Unproven conjectures

Ohhhhhhhhh · Post by **Ohhhhhhhhh** » January 2nd, 2023, 8:43 am

I got one:
Do there exist an object in my rule that is formed in round-block style (see my newest posts in Coexistence in the OCA forum) but eventually evolves into something that breaks the final sequence of the former round block when converting to Life cells? (That is, do there exist a pattern constructed of ‘round-block’ like metacells which can’t work as Life cells in it’s evolution in the rule I posted there)

Apersoma · Post by **Apersoma** » January 17th, 2023, 11:07 am

I'm not sure if due to being Turing complete this cannot be proven, this also may have already been proven but I don't think this conjecture has been proven:
There exists a finite object that exhibits infinite non-repeating growth which can be proven to exhibit infinite non-repeating growth.

An interesting thing with this is that if this can be proven in any Life-like automata then it can be proven in life as you can simply use a meta-cell.

Post by **dvgrn** » January 17th, 2023, 11:38 am

Apersoma wrote: ↑
January 17th, 2023, 11:07 am
There exists a finite object that exhibits infinite non-repeating growth which can be proven to exhibit infinite non-repeating growth.

Depending on your precise definition of "non-repeating", this has already been done in a number of ways. For example, spiral growth, Hydra, and Quadratic_replicator#DOGun_SaGaQR don't exactly have a unit of repetition defining their growth (trivially in the last two cases, since they're not linear growth patterns).

It would also be easy to string together something that would exhibit any type of "infinite non-repeating growth" you might want -- e.g., some kind of "burst gun" building glider guns at increasing distances, attached to something like a caber tosser so that a linear pattern doesn't develop.

Apersoma · Post by **Apersoma** » January 19th, 2023, 9:03 am

I mean that the pattern doesn't have a reasonably predictable growth, that there is no real variation in the objects created, though its hard to get a concrete definition of things like that. Also I was playing around with the highlife replicator & I found something that fits the type of thing I'm talking about for at least 300,000 generations. Idk how to upload a .life file (it tells me I can't when I try) or to export any other file types so I'll screenshot it. Also life viewer doesn't have a large enough area so I'll just upload a screenshot.

AlbertArmStain · Post by **AlbertArmStain** » January 19th, 2023, 9:37 am

Apersoma wrote: ↑
January 19th, 2023, 9:03 am
I mean that the pattern doesn't have a reasonably predictable growth, that there is no real variation in the objects created, though its hard to get a concrete definition of things like that. Also I was playing around with the highlife replicator & I found something that fits the type of thing I'm talking about for at least 300,000 generations.

Do you mean something like the 5N+1 pattern or the 0E0P metacell?

Apersoma · Post by **Apersoma** » January 19th, 2023, 12:53 pm

Yes, also I think I came up with a more formal definition: a pattern that exhibits infinite growth but given a random generation # you cannot give the pattern of that generation without going through every generation before it. If by the metacell you mean using the metacell to replicate the 5n+1 pattern then yes otherwise can you explain what you mean.

Post by **dvgrn** » January 19th, 2023, 9:50 pm

Apersoma wrote: ↑
January 19th, 2023, 12:53 pm
Yes, also I think I came up with a more formal definition: a pattern that exhibits infinite growth but given a random generation # you cannot give the pattern of that generation without going through every generation before it.

I don't think it's necessary to use a metacell in a rule like

Code: Select all

x = 4, y = 3, rule = B3578/S123
2o$3bo$2bo!

to get a pattern that matches that description.

The "infinite novelty generators" that Bill Gosper and others have investigated from time to time seem to fit the bill pretty well, for example. For some of them you might be able to predict 99 point something percent of the ON cells in the configuration at time T, but to get the exact configuration you pretty much have to evolve the pattern.

Unfortunately the pentadecathlon.com link in the above link is down for another week or so while a fan gets replaced in the server, but there are quite a few examples scattered through Nick Gotts' GoL Patterns with Eventful Histories blog (from the very early days of blogging about Life!)

Come to think of it, I'm kind of surprised that people haven't played around more with (2,1)c/6 infinite novelty generators.

AlbertArmStain · Post by **AlbertArmStain** » January 24th, 2023, 8:48 pm

Conjecture: there is no p2 oscillators that have a volatility of 1.00

Chai · Post by **Chai** » January 24th, 2023, 8:57 pm

Isn't this a counterexample (along with all of the other known phoenices)?

Code: Select all

x = 8, y = 8, rule = B3/S23
4bo$2bobo$6bo$2o$6b2o$bo$3bobo$3bo!

AlbertArmStain · Post by **AlbertArmStain** » January 27th, 2023, 4:09 pm

Chai wrote: ↑
January 24th, 2023, 8:57 pm
Isn't this a counterexample (along with all of the other known phoenices)?
Code: Select all
x = 8, y = 8, rule = B3/S23
4bo$2bobo$6bo$2o$6b2o$bo$3bobo$3bo!

I forgot that one.
Conjecture: there isn’t a margolus-neighborhood rule that’s Turing complete

confocaloid · Post by **confocaloid** » January 27th, 2023, 9:57 pm

AlbertArmStain wrote: ↑
January 24th, 2023, 8:48 pm
Conjecture: there is no p2 oscillators that have a volatility of 1.00

Chai wrote: ↑
January 24th, 2023, 8:57 pm
Isn't this a counterexample (along with all of the other known phoenices)?
Code: Select all
x = 8, y = 8, rule = B3/S23
4bo$2bobo$6bo$2o$6b2o$bo$3bobo$3bo!

Here's another phoenix-related conjecture (from a related discussion in Thread for basic questions):

There exists a reasonably small oscillator that is not a phoenix, such that at least one phase consists entirely of newborn cells (without any cells surviving from the previous phase).

Below are some non-examples (pentadecathlon, cross, star, phoenix). The first three are non-examples because every phase has some surviving cells from the previous phase. The last one is a non-example because phoenices are explicitly disallowed in the conjecture.

Code: Select all

#C The Golly ruletable is here: https://conwaylife.com/w/index.php?title=Rule:LifeHistory2&action=edit
x = 64, y = 13, rule = LifeHistory2
26.2H15.HBH$7.2H15.H4BH12.HGAGH$6.H2BH14.HA2GAH11.H5BH10.HBGH$3.2H6B
2H9.2HBA2HAB2H8.HABAHABAH9.GBGB$.2H10B2H7.B2AG2HG2AB7.H3B3H3BH6.HB4HG
H$H4BG4BG4BH5.HBG2H2.2HGBH5.HGBAH3.HABGH5.2GH2.H2B$3BAGBA2GABGA3B5.HB
G2H2.2HGBH5.BAB2H3.2HBAB5.2BH2.H2G$H4BG4BG4BH6.B2AG2HG2AB6.HGBAH3.HAB
GH5.HG4HBH$.2H10B2H7.2HBA2HAB2H7.H3B3H3BH8.BGBG$3.2H6B2H11.HA2GAH10.H
ABAHABAH9.HGBH$6.H2BH14.H4BH11.H5BH$7.2H17.2H14.HGAGH$43.HBH!

("Reasonably small" means "can be viewed in Golly or LifeViewer, with the state of every single cell visible at once".
According to the discussion in Thread for basic questions (p155622, p155624), there should be incredibly large high-period RCT-based solutions. Since the glider has some surviving cells in every phase, there should even be an oscillator where exactly one phase consists entirely of newborn cells.)

pipsqueek · Post by **pipsqueek** » February 4th, 2023, 12:17 pm

pretty random, but I conjecture that there exists no stable or periodic (stationary) object that cannot be hit with a glider to create debris with a larger population than the original object. for example, the block has two collisions that have a greater final population.

Code: Select all

x = 33, y = 7, rule = B3/S23
bo21bo$2bo21bo$3o19b3o3$8b2o21b2o$8b2o21b2o!

another thing I noticed, the block appears is the only stationary object with no glider producing collisions

hotdogPi · Post by **hotdogPi** » February 4th, 2023, 12:45 pm

Create a dense 8000-cell still life (≈130×130). If no glider collision creates a switch engine, it's extremely likely that every glider collision will result in a decrease. (The record methuselah on the wiki for final population is 5828 cells.)

Goldtiger997 · Post by **Goldtiger997** » February 4th, 2023, 1:18 pm

pipsqueek wrote: ↑
February 4th, 2023, 12:17 pm
pretty random, but I conjecture that there exists no stable or periodic (stationary) object that cannot be hit with a glider to create debris with a larger population than the original object. for example, the block has two collisions that have a greater final population.

I think the following 8492-cell still-life (a long^4243 ship) is a counterexample:

Code: Select all

x = 4255, y = 4246, rule = B3/S23
4244b2o$4243bobo$4242bobo$4241bobo$4240bobo9b2o$4239bobo10bobo$4238bob
o11bo$4237bobo$4236bobo$4235bobo$4234bobo$4233bobo$4232bobo$4231bobo$
4230bobo$4229bobo$4228bobo$4227bobo$4226bobo$4225bobo$4224bobo$4223bob
o$4222bobo$4221bobo$4220bobo$4219bobo$4218bobo$4217bobo$4216bobo$4215b
obo$4214bobo$4213bobo$4212bobo$4211bobo$4210bobo$4209bobo$4208bobo$
4207bobo$4206bobo$4205bobo$4204bobo$4203bobo$4202bobo$4201bobo$4200bob
o$4199bobo$4198bobo$4197bobo$4196bobo$4195bobo$4194bobo$4193bobo$4192b
obo$4191bobo$4190bobo$4189bobo$4188bobo$4187bobo$4186bobo$4185bobo$
4184bobo$4183bobo$4182bobo$4181bobo$4180bobo$4179bobo$4178bobo$4177bob
o$4176bobo$4175bobo$4174bobo$4173bobo$4172bobo$4171bobo$4170bobo$4169b
obo$4168bobo$4167bobo$4166bobo$4165bobo$4164bobo$4163bobo$4162bobo$
4161bobo$4160bobo$4159bobo$4158bobo$4157bobo$4156bobo$4155bobo$4154bob
o$4153bobo$4152bobo$4151bobo$4150bobo$4149bobo$4148bobo$4147bobo$4146b
obo$4145bobo$4144bobo$4143bobo$4142bobo$4141bobo$4140bobo$4139bobo$
4138bobo$4137bobo$4136bobo$4135bobo$4134bobo$4133bobo$4132bobo$4131bob
o$4130bobo$4129bobo$4128bobo$4127bobo$4126bobo$4125bobo$4124bobo$4123b
obo$4122bobo$4121bobo$4120bobo$4119bobo$4118bobo$4117bobo$4116bobo$
4115bobo$4114bobo$4113bobo$4112bobo$4111bobo$4110bobo$4109bobo$4108bob
o$4107bobo$4106bobo$4105bobo$4104bobo$4103bobo$4102bobo$4101bobo$4100b
obo$4099bobo$4098bobo$4097bobo$4096bobo$4095bobo$4094bobo$4093bobo$
4092bobo$4091bobo$4090bobo$4089bobo$4088bobo$4087bobo$4086bobo$4085bob
o$4084bobo$4083bobo$4082bobo$4081bobo$4080bobo$4079bobo$4078bobo$4077b
obo$4076bobo$4075bobo$4074bobo$4073bobo$4072bobo$4071bobo$4070bobo$
4069bobo$4068bobo$4067bobo$4066bobo$4065bobo$4064bobo$4063bobo$4062bob
o$4061bobo$4060bobo$4059bobo$4058bobo$4057bobo$4056bobo$4055bobo$4054b
obo$4053bobo$4052bobo$4051bobo$4050bobo$4049bobo$4048bobo$4047bobo$
4046bobo$4045bobo$4044bobo$4043bobo$4042bobo$4041bobo$4040bobo$4039bob
o$4038bobo$4037bobo$4036bobo$4035bobo$4034bobo$4033bobo$4032bobo$4031b
obo$4030bobo$4029bobo$4028bobo$4027bobo$4026bobo$4025bobo$4024bobo$
4023bobo$4022bobo$4021bobo$4020bobo$4019bobo$4018bobo$4017bobo$4016bob
o$4015bobo$4014bobo$4013bobo$4012bobo$4011bobo$4010bobo$4009bobo$4008b
obo$4007bobo$4006bobo$4005bobo$4004bobo$4003bobo$4002bobo$4001bobo$
4000bobo$3999bobo$3998bobo$3997bobo$3996bobo$3995bobo$3994bobo$3993bob
o$3992bobo$3991bobo$3990bobo$3989bobo$3988bobo$3987bobo$3986bobo$3985b
obo$3984bobo$3983bobo$3982bobo$3981bobo$3980bobo$3979bobo$3978bobo$
3977bobo$3976bobo$3975bobo$3974bobo$3973bobo$3972bobo$3971bobo$3970bob
o$3969bobo$3968bobo$3967bobo$3966bobo$3965bobo$3964bobo$3963bobo$3962b
obo$3961bobo$3960bobo$3959bobo$3958bobo$3957bobo$3956bobo$3955bobo$
3954bobo$3953bobo$3952bobo$3951bobo$3950bobo$3949bobo$3948bobo$3947bob
o$3946bobo$3945bobo$3944bobo$3943bobo$3942bobo$3941bobo$3940bobo$3939b
obo$3938bobo$3937bobo$3936bobo$3935bobo$3934bobo$3933bobo$3932bobo$
3931bobo$3930bobo$3929bobo$3928bobo$3927bobo$3926bobo$3925bobo$3924bob
o$3923bobo$3922bobo$3921bobo$3920bobo$3919bobo$3918bobo$3917bobo$3916b
obo$3915bobo$3914bobo$3913bobo$3912bobo$3911bobo$3910bobo$3909bobo$
3908bobo$3907bobo$3906bobo$3905bobo$3904bobo$3903bobo$3902bobo$3901bob
o$3900bobo$3899bobo$3898bobo$3897bobo$3896bobo$3895bobo$3894bobo$3893b
obo$3892bobo$3891bobo$3890bobo$3889bobo$3888bobo$3887bobo$3886bobo$
3885bobo$3884bobo$3883bobo$3882bobo$3881bobo$3880bobo$3879bobo$3878bob
o$3877bobo$3876bobo$3875bobo$3874bobo$3873bobo$3872bobo$3871bobo$3870b
obo$3869bobo$3868bobo$3867bobo$3866bobo$3865bobo$3864bobo$3863bobo$
3862bobo$3861bobo$3860bobo$3859bobo$3858bobo$3857bobo$3856bobo$3855bob
o$3854bobo$3853bobo$3852bobo$3851bobo$3850bobo$3849bobo$3848bobo$3847b
obo$3846bobo$3845bobo$3844bobo$3843bobo$3842bobo$3841bobo$3840bobo$
3839bobo$3838bobo$3837bobo$3836bobo$3835bobo$3834bobo$3833bobo$3832bob
o$3831bobo$3830bobo$3829bobo$3828bobo$3827bobo$3826bobo$3825bobo$3824b
obo$3823bobo$3822bobo$3821bobo$3820bobo$3819bobo$3818bobo$3817bobo$
3816bobo$3815bobo$3814bobo$3813bobo$3812bobo$3811bobo$3810bobo$3809bob
o$3808bobo$3807bobo$3806bobo$3805bobo$3804bobo$3803bobo$3802bobo$3801b
obo$3800bobo$3799bobo$3798bobo$3797bobo$3796bobo$3795bobo$3794bobo$
3793bobo$3792bobo$3791bobo$3790bobo$3789bobo$3788bobo$3787bobo$3786bob
o$3785bobo$3784bobo$3783bobo$3782bobo$3781bobo$3780bobo$3779bobo$3778b
obo$3777bobo$3776bobo$3775bobo$3774bobo$3773bobo$3772bobo$3771bobo$
3770bobo$3769bobo$3768bobo$3767bobo$3766bobo$3765bobo$3764bobo$3763bob
o$3762bobo$3761bobo$3760bobo$3759bobo$3758bobo$3757bobo$3756bobo$3755b
obo$3754bobo$3753bobo$3752bobo$3751bobo$3750bobo$3749bobo$3748bobo$
3747bobo$3746bobo$3745bobo$3744bobo$3743bobo$3742bobo$3741bobo$3740bob
o$3739bobo$3738bobo$3737bobo$3736bobo$3735bobo$3734bobo$3733bobo$3732b
obo$3731bobo$3730bobo$3729bobo$3728bobo$3727bobo$3726bobo$3725bobo$
3724bobo$3723bobo$3722bobo$3721bobo$3720bobo$3719bobo$3718bobo$3717bob
o$3716bobo$3715bobo$3714bobo$3713bobo$3712bobo$3711bobo$3710bobo$3709b
obo$3708bobo$3707bobo$3706bobo$3705bobo$3704bobo$3703bobo$3702bobo$
3701bobo$3700bobo$3699bobo$3698bobo$3697bobo$3696bobo$3695bobo$3694bob
o$3693bobo$3692bobo$3691bobo$3690bobo$3689bobo$3688bobo$3687bobo$3686b
obo$3685bobo$3684bobo$3683bobo$3682bobo$3681bobo$3680bobo$3679bobo$
3678bobo$3677bobo$3676bobo$3675bobo$3674bobo$3673bobo$3672bobo$3671bob
o$3670bobo$3669bobo$3668bobo$3667bobo$3666bobo$3665bobo$3664bobo$3663b
obo$3662bobo$3661bobo$3660bobo$3659bobo$3658bobo$3657bobo$3656bobo$
3655bobo$3654bobo$3653bobo$3652bobo$3651bobo$3650bobo$3649bobo$3648bob
o$3647bobo$3646bobo$3645bobo$3644bobo$3643bobo$3642bobo$3641bobo$3640b
obo$3639bobo$3638bobo$3637bobo$3636bobo$3635bobo$3634bobo$3633bobo$
3632bobo$3631bobo$3630bobo$3629bobo$3628bobo$3627bobo$3626bobo$3625bob
o$3624bobo$3623bobo$3622bobo$3621bobo$3620bobo$3619bobo$3618bobo$3617b
obo$3616bobo$3615bobo$3614bobo$3613bobo$3612bobo$3611bobo$3610bobo$
3609bobo$3608bobo$3607bobo$3606bobo$3605bobo$3604bobo$3603bobo$3602bob
o$3601bobo$3600bobo$3599bobo$3598bobo$3597bobo$3596bobo$3595bobo$3594b
obo$3593bobo$3592bobo$3591bobo$3590bobo$3589bobo$3588bobo$3587bobo$
3586bobo$3585bobo$3584bobo$3583bobo$3582bobo$3581bobo$3580bobo$3579bob
o$3578bobo$3577bobo$3576bobo$3575bobo$3574bobo$3573bobo$3572bobo$3571b
obo$3570bobo$3569bobo$3568bobo$3567bobo$3566bobo$3565bobo$3564bobo$
3563bobo$3562bobo$3561bobo$3560bobo$3559bobo$3558bobo$3557bobo$3556bob
o$3555bobo$3554bobo$3553bobo$3552bobo$3551bobo$3550bobo$3549bobo$3548b
obo$3547bobo$3546bobo$3545bobo$3544bobo$3543bobo$3542bobo$3541bobo$
3540bobo$3539bobo$3538bobo$3537bobo$3536bobo$3535bobo$3534bobo$3533bob
o$3532bobo$3531bobo$3530bobo$3529bobo$3528bobo$3527bobo$3526bobo$3525b
obo$3524bobo$3523bobo$3522bobo$3521bobo$3520bobo$3519bobo$3518bobo$
3517bobo$3516bobo$3515bobo$3514bobo$3513bobo$3512bobo$3511bobo$3510bob
o$3509bobo$3508bobo$3507bobo$3506bobo$3505bobo$3504bobo$3503bobo$3502b
obo$3501bobo$3500bobo$3499bobo$3498bobo$3497bobo$3496bobo$3495bobo$
3494bobo$3493bobo$3492bobo$3491bobo$3490bobo$3489bobo$3488bobo$3487bob
o$3486bobo$3485bobo$3484bobo$3483bobo$3482bobo$3481bobo$3480bobo$3479b
obo$3478bobo$3477bobo$3476bobo$3475bobo$3474bobo$3473bobo$3472bobo$
3471bobo$3470bobo$3469bobo$3468bobo$3467bobo$3466bobo$3465bobo$3464bob
o$3463bobo$3462bobo$3461bobo$3460bobo$3459bobo$3458bobo$3457bobo$3456b
obo$3455bobo$3454bobo$3453bobo$3452bobo$3451bobo$3450bobo$3449bobo$
3448bobo$3447bobo$3446bobo$3445bobo$3444bobo$3443bobo$3442bobo$3441bob
o$3440bobo$3439bobo$3438bobo$3437bobo$3436bobo$3435bobo$3434bobo$3433b
obo$3432bobo$3431bobo$3430bobo$3429bobo$3428bobo$3427bobo$3426bobo$
3425bobo$3424bobo$3423bobo$3422bobo$3421bobo$3420bobo$3419bobo$3418bob
o$3417bobo$3416bobo$3415bobo$3414bobo$3413bobo$3412bobo$3411bobo$3410b
obo$3409bobo$3408bobo$3407bobo$3406bobo$3405bobo$3404bobo$3403bobo$
3402bobo$3401bobo$3400bobo$3399bobo$3398bobo$3397bobo$3396bobo$3395bob
o$3394bobo$3393bobo$3392bobo$3391bobo$3390bobo$3389bobo$3388bobo$3387b
obo$3386bobo$3385bobo$3384bobo$3383bobo$3382bobo$3381bobo$3380bobo$
3379bobo$3378bobo$3377bobo$3376bobo$3375bobo$3374bobo$3373bobo$3372bob
o$3371bobo$3370bobo$3369bobo$3368bobo$3367bobo$3366bobo$3365bobo$3364b
obo$3363bobo$3362bobo$3361bobo$3360bobo$3359bobo$3358bobo$3357bobo$
3356bobo$3355bobo$3354bobo$3353bobo$3352bobo$3351bobo$3350bobo$3349bob
o$3348bobo$3347bobo$3346bobo$3345bobo$3344bobo$3343bobo$3342bobo$3341b
obo$3340bobo$3339bobo$3338bobo$3337bobo$3336bobo$3335bobo$3334bobo$
3333bobo$3332bobo$3331bobo$3330bobo$3329bobo$3328bobo$3327bobo$3326bob
o$3325bobo$3324bobo$3323bobo$3322bobo$3321bobo$3320bobo$3319bobo$3318b
obo$3317bobo$3316bobo$3315bobo$3314bobo$3313bobo$3312bobo$3311bobo$
3310bobo$3309bobo$3308bobo$3307bobo$3306bobo$3305bobo$3304bobo$3303bob
o$3302bobo$3301bobo$3300bobo$3299bobo$3298bobo$3297bobo$3296bobo$3295b
obo$3294bobo$3293bobo$3292bobo$3291bobo$3290bobo$3289bobo$3288bobo$
3287bobo$3286bobo$3285bobo$3284bobo$3283bobo$3282bobo$3281bobo$3280bob
o$3279bobo$3278bobo$3277bobo$3276bobo$3275bobo$3274bobo$3273bobo$3272b
obo$3271bobo$3270bobo$3269bobo$3268bobo$3267bobo$3266bobo$3265bobo$
3264bobo$3263bobo$3262bobo$3261bobo$3260bobo$3259bobo$3258bobo$3257bob
o$3256bobo$3255bobo$3254bobo$3253bobo$3252bobo$3251bobo$3250bobo$3249b
obo$3248bobo$3247bobo$3246bobo$3245bobo$3244bobo$3243bobo$3242bobo$
3241bobo$3240bobo$3239bobo$3238bobo$3237bobo$3236bobo$3235bobo$3234bob
o$3233bobo$3232bobo$3231bobo$3230bobo$3229bobo$3228bobo$3227bobo$3226b
obo$3225bobo$3224bobo$3223bobo$3222bobo$3221bobo$3220bobo$3219bobo$
3218bobo$3217bobo$3216bobo$3215bobo$3214bobo$3213bobo$3212bobo$3211bob
o$3210bobo$3209bobo$3208bobo$3207bobo$3206bobo$3205bobo$3204bobo$3203b
obo$3202bobo$3201bobo$3200bobo$3199bobo$3198bobo$3197bobo$3196bobo$
3195bobo$3194bobo$3193bobo$3192bobo$3191bobo$3190bobo$3189bobo$3188bob
o$3187bobo$3186bobo$3185bobo$3184bobo$3183bobo$3182bobo$3181bobo$3180b
obo$3179bobo$3178bobo$3177bobo$3176bobo$3175bobo$3174bobo$3173bobo$
3172bobo$3171bobo$3170bobo$3169bobo$3168bobo$3167bobo$3166bobo$3165bob
o$3164bobo$3163bobo$3162bobo$3161bobo$3160bobo$3159bobo$3158bobo$3157b
obo$3156bobo$3155bobo$3154bobo$3153bobo$3152bobo$3151bobo$3150bobo$
3149bobo$3148bobo$3147bobo$3146bobo$3145bobo$3144bobo$3143bobo$3142bob
o$3141bobo$3140bobo$3139bobo$3138bobo$3137bobo$3136bobo$3135bobo$3134b
obo$3133bobo$3132bobo$3131bobo$3130bobo$3129bobo$3128bobo$3127bobo$
3126bobo$3125bobo$3124bobo$3123bobo$3122bobo$3121bobo$3120bobo$3119bob
o$3118bobo$3117bobo$3116bobo$3115bobo$3114bobo$3113bobo$3112bobo$3111b
obo$3110bobo$3109bobo$3108bobo$3107bobo$3106bobo$3105bobo$3104bobo$
3103bobo$3102bobo$3101bobo$3100bobo$3099bobo$3098bobo$3097bobo$3096bob
o$3095bobo$3094bobo$3093bobo$3092bobo$3091bobo$3090bobo$3089bobo$3088b
obo$3087bobo$3086bobo$3085bobo$3084bobo$3083bobo$3082bobo$3081bobo$
3080bobo$3079bobo$3078bobo$3077bobo$3076bobo$3075bobo$3074bobo$3073bob
o$3072bobo$3071bobo$3070bobo$3069bobo$3068bobo$3067bobo$3066bobo$3065b
obo$3064bobo$3063bobo$3062bobo$3061bobo$3060bobo$3059bobo$3058bobo$
3057bobo$3056bobo$3055bobo$3054bobo$3053bobo$3052bobo$3051bobo$3050bob
o$3049bobo$3048bobo$3047bobo$3046bobo$3045bobo$3044bobo$3043bobo$3042b
obo$3041bobo$3040bobo$3039bobo$3038bobo$3037bobo$3036bobo$3035bobo$
3034bobo$3033bobo$3032bobo$3031bobo$3030bobo$3029bobo$3028bobo$3027bob
o$3026bobo$3025bobo$3024bobo$3023bobo$3022bobo$3021bobo$3020bobo$3019b
obo$3018bobo$3017bobo$3016bobo$3015bobo$3014bobo$3013bobo$3012bobo$
3011bobo$3010bobo$3009bobo$3008bobo$3007bobo$3006bobo$3005bobo$3004bob
o$3003bobo$3002bobo$3001bobo$3000bobo$2999bobo$2998bobo$2997bobo$2996b
obo$2995bobo$2994bobo$2993bobo$2992bobo$2991bobo$2990bobo$2989bobo$
2988bobo$2987bobo$2986bobo$2985bobo$2984bobo$2983bobo$2982bobo$2981bob
o$2980bobo$2979bobo$2978bobo$2977bobo$2976bobo$2975bobo$2974bobo$2973b
obo$2972bobo$2971bobo$2970bobo$2969bobo$2968bobo$2967bobo$2966bobo$
2965bobo$2964bobo$2963bobo$2962bobo$2961bobo$2960bobo$2959bobo$2958bob
o$2957bobo$2956bobo$2955bobo$2954bobo$2953bobo$2952bobo$2951bobo$2950b
obo$2949bobo$2948bobo$2947bobo$2946bobo$2945bobo$2944bobo$2943bobo$
2942bobo$2941bobo$2940bobo$2939bobo$2938bobo$2937bobo$2936bobo$2935bob
o$2934bobo$2933bobo$2932bobo$2931bobo$2930bobo$2929bobo$2928bobo$2927b
obo$2926bobo$2925bobo$2924bobo$2923bobo$2922bobo$2921bobo$2920bobo$
2919bobo$2918bobo$2917bobo$2916bobo$2915bobo$2914bobo$2913bobo$2912bob
o$2911bobo$2910bobo$2909bobo$2908bobo$2907bobo$2906bobo$2905bobo$2904b
obo$2903bobo$2902bobo$2901bobo$2900bobo$2899bobo$2898bobo$2897bobo$
2896bobo$2895bobo$2894bobo$2893bobo$2892bobo$2891bobo$2890bobo$2889bob
o$2888bobo$2887bobo$2886bobo$2885bobo$2884bobo$2883bobo$2882bobo$2881b
obo$2880bobo$2879bobo$2878bobo$2877bobo$2876bobo$2875bobo$2874bobo$
2873bobo$2872bobo$2871bobo$2870bobo$2869bobo$2868bobo$2867bobo$2866bob
o$2865bobo$2864bobo$2863bobo$2862bobo$2861bobo$2860bobo$2859bobo$2858b
obo$2857bobo$2856bobo$2855bobo$2854bobo$2853bobo$2852bobo$2851bobo$
2850bobo$2849bobo$2848bobo$2847bobo$2846bobo$2845bobo$2844bobo$2843bob
o$2842bobo$2841bobo$2840bobo$2839bobo$2838bobo$2837bobo$2836bobo$2835b
obo$2834bobo$2833bobo$2832bobo$2831bobo$2830bobo$2829bobo$2828bobo$
2827bobo$2826bobo$2825bobo$2824bobo$2823bobo$2822bobo$2821bobo$2820bob
o$2819bobo$2818bobo$2817bobo$2816bobo$2815bobo$2814bobo$2813bobo$2812b
obo$2811bobo$2810bobo$2809bobo$2808bobo$2807bobo$2806bobo$2805bobo$
2804bobo$2803bobo$2802bobo$2801bobo$2800bobo$2799bobo$2798bobo$2797bob
o$2796bobo$2795bobo$2794bobo$2793bobo$2792bobo$2791bobo$2790bobo$2789b
obo$2788bobo$2787bobo$2786bobo$2785bobo$2784bobo$2783bobo$2782bobo$
2781bobo$2780bobo$2779bobo$2778bobo$2777bobo$2776bobo$2775bobo$2774bob
o$2773bobo$2772bobo$2771bobo$2770bobo$2769bobo$2768bobo$2767bobo$2766b
obo$2765bobo$2764bobo$2763bobo$2762bobo$2761bobo$2760bobo$2759bobo$
2758bobo$2757bobo$2756bobo$2755bobo$2754bobo$2753bobo$2752bobo$2751bob
o$2750bobo$2749bobo$2748bobo$2747bobo$2746bobo$2745bobo$2744bobo$2743b
obo$2742bobo$2741bobo$2740bobo$2739bobo$2738bobo$2737bobo$2736bobo$
2735bobo$2734bobo$2733bobo$2732bobo$2731bobo$2730bobo$2729bobo$2728bob
o$2727bobo$2726bobo$2725bobo$2724bobo$2723bobo$2722bobo$2721bobo$2720b
obo$2719bobo$2718bobo$2717bobo$2716bobo$2715bobo$2714bobo$2713bobo$
2712bobo$2711bobo$2710bobo$2709bobo$2708bobo$2707bobo$2706bobo$2705bob
o$2704bobo$2703bobo$2702bobo$2701bobo$2700bobo$2699bobo$2698bobo$2697b
obo$2696bobo$2695bobo$2694bobo$2693bobo$2692bobo$2691bobo$2690bobo$
2689bobo$2688bobo$2687bobo$2686bobo$2685bobo$2684bobo$2683bobo$2682bob
o$2681bobo$2680bobo$2679bobo$2678bobo$2677bobo$2676bobo$2675bobo$2674b
obo$2673bobo$2672bobo$2671bobo$2670bobo$2669bobo$2668bobo$2667bobo$
2666bobo$2665bobo$2664bobo$2663bobo$2662bobo$2661bobo$2660bobo$2659bob
o$2658bobo$2657bobo$2656bobo$2655bobo$2654bobo$2653bobo$2652bobo$2651b
obo$2650bobo$2649bobo$2648bobo$2647bobo$2646bobo$2645bobo$2644bobo$
2643bobo$2642bobo$2641bobo$2640bobo$2639bobo$2638bobo$2637bobo$2636bob
o$2635bobo$2634bobo$2633bobo$2632bobo$2631bobo$2630bobo$2629bobo$2628b
obo$2627bobo$2626bobo$2625bobo$2624bobo$2623bobo$2622bobo$2621bobo$
2620bobo$2619bobo$2618bobo$2617bobo$2616bobo$2615bobo$2614bobo$2613bob
o$2612bobo$2611bobo$2610bobo$2609bobo$2608bobo$2607bobo$2606bobo$2605b
obo$2604bobo$2603bobo$2602bobo$2601bobo$2600bobo$2599bobo$2598bobo$
2597bobo$2596bobo$2595bobo$2594bobo$2593bobo$2592bobo$2591bobo$2590bob
o$2589bobo$2588bobo$2587bobo$2586bobo$2585bobo$2584bobo$2583bobo$2582b
obo$2581bobo$2580bobo$2579bobo$2578bobo$2577bobo$2576bobo$2575bobo$
2574bobo$2573bobo$2572bobo$2571bobo$2570bobo$2569bobo$2568bobo$2567bob
o$2566bobo$2565bobo$2564bobo$2563bobo$2562bobo$2561bobo$2560bobo$2559b
obo$2558bobo$2557bobo$2556bobo$2555bobo$2554bobo$2553bobo$2552bobo$
2551bobo$2550bobo$2549bobo$2548bobo$2547bobo$2546bobo$2545bobo$2544bob
o$2543bobo$2542bobo$2541bobo$2540bobo$2539bobo$2538bobo$2537bobo$2536b
obo$2535bobo$2534bobo$2533bobo$2532bobo$2531bobo$2530bobo$2529bobo$
2528bobo$2527bobo$2526bobo$2525bobo$2524bobo$2523bobo$2522bobo$2521bob
o$2520bobo$2519bobo$2518bobo$2517bobo$2516bobo$2515bobo$2514bobo$2513b
obo$2512bobo$2511bobo$2510bobo$2509bobo$2508bobo$2507bobo$2506bobo$
2505bobo$2504bobo$2503bobo$2502bobo$2501bobo$2500bobo$2499bobo$2498bob
o$2497bobo$2496bobo$2495bobo$2494bobo$2493bobo$2492bobo$2491bobo$2490b
obo$2489bobo$2488bobo$2487bobo$2486bobo$2485bobo$2484bobo$2483bobo$
2482bobo$2481bobo$2480bobo$2479bobo$2478bobo$2477bobo$2476bobo$2475bob
o$2474bobo$2473bobo$2472bobo$2471bobo$2470bobo$2469bobo$2468bobo$2467b
obo$2466bobo$2465bobo$2464bobo$2463bobo$2462bobo$2461bobo$2460bobo$
2459bobo$2458bobo$2457bobo$2456bobo$2455bobo$2454bobo$2453bobo$2452bob
o$2451bobo$2450bobo$2449bobo$2448bobo$2447bobo$2446bobo$2445bobo$2444b
obo$2443bobo$2442bobo$2441bobo$2440bobo$2439bobo$2438bobo$2437bobo$
2436bobo$2435bobo$2434bobo$2433bobo$2432bobo$2431bobo$2430bobo$2429bob
o$2428bobo$2427bobo$2426bobo$2425bobo$2424bobo$2423bobo$2422bobo$2421b
obo$2420bobo$2419bobo$2418bobo$2417bobo$2416bobo$2415bobo$2414bobo$
2413bobo$2412bobo$2411bobo$2410bobo$2409bobo$2408bobo$2407bobo$2406bob
o$2405bobo$2404bobo$2403bobo$2402bobo$2401bobo$2400bobo$2399bobo$2398b
obo$2397bobo$2396bobo$2395bobo$2394bobo$2393bobo$2392bobo$2391bobo$
2390bobo$2389bobo$2388bobo$2387bobo$2386bobo$2385bobo$2384bobo$2383bob
o$2382bobo$2381bobo$2380bobo$2379bobo$2378bobo$2377bobo$2376bobo$2375b
obo$2374bobo$2373bobo$2372bobo$2371bobo$2370bobo$2369bobo$2368bobo$
2367bobo$2366bobo$2365bobo$2364bobo$2363bobo$2362bobo$2361bobo$2360bob
o$2359bobo$2358bobo$2357bobo$2356bobo$2355bobo$2354bobo$2353bobo$2352b
obo$2351bobo$2350bobo$2349bobo$2348bobo$2347bobo$2346bobo$2345bobo$
2344bobo$2343bobo$2342bobo$2341bobo$2340bobo$2339bobo$2338bobo$2337bob
o$2336bobo$2335bobo$2334bobo$2333bobo$2332bobo$2331bobo$2330bobo$2329b
obo$2328bobo$2327bobo$2326bobo$2325bobo$2324bobo$2323bobo$2322bobo$
2321bobo$2320bobo$2319bobo$2318bobo$2317bobo$2316bobo$2315bobo$2314bob
o$2313bobo$2312bobo$2311bobo$2310bobo$2309bobo$2308bobo$2307bobo$2306b
obo$2305bobo$2304bobo$2303bobo$2302bobo$2301bobo$2300bobo$2299bobo$
2298bobo$2297bobo$2296bobo$2295bobo$2294bobo$2293bobo$2292bobo$2291bob
o$2290bobo$2289bobo$2288bobo$2287bobo$2286bobo$2285bobo$2284bobo$2283b
obo$2282bobo$2281bobo$2280bobo$2279bobo$2278bobo$2277bobo$2276bobo$
2275bobo$2274bobo$2273bobo$2272bobo$2271bobo$2270bobo$2269bobo$2268bob
o$2267bobo$2266bobo$2265bobo$2264bobo$2263bobo$2262bobo$2261bobo$2260b
obo$2259bobo$2258bobo$2257bobo$2256bobo$2255bobo$2254bobo$2253bobo$
2252bobo$2251bobo$2250bobo$2249bobo$2248bobo$2247bobo$2246bobo$2245bob
o$2244bobo$2243bobo$2242bobo$2241bobo$2240bobo$2239bobo$2238bobo$2237b
obo$2236bobo$2235bobo$2234bobo$2233bobo$2232bobo$2231bobo$2230bobo$
2229bobo$2228bobo$2227bobo$2226bobo$2225bobo$2224bobo$2223bobo$2222bob
o$2221bobo$2220bobo$2219bobo$2218bobo$2217bobo$2216bobo$2215bobo$2214b
obo$2213bobo$2212bobo$2211bobo$2210bobo$2209bobo$2208bobo$2207bobo$
2206bobo$2205bobo$2204bobo$2203bobo$2202bobo$2201bobo$2200bobo$2199bob
o$2198bobo$2197bobo$2196bobo$2195bobo$2194bobo$2193bobo$2192bobo$2191b
obo$2190bobo$2189bobo$2188bobo$2187bobo$2186bobo$2185bobo$2184bobo$
2183bobo$2182bobo$2181bobo$2180bobo$2179bobo$2178bobo$2177bobo$2176bob
o$2175bobo$2174bobo$2173bobo$2172bobo$2171bobo$2170bobo$2169bobo$2168b
obo$2167bobo$2166bobo$2165bobo$2164bobo$2163bobo$2162bobo$2161bobo$
2160bobo$2159bobo$2158bobo$2157bobo$2156bobo$2155bobo$2154bobo$2153bob
o$2152bobo$2151bobo$2150bobo$2149bobo$2148bobo$2147bobo$2146bobo$2145b
obo$2144bobo$2143bobo$2142bobo$2141bobo$2140bobo$2139bobo$2138bobo$
2137bobo$2136bobo$2135bobo$2134bobo$2133bobo$2132bobo$2131bobo$2130bob
o$2129bobo$2128bobo$2127bobo$2126bobo$2125bobo$2124bobo$2123bobo$2122b
obo$2121bobo$2120bobo$2119bobo$2118bobo$2117bobo$2116bobo$2115bobo$
2114bobo$2113bobo$2112bobo$2111bobo$2110bobo$2109bobo$2108bobo$2107bob
o$2106bobo$2105bobo$2104bobo$2103bobo$2102bobo$2101bobo$2100bobo$2099b
obo$2098bobo$2097bobo$2096bobo$2095bobo$2094bobo$2093bobo$2092bobo$
2091bobo$2090bobo$2089bobo$2088bobo$2087bobo$2086bobo$2085bobo$2084bob
o$2083bobo$2082bobo$2081bobo$2080bobo$2079bobo$2078bobo$2077bobo$2076b
obo$2075bobo$2074bobo$2073bobo$2072bobo$2071bobo$2070bobo$2069bobo$
2068bobo$2067bobo$2066bobo$2065bobo$2064bobo$2063bobo$2062bobo$2061bob
o$2060bobo$2059bobo$2058bobo$2057bobo$2056bobo$2055bobo$2054bobo$2053b
obo$2052bobo$2051bobo$2050bobo$2049bobo$2048bobo$2047bobo$2046bobo$
2045bobo$2044bobo$2043bobo$2042bobo$2041bobo$2040bobo$2039bobo$2038bob
o$2037bobo$2036bobo$2035bobo$2034bobo$2033bobo$2032bobo$2031bobo$2030b
obo$2029bobo$2028bobo$2027bobo$2026bobo$2025bobo$2024bobo$2023bobo$
2022bobo$2021bobo$2020bobo$2019bobo$2018bobo$2017bobo$2016bobo$2015bob
o$2014bobo$2013bobo$2012bobo$2011bobo$2010bobo$2009bobo$2008bobo$2007b
obo$2006bobo$2005bobo$2004bobo$2003bobo$2002bobo$2001bobo$2000bobo$
1999bobo$1998bobo$1997bobo$1996bobo$1995bobo$1994bobo$1993bobo$1992bob
o$1991bobo$1990bobo$1989bobo$1988bobo$1987bobo$1986bobo$1985bobo$1984b
obo$1983bobo$1982bobo$1981bobo$1980bobo$1979bobo$1978bobo$1977bobo$
1976bobo$1975bobo$1974bobo$1973bobo$1972bobo$1971bobo$1970bobo$1969bob
o$1968bobo$1967bobo$1966bobo$1965bobo$1964bobo$1963bobo$1962bobo$1961b
obo$1960bobo$1959bobo$1958bobo$1957bobo$1956bobo$1955bobo$1954bobo$
1953bobo$1952bobo$1951bobo$1950bobo$1949bobo$1948bobo$1947bobo$1946bob
o$1945bobo$1944bobo$1943bobo$1942bobo$1941bobo$1940bobo$1939bobo$1938b
obo$1937bobo$1936bobo$1935bobo$1934bobo$1933bobo$1932bobo$1931bobo$
1930bobo$1929bobo$1928bobo$1927bobo$1926bobo$1925bobo$1924bobo$1923bob
o$1922bobo$1921bobo$1920bobo$1919bobo$1918bobo$1917bobo$1916bobo$1915b
obo$1914bobo$1913bobo$1912bobo$1911bobo$1910bobo$1909bobo$1908bobo$
1907bobo$1906bobo$1905bobo$1904bobo$1903bobo$1902bobo$1901bobo$1900bob
o$1899bobo$1898bobo$1897bobo$1896bobo$1895bobo$1894bobo$1893bobo$1892b
obo$1891bobo$1890bobo$1889bobo$1888bobo$1887bobo$1886bobo$1885bobo$
1884bobo$1883bobo$1882bobo$1881bobo$1880bobo$1879bobo$1878bobo$1877bob
o$1876bobo$1875bobo$1874bobo$1873bobo$1872bobo$1871bobo$1870bobo$1869b
obo$1868bobo$1867bobo$1866bobo$1865bobo$1864bobo$1863bobo$1862bobo$
1861bobo$1860bobo$1859bobo$1858bobo$1857bobo$1856bobo$1855bobo$1854bob
o$1853bobo$1852bobo$1851bobo$1850bobo$1849bobo$1848bobo$1847bobo$1846b
obo$1845bobo$1844bobo$1843bobo$1842bobo$1841bobo$1840bobo$1839bobo$
1838bobo$1837bobo$1836bobo$1835bobo$1834bobo$1833bobo$1832bobo$1831bob
o$1830bobo$1829bobo$1828bobo$1827bobo$1826bobo$1825bobo$1824bobo$1823b
obo$1822bobo$1821bobo$1820bobo$1819bobo$1818bobo$1817bobo$1816bobo$
1815bobo$1814bobo$1813bobo$1812bobo$1811bobo$1810bobo$1809bobo$1808bob
o$1807bobo$1806bobo$1805bobo$1804bobo$1803bobo$1802bobo$1801bobo$1800b
obo$1799bobo$1798bobo$1797bobo$1796bobo$1795bobo$1794bobo$1793bobo$
1792bobo$1791bobo$1790bobo$1789bobo$1788bobo$1787bobo$1786bobo$1785bob
o$1784bobo$1783bobo$1782bobo$1781bobo$1780bobo$1779bobo$1778bobo$1777b
obo$1776bobo$1775bobo$1774bobo$1773bobo$1772bobo$1771bobo$1770bobo$
1769bobo$1768bobo$1767bobo$1766bobo$1765bobo$1764bobo$1763bobo$1762bob
o$1761bobo$1760bobo$1759bobo$1758bobo$1757bobo$1756bobo$1755bobo$1754b
obo$1753bobo$1752bobo$1751bobo$1750bobo$1749bobo$1748bobo$1747bobo$
1746bobo$1745bobo$1744bobo$1743bobo$1742bobo$1741bobo$1740bobo$1739bob
o$1738bobo$1737bobo$1736bobo$1735bobo$1734bobo$1733bobo$1732bobo$1731b
obo$1730bobo$1729bobo$1728bobo$1727bobo$1726bobo$1725bobo$1724bobo$
1723bobo$1722bobo$1721bobo$1720bobo$1719bobo$1718bobo$1717bobo$1716bob
o$1715bobo$1714bobo$1713bobo$1712bobo$1711bobo$1710bobo$1709bobo$1708b
obo$1707bobo$1706bobo$1705bobo$1704bobo$1703bobo$1702bobo$1701bobo$
1700bobo$1699bobo$1698bobo$1697bobo$1696bobo$1695bobo$1694bobo$1693bob
o$1692bobo$1691bobo$1690bobo$1689bobo$1688bobo$1687bobo$1686bobo$1685b
obo$1684bobo$1683bobo$1682bobo$1681bobo$1680bobo$1679bobo$1678bobo$
1677bobo$1676bobo$1675bobo$1674bobo$1673bobo$1672bobo$1671bobo$1670bob
o$1669bobo$1668bobo$1667bobo$1666bobo$1665bobo$1664bobo$1663bobo$1662b
obo$1661bobo$1660bobo$1659bobo$1658bobo$1657bobo$1656bobo$1655bobo$
1654bobo$1653bobo$1652bobo$1651bobo$1650bobo$1649bobo$1648bobo$1647bob
o$1646bobo$1645bobo$1644bobo$1643bobo$1642bobo$1641bobo$1640bobo$1639b
obo$1638bobo$1637bobo$1636bobo$1635bobo$1634bobo$1633bobo$1632bobo$
1631bobo$1630bobo$1629bobo$1628bobo$1627bobo$1626bobo$1625bobo$1624bob
o$1623bobo$1622bobo$1621bobo$1620bobo$1619bobo$1618bobo$1617bobo$1616b
obo$1615bobo$1614bobo$1613bobo$1612bobo$1611bobo$1610bobo$1609bobo$
1608bobo$1607bobo$1606bobo$1605bobo$1604bobo$1603bobo$1602bobo$1601bob
o$1600bobo$1599bobo$1598bobo$1597bobo$1596bobo$1595bobo$1594bobo$1593b
obo$1592bobo$1591bobo$1590bobo$1589bobo$1588bobo$1587bobo$1586bobo$
1585bobo$1584bobo$1583bobo$1582bobo$1581bobo$1580bobo$1579bobo$1578bob
o$1577bobo$1576bobo$1575bobo$1574bobo$1573bobo$1572bobo$1571bobo$1570b
obo$1569bobo$1568bobo$1567bobo$1566bobo$1565bobo$1564bobo$1563bobo$
1562bobo$1561bobo$1560bobo$1559bobo$1558bobo$1557bobo$1556bobo$1555bob
o$1554bobo$1553bobo$1552bobo$1551bobo$1550bobo$1549bobo$1548bobo$1547b
obo$1546bobo$1545bobo$1544bobo$1543bobo$1542bobo$1541bobo$1540bobo$
1539bobo$1538bobo$1537bobo$1536bobo$1535bobo$1534bobo$1533bobo$1532bob
o$1531bobo$1530bobo$1529bobo$1528bobo$1527bobo$1526bobo$1525bobo$1524b
obo$1523bobo$1522bobo$1521bobo$1520bobo$1519bobo$1518bobo$1517bobo$
1516bobo$1515bobo$1514bobo$1513bobo$1512bobo$1511bobo$1510bobo$1509bob
o$1508bobo$1507bobo$1506bobo$1505bobo$1504bobo$1503bobo$1502bobo$1501b
obo$1500bobo$1499bobo$1498bobo$1497bobo$1496bobo$1495bobo$1494bobo$
1493bobo$1492bobo$1491bobo$1490bobo$1489bobo$1488bobo$1487bobo$1486bob
o$1485bobo$1484bobo$1483bobo$1482bobo$1481bobo$1480bobo$1479bobo$1478b
obo$1477bobo$1476bobo$1475bobo$1474bobo$1473bobo$1472bobo$1471bobo$
1470bobo$1469bobo$1468bobo$1467bobo$1466bobo$1465bobo$1464bobo$1463bob
o$1462bobo$1461bobo$1460bobo$1459bobo$1458bobo$1457bobo$1456bobo$1455b
obo$1454bobo$1453bobo$1452bobo$1451bobo$1450bobo$1449bobo$1448bobo$
1447bobo$1446bobo$1445bobo$1444bobo$1443bobo$1442bobo$1441bobo$1440bob
o$1439bobo$1438bobo$1437bobo$1436bobo$1435bobo$1434bobo$1433bobo$1432b
obo$1431bobo$1430bobo$1429bobo$1428bobo$1427bobo$1426bobo$1425bobo$
1424bobo$1423bobo$1422bobo$1421bobo$1420bobo$1419bobo$1418bobo$1417bob
o$1416bobo$1415bobo$1414bobo$1413bobo$1412bobo$1411bobo$1410bobo$1409b
obo$1408bobo$1407bobo$1406bobo$1405bobo$1404bobo$1403bobo$1402bobo$
1401bobo$1400bobo$1399bobo$1398bobo$1397bobo$1396bobo$1395bobo$1394bob
o$1393bobo$1392bobo$1391bobo$1390bobo$1389bobo$1388bobo$1387bobo$1386b
obo$1385bobo$1384bobo$1383bobo$1382bobo$1381bobo$1380bobo$1379bobo$
1378bobo$1377bobo$1376bobo$1375bobo$1374bobo$1373bobo$1372bobo$1371bob
o$1370bobo$1369bobo$1368bobo$1367bobo$1366bobo$1365bobo$1364bobo$1363b
obo$1362bobo$1361bobo$1360bobo$1359bobo$1358bobo$1357bobo$1356bobo$
1355bobo$1354bobo$1353bobo$1352bobo$1351bobo$1350bobo$1349bobo$1348bob
o$1347bobo$1346bobo$1345bobo$1344bobo$1343bobo$1342bobo$1341bobo$1340b
obo$1339bobo$1338bobo$1337bobo$1336bobo$1335bobo$1334bobo$1333bobo$
1332bobo$1331bobo$1330bobo$1329bobo$1328bobo$1327bobo$1326bobo$1325bob
o$1324bobo$1323bobo$1322bobo$1321bobo$1320bobo$1319bobo$1318bobo$1317b
obo$1316bobo$1315bobo$1314bobo$1313bobo$1312bobo$1311bobo$1310bobo$
1309bobo$1308bobo$1307bobo$1306bobo$1305bobo$1304bobo$1303bobo$1302bob
o$1301bobo$1300bobo$1299bobo$1298bobo$1297bobo$1296bobo$1295bobo$1294b
obo$1293bobo$1292bobo$1291bobo$1290bobo$1289bobo$1288bobo$1287bobo$
1286bobo$1285bobo$1284bobo$1283bobo$1282bobo$1281bobo$1280bobo$1279bob
o$1278bobo$1277bobo$1276bobo$1275bobo$1274bobo$1273bobo$1272bobo$1271b
obo$1270bobo$1269bobo$1268bobo$1267bobo$1266bobo$1265bobo$1264bobo$
1263bobo$1262bobo$1261bobo$1260bobo$1259bobo$1258bobo$1257bobo$1256bob
o$1255bobo$1254bobo$1253bobo$1252bobo$1251bobo$1250bobo$1249bobo$1248b
obo$1247bobo$1246bobo$1245bobo$1244bobo$1243bobo$1242bobo$1241bobo$
1240bobo$1239bobo$1238bobo$1237bobo$1236bobo$1235bobo$1234bobo$1233bob
o$1232bobo$1231bobo$1230bobo$1229bobo$1228bobo$1227bobo$1226bobo$1225b
obo$1224bobo$1223bobo$1222bobo$1221bobo$1220bobo$1219bobo$1218bobo$
1217bobo$1216bobo$1215bobo$1214bobo$1213bobo$1212bobo$1211bobo$1210bob
o$1209bobo$1208bobo$1207bobo$1206bobo$1205bobo$1204bobo$1203bobo$1202b
obo$1201bobo$1200bobo$1199bobo$1198bobo$1197bobo$1196bobo$1195bobo$
1194bobo$1193bobo$1192bobo$1191bobo$1190bobo$1189bobo$1188bobo$1187bob
o$1186bobo$1185bobo$1184bobo$1183bobo$1182bobo$1181bobo$1180bobo$1179b
obo$1178bobo$1177bobo$1176bobo$1175bobo$1174bobo$1173bobo$1172bobo$
1171bobo$1170bobo$1169bobo$1168bobo$1167bobo$1166bobo$1165bobo$1164bob
o$1163bobo$1162bobo$1161bobo$1160bobo$1159bobo$1158bobo$1157bobo$1156b
obo$1155bobo$1154bobo$1153bobo$1152bobo$1151bobo$1150bobo$1149bobo$
1148bobo$1147bobo$1146bobo$1145bobo$1144bobo$1143bobo$1142bobo$1141bob
o$1140bobo$1139bobo$1138bobo$1137bobo$1136bobo$1135bobo$1134bobo$1133b
obo$1132bobo$1131bobo$1130bobo$1129bobo$1128bobo$1127bobo$1126bobo$
1125bobo$1124bobo$1123bobo$1122bobo$1121bobo$1120bobo$1119bobo$1118bob
o$1117bobo$1116bobo$1115bobo$1114bobo$1113bobo$1112bobo$1111bobo$1110b
obo$1109bobo$1108bobo$1107bobo$1106bobo$1105bobo$1104bobo$1103bobo$
1102bobo$1101bobo$1100bobo$1099bobo$1098bobo$1097bobo$1096bobo$1095bob
o$1094bobo$1093bobo$1092bobo$1091bobo$1090bobo$1089bobo$1088bobo$1087b
obo$1086bobo$1085bobo$1084bobo$1083bobo$1082bobo$1081bobo$1080bobo$
1079bobo$1078bobo$1077bobo$1076bobo$1075bobo$1074bobo$1073bobo$1072bob
o$1071bobo$1070bobo$1069bobo$1068bobo$1067bobo$1066bobo$1065bobo$1064b
obo$1063bobo$1062bobo$1061bobo$1060bobo$1059bobo$1058bobo$1057bobo$
1056bobo$1055bobo$1054bobo$1053bobo$1052bobo$1051bobo$1050bobo$1049bob
o$1048bobo$1047bobo$1046bobo$1045bobo$1044bobo$1043bobo$1042bobo$1041b
obo$1040bobo$1039bobo$1038bobo$1037bobo$1036bobo$1035bobo$1034bobo$
1033bobo$1032bobo$1031bobo$1030bobo$1029bobo$1028bobo$1027bobo$1026bob
o$1025bobo$1024bobo$1023bobo$1022bobo$1021bobo$1020bobo$1019bobo$1018b
obo$1017bobo$1016bobo$1015bobo$1014bobo$1013bobo$1012bobo$1011bobo$
1010bobo$1009bobo$1008bobo$1007bobo$1006bobo$1005bobo$1004bobo$1003bob
o$1002bobo$1001bobo$1000bobo$999bobo$998bobo$997bobo$996bobo$995bobo$
994bobo$993bobo$992bobo$991bobo$990bobo$989bobo$988bobo$987bobo$986bob
o$985bobo$984bobo$983bobo$982bobo$981bobo$980bobo$979bobo$978bobo$977b
obo$976bobo$975bobo$974bobo$973bobo$972bobo$971bobo$970bobo$969bobo$
968bobo$967bobo$966bobo$965bobo$964bobo$963bobo$962bobo$961bobo$960bob
o$959bobo$958bobo$957bobo$956bobo$955bobo$954bobo$953bobo$952bobo$951b
obo$950bobo$949bobo$948bobo$947bobo$946bobo$945bobo$944bobo$943bobo$
942bobo$941bobo$940bobo$939bobo$938bobo$937bobo$936bobo$935bobo$934bob
o$933bobo$932bobo$931bobo$930bobo$929bobo$928bobo$927bobo$926bobo$925b
obo$924bobo$923bobo$922bobo$921bobo$920bobo$919bobo$918bobo$917bobo$
916bobo$915bobo$914bobo$913bobo$912bobo$911bobo$910bobo$909bobo$908bob
o$907bobo$906bobo$905bobo$904bobo$903bobo$902bobo$901bobo$900bobo$899b
obo$898bobo$897bobo$896bobo$895bobo$894bobo$893bobo$892bobo$891bobo$
890bobo$889bobo$888bobo$887bobo$886bobo$885bobo$884bobo$883bobo$882bob
o$881bobo$880bobo$879bobo$878bobo$877bobo$876bobo$875bobo$874bobo$873b
obo$872bobo$871bobo$870bobo$869bobo$868bobo$867bobo$866bobo$865bobo$
864bobo$863bobo$862bobo$861bobo$860bobo$859bobo$858bobo$857bobo$856bob
o$855bobo$854bobo$853bobo$852bobo$851bobo$850bobo$849bobo$848bobo$847b
obo$846bobo$845bobo$844bobo$843bobo$842bobo$841bobo$840bobo$839bobo$
838bobo$837bobo$836bobo$835bobo$834bobo$833bobo$832bobo$831bobo$830bob
o$829bobo$828bobo$827bobo$826bobo$825bobo$824bobo$823bobo$822bobo$821b
obo$820bobo$819bobo$818bobo$817bobo$816bobo$815bobo$814bobo$813bobo$
812bobo$811bobo$810bobo$809bobo$808bobo$807bobo$806bobo$805bobo$804bob
o$803bobo$802bobo$801bobo$800bobo$799bobo$798bobo$797bobo$796bobo$795b
obo$794bobo$793bobo$792bobo$791bobo$790bobo$789bobo$788bobo$787bobo$
786bobo$785bobo$784bobo$783bobo$782bobo$781bobo$780bobo$779bobo$778bob
o$777bobo$776bobo$775bobo$774bobo$773bobo$772bobo$771bobo$770bobo$769b
obo$768bobo$767bobo$766bobo$765bobo$764bobo$763bobo$762bobo$761bobo$
760bobo$759bobo$758bobo$757bobo$756bobo$755bobo$754bobo$753bobo$752bob
o$751bobo$750bobo$749bobo$748bobo$747bobo$746bobo$745bobo$744bobo$743b
obo$742bobo$741bobo$740bobo$739bobo$738bobo$737bobo$736bobo$735bobo$
734bobo$733bobo$732bobo$731bobo$730bobo$729bobo$728bobo$727bobo$726bob
o$725bobo$724bobo$723bobo$722bobo$721bobo$720bobo$719bobo$718bobo$717b
obo$716bobo$715bobo$714bobo$713bobo$712bobo$711bobo$710bobo$709bobo$
708bobo$707bobo$706bobo$705bobo$704bobo$703bobo$702bobo$701bobo$700bob
o$699bobo$698bobo$697bobo$696bobo$695bobo$694bobo$693bobo$692bobo$691b
obo$690bobo$689bobo$688bobo$687bobo$686bobo$685bobo$684bobo$683bobo$
682bobo$681bobo$680bobo$679bobo$678bobo$677bobo$676bobo$675bobo$674bob
o$673bobo$672bobo$671bobo$670bobo$669bobo$668bobo$667bobo$666bobo$665b
obo$664bobo$663bobo$662bobo$661bobo$660bobo$659bobo$658bobo$657bobo$
656bobo$655bobo$654bobo$653bobo$652bobo$651bobo$650bobo$649bobo$648bob
o$647bobo$646bobo$645bobo$644bobo$643bobo$642bobo$641bobo$640bobo$639b
obo$638bobo$637bobo$636bobo$635bobo$634bobo$633bobo$632bobo$631bobo$
630bobo$629bobo$628bobo$627bobo$626bobo$625bobo$624bobo$623bobo$622bob
o$621bobo$620bobo$619bobo$618bobo$617bobo$616bobo$615bobo$614bobo$613b
obo$612bobo$611bobo$610bobo$609bobo$608bobo$607bobo$606bobo$605bobo$
604bobo$603bobo$602bobo$601bobo$600bobo$599bobo$598bobo$597bobo$596bob
o$595bobo$594bobo$593bobo$592bobo$591bobo$590bobo$589bobo$588bobo$587b
obo$586bobo$585bobo$584bobo$583bobo$582bobo$581bobo$580bobo$579bobo$
578bobo$577bobo$576bobo$575bobo$574bobo$573bobo$572bobo$571bobo$570bob
o$569bobo$568bobo$567bobo$566bobo$565bobo$564bobo$563bobo$562bobo$561b
obo$560bobo$559bobo$558bobo$557bobo$556bobo$555bobo$554bobo$553bobo$
552bobo$551bobo$550bobo$549bobo$548bobo$547bobo$546bobo$545bobo$544bob
o$543bobo$542bobo$541bobo$540bobo$539bobo$538bobo$537bobo$536bobo$535b
obo$534bobo$533bobo$532bobo$531bobo$530bobo$529bobo$528bobo$527bobo$
526bobo$525bobo$524bobo$523bobo$522bobo$521bobo$520bobo$519bobo$518bob
o$517bobo$516bobo$515bobo$514bobo$513bobo$512bobo$511bobo$510bobo$509b
obo$508bobo$507bobo$506bobo$505bobo$504bobo$503bobo$502bobo$501bobo$
500bobo$499bobo$498bobo$497bobo$496bobo$495bobo$494bobo$493bobo$492bob
o$491bobo$490bobo$489bobo$488bobo$487bobo$486bobo$485bobo$484bobo$483b
obo$482bobo$481bobo$480bobo$479bobo$478bobo$477bobo$476bobo$475bobo$
474bobo$473bobo$472bobo$471bobo$470bobo$469bobo$468bobo$467bobo$466bob
o$465bobo$464bobo$463bobo$462bobo$461bobo$460bobo$459bobo$458bobo$457b
obo$456bobo$455bobo$454bobo$453bobo$452bobo$451bobo$450bobo$449bobo$
448bobo$447bobo$446bobo$445bobo$444bobo$443bobo$442bobo$441bobo$440bob
o$439bobo$438bobo$437bobo$436bobo$435bobo$434bobo$433bobo$432bobo$431b
obo$430bobo$429bobo$428bobo$427bobo$426bobo$425bobo$424bobo$423bobo$
422bobo$421bobo$420bobo$419bobo$418bobo$417bobo$416bobo$415bobo$414bob
o$413bobo$412bobo$411bobo$410bobo$409bobo$408bobo$407bobo$406bobo$405b
obo$404bobo$403bobo$402bobo$401bobo$400bobo$399bobo$398bobo$397bobo$
396bobo$395bobo$394bobo$393bobo$392bobo$391bobo$390bobo$389bobo$388bob
o$387bobo$386bobo$385bobo$384bobo$383bobo$382bobo$381bobo$380bobo$379b
obo$378bobo$377bobo$376bobo$375bobo$374bobo$373bobo$372bobo$371bobo$
370bobo$369bobo$368bobo$367bobo$366bobo$365bobo$364bobo$363bobo$362bob
o$361bobo$360bobo$359bobo$358bobo$357bobo$356bobo$355bobo$354bobo$353b
obo$352bobo$351bobo$350bobo$349bobo$348bobo$347bobo$346bobo$345bobo$
344bobo$343bobo$342bobo$341bobo$340bobo$339bobo$338bobo$337bobo$336bob
o$335bobo$334bobo$333bobo$332bobo$331bobo$330bobo$329bobo$328bobo$327b
obo$326bobo$325bobo$324bobo$323bobo$322bobo$321bobo$320bobo$319bobo$
318bobo$317bobo$316bobo$315bobo$314bobo$313bobo$312bobo$311bobo$310bob
o$309bobo$308bobo$307bobo$306bobo$305bobo$304bobo$303bobo$302bobo$301b
obo$300bobo$299bobo$298bobo$297bobo$296bobo$295bobo$294bobo$293bobo$
292bobo$291bobo$290bobo$289bobo$288bobo$287bobo$286bobo$285bobo$284bob
o$283bobo$282bobo$281bobo$280bobo$279bobo$278bobo$277bobo$276bobo$275b
obo$274bobo$273bobo$272bobo$271bobo$270bobo$269bobo$268bobo$267bobo$
266bobo$265bobo$264bobo$263bobo$262bobo$261bobo$260bobo$259bobo$258bob
o$257bobo$256bobo$255bobo$254bobo$253bobo$252bobo$251bobo$250bobo$249b
obo$248bobo$247bobo$246bobo$245bobo$244bobo$243bobo$242bobo$241bobo$
240bobo$239bobo$238bobo$237bobo$236bobo$235bobo$234bobo$233bobo$232bob
o$231bobo$230bobo$229bobo$228bobo$227bobo$226bobo$225bobo$224bobo$223b
obo$222bobo$221bobo$220bobo$219bobo$218bobo$217bobo$216bobo$215bobo$
214bobo$213bobo$212bobo$211bobo$210bobo$209bobo$208bobo$207bobo$206bob
o$205bobo$204bobo$203bobo$202bobo$201bobo$200bobo$199bobo$198bobo$197b
obo$196bobo$195bobo$194bobo$193bobo$192bobo$191bobo$190bobo$189bobo$
188bobo$187bobo$186bobo$185bobo$184bobo$183bobo$182bobo$181bobo$180bob
o$179bobo$178bobo$177bobo$176bobo$175bobo$174bobo$173bobo$172bobo$171b
obo$170bobo$169bobo$168bobo$167bobo$166bobo$165bobo$164bobo$163bobo$
162bobo$161bobo$160bobo$159bobo$158bobo$157bobo$156bobo$155bobo$154bob
o$153bobo$152bobo$151bobo$150bobo$149bobo$148bobo$147bobo$146bobo$145b
obo$144bobo$143bobo$142bobo$141bobo$140bobo$139bobo$138bobo$137bobo$
136bobo$135bobo$134bobo$133bobo$132bobo$131bobo$130bobo$129bobo$128bob
o$127bobo$126bobo$125bobo$124bobo$123bobo$122bobo$121bobo$120bobo$119b
obo$118bobo$117bobo$116bobo$115bobo$114bobo$113bobo$112bobo$111bobo$
110bobo$109bobo$108bobo$107bobo$106bobo$105bobo$104bobo$103bobo$102bob
o$101bobo$100bobo$99bobo$98bobo$97bobo$96bobo$95bobo$94bobo$93bobo$92b
obo$91bobo$90bobo$89bobo$88bobo$87bobo$86bobo$85bobo$84bobo$83bobo$82b
obo$81bobo$80bobo$79bobo$78bobo$77bobo$76bobo$75bobo$74bobo$73bobo$72b
obo$71bobo$70bobo$69bobo$68bobo$67bobo$66bobo$65bobo$64bobo$63bobo$62b
obo$61bobo$60bobo$59bobo$58bobo$57bobo$56bobo$55bobo$54bobo$53bobo$52b
obo$51bobo$50bobo$49bobo$48bobo$47bobo$46bobo$45bobo$44bobo$43bobo$42b
obo$41bobo$40bobo$39bobo$38bobo$37bobo$36bobo$35bobo$34bobo$33bobo$32b
obo$31bobo$30bobo$29bobo$28bobo$27bobo$26bobo$25bobo$24bobo$23bobo$22b
obo$21bobo$20bobo$19bobo$18bobo$17bobo$16bobo$15bobo$14bobo$13bobo$12b
obo$11bobo$10bobo$9bobo$8bobo$7bobo$6bobo$5bobo$4bobo$3bobo$2bobo$bobo
$obo$2o!

The above pattern contains the collision that has the highest population debris, which was 8212. I found that number using this script:

Code: Select all

import golly as g

pat = g.parse("4244b2o$4243bobo$4242bobo$4241bobo$4240bobo$4239bobo$4238bobo$4237bobo$4236bobo$4235bobo$4234bobo$4233bobo$4232bobo$4231bobo$4230bobo$4229bobo$4228bobo$4227bobo$4226bobo$4225bobo$4224bobo$4223bobo$4222bobo$4221bobo$4220bobo$4219bobo$4218bobo$4217bobo$4216bobo$4215bobo$4214bobo$4213bobo$4212bobo$4211bobo$4210bobo$4209bobo$4208bobo$4207bobo$4206bobo$4205bobo$4204bobo$4203bobo$4202bobo$4201bobo$4200bobo$4199bobo$4198bobo$4197bobo$4196bobo$4195bobo$4194bobo$4193bobo$4192bobo$4191bobo$4190bobo$4189bobo$4188bobo$4187bobo$4186bobo$4185bobo$4184bobo$4183bobo$4182bobo$4181bobo$4180bobo$4179bobo$4178bobo$4177bobo$4176bobo$4175bobo$4174bobo$4173bobo$4172bobo$4171bobo$4170bobo$4169bobo$4168bobo$4167bobo$4166bobo$4165bobo$4164bobo$4163bobo$4162bobo$4161bobo$4160bobo$4159bobo$4158bobo$4157bobo$4156bobo$4155bobo$4154bobo$4153bobo$4152bobo$4151bobo$4150bobo$4149bobo$4148bobo$4147bobo$4146bobo$4145bobo$4144bobo$4143bobo$4142bobo$4141bobo$4140bobo$4139bobo$4138bobo$4137bobo$4136bobo$4135bobo$4134bobo$4133bobo$4132bobo$4131bobo$4130bobo$4129bobo$4128bobo$4127bobo$4126bobo$4125bobo$4124bobo$4123bobo$4122bobo$4121bobo$4120bobo$4119bobo$4118bobo$4117bobo$4116bobo$4115bobo$4114bobo$4113bobo$4112bobo$4111bobo$4110bobo$4109bobo$4108bobo$4107bobo$4106bobo$4105bobo$4104bobo$4103bobo$4102bobo$4101bobo$4100bobo$4099bobo$4098bobo$4097bobo$4096bobo$4095bobo$4094bobo$4093bobo$4092bobo$4091bobo$4090bobo$4089bobo$4088bobo$4087bobo$4086bobo$4085bobo$4084bobo$4083bobo$4082bobo$4081bobo$4080bobo$4079bobo$4078bobo$4077bobo$4076bobo$4075bobo$4074bobo$4073bobo$4072bobo$4071bobo$4070bobo$4069bobo$4068bobo$4067bobo$4066bobo$4065bobo$4064bobo$4063bobo$4062bobo$4061bobo$4060bobo$4059bobo$4058bobo$4057bobo$4056bobo$4055bobo$4054bobo$4053bobo$4052bobo$4051bobo$4050bobo$4049bobo$4048bobo$4047bobo$4046bobo$4045bobo$4044bobo$4043bobo$4042bobo$4041bobo$4040bobo$4039bobo$4038bobo$4037bobo$4036bobo$4035bobo$4034bobo$4033bobo$4032bobo$4031bobo$4030bobo$4029bobo$4028bobo$4027bobo$4026bobo$4025bobo$4024bobo$4023bobo$4022bobo$4021bobo$4020bobo$4019bobo$4018bobo$4017bobo$4016bobo$4015bobo$4014bobo$4013bobo$4012bobo$4011bobo$4010bobo$4009bobo$4008bobo$4007bobo$4006bobo$4005bobo$4004bobo$4003bobo$4002bobo$4001bobo$4000bobo$3999bobo$3998bobo$3997bobo$3996bobo$3995bobo$3994bobo$3993bobo$3992bobo$3991bobo$3990bobo$3989bobo$3988bobo$3987bobo$3986bobo$3985bobo$3984bobo$3983bobo$3982bobo$3981bobo$3980bobo$3979bobo$3978bobo$3977bobo$3976bobo$3975bobo$3974bobo$3973bobo$3972bobo$3971bobo$3970bobo$3969bobo$3968bobo$3967bobo$3966bobo$3965bobo$3964bobo$3963bobo$3962bobo$3961bobo$3960bobo$3959bobo$3958bobo$3957bobo$3956bobo$3955bobo$3954bobo$3953bobo$3952bobo$3951bobo$3950bobo$3949bobo$3948bobo$3947bobo$3946bobo$3945bobo$3944bobo$3943bobo$3942bobo$3941bobo$3940bobo$3939bobo$3938bobo$3937bobo$3936bobo$3935bobo$3934bobo$3933bobo$3932bobo$3931bobo$3930bobo$3929bobo$3928bobo$3927bobo$3926bobo$3925bobo$3924bobo$3923bobo$3922bobo$3921bobo$3920bobo$3919bobo$3918bobo$3917bobo$3916bobo$3915bobo$3914bobo$3913bobo$3912bobo$3911bobo$3910bobo$3909bobo$3908bobo$3907bobo$3906bobo$3905bobo$3904bobo$3903bobo$3902bobo$3901bobo$3900bobo$3899bobo$3898bobo$3897bobo$3896bobo$3895bobo$3894bobo$3893bobo$3892bobo$3891bobo$3890bobo$3889bobo$3888bobo$3887bobo$3886bobo$3885bobo$3884bobo$3883bobo$3882bobo$3881bobo$3880bobo$3879bobo$3878bobo$3877bobo$3876bobo$3875bobo$3874bobo$3873bobo$3872bobo$3871bobo$3870bobo$3869bobo$3868bobo$3867bobo$3866bobo$3865bobo$3864bobo$3863bobo$3862bobo$3861bobo$3860bobo$3859bobo$3858bobo$3857bobo$3856bobo$3855bobo$3854bobo$3853bobo$3852bobo$3851bobo$3850bobo$3849bobo$3848bobo$3847bobo$3846bobo$3845bobo$3844bobo$3843bobo$3842bobo$3841bobo$3840bobo$3839bobo$3838bobo$3837bobo$3836bobo$3835bobo$3834bobo$3833bobo$3832bobo$3831bobo$3830bobo$3829bobo$3828bobo$3827bobo$3826bobo$3825bobo$3824bobo$3823bobo$3822bobo$3821bobo$3820bobo$3819bobo$3818bobo$3817bobo$3816bobo$3815bobo$3814bobo$3813bobo$3812bobo$3811bobo$3810bobo$3809bobo$3808bobo$3807bobo$3806bobo$3805bobo$3804bobo$3803bobo$3802bobo$3801bobo$3800bobo$3799bobo$3798bobo$3797bobo$3796bobo$3795bobo$3794bobo$3793bobo$3792bobo$3791bobo$3790bobo$3789bobo$3788bobo$3787bobo$3786bobo$3785bobo$3784bobo$3783bobo$3782bobo$3781bobo$3780bobo$3779bobo$3778bobo$3777bobo$3776bobo$3775bobo$3774bobo$3773bobo$3772bobo$3771bobo$3770bobo$3769bobo$3768bobo$3767bobo$3766bobo$3765bobo$3764bobo$3763bobo$3762bobo$3761bobo$3760bobo$3759bobo$3758bobo$3757bobo$3756bobo$3755bobo$3754bobo$3753bobo$3752bobo$3751bobo$3750bobo$3749bobo$3748bobo$3747bobo$3746bobo$3745bobo$3744bobo$3743bobo$3742bobo$3741bobo$3740bobo$3739bobo$3738bobo$3737bobo$3736bobo$3735bobo$3734bobo$3733bobo$3732bobo$3731bobo$3730bobo$3729bobo$3728bobo$3727bobo$3726bobo$3725bobo$3724bobo$3723bobo$3722bobo$3721bobo$3720bobo$3719bobo$3718bobo$3717bobo$3716bobo$3715bobo$3714bobo$3713bobo$3712bobo$3711bobo$3710bobo$3709bobo$3708bobo$3707bobo$3706bobo$3705bobo$3704bobo$3703bobo$3702bobo$3701bobo$3700bobo$3699bobo$3698bobo$3697bobo$3696bobo$3695bobo$3694bobo$3693bobo$3692bobo$3691bobo$3690bobo$3689bobo$3688bobo$3687bobo$3686bobo$3685bobo$3684bobo$3683bobo$3682bobo$3681bobo$3680bobo$3679bobo$3678bobo$3677bobo$3676bobo$3675bobo$3674bobo$3673bobo$3672bobo$3671bobo$3670bobo$3669bobo$3668bobo$3667bobo$3666bobo$3665bobo$3664bobo$3663bobo$3662bobo$3661bobo$3660bobo$3659bobo$3658bobo$3657bobo$3656bobo$3655bobo$3654bobo$3653bobo$3652bobo$3651bobo$3650bobo$3649bobo$3648bobo$3647bobo$3646bobo$3645bobo$3644bobo$3643bobo$3642bobo$3641bobo$3640bobo$3639bobo$3638bobo$3637bobo$3636bobo$3635bobo$3634bobo$3633bobo$3632bobo$3631bobo$3630bobo$3629bobo$3628bobo$3627bobo$3626bobo$3625bobo$3624bobo$3623bobo$3622bobo$3621bobo$3620bobo$3619bobo$3618bobo$3617bobo$3616bobo$3615bobo$3614bobo$3613bobo$3612bobo$3611bobo$3610bobo$3609bobo$3608bobo$3607bobo$3606bobo$3605bobo$3604bobo$3603bobo$3602bobo$3601bobo$3600bobo$3599bobo$3598bobo$3597bobo$3596bobo$3595bobo$3594bobo$3593bobo$3592bobo$3591bobo$3590bobo$3589bobo$3588bobo$3587bobo$3586bobo$3585bobo$3584bobo$3583bobo$3582bobo$3581bobo$3580bobo$3579bobo$3578bobo$3577bobo$3576bobo$3575bobo$3574bobo$3573bobo$3572bobo$3571bobo$3570bobo$3569bobo$3568bobo$3567bobo$3566bobo$3565bobo$3564bobo$3563bobo$3562bobo$3561bobo$3560bobo$3559bobo$3558bobo$3557bobo$3556bobo$3555bobo$3554bobo$3553bobo$3552bobo$3551bobo$3550bobo$3549bobo$3548bobo$3547bobo$3546bobo$3545bobo$3544bobo$3543bobo$3542bobo$3541bobo$3540bobo$3539bobo$3538bobo$3537bobo$3536bobo$3535bobo$3534bobo$3533bobo$3532bobo$3531bobo$3530bobo$3529bobo$3528bobo$3527bobo$3526bobo$3525bobo$3524bobo$3523bobo$3522bobo$3521bobo$3520bobo$3519bobo$3518bobo$3517bobo$3516bobo$3515bobo$3514bobo$3513bobo$3512bobo$3511bobo$3510bobo$3509bobo$3508bobo$3507bobo$3506bobo$3505bobo$3504bobo$3503bobo$3502bobo$3501bobo$3500bobo$3499bobo$3498bobo$3497bobo$3496bobo$3495bobo$3494bobo$3493bobo$3492bobo$3491bobo$3490bobo$3489bobo$3488bobo$3487bobo$3486bobo$3485bobo$3484bobo$3483bobo$3482bobo$3481bobo$3480bobo$3479bobo$3478bobo$3477bobo$3476bobo$3475bobo$3474bobo$3473bobo$3472bobo$3471bobo$3470bobo$3469bobo$3468bobo$3467bobo$3466bobo$3465bobo$3464bobo$3463bobo$3462bobo$3461bobo$3460bobo$3459bobo$3458bobo$3457bobo$3456bobo$3455bobo$3454bobo$3453bobo$3452bobo$3451bobo$3450bobo$3449bobo$3448bobo$3447bobo$3446bobo$3445bobo$3444bobo$3443bobo$3442bobo$3441bobo$3440bobo$3439bobo$3438bobo$3437bobo$3436bobo$3435bobo$3434bobo$3433bobo$3432bobo$3431bobo$3430bobo$3429bobo$3428bobo$3427bobo$3426bobo$3425bobo$3424bobo$3423bobo$3422bobo$3421bobo$3420bobo$3419bobo$3418bobo$3417bobo$3416bobo$3415bobo$3414bobo$3413bobo$3412bobo$3411bobo$3410bobo$3409bobo$3408bobo$3407bobo$3406bobo$3405bobo$3404bobo$3403bobo$3402bobo$3401bobo$3400bobo$3399bobo$3398bobo$3397bobo$3396bobo$3395bobo$3394bobo$3393bobo$3392bobo$3391bobo$3390bobo$3389bobo$3388bobo$3387bobo$3386bobo$3385bobo$3384bobo$3383bobo$3382bobo$3381bobo$3380bobo$3379bobo$3378bobo$3377bobo$3376bobo$3375bobo$3374bobo$3373bobo$3372bobo$3371bobo$3370bobo$3369bobo$3368bobo$3367bobo$3366bobo$3365bobo$3364bobo$3363bobo$3362bobo$3361bobo$3360bobo$3359bobo$3358bobo$3357bobo$3356bobo$3355bobo$3354bobo$3353bobo$3352bobo$3351bobo$3350bobo$3349bobo$3348bobo$3347bobo$3346bobo$3345bobo$3344bobo$3343bobo$3342bobo$3341bobo$3340bobo$3339bobo$3338bobo$3337bobo$3336bobo$3335bobo$3334bobo$3333bobo$3332bobo$3331bobo$3330bobo$3329bobo$3328bobo$3327bobo$3326bobo$3325bobo$3324bobo$3323bobo$3322bobo$3321bobo$3320bobo$3319bobo$3318bobo$3317bobo$3316bobo$3315bobo$3314bobo$3313bobo$3312bobo$3311bobo$3310bobo$3309bobo$3308bobo$3307bobo$3306bobo$3305bobo$3304bobo$3303bobo$3302bobo$3301bobo$3300bobo$3299bobo$3298bobo$3297bobo$3296bobo$3295bobo$3294bobo$3293bobo$3292bobo$3291bobo$3290bobo$3289bobo$3288bobo$3287bobo$3286bobo$3285bobo$3284bobo$3283bobo$3282bobo$3281bobo$3280bobo$3279bobo$3278bobo$3277bobo$3276bobo$3275bobo$3274bobo$3273bobo$3272bobo$3271bobo$3270bobo$3269bobo$3268bobo$3267bobo$3266bobo$3265bobo$3264bobo$3263bobo$3262bobo$3261bobo$3260bobo$3259bobo$3258bobo$3257bobo$3256bobo$3255bobo$3254bobo$3253bobo$3252bobo$3251bobo$3250bobo$3249bobo$3248bobo$3247bobo$3246bobo$3245bobo$3244bobo$3243bobo$3242bobo$3241bobo$3240bobo$3239bobo$3238bobo$3237bobo$3236bobo$3235bobo$3234bobo$3233bobo$3232bobo$3231bobo$3230bobo$3229bobo$3228bobo$3227bobo$3226bobo$3225bobo$3224bobo$3223bobo$3222bobo$3221bobo$3220bobo$3219bobo$3218bobo$3217bobo$3216bobo$3215bobo$3214bobo$3213bobo$3212bobo$3211bobo$3210bobo$3209bobo$3208bobo$3207bobo$3206bobo$3205bobo$3204bobo$3203bobo$3202bobo$3201bobo$3200bobo$3199bobo$3198bobo$3197bobo$3196bobo$3195bobo$3194bobo$3193bobo$3192bobo$3191bobo$3190bobo$3189bobo$3188bobo$3187bobo$3186bobo$3185bobo$3184bobo$3183bobo$3182bobo$3181bobo$3180bobo$3179bobo$3178bobo$3177bobo$3176bobo$3175bobo$3174bobo$3173bobo$3172bobo$3171bobo$3170bobo$3169bobo$3168bobo$3167bobo$3166bobo$3165bobo$3164bobo$3163bobo$3162bobo$3161bobo$3160bobo$3159bobo$3158bobo$3157bobo$3156bobo$3155bobo$3154bobo$3153bobo$3152bobo$3151bobo$3150bobo$3149bobo$3148bobo$3147bobo$3146bobo$3145bobo$3144bobo$3143bobo$3142bobo$3141bobo$3140bobo$3139bobo$3138bobo$3137bobo$3136bobo$3135bobo$3134bobo$3133bobo$3132bobo$3131bobo$3130bobo$3129bobo$3128bobo$3127bobo$3126bobo$3125bobo$3124bobo$3123bobo$3122bobo$3121bobo$3120bobo$3119bobo$3118bobo$3117bobo$3116bobo$3115bobo$3114bobo$3113bobo$3112bobo$3111bobo$3110bobo$3109bobo$3108bobo$3107bobo$3106bobo$3105bobo$3104bobo$3103bobo$3102bobo$3101bobo$3100bobo$3099bobo$3098bobo$3097bobo$3096bobo$3095bobo$3094bobo$3093bobo$3092bobo$3091bobo$3090bobo$3089bobo$3088bobo$3087bobo$3086bobo$3085bobo$3084bobo$3083bobo$3082bobo$3081bobo$3080bobo$3079bobo$3078bobo$3077bobo$3076bobo$3075bobo$3074bobo$3073bobo$3072bobo$3071bobo$3070bobo$3069bobo$3068bobo$3067bobo$3066bobo$3065bobo$3064bobo$3063bobo$3062bobo$3061bobo$3060bobo$3059bobo$3058bobo$3057bobo$3056bobo$3055bobo$3054bobo$3053bobo$3052bobo$3051bobo$3050bobo$3049bobo$3048bobo$3047bobo$3046bobo$3045bobo$3044bobo$3043bobo$3042bobo$3041bobo$3040bobo$3039bobo$3038bobo$3037bobo$3036bobo$3035bobo$3034bobo$3033bobo$3032bobo$3031bobo$3030bobo$3029bobo$3028bobo$3027bobo$3026bobo$3025bobo$3024bobo$3023bobo$3022bobo$3021bobo$3020bobo$3019bobo$3018bobo$3017bobo$3016bobo$3015bobo$3014bobo$3013bobo$3012bobo$3011bobo$3010bobo$3009bobo$3008bobo$3007bobo$3006bobo$3005bobo$3004bobo$3003bobo$3002bobo$3001bobo$3000bobo$2999bobo$2998bobo$2997bobo$2996bobo$2995bobo$2994bobo$2993bobo$2992bobo$2991bobo$2990bobo$2989bobo$2988bobo$2987bobo$2986bobo$2985bobo$2984bobo$2983bobo$2982bobo$2981bobo$2980bobo$2979bobo$2978bobo$2977bobo$2976bobo$2975bobo$2974bobo$2973bobo$2972bobo$2971bobo$2970bobo$2969bobo$2968bobo$2967bobo$2966bobo$2965bobo$2964bobo$2963bobo$2962bobo$2961bobo$2960bobo$2959bobo$2958bobo$2957bobo$2956bobo$2955bobo$2954bobo$2953bobo$2952bobo$2951bobo$2950bobo$2949bobo$2948bobo$2947bobo$2946bobo$2945bobo$2944bobo$2943bobo$2942bobo$2941bobo$2940bobo$2939bobo$2938bobo$2937bobo$2936bobo$2935bobo$2934bobo$2933bobo$2932bobo$2931bobo$2930bobo$2929bobo$2928bobo$2927bobo$2926bobo$2925bobo$2924bobo$2923bobo$2922bobo$2921bobo$2920bobo$2919bobo$2918bobo$2917bobo$2916bobo$2915bobo$2914bobo$2913bobo$2912bobo$2911bobo$2910bobo$2909bobo$2908bobo$2907bobo$2906bobo$2905bobo$2904bobo$2903bobo$2902bobo$2901bobo$2900bobo$2899bobo$2898bobo$2897bobo$2896bobo$2895bobo$2894bobo$2893bobo$2892bobo$2891bobo$2890bobo$2889bobo$2888bobo$2887bobo$2886bobo$2885bobo$2884bobo$2883bobo$2882bobo$2881bobo$2880bobo$2879bobo$2878bobo$2877bobo$2876bobo$2875bobo$2874bobo$2873bobo$2872bobo$2871bobo$2870bobo$2869bobo$2868bobo$2867bobo$2866bobo$2865bobo$2864bobo$2863bobo$2862bobo$2861bobo$2860bobo$2859bobo$2858bobo$2857bobo$2856bobo$2855bobo$2854bobo$2853bobo$2852bobo$2851bobo$2850bobo$2849bobo$2848bobo$2847bobo$2846bobo$2845bobo$2844bobo$2843bobo$2842bobo$2841bobo$2840bobo$2839bobo$2838bobo$2837bobo$2836bobo$2835bobo$2834bobo$2833bobo$2832bobo$2831bobo$2830bobo$2829bobo$2828bobo$2827bobo$2826bobo$2825bobo$2824bobo$2823bobo$2822bobo$2821bobo$2820bobo$2819bobo$2818bobo$2817bobo$2816bobo$2815bobo$2814bobo$2813bobo$2812bobo$2811bobo$2810bobo$2809bobo$2808bobo$2807bobo$2806bobo$2805bobo$2804bobo$2803bobo$2802bobo$2801bobo$2800bobo$2799bobo$2798bobo$2797bobo$2796bobo$2795bobo$2794bobo$2793bobo$2792bobo$2791bobo$2790bobo$2789bobo$2788bobo$2787bobo$2786bobo$2785bobo$2784bobo$2783bobo$2782bobo$2781bobo$2780bobo$2779bobo$2778bobo$2777bobo$2776bobo$2775bobo$2774bobo$2773bobo$2772bobo$2771bobo$2770bobo$2769bobo$2768bobo$2767bobo$2766bobo$2765bobo$2764bobo$2763bobo$2762bobo$2761bobo$2760bobo$2759bobo$2758bobo$2757bobo$2756bobo$2755bobo$2754bobo$2753bobo$2752bobo$2751bobo$2750bobo$2749bobo$2748bobo$2747bobo$2746bobo$2745bobo$2744bobo$2743bobo$2742bobo$2741bobo$2740bobo$2739bobo$2738bobo$2737bobo$2736bobo$2735bobo$2734bobo$2733bobo$2732bobo$2731bobo$2730bobo$2729bobo$2728bobo$2727bobo$2726bobo$2725bobo$2724bobo$2723bobo$2722bobo$2721bobo$2720bobo$2719bobo$2718bobo$2717bobo$2716bobo$2715bobo$2714bobo$2713bobo$2712bobo$2711bobo$2710bobo$2709bobo$2708bobo$2707bobo$2706bobo$2705bobo$2704bobo$2703bobo$2702bobo$2701bobo$2700bobo$2699bobo$2698bobo$2697bobo$2696bobo$2695bobo$2694bobo$2693bobo$2692bobo$2691bobo$2690bobo$2689bobo$2688bobo$2687bobo$2686bobo$2685bobo$2684bobo$2683bobo$2682bobo$2681bobo$2680bobo$2679bobo$2678bobo$2677bobo$2676bobo$2675bobo$2674bobo$2673bobo$2672bobo$2671bobo$2670bobo$2669bobo$2668bobo$2667bobo$2666bobo$2665bobo$2664bobo$2663bobo$2662bobo$2661bobo$2660bobo$2659bobo$2658bobo$2657bobo$2656bobo$2655bobo$2654bobo$2653bobo$2652bobo$2651bobo$2650bobo$2649bobo$2648bobo$2647bobo$2646bobo$2645bobo$2644bobo$2643bobo$2642bobo$2641bobo$2640bobo$2639bobo$2638bobo$2637bobo$2636bobo$2635bobo$2634bobo$2633bobo$2632bobo$2631bobo$2630bobo$2629bobo$2628bobo$2627bobo$2626bobo$2625bobo$2624bobo$2623bobo$2622bobo$2621bobo$2620bobo$2619bobo$2618bobo$2617bobo$2616bobo$2615bobo$2614bobo$2613bobo$2612bobo$2611bobo$2610bobo$2609bobo$2608bobo$2607bobo$2606bobo$2605bobo$2604bobo$2603bobo$2602bobo$2601bobo$2600bobo$2599bobo$2598bobo$2597bobo$2596bobo$2595bobo$2594bobo$2593bobo$2592bobo$2591bobo$2590bobo$2589bobo$2588bobo$2587bobo$2586bobo$2585bobo$2584bobo$2583bobo$2582bobo$2581bobo$2580bobo$2579bobo$2578bobo$2577bobo$2576bobo$2575bobo$2574bobo$2573bobo$2572bobo$2571bobo$2570bobo$2569bobo$2568bobo$2567bobo$2566bobo$2565bobo$2564bobo$2563bobo$2562bobo$2561bobo$2560bobo$2559bobo$2558bobo$2557bobo$2556bobo$2555bobo$2554bobo$2553bobo$2552bobo$2551bobo$2550bobo$2549bobo$2548bobo$2547bobo$2546bobo$2545bobo$2544bobo$2543bobo$2542bobo$2541bobo$2540bobo$2539bobo$2538bobo$2537bobo$2536bobo$2535bobo$2534bobo$2533bobo$2532bobo$2531bobo$2530bobo$2529bobo$2528bobo$2527bobo$2526bobo$2525bobo$2524bobo$2523bobo$2522bobo$2521bobo$2520bobo$2519bobo$2518bobo$2517bobo$2516bobo$2515bobo$2514bobo$2513bobo$2512bobo$2511bobo$2510bobo$2509bobo$2508bobo$2507bobo$2506bobo$2505bobo$2504bobo$2503bobo$2502bobo$2501bobo$2500bobo$2499bobo$2498bobo$2497bobo$2496bobo$2495bobo$2494bobo$2493bobo$2492bobo$2491bobo$2490bobo$2489bobo$2488bobo$2487bobo$2486bobo$2485bobo$2484bobo$2483bobo$2482bobo$2481bobo$2480bobo$2479bobo$2478bobo$2477bobo$2476bobo$2475bobo$2474bobo$2473bobo$2472bobo$2471bobo$2470bobo$2469bobo$2468bobo$2467bobo$2466bobo$2465bobo$2464bobo$2463bobo$2462bobo$2461bobo$2460bobo$2459bobo$2458bobo$2457bobo$2456bobo$2455bobo$2454bobo$2453bobo$2452bobo$2451bobo$2450bobo$2449bobo$2448bobo$2447bobo$2446bobo$2445bobo$2444bobo$2443bobo$2442bobo$2441bobo$2440bobo$2439bobo$2438bobo$2437bobo$2436bobo$2435bobo$2434bobo$2433bobo$2432bobo$2431bobo$2430bobo$2429bobo$2428bobo$2427bobo$2426bobo$2425bobo$2424bobo$2423bobo$2422bobo$2421bobo$2420bobo$2419bobo$2418bobo$2417bobo$2416bobo$2415bobo$2414bobo$2413bobo$2412bobo$2411bobo$2410bobo$2409bobo$2408bobo$2407bobo$2406bobo$2405bobo$2404bobo$2403bobo$2402bobo$2401bobo$2400bobo$2399bobo$2398bobo$2397bobo$2396bobo$2395bobo$2394bobo$2393bobo$2392bobo$2391bobo$2390bobo$2389bobo$2388bobo$2387bobo$2386bobo$2385bobo$2384bobo$2383bobo$2382bobo$2381bobo$2380bobo$2379bobo$2378bobo$2377bobo$2376bobo$2375bobo$2374bobo$2373bobo$2372bobo$2371bobo$2370bobo$2369bobo$2368bobo$2367bobo$2366bobo$2365bobo$2364bobo$2363bobo$2362bobo$2361bobo$2360bobo$2359bobo$2358bobo$2357bobo$2356bobo$2355bobo$2354bobo$2353bobo$2352bobo$2351bobo$2350bobo$2349bobo$2348bobo$2347bobo$2346bobo$2345bobo$2344bobo$2343bobo$2342bobo$2341bobo$2340bobo$2339bobo$2338bobo$2337bobo$2336bobo$2335bobo$2334bobo$2333bobo$2332bobo$2331bobo$2330bobo$2329bobo$2328bobo$2327bobo$2326bobo$2325bobo$2324bobo$2323bobo$2322bobo$2321bobo$2320bobo$2319bobo$2318bobo$2317bobo$2316bobo$2315bobo$2314bobo$2313bobo$2312bobo$2311bobo$2310bobo$2309bobo$2308bobo$2307bobo$2306bobo$2305bobo$2304bobo$2303bobo$2302bobo$2301bobo$2300bobo$2299bobo$2298bobo$2297bobo$2296bobo$2295bobo$2294bobo$2293bobo$2292bobo$2291bobo$2290bobo$2289bobo$2288bobo$2287bobo$2286bobo$2285bobo$2284bobo$2283bobo$2282bobo$2281bobo$2280bobo$2279bobo$2278bobo$2277bobo$2276bobo$2275bobo$2274bobo$2273bobo$2272bobo$2271bobo$2270bobo$2269bobo$2268bobo$2267bobo$2266bobo$2265bobo$2264bobo$2263bobo$2262bobo$2261bobo$2260bobo$2259bobo$2258bobo$2257bobo$2256bobo$2255bobo$2254bobo$2253bobo$2252bobo$2251bobo$2250bobo$2249bobo$2248bobo$2247bobo$2246bobo$2245bobo$2244bobo$2243bobo$2242bobo$2241bobo$2240bobo$2239bobo$2238bobo$2237bobo$2236bobo$2235bobo$2234bobo$2233bobo$2232bobo$2231bobo$2230bobo$2229bobo$2228bobo$2227bobo$2226bobo$2225bobo$2224bobo$2223bobo$2222bobo$2221bobo$2220bobo$2219bobo$2218bobo$2217bobo$2216bobo$2215bobo$2214bobo$2213bobo$2212bobo$2211bobo$2210bobo$2209bobo$2208bobo$2207bobo$2206bobo$2205bobo$2204bobo$2203bobo$2202bobo$2201bobo$2200bobo$2199bobo$2198bobo$2197bobo$2196bobo$2195bobo$2194bobo$2193bobo$2192bobo$2191bobo$2190bobo$2189bobo$2188bobo$2187bobo$2186bobo$2185bobo$2184bobo$2183bobo$2182bobo$2181bobo$2180bobo$2179bobo$2178bobo$2177bobo$2176bobo$2175bobo$2174bobo$2173bobo$2172bobo$2171bobo$2170bobo$2169bobo$2168bobo$2167bobo$2166bobo$2165bobo$2164bobo$2163bobo$2162bobo$2161bobo$2160bobo$2159bobo$2158bobo$2157bobo$2156bobo$2155bobo$2154bobo$2153bobo$2152bobo$2151bobo$2150bobo$2149bobo$2148bobo$2147bobo$2146bobo$2145bobo$2144bobo$2143bobo$2142bobo$2141bobo$2140bobo$2139bobo$2138bobo$2137bobo$2136bobo$2135bobo$2134bobo$2133bobo$2132bobo$2131bobo$2130bobo$2129bobo$2128bobo$2127bobo$2126bobo$2125bobo$2124bobo$2123bobo$2122bobo$2121bobo$2120bobo$2119bobo$2118bobo$2117bobo$2116bobo$2115bobo$2114bobo$2113bobo$2112bobo$2111bobo$2110bobo$2109bobo$2108bobo$2107bobo$2106bobo$2105bobo$2104bobo$2103bobo$2102bobo$2101bobo$2100bobo$2099bobo$2098bobo$2097bobo$2096bobo$2095bobo$2094bobo$2093bobo$2092bobo$2091bobo$2090bobo$2089bobo$2088bobo$2087bobo$2086bobo$2085bobo$2084bobo$2083bobo$2082bobo$2081bobo$2080bobo$2079bobo$2078bobo$2077bobo$2076bobo$2075bobo$2074bobo$2073bobo$2072bobo$2071bobo$2070bobo$2069bobo$2068bobo$2067bobo$2066bobo$2065bobo$2064bobo$2063bobo$2062bobo$2061bobo$2060bobo$2059bobo$2058bobo$2057bobo$2056bobo$2055bobo$2054bobo$2053bobo$2052bobo$2051bobo$2050bobo$2049bobo$2048bobo$2047bobo$2046bobo$2045bobo$2044bobo$2043bobo$2042bobo$2041bobo$2040bobo$2039bobo$2038bobo$2037bobo$2036bobo$2035bobo$2034bobo$2033bobo$2032bobo$2031bobo$2030bobo$2029bobo$2028bobo$2027bobo$2026bobo$2025bobo$2024bobo$2023bobo$2022bobo$2021bobo$2020bobo$2019bobo$2018bobo$2017bobo$2016bobo$2015bobo$2014bobo$2013bobo$2012bobo$2011bobo$2010bobo$2009bobo$2008bobo$2007bobo$2006bobo$2005bobo$2004bobo$2003bobo$2002bobo$2001bobo$2000bobo$1999bobo$1998bobo$1997bobo$1996bobo$1995bobo$1994bobo$1993bobo$1992bobo$1991bobo$1990bobo$1989bobo$1988bobo$1987bobo$1986bobo$1985bobo$1984bobo$1983bobo$1982bobo$1981bobo$1980bobo$1979bobo$1978bobo$1977bobo$1976bobo$1975bobo$1974bobo$1973bobo$1972bobo$1971bobo$1970bobo$1969bobo$1968bobo$1967bobo$1966bobo$1965bobo$1964bobo$1963bobo$1962bobo$1961bobo$1960bobo$1959bobo$1958bobo$1957bobo$1956bobo$1955bobo$1954bobo$1953bobo$1952bobo$1951bobo$1950bobo$1949bobo$1948bobo$1947bobo$1946bobo$1945bobo$1944bobo$1943bobo$1942bobo$1941bobo$1940bobo$1939bobo$1938bobo$1937bobo$1936bobo$1935bobo$1934bobo$1933bobo$1932bobo$1931bobo$1930bobo$1929bobo$1928bobo$1927bobo$1926bobo$1925bobo$1924bobo$1923bobo$1922bobo$1921bobo$1920bobo$1919bobo$1918bobo$1917bobo$1916bobo$1915bobo$1914bobo$1913bobo$1912bobo$1911bobo$1910bobo$1909bobo$1908bobo$1907bobo$1906bobo$1905bobo$1904bobo$1903bobo$1902bobo$1901bobo$1900bobo$1899bobo$1898bobo$1897bobo$1896bobo$1895bobo$1894bobo$1893bobo$1892bobo$1891bobo$1890bobo$1889bobo$1888bobo$1887bobo$1886bobo$1885bobo$1884bobo$1883bobo$1882bobo$1881bobo$1880bobo$1879bobo$1878bobo$1877bobo$1876bobo$1875bobo$1874bobo$1873bobo$1872bobo$1871bobo$1870bobo$1869bobo$1868bobo$1867bobo$1866bobo$1865bobo$1864bobo$1863bobo$1862bobo$1861bobo$1860bobo$1859bobo$1858bobo$1857bobo$1856bobo$1855bobo$1854bobo$1853bobo$1852bobo$1851bobo$1850bobo$1849bobo$1848bobo$1847bobo$1846bobo$1845bobo$1844bobo$1843bobo$1842bobo$1841bobo$1840bobo$1839bobo$1838bobo$1837bobo$1836bobo$1835bobo$1834bobo$1833bobo$1832bobo$1831bobo$1830bobo$1829bobo$1828bobo$1827bobo$1826bobo$1825bobo$1824bobo$1823bobo$1822bobo$1821bobo$1820bobo$1819bobo$1818bobo$1817bobo$1816bobo$1815bobo$1814bobo$1813bobo$1812bobo$1811bobo$1810bobo$1809bobo$1808bobo$1807bobo$1806bobo$1805bobo$1804bobo$1803bobo$1802bobo$1801bobo$1800bobo$1799bobo$1798bobo$1797bobo$1796bobo$1795bobo$1794bobo$1793bobo$1792bobo$1791bobo$1790bobo$1789bobo$1788bobo$1787bobo$1786bobo$1785bobo$1784bobo$1783bobo$1782bobo$1781bobo$1780bobo$1779bobo$1778bobo$1777bobo$1776bobo$1775bobo$1774bobo$1773bobo$1772bobo$1771bobo$1770bobo$1769bobo$1768bobo$1767bobo$1766bobo$1765bobo$1764bobo$1763bobo$1762bobo$1761bobo$1760bobo$1759bobo$1758bobo$1757bobo$1756bobo$1755bobo$1754bobo$1753bobo$1752bobo$1751bobo$1750bobo$1749bobo$1748bobo$1747bobo$1746bobo$1745bobo$1744bobo$1743bobo$1742bobo$1741bobo$1740bobo$1739bobo$1738bobo$1737bobo$1736bobo$1735bobo$1734bobo$1733bobo$1732bobo$1731bobo$1730bobo$1729bobo$1728bobo$1727bobo$1726bobo$1725bobo$1724bobo$1723bobo$1722bobo$1721bobo$1720bobo$1719bobo$1718bobo$1717bobo$1716bobo$1715bobo$1714bobo$1713bobo$1712bobo$1711bobo$1710bobo$1709bobo$1708bobo$1707bobo$1706bobo$1705bobo$1704bobo$1703bobo$1702bobo$1701bobo$1700bobo$1699bobo$1698bobo$1697bobo$1696bobo$1695bobo$1694bobo$1693bobo$1692bobo$1691bobo$1690bobo$1689bobo$1688bobo$1687bobo$1686bobo$1685bobo$1684bobo$1683bobo$1682bobo$1681bobo$1680bobo$1679bobo$1678bobo$1677bobo$1676bobo$1675bobo$1674bobo$1673bobo$1672bobo$1671bobo$1670bobo$1669bobo$1668bobo$1667bobo$1666bobo$1665bobo$1664bobo$1663bobo$1662bobo$1661bobo$1660bobo$1659bobo$1658bobo$1657bobo$1656bobo$1655bobo$1654bobo$1653bobo$1652bobo$1651bobo$1650bobo$1649bobo$1648bobo$1647bobo$1646bobo$1645bobo$1644bobo$1643bobo$1642bobo$1641bobo$1640bobo$1639bobo$1638bobo$1637bobo$1636bobo$1635bobo$1634bobo$1633bobo$1632bobo$1631bobo$1630bobo$1629bobo$1628bobo$1627bobo$1626bobo$1625bobo$1624bobo$1623bobo$1622bobo$1621bobo$1620bobo$1619bobo$1618bobo$1617bobo$1616bobo$1615bobo$1614bobo$1613bobo$1612bobo$1611bobo$1610bobo$1609bobo$1608bobo$1607bobo$1606bobo$1605bobo$1604bobo$1603bobo$1602bobo$1601bobo$1600bobo$1599bobo$1598bobo$1597bobo$1596bobo$1595bobo$1594bobo$1593bobo$1592bobo$1591bobo$1590bobo$1589bobo$1588bobo$1587bobo$1586bobo$1585bobo$1584bobo$1583bobo$1582bobo$1581bobo$1580bobo$1579bobo$1578bobo$1577bobo$1576bobo$1575bobo$1574bobo$1573bobo$1572bobo$1571bobo$1570bobo$1569bobo$1568bobo$1567bobo$1566bobo$1565bobo$1564bobo$1563bobo$1562bobo$1561bobo$1560bobo$1559bobo$1558bobo$1557bobo$1556bobo$1555bobo$1554bobo$1553bobo$1552bobo$1551bobo$1550bobo$1549bobo$1548bobo$1547bobo$1546bobo$1545bobo$1544bobo$1543bobo$1542bobo$1541bobo$1540bobo$1539bobo$1538bobo$1537bobo$1536bobo$1535bobo$1534bobo$1533bobo$1532bobo$1531bobo$1530bobo$1529bobo$1528bobo$1527bobo$1526bobo$1525bobo$1524bobo$1523bobo$1522bobo$1521bobo$1520bobo$1519bobo$1518bobo$1517bobo$1516bobo$1515bobo$1514bobo$1513bobo$1512bobo$1511bobo$1510bobo$1509bobo$1508bobo$1507bobo$1506bobo$1505bobo$1504bobo$1503bobo$1502bobo$1501bobo$1500bobo$1499bobo$1498bobo$1497bobo$1496bobo$1495bobo$1494bobo$1493bobo$1492bobo$1491bobo$1490bobo$1489bobo$1488bobo$1487bobo$1486bobo$1485bobo$1484bobo$1483bobo$1482bobo$1481bobo$1480bobo$1479bobo$1478bobo$1477bobo$1476bobo$1475bobo$1474bobo$1473bobo$1472bobo$1471bobo$1470bobo$1469bobo$1468bobo$1467bobo$1466bobo$1465bobo$1464bobo$1463bobo$1462bobo$1461bobo$1460bobo$1459bobo$1458bobo$1457bobo$1456bobo$1455bobo$1454bobo$1453bobo$1452bobo$1451bobo$1450bobo$1449bobo$1448bobo$1447bobo$1446bobo$1445bobo$1444bobo$1443bobo$1442bobo$1441bobo$1440bobo$1439bobo$1438bobo$1437bobo$1436bobo$1435bobo$1434bobo$1433bobo$1432bobo$1431bobo$1430bobo$1429bobo$1428bobo$1427bobo$1426bobo$1425bobo$1424bobo$1423bobo$1422bobo$1421bobo$1420bobo$1419bobo$1418bobo$1417bobo$1416bobo$1415bobo$1414bobo$1413bobo$1412bobo$1411bobo$1410bobo$1409bobo$1408bobo$1407bobo$1406bobo$1405bobo$1404bobo$1403bobo$1402bobo$1401bobo$1400bobo$1399bobo$1398bobo$1397bobo$1396bobo$1395bobo$1394bobo$1393bobo$1392bobo$1391bobo$1390bobo$1389bobo$1388bobo$1387bobo$1386bobo$1385bobo$1384bobo$1383bobo$1382bobo$1381bobo$1380bobo$1379bobo$1378bobo$1377bobo$1376bobo$1375bobo$1374bobo$1373bobo$1372bobo$1371bobo$1370bobo$1369bobo$1368bobo$1367bobo$1366bobo$1365bobo$1364bobo$1363bobo$1362bobo$1361bobo$1360bobo$1359bobo$1358bobo$1357bobo$1356bobo$1355bobo$1354bobo$1353bobo$1352bobo$1351bobo$1350bobo$1349bobo$1348bobo$1347bobo$1346bobo$1345bobo$1344bobo$1343bobo$1342bobo$1341bobo$1340bobo$1339bobo$1338bobo$1337bobo$1336bobo$1335bobo$1334bobo$1333bobo$1332bobo$1331bobo$1330bobo$1329bobo$1328bobo$1327bobo$1326bobo$1325bobo$1324bobo$1323bobo$1322bobo$1321bobo$1320bobo$1319bobo$1318bobo$1317bobo$1316bobo$1315bobo$1314bobo$1313bobo$1312bobo$1311bobo$1310bobo$1309bobo$1308bobo$1307bobo$1306bobo$1305bobo$1304bobo$1303bobo$1302bobo$1301bobo$1300bobo$1299bobo$1298bobo$1297bobo$1296bobo$1295bobo$1294bobo$1293bobo$1292bobo$1291bobo$1290bobo$1289bobo$1288bobo$1287bobo$1286bobo$1285bobo$1284bobo$1283bobo$1282bobo$1281bobo$1280bobo$1279bobo$1278bobo$1277bobo$1276bobo$1275bobo$1274bobo$1273bobo$1272bobo$1271bobo$1270bobo$1269bobo$1268bobo$1267bobo$1266bobo$1265bobo$1264bobo$1263bobo$1262bobo$1261bobo$1260bobo$1259bobo$1258bobo$1257bobo$1256bobo$1255bobo$1254bobo$1253bobo$1252bobo$1251bobo$1250bobo$1249bobo$1248bobo$1247bobo$1246bobo$1245bobo$1244bobo$1243bobo$1242bobo$1241bobo$1240bobo$1239bobo$1238bobo$1237bobo$1236bobo$1235bobo$1234bobo$1233bobo$1232bobo$1231bobo$1230bobo$1229bobo$1228bobo$1227bobo$1226bobo$1225bobo$1224bobo$1223bobo$1222bobo$1221bobo$1220bobo$1219bobo$1218bobo$1217bobo$1216bobo$1215bobo$1214bobo$1213bobo$1212bobo$1211bobo$1210bobo$1209bobo$1208bobo$1207bobo$1206bobo$1205bobo$1204bobo$1203bobo$1202bobo$1201bobo$1200bobo$1199bobo$1198bobo$1197bobo$1196bobo$1195bobo$1194bobo$1193bobo$1192bobo$1191bobo$1190bobo$1189bobo$1188bobo$1187bobo$1186bobo$1185bobo$1184bobo$1183bobo$1182bobo$1181bobo$1180bobo$1179bobo$1178bobo$1177bobo$1176bobo$1175bobo$1174bobo$1173bobo$1172bobo$1171bobo$1170bobo$1169bobo$1168bobo$1167bobo$1166bobo$1165bobo$1164bobo$1163bobo$1162bobo$1161bobo$1160bobo$1159bobo$1158bobo$1157bobo$1156bobo$1155bobo$1154bobo$1153bobo$1152bobo$1151bobo$1150bobo$1149bobo$1148bobo$1147bobo$1146bobo$1145bobo$1144bobo$1143bobo$1142bobo$1141bobo$1140bobo$1139bobo$1138bobo$1137bobo$1136bobo$1135bobo$1134bobo$1133bobo$1132bobo$1131bobo$1130bobo$1129bobo$1128bobo$1127bobo$1126bobo$1125bobo$1124bobo$1123bobo$1122bobo$1121bobo$1120bobo$1119bobo$1118bobo$1117bobo$1116bobo$1115bobo$1114bobo$1113bobo$1112bobo$1111bobo$1110bobo$1109bobo$1108bobo$1107bobo$1106bobo$1105bobo$1104bobo$1103bobo$1102bobo$1101bobo$1100bobo$1099bobo$1098bobo$1097bobo$1096bobo$1095bobo$1094bobo$1093bobo$1092bobo$1091bobo$1090bobo$1089bobo$1088bobo$1087bobo$1086bobo$1085bobo$1084bobo$1083bobo$1082bobo$1081bobo$1080bobo$1079bobo$1078bobo$1077bobo$1076bobo$1075bobo$1074bobo$1073bobo$1072bobo$1071bobo$1070bobo$1069bobo$1068bobo$1067bobo$1066bobo$1065bobo$1064bobo$1063bobo$1062bobo$1061bobo$1060bobo$1059bobo$1058bobo$1057bobo$1056bobo$1055bobo$1054bobo$1053bobo$1052bobo$1051bobo$1050bobo$1049bobo$1048bobo$1047bobo$1046bobo$1045bobo$1044bobo$1043bobo$1042bobo$1041bobo$1040bobo$1039bobo$1038bobo$1037bobo$1036bobo$1035bobo$1034bobo$1033bobo$1032bobo$1031bobo$1030bobo$1029bobo$1028bobo$1027bobo$1026bobo$1025bobo$1024bobo$1023bobo$1022bobo$1021bobo$1020bobo$1019bobo$1018bobo$1017bobo$1016bobo$1015bobo$1014bobo$1013bobo$1012bobo$1011bobo$1010bobo$1009bobo$1008bobo$1007bobo$1006bobo$1005bobo$1004bobo$1003bobo$1002bobo$1001bobo$1000bobo$999bobo$998bobo$997bobo$996bobo$995bobo$994bobo$993bobo$992bobo$991bobo$990bobo$989bobo$988bobo$987bobo$986bobo$985bobo$984bobo$983bobo$982bobo$981bobo$980bobo$979bobo$978bobo$977bobo$976bobo$975bobo$974bobo$973bobo$972bobo$971bobo$970bobo$969bobo$968bobo$967bobo$966bobo$965bobo$964bobo$963bobo$962bobo$961bobo$960bobo$959bobo$958bobo$957bobo$956bobo$955bobo$954bobo$953bobo$952bobo$951bobo$950bobo$949bobo$948bobo$947bobo$946bobo$945bobo$944bobo$943bobo$942bobo$941bobo$940bobo$939bobo$938bobo$937bobo$936bobo$935bobo$934bobo$933bobo$932bobo$931bobo$930bobo$929bobo$928bobo$927bobo$926bobo$925bobo$924bobo$923bobo$922bobo$921bobo$920bobo$919bobo$918bobo$917bobo$916bobo$915bobo$914bobo$913bobo$912bobo$911bobo$910bobo$909bobo$908bobo$907bobo$906bobo$905bobo$904bobo$903bobo$902bobo$901bobo$900bobo$899bobo$898bobo$897bobo$896bobo$895bobo$894bobo$893bobo$892bobo$891bobo$890bobo$889bobo$888bobo$887bobo$886bobo$885bobo$884bobo$883bobo$882bobo$881bobo$880bobo$879bobo$878bobo$877bobo$876bobo$875bobo$874bobo$873bobo$872bobo$871bobo$870bobo$869bobo$868bobo$867bobo$866bobo$865bobo$864bobo$863bobo$862bobo$861bobo$860bobo$859bobo$858bobo$857bobo$856bobo$855bobo$854bobo$853bobo$852bobo$851bobo$850bobo$849bobo$848bobo$847bobo$846bobo$845bobo$844bobo$843bobo$842bobo$841bobo$840bobo$839bobo$838bobo$837bobo$836bobo$835bobo$834bobo$833bobo$832bobo$831bobo$830bobo$829bobo$828bobo$827bobo$826bobo$825bobo$824bobo$823bobo$822bobo$821bobo$820bobo$819bobo$818bobo$817bobo$816bobo$815bobo$814bobo$813bobo$812bobo$811bobo$810bobo$809bobo$808bobo$807bobo$806bobo$805bobo$804bobo$803bobo$802bobo$801bobo$800bobo$799bobo$798bobo$797bobo$796bobo$795bobo$794bobo$793bobo$792bobo$791bobo$790bobo$789bobo$788bobo$787bobo$786bobo$785bobo$784bobo$783bobo$782bobo$781bobo$780bobo$779bobo$778bobo$777bobo$776bobo$775bobo$774bobo$773bobo$772bobo$771bobo$770bobo$769bobo$768bobo$767bobo$766bobo$765bobo$764bobo$763bobo$762bobo$761bobo$760bobo$759bobo$758bobo$757bobo$756bobo$755bobo$754bobo$753bobo$752bobo$751bobo$750bobo$749bobo$748bobo$747bobo$746bobo$745bobo$744bobo$743bobo$742bobo$741bobo$740bobo$739bobo$738bobo$737bobo$736bobo$735bobo$734bobo$733bobo$732bobo$731bobo$730bobo$729bobo$728bobo$727bobo$726bobo$725bobo$724bobo$723bobo$722bobo$721bobo$720bobo$719bobo$718bobo$717bobo$716bobo$715bobo$714bobo$713bobo$712bobo$711bobo$710bobo$709bobo$708bobo$707bobo$706bobo$705bobo$704bobo$703bobo$702bobo$701bobo$700bobo$699bobo$698bobo$697bobo$696bobo$695bobo$694bobo$693bobo$692bobo$691bobo$690bobo$689bobo$688bobo$687bobo$686bobo$685bobo$684bobo$683bobo$682bobo$681bobo$680bobo$679bobo$678bobo$677bobo$676bobo$675bobo$674bobo$673bobo$672bobo$671bobo$670bobo$669bobo$668bobo$667bobo$666bobo$665bobo$664bobo$663bobo$662bobo$661bobo$660bobo$659bobo$658bobo$657bobo$656bobo$655bobo$654bobo$653bobo$652bobo$651bobo$650bobo$649bobo$648bobo$647bobo$646bobo$645bobo$644bobo$643bobo$642bobo$641bobo$640bobo$639bobo$638bobo$637bobo$636bobo$635bobo$634bobo$633bobo$632bobo$631bobo$630bobo$629bobo$628bobo$627bobo$626bobo$625bobo$624bobo$623bobo$622bobo$621bobo$620bobo$619bobo$618bobo$617bobo$616bobo$615bobo$614bobo$613bobo$612bobo$611bobo$610bobo$609bobo$608bobo$607bobo$606bobo$605bobo$604bobo$603bobo$602bobo$601bobo$600bobo$599bobo$598bobo$597bobo$596bobo$595bobo$594bobo$593bobo$592bobo$591bobo$590bobo$589bobo$588bobo$587bobo$586bobo$585bobo$584bobo$583bobo$582bobo$581bobo$580bobo$579bobo$578bobo$577bobo$576bobo$575bobo$574bobo$573bobo$572bobo$571bobo$570bobo$569bobo$568bobo$567bobo$566bobo$565bobo$564bobo$563bobo$562bobo$561bobo$560bobo$559bobo$558bobo$557bobo$556bobo$555bobo$554bobo$553bobo$552bobo$551bobo$550bobo$549bobo$548bobo$547bobo$546bobo$545bobo$544bobo$543bobo$542bobo$541bobo$540bobo$539bobo$538bobo$537bobo$536bobo$535bobo$534bobo$533bobo$532bobo$531bobo$530bobo$529bobo$528bobo$527bobo$526bobo$525bobo$524bobo$523bobo$522bobo$521bobo$520bobo$519bobo$518bobo$517bobo$516bobo$515bobo$514bobo$513bobo$512bobo$511bobo$510bobo$509bobo$508bobo$507bobo$506bobo$505bobo$504bobo$503bobo$502bobo$501bobo$500bobo$499bobo$498bobo$497bobo$496bobo$495bobo$494bobo$493bobo$492bobo$491bobo$490bobo$489bobo$488bobo$487bobo$486bobo$485bobo$484bobo$483bobo$482bobo$481bobo$480bobo$479bobo$478bobo$477bobo$476bobo$475bobo$474bobo$473bobo$472bobo$471bobo$470bobo$469bobo$468bobo$467bobo$466bobo$465bobo$464bobo$463bobo$462bobo$461bobo$460bobo$459bobo$458bobo$457bobo$456bobo$455bobo$454bobo$453bobo$452bobo$451bobo$450bobo$449bobo$448bobo$447bobo$446bobo$445bobo$444bobo$443bobo$442bobo$441bobo$440bobo$439bobo$438bobo$437bobo$436bobo$435bobo$434bobo$433bobo$432bobo$431bobo$430bobo$429bobo$428bobo$427bobo$426bobo$425bobo$424bobo$423bobo$422bobo$421bobo$420bobo$419bobo$418bobo$417bobo$416bobo$415bobo$414bobo$413bobo$412bobo$411bobo$410bobo$409bobo$408bobo$407bobo$406bobo$405bobo$404bobo$403bobo$402bobo$401bobo$400bobo$399bobo$398bobo$397bobo$396bobo$395bobo$394bobo$393bobo$392bobo$391bobo$390bobo$389bobo$388bobo$387bobo$386bobo$385bobo$384bobo$383bobo$382bobo$381bobo$380bobo$379bobo$378bobo$377bobo$376bobo$375bobo$374bobo$373bobo$372bobo$371bobo$370bobo$369bobo$368bobo$367bobo$366bobo$365bobo$364bobo$363bobo$362bobo$361bobo$360bobo$359bobo$358bobo$357bobo$356bobo$355bobo$354bobo$353bobo$352bobo$351bobo$350bobo$349bobo$348bobo$347bobo$346bobo$345bobo$344bobo$343bobo$342bobo$341bobo$340bobo$339bobo$338bobo$337bobo$336bobo$335bobo$334bobo$333bobo$332bobo$331bobo$330bobo$329bobo$328bobo$327bobo$326bobo$325bobo$324bobo$323bobo$322bobo$321bobo$320bobo$319bobo$318bobo$317bobo$316bobo$315bobo$314bobo$313bobo$312bobo$311bobo$310bobo$309bobo$308bobo$307bobo$306bobo$305bobo$304bobo$303bobo$302bobo$301bobo$300bobo$299bobo$298bobo$297bobo$296bobo$295bobo$294bobo$293bobo$292bobo$291bobo$290bobo$289bobo$288bobo$287bobo$286bobo$285bobo$284bobo$283bobo$282bobo$281bobo$280bobo$279bobo$278bobo$277bobo$276bobo$275bobo$274bobo$273bobo$272bobo$271bobo$270bobo$269bobo$268bobo$267bobo$266bobo$265bobo$264bobo$263bobo$262bobo$261bobo$260bobo$259bobo$258bobo$257bobo$256bobo$255bobo$254bobo$253bobo$252bobo$251bobo$250bobo$249bobo$248bobo$247bobo$246bobo$245bobo$244bobo$243bobo$242bobo$241bobo$240bobo$239bobo$238bobo$237bobo$236bobo$235bobo$234bobo$233bobo$232bobo$231bobo$230bobo$229bobo$228bobo$227bobo$226bobo$225bobo$224bobo$223bobo$222bobo$221bobo$220bobo$219bobo$218bobo$217bobo$216bobo$215bobo$214bobo$213bobo$212bobo$211bobo$210bobo$209bobo$208bobo$207bobo$206bobo$205bobo$204bobo$203bobo$202bobo$201bobo$200bobo$199bobo$198bobo$197bobo$196bobo$195bobo$194bobo$193bobo$192bobo$191bobo$190bobo$189bobo$188bobo$187bobo$186bobo$185bobo$184bobo$183bobo$182bobo$181bobo$180bobo$179bobo$178bobo$177bobo$176bobo$175bobo$174bobo$173bobo$172bobo$171bobo$170bobo$169bobo$168bobo$167bobo$166bobo$165bobo$164bobo$163bobo$162bobo$161bobo$160bobo$159bobo$158bobo$157bobo$156bobo$155bobo$154bobo$153bobo$152bobo$151bobo$150bobo$149bobo$148bobo$147bobo$146bobo$145bobo$144bobo$143bobo$142bobo$141bobo$140bobo$139bobo$138bobo$137bobo$136bobo$135bobo$134bobo$133bobo$132bobo$131bobo$130bobo$129bobo$128bobo$127bobo$126bobo$125bobo$124bobo$123bobo$122bobo$121bobo$120bobo$119bobo$118bobo$117bobo$116bobo$115bobo$114bobo$113bobo$112bobo$111bobo$110bobo$109bobo$108bobo$107bobo$106bobo$105bobo$104bobo$103bobo$102bobo$101bobo$100bobo$99bobo$98bobo$97bobo$96bobo$95bobo$94bobo$93bobo$92bobo$91bobo$90bobo$89bobo$88bobo$87bobo$86bobo$85bobo$84bobo$83bobo$82bobo$81bobo$80bobo$79bobo$78bobo$77bobo$76bobo$75bobo$74bobo$73bobo$72bobo$71bobo$70bobo$69bobo$68bobo$67bobo$66bobo$65bobo$64bobo$63bobo$62bobo$61bobo$60bobo$59bobo$58bobo$57bobo$56bobo$55bobo$54bobo$53bobo$52bobo$51bobo$50bobo$49bobo$48bobo$47bobo$46bobo$45bobo$44bobo$43bobo$42bobo$41bobo$40bobo$39bobo$38bobo$37bobo$36bobo$35bobo$34bobo$33bobo$32bobo$31bobo$30bobo$29bobo$28bobo$27bobo$26bobo$25bobo$24bobo$23bobo$22bobo$21bobo$20bobo$19bobo$18bobo$17bobo$16bobo$15bobo$14bobo$13bobo$12bobo$11bobo$10bobo$9bobo$8bobo$7bobo$6bobo$5bobo$4bobo$3bobo$2bobo$bobo$obo$2o!")
glid = g.parse("2o$obo$o!")
pop_counts = []
for i in range(4300):
    g.new("")
    g.show(str(i))
    g.putcells(pat,0,0)
    g.putcells(glid,4253-i//2,3+(i+1)//2)
    g.run(5000)
    p = int(g.getpop())
    if p > 8492:
        g.run(10000)
    p = int(g.getpop())
    if p > 8492:
        g.reset()
        g.exit("Collision that produces higher population debris found")
    pop_counts.append(p)

max_pop = max(pop_counts)
max_index = pop_counts.index(max_pop)
g.new("")
g.putcells(pat,0,0)
g.putcells(glid,4253-max_index//2,3+(max_index+1)//2)
g.show("Maximum population: " + str(max_pop))

The script doesn't check the "head-on" collisions, but there's only a small number of those, so I just checked manually. The highest population from a head-on collision seems to be 6371.

PraseodymiumSpike · Post by **PraseodymiumSpike** » February 11th, 2023, 12:49 am

I would like to throw my conjecture into the ring. It is detailed here: viewtopic.php?f=11&t=5942.

pipsqueek · Post by **pipsqueek** » February 22nd, 2023, 1:37 pm

Im sure this one will last long (but it has probably already been thought of)

there exists an elementary replicator in Conway's game of life that fits within a 25x25 bounding box

squareroot12621 · Post by **squareroot12621** » February 22nd, 2023, 5:05 pm

Conjecture: There are no still lives that cannot be cleanly destroyed by up to two gliders.

Code: Select all

x = 68, y = 14, rule = B3/S23
11bo$12b2o13bobo$11b2o15b2o$28bo3$2bo13bo15bo12bo12bo3bo$obo11bobo3b2o
8bobo3b2o5bobo13b2obobo$b2o12b2o2bobo9b2o2bobo6b2o2b2o8b2o2b2o$4b2o12b
o15bo12bobo16b2o$4b2o11bo15bo12bobo16bobo$17b2o14b2o11b2o2b2o12bo$50b
obo10bo$50bo12b2o!

Examples:

One glider destroys the still life.
One glider hits the still life first, while the second glider waits until after the remains of the still life have settled to hit it.
One glider hits the still life first, but the second glider doesn't wait until after the remains of the still life have settled to hit it.
Two gliders hit the still life at the same time.
Two gliders hit each other first before the collision hits the still life.

Post by **dvgrn** » February 22nd, 2023, 9:49 pm

squareroot12621 wrote: ↑
February 22nd, 2023, 5:05 pm
Conjecture: There are no still lives that cannot be cleanly destroyed by up to two gliders.

Have a look at Golly's Patterns/Life/Still-Lifes/random.rle, just as an example -- perfectly valid still life. Does it seem plausible that every still life of that size can be cleanly destroyed by two gliders?

If not, is there a limitation you meant to place on this conjecture?

squareroot12621 · Post by **squareroot12621** » February 23rd, 2023, 9:38 am

dvgrn wrote: ↑
February 22nd, 2023, 9:49 pm

squareroot12621 wrote: ↑
February 22nd, 2023, 5:05 pm
Conjecture: There are no still lives that cannot be cleanly destroyed by up to two gliders.
Have a look at Golly's Patterns/Life/Still-Lifes/random.rle, just as an example -- perfectly valid still life. Does it seem plausible that every still life of that size can be cleanly destroyed by two gliders?

If not, is there a limitation you meant to place on this conjecture?

Now that I think about it, it's almost certainly impossible for every still life of population 2,000 (not to mention anything higher) to be destroyed cleanly with only two gliders. To combat this, I have two candidates for the number of gliders allowed. (For the rest of this post, p represents the population of the still life being tested.)
The first one is p÷5 + [small nonzero number—let's say 1]. This implies it (usually) doesn't take more than the number of cells in the original still life, in glider form, to destroy it.
The second one is log2(p). This doesn't seem to have a CGoL equivalent (at least to me), and the bound is a lot tighter for large values of p, but it still has a very slight chance of working.
If neither of my candidates work, the last resort is to tack on the clause "finitely many exceptions".

hotdogPi · Post by **hotdogPi** » February 23rd, 2023, 10:09 am

It's fifteen.

Post by **dvgrn** » February 23rd, 2023, 11:05 am

hotdogPi wrote: ↑
February 23rd, 2023, 10:09 am
It's fifteen.

Ouch. True enough. RCT strikes again.

(If this isn't clear to anyone, a 15-glider RCT can produce as many gliders as needed to shoot down a still life of any size. For that not to work, there would have to be some still life that can not be cleaned up by any finite number of gliders.)

pipsqueek · Post by **pipsqueek** » February 23rd, 2023, 11:31 am

dvgrn wrote: ↑
February 23rd, 2023, 11:05 am

hotdogPi wrote: ↑
February 23rd, 2023, 10:09 am
It's fifteen.
Ouch. True enough. RCT strikes again.

(If this isn't clear to anyone, a 15-glider RCT can produce as many gliders as needed to shoot down a still life of any size. For that not to work, there would have to be some still life that can not be cleaned up by any finite number of gliders.)

don't forget, the gliders can synthesize other objects. so its really

I wrote: For that not to work, there would have to be some still life that can not be cleaned up by any finite number of constructible objects

but that gives me another question, could such an object exist? If so, I bet it would be some sort of moving object

shuich01 · Post by **shuich01** » February 27th, 2023, 12:40 am

Does a spaceship exist, that CAN BE PROVED to have NO parents except itself? (Not the ones like Sir Robin which is not clear to have one)

Post by **dvgrn** » February 27th, 2023, 10:17 am

shuich01 wrote: ↑
February 27th, 2023, 12:40 am
Does a spaceship exist, that CAN BE PROVED to have NO parents except itself? (Not the ones like Sir Robin which is not clear to have one)

None is currently known, but it's not proven to be impossible.

This problem is analogous to the "still life that must have been present at T=0" and "oscillator that must have been present at T=0", both of which were discovered just last year by Ilkka Törmä and Ville Salo.

The phrasing "NO parents except itself" isn't quite true for any possible "self-forcing" spaceship, any more than for a self-forcing still life or oscillator. If you have a self-forcing finite object, you can always add one ON cell, or any one-tick dying spark, a safe distance away from it, and that will be a distinct parent. A better phrasing might be "no parents that do not include itself"... or I think John Conway's phrase was "(with some
fading junk some distance away not being counted)".

Some discussion of a search for a self-forcing spaceship can be found here. Offhand I'm not finding any extended discussion either on Discord or the forums, but maybe somebody can find something I missed? I just have a few email exchanges with Ilkka Törmä along the lines of

I wrote/Ilkka wrote/I wrote:
>> I'd agree with [Hartmut's] opinion that agars with this kind of self-forcing
>> property are likely to be unusually difficult to turn into a complete
>> spaceship. Agar-supporting greyships are very rare already, even for
>> very easy agars like zebra stripes, so it's going to take some luck to
>> complete a "difficult" agar.
>
> To be honest, I had very little idea about the difficulty of turning an
> agar into a greyship. My instinct was to just throw a SAT solver at the
> agar patch if we manage to find one, and hope it produces a spaceship
> in a reasonable time. But that might be a pipe dream.

Yes, well, it's a good instinct, and it's more likely to find
something than if you don't try!

People who have been in this business for too long sometimes end up
getting too set in their ways. They develop heuristics based on long
experience for what is likely or unlikely to work, which translates
into "this search is worth trying" vs. "that search is too unlikely to
return anything before the Sun burns out, so we won't try that one".

However, a good percentage of new Conway's Life discoveries come from
newcomers who don't know what's worth attempting, so they just try
crazy stuff and figure out how to make it work. The Gemini and
copperhead spaceships, single-channel construction circuitry, the
recent surge in new true-period guns, the 2-engine Cordership, and all
kinds of other things fall into that category.

... That said, all the carefully balanced decorations around the edges
of all of these greyships

http://pentadecathlon.com/lifeNews/grey ... cefillers/

(which are low-period because they're based around simple stable agars)
... took quite a bit of careful searching and engineering to assemble
into a working spaceship.

I don't *think* that even most of those are within easy reach of
completion by an unaided SAT solver. So I guess that would be a first
test: see if you can get a SAT solver to figure out a complete
zebra-stripes greyship. If you find that that's very easy, then it's
a lot more likely that some other more complex agar will turn out to
be within reach also.

When you're looking for spaceship completions of agars with bigger
spatial or temporal periods, the size of the search space tends to
explode in a way that's very difficult to keep under control. Which
is not to say that you shouldn't try -- it's just saying that you
might want to be mentally prepared to spend quite a few CPU-hours
before expecting a solution to appear.

get_snackeTWO · Post by **get_snackeTWO** » April 4th, 2023, 8:21 am

are there any patterns whose predecessor(s) has/have to have an infinite amount of cells (each)?

one way to approach this is to find a pattern whose predecessor(s) converge(s) into an agar that will always leave at least one cell (that isn't supposed to be there) at the edge of it/them.

ConwayLife.com

Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures

Re: Unproven conjectures