Culinary Emojis & Symbols

⣠⣀⠛⠀⠀⠐⠤⠀⠀⡀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⠀⢰⡉
⠛⠉⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⢀⣚⡀⠀⠀⡑⠂⠀⠀⠀⠀⠀⠠⠀⠐⡀⠈⡆⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠀⠁⠉
⠀⠀⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⡬⡉⠀⠀⠔⠂⠀⠀⡐⠀⠀⠀⠀⠐⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣄⠀⠀⠀⠡⠀⠤⠤⠬⠄⠀⠁⠂⠀⡠⠀⠀⠾⠓⢠⣀⠀⠀⠀⠣
⠒⠂⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠞⣄⠚⡙⣨⠀⠀⠀⠀⠀⠠⡀⠀⠛⠀⠀⠀⢀⠀⠀⠁⠃⠈⠛
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡅⠀⠀⠈⠛⠉⠯⠋⠀⠀⠆⠐⠒⠾⠇⠀⠀⠠⠀⢄⠠⣧⠀⠠⠃⠀⠀⢀⠀⠀⡀⡴⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⣔⡄⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠄⠀⣄⡀⢤⡈⠃⠀⣀⠀⠀⠾⠀⠘
⠀⠐⠀⠀⢁⣄⠀⠀⠄⠀⠀⠌⠀⠈⠫⡃⠀⢀⠂⠀⠀⠀⠀⡌⠁⠀⠂⠀⣤⣌⠉⠐⠄⠀⠀⠀⠀⠀⠙⠀⣀⠀⠀⠊⣄⠁
⠂⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⣤⣤⣦⠀⠁⠀⠀⠀⠈⠒⠀⢀⠀⠈⠁⠉⢋⡂⠀⠀⠀⣤⠀⠀⠐⠉⠀⠀⠈⢀⢠
⠈⠀⠀⠀⠀⠀⠐⡬⢠⡀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠤⠈⠷⠀⠀⠀⠆⠀⠀⠀⠤⠄⡀⠀⢄⣀⠀⠑⠇⠀⢀⠀⠀⠐⠀⠀⡀
⠤⢀⠐⠋⠁⠀⠀⢰⡴⢣⠆⠀⠈⠀⠄⠃⠀⠊⡠⡑⠜⠀⠔⠉⡢⠄⠀⠀⠈⠀⡀⠃⠀⠾⠉⠀⠀⢀⠴⠈⠀⠀⠀⣠⣾⠏
⠀⠀⡀⠄⠄⠀⠀⠙⠞⠁⠀⠀⠂⠉⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉
⢀⡀⠿⠀⠁⠠⣀⠀⠀⢀⢤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠤⠀⢠⠒
⠿⠛⠀⠀⠀⠐⠂⠀⠈⠁⠀⠀⠀⠴⠀⠀⠀⠢⠆⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠊⠒
⠀⠀⠀⠀⠂⠀⠀⢀⡁⠀⠀⠀⠈⠉⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠴⠁⣐⠒⠁⠀⡡⠄⠀⠀⠠⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢂⢀⣀⣀⣐⡀⠀⠃⠅⠀⢀⠀⠀⣠⠦⣁⠀⠀⠀⠀⢆
⠤⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⡀⠽⠛⢐⠀⠀⠀⠀⠀⢀⠀⠀⠶⠀⠀⠀⠁⠀⠀⠲⠆⠘⠿
⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡌⡂⠀⠀⠐⠿⠒⣗⠟⠀⠀⡄⠠⠤⣴⡅⠀⠀⢀⠀⡀⠈⣆⠀⢀⠆⠀⠀⠀⠀⠀⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⢠⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣀⠘⠆⠈⠀⠀⠀⢴⠀⠸⠀⠀⠁⠁⠀⠈
⠀⠠⠀⠀⠂⡀⠀⠀⡀⠀⠀⡐⠀⠐⢟⠇⠀⠀⠄⠀⠀⠀⠈⡑⠃⠀⠀⠀⢀⡙⠓⠨⣁⠀⠀⠉⠀⠀⠲⠀⠀⠀⠀⠐⠀⠃
⠄⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠈⠂⠀⠀⠀⠐⠥⠀⠀⠀⠐⠋⠛⠖⠄⠀⠀⠀⣀⠀⠀⠠⠒⠉⠀⠐⠀⢉
⠐⠁⠀⠀⠀⠀⠠⣘⢀⠀⠀⠀⠁⠀⠉⠻⢿⠀⠀⣀⠐⣦⠀⠀⠀⡌⠀⠀⠀⣀⡈⠁⠀⡀⠀⠉⠢⡆⠀⠀⠀⠀⠠⠈⠈
⣀⠀⠠⠖⠂⠀⠀⢡⣨⢇⡄⠀⠐⠀⠀⠆⠀⠄⢀⠠⡲⠀⡠⠒⢄⡀⠀⠀⠐⠀⠀⠃⠀⣬⠛⠀⠀⠀⣠⠘⠁⠀⠀⢀⣴⡗
⠀⠈⠀⠀⡀⠀⠈⠺⡱⠊⠀⠀⠄⠒⠀⠀⠀⠢⠡⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠍

⠀⠢⣀
⣀⠀⠀⠑⠒⠄
⣿⣶⣦⣤⠆⠀⠀⢦⣀
⠀⠀⠈⠹⣮⠀⠀⡀⢈⠑⠄
⠀⠀⠀⠐⣿⣆⠀⢡⠀⢢⡄⡀⡄
⠀⠀⠀⠀⣾⣿⠀⡞⠠⣿⠀⣿⠸⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠻⣯⣼⣇⣰⣿⡀⢿⡄⣇⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡛⢄⣇⠘⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡀⠇⠀⠀⢀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢅⠀⠀⠀⠉⠺⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠚⠀⠀⠄⠀⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣦⣄⣿⣦⣴⣶⣶⣶⣷⣤⣤⣴⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠿⠤⠽⠿⠿⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠒⠒⠚⠛⠉⠉
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠉⠉⠀⠀⠁⠀⠒⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⣀⣀⣠⡶⠾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣉⣀⣀⣀⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⠉⠝⢻⡇⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠙⠛⢶⣄⠀⠀⠈⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⡇⠀⠀⠠⠙⠿⠷⢶⣄⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠶⠃⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠾⠶⠶⣶⣶⡶⠶⠶⠟⠛⠉⠉⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠁⠀⠁⢰⣿
⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠤⡦
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣖⣤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠦⠀⠀⠀⡄⠀⠀⢀⡎⠀⠁⢀⡖⠀⠀⠀⠀⢸⠃
⠀⠀⢸⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⠒⠳⠶⢢⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⠀⠉⠀⠀⠀⣀⡤⠖⠉⠀⢀⣤⢸⡂⠀⠀⡘⠋⠀⠀⠀⠐⣿
⠀⢀⠉⠉⠛⠛⠽⠆⣶⣶⠀⢸⡗⠒⠛⡿⠟⠁⠀⠀⠀⢀⣀⣀⠈⠉⠑⠂⠀⠀⠀⢀⣀⠦⠚⠉⠀⠀⠀⠀⢰⠃⠉⠀⡻⢣⡞⠁⠀⠀⠀⠀⠜⠁
⠀⠈⠻⢿⣶⣤⡄⢀⣀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠉⠀⠀⣀⡠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⢁⡌⠁⠀⠀⠀⢶⣾
⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠀⠁⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⢀⠠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⣇⡄⣴⠉⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⣀⣤⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣿⣤⠍⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⠄⠂⠈⠀⠉⠉⠓⠶⠤⣀⠀⠀⠀⠀⠀⠀⡾⣿⡁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠋
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡄⡀⠀⠀⠀⠸⣿⣿⣿⢷⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠤⠦⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠉⠛⠿⣿⣮⣭⡙⠳⢦⣤⠔⠒⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠠⡶⠋⠉⠋⠉⠓⣆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣷⣀⣠⡦⠔⠋⠉⠀⠀⠀⠀⠠⠎⠈⠐⢦⣄⣀⣀⠀⠀⣸⠷⣦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠰⠛⠙⢸⡟⢛⣏⠀⠀⠘⡇
⠀⠀⠀⠑⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⣠⠀⠀⠀⠀⠈⡿⠁⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠙⠿⠿⢿⣏⣀⣚⢛⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⡀⠑⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠲⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣰⠛⠻⡆
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⢻⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣏⡸⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠦⠶⠛⢻⠶⣤⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⠲⢤⣤⠶⠛⠉⠀⢹⡆
⠀⢀⡾⣧⣀⣈⣇⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⢀⣴⣋⣙⣦⣭⣹⡟⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠘⣇
⣴⣯⣤⡟⠁⠈⠙⢷⣄⠀⠀⠀⠈⠉⠛⠲⢶⢺⠀⠀⠀⠀⣾⣼⣶⣫⡟⠉⠉⢳⣤⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⡏⠀⠀⠀⠙⣧⠀⠈⠛⢦⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣤⠤⠚⠾⠅⠀⠀⠀⢹⡀⠈⠉⣉⠛⠋⡿⠃⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠈⣷
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡴⣷⠀⠀⠀⠀⠀⢳⡀⠀⠉⢀⡼⠁⠈⠁⠀⠀⠀⢷⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⠴⠿⣄⡇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡞⠁⠀⠀⠘⠃⠀⠄⠘⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠈⠉⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠘⠃⠀⠐⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠁⠀⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄⠀⠈⠛⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳⣤⡏⢻⣆⣠⣯⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⢧⣄⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⣀⡈⢳⡏⠉⣻⣾⠙⣧⠈⢿⣹⠆
⠀⢀⡶⠒⠒⠒⠒⠚⠛⠛⠛⢛⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⣟⣉⣉⣉⣉⣹⠂⠀⠀⢿⠘⡇⣠⡤⣤⣴⣿⠟⠁⠀⠀⢸⣏⣉⡙⠳⢴⡃⣿⢰⡿⣧⠀⠻⡄
⠀⠘⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⡴⠟⠉⠉⠉⠉⠉⠲⣄⠀⠸⠀⠀⣿⡀⠁⢹⡇⠀⠀⠀⠀⠀⢀⣀⡿⢦⠀⠙⢧⣸⠃⣼⣆⣀⣽⡦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠛⠛⠻⣿⢦⡼⠃⠀⠀⠀⠀⠀⠈⢿⠙⠛⠓⠒⠚⠛⠚⠛⠉⠁⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣄⣹⣦⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠉⢻⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⠶⠛⠶⣿⣶⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⢁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⠷⠮⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⢀⣾⡭⠽⠧⠬⣍⡉⣿⣋⣽⣇⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡴⠶⠶⢶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡀⠀⠀⣤⠀⠈⠙⠳⢦⡀
⠀⠀⣠⠞⠁⡀⠘⠀⡀⠈⠙⢦⡀⣽⡛⢯⡉⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠰⢦⠀⣤⠈⠁⣠⠌⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠉⠛⠻⢧⣄⣀⡄⠀⠀⠙⢦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠉⠀⢠⠀⠙⣦⠙⣿⢛⣷⠘⡆⠀⠀⠀⠀⢾⠀⠞⠀⠀⠀⠈⣠⠄⠀⠴⠖⠈⢷⠀⠀⠀⠀⠀⠀⢸⣇⠊⣷⠀⠀⠦⠈⠙⠳⣄⣠⠆⠀⠹
⠀⠀⠹⣄⠉⠀⠠⠄⠀⠀⠀⠀⢠⠌⣧⠉⢻⣽⡆⡇⠀⠀⠀⠀⠈⡿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⢸⣏⡴⠏⢠⠖⣛⣉⣽⡳⣬⣻⣦⡤⠶
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠰⠆⠀⠀⠀⠘⡇⢸⢉⣷⠇⠀⠀⠀⠀⢰⡟⠖⠛⠛⠳⢶⠶⠛⠉⠳⠶⠞⣩⡷⠀⠀⠀⠀⠀⢸⡁⠀⠀⣟⢾⣙⣧⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠐⠀⠀⢻⠟⢫⠏⠀⠀⠀⠀⠀⠀⢻⡗⠛⠛⠛⠛⠻⢿⣝⡛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣾⠛⢳⣀⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣀⣨⡿⢦⠾⠃⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡠⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢀⠠⢐⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⣀⣢⢠⣈⣀⣥⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡿⠂⠀⠀⡐⢁⢲⡀⠀⠸⠀⠀⠀⠀⣠⠤⠶⠶⠿⠿⢶⡄
⠀⠘⠈⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠾⠀⠀⠀⠀⠀⠛⢾⡡⠀⢁⡆⠀⠀⠀⢹⠀⠀⠀⠄
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠠⠀⠀⠀⠀⣶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠀⠐⠀⠀⠀⠐⠒⠘


⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⠀⢀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢘⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠰⣆⠀⡀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⡄⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠠⠂⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠲⢎⠣⣄⠀⠀⠈⠀⡃⠈⠠⠈⠀⠠⠀⠑⠠⠀⠀⠀⢀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢙⡧⠄⠀⠀⠀⠀⠐⠨⠤⠒⠀⠡⠀⠀⠀⠀⡁⢈⠀⠠⠋
⠀⠀⠈⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠊⠀⣀⣤⣤⣀⡈⠀⠀⠀⠀⣿⢿⡄⢸⣟⠖⠁⠀⠀⠀⠀⢀⡨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠐⠀⠂⠀⡰⢛⡅⠈⠀⠁⠀⠀⠰⠀⠀⢨⠉⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢋⣀⣠⡠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠨⡀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠠⡬⠀⠀⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠀⠀⠀⠀⠀⢀⣠⠄⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢀⠂⠈⠂⠀⠀⠀⢠⡏⠃⠀⠀⠀⠙⡆⠀⠀⠀⡀⠔⠒⠂⠀⡀⢀⠠⠀⠀⢀⠔⠀⠀⠀⠑⠄
⠀⣀⠀⠀⠐⠚⠛⠛⢲⠇⠀⠀⢀⠈⠀⠂⠂⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⢈⠀⠀⠒⡄⠶⠀⠒⢄⡜⢂
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆⠤⠁⠔⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠘

⠀⣀⠀⠀⠀⠀⡀
⢀⠀⠀⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣰⣤⣤
⠀⠀⡀⠙⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠃
⠀⠀⡇⠀⢣⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⡜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠦⡀
⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠶⠒⠃
⠀⠀⢀⠀⠸⠀⠀⠠⠀⠘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠄⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢊⠈⠁⠁⠀⠀⠀⠉⠉⠀⠀⠉⠂⠒⠢⠄
⠀⠀⣀⠬⠀⡁⠃⠀⣰⠁⠛⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⠤⡀
⠀⢁⠀⢠⡈⠀⠒⠊⡉⢀⣠⠀⠀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⡼⣉⣘⠛⠒⠀⠀⠀⠀⠆
⠀⠐⣝⢦⠀⠈⠉⠉⠁⠄⡉⡀⠐⡂⡤⢠⠀⠈⠁⠀⠀⠀⢀⠀⢀⢀⡀⠄⠄⠀⠀⠀⠩⠉⠒⠒⡆⠀⣾⠀⠠⡀
⠀⠀⠨⣦⡑⢀⠱⠀⠄⢰⣀⣀⣼⣘⠶⠇⠀⠀⠠⠞⠁⡀⡔⡂⡀⠘⠸⢳⠲⠒⠂⠀⠀⠀⠀⡜⠀⡔⢸⠀⠀⠁
⠀⠀⠀⠀⠙⠓⠒⠂⠀⠑⠋⠉⠉⢀⠀⠀⠀⠀⠐⠀⡎⣘⠂⠁⠁⠀⠒⠈⠀⠠⠀⠀⠀⣠⠞⠠⠉⢀⡞⠀⢀⠁
⠀⠀⠀⠀⢀⡀⣀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠐⢨⠧⡜⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠟⡡⣾⣀⡴⠋
⠀⠀⠀⢠⣀⠀⠉⠑⠺⣯⠭⠱⢖⠀⠀⠐⠀⠀⠆⠘⡄⠟⠂⠠⠤⠴⠖⡒⣺⠻⢋⡀⠀⣀⡉⠥⠴⠂⡊⠁
⠀⠀⠀⠀⠉⠂⠀⠐⠀⡄⠳⡠⠤⣴⠁⠀⠀⠀⠘⠑⣧⠀⠈⢤⡤⠔⠋⠀⣀⣔⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠘⠀⠀⣀⠀⠀⠀⠀⣧⠈⡖⠈⠀⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠖⣏⠁⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⣤⠈⢦⢅⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⢀⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠹⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠄⠠⢈⡐⠁⠷⢀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠡⠄⢘⠑⠂⠗⢸⠁⠀⠀⠀⠁⠛⠋⠘⠛⠛⣮⣂⠀⠀⠠⠀⣀⠀⠀⠀⣀⠀⠴⠃⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠘⠁⠘⢆⡈⠡⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡇⠰⢆⡆⢠⠀⠤⢤⠤⡄⢠⡄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠂⠌⡃⠛⠉⡀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠈⠙⠻⠶⠧⠴⠦⠛⠊⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢄⡘⣆⠀⠀⣠⣿⣿⡿⠀⠀⠀⠠⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣞⣿⣿⣿⠃⠀⠀⠰⠀⠉⠉⣠⠀⠀⡘⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠰⠊⠹⣶⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠲⠤⠤⠊⠀⣰⠁⠀⢰⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⢰⢦⠀⠀⠀⠀⣶⣀⣀⣠⣶⢀⡀⠀⠀⠀⠐⠛⡇⠀⠀⠀⠑⢶⣴⣿⠾⠟⠁
⠀⠀⠀⠀⠃⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⢟⣣⠞⠁⠀⢀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⢸⡏⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⣠⡀⢰⠀⢠⣦⡏⢀⠄⢦⣶⣹⣧⣤⣄⠀⠀⠀⣸⠁⠀⠘⢷⣀⠀⠀⠀⣠⣀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠛⠛⠋⠁⠀⠄⠊⠙⢻⠉⠀⠈⠻⣧⠀⠁⠹⡄⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⢤⡆⠀⠈⠢⣀⣀⣀⣶⣶⠾⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠰⠶⠛⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣄⣀⣠⣶⠀⠀⢰
⠀⠀⠀⠀⠀⣴⣾⣶⣶⣶⣶⡊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⡸⠀⠀⠀⠀⠠⠛⠃⠹⠀⠇⠠⠄
⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⡛⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣦⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡀⣀⣄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡸⠆⠦⠾⠬⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⠀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡖⠀⡐⠂⠂⢰⣭⡥⠴⠂⡍⢀⡜
⠀⢀⣄⠀⣀⣀⠀⣀⣀⣀⢸⠠⠄⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠑⢾⡄⠀⠀⠀⠀⠀⢀⠾⣉⠠⠄⣐⡤⣬⠖⠊⠉⠀⠀⢀⡨⠞⢡⡟
⣠⠋⠖⣻⠛⢄⢀⠟⠓⢹⣟⡀⣀⡀⠀⠕⠠⡄⠀⠀⠀⠀⠀⠀⢗⠐⠆⠂⢒⠇⠀⠀⠀⠀⠀⢺⡀⠻⣷⣟⡱⢲⠁⢀⠤⠇⣚⣼⡿⠖⢚⡵⠃
⠀⠀⠓⠊⠁⠉⠉⠉⠉⠩⠈⠉⠁⠉⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣲⣐⡀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣈⠉⠓⠻⣤⠷⢞⣋⡥⠚⠓⠋⢁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠦⠤⠤⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇
⠀⠀⠀⣀⣤⣤⠀⣠⠖⠡⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣰⢲
⠀⠀⠀⠙⣝⡼⠋⠉⠂⠄⠀⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣠⠖⠒⠢⣤⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠶⠧⠬⠷⢄
⠀⠀⠀⢀⣼⣄⣀⣁⠀⢃⣀⣄⣀⣧⡀⠀⠀⠀⢤⠆⠲⠢⣄⣜⣧⠛⠒⠒⣾⣡⣀⣧⢠⢔⠞⡄⠀⠀⠀⠀⠀⢸⠁⠁⠆⠀⠀⢠⡇
⠀⠀⠀⠈⣷⠒⠤⠭⠭⡭⠭⠥⠴⢾⠃⠀⠀⠀⢈⢦⡬⠷⣗⣾⣀⠀⢀⡠⢊⡗⣻⣉⠽⢿⣴⠀⠀⠀⠀⠀⠀⠘⣯⢭⣿⣿⣿⣽⠃
⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣸⣾⣡⣫⠖⣩⣹⣶⠶⢯⣉⡀⣉⡶⠏⣽⠀⠀⠀⠀⠀⠀⠀⢰⡠⠀⠀⠀⠘
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⠀⠠⢀⡟⠀⠀⠀⠀⠘⣟⠲⢬⣈⣉⣙⣦⠀⠀⠉⣽⣛⣡⡴⢚⠟⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠙⣶⢤⣤⣤⡤⢶⡞⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣉⡉⠙⢦⣤⠞⢉⣉⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣀⣄⣺
⠀⠀⠀⢀⡠⠴⠶⠶⢶⣤⣤⡆⠀⡶⣢⠶⡀⠀⠀⠀⠀⠀⠰⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⡴⡋⠨⡁⣀⣠⣤⠯⠞⣤⣾⠞⣵⠾⠃⠀⠀⠀⠀⠀⠀⢀⣤⠟⠛⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⢰⠁⢀⣦⣴⣿⠋⢀⠴⠄⡷⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⢯⢀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠈⠉⠳⡀
⠀⣿⣶⡫⠝⡳⣆⢂⠳⢥⣠⠴⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢰⢻⠛⠛⠛⠛⠛⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠄⠀⠠⠠⠅
⠀⣿⠳⢽⣿⣷⣮⣷⣶⣶⣶⣶⣿⡿⢟⡇⠀⠀⠀⠀⠀⠀⢸⠈⣦⠠⠐⠀⢀⡗⢸⠀⠀⠀⠀⢀⣀⡜⢉⠉⠉⠫⠍⠉⠉⠉⠉⠩⠋⠀⠈⢱⣀
⠀⠘⣷⣤⣈⠉⠉⠉⠉⠉⠉⠉⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠘⢦⣈⣓⣶⣖⣋⣠⠞⠀⠀⠀⠀⠙⠒⡆⢨⣷⣦⣤⡄⠀⠀⠀⠀⠀⠈⡂⠀⢰⠂
⠀⠀⠈⠳⢬⣉⡛⠒⠀⠀⢀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣉⣹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣋⣙⣋⣀⣀⣀⣀⣀⣈⣉⣁⣠⠞

⠀⢂⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠲⠶⠒⠉⠀⠀⠀⠀⡇
⠀⠠⠀⠀⠈⠂⠄⡀⠀⠀⠀⢜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⢠⠊
⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠆⣠⠶⢦⡄⣠⠶⢦⡀⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⢿⣀⣠⠇⢧⣀⣠⠇⣿⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢠⠀⢀⢤⡀⣀⡌⣠⢤⠀⣬⡀⣠⢄⠀⡀⡀⣄⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠛⠇⠳⠤⠀⠟⠄⠳⠼⠂⠟⠅⠣⠴⠃⠧⠇⠏⠻⠸⠤⠃

⠀⠠⠤⠄
⠀⠈⡉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠁⠀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠐⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀
⠐⠈⠀⠀⠀⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠊
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⡪⠂⠀⠀⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠚⠁⠀⠀⠈⠹⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⢀⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠑⠄⠀⠀⠀⣀⠠⠂⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⢀⠸⣦⣴⣷⠖⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⢼⣞⡀⠀⣿⡇⠀⡇⢸⠈⣩⠀⣠⣴⣦⣀⠾⠿⠗⣻⡎⠁⠀⠲⠀⡀⠈⠂⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠠⣌⠛⢾⠆⠀⡇⡇⢸⠁⡟⢠⠇⣶⣿⣿⣿⣿⣧⡄⢼⣧⣴⡇⢀⠂⠀⠁⠀⢠⡻⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣿⣿⣿⣿⣥⠏⠘⣿⣿⣿⣿⣿⣿⠁⢸⠃⢏⣴⢛⣀⡀⡀⠀⢺⠟⠀⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⢸⣿⣷⣿⣿⡏⠀⠀⠈⠻⢿⣿⠛⠁⠀⠉⠈⠀⢰⣿⣿⣿⣿⣿⣤⣀⠾⢦⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⠈⠻⠿⢿⠿⠃⠀⠀⠀⠀⠸⠟⠀⡔⢰⢂⠆⠀⠘⠿⣿⣹⡿⣿⣿⣿⠀⣴⡷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠘⣆⢰⠀⡀⢦⠀⢸⢐⠰⠁⣔⢸⠸⠀⠏⢸⢀⠴⢶⠀⣿⣿⡴⠛⢽⡿⠛⠫⣶⣾⣷⠆
⠀⠀⠀⠀⠀⠀⢱⣶⠆⠻⠿⠷⢹⡜⡆⢷⡘⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡟⣠⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠉⢠⣶⠄⠠⣀⢳⣿⡌⣷⢹⡄⠀⢤⢀⠄⣠⠀⡀⢸⠁⠀⢨⣤⣍⡛⠁⠄⠀⠀⠀⢠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⡴⡆⠈⠙⣿⢷⡸⣯⣿⡀⢫⠈⢂⠉⠀⢃⠁⠀⢰⣿⣿⣿⣿⡆⣠⡄⠀⠰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠇⢀⣴⣼⡏⣷⣿⡞⣷⡀⠀⣿⣧⣶⣿⡇⡀⢸⣿⣿⣿⡿⠃⠙⣡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣉⠉⣿⣿⡿⠷⠘⢳⣶⣿⣿⣿⣿⣏⡿⢸⣿⣿⢋⣴⣶⡞⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣇⠈⠀⠀⠀⠀⠻⣿⣿⣯⣿⣿⡿⢇⣬⣍⠱⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡈⠉⢿⡿⠛⠀⣘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣄⠎⠰⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆

⡧⠀⠀⢠⡖⠦⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿
⠀⠀⠀⠀⠙⡆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢴⣿⣴⣶⣄⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈
⠀⠀⠂⠀⣀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡄⠀⣶⣝⡃⢸⣂⢘⢓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣈⡩⣥⢄⡀⠿⣿⣿⣦⣭⣾⣿⡇⠀⠀⠘⠟⠀⠀⠀⠀⠾⠃
⠀⠈⠋⠀⠀⠂⠀⠀⠀⠀⠀⠈⣷⣷⣶⣷⣿⠀⠀⠙⠿⠿⠋⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠉⠴⠀⢶⠀⠀⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⢠⣶⣷⣦⠄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠐⠀⠀⠀⠠⠀⠀⢸⣿⡿⠗
⠀⠸⣿⠟⠁⢸⣷⣬⣥⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠀⠀⠀⠀⠐⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠀⢄⠀⠀⠀⠀⠙⠿⠃⢀⠆⠀⠠⠗⠀⡀⠤⠤
⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣷⣦⣤⣤
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠉⠄⣤⠛⠿⠿⣿
⠀⠠⠠⠀⠀⠀⠀⠀⢀⡤⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⠈⠀⠬
⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠃⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠸⠆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶

⠀⠀⠀⡀⠀⠠⣴⠥⠠⢄⣠⡤⡄⡀⡀
⠤⠾⠿⠠⠗⠳⠥⠾⠦⠇⠅⠵⠩⠀⠴⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣤⣤⣤⣤⣤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⣿⠰⠰⢸⡇⠆⠆⣿⠇⢀⠀⢴⠖⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⡁⠀⠉⠈⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠭⠭⠭⠤⠤⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠒⠂⣉⣀⠀⠤⠄⠐⠂
⠀⠀⠀⠀⠀⠶⠶⠵⠂⠒⠋⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣶⣽⣯⣿⣿⣿⣝⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⡟⣿⢫⣿⣿⠿⣫⣻⣿⢫⡿⣿⢿⣩⣦
⠀⠀⠀⢰⣶⣶⠂⢠⣤⣤⣤⣤⡀⠳⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢀⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠛⠛⠓⠀⠿⣿⣿⣿⣿⠿⠐⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⢀⡀⠤⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⢊⢉⣀⠠⠤⠄⠒⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⣾⣿⠟⢒⣚⣉⣉⣁⡀⣀⣀⣀⣀⡀⣀
⣿⣿⠛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠠⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⡴⠖⣛⡉⠉⠉⠉⣉⡛⠲⢦⣄⡀⠀⠁⠢⡀
⠀⠀⣦⣦⣦⡆⠀⠀⠀⡐⠁⠀⣠⣾⠟⠈⠁⢀⠄⢨⠦⡌⠀⠀⠁⣄⣈⢙⠦⣄⠀⠈⢂⠀⠀⠀⠀⢐⠢⡀
⠀⠀⣿⣿⣷⡇⠀⠀⠌⠀⠀⡴⠫⠁⠀⠀⠀⠄⠁⠄⡄⡟⠀⠀⠘⢄⢨⣋⣐⣘⣦⡀⠀⠱⡀⠀⠀⢸⠀⠘⡀
⠀⠀⢻⠿⢻⠃⠀⡘⠀⠀⣼⢁⠁⠀⠀⠀⠀⠀⠰⠆⠀⣇⣀⠠⠤⣸⡁⠈⡧⢦⠤⢷⡀⠀⢡⠀⠀⢸⠀⠀⠄
⠀⠀⠀⢹⠁⠀⢀⠁⠀⢰⠇⡈⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⡄⣪⠃⡢⠉⡟⢿⡋⠀⠀⢷⠀⠀⡆⠀⢸⠀⠜
⠀⠀⠀⢸⠀⠀⢨⠀⠀⣸⠀⠃⠀⠀⠀⠀⠀⠀⢀⠜⠰⡆⣤⠉⢀⡶⠈⠈⠉⠉⠉⠢⠸⡆⠀⠀⠀⢸⡎
⠀⠀⠀⢸⠀⠀⢈⠀⠀⢻⡰⠀⠀⠀⠀⢀⠤⠂⠁⠶⠞⢓⢹⠚⠃⠀⠀⠀⠀⠀⠀⢘⢨⡇⠀⠀⠀⢸⡆
⠀⠀⠀⠈⡇⠀⠈⡄⠀⢎⣄⠀⠀⢠⠊⡠⢄⠰⡍⠁⢢⡘⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢡⢀⠤⠏⡒⠓⠂⢸⠁⠠⢀⠕⡆⠴⢃⣠⢱⠄⡀⠀⠀⠀⠀⡰⢡⡏⠀⠰⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠩⠒⠆⢼⡀⠀⢸⠀⡘⢨⠀⢸⠀⠸⣆⣊⡧⠆⢳⠀⠀⠊⣠⠏⠀⡠⠁⠀⠀⡂
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠑⠄⠀⠙⢦⣀⠀⠀⠈⠣⠎⢀⠖⡙⡄⠲⢸⠗⢀⣠⠞⠁⢀⠔⠁⠀⠀⠀⠃
⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠐⢄⠀⠉⠓⠦⣤⣀⣀⠈⠢⣵⣃⣠⠴⠞⠋⠀⣀⠔⠁⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⠉⠉⠁⠉⠀⢀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⢙⠁⠀⠄⣀⡀⠀⠀⠀⢰⡁⣷⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠉⠉⠁⠐⠋⠓⠀⠐⠓⠒⠋⠀⠀⠈⣇⠈⣀⡜⠀⠀⠐⠒⢐⠀⠀⠘⠿⣽⠟⠀⠀⠀⠀⠀⠺⠷⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢞⠉⠀⠀⠀⠀⢀⠀⡠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠚⠿⠟⠃⠀⠀⢀⡁⠀⢤⡀⠀⠰⠷⣾⠿⠄
⠀⠀⠀⢠⠆⠀⠀⢠⠐⠐⢋⠀⠀⠀⢈⠁⠄⠊⠀⠀⠀⠀⠀⠀⣠⠄⠰⠋⣐⣂⠀⠁⠀⠀⠐⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠄⠀⠀⢈⠁⠶⠄⡀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠰⣦⣤⠀⠰⠁⠀⠀⠀⠚⠀⠈⠁⠀⠀⠁⠀⢠⣤⣀⣤⡄⠀⠀⠘⢀⣀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⡀⣤⡈⠀⠠⠤⠴⠊⠁⠀⠀⠤⠄⢀⡀⠀⠀⠘⠄⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠈⠀⠀⠈⢀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠲⡀⠀⠀⠀⠐⠀⠀⡀⣂⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠿⠞
⠀⠀⠀⠓⠄⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⠰⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢦⣤⣤⣤⡴⠀⠐⠿⣽⣦⠿⠀⠀⡀⠊⠑⢀⠀⠀⠉⠁⠀⠉⠡⠀⠰⢁⢶⠦⣔⢢⡀⠾⢏⡽⠃
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠿⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠁⣠⡆⠀⠠⠄⠂⠴⠈⠀⠀⣀⣿⣄⡑⠀⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠛⠃⠈⠀⢠⡤⡤⢤⡄
⠀⠀⠀⠈⠂⠀⠀⠀⢀⣀⠀⠀⠀⠤⠟⠽⠑⠷⠀⠀⢀⡘⢑⡎⠀⠀⠘⠋⣤⠀⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠂⣀⡀⠀⠀⠀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠀⠀⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⠃⠀⢴⢓⡄
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣀⠀⠿⠁⠀⢀⣶⡤⠼⠶⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣷⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣠⣈⣡⡘⠋⠀⠀⠀⠀⠀⢀⡀⠄⢀⡀⠴⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠑⠀⠐⠈⠀⠀⠀⠈⣅⣀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠃⠀⠀⢀⠀⠀⠀⠀⠀⠁⡀⠐⠁⠀⡀⢀⠀⠀⠁⠀⠠⠀⠀⠠⠀⠊⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠠⢐⠡⠂⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠋⢉⠡⡉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢋⠀⠂⠀⠐⠖⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠀⢀
⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠰⢄⠰⠄⠤⠂⠀⢀⡤⠠⠀⠆⠆⠰⠀⠀⠀⠀⠜⠢⢀⡠⠄⠤⠄⢠⡤⠀⠰⠄⠠⠀⠀⡠⠄⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠰⠂⠸⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠐⠀⣈⢐⠂⠀⠀⠃⠠⠄⠆⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠙⠂⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠐⠒⠀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠠⠄⠀⠂⠀⠀⠀⠠⢉⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢉⠁⠀⠂
⠇⠀⠈⠀⠑⠦⠠⠄⠀⠈⡄⠀⢀⠤⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠒⠀⠀⠸⡀⠀⡇⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠥⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠒⠈⠀⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⡀⠀⢠⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠬⢉⠡⡐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠈⠁⠀⢠⣰⡀⠀⠀⠀⠠⠀⢀⠀⠀⢀
⠀⠀⠀⠂⠐⢊⠢⠀⠀⠀⠀⠀⣈⠀⠤⣴⠁⠀⠀⠀⠀⠁⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠐⣀⣴⣿⣿⠏⠀⠀⠀⠈⠋⡀⠀⠡⠁⡀⠀⠤⠀⠔⠀⢀⠀⠀⡀⡀⠁⢀⠄⠀⠀⢼⠿⠟⠻⠿⠿⣷⡀
⠀⡀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠐⠆⠉⠛⠁⠉⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⣜⣠⡖⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⡐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣐⢎⠗⣼⣷⡱⡀
⠀⠀⠉⣠⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡿⢷⣮⠡⠊⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢯⣠⣴⣾⠫
⠀⠀⠀⡆⢀⠀⠀⠀⢀⡴⠖⣢⡶⢶⡄⠀⠘⠀⠀⠀⠸⢛⠿⠟⠀⠀⢀⠂⣵⠁⠀⡱⢍⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⢰⠀⢠⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠇⠀⠐⠀⢀⠀⠀⢶⡷⣷⠆
⠀⡄⠰⠔⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⠫⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠨⣥⠀⠙⣃⠀⠐⠀⠀⠀⠀⠐⠈⠁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⢰⣋⠰⠿⠀⠺⠽⡀⠀⡀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡦⠁⣤⠠⢞⡇⠠⡇⠀⡀⠀⠀⠀⠀⢤⢆⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⡇⢸⠅⣐⡋⢈⠧⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠄⠐⠀⠂⠒⠸⢎⣀⡚⣠⢀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⣫⣑⠂⢦⡀⠀⠀⠀⢠⣴⣶⣤⣤⣤⠒⠀⠀⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣙⣤⠤⢤⡃⠀⠐⠿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⡋⢈⡂⡁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡷⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⢄⡀⠀⠹⣿⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠉⠀⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠘⢷⣤⣄⣀⠀⣀⣠⠜⠁⠀⠀⠀⢀⠀⠘⣄⠀⠤⠂⠀⡅⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠎⠳⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⠦⡴⣣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⣾⣉⠓⠉⣁⣿⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⡁⠀⠀⠀⢻⣏⠙⢯⣉⡿⠀⠀⠀⢈⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢰⠋⠉⠙⠒⠒⢻⡌⠳⢄⣀⡟⠒⠒⠋⠉⠙⡆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡤⠤⠞⠀⠀⠀⠀⠀⠈⡟⠦⠀⣸⠃⠀⠀⠀⠀⠀⠳⠤⢤⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠲⠶⣤⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⡤⠶⠖⠃⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣦⡀⠀⠀⠀⢸⡀⠀⣀⣤⣤⡀⠀⠀⠀⠀⢀⣤⣤⣀⠀⢀⡇⠀⠀⠀⢀⡴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⠀⠀⠙⠶⢤⣀⡀⠉⠉⠁⠀⠀⠙⢦⣀⣀⡴⠋⠀⠀⠈⠉⠉⢀⣀⣤⠖⠋⠀⠀⡗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣦⣤⡤⣄⠀⠈⠉⠛⠒⠶⠦⠤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠒⠛⠉⠁⠀⣠⢤⣤⣴⡇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡄⠀⠀⠘⣧⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⣼⠃⠀⠀⢠⡇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⠷⠴⠋⠀⢻⡀⠀⠀⣴⠟⠻⣆⠀⠀⢀⡟⠀⠙⢦⠾⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠃⠀⠀⠘⠳⠶⠞⠁⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣄⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⣠⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠚⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⣤⠴⠲⣄⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠲⠶⠶⠶⠦⠤⠶⠶⠶⠖⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⣠⠶⠶⣤⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠹⣆⠀⢠⡞⠉⠙⣦⠀⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⠀⣴⠋⠉⢳⡄⠀⣰⠏⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠹⣄⠀⠀⠀⣰⠏⠀⠀⠹⣆⠀⠀⠀⣠⠏⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠚⠁⠀⠀⠀⠀⠈⠓⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠶⠖⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡖⣶⣶⡶⢶⣄⠀⠀⢀⣤⣟⢳⢀⡟⢴⠟⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢀⡀
⠀⠀⠀⠀⢀⣾⣿⣹⣿⠾⢿⣶⣵⡅⠀⣿⡻⣯⣑⠤⢀⣿⣤⣥⣤⠀⠀⠀⠀⠀⢀⠀⢉⠀⠀⠀⠐⠈⠑⢄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠚⠈⠁⠀⠀⢀⠈⠻⡾⡇⠀⠹⢷⣤⣉⣛⣻⣿⣿⠏⠀⠀⠀⠀⣀⠀⢸⣷⣦⣅⡐⠀⠀⣁⣴⣿⠀⠀⢸⡿⢹⠹⢩⡿⢸⠻
⠀⠀⠀⠀⡁⠀⠀⡠⢐⠀⡇⠀⣿⡇⠀⢰⠉⠉⠉⠛⢻⣿⡟⠒⠒⠂⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢼⡯⢮⡄⠺⣿⣿⣸
⠀⠀⠀⠀⢠⠀⠠⠀⠇⠸⠂⠀⣿⠏⠀⠠⠀⠀⠀⠀⠸⣿⣿⡀⠀⠂⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠒⠀⠠⠤⠀⠀⠚⠁⠀⠀⠀⠀⠂⠐⠀⠀⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⡶⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⡤⠀⢠⠤⢤⣤⣄⡀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠛⠛⠋⠛⢿⣿⣷⠀⠀⠀⡄⠀⠐⠀⠟⢹⣿⣿⠓⠐⡠⠮⠉⠑⢄
⠀⠀⠀⠀⠀⣀⣀⣀⣰⣿⣿⣇⣀⡀⣀⢀⣀⠴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⣇⣨⠤⢀⠁⣿⣿⣿⠉⠀⠀⠈⠐⢢⠸⣇
⠀⠀⠀⠀⠀⡊⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⡆⣸⡟⠀⠀⠀⠈⡇⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢸⠃⢆⣧⡀
⠀⠀⠀⠀⠀⠸⢀⠀⠀⢿⣿⣧⡀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠑⠂⠂⠃⠈⠴⠋⠀⠀⠀⠀⠀⠘⠤⡀⣠⠀⢻⣿⣿⡀⠀⠠⠔⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⢀⣀⠤⠔⠊⢉⠉⠑⢢⡀
⢀⠔⠀⠀⡀⠠⠈⠁⠠⠀⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢢
⡏⠀⠈⠀⠁⠀⠀⠀⢀⠀⠀⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⡁⠀⠈
⢃⠈⢀⠀⠁⠀⢁⠀⠀⣀⠀⠀⢠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠼⠁⠲⠏⠘⡆
⠈⡆⢀⠀⢀⣀⠀⠀⡘⠁⠱⡀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠂⠀⠹⢄⣀⣀⡴⠣⡀
⠀⠘⡈⠀⡏⠀⠉⠊⠁⠀⠀⠙⠒⠃⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠈⣆
⠀⠀⢡⡀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣀⣤⣶⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠈⠘⡄
⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⢔⠞⡿⠁⡿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡱⠋⡜⠀⠀⢃⠙⠲⠧⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡸⠁⢰⠁⠀⠀⠈⠳⡄⠀⠀⠑⢟⠲⣉⠆⡔⢦⡀⢀⣠⡀⠀⡇
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣀⡠⠴⡾⠀⠀⡇⠀⠸⡀⠀⠀⠀⠀⠘⡄⠀⠀⢸⠖⣏⣀⡏⠉⠙⢍⢀⠝⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠉⠹⡀⢀⠟⢄⡀⢱⡀⠀⠱⡀⠀⠀⠀⣠⣇⣀⠤⢺⡵⣤⠤⠜⠶⡒⢚⠏
⠀⠀⠀⠀⠀⠀⠀⡠⣖⡊⠭⣶⣓⡚⢄⡀⣨⠭⡍⢒⡶⢍⠑⡲⢭⡁⡠⢄⠀⣨⣄⣀⡱⣤⠤⡸⠃
⠀⠀⠀⠀⠀⠀⠚⠠⠤⢤⠤⢳⢄⣈⣑⣙⡅⠀⠈⡋⠀⠀⡙⠀⠀⡍⠀⢈⠏⢀⡯⠗⠒⠚⡉⢑⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡀⠈⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⣸⠖⢁⠀⠀⠀⠁⠀⡠⡀⠈⠀⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢱⠀⢱⠀⠈⡆⠀⢸⠀⠀⡇⠀⢰⠀⡰⠁⠠⠀⠀⡄⣰⡩⠮⠤⠬⣐⡆⠐⠀⠀⠈
⠀⠀⠀⠀⢀⠠⠄⣠⣇⣀⣀⡠⠤⣧⡔⠋⠒⢼⠀⠈⡄⠀⡇⠀⣘⢠⠃⠠⠐⠀⠀⢷⡁⠀⠀⠀⢀⡠⠃⠡⢀⣀⡀
⠀⠀⠀⢠⠃⠀⠀⠘⠃⠀⠈⢂⠀⠈⠀⠀⠀⢸⡇⠀⠃⠀⠂⠀⠃⠘⣤⢶⣀⠤⡀⠀⠈⠹⢉⠉⠅⠂⠈⣀⡜⠀⢈
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠜⠀⠉⠉⠉⠉⠉⠉⠁⠈⠣⡀⠀⠱⠤⠔⠲⣌⣀⠖⠒⠔⠁⠀⡠⠊
⠀⠀⠀⠀⠈⠒⠤⢀⡀⠤⠊⠉⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⠊
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠤⠀⡀⠀⠀⠀⠀⠤⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⠒⠐⢂⡉⠉⢄⠉⠐⡆⠤⣀
⠀⠀⠀⠀⠄⣄⣠⣀⣀⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢅⡀⠀⣤⠀⠘⣖⠀⣸⣆⡀⣸⠄⢻⠲⡀
⠀⠀⠀⢁⠚⢸⡃⡩⡆⠀⡗⠁⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢰⠎⠉⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⠈⠳⡂⠸⠒⠈⠉⠐⠀⠈⠁⠈⠑⢇⣰⠅
⠀⠀⠀⣖⣂⡯⠀⢴⡁⣨⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⢲⡀⢂⡸⠀⢘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠅⠀⠠⠄⠀⠀⠀⠀⠐⠂⢈⠈⠋
⠀⠀⠀⢠⡠⠕⢞⡷⣿⡿⢾⡀⢨⠀⠀⠀⠀⠀⡆⢃⠡⠴⠀⠘⠾⠇⠀⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠐⠂⠀⠀⠐⠀⠀⠄⠆
⠀⠀⢠⠈⠲⠆⠘⠉⠻⠛⠉⠠⢀⠠⠀⠀⠀⣜⠩⠀⠾⣀⣀⡀⠀⠀⠀⠎⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡁⢀⠀⠀⠀⠉⣿⠀⠀⡌⠱⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠈⢰⡯⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠘⠉⢁⢈⠁⢈⢐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢄⣹⢤⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠜⠁⡌⡄⠘⠈⠢⠈⢸⣄⢀⡸⠀⠀⣸⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⡅⠀⠀⡴⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠀⢇⠀⡨⠤⠄⠉⠀⠀⡘⠉⠙⢀⠙⠷⠺⢍⡔⠠⢤⡀
⠀⠀⠀⠠⡎⠀⠰⠃⠀⡠⠁⠀⡴⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⠉⠉⢃⠐⠀⠀⠡⠂⠀⠴⠂⠈⠀⠐⠀⠀⠀⠙⢦⣀⡴⠆
⠀⠀⣿⠀⠉⡒⠚⠁⠒⠓⠄⣠⠃⠀⡞⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⡀⢠⠄⡘⢤⣶⢀⡄⢹⢀⠜⢁⡼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠙⡀⠘⠀⡹⠂⢠⠚⠃⠘⡧⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠐⢤⢱⠈⠰⡤⠠⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⣘⠁⠀⠀⢸⡇⠀⠐⠉⠂⠖⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣌⠁⠀⠀⠀⠀⠀⠀⠐⢄⣀⡀⠀⡇⠀⠀⠀⢸⠤⠬⠿⠻⠃⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠛⠛⠛⠂⠹⢻⠀⠀⠀⢸⠙⠈⠳⠚⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢺⠤⢮⠹⢟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠀⣄⠀⠨⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⣴⠩⠗⣈⡑⢦⠈⢂⡬⡀⡎⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠂⠈⠱⡀⠀⠀⠀⠀⠀⠅⠈⠚⠤⠝⠘⠏⠹⠀⠎⠐⠑
⠀⠀⢀⢀⠀⣁⣉⠉⠙⣏⣩⡟⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣄⡄⠀⡀⢠⡄⠀⣴⢀⢠⡄⡀⢀⡖⠲⢰⡆⠢
⠀⠀⢸⠀⠀⠉⢠⣷⣋⠉⠁⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡹⣿⠞⣋⡉⢶⠄⢉⣴⠒⣁⣤⠉⠀⠄⣊⢨⠟
⠀⠀⠀⠀⠀⠰⢸⡥⠐⠙⠿⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠄⠘⠆⠀⠀⡜⠀⠀⢰⠈⠘⡆⢵⢀⢰⠃⠛
⠀⢀⠀⠀⠠⠀⠉⠀⠈⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠱⠀⡴⠀⠀⠀⠃⠀⣠⠃⠀⠐⡀⠀⢟⠃⢸⠂
⠀⠀⠂⠄⠀⠀⠀⠄⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠰⠁⡴⠁⠀⡔⠁⣠⠀⠁⣀⠊⣼⡅⡠⠴⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠠⡀⠀⠀⠀⠀⢀⣴⣮⣤⣷⣶⣄⠀⠀⠀⠀⠀⣠⠦⠀⢤⠌⣄⠀⠀⠀⠀⢀⢖⣦⣾⣿⢦⣿⣇⠢
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⢸⠀⠁⡌⠤⠡⠐⠀⠀⠀⠀⢤⣿⣿⣧⣀⣀⣸⣿⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⣿⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠄⣀⠊⠀⠀⠀⠀⠀⠂⠦⠤⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠐⠊⠛⠋⠀⠉

⠀⠀⠀⠀⠀⠀⡐⠋⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⢀⠄⠠⢀⠀⡠⠐⠂⠄⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣀⣀⣀⣀⣀⡤⡎⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⢀⠀⠀⠀⠀⠀⣛⡀⠀⠙⠉⣀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠏⡛⠶⠶⠷⠶⠖⢚⠑⠀⠀⠀⠀⠀⠢⢀⡘⢢⠐⠂⠀⠀⠀⠀⠀⣯⣭⣙⣛⡒⠶⠦⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠒⠋⠀⠀⠀⠀⠀⠁⠐⠀⠉⠍⠉⠛⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠄⡀⠀⠀⠀⠀⢀⣶⣿⠟⢻⣿⣿⣆⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣠⠤⣄⠙⣦
⠀⠀⠀⠀⠐⢁⣀⠀⠀⡀⠀⠀⣈⠄⠀⠀⠀⢸⠉⠛⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠻⢿⣿⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⡇⠸⡇⠄⠸⢀⡿
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⡜⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⢦⣙⠳⠶⠛⠁
⠀⠀⠀⠀⠠⡀⠀⠆⠀⠀⠀⠰⡠⠁⠀⠀⠀⠀⠀⢄⠈⠉⢑⣆⠀⠀⠀⠆⠀⢃⡀⠀⠀⠀⠀⠀⣀⡸⠀⠐⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⠂⠤⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠅⠀⠀⠀⠀⠒⠤⢈⠉⠉⠉⠉⠉⠁⠠⠀⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢨⡙⢿⣿⣿⣿⣿⡧⠸⠅⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣬⠀⠀⠀⠀⠀⠀⠀⠄⠢⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠂⠙⢿⣿⢋⠂⠈⠀⠀⠀⠀⣠⢶⠾⡿⣿⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣭⡌⠀⠀⠀⢀⠴⠚⠒⠒⠶⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⣯⣯⣽⣿⣯⣟⣻⣻⣿⣿⠟⠀⠀⠀⢀⡀⠀⠀⣬⣤⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠋⠙⠉⠋⠈⠀⠀⠀⠀⢂⣼⣀⣠⣤⡌⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢐⠇⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠘⠣⠹⠧⠐⠀⠀⠀⠀⠀⠘⠤⠠⠀⠀⠀⠼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡉⠈⡁

⠼⢀⡀⣀⡄⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢘⢀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠐⠡⠔⢈⠠⠀⠂⠁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠔⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣉⣷⠀⠀⠀⠀⠀⠀⠀⡀⠄⠰⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡠⢀⡉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡖⠂⢁⠀⠀⠀⢀⡠⠲⠀⠅⡁
⠁⢸⠀⠀⠀⢀⠄⠂⠉⠁⠢⢄⠀⠀⢂⡐⡿⠇⠀⠀⠀⠀⢡⠊⠀⢅⡀⠈⢂⠐⠆⠀⠁⠀⠀⠀⠈⠀⠂⠀⠀⠈⡄⠀⠀⡫⡅⢑⣘⣽⠽
⢀⠌⠀⠀⠀⠁⠀⠀⠀⠀⢀⣄⡄⠀⢈⠻⠆⠀⠀⠀⠀⠀⠘⣀⠼⠤⢼⠀⠈⠀⡃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢴⠤⠤⢔⠛⠒⢁⠠⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠤⣀⣠⠞⣠⠑⠔⠁⠀⠀⠀⠠⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠋⠁⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢈⠐⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠈⡀⠀⠀⠀⡉⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡀⠐⠈⠀⠠⢉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠈
⠀⡡⣠⠔⠨⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⢀⠠⠀⠰⢶⠤⢴⠀⠀⠀⠀⢀⣔⠄⠂⠈⠀⠀⣀⠔⠃⠈⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⢢
⠠⠂⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠂⢀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡐⠀⢀⡀⠀⠄⠒⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠄⠊⠃⠒⠈⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠠⠐⠁⠀⠀⠀⠀⠀⠤⠄⠐⠉⠁⠀⠀⠂⠁
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠢⣀⠨⠳⠍⠻⠶⣤⠀⠈⠀⠀⠀⢀⣠⣤⣄⠤⠤⠄⠀⠄⣤⣄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠀⠀⠀⢒⣀⠴⠀⠀⠀⠀⠀⠀⠠⠆⡁⠀⠀⠀⠈⢸⠄⠐⠃⠀⠒⠚⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠉⠁⠀⠀⢠⠀⠀⠀⠀⠀⠐⠁
⠐⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⣇⡠⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⠊⠐
⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠡⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣀⠉⠛⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠦⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⢀⡀
⠄⠀⠀⠀⢀⡠⠒⠀⠀⠀⠀⢉⠖⡂⠈⣍⠉⠙⠒⠀⠀⠀⠀⢀⠔⠈⠀⠀⠠⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠦⠂⠀⠀⠣⠀⠑⠂⠀⡀⠂⠀⠰⠋⢀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠂⠀⣒⠖⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢤⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠀⣀⠀⠀⡁
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠢⡈⠙⡲⡦⣄⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⠀⠀⠀⣀⡠⠬⣒⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊
⡄⢘⡄⠥⠑⠖⠓⠓⠀⠀⠀⠀⠛⠛⠛⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⣀⠄⢈⠠⠀⠀⢀⠟⠛⠛⠀⠀⠀⠀⠀⠀⡐⠃⢄
⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠳⠦⡄⣈⠀⠂⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠃⠀⡀⠱
⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠀⠂⠈⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠈⠂⠐⠉⠐⠐
⡠⠐⢀⡤⠤⠒⠒⠒⢛⢶⣦⡶⠚⠳⠀⠀⠀⢀⠠⠐⠢⡀⠀⠀⢄⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⠀⢁⡂⠤⢄⡀
⠀⡄⠉⠀⠀⢀⠔⠁⠀⢀⠇⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠑⡀⠀⠇⠠⡤⠵⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⡠⠂⢉⠀⠄⢁⡤⠤⠴

⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣖⡀⠢⢗⣦⣀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢠⡀⠀⠀⠀⢀⠀⢀⠀⠀⢠
⠀⠠⢌⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣡⣮⣿⢶⡇⠀⠀⠀⡀⠀⢀⣉⠿⠇⠁⠘⠀⠀⠀⠀⢀⠈⠀⡄
⠀⠀⠘⠀⠂⠀⠰⠔⠁⠀⠀⠀⠀⠀⢠⡆⡆⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠘⠓⡚⢁⣀⠠⠄⢂⠀⠰⠣⡀⠀⠀⠀⡀⠀⣀
⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⢸⠗⠤⠔⠂⠁⣰⠳⡀
⠀⠐⡀⠠⠀⠀⠈⠢⠤⠄⣤⣤⡄⠍⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣅⠄⠀⠀⠈⢴⣰⠂⠀⡀⠀⠈
⠀⠃⢀⠰⠦⠀⠀⠀⠀⠀⠁⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠖⠚⠉⠉⠀⠀⠘⠟
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠆
⠀⠀⢀⠀⠀⠀⢀⠄⡄⠓⣴⡄⠀⠀⠀⢀⠠⢠⠀⠀⣠⢠⡀⠠⠠⠀⠠⢀⢠⢀⠄⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⡀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⡌⡿⣿⣿⡧⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠈⠁⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⣄⠀⠑⠆⠈⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣤⣖⡢⠐⠋⠀⠀⢤
⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⡽⠟⠿⠑⠺⠫⠈⠂⠀⠠⠒
⠀⠀⠠⡀⠀⠁⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⢀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠐⠀⠉⢉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣩⡭⢎⠉⠿⠀⠀⠠⠒⠀⠀⠀⠸⠣⠀⠀⠀⠀⣀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢒⡯⢉⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡤⠦⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⢦⣀
⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣶⣶⣾⠯⠟⠓⠒⠒⠒⣂⡈⢳
⠀⢸⢇⠀⠀⠀⠀⢀⡠⠔⣒⠭⠕⢒⣉⠽⣿⣿⣿⣿⣍⣉⠩⠭⠭⠤⠤⠌⡷⣄
⠀⠈⢎⢣⡀⠀⠀⣿⡈⠩⠴⠒⣉⣩⠤⠒⢊⣻⣿⣿⣿⡶⠒⠒⢒⡒⣒⠊⢹⠈⠣⡀
⠀⠀⠈⢣⡱⡄⠀⢰⠈⠓⠢⠬⠥⠒⠒⢩⡍⢸⣿⣿⠿⣇⠀⢈⠥⠭⣍⢁⣼⣄⡀⠈⠢⡀
⠀⠀⠀⠀⠱⡜⢆⠸⡀⠐⠒⠒⠀⠀⠀⢀⣠⡚⢻⠀⠀⠀⣟⣇⠀⠀⢈⡇⠀⠀⢸⠉⠙⢿⢦
⠀⠀⠀⠀⠀⠘⢎⢣⣧⡀⠀⠀⠤⠆⢰⠁⢠⠝⠚⠢⣤⡞⠉⠈⣷⠊⠉⠳⣶⠖⠋⠳⣄⡸⠉⡗⢄
⠀⠀⠀⠀⠀⠀⠈⢢⠱⡉⠓⠒⠒⠚⣿⣦⣧⣀⠀⠀⣸⢳⡤⠤⠻⣀⠀⣠⢧⣀⣀⣴⣿⣤⣶⡇⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⢛⡿⣟⠓⠒⠒⠤⢤⣈⢦⣤⣤⡤⢒⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢡⠖⢉⡥⣀⠉⠲⠼⠃⢸⠀⠀⠀⠀⠀⠈⣗⣉⠶⣍⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⣄⠉⠛⠻⠿⣻⠟⢋⢄⠀⠀⢸⢀⠋⠀⠀⠉⠑⢒⣒⣁⠀⠀⠀⣀⣀⣀⢟⠛⠛⠋⢟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢆⠀⡴⠋⠀⠀⠸⣌⠲⠤⠞⣸⠀⢀⡠⠔⠊⠉⢀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⣧⠀⠀⠀⠀⠈⠉⣛⡩⠕⠚⠉⠀⠰⠒⠒⠉⠁⠀⠀⠀⢠⠋⠀⢰⠁⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⡗⠤⠤⠔⢒⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣠⠔⠁⠀⠀⠀⢀⣠⠤⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢾⡄⠀⠈⠙⠓⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠉⠉⠀⠀⠀⣀⡤⠖⠊⠁⣀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢫⡳⠤⠴⠖⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⢀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢆⠀⠀⠀⣀⡠⠔⠚⠉⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢳⠒⠉⠁⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⠒⠉⠁

⠀⠀⣀⣄⣤⠤⢠⢤⡤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠠⠤⢤⣀⡀⠀⠀⠀⢀⡀⡄⠤⢠
⠀⠋⢉⣵⣶⣶⣆⠢⢄⢤⠀⠈⠀⠀⡄⢲⢦⠶⣶⣶⠶⠰⠀⠀⠚⢉⣶⣿⢿⣿⡷⣦⢉⠀⠀⠀⡠⡔⢄⢶⣦⡀
⠀⠠⡘⠿⠿⠿⠿⠗⠘⡠⠃⠀⠀⢀⢼⣦⣶⣾⣖⡷⣤⠠⠀⠀⡀⠸⠿⠿⠿⠾⠿⡿⢀⡀⠀⠀⢈⡟⠠⠊⣋⡸
⠀⠀⠈⠩⣉⡭⠥⠤⠅⠀⠀⠀⢀⠀⠳⡸⠍⠹⢉⣉⠈⠀⠀⠀⠈⠁⠖⢂⣀⣐⡀⠀⠁⠀⠅⠄⠀⠂⠭⠭⠄
⠀⠀⠀⠀⡤⠤⠤⠤⠄⠀⠀⠀⠀⠐⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡄⠤⢀⡀
⠀⢀⣀⣤⢮⣤⣦⣤⣤⡐⡀⢀⠀⣤⣤⠀⠀⢀⠤⠴⡄⢀⣸⣇⡄⠀⣀⢀⡀⢀⡴⣿⡳⣄⡀⠈⡵⣴⠀⡶⡄
⠀⡀⠻⠅⢀⠀⠈⢠⡤⡀⢠⠄⠀⠘⣋⠀⠀⢸⠐⠚⡇⢠⢿⡟⢦⡘⠵⠣⠃⠀⢼⠿⣻⠌⠁⠀⠘⠛⠙⠊
⠀⠓⠒⠒⠒⡀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠁⠀⠈⠙⠉⡁⠁⠀⠁⠀⠁⠀⠀⠀⠀⠘⠁⠉⠛⠁⢀⣀⠴⡆⢋⣉⣅
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⡀⣀⣀⢀⠀⠠⠠⠃⣀⢠⢠⠰⠰⠰⠦⠦⠄⠂⠀⠀⠀⠀⠁⠐⠈⠉⠁
⠀⢠⡤⢆⢊⡩⣉⢓⠒⠄⠀⠀⠒⠋⠉⠠⠈⠈⠉⠀⠀⢀⢁⠔⠀⠰⠋⠀⠶⠆⢠⢄⠘⣀⠀⠀⠀⣀⣩⠀⠄
⠀⢀⠄⠆⠈⢉⠉⠀⡁⠀⠀⠠⢂⠒⠠⠀⠠⠈⠁⠐⠀⡎⠮⢂⠌⠀⠀⠀⠀⠀⠁⢨⢈⣿⡇⠀⢲⠙⠉⠤⠐
⠀⠘⠤⠀⣀⣀⠀⠀⠄⠊⠀⠀⠒⠠⠄⠈⠀⠐⠂⠂⠀⠘⠢⠈⢀⣂⣢⣀⠂⠈⠑⠀⠈⠉⠁⠀⠈⠠⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠘⠀⠀⠀⢀⠬⠀⠀⠀⠀⠐⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡵⢡⠀⠀⢸⠲⢤⠀⠀⢠⣦⡀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠇⠀⠀⠸⠁⠀⠀⢸⢀⣀⠀⠀⢀⠈⢀⠀⠀⠾⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠇⠀⠸⠆⣀⡇⠀⢘⠀⠩⡁⠀⠘⢠⣼⠀⠀⢠⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢰⡄⠈⠇⠀⠘⠑⠶⠆⠀⢰⣀⢸⠀⠀⠈⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡈⠀⠀⠀⠙⡇⠀⢐⠆⣤⡅⠀⢀⠈⢹⡀⠀⠸⠰⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⡀⢰⡇⠈⢹⡔⢻⠆⣄⣥⠊⢹⠀⠀⣿⠖⣿⠑⠲⣯⣡⣸⢤⣼⣆⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠾⣷⣆⣴⣷⣿⡇⠐⢾⡿⢿⡄⠈⢿⠿⠿⠓⠶⡿⠿⢿⠦⣌⣿⣿⣿⢄⣈⣿⣶⣾⢟⣳⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⣋⢭⠤⡀⠛⢠⣼⠀⠈⡁⠳⢾⠀⠀⠦⠤⠀⠀⢸⡀⢈⡇⠀⢀⡀⢙⣃⠉⠙⡿⣄⠈⢳⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢷⣿⣇⠉⠈⡄⢠⡀⠀⡉⢠⠐⠧⢦⣼⠀⠀⠀⠀⠀⠀⠐⣠⠙⣃⠀⠈⢫⠈⢻⡻⠶⢷⣤⣍⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠲⢧⣄⣠⣵⣆⠙⡄⠲⣀⠸⣼⠳⡀⠀⣀⠀⢄⠰⡀⠂⣈⢶⣄⡛⢶⣬⣿⣦⡼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠉⠛⠛⠓⠈⢷⣼⣿⣿⣦⢹⣦⣬⡷⣮⡽⠿⠆⠸⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠗⠀⡏⢸⡀⢠⣶⠀⠀⠀⠀⣤⡄⠀⠀⠀⣠⣤⡀⠀⢀⣄⠀⠀⠀⠀⣾⣿⣧⠀⢀⣀⠀⠀⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠁⠀⠑⠜⠉⠀⡀⠀⣰⠋⠸⠀⠀⢸⠏⡩⡇⠀⢸⠏⠀⠀⠀⠀⣿⠟⠃⠀⢹⣯⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠄⠀⢻⠖⠈⠁⣤⡜⢠⠀⢠⡄⠀⣷⠛⠀⢤⠞⠈⠃⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠲⠾⡇⠀⣯⠘⠀⠀⠀⢀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠜⣾⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡄⣀⠀⠀⠊⣁⣼⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡿⠇⠀⡀⣤⣾⢿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡦⠀⡐⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠐⢁⡐⠀⠐⠀⠐⠈⠉⠋⠉⠉⠁⠂



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋⠙⠛⠋⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⣤⠀⠀⠀⣤⠤⠤⠤⣤⠤⠄⠤⣤⠠⠤⠤⣤⠤⠤⠤⢤⡤⠤⠤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⢾⢟⣶⣲⣚⣛⡓⠠⠒⠿⠶⠶⠾⠿⠷⠶⠾⠟⠲⠶⠶⠻⠿⢶⠴⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⢰⡀⢸⢸⠀⠀⠀⠀⡃⠀⠀⡃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠌⡆⢸⢸⠀⡠⢄⠀⠀⠀⠀⡆⡀⠀⠠⠀⢀⡄⡀⡾⠀⠖⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠅⠚⡑⢸⠸⠂⠀⠀⠀⢀⡀⠀⡇⠀⠀⠠⠀⠈⠀⠀⠁⢀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡞⡃⢸⠘⠀⠀⠀⠀⣠⠟⠀⡷⠥⠄⠀⠀⠀⠰⠁⠀⠀⠈⠈⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠍⠅⢸⢸⠀⠀⠀⠀⡇⠀⠀⠡⠤⡀⠦⠄⡄⠒⢀⠒⠂⠀⠀⠀⠉⠀⠁⢀⡀⠀⠀⠀⣔⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢋⠃⠈⠀⠀⠀⠀⠀⠃⠀⠀⠈⣿⣧⠀⠀⢠⠓⠄⠤⠄⠀⠠⠠⣤⡤⣤⢤⢴⡇⠀⠀⡯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣤⣤⣤⡀⠀⠠⠤⠐⠀⣄⠠⠧⠸⠂⢛⣵⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠺⠦⠦⠓⠚⠛⠛⠛⠛⠛⠛⠛⠒⠒⢸⢹⠙⠛⡏⡗⠒⠂⠒⠒⠒⡗⠒⠒⠒⠒⢺⠇⡏⠛⡇⡇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠘⠐⠂⡇⠇⠀⠀⠀⢄⠐⢓⣢⠀⠀⠀⠘⢸⠃⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡁⠀⠀⠀⠀⠀⠈⠉⠙⠢

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠓⡄⠀⠀⠀⢀⠀⠈⢱⡀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡠⠃⠀⠀⠀⠈⠂⠰⠛⠀⠀⠀⠀⠐⢄⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⣬
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡡⣿⣁
⠀⠀⠀⠀⠀⣀⠴⠂⠇⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠠⠤⠀⠸⠁⢀⣱⡿⠙⠛⠛⠦⣀
⠀⠀⢀⡤⠎⠁⠀⠀⠀⠲⠟⠳⣶⢦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⡄⠀⢸⡇
⠀⠀⠸⡄⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡇
⠀⠀⠀⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡊
⠀⠀⠀⢸⠗⠀⠠⢀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⡇
⠀⠀⠀⢸⡌⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⢻⡇
⠀⠀⠀⠈⢆⡀⠀⠀⠇⠀⠀⠀⠁⠁⠀⠀⠀⠑⠄⣀⠤⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡⡏⠆⠂
⠁⠀⠀⠀⠀⠲⠗⣃⠃⢢⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡴⠖⠋
⠀⠀⠀⠐⠀⠀⠀⠈⠓⠢⢀⣉⠙⠓⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠑⠒⠄⠀⢠⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠤⠶⠶⠖⠒⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠂⢀⣀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⢲⣞⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣤⠞⠉⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⡾⠟⢋⠩⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣤⣴⣶⠿⠟⡋⣃⡈⠐⢂⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⢀⣀⣤⣶⡿⠷⠜⠋⠡⠀⠈⠀⠀⠘⢷⡄⠈⢂⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⠿⢛⠉⠁⠒⠙⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⢆⣀⣠⣤⡶⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣦⠸⢛⣩⢥⡲⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢀⡶⠿⣛⠫⢭⣤⠶⣾⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣤⣶⡾⠿⣛⣭⣿⡶⠿⣞⣗⣥⠬⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡐⢨⣿⣷⣾⣿⣏⡦⠽⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠾⠟⠛⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠤⠐⠒⠂⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣠⣤⣤⠶⠖⢒⣻⣿⠿⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡿⠛⠡⠤⠾⢿⣾⡿⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠈⠉⢳⢤⣀⣀⡀
⠀⠀⠀⠀⣀⠤⠒⠊⣉⠤⢠⡗⣦⣤⣼⣇⡀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠠⠤⣈⠉⠛⠒⠦⣄
⠀⠀⠰⠊⠀⢀⣠⣬⣾⠿⢀⣉⣿⣿⠿⣿⣭⣽⣷⣷⣤⡤⣀⣀⠀⣷⠀⠀⠀⢸⣺⣿⠯⠝⠂⠀⠀⠀⠙⠆
⠀⠀⠠⡀⠀⠻⠿⠿⢟⡋⠉⠁⣀⣤⡴⢖⣛⣫⣭⠽⣿⠟⠾⢶⣿⣿⣶⣖⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠈⠒⠦⣄⣀⡀⠈⠀⠈⠛⠛⠋⠉⠁⠀⢶⠿⠶⠚⠛⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠦⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⠤⠤⠴⠖⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠦⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠾⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡀⢀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⢤⠴⠆⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠃⠈⠂⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢀⠁⠄⠀⠀⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⢀⠀⢀⣀⡠⠀⠀⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠐⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢩⠀⢀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢘⠀⠀⢨⠁⠀⢀⠀⣀⡠⠄⡄⠤⠈⠡
⠀⠀⠃⣀⡁⠀⠂⠈⠅⠀⠀⡰⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢂⠘⠈⠀⠐⢈⠀⠀⠸⠀⠀⠈⣉⠀⠈⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠈⠁⠀⢠⠘⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⢀⠀⠀⠀⠀⡄⢀⣡⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡍⠅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠊⠀⠁⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠇⠢⠠⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣄⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢰⡄⠀⡴⠂⠀⡄⡄⠀⢰⠀⠀⠀⠀⠀⠀⠾⠁⢈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠠⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⡄⠉⡁⠘⠒⢒⡓⢊⠉⠙⡆⠀⠀⠀⠀⠀⡀⢀⠀⠤⣁⡀⠀⠀⠂⠀⠀⠀⠀⠠⠒⠉⠀⠄⠠⠈⠉⠒⢄
⠀⠀⠀⠀⢀⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⠌⠥⠢⠳⠈⠁⠭⠄⢤⠄⠀⠀⠀⠀⠀⠁⠃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠤⠤⠀⠤⠠⠔⠆⢸
⠀⢠⠀⠀⢈⠑⠀⠀⠀⠄⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠈⣀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁

⢯⣿⡿⢿⣿⣮⣿⠻⣷⡼⡛⡙⠈⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠓⠯⣙⡤⠇⠃⠄⠊⢰⠀⠀⠀⠀⣀⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠐⠀⠀⠀⠀⠈⠒⠻⠶⠻⠆⠀⠀⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⠀⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⢿⣧⣴⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⠀⠀⠀⠀⢤⣄⣇⠀⠀⠀⠀⠀⠀⠀⠦⣿⣋⠈⠀⠀⠀⠀⠀⢠⣤⠲⠶⢷⢶⣾⣿⡼⠿⠿⠿⠏⢩⣤⣤
⠛⠛⠀⠀⠀⠀⠀⠙⠛⡃⠀⠀⠀⠀⠀⢸⣿⣿⠿⠀⠀⠀⠀⠀⢀⢸⣧⣤⣆⣿⣿⣽⣆⡇⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⢀⠀⣀⣀⣤⣠⠴⣷⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣤
⣠⡤⢀⣻⠇⠀⠀⠀⠀⠀⣖⠀⠀⠀⣴⢿⢿⣾⠴⢶⣴⣿⣿⣿⣷⣾⣿⣿⠼⢿⣿⣿⣿⣿⠀⠀⣀⣤⣾⣿⣿
⣾⣧⢉⠄⠃⠀⠀⠀⠀⠐⠋⢠⣶⣶⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⢼⠀⢸⣿⣿⣿⣿⠓⢮⣍⣿⣿⣿⣿
⣭⣸⠻⡛⠒⠓⠛⠐⠛⠾⠿⠿⣿⣷⣿⣾⣴⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣌⣿⣿⣿⣿⠀⠀⠉⢻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣾⣛⡲⣄
⠀⠀⠀⠀⣰⠞⠩⠍⠩⠉⠭⠙⢦⡀⠀⠀⠀⠀⢀⣴⣒⣚⣓⣒⣦⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⢀⡴⢛⣭⢽⡇⡷⣋⣙⣮⣷
⠀⠀⠀⢸⣧⣬⣥⣬⣤⣬⣤⣥⣤⡷⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣭⡇⠀⠀⠀⠀⠀⣼⠛⠛⢷⠀⠀⠀⠀⢀⡟⣴⣫⣄⢸⡟⣿⠷⣛⡭⡄
⠀⠀⠀⢘⡷⠶⠶⠴⠶⠦⠴⠶⠶⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠙⡆⢸⡇⠀⠀⠀⢸⠰⡇⠳⡞⢹⡤⢖⣋⢹⡇⡇
⠀⠀⠀⠀⣿⠛⢿⡛⠉⠉⢛⡿⢻⠇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠛⠁⢸⠀⠀⠀⠀⠘⣇⢳⡸⣿⠆⣂⡛⢛⡼⢡⠇
⠀⠀⠀⠀⠈⠛⠛⠛⢦⡾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡀⠀⠀⠀⠀⠘⠦⣙⠒⠾⠭⠟⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⣤⢦⡞⢳⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡶⣤⡀
⠀⠀⠀⢠⣿⣹⣌⣧⣼⣡⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠨⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠍⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠂⠙⠮⣷
⠀⠀⠀⠘⡇⠈⠉⠉⠉⠉⠁⢸⠇⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿⠶⣄⠀⠀⠀⢺⣥⠤⣅⣤⢥⣨⠤⣬⡇⠀⠀⠀⠀⢰⠇⠈⠀⡁⠈⣰⠋
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣧⠴⠃⠀⠀⠀⠀⢹⡀⢸⠀⠀⡟⢠⡏⠀⠀⠀⠀⢀⡞⢳⣅⣤⠴⠛⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡒⠚⠛⠒⠒⠒⠚⠓⠒⡶⠀⠀⠀⠀⠀⣧⠘⡇⢸⡇⣼⠁⠀⠀⠀⣟⠋⡶⠋
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠛⠁⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⣠⠟⠓⢶⠚⢧⡀
⠀⠀⠀⠀⠀⡴⠖⠛⠁⠘⢦⡀⠀⠀⠀⠀⣠⠶⠒⢲⡴⠒⠲⡴⠖⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⣹⡄⠀⠀⠰⣟⣛⣛⣛⣛⣛⡷
⠀⠀⠀⠀⣾⠛⠛⠛⠋⠛⠛⢳⠀⠀⠀⢠⣏⣀⣀⣈⣁⣀⣀⣁⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⢀⡴⢯⣀⠀⠉⡧⠀⠀⠀⠸⣄⣤⠶⢋⣽
⠀⠀⠀⠀⢿⠉⢻⡏⠙⡟⠉⡿⠀⠀⠀⢸⣿⠯⠼⣿⠬⠖⠦⠴⣿⠽⢛⣿⠂⠀⠀⠀⢀⡤⢿⡄⠀⠈⠓⢶⠃⠀⠀⠀⠀⢿⡤⠖⢻⠇
⠀⠀⠀⠀⠘⡇⢸⡇⢸⡇⢸⠃⠀⠀⠀⠘⢯⣽⣓⣛⣛⣛⣛⣛⣛⣛⣯⠿⠀⠀⢠⡖⠛⣆⠀⠙⢦⡀⣠⠞⠀⠀⠀⠀⠀⠘⡷⠚⡿
⠀⠀⠀⠀⠀⠻⠤⠧⠼⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠓⠞⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⡟⠷⢶⠀⠀⠀⠀⢀⡴⢶⡀⠀⡴⠶⣄⠀⠀⠀⠀⢰⣟⣚⣳⢀⡼⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢟⡷⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡾⢻⣳⣟⡦⠀⠀⢠⠟⠀⣦⠙⣾⠁⣦⠙⣦⠀⠀⠀⠀⡇⠀⡇⢈⡿⠛⣟⠀⠀⠀⠀⠀⠀⣠⠞⣱⢋⡞⠀⠀⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠟⠚⣧⠟⠀⠀⠀⢸⠀⢰⠏⠀⣿⢠⠏⠀⣸⠀⠀⠀⣠⠇⠀⢷⡏⠁⠀⠈⣷⠀⠀⢀⡴⢚⡵⢾⡵⠋⠀⠀⢀⡞
⠀⠀⠀⢴⠋⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⢷⡘⢃⡴⢿⡌⠃⡰⠋⠀⠀⠀⡏⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠘⣟⡽⠞⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⣤⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠙⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠉⢷⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠒⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠁

⡿⢿⠿⠿⡿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣻⣿⣟⣻⣿⣻⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢰⠀⠀⠀⠀⠀⠀⡀⠉⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢃⡀⠠⢀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠆⠈⠙⠲⣄⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣰⠏⠀⠐⠀⠀⠀⠀⠀⠙⢢⡀⠎⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠃⢈⡿⠷⠀⣀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡛⢦⡀⠂⢄⠀⡤⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢿⡀⠀⠙⢦⡙⠢⡀⠀⠀⣠⠎⠠⠊⠀⠀⠈⠓⢤⣑⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⠀⡙⢦⡀⠀⠉⠒⢄⣀⡴⠃⠀⠀⣀⠀⠀⠀⠀⠄⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠈⠋⢻⠀⡉⠢⣄⠀⠀⠻⠶⢄⠀⠀⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠔⠉⢂⡀⠈⠉⢹⣠⠞⠳⣤⡁⠀⠀⠑⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠄⠠⠀⡵⢢⡀⠈⠡⣴⡾⢧⡈⠓⠦⣄⡀⠘⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠞⣡⠏⡉⣄⡀⠈⠀⡸⠀⢀⣄⣀⣉⡙⠁⡟⠛
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠆⢘⠸⡟⠙⠋⠈⢁⡜⠱⠦⣷
⠀⠀⠀⠀⠀⠀⣬⡁⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⡁⢅⠆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⣶⣶⡤⢀
⠀⠀⠀⣠⠠⠀⣐⣤⠀⠈⠀⠉⠀⠀⠀⠐⠁⠔⡴⣿⡛⠦⣤⣀⠀⠀⠀⠀⠀⣼⡧⠬⠁⠠⠃⢀⣩⣷⡀⠀⠀⠀⠀⣀⠀⠌
⠀⠀⢻⡂⠙⣏⣄⣀⣦⣽⣖⣳⠂⠀⠀⠀⠐⣺⠀⣬⣽⡉⣍⠯⣠⠀⠀⠀⠀⣝⠳⢶⣿⣦⣴⡯⠾⢃⠁⠀⠀⠀⠀⠀⠐⠀⡨⠃
⠀⠀⠈⠁⠐⠃⠟⠿⠿⠿⠋⠙⠁⠀⠀⠀⠈⠉⠉⠁⠈⠁⢈⠁⠁⠀⠀⠀⠀⠙⠛⢛⠰⠆⠀⢁⠀⠉⠀⠀⠀⠰⢯⡈⠁⢀⢃⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠚⠚⠂⠊⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⢀⣈⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀
⠀⠀⠀⠀⣠⣤⣔⠖⡤⣤⣈⡀⢀⠀⠈⠈⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⣍⡋⢷⡀⠀⠀⠀⠀⡄
⠀⠀⣠⡖⠾⠀⡈⢠⡏⢲⢟⠉⡂⡀⠀⠀⠠⠢⣄⠀⠀⠀⣸⠀⠠⠀⠀⠀⠀⠀⠈⠏⠫⢿⣿⣥⣝⣿⣆
⠀⠀⠘⠢⠤⠀⣠⡲⡏⠱⣺⠲⠟⠀⠀⠀⠠⢠⠀⠈⠀⠈⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠐⠒⠊⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⡀⣄⠀⠰⡢⠐⠀⠉⢁⣀⠀⠀⠀⠠⢚⠓⠂⠀⠉⠾⠟⠂⠀⠀⠀⠀⢀⠀⠔⣈⠀⠐⠀⣀⠀⠀⢰⣏⣩⣿⠿⣿⣼⣷⡦⣄⡀
⠀⠀⠐⠘⠈⡥⠰⣀⣤⣤⠔⠀⠊⠀⠀⠀⠻⣖⠒⡐⡃⠀⢀⡀⠡⠂⠀⠀⠔⢀⢀⠀⠀⠒⢀⡀⠀⠐⡀⠀⠈⠙⠱⠤⡼⡿⡊⢢⡵⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠅⠐⠉⠀⠀⠀⠈⠙⠶⢤⡀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠛⠛⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣖⡲⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢳⡏⢀⣀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠸⡉⡝⣛⠛⠉⡆⠻⠀⢸⡿⠿⠛⢣⣴⠿⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⣀⢸⣶⠀⠆⣡⡀⣀⠄⠀⣥⠀⠀⠀⠀⠆⠀⠀⠐⢞⠛⠛⢛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡤⠀⠀⣈⣬⣤⣭⣌⠉⠉⠁⠀⢸⡇⠉⣩⡽⣿⠛⠛⢦⡘⢂⡀⢉⣥⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣿⡇⠀⣜⣿⣿⣿⡝⣿⣠⣴⣾⣶⣿⢛⠏⡘⠀⠘⣷⠀⡸⣠⢴⠀⢸⣿⠘⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠓⠋⠻⢿⣿⣿⢿⠉⠉⠉⣽⣿⡿⠘⢄⣇⠀⠀⣸⣿⣏⡗⠐⠀⣸⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣀⣀⣑⣒⡚⠛⠃⠀⠀⠀⢈⣉⣉⡉⣀⠬⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠶⠻⠿⢏⣸⠛⠻⣯⣹⣿⠿⡛⠫⣿⠿⠿⢿⣟⣷⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡉⠇⣬⢄⡀⢸⡜⠦⠀⠛⠚⡟⠒⠂⠥⠿⠀⣀⣸⣾⣿⡿⡛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠸⠶⠆⠉⣀⡀⢀⠀⠫⢷⣴⣶⣿⣷⠶⣦⡴⠶⣶⣶⡾⠟⣏⣭⣇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀⠀⠀⣸⡦⢄⣀⠀⠀⢀⣈⣴⢸⣽⣿⣿⣿⣷⢸⣿⠀⠀⠁⠀⣠⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠩⠭⣉⣑⣀⣄⡀⠀⠠⠤⠟⠉⠻⢿⣿⠿⠿⣞⣅⣀⠥⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⡿⢿⡉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣉⣉⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠶⣯⣤⣀⣈⣁⡈⠐⠽⢛⣿⣭⣍⡉⠉⠉⡉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠋⠉⠉⠂⠒⠛⠛⠛⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠀⡀
⠀⠀⠀⠀⠀⢀⡠⣴⣿⣷⣶⣄⢀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢷⣶⣧⣼⡀⢠⠆
⠀⠀⠀⠀⠔⠃⠀⠀⢸⠋⢹⡿⣿⣷⣄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿⢸⡏⢹⡟⢻⣦⡾⠂
⠀⠀⠀⠀⠤⠒⠒⠤⢤⣀⠸⣇⣿⣿⣿⣷⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠁⠰⠃⡼⢃⣠⠇⣺⡷⡿⠚⠯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣿⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⣄⣁⣦⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠟⠃
⠀⠀⠀⠀⠀⢀⣤⠤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣾⣷⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⢤⣀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣾⢻⣷⣤⣄⣀
⠀⠀⠀⠀⠈⢓⡦⣴⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⣷⣿⣖⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⣤⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠺⡷⠿⠟⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡇⡀⠀⠀⠀⠲⣦⣄
⠀⠀⠀⠀⣿⡆⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡞⠀⠀⡄⠈⣿⣯⣦⠀⠀⠀⢾⣶⣤⣴⡿⠋⠈⠻⢦⣤⣤⣤⡿⠟
⠀⠀⠀⠀⢿⡟⠀⠃⡘⠱⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣾⠀⠀⠀⢿⠀⢸⡿⡌⡆⠀⠀⠀⠉⠉⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠒⠂⢶⡄
⠀⠀⠀⠀⠘⣿⣄⡀⠠⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⢸⠀⢸⡇⣇⠁⠀⠀⠀⢰⣁⡀⢀⣠⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⢠⠠⢊⡄⠀⠀⡰⠁⠀⠀⠀⠀⠠⡇⢽⠀⠀⠀⠀⠈⠀⢸⣧⣿⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠸⣧⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠖⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠈⡏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠈⠱⠎⡀⢡⠆⠀⠀⠀⢄⢠⡆⠀⠀⠀⠀⡟⢰⡟⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣐⣶⠧⠐⢲⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣈⢳⡄⠈⠀⠀⠀⢸⡌⣿⣦⠀⠀⢸⣷⣾⣿⡟⠀⠀⠀⠀⠀⢀⡂⠈⣽⠟⢻⣿⡿⠦⢴⣾⣏⢀⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣈⡒⠀⠀⠸⣧⣹⣿⣧⡄⣸⣿⣿⡿⠁⠀⠀⣠⣤⡀⠈⣙⣿⠇⠴⣾⣿⣦⣶⣦⣿⣿⠄⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⢿⣿⣿⣧⣿⣿⠟⠀⠀⣤⣀⡀⣼⣿⣿⣍⣥⣴⣾⣟⣿⠩⢿⣿⣯⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣄⠓⠒⠒⠒⢢⡐⠶⠒⠒⢲⡌⠉⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⢿⣶⣻⣶⣶⣽⣿⡿⠿⠿⠿⠛⠛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠬⣿⠠⣤⠤⠤⢼⡅⢠⡤⡤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠠⣀⠀⠀⠀⠀⠁⠀⡀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⠀⠀⠀⠀⢺⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠠⠂⠀⠐⠁⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣏⣤⣄⠠⣄⣸⣇⣤⣀⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡⣿⠈⠉⠁⠠⣽⡆⠉⠉⠴⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⣀⡈⢿⣆⣤⣀⣄⣿⣧⣤⣤⡄⢬⠞⣦⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡎⠀⠘⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣛⣛⣛⣐⣰⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠇⠠⣄⡽⠁⠀⠀⣠⣄⡀⠀⢈⡛⠛⠛⠛⠓⠈⠹⠗⠂⣀⣄⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣞⣉⣿⣿⣿⣿⣶⣶⣶⣿⣿⡇⠠⣄⡀⣍⡁⠛⠷⠦⡹⣿⣛⠛⠛⠶⠶⢶⣤⣤⡤⣼⡿⣿⣧⡀⢀⣤⣴⣶
⠀⠀⢀⣿⣦⡀⣄⢀⣀⣿⣦⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠮⡛⠶⢿⣛⠲⣤⣀⣀⠉⠁⠐⠒⠐⢛⡋⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⠛
⠀⢀⠊⠁⠊⠛⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠢⡀⠙⠳⣴⠛⠛⠛⠛⠶⣶⣤⣄⡀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣷⣆
⠀⠠⡼⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠑⠀⡈⠻⠦⣠⣴⣶⣶⣿⣽⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠊⠭⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠞⠉⠉⣛⠿⡖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠀⠀⠀⢀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⠭⠭⠭⠭⠭⠭⠍⠁⠈⠩⠡⠤⠤⠤⠤⠤⠤⠤⠥⠤⢸⡏⡇⠀⠀⠀⠀⠀⠀⠀⠳⢀⣒⣡⠞⣷⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢡⠀⠀⠀⠀⠀⠀⡠⢶⡟⢅⣀⡠⢓⡶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢸⠀⠀⠀⠀⠀⡰⠁⡸⢧⣀⣀⡠⢼⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡤⠶⠬⠤⠤⠤⠬⠭⡽⢻⠀⢰⠖⠻⠿⠿⠿⠿⠛⠞⣹⠘⠀⡇⠀⠀⠀⢠⠃⡰⠁⠀⠀⠀⠀⢸⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠷⠤⠤⠤⠤⣤⣤⣤⡶⠾⠿⠿⠷⠶⠶⠶⠶⠶⠾⠿⠿⠀⡇⠇⠀⠀⠀⡎⢠⢧⠀⠀⠀⠀⠀⠸⣠⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠒⠚⠒⢄⠀⡀⣸⡀⡇⠀⠀⠀⠀⣀⠽⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣸⡄⠀⠒⠒⠒⠒⣲⣤⠖⠉⠁⠀⠀⠉⠻⣏⠉⠉⠉⢻⠏⠀⠀⠀⠀⠀⠈⣧⢹⣿⠿⢿⠗⠀⠈⣉⣇⣠⠤⠊
⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣠⠹⠿⢯⣉⣉⠉⠉⣈⡠⣏⠀⢀⡤⡶⠶⠞⡶⣼⠉⠉⢙⠃⠀⡖⠒⣐⠂⠩⠝⡇⠀⠈⢙⠇⠒⠊⠉⠁⠀⢸⡀
⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠸⠤⠤⠤⠠⠤⠤⠤⠄⠀⢳⡴⡞⠠⠄⠀⠈⠁⡛⣒⣒⣒⣆⠰⣣⡀⠁⢀⣖⡀⡗⣒⣒⣛⡒⢂⣐⣒⣒⣒⣒⣓⣂
⢸⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠁⠀⠉⠉⠀⠀⠉⠛⢢⣕⣒⣠⡞⠀⠀⠀⠀⠈⠑⠒⡻⣦⣤⡭⠊⣀⢀⣀⣸⠀⢙⣃⡠⠤⠴⠀⣠⠄
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠽⢲⠛⠈⢦⠀⠀⠀⠀⠀⡜⢠⠚⠙⢽⣆⠙⢷⣤⣬⣧⣞⣙⣲⣶⣤⣭⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⢄⠀⠇⢱⡨⣄⠀⠀⠀⠀⠇⠀⠳⢄⣰⠉⠛⠃⠚⣁⠥⠉⠉⠉⠉⠉⠉
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠣⡔⠫⡁⠈⡇⢡⢹⠀⠀⠀⢸⠀⠀⠀⠀⠉⠙⡊⠉
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠈⢦⡈⠢⡅⢸⠀⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣉⣀⣀⣵⣠⡽⢞⠊⠀⠀⠀⠀⡗⠤⠤⠤⠤⠄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⢄⡠⠟⣤⢠⠇⠀⠀⠀⠀⠦⣀⣀⣀⣜⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⡇⢀⠀⠀⠀⠀⠀⡴⠁⡸⠁⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡸⠀⠀⡇⢰⠀⠀⢀⠤⡋⢀⠜⠁⠀⡇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠐⢣⠀⡔⠥⠼⡄⠀⡇⠀⢈⣧⠀⠀⢸⠁⠈⠓⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣠⠜⠀⠙⠦⡀⠛⢢⠘⣄⠈⠈⡆⠀⠸⢄⣀⣈⣋⣉⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣯⣤⣤⣤⣤⣤⣬⣷⣧⣤⣤⣤⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠠⠄⠒⠉⠈⠢⡀
⠀⠀⠀⡐⠉⠀⠄⠂⡀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⡄⠄⠀⠀⠠⠀⠐⠀⠈⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⡗⠄
⠀⠀⠀⠰⠀⠀⢀⡀⠁⡐⠐⢄⠈⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠘⢄⣀⣀⠦⡀
⠀⠀⠀⠀⢃⠀⠇⠈⠉⠁⠀⠈⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠈⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣀⣴⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡩⢣⠂⠀⡑⠤⣆⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡰⠁⠐⠀⡆⠀⠀⠐⢄⠀⠉⠺⠲⡰⢠⢦⣀⣀⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠤⠔⠺⡇⠀⠀⠀⢃⠀⠀⠀⠀⡆⠀⢀⠏⠣⠼⣁⠉⢠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄⡧⢰⡈⠒⣘⠢⢀⡵⠤⢠⠐⢁⠀⠉⡋⠙⣄⠈⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠭⢠⠼⡄⣁⠒⣎⠀⢑⠁⠈⡒⠁⢙⠁⢱⠊⡽⠧⠈⠓⠓⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠇⠈⡀⠰⠀⠀⠀⠀⡁⠀⡄⠀⠖⠉⠀⠀⢀⣀⠤⢄⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠘⡄⡡⢀⣁⠀⠇⠀⠀⠀⠁⡌⠀⠀⠁⡲⠓⠈⠁⠐⡴⠀⠐⠀⠱
⠀⠀⠀⠀⠀⠀⠊⠁⠙⠇⠀⢪⠀⠙⠀⠀⢹⠄⠰⠀⠀⠰⠀⣄⣄⣀⡀⠈⠒⠄⠒⠊⠀⠀⡘⠑⡖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣰⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠉⠢⡀⠐⠤⠒⠀⡠⠒⠀⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠤⠄⠠⠔⠂⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⡛⣁
⠀⠀⠀⠀⠀⠠⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⡐⠦⣄⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⠈⠑⠒⠲⠔⠒⠒⢒⠇
⠀⠀⠀⠈⠑⠒⠒⠢⠤⠔⠊⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣽⡆⠀⠀⠀⠀⠈⣷⣶⣶⣶⣤⣴⣾⡟
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⢁⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⣀⣤⣴⡶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⣲⣶⣄⠀⠀⠀⢀⢤⠄⠶⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⢀⣉⡉⢉⡉⠉⢢⠀⠀⡁⠀⠀⠀⠀⠀⢠⡴⣏⣤⣾⣿⢟⠋⠹⠃⠀⠀⣧⣿⣶⡾⠛⠛⣋⡙⢻⣆⠀⠀⠀⠀⠀⣰⡷⠺⣿⣯⡭⣿⣆
⠀⠀⠀⢸⣿⢶⢻⣽⠀⢸⣷⣾⡇⠀⠀⠀⢀⣴⣛⢠⣶⣿⡟⠁⠰⠈⠀⠀⠀⠀⠈⠉⠙⢀⢰⣿⣻⣿⠀⠃⠀⠀⠀⢀⣾⠏⠀⢂⢬⣿⣷⡄⠾⣧
⠀⠀⢠⠐⣯⣿⣷⣿⡆⢼⣿⣿⠇⠀⠀⢠⣾⣓⣮⣿⣽⢟⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠗⠉⠀⠀⡀⠀⠀⢠⣿⠟⠰⠤⠜⡷⠬⣿⣷⢶⡿⠃
⠀⠀⠈⠢⠀⠀⠈⠉⠠⠞⠋⠁⠀⠀⠀⠉⠲⠾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠁⠠⠒⠃⠀⠀⠈⠛⠒⠒⠂⠀⠀⠀⠼⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢠⠄
⠀⠀⠀⠀⠀⢀⣠⡶⠞⠓⠀⡀⠀⠀⠀⠀⠀⣴⡚⢫⡭⣭⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣧⣅⣼⠦⡀⠀⠀⠀⠀⣀⢠⠒⢠⠀⠀⢶⣶⢂⡄
⠀⠀⠀⢰⠋⠀⠀⠑⢈⡧⢤⣴⣪⠄⠀⠀⠀⣟⢷⡈⠙⠛⠁⠠⠄⢳⠀⠀⠀⠀⠀⠜⠁⣀⠄⠀⠈⠹⣠⣧⠀⠀⠀⠀⡏⠨⠁⠀⠀⠀⠲⣿⡿⡇
⠀⠀⠀⣅⠡⠶⠒⠀⠘⢃⠘⢁⢼⠂⠀⠀⠀⢃⠈⠿⢶⣆⣴⡴⡶⢤⡆⠀⠀⠀⢀⠀⣸⡭⡳⣆⠀⢸⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡗
⠀⠀⠀⢶⡒⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⣈⡉⠈⠃⠀⣸⠇⠀⠀⠀⠘⠀⢿⣿⣎⢯⡇⠈⣷⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣷⡿⠃
⠀⠀⠀⠘⠓⠒⠒⠚⠃⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠓⠛⠃⠁⠀⠀⠀⠀⠀⠦⡀⠉⠉⣩⢅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣄⠂⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⢂⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⣾⠿⠁⡆
⠀⠀⣀⢈⡉⠀⠈⠱⢿⣄⣤⡷⠗⠋⠍⠀⠀⢀⠀⢠⡄⠴⣖⡫⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣶⡞⠁⠀⠀⠀⠀⠀⣾⣁⠎⣁⣹⣥⣿⣾⡇
⠀⠀⠑⠫⠤⠆⠐⠟⣽⠿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠉⠇⠸⠟⠁⠀⡐⠀⠀⠈⠁⠀⠤⠠⠄⣰⣇⢸⡗⠈⠀⠐⠀⠀⠀⡿⢘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠃⠐⠈⠀⠀⠀⠀⣇⢸⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⠔⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠀⠒⠰⠆⠀⠀⠀⠀⠀⠀⡀⠐⡠⠒
⠀⠀⠀⠀⢠⠀⠄⠄⠀⠄⢰⡆⠆⠀⠀⠀⠀⢰⠤⠀⠒⠐⠒⣀⣈⣀⣀⠀⠀⠀⠀⠀⣤⠈⠀⠀⡀⣀⣤⠽⠞⠛⠀⠀⢰⠁⠀⠑⠀⣄⡀⠀⢀
⠀⠀⠀⠀⢸⣄⡀⣀⣀⣰⠀⣿⣤⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢀⡜⢁⡠⠴⠞⠋⠁⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢉⡐⢀⠀⢰
⠀⠀⠀⠀⢀⠁⠀⣿⣿⣿⠀⣿⡿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⠐⠁⠐⣈⣴⡿
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠰⠋⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠼⠿⠿⠟⠃⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⠀⠀⠠⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠠⠋⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⡔⠳⣾⣷⣿⣤⣦⡀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⠟⠋⠛⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣰⣸⣯⣿⣿⣿⣤⣀⠀⠈⢡⣵⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢠⢻⣿⣿⡿⢿⠟⠛⢹⣷⡀⠈⢙⡁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⣾⣿⣷⢀⠈⣇
⠀⠀⠀⡀⠄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⢶⡟
⠀⠀⠀⠈⠁⠀⠀⠀⠀⢽⣿⣿⣿⢿⣿⠆⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⣿⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣻⣿⠭⠛⠁⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠙⠉⠙



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡛⣿⣋⣿⣿⣴⣿⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢶⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡐⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁⠀⠀⡀⠀⡟⡉⠐⢘⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⠆⠀⠀⣦⠦⠿⢀⠁⢨⡉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⠇⠀⠀⠁⠀⡉⠘⠀⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣼⡿⠛⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⣴⣶⣶⣶⣶⣶⣶⣾⣷⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢟⢱⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠀⠀⠀⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙
⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡄⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⢆⠀⠄⠀⠀⣀
⠀⠂⡀⡀⠀⠀⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠿⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠑⠲⠒⠂⠉
⠀⠀⠀⠉⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠠⠑
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣀⡀⠐⡀⣰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢚⠭⠉⠑⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠒⠀⢀⡀⠀⠀⠀⡀⠤⠀⠀⠀⢀⠐⠁⠀⡀⠀⠀⠀⠈⠈⠐⠖⠁⠐⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠱⠆⡉⠀⠉⠐⠀⠀⠀⠀⠀⠸⠀⡠⠈⠂⠀⠐⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣤⠐⠒⠢⠤⣀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠳⣄⠀⠒⢀⡠⢞⠐⠈⠀⠀⠉⠈⠲⡕⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⣦⣄⣀
⠀⠀⠀⠀⠈⠛⠒⠀⠈⠁⠀⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⢀⡘⠇⠤⣬⢉⠋⣩⢀⠀⠀⡠⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠳⣄⠀⠀⡔⣿⣹⢳⣙⣷⢺⡤⡍⢸⡀⠀⠀⠀⠀⠤⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠧⣀⣋⠲⢿⢯⠽⣊⠷⣟⣺⢟⡆⠀⡗⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠡⡆⠙⡝⠲⣶⡉⣷⣿⣉⣟⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢼⡇⢈⡽⠠⠼⠧⣩⠈⠼⠀⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⡠⠂⡑⠀⠀⠀⠀⠈⠨⠛⠃⠳⠄⠤⠀⠤⠰⠇⠀⠀⠀⠀⠀⣠⡤⠄
⣅⣀⠀⠀⠻⠿⣿⣶⡤⠀⠙⠲⣄⠀⠀⠀⠠⡀⠀⠀⢄⠀⡈⠁⠀⣅⠀⠀⠀⠀⠀⢰⠈⠄⠀⠰⠠⠀⢀⠎⠀⡠⠀⠀⠀⢨⣀⠀⠀⢴⣦⡄⠳⠆⠀⠉⠳
⣿⣿⣿⣶⣦⣤⣀⣀⣀⣠⣤⣴⡿⠀⠀⠀⠀⠈⠢⣀⠀⠉⠘⣦⠀⠀⠓⠦⠦⠴⠴⠃⠴⠆⠀⠁⠠⠔⠁⡠⠎⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣉⣁⣀⣀⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠁⠀⠉⠁⠒⣂⠁⠂⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠤⣤⣤⡤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿
⣶⣶⣶⡶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠀⠐⠀⠐⠀⠐⠀⠐⠀⡄⠀⠀⠀⢀⠀⡀⠂⢀⠀⠀⠀⠂⠀⣀⣀⢠⡄⢀⠄⠀⠀⠀⠀⠐⠀⠠⠄
⢈⠀⠈⠀⢈⠀⢈⠀⢘⠀⠁⠀⠀⠀⠰⠃⠀⠀⣈⡀⠠⠄⠀⠀⠉⠉⠀⠁⠉⠀⠄⠀⠄⠀⠀⠤⠀⣠⣤⣤⣄
⠈⠀⢈⣠⣬⣤⣌⠀⠀⠐⣾⣿⣷⣶⡀⢰⣿⣿⣿⣿⣿⣷⡆⠔⢀⣀⠦⠀⡐⠘⠀⢀⠀⢀⠐⠀⠀⣿⣿⣿⣿
⠀⠀⠿⣿⣿⣿⣿⢇⠀⢸⣿⣿⣿⣿⠀⡸⠹⠏⠏⣿⠙⠛⣇⠀⠈⠁⠀⠖⡆⢈⠄⠈⠂⠠⠤⠂⠀⣿⣿⣿⡟
⠀⠂⠓⠌⠉⠉⣡⠈⡄⠀⠙⠛⠛⠃⡀⠈⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⣀⡠⡤⣀⠋⠉⠩⠑
⠀⠀⠠⠀⠀⠀⠀⠄⡠⠀⠀⠒⠄⡤⠁⠀⠀⠀⡨⡀⠀⠀⣔⠳⠠⢘⠍⠉⠩⠇⠠⠊⡩⠄⠀⠁⠀⠀⡤⠀⠄
⠰⠀⠠⠴⠀⠀⠠⠀⠀⢈⠠⢠⠴⠁⠈⠀⢀⠐⠀⣀⣤⣤⣤⣄⠀⡄⠀⠈⠀⠀⠀⠀⠇⠀⠀⢀⢀⡐⠆⠀⠘
⠀⠐⠀⠀⠀⢀⣃⠀⠀⠠⠊⠑⡸⠀⠀⠀⠀⠄⢸⣿⣿⣯⣿⡿⠂⠂⠠⠥⠈⠀⠀⠴⠋⠑⡀⠆⠪⠅⠦⠠⢐
⠀⠘⠄⠀⠀⠟⠛⢓⠀⠀⠀⠀⠖⢆⠁⠄⠀⠂⠈⠉⠉⠅⠀⠀⠀⠈⠉⠀⠀⠴⠀⢀⠄⠑⠃⠈⠢⠿⠁⠑⠬
⠀⣠⡂⠀⠀⢀⣤⡀⠐⡀⠀⣀⢸⠸⡀⠀⢚⡤⣶⣾⡿⣿⢿⡿⣿⣿⢿⠶⡦⣄⠨⠀⢀⠀⠀⠀⡠⠆⠀⠀⢀
⢀⠀⠀⢀⠀⠹⠛⠻⠀⠐⠊⠀⠊⠃⡓⠀⢾⣾⣷⣦⣿⣶⣿⣽⣦⣯⣾⣿⣧⣿⡆⠀⠀⡜⢀⠀⠉⠀⠀⠘⢨
⠈⠀⠀⠈⣤⡤⠤⠤⠤⠄⢠⠄⠀⠀⠀⡀⡘⠿⣿⣿⣯⣽⣽⣭⣭⣽⣿⣿⡿⠟⠠⠠⠼⣷⠚⢠⡁⠠⡄⢀
⠀⠀⠉⣶⠛⠒⠂⠀⠀⠀⠈⢈⠶⠒⠁⢀⠁⡀⢀⢤⣉⡉⠉⠉⠉⣉⡁⠀⠀⠢⢄⡀⠀⢠⠀⢀⠀⠈⠀⠂
⢀⡔⠁⠀⠃⡀⠤⡀⠀⠤⠔⢊⠀⠄⠐⠁⠈⠋⠓⠞⠛⢋⠀⠀⣾⣿⣿⡆⠀⢰⣄⣦⣶⡾⠀⠀⢁⣀⢈⡀⡀
⠀⡀⢀⡀⢀⡀⣀⠀⡀⢀⡀⠐⠢⠀⡆⠀⠈⠀⠁⠀⡀⢈⠀⠀⢹⠟⢻⡇⠀⠸⠛⢋⣡⡜⠀⢻⠀⠄⠀⠂⠂
⠀⡀⠀⠀⢀⠀⢀⠀⣀⠐⢄⣀⣱⢦⡅⠀⡘⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⡿⠿⠁⠀⠊⠀⠀⣀⣤⣴
⠀⢀⠈⠁⠈⠙⢌⠀⢀⡀⠀⡙⠚⡐⢡⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠚⠤⠵⠀⠀⠀⢸⣿⣿⡷⠾
⠀⢈⠀⡀⠀⠡⡑⠄⠀⠀⠀⡄⠀⠉⠈⠁⠀⠉⠛⠛⠛⠹⠀⠀⢀⣠⣣⣤⡀⠐⠀⡀⠢⠀⠀⡀⠘⠋⠁
⠀⢨⠀⠈⠂⠀⢓⠀⢀⡀⠀⠄⠰⠶⠶⠶⠀⠀⠀⠂⠀⡣⠀⢰⡿⢿⡟⠏⠣⢈⠀⠁⢰⠂⠑⠀⠁
⠀⣀⡀⠠⣀⠀⢀⣀⠀⢀⢀⠀⠘⠛⠂⢃⠀⠘⠂⠀⠒⠀⠀⠀⠐⠀⠀⠨⠀⠀⠀⡀⠉⠡⠄⠐⣂⡀⠩⡤⠐
⠀⠓⠪⠁⠒⠀⠐⠂⠄⠜⠚⠀⠸⠿⠿⠿⠀⠺⠿⠹⠏⠿⠽⠧⠻⠼⠆⠀⠀⠤⠇⠃⠀⠀⢰⠁⠈⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠁⠀⣿⠤⡀⡆⠀⠀⠀⠀⢀⣧⢄⠀⡇⣶⡄⢸⡤⠄
⠀⠀⠀⠀⠀⠀⢸⠶⠶⢾⡶⠶⠶⡷⠖⠷⡇⠀⠀⠀⠀⢸⡷⠶⠶⣷⠷⠶⢮⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠷⠈⡟⠁⠀⡇⠀⠀⠀⠀⢸⡇⠉⠀⡿⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⡟⠛⠉⡞⡛⠛⢳⣛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢸⡇⣚⣀⣇⣁⣂⢸⢋⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⡟⣭⠁⣙⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⣶⣶⣤⡶⠒⠃⠀⠀⠀⠀⣯⠭⠤⡭⠭⠤⣥⡤⠤⢼
⠀⢰⡀⠂⢀⣀⣤⣶⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡠⠀⢳⠀⠀⢸⠀⠀⣠⣔⠂⠁⢀⣀⣀
⠀⠖⠛⠋⠉⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡗⠒⠒⡖⠒⠒⣾⠒⠒⢺⠀⠀⠈⠙⠳⠾⠯⠙⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣁⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠘⡇⢀⣀⡃⠀⠀⣻⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣿⣷⡤⠤⠽⣶⣶⠒⠛
⠀⠀⢀⣀⠀⣶⣦⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⢀⣠⡄⠀⠶⡀⣀⣹⠶⣶⡔⠀⠀⠀⠀⠘⣷⣰⣤⣤⠬⣃⠶⣶⠛⠣
⠀⠐⢿⣿⣿⣿⣿⣦⣭⣟⣛⠉⢛⡳⢐⣻⣅⡈⠻⣤⡒⠂⠈⢳⠄⣤⡜⠋⠪⣟⢀⣀⣀⠛⠋⠉⠈
⠀⠀⠀⠈⠛⢿⣯⡉⠽⠿⣿⣿⡵⠖⠉⠀⠛⠂⠀⠙⣿⣾⣝⠃⣀⣙⣆⣴⣶⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⣿⡧⠄⠀⠐⠊⠃
⠀⠀⠀⠠⣒⣁⠰⠃⢀⡠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠆⠀⢤⡀
⠀⠀⠀⠀⠋⠈⠉⠁⠲⢄⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡎⣿⣿⡀⠈⠀⠀⢪⠉⣲⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠻⣿⣧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⡀⡀⠀⠈⠲⡏⠀⠀⠙⢿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠠⠈⡀⠀⠀⠀⠐⠂⠈
⠠⢴⠀⢰⠒⠰⠢⣀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣿⠃
⡲⠚⠛⠉⠐⠒⣄⠉⠒⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠠⠄⠀⠖⠠⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢠⠈⠀⡰⠁⠈⠙⠀⡀
⠀⠀⠀⠀⠀⠀⡾⢭⠹⢸⡁⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠉⠁⠐⠓⠠⢆⠀⠠⢐⡀
⠀⠀⠀⠀⠀⣾⢿⣕⣐⣨⣿⣿⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⢤⣀⠤⠤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢳⣀⠠
⡿⠊⠀⠀⠀⠙⠷⣦⠴⠶⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡴⡎⣀⣄⣄⣵⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⢿⣷⣤⠤⠀⠀⠀⠀⠀⢀⡽⠛⠉⠉⠉⠙⠛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢾⡀⢠⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡀⠂⣀⣀⣤⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠒⠂⠉⠁⠙⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⡀⢀⠄
⠀⠀⠄⠤⠤⠤⠤⢤⣀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠺⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⠊⡁⠁⠀⠀⠹

⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣴⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⣀⢸⣇⡀⠀⣿⡇⣿⣿⣿⢻⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡟⢿⢻⣿⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⣿⡇⠀⣿⣿⣿⡇⠀⣿⡇⣿⣿⡟⠀⢿⡇⠈⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⣤⡀⢸⣿⠀⣿⣿⣷⣿⣾⣿⣼⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⣿⡇⠀⠙⢻⡟⠃⠀⣿⡇⣿⣿⣧⣤⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣾⣿⠀⣿⣶⣶⣶⣶⣶⣶⣶⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣷⣶⣶⣾⣷⣶⣶⣿⡇⢿⣷⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⠤⡤⠤⠤⠤⠀⠀⠀⣄⣠⣠⣄⣄⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣇⢠⣷⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢦⣭⣭⣬⣥⣭⣭⡤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⢶⡶⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⢀⣀⣐⣀⡀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠿⠷⠾⠀⠠⠿⠿⠿⠆⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠾⠿⠇
⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⡍
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣛⣛⣛⣿⣿⣿⡇⣿⡷⠷⠾⠶⠾⠶⠷⣿⡇⣿⡇⠀⣠⣤⣤⣄⠀⢽⡇⣿⡇⠀⠴⠶⠶⠦⠀⢸⡏
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠋⢻⣋⣟⠙⠋⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⡟⠛⣛⣛⣛⣛⠛⢻⡯
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⣿⣿⣿⠀⠀⣿⡇⣿⡇⠀⣤⣤⣤⣄⠀⢹⡇⣿⡷⠶⠶⠾⠿⠶⠶⢾⡯
⠀⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣴⣾⣿⣷⣦⣤⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⣇⣀⣛⣛⣛⣋⣀⣸⡧
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⣀⠚⢀⠀⠀⠁⢀⠭⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣄⣐⢦⡄⠀⠀⠀⠂⠀⠄
⣀⡀⠀⢀⡭⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠐⠀⠀⠀⠩⠥⠶⠾⠇⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠤⡄
⠈⠉⠲⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠁⠀⠀⡅⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣑⠂⠤⣀⡞⠀⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⣁⠀⠀⠑⠒⠠⠤⠃
⠀⠀⢀⠀⠀⠤⠤⠤⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣃⣠⣄⡄⠀⡀
⠀⠠⠀⠀⢠⣥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⠽⠟⠇⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠂⠈⡇⠀⠠⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼
⠀⠀⠐⡏⠉⠛⠓⠺⢼⡀⠀⢄⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡄⠀⢀⡀⠀⢀
⠀⠁⠀⡇⠀⠀⠀⠠⠀⡏⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⡘⠐⠃⠴⢄⢀⡀⠀⠀⠀⠐⢤⡇⠀⠀⠀⠀⠉
⠀⢀⠀⠋⡉⠛⠒⠒⢼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢂⠉⠒⠲⠤⢬⣀⣉⣂⠀⠀⠀⠑⣄⣀⣠⣤⡴⠞⠂
⠀⠀⠉⠓⠲⠭⠭⠭⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⢄⣠⣘⠐⠢⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⢤⣴⣤⢦⣄⡀⠀⠀⢀⣠⡿⢧⠈⡷⣠⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⣿⡟⣾⣇⣿⢦⣍⣵⠀⢠⣿⢻⣏⠦⣈⠀⣾⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠌⠑⠢⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢰⠙⠋⠉⠉⠀⠀⠻⣿⣿⡀⠘⣿⣦⡉⠛⠶⢾⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣷⣄⣑⠂⠄⠀⠀⠃⣠⡇⠀⠀⢸⡿⢿⢻⢛⣿⢿⢿⠅
⠀⠀⠀⠀⠒⠀⠀⠀⣀⠄⢱⠀⢸⣼⠃⠀⡰⠛⠛⠻⠿⣿⣿⡿⠤⠤⠄⠀⠀⠊⠂⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣾⡗⣚⡂⢼⣿⣼⣇
⠀⠀⠀⠀⢘⠀⠀⡈⢰⠁⡮⠀⢸⣿⠇⠀⡁⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣧⣼⣥⣤⣽⣿⣾
⠀⠀⠀⠀⠘⢀⣀⠀⡈⠈⢀⠠⠾⠋⠀⠀⠁⠠⠄⣀⠀⡈⣿⣿⣧⣀⣤⠀⠄⠊⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣽⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠚⣡⠠⡿⢥⣿⣿⣟⡀⠀⡲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠋⠉⠀⠂⠀⠀⠉⢿⣿⡇⠀⠀⢸⠀⠈⠀⢀⠠⣾⣿⣿⠄⠀⠎⠩⢀⡀⠙⡤
⠀⠀⠀⠀⠀⢰⠤⠴⠖⣿⣿⣿⠒⠒⠒⠒⠒⠒⠋⠛⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠘⣿⡇⠀⠀⠘⢶⠞⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇⠑⢄⠂
⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢄⠀⠀⢔⢀⠌⣼⡟⠀⠀⠀⠀⠸⡀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⡰⠁⠘⢼⡖
⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⣿⣿⣧⣀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠦⠀⠹⠿⠿⠆⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⣒⣒⣒⣒⣒⡒⠒⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⣠⠴⠚⠉⠁⠀⠀⠉⢉⡿⣷⣦⠀⠀⠀⠀⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⢀⠀⢠⠊⠀⢀⡕⠀⠈⠐⢈⣵⡿⠁⢹⠟⠠⡐⠲⣦⣄⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡔⠋⠁⢉⢧⡀⠀⣋⡀⢤⡴⠚⢭⢋⣷⣠⠊⠀⠀⠀⢀⢼⠟⣿⡆⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡴⠋⢣⡀⣀⡬⠞⠿⣿⣋⢐⡾⢻⣢⠶⠴⠋⠐⠓⢀⣤⣴⠕⢳⣏⣟⣼⢃⡆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⡀⠀⠈⡃⠀⠀⣀⠘⡜⠋⠁⠈⠙⢶⡶⠒⠲⠿⣿⣋⣻⣧⡖⣩⡍⠵⣹⠇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠻⣄⡀⠣⣄⣮⣹⢿⠀⠀⠀⢀⡀⣼⣽⠗⠶⠶⠶⠻⠷⠚⣧⣈⣵⠞⠋⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⠛⠶⣶⣤⣤⣷⣷⣾⣶⣾⣋⣛⣒⣢⣭⣿⡿⠷⠞⠛⠉⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⢀⡀⠀⡀⠀⣀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⢀⡏⡇⢸⢿⠸⡏⣇⠀⠀⣴⣫⠅⠀⠈⠻⣄⠀⠀⠀⠀⠀⢸⢹⡇⡟⣇⢸⢹⡄⠀⢀⣜⡭⠀⠀⠈⢳⡀
⠀⢸⠁⡇⣾⢸⡀⡇⢻⠀⣸⣿⠁⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡟⢸⡇⡇⢿⢸⠀⣇⢀⣞⡎⠀⠀⠀⠀⠀⢹⡀
⠀⣿⠀⡇⡿⢸⡇⡇⢸⣆⣿⡇⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⢠⡇⢸⢷⡇⢸⢸⠀⢻⢸⢹⠀⠀⠀⠀⠀⠀⡈⡇
⠀⣿⠀⠛⠃⠀⠛⠃⢸⡿⡇⣇⠀⠀⠀⠀⠀⡾⢸⠀⠀⠀⢸⡇⠈⠛⠀⠈⠛⠀⢸⢸⠸⡀⠀⠀⠀⠀⢀⡇⡿
⠀⢿⡀⠀⠀⠀⠀⠀⣸⠃⢧⠘⠶⣤⣤⣤⠞⢁⡟⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡾⠘⡆⠑⢤⣀⣀⡤⠚⢠⠇
⠀⠈⠳⢤⡄⠀⣠⠶⠃⠀⠈⠳⣤⡀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⣤⠞⠁⠀⠘⠦⣄⠀⠀⣀⡴⠋
⠀⠀⠀⢰⡇⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⣇
⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠀⣿
⠀⠀⠀⢸⠃⠀⢸⡇⠀⠀⠀⠀⢸⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⠀⢻
⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⢸
⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⢸⡆
⠀⠀⠀⢿⡀⠀⢀⡇⠀⠀⠀⠀⢿⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠀⠘⡇⠀⠀⢸⠇
⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠉⠓⠒⠋
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⢠⡀⣠⣄⢀⣤⡀⣠⣄⢠⡀⠀⣠⡀⣤⣤⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣿⣼⢿⡇⣿⣾⠈⠃⡇⣿⢸⡇⠀⡿⣇⢸⡇⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠇⡿⢸⠟⣧⡿⢺⣴⠇⣧⡿⢸⣥⣴⠗⢿⢸⡇⢸⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⠤⠤⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠄⠈⠀⡽⢇⡠⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡂⠀⠀⠀⠈⠉⠉⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠤⠀⠀⠀⠀⠄⠀⠀⡰⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⡞⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢩⠔⠒⠞⡰⠁⢠⣟⠁⠀⠠⠤⠤⣄⢀⣰⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡴⠁⢠⠇⠀⠉⠁⠒⠐⠊⠀⠠⢙⠥⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡖⠀⠀⠓⠂⠤⠼⠁⠀⡿⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡀⠀⠀⠀⠁⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠒⠦⢤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠠⠤⠤⣄⣀⣀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠀⠀⠀⣠⠎⠱⡄⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠘⡆⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠠⡋⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠜⠁⠀⠀⠀⠀⢀⣑⣒⡊⠀⠀⠀⠀⠀⠀⠀⠱⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠯⠥⢶⡄⠀⠀⠀⠀⣿⡉⠒⠚⡇⠀⠀⠀⠀⠀⢸⠳⠭⠵⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠢⢼⡇⠀⠀⠀⠀⣿⠈⠉⠓⡇⠀⠀⠀⠀⠀⢸⠙⠒⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⣿⣀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠤⢤⡇⠀⠀⠀⠀⣿⠈⠙⠒⡇⠀⠀⠀⠀⠀⢸⠉⠒⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠧⠤⠔⠒⠓⠒⠒⠒⠒⠋⠀⠀⠁⠉⠀⠀⠐⠒⠒⠚⠒⠒⠂⠾⠤⠄⣀⣀
⠀⠀⢀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠤⣄
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⢰⠁
⡇⠀⠀⠀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢦⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠦⡀
⢧⣀⢀⡠⠎⠈⢧⡀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠑⠤⣀⣀⢀⣀⣀⠠⠔⠋⠀⠀⠀⠀⠁⠀⠈⠒⠤⠤⠤⠔⠉⠀⠀⠈⠓⢤⠤
⠀⠀⢹⠀⠀⠀⠀⠈⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠶⠶⠦⠤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠲⠤⣀⠀⠀⠀⠀⢸
⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⢹
⠀⠀⢸⣀⡠⠤⠖⠒⠒⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠒⠉⠉⠀⠀⠈⠑⠦⢄⣀⣀⠤⠤⠴⠒⠒⠒⠒⠒⠢⢄⣀⣠⠴⢚
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⢀⡸⠆⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠒⠚⠢
⠀⠸⡀⠀⣰⠋⠉⠉⡦⠒⠒⠒⡤⠖⠒⢤⠤⠒⠢⡤⠔⠒⢤⡠⠖⠲⣤⠔⠒⢤⠤⠤⢤⡠⠄⠢⢤⠒⠒⠒⣎⠁⠀⠈⣆⣀⠴
⠀⠀⠈⠉⠙⠢⠤⠴⠳⣄⣀⡠⢇⡀⢀⡸⣄⠀⣀⣧⡀⢀⣠⢆⡀⢀⣧⡀⠀⣧⡀⠀⢀⣇⠀⢀⡸⢇⣀⣠⠞⠒⠒⠚⠁

⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⡄⠀⠀⠀⠙⠻⠿⣿⣿⣿⣶⡀⠀⠀⠙⠻⠿⢿⣿⣶⡀⠀⠀⠀⠀⢠⣾⣆⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠾⣿⡿⠄⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⠄⠀⠀⠀⠀⢀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠙⣿⡿⢥⣄⣀⡄⠀⠀⠀⠈⢻⣿⠯⢤⡀⠀⠀⠀⠀⠈⢹⣿⠿⠿⣿⣿⡆⠀⠀⠀⠈⠙⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣐⣖⡸⢶⡶⡇⠀⠀⠀⠀⠀⠀⣀⡈⠹⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⡿⣷⣯⣵⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉


⣿⣿⢟⠿⠛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣾⣴⣿⣿⣿⣿⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⣽⣿⢸⣿⡇
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⣾⣿⠛⡿⢻⣿⣿⣿⣾⣣⡿⣿⣿⢸⣿⡇
⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣭⣿⣿⣿⣿⢞⣽⣿⣿⣿⣿⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣿⣵⣿⣿⣿⣿⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⢸⣿
⢦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢯⣽⢚⣿⣽⣖⡛⠛⠉⠛⠻⢻⣿⠿⢿⣿⣭⣿⣿⣿⡿⣿⢸⣿
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣟⣿⣛⡋⢨⣭⣿⡉⠁⠀⠀⠀⢀⢸⣟⠘⠂⠀⠀⠻⠿⠟⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠋⡉⠛⠛⠛⠛⠛⢻⢟⣋⣳⣄⣀⣀⣀⣀⣀⣀⡇⢸⣿
⠀⠀⠀⢶⠆⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⢶⡖⣿⠀⠀⠀⠀⠀⠘⠋⠛⠟⢿⣿⢿⡿⣿⣿⣯⡅⢸⣿
⠀⠀⠀⢸⣠⠀⣿⣿⣿⣿⡟⠉⠁⠀⠀⠘⡇⢿⠀⠖⠀⠀⠀⢠⢀⢠⣶⣼⣟⠻⢻⣗⢹⢹⡇⢸⣿
⠀⠀⠀⠘⠂⠀⢹⡿⣿⣿⡅⠀⡀⠀⠀⠀⠇⢹⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⡇⠀⢀⡟⢹⠟⡇⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡄⠀⠀⠀⠀⠀⡀⢸⣇⠀⢀⡼⢸⡇⠀⠈⣿⣿⡇⠀⠀⣷⢈⣀⡄⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⠹⠧⠤⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣇⣀⣈⣿⣿⣇⠀⢸⣿⢾⣏⡇⢸⣿
⠀⠀⠀⠀⠀⠀⢠⣿⢿⠖⠒⠖⠒⠒⠔⠂⠐⢺⣿⣿⣿⣿⣿⡏⠙⠙⣿⢻⣿⠿⣟⣏⣿⡏⡇⢸⣿
⢠⡆⠀⠀⠀⠀⣿⡇⢰⢸⠋⠉⠀⡉⠁⠁⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣺⡟⠠⠀⣿⣿⣷⡇⢸⣿
⠘⠁⠀⠀⠀⠀⢸⡇⢸⣸⠀⣀⣄⣀⡆⣠⣤⠀⢹⣿⠀⠀⠀⠀⠀⠀⢀⣘⣓⡦⢀⣿⣿⣿⡇⢸⣿
⣠⡏⠀⠀⠀⠀⢸⣿⣸⣿⢡⣿⣿⣿⣧⣿⣿⡄⠀⢽⣷⢸⡍⠉⠉⠉⠉⠉⠉⠀⠉⠻⢿⣿⡇⢸⣿
⠁⡇⠀⠀⠀⠀⢸⡿⠋⣉⢼⣿⣟⣿⣿⢿⣿⡇⠀⠀⡉⢐⡄⠀⠀⢀⣀⣀⣀⣀⣀⡤⢤⢬⡇⢸⣿
⣿⣷⠀⠀⠀⠀⢸⣷⣰⣶⣲⣶⣐⣶⣾⣯⡽⠇⠀⠀⣿⠘⣿⠀⠂⢥⣤⣤⡤⠶⠶⠶⠶⠾⠇⢸⣿
⣿⣿⡄⡀⠀⠀⣸⣟⠿⣙⣫⣍⣭⢍⠀⠀⠒⢤⠀⠀⢛⠀⢿⡐⣶⠸⣿⠤⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢠⣽⣯⣭⣙⡤⣄⠶⢤⣴⠿⠗⠻⠖⠂⠀⠀⠒⠆⠀⠸⠂⠄⡇⠘⡀⠄⣧⡐⢄⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣿⣿⡉⠠⣀⠨⢤⡤⠂⢤⡐⠄⣐⠀⠤⠀⠀⠀⠀⠐⣾⡇⢀⡁⠀⣿⣿⣆⡱⣄⠀⠀⡀⢸⣿
⣾⣿⡓⣦⣝⢂⣤⡍⣀⡄⣁⡠⢄⡀⠒⠤⠴⢢⡴⠂⡰⢿⣿⣿⠈⢁⠘⣿⠿⠿⠷⠈⠋⣏⡇⢸⣿
⠋⠍⠋⠡⠐⣉⠄⢈⠁⠒⡩⠔⢁⠀⢀⣠⠆⣁⠘⠡⣴⣋⣽⣿⠀⢸⠀⠘⠢⡄⢡⡄⠀⣿⡇⢸⣿
⠤⣈⠀⠰⢄⡀⠚⠤⠖⠛⠰⡎⣉⠻⢫⣉⠚⠠⣈⡛⠳⢮⣽⣟⠀⣴⠀⠀⠀⣧⠈⠇⡇⡿⡇⢸⣿
⢄⡀⠐⠦⣄⠀⠒⢄⣀⡙⠲⣄⡈⠓⢠⣌⡙⣻⢬⣉⡳⠲⣬⡝⠐⣿⡀⢳⠀⢻⠀⠀⠇⣿⡇⢸⣿

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡛⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⢫⣋⣋⣴⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠻⠁⣤⣸⣿⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉⠉⠁⣠⣤⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⣀⣠⣤⣴⡶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣉⣡⣤⣶⠾⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢋⣡⣴⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠛⠛⢻⣷⡚⠁⣼⠟
⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡿
⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋
⢸⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⣻⣿⠿⠋
⠈⠻⠷⠶⠶⠾⠿⠿⠿⠭⠵⠒⠚⠋⠉