Yummy Food Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀
⠀⠀⠀⣀⣴⣬⡽⠿⠲⣷⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⠀⠀⡠⣄⠀⠀⣀⢀⢀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⢨⣏⠙⠒⠂⠉⢁⢹⡆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠢⡑⠄⠀⠀⠀⡠⢤⠤⡀⠀⠀⢨⠀⣯⠀⡎⠀⠹⡇⠀⢟⣏⡮⠁⠀⠀⢸⠁⢩
⠀⠀⠀⣾⠐⢒⣈⡉⠤⠄⣿⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⢀⠎⠀⠀⠱⣑⡀⠀⠈⠄⢸⠀⠘⠢⡔⠁⠀⢣⢠⠚⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢹⡁⠤⠤⠐⢒⡀⢸⡀⠀⠘⠢⠤⠤⢤⠤⡤⠤⠊⠀⢠⠃⠀⠱⠓⠀⠈⢷⡀⠀⠇⣨⡇⠀⠆⡇⠀⠀⡆⡈⠀⠀⠀⡠⠃⠀⠀⣷⡄
⠀⠀⠀⠀⡷⠖⠬⠵⢂⣒⠭⠇⠀⠀⠀⣇⣂⣈⣀⣁⣀⠀⠀⠧⢤⣦⣤⣤⣤⡤⠬⠇⠀⠀⢐⣠⠀⢁⡇⠀⠀⢇⠇⠀⠀⠀⠧⠤⠤⠤⠬⠬
⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⢸⠀⠠⡤⡂⠀⠈
⠀⠀⠀⠀⠀⣀⠤⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠉⡉⣿⣻⣉⢉⣉⢉⣏⣟⣉⡉⠉⠉⠀⠀⢸⠄⢈⣀⣀⡀⢤
⠀⠀⠀⡠⢊⡤⠊⠉⠉⠁⠢⡑⢄⠀⠀⠀⠀⣠⣖⠉⡄⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠉⢁⣴⠞⠛⢶⡌⠉⢳⡇⠀⠀⠀⠀⠈⣄⣀⠀⠀⣀⡄
⠀⠀⢰⢁⢋⠔⢲⡄⣀⢀⢀⠘⡘⡄⠀⠀⡐⠕⠁⣼⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⣵⣶⢠⣤⣯⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠘⣇⠀⢸⠅⣋⣿⣸⢀⢃⠃⢀⠤⠥⠤⠤⡤⠤⠶⠶⠶⠶⠶⠼⠤⡀⠀⠀⠀⠀⢻⡧⠤⣿⠃⠀⢸⡇⠀⡆⡶⡆⣖⢆⡶⡠⡆⢒⡞⡄
⠀⠀⠀⠣⣩⢲⠉⠀⠳⡄⡵⢋⠜⠀⠈⠋⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠂⠓⠒⠀⠁⠀⠈⠀⠒⠃⠇⠀⠥⠥⠥⠭⠭⠤⠥⠥⠭⠗⠃
⠀⠀⠀⠀⡄⡸⠭⠉⠘⠃⡆⠁⣠⡎⣙⢢⠀⠀⠀⢀⣀⣀⣀⠠⠤⢒⠒⡄⠀⠀⢠⠒⠒⠂⢐⣒⡦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠳⠁⠀⠀⠀⣄⠃⠀⢟⢲⠲⢽⠂⠀⠐⠁⡜⡐⢠⢰⠀⠓⢁⡿⠀⠀⢨⣠⡤⠤⣤⣤⡄⠀⠀⣠⣴⣡⣤⣤⣤⣤⣤⣤⣤⣼⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠈⠀⡌⠀⠀⢻⣄⣀⠃⠘⣀⡡⢴⡩⠎⠀⠀⠘⡇⢀⣰⣿⢷⡇⠀⠀⠇⠊⣠⠤⣄⡤⣤⡤⢠⣄⡌⢱⠈
⠀⠀⠀⣀⠤⠤⠤⠠⣄⠀⠀⠈⠙⠋⠙⠁⠀⠀⠈⠑⠣⠷⠾⠐⠋⠉⠀⠀⠀⠀⠀⣷⠻⠿⠀⣸⡃⠀⠀⡏⢇⢙⠖⢋⢋⡘⠧⠘⠘⢃⡼⢋
⠀⠀⠀⡗⠒⢀⡀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠋⠉⠙⠋⠀⠀⠀⠁⠂⠐⠀⠂⠀⠂⠀⠀⠒⠀⠒⠁
⠀⠀⢠⢸⠟⠂⢒⠘⡇⡀⠀⠀⡏⡇⠤⠤⠤⠤⠴⠥⠭⠽⠥⠵⠤⠤⠤⠤⢄⢈⢸⠀⠀⠠⠒⠊⣑⣒⣉⣓⠒⠤⢦⡠⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠈⢌⢆⡀⢀⠰⡱⠁⠀⠀⡇⡇⠉⠉⠉⠉⠉⠉⠛⠙⡏⠉⠉⠉⢉⠉⠁⡀⢸⠀⠀⡸⢊⠉⡇⢂⢠⢠⠈⡑⠤⣰⠗⡂⠀⠮⠄⠄⠽⡀
⠀⠀⠀⠀⠑⠲⡖⠈⠀⠀⠀⠀⡇⡤⠤⠤⠈⡆⠀⠀⠀⠀⡇⠀⠀⢸⢠⠀⠀⠄⢸⠀⠀⡣⣀⠀⡇⠸⠸⠸⠀⣃⡴⠳⡀⠅⠀⡟⢻⠙⠋⡅
⠀⠀⠀⠀⠀⣨⣇⡀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠀⠀⢸⠀⠀⠉⠢⠽⢓⡒⣒⡲⠩⠔⠁⠀⠈⠁⠀⣆⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠁⠀⡴⢌⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠊
⠀⠀⢠⢰⠰⣠⠤⠤⢤⡴⠖⠚⠛⠉⠀⠀⢀⠤⣒⠒⠀⡰⠖⠉⢳⠁⠀⠀⠀⠀⠀⠀⠀⢴⣶⡖⢲⠮⠅⠒⠀⠀⠀⠀⠀⠀⣀⢴⣂
⠀⠀⡬⠤⠤⠤⠥⠬⠭⠤⢤⠀⠀⠀⠀⡴⢁⠞⡝⠀⠀⡁⠀⣁⠎⢡⠀⠀⠀⠀⠀⠀⠀⠨⣿⠗⠃⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠒⢋⣉⢶
⠀⠀⢇⢆⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⡇⠘⡄⠙⢦⠀⠈⢉⠡⢂⠜⠀⠀⠀⠀⡠⣺⣟⣻⣻⣿⣛⢷⢦⠀⠀⠀⠀⠀⡼⠔⢚⣉⡡⠤⠚
⠀⠀⢠⡓⠕⠀⠀⠠⠤⢺⡄⠀⠀⠐⢄⣉⣀⣈⣉⣉⣀⣀⣁⣈⣉⡰⠂⠠⡆⠐⠓⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⡤⠀⠀⣇⣐⣁⠬⠤⠒⠋
⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠤⠤⠤⢤⣤⣤⣤⠤⠔⠒⠒⠚⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠊⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠑⠺⢧⣄
⠀⠀⠀⠀⠐⠀⢠⠞⡝⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢣⠹⡄
⠀⠀⠂⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⢷⠀⡇⠀⠀⢈⠎⠀⠀⠀⠀⢨⢀⠀⡁⡁⠀⣁⠀⠁⠀⠡⠀⠑⠀⢸⠀⠏⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⣠⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠃⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⣶⣿⢰⣷⢰⣷⢰⣶⣀⣾⡆⣶⣦⣠⣾⡆⢿⣶⣾⠆⢸⣼
⠀⠀⠀⠀⠀⠀⠀⡏⡇⠰⠿⠛⠁⠈⠻⠾⠟⠸⠟⠛⠻⠇⠻⠟⠛⠿⠇⠿⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠄⡀⢤⠀⠄⠀⠀⠠⠄⠀⡠⠄⠠⠄⠀⠤⠀⠄⠀⢤⠀⢸⠋⡆
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡀⠀⠁⠀⠀⠀⠀⠐⠰⠀⠆⠄⠀⠢⠰⠄⠀⡀⠠⠊⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢢⣱⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⡢⠤⠤⠤⠤⠤⢤⣤⣤⣬⣥⠤⠤⠤⠤⠤⠤⠤⠤⢔⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠴⠲⠒⠚⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡄⠀⠀⣀⠀⠀⣤⣀⡄⠀⠀⠀⢀⡂⠀⠀⢀⠐⠲⠂⠀⠀⠀⠀⠀⠀⣦⡦
⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣀⣛⢦⣀⣬⠶⣴⠚⠛⢯⡁⣈⠀⠀⠀⡀⠘⣆⠀⣉⣻⣿⣿⣿⣿⣿⡖
⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠉⠉⠉⠙⢿⣍⣢⣤⠬⠷⢶⡛⠉⠃⠀⠀⠀⠀⠀⠙⠀⣒⣶⠿⢿⠿⠛⠉⠁
⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠘⢿⣁⣈⣳⣤⡴⠛⠞⠀⡀⠀⠉⠀⠀⠀⠀⣭⡀⠀⠀⣀⡀⣀⠤
⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢈⠁⠈⠁⠀⠀⠀⠀⢀⣿⠉⠉⠀⠀⠀⠑⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣷⠀⢀⣿⢳⡟⢁⣰⣶⣧⣄⢀
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠈⠋⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡤⢿⠇⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⣸⠃⣿⣿⣿⣿⣿⡆⣷⡀
⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠹⣿⣧⡙⢿⣿⣿⡿⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢯⣻⣤⣤⠄⠀⠙⠛⠲⠟⠻⠇⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠤⠔⠀⣠⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠐⠂⠀⠂⠀⠀⣹⣷⣀⣠⣤⣶⡶⠶⠶⠶⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢴⣶⣿⣿⠿⠓⠀⠀⠀⠀⠈⠃⠀⠀⠀⠔⠚⢳⡶⣤⡄⠀⠀⠐⢦⠀⠀⠀⠀⠘⠁⠀⠚⠁⠀⠚⠁⠐⠂
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠇⠀⠀⠀⢸⠀⠀⢸⡷⣶⠿⡶⢾⡷⢶⡒⠿⠆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⣤⡶⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠘⠿⣟⣦⣴⣶⡶⣾⡇⠈⠒⠂⠘
⠀⠀⠀⠠⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⣶⠟⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⡀⠀⠀⠀⠆
⠀⢠⡄⣀⠐⠀⠀⠀⠖⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠃⡈⠀⡄⣆
⠀⠈⠙⠛⠇⡵⠚⠁⠀⠀⢀⣴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⢄⡄⠀⠀⠒⠀⠀⠀⠈⠀⠀⡴⠀⢀⠓⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠐⡘⠁⠀⢀⣶⡟⢁⠀⠀⠀⠀⠀⡆⠀⢸⢰⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⠿⢽⡷⢶⠀⠀⠀⠈⢢⡄⠈⠿⢧⠘⠁⠀⠀⠀⠀⠀⠀⢨⠘⢰⠁
⠀⠀⠀⠀⠖⡀⠠⡠⡄⡀⡠⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠐⢃⠔⠀⠱⡈⠅⠀⠀⠀⠀⠀⢀⠀⠤⣦⣄⠀⠀⠀⠀⠀⢠⡇⠀⡴⠶⠟⠿⠇⠐⠲⠀⠉⠀⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⢠⣼⣿⣾⣞⣦⣠⣶⣄⠀⠀⢀⠜⠁⠀⠧⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⣐⠶⣿⣯⣳⢦⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠖⠉⠐⠀⠀⠘⠀⠀⠀⠀⠈⣹⠀⢀⡷⢶⣤⠿⡀
⠀⠀⠀⢀⣀⠀⠙⠻⣦⠙⠋⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⠁⣰⠏⠀⠀⠉⠈⠉⠒⠁
⠀⢰⠃⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡴⣶⠟⠀⠀⠀⠀⠁⢰⠏⠀⠀⠀⢠
⠀⢸⠀⠀⣤⠃⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⢈⢠⠡⠀⡀
⠀⢸⠀⠀⠚⡅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠛⠁⠀⠀⠀⠀⠀⠀⠐⣶⡷⠀⠀⠀⠀⠂⠄⠸⣶⡀
⠀⠸⠀⠀⣷⠄⠀⠀⠀⠀⢀⢤⣄⣠⣀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⡀⡀⡀⠀⠐⠄⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠂⢠⣷⠦⠀⠠⢎⠉⠼⠿⠰⠶⠹⠿⠯⠾⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡧⠤⠠⠡⠱⠡⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠤⠶⠒⠊⠉⠉⠀⠀⠀⠀⠈⠉⠉⠐⠒⠦⢤⡀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠔⠋⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⠃⠐⠀⠀⠐⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠀⠀⠀⠀⢀⠀⡀⢀⡈⠀⠀⢀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡰⠊⢁⡈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⣤⣤⣴⠶⠦⠶⠶⠶⣶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⢁⠔⡚⠛⡳⣦⡓⠺⠃⠁⣿⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠛⠛⠛⠒⢦⣤⢤⣀⡤⠤⢤⣀⣠⠴⠋⢉⣩⠟⢿⣶⡄⠀⠀⡆⣠⠆⠃⡖⠛⠉⠄⠈⡇⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⡀⠀⠀⠀⠀⠀⠀⢳⣤⡄⠛⣦⢀⡤⠤⠖⠚⠉⠀⢀⣼⡿⠛⠀⠀⠀⡸⠃⠆⠳⡤⢶⡎⡰⣧⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣄⠙⠿⣦⣄⠀⣞⠛⠛⠛⠁⠉⠙⠷⠛⢧⡀⠀⢀⣠⣴⠟⠋⡠⠀⣀⣀⣀⠀⠀⠀⠚⢀⡤⠛⢼⡌⣷⠠
⠀⠀⠀⠀⢸⣿⣏⠀⠀⠑⠀⡈⠙⠻⢿⣦⣤⣀⣀⣀⣀⣠⣤⣴⠾⠟⠛⠉⣀⢴⠀⡰⠋⠐⡔⢈⢳⡄⠀⣀⡨⠓⣤⠺⢃⠏
⠀⠀⠀⠀⠀⡘⠿⣷⣄⠀⠀⡤⠶⠦⠄⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣴⣶⠟⢁⠌⠀⡃⢾⡇⠀⣿⠂⡷⠋⢁⡀⠀⢤⡀⠁
⠀⠀⠀⠀⠀⠈⠠⠈⠛⠷⣦⣷⣀⡀⠀⠀⠀⠀⠁⢀⣈⣷⣴⠾⠛⠋⡀⠔⠀⠀⠀⠰⢴⣤⡧⣬⡜⠁⢾⡁⠈⣿⢸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣹⠟⣧⢈⠙⠃⢩⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⠒⠂⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠐⢻⣽⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠉⠠⠘⡡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⢀⣠⣄⠶⠮⠉⠓⠀⡁⢨⠀⠀⠘⠀⣐⠀⠄⠢⠀⠀⠀⠀⡊⠄⠄⡀⠀⠐⠰⢱⠀⠀⢀⠉⢈⠂
⠀⠀⠀⡁⠀⣀⣀⠀⣤⠤⠌⠂⠀⠀⠠⢳⠘⠐⡁⢄⢴⢂⠀⢀⠀⠡⠐⢂⣀⡀⠐⠠⠙⠀⠀⢨⣦⠆
⠀⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⣠⡳⠑⠉⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣠⢒⠂⡉⢙⣢
⠀⠀⠀⠀⠘⠐⢲⠀⡠⢢⠄⠀⠀⠰⠍⠃⠋⠁⠀⠀⣆⣀⣀⣀⣐⡇⠀⠀⣔⡒⢄⠀⢧⠀⠀⠀⠀⠨
⠀⠀⠀⠀⡘⠀⡼⢋⡴⠋⠀⠀⢀⠄⠀⠠⡀⠀⠀⠀⣟⢋⣉⣒⠋⡃⠀⡔⠈⠀⠀⠀⠀⠗⠒⠒⠲⠁
⠀⠀⠀⢸⣧⢊⣔⣗⠀⠀⠀⠀⠂⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡢⠀⠀⠌⠀⠀⣀
⠀⠀⠀⠀⠈⠉⠐⠚⠀⢖⢳⡀⠴⠀⠀⠀⠂⠀⠀⣠⠁⠐⡀⠀⠀⣀⣬⠀⠀⠊⠀⡴⠻⡉⠉⠢
⠀⠀⢀⡄⢀⠀⡀⣀⣀⠀⠁⠀⠀⠀⠀⠀⡠⠐⠁⠀⣁⠈⠀⣑⡀⠈⠉⠁⠀⢀⠞⢑⠌⠀⠀⠀⠑⡀
⠀⠀⢺⠀⢱⠀⡁⠘⠻⠠⠀⢂⠈⠀⢄⠀⣅⣈⣀⣀⣭⣥⣤⣤⠁⠀⠀⠀⠀⣾⠪⠂⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠈⠲⠊⠀⠈⠐⠁⠄⠰⢁⣠⠃⡠⠀⠩⠭⠉⠉⠭⠉⠀⠐⠀⠀⢀⠦⡀⠀⠉⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠠⢀⢀⠄⠀⠀⠀⡄⠀⠂⠠⢀⠀⠀⠀⢀⡃⠉⠨⠄⠀⠀⠀⡄⠡⠐⡄
⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⢀⣀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⣢⠀⠸⠀⠐⠀⠲⠀⠀⣚⠀⠀⠁⣀⠆
⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⢈⠄⠀⡀⠀⠀⠀⠀⠀⠮⠁⠀⠈⣳⡴⡻⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠠⠔⠄⠐⠣⠀⠀⠀⠀⠄⠐⠈⠀⠀⠀⠡⠆⢄⢀⠀⡀⠂⠀⠀⠀⠘⣵⡞⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⢀⣤⡤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠋⠛⠉⢡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⢀⡀⠀⢠⣀⣀⠁⠀⢀⣀⣶⡄⡤⢲⡖⣶⣴⡀⠀⠀⠀⠀⠀⠠⠶
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⠙⢯⡀⣈⣲⣤⠶⠓⢾⡉⠉⠃⠀⢸⣿⣿⣯⠁⠙⣛⣛⣻⣿⣷⣶⣶⠂
⠘⢷⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠻⠛⠛⠛⠛⠿⣏⠣⣀⣈⡷⢤⡒⠛⠻⠀⠀⠘⠻⠿⣿⡇⠠⣒⣲⣿⣿⡟⠛⠉
⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢿⡍⠈⢑⣄⣠⠽⠶⠀⠀⠀⠀⠂⠐⠒⠀⢺⡍⠀⠘⠛⢁⠀⠀⡀
⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠀⢸⠛⠋⠉⠉⠁⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⣿⡄⠀⣸⡟⣼⠇⡀⠐⠂
⠀⠀⠀⠀⢸⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠘⠛⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠀⠀⠀⠀⠀⠀⣿⣧⠀⢿⡇⡟⢰⡇⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⢸⡿⠿⣿⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠀⠀⠀⢀⣿⡿⠀⠘⢿⣷⡈⢷⣄⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢸⡹⣇⣀⣀⠀⠙⠻⠶⠽⠿⢷⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠⠤⠀⢤⣴⣶⣿⣷⠀⠀⣀⣀⣤⣤⣤⣤⣴⣶⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠠⢒⠀⠀⠀⠀⠀⠀⢀⣞⠁
⠀⠖⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡜⠁⠀⠐⢤⡹⠀⠈⡀⠀⠀⠼⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⠀⠀⢠⡄⠀⡠⠀⠀⠀⠀⠀⠉⠡⠀⢁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡀⢤⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣭⡢⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠠⠀⠤⢠⠀⠀⠀⣀⡀⢠⣠⠄⠀⠀⠀⠀⠀⡀
⠈⢀⠰⢒⣶⠀⠀⠀⠀⢘⠓⢀⠿⡅⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⠻⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⣠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⢀⣀⣀⠀⡀⠀⠀⠀⢀⠁⠈⠀⠀⠀⣼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⢀⠁⡀
⠀⠢⠀⠀⠀⠀⠘⠁⠀⠰⡄⡀⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⠈⠀⠈⠐⠠

⠀⠀⢀⣀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆
⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉⠀⠀⠀⠂⠀⠀⢠⣄
⠀⠸⠀⢸⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢠⡾⠁⠉⠀⠀⣀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠴⠂⠀⠘⠁⠀⠀⠚⠉⢀⡀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣠⡀
⠀⠀⡌⠀⠀⣴⠄⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠘⠁⠀⡤⠀⠀⠀⠀⣨⠏⠀⢀⣆⠀⠚⠁⠀⠀⠀⢤
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠀⣀⠤⠐⢀⣀⠿⠒⠈⠀⠀⠀⠘⣇
⠀⠀⣇⠀⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠐⠛⠂⠀⠀⠶
⠀⠀⠙⠀⠀⢤⡄⠀⠀⠀⣠⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠈⠂⣀⣀⠀⠐⠶⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣠⡶⢛⣶⠀⣶⠿⠿⠶⢦⣾⠷⠋⠴⢀⣀⣞⡆⠀⠀⠀⠈⠛⠀⠤⠔⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢡⣿⠃⣠⠶⡀⣶⢲⣰⣿⣸⢧⡟⣿⢈⣜⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠙⣰⡿⢤⠿⣟⡾⠻⠟⣧⣈⡯⠭⣅⠻⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣠⠜⠉⠛⠫⣤⣬⣴⡶⠟⠋⠙⠲⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠀⠐⠛⠃⣀
⠀⠀⠀⠴⣀⠀⠤⠀⠀⠈⠙⠀⠀⣤⡄⠀⠀⠀⠀⠀⣠⠖⠒⣀⠀⠈⠉⠂⠀⠀⠀⠀⠀⢰⣧⠶⠒⠉⢉⠉⠂⠀⠀⠒
⠀⠀⢰⡄⠉⠁⠀⠀⣀⠘⠋⢀⡀⠀⠀⣀⠀⠀⡰⠀⡅⠀⠈⠉⢠⠀⠰⠖⠀⠦⠀⠀⠀⠘⢃⠰⡇⠤⠤⠤⠤⢖⠀⠀⠢
⠀⠀⣼⣿⣦⣈⣁⡈⢙⣀⠀⠋⠉⢀⣰⠁⠀⢈⡇⠀⠒⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠲⠀⠀⠀⠈⠚
⠀⠀⠻⣿⣉⣩⡉⠹⠟⠛⠋⠉⣽⣧⣥⡆⠀⠘⠂⠀⠀⠐⠀⠀⠀⠘⠁⠀⠐⠀⠀⠀⠀⢈⠁⠀⠛⠀⠀⠀⠀⠉
⠀⠀⠰⠟⠿⠗⠒⠶⠶⠶⣾⠛⠛⠉⠉⣠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠤⠀⠐⠀⢠⠠⠀⠀⢸⡔⠂⠀⠀⠀⠲⠆⠀⠀⣄
⠀⠀⠘⣿⠗⢲⡶⠶⢶⡾⢯⠴⠶⠞⠟⢃⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠀⠀⢀⠀⠀⠀⠈⢧⠀⠛⠀⢠⠀⠀⠀⠃
⠀⠀⣾⡟⣲⠶⣥⣤⣤⡤⠬⠴⠖⣒⠉⠍⡄⠀⠀⠀⠀⡁⠀⠀⠠⣤⡄⠀⠀⠘⠀⡤⠀⠀⠈⠲⠄⢀⠀⠀⠤⢀⠤
⠀⠀⠐⠳⠿⠧⠤⠛⣂⣀⣠⣤⣤⠭⠗⠊⠀⠀⠀⠀⢀⠈⢠⡄⠀⠀⠀⠠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣯⣭⣽⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⠉⠉⠴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢀⡀⢀⡀⠀⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⣤⣼⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠄⢀⠀⠀⠀⠀⠀⠀⡇⠀⠄⡀⠠
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⣿⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣀⠸⠀⠀⠀⠀⠀⠀⠇⡭⢶⠠
⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠀⢸⣿⣿⣿⣿⣿⣷⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⠟⠙⠉⠋⠻⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠂⠀⠁⠐⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠁⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣤⣄⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⠸⠃⠘⠃⢀⠠⠄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢠⣶⣶⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆⣈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣌⣻⣟⣁⣼⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣃⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠉⠀⠀⠠⠀⠀⠀⠀⠠⢶⣦⡀⣰⣮⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣯⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣴⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⠋⠏⠹⠟⠀⣿⡇⠀⠸⠏⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⣿⠉⡏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠻⡟⢿⡛⠛⠛⣻⣿⡛⠛⠛⠐⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⢸⣿⣆⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⣸⡇⣴⡆⡇⠀⠹⣆⠀⢻⣿⠁⣀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣀⣬⣭⣄⠀⠀⠀⢀⣠⣴⣿⣷⣾⣷⣧⣀⣀⣘⣿⣿⣿⣿⣷⣿⣀⣀⣀⣈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⡇⣾⠉⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠉⠀⣿⣿⡇⠀⠀⠀⠘⠿⣯⣇⣹⣿⡿⠿⠿⣇⣇⣿⣿⡿⠿⠿⠿⠿⠿⡿⢿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⠃⠀⠀⠛⠙⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡞⠉⢹⡄⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⢙⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣭⣤⣄⢠⣤⣤⡄⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⢸⣿⠀⡇⠀⠀⠀⠀⠀⠛⢻⣿⣀⢀⡂⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢦
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⡏⢓⣓⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣀⢔⣼⡾⠿⢛⠛⠟⠲⢦⣤⡄
⠀⠀⠀⠀⣴⠋⠁⠀⠈⠉⢧⠠⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢄⡀⠐⠋⠀⠀⠀⠀⠀⣱⣿⢾⣿⣝⣻⣿⡬⣤⡾⡿⣱⠁
⠀⠀⢀⠀⢻⣶⣤⣤⣴⣲⣿⡥⣾⣿⣷⣦⣄⡀⠀⠀⠀⢀⣠⣤⠶⣺⡋⠉⠻⣦⡙⢦⡀⠀⠀⠀⠀⠀⣏⠙⠺⠽⠿⢠⡿⠷⠟⠷⠓⡛
⠀⠀⣮⠀⣟⠏⠉⠻⠿⢗⠻⠿⠟⠋⢉⡿⢈⡇⠀⠀⢰⠙⣛⣫⣰⡷⠃⠘⣁⣨⣽⣾⣛⠆⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠈⠑⠤⣭⣶⣄⣣⣤⣬⣄⢀⠈⠁⠐⠁⠀⠀⠀⠀⠠⡇⠀⠉⠉⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⢀⣲
⠀⠀⠀⠀⢀⣠⡴⡖⠞⠉⡳⢶⣤⣤⣀⡐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⣀⡘⠛⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠒⠒⢒⢉⣤⣿⣶⡤⣅
⠀⠀⡐⢂⣼⣭⣳⡶⣬⣅⡲⠠⣺⣿⣷⡌⢢⡀⠀⠀⠀⢀⠀⠀⣐⣋⣡⣬⣗⣳⡿⡝⠳⡀⠀⠀⠀⢠⢾⣿⣡⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⡆⢹
⠀⠰⠀⢞⠿⠿⠷⠿⠝⣿⠯⠡⠷⠿⢛⠟⣸⠇⠀⠀⡐⡣⣶⠿⠛⠛⠉⢁⠔⢉⣀⠵⠐⠁⠀⠀⠀⠘⢌⠢⠛⢃⠙⠶⠿⠛⠛⢛⣋⡤⠔⣁⠜
⠀⠀⠓⠤⣀⠑⠀⠀⠀⠀⠀⢀⣀⣈⣡⠞⠁⠀⠀⠀⠘⠷⣧⡀⠄⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠂⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⢀⣠⠀⠄⠄⢐⡒⢒⠖⠐⠒⣖⢦
⠀⠀⢀⠤⠄⣶⡶⢦⣶⢶⢿⢶⣿⣿⡏⢷⡀⠀⠀⠀⠀⢀⠤⠒⡒⠲⣶⢺⡞⢩⠻⡀⠈⢱⠀⠀⠀⠀⠀⡰⢻⣿⣷⠛⠻⠭⠝⣠⡼⠦⣤⣘⣎⣦⡀
⠀⠰⢣⣯⣽⣭⣙⣩⠏⠹⣬⡗⠺⣿⣷⣾⡿⣆⠀⠀⢀⠁⠦⣰⡄⢳⠈⣃⣸⣁⣿⣿⡿⣿⣷⠀⠀⠀⠀⠇⢸⣿⣿⣿⣖⠶⠛⠬⣛⣓⡖⠁⢸⢸⡇
⠀⠰⣌⠻⢤⣙⢯⣉⡙⠿⠶⠾⠿⠁⠀⡰⢣⡟⠀⠀⢸⣧⠆⣀⢉⡧⠀⢾⠛⠙⢋⡧⠊⠀⣼⠀⠀⠀⠀⠘⢄⠋⠀⠒⠸⡀⠀⠀⠨⠇⣀⡴⢋⡜
⠀⠀⠈⠑⠦⢍⡙⠋⠉⠀⠀⠂⢀⣀⣡⠴⠋⠀⠀⠀⠀⠙⠢⢝⡻⠖⠀⠀⠈⠉⠀⢀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠀⠤⠤⠭⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡆⣜
⠀⠀⠀⡔⠒⠻⣍⢻⡍⣹⠦⣠⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣠⣤⣄⣀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⢿⣽⣿⣿⣷⡤⣄
⠀⣴⣾⡷⣤⡤⠛⠉⠛⡝⠳⢮⣛⡿⢻⣦⡀⠀⠀⠀⢀⣤⣴⡎⢉⣉⠙⣿⣿⣦⣾⠛⢱⠿⣝⢢⡀⠀⠀⠀⢠⡞⢫⠶⣶⡿⠀⠀⠀⠀⣸⣜⣾⡱⡄
⠘⣇⠣⡀⠀⣷⡙⠀⢠⠳⠐⢍⡹⠳⡄⣱⣹⠆⠀⠀⣾⢿⠁⠑⣏⠂⠑⠀⣀⣿⣷⠚⣁⣳⣨⢋⡇⠀⠀⠀⡌⠀⡟⡦⠖⠊⠓⣤⣤⣤⣿⠉⢈⠇⡏
⠀⠈⠳⢤⣄⡘⠻⠶⠶⠶⣶⡐⠒⠒⣛⡽⠋⠀⠀⠀⠘⢎⠀⠠⠌⠉⠁⠈⠀⠉⠥⠤⠒⢚⡵⠟⠁⠀⠀⠀⠘⢄⠐⢌⠂⠄⠾⠁⠧⠒⠉⡠⢊⡼⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠲⠒⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠬⠀⣠⣤⠀⠤⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢿⠈⣧⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⢞⣵⣺⢦⠀⠀⠀⠀⠀⠁
⠀⠠⠶⠶⠆⢱⢰⢄⡆⠀⢁⣒⣂⣂⡤⠀⠀⠀⢸⡄⠸⠂⠈⡦⠀⠈⠈⣁⡀⠀⠀⠀⠀⡴⣩⢟⣾⡽⠃⠀⠀⠀⠀⠀⣰⡞⢹⡆
⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⢧⣄⣥⠔⠃⠀⠀⠉⠁⢀⣨⠀⠀⠀⠈⠉⠺⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣄⠓⢀⡄⠀⠐⠳⢿⣾⠟⠃⠀⠀⠰⢀⡁⠂⢀⡄⠀⠀⠀⣾⣶⣶⡿⠆
⠀⠀⠀⠈⢀⡀⠀⠀⠀⢀⢰⡁⣼⠂⠁⠀⠀⠀⠙⠇⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⣰⡾⠁⡤⠀⠙⠀⠀⠀⠀⠨⠙⠂
⠀⠀⠀⣀⡘⠁⠀⠀⠀⠘⠀⠀⠤⠖⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠡⠤⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠸⠉⠃⠀⠀⠀⢀⣈⠁⠚⡆⢀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⡐⠀⠀⠙⣷⡀
⠀⠀⠀⠀⢠⣆⣠⡀⠀⢰⡁⠂⠀⠀⠀⠸⠀⠀⠉⠂⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠨⠽⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠉
⠀⠀⠀⠀⠰⢷⡽⠂⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋⠁⠀⠀⠀⠀⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠰⠆⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠙⣡⠀⠀⢀⠀⠆⠀⣢⠴⠁⢀⠀⠀⠠⠀⠰⠀⠀⠠⠶⣶⣶⠶⠢⣤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⢠⡄⠀⠠⣀⡝⠀⠐⠶⠀⠶⠋⠁⠀⠀⠰⠠⠆⠀⣤⠄⠀⠀⠀⠃⢄⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠀⡀⠛⠀⠀⢀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠉⠻⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢀⣾⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠤⠊⠀⠀⠀⠀⠀⠚⡄⠈⠒⠀⠀⠀⠀⠀⢠⡄⣤⡈⡷
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠓⠃
⠀⠀⠀⠐⠗⠀⢀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⣄⠀⠀⠀⢀⠀⡀⠀⠠⣿⡟⣭⡛⣷⠀⠀⠀⠀⡴⢤⠀⠀⠀⠀⠛⠃⠀⠀⠛⢃⠀⠀⣬⠃⣠⣥⣀⡤⣀⠀⣠⣾⠿⢶⠃⠉⠁
⠀⠈⠻⠿⠾⠿⠟⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠰⣤⣀⣀⡤⠂⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⡁⠘⣹⠃⣸⣇⡼⠃⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢺⡆
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣶⠆⠀⠀⠀⠘⢻⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢐⣠⣖⡀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⢠⠐⡂⠈⢤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠹⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⠀⠀⠀⠦⠀⣠⡖⠀⠀⠠⠤⠤⠈⠛⠀⠀⠀⢠⣘⣿⣦⡈⠂⠀⠀⠀⠀⣄⠀⢳⡄⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⣤⠤⡤⠤⠆
⠀⠀⠀⠄⠙⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠏⣹⠙⣽⠆⠀⠀⠀⠂⠛⢰⠊⠀⠀⠀⠸⠛⣀⡀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠢⣤⣤⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⣶⠄⠀⠀⣀⡀
⠀⠀⢉⣡⣤⡄⠀⠀⠀⢠⠀⠀⠘⠆⠀⠀⢀⣤⠶⠟⠋⠉⠀⠀⠀⠂⠀⢰⣌⡉⠀⠀⠀⠀⠉⢉⡁⣀⢃⠀⠀⠀⠀⠄⠀⠩⠃⠼⠂
⠀⠀⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠟⠀⠀⠀⣱⣷⠶⠶⠷⠊⠀⠀⠀⠀⢠⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⡙⢻⡏⢉⡟⢛⣏⠋⣹⡿⣻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣴
⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠘⠛⠂⣠⣾⣷⡦⠀⠀⠀⠀⣛⠅⠀⠀⠀⠘⣛⠃
⡏⣾⣿⡇⠀⢠⢤⣤⣤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⢿⣷⡄⠀⢸⣿⣿⡟⠀⠀⠀⢠⢖⣿⣷⡄⠀⢠⢞⣿⣷⡄
⡇⣿⣿⡇⠀⢸⢸⣿⣿⠀⠸⡅⣿⣿⣿⠀⠀⠀⠀⠈⠛⢿⣆⠾⠋⠉⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠈⢆
⡇⣿⣿⡇⠀⠈⢳⡟⠁⠀⠀⠙⢾⡟⠋⠀⠀⠀⠀⠀⠀⣠⡹⣷⡀⠀⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠀⢸⣿⡶⠦
⣇⣿⣿⡇⠀⠀⣨⣇⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⠟⠀⠘⢿⡆⠀⠀⠀⠀⢸⣼⣿⣿⡇⠀⠸⣼⣿⣿⡇⠀⢸⠹⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⣖⣒⣒⣒⣒⣒⠀⠀⠀⣶⣒⣒⣒⣒⣒⠀⠀⠀⠀⠘⢶⠀⠀⠀⠰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣘⣃⡀
⣿⣿⠿⠿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⠶⠶⠶⢾⡅⠀⠀⠀⠀⠀⠀⠀⢰⠀⣆⠀⠀⠀⢰⣿⣿⡄⢸⢸⣿⡇
⣿⣿⡇⠀⣸⣿⠀⠀⠀⣿⣟⢀⡏⢸⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠼⠀⠟⠀⠀⠀⠘⢿⡟⠁⢸⢸⣿⡇
⣿⣿⣮⢰⣿⣿⠀⠀⠀⣿⣿⢸⣿⢸⣿⠀⠀⢀⣠⠤⠜⢮⣉⣩⠞⠡⢤⣄⠀⢸⡛⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⢸⢸⣿⡇
⣿⣿⣯⣬⣿⣿⠀⠀⠀⣿⣿⣼⣿⣼⣿⠀⠀⡞⠀⠀⠀⠀⣴⠀⠀⠀⠀⠈⡇⠀⠳⡘⢿⣿⣿⣿⣿⡿⠃⠀⢸⡇⠀⠈⢩⡍⠁
⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠓⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠃⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠘⠃⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡤⠦⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⣻⠈⡇⠀⠀⠀⢀⣤⣞⠉⠳⣯⡀
⢠⣟⣭⣤⣭⣛⣷⣶⣤⡀⠀⠐⢿⣾⢛⣂⣉⣂⣀⣋⣀⣚⢻⣾⠃⠀⠀⠀⣠⢴⣾⣿⣷⣤⡁⠈⠀⠀⠀⠀⣋⣀⣀⣀⣀⣀⣘
⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡆⠀⠈⠁⠈⢧⣻⣿⣿⣿⡿⠃⠈⠁⠀⠀⢀⡞⢱⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⣜⣿⣿⣿⣿⠟
⣏⠙⠛⠛⢋⣡⠴⠶⠦⠤⠇⠀⠀⠀⠀⠀⠈⠙⡏⠁⠀⠀⠀⠀⠀⠀⠸⠁⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠉⣿⠉
⠈⠙⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠒⠛⠒
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄
⡤⢤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣴⣦⡆⣼⣿⡇⢀⡴⠋⢉⣀⣀⠉⠳⣆⠀⢠⣿⠀⣼⡆⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⡿⢈⡇
⣷⣶⠒⢺⠃⠀⠀⠀⠀⢠⣿⡇⢿⣿⡇⠙⣿⠃⡞⠀⣴⠋⠁⠉⠳⡄⠈⣇⠸⣿⠀⣿⠇⣾⡇⠀⠀⣾⣿⠄⠀⡶⣶⣶⣶⣶⣆
⢺⣀⠴⢾⠀⠀⠀⠀⠀⠀⣿⠀⠈⣯⠀⠀⣿⠀⣇⠀⢷⠀⠀⠀⢀⡇⠀⡿⠀⣿⠀⢻⡄⢻⡇⠀⠀⢸⡏⠀⠀⢧⢻⣿⣿⣿⣃
⢸⡟⠐⣾⠐⣶⣄⣀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠙⣆⡈⠙⠒⠒⠋⢀⡼⠁⠀⣿⠀⢸⡇⢸⡇⠀⠀⢸⡇⠀⠀⠘⠞⠿⠿⠟⠁

⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⢀⠀⠀⠀⡠⠀⠀⠀⡀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⣀⡢⠀⢂⠀⢀⠀⢂⠀⠀⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠄⢠⣂⡉⠦⠂
⠀⠀⢠⡀⠀⠀⠀⠑⠀⠀⠢⢀⠀⠀⠁⠀⢐⣓⡅⠀⠀⡐⡀⠀⠂⠀⠀⠀⠀⡀⠁⠀⠉⠂
⠀⢆⠀⢀⠀⠀⡠⠐⢂⠂⠂⠠⡀⠀⢰⠍⠘⣵⠂⠀⢠⠊⠀⠐⠀⠰⠐⡠⠊⠀⠈⠁⠒⠂⠀⠀⠈⠡
⠀⢀⢄⠈⠀⢈⠀⢀⠤⢀⡦⠦⠏⢀⠤⢄⡀⠻⠀⠀⠈⠂⠠⠛⠑⠀⠀⠀⠀⢀⡀⠁⠁⠀⠂⠁⠂
⠀⢸⠀⠣⠀⠉⠀⠡⠬⠅⠒⠊⠀⡘⠀⠀⡌⠀⢀⠀⠀⠦⠄⠀⣠⣤⢶⣞⣤⠀⢀⠀⠀⠀⠀⡄⠒⠆
⠀⠸⡐⢀⡇⠀⠀⠖⠂⠀⠀⢠⠆⠑⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⡈⠹⠉⠉⠉⡁⠀⢀⠘⠀⠈⠁⠈
⠀⠀⠈⠁⠐⠢⠀⠄⠀⠀⠀⡀⢀⡠⣶⠴⠀⠀⡀⠀⠀⠰⠳⠀⠀⠀⠀⠉⠀⠀⠠⠀⠄⢀⠄⠙⣈⣠
⠀⠓⠀⠀⠀⠀⠀⠀⡄⠀⠄⠐⠂⠉⠠⢊⠐⠃⢃⡲⠖⠀⠀⠀⠀⠤⠀⢀⡀⢈⡀⢀⠀⡀⠀⡀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠴⠔⠒⠂⢉⠴⠀⠀⠀⡀⠀⠀⠂⠅⠀⠀⠐⠈⠠⠈⠀⠃
⠀⢂⠀⠀⠐⡀⠀⠀⢴⡄⠀⠀⣠⠤⠤⠸⢇⣀⠐⠋⡀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⡠⢐⠂⠚⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠁⡀⠁⠀⠀⠀⠂⠠⠈⠁⠀⠀⠀⠂⠐⠉⢀⠀⠀⠀⠈
⠀⠀⠠⢀⠀⠀⡔⡄⠀⢀⠀⠄⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢄⠀⠲⠆⠈⠁
⠀⠀⢀⣀⠀⠀⢡⠁⡀⠠⠁⡆⠀⠂⠀⠀⢀⠀⢰⠂⡀⠀⠀⠀⠀⢀⠰⠂⠀⠐⢣⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠖⠀⠀⠀⡀⠐⠀⠾⠀⠀⠀⠈⠀⠠⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⢀⠜⡄⠀⠈⠿⠂⠁
⠀⠀⠂⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠄⠀⠀⠄⠒⠒⠪⠐⠂⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡐⡀⠈⠁⠠⠒⡀⠃⠀⡙⠀⠀⠀⠀⠀⢀⠀⠀⠠⡰⠠⢀⠆⠄⠂⠀⣀⠀⠀⢀
⠀⠐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠃⠀⠂⠠⠀⠀⠉⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⡉⠀⠀⠀⢩⠃
⠀⢰⢙⠡⠃⠀⠚⠀⠂⠀⠀⡐⠀⠀⡡⠐⠘⠂⠀⢀⡀⠍⠀⠀⠀⠀⠀⡙⠙⠁⠀⠀⠀⠐⠀⠀⠐⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⢛⡯⠉⢉⣉⠉⢩⡍⠉⠛⠲⢦⣄⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠒⠂⣀⣠⣤⠤⠤⣤⡀⠀⠀⠀⠀⠒⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⠃⠀⡴⠛⣉⡤⠴⠶⠶⣶⠟⠘⠂⠀⢠⠄⠀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⣴⠃⠐⠃⠤⠀⠀⠀⠙⠻⠷⠶⠖⠚⠋⠁⢠⠀⠀⠀⠀⠀⡞⠉⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⢶⠀⠀⠀⠀⠴⠆⠀⠀⠀⢀⣠⣀⣀⣀⣼⡃⠀⠀⢸⡇⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠒⣦⠀⢀⡀⠀⢀⣠⣤⣄⡀⠀⠀⣰⠋⠐⠁⠒⠒⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠳⣬⣠⣴⠋⠀⠀⠒⠭⠿⠯⠕⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣁⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡿⣠⡶⠛⣦⢰⡾⠛⢷⡰⡇⠀⢸⡆⢺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠶⠛⠁⢿⣄⣀⡼⠻⡇⠀⢸⡇⢿⣀⣾⣇⠘⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡎⠀⠐⠁⠀⡠⢀
⠀⠀⠄⠀⠀⠐⠀⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠠⠄⢀⡀⠀⢀⡇⢸
⠀⠀⠀⠐⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠂⠀⢂⠠⠄⣁⢀⣈⣉⣀⠉
⠀⠘⠀⠠⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠐⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠞⠀⡉⠒⠢⠻⠤⠤⠀⠔⠉
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠌⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⢄⢴⡆⠀⠀⠀⠀⠠⠀⣀⠈⠙⡀
⡀⠀⠀⠈⠂⠄⣀⡈⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⡉⠻⠀⢀⡤⠂⠀⣎⠂
⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠴⠰⠈⠤⣀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠠⠘⡦⠴⡤⠤⠖⠁⡀⠔
⠀⠀⠈⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠢⡀⠀⠁⠀⠀⠈⠲⠄⠀⠀⠈
⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⣀⠀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢄⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⢀⡠⠲⠀⣶⠤⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡈⠀⠀⠀⠐
⠀⠀⠎⣠⠊⠙⡟⢲⢳⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠲⠤⢀
⠀⠀⣥⠨⡓⡿⣞⠄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠎⠀⠠⣄⢡⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠈⠳⠍⡵⠙⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣⡀⠀⠀⢨⠀⠀⠀⣹⠷⠈⠉⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠘⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⢦⠀⠀⠀⠀⠀⠀⠑⠂⠤⠄⠒⠁⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⡴⠃⠀⠀⠀⠀⠀⠤⠒⠀⠉⠉⠀⠀⠀⠀⢀⠀⠈⠀⠐⠀⢠⠘⠂⠀⣀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⢈⠉⠁⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠂⢰⡀⠲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠐⡀⠀⠀⠀⠀⠘⠈⠀⠈⢰⠃⠈⠁⣈⣀⠀⠀⡀⠒
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠠⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⣶⣿⣿⠆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⠠⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢈⠁⠒⠔⠃⠀⠈⠿⠛⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠐⠒⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠘⠑⠂⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢛⣻⣏⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠟⠛⠛⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡀⠀⠀⠀⣴⠾⠛⢁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⡀⠀⠀⠀⣴⡾⠿⣿⣷⣄⠀⠀⠀⠈⣿⣿⣿⠿⠛⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢲⡿⠀⠀⠀⠘⠏⠀⠘⠛⠛⠁⠀⠀⠀⠀⠿⡿⠋⣴⡻⠆⢹⡿⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⢀⠮⠟⠁⣠⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⣠⣶⣶⣿⣿⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢈⠁⢀⡉⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠰⣟⠛⠛⠛⠳⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠀⣀⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⠀⠈⠉⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢐⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢍⣉⡭⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡑⠀⠀⠀⠀⠘⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⢻⣤⢦⣄⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡻⠁⠘⠁⠀⠀⠀⠀⠀⠈⢿⡁
⠀⠀⠀⠀⠈⡾⢿⣿⣊⣿⣞⣾⣇⠀⠀⠀⠀⠠⣤⣀⣀⣤⣤⣶⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠉⠀⠹⠟⠋⠙⠋⣁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⢒⣟⢡⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⣠⣞⠋⠁⣩⢏⠛⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀
⠀⠀⠀⠀⢠⠞⠋⠈⢻⣾⣓⡾⢀⡟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠁⠀⠀⣠⣾⡿⣍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⡀⠚⠏⢥⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡾⠟⠃
⠀⠀⠀⠁⠀⠙⠀⡤⠟⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠿⣿⣿⣿⣿⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⡀⠖⠁⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠹⡆

⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡲⠀⠙⠉⠛⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠘⣂⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠓⢂⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⡄⠀⡷⢶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⠀⢐⡖⠀⠋⢉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠁⣈⠐⠀⢀⣠
⠀⠀⠀⠀⠀⠛⠋⠁⠖⢠⡻⡄⠹⠁⠀⣠⣤⣤⣬⣠⣬⢇⣾⡤⣏⣀⣤⣀⢠⣆⠁⠀⠀⡼⠃⡤⠴⠛⢉
⠀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠐⠳⠠⠀⡀⣈⢳⣿⡾⢫⡇⠉⣻⣿⡀⠘⠀⢇⣸⣿⣿⡿⢰⣣⣄⠄
⠀⠀⠀⠒⠉⠁⠉⠡⠦⠀⢠⡀⠀⣾⠑⠟⢈⣣⡆⣼⡟⠛⠻⣤⡠⠾⠟⠃⠙⡟⠒⢴⢿⣏⣥⣖⣴⢂⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⣴⣯⣰⢷⡴⡄⠀⠈⢢⣼⠾⠿⣷⣼⠦⣤⣴⣾⣶⣶⣾⣿⠛⠛⣿⣿⣋⣀⣤⢀⡖⠁
⠀⠀⠀⠀⣀⡀⢈⠀⠀⠠⢀⢀⠁⢼⣿⣿⣿⠽⣦⡰⣮⣄⢀⣄⠩⣿⠐⢋⣴⣿⣿⡿⢿⡿⣿⢿⣿⣷⣿⣿⠷⠲⠄
⠀⠀⣴⣾⣿⣿⠂⠀⣤⡀⠀⣈⣳⣂⣸⣿⡇⠀⣙⠀⠀⠰⣿⣿⣿⣃⡴⠿⠛⠉⣿⣧⣿⠁⢻⣦⢿⣿⣿⣶⣶⣙⣆⠂
⠀⠈⣟⣤⣌⠉⣶⡀⠋⢙⡿⠉⠉⢩⣿⣿⣇⠀⢩⠀⠐⠘⢌⠉⠷⢛⣷⣦⣴⣾⠃⠀⠀⠲⣾⠏⣉⣉⣨⢉⠛⡁⢫
⠀⠀⠙⠛⠁⠀⢲⡄⣴⣾⣿⠆⠀⠀⢁⡀⠈⠳⣦⠀⠀⠀⠈⢰⡶⠋⣹⣥⣿⣿⣄⠀⠀⣽⢧⣼⣏⣩⣿⠇⠈⣁⣠⡄
⠀⠀⠀⠄⠀⡀⢼⠗⠰⢾⣁⠊⠀⠀⠀⣋⡙⠆⢠⡀⠠⢤⡈⠁⠀⣠⠋⠉⠀⠉⢻⠿⢿⣿⣤⠍⠙⠉⠉⢈⣠⣛⠛⠀⡀
⠀⠀⠈⠀⠘⣋⣴⣷⠀⣾⡟⣿⢥⣠⠎⣹⣿⠐⢀⢳⣤⣴⡏⢡⠋⠈⠖⢒⣿⣿⠛⠲⠊⣹⣿⣿⣶⣗⣲⣿⣟⣛⡉
⠀⠀⠀⠀⠀⠁⠘⢋⢰⣿⡣⠙⢛⠃⠾⡿⠃⣴⢿⠟⠛⢿⣧⡀⠠⠞⠃⠈⠉⠈⠁⠛⠉⠺⣽⣿⣯⣼⣿⣿⣿⣿⡅⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠋⣨⡛⠳⢊⡡⠾⢿⡯⣤⡄⠀⠋⠀⠀⠀⠀⣀⢠⣤⣀⣀⣤⣤⣤⣙⣿⣿⣿⣿⠋⡿⠑
⠀⠀⠀⠀⠀⠀⠀⣘⣤⣜⠀⠀⣽⢻⡏⣰⣧⣮⢀⣀⣤⡆⠀⣀⣤⣶⣯⠉⠀⢀⡁⠈⠘⣿⣿⢏⣽⣿⠿⠿⣦⣄⠀⢨
⠀⠀⠀⠀⠀⢀⣸⠿⣿⣧⠀⣰⣿⡓⠻⡿⠋⠀⠀⠈⢉⣵⣶⢿⡯⠙⡟⠓⣶⣿⣿⣦⣤⣿⣷⣾⣷⡦⠂⠈⡟⠿⠷⠾⢅⠠
⠀⠀⠀⠀⠒⣻⠟⡦⠸⢷⣠⠛⣿⡨⠂⠀⠀⠀⢀⡴⠟⣿⡟⠸⣧⣼⣿⣦⣹⣿⣿⣿⣿⣿⣿⠏⠙⣿⢾⣿⣷⣖⢃⣠⡀⡼
⠀⠀⠀⠀⠀⡰⣦⡀⠤⠀⣩⠆⠉⠀⠀⠀⣠⣾⣿⡠⠾⠛⢿⣿⡿⠛⠙⣛⣿⣿⡟⠉⠁⠀⣽⡄⣤⡿⢀⣿⣿⣿⡛⣿⣆⢰
⠀⠀⠀⢀⣴⢂⣅⣰⠤⠛⠁⠀⠀⢀⣤⣾⢿⠯⣭⣄⡈⣈⡀⠓⡇⠀⠉⢉⣿⠡⡤⣴⠆⢼⠋⠀⢨⡷⢿⡃⣼⣿⣿⣤⣿⢈⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠶⢶⡤⠰⢾⠟⠉⣅⡀⠘⠷⠦⣀⠉⢭⣙⣹⠿⠿⢿⣿⣾⣀⣤⣀⣼⡗⠚⢻⣅⡼⢿⣿⣿⣿⣿⣿⣬
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠲⠀⡀⠀⠀⢾⡏⠟⠀⠀⠀⣸⣷⣿⠋⠀⣠⠀⠀⠀⠀⢹⣧⡀⣠⣀⣠⣼⠏⠀⣠⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠶⠒⠓⠈⠵⠆⠈⠆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⢰⣿⡇⠀⠀⠀⢀⣾⣿⢻⣇⣀⣀⡀⠀⢸⠏⢻⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⡀⠀⠀⠀⣀⠀⢀⣾⣿⣷⣧⣀⣻⡆⠰⢢⣤⣴⣿⣿⣏⡁⣾⣿⣷⣶⠿⠲⣿⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⣿⣿⣥⣾⣿⡿⠿⠿⠋⢿⠉⠑⠲⠶⠿⣻⢋⣽⣿⣿⡟⡙⠦⣹⣷⠎⠉⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡉⠂⡄⣤⣀⣈⡀⣠⣵⢾⠾⠃⠀⠛⠛⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠋⠐⠻⠚⠫⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣶⣶⣤⣀⣤⣶⣶⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⠟⢛⣛⣛⣛⠛⠻⠿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⣋⣥⣶⣶⣿⣿⣿⣿⣿⣭⣍⣛⠛⠶⣦⣍⡛⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠿⣫⣴⡿⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣦⣍⣙⢷⣤⡙⢿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣡⣾⣿⣿⣿⣿⠿⠛⠉⠁⢀⠀⠀⡀⠀⢀⠀⠈⠙⠻⢿⣿⣿⣾⣿⣦⡙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢏⣼⣿⣿⣿⡿⠛⠁⠀⢠⣆⠀⣿⠇⠰⠻⠀⠞⣾⢀⡤⠄⠀⠈⠻⣿⣿⡿⠿⢆⣙⣉⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢃⣾⣿⣿⣿⠟⠀⠀⢤⣳⠈⠋⠁⠀⠀⢀⡠⠔⡀⠀⠈⠓⠃⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣧⢹⡇⣴⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⣾⣿⣿⣿⠏⠀⣘⣷⠄⠁⠀⣀⠀⠀⠚⠓⣈⣉⣤⣤⣶⣶⢿⣿⠛⣿⢁⣿⢸⣿⣿⣿⣟⢿⣇⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣾⣿⡿⢸⣿⣿⣿⡏⠀⠀⠈⠃⠀⣀⣀⣤⣴⣶⡾⣿⣿⠿⣿⣿⠉⣿⡆⠹⡇⢻⠸⣿⡼⣿⣿⣿⡏⢻⣿⠘⣷⢹⣿⣄
⠀⠀⠀⠀⠀⠀⢹⣿⡇⠿⠿⠛⣛⣠⣤⣴⣶⢿⡿⢿⡟⣿⡏⣋⢸⡇⢹⡇⣸⣿⡄⣿⠇⢦⠻⢸⣆⢻⡇⢹⣿⣿⣿⣻⣿⡇⠋⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⠀⣥⣶⣶⣿⣿⣿⠛⣿⡇⢹⡀⣿⢸⡇⠸⢰⣿⡶⣷⢘⣦⠉⣤⣅⢻⣶⡘⣷⣬⣿⣷⣷⣼⠿⠟⣛⡉⢩⣴⣦⠻⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⢻⣿⡆⢹⡇⢸⡇⣿⡀⣇⢸⣇⢹⣄⣹⣌⣛⣴⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⢰⣾⣿⣿⡇⣸⣿⡿⠃
⠀⠀⣤⣶⣶⣿⡆⢿⣿⣿⣿⣿⣿⡇⣎⢻⡸⣇⣹⣧⣹⣾⣿⣷⣿⡿⠿⠟⠛⠉⠉⠀⠀⠀⡀⡀⠀⠀⠀⣿⣿⣿⣿⠃⣿⣿
⠀⠀⠈⠻⣿⣿⣷⠠⣿⣿⣿⣿⣿⡧⢹⣾⣿⣿⠿⠿⠛⠛⠉⢁⣀⠠⣤⠤⠀⠀⠉⠀⠀⡀⠳⠏⠀⠀⣼⣿⣿⣿⡏⣸⣿⣿⡆
⠀⠀⠀⠀⠈⣿⣿⣧⠹⣿⣿⠿⠟⠛⣉⡉⠁⠀⠀⢠⣶⣠⠀⠀⠒⠊⠁⠀⠀⠀⣤⡀⠻⠟⠂⠀⢀⣼⣿⣿⣿⡟⣰⣿⡟⠉
⠀⠀⠀⠀⢰⣿⣿⣿⢠⣴⣶⣆⢻⣿⣿⣿⣷⣄⡀⠀⠉⠃⠸⣥⠇⢰⣆⠘⣿⠄⠘⠉⠀⠀⢀⣴⣿⣿⣿⣿⠏⣴⣿⣿⡄
⠀⠀⠀⠀⠾⠿⠛⠛⠈⠛⠻⢿⣷⡙⢿⣿⣿⣟⡿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠟⣡⣾⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢶⣝⠻⣿⣿⣿⣿⣿⣿⣯⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⢟⣡⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⢭⡛⠲⣭⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣥⣶⣿⡿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢭⣉⡓⠶⠦⣬⣭⣭⠭⠤⢴⣶⣚⣭⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠛⢿⣿⡿⠛⠛⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢹⣆⣀⣀⣀⢀⣀⣀⠀⠀⡴⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⠞⠳⣤⡤⠜⠉⠀⠀⠀⠀⠀⠀⠙⠢⣷⣀⠤⠾⣴⠶⡟⠛⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡠⠊⠉⠛⢄⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡇⠀⠿⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠙⢦⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣤⠆⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀⢀⡴⠢⠤⠖⠱⢆⡤⠖⠲⠶⣄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢈⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⢦⠀⠀⢸⠀⠀⠀⠀⠀⠀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣄⠀⡀⠀⠀⠈⡇⠀⠀⠀⣯⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠹⣄⠀⢸⠀⠀⠀⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣄⣀⡄⢳⣠⠖⠛⠁⠀⠀⠚⠉⠉⠃⠀⠀⠀⠀⠰⠋⠁⠙⠂⠀⠉⢙⣿⠀⢀⣠⣤⠊⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠻⢬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠖⠉⠀⠀⠀⢀⣾⠀⣾⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⡟⣁⣀⣀⣀⣀⠀⠀⡼⢸⡞⢸⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢳⠀⠀⢸⡗⠒⠋⠉⠙⠛⣧⠀⠀⠀⠀⠈⠳⣄⣀⣀⣸⠞⠁⠀⠀⠀⡸⢿⡅⠈⠉⠉⡏⠀⠠⡇⠈⠀⠘⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⡼⠀⠀⠀⢧⠀⠀⠀⢠⠞⠁⠳⢤⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠞⠁⠀⣧⡄⠀⢸⠃⠀⠀⠷⡄⣀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡘⣆⠀⠀⠀⠈⢧⡀⠀⣿⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⣀⡤⠖⠋⠀⠀⠀⢠⠏⠙⣶⠃⠀⠀⠀⢰⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠼⠒⢆⠀⠀⠀⠉⢻⠟⠓⢤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⡼⠀⠀⢰⡒⠛⠺⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡤⠞⢙⣆⠀⠀⠀⠸⡀⠀⠀⠈⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⡋⠙⠛⠲⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠶⠚⠋⣸⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣞⠉⠓⠶⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡶⠚⣹⡇⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣟⠳⠶⠶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣇⠹⡄⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⡟⢹⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⣼⠀⠀⠀⢸⡟⣗⣿⣿⣺⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡆⢚⠀⡄⣿⣉⣹⣿⣿⣯⣿⣧⣤⠶⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡘⣿⣿⡧⢾⡶⢧⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⠐
⠀⠀⠀⠀⠀⠀⠀⢰⢇⣿⣿⣿⣟⢻⣿⠟⠛⠃⠀⠀⠈⠙⠋⡭⠿⣟⣗⣺⣿⡎⣉⠘⠿⣿⣗⢀
⠀⠀⠀⠀⠀⡀⠀⠚⠛⠿⠥⡈⢈⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣿⣸⠟⠟⠛⠏⠙⠻⢿⣯
⠀⠀⠀⠀⡄⠀⠀⣀⡄⠀⠀⢸⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣛⣵⡃⡄⠠⣰⠀⠀⣰⢻⣿⣿⡆
⠀⠀⠀⡄⣾⣄⡀⣀⣀⣀⣠⣿⣩⣭⣽⣿⣷⠄⠀⠀⢠⣿⣿⣿⣿⣿⣙⠓⠴⠿⠷⠄⣚⣿⣿⣿⡇
⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠷⠾⠶⢾⡶⢶⠾⠿⠿⠾⠷⠿⠿⠿⠾⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⠀⠀⢸⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠀⠉⠉⡏⠀⠀⢸⠀⠀⢸⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⢀⣤⣠⣦⣾⡀⠀⢸⢸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸⠉⠉⠉⠀⠑⠁⠙⣋⠙⠿⠿⣳⣜⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣭⣐⣂⠩⢝⣛⣿⣿⠿⠀⡀⠀⢀⣇⣀⣸⣀⣀⣀⠀⡛⠆⢼⣿⢬⣥⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡟⢫⣽⡾⡎⠉⠉⠉⡏⠉⢸⠀⠀⢸⠀⣻⠆⢀⡄⣪⣿⣿⣿⢹⢀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⢸⣿⡇⢸⡇⣼⢹⢱⠁⡆⠀⠀⡇⠀⠸⠆⠐⢾⠂⠈⡷⠈⣸⢧⣿⠟⢉⡼⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠿⢇⡘⠗⡏⢸⢘⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠙⠞⠛⡢⢋⠔⠁⣨⠦⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠘⠈⠀⡇⠀⠀⣧⠤⠤⠤⠤⢼⠀⠀⠀⠈⠻⡿⢂⡤⠚⠁⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⡆⠀⠀⠃⠀⡀⢚⢦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢩⣿⡍⣙⣤⣿⣄⠀⠀⠀⢰⢁⡉⠀⠼⢧⣠⡤⠤⠤⠤⠤⠤⠤⠄⢰⠳⠃⡠⠌⢢⠀⢠⣆⠀⠀⢹⣿⡇⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠮⢙⡰⣿⣿⢿⠇⢸⠀⢸⣿⠐⠂⢰⠍⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⡄⣸⠴⢤⡀⠡⢸⡿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⣦⠀⠀⡗⠘⢿⣤⡐⠳⠛⣼⠟⠤⠤⠤⠤⠤⠤⠤⠤⠘⣷⡗⠤⠔⡃⡀⣬⠁⠀⠀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⡀⠰⡄⠀⡇⠀⠀⡀⢹⣤⣴⣇⡀⠄⢠⡄⠀⠠⠄⠀⣤⡀⠈⠃⠀⡰⠁⠀⣾⡇⠀⢀⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣶⣶⣴⣟⠊⢸⡇⣤⣶⡾⣿⣋⡀⣰⠄⡶⠀⠀⠀⠀⠀⠘⣧⣀⣀⡜⠁⠀⠀⢿⡇⣾⣼⡇⢸⠇
⠀⠀⠀⠀⣀⠤⣤⣶⣿⣿⣿⣷⣬⣍⠙⠳⠤⠵⣿⣋⡐⣿⡇⠀⠨⣤⣇⣀⣀⣀⡀⣠⡀⠹⠻⡻⣧⣤⣀⠀⢸⣿⣿⡟⠀⠸
⠀⢠⣶⠉⠀⠀⠻⣿⣿⡿⠿⠿⠛⠋⠀⠄⠀⠀⠀⢹⣷⠈⡃⠀⠀⢀⣠⡅⠀⣉⠄⢸⡏⠳⢤⣻⣮⣶⡆⠃⢸⡟⠁⣀⣤⣶⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⣼⣿⠀⠥⠛⠟⢫⣾⣷⠀⢸⣷⣶⣶⣴⣯⡍⠉⢹⣿⣿⡿⣳⣾⣿⡿⣿⣧
⠠⡟⠁⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡄⢰⢦⣩⣿⣆⢠⡄⠲⠀⢯⣍⣣⣼⠯⠉⠉⠉⠉⠡⠚⢸⠟⢁⣴⣿⣿⡿⣿⣿⣿⡀
⠀⠀⣀⣈⣉⡟⠙⠋⡿⠛⠛⢻⠛⠉⡿⠑⣦⡄⠀⢹⣿⣷⡠⢷⠂⠓⠂⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢠⢔⣿⣿⣿⣿⣽⣿⣿⣟⡧
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣷⠘⡆⠻⣿⣧⠈⠇⢈⠁⠀⡀⠀⠀⡤⠀⠀⠀⠀⠠⢸⣿⢟⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣇⠠⣑⠌⠁⡡⡀⠈⡄⠐⢽⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠻⣿⣿⣿⣿⠀⠀⢿⣿⠆⠻⠿⠾⢰⣧⠀⢰⠀⠈⠻⣦⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠀⠀⢸⣿⣦⣤⣄⣰⣿⠃⠀⠈⡄⠀⠀⠑⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢏⡾⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠉⠙⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⠿⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠄⢤⣄⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢠⠀⠀⢀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆⡈⢁⠀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠜⠢⠀⡂⠀⠀⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠡⠴⡂⠀⠀⢩⡸
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠒⠐⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⢀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠶⠶⠚⡠⠁⠀⠀⠀⠀⠁⠀⡐⢁⠐⠁⠀⠀⡠⠖⢦⠀⠀⠑⠦⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣀⠀⠀⠀⠂⠰⠁⠁⠀⠀⣀⠀⠧⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠇⠀⠀⠀⠀⠀⠀⢑⣰⠉⠀⠀⠀⠀⢔⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠎⠀⠐⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⡆⠀⡀⠀⢷⣀⡀⢀⡠⠂⠀⠀⠐⠋⠀⠀⠈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⠒⠀⠀⠀⠄⡂⠇⠀⠀⠉⠉⠉⠀⢄⢠⠷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⣀⣴⣾⣥⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠁⠀⢀⡰⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠋⠀⠀⠶⠶⠖⠀⠈⠀⠀⠀⠙⠋⠉⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⡿⢶
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠛⠛⠛⠛⠋⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠰⠓⠀⠀⠀⠓⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠤⠄⠀⢰⠠⠀⠀⣧⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢯⡰⡙⠷⠀⠀⠀⠠⢄⣸⠀⠀⠀⣼⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡉⢻⡀⠀⠐⠳⣄⡀⢀⣠⠄⠀⡏⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠐⢛⢤⣌⣩⢷⣄⠀⠀⠀⠀⡀⠀⠀⡼⠁⠀⠀⣸⣏⡆
⠀⠀⠀⠀⠀⠐⠛⢠⠾⠉⢸⠈⠓⣦⢤⠤⡭⢶⢻⣦⡀⠀⢀⢾⣍⠣⢞⠂
⠀⠀⠀⠀⠀⠀⣴⣿⠚⢲⣤⠀⣰⠃⠘⠀⠱⢀⢁⢳⠱⢄⠀⢱⢉⠖⠁
⠀⠀⠀⠀⠀⣼⠋⠸⠀⢸⢸⢻⠃⠀⢰⢆⢀⠺⢇⡇⠻⡞⠀⠸⠘⡀
⠀⠀⠀⠀⢰⢹⢰⡀⠀⢸⢈⣨⠆⠀⡄⡇⠁⢀⣨⠕⠁⢸⢠⠃⠀⡇
⠀⠀⠀⠀⣾⢸⢘⢿⣠⡼⠋⠹⣄⣠⢧⠇⣴⣉⣴⡶⡖⠋⠛⠀⢠⡃
⠀⠀⠀⠀⣿⢸⢸⢸⢹⢳⡄⠀⢳⡤⠋⣸⢡⣭⣾⠀⠈⠢⢂⣁⠉⠉⡂⠠⣀⣀
⠀⠀⠀⠀⣿⢶⣼⣼⣈⣈⢹⣄⠀⠀⢀⢏⣸⣼⣇⣠⣤⢷⠒⠀⠀⠈⠉⢀⠛⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⢻⠀⠀⠉⠉⠉⠉⠙⢦⣠⣾⣿⣿⣿⣿⣿⣧⣀⠑⠢⠤⠔⠒⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠉⠉⠛⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⢰⡿
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠻⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⣤⣤⣴⣿⣀⡀⠀⠈⢧⠸⣇⣩⣿⡟⠁⠀⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⢦⠀⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣷⣿⡿⠿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⢿⣿⣵⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⣸⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠁⣠⣴⣿⣿⣿⡿⣡⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⣾⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠛⠛⠛⠿⠟⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠋⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠶⢦⠀⠠⢴⠶⠒⠒⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠃⠀⠀⠐⠆⠈⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣭⠁⠀⣀⡀⠄⠀⠀⠀⣠⡿⣸⠃⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⣷⡈⠿⠿⠟⠀⠀⠀⣠⡼⠋⠜⠁⠀⢀⡆⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠋⠁⠀⠙⣿⣷⠀⠀⠀⠀⣠⣾⣟⡥⠊⠀⠀⢀⡞⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠐⠛⢯⡾⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣾⣿⡿⣆⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⣤⠾⠗⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠁⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢂⣨⡷⠞⢿⠲⠬⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⣩⢷⡂⠈⣦⠀⠀⠉⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠾⢻⣧⡼⠃⠀⢴⣿⠈⢳⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣉⣤⣤⡶⠾⢻⠀⠀⠙⠛⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢍⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠂⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⣷⣿⣧⡀⠀⣤⣧⣽⣿⣏⠐⢾⡉⣶⠄⡀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠶⠶⠶⠶⠶⠶⠶⠶⠗⠒⠾⠾⠿⠿⠿⠷⠿⠿⠿⠿⠿⠟⠻⠾⠛⠛⠒⠃⢘⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⡤⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢝⡉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤
⠀⠀⠀⣧⣀⢨⠀⢴⣲⡄⠘⠊⠁⠀⠀⠀⠀⣧⣗⡖⢰⠐⡆⣎⣱⠀⢼⣿⣧⠀⡿⢿⡟⠿⢻⣿⡇⢸⣿⠿⣿
⠀⠀⠀⠿⠛⠘⠶⠸⡽⠇⠀⠀⠀⠡⣰⠀⠀⠃⠉⠉⠘⠋⠙⠉⠁⠀⠀⠉⠀⠀⣗⣛⣇⣶⢸⣜⣧⣈⣻⣘⣿
⠀⢸⣄⡸⠏⢾⣭⡇⢀⡀⣀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⢠⡄⠀⠀⠀⠀⢘⣷⠀⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿
⠀⠘⠛⠁⠀⠀⠉⠀⠸⣿⡷⠄⢠⣾⢿⣿⣿⠿⣿⠿⣶⡐⠛⠶⣤⣤⡄⢨⣽⠀⠀⠀⠰⡿
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⣿⣇⣻⣜⣼⣜⣻⣀⣾⡇⠀⠀⠀⠁⠀⠀⠾⠀⠀⢻⡀⡀⣆⢸⡀⣏⣰
⠀⢑⡈⣁⠀⡅⢈⣉⠉⡁⠀⠀⠹⣧⣭⣭⣍⣝⣇⣤⣿⠃⠀⠀⠠⠀⠀⠐⣲⠀⠀⣬⣅⢀⣬⣠⢤⢬⣤
⠀⠨⠆⡟⢱⡿⠸⣧⡄⡇⠀⢀⠀⢈⠛⠻⠿⠿⠛⠋⠁⡄⠀⠁⠀⣦⠀⠀⠀⠀⠀⠁⠉⠋⠉⣉⡈⠈⠉
⠀⠀⢀⣤⠀⢀⡀⢠⠴⠲⠶⠇⡀⢈⡀⠀⣤⡄⡀⠀⣀⡀⣐⡒⢂⢀⠀⡀⠀⠀⠀⢀⠀⣀⢀⡝⢁⣄⢀
⠀⠀⡀⠉⠀⠘⠃⢠⣄⣠⣤⡀⠇⠔⠋⠀⠇⠀⢧⠇⠿⡇⠻⠟⠸⠞⣀⣄⣀⡀⡀⠨⠂⠏⠸⠣⠻⡤⠸
⠀⠀⣷⣀⢀⡄⣄⢀⡔⢢⡀⠑⠀⣄⣠⢀⣤⡀⣀⣀⣀⣠⣤⡄⡤⢠⣄⣠⠍⠁⠀⡴⢰⡆⠀⣤⣠⡄⣆
⠀⠀⠛⠛⠀⠛⠋⠀⠛⠛⠀⠀⠀⡟⢻⣿⣤⡟⡿⣿⣝⡦⢸⠀⠧⢸⣞⠨⡷⠀⠀⠀⠀⠁⠈⠛⠉⠀⢈⡀
⠀⠀⠀⠀⠆⠀⠐⠀⠀⠠⠀⠀⠀⠁⠈⠀⠉⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡤⣶⣿⣿⣿⣿⣿⡷⣦⣌⠁
⠀⢠⠄⣤⡄⣶⢠⡶⠆⣤⠀⢰⣶⣤⣤⣤⣤⣤⣤⣤⣄⠀⢐⡀⠨⣭⠀⣰⣿⡇⢿⣿⣏⣹⡅⡿⡇⣿⢫⣧
⠀⠐⠃⠋⠐⠏⠈⠷⠆⠛⠀⢸⣯⣽⣿⣹⣼⣯⣽⣬⣽⡇⢀⡅⠰⠾⠀⣿⣿⣷⡶⣿⢿⢲⢿⢾⠷⢶⠿⣿⠂
⠀⠆⠶⠴⢺⡼⠾⠸⠰⠿⠀⢸⣿⣟⣻⣿⣏⣏⣏⣿⣿⡃⠀⠀⠾⠙⠆⠘⢿⣿⣧⣥⣾⣈⣦⣾⣾⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⠛⠛⠛⠛⠉⠉⠉⣍⠉⠀⠀⠃⠈⠉⠀⠀⣤⡌⠛⠛⠿⠿⠿⠟⠛⠉⠀⠶
⠀⣿⠿⣿⡿⡿⣿⢶⠶⣶⡆⠀⠀⠀⢀⠀⠀⢀⠀⡁⢠⣤⡠⢄⣠⢄⣠⡄⠙⠁⢀⣤⢠⡄⣤⣰⡆⠀⣴⣤
⠀⣿⣾⣿⣶⢿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠁⠁⠀⠁⠀⠈⠈⠙⠋⠙⢋⡈⠁⢠⡄⠘⠷⠌⠧⠏⠘⠧⠖⠿⠷
⠀⣷⣺⣠⡜⣈⣇⠺⣿⢼⡇⢰⣶⡆⠀⠀⠿⠘⠗⠟⠀⠶⠼⠻⠥⢸⠄⠀⡀⠀⠰⠲⠶⠶⣰⡴⣇⣶⣾⡇
⠀⠈⠉⠙⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡠⠚⢁⣴⠮⠭⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡠⠔⠊⠁⢀⢀⠀⣸⢽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⠘⠚⠁⠀⠉⠉⣡⣛⡛
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠋⠀⠃⠀⠀⠐⠀⢉⠤
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠠⣀⠀⢀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠢⣀⢀⡠⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠈⠂⢀⠂⣖⠀⢀⡀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⣅⠀⠀⠀⠀⠀⡗⠀⠏⠀⠀⣀⡀⠀⠰⠃⣤⣏⠀⢀⣠⡂⠀⠀⠀⣶⡃
⠀⠀⠀⠀⠀⢀⠘⠋⠀⠑⠄⢀⣀⣂⣀⡢⠐⣻⡟⠳⣀⠌⠀⠱⠀⠀⠀⠀⠀⠀⠀⠸⢿
⠀⠀⠀⢀⡄⠀⠀⠀⡠⠊⣝⡓⣒⣒⣒⡙⠾⠿⠷⠐⠁⠀⠀⠀⠂⠀⠀⠀⠠⠌⠉⠀⠄⠐⢠⡀
⠀⠀⡀⣅⣱⡀⠀⠀⠐⣠⢺⣷⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡐⠦⠄⠈⠀⠀⡘⣸⣂
⠀⠀⠀⠀⠀⠀⣀⣉⣀⡤⠀⠙⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣐⣤⣽⠒⠛⣤⠀⠄⣤⠖⠒⠋⠉⠉⠉⠉⠉⠙⠒⠷⣔⢄
⠀⠀⠀⠀⠀⣿⣿⡟⠀⠈⠻⢄⡀⠙⠖⠒⠆⠦⠦⠤⠦⠶⠖⠒⠚⢁⣀⠴⠁
⠀⠀⠀⠀⠀⠈⠉⠧⠤⠤⠠⣀⣃⣑⣀⠖⠲⠶⠶⠶⠶⠒⠒⠚⠋⠉

⠀⠀⠀⡀⠄⢀⠆⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⢀⡠⠔⡠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯
⠀⢀⢢⢨⣰⠁⢐⣤⡆⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⢰⠶⠂⠀⠀⡰⠉⠴⡀⢁⠸⠆⠀⠀⠀⠀⣤⠤⠤⠤⠾⠿⢦⡄
⠀⠸⠈⠉⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⢰⡆⠀⠀⠀⠀⠐⠿⣾⢉⡀⠒⢰⠀⠀⠀⠀⠣⠀⠀⢀⡀⠤⠀⡁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣤⠁⠀⢀⡄⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠉⡄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⢡⡖⠀⠀⠀⠋⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⢣⠀⠀⠀⠁⠀⠀⣀⢀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠖⠑⠊⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⠋⠁⠀⠈⠀⠄⠀⠀⠀⠀⠀⣰⠈⢷⠀⢠⣠⠀⠀⠀⠀⡄⠲⡀⢀⡀⠀⡀⠀⠄⢀⠸⠙⠀⠀⠀⠀⠠⠈⡃
⠀⠀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⣘⢦⠀⠀⠀⠈⠢⡑⠄⢠⠀⠀⠀⢂⠀⠁⠂⠀⠀⡀⢀⠀⠀⢁
⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⡿⠔⠀⠀⠀⠀⠀⠐⠀⠄⠂⠀⠠⠔⠁⠀⠀⠸⡀⢀⠀⠀⠏
⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢀⠶⠁⠈⣀⣀⣀⠀⠉⠀⠀⠀⠈⣲⣷⡀⠘⣶⢧⠖⠀⠀⠀⠀⠀⠀⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⡀
⠠⠀⠤⠘⠉⡽⢏⠉⠐⠀⠀⠀⠀⢹⠀⠁⢸⡙⠳⠀⠀⠀⠀⠀⡠⠉⠉⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡠⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠉⢰⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠑⠚⢻⠟⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⡄⠀⠀⠀⠀⠀⢠⡴⡆⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⢌⠄⡝⠁⠉⠀⠀⠀⠀⢠⡇⠂⠀⠀⠀⠀⠹⡀⠀⠀⠀⡠⠂⠉⠀⠀⠀⢀⠀⠆⠀⠀⡠⠚⠀⠀⠀⡌⠃
⠀⣀⠀⠐⠒⠛⠛⠛⠓⢲⠃⠀⠀⢀⢈⠂⢜⠖⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠄⠀⠀⠀⠀⠀⠨⠀⡁⠀⠀⢁⠄⠒⠀⠘⠢⣄⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢃⡠⠌⡠⠂⠀⠀⠀⠀⠀⠘⡆⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


⢀⠉⠃⣶⣴⣶⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠹⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⢰⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡟⠛⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⣀
⠀⠀⢾⠀⠀⡇⠀⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣉⣷
⠀⠀⠘⠀⠀⡇⠀⠸⠀⠀⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠄⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⠀⢀⠐⠤⠀⠠⠌⠁
⠀⠀⠀⠂⠀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠁⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠐⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡄⢥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⠤⠒⠢⣀⣠⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠒⠒⠊⠉⠉⠁⠀⠀⠆⠀⠀⠀⠀⢠⠀⠁⠈⠙⠦⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠊⠀⠀⣀⠀⠐⠂⠀⠺⠅⠀⠀⠀⠰⡇⠀⠀⣄⠀⠀⢠⠀⣤⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡾⠁⠀⠀⠉⠃⠰⠦⠀⠀⠀⠤⠀⠀⣀⠀⠀⠀⠘⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⣠⠴⠖⠲⠚⠒⠶⠲⠤⠖⢦⣀⡠⢄⣁⣀⣀⡴⢶⣀⣀⠈⢉⡴⠞⠉⠁⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠓⣰⠊⠁⠀⢦⣠⠦⠃⣀⣀⠀⠀⠀⢡⣆⡀⠈⠀⠁⣤⡀⠉⠉⠛⢾⣀⠀⠚⠂⠀⠰⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣸⠅⡠⢄⠀⠀⣀⠀⠀⠃⠈⠀⠀⠀⠀⠈⠀⢀⡀⠀⠈⠁⠀⠀⢀⡀⠉⣷⠀⠀⣠⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠸⡇⠀⠇⠀⠀⢠⡞⠻⠿⠷⠾⠷⠾⣗⣚⣻⡥⣤⡿⠿⣿⣲⡂⠀⠙⠀⠀⣸⠇⠀⠀⠀⢠⠆⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠻⡀⢁⡏⠀⠀⠀⠐⠦⡝⠦⣅⡲⢄⡰⠤⠀⢘⢻⡟⢁⡤⢒⣽⢡⠟⠂⢀⣄⠀⢈⡇⠀⢀⡀⠀⠀⠐⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⣧⠀⡴⢦⠀⠀⢳⣴⡶⠬⣑⠮⠥⠴⢞⣀⣿⣥⣾⣭⠟⣞⠀⠀⠀⠚⠀⠸⡄⠀⠘⠃⠀⢤⡀⢰⡃
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⡀⠀⠀⠀⣀⠙⡇⡇⠀⢨⣿⣴⠿⠯⠖⠛⠳⠭⣍⡓⢬⢡⡆⠀⠓⠂⣠⠇⢠⡄⠀⠀⠘⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠄⠠⣏⠁⣠⡀⠀⠀⣁⣧⠃⢠⣿⢋⡿⠤⣍⡁⠀⣒⠦⠀⢳⣈⡇⣧⠀⢲⡆⠈⣳⠀⠀⠀⠰⠂⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢧⡄⠀⢏⠀⠀⢓⠄⢀⡌⣿⠀⢸⡷⡏⠉⢓⡒⠻⢷⡦⣽⣦⠴⡫⢤⢘⡤⠙⠁⠸⡅⠀⢀⡀⠀⠐⠃⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⣼⠁⠈⠁⠀⣠⠃⢿⠇⢸⢠⣚⡷⠤⢍⣙⣀⣉⣲⠽⢾⡡⠾⡞⠁⠀⠀⣴⠃⠀⠈⠁⢀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢸⠆⠀⢀⠀⠒⠒⣎⣓⣮⣴⠛⠖⠲⣆⣤⣤⠖⠶⠒⠚⠓⠂⠀⠐⠒⠀⣹⠂⠀⠶⠀⠈⠀⠀⣞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠸⣄⠀⠣⡄⠀⢀⠁⠈⠃⠈⠁⣆⠀⠈⠀⣠⣄⣀⠀⠀⢠⠀⠀⡀⠀⢈⡇⠀⠀⠀⠀⠘⠁⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⠈⢿⠀⠙⡛⠊⠀⢠⠀⣀⣀⠀⠀⡀⠰⠁⠈⠈⠀⣀⠈⠉⠉⠁⠀⢻⠀⢀⣤⠀⠛⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⠀⠀⠉⣉⠉⠦⣀⣤⡉⠉⢁⣄⠘⢉⡀⢀⡀⠀⣄⠈⢡⣀⣠⡦⠶⠋⠀⠀⢀⣀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣇⠀⡈⠁⢀⠀⠀⠈⠉⣉⣀⠉⠉⠉⢁⡙⠊⠉⠙⣫⠈⢉⣀⣀⡴⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠋⠓⠶⠞⠳⠤⠴⠤⠤⠴⠦⠥⠖⠲⠖⠋⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣟⣠⣺⣆⣾⡏⣼⢰⡇⣴⢳⣦⡖⣴⣴⣤⣇⣔⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠁⠉⠁⠁⠺⠀⠉⠉⠈⠁⠉⠈⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠂⡬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠙⠀⠀⣰⣦⣄⡀⠀⠀⢀⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⡀⠿⣧⣶⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠙⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⢇⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⢋⢈⠀⣿⣿⣿⠿⠁⠿⢿⣿⣿⡿⠟⠋⠀⠀⣹⠀⣟⣛⡃
⠀⠀⠀⠀⠠⣤⣴⣶⣶⠀⣂⣀⣉⡸⡗⢶⣿⣶⣶⣶⣶⣶⠒⠀⠀⣁⠀⠀⠀⠀⠉⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⣍⣭⣭⣭⣭⣡⣤⣭⣭⡁⠀⠀⠀⠐⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡆⢘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠇⠸⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⢐⢤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣀⣀⠀⠚⠀⠀⠀⢁⡤⠠⡀⠀⠻
⠀⢀⠉⠀⡄⡁⢀⠀⠠⢄⡀⠈⢀⠄⠀⠀⢂⠠⣆⠄⠀⠀⠀⢀⠀⠀⠀⠀⢸⣅⡈⠙⠁⠋⠋⠐⠀⠀⠢⡀⠀⠂
⠀⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⡀⠙⠐⠅⠀⡀⠀⠀⠀⠀⣎⠙⠻⣷⣦⡇⠁⠀⠀⠀⣀⠈⠀⠊⠠
⠀⠘⣆⠀⠈⠲⠀⢀⠀⠀⠄⠒⠀⠡⠀⠀⠀⢀⠀⢀⣀⣦⠀⠀⠀⠀⠀⠀⠻⣷⣂⢄⡉⢁⠀⠀⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠐⠆⠀⠀⠐⠀⠀⠀⠀⠈⠙⢛⠀⠀⡄⡀⠀⣠⣄⠈⠙⠷⠃⠄⠀⠀⠀⠈⠠⠄⠂
⠀⠀⠀⠀⠄⠀⠀⠁⠈⠀⠀⠀⢀⠀⠀⠀⠠⢄⠂⣈⠄⠀⠈⠁⠀⠉⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠐
⠀⠰⡦⠀⠀⠔⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠁⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠖⠠⠀⠀⠀⠀⠀⢀⢀⣴⣤
⠀⠀⠀⠀⠋⠁⠁⠢⣄⡀⠢⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠃⢘⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠠⠔⠀⠀⠀⠀⣠⣴⣦⣤⣄⢤⠤⡖⠲⣶⣿⣿⣷⣄⠀⠀⠁⠀⠀⠀⠀⠀⡀⣼⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠱⡄⠀⠀⢸⠋⣽⣿⣿⣿⢺⣾⡗⣺⣿⣿⢿⣿⢸⠀⠀⠈⠀⠀⠀⠀⠺⡀⠙⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⡇⣞⠊⣆⣻⠸⣿⣇⣯⣒⣤⣧⣝⡸⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠈⡀⠂
⠀⠠⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢘⣷⣢⠤⠈⠛⠛⠛⡛⣋⠉⠉⠉⠉⠉⢉⠉⠐⠆⡀⠀⠉⠂⠀⡄⠁⠀⠀⢈⡈⠂
⢠⠁⠀⠀⠀⠀⢁⠀⠀⠀⠑⠰⡉⠀⢅⠀⡀⠀⠀⠀⠀⠔⠂⠉⠀⠀⠀⠀⠀⢊⠄⠄⠀⠀⠀⠀⠀⣐⣛⣏⡿⢟⣦
⠘⠀⠠⢀⡀⠠⠂⠀⢰⠂⡁⠀⠏⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⢀⠀⣀⠑⠂⠈⠀⠀⠀⠀⠀⠈⠁⠴⣦⢴⠚⠉
⠀⠁⠀⠀⠀⠀⢀⠤⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢠⠀⠀⠰⠃⠼⠉⠀⠸⠄⠀⠀⠀⠀⠀⠀⡤⣀⣀⠤⡤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠣⠀⠰⠂⠀⠀⡶⠝⡦⢀⠀⠓⢤⡧⣤⣀⣀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠒⠁⠈⠀⠀⠆⠀⠈⠉⠁⠀⠤
⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⠇⠀⡀⠀⠄⠀⠀⠐⠄⠀⢀⠀⠀⠀⡀⠀⠠⠌⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⢀⡆⠈⠀⠀⠀⠀⠁⠄⠀⠀⠆⠀⠐⠀⠀⠠⠁⢀⠀⠀⡀
⠀⠀⠀⠀⣠⣀⠉⠹⢦⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠟⠯⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣻⣻⣟⣻⣿⣿⣿⣟⣟⣻⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣻⣿⣻⣻⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣻⣿⣻⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣯⣿⣿⣯⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣯⣭⣭⣭⣭⣭⣭⢭⣭⣭⢭⣭⣭⣭⠭⣭⡭⡭⢭⣭⣭⣭⣭⣭⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢹⣿⡜⡈⢸⢘⢹⡧⢹⣸⣿⡇⣧⡳⣿⡏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣧⣷⣾⣼⣿⠴⣾⣿⣿⣧⢧⡵⣿⡿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡘⠁⡇⡇⡇⠱⡇⣓⣿⠀⣿⡘⢸⢸⢺⡞⣼⡿
⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⠿⠿⠿⠧⠷⠥⠧⠷⠵⠭⠯⠶⠭⠷⠼⠬⠼⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣖⣖⣶⣖⣶⣶⣷⣶⣶⣶⣲⣶⣶⣷⣶⣶⣖⣶⣖⣶⣲⣶⣶⣶⣾⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣛⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣿⣟⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣯⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣻⣿⣟⣿⣻⣟⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠻⢟⣦⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠁⠈⣇⣀⣠⠛⠛⠳⡀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠻⣶⠖⠺⡏⠀⠙⣦⣀⡴⠋⠒⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⣀⣠⣿⢦⢾⡤⠤⠿⣄⠀⢅⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠒⠋⠉⠋⠀⠘⢄⣄⠑⢄⠈⠢⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡇⢀⣀⡴⠶⠐⠓⠘⠒⠛⠦⣀⣑⣄⠀⠳⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⢇⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⠋⠀⠀⣠⠖⠚⠉⠉⠑⣦⠤⣀⠀⠀⠀⠈⢦⠃⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠀⡈⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⠒⠉⠓⡄⠀⠀⠀⡟⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠱⡇⠀⠀⠸⡈⢦⣀⡀⠀⣰⡇⠀⠀⠀⢻⠀⠀⠀⡗⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⢱⠀⠀⠀⣷⠊⠁⠈⠙⠣⡘⢄⠀⠀⢀⡇⠀⢀⡧⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢈⢲⠀⠀⠀⢻⣆⠀⠀⠀⢠⠇⠈⡳⠒⢁⠇⠀⢸⡗⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⠁⠣⡀⠀⠀⠙⠷⠦⠤⠾⠦⠾⠤⠤⠎⠀⠀⡜⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢢⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠥⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣉⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⡀⠀⠀⠀⣀⠀⢀⣤⢄⡀⠠⣤⣤⣤⠀⣀⠀⠀⢀⣄⣀⠀⣀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣷⢸⡇⠀⢁⢀⣶⣶⣶⣤⠀⣿⢨⡗⠀⢸⡇⠀⠀⢸⣿⠀⣿⡄⠁⢰⡇⠘⡀⣧⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢰⠏⢸⣧⡄⠂⣿⣾⣎⠉⣿⡇⣿⢻⡄⠀⢸⡷⠂⠀⡆⣿⠀⢻⣷⡀⣸⡇⠀⡇⣿⢧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢠⡄⢸⡇⠀⠀⠘⢿⣿⡿⠟⠀⣿⠈⣧⠀⢸⡇⢀⠀⡓⢻⡆⠀⢹⣧⢾⡆⠀⠇⣿⠈⢧⢸⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣘⣁⣼⣗⣒⣇⣀⣀⡀⠂⠀⠀⠛⠂⠙⠀⠚⠓⠛⠼⠄⠸⠧⠀⠴⠋⠘⡳⠊⠐⠛⠆⠈⠛⢰⣿⡿
⠀⣴⣶⣄⠀⠀⠀⡠⠒⠩⢴⡖⢲⡆⠐⠀⢰⡆⠈⣭⢉⠑⠓⠒⠶⠶⠤⣄⣀⣀⠀⡀⠂⠀⠀⠀⢀⡐⠒⠈⢀⣠⠔⢁⡿⢛⣡⣤⣤⣄
⠀⠈⠻⢿⣷⣄⠈⡀⠀⠀⠘⣇⠸⡏⢈⠐⢸⡇⢰⠇⠀⠤⠀⠀⣾⠀⣴⢢⢠⡌⢩⠉⡭⠟⣻⡒⢒⠒⡛⡭⠅⠀⣤⠀⢚⣛⡛⠿⠿⠟⠁
⠀⠀⢀⣤⣴⠖⡀⠉⢀⡠⠤⠥⠤⠤⠤⣤⢈⣁⣘⠀⠀⠀⠠⢀⡿⢸⠇⡜⣾⠉⠑⢸⡧⢀⡏⠸⣿⢀⠀⡗⠀⠀⠁⢀⠈⠻⣿⣿⣶⡄
⠀⣴⣿⣿⢏⣼⡇⡞⠁⠀⠀⠀⣠⣴⣶⠶⣄⡀⠀⠉⠩⢉⣒⠓⠲⠾⠤⠤⢏⣀⣂⡺⠠⠈⠇⠀⠿⠘⠃⢓⣢⠴⠒⠁⠀⠀⠀⠉⠛⠃
⠀⠙⠛⠁⢸⣿⡇⠑⠚⠀⠀⣰⣿⡟⠀⠀⢸⣿⡶⠆⠀⠐⠂⠬⠍⠉⠀⢀⣄⡀⣠⡍⠉⢉⣭⡉⠩⠭⠍⠐⣠⣴⠶⢦⠀⠀⣀
⠀⠀⠀⠀⠘⠛⢁⣴⣦⠀⠀⣿⣿⡇⠀⢀⡾⠃⣀⣤⡄⢀⣀⠈⢀⣀⠀⠈⢿⣿⠟⠁⢠⣿⠏⡟⠀⠀⠀⢰⣿⡇⠀⣸⠂⠺⢻⠇
⠀⠀⠀⠀⠀⠀⠸⣧⡁⠀⠀⠸⣿⢿⣴⠟⡵⠚⣹⣿⡷⢿⣿⠟⢻⣿⡇⠀⢀⣅⠀⢠⣿⡟⣸⠃⣀⣤⢤⢸⣿⣿⣴⠏⢀⡴⠋⢀⡀
⠀⠀⠀⢰⠀⠀⠀⢈⠙⠛⠛⠛⠛⢿⣿⣆⠀⣴⣿⡿⠀⡾⡿⢀⡿⣿⢀⣴⣿⠏⠐⢿⣿⡷⢃⣴⣿⠃⣼⠐⠟⣿⣿⣶⠋⢀⠎
⠀⠀⠀⠈⢦⣰⣊⡠⠂⣴⠶⠦⠀⠈⣿⣿⡄⣼⣿⠇⢰⣿⠇⣸⣿⠃⢠⣿⡟⠀⢀⣾⣿⠀⠘⡿⣧⠞⠁⣠⢞⡵⢻⣿⡇⢈⡤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡀⠀⠀⣰⣿⡿⢱⡿⠟⠀⠾⠟⠀⠻⠿⠶⠻⣿⡷⠖⠋⠻⢿⡤⠞⠻⠿⠦⠚⠁⣼⠁⣸⡿⡕⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⢰⠈⠻⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠁⠀⠠⣶⠠⢀⡴⠀⢠⡦⡄⢠⣤⠀⣦⠈⡄⠈⠉⣄⣀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠊⠉⠉⠈⠁⠀⠄⠀⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⢸⠯⠀⠘⡏⠀⠀⠰⠀⠀⠀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠇⠀⠘⠗⠀⠿⠀⠠⠀⠇⠀⠀⠀⠆⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠡⢄⣀⠀⠀⠀⠓⠂⢄⡆⠀⠈⢀⣀⣀⠀⣉⠀⣀⣉⣀⡀⠀⢉⡩⠉⠀⠀⢀⡀⠤⠛⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⢋⣥⠄⣩⠠⣬⡙⠛⠛⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢀⣿⡆⠙⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠉⠉⠁⠀⠀⠀⠐⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⣀⣀⡠⠶⠾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣤⣤⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠁⠍⠻⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⡀⠀⠉⠹⢦⡀⠀⠀⠈⠂⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠐⠉⠛⠛⠳⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠶⠛⠁⠀⠀⠹⢦⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⠄⠀⠠⠴⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠸⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠋⢀⡀⠀⠀⠀⢩⡿
⠀⠀⢠⣀⠀⠀⠀⠀⠉⠛⠲⢿⣆⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠤⠀⠀⠈⠁⠀⣀⠼⠀⠀⠀⡞⠀⠀⢀⣿⠀⠀⠀⠀⣸⡅
⠀⠀⠼⢿⣗⡦⣄⣀⣀⡀⠀⣤⣀⣠⣭⣥⡿⠋⠁⠀⠀⠀⠀⠀⠤⢄⡀⠀⠉⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⢠⠾⠇⢣⣤⢀⠔⠀⠀⠀⠀⢀⡿
⠀⠰⣤⣄⣀⠀⠉⠈⠛⠃⢀⣿⠀⠀⠘⠁⠀⠀⠀⠀⠐⠒⠲⠤⠀⠀⠀⠀⣀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠁⠿⠀⠀⠀⢀⣠⡏
⠀⠀⠈⠙⠛⠛⠤⠶⣶⡄⠸⠃⠀⠀⠀⢀⣀⡀⠉⠉⠀⠀⠀⢀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⢀⢀⡴⠚⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢞⡘⠇⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠈⢂⣾⡿⠉⠁⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠈⠹⢿⣤⣤⡶⠶⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠀⠀⠙⠻⢿⣾⣽⣛⠳⢦⣄⣀⠠⠔⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠦⣄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠛⠻⡷⢶⣏⠉⢠⣄⠴⠒⠛⠁⠀⠀⠀⡠⠂⠂⢬⣀⠀⠀⠀⠀⢈⡶⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠴⠛⠋⣿⠿⣶⡉⠀⠘⣇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡄⠀⠀⠀⠙⣾⠟⠀⠀⢠⡏
⠀⠀⠀⠀⠉⠻⠿⣶⣶⣀⣐⠲⣶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠘⢤⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠶⠿⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣠⣼⠃⠀⠀⠭⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣰⡿⠯⠭⠉⢻⠋⠀⢻⡀⠀⠀⢀⠇⣹⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⠀⠀⠙⡿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡶⠚⠉⠩⢭⠻⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⢀⣿⣄⡀⠀⢀⣼⣀⣀⣀⡀⣠⣏⠀⠀⠀⠀⠀⢀⡿⠉⠉⠭⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⣱⠖⠻⡟⠉⠉⠉⠉⠉⣿⡟⠛⠋⠁⢹⣦⣄⣀⣀⡴⠛⢇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡛⠛⠒⣎⠀⠀⠀⢸⣄⡀⠀⢔⣠⠿⠷⣦⣤⠖⠛⠛⡿⠀⠀⠀⠀⠈⢦⣄⣠⠤⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠹⣄⣀⣠⡜⠀⠀⢹⡏⠀⠀⠉⠂⣿⠀⠀⠀⠱⣜⠦⠤⠤⢢⡿⠛⠷⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⣰⣿⠿⣇⢠⡀⠀⣨⣇⠀⠀⠀⢀⣿⡀⠀⠀⣀⡿⠿⢷⣾⡏⠀⠀⠀⢹⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠉⠀⠀⠸⠓⠚⢿⠟⠛⠓⢶⠒⢿⠟⡋⠉⠛⢏⠀⠀⠀⠈⠳⡄⠀⢀⠎⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣧⡀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠈⡆⣀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⣟⠋⠁⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⡶⠾⣅⡀⠀⣸⣤⣀⣀⡴⠁⠈⢦⣀⣀⣠⣾⣀⠀⣀⣠⠾⠟⠓⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢄⠀⠈⠉⠉⠉⠉⠙⠛⠒⠲⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠉⠑⠒⠈⠙⠚⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢣⠈⠒⠤⣀⠐⠤⣀⣀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡣⣄⡀⠀⠈⠉⠉⠉⠉⠉⠁⠒⠉⠳⢄⡀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣅⣀⣀⠤⠤⠤⠤⠤⠤⣀⣀⡀⠉⠓⣲⣤⡴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢉⣘⠉⠀⠛⢉⣁⠘⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠈⣀⠀⢀⡀⢀⣀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠚⢂⠋⢣⠚⠂⣸⣿⠏⢹
⠀⠀⠀⠀⠀⠀⢸⣿⠏⡈⢿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠆⠀⠀⠀⠈⢩⣤⠋
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠤⠄⠒⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠶⠀⠀⠀⠶⠀⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣤⠤⠤⠴⠖⣺⡁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⡀⡀⠀⠀⢀⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⡿⣏⢳⣶⠋⠉⣀⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣄⣈⣀⣠⡴⠋⢹⣿⣿⣿⠇⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣅⠠⠚⠈⡟⠹⠶⢊⣽⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⡍⠉⠉⠛⢳⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣠⣶⣶⣶⣶⣿⣾⣼⣿⣿⣧⠀⠀⣧⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⣿⣷⡀⣤⠴⠞⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⡹⣿⣿⡟⢷⠁⢸⡇⠀⠀⢠⣿⢿⡿⢋⡿⠋⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠙⣿⡟⠀⠸⣆⡼⣇⠀⢠⡿⣿⠀⠀⠁⠀⠀⠀⠈⠀⠈⣿⣿⠋⠑⠁⠀⠉⠉⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⣿⠀⢹⣤⡟⢸⡙⡆⠀⠖⠀⠀⠀⠶⠀⢀⣿⢹⠀⠤⠄⠀⠀⠠⠤⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡇⢹⡆⠀⢸⡄⠀⢿⠀⢠⣿⢇⠀⢴⣐⣒⣐⡆⠀⢈⣿⣿⡀⠀⢠⣤⣤⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢷⠀⠀⣰⠏⣿⣴⣿⣾⣿⣯⣵⠒⠚⢯⡀⢉⣿⣶⣾⣿⣭⣥⠤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠗⢻⡇⠀⠀⠈⠳⠴⠀⣠⢿⣿⣿⡟⠹⡏⠀⠀⠀⠀⣱⣿⣿⣿⡟⢿⠋⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠻⣟⣻⢿⠣⣤⠷⠤⠴⠂⢀⣷⠾⣿⡿⣄⣸⢦⣀⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠴⠤⠤⠦⠶⠒⠛⢶⠋⠀⠙⠲⠤⠤⠔⠋⡏⠯⣵⠃⠈⠣⢤⣀⣠⠴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⣤⣤⣤⣤⠤⠴⠇⠀⠻⠤⣤⣤⣤⣤⠤⠴⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢾⣀⣟⣠⢶⣰⢆⢀⣴⡧⠒⣦⠒⣄⢀⢾⡖⠳⡴⢲⡀⣰⡇⣸⣇⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡏⠀⠈⠁⠀⠉⠈⠁⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠉⠀⢉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢦⠀⠀⢀⡴⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⣠⠞⡴⢣⣏⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠚⠓⠛⠉


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⠀⣺⠃⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢰⡆⣾⣠⠇⠜⡴⢆⡇⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⢀⠔⣹⠀⠈⠀⠁⡎⢀⠏⠓⠁⠀⠀⠀⣡⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢨⣠⠏⠀⢠⢠⠀⣠⠅⡤⠀⠀⠠⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⣿⠉⡦⣟⡀⣟⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⡤⠀⠀⢠⠤⠀⠀⢀⠞⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣏⡴⢠⠆⣄⡖⣠⠂⢈⡶⠀⢿⢀⡖⢀⡞⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣸⠋⠹⠜⠈⠃⠙⠂⠸⡧⠁⢸⡎⠀⠹⠧⢪⡯
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⠜⠅⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠈⠒⡄⢠⣶⣶⡄⣠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠄⠀⠐⠄⠀⠀⠀⢨⡶⠿⠿⢿⡅⠀⠀⠀⠠⠂⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠃⠠⠀⣈⣴⣒⣒⣦⣁⠠⡄⠘⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢀⢺⢺⣭⣥⣬⣭⠳⡷⡀⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠰⠖⠒⠲⠶⠀⢇⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠙⢿⠛⠁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠌⠉⠐⠒⠂⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠂⠀⡄⠀⠀⠀⠂⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠂⠀⠀⠀⠀⠀⠀⢠⢄⡄⠀⠠⠤⠄
⠀⠀⠉⠋⠀⠀⣀⣤⠊⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⡤⠀⠠⣴⡒⠒⢂⣏⠀⠇⢷⡀⡀⠀⠀⠀⠀⠀⠀⠀⡱⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡞
⠀⠀⠀⠀⠀⠈⠣⡠⠤⠤⠐⣲⡖⠀⣨⣥⣶⣀⠀⠠⠈⠉⠙⠚⠉⠁⠠⠀⠙⠻⣛⢕⠂⢀⣁⡠⠤⠖⠉⠀⠀⡎⠀⠀⠀⠀⠀⠈⠰⢶⡿⢖⣠⣤⡤⠤⠤⠀⢸
⠁⠀⠀⠀⢀⠀⠀⠑⠲⠶⠛⠉⠀⣈⣁⠤⠄⠀⠀⠀⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠧⠤⢄⣒⠉⠉⠥⣤⣏⡀⠄⠒⠁⠀⠀⡀⠀⢸
⠀⠀⠀⢄⠀⠀⠂⠀⠁⠀⢉⡩⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠶⠨⠤⠄⠀⠂⠀⠈⠁⠀⡌
⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⣠⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠉⠂⠀⠀⠇⠀⠀⢀⠀⠀⠀⢀⠀⣙⡦⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⣦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡃
⠢⠀⠀⠐⠁⢀⡞⠊⠀⠀⠒⠀⠈⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣿⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠔⠒⠈⠓⠒⡂⠀⠀⠀⠀⠀⠠⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⣦⠀⠀⠀⠀⢀⠠⠐⠀⢀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⡠⠘⠁⡠
⠀⠀⢹⢿⠃⠀⠀⠀⠀⠀⠁⠀⠈⠄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠠⠃
⠀⠀⡈⠓⠲⣦⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠈⢇⣦⠤
⠀⠚⠁⠀⢷⣏⡄⢀⣀⣤⠤⠄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠡⠐⢋⣤⠄⠈⠀⠖⠀⢀⣀⠀⠁
⠀⢄⠀⠀⠘⣦⢿⡧⠄⠀⠀⠀⠀⠀⣠⠴⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠠⠇⢀⠀⠀⡨⠋⡠⠐⠃⣀⡤⠊⢩⡇⠸⡅
⡀⢀⡠⠀⠀⠘⣮⢤⠀⣈⡄⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠓⠒⢄⠀⢀⢎⠀⠀⣀⠄⠈⣹⣥⠀⡼
⡀⠀⡸⠀⠄⠀⠘⡭⣦⣬⠴⠒⠀⠐⠀⠀⠀⠀⡄⠀⢀⠴⠀⠚⠃⠈⠈⠁⠐⠠⡀⠀⠀⡀⢀⡰⠀⠁⠈⣰⠶⠒⠂⠲⣄⢀⣠⠔⠊⣧⡆⠀⣿⠟⠋
⠁⠈⠀⠀⠀⠠⠀⠘⡎⠀⠀⠀⠀⠀⡃⠀⢀⡠⠃⡴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠻⣿⡉⠐⠶⠒⠧⢤⣀⣀⣦⠚⠉⣇⡄⠀⡿⠗⠈⠀⠀⠀⠄⡠⠤
⠀⢠⡀⠀⠐⠀⠃⡀⠙⠤⣀⣀⣀⢠⡅⠂⠁⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⢧⡀⣲⣦⡀⢘⣿⡀⢼⣣⠀⣯⠟⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠇⠀⡄⠀⣀⠔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⠿⣵⢆⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠀⠀⠀⠈⠁⠒⠛⠷⠼⠿⠊⠁⢀⠔⠁⠀⠃⢡⠀⠀⡠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠒⠉⣹⣩⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣁⡨⠴⠚⠉⠉⠳⡉⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣶⠠⢷⢤⣤⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣭⣶⣿⣿⣾⡆⠺⣶⣿⣿⣻⢮⣑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣾⣟⣥⣼⣿⡿⠻⠙⠟⠻⡛⠿⣿⣷⣿⣦⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣹⣿⣿⠿⠟⠋⠉⠀⠀⠀⠘⠀⠈⠢⡈⠙⠿⣿⣧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢌⠻⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢹⡄⠀⠁⢠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠤⣍⡑⠒⠢⠤⠤⠄⣀⣀⣀⣰⣀⣀⣀⣀⣠⣄⡠⠤⠜⠚⢉⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢝⠺⠯⠙⢓⠒⠲⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⣒⣒⣛⡍⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣦⣌⣀⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣢⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣿⡿⢛⣿⣿⣿⣶⣶⡶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣯⣿⠁⢸⣿⡿⢿⣿⠏⣾⡿⢡⣿⣿⣿⣿⣿⣿⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢹⣿⡄⢸⣿⠁⣿⣟⠠⣿⠃⣾⠏⣼⠟⣽⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣦⣿⣦⣼⣿⢰⣿⠠⣿⣶⣿⣦⣿⣿⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣿⣿⠩⣿⡟⢿⡿⡦⢿⣷⠾⢿⢻⣯⣿⡟⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⠀⣿⣷⠘⣿⡇⢸⣿⠈⢾⠧⣹⣿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣿⡾⢿⣷⣿⣧⣾⠿⢾⡿⣿⣿⡏⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⣿⣧⢰⣿⣿⠀⣿⡆⢸⢇⣿⣿⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⣿⣿⠸⣇⡿⢀⣻⣷⡀⣸⣧⡟⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⣿⢀⣽⡏⢸⡿⡟⢫⣿⣽⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢌⡛⠿⢿⣿⣿⣿⣿⣿⣷⢏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠭⠭⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠙⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠈⠻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢉⡉⠙⢿⣷⡄⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡄⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⢿⣷⣀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣶⣶⣶⣶⣾⣿⡿⠿⠟⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣭⣭⣭⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⣿⠿⠟⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣅⡀⠀⠀⠀⢠⣾⡿⠿⣷⡄⠀⠀⠀⠀⢀⣴⣶⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠈⣩⣤⠀⠀⠉⠀⠀⠀⢠⡞⢁⡀⠙⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⣹⣾⡷⣄⠀⠀⠀⢠⡟⠀⣭⣤⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⠀⠀⠀⠀⠀⠙⠋⠁⠉⠀⠀⠀⢸⣧⠸⣿⠃⢿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣛⡻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢹⣿⡆⠀⠀⠀⠀⠀⠀⣠⣴⡾⠃⠀⢠⣶⠆⣠⡔⡆⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⠓⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⣀⡀⠈⠁⠘⠋⠙⠻⣦⡀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠀⠀⠀⠸⣿⣟⠛⠛⠻⠿⠶⠶⣶⣤⢽⠇⣸⡇
⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣶⡟⠁⠀⢰⡟
⠀⢀⣴⠾⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⠛⠛⠛⠋⠙⠛⠲⠾⣧⣄⣀⠀⣠⣤⡄
⠀⣟⠹⡆⠸⣧⠈⣷⠀⢠⡾⠛⠛⢶⣄⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⢹⣌⠛⢶⣄⡀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⡇
⠀⢻⡄⢻⡄⢹⡆⠘⣧⣿⠀⢳⣤⣀⣹⡶⢿⣇⠙⢷⣦⣀⠀⠀⠀⠀⠙⠛⣠⣝⢿⣿⡿⠶⣶⠾⠟⠿⠶⣿⣿⣷
⠀⠀⢷⠀⢷⡀⢻⡄⠸⣿⠀⠘⣿⡿⠋⢠⡾⢧⡀⠀⠈⠛⠷⣶⣤⣀⣀⣀⣨⣽⣤⡉⠙⢿⣿⣛⣛⠛⠻⣿⡈⢿⣆
⠀⠀⠘⣧⠈⣧⠈⢿⠀⠉⠁⠀⢼⡇⠀⣾⡇⠈⠻⣦⣀⠀⠀⠀⠉⠙⠛⢛⣽⣧⡈⠻⢦⣄⡈⠉⠛⠿⠟⠛⠛⠈⠻⣷⡄
⠀⠀⠀⠹⣆⠘⠇⠀⠀⠀⠀⠀⠘⣷⡀⢻⡇⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⣸⣧⣈⠛⢷⣤⣈⠛⠳⠶⡤⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣠⣴⡶⠿⠃⠀⢿⡀⠀⠀⠀⠀⠙⢿⣦⡴⠞⠉⠈⠙⠷⣦⣈⠙⠻⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠈⣿⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣠⣾⣿⣷⡄⠀⠀⠀⠀⣸⠟⠻⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠘⣿⣄⠀⠀⠀⣸⡿⠈⠻⣦⡀⣴⠿⣿⣿⣿⣷⠀⢰⡟⠿⣷⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠁⠀⠀⠘⠛⠁⠀⠀⠈⠻⠏⢀⣿⣿⣇⠹⣷⡿⠙⢷⣦⣌⣀⣤⣴⡾⠿⠿⠷⠶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⡗⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⡤⢴⢶⣲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⣠⣔⢶⣾⣶⣾⣶⣦⣤⣀⠀⠀⠀⠀⣀⡤⠴⠶⣦⣤⡀
⠀⠀⢢⣥⣄⣻⣷⣿⣿⡿⠢⡀⠀⠀⠀⢰⡿⣿⣿⣶⣿⣿⣏⣾⣹⣿⣇⠀⠀⣞⡁⣄⣀⡀⠔⠉⠉⠵⠦⡀
⠀⠀⠐⡄⠀⣿⣿⡿⣅⡀⠱⠍⢦⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⡙⡂⠳⠞⣲⣄⠀⠀⠐⠚⢳
⠀⠀⠀⠈⠦⠿⣿⡇⠀⠙⠲⡟⣻⠁⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢄⠀⠀⠀⠌⢷⡤⢐⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠂⠒⠠⠍⠯⠟⠊
⠀⠀⠀⠀⣀⣠⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣒⣲⢦⡤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣀⡀
⠀⠀⣠⣾⠭⠤⢔⣀⡀⠠⠽⠛⢶⡄⠀⠀⠀⣡⡊⢀⣼⣿⣿⣿⣿⠳⢄⠀⠀⠀⢘⢥⣄⣾⣿⣿⣿⣇⡽⣶⣤⣀
⠀⠀⢿⠴⠖⠒⠒⠢⢍⡓⠦⣀⠤⠼⢶⡄⠀⣧⠀⢸⣿⣿⣿⠛⠶⢍⣫⣱⣦⡀⢜⠓⢶⣿⣾⣿⣿⣿⣚⣭⣟⣽
⠀⠀⠀⠀⠠⠀⡀⠀⠀⠌⠑⣿⣄⣀⡼⠇⠀⠈⠂⢿⣿⣿⡿⠀⠀⠀⣻⣹⣿⣧⠘⢶⣼⣿⣿⣿⠟⠶⠼⠭⠖⣺
⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠐⠊⠉⠷⠟⠃⠀⠀⠈⠉⠙⠛⠶⠷⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠶⠖⢚⣳⣖⣒⣤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⣋⡉⣉⡉⠒⠢⣄⠀⠀⠀⠠⢾⡛⣧⣟⣾⣽⣿⣆
⠀⠀⢿⣶⣦⣶⣿⣿⣿⡿⠟⠛⠲⢄⠀⠀⠀⠀⢮⠁⠂⢗⢺⣓⢋⡴⠇⠀⠂⣧⠀⠀⠻⣄⠩⠓⠚⠟⠳⣋⣩⡆
⠀⠀⢠⡐⢺⣿⣿⣿⢿⡲⣄⠀⠀⠀⠙⢄⠀⠀⢿⣷⣥⣀⣀⣀⣄⣨⣤⣶⣋⣹⠀⠀⣧⣼⣿⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠁⠻⣿⣿⣿⠐⠈⠳⣵⣄⠀⢀⡤⠟⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠐⠪⠤⠬⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠙⠿⠿⣿⣿⠿⠿⠛⠁

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣾⠟⠉⠻⣷⡀⠀⣿⡇⠀⠀⠀⣸⡇⠀⢠⣾⠟⠉⠻⣷⡀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⡏⠀⠀⠀⠹⣷⠀⣿⣿⠀⠀⠀⣿⠀⢠⣿⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⠀⢻⣿⠀⠀⠀⣿⠀⣼⣿⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⠀⢸⣿⡆⠀⢸⡇⠀⣿⣿⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢿⣧⠀⠀⠀⢰⡏⠀⠀⣿⣇⠀⣼⠇⠀⢸⣿⡖⠋⢡⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣄⠀⣀⠘⢿⣦⣀⣴⠟⠀⠀⠀⠘⣿⣤⡿⠀⠀⠀⢻⣷⣄⣼⠇
⠀⠀⠀⠀⢀⣉⠀⠀⠀⢀⣀⠀⣀⢈⣉⣉⠉⣀⠀⣉⡉⠁⠀⠀⣀⣀⣀⡈⢉⣀⡀⠀⠀⠀⠈⠉⣁
⠀⠀⠀⠀⢯⠈⠣⣀⠀⠈⣿⣠⣿⣾⡟⣿⣦⣿⠀⣿⡇⠀⠀⠀⠉⣿⡟⢱⣿⠻⣷⠀⠀⠀⣠⠞⢉⡇
⠀⠀⢠⠤⠬⣗⡶⠬⠷⠦⢹⣿⡇⣿⡇⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⠀⠶⠯⠵⣖⡯⠤⢤
⠀⠀⠈⠓⠒⣫⠽⢒⡻⠛⠈⣿⠀⣿⡇⣿⡿⣿⠀⣿⡇⠀⠀⠀⠀⣿⡇⢸⣿⢀⣿⠀⠻⣗⠲⢭⡓⠒⠋
⠀⠀⠀⠀⠀⠧⠤⠊⠀⠀⠀⣿⠀⠻⣷⡿⠃⢿⣷⡿⠀⠀⠀⠀⠀⣿⡇⠈⢿⣾⠟⠀⠀⠈⠳⠤⠇
⠀⠀⠀⢠⣤⣤⣤⣤⣤⡀⢠⣤⡄⢠⣤⣤⣤⣤⣄⠀⢀⣤⣴⣦⣤⡀⢠⣤⣤⣤⣤⣤⠀⢀⣤⣶⣶⣤⣄
⠀⠀⠀⢸⣿⡏⠉⢹⣿⡷⢸⣿⡇⢸⣿⣏⣉⣉⡉⢀⣾⣿⠛⠙⠿⠟⢸⣿⣏⣉⣉⡉⠀⣾⣿⣏⣉⣛⠋
⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⢸⣿⡇⢸⣿⡟⠛⠛⠃⠸⣿⣧⠀⠀⢀⡀⢸⣿⡟⠛⠛⠃⠀⢈⡛⠿⠿⣿⣷
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⢸⣿⣷⣶⣶⣷⠀⠻⣿⣷⣾⣿⠟⢸⣿⣿⣶⣶⣿⠀⢿⣿⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣄⣠⡄⠈⠁
⠀⠀⠀⠾⠷⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠘⣿⣿⠃⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠓⢦⡟⠀⣸⠃
⠀⠀⠀⠀⠀⣠⣞⡱⠶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣤⠤⠖⢺⡥⣤⡿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⣄⣤⠴⠛⠉⢹⡄
⠀⠀⠀⣴⢷⣀⣈⣇⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⣰⣞⣙⣦⣭⣹⠛⡆⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⡤⠤⣄⡀⠈⣇
⠀⠀⠾⠷⡞⠁⠀⠙⢷⣄⡀⠀⠀⠉⠙⠓⡞⡇⠀⠀⠀⡿⠿⣾⣽⣉⣈⣹⡾⠁⠀⢻⡀⠀⠀⠀⠀⠀⠈⢳⡄⢰⠃⠀⠀⠀⢳⠀⠈⠙⢦
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠳⠶⢶⣶⡚⢙⠃⠀⠀⠀⢹⡄⠀⠠⠈⢁⡟⠠⠀⠀⠈⣧⠀⠀⠀⠀⢀⡴⠋⠀⠸⣆⠀⠀⢀⡼⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⢀⡿⢹⠃⠀⠀⠀⠀⢳⡄⠀⢠⠞⠀⠀⢠⠀⠀⠸⡄⠀⠀⠀⣾⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠙⠾⠀⠀⠀⠀⠀⠀⠙⢦⠏⠀⠀⠀⠀⠀⠈⠀⢳⡀⠀⠀⠙⢦⣤⣤⠴⠚⠛⠛⠛⠲⠦⢤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⠀⠀⠄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠁⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢰⣛⣧⠀⠀⠙⠲⠶⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⡴⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣆⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⡉⣷⣿⣉⣷⡴⢧⣠⣄
⠀⠀⠀⠀⣀⣀⣀⣀⣸⣷⣇⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣤⣾⣤⣽⣦⡄⠀⢸⡇⣞⠀⠀⠀⢀⣴⡿⠂⠀⠀⡤⣤⣽⡁⣠⢿⠇⣷⡀⠳⡟
⠀⠀⠀⢾⣭⠭⠥⠤⠤⠤⠤⠤⠴⢦⡼⠇⠀⠀⠀⠀⢀⡷⠶⠶⠶⠶⣇⡀⠀⣷⠘⢰⠛⠓⢿⡏⠀⠀⠀⠀⠓⠒⣦⡉⠳⣼⢠⡏⢳⡀⠹⣄
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢹⠀⣩⠶⢾⣷⣄⣸⠇⠀⠀⠀⠀⠐⣶⠷⠷⣤⣼⣿⡤⠿⠗⠚⡿
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣀⣧⡀⠀⣹⠊⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡏⠉⠝⣯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⢛⠲⣿⡾⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣘⣆⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⠋⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⣠⢖⣶⣒⡦⠴⢦⡤⢦⡄⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⡴⠛⠉⠁⠈⠉⠳⢼⡛⣻⠿⣟⠲⣄⠀⠀⠀⠀⠀⢀⡴⠛⣍⠀⣀⠓⢍⡙⠲⣄⠀⠀⠀⠀⠀⠀⠰⣟⡛⠲⠦⣾⡁⠀⠀⠈⠙⢦⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠐⠃⠀⡀⠹⣍⠳⡿⢲⡌⣧⠀⠀⠀⠀⡏⠰⠂⠈⠀⠉⣀⠈⠡⡴⠎⣧⠀⠀⠀⠀⠀⢸⡏⠛⡆⠀⠠⠉⠛⢧⣀⣠⠀⠙⣆
⠀⠀⠀⠘⢦⡉⠀⠰⠀⠀⠀⠀⢠⠜⣦⠙⣿⡧⣻⠀⠀⠀⠀⢹⠶⠶⠶⠶⠾⠷⢶⡶⠶⠶⣾⠀⠀⠀⠀⠀⢸⣏⡴⠃⡴⣚⡛⣽⡲⣌⣳⡤⠶⠛
⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠒⠀⠀⠀⠸⣆⣏⣿⡏⠀⠀⠀⠀⢾⡓⠛⣙⣓⣶⣚⣉⣙⣓⣚⣩⠇⠀⠀⠀⠀⢸⣁⠀⢸⡗⣯⣷⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⡈⠀⠀⣿⢩⡟⠀⠀⠀⠀⠀⠈⢿⡉⠉⠉⠉⠙⠻⣍⡉⢁⡽⠀⠀⠀⠀⠀⢸⢉⣷⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⢸⠟⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⠀⢹⠫⡛⣆⠀⠀⠀⠀⠀⢀⠯⠂⠄⠹⠉⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡀⠀⠹⢦⡀⠀⠀⠀⢠⣾⠃⣰⡇⠀⠈⠓⠬⣼⡗⡄⠀⠀⢰⣿⢤⣀⣠⣤⣦⣀⣤⣷⡆
⠀⠀⠀⠀⢰⢫⠇⠀⠀⠁⠀⠀⢣⢹⡀⠀⠀⣸⣿⡀⠁⣇⠀⠀⠀⠀⠀⢿⡇⠀⠀⣾⣟⠌⠀⣀⣀⣃⣀⣀⣷⣃
⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⡆⣧⠀⠰⣽⣷⢳⠀⠈⠑⠒⠦⠤⣤⣘⡟⡆⢰⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⣿⠀⡆⠀⠀⠀⢰⠀⠀⠃⢸⡆⠀⣿⣿⡌⡇⠀⠀⠀⠀⠀⠀⠀⣷⡇⠈⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢸⢻⡀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠸⣿⣽⡇⢧⣀⠀⠀⠀⠀⠀⠀⣧⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠘⣾⡇⠀⠘⠀⠀⠀⠀⢀⠀⢸⡇⠀⣟⡾⡇⠀⠈⠙⠲⠦⢤⣀⣇⣷⡇⠀⠛⢿⣿⡟⠛⣻⣛⣛⣿⡿⠁
⠀⠀⠀⠀⣿⡇⡆⠀⡀⠀⠀⠀⢸⠀⣿⠁⠀⠘⡷⣿⣆⠀⠀⠀⠀⠀⢀⢩⡷⠁⠀⠀⠘⢿⡯⠉⢽⠋⢙⠟
⠀⠀⠀⠀⢟⢧⡀⠀⡇⠀⠀⠀⢸⢀⡇⠀⠀⠀⠳⣿⣿⣦⣀⠀⠀⠀⡈⡼⠁⠀⠀⠀⠀⠀⡖⣰⢩⢙⠉⡇
⠀⠀⠀⠀⠈⠛⠛⠦⡇⠀⢸⠀⢰⠟⠀⠀⠀⠀⠀⠀⠉⠳⣍⠙⢓⡶⠞⠁⠀⠀⠀⠀⠀⢀⡃⠁⠊⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣌⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⣃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠆⠰⠄⠀⠀⠠⠀⠀⠤⠰⠠⠤⠠⠀⠰⠂⠰⠠⠀⠀⠀⠀⠰⠠⠂

⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢰⣿⣦⢩⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤
⠀⠀⠀⣡⣧⢸⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠟⠿⠿⣧
⠀⠀⠀⣯⣍⢈⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡁⠀⠀⠀⢠⡼
⠀⠀⠀⣟⣋⢘⣻⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠧⣗⠺⠿⠿⠆
⠀⠀⠀⣿⠿⠘⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠰⣿⣶
⠀⠀⠀⠛⠃⠠⠾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⣴⣿⢰⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀⠀⠀⣄
⠀⠀⠀⣷⣶⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡇⣀⡀
⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠿⡶⢒⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠰⣾⣿⣿⣿⣿⡇⣀⣶⡤⠸⣿⣿⣿⣿⣿⣟⣽⣯⣽⣿⣿⣿⣿⣿⣿⣭⡽⣿⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣿⣿⣿⣿⠞⠀⠀⠈⠉⠉⠋⠉⠉⠁⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠿⢅⣴⣶⣶⣾⣷⣆⣀⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⠿⠋⣠⣴⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣩⣿⣿⣍⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣦⣭⣤⣮⣬⣦⣴⣿⣽⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⣸⣿⣿⣷⣾⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢁⣠⣴⣿⣿⣿⡟⣡⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠿⠟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠶⢦⠀⠠⠴⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠐⠆⠈⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣭⠁⠀⢀⡀⠄⠀⠀⠀⣰⡟⣸⠃⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⣷⡈⠻⠿⠛⠀⠀⠀⣠⡾⠋⠜⠁⠀⢀⠄⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠋⠁⠀⠙⣿⣧⠀⠀⠀⠀⣠⡾⣛⡴⠂⠀⠀⢠⡞⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠀⠛⢭⡞⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⣿⣿⡿⣄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⢶⣤⠶⠓⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢂⣠⡷⠞⢿⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⣡⢷⡀⠈⣆⠀⠀⠉⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠾⢛⣧⡼⠃⠀⢤⣡⠈⢳⣄⡀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣯⣩⣤⣤⡶⠾⢻⠀⠀⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢄⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⡶⣿⣥⡀⢀⣠⣦⣽⣿⣇⠰⢮⡁⣦⠀⡀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠶⠶⠶⠶⠶⠶⠶⠶⠆⠐⠾⠾⠿⠿⠿⠷⠿⠿⠿⠿⠿⠛⠟⠺⠟⠛⠒⠂⢘⣿⣿⣿⣿⣿⣧⣠⣤⣤⣤⣤⣤⣤⣤⡤⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣮⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠠⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠆⠰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠐⠉⠀⠈⠋⡀
⠀⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠁⠁⠒⠦⠴⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠐⢿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⣤⢬⣉⡅⡉⠽⠉⠿⠯⠶⠷⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠽⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢄⠀⠁⡀⢠
⠀⠀⠀⠐⢪⣷⣻⠯⡑⠀⠳⠟⣓⡃⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠹⠧⠃⡁⠤⠚⡤
⠀⠀⠀⠀⢸⡋⠚⠧⢵⠒⢲⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⣒⠙⠉⣀⢐⠸⡆⣀⡚⡀
⠀⠀⠀⠀⠀⣷⠋⠠⢈⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡟⠻⡶⢄⠻⣯⠑⣾⡟⢘⡟⣾
⠀⠀⠀⠀⠀⠘⣆⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢛⢯⠟⣾⣠⣿⣯⣽⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠚⠾⠉⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⣠⡄⠀⠀⠀⣠⠶⡆⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡤⢦⠀⠀⠀⢀⣼⠃⠀⣰⠋⡿⠀⡟⠀⢀⡼⠁⢸⠇⠀⢀⣾⠃⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣶⠀⠀⢀⡴⠋⣍⡴⠋⠀⡼⠀⠀⢠⢾⠋⠀⣰⠁⠸⡇⢠⠃⣠⠟⠀⢀⡟⠀⣰⢋⠟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣁⡴⠋⠀⣠⠞⠁⢰⡟⠀⠀⢰⠃⢀⡴⠃⡞⣠⠾⡇⠀⢀⡽⠛⠛⠁⠀⠀⠸⠦⠞⢁⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⢀⡴⠃⠀⢠⡟⠀⠀⠀⣇⣠⠞⠀⣸⠖⠁⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣠⠴⠋⠀⠀⠀⠛⠀⠀⠀⠀⠉⠀⣠⣾⠃⠀⠀⣠⠋⡹⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡏⠀⠀⢰⠏⡰⠃⠀⠀⠀⠀⠀⠀⡞⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢠⠟⠀⠀⢀⢏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠎⠀⠀⠀⣼⠏⢀⠀⠀⠀⠀⢀⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠤⠦⠀⠀⣼⣡⠞⠉⡳⠀⠀⣠⠏⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢠⣾⡿⠁⠀⣠⠃⠀⣠⡿⠊⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⡰⢃⡞⠀⠀⢠⡏⢀⡜⢫⡀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠞⠁⣼⠁⠀⠀⠘⠗⠋⠀⠀⠉⠉⠀⠀⠀⢠⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡏⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠇⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⡜⠀⠀⠀⠀⣾⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⠃⠀⠀⠐⠋⠀⠀⡾⠀⠀⠀⣀⣰⣁⣠⠀⠀⣸⠟⠀⠀⢠⠖⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⢠⠀⠀⠴⣾⠟⠛⠃⠀⣹⠏⠉⠀⠀⣰⠏⠀⠀⢠⣃⡴⠋⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣴⠏⠀⠀⣴⠏⠀⠀⢀⡴⠻⠀⠀⢀⡼⡟⠀⢀⣰⡏⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢠⠞⡏⠀⢠⠞⢸⠀⠀⣠⠎⢠⡇⠀⣰⠏⠀⣇⣠⠞⠁⠷⠤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡴⠋⢸⢀⡴⠋⠀⠸⣤⠞⠁⠀⠀⠓⠊⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠚⠀⠀⠘⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡞⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢰⣧⠎⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⣀⣤⣤⠀⠀⠀⢀⡴⠊⢉⡟⠀⠀⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⡿⢃⣠⡄⠀⠀⠀⢀⡶⠀⠀⢀⡾⠉⣇⡴⠋⠀⡞⠀⠀⣰⠋⠀⢀⡾⠁⢀⡾⠁⢸⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠷⠒⠃⠀⢠⣞⡴⠋⠀⡇⠀⠀⣠⡿⠁⠀⣠⠋⠀⣼⠏⠀⠀⡼⠁⢀⣾⠃⠀⢀⣾⢃⣴⠋⠀⢀⣼⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⡰⢻⠟⠀⠀⣸⠁⢀⡴⢹⠁⢀⡼⠁⠀⣰⠏⠀⠀⢸⣇⡴⠋⠳⣤⠴⣫⠟⠁⠈⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⢠⠞⢡⠏⠀⠀⢰⡇⡠⠏⠀⢯⡴⠋⠀⠀⠀⠋⠀⠀⠀⠀⠉⠀⠀⢀⡴⢊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡴⠋⠀⠟⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠙⠛⠁⠀⠀⠈⠷⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠀⠀⠀⠀⠀⢾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⠶⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠒⠛⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠾⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣤⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣉⣻⣩⣽⣛⣟⢩⣽⡟⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⠳⢶⣄⠐⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢛⣩⣽⡿⠷⣿⠿⢿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢁⣴⠟⠉⠀⠀⠀⠈⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⣰⡟⠁⠀⠀⠀⣠⣤⣤⠀⠀⠀⠶⠳⢶⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⢰⡟⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠛⡉⢢⡜⠋⡿⠙⠟⣿⠛⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇⠀⠀⠠⣏⠲⢀⡁⠤⠀⠉⣠⡴⠟⣡⡽⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣇⡀⠀⠀⠀⣀⣴⡿⠃⠀⢸⡟⠀⠀⣰⠛⢶⠤⠴⠶⠚⢫⣥⣴⣶⡿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⡄⢻⣇⠀⠀⠀⠀⠾⠋⠀⣿⠛⠛⢛⣿⠋⠀⠀⠀⣼⡇⠀⠀⠈⢻⣻⠶⠳⠟⣲⣾⠵⠞⢋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢁⣸⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⣠⣾⡛⣿⣷⣦⣀⠀⠉⢿⣍⣉⣩⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡏⢹⣏⣀⣀⠀⠀⠀⠈⠻⣶⣤⣀⡀⠀⠀⠀⢀⣀⣠⣴⣾⣯⣉⣷⡘⣿⡟⢿⣷⣦⣾⠏
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠈⢧⣼⠋⠉⠉⣻⡄⠀⠀⣠⣿⡏⠉⠛⠛⠛⢿⠛⢉⡵⠛⠓⢤⡏⠉⠁⠘⣿⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⣤⣤⣤⣤⡤⠶⣾⡿⠀⠀⣴⡿⢻⡇⠀⠀⠀⠀⠘⠟⠉⠀⠀⣠⠏⢷⡀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠛⠛⠛⠉⢹⡇⢀⣼⠟⠁⣿⠃⠀⠀⠀⠀⢀⣀⣤⠴⠚⠁⢀⡾⠁⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡦⠀⠀⠀⠀⠀⢸⡷⠟⠋⠀⢰⡟⠀⠀⢠⠶⠛⠉⠁⠀⣀⡤⠚⠁⠀⣀⣀⣤⣄⣀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡖⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠁⠀⠀⡾⠀⠀⠀⢠⠞⠁⠀⠀⠀⠛⠉⠀⠀⠀⠈⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⣠⡾⠀⠀⠀⣼⠇⠀⠀⣸⡥⠶⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⣴⢿⣿
⢰⠖⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣄⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣿⣷⣄⠀⠀⠀⢸⢧⡿⢹
⢸⣇⣄⣀⡀⣀⠀⡀⠀⠀⢀⠀⡀⣼⢿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⠋⠈⢻⡀⠀⠀⣾⣼⠁⣼
⠘⢋⡟⠉⠛⠛⠿⠛⠞⠳⠟⠿⠻⠏⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⢸⣿⣶⣄⣿⣿⢰⠏
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠘⣿⡇⠀⠀⡿⠀⠀⠙⠻⡿⠋
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⢻⡇⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⢿⣷⣶⣿⣷⠀⣸⠃
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⠘⣷⠀⠀⠀⠉⠻⢶⣦⣤⣀⣀⣀⣀⣀⡀⠀⢈⡋⢁⣀⣀⣀⣀⣀⣤⣤⣶⠾⠟⠋⠈⠙⢿⣶⠏
⠿⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠐⠇⠐⠉⢓⣹⠆⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠈⠁⠀⠄⠀⡀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠐⠀⢀⠐⠂⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠴⠁⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠀⠀⣎⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠰⠃⠀⠤⢖⠀⢀⠀⠀⠒⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠐⠁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⢢⠀⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣽⣽⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣽⣿⣯⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⢂⣀
⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⣠⣤⣤⣈⠁⠻⢟⣀
⣸⡿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠛
⣿⡇⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠙⢿⣦⣴⣾⠿⣿⡇⣼⡿⠀⣀⡀⣾⡟⢻⣿⡿⣿⡆⣾⡟⢿⣿⠛⣿⡆⣿⡏⠀⢀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⠁⠀⢀⣿⠁⣿⡇⢀⣿⡇⠻⡧⠀⠻⠃⠸⠇⠙⠃⠘⠋⠀⠙⠃⠙⠿⢶⣿⡿⠀⠀⢸⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⣤⣤⣤⣾⠟⠀⠘⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢾⠿⠋
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢇⣴⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⠉⠉⠉⠉⣉⣉⡉⠉⠉⠉⠉⣿⠉⠉⠉⠉⢉⣉⣉⠉⠉⠉⠉⢹⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢰⡁⠀⣹⠀⠀⠀⠀⣿⠀⠀⠀⠀⣎⠀⢈⡇⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⣰⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⢀⡤⠽⠿⠥⣄⠀⠀⠀⣿⠀⠀⠀⣠⠬⠿⠯⢤⡀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢠⠧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣇⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣸⠇⣸⠤⠤⢤⣀⡟⣲⠁⠀⢀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣇⣸⡇⠀⠀⠀⠀⡤⠤⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⢸⣏⡀⠀⠀⠀⣈⣿⣃⣴⠚⣧⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⣧⡏⢉⠑⢄⠀⠀⠸⣄⢀⡼⠀⠀⠀⠀⣿⠀⠀⠀⠀⢯⡀⢀⡇⠀⣠⠞⠉⠉⠉⠑⢶⠋⠉⠉⠙⢶⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣷⡋⠤⠀⠠⠈⣷⠤⣶⣾⡛⠒⠦⠀⠀⠀⣿⠀⠀⠀⡠⠖⠛⠓⠢⣄⡧⣤⣀⣀⡀⠀⢘⣆⣀⣀⣠⡤⡇
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀⢀⠀⢹⣦⠤⠤⠤⠤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠴⣇⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣼⠉⠙⠛⠦⠔⠳⠤⠖⠦⠴⠓⠒⠋⠉⠁⠈⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠘⢤⣀⡠⠴⠲⢄⠀⠀⠀⣠⠤⣄⣀⣀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⣀⣠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠑⠒⠊⠁⠀⠀⠉⢉⡿⠴⠶⠶⠴⠶⠶⠶⠶⠶⠶⠦⠦⠦⠤⠤⠤⠤⠦⠴⢼⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⣤⣤⣀⣀⣤⣤⠤⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇⠀⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠲⠦⠤⠤⠴⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣠⠴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⣼⠏⠀⠀⠀⣀⣠⣀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⣠⣞⡋⠀⠀⢀⣾⣿⠁⣸⠇⣴⣿⣋⣰⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠙⣿⣧⠀⣼⣿⠉⠉⠁⣰⣿⠏⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢠⠴⠖⢲⣾⡿⠴⠻⣿⣀⡠⠜⠉⠿⣦⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⢿⣯
⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢲⣆⠀⠀⠀⠸⣿⠀⠙⠷⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣺⡭⣺⣏⣛⣻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣼⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⢍⡭⠴⣯⣍⣉⣻⡎⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣠⣾⡿⠋⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠹⣬⡭⠟⠳⠦⠇
⠀⠀⠀⠀⠀⠀⣼⣿⣷⣞⠋⠁⠀⢠⣍⠁⠀⢠⣄⠀⠀⣀⣄⠀⠀⢀⣤⣄⢀⣿⣿⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⢠⣿⡿⠈⣿⣿⡄⠀⣸⣿⠀⠀⣼⣿⣠⠎⣹⣿⠀⢠⣿⡟⠛⣺⣿⡏⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⢀⠅⠐⠂⠈
⠀⠀⠀⠀⠀⢸⣿⠇⠀⣿⣿⡇⠀⣿⣏⣠⠞⣿⡿⠁⢰⣿⡇⠀⣸⣿⡀⣀⣿⣿⠁⢀⡆⡠⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠸⣿⣇⣠⠈⠉⠀⠀⠉⠁⠀⠈⠻⠦⠞⠁⠈⠉⠁⠹⢿⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠔⠃⠈⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠐⠁⠀⠁⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠑⠤⢀⣀⡤⠤⠄⠠⠤⢄⡀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠘⠀⠀⠀⠣⡀⠠⡀⠀⠀⠀⡂
⠀⠀⢠⠂⠀⠀⠀⠐⠀⠀⢎⠀⠤⠐⠁⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠢⡤⠔⠊⠀⠀⠒⠒⠁⠀⠈⠒⠀⠰⠀⠀⠀⡀⢀
⠀⠀⠈⠦⣀⠠⠐⠢⡀⠀⠈⢄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠔⠒⠒⠲⢄⠀⠀⠀⠀⠠⢁⠀⠀⠘⡉⠁
⠀⠀⠀⠀⠠⠤⠤⠊⠈⠢⠀⢀⠴⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠵⣀⠀⠀⠀⠀⠈⠢⡀⠈⠒⠒⠆
⠀⠀⠀⠀⢠⠀⠀⠀⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢡⠀⠀⢀
⠀⠀⠀⠐⢡⠔⠁⠀⠀⠀⢀⣀⡀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡣
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡅⠤⡀⡘
⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣀⡠⠤⢄⠀⢀⡞⠉⠱⡄⡴⠋⠀⠉⢦⡴⠋⠉⢦⣠⠖⠛⠲⡄⢀⡠⢄⠀⠀⠀⠀⠀⠁⠀⠘⡆
⠀⠀⠀⢹⡀⠀⠀⢀⡞⠉⠉⢳⠀⠈⡇⢸⣧⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠙⠉⠀⠀⣷⠚⠓⣄⠀⠀⣀⣀⡴⠤⣄
⠀⠀⠀⡠⠓⠒⠦⠾⠁⠀⠀⣎⠀⠀⢸⠘⣿⡄⠀⢸⡀⠀⢠⡄⠀⢀⡄⠀⠈⡇⠀⢀⠀⠀⠀⠀⠀⣿⡄⠀⠘⠒⠋⠉⢹⠀⠀⣸
⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠈⠧⡽⠇⠀⢸⠇⠀⢸⣿⣶⣾⡇⠀⢀⡇⠀⣿⣦⣤⡟⠀⠀⣿⣿⠀⠀⢀⣤⣶⠋⠀⣰⠃
⠀⠀⠻⣿⣷⣶⣤⡀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⣼⣦⣀⡼⠉⠀⢿⣷⣤⣾⣄⡴⠋⠁⣿⡇⠀⣰⣿⠇⠀⢠⠏⢸⣿⣀⡔⠁
⠀⠀⠀⠀⠹⡙⢻⣿⡄⠀⠀⠹⡝⢿⣷⣤⣤⣴⠞⠉⠛⠋⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠛⠟⠋⠙⣿⣦⣠⠞⢠⣼⠛⢧⡇
⠀⠀⠀⠀⠀⠏⠂⢿⣷⡀⠀⣠⠇⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠿⢖⡿
⠀⠀⠀⠠⠊⠀⠀⡎⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠋⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠸⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⢀⠀⢀⡠⠃⠉⡠⠤⠤⢀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡉⠁⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠂⠀⠀⠀⠀⣀⠜⢄⠁⠀⠠⠁
⠀⠀⠀⠐⠉⣠⠤⠅⠴⠊⠀⢀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠠⠤⠤⠤⠔⠚⠁⢀⠄⢇⠀⠀⠈⠒⠁⠀⠉⡆
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠎⠀⠠⠀⠈⣑⠲⠂⠀⠒⠂⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠈⠀⠐⠐⠊⠀⠀⠀⠃
⠀⠀⠀⠱⣄⡀⠀⠀⠀⠑⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠐⠢⡀⠈⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠙⠒⠒⠐⢄⣀⡠
⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⡇⠀⠀⣀⣠⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢁⡾⠁⢠⣾⡿⠟⠋⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣷⠟⠁⠀⠘⠟⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⡀⠀⢸⣿⣇⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⠁⠀⣴⠶⣶⣿⠆⠀⣴⣷⠀⢀⣾⣧⡾⢿⣿⡆⢸⣿⡏⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⣰⣿⣿⠀⢀⡿⢰⣿⡿⠀⣴⣿⡟⢀⣼⣿⡟⢀⣿⣿⠁⣿⣿⣿⡿⢿⡏⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣴⠟⠹⣿⣀⡼⠃⠘⢿⣷⡾⠋⢿⣷⡾⠛⠿⠃⢸⣿⣇⣼⠟⣿⡇⠀⠸⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠙⠃⠀⠀⠀⠁⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠀⠀⣀⠀⢴⣶⣶⠆⠀⠲⣿⠟⠂⠀⢿⣿⡟⠀⠰⣿⠟⠀⢠⣶⠶⠿⠿⠿⠟⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢰⣿⡇⠀⣾⠇⠀⠀⠀⣿⠀⠀⠀⢸⡿⣷⡀⠀⣿⠀⠀⢸⣿⠀⠀⣀⣠⣦⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣾⠏⣿⢀⣿⠀⠀⠀⢀⣿⠀⠀⠀⢸⡇⠹⣧⢰⣿⠀⠀⢸⣿⠛⠛⠛⠛⠿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢹⣿⡟⠀⠀⠀⢸⣿⡀⠀⠀⣿⡇⠀⢹⣿⡟⠀⠀⠸⣿⣀⣀⣀⣀⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⠇⠀⠰⠿⠇⠀⠀⠘⠛⠛⠋⠀⠰⠿⠟⠀⠘⠿⠟⠃⠀⠀⠛⠋⠉⠉⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣾⠟⣷⠀⠀⠀⠀⠀⣀⣤⡶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⢶⣤⠀⠀⠀⢀⣾⣿⣃⡴⠋⢠⣶⣿⢿⡷⢀⣶⡿⢛⣿⠀⣸⣿⣯⠾⠃⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣭⣤⣤⣿⣿⠿⠛⠁⣾⣿⠓⠛⠁⣠⣿⣿⠃⠀⠀⣀⣤⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⠀⠀⣠⠾⠋⠁⣿⣿⠻⡇⠀⠈⢿⣇⣀⣠⡞⢻⣿⣀⣀⡼⠋⢻⣿⣇⣤⠾⠋⠁⠀⠀⠀⣤⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⢿⣿⠀⣷⠀⠀⠀⠉⠉⠁⠀⠀⠉⠛⠉⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⠸⣿⣠⡏⣠⣤⣤⣴⡆⢠⣶⡶⠄⢠⣦⠀⠀⢶⡶⠀⣴⠶⢾⡇⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠀⣿⠀⠀⠈⠁⠀⢸⡇⠀⢠⡿⣧⠀⢸⡇⠀⣿⣤⣴⡄⠀⠀⠈⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠄⠀⠀⢠⣤⣤⣿⣶⠶⣾⡇⠀⢸⡇⠀⢸⡇⠸⣧⢸⡇⢠⡿⠀⠉⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⠀⣠⣼⣧⣄⢸⣧⠀⠹⣿⠁⢸⣧⣤⣶⠀⠀⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢰⠀⡄
⠀⠀⠀⠀⢀⠀⠘⠉⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠁⠀⠀⠀⠀⠂⠐⠀⠈⡄⠀⠄
⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠤⡆⠀⠈⠀⡀⠀⠀⠀⢀⠐⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠄
⠀⠀⠀⠀⠀⠑⠊⠀⠁⠈⠀⠀⠀⠚⠀⠔⠀⢀⠀⠀⠀⠀⠀⠀⠘⠐⠠⠀⠁⠀⠀⠀⠀⠀⠀⠊⡩⠁
⠀⠀⠀⠀⠀⠀⠆⢀⠈⠑⡂⢸⠀⠉⢀⡁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢉⡅⢸⠘⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⡇⠈⣃⠀⠀⡠⠔⣻⠃⠀⠀⠀⠀⡀⠄⢀⠄⣀⠤⠤⠦
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞⠁⢀⡠⠤⠖⠛⠁⠐⠉⠂⠀⡀⢀⠉⠃
⠀⢀⠔⠁⣀⠀⠉⠁⠀⠀⠀⠀⢀⠀⠑⠁⠀⠀⠈⠀⢀⠀⠀⠀⠄⢚⠈⠁⢹⡋⠉⠃⠀⠀⠀⠠
⠔⠁⠀⡴⠁⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣼⠟⣦⣄⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠐⠈⠀⠀⠀⠀⠀⢰⠁⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠏⠀⠀⠻⠂⣀⠠⢐⡡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢒⣒⡫⠭⠒⠊⠁⠀⠐⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠠⠔⠚⠉⠀⠀⠀⠀⠀⢀⢈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚
⠀⠀⠀⡠⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⠓⠀⠀⠀⠀⠀⡄
⠀⠀⢸⠀⠀⠀⠀⠂⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⠛⠛⠃⠀⠀⡀⠀⠀⠀⢀⣎⡤⢀⡀
⢠⠑⠸⠀⠀⠀⠠⠂⢘⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠤⠐
⠈⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⣇⣴⡲⢃⣐⣸⠂⡀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠄⠀⠀⠀⢀⠃⠀⠀⠀⠀⠠⡞⣿⠊⢉⡏⠀⠀⡄⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⡰⠀⠇⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠡⠚⠏⠿⣛⣀⢀⣀⠤⡤⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠘⠒⠖⢂⡙⠁⠀⠀⠠⠂⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠠
⠀⠀⠀⠁⠀⢀⡐⠾⠃⠀⠀⠀⠀⠠⠌⠁⣀⣀⣉⣁⣀⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠂⠀⠤⠀⢀