Cocoanut Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡯⠈⣀⠙⠿⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠾⠛⠀⠀⠀⠀⠀⠀⡙⣄
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡐⠘⣆⠀⣀⡀⠠⠤⠤⣀⣀⡀
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠀⢣⠰⢁⡴⠋⠕⠀⢀⣈⡁⡈⣁⣀⠺⢵⣦⡀
⠀⠀⠀⠀⢸⡇⣰⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠄⢠⡫⠁⠀⡴⠊⠁⠀⠀⠀⠀⠀⠙⢄⡙⣷⡀
⠀⠀⠀⠀⢸⣿⣿⠀⢠⠀⠀⡇⠀⡄⢰⢀⢰⢠⣿⠁⠀⡜⠀⠀⠀⠀⠀⠀⢀⡠⠄⡐⠃⣸⣷
⠀⠀⠀⠀⠈⢿⣿⡄⠜⡆⠂⡇⡆⣷⣼⣼⡇⠈⣿⠀⠀⣇⠀⠀⠀⠀⠀⡜⣵⣶⠿⠿⠛⠻⢿⠃
⠀⠀⠀⠀⠀⠘⢿⣷⣀⣻⣦⢱⣿⡟⢿⣿⡇⣾⢻⡆⠀⠘⡀⠀⢀⠀⡠⠀⣿⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀⠈⣉⣉⣉⣤⡾⠃⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠟⠛⠋⠉⠀⠘⢿⣝⢟⡻⢿⠏⠉⠳⠀⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣓⣬⣀⣀⠀⣀⣄⡼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣄⣢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⣙⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⣹⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡈⢹⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡚⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡴⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠙⢿⠁⠹⣶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠈⠉⢛⠗⠈⠳⡄⠈⠆⠠⠛⢛⠳⣄⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⣠⠤⠄⠀⠀⠀⠉⠀⠀⣀⠤⠶⠒⠒⠒⠒⡇⠀⠀⠐⢩⠀⠘⠳⣄⠶⠠⠘⠓⠚⠛⠉⠉⠉⠉⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣇⠀⠀⠘⣧⡀⠀⠀⠀⢁⡀⠤⠀⢲⠒⠒⠒⠒⠒⠲⠤⠼
⠀⠀⠀⠀⠀⣿⠈⠉⠒⠢⢤⣔⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠓⡆⠀⠀⠙⠒⠖⠒⠋⠁⠀⠀⣸⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠒⢦⣤⣀⣟⣷⠯⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠘⢤⣀⠀⠀⢀⡄⣀⣀⣠⠴⡃⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⣹⠛⠎⢱⣦⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠋⠹⡇⠉⡅⠀⢢⠙⢦⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⡏⠀⢳⡿⠶⠶⠶⠶⠶⠀⢀⣀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢹⠀⠈⠇⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠤⠤⣴⡻⣦⠈⢻⡥⠭⣭⣄⣀⡳⣄⠈⢟⠲⢄⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣠⢾⠃⠀⡇⠀⠀⠀⠀⠈⢧⠈⢷⠀⠀⠀⠀⠹⣌⢢⡀⢦⡀⠈⠓⢦⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣀⡴⠚⠁⢸⣀⠀⠉⠢⣄⠀⠀⠀⠈⢧⠈⢧⠀⠀⠀⠀⣨⠞⠁⢈⠧⡀⠀⠀⠈⢳⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⡇
⢀⡠⠴⠚⠱⢂⣠⠖⠋⠈⠓⠦⣄⡈⠙⠂⠠⠤⠬⢧⡬⠧⠠⠒⠋⢁⡤⠖⠁⠀⠀⠉⠲⢤⡀⠙⠉⢦⡀⠀⣸⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾
⡁⢀⢠⠴⠖⠉⠀⠀⠀⡀⠀⠀⣠⠟⠙⠙⠓⠒⠒⠒⠂⠒⠒⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⢿⠰⠋⢰⠇⠘⠀⠀⠀⠀⠀⠀⢠⠇
⢻⡀⠀⠀⠀⠛⠀⠀⠈⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠺⣧⢰⡎⠀⠀⠀⠀⠀⡀⠀⢀⡞
⡀⢧⠀⠀⠀⢀⡤⠀⢀⡴⠃⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⢸⢰⡇⠴⠁⠀⠀⠠⠃⠀⡞
⠁⠈⢧⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢨⡇⠀⠀⠀⠀⠀⢀⠌
⢸⠀⢸⠧⢤⡖⠉⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⢻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⡠⠊⠀⡠⠊
⠈⡄⠘⡇⠀⠉⠱⡦⢤⣀⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡴⠁⠀⠀⢸⠵⠊⠀⠠⠊
⠀⢡⠀⠇⠀⠀⠀⢷⠀⠈⠉⠙⠒⠲⢅⣀⣀⠀⠀⠃⠀⠀⠀⢀⣸⣀⠀⠀⠀⠀⠀⠀⢀⡀⠔⢻⠁⠀⠀⢀⡟
⠀⠈⢆⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠁⠈⠁⠀⠀⠉⢹⠟⠛⠛⠛⠋⠉⠀⢀⠎⠀⡄⠀⡼⠁
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡼⠃
⠀⠀⠀⠘⢿⡆⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡜⠁
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠰⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠄⠀⢀⡄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣷⣄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡴⠋⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠳⠆⠁⠦⣄⠀⢀⣀⢀⡤⠀⠀⠈
⣾⣾⣶⡾⣿⣶⣾⣿⣿⣿⣿⣿⣶⣾⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣷⣾⣷⣾⣶⣶
⣿⣿⣿⣀⣀⣠⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠⢄⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠓⠺⣉⠙⣒⠻⢄⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠋⠉⠉⠉⣲⣦⣬⣥⣄⣑⠢⢵⣦⡀⡼⢀⡠⠤⠤⠤⣤⡤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⠀⠀⠀⠀⠙⠓⢮⢯⡣⣨⠌⣠⡷⠚⠂⠀⠀⠀⠀⠉⠲⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⠤⠤⠒⢾⣟⠟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⡠⠖⠋⣠⡴⡾⠿⠋⠙⠗⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠻⠿⢶⣿⠋⠈⠀⠀⠀⠀⠀⢰⣴⣷⡀⠀⠐⢤⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⣷⡀⠠⠠⢉⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢞⠀⠙⢦⠴⣶⣬⣵⡶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⢀⡼⢇⠀⠀⠀⠀⠀⠀⠀⢘⡄⠈⠀⠀⠘⡄⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢤⡀⠀⠀⣠⡾⣠⡾⠃⢀⠀⠀⠀⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠛⠋⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠳⢦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⡀⠤⠒⠒⠓⠒⠦⠀⠙⣮⡙⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠁⡠⡠⢚⠏⢿⡄
⠀⠀⠀⠀⠀⠀⠠⠂⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⣇⠀⠘⢦⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠻⣧⣴⡃⠀⠈⣷⡀
⠀⠀⠀⠀⢀⡾⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣿⠀⠀⣸⣧⣴⠞⢛⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⣾⣟⠉⠉⠛⠛⠿⠃
⠀⠀⠀⢠⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡧⠀⠘⣿⣿⠻⣿⠿⢯⣥⣤⣤⣀⣀⣀⣀⣤⣤⣤⣴⠾⠛⠹⡆
⠀⠀⠀⢸⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⡇⠀⢲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⣿⡆⠀⣿
⠀⠀⠀⣿⡁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡜⠁⢠⡾⠁⠀⢸⣿⡇⡴⠢⠈⠉⠀⠀⠀⠀⢀⡀⠩⠭⠥⠤⠼⢻⡷⡄⣿
⠀⠀⢀⣿⣷⡀⠸⣄⠀⠀⠀⠀⢀⠀⠚⠕⠉⣀⣴⠟⠀⠀⢀⣮⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠇⡟
⠀⠀⠀⠻⡈⠻⢦⣈⠙⠒⠒⠒⠚⠛⣀⣴⠾⠋⠁⠀⣀⣈⣦⣼⣿⣇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⢸⠇
⠀⠀⠀⠀⠸⣈⠀⠙⠛⠻⠶⠚⠛⠛⠉⢁⣤⢤⣦⠴⠿⢿⣿⣿⠏⢸⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢏⡟
⠀⠀⠀⠀⠀⠈⠳⢄⡀⠐⢤⣀⣀⢀⡂⢹⣧⠀⠠⡀⠀⠀⠙⠣⢄⣀⣣⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⢿⣿⣿⣿⣿⣿⣷⣄⠀⠃⠠⡀⠀⠀⠀⠈⠉⠓⠢⣄⡀⠀⠀⠀⢀⠠⢤⣐⣂⣥⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠀⠒⠒⠛⠙⢛⢿⡻⠷⢦⣀⡈⠐⠂⠀⠀⣐⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⢠⠞⠳⠠⠀⢀⠀⠀⡀⠤⠤⠴⠋⣈⣶⡄⠈⠁⠀⠉⠩⢭⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢿⣦⡄⠀⠀⠀⠀⠀⢀⣠⠶⢲⣿⣿⠟⠣⠴⢤⣶⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠛⢿⣄⡉⣉⠉⣀⡠⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⠶⠾⠛⣻⠛⠛⣟⣻⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠻⠧⠔⠂⠀⠀⠁⣀⠠⠤⠤⠄⠀⠒⠀⠤⣿⣟⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠁⠀⠠⠖⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠉⣉⣿⣿⣧⡶⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠤⢛⣻⣛⣛⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢈⡤⡺⢋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠐⢒⣥⢊⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢼⡿⡹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣼⣡⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣼⢷⠃⢻⣿⠛⣿⣿⡀
⠀⠀⠀⠀⣰⡿⢃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⢮⡄⠸⠇⡁⣧⣿⡇
⠀⠀⠀⢀⡾⣷⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⢏⡿⠡⣸⢸⣧⣿⣿⣧
⠀⠀⠀⢸⡇⣏⡄⠀⠀⠀⡐⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡿⢋⣾⣃⣿⣏⡟⢻⣽⣿⣿
⠀⠀⠀⣿⠃⣯⡇⠀⠀⠀⠀⠀⠀⢠⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀⠀⠀⣀⣷⣿⣡⢾⣿⢟⡿⣼⢡⡿⣽⣿⣿
⠀⠀⠀⡿⢹⣿⠃⠀⠀⠀⢀⠒⡠⢁⠞⠀⠀⠀⠀⠀⢀⠰⠂⠀⠈⠀⠀⡠⠈⡀⠁⡠⣼⣣⣿⣿⢯⣬⢎⡾⣽⢇⣼⣷⡏⣿⡇
⠀⠀⠀⣧⢻⠸⠇⠠⠠⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢊⢜⡕⡡⠋⢀⣿⣏⡿⣱⣿⡾⣽⠿⣰⣿
⠀⠀⠀⢹⣿⠀⡇⠇⣸⠀⢇⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡢⠊⠀⠀⠐⢁⡔⢴⡯⣺⠟⢡⡿⢫⠞⣰⡟⣻⣴⠇⣜⣿⠃
⠀⠀⠀⠘⣿⣇⣇⠀⢸⢀⣎⠀⠊⢀⠆⠀⡐⠅⠠⠀⢀⣼⠋⡄⠀⠀⣠⠂⠩⡲⢫⣼⣇⣴⢞⡴⣫⠾⢋⡼⣹⣿⣰⣿⠃
⠀⠀⠀⠀⢻⣯⢹⣀⢸⣼⢸⠆⠀⠀⠀⠊⠀⠊⣀⣤⠞⠁⠈⡀⠐⠋⣡⠖⢋⡠⠟⣋⡴⢛⣺⡾⢋⡴⠟⣻⡟⢎⡿⠃
⠀⠀⠀⠀⠘⣿⡸⣧⣸⡇⣾⢠⠅⡀⠀⢀⠀⣪⠟⠁⣀⠴⠊⠁⡶⠋⣁⠀⠉⢔⡾⣫⡴⠿⠕⣊⠞⣣⣼⣫⢾⠟⠁
⠀⠀⠀⠀⠰⢻⣷⣿⣿⣿⣿⠭⣪⠄⣐⡵⠚⠡⠔⢋⣡⣤⣶⣏⣒⠊⠁⠀⠈⠐⠉⢉⢤⡶⠋⢑⣾⣫⣟⠵⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣗⣨⡶⢟⣛⣓⣖⣾⣛⡛⠽⠛⠋⢈⣁⣤⣤⠂⠀⡰⣆⢥⣠⡴⣟⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣿⣿⠛⢛⡍⢐⠲⣒⣚⣭⠥⢄⣔⣤⣴⣖⣬⠷⣺⣽⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠻⠻⠿⠿⠷⠾⠿⣿⣷⣫⣉⣛⢩⡭⡟⢛⣯⠟⣉⣉⣩⣵⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠉⠋⠉⡼⠛⠉⠉⠋⠉⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⡴⡽⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⠇⡇⠀⠀⡜⢀⠇⠀⠀⣠⢖⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠒⠒⠒⠦⠤⢄⣀⠀⢣⠹⡄⢸⠄⢡⠀⡸⠁⡜⠀⣠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠁⠀⠠⠔⠒⠊⠀⠀⠀⠀⠀⠈⠉⠳⢦⣱⡸⡤⢸⠀⡇⢠⣣⢞⠵⣋⡤⠔⢒⡺⠋⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠀⠀⠉⢧⣧⠀⣇⣇⣾⣵⣟⡫⠐⣢⠔⠋
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⣀⡠⣤⣶⠶⠿⠛⠛⠛⠋⠉⢻⣶⠋⠀⠀⣀⡈⠉⠛⠦⣤⠄
⠀⠀⠀⠀⡰⢁⠂⠀⠀⢀⡤⠊⠀⢀⠤⢒⠍⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡇⠀⠠⡏⠁⠈⠑⠲⢄⣀⠙⠢⣀
⠀⠀⠀⡰⢁⠆⠀⠀⡠⠉⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢠⠃⠀⠸⡀⠈⡇⠀⠀⠀⠀⠀⠈⠳⣄⠈⠓⢄
⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⡪⠊⠁⠀⠀⡠⠔⠀⠀⠀⠐⠊⣁⣀⡀⠀⡏⠀⠀⠀⢳⡀⠘⢎⠀⠀⠀⠀⠀⠀⢀⠓⡀⠈⢧
⠀⠀⠀⡇⠀⠀⠀⡠⠊⠊⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⠀⠀⠈⠉⠑⠣⢤⡔⠀⠑⢄⠀⠳⢄⠀⠀⠀⠀⠀⠀⢻⠀⠸⡀
⠀⠀⠀⡇⠀⢀⠌⠀⠁⠀⢀⠤⠒⠊⢀⠔⠉⠀⠀⣀⠴⠒⠂⠴⠄⡀⠀⠀⠀⠈⢦⡀⠀⠑⠦⣀⡙⠒⠲⠤⠤⠤⠞⠀⢀⡇
⠀⠀⠀⡇⠠⠂⠀⠀⠀⠀⠀⠤⢔⡞⠁⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠓⣆⠀⠀⠈⣷⣄⣀⣀⡀⠉⠓⠢⠤⠤⠤⠤⢤⠞
⠀⠀⠀⠣⠤⠤⣀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⣷⠃⠀⠀⠈⢢⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣀⡏⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠒⢶⠃⠀⠀⠀⠀⢸⠆⠊⢀⣴⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠺⣤⣦⡶⠶⠢⠾⠶⠿⢻⡖⣒⣒⣲⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⣀⠽⠦⣀⠀⠀⣀⣼⣿⣿⡛⡀⠀⠀⠀⠀⢸⠯⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⠙⠲⠒⠚⠉⠉⠀⢀⡔⠋⠉⠉⠀⠀⡟⡸⠁⠈⠢⣄⣀⣀⣜⡙⠛⠛⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⢄⣀⠀⠀⢀⣀⣀⠤⠴⠚⠙⠢⣤⠤⠤⠚⣠⠃⠀⠀⠀⠘⡿⣦⣑⠉⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠭⣭⣉⣀⣀⣠⣴⡦⠤⠒⠉⠒⠒⢺⡧⣀⣀⣤⢲⠺⡕⠌⢮⠓⠬⣀⣈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⢧⠈⡇⠈⢮⡀⢣⠀⠀⠈⠉⠙⠓
⡰⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⢦⣇⠀⠀⠙⠦⣧
⡇⠀⠀⢤⣘⢴⡁⢠⡘⢶⡔⡆⣤⢠⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠁
⣽⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠄⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠐⠛⠚⠸⠓⠛⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠒⠛⢩⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢶⠎⠉⠀⡠⠁⣠⡾⠏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⣠⣾⢿⣹⡶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⡦⢄⠜⢧⢘⠷⡆⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⡀⣷⣿⠮⡳⢸⡎⣧⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠀⠀⡀⠀⠀⠀⣀⢴⠻⡅⠉⢧⠹⡞⢿⣆⠁⠈⠧⣄⢻⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣦⢶⠤⠀⠁⠀⢀⠔⢾⣥⢀⠃⠃⡜⣆⠀⠑⠀⡈⡣⡀⠀⢻⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⠀⠀⣀⡤⢶⡿⣤⠀⢢⣄⠱⣆⢤⠈⠈⠀⢰⠀⢻⡀⠹⠀⢠⢁⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡶⣶⣿⣿⣟⢀⢳⣜⠄⣼⡝⢟⠼⡌⠃⠘⢦⡈⠄⠀⠁⢰⡇⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⣿⢿⡧⠙⢿⣆⠺⡎⢿⡠⣿⡄⣿⣷⢀⠠⠸⡄⢸⠇⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡙⠷⢤⡐⢤⡱⣜⠃⠢⡱⡌⠻⡄⢧⢇⠻⠈⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣷⣻⣦⣽⣮⠤⣀⠳⢬⡀⣜⠘⠈⢸⣶⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣷⣬⣵⣮⣳⣮⣥⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢤⠤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⡔⢂⣧⢔⣂⡀⢐⡒⠀⠴⣮⣭⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⠀⡀⢀⣤⢂⣀⢭⣭⣕⡶⢒⣒⠲⠶⢬⣍⣍⣻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣥⣀⠀⠀⠂⠋⢍⣫⣥⣶⣿⠿⠿⢿⣒⣲⣿⣟⣷⣿⣟⠻⡝⡄
⠀⠀⠀⠀⠀⠀⣤⠐⠃⠈⠀⠀⠀⠀⡺⠿⣛⣫⣵⣒⡌⠿⠻⠛⢯⡉⢭⣷⣻⣾⣿⣾
⠀⠀⠀⠀⠀⠀⢰⠐⠈⠈⠀⡠⠔⡉⣰⢪⣬⣭⡥⠉⠀⣀⡀⢀⡀⠐⣹⡿⣻⣿⢏⡏
⠀⠀⠀⠀⠀⠀⢸⠀⣤⠕⣋⢐⠾⣛⣁⡍⠾⠐⠓⠙⠉⠀⢞⣛⣿⣛⣵⣾⢿⡷⢿⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠁⠞⠁⡈⠘⠉⠙⠛⠁⣠⡔⠀⠀⢐⣄⣿⢟⣿⣬⣷⣯⡷
⠀⠀⠀⠀⠀⠀⠀⠻⣌⣢⣤⡏⠀⠐⠒⠀⠠⠀⠀⠀⠛⢷⣾⣿⣧⢿⣿⣿⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣶⣀⠠⠀⣠⠞⡀⠰⠂⠰⢀⣼⣾⣿⣿⡷⠛⠉⠁⠀⠉⠙⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣦⣶⣤⣶⣿⣤⢶⣹⣿⣯⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⢰⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⢷⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣖⠸⡿⢛⡛⠟⠛⠋⣽⣩⣧⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣽⣤⣤⢂⣘⣂⣠⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡿⠀⠀⠀⢀⠄⠀⠀⠄⠐⠀⠂⠀⠈⠂⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢀⠃⡠⠀⠠⢀⠂⠇⠠⠂⠀⠀⠏⠁⠀⠀⠀⠀⠸⠀⠀⠀⠡⠀⠀⠂⠐⡀
⠀⠀⠀⠀⠀⠠⢃⡴⠙⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠓
⠀⠀⠀⠀⠀⠀⣰⠡⠀⠀⠁⠄⠀⢠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⡄⠠⣠⡐⣆⠂
⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⢈⠄⢠⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢐⠀⠁⠀⠁⢲⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠈⢀⠘⠀⢐⠀⠀⠀⠀⠀⠀⡀⠀⠁⡀⠀⠀⠈⢀⠏⢁⡁⠛⠀⠰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠸⠚⡔⠐⠉⠁⢀⠀⠀⠀⡀⠁⠀⠀⠉⠀⠃⠺⡘⠀⠘⠁⠠⠀⠀⡀
⠀⠀⠀⠀⢰⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠀⡹⠀⡄⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⢰⡇
⠀⠀⠀⠀⠸⡔⡇⠓⡤⢤⡄⡈⡄⢀⡴⠂⡆⢸⢸⠢⠹⢄⡇⠙⠀⢠⠀⠀⠀⡀⡀⢐⡆⡤⣿⠇
⠀⠀⠀⠀⠈⠁⢳⣤⠋⢸⡗⡇⣿⢆⢡⢠⣧⠲⢀⠐⢀⡀⡒⠸⠀⡜⠈⠐⠠⠃⠑⢻⠡⣷⣹
⠀⠀⠀⠀⠀⠀⢳⡻⡆⣟⠏⣇⡃⢘⣈⡄⣿⡄⡈⡄⢘⡤⠉⠀⢀⠁⠈⡁⠀⠠⣶⢫⡴⡘⠁
⠀⠀⠀⠀⠀⠀⠘⢱⠀⢻⡹⢨⡇⠺⣿⠃⡷⠃⠀⡄⠈⣞⢀⠀⡿⠃⢠⡧⢆⠘⠻⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⡧⡴⣾⡠⣷⢄⣆⣾⢰⣸⡘⣼⣷⡗⢠⣰⣿⣷⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣕⠟⢿⣿⣞⣿⣽⡿⡼⣽⢶⢿⣿⣷⡿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣮⣗⣿⡃⣳⣇⣽⣯⣤⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠋⠉⠉⠛⠛⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣠⣤⡤⢤⣤⣤⣀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣶⠛⠉⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣹⣿⡄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡟⢻⣿⡄⠀⠀⣧
⠀⠀⠀⠀⠀⣀⣤⠴⣖⣛⣛⣋⣛⣛⡛⠛⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣄⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠀⡐⢫⣿⣷⠀⠀⠘
⠀⠀⢀⣴⣾⠿⠞⠛⠋⠉⠁⠀⠀⣈⣉⡉⠙⠒⠦⣌⡙⠳⢤⡀⠀⠀⠀⠀⠀⣿⣇⢸⠛⢧⡀⠀⠈⠙⢷⣦⣄⠀⠀⠀⠀⠀⢾⣿⣿⠏
⠀⣴⣿⣯⡵⠖⠚⠛⠋⠁⠀⠀⠀⠀⠈⠉⠙⠒⠢⢤⣈⡙⠲⢿⣶⣄⠀⠀⠀⢻⣿⠸⡄⢾⠻⣦⡀⠀⠀⠉⠛⠷⠦⣴⣶⣶⠿⠋⠁⠀⠀⠀⣰
⣼⣿⡋⠁⠐⠒⠒⠛⠒⠒⠒⠒⠶⠲⠦⢤⣄⣉⡒⠢⢤⣈⡙⠲⢬⣿⣷⡀⠀⠈⢿⣷⢧⡘⠀⡏⢻⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠟
⣿⣿⣟⠓⠶⣤⣄⣙⠛⠓⠒⠒⠤⢤⣄⣀⡀⠈⠉⠙⠲⣄⡉⠙⠢⣝⢿⣿⣄⠀⠈⢿⣏⣳⠀⣷⠘⣠⠞⢉⠿⢳⣶⢶⣶⣶⣾⣿⣿⣿⡿⠃
⣿⣿⡙⢷⣄⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠉⠙⠲⠤⢤⣀⡉⠓⢦⣌⡻⢿⣿⡆⠀⠀⠙⢿⣦⣿⡞⣡⠔⠁⣐⣫⠴⠋⣹⣥⣾⣿⠿⠋
⠹⣿⣿⡦⣍⠻⣦⡀⠲⢄⣀⠈⠙⠒⠦⠤⠤⢤⣤⣀⣀⠀⠉⠓⠲⢭⣿⣾⣿⣿⡄⠀⠀⠀⠉⠛⠿⣿⣶⣿⣿⣶⣿⣿⡷⠿⠋⠁
⠀⠙⢿⣷⣮⡓⠤⣉⠓⢄⡈⠙⡒⠒⠲⠤⠤⣤⣀⣤⣭⣉⣉⣉⣁⡤⠬⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠈⠻⣿⣿⣶⣤⣉⡲⣽⡲⠮⣭⣓⡒⠲⠤⠤⠤⣤⣶⣶⣶⣖⣚⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⠻⢿⣷⣌⣭⡛⢯⣛⠶⢿⣭⣍⣭⣭⣭⣭⣵⣶⣾⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣽⣛⡭⣿⣛⣛⣛⡻⢯⣭⣭⣶⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣵⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢱⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠄⠈⠉⠙⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⠤⠴⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣛⠛⠿⣿⣿⣿⣿⢛⣩⣭⣭⣹⣿⣿⠿⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠿⠿⠿⠿⠟⠛⠛⠉⠁


⣿⢿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⣒⡲⠖⠚⠉⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⣠⠖⠋⠉⢙⣆⠀⠀⣄⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⢀⡠⠚⠁⠀⢠⣶⠟⠉⠱⡀⠀⢳⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠊⠀⠀⢀⣔⠝⠁⠀⠀⠀⡇⠀⠀⢳⠀⠀⢄⠘⢆
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⠜⠁⠀⠀⠠⠪⠋⠀⠀⠀⠀⠀⠃⠀⠀⠈⣇⠀⠈⠄⠈⢷⠁
⠀⠀⠀⢀⢠⡞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢀⠄⡾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⢠⠋⢰⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡈⠧⠏⢄⡀
⠛⠀⣾⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠤⠠⡪⠀⠀⠀⠀⠈⠉⠲⠂⠢⠀⠀⠀⠀⠂⠤⡀⢀
⠀⠀⣿⠐⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⢸⠀⠀⡀⢚⠄⠒⠊⠉⠁⢀⡠⠞⠑⠢⠀⠠⠤⠀⠀⠀⠀⠀⢀⡀⠀⠐⠪⢕⡢⣄
⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠒⢸⡦⠊⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⡇⣸⡀
⢠⠊⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣠⡠⠤⡠⠔⢋⠔⠙⡇
⠉⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡔⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠋⠠⣴⠒⢡⠤⠖⠀⠊⠁⠀⠀⠷
⠀⠀⠘⣇⠀⣇⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣠⠃⡴⠉⡆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠹⣆⢹⣃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣠⠞⢡⠞⠀⠀⠸⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠙⣮⣿⡀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⢀⠇⠀⢸⡰⡂⠀⠀⠀⠹⡀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⡠⠚⡡⠚⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⢸⠀⠀⡞⠀⠀⠀⢀⡞⠀⠀⣸⡧⡡⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡠⠔⡉⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣈⣇⣸⡇⠀⠀⣠⠞⢀⣠⠾⣋⣹⣜⠮⣀⠄⢀⢀⣀⣀⡠⠤⢒⡊⠅⢶⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠇⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠘⢦⡀⠉⠁⠒⠒⠒⠈⠉⠁⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⠈⡄⡀⠀⠀⠀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠏⠀⠀⢀⣼⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠋⠢⢄⡀⠀⠀⠀⠀⠀⡀⠐⠤⣀⠀⠀⠀⠀⠀⠘⣤⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠗⠢⢤⣀⣀⡀⠑⠒⠤⠭⣷⣶⣶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⣋⣡⡽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⣋⣥⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢟⣫⣽⣶⣶⣿⣿⣿⣿⡷⣶⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⢛⣻⣵⣾⣿⡿⠋⣩⡿⠛⠛⠻⠿⣿⡋⠉⠁⠈⠙⣷⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡶⠟⢋⣡⡴⠞⣫⡿⠟⠉⠙⠷⠶⣿⡀⠀⠀⠀⢀⣾⣇⣀⣀⣤⡶⠟⠉⠻⣦⡀
⠀⠀⠀⠀⣠⡾⢋⣴⠾⠋⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠞⠛⠁⠉⠉⠉⠁⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢰⡟⣴⠟⠁⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠈⢿⡏⠀⠀⠀⢰⡏⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠼⠋⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠴⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠛⠶⠤⢤⡤⠤⠴⠶⠒⠋⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⢀⣀⣠⣤⣤⣀⣀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⣿⣿⡄⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⣿⣽⡇⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠘⣿⣿⡝⣦⣿⣿⣧⣿⣿⡯⠤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⠿⣿⣶⣽⣻⣿⣾⣿⣿⣿⡏⢀⣴⣶⠶⠦⠄⠈⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⢁⡈⠩⠤⣌⠻⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⠁⠀⠀⠀⠀⠀⠀⢄⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠈⣁⣀⣾⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣆⠘⠿⠀⠀⠀⠀⠀⠀⠀⠹⠦⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⠙⢛⣿⠿⣿⣭⣿⣿⣿⣿⡿⣿⣿⣿⣧⣷⣄⠀⠀⠀⠀⠀⢠⣀⠐⢜⢿⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠈⠉⠻⠻⣿⠿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠁⠒⠿⣷⣾⣿⣿⠂⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠄⣠⣒⡀⠄⠀⠀⣀⣴⣶⢿⣻⠿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣤⣤⣄⣀⣀⣠⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠷⠶⠭⠉⠈⠁⠀⢄⣩⣴⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣶⣶⣾⣿⣿⠟⠛⠿⣿⣿⣿⣷⢦⡹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⠿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⡿⠭⡁⠀⠁⣠⠴⣿⡙⢿⣮⡀⠙⠪⣙⠋⠉⠉⠈⢸⡿⠛⠉⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢰⡏⢻⣴⡿⠁⠀⠙⣿⣦⣴⣿⣿⣟⠀⠀⠉⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣷⠟⠉⠀⠀⠀⠀⠈⠙⠻⠿⠿⣷⣶⣶⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢠⣾⣿⡿⠿⣿⡿⠟⠉⠉⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣴⠋⠀⠈⠉⠀⠀⠙⠛⠋⠁⠀⠈⠙⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⣦
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣧
⠀⢠⡟⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸
⠀⡾⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈
⣸⠃⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸
⣿⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡞
⣿⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⢹⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣾⠀⠉⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠘⣧⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢰⠟⠛⠒⠶⠤⣤⣤⣤⠴⠋
⠀⠘⣧⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠏
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁
⣀⢀⣀⣀⣀⣀⣀⣀⣈⣙⠳⣶⣤⣴⣶⢛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⢦⣄⡀⢀⣤⣶⠛⠉⠉⠛⠉⠈⢋⡛⢛⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠁⠀⠀⡀⠀⠈⠙⠻⣿⣿⠥⢊⣩⣶⡞⠋⠉⠀⠉⠉⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠸⣧⠀⠀⠉⠉⠉⠒⢀⡀⠈⠛⢾⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡥⠹⣇⠀⠀⡀⠀⠀⠈⠉⢶⣄⡀⠿⣿⣿⣿⣿⣏⠠⠀⢀⣤⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠘⠁⠉⠛⢦⡙⢧⣤⡶⠀⢅⣿⡆⠀⢹⣿⣿⣿⣿⣷⣷⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣠⣤⣽⣦⣉⠻⣿⣯⡰⣶⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⢀⣼⣯⣾⣿⣿⣿⣷⡈⠛⠓⠛⠁⢰⡿⢛⣩⣭⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣺⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⠿⠟⠛⣛⣛⣛⠿⠟⢁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣾⡿⣿⠟⠋⠉⠀⠒⠊⠉⠉⠉⠒⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣎⡳⠈⠻⣟⠶⣜⠳⣤⠴⣶⣇⡀⣐⢒⣛⡂⢉⣡⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠤⠄⠈⠳⣄⠠⣌⠻⢎⡛⢮⣑⠢⣍⠛⠮⠑⠮⣵⣒⠾⠭⠭⣭⣉⣉⡉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⡛⢦⡙⢦⣍⠳⣌⠻⢦⣄⡲⠦⣌⡙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠳⠄⠙⠢⠈⠙⠒⠀⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣰⣯⣍⣭⣭⣍⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠳⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣴⣾⡿⠿⠿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⣿⠋⠀⢀⣀⣀⣀⣀⡀⠉⠛⢿⣦⣄
⠀⠀⠀⠀⣰⠏⢀⡴⢛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣸⡟⠀⣰⡟⠉⠉⠉⠉⠛⢷⡄⠀⠉⠻⣷⡄
⠀⠀⠀⢰⡏⣀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣿⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠈⢿⣦⡀
⠀⠀⠀⢸⣟⣽⠳⣟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣿⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡀⠀⠹⣷⡀
⠀⠀⠀⢸⡟⠁⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣷⡀
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠹⣷⡀
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⣸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠙⠳⠶⠶⠞⠋⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣤⣤⣀⡀⠀⠀⢀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢤⣤⣤⣄⣀⣀⣀⣠⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁




⣿⣿⡿⠿⣿⠿⢿⣿⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣾⣶⣷⣶⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⣶⣶⡶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣿⣿⣿⣿⣿⣍⣙⡂⠙⢹⣿⣶⡤⡄
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⠛⢻⣿⣷⣤⣬⡉⠁⠉⠙⠛⢻⣿⣿⣾⣦⡀
⠀⠀⠀⢀⣠⣞⣁⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠒⠲⠦⠤⠀⠀⠀⠈⠙⠿⣿⣿⣄
⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⠒⠂⢀⣈⠉⠑⠂⠄⠀⠀⠀⠈⢑⣒⡺⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠱⣝⣿⣿⣿⣷⣄⡀⡉⠚⠦⢤⣶⣀⡒⠢⠶⣈⣙⣿⣿⣿⣿⣿⣿⢿⣟⣛⣻⣿⣛⠳⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣏⠻⣿⡯⠒⢀⡠⠄⢉⣉⣠⣬⣉⣙⣿⣿⡿⣉⢔⣋⣉⣉⣉⡁⠉⠛⢮⣌⠛⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣒⡋⢿⣶⣦⣭⣿⡿⢿⣿⣿⣿⣿⢻⠁⠜⠋⠉⠉⠀⠀⠉⣢⡀⠀⢹⣶⣈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡀⠀⠀⠠⠹⣿⣶⣿⣿⡁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠀⠀⠈⠑⣿⣿⣿⣷⡟⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣦⣭⣿⣯⣽⠤⠒⠿⣿⣹⠈⢄⠀⠀⠀⢠⠀⠇⠀⣿⣿⠏⣿⠁⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠸⣿⢦⡈⠳⠄⠀⠀⠀⢀⣠⣟⣿⡾⠧⣸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡝⠳⣶⣤⣶⣶⠿⠾⠟⠋⣠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣤⣌⣉⣤⣤⣤⣿⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⢿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠉⠉⠩⠟⠛⠻⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠂⢠⠂⠀⢀⡀⠀⠀⠀⣀⣈⣏⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⢰⣿⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢅⠷⠀⠀⠀⠀⣀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠁⠀⠀⠀⠀⢽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣞⣲⣲⣾⣿⣿⣿⣿⠲⠶⠦⠤⠤⠤⠖⠒⠒⠊⠉⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠾⣥⣔⡀⠀⠀⠀⠀⠀⠀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠰⠶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⣒⡒⠒⠊⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⣠⠔⠋⠉⢉⣧⡀⠠⢄⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⡠⠞⠁⠀⣠⣾⠟⠁⠻⡀⠀⢣⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⣠⠞⠁⠀⢀⢔⠟⠁⠀⠀⠀⡇⠀⠀⢧⠀⠀⠀⠙⣄⢀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡔⠁⠀⠀⠠⠢⠃⠀⠀⠀⠀⠀⠁⠀⠀⠈⠆⠀⠀⠄⠘⣇
⠀⠀⠀⡠⣶⠃⠀⠀⠀⠀⠈⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀
⠀⡠⢢⡏⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀
⣼⠁⣼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠉⠐⠂⠄⣀⠀⠀⢀⣀⣀⡀
⠁⠀⡿⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠣⡀⠀⠀⠀⠀⠀⠀⣆⠀⣐⡠⠥⠀⠀⢀⡤⡀⠀⠈⠁⠉⠁⠀⠈⠀⠀⠉⠒⢀⠠⢀
⡀⠀⣧⠂⠀⡀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⡠⢸⠀⡠⠂⠂⠁⠀⠀⢀⠠⠒⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⠒⠒⠂⠄⠀⠉⠲⠙⡆
⠀⡰⡇⠀⠀⡁⠀⠀⠀⠀⠀⠙⠀⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⢸⢋⠊⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⡰⢿
⠜⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⢀⣥⠋⣋⣍⣉⠤⠊⠀⢸⡄
⠀⠀⢸⡄⠘⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⡟⢠⠚⡉⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢷⡀⣗⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠈⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⡠⠋⡰⠃⠀⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⢳⣸⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⢠⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⡠⢊⡠⠊⠀⠀⠀⠈⡀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⡇⠀⢠⠂⠀⠀⠀⡰⠁⠀⢸⣇⢂⠀⠀⠀⠀⠐⠀⠐⠀⠉⠀⠀⢀⡠⠔⡩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣷⢀⡞⠀⠀⢀⡴⠁⢀⡴⠋⣹⡳⢕⠀⢀⠀⠀⠀⢀⣀⠠⠤⢚⢡⠐⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠿⠶⠟⠛⠛⠉⠁⠑⣄⠉⠐⠒⠉⠉⠒⠂⠀⠁⠀⠀⠳⡀⠀⠀⠀⠀⢀⠈⡀⡀⠀⠀⠀⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡟⠁⠀⢀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠦⣀⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠀⠀⠘⣄⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠤⢄⣀⣀⡁⠒⠦⠭⣷⣶⣶⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢂⣀⡀⡀⣀⣀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠛⠙⠘⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⡠⠴⢚⠉⠉⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠻⠉⠀⠀⠊⣠⣾⣟⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠓⣽⠙⣿⣻⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣹⣏⢶⡈⣧⢬⢻⣤⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠅⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⡦⣦⢿⣿⠳⡅⢻⠈⢺⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⢀⡀⠀⠠⠀⠀⠀⣠⠔⠛⡍⠇⢠⡳⠘⠆⠙⢣⡀⠌⠱⣦⢿⣾
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⠛⠋⠋⠀⢀⣠⠔⠋⣙⠋⢤⡀⠀⠣⠳⡀⠀⠘⡌⠸⣆⠀⠻⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣤⣴⣾⠉⢫⠻⡇⢸⡳⡾⣻⡹⡄⢠⡀⢱⠀⠙⠀⢠⠀⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣽⣟⢿⣿⣮⠲⣿⡅⢹⡇⣽⢈⣧⢀⣦⡍⠂⠀⢢⠀⣼⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⢿⣯⡹⣦⣈⠉⡀⠻⡸⡏⠙⢇⠙⢿⠙⡴⡸⣆⠛⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣯⡷⣌⡳⣝⣀⠀⢦⣓⢈⠃⠳⠃⣦⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣿⣿⣿⣤⣙⣢⣽⢧⣙⣂⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠉⠉⠉⠙⠛⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣠⣤⠴⠶⢶⣤⣀⡀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠉⠉⠻⢷⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣽⣿⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⣻⣿⡀⠀⠘⣆
⠀⠀⠀⠀⣀⡤⣖⣻⣭⣭⠭⠭⠭⢭⣉⣉⡛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣷⣄⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠠⢍⣸⣿⡇⠀⠀⢸
⠀⠀⣠⣾⠿⢛⣉⣁⣀⠀⠀⠀⠠⠤⢤⣀⣉⠙⠲⢬⣙⠳⣄⡀⠀⠀⠀⠸⣟⡆⡏⢙⣦⡀⠀⠈⠙⢷⣶⣀⠀⠀⢀⡀⣻⣾⠟⠁⠀⠀⢸
⢀⣾⡿⠗⠛⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⢈⣉⠓⠢⠤⣝⡛⠿⣦⡀⠀⠀⢿⣧⢳⠸⡇⢻⣦⡀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⢀⣠⡟
⣾⣿⣤⣀⡈⠀⢀⣀⣈⣉⣉⠉⠉⠉⠛⠒⠦⠬⣍⡓⠲⢤⣉⠳⢿⣿⣄⠀⠈⢿⣏⢧⠁⢻⢨⡟⢳⡦⣤⣀⡀⠀⠀⢀⣀⣤⣴⣾⣿⠟
⣿⡿⢦⡈⠙⠛⠲⢤⣀⠀⠈⠉⠙⠒⠲⠦⢤⣀⠀⠉⠓⢦⣀⠙⠢⣽⣿⣆⠀⠈⠻⣮⣇⢸⢀⡴⢋⡴⢋⡽⢛⣻⣿⠿⣿⣿⣿⠟⠁
⢿⣿⣦⡙⢶⣄⠀⢀⡈⠙⠲⠤⣄⣀⠀⠀⠀⠈⠉⠑⠒⠦⣌⡙⢶⣬⣻⣿⡆⠀⠀⠈⠻⢿⣿⣴⣋⣤⣶⣚⣭⣤⣾⣿⡿⠟⠁
⠈⢿⣿⣍⠲⣈⠓⠦⣉⠓⠢⠤⣀⣈⣉⠉⠉⠙⠓⠲⠦⠤⠤⠌⠙⢻⣿⣿⣿⡀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠟⠛⠉⠁
⠀⠀⠹⣿⣿⣦⣉⠒⠬⣳⢤⣐⡢⠤⣈⣉⣉⣉⣉⣉⣑⣒⣛⣫⣭⣭⣾⣿⡿
⠀⠀⠀⠈⠻⣿⣿⣍⠓⠾⣷⠮⣭⣷⣶⠶⠲⠾⠿⣛⣛⣛⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⠿⣖⣾⠿⠿⠿⣿⣟⣛⣛⣫⣭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣾⣿⣿⣿⣶⣾⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢒⣲⣒⠊⠉⢢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⡠⠚⠁⣠⡼⢦⠐⠢⡀⠙⠢⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡠⠊⠀⢀⡼⠋⠀⠀⠇⠀⠱⡀⠀⠘⢆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠜⠀⠀⡠⠝⠁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠈⢧
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⡰⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠂⠄⡀
⠁⢸⠇⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⣀⠀⣐⠂⠉⠀⣠⣀⠀⠙⠈⠉⠁⠈⠁⠐⠂⠠⢀⡀
⠄⢸⠆⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⡎⡆
⡠⢸⡄⠀⡆⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠤⠤⢊⠄⢳
⠁⠈⡇⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢂⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⡞⡡⠒⠁⠈⠀⠀⠘
⠀⠀⠹⡀⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⡠⢊⠔⠁⢀
⠀⠀⠀⠱⣼⡆⠀⠀⠀⢸⠀⢀⠀⠀⠀⢀⠃⠸⡴⠀⠀⠀⠋⠀⠀⠀⣀⠄⠊⠁⠀⡠⢊⠄⠈⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⠀⣸⠀⠀⢀⠎⠀⣰⢷⣅⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠳⠧⢤⣴⣯⡴⠾⠗⠚⢣⡑⠀⠤⠖⠲⠌⠉⠂⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⢀⠐⠤⣀⡀⠀⣀⣱⠔⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣒⣲⣤⣬⣭⣿⣿⣟⣋⣁⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣉⣉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⢩⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢠⡿⠀⠘⣿⠀⠀⠀⠀⣠⣶⠾⠛⠛⠉⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⢿⡆⠙⠻⠶⣤⣄⣀⠀⠀⠀⣀⣤⠶⠛⠛⠛⠛⠷⣦⣼⠙⠳⢦⣤⣾⣁⠀⠀⢹⣇⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⣷⡄
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠉⠙⠛⣳⠾⠋⠀⠀⠀⠠⠶⢤⣄⠀⡏⠀⠀⠀⠈⠉⠙⠛⠻⠶⣿⣾⠟⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⠛⠉
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢸⠿⠶⠶⣦⣄⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠑⢤⡀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣀⡴⠋⠀⠀⣠⡾⠋⠙⢶⣤⣀⣀⣀⣀⣀⣠⣤⡶
⠀⣀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣠⠤⠤⠤⠹⢿⣦⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⢷⣄⠀⠀⠀⠙⢷⡶⠞⠋⠀⠀⣠⣾⠋⠙⠳⠦⠤⠌⠉⠉⠉⢉⣩⡿⠋
⠈⢿⣟⡛⠛⠛⠛⠛⠛⠋⠉⠁⠀⣠⣤⡴⠶⠛⠛⢛⣿⣷⣶⣤⣤⣤⣤⣿⡆⠀⠀⠀⢻⣆⠀⠀⠀⢈⣧⣤⣤⠶⠛⠙⠛⠛⠛⠻⠿⠶⢶⣶⡿⠟⠛⠁
⠀⠀⠉⠛⠷⣦⣤⣄⣀⣀⣈⣈⣁⣀⣀⣀⣤⡴⠞⠛⠁⠀⠀⠉⠉⠉⠉⠉⢿⣤⣀⣀⣈⣿⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⢀⣤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⢻⣆
⠀⠀⣰⡟⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣆⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⢿⣆
⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠊⠐⠀⠀⠀⠀⢀⠀⠀⠘⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠂⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡀⠀⢻
⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠠⠴⠋⠀⠀⠀⡀⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢸
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⢸
⣿⠀⠀⢀⠀⠀⠀⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⣼
⢿⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠑⠞⠀⠀⠀⠀⠀⠀⠀⠠⠒⡆⠀⠉⠆⢠⣿
⢸⣧⠀⠀⠸⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠓⣦⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠘⠀⠀⢀⠐⠂⠀⢸⠀⠗⠀⣾⡟
⠀⢿⡆⠠⠀⠀⠀⠀⠰⡆⠀⠀⡄⡄⠀⠀⠀⠠⡇⣹⠀⠀⠀⠀⠀⠸⣦⠟⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⠀⠀⠡⠀⠀⡺⠤⠂⠀⣀⠀⠀⣸⡿
⠀⠈⢿⡄⠑⠀⠀⠄⠀⠁⠀⠀⠶⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⣠⠞⠁⠀⣰⡿⠁
⠀⠀⠈⢿⣆⠀⠀⢙⠆⠀⠀⢡⢄⠀⠀⠀⠒⢀⠀⠀⠀⠀⠘⢀⡄⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣀⠀⠀⠰⠀⡠⠀⢠⣿⠃
⠀⠀⠀⠀⢻⣦⠀⠙⠀⠀⠀⠘⢬⠆⠀⠀⠐⣍⠳⡀⠀⠀⠀⠘⣇⣸⠇⠀⠀⠀⣀⣀⠀⠀⠈⢠⡈⢦⠀⠀⠀⠀⣿⡠⠁⠀⢼⠍⠀⠀⢰⠊⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠓⠁⠀⠠⡤⣀⠈⠁⠀⠀⠀⠀⠈⡨⢠⡄⠀⠈⠷⠾⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠄⠀⠐⡖⢡⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠐⢨⡆⠀⠀⠊⡤⣀⠀⠀⠀⠀⠇⣸⠆⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠴⣁⠄⠀⠀⠉⡁⠀⠄⠘⢀⠀⠐⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⡳⣌⠀⠀⠀⣀⡀⠉⠀⠀⠀⠉⣉⢳⡄⠀⠀⣴⠛⣠⠀⠀⢀⣄⠀⠀⠀⢀⣀⠀⠀⠜⠋⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢂⠀⠀⠈⠀⠀⠀⠀⠸⡈⣦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠃⠴⠀⠀⠰⡆⠄⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠀⠀⠀⠢⡄⠀⠒⢠⠈⠁⠀⠀⠈⢁⢱⡄⠀⠒⢉⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡒⠂⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠠⡀⠈⠀⠀⠈⠀⠀⠀⠆⢤⠀⠀⠁⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠙⠀⠀⠀⡀⠁⠀⠀⠀⠘⠁⠀⠀⠐⠂⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠂⠀⠉⠐⠆⠀⢠⠤⢄⠀⠀⠀⠀⠔⡚⠂⢠⡴⠂⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠰⠁⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠈⡧⠀⠀⠀⠰⠒⠀⠀⠀⠀⠚⠙⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⢀⣀⠀⠀⠠⣦⠤⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣦⣤⣀⣉⣁⣀⣠⣴⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⣀⠀⣠⣤⠒⠘⠚⠛⠛⠛⠶⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠁⢀⣀⣀⠈⠙⠿⣿⣒⣩⣶⣟⠉⠁⠉⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⢷⡀⠀⠀⠀⠁⠤⣀⠉⢻⣿⣿⣿⣤⠀⠀⠀⢨⣷
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠆⠳⢤⡐⢄⣀⡄⡜⣷⠀⠹⣿⣿⣿⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⢀⣤⣽⣮⣙⢻⣿⡼⣦⠀⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⡠⣾⣿⣿⣿⣿⣧⣉⡉⠉⣠⣟⣩⣵⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣵⣿⠿⠉⡡⠦⠂⠒⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⣿⣿⣿⡿⣔⠎⠻⣿⢥⡲⣄⡤⣴⣀⡀⢐⣚⠑⢀⣠⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠠⠀⠈⠳⣄⢬⡓⢍⠲⣕⠪⣍⠚⠙⠫⢶⣚⠋⠭⠭⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠢⠙⠦⡑⠬⡑⠦⢍⠒⠮⠉⠒⠂




⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⢰⣿⡿⠿⠟⠛⠛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠻⣿⣶⣾⣿⣿⣿⡒⠒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⣤⣜⣁⡀⠀⠀⣉⣉⣉⡀⠀⢄⠀⣀⣤⡷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣯⢿⣿⣷⣿⣽⡽⣿⣿⣯⣿⣯⣭⣿⣻⣿⣽⣿⣿⣾⢷⡀
⠀⠀⠀⠀⠀⠀⣼⢷⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣽⣯⣿⢽⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢰⣏⣿⡟⠉⢿⣿⣿⣟⣿⠁⠀⠙⢾⡿⠁⠀⢹⡾⠉⠉⣿⣿⣿⣾⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣧⣶⣿⣿⣿⣿⣿⡄⢀⣶⡘⣇⣶⡄⢠⣿⣶⣶⣟⣿⣿⣿⡇⠀⠀⢠⠋⠉⠙⣿⣿⠛⠳
⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠛⣡⣿⣿⣥⣾⢿⣷⣿⣿⣿⣿⢻⡇⠀⢀⢾⠀⢱⣴⣿⡗⠐⢚
⠀⠀⠀⠀⠀⠀⢻⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣥⣴⣾⡈⣀⢹⣿⣿⡗⢒⡟
⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣦⣟⡿⠋⠉⠁⠀⠈⠁⠀⠉⠉⠉⠉
⠀⠀⠀⢠⣿⡟⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣥⣶⣻⣭⣾⣿⣿⠟⠁
⠀⠀⡔⢺⣿⠄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⢠⠊⠑⠮⠡⠚⢢⠀⠀⠀⠀⠀⠀⠉⠙⣿⡿⠻⠿⠛⣿⡟⠉
⠘⡆⠀⠀⠀⣴⣸⠂⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⣿⡇
⠀⠙⠚⠦⠤⠊⠀⠀⠀⠀⡠⢴⣶⣞⣿⣿⣿⣦⢠⣴⣿⣿⣟⣲⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠙⢿⣿⡿⠋⠈⠻⣿⣿⡟⠉⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠉⠒⠲⠬⠷⠚⠁

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

⠀⠀⠀⣼⡀⡶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠠⠀⠀⠀⠀⣀⠠⠔⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠈⠈⢻⠄⢀⣴⠀⠀⠙⡦⡀⠀⢀⠀⠀⠀⠑⠤⣤⣠⠤⠀⠉⠁⠀⠀⠘⣿⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠃⢿⠛⠁
⠀⠀⢠⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠊⢲⣎⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠠⣤⣴⡿⢀⢨⣿⣦⡀⠀⢀⠜⠉⠁⣰⣿⢿⣷⣀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⡀⠀⠀⠀⡠⠀⠁⢀⠀⠀⠀⣸⣿⠁⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢹⣿⣷⠉⠐⠆⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢰⡃⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠠⠃⠀⠀⠸⠀⠙⢿⣿⣿⠀⠀⠀⢸⣿⠿⠁⠀⠀⢀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⢷⣄
⠀⠀⠀⠙⠀⠁⠀⠀⠀⠠⣿⣶⣶⣤⣿⣿⠋⠀⠀⡴⠁⠀⡀⡀⠀⠀⡀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠀⣀⠀⠑⡄⠀⠉⠏⠉⠀⠀⠀⢠⢴⠄⠀⠙⣦⠀⠀⢲⡀
⠀⠀⠀⣄⠀⢀⡀⠀⠀⠀⠋⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠇⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢠⣄⠀⠁
⠀⠀⠘⢣⡼⢿⣤⣤⢄⣴⡆⠀⠀⠀⠀⠒⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣶⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠉⣀⣾⠁⠙⠀⡽⣋⠱⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢠⣿⠯⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢀⣶⡄⠀⢀⣀
⠀⠀⠀⠦⠛⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠐⣶⢀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢲⡄⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠋⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠒⣶⠀⠀⢰⡄⢠⡄⣘⣾⣿⣿⡳⣆⠀⠀⠀⠀⠀⢀⢀⣿⣆⡀⠀⠀⠀⠀⠀⠉⠚⠂⠀⠘⠇
⠀⠀⠀⠀⣶⠆⠀⠀⠀⠸⢿⡇⠉⠀⠀⠈⠉⠘⡾⠛⠟⠉⠙⢿⡌⣧⠀⠀⠀⠠⠈⠈⢻⣿⣷⡄⠀⠀⢀⢺⣿⡖⣶⣶⡄⠀⢀⠀⠀⠲⣶⣄⠢⣠⣦⢴⡞⠁
⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀⠈⣀⠰⠂⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠸⣷⣿⣇⢻⣿⡇⠀⠀⠀⠀⠀⠈⠉⣁⠟⢁⣀⣠⣄⡀
⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠒⡏⠀⠈⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⢰⣷⠀⠈⠙⠋⠈⠛⡡⢴⡒⢶⡄⠀⠠⣾⣈⠀⢻⡇⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⣧⠸⡑⣌⣿⠀⣌⢿⣿⣿⣺⢷⢼⣿⠇
⠀⠀⠀⠀⠀⠀⣀⠠⠂⠀⠀⢤⣤⣤⣤⡀⠀⠀⠀⠙⠛⠂⠀⠈⠀⠳⡾⠿⠋⠀⠀⠀⢴⣦⣒⠶⢻⣀⣤⣴⠋⠀⠀⠀⠘⠷⠬⠟⠃⠀⠹⣿⣿⡿⠁
⠀⠀⠀⠠⠾⠟⠉⠰⢀⡀⠀⠀⠙⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⢀⡀⠀⢸⢓⣯⠉⡄⠴⠶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢲⠂
⠀⠀⠀⠀⠀⠀⣶⣶⣿⠁⣹⣾⠉⠁⠀⠀⠀⠀⠀⠀⣆⡀⠀⠘⠿⡇⠀⠀⣠⡾⢿⠀⠀⠀⠈⣇⠁⠀⠀⠸⠇⣥⠆⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠐⠿⠛⠻⠇⠁⠀⠀⠀⠀⡶⠤⠀⠀⠀⠴⠇⠀⠀⠀⠀⠰⢾⡯⠟⠁⠀⠀⠀⠴⠋⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠘⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⣿⡿⠟⠛⣿⡿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⢀⣼⠋⠀⠀⢠⡿⠀⠈⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢾⠿⠶⢶⣤⣿⢁⠀⠀⢠⡿⠁⠀⠀⣿⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠻⣶⣿⣡⣀⡀⢰⡟⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠉⠻⣿⠷⠷⢶⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣦⣤⣤⣤⣤⣼⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⢿⣭⣜⣷⣄⣀⣰⣿⣩⣭⡿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⡉⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠛⠷⠶⢶⡶⠶⠿⣦⣄⣀⢀⠀⣀⣠⡶⠟⠛⠷⢶⣤⣤⣤⡶⠾⠋⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠋⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡄⠀⠀⠀⠀⠢⡉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⠀⠀⣀⡼⠧⢖⣒⣋⠭⠭⠒⠒⠒⠒⣲⢈⣧
⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡷⣏⠔⠂⠉⠁⠀⠀⠀⢀⣀⠤⢔⣪⠵⠊⠸⡆⢀⡤⠴⠚⢩⡙⢢⡀
⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣒⣒⣒⣒⣒⣪⠭⠵⠒⠊⠉⠀⠀⠀⠀⡟⡁⠀⠀⠀⠀⠀⠀⠈⢢
⠀⢀⡞⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⣼⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠲⠦⠤⠤⠖⠒⠋⠁
⠀⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⡜⠁⠀⠈⠓⠦⣄⣀⣀⣠⣤⣤⡤⠞⠚⠁
⠸⣏⡀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠒⠂⠁⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠉⠳⢤⣄⣀⠀⠀⠀⠐⠂⢉⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣉⡡⣤⣤⣶⣦⣦⣾⡍⣙⣓⡲⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡼⢁⣴⣬⣿⣻⡟⣻⣿⣽⡷⣿⣿⣾⣿⡿⣣⣤⣍⡓⠦⣀
⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⠻⠛⠿⣿⣯⢷⣿⣿⣷⣬⡑⢦⡀
⠀⠀⠀⠀⢸⣿⣷⡈⠛⣛⣿⣿⣟⣿⣿⣿⣿⣗⣤⡀⣼⣾⣷⣻⣟⣻⠿⣿⣕⣠⠹⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣦⡙⢿⣿⣿⣿⡽⣿⣿⣿⣿⣷⣿⠟⣫⡍⠙⢙⠛⠷⣾⣯⠀⣷
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣌⡉⠉⢾⣿⣿⣿⣿⡲⠀⣂⣻⣿⣧⡄⠄⠉⠀⠛⢦⡏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⠿⠀⠐⢀⠀⠀⢀⣣⣤⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣥⢤⠆⢈⠛⣷⣴⡆
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⠦⠄⡒⠂⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⢯⣈⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⢮⠻⠾⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠦⠀⢴⣶⠇⠢⠈⢿⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠷⠀⠀⠀⠀⡆⡄⠀⠏⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣦⣄⣠⣠⣾⡇⣉⠀⠀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠞⠦⠀⠙⠻⢿⣿⣷⣿⡞⢉⡄⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠙⢿⣯⣴⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠋⢉⠉⠉⠛⠻⠋⢻⣿⣿⣖⠀⠀⠀⠀⠘⢿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⢂⠀⠀⠀⠀⠐⠀⣀⠙⣿⣿⣿⣿⡟⠛⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣡⢁⣀⣠⣿⡟⠃⣬⣻⣿⣿⣷⣿⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣼⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠤⠌⣉⣐⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⠼⣆⠱⣤⢤⡤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠁⠰⠶⣿⣿⣿⣧⡘⠿⠿⠛⠀⠀⢈⡁⠲⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⠁⠀⠀⠀⠀⠀⠀⣠⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣶⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣷⣷⣷⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⠶⢦⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⢀⡠⠤⠴⠦⢤⡈⠙⢻⣝⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠉⠉⢩⢾⠿⣧
⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⢰⡀⢻⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣁⣱⠊⠀⠹⣇
⠀⠀⠀⠀⠀⣰⠆⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠀⠀⢼⡆⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣼⡿⠛⠶⠾⣴⣿⡆
⠀⠀⠀⠀⣴⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⡇⠀⢲⣿⣿⣿⣤⣶⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡿⢷
⠀⠀⠀⢰⡿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⣬⣿⣿⠀⠓⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣯⣦⠀⢸⡇
⠀⠀⠀⣼⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠋⢀⣾⠃⠀⣸⣿⡏⢀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠐⠒⠒⠀⣿⣿⣄⠀⡇
⠀⠀⠀⢿⣇⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⡤⣠⠞⠁⢠⡾⠃⠀⠀⡸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⡿⢸⢀⡇
⠀⠀⠐⣿⠻⣦⣀⠹⢦⣀⣀⣀⣐⣦⡄⠈⢁⣤⠾⠋⠁⠀⢀⡀⢻⣿⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡼⢸⠃
⠀⠀⠀⠈⢣⠀⡙⠷⣦⣄⣈⣀⣠⣤⣴⠾⠛⠁⢀⠀⢠⣾⣾⣿⣿⡿⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢇⡟
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠉⠁⠀⢀⠠⣶⠚⠚⡚⠉⠉⠻⢿⡟⠁⠘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡜⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠙⣲⣶⣤⣶⣤⣿⣧⡀⠑⢈⠄⠀⠀⠉⠒⠢⠾⢬⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⣿⣿⣿⣿⣆⠀⠀⠒⢄⡀⠀⠀⠀⠀⠈⠉⢳⣆⣐⣀⣀⣒⣶⣶⣬⣥⣶⡾⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠈⠉⠉⠉⠉⠁⠀⠉⡻⣝⠛⠳⢦⡄⠀⣀⣠⣤⣤⣴⣶⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⢠⠏⠙⠒⠂⠀⠄⠀⠠⠒⠚⠒⢊⣠⣼⣿⠆⠀⠀⠀⠀⠐⣺⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣷⣦⣀⠀⢄⣀⣀⣀⡤⠞⣛⣽⣿⠟⠉⠑⠛⠼⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧⢄⡀⠀⠠⠤⠞⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀⠀⠈⢀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠴⠀⠀⣀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠠⠊⠀⠀⠈⠀⡂⠥⠤⠤⠤⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠒⠖⠠⣄⠠⡴⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴⠠⠀⢄⠀⠄⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⢰⠋⠀⠈⢢⣀⠈⠒⠄⠀⠀⠀⠀⢀⣠⣶⣌⠢⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠋⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⢿⣿⡿⠋⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠐⢠⣤⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠂⠀⠀⢠⠔⠏⠀⠠⣀⡀⠀⠀⢀⡠⠄⣤⣤⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⢿⠋⠙⢉⡄⠱⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠠⠃⠀⢤⠀⠀⠀⠀⠀⠀⠈⠳⠂⠐⠈⠂⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟
⠀⠀⠀⠀⠘⢰⠀⠀⠀⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠘
⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠉⢀⣹⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣴⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⣒⣾⡏⠉⣳⡶⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠘⠛⠋⢀⡀⠉⠛⠃⠈⠗⣄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠂⠀⢀⠁⡃
⠀⠀⠀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘
⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠰⠁⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢰⠏⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⠆⠀⠀⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢀⠀⡗⠀⠀⠀⡀⠂⠀⠀⠐⠉⠁⠀⠀⠒⠂
⡁⡄⠀⣀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠂⡎⠁⠠⠀⠊⠀⠐⠀⠀⠀⠀⠀⠀⠠⣀
⠓⠇⣄⡈⠣⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠢⡠⠊⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠖⠒⠛⠲⠤⠄⡀⠀⠀⠀⠀⠀⢢
⠸⣶⡞⣿⡠⣶⡦⣄⠀⠀⠀⠀⠈⠀⡀⠊⠀⠠⠀⠀⠀⣠⣴⣿⡿⣉⠅⠀⠀⠀⠀⠐⠊⠀⠸⠎⠉⠀⠀⡤⣿
⠀⢿⣧⣿⣇⣿⢷⣧⣻⣦⣆⠀⣼⢰⡷⡀⠀⠀⠀⠀⣼⣿⣿⣿⣝⢅⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⢠⣿
⠀⠈⢾⢿⢩⣀⢈⣿⡟⠇⣧⣡⡇⣿⡗⠂⠀⠀⠠⠔⠻⢭⡿⠃⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⣠⡿⣿
⠀⠀⠀⠱⢿⣿⣼⣵⣿⢘⣿⣸⡷⡀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⣿⠞⠅
⠀⠀⠀⠀⠀⠑⠋⣯⡻⣻⡿⠸⠿⡧⡺⢿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠈⡃⠰⣫⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠛⠛⠛⠛⠑⢍⠛⣿⣰⣲⣄⣠⡀⣄⢠⢀⡐⡄⠄⡍⡠⣔⡷⢞⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠈⣬⣻⣿⣿⣌⡟⣬⢀⡏⣠⣕⣷⢿⣷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠻⠿⠿⠽⠯⠽⠔⠚⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣤⣀⠖⠃⠈⢉⣉⣁⣠⣽⣦⠀⠀⠀⠀⡀⠐⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣸⣿⣿⣿⣯⡀⠀⠀⢈⣿⣿⣿⣿⣿⣆⠄⠀⢰⣧⠀⠀⠙⠓⢢
⠀⠀⠀⠀⠀⢀⣀⣄⣉⣹⡿⢿⣿⣟⣻⡗⠛⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣯⠴⣥⡆
⠀⠀⠀⠀⢀⠁⣹⣿⣿⣿⡄⠉⠀⣀⣠⣤⣾⣅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠏⠛⣿⢷⣴⣿⣶⣶⡄
⠀⠀⠀⠀⠀⢻⡫⢟⣽⡿⣿⢦⣾⢯⣴⣿⣿⣿⣯⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠂⡐⢛⣿⣿⣧⣴⣦⡀
⠀⠀⠀⢀⣧⣶⣿⣾⣿⡿⢻⣿⣿⣿⣿⣿⡏⢁⣬⣽⠳⣿⣯⣀⣀⣠⡄⠈⣀⣠⣤⣴⣿⣿⣿⣿⠏⠉⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠻⠿⠿⠛⠛⠙⠛⠿⠿⠿⠿⠿⠛⠛⠉⠉⠛⠛⠛⠿⠟⠛⠛⠛⠋⠁

⠀⠀⠀⢀⡠⠔⠂⠀⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣒⡒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣉⡑⢒⣤
⠀⢀⡔⠉⠀⠀⠀⠀⢀⣜⣴⠀⢣⠀⠀⠀⠀⢠⡶⢤⡀⠀⠀⠀⠀⠀⠀⡠⢿⣽⣹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⠤⡀⢸⡏⠉⠉
⠀⠎⠐⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⢣⠀⠀⠀⠈⢧⡐⠌⡑⢂⣀⣒⡮⠝⣠⠎⢨⡯⡇⠀⠀⠀⠀⠀⠀⠀⣰⣡⠚⠓⢲⣉⣱⣏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣮⠋⡒⠤⠤⠤⠤⢒⠫⣀⠔⡱⠁⠇⠀⠀⠀⠀⣀⡤⠲⣁⡜⠁⠈⢳⢈⠀⢀⡏⢳
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠈⣶⢚⠽⠿⠿⠍⠒⢋⡡⠊⠀⡘⠀⠀⠀⠀⢎⣠⠓⠴⡁⠙⡖⢒⠛⠒⢏⣁⣟⢹
⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠑⢄⠉⠁⠒⠀⠉⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⠓⠚⠬⡹⢍⡹⠤⠤⠾⠴⠋⠉
⠀⠀⠀⠈⠉⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠈⠢⣀
⠀⠀⠀⠀⠀⠀⡀⢰⢆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⠶⠲⡖⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⢀⣱⡘⠈⣎⠟⡄⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠈⠓⣄⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⢀⠎⠀⠖⢠⡝⢦⡉⠠⣇⡤⠒⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡸⢀⡴⡫⠤⣤⢄⡀⠀⠀⠀⢠⡇⡆⠀⠀⠀⠀⠀⠈⢦⠀⠀⢸⡀
⠀⣰⢡⠀⠛⠀⢠⡄⢈⠙⢦⢠⡬⠆⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠈⣠⡿⣟⠃⠄⡨⢃⡙⡦⡀⠀⠘⡇⠳⢆⠀⠀⠀⠀⠀⣸⠀⠀⢸⠇
⢰⠃⢀⠀⠐⠆⢀⠀⠈⠁⠘⡆⢻⡀⠀⠀⠀⠀⠈⠑⠢⠤⡤⠤⠚⢱⡏⣹⣏⡹⢌⣁⡌⡇⢳⡀⠀⠈⠲⠬⣙⣁⣀⡠⠴⠧⠤⠖⠋
⣦⠁⣈⠀⢠⠀⠀⣤⠈⢋⡸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡞⢙⠉⠒⡌⡰⠁⡠⠟
⢧⣀⡄⠰⠆⣀⣤⡤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⣭⣮⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣿⣦⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣄⠀⣀⠤⠒⣒⡶⣤⠄⠀⠀⠀⠀⠀⠐⠲⢶⠶⢼⠹⡿⣿⠟⢻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡌⢶⠅⠂⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠚⠆⡧⠚⢈⣩⠽⠒
⠀⠀⠀⠀⢀⣤⠤⢤⣀⠦⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠹⣼⠓⠢⠤⠔⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⣭⡽⠯⢷⡛⠛⢿⢶⠈⠶
⠀⠀⡠⢚⡥⢂⡛⠰⠮⠗⢘⣛⢲⡄⠙⢦⠀⠀⠀⠀⣾⠸⣅⠀⠈⠚⠛⠁⠀⠀⠀⢂⡇⠀⠀⠀⠀⣠⡖⠩⠥⠄⠩⠬⢽⣻⡕⢸⠙
⠀⡸⠁⠚⠉⠰⠗⠛⣼⠉⠺⠧⠀⠀⠀⠈⡇⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⡴⠁⢠⣀⡀⣄⣀⣆⣀⡄⡇⠈
⠀⢧⢆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠼⣸⠁⠀⠀⢸⠛⠉⠈⡀⠀⠃⠀⠀⠀⣿⠃
⠀⠈⠯⣓⠉⠒⠒⠦⠆⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠘⡂⠒⡗⠂⡏⠈⣏⡴⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠉⠑⠒⠚⠁⠀⠀⠀⠀⠀⠙⢯⣀⡃⣸⣃⠼⠋

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣴⣿⣿⣿⣶⣄⠀⠀⠀⠀⣠⣴⣤⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⡀⠀⠀⠀⠀⡀⣀⠀⣄⣲⣄
⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⣶⣼⣿⣿⣿⣿⣿⣤⠀⠀⣾⣷⣿⣶⣿⣿⣿⡆⠀⠀⠀⠀⢷⣶⣀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⠦⠖
⠀⠸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠙⠛⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⢀⣰⣾⣿⣷⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⢠⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠄⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⢾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⡀
⠀⠀⠀⠈⢻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠘⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⣿⣆⠀⣀⠀⠀⠀⢠⣾⣿⣿⣶⣦⠀⠀⢀⡮⣿⣿⣿⣿⠆⠀⠀⠴⢶⣶⣷⣿⡿⢦
⠀⠀⣴⢊⣹⡿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣇⠀⢸⣷⡀⠛⣻⣿⣏⠀⠀⠴⠟⢻⡟⠙⠛⠂
⠀⠀⣿⣧⣻⣿⣺⣿⣿⣿⣿⣿⠇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠻⣿⣾⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢶⣶⣶⣶⠆⠀⠀⠀⠈⠿⡿⠟
⠀⠀⠀⠀⠀⡀⢠⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠠⢀⣀⡀⣀
⠀⠀⠀⢶⣺⣟⣟⣿⣿⣓⠖⠀⠀⠀⠀⣤⣴⣶⣿⣶⣦⡄⠀⠀⠀⢀⣀⡀⢈⣠⣤⠀⠀⠀⠀⣦⡿⡛⣯⡻⣿⣷⡄⠀⠀⠀⠀⠀⠠⠀⠀⠠
⠀⠀⢰⣟⣿⣿⣯⣿⣿⣿⣷⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣇⢻⣼⣧⢘⣻⡇⠀⠀⠀⠀⠀⠀⠀⠒⠁⠄⠂
⠀⠀⠈⠉⠉⠉⠈⠁⠉⠈⠉⠁⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣦⡻⢿⣸⣿⡇
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣄⡄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⠻⣿⣿⣶⣿⣿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣷⠟⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⡀⠂⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⢀⡤⠌⠀⠀⠀⠀⠀⠢⠂⠠⠀⠀⠀⠀⠀⠀⠀⠈⠸⠅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⠄⠀⠀⠀⠁⠈⠀⠀⣰⠶⡀⠀⠀⣉⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠀⠀⠀⠀⢸⣿⣾⣇⣾⣿⣾⣿
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣽⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣿⣿⠿⠻⠿⠛⡿⢿⠿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⡒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣍⡓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢥⣉⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡼⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠉⢻⣔⢛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠀⣀⣀⡉⢫⡀⠳⡒⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠴⠒⠀⠀⢀⣀⣀⣀⣰⠋⠀⢱⡄⠙⣄⠉⡉⠙⣆⣀⣀⣤⣤⡤⠤⠤⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠐⠋⠁⠀⠀⡀⠀⠀⠂⠉⠉⠁⠀⠀⣇⠀⠀⢥⡇⠀⠈⠓⠉⠀⠀⢀⣀⣠⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⢰⠀⠢⠤⣀⣀⠜⠁⢀⡄⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠚⠉⢙⡦⡄⠈⠓⠤⣄⡠⠜⠁⠀⢈⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠐⠲⠤⣄⣉⣳⢶⣮⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠱⣀⠀⠀⠀⣀⠀⠀⣠⣞⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⢹⠟⠚⣱⡄⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⡻⠒⠉⡇⠹⡅⠠⡌⢣⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠼⣇⠈⣾⡒⠒⠒⠒⠒⠀⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣧⠀⠙⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⠆⠛⠛⠛⢦⠘⣗⠒⠒⠒⢬⡳⣄⠹⡝⠲⢄⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠞⡻⠀⠸⣀⠀⠀⠀⠈⢧⠘⡆⠀⠀⠀⠙⢎⡆⠹⡄⠐⠉⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸
⠀⢀⣠⠔⡋⠀⣠⠞⠲⣄⡈⠓⠤⠀⣀⡈⣣⡘⣄⢀⡠⠖⠉⣠⠔⠁⠀⠄⣀⠐⠻⠢⡀⠀⢀⡇⠀⢀⡀⠀⠀⠃⠀⠀⡜
⠊⠁⢀⡤⠖⠋⠀⠀⠀⠀⢉⡷⠂⠠⠤⠤⠭⠭⠥⢤⠤⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⣀⠹⡆⠼⢁⡆⠘⠁⠀⠀⠀⠀⢠⠃
⢷⠈⠀⠀⠐⠀⠀⠘⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠈⠓⢷⡀⡎⠀⠀⠀⠀⢀⠀⢀⡎
⠈⣇⠀⠀⢀⡤⠀⣠⠞⠀⠀⣠⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠇⡆⠔⠀⠀⠀⠚⠀⡜
⠀⠘⣆⠀⠀⣠⠞⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠄⠀⠘⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡇⠀⠀⡠⠀⢀⠌
⠘⠀⢫⠑⠮⣀⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡄⠀⢠⠞⠀⠀⡇⣠⠞
⠀⡇⠸⠀⠀⠈⣏⠓⠒⠤⢄⣠⡏⠀⠀⠀⠴⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⢸⠋
⠀⢹⡀⠃⠀⠀⠹⠀⠀⠀⠀⠀⠉⠒⢲⠒⠶⠶⠒⠂⠀⠑⠒⡶⠤⠤⠄⠒⠂⠁⡜⠀⡀⢀⡎
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡞
⠀⠀⠀⠻⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢇⠀⠀⠲⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠑⢤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡠⠂⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢄⡀⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡋⣡⠼⢭⣿⣯⡝⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⣿⣿⣝⣹⣽⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠗⠫⣥⡤⠤⣄⠀⠉⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣄⣾⣿⡾⢛⣿⡣⢻⢸⠃⡯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣶⠿⠇⠀⢀⡒⢀⠔⠈⠒⣻⡗⠂⠀⠀⠀⠀⠀⠀⠀⣠⠎⡠⠒⠀⠀⠀⠉⠻⣽⣿⢫⣯⡜⣸⡇⣿⣿⡇
⠀⠁⠀⠀⠀⠀⢱⣿⣷⣬⣯⠭⣭⡝⠛⠁⣺⠏⠁⠀⠀⠀⢴⣄⣂⣀⣼⣿⠀⡇⠀⠀⠀⠀⠀⠀⣿⠏⣾⢁⣰⢟⣽⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣷⣟⣿⡿⠋⠀⠀⠀⠀⠀⠸⣷⡿⣼⣿⣿⡄⢣⠀⠀⠀⠀⢀⠀⣿⡧⡳⢋⣡⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣦⣑⠂⠀⠀⢀⣺⣿⣯⣴⣽⣯⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⠿⣿⠿⠟⠁⠀⠉⠙⠛⠋⠁
⠀⠇

⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⢺⠒⢄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⣑⣤⣵⢂⡀⠀⠀⠀⠀⠀⡹⠺⣄⠀⠀⠀⠀⠀⡱⠤⠵⣋⡜⠀⠀⠀⠀⠀⠀⠀⢸⠆⠑⡄
⠀⠀⠀⠀⠀⢎⠆⠀⠉⠁⠈⢣⠀⠀⠀⡸⠀⠀⠘⡄⠀⠀⠀⢸⠰⠀⠂⠂⢸⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⡜⡁⠀⠀⠀⠙⡄⠀⠀⠈⢎⢘⢀⢁⠆⠀⠀⣀⠠⠴⠚⢁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣠⠃⠀⠀⢇⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠒⠊⠀⠀⠘⢥⣉⣉⣉⣁⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠉⠉⠁⠀⠀⠀⠀⠑⠒⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢢⠀⠀⠀⠀⠀⢀⡤⠤⠼⡤⢮⡀
⠀⠀⠀⠀⠀⢀⣴⠍⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡤⢴⡺⠯⢷⡼⠤⠤⡀⠀⠀⡏⡎⠀⠀⠘⡄⠈⡆
⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢰⠚⢄⡠⢇⠀⣰⡿⠶⡖⠁⠀⠀⡗⠂⠀⠀⠐⠁⢀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣟⡩⠻⢄⠀⡏⠉⣧⠠⠏⠀⠀⠀⠘⠦⣀⣀⣀⠴⠊
⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⠤⠖⠁⠀⠀⠀⠸⠤⠷⠤⠚⠐⠉⠉⠁⠀⢠⢤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⡌⠁⡈⠀⠄⢀⠀⢁⠀⠂⡈⡸⢰
⠀⠀⠀⠀⠀⠀⢸⠦⡸⠙⣤⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣦⡀⠂⠠⢈⠀⡄⠐⠀⡰⣡⠃
⠀⠀⠀⠀⠀⠀⢸⠳⢽⢊⡤⢻⠀⠀⠀⠀⡴⠊⠁⣶⣀⠤⢄⣀⠀⠀⠀⠀⠀⠙⠪⢕⡲⠤⠤⠤⣒⡭⠚⠁
⠀⠀⠀⠀⠀⠀⣠⠓⠻⣟⠙⣧⡀⠀⠀⠈⠓⠒⢩⣋⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣎⠈⣦⡊⠈⡱⠧⣵⠀⠀⠀⠀⠀⡇⡃⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⠴⢒⠩⠭⣑⠒⠤⢄
⠀⠀⠀⠀⠀⡟⠻⣄⣩⠾⢄⣰⢹⠀⠀⠀⠀⠀⠳⣁⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⢳⠶⣊⠑⢢⠼⣉⠏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠁⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠑⠶⣋⡱⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⢀
⠀⡀⠀⠄⠀⠀⠈⣀⣀⣤⠴⣷⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⠤⠤⠴⠶⢲⣶⣦⡀
⠀⢤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠹⡟⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢾⣆⠀⠀⠀⠀⣠⠴⠚⢁⠎⢸⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⣤⠔⠋⠁⠀⢀⠎⠀⠀⣇⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢿⡦⣄⢀⡞⠀⠀⠀⠸⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⡿⢷⣦⣄⣀⠀⣧⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⠋⠀⠀⠈⠉⠙⠛⢻⡿⠶⠟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣦⡤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⣀⣀⣮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⡙⠧⣸⣏⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⢺⣿⠟⢒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠉⠙⠓⠒⠶⠾⠭⠤⠤⠤⠤⠭⠷⠶⠒⠒⠛⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠧⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣇⢸⠟⠲⢭⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡜⡆⠀⠀⠈⠒⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠹⣌⢆⠀⠀⠀⠀⠑⢝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠈⠳⣕⠄⡀⠀⠀⠀⠡⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢦⡀⠀⠈⠳⢬⡒⠄⡀⠀⢰⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⠉⠓⠲⢤⣥⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠚⠉⠓⣲⣖⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠁⣠⣶⠆⠀⠉⠀⠀⠀⠌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⠐⡌⢧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡐⡈⣷⡄⢀⣠⣠⠤⠴⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠹⡀⠆⠁⣠⢞⢫⠍⠀⠀⢀⣉⣀⣈⣀⠒⠲⢭⣒⢤⡀
⠀⠀⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠁⢠⢞⠕⠁⠀⣀⠴⠚⠉⠈⠀⠁⠉⠙⠓⢦⠙⢳⣿⡄
⠀⠀⠀⠀⠀⢸⣇⣼⣿⠀⠰⠀⢀⢐⡆⠀⠁⠀⠀⠀⠀⠐⢠⣟⠊⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢹⣿⡀
⠀⠀⠀⠀⠀⢈⣿⣼⣷⠀⠰⡄⢠⠈⡇⡀⡇⠇⣷⢠⡜⠄⡿⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⣍⣁⣼⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⡁⢇⠈⡄⡇⣇⣷⣦⣿⢸⡇⡀⢰⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡎⣰⣾⡿⠟⡟⠋⠟⠿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡰⢸⣷⡀⣧⣹⠹⣿⢹⣼⡇⣴⡾⣿⡄⠀⠘⢇⠀⠀⠀⠀⠀⣸⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣧⣸⣿⣿⣽⣼⣿⣧⣿⣷⣿⣷⣀⠀⠈⠒⠒⠒⠒⠚⢁⣰⠏⠃⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⢹⣿⢶⣤⣤⣶⣾⣷⡾⡿⡏⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⢝⣦⣙⢮⡛⠻⡛⠀⠀⠁⠀⠀⣠⡆⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣓⣬⣀⣀⠀⠀⣀⣄⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠵⠋⠁




⣶⣶⣶⢶⠾⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⡶⣶⣾⢶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⠟⠉⠁⠀⠀⠀⠁⠉⠐⠂⠤⣀
⠀⠀⠀⠀⠀⣠⠔⠁⡠⠊⠀⠀⣀⠄⠀⠀⠀⠄⠀⠄⠀⢀⠀⠈⠙
⠀⠀⠀⡠⠠⠃⢀⠈⠀⠀⡴⠊⠀⠀⠀⠀⠔⠁⠀⠀⡐⠀⠀⠀⢠
⠀⠀⡠⠡⠁⠀⠂⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⡇
⠀⠰⠁⠁⠀⠀⠀⠀⡈⠀⢀⠆⠀⠀⠂⠀⠀⠂⠀⠰⠀⠀⠀⠸⠀⡏⠄
⠀⠀⡞⢰⠀⠀⠀⠀⠁⠀⠊⠀⠀⠂⠀⢀⠂⠀⠀⡜⠀⠀⠀⠀⠀⡇
⠠⠊⠀⠘⠀⠀⠔⠀⠀⠀⠀⠀⡔⠀⠀⡀⠀⠀⠈⠀⢀⠀⠀⠀⠰⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⠺⠀⠀⠀⠀⠀⡠⠀⠠⠊⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠁⠈⠑⠢⢄⡀
⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠤⠤⠄⠀⠒⠂⢀⡉⠡⠀⠂⠀⠈⠉⠁⠁⠂⢌⠢⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⡠⠊⠌⠀⠀⠀⠀⠀⠀⠃⠀⠒⠀⠁⠀⠀⣀⠠⠤⠄⠠⠤⢀⠀⠀⠀⠀⢆⠳
⠀⠀⠀⠀⠑⠀⠀⠀⠐⡒⠀⠀⡀⠄⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡨⠊⠀⠀⠀⢁⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠎⠁⢴⠋⠀⢃
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠠⠀⠤⠤⠄⠤⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⢘⠀⠈⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⢠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠄⠀⠀⢀⠆⠀⠀⡈⠉⠐⠀⠀⠤⠔⠊⢀⡠⠊⠀⠐⠀⠃⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠅⠐⠢⠄⠀⠤⠄⠊⠀⠀⠉⠒⠂⠀⠒⠊⠁⡀⠀⠠⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⠠⡀⠀⠀⠀⠀⠐⡀⠰⡀⠠⠀⢁⠀⠃⠀⠀⠀⡄⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⢄⠑⢄⠑⠌⣀⠈⠀⠑⢄⠀⠀⠀⠆⠀⠇⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠥⣤⣀⠀⠀⡑⠀⠑⢀⣀⠤⠂⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⡖⠲⣄⠀⢀⠴⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠶⡁⣰⣁⣀⡀
⠀⠀⠀⠀⠶⣉⠉⠉⢙⢃⣶⢧⣦⢋⡤⠖⠛⡩⠍⣀⠤⠀⠉⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⢀⣄
⠀⠀⠀⠀⢀⠔⠓⠈⣺⠾⠾⠾⣿⣿⣧⡀⠀⣒⠭⠒⣈⣀⣀⠀⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣤⠋⠈⡆⠀⠀⢀⣀
⠀⠀⠀⢀⠗⠊⠉⠈⢳⡀⢀⣾⣿⠏⠀⠑⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢿⢀⢀⠷⠊⠉⢀⡇⣀
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠱⠎⠡⠉⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣀⣀⣤⡴⠶⠶⠶⢤⣤⣤⣀⣀⡜⠀⢋⡬⢈⡨⣇⠐⢋⣠⠞
⠀⠌⠀⠀⠀⠀⡠⢒⠤⡲⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⠛⢉⣠⠔⢲⠖⠒⢄⠀⠉⠉⠀⠀⠸⠜⠛⠞⠀⢀⣼⠟⠁
⡸⠀⠀⠀⠀⠈⠀⠁⠈⠀⠊⠁⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢆⠀⢀⢖⠕⢀⠤⡌⣁⠹⠤⡾⠦⢴⡋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇
⡇⠀⠀⠀⠀⠀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢰⠝⠡⢈⣴⠟⢡⠊⢣⡠⠋⣥⣤⣤⠷⠤⠖⠉⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣐⣆⣲⠸⠄⠀⢠⢿⠃⡠⠾⣄⡠⢧⡀⣸⡁⢘⣤⡖⠙⡶⠉⠀⠀⠀⡠⡖⠒⢲⢉⣦⡀⠈⣷⡄
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⣻⣒⠹⠇⠀⠀⣟⠇⠈⠀⠀⠸⠤⣔⣉⡜⠙⢧⣦⡷⠾⡀⠀⢀⡮⣉⠀⣸⢤⠿⣏⢀⡽⢆⢻⡝⡄
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣘⢓⢳⠹⠏⠂⠀⣎⠏⢀⡰⠉⣏⣀⡠⠋⣨⠧⣀⡞⠉⣧⣶⡃⠀⡏⠀⠀⡏⢣⣬⣀⡜⠻⡀⡜⢸⡏⢽
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⢦⢙⣒⡛⠎⠯⠧⠄⢸⡏⠀⡏⠑⠺⣁⣀⢹⣽⣁⣠⣨⠛⠒⡏⠀⣹⠀⢸⢦⡾⠤⢞⡔⠛⠧⣤⡽⠁⣼⠀⢛
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠰⠈⡄⠀⠘⡝⣖⠲⠈⠹⠌⠏⠀⣾⠀⡠⠓⠒⣴⠉⠹⡏⢠⣹⢽⡝⠂⠲⣏⣉⢱⡇⢸⠸⣴⣲⣘⣤⠯⢷⠁⡸⡰⡏⠀⣼
⠀⠀⠈⢆⠀⠀⠀⠀⠄⠁⠡⡀⠀⠐⠑⠐⠀⠩⠀⠑⠀⠀⣿⡄⢣⡦⠷⣸⠊⠚⣿⢿⡁⠞⣧⠴⠾⠟⠙⡿⠓⢣⠔⠚⣇⡈⢧⡤⢬⠟⢁⡷⠁⢐⣿
⠀⠀⠀⠈⠣⡀⠀⠀⠀⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣼⣇⠘⣷⣀⣜⣠⢴⣅⠀⣼⠉⣹⢴⣦⠗⠸⣆⣠⡧⠶⡾⠛⠳⡏⣀⠎⡠⡺⠁⠀⢴⡿
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⢜⠫⠪⣿⡀⠀⠳⡀⡧⠤⣜⠉⢙⠛⠁⢴⢛⠦⡇⢀⣇⣀⣄⣧⡞⠉⣹⠁⣰⡱⠁⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⢀⣠⠠⡢⢐⢅⣊⡵⠬⠞⠉⠳⣤⡀⠳⢧⡔⣋⣉⡁⠀⡠⠼⢇⢀⡸⡏⠀⠉⣏⠀⢸⠞⢁⣴⠟⠁⠔⢘⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠙⢮⣦⠀⠈⠁⠀⢹⣠⠧⢤⡼⣍⡞⠛⡟⠉⣉⠖⢁⣠⡿⠃⠀⠀⢈⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⣀⠀⠀⠉⠛⣆⣈⣦⣠⠟⢉⣁⣴⣿⠟⢁⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⢷⣶⣶⣶⠦⣴⡦⣭⠿⠟⣋⢥⣰⣵⠞⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣶⣶⣿⣷⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⡶⠷⢿⡛⠛⠿⠿⣿⣿⣲⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⣏⣉⠥⠀⠀⠐⠒⠀⠀⠀⠈⠉⠉⠉⣍⣍⣉⡙⣿⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠚⠁⠀⣉⠀⠀⠀⠀⠤⠒⠂⠉⠉⠉⠁⠀⠀⠐⠲⠴⠬⣿⣿⡆⢉⡻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣞⣫⠟⠊⠁⠀⠀⠀⠊⠁⠀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠀⠉⠉⠉⠁⢒⣭⠿⢿⣿⣽⣛⣛⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣶⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠨⠁⠠⠒⠉⣥⣯⣤⣬⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡫⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠤⠂⠀⠀⠈⠀⠠⠀⠀⠀⠀⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠤⠖⣪⡴⢋⠞⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⢠⢾⣿⢹⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⠟⣰⠃⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠃⣾⣧⡏⡾⣿⡿⣿⡟⣿⡀
⠀⠀⠀⠀⠀⢠⣏⡾⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠔⠁⣸⡏⡸⣠⢸⣿⠁⠼⡏⣿⡇
⠀⠀⠀⠀⠀⣾⣏⢡⠠⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣴⡟⡜⣱⠇⡈⡇⣠⡄⣷⣿⣷
⠀⠀⠀⠀⢠⡟⡿⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⡟⣰⡟⡰⣸⢣⣿⣿⣿⣿⣿
⠀⠀⠀⠄⣿⠇⣷⣀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣼⠛⣰⣿⣡⣿⡟⣼⠃⣏⣿⢿⣿⡆
⠀⠀⠀⢠⣿⢸⡇⡇⠀⠀⠂⠄⠀⠀⠀⠀⠀⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⣦⡾⡅⣴⢷⢿⡟⣼⢰⡇⣼⡏⡏⣾⣿⠃
⠀⠀⠀⢸⡿⢾⠷⡇⠀⠀⠀⠀⠀⡠⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⡿⣃⣼⢃⢃⡏⣼⢳⡿⢠⣿⣱⠟⣿⡿
⠀⠀⠀⢸⡇⣼⠚⡇⠀⡐⠀⠀⠘⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠂⡠⢂⠞⣡⢋⠞⠁⢹⣿⣟⣾⢃⣿⢣⡟⣿⣾⢠⣿⡇
⠀⠀⠀⠸⣇⣿⠈⡃⢰⠁⠀⠀⡄⠀⡰⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠊⠀⡀⣠⠀⠀⠀⢂⠄⠊⡠⣠⠞⣱⢣⠆⣠⣿⢟⡼⢁⣿⣿⠟⣸⠏⢣⣾⣿
⠀⠀⠀⠀⣿⣿⠀⡷⠘⡀⡆⠀⠃⡔⠁⡀⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⢠⢞⠜⠁⠄⠀⠘⢁⣴⢊⢞⠵⢊⡿⡁⢰⡿⢫⡞⣠⣾⢋⣟⣼⢇⢠⣫⡟⠅
⠀⠀⠀⠠⢹⣿⣦⣦⠀⡆⡇⢠⢾⡀⠐⠀⣠⠂⠀⠀⡡⠂⠐⠀⠀⣰⠟⠁⠀⠀⠀⣠⡔⠈⢕⡕⢡⣴⡿⣪⣶⢋⡴⢋⡾⠟⢣⡞⣽⡟⠀⣼⡿
⠀⠀⠀⠀⠘⣷⣽⢸⡆⡇⡇⣾⢸⡇⠀⡰⠁⠀⠚⢉⠔⠀⢀⣠⠾⠋⠄⠈⡀⢔⠏⢁⣠⠶⠋⣠⡾⠛⢀⡵⠳⣿⣴⠟⢁⡶⡿⣺⡟⡌⣹⡿⠁
⠀⠀⠀⠀⠀⢸⣿⠀⣷⡇⣇⡇⣼⡅⠰⠡⠠⠂⠀⠁⡠⢒⡿⠁⠀⢀⡠⠞⢀⣠⡴⠋⠁⠀⠚⣡⠴⠾⢋⣴⡟⣉⠅⣲⡿⠊⣶⢟⣰⣾⠟
⠀⠀⠀⠀⠀⢠⣿⣧⣹⣷⣿⣿⣿⠰⢋⡔⠁⢀⠔⣫⠴⠋⣀⡤⠖⠉⠁⣠⡴⣉⡠⠔⠒⡀⠠⢐⠯⠶⠋⠉⣀⣤⠞⡩⣪⡾⡻⢋⡝⠁
⠀⠀⠀⠀⠀⠘⠹⣾⣿⣿⣿⣿⡿⢖⡥⢚⣤⣥⡊⠁⠐⣋⣡⣤⣶⣚⣭⡗⠬⢕⠀⠌⠀⡀⠈⠀⠀⡠⢆⡽⢋⣀⣬⣞⣯⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣥⡾⠟⣍⣉⣉⣭⣭⣿⡭⠍⠲⠋⠉⣀⡥⠤⠤⢴⡎⠀⠀⠜⣯⡔⣭⡴⣛⣫⣾⡽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣽⣷⣶⣿⢿⣟⠛⠛⣷⠂⠐⠲⠖⣊⣩⡭⣤⠆⣄⣠⠴⣖⣊⣭⠶⣚⣯⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⢿⣿⣭⣵⣿⣿⣻⣷⣒⠛⠻⢛⣛⣨⠽⠷⣟⣳⠾⠋⠋⠉⣋⣥⣾⠯⠞⠋⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⠒⠋⠉⠉⠛⠻⠶⠻⢧⡯⠶⠛⠱⠖⠛⠛⢉⡝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠑⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⡘⢄
⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⣀⠉⠪⡣
⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡦⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣈⠢⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠄⠀⠀⢀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠐⠈⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⢀⣠⣴⡶⠾⠛⢛⠛⠛⠷⣶⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡉⠀⠀⠀⠀⠄⠀⠀⠀⠚⠦⢄
⠀⠀⢀⣔⠿⠋⠀⠀⣀⡠⠼⠤⢄⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢦
⠀⣼⡿⠃⠀⢀⡴⠊⠁⠀⠀⠐⠂⠙⢧⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢧
⢠⣿⠁⠀⡠⠋⠀⠀⢀⠀⠀⠀⢠⠀⠀⠑⠄⠀⠙⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⠁
⣸⡇⠀⠶⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠁
⢻⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⡃⠁
⠙⣿⡄⢀⠱⡀⠀⡐⠄⠀⢀⡀⠀⠀⢀⣰⠃⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⠀⡘⠃⠀⠀⠘
⠀⠻⣷⡀⠀⠉⢢⡈⠀⠀⠀⠀⠀⢠⡔⠉⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡄⠀⠀⠂⠀⠀⠐⠀⠀⠀⡀⢐⠁⠂⠀⠀⠀⡰⠃
⠀⠀⠈⠺⣦⣄⡈⠀⠉⠒⠋⠙⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣖⡀⠀⣤⠄⠦⠌⠊⠁⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠉⠛⠻⢶⣖⣲⣦⣶⣶⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠄⣀⣀⡀⠀⣀⠀⠔⠂⠁
⣶⣶⡶⡶⢶⣶⣶⣶⣶⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢇⡀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣉⠒⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣙⢳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣌⠙⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣅⡸⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣋⡽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠶⠶⠶⠒⠒⠒⠂⠻⢦⡶⠛⣦⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⢦⡄⠷⡄⠈⢧⠈⢙⠶⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⣀⡀⠀⠀⠀⠐⠋⠉⠀⢀⣀⣀⣤⣤⡄⣴⠋⠀⠀⡸⠄⠀⢷⣄⠀⡀⢈⣳⡤⠤⠤⠤⠶⠶⠒⠒⠒⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⢇⡇⠀⠀⠉⠻⠁⠀⢀⡀⣀⣠⣤⣤⣤⣄⣀⣀⢸⡇
⠀⠀⠀⠀⠀⢠⠀⠤⣀⣀⠀⠀⡰⠋⠀⢀⡀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠙⣦⣀⠀⠈⠳⣤⣀⣀⣀⡴⠃⠀⠁⢹⡄⠀⠀⠀⠀⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠘⠤⢄⣀⡈⠙⠛⢧⣤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠨⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡞⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠟⠲⠾⣼⣟⡹⣆⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠳⣤⣤⣤⣴⠖⢤⠖⠒⠉⢦⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠋⠈⢤⡽⢦⠀⡼⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⡇⠈⡆⠀⢹⡄⠙⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠾⠐⠒⠚⣦⠀⢻⣁⣙⣉⣉⠉⢉⡁⠒⢤⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠓⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⢡⠖⠪⠙⠛⠛⢧⠀⢻⡖⠒⠒⠒⠲⣍⢦⡀⠹⣍⠓⢦⣄⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡴⠛⡇⠀⠸⡀⠀⠀⠀⠀⠈⢧⠀⢳⡀⠀⠀⠀⠈⢧⣙⡄⠹⡆⠀⠈⠙⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⡇
⠀⠀⠀⢀⣠⠖⠋⠀⢨⣧⣀⠀⠙⠲⣄⡀⠀⠀⠈⢧⠀⢷⠀⠀⠀⣀⡴⠛⠀⣀⠟⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⢸⠆⠀⠀⡀⠀⠀⠸⠃⠀⠀⢠⠇
⣀⠤⠒⠉⠐⢃⡤⠞⠉⠀⠈⠑⠢⣄⣀⠉⠒⠒⠒⠴⠷⠼⠗⠐⠊⢁⣠⠴⠊⠁⠀⠀⠈⠉⠒⢤⡀⠁⠙⣦⡀⠀⡟⠀⡀⢰⠇⠀⠀⠀⠀⠀⠀⣼
⣄⠀⡤⠶⠊⠁⠀⠀⠀⡀⠀⠀⢀⠜⠁⠉⠉⠉⠉⠉⠉⠉⠉⠙⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠳⢤⡘⣏⠘⠁⣼⠁⠈⠀⠀⠀⠀⠀⠀⢠⠇
⢻⡀⠀⠀⠀⠈⠀⠀⠀⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⡆⢿⠀⠀⠀⠀⠀⠀⡀⠀⠀⡞
⡀⢳⡀⠀⠀⢀⡴⠀⢀⡴⠋⠀⠀⠀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⠀⠀⠀⠀⡍⢰⡀⠞⠀⠀⠀⠰⠃⢀⡼
⠁⠈⢷⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⡇⠀⠀⢀⠀⠀⢀⠞
⢸⠀⢸⡇⣤⡴⠋⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠀⠀⠀⢻⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢸⠁⢀⡴⠃⠀⡰⠋
⠈⡄⠘⡇⠀⠉⠓⡶⢤⣀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⠞⠀⠀⠀⣿⠴⠋⠀⠠⠈
⠀⢱⠀⢻⠀⠀⠀⢱⡀⠀⠉⠑⠒⠠⢾⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠘⡿⠀⠀⠀⢰⡇
⠀⠈⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⣻⠋⠙⠋⠉⠉⠉⠉⠀⠉⢹⠖⠒⠒⠒⠊⠉⠁⠀⣸⠃⢠⠀⢀⡞
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡞⢀⡜
⠀⠀⠀⠘⣿⣆⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡞
⠀⠀⠀⠀⠈⢻⡀⠀⠀⠉⠀⠀⠀⠀⢰⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠞⠀⠀⡀⠀⠀⢀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⡴⠃⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄⣰⣄⡑⢤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠋⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣭⣿⣷⣶⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡥⢬⣟⣛⠛⣛⣛⣛⠛⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⠒⠀⡠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠆
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠤⠀⠐⠠⠞⠛⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⢀⡆⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖
⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠈⠈⠻⠶⠶⠶⠊

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠠⠆⠉⠀⢳⣧⡴⣊⢁⠙⢧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⠗
⠀⠀⠀⠀⠀⠆⠘⠁⢀⠗⠁⢤⣭⢉⠙⠉⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡀⠐⠤⠄⠄
⠀⠀⠀⠀⠤⠀⡙⠋⠛⠤⣈⠂⠉⠉⠠⠠⠤⠈⠓⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠴⠛⠣⠞⠀⠀⠃
⠀⠀⠀⠀⠀⠸⠃⠄⠀⠘⠋⡄⠀⠀⠀⠀⡄⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣏⠁⠀⢀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠐⠊⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡔⠒⠛⠹⣷⣤⠘⣁⣨⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠾⡆⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⢯⣽⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠐⣀⣐⡤⣠⠋⠀⠛⣄⠘⠂⠀⠀⠀⠀⠀⠀⣊⠁⠀⢠⠄⢀⠋⣱⠊⠿⠂
⠀⠀⠀⠀⢀⠀⠚⠁⠀⢨⠀⠱⣦⠉⠀⣷⠂⠀⠀⠀⠀⠀⠀⢁⠈⠲⠢⡔⠋⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠊⠀⠁⠀⠀⠀⠀⢆⠀⠁⠀⠀⠀⠀⠀⠀⠈⠈⠷⠜⠻⠦⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠂
⠀⣀⡀⡀⠀⡀⡀⡀⡀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣾⠟⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠿⣿⣤⣿⡿⠟⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⡇⠀⠀⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⠿⣿⣿⣿⡿⢿⣿⡿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠘⠁⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣠⡾⢻⣿⠙⢷⣤⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠋⠀⢸⣿⠀⠀⠙⢷⣾⡇⠀⠀⢀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢁⣴⡾⠛⠉⠉⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠉⠙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡾⠻⢷⣴⣶⣾⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⢿⣶⣶⣴⡾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⠶⠶⠶⠶⠿⢷⣶⣦⣬⣭⣛⡛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠋⠉⠁⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣹⣿⡆⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠿⠶⣶⣼⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠛⠿⠿⠶⠶⠶⠶⠶⠾⠿⠟⠛⠛⠉⣿⠿⢶⣶⡶⠿⠛⠋⠉⠛⠻⢶⣦⣤⣴⠿⠋⠀⢠⣤⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣾⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠿⠿⠷⠶⠶⠶⠶⠾⠿⠿⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠻⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠶⢶⠶⢶⣶⣶⠶⠶⠾⠟⠛⠁⠉⠛⠻⠷⣶⣦⣤⣤⣤⣤⣴⡶⠾⠛⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠔⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⢀⠠⣀⠀⠀⠀⠀⠀⠀⣖⠥⢂⣠⠶⡄⠐⠂⠀⣠⠀⠀⠠⠈⠁⢶⡦⠿⣀
⠀⠈⢄⠈⡀⠸⡃⠀⠀⠀⠀⡄⠀⠀⢰⠁⠀⡀⠀⡀⠑⠮⠉⠂⠀⠀⠀⠀⠈⠉⠏⠈⠁⠈⠁⠀⠊⠁⠀⠀⠀⠠⣦⣷⠺⡴⣯⢧⡀
⠀⠀⠀⠉⠉⠀⠙⠀⠀⠤⠞⠁⠀⠀⠈⢇⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠘⠑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂


⠀⠀⠀⠤⢀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢈⣛⣦⣀
⠀⠀⠀⠀⠈⠈⠀⠂⠒⠉⠀⠀⠀⠀⢰⠀⠀⠀⡀⢀⠄⣀⡤⠀⡀⠀⠀⠀⣠⠰⠆⢘⣤⡆⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠁⠜⡙
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠤⠄⠊⡄⠑⡀⢀⠙⠀⠀⠀⠹⣄⡬⠝⠀⠳⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⡆⢀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⣉⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄⢀⠔⠎⠛
⠀⠙⠛⠀⠀⠈⠉⡒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⢁⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠖⠛⠛⢓⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⠉⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⡠⣄⡀⠀⣀⠀⢀⡆⠔⠀⠀⠀⠀⠀⢀⠠
⠀⢁⠀⠆⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⡑⠀⠀⠁⣿⢳⠆⠀⠀⢀⡤⠊⠁⣀⠀⠀⠀⠐⠃
⠀⠀⠀⠄⠢⠀⠄⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠋⠋⠀⠀⠀⡈⠀⠀⠀⠈⢀⡰⠈⠄⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠂⠱⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⡀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⣦⡀⠀⢿⣿⣧⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣴⣿⣿⣿⣷⡀⠸⡯⠙⡇⠀⠀⣴⣿⢿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠻⣿⢻⣿⣿⣦⣙⡆⡇⠰⣇⣴⡿⠟⢡⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢷⣶⣤⣤⣭⣷⣝⣿⣛⣿⣛⣓⢶⢿⣿⡶⠶⣀⣠⣟⣁⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⣤⢶⡚⠟⣫⣀⣭⢹⡟⠻⢞⣱⣿⡟⢩⣾⢉⣙⣓⢿⡛⠒⠶⢿⡿⠿⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡀⣶⢸⣝⡿⢦⣴⢰⣿⡙⣿⣷⣿⣛⣿⣽⣿⡿⣦⢺⣷⣴⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡇⢸⣥⣏⢻⣿⢃⣬⣿⣏⣿⡿⢿⣧⣻⣿⣿⣿⢿⣷⣿⡶⣦⢿⣿⣷⣬⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⠈⣴⡀⣅⢻⣯⣁⣼⡛⢿⣛⣻⣷⣽⣿⣿⣿⣻⣿⣼⣿⣿⢧⡅⣦⣿⣽⡜⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⣴⠈⠑⣏⣷⣼⣷⣭⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏⢻⣾⣿⡿⢻⣾⣷⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠻⣂⠚⣮⠁⣿⣙⡦⣻⣤⣽⣿⣯⣻⣿⣿⡿⣻⣿⣸⣿⣾⣿⣿⢧⡻⣿⡶⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿⣦⠻⣷⠛⣶⢳⠘⣛⠻⣿⣟⡻⣿⣿⠟⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⢉⣿⣦⢰⡬⣉⠸⣿⠇⠻⣿⣿⡟⢿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⢻⣍⠘⢯⣼⡅⠋⣿⣳⣬⣿⣿⣿⣿⣏⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⠻⠰⣶⡌⠁⢰⣮⢻⣿⡴⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠱⣇⢙⣇⡸⠿⣿⣼⣿⡿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢹⣿⢿⣿⠀⣾⣿⣻⠱⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠟⣿⠛⣦⡝⠻⣃⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⣿⠏⢴⣦⡍⣿⣿⣻⢿⣿⣾⣿⣏⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⣦⠺⡆⢶⣏⣹⣿⣾⣿⣿⣛⣿⣟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣤⡰⡷⣿⣷⣏⣰⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⢿⣿⣟⡛⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣤⣄
⠀⢀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠸⣿⣿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠛⢻⣿⣿⣿⣿⣭⣽⠭⣭⣭⣙⣛⠛⠛⠒⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠋⠰⢐⠖⠂⠀⠉⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⡋⠀⠉⠂⠀⠈⠉⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣷⣻⢶⣦⣾⣁⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠲⣌⠑⢒⣢⣴⣶⣾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⣿⣿⣿⣿⣶⡿⢍⣍⣿⣛⡿⣻⣛⣻⣿⣿⠋⠉⠙⣿⣛⣿⣷⣿⣿⣿⣽⣾⣿⢂⣴⣼⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣳⣻⣿⣿⡿⡿⣛⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⣿⣻⣿⣿⣹⣧
⠀⠀⠀⠀⠀⠀⢰⣿⣱⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⡽⣿⣹⣇
⠀⠀⠀⠀⠀⢀⣿⢷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⣷⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣹⣇
⠀⠀⠀⠀⠀⣼⡇⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡏⣿
⠀⠀⠀⠀⠀⢿⡇⣿⣽⡿⣿⣽⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢳⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⢸⣇⣿⣻⣧⣿⢾⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣟⢿⡿
⠀⠀⠀⠀⠀⠘⣿⣻⣷⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢼⣳⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣟⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⠿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣟⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⢋⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣷⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉
⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣴⠚⡩⢿⣿⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⢟⣟⣿⣄
⠀⠀⠀⠀⢸⡿⢛⡉⡤⠠⠄⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣷⢛⣿⡙⡇⡃⣯⣧
⠀⠀⠀⠀⠸⣻⣟⣠⠠⠤⢄⡄⣀⡾⠏⠀⠀⡀⠀⠀⢠⡎⠐⠁⠀⠀⠀⢹⣿⢱⠗⣨⢇⢿⣿
⠀⠀⠀⠀⠀⠛⢿⣿⣯⣽⣵⣲⠞⠁⠀⠀⠀⢻⣿⣿⣿⡇⢀⠀⠀⠀⠀⢀⣧⡿⠚⣡⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢦⣁⣀⢀⣀⡾⣯⣴⣿⣽⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⡾⢷⡄
⠀⠀⠀⠀⠀⢀⣴⠶⠟⠷⢿⣧⣿⡶⠟⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⡆⠀⠸⣷⡿⠁
⠀⠀⠀⠀⠀⠚⠛⢻⣿⠿⣿⣿⣿⡿⢿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠉⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⢰⡟⣡⡾⠋⣿⠈⠻⣦⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⣿⠀⠀⠈⠻⡟⢀⣠⣴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣿⣏⣀⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣄⣈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣤⣤⣤⣴⣿⣤⣭⣙⣛⠷⠶⠶⣶⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠟⠛⠋⠁⠈⢷⡄
⠀⠀⠀⠀⠀⠀⢰⣟⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣿⣆⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣴⠟⠶⢦⣬⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠋⢹⡟⠷⡶⠾⠛⠛⠉⠙⠛⠷⣦⣴⡾⠋⠁⢠⣆⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠿⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣶⠶⠶⠶⠶⠶⢶⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣤⣤⣤⣀⣀⣀⣤⣤⣤⣼⠿⠛⠷⢦⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠗⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡟⡌⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢼⣿⣼⣿⣿⣿⣫⣶⠄
⠀⠀⠀⠀⠀⣰⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣻⣸⣿⣿⣿⣿⣿⣿⣿⣢⡼⠃
⠀⠀⠀⠀⢸⣭⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣲⠿⢻⣉⣿⣿⣿⣿⡿⣛⣯⣖⣿⡂⡆
⠀⠀⠀⠀⢾⣿⣯⣶⣶⣂⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⢢⣋⡻⣿⢿⣿⠿⠷⠳⣱⣿⠃⠁
⠀⠀⠀⠀⠸⣿⣷⣽⣾⣿⣄⠠⠶⣶⣨⡀⣀⣠⠆⠀⠀⠀⠀⠙⢯⣇⢠⡔⣹⣆⡖⣶⣞⢠⠟⠁⠈
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡛⠉⠉⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

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