Celebrating Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⣙
⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢧⣤⠆⠀⠀⠀⠀⠀⠀⠀⠲⠀⠋⠱⠂⣤⣤⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡰⠋⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠔⠀⠒⠀⠀⢀⠀⠂⠈⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠩⠭⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⣄
⠀⢀⣀⠀⠀⠀⠀⠰⠪⣺⠀⠀⠀⠀⠀⠀⠈⠒⠒⢸⣧⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠰⠂
⠀⢈⣷⡀⠀⢀⣊⡐⠥⢀⢱⠁⡨⠀⠀⠀⠀⠀⠀⢸⡟⡀⠈⠢⡄⠠⠔⢁⡀
⠀⠀⢨⡇⠀⠀⠀⠈⠐⢧⡶⠋⠦⡀⠀⠀⠀⠀⠂⣸⡇⠈⠢⠀⠀⠀⠎⠉⠪⣕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠘⠢⡆⠀⠀⠀⠀⠀⣿⡁⡀⠀⠀⠀⠀⢱⣉⣄⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢄⣑⣠⠫⡤⡀⠀⠀⠀⣁⠋⠆⠀⠀⠀⢘⠀⣈⠤⢳⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠲⠇
⠀⣜⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠑⠃⠀⠀⠀⠀⡐⠀⠀⢀⠄⡾⢄⢘⡖⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠉⠉⠀⠀⢀⡄⡸⠳⡆⠀⠀⠀⠸⡧⡀⡶⡼⠀⠀⢀⠤⡶⠑⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⢔⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⡌⢀⡨⣿⡿⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠙⠒⠉⡁⡿⢶⡈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠖⠤⣤⠚⣴⠏⢉⣿⡆⣡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡩⣚⠓⠀⠀⠀⠀⠈⡳⠏⠀⠈⢩
⠀⠀⠀⠀⠀⢀⠤⣎⠕⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠐⠁
⠀⠀⠀⢀⠔⠁⡠⠇⠢⢀⠀⠀⠀⢀⣠⠜⠉⠚⠀⢀⠂
⠀⠀⠀⠘⠐⠊⠀⠀⠀⠀⠐⠂⠉⢀⠊⠀⠀⠀⠀⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠉⠐⠫⠥⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⢠⡄⠀⠚⡉⡦⠀⠀⠀⠀⠀⠠⠂⠠⠂⠄⡐⡃⠘⠀⠂⠀⣸⠀⢠⠀⡄⣀⠇⡄
⠀⠀⠀⠀⠀⠀⢾⠻⢶⣛⡒⢚⣛⠚⠛⠚⢻⠋⠐⠰⣖⠄⠀⠀⢠⠄⡄⠀⠄⠀⠀⠀⠀⠀⠛⡈⠘⠀⠀⢹⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣋⣟⠐⢛⣘⡟⣌⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⢿⣯⠗⠧⡟⠈⢀⡅⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀
⠀⠀⠀⠀⠀⣰⡳⠀⡌⠃⠀⣾⣦⣿⡴⠀⢌⠱⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠻⣮⠿⢿⣺⠿⣯⡿⠃⢀
⠀⠀⠀⢀⠀⢚⡃⠀⢸⠇⠀⣽⣧⣽⣏⠀⠘⡇⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠾⠹⠦⠈⠁⠀⢸⡀
⠀⠀⢠⡎⢨⡁⢩⣧⡼⣆⢘⠄⠘⢒⠨⣦⡰⢷⢼⣆⡄⠀⠀⠀⠆⠀⡀⡄⠠⡀⠀⠀⠀⠀⠀⠀⠪⠀⠁
⠀⠀⠀⠀⠀⠀⢌⠛⡷⣲⣯⣄⠤⠤⠤⣾⢊⠛⠀⠁⡀⠀⠀⡄⠉⠁⠃⢋⠀⠁⠀⠀⠀⠀⡄⢀⠞⢀⠀⠀⠄⠨
⠀⠀⠀⠀⠀⠀⠀⠁⠿⢥⠗⢺⠛⣻⠛⣳⡒⠦⠥⠀⠀⠀⠸⠇⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⢿⠀⣿⡀⠙⡧⠀⢸⡓
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣧⠈⠀⢯⣧⠐⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣶⠀⠸⣾⣄⠈⠀⠀⠀⠀⠀⠀⡀⢰⠀⢷⠀⠀⠀⢰⠐⢂⠀⡀⠀⡄⢨⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣏⡋⣠⠰⣿⠏⢃⠀⠀⠐⠷⠀⠀⠁⢸⠀⣸⣴⢰⠀⡏⠸⠋⠂⠓⠂⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⠁⠻⣿⣿⣿⢁⣠⠀⠀⠀⠀⠀⠀⠘⠀⠃⠈⠀⢀⠇⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⢹⣤⠘⠿⠉⠻⡆⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠈⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠊⠁⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠒⠢⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠢⣀⠀⠀⡁⠁⠀⠀⠀⢄⠀⠀⠀⠀⠋⠛
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢏⠀⠁⠁⠸⠝⠀⠀⠀⠈⠁⠀⢠⠂⠀⠒⢄⠀⠠
⠀⠀⠀⠀⠉⠒⢤⡤⠆⠁⠀⡠⠊⠀⠀⠀⠑⡤⡀⠀⠀⠀⠀⣚⠐⠀⡠⠏⢠⠄⡸⣝⢷⡀⠑⠄⣀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠑⢄⠀⠀⠀⢈⠦⣼⠤⢤⣤⡐⠽⢀⠜⠁⢸⡸⡐⠌⣧⢫⣷⡰⣹⠘⠙⠉
⠀⡠⠂⠉⠉⠉⠢⣄⠑⠣⣤⡄⢠⠓⢄⡔⢁⣜⠤⠂⢉⣏⡧⠔⠁⠀⠀⠀⠳⡱⣌⡮⠱⠟⡇⠬⠆⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠄⠆⠀⡎⠀⡆⡄⠋⠀⠗⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣁⠀⡰⢃⡤⢄⣆⡤⢣⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠠⠚⡝⠀⠀⠀⠠⡔⠦⢄⣀⣀⣀⣀⣀⠠⠤⢠⠆⠙⠽⢾⡉⠑⢣⠀⢤⣜⡀
⠡⠀⠀⠀⠀⠀⠀⠀⠰⠽⠀⣀⠀⠀⠑⠄⠀⠀⠀⠈⢦⡔⠤⡼⣀⠀⠀⠀⠀⠾⡔⠒⠊⢁⠔⠊⠀⠀⠀⠈⠉
⠀⠑⠢⢄⣀⡠⠐⢀⡄⡀⠑⠊⢰⠑⠄⠀⠐⠃⠀⠀⠀⠉⠂⠤⠌⠂⠒⠀⠀⠀⠈⠲⡊⠁
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢬⡅⢀⠆⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠏⡽⠢⣀⣀⠀⠀⠀⡀⣀⠠⣤⡶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠃⢀⡔⠁⠀⡐⠁⠐⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠄⠏⠀⠀⠀⠁⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛
⠀⠀⠸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⡀⠀⠀⠀⠀⠀⠀⢰⡄⢠⡟⢳
⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢈⡹⠀⠀⠀⠀⠀⠀⠀⠸⠇⠙⠁⠈⠀⠀⠀⠀⠀⠀⠠⠾⠣⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⢀⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⡀⠀⠀⠀⠀⠀⢿⠇⠀⠘⠁
⠀⠀⠀⠀⢸⣶⣶⣶⡇⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⡄
⠀⠀⠀⠀⢸⣿⠉⣿⡇⠀⠀⠀⠀⠘⠿⣿⣷⣦⠸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠁⢈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⢸⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠸⡏⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠘⠁⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⡆⠀⣤⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠨⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠰⡖⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡃⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠀⠈⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢷⡀⣼⡄⢀⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠉
⠀⠠⠀⢀⣧⡀⢨⡏⠀⠈⠙⣾⣶⠋⠀⠈⣇⠀⣬⡄⢠⡏⠀⢹⡀⢠⣧⠀⠀⠀⢸⡄⢠⣯⠄⣼⠀⠀⣸⣤⠀⢀⡄⠠⣄⠀⢠⣶⡄⢠⡇
⠀⠀⣠⢶⣿⡶⠋⠀⠀⠀⢀⣿⣿⠀⠀⠀⠈⢳⣾⡶⠋⠀⠀⠀⠙⣾⣷⡖⠲⣤⠀⠙⠲⣿⣞⠁⠀⣀⣼⣷⡞⠋⠀⠀⠈⠙⣶⣿⡶⠋
⠀⠀⠸⣾⣿⡇⠀⠀⠀⢠⡞⠁⠈⢷⡀⠀⠀⢸⣿⡗⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⠀⠀⢻⠈⣿⣷⠀⠀⠀⠀⢠⣿⣿⣇⠀⠆
⠀⠀⠀⢸⡏⡇⠀⠀⠐⠋⠀⠀⠀⠀⠻⠀⠀⢸⡇⣏⠀⠀⠀⠀⠘⣿⢻⠛⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⠘⣇⠀⠀⠀⠘⣿⣿⠛
⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠇⠀⠀⠀⠀⠀⠿⠹⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠠⠟⠰⠇⠀⠀⠀⠀⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠊⡌
⠀⠀⠀⠀⢰⢾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣨⣯⣤⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⢻⡟⣹⠋⠉⠁⠀⠀⠀⠀⠀⢸⣯⣿⣻⡿⠙⠋⢠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠳⠀⠃⠀⣞⡀
⠀⠀⠀⠀⠀⢘⣧⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣏⠛⣦⠀⠠⠆⠃⠀⠀⠀⠀⠀⠀⠂⠀⢹⡇⠠⠀⣤⣤⣀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⣸⡏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡿⠀⠀⠀⠀⢠⡄⠀⠀⠀⢰⣇⠀⠀⡝⣇⡀⠻⢿⣿⣿⡿⠏⠀⠈⠉
⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⠀⣿⢿⡄⠀⢸⣿⣿⡄⠀⢰⠈⢻⣿⣼⣿⣿⣧⣤⡀⠐⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢻⣶⣶⣩⣭⣴⠇⣭⣳⣼⣿⡿⣽⠏⠿⡿⠇⠀⣠⣴⠿⠋
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⣻⠛⣿⣿⣿⠀⠻⠿⠻⣿⣿⣏⠻⣶⣿⣿⡟⠋⠁
⠀⠀⠀⣿⡷⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣻⣿⣿⠛⣿⣿⣿⣿⢹⣿⢸⣿⣿⣿⣷
⠀⠀⠀⣶⣶⣀⣀⣀⡀⠀⢀⣄⣀⣀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⣿⡗⣿⡷⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⠉⠉⠉⠀⠀⠀⠉⠉⢩⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⡇⣾⡛⣿⡿⣿⡿⢸⣿⠾⢿⣿⢿⣿⠛
⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢸⣿⠙⠃⣿⡇⣿⡇⣿⡇⣿⠀⠀⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⣼⡇⠀⠀⠙⠃⠙⠃⣿⡇⣿⠀⠀⠀⠀⢸⡿⢸⡿
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⣿⠃⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠳⠀⠈⠁⠀⠈⠀⣀⡲⠀⠄⠀⠀⠀⠆⠐⠠⠀⠀⠙
⠀⠀⠀⠀⢰⣿⣿⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⢻⠁⠀⢁⠚⠒⡄⠸⠏
⠀⠀⠀⠀⠀⠙⢫⢣⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠀⠀⠀⢠⠤⣤⡆⡀⠘⠁⢀⡀⠗⠲⠀⠀⢀⠀⠠⠤⠰
⠀⠀⠀⠠⣠⣴⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠾⠃⠀⠀⠀⠈⠀⠀⢈⣤⡵⠖⣶⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⠟⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠀⠈⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⠂⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⣸⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠒⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣀⠄⠈⣁⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⠀⠂⢸⠁⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⢿⣷⠀⠀⠀⠀⢀⠀⠒⠒⠒⠒⠀⠂⠒⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⠁⠀⠠⠼⠃⠀⠂⢀⠀⠄⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠆⠀⣰⣿⡟⠀⠀⢿⡷⠈⠀⠀⠁⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠆⣠⠀⠀⠀⠀⠢⢤
⠀⠀⠀⠀⠀⠈⠱⠀⠈⢻⣷⠀⢀⡾⠃⠀⠀⠀⢠⣶⣿⡃⠀⠀⠀⠘⠆⠀⢀⡃⣤⡴⢦⡀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠐⢃⠀⡀⢈⡇⠈⠉⠈⠀⠀⠄⠀⠘⠿⠿⠟⠀⠀⠐⠀⠀⠀⣤⡶⠟⠁⠀⣰⣾⠿⠷⣦⠈⠒⠂⠀⠨⠁⡄⢈⡁⠀⠀⠀⠀⢠⠀⠂
⠀⠀⠀⠀⣀⣰⠊⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢴⡆⠀⠀⡄⠀⠀⠁⡄⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡌⠁⠀⠠⡄⠀⡀
⠀⠀⣤⣿⠛⠃⠀⠀⠇⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⡘⢣⠀⠁⠠⠀⠀⠀⠐⡈⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠒⠂⠀⠀⠆⠀⠀⠀⠀⠀⠉⠂⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⣠⠀⠀⢀⣠⣴⣶⡦
⠀⠠⠆⠀⠀⠀⠀⠋⠀⠠⠀⠙⢁⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠚⠛⠛⢻⡦⠤⠁⡀
⠀⠚⠂⠀⠀⠀⠄⠀⠀⠀⣀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠐
⠀⠀⠃⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡒⠂
⠀⠀⠀⠀⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠐⠐⠂⠄⠈⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⠄⠒⠀⡠⠂⠐⣇⣠⠄⠢⠀⢀⠠⢀⠐⠀⠖⠰
⠀⢠⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠉⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠
⠀⠀⣤⡄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⠀⠀⠀⠁⠀⠀⠂⠁⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠈⠂⠀⠲⠶⠄⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡊⠀⠀⠀⠀⠀⣀⠠⠏⠀⠀⠀⠀⢠⡄⣀⣀⣀⣀⡀⣀⣀⠀⠀⠀⣴⠁⠀⠀⠀⡆⠠⣤⡤⡀⢀⠁⠃⡏⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠃⠨⠀⠈⠀⠀⠐⠛⠃⠀⢨⠀⠀⠀⠒⢠⡈⠉⠉⠉⠀⠀⠀⢉⠛⢙⠛⡀⠠⡇⠀⠀⠈⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠃⠈⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣥⣬⣥⣤⣤⣼⣦⣴⣾⣵⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢖⠀⠀⠀⠀⢀⠾⠐⠞⠀⠀⠀⢀⣔⠈⠨⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠘⠉⠀⠀⠀⡰⢅⠙⠊⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⠀⠀⠀⠀⠀⠀⣀⠘⢍⠒⠁⠀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠀⠀⠀⠀⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠛⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡴⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠀⠀⠀⠀⠀⠀⠀⢠⠰⣀⠀⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠃⠀⣀⠀⠀⠀⠀⠀⢀⠛⠄⡤⠀⠀⠀⠀⠀⠀⠐⠣⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⠌⢃⠇⠂⠀⠀⠈⠑⡀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠢⡀⠀⢅⢀⡁⠀⠀⢠⡒⡀⢹⠜⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⠀⠈⢄⠀⠀⠈⠲⡄⢆⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⢐⠋⢴⠘⠈⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠁⠌⠀⠀⡠⠂⠀⠑⢄⠀⢄⠶⢆⠀⠀⠀⠠⠁⢈⠀⠀⠀⠀⠶⠅⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠌⠀⠀⡠⠐⠁⠈⠢⣀⠀⠡
⠀⠀⠀⠀⠀⠈⠈⢀⠔⠁⢀⠔⠊⠀⢀⠠⠐⠈⢀⠁⠖⠃
⠀⠀⠀⠀⣠⠀⡠⠂⡠⠐⠀⡀⠄⠂⡁⠄⠂⠈
⠀⠀⠀⣠⢃⢌⠄⢊⠄⡀⠅⠐⠈
⠀⠀⢠⣿⣶⠵⠚⠉
⠀⠀⠉⠁

⣿⣿⣿⣿⣛⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⣿⣟⣛⣛⣟⣻⣿⣛⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⡔⡂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣡⡀⠀⠀⠀⠈⠠⠿⠂⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠤⢄⡀
⠀⠀⠀⠀⠊⠀⡏⡇⠀⡇⢇⠀⠀⠀⠀⢠⢤⣤⡤⡐⡓⡌⢀⢎⢟⠤⠇⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢀⡦⠒⠤⣀⠀⠒⠤
⠀⠀⠀⡀⠀⠀⢠⢧⠠⣃⢹⢀⢪⠛⡌⡇⡇⢇⢘⡸⢣⠡⠡⠃⠀⠁⣍⠇⠀⠀⠈⠏⠠⣲⠀⢸⠹⡀⠄⠀⠀⠀⠀⣁⣀⣀⡠⣤⣀⣄⠀⠈
⠀⠀⠀⠀⠀⠀⢸⢰⠉⠈⡌⡎⠪⠖⠃⠃⡇⡏⠀⠀⠸⠀⠀⠈⠉⠃⠉⠀⠀⠃⠀⠀⠀⠫⣑⣪⡆⣧⢊⡿⢱⢄⢏⡆⡆⡟⢸⢸⠁⠀⠀⠀⡂
⠀⠀⠀⠀⢀⡀⠚⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢰⠒⡄⢸⡏⡠⡀⢔⡒⡔⢲⢹⠀⡤⣀⡀⣠⢣⠋⢾⣤⣲⢆⠓⠭⠲⠟⠘⠚⠀⠀⠀⠀⠐
⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠠⠚⠱⠂⢸⢰⣞⠆⡿⡔⣉⣬⢹⣡⠣⣸⠄⠀⠈⠂⢒⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠈⠰
⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠼⠼⠘⠦⠃⠈⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠛⣏⠀⠀⠺⠦⠒⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠄⠀⠀⠀⠀⠠⠀⣅⠀⠐⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠁⠉⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠌⡐⣁⡠⠤⡄⢀⣾⣧⡆⡗⠚⢻⣧⡀⠑⠄⣀⠀⠫⡀⡸⠀⠀⠀⢅⠄⢀⠀⣔⠙⣄⠀⠀⠦⠀⠶⠈⢫⡉⡍⢠⠴⠒⠒⠲⣤⠀⡋⠉⡇
⠀⠀⢸⣴⠋⣀⣤⣶⣷⣲⢣⠀⣧⠧⡰⢱⢋⠙⣆⠀⠀⠀⢰⣾⣷⠀⠀⠄⠀⠀⠀⣮⣤⣠⣈⣧⡀⠀⢠⣀⣀⠀⢩⣡⣼⣶⣶⣶⣶⣧⠠⠟⠒
⠀⠀⢠⣨⢿⠿⠏⢘⠀⣧⢀⠳⢁⡰⢡⣯⠖⣾⠾⣇⡀⠀⡼⢠⠏⢾⠛⢷⣀⠀⣟⣿⢺⠓⠋⣹⣟⠴⣞⠉⠃⠀⡿⣁⣿⠙⢆⠛⢈⡿⢞⠀⢰
⠀⠀⠰⠘⠛⢦⣀⢚⣠⠟⠉⣢⡔⠱⡘⡇⠀⠈⢉⣼⢃⣴⣗⠜⣴⣦⠠⣸⠋⠓⢿⣟⡶⢥⣴⠛⡧⠒⣧⣀⣀⣴⡣⢏⣹⣦⣭⣴⣞⣵⣽⢬⣻⣤
⠀⠀⠀⠣⠀⠈⠉⠭⠉⠀⣼⣁⣃⠀⠑⠷⣄⣀⣠⣾⠿⡁⣼⠶⣏⢨⡀⣻⣀⡤⠖⡟⠿⢾⠁⡈⠀⣉⢈⡙⢹⢿⠹⣄⢩⣵⣶⣿⡍⣛⣿⠿⣍⢹
⠀⠀⠀⠀⢇⢀⣀⡴⠊⠉⢀⡠⣤⣷⡄⠀⠈⢉⠟⢱⢫⠖⠁⠀⠘⢆⢣⠻⡇⠠⡇⠀⠀⣿⠀⠀⠀⣼⣩⣥⣤⡤⠀⡬⢤⡍⠭⡁⣤⣿⣿⠀⡏⡽
⠀⠀⠀⠀⠀⡟⠻⠪⢿⣿⠛⡿⣉⡟⣧⠐⢂⡏⠀⣇⡼⠻⠶⢲⠶⣶⡗⡄⠻⣄⣂⣠⣔⠛⣶⡀⣠⣷⢿⡿⣿⡷⢺⠁⣾⠀⣼⠀⠉⣸⢗⡜⠀⡇
⠀⠀⠀⠀⡾⠛⡃⠀⠈⢧⡉⠙⢃⣠⠏⠀⡠⡇⠀⢟⣷⠄⢀⡼⠁⣸⢣⠁⠀⣸⠏⢳⣬⣟⠄⠈⣼⢿⣯⣠⣈⣷⠈⣀⠜⣶⣤⣤⡾⠓⠊⠀⢰
⠀⠀⠀⢀⣀⣶⠿⠒⠴⢯⣟⡟⡻⠋⠁⣉⢴⣯⣶⣌⢳⣄⣈⣠⡞⢉⠎⣴⣻⠋⠀⠀⠈⢯⢇⣰⣇⠸⠆⠐⢉⣏⡼⠡⠤⠠⠍⠉⠤⢀⣀⠴⠃
⠀⠀⢀⠈⠉⠑⡄⢀⡴⢿⠝⢓⡦⠀⠘⣲⣿⠫⢝⣷⣹⢏⠛⢁⣄⡘⠀⠻⣿⡻⠋⠙⠛⢻⡄⢨⣝⠷⠶⣶⠯⠌⠤⠤⠤⠤⡆⢻⡆⣀⡇
⠀⠀⣼⠷⢾⠀⠱⣼⠃⠀⠀⢺⡇⢀⠐⣷⠀⠀⠀⣽⠀⢸⢨⡏⣉⡿⠀⠀⠹⣆⣀⣀⣀⡿⠀⢞⢈⠗⠈⠀⠀⠀⠀⢀⣀⠞⠁⠙⠁⠀⢰
⠀⠀⠙⠢⡌⠣⠀⡼⠳⢤⠶⢟⠙⣯⣀⠜⠛⠾⠛⠋⠢⣠⠎⣽⠁⠡⠀⠀⠀⡎⠉⠉⠉⠑⠂⠼⠈⡀⠀⠀⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠠⠤⠤⣶⣶⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⣷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣽⣿⣿⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⠟⠛⠉⠁⠀⣤⣾⣿⣿⣯⡍⢉⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⣬⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣭⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⠁⢹⣿⣿⠇⠀⠀⢀⣤⣴⣶⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀⣘⣿⡏⠀⠀⠀⡿⠟⠛⠉
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⣰⠛⡿⠋⣿⣶⠀⠀⡄⠰⠀⢾⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢿⣤⣈⣀⠀⠱⡶⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⢠⣴⣆⠐⠀⢀⠠⠄
⠀⠈⣿⣿⡇⠀⠤⠀⠀⠀⣠⣤⣶⣤⠀⠀⠀⢀⣾⣿⣏⠀⠀⠀⠀⣦⡹⡆
⠀⣴⣾⣿⣇⠀⠀⠀⠀⠀⠸⣇⠀⠈⣄⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⣍⡻⢷⡄⠰
⠀⠸⣽⣿⣿⣇⢰⠀⠀⠀⠀⠘⣄⠻⣾⣷⣶⣦⣿⣿⡋⠸⡧⠀⠀⢹⣷⣦⣴⠆
⠀⠀⠀⡾⠁⢡⣜⣀⡄⢀⡀⠀⠘⢧⠈⣭⣿⣿⣿⣿⣿⣆⠀⢹⠀⠺⠁⡿⠗⣤
⠀⠀⠸⡆⠀⡴⠉⠁⣠⠞⠁⠀⠀⠈⣇⠸⣿⡻⣿⣿⣿⣿⣧⣾⣧⢰⠄⣇⢺⡄
⠀⠀⠀⠘⠒⡿⠚⠋⠁⣀⣠⣶⣤⣤⣯⣴⡎⢻⡝⢿⣿⣿⣿⣿⡿⠁⠘⣷⣄⡀
⠀⠀⠀⠀⠀⢡⡀⣰⡿⠋⠁⠀⣀⣹⡟⢉⣻⣧⣽⣿⣛⠛⣹⡟⠁⢰⣦⡿⣯⣁
⠀⠀⠀⠀⠀⠀⠣⣘⠀⠀⠐⠀⣹⠟⢠⣾⠿⢋⣹⣾⣧⣠⠏⠀⠀⠀⢛⡷⣿⠸
⠀⠀⠀⠀⠀⠀⠀⡿⠁⠓⠚⠻⠃⣤⣾⠉⣠⡾⣿⣿⣿⡇⠀⠀⠀⠘⣯⣧⡉⡀
⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⢤⡀⠀⠹⣇⠀⣏⡀⢈⣿⠿⣷⠀⠀⠀⠐⣿⠻⠇
⠀⠀⠀⠀⠀⠀⠈⢉⣹⠃⠀⢹⠀⢀⠛⠀⢹⣇⠻⣿⡳⣾⠃⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢦⠍⠀⢺⠁⠀⠀⢹⠐⢿⣵⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠓⠲⠲⢆⣀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠈⠀⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠶⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣠⠀⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⣿⣡⣿⣯⠛⠁⠀⢸⡹⠋⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⡙⢣⣀⣽⣿⣿⡀⢀⣽⣍⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠻⠛⠿⠹⢿⣷⣾⣿⣟⣡⣄⣷⣶⣷⣄⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⢀⡤⢠⢾⠀⠀⠀⠀⢠⡸⠇⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠘⡡⠀⠀⠀⠀⢸⡇⢸⡜⢸⡎⡰⠀⠀⠐⣒⢀⠂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⠰⡈⠀⡀⠀⠣⠜⠣⠚⠓⠉⠉⠁⠀⠠⠈⡠⠃⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⢱⠀⠀⡄⣠⢀⣶⢰⢦⢰⢢⣄⢰⠀⡐⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⠀⡧⡆⣼⣼⢸⠋⢸⠁⢸⠇⡜⠀⠀⠀⠠⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠚⠀⣀⠁⠇⠛⠃⠘⠘⠀⠘⠀⠈⠀⢰⡳⠀⠛⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⡠⣾⠏⠀⢀⡀⢠⣞⠇⠀⣼⠇⡴⡏⣸⠷⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠖⠊⢀⡏⣠⠞⣽⠁⣾⠋⣠⠎⢾⠞⠀⠗⠁⣶⡷⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⢠⠀⠈⠛⠁⠀⠓⠋⢉⠋⠀⣠⡀⠀⣷⣀⡀⠀⠀⠶⣦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⠤⠖⢳⡄⢰⡿⢃⣾⢹⣇⡰⠃⢸⠁⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡷⠛⠶⠋⠉⠀⣉⢀⡀⠸⣤⣠⡴⠋⢠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢖⡄⢀⢾⡇⢀⠞⡶⢹⡎⢸⡇⢹⠀⠀⠀⠀⠘⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠾⠁⠈⢐⡇⣮⠇⡽⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⣀⣀⡾⠀⠟⣴⣿⣯⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⢻⣄⠀⢉⣡⠀⢀⡶⢸⠏⢀⡶⢀⡟⠻⣦
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣶⣿⠇⣼⠟⠛⠛⡇⠀⠚⠁⡄⠀⢨⣴⠿⢃⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣇⢠⣾⣟⣡⡏⣸⠏⢀⣴⣿⣷⣤⣴⣾⣿⣤⣤⣴⣾⣿⣟⣡⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣻⠟⠋⠉⠉⣀⠉⣀⠛⢁⣴⠀⣸⠃⢈⡤⢀⡉⠀⣡⠄⢈⠁⢀⡟⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠀⣿⠀⡟⠀⠰⠃⢰⡏⢠⡿⠃⢨⠁⣼⠟⠀⡍⠀⠞⠀⠘⣉⠀⠉⣿⡄
⠀⠀⠀⠀⣿⠙⠶⠟⠋⠀⣸⡇⠀⢿⣤⣴⣦⡔⠁⣦⣤⣶⠇⢰⣤⣴⣾⣧⣴⠎⣰⣿⠟⠻⢷⣿⠇
⠀⠀⠀⠀⠹⣷⣄⣀⣠⣾⣿⣧⣀⣀⣿⡍⡿⠀⢸⣿⢉⡏⠀⣿⠃⠘⠷⠟⠃⣰⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠙⠛⠛⠋⠘⣷⣤⣿⠇⣿⣄⣰⣿⣆⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠋⠙⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠀⠀⠀⢱⣠⠔⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠙⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣄⠐⢀⡜⠁⠄⠀⢀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⣻⠟⡝⡟⢷⣶⣤⣀⣀⠞⠁⠀⢀⠀⠀⠈⠧⠀⠀⢈⣀⡀⠈⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⢀⡬⠐⠋⠘⠁⠁⠀⠐⠦⠙⢷⣦⣀⠀⠈⠙⠂⠀⡠⠚⠉⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣯⡣⡀⠒⠀⡼⠁⣰⠃⠀⠁⠀⠀⠀⢳⠐⠚
⠀⠀⠀⠀⠀⠀⠐⠟⡴⢡⣇⠛⠀⡀⠀⠀⠀⠐⠂⠀⠈⠀⢀⠀⠛⢸⣻⡷⣵⡀⠀⠱⡀⠹⣄⣀⣀⡤⠀⢠⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠏⠀⠇⠻⠁⠀⠀⣹⢶⠤⢍⡭⠤⠖⠁⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠦⢄⣀⣀⡠⠴⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⣀⠀⢰⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠦⠤⠤⠤⠤⠔⠚⢿⢄⡀⠀⠀⣀⢀⡠⠊⠁⠀⠀⠀⡇⠀⠀⢇
⠀⢠⠊⢉⣚⠉⢹⠄⠀⢀⣀⣠⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠑⣾⡷⠏⠀⠀⠀⠀⠀⠀⣃⣀⠀⠈
⠀⢿⢠⠋⢀⢱⠈⠓⡄⠀⠞⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠁⠀⠀⠀⠀⠀⣀⣴⡉⠵⠮⣗⠒⣄
⠀⣰⠛⢻⠾⠊⡤⠞⠁⠀⠀⠀⠀⠘⠓⠋⢹⡏⠉⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣅⢎⣥⡼⢴⠃
⠀⠈⠋⢉⣓⣚⣆⡴⣦⣀⡠⠤⠤⠒⠒⢃⣸⠇⠉⠉⠁⣇⡀⠉⠙⠓⠒⠒⠦⠤⢄⣀⠉⢱⣌⡹⠯⣀⡼
⠀⠀⠀⠈⠓⣮⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⡀
⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⠔⠋⠄⡰⠀⠀⠀⠂⠠⠀⠀⠂⠱⠘⠀⠶⠂⠋⠇⠃⡇⠱⠀⠀⠰⠂⠁⠀⠀⠴⠀⠆⠀⠸⠉⠱⠋⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⠛⠻⠟⠛⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⡥⠄⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠘⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡐⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡤⢴⠆⠀⠀⠠⠂⠀⠀⡠⠀⠁⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢌⣀⣠⡔⢈⡀⠠⣤⠐⠈⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢹⣧⣼⡷⠀⠀⠀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠐⢻⡀⠀⠀⠀⠙⠈⠁⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠁⠀⢀⠠⠀⠐⠛⠊⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠑⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣽⣷⠇⠀⠀⠀⣷⣿⣫⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡻⠃⠀⠀⠀⠀⠘⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣻⣿⣛⣟

⠀⠀⢠⡤⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⢤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤
⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⢀⣀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⡇⠀⠀⠐⣿⠇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠰⣿
⠀⠀⢸⣄⠀⣼⠏⠀⠀⠀⣼⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣄⢀⣼⠋⠀⠀⠀⣼⣿⣿⣿⣷⣶⣄
⠀⠀⢸⣿⣿⠋⠀⠀⠀⠸⠿⣿⣿⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠸⠿⣿⣿⣿⠿⡿⠟
⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀
⠀⠀⢘⡃⣀⠀⢀⣀⠀⢀⣀⠙⢛⣛⢓⡀⢀⡀⠀⢐⣛⠛⢛⣛⢁⡀⣀⢀⡀⠀⣀⢀⡙⢛⣛⠀⣀⡀⢀⣘⡋
⠀⠀⢸⣷⣿⠀⣿⣿⡇⣿⣽⠇⣿⣽⠏⢻⡟⠀⠀⣿⢻⡇⣿⣯⢸⡏⣿⣿⡇⠀⢹⣿⠁⣿⡯⢸⣏⣿⢸⣿⣿⠂
⠀⠀⠘⠃⠛⠀⠛⠙⠃⠛⠀⠀⠛⠀⠀⠘⠃⠀⠀⠛⠘⠃⠛⠛⠘⠛⠛⠛⠁⠀⠘⠛⠀⠛⠛⠘⠋⠛⠘⠋⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⠠⠁⠑⠒⡢⠀⠀⠒⠒⠒⡆⠀⠀⠒⠒⠒⡆⠀⠀⡐⠉⠉⠉⢃⠀⢀⡀⠤⠀⠀⠠⠄⣀⠠⠄⠒⠒⠒⠠⢤⠄⠒⡀⠀⠀⡠⠤⠄⢀⠀⠀⡀⠺⡄⡴⠄
⠀⠉⢄⠀⠀⠀⡁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡐⠀⠀⣀⠀⠀⠆⠸⠀⠀⠀⣀⠀⠀⠀⠱⡀⢀⡀⣀⠀⠀⠑⠀⠐⡀⡐⠀⠀⢀⠊⠀⠀⢉⡳⢬⠒⠶
⠀⠀⠘⠒⠉⠉⠁⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⡇⡰⠀⠀⠐⠉⠆⠀⠈⡌⠀⠀⠀⠀⠈⡂⠀⠀⡁⢸⡀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠠⠂⠀⠀⠀⠈⠁⠘⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡧⠁⠀⠀⠉⠉⠁⠀⠀⠸⡀⠀⠀⠉⠉⠀⠀⡠⠁⠀⠀⠀⠀⠀⡠⢣⠀⠀⠀⡰⠁⠀⠀⣀⠀⠀⠀⠀⢀⠐
⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⡇⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠄⠐⠘⠀⠀⠀⠄⡄⠂⠈⠀⢈⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠁
⠀⠐⠄⠔⠁⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⣀⣀⢀⡇⠤⠊⢸⠀⠀⠀⠠⠀⠠⡔⠀⢀⡄⠀⠀⠀⣄⠀⢀⠀⡅⠀⠀⠀⢈⡀⠀⢀⡇⠀⠀⠀⡀⠠⢄⡐⣂⢀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠤⡍⠂⢑⠀⠅⠊⠔⠄
⠀⠀⢀⡂⠊⡕⠈⡢⠀⣈⡢⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠰⢄⡀⠀⠀⠀⠀⢀⡀⢰⠀⠀⡀⠀⠀⠀⢀⡠⠧⣀⠀⠀⢀⡠⠤⢀⠀⠀⠠⠉⠄⢨⢩⣄⢓⣊⢘⡔
⠀⠀⡃⠐⡦⠈⢰⠄⣈⠢⡐⠉⠄⠀⠀⠀⠀⠀⠀⠀⠨⢤⠬⠀⠀⠀⠀⢀⢀⡑⡎⡞⣁⠀⠀⠀⠀⠀⠧⡤⠅⠀⠀⠋⡠⠀⠀⢡⠀⠠⠄⡀⢊⠤⢄⠪⠀⠑⠐
⠀⡨⠉⠴⠈⠃⠰⠆⢈⡀⠤⡀⢂⠀⠀⠀⢈⡰⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠔⠁⢆⠈⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⢂⠀⠒⢁⠜⠀⠀⠰⠔⢃⠀⡌⠄⣂⠈
⠀⠑⡂⡌⠂⡉⠀⠦⠈⠰⠡⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠰⣀⠁⠸⡈⠙⢀⣐⠊⠀⠊⠀⠀⠢⡀⠀⠀⠏⠉⠀⠱⠄⠀⠀⠀⠀⠀⠲⠄⠀⠲⠀⠀⠀⠄⠐⠣⡀⠀⠀⠐⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠊⠑⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠇⠀⠀⠀⠀⠀⡀⣀⠀⢀⢀⠀⠀⠀⠃⠀⡘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠋⠉⠀⠘⠄⡀
⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠘⠂⠂⠐⠀⡆⠀⠀⠀⠀⣠⠁⠀⠀⠀⠠⢀⠃⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⣀⡀⠠⠈⠁
⠀⠀⠀⠀⡀⢀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⠐⠀⠀⠀⠋⠀⠀⣆⠀⠀⠟⠀⠀⢀⠂⠀⠀⠖⠀⠀⠀⠀⠀⠈⠃
⠀⠘⡀⠈⢄⡠⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠒⠆⢡⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠀⠌
⠀⠀⠐⠢⠀⠠⠔⠁⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠈⠢⠀⠀⣄⢀⢀⢀⡀⠀⠀⠀⡀⠀⢆⣀⣀⣀⠄⠀⢃⠀⠀⠀⡈⠀⠀⠀⢀⣀⢄⠠⠂⠄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⢬⠄⠴⠀⡄⠌⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡼⣣⠞⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⡊⠈⠢⠀⠀⢀⢌⠁⡜⣀⠘⠃⢰⠈⠦⠀⠒⠄
⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠋⢹⡏⠓⠂⠀⠀⠰⠊⢑⠆⠀⠀⠀⠀⠀⠀⠖⠉⡠⠀⠀⠀⠀⠈⠁⠀⠀⠔⠂⢉⡀⢡⠘⠋⠠⠆⡐⠢⡨
⠀⠀⢄⠊⠀⠀⠉⠇⠀⠀⠀⢎⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠚⠀⠀⢀⠄⠄⠀⠀⠘⡚⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠂⡀⡮⢀⠛⢤⠈⠐⡲
⠀⠀⠀⢁⢀⡀⣠⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢀⡈⢢⠀⡠⠦⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠈⢂⠀⠀⠐⠂⠒⢢⠀⠀⠈⠁⠁⠉⢹⠀⠀⠀⠄⠀⠦⠠⠀⠀⠂⠉⠀⠀⠉⠀⠲⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⢄
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢆⡰⠁⠀⢀⠎⠀⠀⠄⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠀⠃⠀⠀⠀⠀⡔⠠⡀⠀⠈⡆⠀⠀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⣀⠪⢘⠈⡡⠁⢊⡂⡄⠀⠀⠀⠱⡀⠀⠈⠁⠀⠠⠊⠀⠀⠀⠉⠁⠀⠀⡄⠀⠈⠀⠀⡐⡀⠀⠐⡀⠀⠀⠀⠧⠄⠁⠀⠀⠆⠀⠀⠈⠁
⠀⡠⠧⠑⠤⢇⣙⢊⠤⠘⣠⠀⠀⠀⠀⠐⡄⠀⠀⠐⠁⠀⡇⠀⠀⠄⠂⠐⠂⠃⡜⠀⠀⠰⠀⠰⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⡄⢀⡄
⠀⠠⡋⠔⠘⠌⡨⡘⠄⡀⠤⠀⠰⡉⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⠀⠀⢀⡀⠀⠀⢃⠀⠀⡧⠀⠀⠈⠂⡄⠀⠀⠀⠀⠤⢘⢒⠠⠐⠂
⠀⠀⠠⠊⠄⣀⠄⢀⡰⠩⠆⠀⠀⠀⠀⠀⣅⣀⣀⡄⠀⠀⠠⠤⠤⠤⠤⠤⠤⣤⠄⠠⠁⠀⠀⠀⠡⠀⠀⠀⡤⠤⠂⠑⢄⠀⠀⡃⠀⠀⠀⠀⠔⠂⠥⠘⠂
⠀⠀⠀⠀⠘⠈⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣤⣿⣷⣾⣷⣶⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣼⣿⡏⠀⠀⠀⠉⠉⠈⠙⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⠟⠋⠛⠛⠿⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠏⠋⠉⠈⠁⠀⠈⢻⣿⣿
⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠘⣿⡇
⠀⠀⠀⠈⣜⠀⠀⠀⠁⡀⢀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠗⠎⠀⠄⠀⠁⠄⠠⠀⠀⠀⠀⠐
⠀⠀⠀⢠⣿⣦⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠠⡉⠈⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀
⠀⠀⠀⣸⣿⣿⣿⣿⠗⠐⢿⣿⣷⠀⠀⠀⠂⢀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡛⠃⠓
⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠈⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎
⠀⠀⠀⠈⠉⠉⢱⠀⠀⠀⠀⢈⠁⠀⢠⠀⠀⠀⠀⠀⠈⠩⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠦⠲⠀⠀⠀⠀⠸⠲⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢒⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠥⡄⠈⢴⠀⠀⠉⡙⠀⠀⠀⠀⠈⡤⠏⠘⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠠⢺⠇⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠛⠒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣡⠔⠊⠀⠠⢄⠠⠤⠤⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢹⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠠⠖⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣸⠁⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⣸⠁⢀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⠁⠀⠀⠀⠀⣟⢸⡇⠀⣼⠁⣿⠸⣇⠀⡿
⠀⠀⠀⠀⠀⢰⠃⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⣸⠃⠀⠀⠀⠀⣷⠘⠧⠆⠻⠎⠿⠀⠸⠇⠳⠄
⠀⠀⠀⠀⠀⡾⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡾⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣇⠀⠁⠁⠀⢠⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠇
⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⢀⣈⣉⠀⠀⠠⠀⠀⠀⣵⡀⠀⣰⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠳⠦⢤⣀⣈⠙⠃⠋⠀⡿⠁⠀⠀⠀⢀⣠⠔⠒⠛⠉⠉⠈⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢀⣀⡀⠀⠉⠉⠛⠒⠚⠁⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⣠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⡀
⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢰⠃⠀⠀⠀⠀⢀⠀⠄⣀⠃⠀⠀⢆⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢆⠀⠀⠀⠀⡎⠀⡸⠀⠉⠓⠒⠢⡌⢁⠀⠀⠀⠀⢣
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⠏⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡰⢠⠄⠃⠀⠀⠀⠘⡆
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⢨⠀⠀⠀⠀⠴⠘⠠⢀⣀⠀⢼⠃⡀⡑⠀⠀⠀⠀⠀⢹
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠐⡄⠈⢍⡁⠠⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⡤⠴⠃
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠉
⠀⠀⠀⠉⠙⠒⠒⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⢀⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⠤⣄⣀⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣤⣈⡙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣄⣉⠀⠉⠲⢤⡉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⡛⠛⠛⢿⡭⢿⣙⣛⡛⠿⠿⢿⣿⣶⣦⣄⡉⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⠎⠀⠀⠀⠈⠉⠙⠒⠲⠤⣍⣙⡻⠿⣷⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣴⠾⠀⠀⠀⠀⠀⠀⠀⣠⣈⠉⠐⢢⣽⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠈⠀⣀⠀⠀⠀⠀⢀⡤⠀⠈⠙⠷⠀⠀⣿⡧⠀⠉⠛⠢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢀⡠⠿⠤⠄⠀⢠⡏⠀⠀⢸⠀⠀⠀⢸⣿⡟⠓⠲⠶⠶⠶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣀⠀⠀⠂⠙⠂⠀⠀⠀⠉⠀⠀⠀⢛⠭⣹⠂⠀⠀⠀⠀⠶⠖⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠈⠉⠳⣦⠤⠴⠤⠄⠀⠠⠵⠂⠀⢀⡀⢀⡴⠃⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⣉⠉⠉⡉⠉⡿⠈⠻⣦⡀⠀⠈⢿⣶⣶⣶⠖⠁⠀⠀⠀⣠⠛⠋⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣾⣵⡏⢠⡇⠀⠀⠈⠙⢦⡀⠀⠉⠉⠀⠀⠀⠀⡠⠞⢻⡄⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣰⡄⠀⠀⣀⣸⣄⡀⠀⠀⠀⠈⠙⢦⣄⣀⡀⠤⡔⠊⠀⠀⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⠛⠻⣥⢤⡖⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢀⣤⠞⣻⢼⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⠴⠶⣄⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣾⣀⣵⣻⠟⠂⠤⠌⠁⣼⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠻⣄⣠⠟⠀⣸⡤⢚⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢩⡟⢁⠈⠂⠀⠆⠤⠁⠴⠬⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠶⣤⣀⠀⢀⠁⢀⡾⠓⣤⣄⣀⣀⣀⠀⣀⣼⣤⠃⣉⡉⠰⠌⠀⠐⣶⠤⠀⠠⠤⠌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠶⠚⠉⠀⡸⠒⡬⠄⢘⡀⠜⠁⣜⠡⢟⠉⡷⢦⣸⠃⣉⡓⢠⠗⣤⣀⣶⠤⠀⢠⠤⠄⠀⠽⢦⣀
⠀⠀⠀⠀⠀⠀⠠⣿⣠⣤⣤⣤⣤⣤⠇⠰⣦⣰⡋⠁⡼⠇⣹⠷⣨⠿⣷⢤⣁⡰⠏⣉⡛⢠⠏⢻⣌⡷⠲⠞⠀⣶⣤⠀⣸⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠳⠶⣾⣦⣴⣦⣵⣶⢿⣧⢈⣁⠠⠏⢉⡃⢠⠏⢙⣇⡜⠲⠤⠁⡴⠦⠏⢸⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣭⣭⣍⣉⣉⣉⡉⠉⠙⠛⠒⠒⠲⢶⠀⠀⠀⠀⠙⢷⡉⡁⠀⠏⢉⠛⢀⡏⢙⣦⠞⠲⠄⠁⡰⠒⠒⢠⡖⠛⣷⡀
⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣉⠈⣉⣉⠁⠀⣀⠄⠂⣠⡤⠂⠀⠀⠀⠀⠀⠈⢻⣏⠛⠀⠎⢈⣭⣄⠃⢸⣧⣰⠂⠤⠁⡾⠓⠚⠁⡗⠻⣷⡀
⠀⠀⠀⠀⠀⠰⠶⠤⠤⠤⠤⠤⠄⣀⣁⣀⣈⣁⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡉⣀⠛⢠⡤⠤⠈⢻⡇⡔⠒⠄⠁⡼⠙⠒⠀⠾⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣭⣥⡜⢰⡖⠒⢨⣷⠃⡾⢀⣀⡀⠸⠉⣛⠂⠼⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣞⣢⡀⠀⢻⡶⠦⠌⣼⠛⢾⣿⣭⣁⡝⣴⣭⣡⣼⣿⠟⢒⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡴⢋⣡⢉⠦⣌⠻⢷⡒⢠⠞⢾⠟⣲⣬⣶⣿⣿⣿⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠒⢡⠟⣡⣔⡆⢈⠳⣝⠢⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣯⠴⣭⢃⠟⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠃

⣞⣟⣉⣉⣉⣉⣉⠉⠉⠉⠙⣶⣶⡄
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣛⣙⣿⣻⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣟⠋⢹⣏⠉⢉⣿⠳⣮⣛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣿⠀⣼⠃⣠⠞⠛⣯⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠤⠤⠼⠦⠼⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠧⠿⠶⠧⠾⣧⣤⡴⠛⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢦⣄⣀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡞⠁⠙⣿⣦⡈⠙⢻⡿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡴⠋⠀⠀⠀⠈⢧⣙⣶⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠎⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⣿⣿⣿⣿⡿⠋⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠛⠛⠛⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⠀⠀⣿⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠉⠀⠀⢹⡀⢀⣿⠀⠀⠉⠉⠉⠙⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣄⣀⣀⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⡀⠄⠒⠂⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⠢⢄
⠀⢸⠋⠉⠉⠉⠙⠛⠒⠀⠀⠀⠀⠚⠀⠉⠉⠉⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠱⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⣢⣀⡀⠀⠀⠀⠀⠀⠘⢆
⢸⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠆⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⠀⠀⠀⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠆⠀⠀⠀⠋
⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⠓⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡼
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡾⠁
⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⠒⠒⠒⠲⠶⠶⠶⠶⠶⠦⠤⠤⠶⠞⢃⡴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠿⣭⣭⣥⣤⣤⠤⠴⠶⠶⠶⠾⢿⣿⣭⣐⣒⣒⣂⣀⣀⣠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠉⠛⠓⠶⠶⠶⠶⠶⠶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠻⣤⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠒⠒⠒⠛⢧⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠉⠒⠦⢤⣀
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢀⣆⠈⠙⠓⠶⠶⠶⠶⠶⠤⣤⣤⡤⠶⠶⠶⢿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠈⠙⠓⠻⠦⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⢧⣀⡀⠀⠀⣄⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠳⠶⠶⢿⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠦⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣄⣹⡄⠀⠘⠦⠀⠀⠤⠤⢀⣀⣀⠤⠂⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⠤⠄⠀⠀⠈⠉⠀⣀⣀⣀⣤⣤⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⡀⣺⣦⠀⠀⠀⢹⡿⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠛⡋⡁⠀⣠⣤⡘⣿⠣⡇⠀⣴⡄⡆⠜⢡⡄⠀⡇⡏⣿⠇⠀⢀⡀⠀⣀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠻⣠⣫⣷⣼⣧⣾⣷⣸⠦⡷⠛⠛⠉⠙⠿⠋⠀⠈⠳⠶⢏⣼⡧⣾⣯⣼⡛⣇⢘⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡶⠃⠉⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠛⠛⢾⣤⠖
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣄⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⠃
⠀⠀⠀⠀⠀⠀⡌⣁⣈⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣟⣿⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡷
⠀⠀⠀⠀⠀⠀⠈⣹⣿⡉⣀⣈⠿⠿⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢟⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢒⣒⣒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣍
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠘⣍⣉⣏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿
⠀⠀⠀⠀⠀⠀⣧⡉⠐⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⣬⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠖⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠈⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣃⣠⡄
⠀⠀⠀⠀⠶⣿⡄⢈⣏⠰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠙⠋⠁

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

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠤⠤⠀⡀⠀⠀⢀⡀⠀⠀⠀⡄⠀⠀⠄⠀⡀
⠀⠀⢠⡠⠉⡁⠀⠲⠀⡲⠂⠀⠒⠂⠐⠒⡀⠈⠁⡄⡄⠀⠀⠀⢺⠀⠀⠈⠀⢠⡦⣤⠀⠀⠐⢀⣉⣠⢀⣄⣠⣀⡀⠉⠄
⠀⠀⠘⠀⠀⠟⠁⠀⡗⠀⠀⣶⠀⠘⣞⠀⠘⡇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⠀⢀⡉⢘⣝⣏⡿⢅⣋⡜⡏
⠀⠀⡄⠀⠀⠀⢒⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠆⠀⠀⠀⠀⠀⠬⠤⠐⠁⠀⡸⠠⠁⠀⠀⠀⢸⠻⡿⢿⡉⡿⢳⠇
⠀⠀⠀⠀⡧⠀⠀⠀⡐⠀⠀⠢⡎⣀⣠⣤⡀⠀⠀⣁⠉⠄⠉⠀⡄⠀⠮⠂⠀⡗⠚⠀⠀⠀⠂⢰⣴⣶⢠⣶⣴⡖⡇⢁
⠀⠀⡀⠶⠶⠶⢀⠀⣶⣶⣶⡆⠈⢿⣿⠿⠁⠀⡘⠰⢆⠒⡎⠐⠀⠀⢠⠀⢸⠁⠀⠀⡧⠃⠐⠠⠡⠌⠭⢀⠀⠅
⠀⠀⢍⠉⠁⠈⠉⠀⠈⢻⠋⠁⢠⠀⠈⡇⠀⠀⠆⠀⠀⠔⠁⠀⠀⠀⠀⠀⡜⠀⠈⠈⢓⢄⠀⠂⠄⠀⠈⠀⠠⠄⠠⠤⠄
⠀⠐⠚⠀⠀⡔⢆⠀⠀⡞⠀⠐⠀⠀⠠⠳⠠⠀⠅⡰⠁⠠⡔⠠⣶⢢⠀⠶⣴⡆⠀⢤⢘⡀⠑⠄⠀⠀⠈⠀⠅⠰⠇
⠀⡰⠀⠀⠀⡃⢸⠀⠂⠉⠀⠀⠀⡀⠄⠀⠀⠀⠊⠀⠀⠀⢃⡄⠽⠾⠠⠴⠼⠇⢠⢋⠈⠀⠀⡄⠐⠄⠀⡀⠐⠂
⠀⠁⠀⠀⠀⢁⢸⢀⡤⡄⠀⡦⡉⠀⠀⠀⠐⡄⢀⣤⡴⣶⣶⣶⢶⣦⣤⡀⠀⢀⠀⠀⠀⠗⠁⠐⠀⠀⠀⡆⠨
⠀⠄⠀⠀⠃⠀⢀⠎⡰⠁⠀⡙⢮⡒⢐⡩⠰⢠⣿⣿⢦⡦⠶⣶⡴⢴⣿⣿⡄⠀⡿⠒⠂⠠⠄⠠⠀⠀⠀⠈⠀⠤⠚⠀⠠
⠀⠂⠀⠀⠀⠀⢎⡠⠁⢀⠂⠑⢄⠉⢁⠄⠀⢸⣿⣿⣰⣄⣐⣇⣠⣸⣿⣿⡇⠰⠁⡀⠀⠄⢀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠉⠀⡀⠀⠘⣿⡏⠃⠁⠼⠁⠛⠀⣿⣿⠃⠄⠀⠐⠀⡥⠀⡔⠀⣁⠠⠀⢠⠁⠰⠂⣀
⠀⠀⠀⢀⠘⠄⠀⢠⠏⠀⠀⠀⠀⠌⠀⠑⢤⡀⡈⠛⠺⠿⠿⠿⠿⠟⠛⠁⢸⠀⠀⠀⠆⠨⠔⠀⠀⠄⠢⠄⠠⡀⠀⢰⣀
⠀⠀⠰⠄⠐⠄⠘⠠⠆⠠⠒⠀⠈⠀⠄⠤⢈⠀⠀⡣⠀⠀⣖⠄⠀⠐⠀⢐⠀⠉⠀⠀⠀⣰⠀⠀⠀⠂⠀⠠⠂⠀⠀⣸⢸
⠀⠀⠀⠀⠒⢂⠈⢀⡙⠀⣀⠀⠀⢠⣠⢄⠀⠀⠀⠀⠀⡄⡀⠀⠈⣐⠎⠍⠍⠲⢄⢀⠀⡌⣠⣤⣤⣤⣤⣤⣤⣤⠀⡇⠸
⠀⠀⠀⠉⠴⢋⠐⠀⡙⠦⠀⠁⠀⠀⠱⠊⢠⡴⠦⠀⠀⠀⠀⠀⢚⠻⠀⣁⣀⠸⠟⠀⢠⠃⣿⣿⣿⣽⣽⣿⣿⣿⠀⠿⡃
⠀⡐⠆⠀⠀⠂⠐⠀⠘⠀⠀⠀⠀⠰⠞⠛⢀⡤⡄⢠⠂⠈⠁⢂⠈⢬⡀⠛⢳⣾⠼⠀⠠⠀⠈⠉⠁⠀⠸⠃⠀⠀⠈⡃
⠀⠁⠄⠀⠢⠀⠀⠀⠀⠀⠀⢈⠻⡄⠀⢀⠙⠲⠃⠆⠀⠀⠀⠀⠆⠀⡅⠁⠁⠀⠀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠰⡀⠀⠀⠀⢨⠀⣞⠠⠤⠀⢶⠑⢌⢦⠐⠠⠂⠀⠐⢄⣀⣀⠜⠀⠀⠈⠀⠀⢀⠌⠍⠀⠀⠀⠀⠀⠄⡈⠀⠀⠘
⠀⢱⡆⣶⢺⡈⠀⠁⠈⠀⠀⡉⠀⠀⠑⠃⠀⢀⡹⢐⠀⠘⠁⢆⠀⠀⡐⢀⠈⠀⢀⠀⠯⠂⠀⠀⠁⠂⠀⠀⠀⠀⠈⠀⠂
⠀⠠⣯⢀⢰⡇⠀⠀⠠⠀⠀⠀⠀⡌⠂⠀⡠⣊⠖⠁⠀⠀⠀⠀⠹⠁⠀⠌⠀⠠⠂⢠⣠⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠻⠼⠞⠃⠀⠁⠄⠀⠔⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⠀⡀⡀⡠⢸⠠⡂⢠⠠⡀⡄⡂⠄⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢖⠂⣆⠗⠁⠇⠀⠣⠸⠀⠚⠘⠀⠃⠃⠁⠀⠀⡏⢀⠇⠄⠐⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠤⠄⠤⢄⠈⠁⠀⠈⢁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠎⠉⠀⠁⠈⠀⢀⣀⠀⠈⠑⠒⠖⠢⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⠉⠁⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⡉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠐⠢⠭⢥⡝⠀⠀⠁⠀⣀⠖⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠄
⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠷⣮⡍⠁⠈⢣⠀⢀⣀⠆⠁⠀⠈⠙⠔⠆⠤⠤⠦⠀⠀⢀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⠆⠋⠁⠀⠀⠀⢹⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢇⠀⢁⠏⡼⠀⠀⠀⠀⠀⠠⡘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⠀⠀⠀⠀⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠈⢢⣀⠜⠀⠀⠶⠀⠀⠀⡀⡄⢂⠀⠀⠀⠰⡇⠀⠀⠀⠠⠦⠀⠀⠣⣤⢠⡀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⣦⣀⠀⠀⠀⠀⠀⢀⣠⠞⠓⢤⣀⠀⠐⠐⠀⠀⠀⠀⢀⡠⠔⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠐⠒⢲⣙⠷⡀⠈⠑⠀⠓⠋⠁⠀⠒⠒⠂⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⡿⠃⠀⠸⠄⢠⣆⠀⠀⠀⣀⠀⣀⠐⠤⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⣈⠀⠛⠂⢸⠀⠉⠉⠂⠴⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⢀⠄⠉⠁⠰⠦⢼⡀⢀⢀⠀⡀⡀⢄⡒⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠃⠴⠻⠦⠐⠛⠒⠀⠀⢘⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠐⠀⠀⢀⠀⡀⠐⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡁⠀⢈⢩⡀⠀⠀⡀⣄⡄⠀⢈⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠷⢶⣤⡀⠀⠀⢀⣤⡶⠾⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠴⣶⡄⠀⠀⠀⠀⠀⠀⢠⠶⣦⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⢿⠿⠃⠀⠀⠀⠀⠀⠀⠘⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠛⢛⣁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⣿⣿⡇⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁

⠀⢀⡇⠀⠀⠒⡊⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⠀⠀⠐⢒⠁⠀⠀⠀⠀⢠⠁⠀⠀⢀⠃⠀⠀⠒⡊⠀⠀⠀⠀⠀⡄⠀⠀⠀⣘⠀⠀⠐⠲⠁⠀⠀⠀⠀⢰⠁
⠒⠈⠁⠀⠀⠀⠱⠀⠀⠀⠀⢸⠁⠒⠒⠂⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⡏⠐⠂⠒⠈⠁⠀⠀⠀⢠⠀⠀⠀⠀⠸⠁⠒⠒⠂⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⡏⠐
⠄⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠄⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⠀⠉⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⢢
⠀⠀⢸⡀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣇
⠐⠠⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡤⠀⠂⢄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢠⠄⠐⢠⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡄⠐⠂⢄⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⢠
⠀⠀⡅⠇⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡅⠃⠀⠀⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠸⠸⠀⠀⢀⡀⠀⠀⠀⠀⠀⠆
⠀⢰⡅⠀⠀⠉⠅⠀⠀⠀⠀⢀⡇⠀⠀⠀⡆⠀⠀⠈⠹⠀⠀⠀⠀⠀⣸⠂⠀⠀⢰⡂⠀⠀⠉⠇⠀⠀⠀⠀⢀⡇⠀⠀⠀⣶⠀⠀⠈⠹⠀⠀⠀⠀⠀⣸
⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠈⡒⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⢑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⢰⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⡀
⠀⠀⠸⠄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠧
⠀⠑⡄⡀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠞⠀⠈⢢⢀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠰⠂⠀⠑⡄⡀⠀⠀⠀⢘⠄⠀⠀⠀⠀⠞⠀⠈⢢⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰
⠀⠀⠇⠑⠀⢀⠔⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⠂⠀⡠⠂⠀⠀⠀⠀⢀⠃⠀⠀⠀⠂⠑⠀⢀⡔⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠈⠂⠀⣠⠂⠀⠀⠀⠀⢀⠃
⠀⠸⠃⠀⠀⠀⢣⠀⠀⠀⠀⢰⠇⠀⠀⠀⠇⠀⠀⠀⠘⡀⠀⠀⠀⠀⡼⠀⠀⠀⠸⠂⠀⠀⠀⢁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠟⠀⠀⠀⠈⡀⠀⠀⠀⠀⡞
⡀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⡀⢀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠈⠀⡀⢀⠀⠂⠀⠀⠀⠀⠁⠀⡀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄
⠀⠀⢸⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡄
⠀⢀⠘⠃⠀⠀⠈⢃⠀⠀⠀⠀⠀⡀⠀⢀⠀⠛⠀⠀⠀⠙⡀⠀⠀⠀⠀⢀⠀⠀⣀⠘⠃⠀⠀⠈⢣⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠀⠀⠀⠙⡀⠀⠀⠀⠀⢀
⠀⠀⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢱⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⡀⠀⠀⠀⢠⠀⣥⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣧⣄⣷⣶⠀⠀⠀⠀⠀⠁⠐⠂⠜⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠑⠒⣿⠀⠀⠀⠀⠀⠆⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠀⠀⠀⠀⢰⠀⠀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠀⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠦⠈⠾⠃⠀⠀⠀⠀⠀⠣⠀⠠⠾⠃⠀⠀⠀⠸⠆⠀⠶⠃⠀⠀⠀⠀⠠⠄⠠⠶⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠴⠟

⠀⠀⠀⠀⣀⡀⠀⢠⣰⢄⡀⠀⠀⠀⡤⠄⠀⠠⠀⢤⠀⠀⢠⠂⠐⠒⠂⢲⡄⠀⠀⣠⡤⢀⠀⣤⣤⣄
⠀⠀⠀⠀⠹⡄⠀⠈⢹⠟⠀⠀⠀⠀⢂⠀⠀⠀⠀⠘⠀⠀⠀⢂⠀⠀⢀⠞⠀⠀⠀⠣⠀⠀⠀⠀⠀⠉⠀⠀⢠⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠙⢻⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡟
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠀⠀⠀⠐⠋

⠀⠀⠀⠀⣀⡀⠤⠄⠀⢀⡀⠀⠀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢏⠀⡀⢀⡀⢻⡇⠀⠀⠀⠘⠓⠛⠛⢛⡗⠀⠀⠀⠂⠀⠈⠀⡶⠀⠀⠀⠀⠃⠀⠀⢹⡇⠀⠀⠀⠐⠗⢒⣆⣰⠛⣿
⠀⠀⠀⠀⠘⡀⠀⣀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⢄⡋⢿⢛⡇⣿
⠀⠀⠀⠀⠀⢟⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⢀⠐⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⢀⡁⠀⠒⠊⠀⡁
⠀⠀⠀⠀⠀⠘⠃⠀⠚⠃⠀⠀⠀⠀⠀⠙⠀⠒⠛⠀⠀⠀⠀⠘⠀⠐⠛⠁⠀⠀⠀⠀⠀⠂⠀⠚⠀⠀⠀⠀⠈⠓⠂⠀⠈⠛⠃

⢰⣦⣀⣀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠆⠰⣄
⠹⡿⠋⠉⠁⠀⢀⣀⣴⠀⠀⠀⠀⢀⣄⠀⠀⠉⢻⠃⠀⠉⣤⣠⠖⠿⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠿⡿⢀⠀⣀⠀⠀⡌⣆⠀⠀⠀⠀⠀⢀⡉⠛
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣀⣴⡿⠟⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⡠⠀⠀⠀⠀⠍⢃
⢸⣿⠀⠀⠲⢶⣶⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢨
⢠⣤⣠⡀⠀⠸⠿⣦⣤⡄⠀⠀⠻⠁⠀⢀⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢴⣌⡙⢁⠀⠀⠀⠀⠀⠛⢠⡄⢀⣠⠀⠈⠙⣿⡶⣦⠀⠀⠙⠛⠀⠀⠀⣀⢀⡀⢸⠙⠀⢰⡆⠀⠀⠀⠀⠸⠦
⠀⠙⣿⢾⡇⠀⠀⠀⢀⣀⠈⠁⠀⢂⣤⡀⢸⠇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠛⠘⣇⠀⠒⠀⢨⠷⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠋⣙⣢⡴⢶⣤⡈⠇⢀⠆⢸⣀⣈⠞⠷⠁⠀⠀⠀⠀⠀⣀⣀⢀⡀⢰⣦⠀⢶⣶⣶⣆⠀⠀⠀⠀⠀⢾
⣰⣦⣄⠀⠀⠁⠀⠀⠸⣿⠃⠀⠀⠈⠉⠉⡇⠀⢷⠀⠀⠐⠛⢿⡝⣧⣀⠁⠰⠟⠧⣀⡍⠋⠙⠇
⢸⣿⣏⠀⢀⡀⠀⠀⣠⣿⡆⣴⣤⡄⠀⢀⠁⠀⠀⣇⠀⠀⣤⠼⢷⣿⣟⢀⣄⠀⠸⠃⡷⣀⠈⣁
⣾⣿⣿⠀⠀⣵⣤⡶⢿⡻⢿⣿⣿⢿⣯⡝⠀⠀⣰⣿⠀⢠⣿⣿⣿⣿⣿⣿⣷⣾⠁⠀⢠⣿⣀⣸⠇⠀⠀⣤⡶
⠺⠿⠟⠀⠀⠉⠏⠀⠀⢰⣦⡌⠁⠀⠀⠀⠀⠀⢰⣿⠀⣼⣿⡿⠋⠉⠙⠿⠿⣿⠀⡀⠀⠲⢮⠁⠀⠀⠸⣿⡄
⣠⣤⣤⣤⣄⠀⠰⣄⢀⣼⣿⣶⡖⠀⠀⠀⠀⠀⠈⠉⠀⢨⠇⠀⢀⠐⠀⠀⠀⠸⢣⣿⣄⠀⠀⣗⠀⡿⠀⠿⣷
⢸⣿⣿⣿⣿⣷⣆⠙⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠈⢴⢯⣽⢷⣄⠀⠀⠀⣾⣿⣿⣶⣌⢿⠀⠀⠀⠀⠹
⠘⢿⣿⣿⣿⣿⣿⡄⠸⣿⣿⠿⡿⣿⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠜⢁⣠⣭⡈⠛⠋⡴⢨⣿⣿⣶⡦⡄⠀⡀
⠀⠀⠈⠀⢹⣿⡟⠀⠀⠙⠛⠓⠂⢸⣿⣿⣿⠟⠼⠛⠁⠛⠀⢀⠀⠀⠙⠋⠀⠁⠀⢀⣀⣼⣿⣿⣿⡁⠀⠀⡤
⠀⡆⠶⠂⠀⠉⠀⠀⢠⠤⠀⢤⡀⢸⣿⣿⠟⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣴⣦⢉⡟⠻⠿⠿⢧⣀⡀
⣺⣧⣤⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⠉⠉⣠⣄⣤⡰⢶⣤⠤⣀⠀⠀⠀⠀⠠⠛⠁⣾⣷⠀⢶⣶⣿⡿⠟⠛
⠈⠻⣿⣄⠀⠀⠀⠀⠀⢲⣿⡏⠈⣯⠀⠀⢠⣇⠀⢻⠑⠟⠧⠀⠉⣀⣴⣷⠲⡆⠀⢠⣷⣾⡀⢘⣉⣿⣧⣴⣶
⢐⣁⣠⣿⠀⠀⠀⠀⠀⠈⣽⡇⠀⠉⠀⣠⣤⣀⠀⢀⡀⢰⣶⣶⡾⢻⣿⣯⣰⡧⠞⣿⣿⣯⢷⣿⣿⣿⣿⣿⡿
⢻⣿⣿⣿⣷⣶⣶⣦⣤⣤⣿⣷⣴⣾⣿⣧⡌⢙⣿⣿⣷⣀⣿⣏⠐⢾⣿⣿⣟⣃⠈⢯⣉⣉⣈⣿⣿⣿⡿⢿⣿

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⡠⠒⠈⠁⣆⠀⠀⢀⡇⠀⣠⡴⠒⠒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢀⣿⡟⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⡃⠀⠀⠙⠁⠀⢀⡼⠁⣸⠋⠀⢀⣀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣉⠷⡦⠤⢤⣄⠀⠀⣿⡀⠀⠀⠀⣼⡿⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠐⠤⠀⠀⠤⠔⠋⠀⠀⠹⣄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⡞⠁⢠⠏⠠⣤⡿⠀⠀⠘⠿⠂⠀⣰⣿⠃⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⠀⠀⠙⢿⣤⣀⣀⣀⣠⡤⠤⢖⣲⣿⣿⠿⢿⣿⡟⠿⣶⣤⣿⠏⠀⣠⠶⢛⡦⢀⣶⡤⢶⣀⣶⠴⢲⡄⣴⠆⠀⣶⠆⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠀⠀⠀⠘⢿⣦⣤⣤⣤⠶⣚⡿⠛⠉⠀⠀⣼⡿⠀⠀⢸⣿⡟⢠⡾⢃⣴⡿⢡⣾⢯⡄⣼⣿⢃⡀⣼⢱⡏⣠⣾⡏⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈⣉⣠⡴⠚⢡⡄⠀⠀⠀⣰⣿⠃⠀⠀⣸⣿⠁⢿⠿⠋⠸⠿⢡⡏⠘⠛⢱⡏⠘⠛⠁⠘⠛⢡⡟⢀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠟⠛⠉⠁⠀⠀⣾⡇⠀⠀⢀⣶⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡿⠀⠀⠀⠀⠀⠠⡾⠁
⠀⠀⠀⣠⠔⠂⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣧⠀⠀⣾⡿⠀⢀⣀⠀⡀⠀⡀⠀⠀⢀⡤⢺⡏⠀⠐⢸⠇⡀⠄⠀⠀⠀⣼⠃⠀⠀⠀⣴⣶
⠀⣠⠊⠀⠀⠀⠀⡄⢰⡄⠀⢻⠀⠀⠀⠀⠀⠀⢰⣿⠃⢿⠀⢰⣿⢡⣾⣫⢜⢼⡏⢰⡟⢀⡴⠋⠀⢈⡤⠄⠀⢠⠊⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⣿⠃
⣼⠁⠀⠀⠀⠀⠘⣆⠀⠀⢀⡞⠀⠀⠀⠀⠀⣠⡿⠃⠀⢸⣆⣿⠇⣿⣏⡠⠋⢸⡷⢹⣷⠏⠀⢀⡴⠋⠀⠀⠀⢠⠀⠀⠀⣀⠴⠁⠀⠀⠀⢀⣿⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠸⣿⡟⠀⠈⠉⠀⠀⠈⠁⠈⠁⠀⣰⡿⢁⠔⠒⡆⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⣼⠃
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠿⠁⠀⣠⠖⠒⢦⡀⠀⠀⠀⣼⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠈⣿⠀⠀⣼⣿⢃⡴⢊⡗⣠⠖⣲⠄⠸⣧⣠⡄⠀⠀⠀⠠⠃
⠀⠀⠈⠛⠛⠳⠶⠖⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⢀⣼⣿⠇⣾⠵⠋⣼⣃⢴⡏⢀⠀⣰⡟⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠈⠙⢦⠀⠀⠀⠈⠛⣹⣿⠏⡀⠙⠒⠊⠙⠁⠘⠞⠁⠀⢹⣇⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⠊⠉⢳⡆⠀⠈⡇⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⡀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠄⠊⠁⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠀⠈
⠀⢦⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣠⠔⠊⠁⠀⠉⠑⢦⡀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣀⣀⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣧⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⠞⠁⠸⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠔⠉⣠⡟⠀⣆⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠈⠓⠶⣄⠙⢷⣄⠀⠀⠀⠀⡠⠐⢁⣠⣶⠟⠋⢀⣼⠇⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠈⢀⠀⢀⠀⠉⠙⠳⣎⠳⣆⢀⣉⡵⠞⠋⢁⣡⠴⠞⠋⠁⠈⣠⢏⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠙⠉⠀⠀⣰⠟⠁⠀⠀⠀⠀⣰⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣀⡤⠖⠛⠁⠀⠀⠀⠁⠀⣼⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⠀⠀⠀⠀⠀⢀⡾⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣧⣄⣤⣗⣉⠙⠛⡛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠾⢿⣦⣴⣖⣭⠻⢻⡲⢦⢤⣄⣄⣀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢤⣬⣆⡐⠈⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢰⡿⣿⣻⣦⢤⣸⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢁⡔⢀⣤⡜⠂⣿⣷⡝⢢⡀⠀⡺⣵⡿⠙⠽⠷⠶⢤⠈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⣸⢠⡃⣿⡿⠛⠉⠀⠀⢻⣿⣿⣿⡇⠠⡖⢋⣤⣀⠀⠀⠀⠀⠰⠉
⠀⠀⠀⠀⡀⡺⢿⠿⠷⠛⠚⠉⢹⠀⠀⠀⣀⣤⣌⢿⣯⣾⠄⢠⡇⠀⠛⠛⠀⣴⣦⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡾⠛⢛⣉⣀⣂⠉⣁⣴⢾⡇⠀⢀⡀⠀⠀⢉
⠀⠀⠀⠀⠑⠀⠀⠴⠶⠦⠤⠤⠤⡄⣻⣏⠹⠛⡿⣻⣿⣿⠋⠀⢻⣏⠻⠟⣧⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣬⣮⣵⣿⣿⣻⣶⡆⠈⠛⢿⠞⢩⠂⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣀⡄⢹⢨⣼⣿⠿⢿⡿⢛⣁⡄⠀⠄⠀⠀⠀⣹⣻⡝⠿⠧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣣⡉⠁⢈⡘⠟⠛⢛⣿⣅⣈⠉⣁⣀⣀⣁⡉⠁⣿⣥⣴⠤⣤⣤⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣴⣶⣳⣟⣽⣿⣿⣯⡄⠸⡍⢿⣥⠄⠀⠀⣿⣿⣿⣆⠀⠠⠚⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠛⣸⣿⣿⣿⣿⠀⠀⠈⠙⠆⠀⠀⢠⣿⣿⣿⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡄⠀⠀⢸⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠁⠀⠀⣿⣿⢏⠓⠁⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠻⣿⣿⣿⣿⡿⠀⠀⠀⣘⣄⠀⢰⡿⠁⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠬⠉⠉⠉⠙⠛⠿⢾⣯⡬⢷⠈⠛⠋⠻⢾⠿⣟⣡⣤⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠔⠂⠌⠰⠀⠪⠠⠍⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡐⠀⠐⠒⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢟⣛⣩⣭⣭⣛⣓⡀⠀⠀⠀⢮⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⠵⣾⢿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡼⠁⠈⠀⠀⠀⠀⠐⠒⠲⠄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⢀⠤⡀⠀⠔⡡⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⣄⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠃⠀⠈⢀⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⢰⠚⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⣄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢙⠂⠤⠞⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⣠⠔⣻⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢠⢂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢇⡉⣉⡠⣺⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡠⠚⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⣌⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⣀⣠⡴⢾⠁⠒⠒⠉⣁⡠⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢋⡀⢀⡞⢰⠒⠊⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠒⠒⠒⠉⣀⣤⡆⠀⠉⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡴⠂⠤⠤⠤⠤⠖⠚⠦⠔⠒⠋⠁⡼⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⠈⠙⠲⠤⣀⡉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠲⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣄⢀⣀⣠⠋⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡭⢷⡄⠀⢀⣀⣀⣀⣈⠑⠲⠦⢤⣤⣀⣀⡀⠀⣀⡁⠀⠀⠀⠀⠀⢸⠀⡟⠈⠀⠀⠈⠉⠉⠉
⠀⠀⠒⠄⠀⠀⠀⠀⠀⡰⢮⡠⠚⠁⠀⠀⠛⠉⠉⠉⠁⠈⠉⠁⠢⢤⣀⡀⢀⠉⠉⠉⠉⠴⡦⠀⠀⠀⢠⠋⡰⠃
⠘⢌⠢⡀⠈⠑⠢⢄⡘⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⣸⠣⠤⠔⣊⡭⠛⠁
⠀⠈⠱⣈⠢⡀⠀⠀⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠏⠙⠋⠉⠁
⠀⠀⠀⠈⠑⢌⠳⢄⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢹⠀⡄⠀⢀⣏⣼⠁⠀⢀⡄
⠀⢀⠀⢀⠀⠀⠙⢇⡂⢄⠰⣆⢸⣄⠁⣶⢾⢾⠇⢀⠔⠙
⠀⠘⣆⠀⠳⣄⡀⠀⠙⢆⢄⢰⣿⢸⠄⠁⡾⡟⢀⠎⠈⠀⠀⢸
⠀⠀⢙⢦⡀⠀⢽⡦⣄⠘⡌⢾⢹⠈⠀⠀⢣⠁⡌⡀⡤⠀⠀⠘
⠀⠀⠀⠱⡙⢆⣀⡱⢄⡑⢺⡌⢄⠀⢀⡆⣜⡜⢰⡇⡃
⠀⠀⠀⠀⢙⠊⢈⠴⣁⠈⢂⠑⣌⣶⢸⡰⠋⠄⡽⠚⣍⠉⠆
⠀⠀⠀⢠⢂⣴⡋⠀⡈⠳⣄⠳⡈⣇⠸⠁⠈⡰⠁⠐⡠⠓⢬⡑⠄
⠀⠀⣴⠗⠁⠀⠙⢿⣦⠀⠙⢧⡱⣿⠀⠀⢠⢣⢂⠔⠁⠀⠀⠈⡉⠒⠦
⠀⠈⠀⠈⠳⡤⢄⡀⠑⣅⢄⣀⠃⣿⠀⢰⢱⣧⠞⡀⠀⢴⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠐⠚⣍⠈⠡⠘⢇⢧⠀⣈⢸⡟⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠒⠶⠆⠜⠡⠎⢁⣈⠳⢦⠘⡎⣾⠄⠃⢈⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣳⡀
⠀⠀⠀⣀⠔⠀⠀⠀⠀⠙⢾⣧⠘⣸⣟⠂⠛⡎⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣤⣄⣸⣋⣳⣤⣤⣄⣀
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣿⡀⢰⠁⠀⠀⠀⠀⣠⠏⡞⠀⠀⠀⠀⢠⠞⠉⠀⠀⢀⠀⠈⠀⠀⠁⠀⠉⠙⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⣁⠀⢸⡆⣠⠖⡪⠙⠃⠈⠙⠉⠁⠑⢲⡏⢀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠔⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⣾⡿⠁⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠳⠋⢠⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠈⢿⢛⡋⢐⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡆⢀⣧⠐⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠤⠾⣷⣿⣿⣿⡄⠄⠀⢆⠀⠀⠀⠀⠘⠀⢀⣜⣻⣷⡔⢸⡀⠀⠀⠀⠀⠀⢰⡿⢀⣞⣵⢿⢯⣿⣿⣷⣒⡒⠒⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢐⣶⠾⠋⠀⠰⡏⠉⠉⠻⢦⣨⣤⡀⢀⣠⣿⠾⡟⢾⣽⣿⣿⣿⣿⣄⣀⣀⣀⣠⣟⣱⣛⣛⣷⡄⣙⣻⣿⡻⣿⣷⣤⣈⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠛⠺⠍⠀⠀⠀⠀⠀⢙⣦⠀⠀⢠⢯⣼⣥⣤⣤⣀⣄⠀⠠⢬⡙⣹⣝⣉⣉⣉⣉⣩⠉⣯⢦⠛⢡⡿⡿⠁⠘⠃⠀⣀⠘⠛⠋⠛⢝
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠩⠀⠀⢠⣀⣀⣤⡞⠁⠄⠀⢸⠀⣧⠀⠀⠀⠀⠀⣀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⣄⠱⢄⡐⡖⠒⠁⠀⠀⠀⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠀⠀⠀⠙⠋⠉⠉⠠⡀⠀⣸⡆⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⢤⢦⠀⢸⠳⠃⠀⠀⡇⣄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⣀⣀⡇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⠱⠎⠀⠀⠀⢀⡇⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠃⠀⠀⠀⠀⠀⠒⠀⠀⢀⣀⡇⢾⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣈⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠧⠤⠴⠶⠒⠚⠛⠛⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⠚⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⣀⡉⣒⡶⢤⣍⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠠⡹⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣾⣿⣿⣿⣿⣿⣿⣧⣿⣭⢫⣞⣿⣿⠐⣷⠻⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠸⢸⡟⠛⠛⠛⠋⠙⠁⠉⠋⠿⢻⣾⣿⣿⣼⠘⢢⡟⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⣂⠛⢹⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢿⣴⣯⢟⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣿⣿⣯⣐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡇⠀⣷⣤⣤⠀⠀⠀⠰⠿⣿⣯⣭⣍⠑⠀⠘⣿⣿⡷⣭⣋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠹⠾⠦⠀⠀⠀⠀⠀⠁⠀⠈⠙⠃⠀⠀⠹⣿⣿⣦⠌⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡳⣄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣻⣿⣿⣮⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⣀⢀⣼⣿⣿⣿⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⠛⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⡿⢹⢸⠹⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠰⢸⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣿⣿⣿⣿⡃⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡲⢤⣀⣀⣀⠠⠒⠉⠀⠀⢠⣿⣿⣿⣿⡇⠀⠁⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⡃⠀⠣⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣧⡰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⢦⣤⡂
⠀⠀⠀⠀⠀⡀⠀⡀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠀⠶⢮⣭⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠊⠢⠙⢿⣷⡖
⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠛⢀⠀⠀⠹⣆⠀⠀⠀⠀⢠⣿⣿⡿⣿⣧⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠈⠘⡉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠹⠀⠀⠀⢀⠃⣿⣿⠃⠘⢿⣷⠀⠀⣀⣀⢿⢿⡀
⠀⠀⠀⡀⠹⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⠀⢀⠂⢠⣿⣡⢖⡒⢚⠻⡈⠋⠉⠀⠀⠂⠃
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⢝⠉⠑⠋⠀⠀⠀⠈
⠜⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⢠⡄⠀⣼⠁⠀⠀⠀⢀⣀⡀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣴⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢈⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣛⠂⠀⢀⣠⢶⣀⡀⢀⣄⠛⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠁⠀⡄⡇⡄⡀⠂⠶⣠⠸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠙⢿⡉⠉⠉⠩⠩⠩⠩⠩⠍⢹⠃⠀⠁⠸⠭⠄⠀⠀⠀⠡⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢧⠀⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢲⠖⡐⡒⠀⢓⣃⠱⢇⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠣⠻⣉⡦⣎⠙⠃⠀⠉⠁⠑⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠆⠈⢘⢭⠀⠠⠄⡀⠀⠰⠣⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠠⠀⡴⣎⢨⢦⠀⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠃⢨⠀⠈⣿⡗⢡⡏⠀⠀⢣⡀⠀⠀⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⡣⢬⠁⠄⡬⠋⠀⠠
⠀⠀⠀⠀⣤⠀⠁⣉⡀⠀⢘⡇⠀⢠⢿⣴⢬⠷⡀⠀⠈⡇⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠓⠀⠀⠀⢀⠰⣄
⠀⠀⠀⣠⡄⠈⡁⠈⣽⣄⡼⣇⡀⢂⠄⠈⠖⠠⢄⢀⣰⠿⡄⣴⡄⡄⠀⠀⠀⢠⠁⡀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘
⠀⠀⠀⠉⠁⠀⠀⢀⠸⢷⣆⠌⡝⢁⠀⠁⣀⡁⣠⡡⡐⠶⠀⠉⠀⠀⠀⠀⢀⠘⠌⠃⡫⠨⠈⠀⠃⠀⠀⠀⠀⠀⠸⠀⢀⡖⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠥⠘⢛⣛⣭⡤⢷⢶⢬⣭⣐⣀⠂⠀⠀⠁⠀⠀⢼⠀⢐⠀⠅⡠⡆⡀⠀⠀⠀⠀⠀⠀⠉⢐⠾⠀⡀⠂⠁⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⡍⠀⢑⠀⣖⡆⠐⢇⡄⠉⠙⣅⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣃⠀⢿⠀⣛⣇⠀⠠⠖⡀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣸⡄⠈⠄⢹⡽⡄⠸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⡶⣤⠀⠀⣆⣥⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢱⡄⠀⠀⠀⠠⡦⠤⠂⠀⠀⠀⠀⡀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠃⠿⠀⠀⣧⣿⠗⡄⠀⠀⠀⢠⣤⠀⠀⠸⠀⢸⠀⠈⡇⡀⢀⠄⢸⠂⡆⡆⡤⣃⢤⠘⠇⠆⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⠀⣮⣀⣿⣼⣠⠝⠀⡀⠀⠀⠉⠀⠀⠀⠀⢸⠀⣸⠓⠇⠘⠂⢸⠀⠁⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢁⡛⠀⠘⡮⣙⣿⣟⠰⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠏⠑⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢡⣦⠈⡿⠃⠈⠶⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⠠⠿⡧⢠⡆⠀⠀⠀⠀⠀⢠⠏⡁⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠼⣶⣷⡂⠀⢀⣁⡀⠶⣶⠦⣀⠠⠌⣹⠃⠀⠈⠉⠁⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠸⡄⣀⣴⠀⠀⠀⠀⣠⣽⣦⠜⢻⣯⠏⠸⣦⠆⣠⠉⣡⡀⢈⡛⣛⢀⢲⡎⠀⢰⡗⠂⠠⠼⠎⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠀⠀⠀⠀⠀⣆⠀⢉⡆⠀⠐⠒⠒⠂⠚⠲⡂⣈⠾⠃⠀⠈⠝⠀⠀⠀⠸⣿⣤⠦⠀⢀⠀⣮⣄⢀⣀⣀⡀⠀⢠⡏
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢳⣆⣦⠀⠀⠀⠀⠙⢀⠄⠁⠓⠛⠛⠗⠛⠒⠂⠀⠟⠴⠓⠀⠢⣄⠴⠂⢠⡤⠄⠀⠤⠄⠹⣴⠃⠀⡄⠀⠈⠉⠉⠙⠓
⠀⠀⠀⠠⠀⢆⡀⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠐⠋⠉⠋⠉⠙⠻⡼⠷⠤⠤⠒⣶⣾⡿⡦⠀⢠⣤⡔⣈⢀⠒⠦⠶⠂⠀⠻⡀⠦⣀⣀⡀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢆⠀⠀⡀⠀⠀⠀⢡⣧⡀⣀⠀⠀⢀⣀⣀⣤⠀⠀⠔⠀⠀⠀⠐⠪⢿⠃⠀⠀⢤⠘⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠉⠙⠒⠦⠤⢀⣀
⠀⠀⠀⠀⠘⡦⢀⣥⠀⡀⠀⠈⢈⡷⠉⠀⠶⠞⠛⠋⠃⢶⠀⡀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⡀⠀⠆⢚⡶⢶⣶⠶⠠⠶⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠈⡋⠁⠀⢠⠞⠠⢄⠀⠀⢠⣤⠴⠤⡍⣀⣼⢧⡤⠤⠤⠄⣀⣴⣐⣦⢦⣤⡯⠟⠲⠛⠉⠉⠀⠀⡆⣄⡀⠀⠱⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⡄⠀⢰⢀⠖⠀⠀⠀⣠⣬⣥⠦⠀⠀⠀⠻⣿⠗⠀⡗⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡁⠀⠀⠀⠙⣄⠀⢀⡀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⢀⠀⢨⠁⠄⠀⠀⠀⠠⠤⠤⠤⠤⠴⠶⠶⢻⡬⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠒⠋⢩⠀⠠⠤⠤⠤⠈⠧⠤⠕⢲⠒⠃
⠀⠀⠀⠀⠀⠀⠘⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣸⡅⣀⣠⣤⡤⠤⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⡆⠐
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢶⡈⠂⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠙⣦⣀⠁⠀⡀⠀⠀⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠁⢨⡃⠇
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢻⠀⠀⢈⣷⣤⡈⠒⠀⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⡀⠀⠀⠀⠀⠀⠀⢸⣉⠁
⠀⠀⠀⠀⠀⠀⢀⡇⠀⣄⣀⡤⠤⢺⡇⢘⠁⠀⠀⠈⠙⠲⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣆⡷⡄⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⢸⡇⠘⢻⣧⠘⠣⣄⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠀⠰⣆⠀⠀⢀⣴⣋⣿⢰⡄
⠀⠀⠀⠀⠀⠀⢯⠀⣀⠇⢸⠇⡄⠈⣿⠀⠳⣌⠑⢄⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⣤⣤⢼⣦⣴⣿⣭⣭⣿⠘⡇
⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⣸⡆⣿⣮⠿⢶⠺⠆⠑⢦⡙⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀⠀⢿⣇⡇
⠀⠀⠀⠀⠀⠀⠘⠧⠃⠀⣿⠀⡇⠀⠀⢸⡐⡀⠑⢄⠙⣿⣏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠠⠀⠀⢀⡸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⠀⢸⣿⣧⡀⠀⠙⣿⢻⡷⠶⠾⠟⠛⠛⣩⣭⡵⠶⠛⠛⠛⠻⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⢸⡯⠿⣿⡢⡀⠀⢻⠠⠛⠂⠀⠈⠉⠀⢸⣞⠀⠀⠀⠀⠀⠀⢱⣿⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⢸⡇⡀⠈⢿⣾⣦⣽⡄⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠱⣝⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⡠⠊⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠒⠒⠒⠒⠠⠄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢤⡀⠀⡰⠁⠄⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠐⠂⠀⠀⢂⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠑⠒⢄⡀⠀⡀⠀⠅⠀⠀⢳⢠⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⣼⠼⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⡀⠂⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠇⠆⠀⠀⠀⠀⢠⡀⠰⢒⣞⡠⠛⠤⣻⠄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠐⠁⠀⠀⠔⢡⠀⢀⠌⠀⠀⠀⠀⠀⠂⠈⠑⡏⠀⠉⠀⡠⠂⡌⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠑⢄⠀⠀⢀⠴⠁⠀⠀⢀⠴⢋⡀⠀⠀⡌⠀⠈⠒⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⠚⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⡀⠀⠉⡞⡁⠀⡜⠆⠈⠁⠀⠐⡷⠀⢸⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠁⠀⣠⠆⠀⣔⠆⠀⣧⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠠⠰⠀⠀⠀⠀⠀⣷⠀⡸⠀⣠⡄⢈⠁⠀⡇⠀⠀⠀⠒⠚⢹⠠⠚⠁⠊⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠃⡆⡇⢰⠔⢁⣏⠼⠜⠀⠀⠀⠠⠔⢈⠇⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠎⠀⠸⡇⠐⠐⠂⢀⣀⡠⠄⠀⠀⠒⢂⠌⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⡠⠔⠊⠉⠀⠀⠀⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠠⠤⠀⠀⠒⠒⠈⠁⠀⠎⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⣀⡠⠔

⠀⡁⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠲⠄⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⠀⠛⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠠⠀⠀⠀⡄⠂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢀⠀⠀⠀⢠⡀⠄⣂⡈⠢⠁⠀⠀⠀⡀
⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠐⠋⠼⠳⠀⠀⠀⠀⠀⠚⡓⠣⠈⠁
⠀⡀⠐⠂⢀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡀⠀⠀⠀⠀⣀⢀⠂⠀⠀⠀⠀⠀⢐⡡
⠀⠈⠁⠠⠿⠃⢀⠀⠀⠀⠠⣤⡾⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠙⠦⠜⠀⡉
⠀⠀⠀⠀⠀⠀⠁⠠⣧⡄⠀⠀⠀⠐⠚⠓⡰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⢀⠀⣂⣾⠁⠈⠀⠀⠀⠀⠀⠸⢍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠸⣾⣿⣏⠀⠀⠀⠀⠀⠀⢀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠂⠀⠀⠠
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⢠⡞⠉⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡾⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⣤⣦⢾⢿⣿⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠒⢫⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⣠⣴⡒⢿⠆⠀⠩⢷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠁⠀⠽⣥⠉⣿⡄⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠙⢿⠀⠀⠰⠗⣶⣈⠉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣦⠀⠀⠣⣀⠀⠀⠁⠸⢺⡟
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠃⢉⠞⠀⠘⣦⣬⡝⠲⣶⣖⡿⠁⠀⠀⠀⠀⠀⣠⠔⣲⣤⠤⣄
⠀⠀⢀⡞⠁⢰⣿⣿⣿⢾⠁⡝⢎⢮⢫⢦⠀⠀⠀⣼⠁⣔⣁⡀⠀⠀⠉⠀⠀⣾⢿⡛⢓⠄⠀⠀⠀⠀⢰⣧⢰⣿⣵⣆⠀⣀⡀
⠀⠀⣾⠁⠀⠈⢿⣿⣿⡎⣿⡙⢾⣮⠎⣾⣆⣠⣴⣣⢤⢬⣉⣡⠊⠀⠀⠀⢀⣀⣀⠕⠋⠀⠀⠀⠀⠀⠈⠻⣿⠿⣿⣿⣷⡿⠿⣶⣄
⠀⠀⣿⠀⠀⠀⠀⠙⠛⢣⣿⡧⡿⠛⢛⠽⠉⠁⠈⢇⠀⠳⠀⠹⠄⠀⣀⠴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡙⢦⠀⠀⠀⠈⠉⠀⢶⡶⢮⡄
⠀⠀⠘⢧⡀⠀⠀⠀⣠⠞⠁⢈⣡⠖⠁⠀⠀⠀⠀⠈⠓⣤⣤⣤⣶⠈⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⢤⠀⠀⠀⢤⣄⡀⢸⣧⣿⡇
⠀⠀⠀⠀⠉⠓⠒⠋⠁⠈⠉⠁⠃⠀⠀⢠⣤⣴⣶⡿⣻⡿⠻⣿⠇⢠⣾⣿⣷⣄⣀⠀⠀⠀⠀⣸⠁⢀⠖⠁⠀⠐⣿⣦⡀⢁⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠁⢀⠤⣿⣐⣻⡭⠭⣿⣿⣿⣿⣿⠂⢀⡏⢰⢦⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⢸⠩⣙⣙⣤⣬⢳⣿⣿⠟⢉⣵⡶⢾⠁⠸⠶⠎⠁⠀⠀⠀⣠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣸⣿⠇⠰⣿⣯⣤⣈⠲⠤⢤⡤⠤⠴⠖⣰⣿⡟⠛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣼⣿⣿⣿⣿⡿⣫⢴⠀⠀⠀⠉⠉⢿⡿⠟⢀⡞⠀⠀⠀⣼⠛⣫⣥⣄⣀⡬⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⣿⠏⠜⠘⠺⠀⠈⠉⠐⠲⠤⣤⠴⠎⠀⠀⠀⣼⣿⣤⣶⣦⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡉⠠⣉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠉⠉⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡔⠂⠐⡄⠀⠀⣿⡣⠄⠙⠀⠈⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢘⣃⡀⡀⠀⠀⢘⣖⣟⡠⠂⠀⠀⣿⡠⢄⠀⠲⢘⠀⠀⠀⠀⠀⠻⣷⠄⢀⡉⠁⠟
⠀⠀⠀⠀⢸⣥⣅⢛⣄⠀⠈⣼⠋⠀⠀⠀⠀⢸⠟⢢⠒⠂⠈⠀⠀⠀⠀⠀⠀⠘⣷⠄⡒⠊
⠀⠀⠀⠀⠀⣿⡯⠉⢩⡙⠡⠸⠀⠀⠀⠀⠀⢿⣦⠿⠰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢹⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⠓⢄⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡦⢠⠛⢸⠀⠀⠀⠀⠀⠀⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠢⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠖⠀⠁⣄⠁⠈
⠀⠀⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠐⣠⠶⣌⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣾⣦⠤⠦⣻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣭⡏⠀⠩⠃
⠀⠀⠀⠀⠀⠀⠘⠛⠿⢀⡀⠀⠀⠀⠀⠀⠀⣯⣁⠌⠂⠒⢙⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣧⢄⠀⢀⢘⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢁⢨⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⡀⠀⠀⠀⠀⣿⠟⠶⠄⠛⠛⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣀⡀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆
⠀⠀⠀⢀⣀⣉⡉⠉⠉⠀⣸⡄⣴⣶⣾⡶⢿⣦⠾⢶⣿⣷⣶⣶⣶⣶⣶⣶⣶⡒⣢⣤⣸⣾⣿⣿⣿⣶⣾⠢⠀⠀⢀
⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⢹⣀⣀⣍⣀⣀⡁⠀⣤⡗⠚⠛⡛⠛⠛⠛⠋⠙⠉⢛⣿⡛⠛⠛⠋⠛⢻⣿⡖⠀⠀⠘⠇
⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⣠⣠⠱⡟⠋⠁⠄⠐⣖⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠄⠥⠀⣀⡴⠖⠛⠀⠱⡀⠠⢤⣶⢀⣶⡀
⠀⣀⢨⣄⠉⠀⠀⢀⡀⠀⠈⡈⠀⢣⠀⠀⠀⣸⣿⣀⡀⠀⠀⠂⠀⠈⠁⠛⠠⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⣷⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠁⣁⢀⡀⣀⢸⠀⠀⠀⠈⢉⠉⠁⠁⠀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣷
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⢤⡤⠅⠨⠀⠀⠀⠀⣚⣛⡃⣸⣻⢛⢅⣴⣿⣿⣷⠄⢀⣤⣄⠀⠀⠀⠀⠀⠀⢰⣶⣤⣻⡿⣴⣿⡦
⢀⠂⢀⠀⣠⠤⠤⠀⢠⣤⣬⣥⣤⣤⠀⠀⢤⣬⠀⢀⣅⣈⠉⢴⣦⣝⣷⡬⢿⡅⠉⡟⠩⠀⠀⠀⠀⣉⠇⣚⠻⢩⣿⣶⣾⢿⣷
⠈⠴⠠⢀⣄⠀⠀⠀⠀⠟⠘⣿⢻⠗⠀⠀⠁⠀⠀⠈⠳⠟⠀⠘⠙⠛⠛⠑⠰⠂⠂⠁⠠⠾⠇⠿⠖⠻⠚⠹⠏⠸⠯⠿⠿⠻⠿
⠀⣠⣇⠀⢩⣆⢀⠀⠠⢤⠀⠉⢀⣄⡀
⠈⠉⠉⠞⠳⠋⠁⠀⠐⠿⠷⣀⣿⣿⣷
⠀⠀⠀⣄⣤⠇⡤⠀⠀⢀⣴⠿⠛⢻⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⠤⠀⠀⠀⠀⢀⡀⠁⠃⠀⠀⢸⠉⠉⠒⣄⣁⠰⠖⠲⠒⠲⠶⠶⠶⢶⣶⠶⠆⠀⠔⠀⠀⠂⠀⠶⢦⣶⢦⡖⠲⠖⠶⠖⡀
⠀⠠⠄⠀⠀⠀⠁⠀⠗⠧⠆⠠⠰⠞⠀⢤⣴⣿⣿⣤⣤⢀⢀⣤⣤⣀⢄⣸⣿⣧⢤⣤⣤⣤⣤⣤⣤⣤⣾⢹⣦⣤⣤⣤⣤⡌
⠀⠀⣤⣶⣄⠻⡴⢇⠀⣸⢇⠴⢥⣤⣿⣿⣿⣯⣒⠀⠀⣿⠙⣧⡤⢈⠋⢹⣾⠗⢼⣏⣿⣏⣬⣩⣽⣿⣏⣬⡋⢻⣯⠈⣀⣤
⠀⠀⠈⠉⠉⠀⠀⠀⠺⡿⢻⡃⠀⠀⠁⠠⢩⣽⣿⣧⢸⣿⡋⣁⣀⢺⡆⣿⣻⡀⢸⡏⣿⣿⣿⣿⣦⣆⣿⠛⠛⢋⣽⣸⠨⠁⠞
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⣷⣤⡤⢤⠰⠿⣿⣿⣿⣾⣿⠀⠀⢙⣿⢁⣿⠘⠀⡿⠇⣽⡿⡙⠿⣷⣿⣿⣰⣶⣾⠿⠈⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠈⠀⠀⡟⡿⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠁⠁⠀⢩⢽⡇⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠸⠏⠀⠀⠀⠛⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠐⣆⠀⠀⠸⣦⣄⣠⣾⠃⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣼⡆⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠰⢿⣾⠃⠀⠀⣀
⠀⠀⠀⠀⣼⣿⡆⠀⠀⠁⠀⠻⠷⠀⢀⣀⣀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣶⣦⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢠⣦⣅⡀
⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢿⣿⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣹⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡇
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡿⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⡇
⠀⠀⠀⠀⠀⠰⠄⠀⠠⠒⠀⠀⠠⠀⠹⠀⠸⠧⠀⠘⠉⠩⠅⠀⠀⠠⠄⠄⠀⠀⠠⠄⠀⠀⠠⠤⠀⠠⠄⠠⠄⠀⠛⠀⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠋⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠀⠀⣼⡟⠀⠀⡀⠀⠀⠀⢠⣾⠂⠀⠀⢀⣶⠆⠀⠁⢀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⠛⣿⠂⢠⣿⡗⢩⣿⠀⣾⡧⠊⣿⠂⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠇⢰⡟⢁⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢤⣼⠟⢀⣿⠃⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠘⠛⣽⡏⠙⠋⠁⢰⡿⠙⠛⠉⠀⠀⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⣴⠞⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⡆⢀⣴⡷⠀⠀⢰⣄⠀⠀⣶⠄⠀⠀⠀⠀⠀⠐⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠉⠉⠉⠛⠛⢻⣾⢿⣶⣿⣯⣤⣀⣠⣼⠟⠀⣼⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣼⠏⢠⡿⢁⣭⣭⡍⢉⣡⣤⣴⡟⠀⠀⢠⣴⠶⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⠀⣴⡿⢁⣼⠇⢀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡃⢀⣀⣤⠟⠁⣿⣧⠶⠋⢰⣿⣥⢾⣿⠀⢸⡟⠁⢼⣇⡤⢿⣤⡶⠻⣧⣴⠞⢿⡥⠊⣿⡤⢺⣿⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠐⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣬⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡇⠀⠀⠀⡸⣿⠙⣦⠉⠉⠉⠛⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣹⠇⠸⣿⣄⠀⡾⣷⡇⠰⣏⠀⠀⠀⢠⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⣀⣤⡿⢦⠀⢿⠻⡟⢃⣿⠀⠀⡞⠀⠀⠀⡏⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠾⠛⣉⣧⣷⣾⠀⢸⡼⠇⢸⡏⠀⡜⠀⠀⠀⢸⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⠖⢻⡏⠉⠀⠸⣆⠈⣷⠀⢸⡇⣸⠁⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⢿⡇⠀⠀⣿⠀⠀⠀⠹⣆⢸⡇⢸⣧⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠛⣿⠁⠀⠀⠸⡆⠀⠀⠀⠹⣦⡇⣼⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠁⠀⢀⡟⠀⠀⠀⢰⢷⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⣀⣴⣾⣿⡟⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡸⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣰⠁
⠀⠀⢀⣠⣾⣿⣟⣻⣿⣏⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣸⣃⣀⣿⣀⣀⣀⠀⠀⣼⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⣰⠃
⠀⠰⠯⠟⠉⠿⢿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⣽⣷⣾⣇⡀⠀⢀⣮⣤⣄⡀⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣼⣿⡏⠁⠀⠀⠀⠉⢹⡛⠛⣶⣄⠀⠀⠀⠈⠛⠿⣿⣶⡋⠁⠈⢙⡿⣴⠏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⣯⣿⣤⣄⣄⣀⣀⣀⣈⣙⣿⡶⠦⠞⠿⠏⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⡏⠉⠉⠉⠉⢈⡏⠉⠹⣏⠉⠁⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⣸⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣀⡤⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⣷⠀⢸⠷⡶⠶⠋⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⡇⠀⣼⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⡇⠸⡇⠀⠀⠀⠀⠀⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⢀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⡖⠀⠀⠸⣥⢤⠄⣴⠀⠐⠄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⠀⡿⢸⠃⢠⠖⡆⠉⢹⠇⠠⠁⣟⡰⠇⠀⠀⣎⢀⡼⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⠦⠀⠀⡇⣼⠀⠸⡄⠔⠁⢙⠂⠁⠀⠀⣀⠆⠀⠀⠀⣰⡂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠻⢦⡔⠊⠀⠉⠀⠀⠀⢀⡆⠀⣾⠉⠉⣉⡉⣄⢠⡖⢂⠀⣿⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠠⢰⡇⠇⢀⡔⠀⡀⢨⠁⠈⣇⢠⡇⢠⡏⣸⢡⡇⠸⡅⠿⢈⠼⡇
⠀⠀⠀⠀⠀⠀⠀⣰⡃⡿⠆⢸⡗⢰⠄⡙⣹⠃⣿⢀⡖⢻⠘⠇⠚⢀⢁⠀⠉⠀⠀⠀⠊⠰⠃
⠀⠀⠀⠀⠠⠂⠀⢻⡄⠀⡠⢾⠁⠺⠔⠁⠙⠀⠈⠀⠣⠞⠀⠀⢠⡟⠈⠀⠀⠀⠠⡞⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡴⠂⠁⠀⢀⡀⠀⣤⢀⣄⡖⢸⠇⠀⠀⠀⠀⡀⠉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠇⠀⡎⢰⠆⡏⠸⠘⢇⡘⡀⠀⠀⠀⢸⡀⣲⠈⣦⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⣠⠔⠒⢄⠀⠀⠉⡴⢀⠀⠀⠀⠀⠀⠘⣇⢁⠠⡄⣤⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⠃⣎⠃⠠⢀⡴⢸⢁⡟⢠⠖⡀⣶⢀⣦⡏⢸⢿⠁⡟⠀⣰⠃⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢷⠈⠁⠀⠈⢁⠎⢸⠁⢿⠠⢇⡏⠚⢹⠃⠉⠠⢰⢗⡋⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠴⠒⠀⠀⠀⠙⠒⠒⠒⡁⡀⠀⠀⠀⠀⠸⠇⠀⢸⠀⣀⠔⠉⢺⡥⣤⠀⠸⠇
⠀⠀⠀⠀⠀⢰⡏⠀⢀⡄⣰⠛⠙⠀⠀⠈⠳⠤⠂⠀⠀⠀⡶⢰⢰⡏⢹⡃⣾⢀⠊⠰⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠉⠀⡞⢡⡏⢠⠖⠆⡇⢸⠀⠀⠀⠀⠀⠐⢇⣾⣘⣂⠀⠁⣀⠤⠖⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⡇⠻⠤⠂⠙⠈⠁⠀⠀⠀⠠⡞⣩⠋⢈⡩⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢠⡞⠉⠃⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⡜⠻⠄
⠀⠀⠀⠀⠠⠔⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⣴⡴⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠸⢀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⡼⡿⠿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠸⢰⣿⡿⣿⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠄⠒⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⠟⠏⠈⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣤⣯⠤⡀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣰⠃
⠀⠀⠀⠀⢀⡙⠻⠿⠷⠾⠿⣫⡄⠀⠀⠀⠀⠀⠀⠈⠲⢼⡷⠀⠀⠀⢠⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⢤⠇
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣁⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠂⠒⠚⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠢⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠛⣿⡿⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠲⠤⡌⣉⠀⡤⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⣼⡄⠀⠀⠘⠙⠓⠒⠒⣒⣲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺⣿⣧⡠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢻⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣷⣂⡀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⠧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣿⣷⣦⠀⣡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥
⠀⠀⠀⠀⠀⢀⣿⣻⣛⡓⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠲⠤⠭⠭⠙⠂⠈⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠉⠉⠀⠐⠒⠒⠂⠠⠤⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁
⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣆⣠⠃
⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡟
⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢡⠞⠙⠒⠦⣄⡀
⠀⠀⡟⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⡰⠋⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠣⣀⡀⠀⠀⠈⠉⠀⠒⠲⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡔⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⠟⠑⠢⢄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠉⠉⠐⠢⠄⠄⠀⣀⣀⠠⠊⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠓⣄⡀⠀⠀⠀⠀⠉⠉⠉⠁⠶⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⣠⡾⢽
⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠲⠶⠖⠒⣉⣀⡤⠤⠤⠀⠀⠀⠀⠀⢀⠞⣿⡯⡅⠿⡿
⠀⠀⠀⠀⠐⣄⠀⠄⡄⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⣀⠀⠀⠀⠀⢀⡠⠖⠁⢀⡿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠑⢄⡁⠠⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠂⠀⠀⢀⣀⠤⠔⢊⠁⡐⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⡇⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢊⢩⠀⠀⠀⠀⢄⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢇⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠁⠠⣧⠘⡈⠀⣃⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⡀⢀⠀⠰⠀⠸⠀⣁⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⠼⢤⡤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠆
⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⣰⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠀⢈⡿⣦
⠀⠀⢀⣹⣟⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠶⢶⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⠆⠀⡄⠀⠀⠀⠀⠀⠈⠟⠀⣾⠡⣼⡀
⠀⠀⠈⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠅⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠘⠋⡀
⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢠⡟
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣿⣆⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠏⢿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣁⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠈⣿⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⣀
⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻
⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠚⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⠀⠀⠈⢻⡄⠀⠀⢀⣤⠤⠖⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠒⠂⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠀⠀⠀⢸⡟⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠚⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠂⠀⠀⠀⢻⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷⠀⢳⣄⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠙⠷⠶⠖⠛⠋⠁⣀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⢇⢻⠀⢹⡞⢸⡼⢪⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠃⠈⠈⠁⠀⠀⠈⠁⠋⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⡹⢀⣤⡀⠀⠉⠀⠀⠠⢀⣀⠀⠀⢠⡀⠀⠘⠁⠀⢀⠇
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠐⠋⣰⠋⠀⠀⣀⠀⠀⠀⠰⠂⡀⠉⢱⠟⠲⠦⠴⠶⠚⠁⠸⠀⠀⠀⡀
⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣰⠃⢠⡆⠀⢑⡦⢀⡼⠀⢸⡋⢠⠋⣴⠀⣴⢂⡄⢀⡴⢚⡁⠀⢸⡃
⠀⠀⠀⠸⣇⠀⠀⡀⠀⠀⠏⠀⠘⠀⠀⠘⠀⠘⠁⠐⠾⠃⠇⠘⠁⠈⠁⠺⠁⠘⠁⡘⠃⠐⠼⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢥⡶⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡷⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠸⠚⡖⠀⣶⢰⠀⣾⡀⠈⠎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠒⠒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠞⠑⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠁⠉⠃⠁⠀⠑⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢰⢎⡀⢀⣰⡄⠀⠔⠄⠠⠀⠀⢙⠀⠀⠄⠂⠋⠀⡀⠀⠀⠂⢀⠄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠾⠟⡗⢚⢁⡀⠀⠈⠁⠀⠂⢅⢣⣑⡀⠃⠀⡀⠀⠀⠀⠈⠀⠐⠀⠈⠍⠀⠐⠂⡈⠄
⠀⠀⠀⠀⠀⠀⠘⠆⢑⣄⠈⡠⠛⠶⢉⢃⠀⡀⠰⢳⠖⠲⠀⡾⠁⠀⠠⡁⠂⠐⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠂⠀⠀⠁⠄⠀⡈⠠⠀⡀⠀⠔⠉⠀⠈⠢⡀⠀⡀⢠⠀⠀⠀⠀⠉⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠠⠀⠨⠾⠀⣀⣀⠀⠀⠀⢀⠀⢐⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠈⢉⠐⠀⠀⠖⠋⠀⠀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⡞⠒⠒⠒⠂⠀⠀⠀⠀⠀⠃⠀⠠⠆⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⣈⡈⢄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠀⠀⠀⠀⠈⠉


⣶⡖⢲⡶⣶⣶⡶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠔⠚⠝⠉⠉⠙⠓⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠁⠀⡘⠀⠀⠀⠐⠀⠀⠑⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢛⣉⣩⡤⠤⠤⠤⠤⠠⠤⠤⠍⣹⣛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠒⠫⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢂⠀⠀⠁⠀⠀⠀⠈⠀⢀⠀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠠⡁⠀⠀⡀⠀⢠⠁⡠⡣⠊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠳⠚⠒⠒⢋⠁⠀⢠⠁
⠀⠀⠀⠀⠀⡴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⢤⡀⠀⠀⠀⠸⠀⢀⠆
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣀⡅⠀⠀⠀⠀⣇⡎⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠐⠀⠒⠀⠁⠈⠁⠀⡄⢉⡀⢀⡀⢀⡀⣀⠅⠀⠀⣤
⠀⠀⠀⢀⠌⠀⡘⠀⢀⠀⠀⠀⢀⠀⠃⠀⢠⠀⠀⣨⠇⠸⠇⠸⠂⠺⠂⠀⢼⣿⡧⡀
⠀⢀⠔⠁⢀⠔⠀⠀⠂⠀⠀⠀⠘⠀⠀⡀⠀⠡⠀⠈⠢⡄⠀⠀⠀⠐⠠⠂⠳⠙⠙
⠺⠷⠶⠲⠷⠶⠖⡾⠲⠶⠷⠖⠶⠷⠖⠾⠖⠶⠺⠖⠶⠶⠷⠀⢀⠔⡠⢀⠁⠀⠐⡀⠄⠢⡀
⠀⠀⡀⠀⡆⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⢀⠁⡀⠐⠁⠔⠁⠄⢀⠀⠀⠀⠈⠂⠈⠂⢀
⠀⠀⢁⠀⢀⠀⠀⢰⣲⠚⠓⣦⡞⠓⢒⣾⠀⠀⠰⠀⢰⣉⣀⣤⣎⣀⣬⣠⣬⣀⣤⣄⣥⣀⣱⣤⣀⣁⣦
⠀⠀⠘⠀⠈⠀⠀⢸⡿⠀⢀⣿⡇⠀⠀⡇⠀⠀⡀⠀⡀⠀⠄⠰⠀⠀⡀⠀⡃⠀⢀⠀⢠⠀⠀⠃⠐
⠀⠀⠀⡄⠀⠀⠀⢸⡟⢰⣸⣿⣧⣴⠀⡇⠀⠀⠇⠀⠁⠀⠰⠀⠆⠀⢸⡏⠉⣿⡋⠙⡏⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻⣿⣿⣿⣟⠧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣷⡇
⣶⣶⡶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣾⣶⣶⣶⣷⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣌⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠐⣿⣧⣻⣿⠿⣠⣭⣿⣟⣿⣿⣧⣤⣤⡄
⣿⣦⣄⣀⣀⡀⠀⢛⣿⣿⣿⣾⠄⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢸⠋⣿⢏⣼⡿⠟⠋⠁⠉⣿⠿⠿⣿⣿⣶
⣿⡿⠛⡉⠉⠀⠀⣿⣿⣿⣿⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡾⠋⠀⣀⣀⡀⢀⣀⡀⠀⠈⢿⣿
⣿⣟⣀⣧⢠⡀⠀⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⣿⣿⣷⡄⠀⠀⢶⠒⠦⠀⠤⠄⠐⠉⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀⠈⣿
⣿⡏⣿⣎⣿⠃⠀⠀⠈⠙⢿⣿⣿⣿⣧⣤⣴⣆⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⠟⠀⠀⠀⠁⠀⣀⠉⠋⠀⠛⠛⠛⠛⠁⡼⠛⠉⠉⠻⣿⣿⠃⠀⣾
⠛⠣⣬⡛⡄⢀⡠⠖⠄⠀⠀⠙⠻⠿⠿⠟⣥⢿⣿⣶⣴⣾⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⢸⠇⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡚⠛
⠀⠀⡈⠑⠀⠋⠁⠀⠀⠀⠀⠲⣴⠦⢀⣿⣿⠈⠻⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⣰⣿⡻⢿⣶⣶⣶⣶⣶⣶⣤⣴⣶⡟⣽⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⣰⣿⡿⠃⠀⡌⠉⠉⠉⠉⠉⠛⠉⣁⣾⣿⣧⡙⢷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⣿⠟⠀⠀⠀⣿⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⠛⠿⠯⠰⢦⣄⠀⠀⠀⢆⢻⣧⡀⠀⠉⠛⠷⠦⣤⣤⣤⣴⠖⠀⠀⠀⢀⣤⣤⣿⣿⡟
⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⢿⡶⣦⡀⠀⠘⠿⣷⣦⣄⣈⣁⣉⣙⣻⡶⣲⡄⠂⠁⣾⣿⣿⣶⣄⣀⣀⣾⣿⣿⣿⣿⠁
⠁⠀⠀⠀⣾⣿⣿⣿⡻⣿⣿⣿⣿⣻⣿⠟⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠞⣫⣿⠛⣹⢶⣿⣯⡀⠀⠀⠉⠛⠿⣿⣿⣏⣿⣿⠏⠙⠿⠃
⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⣼⣿⡇⢠⡸⣧⡿⢿⣿⣷⣦⣀⠀⠀⠀⠈⠙⠛⠋⠀⣦⣀⣀⣤
⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣜⡏⠀⠀⣿⣿⣷⠀⢱⣽⣿⡦⠙⢿⣿⣿⣿⣶⣤⣦⠀⣀⣀⣠⡏⠻⡿⠟
⡄⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⣿⣿⣿⠀⠸⠯⣿⣇⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⡄⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⣿⣿⡏⠀⢠⠀⢸⣿⠀⠀⠀⠀⠉⠉⢀⠈⣿⣿⣿⠁
⢿⣿⣦⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⠛⠛⠁⠀⢀⣴⣿⡿⠁⠀⢾⠀⢸⣿⡄⠀⠀⠀⠀⠀⡇⢸⣿⣿⣧
⣈⣻⣿⣷⣄⣀⣀⣻⣿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣶⣿⣂⣀⣻⣷⣾⣿⣿⣟⣁⣀⣐⣊⣀⣸⣿⣿⣦⣀⣀⣀⣀⣷⣀⣻⣿⣿⣷⣄⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠛⠛⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠘⣿⣿⡀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⢀⣼⠛⣿⣿⠁⠀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣀⡀⣹⣿⠷⢤⣀⡀⢀⣼⣿⣦⠀⠀⠀⢠⡟⠁⢀⡿⠿⣄⣀⣤⣶⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠉⠉⠛⣻⣧⣀⠀⠀⠙⠻⣿⡿⠉⢷⡀⢠⣿⣷⣴⠋⠀⠀⢸⠿⠛⠋⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣿⣿⣿⡿⠛⠲⢤⣄⣈⢧⡀⠈⢷⡞⢹⡟⣁⣠⣤⣶⣇⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⢤⣄⣉⠙⢻⡦⢸⡇⢿⣿⣅⣠⡴⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠿⣿⣿⠉⠋⠉⠉⠉⢻⠋⠉⠉⠉⠛⠛⠓⠒⠒⠲⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣀⣀⣠⣤⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⡇⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠦⢤⣤⣤⣤⡼⠷⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢐⠒⣠⠂⡖⢒⡖⢀⣤⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⠢⠒⠀⠀⠀⠐⠀⠀⠀⠀⣂⡄
⠀⠀⠀⢰⠋⠻⣶⣦⣤⣀⡀⠀⣠⣄⠀⠀⢀⣆⠘⣶⠙⣶⠁⢸⠀⠙⢮⠀⣾⢀⡿⠁⡶⢲⡤⠄⣀⣀⠀⠁⢢⡀⢀⣏⠉⠀⠀⠀⠀⠀⠁⣉⣿⠇
⠀⠀⠀⣼⣀⣬⣿⣿⡿⠋⠁⠀⠾⢧⣴⠃⠀⣿⢠⠈⠀⠀⠂⠈⠈⠁⠮⠐⠃⠸⠇⢰⠃⡌⢹⡜⢡⠞⠣⠉⢻⣷⠞⢸⣿⣿⣿⠿⠛⠉⡇⢻⣽
⠀⠀⠀⠻⣿⠀⠈⢹⠁⠀⠀⠀⠀⠀⣿⣷⠦⡹⠞⠛⠛⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠹⣀⠏⠠⠞⠃⣿⠸⣿⠁⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⠀⠹⣷⣄⠀⠀⠀⠇⢫⡙
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⣑⣾⡏⠀⠀⠀⠀⠀⡠⠒⣤⠀⢂⠔⢲⡀⡖⠀⠏⠀⠉⣡⠒⠠⡀⠀⠀⠀⣶⡇⠀⠀⠘⢿⣿⢶⠞⡁⣜⣏
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⡀⠀⠀⠀⠠⠁⠀⡼⠀⠸⠤⠞⠸⠇⠜⠀⢠⠞⢹⡆⣰⠟⠀⠀⠈⣰⡟⠀⠀⠀⠀⠿⡇⠀⠈⣿⡏
⢀⣤⣶⣏⠉⠉⠁⠐⠐⠒⠀⠄⠀⠀⢻⡇⠁⠀⠀⠀⣦⠖⠐⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠓⠶⠏⠀⠀⠀⠀⡌⢓⣶⣾⣶⠶⠤⠙⢆⡌⠗
⣼⣿⣿⣿⠟⠛⠉⠉⠁⠂⠀⣠⡀⠀⣤⠥⡤⢀⠤⠤⢿⠤⢤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⣛⠿⡆⠀⠀⠀⠘⠃⣿⢶⡤
⠘⠻⣿⠟⠀⠀⡠⢀⠀⣤⠀⣖⡶⢸⡯⠃⢻⡎⠀⠀⡸⢳⡜⢀⣯⠁⢲⣀⣿⢡⠆⠒⢂⠤⠀⠀⢀⠀⠀⠈⡄⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠉⠸⡇⠠
⠀⠀⠀⠁⢐⠁⡇⢿⠰⠛⣆⣛⡀⡬⠥⡴⠚⠒⡖⠒⢳⢠⠥⠼⢷⣆⣘⡃⠹⠃⠀⠀⢸⡗⠁⣶⠂⢀⡎⢹⢗⣆⣿⠷⣄⡀⠀⠔⣤⡀
⠀⠀⠀⠀⠈⠀⣣⣥⣂⠉⠛⠛⠐⠛⠛⠓⠀⠈⢀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠸⢁⡘⢧⡤⠃⠇⣼⣻⣼⡛⠓⠈⠛⠛⠿⠿⠿⠷⢦⣤⡄
⠀⠀⠀⠀⠀⠻⣟⢛⠛⠛⠉⠀⠂⠀⠀⢀⡠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣄⣀⣀⣀⣀⣀⣤⠾⠛⠁

⠀⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⠀⡀
⠀⠀⢀⡾⠙⣄⢿⣿⣷⣶⣶⡤⠠⠥
⠀⣠⠎⠀⠀⠈⢿⣿⣿⣿⣿⣇⢀⡤⡄
⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⡀
⠀⠀⠀⢀⠀⠀⠀⢈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⡀⠈⠋⠉⠀⠀⠄⠂⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡟⢺⡟⠀⠌
⠀⠠⡀⠀⠀⠀⢸⠀⠀⠀⢤⡀⠀⢨⡄⢠⡄⠼⠀⠀⠂⢀⠆⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣠⣄⡼⢀⣿⣿⣦⡄
⢠⠦⠁⠀⠀⢀⣹⠀⠀⢐⡋⠀⢀⣿⡷⢃⣀⠐⠀⠀⠈⠁⠀⠀⣺⣟⠁⠀⠀⠀⠀⠀⠈⠛⠛⣧⣾⣻⣿⡟⠄
⠀⠀⣀⡤⠔⠊⠻⢦⠀⠀⢹⡆⢠⢬⡅⠀⢈⡇⠀⣶⠀⠀⠀⢪⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⣿⠒
⠀⣈⠍⠀⠀⠀⠀⠀⠀⠂⣼⡇⢰⣌⣿⠀⢘⠓⠀⢨⡅⠀⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⢠⡽⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣞⢻⠁⠀⠸⠀⠈⢛⡅⣀⢹⣿⢛⣷⣿⣏⠀⠀⠀⠀⠀⢀⡀⡠⠀⠀⠀⡹
⠸⠀⠸⣷⣞⡿⠆⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⢘⣼⡇⢡⠀⡀⡀⠈⣿⣿⡄⠄⠠⠀⢀⠘⠤⠷⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⢰⣾⣿⣷⠀⢀⠀⠀⠈⢫⣵⣾⣦⣷⣷⣟⣿⣿⣷⠄⠀⠠⠿⢿⠂⠀⠀⠀⠀⠀⢠
⠰⣶⣷⣄⣀⠀⠀⠀⠇⡀⠈⣿⡿⠙⠀⠈⠷⣾⣠⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣻⠀⠀⣴⣿⣿⣦⣀⡀⠀⠀⠈
⢰⣶⣤⣭⣿⡏⣵⣤⣀⣥⣀⣙⣄⣀⡠⠤⠤⠀⢻⣿⠛⢻⣿⣿⡿⣿⣿⡿⣿⣿⡀⣴⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠉⠉⠛⠿⠿⠶⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⢝⠂⢾⣇⣀⠈⠉⠉⠿⠿⠿⠿⠿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⢤⠄⡀
⠀⠀⠀⢀⠜⠁⠀⢀⣀⠀⠀⠙⢆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢸⣀⡀⠐⠁⠀⢑⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠸⡄⠂⠌⠀⠀⠀⠃⠀⢀⡐⠁⠈⠃⠀⠀⠀⠀⠀⠐⠴⠐⠐⠁⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⠀⠀⢸⠒⠄⠠⠀⠀⠀⠁⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠌⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⢚⠀⠀⡂⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠱⠤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠈⠀⠀⡠⠂⣀⣀⠀⠀⠘⡄⠂⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢣⠔⠈⠀⠁⠉⠅⠀⣰⠃⠀⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⢥⠀⠀⠸⡄⠀⠀⠀⠂⠉⠀⢀⡄
⠀⠀⠀⠘⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠮⠤⠤⠤⠐⠁⠀⠀⠀⠣⠤⠤⠤⠤⠄⠀⠀⠤⠊⠀⠀⠀⠈⠒⠂⠤⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠠⠁⡌⠀⢀⠀⠀⢠⢤⠀⠀⡔⠀⠀⢀⡆⠰⠀⠀⢐⠐⠒⠠⠀⢀⠒⢒⠒⠢⡀⠐⣲⠀⢠⠀⠂⠀⠀⠠⠡⡄⠄⡠⠀⠄
⠀⠀⠀⢠⢀⡑⠆⠃⠰⠀⣠⠄⠀⢐⠀⠀⡃⠐⠀⢐⠰⠆⠤⠀⠃⠰⣈⠂⠘⢨⠀⠩⠝⠀⠅⠆⠸⣀⡌⢠⠃⠐⠀⠀⢓⠠⡀⢘
⠀⠀⠀⠐⡀⡅⠠⠨⢈⡁⠀⠀⠀⠈⠂⠖⠀⠀⠀⠀⠈⠁⠈⠀⠇⢠⠄⠀⠂⠨⠀⡤⠀⠈⠀⠈⠢⢤⠀⡀⠀⠀⠨⣀⣁⠆⠐⠈⡀⢀⠄
⠀⠀⠀⠈⠀⢠⠂⠘⠀⠠⡘⠀⠅⠘⠁⠑⠀⠀⢐⢀⠎⢂⠀⡆⠃⣠⠀⠀⠀⢸⣀⠄⠀⠀⠀⢂⡐⠊⡠⠃⠀⠀⠀⠀⠀⠀⠣⠀⠠⠂⠤
⠀⠀⠀⠀⢀⠐⠀⠀⠑⠀⠀⠀⠐⠂⠀⠀⠒⠁⠈⠉⠀⢀⠉⡐⢈⡁⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠪⠈⢠⠤⠂⠒⡀⠁⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡀⠆⠠⠁⠁⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠌⣀⠴⠊⠀⠀⢀⠠⠀⠆⢉⠂
⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠄⡫⠀⠂⠐⠄⠀⡌⠀⠃⠀⠀⡂⠀⠀⠀⡰⠃⠘⠁⠀⠀⠀⠀⠀⠈⠀⠂⠂⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠀⡁⡈⡄⠀⠀⠀⢠⠀⠠
⠀⠀⠀⠀⣤⠈⡀⠀⠀⠀⢀⠄⠠⡀⡠⡀⠀⠀⣀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠈⢆⡀⠈⣁⠀⠀⠀⡠⠤⠤⡀⠀⡀⠤⠤⠀⠀⡤⡄⡀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠐⢡⡈⡀⠀⠁⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡘⠀⠯⠂⡐⠐⠀⠀⠀⠀⠀⠀⠂⡠⣈⠕
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠄⠙⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠄⠁⢀⡔⠊⠀⡇⢨⠀⠀⠁⠀⠀⠒⠁
⠀⠀⠀⢅⠀⠀⠤⡠⠀⠐⠀⠀⠩⠂⠀⠀⣄⠀⠀⢀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠤⣀⣉⡠⠎⠀⠱⣄⣉⡤⠃⠱⣀⡠⠠⡱⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠻⠷⢿⠟⡿⢻⡾⠁⠞⠟⠞⠻⠞⠠⠿⠿⠟⠿⠻⠟⠁


⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀
⠀⠀⢾⣿⣿⣷⠀⣾⣿⣿⣷⠀⢼⣿⣿⡄⠰⠿⣿⣿⡆
⠀⠀⣰⣿⣿⠏⠸⣿⣿⣿⣿⠀⢀⣿⣿⡇⠀⣚⣿⣿⡇
⠀⠀⠻⣿⣿⡿⠀⠻⣿⣿⠏⠀⠘⣿⡿⠁⠘⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠚⠂⠀⠀⠐⠀⠆⠀⠀⠀⠂⠒⠀⠀⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡟⠀⠀⢰⣿⡏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠸⣿⣿⣏⠁⠀⠀⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣖⣛⡻⠭⠽⣟⣓⣒⠦⣤⣀⠀⠀⢀⣠⠴⢖⣚⣛⡯⠭⠽⣟⣓⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠕⠋⣁⡤⠤⢤⣄⣀⠀⠈⠉⠒⠮⣝⣛⠭⠒⠋⠉⠀⢀⣀⡤⠤⢤⣌⡉⠲⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⡱⠃⣠⠊⠁⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠉⠉⠛⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠙⢦⠈⢳⣹⡄
⠀⠀⠀⠀⠀⠀⢸⢣⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⢀⣀⠀⠀⠀⠀⣈⠀⢀⠀⡀⠈⡇⠀⡇⣷
⠀⠀⠀⠀⠀⠀⢸⢸⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠥⣄⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⢐⠄⠉⠀⢀⡇⠀⡟⣿⠀⠀⠀⢠⠖⠢⡴⠋⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠘⣇⢇⠀⠹⡄⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠑⡄⡴⠂⠐⠢⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⢣⡏⠀⢀⠤⢼⡀⢀⡇⠀⡸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠙⣎⢦⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⣻⠀⡄⠀⠀⢱⠀⠀⠀⠀⠀⠀⣼⠀⢠⢫⡞⠀⠀⠸⣄⠀⠙⠒⢄⠉⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠀⢘⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡼⠁⠀⠀⠀⡄⠀⠀⠓⠦⠤⠶⠋⠀⠑⠦⠤⠞⠁⠀⢠⠄⠀⠀⠀⢹⡀⠸⡟⡇⠀⠀⠀⠀⠀⡇⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⣼⠁⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⢳⠀⡇⡇⠀⠀⠀⣠⠞⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⢳⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠤⠤⠤⠤⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠒⠒⠋⢁⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢿⢹⠒⠚⠋⠉
⠀⠀⠀⠀⢀⣠⠴⣾⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢸
⠀⠀⢀⡴⠋⢀⡤⣿⣾⠀⢸⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡆
⠀⠀⡞⠀⢰⠋⠀⡇⡆⠀⣸⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⢸⡇
⠀⢸⠃⠀⣿⠀⠀⡇⡇⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⢏⡇
⠀⢸⠀⠀⠙⢢⠀⢷⢱⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡸⢸⠃
⢰⠃⠀⢀⠀⠘⠒⢮⢧⡳⣌⡓⠢⠤⠤⠤⠶⠒⠒⠲⠤⣄⣀⣀⣀⣀⣠⡤⠔⠒⠒⠲⠤⠤⠤⠴⠒⣁⠔⣱⠃
⡟⠀⢰⠻⡑⠲⠶⠋⠀⠙⠲⢭⣝⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡭⠵⠋⠁
⢧⣀⡼⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⠉⣿⢹⠉⣿⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠛⠒⠦⣼⠀⣿⢸⠀⣿⡤⠖⠚⠛⠋⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠉⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣇⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣆⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢁⡈⢿⣆
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢛⠉⢆⠀⠈⡴⠉⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢿⣶⣤⣤⣀⣀⣀⣀⣀⢀⣀⣀⣀⣤⡴⢖⠾⡉⣿⣗⠐⠤⡌⠀⠀⢡⢤⠂⣺⣿⢉⠷⡶⢤⣤⣀⣀⣀⣀⡀⣀⣀⣀⣀⣤⣤⣶⡯
⠀⠀⠀⠀⠈⢿⣿⠒⠭⡋⠉⠛⣽⠻⡝⠃⣤⠊⢀⡾⣛⢻⡌⠻⣷⣌⠡⠆⠰⠌⣡⣾⠟⢡⡟⣛⢷⡀⠑⣤⠘⢫⠟⣯⠛⠉⢛⠭⠚⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣟⣹⣯⣂⠤⠘⡀⠀⠀⡑⠲⠟⢰⡿⣤⠇⣠⣄⡝⠷⣆⣰⠾⢫⣠⣄⠸⣤⢿⡆⠻⡶⢎⠀⠈⢀⠃⠤⣐⣿⣏⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⡟⠋⣫⢟⢓⢦⡑⠀⢈⠛⢤⡴⠟⠂⣼⢫⣿⠃⠀⠸⠗⠀⠘⣿⡟⣧⠐⣺⢦⡠⠋⠃⠠⢊⣵⡿⡿⣍⠙⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⢧⠯⠈⠳⢿⠀⠀⣁⠀⠀⠀⣀⠙⠿⣿⠀⡀⢀⡀⢀⠀⣿⠿⠋⣀⠀⠀⠀⣈⠀⠀⣿⠞⠁⠝⡼⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⡀⢐⡏⡇⠈⠟⣰⣷⠄⣀⢤⣼⡛⢦⡳⣏⣹⢞⡴⢛⣧⡤⣀⠠⣿⣆⠻⠀⢸⢻⡀⠀⣦⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⡏⡇⠀⠀⢫⠋⠀⠧⠞⢀⡟⢸⣿⡎⢱⣿⡇⢻⡀⠣⠼⠀⠙⡝⠀⠀⢸⢹⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣇⠀⠀⠘⢠⣫⠀⠀⣾⡇⡏⠀⠀⠀⠀⢹⢸⣧⠀⠀⣝⡄⠃⠀⠀⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣘⣦⠿⣟⠻⢷⣷⠀⠀⠀⠀⣾⡾⠟⣻⠿⣴⣃⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢾⢤⣞⣻⣳⣄⣠⣞⣟⣳⡤⡷⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⠆⠸
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣄⠀⠀⠀⣀⠤⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠘⠉⠁⠒⢄⠀⠀⡀⠀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠳⠶⠚⠁⠀⣡⣀⠔⠁⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠒⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⠟⢉⡍⠀⠀⣇⠀⠉⠉⠓⠛⠒⠒⠒⠒⠒⡟⠀⠀⠰⡟⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢈⡶⢹⠀⠀⠀⡇⠈⠐⠒⠀⠀⠤⠄⠀⠒⡾⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⢻⠀⠀⠀⠸⡆⠀⠀⠤⠄⠀⢀⣠⠞⠀⠀⠀⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⠶⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠃⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠒
⠐⠂⢉⡆⠰⠒⠈⠀⠀⠀⠀⠁⠒⠂⠤⢄⣉⡑⠢⠤⣀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢀⣀⠤⠐⣀⠔⠉⢦⡀⠀⠀⢀⠀⠠⣔
⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣌⡉⠒⠺⠛⣿⠶⠶⠶⣶⠶⠶⠟⠉⠀⢒⣂⣈⣭⠤⠔⠒⠉⠁⠀⠀⠀⠉⠓⠀⢧⠘⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡰⠁⠘⠒⠛⠁⡶⠂⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠉⠑⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⡴⠀⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣠⣤⣴⠞⢉⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠢⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣀⠇
⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠛⠛⠿⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡼⢁⠄⠀⠀⠀⠀⠀⠒⠢⢤⣄⡀⠉⠛⠒⠖⠛⠁⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⡜⢡⠏⠀⠀⠀⠀⠀⢀⡤⠶⠢⠈⠙⢦⣄⠀⠀⠀⠀⣀⣴⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣆⠀⢰⡏⠀⣠⣿⣿⡄⠀⠙⠻⠿⢿⡿⠟⢃⣄⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣥⡤⠄⠀⠀⠀⠀⠹⣆⣹⣇⠀⠈⠋⣱⠁⠀⠀⠀⠀⣾⠁⢠⣾⡿⣸⣧
⠀⣀⣀⣀⠀⠀⢀⣴⠞⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢿⣦⣀⣩⡼⠉⠉⠛⠳⢦⡀
⣾⠋⠉⠉⠛⠶⠟⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣄⣀⠀⠀⠀⠀⠉⠉⠉⠀⣴⣄⠀⠀⠀⠙⣦⡀
⠘⠻⢶⣦⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⡇⠀⣼⠀⢀⣽⣿⠿⠿⠟⠋⠀⠀⢰⡟⠉⢳⡄⠀⠀⠘⠷⠶⠤⣤
⠀⣠⠞⠉⠀⠀⣀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣼⣤⣼⣷⡾⠟⠉⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⡼⠃⠀⠀⠀⢀⣀⣀
⠠⣿⠀⠀⢠⡏⢸⡇⠀⢸⣷⠀⡄⡄⡀⠀⠀⠀⠐⢦⣀⠀⠉⠉⢀⣀⣠⠔⠂⠀⠀⠀⠀⣠⡟⠁⣴⠋⢀⣴⢶⡆⠀⣿⠀⠉⠙
⠀⠻⣦⣤⡿⠁⠸⣧⣤⠎⢻⡄⢣⢡⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠳⣤⡾⠃⢸⣧⠀⢸⡄
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢿⡌⢧⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠱⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠠⡀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⡇⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠈⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⡁⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡓⠄⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠏
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢴⠶⠖⠲⠛⡛⠯⠽⠛⠿⠛⢛⡛⣿⣶⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⢋⡉⠰⠅⠚⠶⠉⠁⠈⠉⠉⠀⠒⠒⠒⢒⠶⠬⠄⠉⠧⣭⡹⢿⢿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠃⢥⡄⠾⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠄⡀⠉⢸⡻⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈⡭⠁⠑⠒⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠰⣂⣽⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡓⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠌⠀⠛⡶⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣄⠾⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠐⢡⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣆⠑⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠂⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡧⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠌⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣂⡭⣄⣼⣟⢁⣀⣁⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢦⣿⣿⣿⣿⡿⢀⡀
⠀⠀⠀⠀⢀⡤⢚⣥⣶⠏⠁⠈⠓⠻⠿⠶⠶⣴⣿⣝⣀⣴⣄⠐⠲⠂⢀⡂⠤⠀⣀⠀⠀⠀⠰⠀⠂⢈⠞⣆⣸⣿⣿⣿⣿⡧⢀⠈⠁⠂⠄⡀
⠀⠀⢀⡴⣫⣾⠟⠙⠻⠛⠒⠒⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢶⣿⣥⣄⣀⡁⠒⡒⠐⢎⣹⡈⠀⣠⣼⣿⣿⣿⣿⡁⠀⠨⢑⠢⢄⠨⢑⠢⣀
⠀⢠⠎⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⣿⣭⣖⣥⣿⣿⣿⣿⣟⣤⠑⠂⠀⠘⠋⠀⠀⠱⣮⣗⢄
⢀⡏⣸⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠠⠐⢢⠤⣤⣄⡀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠐⠊⠒⠀⠀⠀⠈⠈⢻⣯⡳⡀
⣸⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠐⠒⣀⠽⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢄⠀⠀⠀⠀⠘⣷⡹
⣿⢸⣿⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠽⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⡇⢸⡜⡆⠀⠀⠀⠀⠘⡇
⡿⢸⣿⢅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⣥⡧⠶⠤⣤⡀⠀⢹
⣇⠈⣿⡡⢒⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣂⠉⢀⠀⠀⠀⠀⠀⠀⠚⢧⡀⠘
⣿⠀⣿⣎⠥⢂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣇⣸⣇⣰⣖⣀⣀⣤⣤⡶⡊
⢹⡄⢹⣷⣊⠥⠒⡀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠛⢋⢹⠀⡇⡿⠛⢥⡤⠀⢀⣇
⠈⢷⣄⠙⠷⣶⣩⡔⣊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠰⠛⠁⠀⠀⠠⠀⣼⣿
⠀⠈⠙⠿⣶⣤⣉⡛⠻⠶⣦⣴⣀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣾⠋⡶⡄⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣤⣬⣉⡛⠻⠷⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣻⣀⣷⣇⣤⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⣶⣤⣬⣉⡉⠐⠃⠒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣁⠀⠀⠀⠀⠀⠀⠀⢔⣊⡽⢿⣟⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣯⣥⣤⣤⠤⠤⢒⣐⣩⣭⡷⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠷⠶⢶⣦⣤⣤⣤⣤⣴⠶⠶⠿⠛⠋⠉⠁