Border Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣞⠓⠢⢀⣤⣄⣐⣒⣒⣂⣠⣄⠀⠚⢛⡆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣹⡿⠒⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠑⠚⣭⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡖⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⣾⣄
⠀⠀⠀⠀⠀⠚⠟⢶⣴⠏⠀⠅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠅⠈⢷⣴⠶⠛⠃
⠀⠀⠀⠠⡾⠟⢡⢾⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⢦⠙⠻⠦
⠀⠀⠀⠀⠀⠠⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡣⠀⠀⣀⡀
⠀⢀⢙⡛⣲⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⠏⣉⣁⡀
⠶⠟⠋⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⠙⠓
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⠎⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢆
⠀⠈⢆⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠜
⠀⠀⠈⢾⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⢸⠎
⠀⠀⠀⠈⣧⠀⠀⢀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⡀⠀⠀⢠⡏
⠀⠀⠀⠀⠸⡣⡀⠈⢳⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠶⠁⠀⡠⡻
⠀⠀⠀⠀⠀⠱⡱⡼⠇⢼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠱⠇⡰⡱⠁
⠀⠀⠀⠀⠀⠀⠑⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢶⣿⢲⠂⠀⠀⠀⣠⠀⠂⡀⠀⠔⠋⠉⢉⢢⡀⢀⠀⠀⠠⡦⣶⣴⠧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢺⠟⢶⣇⠔⠁⡮⠝⢢⠃⡶⣦⡀⢰⠩⠟⢠⠀⠡⣰⡶⠶⣗⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠃⠓⠀⣥⠓⠉⣮⠤⠌⣉⠉⠑⢢⣁⠠⠚⠙⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣊⠐⠺⠖⠀⠑⠆⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢠⢄⣀⠀⢆⡤⡄⢀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⣩⣶⣦⣏⠈⡘⣷⣿⣷⣧⠀⣁⠋⠐⠀⠉⠀⠀⠐⢚⠋
⠀⠀⠀⠀⠀⠀⠻⣿⣻⣿⡆⠈⣽⣟⣿⣿⡦⠐⢃⠀⠀⣄⡐⠀⠳⣄⠲⠦⠄
⠀⠀⠀⠀⠀⠸⣄⣀⣧⣦⣀⠀⠑⢞⠉⠉⠀⠀⠀⠀⡗⠈⠛⠂⠀⠈
⠀⠀⠀⠀⠀⠉⣬⣿⣿⡿⡟⡀⠄
⠀⠀⠀⠀⠀⣰⠽⢿⣿⣿⠃⠁
⠀⠀⠀⠀⠰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⡶⢐⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠈⠁⠀⠠⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠐⡼
⠀⠀⠀⠀⠀⣠⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⢠⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠙⠠⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠘⠻⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⠛⠦⠁⠀⢀⣴⣖⣿⣯⡦⣠⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠈⠛⠀⠈⠀⠉⢀⠘⠻⢿⣿⣿⠁⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠐⠠⠂⠀⠉⠰⡠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⢛⠿⢛⡛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠒⠛⣋⣉⣉⣉⣙⣛⡓⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣉⣠⠴⠖⠚⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠓⠲⠦⣭⣙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢍⡲⢄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⢦⡤⢀⡀⠀⡔⠈⢹⠃
⠀⠀⠀⠀⠀⡴⠋⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣦⣹⠘⣇⡎⡸⠀⣀
⠀⠀⠀⢀⡞⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⡢⣸⠁⡔⠁⣯
⠀⠀⢠⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢅⡀⠀⢻⣷⣜⡌⣧⡣⠏⢀⡀
⠀⢠⠏⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠉⠑⠺⣿⣹⡇⡴⠋⠙⡇
⠀⡾⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠬⣿⣷⡧⠧⣏⣴⡁
⢸⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⢻⣧⡖⠁⠀⢳
⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠺⣿⣃⠤⠂⣀
⡏⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠛⠘⣿⣼⢎⠉⠉
⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⣆⠈⣿⠘⣄⠀⣠
⣷⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠟⠀⠀⠉
⢹⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣿⣆⣶⣆⣀⡁⢠⠀⡾⠚⠓⠄
⠈⣇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣩⣙⣇⢿⠿⠀⠈⢴⣻⡇⠂⢀⡸
⠀⠹⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡤⢷⡜⣦⣴⠉⠉⠀⡹⢣⣦⣄
⠀⠀⢹⡜⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣊⠍⣤⡹⠟⢲⣴⣾⣶⠛⣛⡿
⠀⠀⠀⠹⣌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠿⡇⢟⣺⠋⣡⢺⡲⢬⢄⡄⢩⣼⢹⣋⠕⣲
⠀⠀⠀⠀⠘⢦⡳⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡿⢰⣆⣠⡀⣾⣽⣿⡄⢀⡂⣠⡐⣿⠥⣋⠜⢋⣸⡿⣷⡾⠥
⠀⠀⠀⠀⠀⠀⠑⣬⣿⡒⢤⡀⢀⠞⢦⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠺⡋⡿⡡⢳⠏⢠⡀⢰⣁⡴⡧⠭⠭⡼⢤⣾⠿⢿⣟⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣷⣧⣸⢀⠀⣃⠊⠳⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢿⣿⠏⢉⠱⡇⣥⠚⡳⢾⢦⡍⠇⠀⣤⡎⠄⠀⢠⣴⣼⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠻⢿⣿⣶⣙⡄⡄⡐⡠⠒⠉⠳⣡⡭⣉⣳⣀⠔⠸⡀⠀⢀⠿⣿⠇⠑⢃⡵⢣⣊⡦⠊⠉⢡⠒⢲⣿⣾⣧⡯
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⢽⠒⢚⣛⠻⣿⣿⣿⣷⣧⣄⣐⣄⣹⣀⣀⣙⡁⠀⠐⣸⣳⡧⠀⢘⣷⡆⣭⢼⢁⣠⣶⠠⢤⣼⣷⣡⣺⡿⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠊⠔⠁⠔⣻⢃⡤⠤⡟⢨⠿⠛⢻⣯⡿⣟⣉⡡⣹⠋⠠⠉⣤⡤⢚⢿⣞⣛⣷⣾⣿⣧⣒⣿⠾⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣍⣀⣉⣽⡁⠀⠠⠃⡌⠙⠀⠈⡇⠘⠄⠀⡰⠂⢶⣿⢢⢏⠔⣹⡿⢻⡉⢄⠉⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣢⣚⣣⣤⣤⣊⣁⣀⣀⣀⣀⣀⣸⣗⣁⣘⢚⣁⣂⣯⣁⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⣠⣆⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⣠⣄⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣿⣿⢰⣄⠻⠃⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⡿⢀⣦⢿⣿⣾⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣽⣿⠝⣽⠇⠈⠛⠲⡟⣣⣿⠀⠀⠀⣀⣀⠀⠀⠀⣟⣦⡹⠶⠚⠁⠈⣻⣩⣽⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠘⢇⠀⡀⢀⡿⢧⣦⣤⣶⣿⡍⠉⣿⣶⣤⣴⡾⢿⣀⠠⡀⣰⠏⠐⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡍⠄⠀⣒⣾⠛⣿⠁⠀⠀⢸⡤⠤⠶⠶⠶⠦⠤⢤⡌⠀⠀⠈⢾⠛⣷⡒⠀⠠⢫⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣶⠊⠉⢹⠙⠝⠳⠤⢠⣀⠀⡶⡈⠆⠀⠀⢲⡀⣀⣄⠤⠜⢫⠟⡏⠋⠑⢶⣢⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⢻⢟⡶⡄⢈⡀⠀⠀⣖⣀⠃⠘⡴⢠⠘⠃⡄⢦⡅⠘⠀⣰⠀⠀⠀⡋⠀⣶⠛⡟⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠋⠁⠀⠀⢀⣯⣾⠘⣡⡎⡍⠀⣰⢫⣍⠹⠆⠀⠀⠀⠀⠀⠀⠰⠏⢹⡟⣆⠀⢈⠱⣄⠣⣹⣬⡀⠀⠀⠈⠙⠳⠦⣄⣀
⠀⠀⢀⣴⣶⠫⠝⠉⠀⠀⢀⣠⢃⣴⠟⠋⠁⠀⠁⠀⠆⠃⠈⠘⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠈⠐⠉⠀⠀⠀⠀⠉⠻⣆⡘⣆⠀⠀⠀⠘⠯⣻⣶⣤⡀
⠀⠀⢸⡏⢿⣧⠐⠷⢂⣽⣏⢁⡾⠃⠀⠀⠀⠀⡰⢆⠤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⡠⣖⠀⠀⠀⠀⠸⢧⠘⢛⣿⠥⣰⠦⢰⣿⢻⡇
⠀⠀⢸⡇⠀⠛⢦⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣧⠉⠁⠀⠀⢰⡿⠈⢸⡇
⠀⠀⢸⡇⣀⡄⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢠⡀⢸⡇
⠀⢀⣼⡵⠻⢙⠂⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠾⢿⣟⢃
⠀⠈⢹⡇⡷⠀⠱⠆⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡴⠃⡸⢼⡏⠛
⠀⠀⢸⣷⣰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣇⣼⡇
⠀⠀⢸⡏⡘⠧⣀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⢏⢹⡇
⠀⠀⢸⡇⠷⢠⠈⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠋⣙⢼⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠉⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⢧⣄⡀⠀⠀⠀⠀⠀⠀⣸⠿⣦⡀⠀⠀⠀⠀⠀⣠⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣄⠀⠀⠀⠀⠀⠀⣴⠿⣇⠀⠀⠀⠀⠀⠀⢀⣠⡼⠇
⠀⠀⠀⠀⠈⠉⠓⠶⣤⣀⠐⠂⢻⣴⣿⣋⡗⠀⠀⡀⣀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⢀⢀⠀⠀⢺⣝⣿⣦⡟⠐⠂⣀⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⣌⣙⠹⠙⢶⣅⡀⠀⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠀⢀⣨⡶⠋⠎⣍⣡⡴⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠰⠂⠉⠛⠶⢦⣈⡛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠶⢛⣁⣴⠶⠛⠋⠱⠆⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⢘⣭⠙⢷⣦⣍⣙⠓⢶⣦⡤⣤⣤⣤⣤⢤⡴⠶⠚⣋⣭⣴⡾⠋⣩⡃⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣿⢍⢁⡼⠉⠈⠢⢀⠀⠙⠋⡛⠲⢤⣄⡀⠀⠀⢀⣠⡴⠖⢛⠉⠋⠁⡀⠔⠁⠈⢳⡀⣩⣿⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠉⠛⢹⠀⠀⠀⠠⢄⡀⠐⠠⠄⠀⢠⡬⠽⠓⠚⠯⢥⡄⠀⠡⠀⠂⢀⡀⠄⠀⠀⠀⡏⠛⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢤⡀⠈⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠁⢀⣤⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⠀⠂⠐⠀⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠈
⣶⣶⣶⣶⣶⡾⢶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣷⣾⣿⣿⣶⣿⣷⣷⣾⣷⣶⣶⣷⣿⣿⣾⣶⣶⣿⣶⣿⣷⣾⣷⣾⣷⣾⡶⣶⠶⡶⠶⠶⣶⡶⢶⡿⠷⡶⡾⠷⠶⢿

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⡀⠀⠀⢈⠄⠀⠂⢀⡹⠿⠧⠂⠉⠘⢁⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠰⠏⠀⢰⠃⠊⠀⠠⠋⠀⠀⡀⢀⠢⡉⠌⣡⠠⠽⡄⠀⠀⠀⠀⠀⠀⠉⠀⢂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡆⠈⢠⠀⠀⠀⠀⠀⠈⠂⠉⢞⣽⣥⠐⠂⣵⠀⠀⠀⠘⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⡇⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡉⠀⠀⠀⢠⣤⠀⠀⠣⣀⡠⢂
⠀⠀⠀⠀⠀⢺⡂⠀⠀⡀⡀⢀⠀⠀⠀⣁⠗⣀⠢⣄⠉⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠠⡖⠀⠀⠀⢴⠇⢹⣦⠀⠀⠀⡀⡁
⠀⠀⠀⠀⠀⠘⠃⠀⠈⠲⡂⣀⠅⠀⠀⢸⠑⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⡇⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠈⠀⠐⠚⠒⠠⠼⠶⠤⠤⠄⢀⣀⣀⣤⣤⣒⣉⣸⣠⡠⣽⣦⣔⠀⠀⠀⢁⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⢠⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠄⠀⠀⠀⠀⠑⡆⠁⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢺⡈⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠉⠆⠐
⠀⠀⠀⠀⠀⠀⢠⡈⠀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠲⣤⡠⠊
⠀⠀⠀⠀⠀⠐⢮⣧⠂⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣠⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢦⣇⣼⡵
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⡈⠃⠀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠁⠠⠐⠾⠐⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠴⠂⠐⠠
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠪⢷⣸⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡤⢀⡄
⠀⠀⠀⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠙⠼⠧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣰⠤⠤
⠀⠀⠀⠀⠀⠀⡀⠀⢂⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⢠⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⣰⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡄⠑⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡀⠀⠀⣤⡘⠏⢠⣿⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣧⣴⡆⣿⣆⠀⣿⠇⣀⠻⠑⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠻⠋⣴⡎⢿⠀⠛⠛⠁⠠⠚⠛⠋⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⠛⠃⠀⢀⠀⠀⠀⠄⠀⠀⢄⠘⡀⢹⡀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠕⠀⠀⠀⡀⠚⠀⣀⡀⠀⠀⢃⠀⠀⡀⣀⠘⠮⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠐⡀⠀⣀⡀⠀⠀⠛⢫⡆⠀⠀⠐⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠁⠈⠁⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣤⠀⠀⠀⠉⣶⢤⡴⠀⠘⢻⠂⢀⡀⢀⡄⠠⢴⠂⠐⠠⡂⠴⠇⡒⢦⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠖⠀⡙⠓⠶⠿⠓⣷⠌⣈⢃⠀⣀⡄⢀⠐⠀⠀⠐⠂⠈⠱⠘⠩⠖⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⣠⣴⠆⢀⡁⠄⠉⠀⢣⠉⠨⣁⠌⡋⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠀⠨⠦⢀⠐⠀⠘⢣⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠊⠀⡔⠄⠀⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣛⣩⣭⣴⣶⣶⣶⣶⣦⣭⣍⡙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣥⣶⣿⣿⣿⡿⢿⣿⡿⠛⢿⣿⣿⣿⣿⣷⣄⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⣡⣴⣿⣿⣿⣿⡇⢹⠁⠀⠉⠀⠀⠈⠉⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣼⣿⣿⣿⣿⣿⣿⣿⡘⣤⣄⢈⣟⡩⢶⡄⠈⢹⣿⣿⣿⣿⣿⡄⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⣿⣿⣿⣿⣟⠉⠉⠁⠙⠈⠙⢲⣳⣋⡄⠀⠀⢉⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠠⢤⠞⠀⠈⢇⠀⠀⠐⣾⣿⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⣬⠀⠀⢨⡛⠤⠤⣤⣼⣿⣿⣿⣿⡟⢨⡇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣆⢠⣾⣿⣷⣦⣾⣿⣿⣿⡿⠋⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣿⣿⣿⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⣿⣿⣿⣿⡇⣿⠁⠀⠀⠀⠀⣀⣘⣛⣷⣦⣸⣿⣷⣀⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣵⣾⣿⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⢰⠀⠀⠀⠀⣶⣦⣆⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣏⣭⣥⠻⣿⣾⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⢀⡾⠁
⠀⢸⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⣿⣿⣇⠀⠀⠀⠀⠈⣽⣿⡏⢴⣦⡟⣶⣝⣈⣏⠉⠁⠀⠀⠀⠀⠀⣰⠟⠁
⢀⡇⠀⠀⠀⠀⡿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢿⣆⠀⠀⠀⠀⠈⢹⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⢀⣠⠞⠁
⣾⣶⡄⠠⡄⠀⣷⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣀⠀⠀⠀⠀⠀⠉⠹⡿⠋⠈⠻⠇⠉⠁⣀⣤⠶⠛⠁
⣿⣿⡂⠀⣧⢠⣿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠛⠉⠁
⣿⣿⡇⠀⡿⢸⣧⡄⢠
⣿⣿⣷⣾⡇⢸⣿⣯⢠⡇
⣻⣿⣿⣿⡁⣸⣿⣿⣸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡅⠀⠿⠿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⣸⡇⠀⠀⠀⠀⢨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡞⡷⣤⣀⣀⣀⡴⠒⠒⠒⠲⠦⠤⠤⠤⢤⣤⣾⢳⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢠⢏⡞⠀⠀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡳⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⢫⠎⠀⠀⠀⡴⠃⠀⠀⡰⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠿⣄⡀⠀⡰⣣⠏⠀⠀⠀⠘⠦⠤⠖⠋⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠳⡝⣄⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⢀⡴⠙⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⠀⣠⠖⠲⣄⡤⢤⡀⠀⠀⠀⠀⠀⣄⡀⠀⠙⠲⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠁⠀⣠⠏⠀⢀⣽⣄⡀⠀⢀⡀⠀⠙⠢⣄⣀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣶⠁⠀⣠⠞⠀⠀⣷⣀⠀⠙⠢⣄⣀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢺⡇⠀⢠⠞⠁⠈⡧⣄⠀⣸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢯⡀⣠⣞⣁⡸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢰⡿⠛⠻⣿⣿⡛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⡛⢛⣿⣿⠟⠛⢷⡆
⠀⠀⠘⠷⠿⠀⢸⣿⣷⣵⣄⢀⣈⣝⠷⣤⡀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⢀⣤⠞⣫⣀⡀⣠⣯⣾⣿⡇⠀⠿⠾⠃
⠀⠀⠀⠀⠀⣤⣾⣿⣧⣘⠙⡷⡦⠬⢵⡝⣝⢷⣄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣾⡻⢣⡮⠥⣴⢾⢻⣁⣼⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠙⢿⣿⣿⡈⠑⣧⠯⣦⡀⢡⠘⡇⢛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡛⢸⠁⡎⢀⣼⠽⣼⠋⢁⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣀⣿⣿⡟⢲⡁⡴⠶⠽⣜⠦⣸⡈⣸⠙⣧⡀⠀⣴⣆⠀⢀⣼⠋⢣⢀⣇⠴⣡⠯⠖⢦⢈⡖⣻⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⠷⣷⠄⣀⡈⢷⣄⠑⢾⡀⠘⣿⣔⣿⣿⣢⣿⠁⢠⡷⠊⣠⡾⢁⣀⢀⣿⠾⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣦⣤⣽⡶⣦⣀⣌⣑⡢⣝⣲⣾⣿⣿⣿⣿⣷⣖⣫⣔⣋⣥⣀⡴⢶⣯⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⣶⣶⡶⠾⣿⠟⠛⠟⠋⣼⣿⣿⣧⠙⠻⣟⡿⡿⠷⢶⣶⣶⣾⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⡫⠁⡠⠞⠡⢠⠀⢀⣼⣿⡻⢿⣿⣧⡀⠀⡝⡌⠳⠄⠈⢝⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠋⡰⣋⣠⠤⣧⣾⠶⠋⣸⢿⣿⣿⡿⣇⠛⢶⣷⡜⢤⣄⡙⢆⠙⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡾⢋⠎⠀⡰⢁⠃⣀⡴⢻⠟⣿⣿⠛⡟⢦⡀⠙⡘⢆⠀⠱⡙⢷⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣞⠀⡰⠀⣸⠔⢁⠁⣸⠀⠻⠟⠀⣇⠈⡌⢢⣇⠈⣆⠀⣷⣾⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣴⡇⢠⡟⠠⢹⢀⡟⠀⠀⠀⠀⢻⡀⡇⠄⢻⡄⢸⣦⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣶⣿⠞⠀⠀⠀⠀⠀⠈⢳⣿⣶⣼⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡆⠀⢸⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡇⠀⢰⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⡶⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢶⡦⠶⠋

⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠶⠶⠶⢶⠾⣿⣿⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣷⣤⣤⣤⣤⣼⣿⠀⠀⠀⣠⣦⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡏⠉⠉⠉⠉⢹⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣧⣤⣤⣤⣤⣼⣿⠀⠀⠀⣠⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡟⠉⠉⠉⠉⢹⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣧⣀⣀⣀⣀⣸⣿⠀⠀⠀⣠⣴⣶⣤⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣦⣴⣦⡄⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⡏⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣠⣿⣿⣟⠀⣰⣿⣿⣧⠀⣰⣿⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠙⠿⠿⠿⠃⠘⠻⠿⠟⠛⢿⣷⣤⡄⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⡻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⠀⠀⠲⣶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⣁⢀⠈⠀⣀⣤⣼⣿⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⣿⣴⣀⢀⣇⣈⣿⣻⣿⣿⣿⣷⣶⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⠿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣝⣿⣿⣿⣿⡉⠻⢻⠟⠻⡀⠌⠉⠹⠄⢹⣦⡀⣽⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣽⣿⣿⠏⢑⣦⣾⣷⣄⠄⠀⠀⠀⠀⠦⣨⣿⣷⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⠣⣿⣧⣀⣈⡀⢀⠀⠀⠀⠀⢸⡟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⠋⠙⣿⣋⣀⣀⣴⣶⣄⢸⣷⣬⠿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣾⣿⣿⣿⣟⣉⣿⣿⢿⣿⣼⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⡏⢹⡿⠏⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡛⡈⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠅⢈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣟⠃⠀⡼⠷⡄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⣀⡀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⣀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡫⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠲⣤⠤⠤⠤⠤⠐⠒⠚⠉
⠀⠀⠈⠑⠶⠶⠤⠤⠶⠶⠤⣤⡎⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡳⠦⠤⠰⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠤⠴⠀⠄⠈⠆⢀⠀⢄⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⡀⠐⠁⡀⠀⠀⢀⢀⠌⢀⣤⡤⣤⠀⠀⠀⠐⠀⠀⠀⠀⢀⢄⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⡠⠞⠴⠚⠓⠈⠁⠀⠙⠥⠤⠤⠤⠤⠒⠓⠚⠉⠉⠉

⣶⡶⢶⡶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠘⢩⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⡐⠀⠣⠀⠀⠀⠰⠘⢃⡀⠀⠀⢉⠖⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷
⠀⠀⢴⠌⠁⠀⢀⠁⠀⡃⠀⠀⠀⠀⠇⡀⢡⡀⠀⠀⠀⠁⠞⡀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠘⡏⢀⣴⠆
⠰⣙⠂⠀⠀⠀⠠⠀⡐⠅⠀⠀⠀⠀⠈⡥⠨⡅⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢄⡇⠘⠋⣀
⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠴⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⡇⠀⣾⠟
⠀⢀⡄⠶⠃⡛⢐⡋⢐⠃⠰⠆⠀⠀⠀⠒⠰⠆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢷⠊⠁⣤
⠚⡀⢤⡘⠂⠙⠀⠁⠈⠀⠺⠉⠀⠀⠚⡷⠲⠀⠀⠀⠀⢸⣿⡆⠀⣴⡇⠀⠀⠀⠀⠀⣤⡀⠀⠘⡄⣸⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⡙⠓⢸⡿⠃⠀⠀⠀⠀⠀⠈⠉⠁⠒⢺⠁⢠⣾
⠄⣀⠀⠀⠀⠀⠀⠈⠳⣾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠊⠀⢀⡀⠀⠀⠀⠀⠀⠰⣶⣄⣀⣣⡜⠁
⣀⠀⠈⠜⠑⢂⡄⠀⠀⠀⠉⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠰⣦⣄⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠹⣄⡼
⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⢰⡄⢀⣿⠟⠀⠀⠀⠀⠀⠀⠉⠛⢃⡼⠋⠀⠀⠀⢘⣷⠶⠃⠀⠙⠛⠋⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢿⣷⣯⡄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣴⡿⠀⠀⠛⠁
⠀⠀⠀⠀⠀⢀⣄⠀⢸⣿⣔⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡀⠀⠛⠁
⠀⠀⠀⢠⡀⠘⣿⣠⡊⠛⠛⠋⠀⠀⠀⣦⠗⠀⠀⠀⠀⣶⣄⠀⠘⠁⢀⣤⠄
⢀⡄⠀⢸⣇⣔⠛⠻⠟⠁⠀⠀⠀⠀⠛⠈⡶⠁⠀⠀⠀⠘⠻⢧⠀⢰⡿⠟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠
⢸⣇⡤⠊⠙⠛⠛⠀⠀⠀⠀⣀⢀⠀⠀⠳⡆⠀⠀⠀⢲⣦⡀⠀⠛⢁⣤⡦⠀⠀⠀⠀⠀⠀⠈⠠⢠⠄⠄⡀⠅
⠚⠻⠿⣷⠆⠀⠀⠀⠀⠀⢠⡹⠟⣀⠀⠀⠀⠀⣀⠀⠈⠻⡗⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡈⠁⠀⠀⠀⠀⢹⣷⡄⠀⠐⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⠀⠉⠃⠀⢀⣴⣾⠗⠀⠀⠠⣄⠆⢀⡀⢀⠠⡄⠤⠈⠃⢠⡆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢿⣦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠂⠤⠃⡬⠀⡤⠰⠆⠘
⠀⠀⣠⡿⡀⠻⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠀⠀⣬
⠀⠀⠹⠁⠐⣤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⡀⠀⠀⠀⠀⠤⡝⠂
⠀⠀⠀⢀⣴⡀⠳⢟⠛⠓⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⡁⠀⠀⢠⠜⠃
⠀⠀⠀⠸⠟⠁⠀⠀⠑⠦⣔⠶⠿⠖⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠆⡀⠀⠀⠀⠀⠀⢬⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⠑⠒⢤⣤⣄⠀⠀⠀⠀⠀⠀⠠⡅⠀⠄⠀⠀⠀⠀⡀⠦⠠⠆⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠂⠠⢂⠀⠀⠀⢠⠙⠀⠖⠀⠀⠀⡄⢦⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣀⣀⡀⠀⠊⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢜⠇⠀⠀⠀⠀⠉⠳⣬⣵⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠈⠀⠀⠀⣀⠀⠀⠀⠈⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢿⠃⠀⠀⠀⣤⣨⠷⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⠞⡟⠀⠈⡀⠀⠀⠀⠀⠁⣤⣠⠽⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠀⠀⠀⡤⠀⠃⠀⠀⠀⠀⢸⡢⠐⡂⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⢀⠊⢀⣤⣘⡄⢀⣼⡓⠚⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢁⠘⠋⠉⠀⠈⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠧⠂⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠜⠁⠀⠈⠠⣠⣠⡤⠤⠄⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⣀⣤⣤⣿⣿⡆⠀⠀⠀⠀⠀⢀⠄⠉⠃⠐⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠃⠀⠒⠈⠀⠀⠠⠈⠛⢷⣄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣹⣑⠈⠉⠉⠙⠛⠒⠒⠶⠒⠒⠋⠁
⠀⠀⠀⠀⣀⠀⠈⠛⠛⠒⠂⠠⠤⠀⠀⠠⠤⠄⣈⡿⠛⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢤⡢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢤⣀⣀⣄⣀⡀⠀⠀⠀⠀⢀⣰⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣶⡶⠖⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣤⣤⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⢠⣀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣬⢿⣿⣮⣥⣮⣿⣿
⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⣿⣽⣷⣽⣿⣿⣿
⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣔⢠⣵⣾⡿⢿⣟⣿⣿⣿⣿
⣿⣿⡏⠃⠀⠀⠀⠀⣀⣠⣔⣬⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣻⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⡀⢠⣤⣴⠀⠘⣻⣿⣿⣿⠟⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣈⢻⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⡻⣿⣦⡈⠇⠀⠀⣿⣿⣿⣿⢴⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣮⡛⢿⣦⡀⠀⢿⣿⣿⣿⠞⠋⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣬⣻⣣⣿⣿⣿⡟⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢦⣼⠛⣿⠯⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⡿⣏⣿⣿⣿⣦⡉⠶⠄⡀⠀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⠛⣭⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣿⣧⣹⣿⣯⠀⠐⠸⣧⣼⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⢹⣿⣿⣿⣿⣿⣿⣠⣔⣳⣴⣼⡻⢦⡁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣼⣿⠉⣿⣿⢻⣿⣧⣽⣿⣿⣿⢿⣾⠀⠀⠀⣼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣧⣸⣿⣉⣽⣿⣿⢙⣿⣷⣶⣂⣼⣥⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣩⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠏⣿⣿⠁⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣉⣙⣫⣉⣉⣁⠀⠀⠀⠀⠀⠀⢸⡁⣀⣴⣿⣷⣾⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡯⠉⣿⡏⣴⢤⠄⠀⠀⡀⠘⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⠻⣿⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣛⣀⢀⣼⣧⣤⣶⠀⠀⠼⠇⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣿⣿
⣿⣿⠀⢻⡀⢰⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⠟⠋⢹⡇⣍⠀⠠⠀⠀⢀⡄⠀⠀⣿⣿⣿⠋⢻⣿⣿⣿⡁⠙⣿⣿⣿⠈
⣿⣿⣷⣾⣶⣎⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣷⣄⠀⢼⣇⣏⡀⠘⠀⠀⠈⠉⠀⣤⣘⣻⣷⣤⣼⣿⣿⣿⣷⣾⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⡿⢿⣿⠃⣾⣿⣿⣿⣧⣤⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⢻⣿⣿⣿⣿⡟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠃⠈⠅⠀⢸⡟⢿⠟⢻⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⠉⣿⣿⣿⡏⣟⢻⣿⣿⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄⢀⣀⣀⣼⣿⡄⠀⠀⢸⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠛⠛⠛⠻⠟⠛⢿⣿⣶⣶⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⣄⢸⣿⣻⣿⡿⢁⡀⠀⠀⠠⢤⣤⣤⣤⠈⣩⣭⣭⣭⣽⣯⣽⣭⣽
⣿⡏⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⡏⠻⣿⣿⠀⠉⠉⠙⠃⠁⠈⠛⠛⢋⣽⡟⠃⠀⠀⢠⡆⠛⢿⣿⣾⣿⣿⣿⣿⡖⠒⢻⣿⣿
⣿⣧⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⣿⣻⣷⣞⣣⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⡆⠈⠉⢛⠋⢹⠿⣿⠛⠻⣾⣿⣿
⣿⣿⣿⣿⡟⣹⣧⣿⣿⣿⣿⣿⣿⣿⣤⣭⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⠏⣿⢿⡇⠀⠀⠀⢿⣿⣼⣧⠀⢸⣷⣿⢷⠁⢴⣶⣶⣾⣿
⣿⣿⣿⣿⣷⣿⣿⡿⡾⣿⣿⣧⣬⣿⣾⣿⣿⣿⣿⣿⣷⠀⠀⢠⡀⠀⠸⠀⣿⠀⠇⠀⠀⠀⢸⡟⢿⣇⣼⣶⣆⣠⣾⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣷⠿⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⢿⠆⣠⠈⠀⡍⠀⠀⢻⠀⠀⠀⠀⠀⠸⣧⣼⣧⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⣿⢟⣽⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣯⣭⣤⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠋⡁⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣣⣠⣆⠀⠀⡄⠄⠀⠀⢀⠏⣹⣿⣿⡿⢻⠿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡅⢂⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣻⣿⣭⣿⣧⡿⣿⢿⣵⣒⡀⠸⣿⣾⠀⣷⣾⠷⣰⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠻⢷⣶⣿⣿⣾⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢻⣇⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⢀⡾⠛⠷⣦⣤⣄⣠⡾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠾⠛⠻⣦⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢠⡿⠁⠀⠀⠀⢀⣼⠟⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⣠⡿⠁⠀⠀⠀⢀⣾⠃⠀⠀⣠⡿⠋⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠸⣧⣤⡴⠟⠋⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢸⣏⡀⠀⠀⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⢘⣷⡀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠉⠻⢶⣼⠏⠙⣷⣀⣤⣤⣄⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠈⠙⢷⣤⣀⣴⠟⠉⢿⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⢹⡿⠋⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠀⠈⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣴⠟⠁⠀⣠⡾⠛⠻⣦⠀⠀⠀⠀⠘⠷⣦⣀⠀⠀⠈⠛⢷⣦⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠀⢀⣴⠏⠀⠀⣠⣿⣤⡀⢀⣀⠀⠀⠈⠙⠻⢦⣤⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣇⠀⢀⣼⠏⠀⠈⣿⠀⠉⠛⠶⣦⣄⣀⣠⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣧⡀⢀⣾⢿⣤⣄⣀⣀⣴⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣤⡙⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣍⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣼⣿⣿⣿⠏⠻⣿⣿⣿⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⠀⠘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠀⠀⢀⠲⠶⣤⠀⣠⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠹⠀⠀⠀⠀⠑⠛⠁⠈⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⢹⠇⠲⡄⠀⠀⠀⠀⠈⠠⡤⠄⠈⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢸⡄⠀⠘⢦⡀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠹⠉⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠚⠁⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠙⢦⣄⣀⡤⠊⠀⠀⡔⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠒⠤⡀⠀⠀⠀⢸⡀⠀⠀⢳⡀⠀⠀⣨⣽⣯⠀⠀⠀⠘⠀⠀⠀⢠⠀⢸
⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠘⢦⠀⠀⠀⠛⠒⠂⠈⢧⠀⠀⠈⢻⣯⠈⠀⠀⠀⢀⠀⠀⣾⠀⢸⡄
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡼⠀⠀⠀⠳⡀⠀⢻⣿⣧⠀⠀⠀⡌⠀⠀⡇⠀⠀⣧
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠱⣄⠀⠀⠀⠙⠄⢸⣿⣿⣇⠀⠀⠀⠀⢈⡇⠀⠀⣿
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠨⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⢢⡙⣿⠁⠀⠀⠀⢠⣏⣀⣀⠀⠘⣇
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⢠⣯⣿⡿⣋⠀⠀⠳⡄
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⢙⡿⠋⠀⠀⠀⠀⠙⢦⡀
⠀⢠⡃⠀⠀⣀⢴⣾⣡⡴⣾⡶⠗⠒⠒⠒⠚⠋⠉⠉⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠙⢦
⠀⠸⣅⠀⡜⠡⢋⠔⢫⠞⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠴⢞⠉⡡⠀⠈⠑
⠀⠀⠈⢂⠀⠠⠃⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠚⠓⠒⠚⠋⠒⠒⠒⠀⠀⠌⠄⡤⠀⠋⢀
⠀⠀⠀⠈⠃⠀⠀⢀⣀⣀⡤⠤⠤⠤⠤⣤⣤⣤⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠚⠉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃



⣿⢿⠿⠿⠿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠻⠏⠉⠀⠀⠀⠀⢀⠲⣿⣷⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⡠⣆⡄⠀⠁⠀⢦⡄⠈⠙⠛⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣀⠠⠤⢂⡰⣣⣮⢷⣩⡥⠤⠄⠈⠁⠒⠰⠶⠆⢉⢆⡀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⢖⣯⣵⣏⣇⣿⣾⢿⡟⣢⠁⡔⠀⠠⠐⠀⠀⡄⠘⠬⢵⢋⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⢀⣤⣄⣁⡉⢋⢽⣿⣿⣟⣫⣿⠻⣧⠀⠓⡠⢉⠧⢦⣧⠀⠠⣀⣤⠋⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠯⡷⡿⣿⡇⣹⣺⡯⣬⡯⢿⣿⡦⠍⣰⡆⢣⣈⠙⠂⠁⠅⢀⠜⠉⠡⠄⢠⡴⠶⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢷⣾⣿⣿⣿⢿⢉⣿⡞⠕⢡⣧⠴⠊⠹⡙⠀⢹⡖⢲⣔⣶⡂⠀⠀⠐⣦⠛⣃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡽⣷⣯⣿⣽⣐⣿⠛⡢⠺⠋⣉⣁⡀⡙⢤⣹⠘⡉⢦⣼⣯⡶⠈⢆⣼⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⣻⣹⣿⣿⣟⣷⡿⣴⢏⣠⠖⠋⠉⠀⠈⠉⢷⣟⢀⡷⠳⣼⠟⡉⣓⣾⡋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⡫⢷⡧⣯⡝⣿⣯⣿⣿⣿⠀⢀⠀⠀⠀⠀⠈⣿⡿⡻⢄⣹⠞⣱⣼⠷⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣭⣗⣯⣏⣷⡫⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⢰⡴⣌⢹⡼⣤⣏⡱⠊⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣿⡿⢯⣻⡟⣯⡝⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣦⠙⣾⣉⢻⡤⠆⢸⣶⡒⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⠚⠋⣳⣿⡐⣿⠁⠀⠀⠀⠀⠀⠀⠶⠟⠋⣰⢋⣴⣇⠛⣾⡅⡂⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣦⣀⢸⢸⣿⠀⠀⠀⠀⠀⢑⠄⠀⢠⣾⣿⣦⣹⢯⢟⢻⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⠌⠛⣾⢿⡄⠀⠀⠀⠠⠀⠀⠀⠀⢰⣽⣿⣿⣧⣃⢜⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢾⠑⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢻⢏⡴⢊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂⢻⡿⣦⡀⠀⠀⠀⠀⢀⣆⠀⢈⡠⢻⣟⣉⠭⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⡜⠄⣿⠛⠲⣶⠲⣺⠟⢳⣿⣠⣂⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣱⠋⢉⠽⣿⣗⡉⠙⢣⡤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢰⠋⠀⣜⠀⠉⢣⡀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠐⠊⠉⠓⠰⠖⠘⠃

⠀⠀⠀⢠⠂⠠
⠀⠀⠀⠀⣀⢀⣭⠇⠈⠀⠸
⠄⠀⠀⢄⢀⡉⠁⡠⠂⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢄⡦⡀⠀⠀⠎⡏⢀⠔⢡⠀⠉⠐⣀⣴⣶⡁
⠀⢠⠃⠀⠀⢠⠇⠂⢀⣻⡿⢓⣴⠿⠿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠆⢤⠔⠀⢂⣖⡡⠤⣰⣯⡶⠋⢁⡤⠤⡌⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢠⠋⠀⠌⡼⠙⠃⣴⢡⠏⠀⠀⡏⢀⣤⡟⠀⡘⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⢠
⡼⠁⠀⣜⠁⠀⣼⠃⡟⠀⠀⠀⠣⡈⠑⠂⠀⡀⠀⠁⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠴⠦⣄⡈
⡇⠀⠘⠡⠈⠀⠋⠂⢻⠀⠀⠀⠀⠁⠀⠐⠹⠻⠀⠄⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠤⣠⢀⡴⠃⠙⠀⢀⣤⣄⠀⡃
⡁⠠⠀⠇⠀⠠⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠖⠋⠉⠐⣄⢠⠝⠉⠉⠁⠲⢄⠀⠘⠥⠀⡁
⡟⠈⡰⠀⠀⠸⣆⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣠⠴⠚⠑⠢⣞⠁⢸⡃⠀⠀⠀⠀⣤⢀⡇⠀⠀⠀⠈
⡇⠀⠁⠀⠀⠀⢣⠑⠀⠀⠁⠈⠑⠤⠤⠤⠀⣀⣠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⣤⠚⠃
⢧⡤⠀⠀⠀⠀⠋⢣⡀⣀⡀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠂⣉⡁⠢⡈⠀⠠
⠈⡄⠀⠠⠀⠀⠐⠀⢛⢦⡂⠀⢖⠀⡀⡀⠁⡲⠂⠀⠀⢀⢔⠀⠀⠀⠀⠙⣆⣿⠀⠀⠐⢆⠀⠀⠀⠀⠔⠚⠋⠀⢄
⠀⠀⡀⠂⠀⠄⢀⠀⠠⡀⠉⠛⠶⣤⣤⣄⣉⡀⣤⠔⠈⠀⠁⠀⠀⠀⡀⠀⠘⢿⡂⠀⠂⠈⠑⠀⠀⢀⣈⣁⠀⡀
⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⡘⢡⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠧⠀⠀⢀⠀⣀⠴⠄⠐⠒⠒⠲⢄
⠀⠀⠀⠙⣮⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⢀⠀⢢⣀
⣀⠀⠀⠀⠘⠷⣄⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡰⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⡉⠀⠙⠉⠀⠀⠀⢳
⠀⠀⠈⠂⠠⡀⠈⠓⢤⣝⣤⣀⣐⡢⣉⡁⠤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠆⣤⡆⠀⠜
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉⠁⠉⠁⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠉⠛⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣲⣶⠶⠂⠀⠀⠀⠀⠀⢹⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⣰⠋⠠⠙⠃⠀⠀⠀⠀⠀⠛⣅⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠛⢹⠐⠀⠀⠀⠀⠀⢠⡙⠲⢀⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢻⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⡴⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⢻⡄⠀⠀⢳⡀⠀⠀⢠⠀⠀⠀⠀⢀⠀⢀⡀⠇
⠀⠀⠀⠀⠀⠀⠘⠁⢠⣀⠀⠀⠀⣷⠀⠀⠀⢳⡀⠀⡈⢦⡀⠀⠀⠼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢸⡀⠀⠀⠈⣧⠞⢃⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⡟⠙⢣⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣾⣀⣠⠚⠇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⣿⠂⠀⢤⡄⠀⢸⡆⠀⠀⠀⠀⢠⠀⠀⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣿⠀⠀⡠⣣⠊⠁⠀⠀⢀⣀⣸⣇⠀⠀⣀⠤⠬⠷⢔⣄⡀⠀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠚⠒⠛⠛⠛⠛⠛⠚⠋⠉⠉⢉⠀⢻⠁⠀⠀⠀⠈⠉⢛⠛⢦⡀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠁⢸⡇⠀⠀⠀⠀⠀⠤⣍⣲⢽⣆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣯⣤⣤⠞⠓⠲⠶⠶⢤⡭⠶⠋⠁⠀⠨⠇⢁⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠶⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⢸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢛⣫⣭⣭⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢋⡾⢫⣵⡶⢂⣭⠳⣌⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡏⣼⢱⡿⢋⣴⣿⠟⣡⢹⡌⣿⣿⠟⣨⢉⢱⣶⣬⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⢹⡌⢴⣋⠔⣡⣾⠏⣼⢱⣿⣇⣃⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡙⢦⣥⣚⣫⣥⠞⣡⣿⣿⣿⣿⣿⣿⡿⣛⢿⣿⣿⣿⣿⠿⠏⢴⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⣩⣾⣿⢇⡙⠿⢋⣵⣾⣿⣷⣝⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⢟⣵⡿⢋⣴⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡺⣿⢟⣵⣿⣿⠰⡿⢋⣥⣭⣙⡛⣩⣽⣿⣿⡧⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢋⣭⡹⠷⢶⣿⣿⣿⣿⣿⣮⡻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢰⡿⢋⣴⣿⠃⠿⣿⡿⣿⣮⡻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠿⢟⣵⣿⢇⡻⣷⣌⠻⣿⣮⡛⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠘⠛⣵⣿⢏⣌⠻⣷⡌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢃⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡟⡹⠂⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡲⠀⠀⠀⠀⣀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡡⣄⠀⠀⠀⠀⡁⠑⠄⠈⠿⢋⡠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣛⣂⡁⠀⢀⣦⣄⠱⡀⢸⡜⢠⡁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡿⢐⡀⠀⠀⣿⣿⡆⠈⢹⠗⢁⣀⡀⠀⠀⢀⠠⢴⠈⢁⡠⠄⢲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⡀⠀⠰⣦⠀⠀⠀⠀⢑⣿⠅⡃⠀⠀⢈⠛⢇⠀⠆⣴⣿⣿⠀⢀⠖⠁⠀⣨⠔⢁⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⣑⢄⠈⠆⠀⢠⣄⠘⢽⣦⡎⠀⠀⢨⠉⢂⢳⣸⡿⠟⠁⢠⠃⠀⠁⣴⠕⠊⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠳⣜⠀⢘⠋⠰⡒⣿⡹⠀⠀⠀⢱⠞⠚⠓⠠⠄⣀⡄⠀⠀⡞⡁⣀⢀⡜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡀⠀⠈⢇⠀⠀⢰⣶⡻⣎⠅⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠑⢞⠉⠁⡠⠊⠀⢠⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠁⠐⠚⢳⡀⠀⣇⠬⠛⠞⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠏⠛⠤⡀⠀⣃⣠⢊⣀⡔⠉⠉⢉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠛⠣⢄⡀⠀⠀⢣⡔⠁⠀⠠⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠈⠢⣀⠄⠀⠀⠀⠙⢿⢤⠤⠠⣁⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡉⠒⠤⡈⠉⡰⠋⠀⠀⠀⡠⠒⠉⠉⠉⠀⠒⠇⢀⠤⠤⡀⠀⠈⠆⠀⠀⠀⠀⠀⠇⠱⢄⡈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣀⢘⡏⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡰⠴⢅⠀⠀⠈⠆⠀⢸⠁⠢⢄⠀⠀⠘⠐⠖⠒⢤
⠀⠀⠀⠀⠀⣀⠤⠒⠐⢒⠐⠐⠬⢟⡁⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⢡⠀⠀⠸⢀⢶⠀⠀⠀⠱⣠⢏⠑⠌⠓⠀⠃
⠀⠀⣠⠖⠉⠈⠢⣀⠀⠀⠳⣀⠀⠀⠈⠳⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠙⠁⠀⡠⠋⠁⠀⡆⠀⠀⠀⠸⠀⠑⠼
⠀⠜⡡⠔⠒⠉⢉⣉⡭⠽⠖⠚⠳⢤⣤⡀⢵⡀⠀⠀⠈⢆⠀⠀⠀⢀⠔⠚⢄⢀⡠⠊⠁⠀⠀⢠⠁⠀⠀⠀⠀⡗⠀⠀⣀
⣼⠬⠄⠀⠠⠶⣉⠀⠀⠀⢀⠤⠊⠁⠀⠀⣀⠕⣄⠀⠀⣠⠟⠒⠒⠉⠣⡀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⡘⠀⣤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠃⠀⠀⠒⠐⠈⣔⣪⡗⠟⣍⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠄⡤⠊⠁⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣲⠾⢭⠆⠉⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⠐⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣨⠟⡜⠄⠀⠀⡠⠒⠉⠑⢄⡀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢾⢱⠑⠁⠀⣠⠊⢀⡀⠤⣲⠋⠉⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⢟⢢⠉⠀⠀⢰⠋⠉⠀⢀⠜⠃⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⡗⠄⠉⠀⠀⠀⡆⠀⡠⠴⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢔⣸⡗⡔⠁⠀⠀⠀⠀⡏⠁⠀⠏⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⢰⣩⡟⠏⠁⠀⠀⠀⠀⠀⠃⠀⠸⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠠⣉⠌⠁⠀⠀⠀⠀⠀⠀⠈⠀⡆⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡷⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣆⡤⠖⠚⠛⢳⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠾⠛⠁⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠋⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⢠⣤⣶⣶⣾⡋⠉⠉⢉⡽⣿⣶⣄⠀⠀⠙⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠃⠀⢀⣼⡵⠋⠹⠿⢿⠀⢠⡏⠀⠛⢛⡟⣇⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡾⢹⠁⠀⠀⣠⠞⠀⠸⠷⣤⣠⡞⠀⢹⡄⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⡶⠀⠀⢀⡞⠁⠘⠷⠶⠚⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣤⣶⠟⠀⠀⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠀⣾⠀⠀⠀⣠⠄⠀⠀⠀⠈⠉⠉⠉⠁⣴⣤⡀⣿⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠛⢲⡄⠀⠈⢻⣄⣿⠀⠀⠚⠉⠳⢦⣀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢡⠖⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣽⣇⠀⢀⡏⡙⠻⠀⠀⠀⠀⠀⠀⠉⠛⠒⢀⣀⠜⠁⣀⣤⣤⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣠⣿⠀⠀⣧⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣁⣀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡤⣶⣿⠀⠀⠘⢷⣄⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⠽⠛⠛⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⣿⢸⡇⢀⣤⠤⠄⠀⠿⠿⠧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠚⠓⠀⣿⠙⠛⠛⠛⠛⠒⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⢸⡇⣸⠀⠀⠀⠀⠀⠀⣀⠠⠿⣦⡄⠀⠀⢀⣶⡛⣯⣤⡶⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⢻⢸⡇⣿⠀⠀⠀⠀⣠⠞⠁⠀⠸⣿⡁⠀⠀⢸⣿⠛⣾⠁⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣸⡇⣿⣠⡴⠖⠒⡯⠀⠀⠀⠀⠈⠛⠒⠚⠛⠋⠀⠹⣶⠟⠁⣸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣇⢸⣿⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠞⠋⠈⢷⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢻⣿⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠻⣾⡟⠈⣿⠀⢰⠃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢳⣄⠀⠀⣿⡇⢀⡿⠀⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⢹⡇⠀⠙⣶⣾⢿⣿⡏⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⠁
⠐⠛⠛⠓⠲⠶⣾⡏⠸⡇⠀⢷⡀⠀⣸⣿⠷⣿⡿⠶⠿⢤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣤⣶⡿⠃⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠙⠷⠞⠻⢦⣼⠿⣶⡿⠛⣿⣿⠛⠲⠶⠤⣤⣄⣀⣉⣉⣉⣉⡉⠉⠉⠛⠛⠒⠒⠶⠶⠶⠤⠴⠿⠿⠧⠶⠤⠤⠤⢤⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠏
⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠉⠛⠛⠛⠓⠲⠶⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⡤⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡉⠈⠣⡀⠀⠁⠉⠀⠀⢳
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠾⢷⡋⠀⠈⠲⢶⣀⠠⢂⠘⡇
⠀⠀⠀⠀⣰⠋⠀⠀⣀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢁⡄⠀⠀⠙⢆⠀⠀⠸⣇⢈⠤⠀⠸⡀
⠀⠀⠀⢰⠃⠀⢠⠞⠉⠀⠀⠀⠐⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠡⠂⠀⠉⠳⡄⠀⠀⠈⢳⡄⠀⠹⣆⠀⠀⠘⢷
⠀⠀⢀⠏⠀⢀⡏⠀⠀⠀⠀⢠⠂⠀⠀⢈⡆⠀⠤⠔⠒⠁⠸⠛⠣⡀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠹⡖⠂⡀⠀⠀⠀⢸
⠀⢠⠎⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡄⠀⠀⠀⠀⢠⡀⠀⠀⠁⣀⠘⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠤⠶⠦⣀⠀⣂⣳⣄⡀⠀⠀⠀⢻⠀⣠⠒⠡⠀⠀⠀⠀⢸
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡠⠞⢻⣆⠀⠀⠘⠣⡹⣀⠔⠃⠀⠀⠀⢸
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡠⠊⠁⠀⠀⠋⠳⢄⣤⢴⢍⡀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⢦⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠑⠂⠤⠄⠠⣆
⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡠⠖⢙⣧⡀
⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠩⠀⢀⠎⠀⣿
⠀⣠⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣅⣀⠠⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈
⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣵⣿⡿⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⣫⠟⣵⣌⣛⡟⠁⠀⠀⠉⠓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢫⡀⠀⣠⠞⣡⣾⣿⣿⣿⢠⡞⣠⠆⠀⠀⠀⠀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣀⣧⡞⣡⣾⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⠞⢃⣴⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀
⠀⠀⠀⠀⠀⢠⠏⢠⣄⡴⢃⠴⠋⠀⠘⣜⣆⠀⠀⠀⠀⠀⢀⢄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠃⣾⣷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⡞⠀⢀⡏⠐⠣⡀⠀⠀⠀⢈⣨⣤⣶⣶⣶⣿⣿⡼⢟⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⡸⢁⡴⣯⣀⣠⣐⣁⣤⣶⣾⣿⣿⣿⡿⣿⡏⢹⣿⣿⣷⣄⡀⠙⠲⢦⣤⣀⠀⠀⠀⠀⣠⡆⠐⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱
⠀⠀⠀⠀⢣⣞⣵⠟⢹⣿⠛⠛⠻⣿⢿⣿⣫⣿⣾⣿⣷⢘⣿⣿⣿⣿⣿⣷⣶⣦⣤⣭⣶⣦⣴⡾⢻⣿⠇⠀⢸⣿⣿⣿⡁⠟⣿⢹⣿⣿⠸⡸
⠀⠀⠀⣰⣿⠟⠁⠀⠈⠻⢶⡀⠢⡘⣷⠾⢿⣿⡿⠣⠬⣉⠛⢦⣌⠁⡹⣿⣿⣿⡿⣿⡿⠿⣟⢹⣿⡟⠀⠀⣿⣿⣿⣿⣷⣤⡇⣾⣿⡏⠀⡃
⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠙⠦⠴⣯⠀⠀⠙⢯⣀⠀⢀⡵⠀⠉⠛⠶⠶⣭⣭⡭⠿⠟⠲⠶⠤⢽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄⡀⣸⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣤⡤⠞⠀⠀⣠⠞⠉⠁⢀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⡞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡖⠛⠳⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸⣠⠟⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠒⢦⡀⠀⠀⣹⠀⠀⠀⠀⠀⠀⣸⠟⢦⣴⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠓⢶⠞⠁⠀⣠⠏⠀⠀⠀⠀⠀⣰⠋⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⣼⠃⣠⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⡀⠀⠀⠀⠀⢀⡼⠁⣴⢿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠅⠀⠀⠀⢀⡾⢁⡾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⣿⣶⠟⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⡆⠀⠀⢸⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣀⣤⣤⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⡄⣠⣤⢠⡞⢡⡤⢤⡉⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠃⠛⢸⡄⢿⣀⣠⠇⣸⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣭⣥⡴⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣭⣭⣭⣭⣭⣭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣄⣴⡆⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⢰⣦⢠⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⢻⠃⠿⢌⣥⢺⡇⠀⠀⠀⠀⠀⠀⢹⡗⣬⡡⠿⠘⡿⢿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠉⠁⠹⡄⠀⠀⣳⣯⣇⣤⣶⡚⢓⣦⣤⣸⣽⣎⠀⠀⢠⠇⠈⠉⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠄⢀⣲⣽⣻⡎⠀⠀⡡⠤⠤⠶⠶⠤⠥⣌⠀⠀⢱⣞⣯⣆⡀⠜⢭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣾⡈⠈⡌⠛⠙⠒⠤⡄⡴⡆⢇⡰⢑⢆⢠⠤⠒⠋⠛⢡⠉⢑⣶⣤⡈
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢠⢫⣟⢀⡠⠀⠀⣻⠤⣅⠐⠁⠂⠐⠈⠂⣨⢤⣟⠀⠀⢆⠐⣻⡽⡈⠉⠓⠦⣄⣀
⠀⢀⣠⡴⡺⠋⠁⠀⢀⠆⣠⠿⠛⠁⠚⠘⠦⠘⠱⣧⠈⠀⠀⠀⠀⠀⠀⠁⣾⠎⠃⠔⠁⠓⠈⠛⢷⡄⢠⠀⠀⠉⠻⡶⢤⣄⡀
⠀⣼⢻⣇⠰⠆⢐⣾⠋⡼⠃⠀⠀⠀⡠⢄⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡠⠄⠀⠀⠀⠹⣧⠓⣲⡆⣠⠄⣽⡿⡇
⠀⣿⠀⠙⠧⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠀⠀⡰⠟⠀⡇
⠀⣿⣠⣦⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣤⣄⡇
⠴⣿⣩⠈⢦⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡠⠋⣝⡿
⠀⣿⣅⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⢠⣹⡇
⠀⣾⠉⢧⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡸⡙⡇
⠀⣿⠘⠰⠈⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⡄⠆⡇
⠀⣿⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠿⣀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠉⠓⠦⣤⣀⠂⢻⣼⣟⣷⠀⠀⠀⢘⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡃⠀⠀⠐⣮⣻⣧⠗⠐⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣌⡋⠳⢤⡄⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡴⠋⢘⣥⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠀⠀⠉⠻⠶⢭⣛⠶⢤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⡤⢖⣋⡥⢶⠟⠉⠀⠀⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣶⠀⢠⠖⠙⠈⠙⠛⠖⠦⣍⣉⠉⠉⠉⠉⣉⣭⠴⠺⠛⠉⡡⠋⠢⡄⠀⣾⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠛⠇⠀⠀⠀⣀⠀⠀⠀⠀⣉⠹⠶⠶⢋⣁⠀⠈⠀⠀⣈⠀⠀⠀⢹⠛⠛⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠐
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⣧⣤⣤⣤⣤⣬⣷⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣿⠟⢻⡟⠛⣿⡲⠶⣤⣀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠖⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠆⠀⣠⣶⣋⡁⠀⣠⠞⠁⠀⢸⡇⠀⠈⠳⣄⠀⢈⣙⣶⣄⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠉⠉⣿⠟⠓⠲⠶⢾⡷⠶⠖⠒⠛⣿⠉⠉⠀⠈⠻⣦
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢀⣾⣁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣈⣣⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠉⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣤⣤⠶⠞⠛⠉⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⡽⠟⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢠⡾⢋⣥⣤⣍⡙⢦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⢀⣠⡴⠞⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⡿⢠⡏⣠⠞⠉⢻⡌⣷⠀⠀⢸⣄⣀⣀⣀⣀⣀⠀⠀⢀⡀⠘⠛⠋⠁⠀⠀⠀⠈⠙⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢿⡘⣿⣡⡞⣁⡾⢁⡟⠀⠀⢸⡁⠀⠀⠀⠀⠉⢳⡶⠋⢹⡶⢶⣄⠀⠀⠀⠀⠀⢤⡀⠙⢿⡟⠁⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣤⣉⣉⣩⡴⠟⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠘⢷⡾⠋⣠⡼⠋⣻⡄⠀⠰⣤⡀⠙⣶⠟⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡄⠛⠾⣏⣠⡾⠋⣻⠶⣄⣈⣿⠞⠃⠀⣸⠇⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢻⡄⠀⠈⠉⠳⠞⢻⡴⠟⠉⠁⠀⠀⢠⠏⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣤⡤⠿⣶⠒⠚⠛⢻⡟⠛⠛⠲⣶⠷⢤⣤⣀⣠⡾⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠈⠷⣄⠀⢸⡇⠀⣠⠞⠁⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠿⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣤⣤⠄⠀⠀⠀⠀⠉⠛⠓⠿⠷⠾⠷⠾⠿⠚⠛⠉


⡖⠒⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠒
⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢠⠤⢄⠀⡀⢤⠤⠀⣠⠀⢠⠤⡄⢠⠀⠀⡠⠄⠀⢀⠠⠄⠠⡤⠄⡤⢄⡀⡠⠤⡀⢠⠀⡄⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⢸⠀⢀⠂⡇⢸⡃⢰⠄⠆⢸⠒⢣⢸⠀⠀⡗⠀⠀⠈⠑⠄⠀⡇⠀⡇⢺⠰⡇⠀⣸⢸⠻⡀⢸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣾⣶⣶⣶⣷⣶⣶⣷⣶⣷⣶⣶⣾⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣮⣵⣾⣯⣵⣶⣦⣄⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠤⣄⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠄⠀⠄⠀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠁⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠀⠀⠂⢐⡶⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣧⡀⠀⢀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢿⣿⣷⣦⡄⠀⠴⠄⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠈⠣⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠉⠘⠂⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡷⠶⣤⡀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠈⠁⠀⠐⠧⠄⣀⡀⠀⠈⠛⠛⣛⠋⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣀⠋⠈⣩⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣆
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢧⡀
⠀⠀⠀⠀⢸⣇⣀⣀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡹⠆
⠀⠀⠀⠀⠀⣹⠟⠛⠛⠿⢷⣦⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠶⡾⠉
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡹⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡀
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠐⠚⠆⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⣇
⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠈⠱⠦⣀⠀⠀⠀⠀⠀⢛⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙
⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⠎⠀⠁⠀⠀⠀⢢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠈⠁⠉⢹⠀⠀⠀⠀⠀⠒⠒⠒⢶⠚⠃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠓⠤⢄⠀⠀⠐⠒⡶⢋⠻⠇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⢒⣶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠂⠁⠀⠀⠀⣰⢋⣴⠟⠁⠀⢀⠀⠀⠀⠈⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠⠴⠒⠛⠒⠒⠤⣄⡀⠀⠀⠀⠀⣀⣄⣪⠞⠁⠁⠀⠐⠤⠴⢴⡖⣨⠔⢃⠊⠀⠀⡐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⣶⡶⠿⠾⢟⣁⣀⣀⡔⠀⠀⢀⡼⠋⠀⠀⡠⠂⠀⠀⡀⠀⠀⠀⡀⠀⠀⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⡠⢃⣼⠷⠂⠀⠉⠉⠉⠉⠿⢿⣿⡿⠿⠻⠻⠗⠒⠚⠁⠀⢀⣤⡀⠓⠈⢁⡠⠈⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠺⣷⣼⣶⡟
⠀⠀⠀⠀⠀⣀⣄⣴⡯⡀⠂⠀⠀⠀⢀⣤⣶⠾⠋⠉⠀⠒⠂⠄⠀⠀⠀⡰⠊⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⠤⢤⣌⣻⣿
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣤⠤⠠⢄⠤⠤⢶⡕⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣰⠟⠉⣀⣨⡽⠯⠅⠄⡀⠤⠤⠀⠂⠉⠀⢀⡀⠤⠀⠉⠀⠘⠀⠠⠀⠰⠄
⠀⠀⠀⠀⠀⠁⠀⢸⠟⣁⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆⠀⠀⠀⡌⠀⠃⠀⣄
⠀⠀⠀⠀⠀⠰⠐⠱⠊⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠄⠀⠀⠀⠉⠰⠶⢦⠄⠈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⢠⠀⠀⣠⠊⠠⠄⠈⠶⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠣⠀⠀⠀⢨⡄⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⢀⠀⢠⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠰⢼⣶⣄⢀⠀⠀⡾⠒⢉⠀⢐⠂⠀⡤⠀⠀⠀⠀⠀⠺⠟⠙⠃⠀⠀⠀⠈⡄⣾⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠻⣿⣷⠖⠋⠁⠀⠈⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⡇⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠐⠂⣀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣀⠀⠐⠤⠀⠀⣄⣹⣶⣤⡴⠃⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⢷⠀⠀⠀⣠⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢀⡤⠒⠂⠈⠉⠛⢿⠁⠀⣀⣀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡟⠈⠀⠀⢀⣷⠞⣥⣾⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡰⠋⠀⠀⢀⠀⢀⠰⡀⠛⠉⠩⠄⠀⠁⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳⡄⠀⠀⣼⠃⣀⠟⠛⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠉⠻⣶⣧⡐⠀⠒⢀⡀⠀⠀⡀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⢿⣼⢰⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠚⢛⢿⣿⣿⠂⡀⠈⠁⢀⣸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⢸⣿⡼⠀⡠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠙⠀⠁⠀⠀⠀⢸⠔⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣠⣤⣤⢤⣤⣤⣙⢳⣄⠀⢀⣴⠟⣉⣀⣀⡀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⣠⡾⠟⠉⠀⠀⠀⠀⠈⠙⠷⣿⣧⣿⣵⠟⠋⠉⠉⠛⢷⣄⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⢁⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠉⠛⠛⠲⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⣤⣄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠏⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⢀⣤⣤⡀⠀⠀⠀⣿⠁⠀⠀⣀⣀⣀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠙⢷⡄⢘⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⣿⠉⣿⡗⠀⠀⠀⣿⠀⠀⢰⣿⠋⠙⣧⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⣀⣀⣀⣘⣿⡇⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⡀⠀⢻⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠁⠀⣿⠀⠀⣠⡶⢷⣦⡀⠀⠀⠀⠀⢀⣿⡿
⠀⢠⣴⠟⠋⣉⣉⣙⣻⣿⡄⠀⠀⠀⠀⢸⣷⣤⠀⠈⠻⣦⠈⣿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡟⢀⣼⠏⠀⢶⡿⠃⠀⠀⠀⢀⣼⣿⣤⣤⣄⣀⡀
⢰⡟⢀⣴⠟⠋⠉⠉⠉⠉⠛⠻⠶⣦⣄⡀⠈⠁⠀⠀⠀⠙⣷⡘⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⢡⡾⠃⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⠛⠻⣯⣍⠻⣦⡀
⣿⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⠀⠀⠀⠈⢻⣿⣦⣄⡀⠀⣿⡄⢀⣤⣤⣼⣷⡟⠁⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠹⣆⠈⣿
⢿⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⣼⠋⠁⠉⠙⣷⣼⣷⠟⠁⠀⠙⣿⡀⠀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼
⠸⣧⠈⣷⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⣾⣷⠟⠉⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⢠⡿⢠⡿
⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣤⡀⢀⣠⣿⣇⠀⠀⣠⣾⣏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣿⠇⠀⠀⠀⢠⡟⢁⣿⠁
⠀⣿⠀⢸⡇⠀⠀⣠⣤⠀⠀⠉⠛⠛⠿⠶⠶⣦⣤⣤⡾⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣷⡿⠛⠉⠉⠉⠙⢷⣄⣠⣤⣴⡶⠶⠟⠋⠁⠀⣠⣤⡀⣿⠁⢸⡇
⠀⣿⠀⢸⡇⠀⠈⠿⠿⠃⢀⣠⣴⠶⠶⠶⠾⠟⠛⢻⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣼⠿⢿⣶⣶⣦⣤⣤⣀⠀⠀⢿⡿⠃⢹⡇⠸⣷
⢰⡿⠀⠘⣿⠀⠀⠀⠀⢠⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣶⣶⣶⡿⠟⠉⠙⣿⠋⠈⠙⠻⣶⣶⣶⡞⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠈⣷⠀⢻⡇
⠸⣷⠀⠀⢿⡀⠀⠀⠀⠈⠿⣶⡿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠞⢻⡏⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⠉⠛⠛⠶⢦⣤⣀⠀⠀⣷⣦⡾⠃⠀⠀⠀⠀⣿⠆⢸⣿
⠀⢿⡄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⢻⡄⠀⠀⠀⣸⣿⣷⣄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⠙⠛⢶⣄⠁⠀⠀⠀⠀⢀⣴⡟⠀⣸⡇
⠀⠈⢿⣄⠀⠀⠛⠷⣤⣤⣤⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣼⣿⢶⡶⠾⠋⢸⡏⠙⠛⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣿⣟⣥⣤⡾⠟
⠀⠀⠀⠙⠻⠶⠶⡶⢶⣿⡟⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⢟⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⠻⣦⠀⠠⣶⣄⠀⠀⠀⠀⠀⢻⡌⠙⣯⡉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡇⠀⠀⠀⠀⠀⣾⡛⣃⣴⠟⢁⣾⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣇⠙⠷⣦⣼⠟⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⢻⣄⡀⠀⠀⠀⠈⠛⠋⠁⠀⣸⡇⢀⣀⠀⠀⠀⢰⡟⠀⠀⠀⢰⣿⣼⡿⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⠛⠳⠶⣤⣄⠀⣴⣶⠀⠹⣷⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠋⠁⠀⠙⠟⢁⣀⣀⣀⣀⣠⣾⠋⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠙⢿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⣉⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠀⣠⡾⠃⠀⣠⣴⡶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠻⣦⡀⠀⠀⠀⠀⣠⡾⣿⠟⣿⠻⢦⣤⣴⠾⠋⢀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⠛⠷⠶⠶⠛⢋⣴⠏⠀⠘⢷⣦⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠶⡶⠲⢲⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⡏⠉⠉⠉⠉⠉⠉⣿⢠⡶⠶⠶⠶⢶⣤⡶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠤⢸⡇⠀⠀⠀⠀⢧⣀⣄⣠⣼⠇⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⣿⣷⣦⣤⣶⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠂⠒⢸⡇⣤⢤⣤⣤⣤⠤⠄⢤⢤⡄⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⣿⡇⠟⠙⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠥⠥⠼⠃⣿⣸⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⣿⠸⠦⠤⠤⠤⠼⠿⠧⠤⠤⠤⠼⠇
⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠒⢲⡄⣿⣿⣿⣏⠩⣿⣿⣿⣿⡇⣇⠀⠀⣀⣀⣀⣀⣿⢰⡞⠛⣻⣶⣝⢿⣿⡟⢳⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠨⡇⣿⣿⣏⣈⣶⠾⣯⣍⣹⡇⣈⠈⠉⠉⠩⠭⠭⣅⢸⡇⢠⣿⣿⣽⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⣍⣻⢷⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⣿⠾⢟⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⡇⣿⣿⣿⣿⣿⣤⣿⣿⢿⡇⡇⠘⠛⡃⠃⠀⠀⣿⢸⡇⢸⣿⣿⣿⣿⡹⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠻⠿⠿⠿⠿⠿⠿⠷⠾⠇⣇⣀⣉⢁⣉⣉⡀⣿⢸⡇⠈⠿⣫⣿⣿⣷⣯⣿⡇
⠀⠀⠀⠀⠀⠘⠓⠒⠒⠐⠂⠂⠒⠃⠀⠀⠀⠀⡖⠒⠒⠒⢲⡆⡇⠈⠀⠀⠈⠀⠀⣿⢸⡇⠀⠀⠙⠋⠁⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡇⠷⠤⠤⠤⠤⢤⣤⠿⠘⠓⠒⠒⠒⠒⠒⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠴⠦⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡇⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⣶⣶⣶⣶⣶⣶⣶⢶⠶⢶⠆⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠃⠀⢸⡓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⠛⣰⣦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢻⣿⣿⣶⣤⣀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣸⣿⡒⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⠀⠀⠀⠉⠙⠛⠛⠛⣿⣿⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠿⠿⠿⠟⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣀⣀⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠉⠉⠉⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⣸⡏⠀⣿⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⠀⢀⠸⣷⡀⠀⣤⣀⠀⡀⠀⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⣿⠇⠀⠒⣿⠁⢸⡄⢻⣧⠀⢈⣯⠀⢹⡶⠲⢶⣆⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠘⠸⡟⠸⠀⠐⢿⠀⠀⠃⠈⢿⢷⠛⠻⠏⠉⠙⠇⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣥⣝⢆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣹⣇⠀⡉⠛⠻⢷⣤⡄⠈⠣⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠄⠐⠉⢴⠿⠛⠻⢿⠀⡀⠀⠀⠈⠉⠳⢤⡙
⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⣾⣄⠀⠀⠀⠀⠛⢷⣆⡆⣀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠙⢿⡓⠦⣄⡀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣟⠀⠀⠀⠱⣦⣄⠀⠀⠀⠈⠓⠺⢿⣦⣀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⡙⡛⠿⠿⣆⣠⡁⠙⢻⠶⣷⣂⡀⠀⢨⠟⢻⣟⠁
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣽⣄⡻⣿⣧⣀⠀⠘⠿⣿⣦⣦⣔⣾⣿⣿⣿⣿⡶⠶⠛⢷⣄
⠀⠀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣴⣤⣌⣏⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠈⠑⠚⠓⠚⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣤⣤⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣀
⣿⣯⣤⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠖⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣤⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠛⠛⣋⣉⡁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡴⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣉⣉⣉⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠶⠶⠶⠶⠞⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢙⣛⣋⣉⣉⣉⣩⣭⣥⣤⣤⣤⡴⠶⠶⠶⠶⠶⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣉⣉⣉⣉⣉⣁⣀⣤⣤⣤⣤⣤⡤⢤⠴⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⢉⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠉⣉⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠲⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣤⣤⡤⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣋⡙⠳⣦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣾⣿⣿⢳⣦⠹⣆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣾⣿⣿⣯⣹⡇⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠹⣯⣟⣻⣿⡿⢁⡿⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣉⣉⣩⣴⠟⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣤⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⣤⡤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠀⠉⠁⠀⠀⠀⠀⠀⠙⠁⠓⣤⠄⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⢠⣄⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⣾⣿⣶⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠁⢶⣄⡀⠂⢀⡀⠀⣀⣠⡄⠀⠀⠀⠠⠄⣀⠀⢀⣀⣠⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠃⠐⣤⠉⠻⠓⣤⡤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠻⢿⣏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠁⠤⢺⡿
⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠉⠀⡄⠀⣄⠀⠰⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⣀⣰⠦⠘⠛⠃⣼⣧⢀⣄⠂⠀⣼⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣶⣦⣄⣀⣀⠀⠀⠀⠁⠀⢠⡚⠉⠀⠄⠀⠀⠀⠀⠀⠀⢸⢿⣶⠉⣉⠉⠁⠸⠻⢆
⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠙⠲⠶⠦⣤⣼⣅⣂⣴⣾⣿⣦⠒⠀⣠⣿⡯⠛⠁⠾⠛⢠⠆⠰⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⣶⣥⡄⠋⠹⠿⢿⣿⣿⣥⠞⣋⣁⡀⠀⠀⠀⠀⢁⣴⣦⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⠷⠄⠀⠀⢉⠳⣶⣿⣿⣿⣧⠙⠁⠀⠀⣘⠋⢀⣴⠞
⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠁⣴⡟⠻⣷⣌⠀⠈⠛⣿⣿⣿⢀⣤⣾⣷⣾⠟⠙⣉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣄⠙⠃⣠⣿⢋⣴⡀⠀⠜⠻⣿⣉⣤⡀⠀⠀⠀⠘⢻⡇⠈⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣀⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠉⣉⡙⠛⡛⠷⢾⣿⣿⡄⠈⠄⠹⣿⣿⣿⡄⠃⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠁⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠻⣿⣁⠟⢢⣌⠙⠻⠂⠀⠂⡹⡿⠋⠀⠀⠐⠀⠾⠟⢢⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠘⠏⣀⡄⠀⠑⢦⡀⠀⠀⠠⢿⣀⣀⣀⣀⠀⠠⣬⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⢤⣀⡀⠀⠀⠀⠲⠄⠙⠶⣶⣿⣦⣸⣦⡀⠀⠸⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣀⠀⠀⢠⣴⣿⢿⡟⢉⡙⢷⡈⢻⣭⡔⠒⠒⢤⣤⣀⠀⠀⠀⠈⠛⠿⣷⡄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣀⠀⢈⠙⠿⡆⢿⣅⣼⡿⢀⠘⣅⠚⢧⣀⡐⠛⣧⡀⠀⠀⠀⠀⠈⢻⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠦⠄⢀⡀⠈⠛⠛⠰⢿⣷⣄⡉⠶⠋⣡⣶⢄⣙⣤⢀⠀⠀⠀⠀⠑⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠇⠀⠀⠀⢻⣷⣤⣄⣀⣀⣌⠀⠀⠀⠀⠈⠙⠋⠙⠟⠳⠦⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⡄⠀⠀⠀⠀⣧⣿⣿⠿⣿⡿⠷⠚⠛⠻⣯⡄⢠⡶⠂⠴⠤⠄⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠸⢸⣿⠀⣿⢁⡀⠀⠀⠀⠈⣄⣴⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠃⠀⠀⢀⠀⠠⢶⡚⢿⣷⣿⠎⢡⠀⠀⠀⠀⠈⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠀⠀⠀⡀⠂⣈⣿⣸⣿⣿⢠⡆⣤⠂⠀⠀⠀⠈⡴⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⠋⠀⠀⠈⠠⠈⠓⠀⠉⠹⣿⣿⡀⠀⠁⠞⢉⠀⠰⠀⠰⢆⡀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⣿⣟⠁⠀⠀⠀⠉⠀⠂⠀⠀⠈⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣦⠀⠀⠀⠀⠀⠒⢯⡄⢀⠀⣿⣿⠀⠀⠀⢇⡈⠀⠀⠀⠀⠀⣥⡄⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣠⣤⣿⣷⡀⠀⠀⠀⠀⠁⣰⠋⢶⣿⣿⡸⠇⠳⠀⠡⠄⠀⠀⠀⢸⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠉⢡⣿⣡⣿⣿⡦⠀⠀⠀⠠⠀⠀⠴⣿⣿⡄⠞⠀⠀⠀⠀⠀⠀⣰⣿⣏⣹⣿⢠⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣸⣿⠿⠋⠉⠀⠈⠁⠀⠀⠀⠁⠀⣿⣿⠇⡀⠈⠀⠀⠀⠀⠚⠛⠛⠿⢿⣿⣏⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠸⠃⢀⠄⣀⣀⣤⣤⣼⣿⣿⣆⣁⣤⣀⡀⠛⠀⠀⠀⢤⡀⠀⠈⠛⢣⣄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡇⠀⠀⠐⡄⠀⠀⢠⣶⡿⠛⠉⠉⠉⣿⡿⣿⠋⠉⠙⠛⠷⣷⣀⡀⠀⠹⠃⡄⠀⠀⢨⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢊⠀⠀⠀⡄⠀⠀⢰⣿⠃⠀⠈⢀⠀⠰⣿⠀⢻⣆⠀⡀⠁⠦⠈⢿⣄⠠⠀⠀⠐⢄⠀⠀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠁⠀⠠⣿⠇⠀⠀⠠⠈⠀⠀⡏⠀⠘⡇⠀⠳⢆⡀⠀⠀⣿⣄⠀⠀⡇⠘⠀⠀⠻⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⠃⠀⠀⠈⢠⣿⠀⠀⠀⠠⠄⠀⣦⡀⠀⠀⣤⡀⠀⣈⠀⠀⠀⢿⣯⠀⠀⡇⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⡀⠀⡀⠀⠀⣿⡄⠈⠀⢀⠈⠀⠀⡾⠀⢸⣇⠀⠀⠉⠠⠀⠀⣿⡏⠀⠀⡆⠀⠀⠀⣿⠾⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⡀⠳⡀⠁⠸⢿⣆⡀⠀⠀⠀⠀⢳⣄⡰⠏⠀⠀⠀⠀⢀⣼⡿⠄⠀⠀⠃⠾⠀⠀⣈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⢀⠀⠁⠀⢣⡀⠀⠈⢻⣿⣦⣀⠀⠀⠈⠀⠀⠀⠀⢀⣴⣾⣿⠿⠁⠀⢀⠈⢠⠂⠀⢠⣼⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⡄⠀⠀⠀⠀⡄⠀⠀⠙⢻⡟⣷⣄⠀⠀⠀⠀⣴⣿⣤⡿⠇⠀⠀⡰⠆⠀⠈⠀⠠⡌⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⠁⢄⡀⠀⡀⠀⢆⡀⠀⠀⢻⣿⠙⣧⡄⠀⣿⣏⣸⡟⠛⠀⢀⠐⠀⣠⠂⠀⢀⢷⣦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠳⠄⠘⠠⠼⠃⠀⠀⠈⢽⣿⠟⠷⢴⡍⢻⣿⠁⠀⠀⠠⠦⠄⠁⢀⡰⠄⠀⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡤⠀⣥⡄⡀⠀⠀⠀⠉⣼⣿⠀⠀⠀⡀⢸⣿⣵⠀⠀⠀⠀⢠⠀⠾⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠈⠁⠴⣉⣁⣾⠟⠙⣷⣦⣤⣴⣿⠛⢿⠇⣀⠒⢰⣧⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣿⡏⠁⠀⢰⡿⠋⠉⠉⣩⡟⠓⠒⢾⣧⠠⠄⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⢽⡟⠀⠁⠂⣿⠇⠐⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⣉⣭⣿⡿⠿⠟⠛⠛⠿⠿⠷⣶⣶⣤⣤⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣰⡿⠻⠿⠷⠶⠾⠿⠿⠛⠛⠉⠁⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⢿⡇
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⣇⣠⣴⡾⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢠⣿⠛⠉⠁⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⢠⣿⠃⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢻⣇
⠀⣾⣧⣀⠀⢀⣴⡿⠛⠛⢿⣦⣀⣾⠟⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⣀⣠⣼⡿
⠀⠀⠉⠛⣿⣾⠋⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⣸⣷⣶⣤⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠉⠛⢿⣦⣄⠀⠀⠀⠀⠀⢹⣿⠛⠛⠉⠁
⠀⠀⠀⢰⣿⠁⠀⠀⠀⢀⣾⠟⠀⠀⠀⢀⣼⠟⠁⠀⠈⣿⣄⣀⠀⠀⠉⠛⠿⣶⣄⡀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣠⣾⠏
⠀⠀⠀⠘⢿⣆⣀⣀⣴⡿⠃⠀⠀⠀⣠⡿⠋⠀⠀⠀⣰⡿⠛⠛⢿⣆⠀⠀⠀⠈⠙⠻⢷⣦⣀⠀⠀⠀⣸⡿⠙⠋⠁
⠀⠀⠀⠀⠀⠙⠛⠛⣿⡅⠀⠀⢀⣼⡟⠁⠀⠀⢀⣾⠟⠀⠀⠀⢨⣿⠿⣶⣤⣀⠀⠀⠀⠉⠻⣿⠶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⠿⣿⡄⠀⠀⣰⣿⠃⠀⠀⠀⣰⣿⠃⠀⠀⠉⠛⢿⣶⣤⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⢿⣄⣀⣠⣾⠟⠛⠿⣶⣤⣤⣤⣴⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⢠⢂⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⢧⣀
⠀⠀⠐⢀⠴⠠⠒⠈⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠢⠠⠾⢧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠉⠃⠀⠀⠀⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡂⡄⠀⣀⡀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⢠⠖⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀
⠒⢀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠐⢨⡼⣉⠑⠶⠤⠤⠄⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠭⠏⠀⠀⠀⠀⠀⠀⠈⠒⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣞⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠠⠀⠈⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡘⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢠⠀⠠⠗⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠖⠂⠀⠴⠷⠚⠉⠈⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⠼⢴⡞⠀⠀⠀⠀⡠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠉⠙⠟⠀⠀⠁⠀⠀⢠⢀⡷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⠋⢇⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠀⠀⠀⢀⡤⠄⠀⢀⣀⢀⠀⠐⠒⠠⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⢀⠠⠀⠔⠂⠀⠉⠈⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠴⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄
⠁⠉⠀⠀⠐⠓⠀⠤⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠷⠍⠉⠒⢄⡠⠒⠉⠩⠾⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠄⣀⡇⠀⢀⡶⣠⢠⣨⣅⡄⣄⣶⡀⠀⢹⣀⠠⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⢀⣳⡼⡲⣼⠾⣇⣺⣗⣸⠷⣭⢖⢧⣞⡀⠀⠀⠩⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣻⢚⣾⣑⣵⠶⠿⠶⠟⣁⣈⠻⠶⠿⠶⣯⣊⣷⡓⣟⠀⠀⠡
⠀⠀⠀⠀⠀⢀⡤⠼⢤⣰⢞⢻⣅⣽⠃⡴⣖⣦⣼⣭⣽⣧⣴⣲⢦⠘⣯⣨⡟⡳⣆⡤⠧⠤⡀
⠀⠀⠀⢠⢴⡇⠀⢀⢺⡫⢱⡟⢉⡤⣤⡿⣛⣫⣲⣾⣷⣶⣝⣟⢿⣤⢤⡉⢻⡟⢝⡖⡀⠀⢸⡦⡄
⠀⠀⠀⠈⡇⠁⠘⣫⣲⡟⢻⡇⠸⣽⡿⣰⣴⣿⡿⣿⣿⢿⣿⣦⣗⢿⣯⠇⢸⡟⢻⣔⣝⠃⠈⢸⠁
⠀⠀⠀⠀⠘⢄⡀⣲⣩⣹⠟⢡⠖⣿⣨⣾⣿⣯⣿⡿⢿⣿⣽⣿⣷⣅⣿⣲⡌⠻⣏⣍⣖⢀⡠⠃
⠀⠀⠀⠀⢠⠊⠁⠽⣙⣹⣦⡘⠧⣿⢹⢿⣿⣟⣿⣷⣾⣿⣿⣿⡿⡋⣿⠽⢃⣴⣏⣋⠯⠈⠑⡄
⠀⠀⠀⢀⡇⡀⢠⣝⡝⣧⣼⡇⢰⣻⣷⢽⠻⣿⣷⣿⣾⣾⣿⠟⡯⣾⣟⡆⢸⣧⣼⢫⣫⡄⢠⢸⡀
⠀⠀⠀⠘⠺⡇⠀⠈⢼⣕⡼⣧⣈⠓⠛⣷⣽⣝⠝⢿⡿⠫⣫⣯⣾⠛⠚⣁⣼⢧⣪⠯⠁⠀⢸⠗⠃
⠀⠀⠀⠀⠀⠈⠒⢲⠚⠹⢮⣼⡋⣻⡄⠳⠯⠟⢻⣛⣟⡟⠻⠽⠞⢠⣟⢙⣧⡵⠏⠓⡖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣽⢬⢿⡩⣻⠶⣶⠶⣦⡉⢉⣴⠶⣶⠶⣟⢍⡿⡥⣯⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢘⣧⣂⠀⠀⠈⡽⢳⠵⣻⢶⡏⢽⡯⢹⡶⡟⠮⡞⢯⠁⠀⠀⣐⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠉⡇⠀⠈⠿⠙⠘⢙⡋⠃⠋⠾⠁⠀⣸⠉⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡶⣂⣀⠤⠊⠑⠤⣀⣐⢶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⠶⠦⠳⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠛⠁⣰⢶⣾⠊⢈⢈⣤⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣧⡀⢛⣉⠉⢨⡁⠛⠚⢺⡏⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⠉⠉⠛⠻⢧⠆⣄⠀⡅⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⠀⠀⠀⠀⢀⠷⢧⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢈⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⣠⠞⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⢫⠀⠀⠀⣠⠟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⣰⠏⠀⠀⢂⠈⠓⢲⠎⠀⠀⠀⠈⠑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⢀⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⡾⢫⠀⠀⠄⠈⢀⠀⠠⠁⢀⠀⢈⡀⠉⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⣠⣜⣹⠟⡉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠎⠀⠀⠀⠀⠀⠐⢀⠀⠀⡀⠈⠀⠀⠀⢀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⣀⠤⠒⠈⣩⠿⠃⠢⡀⣠⡏⠝⠉⠛⠛⠓⠒⠀⠀⣤⡟⢀⡇⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⠰⣄⠀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢞⠱⣅⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⣀⡀⠀⠁⠀⠀⠂⠀⠀⡶⠀⠀⡁⠀⠀⠀⢀⠀⠀⠀⠐⢀⠟⠳⣄⠀⠄⠀⠠⠀⢳
⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠉⠓⠶⣀⠄⠈⣀⣼⠃⠀⠀⠀⠄⠂⠀⠀⠄⠀⠈⠀⡜⠀⠀⠈⠳⣄⠀⠀⠄
⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠊⠉⠣⡈⠢⡀⠀⠀⠀⠀⡀⠰⡅⠀⠀⠀⢈⣱⡿⢛⡿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐
⠀⢸⡟⠻⣦⣄⠀⠀⠀⠀⢀⠀⠀⠀⠳⡀⠀⠙⣆⢹⣦⣠⠖⣉⠤⠚⠁⢀⣤⡶⠛⠁⣠⡞⠁⠉⠀⠀⠈⠐⠀⠈⠀⠀⠤⣴⠀⠀⠀⠀⠀⢀⡟
⠀⢸⡇⠀⠈⠛⢷⣄⡀⠀⢸⠘⡄⠀⠀⠹⣄⠀⠀⣡⠤⠒⠋⠁⣀⣴⠾⠛⠛⠒⠛⠉⠉⠳⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⡼
⠀⢸⡇⠀⠀⠀⠀⠉⠻⣦⡀⠁⢱⡄⠀⠀⠈⠲⠋⠀⢀⣠⣴⠟⠋⠁⠀⠀⠀⠀⢀⣤⠖⠀⠀⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣴⠋⠀⠀⠁⣠⠞⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠐⢰⡾⢧⡔⢃⣀⠈⠉⣧⠰⠞⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣠⣴⠾⢻⡇⠀⠀⠀⠀⣈⣢⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢻⠖⠁⠀⡼⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⠁⠀⠀⢀⣀⣴⠛⠦⠤⠚⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣀⠢⣤⡤⠖⢺⣿⠋⠉⠛⠛⠛⠛⣿⠋⠉⣿⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢻⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣇
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⡿⣆⠀⠀⠀⠀⠀⠈⢧⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡏
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠹⣆⠀⠀⠀⠀⠀⠘⡇⢸⡿⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣷
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠀⠀⠹⣆⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿
⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣀⡀⣀⣀⣼⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣿⣀⣤⡶⠟⠋⠉⠉⠉⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣿⠉⠀⠀⢀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠉⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢰⡟⠋⠁
⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣶⡾⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢂⣴⣶⡄⠀⠀⢸⣿⣿⣿⡟⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡿⠋⠙⢿⣿⣿
⠀⠀⠀⣿⠀⠐⠒⠒⠒⠒⠒⠒⣠⣾⣿⣿⡟⠁⠀⠀⢸⣿⣿⣿⠀⣿⣯⣭⣭⣭⣭⣭⣭⠟⠁⠀⠀⣠⣿⣿⣿
⠀⠀⠀⣿⠀⢨⣭⣭⣭⡍⣡⣾⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⡷⠶⠶⠶⣶⠞⠁⠀⠀⢀⣼⣿⣿⣿⣿
⠀⠀⠀⣿⠀⠐⠒⠒⢂⣴⣿⣿⡿⠋⣴⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣯⣭⣭⡽⠋⠀⠀⢀⣴⠋⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠀⠈⠉⣁⡺⣿⡿⠋⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣿⣷⣶⡾⢅⡀⣠⣴⣿⣿⡀⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣩⣭⢁⠀⣠⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⢿⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣦⣶⣶⣾⣾⣾⣿⣿⣿⠇⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⠀⠀⠀⠠⠿⢃⣀⣀⣀⡀⠀⠀⢀⡀⢹⣾⡟⠀⠀⡈⠻⠀⠀⠀⠀⠀⠈⠁⠀⣆⠋⠀⢦⣤⣀⠉⢤⠀⠙⠻⠿⠀⠀⠈
⠉⠁⠈⢣⠆⠀⠀⠀⠈⠉⠉⠉⢀⣤⡀⢀⡛⣃⣉⣤⣶⣠⣼⣄⠀⠉⠀⠀⠀⠀⠆⠀⠸⣴⡇⢠⡉⠛⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁
⠀⠀⢰⠇⢠⡞⠁⠀⢷⡀⠈⠛⠳⡄⠀⡌⣠⠹⣿⢿⣿⡿⢯⣉⣽⣧⠛⠀⠉⠁⠀⠀⠀⠘⠃⠈⠙⠂⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢲⡶
⠀⠀⠛⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣍⣠⣿⡆⢿⣇⣀⠉⠛⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠉⠓⠈⠟⠃
⠆⠀⠀⠸⣧⠐⠛⠀⠀⠀⠀⣠⠀⠛⢀⡀⠘⢿⣽⡿⠀⠉⠛⠛⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠉
⡄⠀⠀⢀⣿⡀⠀⠤⠀⢀⣠⣠⣀⠈⠀⠀⠀⠘⠋
⠷⠀⠀⢻⢆⡀⠺⠀⣠⠛⠋⠉⠉
⠀⠀⠀⢀⣬⡁⠀⠈⠀⢞⠁⢠⡤
⠀⠀⠸⣿⣯⡀⢻⣦⠀⢸⡆⠘⣿⣦⡄
⣾⡿⠀⡸⠟⣻⠿⢿⡆⠈⠁⣶⠘⡏⠁
⡿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⡄
⠁⣶⡶
⠞⢋⣠⣤⣶⣦⣤⣄
⣴⣿⣿⣀⣤⣾⠋⠁
⣧⣼⣟⠛⠻⠿⠁
⣹⣉⡉⠁
⠛⠿⣻⣷⡀
⠖⠰⠟⠋⠉
⠶⢶⡆

⢠
⣸⠇⢠⣤⡇⠀⢀⡀
⡟⠀⢾⣉⠣⡾⠛⠁
⠀⣰⢿⡏⠀⠀⠰⠤⠴
⢼⣿⡀⠑⠀⠀⠀⠠⡶
⠀⢹⡇⠀⠐⢶⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⢉⡀⠀⠀⠀⢰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣹⠀⠙⢿⠻⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣰⡇⢠⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦⣄
⠿⢰⣿⠁⠀⢙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣿
⠀⢺⡏⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠴⠛⠀⠀⠉
⠀⠈⢿⣣⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣄⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠞⠻⣷⣦⡀⠈⠰⠶⢿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠐⡿⠁⣿⡄⠀⠐⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⡀⣻⡧⠀⢰⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⠒⣦⣤⣄⣀⣶⣯⣽⡿⠛⢃⡀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣈⣤⣍⣧⣠⣎⣀⣴⣌⣰⣾⣋⣷⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡞⠒⠒⠒⠒⠒⠒⢿⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠦⠤⠤⠤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠴⠤⠤⠤⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡏⠉⠙⣷⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⣧⣤⣤⡿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡟⠛⠛⣷⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⣧⣤⣤⡇⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡟⠛⠛⣷⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⣧⣤⣤⡯⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡿⢠⣦⠀⣀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠟⠙⠞⠻⢦⠄⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈

⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣀⣃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣙⣧⡙⡇⢴⣿⠿⠟⠃⠀⠘⠖⠤⣐⠤⢀⡀⠀⠉⡠
⠀⠀⠀⠀⢈⣭⣇⣛⢰⣶⣄⠀⠀⠚⠀⠀⠀⠀⠉⠀⠀⠩⠿⠃
⠀⠀⠀⠀⡾⠟⠅⠟⡠⠙⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠄⠶⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⣤⡾⠁
⠀⠀⠀⠀⢰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣤
⠀⠀⠀⣰⣧⠁⢠⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠
⠀⠀⠀⠈⢁⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠿⠤
⠀⠀⠀⠀⠈⣄⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡟⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠠⠀⠄⢀⣀⡀⠀⠀⢀⠀⣰⣷⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢁⡀⠀⠀⠀⠀⠀⠠⠽⣿⣷⣦⣼⣓⣿⣧⡊⠀⡼
⠀⠀⠀⠀⠀⠤⠀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⣀⠀⠓⠀⠀⠀⠁⠀⠀⠀⠈⠉⣩⢜⡛⣙⡻⡥⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠂⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⠋⠻⠈⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣛⣻⣿⣛⣛⣻

⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠴⣄⢀⡴⠀⠀⠀⠀⠀⠀⡔⣛⠲⣤⠒⣑⣦⠀⠀⠀⠀⠀⠀⡠⠊⣙⢦⠀⠀⠀⣠⠔⠒⠚⠓⠲⡄
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡀⠈⡇⠀⣀⠀⠀⠀⠀⢦⣙⠋⠀⢇⠀⢛⣣⠆⠀⠀⠀⢰⠀⢃⠀⠙⠁⠀⠀⠜⠁⠈⡧⠀⠀⠀⡼
⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠠⠤⢞⢙⠦⠌⠀⠀⠀⢀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠠⠀⠀⠄⣉⠀⠀⢘⣇⠀⠀⠀⢀⣋⠅⠀⠀⠈⠄
⠀⠀⠀⣤⠸⡆⣄⠀⠀⠀⠀⠐⠀⠈⡏⠀⠚⠀⠀⠀⠀⠴⣊⣄⠈⡖⠀⣠⡐⠆⠀⠀⠀⢸⠁⡌⠀⣠⡀⠠⠀⢢⡀⢀⡷⠀⠀⠈⢳
⠀⠀⠀⢸⡇⠇⣈⣒⠀⠀⠀⠀⠴⠞⠙⠶⠀⠀⠀⠀⠀⠀⢧⣋⡠⠛⢄⣉⠝⠀⠀⠀⠀⠀⠀⠱⣌⣋⠝⠀⠀⠀⠙⠥⢄⣀⣠⠴⠋
⠀⠀⠀⠸⠧⠤⢤⣌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠳⣦⠀⠀⠀⠀⠀⠀⣄⢰⢀⡞⠋⣡⠤⢤⣄⡀⠀⠀⢠⡀⡦⠀⣰⠀⠀⢸⡃⠈⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣥⣸⡇⠀⠀⠀⠀⠤⠬⠈⢸⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⣣⣣⡼⠃⠀⠀⠀⢇⠀⠀⢰⠗⢲⡄
⠀⠀⠀⠀⢠⢄⢀⣶⠀⠀⠀⠀⢴⡋⠝⠻⣿⡷⠃⠀⠀⢀⡴⠒⠒⠀⠘⡇⠀⠀⠒⠒⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢼⣦⣤⣯⣠⠞
⠀⠀⠀⠀⣀⣿⠝⢿⣴⣢⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠈⠀⣴⠞⠉⠙⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠈⠛⢻⣳⢾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢦⣤⠤⠴⠾⠃⠀⠀⠀⠀⠀⠀⣈⣁
⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠀⢰⣶⣄⣴⡆⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢶⡤⠤⡤⠔⠁⠀⠀⠀⢬⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋⣿⣥⡀⠀⠀⠀⠀⢀⡔⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢻⢢⠀⠀⠀⠀⠀⢀⠢⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡏⠛⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠉⠀⢀⠞⠀⢣⠀⠀⠀⠀⢠⡑⢊⡅
⠀⠀⠀⡇⠞⣠⡖⠀⣀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⢌⡡⠆
⠀⠀⠀⠇⢰⢋⣴⠛⠁⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠢⠔
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠁⣸⠃⠀⠀⠀⢀⣀⠀⢠⣇⠔⠂⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡇⠀⠀⣙⣊
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠈⠑⣼⡏⢀⣤⡤⠄⠀⠀⢀⣀⡀⠉⢀⣀⠀⠀⠀⠀⡨⠒⠑⢦⡈⠁⠀⠀⢬⡥
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⣠⣤⣤⣼⣧⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠁⠄⠀⠠⠃
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠰⠋⠉⠓⡤⠚⠉⠙⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡶⠚⠲⢄⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⡀⣦⠀⠀⣠⠖⠒⠀⠀⠒⠲⣄⠀⠀⣴⢀⣠⡤⠶⠶⢤⡀⠀⠀⠀⠀⡠⠖⠛⢶⡀
⠀⠀⠀⢸⡀⣎⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⣀⠀⠙⢮⡃⠀⢿⡀⠀⠀⠀⠀⢀⡿⠀⢘⡵⠋⠀⣀⡀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣱⢀⡇
⠀⠀⠀⠈⠻⠮⣥⣤⣤⡤⠤⠖⠒⠛⠉⠁⠀⠤⠤⠀⠈⠑⠊⠙⠲⠤⠤⠖⠋⠑⠊⠁⠀⠤⠤⠀⠀⠉⠓⠒⠶⠤⢤⣤⣤⣬⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⡞⠉⠀⢠⣀⣀⠀⠀⠠⠀⠀⠀⢀⠀⠤⠐⠉⠀⠀⠀⠀⠉⠐⠂⠠⠤⠤⠄⠲⡎⡇⠀⠀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠋⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠑⢠⠇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠞⠀⠀⠀⠀⠀⠙⢄⡀⠄⠀⠀⠀⠀⠀⠀⡂⢣
⠀⢄⡀⡀⠄⠠⠀⠀⢸⠀⢀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠞⠃⠀⠀⠀⠀⠀⢄⠀⠀⠈⠳⣖⠀⠉⠀⠈⠀⢣⠸⡆
⠀⠀⠈⠉⠑⠳⠦⠤⢬⠷⠬⣌⡧⣄⢀⡀⠀⢀⣀⣀⡀⠀⠀⠀⢠⡀⠀⠱⣄⠀⠀⠑⢤⣀⠀⡀⠛⢦⡠⠖⠈⠉⠓⠓⠤⠤⠤⠬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣜⠉⢩⠀⠀⠹⠆⠨⣄⠀⠙⣤⡀⠀⠳⢤⡀⠀⠈⢻⢤⣈⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡈⢧⡀⠸⣄⠀⠈⢦⡀⠀⠱⣦⣔⣂⡛⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠛⠉⠉⠉⠉⠛⠛⠁

⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⠀⠀⠀⠀⠀⢻⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂
⠀⠹⣶⣤⡀⠀⠀⠀⠀⠀⠀⠸⠿⠦⠀⠀⠀⠀⠘⣿⣿⣿⠇⠄⠀⠀⠀⣀⣤⣤⣤⣀⣠⡴⠋⠁
⠀⠀⠻⣿⣽⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡨⣽⣿⣯⠚⣀⠖⠀⠀⠈⠻⣿⣿⣿⡥
⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣥⣴⣞⣻⣾⢷⣿⣃⠀⣙⣠⣼⣿⠟
⠀⠀⠀⠀⢻⣿⣿⣿⣷⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣭⣿⣿⣿⣿⡇⠞
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⠟⢡⠦⣭⣽⣿⣿⣿⠷⡶⠮⠙⠛
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⣹⣿⣿⣷⠴⣿⣧⠀⠈⢦⣬⣿⣿⣿⣿⣏⣠⠀⠀⣰⣷⣄⡀
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠙⢘⣩⣿⣿⣿⣿⡿⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⣼⠿⢿⣟⡻⣷⣦⣄
⠀⠀⠀⣼⣿⠿⠁⠀⠀⢀⣤⣾⣿⣿⡿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⠻⣮⣿⣿⣦
⠀⠀⠘⠋⠁⠀⠀⠀⣰⣿⣿⣿⡿⠋⠤⢾⣿⣿⠟⠛⠛⠛⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⢀⡀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢢⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⢠⠶⡄⢀⣴⣿⣾⣶⣀⢠⡶⣄⡴⡄⢀⣰⣿⣾⣷⣀⢀⡴⣄⡴⣦⢀⣰⣿⣶⣷⣅⠀⡴⣦⡴⢦⠀⣠⣿⣷⣷⣇⡀⣴⢦⡀
⠀⠘⠦⣴⣁⠀⡽⢯⠄⣈⣢⠴⠛⠷⣤⣁⠀⢼⢿⠄⣈⣡⡴⠟⠳⣤⣊⡀⢼⠿⡅⢀⣱⡤⠞⠳⢤⣎⡀⠨⠿⡇⢀⣙⡤⠾⠁
⠀⢘⣋⠹⢿⠤⠀⠀⡤⡿⠏⢙⣯⣛⠉⠿⡤⡄⠀⡤⡼⠏⢙⣫⣟⠉⠿⡧⡄⠀⡠⣼⠟⢙⣫⣝⡉⠻⣧⠄⠀⠠⢼⠿⠉⣛
⠀⣼⡛⢦⢰⠞⠦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠰⠞⢾⢠⠞⣻⡄
⠀⠈⡥⠊⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠢⡍
⠮⣿⣧⣤⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢠⣤⣿⡯
⠾⢿⡟⠙⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠘⠙⣿⠿
⠀⢀⡑⢤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠔⣁
⠀⢻⣤⡞⢸⢢⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⢺⠘⣦⣼⠃
⠀⠻⠍⣹⣼⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢹⣼⡋⠽⠃
⡠⣀⡎⠀⠛⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⠂⠈⣦⡠
⢹⣿⣿⣾⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣾⣿⣯
⠉⠛⣇⠈⣄⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣄⡌⢀⡟⠋
⠀⣤⠎⣰⢿⡉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣹⢷⡈⢶⡄
⠀⣸⠿⣯⢸⡕⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⣽⢨⡿⢿⡀
⠀⠙⣃⠚⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡞⠢⡛⠁
⢤⣶⣇⢠⠉⠹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠁⢡⣀⣷⣦
⣼⣿⡿⠻⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠻⣿⡿
⠀⠈⠣⣀⣶⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣆⡠⠋
⠀⢾⣥⡾⢹⢄⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢼⠹⣦⣽⠆
⠀⢾⡉⢳⣸⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢻⣰⠋⣹⠆
⢀⢀⡔⠉⠿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⠏⠑⣄⢀
⠳⣿⣷⣴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣴⣿⡷
⠚⠿⡏⠘⣀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣀⡘⠈⡿⠟
⠀⣠⡍⢢⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢧⠊⣥⡀
⠀⢙⡶⠋⢘⠳⠛⠀⡠⡀⠀⢠⣀⣤⠀⠀⡀⡀⠀⡀⡀⠀⢀⣤⣤⠀⠀⡀⡀⠀⡀⣀⠀⢀⣄⣠⡀⠀⡀⠀⠘⠣⢻⠈⠳⣾⠁
⠀⠸⠦⣼⣿⠉⠀⠀⠉⣿⣧⠴⠯⠶⣤⣿⠉⠁⠀⠉⣹⣧⡴⠯⠷⣤⣾⡏⠁⠀⠉⢹⣷⡤⠮⠵⢤⣾⡏⠁⠀⠈⢹⣿⡤⠾
⠀⢰⠋⡙⢄⣀⣽⣯⣀⣠⢊⡙⣶⡟⡙⢄⣀⣹⣿⣁⣀⢜⡙⣷⡞⣉⢦⣀⣹⣿⣅⣀⠜⡉⢳⡞⢉⠣⣀⣨⣿⣅⣀⡴⣉⢳⠄
⠀⠈⠛⠁⠀⢙⡿⢿⡛⠀⠈⠛⠉⠙⠁⠀⢘⡿⠿⣟⠀⠀⠛⠁⠙⠋⠀⠸⡿⠟⣟⠅⠀⠙⠋⠙⠋⠀⠈⣿⠟⢟⠇⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⣤⡐⠲⣦⣤⣦⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣶⣦⣴⢶⣢⡤⠤
⠀⠀⠀⠀⠀⡜⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⢿⣿⣿⣦⣬⣉⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⡛⢻⣭⡿⢾⣗⣿⡟⠃
⠀⠀⠀⠀⠠⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⢿⣿⣿⡿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠠⠀⠀⠀⠀⠀⠀⣹⣿⣿⣶⣌⡙⢿⣿⣶⣿⡅
⠀⠀⠀⠀⢀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢗⣉⣑⠲⠐⢠⠀⠀⠀⠀⠀⠀⠀⣻⣾⣻⠆⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⣧⣌⠻⠿⡁
⠀⠀⠀⠀⠀⠂⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣿⣿⢟⣶⣿⣿⣿⣿⣶⣤⠄⠀⠀⠀⠀⠀⠚⢞⠋⣟⠠⣀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⢿⣭⣿⣿⣿⣿⣿⣿⡿⢠⠆⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠀⠁⠀⠀⠀⠀⠀⢻⡇⣿⣿⣿⣿⣿⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠠⢷⣄⡀⠀⠠⠀⠀⣾⣿⣿⣝⣿⣿⣿⡟⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠱⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢀⠀⠈⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠀⠉⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⢀
⣀⣐⣒⣒⣒⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣠⡔⠀⠀⠀⠀⠀⠀⠀⣀⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣀⡀⡄
⠀⠀⠀⠀⡖⠀⠀⠀⠀⠃⢀⠛⠐⠀⠀⠀⠀⠀⠀⡀⡉⠙⡄⡠⢀⠉⠂⠀⠐⠈⠀⢀⠡⠏⠩⢀⡀⠀⠀⠀⠀⠀⠀⠙⡀⠸⠀⠀⠀⠀⢰⠄
⠀⠀⠒⠒⠛⠚⢗⠒⠒⢚⠺⣷⢒⣚⠿⡃⠀⠀⠘⡿⠁⢀⣀⠀⠜⠙⠗⣿⠺⠇⠣⠈⣀⡀⠀⠻⠃⠀⠀⢘⠿⣓⡒⣺⠗⠓⠒⠒⡺⠗⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠘⠋⠏⠉⠉⠉⠨⠶⠂⠀⠀⠀⠠⢠⣄⠀⠈⠠⡶⠄⠈⠀⠁⠀⠶⠆⠁⠀⢠⡄⠆⠀⠀⠀⠈⠶⠏⠉⠉⠉⠹⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⢠⣄⡄⣀⣀⣀⠰⢶⡄⠀⠀⠀⠀⠘⠛⠀⠀⡘⠷⠂⠀⠀⠀⠐⠾⠇⡀⠀⠘⠃⡅⠀⠀⠀⢀⡶⠆⠀⣀⣀⣠⣀⡴
⠀⠀⠀⠠⢠⢤⣦⠁⠠⢤⢴⣿⠀⠁⣤⣄⠐⠀⢠⣵⡀⠈⠉⠁⢠⡤⡦⣶⢴⡆⡤⠀⠉⠁⠀⣰⡄⠀⠀⢠⣤⡄⠁⢼⡦⠄⠤⠀⢴⡤⣤⠤⠄
⠀⠀⠀⠀⠧⠀⠀⠀⠀⡄⠈⣡⠤⠀⠁⠀⠀⠀⠀⠁⣁⣒⠂⠑⠈⠀⠤⠀⠢⢀⠈⠈⡐⢂⣈⡈⠁⠀⠀⠀⠀⠁⠠⢤⠁⢠⠀⠀⠀⠀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣙⠣⠀⠀⠀⠀⠀⠀⠀⠉⠉⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠉⠃⠀⠀⠀⠀⠀⠀⠢⣋⠣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈⠛⠛⠞⠛⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠔⠒⠦⡀
⠀⠀⠈⠀⠂⠒⠒⠓⠚⠚⠑⠒⠚⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠁⠀⠀⠀⠀⠀⠠⠀⢼⠉⠁⠀⠀⠀⠉⢹⠤⠠⡀
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⢸⠓
⠀⠀⠠⠀⠖⠒⠒⠖⡲⠲⡖⠒⠰⢒⠒⠰⠀⠆⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠔⠡⠄⢸⠀⠀⠀⠀⠀⠀⢸⠀⠤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠿⠚⠑⠾⠂⢠⠀⠀⠀⠀⠀⠀⡀⠂⠚⠀⢻⠀⠀⠀⠀⠀⠀⢸⠉⠀⠂⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠍⠳⡌⠀⢾⠀⠀⠀⠀⠀⠀⢸⠆⠌⡴⠘⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠁⠀⠐⢀⠄⠀⠀⠀⠀⠀⢸⠀⠀⡀⠹⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⠶⠾⠧⠒⠒⢀⣠⣔⡐⠒⠢⠿⠦⠾⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠍⣠⡴⠃⠀⢾⠀⠀⠀⠀⠀⠀⢸⠆⣢⠳⢤⣈
⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣶⣦⡀⠀⠀⠀⠀⠤⠦⠤⣼⠀⠀⠀⠀⠀⠀⢸⡨⠤⠤⠌⡀
⠀⠀⠀⠀⣠⣾⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣄⠀⠀⠀⠂⠐⠂⢸⠀⠀⠀⠀⠀⠀⢸⠀⠒⠠⠊
⠀⠀⠀⠀⢈⣾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⢷⡎⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⡔⠁
⠀⠀⠀⠰⣧⣿⣾⣟⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣷⡗⠀⠀⠀⢀⠄⢸⠀⠀⠀⠀⠀⠀⢸⠀⠤
⠀⠀⠀⠘⢷⣷⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣽⡷⠇⠀⠀⠀⠐⠀⢻⣀⡀⠀⠀⠀⣀⣸⠓
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣧⣾⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⣽⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠾⢶⡤⠤⠄⢘⠹⠍⣁⠠⠤⣴⠾⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣻⠋⠀⠈⠀⠀⠀⠀⠀⠀⠠⢠⠀⠉⠠⠙⣿⠿⠁⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⡀⢤⡢⡀⠑⠄⠀⠀⠂
⠀⠀⠀⠀⠀⡄⠠⣄⢮⠒⠦⠑⠌⠋⠀⠈
⠀⠀⠀⠀⠀⠙⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⣾⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠚⢌⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠈⠀⠁⠀⠀⠄⠀⢀⠔⡠⠀⡴⢿⡟⠁
⠀⠀⠀⠀⠀⠀⡄⡒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢁⠈⣰⠎⡠⠋
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⠠⠤⠀⠒⠊⠁⠀⠀⠀⠠⠈⠀⢁⡴⢃⠜⠁
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠋⠈⠉⠁⢀⣀⣀⠠⠄⠀⠐⠂⠀⠀⠀⠔⠁⢊⡠⠃⣠⠋
⠀⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠒⠂⠁⠁⠀⢀⣀⣀⡀⡀⠤⠒⡰⠀⠔⣠⢟⢀⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠒⠂⠊⠁⠀⠀⠀⠀⠀⢀⠀⠠⢲⡴⣏⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠤⠤⠤⠀⠂⠉⠁⠀⢂⠀⢠⡎⣠⠯⠤⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠤⠤⠄⠐⠂⠸⠣⣀⡴⣧⠞⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠠⠤⠀⠐⡆⠀⡠⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⠀⠀⠤⠤⠴⠟⠡⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⢰⠖⠒⠚⠻⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡀⠀⠀⠀⣀⣀⠤⠔⠒⢛⣋⣉⣩⣥⣥⣤⣶⠾⡿⠽⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣝⣒⣪⡭⠤⠖⢒⠚⠋⠭⢍⣀⣀⣠⣤⣤⣔⣶⣶⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠛⢉⣐⣉⠠⠎⠁⠚⠋⠏⠋⠀⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠄⠄⠤⠄⠀⠀⠀⠀⠀⠄⠔⠔⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡀⠀⢀⣤⡀⣄⢠⠀⢦⡤⣶⡄⢠⣄⡴⠀⢶⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⠀⠀⢺⣠⡾⢹⠹⠃⠘⠇⠏⠓⠞⠙⠳⠖⠘⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣤⡤⠤⠤⠤⠴⠒⠒⠒⠒⠒⠒⠛⠛⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠤⠤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠚⠉⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠶⠶⠶⠒⠒⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠠⠦⠤⠄⠀⠀⠀⠛⠒⠒⠉⠛⠂⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠖⠒⠛⠛⠋⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⠉⠉⠉⠉⠀⠀⠀⠀⢠⣤⡤⠴⠖⠚⠛⠃⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⡀⠀⠀⢀⣀⣠⡤⠴⠒⠛⠛⠋⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠂⠀⠈⠉⠀⠀⢀⣀⡀⠀⠀⠀⠈⠙⠂⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠒⠚⠉⣉⣀⣤⠤⠶⠆⠀⣀⣀⣤⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠐⢛⣋⣩⡥⠴⠶⠒⠛⣫⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⠖⠚⠛⢉⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠲⠆⠀⠀⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣯⣤⣤⠤⠤⠶⠶⠚⠛⠋⠉⠁⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⠛⠃⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠠⠀⠀⠀⠐⠒⣂⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣠⠦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢧⣤⠼⠀⠀⠀⠋⠙⠉⠉⣉⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⣀⣀⣤⣤⠶⠶⠞⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁

⠀⠀⠀⠆⠻⠂⣤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣠⣤⡀⠀⠴⠂⠀⠀⠀⢀⡜⡿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠖⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴
⠶⣶⣿⣕⣽⣿⠀⠒⠋⠀⠀⢠⢏⡾⢡⢫⡟⡴⡦⠀⠀⠀⠀⠀⢀⣴⡿⠛⣿⠟⢀⣴⠾⣿⣿⣿⠇⠀⠀⠀⣀⣠⣤⣴⢶⣶⠾⠟⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠉⣿⣿⡟⠀⠀⠀⠀⡰⣣⡟⡱⣱⢏⢞⡽⢡⢶⠀⠀⠀⣠⠞⠋⠓⢚⣩⠾⢿⣁⣀⡼⠟⣋⣤⣴⣾⣿⣿⡿⠋⠀⢸⣏⠀⠀⣠⣿⣿⣿⡿⠋
⠀⠀⠀⣿⣿⠁⠀⠀⢀⡜⣵⣟⢜⡼⣣⣫⡞⡱⢣⠟⣰⣶⠰⠋⠀⣠⡴⠋⠀⠀⣀⣬⣴⣾⣿⠿⠿⠿⠿⠿⠿⠷⠼⣀⣀⣙⣛⣛⣛⣉⣉⣀⣠⣤⣴
⠀⠀⢰⣿⡇⠀⠀⢀⢞⣾⢯⣪⢟⣵⣽⢋⢜⡵⣫⣪⣾⠋⣀⡠⠞⠁⢀⣠⡶⠟⠛⠉⠁⠀⢀⣀⣤⣤⣶⣶⣿⣿⠟⠉⢉⣿⠋⠉⠉⣿⣿⣿⣿⡿⠋
⠀⠀⣾⣿⠀⠀⢠⣿⣿⣳⡿⢫⣮⡿⣵⣵⣫⢞⣿⢟⡵⣫⡿⠃⠠⠞⠉⠁⠀⠀⣀⣤⣶⣿⡿⠿⠿⠿⠿⢿⣿⣧⣐⡆⠈⠿⣷⣶⣾⣿⠿⠟⠋
⠀⢠⣿⠇⠀⣰⡏⢙⡻⢿⣷⣿⣯⣫⣿⣿⡿⣻⢕⣥⠾⣋⣤⣤⠀⠀⢀⣤⠶⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣭⣭⣤⣤⣤⣤⢤⣤⣤⣶⣶⣶⣶⡶
⠀⣼⡿⠀⢰⣿⣿⣿⣷⣶⡙⢿⣿⣿⢿⢯⣪⡶⣋⢵⣺⡿⣟⣡⣄⠚⠉⠁⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⢾⣧⣀⢀⣽⣿⣿⣿⡿⠋
⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣯⣤⠹⣿⣷⣯⣷⡯⣟⡯⢗⣫⡵⠞⠁⢀⣤⠶⠛⠋⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⣙⣛⣋⣀⣀⣙⣛⣛⣛⣛⣋⣉⣀⣀⣀
⢰⣿⣇⠀⢸⣿⣿⢋⣍⢻⣿⣷⡆⢿⣟⣯⣷⣯⣷⠾⢯⣷⣾⡿⠂⠈⠀⢀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⢛⠉⣹⣿⠛⠙⠻⣿⣿⣿⣿⣿⣿⡟
⣸⣿⣿⣄⠈⢻⣿⣦⡼⢸⣿⣿⠆⣸⣿⣯⣭⣴⡖⠛⠯⣭⣤⡄⠠⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⠉⠙⠛⠻⠼⠃⠛⠿⣦⣤⣶⣿⣿⣿⣿⠿⠋
⢿⣿⣿⣿⣷⣤⣬⣭⣴⣿⣿⣿⠄⣿⣿⣷⣶⠶⠿⠿⠟⣍⡉⢀⣠⡤⠴⠶⠶⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢙⣿⣷⣶⣶⣶⣬⣥⣉⣀⡀
⢸⣿⣿⣿⣿⣿⡏⡛⠿⠟⠿⢀⣾⣿⣿⣛⣛⣛⠿⢿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣇⢲⡄⢸⣿⠉⠈⠉⢻⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠻⣿⣿⣿⣿⣇⢹⣶⣶⣿⣿⣿⡿⣿⣭⣛⣩⣭⠙⠉⠈⠉⠉⠙⠛⠛⠛⠻⠿⣿⣶⣶⣶⣶⣦⣤⣤⣍⣉⠀⠈⠻⢷⣶⣴⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠈⠛⠻⠿⠿⣿⣿⡿⣿⣿⢯⣟⠶⠿⠆⢩⣥⠤⠤⠶⠶⣶⣶⣶⣤⣤⣤⣄⣀⡈⠉⠛⠿⣿⡟⣍⠉⣽⣿⠿⠷⣶⣤⣭⣉⡉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣶⣦⣬⣙⠛⠀⢿⣧⡀⠀⠀⢹⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠩⡈⢿⣿⣶⣤⡙⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⣄⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠷⡀⠻⠣⠸⠀⣹⠞⠑⢶⠖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⡹⠟⠛⠛⠻⢄⠀⠀⠘⠄⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠀⠀⠈⢿⣷⠦⣸⡀⠠⡗⠀⠀⠀⠀⠈⠧⠀⠀⡀⠀⢠⠟⠛⠙⢶⡤⢤⣤⠖⠚⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠓⢦⡀⠀⢱⣤⣈⣷⣦⣿⡆⠀⢀⣀⠀⠀⠀⣦⣷⣴⡇⠀⠀⠀⢈⣀⣈⣿⣦⡞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣄⣿⣿⣾⠉⠛⢻⣿⢿⠟⢳⣤⣇⠈⠑⣆⢀⡀⠉⠹⣿⣆⣠⠞⠉⠉⠉⠙⣿⡉⠉⢙⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⣸⠁⠀⣠⠾⠿⣶⠀⠀⠈⢓⡟⢻⠦⣾⠿⢿⡀⢀⡦⠤⣴⣿⠤⠞⠋⢁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⠷⡄⠀⠀⠛⠀⠴⠁⠀⢠⠟⠛⣏⣸⣋⡉⠻⡄⠀⠀⠀⢹⡟⠀⠀⠘⠹⢓⣦⣾⡉⠁⣹⠟⠉
⠀⠀⠀⠀⠀⠀⣀⣤⡔⢲⣧⠀⠀⠀⠀⠀⠉⠐⠛⡀⠀⢄⡠⠴⠿⣄⢀⡏⠁⠈⠉⢳⡘⣆⠀⠀⣰⠀⠀⡤⠂⠀⠈⠉⠛⣇⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⣑⣺⣧⣀⣀⡠⠲⣤⣬⣐⣛⣋⣡⠾⠇⠀⠀⡼⠋⣱⣤⠶⣤⣸⣧⣿⣷⣿⣷⡄⠀⠀⣀⣤⣄⣄⣴⣧⣤⣀⡀
⠀⠀⠀⠀⣀⣤⣶⡊⣉⣩⠿⠟⠛⢧⡀⢠⠞⠉⠀⠀⠀⠀⠀⢠⡞⠀⠀⠻⣤⣤⡄⡈⠋⠰⣶⣤⡻⣿⠋⠉⠉⠀⠈⠹⣿⣟⠀⠀⠉⠱⣦⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠓⠳⠶⢦⣠⠞⠛⠓⠖⠋⠀⠀⠀⠀⠀⠻⠦⢤⡤⠤⠀⢉⣁⣾⡀⠀⢀⠀⠀⠀⠈⣻⣿⣿⠟⠉⠉⠛⢳⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⢬⣿⣏⡀⠀⠀⢹⡆⠀⠀⣿⣿⣟⠻⢷⡶⠶⠤⠚⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣾⣃⣀⣤⣿⣿⣿⡅⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⣿⡓⠢⠤⢤⣙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠈⢣⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⡤⠤⠶⠶⠶⠒⠒⠒⠒⢛⣛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣒⡛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢋⣭⡅⠀⣷⡤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡥⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢸⡥⢋⡴
⠀⠀⠀⠀⠀⠀⠀⡼⣇⠉⠛⠿⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠈⣷⠏⡰⠂
⣤⠤⠤⠤⠶⠖⢺⡷⠄⠀⠀⢠⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠞⣡⠄
⢻⠀⠀⠀⠠⢯⣿⣙⠀⠀⢠⣟⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⢸⡇⠀⠀⠐⣾⢧⡈⠀⣰⣏⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⣠⠀⠀⠀⠀⠀⠀⢀⡞⣡⣍⠋⢽⠋⡛⣦⡀
⠈⡇⠀⠀⣉⣟⠦⠀⣴⠧⠶⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠆⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠀⣧⡞⢡⠄⠀⠀⠀⠀⣰⢋⡞⢹⡃⠀⡸⢛⡿⣿⡇
⠀⡇⠀⠠⢼⡏⠁⡼⠷⠖⠀⢛⣋⣋⣉⣩⣭⣥⠤⠤⠶⠶⠒⠒⠛⠛⠉⣉⣉⣁⣀⣄⠀⠀⠀⠀⢻⡴⢋⡄⠀⠀⢀⣼⡵⠋⣴⠏⠳⣞⣱⢋⡴⣹⠃
⠀⣧⠀⢐⣺⠀⣼⡛⠉⠀⠀⢉⣉⣁⣀⣤⣤⠤⠤⠴⠶⠖⠒⠚⠛⠉⠉⢉⡉⠀⠀⠀⠀⠀⠀⠀⢸⣥⠏⡤⠀⣠⢿⡟⣡⠞⠁⣤⠳⢤⣩⠟⠛⠁
⠀⢿⠀⢨⣽⣼⡋⠁⠀⠀⠀⠉⣉⣉⣁⣀⣤⣤⠤⠶⠒⠒⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⣡⠞⠁⣼⢾⠁⢀⡰⢬⣑⣲⠋
⠀⢸⡀⠐⣿⣯⠁⠀⠀⠀⠀⠈⠉⠉⠉⢁⣀⣀⣠⣤⡤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⣛⢲⡾⠉⠀⡐⢦⣙⣲⠟⠁
⠀⢸⡇⢈⣿⠆⠀⠀⠀⠀⠀⠐⠛⠛⠋⠉⠉⠁⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠴⠶⠖⠒⠀⠀⠀⠀⠀⢸⣷⡵⠋⠀⠀⠦⣙⢢⡼⠃
⠀⠈⡇⠀⢾⡆⠀⠀⠀⠀⠀⠰⠶⠶⠒⠚⠛⠛⢋⣉⣉⣡⣤⣤⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢤⡙⠲⣤⠏
⠀⠀⡇⠀⣩⡇⠀⠀⠀⠀⠀⠀⠶⠒⠒⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⡙⠦⣬⡟⠁
⠀⠀⣷⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡰⢜⡲⣭⡶⠋
⠀⠀⢻⠀⢈⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠹⢤⣙⣲⣿⢋⡞⠁
⠀⠀⢸⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡀⠀⡀⠀⠀⠀⠀⠶⠤⠤⠶⠚⠀⠀⢠⡏⡀⢬⣳⠞⠁⢹⠏⡴⠂
⠀⠀⠸⡇⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡾⢁⡼⢁⣾⢁⡖⠀⣴⠀⠀⡀⢠⠦⣤⣯⢗⡿⣋⡵⠀⠒⠸⢟⡱⠋
⠀⠀⠀⣧⠀⣩⣧⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⣡⠞⠧⠋⠳⠛⠧⠊⠙⠒⠋⠉⠉⣀⣀⣀⣈⣠⣥⣽⡤⠚⣁⣟⡟⣡⠆⣰⠂⣠⠀⣀
⠀⠀⠀⢻⠀⠐⣻⠀⠀⠀⠀⠀⣈⣘⣤⣞⣤⣥⣤⠤⠴⠶⠶⠶⠒⠚⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡼⢁⡞⢁⠞⢁⡼⠁⡴⢃⡤⢀⠀⡀
⠀⠀⠀⢸⡆⠠⢽⡆⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠏⣰⠋⣠⠟⣠⠞⣠⠏⡴⢋⡜⢡⡞⣠⠆⡀
⠀⠀⠀⠀⣇⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⡴⠁⠀⠁⠀⠁⠈⠁⠞⠀⠋⠀⠏⣰⠃⡼⢡
⠀⠀⠀⠀⢻⠀⢩⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⣠⠊
⠀⠀⠀⠀⢸⡆⠐⣺⡄⢧⠻⠰⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠴⢶⣒⣒⣚⣛⣿⣋⡟⢉⡟⢁⡴
⠀⠀⠀⠀⠀⣇⠀⠺⣧⣤⣤⣤⡤⠤⠤⢴⣶⣶⣒⣒⣺⣿⣭⣭⠭⠤⠶⠖⠒⠚⠋⠉⠉⠉⢁⣀⣀⣽⠋⣠⠏⠀⠋
⠀⠀⠀⠀⠀⣿⠀⠐⠒⠒⠒⠚⠛⠋⠉⠉⠉⣉⣉⣀⣀⣀⣠⣤⡤⢤⠶⢶⡖⢒⡾⢛⡿⢋⡿⠉⡽⠁⡴⢡⠖
⠀⠀⠀⠀⠀⠸⠶⣶⢶⡖⣲⠞⣻⠛⣻⠋⣹⠋⣹⠋⣠⠞⣱⠋⣰⠋⢰⠏⠠⠏⠀⠞⠀⠛⠀⠈⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢟⣛⣭⣽⣿⣿⣶⣤⡀⢀⡻⣃⠀⣠⣴⣾⣿⣿⣭⣍⣛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢫⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣮⠻⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠷⠌⠻⠿⠿⠿⢟⣵⣿⡿⣫⡻⣿⣷⣝⠻⠿⠿⠿⠋⠴⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠐⠆⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⢀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡋⠉
⠀⠀⠀⠀⠀⢸⡡⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⠦⠼⠂⠒⠀⠀⠀⠀⠀⠜⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⡿⣣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⢄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡘⢃⡞⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠌⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠔⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⢀⣄⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣶⣤⣤⣄⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⢀⣾⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⢀⣾⡿⠁⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⢀⣾⡿⠁⠀⢰⣿⣿⣿⣿⠋⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⢀⣾⡿⠁⠀⢠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⢀⣾⡿⠁⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⢺⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠻⣿⣿⣿⠟⠀⠀⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠉⠻⣿⣦⣀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣤⣤⡀⠀⣀⡀⠀⠈⠻⢿⣦⣄⠀⠀⠙⢿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣀⡙⢿⣶⣄⠀⠀⠙⠻⣷⣦⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣿⣦⣄⣀⣼⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⣿⣿⠟⢿⣶⣴⡿⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣈⠓⠲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠻⢿⣿⣿⡿⠟⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠐⣛⣲⣶⠄⠴⣶⣒⠂⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠼⢄⠠⠄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠄⠀⢀⣤⠤⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣄⠀⠀⠂⠀⢀⣠⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣿⠉⢻⣿⣷⣦⣤⡤⢞⡽⠁⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠚⠁⠀⠀⠀⠘⣧⠀⠙⠦⠉⠁⡤⠊⠀⠀⠀⠀⠀⠈⠙⠲⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢤⡀⡼⠁⢸⠀⠀⠀⠀⠀⠀⢹⣇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠤⠀⢤⠖⠀⢿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⠀⠀⡈⠻⠄⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⣤⣤⠼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠈⠀⠀⠀⠂⢤⠈⠀⠈⠛⠛⠛⠛⠒⠒⠒⠚⠛⠛⠓⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛
⠀⠁⠀⠀⠈⠂⣄⣀⣀⣀⣤⣤⣤⣾⣿⣿⣷⣄⣀⣁⣖⢢⠄⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣵⣟⡓⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠐⠂⢁⠜⣡⡾⠍⠉⠉⠑⠀⠀⠉⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠛⠛⣿⠟⢿⣿⠿⡿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⡠⠠⠐⠂⢉⠴⣡⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣄⢀⢠⠀⠀⢩⠀⢘⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⠞⠁⠀⠀⢀⡴⣢⡾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣼⣿⠉⠁⠀⠈⢹⡞⠀⠀⠠⠀⡆⣞⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡼⠁⠀⠀⣤⡴⢋⣴⣯⣷⣇⠂⠐⠀⢀⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⣀⠀⢃⡄⣿⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣞⡵⠋⠀⠀⢀⡼⢋⣴⣿⣿⣿⣿⣿⠿⡿⣶⣿⣿⣴⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⠎⡇⣏⢹⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⢠⣤⠞⣵⣿⡿⠿⣏⣧⣾⣯⣴⣵⣩⠥⣿⣿⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣤⡷⣿⢸⣿⢧
⠀⠀⠀⠀⠀⢠⡏⠀⢀⣠⣾⢞⣵⠞⣛⠛⠿⠛⡛⢿⡯⢍⣙⡛⠿⢾⣿⣿⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⣧⠀⣯⢱⡟⣿⢿⢸
⠀⠀⠀⠀⢠⣏⠀⠀⢀⡿⢫⣿⠁⠀⠀⣹⠁⢿⠋⠁⠈⠂⠉⠉⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡠⢤⠀⠀⢸⣿⣦⣽⡈⣧⣿⣾⡇
⠀⠀⠀⣠⠟⡘⠀⢀⣾⣵⠏⠸⣦⣖⡒⡛⠀⢟⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠣⠜⠀⠀⠸⣸⡿⣿⣇⣿⣿⡿⠅
⠀⠀⠀⢧⣊⣤⣶⡿⣿⣿⠁⠀⠙⢿⡙⠛⣿⣿⣿⣾⡅⠀⠒⠓⠒⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⢤⣦⣼⠀⠀⠀⠀⢠⣟⣿⣿⣾⣿⣷⡿⣳
⠀⠀⠀⣠⠟⣩⣎⣴⡿⠃⠀⠀⠀⠀⠉⠳⣬⣉⣿⣿⣷⣶⣶⣶⣴⣶⣶⣦⣽⣿⣿⣿⣮⣶⣶⣶⣾⣿⣿⣦⠤⡄⣄⠉⣉⣙⠛⣛⠿⢾⣾⣿⣽⣿⣯⣿⠾⠋
⠀⢀⣴⣷⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⣿⢿⡿⠧⠬⠉⠭⠿⠽⠏⠛⠛⣿⠛⠛⠛⠿⠉⠉
⢀⣾⠟⠁

⠀⠀⠀⢀⣠⡎⢭⠆⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⢭⠆⠀⢀⠤⠤⡄
⠀⢐⢀⡊⡀⠑⢀⣆⠀⠀⠸⢇⠜⢀⠐⡖⢄⣠⣄⠀⠀⠀⢔⢀⡊⡀⠑⢀⣆⠀⠀⠸⢇⠜⢀⠐⡖⢄⣠⣄
⢆⠞⡑⠢⡉⠓⠢⡌⠁⠐⣦⠀⠋⠤⢱⢃⡌⠀⡞⢀⠐⢆⠞⡑⠢⡉⠓⠢⡌⠁⠐⣦⠀⠋⠤⢱⢃⡌⠀⡜⢀
⠼⠀⣁⣠⣃⠀⣬⡁⣶⠲⠉⠗⢹⣎⡈⣾⠋⣱⠗⢏⡃⠼⠀⣁⣠⣃⠈⣬⡁⡴⠲⠉⠗⢹⣎⡈⣾⠋⣱⠟⢏
⠌⢁⠒⠔⡂⣻⠁⢿⣊⡀⢖⣲⢀⢴⡃⣚⢆⣄⡴⡦⢻⡌⢁⠒⠔⡂⣻⠁⢿⣊⡀⢖⣳⢀⢴⡓⡚⢆⣄⡴⠦
⠂⠚⢄⢀⠢⡁⣨⡆⢮⣤⠀⣄⢰⡖⣛⠆⢔⣩⠛⣀⠩⠂⠚⢄⢂⡢⡁⣨⡆⢮⣤⠀⣄⢰⡖⣛⠏⢔⣩⠛⣀
⢥⠑⠐⠉⠉⠀⠃⠘⠪⠍⠛⠅⢉⢤⡈⢁⠈⠁⠀⠁⡤⢅⠑⠐⠉⠉⠀⠃⠘⠪⠍⠻⠅⢉⢤⡈⢁⠈⠁
⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⣃⠄⠀⠀⠈⠠⣙⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⣃⠄⠀⠀⠈⠤

⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⡀⣠⠖⢠⣠⠒⣆⠀⡀⠀⠀⠀⠀⠀⢀⢄⣄⠤⡖⠀⣦⠄⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄
⠀⠀⠀⢠⡑⢿⣭⣽⢷⣭⡿⠚⡡⡀⠀⠀⠀⠀⢸⡈⠁⣦⡳⠴⣣⡆⠉⣰⠀⠀⠀⠀⠀⣀⣀⡉⠉⡄⢠⠉⢁⣀⣀
⠀⠀⠀⠢⠄⡶⠈⣏⡘⡍⢴⡢⠤⠃⠀⠀⠀⠀⠈⠿⡷⠾⡟⠈⡿⠶⡯⠿⠀⠀⠀⠀⠈⠽⠛⠟⣋⠁⠈⣙⠻⠛⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠃⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡺⢓⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢢⡔⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣘⠂⡓⢺⠑⣓⡄⣄⣀⠀⠀⠀⠀⠀⡶⢶⡷⣍⣩⢿⡦⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠐⠀⠀⠀⠹⠟⠋⠉⠀⠀⠀⠀⠀⠟⠁⢙⣸⣇⡋⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠖⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢷⡾⠣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡴⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠀⡄⠶⠀⡀⠤
⠀⠀⠀⠠⡄⠀⢰⣣⢻⢰⠀⠀⣠⠄⠀⠀⠀⠀⠀⢀⢬⡚⣣⣝⢃⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠃⠀⠐⠙
⠀⠀⠀⠁⠖⠒⠺⣇⠟⡾⠒⢒⠒⠁⠀⠀⠀⠀⠀⡿⠾⣟⣩⣇⡟⠾⢵⠀⠀⠀⠀⠀⠀⠀⠙⠀⢙⡢⠀⣴⡋⠀⠛
⠀⠀⠀⠀⠈⣁⣿⠿⠀⠿⣯⣘⠀⠀⠀⠀⠀⠀⠰⢗⣲⡷⢪⡰⢷⣖⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⡤⡌⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠘⠃⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣤⢦⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢖⠀⠀⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠟⠲⢍⢋⠵⠚⠿⣤⠀⠀⠀⠀⠀⠰⢉⣻⡬⠌⠮⣬⣛⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣈⢾⣿⢋⡀⠀⠃⠀⠀⠀⠀⠀⠀⠉⢲⣊⡌⢀⢲⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢃⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡿⡹⠂⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡠⠀⠀⠀⠀⣀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⡡⢀⠀⠀⠀⠀⡅⠑⠄⠈⡿⢋⡠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⣂⡁⠀⠀⣦⣄⠱⡀⢨⡔⢠⡁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡿⢐⡀⠀⠀⣿⣿⡆⠈⢹⠗⢁⣀⡀⠀⠀⢀⠠⠴⠀⠀⡀⠌⢒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣀⠀⠰⣦⠀⠀⠀⠀⢐⣿⠄⡃⠀⠀⢈⠙⢇⠀⡎⣴⣿⣿⠀⢀⠒⡁⠀⣠⠔⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣑⢄⠀⠆⠀⢠⣄⠘⢽⡆⡈⠀⠀⢀⠉⢢⢱⣸⣿⠟⠁⢀⠂⠀⠀⣰⠕⠊⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠳⣜⠀⢘⠋⠀⡒⣶⡡⠀⠀⠀⢱⠞⠚⠓⠠⠄⣀⣌⠀⠀⡞⠁⣀⣀⡔⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡀⠀⠈⢃⠠⠀⢰⣶⠻⣌⠅⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠑⢞⠁⠀⡠⠊⠀⠠⠊⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠁⠐⠚⢳⡀⠀⣆⠬⠛⠞⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠇⠛⠤⡀⠀⣃⣠⢊⣀⡔⠈⠉⢁⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠙⠡⢄⡀⠀⠀⢣⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠈⠂⣀⠄⠀⠀⠀⠙⠻⢤⠀⠠⣁⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡉⠐⠄⡈⠉⡰⠋⠀⠀⠀⡠⠒⠉⠉⠉⠀⠒⠇⢀⠤⠤⡀⠀⠈⠂⠀⠀⠀⠀⠀⠃⠱⢄⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣀⢘⡏⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡠⠴⢁⠀⠀⠈⠆⠀⢸⠃⠢⢄⠀⠀⠘⠐⢖⠒⢤
⠀⠀⠀⠀⠀⣀⠄⠐⠐⢒⠀⠒⠨⢟⡁⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡎⠀⠀⠀⢡⠀⠀⠸⢀⠾⠀⠀⠀⠑⣀⢏⠑⠌⠑⠀⠃
⠀⠀⣠⠖⠁⠈⠢⣀⠀⠀⠱⣀⠀⠀⠈⠑⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⡀⠀⠙⠁⠀⠠⠋⠁⠀⡇⠀⠀⠀⠘⠀⠑⠼
⠀⠜⡡⠔⠒⠈⢉⣉⡭⠭⠒⠒⠳⢤⣤⡀⠵⠀⠀⠀⠀⢂⠀⠀⠀⢀⠔⠚⢄⠀⡠⠊⠀⠀⠀⢠⠁⠀⠀⠀⠀⡗⠀⠀⣀
⡼⠬⠄⠀⠠⠖⣉⠀⠀⠀⢀⠤⠂⠀⠀⠀⣀⠕⣄⠀⠀⣀⠟⠐⠂⠉⠣⡀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠘⠀⣤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠃⠀⠀⠀⠐⠈⣔⣪⡗⠟⣍⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠄⠤⠊⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣲⠾⢭⠆⠈⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡨⠟⡈⠄⠀⠀⡠⠒⠉⠑⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢾⠑⠐⠁⠀⢠⠊⢀⡀⠤⣲⠋⠀⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⠿⢠⠁⠀⠀⢰⠋⠁⠀⢀⠜⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡗⠄⠉⠀⠀⠀⡌⠀⡀⠰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢔⣸⡗⡄⠀⠀⠀⠀⠀⡏⠁⠀⠏⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⢠⣫⡟⠉⠁⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠠⣈⠌⠁⠀⠀⠀⠀⠀⠀⠈⠀⡆⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠰⣆⠀⠀⢀⠏⢠⠞⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀⠀⠀⠘⢦⡀⡄⣿⠀⢀⡟⠠⠃⢀⡴⢛⣤⠆⠀⠀⠀⠀⠀⢀⣠⣾⣧⣄⡀
⠀⠀⠀⠀⠢⣬⣷⣤⡙⢾⡶⣀⠀⠀⢹⡀⠀⠀⡜⣴⢣⢖⣩⠶⠋⠀⢠⠖⠀⠀⣴⣾⣶⣿⣬⣭⣬⣿⣷⡄
⠀⠀⠀⠀⢤⡈⠙⠻⢷⣤⡙⢿⠦⣀⠀⣏⢸⡄⣻⣞⡥⠚⠡⠐⣊⡠⠄⠀⣀⢼⣭⣍⣉⣉⣉⣛⣛⣛⣛⣻⣀⡤
⠀⠀⠀⠀⠀⠉⠓⠦⢄⡉⠻⢦⡳⢜⣧⣿⣌⣿⠿⣋⡠⠖⠛⢀⡁⠀⠀⠀⢿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡑⠂⣁⣀⣼⣿⣿⢿⣿⣅⠉⠛⠃⠀⠀⠀⠀⠀⠈⠣⣼⠇⠀⠷⠀⡴⠀⢀⣦⣾⠶⢯⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠿⣫⣿⣿⢿⡝⣳⣷⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⡳⣦⣤⣴⣾⡿⠫⠜⠛⠓
⠀⠀⠀⠀⠀⠀⡠⠚⢀⠖⠀⢲⠃⢸⣿⣾⡿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣿⠟
⠀⠀⠀⠀⣠⠞⠀⢠⠎⡜⢠⡇⡌⣣⢹⡟⠷⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠘⠃⠀⢠⠆⡰⠀⣾⠠⢰⠇⡜⠹⠆⠀⢹⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⢠⠃⣰⠃⢰⡟⢠⡟⣰⠃⠀⠀⠀⣼⡏⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠠⠋⠰⠁⠀⡎⢠⢏⠁⠟⠀⠀⢀⣰⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠁⠀⠀⠀⡸⢠⠉⠀⠀⠀⠀⢠⣿⡊⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢸⠀⠀⠈⢫⣦⠘⠃⣸⣇⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⣼⠀⠀⠐⠁⠠⠀⠀⠀⢸⡆⠀⠀⠘⠿⠷⣾⣿⣿⣿⣆⠹⣷⡶⠖⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠀⠀⠂⠀⠃⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠎⠹⣿⣿⣿⣧⡘⢿⡄⡦⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠐⣌⠻⣿⣿⣷⡈⠞⠁⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠈⢻⡌⢿⣿⣿⣄⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠻⣆⢻⣿⣿⣷⣤⣾⠿⢏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⣿⣿⣿⣿⣷⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⣿⣿⣿⡛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⢰⡆⣈⡟⠛⡟⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⣣⡤⠞⡱⠋⠠⣤⡋⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣴⣬⠛⢋⣴⠞⠁⠀⢈⣿⠇⠀⣟⡷⠀⠰⣼⣶⢎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⡧⠽⠙⠃⣠⡾⠋⠁⡰⠂⠀⣿⡾⠀⠀⢿⣧⡈⡤⠀⠻⣐⣻⣵⠶⣬
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣿⡣⠦⠉⠛⠁⣀⣴⡿⠋⠀⢁⡴⠀⠂⡴⢟⠇⠠⠀⢸⣿⣷⡘⡄⢠⠙⠋⢻⡆⠰⢿⣠⡿⠷⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠰⠟⠁⠀⣠⣴⣿⠟⠁⠀⠀⣠⡞⠁⠀⠘⣷⡋⢈⠀⢠⡄⢿⡿⣷⡌⢧⠐⠀⠈⠲⣶⡿⠙⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⣤⡘⠋⠐⢀⡘⢛⡹⠇⣉⠀⠄⠠⠨⣟⣫⣿⣆⠳⡀⠲⠂⠈⠁⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⣤⣻⠿⠁⠒⢀⣾⣧⠟⠁⠀⠈⠛⠀⠠⠄⢻⡿⣿⠙⣧⡹⣆⠀⠂
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⢰⣾⣁⡟⠀⠛⠀⣤⣴⢻⡟⠀⠀⠀⡶⠂⠂⠀⠈⢇⣘⣠⣿⣷⣜⢷⡄⠀⠋
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⣸⠶⣭⠉⠀⢠⢠⣟⠈⣥⡌⠁⠀⠀⠀⢰⡄⠐⠂⠂⠘⣿⡟⣯⡉⢹⣆⠻⣦⡀⠘
⠀⠀⠀⠀⢀⣿⣿⣿⠃⠰⠀⢠⣯⣴⠏⠈⠀⠀⠾⠿⣶⣋⡀⠀⠀⠀⠁⠉⣤⠰⠀⠀⠓⠘⢷⣭⣥⣾⠿⣧⡙⣿⣦⡟
⠀⠀⠀⠀⢸⡏⢹⡿⠀⣈⠁⠶⢶⡇⡈⠀⠁⢘⣠⣾⠇⢹⣿⠀⠀⠠⠀⠀⠸⣂⠈⣁⠀⠠⠈⢿⣏⢼⣁⠈⣿⣎⢿⡿⢶⡄
⠀⠀⠀⠀⠘⠀⠘⠃⠀⠈⢐⣿⠟⠀⠁⢀⠀⣮⡉⠉⣤⣀⡉⢀⠀⠀⠀⠀⠤⢩⡄⣈⠀⠀⠲⠀⠻⣯⣥⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡿⠀⡀⢀⠀⢰⣿⣷⣤⡿⠋⠐⠀⠀⠀⠂⠀⠀⠀⠘⡆⠘⠃⠐⠆⢠⠹⣿⣏⠰⠆⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠄⠀⠀⠀⠀⠁⣠⣿⠻⣿⡇⠰⠀⠀⡉⠀⠀⡬⠀⢰⠆⢠⡐⠃⠀⣤⢘⢿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠋⠀⠈⠓⢄⡈⢉⣁⠬⠶⠤⠦⠾⠶⠮⠤⠤⠤⢤⠬⠬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠙⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡱⠃⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣋⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠞⠁⠀⣿⣿⣿⢣⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⢰⣿⣿⣯⡟⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⠃⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⣿⠀⢠⣼⣿⣿⣿⡏⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡤⠾⣿⣿⣿⡟⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣷⡾⣻⣿⣿⣾⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣷⣶⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠛⠋⠉⢀⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣧⡀⣠⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠛⠙⢿⣿⣿⡿⡿⣏⣉⣵⢿⠞⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⣾⣿⣿⣷⣿⣿⠿⠟⠁⠀⣀⣠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣄⠀⠀⠀⠀⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁