:::::::::::::::::11111:..........................................1.  :5..................:::::1:111::::::::::::::::.............
:::::.:::::::::::11511:..................................:11::..:1.  :5..................:::::::111111111:::::::::..............
:::::...::::::::111111:..............................:11555566655551.:5..................:::::111111111:::::::::::..............
::..::...:.:::::::1111:............................:1111555666666666661:................::::::155511:1:11::::::::...............
:::.:.....::::::::11111...........................:111155566665566665665:...............::::::55551511::::::::..:...............
::::..:.:.:::::::::1511.........................:11111555555555:155555665:.............::::::1655551:1:::::::.::................
::::.....:.:.::::::1111........................:11::11551111151::155556655::...........::::::1665551::1111:::::............. ...
::::::.....::::::::1111.......................:1111111151:11111::1115555655:..........:::::::1555551:11111::::::................
::::::::.:...::::::111:.......................:1111:11:1::::1::..:1155555511:.....::..:::.:111111551111111:::::.................
:::::::::....::::::1111......................::155:::::::::::::..::111155511::.....:.:1:11:::::::111::161:::::::........ ...... 
::::::::::...:.:::1111:.....................:115511::::::::::::..::::111151:1......:::1::::::::1:511111511:::::......... .......
:::::::::::..:::::1111:.....................:1161111111:::::11:.:::::::::5::5.....:::::::::::.:11::11:555:::::::................
.:::::.:1::::.:::::151:.....................:115811::..::.:::11..111:51116151:::::::::::::::::::::::15556::::::........  ......:
:::::...:1:::::::::111:....................:::5561:::...:51:11:::.:1:5551666688888:..:::::::::::::::115661:::::.......... ......
.::::...::1::::::::1111...................::511511::.....:15.5.:..:1:11656665111::::::.:11::15111:::115581:::::.............1...
:::::....::1:::::::111::.................::.1::15::::.............:.566856865::::::::1:.:1:161111:11115581::::::.............1::
:::::....:::1::::::111::.................::::1:111:::.............:::::1:886:::....:11:::...:51111111556651::::.................
::::.....:::1:1::::111:::...............::::::118:::::.........:...::..:18661::....::5::.:.....1515555568811:::............. .. 
.:::.....::::11::11115:::..................11:1561::::.........::..:::::5866::1::::::::...:......:6666886511::::................
::::.....::::11:111155::::.............:...::11111:::::.......:..:::::::58661::111:::::.. .:.....:6665111151:::::.......... ... 
:::::...:::::11:1111551:::.................::::116:::.:...........:::::188665::::::::::.. .......:65551111111::::........ ... ..
:::....::::::111111155::::................:::5:1111:.::..  ...::::::.::668666:::::::::::....:....:5511:::::11:::::...... ..... .
.:......:::::111:11155:::::..............::::51::111::::.....::. :11::56666561::::::::::....   ..555511:::111::::.............  
........:::::111:::1151:11:.::..:..:....::.:15615:1151::::...:.::::1::66665655:::::::::::..... ..555151:::::11:::::..........   
........:::::111::::::::1::::1:..11:....:::.:556611::55:::.:...::11:1866655551:::1::::::........:551111:::::15:::::......... . .
.......:::::::11::::::::::::::...::::::::::::1665551:1155:.::...:::1686516115555151551::........:551151::::::11::::.......... ..
........::::1:11::::::::::..::1....:...::::1::565611111111151::::1166651511111111111555::.......:5551111::::::51:::::...........
........::::1111::::::::::::::15:..:::::..:.::1566551115::::::::1156561:1:115151111155551:.......1551111::::::11:::::.......... 
........::::1151::1:::::1:1111115:..:1:1::...:155555111:1::::::::155651151111111111115555:.......:551111::::::151::::...........
........::::1151::11:::::5111:111:...:611::::115556515:1:::::::::1:15555511:115:111115555:::......:551111::::::111:::::.........
........::::11511:11:1::1:::...::....::::111111155551:::::::.:::::::5155511:1151::11155555::......:5551111:::::111:::::.........
........::::115111111::11:.....:.   .::1:161111155555:::::..:::::::::1::511::1111:11111555:::.....:1555111:::::1111:::::........
.......:::::1165511111156:. ...:..  .:51155:::1155651::::::::..::::::::1515551511::11111555::......:5551111::::11111::::........
.......:::::1166551155586:. ........::551511:11156111::1:::........:::::111511111::51111155:::.....::5551111:1:11151::::::......
.......:::::15666686555666:... .....::5156:51:155111:::::........::.:::::11151:111151::11151::......:155555111111111::::::......
.......::::1111111111555666..  .....:1556:15111511::::::.......:.....:.::11111:.11:1:::::1551:......::555555111111151::::::.....
......:::::111111::11155566:........:5516:1511111::::::.......:...:...::::11111:1:111::::1151:......::1555555111111111::::::....
......:::::11111:::111155661:.......:515111511111:::11::::....:...:::::::::11111:1:1::::::111::......::555555111111151::::::::..
.....:::::1111::1::111155661:......::555:1151111:::1:::::......:::::::::::::1:::11::11:::::11::......::15555151::::15:::::::::..
.....:::::1111:11::111155651:..::::::5511:11111111::::::::......::::::::::::111:11:111::::::11:......:::11151551::::1511:::::::.
.....:::::11111::::111555651:.....::156:1:51:51::::::::::.........::::.::::::::111:::::::::::1:......::::155111::::::::::::.::::
....:::::1111111::1111555651:.....::15511:1:1:::::::::::..........:::::::::::::11:::1::::::::1:........::11111111511::1::.::.:::
....:::::1111111111115555651:.....::1551111:1:::::::::::............::...:.::::::1::.:::::::11:........:::111:1111:11155::.:::::
....::::11111111111115555655:.....::1551:1:11:::::::::::.....................:::1::..::1::::11:........:..:111111151::55:::.:.::
...:::::11111111111155155651:.....::11511:5111::::::::::.....................::::::::::51:::1::...........:111:555::::511:::::.:
...::::111111111111151555661::....::15511:5111::::::::............:...........:::11:.:::51:::1::..........::5151:551:55111::.::.
..:::::111111111111115555661::....::11555:5111::::::.............::::..........::::1::51:11::1:::..........1615111511:11111::::.
::::::11111111111111555556511:....::11155151111::................:::::.........::::15::51:1::1:::::........:65111151155551:::11:
::::::11151111111111155566511:....::::155155511::.................::::::::::::::::1151:15:11:11:::::......::11551515111511:11111
:::::11115551111111115556611:::...:::111655511::....................:::::::::::1111561:56::5::11::::.......:65511515115111::5151
:::::11115511111111515556811:::::.:::115565551::......................::::::1111111155::551151111::::.......11155151555111:11155
:::::11155511111111555566611:::::::::1115555111:::::.:.................::::::::11::1151.15151151111:::...:::11111111115111511:55
:::1111155551111111555566511:::::::::1115615511::::::::::::............:.:::::::::::151::511:::1551::::..:1511111111111165111116
::11111555551111115555668511:::::::::111161151111:::::::::::............::::::::::::1511::1:::::::5111::::5555511111155565511111
:111115555551111115555666511:::::::::11:161:15551111111::::::...........::::::::::::1111::1::::::::::::5151151115555555516511111
11111156555551111155566665111:::::::::115511116665551111:::::.....:::.:..::::::::::::11:::1:::::::::::::155551111511115565511111