Lazy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠉⠉⠉⠀⠀⠀⠀⠁⠄⠠⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠐⠆⠀⠀⢣⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⡆⠀⠀⠀⠐⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠄⠈
⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠐⠖⠀⠀⣀⡀⢀⠠⠐⠋⠀⠀⠀⠀⠀⠠⠀⠀⡔⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⡠⠤⣀⠂
⠀⠀⡐⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢐⡰⠒⠀⠁⠀⠄⠀⠀⠀⠢⢄⡈⠀⢀⣀⡠⠊⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠐⠒⡒⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⡠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠊⠀⠠⠄⠐⠂⢐⠆⢀⠠⠗⠀⠐⠒⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠄⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠙⠓⠂⠀⠀⠀⢀⡄⠀⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠉⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠀⠀⠤⠤⠤⠌⠀⠀⠤⠄⠀⠤⠤⠀⠂⠂⠩
⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠲⠶⠒⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢣⡙⢄⠀⠈⢻⡛⠛⠛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⡀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⡃⣇⠀⠀⠘⣧⠀⣀⠄⠀⠀⠀⠀⠀⠀⠁⠑⠀⠤⠤⣤⣤⣴⣶⡿⠉⠀⣹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⡅⡇⣠⣔⠒⠛⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⣠⣾⡿⠉⠋
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡆⠀⢩⣞⣅⡀⡀⢤⠠⠀⠀⡀⢀⣴⣶⡿⠟⠁⠀⣠⣾⣿⣿⢣
⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⠹⣿⠯⠐⠚⠛⠛⠟⠛⡷⠿⢷⣾⣿⡿⠛⠁⠀⠀⣠⣾⣿⣿⣿⡟⣾
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⠀⠀⣀⡀⣔⠀⠀⠀⠀⠀⠁⢀⢀⣀⢀⣴⣶⣿⣿⣿⣿⣿⠃⠨
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣟⣒⠀⢀⠀⠀⢠⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⢏⢄⡇
⠀⠀⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢛⣉⣙⠛⠛⠛⣛⠋⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⢿⡼⠁
⠀⠀⠀⠼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣷⡶⠦⠾⠿⠶⠷⠳⠤⠴⠤⢤⣤⣴⠷⠋⢵⡟
⠀⠀⠀⠘⠻⠻⠿⣿⣿⡟⣿⣿⣿⣿⣷⣄⡀⠹⣶⣤⣴⣤⣤⣄⣄⣠⣤⣤⣤⣤⠤⢤⣀⡀⣼⠛⠓⠚⠓⠒⠛⠛⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⣿⣿⣦⣌⠛⠛⣟⠿⠿⠛⠿⠻⠿⢿⣶⣶⣤⣬⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠤⢠⠄⢠⣄⣀⣀⠀⢀⡁⣁⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠉⠁⠈⠉⠁

⠀⠀⠀⠀⠀⢀⡴⠂⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡀
⠀⠀⠀⠀⠠⠈⠁⢀⠀⠀⠀⠀⠀⠄⠠⡤⠄⢤⡤⢠⡄⠶⠀⠛⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠡⣤⠀⠈⡄⠀⠀⠀⡧⠔⠒⠗⠒⠒⠳⠼⠧⠤⢀⣥⣿⣦⠀⢴⠆⠀⠀⢠⣶⣄⠀⠀⠿⠀⠀⠀⠀⠐⠠⠄⡀
⠀⠀⠀⠀⠀⡩⠋⣑⣷⡀⠀⠀⠁⠤⡴⠃⠂⠂⠁⠀⠀⠀⠀⠀⠉⠫⡀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⢠⣿⣷⠀⣶⠀⠈⠐⢄
⠀⠀⠀⠀⠠⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢶⠄⠀⠀⢰⡦⠀⠀⠈⠛⠋⠀⠀⠀⣠⣤⠀⠐⢄
⠀⠀⠀⠀⠸⠟⠐⣶⣾⠁⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣿⠃⠀⡀⠁
⠀⠀⠀⠀⣀⣀⡠⠛⠋⠀⠑⠄⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⢀⣠⡜⠀⣿⣿⠂⢀⣄⠀⢠⣾⣦⠀⠀⠛⠁⠀⠀⢀⣄⠀⠀⠘⠋
⠀⢀⣒⠁⣶⠀⠀⠀⠀⠀⠀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠈⣥⢀⡈⠁⠀⢈⡉⢀⠈⠿⠏⠀⣀⠀⠀⢀⣤⠀⠉⠐⠀⣤⠈⡀⠀⡀⢀
⠀⢿⣿⡇⠀⠀⠄⠀⠀⠀⠛⡤⠇⣀⣀⣀⠀⣀⣀⣀⡀⢀⠀⠀⢀⠀⠰⡎⠉⠁⠉⠀⠀⡀⠝⠒⠄⠀⠛⠀⠀⢿⣿⠇⣴⠁⠀⢈⡤⠚⢈⣵⣦⠀⣨⡄⢀
⡆⠈⠛⠡⣦⠀⠐⡀⠲⠀⠀⠈⠐⡆⠠⠄⢀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠒⠲⣤⠦⠀⢠⣾⠀⠀⢀⢀⡠⠀⠀⠠⢤⣥⣴⠁⠀⢀⠋⢴⠆⠘⢿⠟⠀⠈
⠇⠿⠂⢰⣿⣧⢠⡀⠀⠁⠀⠀⠀⠈⢠⠀⢠⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⢠⠟⠁⠰⢲⠟⠉⠁⣿⡄⠀⠀⢠⣤⡀⠀⣠⡄⠀⣰⣶⡄
⠀⢄⠀⠈⠛⠃⠈⢁⡀⢀⠀⠀⠀⠀⣨⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣬⠏⠀⠀⠀⣿⣧⢀⠀⢻⣿⠇⠈⠀⡀⠀⠹⠿⠃
⠀⠀⠈⠐⠀⡄⠠⣿⣿⡆⠀⢀⡈⢁⣸⠠⢥⢀⠑⠢⣀⠀⠀⠀⠀⢠⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢩⣿⣾⢰⡆⠀⠀⠀⣿⣿⡄⠀⣦⡠
⠀⠀⠀⠀⠀⢘⠀⣉⠉⠙⣦⡙⠁⠀⠊⠀⠉⢚⣴⣶⡄⠱⠆⠀⠀⢲⡗⢦⠅⣀⠀⠀⠀⠀⠀⣀⣀⡠⡧⠴⠐⠂⠈⣿⣿⣍⠀⣠⣤⠀⠀⠙⠋⡶⠈⠉
⠀⠀⠀⠀⠀⢸⠀⠛⠀⢸⣿⡇⠀⣶⢼⣶⠂⠀⠹⠿⠇⢠⣾⣷⣀⣀⡀⣰⣶⣦⠉⠿⠀⠉⠈⢿⡿⣀⠀⢰⣿⣷⠀⠛⠋⣶⠀⢿⣿⠇⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠉⣁⠚⠛⠃⠠⠤⠊⠈⠂⢺⡇⠀⠀⣴⣦⡀⠀⠟⠀⠘⠿⠋⠀⠀⠰⡷⠀⠀⠀⠛⠁⠈⠻⠋⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠄⠒⣁⠀⠀⢸⡏⣿⡀⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠆⠜⠛⠛⠿⠥⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣉⠶⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠉⠇⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣭⠒⡋⢱⠀⠀⠀⠀⠘⠁⠀⡙⣥⠸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⢀⠼⠄⠀⠀⠀⠈⢦⡀⠀⠀⣀⣤⠤⠤⠤⣄⣤⠀⠀⠀⢠⠃⠀⢀⣘⠃⡌⢳⠀⠀⠀⡞⠁⠘⠟⠀⢒⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠯⠶⠼⠅⣅⣠⠋⠀⠈⠉⠃⠸⠀⠀⠈⠛⠀⠔⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣛⢙⠉⠀⢻⡰⠂⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠸⠤⠄⠀⣠⠶⠋
⠀⢀⣀⣤⡼⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⡠⠔⡏⠨⠇⠀⠀⡖⢨⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⢡⠁⡄⠁⠀⠀⠀⠀⠀⠀⡀
⢀⣼⠀⠀⠀⠀⠀⢀⣀⣀⠀⠺⢤⡀⠀⣌⣀⣀⡂⠈⠅⠀⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⢨⠆⠀⠀⠀⠀⠀⡼⠁
⠛⠢⠤⠖⠉⠙⠛⠃⠀⡠⠤⢤⠴⠛⠋⠉⠁⠈⠹⡄⢙⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠃⠀⠀⠀⢰⠋
⠀⠀⠀⠀⡀⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠆⠀⠀⠀⡜
⠀⠀⠀⢮⡁⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣠⠤⠤⣶⠫⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢐⣊⠤⡀
⠀⠀⠀⠀⠻⠤⠶⠚⠛⠚⠋⠀⠉⠁⠀⠀⠀⠀⠈⠙⠣⢿⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠀⠀⠀⠙⠚⢢⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠲⠖⠓⠲⠶⠤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣳
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣲⣞⣛⣶⣴⣙⣓⣒⣋⣉⣉⣈⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠉⠁
⠀⠀⣼⠷⢦⣄⡀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡀⠀⠀⠀⠀⠀⢀⢤⡠⠄⠤⢄⠀⠀⢠⢊⠋
⠀⠀⠀⠀⠀⠈⠛⢗⢄⠀⠀⡇⠀⢱⠀⡀⠤⣀⠀⠀⠀⠀⠀⣏⣉⠉⡇⠀⠀⠀⠀⠰⡅⠀⠑⣴⡄⠀⠑⡴⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡕⢤⡃⡠⢼⠉⠀⠀⠀⢑⠖⠢⢄⣸⡀⣩⡧⠧⠒⠊⠉⠒⡎⠀⠀⢀⣩⠉⣶⠎⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⢌⡐⠪⢅⣢⡎⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠺⠵⣴⣝⣢⣁⠔⠁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠑⠤⣈⡏⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠉⠐⠂⠀⠤⠦⠤⠤⠤⠤⠒⠂⠉⢛⠉⠉⢹⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠤⠄⠐⠂⠉⡠⠃⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣀⣸
⠀⠒⠒⠂⠒⠂⠒⠒⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⡅⣦⡍⠆⠀⠀⠀⢂
⣠⠔⠀⠉⠈⠁⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠀⠉⠒⠀⠀⠀⠀⠈
⠣⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⣴⡆⠄⠀⠀⡜⠀⠄
⠀⠑⡀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠁⠙⠁⠀⠀⠈⠃
⠀⠀⠘⡄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢀⠔⠒⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠉⠓⡀⠀⠀⠸⠀⡀⡇⢄⢀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠄⠁⠈⢑⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠈⠀⠐
⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠤⠀⠀⠠⠄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠈⠐⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⢠⢈⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⣀⣀⡤⣊⡁
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠈⠀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠉⠉⠁⠈⠐⠂⠤⠤⠼
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣶⣦⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢁⣀⣈⡉⣀⣶⢤⡐⠦⡤⠤⠤⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⣨⣿⢭⠳⣤⡼⠀⢙⣷⠀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠤⠀⠠⠒⠎⠀⠤⠤⠠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⠁⠈⠐⠳⣌⣑⣦⠪⡾⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠂⠀⠀⠀⢠⠀⠄⢸⠀⠫⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠀⠀⠈⡿⠀⡐⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⣁⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⠀⠤⠀⠀⠀⡠⡿⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⢠⣀⣀⣀⣀⣀⣈⢸⠀⠰⢸⡇⠀⠀⠀⠀⢠⡤⣤⣤⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⢀⢀⡣⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣄⣶⡂⠐⠀⠀⠀⠀⠀⠘⠀⢀⣺⡇⠀⣠⠔⢈⢉⣁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣠⠿⠵⠶⠶⠇⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠒⠓⠛⠓⠒⣶⡴⢶⣶⠒⠒⠓⠛⠒⠛⠊⠀⠀⠀⠑⡍⠀⠀⠀⠀⠐⠀⠀⠀⢀⠴⠊⠁⠄⡀⠀⠀⠀⠀⡴⡀
⠀⠀⠀⠀⠀⠀⢼⢇⣰⣂⣀⣀⣘⣉⣉⣉⣉⣉⢓⣒⣲⣶⣶⣖⡆⠔⠲⡀⠀⡀⠀⠀⠀⠐⠂⠌⢀⡖⠁⠀⣀⡀⠀⠀⠆⠀⠀⡞⢈⡅
⠀⠀⠀⠀⢀⠀⡈⣆⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢄⡇⠙⢞⠁⠠⢣⡀⠀⠀⠀⣀⣂⣈⡁⠀⣊⡀⣱⠀⠀⠰⢀⠈⠀⠸⠁
⠀⠀⠀⠀⠹⡭⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠁⣦⡀⠀⠀⣇⠀⠉⠁⠈⠀⠀⠀⠈⠣⡀⠀⠉⠁⡀⠠⠚⠁⢀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⡇⠘⠛⠉⠉⠑⠒⠴⠤⠤⠤⠤⠤⠤⠾⠢⠤⠤⡶⠥⠟⠒⠋⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⠀⠀⠀⢊⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡃⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣀⣄⣀⣴⣶⣦⣴⣶⠶⠲⡶⢲⣀⣸⣨⡗⣷⣷⣷⠤⢦⣤⠤⠤⢤⡬⢬⣤⣤⣤⣤⣀⣀⣥⣥⣼⠶⠶⢶⠾⠃⠈⠑⠂⠉⠀⠄⠒⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠂⠀⠈⠀⠠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠠⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⢹⠄⠤⢀⠄⢳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠿⠄⠤⠀⠀⠓⢃⠀⣸⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⢆⠐⠂⠘⠚⢤⣤⠠⠤⠔⠁⠘⣧⠯⠀⢹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢺⣧⠘⣄⡀⠀⠀⣠⡿⠀⠀⡘⣿⢠
⠀⠀⠀⠀⠀⢀⣴⠻⣷⣄⠈⠻⢷⡘⣿⡼⢋⣭⡆⠀⢰⡇⣿⡄
⠀⠀⠀⠀⠀⣿⡹⣧⡙⣿⡟⠀⠀⠉⠀⠑⠿⣿⡇⠀⢼⣇⢸⡇⠆
⠀⠀⠀⠀⠀⢿⣱⡜⣷⡌⢿⣷⣄⠀⠀⠀⠀⠀⠁⠀⠘⢿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄
⠀⠀⠀⠀⠀⠈⢿⣽⣮⢿⣆⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡈⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠻⣾⠷⣻⣧⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠆⠀⠀⠀⠈⠀⠀⠈⠀⠀⠒⠀⡖⠠⠠⢴⠐⠂⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡟⣝⢷⣌⢻⡄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠑⠤⣤⣤⣤⠼⢦⡀⠈⣤⣶⣆⣠⣞⣁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣻⣿⣦⠻⡀⠀⢀⡾⠁⠀⠀⢀⣤⣴⣮⣥⣤⣤⣤⣄⣀⡀⠀⠀⠀⠘⠛⠿⠀⣷⣦⣤⡜⣻⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣷⣷⣠⣾⡿⢷⡶⢿⣿⣿⣿⣯⣭⣽⣿⣛⣛⡿⠿⠷⣶⣤⣬⣽⡛⢾⣿⠠⠛⠉⠉⠙⠒⠤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠿⠾⠷⡾⣧⡼⠿⢼⣿⣸⣿⢸⣷⠉⣾⡏⣻⣟⣛⠷⣶⣶⠙⡿⠃⠈⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡄⢰⡶⠂⠀⢰⡿⡵⢞⡪⠓⠋⠁⠀⠀⠀⠀⠀⡀⢉⠉⠓⠛⠣⠿⣇⣽⡏⡸⠟⠁⠀⠀⠀⠠⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⣸⡥⠊⡡⢤⠇⣢⡀⢀⣰⠀⠠⠙⠙⠉⠑⠀⠀⠀⠀⣸⡟⠉⠀⠀⢀⡠⢀⡥⠚⠁⠀⠀⡄⠀⠆
⠀⠀⠀⠀⢀⡸⠀⢀⡀⢶⠸⠟⠏⡾⢠⢗⡀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢌⠟⠀⠀⡀⢔⡡⠞⠁⠀⠀⠀⠀⠀⠊⠀⠁⠶⡄
⠀⠀⠀⢆⠈⠀⠙⠨⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⡶⣀⠐⣞⢀⡠⢊⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠛⠳⡌⠛⠛⠹⢸⡿⣫⣞⢡⡄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣩⠞⠋⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⣦⣤⣤⣦⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠒⠒⠂⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢂⢀⣀⡈⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠘⠁⠶⠾⣿⣿⣿⡆⠀⢠⣿⣿⣿⡿⠿⠓⠈⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣀⠈⠛⠛⠁⠒⠀⠙⠛⠛⠀⣠⣴⣾⣿⣿⣷⡄⠀⠀⣠⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⡀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡇⣠⣞⣩⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠻⠿⠿⠿⠿⠿⠿⠛⠟⠛⠛⠛⠛⠀⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⣀⣀⣀⡀⠠⡆⢀⣀⣀⣀⣀⡀⠀⠀⣿⠀⣀⣀⣀⡀⠀⠀⢠⢀⠀⣀⣄⣀⣀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡍⠛⠉⢿⣟⣛⣋⠉⠉⠙⠛⠛⠛⠉⠉⠉⣿⡍⠙⠛⠚⠛⠯⡽⠟⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⠛⠻⠶⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⢷⡐⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⢀
⠀⠈⠃
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠂
⠀⡀
⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣦⠆⠀⠐⠀⠀⠀⠤⠤⠀⡀
⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠈⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡃
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠄
⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣄⣿⠤⠇⠀⠑⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣬⡀
⠀⠨⠊⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠘⠀⠰⠂⠀⠀⠀⠀⠠⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣰⣶⣀⣄⣤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⢰⣿⣿⣾⣿⣦⣠⡄⠀⢲⠀⠒⠂⠀⠚⠳⠀⠀⠀⠀⠒⠂⠶⠆⠀⠀⠈⠈⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠀⢨⣃⡀⠂
⠀⠀⣿⣿⠻⠁⣾⡿⠁⠀⢹⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠙⣿⡦⠐⡟⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⡤⠄⠈⡉⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠀⠠⠄
⠀⠀⠀⢟⡛⠛⢛⣳⠶⠶⠾⠆⠀⢀⠔⠁⠀⠀⠈⠉⠁⠀⡧⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠈⠀⢀⠂⠀⠀⠀⠀⠀⠀⠤⠔⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠹⣿⣷⣦⣶⣤⣤⡖⠰⡟⠀⠀⠀⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠀⢹⢿⣿⠄⠤⠤⠭⠹⣟⠀⠀⠀⠀⠺⣙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡟⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠠⠠⠤⠀⡤⠤⠀⠶⠤⠀⠤⠤⡤⠄⠤⠄⠄⠦⠤⠤⠀⠤⠤⠠⠦⠤⠰⠤⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠰⠲⠀⠂⠀⠆⠰⠂⠐⠂⠂⠰⠆⠀⠀⠖⠔⠀⠐⠀⠃⠤⠲⠂⠐
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣀
⠀⠎⠉⠑⡆⠀⡇⠀⠀⠹⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠤⣤⢡⣖⣒⣛
⠈⠄⢀⡠⠃⠀⠈⠒⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠀⠄⢀⠃⠀⢈⠷⠠⣤⠤⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⡀⠀⢀⡠⠀⢂⡠⠂⠀⠔⢁⢀⣶⠪⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠘⣍⠉⢻⡿⠟⢒⡎⠀⠀⠂⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠻⠒⠋⠀⠀⡤⣜⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠀⠀⠀⠀⠀⠐⢋⡤⠤⠈⡀
⠀⠀⠀⣀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠂⠴⠀⢀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣈⣁⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⢀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⡎⢹⠴⣴⣩⢈⡇⠀⠬⠭⠥⠄⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⢀⠿⠽⣏⠓⠒⠒⠒⠂⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠉⠂⢄⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠦⠙⠦⣀⠀⠀⠀⣠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠉⠀⠀⠀⢈⠆⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⣶⣶⣶⠄⠛⠂⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⣀⣴⠂⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⡶⠟⠻⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢀⣠⣿⡿⠤⢄⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⡞⡟⢱⠞⣘⡆⠀⢸⠀⣠⡟⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢦⡉⠁⠉⠉⠉⠉⣉⣀⡠⠤⠴⢲⠞⠁
⠀⠀⠀⠀⠀⠀⢁⠈⠈⠁⢸⠅⠀⠒⠋⠈⠁⠈⠀⡼⢩⠖⠒⢒⠀⠠⠄⣀⠀⡼⠁⠀⠀⢨⠗⠒⠀⠉⠁⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠏⠀⠀⢀⠄⠠⠤⠀⠐⠒⠃⠒⠛⠃⠀⠀⠀⠀⣸⠃⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⢠⠀⠀⢀⡞⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⢀⠀⢀⠈⠀⢀⠀⠀⠒⠋⠑⢤⡀⠀⠀⠐⠂⠐⠛⠉⠉⠷⣏⡀⠀⢠⠃⠀⣀⡠⠤⠀⠐⠛⡽⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠁⠀⠀⠀⢫⣙⠂⠴⠋⠀⠓⠂⢉⣉⠉⠠⠄⠒⠁⣯⠗⠒⠚⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠾⠗⠊⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠠⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠂⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠅⣀⠄⠀⠤⠋⠑⢇⠠⢜⠄⡐⠀⠀⠀⠀⠈⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠂⠽⣶⡧⠤⡠⠂⠀⠸⢋⢱⣌⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢀⠄⠙⠁⢀⢴⠂⢀⡶⠟⠁⠀⠀⠁⡄⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠑⠤⠴⠒⠁⠀⢀⠴⡿⡡⠒⠉⠉⠢⡀⠐⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠐⢪⠕⠉⡌⠀⠀⠀⠀⠀⣱⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⢀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠀⠀⠀⠀⠀⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠋⠀⡶⠒⠀⠀⠐⠠⠄⠠⠤⠀⠒⠉⠀⠀⠀⢂⣆⠀⠀⠀⢰⠀⠈
⡀⣶⢶⠐⡠⠀⢃⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠉⠐⠆⠀⠀⡊⠘⡦
⢉⠀⢀⡃⠄⠂⠁⣀⠉⠷⠦⢄⣀⡀⠀⠀⠀⠀⡏⠉⠁⡰⠂⠀⢀⠀⠀⠰⡀⢰⡁
⠰⠀⠈⡁⠀⡀⠤⣇⠀⠀⠀⢀⣀⣉⣭⣥⣤⣶⡇⠀⠀⠁⠀⠀⠁⠉⠀⠼⠃⡈
⠀⠐⠉⠓⠀⠀⢀⣈⣂⡀⠰⠆⠛⠧⡄⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢖⡒⢉⠁
⠀⠀⠀⠀⠀⠀⠈⠪⠤⠴⠖⠂⠀⠈⠁⠀⠀⠉⣓⢒⣒⠊⠉⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣴⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⢛⣛⠛⠛⠛⠿⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠟⠻⡷⠀⠀⢀⣿⣿⡻⠛⠻⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡄⠀⠀⣨⣴⣀⠀⠀⢠⣿⣿⠀⣠⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣅⣠⣿⣿⣨⣿⣷⣄⣸⣿⣿⠀⣨⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣯⣿⣯⣿⣿⣯⣽⣿⣿⠀⠻⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣻⡟⠛⠛⠛⠻⣿⡿⣟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠀⠂⣄⣀⡔⠋⠀⣸⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⠁⠐⠀⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣿⣟⣛⣛⣻⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⠃⠲⠤⣄⡀⣘⠂⢠⣄⠀⠀⣿⣧⠀⢠⠎⣼⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣇⠀⠀⠀⠀⣀⠉⠀⠞⠀⠀⣰⣿⡿⠂⣿⠀⣿⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⢸⠰⣆⡠⠆⠀⠀⠉⣽⠀⣿⠀⣿⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⡆⠀⠀⠀⠸⣄⠉⠁⠀⠀⡰⠀⠀⠀⢸⡆⢹⡇⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠤⠷⠤⠐⠚⠧⣨⣖⠂⢀⡔⢦⣄⡀⠀⠸⡇⢸⡇⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⣤⣄⡀⠀⠀⠀⠀⡠⢤⣄⣀⣸⡄⡀⢠⡀⠄⠀⢀⠀⠀⣀⣼⠉⡐⠁⡄⠀⠈⠉⠛⠦⣿⢸⡇⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣇⣇⢸⡇⠀⠀⠀⠈⣇⠀⢳⡀⠀⢀⠇⠀⡣⠀⢠⠂⢠⡼⠋⠀⢄⡀⠀⢥⣄⣀⠀⠀⠀⡸⣸⢣⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⢸⣷⠰⣿⡒⠲⠦⠤⠤⡥⣄⣀⣁⣈⣀⣤⢈⠐⠋⠀⠀⢠⡏⠀⠀⢠⠇⠉⢙⣒⣴⡟⠋⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠻⠰⣞⣿⡷⠈⢳⣀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⣬⠃⡀⠈⣀⣤⣤⣶⡶⠿⠟⠋⠉⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣁⠈⠉⣉⠒⠚⠛⠶⢤⣤⡔⣿⢰⡇⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⢸⡇⠤⢤⣤⣄⣀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠐⢀⠀⠀⡄⡀⠀⠻⡠⠤⠤⠤⠴⢶⠒⠈⠀⠀⠀⠀⠀⠀⠀⢻⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠃⠃⢰⢠⠇⠀⠀⠀⢳⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠿⠿⠦⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⢈⢸⠀⠀⠀⠀⠈⠇⠑⠐⠒⠲⠶⠤⢤⣀⣀⠸⠀⡿⢀⣀⣀⣤⠤⠶⠶⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠂⢀⡄⠂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠊⠁⡀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢄⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⠦⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠐⠀⠐⠂
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇
⠀⠈⢧⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠂⢀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠘⣇⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢀⠔⠉⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⢹⡄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠈⠅⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠘⢄⠀⠀⠀⢀⣼⠂⠄⠀⠀⠀⠠⠀⠐⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡆⠀⣸⣄⣀⣀⣀⣀⣑⣀⣀⣙⣛⣀⣠⡀⠠⠤⠀⠀⠀⠠⠀⠄⠐⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣷⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠈⢢⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢢⠀⠀⡹⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠃
⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡔
⠀⠀⠀⠀⠀⠘⡏⠁⠀⠒⠒⠀⠀⠠⠄⠤⠄⢡⡀⠀⢀⠜⠀⣀⡀⡤⠀⠀⠀⠀⠀⠠⠃⢀⠎⠀⠀⠀⠐⠒⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠂⠀⠀⠀⠀⠀⠀⠆⠄⠀⠄⠀⠀⠀⠦⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢨⠤⠄⠰⠃⠀⠀⠀⠀⡠⠁⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⢠⢁⡀⠁
⠀⠀⠀⠀⠀⠀⠨⡉⠑⠒⠆⡤⢀⣀⠀⠀⠀⠀⢀⡀⠼⠐⠚⢠⠀⠠⠀⣀⠁⠀⠀⠉⠈⠐⠀⠀⠀⠠⠀⠀⠀⠐⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠉⠀⠀⠈⡍⠁⠚⠉⡈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡤⠀⠐⠒⠃⠀⠐⠂⠋⡐⠀⠀⠆⠀⠀⠀⠀⠆⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑⣄⠐⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠸⠆⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⡤⠤⠅⠀⠀⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⡐⠒⣂⠂⡢⠀⠀⠀⠀⢎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣦⠄⠉⠁⠀⠀⠀⠘⡌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣦⡗⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠸⠋⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⡀⢀⠏⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⠘⠀⠀⠀⠀⠀⠐⠔⠰⠥⢽⠘⠞⣮⣩⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢁⠂⠈⠀⠀⠈⠀⠺⠏⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠉⠐⡃⣀⢰⡇⢠⠀⠀⠀⠀⠇
⠐⠂⠀⠀⠈⠐⠇⠁⡀⣀⡰⢃⡎⢂⢴⣿⣰⢰⠂⠄⠄⡀⠀⠀⠀⠀⠀⠙⢿⣿⡇⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠑⠈⠁⠠⠈⠰⣇⠙⠻⠞⠜⠀⠀⠀⠀⠀⠀⠐⡀⠘⠀⠈⠀⠀⠀⠀⡆
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢉⡀⠀⠐⠖
⠀⣄⡀⠀⠀⠀⠀⡠⠄⠀⢀⠠⣂⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠈⠂⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠨⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣇
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠃
⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠁⠀⠉⠙⠳⢦⡀
⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⣤⣤⣤
⢹⣟⠛⠛⠋⠉⠉⠉⠉⠹⣏⣹⣿⡿⠀⠀⠀⠀⠀⠉⠉⣿⠃⠀⠀⠘⢧⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⣿⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠘⠀⢆⢀⣶⠀⣿⣯⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠙⠆⣿⡧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⣶⣶⡖⢰⠆⢠⣿⣷⣶⣤⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⣿⡇⣾⢀⣾⣿⠝⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⢰⣿⣼⣿⢜⣿⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠳⠶⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠁⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣀⡀⠀⢠⠂⠉⢲⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠔⣒⣢⣄
⡎⠀⠀⢹⠀⠰⡀⠀⣠⠇⠀⡎⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⣦⠀⠀⠀⢠⠞⠳⣆⠮⠥⠤⠤
⠑⠠⠤⠊⠀⠀⠈⠉⠁⠀⠀⠑⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡇⠀⠐⢠⠏⠀⣠⠞⠁⠲⣖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⣀⣀⡼⠋⢉⡧⠋⢀⡔⢡⠤⠼⠍⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠄⢧⠤⠌⣿⠋⢉⡽⠁⠀⣞⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⠗⠉⠀⠀⢸⣺⠅⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⢉⣴⡶⠂⣸
⠀⠀⢠⡄⠂⠀⠴⡦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣬⣉⣒⣀⣂⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠾⠓⠤⣄
⠀⠀⠈⠛⠵⣂⡤⢀⠀⠈⠙⠢⣄⡀⠀⠀⣀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⢀⡜⣇
⠀⠀⠀⠀⠀⠀⠈⠉⠘⠓⠒⢺⠃⣿⢒⠯⣴⣸⡀⠀⠲⠤⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⢠⠎⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠬⠗⠺⢍⠙⠛⠒⠒⠒⠛⢛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⡀⠙⠲⣄⡠⠃⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠢⠙⠲⣄⣀⠄⣀⣼⡇⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⢀⡹⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⣶⣶⣶⡶⠞⠛⠋⡝⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣀⣀⡤⠞⠉⠀⠀⢀⣠⣴⡞⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡿⠋⠀⠀⠀⠀⠈⠐⠒⠠⠤⠤⠤⠄⠀⠒⠒⠉⢉⠔⠉⠀⠀⣠⣴⡾⠟⢻⠏⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣀⣩⣿⡿⠧⠤⣌⡴⠃
⠀⠀⠀⠀⠀⠀⣸⢹⡋⡗⠉⣹⠄⠀⡇⢀⣴⡋⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠯⣉⠉⠉⠉⠉⢁⣀⣀⡠⠤⠤⢒⡶⠋
⠀⠀⠀⠀⠀⠈⡗⠉⠉⠀⡿⠐⠒⠊⠉⠉⠀⠈⠠⠞⡱⠃⠒⠒⠒⠲⠆⡀⠀⣼⠁⠀⠀⢨⠗⠂⠉⠉⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⣸⠁⠀⠀⣠⠤⠤⠐⠒⠒⠚⠓⠒⠛⠁⠀⠀⠀⠀⣽⠃⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⡄⠀⠀⣰⠃⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⢸⡀⣀⣰⠃⠀⡀⠠⠔⠒⠉⠳⣄⠀⠀⠐⠒⠒⠚⠛⢋⣉⠧⣎⡀⠀⢠⠏⠀⢀⣀⠤⠔⠒⠚⣭⠋
⠀⠀⠀⠀⠀⠉⠙⠓⠈⠁⠀⠀⠐⢏⣑⠂⠔⠋⠐⠒⠒⠈⣉⠉⠤⠤⠒⠃⣯⠗⠒⠒⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠾⠔⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⣀⣀⣀⣀⣀⣈⣁⣀⣈⣉⣑⣀⣂⡒⠀⠂⠐⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⡿⠛⠛⠛⠛⣛⣛⡛⠛⠛⠛⢻⣿⡇⠀⠋⠉⠉⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⠛⠻⡧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣠⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇⠀⠀⠄⠀⠈⠁⠈⠐⠀⠀⢸⣿⡇⠀⠘⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣯⠥⠈⠭⠥⠭⠭⠭⠠⠩⠨⣿⣿⡇⠀⢰⣛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢠⡿⠀⠀⠀⠀⠀⢻⣿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢴⡶⣿⡇⠀⠀⣄⣀⣤⠋⠁⠀⣼⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣩⠵⠖⠻⣿⡻⢮⣿⠄⠠⢛⡿⠋⠄⠀⢀⣟⢿⣿⣿⠿⢿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣳⡤⠿⠛⢋⣻⣧⡻⡇⠀⣌⠻⣧⠀⠀⣰⡻⣶⣿⣩⣛⣾⡌⢯⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣠⢋⠷⡴⠷⠻⣿⣦⡹⣾⠀⠻⣷⣤⡀⢠⡝⣷⣘⣷⣏⣹⣆⢳⣎⣧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡏⡜⣸⢧⡾⠚⣛⣿⣷⡹⣿⣧⡈⠻⣧⣯⢻⣼⠿⠶⣴⣿⣽⢾⢿⡼⡞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣼⣹⠃⣾⣻⣋⣭⠼⣿⣿⡙⣍⠻⣶⣾⣜⣷⣟⣻⣶⠟⠁⠀⡀⡞⣿⣻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣵⢧⣏⣸⠧⣽⣷⣶⡾⣟⡟⠳⠾⣷⣼⣷⣿⣟⠻⢿⣯⣴⣖⣶⠞⠷⢼⢽⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡧⣼⠤⣿⢑⡿⠋⠀⠀⣯⣍⣙⠓⠶⠤⣥⣉⣛⡗⠶⣤⣈⡉⠉⠋⠙⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢰⡟⢘⣯⣾⡷⣶⣂⣾⢶⣯⣍⡙⠛⠲⠦⣬⣍⡛⠲⠦⣄⡉⠉⠛⠚⠛⠚⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣼⡏⢹⣿⡿⣝⣳⠮⣉⡛⠲⠿⣽⣿⣶⢤⡤⣈⡙⠻⠶⣤⣍⡉⠛⠘⠛⣉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠹⣿⡻⢤⡙⠳⢬⣉⡛⠂⡦⢀⡍⣙⠃⣿⡿⢿⣛⣿⠿⡟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣘⣧⡀⣽⠶⢦⣤⣿⣾⠒⠚⢻⠿⠛⢛⣉⣉⣄⣴⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣛⣛⣓⡛⠒⡶⠏⠄⠀⢸⠞⠟⠛⠉⢉⣁⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣭⣉⣉⣉⡉⣙⢛⡃⠄⠀⢸⡖⠓⠘⠛⠉⠉⢈⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣄⣔⡵⠚⢢⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣤⠌⠀⣌⠑⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠊⠀⠠⠀⠒⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⡚⢓⣈⠀⠀⠀⠀⠀⠀⠀⠀⡞⡄⠀⡈⢀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠂⠁⠀⠐⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠳⠴⠤⠀⠀⡺⠒⢀⡾⠁⠐⠂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠊⢀⣀⣀⣈⣡⡠⡠⠾⠀⠀⠈⠰⠅
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣜⣠⡃
⠀⠀⠀⠀⠀⠴⡶⡆⠀⠀⠀⠀⠀⣻⣦⣤⣤⣤⣼⣿⣶⠿⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠳⣼⣉⣥⣤⣩⣌⣈⣁⣉⣿⣭⣅⢖⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠧⠤⡆⠠⠀⠀⣿⠁⠀⠀⠀⢂⠂⢰⠇⢀⠐⠂⠠⡄⠢⠀⠁⠄⠁⡠⠒⠏⠀⠈⠀⠐⠠⠈⠀⠄⠁⠀⠁⠁⣼⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠲⠶⡴⡶⠐⠶⠲⠶⠆⠴⠶⠅⠀⠈⠢⣘⠄⠂⠀⠅⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠉⠁⠈⠀⠁⠐⠑⠳⠖⠚⠓⠚⠒⠚⠓⠛⠒⠚⠒⠓⠲⠶⠏⠠⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⣴⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠉⠉⠉⠀⠈⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠂⣁⠢⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡀⠊⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠆⠶⠤⣴⠿⣀⠀⠀⠀⠀⠀⠁⠀⠸⡁⠀⠐⠡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠲⠤⠤⠀⠀⠗⠀⣰⠃⠀⠁⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⣀⣀⣀⣀⣀⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠊⠭⠤⠬⠭⠤⠤⠞⠃⠀⠀⠘⠁
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠈⠉⢻⡿⠿⠿⠿⠿⣿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠐⠛⣇⠀⡀⠀⠀⢨⡿⠿⠶⢶⠿⠻⢿⠇⠀⢀⠀⠠⠀⢀⡀⠀⠀⠈⣳⠒⠒⠒⠒⠠⠠⠠⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠘⠊⢇⣉⣀⡸⣃⠀⣀⣀⣐⡀⢚⣡⠆⠑⢄⠣⡈⡀⠀⠂⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠁⠈⠀⠉⠁⠉⠉⠁⠀⠤⠰⠵⠄⠨⠁⠄⠤⢼⣤⣠⡤⣤⠤⣤⠤⠤⢠⣤⡤⣤⣥⡤⣀

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠓⠒⠤⠀⣀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣽⣭⣽⣯⣿⣿⣿⣾⠷⢾⣶⣀⠀⠤⠖⠒⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠒⠢⠀⠤⢀⣀⣀⡀⠉⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣀⣀⣀⠤⠀⠤⠒⢺⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠉⠀⠉⠈⠈⠉⠁⠘⠛⠐⣿⣿⣿⣿⣿⣿⠀⠈⢡⣇⠀⠀⢰⡆⠀⠀⠀⠀⣷⡄⠀⠀⠀⣿⡟⠛⠋⠀⠉⠉⠉⠉⠀⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠄⢠⣼⣿⠀⠀⠀⠰⣿⣷⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠐⠂⠀⠉⠉⠉⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠷⠰⣷⡶⣿⣷⡆⠀⢸⣿⡇⠀⠈⠉⠁⠀⠐⠂⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⠄⠐⠒⠉⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⣼⣿⠉⠉⠒⠂⠠⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠐⠉⠁⠀⠀⠀⢀⡠⠔⠊⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬⣥⣿⣿⠢⢤⡀⠀⠀⠀⠈⠉⠃⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⠿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⣻⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⢛⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠄⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢢⡀⣰⣿⣿⣿⣷⡀⢠⠎⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣷⠀⠀⠙⠁⢻⣿⣿⠏⠘⠁⠀⢀⣿⣿⣿⡿⣋⣼⣿⣿⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⣼⡿⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⣿⡀⠀⠀⣼⣿⣿⡇⠀⠀⢰⣿⣷⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣧⠀⢠⣿⣿⣿⣷⠀⢀⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⣿⣀⣈⣩⣉⣉⣉⣉⣉⣉⣉⣉⣉⣍⣉⣉⣀⣉⣉⣉⣠⣈⣉⣉⣉⣉⣀⣀⣉⣉⣉⣀⣉⣉⣉⣉⣉⣉⣉⣉⣍⣉⣉⣀⣼⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠰⣏⠀⠀⢀⡀⠀⠀⢀⠀⡀⣈⡀⠀⠈⡅⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⠀⠸⣆⣿⣶⣐⣶⣀⡈⠛⠓⠀⡀⠀⠀⣧
⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣳⣽⣷⠀⠀⠀⠳⣷⣶⢿⠀⠀⠀⠀⢀⠄
⠀⠀⠀⡤⠤⢜⡛⡄⠀⠄⠀⠂⠈⢹⣿⣿⡋⠿⣿⣿⣆⣼⣿⣷⡄⠀⢸⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⣶⢖⣤⢄
⠀⠀⠀⠀⠀⠀⠹⣼⡤⣠⠶⠖⠛⠛⠛⠛⠛⠛⢳⠟⠛⣻⣿⠟⠋⠙⣟⢻⣟⣛⡷⡘⠛⠻⠒⠒⠖⡲⠖⠖⠒⠺⠧⣼⣿⠁⠁
⠀⠀⠀⠢⠄⠀⢀⡟⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⠿⢥⣭⣿⣿⣇⠀⠀⣿⣷⣤⣟⠈⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠚⠻⡇
⠀⠀⠀⠀⢀⠀⠘⣇⡀⠀⠀⠀⠀⢰⣤⣀⣙⠓⠒⠶⠿⠟⠛⠻⠤⠼⠻⠿⠷⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡃
⠀⠀⠀⠀⢸⠀⠀⡇⠉⠉⠉⠉⠁⠈⠙⠛⠛⠻⠿⠿⠿⠟⠻⠗⠒⠒⠒⠒⠚⠛⠛⠛⡂⣀⣉⡩⠃⠀⠐⠒⠒⠒⠚⠛⠁⡇
⠀⠀⠀⠀⠸⠀⠀⡇⠠⠤⠄⠠⠴⠶⠶⠶⠾⠀⢠⠀⠀⠀⠠⠄⢀⣀⣀⣠⣤⡤⠤⡅⠀⡀⠀⠀⠤⠤⠀⠀⣀⣀⣀⣤⡄⡇
⠀⠀⠀⠀⠠⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣠⠀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⠀⠠⠄⠀⠈
⡔
⢳⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢇
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⣇⠀⢰⠀⠀⠐⢄⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢸⡀⠘⠂⠀⠀⠀⠀⠂⠈⡡⠒⠂⡀⠀⠀⠄⠀⠠⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢹⠁⠀⠂⠀⠀⠀⠠⠀⡤⠀⢠⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⢐⡀⠀⠘⠒⠒⠒⠒⠒⠒⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢉⠐⠂⠤⠀⣀⠀⠀⢀⡀⠄⠐⠠⠀⡄⠀⠁⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⣁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠒⠀⠈⠁⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠉⠉⠁⠀⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠁⠢⠀⠠⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢁
⠀⠀⠀⠀⠀⠀⠀⣎⡁⠀⠤⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠈⠋⠀⣤⠈⠁⢀⣗⠂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣛⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⠄⠀⠠⠄⠀⠠⠄⠀⠠⠄⠀⠠⠄⠀⠠⠄⠀⠠⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⢀⡀⠀⢠⠀⠀⣀⠀⠀⣀⠀⠀⣀⠀⠀⡄⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⣦⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⣴⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⠦⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⣀⣠⣄⣀⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣄⣀⣄⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁





⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶⡶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠿⠤⠤⠤⠶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠠⢤⣀⣀⣀⠀⡀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⣶⠃⠀⠀⠀⣿⢀⣯⡀
⠀⢀⣠⣤⣤⣤⣤⣤⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢠⣿⠇⠀⢀⣠⣤⡟⢸⣧⡇
⣼⠏⠉⠙⣷⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣀⣀⣠⣿⣯⣤⠴⠿⠿⠟⠛⠛⠋⠛⢶
⣿⠀⠀⠀⢻⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠹⣧⠀⠀⢸⡇⣀⣀⣿⠴⠶⠞⠛⠋⠉⠙⠛⠛⠛⠋⠛⠛⠛⠓⠶⠶⣦⣤⣼⣧⣤⣄⣀⣀⣀⣀⣾⣀⣀⣸⡏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢸⡇⠀⣸⠛⠛⠶⠶⠶⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡟⠛⠛⠛⠶⠶⠶⢦⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⢘⡇⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⣾⠉⠙⠓⠒⠲⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡏⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠛⠛⠛⠲⠶⠶⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⣿
⠀⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⣀⡤⠖⠚⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠶⠶⣤⣤⣄⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⢶⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡄⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠳⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⠶⢤⣼⣤⣷⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣀⡀⠀⣄⣀⣀⠀⠀⠀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⢸⡀⠀⢸⠀⠀⡗⠋⡇⠀⠧⠁⢹⠂⡀⠠⠥⣼⠤⠤⠤⢬⠤⠤⠤⠤⠤⠦⠥⠤⠤⠄
⠀⠀⠀⠸⡇⠀⢸⡄⠀⡇⠀⡇⣄⣤⣀⢸⠇⡀⠀⠀⠏⡆⠀⠀⢰⠀⠀⠀⢠⠐⠂
⠀⠀⠀⢀⡿⡀⠸⡇⡤⣧⠀⡧⠏⣿⣷⢸⠀⡋⠀⢰⠀⡇⠀⠀⢸⠀⢰⡀⠸⠀⠀⡴
⠀⠀⠀⠈⠳⠁⠀⣟⡿⠋⠀⠋⠣⣿⠏⢸⠀⡇⠀⢸⠀⠧⢀⠀⢸⠀⠀⢣⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠶⣤⠀⠉⠀⢸⠀⠩⡇⢸⠀⠀⠈⠀⠈⠀⠀⢈⠶⢁
⠀⠀⠀⠀⠀⠁⢀⣤⣾⢶⡛⠦⣀⠀⠀⢸⠀⠉⡏⢹⠈⠉⡜⠉⣉⣉⣉⡁⠀⠈⠁⢀⡉⠈⢷
⠀⠀⠀⣀⣴⣾⡿⠋⠣⡘⡆⠈⡈⡗⠀⢸⠀⠈⠁⢸⠀⢀⣧⣤⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸
⠀⠀⠀⠈⠙⠿⣿⣶⣤⣙⢿⠀⠈⢱⠀⢸⠀⠀⠀⢸⠀⢸⣠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡌⠙⡿⣿⣿⣿⣼⣻⢆⡘⠀⢀⣀⣘⣀⢸⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡇⡇⠀⠹⣍⣹⢿⣿⣿⣷⣯⣦⣄⠀⠀⠀⠀⠇⠸⠀⢀⣀⣤⣶⣾⣷⣄⠰⠃⡞
⠀⠀⠀⠀⠀⡇⢰⠆⠀⠈⠳⣥⠉⣻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⠿⠟⠋⣉⣙⣿⣿⣶⣅⡀⣀⡾⠃
⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠓⣍⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠿⠟⠉
⠀⠀⠀⢠⠀⡇⠀⠁⠀⠀⠀⠀⠀⠈⠱⣄⣀⣉⣙⣛⣛⣻⣙⣉⣉⣉⣉⣽⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠁⠙⢿⡍⠁⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠛⠛⠲⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣽⠉⠉⠉⠉⠉⠉⠉⡏⠃⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⢸⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣼⢸⣜⣀⣀⣒⣒⣒⣀⣒⣣⡂⣮⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠉⠿⠉⡈⠉⡟⠁⠀⠙⣯⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢀⡆⠐⢦⣖⠥⣶⡠⠂⢸⣆⠀⠄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡸⡇⠀⢺⢞⣶⡿⡆⠀⠸⠘⡆⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⠇⡇⠈⠉⠀⠆⠀⡏⠀⡇⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⠀⡇⠈⢸⠤⠖⠰⡏⠀⢱⠀⣷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⢒⡚⢠⠁⢀⡄⠀⣀⠀⣇⡀⠘⠀⡼⡌⠁⠀⠀⠀⠀⠀⢶⣦⣄⣀⣤⣴⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠰⣬⠃⡀⠀⠈⠅⢰⠉⡇⢹⠀⠀⠃⠠⠷⠃⠀⠀⠀⠀⠀⠀⠉⢻⡏⠈⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⢰⠀⡏⠀⢸⠈⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢶⣷⣶⣦⣄⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢸⠀⠀⠀⡇⢁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣾⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠁⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣞⡻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠠⠄⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒



⣀⣀⣀⣀⣀⣐⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣂⣄⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠒⠖⠒⠒⢂⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠠⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠐⢀⠀⣼⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⠔⠈⠉⠁⠀⠉⣀⣀⣀⠀⢀⡀⠉⠉⠐⠢⢄⠀⠀⣾⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⠀⣠⣴⡟⣭⣿⡟⠉⠠⣿⣿⣶⣿⠂⠀⠀⠡⠀⣿⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⣻⠛⣉⣉⣿⡇⢀⣆⠀⠉⣁⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇⠀⣀⠰⠇⠐⣉⣓⠸⠇⠶⣉⠙⢣⢉⠀⠻⠇⢀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠈⠋⣼⠂⢂⣀⠦⠀⠀⠐⣄⠘⠃⢀⠄⡶⢹⠔⠃⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠢⠉⠀⠈⠏⠀⠀⠄⠁⠀⣼⢀⠚⠁⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢅⣈⡀⠈⠙⢂⠈⢁⠘⠁⠀⠀⠀⡈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣉⠒⠠⠤⢀⣉⡀⠊⠀⠉⢀⡀⠀⡀⡀⠠⠊⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠐⠒⡒⣈⠉⠭⠭⠥⠤⠔⠖⠒⠒⠂⠂⢀⣀⣄⢀⠀⠀⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠰⠐⠒⠒⠒⠀⠀⠠⠠⠤⠤⢤⠤⠀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠃⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⢒⠀⠀⠁⠀⡀⠀⠐⠀⢈⠐⠀⠁⠃⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠈⠐⠂⡀⠀⠁⠁⠀⠀⢠⠀⠀⠀⡆⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⡤⠄⠄⠀⢀⣀⣀⣀⡁⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠨⠀⡇⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⢉⠉⠉⠈⠑⠛⠛⠓⠒⠚⠉⠬⠬⠶⠦⡄⠠⡜⠂⢀⣀⣤⣧⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠜⠉⠉⠉⠉⠉⠹⠉⠋⠉⠉⠉⠑⠢⠤⡇⠀⠗⠒⠒⠒⠒⠺⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠙⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠈⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠃⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⠒⣤⡄⣀⠀⠀⠁⠀⡁⠀⠔⡟⠧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠈⠁⠀⠀⠀⠈⠀⠈⠂⠀⢰⡄
⠀⠀⠀⠄⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠔⠐⠒⠀⡀⢀⠀⠀⠀⠈⢇⠉⠉⠉⠀⠈⡆
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⢀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠠⠄⠀⢄⠀⠃
⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⣄⡰⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⡃⠀⠀⣀⣀⠀⢀⡀⠀⠀⣀⣀⣀⡀⠠
⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⢀⠂⠀⡀⢠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⣀⠁⠨⣼⣿⡟⠛⡟⢉⡏⠉⣏⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠁⠃⢀⡀⠁⠀⡀⠘⠈⠀⠉⠍⠐⠠⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⡀⠤⣷⢞⢁⣀⣭⠽⠧⠴⠒⠋⡇
⠀⠀⠤⢐⡆⠉⠋⠉⡌⠀⠀⠀⢢⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠁⠂⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⡈⣉⡉⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⡀⠀⠄⠤⠀⠀⠤⠄⡉⢱
⠀⠀⠀⠀⠀⠀⣾⢸⠈⠆⢐⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⡒⠒⠊⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⡏⢸⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⡇⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⢡⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢸⣿⣿⣿⣭⣭⣿⣟⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠘⡇⢸⠟⠻⠿⢿⣯⠭⢿⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡈⢴⠅⣴⣿⠵⣕⢼⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⢴⠎⢳⠤⠴⢟⢚⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠨⡇⡇⠰⠆⢀⠉⣋⢁⢸⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡄⡇⡇⠲⢲⣎⣋⠟⣿⣸⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡅⠓⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⡤⠤⠤⠖⢒⣉⣠⠁⡇⢇⡺⡆⠙⠟⠛⠝⢩⢸
⠀⠀⠀⠀⠀⠀⢸⠈⠪⠤⠬⠤⠈⠉⠭⠭⠭⢭⡭⠭⠭⠭⠉⠉⠁⠁⠈⠁⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠄⠰⠃⠸⠿⠿⠿⠿⠿⠿⠟⢸
⠀⠀⠀⠀⠀⠀⠈⠧⣄⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠉⠉⠉⠉⠙⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢀⣠⠴⠚⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠳⠒⠒⠛⠣⠀⠀⠰⠚⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠁⠸⠿⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⣔⠋⠉⣀⣩⣿⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠶⠀⣠⣄⣀⡀⠀⠀⠈⠓⠢⢤⠴⠶⠖⠶⠒⠒⠒⠲⠶⠤⠤⠤⠿
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠓⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠚⠉⠀⠈⠉⠉⠓⠲⠤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡠⡄⢤⠤⠀⠀⠠⡤⠀⠤⡀⡄⡀⢠⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⡇⢇⡿⢸⠀⠀⠀⠀⡇⠘⣀⡇⣇⠄⠖⢧⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⣦⠤⠤⠤⠤⠤⠤⠤⢶⡶⠶⢦⡤⠤⠤⠤⠤⠤⠤⠴⣦
⠀⠀⠀⠀⠀⠀⣴⠚⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⢳⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠀⢸⡇
⠀⠀⠀⢀⣴⠞⠋⠉⣻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢿⡉⠉⠙⢶⣄
⠀⠀⠐⢿⣥⣤⡀⢰⠋⠈⠛⠛⠛⠋⠉⠉⠁⠀⠀⠐⡗⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠈⠳⠆⣤⣤⣽⠗
⠀⠀⡰⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢳⠒⠒⠚⢶⡀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠉⠻⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠿⠿⠿⠇⠉





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣗⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⣽⠟⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⣡⣾⣯⣕⣶⣤⣄⠀⠀⢄⣤⣤⣤⣶⣤⣤⣤⣤⣤⣀⣀⡀⢿⣿⡏⠙⠳⣄⠊⠟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡿⠇⠉⠀⣸⣿⡿⠇⠀⣲⠆⢀⣉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢎⠻⡃⠀⡐⠀⣢⡾⠛⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⢦⣶⣿⣿⣾⣷⡆⠀⢰⡟⠉⠀⠀⢶⡀⠀⠀⢹⡇⠀⠈⢿⣿⠁⠉⢿⣿⣿⠏⢸⣧⣁⠀⠀⢸⠀⢶⣤⣻⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⢠⢿⣷⣤⠀⠀⢷⠀⠀⠀⠺⠃⠀⠀⠻⠧⠀⠀⠀⢹⣿⣶⣿⣿⣿⣷⣶⣒⢡⡘⢿⣷⣤⣼⣿⣿⡿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢊⣿⠇⠀⠀⠈⣡⡄⠀⠀⢴⠶⠆⠀⢀⡀⠀⢠⣾⣿⡟⠙⣿⣿⣿⣿⣿⣧⣿⣿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣁⣄⣀⣰⣄⠘⠷⠤⠀⠀⣤⠀⠀⢻⡇⣠⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⢿⣿⣿⣿⣧⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠋⠉⠉⠉⠉⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⣀⣀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢨⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠰⠙⡀⣀⡀⢀⡀⠰⢑⠀⠀⠀⠀⠀⡉⠄⠀⣀⣀⠀⡄⣀⣀⡀⠀⡎⡀⠀⠀⠀⠀⢈⠡⠀⢀⣀⣀⢸⠀⠀⠀⠀⢠⣀⣀⣀⠀⢀⠋⠆
⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⣃⡀⠀⠀⠀⠀⠀⢃⢈⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠈⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡈
⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⡸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣏⣿⣿⣽⣿⣾⣯⣿⣿⣟⣾⠃⠀⠀⠀⠀⠘⣿⣻⣿⣯⣿⣷⣿⣿⣿⣿⣷⣿⣯⣿⣿⣏⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠀⠀⠀⠀⠀⠀⢹⡽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣀⣤⣤⣄⡀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣆⠀⠘⢧⣤⣿⣿⣿⡿⠃⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⠀⣿⣿⣿⣿⣿⣿⠋⢻⣠⡾⠿⠿⠏⠉⠉⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⢀⣀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠃⠀⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡂
⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⣠
⠀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⣠⣤⡄⢰⡖⠛⣧⠸⣷⢿⣄
⠀⠀⠛⢻⡏⠁⢸⡟⠙⣷⠈⣥⠞⣿⡈⣷⠀⠻⠀⠛⠀⠉
⠀⠀⠀⠈⣿⠀⠀⣿⠀⠹⠂⠛⠋⠉⠁⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡀⠀⣦⠘⣇
⠀⠀⠀⠀⠀⠀⠙⢷⣴⡟⢠⡞⠙⢷⡘⣧⠀⣿⡄⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠷⠤⠞⠁⠙⠋⠉⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠈⠀⠀⡀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠂⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠌⠀⠀⠈⢐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠈⠁⠀⣀⣀⢠⠤⢤⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⢀⣀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠈⠇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱⠀⠀⢲⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢣⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠊⣤⣄⢠⣄⠀⢧⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⠀⠈⠆⠀⠈⠄⠀⠀⠀⠀⠀⢰⢦⣃⢋⢻⡌⠶⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣇⠀⠈⠄⠀⠘⣄⣀⠤⠄⡶⡎⡇⠛⠈⠈⢁⡞⡩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠀⠈⠄⠀⢀⣀⠤⣔⢧⡘⠃⠀⣀⠠⠞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠱⠀⢀⡠⠂⠉⢀⡼⠓⠤⢈⢶⠊⠀⠀⠀⠘⡀⠈⠉⠁⠒⠒⠒⡖⠲⢄⠀⠀⢀⠀⠀⠂⠁⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠛⠒⣨⠝⡟⠹⡦⣄⠀⠈⣧⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⣁⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠎⠀⠀⠑⢄⠉⠒⠃⢃⠀⠀⠀⠀⠘⢄⠀⠀⢸⠯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⡜⠀⠀⠀⠀⠀⠑⢤⡀⠀⢃⠀⠀⠀⠀⠀⠳⣄⠀⡖⠀⡞⠫⢄⣀⠠⢀⠀⢀⠤⠐⢨⡒⠞⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠡⡀⠀⠀⠀⠀⠈⠓⡆⢰⠁⠀⠀⠀⠉⢱⢸⠀⠀⠀⠀⠈⠔⠊⠁⡌
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠉⠁⠈⠉⠉⠉⢹⠁⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢇⡘⠲⢤⣀⠀⠀⡜⠀⡄⠀⡠⠔⢻⡠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⣚⣀⣠⠤⠖⠚⠁⠈⠢⣄⠀⠀⠀⠀⠈⠑⡦⠄⣉⠛⠁⠠⠁⢸⡁⠠⣾⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⢹⠢⢄⠀⠀⠀⠘⣄⠀⢉⣒⡶⠲⣁⠁⢘⡟⠰⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡄⠀⠀⠈⡗⠉⠙⢱⣄⡜⢙⡜⡁⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⢘⠀⠀⠀⡇⠀⠀⠸⢄⡀⠀⠹⠀⡞⢹⢠⡇⡜⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⢈⡆⠰⣰⠀⢸⡜⠋⠣⣠
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠘⠁⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⠝⠉⠉⠀⠀⠒⠒⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⡠⠊⠀⡠⠃⡠⠂⢀⠔⠁⡀⠀⢠⠃⠀⢈⠛⠚⠤⠐⠀⢀⠀⠙⠩⠭⠛⠁⠀⠸
⠀⠀⠀⡠⠴⠁⠀⢠⢁⠜⠁⢠⠂⢠⠎⠀⢀⠎⠀⠀⠉⠀⠤⠤⠤⠤⠝⠣⠤⠤⠤⠤⠀⠁⠀⢇
⠀⠀⠰⠁⡇⠀⠀⠈⠁⠀⠀⠠⠔⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⡇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⡀⠀⣀⣀⠐⢄⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⠀⠈⡱⠦⠤⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢀⡀⠘⠸⣄⣀⣀⣼⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠌⠠⠂⠀⠀⠀⠀⠀⠒⠒⡒⠲⠒⠚⠫⡁⠀⠀⠀⠀⠀⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠠⠤⠬⠠⣀⣀⣐⣀⡃⠀⠀⣀⠜

⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⢀⣴⣷⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀
⠘⠿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠂⠀⠚⠀⠀⠓⠀⠀⠃⠀⠐⠂⠀⠘⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢀⡤⠶⠬⡇⠀⠀⠀⠂⠀⠐⠂⠀⠐⠂⠀⠒⠀⠀⠒⠀⠀⠀⡿⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢹⠀⠐⠂⠀⠒⠀⠀⠒⠀⠀⠂⠀⠐⠂⠀⠐⠀⢸⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡄⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠇





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣧⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣯⣧⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠛⠻⠿⣿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠈⣿⣧⠈⢿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠻⠿⣷⣶⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠘⣿⣆⠈⢿⣧⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠘⢿⣦⣀⡙⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠊⠂⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠄⠠⠀⠀⠒⢄⠀⠠⢀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠑⠀⠀⠳⡀⠀⠀⠀⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⣠⠄⠁⠘⠀⠀⠀⠀⠈⠓⠀⠐⡆⠀⠀⢀⠠⠀⢄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢀⡀⠀⠀⠀⠒⡅⢀⠀⠀⠀⡀⢀⣀⡀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡐
⠈⠢⠀⠀⠘⠀⠀⠀⢁⠀⡀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⠀⠠⠠⠐⠀⠐⡄⠀⠀⠂⡐
⠀⠀⠀⠐⣳⢰⡤⠒⠓⠄⠂⢀⠀⠀⠐⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠨⠒⠀⠀⠂⠤⡀⠀⠀⠀⠀⠦⠀⠀⠈⠃⠀⢠⠀⠀⢠⠆⠀⠀⡘
⠀⠀⠀⠻⠍⠃⠀⠀⠀⠀⢤⠂⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠂⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠓⠀⠀⠀⠀⠈⢀⠠⠈