Snowflakes Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡃
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸⠀⣇⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⡀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣒⠄⢠⡀⠄⠀⠀⢀⠙⠀⡋⡀⠀⠀⠀⢀⡀⠠⣚⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣉⠻⢀⠂⡀⠀⠀⡇⠀⠐⠀⢚⣩⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⡀⠀⠉⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠉⠠⠀⠀⠀⣠⠒⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢁⠀⡀⠀⠀⡀⠇
⠀⣀⠀⠀⠀⠉⠁⠠⠔⠁⠀⠀⠄⠀⠀⠈⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠖⣀⠠⠄⠀⢠⠀⠁⠓⠀⠄⡐⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠃⡀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠱⠞⠋⠀⠁⠀⠀⠀⠅⠖⠉⠀⠹⠒⠦⣀⡆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⢾⠀⡷⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⢰⠭⠶⠀⠠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⢈⡄⠈⠁⠀⠈⠉⢠⡔⠀⠂⠀⢀⡀
⠀⠀⠀⠬⠳⣤⠀⠀⠀⠀⠠⡄⣧⠀⠀⠀⠀⢠⣀⡨⠆⠉⠀⠀⠀⠀⠀⠀⠆⠀⠶⢭⡚⠒⠃⠀⠀⠀⢼⠀⠀⠀⠈⠀⡈⠰⢗⡊⠵⠂⠠
⠀⠀⠀⠀⠀⠁⠀⢃⡶⢄⡀⠄⢃⡀⠰⣂⠐⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⠀⢄⡀⠀⠐⢿⠀⣰⡶⠞⠉⠀⠀⢤⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠁⠈⢀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⠄⠀⠙⢷⠤⠌⠁⢫⣀⣄⣀⡀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠄⡰⢖⠁⠐⠄⠰⠀⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣠⡞⠘⣧⠀⠉⠳⠄⠀⢠
⠀⠀⠀⣀⡠⢷⠈⠁⠈⠀⢠⣦⢠⠀⠈⠉⠉⢠⣦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢆⡀⠠⠒⠋⠉⠀⠀⡟⠀⠀⠀⠀⠀⡳⢆⡀⠀⢀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⠒⠄⠀⠀⠀⠀⠀⠀⠀⠈⠡⠞⠉⠈⠃⢠⡆⠀⠀⠀⠇⠀⢠⡄⠜⠈⠛⠰⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠚⣠⢰⡖⠒⢀⠂⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠁⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⢤⡤⣒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠨⣘⡯⠀⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⢇⡀⠁⣀⠔⠛⠭⠀⠀⠀⠀⠀⠀⠀⡲⢤⣄⡄⠀⡀⠇⢠⠀⣸⣴⠾⡓⢄⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠓⣄⣾⠕⣫⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠊⠔⠋⢑⣚⣿⣷⣊⣀⠀⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠐⢻⠟⠉⠉⠩⣭⢛⠟⣍⠓⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⢹⠙⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠁⡜⠀⠘⠁⠀⠀⠉⠲⣶⡄⠀⠀⠀⠀⠀⠀⠤⣐⣒⠾⠻⠀⠈⠀⢋⢷⣒⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠄⠀⠀⠀⠀⠈⡌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣙⣇⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⡀⠡⠀⣤⠀⣂⠗⠠⠀⠀⠀⠀⠀⠀⢴⡰⡀⠠⡀⡀⠀⣇⢘⠀⠀⢠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠽⠓⠤⠬⣙⣬⣠⡧⠊⣩⡅⠀⠠⠤⠀⠀⠀⠀⠩⠭⠛⠢⢔⡳⣄⡿⢁⠤⠒⠛⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠓⣂⢟⠿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡻⡿⣓⠒⠣⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠠⠎⠰⠈⠖⠈⢹⠳⡶⠀⠀⠀⠀⠀⠀⠀⠉⠀⢁⡔⢡⢇⠈⠑⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠙⠀⠀⡀⠀⠀⣃⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠿⠀⠀⠄⠀⠀⠸⢱⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠐⡹⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡙⢴⡧⢊⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⣸⣇⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣤⢸⡇⣤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠙⡇⣬⡀⠆⠸⠀⣷⠀⠀⠓⢦⢣⣄⠰⣿⣺⣷⣿⠆⣠⡜⡴⠞⠀⠀⣾⠀⠗⠰⢀⣭⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠝⠿⣶⣦⡁⣤⣤⣄⢸⡯⣟⣷⡖⣡⣌⢲⣾⣻⢽⡇⢀⣤⣄⢈⣤⣴⠿⠫⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⡤⠉⣛⣿⣾⠯⠼⠻⡟⠉⡅⢿⣿⢸⠉⢻⠿⠧⢽⢷⣷⣛⠉⢤⡀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠾⠛⡆⢿⣷⣮⣓⣼⡼⢧⣷⣒⣵⣾⡷⢠⠻⠷⠋⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⠴⠾⣟⣿⠂⠪⢭⣿⠉⢄⡠⠉⣿⡭⠕⠐⣿⣻⠷⠦⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠙⠻⢿⡿⢂⣚⣭⣿⣄⡈⢉⣠⣿⣭⣓⡐⢿⡿⠟⠋⠙⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⣴⣿⣶⠃⠿⠿⢋⠔⡻⢻⡟⡟⠢⡙⠿⠿⠘⣴⡿⣦⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⣉⣤⣵⢿⣿⣯⢱⡾⣧⣠⠇⣿⣿⢸⣀⣼⢷⡎⣽⣾⡿⣮⣤⡉⠡⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣈⣱⣾⠛⠋⣄⠙⠋⠁⢼⢟⣯⡿⠳⣌⣡⠞⢿⣽⡻⡇⠈⠙⠋⣠⠛⠛⣶⣆⡁⢄
⠀⠀⠀⠀⠀⠀⢀⡴⠦⠩⠁⠂⠼⠀⠟⠀⠀⠶⠋⡎⠁⠰⣿⢿⡿⣿⠆⠈⢱⠗⠦⠀⠀⠿⠀⡦⠐⠨⢍⠰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⡉⣹⡏⢉⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡁⢹⠏⢈⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢹⡏⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡿⠏⠋⠻⣏⡀⠀⠀⠀⠀⠀⠀⢘⠿⢙⡙⢿⣁⠀⠀⠀⠀⠀⠀⠲⣾⣶⣿⣿⣮⠴⠀⠀⠀⠀⠀⠀⠑⠄⣒⠤⠁
⠀⠀⠀⠀⠀⠀⠙⣿⡄⡉⢠⡟⠉⠀⠀⠀⠀⠀⠈⢻⣧⢙⠃⣼⠋⠁⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⡿⡤⠀⠀⠀⠀⠀⠉⠀⡡⢛⠪⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠝⠟⠈⠙⠀⠀⠀⠀⠀⠀⠀⠘⠩⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠎⠋⠮⠑⠀⠀⠀⠀⠀⠀⠀⠚⠀⠰⠀⠈


⠀⠀⠀⠀⠀⠀⢀⡄⢐⢂⣔⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⡴⡴⡠⠀⠀⠀⠀⠀⠀⠀⣄⠦⣶⢖⡄
⠀⠀⠀⠀⠀⠀⣄⠐⣾⣿⣷⠢⠆⠀⠀⠀⠀⠀⢀⡀⠐⢬⡌⠄⠤⠀⠀⠀⠀⠀⠀⠈⣟⢲⣿⣷⢺⢒⠀⠀⠀⠀⠀⢘⡊⢡⣷⡎⠬⠅
⠀⠀⠀⠀⠀⠀⠀⣬⠹⠛⠏⡅⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⡹⣤⣉⣧⢟⠂⠀⠀⠀⠀⠀⠐⢢⢄⢸⢴⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠖⠞⢶⣀⠀⠀⠀⠀⠀⠀⠀⡰⢈⠬⢤⡔⠄⠀⠀⠀⠀⠀⠀⠀⠢⣴⠛⠶⠶⠂⠀⠀⠀⠀⠀⠐⢶⣶⣿⣶⣗⡄
⠀⠀⠀⠀⠀⠀⠂⣿⡸⠽⢀⡧⡂⠀⠀⠀⠀⠀⠐⠂⣗⡺⢇⡿⡘⠀⠀⠀⠀⠀⠀⠰⠈⣿⠶⡤⠤⠠⠀⠀⠀⠀⠀⠾⢿⠿⢿⠿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠎⠳⡓⠋⠒⠀⠀⠀⠀⠀⠀⠀⠠⠊⠍⡍⠈⠂⠀⠀⠀⠀⠀⠀⠀⠰⠋⢢⡖⠲⠀⠀⠀⠀⠀⠀⠀⠴⠰⢰⠦⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⢀⣸⣇⡀⣄⣤⠆⠀⠀⠠⣼⡆⢹⡟⢁⣿⡤⠀⠀⠰⣤⣆⢶⣼⣇⡶⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠋⠙⣿⡍⠀⠀⠀⠀⣛⡋⣙⣿⣿⣟⢉⣛⡀⠀⠀⠨⣭⣿⣿⣿⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠷⡾⠟⡶⣤⡀⠀⠀⠸⢿⡏⢹⣇⠉⣿⠏⠀⠀⢀⣴⡶⣻⡿⡿⣟⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠏⠓⠈⠀⠀⠀⠀⠀⠀⠉⢼⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠦⣽⠴⣀⣴⡶⠀⠀⠲⣤⣀⠀⣹⡁⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣳⣾⣞⣛⠌⠀⠀⠀⠀⠀⠉⣛⣾⣶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⡇⣿⢬⡛⣶⣦⠀⠀⣠⡶⠞⠉⢺⠒⠉⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠘⡏⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣷⡚⠉⠁
⠀⠚⠒⠂⠒⠂⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⡇⠉⢻⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⠀⠀⣿⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⣿⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⡈⢻⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣸⣇⠀⣶⠀⠀⠀⠀⠀⣤⣘⣿⣁⣤⠀⠀⠀⠀⠀⣴⠆⣰⡟⢀⣠⣴⠾⠛
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⠿⢿⣦⣿⡀⢴⡀⢠⣤⡈⢻⡿⠋⣡⣄⠀⣠⡀⢰⡟⣰⣿⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠶⠿⠛⢷⣾⣇⠘⠻⣇⢸⡇⢀⡿⠛⢀⣿⣤⡿⣿⣉⡉⠛⠛⠳⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣉⠙⠳⣦⣽⣾⣷⣟⣠⡶⠟⠛⠿⢦⠄⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠗⠲⢶⣿⣿⣿⣿⠷⠶⠶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠐⠻⣶⣤⣴⠞⢋⣽⢿⡿⣟⠻⢦⣄⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠐⠷⠶⢦⣤⣤⣈⣉⣿⣾⠛⣿⠁⣴⣾⠁⢸⡇⢹⣦⡄⢹⡿⢷⣤⣶⠶⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣿⠏⣼⠇⠈⠋⠀⠉⢉⣠⣾⣧⡈⠛⠃⠸⠷⠨⣿⠻⣷⣶⣿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣤⡶⠟⠋⠁⣼⠏⠰⠟⠀⠀⠀⠀⠀⠛⢉⣿⡍⠛⠀⠀⠀⠀⠀⠶⠀⢻⡏⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣧⡈⠛⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⣿⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿⠀⠀⠻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣹⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠄⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⣻⣤⡀⠀⡀⢀⢺⣗⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠄⡄⠢⡝⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⡳⣦⢰⠟⠎⣀⣲⠵⣛⠫⠁⠀⠀⠀⠀⡀⡀⠠⣦⡀⢫⢛⠌⣠⡞⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣰⢒⢿⠐⣏⠂⠁⠀⠀⠀⠀⠀⠀⢐⠭⡻⠓⠂⠨⣷⣿⡯⠤⠄⢶⢶⠆
⠀⠀⠀⠀⠀⠀⢀⣠⡵⢿⠛⠸⠹⡾⠅⠋⠛⢥⡢⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛⣡⢂⣝⡌⠱⠶⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⢭⠏⡂⠀⠀⠀⠸⠱⠆⠀⠀⠀⠀⠀⠠⢐⣸⡆⠀⠃⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣟⡠⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠹⡅⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢤⠀⠀⠁⢀⠀⣨⠾⠡
⠀⠀⠀⠀⠀⠀⠠⣁⡀⠀⠀⠙⡇⢀⠀⣆⢠⠶⡀⠀⠀⠀⠀⠈⠟⡺⠤⢀⡀⠀⠣⣸⣀⡪⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠊⠔⠩⠛⠒⢴⣶⣅⣊⠉⠑⠉⠂⠁⠀⠀⠀⠐⠋⠀⠀⢀⣀⠉⢶⡉⢹⢐⠊⠛⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⠔⢹⠱⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠔⡱⢻⠙⢆⠈⠹⡳⡣
⠀⠀⠀⠀⠀⠀⠀⠤⢄⡶⠉⠀⠀⠐⡙⣦⠴⠤⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠘⢁⡌⠀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠁⠀⠀⠀⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢱⢯⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⢿⡿⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⠀⠙⢿⡿⠋⠀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢻⣿⣿⡄⣿⢸⡇⣿⢠⣿⣿⡟⠀⠀⠀⠀⢠⡄
⣀⣀⡀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⣬⣭⣿⣿⣸⣇⣿⣿⣭⣥⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⢀⣀
⠈⢿⣿⣿⣦⢹⡇⠀⠹⣿⣿⢠⡦⢸⣷⣄⡀⠀⠈⢻⡟⠁⠀⢀⣠⣶⡇⢴⡀⣿⣿⠏⠀⢸⡇⣴⣿⣿⡿
⠀⠀⠙⣛⣛⣿⣿⣜⡻⢾⣿⡿⠁⠘⣿⣿⣇⢠⡆⢸⡇⢰⡄⣸⣿⣿⠃⠈⢿⣿⡷⢟⣣⣿⣿⣛⣛⠉
⠀⠀⠀⠉⠉⠀⢶⣭⣛⢶⣽⣇⠀⠠⣬⣝⣿⣿⠁⢸⡇⠈⣿⣿⣫⣥⠄⠀⣸⣯⡶⣛⣭⠶⠀⠉⠉
⠀⠀⠀⣠⣾⣿⣶⡾⣿⠟⠛⠙⠻⣦⣄⡈⠉⢿⡄⢸⡇⢠⡿⠉⢉⣠⣴⠞⠋⠙⠻⣿⢷⣶⣿⣷⣄
⠀⠀⠉⠛⠛⠛⠋⢼⠏⢀⣀⠐⢶⣄⠉⠛⢶⣤⣻⣾⣷⣟⣤⡶⠛⠉⣠⡶⠂⣀⡀⠹⡧⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡷⣿⡷⠶⠶⢾⣿⣿⣿⣿⡷⠶⠶⢾⣿⢾⣿⣿⣿⡷⠆
⠀⠀⣀⣤⣤⣤⣄⢺⣆⠈⠉⠡⠾⠋⣀⣤⡶⠛⣿⢿⡿⣯⠛⢶⣤⣀⠙⢷⠌⠉⠁⣰⡗⣠⣤⣤⣄⣀
⠀⠀⠈⠙⢿⣿⡿⢷⣿⣦⣄⣠⣴⠞⠋⢁⣀⣾⠃⢸⡇⠘⣷⣀⡈⠙⠳⣦⣄⣠⣴⣿⡾⢿⣿⡿⠋
⠀⠀⠀⣀⣀⠀⠶⢛⣭⡾⣿⡏⠀⠐⠛⣫⣿⣿⡀⢸⡇⢀⣿⣿⣝⠛⠂⠀⢹⣿⢷⣭⡛⠶⠀⣀⣀
⠀⠀⣀⣭⣽⣿⣿⢋⣵⢾⣿⣷⡀⢰⣿⣿⡟⠸⠇⢸⡇⠸⠇⢻⣿⣿⡄⢀⣾⣿⡷⣮⡙⣿⣿⣯⣭⣀
⢀⣼⣿⣿⠟⣹⡇⠀⣠⣿⣿⠘⠗⢸⡿⠋⠁⠀⢀⣼⣧⡀⠀⠈⠙⢿⡇⠺⠃⣿⣿⣄⠀⢸⣏⠻⣿⣿⣧
⠉⠉⠉⠁⠀⠈⠀⠀⢹⣿⠟⠁⠀⠀⠀⢛⣛⣿⣿⢹⡏⣿⣿⣛⡛⠀⠀⠀⠈⠻⣿⡏⠀⠀⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣼⣿⣿⠇⣿⢸⡇⣿⠸⣿⣿⣷⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉⠀⣠⣾⣷⣄⠀⠉⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣾⣷⡙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠅⢀⠔⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠠⡀⠀⢐⢐⠀⠀⡠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄⢠⠂
⠀⠀⠐⡖⢢⠀⠀⠀⠰⡀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠃⠀⢀⡰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠀⢀⡀⠉⡃⠁⣀⠀⠀⠀⡐⠀⠀⠄
⠀⠀⠀⣀⣀⡉⠤⡠⠀⠁⠀⠀⠀⠨⠀⠀⠀⠀⢘⠀⠤⠁⠀⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠬⡀⠀⢁⠐⠒⢈⠀⠀⢀⠀⢅⢋⣀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠒⠄⠀⡀⠸⠐⠀⣄⠠⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠗⢄⡐⢖⣀⠀⠳⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡐⠂⢨⢣⠣⣉⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⢰⠆⠀⢀⠐⠍⢀⠄⡀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⡠⠌⠂⡠⠈⠁⢈⠑⠶⡀
⠀⠀⠀⢀⣀⠀⠀⢀⡀⠘⠉⠀⠈⠀⢨⠀⠂⠀⠀⠀⢠⣦⠄⠤⠄⠀⠀⠀⠀⠀⠀⣀⠄⠘⢲⠃⠀⠀⠀⢘⡄⠄⡘⠀⠠⠂⠤⠁
⠀⠀⠀⠀⢀⣠⠄⠉⠁⢠⠀⠀⠀⠀⠰⠀⠀⠀⠀⢆⠀⠠⠈⢃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢔⡢⡀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠔⠀⠁⢠⠃⠀⠂⢠⠔⠁⠀⢠⠀⠐⢄⠀⠘⠀⠀⠳⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⣉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠁⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢾⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠙⠀⠰⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠐⠀⠐⣦⡀⠀⢹⠀⠀⠀⣐⠂⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠠⡀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢦⣀⠀⢠⠈⠲⡟⢄⡀⢀⠃⠀⢀⣈⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈⢆⠈⠐⢀⠴⠁⠀⠈⢀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠙⡛⠈⠁⠀⠁⠘⠀⢚⠶⡾⠋⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢀⡆⠙⠰⠁⡈⠀⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠖⡊⠉⠄⠈⠠⠂⠄⠀⡠⠒⠀⢀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⡈⠉⠀⠀⠈⠁⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⠀⠀⠀⣠⣭⡄⢂⠀⠀⠁⠀⠀⠃⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⡀⠀⠏⠀⢀⠀⠫⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠉⠁⠎⢈⠇⠀⢠⠁⠂⠞⢁⣄⠀⠀⠤⠅
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢠⠔⠉⣈⠀⢤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠊⠀⡀⠀⠀⡸⠂⠁⠠⣦⠀⠀⢬⠀⠀⠀⠃⠤
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠆⠀⢁⡀⠀⠸⠀⡀⠀⠰⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠁⠀⠘⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⠄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠞⠀⠼⠈⢆⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣧⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣼⣦⠄
⠀⠀⠀⠀⠀⢲⢧⣆⢈⣿⠁⣶⡼⡆⠀⠀⠀⠀⠀⠀⢲⣿⣀⠈⡇⢀⣸⣶⠂⠀⠀⠀⠀⠀⠐⣶⡇⡀⣰⡄⣀⢿⡶
⠀⠀⠀⠀⠀⠀⣉⢉⣟⢉⣿⣉⣉⠀⠀⠀⠀⠀⠀⠀⣉⠀⣉⣿⣿⣏⡁⢉⡁⠀⠀⠀⠀⠀⢈⣉⠀⣹⡉⣹⣏⠀⣉
⠀⠀⠀⠀⠀⠴⡞⡏⢈⣿⡉⠽⢳⠆⠀⠀⠀⠀⠀⠀⠼⣿⠉⢀⡇⠈⢻⠿⠄⠀⠀⠀⠀⠀⠠⠿⡇⠁⠹⠃⠉⣾⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⡟⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢻⠟⠂

⠀⠀⠀⠀⠀⠀⡀⠀⣒⣿⣃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣧⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣼⣦⠄⣀
⠀⠀⠀⠀⠀⡾⢷⣇⡈⣿⢁⣾⡾⢧⠀⠀⠀⠀⠀⠀⣳⣿⣀⣨⣇⣀⣼⣶⡂⠀⠀⠀⠀⠀⠐⣶⠇⣀⢰⡆⣀⢿⣞
⠀⠀⠀⠀⠀⠀⣍⣈⣽⣿⣯⣁⣩⠀⠀⠀⠀⠀⠀⠀⣉⡀⣸⣇⣈⣯⡀⣈⡁⠀⠀⠀⠀⠀⢈⣁⠀⣩⣿⣿⣍⠀⣉
⠀⠀⠀⠀⠀⠹⡟⠏⣀⣿⣀⠿⢻⠏⠀⠀⠀⠀⠀⠀⠾⣿⠁⢈⣏⠈⢹⠿⠄⠀⠀⠀⠀⠀⠠⠿⡇⠁⢸⡃⠈⣾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡔⠶⣿⠶⢢⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡯⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠲⢿⡷⠂⣄⡀
⠀⠀⠀⠀⠀⣨⡿⢧⣤⠿⣤⡼⢿⣁⠀⠀⠀⠀⠀⠀⠛⠿⣤⣘⣇⣠⡾⠟⠁⠀⠀⠀⠀⠀⢀⣿⠦⣄⡼⢧⡤⠞⣿
⠀⠀⠀⠀⠀⠰⣄⣤⠷⣤⠿⣄⣠⠆⠀⠀⠀⠀⠀⠀⡀⣄⣤⠟⡟⢦⣄⣄⠀⠀⠀⠀⠀⠀⠠⣦⣠⡼⣤⡼⢧⣀⣴
⠀⠀⠀⠀⠀⠘⢹⡆⣀⣿⣀⢰⠏⠃⠀⠀⠀⠀⠀⠀⠛⠉⠀⢸⣯⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠛⡧⢀⣸⣇⡀⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠂

⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠
⡿⣟⣿⣷⣟⢯⣟⣷⣾⢟⡻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣷⣯⣵⣿⣞⡱⣟⣷⣿⣾⣵⣾⣿⣿⣿⣿⣯⡿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠒⣄
⣿⣿⢿⣷⣿⣟⢿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣷⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠐⡒⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠟⠛⠉⠁
⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⡿⣿⣯⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢑⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰
⣿⣿⣝⣻⣿⣗⣿⣿⣝⣿⣿⣿⣿⢿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠠⠈⠁⠀⠀⠀⣂⡜⠀⠘⠁⢀⠮⠁
⡿⢿⢿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣻⣿⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠤⠠⢞⡲⠄⡀⡀⠀⠀⠀⠀⠁⠀⡐⢀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣀⡈
⣿⣿⣟⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡆⠀⠘⠇⠀⠀⠀⠠⡌⠀⠠⠀⠀⠁⠄
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢤⠀⠛⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠠⠀⢀⣀⠀⠀⠀⠁⠀⠀⠀⠀⢄⠀⠒⠂⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⢷⣿⣿⣿⣾⣿⣟⡿⣿⠀⡀⠁⠀⢰⠫⠁⠀⣧⠐⠈⣁⣀⠠⡠⡀⠄⠀⡄⠀⠀⠠⢀
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⢷⣿⣿⣿⠀⠁⡀⠀⠘⢔⡀⣂⠞⠀⢠⠀⠀⠈⠀⠁⡀⠨⠄⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⠠⠄⢀⠀⠈⠈⢀⠐⠄⠀⠀⠀⠀⠀⠀⢊⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠺

⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣄
⠀⠀⠀⠂⠄⠀⠂⠸⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⡆⠠⢘⡁⠄⣒⠤⠂
⠀⠀⠠⠠⠤⠄⠰⣚⡆⠠⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢐⢸⢔⡂⠄⠁
⠀⠀⠀⠀⠔⠂⡐⢈⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⡒⠨⢘⠂⠁⣖⢥⡀
⠀⠀⠀⠀⢀⡄⠀⢸⠀⠑⠀⠀⠀⠀⣀⠀⡭⠀⡀⠀⠀⠀⠀⠀⠀⢪⡕⠀⠀⠀⠀⠀⠀⠀⠠⢞⡃⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⠘⠀⠟⡐⠁⣀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠴⢙⠁⡀⡢⣔⡀⡈⡋⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠬⠔⢾⣾⣇⢀⢠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠊⡜⢠⣤⠀⡑⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠙⡋⠋⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠑⠈⠤⡥⠄⠎⠄⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠂⢀⡉⠌⡀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣸⡇⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢻⣷⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣾⡇⠀⠀⠀⠀⠀⠀⣄⢸⡇⢀⡀⠀⠀⣷⠀⠀⢀⣼⠿⠷⠶⢶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠙⢦⡀⠀⠀⢠⠀⠈⢻⡿⠋⠁⠀⠀⢸⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⠇⠀⢸⣿⠀⠀⠀⢀⣼⠛⠛⠛⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠚⠿⢿⣄⠀⢸⣿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢷⣼⣿⣴⠟⠁⠀⠀⠀⠀⣠⡶⠃⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠶⠶⠶⠶⠶⠶⣾⡿⠶⠶⠶⠶⣶⣿⣿⣷⠶⠶⠶⠶⠶⠾⣿⡶⠶⠶⠶⠶⠾⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⣠⡾⠋⢸⣿⠙⢷⣄⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⡾⠋⠀⠀⢸⣿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠀⠀⢀⡴⢿⣿⢧⡀⠀⠀⢙⣿⣟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠸⠃⠀⠀⠉⠀⢸⣿⠀⠻⡄⠀⠈⡇⠙⢷⣄⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⢦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⣿⠘⣷⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠉⠀⠘⣷⡀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠀⠀⠀⠀⠀⡴⡁⠀⠀⡰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣀⠀⠀⠀⠀⠁⠊⠀⠃⢤⡌⢉⢤⠘⠂⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⢀⠠⣰⠆
⠀⠀⠀⠀⠀⠀⠼⠁⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⡾⡇⠘⠃⠀⡷⣖⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⡀⡤⠿⣩⠻⢦⢄
⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠇⠁⠀⠀⠘⠐⠹⣇⠀⠀⠀⠀⠀⠀⠈⠁⠛⢟⣟⡺⡿⠓⡗⠾
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣄⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡺⠞⣽⡍
⠀⠀⠀⠀⠀⠀⠙⢄⡘⢁⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢰⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠎⠁⠀⠀⠚⣏
⠀⠀⠀⠀⠀⠉⢩⠉⢫⡉⠁⠀⠀⠀⠀⠀⠀⠢⢄⡱⣄⣠⢀⣠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠶⠀⠀⠀⠁⠀⠀⠁⠀⠀⠰⠀⠀⠦⠶⠶⠀⠶⣿⡿⠶⠀⠶⢾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡀⡴⠀⢠⡀⣠⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠘⢫⠙⠊⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠬⣽⣾⠁⠀⠀⢳⣿⣁⣀⡀⠀⠀⠀⠴⠆
⠆⠀⠀⣆⠀⣤⣃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⠀⠘⢆⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⡀⠀⠀⠀⢺⣧⠐⣼⡟⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣤⠂
⠀⠀⠀⠸⣤⣁⣤⠄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣹⣄⣠⣤⣌⣽⣾⣁⣤⣤⣀⣼⣡⣀⣄⣀⠀⠀⠀⠀⠀⣀⣀⣉⣤
⠞⠀⢳⣴⠉⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠆⠀⠀⠀⠀⠉⠈⠉⡹⠃⠈⠈⣀⡞⠙⣤⠉⠉⠈⠻⣍⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣈
⣦⢦⣜⡉⠁⡴⠀⡼⠁⡀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠾⠁⠈⠞⣇⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⡀
⣶⢿⣺⠗⠺⡗⠺⣷⠚⠗⠂⠀⢀⡀⠀⠀⠀⣇⠈⠳⡄⢠⣤⠀⢀⡴⠚⢹⠀⠀⠀⠂⠀⠀⠈⠉⣩⡟⣆⠀⠀⢠⠟⣯⡉⠓⠀⠀⠀⠀⠀⠀⠠⠷⠆⣾⠖⡿⠒
⠟⠛⢣⣀⡀⠈⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢳⠨⣟⢀⠎⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠘⠄⠀⠋⠀⠚⢯⡀⠀⠀⠀⣀⠀⠀⠀⠀⣰⠃⠘⢁⣀
⢧⠀⠞⢫⣍⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢶⣌⠓⣼⠤⠥⣼⠤⢚⣡⡴⠆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣤
⡀⠀⢠⠏⣧⣄⠀⠀⠀⠀⠀⢠⡤⠖⠒⠒⠒⠦⢤⣹⠁⠀⠀⠈⢷⣉⣤⠥⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡏
⠀⠀⠋⠀⠋⢣⠀⠀⠀⠀⠀⠀⠉⠑⠲⠶⠒⢒⣉⡽⣄⠀⠀⣀⠞⣑⠲⠤⢤⡤⠬⠟⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠁⠀⣀⠀⠀⠀⠀⠀⠐⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⢠⡽⡞⢉⡴⢻⢙⡏⣟⠲⣌⠛⠷⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠐⠄
⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡾⠸⣧⠸⡄⠈⢧⠀⠀⠀⠀⠄⠀⠀⠀⢆⢀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠈⠀⠀⠀⡇⣠⠞⠁⠘⠓⠀⠙⠦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠉⢣⣄⠐⣤⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠎⠀⠀⠀⠀⠀⣀⠈⢃⣀⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⣀⢀⡀⣄⣠⣬⠉⠈⢣⣤⢂⣀⢀⣀⣀⠀⠀⠀⠤⠀⠀⠈⢧⢀
⠀⠀⢀⡀⠀⠀⠉⢁⡈⢛⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠊⢨⡦⠠⣮⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣯⠖⡀⢂⡴
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠑⠀⠀⠀⠀⠶⠂⠀⠀⠀⢶⡀⢀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠘⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠼⠖⠱⣞⡉
⣴⣷⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡄⡜⠡⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠷⠶⡾⡾⠖⢺⠀⠀⠀⢰⠧
⠌⠋⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠡⢻⡽⣞⢃⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢓⡶⣀⢶⠐⠂
⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡀⠀⠀⣠⠎⠰⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⣲⠟⠆⠁⡸⣷⡂
⠀⠰⠆⠀⠀⠀⣀⢃⡜⠀⠀⢡⣘⣁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠄⡀⠀⠀⠀⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠙⡆
⠀⠂⠀⠀⢀⠀⠀⠀⢡⡄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠊⣻⡔⠀⠀⠀⣦⣟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠂⠠⠄⡤⢡⠠⡄⢠⠁⠈⠤⠤⠠⡆⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⣀⢹⡔⠙⢴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠁⠀⠀⣤⠃⠘⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠐⠒⠶⡷⢶⢾⡦⢼⠄⣾⣿⡆⢼⠥⡮⣴⢴⢤⠀⠄⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⣿⡇⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⣿⡇⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⣿⣿⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⣿⠋⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠈⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡟⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣽⣧⠀⢸⡇⠀⠀⠀⠀⠀⠸⣷⣤⣿⣠⣶⠇⠀⠀⠀⠀⠀⢀⣿⠃⣰⡟⢀⣠⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⠶⠾⠿⠿⣦⣼⣇⠀⣿⡀⢠⣶⣦⠈⢻⣿⠋⢀⣤⣄⠀⢠⡄⠀⣾⣇⣰⣿⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⠾⠿⠿⣶⣿⡇⠈⠛⢿⡀⢸⣿⠀⣸⡿⠛⠀⣿⣧⣼⣿⣿⣋⠉⠛⠛⠻⠷⢶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠛⠻⢷⣤⡈⢷⣸⣿⣼⠏⣀⣤⣾⠿⢿⣥⣄⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣍⣻⣿⣿⣿⣿⣾⣛⣉⣀⣤⣄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠁⣈⣭⣿⣿⣿⣿⣿⣯⣉⠉⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣀⠙⢛⣷⣶⡾⠛⠉⣰⠟⣿⡏⢿⡍⠛⢷⣦⣤⣴⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⢶⣦⣤⣤⣀⣩⣿⣿⡟⢹⡿⠀⣴⣾⡏⠀⣿⡇⠈⣿⣦⡄⢸⣿⠿⣶⣶⡶⠾⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⠏⢹⡿⠀⠘⠃⠀⠙⠛⠁⣠⣿⣧⡀⠛⠟⠁⠘⣿⠀⢹⡟⠻⣶⣶⣶⠶⠿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⣾⠏⢠⣿⠃⠀⠀⠀⠀⠀⢰⠿⠋⣿⠛⢿⡆⠀⠀⠀⠀⠀⢸⡇⠀⢻⣟⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⣼⠏⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⡀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⣠⣿⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⣿⣄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢸⣿⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⢸⣿⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠴⠒⠂⠀⠉⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠉⣠⠔⠊⣀⣀⣈⢉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠞⣁⡴⢧⣄⠠⠶⠶⠤⠰⠶⣄⡀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡾⢁⠀⢀⣿⠷⠆⠀⠤⣭⠏⢴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⠸⠋⠀⣀⣉⣫⡥⠩⣟⣓⡉⠙⠓⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⠈⢸⠘⠀⡄⠀⢀⠐⢒⡂⣄⣓⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠸⠰⣇⠋⠰⠈⡀⠡⠍⠰⠸⢀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⠁⡀⡀⠃⠘⠧⠙⢳⣤⣤⣤⣤⡾⢋⡹⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠸⡀⢃⡅⢰⡘⠦⠠⠀⡿⠁⠈⢻⠧⠠⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠁⣸⣿⣄⠉⠂⡴⠀⡇⠀⠀⠨⠗⠄⠞⢃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠻⣷⣾⠁⠀⠐⢦⡴⠂⠀⣸⣾⠛⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣾⣿⡉⢦⡀⠈⠳⢦⠀⠚⠃⢠⡴⣋⣠⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡟⢳⡄⠁⠀⠀⠈⠛⠾⠟⢩⡾⠋⢉⡡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠘⠻⣦⡀⠠⣀⣀⠀⠠⠏⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⣄⡀⠀⠙⢦⡈⠙⠛⠃⠀⠀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠢⡄⠁⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⠀⠀⠀⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢰⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣈⣠⡿⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡌⢸⡷⢁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⢸⡧⠠⠶⠃
⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⡀⢀⠀⠀⢀⠀⣦⠀⠀⣴⢸⡇⣦⠀⠀⣴⠀⠀⠀⠀⡀⢀⡀⠀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣐⠶⣌⡄⠃⢸⠇⠀⠈⢻⡙⣦⣄⠻⡿⢿⠿⣡⣴⢋⡞⠁⠀⠸⡇⠸⢁⣃⡶⢎⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣈⠚⢿⣦⣔⡷⣦⠘⣟⣿⣿⡏⣴⣦⢹⣿⣿⣿⡃⣴⢾⣦⣴⡾⠛⣋⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⡴⠂⣸⣝⣿⡟⢚⣉⠣⡁⢠⢻⡟⡄⢈⠜⣉⡓⢻⣿⣫⣅⠐⢦⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣉⣩⣷⣘⠿⢿⣮⠿⠟⠻⢿⣵⡿⠿⢃⣾⣍⣋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢮⣽⣿⣿⡃⣈⡵⣿⠀⠰⠖⠀⣿⢞⡉⢘⣿⣾⣟⣱⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣩⣙⡿⢡⣶⣾⢟⣶⣦⣴⣶⡻⣷⣦⡍⢿⣋⣉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠳⠄⢙⣫⣿⣧⢬⣉⡔⡁⠘⣼⣧⠃⢈⢢⣉⡥⣼⣿⣝⡋⠠⠞⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣩⣤⡾⠟⠹⡷⠟⢠⣯⣿⣿⣇⠻⠟⣸⣿⣿⣽⡄⠿⢾⠝⢿⣷⣤⣭⡥⢀
⠀⠀⠀⠀⠀⠀⠀⣬⡱⠞⢩⢁⡄⢸⡆⠀⢀⡼⣡⠟⢋⣴⣷⣾⣦⠙⠻⣼⣇⡀⠀⠰⡇⢘⠙⡟⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠿⠀⠀⠻⢸⡯⠟⠀⠀⠻⠉⠉⠀⠀⠁⠈⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠂⢺⡗⠐⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢃⢾⡇⡘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣿⡇⠀⠀⢸⣿⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⣿⣿⡇⠀⠀⢸⣿⣿⠟⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠈⢿⡇⠀⠀⢸⡿⠁⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠈⢿⣷⡀⠀⠀⠁⠀⠀⠈⠀⠀⢀⣾⡟⠁⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⣠⣤⣶⣤⣄⢰⣿⠋⠀⠙⣿⣆⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣼⣿⠋⠀⠙⣿⡆⣠⣤⣶⣤⣄
⠀⠀⠀⠀⢰⣿⠋⠉⠙⠻⢿⣿⣧⠀⠀⠘⣿⣆⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⣰⣿⠃⠀⠀⣼⣿⡿⠟⠋⠉⠙⣿⡆
⠀⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠈⠛⠧⠀⠀⠘⣿⣆⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⣿⠁⠀⠀⠀⠀⣰⣿⠃⠀⠀⠼⠛⠉⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⢉⣻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠘⣿⣆⡀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢀⣰⣿⠃⠀⠀⠀⠀⠀⢀⣤⣶⣿⣟⠉
⠀⠀⠀⠀⠀⢠⣿⡟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣀⣿⡇⠀⠀⢸⣿⣀⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢻⣿⡀
⠀⠀⠀⠀⠀⠘⣿⣦⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠈⠙⠻⣿⡇⠀⠀⢸⣿⠟⠋⠁⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠿⣷⣦⣀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⣠⣴⣾⠿⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⠖⠀⠀⠀⠀⠀⠀⠲⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣶⡿⠟⠉⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠉⠻⢿⣶⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢠⣿⠟⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⢀⣠⣴⣿⡇⠀⠀⢸⣿⣦⣄⡀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠈⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⣿⡇⠀⠀⢸⣿⠉⠛⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⣠⣽⣿⠿⠛⠁⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠈⠹⣿⡄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣯⣄
⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⣀⣤⡖⠀⠀⢠⣿⠏⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⡀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢲⣤⣀⠀⠀⠀⠙⠻⣷⡄
⠀⠀⠀⠀⠸⣿⣄⣀⣠⣴⣾⣿⡟⠀⠀⢠⣿⠏⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠹⣿⡄⠀⠀⢻⣿⣷⣦⣄⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠸⣿⣄⠀⣠⣿⡏⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⢹⣿⣄⠀⣠⣿⠇⠙⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⢀⣾⡿⠃⠀⠀⡀⠀⠀⢀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢀⣾⡇⠀⠀⢸⣷⡀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣿⣿⡇⠀⠀⢸⣿⣿⣦⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⡇⠀⠀⢸⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⡌⠂⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢣⣸⠀⠈⠙⠃⠀⠐⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⣍⡆⠀⠀⠀⠠⠀⠀⠈⠀⡏⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠉⢸⠆⠀⠀⠀⢁⡦⠀⠀⢇⡏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⢿⡷⠐⣏⣠⣖⡒⠉⡁⠀⣠⠊⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡖⢠⡾⢋⠅⡼⢟⣡⣄⠄⣰⠃⡀⠀⡀⠉⠳⣄⠐⠁⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣮⡰⣇⠈⢧⠸⢊⣴⢋⡜⠁⣼⠃⢸⠀⠀⠈⠛⢆⠈⠢⠄⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡲⣆⠹⣿⠇⢸⢠⢺⡎⢸⢀⢸⡎⢀⡟⠀⠈⠉⠒⠄⠀⠀⡀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⡉⠟⣸⠇⠠⠟⠈⢯⠃⣟⢸⠸⡆⠸⠁⠀⠀⢀⠀⠀⠀⠴⣿⠏⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣀⢤⠞⠁⠀⠀⠓⣀⠀⠈⣦⠀⠀⠀⠈⢧⠙⠮⠧⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣤⣦⠀⠶⠆⠛⠛⠋⠀⣤⣤⡤⠀⠙⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢀⣄⠤⠠⠖⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⡀⣿⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀⢠⡄⠀⠀⠸⣧⠀⢠⡶⢶⣦
⠀⠀⠀⠀⠀⠀⣾⠛⢻⣆⠀⢻⡇⠀⠘⢁⡀⠀⠀⣿⠀⠀⠠⡄⠀⠀⠀⢰⣟⣤⡿⢧⡶⠟
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠙⠷⣾⣧⡀⠀⠈⢡⡄⠀⣿⠀⢠⡦⠀⠀⣀⣴⠿⠿⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠛⠉⠻⢶⣤⣈⢻⣆⣿⣠⣿⣡⡶⠟⠋⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣈⣙⣿⣿⣿⣿⣿⣭⣤⣤⡄⠠⡄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠉⣉⣭⠿⣿⣿⣿⡻⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣤⣤⣤⣴⠞⠋⠁⣴⠏⣿⡍⢷⡄⠈⠛⠷⣦⣤⣤⡴⠾⠋
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡾⢻⡟⠀⠀⠀⡘⠋⠀⣿⡇⠈⢋⡀⠀⠀⠀⢹⡿⢶⣤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣁⣼⠇⠀⣾⠃⠀⠀⣀⠉⠀⠀⣿⡇⠀⠈⢁⡄⠀⠀⢸⣷⠀⠈⢿⣤⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠀⠀⠀⠈⠀⢀⣼⢿⣿⣆⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢸⡇⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠃

⠀⠀⠀⠀⠀⠀⠀⣀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀
⠀⠀⠀⢀⡀⡄⢀⡈⢻⡟⣁⠀⣤⢀⠀⠀⠀⠀⠠⣼⣿⣧⠀⣴⣿⣿⡤⠀⠀⠀⠀⠀⠶⣾⣺⣭⣭⣄⣷⠶
⠀⠀⠀⢨⡿⠿⣬⣿⣼⣷⣯⡴⠿⣯⠀⠀⠀⡀⢀⡘⢿⣿⣶⣿⣿⠛⣀⢀⡀⠀⢠⡎⣴⣻⣿⣿⣿⣿⢿⣮⢱
⠀⠀⠀⠀⠰⠷⢶⣿⣿⣿⣿⠶⠷⠀⠀⠀⠠⢿⣿⣿⣿⡇⠀⢈⣿⣿⣿⣿⠥⠀⢦⣬⣷⣽⣿⠋⠙⣿⣿⣿⣧⣴⠂
⠀⠀⠀⢈⣿⣿⢋⡿⢻⡿⣯⠻⣿⣏⠁⠀⠀⠋⠉⢉⣽⣿⣶⣾⣿⣍⠉⠙⠃⠐⢛⡽⣿⣿⣿⣷⣾⣿⣯⣟⢿⠛⠂
⠀⠀⠀⠀⠀⠃⠈⣡⣾⣧⡉⠀⠛⠀⠀⠀⠀⠀⠠⢾⣿⡿⠁⠿⣿⣿⠦⠀⠀⠀⠀⠳⠘⣾⣿⣿⣿⣿⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠋⠙⠀⠀⠀⠀⠀⠀⠛⢻⠈⠷⠽⠁⡿⠙⠂



⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠲⣶⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣷⠞
⠀⠀⠀⠀⠀⢽⣿⣷⣀⣶⣿⣿⠀⠀⠀⠀⠀⣰⡀⣾⠛⠷⣿⠾⠛⣿⠀⣦⠀⠀⢠⣿⡤⣿⣇⣸⣇⣻⠿⠂⣿⣤
⠀⠀⠀⢀⢠⣹⣿⣿⣿⣿⣿⣏⣡⢀⠀⠀⠐⢋⣿⣿⣴⡿⠟⠿⣦⣿⣿⡛⠣⠰⠞⡛⠛⣶⣿⠟⠛⢿⣶⠞⣛⠳⠆
⠀⠰⠿⢾⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠾⠆⠰⣿⣍⠰⣿⠀⠿⠇⣽⠇⣉⣿⠆⠀⠐⣿⠗⣿⣧⠀⠀⢸⣿⠛⠿⠃
⠀⠀⠀⠀⠘⣩⢿⣿⣿⣿⣿⣏⡙⠀⠀⠀⠠⣤⡽⣿⠻⡷⣶⢾⠟⣿⣿⣥⡆⠈⢻⣷⡞⠙⣿⢿⣿⢿⣋⠻⣶⣟⠃
⠀⠀⠀⠀⠀⣺⣿⡿⠋⠿⣿⣿⠀⠀⠀⠀⠀⠙⠂⢿⣦⡶⣿⠷⣦⣿⠀⠋⠀⠀⠀⠿⠀⠻⠿⣸⣇⠸⠻⠁⠿
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⡏⠓


⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢰⠀⣤⢸⣶⣆⠀⠀⠀⠀⠀⠀⢀⡤⢄⢰⡆⡠⢤⡀
⠀⠀⣶⣷⣦⣰⡶⠟⠻⠶⣦⣰⣾⣷⡆⠀⠀⠰⣽⣻⣼⣿⣿⣽⣫⡵⠀⠀⠀⠀⠀⣤⣹⡆⠙⣻⣟⠋⢰⣅⣄
⠀⠀⠉⠛⣿⠋⣴⣿⣿⣶⡈⣿⠛⠋⠁⢠⣜⡶⣿⣿⡿⣟⡿⣿⣿⡧⢖⣢⠄⠀⢠⢬⠿⢿⣶⣾⣷⣶⡿⠿⡵⡄
⠀⠀⠀⣘⣿⡀⢿⣿⣿⣿⠇⣼⣃⡀⠀⢻⠿⣻⣿⣿⣯⡿⣯⣿⣿⣿⡻⢿⡓⠀⠱⠰⣦⣤⣿⣿⣿⢿⣤⣴⢦⠇
⠀⠀⣿⣿⣿⢷⣦⣉⣉⣡⡾⢿⣿⣷⡇⠀⠈⢁⣽⢿⣿⣿⣿⣿⢿⣅⠉⠁⠀⠀⠀⠚⢻⡏⢁⣿⣯⡈⢹⠛⠃
⠀⠀⠈⠃⠀⠈⠁⣿⣿⡏⠁⠀⠈⠃⠀⠀⠀⠨⣶⣿⢹⡏⢻⢹⣿⡮⠁⠀⠀⠀⠀⠀⠙⠦⠍⠹⠏⠫⠔⠃
⠀⠀⠀⠀⠀⠀⠐⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠈⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣉⣤⠒⠒⢲⠒⠠⢌⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠋⠐⣎⢦⠀⠘⡀⠀⣠⠜⣦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢠⠃⣼⣁⠀⡀⠈⣆⠻⠀⡦⢊⠴⠊⠀⠱⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠂⠠⢤⣄⡉⠀⡀⠀⡋⠒⠒⠀⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣁⠀⠀⣠⣞⡵⠞⣳⡌⢫⠉⠁⠀⢐⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠻⠙⢫⠋⠁⠈⠀⡇⢿⠉⢦⡱⡀⢀⠎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠉⠀⡀⠀⢀⡸⠀⢀⡱⠞⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠈⠈⣿⡉⢤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⠀⠀⠀⢀⣀⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠁⠀⠉⠉⠉⠁⠀⡀⠄⠂⠙⡗⠲⣤⣀⣀⣀⣤⠔⠚⠉⠀⠀⠀⠀⠀⠙⢆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠀⢀⠔⠈⠁⠀⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⡈⠀⠠⠂⠁⠑⢄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⣇⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡔⢃⠀⠀⣀⣀⣀⣀⠀⢦⠀⠀⠀⠀⢸⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠇⠀⠀⠀⠈⢠⡡⣀⠤⠒⠉⠀⡀⠀⠀⡏⠉⠉⠉⠀⠀⢱⠀⠀⠀⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⢀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⡠⠉⠀⠉⠓⠴⢦⡂⠀⠀⠀⠀⠀⡕⠸⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⡄⠀⠀⠀⠀⡰⠁⠀⢠⠧⢄⡀⠀⢩⠁⠒⠒⠂⠐⠈⠁⠀⠀⡶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣁⠀⠰⠃⠀⠀⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡀⠀⠀⠀⠈⠢⢀⡀⠀⢀⠄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣄⠙⠶⢤⣀⣀⣀⣀⡀⢀⣀⣀⡠⠴⠚⠋⣠⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠙⠲⠤⣤⣀⣀⣈⣉⣀⣀⣤⠤⠖⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠊⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⡀⢠⠄⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠈⡀⠀⠀⢀⡀⢹⢦⣘⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠄⠄⠀⠀⡁⠤⠘⣁⠠⠐⠂⢢⣁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠀⠰⠤⠐⠞⢀⣀⡀⠀⠀⠠⠉⠱⠒
⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠶⠵⢆⡠⠀⠠⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⡠⠐⠀⠀⠀⠀⠒⢄⠀⠀⠀⠐⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠴⠀⠔⢄⡀⠀⡠⢁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡀⠘⠀⢰⡆⠀⠰⡦⢠⠁⢘⠅⠕⣨⣀⠀⢀⡄⠀⡇
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⡀⠀⢨⠀⠂⠀⣤⠀⠀⣀⠁⠁⠀⢀⡔⠁⠈⠑⢀
⠀⠀⠀⣠⠀⠀⠪⡜⠒⠒⡄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠤⠈⠃⠀⡄⡠⢚⠀⠀⠀⡀⣶⢓
⠀⠀⠀⠁⠀⠀⠁⠉⣉⣩⢇⡀⠀⠀⠀⠀⠀⡀⠆⠤⠌⢠⠄⠊⢰⠀⢐⠦⢈⠀⠈⠃
⠀⠀⠀⠀⠀⠄⡀⠤⢤⣤⠺⠂⠀⠀⠀⠀⡀⡘⠉⠁⠐⠉⢄⣧⢀⠓⠂⠉⠁⠒⢘⠀⠀⡄⡀⡌
⠀⠀⠠⡏⠈⠁⢀⠀⠮⠘⠈⢀⠀⠀⠀⠀⠳⡃⠠⠬⠉⠐⠀⢙⠃⠀⠨⠀⣍⡍⢩⠑⠉⠉⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⣴⠊⠁⠀⠀⠀⠀⠑⡒⢒⠒⠊⠀⢠⠀⠀⠀⠐⠈⣣⣼
⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⣃⢇⠀⠀⠢⢀⠀⠀⠀⠉⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⣤⣤⠄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠮⡥⠉⢡⡽⠷⡜⠁⣤⢾⣷⡈⠟⡃⣸⡷⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⢈⣧⣶⢶⡰⣟⣽⢳⣧⢻⣿⢯⣶⣷⣾⡽⣿⡿⠈⠽⠛⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣏⣏⡬⢿⣿⠛⠓⠈⠀⠀⢀⣀⣠⣤⣀⣉⡉⠁⠻⣿⣃⣴⣿⣼⠏⢤⡀
⠀⠀⠀⠀⠀⠀⣼⣃⡏⢰⣿⣶⠊⠁⠀⢀⣤⢞⡟⢋⣹⠯⣌⣿⣷⣿⣂⣦⠀⠐⡍⢻⣟⠁⢃⠷⡀
⠀⠀⠀⠀⠀⢸⡩⢮⡕⠆⣻⠁⠀⣠⡾⡹⢿⣭⡽⣶⣿⣿⡶⠟⡛⠈⠀⠁⠀⠀⠐⠀⠘⣿⣯⠚⡧
⠀⠀⠀⠀⠀⢺⣶⢄⡟⢈⣿⠀⠀⣿⣟⣷⢭⣍⡁⠻⣿⣿⣷⣋⢽⣀⡀⠀⢀⡔⠀⠈⠀⢸⡷⢾⡶
⠀⠀⠀⠀⠀⢨⡹⠾⣷⡈⠿⣦⡴⣿⡋⠀⠠⣄⠴⠷⣌⠳⣤⡘⢦⣈⠙⠓⠋⠀⠀⠃⠀⠐⡷⢶⡁
⠀⠀⠀⠀⠀⠀⢻⡄⠾⣛⠛⣫⣽⡏⠂⢀⣲⡃⠀⠀⠀⠙⠚⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⣼⡯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠨⢙⠘⠛⠛⠊⠁⠀⣤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣸⡷⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠆⠐⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡞⣩⣹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣻⢯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⠆⠳⣿⣵⡸⠏⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣤⣴⣴⢶⣾⣾⠉⢿⣿⣣⣾⣾⣿⣿⣿⣿⣿⡶⢦⢤⣀⡀
⠀⠀⠀⠀⠈⠀⠀⢠⡤⣦⢦⣼⠿⢛⡻⠟⣷⣀⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣟⡷⢼⠯⠇⢀⣦⣄
⠀⠀⠈⢀⣤⣶⠿⠿⠳⣷⣿⠝⠓⠉⠉⢁⡴⢻⡟⣿⣿⡿⠟⠋⠉⡁⠀⠠⠠⠠⠠⠡⠉⠛⠷⣤⣶⢿⣮⣛⣉⣡⡄
⠀⢀⠶⣿⠯⣍⢿⣿⠟⠉⠀⠀⠀⠀⢠⣯⣷⣮⣛⡿⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⡃⠛⠋⢩⣿⡆
⠀⣼⠲⠞⠧⠙⣼⡏⠀⠀⠀⠀⠀⠀⣾⡌⢻⣿⣿⣇⡀⠀⠀⢀⣀⣠⣤⡔⢲⣖⣶⣶⣶⡄⣀⠀⠀⠈⡿⣿⣿⡷⣿⢛
⠀⣿⠛⡿⢷⡞⢿⠃⠀⠀⠀⠀⠀⠀⢺⣵⡆⢥⡄⣿⣷⠶⢋⡽⠛⢛⣯⠒⣩⡭⣬⠉⣷⠀⣾⣗⣄⠀⣷⣮⣁⠸⢿⡞
⠀⢹⣺⢳⣿⢏⡐⣜⡦⠀⠀⠀⠀⠀⠈⢷⣶⣗⣲⢿⡶⢃⣴⣲⣮⣅⣀⡼⠿⠿⠯⢿⣯⠈⢀⣡⣥⣿⣭⣻⣭⣧⡍⣠
⠀⠈⢿⣿⣥⢾⣿⢩⢮⢀⣷⣄⡀⠀⠀⠀⠉⠻⠿⢮⢡⣼⠽⠿⠛⠉⠁⠀⠀⠀⠀⢀⣨⣿⢮⡽⢿⣿⣆⣫⣭⠟⢠⠇
⠀⠀⠀⠻⣿⢛⣏⡘⢫⡠⣽⡶⢶⣝⠒⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣯⠿⣉⡧⠔⠘⣇⢻⡟⠋⣰⠃
⠀⠀⠀⠀⠈⠙⡯⣿⣌⣱⣮⠿⣑⡛⢈⡳⢠⣾⢻⣿⠱⡴⢇⣾⣉⣻⣻⣿⣿⣿⣿⣿⣷⣯⣼⢀⡜⣿⣶⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠍⡙⠓⠾⢿⣿⣌⣡⣿⡴⢟⣙⡃⢀⣾⣟⣻⣿⣓⡿⣿⣿⣿⣿⠿⠞⢹⠌⢻⡾⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⢀⡉⠉⠁⠙⠛⠻⠿⠛⠿⠟⠟⠇⠃⠛⠉⢉⡀⠄⠒⡧⢀⣼⡃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠀⠈⠈⠀⠀⠀⢜⡑⢿⢐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠃⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⢦⣤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⠶⣆⣰⣯⡿⠟⢻⣽⣿⣦⣅⠀⢀⡠⢲⣭⣵⣟⣻⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⢿⣁⣀⣀⣀⣀⣩⣥⡿⣸⡆⢣⣵⣟⣻⣾⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣻⣖⣎⣝⢣⠮⣝⣿⣿⡆⡾⣷⡸⣃⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⣉⡛⣩⣟⡿⠛⠉⣿⣿⢚⡷⠟⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⣀⣼⣫⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⠀⣿⣷⣦⢠⣶⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⣰⡄⠛⢿⡿⠛⢠⡄⢀⡀⠀⠀⠀⠀⡀⢠⡀⠀⠻⣿⠟⠀⢀⡄⢀
⠀⠀⠀⠀⠀⣀⠿⠋⣭⢈⣽⠻⢟⡀⠀⠀⠀⠀⠀⢈⣻⣿⣧⣴⢻⡟⣦⣼⣿⣟⠁⠀⠀⠀⠀⣙⣿⣷⣄⣤⣿⣤⣀⣾⣷⣏
⠀⠀⠀⢴⣿⣿⡣⣶⠽⣾⢵⡦⢻⣿⣷⡆⠀⠀⠀⢈⣉⠀⣯⣹⣿⣿⣏⣿⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠛⣣⡀⠿⠘⢷⣠⡟⠛⠁⠀⠀⠀⠀⢀⣽⣿⡟⢯⣼⣧⠽⢻⣿⣯⡀⠀⠀⠀⠀⣛⣿⣿⠛⠻⣿⠟⠛⢿⣿⣛
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⣴⣾⣷⣦⠘⠃⠈⠀⠀⠀⠀⠀⠉⠘⠃⠀⣰⣿⣦⠀⠘⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⣠
⠀⠀⠀⠀⠀⣠⡤⣄⢰⣯⣿⠀⣤⢦⡀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣿⣿⣯⣷⣴⣄⠀⠀⠀⠀⠀⠀⢀⠀⠈⣷⡄⢻⡏⢠⣾⠃⢀
⠀⠀⠀⠀⠀⠙⢷⣻⢾⡏⣿⠯⣷⠟⠁⠀⠀⠀⠀⠀⠀⣯⣽⣵⡏⠺⠗⢹⢸⠷⣷⠀⠀⠀⠀⠠⣬⣷⣀⡘⠿⣼⡇⡿⢃⣴⣯⡤
⠀⠀⠀⠀⣶⣳⣿⢿⡋⠀⠀⢹⣻⣻⣳⣗⠀⠀⠀⠀⣿⣿⡳⡄⠀⠀⠀⠈⢁⢿⣿⣷⠀⠀⠀⣤⣤⣠⣍⠛⢶⣿⡷⠞⣋⣅⣀⣀
⠀⠀⠀⠀⠉⠉⣹⡿⣷⡤⢴⣫⢿⣋⠉⠁⠀⠀⠀⠀⢿⣿⠟⡁⡀⠀⠀⢀⣈⣻⣿⡿⠀⠀⠀⠁⠉⣉⣩⠶⠛⣿⠛⠶⣌⡋⠙⠙
⠀⠀⠀⠀⠀⠸⣳⡟⢛⡯⣿⠋⢷⣫⠇⠀⠀⠀⠀⠀⠘⢿⣻⡇⣧⢾⡦⣼⡨⣭⡽⠀⠀⠀⠀⠈⢹⠏⣠⡿⠃⣹⠘⢷⡈⠹⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡿⡿⠿⠓⠛⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡿⣇⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣇⠀⣻⡟⠀⠀⣀⡀⠀⠀⠀⠀⠀⡄⠀⣤⣄⣙⣋⣠⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠨⣷⡄⣺⣗⢀⣾⡇
⠀⠀⠀⢠⣶⣄⡴⠛⢿⠉⡟⢛⣦⠾⠿⠃⠀⠀⠀⠀⣠⣧⣸⣿⠛⢿⡿⠛⣿⣇⣼⣄⠀⠀⠀⠀⠸⢿⣶⣿⣿⣿⣿⣿⣿⣴⣿⠏
⠀⠀⠀⠀⠉⣿⠓⠒⣾⣿⣷⣉⡘⣧⠀⠀⠀⠀⠀⠈⣁⣴⡿⠿⣷⠞⠛⣾⠿⢿⣦⣀⠉⠀⠀⠲⣶⣶⣿⣟⠏⠀⠉⠙⣿⣿⣧⣶⠶
⠀⠀⠀⢀⣀⣹⣆⠋⢩⠛⣆⠈⣹⠿⣶⡆⠀⠀⠀⢀⡉⠻⣿⣶⡿⢦⣤⢿⣶⣾⠟⢉⣀⠀⠀⣠⣤⣿⣿⣿⡀⠀⠀⠀⣾⣿⣿⣤⣀
⠀⠀⠀⠸⠿⠇⠙⢦⣶⣤⣼⣴⠋⠀⠈⠁⠀⠀⠀⠀⠙⡟⢹⣿⣤⣾⣿⣤⣿⡏⢻⠋⠀⠀⠀⠉⢉⣼⣿⣿⣷⣴⣦⣾⣿⣿⣏⡉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠋⣨⣅⠉⠛⠁⠘⠀⠀⠀⠀⠀⠚⠛⢠⣿⠟⢿⡿⢻⣿⡈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠹⠏⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⠁⢀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⣫⡆⢐⢮⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠺⠂⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣤⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⣀⣤⣠⡋⠈⢩⣤⣶⣦⠄⠀⠀⠀⠀⠀⠐⠛⠢⣤⡤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠚⢈⡶⠭⢶⣁⠉⠀⠀⠀⠀⠀⠀⠀⣔⡶⠊⠉⠈⠐⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣠⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠂⠙⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣠⢀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠁⡀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣖⡴⠈⠪⠞⢱⢰⣲⠂
⠀⠀⠀⠀⠀⠀⠐⠷⡵⠄⡦⢱⡎⣥⢀⡴⣠⡀⠀⠀⠀⠀⠀⠀⠬⣖⣭⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⣓⠊⢑⡊⢰⠉⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠻⡂⠀⠘⠈⠀⠀⠀⠀⠀⡀⠶⠀⠔⠙⠂⠀⠶⠀⠀⠀⠀⠀⠀⣠⣖⢭⠃⣨⡁⢹⣱⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠠⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⡰⠲⠔⢦⢸⣷⠂⠀⠀⠀⠀⠀⠛⣨⣄⠀⠭⢀⣸⡀⠓⠀⠀⠀⠀⠀⠘⣂⣅⡀⠸⠇⣀⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣁⠀⠀⣁⡶⠈⠁⠀⠀⠀⠀⠀⢈⡀⢈⡹⣿⢎⠀⣀⡁⠀⠀⠀⠀⠀⠀⡀⢈⣉⠾⠦⣉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠳⢞⠦⠆⢰⠯⡄⠀⠀⠀⠀⠀⡤⢘⠇⢀⣖⠀⢸⠑⡴⠀⠀⠀⠀⠀⠠⠌⠋⠁⢸⡆⠉⠏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⠛⢛⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣬⣉⠙⢀⡄⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡧⠥⡬⠀⠥⠬⠼⢿⣄⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⠊⠀⠰⠀⠀⠀⠈⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢰⠞⠉⠉⠉⢳⡀⠀⠀⢀⡞⣁⣀⣀⡠⠤⠤⠖⠒⠀⠒⠢⠐⠄⠳⢤⣙⣧
⠀⡴⠖⠛⠂⠀⠀⠀⣸⡃⠀⣴⠛⠏⠠⠀⠀⡆⠀⠈⠀⠀⢘⠀⢰⠀⢠⠀⠘⡀⠉⣧
⢸⡇⠀⠀⠀⠈⢢⠀⠈⢿⡀⡏⢠⠀⢈⠀⠀⠁⠀⠀⠂⠀⠈⠀⠀⡄⠀⠀⠀⡇⠘⣸
⠀⣿⠂⠀⠀⡀⠈⠀⠀⣸⡿⠛⠀⢤⣚⣩⣭⣩⣒⡉⠉⠀⠴⠖⠒⢆⣀⡐⣖⣳⠂⠉⢳⡄
⢀⣸⡇⠀⠀⠁⠀⣤⠞⢹⠃⠀⠀⢰⠀⢀⠊⣴⡿⢷⠀⠀⠀⡴⢷⣦⠑⡄⠈⡇⠀⠀⠈⣷
⡟⠀⠀⠀⣆⠀⠀⡹⠶⠛⠠⡀⢀⡸⢠⣬⣄⣛⣿⠞⣠⣤⣄⢻⣿⠟⡠⣁⢀⡃⠀⠀⠀⣿
⠻⢤⣠⣤⠁⣀⢀⣠⡶⠓⠲⣦⣠⣾⣻⠟⠟⠩⢋⠕⠛⣏⠙⢌⠫⠑⠟⢿⢙⣷⣤⡤⠞⠁
⠀⠀⠀⠈⠉⠉⠉⠁⢀⣴⠞⠋⠉⠙⡇⠀⠀⠀⠀⠀⠚⡍⠂⠀⠀⠀⠀⠀⡋⠉⠉⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠤⠔⠊⠘⠀⠀⠀⠀⠀⠀⠜⠙⢆⠀⠀⠀⠀⠀⡈⠉⠑⠤⢤⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣀⣀⡀⢳⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⣈⣢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡸⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠄⠊⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢸⠒⠂⢲⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠤⢽⡇⠀⠐⠒⠀⠤⢼⠀⠀⠀⠀⠀⠀⡸⠄⠒⠊⣿⣤⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠁⠀⠐⠒⠂⢎⣰⣣⣆⣴⣰⣠⠗⠒⠈⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⡽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣛⣦⣤⣀⣀⣀⣤⣐⣿⣾⣓⣠⣄⣀⣀⣠⣴⣞⣯⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠉⠀⠀⠀⠈⠀⣼⣿⡀⠈⠀⠀⠀⠈⠉⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⢷⡳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⢶⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⣀⣀⣼⠃⠀⣄⠠⠤⢶⢀⡉⠀⠀⢀⣦⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢿⣿⠀⢰⣿⠀⠀⠀⠋⠈⠁⠈⡤⠟⢻⣿⡇⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡀⡙⣄⢼⣏⡀⠀⠀⠠⠑⢲⡁⠠⠾⠾⢿⡇⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠸⡇⠀⠘⣿⣦⣤⡀⠀⠨⠦⠀⠄⠀⠀⠉⠙⠁⠉⡏⣶⠂⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣭⣇⠀⢷⡀⠀⠘⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣤⣄⠀⠀⠀⢀⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⢸⣿⣤⣀⠹⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢀⣠⡾⠟⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠄⠀⠈⠛⠷⣝⣟⠻⣷⣟⣷⣤⡀⠀⠂⠁⠀⠀⢀⣠⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠈⠛⠿⣿⣿⣏⣉⠀⠀⠀⢀⣠⣴⣿⣿⠋⠀⢀⣤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠑⢦⣀⡀⠈⠛⢿⣿⣷⣤⣀⣀⣀⣴⡿⢁⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠁⣽⣦⣤⣤⠛⣩⣿⡿⠿⠿⠛⠂⠉⡉⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠙⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣦⣀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠁⠄⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣾⣿⢿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⣠⣄⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣷⣶⣿⣦⡀⠈⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢰⣶⣾⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣸⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠀⠀⢴⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠛⠁⠀⠀⠀⠀⠉⠉⠉⠙⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⡉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣿⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣿⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠙⢧⡘⣿⢋⣤⠄⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⢻⡄⢀⡄⠀⠀⠀⠀⣈⠻⣿⠛⡁⠀⠀⠀⠀⢀⡄⢀⡾⠁⢀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣻⣾⣷⣘⣧⢀⡄⠀⣀⡙⢷⣿⠞⢉⠀⠀⡀⠀⣾⢁⣾⣥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣡⣤⣼⠿⠿⣤⣷⠘⠿⣇⢸⡇⢀⡿⠇⢰⣏⣼⣿⣟⠛⠳⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⠙⠳⣦⣹⣾⣧⣟⣠⡴⠟⠻⢧⡌⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠒⢲⣿⣿⣿⣿⠷⠶⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡘⢳⣦⣴⠞⢋⡽⢻⡟⣟⠻⢦⣤⣤⡴⠄
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢦⣤⣽⣿⡟⣹⠇⢰⣾⠁⢸⡇⢸⣶⡄⢿⠛⣶⣶⡟⠛⣋⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⡿⢁⡿⠀⠈⠀⠀⣁⡴⣿⢷⣄⠉⠀⠘⠁⢻⡍⢿⡿⣯⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠟⠉⠁⢀⡾⠁⠘⠁⠀⠀⠀⠀⢈⣤⣿⣦⡉⠀⠀⠀⠀⠘⠁⠘⣧⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠐⠋⣡⣿⡌⢻⣄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⣿⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠙⠶⢶⣄⣀⠀⠀⠀⠀⣀⡶⠛⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠉⠙⠷⠲⢦⡼⢧⡀⠦⢄⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡀⠀⠀⠀⠔⠲⡤⢄⢀⠀⠀⢀⣈⢥⠀⢈⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠀⠀⢀⠉⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⠒⠃⠀⠀⢠⠀⠀⠀⠀⢀⣄⣼⠃⠰⠚⠁⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⣀⡴⢿⣰⠀⢀⣘⣿⣄⣠⣄⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣴⠗⠚⡅⠐⠂⢹⡆⣸⠋⠁⠀⠀⣬⡟⠉⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠀⠀⠀⠓⠋⠀⠀⢠⠄⠀⠀⠀⢻⣧⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⠀⠀⠀⠀⠫⠇⠀⠀⠀⠀⠀⠀⡀⢺⡧⠤⢤⡈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣸⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡆⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⣿⡗⠒⠚⢁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠒⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡦⣿⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣑⣑⣚⣘⣃⣄⣤⣤⣤⠤⠤⠬⠶⠮⢕⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢠⡞⠁⠐⠂⠬⢍⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣋⠭⠄⠂⠈⠙⣦
⠀⠀⠀⢸⡖⠚⢋⣉⣓⡒⠦⢝⡮⠷⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠴⠭⣞⠥⠖⣚⣋⣙⠛⠒⣿
⠀⠀⠀⠈⢷⡉⣉⠀⠨⢭⣍⣻⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣼⣋⣭⠍⠀⣈⡉⣸⠇
⠀⠀⠀⠀⠘⢧⡠⠤⠖⠒⠒⠒⠛⠦⣄⠀⠀⠙⢦⠀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠞⠒⠒⠒⠒⠦⠄⣰⠏
⠀⠀⠀⠀⠀⠈⢷⣐⠊⠉⢉⣉⣉⡙⠛⠛⠒⠦⣄⡳⣐⣢⡴⣁⡤⠖⠛⠛⠛⣉⣉⣉⠉⠉⢒⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠧⣤⣤⠬⣭⣭⣭⠯⠭⢽⣏⢘⣿⠭⠭⣯⣭⣭⡭⢤⣤⡬⠿⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣁⠤⠄⠐⣶⠤⠒⠊⡝⣿⢾⡿⡑⠒⠤⢴⡒⠀⠤⢄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⣉⠤⠒⢈⡏⠀⠀⣠⢾⢀⡏⡘⡇⠹⢆⡀⠀⠙⣏⠐⠢⢌⠓⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠤⠂⡩⠳⡴⢺⠁⠀⣸⢀⢃⢹⠸⠀⢻⠲⡴⠫⡁⠢⣄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⢠⠊⠀⡜⠀⠇⠀⢰⠇⠈⠃⠈⣿⠀⠈⡄⠑⡀⠈⢦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣇⠀⡘⠀⠀⡆⢀⡞⠀⠀⠀⠀⠸⣆⠀⠇⠀⢸⠀⢈⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠶⠚⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢱⡆⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⠀⣾⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⠈⣿⡇⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠦⣄⣿⣷⠀⣿⠤⠃⠀⠀⠀⠀⡞⠓⡄⠀⠀⠀⠈⡷⠞⣀⣠⣤⠾⠓⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⠃⠀⠀⠀⠀⠀⠀⢸⡞⠁⠀⢀⣤⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣠⣴⣾⡿⢿⡋⣉⣀
⣞⣻⣦⣤⣤⣤⣄⣀⣀⠙⠳⡀⠀⠀⠱⣤⣇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣠⣾⡿⠿⠋⠁⠀⠀⠀⠻⠼⠂
⠈⠉⠀⠀⠉⠙⡛⢻⣿⣿⣿⣿⣶⣶⣶⣦⣬⣷⣄⣀⣀⠀⠀⢀⡿⣤⣀⣀⡴⠿⠋⠙⠒⠲⠟⣛⡆
⠀⠀⠀⠀⠀⢨⣩⠏⠀⠀⠀⠀⠀⠉⣹⠛⠛⠛⠛⠉⠉⠙⢲⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⢠⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢤⣾⡏⠀⠀⠀⠀⠀⠀⣟⢿⣷⣶⠒⠛⠳⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠿⢁⣾⣿⠁⠀⠀⠀⠀⠀⠀⡽⣄⠙⠿⣳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠙⣆⠀⠀⠀⠀⠀⠸⣦⠟⠀⠀⢹⢿⣿⣦⣀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⢠⣾⡿⠁⠀⡼⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠙⢿⣿⡙⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣾⣿⠃⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠟⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠐⢇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣧⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⢄⢸⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠤⣯⡙⣇⡟⣩⡧⠄⠀⠀⠀⠀⠀⢀⠛⠺⡀⡵⠚⣃⠀⠀⠀⠀⠀⠀⢢⣇⡀⠍⢀⣸⡔⠀⠀⠀⠀⠀⠀⣖⢲⠘⡞⣰⠒⠆
⠀⠀⠀⠀⠐⢛⣭⠜⡿⡿⢥⣝⠓⠀⠀⠀⠀⠐⢫⠝⢒⡿⡖⠚⢽⠒⠀⠀⠀⠀⠀⢅⣀⠼⠿⠥⣀⡤⠀⠀⠀⠀⠀⠀⡨⢡⠝⡟⢥⠭⡀
⠀⠀⠀⠀⠀⢡⠾⡺⢇⠿⡺⢦⠁⠀⠀⠀⠀⠀⠀⢲⣽⡀⣼⡴⠂⠀⠀⠀⠀⠀⠀⠈⠇⣠⣦⡀⠸⠁⠀⠀⠀⠀⠀⠀⠉⠊⢰⣹⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⢯⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡯⠄
⠀⠀⠀⠀⠀⣾⢼⣄⠽⢅⣼⣴⠆⠀⠀⠀⠀⠀⠑⠛⠮⣭⡵⡞⠚⠀⠀⠀⠀⠀⠀⣤⣉⡗⠛⢾⣉⣄⠀⠀⠀⠀⠀⠘⣺⠧⡴⠳⡤⢶⡚
⠀⠀⠀⠀⠀⠀⠡⣼⠆⢮⡠⠁⠀⠀⠀⠀⠀⠀⣔⡶⠫⣽⠝⢳⣲⠀⠀⠀⠀⠀⠀⠉⣠⠗⣶⠻⣤⠁⠀⠀⠀⠀⠀⠀⠀⣀⡗⠒⣅⡀
⠀⠀⠀⠀⠀⠀⠹⠏⠃⠋⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠎⠃⠀⠋⠗


⠀⠀⠀⠀⠀⠀⠀⠠⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣗
⠀⠀⠀⠀⠀⣴⡀⢢⣸⣤⠂⣰⡄⠀⠀⠀⠀⠀⢚⡾⣀⣹⢀⡴⡞⠀⠀⠀⠀⠀⠀⠯⢧⡤⣓⢤⠼⠽⠀⠀⠀⠀⠀⠘⢳⢦⡔⡗⣤⢶⠓
⠀⠀⠀⠀⠀⠉⡨⢿⣁⣸⠯⠌⠁⠀⠀⠀⠀⠀⠠⣤⠜⢿⠣⣤⡄⠀⠀⠀⠀⠀⠀⡤⡤⢎⣚⡼⣤⢄⠀⠀⠀⠀⠀⢀⣠⡼⣞⣟⠾⣤⡀
⠀⠀⠀⠀⠀⠀⣤⡎⢹⠉⣶⡄⠀⠀⠀⠀⠀⠀⠉⠘⠠⢾⠦⠈⠘⠁⠀⠀⠀⠀⠀⠑⠁⢠⢷⠄⠈⠊⠀⠀⠀⠀⠀⠈⠉⠁⢐⣗⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠶⣴⣀⡹⣁⣰⡴⠆⠀⠀⠀⠀⢀⡴⣠⡐⣿⠕⣄⡰⡀⠀⠀⠀⠀⢀⣄⠐⣄⣉⡠⠀⣀⡀⠀⠀⠀⠀⠀⠰⠧⡈⡏⡰⠷
⠀⠀⠀⠀⠀⠈⣀⣗⡀⣐⣇⡈⠀⠀⠀⠀⠀⠘⠛⠝⢓⡾⣚⠫⠗⠃⠀⠀⠀⠀⠈⢉⣑⣎⢉⡷⣉⠙⠀⠀⠀⠀⠀⠀⠷⠒⣿⣩⡗⠲⠇
⠀⠀⠀⠀⠐⠿⠻⢀⣽⣅⠘⠛⠗⠀⠀⠀⠀⠀⢠⡽⡟⠁⢟⠟⡤⠀⠀⠀⠀⠀⠀⠀⣤⠊⡍⠱⣄⠀⠀⠀⠀⠀⠀⠀⠐⠞⢀⣇⠸⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⠀⠆⠀⣤⡊⢀⠀⢻⠀⠀⠐⠠⠊⠁⠀⠒⠒⠲⠤⠤⣀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠄
⣡⢈⣹⣿⡑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢠⡀⠀⠀⠀⠀⢀⣴⠚⠁
⢥⠘⣩⣋⣋⡷⢶⠶⠊⠀⢠⠀⠀⠀⠀⠀⣠⣰⡭⠖⢋⠴⠃⠀⠀⠀⠀⠈⠱⠀⢀⠤⡘⠋
⠀⢘⣻⣿⣿⠿⢁⠔⠤⠂⠀⠀⢀⠠⠴⢀⡤⢯⠄⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄
⢞⣞⢹⣿⣿⣫⠕⠦⠄⠀⠀⠀⠈⠀⠀⠀⠀⠙⣸⢷⠂⠀⠤⠌⠤⠀⠀⠀⠀⠀⠀⢀⠹⡍⠿⠛⠋⠀⠉⠂
⠲⣴⣯⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⣯⡛⠿⢧⣄⠀⠣⢀⡀
⠸⠛⠉⠁⠀⠀⠀⠀⡀⠈⣛⡁⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡾⢆⠧⠽⣥⠀⠈⠁⡠⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣖⠀⠁⠀⠰⣆⠀⠀⠀⠀⠀⢐⡘⠂⠒⣙⣷⠀⣠⣤⣶⠖⠉
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠐⠀⠀⠀⠑⣶⠟⡅⠆⠀⠀⠀⢨⠄⠀⢼⠀⠀⠀⠀⠀⠀⠀⠚⢹⣦⡀⠈⠣⠴⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠴⠉⠀⠀⠀⠀⡿⠀⠀⠐⠠⠁⣤⡀⠀⠀⠀⠃⢸⡷⠁⠁⠀⠠⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣬⠯⡶⣰⠀⠀⠚⠁⠀⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡾⣫⡾⢙⣥⢰⠀⠀⠀⢀⠀⠠⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠩⢭⠄⡟⢡⣿⠀⢂⡀⠉⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠍⠓⠀⡸⢁⣿⡏⣐⣿⡶⠀⠀⠈⠱⢦⠀⠦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⠏⣠⡽⡶⠯⠥⠀⢰⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠈⠉⠀⢀⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⡠⣏⣛⡨⠈⠀⠀⠀⠀⢀⡄⠈⢣⠂⢁
⠀⠀⠀⠀⠀⠒⠶⠀⠉⠁⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠰⠃⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡆⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢰⠄⢀⣴⡞⠋⠁⠀⠙⠀⠀⠐⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠐⠠⠄⠀⠀⠀⠀⣠⣤⣀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠩⠤⠰⢒⣲⣲⣟⣉⣡⣆⣖⣶⡶⡤⢄⣉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⣿⡷⠴⠛⠻⠿⠿⢿⢟⢻⢛⡛⠛⠃⢠⣤⣾⠃⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠃⠂⠈⠑⢾⣿⢿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣶⡤⠊⠀⡠⣿⡟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠁⠕⠶⣤⣀⡀⠙⠻⣿⣿⣿⣹⣿⣿⣿⣿⠿⠋⠀⣀⣬⣤⢟⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⡿⣿⣶⣤⣀⡉⠛⢷⣆⡈⠛⢿⣿⣽⡿⠛⢡⠴⠶⠛⢉⣩⣴⠞⠋⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⣴⣬⡿⠀⠀⠉⠛⠛⠿⢷⣬⣥⡶⢤⣽⢫⣴⢶⣀⣤⡴⠶⠛⠉⠀⠀⠈⠁⠈⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣞⣱⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠊⠋⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠠⠟⠻⢏⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢎⢽⡄
⠀⠀⠀⠀⠀⠀⣗⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠻⡀
⠀⠀⠀⠀⠀⢸⣶⠁⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡰⠀⠀⠈⠥⠀⣧
⠀⠀⠀⠀⠀⣿⠘⠄⠄⠈⠳⢘⠲⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⠋⢻⡤⠂⠐⠠⢰⣽
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠐⢮⢀⣦⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⠞⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⡿⠃⠁⠀⠀⠀⠀⣴⣆⣿⡜⠇⢠⡐⡠⣠⠀⠘⢁⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢻⣾⡿⠄⡖⡶⠆⠀⠀⠐⣿
⠀⠀⠀⠀⠀⣯⡆⠀⠀⠀⠀⠚⠟⢻⡿⣟⣿⣒⣛⣛⣈⣀⢀⠏⢐⢄⡟⠁⡽⠋⠉⠱⣖⠶⠺⡗⡻⢿⡇⡇⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢇⡗⠀⠐⠠⠶⢻⣿⡝⠫⠍⠀⢹⠟⠛⠇⡮⠀⠴⠮⠒⠀⠀⠀⠀⠈⠁⠀⠀⠫⠞⢹⡗⠦⠄⠀⠀⠀⠀⢰⡾
⠀⠀⠀⠀⠀⢸⠜⠉⠀⠀⠀⠀⠸⠋⠙⠀⠁⠀⠀⠀⠀⠀⢳⣦⣾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣥⣽⢿⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢺
⠀⠀⠀⠀⠀⠀⢻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡑⢀⡻⣿⠛⣛⠩⣶⢤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠆
⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⡄⡀⠀⠀⡀⠄⠀⢨⡴⣟⣫⣻⡿⡖⠱⠘⠈⠁⠹⠃⢽⡠⣢⣠⣔⠀⢀⡀⠀⠀⠀⠀⣧⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣀⡲⡶⣿⡳⠛⠟⡿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢧⡙⣲⠤⢆⣠⣤⣶⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢩⠏⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠉⠉⢡⢁⣞⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠋⠄⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠈⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠈⠀⠚⠛⠛⠒⠒⠒⠠⠒⠚⠟⠉⠉⠛⠊⠉⠁⠀⠀⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠶⠄⠄⠖⢦⠐⢶⡶⠶⣶⣠⢶⣶⣶⡶⠲⠹⠟⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⡰⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⠒⠋⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠬⠳⡀
⠀⠀⠀⠀⡼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⣠⡇⠀⠲⣄⠀⠀⣠⡟⣡⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣇⢠⣀⠀⣀⣹⢦⡀⠻⣄⣴⠟⡇⠀⠀⠹⡳⡜⡝⡴⢹⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣿⢀⣙⠻⡦⣹⣾⣌⡦⠾⠴⠴⠣⠶⣦⣄⣸⢠⡷⢁⠟⣿⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢹⡀⠉⢳⣝⣜⢿⠏⠀⠀⠀⠠⠊⠀⠈⢷⡇⢸⡇⡜⢸⣿⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⢱⠛⠍⠉⢻⣾⡀⠀⠀⠀⠀⠀⠀⣀⣼⣇⣸⣷⠋⠉⠉⣹⠉⢹⡄⠀⡇⠀⢀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠉⠑⠚⠉⠉⠉⠉⠀⠀⠈⠁⠈⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⡀⡀⡀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠒⠋⠉⠉⠉⠙⠲⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠳⠚⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣐⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⡀⢀⣀⠔⠊⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⣀⣔⣁⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⢀⢀⡀⠀⣀⣤⠤⠜⣯⠑⠀⠉⠳⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢸⡀⠉⠁⠈⠀⠀⠂⢹⡧⠀⠀⠀⠀⢸⠄⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠠⢧⠀⠀⠀⠀⠀⠠⣼⠁⠀⠀⠀⠐⣼⡇⠀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡆⠀⠀⠀⠐⢀⡟⠀⠀⠀⠀⠀⢱⡃⠀⣀⣀⠤⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⢅⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⡎⠔⠊⠁⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⢻⠀⠄⠀⠩⠚⠁⠀⠀⠘⠀⠀⠀⠠⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠚⣧⠀⣠⠖⣡⠬⣆⢰⢩⣡⣈⠒⠢⠌⠋⢀⡤⠾⠶⢦⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⠘⠯⡴⠋⠀⠀⢰⠆⠀⠀⠀⠉⠑⠒⡔⠁⠀⢀⠤⠚⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣺⣆⠀⠀⠢⢀⡴⠊⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⠳⠶⠶⠒⠋⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠰⣦⠀⠀⢺⣇⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⣤⢘⣇⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣆⠀⡐⡿⠁
⠀⠀⠀⠀⠰⠾⠾⠒⡒⣇⣪⡓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣟⢆⢸⢃⣤⡼⠞⠃
⠀⠀⠀⠀⠀⠀⣐⡶⠋⢐⣇⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⣨⡭⠝⡿⡗⠤⣶⣴⡄
⠀⠀⠀⠀⠀⠐⠋⠂⠀⢐⡗⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠁⣺⡇⠈⢶⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠
⠀⠀⠀⠀⠀⠀⢬⢵⠷⣛⠀⠀⠀⠀⠀⠀⠀⠠⡄⣆⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⢠⡥⠀⣀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⡺⡿⡖⠀⠀⠀⠀⢀⠀⠀⡘⠣⣀⣀⡔⠓⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠼⠉⠉⠉⢉⡽⠯⣉⠉⠋⠉⠙
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠋⢀⡆⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣥⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠀⢨⣇⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠉⡴⢰⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡤⢀⠴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡾⠛⠉⠠⠤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠳⣤⣤⣤⡤⠴⠚⢁
⠀⠀⠀⢠⠁⠀⠈⠁⠀⠀⢀⣀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠟⠛⠀⠑⠒⠒⠒⠛⠋⠉⡠⣄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠒⠚⠉⠁⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⠶⠶⠖⠒⠒⠒⠒⠶⠤⢬⣽⠓⠦⢤⣤⣀⣀⣀⣀⣀⣤⠴⠶⠛⡏
⠀⠀⠀⢰⠀⠀⠀⠀⠈⠁⠀⣤⠀⠹⠓⠒⠶⠦⠤⠤⠤⠤⠶⠒⠚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢠⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠶⠀⠀⠀⠀⠿⠀⠀⠀⠘⠃⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠰⠆⠀⠠⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠛⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣴⣲⠭⠖⠛⠛⣛⣛⣲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⡶⢒⣛⠭⠛⣛⠳⠶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣶⣶⣖⣺⠯⠟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣾⣷⣾⣿⣿⣾⣟⣫⣤⠀⠀⠙⢛⣻⣿⣬⣙⣻⡿⢿⣿⣿⣿⠯⠭⣀⠂⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠉⡛⢙⣛⠿⣿⣿⣿⣿⣿⣯⣀⣀⡀⠀⠉⢭⣿⣿⣿⣭⣭⣝⡻⣯⡀⠀⠀⠀⠀⠻⣮⢣⡀
⠀⢠⣦⡆⠤⢰⣪⣵⣤⣶⠿⠿⢿⣿⣿⣄⠻⢿⣿⣿⣿⣿⣷⡦⠭⣀⠐⣮⣟⣻⡿⣶⣂⠀⠀⠑⠄⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠹⢿⣿⢿⣿⡿⠟⠿⣵⣿⣿⡎⣿⣿⣿⡋⢙⢻⣿⣿⣿⣿⣏⡓⠆⠸⣿⡷⢦⠁⠀⠨⣅⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧
⠀⠀⢠⠃⢰⡟⠁⠀⠀⠀⠀⠉⢸⣿⣿⡿⣼⣿⠛⢻⣿⣿⣿⣿⢿⠑⠱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣤⠀⢣⠀⢹⣿
⠀⢠⡇⢠⣼⣽⡟⠀⠀⠀⠀⠀⠀⠂⢽⣿⣿⣿⠠⣜⣿⣿⣿⣿⣷⡀⢀⠿⠀⠀⢀⠀⢀⠀⠀⠀⣰⣷⣆⣿⣠⠈⡤⣞⣿
⠀⠘⣿⠻⣿⣿⣿⣷⣶⣦⣤⣾⠐⠄⢺⣿⣿⡇⣀⣿⣿⣿⣿⣿⢷⡁⢮⠇⠀⠀⡘⣧⣂⣧⣶⣾⣿⣿⣿⣿⣸⠄⣷⣿⣼
⠀⡴⠃⣴⡏⠉⠉⠹⢟⣻⣿⣿⡧⣀⢻⠛⣿⣾⣿⣿⣿⣿⣿⣿⣤⢀⣄⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿
⣼⣁⣤⣿⡅⠀⣠⡜⢻⣿⣿⣿⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣾⣤⠀⠘⣌⣿⣿⣿⣿⡟⣿⣧⣿⣿⡿⠟⢸⣿
⠙⣾⡛⣿⣿⣿⠿⣿⡿⠟⢉⣿⣿⣾⣷⣺⣹⣟⣿⡏⣭⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣟⣷⣿⣿⣿⡿⠁⠀⣼⠃
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⡟⣸⣶⡆⠀⢿⣿⣿⣧⢻⣿⣿⣿⠟⢁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⣿⣿⣿⣿⣿⣶⣽⣍⣿⣿⣶⣿⣧⠀⠀⠈⢿⣿⣿⣨⢿⡿⡋⢠⡞⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⡿⠃⠘⣿⣿⣿⣿⣅⠀⠀⢸⣾⡿⠀⢿⣾⣽⣿⣯⡾⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣟⠁⠀⢸⣿⣿⣇⣠⣼⣿⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢎⣄⡿⣿⣿⠁⠀⠀⣀⣿⣟⡋⠅⣀⢀⡾⠿⠛⢯⣏⣏⣭⣭⡭⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⣯⣯⡦⠼⠟⠀⢠⡞⡟⣽⣹⡌⢀⣠⠟⠁

⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠕⠊⢀⣈⠍⠉⡉⡩⣰⡼⠿⣀⣀⠀⠀⣄⣠⣀⠀⠀⠀⢁⠤⢀
⠀⠀⠀⠐⠃⢹⣷⣀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⡐⣲⣿⣚⣎⣘⣟⣳⣪⣿⣿⣿⣿⣿⣽⣶⣿⣿⣞⣻⣿⣿⣶⠦⣠⣝⡤
⢢⠀⢀⠀⠂⠰⣿⡹⣄⡀⢄⠀⠀⡨⣧⡤⡾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠘⢇⠀⠀⠀⠀⠘⣿⣎⢷⣾⣧⣚⡰⠿⣿⠓⠹⣟⠉⢻⡏⢻⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠳⡀⠀⠀⠔⢈⠿⣿⣿⣿⣿⣄⠀⠘⢧⣄⣻⣆⠀⣻⣞⣿⣿⣹⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢤⡀⠙⢶⣦⣄⡄⡸⠏⠛⢯⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠿⣿⣾⣽⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⡀⠀⠙⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣾⡛⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠑⠷⢯⢄⣀⣙⣿⣿⣿⣿⣿⣿⠏⢀⣼⣿⡿⠉⠰⠛⠛⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠦⠥⠤⢴⠶⢛⣻⣿⣿⣿⠋⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠺⠋⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠒⠤⠤⠤⠶⠛⣻⣿⣿⠛⠀⠀⢸⡟⠃⠃⠀⠀⠀⠀⠀⣀⣀⣈⣛⢿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣷⣸⣿⣝⠿⠋⢿⡟⠉⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⡀⢠⡀⠀⠀⠀⢄⠀⠆⣸⣿⣿⣿⣿⣿⣿⣷⣿⣏⠀⠀⠀⠀⢀⣾⣿⠇⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠃⢸⣷⡄⠀⠀⠀⠈⠇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⠳⠀⠀⠀⣻⡿⠉⠈⠋⢁⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠀⣴⣶⣌⣻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠸⡟⠓⠀⠀⠀⠀⠀⠀⠘⠝⠛⣟⣻⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠃⠴⠄⠀⠀⠀⠀⠀⠀⠀⠞⠻⣿⣿⠛⢁⠀⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠈
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣶⣦⣦⣤⣀⠀⠀⠀⠀⠀⠀⠟⠟⠀⠉⠀⠀⠀⠀⠀⠤⢾⣿⣿⣿⡟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠁⠻⠏⠙⣸⡢⢼
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⣿⣇⠀⠀⠀⠀⠹⣿⣟⣿⣿⣿⣯⣉⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢀⣥⢃⢳⢾
⠀⠀⠀⠀⠀⠂⠿⡿⠿⢛⣁⡀⢺⣍⠀⠀⠀⠀⠀⠙⢿⣿⣯⣿⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠋⣀⣀⢤⡾⣿⣿⡨⢥
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡆⣴⣶⣾⡿⢀⣠⠖⠀⣁⣜⣳⣮⣿⣿⣿⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⣿⣿⣦⡐⠠⠀⠀⢀⠀⠈⠛⠻⠿⡿⣷⣿⠿⠟⣃⣈⣢⣴⣿⣿⣯⣿⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠃⠘⢿⣦⣄⡀⠀⠉⠀⠀⠠⡐⣤⣢⡓⣾⣯⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠛⠻⣿⣶⣬⢶⡤⠰⠇⠄⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠂⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠿⢧⣀⣀⣀⣀⣴⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠌⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣦⣄⠀⣿⠀⣠⣴⠞⠃⠀⠀⠀⣰⢤⡹⣽⢃⣤⡆⠈⠀⠀⠀⠀⠀⠀⠶⠀⠰⠇
⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⢉⣓⢾⣞⡉⠀⢐⠀⠀⠀⠀⢈⣛⣻⣿⣟⣋⡁⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠠⡷
⠀⠀⢂⠨⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣤⠾⠋⠁⣾⠀⠙⠻⢦⡀⠀⠀⠀⠻⠞⢱⣻⡜⠾⠇⠀⠀⠀⠀⠀⠀⢐⡴⠀⠰⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠤⣤⢠⣬⣼⣥⡤⢤⡤⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠄⠠⠀⠀⠀⢀⡀⢀⢀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠻⡦⠀⣴⠦⠄
⠀⠀⠘⢣⣿⣯⣝⣿⣿⡜⠁⠀⠀⠀⠀⠂⠀⠀⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡉⠀⢉⡤⠀⠀⠀⠀⠀⠘⠶⠖⠀⠀⠀⠉
⠀⠀⢰⣮⢟⣿⣽⣿⡿⢴⡆⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⡄⠡⢔⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⣰⠄⢀⡀⠘⠛⢧
⠀⠀⠉⠉⠀⠡⣭⡍⠀⠉⠉⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⠭⠘⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⢓⣿⢿⢠⡄⣠⡄
⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠑⢣⣄⣻⣠⡄⠪⡥⠀⠀⠀⠀⠀⠠⠠⠡⠀⠀⠀⠀⠀⠀⠀⢩⢻⡶⣍⣹⣩⡶⣟⣯⠁
⠀⠀⠀⠀⠠⠘⠛⠣⠀⠀⠀⠀⠀⠀⠴⢄⡠⠜⢻⠳⢆⡠⠦⠀⠀⠀⠀⠀⠀⠡⠡⠌⠀⠀⠀⠀⠀⠀⠰⣰⣥⠞⣿⠳⣮⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠆⡀⢭⢀⠰⠮⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠫⠆⡹⣿⢾⠱⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠍
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠰⣶⢫⠧⣩⠉⣏⠴⡜⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠢⣤⣾⢾⣆⣤⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢙⡛⢴⢽⣿⡯⡦⢚⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣽⣻⣯⣿⠋⠀⠀⠀⠀⠀⡀
⠀⢀⣮⣱⡄⠾⠭⠗⣀⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠷⢾⣹⡷⢿⣑⣄
⠀⠀⠉⠉⠁⢏⣒⡟⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠞⠛⠛⠛⠛⠶⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⢀⣀⣴⠟⠋⠉⠻⠋⠀⠀⠈⢻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠙⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠻⡶⠛⠛⠛⠷⣦⣰⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠷⣦⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣽⣿⢭⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢤⡆⠀⠀⠀⠀⠀⠀⠀⠈⠾⠽⠶⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣺⣗⢺⠂⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣻⡟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⠀⠀⠀⢾⡷⣽⠆⠀⠀⠀⠀⣴⡖⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠸⣗⡿⣗⡟⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢲⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠙⠀⠀⠀⠈⠩⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣺⢿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⡀⠀⠠⠀⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣽⠇⠀⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢀⡀⠀⠀⠀⠦⠹⠴⠋
⠀⠀⠀⠀⢷⡶⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠻⡆⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⣴⡀⠀⠀⠓⠚⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠉⠉⠤⠄⠈⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⡆⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⡰⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠐⠂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⢄⣶⣿⣿⣤⣰⣿⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣟⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⢼⣧⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡁⣸⣇⢈⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⢸⡇⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⠇⣭⡀⠆⢸⠀⣷⠀⠀⠳⠦⢧⣄⠐⣿⣾⣷⣿⠆⣀⡼⡰⠖⠀⠀⣾⠀⡗⠰⢀⣬⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠝⠟⣶⣤⡁⣠⣄⡀⢸⡦⣟⣷⡖⣡⣌⢢⣾⣻⢵⡇⢀⣠⣄⢘⣤⣴⠿⠏⡅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀⣬⠉⣻⢾⡾⣿⠼⠿⡟⠋⡃⣿⣿⢈⠙⢻⠿⠧⣿⢷⡷⢟⠛⣥⡐⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠻⠾⠟⡄⣾⣷⣬⡲⣼⡾⢷⣧⢔⣥⣾⣷⢠⠻⠷⠟⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⠴⣶⣟⣷⠂⠬⣝⣿⠉⢀⡀⠉⣿⣫⠥⠐⣾⣻⣶⠦⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠺⠿⣯⡿⠄⢒⣫⣿⣀⠈⠁⣀⣿⣝⡒⠠⢿⣽⠿⠖⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⣴⢶⣦⠃⢿⡿⢛⠕⢻⢿⡾⡟⠮⡛⢿⡿⠘⣴⡶⣦⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠈⢛⣄⣵⢿⢷⣟⢲⡶⣧⣄⡅⣿⣿⢘⣠⣼⣶⡖⣿⡾⡿⣮⣀⡛⢁⠴⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢘⣢⣾⠟⠛⡅⠙⠋⠁⢸⢗⣯⡿⠧⡙⢋⠼⢿⣽⠺⡇⠈⠙⠋⢈⠛⠿⣶⣔⡂⢄
⠀⠀⠀⠀⠀⠀⢀⣴⡆⡛⠅⠆⢼⠀⡿⠀⠀⠴⠎⡞⠉⠰⣿⢿⡿⣿⠆⠙⢣⠑⢦⠀⠀⢿⠀⡆⠰⢨⢛⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢸⡇⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⡁⢹⡇⢈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡠⢻⡗⠌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠘⠃⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠚⢁⡠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣡⡌⠱⣄⡏⠀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠉⠢⣡⢠⠎⠀⡀⢹⡆⢀⣤⠶⢤⡀⠀⠀⠈⠓⠀⡆⢠⡶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣶⠀⠀⢹⡟⠀⠀⠙⠊⠁⢻⣤⠄⠀⢱⠀⠀⢀⣠⣮⣤⣀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⠀⠀⠀⢠⠶⠶⢆⠈⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠴⠚⠉⠁⠀⡀⠈⣇
⠀⠀⠀⠀⢠⣤⡄⢸⡀⠀⠛⠀⠀⠀⢏⠀⠐⠊⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣀⣤⠾⠿⠤⠤⡀⠀⠀⠈⠷⠾⠃
⠀⠀⠀⠀⠹⠦⠇⢀⣙⣶⣤⣤⣀⣀⡈⠳⣄⡀⠀⠀⠀⠀⠀⡬⠓⠶⣤⠴⠋⠁⠀⠀⠀⣀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢰⢉⣄⠀⠀⠀⠀⡠⠖⠛⠉⠉⠛⠒⠒⠒⢺⡇⠀⠀⢸⠂⠀⠀⠀⠀⠀⠱⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⢘⠀⠀⣤⡄⠀⠀⠀⠀⠀⠈⢻⠶⠖⠛⠢⣄⠀⠀⠀⠀⣴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⢳⣄⠀⠀⠙⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠷⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⢹⡿⣶⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣀⡤⠞⣿⠀⠀⢀⡀⠀⣠⠲⠀⠀⡇⠈⠳⣄⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢺⠀⠀⠋⢹⡆⠹⠶⠤⠞⠀⠀⠀⠈⢳⡦⣄⣉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢲⡆⠀⢀⡞⠀⠀⠓⠤⠴⠛⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⡷⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⣀⡴⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠖⠁⠸⢧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⡀⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠴⠇⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⠤⢠⢤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣸⠤⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠉⣿⠇⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠋⢴⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠂⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⢀⡄⠐⠀⣴⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣤⣠⣤⣠⣤⠞⠉⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠐⠀⠁⠀⠢⠄⣠⠀⠀⠀⢦⡆⠠⠠⠘⠂⠉⠃⠀⠙⠀⠸⣶⠆⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣿⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣯⣭⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢿⡃⣴⠂⡀⠀⠀⣰⠏⢷⡀⠀⠀⡀⢲⡄⣻⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠾⣿⠁⡼⠃⠀⣰⠃⢠⠀⢳⡀⠀⠻⡄⢹⡿⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠛⠲⠾⣿⠁⠀⣴⠃⠀⣾⡇⠀⢻⡄⠀⢹⡿⠶⠚⠛⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠛⠲⠦⣤⣀⣀⠸⣆⣼⠃⠀⠀⣿⡇⠀⠀⠻⣄⡾⢀⣀⣠⡤⠶⠚⠛⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠻⣦⡀⠀⠈⠉⢽⣿⡿⠃⣴⢀⡏⣇⢰⡄⢻⣿⣿⠍⠁⠀⠀⣠⡾⠃⣸⠃
⠀⠀⠀⢀⢲⡀⢷⠀⣶⠀⠈⣧⠀⠈⢿⣶⣄⠰⠦⣤⣻⡼⠁⢸⡇⣿⠀⠹⣼⣣⡤⠶⢀⡴⣾⠏⠀⢠⡏⠀⢰⡆⢰⠆⣰⢂
⠀⠀⠀⣨⠿⠳⣾⣇⣸⡆⠀⢸⡄⠀⢀⡙⢮⡳⢦⡀⣬⣷⡞⢸⠃⢻⠘⣶⣯⡄⣠⠶⣫⠞⣁⠀⠀⣼⠁⠀⣾⣀⣿⡶⠻⢯⡀
⠀⠀⠀⠀⠴⠛⢁⡤⠟⠛⠲⢤⣷⣷⠈⣧⠈⠳⣄⠙⢦⣌⣧⣼⠀⢸⣤⢏⣤⠞⢁⡴⠋⢠⡏⢰⣷⣧⠴⠚⠛⠧⣀⠙⠳⠄
⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⠶⠛⠿⠛⣛⡾⢦⣿⡈⢧⡀⢈⠻⣿⢸⢸⡿⢋⠀⣠⠟⣸⣧⠾⣞⡛⠻⠟⠳⢦⣄⠀⠀⠁
⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠐⢛⣁⣀⣚⣉⣉⣳⣿⣮⣳⣾⣾⣾⣶⣫⣾⣷⣏⣉⣙⣂⣀⣙⠓⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠰⢯⣁⠀⠒⠾⠿⠿⠿⠯⣭⣭⣍⣉⣀⣀⣀⡒⢒⣿⣿⣿⣿⣿⣖⠒⣂⣀⣀⣈⣩⣭⣭⡭⠿⠿⠿⠿⠖⠂⢀⣩⠷
⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠐⠦⣄⡀⢲⣤⡭⢿⡿⢋⡼⣻⢿⢿⡻⣌⠻⣿⠯⣥⣴⠂⣀⡤⠖⠀⠀⢀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠠⣄⡀⠀⠉⠓⢦⣷⣦⠶⣿⠋⠿⣠⠟⠀⣠⢾⣿⠸⢸⣿⢦⡀⠘⢧⡸⠏⢻⡷⢦⣾⣧⠖⠋⠁⠀⣀⡤
⠀⠀⠀⣀⠘⠶⣄⣉⣷⡶⠚⢋⡟⠟⢠⡏⢠⡞⢁⡴⣛⣡⡏⢹⠀⢸⠉⣧⣙⡳⣄⠙⣦⠈⣇⠘⠟⣏⠛⠲⣶⣏⣁⡤⠞⢀⡀
⠀⠀⠀⢩⢿⡖⢻⠏⣸⠃⠀⣸⠁⠀⢀⡴⣫⠖⠋⣀⣩⡟⠳⢸⡆⣾⠰⠛⣯⣁⡈⠓⢮⡳⣄⠀⠀⢹⡀⠀⢻⡈⢿⠛⣾⢯⠁
⠀⠀⠀⠀⠚⠀⠟⠀⠋⠀⢠⡏⠀⣠⡾⠟⠁⠘⢋⣉⡿⠹⡄⢸⡇⣿⠀⡼⠹⣏⣉⠛⠀⠙⠻⣦⡀⠀⣧⠀⠘⠃⠘⠇⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠾⠋⠀⢀⣀⣤⠽⣿⡿⠄⠙⠀⣧⡏⠘⠁⠼⣿⡿⢥⣄⣀⠀⠈⠻⠆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⠶⠚⠋⠉⠁⠀⣰⠃⠹⣄⠀⠀⣿⡇⠀⢀⡼⠁⢳⡀⠀⠉⠉⠛⠲⠦⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⢻⠿⡄⠀⠹⣆⠀⢿⠇⢀⡾⠁⠀⡼⢿⠛⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⢺⡿⣄⠹⡄⠀⠘⣆⠘⢀⡞⠀⠀⡼⢁⡼⣿⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢚⡿⣄⠙⠆⠀⠀⠀⠘⣦⡞⠀⠀⠀⠀⠞⢁⡼⣟⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠙⣧⣀⡄⠂⢙⣳⡾⠈⢷⣬⠾⠏⠿⣷⣩⣠⠟⣵⣿⠛⠙⡄⢀⠀⠀⠀⠀⠀⠀⢿⣷⣾⢃⡴⠂
⣐⣛⠘⢻⠀⠀⠉⠀⢐⡾⢻⣞⣠⠅⠾⢿⣧⣼⣿⣿⡇⣸⣥⣿⣤⡀⠀⠀⠀⢀⠘⢽⣻⣿⣿⡶⠂⣤⣠
⠿⠻⢇⡘⢠⠴⢀⠀⠁⠒⡟⣿⠁⡀⠀⠤⢸⣿⡿⢇⣰⣿⣿⣿⠣⣦⡀⣠⠀⢼⣿⣨⡿⠿⢉⣿⣧⣜⣿
⠀⣠⠊⢀⠹⢧⣼⣰⠔⠂⠀⠫⠀⠁⢀⣠⠄⠘⣇⠀⣿⠻⣿⣥⣴⢻⣿⡯⠀⡨⢿⣿⣷⡀⣛⣻⣿⣺⣿
⣀⣀⣁⠢⠀⢀⡈⠁⡤⠀⠀⣀⠀⠀⠀⢀⠀⣈⡷⠞⠀⠉⠠⢟⡙⢿⣿⣿⠿⠃⣾⣿⣈⣁⡉⣿⣽⠾⢿
⢠⠬⢋⡁⢘⠋⠀⠀⡘⣧⣞⡡⠄⡀⠀⠁⠀⢸⣇⣄⠂⠀⠀⠉⠀⡠⠞⣿⡾⠾⢿⢻⡟⣿⠛⢹⡧⠃⢼
⠚⠛⢛⣋⣿⡳⠤⢀⡀⠞⠻⣯⣉⡠⠀⠀⠀⢠⠁⠁⠁⠀⠀⠀⠉⢐⡲⢼⣧⡤⠸⠋⠃⠧⠀⠈⢀⡞⠋
⢲⠖⢋⡀⠸⡄⢀⡾⠧⢄⠠⠋⢿⣴⢒⠆⡀⠘⠀⠀⠀⠀⢀⡀⠀⠷⢧⣽⣷⢒⠀⣞⣠⠀⠀⠀⠾⠃⠁
⠀⠀⠒⠒⢓⠛⣝⡻⠆⠀⢀⠀⡨⣻⣧⡈⠀⣰⠆⢀⡶⠀⠀⢱⣄⠀⢶⢐⠏⣽⣿⣟⣁⡀
⠀⠀⠋⠉⠁⢀⡟⠻⠶⣖⢋⠤⠀⠀⠋⠱⣤⢁⡴⠟⡀⠀⠄⢔⣉⣡⡜⠋⢃⠉⢻⡉⠻⣷⠀⠀⣲⣄⣾
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⡃⢀⡀⠀⠀⢊⢹⣿⡔⣊⣁⣄⠀⠒⠢⢌⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛
⠞⠀⠀⠀⠀⠁⠀⠀⠠⣄⣽⣎⢀⣴⠀⠀⢞⡉⢿⡿⠭⡅⠀⠴⢛⡽⢷⣆⠈⢀⣀
⡷⢀⠀⢠⡆⠀⡆⠀⠀⠉⣩⣷⣿⠁⠀⠀⢤⣔⠛⣷⠊⠁⡄⢰⠈⠐⠁⣸⣄⣩⣥⠄⠀⢀⡠⣸⡃⡀
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠄⠠⠠⠤⠀⢀
⠀⢀⣰⣶⣟⠲⢶⢖⠳⣘⣫⣶⠿⠿⠞⠛⢓⢹⠄⠂⡈⣡⢰⣺⣦⣷⣠⡄⠒⠚⠚⠇⡴⡂⢄⣃⣀⡀⢀
⠀⣠⡼⢖⣀⣤⣯⣥⠴⠂⣿⠃⠀⣀⠀⣄⣾⢻⠀⣀⠝⠨⠧⢸⡽⣏⠉⠳⢄⣄⣤⢤⡀⣤⣴⣛⣃⢼⣌⡙⣤
⢀⠏⡀⠈⠁⢈⢇⣘⣆⢀⡼⡆⠒⠉⢣⣀⢯⡘⡆⠀⠠⠤⠀⠈⢃⡷⠲⠆⠀⠀⠐⠊⠏⠁⠀⠉⠹⡀⠀⢈⣛⠁
⠊⢿⡾⠠⣿⣾⣹⡽⣝⢧⣀⣈⣀⠀⣉⡠⠀⠘⣇⠀⠐⢠⣯⠴⣟⢲⣄⢀⣐⣆⡀⢀⠶⠂⠈⠛⠂⠀⠃⣀⠉
⠀⢀⠇⠀⠀⡞⡩⠙⣶⡾⠟⠛⠻⡛⠻⣟⡣⢾⣿⣭⣶⣿⠋⠛⠉⣠⣟⠦⢌⠿⣻⣿⣾⠛⡯⡀⠠⠂⠀⠀⢀
⠀⢨⠔⠊⡰⣠⠇⢡⣿⠷⣶⡶⠀⠹⢷⡟⠙⠷⢼⣮⢻⣻⣧⠄⠞⢻⣯⣿⣃⣼⠇⠀⠈⠛⣧⣼⡁⠀⠀⠀⢨⢰⡀
⠰⠖⠶⠂⠤⠀⠀⠈⣩⡗⠈⠀⢴⡄⠀⡓⢊⠒⠶⠶⣾⡽⡈⠋⣄⣀⡏⣩⣷⡋⠀⢀⣀⣀⢸⣿⣖⡆⢸⣄⠱⣣⠂
⠀⠰⠀⠀⢘⠄⠀⠀⠀⠱⢤⣀⠤⡄⣰⡀⠙⢂⠀⠀⢪⡄⠇⡠⡤⠀⣤⢸⡂⠛⠃⢀⠁⢉⠾⣟⣿⠇⠀⠈⣄⠉
⠀⠃⣈⠉⠩⠓⠒⢲⡞⢁⠘⢿⣟⣻⠷⠖⢶⣿⣦⣐⣿⣧⣤⣀⢀⡼⠗⠛⠗⠢⡄⠛⠋⠜⠃⣁⣀⡀⠀⣀⡄⢀
⠀⢶⠉⡚⡶⠞⠶⡖⡽⠎⠃⠼⢸⣵⠴⠚⠛⠛⠿⢏⡙⠛⡛⠛⣻⠆⠀⠀⠀⠀⠙⢶⣵⣧⣼⡿⣭⣙⢷⣄⣀⠆⣃
⠀⠈⢻⠉⠀⠀⠃⠞⠀⠀⠀⠀⢈⢻⣾⣷⠄⠺⣿⡆⣿⡇⠉⣉⣿⠆⠂⠰⠶⠈⠐⢀⣏⣽⠻⠋⣹⡛⠿⠻⡆⠀⣹
⠀⠀⢩⠁⠀⠀⠀⠀⣀⡀⡵⠖⣶⠞⣇⠀⢀⣀⠀⢀⡋⠀⠘⠛⠣⡄⠷⠀⠀⠀⠀⠊⠉⠈⡆⣀⣭⣩⠀⠜⠀⠙⠃
⠀⠀⢨⡇⠤⢖⠨⠱⢠⠀⠀⠀⠀⠀⣨⣁⠠⣠⠀⡈⠀⠀⠀⠀⣰⣬⠀⠂⢀⠀⠀⠀⠀⠀⣙⢏⣁⠤⠀⠰
⠀⠀⣚⠦⣿⡴⣴⠂⠟⠀⠸⠁⠀⠀⣸⣭⠓⠻⢺⣾⡃⢤⢠⢤⣼⣿⣲⢶⠃⠘⠿⠗⢀⣶⠳⠾⠲⣄⠀⠒⠿⢻
⠀⠀⠀⡞⢿⣠⣤⠠⠒⠓⡆⠈⠀⣜⢟⣁⡈⠚⠓⢋⣷⠻⠇⡆⠨⡿⢿⠀⠀⠀⠀⠀⠀⣹⠈⠁⠰⠟⠛⡖⣺⣿⢧
⠀⠀⠀⢀⠈⠎⠘⢲⣥⠀⢈⢶⣺⢶⠊⠛⡛⡁⠸⡈⢻⠀⠀⠓⠼⠀⢸⡏⣡⠶⠄⠤⣸⠛⠟⢀⡄⠀⠀⢰⠿⠛⠈
⠀⠀⠀⠉⢠⡔⠓⠂⣶⠒⡡⡶⠀⠛⠀⠀⢀⡁⠀⢉⢠⠀⠀⠚⠻⢂⡞⠼⢿⡷⢶⣟⡹⢠⡀⠀⠀⠊⡠⠀⠆⠄
⠀⠀⠀⠀⠠⠱⡤⠀⠄⠀⡄⠀⠉⣥⠀⡠⢬⣁⣀⡠⠈⠀⠀⠤⠀⠈⠊⠉⠸⠉⠓⠛⠀⠀⠘⠃⠄⠀⠐⠈

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠓⠲⣄⡀⢀⣠⠤⠶⠒⠒⠶⠦⣤⣄⡀
⠀⠀⠀⣬⢰⣷⢢⣦⣢⣄⠀⠀⠀⠀⠀⠀⢀⢀⡔⢁⠿⠇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠿⢿⠀⣿⢸⡏⢛⢿⣆⡤⠒⠠⡦⠎⠉⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⢢⠙⠓⠀⠸⡈⠹⡇⣷⡄⠙⠞⠃⠀⠀⠀⠀⢀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠈⠦⣤⡀⠀⣷⠀⢹⡎⠀⠀⠀⠀⠀⠀⣀⠺⠋⣴⣶⣄⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠰⢭⣰⣿⡄⣟⠷⢀⠀⠀⠀⠀⠀⢸⣷⣤⣼⠟⠛⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣾⡟⡷⠠⡦⢇⡴⡾⣧⣈⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡋⠁⠀⠹⣈⠙⢻⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡙⠋⣹⠇⠈⣀⠚⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣼⣐⡉⢀⣼⣽⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢩⣯⣽⣯⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⢠⢠⠇⠀⠀⠀⠀⠀⠀⠀⡘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⢀⡏⢀⣶⠋⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠞⠁⠀⢠⢴⢖⡤⢀⠀⠀⠀⣰⠃⡰⣡⣞⠔⠟⠛⢦⣀⠀⠀⠀⣀⣴⠋⠉⠉⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠰⢫⡟⢥⠏⣠⢀⣾⡣⡾⠓⠩⠃⠀⠀⠀⠀⠈⠛⠒⠛⠵⣭⠽⢦⣀⡤⠋⠁
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠄⡀⠀⣤⡀⠀⣀⣠⡴⠟⠉⠉⠀⠉
⠀⠀⠀⣀⡪⠿⣉⡤⠒⢀⣀⠀⠀⠉⠴⠾⠻⡟⠁
⢠⣴⣯⡫⢲⢗⣭⣴⢞⡃⠀⠀⠀⡀⠀⠀⡼⡇
⠋⢠⠟⣩⠷⠛⣺⡵⠽⣿⣲⡤⠥⠬⠬⠭⠚
⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣘⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠢⣸⢁⠔⠁⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠠⢦⣠⠀⠀⢀⠀⠀⠙⣄⠀⠀⢸⠃⠀⠀⣠⠋⠀⠀⡀⢀⠀⣄⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠱⠧⣀⡄⠀⠀⡿⢝⠦⣼⣤⠴⡻⣻⠀⠀⢠⣀⠼⠎⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠒⢄⡟⢸⢷⢼⠤⡾⡇⢿⡠⠒⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⠴⢚⣩⠟⢬⣶⣼⠔⠻⣍⡓⠦⣄⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠲⢬⣓⣤⢔⢿⢻⠢⣤⣋⡥⠖⠋⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠤⠊⣧⢸⡮⠼⠦⢵⡇⣾⠑⠤⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡰⡖⠈⠃⠀⠀⣷⣪⠖⢻⠛⠲⣵⣼⠀⠀⠸⠁⢲⢆⣈
⠀⠀⠀⠀⠀⠀⠀⠐⠖⠉⠀⠁⠈⠀⠀⣴⠋⠀⠀⢸⡀⠀⠀⠙⣄⠀⠀⠁⠀⠀⠋⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢀⠔⢩⡈⠢⡀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠲⢦⣄⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣀⣀⣀
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣻⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡴⢾⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢫⡟⠛⠛⠻⣤⣞⡃
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠙⢦⣤⣀⣀⣠⣤⡞⠉⢳⣦⣤⣀⣀⡀⠀⢀⣀⣤⣏⡿⣠⣭⡗⠀⠀⠀⣿⠉⢿⠄⢀⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⠹⣤⣤⣤⣽⡜⢯⣩⣟⢻⣍⣧⠙⣴⣧⣴⠟⣦⣤⡾⠡⣿⡭⠤⠟⠼⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⢂⡶⢶⣲⡶⣠⠶⠶⣦⡴⢶⡶⣀⠰⡖⢶⣔⡶⠒⣆⢲⡒⠒⠓⢶⣘⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢾⡉⢰⡇⠀⠀⢸⣗⠛⢰⠋⣷⠙⣻⡏⠀⠀⠘⣧⠛⢶⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢧⣤⣤⣤⠟⡴⠞⠛⠳⢷⡙⣦⣀⣀⡴⣷⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡴⠒⢲⢆⡘⣇⠀⠀⠀⣰⢃⡄⢶⠶⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣷⠙⢲⣶⠚⢡⡏⠹⣎⢧⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⢁⢺⡄⠙⠶⠛⠹⠷⠖⠋⠀⣸⠂⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠸⠀⠁⠈⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⠃⠀⠄
⠀⠀⠀⢠⣄⣀⠀⢪⣩⣆⢠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⡇⠰⠀⠀⠀⠐⠀⡔⠀⠁⠀⡁⠀⠆
⠀⣀⠐⢦⡀⠙⣷⣘⢳⠏⢰⢀⠏⠰⠀⠀⠀⠀⠀⡔⠡⡐⢤⠤⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⠀⠀⠈
⠀⠸⣆⠀⠙⠄⠈⣿⢼⠇⠰⣎⡴⠓⠄⢀⢔⣤⡞⠀⢀⠇⠈⡆⢠⠔⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠈⠑⢄⢸⣆⢻⣶⡆⠐⣽⠁⠀⠀⢈⠘⣿⡇⠀⢨⡆⠀⢿⢀⡟⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⢦⠻⡈⣻⢃⢣⡏⠀⠀⠀⠀⠄⠻⣷⡄⠸⣆⣀⡞⣼⢁⠇⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⡄⠀⣄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠣⣷⣿⣾⠋⠀⠀⠀⠀⠀⠀⠣⠼⡿⠿⠋⠜⡿⠑⠁⠀⠀⠀⠀⠀⠀⠈⠯⣤⠀⢳⠆⠀⢰⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⠘⠀⠀⠀⠀⠀⠀⡴⠒⠂⣴⠶⢄⡀⢳⣼⣇⣼⣿⠷⠚⠃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠑⣄⡀⠈⠷⣇⡙⢶⣍⢯⠉⣤⣤⡶⠿⢛⡋⡳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⠀⠹⢦⣦⡭⣷⣶⠽⠷⠦⣤⠤⡤⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣉⣀⣀⣑⣀⣐⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⣟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢰⣄⡀⠀⠈⠻⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣾⠋⠁⠀⢀⣠⠂⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠘⣿⣶⠆⠀⣰⣿⣿⠯⠉⠁⣀⣀⣀⣀⠹⣿⢿⡿⢃⣀⢀⡀⠈⠉⠙⢿⣿⣿⡀⠠⢤⣼⡿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣿⣿⣿⣿⠟⣉⣀⣰⠾⠛⠋⠉⠉⠉⠳⡝⠘⡵⠋⠉⠉⠙⠛⠷⢦⣀⣈⡛⢿⣶⣾⣿⡇⠐⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⣿⠋⣴⡾⢿⣂⣀⠀⠀⠀⠀⢀⠀⡀⢷⠸⢧⡀⢀⠀⠀⠀⠀⠀⣀⡹⢷⣦⡝⢿⣿⣷⣄⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⣿⡟⠁⠈⢁⣴⠞⠛⣉⣁⣀⠘⢶⡌⣧⠀⠀⠀⠀⢠⡏⣴⠖⠀⣀⣙⠛⠻⢦⣌⠁⠀⠻⣿⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢫⣾⠃⠰⠋⠀⠀⠀⠀⠀⠉⠳⣮⣿⡏⠀⠀⠀⠀⠈⣿⣧⡴⠋⠁⠀⠀⠀⠀⠙⢧⠈⢷⣜⠇⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠠⠟⡉⠀⠀⣾⡀⣀⣤⣶⢿⣷⣮⣿⡿⠷⠄⠀⠀⠀⠴⠿⣿⣯⣶⡿⢶⣤⣀⠀⢸⡀⠀⠘⠻⡆⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⠀⠉⠀⢀⡀⠙⠟⠹⣯⡙⢛⣻⣿⠋⠀⠀⢀⠀⠀⢀⠀⠀⠉⣿⣟⡛⠚⣩⡟⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠰⣿⣿⠏⣰⡟⠀⠀⠀⢀⠎⠁⠀⢦⣄⣈⣹⣿⠋⠁⠀⠀⢀⣈⣁⣈⣁⡀⠀⠀⠈⠛⢿⣞⠉⣀⣤⠀⠀⠱⡄⠀⠀⠀⠹⣦⠹⣿⣿⡆
⠀⠀⠀⠀⢈⣿⡏⢠⣿⠃⠀⠀⠀⠁⣴⠀⠀⠈⣿⣿⢋⣷⠃⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢶⡝⢿⣿⠏⠀⠀⣤⠘⠀⠀⠀⠈⣿⡆⢹⣿⡃
⠀⠀⠀⠀⣼⣿⠀⢸⣿⠀⠀⠔⡀⠀⠹⣆⠀⠀⠸⠃⣾⣯⡀⣼⣹⣿⣛⠻⣿⣿⡟⣛⣿⣿⣷⠀⣸⣿⡘⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⣹⡇⠀⣿⣷
⠀⠀⠀⢠⣿⣿⡀⠘⣿⡇⠀⡾⠀⠀⠀⠙⣦⡀⠀⣼⣿⡿⠁⠘⠘⣿⠟⢡⣿⣿⣆⠻⣿⠏⠋⠀⢻⣿⣧⠀⠀⣰⠟⠀⠀⠀⢷⠀⢀⣿⡇⠀⣿⣿⡆
⠀⠀⠀⠀⣿⣿⠇⠀⢹⣇⠀⠁⢸⠀⣦⡀⠈⠛⠶⢿⣿⣧⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⢸⣿⡿⠶⠟⠁⠀⣰⡄⡆⠈⠀⢸⡟⠀⢸⣿⣿⠁
⠀⠀⠀⠀⢻⣿⡄⠀⠀⢿⣧⠀⠘⣷⣿⣿⣴⡆⠀⠸⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠰⣿⣿⡇⠀⢰⣄⣾⣿⣿⡇⠀⢰⣧⠁⠀⠀⣿⡿
⠀⠀⠀⠀⠘⣿⣧⣦⡀⠈⢿⡇⠀⠹⡏⠻⣿⣷⢰⡆⣿⣿⣀⡴⢎⣠⣴⣿⣿⣿⣿⣦⣀⠱⣤⣀⣿⣿⢠⡆⣾⣿⡿⢹⡟⠀⢰⣿⠏⠀⣀⣴⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠸⣷⣷⣄⠀⠀⠈⠿⣿⣷⠸⣿⣿⣿⠋⢹⣏⣏⣏⣿⣿⣹⡏⠻⣾⣿⣿⡇⣼⣿⡿⠋⠀⠀⣠⣶⡾⡏⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⢸⣿⣿⣷⣄⡀⠀⠹⢿⡆⢿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⡿⢰⣿⠏⠀⠀⣀⣶⣿⢿⠃⠁⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣦⠀⢹⣿⣿⣿⣷⣆⡄⠘⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⠃⢀⣠⣼⣿⣿⣿⢸⠀⣰⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⡟⠟⡿⣿⣿⣿⣿⣿⣿⣽⠿⢻⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⡆⢀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⡿⠁⠀⠉⠻⢿⣿⣿⣿⣿⣿⠀⣈⠻⣿⡿⠏⣀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⡿⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⡉⣃⡀⣀⡏⢉⣇⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣆⠙⢿⣿⣿⡟⠁⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⠛⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠋