Phrases Emojis & Symbols

⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢹⡀⡄⢀⠂⠀⠂⠢⠀⠀⠀⠀⠀⠀⠺⣄⣤⠤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠦⠆
⠀⠀⠀⠀⠀⣞⠛⡗⣗⡠⡕⣒⠛⡳⡇⠀⠀⠀⠀⣤⠘⠋⣘⣋⠑⠌⢀⠀⠀⠀⠀⠀⠀⡦⠴⠶⠷⡦⠄
⠀⠀⠀⠀⢀⡘⠤⠇⡈⠋⣁⣈⣒⡉⣩⠄⠀⠀⠀⠙⢲⢰⣷⢰⣶⢹⠉⠀⠀⠀⠀⠀⢀⢄⣐⣂⣛⢠⢤
⠀⠀⠀⠀⠈⡛⢛⠋⠉⠀⠍⠍⠅⠅⠭⣄⠀⠀⠀⠀⢈⠉⠠⠄⠉⠈⠀⠀⠀⠀⠀⠀⠘⠀⠉⠼⠀⠂⠉
⠀⠀⠀⠀⠀⢻⣘⣣⣶⣒⣞⣾⣯⣷⣤⣧⠀⠀⠀⢰⢘⣶⣌⣋⣴⠀⣤⠀⠀⠀⠀⠀⣄⢀⣓⠚⣚⠀⠀⣠
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠛⠋⠀⠙⠙⠛
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠣⠼⠘⠆⠇⠀⠀⠀⠀⠀⠀⠀⠘⠟⢳⠟⠿⠾⠀⠀⠀⠀⠀⠀⢀⡖⠊⡉⣡⣐⡄
⠀⠀⠀⠀⣰⣿⠀⣴⢄⠉⢁⡤⠷⣷⡄⠀⠀⠀⠈⠁⡏⣠⣠⣄⣀⡆⠀⠀⠀⠀⠀⣀⣋⠁⣁⠉⠉⠉⡀
⠀⠀⠀⠀⢻⣷⠈⢷⡺⠜⢋⠣⠰⡿⠇⠀⠀⠀⠀⠀⠉⠑⠛⠧⠴⠀⠀⠀⠀⠀⠀⠀⠒⣶⢒⢒⠶
⠀⠀⠀⠀⠀⠉⠀⡟⢃⣰⢩⡀⠀⠀⠀⠀⠀⠰⠆⠎⣡⡖⡇⣰⡀⣏⢐⠂⠀⠀⠀⢠⡌⢙⠛⡈⢠⠄
⠀⠀⠀⠀⠀⠀⠠⠑⠚⠿⠛⠋⠔⠀⠀⠀⠀⠀⠀⢌⠡⠁⠁⠒⢂⡷⠀⠀⠀⠀⠀⠈⡟⠺⠎⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠃⠀⠢⠐⠐⠙⠃⠊⠈⠘⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠰⠒⠐⣀⠀⠀⠸⠃⠀⣠⠒⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠎⠀⢀⠞⡁⢀⠄⠀⠀⠀⣤⢐⠐⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⡌⢀⣤⡈⠀⠀⠁⢀⢰⠃⠀⡟⡜⠉⠀⠀⠀⠀⠐⢄⠂⠀⠀⠄⠠⠚⠁⠒⠂⠀⠈⠒⠚⠁⠀⠀⡠⠀⢀⡠⠄⠐⠂⠀⠁⢨⠀⡀⠀⠀⡄⠐⠀⠤
⠀⠀⢱⠘⠂⠻⠄⢄⢀⡜⠈⣇⢀⠇⢧⣀⡞⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠐⠒⣨⡉⠀⠀⠐⠀⠒⠀⠁⠀⠀⠁⠀⡀⡀⠀⠀⠀⠸⠀⠇⠠⠐⠁⠀⠀⠀⠠⠀⢀
⠀⠀⠈⠀⠀⢀⢤⡀⠁⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣉⣤⡀⠀⣺⠀⡄⠀⣄⠑⠂⢀
⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠊⠀⠠⠀⠠⠀⠠⠁⠀⠀⠀⠀⠀⠀⠄⠕⣀⠀⠠⠀⠀⠀⢀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢾⠁⠄⢹⠸⡇⠀⠊⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠰⡄⠇⠀⠂⠰⠀⡠⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠅⠼⠁⠎⠜⠣⠟⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⢠⡆⠀⢸⠀⡀⣸⠀⠈⠀⢡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡀⠀⡠⠀⡔⠁⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⡴⢀⢀⡄⢀⡤⢄⠀⠀⠀⢀⠀⠀⠀⠀⢰⠰⡼⠠⠴⠃⠀⠐⠁⠀⣀⢀⣸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠚⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢠⣤⠞⠐⡏⠊⣧⢾⠀⡀⡀⡈⠐⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠄⠂⠀⠀⠀⠈⠉⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⡄⢜⠫⠴⠃⢆⣼⠘⠦⠴⠓⡁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠥⠄⡂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠁⠀⠀⠂
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢡⡠⠤⣀⣠⠄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠⠲⢀⡄⢒
⠀⠀⠀⠀⠀⠘⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣚⣒⣀⠀⠀⠈⠑⡄⢸⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠒⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⣤⣴⣦⣤
⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠚⠛⠓⠒⠻⠿⠀⠀⠀⠳⠄⠀⠲
⠀⠀⠀⠀⠀⠐⠰⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⡀⣀⡀⠀⠀⠀⠀⠠⠀⠤⠤⠂⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⠂⠀⠀⡄⡀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠐⠂⠐⠠⠀⠀⠀⠀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠒⠃⠋⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠈⠛⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⢘⡆⠀⡀⠀⠀⣚⠄⠀⠀⠀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⢈⣀⣁⣀⡀⠀⠀⠀⠀⠀⠽⠁⠀⡇⠀⠀⢼⠄⠀⠤⢤⠄⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡀⡀⢠⡀⢀⢠⢄⠀⠀⠀⠀⠀⠀⠠⠆⡀⠤⢦⡀
⠀⠀⠀⠀⠀⠸⡆⠀⢰⢸⡙⡇⢸⡠⠁⠀⠀⠀⠀⠀⠠⠻⠷⢶⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣽⠚⣟⣁⢠⣈⢩⢡⡄⠀⠀⠀⠀⠀⠀⠉⠭⡉⡀⠀⠀⠀⠀⠀⣠⡂⢰⢅⣀⡠⠄⡤⣆⢦⣤
⠀⠀⠀⠀⠀⠀⢹⠁⣸⠈⠉⠴⣻⠋⠀⠀⠀⠀⠀⠐⠺⠿⡚⠟⡇⢂⠀⠀⠠⠴⠛⢳⢦⣤⡤⢠⠤⣭⣼⠶⠛⠲⠄
⠀⠀⠀⠀⠸⣿⣷⠎⠀⠐⠀⠚⠒⠘⣿⣿⡇⠀⠀⠀⢨⣮⡁⠈⠀⣀⠀⠀⠰⠮⠤⣠⠀⡸⠱⣏⡷⠉⡏⢀⠤⠥⠄
⠀⠀⠀⠀⠀⠙⠋⠰⠋⠉⠛⠋⠋⡗⠈⠉⠀⠀⠀⠀⠀⢯⣍⢉⣩⠝⠁⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠐⡋⣀⡀⠀⣈⠓⠀⠀⠀⠀⠀⠀⠘⣐⡤⣩⣠⡤⣬⠑⢄⠀⠀⠀⠀⠀⣹⣒⣝⣓⡨⠠⠼⠃
⠀⠀⠀⠀⠀⠀⡄⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣦⡎⠐⣄⡀⠊⠀⠀⠀⠀⠀⢠⣠⣯⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠳⠈⢓⠛⢻⠘⡙⠀⠀⠀⠀⠀⢀⣊⡁⢘⣛⠙⡃⠁⠀⡤⠀⠀⠀⠀⠀⣤⡉⣿⣭⡭⠡⠖
⠀⠀⠀⠀⠀⠀⠀⣱⣛⣾⣦⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⡆⠞⠓⠚⢶⠂⠀⠀⠀⠀⠀⠀⢲⡠⣭⣈⣁⡴⣺
⠀⠀⠀⠀⠀⠀⠈⠈⢙⠛⡛⢿⠝⠀⠀⠀⠀⠀⠀⠀⢀⣁⡖⡴⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣽⣿⣽⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢀⠈⠐⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⣀⠔⠉⠉⢢⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠐⣲⠒⠐⡀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢳⠦⣠⢠⣦⠦⣌⠉⠢⡀⠀⠀⠀⠀⠈⢺⣢⠖⣴⠦⠀⡇⠈⣻⠆
⠀⠀⠀⠀⠀⠀⢸⠩⣇⠈⢀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⣾⠜⣴⠃⢢⢀⠀⠰⠁⠀⠀⠀⠀⠈⠊⠁⢻⠿⠿⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠚⣦⠉⠧⠿⠽⢳⡎⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⢸⠿⠿⡲⠈⠋⠡⢀⠀⠀⠀⠀⠀⠀⠰⣶⢾⢲⣦⣾⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡐⢦⣸⢠⢤⠸⣶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⢐⣒⣢⡄⠀⣀⢀⠛⠘⠃⠀⠀⠀⠀⠨⢦⡌⢸⣯⣬⣤⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⡄⢾⢦⣿⣾⣷⣪⣿⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠃⠉⠉⡩⢟⠁⠀⠀⠀⠀⠀⠀⠀⢶⠀⣬⣍⢓⠂⢀⡤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡏⢿⠛⢻⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣁⡎⣸⢣⣔⣅⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣙⡛⢛⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠉⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢰⠀⠠⢐⠈⠈⢈⠑⠀⠀⠀⠀⠀⠀⠀⠈⣹⡤⣿⣚⢬⠝⢶⠄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⣧⠀⠀⢸⡄⠀⢠⠆⠀⠀⡀⠀⠀⠀⣾⠛⢻⢺⠒⡀⣝⠖⡚⠛⣓⣿⠀⠀⠀⠀⠀⣶⠂⠏⢨⣈⡉⠀⠫⠀⢰
⠀⠀⠐⣄⡀⠰⠓⠤⡔⠉⠂⠀⢉⡑⠐⠛⢆⣠⡴⠁⠀⠀⠀⠹⣄⣸⠃⠻⠖⠃⠉⠻⠔⠗⢛⣀⠀⠀⠀⠀⠻⢲⠀⢰⣶⠠⣶⡎⣿⢸
⠀⠀⠀⠈⢄⢲⣦⡄⢨⡟⣒⣒⣘⣚⠋⠶⡖⡰⠁⠀⠀⠀⠻⣷⣴⣤⠶⠆⠀⠟⠷⠾⠞⠆⠟⠁⠀⠀⠀⠀⠨⠸⠴⠼⠛⠀⠿⠇⠿⠘
⠀⠀⠀⠀⠀⠾⡷⠾⠛⠛⠙⠙⠛⠛⠻⠿⠶⠁⠀⠀⠀⠀⠀⣄⢒⡖⠀⢀⡀⢉⣉⣉⣍⡉⠉⣽⠄⠀⠀⠀⢠⢀⡌⢀⣨⣁⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣿⣯⣽⣯⣭⣿⣶⣷⡶⠾⠆⠀⠀⠀⢻⢀⣽⣿⣞⣉⣾⡗⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠁⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⠀⣖⣦⡆⣦⣴⣦⣶
⠀⠀⠀⠀⢀⠀⣀⢀⡀⠉⢒⡘⣋⠀⣀⡀⢀⠀⠀⠀⠀⢀⡀⠛⡀⠀⢀⠈⠓⢒⡒⠜⠀⠀⠐⠗⡀⠀⠀⠀⠘⠟⣀⣛⣀⣛⣉⣃⣛⣉⠙⡙⢀⣠
⠀⠀⠀⢀⡀⠘⢧⣹⠿⣿⣿⢻⣿⣎⣿⠁⠀⢀⠀⠀⠀⢸⡇⢰⡇⣼⠉⠃⣿⢸⡇⡇⣾⡍⢸⣏⠟⠀⠀⠀⢠⡞⠿⠦⠿⠴⠧⢴⠾⠿⣴⣵⠛⠛⠁
⠀⠀⠀⠀⢠⠈⢉⠉⢀⢀⣉⢁⣈⣀⣈⠁⢀⠀⠀⠀⠀⠸⠇⠈⠷⠘⠒⠃⠘⠚⠳⠃⠹⠆⠸⠋⠒⠀⠀⠀⠾⣧⣿⠵⣧⣿⡿⢻⠀⠰⡷⡟⡧⣿⠄
⠀⠀⠀⠸⠿⠯⠘⠷⠎⠻⠍⠻⠍⠿⠴⠁⠾⠞⠀⠀⠀⠀⣠⣆⣠⡞⢁⠀⡏⢸⣇⠀⣿⠃⢄⣶⡀⠀⠀⠀⢰⡦⢴⡁⠚⠒⠤⠆⠀⠐⠂⡹⡖⣶⠂
⠀⠀⠀⣶⠰⡆⢲⡆⢶⡲⣶⣠⢰⢲⣤⣆⣰⢰⠀⠀⠀⠀⠛⠛⠈⠷⠾⠀⠇⠸⠟⠆⠻⠀⠉⠛⠁⠀⠀⠀⣰⣑⣇⣁⠙⠘⠸⠐⠚⠋⠃⣁⣵⣸⡄
⠀⠀⠀⠙⠀⠉⠈⠃⠉⣁⠈⠟⠘⠊⠈⣉⠉⠝⠀⠀⠀⠀⠀⠠⠀⠂⠀⠈⠉⠁⠀⠀⠁⢰⣿⡆⠀⠀⠀⠀⠀⣡⣍⢀⡆⢠⢠⠀⣴⢀⡄⡄⣀⣄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠋⠘⠉⠈⠛⠃⠋⠁⠹⠃⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⣿⠀⣴⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄⠈⣧⠸⡇⣿⢰⡇⣰⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⡀⠀⣀⡄
⠀⠀⠀⣠⠀⣿⠀⠀⠀⠀⣀⢠⠁⢀⠀⢀⣼⠀⠀⠀⠀⠀⠐⢮⡳⣜⣇⣧⢿⣸⣱⢣⢞⡥⠖⠀⠀⠀⠀⢰⣤⡄⢻⣤⡇⣐⢠⣦⢸⣧⠀⠄⣤⢀
⠀⠀⠈⢧⡀⣿⠀⢸⡁⠁⡟⢸⠠⣟⠰⠇⢿⠀⠀⠀⠀⠀⡄⣀⢠⣨⢤⣠⢤⣠⢁⡥⡈⢠⠤⠀⠀⠀⢠⠾⡍⢀⠼⠀⠓⢓⠉⡟⡙⠹⠂⠐⣾⡿⣂
⠀⠀⠀⠔⢳⢉⠀⣶⢀⠀⠀⢠⡆⣸⣄⣠⠌⠁⠀⠀⠀⠀⢧⠿⠜⠻⡴⠻⠯⠸⠼⠧⠃⣸⡽⠀⠀⠀⠈⢳⣄⢟⣶⡆⣴⣮⣰⣶⢣⢾⠆⣷⣠⣶⢧⡆
⠀⠀⠀⣘⠿⣟⠀⠳⢘⣓⠀⠘⡇⠘⣑⠛⢄⣀⡀⠀⠀⠀⣠⢤⡇⣡⠐⢢⣀⣂⡠⣐⠖⣥⡇⠀⠀⠀⠓⠚⠉⠋⠋⠋⠁⢙⡙⠙⠙⠉⠃⠙⠙⡙⠁⠃
⠀⠀⠀⣿⡟⢹⡷⣼⡏⢙⣧⢸⣿⣄⣿⢰⣿⠉⠉⠀⠀⠀⠻⠾⠗⠫⠎⡿⠰⠛⠯⢉⣦⠹⠖⠀⠀⠀⠀⠀⠀⠺⠟⠀⣪⠵⠚⠛⠛⠲⡕⢄⣀⠜
⠀⠀⠀⣿⡗⢻⡇⢻⡇⢈⣿⢸⣿⢻⣿⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⣤⠤⣥⢦⣴⣤⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠠⡀⣠⠇
⠀⠀⠀⠛⠉⠛⠁⠈⠙⠛⠁⠈⠋⠀⠛⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠈⠁⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣶⢀⡀⠀⠠⠔⠒⠒⡄⠀⢀⡀⠀⠀⠀⠀⠀⢲⣿⡿⢄⠀⠀⠀⠀⠀⢀⠀⡾⠇⠀⠀⠀⠀⠀⠀⠀⡈⢂⠂⠘⠐⠠⢃⡀
⠀⠀⢠⡖⡆⣿⠛⣴⢷⣄⣶⣴⣶⢀⣴⢶⠨⢳⡆⠀⠀⠀⠛⠈⠀⠃⢸⡷⢾⢴⡟⡷⣿⣋⠗⠀⠀⠀⠀⠀⠀⠉⠒⠬⠀⠀⣀⠀⢀⠡⠒⠊⠁
⠀⠀⠈⢻⣴⣯⣼⣇⣰⢻⡿⢸⣧⣾⣏⣱⠃⣿⡴⠀⠀⢸⢷⣄⢀⡄⠘⠃⠘⠈⠓⠂⠛⠙⠂⣼⠇⠀⠀⠀⣴⣮⢹⣶⣶⣦⣴⢶⣠⡆⡧⢡⢶⡄
⠀⠀⠀⠉⡀⠡⢀⣭⣁⢀⡆⢠⣁⠀⣿⠁⠄⡈⠀⠀⠀⠈⢸⣿⢀⣴⠋⣳⡾⢱⡏⣼⢫⡿⣱⡏⡀⠀⠀⠀⣟⣷⣸⣷⣧⣧⣿⣸⣿⡟⣷⢸⣻⡅
⠀⠀⠐⣦⣿⡶⢺⣇⣿⢸⡇⢸⣿⠃⣿⠐⣦⣿⣔⠀⠀⢀⠸⣿⠎⠙⠛⠁⣻⣿⠛⠙⠋⠛⠙⢋⠀⠀⠀⢀⡉⡉⣈⡉⡉⠉⡈⠉⣌⢁⡉⣈⡍⠁
⠀⠀⠀⠉⠉⠉⠀⠽⢋⣈⣃⠙⠙⢃⠉⢀⣍⡉⠉⠀⠀⢩⢁⣠⢀⡤⣀⡅⣙⣅⣀⣤⢀⣤⣀⣭⡀⠀⠀⠸⠇⡞⢇⠜⢿⢺⠀⠸⠹⠼⠱⡏⣇
⠀⠀⠀⠀⠰⠀⠁⠀⢀⡀⠀⠀⠀⣀⠀⢹⠿⠇⠀⠀⠀⣿⢼⣿⣿⡗⣾⡧⣿⣿⣿⣿⠘⢷⡌⢷⡄⠀⠀⠀⠠⣼⡤⣰⠶⣦⢶⡶⣶⡂⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠈⠁⠀⠀⠁⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠉⠁⠈⠁⠉⠈⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠀⠰⠦⠀⠀⣀⣀⠀⠀⣮⡹⠷⡀⠀⠀⠀⠀⠀⣦⠀⡄⣀⡀⣀⠀⣀⠀⣠⢤⡀⠀⠀⣶⣤⡤⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣶⣦⡀⡇⠀⠸⣯⣿⡇⠀⠉⠑⠀⢃⡀⠀⠀⠀⠀⣿⠿⡇⣿⠀⣿⡀⣿⡀⣷⣴⡇⠀⠐⢿⣿⠿⠄⢸⣿⢛⣻⡇⠘⠃⢹⣭⣿⡇⢰⣿⣿⢛⣿⡇
⠀⠀⠀⠀⠿⠿⠟⠁⠷⠶⠰⣦⣼⠇⠀⠀⠀⠀⠀⢉⣈⡆⠀⠀⠛⠀⠃⠉⠁⠙⠋⠙⠛⠈⠉⠀⠀⠀⠀⠁⠀⠀⢸⣟⠶⢹⡇⢰⡆⢸⡜⢿⡇⠈⠛⣿⠘⣿⡇
⠀⠀⣶⠀⠀⢴⡶⢠⡖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡀⢸⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢹⣷⣦⠘⠓⠘⢿⣾⠟⠀⢰⣄⣤⠆⠀⠀⠀⢀⣤⣶⣶⣿⣿⣶⣶⣤⣀⠀⠐⣿⣄⠀⠀⠀⠀⠀⠀⣠⣽⡃⠀⠀⠀⠀⠀⣌⡉⠉⠉⠉⠉⠉⠛⠛⠛⠛
⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⠷⠀⢀⣼⣿⣿⣿⣿⣿⡟⢿⣿⡿⢿⣷⡀⠋⠙⠿⣶⣤⣤⣴⠀⢨⣭⡍⠀⠀⠀⠀⠺⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣾⣿⡅⢶⡇⠿⢸⡆⠾⢿⠀⡠⣿⣷⠀⠀⠀⠀⠘⠋⠁⠀⢈⣹⡧⠀⠀⢸⡇⠀⠄⢠⡆⢰⡦⠀⣿⠀⣠
⠀⢨⡀⠠⡦⡄⠄⣠⠀⠰⢦⣄⢤⠤⠀⠀⠀⢿⣿⡷⠶⠿⢶⠿⡿⢶⡾⠷⠲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠷⠆⠑⠘⠧⠎⠳⠆⠿⠶⠛
⠀⠀⣁⡀⢀⣀⠀⣤⠀⢀⣤⡄⠀⣀⠀⠀⡄⠈⢿⣷⣶⣵⣶⣤⣿⣭⣤⣴⣼⡿⠃⠠⠄⠀⠠⠄⠀⠀⠀⢈⣹⡇⠀⠀⢰⣶⣦⡖⣤⣤⠤⠔⣶⢲⢢⡦
⠀⠀⣙⡆⢸⠟⢡⡟⡇⢻⣇⣀⢸⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⠿⠟⠋⠀⣠⠀⠀⠉⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠛⠉⠙⠑⠃⠉⠈⠙⠓
⠀⠀⠈⠀⠈⠀⠈⠁⠁⠈⠉⠉⠀⠉⠀⢀⡖⠁⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⣶⣦⠀⢀⣠⡄⢀⠿⢏⠉⠯⠉⠁⣤⠤⢤⣀⠀⢰⡶⠶⢠⡀⢀⠀⣤⣴⢀⣌⣤⠁⡆⢰⠀⢠⠀⠀⠀⠀⠀⢀⡤⠀⣤⣄⢰⡆⢀⣴⠶⠀⣠
⠀⠀⠀⠀⠈⠁⠀⠈⠻⠇⢐⣄⡔⢀⣤⣀⡀⠿⠤⠴⠛⠀⢸⡏⠀⠸⣇⡼⠀⡿⣿⠸⡿⣿⠀⢙⡾⠀⣀⢀⡀⡐⢀⡀⠠⣽⠆⡟⠉⣾⢻⠘⣷⣤⠀⣏
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⠉⠙⢧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠋⠘⠃⠿⠌⠛⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⣿⣶⣦⠀⣯⣉⡧⠀⣾⣁⣹⡇⠀⠀⠁⢸⣧⣼⡇⣴⠒⣦⢰⣦⣶⡆⡶⠦⠻⣿⠗⣾⡃⣶⠖⣦⢾⡛⠀⠀⠀⠸⠃⠸⣇⠀⡄⡿⣧⣿⠆⢹⣤
⠀⠀⠀⠛⠛⠋⠀⠉⠋⠁⠀⠈⠛⠋⠁⠀⠀⠀⢸⡏⠙⡟⢿⣤⣿⢸⡿⣿⠣⣍⣷⠀⣿⠀⢿⡤⣻⣿⡁⢦⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠘⠃⠘⠛⠈⠛⠁⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⠀⠻⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠐⠆⠀⣄⣤⡄⠀⢀⣴⣿⠉⣿⣿⢿⣿⢿⣿⠟⣿⣿⠉⣿⣿⣦⡀
⠀⠀⣖⠂⢰⣶⡄⣿⡇⢠⡿⠛⠀⣴⠀⠀⣿⣿⣷⣶⣶⠶⣶⣶⣶⣴⣤⣤⣤⣤⡄⠀⣙⡁⠠⠤⣤⡄⢀⣾⣿⣿⠀⠿⣿⢻⣇⢰⣷⡄⡾⢿⠠⢿⡇⣼⣷⡀
⠀⠀⠶⠇⢸⠉⠠⡿⢳⠘⣿⣶⠄⠿⠄⠀⢻⣿⣈⣹⣺⠀⢯⡐⣯⣚⣸⣨⢙⣽⡇⠀⢈⡃⠰⠶⣭⡄⢸⣿⣿⣿⣶⣶⣿⣷⣿⠦⣼⠷⣶⣿⣶⣶⣿⣾⣿⡇
⠀⢀⡀⣀⠀⣀⣰⢄⡄⢠⢠⡄⡀⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⢿⣿⣿⡇⠀⢈⠍⢈⣥⣤⡀⠀⢿⣿⣿⢹⡏⠹⠇⣭⠠⣇⠛⢀⡇⢸⠹⡆⣼⡿⠁
⠀⠘⠂⠛⠒⠋⠸⠦⠛⠋⠘⠃⠓⠛⠀⠀⢸⣿⣎⣯⣽⣿⣧⣧⣶⣸⣦⣹⣷⣿⡇⠀⠐⠀⠘⣃⣈⠃⠀⠀⠻⢿⣾⣷⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣉⠉⠁⠀⠀⢈⡋⠈⠁⠉⠀⠀⠀⣄⣀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⢰⣶
⠀⢲⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀
⠀⢾⣿⠉⣿⣿⠋⣿⢹⣿⡝⣏⣋⣿⣷⠀⠀⠀⠀⠀⠀⣆⢠⣄⠀⢶⣠⠤⠀⢸⢻⣰⣎⣲⢰⣎⣶⢸⣿⠀⠀⠀⠀⢠⣾⠛⢸⡇⢰⡗⠺⣿⠃⠀⣾⣿⡿
⠀⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⠀⠉⣉⡀⠀⠀⠀⣤⠀⠀⠿⠶⠄⠿⠾⠃⠀⠿⣶⠇⠻⣯⠶
⠀⣿⣇⠾⡇⢀⣹⠀⢻⡁⢴⣾⡏⣹⣿⠀⢰⣤⣴⡄⠀⠀⠀⣾⡀⣶⡆⣼⠃⠀⢰⣀⣼⡤⣟⠃⣼⡃⠀⠀⠀⠀⠀⠠⣤⣄⣤⣠⡀⣴⠀⣶⠀⣰⣦⣶⡦
⠀⠿⠷⣶⣧⣿⣧⣼⣼⣧⣤⣼⣧⡽⠿⠀⠘⠻⠟⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠁⠛⠙⠀⢠⣦⠀⠀⠈⠀⠉⠛⠉⠁⠺⠃⠙⠖⠛⠗⠛⠓
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣷⣼⣿⡆⢰⣶⣿⣯⣿⠀⢸⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣀⣀⠈⣿⠻⠿⣷⡀⣸⡏⢸⣿⢠⣿⠁⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⣿⣍⣿⠇⠛⠃⠀⠉⠀⠀⠀⠀⠉⠈⠛⠿⣰⣿⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣳⠆⡈⠉⠁⠀⠀⣴⡆⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠙⢛⠰⣞⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠏⠘⣁⡀⠒⠉⣿⡟⠒⠒⢒⠚⠉⢀⣴⡟⣀⡀⠀⠀⠘⣃⡹⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢼⡟⢁⠤⣾⡿⠀⢠⣾⣋⠟⢀⣼⡿⠋⠀⣿⣄⣠⣾⡏⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⡠⢼⣿⠁⢰⡿⢁⣴⣿⠋⢁⡤⣺⣿⡡⢴⣾⠏⠁⣀⣸⣷⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢠⡏⠀⢸⡿⠀⠻⠷⠋⠈⠻⠖⠋⣰⡿⠙⠒⠋⠁⠀⡏⠁⢠⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠙⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⣿⡆⢸⣿⡆⠀⣿⣿⠂⢸⣿⠿⠿⡆⠀⣿⡿⠿⣶⣄⠀⣿⡇⠀⣺⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⡈⠁⠀⣿⡇⢠⣿⡇⠀⢸⣿⣴⡆⠀⠀⣿⣇⣠⣾⡿⠀⣿⣇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠿⠃⠀⠀⢻⣿⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⡟⢻⣿⡀⠀⠙⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡄⠀⢸⣿⣿⣿⠀⠀⢸⣿⣶⣿⣿⠀⣿⡇⠀⣿⡇⠀⢰⣶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⠀⠀⠋⠉⠁⢀⣤⣶⣿⣿⣶⣤⡀⠈⠀⠀⠙⠻⠀⠸⣿⣦⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠈⢙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡸⣷⠀⣦⠀⢠⣦⣄⡈⠻⠇⠀⠀⠀⠀⠀⢹⣿⠀⠠⣶⣇⠀⣦⢀⣿⢃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣭⠷⠈⢠⣿⡿⠻⣿⣧⠀⢰⣶⣶⣶⣶⠈⣿⣇⠀⣿⣿⡀⠡⠾⣭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⣿⡿⠁⢀⣿⣿⠀⣾⣿⣀⣿⣿⡀⠙⢿⣿⠿⣿⣧⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣧⣴⣾⡿⠃⣼⣿⠟⠛⠻⣿⣧⠀⠀⣤⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⢼⣿⣿⠀⠀⠀⣿⣿⡧⠀⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⣴⡆⢠⣄⢰⣶⠀⠀⠀⢠⡶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣷⠀⠀⢰⣿⣿⣼⢿⡇⠸⣧⡼⣿⣀⡀⠀⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⣸⠸⣿⡏⢸⡇⢀⡴⢺⡿⠀⠀⠀⢻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣄⠙⠀⠙⠁⠘⠃⠘⠦⠞⣡⠄⣤⡄⠘⠛⢁⣀⣀⣀⣀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠘⣿⣀⠀⠀⢀⡀⠀⢀⡀⢀⠘⢶⡿⠒⢚⡉⠉⠀⠀⠀⢠⣿⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢋⣽⣧⠜⢡⣾⠇⢰⣿⡿⢰⡿⣹⡿⠀⣿⠃⢠⣿⡟⢀⣾⡟⡂⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡥⣾⠃⠀⣼⡏⣠⢾⣏⠴⠻⠟⣿⠃⣰⣟⡴⠻⣇⡴⢋⣽⣯⠀⣿⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⢏⣀⠀⠈⢉⣁⠀⠀⠀⠀⠀⠻⠔⠁⠀⠀⠀⠀⠀⣎⣸⠟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣱⡿⢹⠀⢰⡟⢹⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠃⠀⣿⣣⠏⣴⢦⠀⣶⠓⢸⣿⠈⢠⡮⢠⣆⣠⡀⢀⣴⠶⣿⡆⣴⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢦⢼⣿⢥⣄⣸⣿⠁⣸⡿⢂⠜⣿⡔⠈⣿⡖⣿⠃⣼⡟⣿⡇⣼⣧⢞⣿⠋⣹⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡴⣿⠀⠻⠚⠉⠓⠋⡞⣿⠇⡼⢻⡇⠙⠊⠘⠁⣿⡰⢁⠔⢹⡟⠸⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠧⠾⠁⠀⠀⠀⠀⠈⠀⠺⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⢀⡶⠻⣦⢀⣾⢿⡄⣷⠀⠀⣿⠀⠀⠀⣾⣆⠀⣰⣷⣾⠟⠛⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠍⢸⡇⠀⠛⢸⣇⣸⡇⣿⠀⠀⣿⠀⠀⠀⣿⠻⣶⡟⣿⣿⣧⡄⠀⠡⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠖⠸⣧⣀⡿⢻⠋⢹⡇⣿⢀⠀⣿⣀⠀⠀⣿⠀⠉⠀⣿⣿⣇⣀⠀⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈⠋⠁⠈⠀⠈⠁⠉⢙⣁⣉⠉⠋⠀⠉⠀⠀⠀⠉⠈⠉⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡴⣶⢀⣀⠀⢿⣅⠈⠆⢠⣷⢠⣦⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⡏⣿⡇⢸⣿⠁⡏⢹⣿⡏⣿⡿⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢸⡿⢸⣿⢠⠿⣇⡴⠁⠸⡿⠁⣿⠇⣿⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⣠⡞⠁⠀⠼⠃⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠰⣿⡀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⢀⣼⡿⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠙⠳⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⠀⢀⠈⠁⠀⢀⣾⣟⡡⠚⠁⠀⣠⣴⠟⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡀⠀⠀⢀⣀⠀⢀⡠⣤⠀⡰⠊⢀⣼⣿⠃⢰⣿⠇⠀⢀⣾⡿⠉⠀⠀⢠⣾⡟⢁⣠⠞⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⢀⣾⠏⡰⠋⣴⢯⠎⠀⢠⣾⡿⠁⢠⣿⠏⠀⠀⣼⣿⠁⠀⠀⢠⣿⡟⠋⠉⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠈⣿⣿⠀⣼⡟⡜⠀⣼⣿⠃⠀⢠⣿⠟⠀⠀⣼⡿⠀⢠⢾⣿⡇⠀⠀⢀⠾⣿⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⣿⠏⠀⣿⡟⠀⠀⢿⠃⠀⢠⣿⡏⠀⢀⠎⠈⠻⠖⠁⢸⣿⡇⠀⡠⠋⠀⣉⣛⣛⠁⠀⠀⢠⣾⠄⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣠⠾⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠿⣧⡤⠋⢀⡴⢋⠇⠀⠀⠻⠿⠛⠁⠖⠛⠉⠉⠉⠙⠓⣶⣿⡏⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⢁⣀⣀⠀⢠⡤⢤⡄⢀⡄⣠⣤⡀⠀⠀⠀⣴⠟⡠⠋⠀⠀⠀⠀⠀⣀⣀⠀⣠⣴⠖⠁⡆⣰⣿⠏⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠸⣄⠁⠀⣼⠁⡼⠳⣾⡾⠓⠚⠁⠀⠀⣼⡿⢊⡤⠶⣦⡀⢀⣴⠟⢁⠔⠰⣿⣇⠀⠚⢡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠐⠤⠟⠀⠀⠃⠘⠃⠘⠉⠳⠴⠋⠀⣠⢴⣿⡱⠋⢀⡀⢼⡗⣾⡟⠀⠀⠀⠀⠹⣿⣦⠀⣸⡟⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠴⣶⡄⠀⠀⣀⢤⣄⠐⠒⠉⠀⣼⡿⠁⡖⠁⡠⠟⠀⢿⣇⢀⡔⢁⡀⢀⣿⡟⠀⢿⣇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⡔⠁⣰⣿⠃⣠⠚⢁⣼⡿⠀⣀⡀⠀⠘⠃⠀⣩⠟⣳⠀⠀⠈⠉⠉⠀⠀⠉⢉⡁⠀⠀⣀⠉⣡⣄⡠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢧⠎⠀⣰⣿⢇⠞⠁⢀⣾⡟⠑⠋⠉⠉⠙⠒⢲⡾⠗⠊⠁⠀⠀⣀⣤⢤⡀⠀⣴⡿⠃⠀⣾⠏⣰⡟⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢰⣿⣿⠋⠀⣠⣿⡟⣠⡶⠋⠙⣦⡄⢠⣿⡥⠚⠙⡿⣠⡾⠋⢀⠜⢀⣾⠟⠀⠀⣼⡏⢰⡟⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢠⣿⣿⠃⠀⢰⣿⠏⣼⠏⠀⠀⣼⡟⢠⣿⣋⡠⠤⠊⢱⣿⠗⠚⢁⡄⣸⠏⠀⠀⣼⡟⢠⡿⢧⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣾⣿⠃⠀⢠⣿⡟⢸⡏⠀⠀⣴⡟⠀⣼⡏⠙⢻⣦⡀⠈⠻⠦⠔⠋⡀⢿⠀⢀⠜⢹⡇⣼⣃⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⡇⠀⠀⢸⣿⠃⠸⢧⡤⠊⢿⡤⠜⣿⠃⠀⠀⠙⢿⣦⣤⣤⣤⠞⠁⠈⠓⣁⡤⠴⠒⢻⣅⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠘⣿⣆⠀⣀⠀⢀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠈⠉⢁⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠳⣤⣤⣄⣀⣤⣤⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⡞⢹⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠘⢧⡙⢦⢹⡸⡴⢋⡼⠃⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡘⢵⡼⡝⠀⠀⠀⠀⠀⠉⠚⢿⡿⠓⠉⠀⠀⠀⠀⠀⢣⣣⡫⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠟⠀⠀⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢹⠀⠀⡏⠀⠀⢾⠆⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠣⡀⠸⣤⠎⡅⠀⣠⡤⡀⠰⡖⠂⠀⣤⣄⠀⠐⠂
⠀⠀⠀⠀⠀⡞⠛⠲⢤⡀⠀⠀⠀⢰⣦⡜⠀⠀⣠⠇⠀⠯⢊⠄⠀⣸⠆⠀⠉⠁⢀⡤⠖⠛⢳
⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠦⠄⠀⠀⠉⠰⠿⠩⣧⣀⡤⣠⣤⡀⣤⠀⣤⠀⠠⠴⠛⠋⠙⠛⠋
⠀⠀⠀⠀⠀⠀⣶⣫⠽⠂⢀⠀⠀⣠⡖⠋⣹⡆⠈⣿⠀⢻⣼⡇⢻⣠⡟⠀⠀⡀⠐⠯⣝⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡝⠀⡜⠸⠀⠀⠈⠁⢀⣉⠀⠀⠉⠀⣠⣉⠀⠀⠀⢫⡳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣣⠞⠀⠀⣇⢣⠀⠀⠀⣼⠏⣨⡇⠀⣠⡟⠉⢻⠀⣤⠀⠀⠳⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠺⠷⠶⠊⢙⣚⣁⣛⣿⣃⣃⣀⡘⠛⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡞⣻⣟⠛⣉⡉⡍⠉⠹⣿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠘⣽⢫⣿⣆⣸⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣇⢸⡼⠛⣥⢟⡏⣆⣀⣓⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢉⠉⡝⡏⣍⣽⢹⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⠿⠿⠽⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢣⣉⣀⠀⣌⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⣹⢦⣰⡄⣶⣯⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣤⣒⣶⢀⣤⡖⡄⣾⢨⡂
⠀⠀⠀⠀⠀⠀⠀⢦⣀⠹⡇⠿⣼⠛⠧⠟⠟⠓⢠⣎⠀⠀⠀⠀⠀⠀⠀⠐⢙⣄⡃⣁⣉⢩⡉⢹⣯⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣻⣦⡀⢸⣷⣾⠟⡶⠣⠾⠊⠀⠀⠀⠀⠀⠀⠀⢠⠆⣘⣛⡄⡈⠁⠀⡀⡉⣽⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⢠⢬⡅⠚⠚⠀⠀⣨⡭⣽⠇⠀⠀⠀⠀⢀⣰⠇⢳⠹⠻⠃⢙⣗⠛⠓⠓⠏⢘⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⠚⠹⣷⣗⣮⠿⢏⣰⡟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡆⠘⠏⠉⠁⠾⠀⠺⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣶⣤⣤⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣤⣖⡗⡒⣒⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⣀⣰⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠟⠳⠎⠷⠧⠛⠥⠆⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠋⠉⠙⠙⡋⠿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⣿⡧⢐⣂⠰⠷⠶⠜⠂⡀⣃⡀⣼⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠛⢂⠙⠛⢂⣠⣐⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿⠀⢸⣾⡗⠚⡇⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠰⡇⠟⠿⠿⠽⠻⠜⡈⢃⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠴⠼⠛⠃⠀⣇⡇⢸⠇⡌⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠘⠀⡿⠥⢈⠉
⠀⠀⠀⠀⠀⠀⠀⢨⡇⢄⡰⠄⠘⠚⠂⢀⠘⣂⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⡶⣶⠼⡠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣥⣴⡎⡿⢻⢀⣆⡄⠀⣣⠀⠀⠀⠀⠀⠀⠀⠷⣠⣤⡶⡄⠀⣶⣧⣄⣀⣀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠃⣴⢫⣿⣿⡤⠴⠟⣾⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠎⠁⠉⠀⠈⠙⠉⠙⠻⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⣀⠀⣤⡀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡀⡄⢠⡤⣠⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡟⣷⢿⠿⢿⣅⠀⠀⠀⠠⠋⠿⡈⠈⠲⠀⠀⠀⠀⠀⠘⣧⢿⣿⡗⢷⣤⣚⡸⠀⠀⠠⣄⣀⠀⣤⣤⣶
⠀⠀⠀⠀⢸⣇⣭⣀⣹⣼⣿⠀⠀⠀⠘⠀⢠⣀⢇⠄⠂⡆⠀⠀⠀⠀⠠⢆⡆⠷⡜⡆⣷⡆⠀⠀⠀⢻⡿⡆⢿⠿⠏⠆
⠀⠀⠀⠀⢸⣾⣬⣧⣾⣿⣿⠀⠀⠀⠀⠙⠌⠟⠈⠁⠈⠀⠀⠀⠀⠀⣶⣄⣶⣲⣰⢠⡤⢰⠀⠀⠀⢀⠀⠀⠀⢠⠐⢄
⠀⠀⠀⠀⢸⣿⠿⣏⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠛⠈⠃⠚⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⣶⣴⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣧⡆⣶⡆⢰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⣦⣤⣶⠀⠄⠀⠀⠀⠀⠀⣯⣥⠩⠭⠭⠭⣭⣽⡄⠀⠀⠀⠀⡤⢤⣤⣤⡄⠀⠀⠀⠀⠀⢠⢤⡄⢰⣤⠀⠆
⠀⠀⠀⠀⠀⣀⡀⡀⢰⣖⣿⠀⠀⠀⡐⡃⡐⡛⡁⣀⢘⢂⡀⠀⠀⠀⣼⠓⡒⡶⠞⠞⣦⡀⠀⠀⠀⣾⢸⣷⣿⡸⣶
⠀⠀⠀⠀⠀⣿⡏⢷⣿⠿⠙⠀⠀⠀⣿⢱⣷⣏⢏⣿⢻⢸⠇⠀⠀⠘⠿⢧⣇⣧⣄⣽⣼⠗⠐⠀⠀⢘⣉⠏⠈⢡⡏
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣿⣼⣿⡇
⠀⠀⠀⠀⠀⣤⠀⡄⠀⠀⡠⡤⢤⡄⢀⠀⡄⡀⠀⠀⠀⠀⠀⡠⣤⣄⠀⣤⣠⣤⣀⢀⡀⠀⠀⠀⠀⣴⢱⣮⣯⣯⣧
⠀⠀⠀⠀⢸⢿⣰⣇⢷⢼⡣⡧⣿⡿⠼⠔⡟⠏⣧⠀⠀⠀⠈⠿⠭⠟⠀⠛⠙⠋⠃⠚⠁⠀⠀⠀⠀⢸⡜⠇⠃⠸⠵
⠀⠀⠀⠀⠈⠸⠇⠉⠀⣠⣀⠥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⣏⢰⢃⢸⠙⡇⣾⢺⡅⠀⠀⠀⠠⣬⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠈⠃⠈⠃⠘⠀⠃⠋⠐⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⡀⠂⠀⠈⠠⠈⠐⢉⠂⠈⠅⠀⡐⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠌⡠⢀⢀⠀⢀⠘⠂⠀⠀⠀⠱⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠈
⠠⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⠀⠈⠀⠡⢠⣉⠢⠁⠐⠇⠑⠘⠀⡀⠉⢁⠁⠀⠀⠀⠀⢣⡐⠶⡄⠂⠀⠆
⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⣀⢘⣤⡤⡌⠂⠀⠀⠀⠀⠀⢀⡠⡄⠀⠀⠂⠈⠉⠀⠀⠀⠀⡀⠠⢄⠒⠀⠸⠉⠁⠀⠀⠃⠀⠐⠀⠲⡀⠉⠀⠁⠁⠄
⠙⠁⢀⠀⠀⠀⢒⠐⣿⣀⡩⠺⠟⠓⠃⠁⠀⠀⠠⠚⠀⠀⠀⠀⠁⢂⡁⠂⠈⠐⠀⠑⠀⠀⠄⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠀⠀⠂⡠⠄⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⡀⠊⡠
⠂⢄⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠠⡠⠀⡁⠁⠀⡤⠂⠀⠀⢀⠉⠃⡐⣰⡤⠠⠤⠄⠈⠁⠀⠀⠈⠀⠐⠀⠒⡈⢀⡀⠄⡀
⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡀⠀⣀⠀⠠⠂⠀⠀⡋⠀⡕⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠉⠈⠀⠑⠀⠀⠔⠈⠀⠀⠀⠀⠀⠈⠀⢁⠂⣸⠍⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠁⠂⠀⡆⡒⠂⠇⠀⠈⠀⠀⠀⠀⠀⠫⡈⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠁⠂⠀⠠⠀⠄⠃⠀⠀⠀⠀⠀⠤⠌⠄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⢈⠀⠀⠀⡀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠈⣀⠐⠁⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⡀⠀⠀⢀⠀⠐⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⢐⠂⠨⠙⡌⢢⡱⠀⠀⠠⠀⠀⠔⠁
⠀⠑⠄⠀⠔⠀⠀⢀⠐⠀⠀⠀⠠⠀⡠⠀⠀⠀⠉⠀⠂⠀⠁⠀⠀⠀⡐⠀⠀⠠⠀⠄⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠀⠀⠨⠐⠅⠈⠠⢈⠁⡁⠀⠀⠀⠀⠁
⠀⢀⠀⢀⠁⠀⠉⠀⠀⠀⠠⠄⡀⠚⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠈⠂⠀⠑⠘⠂⠀⡀⠀⠀⠀⠀⠀⢠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠈⢀⢀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐
⢀⠀⠀⠒⠒⠂⠀⠒⠒⠐⡀⠀⠀⠀⠀⠀⠀⠨⠿⠃⠹⢠⡍⠉⡹⣷⠆⠃⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡄⢀⡠⢀⠄⢀⡀⢀⡀⠀⢊⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠁⠀⠱⢉⠀⠐⢃⠠⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢌⠄⢀⠀⣀⠀⠀⠁⠉⣤⠀⠀⡐⠀⠄
⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢸⠁⡈⠘⢠⢄⠡⢡⠲⠀⠸⠀⠬⠦⢀⠀⠀⠂
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢸⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣿⣿⡇⠀⠛⣹⠃⠀⠀⣼⣿⡿⠃⠀⢠⣆⠀⠀⠀⠀⠈⢀⠀⠁⣀⠀⠐⢄⠀⠀⠀⠀⠈⣨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠃⠀⠀⠀⠈⠿⠃⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠳⠀⠀⠀⠀⠁⠂⠼⠇
⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⢐⡀
⠈⠁⠀⠉⠀⠀⠐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⡄⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠃⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢀⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣧⠸⣿⣷
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠄⠀⠀⠀⠍⡟⢀⣼⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢻⣿⡆⠹⣿
⡆⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠼⠛⠿⠃⠀⢀⠀⠀⠀⠀⠀⢀⣿⢅⡅⢠⣤⠘⣿⣷⠀⢿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢈⠆⠀⠀⣈⡓⢦⡀⠀⠀⠘⠛⢸⡇⠸⠏⠀⠹⣿⣿⣿
⣿⣇⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⣥⠈⠀⠀⠈⠁⠉⠢⡉⠀⠀⢠⠆⢸⢿⡆⠀⠀⠀⢿⣿⣿
⣿⡿⡄⠀⣾⠀⠀⠀⣄⢠⡆⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡄⢀⠏⠀⠀⠀⠀⠀⠂⠤⠁⠀⢀⣦⠀⢿⣾⡇⠀⠀⠀⠸⣿⣿
⠸⣾⣧⡀⢯⠀⠀⠀⠈⠋⠀⠀⠈⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠻⠀⠀⠀⠀⠀⢻⣿
⠃⠙⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢰⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⡀⢁
⣠⣿⣿⠏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠿⢋⣼⣷⡈⠁
⣿⣿⡿⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡜⠃⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⣰
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡤⠀⠀⠀⢸⣿⣿⡿⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⢹⣯⢿⠇⠀⠀⠀⠀⣴⣿
⣿⣯⠀⠀⠀⠲⠋⠀⠠⠶⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⣾⣿⣿⠃⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣶⠀⠀⠀⢾⣿⡟⠁⠀⣼⣇⣼⣿⡏⠀⠀⠀⠀⢴⠿⣿
⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢠⣾⣿⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠟⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠸⠆⣴⣿
⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢁⠂⠐⣉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⡇⠀⠀⢠⣤⠀⠀⣠⣼
⣿⡇⠘⠃⠀⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⡞⠠⠰⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⣴⡿⠁⠀⠀⠻⣿
⠍⠑⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⡼⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡴⣀⣀⡀⠀⡀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⣾⣿⡿⣸⣟⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⢀⠐⠁⠀⠀⢀⡀⣀⠀⠀⠀⠐⢄⠀⠀⠠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣿⣀⣸⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣷⣁⣀⣀⣘⣄⣈⣠⣀⣀⣀⣄⣀⣀⣤⣀⣀⣀⣀⣺⣿⣇⣀⣀⣀⣀⣠
⣿⣿⡟⠛⠿⠛⠻⠻⣟⠟⣿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠣⡀⠈⢢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢌⠂⣀⡸⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⣀⡸⠈⢃
⠀⠑⠦⢀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⢀⣠⠚⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡈⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡈⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠁⢀⠜⡢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠐⠊⢀⠜⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠋⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠰⠉⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠮⡔⠋⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡔⠉⢀⠜⡡⠊
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠑⢲⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢒⡡⠊
⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⢉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡔⢉⢇
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢
⠠⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢌⠲⣀⠙⠦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢌⠲⡄
⡀⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡄⠙⠆⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌
⢌⠲⣀⡸⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣀⠸⠉⢃
⠀⠑⠧⢀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⢀⣠⠚⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡘⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠦⡘⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠃⢀⠜⡢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠃⢀⠜⡢⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡔⠃⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠉⢠⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠮⡔⠊⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⡤⠃⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠑⢲⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢲⡡⠊
⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢉⢇
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⢁⡔⠉⠤
⢠⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀⠈⢢⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯⣳⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⡿⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢠⠏⢠⠞
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡰⠁
⢠⠞⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠉⠳⣤⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⡴⠃⠀⣀⠞
⢸⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠉⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢸⢉⡄⢸⡾⠁⠀⣰⠋
⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⢀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⢤⢼⠟⣷⠋⠀⢠⡞⣁⡞
⢸⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡙⡛⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡁⢸⡾⠁⠀⣴⢏⠞⠕
⢸⡇⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠤⠤⠤⣤⠏⠀⢀⣼⠁⠘⠃
⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡶⠃⠀⢠⠟⠽
⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⢻⠀⢀
⢸⡇⢸⣿⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⡃⠀⢀⠞⢀⣿⠀⠈
⢸⡇⢈⢻⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣠⠊⠀⢈⣁⠀⣤
⢸⡇⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣠⠞⠁⠀⠀⢿⣨⠀⣿
⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠁⠀⠀⠀⠀⢼⡏⠀⠉
⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿
⢸⡇⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿
⠀⡇⠀⠻⡦⠀⠀⠠⠤⠤⠴⠦⠰⠶⠖⠒⠲⠒⠒⠒⠒⣾⡴⠒⠂⠐⠶⠂⠀⠰⠦⠀⠤⠤⠤⠤⠤⠤⠤⠾⠇⠀⡃
⠀⠙⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠁⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠔⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢸⡀⠸⠞⡆⠀⣿⠁⠠
⣀⠀⠀⠀⠀⠀⠀⣿⡙⣷⣾⣔⠰⣀⣀⡤⠤⢤⡶⠀⠀⠀⠀⠀⠀⠀⠠⠘⠷⠖⡂⢘⡀⠻⠀⠈
⠘⣿⡙⠲⣗⡢⠿⡭⣬⣥⠤⠤⠒⠉⣿⠁⠐⡿⠓⠀⠀⠀⠀⢰⣿⣇⢀⢠⢤⠀⠁⠉⠃⣀⣐⣿⣾⣦⡄
⠉⠻⣯⡀⣇⡽⠾⡴⣤⡴⠶⢶⡖⣛⣿⡤⠞⠁⠀⠀⠀⠀⠀⣻⣿⡃⠀⡿⡉⣴⡆⣶⣪⣿⠁⠈⣻⣿⠇
⠀⠀⠈⠙⠛⠉⡷⣶⣶⡖⢲⡮⠽⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠀⢑⣯⡙⠊⠝⢱⠘⠒⠈⢿⠟⠁
⠀⠀⣠⡄⣶⠒⠰⣤⢠⡖⢠⢠⢰⡂⣯⡈⠧⣄⠳⠁⠀⠀⠀⠀⠈⠁⠀⢸⠜⠅⠀⡼⢉⡀
⠀⠀⠈⠁⣏⡀⠰⠻⡜⣧⠼⣦⠀⣼⠻⡴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⣺⣇⣯⣏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠉⠉⠙⠇⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⡠⠄⢨⣯⢰⣄⡆⡂
⠀⠀⠀⠀⠀⠀⠑⠒⡘⠉⡉⠈⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⢻⠁⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⢸⡯⣉⣿⢩⠭⠉⢩⣭⣏⣹⣁⣤⣸⣁⣀⣼⢗⠰⠶
⠀⠀⠀⠀⠙⢣⡄⣀⡀⡉⡅⡐⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⡤⠈⠀⠀⡀⠀⠀⠀⣤⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠂⠁⡤⠒⢠⡀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣀⢳⣀⣤⠈⡏⢠⡖⢀⡯⡄⢀⠁⢸⡇
⠀⠀⠀⠀⠀⢰⢰⣼⣇⣭⣻⢡⣖⣿⣤⠀⠀⠀⠀⠀⠀⢸⡇⠳⠋⠚⠛⢊⣌⣨⡍⡩⡅⠃⠓⣁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠋⢙⣉⡥⡅⡴⡆⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠑⠌⠿⠘⠙⠧⠶⠥⠴⠐⠇⠀⢸⡇
⠀⠀⠀⠀⠀⢀⠈⢻⠸⠷⠧⢟⣡⣦⣆⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠹⠲⡶⡶⢶⠶⠞⠛
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠽⢷⣷⡹⣶⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣉⣽⣦⣀⡀⠈⠙⠻⢷⣶⡄⠀⠳⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠄⠀⠉⠠⣾⠛⠛⠻⢿⡀⣀⠀⠀⠀⠀⠉⠳⢤⡈⠂⡀
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⣀⣼⣯⡀⠀⠀⠀⠀⠛⢿⣶⣰⢄⡄⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠂⠀⠀⠀⠀⠀⠙⠿⣿⠦⢥⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⠇⠀⠀⠀⣲⣤⣄⠀⠀⠀⠈⠑⠶⢽⣷⣦⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣴⢶⡀⢀⠋⠻⢷⣦⣰⡠⠀⠀⠀⠘⡿⢿⡷⠖⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣼⡆⡴⣶⣶⠀⠈⠈⠻⣾⣧⣄⣼⠀⣙⣿⣷⣶⣶⣬⣥⣀⣿⣦⡀
⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⣽⣻⡿⣦⣤⢘⠉⢻⢿⢿⣿⣾⣿⣿⠿⠛⠛⠋⠁⠀⠈⠻⢦⣀
⠀⠀⠸⠿⠿⢿⢟⣿⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀
⠀⠀⠀⠈⠉⠉⠁⠉⠀⠉⠛⠻⠿⠿⠻⠿⠿⠿⠟⠿⠓

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡟⣆⡠⣤⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡩⢄⡏⣣⣊⣑⢊⠃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⡀⠑⣞⢁⣉⠉⠉⠛⣡⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⢸⣧⡾⢦⠀⠀⡴⣤⣒⡯⢆⣐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠃⢀⠘⣘⠛⣠⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢿⠸⣇⢸⣶⡶⡡⠾⡕⠾⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡗⢻⢸⡋⠀⠳⣄⠸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠉⠈⠪⠶⣉⠀⢀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠨⢟⣁⣈⣬⣷⣥⣴⣯⣤⡱⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠀⡴⢢⣠⠀⡀⣾⠁⠇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⣾⣶⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⡄⣾⠉⣸⣿⣠⡇⢻⡾⣾⢹⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⢉⣿⣁⠘⠁⢉⠨⠽⡅⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢛⣿⡿⠿⠿⢿⠛⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⢠⢠⡀⢀⡤⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆⢠⠂⠘⠶⠴⠾⠿⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡆⣇⠀⢸⡎⣧⠄⣿⠂⠀⣾⣇⡤⢲⠆⠀⠀⠀⠀⢯⡴⠀⣷⢸⡤⢀⣀⡀⢿⣄⠀⡠⣇
⠀⠀⠀⠀⠀⠐⠭⣉⣹⣾⣇⠻⠐⠊⠃⠘⡁⠙⠂⣠⣿⣟⠭⣁⠀⠀⠀⠀⠀⠀⢠⡌⣹⢻⣁⣿⠼⣥⠞⣏⣸⣤⣿⡀
⠀⠀⠀⠀⠀⠀⢠⡎⠔⣫⡥⢤⡀⠀⠉⠉⠁⣤⡤⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⢤⡿⣋⠀⣍⢠⣤⣴⣦⠨⠄⠈⣽⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⠘⠉⣱⡴⣿⡾⡞⢦⡠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈⢨⣍⣬⡀⣤⡀⣤⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⣾⠀⢉⣻⠆⢐⡖⠁⢰⣶⡯⢃⣤⣄⣠⠀⠀⠀⠀⠀⢀⣀⣉⣘⣥⣿⣵⣯⣧⣼⣬⣁⣀
⠀⠀⠀⠀⠀⠀⢴⣾⣿⣷⣄⡙⡏⢁⣤⣿⠰⣟⣀⣩⣿⣿⣿⠿⠛⠀⠀⠀⢀⣠⣼⣿⢿⡯⣿⢿⣿⣿⣿⣿⡿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⣏⣻⠿⢷⡶⢤⣤⡶⠟⣿⣥⠋⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣄⣴⣿⠶⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⠸⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣌⠣⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠂⢑⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⣦⡀⠸⢷⡄⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⠘⢿⣦⡀⠠⡀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠢⣄⠀⠀⠀⠈⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣹⣷⣄⠙⢷⣦⡄⣀⣀⡀⠹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢻⣸⣿⣷⡀⠙⢿⣿⣿⣧⠀⠀⢣⡀
⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠿⣦⡀⠹⣿⣮⢷⠀⠀⢳⡀
⠀⠀⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢢⡆⠉⢐⣸⢿⣷⣿⡖⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⣶⣬⣳⣤⡀⠀⠀⢀⢀⣀⠀⣀⡀⠀⣀⣀⣀⣐⣘⣉⣠⣉⡻⠦⠀⢏⠀⠀⢙⣿⣿⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣿⣿⠿⠿⣿⡿⠿⢿⣿⣛⣿⣿⣷⣶⡾⠷⠿⣜⢿⣇⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢠⣤⣐⢷⡶⢛⣫⡵⠟⠉⠁⠙⠛⠛⠻⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠭⠟⠦⣤⠞⠳⣌⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣽⠟⣉⣥⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣀⠈⠳⢾⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁




⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⢰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⡇
⠀⠀⢸⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⣀⣤⣤⣄⠀⠀⣤⣤⣤⣄⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⠉⢻⣿⡀⢰⣿⠏⠙⣿⣧⠀⣿⡏⠙⣿⡇⢸⣿⠉⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠘⣿⡇⣿⣿⠀⠀⢸⣿⡀⣿⣷⣴⣿⠇⢸⣿⣷⣶⠀⠀⣄⡀⠀⢸⣷
⠀⠀⢸⡇⠀⣀⣶⠀⣿⣿⠀⢸⣿⠇⢻⣿⠀⠀⣼⣿⠀⣿⡟⠉⠁⠀⢸⣿⠀⠀⠀⠀⡟⠛⠀⢸⣿
⠀⠀⢸⡇⠀⠉⠃⠀⢿⣿⣶⡿⠏⠀⠈⠿⣷⣾⡿⠃⠀⣿⡿⠀⠀⠀⢸⣿⣶⣶⡶⠀⠁⠀⠀⢸⢹
⠀⠀⢸⡇⠀⢀⣤⣤⣔⠲⣄⠀⡠⠴⣦⣄⠀⣠⡶⢲⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣴⠖⠆⠀⢸⢸
⠀⠀⢸⡇⠀⠊⠸⠀⠈⢇⣿⡟⠀⠀⢸⡿⢰⣿⡡⠃⠀⢀⠀⠀⠙⠇⠀⡀⠀⣰⣿⡣⠊⠀⠀⢸⢸
⠀⠀⢸⡇⠀⢄⢠⠈⡇⠸⣿⡇⣀⣤⠞⠁⣼⡏⠀⢀⡾⠁⢸⣿⠀⣰⠏⠈⠂⣿⡯⠒⣦⠀⠀⢸⢸
⠀⠀⢸⡇⠀⠈⠉⠛⠐⠁⠿⠃⠀⠈⣷⠀⢻⡇⠀⣸⡇⢀⢾⡏⢠⣿⠀⠀⡰⣿⢤⡞⠃⢰⠀⢸⢸
⠀⠀⢸⣷⠀⠹⢏⠀⠀⠀⢎⠈⣃⣼⠟⠀⠈⠳⠔⠁⠉⠁⠈⠷⠊⠙⠧⠐⠁⠈⠀⠻⠔⠁⠀⢸⢸
⠀⠀⢸⣿⢠⣤⠀⣤⡄⢠⣤⠈⢁⣤⣤⣄⠀⢀⣤⠀⠀⠀⣤⡄⠀⣠⣤⣤⡀⠀⢠⣄⠀⢠⣤⢸⢸
⠀⠀⢸⣿⢸⣿⠀⣿⡇⢸⣿⠀⣾⡏⠀⣿⡇⢸⣿⡇⠀⢰⣿⡇⢀⣿⠃⢹⣷⠀⢸⣿⡀⢸⣿⢸⢸⡆
⠀⠀⢸⢸⢸⣿⢰⣿⣧⢸⣿⠀⣿⡇⠀⣿⡇⢸⣿⣿⠀⣼⣿⡇⢸⣿⠀⢸⣿⠀⢸⣿⣇⢸⣿⢸⢸⡇
⠀⠀⢸⢸⠈⣿⢸⡿⣿⢸⡏⠀⣿⡇⠀⣿⡇⢸⣿⣿⣦⣿⣿⡇⢸⣿⡀⣸⣿⠀⢸⡟⣿⣾⣿⢸⠘⡇
⠀⠀⢸⢸⠀⣿⣿⡇⣿⣿⡇⠀⣿⡇⠀⣿⡇⢸⣿⢻⣿⡏⣿⡇⢸⣿⠛⢻⣿⠀⢸⡇⠸⣿⣿⢸⠀⡇
⠀⠀⢸⢸⠀⣿⣿⠁⢸⣿⡇⠀⠹⣿⣴⣿⠃⢸⣿⠈⣿⠁⣿⡇⢸⣿⠀⢸⣿⠀⢸⡇⠀⢿⣿⢸⠀⡇
⠀⠀⢸⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣠⡇
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣀⢐⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠐⠒⢀⠀⠀⠀⠀⠆⠠⠂⠴⠀⠀⠀⠀⠊⢀⠀⠉⠂⠀⠀⠂⠖⡀⢠⠧⠉⠀⠀⣞⢐⠠⠄⢻⠀⠀⠀⠀⠐⠆⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠰⠄⠀⠀⠠⠄⠀⠈⠀⠄⠁⠄⠀⠉⠀⣤⡿⠿⠿⠿⣶⡄⠀⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⢠⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⡀⡀⠀⠀⢀⠡⠂⠄⠂⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⢀⢠⡄⣀⣀⠀⠀⢈⣈⡀⠁⠄⠥⠀⠀⠈⠀⠃⠂⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠒⠤⠄⠀⠀⠀⠀⠲⠀⡀⠀⠀⠀⠀⠒⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠴⠤⠴⠦⠴⠀⠀⠀⠰⠖⠠⢠⠀⠀⠀⠀⠤⠈⠤⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠸⠨⠍⠙⠀⠀⠀⠀⠸⠋⠒⠀⠀⠀⠀⢠⠂⠀⠀⠶⠀⠀⠀⢀⣤⠀⣄⡀
⠀⠀⠀⠀⣐⢢⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⢀⢳⠞⠀⠀⠀⠀⠀⢠⠀⠂⠆⠀⠀⠀⣶⠉⠛⠓⠖⠀⠀⠘⣽⣿⣿⣟⣭⡇⠀⣀⣾⣠⣆⣴⣶⠄
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠊⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠉⠓⠓⠒⠁⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠈⠛⠉⠉⠉

⠀⠀⢀⠤⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠰⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⠀⢶⠄⠀⠈⠶⠆⠀⠀⠀⣙⠈⠀⠀⠀⠀⠀⠉⠃⠈⠋⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣴⣄⠀⠀⠀⠀⠀⢈⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠠⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡤⠤⠄⢀⣀⠀⡸⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠈⡉⠉⠉⠁⠀⠀⠒⠂⠐⠈⠉⠉⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⠤⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠘⠉⠭⠽⠟⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠻⠛⠛⠓⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⣄
⠀⠀⠀⠀⠀⢀⡴⢚⠁⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⡀⠀⢀⣠⡤⠖⠛⣉⠥⠄⠠⠜⠻⣦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠁⠀⠔⠊⠉⠴⠊⠩⡝⢳⣄⡀
⠠⢶⠤⣰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⢣⡺⡤⣿⣌⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣠⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡲⠤⣄⣀
⡠⢀⠙⠺⠻⣷⣶⡤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣩⡾⡃⣀⣚⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣤⣽⣦⣀⠤⢶⢺
⠀⠐⠣⡅⣙⢄⣋⣭⣛⣓⣶⠶⢶⣤⡤⣤⡴⠶⠶⠶⠶⠚⡟⠛⠶⠿⢱⣚⡏⠩⠈⠓⢄⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢿⢿⠿⠿⠟⠛⠉⠉⢀⣀⣼⠿
⠀⠀⣾⣷⡔⠀⢨⠃⠂⠘⠑⠷⢶⣧⣲⡖⠃⢂⡵⠷⠒⠛⣓⣲⡒⠄⡽⣿⡀⠀⠀⠀⠀⠙⠢⣀⣴⡟⠛⢿⡟⠀⣠⣲⣷⣲⠶⢶⣒⠚⠿⢍⡳⢤⣤
⠀⠀⡟⠬⡙⠗⠦⣤⣀⠀⠀⣀⣀⠀⠀⣙⡉⠀⢀⠭⠒⣈⠡⠖⠴⠼⢂⣿⡁⢠⢠⡔⠀⠀⢠⣾⡇⠘⡳⡖⠀⡴⣱⡁⢸⡌⠉⢳⢦⣍⡒⠤⣉⣲⠖
⠀⢀⠛⣦⡘⠀⢀⡈⠉⠛⠖⠀⣀⣀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣠⠎⢱⠙⢦⡸⢃⠄⠀⣾⣿⡇⠀⣷⡉⢙⡴⣝⢧⡀⣷⠀⠈⣶⣄⣹⣲⣇⡰
⠀⠐⡀⠈⠀⠩⠴⠿⠧⠤⠤⢤⣁⣉⣥⣌⡱⣶⡴⠭⢄⣒⣂⠭⠔⠋⠀⡸⠀⠀⠙⢼⠃⢠⡟⣿⣿⠀⠸⣿⡋⠵⢾⣭⣏⣻⡖⠐⡧⣄⣈⣉⣏⣹
⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠙⢮⡇⠈⢻⠇⠀⢳⡉⠲⣤⣄⠤⣞⠛⢟⠿⣓⠊
⠀⠀⠀⠀⠈⠉⠒⠛⠛⠉⠁⠲⠶⠶⠶⠦⠤⠤⠄⠀⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢿⠭⡛⡘⣤⡉⢉⠇⠈⠑⢤⣙⡚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣈⣆⠱⣸⣌⣄⠉⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠙⡾⠋⡏⠀⣷⢸⠀⡷⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢀⠄⠀⠿⣤⣴⣼⣾⣴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠚⠁⠈⠂⠋⡀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣩⠉⢷⢸⢀⡀⠀⠀⠠⣶⡄⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢺⡟⠓⠓⣠⡐⠟⣻⡛⢺⡇⠘⡓⠒⠆⠀⠀⠀⠀⠀⠀⠉⢀⡐⢺⡾⡟⢰⣟⣿⠁⡽⡿⢠⡏⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⡷⠆⠺⣟⣡⣜⡇⣴⣦⣸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡾⠁⠳⠞⡉⠈⣉⡀⠓⠊⠙⠳⡿⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⢾⠦⣠⠦⠨⠵⠀⣀⣉⠀⠀⠀⠀⣀⠀⠀⠀⠚⢹⣏⠰⠆⡾⠆⠿⠻⠻⠟⠈⠃⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⢿⡷⠒⠙⠙⠟⠋⠀⠿⠳⠇⠀⠐⡍⠙⠛⠛⠛⠀⠿⠟⠀⠀⠀⠈⠁⣠⠰⣶⢶⣶⢠⣷⡌⢺⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⡿⠟⢷⠟⠳⠛⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣥⣬⣥⣭⣥⣥⣬⣤⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠚⠛⠊⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠿⣿⢽⡿⣿⣯⣝⣿⢻⣿⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⢡⣶⠆⢻⡋⢳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡟⣧⢲⣴⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣥⣤⣬⣭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⣰⣃⠀⠈⢈⣀⠀⣄⣠⠆⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣾⡇⢸⡵⣾⢡⢴⠤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣜⢦⢂⡉⠘⠆⠲⠜⠉⠓⣪⠼⣞⣉⡛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⣝⣓⠘⢁⣘⡊⢠⣄⠀⠀⠀⠀⠀⠀⠐⡖⠛⠛⠹⠿⢧⣤⣤⡤⠤⡤⠤⣦⠶⣿⠿⡟⠉⠙⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⡂⠀⠀⡁⠀⢸⡏⢡⡟⠙⣧⠙⢲⡏⠀⣇⣀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣽⣳⣤⢤⣴⣤⣶⣿⡤⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣇⣈⠚⣁⠈⠳⠞⠃⣀⣘⣣⣤⠌⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣨⡉⠉⣁⣠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠋⠉⠛⠉⠁



⡿⢿⠿⠿⠿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠈⢁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣡⣊⣽⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⢧⣄⣴⠗⡢⡀
⠀⠀⠀⠀⠀⠀⢀⠌⡜⠙⠉⢎⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠀⠀⠀⠀⠀⠑⡔⡄
⠀⠀⠀⠀⠀⢠⠂⡘⠀⠀⠀⠀⠆⠱⡀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠚⠚⠤⠤⠤⠤⠤⠤⠤⠐⠒⠤⡄
⠀⠀⠀⠀⢀⠃⠀⠃⠀⠀⠀⠀⠘⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡌⠀⠰⡦⣠⡄⣤⡄⡦⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠇⠿⠾⠻⠼⠧⠀⠀⠀⡇
⠀⠀⠀⢰⠀⠀⢀⡁⣉⣉⢁⡉⣉⡀⠀⠘⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⡔⣶⡶⣴⡔⣶⠀⠀⠀⡇
⠀⠀⠀⡆⠀⠀⠚⠓⠛⠛⠘⠓⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠀⠂⠀⠂⠐⠐⠂⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡜⠀⠈⠉⠁⠐⠒⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠂⠤⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠧⣤⣶⣦⡜⢤⡄
⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣛⣘⣔⣺⠉⠇
⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢰⢰⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠅⠀⠀⡇⠀⠈⢢
⠀⠀⡇⠀⠇⠾⣴⣶⢠⡄⠀⠈⢨⠀⢸⡤⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃
⠀⠀⠁⡴⡆⣤⣤⢠⣈⡁⠀⡆⢸⠔⣁⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⣠⡄⣤⢠⡤
⠀⠨⣀⡀⠀⠀⠁⠉⠃⠛⠀⡇⡸⢋⡼⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣁⣉⢁⡉⣉⡀
⠀⠀⠀⠀⠉⠐⠒⠢⠄⣀⣀⣶⠔⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠛⠚⠓⠙⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣃⢸⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⡏⠀⠀⠀⠀⢀⡠⢄⢴⠊⠉⢱⡀⡏⠉⠀⣁⢀⠖⠤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠰⡁⠀⠈⢎⡆⠀⠀⢣⠡⠀⠀⢠⡌⠀⠀⡰⡰⠁⠉⢢
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠀⣧⣤⣤⣤⣀⣱⡀⢺⠁⠘⡀⠀⠀⣾⠀⠀⢸⠁⠀⢠⠛⠳⡄⢀⠎
⠀⠀⠀⢰⡉⢖⠉⠉⠀⠀⠀⠘⠤⠃⠀⠀⠀⠉⢁⡣⢉⣇⠀⢇⠀⠀⢹⠀⠀⡍⠀⠀⠸⠀⡸⠀⡎
⠀⠀⠀⢸⠪⠭⢉⣛⣒⣛⠛⠚⠶⠚⠛⣛⣚⣛⡉⠭⠑⡟⡀⢸⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠇⣼
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠧⣀⡇⠀⠸⠀⢸⠀⠀⠀⣃⡴⠊⠸
⠀⠀⠀⠀⡇⠀⠀⠀⣼⢷⡀⠀⠀⠀⢠⡾⣦⠀⠀⠀⢸⡀⠀⠈⠉⠒⠓⠒⠚⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠈⠁⠀⢁⣴⣶⣦⡉⠀⠈⠁⠀⠀⡏⡇⠀⠞⠋⠳⠀⠀⠀⠀⠞⠉⠳⠀⢰
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣿⡟⣻⠁⠀⠀⠀⠀⢠⠄⢻⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⠀⣀⠀⢼⢀⣸⡀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⡝⡤⠖⢀⣉⣛⠫⠽⠿⣓⠒⠶⣶⣶⣶⣶⣤⣬⡿⣍⡓⠛⣉⣐⡶⣚⠭⠭⠓⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡴⠛⢒⡒⢛⡒⠢⠤⠤⠒⢬⠲⣦⣄⣢⣶⠖⠥⠦⠶⠶⠛⠛⠛⠚⠲⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠉⢲⠋⠀⠀⠰⠃⠈⠁⠺⡄⠘⣀⠘⢣⡄⠰⠂⣰⠂⡤⢸⡇⣨⡃⠘⠁⠀⠀⠀⠱⡖⠁
⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠆⠤⠤⠤⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠤⠤⠄⠒⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣴⣤⣦⠀⢴⡴⠶⠛⣠⠠⠤⠤⣤⠄
⠀⠀⠘⠳⡍⠉⣿⣓⣶⣞⣶⣅⢒⣶⢲⣉⢩⡭⡇⢀⣘⡡⠄
⠀⠀⠀⠚⠒⠒⠛⠙⢻⠉⠸⠋⠘⣛⣀⣙⡠⠥⠉⠁⢰⠂⠀⠀⠀⠀⠀⣠⠞⣳⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⣠⢆
⠀⠀⠀⠀⢙⣶⣤⣴⡦⠉⠛⠻⠛⠚⡃⣀⢀⣠⣤⢰⡛⢥⠀⠀⠀⠀⠳⡧⠶⠋⠀⠀⠸⣸⢀⠀⠀⢤⣾⣿⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠆⠀⣾⣵⣀⡏⢹⣈⡟⠙⣇⡌⠻⣜⣋⢳⠀⠀⠀⣠⣄⠈⡏⠙⣦⣾⠡⣿⠃⣬⢰⢲⢠⠉⣦⣜⠆⡰⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⢰⣟⡂⠺⡁⠻⣍⠓⠲⠋⠀⠀⠀⢸⣿⣦⣌⣶⣿⡽⢷⡙⣖⡙⣚⡗⣉⣚⠁⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠷⠎⠓⠂⠘⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠿⠁⠀⠀⠀⠙⠁⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠠⢸⠃⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣼⢃⣀⣀⡴⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣰⣧⡶⣆⠀⢰⢦⣴⡮⢅⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢷⡟⢿⣹⡏⠀⢷⠟⠁⣶⠆⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡿⣇⣼⢶⠫⢚⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣉⢁⡌⠁⠈⠉⠀⠀⠀⡾⡇⢠⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠚⡡⡀⢠⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⣼⠁⢀⢀⡄⡀⢀⠀⣿⡃⢻⡏⠀⠀⠀⠀⠀⠀⢠⡼⡇⢠⡯⢱⣶⢠⢸⣁⣁⢾⡇
⠀⠀⠀⠀⠀⠀⠀⡔⢡⡏⣰⣟⡿⢻⣇⣾⡾⢏⣹⠟⣧⡄⠀⠀⠀⠀⠀⠸⣥⢧⠼⣧⠏⠿⠻⠞⢫⡟⠘⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠉⠉⠁⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠀⠀⠀⣠⠤⠀⠀⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠒⠤⡄⠴⡴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠞⠣⠒⠗⠒⠀⠀⠀⢄⢠⠤⠄⠤⣤⠲⠈⠀⡠⠶⠈⠑⠀⠤⣥⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣂⣀⠁⠀⠈⠀⠀⠀⠀⠀⢂⠤⣎⣁⠠⠄
⠀⠣⠀⠐⠠⠄⠀⠀⠀⠤⠀⠀⠀⢠⠞⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠐⠁⠀⢠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠓⠦⢀⡀⠀⡠⠖⡩⠄⠀⠀⠀⢸⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠭⠔⠉⠀⠀⠀⠀⠀⠘⡇⡞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠄⢠⡄⠀⠒⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠀⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠈⠀⢠⠘⣠⠀⠅⠤⠀⠃
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⢀⡌⠀⠈⠀⠸⠁⠐⠀⠀⢀⠁⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠠⠴⠄⠊⠀⢀⠘⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡜⠚⠀⠁⠂⠀⠀⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⣴⠄⢀⡀⠙⠂⡀⢀⡀⠀⠀⠐⠧⡄⠣⡀⠀⠀⠀⠀⠀⠛⡠⠄⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⢠⣄⣀⠀⠀⠀⢀⠀⠐⠠⠤⠀⠉⠈⠒⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠠⢌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠈⠀⢀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀
⠰⢦⡀⠴⠄⠦⠔⠃⠀⠀⣀⠤⢠⡄⡶⠠⢄⠀⡆⠀⠀⠀⡀⠀⡝⠤⢀⡀⢠⡄⢤⣤⠀⣀⡠⠄⠀⡢⠄⠠⠄⠀⠀⣀⠤⠀⢨⣅⡰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⡥⠀⣶⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣛⡀⠀⢠⠀⠀⠘⠡⡤⠀⠁⠀⠕⠀⢀⡀⣤⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠐⠈⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢩⠁⠀⣠⡀⠑⠓⠐⠆⠀⠀⠀⠀⠈⠉⠀⠉⠀⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⣀⣀⣈⡀⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠈⠁⠉⠀⠦⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⠀⠀⠐⡶⠀⡀⠀⠀⣀⡀⠀⠁⠀⠄⠀⠺⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠔⠀⠀⠠⠤⠀⡀⠠
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠌⠓⠀⠀⠁⠀⠒⠀⠀⠀⠑⠠⠌⠂⠉⠐⠂⠉⠀⠀⠀⠀⠔⠀⠑⠒⠂⢀⣁⡀⠀⠈⠁⡠⠀⠀⠀⠄
⠀⣤⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠆⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠀⠀⠀⢈⠄⠠⠐
⡇⠀⠀⠁⢄⠘⠦⣄⢠⡄⠔⠀⠘⣰⠀⠀⠀⣀⣦⠄⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠡⠀⠀⣤⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡀⠘⢇⣀⠀⣀⠀⠔⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢋⡤⠀⠀⠀⠀⠐⢀⠁⠀⠀⠠⠒⠈⠉⠉⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠇⠀⠀⠀⠀⢀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠤⡀⠀⢀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⢰⠀⠀⠃⢄⣀⡀⢀⣀⡰⠞⠀⡈⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠊⠔⣈⠉⠋⣀⠲⠀⠀⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣊⠤⠖⠶⠤⡑⠀⠀⠡⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⣀⡀⣀⣀⠈⠁⠈⠣⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⣀⠀⠀⠀⠀⠀⠆⠀⠴⠀⠀⢀⠤
⠀⠀⠀⠀⠓⠈⠜⢉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣰⠁⠀⠀⠀⠀⢠⠈⠁⠜⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⢞⡵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣄⣤⣤⡤⠐⣡⣶⡋⢀⣾⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⣡⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⣉⣴⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣾⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣉⣖⣫⣾⣿⡿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣠⢻⡤⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣀⢟⡽⢷⣤⣤⡆⢀⣀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⢀⢀⠛⠋⠀⠀⠙⠛⠋⠹⠿⢻⠿⠿⠛⠛⠛⠛⣛⠛⠻⢿⣿⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣇⠀⢻⣿⣿⣿⣿⣷
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⢿⡿⠟⠛⠛⠛⠋⠛⠛⠉⠁⠀⠀⠀⠀⠀⢄⣸⣇⢿⣿⣟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠁⠀⠙⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣘⣛⣛⣛⣛⣋⣙⣛⣛⣛⣛⣃⣙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣒⣒⣒⣒⣒⣒⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⢠⡿⢛⣛⣛⣛⣛⣛⣛⠛⢻⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣏⣉⣉⣉⣍⣿⡇⣿⣿⣿⡇⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢠⣿⣧⣤⣤⣤⣤⣿⢡⣿⣿⣿⢃⣏⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠘⠿⠿⠿⠿⠿⠿⠟⢸⣿⣿⣿⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠇⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢘⣵⣾⣿⣦⡁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢿⣶⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⢸⣿⡇⠀⠀⢸⣿⣦⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣶⡄⠀⢻⣿⡇⣼⣿⠃⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⢸⣿⣿⣿⣧⣤⣤⣀⠀⠀⢁⣤⣶⣶⣦⠀⠀⠀⣾⣿⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⠻⠁⠀⢸⣿⡿⠋⠉⠀⢹⣿⣷⡀⣾⣿⠋⣰⡿⠀⠀⠀⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣼⣿⢹⡇⠀⠀⢀⣼⣿⡇⠀⠀⠀⣸⣿⣿⢻⣿⡿⠛⠉⢀⡾⠀⠀⠙⠉⠁
⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢠⣿⡟⢸⡇⠀⢠⣿⠉⣿⡇⠀⠀⣰⣿⣿⠏⠈⢿⣿⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣠⣤⣤⣄⣀⣸⣿⠇⠀⠀⣸⣿⡇⢸⡇⠀⠈⢿⣄⣀⣀⣴⣾⣿⠟⠁⠀⠀⠀⢈⣉⠉⠀⠀⠀⠀⠀⢠⣶⣆⠀⣸⣿⡀
⠛⠷⣤⣤⣭⣿⣿⠓⠒⠲⣿⣿⡷⠾⠃⠀⠀⠀⠈⠉⠙⠉⠉⢰⣦⣴⡟⢻⣦⢸⣿⡆⢀⣴⠶⣶⡄⢸⣿⣿⠀⣽⣿⣇
⠀⠀⠀⠀⢀⣿⣿⠀⠀⢀⣿⣿⠇⠀⠀⢠⣶⣿⠟⣿⣆⠀⠀⣿⣿⡟⣀⣼⡿⢼⣿⣿⡿⠁⣀⣿⡟⠙⣿⣿⣦⣿⣿⣿⣤⠴⠒
⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⢀⣴⣿⣿⡏⣼⣿⣿⠀⣼⣿⣿⣿⣽⠿⠁⠈⣿⣿⣧⣞⣵⡟⠁⠀⠀⠉⠉⢀⣿⣿⣇
⠀⠀⠀⠀⠸⠿⠃⠀⠀⢸⣿⣿⣴⠟⢹⣿⣿⣿⠇⣿⣿⣰⡇⣿⣿⣇⠀⠀⠀⠀⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⣰⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠈⢿⣿⡟⠀⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⣿⡟
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢸⣿⣿⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⢀⣴⡖⠰⠂⠘⠿⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⡤⠔⠚⠉⣁⣠⠼⠛⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⣀⣛⠋⠀⣾⣼⣠⣿⣖⣲⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠻⣟⠯⢭⣁⣀⠀⢀⡤⠖⠚⣛⡶⠒⠀⣠⠴⣋⠽⠛⣁⣼⠿⠯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠳⡀⠀⠹⣝⠻⢟⠛⠛⠲⢶⡶⠾⣿⣛⠛⠋⠙⠛⠒⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠼⠂⠀⠈⠓⢤⣑⣄⠀⠀⠈⠓⠲⠶⠽⣦

⢀⡀⠀⠠⠅⠀⠀⡠⠂⠈⠢⡈⠁⠠⠄⠄⠀⠂⠀⢀⠴⠀⠐⠛⠻⠀⠸⠇⠄⠄⢄⠀⠀⠊⠅⠀⠀⡠⠊⠉⠠⢀⠇⠘⡄⢀⠀⠀⠀⢀⠴⠀⠐⠛⠳⠁⠸⠔⠠
⠀⠀⠈⠀⠐⠀⠂⠁⠀⠀⢀⠜⠀⠀⠖⠀⠨⠀⠠⡀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠑⠄⠀⢀⠘⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀
⠺⠂⠳⣀⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠠⠀⠠⠃⠀⠈⠠⠈⠀⡔⠓⡜⢂⠀⣾⠃⠺⢆⠽⣠⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠂⠔⢂⠀⣺
⠀⠘⠂⠁⠀⠀⡠⠐⠀⠁⠐⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠈⠲⢪⡖⡛⠀⢙⠒⠂⠛⠛⠏⠀⠀⠠⠐⠀⠀⠐⠢⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠈⠶⢢⠔⡛⠀⢛
⠀⠀⠀⠀⠀⠀⡶⠤⣂⢴⡤⢴⡆⠀⡏⠀⠄⢩⠂⠀⠀⠆⠐⠈⡧⢾⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠄⣂⢠⡆⢶⡆⠀⡍⠀⠈⢩⠂⢰⠀⠀⠀⠈⡳⢮⠃⠀⠈
⠀⠀⠉⠀⠀⠀⠉⠉⠷⠘⣣⠍⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠆⠀⠐⠂⣀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠳⡜⣫⠝⠁⠀⢠⠀⠀⡀⠀⠀⠑⠀⠆⠀⠐⠂⢀⢀⡀
⠀⢀⠊⠀⠈⢢⠀⠀⠀⠈⠁⠀⠀⠀⠸⠄⠀⠄⠀⠀⢀⣲⠦⠀⠀⡁⠀⠀⡀⣥⠀⠠⠈⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⣶⠦⡀⠰⡉⠀⢀⡀
⠀⢨⠀⠀⡠⠂⢀⢀⣑⠄⢀⣴⠤⠂⠀⠀⠀⣦⣡⡾⠟⠁⠀⡀⠀⠀⠂⠀⠀⡀⠀⢀⡀⠀⡀⠂⠀⢂⡐⠄⢀⡕⠴⠠⠀⠀⠀⣤⣱⡾⠟⠋⠀⠀⠀⠁
⡄⢢⠘⠈⠀⠀⢈⠠⡔⠲⠵⠷⣄⠒⠀⠀⠈⢜⠁⠀⠀⠠⠊⠀⠀⠀⠒⠐⠀⠀⠄⠡⠚⠈⠀⠀⠄⠀⡴⠲⠾⠶⣄⠂⠀⠀⠀⢎⠀⠀⠀⠠⠊⠀⠀⠈⠂
⢀⡁⠀⣀⠀⠀⠈⢐⠂⠠⠄⢂⠄⢀⠀⢠⣂⠀⠀⠀⠀⠀⠘⠀⠇⡈⣄⠀⠀⠀⢀⡀⠀⣀⠀⠀⠐⢐⠂⠠⠄⢂⠄⠀⠀⣘⣀⢀⠀⠀⠀⠀⠸⠁⠇⡘⡀
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡯⠇⠀⠀⢀⠀⡰⠂⠺⠀⠀⠠⠀⠌⠢⠰⠁⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣠⡿⠇⠀⠀⢀⠀⡯⠒⠲⡀
⠀⠃⢀⠀⠀⠀⣠⠄⠒⠀⠲⠀⠐⠂⠁⠂⠈⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⠃⠀⢠⢄⡒⣀⢶⣄⠐⠂⠑⠐⠈⠁⠐
⠀⠂⠁⠐⠊⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⡀⡀⡀⠀⠄⢀⡀⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⡆⣀⠠⠀⠒⣀⠁⠀⠦⢷⠀⠘⡉⠁⡙⠀⠀⠀⠉⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⣂⣀⠠⠀⠒⡀⠁⠀⢨⠷⠄⠘⠃⠉⠛⠀⠀⠀⠉⠀⠀⠉
⠉⠀⠉⢉⡄⠀⠀⠀⠀⢀⠨⠀⠁⢀⣀⡀⠄⠀⠠⠀⠀⡀⠴⣀⢦⠀⢀⡁⠉⠀⠉⠀⠋⢉⡆⠀⠀⠀⠀⠀⡤⠀⡃⠀⢌⡄⣄⠀⠃⠀⠂⠠⠴⣐⢦⠀⢀⡀⠉
⢉⣑⠈⢛⠄⠀⠀⡠⠊⠈⠐⡈⠃⠀⠖⠀⢀⠂⠀⣀⠖⠐⠒⠋⠺⠀⠰⡃⣀⣄⢢⣄⠨⢋⠖⠀⠀⡀⠊⠈⠀⢀⠃⠐⡔⠀⠀⠀⠀⠀⠔⠐⠒⠉⡳⠁⠘⡏⣑
⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⢀⠘⠀⠀⠔⠀⠰⠀⠨⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢋⠐⠀⠀⢀⠜⠀⠀⠆⠂⢀⠀⠈⡀⠀⠀⡠⠈
⠿⣆⡵⣠⠀⠀⠈⠃⠈⠃⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠂⠊⠀⡐⡁⣜⢂⠀⣷⢃⡿⢂⠵⣠⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠂⠂⢀⡜⡁⣄⢂⠀⣾
⠒⠛⠈⠁⠀⠀⡀⠂⠁⠀⠁⠢⠀⠀⢀⣀⣃⣀⠀⠀⠤⠀⡀⠒⠢⢔⡚⠁⠙⠐⠓⠛⠋⠇⠀⠀⠀⠀⠉⠉⠁⠢⠀⠀⢀⣀⣂⣀⠀⠀⠤⠄⡈⠖⠢⢔⡺⠀⢋
⠀⠀⢀⠀⠀⠀⡷⢒⣒⢒⡒⢶⡇⠐⡅⠀⠀⢨⠂⢀⠀⠆⠀⠈⡗⠺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⢒⣂⢒⡒⢶⡆⠐⠍⠀⠀⢨⠂⢰⠀⠀⢐⠈⡷⢮⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠌⠶⡜⣣⠍⠀⠀⢀⠀⠀⠈⠀⠀⠁⠒⠒⠀⠐⢂⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠌⠷⠜⣯⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠒⠂⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠆⠀⠀⣐⣶⠶⡄⢠⣁⡀⣀⡀⡤⠀⠠⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣶⠶⡀⠰⣁⠀⣀⣀
⠀⢠⠀⠀⡀⠂⢀⢀⡠⠄⠠⡔⠴⠂⠀⠀⠀⣤⣦⡿⠟⠁⠀⠈⠀⠀⠂⠀⠀⡀⠀⢠⠀⠀⡠⠂⠀⢀⡈⠄⠨⡔⢤⠢⠀⠀⢠⣔⣤⡿⠟⠁⠀⠄⠀⠁
⡔⢢⠊⠀⠀⠀⠀⠀⠌⠒⣋⠶⡴⠒⠀⠀⠈⢊⠀⠀⢀⠄⠊⢀⡀⢈⠁⠂⠉⠀⣔⠠⠈⠁⠀⠀⠁⠀⡌⠒⣟⠧⢴⠒⠀⠀⠀⢎⠀⠀⠀⠠⠊⣀⡀⢈⠁⠂⠉
⢀⡁⠀⣀⠀⠀⠈⠜⠂⠰⠄⢀⠄⠀⠀⢠⡇⠀⠉⠁⠀⠀⠘⠒⠃⡌⣄⠀⠀⠀⢀⡁⠀⣀⠀⠀⠀⠈⠊⠡⠤⢈⠄⠀⠀⢘⡄⠀⠉⠉⠀⠀⠘⠒⠂⡬⣄
⠁⠈⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠯⠇⠀⠀⢀⠀⡸⠂⠸⠀⠀⠠⠁⡀⠃⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⡀⠀⠀⣨⡿⠅⠀⠀⢠⠀⡯⠂⠒
⠀⠁⠀⠀⠀⠄⣠⢀⡔⠭⣳⠄⠘⠄⣉⣀⢈⡁⠜⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⠃⠄⣠⢆⡔⢭⣳⢄⠘⠆⣉⣀⣈⡁⠜⠀⠀⠀⠁
⠀⠂⠀⠐⠀⠀⠁⠂⠀⠀⠀⠐⠇⠀⠀⡀⠂⠀⣀⣀⡀⠀⠄⢠⡀⠀⠀⢰⠀⠀⠀⠂⠀⠑⠀⠀⠡⠀⠀⠀⠀⠈⡆⠀⠀⠠⠂⠀⣀⣀⣀⠀⢀⢠⡀
⠀⣀⠀⠀⠀⠀⣎⠀⠄⠀⠀⢈⠀⠀⠲⢿⠀⠘⠅⠀⠜⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⣀⠀⠀⠀⠀⣂⠀⠄⠐⠀⣀⠀⠀⢰⡷⠀⠸⠁⠀⠘⠀⠀⠀⠀⠀⠈⢀
⣁⣀⣉⣈⡀⠀⠀⠀⠀⠀⡈⣀⣁⢀⣀⣀⣄⠀⠠⠠⠀⣀⡒⣑⢢⡀⢀⣀⣁⣀⣉⣀⣃⣀⡂⠀⠀⠀⠀⢀⡤⣀⣃⢀⣌⣄⣀⠀⠃⠀⠂⣀⠐⣑⣦⡀⢀⣀⣁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⣀⣈⡓⡷⣶⢴⠤⠴⠷⠻⣉⣡⡐⠒⠒⡲⠆
⠀⠀⠈⣑⠆⠀⣏⣥⣶⣵⣷⡌⣽⡍⢯⠇⡆⣿⣀⠨⠕⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⣉⠉⠁⠁⠏⢀⣛⣀⣩⣥⠬⠤⠒⠁⠀⣰⡃⠀⠀⠀⠀⠀⡜⢉⡗⠀⠀⡠⡄⠀⠀⠀⠀⣦⣤⣳⣀⡀
⠀⠀⠀⠀⠨⡓⠶⣿⠂⢈⢉⡉⣉⣩⣤⠤⣴⠶⣸⣎⠒⠀⠀⠀⠀⢹⣗⣋⠀⣀⣀⣧⠇⡄⠀⠐⠿⠛⢛⡛⠿⣧⡀
⠀⠀⠀⠀⠈⠀⠐⠧⠳⡼⠀⢧⣼⢁⣻⢚⢈⡯⠥⣸⠀⠀⠀⢶⣧⠈⢇⣈⡷⣧⣺⡏⣸⡇⣯⣇⢇⡽⢾⣛⡜⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡀⣿⣏⢈⣶⠈⡷⠈⢉⠁⠀⠀⠀⠘⠻⣷⣶⡿⠿⠙⠳⠈⣶⢠⡞⠲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡉⠈⠉⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠃⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡾⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⢃⣄⠀⠀⣀⢀⣠⣖⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣼⣷⠿⣷⠋⢾⣹⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⢻⠙⣾⢿⠈⣧⡴⢣⢟⢭⠶⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⠛⠀⠛⠃⠀⠈⢡⣤⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠈⠛⠁⠤⢔⡉⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠿⠃⡿⠀⠀⢀⠀⠀⠀⣿⡏⠶⡟⠀⠀⠀⠀⠀⠀⢀⣸⠀⣠⡖⣤⡄⣀⡎⡐⢨⣿
⠀⠀⠀⠀⠀⠀⢀⠔⣸⠇⣼⢿⡿⣾⣰⣧⣿⢛⡶⣇⡀⠀⠀⠀⠀⠀⣿⣘⣇⣿⣰⠻⡷⢧⠿⣻⠅⢿⠄
⠀⠀⠀⠀⠀⠀⠘⠶⠛⠚⠙⠋⠀⠛⠁⠁⠈⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠓⠢⠀⠐⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠃⠋⠀⠰⠶⢦⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠤⠄⢀⣘⡋⠲⠶⣶⣾⠿⣿⣿⡳⠶⠒⠒⠂⠀⠀⣀⣠
⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⣸⣿⣿
⠀⠀⠀⠀⠸⣧⠀⠄⠀⠀⡄⢠⠀⠀⠀⠐⡇⠀⠀⠠⠈⠃⠀⣠⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠋⠉⠉⠀⠀⠨⠭⠉⠉⠉⠀⠘⠛⠛⠛⠟⠙⠉⠉⠤⠄
⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠁⢸⡆⠀⠀⠀⡇⠀⠰⡆⠀⠘⣾⠇⠀⠀⢨⡇
⡀⠀⡀⠁⠀⠀⠐⠀⠀⣄⠀⠀⡀⠀⢠⠀⠀⠆⠀⢰⠀⠀⠉⢠⠦⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣙⠀⠈⠂⠂⠀⠀⡀⢬⣿⡄⠀⠀⢸⠀⠀⠰⠂⣀⢸⠀⠀⢰⣇⠀⠹⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣷⡄⠀⠀⠀⠀⠉⠀⠘⠃⠀⠀⢸⠀⠀⠀⠀⠻⠀⠂⠀⠀⠃⠀⣀⣀⣁⣠⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠆
⠀⣄⡀⠀⠀⠘⠓⠒⠉⠛⠚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⠁⠀⠀⠀⠀⣀⣀⡀⢀⡀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢀⡤⠚⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠚⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠠⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡨⠄⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿
⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠶⠤⠤⠶⠶⠶⠾⠿⠶⠤⠤⠄⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⢀⣀⡀⠀⢌⠐⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⡐⠀⠈⠁⢀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠐⢂⠀⠒⠂⠀⠀⠀⠖⠒⠀⠨⠃⠀⠀⠀⢠⠀⠀⠠⠀⠀⠀⡴⡏
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠘⠄⠀⡤⠈⠀⠀⠀⡠⣜⠀⡈⠃⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠁⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠜⢀⣀⢈⡉⢁⡀⠐⠓⠔⠂⠀⣀⣁⡀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⡧⠶⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠈⠀⠀⠀⠀⠀⠠⡴⠙⢆⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⠒⠒⠒⠐⠐⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⣤⣄⠀⡀⣀⣀⣄⠁⡀⢈⠁⠀⠀⢀⡀⣀⢀⣀⢀⣀⣀⠀⢤⡤⠒⠒⠂⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠉⠚⠁⠀⣤⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⠐⠀⠀⠂⠀⠁⠀⠀⢀⡠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠄⠀⡜⢀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢃⠀⠀⠀⠀⠀⠀⢠⢤⡴⢠⠆⢀⠀⡴⠂⠀⢀⣠⢠⠆⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠱⠂⡀⠰⠄⢎⠄⠀⠀⠀⠀⠀⠙⠀⠀⠏⠐⠇⠘⠑⠠⠇⠈⠈⠎⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠐⠒⠒⠛⠃⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⣀⡀⠀⠀⠀⢀
⠀⠀⠀⢸⠠⠀⠠⠔⡄⠀⠤⠜⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠁⠘⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡘⢀⢦⠆⡠⠀⣠⠏⡠⢤⠋⣄⠀⠀⠀⠐⠈⠀⠀⠀⠀⠁⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢠⢰⡲⠉⠀⠀⠀⠀⠀⠁⠀⠈⠘⠱⠀⢠⠄⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠘⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠰⡎⠄⢠⠂⠀⡴⡱⠀⠀⠀⠀⠀⢀⠎⢀⠐⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠈⠀⠃⠜
⠀⠀⠀⠀⠈⠉⡀⠁⡈⢈⠈⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠐⡀⠂⠈⠜⠄⠞⠈⠆
⠀⠀⠀⠀⠀⠔⠁⠴⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⢀⣀⠀⠜⠒⠀⠰⡖⠚⠰⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠔⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⢁⠀⠀⣤⠄⠀⠀⠀⠀⠀⣌⠠⠄⡄⢀⠀⡀⡤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠠⠀⠄⠀⠀⢀⢈⠀⢰⣆⠀⠀⢀⡂⠄⠀⡁⠀⠀⣀⡀⣈⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢐⣻⠵⠀⠀⠁⠀⠈⠈⠀⠉⠀⠠⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠂⠊⠠⠀⠐⡆⠀⠀⠄⠠⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠰⠄⠄⢀⡰⢠⠆⣀⢢⠄⠤⠀⠀⠀⢸⠀⠆⠀⡤⢢⠀⠠⠤⡜⠱⠄⡔⠡⠤⠞⠠⡄⠀⠰⠀⡀

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⡆⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠠⢄⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠈⠙⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⣔⠃⠋⠓⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠠⠀⠂⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⢈⠉⠈⠀⠀⠀⠀⡌⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⡀⠀⠀⠀⠀⠈⠂⡀⠀⠂⡀⠈⠁⠁⠄⠀⡁⠀⢀⠠⡄⢀⠈⠀⠀⠠⠄⡀⣀⢀⠀⣼⣇⢄⠀⠀⠀⠈⠀⠀⢀⡀⠠⠲⠀⢀⡀⢀⠀⠀⠐⠁⢁
⠀⢰⡀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠀⠀⠁⠐⢁⡄⠀⡀⠈⠑⡽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⣤⡠⡤⣤⡴⡀⠈⢤⡀⠔⢀⠠
⠀⠀⣦⣄⡠⠆⠀⠒⠁⠉⠀⠀⠀⠀⠡⠄⠠⡁⠀⠀⠁⠀⠀⠀⢀⠌⠀⠀⢨⡕⠀⠀⡀⢠⠀⠀⠀⠠⠀⠀⠠⠀⠦⠄⠘⣄⢋⠀⠤⠂⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠂⠀⠀⢀⡀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠐⠀⠄⠀⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠠⠄⡀⠀⠀⢘⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌⠡⠒⢈⠀⠂⠀⠀⠀⠀⠐⠀⢀⣀⠈⠀⠀⠣⠊⠁⠆⠀⠀⠀⡀⠀⠀⠀⠔⠁⠀⠀⠀⠰⠀⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠂⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣄⣄⣀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⠊⢀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢠⣶⣿⣿⣿⠛⢛⡛⡻⡟⣿⣿⣿⣶⡄⠀⠁⠀⠉⠀⠠⠸⡈⣈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⡐⠂⠠⠁⠀⠀⠀⠀⠀⠑⠄
⠀⠘⡒⠐⠈⠀⠀⢀⠀⢀⣿⢛⡟⣿⢻⡛⢛⣿⢛⡛⠻⠟⠟⢻⣿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⢀⠀⣂⢀⣀⣀⣀⠀⠀⡀⡂
⠀⠀⢡⠀⡄⠀⠀⠀⠀⠘⣿⢨⠁⢹⡜⣿⢸⣿⢈⡁⡇⠀⠀⡆⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⡂⠀⠀⡁⠀⠁⠀⠀⠇⠀⠍⠛⠋⠀⠛⠀⠐⠈⠁
⠀⠀⠀⠆⠃⠀⠀⢀⠀⠀⠹⣼⣼⣮⣭⣿⣼⣿⣼⣧⣡⣬⣤⣴⠏⠀⠀⠀⠀⠰⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠉⠛⠛⠛⠻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠂⠀⠀⡀⠀⠠⠄⠁⠀⠀⠀⠀⠈⠀⠀⠀⢐
⠀⠀⢅⠀⠀⠀⠂⠀⠒⠠⠀⠀⢠⠐⢀⠀⠀⠠⢀⠀⠠⡀⠀⠀⠀⠀⠄⠀⠀⠠⡈⠀⡀⠔⠀⠄⠀⠀⣀⣀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢉⠀⠸⠀⣕⠐⠘⠂⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⢀⠗⠁⠀⠀⠉⠄⠀⠀⠂⠈⠂⠀⣈⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⡀⠀⠐⢀⠀⠀⠘⠕⠀⡀⠀⠀⢘⡂⠀⠀⠆⠀⠀⣀⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠑⠂⠀⠘⠀⠰⣀⣀⠬⠃⢈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠬⠄⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠰⠸⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠖⠃⢀⠄⢀⠀⠒⠑⢀⠀⠀⠠⠀⠀⠀⠃⠁⠦⠀⠐⠀⠅⠀⢸⠀⠁⠈⠀⠂⠀⠐⠀⢴⣊⠖⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠠⠤⠆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠨⠂⠀⠀⠠⠊⠀⠀⢄⠀⠀⢀⡈⠀⠂⢰⣀⡠⡰⠱⢡⠄⠀⠀⠀⠀⡆⠀⠠⠀⠠⠀⠁⠒⠈⠀⠤⠀⠀⠀⠀⣠⠀⢀⠠
⠀⠈⠀⠀⠀⠄⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠠⢇⡀⠀⢸⢆⡀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠐
⠀⠢⠀⠠⠄⠂⠁⠀⠀⡀⠀⠀⡠⠔⠊⠁⠁⠀⠀⠈⠍⠀⡄⠀⠀⠈⠚⠚⠁⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⡄⠀⠀⡀⠀⠀⡄⠀⠄
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠑⠂⢀⠉⠀⠐⠀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠁⠀⠠⠤⠄⠀⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠓⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⣎⣉⣳⡀⠀⠀⠀⠀⡤⡤⠒⡶⣠⠒⡦⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⢠⠮⠭⠭⠭⠽⠄⠀⠀⠀⣸⠥⠄⠬⠦⠨⣆⠀⠀⠀⣜⠁⣼⡙⣧⢎⢫⣾
⠀⠀⠀⢠⡗⡒⡒⢖⠠⣒⡲⣶⠾⡀⠀⠀⠀⠘⡎⠉⠉⠉⢹⠁⠀⠀⠀⠙⣟⢻⡭⡛⢹⠁⠀⠀⠀⢹⠙⠓⠓⠚⠚⢉⡇
⠀⠀⠀⠀⢹⠒⠾⡉⣘⢿⠓⠞⡟⠀⠀⠀⠀⠀⢣⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡟⢤⣺⠃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠘⠳⣰⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡁⡝⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡤⢒⣂⡉⣐⠲⡄⣠⢤⠀⠀⠀⠀⠀⣀⠤⢤⠒⠢⡄⠤⡀⠀⠀⢀⡠⠔⠒⠒⠠⢄⠀⠀⠀⠀⠀⢀⠤⠒⠢⢄
⠀⠀⠀⢠⢋⠖⠧⠎⢀⡠⡫⠞⠹⡆⠇⠀⠀⢠⠞⠁⠀⠀⠣⡀⢣⣀⣈⠆⠀⣎⣀⣀⣀⣀⣀⣠⡕⠀⠀⠀⢠⠋⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠈⠆⠏⠋⠻⠒⡿⢭⢅⠙⠂⠀⠀⡜⠣⡀⠀⠀⢀⡝⠁⠀⠀⠀⠀⠈⡄⢠⠈⡄⠰⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⢆⠳⢖⢐⢢⣀⡰⢋⡞⠀⠀⠀⠀⡗⢄⣈⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⢡⣘⠀⢃⣃⠎⠀⠀⠀⠀⡼⢑⣤⠴⠊
⠀⠀⠀⠀⠀⠑⠢⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⢇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⢭⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⢖⣂⠴⡒⣒⣄⠀⠀⠀⠀⠀⡤⠤⠤⠧⠧⠤⣄⣀⡀⠀⠀⠀⢸⠀⣇⠾⠼⠄⠀⠀⠀⢀⡔⡢⣄⡠⢚⠦⡀
⠀⠀⠀⠀⡎⡡⠒⠉⠒⠒⠒⢝⢦⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⣯⣗⠅⠀⠀⠀⡸⠀⡧⠋⠈⠣⡄⠀⢠⠊⠀⢱⠈⢳⠸⡄⠈⠆
⠀⠀⠀⢸⡴⠁⠀⠀⠀⠀⠀⠈⢿⠂⠀⠠⡆⠀⠷⠤⠄⠖⠋⠃⡲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠸⡀⢀⠇⠀⢸⠀⡇⠀⡄
⠀⠀⠀⠸⠤⠤⠤⠀⠒⠀⠀⠤⠊⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠀⠑⢤⣃⠴⠛⢄⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠤⠤⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠀⣞⣵⣵⠗⠺⡄⠀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⠀⠀⣠⠊⠱⢼⢌⢷⠀⠀⠀⣠⣀⡠⠤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⢰⣊⠭⣔⡺⣽⠝⠁⠀⠀⡇⠀⠀⠀⡞⣚⠓⠙⡆⠀⠀⠀⠀⣴⠥⠔⠚⠉⢉⡏⠀⠀⢸⠀⠘⠀⣀⠈⠀⠀⠋⠀⢹
⠀⠀⠀⢎⣪⠛⠊⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⠹⠀⡇⢰⠃⠀⠀⡠⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⣞⡋⢛⡓⠒⡞⠉⣖⡛⢳⣋⡢
⠀⠀⠀⠈⠡⡀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠸⠋⠁⠸⡄⠀⠀⠣⢄⡀⠀⠀⡔⠁⠀⠀⠀⠀⠘⠬⠅⠈⠫⠬⠍⠤⠬⠥⠜
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡄⠠⠃⠀⠀⠀⠀⠈⠢⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡼⠁⠂⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⢇⡀⢀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⢸⡇⠀⠀⢀⠀⠀⢀⣶⠀⣀⠀⢀⠔⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣧⠀⢹⡇⠀⣼⠃⣵⡆⢸⡇⠀⣿⡄⠁⠀⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⢸⡇⢠⣿⢀⣿⠀⠜⢧⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡿⠀⠀⠳⠂⠙⠃⠘⠞⠀⠀⠠⢻⡇⠀⠀⡠⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⠠⠄⠀⠀⠀⠀⠠⠀⣾⡆⠀⢀⡂⣼⠃⢀⠌⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠡⠞⡉⠀⢀⠀⢰⡆⠀⢠⡅⢠⣿⠀⢀⡂⠙⠁⢀⢋⡤⢠
⠀⠀⠀⠀⠀⠀⠀⣿⢇⣀⡀⢅⡄⠈⡄⠈⢷⡄⣿⠃⢸⡏⠀⣾⠃⣼⠃⢢⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠢⠐⣿⠇⠸⣷⢺⡇⠀⠇⢠⠚⡇⢹⣄⢿⡇⠀⣿⣠⢿⡌⢸⡇⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣞⡏⠈⠓⠊⠀⠘⠘⠁⠀⠁⠸⡇⢸⠀⠁⠈⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣸⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠂⠀⢰⠃⠀⠉⠙⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠌⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡘⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠉⠉⠛⠛⠶⠶⠶⠶⠖
⠀⠀⠀⢸⠀⠀⠀⠐⢄⡰⢀⣀⣼⣠⣤⣼⡧⠴⠚⠁
⠀⠀⠀⠸⠄⠀⣠⡤⠾⠟⠉
⠀⠀⠀⠀⡴⡫⠁⠀⡆
⠀⠀⠀⢠⣧⠣⣀⣀⠄⠀⠀⠀⣠⣤⠤⢤⣄⣀⣀⣀⣀
⠀⠀⠀⢸⡀⠙⣲⠒⠒⡖⠋⠉⠓⠢⣵⠯⣀⣀⠈⡍⠙⠒⠦⣤⣤⣀⣀⣀⣀⠀⠄
⠀⠀⡀⠀⠙⠚⠑⠠⡜⠳⢄⡤⠤⡀⢸⠀⠀⠈⠻⡓⠒⠠⢤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠴⠶⠶⠶⠶
⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠀⠉⠑⠚⠚⠼⠁⣐⣠⠇⡊⠘⣸⠃⠀⠈⠉⠓⠒⠒⠒⠒⠛⠉⠉⠁
⠀⠀⠈⠁⢩⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⣿⠋⠁⠀⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠋⠀⣿⠀⢀⣴⠏⠀⠀⠀⠀⢠⡶⠋⡁⠀⡀⠀⡀⠀⣠⡄⢸⠁⡠⢀⠀⠀⣀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠟⠁⢀⣀⠀⠀⢰⠟⢀⡾⠁⡼⢁⠀⠈⢰⡷⠃⠼⣏⣴⠏⣑⢰⡇⣸⡇⣰⠇⣠⠖⠆
⠀⠀⠀⠀⠀⠀⠴⣿⠉⠑⡆⣴⠏⠀⠀⠀⡟⢀⡾⠁⣼⠃⣼⠀⡇⢸⣀⠎⡀⣿⢺⡀⠀⡾⢡⠟⣰⠏⣼⠃⢁⠠
⠀⠀⠀⠀⠀⠀⢠⡇⢀⠜⠁⣇⡠⠂⠀⠀⠓⣹⠃⠀⠻⠀⠻⡴⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠞⢠⡏⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠔⠀⠀⠀⠀⠀⠀⠀⢆⣀⡼⠃⠀⣠⠖⠀⠀⠸⠃⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣄⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠄⠀⠀⠉⠀⠀⢠⡏⠐⠀⠀⠀⢰⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡄⠀⠈⢀⣰⠞⢣⠀⠀⢿⠀⠄⣾⠀⠀⣠⣄⠀⠀⢸⡁⠀⠀⢀⡀⠸⡄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⠀⢰⡇⢀⡞⠀⠠⠹⣇⢰⡇⠀⣼⠧⠊⠀⠀⢻⠀⠀⣰⠣⠀⠀⢷⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣇⢀⠁⢸⠃⢸⠇⠀⠁⠰⡗⢸⠃⢰⡏⠀⡀⠀⠀⢸⡆⠀⣿⠀⡠⢁⢼⡄⡜⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠹⠆⠀⠈⠁⠸⠄⠀⠄⢸⠇⠸⡠⠙⠧⠊⠀⠀⠀⠀⢧⡀⠘⠋⢠⠂⣼⠁⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠛⠋

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠁⠀⠀⢀⠠⠤⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠤⡀⢤⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠤⠐⠀⠈⠀⠠⠀⡀⣤⠀⠤⢤⡌⠛⠂⠀⠤⠆⠉⠉⠁⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⣀⣡⡒⠦⠤
⠀⠂⠀⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⡀⠞⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠁⠒⠦⢀⡀⢀⡤⢊⠡⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠔⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠥⠖⠁⠀⠀⠀⠀⠀⠸⡄⠃⠀⠄⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠄⠤⠀⢤⠄⠀⢂⠀⡰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡆⠀⠀⠄⠂⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠄⠃⡤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⢀⠀⠘⠀⠐⠄⠀⠀⠁⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⠀⠀⠀⡐⠁⢠⡕⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠇
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⠂⢀⠀⠙⠂⠀⡀⠀⠀⠀⠑⢧⠘⠀⠀⠀⠀⠀⠀⠐⢁⠤⠀⠀⠘⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⣀⠀⠈⠀⠀⠀⠀⠢⠤⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠠⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠁⠀⡄⠀⠊⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠦⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠲⡀⠶⠄⠦⠐⠃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠁⠤⠄⠀⠀⠀⠤⠄⠀⢀⡀⠀⢀⠠⠐⠠⠀⠀⠀⠠⠄⠀⠀⢀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣁⡀⠠⠄⠄⠀⠈⠠⠄⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠠⢤⠄⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠠⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠨⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠉⠉⠀⠦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠖⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠐⠈⠁⠀⠂⠀⠀⠀⠀⠐⠒⠈⣀⣁⠀⠀⠀⡁⠀⠀⠀⠀⠃
⢀⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⢀⠀⠀⢀⠀⠀⠐⠢⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠈⢂⠘⠢⠄⠀⠠⠒⠀⠈⡠⠀⠀⢀⡄⠆⠆⠀⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠰⠀⠂⠀⠀⠀⠀⠁⠂
⠀⢀⠀⠀⠀⠱⡀⠀⠄⠒⠀⠀⢰⠁⠀⢰⠑⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠊
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⢆⣀⣀⡀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠈⠉⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⢀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢠⠄⠀⠀⣤⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠢⠄⡈⠣⡙⠃⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⡐⠒⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣤
⠀⠂⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡀⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠶⠾⡄⠀⠁⠀⢂⠐⠃⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠑⠀⠈⣉⠲⠀⠀⠀⠀⠀⠀⢀⡉⠀⠭⠭⣝⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣑⣤⣤⡤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⡔⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡐⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠜⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⢀⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠢⠤⠄⡀⠀⠀⠀⠀⠀⡇⣃⠠⠤⢢⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⠡⠀⠀⡠⢚⠠⠀⡰⡡⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⣤⣠⣤⡴⢅⣧⣽⣿⣷⣆⡀⡐⡐⢁⠠⠐⡚
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⢠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠊⠁⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡞⣺⣿⣿⣿⣿⣷⣽⡿⢛⠡⢋⠡⠔⠂⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠙⠛⠻⢿⠖⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⢸⠀⠀⡀⠄⠂⠁

⠀⠀⠀⠀⣤⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠝⢱⠀⠼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠍⠱⠀⠼⢉⡀
⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⡴⠋⡏⡩⠦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡴⠫⡎
⠙⢣⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⠅⠜⢃⡶⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠰⠤⠒
⡄⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠖⡼⣿⡆⢊⠀⠀⠀⠌⠄⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣖⣾⣻⡆⠊⠀⠀⠀⠌⠆⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠀⠀⠀⠀⠶⢋⠘⠃⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠶⠛⠘⠇⢦⡴⠂
⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠨⣁⠀⡤⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣀⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⡠⠦⡴⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠢⡤⠀⠀⠀⠀⠆
⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃
⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⢀⠉⡰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡰⠉⠆
⠀⠀⠀⠀⡶⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠃⠠⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠜⠹⠀⠼⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱⠀⠍⠹⠀⠨⢡⡀
⠦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠀⠀⠀⣴⠁⡏⠩⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡰⠉⡏
⠙⡃⡶⠀⠀⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠜⠃⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒
⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆
⣗⠺⣻⡆⢂⠀⠀⠀⠌⠂⢉⠿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⣊⣖⢾⣹⡖⠊⠀⠀⠀⠈⠂⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠖⢋⠘⠃⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡴⠀⠀⠀⠀⠷⢛⠘⠃⢢⠴
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣁⠐⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣁⠂⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡰⠦⠶⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡤⠲⡴⠐⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠉⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠈⠉⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠂⠐⠀⠀⠀⠐⠈⠒⠒⠀⠁⠁⠘⠘

⠀⠀⠀⠀⠀⠀⠀⢞⡀⢠⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⣰⣶⠶⠦⠐⠶
⠀⠀⠀⠀⠀⠀⡀⢠⠿⡹⡵⠰⣋⠛⠀⠀⠀⠀⠀⠀⠧⠖⠒⠻⠶⠦⠀⠀⠀⠀⠀⠀⠘⣋⡉⢀⡦⡂⣀⠀⡆
⠀⠀⠀⠀⠀⠸⡯⡐⢀⣲⠂⣂⡀⣄⡾⠀⠀⠀⠀⢠⢤⣀⣃⣈⡃⣴⡄⠀⠀⠀⠀⠀⠘⠽⠛⠛⢫⢗⠿⠯⠷⠧
⠀⠀⠀⠀⠀⠀⡇⣇⣈⣿⠁⣿⡇⡇⡀⠀⠀⠀⠀⠈⠂⠉⠰⠆⡒⠈⠁⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⢥⠐⡆⣀
⠀⠀⠀⠀⠀⠀⡃⣉⠉⠐⠂⠀⠑⠁⠁⠀⠀⠀⠀⣀⠀⠙⠒⢒⠃⠀⢀⡀⠀⠀⠀⠀⠺⠺⣶⣄⡖⢲⡀⡇⠉
⠀⠀⠀⠀⠀⠀⡇⢙⣶⡮⠛⣥⡆⠀⣥⠀⠀⠀⠀⠀⠿⠛⠂⠙⠛⠻⠎⠁⠀⠀⠀⠀⠀⠀⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠑⠛⠛⠉⠉⠃⠀⠛
⠀⠀⠀⠀⢀⠀⣄⠀⠐⠴⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⡄⢠
⠀⠀⠀⠀⠀⢁⢸⢟⡶⠆⢗⣤⣇⠀⠀⠀⠀⠠⡤⢤⡄⣨⠇⠛⢓⡠⢶⠂⣰⠇⠀⠀⢀⡄⠀⠓⠩⠬⠈⢀⣀⡀
⠀⠀⠀⠀⠀⠲⠅⢰⡒⢒⢀⠀⠒⠀⠀⠀⠀⠈⠻⣨⣿⠶⢤⠤⢤⣖⠿⠴⠃⠀⠀⠀⣿⡏⢰⣛⡤⣤⣰⠊⢻⣿
⠀⠀⠀⠀⠀⢠⣬⣽⣿⣿⣶⣧⣄⡀⠀⠀⠀⠀⠀⡀⡅⢉⠛⡋⡛⢉⢤⠰⣀⡤⠀⠀⠛⠟⠀⣧⠉⢨⠆⠁⠘⠋
⠀⠀⠀⠀⣾⣿⠿⠿⠿⠿⠿⠿⢿⣿⡅⠀⠀⠀⠈⠉⠇⠘⠧⠧⠣⠀⠿⠤⠊⠀⠀⠀⠀⠀⠘⣁⣤⣇⣖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄⠄⠀⡐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠰⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠙⠓⠒⠒⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠛⠉⠙⠒⠲⢤⡀⠀⠀⠀⢀⣸⠤⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠖⠋⠁⠀⠠⠖⠡⠟⡷⣄⡀
⠀⠀⠀⠀⠀⠐⡒⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡈⠹⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢟⣹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⣲⣄⣀⢤⠄
⠀⠀⠀⠀⠀⠀⢁⣮⠆⢽⡍⢿⣖⢶⠶⢶⠒⣒⣚⣹⠉⠞⣳⡽⠉⠈⠢⣀⠀⣀⣤⣴⡶⢛⣟⢛⡛⣉⣁⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠸⢛⠦⢄⣀⠀⠈⠉⠙⡓⠀⣉⠀⠘⠋⡥⢎⡟⢠⢀⠀⠀⣽⠉⢤⡏⠀⡎⢻⠛⢯⣄⡈⢙⣭⠗
⠀⠀⠀⠀⠀⠀⠘⠦⢀⣠⡌⠛⠁⠤⢄⢠⣈⣁⡀⠀⡀⣠⠎⠁⠣⣌⠄⢸⣿⡄⢸⣬⣖⡽⠄⣇⢀⠦⠽⢾⡜
⠀⠀⠀⠀⠀⠀⠐⢄⢀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠉⠁⠈⢀⠄⠁⠀⠈⠢⣥⠙⣧⠈⣟⠬⣉⣁⡟⢴⣟⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠙⡓⡁⢶⠨⠇⠈⠂⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠘⠏⠇

⣿⣿⠻⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣤⡶⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠸⠟⠀⠀⠠⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠐⠤⠊⠀⠈⢆⡀⠀⠀⠀⠀⠀⠠⡤⠤⠶⠦⠤⡤⢤⣄
⠀⠀⠀⠀⡨⡉⠩⠉⠅⠄⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡼⢻⠼⢴⡟⠛⠂⠈⡆⠀⠀⠀⠀⢀⣯⣛⣝⣗⣀⣇⡠⠟
⠀⠀⠀⢈⣖⠷⡤⣤⢴⣀⢿⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢹⣧⣿⡀⢣⢤⠀⠁⠀⠀⠀⠀⠀⢀⣀⣏⣉⣡⣤
⠀⠀⠀⠀⠙⡄⢹⠍⡉⢞⣨⡌⠀⠀⠀⠀⠀⠀⠀⢔⣁⡀⡘⠍⠉⠩⠤⠠⠵⠦⠀⠀⠀⠀⢂⡘⠟⠿⢛⡚⠛⣢⠇
⠀⠀⠀⠀⠀⣬⣌⣶⣤⣮⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠞⠓⠚⡳⡗⠀⠀⠀⠀⠀⠀⠈⡍⢀⡚⠹⠝⠈⣁⣤
⠀⠀⠀⠀⠈⢈⠛⡝⢿⠿⣟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⡃⡔⣰⢂⢔⡁⡂⠀⠀⠀⠀⠀⠀⠹⣾⡛⠷⠶⢞⣡⠇
⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡴⡀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡆⠠⡡⠀⣀⡍⢃⠀⠀⠀⠀⠀⠀⢈⣷⣺⣯⢱⠏⠷
⠀⠀⠀⣧⠀⠀⣷⠀⠀⣼⠀⢀⡎⠀⠀⡄⠀⠀⠸⡏⠙⡏⣏⠤⡍⣯⡍⢩⢾⠀⠀⠀⠀⠀⣿⠸⠁⠦⠤⠄⣉⣀⣴
⠁⠆⠐⢉⠑⠪⣄⣈⡉⢤⣨⢉⣑⠒⡞⠀⠀⢀⣠⠑⠴⠃⡈⠋⣁⡀⣑⣉⢉⡥⠀⠀⠀⠀⠃⣷⠀⣿⠃⣿⡇⡏
⠀⠈⢄⣟⣋⣴⣯⢥⢥⣤⣤⣬⣝⡜⠀⠀⠀⠀⠙⠛⣛⡋⡋⠀⠅⠭⠭⠬⠬⢅⡀⠀⠀⠀⠀⢈⠍⠡⠤⠁⠡⠁
⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⡷⠺⣤⣴⢶⣼⣴⣞⣳⣀⣸⡅⠀⠀⠀⣧⠸⣤⣎⠗⢇⡦⠀⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣁⣸⣟⣛⣋⣉⣓⣀⣿
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣯⡽⢶⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀
⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠦⣦⠞⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠡⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠐⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠄⠀⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠉⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣿⠃
⠀⠀⠀⠀⡀⢴⡿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢍⠀⠀⢸⡿⠋⡐⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠑⠂⠉⠛⠛⠉⠁⠀⠀⠀⠀⢤⡀⠀⠈⣇⠈⠁⠀⠁⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⣀⢹⣁⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡏⠐⠦⢽⣄⣀⣠⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠀⠀⠀⠀⡇⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣜⢂⡀⣄
⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠑⠪⣐⠠⡄⠀⣨⡥⠮⠀⠂⠁
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀⠀⠀⠀⠀⠁⠒⠉
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠻⢿⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡩⢣⠀⣤⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠓⣀⢦⠠⠤⡏⠇⠰⠰⡅⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢆⡰⢌⡄⠹⡤⠿⠲⠁⣎⡹⠆⠡⠀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣄⢀⡸⠒⠎⠘⡀⡠⠞⢢⠀⠨⠁⠈⡀⢂⠈⠎⠖⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢹⠇⣤⠋⢄⠀⠑⢻⠲⠉⢇⠀⠁⠡⠐⠀⣃⣸⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠀⠀⠀⠀⠀⣀⡇⠀⠈⢆⠈⡆⠀⠈⠓⠋⢇⢃⠘⡆⠀⠀⣣⡶⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⢸⡗⠶⠦⢤⣬⣤⣽⣄⣦⣤⣥⣸⣬⣤⡴⣶⠞⠉⠀⠀⠀⠀⠀⡇
⠀⠀⣠⡤⠔⠒⠂⠀⣈⡧⡤⠓⠒⠤⢤⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤⣤⣤⣤⣧⣤⣀⣀
⠀⣼⣏⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⢟⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠻⢷⣦⣤⡀
⠀⡷⠬⣍⣛⣒⠚⠛⠒⠒⠒⣒⣚⡉⠥⠚⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢉⡁⡄⠀⠀⠠⠀⠂⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⡏⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠈⠀⡇⠀⠸⡆⠀⠀⣀⣴⠾⠋⠁⡠⢰⠄⠉⠀⠂⢂⣠⠤⠖⠒⡈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢿⣷
⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⡀⠀⠀⢀⡇⠀⠀⣇⣠⡾⠋⠁⠀⠀⢀⣈⣀⣤⠤⣤⠴⠿⠤⠤⣤⣉⣀⠀⢴⡴⠀⠉⠉⠠⡠⠆⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⢀⠀⠐⠊⠉⠁⣠⠔⠋⠀⠀⡄⠀⣀⠀⠈⠉⠛⠲⣄⠀⣆⠜⠀⠀⠀⠀⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⢸⣷⠟⠁⠀⠀⠺⠈⢀⡠⠂⣤⠞⠁⠀⢀⡀⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⡆⠀⣠⠞⠁⠐⠁⠐⠒⠁⢠⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⡟⠀⠀⠀⠀⠀⠀⠋⠀⡴⠃⠀⠀⠸⠥⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⢀⣤⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⣀⣤⠞⠋⣠⡇
⢸⡇⠀⠀⠁⠀⠀⠀⠀⡜⠀⠀⢨⣿⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠉⣀⣤⠶⠛⠉⢀⣤⠞⠉⡷⢤⡀
⣿⡇⠀⠀⠀⠀⠀⢠⠎⢀⡀⠔⠉⠳⣍⡛⠿⢿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠛⢉⣁⣤⠴⠞⠋⠉⠀⣀⣤⠾⠋⠁⣀⡼⠃⠀⣿
⣿⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣇⠙⠓⠦⢤⣈⣉⡉⠉⠉⠉⠉⠉⢉⣉⣁⣠⣤⠴⠖⠚⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⣀⣴⠞⠋⠀⠀⢠⣿
⣿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢦⣄⣀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⢀⣀⣤⠶⠛⠉⠀⠀⠀⢀⣴⡿⠁
⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦⣌⠉⠙⠛⠓⠒⠲⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁⢀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡿⠋
⣿⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠶⠤⢤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁
⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⢛⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⢿⣝⡛⠻⠷⠶⠿⠿⠟⢛⣋⣩⡴⠖⠛⠁⠀⠉⠛⠷⠶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠛⠋⠁
⣤⣤⣬⣭⣿⣿⣷⣾⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣏⣼⣉⣯⣩⣿⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣼⣛⡲⢤⡀
⠀⠀⠀⠀⢠⠖⠋⡍⠉⡉⢉⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠶⠾⠷⠶⣦⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⢚⣩⣭⡇⡿⢟⡙⢦⣹⡄
⠀⠀⠀⠠⣏⣀⣃⣀⣁⣀⣁⣘⣀⣸⡆⠀⠀⠀⠀⢾⣉⣉⣉⣉⣉⣉⡇⠀⠀⠀⠀⠀⢠⡟⠒⠻⡆⠀⠀⠀⠀⢠⡟⣴⣋⣐⢺⡇⣷⡯⢟⣫⣍
⠀⠀⠀⠀⣯⠤⠤⣤⡤⠤⣤⡤⠤⣽⠇⠀⠀⠀⠀⠈⣯⠈⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⣾⠛⢳⠀⣿⠀⠀⠀⠀⣾⢰⡇⢯⡽⢸⣧⠵⣚⠉⡇⢹
⠀⠀⠀⠀⢳⠶⣶⡒⠒⠒⠒⣶⠶⣾⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡶⠛⠀⡟⠀⠀⠀⠀⢹⡌⣇⢰⣷⡌⠄⠺⠿⣰⢇⡿
⠀⠀⠀⠀⠘⠳⠾⠷⣦⣠⠾⠷⠖⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣇⠀⠀⠀⠀⠀⠻⣌⠳⢭⣴⣏⡷⠞⣣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠟⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⢴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢀⣴⠻⡌⢿⢸⡟⣸⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡅⠻⣜⣳
⠀⠀⠀⠈⡏⠛⠛⠚⠛⠒⠛⠋⣿⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⣦⣀⡀⠀⠀⠀⢠⡞⠉⠠⠈⠠⠉⠄⠈⢳⡄⠀⠀⠀⠀⢀⡞⠰⠀⠄⠠⠈⡽
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⢁⡿⠀⠀⠀⠀⢹⡏⠹⡟⠉⢹⡏⢩⡟⠁⠀⠀⠀⠀⣸⣇⠐⠀⢂⣠⠞⠁
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⣤⣼⣧⣤⣤⣤⣤⣿⣭⣤⠀⠀⠀⠀⠀⢷⠀⣿⠀⣸⠁⣼⠁⠀⠀⢀⡤⡼⣃⡼⠓⠛⠉
⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠾⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣤⣤⣤⣤⣤⠞⠀⠀⠀⠀⠀⠘⠧⠼⠤⠿⠴⠃⠀⠀⠀⠈⠳⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣉⣳⣆
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⣄⠀⠀⠀⠀⣾⣁⣈⣹⣄⣙⣦
⠀⠀⠀⠀⢀⣾⣩⣥⣀⣠⣩⣧⠀⠀⠀⠀⢀⡞⠉⠉⢹⠏⠉⠉⡟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠲⢾⡀⠀⠀⠈⢷⠖⠲⠖⣶⣶⡞
⠀⠀⠀⠀⢻⣥⣄⣠⣤⣀⣤⣬⡇⠀⠀⠀⣼⢶⠶⠶⡶⠶⢶⠶⠶⡶⠶⢶⢾⡆⠀⠀⠀⠀⠀⢀⡴⠋⠳⢤⡀⢨⡇⠀⠀⠀⠘⣷⠖⢋⣡⣼⠁
⠀⠀⠀⠀⢸⡄⠈⡇⠀⣿⠀⣸⠃⠀⠀⠀⣿⣯⣛⣛⣟⣛⣋⣛⣫⣿⣚⣉⣿⡇⠀⠀⠀⢀⡴⠛⠳⣄⠀⠀⠙⣿⠀⠀⠀⠀⠀⢹⡞⢋⣠⡇
⠀⠀⠀⠀⠀⢷⠀⣷⠀⡟⢠⡏⠀⠀⠀⠀⠘⠲⠾⠭⠭⣬⣭⣭⣬⠭⠽⠷⠚⠀⠀⠀⢿⣉⠹⡄⠀⠘⣦⣠⡾⠃⠀⠀⠀⠀⠀⠈⣿⠉⡿
⠀⠀⠀⠀⠀⠘⠓⠛⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣻⠙⠖⡦⠀⠀⠀⠀⣠⠞⠳⣄⢀⡴⠛⣦⠀⠀⠀⠀⠀⣯⠭⣽⡇⣴⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⣏⡽⠷⣤
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⣷⠛⣯⣿⣹⠆⠀⠀⣰⠋⠐⣦⠈⣯⠀⢶⠈⢳⡀⠀⠀⠀⢸⠀⢸⠀⣹⠏⢹⣇⠀⠀⠀⠀⠀⠀⣠⢞⡵⣫⡞⠁⠀⠈⡇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡟⠛⢻⡾⠃⠀⠀⠀⢿⠀⣰⠃⠀⣽⢠⡏⠀⢸⠇⠀⠀⢀⡾⠀⠸⣾⠁⠀⠀⢸⡇⠀⠀⢠⡖⣫⡵⣫⡴⠋⠀⠀⢀⡼⠁
⠀⠀⠀⢰⡋⠀⠀⢀⣴⠏⢀⡴⠋⠀⠀⠀⠀⠀⠈⢧⡈⢁⡴⠳⣌⠃⣰⠏⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠸⣏⡽⠛⠁⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠙⢦⣴⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠘⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠉⢳⣄⣀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠛⠓⠒⠒⠚⠃⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢢⡀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⢀⡄⠀⡀⢀⡈⠀⠀⠤⠛⠈⠁⠀⣄⠀⠀⣾⣿⣿⢿⣻⠀⠉⠃⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⡄⠀⠀⠀⠘⠛⠀⡘⠛⠃⠀⠀⠘⠁⠶⠀⠀⢀⠀⠀⠛⠛⠛⠋⠁⡀⠀⠀⠘⢡⣿⡦
⠀⠀⠀⢀⢀⡀⠀⠀⠠⠀⢰⣿⣆⠀⠀⠀⠀⠉⠄⠀⠀⢀⡀⠀⠴⠀⠀⠂⠀⠀⡉⠀⠀⠀⠠⢀⠕⠛⣈⡃
⠀⠀⠀⠙⠉⠁⠠⠄⢠⣤⠘⠋⠉⠀⢠⣶⡖⠀⣤⣄⠀⠿⠟⠁⠀⠀⠀⢰⠀⠄⢀⠄
⠀⠀⢈⠂⠀⠀⢀⡀⠈⠙⠀⠶⠿⠀⠿⣿⠀⢠⣿⡇⠀⠾⠀⠀⠁⠈⠊⠄⡠⠀⠠⠄⠀⡀⠀⠁⠀⠀⡂⠀⠀⠈⠁
⠀⢀⡠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⢨⡍⠉⣀⠀⠀⠀⠁⠀⣦⠀⠀⠀⠀⢀⠂⢀⡄
⠀⠀⠀⠁⠀⠀⢀⠀⠀⢀⠀⠄⠄⠀⠃⠀⢸⡇⠀⢨⠗⠰⠄⣦⠀⣿⠀⠹⢢⡇⠀⣰⣾⣧⠀⠀⠀⠀⠀⣠⣶⡈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠁⠀⠀⠀⢸⡇⢀⠸⣀⠀⡆⣿⠀⣻⡄⠀⣾⠁⢀⠀⠉⠛⠀⠰⢦⣤⠀⠻⠟⠁
⠀⣀⠤⡀⢴⡆⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠙⣁⠀⠙⠋⠈⠉⠉⡀⣉⠁⠴⠟⠀⠘⣿⣶⠂⠰⣿⣷⣷⠀⡾⠂
⠀⠄⠄⠇⠈⠙⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠚⠁⠛⠃⠀⢀⠀⠀⠀⠀⢀⣟⣾⢾⣮⠁⢀⣬⣄
⠀⡀⠅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠄⠀⠠⠊⠀⠀⠠⠆⠀⠀⠘⠣⠄⠀⠸⣭⣿⣿⡗⠀⠈⠛⠋
⠀⠀⠀⠒⠒⢒⠂⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⠀⠀⠀⠰⠂⠓⠀⠀⣛⣳⠶⣶⠅⠀⠀⠀⡾⠖
⠰⠶⠓⠒⡓⠒⠓⢈⠀⠀⠂⠠⠤⠀⠘⠀⠀⡤⢠⡠⣄⠛⠿⠟⠉⠀⠀⠀⠠⠀⣴⡆⠠⢼⣭⣭⣟⠀⠀⢠⠒⣀⡀
⢈⡙⡒⠘⠀⠀⠠⠀⠀⠈⠉⣁⡳⡀⠀⠀⠀⠀⠄⠈⠃⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⠀⠼⠒⠱⠹⡛⠀⠀⠘⠀⠡⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢀⡀⠀⠀⠀⠀⠀⢀⢀⢀⡠⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠍⢳⣾⣶⣖⣊⠂⠁⠂⣀⡌⠓⣗⣲⣾⣴⠟⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠹⠁⢻⡄⢋⠏⢻⠈⢁⣤⠈⣽⢁⡟⠁⠈⢸⡏⢯⠓⣰⠋⢹⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⣷⡟⠀⠀⠀⢩⡏⢙⣿⢿⣄⣴⡄⠀⠀⠈⣷⣿⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣷⡌⠁⢀⡀⠀⠀⠛⠛⠋⠘⠛⠛⠀⠀⢀⡀⣫⣥⠄⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣽⡿⠀⣸⡏⠛⠷⠀⢠⣾⣷⡄⢀⣶⠿⢟⡇⢹⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠭⢿⣥⡀⣿⡷⢾⠆⠀⣿⣅⣸⢷⢸⡏⠀⠈⠁⢨⣿⣴⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⣿⣇⣀⣶⢠⣿⡍⢸⣿⣼⣷⣀⣜⡆⢰⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⡿⠃⣿⣛⠉⡁⣠⠀⢠⣄⣄⣀⡉⠉⣙⡀⠿⣿⣄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠿⡟⢉⣤⡶⠦⠈⠀⠇⠿⠂⠟⠛⠘⠸⠇⠈⠩⢥⣤⣄⡁⠘⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣞⣀⠛⢋⣴⠃⢰⣴⢠⣶⣰⡖⣲⣶⣲⠶⣴⠀⠲⣬⠻⠇⣘⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡿⠻⢿⣾⡁⢋⡈⠈⠙⠙⠛⠋⡁⠋⠁⠈⠋⠈⣃⡉⣴⣿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣷⢸⡇⠀⠀⠀⢠⣿⢻⣧⠀⢠⣾⠿⢟⡇⣿⣿⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣠⣴⣿⠇⣼⡇⠀⡀⠀⡾⣧⣼⣿⠀⣿⡇⠀⢀⠀⣿⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠋⠁⠀⣿⣧⣼⡇⠠⠿⠿⠹⠿⠆⠹⣿⣶⣽⠀⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡄⠀⠀⠀⠉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡉⠀⠻⣿⣦⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠛⠁⠀⣴⣾⣿⠟⢋⣽⣿⣶⠚⠓⣶⣿⣿⠟⢋⣩⣷⣦⡈⠙⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡄⣼⣟⣋⡤⠞⣉⣿⣿⣿⡇⢸⣿⣋⣤⠞⣋⣽⣿⣿⣧⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠆⢻⣿⣿⣷⣾⣿⣿⡿⠋⠁⠈⠙⢿⣷⣾⣿⣿⣿⣿⡟⠰⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠓⠒⠯⠝⢻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⡀⡥⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠞⡃⠠⡠⢹⣦⣾⣟⣽⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣻⣿⣿⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⠙⢋⡿⠣⣮⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣏⡉⠙⠁⠀⠀⠒⠦⠈⠉⠉⠉⠿⣿⣿⣿⣿⡟⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠻⠛⠲⠶⠶⣄⣲⣀⡀⡒⠒⠺⠽⠛⠛⢋⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣛⣉⣤⣶⣶⣮⠙⠉⠉⠉⠉⠉⠉⢉⣭⣶⣶⣤⣀⣾⣿⣿⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⣭⣙⡻⣿⣿⣿⣷⡄⠀⠀⢀⣴⣿⢿⡟⣛⣹⣿⣿⣿⣿⢾⣾⡏⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠆⣈⡴⣋⠿⡝⢁⣙⠳⢶⡟⡇⠈⠀⢽⠋⡛⠞⢻⠁⢀⣰⡗⣵⠐⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡔⢡⠗⡂⣨⣍⠳⢮⠀⣀⣚⠋⠘⠀⠀⠀⢡⣴⣿⣉⣸⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣏⡟⠳⠓⠜⠉⠉⠐⠚⠛⠿⢆⠍⣀⣎⣹⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠤⠄⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣠⣤⠀⠀⡀⠀⣤⡄⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣿⣿⡇⣰⣿⣿⠀⣿⡇⢀⣿⡇⠀⠀⠀⢰⡟⣵⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣏⡇⠀⠀⢸⡟⣿⣷⡿⢹⣿⠀⠙⠷⠞⣿⣧⠤⡄⠀⢸⣧⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⣼⠇⣿⣿⡇⢸⣿⠀⢠⠔⠋⣿⠃⠀⠀⠀⠘⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⣀⡀⠛⠀⠘⠛⠁⠘⠛⠀⢿⣤⡼⢋⣀⠀⣠⡄⠀⠻⠟⠉⠀⠀⠀⢀⡀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣰⣿⣧⡤⠴⠖⠒⠛⠉⠉⠉⠉⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢴⣦⠀⣠⠟⣲⣦⠀⢀⣴⣦⠀⣠⣤⣤⣴⡄⢠⣿⡏⠀⢠⣴⣦⠀⢀⣤⣄⠀⢰⣿⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢋⡴⢿⣿⠞⠁⣰⣿⠇⠀⣿⣿⠞⢰⣿⢋⣾⡿⠁⢸⣿⠀⢠⣿⡿⠃⣠⣾⣿⣈⠔⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠴⣿⠇⠀⠀⣿⡏⢀⡴⣿⣇⡴⠻⠿⠋⣿⠃⢀⣿⣇⡴⠻⣿⣠⡴⢋⣼⣿⡇⠀⣿⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⡟⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢿⣠⠟⠀⠀⠀⠀⠀⠀⢀⡎⢀⣿⠃⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠴⢫⣾⢿⡆⠀⢀⣶⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣸⠃⢀⣾⡏⢰⠇⠀⠀⠀⢀⣀⠀⢰⣾⠛⠆⠀⠾⠂⠀⠀⠀⠀⠀⠀⢀⠀⣤⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡴⠃⠀⢸⣿⣡⠋⣰⡿⡷⠀⣿⡏⠃⢸⣿⡀⠀⣾⡗⢰⣿⣠⣶⡄⢀⣾⡟⢻⣿⡇⣰⣿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣿⣿⡤⣄⣀⣼⡟⠁⢀⣿⠗⢁⡔⣿⣧⠒⠈⣿⡷⢺⣿⠁⣼⣿⢃⣿⠇⢸⣟⡰⢋⣿⠟⢉⣿⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣠⣿⡏⠸⣧⡴⠋⠿⠴⠋⡴⢻⣿⠀⡴⢻⣷⠈⠿⠞⠘⠟⢸⡿⢠⠇⢨⠔⣻⡿⢠⡏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣿⠃⠀⠀⠀⠀⠀⠀⠘⠧⠼⠃⢰⡇⢸⡟⠀⠀⠀⠀⠀⠘⠛⠁⢰⡇⣠⡿⠁⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⣀⣀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⣙⠋⠀⠀⠀⢀⡀⠀⠀⢀⡀⢈⣉⣁⣄⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⢀⣾⠛⢻⣷⠀⣾⠟⣿⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⡀⢀⣿⣿⢸⡏⠉⠉⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡉⢸⣿⠀⠀⠛⢸⣟⣀⣿⢀⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⡿⣷⣾⢻⣿⢸⣧⣤⡄⠀⠉⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⡤⠸⣿⠀⢠⣷⢾⡟⠛⣿⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠙⠋⢸⣿⢸⡏⠉⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠻⢷⡾⠃⢸⠇⠀⠿⠘⠿⣶⡶⠸⠿⣶⣶⠄⠀⢿⠃⠀⠀⠸⠿⠸⠷⠶⠶⠆⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢤⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡼⣿⡆⣠⣤⡀⠹⣧⣤⠈⢣⠀⣿⣿⣰⣶⣆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⢫⣿⡇⢠⣿⡟⠉⡻⠉⣿⣿⡇⣿⣿⠎⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇⢸⣿⠁⣼⣿⠇⣠⠇⠀⣿⣿⠀⣿⡟⠀⣿⡇⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠛⠀⣿⡏⣼⠃⠙⠛⠁⠀⠀⠉⠁⠀⠙⠁⠈⣿⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡝⢿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠻⢶⣤⣀⣠⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⣀⣤⣠⣾⣿⣿⡿⠋⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣠⡴⢟⣽⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣀⡀⢰⡶⠶⠶⠶⢶⡆⠀⠀⠈⣿⣿⡀
⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣠⡾⢋⣴⣿⣿⣿⠟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⣷⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⡇
⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢠⣾⣫⣴⣿⣿⣿⠟⠁⠀⣠⡾⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣧
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⡇⠀⢀⣾⣿⣿⣿⣿⣯⣥⣤⣤⣘⣫⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡞⣁⣠⣾⠟⠛⠛⢿⡍⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⡟
⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣧⣀⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⣄⠀⣸⡇⠀⠀⣼⣿⡇
⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⡻⣿⠟⠉⠉⠛⠛⠛⠷⠶⠶⠶⢶⠶⠶⠶⠶⠿⠶⢶⣤⣤⣤⣤⣶⡶⠶⠶⠿⠆⢰⡏⠺⣧⡽⢃⣿⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢀⡘⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠃⠀⠀⣼⣿⡟
⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⢀⡀⠈⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣿⣧⠀⢰⣟⠁⢀⣠⣴⠾⠛⠉⠉⠙⠻⣦⣄⣀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠠⠤⡀⠀⢝⢤⡀
⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠴⡶⠴⠂⢀⣀⣂⡀⠀⠀⠈⠀⢀⠐⢁⡔⠐⠄⠀⠀⠀⠈⣏⢳
⠀⠀⠀⠀⠀⢂⠝⠁⢀⠜⠁⠀⠀⠀⠀⠀⢀⠀⡀⡠⠀⠀⢀⣖⢻⡓⢼⡽⠷⠆⠀⠀⣐⠀⡎⠀⠀⠀⡇⠀⡇⠀⢸⡈⡇
⠀⠀⠀⠀⢁⠀⠄⢴⡏⠀⢀⣀⣀⡀⡠⢀⠂⠐⠐⢁⡀⢠⣿⣭⡆⣏⣀⡈⠓⢀⠀⠀⢨⠀⢇⠀⠄⣀⠇⢈⡇⠀⢸⡤⡃
⠀⠀⠀⠈⠃⠠⠀⡘⠈⠉⠀⠀⠀⠈⠀⡈⠀⠀⠁⠉⢀⣿⡈⡿⢤⠋⡉⠲⣻⣷⣀⢄⠈⠧⡀⠉⠈⢁⣠⠎⠀⢠⡟⣸
⠀⠀⠀⢀⠀⡆⡇⡇⣀⣀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠀⣨⡷⠊⣤⠞⢿⡇⠀⣉⣹⠈⠂⣠⣄⣀⣉⠀⢉⣁⣠⡾⡏⠔⠁
⠀⠀⠀⢀⣇⢳⠁⠁⠀⠀⠀⠀⠀⠀⠀⢁⣨⠀⠇⠀⡹⠁⣾⡴⠒⠻⡿⠞⠻⡕⠀⠀⠈⠁⡬⠭⢍⡭⠏⠐⠂⠁
⠀⠀⠀⠀⠘⣌⠶⣔⡀⠀⠀⠀⠀⠀⠀⠰⠰⣆⢂⠀⠘⣿⣻⣾⣲⡂⢰⣾⠶⣇⣀⣀⣂⣤⡬⠀⠀⢠
⠀⠀⠀⠀⠀⠊⣺⣷⣷⣄⣀⠀⣀⡀⡀⢠⣣⡣⣊⣢⡀⠘⢿⣿⡿⡂⢯⡹⠂⣠⣤⣤⠀⠀⠙⢳⡖⠢⢁⣀⡰
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠀⠃⠉⠙⠋⠽⠉⠁⠻⡻⣻⡇⣼⣶⣞⣯⣭⣏⡙⢻⣻⠏⠛⠒⢭⣍⣉⠂⠐⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠈⣣⣌⡀⠙⠾⣟⠧⣍⣘⣥⠾⢛⠛⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠛⠉⠉⠙⠦⠤⠀⠀⠐⠘⠁⣰⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⡇⠀⠂⢠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⠀⢁⢰⡇⣀⠂⣀⡆⢸⡇⠀⠀⡀⠀⣘⢃⠃⡀⠀⠓⠘⠀⢀⠀⠀⠀⠀⠀⢈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠸⡟⠌⠃⠼⠁⠈⠁⠀⠀⠀⠀⠼⠂⠁⢠⠘⠃⢀⠐⠆⠁⠠⠀⠀⠀⠘⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠛⠒⠘⠓⠟⠛⠃⠚⠈⠘⠾⠟⠲⢻⠖⠖⠘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⣀⢀⣄⣀⣤⡆⢀⠀⢘⡇⢛⡀⠃⠆⣹⣆⠳⠈⣛⠀⠀⠄⠀⠀⠸⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣈⣿⣿⣿⡿⣿⢿⣿⠟⠃⠸⢀⣨⠁⣾⣧⣧⣀⣉⣄⣠⣀⣉⣤⠀⠠⠤⠄⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠯⠽⠓⠿⠽⠺⠂⠸⠇⠈⡽⠰⠸⠿⠿⠿⢿⠿⠿⠿⢿⣿⠇⠠⠤⠄⠙⢂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠄⠀⠀⠀⢳⡔⢦⡐⢤⣄⠰⠄⡄⠐⠆⠐⠂⢰⠀⠘⢰⡆⣾⣿⠗⠒⠒⠂⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠈⠀⢉⠸⡇⠁⡀⣁⢀⡿⢀⢟⣈⣠⣸⣀⣃⣿⣿⡿⠛⢛⠓⢢⣬⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣟⠣⣼⣽⡧⢞⠛⣛⢻⣧⠌⠌⢻⣿⣯⣽⣿⣿⣿⠀⠈⠛⠥⠶⡶⠖⢠⣤⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⠀⢐⠋⠀⠀⠀⣲⢁⡄⣀⢻⡷⢈⣉⣿⣿⣿⣾⣿⣿⣿⡥⠀⠁⠶⠶⠦⠘⠰⣿⡷⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠿⠿⠿⣿⠖⠲⠦⣿⣦⠍⠯⢹⡟⠀⠀⢾⣿⡿⠬⠻⢿⡿⠦⠉⡭⠉⠉⣥⣭⠐⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⡁⠰⣯⢉⡁⡂⣿⠀⡆⠀⠆⠰⡆⠇⡘⠀⠀⢰⡆⣰⢀⠰⠀⠄⠀⠄⠀⠀⠘⣿⣯⡁⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁⢺⣿⣾⣿⣷⣿⡇⢣⡄⢀⣈⣃⡠⠄⣀⠀⢀⠀⣋⠀⢠⣄⣄⣀⠀⠀⢀⢈⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠀⠁⠀⢶⠰⠂⠰⡎⠉⡄⢰⠆⠋⡀⡌⠐⠛⠈⠀⠀⠈⣉⠉⠀⠀⠈⣻⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠈⡁⢀⣉⣄⣀⢀⣋⣤⣀⣈⣁⣤⣴⣴⣶⠀⡁⠂⡆⠀⡀⠀⠀⠀⠀⠘⠃⠉⠀⣿⣯⡀⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⢛⡅⢨⣿⣿⣿⡟⣉⠻⢉⢻⡟⢿⠛⠻⡟⢂⡳⡃⣐⢒⠓⠀⠀⠍⠉⠁⠈⠀⠐⢛⠃⠀⢦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⢋⡄⢰⣿⡿⣿⡇⣨⠘⢈⠸⠱⠸⠀⢀⠁⢦⡹⡇⣿⢸⠀⠀⢠⣄⣭⣍⣀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢀⣤⣼⣤⣼⣦⣤⣼⣤⣦⣼⣧⣿⣦⡔⠀⢈⠁⠀⢤⣤⣄⣀⠀⡀⠀⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠶⢀⠀⠀⠀⠀⠉⢰⠀⢄⠃⠀⢸⠀⠀⠀⠈⠋⢹⠋⠘⠏⠻⠛⠟⠻⢿⠟⠻⠟⠗⠀⠀⢁⡄⠘⠿⠃⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠁⠈⡳⡘⠂⡇⢸⠀⠁⠘⠇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣀⠀⢀⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠈⠀⠈⠈⠀⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠐⠒⠶⠖⠲⠆⠀⠀⠰⠒⠦⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡍⣷⠀⠀⢀⡄⣶⣤⣠⣴⠀⣶⣄⡰⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣇⠀⠀⣽⠀⠀⠘⠃⠁⡉⡉⠀⢀⡀⠁⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠋⢀⡇⠸⠀⡖⠀⠏⡖⡸⠂⣾⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠛⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛
⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠒⡰⠄⢢⣎⣁⠀⠐⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠶⠒⣒⡒⠲⢤⡀⠀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠖⠻⡄
⡟⠓⠺⣄⠀⢀⣇⣀⣹⡄⠀⢸⣄⠀⠀⠂⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⢀⠀⠈⢑⡦⢷⡀⣌⠐⢣⡄⢀⣀⡰⠟⢫⣾⠟⠁
⠇⠀⠀⠀⠉⠉⠀⠀⠀⣹⢿⣧⡎⠀⠀⠀⠀⠀⠀⠀⢸⡂⡈⠀⠀⡐⢀⡀⣈⢀⣀⣤⣾⠁⠉⠀⠛⠓⢀⣤⠶⠛⠉
⢰⠀⠀⠀⠄⠀⠀⠀⡐⠉⠀⢧⠀⠀⢐⠀⠀⠀⠀⢴⠉⠻⠽⠿⣭⠿⣯⠽⠛⣛⡻⢟⡟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⠸⠀⠀⠀⠀⠀⠀⠐⢀⣠⠴⠚⠀⠀⠀⠉⠉⠁⠀⠈⠲⢍⣀⣒⣐⣒⣀⡨⠭⠄⠒⠉⠀⠀⠰⠀⠀⠀⠀⠈⠀⠈⠁⡆⠀⠀⡀⠀⠀⠨⢆
⠀⠉⠙⠛⠛⠒⠚⠞⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠱⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡨⠓⠀⠀⠀⡈⠓⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⣼⠃⠀⠀⠀⣤⣶⠶⣤⣤
⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠰⢄⣨⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠢⡀⠙⢆⠀⠀⠁⣆⠀⠀⠀⡇⠀⠀⠀⠀⠁⢀⠠⠐⡄
⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⢀⠎⠀⠀⠐⠦⠀⠀⡀⢀⣨⡦⠠⠇⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⡁⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⢀⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⢂⣤⠾⠛⠁⠐⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠄⢙⣣⡄⠀⠀⠈⠀⠉⠀⠀⠀⠀⢸⣀⣴⠟⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠘
⠀⢀⠄⠒⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡤⠒⠛⠛⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⡤⢀⢄⡀
⠀⡀⢰⠀⠀⢧⠀⠀⠀⠀⣠⣄⣴⣄⠐⢃⣀⡀⠀⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⠀⢀⣠⢼⠀⠀⠤⣜⠷⠻⣇⢱⠈⡁⠀⠀⠀⠐⠀⠀⠈⠠
⠀⠄⣸⠀⠀⢸⠀⠀⢠⣾⠏⡠⠊⠀⠀⠀⠀⠉⢶⠀⠀⡟⠀⠤⠀⠀⠀⣠⣤⣶⠿⢳⣻⡀⠀⠀⣿⠄⠀⠟⣸⣄⡿⠃
⠀⡇⣇⠀⠀⣼⠀⠀⢼⡫⠜⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⣤⡤⠶⠊⣙⢋⠽⣷⢦⣎⡥⢴⠋⠀⡋⠘⠚⠷⠛⢛⡇⠀⠀⠀⠀⠀⡀⠠⠤
⠀⢶⢸⠀⠀⡇⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠀⠠⠃⠀⠀⠈⣼⣄⣸⣭⣴⡶⠿⠋⠃⣱⠎⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠃⠀⠄
⠀⢸⡌⠀⢰⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢀⣀⣈⣉⣀⠤⠒⠊⠁⠀⠀⠀⠀⠃⠀⠀⠠⠓⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠳⣤⠟⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣠⡌⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠐⠖⠒⠲⡤⠠⢤⡶⠀⠀⢀⠤⣠⠶⠶⠚⠋⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡆⢀⣬⡦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠂⠀⠀⠁⢨⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⠦⠂⣀⣒⠀⠉⠝⠃⠚⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⠤⣽⣋⣛⣛⣛⣛⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄
⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣆⠀⠀⣿⣿⣿⡇⠀⠀⣠⣾⣶⡄
⠀⠀⠀⣿⣿⢿⣧⢰⣿⠏⣿⣷⢀⣴⣿⣿⣿
⠀⠀⠀⢹⣿⠈⢻⣿⣿⠀⢿⣿⣾⠟⣿⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠙⠃⠀⠈⠛⠋⢠⣿⡿
⠀⠀⠀⠀⣿⣧⢀⣠⣤⣤⣤⣄⡀⣸⣿⠇
⠀⠀⠀⠀⠙⠛⠻⢛⣛⣛⣛⠻⠿⣿⡍
⠀⠀⠀⠀⠀⡤⢞⣭⣿⡿⠿⣷⣄⠈⠛
⠀⠀⠀⢠⢞⣴⣿⠟⠁⠀⢰⢿⣿⣷⡄
⠀⠀⣰⢫⣾⡿⠃⠀⠀⢀⡞⣸⣿⣿⡇
⠀⢰⣯⣿⣿⠃⠀⠀⣠⣟⣴⣿⣿⣿⡇
⢀⣿⣿⣿⠇⠀⠀⠀⠹⢿⡿⣿⣿⣿
⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⢧⣄⠀⠀⠀⢀⡀⠀⠀⠀⢀⡠⢤⣤⣀⠀⠀⠀⣀⠤⣤⣄⠀⠀⠀⠀⠀⢀⣤⣄
⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⡟⣸⢻⣷⡄⠀⡿⣿⣦⠀⢠⢎⣾⣿⠟⣻⣧⢀⠞⣵⣾⡿⢿⣷⢀⣿⣦⣰⣿⢻⣿⣷⡄
⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⡿⢠⡟⣸⣿⠃⢸⠇⣿⣿⢀⣏⣾⣿⣃⣴⣿⣿⣿⣾⣿⠟⣠⣿⡿⣸⢸⣿⡿⢁⡞⣼⣿⠇
⢿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⠁⣼⣧⣿⡟⢀⣿⣼⣿⡇⢸⣿⣿⡟⠛⠛⢋⣼⣿⣿⡿⣾⡿⠟⣠⣿⣿⣿⠃⡾⣰⣿⡟
⠸⣿⣿⣿⡄⠀⣸⣿⡜⣿⣷⡀⢹⣿⣿⢃⣾⢿⣿⣿⡇⠘⣿⣿⡇⠀⣠⣾⠻⣿⣿⡇⠀⣠⣾⠿⣿⣿⠇⣸⢣⣿⡟⠀⣶
⠀⠙⢿⣿⣿⣾⣿⣿⣷⢹⣿⣷⠀⠙⠿⠿⠋⠀⢿⣿⣄⣼⠛⢿⣿⣾⠿⠁⠀⠙⠿⣿⣿⠿⠃⠀⠙⠋⠀⣿⣾⡿⠁⢰⣿
⠀⠀⠀⠙⠻⠿⠟⠋⢻⣧⣻⣿⡄⠀⠀⠀⠀⠀⠀⠉⠋⠁⢀⣀⣠⡤⠴⠶⢒⣚⣛⣻⣿⣿⣿⣷⣦⡀⠘⣿⣿⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣶⡤⠀⠀⣀⣠⡴⢖⣛⣭⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⢿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣠⣶⣿⣿⣷⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢠⠤⣄
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠉⣓⡏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⣠⠰⠯⡞⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠒⣋⣽⡗⠾⣷⣆⠀⠀⠀⠀⠀⢠⠞⠉⠙⠒⠚⠉⠀⠈⡇
⠀⢀⣼⣩⠗⠒⠷⣄⠀⠀⠙⠒⠤⢄⣤⠀⠀⠀⣿⣎⣴⡗⠒⢿⣱⠋⠸⡄⠀⠀⠀⠀⠘⢦⡀⢠⠞⠉⠙⢲⡀⠙⢦⡀
⠀⠀⠀⠸⡄⠀⠀⠈⠓⠦⣤⣤⣤⠜⠺⠀⠀⠀⢳⠉⠉⡑⠛⡿⢁⠀⠀⢳⠀⠀⠀⠀⢀⡴⠃⠸⡄⠀⠀⣸⠇⠀⠀⢹
⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⢉⡟⡿⠀⠀⠀⠈⢧⠀⠀⡼⠁⠀⣠⠀⠈⡇⠀⠀⠀⡏⠀⠀⠀⠉⠓⠚⠁⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠹⠇⠀⠀⠀⠀⠀⠳⡞⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠳⠤⠤⠖⠚⠉⠉⠓⠲⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡀⠀⠛⠀⠐⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⡀⠘⢦⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣏⡞⠉⠀⠀⠀⠀⠀⠀⠀⠘⢲⣇⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠲⣄⡶⢾⢉⣗⢀
⠀⠀⠀⠀⠀⠀⠀⣸⣹⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣞⣘⣦⡀⠀⢰⡇⡆⠀⠀⠀⣠⡶⠀⠀⣀⣈⣷⠉⣹⡞⢻⡈⢯⡇
⠀⠀⠠⣯⡭⠭⠭⠭⠭⠭⠭⢤⡽⠆⠀⠀⠀⢀⡧⠤⠤⠤⢧⡀⠈⡇⠃⡞⠳⢾⡏⠀⠀⠀⠿⠲⣬⠙⢧⡇⡿⢳⡀⢳⡀
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⠀⡵⠲⢿⣤⣼⠇⠀⠀⠀⠀⢷⠻⠷⠤⠿⠧⠟⠓⢫⠇
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣬⣷⣄⣸⠇⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣄⣧⣀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣇⢀⢀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⢾⠑⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⣻⡿⠓⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢠⣴⣶⣲⡤⢤⡤⢤⡄⠀⠀⠀⠀⠀⠸⠋⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠈⠉⠙⠒⠦⣄
⠀⠀⠀⣠⠛⠉⠀⠈⠙⠺⣏⣻⡻⡟⠲⡄⠀⠀⠀⠀⡤⠚⢭⡀⣄⠓⣩⠛⢦⡀⠀⠀⠀⠀⠀⣯⡙⠒⠶⣇⣀⡀⠈⠙⢦⡀
⠀⠀⠀⡇⢀⠀⠀⠈⠀⠠⠈⢣⡙⣟⣷⢹⠀⠀⠀⠸⣅⠋⠀⠀⢡⠄⠀⠒⠃⢳⠀⠀⠀⠀⠀⣧⢙⡆⢀⣂⣉⡓⢤⡖⠀⢳⡄
⠀⠀⠀⠘⠦⣀⠈⠀⢀⡀⠀⠃⢳⢈⡿⣿⠀⠀⠀⢀⣯⣩⠭⣍⣉⣭⠿⣍⣩⠿⡄⠀⠀⠀⢰⡗⠋⢰⣫⢶⣾⣯⡷⠟⠛⠉
⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠈⡿⢻⠏⠀⠀⠀⠀⢳⡶⠖⠒⠻⠶⣖⠒⠒⣻⠁⠀⠀⠀⢸⠗⣦⣸⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠷⠋⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⡤⠬⠷⠞⠃⠀⠀⠀⠀⠸⠛⠉

⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡖⠭⠒⢀⡍⡁⣈⡠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠃⠢⠀⠒
⠀⠀⣀⠁⠀⠀⠀⠈⠀⠀⠀⢀⡰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⡐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠖⠀⠀⠊
⠀⠀⠁⠀⠀⠀⠒⠒⠒⢒⣈⣩⠴⠚⡅⠀⠀⠀⠀⠀⠀⡠⠞⠍⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠐⠒⠒⢀⣀⡠⠤⠖
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡀⠠⠔⢻⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠀⢠⠊⠁⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⢀⣠⠄
⠀⠀⢸⠄⠀⡀⠀⠀⠀⠀⢀⣀⡤⢾⠀⠀⠀⠀⠀⠀⠇⠀⠀⢂⠘⠀⠀⠠⠤⠐⢊⠁⠁⡔⠊⡥⠀⠀⠀⠀⠀⠀⢩⠝⣀⢋⠼⡟⢣⠉⡄
⠀⠀⠘⠀⠄⠀⠈⠉⠉⠭⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠔⠁⠀⠞⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⢼⣤⣦⣼⣤⢧⢿⠁
⠀⠀⠀⡇⠀⠀⡀⠄⠐⠀⠀⠙⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢜⣕⢕⡵⡡⡏
⠀⠀⠀⠘⠀⠀⠀⣀⣈⣀⡠⠴⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡯⡪⣾⢮⡇
⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢠⡆⠀⠀⠀⠀⠀⠀⣀⠄⠘⠀⠀⡚⢀⡀⠀⠃⢦⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠞⠁⠀⠀⢀⣠⠀⠀⠀⠀⣀⢄⠈⢱⠚⠇⢸⠁⠞⠂⡜⠓⢀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠐
⠀⠀⡠⠖⠂⠒⠉⠈⠁⣄⣀⣠⠞⠁⠘⠉⠀⠀⠀⠀⠁⠈⠃⣰⠸⠀⠟⠲⠀⣼⠇⠀⠈⠀⠀⠀⠀⡸⠤⠠⠄⠤⢀⡀
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠂⠅⠧⠼⠿⠏⠀⠀⠃⠀⠀⠀⠀⠀⣺⣁⣊⣐⣂⠐⠋⠻⠐⠠⢀⠤⠀⠈⠆
⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠌⢀⡘⡈⠀⠀⠀⠀⢄⣁⣠⠎
⠇⠀⠀⠀⠀⠀⠀⡀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢨⠆⠀⢀⡈⠉⠀⠒⠃⠐⠂⠐⠀⠜
⠀⠀⠀⠀⠀⣀⣴⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⡀⠀⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⠀⠤⠌⠀⠉⢐⡋⣘⠁⢀⠀⢀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⢀⣠⠖⠊⠉⠄⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⢸⠁⠄⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢧⡀⠀⣀⡀
⠀⣠⠋⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠂⠀⠀⡄⠀⡄⠀⠠⠀⠀⢀⡀⠀⠀⠀⢸⠁⠀⠈⠃⠪⡁⢟⣠⣄
⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⣡⠞⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡒⢠⠉⠂⡠⠀⠀⡄⠀⠘⠀⠀⠀⠀⠈⠓⠀⠤⠘⣤⣗⣲⣄
⠈⢙⡁⠶⠄⠤⣤⠤⠤⡬⢄⠒⠚⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⡁⠂⡠⠊⠀⢀⡰⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡢⡑
⠀⠈⡀⠀⠉⠀⠐⠈⠀⠐⣁⠤⠚⢀⡁⠴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠕⠊⠀⢀⡴⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞
⠀⠘⠀⠘⠀⠤⠶⠒⠒⠒⠀⠚⠩⠉⠂⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢠⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠂⣒⣨⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠉⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⣠⡖⠉⢉⠇⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⣿⡀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⣾⠟⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠈⠛⠓⠛⠉⠀⠀⠀⠀⠀⡠⠲⣶⡄⠀⣀⠁⠀⢠⣿⡯⠔⠁⢀⣤⡾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⣴⠄⡠⢒⡖⡠⠊⢀⣾⡿⠀⣾⡟⠀⢀⣿⡏⠀⠀⢠⣾⣏⠤⠞⠁⣠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⠀⣼⡏⡜⢁⣿⡟⠀⢠⣿⠏⠀⣸⡿⠀⢀⣾⡿⠀⠀⢀⣿⡏⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⠀⣿⡟⢀⣿⠏⠀⣾⠏⠀⢠⣿⠋⠀⡰⠻⣧⠔⠁⣿⡇⠀⣠⠊⠙⠷⠴⠚⠁⠀⣠⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⣰⠟⠀⠈⠛⠀⠀⠈⠀⠀⠸⣿⣀⠜⢀⡴⢒⠀⠀⠹⠿⠞⠁⠴⠚⠛⠛⠒⠦⣴⣿⠃⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠉⢋⡉⣀⣀⠀⢤⡤⣤⠀⡄⣠⢤⠀⠀⠀⣠⡟⡰⠃⠀⠀⠀⢀⣀⣀⢀⣤⠖⠂⡂⣰⡿⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢧⡁⠀⡞⢰⠟⣾⡟⠓⣚⠀⠀⢰⡿⢋⠴⠶⣦⠀⣴⡟⠡⠀⢸⣿⡀⠈⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠑⠉⠀⡈⠁⠈⠀⠁⠙⢚⣁⠤⠖⣿⡗⢁⠀⠀⡿⢹⡏⠀⢀⠀⠀⢹⣿⠀⣼⡇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⡴⢋⣿⠇⢀⡴⢚⣷⠄⠀⠀⠘⡿⠀⠫⣤⣊⠀⠘⠷⠤⠋⠐⠤⠾⠋⠀⠙⠷⠊⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⢇⠎⠀⣼⡟⡴⠃⢠⣾⢏⠴⠖⠶⠤⢄⣠⡞⠥⠊⠀⠀⢀⣀⠀⠀⣠⡶⠀⢠⡖⣠⡿⠊⠁⢸⡇
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣼⣿⠞⠀⣰⣿⢋⣤⠖⠲⣤⠀⣼⣏⠴⠲⡆⣠⡾⠋⡨⢀⣼⠏⠀⢠⡟⢠⡟⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⢰⣿⠇⠀⣸⣿⠋⠀⣰⣿⢣⡞⠁⠀⣼⠏⣸⣟⣁⠤⠚⢹⡿⠐⠊⡀⣸⠇⠀⢠⣿⢁⡿⢥⣤⠾⠋
⠀⠀⠀⠀⠀⣼⡏⠀⢠⣿⠏⠀⢰⣿⠇⣿⠀⠀⣼⠏⢠⣿⠉⠹⣷⣄⠘⠳⠖⠊⡀⢿⠀⡰⠁⠇⢸⣇⠠⣄⡀
⠀⠀⠀⠀⠀⠿⠀⠀⠘⠟⠀⠀⢸⣿⠀⠛⠒⠉⠻⠖⢹⡏⠀⠀⠈⠻⠷⠶⠶⠚⠀⣀⣩⠴⠒⠊⠙⢧⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠤⠀⠰⣄⠀⠀⠁⠀⠀⠀⣀⣀⣤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠈⠉⠒⠲⢤⣄⣀⠀⠀⠀⢀⣀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⠚⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⡀⠻⢬⢝⡞⠿⣧⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⢉⣤⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠻⠷⢶⣾⡿⢷⡶⠶⢟⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣤⠖⠋⣡⣦⡶⠖⠋⠁⢀⣠⣴⣾⡿⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣿⡶⠟⠋⠁⠀⣀⣤⠶⠛⢩⡟⢱⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⢀⣠⡴⠟⣻⣀⣀⣠⡾⠀⠈⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⢴⡚⠁⠀⠀⣀⣴⠾⠛⢻⡏⠉⠙⣛⡿⠟⠃⠀⣀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⠤⠺⡙⣆⠀⢻⣤⣶⡟⠛⠛⠃⢀⡼⣡⠔⠋⠁⠀⠀⠀⠀⠈⣽⠃
⠀⠀⠀⠀⠀⠀⠀⡟⣴⠛⠙⣆⠀⣹⣽⠶⠛⠁⠈⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠀⠀⠀⠀⠀⠀⣼⠃⢧⣀⣠⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞

⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢀⡀⢠⣄⣼⠂⡀
⠀⢰⡞⠋⠁⠀⢷⠀⢻⠳⡄⡟⠀⡏⠈⢳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣿⠋⠈⠃⢬⠟⠁
⠀⠀⢿⡁⠀⠀⠸⠆⢸⣀⣙⡇⠀⣇⠴⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣹⠰⠌⡷⣟⡤
⠀⠁⠈⡷⢶⣚⣯⠍⠉⠉⠉⠉⠉⠛⠒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶
⠀⠀⢶⡿⣀⡤⢷⠔⣾⢘⡷⠺⣇⣿⣀⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣐⠛⣂⠀⣀
⠀⠀⠀⣾⠁⠀⣸⠀⠈⠉⠀⡴⠚⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠦⣇⡇⡿⠀⣷⢳⡇⡧⠶⠆
⣴⣶⣤⣜⣲⠖⠋⣀⣀⠀⣤⢱⣋⡅⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⡁⣥⣉⡄⠉⣡⣹⠁⣴⣄
⢻⡿⣿⣿⠟⢀⠀⠉⠈⠀⠈⠀⠀⠁⢀⠸⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⠀⠈
⠈⠳⠿⠃⠀⢽⠻⠝⠣⠿⠯⠟⠷⠛⣻⠄⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣿⡶⡴⡶⠶⡴⣾⢟⡔
⠀⠀⠀⠀⠨⠜⠀⠀⠀⠀⠀⠀⢐⣋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣅⣍⠉⢉⡄⣤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠩⠟⠉⠙⠏⠉

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣴⣿⠟⠋⡍⠍⢙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠐⠢⣄⡴⠉⠀⠀⠙⡆
⠀⠀⠀⠐⠿⠃⠀⠠⠂⠰⠈⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣦⢦⢠⡄⡀⣤⣦⣤⠉⠹⠤
⠀⠀⠀⠀⠛⠘⣙⣛⢃⠁⡄⢃⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⡋⠸⡊⠏⡽⠏⢄⠈⠉⠀⢀
⠀⠀⠀⡏⣸⠇⠈⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⢻⣇⣷⡇⠀⠘⣤⢦⠀⠁
⠀⠀⠠⣷⡔⠛⣟⣾⣟⣻⣧⡞⣗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠸⠏⠟⠻⠟⠀⠁⠀⠓⣤
⠀⠀⠀⠈⣑⠄⢸⡄⠉⡀⢺⣁⢸⡌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠃⣒⣒⣳⣤⠄⡉⣍⡍⡈⠉⠉
⠀⠀⠀⠀⠈⢛⠎⣇⣏⠯⡜⢹⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠟⠘⠚⠚⢉⣿⡟
⠀⠀⠀⠰⠌⠻⣾⣾⣿⣛⣿⣵⡟⢧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠇⣠⠤⣠⠄⢁⡼⠀⠠
⠀⠀⠀⠀⠉⢄⠁⡱⠸⢻⠋⠻⣇⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡖⡦⢿⡰⢏⣼⣣⡶⡆⠫
⣀⣀⣀⣀⣀⣀⣁⣁⣢⣌⣐⣃⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢄⡀⠛⠛⠛⠓⠃⠀⠀⠃⠑⠒⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠸⠤⣧⠀⠀⡆⠘⢵⠶⠟⠸⠿⠆⠗⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠟⢠⠀⡇⢀⠄⣤⡀⣰⢠⡄⡀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠀⠃⠃⠇⠸⠣⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠾⠁
⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣀
⠀⠔⢂⠶⠘⣆⣁⡀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠶⠖⣒⡒⠒⠤⡀⠀⠤⠒⠀⠀⠀⠀⠀⣠⠖⢻⡀
⡏⠙⠳⣄⣀⣭⠤⣽⣄⣀⡼⡄⠀⠂⠀⠀⠀⠀⣯⠀⡀⠀⠀⠀⠀⠀⠈⢶⠼⡄⢌⢑⣦⠄⠀⠠⠟⣩⠾⠛⠁
⠇⠀⠀⠀⠀⠀⠀⠀⡜⢻⠾⠃⠀⠀⠀⢀⠀⢀⣧⣠⣀⣀⣌⣠⣄⣦⣤⣴⣾⠇⠀⠄⡉⣁⠴⠚⠉
⢰⢰⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠀⠄⠀⠜⠀⢧⡈⢙⣛⣚⣛⡓⠋⠍⢝⡪⠟⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠋⠢⡀
⠘⠤⢤⣤⣤⣠⣦⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠚⠃⠉⠁⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠆⠀⠀⠁⠰⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠯⠄⠉⠙⠲⣄⠀⠀⠀⢹⡀⠀⠀⠀⢠⠏⠀⠀⠁⢀⣤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⣀⡒⠁⠀⠂⠀⠀⠀⠀⡠⠁⠂⠀⠀⠀⠢⡀⠑⢄⠀⠀⠃⡀⠀⠀⠘⠀⠀⠀⠈⠍⠉⡉⣝
⠀⠀⠀⠀⠲⠅⠀⠀⠀⠀⠀⠉⠁⠀⠀⢄⠀⠀⠀⣰⠁⠀⠀⠆⠀⠀⠀⣈⣦⠄⠆⠀⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠐⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⢀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⣠⡴⠚⠉⠀⠘⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠀⡆⠀⠀⠀⠀⢰⣼
⠀⠀⠀⠀⠀⠠⠠⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠛⠁⢀⣠⣤⡦⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠔⢉⠉⢳⠀⠀⠀⠀⠀⢀⡀⢀⡀⡀⠀⠀⠀⠀⣠⠞⠙⠠⠁⠉⠉⠀⠉⢱⡀⠀⣀⣠⣁⣉⣡⡀⡀⠀⠀⠸⣽⣋⣦⣄
⠀⠀⢆⠀⢸⡄⠀⠀⣴⠟⢪⠟⠈⠐⠒⠣⣄⠀⢠⠏⠀⠀⠀⠀⠀⣀⣥⣾⣽⠀⠀⢉⣏⠉⠹⡟⡇⣧⠄⠀⠀⠈⠉⠀⠈
⠀⢰⡃⠀⢸⠃⠀⣺⣛⠔⠁⠀⠀⠀⠀⠀⠈⡀⠸⣄⣀⣤⠔⢲⠟⣿⣥⡴⣚⣡⡆⠀⡇⠢⢴⡽⠿⣏⠀⠀⠀⠀⠀⠀⢀
⠀⡇⡅⠀⢸⠀⠀⠈⠓⠢⠤⠤⠀⣀⠀⠀⠤⠁⠀⠈⣭⣄⣀⣋⣭⣾⡟⠋⢱⡜⠀⠀⢇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠁⡠
⠀⢹⠁⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣀⣉⣉⡠⠴⠒⠉⠀⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠉
⠀⠈⠣⡜⠁⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⣀⣤⣴⠟⠛⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⢶⠈⠢⡀
⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⡙⠉⠉⠛⠉⠑⡉⠀⠠⠐⠗⠛⠉⠉⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⡿⣼⢄⣶⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠆⣀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠰⠊⡼⠑⣇⣈⢠⢴⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣾⠁⢀⣤⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠈⠃⠀⢻⠳⠎⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠄⠀⠀⠀⡀⠤⡀⠀⠄⠀⠀⠀⠀⠑⡄⡇⠀⠏⢛⠸⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠇⠂⠆⠀⢦⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⣹⠀⡾⡇⢸⡇⠀⠸⡎⠀⠀⠀⠀⢀⠀⠊⠰⠄⠀⠈⠂⠀⡄⠀⡅
⠀⠀⠀⠀⢀⣠⡇⣀⠀⢊⣄⠠⡄⠀⢠⢀⠀⡠⢦⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠃⡠⠀⠀⠀⡇⠀⠀⠀⠀⢼⠀⠀⠀⣴⢰⡄⣟⠀⣇⠐⠁
⠀⠀⠀⢰⢹⢹⡧⢸⣀⡷⡇⠼⢤⣾⢸⠀⢼⡇⠄⡗⠀⠀⠀⠀⠀⡁⠸⡄⢀⠀⢃⡂⠀⣠⠂⠀⠀⠀⠀⢸⠀⢸⡇⠛⠰⡇⡏⠀⣷⠀⠄
⠀⠀⠀⠈⠸⡌⠇⠈⠉⠀⠑⠁⠌⢿⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⡞⢠⡆⡆⢰⢀⡆⠃⠈⠁⠀⠀⠀⠀⠀⠸⡄⠌⠃⠀⠀⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠣⠀⠃⢇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⡆⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⣰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡾⡀⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠤⡄⡀⢠⡄⡇⡏⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠀⠀⢠⠧⡖⠀⠀⠀⠀⠀⠀⠀⣇⠼⢸⡐⠇⠃⠇⡇⠿⠈⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⡏⠀⢸⠠⢄⡀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⢠⠀⢑⠀⠀⣀⠀⢸⠀⠀⠈⡀⠀⠀⣄⠀⠀⠁⣴⠐⠢⡀
⠀⠀⠀⠀⠀⠀⢀⢡⡀⢧⠀⢿⠀⠸⡁⠈⢻⠇⠀⠀⠀⣿⠀⠀⠨⢅⠀⡇⣿⠀⢸⠉⢠⡏⠀⣼⠀⠀⢀⡷⠤⠀⣸⢰⣻⠀⠛⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠈⠟⣃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢹⡀⠰⠁⣿⠀⠁⢻⠀⢸⠀⠈⠧⠀⠃⠀⠀⠀⡗⠀⠀⠻⠀⠘⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⠎⠀⢳⢀⣨⣆⢠⡴⢹⠃⠀⠀⠀⠀⠀⠁⠠⠀⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢀⡀⢆⡀⡗⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡿⠄⠳⠂⠓⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠀⠈⡇⢇
⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠈