Makan Emojis & Symbols

⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠒⠒⢄⠀⠀⢀⠄⠒⠒⠒⠒⠒⢄⠀⠀⠠⠐⠒⠒⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣠⣀⣀⣨⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠄⠀⣧⠀⠀⠀⠀⠀⢠⠊⠸⢠⠀⠀⠀⡄⠘⠀⠀⠀⢸⢀⠁⠀⠀⢨⢀⠁⠀⠀⡁⠈⠀⠀⠁⠈⠀⠀⠈⡀⠁⠀⠈⡁⢁⠀⠑⡄⠀⠀⠀⠀⠀⣸⠀⠠
⠀⠀⠐⡆⣿⠀⠀⠀⠀⢀⡏⢀⡏⣼⠀⠀⢠⣅⡏⠀⠀⠀⣭⣨⠀⠀⠀⡍⣸⠀⠀⠀⣏⣩⠀⠀⢸⣸⡅⠀⠀⣇⣏⠀⠀⢩⡸⡅⠀⢡⠀⠀⠀⠀⠀⣷⢲⠂
⠀⠀⠀⠁⢹⠉⠉⠉⠉⣏⣀⣀⣀⣆⣀⣀⣘⣠⡀⣀⢀⣀⣄⣀⢀⣀⣀⡇⣀⣀⣀⡀⣄⣀⣀⣀⣸⣀⣄⣀⣀⣀⣀⣀⣀⣀⣄⣠⣀⡀⣋⠉⠉⠉⠉⡏⠈
⠀⠀⠀⠺⣬⠭⡍⠀⢼⠀⠀⡞⠸⠂⢀⣀⢶⣰⡀⠀⠀⠐⠆⡖⠀⠀⢰⢂⡷⠶⠶⠦⡷⣲⠀⠀⠐⠆⠗⠀⠀⣺⢸⠀⠀⠀⢒⠘⡆⠂⢸⠅⠀⢨⠭⣥⠟
⠀⠀⠀⠀⣿⢠⣀⡀⠀⣹⢰⠓⡏⠉⠀⠀⠀⠐⠀⠈⠁⠐⠖⠧⠀⠒⠉⠈⠀⠀⠀⠀⠀⠀⠈⠈⡏⡃⠉⠀⠀⠸⠈⠁⠁⠐⡞⠲⠒⡆⣏⢀⣀⣀⡄⣿
⠀⠀⠀⠀⣿⣜⣒⣒⣒⣚⣸⠀⡇⠀⠀⠀⠀⢮⠥⠤⠤⠤⡵⠆⠀⠀⠀⢮⠥⠤⠤⠤⡵⠄⠀⠀⡷⡥⠤⠤⠤⢬⠶⠀⠀⠀⡇⠀⠀⣧⣓⣒⣒⣒⣣⣿
⠀⠀⠀⠀⣿⠈⠀⠀⠀⢸⢐⠀⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⡇⠀⠀⠀⠁⡿
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠚⠀⠣⠆⠀⠀⠐⠂⠀⠀⠀⠀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠀⠐⠂⠀⠀⠓⠀⠀⠀⠀⠀⠛⠀⠀⠀⠢⠔⠀⠓⠀⠀⠀⠀⠐⠂

⠼⢿⠀⣀⣀⠀⢀⣀⡀⠀⠁⠛⣛⣛⠛⢉⣋⡛⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠰⠀⠀⠐⢠⠀⠀⠀⠀⠁⠀⠀⠀⠓⢦⠤⠤⢤
⠀⠈⠀⡁⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠒⠂⠀⠀⣨⠀⠀⢠⠀⢰⠀⢸⠀⠀⢸⠀⠀⡆
⠀⠨⠀⠄⠄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⢀⡘⢳⡄⣀⣀⣀⣠⣠⡐⠠⠘⠀⢀⠀⠀⠀⠀⠅⠘⠀⠀⠀⠀⢸⠘⠙⠀⠀⠸⠀⠉⠁
⠤⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠀⠀⠀⠀⠀⠈⠢⡠⠤⣀⡾⠀⢀⠔⡘⢦⡠⢆⡴⢛⠿⡺⣄⢀⡾⠿⡤⠤⠤⠤
⠀⠀⠀⢰⠶⡆⠀⡖⠒⠀⠀⠀⠈⠉⡇⠀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⢪⡛⠛⠛⠀⠀⠀⠀⠁⠶⢀⠂⠔⠠⡀⢊⠜⠰⠉⠃⣄
⠀⠀⠀⠘⠀⠀⠀⡁⠀⣀⣠⡀⠀⠀⠇⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⢀⡀⠀⢀⣀⠀⠙⠁⠀⠀⠀⡀⡃⠀⠀⠈⠋⣐⠐⠀⢁⠎⡠⢀⠀⠀⠉
⠒⢰⠶⠻⠀⠃⠀⠂⠐⠁⠀⠐⠐⠂⢀⡀⠀⡋⠉⠀⡏⠉⠀⠀⠀⠈⠅⠅⠀⠀⠄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠐⠁⠒⠀⠀⠐⠀⠐
⠜⠁⢰⣴⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠄
⠀⠀⠘⠛⠀⠀⠀⠑⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡀⠀⢨⠀⠐⠀⠀⠀⣤⡕
⣆⠀⠀⡄⣄⠠⢰⠀⠀⠩⠉⢉⡉⠁⡏⡉⠀⠖⠒⠀⠖⠒⠀⠀⠀⠐⠒⠆⠀⡶⠶⠆⠀⠀⠀⠰⡾⠄⠤⠤⠣⠤⢄⣠⠦⠙⠀⠀⠀⠀⠀⠈⢀
⢹⡅⠔⠃⡟⡀⢸⠀⠀⢰⠀⠨⠄⠀⠇⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⠀⣀⢃⣤⡃⠄⠀⠀⣀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠷⠀⠀⠀⢄⣈
⣬⣥⡅⠠⣮⣤⣼⣤⣤⣈⠀⡨⠠⠀⠀⠈⡀⠉⡁⢄⠐⠄⠐⠆⠒⠄⠘⢠⠴⠓⠐⠂⣼⡕⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣰⡒⠚⠛
⢃⡐⠘⠈⢁⠡⡀⠄⢨⡄⠋⠀⠀⠈⠋⠉⠁⠈⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⣀⡀⠀⢀⣀⡄⠀⠀⠉⠩⢭⡉⠉⠉⡉⠉⠁⠀⡀
⢢⠐⡌⢂⢀⠨⠀⡘⠂⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⠄⠄⠀⠀⠀⠀⠂⠇⠀⠀⠂⢀⠠⠎⠱
⠀⡡⢈⠊⢀⢚⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⢀⠟⡠⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⠸⠠⠞⢠⠀⠀⠨⠁⠈⡅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⡄
⡁⠰⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⣤⣬⣤⡀⠀⠀⠀⠀⣀⣆⡇⠀⠀⠀⠀⠀⢰⠚⡇⠀⠋⠉⠀⠀⠀⠈⡉⡇⠀⢨⠀⢀⡇⠂
⠀⠀⠀⠸⠃⡀⠀⠀⠀⠀⠀⠀⠘⠀⣤⡄⢡⠤⠤⠤⠤⠤⢤⠄⣔⣤⣤⠤⡴⠶⣆⡀⣴⠄⢨⢤⣥⠀⠄⠀⠀⠀⠀⠀⠄⠇⠀⠤⠀⠸⠇⠀⡀
⣀⢀⣄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠈⠁⠀⠘⠀⠀⠀⠀⠀⡠⠈⠈⠑⢆⣤⠤⠶⠤⠀⠠⢄⡤⡶⠆⠑⠀⠁⡂
⠈⢉⠝⠉⢭⣮⡽⢤⢍⣮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠣⣄⠀⠀⠀⠀⠀⡀⠊⠀⢸⣿⠀⠀⠑⢦⡀⠀⠀⠀⠀⠁⠘⠒⠈⠈⠉⠉
⠀⠁⢠⡕⠀⠀⠀⠀⠀⠳⠒⢛⠛⠛⣛⣛⠛⠀⠀⢀⣀⡀⠀⢀⢀⡀⠠⣤⠤⠦⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂
⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠤⠄⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⢀⡇⠀⡖⢈⠀⢴⡆⠈
⢀⠀⠀⠄⠀⡀⠀⠑⠤⠀⠐⠆⠀⠀⠂⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠅⠀⠁⠁⠀⡇⢰⠀⠸⡥⢁⠀⢀⠀⠠⠤⠀⠀⠂⠂⠒⢰
⠉⠀⠀⠈⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢄⠉⠞⠃⠝⠰⠻⢀⠜⡛⢻⡍⠈⠉⠇⡞⠐⠈⠀⠀⠀⠐⠀⡇⡆⠀⢸
⠀⠶⠶⠶⠶⣧⠴⠄⠄⠠⠴⡏⣱⢤⡏⠉⠁⠀⠀⠐⠋⠀⠀⠀⢀⠀⠙⢣⣌⠐⠀⡠⢁⠊⡘⠁⠉⡱⢀⡀⠱⠒⢨⣄⠀⡀⠠⡠⢧⡷⠛⢾⢀
⠉⠷⠷⢉⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠈⠠⡅⠀⠀⠊⠰⠁⠄⠀⠆⠈⠃⠽⠉⢈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠔⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠆⠀⠀⠁⠀⠈⠁⠀⠉⠉⠠⠹⠿⠇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢐⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⢀⠄⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠃⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⠀⠠⠀⠡⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡀⠀⠀⢀⠔⠂
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⡰⠀⠀⠠⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠
⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢡⠀⡐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣠⡟
⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠀⠁⠈⡀⠀⠁⠀⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⢻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠂⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡟
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣦⣦⣤⣤⣴⣤⣤⣴⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠫⡜⠃⢺⣍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⡄⠸⠿⢸⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⢴⣤⠛⠄⠀⠀⠀⠀⠀⠀⢿⠙⠛⡆⠘⠋⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠒⢈⠀⠀⠀⠀⠀⠀⠈⣇⠀⣃⣀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣧⠀⣄⠀⡀⠀⠀⢌⠃⠈⢧⠀⠀⠀⠀⠀⣀⣽⣆⠙⠁⣠⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠘⠃⠀⠀⠀⢚⠃⠀⢸⣀⣤⣶⣾⣿⣿⣿⠀⢯⡽⠃⢸⣿⣷⣦⣤⣀⡀⠀⠀⡴⠊⣍⠒⠒⠛⠺⠿⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⡀⠐⠲⡐⢮⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⢳⠌⠛⠂⠉⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣐⠚⣣⢀⣀⠷⠚⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⠀⣿⣿⣿⣿⢸⣿⣿⣿⡇⢸⠠⠀⠀⠠⠀⢠⡍⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠽⠛⠉⠉⠒⠢⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣿⣏⣩⣾⣿⣿⣿⡀⢠⠉⠑⠀⠘⠀⠀⡜⠘⢆
⠀⠀⠀⢀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⢣⡰⠶⠀⣀⡴⠃⢰⠘⡆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠙⠒⣊⢅⠘⠀⠆⠐⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⡆⠤⠤⣾⣿⣿⣿⣿⠁⠀⠀⣀⣈⡷⢡⡀⠁⠘⣎
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡠⡟⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣏⠀⢠⡎⠷⣤⣆⠀⠀⠀⠆⠸⡆
⠀⠀⠀⢻⣆⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣄⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⢀⠀⡀⠀⢳⡴⠄⠰⠆⢘⠀⠀⠆⢿⠀⠀⡴
⠀⠀⠀⠀⠉⠉⠓⠚⠛⠛⠛⠛⠛⢫⢣⠀⠀⠒⠢⢤⡀⠀⠀⡘⢆⢠⠀⠀⠀⠐⣶⡍⠘⣛⡛⠣⠦⠀⠄⠀⠳⠴⠦⡔⣏⠘⠃⠰⠸⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠖⠒⡀⡇⡆⠀⢀⠔⡗⠈⢶⣾⠕⠋⠳⡳⡀⢞⠉⠠⠐⠤⠒⠉⢑⠄⡰⠀⢨⠋⠉⡿⠃⣄⣀⡢⣔⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⠰⠀⢀⡴⠁⠀⠀⠳⣄⠀⠀⠱⢷⠈⠙⢳⡄⠢⠴⠖⠋⠒⠒⠒⠋⠀⢰⠇⠤⠸⡶⠁⢈⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡄⡐⠁⠀⠀⠀⠀⠀⠙⢧⣀⠀⢸⠀⠀⠀⠳⠄⠒⡒⠒⠶⠶⠶⠶⠂⠉⢠⡀⢰⠓⡆⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢱⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢁⠇⠀⠃⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⢛⡿⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠰⠙⠀⠀⢣⡀⢾⠁⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠛⣻⡷⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠋⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⢤⣀⠀⠈⠳⣤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠓⢒⠒⠶⠶⠶⠶⠤⠤⠤⠤⠤⢤⡤⠴⢾⠟⠋⠙⠚⠛⣿⡿⠂⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠁⠀⠠⠀⡀⠀⠂⠂⠀⠀⡀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⣦⠀⠉⠁
⠀⠀⠀⠀⠀⢀⣤⠖⠛⠋⠛⠦⢤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣬⡦⢤⣄⣠⡶⠛⠛⠃⠠⣾⣳
⠀⠀⠀⠀⠀⠺⣥⣀⣠⣤⠤⠖⠒⠀⠀⣀⡤⠴⡶⠀⠀⣀⡄⠀⢠⢴⠀⣀⢀⡴⠋⠈⠳⣄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣀⡤⠶⠚⠉⠁⠀⠀⠷⠶⠚⠁⠳⠖⠁⠀⠛⠉⡟⠀⠀⠀⢠⡿⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣈⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⢄⡀⠀⢸⡁
⢀⣤⠶⠒⠛⠛⠉⠉⠉⠀⠀⠀⠙⠲⣌⣈⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡷⠚⣻⢿⡋⠉⠉⠉⠉⠙⠛⠓⠒⠲⠦⢤⣄⡀
⣿⠀⠀⠀⠘⠀⠀⠓⠒⠒⠒⠒⠂⠲⠦⠽⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⢛⣋⣁⣠⣤⡭⠥⠤⠤⠤⠤⠔⠒⠂⠀⠀⡀⠀⠀⠀⠉⠳⢦
⠈⠛⠒⠶⠤⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡄⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣏⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠶⠖⠒⠒⠛⠋⠉

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢸⠁⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹
⠀⠀⠀⠘⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡌
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡖⠑⡆⠀⡖⠳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠃⠀⢧⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⡆⠀⡗⠲⡇⠀⡗⠺⡇⠀⡷⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⠀⢠⠃⢀⠇
⠀⠀⠀⠀⢹⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡇⢀⡇⠀⣇⢀⡇⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⢸
⠀⠀⠀⠀⢸⠀⠸⡆⠀⠉⠉⠉⢹⠉⠉⠉⢹⡏⠉⠉⠉⠉⢹⠀⠀⡏⢹⠃⠀⡏⠉⡇⠀⢸⠉⠉⠉⠉⠉⡏⠉⠉⠉⢹⠉⠉⠉⠁⠀⡏⠀⢸
⠀⠀⠀⠀⢸⡄⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠀⢀⠃⢸⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⡆
⠀⠀⠀⠀⠈⣇⣀⣃⣀⣀⣀⣀⣸⠀⠀⠀⢸⣀⠀⠀⠀⠀⠸⠀⠈⠧⠜⠀⠀⠱⠤⠃⠀⢸⠀⠀⠀⠀⣀⣹⠀⠀⠀⢸⣀⣀⣀⣀⣸⣁⣀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⡇⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢬⠀⠀⠀⠀⡇⢹⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡏⠉⡛⠉⠉⠉⠉⢹⡆⠀⠀⢸⠉⡇⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡏⢹⠀⠀⠀⡟⠉⠉⠉⠉⢹⠋⠉⡇
⠀⠀⠀⠀⢠⡇⠀⡏⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⡇⠀⠀⠀⡏⠀⢸⠁⠀⠀⠀⠀⠀⢹⠀⠈⡆⠀⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⡇
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠇⠀⠀⠀⡇⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⢸⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⠀⣧⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⢸⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⢧
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⢸⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⢸⡇⠀⢀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡀⢸⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠃⠀⠀⢸⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠛⠒⠐⠋⠃⠚⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠘⠒⠃⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠃⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢠⠤⠤⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠁⠠⠆⢀⢠⠌⢳⠀⢀⠀⠀⠀⠀⠀⠀⢠⡥⣀⣈⣉⣉⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⠀⠀⠀⠀⢰⠏⢠⣄⠀⠀⠀⡤⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠾⠁⠀⠀⠀⠀⠀⣾⠀⠈⠁⢀⠀⠀⠀⠠⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠛⠀⠀⠀⠀⢀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢠⡄⠀⠀⠉⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠤⢤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡤
⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢐⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀
⠀⠀⠀⠀⠀⣼⣁⠉⠀⢘⢙⢃⣡⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣾⣤⣄⣀⣀⠀⠀⠻⠿⠦⠴⠮⠽⣶⣭⡶⠭⠶⠭⠾⠿⠗
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠰⢄⣠⣄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣏⣿⡗⢐⡏⣰⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠉⠉⠃⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢃⠀⠀⠀⠀⡘⠛
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠰⠀⠆⠐⠀⠀⠀⠀⠀⠀⠇⠛⢨⠶⢶⡄⠏⠸
⠀⠀⠀⠀⠀⢰⢦⣴⣤⣴⣄⣠⣦⣤⣦⣀⣥⡆⠀⠀⠀⠀⢤⣶⣤⣶⣤⣴⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⠟⠃
⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠨⠀⠉⠙⠁⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣛⠛⣛⡛⠛⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣟⠿⣿⢿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡶⠿⠋⠉⠙⠊⠁⠉⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠛⠀⠀⠀⠲⠄⠀⠀⠒⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡎⠀⠀⠀⢢⠆⠀⠀⡤⢻
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠬⢦⣑⠀⠀⠀⠀⠀⠐⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠷⣦⡀⢣⡀⢄⡀⠀⠀⠸⠏⢀⠴⡃⠀⠠⠤⠤⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠤⠄⠈⠻⣄⢷⣤⢊⣿⣓⠒⢚⠁⠠⢌⡽⠶⣤⣤⣄⣀⠤⠂⡩⣍⣴⠞⠉⣠⡭⠟⠃⠤
⠀⠀⠀⠀⣴⠃⢀⡐⣒⠒⠢⠄⠻⣷⢩⣷⣿⠏⠓⠦⣙⣦⣾⣭⣶⣿⣾⢿⡟⠖⣾⡶⣛⡤⣰⡾⣯⣖⣖⣢⡞⠉⠓⠋
⠀⠀⡴⠛⢯⠡⡀⠛⢮⡙⠲⠤⠀⠙⢿⡿⠧⣀⢀⡴⠋⠿⣯⠶⣼⠯⠝⠒⣥⡾⠁⠀⣾⠁⠙⢳⡟⠀⢼⠎⢹⡄
⠀⢸⠁⡎⣽⠷⣿⣦⣜⣿⣦⣀⠀⠀⠀⠳⣄⠀⠉⡗⣄⣀⢤⡘⠯⠄⠀⢸⣏⡈⠀⠸⣧⣤⡄⠚⢧⡌⠚⠢⣼⠃
⠀⢸⡀⣿⢀⡀⠐⠻⣿⣿⣿⣿⣗⠦⣠⠊⠈⡳⠤⠇⠿⢛⣷⣤⣾⣶⣥⣤⡐⠠⣤⣤⠰⣦⣤⣤⣒⣶⣿⣶⣿⣆⡀
⠀⠈⢧⠈⠈⠁⠀⠀⠈⣻⣿⠿⠟⠓⠛⣧⣌⡀⠀⠀⠈⢛⡻⠿⣿⣿⣭⣭⣭⣽⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠹⡳⡄
⠀⠀⣘⣦⡤⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⢯⡯⣛⢦⣀⠀⠈⠛⣿⣿⣿⣿⣶⣿⠿⢩⣽⣿⣋⣿⣿⣿⣿⣿⡿⠋⠀⣠⢏⡟
⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣵⣲⠥⣀⣉⣛⠛⠛⠿⠿⠿⠿⠷⠼⠯⠟⠛⠛⢋⣉⣠⠤⣖⣫⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠿⠿⠿⠿⣿⣿⣶⣶⣶⣿⣿⠯⠭⠿⠓⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠬⢉⣉⣉⠁⠀⠒⠒⠒⠠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠁⠉⠁⠀⠁⠀⠀⡂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡘⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣈⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠤⣀⡀⠀⠙⠓⠢⢄⣀⠀⠀⠀⢀⠀⠀⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠂⠀⡈⠓⠲⠤⣀⡀⠀⠉⠲⠤⣀⡀⢀⠇⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⡠⠈⠁⠒⠼⠄⣼⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⢀⠤⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡀⠐⠁⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠓⢤⣀⠀⠀⠀⣀⠐⠁⠀⠀⠀⠀⠠⠊⠀⣠⠶⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡰⢀⠃⢨⠁⠢⣄⡀⠀⠂⠌⡀⠐⠀⢀⠴⠋⠘⡀⠄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠂⠀⡆⢠⠁⠆⠈⠒⢤⣀⢀⡠⠖⠁⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠂⠌⠀⡸⠀⠀⠰⠀⠀⠀⢸⠀⠉⡁⠀⠀⠀⠀⠀⠁⠸⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠁⠀⠄⡐⠀⠀⣅⠀⠁⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⢰
⠀⠀⠀⠀⢠⠇⠀⡈⠐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡜⠀⢰⠀⡆⠀⠀⠀⠀⠀⡄⢀⠀⠈⡀
⠀⠀⠀⠀⢎⡀⠐⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⡇⠀⠀⠀⠀⠀⠠⣘⣀⠤⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠄⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⢀
⠀⢐⢀⠀⠀⠤⡤⠀⠀⠀⣀⠀⠐⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⢨⡑⠳⠶⠄⠠⠤⠤⠤⠤⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠁⠀⠀⠭
⠀⠀⠙⢗⠤⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠔⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠠⣄⣀⠈⠙⠂
⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⡀⡀⠀⣠⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠛⠋⠉⢉⡅⠻⠉⠉⢐⢊⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠄⣀⠀⡄⠀⢀⣉⠠⢄⣀⠀⠀⠀⠀⠘⠻⠄⠁⠤⠤⣤⣤⠬⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⢸⢯⡉⢦⣀⠛⠦⠰⠀⠡⡀⢰⠀⠀⠀⠀⠀⢂⠒⢀⠀⠀⠈⠐⠀⠀⠐⡠⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠘⢾⣴⢲⡾⠳⣜⣃⠉⡗⠘⠓⠟⠧⢁⡀⠀⠀⠑⠅⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠈⢿⣉⣙⡊⢶⠉⠈⠙⠑⠒⠒⠠
⠀⠀⠀⠀⠀⠙⠿⡝⠈⠦⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠛⠢⠵⢠⣄⠄⢀⡀⠂⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠦⠈⠂⠈⠁⠈⠁⠀⠀⠀⠀⠙⠤⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣈⣀⠀⠒⠒⠲⢶⡶⡶⡄⠐⡄⠀⠐⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⣓⠬⠤⠔⠁⠉⠛⠁⠸⠴⠤⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠶⡶⠿⡴⢄⣀⣀⠀⡀
⠀⠀⠀⠀⠠⠉⠒⠂⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢮⠙⡈⢏⣰⣄⣠⢐⣄⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢐⠢⠤⠤⠈⡧⠬⠤⠀⠫⠄
⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡤⠀⠀⠀⠈⠁⠀⠀⢀
⡄⠈⠈⡍⣉⣙⣛⡓⠒⢓⠒⠶⠶⠂⠴⠾⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠷⠶⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⡎⠀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠣⠶⠶⠤⠤⠤⠤⠤⠤⣤⣄⣀⣀⣰⠇⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠊⠓⠒⠒⠒⠲⠶⠤⠤⠤⠤⣤⣤⣼⠀⡌⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡋⣲⠒⠒⠒⠶⠤⠤⠤⣤⣀⣀⣀⣀⡇⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡏⠉⠉⠛⠓⠒⠒⠶⠤⠤⣤⣀⣈⣹⡇⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⡏⠉⠑⠒⠒⠦⠤⢤⣀⣀⣀⠀⣸⠀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⢀⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡧⣘⡠⠅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠤⢤⣀⣀⡇⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠴⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣍⣀⠂⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⡩⠄⣶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⠉⠓⠲⠤⣍⣑⡒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢊⣥⠴⠊⠁⢀⡀⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡟⢰⡤⢄⣀⠀⠈⠉⠓⠲⠦⣬⣉⡑⠒⠖⠒⣉⡤⠖⠚⠉⠀⣠⣴⣞⣉⡇⢘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠘⡇⠀⠀⠉⣓⣶⡤⢄⡀⠀⠀⢹⠛⢻⠋⡏⠀⣀⡴⠶⣉⣀⠀⠈⠉⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠊⠓⠶⢶⣟⠉⠀⢀⡤⠜⠋⠓⢺⡀⢸⠀⣿⠉⠁⠀⠀⠀⠈⠉⠑⢲⣧⣤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣀⠀⠀⠉⠉⠛⠳⢤⣤⣀⠀⢸⡇⢸⠀⣿⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⣿⠉⠑⠢⢄⣀⠀⠀⠈⠙⠛⢻⡇⢸⠀⣿⠀⣀⣤⡶⠋⠁⠀⢀⡤⡆⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠀⠀⠀⠀⠈⠉⠒⠦⣄⣀⠠⡇⠸⠀⣿⠞⠋⠁⠀⣀⠴⠚⠁⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠈⠀⣿⢀⣠⠔⠋⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⡆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⣀⢀⠀⠀⠀⠄⢠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⡶⠶⠓⠓⠷⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⣤⣴⣶⣶⣿⢿⠾⢶⣶⣦⣬⣋⠛⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⣾⠟⠋⠁⢉⡞⠁⠀⢀⡼⠟⠉⢻⡿⢿⣦⡐⠻⣷⣄
⠀⠀⠀⠀⠀⢠⡾⢋⣴⣿⠟⠉⠀⣀⡔⠻⠀⠀⠔⠙⠦⣀⠔⠀⠀⠠⡏⠘⢦⡘⢝⢦⡀
⠀⠀⠀⠀⢰⡟⢀⣾⠛⠻⣀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠉⠂⣀⠀⠀⠀⠂⡀⠑⡌⢻⣿⡆
⠀⠀⠀⢠⡟⠀⣾⢿⣆⡀⠉⠒⢄⠀⠈⠐⢦⡠⠊⠑⠤⣠⠆⠀⠑⠤⠀⠀⢀⠎⠠⠈⢿⣧
⠀⠀⠀⣼⠃⢸⣏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠠⠖⠀⠀⡠⠛⠄⠀⡆⠈⢿
⠀⠀⠀⣿⠄⢸⡟⠀⠀⢀⠔⠣⡀⢀⡴⣣⣄⠠⣴⣛⣷⣿⣄⠁⠠⡀⠾⡁⠀⠀⠘⣿⠀⣿
⠀⠀⠀⣿⡄⢸⡇⠀⠰⢇⠀⠀⢀⣿⡀⠈⠛⠛⠻⣿⣉⢉⡻⣦⣄⠈⠀⢌⡢⣄⠀⣼⠀⣿
⠀⠀⠀⢸⡇⠘⣿⡀⠀⠀⠰⢄⡀⠉⠹⠓⢦⡀⠀⠈⠙⢿⣷⠟⠉⠓⢦⡄⠠⡨⠿⣿⢢⡿
⠀⠀⠀⠈⣿⡄⠹⣯⢢⠄⠀⠀⢹⠖⠀⠀⠀⠙⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡁⣰⢃⣾⠃
⠀⠀⠀⠀⠈⢿⣄⠙⠇⠀⣠⠞⠁⠂⠀⣠⠎⠀⢀⡴⠛⠀⠀⢀⠴⠂⠀⢀⢘⡿⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠧⠀⠀⠠⣄⠀⠀⠘⠛⡀⠀⠀⠐⠷⣄⠀⢢⡽⠋⢀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠄⠈⢳⣤⠀⠀⠙⣦⡄⡀⠀⠠⠟⢋⣤⡼⠛⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡈⠈⠙⠛⠋⠋⣀⣁⣤⠴⠞⢋⣥⣤⣴⣶⣶⣶⢤⣄⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠛⠛⣿⠟⠛⠛⣩⡴⢞⣽⠛⠁⠀⠀⢠⠀⠙⠳⣬⣜⡳⢦⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⣹⠂⠀⢠⡞⠁⣤⢴⣾⣩⣷⣿⠃⠀⢀⠀⠀⠀⠀⠐⠀⢻⡟⠏⠶⣿⣷⡀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⡟⠀⢠⡟⠁⠀⣾⣷⣿⡋⡇⣿⠀⠀⠀⠀⢀⢁⣄⠀⠀⢸⣿⡆⠀⠈⡟⢻⣆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣾⠃⠀⣾⠁⠀⣼⣿⡿⣻⠧⣅⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠙⢣⠀⢀⠇⠸⢿⡆⠀⠘⣧
⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⢠⣿⣿⢹⡿⡴⢛⣣⣉⠟⠶⣤⣄⣠⣤⣾⠇⣀⣦⣰⣴⣤⠆⣳⠀⢿⠀⠀⣿⡀
⠀⠀⣴⠋⠀⣠⡤⠶⠤⣄⠀⠀⣿⠀⢸⡇⠀⠸⣿⠃⢀⡾⠛⠉⠉⠉⠛⠲⢾⡉⠀⢹⣷⠟⠉⠁⠉⠉⠙⠳⣟⠃⢸⠀⠀⢸⡇
⠀⣸⠃⢠⡞⠁⠀⠀⠀⠀⠳⠀⢸⡇⠘⣇⠀⠀⣿⢠⡟⠀⠀⣀⠀⠀⠀⠁⠀⢳⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⠀⠀⣸⡇
⠀⣏⠀⢾⠀⠀⠀⠀⠀⠀⠈⠆⢸⡇⠀⢻⡄⠀⠹⣿⠀⠀⠀⠀⣉⠀⠈⠀⠀⢸⣾⡇⠀⠀⠀⠤⢤⠬⠣⡀⢀⣿⠀⠀⢠⣿⠃
⠀⢻⡀⠘⢇⠀⠀⠀⠀⢀⠐⠀⣼⠃⠀⠘⣷⡀⠀⢻⠀⠈⠀⠉⠀⠀⠀⠀⠀⢸⡏⣷⡀⠀⠐⠀⠀⢀⠀⠁⣼⠇⠀⢠⣿⡟
⠀⠈⠻⣆⡀⠈⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠘⣷⡀⠀⠑⣤⣀⠀⠀⠀⠀⢀⣴⠃⠀⡏⠷⣤⣀⡀⠀⣀⣠⡾⠋⠀⣰⢿⡟
⠀⠀⠀⠈⠙⠻⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠈⠻⢿⡶⠖⠚⣿⠁⠀⠀⡇⠀⠈⣝⢙⡉⠉⠁⠀⣠⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠉⠁⠀⠛⠤⠀⠠⠴⠄⠀⠉⠀⠀⢀⣠⢾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⣤⣄⣀⣀⣀⠀⢀⣀⣀⢠⡴⣾⣻⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣮⣭⣽⣿⣽⣿⣿⣿⣿⣽⣿⣷⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠿⠭⣽⣛⡷⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⢶⡶⠶⣶⠶⢶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⠀⠀⠈⠉⠙⠛⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠦⣀⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠻⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠖⠛⢿⣤⣼⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣄⣹⠀⢸⡇
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣾
⢀⣼⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⢊⣡⣿⡏
⠸⣷⣄⡀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⢋⡤⠖⣩⡿⠋
⠀⣿⠉⢻⣶⣄⡀⠀⠀⠀⠈⠙⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠞⣉⣴⡞⠙⢳⣄
⠀⣿⠀⢸⡇⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣩⣴⠾⠋⣡⣴⠟⠉⠈⢻⣆⠀⢿⡄
⠀⣿⠀⢸⡇⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣡⡴⠟⠉⣠⡴⠟⠉⠀⠀⠀⠀⠀⢻⡇⠸⣷
⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣠⠞⠁⣠⠞⢉⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⢀⡾⠋⣠⠞⣡⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⣼⠃⣰⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠸⣧
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠶⠃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⡆
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣇
⢸⡷⠶⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢹⡄
⣿⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠞⠁
⠛⠶⣶⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⣸⡇

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀
⠀⠀⢰⡚⠛⠉⠁⡀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⡦
⠀⠀⠀⠉⠣⣄⠀⠀⠀⠁⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠖⠋⠉
⠀⠀⠀⠀⠀⣈⣙⣓⣚⡋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣺⠿⠗⠋⠉
⠀⠀⢰⡞⠛⠉⠀⠀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⣀⡠⢴⣲⡯⠗⠛⠉
⠀⠀⠀⠉⢧⠀⠁⠀⠀⢀⣠⡤⠏⢀⡠⢤⣒⡭⠗⠚⠉
⠀⠀⠀⠀⠈⠓⠒⠒⢚⣉⣤⣶⠿⠗⠋⠉
⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠻⠶⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠒⣒⣋⣽
⠀⠀⢀⣼⡿⠋⠀⠀⠄⠀⠊⣰⠋⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣯⠭⠿⠶⠒⠛⠛⠉⠉⠁
⠀⠀⠸⢤⡀⠀⠀⠀⣀⣠⣶⣥⣤⣶⣶⠶⠿⠭⠽⠒⠚⠋⠉⠉⠉
⠀⠀⠀⠀⠾⠿⠿⠛⠛⠛⠉⠉⠁

⠶⢤⠴⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠤⠀⣀⡀
⠄⡘⢀⡇⠼⠒⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⣤⣤⣤⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣈⠉⠙⠎⠙⡓⠲
⣒⣛⣚⣓⣗⣓⣚⡳⢤⡀⠀⠀⠀⠀⠀⣠⣾⢿⣲⡶⠤⠾⠥⢤⣄⣸⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠢⢐⣤⠴⢯
⢀⠴⠒⠞⠛⠳⣦⠉⠓⣽⡄⠀⠀⠀⠀⢿⡞⣩⢂⡰⠶⢠⡢⢦⡰⠈⢗⣼⠇⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣴⠊⠀⠀⣈⡆
⣇⢀⡁⠊⠀⢔⣽⡧⠔⡿⠀⠀⠀⠀⠀⠘⢿⣾⣧⣼⣿⣷⣶⣷⣿⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡙⠻⠶⠶⠶⠿⠷
⡈⠉⠉⠉⠉⠉⢁⡤⠊⠀⠀⠀⡄⠀⠀⠀⠀⠙⣶⠬⠭⣭⡭⠯⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠦⠤⠤⠴
⠛⠷⣶⣶⣶⡾⠟⠀⣀⠀⡴⠒⠋⠀⠀⠀⠀⠈⢻⣦⣀⣀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⡎⢙⡏⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣞⠛⠛⢶
⣠⠶⠦⣄⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣥⠞⣫⣾⠋⣿⡁
⠃⢄⠀⠸⡆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡄⠐⠁⣪⢿⠾⠦⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣋⣡⠉⡀⠜⢙⠉⠃
⠀⠀⣱⢞⣁⣀⠀⠀⠀⠘⡄⠈⠁⠀⠀⠀⢀⠀⢠⠖⠛⠙⣤⣀⣽⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠞⠁⢏⠩⢚⠰
⠛⠚⡱⠋⠀⠈⠙⢦⠉⠉⠁⠀⠀⠀⠀⠠⢂⠀⢾⠐⠀⠀⡼⡇⠀⠹⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣤⣦⣤⣤⡴⠾
⠀⢸⠃⠈⢲⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⢠⡤⠊⠁⠛⡂⢰⡑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⣒⣂⣰⣤
⠀⠘⢆⡀⣸⣂⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟⢺⢂⠘⠀⠀⠀⠀⠹⠇⠷⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢈⠝⠂⠀⠀⠀⢚⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣀⣀⡀
⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣱⢳⢳⢃⡟⣹⢋⠟⡿
⠉⠁⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⠟⠀⠀⠀⠀⠀⠀⢰⣧⢏⢯⠇⡞⣴⢣⢏⠞⣰
⠖⣱⢶⡶⣤⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⣴⣟⡤⠤⢶⡷⠦⠀⠀⣿⡟⡘⡜⡘⣼⢡⢣⠊⣼⡿
⣾⠿⢷⣸⡉⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡤⠚⠉⠹⣿⣶⣾⠟⠁⠀⢠⡞⠀⠀⠀⢰⡏⠁⠙⠁⢰⢣⠣⠃⣼⡿⣱
⣌⣱⡴⣷⣦⣙⣧⠏⠀⠀⠀⣠⣿⠃⠀⠀⣠⠋⠀⠀⣠⣾⠿⠙⢿⣦⣀⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠌⠀⣼⠟⣱⠏
⠈⢹⣷⠥⢿⡶⠀⠀⣀⣤⣾⠟⠁⠀⠠⡾⠿⠤⠶⠞⡿⠃⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⢸⡏⣰⠏
⣶⣶⣶⣶⣶⣶⡾⠿⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣁⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣶⣶⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⠤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠒⠛⠲⠾⠾⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡉⠐⠒⠒⠶⠦⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠐⢈⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠗⠐⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣮⣵⣬⣮⡓⢒⣫⠯⠉⠛⠛⣛⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠮⡭⠤⠀⠀⢠⢖⡪⢺⠆⠰⣍⣉⣛⡻⠷⠿⣶⡒⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠒⡼⠀⡠⢖⠕⡡⠖⠉⠉⠉⠉⠀⠀⠈⠉⠓⢲⠼⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢰⢗⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⡋⡩⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⢛⠛⣛⡿⠖⠛⢋⣉⡤⠄⢖⣊⣳⡂⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠘⠷⠶⠖⠛⠉⠁⠀⣀⣀⣤⣬⣽⣦⠘⣄⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠛⠛⠻⠷⢖⡤⡒⠋⠉⢉⣒⣂⣠⣬⣧⠘⣦⣤⣄⣬⡍⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣈⣛⣛⣛⠻⠿⠿⠿⠿⣛⣛⣛⣫⣭⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠘⠲⠤⣤⣤⣀⣤⡔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⣧⠈⣉⡉⢁⠀⢀⡀⣀⣀⣀⣀⠤⠴⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⢿⡀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣤⣄⣀⠀⢀⣠⣤⠤⠀⠀⠤⠤⠤⣤⣤⣤⣤⣴⣾⣍⣀⣀⣻⡀⠉⠉⠉⠉⠉⡼⠋⠉⠈⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡿⠛⠁⠀⢠⡰⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⡍⠉⠛⠛⠛⠲⡾⠷⠶⢤⣤⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠋⠁⠀⠀⠀⠀⠀⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣇⣤⡶⠶⠟⣾⠓⠚⠓⠲⢦⡀⠀⠈⠉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⣄⠀⠀⢀⣤⠶⠚⣩⣶⡾⠛⠁⠀⠀⠁⠶⠞⠃⠀⠀⠀⢹⣦⣤⠞⠁⢸
⠀⠀⠀⠀⠀⢠⣶⡛⠋⠙⣇⠀⠉⠉⠛⠛⠛⠷⠶⢶⣤⣤⣤⣤⠼⡧⡙⡂⠜⣋⡤⠖⢿⣿⡟⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠾⠿⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⣷⣽⣿⠞⢉⣤⣴⠋⣹⡇⠼⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠾⣷⣶⣾⣍⣷⡀⣀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠂⣰⢂⡿⠂⠀⠀⠀⠀⠀⡔⠒⠲⠦⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡷⠟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⡜⢀⠀⠈⠣⣄⣀⣀⣀⣀⡀⢀⣀⣴⠏⠀⣴⠃⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣒⣒⣂⠀⠀⠀⠀⠈⠉⠉⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠶⠶⠞⠛⠉⠀⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠛⠉

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠖⠚⠛⠛⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡞⠋⠛⠟⠉⢻⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⠀⠀⢧⣀⠀⠀⣠⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠈⠙⠻⠃⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠳⠶⠦⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣤⡴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣙⣿⡿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣛⡳⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⠶⣚⣫⡽⠖⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠉⠛⠒⠶⢭⣍⣛⡓⠶⠖⣛⣭⠵⠖⣋⣩⣤⡶⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⣿⠛⠶⠶⣤⣄⣉⠉⣿⢋⣩⡴⠶⠛⠉⠁⠘⡇⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⡿⠀⠀⠀⠀⠈⣿⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣧⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢻⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⠀⣼⠃⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡆⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠻⣾⣇⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣤⡾⠃⠀⠀⠀⠀⠀⠀⢻⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣼⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠤⠀⣀⠀⣰⡧⠴⡗⠚⣻⣁⣸⣦⡤⠖
⠀⠀⠀⠀⠀⠀⠤⠴⣿⣚⡽⠛⠁⢸⠀⢠⡿⡆⢸⠀⢰⡇⢰⡇⢈⡽⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣟⣁⡤⢤⡤⢼⠁⢸⠃⢻⣼⠀⢸⡇⠀⠛⠋⢠⠀⠀⢀⠀⠀⢀⡼⣣⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠉⣇⡤⠖⠋⠀⠻⠴⠺⠀⠀⠛⣤⠀⢠⡄⣷⠖⣾⡴⣦⠞⠀⢀⣞⢞⡵⠊
⠀⠀⠀⠀⠀⢀⡤⠾⡏⠀⠀⠀⠀⠀⢠⣀⣿⣠⠄⡟⠿⠿⢹⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣦⢶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢀⣀⣤⣾⡜⠳⣻⠿⠂⠧⠖⠂⢀⣀⢀⣀⣤⣴⠶⣖⣉⣉⣉⠉⠒⢬⡁⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣲⣾⡧⠛⠉⡏⠟⠈⠋⠀⠀⣀⡠⠊⠁⠀⠫⣴⢣⣀⠷⠈⡧⢄⠈⢳⠀⠀⠈⠳⢄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⡰⠂⡏⠀⠸⠀⠀⠀⠁⢀⣠⣴⡖⠉⡱⠁⠀⠀⠀⠁⠙⢗⣭⠷⣴⡳⠌⡇⢸⠯⡉⢳⡀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠑⠞⠁⠀⠀⣀⡤⠖⠋⠁⡟⠋⡻⢤⡃⠀⡔⠒⠂⠉⢂⡜⠁⠂⠀⠙⣞⣠⠷⣄⡹⢸⡣⢚⣶⠤⡈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⡀⢀⡀⠄⠠⡈⠒⠌⠒⢦⣶⣆⡀⡌⠀⠀⠀⣀⣀⠈⢏⡲⠗⠧⣞⠔⣱⠋⡰⣁⠠⢠⠈⠲⡀
⠀⠀⠀⠀⠀⠀⣼⠡⣴⢤⠐⠢⣀⠢⡕⠂⢁⠠⠐⡧⠠⠠⡈⠛⢶⡃⠀⡎⠀⠀⠈⣤⠋⠀⠀⠀⠈⢾⠃⢜⠔⢁⠔⡦⢀⡦⢿
⠀⠀⠀⠀⠀⠀⡟⣆⠀⠸⡇⠦⠀⠂⠒⣈⠠⡄⠰⣄⠢⠀⣴⣦⣶⡌⠑⠧⣶⡄⢐⠁⢠⠄⠐⠒⢢⠈⢟⠳⣪⡭⠞⠋⠁⠀⡼
⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡃⠘⠙⠣⠉⢮⢹⣈⠃⢈⣀⠴⢯⡁⡠⠛⠉⠙⢪⡑⠧⡀⢢⢠⢰⣄⣤⠤⠚⠋⡁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠳⣍⡀⡳⡜⠛⠛⡿⠉⠀⠀⠀⡸⢁⡴⠒⢢⠀⣇⣀⣨⠽⠚⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠉⠳⢤⣀⢸⠁⢠⠊⠑⡄⣇⣸⣠⡤⠜⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⣚⠋⠉⠁⠀⠀⠒⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠁⠁⢀⣀⡤⠴⠒⠋⠁⠀⢀⠀⣠⡀⣴⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠙⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⢠⠟⣷⠁⠿⠘⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⡀
⣿⣯⢭⣟⡛⣛⣛⠛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⢖⡚⠩⠭⠭⣍⡛⣒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡀⢀
⠀⠀⠀⠀⣠⢞⢩⢾⡃⠠⠔⠥⠀⠀⠀⠉⠁⠨⡑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣙⠢⣑⢄⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⡀
⠀⠀⠀⣰⢣⡏⠀⠦⠾⠚⣆⢣⡀⠀⠀⠠⠀⠀⣸⣮⢳⡀⠀⠀⠀⠀⠀⠉⠑⠒⠚⢛⣾⣿⡿⠁⠀⠀⠀⠈⢿⠻⠣⠎⠈⠁⠈
⠀⠀⢠⠇⣿⠁⠀⠀⠀⣠⣿⡘⣿⠶⣤⣤⡤⠚⠿⠙⣇⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⡁⣀⠀⣀⡄⢀⡸⠟⠒⢄⠀⠀⡠⢰⢦
⠀⠀⢸⢰⡇⣀⠀⢰⣯⣨⡼⡈⣷⠠⣿⣿⠀⠀⠀⠀⠨⣹⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⠿⢿⣿⣿⣾⣿⣿⣟⠁⠀⠀⢸⣷⡾⢷⣫⡞
⠀⠀⠸⡄⣿⣿⣤⣾⣻⣟⠒⠽⣯⣼⣿⠇⠀⠀⠀⠀⡖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣭⣭⣭⣭⣤⣤⣶⣶⣾⣿⡿⠁
⠀⠀⠀⢳⡸⣿⣿⣿⢷⣽⣻⣟⣿⣿⣿⡤⡄⠀⢠⡔⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠙⢌⡻⣯⡺⣿⣿⣿⣿⣿⣿⣿⣧⠴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠢⢭⣛⣛⠛⠛⣛⣛⣫⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡀⡀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣷⣿⣯⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣠⡾⠏⠣⢄⣀⣀⡔⠁⠀⠈⢙
⠀⠀⠀⢀⣴⣶⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠞⠻⣶⣧⣄⠀⠀⠀⢠⡑⠒⠂⠈⣀⠀⠀⣀⡜⠏⠋⠀⠀⠀⢀⣾⡳⡄
⠀⠀⠐⢜⡿⣾⡏⠈⢽⣷⣿⣿⠉⠉⠋⠙⠉⠉⠆⠀⠀⠀⣼⡿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣋⡁⠀⢀⡠⠦⠴⡿⠟⣋⠴⠁
⠀⠀⠀⠀⠉⠒⠯⠤⣜⣛⣿⡿⠤⠤⠤⠤⠤⣄⣘⣢⡤⠭⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⠀⠉⠉⠀⠈⠛⠛⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠴⣾⠋⣽⣹⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠖⢋⣩⠖⠁⠀⠀⣀⠀⣾⣰⡇⡜⣿⢸⣇⠞⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣠⠖⡋⠁⣧⠴⠟⠒⠛⣻⠆⢰⡷⡟⡿⠑⠟⠀⠏⠀⡁⠀⢰⠇⣰⠇⠀⢀⣠
⠀⠀⠀⠀⣴⡯⠖⠋⠀⠀⣧⠀⠀⣠⠞⠁⠈⠙⠚⢠⠀⢀⢠⠀⣤⢸⣷⢛⣾⠞⢹⠀⠀⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠀⣸⠀⠿⠻⠞⣿⣼⠙⠋⣿⠀⠘⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠀⠀⠀⣠⢤⡖⠀⠀⣿⣠⡴⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠋⠁⠀⠀⠀⢀⣀⡠⢤⠔⠶⣒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠛⠉⠁⢢⡗⠀⠒⢠⠙⢆⠈⢲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠊⠁⠀⠀⣠⡄⡰⠒⠾⢭⡢⢤⡊⢀⣠⠤⠃⡠⠗⠒⠐⢸⠀⡰⢀⡬⠔⢊⣉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣄⠎⠲⠃⠈⠁⠀⠀⣀⠓⠂⠉⠒⢤⣠⠊⢀⡀⠴⣒⠡⠶⠵⢍⠀⢎⢹⣂⠇⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠃⡄⠀⠀⠀⠀⠀⠀⠤⠏⠁⣨⡤⠒⠂⣏⢙⠤⣠⠊⢠⠂⡏⠌⡲⠑⣤⣈⡤⠖⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠐⠀⢀⣀⣶⣲⠃⠀⠀⡇⢀⣀⣰⣾⠄⠑⢩⠛⠲⣝⣓⣨⠴⠚⠉⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠳⢤⣀⡔⡉⠀⠀⠀⣱⠼⠾⣔⠋⠀⠀⠈⢣⣀⣠⠷⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠙⠧⣄⣀⡞⠠⠀⠀⠈⣧⣠⠴⠒⠉⠁⠀⠀⠀⠈⠁⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠈⠉⢛⣒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣈⣁⣀⡤⠴⠚⠉⠁⠀⠀⠀⣀⡴⡴⠖⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠋⢉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣎⠻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣟⠋⢍⢢⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⢶⣾⣿⣿⣿⣿⡿⠟⠣⡺⣝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠈⣇⢀⣉⣁⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⣿⣿⡿⣿⣿⣿⢟⣩⣀⠀⠀⣽⣝⢷⣝⠻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢳⣀⣀⣤⣶⣶⢳⣟⣿⣿⣿⠙⠿⠋⣿⣿⣯⣿⣿⣠⣾⣿⣿⣦⠻⣷⣮⡻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠈⠋⢻⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣻⣭⣽⣿⣿⣟⢿⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣜⢿⣿⣿⣿⣿⠿⣻⣿⠿⣛⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣶⣶⣶⣿⣿⡇⣾⣿⣿⣿⣿⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣶⣭⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣤⣤⣄⣀⣠⣤⡴⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢸⡀⠀⠀⠀⠁⠀⠀⣷⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣷⡶⠞⠛⠛⠛⡏⠹⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢻⣇⠀⠀⠀⠀⢷⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡿⠀⠀⠀⠀⢸⠀⢰⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⡇⠀⠀⠀⠈⡇⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢷⢣⠀⠀⠀⠀⡇⠈⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣼⣤⣤⡶⠾⠟⠚⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⡇⠀⠀⠀⢀⣀⣤⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡷⣶⠛⠛⠉⢹⡄⢹⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢹⣸⡀⠀⠀⠸⡇⠸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡏⣇⠀⠀⢀⡇⢰⠄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⡾⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣫⠉⠉⠛⠛⠛⠒⠒⠶⠶⠶⡖⠒⢶⡤⠴⠖⠛⠋⠉⡩⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢺⡟⠛⠛⠻⢶⡶⠶⢶⣴⡇⠀⢨⣧⡤⠶⠶⠛⢻⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠘⡇⠀⠀⠀⢸⡇⠀⢸⠅⡇⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠘⡇⠀⢸⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⡇⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠀⡇⠀⠀⠀⢰⡇⠀⢸⢀⡇⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠘⡇⠀⠀⠀⢸⡇⠀⢸⣸⠇⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣸⣰⡇⠀⠀⠀⠘⠓⠶⠛⣽⠀⠀⠀⡟⠀⠀⠀⠀⢸⣇⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠃⠀⠀⠀⠀⠀⠁⠈⠁

⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⢀⠤⠔⠒⠒⠢⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⡀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠒⠢⠤⠋⠙⣦⣀
⠀⡠⠔⠋⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠁⠑⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠜⡠⠔⠒⠒⠠⠄⣶⠤⣑⠂⣄
⠸⣀⠀⠀⢠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠃⠀⠨⠀⠀⠀⡠⡔⠋⠀⠀⠂⠈⡹⠯⠶⡄⡀
⠀⠈⠑⢢⢄⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠂⢡⠁⠀⡄⠀⠂⢇⡔⠉⠀⠀⠀⢋⠤⠒⠉⠠⠄⠀⢹⣌⡑⠢⣄
⠀⠀⠀⢸⠀⠉⠒⠤⡈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⠤⠀⠀⠘⠢⡀⠀⠄⢀⣠⣦⡲⠀⡀⠂⠁⠀⠈⢀⡀⠄⠊⠁⣠⢹⠀⠀⠉⠂⢄
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠑⠢⢌⠑⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⡋⠀⣰⠥⠴⢦⣤⣌⡂⢁⠈⠢⢄⢩⣴⡶⢶⠵⣄⠑⢀⣞⡉⠀⠂⠀⠀⠁⠀⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠉⠒⠄⡉⠒⠀⠒⠊⠀⡰⠧⢭⣚⡥⢤⣥⣇⣀⣼⠚⠉⠉⠂⠆⠀⠀⢰⠁⠀⠀⠙⠉⠁⠙⢢⣀⣀⠀⠀⣀⢇⡠⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠈⠑⠠⢀⠀⠀⠑⢤⢾⡁⠀⠀⠀⠀⠉⠛⢦⠀⢀⠀⢠⣄⠠⡀⢀⠠⠴⡁⠀⠀⠀⠈⠂⠈⡉⠄⠊⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠉⠒⢄⡀⠉⠃⠀⠀⠀⠀⢀⡀⠜⣀⣀⢠⣌⡨⠏⣘⠁⡀⢠⠈⠁⠀⢀⡠⠒⠉⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠁⠀⡎⠀⢀⠀⠀⢙⡄⠃⠀⠓⠁⣀⠤⠊⠁⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠁⠢⢄⡀⠀⠃⠐⠀⠀⠀⠈⠃⢀⡠⠔⠈⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠈⠐⠤⣀⠀⠀⣀⠤⠂⠁⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⣀⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⡀⠀⣐⣲⣶⡒⠠⢀⠀⠀⠀⢤⠤⠦⠴⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢄
⠀⠀⠀⠀⠀⠀⠈⠴⠀⠂⠈⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠡⠆⠐⠈⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣶⣍⣩⣥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖
⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠰⠂⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⣴⠋
⠀⠀⡴⠟⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣷⣶⡋⠀⠀⢠⡏⠀⠀⠀⠀⣠⠾⠁⠀⢀⣀⢀⠄
⢀⡾⠃⠀⢀⣔⡑⢂⣠⣴⠀⠀⠀⠀⠐⢤⣤⣤⣾⣧⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣀⡌⠐⣀⣴⡆⠀⠀⠀⠀⠦⣤
⠀⠁⠀⠀⠀⣿⣿⡏⢩⣿⠀⣀⠀⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠉⣽⠇⢀⡀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠈⣷
⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠶⢬⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠸⢦⣿⠀⠀⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠈⢷
⠀⢤⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⣠⠀⠀⢸⡗⢦⣬⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠘⠃
⢠⣶⡶⣃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠠⠀⠘⢧⣸⣿⣋⡔⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣞⡀⠀⠀⠀⠘⠃
⠸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠉⣷⢤⣇⣴⣴⠀⠀⠀⠀⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣻⣿⣿
⠀⠀⡀⠀⠠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢄⡃⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴
⠀⠒⢠⠶⠦⠶⡎⠀⠴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⠂⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠂⠴⠦⠰⢶⠁⠠⠄⢠
⠐⠻⠇⢀⣛⣁⣼⣞⣲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠌⠖⠀⠀⠀⠀⢰⣄⡈⣋⡀⠿⠚⠿⠀⣈⣁⣤⣷⣓⣾⡿
⢀⣉⣤⢾⣿⣷⡟⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣨⣿⢦⣀⣈⣡⡴⣿⣿⣾⠛⠛⠋⠁⠀⠀⠀⠀⠀⡀
⢸⣿⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢼⣿⣿⣿⡷⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⠉⠀⠀⠀⠀⠀⢰⣤⠄⡀⠀⠀⠀⡀⠈⠻⢿⠿⠟⠥⣀⠀⠀⠀⢤⠤⠤⠴⠠⣤⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠰⠁⠂⠈⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠆⠰⠈⠀⠀⠀⢾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣭⣉⣩⣭⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡧
⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡄⠰⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣤⠏
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣴⣶⣴⣶⣴⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢨⡿⠀⣰⡿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠃⢠⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣼⠇⢠⡿⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⢠⡿⠃⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡟⠀⣾⠗⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀⠠⠄⠒⠂⣈⣉⠉⠥⠀⢀⡿⢠⡿⠀⣼⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠰⠁⠀⠀⠞⠁⠀⠀⠀⠀⠀⣾⠃⣾⠁⣰⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢢⡀⠀⠀⠀⠈⠲⠄⣀⠙⠲⢄⠀⠀⠀⣸⠏⣼⠇⢠⡟⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⡙⠫⣝⢷⣦⣀⣀⣩⣭⣭⣴⣦⣤⣤⣦⣤⣶⣤⣤⣰⡟⣰⡏⢀⡿⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⢡⣤⡙⢿⣍⣉⣳⣈⠻⠿⣍⡠⠤⣄⠠⡤⣘⠀⠡⣄⠀⢈⣿⢡⡿⠻⣿⢁⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⡘⠓⢽⡿⢧⣌⠁⢞⠈⢷⠀⠈⠀⠀⠈⢄⡀⠀⠀⣸⠃⡼⠁⡼⢁⣾⠋⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⣹⡿⠿⠷⣶⣯⣉⡑⣭⡀⢸⡶⢄⠀⠨⠀⢀⠁⢰⣶⣧⣼⡧⣾⠷⢾⣷⣶⣤⣄⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣠⣾⠋⠁⠀⢒⡂⠀⠍⠉⠻⠿⠛⣷⣶⡏⡐⠀⠈⣀⠜⡋⠀⠌⠀⡤⠀⣤⣞⣉⣍⢙⠻⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣾⡯⠄⠀⢾⡶⣤⣥⣤⣤⣄⣘⠆⠈⠠⣼⣦⣑⣤⠞⡡⠀⡠⢀⠔⡠⠄⠀⢿⣻⡿⢻⣿⡷⠾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⡟⢻⠿⣯⣽⡇⢀⠀⠈⠉⠙⣯⡀⢢⡒⢡⣾⡿⡡⢊⡤⢊⣤⡪⢶⣤⣠⣴⣼⣿⠟⠻⣿⠀⣄⣞⡷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⢧⣎⢘⣷⠐⠚⢇⡀⠀⠈⢻⡅⣰⡿⢋⠜⡰⣡⢜⡠⢋⠔⢉⡿⡁⠠⠁⣬⠆⢘⣿⣷⣎⣁⣠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠷⢶⣾⣦⣿⣄⣐⣂⢻⣀⡐⣾⡷⣛⢖⡡⣚⢚⡵⣿⣷⣥⣶⣽⣇⣵⣾⣯⣷⣶⠿⠿⠟⠛⠋⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠳⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⠶⠶⠿⠛⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣮⣦⣤⣀⣀⣀⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣯⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣿⣿⣿⣿⠟⢉⣉⣈⣹⡿⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⣿⣿⣿⣤⣿⡇⢺⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠘⣿⣿⠁⢠⣾⣿⠿⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⣿⣿⣿⠀⣿⡇⢻⡇⢸⡇⢸⢿⡧⢾⡏⠴⣦⣽⣧⠈⣶⣾⣿⡿⠁⢰⣿⣿⡄⠘⣿⠀⠸⣟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣿⠇⣿⡃⢸⡇⠘⡇⠀⠊⠁⢸⡟⠳⠖⢸⣷⠀⠿⢿⡿⢧⣰⠿⠟⠛⠻⠀⠘⡧⣀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢿⣿⠿⠋⠁⠂⠀⠐⠒⠁⠈⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠶⠋⣠⢞⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⣋⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠋⣠⡶⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠉⣤⢞⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠷⣄⡀⡀⠀⠀⠀⣀⡴⠞⢁⡴⢚⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣀⣉⣛⣛⣛⣋⣉⡤⠶⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⠉⠉⠉⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⢉⣉⣉⣉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣒⣚⣓⡒⠦⣤⡀
⠀⠀⠀⠀⣠⠞⢁⣤⣪⡬⠶⣶⠶⡦⢯⣷⣤⠈⠳⡀⠀⠀⠀⢀⡔⣩⡴⠿⠛⢣⠹⠇⠛⠛⠲⣍⠳⣄
⠀⠀⠀⣰⠃⣽⣿⡿⠹⡇⠀⡇⠀⠇⠀⡄⠙⢷⡄⠙⡄⠀⢠⢏⣾⠧⠤⠐⢀⠀⠀⠀⠂⠘⠀⠨⠷⠙⣆
⠀⠀⠀⡇⢰⣿⢿⡵⢜⡷⠔⣤⣴⡅⣠⢡⣠⢼⢻⠀⢹⢀⡏⣾⣁⣤⠀⢂⡠⠀⠠⣄⢲⡄⢠⡠⠔⠢⢸⡀
⠀⠀⠰⡇⢸⡇⢨⠀⠸⠀⠈⠁⢸⠋⠈⠋⢹⠈⠁⠀⢸⢸⡷⣿⡄⠘⠀⢸⠀⢠⣴⡟⠈⡅⠀⡀⠠⠀⠘⡇
⠀⠀⠀⢧⠈⢧⡲⢀⣶⢀⣾⣀⡼⣀⣼⣤⣜⢰⡘⠀⣾⠸⣇⠟⠂⠀⠁⠀⠀⠻⣏⣿⠀⢀⡠⠤⠀⢷⢰⠇
⠀⠀⠀⠘⢧⠈⠿⠑⡟⠑⡗⠉⡖⠋⡙⠋⣙⠝⢁⣼⠃⠀⠹⡌⢀⠀⢀⠠⠆⠀⢟⠉⠁⡀⡀⠀⡦⢃⡞
⠀⠀⠀⠀⠈⠳⣄⡉⠓⠀⠧⠀⠧⠀⠗⠂⢀⣴⡿⠃⠀⠀⠀⠻⢦⡄⢤⣄⠀⡃⠈⠀⢈⣅⣡⢀⡵⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣿⣓⣐⣛⣨⠭⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠠⠀⠂⢄⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⠠⠂⠁⠀⢀⡠⠖⠃⠂⢄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⡀⡀⣤⣦⣀⠀⡤⠒⠁⠀⠀⢀⠠⠚⠁⠂⠄⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⡄⣤⣤⢤⣀⠈⢁⡬⡝⣦⣤⣤⡀⠂⠁⠀⠀⢀⠠⠊⠉⠑⠀⡀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⢠⠔⠋⠁⠀⠀⢀⣤⣤⣤⣀⠈⠁⡬⡜⢶⣶⢧⣅⠈⠁⡀⡥⡤⢄⡀⠊⠀⠀⠀⢀⣠⡞⠉⣹⡤⠠⡀⠀⠀⠉⠓⢤
⠀⠀⠀⢸⠀⠀⠀⠀⠰⠋⠉⠛⢉⣽⣧⣄⣡⡄⠀⠁⠀⢈⢀⣺⠉⠀⠀⠀⠈⡆⠀⣠⡞⠅⣹⠭⢾⠿⢀⣴⠷⠉⠁⠀⠀⠸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠋⠁⡌⠗⠚⠲⢤⠋⠀⠈⢱⠒⠀⠨⠤⣕⢤⣌⣩⣞⣧⢀⣼⠗⠋⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠂⠀⠀⢀⡀⠇⣀⡄⠘⠠⢀⠀⠀⢢⠤⠙⢩⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠈⠉⠁⡠⢒⣂⠳⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣤⠾⠛⠛⠾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣄⣀⢀⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠉⠉⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣼⠃⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢹⡟⠉⠛⠉⢻⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿⠋⠛⠉⢻⡟⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣟⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣇⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣽⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁


⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⢾⣃⣸⣯⣹⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠟⠀⠀⢀⠁⠀⠀⠀⠙⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡖⠀⠀⠀⠀⠁⠀⠈⠃⠐⡏⠀⢘⠆⠀⠁⢲⠀⠀⣀⠇⠀⢠⠞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠃⠀⡆⠰⢀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠘⢧⡀
⠀⣀⠀⠀⠠⠯⢸⠢⢠⢠⡈⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠐⠓⡀⠀⠈⠁
⠀⡁⣀⡀⠀⠀⠙⠱⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⢀
⠐⢻⠵⠂⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠄⠁⠀⠐⠀⠁⠀⠀⠀⠰⣁⠈⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⣀⣀
⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠦⣵⢿⡷⣯⣤
⠀⣏⠀⢳⣔⡀⠀⠀⠀⡀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⣂⡿⢿⣟⡶⡿⣗⠈
⠀⡏⠻⠾⠏⡦⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡽⠷⣴⠷⡍⡛⠒⠀⠆
⠀⡇⡂⠘⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣄⢠⣾⠧⢓⡀⠀⠀⡤
⠀⠁⠑⢀⠉⢀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣜⠹⣀
⠠⡆⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠔⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣸⠉⠙⠓⠲⠯⠭⣷⣒⡶⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠾⢭⣱⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡹⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⠉⡟⠓⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡞⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡟⣸⠁⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⣄⣀⣰⠃⢸⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢀⡏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠣⠼⠞⠓⠒⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⡸⠀⡼⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠢⠤⢀⣠⠃⢰⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣞⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⢸
⠀⠀⠀⠀⠀⠀⣴⢏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⢾
⠀⠀⠀⠀⠀⠀⢹⠀⠈⠉⠛⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠼⠁⢸
⠀⠀⠀⠀⠀⠀⢸⠙⠒⠤⣄⣀⡀⠀⠈⠉⠙⠓⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⡠⠊⠁⣠⠞⡇⢰⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⢀⠈⠉⠙⠒⠦⠤⣄⣀⡀⠀⠀⠉⠉⠛⠒⢶⠞⠁⣀⠞⠁⠀⡇⢰⡀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⠈⡏⢹⡓⠒⠤⣤⣀⣸⣠⢾⠁⠀⠀⠀⡇⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⠀⣿⠀⢸⠁⢸⠀⠀⠀⠀⡇⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⣀⣇⡼⠁⠀⠀⣿⠀⢸⡅⢸⠀⠀⠀⠀⡇⢰⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⠀⢸⡇⢸⠀⠀⠀⠀⡇⢸⠂⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⢸⠀⠀⠀⠀⠉⠛⠛⠁
⠀⠆⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠸⣄⡀⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⢸
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠲⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣠⣶⡶⣿⣿⠿⠿⠛⣿⣶⣶⣯⣉⠻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⣿⠋⠁⢈⡴⠃⠀⣀⡜⠛⠁⠸⢟⠿⡷⢌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢠⡾⢁⣾⣿⠋⠀⠐⡴⠊⠑⢤⠐⠁⠉⠲⡎⠀⠀⠘⠃⠈⠳⡌⢮⢧⣄
⠀⠀⠀⠀⠀⢠⡟⢠⣿⡇⠈⠳⣄⠀⠠⡠⢀⠀⢁⢤⡀⠀⢈⠶⢄⠀⠀⠉⠦⡨⠆⢻⣿
⠀⠀⠀⠀⠀⣿⠀⣾⠋⢿⠂⠀⠈⠑⠀⠀⠀⠙⠁⠀⢈⠟⠁⠀⣀⠉⠀⢀⣔⠀⢈⠈⢿⡆
⠀⠀⠀⠀⢠⣯⢀⣿⠟⠁⠀⢠⡔⠀⠀⣠⢀⠀⢀⡴⢦⣤⣀⠜⠁⠀⣴⠃⠈⠁⢾⡆⢰⡇
⠀⠀⠀⠀⠸⣏⠈⡷⠀⢠⡜⠁⠈⡠⣾⠀⠻⠷⠿⣶⠾⠛⢿⣄⡀⠑⠈⡣⣀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣿⡄⠀⠈⢢⡀⠈⠻⣷⠦⣀⠀⠈⠻⢿⣷⡾⠋⠢⣄⡜⠉⢻⢶⡯⣸⠇
⠀⠀⠀⠀⠀⢹⣇⠘⣟⢤⡄⠁⠈⢳⠖⠁⠀⠈⠛⠀⠀⣠⠋⠀⠀⠀⠈⠀⠀⠃⡼⠡⡿
⠀⠀⠀⠀⠀⠀⠻⣧⠘⢏⡀⣠⠞⠁⠀⠀⣠⠃⠀⣠⠔⠁⠀⢀⣴⡂⠀⣀⢸⡟⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⠧⠀⠀⠠⡄⠀⠀⠛⢃⠀⠀⠈⠻⢄⡀⣺⡿⢋⣴⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠤⠈⣳⣄⠀⠈⢳⡤⣀⠀⠠⠟⣉⣤⠟⠋⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⣤⣀⣈⣉⣉⣉⣠⣤⡶⢞⡛⣭⣴⠶⠶⠶⣶⣖⠤⣄⡀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠉⠉⣹⠟⠋⠉⣥⣶⣋⡼⠋⠀⠀⠀⠢⠀⡉⢳⣶⣿⢷⣦⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣿⠀⢀⡾⠁⠘⣶⣿⡷⡿⢿⠁⠀⠀⠀⠀⡀⠀⠁⠈⣷⡝⠘⠻⣿⣆⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣸⠇⠀⣼⠁⠀⣼⣿⣿⣇⠇⣸⠀⠀⠀⠀⠀⠘⠢⠀⢀⡟⡇⠀⠀⡇⢸⣧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⣿⠀⢰⡇⠀⢸⣿⡿⣼⣏⡷⣌⠷⣤⡀⠀⠀⠀⢀⣴⠊⢁⢉⡃⡐⡃⢾⠹⣇⠀⠘⡇
⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⠀⠀⠀⣿⠀⢸⠁⠀⣾⣿⠃⢃⣮⠶⠾⠾⢥⣍⡿⠟⠛⣿⣩⠶⠟⠛⠳⠾⣥⡶⡄⢻⠀⠀⣿
⠀⠀⠀⣼⠃⣠⠞⠉⠁⠈⠉⢆⠀⢻⡀⢸⡅⠀⢸⡇⣰⠏⠀⡀⠀⠀⠀⠀⠙⣆⢠⡟⠁⠀⠀⠀⠁⠀⠀⠹⡄⠘⠀⠀⣿
⠀⠀⢰⡗⠀⡏⠀⠀⠀⠀⠀⠈⡄⢸⡇⠈⣇⠀⠘⣷⡏⠀⠀⠈⠐⡀⠀⠀⠀⣽⣾⠀⠀⠀⠀⠀⣀⠤⠀⠀⣿⠃⠀⢸⣿
⠀⠀⠈⣇⠀⠳⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⢹⣆⠀⠸⡇⠀⠈⠁⠉⠀⠀⠀⠀⣸⢻⣆⠀⠤⠤⠚⠁⠀⠁⣼⡏⠀⢠⣿⠇
⠀⠀⠀⠙⢦⡀⠈⠒⠀⠀⠈⣠⡾⠃⠀⠀⠀⢻⣆⠀⠙⢤⡀⠀⠀⠀⠀⢀⡴⠃⢸⡟⢦⣀⠀⠀⠀⣀⣼⠋⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⢿⣶⡖⠒⡟⠁⠀⢸⠅⠀⢉⡛⣏⠝⠉⠀⣀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠈⠁⠀⠓⠂⠀⠜⠒⠂⠈⠁⠀⢀⣠⢾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠴⠖⠒⠒⠛⢻⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢤⠲⠖⡖⠖⠒⡆⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡇⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⡀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢸⠀⠀⡇⡇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⢸⠀⠀⡇⡇⠀⡄⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⡇⠀⡇⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢰⠀⡇⠇⠀⠃⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⠀⣇⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠀⠋⡀⠀⢸⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⠀⡆⢸⡇⠀⢸⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣸⣸⣄⣇⣸⣇⣀⢈⡀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⠉⠭⠙⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠁⠒⠒⠀⠢⠤⠤⣀⠤⠖⠒⠂⠉⠁⣀⣀⢤⠴⠓⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠱⠒⠢⠤⢤⣀⣀⣨⣤⡔⠒⢻⡭⣭⣤⣄⣰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣸⠛⠒⠶⢼⠀⠀⠀⡟⢧⠀⡏⠀⠀⠀⠀⠈⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠈⢳⠀⢸⠁⢸⠀⣧⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡀⢸⠀⢸⠀⡆⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠸⡇⢸⡄⠘⠧⠇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠤⡤⢀⡀⠀⠀⠴⠶⢤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠰⢤⡤⣀⣀⢀⠃⠒⠒⢦⢈⠗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠘⢩⠏⡧⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠠⣵⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠃⠀⠀⣠⠞⠀⠑⢬⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠆⠀⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀⠉⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⢀⣿⠗⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⣀⠀⠀⣠⠴⢥⣌⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣆⣀⡀⣸⠵⠓⠲⣄⣹⢾⠈⠉⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⠃⠀⠀⠀⡽⣽⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠨⢤⡍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠠⠀⠂⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣷⣿⣧⠀⣀⠀⢷⠃⠀⠀⠀⠀⡀⠄⠀⠉⡁⠀⢃⣬⡁⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠁⠀⠉⠀⠁⠀⠀⠀⢀⠈⠀⡄⠀⠀⢰⣦⡼⡿⠛⠉⠀⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢰⣶⣴⠿⠛⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠒⠠⠃⠒⠦⠿⠿⠿⠿⠛⢷⣝⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠞⠛⠙⠉⠉⠉⠉⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡠⣤⡴⠶⠒⠒⠶⠶⢤⣀⡀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⢀⣴⡾⣋⡠⣶⡶⣾⢸⠿⢷⡖⣶⣦⣝⣳⢤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠰⣿⣶⣯⢼⡿⢿⣷⠀⠀⢸⢸⠀⢈⠃⠀⠋⣽⢸⠿⣿⣦⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠀⢠⣿⣷⣿⢸⠀⢸⡟⠀⠁⡾⠀⠀⢸⠀⠀⠀⡟⠀⠀⢹⢹⣷⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢹⡆
⠀⠀⠀⠀⢠⡏⠀⢀⣿⣿⣋⡿⡲⣄⢶⢳⠄⢠⡟⣀⣠⣬⠖⠀⠀⢧⠆⠀⡞⣸⠹⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⢸⣿⡏⠿⣻⠋⠉⣦⡵⠋⠃⣈⡵⢍⣿⠟⣢⡺⡴⣗⡲⡞⢨⡂⢹⡆⠀⢸⡇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⢠⡇⠀⠀⣿⠀⠀⢸⠁⠀⠀⡟⠏⠀⢸⠹⠁⢻⡇⠊⠉⠀⡇⠀⢸⡇⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⡇⠀⠘⣯⠀⢸⡀⠀⢠⡏⠀⠀⣾⠀⠀⠀⣧⠀⠀⣸⠀⠀⢀⡇⠄⠀⡰⠀⠀⢸⡇⢠⡾⠁⢀⡤⠤⠤⢤⡀⠠⢸⡇
⠀⠀⠀⠀⠀⢻⡄⠀⠹⣤⡘⡃⢄⣸⣅⢄⣨⣽⡅⢀⣤⢱⣀⣐⡟⢧⡤⣨⡁⢞⠃⠇⠀⢠⣿⢣⡏⠀⡴⠋⠀⠀⠀⠀⢙⠄⠸⡇
⠀⠀⠀⠀⠀⠘⣷⡀⠀⢻⣧⡝⢪⡽⡽⠦⣰⣿⡷⠟⠛⠛⠛⠛⠿⠿⠿⢿⢶⣯⡞⠀⢠⣿⡟⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠙⣇⠀⣼⠾⠛⢋⣡⣴⣶⡾⢻⣿⡿⢿⣿⣶⣤⣉⡛⠿⡷⣿⡟⠀⠘⣇⠀⠳⡀⠀⠀⠀⠀⡠⠁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣨⠟⠁⣴⣾⢿⢟⡟⠀⠀⡼⠛⠀⡀⠛⠂⡾⠀⠙⠶⢌⠲⣿⣷⡀⠙⢷⣀⠈⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⣠⣾⠏⠀⠀⣾⠁⠀⡼⠉⠒⠴⢀⠀⠀⠀⠀⠓⠠⢌⠃⡌⢻⣷⡀⠀⠉⠛⠲⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣰⣿⠟⠂⢤⡞⠀⠉⠒⠄⢀⡀⠀⠀⠌⠑⠢⡄⠀⠀⣌⠀⠀⣄⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣸⡿⠿⣀⠀⠀⠈⠰⠠⢤⣀⠋⠉⠓⡞⠀⠀⣴⠀⠀⡼⠁⠉⠐⢿⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⣧⡀⠈⠁⠒⠴⠀⠀⠀⠁⠀⠀⣌⣠⣤⣠⠂⠠⣘⠓⠤⣀⡀⠀⢿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⣿⠉⠟⠀⠀⠀⠀⠀⢀⡆⣄⡠⣾⣭⣾⠟⠻⢦⣤⣀⠀⠈⠊⠉⣻⢿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⡞⠁⠀⠠⠋⠂⢀⣜⠈⠛⠛⠛⠛⢶⣶⣾⣷⡏⠈⠙⠻⠁⠀⠁⢰⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⡧⠀⠰⢧⡀⠀⠐⠻⠿⡶⠢⣤⣠⠀⠀⢈⡟⠀⠀⢀⠀⠀⠀⠾⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢻⣦⠀⠀⠈⠗⠠⢤⡤⠁⠀⠀⠉⠀⢀⣼⠀⠀⢀⠾⠁⢂⣾⡞⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠻⣗⡰⡖⠀⢀⡼⠁⠀⠀⡼⠀⢀⡾⠁⠀⠁⠛⠒⠤⣤⡟⣁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⢆⣀⡼⠁⠀⠀⣌⠀⠀⠈⠁⠲⢤⣀⢀⡀⠔⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣈⠙⠂⠀⠀⡀⠉⣲⣦⣀⣤⠾⠃⣉⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⡒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣷⣴⡁⠔⠐⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⢀⣼⢳⣒⡭⢛⡷⢺⣿⡟⢸⢿⠃⠀⠀⠀⠠⠐⠁⠀⠂⢀⡠⠄⠤⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⡴⣽⣺⣎⢻⣭⠏⠑⠤⣠⣇⠿⠿⠶⠤⠤⣀⠁⠀⡀⣄⡤⠊⠀⠀⠀⠐⡀⢠⠀⠈⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠐⠐⠉⠁⠀⠈⠓⠳⣽⡗⠣⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⣈⣧⡖⠉⠠⠁⠀⠀⡀⠐⠂⣁⡀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⡠⠒⠁⡀⠐⠀⠂⠀⢀⣄⢠⠬⡁⠂⢇⣀⠀⠀⠀⠀⠀⠠⣠⠊⣠⣤⣤⣈⠃⠤⡆⠁⠀⠀⠀⠀⠙⠀⠀⠇
⠀⠀⠀⠁⠀⠀⡄⠁⠀⠀⠈⠁⣾⠆⠀⢧⠘⠚⣀⠇⠀⢀⣀⠉⠂⢀⡀⠀⠀⠃⠀⠈⠀⠀⠉⠀⠀⠈⡄
⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠓⠊⠀⠀⠀⠈⠂⠰⣆⠀⠀⠀⠀⠀⠶⣛⠀⢠
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⡀⠀⠸⡱⠀⠀⠀⢀⠀⠀⠀⡤⠒⠒⠦⡀⠔⢢⠀⠀⠈⠢⣐⠲⠶⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠣⠞⡵⠀⡸⠈⠁⠀⠀⠀⠀⠀⠙⠈⣁⠄⠂⠁⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⠠⠴⠀⢉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠑⠬⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠓⢭⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡯⣉⠪⡻⢗⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣄⠀⠈⠙⠛⠃⠀⠉⢳⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠙⢲⢄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡇⠀⢸⠀⡟⢦⡀⠀⠀⡇
⠀⠀⡤⣄⣠⣤⠦⠵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⠀⡇⠀⡍⠓⣤⣇
⢀⡠⢖⠋⠉⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⢤⡀⡇⣿⠀⢸⠀⡇⠀⡇⠀⡇
⢰⠀⠀⠀⣀⠀⠒⡋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣒⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⢾⡀⢸⠀⡇⠀⡇⠀⡇
⠰⠤⠆⠉⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣇⠀⡇⢰⠃
⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢳⢮⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⣸
⠀⠀⡇⠀⠀⠀⢀⡧⢊⠔⢠⡨⠨⡉⠉⠉⠉⡩⡳⢸⠀⢸⠄⠈⠲⢭⡲⢄⣀⣀⣀⣀⡤⠤⠤⠤⠄⠒⠒⣒⣚⡇
⠀⠀⡇⣨⠴⠊⠁⠀⢨⠒⣫⡛⢻⠀⣀⡴⠪⠊⠀⢸⠀⢸⠀⠀⠀⠀⠙⢾⡤⠤⢤⢴⠒⢲⡖⠉⠉⡏⠀⠈⡇
⠀⣔⣋⣤⣤⣤⣶⡦⣤⣭⣤⢬⡕⢉⣹⡶⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⠀⠸⡇⠀⠀⢳⠀⠀⡇
⠀⠀⡇⡠⠄⢀⣠⣤⣤⢠⠀⢸⠖⠋⢹⠀⢰⠀⠀⣾⠀⠸⡆⠀⠀⠀⠀⠀⡇⠀⢸⡿⡄⢀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⡇⠈⡏⠉⠉⠁⢹⠉⠀⠘⠀⠀⢸⠀⢸⠀⠀⣏⠀⢀⡇⠀⠀⠀⠀⠀⣇⠀⠀⡇⠈⠉⠀⠀⠀⢸⠀⠀⡇
⠀⠀⡇⠀⡇⠀⠀⠓⠃⠀⠀⠀⠀⠀⢸⣀⣠⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⡇⠀⡇⠀⠀⠀⠀⢠⠀⢠⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣷⠀⠀⠀⠀⠀⢸⡀⠀⡇
⠀⠀⠣⠴⠀⠀⠀⠀⠀⠘⠶⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠿⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⣉⣦⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⠶⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣠⡴⠞⠋⠉⠀⠀⢀⣀⣤⠶⡞⠋⢉⣹⠆
⠀⠀⠀⠀⠀⠀⢰⡶⢤⣤⣤⣄⠀⠀⣀⣤⠶⠛⣁⡤⠶⠛⠉⠀⠀⢀⣀⣤⠶⠚⠋⣁⣸⡤⠷⠛⠋⠁
⠀⠀⠀⢠⡾⢋⢻⢥⣂⣰⡄⢸⣷⣛⣩⡴⠖⠋⠉⠀⣀⣠⡤⠶⠛⠋⣁⣤⡴⠞⠋⠉
⠀⠀⣰⠏⣤⡍⢊⠀⣉⡙⠙⡄⢸⡏⠁⢀⣠⡤⠶⠛⢉⣡⣤⠶⠚⠋⠉
⠀⠈⢻⡆⢔⣩⠖⢢⡄⠰⣌⣡⡼⠷⠚⢋⣡⣤⠶⠚⠋⠁
⠀⠀⠈⣷⠰⢍⣡⡼⠶⠛⣉⣡⡴⠶⠛⠉⠁
⠀⠀⠀⠈⢻⣏⣥⣶⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡤⠖⣚⣋⣉⣉⣉⣁⣀⣀⣤⣤⣬⣭⠭⠭⠭⠭⠥⠤⠤⠤⠭⠭⠭⠭⠭⠽⣷⣶⣤⣀⡀
⠀⠐⣏⠙⢛⣻⣿⣿⡿⠿⠿⠿⠿⠿⠭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⠥⠤⠤⠤⠤⣤⣬⡉⢧
⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠟
⠀⠀⠀⠈⠲⠿⠶⠒⠒⠒⠶⠚⣶⣄⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⡶⢄⡤⠶⢶⠻⠋
⠀⠀⠀⠀⢀⠀⣨⠿⢟⣿⠿⠷⢿⡿⠯⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⠝⠋⠀⠂⢸
⠀⠀⠀⠀⡾⡜⢡⠖⠉⠀⠀⠀⢸⣷⠃⣀⡬⠓⢦⠀⠀⠀⠀⠀⣠⠔⢋⣩⠽⠋⠁⢠⣤⢀⠀⢸⡷⣄
⠀⠀⠀⢰⢇⣷⠃⠀⠠⠴⠶⣦⢼⠿⠋⠀⠀⠀⠈⢳⡀⠀⠀⣴⣧⠴⠋⠁⠀⠀⠀⠈⠁⠘⠃⠘⡇⠀⠙⢆
⠀⠀⠀⣸⢸⡇⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠚⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠃
⠀⠀⠀⡏⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⢸⣠⠾⠃
⠀⠀⠀⡇⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡤⣴⡄⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⠦⢼⣿⡆
⠀⠀⢸⡇⡏⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣹⣍⡉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣠⣿⣤⣼⢸⠁
⠀⠀⠀⢧⢧⡀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⣿⠯⣙⠓⠒⠚⠛⠛⣉⣭⣿⣟⣛⠻⢧⣤⣄⣸⣿
⠀⠀⠀⠈⢷⠬⣝⣛⣛⣓⣒⣒⣒⣒⡿⣺⣥⣄⡏⠈⠳⠈⠉⠓⣖⣚⠉⢁⡼⣍⣛⣿⢻⡽⢯⣉⡏⡧
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠉⠉⠉⢸⣿⠁⠘⢿⣲⣠⣶⣤⣴⣚⣁⣘⣞⣉⣀⣉⣩⣯⠬⠤⠚⡹
⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣀⣀⣀⣘⣋⣀⣀⣀⣀⣉⣀⣀⡀⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⡇⠀⠀⠀⠀⣀⣀⣹⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢹⣿⠛⠛⠉⠉⣯⠉⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠸⣿⡀⠀⠀⠀⢸⠀⢳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡿⡇⠀⠀⠀⠸⡇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⢛⠀⠀⠀⠀⡇⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡼⡀⠀⠀⠀⣿⣀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡷⠷⠶⠛⠛⠉⠉⠇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢶⣀⣀⣠⣤⣤⠖⢻⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣹⡉⠀⠀⠘⡇⢸⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣏⣇⠀⠀⠀⡇⠈⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⢸⣀⣤⣤⣿⣠⣦⣤⣷⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠋⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠶⠤⠤⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⢶⠖⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⡇⠀⢸⢉⣀⣠⣤⣤⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡄⣧⠀⠀⠀⢸⡇⠀⢹⢻⡇⠀⢸⡏⠉⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⣿⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⣿⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⢸⡇⠀⠀⠀⠀⣇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⣿⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⣿⠀⠀⠀⠀⡇⠀⢸⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠃⡟⠀⠀⠀⠀⡇⠀⢸⣸⠃⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢰⣀⡇⠀⠀⠀⠘⠷⠶⠞⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠾⠁⠀⠀⠀⠀⠈⠉⠉

⣿⣟⢹⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣿⣵⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢦⡟⠈⢻⣿⣿⣿⡀⢚⡠⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢿⣿⣷⣾⡿⣶⡜⣿⣿⣿⣃⢛⣷⣿⣯⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣾⢻⣿⣿⣿⣫⣿⣯⣥⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠿⣿⣻⣿⣾⣻⣿⣿⣆⣾⠉⣧
⠀⠀⠀⠀⢠⣦⣀⠀⠀⣀⡉⣿⣷⢻⣿⣿⣿⣿⣿⣫⢻⢫⣾⣿⣿⣿⣿⣷⣯⣾⣽⣿⣿⣧⣿⡆⢀⣠⣦
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣽⣇⣘⣿⡇⠻⣿⣿⣬⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⡇⢿⣷⣟⣟⣿⣷⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣷⢶⣿⣯⣿⣵⣭⣭⣭⣭⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⠯⣻⣹⣹⢿⢹⣟⣿⣯⣿⡯⣿⣋⣷⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠚⠐⠒⠒⠒⠒⠒⠒⠒⠏⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡤⠀⠀⠀⠀⣀⣀⣀⣀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⠀⠐⠒⠒⠒⠒⠶⢾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠤⠄⠤⠠⠄⢀⣀⣀⣸⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠉⠉⠀⠒⠒⠒⠠⠤⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠤⢀⣀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠒⠈⠈⠈⠈⠒⠒⠢⠤⢀⣀⣘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢱⠂⠨⠄⣂⠀⠄⢀⠀⠀⠀⠀⠀⡀⠄⣂⠤⠒⢈⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠒⠠⠄⣈⠉⠒⠢⢬⣀⣈⡥⠒⢉⡀⠐⠾⢽⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡖⠢⢤⡖⠋⢁⡰⠒⢤⠀⠀⡶⠊⠉⠁⠀⠂⢤⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⣤⢀⠈⠈⠓⠦⢤⣀⠀⠀⡇⠀⠀⣠⠴⠚⠁⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠂⠤⣀⠈⡀⡇⣷⠖⠋⢀⠠⠒⠉⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠂⠀⠀⠀⠀⠀⠀⠈⡇⡇⣧⠴⠊⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⡇



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠠⡀⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣦⣄⣠⣴⣛⣉⢀⡴⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡼⠃
⠀⠀⠀⣀⣤⣶⣿⣟⣛⡟⠙⢻⣾⡿⠽⠟⠒⠛⠺⠿⣿⠹⠟⠹⡟⢰⡟⢠⡟⢣⣾⠋⡾⢋⡿⢻⣿⠛⣿⡿⢿⣿⣾⣿⣶⣶⣠⣄⣀⠀⠀⠀⣰⣏⣀⣰⠇
⠠⢶⡿⠋⠉⢰⣴⣿⡧⠇⠀⠀⠈⣻⣶⣶⣶⣞⣿⣿⢻⠿⢿⡟⠛⠳⢶⡾⣶⣦⠀⠀⠀⠈⠀⠚⠃⠀⠉⠁⠘⠋⠘⠛⠟⠛⠛⠻⠟⢿⣿⣾⣿⣿⣻⡏
⣤⣠⠹⢦⠠⣌⠛⠛⠁⠁⠀⠰⠀⣸⡗⢹⠉⠀⠀⠀⣀⣀⣠⡤⠤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢾⠟⠛⠛⠛⢿⣿⣿⣼⣧
⠈⠙⠻⠶⣾⣭⣀⣀⠀⠀⠀⣾⣆⣾⣧⠭⣷⣶⣞⣁⣀⣀⣒⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠀⠁⠀⠀⠀⠀⠀⠀⠹⣮⠉⠹⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠾⢯⣭⣿⣿⣟⣛⣛⣭⡽⠿⢿⣷⣶⣶⣶⣶⣶⣶⣿⡿⣯⣭⣭⣵⣶⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢳⣾⣿⣯⣭⡭⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠙⠻⣿⡛⠛⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣽⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⢚⣂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⣛⣩⣥⠴⠶⠚⠛⠉⠉⣀⣠⣤⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢛⣋⣩⣤⠶⠞⠛⣉⣁⣤⣤⣤⣶⡿⢿⣛⣻⣭⡽⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⣡⢞⣫⣍⢹⡶⣤⣠⡤⠶⢞⣋⣩⣥⠶⠞⠛⣉⣉⣤⣴⡶⠿⢿⣛⣛⣭⡽⠷⠞⠛⠉⠉⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡀⠀⣀⣄⣼⠿⢿⣷⣿⣼⣿⣿⣾⢿⣯⣷⠖⠛⣉⣉⣤⣤⣶⠾⣟⣛⣭⡽⠶⠚⠛⠉⠉⠁⠀⠀⣀⣀⣤⣤⠶⠶⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠈⢠⣞⣭⣾⣿⣿⣷⣿⣿⡿⣯⡻⣏⢷⡹⡏⢿⣟⣿⣿⠿⠟⠛⠛⠉⠁⢀⣀⣀⣤⡤⠶⠶⠚⠛⠋⠉⠁
⠀⠀⠀⢰⣿⣿⡿⠿⢛⣋⣩⣿⣿⣿⣎⣷⢻⠈⣿⣷⢸⣏⣁⣀⣠⣤⠴⠶⠟⠛⠋⡉⠁
⠀⠀⠀⣼⣿⣵⣶⣿⣿⣿⡿⠷⣿⣿⡟⣿⢸⣼⣯⣇⣼⣿⠉⠁
⠀⠀⢰⣿⣿⣿⣛⣩⣥⣴⣶⣾⣿⡿⣹⢇⣾⣽⣿⣿⡟⢯⣷⡄
⠀⠀⢾⣼⠃⠉⠉⠘⣿⣷⣿⣿⣿⣹⢻⣿⡿⣿⣿⡟⣧⠘⠿⠃
⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⢹⣿⡧⡏⣾⢸⣿⣿⣿⣿⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿⣧⣿⣧⢿⣿⡿⣿⡏⣿⢉⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣷⣿⣿⣹⣧⡻⣷⣿⢷⡹⣿⠿⢻⡇⡿
⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣯⣷⣜⣿⣿⣳⣼⢷⡌⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⢻⣿⣿⣿⣿⣿⣞⣿⣿⢿⣧⣿⠀⠙⢿⡝⣦
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣷⣿⣿⡙⢧⣽⣿⣿⣿⣷⡟⠀⠀⠀⠷⠟
⠀⠀⠀⠀⢀⠀⢿⢻⡄⠀⠀⣿⣿⡇⣿⡷⢾⢿⡟⠉⢿⣷⡀
⠀⠀⠀⠀⠈⠣⠈⢷⣿⡄⠀⣿⣿⣇⣿⡷⢏⡼⠃⠀⠈⢻⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢿⡙⣿⡿⢳⠏⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣫⣾⣟⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⣳⢿⣿⣿⣿⣷⣶⣟⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣽⣾⣿⠛⠁⠀⢻⣿⣄⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⠀⠀⠀⠀⠹⣟⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠶⠶⠚⠛⠛⠛⠛⠒⠶⠶⣤⣀
⠀⠀⠀⢀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠈⢳⣄
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⡀⠀⠀⠀⠸⣇⢻⣷⡀⠀⠀⠀⠙⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢻⡻⣦⠀⠀⠀⠻⣆⢻⣿⣄⠀⠀⠀⠘⣇
⣿⠀⠀⠀⠀⣾⠻⣦⡀⠀⠀⠀⠈⢳⡄⠀⠹⣿⣇⠀⠀⠀⠘⢧⣹⣿⣆⠀⠀⠀⢻⡄
⢻⠀⠀⠀⠀⣿⠀⢪⣷⡀⠀⠀⠀⠀⠹⣦⠀⢹⣿⡄⠀⠀⠀⠈⢷⢿⣿⣆⠀⠀⠘⣇
⠸⡇⠀⠀⠀⠘⣧⡀⢿⢿⣄⠀⠀⠀⠀⠈⢷⡀⢿⣷⠀⠀⠀⠀⠘⣇⢻⣿⡀⠀⠀⢿
⠀⢻⡄⠀⠀⠀⠘⣧⠈⢷⣻⡆⠀⠀⠀⠀⠈⢷⠸⣿⣇⠀⠀⠀⠀⢿⢸⣿⡇⠀⠀⢸⡇
⠀⠈⣷⠀⠀⠀⠀⠘⣆⠈⢿⣿⡀⠀⠀⠀⠀⠸⡇⣿⣿⠀⠀⠀⠀⢸⡜⣿⡇⠀⠀⠈⣧
⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄⠘⣿⣇⠀⠀⠀⠀⠀⣿⢹⣿⡆⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⢻
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⠀⢹⣿⡄⠀⠀⠀⠀⢿⡌⣿⡇⠀⠀⠀⢸⡇⣿⣿⠀⠀⠀⢸⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄⠘⣿⣇⠀⠀⠀⠀⢸⡇⣿⣇⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠈⡇
⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇⠀⣿⣿⠀⠀⠀⠀⢸⡇⣿⣿⠀⠀⠀⠀⢻⣾⡿⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⠀⢸⣿⠀⠀⠀⠀⠸⣇⢹⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⢹⣇⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡛⢷⣦⣄⡀⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠙⠶⣍⠻⢿⣶⣄⡀⠀⠈⠛⠳⢦⣄⡀
⠀⠀⠀⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠒⠭⣝⠳⣤⡀⠀⠀⠈⠑⠦⣝⠻⢿⡶⣄⡀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠰⡇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠙⠷⣄⡈⠳⢦⣙⠳⣤⡀⠀⠀⠈⠛⢦⣍⣪⣿⡄⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⡇⠀⠀⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠠⢭⣟⡶⣤⣀⠀⠀⠈⠙⠶⣤⡉⠳⢮⡙⢦⡀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⡀⠄⠀⠈⢷⡀
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠈⠛⢦⡈⠙⠳⢯⣟⠶⣄⡀⠀⠈⠙⠶⢦⣍⣂⣹⡆⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠸⣇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⠀⠀⠀⠈⠑⠦⣄⡈⠙⠪⣝⢶⣄⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠙⠷⣦⣌⣡⣹⡆⠀⠀⠀⠀⢀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡴⠶⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠉⠉⠉⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⡀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠀⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⠾⠟⠉⠀⢰⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⣸⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢻
⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⢻⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠀⠀⠀⣀⣼
⠀⠀⠀⠀⠛⢦⣄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⣿⢀⣠⡴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⢒⣛⣛⣶⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⣋⣉⣭⣤⡶⠾⠟⠛⠋⢉⣙⣯⡳⣝⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢲⠞⢁⣴⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠼⠳⠽⠟⠛⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⢉⣀⣀⡴⠃⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⡪⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠿⣄⠀⠀⣠⣖⠋⠀⠉⢑⣲⣾⣆⠀⢀⡀⠤⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠊⠉⠀⢀⡠⠝⢳
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠛⢲⡏⠉⠛⠳⣾⡿⠟⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠉⠁⢀⣀⡤⠴⠒⠊⠉⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢸⠃⠀⠀⠀⣿⠤⣄⣀⣀⠀⠉⠁⠒⠀⠠⠤⠐⠒⠉⠁⢀⣀⣤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣝⣲⢶⡾⣶⣦⣄⠀⣿⠀⠀⠈⠉⠛⠛⠶⠶⠦⠤⠤⠴⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⢒⣋⣭⢴⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠻⣇⣤⢄⢹⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠖⢚⣋⣭⢴⠶⠟⠛⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡄⠀⡏⠰⠜⢸⣿⡯⢭⣙⡓⠲⠤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡶⠶⠞⢛⣋⣥⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡿⡇⡇⠉⠙⠛⠶⢶⣤⣭⣉⣉⣉⣩⣭⣤⡶⠾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠠⢄⢸⡿⡇⡇⠁⠒⠠⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⠀⠘⢮⣊⣼⠟⠃⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡉⠒⠠⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣈⡉⠒⠠⢄⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠖⠒⠋⠉

⠀⠠
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄
⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⠶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠃⠀⠑⠢⠂⣠⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠀⠀⠈⠔⠁⠀⠣⣄⠀⠀⠀⠀⢀⠤⠒⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⣖⡩⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠑⠂⠠⠀⡀⠊⠀⠀⠀⠀⠀⠁⠈⠆⠀⠀⠀⠁⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠐⡀⠀⠀⠈⠀⢀⠀⢠⠁⠀⠁⢀⡀⡀⠘⠀⡤⠀⠀⠈⠩⠍⠑⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⡀⠈⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⠀⠀⡕⠀⠀⠘⠢⠈⠁⠀⠀⠂⠂⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⠀⠀⡶⣶⣶⣶⡀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⢋⠀⠐⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⢀⣠⠒⠁⠄⠒⠀⠒⠒⠀⠈⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠁⠂⠀⢀⡀
⠀⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠉⢀⡠⠒⠉⠀⡀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⢀⡀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⣀⡸⠒⠂⠈⡁⢀⣤⡀⣀⣀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠘⠦⢤⣀⠤⠤⠀⣩⡴⠐
⠀⠀⠀⣀⠱⠤⠀⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢂⡜⠉⠀⠁⠀⢀⣀⣁⡠⠀⠀⠀⠙⠶⠶⣒⠐⠒⠂⠤⠤⠴⠚⠉
⠀⠀⠘⠁⢀⡠⠄⠀⠛⠀⡱⡀⠧⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡁⢙⣒⢒⣉⠁⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠤⢶⡤⣀⣀⣀⠠⠴⠒⣧⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠘⣧⠀⠉⠙⠈⠶⠀⠄⠛⢪⣀⣠⠤⢶⣛⡋⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠁⠀⠸⡄⠈⢋⠀⣤⣇⠀⠀⠀⠉⠂⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣹⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⢈⠃⠘⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⠤⠤⣤⣶⡶⠶⠾⠛⠋⠀⠀⠀⠴⠶⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠒⠤⠔⠷⢂⡀⠐⠸⠱⣎⡀⢤⠤⢤⣤⠀⣀⠀⠀⠤⢤⡴⠟⠀⠀⢠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠖⣄⡐⠂⣡⠤⡏⠂⠞⠓⣛⠛⣟⣩⣭⣤⣤⡶⠖⠊⠁
⠀⠀⢠⣄⡠⠔⠒⠋⠉⠀⠀⠀⠉⠀⠈⠑⠳⢤⡭⢄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⣀⠠⠄⣀⠀⢀⣐⢁⠽⠛⠳⠰⠶⠤⠖⣞⣳⠻⣛⢉⡉⣉⠁⠉⠂
⢠⠔⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡎⢀⡀⠀⠀⠈⠑⠂⠠⠤⠤⠀⠀⠊⠉⠈⠉⠙⢧⠦⣊⢀⠴⠶⠘⠛⠉⠀⠀⠉⠙⠛⠛⠀⠀⠢⣄
⡘⠈⣡⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠖⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢅⣤⣼⣙⢦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠳⠽⠧⠼⠐⠶⠆⣠
⠘⡏⠁⠀⠀⠈⠛⢎⡙⡛⠓⠀⠛⠛⣒⢀⡉⠉⠀⠀⢈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇
⠀⠈⠂⢀⡀⠀⢀⣸⠟⠉⣀⠀⠀⠬⠵⢶⣭⣆⡉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⣟⠟⠀⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠐⠀⠀⠈⠁⠀⠀⣄⣀⠀⠂⠈⠉⠀⠈⠁⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢰⣆⣠⣀⢈⣉⣁⣤⣄⣈⢀⣺⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣛⣽⣿⡄⠀⠀⠀⠀⠘⠛⠻⢃⣬⠉⢙⡛⠛⠉⠜⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠋⠉⠛⠁⠀⠀⠀⠀⡆⠀⠀⣤⡾⠛⡾⣿⢿⣿⠿⣷⠀⠀⠈
⠀⠀⠀⠀⣄⣰⠐⡠⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⢦⣆⣾⣶⣾⣴⣦⣴⡄⠀⠠
⠀⠀⠀⠀⠈⠉⠉⠳⠮⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⡉⠉⠉⠛⠭⠯⣉⡙⠁⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣿⣷⡼⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠠⠀⠮⠽⠿⠄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠱⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠲⣦⣖⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢉⡞⣳⣛⣻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠫⢠⣥⣼⣷⢚⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⡁⠀⠀⠀⠀⠀⣰⣾⡯⣽⣿⣧⣴⡀
⠀⠀⠀⢀⣴⡀⠂⢀⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⣤⢀⣄⡀
⠀⠀⠀⠀⠙⠛⠃⠭⠀⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠩⠿⠿⠏⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠠⠀⠀⢀⣀⣠⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⢿⣿⢵⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠷⠶⠒⠛⠁⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦
⠀⢀⠀⠀⠠⣰⡏⠡⢄⡅⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡶⠶⠶⠆
⠀⠀⠁⠀⠀⠀⠁⠙⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣄⠤⣄⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⡦⠛⢉⣠⡴⠋⣀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠱⠟⠐⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⣹⠀⠴⠻⠯⠃⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⠶⣏⠈⢻⣖⣚⣛⣛⣛⢩⣉⣭⣭⣿⣷⠶⠖⠛⠛⣷⣎⢧⡀
⠀⠀⠀⠀⠀⣿⢡⣶⣶⣾⡉⠷⣔⠊⢍⡚⠻⣿⣿⣿⣿⡎⢿⣿⠟⢁⣠⣴⠶⠚⠉⠛⢻⣧⣳⡀
⠀⠀⠀⠀⠀⢻⣆⢿⡗⠀⠙⢦⡀⠙⣄⠙⣄⠹⣽⣽⣶⣷⡞⢿⣷⠏⠀⣀⣀⠤⠀⠂⣺⣿⡷⠻⣄
⠀⠀⠀⠀⠀⢸⣿⡌⣧⠀⠀⠀⠻⣄⠘⡆⠸⣦⠿⠿⠿⠿⢟⣘⣛⣃⠈⣭⣤⡴⢲⡶⠶⢾⣿⣶⡙⣦
⠀⠀⠀⠀⠀⢸⣿⣷⡘⢒⣂⣠⣤⡭⢤⣶⣶⠶⠖⡻⠟⠛⣩⣌⡙⢿⣷⡹⠁⣇⠀⢿⡟⠛⠛⣻⣿⣜⢧⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣧⢹⣿⡉⠐⣝⡦⠈⠀⠐⠮⠁⠀⣀⠠⡅⠀⣠⣌⠛⢄⠸⢦⡈⠻⣿⣛⣉⣉⣽⡮⠿⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⢻⣿⣦⡀⠀⣼⠃⠄⢂⣀⠘⠽⢲⣴⠦⠀⢁⣶⣛⣒⣦⣭⣭⣿⣿⣷⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣼⣿⣿⣿⣦⣬⣥⣤⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠂⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣄⠀⠀⢀⡀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠁⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⡈⠀⠀⢸⢷⣔⣂⣐⢶⣉⡫⣥⣾
⠀⠀⠀⠄⠀⣀⣤⣨⣧⡤⠀⠀⠀⠀⠀⢀⠆⠐⢦⠀⠀⢀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠉⠒⠉⠉⠛⢋⡁⠁
⠀⠀⠀⠀⠒⠈⡞⠯⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠛⠡⠀⠀⡹⠖⠲⠾⢾⣧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⣂⠀⣀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢀⢀⠀⠀⠀⠀⠀⠀⡐⢈⠁⠶⠡⠠⡄⠂⠀⠀⠀⠀⠀⠀⠐⠓⠐⠀⠒⣲⠂
⠀⠀⠀⠀⢐⡄⠀⠂⠀⠈⢂⠀⠀⠀⣉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⡄⣀⣀⠉⠀⠀⠆⠉
⠀⠀⠀⠀⠀⡙⣄⣠⣰⣤⡤⠷⠒⠚⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠞⣈⣭⣷⠇⠁⡂⠀⠀⠀⢀⠄
⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢴⡀⠀⠀⠀⠀⠒⠾⠀⣠⣾⣯⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠐⠢⢄⡀⠀⠈⠉⠀⠠⠀⠀⠈
⠀⠀⠐⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠘⣢⠤⠠⠀⠐⠀⠀⡀⡀⢠⣆⠀⠀⠀⠀⠈⠑⠪⢄⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠒⠀⠒⠉⠀⠐⠀⠀⠉⠃⠀⠀⠀⠀⠘⠤⡀⠂⢀⣶⠈⠀⠀⠈⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⢀⣠⠤⠀⠒⠒⠒⠒⠂⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠃⠀⢨⡄
⠀⠀⡀⠋⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⡀⢳⡄⢀⠀⠨⠤⠴⠂⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠤⢸⠦⠄⠀⠀⠀⠀⡟
⠀⠀⡕⠀⣤⡶⣞⠿⢭⢵⣿⡆⠤⠤⢴⡚⡏⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠙⠲⢵⣛⢩⡙⢶⠾⠵⠞⣚⣤⠟⠉⠁⠀⠀⠀⠀⢀⠈⠀⠐⠘⡇⠐⠈⢉⠀⠠⠀⠀⠀⠀⠀⠀⠑⢄⣀
⠀⠀⠀⠀⠠⡀⠀⠉⠙⠋⠉⠉⣁⡄⠈⠀⠀⠀⠑⠀⠀⠉⠂⠀⡤⠚⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⢄⣀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠐

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠰⡶⡄⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣪⠲⣴⣿⠖⠾⢦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣦⡑⢦⡀⢆⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⢷⣾⣿⡾⠷⠊⠲⠤⣤⣀⣼⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠻⡴⣴⣿⡗⢯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢾⣧⡙⣿⣿⣤⣀⡀⠀⢀⣿⠋⠀⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⢻⣦⡀⠀⣀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⣿⣿⣿⣷⣿⠏⠀⠀⢀⡠⣾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⣾⣶⣿⣀⠶⠀⠠⣤⣄⣠⣠⣄⡀⠀⠀⠀⢰⡟⠻⣌⢮⡻⣿⣻⢿⣿⣷⣤⣴⢿⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠳⣮⡟⢾⣿⣟⡷⠤⣀⢀⡹⣿⠁⠀⠉⠁⡄⠠⠟⠀⠀⠈⠙⠿⣶⣬⣭⣽⣿⣿⠷⠋⠀⢄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢻⢎⢻⣿⣿⣧⣼⣿⣿⡿⠀⠀⠀⢠⣟⣦⠀⠀⢀⣤⣴⣌⡉⢙⠢⣽⣿⣿⣶⣷⣦⣖⠣⢼
⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣷⡄⠀⠀⠀⣙⠷⣝⢿⣿⣿⢿⣿⣇⠀⢀⣶⡔⠁⠀⠀⠑⢖⠒⢾⡯⣙⢶⡑⣿⣷⣦⣶⣤⠀⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡹⣆⢠⡞⠁⠑⢀⡈⠻⣧⣬⣟⢿⣿⣿⡞⠀⠀⠀⠀⢀⠸⣧⣀⣹⣌⣧⣿⡿⣿⣿⣿⡴⣆⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⡜⣾⠃⠀⠀⠀⠉⠂⣌⡈⠙⢦⣿⢿⣶⣤⣀⡤⢄⣤⣼⠿⣿⣿⣿⢿⣿⠀⠁⠙⢿⡌⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⢷⣼⡄⢀⣀⣀⣠⣤⣌⡙⠤⢭⡝⣿⣭⣭⣽⡾⠛⠛⠉⠙⢿⣿⣧⠀⣿⣄⡀⠀⣠⣷⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⡗⠦⣄⡀⠉⠙⠉⡉⢕⣒⣶⣿⡤⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢻⡄⠀⠙⠿⣷⣷⣌⣦⡼⡏⠻⢿⣧⡖⠀⣤⣦⣾⡿⠈⠙⠻⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣀⣠⣿⠁⠀⠹⣿⡅⠀⠀⠙⠯⣛⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠘⣧⡄⠀⠀⠀⠈⢧⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⢄⣠⣿⣿⣶⣦⢴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠭⢽⡭⠿⠻⠭⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢿⡟⢿⡿⣿⣿⠿⠿⣿⢿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣧⣿⣿⣼⣿⣿⣹⣾⣾⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿