
....................................................................................................................................................................................
...........................................````````.................................................................................................................................
........................................``````````````...............`..`..........................``.``............................................................................
......................................````````````````...............```````````....................................................................................................
.....................................````````````````.........................``......................``````........................................................................
.........................................````````````................```````````.`..............`````.``............................................................................
................................................`````..............```````.`.....................````.```````............................````.......................................
.....................................................................`................................````..````...........................````.....................................
.............................``...................................```````..................;..................``........................`.....```...................................
............................```....```.......................................................;;;;++;;;.........`..........................``...```..................................
..........................`````...``````.................`.................................;+;;;+++++++;............................................................................
........................```````...``````................................................+++++;;;++++++++;;..........................................................................
.......................```````....``````````````........................................;+++++++++++++++;;;.........................................................................
......................````````...```````````````````.....................................;++++++++++++++;;+;.......................................``...............................
......................```````....``````````````````````................................;;+++++++++++++++++;;;....................................````....``.........................
....................```````.......``````````````````````...........```.................;;+++++++++++++++++++;..................................```````...```........................
.................`````````........```````````````````````..........``````..............;;+++++++++++++++++++;;..........................`````.````````...````.......................
................`````````.........``````````````````````............``````............;;;+++++++++++++++++++;;..........................``.```````````...``````.....................
..............```````````.......````````````````````````............``````.............;;;;;;;;;;;;;;;;;+++++;......................``````````````````....`````.....................
..............```````````.....````````````````````````.............``````..``.......;;;;;;;;;;;;;......;;++++.......................`..```````````````.....````.....................
................`````````....````````````````````````...............```````.........;;;;;;;;;;;.........;;+++...............................``````````.......``.....................
..................``````.....```````````````````................`...................;+;.;;;;;;;;.........;+++......................`..````````````````..............................
..........``.......`````.....``````````````````.........`.......`...................;;;.;;;;;;;;........;;;++.........................``.````````````...............................
.......``````................`````````````````.........``.......``..................;;;.;;;;;;;;.........;;++...............................``.````````.............................
.......```````...............````````````````.........```.......```.................;;;;;;;;;;;;;;.......;;++..............................`````````````............................
.....``````````.............``````````...............````.......```.................;;;.;;++;;;;;;;......;;+;..............................``````````````...........................
....```````````............````````````.............`````.................``.`.......;..;;;;;;;;;;;;;;;..;++;...............................``````````````..........`...............
...`````````````..........````````````.............``````.......`.....````````.......;;;;;;;;;;;;;;;;;;;;;;+;...............................``````````````..........................
...`````````````.........```````````...............``````.............``````````.......;;;;;;;;;..;;;;;;;;;;.....................................`````````..........................
...````````````..........``````````................``````.............````````````.....;;;;;;;;;..;;;;;;;;;...`..................................````````.................```.......
.`````````````````.......`````````.......```.......``````...........`.`````````...;;...;;;;;;;;;...;.....;;...``.`................................````.`.................``````.....
.```````````````````....`````````.......`````......``````.........```````````````.;;...;;;;;;;;;.........;;;.......................................````````.............```````.....
.``````````````````......```````........``````.....``````........````````````````..;...;;;;;;;;;.........;;;.........................................```.``.............`````````...
.````````````````````....````..........``````````...`````........``````````..``....;...;;;;;;;;;;;.......;;;..`..`....................................```.`............```````````..
.````````````````````..................```````````..`````........`````````````````..;..;;;;;;;;;;;......;;;...`..`.................`...................````.............```````````.
.````````````````````.................```````````....````.........````````````````..;..;;;;;;;;.........;;;.......................``.....................``............````````````.
.``````````````````...................``````````......```..........```````````````.....;;;;;;;;........;;.....`..``.`.....................................```........```````````````
.``````````````````...................````````....................````````````````.``..;;;;;;;;;.......;;...................................................``......````````````````
.``````````````````...........````......``````.....`.............`````````````````.```.;;;;;;;;;;;;;..........................................`....................`````````````````
.``````````````````...........`````......`````....````...........`````````````````.```.;;;;;;;;;;.;;...............................................................`````````````````
.``````````````````......`....``````.....````.....````...........```````.``............;;;;;;;;;;..;;;;.......`..`.................................................`````````````````
.```````````````````....```....`````.............`````...........`````````````````.```..;;;;;;;;...;;;;............................................................`````````````````
.```````````````````....````...`````............```````...........````````````````.......;;;;;.....;;;;.......`.............................`......................`````````````````
.```````````````````....````.....`.............`````````...........``````````````......;;;;;;;;;.;;;;;;......................................`......................````````````````
.```````````````````....````...........``......````````..............```````````.......;;;;;;;;;;;;;;;;;................................................`...........````````````````
.`````````````````......````.........`````.....`````````.............``````````........;;;;;;;;;;;;;;;;.+....................................................`......````````````````
.```````````````........`````........```````...`````````.......`.....`````````.........;;;;;;;;;;;;;;...++;............................`....................``.....`````````````````
.``````````````........``````........```````...`````````.......``......````............;;;;;;;;;;;;;;;..+++;................................................```....`````````````````
.```````````.........``````````......````````..````````........```.......````...........;;;;;;;;;;;.;..;+++++;..........................`......`............```.....````````````````
.``````````..........``..```````.....````````..````````........````...................;.;;;;;;;;;;;;;..+++++++;;;;.....................``....```............```.....````````````````
.``````````................````......````````...```````........```....................;.;;;;;;;;;;;;...+++++++;;;;;;;;......................```.............```.....````````````````
.`````````...........................````````...```````........``.....................;;;;;;;;;;;;;....++++++++++++;;;;;;;;.................````..........``````.......`````````````
...`````..............................````````..```````............................`..;;;;;;;;;;;;;....+++++++++++++++++++;;;...............``..`.`.......``````.......`````````````
....```................................```````..```````............................`..;;;;;;;;;;;;.....+++++++++++++++++++++++;;;...........````..........```````.........``````````
....``.................................``````....``````...............```.....;;;;....;;;;;;;;;;;.....;+++++++**++++++++++++++++++...........````.........```..............`````````
.......................``...............``.```...``.```.............````....;;;;;;....;......;;;......++++++++****++++***+*+++++++;............``..........................`````````
...........`````......````.`............``````...``````............````...;;++++;;....;;;;;;;;;......;+++++++*****+++++**+*++++++++........```..`...........................````````
...........`````..`````````.....```......`````...``````............``....;;+++++;;....;;;;;;;.......;++++++++*****+++++**++++++++++;.......``.``.............................```````
.........```````..``````````....```......`````......``.................;;+++++++;;....;;;;;;;.......+++++++++****++++****+++++++++++..........``..............................`````.
.........````.`````````````.....``........`.``......``..........``...;;+++++++++;;....;;;;;;.......;+++++++++*+**++++***++++++++++++...........................................````.
.........```````.````````..................```..................`..;;;++++++++++;;....;;;;;;.......++++++++++****+++****++++++++++++..........................``......``........``..
........``.```...````````.......```.`......`.....................;;;+++++++++++++;;;+.;;;;;;.;;;..;+++++++++**+***++****++++++++++++..........................````.````````.........
........``.`````.````````......```...............................+++++++++++++++++++;.;;;;;;;+++++*++++++++++++***+*****++++*+++++++;............................```..``````........
.........```````..````..`......```...............``..............+++++++++++++++++++;;;;;;;;.....;+++++++++++++**+******+++**++++++++;...........................``...```````.......
..........``.```.````````......................````..............++++++++++++++++++++;;;;;;;;+++++++++++++++++***+******+++**+++*+++++.........................``..`..````````......
.........```````````.```.......................``````............++++++++++++++++++;;;;;;;;;.;;;;+++++++++++++*********++++**+***+++++;...............`........``..``.````````......
.......```````..`````````......................```````...........++++++++++++++++++++;;;;+;;;;;;;+++++++++++++*********++++**+***+++++;..............``...............`````````.....
.......````````.`````````.....................````````..........;+++++++++++++++++++;.;;;;;.;+++++++++++++++++**++*****++++****+++**++............................``..`````````.....
........```````..`````.``.....................````````..........;++++++++++++++++++;;;+++;;;;...;++++++++++++***+******++++****++***++;...........................``..````.```......
........```..``...............................````````..........;++++++++++++++++++++++;;;+++++++++++++++++++**********++++****++***+++;........................`......```````......
.......````````.```.``.........................```````..........;++++++++++++++++++;;;;...;;;;;++++++++++++++**********++++****++***++++.........................`....`..`````......
......``.````...................................................;++++++++++++++++++++++;;;;;;;;;+++++++++++++**********++++****+***++*+++.........................``...`.``````.....
......```````..................``..............```````..........;++++++++++++++++++++++;.;;++++++++++++++++++**********++++********+***++..........................`...``..`````....
..............................``...............```````...........++++++++++++++++++;;;;...;;;;;++++++++++++++*********+++++********+***++;..............................``.`````....
................................................``.```...........++++++++++++++++++++++;..;+;;;++++++++++++++*********++++********+**+*+++;.................................````....
...........................``......................``............+++++++++++++++++++;;;...;++++*+++++++++++++*********++++********++++**++++;..........``.................```````...
..........................```.``.................`````...........++++++++++++++++++;;;;...;;;;;++++++++++++++*********+++*********++++**++++++......`.```..................``````...
............`...`.........``.```.................`````...........++++++++++++++++++++++...+++++++++++++++++++********+++++***********+++++++++;......``````.................`````...
...........```.```........`......................````............++++++++++++++***+;;;;...;;+++++++++++++++++*******++++++************+*****+++;........`````.................```...
..........````.``.`.......`.......................`.`............+++++++*++++++***++++;;;.;;;;+++++++;+;;..;;;;+++**++++++******************+++++;...`````````......................
.............``````......``..`....................````...........+++++++++++++****+++++;;;+++**+++++;;..;;;;;;;;++**++++++*********************++++;.``````````.....................
........````....```..........`....................````...........+++++++++++++***++;;;;;;;;;;++++++++;.;;;;;;;;;;+**++++++***********************+++;.`.`````.`.....................
........``````.``..................................```...........+++++++++++++****++++++;;;;;;++++*++;;;;;;;;;;;;;++++++++**********************+++++...````````....................
.......``````..``..........```...........`..........`............+++++*+++++++****++++++;+++***+*++++;;;;;;;;;;;;;;++++++++**********************++++.``````````....`......`........
..........`````````.........``.``..................```...........+++++**++++++****+;;;;;;;;;;+++***+++;;;;;;;;;;;;;;+++++++**********************++++;..````````....``.....``.......
......``.`.....```..................................`............++++***++++++***+++++++;++++++*****++;;;;;;;;;;;;;;;++++++**********************++++;......```......`.....```......
......```````..................................`....`............;+++***++++++***++++++;;+++*********+;;;;;;;;;;;;;;;+++++++*+*******************++++;....````.............`````....
.......`.``.`..```............................``.................;+++****+*******+++;;;;;;;;;+********+;;;;;;;;;;;;;;+++++++++**********+****++***+++;....``.........``.....`````...
..........`.....`..............................`...............`..+++****++*******+**+++;+++++********++++;;;;;;;;;;;++++++++++++++++++++****+++***++;....``........``......`.......
..............................................................``..+++*****+*++****+++;;;;+++***********+;;;;;;;;;;;;;+++++++++++++++++++++++*++++***++..............`.......``````..
.........``.......................................................+++****+++++****+++;;;;;;;++*********++;;;;;;;;;;;;+++++++++++++++++++++++*++++***++....```..............```````..
..........`.......................................................+++****+++++****++***+;+++************+++++++;;;;;;;++++++++++++++++++++++*+++++***+.....`.........`......`````...
..................................................................++*****++++++**++;;;;;;+++******************++;;;;;;+++++++++++++++++++++++++++++**+......................```.....
............................................``....................++*****++;;++***++++;;;;;;+*******************++;;;++*++++++++++++++++++++++++++++*+;.............................
............................................```...................;+++***+;;;+****++++*+;+************************+++++**+***+++++++++++++++++++++++++;.....................```.....
............................................`.....................;++****+;;++***+++;;;;;+++*******************************++++*+++++*********+*++++++;.............................
.............................................``..................;++++***+;;++*******+++;;++******************************++;;;;++++++****++++++++++++..............................
.............................................```.................;++++++++;+++****++++++++********************************+++;++++++**++**++**+++++++;..................;;..........
..............................................```................;;++;;;++++++****+++;;;;;;+*******************************++++***+****************+;.;;................;;;.........
.................................;...............................;;+;+;;;.;++*****++**++;+++*****************************************************++;.;;;;...............;;;.........
..........................;...;.;.................................;++;;..;;++*****+;;;+;;+******************************************************+;..;;;;;...............;;;.........
..........................;.;;.;;................................;++;...;;++********++++;+++**********************************************++;;;.....;;;;;...............;;;.........
.............................;;;;;..............................;++...;;;+++******+;++++++***********************************+;;;;++++;;;...........;;;;;................;;;........
.............................;;;;;..............`...............;;...;;;+++*******++;;;;+++******************+++*************+;.........;;;;;;;;;;;;;;;;;;;;;;;;.....;;;;;;;........
.............................;;;;;;.............................;.;;;;;;++++***********++++******************+;;**************;......................;;;;;;;;;;;;....;;;;;;;........
.............................;;;;;;;;...........................;;;;;+++++++******++;;++++*******************+++**************;......................;;;;;...............;;;........
........;....................;;;;;;;;;..........................;;;++++;;;++*******+++;;+++***********************************;;.....................;;;;;...............;;;........
........;...;................;;;;;;;;;.........................;;;;;;;;;;+++***********+++************************************;;......;;;.........;;;;;;;;...............;;;........
........;;;;;................;;;;;;;;;.........................;;;;;;;;;;;++********++++++************************************+;......;;;;.......;;;;;;;;;...............;;;........
.......;;;;;;................;;;;;;;;;;......................;;;;;;++++;;;++********+++++++***********************************+;.......;;;.......;;;;;;;;;...............;;;;.......
.......;;;;;;................;;;;;;;;;;;.....................;;;;;;+++;;;;++*********++++*************************************+;......;;;;.......;;;;;;;;;;..............;;;;;......
.......;;;;;;................;;;;;.;;;;;;..................;;..;;;;+++;;;;++*********++++*************************************+;......;;;;;......;;;;;;;;;;..............;;;;;......
;......;;;;;;................;;;;;..;;;;;;.;..............;;;...;;;+++++;;++*********++++*************************************+;;.....;;;;;;...;;;;;;;;;;;;..............;;;;;......
;......;;;;;;...............;;;;;;..;;;;;;;;;;...........;;;;...;;+++++;;+;+*********++++*************************************+;;...;;;;;;;;;;;;;;;;;;;;;;;..............;;;;;......
;......;;;;;;...............;;;;;;...;;;;;;;;;............;;;....;+++++++;.;******+**++++**************************************;;.;;;;;;;;;;;;;;;;;;;;;;;;;..............;;;;;;.....
;......;;;;;;...............;;;;;;.....;;;;;;............;;;;....;;+**++;;;;******+++++++**************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;..............;;;;;;.....
;.....;;;;;;;...............;;;;;......;;;;;;...........;;;;;......;;;;;;;;;******+++++++**************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;.....;.....;;.;;;;;;.....
;.....;;;;;;;...............;;;;;;......;;;;..........;;;;;;;.......;;;;;;;;******++;;++++*************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;..............;;;;;;.....
;;.;;.;;;;;;;..............;;;;;;;;;....;;;...........;;;;;;;.......;;;;;;;+******++;;++++**************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;.;;...........;;;;;;.....
;;.;;.;;;;;;;;;;;;;;;;;..;..;;;;;;.;...;;;;;.........;;;;;;;;.......;;;;;;;+******++++++++**************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;..;.;;.....;;;;;;.....
;;;;;;;;;;;;;;;......;;.....;;;;;;.....;;;;;........;;;;;;;;;.......;;;;;;;+*****+++++++++**************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;.....
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;...;;;;;;;........;;;;;;;;;......;;;;;;;;+*****+++++++++***************************************;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;..;;;;;;;;;.;..
;;;;;.;;;;;;;;;;;;;;;;;;;;;;;;;;;;;.;;;;;;;;;;.....;;;;;;;;;;.....;;;;;;;;;+*****+;;+++++****************************************;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;....
;;;;;;;;;;;;;;;...;.;;;;;;;;;;;;;;;;;;;;;;;;;;;;...;;;;;;;;;;....;;;;;;;;;++*****+;;+++++******************+++*******************;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;..
;;;;;;;;;;;;;;;;.;;.;;;.;;;;;;;;;;;;;;;;;;;;;;;;...;;;;;;;;;;...;;;;;;;;;;++*****+;;+++++******************+++*******************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;.;;;;;;;;;;;;;;;;;;;;;;;;...;;;;;;;;;;...;;;;;;;;;;++*****+;++++++*******************++*******************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;..;;;;;;;;;;;.;;;;;;;;;;;++*****+;+++++++***************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;.;;..;;;;;.;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;++*****+;+++++++***************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;++*****+;+++++++***************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;+++*****+;+++++++****************************************;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;+++*****+++++++++****************************************;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;++******++++++++++***************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;+++******++++++++++***************************************+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;