⠜⠎⠄⠜⠌⠇⠜⠉⠄⠜⠌⠇⠜⠞⠄⠜⠌⠇⠜⠃⠄⠜⠌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠗⠁⠝⠵⠀⠨⠛⠗⠥⠃⠑⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠞
⠀⠀⠀⠀⠀⠨⠏⠁⠗⠁⠀⠉⠕⠗⠕⠀⠍⠊⠭⠞⠕⠀⠁⠀⠉⠥⠁⠞⠗⠕⠀⠧⠕⠉⠑⠎
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠕⠨⠝⠨⠉⠨⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠑⠗⠧⠊⠉⠊⠕⠀⠨⠃⠊⠃⠇⠊⠕⠛⠗⠷⠋⠊⠉⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠄⠀⠨⠇⠁⠀⠨⠉⠕⠗⠥⠻⠁⠂⠀⠼⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠓⠚⠃⠚⠀⠨⠍⠁⠙⠗⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠞⠑⠇⠋⠄⠒⠀⠼⠊⠁⠑⠓⠊⠙⠃⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠚⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠧⠕⠇⠥⠍⠑⠝⠀⠾⠝⠊⠉⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠗⠁⠝⠵⠀⠨⠛⠗⠥⠃⠑⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠁⠛⠓⠛⠤⠼⠁⠓⠋⠑⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠗⠍⠄⠀⠨⠁⠄⠀⠨⠃⠁⠗⠗⠊⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠼⠋⠦
⠀⠀⠜⠎⠄⠜⠏32768⠐⠓⠄⠉33256⠮32512⠓301536⠫⠄⠀⠀⠀⠀⠀⠀⠀32768⠓⠄⠉33256⠮32512⠓301536⠫⠄
⠀⠀⠜⠉⠄⠜⠏30768⠐⠋⠄⠉31256⠿30512⠋281536⠹⠄⠀⠀⠀⠀⠀⠀⠀30768⠋⠄⠉31256⠿30512⠋281536⠹⠄
⠀⠀⠜⠞⠄⠜⠏281024⠐⠹28512⠙251536⠸⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀281024⠐⠹28512⠙251536⠸⠳⠄
⠀⠀⠜⠃⠄⠜⠏211024⠸⠹21512⠙211536⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀211024⠹21512⠙211536⠹⠄
⠼⠁⠀⠰⠆⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠞⠂⠀⠀⠓⠑⠊⠇⠊⠛⠑⠀⠨⠝⠁⠉⠓⠞⠖
⠼⠃⠀⠰⠆⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠞⠂⠀⠀⠓⠑⠊⠇⠊⠛⠑⠀⠨⠝⠁⠉⠓⠞⠖
⠼⠉⠀⠰⠆⠨⠝⠕⠉⠓⠑⠀⠙⠑⠀⠨⠙⠊⠕⠎⠂⠀⠝⠕⠉⠓⠑⠀⠙⠑⠀⠏⠁⠵⠂
⠜⠎⠄361024⠨⠱36512⠑341536⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀351024⠹35512⠙321536⠐⠳⠄
⠜⠉⠄271024⠸⠺27512⠚291536⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀301024⠫30512⠋301024⠫⠉32512⠓
⠜⠞⠄241024⠸⠻24512⠛241536⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉231024⠸⠫25512⠓⠜⠙281024⠐⠹⠉27512-1⠣⠚⠜⠲
⠜⠃⠄181024⠘⠳18512⠓181536⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉211024⠸⠹21512⠙⠜⠙21512⠸⠙⠉22512⠑⠉23512⠋
⠀⠰⠆⠁⠇⠇⠑⠎⠀⠎⠉⠓⠇⠜⠋⠞⠂⠀⠀⠀⠀⠀⠑⠊⠝⠎⠁⠍⠀⠺⠁⠉⠓⠞
⠀⠰⠆⠨⠛⠕⠞⠞⠑⠎⠀⠎⠕⠓⠝⠂⠀⠀⠕⠀⠺⠊⠑⠀⠇⠁⠉⠓⠞
⠀⠰⠆⠉⠇⠁⠗⠕⠀⠎⠕⠇⠀⠃⠗⠊⠇⠇⠁⠀⠽⠁
⠼⠑⠀⠜⠎⠄331024⠐⠪33512⠊35768⠙⠄34256⠾33512⠊
⠀⠀⠀⠜⠉⠄281024⠐⠹31512⠛33768⠊⠄32256⠷31512⠛
⠀⠀⠀⠜⠞⠄261024⠸⠪28512⠙28768⠙⠄28256⠽28512⠙
⠀⠀⠀⠜⠃⠄241024⠸⠻24512⠛24768⠛⠄24256⠿24512⠛
⠀⠀⠀⠀⠰⠆⠝⠥⠗⠀⠙⠁⠎⠀⠞⠗⠁⠥⠞⠑⠀⠓⠕⠉⠓⠤
⠀⠀⠀⠀⠰⠆⠨⠇⠊⠑⠃⠀⠁⠥⠎⠀⠙⠑⠊⠝⠑⠍
⠀⠀⠀⠀⠰⠆⠽⠀⠇⠕⠎⠀⠷⠝⠛⠑⠇⠑⠎
⠜⠎⠄32768⠐⠓⠄33256⠮32512⠓301536⠫⠄
⠜⠉⠄30768⠐⠋⠄31256⠿30512⠋281536⠹⠄
⠜⠞⠄28768⠐⠙⠄28256⠽28512⠙⠜⠉25512⠸⠓⠉28512⠐⠙⠉⠜⠙⠄27512-1⠣⠸⠚⠜⠲
⠜⠃⠄21768⠸⠙⠄21256⠽21512⠙211536⠹⠄
⠀⠰⠆⠓⠑⠊⠇⠊⠛⠑⠀⠏⠁⠗⠗
⠀⠰⠆⠨⠛⠪⠞⠗⠊⠉⠓⠑⠝⠀⠍⠥⠝⠙⠂
⠀⠰⠆⠉⠁⠝⠞⠁⠝⠦⠙⠕⠀⠑⠎⠴⠞⠷⠝
⠜⠎⠄331024⠐⠪33512⠊35768⠙⠄34256⠾33512⠊
⠜⠉⠄281024⠐⠹31512⠛33768⠊⠄32256⠷31512⠛
⠜⠞⠄261024⠸⠪28512⠙28768⠙⠄28256⠽28512⠙
⠜⠃⠄241024⠸⠻24512⠛24768⠛⠄24256⠿24512⠛
⠀⠰⠆⠨⠓⠕⠇⠙⠑⠗⠀⠅⠝⠁⠗⠑⠀⠍⠊⠞
⠀⠰⠆⠙⠁⠀⠥⠝⠎⠀⠎⠉⠓⠇⠜⠛⠞⠀⠙⠊⠑
⠀⠰⠆⠛⠇⠕⠦⠗⠊⠁⠀⠁⠴⠀⠨⠙⠊⠕⠎⠀⠛⠇⠕⠦⠗⠊⠁⠀⠁⠇⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠑
⠼⠓⠀⠜⠎⠄32768⠐⠓⠄33256⠮32512⠓301536⠫⠄
⠀⠀⠀⠜⠉⠄30768⠐⠋⠄31256⠿30512⠋281536⠹⠄
⠀⠀⠀⠜⠞⠄28768⠐⠙⠄28256⠽28512⠙251536⠸⠳⠄
⠀⠀⠀⠜⠃⠄21768⠸⠙⠄21256⠽21512⠙211536⠹⠄
⠀⠀⠀⠀⠰⠆⠇⠕⠅⠅⠊⠛⠑⠍⠀⠓⠁⠗⠗⠂
⠀⠀⠀⠀⠰⠆⠗⠑⠞⠞⠑⠝⠙⠑⠀⠎⠞⠥⠝⠙⠂
⠀⠀⠀⠀⠰⠆⠨⠗⠑⠽⠀⠉⠑⠇⠑⠎⠞⠊⠁⠇⠂
⠜⠎⠄⠜⠉361024⠨⠱36512⠑⠜⠙38768⠨⠛⠄36256⠵34512⠚
⠜⠉⠄⠜⠉311024⠐⠻31512⠛⠜⠙29768⠐⠑⠄31256⠿31512⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠜⠞⠄⠜⠉271024⠸⠺27512⠚⠜⠙27768⠸⠚⠄27256⠾29512⠑
⠜⠃⠄⠜⠉251024⠸⠳25512⠓⠜⠙⠄257681⠩⠸⠓⠄252561⠷255121⠓
⠀⠰⠆⠎⠉⠓⠇⠁⠋⠞⠀⠓⠊⠍⠍⠇⠊⠎⠉⠓⠑⠗
⠀⠰⠆⠨⠉⠓⠗⠊⠎⠞⠀⠊⠝⠀⠙⠑⠊⠝⠑⠗⠀⠨⠛⠑⠤
⠀⠰⠆⠙⠥⠑⠗⠍⠑⠀⠝⠊⠻⠕⠀⠨⠚⠑⠤
⠜⠎⠄⠜⠏⠏351536⠨⠹⠄⠉⠜⠞⠑⠝⠄371536⠨⠫⠄
⠜⠉⠄⠜⠏⠏301536⠐⠫⠄⠉⠜⠞⠑⠝⠄3115361⠩⠐⠻⠄
⠜⠞⠄⠜⠏⠏281536⠐⠹⠄⠉⠜⠞⠑⠝⠄281536⠐⠹⠄
⠜⠃⠄⠜⠏⠏261536⠸⠪⠄⠉⠜⠞⠑⠝⠄22153618⠸⠱⠄⠔
⠀⠰⠆⠗⠥⠓⠄
⠀⠰⠆⠃⠥⠗⠞⠄
⠀⠰⠆⠎⠾⠎⠄
⠼⠁⠁⠀⠜⠎⠄⠜⠗⠊⠞⠄⠄35768⠨⠙⠄32256⠐⠷30512⠋32768⠓⠄31256⠿⠜⠏⠏29512⠐⠑⠀⠀⠀⠀⠀283072⠝⠄⠣⠇⠣⠅
⠀⠀⠀⠀⠜⠉⠄⠜⠗⠊⠞⠄⠄32768⠐⠓⠄30256⠯28512⠙27768⠚⠄26256⠮⠜⠏⠏27512⠸⠚⠀⠀⠀⠀⠀⠀283072⠝⠄⠣⠇⠣⠅
⠀⠀⠀⠀⠜⠞⠄⠜⠗⠊⠞⠄⠄30768⠐⠋⠄28256⠽25512⠸⠓22768⠑⠄22256⠵⠜⠏⠏24512⠸⠛⠀⠀⠀⠀⠀233072⠏⠄⠣⠇⠣⠅
⠀⠀⠀⠀⠜⠃⠄⠜⠗⠊⠞⠄⠄25768⠸⠓⠄25256⠷25512⠓18768⠘⠓⠄18256⠷⠜⠏⠏18512⠘⠓⠀⠀⠀⠀⠀213072⠸⠝⠄⠣⠇⠣⠅
⠀⠀⠀⠀⠀⠰⠆⠎⠉⠓⠇⠁⠋⠀⠊⠝⠀⠓⠊⠍⠍⠇⠊⠎⠉⠓⠑⠗⠀⠗⠥⠓⠄
⠀⠀⠀⠀⠀⠰⠆⠨⠉⠓⠗⠊⠎⠞⠂⠀⠊⠝⠀⠙⠑⠊⠝⠑⠗⠀⠨⠛⠑⠃⠤⠀⠃⠥⠗⠞⠄
⠀⠀⠀⠀⠀⠰⠆⠙⠥⠑⠗⠍⠑⠀⠝⠊⠻⠕⠀⠨⠚⠑⠤⠀⠀⠎⠾⠎⠄
⠼⠃
⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠂⠀⠓⠑⠊⠇⠊⠛⠑⠀⠨⠝⠁⠉⠓⠞
⠨⠓⠊⠗⠞⠑⠝⠀⠑⠗⠎⠞⠀⠅⠥⠝⠙⠛⠑⠍⠁⠉⠓⠞⠆
⠙⠥⠗⠉⠓⠀⠙⠑⠗⠀⠨⠑⠝⠛⠑⠇⠀⠨⠓⠁⠇⠇⠑⠇⠥⠚⠁
⠞⠪⠝⠞⠀⠑⠎⠀⠇⠁⠥⠞⠀⠧⠕⠝⠀⠋⠑⠗⠝⠀⠥⠝⠙⠀⠝⠁⠓⠆
⠨⠉⠓⠗⠊⠎⠞⠀⠙⠑⠗⠀⠨⠗⠑⠞⠞⠑⠗⠀⠊⠎⠞⠀⠙⠁⠄
⠨⠉⠓⠗⠊⠎⠞⠀⠙⠑⠗⠀⠨⠗⠑⠞⠞⠑⠗⠀⠊⠎⠞⠀⠙⠁⠄
⠼⠉
⠨⠎⠞⠊⠇⠇⠑⠀⠨⠝⠁⠉⠓⠞⠂⠀⠓⠑⠊⠇⠊⠛⠑⠀⠨⠝⠁⠉⠓⠞⠖
⠨⠛⠕⠞⠞⠑⠎⠀⠨⠎⠕⠓⠝⠂⠀⠕⠀⠺⠊⠑⠀⠇⠁⠉⠓⠞
⠨⠇⠊⠑⠃⠀⠁⠥⠎⠀⠙⠑⠊⠝⠑⠍⠀⠛⠪⠞⠞⠇⠊⠉⠓⠑⠝⠀⠨⠍⠥⠝⠙
⠙⠁⠀⠥⠝⠎⠀⠎⠉⠓⠇⠜⠛⠞⠀⠙⠊⠑⠀⠗⠑⠞⠞⠑⠝⠙⠑⠀⠨⠎⠞⠥⠝⠙⠂
⠨⠉⠓⠗⠊⠎⠞⠂⠀⠊⠝⠀⠙⠑⠊⠝⠑⠗⠀⠨⠛⠑⠃⠥⠗⠞⠄
⠨⠉⠓⠗⠊⠎⠞⠂⠀⠊⠝⠀⠙⠑⠊⠝⠑⠗⠀⠨⠛⠑⠃⠥⠗⠞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠊⠝⠀⠙⠑⠀⠇⠁⠀⠕⠃⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀