Financial Emojis & Symbols

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⣄⢤
⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⢤⡄⠀⠀⠐⡤⡀⢀⠀⠉⠁⠀⠀⠀⠀⠁⡄⠀⠀⠆⢀⠀⣯⡼⠏
⠀⠀⠀⠀⠀⠀⠀⢐⣦⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡏⠀⠀⠶⠛⠀⠀⢀⡴⢮⣿⣤⠀⠈
⠀⠠⠚⡠⠟⠀⠖⡾⠋⠁⠉⠑⠠⣀⠀⠀⠀⢒⠢⢈⣻⠋⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠙⢏⡺⣄⠸⣯⡀
⠀⠑⠚⠁⠀⢀⠋⠀⠀⠀⣿⣶⣄⠀⠑⠄⠀⠉⠀⠞⠩⣠⠄⠀⠀⠄⢀⣴⡶⢶⠆⠀⠀⠀⠈⠙⢅⠀⠈⠁
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⣿⣿⣤⡀⠀⠀⠐⡀⠀⠀⠚⠁⠀⠀⢀⣲⠋⣞⣲⣶⠂⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠹⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠈⢾⣓⣒⣲⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠙⣿⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠳⠶⠆⠀⠀⠀⠑⠤⢀⡀⢀⣀⠀⠀⠀⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠈⢁⠈⠒⠂⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃
⠀⠀⢰⡇⡶⠄⠀⠙⠧⠀⠀⠀⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠰⣄⠀⢀⣤⢄⣀⣀⡀
⠀⠀⠀⠙⢤⣤⡀⠀⠀⠀⠀⠀⠁⣤⠾⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢹⡄⠀⠻⢆⠰⠖⠚⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢠⠞⠁⢠⡀⠀⠀⠠⠖⣸⠆⡇⠀⠀⢸⠀⠀⠀⠈⠓⠦⣄⡉⠉⠀⠀⢷⡂
⠀⠀⠀⠻⠖⠀⠀⣠⠞⠀⠴⠃⠀⠀⢸⠀⢠⠀⠙⠋⠀⠀⡇⠀⠀⠸⡄⠀⠀⣦⠀⠀⠀⠉⠲⣄⡀⡀
⠀⠀⠀⠀⠀⢀⡴⢃⡀⠀⠀⣷⠀⠀⢸⠀⢘⠀⢠⣤⠀⠀⡇⠀⠀⢨⡅⠀⠀⡧⠀⠀⢀⠀⠄⠈⠉⢫
⠀⠀⠀⠀⡰⠋⠀⠀⡇⠀⠀⣿⠀⠀⣸⠀⢸⠀⠈⠳⠂⠀⡇⢠⠀⢘⡃⡀⠀⡏⠀⠀⠀⡅⠐⠀⠀⠀⢧
⠀⠀⠠⠎⠀⢲⠀⣀⣇⣀⣤⣿⣠⣤⣿⣄⣼⠀⠀⠀⠀⠠⠧⠼⠶⠾⠦⠷⠴⠷⠤⠦⢤⣇⣀⠀⠀⠀⠈
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠴⣄⣀⠀⠀⠀⠀⡀⠀⡰⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢉⣇⣠⣤⡄⢀⣀⢰⠞⠀⠀⠺⢃⡇⠀⢠⠫⠁⠀⠀⣠⠤⠷
⠀⠀⠀⠀⢀⡱⠖⠁⣀⡟⣹⣖⣢⡾⣿⠃⢨⡿⠉⠻⠀⠀⠀⠛⠃⠀⠈⠈⠉⠀⡴⠕⠀⣀⠐⣄⠀⠀⢀
⠀⢁⢀⣑⣺⠁⠀⣿⣛⠐⠂⣿⠁⠀⠋⣡⡴⠆⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠆⠸⠍⠀⣿⠀⠀⠠⣄
⠀⠘⣠⠄⢸⢇⣀⢿⢟⢀⢀⡹⠖⢋⠄⠉⠁⠈⠁⠀⣠⡨⠤⠀⠠⣀⣀⣈⠀⠀⠀⠈⠂⠶⠚⠁⢀⢔⠀⢀⠠
⠀⠈⠀⠀⠰⠺⠿⠞⠟⣄⣀⣉⣼⣀⠀⠄⠂⠀⠠⡎⣸⠻⢌⣪⡝⢤⠛⠳⠄⢀⡀⠂⠀⠀⠐⠊⠝⠄⣶⠀⠁
⠀⠀⠈⠓⢢⣬⣓⠆⢀⣠⠬⠋⠋⠁⠀⠀⠀⠁⠀⢙⡉⣹⢞⡿⠧⠾⠒⠁⠀⠉⠁⠀⠀⠀⠈⡁⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠡⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠛⠛⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠁⠀⠀⠀⠉⠻⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠰⠶⢶⣤⣀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠙⠳⣄⠀⣸⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠹⣧⣿⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠈⠀⠉⠉⠈⠉⠉⠈⠁⠁⠉⠀⠈⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠁⠀⠀⠈⠉⠻⠇⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢠⣤⣤⣼⣿⣿⣥⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠈⠛⢻⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⣀⣸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⢶⣶⠶⠶⠶⠶⢶⡶⣶

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄
⠀⠀⠷⣅⣡⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠠⣆⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢄⡀⠀⠀⡾⢋⣷⠍
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢄⡀⠀⠀⡄⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⡀⢡⠆⣴⠇⠀⢀⣠⡄⠀⠀⠀⠀⣈⣦⣤⡀⠉⠀⠆⠀⠙⠋⠁
⠀⠀⠀⣀⠀⣀⠀⠐⠀⣠⣿⡿⢐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢺⣶⠟⠀⠀⠛⠉⠀⠀⢀⡠⠜⠛⠻⠿⣿⣁⠠⣀⠀⢀⡄⠄
⠀⢀⠊⢡⠄⠟⠀⣘⢛⠋⠁⠀⠀⠀⠈⠑⢄⡀⠀⠀⠈⢢⣙⠆⢀⣝⠁⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠈⠫⣘⡛⡆⠈⢷⣼
⠀⠘⠒⠋⠀⠀⠀⠈⠁⠀⠀⠀⢘⢿⣦⣄⠀⠈⠲⡀⠀⠉⠀⢑⠞⢩⣱⡄⠀⠀⡔⠁⣠⡴⣶⣶⡶⠀⠀⠀⠀⠁⠉⠻⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣞⣿⣿⣉⠀⠀⠀⠀⢤⡀⠀⠀⠀⠶⠋⠀⠀⠄⣤⡴⢷⠾⡤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⢓⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠐⠓⣇⣼⣁⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣸⣷⢿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⠻⠽⠥⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠏⠀⠀⠀⠀⡘⠀⢀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠑⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠘⠗⠶⡦⠀⠀⠀⠙⠢⢄⠀⠀⠀⢀⡀⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠲⠶⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢴⣾⠻⠆
⠀⠀⠀⢠⡤⢀⡀⠀⠀⣶⡆⠀⠀⠀⠀⠀⡀⠀⣸⠇⠀⡆⠀⠀⠀⠀⠀⠃⠀⠘⠓⠂⠀⠀⠀⣀
⠀⠀⠀⠸⡤⠊⠁⠄⠀⠀⠙⠁⠀⠀⠰⡎⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠈⢷⠀⠀⢸⣏⠑⠶⢦⡒⣤⠄
⠀⠀⠀⠀⠈⠠⠵⢦⠀⠀⠀⠀⠀⠀⠀⢀⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠂⢸⡇⠀⠈⠛⢦⣊⡋
⠀⠀⠀⠀⡀⠀⠀⣸⠃⢀⠀⠀⠀⠀⣠⠟⠀⠀⣤⠀⢰⠀⢀⡴⠆⣼⠆⣄⠀⠀⠀⢸⠀⠀⠀⠠⠀⠙⠳⢤⣄⡈⠉⠁⠀⠈⢿⡆
⠀⠀⠀⠀⢯⡴⠀⠁⠀⢀⡶⠂⢀⡼⠃⠀⠀⠀⢸⠀⢸⠀⠘⠞⠋⠁⠀⣿⠀⠀⠀⢸⠄⠀⠀⠀⣄⠀⠀⠀⠈⠙⠢⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⡄⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠻⠀⠀⠀⠁⠄⠀⠈⠻⠶⡶
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠒⣦⠀⠀⠀⡿⠀⠀⢀⡛⠀⢸⠀⠐⣯⠓⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⠀⢰⠄⠁⠆⠀⠀⠘⣆
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⢸⡇⠀⢸⠀⠀⠀⠉⠀⠀⣿⠀⡦⠀⢨⡄⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠂⠀⠀⠛⡄
⠀⠀⠀⠰⠋⠀⢐⡆⢀⣀⣧⣀⣴⣼⣯⣠⣤⣼⣧⣤⣼⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠾⠷⠾⠷⠶⠶⠦⠴⢦⣼⣦⡀
⠀⠀⠀⠐⠀⠈⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠚⢻⡇⠀⣀⣀⠀⠀⠄⠉⣨⡿⠀⠀⢀⣶⠀⡷⠀⠈⢠⠖⠆⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠤⡀⢀⡤⠀⢠⡤⢀⢀⡀⢀⣸⣿⠀⠸⣷⡷⣿⣾⠃⠀⠚⢀⣿⡄⠀⠀⢀⣡⠔⠁⠀⣰⠋⠊⣀⡀⠀⠑⠛⠉⠉
⠀⣀⠀⡀⠀⢰⣦⠛⠁⣠⣄⡫⠉⠙⣮⡵⠿⢻⣧⡀⢸⠟⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠜⠁⠁⢀⣤⡀⢳⡄⠀⠀⠀⠄
⠀⠨⡈⣅⣙⣹⡇⠀⠈⣿⣋⡉⠉⢙⡿⠀⢀⠚⢀⣽⡗⠒⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠸⠀⠻⠅⠁⣸⡄⠀⠀⠀⣦⠄
⠀⠀⠃⣀⡀⢸⣗⣀⣀⡿⠶⠂⡀⠀⢯⠔⠋⣀⠈⠙⠁⠊⠉⠀⠀⡀⣈⣄⡀⠠⢀⠀⠀⠀⡉⠀⠀⠀⠀⠑⠠⠤⠾⠊⠀⢀⡜⠁⠁⠀⡄
⠀⠀⠒⠑⠀⠀⣤⣽⣇⣻⣮⠄⠉⠀⠂⢀⠊⠁⠀⣀⠠⠄⢀⣤⡾⣹⣯⡒⠠⡞⢟⣉⠹⣾⣄⠀⠀⠀⢠⡒⠄⠀⢀⡤⠒⢷⡈⣤⠀⡙
⠀⠀⡐⢠⣄⠈⠠⣌⣉⠈⠉⠄⠰⠶⣚⠯⠗⠊⠉⠀⢀⢀⠉⠙⣕⠾⢬⣉⣿⣿⠂⢸⣇⣤⠉⠁⡐⠶⠀⠀⠀⠀⢠⠤⠈⢴⠇⠘⠃
⠀⠀⠀⠀⠈⠘⠳⠮⢅⡀⢠⠴⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣴⣭⣽⣛⣛⣋⣉⠀⣀⠀⠀⠀⠀⠀⠀⠀⢘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠐⠒
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣥⣬⣧⣴⣤⣵⣬⣼⣯⣵⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⣀
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢺⡷⣾⣿⣷⢾⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡤⣾⡖
⢀⣴⡆⢸⠀⣶⣤⠀⠀⠀⠀⠀⠘⠇⢻⣿⡟⠸⠃⠀⠀⠀⠀⠀⣿⡏⠉⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⡇
⣾⣿⣿⢼⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣿⡇
⠛⠛⠛⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⡹⠃⠀⣤
⠀⣤⣴⣯⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠀⠀⠀⠀⠀⠀⡤⠒⠊⠀⢤⣄⣠⣿⡆
⠐⢷⣿⠟⠳⣤⣀⠀⠀⠀⠀⠀⠸⣿⣿⠳⢤⣀⡀⠀⠀⠀⠀⢠⣾⣿⣤⣤⣀⣘⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢹⣿⡇
⠀⣼⠛⣧⠸⣿⠿⠇⠀⠀⠀⠀⢸⡿⢿⡄⣿⡿⠷⠀⠀⠀⠀⢘⣿⣷⢾⡏⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠸⠏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⠿⢠⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇


⠀⢀⣠⡤⣤⣀
⣰⠛⡿⠤⠼⢿⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢀⣀⣠⣆⣰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⡷⢺⡗⠒⠒⢾⠒⡇⠀⠀⠀⠐⣶⣾⡏⢯⢹⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣶⡆
⠹⣶⣷⠒⢒⣿⡴⠁⠀⠀⠀⠀⢿⠿⠷⣖⣫⡭⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠿⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁

⠀⢀⡠⠄⢤⣀⠀⠀⠀⠀⠴⠖⠒⠀⠀⠀⠀⢀⣴⡾⣆⠀⠀⠀⠀⢠⢲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣧
⠀⢻⣿⣤⣤⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⢺⣿⣿⣧⣽⡶⠀⠀⠐⢡⠏⠀⠀⠀⠀⠀⠲⣿⣿⡿⡀⠀⠀⢰⡄⠀⡀⢰⣆
⠀⠘⠿⠿⠿⠕⠀⠀⠀⠀⠈⠁⠀⡇⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢼⣶⣶⣾⡇⠀⠀⠉⠁⠀⠀⢩⡍
⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⣏⠀⠀⠂⠀⠅⡆⠀⢠⣶⣶⣶⣶⠄⠀⢰⣿⣿⣿⣿⡇⠁⠀⠀⠀⣱⣀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠄⠀⠀⠰⡥⠤⢽
⠀⣇⠀⠀⠀⠀⣃⡇⠀⢰⢘⢘⣋⡃⡄⠀⢸⣿⣿⣤⣼⡟⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⣹⣿⣿⣿⣿⠂
⠀⠈⠁⠀⠀⠀⠉⠀⠀⠘⠤⠤⠤⠠⠂⠀⠈⠻⠿⠿⠿⠍⠃⠀⠀⠀⠈⠛⠉
⠀⠀⠤⠀⠀⠀⠀⠀⢠⠤⠤⢤⡀⠀⠀⣤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⢠⡤⠤⠤⡄⠀⠀⢀⣀⣀⣀
⠀⠀⠨⣧⠀⠀⠀⠀⠀⠐⠲⡆⡇⠀⠀⡇⣤⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡽⡀⠀⠀⢸⡧⠐⠀⡇⠀⠀⠸⠤⠶⢿
⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠔⢃⠀⠀⢸⡀⠀⠀⡇⠀⠀⢸⠩⠭⢹
⠀⠀⠓⠒⠒⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠈⠉⠀⠉⠁⠀⠀⠈⠉⠉⠉
⠀⡴⠒⢦⣤⣤⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣄
⠀⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣧⣤⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠉⠁⠀⠀⠸⡿⣹⣿
⠀⠛⠛⠛⠛⠛⠃⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠀⠐⠒⠶⠖⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⣠⡶⠒⠶⠀⠀⠀⢠⡖⢲⡄⠀⠀⢀⡤⠲⢤⠀⠀⠀⢀⣀⣀⢀⠀⠀⢀⣤⣄⡀⣄⠀⠀⠀⣴⠛⡆⠀⠀⠀⠀⣠⣄⡀
⠨⣿⡿⠏⠀⠀⠀⠀⠺⡷⠂⠀⠀⠀⢾⢦⣈⢻⡇⠀⠀⢰⡎⣀⣰⡆⠀⢸⣿⣿⣅⣙⠀⠀⠀⣿⣛⣿⠀⠀⠀⠐⣿⣿⠇
⠀⠈⠛⠛⠛⠀⠀⠀⠘⠛⠲⠂⠀⠀⠈⠳⠴⠚⠁⠀⠀⠃⠀⠀⠐⠁⠀⠘⠛⠛⠛⠛⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠘⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣶⣶⡦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠒⠉⡶⠀⠠⣄⠈⠐⠽⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠊⠀⠀⢀⠁⣐⠀⣇⠱⡦⠀⠈⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠀⠀⠀⢸⠺⣿⠇⣇⠼⡄⠀⠀⠈⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⡄⠀⠀⠀⠀⡇⠀⠀⠀⡤⠚⠂⠉⠀⠀⠀⠘⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⣴⠶⠞⠛⠉⠀⠀⠀⠀⠙⣛⢦⡀⠀⢇⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⢹⠃
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠠⠼⠟⣂⡿⠀⠘⢎⢄⠀⠀⠇⠀⠀⢀⡀⠀⠐⠈⠠⣢⠏
⠀⠀⠀⠀⠀⣠⠴⣲⠿⣷⣶⣶⣶⣶⣿⣿⡟⠉⠀⠀⠀⠈⠳⢕⡤⣘⠈⠀⠀⠀⣀⠠⣢⠕⠁
⠀⠀⠀⠀⠊⣠⠞⢁⡾⠁⠀⠀⠀⠀⠨⠭⠽⣦⠀⠀⠀⠀⠀⠀⠉⠓⠒⠿⠾⠓⠚⠉
⠀⠀⠀⠀⠘⠁⢠⡞⠁⠀⢀⡠⠢⠴⡈⢹⣭⣽⣧
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡆⢴⢰⡆⠤⠄⠤⠤⠼⣇
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢰⢠⡄⡝⠄⠩⠭⠭⢽⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠐⡒⠬⠸⠇⠆⡰⠴⠧⠉⣋⣽⣿⣿⠛⠐⠒⠒⠲⠖
⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠈⠒⠤⢆⠮⢥⣀⣀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠸⣇⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠙⠓⠀⠤⠀⢤⢀
⠀⠀⠀⠀⠀⠈⠙⠓⠾⣦⡀⠀⠀⠀⠀⠈⠉⠒⠛⣿⣿⣤⠄⣀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠒⠛⠀⠀⠀⠀⠿⣿⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⢠⡀
⠀⠈⠳⢬⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⣤⡠⠀⠀⠀⠠⣀⠀⢀⡀⠙⠃⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⡀⠀⣏⣹⠞
⠀⠀⠀⠀⠀⠀⠀⡀⠢⣠⣄⣰⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⣰⣃⡿⠁⢀⣤⠖⠀⠀⠀⢀⣜⣶⣦⡀⠀⠃⠀⠉
⠀⠀⡤⠖⢴⠄⢸⣤⣾⠟⠋⠛⠣⣀⡀⠀⠀⠀⢀⢠⡀⠀⢼⠟⠁⠀⠀⠀⠀⠀⠤⠒⠉⠉⠋⠛⣧⣂⣦⠀⢰⡐⡄
⠀⢰⣠⠎⠁⠀⠸⠔⠁⠀⠀⣤⣄⡀⠙⠢⡀⠀⠠⠗⠂⣴⠿⢀⠀⠀⠀⡐⠉⢀⣀⣀⣀⠀⠀⠀⠀⠲⣧⠃⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢠⣾⣾⠟⠀⠀⠈⠂⡀⠀⠈⢃⣨⠟⠁⠀⠜⣀⣼⣭⣋⣙⣁⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠘⠿⢿⣷⣶⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠸⢽⣰⡗⠛⡛⠁⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣤⣌⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠈⠻⢭⡭⠼⠃⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠛⢻⠿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠈⠀⢤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠁⠀⠀⠛⠲⠆⠀⠀⠀⠑⠢⠀⢀⣀⣤⠀⠠⡀⠠⠔⠊⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛
⠀⠀⠀⡾⢰⠦⡀⠀⠻⣥⠀⠀⠀⡀⠄⠀⡜⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢉⠀⠀⠀⢠⡄⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠙⢍⣠⣁⠀⠀⠀⠀⠀⠀⠁⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⢷⡄⠉⡽⠀⠚
⠀⠀⠀⠀⠀⠉⢩⡆⠀⠀⠀⠠⢂⣰⠏⢀⡀⠀⠄⠀⢠⣤⣶⡄⡆⠀⠀⠀⣿⠀⠀⠄⠘⠧⣄⡀⠛⠶⠃⠀⢠⣤
⠀⠀⠀⢰⣂⡤⠉⠀⢈⣤⢈⢁⡾⠉⡇⠀⡿⠀⡀⠀⢿⡿⠋⠀⡇⠀⡁⠀⣯⠀⠀⢠⡐⠦⡀⠙⠿⢦⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠉⣄⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠐⠀⠀⠙⠶⢶⣤
⠀⠀⠀⠀⠀⢠⠞⠁⠰⡆⠀⠀⣿⠀⠀⢀⡃⠀⡇⠀⠾⡛⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢉⠀⠀⠐⣄⠀⠀⠀⠀⢣⡄
⠀⠀⠀⢀⡴⠃⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⡇⠀⠀⠉⠀⠀⡇⠀⡆⠀⡇⠀⡄⠀⠀⠀⡀⠀⣧⠀⠀⠀⠀⠀⢣
⠀⠀⠀⡋⠀⣨⣇⣠⣴⠧⠴⠶⠿⠤⠷⠾⠷⠤⠇⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠚⠛⠛⠛⠒⠓⠶⠷⠤⠄⠀⢀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢤⡀⠀⠀⠀⠀⠒⡦⢤⡀⠀⡠⠀⠠⡀⠀⠔⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⢹⣄⣤⣆⡄⠀⣀⠀⡞⠁⠀⠀⠟⢠⠇⠈⢠⠫⠁⠀⠀⣀⡤⠼⠇
⠀⠀⠀⠀⠄⣈⠿⠞⠉⣀⠟⠙⣑⣆⣴⢿⡏⠀⣽⣟⠙⠿⠀⠀⠀⠚⠛⠀⠀⠀⠚⡁⠀⡰⠕⠀⠀⠀⢤⠀⠀⠀⢀
⠀⢓⢐⣒⢲⡟⠀⠐⡿⠟⠓⠈⣿⠏⠁⠼⢃⣢⠥⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠊⠀⡄⢰⣏⠁⣸⡇⠀⠀⢨⡀
⠀⠸⠃⠈⢉⣿⠀⢀⣿⡷⠀⠀⢽⣢⠎⣀⠘⠛⠒⠚⠁⠀⢀⢘⣁⠀⠀⠀⣀⢀⣘⠉⠀⠀⠐⠤⣤⠴⠟⠀⢀⡌⠘⠉⢀
⠀⠀⠊⠃⠀⢭⣽⣧⣷⣞⠈⢀⠳⢀⡞⠉⢁⡠⠤⠀⣀⡴⠹⢿⠄⢠⡶⣏⡩⣶⢇⠀⠀⠀⡄⠂⠀⢀⡤⢒⣏⠨⡄
⠀⠀⠐⣤⣈⠀⢬⣍⠈⠍⠊⢵⢖⠿⠗⠊⠁⠀⡄⡈⠙⢷⠶⢮⣹⣷⡟⢈⣧⡤⠈⠀⠰⠺⠀⠀⠀⠰⠤⠈⢾⠄⠋
⠀⠀⠀⠈⠐⠛⠳⠦⠤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠾⣴⣿⣭⠭⠥⠄⠠⠀⠄⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠕⠀⠀⠁⠪⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⡥⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⣀⣀⡐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠐⠁⠀⠀⠀⠑⠌⠄⡀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠠⠦⠤⠶⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠘⢏⠘⠁⡃⠀⢀⠀⡁⠀⠉⠀⠀⠐⠒⠊⠉⢉⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⠃⠀⠀⢣⡁⠀⠀⠀⣀⣀⣀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⣉⣁⠀⢄⠀⡄⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠤⣖⣤⡶⠄⡀⠀⢀⠈⠉⠉⠉⠉⠉⠈⢁⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⠀⠀⠨⢆⠈⢀⠰⣠⠀⠀⠀⠀⡃⠠⠀⢀⣀⣀⣀⡠⠔⡇⠀⠸⠦⢤⠤⢠⣤⣶⣾⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⢀⣀⣤⠇⠀⢀⡦⠀⠀⠀⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠈⠓⠒⠲⠅⣀⠀⣇⡀⠉⠉⠛⠛⠛⠙⣸⠀⠀⠀⠁⠀⠀⠀⠤⠰⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢠⠀⠉⠉⠂⠐⠂⠀⡇⠀⠙⠀⠀⠄⠤⠤⢶⠞⢿⠀⠀⠰⠇⠀⠀⠀⣀⣀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠶⠶⠦⠀⡀⠀⠾⠁⠀⠠⣤⣤⣤⣦⡇⠀⢠⡓⠀⠀⠀⠀⠀⢀⡼⠀⠀⢐⠀⠀⠀⠈⠈⠁⠁⢤
⠀⠀⠀⠀⠀⠀⣆⠈⠀⢐⠀⠒⠒⠉⢀⠀⢠⡀⠀⠈⠉⠉⠉⠁⣧⠀⠀⢀⠁⠀⠚⠓⠛⠩⢰⠄⡀⠈⠀⠀⠀⠤⠤⠤⠶⠟⡇
⠀⠀⠀⠀⠀⠀⠑⠠⠄⠠⢤⢤⣤⡴⠊⠁⠘⠢⠤⣀⣤⢤⡤⠶⠁⠔⠈⠀⠅⣀⡤⣤⣤⠔⠋⠀⠀⠲⣌⣀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣦⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠀⠤⠤⠤⠀⠤⡄⠀⠀⠀⠀⢀⠜⡀⠠⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠸⣧⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠳⣄⠀⢀⡠⠒⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠂⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢐⣈⢀⠇⣛⣾⠇
⠀⠀⠀⠀⠯⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠷⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣦⠀⢀⡄
⠀⠀⡀⢀⣀⡠⠎⠀⠀⠈⠉⠉⠙⠙⠉⠉⠀⠀⠀⠀⡀⠀⢀⢰⠀⠀⣮⣤⣦⣴⣶⠀⠀⠀⠀⠙⢀⠀⡀⣻⠇⠉
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠚⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣁⠒⠉⠐⠴⠴⠒⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠤⠀⠀⠀⠀⠀⠀⠀⠛⠓⠦⠆⠀⠀⠐⠀⡁⡀⠖⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠆⠀⠀⠀⠀⣠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢀
⠀⠀⠀⠀⠀⠠⣤⡦⠶⠟⠉⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠓⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⠀⠘⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⢀⡀⠠⡆⠀⠀⠀⠈⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣿⣸⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠡
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⢻⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠹⡷⠈⠉⢀⢐⠂⠀⠀⠀⠀⢀⠀⠺⠇⠀⠀⠂⠀⠀⠀⠈⠉⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠒
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡔⠀⠀⠀⠀⠆⠀⠀⠀⠺⢠⣠⠔⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣐⠂⠁⠐⠚⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠂⠂⠐⠒⠁⠀⠀⢀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠳⠜⠜⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⡆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈
⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠲⠒⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠠⠶⠀⠀⠀⠀⠀⡀⠀⣠
⡿⠋⢁⡄⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢠⠜⠀⠀⠀⠐⣠⣴⣿⣿
⠁⠀⠺⡤⠀⠀⢸⣿⣿⣿⡿⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡄⠀⠀⠤⠄⠀⣼⣿⡿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣶⣤⣤⣴⣾⡿⠋⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠄⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠈⠀⠁⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡐⠠⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡿⢋⠀⠀⠀⠑⠀⡀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠀⠀⢀⠄⠀⠀⠀⠀⠀⢿⣿⣿
⠁⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠈⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠲⠄⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢄⣀
⡠⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⠖⠐⠀⠁⢀⠤⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲
⠀⠀⠀⠁⠀⠀⠀⡀⠀⣄⠀⠈⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⢓⡆⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡖⠀⠘⡅⠀⠀⠀⠀⠀⢉⠂⠐⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⠀⠉⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠒⠢⡁
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠿⢤⡀⣀⠠⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⣀⠫⠀⠀⡀⣀⡴⡃⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣠⡾⣿⢻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠛
⣇⠀⠀⠐⠀⠀⠀⠀⣀⣤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣀⣿⢸⣷⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘
⠀⠄⠀⠀⠀⠀⢠⣿⣯⢿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣾⣿⣶⣄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠋⠉⠙⠛⠒⠦⣄
⠀⠀⠀⠀⢠⠖⠋⠀⣠⠤⠖⠒⠒⢒⠦⣄⡀⠈⠳⣄
⠀⠀⠀⣰⠋⠀⣰⠋⠁⠀⠀⡤⠶⢾⡀⠀⠙⣆⠀⠈⣇
⠀⠀⢰⠇⠀⣸⠁⠀⠀⠀⠘⣧⠀⠀⠙⠀⠀⢸⡆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢛⣉⣉⣉⣉⣉⣉⣉⣙⠓⠲⢤⣀
⠀⠀⠸⡆⠀⠸⣆⠀⠈⢳⡤⠴⠞⠀⠀⠀⣰⠋⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡴⢋⣉⡵⠀⢀⣠⠖⠒⢲⣭⠽⠳⡄⠈
⠀⠀⠀⢻⣆⠀⠈⠳⢤⣌⣀⣀⣀⣤⠴⠋⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠲⠤⣽⣛⣋⣁⣀⣀⣨⡥⠴⠚⠁⣠
⠀⠀⠀⠀⠙⣿⣦⣄⣀⡀⠀⠀⢀⣀⣠⣴⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣯⣟⣻⣿⠿⢿⣿⣿⠿⢿⣿⣛⣯⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠖⠲⠶⠶⠤⢤⣀⣸⡿⣷⣯⣟⣻⣿⡿⠿⠿⠿⠿⣿⣿⣻⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⠴⢖⡒⠛⠛⣛⣻⣖⡲⠦⣤⡉⠛⣷⣯⣿⣻⣿⠿⢿⣿⣿⠿⢿⣿⣛⣯⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠻⣔⡒⠻⢤⠤⠞⠁⠀⠀⠟⢉⣠⠟⠀⢸⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣭⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣈⡉⠙⠛⠒⠒⠒⠒⠛⠋⢉⣁⣤⣶⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣝⣿⢿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⢿⣫⣾⣿⣻⣿⣿⡿⠿⠿⣿⣿⡿⢿⣿⣻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣽⣻⢿⣷⣿⣿⣯⣭⣭⣽⣿⣿⣶⣿⢿⣫⣿⡿⠛⠉⠀⢀⣀⣀⡀⠈⠙⠻⣿⣻⣽⣾
⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣄⣀⢸⣷⣝⣿⢿⣷⣿⣿⣭⣿⣿⣭⣿⣿⣶⣿⢿⣿⡟⠀⢀⡴⠚⠉⠉⠉⠉⠛⠦⣀⠈⠻⣯⣿
⢀⡴⠋⣉⡤⠴⠶⠒⠒⢒⣒⣶⠶⠤⣌⡙⠻⣿⣿⣿⣷⣿⣿⣿⣭⣭⣿⣿⣿⣷⣿⣿⣿⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠘⣿
⣏⠀⠸⣁⠶⠾⣥⣤⡴⠋⠁⠉⠿⠛⢁⡽⠀⢈⣿⣷⣿⣯⣽⣿⣿⣿⣿⣯⣽⣿⣾⣿⣇⠀⢸⡇⣤⣾⠁⠀⠀⡴⠚⢶⡄⠈⣇⠀⢹
⣿⣶⣄⣈⠙⠓⠒⠲⠶⠶⠶⠒⠒⠋⢉⣀⣴⣾⣿⣷⣿⣯⣽⣿⣿⣿⣿⣯⣽⣿⣾⣿⣿⠀⠘⣇⠀⠙⢦⣤⠞⠁⠀⣰⠟⠃⣿⠀⢸
⣿⣝⡿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⣟⣽⣿⣷⣿⣿⣭⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣧⠀⠘⣆⠀⠀⠀⠀⠀⠀⠉⠀⢠⠏⠀⢸
⣿⣝⡿⣷⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿⣶⡿⣟⣽⡇⠉⠙⠛⠛⠛⠿⠿⠛⠛⠛⠋⠉⠀⠻⣿⣷⣄⠈⠓⢦⣄⣀⣀⣀⣠⠴⠋⠀⢠⠏
⠘⠿⣿⣷⣾⣯⣭⣿⣿⣿⣿⣯⣽⣿⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠉⠉⠉⠀⠀⣠⠴⠋
⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣷⣶⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠓⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⢨⡅⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢈⠒
⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣠⣈⣀⢠
⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣜⣧⣄⠀⠀⠀⣤⣤⣤⣴⣤⠀⠀⡠⠀⠤
⠀⠀⠀⠀⠐⣤⠀⢀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣍⠀⠀⠀⣿⡿⢿⣿⣿⣷⣄⣨⠆⠀⠀⠀⠀⠀⠀⠀⡗⠀⣈⣁
⠀⠀⠀⠀⠸⣀⠀⠺⡀⠇⠀⢠⠀⠀⠀⠀⣴⣿⣿⣿⡯⠻⣦⠛⠀⠀⠀⠉⢠⣾⡉⠋⣿⣿⡷⠀⠀⠀⠀⠰⣤⠆⠀⡇⠀⠈⠉
⠀⠀⠀⠀⠘⠈⠉⠀⠉⠀⠁⠉⠀⠀⠀⠀⠈⣿⡿⣿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃

⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠆
⠀⠀⠀⠀⠀⠘⣿⠋⣭⠛⣩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠆⠀⣙⣛⠁⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⡀⢰⣦
⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⠟⢭⣷⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⢸⣿⢸⣿
⠀⠀⠀⠀⠀⣠⣭⣤⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⣿⣦⣘⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⠿⠸⠿⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣙⠳⣄
⠀⠀⠀⠀⠀⢨⣿⡿⠻⢿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⣳⠀⣸
⠀⠀⠀⠀⠀⠸⣿⣿⣴⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠚⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣾⣿⣿⣿⣿⢾⣿
⠀⠀⠀⠀⠀⠈⠙⠋⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠛⠉⠀⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⡆⠀⠀⠀⡀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇⠀⠀⢸⣭⢉⢡⡀⡄⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⣙⣛⡛⠛⢛⣛⣛⠛⠛⣛⣛⣛⠛⠛⣛⣛⡁⠀⢸⡇⠀⠀⠈⣿⣿⣼⣿⣿⡟
⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⣶⣶⣤⡀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⢸⠀⡇⠀⠀⢱⢸⠁⠀⠀⡇⢸⠀⠀⠈⠆⢸⡇⡠⠚⠉⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⣰⡿⠛⠁⢀⣶⣦⣀⡈⠙⢿⣦⡀⠀⠀⠀⡇⠀⠣⠤⠤⠼⠀⠧⠤⠤⠞⠘⠤⠤⠤⠃⠸⠤⠤⠴⠃⢘⡟⠁⠀⠀⠀⢠⣦⣀⡀⠀⠀⠀⠳⡀
⠀⠀⣸⡿⠁⠀⣰⠟⠉⠉⠉⠉⠀⠀⢻⣿⠉⠙⠉⢳⠀⡔⠀⠀⢲⠀⡖⠊⠒⢦⢠⠂⠀⠐⡆⢰⠂⠀⠓⡄⢸⡇⠀⠀⠀⣾⠉⠉⠉⠉⠀⠀⠀⠀⢣
⠀⠀⣿⡇⠀⠀⠙⢷⣤⣤⣤⡀⠀⠀⢸⣿⣄⣀⣀⣼⡀⢇⣀⣀⣸⠀⣇⣀⣀⡸⠸⣀⣀⣀⡇⢸⠀⠀⠀⡇⢸⡇⠀⠀⠀⠘⠳⠶⠶⣦⠀⠀⠀⠀⠈⡄
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣸⡿⠀⠀⠀⠀⢹⡠⠤⠤⢤⠀⡤⠤⠤⣄⢀⠤⠤⠤⡄⢸⠀⠀⠀⡇⢸⡇⠀⠀⠀⣠⣤⣤⣤⡾⠀⠀⠀⠀⠀⡇
⠀⠀⠈⢻⣧⡀⠘⠛⣿⣿⠛⠁⢀⣴⡿⠓⠒⠒⠲⡖⠋⡇⠀⠀⢸⠀⡇⠀⠀⢲⢸⠀⠀⠀⡇⢸⠀⠀⠀⡅⢸⡇⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠙⠻⣷⣦⣤⣤⣴⣾⡿⠋⠀⠀⠀⠀⢀⡷⣄⠉⠊⠁⠉⠀⠉⠈⠀⠁⠀⠁⠀⠈⠁⠈⠁⠀⠈⣀⠜⠑⠦⣄⣀⡀⠀⠀⠀⠀⣀⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀
⠅⠌⠀⠀⡀⠀⠀⠀⡤⠈⠀⠐⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠐⠉⠄⠀⠈⠀⠀⡄⠀⠀⠀⡤⠈⠀⠁⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠠⠈⠀⠀⠂⠂⠀⠀⠀⠐⠁⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⢀⠊⠀⠀⠂⠂⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢀⡸⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⡸⠨⡀
⠀⠀⠀⠀⠉⠚⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠠⣆
⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⠀⠀⠸⠸⠷⠒⠦⠌⠀⠀⠀⠠⢀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠅⠹⠄⠀⠀⠰⠸⠷⠒⠦⠆⠀⠀⠀⠠⢀
⠤⠄⠀⠀⡝⠃⡾⠀⠀⠠⠀⠂⡀⠀⠀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⡌⡤⠤⠀⠀⠀⡝⠃⠚⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠀⢄⠀⠀⠀⠠⠀⡈
⠀⠀⠀⠐⠐⠒⠋⠀⠰⠆⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⠐⠀⠒⠊⠀⠰⠆⠀⠁⠀⠀⢀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⡄⢀⠀⠀⠠⠀⠀⠀⠀⣀⠂⠔⢣⡀⠀⢠⠆⠀⢀⠀⠀⠀⠀⢀⠀⠀⠐⠀⡄⠀⠀⠤⠄⠀⠀⠀⣀⠀⠔⢣⡀⠀⢠⠆⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠐⠂⠂⠀⠁⠀⠈⠂⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠈⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠆⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠄⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⢀⠤
⠀⢁⠀⡴⠂⠀⠀⠠⠊⠀⢀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⡤⠁⠀⠀⠀⠋⠀⠀⠀⣀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠁
⠀⠀⠀⢀⡀⠅⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡀⠀⣀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠂
⠀⠀⠀⠀⠤⠥⠀⢀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠐⠊⠈⠂⠀⠀⡀
⠠⡀⠀⠀⠀⠂⠀⠁⠀⠀⠀⢢⡀⠀⠀⢠⠠⣎⢿⣁⣣⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢢⡀⠀⠀⢠⠠⣮⢝⣁⡋
⠐⠸⠀⠀⢠⣄⣤⠀⠀⠀⠀⠈⠃⠀⠀⠈⠈⠁⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⢐⠀⠀⡠⣄⢠⡄⠀⠀⠀⡈⠃⠀⠀⠈⠈⠁⠀⠉⠁⠀⠀⠀⠈
⠉⠁⠀⢀⠃⣀⡆⠀⢐⡈⠀⠀⠀⠀⠀⠀⠀⠨⠀⠑⠀⠀⠀⠀⠠⠇⠉⠉⠁⠀⢀⠃⣀⡠⠀⢒⡊⠀⠀⠀⠀⠀⠀⠀⠨⠀⠑⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⠈⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠄⠀⠀⠉⠂⠀⠄⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡄⠀⠀⠀⡀
⠀⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠁⠀⠀⠠⠈⠂⢡⡜⠁⠀⠜⠁⠠⡀⢀⠀⢡⠀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠁⠀⠀⠠⠂⠀⢡⡜⠁⠀⠘⠁⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢀⠀⢀⣀⡀⠀⠔⠠⠴⠦⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈⢀⢨⡄⠁⠀⠀⠀⠀⠀⠤⠤⠶⠂⢀⣍⣍⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠄⢠⠀⠀⠀⠀⠀⠀⠴⢃⡀⠀⣄⣠⢕⡢⠤⠤⣄⣤⡀⡀⠀⠀⠀⢂⡠⠄⠒⠃
⠀⠀⠀⡀⠀⠀⣐⡠⣀⠂⠤⠤⠤⠔⠇⠉⠀⢺⠙⠀⠈⠉⠁⠀⠩⠌⠀⠁⠐⠋⢉⢁⠄⢀⡆⠠
⠀⠀⠀⠀⠁⢘⠁⠀⠁⡁⠀⠀⠀⢀⡿⠄⠤⢼⡉⡌⠁⠂⠛⠓⠷⠶⠄⠐⠪⠭⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⣇⠀⠀⠒⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣷⠟⠙⢮⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠞⠁⢠⠔⠢⡙⢷⣵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⡾⠁⠀⠀⢣⣀⡠⢗⣮⠶⣮⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡽⢋⣠⡤⣀⡠⣔⣭⠞⠋⢀⣀⡈⢧⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⠋⢠⣿⡿⣛⡽⠞⠉⠀⠀⠠⡋⠀⢙⠌⢳⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣵⠟⢁⠤⣪⡵⠚⢉⣴⣶⡢⡄⠀⠀⠑⠒⠊⣀⡴⢟⠼
⠀⠀⠀⠀⠀⠀⠀⡖⠒⠛⠚⠓⠚⠓⠛⠓⠒⠒⠛⠛⠚⠓⠚⠒⠒⠒⠒⠛⠛⠚⠓⢲
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢽
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠼⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠙⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣑⣒⣁⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿

⠀⠀⠀⢈⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⢀⣿⡹⣯⡀⠀⠀⠀⠀⠀⣤⣤⣼⣷⣿⣂⠀⠀⠀⠀⠀⣿⣴⣂⣀⡦⡄⠀⠀⠀⣴⣿⣿⠿⢻⣿⠶⠀⠀⠀⠀⢰⣿⣿⣿⢿⡀
⠀⠀⠘⠿⠶⠿⠃⠀⠀⠀⠀⠀⠛⠛⠷⠶⠋⠁⠀⠀⠀⠀⠤⠿⠿⠽⠿⠧⠤⠀⠀⠀⠀⠙⠿⠾⠿⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠾⠁

⠀⠀⢠⣶⣶⣶⡀⠀⠀⠀⠀⠀⢀⣠⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⡄⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖
⠀⠀⢸⣿⣿⣷⢲⡄⠀⠀⠀⠀⠾⢀⣞⠹⣿⠓⠀⠀⠀⠰⣟⣿⠀⠀⢸⣏⡷⠀⠀⠀⠀⣶⣒⣚⣛⣓⡂⠀⠀⠀⠀⠀⣰⣟⢽⣦
⠀⠀⠈⠙⠛⠙⠚⠁⠀⠀⠀⠀⠦⠌⠏⠠⠟⠁⠀⠀⠀⠀⠈⠁⠳⠶⠂⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⠯⠇⠀⠀⠀⠀⠀⠙⠿⠾⠋

⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⢾⣿⣾⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣤⣤⠀⠀⠀⠀⠀⢀⡴⣤⡐⢀⠇⠀⠀⠀⠀⠀⣿⣿⣽⣭⣿⡛⠋⠀⠀⠀⢰⠀⣺⠀⢨
⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠘⠯⠿⠃⠁⠀⠀⠀⠀⠘⠛⠛⠒⠚⠓⠛⠁⠀⠀⠀⠀⠀⠂⠤⠄⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠖⠒⠚⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢉⣡⣤⠶⠖⢶⣄⣀⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢋⣠⡴⠞⠋⠁⠀⠀⠀⠀⠉⠉⢻⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣻⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⣴⠞⠁⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⢉⣉⣉⣡⣤⣤⣌⠉⠉⠉⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣁⡴⠋⠁⢀⣀⣤⡴⠞⠋⣉⣤⡴⠶⠛⠛⠉⠉⠉⠀⠀⠀⠹⢦⣄⡀⢸⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢋⣠⠞⠋⣀⣴⠾⠛⢉⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣁⣴⣛⣥⠶⠛⣉⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⡿⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⣁⣤⡾⠿⠛⣉⣤⠶⠛⠉⢀⣠⣤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠘⣇⠀⣧⠹⣆⠘⣧
⣠⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⡿⠷⠞⠛⣉⣡⡤⠶⠛⠉⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⡼⢋⣤⠶⢤⡉⢳⡄⠀⠀⠀⠀⢻⡀⢹⡶⠛⠀⠘⣧
⢿⡀⠈⠉⠉⣉⣉⣉⣉⣤⣤⡴⠶⠞⠛⠉⠁⠀⠀⠀⠀⣰⠟⠁⠀⣠⠶⠦⠤⣀⠀⠀⠀⠀⠘⣧⣸⠃⣾⠑⢿⡀⢹⡆⣿⠀⠀⠀⠀⠘⣇⠈⣿⠀⣀⣀⣈
⠸⡇⠀⣀⣼⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⠛⢀⡀⠀⢸⡆⠀⠀⠀⠀⢸⣿⣇⠹⢦⣭⣥⠞⢠⡟⠀⠀⠀⠀⠀⢿⡀⢹⡋⠉⠉⠉
⠀⢿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⡇⠀⠈⠓⠺⠿⣤⠀⠀⠀⠀⠀⡇⠙⠳⢦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠸⣇⠘⣇
⠀⠸⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠻⣤⣀⣀⠀⠀⠘⣇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⡀
⠀⠀⣿⠀⢻⡀⠀⠀⠀⠀⠀⣠⠞⢋⣉⣉⡙⠳⣄⣷⠀⠀⠀⠀⢠⡞⠋⠙⡇⠀⢠⡟⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠘⣇
⠀⠀⢸⡇⠸⡇⠀⠀⠀⠀⢰⡏⣰⠏⣵⡌⢹⡆⢹⣿⡄⠀⠀⠀⠀⠻⣄⣀⡀⢰⡟⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡿⠀⠀⠀⢿⡀
⠀⠀⠀⢿⠀⢿⠀⠀⠀⠀⠸⣇⠹⣆⡘⢛⣼⠃⣼⠁⢳⣄⠀⠀⠀⠀⠈⠉⠛⠋⠀⢀⣴⠟⠀⠀⠀⢀⣀⣤⠴⠚⠛⠉⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣸⡇
⠀⠀⠀⢸⡆⠸⡇⠀⠀⠀⠀⠘⠷⣬⣉⣉⣥⠾⠁⠀⠀⠙⠷⣤⣀⣀⣀⣀⣀⣤⠶⠋⠁⣀⣤⡴⠞⠋⣉⣤⠴⠖⠛⠋⠉⠁
⠀⠀⠀⠀⣷⠀⢿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣀⣤⠶⠛⢉⣠⡴⠞⠋⠉
⠀⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢉⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠈⣷⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⣉⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⢹⡄⠀⠈⢻⣄⣀⣠⣤⣤⡤⠴⠶⠛⠋⣉⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠈⠷⢤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠛⠋⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⡤⠖⠲⣄⣀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡇⠉⠀⠀⠘⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠆⡄⠀⡗⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢩⠃⠸⠂⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠛⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡿⠿⣿⣿⣧⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⣿⣿⡀⣿⣿⡇⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⣀⡀⠈⠉⠀⠀⠀⠀⠀⠈⠄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠄⠊⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠻⣿⣿⡇⠀⠀⠀⠀⢀⠤⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⣿⣿⡇⠀⣰⣿⣿⡇⠀⠀⠀⠁⠄⠒⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠑⠀⠀⠀⠀⠈⢿⣿⣿⣦⣿⣿⣷⣾⣿⣿⠟⠀⠀⠀⠀⠀⢀⠡⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠦⠀⡄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠐⢈⠠⠔⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⡄⠈⢁⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⠤⠤⠤⠶⠶⠒⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⣳⣧⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⢉⡱⠀⠀⠀⠀⡀⠀⠦⠄⠠⢒⣼⠒⢐⢚⣺⠀⣻⡃
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠥⠤⠄⠒⣒⢲⡂⢎⢫⣻⡦⠭⢯⠟⡖⠋⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⡐⠀⡄⠀⠂⠀⣀⠀⠀⠀⠀⠓⠂⠋⠉⠉⠉⠁⠹⠀⠚⠚⠁⠀⠀⠖⠀⠀⠐⠨⢍⣀⠀⠀⢄
⠀⠀⠀⠤⢶⡤⠀⠀⠀⣠⠐⣲⣾⡞⠨⢵⣶⠅⠐⣖⣈⢥⡀⠶⢁⠁⠀⠀⢀⠀⠀⠀⢈⡐⢁⡢⣀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣈⣤⠴⠧
⠀⠀⠑⠤⡐⠀⠐⠀⢄⠙⠒⢋⣜⣿⣀⢘⣻⠤⢀⣰⣏⡿⣥⡀⠀⠁⢂⡐⠀⠌⣃⢠⠐⠀⠦⢄⠠⠑⠤⣏⣀⣈⣟⣶⡞⠉
⠀⠀⠀⠀⠈⠁⠠⡀⠀⢢⠄⠀⣠⠤⢉⣉⠩⢅⠀⠒⠾⣟⠉⠤⠴⠂⢀⡌⠀⢠⠈⠃⠄⢀⣀⡀⣰⡄⠴⠄⠵⢤⠶⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢡⣒⡶⠃⠀⠐⠁⠄⢬⡼⠿⣾⠷⣀⠀⠀⢉⡁⠀⡀⢀⣀⡀⣀⣠⣠⣜⣠⠒⠡⢶⡄⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡛⠉⠁⠀⠈⣿⣦⠟⠋⠛⠛⠋⠉⠀⠉⠁⠈⠀⠁⠀⠀⠌⠠⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣢⣀⡰⠆⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠴⠖⠚⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠴⢤⡀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠈⠾⠁⢍⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢦⣾⣴⣋⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⣩⡞⠟⠫⠢⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠘⠑⠹⠀⢀⣠⡀⠀⠀⢻⡄⣀⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠃⠀⠰⢛⠉⠉⠀⠀⠀⢣⣤⣉⣁⣀⢠⣶⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣬⣥⣥⠆⠀⠀⠀⠄⠀⠡⠤⢈⠉⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢖⠒⠀⠀⡀⠰⡟⠄⢰⡆⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⠀⢀⡀⠀⠀⠾⠫⢄⡤⠀⣀⣰⠀⠀⠉⢠⣿⠥⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠻⢶⣤⣀⡀⣉⣤⣾⢿⣿⣶⣤⣠⣿⠃⢀⣉⣠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⡶⣃⡀⢀⠀⠀⢈⣹⢿⡿⣿⠆⡀⢀⠈⢉⣿⠗⠒⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⡀⠀⠾⢋⣠⣶⣿⣾⣇⡀⠉⠈⠠⠟⠀⣼⣿⠒⠒⠶⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⣶⣶⣿⣿⠿⠋⠙⠿⣿⡿⠶⢄⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠙⠓⠄⠙⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠟⠁⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢲⣄⢀⠀⠀⣄⠀⠀⠀⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠙⢿⣷⡀⢺⡆⢀⣤⡀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⢸⣿⣿⣮⣷⣿⣷⣏⡀⠸⣆⡀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⡴⣶⣿⣿⣿⣿⢿⠟⠋⠙⠿⣶⣾⣿⣷⣶⣶⣦⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⢁⣾⢋⡿⢹⠁⡏⠘⠁⡀⠀⠀⡆⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣾⣷⣾⢣⠏⠀⣠⠀⠈⠀⡆⢀⣡⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⢀⣠⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠌⠀⢀⣿⣄⣀⣰⣠⡿⠿⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⣀⣠⣔⣯⣽⣯⣴⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠄⠀⠀⠈⡛⠛⠛⠁⠀⠀⣗⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠃⠄⠀⠀⠀⣰⣧⡀⠠⣠⠀⢰⣿⣤⣤⣤⣤⣴⡶⠋
⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⡟⢿⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⣠⣾⣿⣿⣿⣶⡶⢟⢫⢁⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⡼⡿⠃⠈⡏⠛⠉⢹⡇⢸⠀⠀⣿⠛⠉⠀⠀⠀⠀⣤⣶⣿⡿⠀⠀⠀⠀⠰⣿⣿⢹⡇⢤⡁⠀⠀⢀⣿⠆⢀⣀⣀⣀⣰⣸
⠀⠀⠀⣇⠀⡤⢠⠀⣄⣸⣸⣿⢸⡄⠀⢸⣾⣷⣶⠦⠼⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣾⣇⠈⣿⣶⣤⣾⡿⠿⠿⣿⣿⣿⡿⠿⡀
⠀⠀⢠⣿⣤⣶⣿⣾⣿⣿⣿⣿⡈⣇⠀⠀⢿⣯⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⠀⠀⠸⣿⣿⠿⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡇⠀⠀⢿⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣿⠀⣿⡆⢻⣿⡆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡀⠀⠘⡇⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣿⣀⣿⣧⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⠀⠀⠀⠀⠘⢹⣿⣷⣤⣀⠀⠀⠀⠀⠀⠙⠻⣿⡿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃
⠀⠀⠀⠈⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠃⠀⠀⠀⠀⠲⣼⣿⣿⣿⣿⣽⡖⡀⠀⠀⠀⠀⠛⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣾⣷⣶⣶⣤⣤⣤⡄⣀⢀⣀⣀⡀⠀⢀⣠⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠉⢿⣿⣿⣿⣿
⠀⠀⠠⣶⣴⣶⣶⣿⡟⣩⡤⠉⢻⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣟⠛⠛⠉⠉⠀⣰⡞⣻⣶⡄⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⢀⣹⣿⣿⣿⣿⡀⠙⣛⡷⢀⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⡿⡆⠀⠀⠀⠀⣿⣦⠤⢹⡿⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⢳⢻⣿⣿⣿⣿⣦⣬⣵⠿⠛⣋⣉⣉⣉⠁⠀⠀⢸⣿⣿⣿⡜⡄⠀⠀⠀⠈⠛⠛⢋⣠⣤⡶⠶⠶⠶⣿⣿⣿
⠀⠀⠀⠈⢧⡛⠛⠛⠛⣉⣡⣴⣶⠿⠟⠛⠛⠛⠂⠀⠀⢸⣿⣿⣿⣷⡙⣆⣀⣤⡶⠶⠾⠛⢉⣀⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣄⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣿⣿⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⢈⣩⣤⣶⣶⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⣴⡾⠟⠋⠉⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⣠⣴⠿⠛⠁⠀⠀⠀⢀⣀⣠⣤⣬⣤⣤⣭⣭⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⣩⣴⡿⠛⠁⢀⣀⣤⣶⣶⠿⠟⠛⠋⠉⠉⠉⠙⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢛⣉⣥⣴⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠉⠁⠀⣠⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⢡⡆⣷⣴⣿⣿⣿⣿⡄⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠘⠃⠙⠛⢿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣶⣿⣶⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⠇⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⣧⣈⡃⢨⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣀⣤⣴⣶⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠷⠾⠿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣍⣉⣍⣩⣭⣥⣤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⡉⠉⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⡄⠀⠀⠀⠀⡆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣽⣀⣴⣀⣀⣧⣿⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡹⠿⠿⢿⡿⢿⠟⢏⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⡼⠁⠀⠀⠈⠃⠀⠁⠈⠳⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢴⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠞⠀⠀⠀⠀⠀⠀⠀⢑⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢦⣠⠀⠀⠀⢀⣀⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠑⠡⠀⢠⡟⠉⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠐⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠸⠆⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠚⠏⠘⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢰⡏⠰⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⡃⠀⠀⠀⠀⠛⠶⣤⣀⣤⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠠⢊⠖⡴⡠⢢⠄⡄⠀⠀⠀⠞⡜⠡⠃⠀⢀⣴⢤⣤⣻⣤⣤⣶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⣄⣀⣈⣈⣁⣠⣤⣤⣤⣤⣄⣀⣀⣠⡴⠞⠋⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⡀
⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠈⠑⠚⣩⠟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠁⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⡤⠴⢖⠶⠦⣄⡀
⠀⠀⠒⠂⠀⠀⠈⢳⣀⣈⣀⡜⠁⠀⢀⡠⠖⠉⠀⠈⠁⠉⠉⠁⠈⠓⢄⡀⠀⠀⠙⣄⣀⣀⣀⡞⠀⠀⠠⠖
⠀⠀⠀⠀⠀⢀⡤⠚⠻⠛⠟⠣⣄⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⡼⠛⠿⠛⠛⠳⡀
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⠖⠉⠉⠒⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⡰⠁⠀⠀⠀⡖⠉⠂⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢣⠀⡔⠉⠂⠀⠀⠀⠈⢣
⠀⠀⡇⠀⠀⠀⠀⠉⠒⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡼⠀⠉⠒⢢⠀⠀⠀⠀⢸
⠀⠀⢣⠀⠀⠀⠀⠐⠶⠋⠀⠘⣆⠂⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠐⠶⠊⠀⠀⠀⢠⠏
⠀⠀⠢⢳⢄⣀⣀⠀⠀⠀⣀⣀⣨⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣇⣀⠀⠀⠀⠀⢀⣠⠔⣁⣀
⠀⠀⠀⠀⠐⠉⠜⠉⠜⡡⠋⠵⢋⠔⠡⢏⡝⡹⠋⡹⠋⡹⢋⡝⣩⠟⡽⠁⠋⠐⠱⠋⠉⠟⠝⠁⠊⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠠⣉⠄⣀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣨⣥⡴⢶⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠗⠴⢀⠲⣦
⠀⠀⠀⢠⠚⠅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣶⡶⠀⠀⠀⠀⠀⠀⠀⢘⢲⡌⣾⣀⢺⡷⠀⠀⠀⠀⠀⠀⠀⠘⢯⣈⠉⠀⠑⡼⠃
⠀⠀⠀⠈⠂⠤⢀⡤⢄⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣐⣀⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠙⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⠊
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁


⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠐⢾⡿⢤⠬⢿⠖⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠈⣁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⠞⠛
⠀⠀⠀⠀⢸⡆⢸⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⣦⣄⣀⡇⠀⠀⠀⠀⠀⠀⠰⢀⠒⠒⡀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠤⣶⡀
⠀⠀⠀⢀⣼⣧⣾⣧⣾⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠠⠩⢰⣶⡆⠀⠀⠀⠀⠀⠀⢠⣤⣄⣟⣿⢰⣻⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⡀⠀⣚⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢸⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢴⠆⠄⣌⡳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠒⢢⡈⠁
⠀⠀⠀⠀⡇⠀⠰⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⢸⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠷⢆⠀⢾⣏⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⣾⣶⣧⡄⠈⠄
⠀⠀⠀⢠⣭⣭⣥⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣼⠀⠀⠀⠀⠀⠀⠀⠈⠠⡯⠿⠀⢋⡵⠁⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡗
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣿⣏⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⢉⡉⣵⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁
⠀⠀⠀⠀⣟⡛⡚⣂⣛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠇⠺⠗⢸⠁⣸⡇⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠉⠉⡍⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣛⣶⡀
⠀⠀⠀⠀⡇⡇⡇⡇⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⠀⣀⣀⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⢆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⡀⡄⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⣛⣛⡛⠛⠛⣛⣛⣛⣛⣛⣛⡫⡉⠱⠀⠉⢸⣿⣿⣿
⠀⠀⠀⠀⣰⠆⠂⠈⠀⠉⠉⣴⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⡴⠐⠀⠂⠈⠉⢉⡴⠁⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⣄⡿⠀⠀⠀⡀⠀⠀⢠⡰⣶⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣠⡀⠀⢀⢜⡇⠀⠀⠀⠀⠀⠀⢀⡴⣶⡆⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣝⠝⠀⢰⣘⡧⠀⠀⢀⡷⠀⠀⠘⠙⠋⢁⣀⡤⢞⡤⠀⠀⠀⢸⣿⣿⣿⠀⠀⠨⣍⠜⠀⢨⣸⡇⠀⠀⢠⡇⠀⠀⠈⠛⠉⢀⣠⡴⣆⡆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣷⣄⡀⣿⡇⠀⢀⣀⣀⣠⣬⣴⠾⠛⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⣈⣻⣷⣄⢐⣿⡃⡀⠀⣀⣀⣠⣭⡴⠟⣫⣴⣿⣿⣿
⠀⠀⠀⠀⠶⠔⠒⠂⠘⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠐⠶⠐⣒⣂⣉⣉⣉⣉⣈⣉⣙⣛⣛⣋⣭⣭⣭⣴⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⠒⠛⢐⣤⣀⠀⠀⠀⢠⣴⣾⣿⣿⣶⡤⠀⠀⠀⠀⢀⣤⠤⢤⠠⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢻⣾⡿⣷⣿⠃
⠀⠀⠀⢾⣹⡇⠀⣿⣧⣿⠆⠀⠀⠀⢹⠀⢸⠀⢸⠀⠀⠀⠀⢰⣿⣷⣬⣿⣠⡾⠀⠀⠀⠀⢰⠾⣧⡿⢷⠀⠀⠀⠀⠀⢸⣯⡿⣯⣿
⠀⠀⠀⠀⠙⠄⣄⠬⠋⠉⠀⠀⠀⢀⣾⣄⣾⣄⣼⣄⠀⠀⠀⠘⠟⠛⠻⠻⠋⠀⠀⠀⠀⠘⠛⠒⠛⠓⠚⠛⠂⠀⠀⠀⠺⣿⣿⣿⣿⠆

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⣴⠹⡍⢩⠏⢦⡀⠀⠀⠀⢾⢉⢹⡄⢤⡄⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠈⣃⣜⢉⢟⡖⢤⠀⠀⠀⠀⢠⣤⠯⢧⣀
⠀⠀⢺⡇⣻⡇⣿⣿⠀⢸⡧⠀⠀⠀⢨⣧⣯⣵⣼⡄⠀⠀⠀⠑⣺⣿⣿⠀⣿⡒⠁⠀⠀⢺⠋⠀⢹⠺⠤⡎⠀⠀⠀⢶⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠉⠻⣰⣣⣞⣆⠞⠀⠀⠀⠀⢸⣿⣿⣿⣽⡇⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠈⠒⠐⠻⣄⡛⣤⠀⠀⠀⠀⠙⣿⠿⢿⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣤⣤⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣸⣷⡆⠀⠀⠀⠀⠀⠀⢠⡿⠛⠿⣦⠀⠀⠀⠀⢠⠻⡈⢹⠐⢒⡆⠀⠀⠀⠀⣴⣶⣶⣶⣶⣤
⠀⠀⠀⣯⣽⣿⢺⢺⠾⡷⡇⠀⠀⠀⠂⠙⠛⡉⠛⠶⠄⠀⠀⠀⢘⠗⠀⠐⢟⠀⠀⠀⠀⠙⠒⠃⢸⠀⣎⣘⡄⠀⠀⠀⠘⢿⣿⣿⡿⠁
⠀⠀⠀⠛⠛⠛⠛⠿⠿⠋⠀⠀⠀⣠⣶⣶⡄⠂⠀⠀⠀⠀⠀⠠⣿⣿⣶⣾⣿⡧⠀⠀⠀⠀⠀⣀⣸⣀⡈⠁⠀⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠻⠛⠻⠂⠀⠀⠀⠀⡇⢴⡦⠀⣿⣻⣿⡇⠀⠀⢠⢝⢿⣿⡿⣆⡀⠀⠀⠀⢀⣀⣴⣒⣲⣆⣀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣷
⠀⠀⠀⠀⠀⠘⠂⠊⠀⠀⠀⠀⠀⣥⣤⣤⡄⠛⠛⠛⡁⠀⠀⠇⠀⠑⠀⠛⢩⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣦⢸⡇⢿⣼⡿
⠀⠀⠀⠠⣾⣿⣾⣼⣿⡆⠀⠀⠀⣿⣯⣸⡇⠐⠟⠀⡇⠀⠀⠈⠢⢤⡄⢴⣿⣿⠂⠀⠀⠀⠿⠿⠷⠿⠿⠇⠀⠀⠀⠀⠉⠈⠁⢿⣾⠟
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣛⣩⣭⣭⣝⣓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡶⠋⠁⠀⣀⡀⠀⠉⠛⢮⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠋⠀⠀⣴⠛⣫⡙⢳⡄⠀⠀⢻⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡏⠀⠀⠀⢿⡀⠻⢿⣟⠃⠀⠀⠀⢿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡇⠀⠀⠀⣤⣽⣶⡄⠙⡇⠀⠀⠀⣼⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡀⠀⠀⢻⣄⡻⢃⣰⠇⠀⠀⢠⢏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡻⣤⡀⠀⠈⠻⠏⠁⠀⣀⡴⣫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣽⣓⡶⠶⠶⢶⣚⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣻⣭⠙⠢⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠸⠦⠬⣽⡬⠤⠞⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠖⡛⣾⡓⠲⣄⠀⠀⠀⠨⣈⠛⠲⠶⠦⠀⣒⣘⡇
⠀⠀⠀⠀⠀⠀⠆⠣⣄⣙⣧⣁⡤⠞⢰⠀⠀⠸⢈⣉⡛⠛⠛⢛⢉⡠⡆
⠀⠀⠀⠀⠀⠀⢼⠲⠤⠤⣤⣤⠴⠖⢐⠂⣀⣀⣤⣌⣉⣉⣉⣉⣡⣴⠡
⠀⠀⠀⠀⠀⠀⢉⠘⠲⠶⠦⠤⠴⠒⡋⡎⠁⢦⡿⠆⠈⣫⢩⣉⣡⣤⣆⣀⣀
⠀⠀⠀⠀⠀⠀⢘⢉⡓⠒⠶⠶⠖⠛⢃⣈⠓⠒⠛⠒⠊⣁⣜⢽⠉⢡⣽⠶⠉⢙⡔
⠀⠀⠀⠀⠀⠀⢰⣌⣉⢓⣶⣶⣶⣯⣭⣨⣉⠛⠛⠛⠛⣉⡨⣈⠓⠒⠿⠗⠒⢋⣨⢣
⠀⠀⠀⠀⠀⠀⠀⠤⡅⣏⠀⢤⣟⠃⠀⡱⣩⣉⣉⣉⣉⣥⠺⡩⣉⠚⠓⠚⠛⠛⣁⡌⠀⠀⠀⠀⠀⠀⠀⡀⢠⠖⢲⠄
⠀⠀⠀⠀⠀⠀⠰⠸⣦⣌⣉⡓⠛⢚⣉⣠⣎⣭⣉⣉⣤⣤⡾⣦⣈⣉⡉⠉⣉⣉⢅⣇⣀⠠⡤⠤⠐⠂⠉⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⣷⡿⠿⡿⠭⢽⡏⠉⠉⠉⠉⢩⣥⣤⠔⠺⠋⠛⠛⠛⠛⠉⠉⠍⡀⣀⠀⠐⠀⠀⠠⣞⣯⠵⠛⠀⠀⠆
⠀⠀⠀⠀⠀⢀⡔⣇⡀⢷⣏⠃⢀⡽⣵⡶⠦⠖⢊⣥⣴⣶⣶⠶⠀⠀⠐⠈⢀⢰⡄⠉⠁⠀⠐⠁⠀⠀⢀⣀⣠⡄⠾⠒⠚⠁
⠀⠀⠀⠀⠀⠸⠠⢤⣭⣽⣿⣛⣻⣏⣀⣀⣀⣀⡀⠉⠉⠀⣀⣀⣀⣀⣀⣀⣀⣡⠤⠤⠄⠶⠒⠒⠊⠻⠷⠯⠯⠟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠓⠤⣤⣤⣠⣤⠤⠪⣿⣦⣶⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣭⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣀⣸⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠉⠙⠻⢷⣦⣤⣤⣶⠾⠟⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣴⡿⠁⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡍⠉⠁⠀⠀⣿⡆⠀⠀⠀⠀⣴⡿⠋⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣼⣷⣤⣤⣤⣼⣯⣤⣤⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⣤⡄⣤⡀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⣾⣿⠟⣿⡏⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣿⡇⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⡟⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⡇⣿⠇⣸⣿⡿⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠀⠀⠈⣿⡏⣿⡏⠀⠀⠀⠀⠀⢀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⡶⣦⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⠀⡄⢀⣀⣤⢘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⢆⡀⠤⢻⣤⠄⢠⣤⣷⣇⣴⣿⣆⣴⣤⡄⠻⢳⡀⣴⠁⢸⣿⠀⠁⣿⣿⣿⣿⣇⡀
⠀⠀⠀⢠⣤⣸⣷⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡧⣬⠨⣅⣿⣠⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠋⠉⠁⠙⠛⠛⠛⠓⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠁⠀⠄⣇⠀⢃⣣⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠚⠈⠀⠈⠀⠂⠊⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠒⠆⠀⠀⢠⢀⡮⡕⠀⣴⠂⠀⡤⢤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠀⠄⠒
⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠐⠛⠂⠰⠇⠀⣛⡺⠔⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢁⠓⡀⠀⡹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀⣠⠄⠀⠈⠀⠀⢤⢾⢆⠀⠀⣀⠀⠀⠀⠁⢀⣀⠠⢀⠀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢹⠶⠚⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠤⠤⠀⠐⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢤⣄⣤⠶⡻⠲⢤⢤⣤⡶⣛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡚⠾⣯⡮⣳⡗⣐⣱⡱⣡⡟⣊⣿⡓⡒⡲⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢭⣿⠋⠕⣻⠾⠾⢽⡇⠀⠉⢉⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢦⣿⡆⢰⣸⣀⠀⣿⣶⡔⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡬⠗⣲⠿⣧⣼⡿⠿⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣻⢿⡿⢳⢞⣹⣥⣇⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣾⡷⡷⡿⠻⢯⢿⡇⠋⠛⡶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠊⡸⠋⠀⠀⠀⠀⠈⠂⠙⢦⠀⠀⠰⢡⠋⠗⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡁⡄⠀⠈⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢃⠔⢉⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⢠⠂⠁⠀⠀⣀⢤⠄⡦⡼⡻⡪⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢣⠊⡠⢛⢦⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠸⠜⠀⠀⠀⠀⣼⠕⢕⣱⣞⡺⡫⣪⣜⢝⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠔⡡⢊⡵⣄
⠀⠀⠀⠀⡠⠊⠀⡀⡄⠁⠀⠀⠀⠀⢸⢕⣵⡟⠁⢸⡯⡾⡟⠲⢵⣿⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⡥⢊⠔⡹⢆
⠀⠀⢠⠎⠀⡄⠆⠁⠀⠀⠀⠀⠀⠀⠸⣷⢝⣷⣄⣸⡪⣪⡇⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠔⣁⠞⡵⢡⢧
⠀⣰⠃⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⣝⠯⡪⣺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡡⠊⡰⡱⢋⣇
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⡾⣻⢋⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢊⠜⡡⣣⣻
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢸⡫⣪⡏⠻⣕⢕⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡴⢋⢜⢔⡕⣽
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡽⠻⣄⠀⢸⣾⣾⠇⠀⢹⣟⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠖⡵⣫⣮⢞⢾
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡪⣺⡷⡿⣻⡿⡦⡶⣿⢿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡵⣫⢞⡵⡵⣣⢿
⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢾⡯⡫⣪⣮⣬⠿⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡡⢚⡵⡣⢊⠜⣡⡏
⠀⢣⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣩⠔⡡⢚⠔⡡⢊⡴⠁
⠀⠀⢣⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠘⢁⠞⡡⢊⠔⣡⢊⠔⣹⠗⠒⠒⠒⠒⠀⣀
⠀⠀⠀⠱⣄⠃⠇⡄⡄⠄⠀⢀⠀⠀⡀⡠⢠⢎⡴⣣⠔⡡⢊⡤⢊⡤⢃⠌⡠⢣⢎⡔⡱⡳⢁⠎⡰⢫⠊⡵⡣⠾⠥⠥⠤⠬⠤⠭⠭⠭⠭⠬⠤
⠀⠀⠀⠀⠈⢳⣄⡉⠃⠆⠇⠸⠐⠰⠰⠡⠃⠊⠐⠁⠊⠐⠁⠐⠁⠚⠡⠊⠔⡡⢊⢌⡜⡠⢃⠎⡔⣡⠾⠎⠩⠩⠭⠍⠩⠭⠭⠭⠭⠭⠭⠉⠉
⠀⠀⠀⠀⠀⠘⠛⣛⣓⣦⣤⣤⣤⠔⢶⣶⠶⣶⣶⣶⣾⣿⣭⣭⣭⠍⣉⣀⡀⣔⣱⣋⣞⡰⠧⠾⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⣽⢋⣁⣀⣉⡭⠭⠭⠭⠭⠿⠍⠭⠿⠾⠿⠉⠹⠿⠿⢿⣭⣭⣭⣯⠭⠭⠭⠭⠈⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠀⠀⠀⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣄
⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣋⣩⣤⣶⠶⢶⣦⣬⣍⡛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠞⠋⠁⠀⠀⣀⡀⠀⠀⠉⠛⢷⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣰⡟⠁⠀⠀⢀⣤⣾⠟⠿⣦⣄⠀⠀⠀⠙⢷⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⡏⠀⠀⠀⠀⣿⠁⢠⣾⣆⠀⣻⡆⠀⠀⠀⠈⢿⡌⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣿⠀⠀⠀⠀⠀⢿⡄⠈⠻⢿⣟⡛⠁⠀⠀⠀⠀⠸⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⠀⠀⠀⠀⠀⣈⣛⣷⣤⡀⠈⢻⡆⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡀⠀⠀⠀⠀⣿⠉⢹⣿⣇⠀⢸⡇⠀⠀⠀⠀⣸⡇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⡀⠀⠀⠀⠹⣧⣌⡛⣁⣤⡾⠃⠀⠀⠀⣠⡿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⢿⣄⡀⠀⠀⠀⠹⠿⠿⠁⠀⠀⠀⢀⣴⢟⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⡻⢶⣤⣄⣀⣀⣀⣀⣤⣴⠾⣋⣵⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿
⣿⠀⠀⠀⠉⠉⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣭⣭⣭⣭⣭⣥⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠉⠉
⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⠛⢦⣄⡀
⠀⠀⠀⠀⠀⢰⠇⡼⠓⠺⢍⠓⠦⣤⣀⣀
⠀⠀⠀⠀⠀⣾⢰⠇⢸⣷⠀⣳⡀⠀⠂⠌⠩⣛⠓⠶⠶⠤⢤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⢠⡇⠈⢤⡛⠁⣠⠏⡡⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠂⠊⠚⠉⠭⢝⣓⠲⢦⢤⣄⣀⡀
⠀⠀⠀⠀⣼⠃⢰⠀⠙⠛⠛⠁⠀⠠⠀⡄⠀⠀⢀⠉⠀⣀⡀⠀⠐⠆⠀⠰⠄⠀⠀⠉⠉⠒⠢⣬⣍⣻⣶⣤⣀
⠀⠀⠀⢰⠇⠀⣼⠀⠀⠀⠀⠀⠨⢱⠀⠀⠀⠀⢈⡴⢚⠋⠉⠻⡻⢦⡒⠠⠀⠀⠀⠀⠀⢠⣼⠋⠀⣤⡌⢧⠉⡷
⠀⠀⠀⣾⠁⡖⠛⠲⣄⠀⠠⢠⠁⠀⠀⠀⠀⢠⠋⣄⠀⠀⠄⠀⡈⠘⡅⠀⠀⠖⠲⠀⠄⠀⣺⡀⠰⠾⠀⢸⢠⠇⠀⠀⠀⢀⣤⠞⠻⡆
⠀⠀⠀⣟⠀⠇⠰⡇⣸⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⢀⠁⢀⠀⠔⠃⢰⠁⠀⠀⠀⠀⠀⠑⠀⠈⠛⠲⠶⠾⠋⡞⠀⣀⡴⢚⡽⠛⠛⢦⡸⡄
⠀⠀⠀⠈⠙⠾⣶⣖⡫⠀⢀⡀⠀⡠⠮⠽⠸⣒⣉⣠⡀⠀⠷⡀⢠⢋⣦⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠎⣰⠷⢛⠥⢶⡟⠰⢿⠀⠀⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⢥⣥⣠⣀⣀⡀⣤⠀⠀⣉⣉⠁⠛⠚⠷⠢⠀⠒⠂⠀⠀⠀⠀⠀⣄⣼⢠⡟⠉⠀⠀⢠⣧⣀⠉⢁⡼⠃⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠓⠶⠶⢯⣭⣥⣌⣒⠆⠠⢄⡀⢠⠎⣩⢻⡇⢸⠇⠀⠀⠀⢀⠈⠻⠛⠁⠀⠀⢵⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠒⡋⠩⠀⠈⠙⠙⠓⠶⣮⣝⣆⣛⡼⢂⡿⠀⢠⡄⠂⠈⠀⢢⠀⠀⠀⠀⢾⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢫⡩⠇⠒⠦⣌⡈⠀⠀⠀⠀⠀⠀⠈⡁⠀⣠⢞⠛⠷⣤⣾⢇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⢫⡉⢳⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⡆⠲⣾⠄⢸⡇⠆⠀⠀⢀⠀⠀⠀⠁⢸⠃⠆⠀⠠⠀⢻⡀⢣⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⣌⣩⣮⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠖⠶⠦⠼⣧⡙⠦⣚⣃⣼⠿⠀⠀⠀⠠⡀⠀⠀⠀⢸⠐⠦⠠⠀⢀⣸⠀⠐⣏⢴⣂⣠⡈⠀⡀⠄⣂⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢴⡶⣏⠸⠉⣉⡉⠓⣌⣷⠀⠠⣀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⢘⡄⠀⡄⠢⡀⠈⣓⠦⠛⠘⣉⠤⣈⣨⠶⡟⠉
⠀⠀⠀⠀⠀⠀⡠⠻⢸⡁⣿⠸⡄⢹⣟⠀⣽⠹⣧⠀⠱⡆⠀⠀⠀⠒⠈⠀⠀⠀⠀⡲⣍⡮⠀⠐⠉⣁⡠⣄⣲⡭⠶⠛⠉⢱⠀⣧
⠀⠀⠀⠀⠀⢸⢡⠀⢸⡅⢿⡇⠈⠾⠥⡴⠿⠁⠸⣇⠀⡍⠉⣬⠙⣆⠀⠀⠀⠀⣲⠉⠁⣀⣐⣦⡽⠶⠛⠉⣁⠀⠀⠀⠀⣸⡆⢹
⠀⠀⠀⠀⠀⡌⠸⠂⠘⡇⠈⣷⠀⢢⠄⠀⠀⠀⠀⠹⣆⠘⠦⢘⢣⡜⣀⣀⣬⡥⠶⢶⠟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢇⠸⡇
⠀⠀⠀⠀⠀⡇⢸⡇⠀⣷⠀⣻⡄⠘⣇⠀⠀⠀⠠⠠⠜⠶⠒⠛⢛⡛⠉⠁⢉⠀⢤⡆⠀⢸⢂⡤⠀⠀⡠⠄⠀⠀⠀⢸⠸⠧⡸⠀⣇
⠀⠀⠀⠀⠀⡇⠸⠇⠀⣿⠀⢸⡇⠠⡃⢡⡌⢢⠀⠀⠀⠀⠀⢀⠪⠙⡖⢁⣈⣄⠀⠩⠶⠼⠔⠷⠓⢲⡀⡠⠄⢀⣒⣩⣷⣾⠷⠚⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⣾⢿⠀⠳⢀⣛⣼⢃⠀⠀⢄⠠⠍⠉⠉⠀⠀⠤⠄⢀⣠⣤⣀⣖⣦⣭⠶⠶⠗⠛⡟⣩⠙⡇⢿
⠀⠀⠀⠀⠀⡇⢰⠀⠀⢹⡄⠙⢮⢛⡷⢛⠻⠗⠻⠖⠖⠾⡶⠶⠿⠿⠿⠛⢛⡛⡩⡩⠉⠥⠀⠂⡶⠠⠀⠴⢔⢧⣝⡵⠃⣾
⠀⠀⠀⠀⠀⢇⠸⠀⣰⠎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⣉⣉⣉⣉⣛⣛⣛⣛⣏
⠀⠀⠀⠀⠀⠸⢠⡾⠫⠍⠤⠤⢶⠶⠶⠀⠀⠀⠀⠐⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⡉⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠙⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣶⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠢
⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⢤⡀⣶⠐⡆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⢠⢒⠀⠀⠀⠳⢤⢿⡎⢳⡛⠛⠀⠁⢧⠀⠀⠀⠀⠀⠀⠀⠊⠀⢒⡏⠘⢀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠈⠀⠀⠀⠄⠠⢶⡄⠈⠀⠀⢠⠘⠄⠀⠀⠠⡄⠀⠠⠀⠀⣸⠁⠀⠂⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠐⡶⠃
⠀⠀⠀⠀⢀⠠⠄⢰⠎⠢⠙⠃⠀⠀⠤⠐⠀⠁⠀⠈⠀⠇⠀⠀⠀⢀⠏⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡠⠂
⠀⠀⠀⠀⠀⠀⠂⠈⠳⡄⠁⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⡒⠀⠀⡟⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠄⠀⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⡔
⠀⠀⢀⠀⠀⢠⠀⠠⢠⡀⣤⡴⠀⣾⣆⠀⠀⠀⠀⠀⠀⢠⣢⣄⡀⠀⠀⢀⠀⠀⠀⢀⠰⠛⠀⠀⠀⠀⠀⠀⢀⠐⠀⡤⠀⢀⠞
⠀⠀⢸⠀⠀⠀⡆⠂⣰⠃⠸⢀⡀⡟⠻⡄⠀⠀⠀⠀⠰⠵⠿⠟⠘⠛⠋⠀⠀⠑⠛⠛⠀⠀⠀⠀⠀⠀⠀⠠⡘⠂⠀⠀⡠⠋
⠀⠀⢸⣆⠀⠈⠀⠈⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⠫⠆⢀⡔⠁
⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠤⠔⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡠⠂⠉⢁⣌⠃⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⢤⠀⢸⣁⠀⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⡈⠀⡞⠓⠨⣇⣤⢡⡤⠘⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣷⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⢤⡈⣀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⡞⠡⡼⣹⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⣽⢿⡍⣹⣿⣷⣸⣆
⠀⠀⠀⠀⠀⡠⢚⠙⢿⣿⡇⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣇⠉⠈⢿⣪⠟⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠃⣚⡠⣼⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡲⢍⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣔⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠒⠠⠤⠞⢡⣤⠀⠀⠀⠀⠀⠀⢰⡶⠒⡲⣒⣒⡲⡒⠲⣶⠀⠀⠀⠀⠀⢀⣾⠃⢸⣿⡦⠄⠛⠉
⠀⠀⠀⠀⠀⢠⣅⠐⣿⡇⣶⡆⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⠶⡹⣯⢜⡷⡱⠆⢸⠀⠀⠀⠀⠀⠘⠛⠃⠉⠈⡆
⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠸⠷⠤⣱⡯⠭⠷⠥⠴⠿⠀⠀⠀⠀⠀⠀⠀⡔⢪⠖⣩⡒⣴⢢
⠀⠀⠀⠀⠀⠈⠩⠤⠉⠡⠉⠡⠌⠩⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡺⣄⡞⣠⣟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣄⡤⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠽⣋⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣶⣄⠁⣠⠟⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⢶⣿⣦⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠦⡝⢻⣿⣿⠃⠀⠀⠀⠀⣠⡞⠁⡘⠷⡧⣯⠞⠁⠻⣧⡄⠀⠀⠀⠀⣿⣿⣿⣿⡀⣫⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⣄⣁⣠⠞⡅⣿⣦⣴⡿⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠱⠚⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡔⣤⣐⢦⣄⡰⣥⣄⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠠⠤⠄⠐⠊⠀⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣣⠶⣿⡦⠾⣷⠶⣿⣤⡽⠞⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠁⠀⠆⠀⠀⠀⣁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢠⡿⠀⣼⠃⣰⡟⠀⠀⢀⣀⠀⠈⢙⣟⣂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠂⠀⠀⠀⠉⠀⠈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⣼⠇⣼⠇⣰⡟⠀⠀⠀⢟⣿⡇⠀⠀⢳⣍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠀⠀⠆⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⢴⣿⣴⡿⣶⡿⠐⢀⣀⠓⠀⡀⠀⠀⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⠇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣿⣵⣿⣶⣿⣴⣎⡍⠉⠙⢦⠈⠄⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠀⣤⠤⡤⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣽⢿⠿⣿⡇⠻⠿⠻⣿⣸⡇⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠄⢠⣠⣨⡜⠂⠑⠀⠀⠀⠀⠀⠀⢠⣻⣟⡯⣿⣿⣿⠏⠀⢻⣿⣦⣀⣘⣩⠟⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⡄⠈⠀⠇⢀⠐⠀⡄⠀⣀⠀⠀⠀⠒⢿⡿⠿⠿⣿⠃⠀⠀⣈⠉⠃⡄⠄⠀⣸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠊⠀⠀⠀⠀⡇⢠⠈⠀⢠⡆⠀⠀⠘⢉⠍⠉⠈⠱⠴⠅⠉⠉⢈⣭⠍⣭⡍⠉⠈⠉⠉⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠙⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠠⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⢠⢃⠀⠠⠀⡀⠀⠀⠀⠀⢠⣎⢊⣄⠈⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠨⠀⠆⠐⢠⡄⠀⢠⢠⠀⠀⡀⠀⠀⠀⡄⣄⠀⢠⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠰⡄⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⡄⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠂⠡⡂⠀⠀⠀⢘⠀⠀⢂⠀⣰⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⡇⠀⠀⠀⢈⡀⠀⠀⠀⡆⠀⠀⠀⠤⠀⠀⠤⠀⠄⠀⠀⠀⠠⠠⠀⠤⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠁⠡⠀⠀⠀⠁⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠒⠒⠂⠒⠀⠂⠒⠐⠂⠐⠒⠒⠒⠀⠓⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠁⣉⢀⡉⠀⠈⡀⢈⠈⠉⢈⠀⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⠀⠀⠀⠀⢀⣆⣀⡀⠔⢠⣀⠀⠀⣀⠀⡀⠀⢀⡀⢀⢀⠀⣀⠀⡇⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠔⠀⠀⠀⠀⠘⠂⠀⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠


⣾⣿⣿⣶⣶⡷⢿⣾⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⢷⡿⠿⡿⢶⣶⣿⡿⠶⠶⢶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠉⢉⣉⣭⣉⠉⠁⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠤⠤⠾⠁⠀⠿⠤⠤⠤⠖⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣸⡆⢻⣾⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠉⠉⠉⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣦⢰⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣀⣧⢼⠦⣄⠀⠀⠀⠀⠈⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣼⠉⡇⢸⠀⠈⣧⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢻⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠙⡷⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢠⡀⠀⡇⢸⡆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⠲⣷⢼⡗⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣉⣈⠁⠀⠀⣀⣀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠒⠂⢾⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣿⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠐⡆⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⢹⣿⣿⠀⠀⠀⠀⡸⠄⠀⠀⠀⠘⣷⠀⠀⢰⠁⠀⠀⠀⠀⢿⡌⠿⢶⡂⣠⡤⣤⣤⠉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠸⣄⠠⢰⣿⣿⡏⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢷⡟⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣀⣤⣀⢉⠲⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣌⣿⡇⠀⠀⠶⢖⠂⢤⣐⡀⠰⠀⢀⣠⣤⡴⠦⠤⠦⠸⣿⣉⠀⡀⠀⠘⣿⣿⣇⡀⢠⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⣿⠁⠀⢀⠀⣀⣤⠴⢞⠿⠛⡺⠋⠁⠀⠀⠀⠀⠠⠄⠀⠈⠑⢮⣠⣄⠹⣿⣿⡇⣠⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣿⣋⣁⠀⡨⠟⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⣧⡘⠏⠀⢰⠈⠉⠉⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠿⠿⣤⣤⠟⠀⠀⠀⠀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠹⣷⡄⠲⣈⢠⡍⠙⠃⠓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣄⣤⣤⠃⠀⠀⠀⣰⡿⢿⡿⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠹⣿⣿⣿⡑⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⣼⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣿⣿⡿⢏⣉⡀⠬⡄
⠀⠀⠀⢀⠀⠀⠀⠀⢀⢼⣅⡀⠀⠀⠀⣀⣴⠀⠀⢿⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠟⢻⣷⡄⠠⢀⣖⠁
⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⡀⠉⣉⢉⣉⣁⠤⢣⠀⠀⠙⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣾⣿⠟⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠀⢀⠀⠀⠀⠀⢿⡇⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡆⠸⡿⠁⢀⡷⣤⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣁⠐⠒⠂⠓⠀⠀⠀⠀⠐⠈⠀⠀⢶⡀⠸⡇⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⡁⠀⠀⣰⡿⠟⢛⠻⢿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠃⠤⢤⠬⠀⠀⠀⠐⠂⠀⠀⠀⠀⣆⠻⢶⣷⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣼⣀⣠⡾⢻⡁⣄⣉⡉⠂⣿⣿⡿⠁⠠
⠀⠀⠀⠀⠀⠀⣞⣀⡒⢒⡏⣀⣉⣀⣈⡁⠀⠀⠀⠸⣆⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⣠⣾⣿⣿⣿⣷⣍⡑⠬⣭⣭⣶⣿⡏⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠭⠶⠄⢤⣬⡤⠤⠄⢚⠀⠀⢻⣷⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⣰⣿⣿⡿⠊⢙⣿⣿⣿⣿⣿⣿⣿⣷⣾⣵⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠠⠀⠐⠀⠻⠷⣶⣾⣿⣿⣷⣤⣀⡆⠀⠀⠀⠀⠀⠀⠆⠙⣿⠟⢁⣴⣿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⣿⠥⠯⣀⡀⠀⠀⣈⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⣴⣿⣿⢡⠠⠿⢦⡙⣶⢺⣾⡿⠁⠈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠉⠻⣿⣦⡑⠿⠟⣡⣿⡿⠛⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠈⠑⠒⠒⠤⠭⠭⠭⣉⣛⣋⣉⣉⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡜⠀⠐⣶⠾⠤⢤⣀⣠⣤⣤⡀⠀⠀⣤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠼⠏⢀⠀⠙⠃⠹⠛⠛⠒⠺⣿⠯⠁⢠⢫⠇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣛⣡⠥⠤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠈⠁⢀⢤⢮⠎⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣋⠭⠔⣒⠀⠀⠀⠰⣄⢠⣀⠈⠉⠉⠉⠙⠓⠒⠦⠌⠉⠓⢦⠀⠄⠔⣵⡵⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠟⠳⠶⠦⢤⣤⣤⣤⡤⠶⠖⠋⣐⣒⣭⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠏⠀⠀⣐⣶⠾⣅⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣈⠥⠒⢋⣡⠴⠶⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠏⠀⠀⠀⠈⢿⣭⣶⡶⠿⣙⡛⢿⡦⠀⢀⡴⠋⢀⡴⠚⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⠒⠦⠤⢤⣄⣀⠀⠀⠀⠀⠼⠋⠓⢠⠋⢀⣴⢋⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢭⣙⡓⠦⢤⡀⠀⢠⠃⢀⡞⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⠀⡾⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠿⠿⣒⠮⢭⣴⣾⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⡸⣧⡀⠰⢶⡄⢤⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠻⣽⣇⢻⠀⠉⠙⢻⠃⣀⣬⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢶⣿⢿⣿⣇⠀⣠⣡⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢞⡶⡿⢃⡿⢹⠟⠻⢏⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⣵⠏⠈⢀⣾⠃⠀⠀⠀⠈⠳⢄⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⢋⣵⡞⠘⢃⣾⠁⠈⠁⣶⣄⣘⣷⣆⡀⠀⠢⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⣴⣿⠟⠁⠀⠈⠁⠀⣠⣾⣿⣿⠿⢿⣿⠛⠛⠂⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⣠⣿⠇⠀⠀⠀⠀⠀⠠⣿⣿⢿⣿⢀⣸⣿⣤⣄⡀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣾⣤⡄⢶⣾⡀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠛⠻⣿⡆⠀⠀⢠⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢹⣿⠀⣼⣿⠀⣠⣿⣿⠀⠀⠘⣿⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⣿⣿⣿⢹⣤⠀⠀⠰⣶⣤⣾⣿⣠⣿⣿⣾⣿⡿⠃⠀⠀⠈⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠉⢿⣿⠸⡿⣦⡀⠀⠀⠙⣿⡿⢿⣿⡿⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢀⠈⠀⠃⠁⠀⠳⠀⠀⢸⡿⠁⠸⠟⠁⠀⢀⢀⣰⣿⣾⠀⢀⡔⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣶⣆⣄⣀⣀⣀⠀⠀⠈⠁⠀⠀⠀⡠⠾⠛⢿⣿⣿⣯⣤⣾⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⠿⠿⢿⣿⣷⣤⣤⣀⣀⣠⠴⠧⠶⠦⣤⣽⡵⠧⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣶⣦⣴⣶⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠋⣉⣁⣀⣉⠉⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠀⣿⣿⡿⠛⣉⣉⣉⣉⣉⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣉⡉⠉⣉⣠⣿⣿⣧⡈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠀⢀⣤⣤⣀⠀⠀⢀⣾⣿⠛⡁⢈⣙⣿⣷⡀⠀⠀⣀⣤⣤⡀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⣿⣿⣿⣿⡆⠀⣼⣿⣿⣄⡁⠘⠻⣿⣿⣧⠀⢰⣿⣿⣿⣿⡆⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠻⢿⡿⠟⠁⠀⠸⣿⣿⠛⠃⠘⣀⣿⣿⠇⠀⠈⠻⢿⡿⠟⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣇⣸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣼⣧⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠁⠀⠀⠈⢿⣿⡇⠀⠀⣿⣸⣇⠉⠀⠀⢸⣿⡿⠁⠀⠀⠈⢿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣷⠀⠀⠀⠀⣼⣿⡇⠀⠀⡀⢹⡏⣿⠀⠀⢸⣿⣧⠀⠀⠀⢀⣾⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⢿⣿⣿⣶⣶⣿⣿⣿⣿⣄⠀⠙⢻⡟⠁⠀⣠⣿⣿⣿⣿⣶⣶⣿⣿⡿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠬⠥⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⡟⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⢛⣿⡟⠛⠛⠛⠛⣿⡟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣾⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣾⣿⡇⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣾⣿⡇⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠳⠾⠋⠉⠩⡔⠲⠀⣩⠍⣱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣭⣥⠤⣀⠀⠀⠀⠈⠙⢀⣮⣥⣾⣻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠂⠉⠁⠀⠀⠉⠙⠛⠶⠤⣀⣴⣿⣯⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠲⠋⡍⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡟⠂⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣪⠑⠊⠀⠀⠀⠱⢤⠀⢈⠑⣅⡨⢯⢟⣦⠠⣣⢡⣿⣿⣿⡛⢪⣦⣾⣿⣇
⠀⠀⠀⠀⠀⠀⣄⠒⢉⡴⠞⠅⢉⡁⠀⠀⠀⠀⠀⠀⠉⠉⠉⡠⢒⣽⣿⣿⡀⣱⣿⣾⣟⣀⣴⣟⣽⣯⢏⡾
⠀⠀⠀⠀⠀⢰⡿⣛⠲⠤⣌⣓⠠⣌⡀⠀⡠⠤⣤⡄⡠⣰⡭⣺⣿⣿⣿⡿⢀⣽⣟⠂⠀⢀⢹⡷⡿⣱⣏⡀
⠀⠀⠀⠀⠀⢘⡇⠈⢛⣒⢦⢭⣙⣶⣍⣉⠤⢞⣩⣔⣮⣷⣿⣿⣿⣿⣿⡝⠋⠁⠀⠀⣠⡼⢪⣿⣷⣯⣒⡚⠑⢶⠤⢄⣀
⠀⠀⠀⠀⠀⠘⠣⢄⡀⠠⢍⣋⠒⠮⢙⠿⠯⣗⣿⣟⣯⡿⣿⣿⠋⠓⠂⢀⣩⡿⣿⣪⣳⡼⢾⣿⡥⠴⠚⣇⣀⡂⡰⠔⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣦⣭⣛⠲⠬⣴⠒⣾⣿⡿⠟⠷⠂⠀⠀⠉⢁⢎⣾⣿⠧⡳⣡⡎⠁⠀⢠⠂⠉⠚⠵⢖⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡺⠗⠂⢉⣉⠒⠤⣼⠏⠽⠀⠉⠁⠀⠀⢀⢔⣵⣟⣽⣿⢀⡴⠃⢀⡠⠕⠁⠀⠀⠀⠐⠒⠈⠙⡏⢙⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⡎⠤⠸⠥⠀⢓⣀⠠⠬⢗⣒⠀⠀⡠⠔⣒⡖⢒⣵⡷⣳⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⣀⠘⡀⠈⢐⣡⠔⣫⡀
⠀⠀⠀⠀⠀⠀⢸⡯⠭⠍⢀⣒⣒⠒⠀⠉⠩⠍⠋⢉⡀⠐⠫⢒⠽⣣⣮⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⠯⢒⡩⢔⣫⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠭⠔⢒⣒⣒⣀⠭⠍⠭⠤⠶⠒⠀⠭⠽⠤⣾⣿⡿⡿⠿⣶⣖⠒⢲⣖⠢⢄⣀⡠⠄⢀⡢⢭⣒⣬⣴⣾⢿⣿⡯⢛⠯
⠀⠀⠀⠀⠀⠀⠀⠈⣟⢆⡳⣖⠶⡴⠤⢭⠭⡭⢩⠏⡭⡩⢭⠍⡽⣿⡫⡂⠀⠈⠙⣯⣒⠦⡭⣤⣖⠲⢽⣗⣿⣿⣿⡿⠿⢛⡉⢔⣚⣽
⠀⠀⠀⠀⠀⠀⠀⠨⡎⠁⠉⠊⠑⠦⣀⢁⠊⠐⠑⠠⠊⠔⠡⠢⢂⡜⣿⣾⡀⠀⠀⠀⠱⠍⢨⣿⣿⣾⡿⠿⢛⡩⢕⡂⢬⡰⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠈⠙⡳⣖⠈⣉⡽⠖⢲⣶⣿⣿⣿⣿⡿⡶⠄⡀⠀⠀⢸⡿⠽⣔⣶⡯⠿⠛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠘⡟⡙⠢⣴⢾⣿⣽⣿⣿⡷⠝⠋⠀⠀⠈⠐⠠⠜⠛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠈⠮⠀⣼⣿⣯⠿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠐⠀⠀⠄⡠⢀⠄⡠⢀⠀⢀⠀⡠⠀⠀⡀⢀⠄⡠⢀⠄⠀⠀⡠⢀⠄⠀⢀⠀⡠⢀⠀⡠⢀⢄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠊⢔⠄⡀⠄⡀⢀⠄⡠⠔⡁⢀⠅⠠⢊⠄⡨⢀⠀⣀⠄⠀⡠⡠⢊⠔⠡⢀⠔⡡⢊⠔⡡⢊⠔⡁⠨⠪⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠐⠁⠊⠐⠁⠐⠀⠊⠐⠡⠂⠄⠡⢂⠀⠡⠪⠈⠄⠁⠊⠐⠁⠈⠀⠁⠈⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⣤⣀⠉⠙⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⣤⣀⡈⠉⠛⠿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣦⣀⣠⣤⣴⣶⣷⣾⣷⣦⠀⢀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦⣤⣽⣿⣉⠉⠁⠀⣠⣾⣯⠵⠞⠛⠉⠉⠉⣈⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉⠉⠉⢉⣽⣿⠿⠛⢻⣄⣠⣴⣿⣾⣶⣶⣤⣤⣶⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢿⣿⣶⣾⣿⠿⠟⠋⢉⡾⠉⠉⠉⠉⣩⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠻⣷⣄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⢟⣀⣤⣴⠶⠾⠷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣤⠶⢿⣻⣿⣿⣯⣤⣶⣶⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠉⠙⠛⠿⠿⠶⠶⣶⢶⣦⣤⣶⡾⠟⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣠⣼⣿⣾⡿⢿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠉⠙⣧⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠈⢷⡀⠀⠀⠸⣇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆
⠀⢀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⡁⠀⠀⠘⣷⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠸⣇⠀⠀⠀⢹⣧⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣶⣤⣿⣶⣶⣾⡿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠘⢿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⢀⠀⠀⠀⠠⢄
⠀⠀⢀⠠⢄⠀⡠⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⢑⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⣄
⠀⠐⠁⠄⡲⢸⡄⠀⠈⢂⠀⠀⠀⠀⣤⣀⣀⠠⠄⠀⠠⢦⠀⠀⢠⠾⠟⠄⠀⠀⠀⠀⡀⠀⠈⢀⠀⠀⠀⠀⠠⠐⠀⣀
⠠⢂⣂⠔⠁⢻⠈⠢⢄⣠⢣⡀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠐⠄⠀⠀⠁⠀⠀⠐
⡏⠚⠁⠀⡀⠀⠂⠀⠀⠈⠃⠀⠀⢰⡆⢈⠀⡀⠄⠐⢀⡖⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠙⠓⠛⠢⠄⠆
⠙⠀⠀⠊⠀⠀⠀⠈⠑⠂⠀⠁⠀⠸⣂⠈⠀⠀⣀⡴⠚⠀⠀⠀⠈⠒⠀⠀⠀⢀⡀⠘⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⠊⠰⠃⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠯⠄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠋⠉⠓⠮⠁⠒⠄⠀⠀⠀⣕⡢⠀⠀⢀⠆⠸⢀⠀⠀⠀⢀⠆⠈⠁⠐⠒⠒⠀⠡⢆⡀⠀⣐⡡⠀⠀⠀⢒⠒⠒⠂⠀⢄
⠀⠀⠀⠀⢸⠀⠀⢀⠀⠈⡀⠀⠀⠀⢘⠜⠀⠀⣠⢇⣗⣀⡤⣄⠀⠀⠈⠃⠀⠤⠤⠤⠄⠐⠒⠚⠁⠀⠇⣀⣀⣀⣀⠼⢀⣀⣀⡦⠔
⠀⠀⠀⡀⣰⠇⣘⠉⠑⠀⣐⠀⠀⠃⠂⠀⠀⠠⠃⠒⠀⠀⠀⠈⢢⠀⠀⣠⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢲⠀⠀⢠
⢠⠂⠀⠀⠀⠀⠈⠛⠃⠠⠼⠀⠀⠃⠀⠀⠀⡆⠀⠀⠀⠐⠀⠀⠀⠀⠀⡱⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⠔⠉⠙⠆⢣⠄
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠈⠐⠠⡀⠱⢊⡁⠈⠲⡄⠀⠀⠀⢹⠀⠰⠤⠔⠁⡸⠄⡀
⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠁⡇⠀⠀⡰⠊⠸⣀⠤⢃⢔⡑⠁⠀⠀⢀⠼⡀⠀⠀⠀⠈⠀⠀⣰
⠀⠈⠑⠠⢤⡄⢤⡠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⣤⡀⠀⢄⡠⠔⠛⠌⢢⠀⠀⠈⢲⠃⠀⠀⠀⠈⠓⠚⠁
⠀⠀⠀⡤⡀⠀⠀⠐⠐⠃⠀⠦⢤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢩⠣⣀⣠⠆⡸⠀⠀⠀⠘⠠⠄
⠀⠀⠀⠀⠁⠀⠰⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠈⠀⠀⠀⠠⡀⢀⡔

⠀⠀⢀⣀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣷
⠀⠀⢿⣿⡂⢀⡨⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣾⡿⣷⣞⣿⣦⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢠⣶⣒⡶⠂⠀⠀⠀⡄⠀⠀⠀⢨⣯
⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠐⡚⠋⠙⡇⠀⠀⠀⠸⣽⣿⡟⠛⠁⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣷⠀⠀⠀⠛⠀⠀⠀⠘⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠤⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⢀⣠⣄⣠⣀⡀⠀⠀⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢘⢿⢻⠿⡟⡃⠀⠀⣿⣿⣟⠙⡇⠃⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠠⠿⠿⠀⠀⢐⠚⠒⠒⠃⡇⠀⠀⣿⣿⣿⣿⠦⠇⠀⠀⠀⠀⠹⣿⣽⠟⠀⠀⠀⠻⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠲⡄⠀⠀⣴⠒⣒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠀⠀⠀⢰⡟⠛⠛⢳⠀⠀⠀⠠⠄⠀⢀
⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠁⠻⢿⡇⡇⠀⠀⠿⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠱⢻⡀⠀⠀⢸⡗⠛⠉⠀⠀⠀⠀⠀⠀⢀⣻
⠀⠀⢸⡗⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠠⡆⢺
⠀⠀⠀⠙⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠈⠉⠉⠉
⠀⠀⡴⠖⢦⣄⣠⣀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣤⡄⣀⠀⠀⠀⠠⠤⠤⠤⠤⡀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⢰⣷⣿⣿⣿⣠⡀⠀⠄⠀⠀⠀⣀⡇⠀⠠⠐⢂⡐⢁⠀⠀⠀⣠⢴⠏⠉⠀⠀⠀⣾⣿⣛⣿⡇
⠀⠀⠿⠟⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠀⠚⠛⠛⠛⠛⠛⠓⠀⠀⢠⣤⣤⠠⠃⠀⠀⠀⣨⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠴⣤
⠀⠀⡜⣷⣶⠂⠀⠀⠀⢀⢀⣀⡈⠀⠀⠀⢠⣏⠂⠦⣳⠀⠀⠰⢒⠛⠀⢈⡆⠀⠀⣿⣿⣿⠀⠷⠀⠀⠀⢾⣶⣾⡄⠀⠀⠀⢸⣷⢸⡇
⠀⠈⠙⠬⣁⠰⠀⠀⠀⠀⠰⣧⣀⠀⠀⠀⠘⢏⠓⠃⠜⠀⠀⠰⠚⠃⠀⠘⠇⠀⠀⣿⣿⣿⡆⠃⠀⠀⠀⠺⠥⠿⠃⠀⠀⠀⠈⠻⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣉⣖⠒⠂⡶⡞⢛⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠸⠦⢸⠃⠋⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀⠀⠈⢀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡬⠉⠉⠭⠥⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣅⡿⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠉⠉⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢶⣁⡀⠀⠉⠀⠀⢀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⢹⣆⠀⠀⠻⡟⣷⠀⠀⢼⢏⡵⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⣴⣷⢿⣶⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⠶⠛⠂⠀⢿⠉⢦⠀⠀⠹⣾⠀⢀⡴⠋⠂⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⢸⣷⣼⡸⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠆⠳⡀⠀⠀⢀⡈⠳⠮⢷⡀⠀⢘⣶⠫⢐⣠⢗⣪⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⠃⠀⠀⠀⠉⢻⡿⣷⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⡄⠑⡄⠔⠎⢉⣠⡤⣺⡗⠈⢀⣿⣺⡽⠚⠉⣀⣬⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠏⠀⠀⠀⢀⡀⢸⡃⡟⣿⡆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠘⠌⢦⠈⣆⣠⡤⢶⣻⣽⣧⠤⡞⠁⠀⠹⣶⠎⣫⣵⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠸⣿⣾⣶⣿⡿⠁⠀⠀⢰⠀⢹⡀⠀⠀⠀⠀⠀⠈⢦⠱⠿⡖⠛⠉⢁⣠⠤⠖⢻⡎⠀⠀⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⢀⠀⠀⠀⠀⠀⠟⠹⠃⠀⠀⠀⠀⡼⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⣦⢉⣠⡤⢖⣩⠼⠷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⢀⠈⠈⣆⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⡽⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣤⡤⠶⠲⠤⠴⠶⠶⣤⣤⣤⣤⡴⠶⠛⠒⠋⠉⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣤⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡷⢚⡶⢻⡗⢻⡧⠽⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠆⠸⢣⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⢁⡞⢠⡟⠀⢀⣤⣄⠀⢹⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⢠⠂⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣯⣾⣥⡏⠀⠀⠂⢈⠋⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣾⣽⣷⣯⣴⣋⢉⡑⣌⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠖⠰⢈⠲⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣿⣇⠛⢙⢿⡟⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠘⠚⠉⠀⢀⠀⠀⠀⠀⠤⣿⣿⣿⣿⠋⠀⠘⠻⣓⠒⠉⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⢴⠀⠀⠙⠁⠀⠈⠢⠆⠉⠀⣤⠉⣥⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠊⠀⠀⢀⠀⡀⠀⠐⡓⡘⠃⡀⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠨⠀⠀⠈⠄⠁⠁⠀⠁⠁⠄⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠀⣂⠀⠀⠀⠄⠀⠁⠰⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠁⠀⢀⠀⠀⠀⡁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⢐⠀⠐⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠛⠋⠁⠀⠀⠀⠀⢠⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⢰⠀⠀⠀⣰⠋⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣟⣭⠿⠷⠤⣾⣿⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣠⣤⣴⣶⣶⣤⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢁⠼⠁⠀⠘⢧⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢀⣸⣷⣼⣷⣄⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢠⣿⢿⣿⠹⣿⠛⠃⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⡀⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⢀⠞⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠛⠛⠻⠶⠶⠶⠶⠶⠿⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠶⠦⠇⡑⠆⢠⡄⠘⢔⠀⠀⣡⢂⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣴⣀⣤⣀⣷⣋⣚⣂⠾⠟⢤⣯⣭⣶⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠒⠉⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣶⣶⣶⣶⣶⡶⠶⢶⣶⠶⠶⠒⠋⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠁⢿⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⢦⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣾⣶⣄⠀⠀⢠⣿⣿⡰⠇⣷⣾⣿⣧⠀⠀⢀⣴⣾⣶⣄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⡿⠀⠀⢸⣿⣿⢿⡆⣦⢹⣿⣿⠀⠀⠸⣿⣿⣿⡿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠈⠙⠉⠀⠀⠀⠈⠻⣿⣤⡁⣩⣼⡿⠃⠀⠀⠀⠈⠙⠉⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣿⣿⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣛⣛⣛⣛⣛⡛⣿⣿⣷⠀⢰⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⡾⠁⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⣣⣿⣿⣿⣿⣿⣧⡻⢿⣿⠀⠀⠹⣆⠀⠀⠀⣿⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢀⣀⣀⣉⠀⠀⠀⣿⣿⠀⠀⠀⣉⣀⣀⣀⣀⣀⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⢻⣿⣿⣿⣿⣿⣿⣿⡟⣡⣿⢸⣿⡿⠋⠀⠀⠀⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠈⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠊⢉⣛⠛⣛⣋⠁⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡎⡛⢿⣿⣿⢟⡉⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⣿⣷⣶⣶⣿⡇⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⣠⣿⣿⡿⢋⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⢸⣿⣿⢸⡇⣿⣿⣿⣿⣿⢠⣴⣶⣶⣶⣶⣶⡄⣿⣿⣿⡇⠿⠷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⢸⣿⣿⢸⡇⢸⣿⣿⡿⢛⣈⣛⣛⣛⣛⣛⣛⡃⢿⣿⣿⡟⠿⠇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⣧⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣦⠸⠿⠿⢰⣶⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣭⣍⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠤⠶⠖⢲⡄⠀⠀⠀⣠⡞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠒⠒⠀⠐⣆⠀⠛⡀⠀⠀⠀⠀⠀⡀⡇⠀⣠⠞⠉⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡈⢧⠰⣆⠀⠀⠠⠘⢆⠀⡇⠀⠀⢀⠈⣐⠌⠑⠾⣍⡀⢀⠀⠀⠀⡠⠊⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⢧⠀⢀⡴⠖⠒⡈⢧⣳⢤⡴⠀⠘⠉⠀⠀⡀⢤⢝⣦⠑⣤⠞⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⢀⠷⠚⠁⠉⠀⣀⣀⡿⠛⢶⣖⠤⣀⠀⠀⠍⢂⠎⡘⠁⢸⣤⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⣧⠅⠀⡰⠶⠾⠿⢛⠯⣄⡀⠀⠈⠑⠪⣆⢀⢎⢎⡼⣧⣤⠾⢿⡅⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠿⣦⡔⠁⢬⣆⡴⠉⠀⠳⢬⣒⣄⡀⠀⠈⢳⣧⠾⠛⢋⣤⠾⠋⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠢⣌⡙⠲⢿⣫⣤⣤⣀⣀⢀⣀⣀⣼⣧⣀⠤⠿⠶⠟⠋⠁⣠⡴⠋⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠁⠀⠠⣉⣉⡉⢉⣉⡁⠀⠀⢀⠤⠤⠤⠶⠖⠚⠋⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⠁⠀⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣀⣤⡤⠶⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣤⡤⠶⠶⠛⠁⠀⠀⠀⠀⡄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠹⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠀⢀⡠⠖⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠞⠋⠉⠉⠛⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠛⠒⠚⠓⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⣠⠒⠉⢁⣦⣀⠀⠀⠀⢠⣶⣿⣿⣷⣶⠄⠀⠀⠀⠀⣰⠖⡶⠒⢶⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠈⣾⡿⣿⣿⣻
⠀⢸⣏⡗⠀⢿⣧⣽⠂⠀⠀⠀⣿⠀⣿⠀⡇⠀⠀⠀⠀⣿⣿⣦⣷⣥⡾⠀⠀⠀⢀⣰⠿⣦⡿⣇⡀⠀⠀⠀⠀⣿⣼⣟⣿⢿
⠀⠀⠈⠂⠤⠄⠋⠁⠀⠀⠀⢠⣿⣤⣿⣤⣿⡀⠀⠀⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠘⠛⠚⠛⠃⠛⠛⠀⠀⠀⠐⢭⡭⠭⣭⠟

⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⣤⢼⡈⣧⣰⠋⢳⡀⠀⠀⠀⢏⠤⣻⡈⠶⠀⠀⠀⢠⠒⣒⣒⡒⣒⠒⡄⠀⠀⢀⡄⠮⣰⡩⠉⡶⠀⠀⠀⢀⣶⣞⣻⣦⡄
⠘⢷⣼⠇⣼⢿⠀⢘⠗⠀⠀⠀⣾⣿⣷⣷⣷⠀⠀⠀⠀⢱⣿⣿⡇⢻⡎⠀⠀⠀⢿⠀⠀⡘⠑⡚⠁⠀⠀⠐⢿⣿⣿⣿⣿⡿⠂
⠀⠀⠘⢾⣭⣯⡷⠋⠀⠀⠀⠀⢿⣿⣿⣷⣿⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠉⠉⠙⢦⠁⠆⠀⠀⠀⠀⠻⠛⠛⠿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⡤⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⣾⢿⣿⢿⠿⡿⡷⡀⠀⠀⠀⠠⣿⡿⢤⣀⡀⠀⠀⠀⠀⣿⠁⠉⣿⠀⠀⠀⠀⣜⣈⡄⣾⠀⡜⢇⠀⠀⠀⠸⣿⣿⣿⣿⡟
⠀⢿⣿⣿⣽⣭⣿⡯⠁⠀⠀⢀⣀⡀⢀⠀⠈⠉⠀⠀⠀⣠⣮⣀⣀⣵⣄⠀⠀⠀⠀⠁⠀⣿⠐⠳⠞⠀⠀⠀⠀⠘⢻⡿⠋
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠶⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⣾⢶⡄⠀⠀⠀⠀⡆⣩⡉⢸⣿⢿⣦⠀⠀⠀⣰⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤
⠀⠀⠀⠰⣄⡰⠀⠀⠀⠀⠀⠇⠙⠁⠸⠿⠿⠿⠀⠀⢰⠉⠪⣛⣹⣾⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⣶⢸⡇⣿
⠀⠀⣴⣶⣰⣰⣶⡄⠀⠀⠀⣿⠛⣿⡇⢠⡆⢸⠀⠀⠈⢆⡀⠀⣀⣼⣷⡄⠀⠀⠀⣿⣿⣭⣿⣿⡄⠀⠀⠀⠸⠃⠟⢸⡏⣿
⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠛⠛⠛⠃⠀⠀⠊⠀⠀⠀⠀⠀⠁⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢻⣿⣿⣿⣿⣿⣿⣿⢏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣤⣄⢨⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣾⣿⣿⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠇⠸⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏⠁⢀⡀⢀⡀⠈⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⡇⢸⣿⣄⣠⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠁⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢠⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⡇⢸⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠁⠈⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⢒⠋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠒⠉⣁⣠⠤⣤⠀⢿⣧⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠒⠉⣉⣀⡠⠤⠒⠒⠉⠉⠀⠀⠀⠹⣄⠘⠛⣁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠛⠉⣉⡠⠤⠶⠶⠞⠯⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠒⠈⣉⣀⡤⠤⠖⢒⡽⠋⠁⠀⣠⣄⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣷
⠀⠀⠀⠀⠀⢠⠔⠒⠈⠉⢁⡠⠤⠔⠒⠉⠉⠁⠀⠀⠀⡰⠋⠀⠀⢀⣴⣿⣿⡿⣷⡦⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡀
⠀⠀⠀⠀⠀⠈⡄⠀⠻⢄⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣿⡟⠀⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡇
⠀⠀⠀⠀⠀⠀⢱⠀⠀⣃⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠻⣿⣦⣼⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⠿⣿⣶⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⣷⢲
⠀⠀⠀⠀⠀⠀⠀⢻⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢻⣿⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⡄⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢠⣤⣀⣀⣻⣷⣴⣿⠟⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢩⠆⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠛⠿⠿⠿⣿⡟⠁⠀⠀⣠⠎⠀⠀⢀⣀⣠⠤⠔⠒⠉⢉⣁⡠⠤⢴⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠉⠀⣀⣤⠾⠵⠒⠚⠉⣉⡠⠤⠴⠒⠚⠉⠉⠀⢀⣀⢼⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣧⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡭⠷⠞⠛⠋⢉⣀⣤⡤⠖⠒⠉⡹⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⢠⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡆⠀⢱⠀⢀⣀⣀⠤⠔⠒⠊⠉⣉⣠⠤⠴⠶⣾⣿⣿⠟⠋⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄⠀⣹⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠽⠀⠈⠋⣉⣀⠤⠴⠒⠚⠉⠙⠦⣀⠀⠀⠀⠀⠈⠋⠀⢀⣠⣔⣋⣀⠤⠤⠴⠒⠒⠚⠋⢉⣉⣀⠤⠤⠴⡶⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢧⠤⡔⠒⢯⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣩⡵⠶⠶⠒⠒⠊⢉⣉⣁⣠⡤⢤⡤⠖⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⡄⠸⡇⠤⠤⠔⠒⠒⠉⡉⣉⣁⡠⠤⠤⠔⠒⢲⣿⠛⠋⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⡉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢀⣉⣀⣤⠤⠔⠖⠒⠚⠋⠉⠉⠀⠈⠑⠢⣄⣀⡀⠀⠁⢀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣉⣉⣁⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣈⣉⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡆⠀⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⢀⡀
⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡾⡿⠀⠀⠀⠀⠀⣿⣧⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧⢴⣶
⢠⣶⡆⢸⠀⣷⣦⠀⠀⠀⠀⠀⠛⠘⣿⡿⠃⠃⠀⠀⠀⠀⠀⣿⣏⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿
⣿⣿⣷⢿⢼⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿
⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀
⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠈⠀⢰⡆
⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠁⠀⠀⢀⠀⠀⠀⠠⠭⠤⠤⠤⠿⣴⣿⣿
⠈⢹⣿⡁⣩⣷⣶⡀⠀⠀⠀⠀⣻⣿⡏⣙⣷⣶⡀⠀⠀⠀⠀⣿⣿⣻⡷⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢠⡟⠈⣿⠘⠛⠉⠀⠀⠀⠀⢀⡿⠉⣿⠘⠛⠉⠁⠀⠀⠀⠀⢻⠛⣹⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⣀⡀
⢠⢾⣿⣉⣹⣷⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤
⣯⢼⡧⠤⠤⣷⢼⡆⠀⠀⠀⢠⣤⣴⢺⡛⣿⣷⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣤⣶⣶⣶⣦⣤
⠳⣼⣧⠴⢤⣧⡼⠁⠀⠀⠀⠸⣿⣿⣦⢵⣛⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠈⠛⠒⠛⠋⠀⠀⠀⠀⠀⠀⠓⠖⠚⠋⠁⠀⠀⠀⠀⠀⠘⠟⠟⠛⠛⠻⠻⠃⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠆⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠠⠤⣤⣄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⠻⣦⠀⣸⠃⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠘⣷⡟⠀⠀⠀⠀⣠⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⢀⣠⣼⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢀⣾⣿⠟⠉⠉⠻⣿⠗⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⣀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⢶⣾⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣉⠉⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⢛⣻⣭⣉⠀⠀⠀⠙⠻⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠛⢛⣉⣡⠤⠒⠲⢿⣿⣿⣷⣦⡀⢿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⡁⠶⢿⣧⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⢀⣾⣿⣿⡇⢰⣯⣃⠈⢿⣿⣿⣿⠇⠸⣿⣿⣿
⠀⠀⠀⠀⠈⣭⣤⣤⣤⣤⣭⣭⣥⣬⣭⣤⣤⣤⣬⣭⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⡖⠛⠛⠛⠛⠓⠒⠒⠛⠓⠛⠛⠛⠛⠒⠒⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⢀⣴⠖⢶⣄⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⣠⣿⣿⣿⠟⣉⣍⡛⣿⣿⣿⣧⣀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣧⣌⠻⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢛⣭⣛⣿⣟⠀⠛⢮⡁⢸⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣶⡄⠀⠀⠘⠷⠦⠾⠋⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡁⠈⢙⣿⣛⣛⣂⣙⣋⣥⣿⣿⣿⡟⠉⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿