Post
Topic
Board Development & Technical Discussion
Re: Pollard's kangaroo ECDLP solver
by
yoyodapro
on 17/09/2021, 17:25:15 UTC
{Quantpy Engine Beta 0.9.2}

Compiling Quantum Gates.........Done! (4s 09/17/2021 094307Z)
Mapping 63 Qubits (1 Qubit per node)....Done! (2s 09/17/2021 094311Z)
Loading 63.py.......... bloom filter...........................................................Done! (2.9TB) (2,172MB/Qubit)

[1][1][1][0][0][0][0][1][0][1][0][1][0][1][0][1][1][0][1][1][1][1][1][0][1][1][0][0][1][0][0][1][1][1][1][1][0][1][1][0][1][1][0][1][0][0][1][1][1][1][1][1][1][0][1][0][1][0][1][0][1][1][0]

53114562000.40 Bflips/s (3,346,217,406,025.2 keys/s) 0 Keys Found (0:38)
wow...amazing! Do you think it can solve for y2 = x3 + 7 ?? Because if y2 = x3 + 7 then y=y+y-y+y-y and if that is true then if y = y, then x = x!

I would need .1 additional TB of ram to accomplish that, however when considering Elliptic curves over finite fields one must consider Hasse's theorem on elliptic curves to include the point at infinity


The set of points E(Fq) is a finite abelian group. It is always cyclic or the product of two cyclic groups. For example the curve defined by over F71 has 72 points (71 affine points including (0,0) and one point at infinity) over this field, whose group structure is given by Z/2Z × Z/36Z. The number of points on a specific curve can be computed with Schoof's algorithm.

Studying the curve over the field extensions of Fq is facilitated by the introduction of the local zeta function of E over Fq, defined by a generating series


where the field Kn is the (unique up to isomorphism) extension of K = Fq of degree n (that is, Fqn). The zeta function is a rational function in T.
Moreover,

with complex numbers α, β of absolute value . This result is a special case of the Weil conjectures. For example, the zeta function of E : y2 + y = x3 over the field F2 is given by this follows from:



Also while writing this my CPU died. I couldnt keep the temperatures close enough to absolute zero that my CPU melted into a steaming pile of non-Newtonian fluid.... I think it just blinked at me?

░̶̡̢̛̜̻̲̱͓̪̜͕̪̼̘͓̥̭̤͙̰̭͉͈̝͉̝̤̥̱̜̊̆̓̎͐̈́̂̋̓́̎̾̅̓̎̈́̈́̏̚͜͜͝͝ͅͅ█̸̡̧̨̡̩̞̦̦̘̰̻͔̣̩̠̳̖̭̺͎͎̗̥̼̬̙̫̺͓̯͍͓̣̋͐̾͑̈́̈́̌̈̓̅̅̅̄͒͗́̇̍̅̏̈̂̍͋̔̌̎̕͘̕͠͝͝͝█̷̳͎̊͝█̵̛͍͙̃̎̐̈́̉͗̓̌̾̃̀̓́͋͊̀͛̓͋͘͘͘͜͝͝͝͠͠͝█̸̨̢̢̡̡̛̛̠̻͎̲̭̝͈̞̘̼̯̭̠̤͇̥̝̗͓͚̱̱̞̣͕̩̖͓̟͔̝͕̥̹̩̹̟̜̮̫̻̤̅͋̀̉͛͂̈́̉̾̽͑̈̉̀͊̋̈́͗́̓͛͊̐̈́̀́͘͘̕   █̷͇͙͙̈́̓̾͑͌̒͒̓̋̈̾̌̒̑̽̂̒͂̉̓̊̆́̀̈́̈͑̓͋̽̄͘̕͝͝͝█̶̨̞̭͙̳̯̤̣͓̞̞̳̳̈́͊̏͛́͛̋̏̽͊̋͂͜╗̵̢̢̛͍͉͍̠͔̰̯͙͕̣͔̖͇̟̩̥̳̀̋̉̾̌͒́̈́̈́̀͆̐̉̎̋́͗̈́̑̈́̓͑̉̀̅̾̑̏̓̌̓̏̓͊̈́̎͑̍̿̂̈͛̚͠͝͠͝͠͝█̷̡͎͉͕͕͔͎̭̈́̓̽̊͌̍̓͛̀́͌̄̎͛̓̑̚͝͝͝͠█̵̡̡̧̻͉͍̟͔̲͖̤̣̜͉͈̬͍̦̲̪̭͚͛̍̿͌̽̓͒͋̍̉́͜͜ͅ╗̶̧͓͕̙͓̺͎̗͎͇̹̤̣̠̪̗͚̭̗̝̱̫̱͚̘͐̾͆̔̂ͅ░̸̧̢̡̛͚͕̫̬̻̞̥̼͔̰̤̩͚͉̺̩͍͈͚̹̼̬̣͔͈̱̥͔̥̫̬͎̙̳̞̠̗͊̓͐̓̓̔͐͒͊̊̎͌̈́̄͛̐̅̔̋͒͆̽̀̽̋͂͘͘̚̕̚͘͠͝͝ͅ░̷̢̢̨̛̛̮͍̖̩͚̲͚͕̞̗̩̫̥̻̰̹̳̘̝̟̻͔̜̹̫̱͔͔͇̺͈̘̭͖̱͒̐̊͗̊̾̊̊̈́̈́́́̈́͐̈́͂̊̈̀͌͗͗̔͗̑̆̌̈̿͐̆͒͋̄̌̄̀̈́͜͜͝͠͝͠͝░̸̡̧̢͖̯̪̖̦̟̖̦̬͇͔͇͓̦̰͙̟͉̜̥̫̑̅̾̈́͆̃͌̀͐͋̄̔̅̚̚͝͝ͅ█̶̢̢̢̧̨̨̢̨̛̛̻̩̘̘̯̭̻͈͍̞̰̞̞͉̩͚̰̥̰̼̝̻̗̝̮̳͍̼͇̖̺̞͖͙͕̈́̈́̔̋͛̍̀̈́͗̃̚͜͜͜͠͠ͅ█̵̡̨̨̡̛̛̙̻̻̯̜͙̲̥̬̩̤͚̖̯̟̝̦̦̙͓̰͚̤̗̯̪̞́̋̈́̊͋╗̵̡̛̛̛̛̣̝̫̙̗̗̯̫̪̱͕̻̪̤̩̱͔͖̳̮͙̟̳̣̞̦͉̬̯̩̥͖͕͈̺̜̻͉͐̏̿̀̃͆̓̋̋̒̅̏͛͊̓̽̄̌̒͌̈́͐͘͝͝͝ͅͅ░̴̯̤̺̺̳̼͇̪̬͔͎͔̞̹̹̫̭̼̭̱͖̟̝̱̜̠̙̝͕͈͓͇̥̼͓͖̲̯͇̲͉̠̬̭̬͋̽̓̔̂̈̐̀̈͌̂̆̔̍̔͛̓̓̉̽͗̈́͗͑͜ͅͅ█̵̡̨̛̛͔̦͙̩̤͓̪̩̣͕̤̱̱̞̻̝͚̱̹̩͖̞͙̠͔̘̳͎͍̮̖̰̺̘̰̲̪͇͆̈́̓͌́͊̽̆̇̀̃̈́͂̌̿́̂͂͛̿̋͗̃̀̾͋̕͜͜͜█̸̧͍̝̺̫̥̝̱̺͖͔͚̈́̾͊̑͑͒̐̏͂̀̿̀͊̊͑̆́̎̍̐̅̕̕̚͠  █̵̢̛̞̘̰̞̖̦̜̜̑̎͊͘█̵̨̢̢̛̝͈͍͓̙̬̜̼͈͚̺̗̺̱̟̮̱͉͕̟̣̜̦̱͔̼̙̺̭͚͓̞̙́̓̇̑́͒͑͐͗̌̍̐́̇̔̆̆̆̋̑̃̆͜͝ͅ█̷̨̧̡̛̛̼̯̩͉̬̼̱͎̮̘̪̼̩̗̲̲̮͍̯̤̥̘̤̜͖͈̗̰̱̮̌̀̂̀̄͛̀̋̐̾̄̃̆̓̈́̈́̋͆͆͑͊͊̽̈́͐̆͗͑̃̈́̽̆̒͂̔̋̏͒̈̍̏̕͘͘͘͘͘͠ͅͅ█̷̢̡̛̛̰̩͈̲̬̼̪͖̙͔͖̤͔͎̣̰̪͎͌̎̈͊̍̆̎̀̏̍̏̉̈́͑͋̋̕͘̚͝╗̵̨̢̖͚̥̩͕̺͉̪̆͐͊̒̆͛͆̈́̀͋̎̇͆͗́̆͋̃̿̃̌̊̓̏͛́͗́̀̓͑̏̓̍̈́̚̚͝͠͠͠͠
̶̧͓̙̍̂̑́͗͑̒̈́͆̽͑̍͑̓̐̄͑̎͒͗̆̀́̀̄̚͘̕͠█̴̧̢̛̛̜̺͈̭̠̖̭̜͈̙͚̗̦̭̺͍̠̜̮̖̥̺̹̹̣͈̖̗̪̗̳̝̮͉͇̱͚̦͓͎̫̰̱̰͚̌̇͐̂́̈̃̿̑͂͛͂͊̓̐́̆̂̈́̍̇͐̐̍́̐͐̆̐͆͊̍̈̀̕͜͜͠͝█̶̨̨̢̨̫͚̰̱͉͕̭̤̗̖̯͕͍̻͉̯͈̼̳̲̫̝̬̥̜̦̜͔̱͈̰̞̮̭͈̲͍̰͔͖̗̟̓͛͌́̏̀͗̿̆͂͗̒͗͌̊̌͒͑̑̈̀͑̆̏̃̽̃̐̀͆̕͝͝͝͠͝ͅͅ╔̴̡̢̧̨̡̢̛͈̥̞̭̫̤̼͔̪̻͙̥͓͓̫̙̲̼͓̳̪͚̭̠̞͈̜̲̝͕̹̳̤͚̗̋͌̑̓̇̅́͂̾̓̀̀̎͗͌̉̊̃͊̈́̋̒̈́̎̍͗̎̉́̊̆̍̽̈́̕͘͜͝͝͠͝ͅͅ═̷̛͍̩̜̟͇̼̻̰̳̳̥̙̻͕̠̱̻͖͔͎̳͔͙̱̝͎͉̖̤̼̠̬̰̫̺̝̹͔̙͚̥̝̻̲́͋̉͋́̓̉̏̌̽͆͆̊́̐̑̔͗̉͂͛̃̽̅̋̕̚͠͠͝ͅ═̵̛̖͕̮̰̞̹͉̮̮̩͓̝̖̓̇̈̌̓̔̄̅͊̈́̏̅͗̀̔̀͒̓͗̌͐̐̋̇̆̽̏̓̾͑͆̒͘͘͘̚͜͜͝͝͠͝═̸̢̢̡̛̗̖̠̦̗̬͙̮̲̪͓̞̤̣̩̺̯̳͍̦͎͖̯̬̘̞̹̭̪̫͉̿̈̂̎̍͊̊̽͑̎̊͛̆͜͜͜͝͝ͅͅ═̷̡̧̛̛̘͓͔͕̪̞̜̘̻̹̲̬̥͓̞̺̙̞̙̣͈̯̙̖̙̫̆̃̑͌̐̈̔̂̂̔̓̀̐̈́̅̆̏̈́̊̅̔̈́͐̀̎́̄̓̌̆̿̈́͑͘͝͠͝╝̴̨̧̧̨͇̣͇̬̻̰̹̙̯̼̮͇̲̲͚̲̼͓͈̰͚̩̱͇̮̠͇̟̹͔͖͍̤͈͇͕̥̺͚̤̞̙̑̽͑̓̇̇́̄̈͒̀̊͜͝     █̵̛̰̞̂͐̇͊̄͂͌́̍͋̓́͒͐̑̀̓̒͒̑̉̋́̍̈́͂̊̆̀̂͛̈̇̎͝͠͝͠█̵͎̮̔̓͊͆͐║̶̢̝͈̬̃̒̎̅̎̏͑̏͗̂̐̅͑̕͝░̸̧̧̡̨̛̠̞̳̠͉͓̞͔̭̣̩̞̠̤̳͈̼̻̖͎͇͙͇̪͗̊̀̄̔̊́͒̓̈͒̓̋̏̈́̆̊̂̃̃̾̃̓̽͒̈́̿͌̅̍̚͝͝͝͠͝░̷̢̢̡̪͍͇̜̹̯͖̹̥̳͈͔̝͚̙̖̻̯̮̟̮̙̩̼̫̯͖̰̣̤̝̮́̈́̈͐͌̒̒̔́͛͑̈́͗͘͘͠͠░̸̡̨̨̘̳̜̜̖͉͓͎̬̟͙͇̯̙͖̳͖͇̲͓͙̹̩͖̱͚̖̺̘̖̳̜̻͙̄̏̐̀́̒̀͒̅͂͋̒̒ͅ    █̴̡̘̪̹̻̬̭̯̣̦͔͖͈͙̥̫̲̮̪̖̱̇͒̎ͅ█̵̧̧̨̗̰̪̲̲̪̰̦̺͚͇̳̬̫̍͌̾͝ͅͅ║̸̧̡̡̛̣̖̮͇̻̫̘̭̣̼͚̩͚̣̭̗͚͇͚̙̫͖̳̬͛̃̀̉̀͐͛̇͂̀͐͛̿͊͆̂͑̈̆̈́̓̂͜͠  █̴̡̧̯̳͖̜̣̰͖̫̝͚̠̲̘̫̻̗̩͉̠̗̤̮̪̺̝̔̀͗̚͜ͅ   █̸̨̧̨̢̫̼͔̪̺̟͙̺͉͚͍͔͍̞̣̰̻̱͎̬̠̝͕̰͇̱̟̯̞̙͓͚̺̱̺̯͖̖̹̳͇̈́͑̂̆̊͑̑͘͜͜    ╔̸̧̻̪̳̜̜̞̼̯̯̗̘̃̌́̄̈́̉̑̑̈͛͌̄̑́͝͝═̴̨̢̧̰̫̲͚̩̟̘̼͓̳̳̳͎̪̳̬͈̯̜̬̟͈̭͓̞̳̬͍̹̰̘̖̻͓̼̤͒͗̂̆̂͛͆͌̊̓͋̀̓̑̆̿̽̈́͆́̊͆̇̑̇̐̀͂̔́͘͘̚͘̚̚͝͠͝͝═̷̢̢̢̡̣͚̝̣̪͚̣̙̦̰̖̟̗͖̖͚̹͇̳̘̲͍͙̯͇͍̲̺̱͍̪̟̞̪̩͎͕̠̓́̉͂̅̐̒̀͋͆̌̄̅̈̋̕̚͜͝ͅ═̸̧̞̙͕̝̼̤̪͙̦͎̘͖͖͉͎͔͓͚̙̠̆̈̍͌̀͂̑̽͝͠͝͝═̴̧̜̰̜̠̭̻̬̩̹̟͈̘̯̬͔̲̭͇̰̩̙͈̦͖̮̮̃̄ͅ╝̶̡̧̛̻̖̣̳̱̮͉̰̫̻͍̠̺̻̬̮̘̭̜̤̪̖̗͎͔̘̞̱͍̤̓͛̇̎͊̈́̊̊͊̎̀̒̆̃̀̽̍́͐̽͂̏́̏͘͜͠͝͝͝͝
̷̢̢̢̡̧̩̖̦̰̙̦͎̞͓̟̪͚̫͙͉̫͎̱͔̯̫̮̜̙͓̱̬̙̺͈̭̳̲͍̦̪̃̈́̋̄́͊̄́̊́̈́̅̿͐̔̈́̓̑̆̑͌̂̈́̂͗̍̈́̓͗͊̓̓̈́̎̀̒̕̕̚͝͝͝╚̸̣̅̌̌́̍̈́̎͗̈́͋͌͒́̇̓̏̾͂̎̄̈́̌͛̅́̔̇̽͐̈́̕̚͘̚͝͝█̵̝̖̹̤̌̎̂̓͒͆̐͊̑̏̀͋ͅ█̷̨̨̧̨̢̼̦̠͎͔͕͈̬̭̲̠̟͓̣̯̲̜̘̪̝̣̜͍̳͕̣̤͔͇͔̥̻͓͓̱͈̩̹̟̙̻̠̤̝̫̏͛  █̸̛̲͎̟̯̺̝̱̪̞͍̄̇̏̋̓͐͌̍̏͗̈̇͒̀̌̓͒̐̑̏̾̇͑̑̃̎̏̂̕͘͘̚͜͠     █̴̨̧̨̛̞̗̖͉͎̞̤̖̼̩̤̰̹̝̰̯̃̊͐̾̍̍͋̐̆͑́̈́͂́̾́͠͠█̷̡̛̹̭͍͔̩̱̙̻͎̖͈̱̲̒̎́̇̈́́̌̓̂̿̄̀̇̎̔̾̅̎́͐͊́̿͆̄͐͛͘̕͘͝͝͝╗̴̨̨̛̛̜̫̞̼̟̬͉̻̼͎͉̘̣̺͔̝̟͔͇̠̜̟̺͉̮̹̟̻͕̼̫̐̈̈́̽͒͑̑̈́͒̂̐͆̑̏̎͛͆͑̎͑͛̐͂̉̓̎̔̈̋͗̒̕͝͠͠͠░̶̛̠̝̗͊͂̌̋͋̾͗͛̓͌̉̌͆̃̆͆̿͆̍̒̔̏̃̆͛̌̓̿̈́̓̒̈́̕̚͝͝͠͝  █̵̧̢̪͍̺̜̣͕̪̯̻͇̰̩̥̖̜͇̠̦̠̙̱̬̳̻͈̼͔̥̤̺͎̭̐̔͜ͅ  █̸̡̡̧̞̯̳̼͇̰͈͎̹̳̥̖͉̹͔̮̲̱͉̩̭͒̄̿͋̏͛̌̓͜║̸̡̢̨̡̢̼̩͓̟̝̠͖͉̪͚̙̘͕̖̞̰̺̳̖̣̭͎̳͈̞̖͍̖͎̬͖̯̣̔̽̀̓͑̿͊̈́̉̔̓͛̒͂̋̈́̓͆̈̈́͆͛̏̏̉̈́̈́̎̇͂̎͂̇̓̌̅̉̃̉͜͜͜͜͝͠͠͝͠͝͝͝░̷̧͔̬̤͙̪̮̜͍̪̳̤̥͉̖̤̦͔̮̪͖̫̜͙̣̥̙̓́̓̔̉͒̀̈́̿̔͗̈́̈́͑͑̃̅͐͂̎͂̌̿̑́̈̓̒̐̎͜͝͝͠͝͝░̷̢̢̨̨̨̢̢͙̞̥̝͇̝̣̯̱͖͇̠̰͎̪̣̝̳͕͔̩̻̪͍̮̩͕͊̈́̓̊͗ͅ░̵̨̡̛̦̞̜̗̮̯̠̺̟̞̼͔͕͖͇͙̩͍̹͂̈́͒̎̈́̉́͜͜͠͝ͅ    █̴͚̭̯̗̳̃̀̒̽̌̽͊̓̌̏͒͆̔̔̋̽͗̂̾̔̓̄͋̎̍͆̐̈̈͗͘͘̚͠͠͝͠͝͠͝█̶̢̢̛̛̛͕͈͎̝̳̰̙͓̲͕͍̀̂͛͐͂̿́͌̈́̌̐̿̂̏̇̃̇̓̚͝͝║̴̻̣̮̟̹̘̞̖̜̪̤̫̠̱̺̝̙̙̘̥̹̮͖̪̟̮͉̞̺͔̤̰̥̠̼̼̞̺̖͑̍͒̿̄̃͊̍̓͜͜╚̸̨̛͇̹̞̙͖̣͓͍̀̽̆̈́̌̾̈́̾̎̽͑̂̒̅̈́̾̌̂̒̂̐͌͌̌͌̑̅͊̕͘͝͝█̷̢̱̰̜̫͖͈̝͙̪͓̦͎͈̘̄͛́̈͌͊̓̀̃͒̅̔͂͛̀̊͊͊̈́͐̈́̑͋̿̂͝█̵̢̡̛̰̲͉̲̺̝̝̫̈́̈̋̀̀̐͆͒̊͋̓͛̆͌̍̓̾͛͆͐͌̎̋̅̍͛̑̈̓́́͋́̽̾͒̃̚͘͠͠͠͝͠͝   █̶̨̨̛̱̜̯͑̅͂̋͋̐̂̈́́̍̇̓̇̇̅̀͠͠█̷̢̡̨̛̜̹̳͇̰͓͔̞̆̊̄̈́̍̑̽̐́̊͂̈́̂̒̽̇̋̅̾̓͆̅̀͐̌̒͑́̎͘̕̚͜ͅ█̴̨͎͍̱̜̺͈̝͔̣͇̹͈̤̿͛̃̀͒̾̇̈̉̀͐̀͊̑̿̚͝͠͝╗̴̧̛̪͚̖͙̫͍̼̎̈́̉̃̀̇̋̑͂̂̔̐̐́͒̅̽̌͒͒̅̂͛̀͐̆͌̾̅̓̕̕͜͜͝͝͝ͅ░̸̡̧̧̫̺̬̲̪̺̖̘̺̹̟͔̤̤͍̪̺͎̙̠̬̤̦̩̼̙̩̫͍̠͙͎̗̳̀̊̿͛̈́̿̐̔̒̈́̋͛͐͂͋̈̒̉̋̓̀͑͊̇̂̈́͆̒̉̑̓͊̏̀̅̅͘̚̕̚̚͝͠ͅ
̸̢͕̗̞̬̠̘̩̼̮͓͎̥̗̼̠̤͕͇̳̣̹̦̦̘̺͇̯̩̥̻͙̬͐͗̈́̀̀̊̇̐̎́͂͊͂̈́̄͐̒̈́̿̓̄̒͆̎̍͐́́͘̚͜ͅͅ░̷̨̨̛̛̙͉̳̯̩͉͚̜͍̘̩͇̘̼͖̬̲̝̹̞͎̮̝̰̩̦͇͖͙̠̞̪̮̪̣̇̒̅͒̓̒̌̎͛̄͆̎͌̐͊̈͊͐̓̏̎͝͝͝͝ͅͅ╚̷̧̢̢͖̝̥͚͍͉͇̤͚̰̼͇̫̮̱̮̼̰͖̞̫͉̩̲̹͈̘͕̳͇́̆͂̈́͂͋͌̌̀̔̑̋̂͌͊̍̈͒̑̇̋̌̾̋͆̿̐̓̀̇͛͐̀̒̊̽̐̊̈́͑̈́̚͝͝ͅͅ═̷̛̟̈́̅̑̾̏́̉̈́̍̐̿̊̇̀̕͘═̷̧̼͈̩̫̭̖̫̠͓͂͗̾̈́̋̈́̊̀̆̎̓̐̋͗͜͝═̶̳͓͉͈͙͖͔̭̹̯͍̣̎̓͌͋́́̃́̂͊̈͆̈̀̔͋̕̚█̷̯̹̯͙̹̗̼̻̺̮̽̉͐͂̀̎̂͗̾̈́͝͝█̸̢̨̡̡̝̭͖̟̥̱̗̥̗̻͈̦̙͚̰͉̹̈́̊̄̔̿͐̈͆͒̋͆̈́̎̃̿͆̇̚͝͝ͅ╗̵̦̞̻̯͍͙̥͇̹̗͎͕̘͖͙̮̠͚̹̈́̊̒̊͑̿̈̏͒̽̑̓̽̈́̓͊̓̕̕͜͜͠͝█̶̡̧̧̜͍̦̖̣͈͖̟̰̠͇̜̱̭͖̟͙̹̱̣̭͔̠̮̮̠̹̲̠̺̰̰̘̩̠̘̤̙͇̠̠̝̽͊̏͜ͅ█̵̢̛̖̯̞̏̈́͆̽̒̔̒̅́̒͊̃́͂͑́̍͒͒̈́͐̔̈́̿͂̌̈͆̔͑̏͌̏̎̉̚̕͜͝║̸̨̡̧̦̺͕͈̱͕̙̭̤̲̭͈̜̜̳͙͈͕̮̦͚̹̠̩̫̲͙̮̝͍͈̄͑̃͊̏̌̆̓̓̽̃̍̈́͐͒͊͌̂́̊͐̒̓̌͆͌̏̀̽̈́̒̔́͑̎͐̽́̆̃̔̃͗̕̚̕͜͝ͅͅͅ░̷̢̨̘͔͙̥͇͚̝̖̭̝͙̭̦̦̗̱̠̟͚̠͇̫͔̗̤͚̤̩̯̻̦͉͇̖͚̣̖͓͔̻͉̜̼̰̼̞̪̉̀̃̔̈́̂̊̈́́̈́̒̔̀̌̽̀̔̄̍̔͑̐̈́̈́̀͗͛̽̇̄͒̀̑̉͂͘̕̕͠͠͠͠͝͝͝͝░̸̡͚̟̩͔̥̃̀́░̶̢̢̩̰̳̜̻̮͇̘͓̳̣̜̜̩̲͇̜̮͚̺̺̤̪̲͆̀̓̈́̓͊̒̏̌̆̍̔̇̎̌͌͋̓͆̐̇̋͋̀͜͜͠͝͝ͅͅ█̴̢̢̧̧̞̭͈̳̖̳̤̫̻̪̤͎̹̫̼̺̺̮̺̥̋͘͜█̶̧̡̗͕͍͖̩̬̫̫͕̬̖̩̬̳͂͂͆̌̈́̏͌͗║̷̧̣̣̝͓͔͉̘̻̙̼͇̺̙̹̲̬͙̙̖̘̗̫͑̂̇̂́̈́̈͛̈́̈̒̃̇̾̀̀͛͋̄͘͘͠ͅ░̶̨̢̦͔̘̯͕̲̯̩̭̼̤͍̝̱͔̟̣̙͈̪̼̩̱̣̺̤̗̪͋̍́͂̔̐͆̑̈́̐̾̈́̚͘͜ͅͅ╚̵̡̧̢̛̠͚̭͎̝͍̳͇̬̻̗̪̞̭͈̼̪̺̞̥̼̮̩͍͓̝̞̪̻̗͇̟̬̳̯̖̭̼̯̻̮̓͂͛́̆͌̃͗̾͆̑̅̒̈́̒́̿͛́̊̌̾͌̓̓́͛̎̕͜͠͝ͅͅ═̸̧̧̧͖̦͍̭̭̯̩̭̳͈̟͓̥͈̦̮̲̼̳̹̜̹̯̭͍͔̱͕̱̖͈̭̩͕͕̏̓̑̂͝═̸̧̧͇̭̬̩̬͔̗̰͙̜̥͎͈͇͈͚̞̰̹̲͑̂̀̽̈͒̋͐̎̄̈́̉͌́͑̚͝͠═̶̨̢̻̙̝̭̲̲͖̟̙̠̩͉͖̲̭̲̼͎̦͔͎̥͖̫̰̟̖̞͇̫̪͉͖̖̒ͅ█̶̢̟͓͕̲̉̌͂̿̊̂̔̽́͐̐͛̎͗̏̐̑͌̽͂̈̐́̓́̃͐͂̀̐̾̎̏͘̕͘̕̕̚ͅ█̴̢̛̖̬̝͇̦̦̭͔͈̫͙̪̊̑̽͑̏͊̓̇̄͒͆͐̀̒̽̉̈́͛̿̓͊̏̒͐̾͐̓̾̿̓͐͌̕͝͝͝͠͝͝͠╗̸̩͚̗̓́̉͌̚̚͝
̷͉̠̘̩̙͆͑͊̈́̌̉̂͆̓͑͊͛͝͠█̶̨̡̢̜̬̘͙͈̹̥̩̩̭̼͇̻̣͇͙̤͍̻̃̅̽͒͆̈́̊̃̌̏́̀̿̌͠͝ͅ█̵̨̡͇͖͉͉͓͎̺̹̳̠̪͎͈͉̻̪̩̳͙̳̭̺͉͓̈́̑̅͑̏̈́̆̂̍̿̂̿̈́̉̃̾́̄̄̒̈̇̿͆͌͑̿̓̍̑̕͘̚͜͠█̷̨̢̲͈̪̞̟̗̜̼̗̹̖̮͓̹͔̪̰̦̻͔̳̞͎͇͖̪͍̣͚̤͇̣̇͂̃̐̾̉͐̀̈́̍̿̊̎̿͌̍̄͛͆̃̈́̚͜͠͝█̸̨̢̨̧̨̜̹͙̩̝̣̪͉̜͈͍̬̹̣̠̘̦̙̯̮̙̪̬̥̰̤͖̰̱̜̳̝̤̮̘͕͓͍̆̊͛͗̒͘͜͜ͅͅ█̷̨̨̛̜͍̤̻̙̭͍̜̫̦̖̠̳͎̲̜͚̹̥̹̫̠̬̪͚̜͕̳̪͇̩̩̝̋͂̓͆̎̀̆̾̏̍̑̄̆̈́̀̓́̅̓͒̇͂͂͐͒̈́̏̆̒̊́͘̕̚̚͜͜͝͝͝ͅ█̷̼̹̬͎̺̺̙̝̪̙̠̝̔̒̇̿́̒̀͗̆̂̾̅̇͌̏̏͑̓̒͊̋̇̆̊̿̀̈̊͒̏̚̕̕̚͜͠͝͝͠͠ͅ╔̸̡̢͕̦̗͚͙͕͖͚̣͙̟͇̮̰̪̒̈̿̐̂͑̈́́̇͌̌̍̐̀́́̑͐̽̂͋̉̌̓́̄̚͘͠╝̶̨̛̟͇͙̰̦̩͓̖̜̩̘͙̫̟̭̻̑̀̿̋̇̓̀͗̓̔͐̐͂̇͛̆͆͂̆̿̒̅͒́̎̄͆̏̎͒̿̈͆̈̈́̑̄̔̊̽̒̾͋͂̀̕̚͝͝ͅ╚̴̛͍̣̐̔̄̑̓̅̀̈̄̆̽̌̅̃̈́͐͌̃͒͊̌͗̓̾̿̊̊̏̀͒̉̓̍̌̓̏̋͘̚͝█̸̢̡̡̡̛̛̱̯̱̩̟͇̻̺̙̯̭̬̭͙̮̲͎͕̯̆̃̌̎̂̉̀̄͆̿̒̏̑͑͆͒̔̍̍̈́̓̇̓͋̃̓͐̄̋̏̕̕͠͝͠͝█̴̨̢̨̩̦͙͖̳͉̳͇͖͉̙̘̱̥͕̖̻̼͎̘̼̜̹̫̦͎͇͔͙̯̱̖̝̻̲̟͖̯̍̎̅̕█̷̡̛̟̩̣̮̎͐̀́̓̈̎̌̊̓͊̏̎̐̌̽͘͘̕͠ͅ█̵̢̝̲̦̤̘̺̝̤̥̜̤̟̰̟͙̭̯̠͔̮̫̩̓̈́̏̂̄͂͗̏͐̔̓͋̐̈́̊̿̚̕̚̚͜͝ͅ█̸̧̛̛͓̪̥̥͎͕̼̲̗͚͇͓̞͖̘͉̺̪̟̖̊̈́̅̂̿͑̂͑͜ͅͅ█̴̨̛̛̮͕͕̭͔̘̮͙͚̥̖͈̼͕̦̱̮̪͋̐͛͛̄̿̅̀͜͠͝ͅ╔̷̧̲̪͎͙̦͙̫̭͉̐̆̂̅̔̈́́̌͗̂̐̽͊̕╝̴̧̡̗͙̞̠̫̙̟̗͔͕͚̹̳̙̺̥̣̻̣͉̱̗̺̪̗̞̗̜̎̽͑̍̓̐̊͋̃̾̊͛̆̀̊̄͋̅̈́̋̏͊́͗͌͐̓͂́́̍̇͐͊̀̕̕͠͝͝ͅ█̷̢̨̡͕͖̙̜͕͉͓̜̹͖̤̭̠͙̱̙̺͖̙̓̏̇̃͜͜͜ͅ█̴̧̗͕͉̺͇̭̟̝̻̩̥̙̗̪̫͎̄̈́̄̈̎̿̈͐̍̄͑͊̀̈́͘̕͘͠͝█̵̢̛̛̛̗̻͎͕̽͂̉́͆̏͂͌̓̀́͂̏̎̐̋́́́͘̕̕͜͠͝͝͝     █̴̡̻̬̪͓͎̣͚̟̬̮́̽̈͛̍͒̚͝ͅ  █̵̧̨̡̨̧̭̠͓̟̜̫̪̳͓̹͙͚͕͎̰̰͈͎̬͍͉͖̜̺̜̻̪̙͉̭̭̦̗̲̘̥́̾̀́̽͒͌̊̓̄̂̑̎̄͊̌̀̓̿̒̑̊͘͜͜͝͝͠͝͝͠ͅ█̷̡̨̧̛̠̬͚͔͕̭͈̝̯͕͉̜͓̎̇̒̄̾̂̔͒̏̐͐͒͊̎̍̊́͘╔̷̙̭̠̪͕͍̒̀̀̕╝̸̢̧̺̖̫̬̺̼̰̰͔̻͉̳̗̦͖̟̖̮̺̗̬̖̱̩͎̭̼͖̌̅̈̃̓̊̇̿̇́̔̄̌͋̒͑̋̋̽̆͑̎̃̓͋̂͆̓̀̀̀̔̉̀̇̇̓͑͌̕͠͝͝
̵̨̨̼̝̫͉͇͇̜̬̭̼͉͙̹̤͎̠͖̭̼̗̝̼̖̜̰͔͉̲̰͎͌̇̃͂̏́̈̓̽̊́̈́̑̚͜͝͝͝͝͝ͅͅ╚̵̨̧̨̝̩̺͔͙̞͔̫̊̊͋͐̓͗͒̽̀̂̇́̾̽̽̓̀͑̐͒̌̀͆̏̔̍͂̂̉͑̌̓̈̿́̈́̐̕̚̚̕͝͠͝͝═̷̨̢̫̝̣̗̬̖̣̱͓̳̖̪̈̈́́̒͊͛̊̌̒̓̅̂͋̾̃̑͊̆̉͐͌̀͆́͒̿͆̊̀̅̈́̃̄̄̓̆͌̔̏̇͋͂͝͠═̸̨̨̡̛̼͍̼̰̞̪͈̥͇̫͉͔̳̺̱̣̪͓̜̞̹̝̰̫͉̹̗̮̆̑̎̅̂͑͑́̊͋̈́͒̈́̀̂̑͊͗́̋́͐͘̚͝ͅ═̶̡̡̢̥̟̭̬̳̝̳͕͍̥̬͓̦̑̆̿̇̈́͊̈́̊͐͋̓̀̃͒̃̑́̌́̀̔͝͝═̵̧̧̨̛̺̪̪̟̰͙̥̣̮̳͖͋͆́̃́̒͑̃͊͛́̂̒̂̔̿̅̈́̓̑̏͋̌̎̍͗̄̋̏̌͆̔̅̊̓̽͘̚̕̕͝͝═̴̢̨̨̨̢̛̹͎̮̩̜͈̬̦̮̫̲͖̫̱̻̤̱͉̝̟̲͕̣͓̹̅̓͌̓̈́̄̀̅͋̓̀̾̌̾͛̌͒͂̉͗̋̂̃̌͊̾̉̅̚͘̚͘͘̕͝͝͝͝╝̵̨̡̨̛̣͓͚̤͔̜̬̥̼̹̬̘͎̠̬̪͉̳̳͓̼͖͔̲̦̲̫̗̠̥̫̳̩́̇͐̂͐̽̿̿̓̆̀́͐̇̕̕͜͠ͅ░̶̡̛͓͔̯͉̮̺͑̈́̀̏̌͋͂̾̊͆͛͌̊̓̕░̸̡̡̧̨̙̱͕̘̯͕̗̘̯̘̘̼͙̦̳͕̺̫͊̀̑̔̌̆̌͐̀̋̀̏͐̈̉̄̇̊̀̽͒͌̂̌̊̄̔̋̓͆̓̉̅̀̅̎͆̅̐̃̓̕̚͜͜͜͝͝͝͝ͅ╚̴̢̢̧̧̨̥͚̹͖͓̪̥̱̫̯̱̯̺̗͓͇̰͍͕̞̖̠͉̫̻͍̝͍̬̝͉̣̥̫͉͉̜̰͍̜̲͖̿̈́͌̂͑̔͌̃̀̏́̃̎̒̃̅̃̈͑̆̕͘̕̚͝͝͝ͅ═̶̢̹̫̬̮̖̱̞̣̜̘̘̪̺̜̩͔͓̺͙̰̜̗͉̥̩̥̜̘͗͘͝ͅ═̵̧̡̬̼̬̩͎͈̟͉̗͇̬̹̳͎̼̼̹͈̝͔̹̝̯̮̼̮̩̺̘̪̗̃͛̄͐̎̉́̆͐͒́̎̈͑̕̚͝ͅ═̶͍̖̻͈̹̘̙̞̫͍͙͍͚̯͇̗̜̳̖̀́═̶̡̨̨̪̘̮͔̖͍͓̘̰͚͍͋͑̾̆͋̈́̏̅̓̈̇͌̉̃̍͋̑̋̔̋̏͋̚͜͠͝═̶̧̨̧̨̨̙͉̩̠̘͓̬̺͕̘͍̭̮̲̺̼͉̬̔̓̈́͊͐̿͐͆͆̒͂͊̃͛̕͘͜͝͝͝╝̵̛̹͕̩̞̳̠̯̰̦͇̹͎̤̩͇̳͚͈̌̔͊̓̇̀̈́̎͗̊͊͒̒̔́̐̉̿̓͗̎̈́͑̓̈̎̆́̐̃̌̉̎̓̃̋́̇́́̃̈́̓̎̕͠͝░̴̨̨̧̧̢̧̩̝̩̖̟͚̦̳̘͖̰͚̯͚͇͔̱͕͉̰͓̬͈̱͈́̊̈̈̏̓̓̅̀́͜͝╚̸̢̨̛̛͇̼͓̯̬͍͇̯̰̙̺̹̥͍͔͓̫̺̲̠͖͍̠͔̠͖͈͉͇͚͉̻͈͇͇̱̼͉͓̘̯̖̙̮̾͌́̍̉̿̾̀̾̎͒̈̑͂̈́͗̿͗͘̕͜͠͝͝͝═̷̡̢̧̡̡̢͎͖̪̟͕̖̘̼͍͕̰͉͉͎̟͎̦̖̜̠̙̩̠̬̦̖̻͉̮̯̱͈̦̯͓͖͖̟͍̰̮̽̓͐̈́͊͛̑̆̔̔͒͐̇̈́̍̉̒͆̉͜͠ͅ═̶̧̧̨̧̭͈͉̲͎̖̙̳͚͎̦͇̫̱̯̯̯͇͕͓͙̺͚͚̘͓̭̲̯̣̠̞̲̱̤̙̱͍͉̬̹̎̊̇͆̏͜͝͠═̴̡̨̨͎̳̮̻͙̪̙̩̭̰͚̰͎͇̦̙̳̘̠͎̹͎̮͇̟̥̼̤̥̙̦͓̳̯̪͙͍͓̦̥̫͂̀̈́́̈̒͆̈́̊̒̒͛̋̃̕͜═̸̡̧͎̭̲̲̝̺̪̘̱͚͔̲̱̯̺̏̂̆̌̽̚͜═̵̧̢̡̛͎̗̮͖̻̺̰̤͇̗̳̘̗͉͖͓̮͎͇̙̬̹͎͙̫̲͍̘̘̪̱̳̯̭̤̋̔̀͒̉͛́̐̄̓̌̍̂̆͗̎́̌̀̕̕͜͝͝͠ͅ╝̶͇͌̎̎̈́̓̌͂̈́͠░̸̢̨̡̡̛̛̗͇̬͉̼͙̟͓͔͎̠͍͔̯̳̦̮̜͇̫̻̣͙͔̃͒̊͐̈́͊̈́̈̈́̉̃͐̍͂̒͛̀̈͆̊́̚͝͝͝ͅͅ