Birthday cake Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢦⡀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⢰⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢦⣷⠀⠀⠀⠀⠀⣰⣷⣬⡇⠀⠀⠀⠀⢀⣼⣶⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣸⣿⠀⠀⠀⠀⢸⣿⢀⣼⡏⠀⠀⠀⠀⢾⣏⣀⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣫⠿⣇⠀⠀⠀⠀⢀⣏⡹⠿⡄⠀⠀⠀⠀⢸⣛⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡠⠖⡏⠀⠀⠀⠀⢸⣁⡤⢖⡇⠀⠀⠀⠀⢸⣁⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⢋⣿⠀⠀⠀⠀⢸⡧⠒⢉⡇⠀⠀⠀⠀⢸⠵⠚⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢚⣩⣧⠀⠀⠀⠀⢸⡶⢚⣩⡇⠀⠀⠀⠀⢸⠔⣋⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⡤⡟⠀⠀⠀⠀⢸⠋⣉⡤⡇⠀⠀⠀⠀⢸⢋⣡⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡥⠒⣧⠀⠀⠀⠀⢸⣏⠥⠚⡇⠀⠀⠀⠀⢸⣩⠴⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⢚⡏⠀⠀⠀⠀⢸⡥⠴⢚⡇⠀⠀⠀⠀⢸⡤⠖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠷⠾⠥⠿⠤⠖⠒⠒⠚⠓⠚⠛⠓⠒⠒⠒⠒⠺⠶⠯⠽⢄⣀⣀
⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠢⢤⣀
⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⢀⡤⠒⠢⣄⠀⠀⠀⣀⠀⠀⡞⠉⢧⠀⠀⢰⠋⠀⠉⢇⠀⡞⠁⠹⡄⠀⢀⡞⠉⠉⢳⡀⠀⣠⢤⡀⠀⢀⠀⠀⣷
⠀⠀⠀⠘⡇⠀⠀⡾⠀⠀⠀⢸⠀⠠⡏⠉⡇⠀⡇⠀⢸⠀⠀⡅⠀⠀⠀⣀⠀⢻⠀⠀⡇⠀⢸⠀⢀⠀⠀⡇⠀⡇⢰⡇⠀⢸⢳⣤⠏
⠀⠀⠀⠀⠳⣀⣠⠃⠂⠀⠀⢸⠀⠀⡇⠀⠣⠤⠃⠀⡞⠀⠀⢹⠀⠀⠀⡇⠀⠸⣤⠀⡇⠀⠸⡀⠀⠀⢸⠁⠀⡇⠀⠓⠲⠋⡼
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⣹⠠⠀⠀⠀⠘⡇⠀⠀⠘⡆⠀⠰⡇⠀⠀⡇⢰⠇⠀⠀⢧⢀⠀⠘⢤⡤⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠈⠀⠀⠀⠙⡚⠁⠀⠀⠀⠀⠸⡅⠀⠀⢀⡇⠀⠒⠙⠒⠚⠁⢸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⢀⣀⡤⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢤⣀⡀
⢀⡠⠖⠋⠉⠀⢀⣠⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣄⡀⠀⠈⠙⠲⢤
⡎⠀⠀⠀⠀⢼⠉⠀⠘⣆⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠉⣷
⠙⠦⣀⠀⠀⠈⠓⠦⢤⣀⣉⠓⠒⠲⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠴⠒⠒⣋⣁⡤⠴⠚⠁⠀⠀⣀⡴
⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡈⠉⠉⠙⠒⠒⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠒⠋⠉⠉⢁⣀⣀⡤⠤⠖⠚⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣙⣓⣒⣒⣶⣲⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣖⣶⣒⣒⣒⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡄⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡎⠀⠀⢰⠃
⠀⠀⠀⠀⠲⠬⠥⡤⣬⣭⣬⣭⡵⡇⠀⠀⠀⠀⠀⢀⠠⢼⠤⠀⢰⡧⠤⢤⡧⣀⠀⠀⠀⠀⠀⠀⠀⢀⣁
⠀⠀⣠⡒⠓⠶⠶⠤⠶⠶⠶⠾⠟⢓⣠⠀⠀⠀⠀⠀⠒⠶⠶⠦⠤⠤⠴⠶⠶⠖⠇
⠀⠀⢨⠉⠙⠛⠛⠳⠚⠻⠛⠛⠙⠋⢽⠀⠀⠀⠀⡏⠁⠚⢀⠆⠀⠀⠜⠀⠒⠀⡆
⠀⠀⠈⡄⠈⠀⠀⠀⠐⠚⠀⠃⠃⠀⣼⠀⠀⠀⠀⢷⠠⠤⠄⡀⢀⡠⢂⠤⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠙⠛⠒⠒⠶⠖⠶⠖⠓⠒⠋⠉⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉

⠀⠀⠀⠀⠀⢶⣈⣹⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⢸⠀⠀⠀⡆⠀⡄
⠀⠀⠀⠐⣛⣉⡥⢴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⠺⠖⠺⠛⠈⠿⠉⠏⠉⠏⠉⠟⠐⣢
⠀⠀⠀⠈⠁⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆⣙⠒⠒⠒⠒⠒⠒⡒⠒⢒⣒⡋⡉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠠⠀⠀⠀⠀⠀⠀⢁⠌⠁⠖⠁⡐⠃⠈⠀⠛⠀⠉⢙⣐⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⠉⠉⠒⠚⠛⠒⠚⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢨⠀⠀⠀⠖⠄⢀⠒⡒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠶⠦⠶⠶⢾⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⡀
⠀⠀⠀⣴⡪⡩⣍⣉⡆⠀⠀⠀⠀⣼⠉⠈⠒⠒⠶⠶⠶⠘⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠠⠟⡉⠟⠫⠍⠟⢓⡀
⠀⠀⠀⡇⠐⠊⠁⠂⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⢘⠛⠛⠛⠛⠛⠛⣛⣛⡀
⠀⠀⠀⡗⢒⠶⠒⠚⡇⠀⠀⠀⠀⣿⣿⠠⠤⠴⠂⠖⠀⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢘⣉⣉⣉⣙⣛⣛⣋⡉
⠀⠀⠀⢠⣀⣀⣠⣤⠄⠀⠀⠀⠀⢸⣌⡊⠀⠀⠀⠀⠀⠠⣼⠀⠀⠀⠐⠂⠀⠖⡆⠀⠀⠀⢘⠿⣷⣭⣮⣾⣿⣿⡷
⠀⠀⠀⠨⠌⣩⡥⠠⠀⠀⠀⠀⠀⠸⢦⣄⣉⣙⣓⣒⣒⣂⡏⠀⠀⠀⠀⠀⠀⠃⠇⠀⠀⠀⠈⢿⣿⣾⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠚⠓⡀⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⣀⠀⠀⠀⠳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠾⠆⠀⢀⠟⡆⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢠⠎⠀⠱⠀⠀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⣃⠄⠀⡋⠀⢠⠀⡇⠀⡴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠳⢄⡣⠜⡀⢘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢱⠀⠇⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂⠉⡉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠙⠃⡅⠀⠀⡇⠀⠀⠀⠀⠤⠤⠀⠠⠀⠒⠒⠒⢂⣤⡔⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠡⣌⠉⢛⠀⠀⢠⠤⣀⣄⡀⡀⠀⣀⡀⠀⠀⠀⠲⠂⡀⠱⠁⠀⠀⠀⠀⠀⡀⠀⣠⡀⠦⠤⣇⣀⠄⠐⠁⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢣⠀⠀⠉⠁⠒⠛⠓⠈⠁⠎⠤⠥⠤⠥⠤⠤⡤⠤⠤⠀⠠⠀⡀⠒⠒⢚⣂⠀⠀⠈⠉⠁⠀⠓⠀⠈⠀⠀⠀⠘⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⣤⣠⡤⣄⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠁⠈⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣀⠀⢤⣼⢶⣄⣠⢏⢧⡨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠳⠙⠡⠋⠐⠩⣻⡷⠄⠀⢰⠹⡇⠠⣤⡾⣫⢛⡽⣲⠖⡲⢋⠔⣡⢜⣿⡂⠀⣰⢟⢟⡽⡫⠣⠢⠪⠃⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡗⢈⣳⣒⠤⣰⣆⣀⡈⠛⣦⠠⠆⠈⠛⠹⠋⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠉⠉⠘⡙⠁⢁⣀⡀⢠⡄⡀⠤⠰⠆⢺
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠎⠱⠦⠴⡤⢬⣸⣗⣈⣲⠠⠿⠔⣂⡐⠤⣶⠴⠂⣲⠠⡿⠤⠒⣂⡒⠚⠓⢊⣡⣤⣍⣉⣉⡴⢲⡳⠖⢻
⠀⠀⠀⠀⠀⠀⠀⣠⡗⣦⢆⠄⡀⢀⠀⠉⠀⠈⠁⠽⠉⠙⠛⠋⢽⠉⠛⠋⠛⠉⣤⠈⠓⠚⠋⣭⠉⠛⠛⠉⠀⠛⠀⢀⢀⢀⡼⣥⣤⢨⣀
⠀⠀⠀⠀⠀⠀⡼⠀⠛⢶⣥⣊⣔⡡⡢⢚⠔⡠⣠⢆⡤⡠⢀⠴⡤⢂⠄⡀⣀⢀⡀⡠⢠⢀⣄⣀⡰⣢⢂⡖⣴⡿⠿⠛⠛⠛⠚⠘⠉⠀⢻⠳⡀
⠀⠀⠀⠀⠀⢰⢥⡶⢤⣤⠀⡀⢀⠉⠙⠓⠾⠾⠵⠯⠞⢛⣷⣛⡒⠓⠮⠶⠵⣫⡾⠾⠓⠋⠉⠉⠉⠉⠉⠙⠋⠀⠀⢀⠀⠀⠀⣴⣲⣄⠀⠀⡛
⠀⠀⠀⠀⠀⠀⠟⢧⡓⣷⡺⡫⣻⡀⠐⣧⣦⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣀⠀⠀⠀⢀⣤⣶⡲⣤⣴⢿⣧⣀⡠⠛⠛⠛⠗⡞⠁
⠀⠀⠀⠀⠀⣶⠠⠤⠀⠀⠈⠈⠪⠿⠴⠾⣻⣤⣿⣟⣽⠉⠀⣾⡻⣧⣤⣶⣛⣿⣦⣶⣣⣮⣧⡀⣤⣼⠟⠓⠙⠘⠋⠁⠀⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⣿⡀⢠⠄⣀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠈⠛⠳⠜⠛⠛⠛⠉⠈⢈⠁⠉⠀⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⢀⣲⡇
⠀⠀⠀⠀⠀⣿⣌⣙⣃⣬⣩⣝⠋⠋⣉⣉⠣⣐⣶⢀⣤⣀⣰⣄⢠⠄⠠⣀⣤⣀⣀⣄⡀⢠⡄⠀⠀⢠⡦⣀⠤⠤⠾⠷⠊⣈⣻⣉⣀⣤⡥⡇
⠀⠀⠀⠀⠀⣠⠈⠉⠉⠁⠳⠈⠙⠋⢩⡍⠱⠿⠿⠦⡶⠦⢤⣭⡤⠖⣓⠫⣭⣁⣠⠤⢬⣟⣋⣡⠬⠽⣯⣅⣤⠶⣶⠲⠛⠡⠮⠉⠉⠀⠁⡖
⠀⠀⠀⠐⣒⣻⡷⢹⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠸⠂⠀⠀⠀⠛⠀⠀⠀⠀⠀⣉⢀⠀⠄⠄⠂⠀⠀⣠⡴⠄⠀⣀
⠀⠀⣉⠤⠔⢂⡱⠦⢄⡉⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢄⡠⡠⢂⠄⡰⣠⢢⢂⠜⠜⠁⠀⠁⠀⠀⢀⣠⠄⢒⠽⠋⢀⡤⠊⠁⣀
⢀⡠⠄⠒⢉⡠⠔⠒⢉⡡⠝⠓⠒⣠⠤⠄⢀⣀⠀⠀⠁⠐⠁⠈⠊⠐⠋⠚⠱⠋⠊⠐⠁⠊⠈⠀⠀⢀⣀⡀⠤⣤⠖⠂⡩⠛⣁⠔⠁⡠⠖⠁⣀⠔⠋⣠⠖
⢠⠔⠂⠉⣀⡤⠖⠈⣁⡤⠒⠋⠁⣀⡤⠖⠉⠉⢀⣉⠍⠉⠀⡂⠴⣒⠴⠖⢒⡴⠖⠀⣉⠝⠋⢉⡴⠋⢁⠴⠋⢀⠔⢋⡤⠊⣀⠔⠋⢀⡴⠊⢁⡴⢊⡠⠖
⠀⠖⠊⢉⣀⠤⠖⠋⠁⢀⡤⠖⠋⠀⣀⡤⠖⠈⠁⣀⡤⢖⣩⠔⠊⢀⡤⠖⠁⣠⠔⠋⢀⣠⠞⢁⡠⠞⠁⡠⠞⣁⠔⠁⣠⠞⠁⡠⠚⠁⡠⠒⠁⠀⠋⠀⠈
⠀⠀⠊⠉⢀⣀⠤⠒⠊⢁⣀⠤⠐⠉⠁⢀⡠⠔⢋⣡⠖⠉⢀⡠⠖⠁⢀⡤⠊⠁⣠⠔⠉⢀⡴⠋⢀⠔⠊⡠⠞⢁⠴⠊⢠⠔⠉⠀⠀⠈
⠀⠀⠀⠀⠉⠀⠀⠤⠒⠉⠀⢀⡠⠔⠊⠁⡠⠔⠋⠀⣠⠔⠉⢀⡠⠒⠁⢀⡴⠋⠀⣠⠞⠁⢠⠖⠁⠀⠊⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⢀⠀⠀⢣⠆⠀⠀⢠⠀⠀⠀⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠀⠀⠠⣋⡆⠀⡆⡆⠀⢠⣀⠀⠀⠀⡙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢠⢉⠀⠀⡇⢡⠀⢠⢃⠀⠀⢰⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠤⠄⢺⢸⠒⠒⣇⡜⠒⢺⠸⠒⠒⢺⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠣⠇⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠒⠁⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠢⢄⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⠤⠔⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡆⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢀⡀⠀⠀⣀⣀⠞⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣧⠏⠀⠀⠑⠒⠒⠒⠉⠙⢆⡴⠁⠀⠱⠀⡁⠈⠢⠴⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣦⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡄⠀⠀⣏⢸⠀⠀⠀⣼⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⠁⠀⠀⣹⣯⠀⠀⠀⠻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡇⠀⠀⣧⢾⠀⠀⠀⣾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡇⠀⠀⣧⢾⠀⠀⠀⢿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⢾⢹⡗⠒⠒⢿⡼⠓⠒⠒⢿⢹⡗⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⢤⣄⣀⣈⣉⣡⣈⣀⣀⣈⣀⣀⣀⣈⣉⣡⣤⡭⠴⠞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⡆⠀⢀⡭⢯⡉⠉⠉⣭⡍⣩⣍⠉⠀⢠⢤⡄⢸⡿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣧⢀⡞⠀⠄⢧⣀⡼⠣⠙⡁⢹⡀⠀⡟⠐⠙⠚⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣈⣉⣀⣁⣐⣀⣉⣀⣐⣀⣀⣂⣛⣚⣁⣈⣀⣂⣐⣀⣟⣀⡀
⠀⠀⠀⠀⠀⢀⣞⠉⠉⠉⣩⡭⢭⣉⠉⠉⠉⠉⠉⣩⡭⢭⣉⠉⠉⠉⠉⣩⠽⠿⢭⡉⠉⢳
⠀⠀⠀⠀⠀⢸⠛⠲⠶⠛⡁⠐⠀⠈⠳⠤⡤⠴⠚⠁⡒⠀⠉⠓⠶⠶⠛⠁⠀⡁⠀⠉⡙⢹⡇
⠀⠀⠀⠀⠀⢸⣄⠀⢀⣠⣥⣄⡉⢀⣂⣠⣈⡀⠠⠀⠁⢀⣨⣤⣤⣀⡀⠁⠀⣀⡤⠖⠒⢾⡇
⠀⠀⠀⠀⠀⢸⣏⣉⣉⣤⢤⣌⣉⣉⣡⠤⣤⣉⠛⠒⣛⣉⡤⠴⠦⢬⣉⣉⣉⣩⡴⠖⠚⢺⠇
⠀⠀⠀⠀⠀⠀⣧⠉⢉⢀⡀⣤⢉⡉⢀⢠⡀⢩⠉⡉⠉⠁⡀⢰⠀⡀⣈⠉⣉⠀⣀⠀⡄⢸
⠀⠀⠀⠀⠠⠤⠿⠶⠾⠾⠷⠿⠴⠧⢼⣼⣧⣼⣤⣷⠼⠦⠷⠾⠶⠷⠿⠶⠿⠶⠿⠴⠷⠟⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⢹⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⡇⠀⠀⠀⠀⠀⢀⡾⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡞⠀⠀⠀⠀⠀⠀⠹⣄⣀⡼⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡭⣭⣀⠀⠀⠀⠀⠀⢠⣶⣛⣩⣤⡀⠀⠀⠀⠀⠀⢠⡤⠷⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣍⡁⠛⢻⠀⠀⠀⠀⠀⠠⣧⣉⠉⢸⡇⠀⠀⠀⠀⠀⢸⡟⠛⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠙⠛⢻⠀⠀⠀⠀⠀⠀⡇⠀⠙⢻⡇⠀⠀⠀⠀⠀⢸⡋⠛⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠶⣤⣼⠁⠀⠀⠀⠀⠀⡏⠑⠦⣼⡇⠀⠀⠀⠀⠀⢸⠗⣤⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢸⡅⠀⠀⠀⠀⢠⣇⠀⠀⠐⡇⠀⠀⠀⠀⠀⢸⠁⠀⠉⢹
⠀⠀⠀⠀⠀⡴⠋⠙⠲⣄⠀⢀⡤⠤⠤⠾⣿⡲⢤⣼⠧⠒⠒⠒⠦⣤⡏⣱⠖⠚⠛⠒⠲⣄⠀⣠⠼⠷⢤⣄⣼⣄⡤⠴⠒⠦⣤⡀⣠⠤⠤⢤⡀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠉⣿⠏⠀⠀⠀⠀⠈⡿⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢸⡏⠙⠲⠶⠖⠲⢤⣄⡀⢀⣀⣤⠶⣄⡀⠀⠀⠀⢀⣠⠴⣦⡀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⢀⠾⣤⡀⠀⢀⡼⠉⠳⠶⠶⠖⢿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠑⠋⠉⠀⠀⠈⠑⠲⠶⠶⠞⠉⠀⠉⠓⠲⠚⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣀⣀⠀⢸⡇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⡸⠋⠉⠁⠙⠻⣇⣰⠟⠉⠀⠀⠀⠉⠙⣆⣀⡴⠞⠛⠛⠉⠙⠛⢦⡀⢀⡴⠛⠋⠉⠈⠉⠛⢦⣀⡴⠖⠛⠛⠓⠶⣄⣀⡴⠚⠛⠛⠛⠳⢦⣸⡶⠞⠛⠲
⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠟
⠙⢦⣄⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣠
⠀⠀⡏⠉⠉⠐⠋⠉⠓⠶⢤⣤⣤⣤⡤⠖⠚⠢⣤⣀⣀⣀⣀⣀⣤⠶⠚⢶⣀⠀⠀⠀⠀⢀⣠⠾⢧⣀⡀⠀⢀⣠⡞⠛⢦⣤⣀⣠⡴⠃⠈⠙⠒⠒⠋⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠑⠓⠒⠒⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡇
⠀⠀⡇
⢀⣠⢧⡤⣄⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀
⣞⠁⠀⠀⠈⠙⢦⣠⠞⠋⠉⠉⠉⠙⠓⣦⡴⠚⠉⠉⠁⠀⠈⠉⠳⣄⣠⠞⠉⠀⠀⠀⠀⠉⠳⣤⡜⠋⠉⠉⠙⠳⣄⢠⡞⠋⠉⠉⠉⠙⢳⣤⠞⠉⠉⠉
⣏⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉
⠈⠳⠶⣤⣄⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡴⢶⣄⠀⢀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠲⠶⠶⠶⠖⠉⠉⠛⠶⠦⣤⣤⣤⡴⠶⠋⠉⠻⣦⡀⠀⠀⢀⣤⠴⠋⠳⣤⣄⣀⣤⡴⠋⠉⠳⠶⠦⠶⠞⠁⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⢀⣿⠹⣇⠀⠀⢠⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠘⣧⣤⡟⠀⠀⢸⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⣬⣿⣤⠀⠀⣀⣹⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣻⣿⠀⠀⢠⣿⡴⣿⠀⠀⣿⣩⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⣡⣿⠀⠀⢸⣏⡴⣿⠀⠀⣿⡡⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢠⣿⠀⠀⢸⡏⡰⣿⠀⠀⣿⢁⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⢉⣿⠀⠀⣸⣟⣀⣿⣀⣀⣿⣁⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⣦⣤⣤⣤⣤⢦⣤⣀⣀⡀⠀⠂⠀⠀⣀⣀⣨⣤⡶⢦⣤⣤⠶⠶⠾⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠒⠒⠉⠳⠤⠤⠔⠋⠻⣍⣛⣛⡿⠛⠻⢍⣉⣀⡤⢊⡁⠑⠢⠔⠊⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣤⣤⣬⣤⣤⣌⣀⣬⣥⣤⣤⣄⣐⣀⣀⣒⣀⣀⣀⣀⣀⣤⣥⣤⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣿⣤⣧⣀⣍⡀⣹⠉⢹⠁⢹⠀⢹⠉⢹⠉⢹⠉⢹⠉⢹⠉⡏⢹⢀⣇⣰⣼⡷⠾⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⢠⡄⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠳⠿⠶⠾⠶⠾⠶⠾⠶⠾⠶⠿⠾⠛⠛⣛⠉⠉⠀⠀⠀⠀⠛⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣠⣤⠀⢴⠄⣀⡀⠁⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢀⢀⡀⠉⠠⠀⢀⣿⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠻⣤⣤⡴⠟⠛⠛⢷⣤⣀⣀⣠⣴⠿⢷⣴⣦⡈⠈⠋⠀⣀⣴⠟⠛⠛⠶⠶⠶⠟⠁⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠄⠀⠀⠀⠀⠀⠃⠀⠀⠉⠉⠁⠀⣀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠠⠄⠀⠀⠀⠀⠀⠈⣁⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⣤⣤⣄⣀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⣀⣀⣠⣤⣤⢶⣶⠟⠛⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣷⣀⣠⡿⢿⡉⠛⠛⣿⣿⠲⠶⠶⣶⡶⠶⢶⣶⡶⠞⠛⢻⣿⠛⠉⣹⠿⣧⣀⣸⣟⣷⣾⠿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⠛⠛⠳⠾⠿⢶⣾⣯⣽⣦⣤⣾⣋⣷⣤⣾⣍⣿⣦⣴⣿⣽⠷⠾⠿⠟⠛⠛⠉⣉⣠⣤⣶⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⢿⡟⠶⣶⣶⣤⣤⣤⣤⣤⣈⣉⣉⣉⣉⣉⣉⣀⣀⣠⣤⣤⣤⣤⣴⣶⠶⢻⡟⢿⣁⣿⠙⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⡈⣷⡾⠃⢸⣇⣴⠏⠹⣇⢠⡿⠙⣯⢉⣽⠋⢻⡍⣼⠏⠹⣇⣼⠃⠘⣧⣾⠁⠈⣿⣇⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢦⣤⣿⣃⣀⡀⣿⡟⠀⠀⢻⣾⠃⠀⠈⣿⡏⠀⢀⣻⣿⣀⣤⣼⣿⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⠀⠀⠀⠀⠀⠀⣠⠎⠱⡄⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠈⡆⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡋⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠜⠁⠀⠀⠀⠀⢀⣑⣒⡊⠀⠀⠀⠀⠀⠀⠀⠱⠄⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠯⠥⢶⡄⠀⠀⠀⠀⣿⡉⠒⠚⡇⠀⠀⠀⠀⠀⢸⠳⠮⠽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠢⢼⡇⠀⠀⠀⠀⣿⠈⠉⠓⡇⠀⠀⠀⠀⠀⢸⠙⠒⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⣿⣀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠤⢤⡇⠀⠀⠀⠀⣿⠈⠙⠒⡇⠀⠀⠀⠀⠀⢸⠉⠲⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠧⠤⠔⠒⠓⠒⠒⠒⠒⠋⠀⠀⠀⠉⠈⠀⠐⠒⠒⠛⠒⠒⠂⠾⠤⠤⣀⣀
⠀⠀⢀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠤⣄
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⢰⠁
⡇⠀⠀⠀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠑⢦⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠦⡀
⢧⣀⢀⡠⠎⠈⢧⡀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠑⠤⣀⣀⢀⣀⣀⡠⠔⠋⠀⠀⠀⠀⠁⠀⠈⠒⠤⠤⠤⠔⠉⠀⠀⠈⠓⠤⠤
⠀⠀⢹⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠶⠶⠦⠤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠲⠤⣀⠀⠀⠀⠀⢸
⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⢹
⠀⠀⢸⣀⡠⠤⠖⠒⠒⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠀⠀⠈⠑⠦⢄⣀⣀⠤⠤⠴⠒⠒⠒⠒⠒⠢⢄⣀⣠⠤⢚
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⢀⡸⠆⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠒⠚⠢
⠀⠸⡀⠀⣰⠋⠁⠉⠦⠒⠒⠒⡤⠖⠒⢤⠤⠒⠢⡤⠔⠒⢤⡠⠔⠒⣤⠴⠒⢤⠤⠤⢤⡠⠔⠢⢤⠒⠒⠒⣎⠁⠀⠈⣆⣀⠴
⠀⠀⠈⠉⠉⠢⠤⠔⠳⣄⣀⡠⢇⣀⢀⡸⣄⠀⣀⣧⣀⢀⣠⢆⡀⢀⣧⣀⠀⣧⡀⠀⢀⣇⠀⢀⡸⢇⣀⣠⠞⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡠⠀⠀⡀⠀⢀⠀⠀⢀⢀⠀⢀⣶⠆⠀⠀⠀⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⠀⠰⢡⢣⢂⠎⠀⡘⢸⡄⠀⢸⢸⠀⣼⠏⢀⠀⡄⡄⠀⣏⡏⡀⠀⣀
⠀⠀⠀⠀⠀⠠⡀⢀⡀⠀⠀⠀⠀⠘⡜⠀⠀⠀⠏⠎⠀⢀⠃⢻⠀⠀⠘⠀⠰⠏⣰⠃⠀⣧⡇⠸⡻⡰⢁⢞⡁
⠀⠀⠀⠀⠀⠀⣈⠢⡙⢦⠀⠀⢀⠀⠘⠀⣿⡀⠀⠀⠀⢸⠀⠋⠀⠀⢀⣴⠀⠀⠁⠀⠀⠃⠀⢀⡁⠰⡣⠋⠀⠀⠀⢀⡤⣚⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢌⠳⠅⢀⣿⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣮⡟⠀⠀⠀⡄⠀⠀⠀⣞⡇⠈⠁⠀⠀⢀⠐⠉⢈⣁⡠⠤⠄
⠀⠀⠀⣀⣐⠢⠤⣀⡀⠙⠂⢘⣼⠀⠀⠀⡞⣷⠀⠀⠠⢳⡀⠀⠀⢰⢻⡆⠀⠀⢰⢹⡀⠀⢠⣾⡆⠀⠀⠀⢰⣻⠀⠈⠐⠒⠒⠘⠃
⠀⠀⠀⠀⠈⠉⠓⠒⠪⠄⠀⣴⣷⡆⠀⠀⡇⣿⠀⠀⠀⢻⡇⠀⠀⢸⢀⡇⠀⠀⠈⣾⡀⠀⢸⠀⡇⠀⠀⢠⣾⡇⠀⠐⠒⠲⠶⠭⠭⢥⣄⡀
⠀⠀⠀⠀⣒⡒⠫⠭⠙⡁⠀⢻⠀⡇⠀⠀⡇⣿⠀⠀⠀⡓⣿⠀⠀⢸⢸⡇⠀⠀⢸⠋⣿⠀⢸⠀⡇⠀⠀⡸⢰⡇⠀⠲⠭⣒⡢⠄
⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⢸⠀⣷⠀⠀⡇⢿⣀⣠⠬⠄⣿⠤⠤⢾⢘⡧⠤⠤⢼⡆⣿⣀⣸⠄⡇⠀⠀⡇⣸⠀⠀⠀⠀⠀⠉⠓⠲⠤
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡼⡀⢿⠉⠹⣳⣞⡦⠀⠀⡇⣿⠀⠠⡞⣼⢷⡄⠀⠘⡇⣿⠀⡸⠀⣏⡒⢲⠁⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣠⣇⣸⣄⠀⠈⠉⠀⠀⠀⡇⢸⠀⠀⠉⠉⠉⠀⠀⠀⡇⢹⠀⠑⠿⠷⠃⣸⢰⡇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⠞⠗⠋⠀⠀⠀⠀⠀⣖⠣⢾⣦⠀⠀⠀⠀⠀⠀⢮⣳⣞⡷⠀⠀⠀⠸⢜⣺⠽⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣃⡤⠞⡗⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⣀⣤⣀⡀⠀⠀⢠⠖⢦⣀⡟⣦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠑⠛⠉⠉⠑⢄⣀⡤⠞⠋⠉⠑⢄⣀⣠⡾⠁⠉⠁⠉⠛⠉⠀⠀⠉⠳⢤⡼⠀⠀⠀⠀⣻⣢
⠀⠀⠀⠀⠀⠀⠀⠘⣟⠣⣀⠀⠀⠀⠀⢀⣀⢶⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⢦⣠⠀⠀⢀⣀⣤⣾⢿⠁⡠⠤⠤⢤⣀⣀
⠀⠀⠀⣠⠴⠒⠋⠉⣸⠉⠻⢝⣓⡒⢖⣼⠂⠈⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠮⡁⠀⢯⡽⠿⠻⠟⠉⠁⢸⡧⡄⠀⠀⠀⠀⠈⠙⢦
⠀⠀⣞⣁⣀⠀⠀⠀⢝⣄⡀⠀⠀⠈⠉⠉⠚⠑⠻⠦⠯⣽⣒⣒⣒⠶⡶⣖⢒⡒⣏⡭⢽⠴⠲⠉⠉⠁⠀⠀⠀⠀⢀⡼⡣⠇⠀⠀⠀⠀⣀⣀⡼
⡠⠊⠉⠉⠉⠀⠀⠀⠀⠙⠼⣶⡤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠙⠛⠋⠉⠛⠁⠀⠀⠀⠀⠀⢀⣀⠤⣶⣮⠽⠋⠁⠀⠀⠀⠀⠈⠉⢙⡇
⠙⠦⠤⠤⡤⠶⠃⠀⠀⠀⠀⠈⠉⠓⠽⠿⣗⢦⣤⣀⣤⠤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⣤⣴⣒⣺⣭⠽⠛⠛⠁⠀⠀⠀⠀⠀⢠⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠳⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠙⠓⠚⠛⠓⠋⠙⠛⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠙⢯⣁⣀⣀⠀⣀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢽⣷⠤⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠳⠦⣤⣤⣤⣀⣤⣤⡾⠗⠀⠀⠀⠀⣠⣾⠃⠀⠀⢀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡠⡠⢀⢀⢀⠀⡀⡀⢀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠠⠂⠈⠀⠀⠀⡀⢈⠀⠀⠁⡀⠊⠄⠀⢡⣁⠂⠊⠊⠐⡁⢀⠀⢂⠀⢀⡀⠢⠊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⢂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⡈⠐⠈⠀⠀⠀⠆⠱⡀⠀⠀⠀⡈⠱⡀⠀⠀⠀⠜⢣⠀⠀⠀⡌⠱⡀⠀⢘⠈⣆⠀⠀⠀⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠄⢀⠇⠀⠀⠀⠄⠇⠅⠀⠀⠸⡀⠈⠇⠀⠀⠇⠀⠑⠀⠀⢐⠘⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⡡⢂⠀⠁⡴⠂⠐⢠⠀⠀⠀⠀⠓⠀⠀⡀⠀⠌⠚⠢⠀⢀⠐⠛⢠⠁⠐⠉⠹⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠊⠀⢸⠀⢰⣤⠡⡊⠀⠀⡲⢽⠠⡪⠐⠴⠀⠠⠀⠈⡄⢠⢸⡆⣳⢀⡀⡄⢀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠧⠻⠈⠂⠀⠦⢰⢸⠀⠐⠄⠨⠠⠀⠀⠕⡇⠜⡇⠂⠐⠸⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢹⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⢨⢤⠀⠀⡇⠸⡇⠀⠘⠨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⡆⠀⢸⡀⢀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠈⢈⠁⠀⣀⢈⢉⠉⡁⡈⡩⠈⠉⡉⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⡀⢒⣈⡀⠀⠀⠠⠂⠔⣁⣊⣊⣊⣀⠁⠐⠔⠡⠢⠀⣂⣊⣈⡐⠐⠀⠌⠄⠄⢂⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠈⠉⠂⠈⠓⠒⡰⠊⠉⠁⠑⠀⠀⡉⠉⠓⠒⠒⠒⠓⠁⠀⠲⠋⠉⠑⠂⡮⠉⠉⢉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠶⠷⠶⠶⡖⣖⡶⠿⢶⣶⣶⢶⣶⢶⣶⡖⣴⡶⣖⢢⠯⠯⠽⠿⠭⡟⠿⠽⠽⠿⠏⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠈⠀⢠⡄⠈⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢂⠀⠀⡀⠄⢐⠆⠂⣀⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣥⠤⠠⢤⢤⣄⢠⣭⠤⡤⡬⠥⠤⡤⢠⣤⣐⣂⢀⢤⢤⢤⢽⠉⣉⡉⢹⣭⡉⠙⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡉⠉⠉⢩⠉⠉⠉⠩⠈⠉⠉⠉⠩⠁⠉⠩⠉⠉⠙⠛⣉⠉⢙⣩⣉⣉⣛⣝⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠒⠀⠐⠀⠈⠉⠀⠀⠀⠀⡉⠁⡈⠉⠁⢉⠀⡁⢈⢉⠉⢀⢉⡩⠄⠄⡉⡈⣉⢉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠧⣀⡹⠦⣄⠠⢑⡴⠦⠞⠉⠳⢌⣠⠷⢢⡐⠐⡡⠖⣄⠁⢠⠞⠙⠳⣬⢐⠝⡇⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⡘⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⢧⣋⠞⠁⠀⢀⠀⣀⣀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⡀⠀⣀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠑⠀⠑⠁⠊⠓⣐⣓⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⡆⢠⢒⣔⢢⠀⠜⣩⡍⠍⢉⠤⡤⢌⠀⠩⢭⠍⡍⢩⢭⡬⢍⠉⡕⡬⢢⠀⠔⣦⠒⠰⣞
⠀⠀⠀⠀⠀⢀⡀⣀⣘⢋⡀⠈⠊⠩⠃⠀⠈⠟⠿⠃⠀⢪⡱⠞⠀⠐⠒⣴⠃⠈⢟⣲⠏⠀⠁⠉⠞⠀⠩⠙⠂⠀⠹⠀⡀⣠⡀⡀⡠⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠐⠉⠛⠉⠛⠉⠛⠙⠛⠰⠒⠒⠒⠲⠒⠶⠒⠶⠲⠶⠰⠶⠴⠖⠶⠖⠶⠒⠲⠂⠜⠫⠋⠑⠉⠊⠈⠁⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣇⠀⠀⠀⠀⠀⠀⠀⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀⣸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⠘⡆⠀⠀⠀⠀⠀⢠⡟⠀⠘⡆⠀⠀⠀⠀⠀⣰⠃⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⠸⠃⠀⠀⠀⠀⠀⠈⠳⣽⠴⠃⠀⠀⠀⠀⠀⠘⠆⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠳⡄⠀⠀⠀⠀⠀⠀⣴⠛⣦⠀⠀⠀⠀⠀⠀⢠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡄⡗⠀⠀⠀⠀⠀⠀⡇⣠⣿⠀⠀⠀⠀⠀⠀⣿⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⢻⠀⠀⠀⠀⠀⢰⡇⣠⡟⠀⠀⠀⠀⠀⢀⡟⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢸⡀⠀⠀⠀⠀⢸⡇⣁⡿⠀⠀⠀⠀⠀⢀⡇⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣿⠶⠾⠶⠶⠶⠶⠶⠾⠷⠿⠿⠶⠶⢶⣶⣶⣼⣧⣭⣿⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡁⣄⠀⣰⡟⠁⠀⠉⠻⣦⡐⠦⠤⠤⠖⣡⣴⠟⠉⠉⠉⠻⣦⣄⠐⠤⣤⣤⡤⠔⢀⣴⠟⠉⠉⠻⣦⡀⢠⢆⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠷⣶⡶⠟⠀⠀⠀⠀⠀⠈⠛⠻⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠾⠛⠁⠀⠀⠀⠀⠈⠻⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠛⠛⠛⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠶⠈⣿
⠀⠀⠀⠀⠀⠀⣠⣴⠿⢷⣤⣤⣤⣤⣤⣤⡶⠾⠛⠛⠛⠛⠛⠛⠶⣶⣤⣤⣤⣤⣴⠶⠾⠛⠛⠻⠶⢦⣄⣀⢀⣀⣠⣤⣤⣴⣿⣀
⠀⠀⠀⠀⠀⠰⣿⠀⣀⣀⡀⠀⢉⣉⣁⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣉⣉⡀⠀⣀⣀⣀⣀⠀⠀⢀⣉⣛⠛⠋⠉⣀⣀⣀⢈⣿
⠀⠀⠀⠀⠀⠀⠙⠷⣦⣭⡶⠾⠛⠉⠉⠙⠻⠶⣦⣭⣥⡶⠶⠟⠛⠋⠉⠉⠉⠛⠷⠶⣮⣭⡶⠶⠟⠛⠉⠙⠛⠷⠶⢾⣿⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠐⠶⠶⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠶⠶⠶⠖⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠶⠶⠖⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠟⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠈⡌⠀⠀⡈⠙⠀⠀⠙⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠆⠀⠆⣄⡀⠀⡀⠹⠀⠘⠠⣄⠀⢠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠆⠀⠆⣄⡃⠀⡉⠛⠀⠰⠤⣄⠀⢀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠐⢦⡠⡄⠀⣃⢴⡏⠛⣦⣴⠠⣴⡆⢨⢉⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢾⣥⣡⣷⣿⠐⢼⠷⣇⠉⡿⠾⠗⠾⠷⢿⠄⣸⣿⣿⢈⣻⣷⣾⣲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣰⡏⠥⠢⠈⠐⠾⠀⣁⠙⡇⠀⠓⠂⠀⠐⠄⣼⠀⢠⡄⢥⣌⣹⡷⢌⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⣇⣄⠂⣁⣀⢆⠀⡉⢻⣣⡀⠀⠀⠀⠀⠒⡑⢀⡀⢦⣈⣯⣉⣿⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠆⠱⣼⣶⣷⡔⣦⣑⢮⣷⠷⠌⠶⡿⠷⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡁⠸⠘⠄⡸⠃⠀⠀⣼⢧⠀⠀⣶⢷⠀⢠⡶⠀⠀⢠⣿⡿⠀⣴⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠐⠂⠐⠃⠀⠀⠸⡧⠚⢀⡸⢁⠀⣀⠀⡏⠄⢀⠾⠳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠸⠁⠀⠀⠁⠈⠲⠏⠀⡇⠀⠀⠀⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠅⢻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣤⣿⠐⠀⣀⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⢀⡀⣀⠤⡄⠀⠛⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠹⣷⠀⠀⠀⣼⡟⠀⢻⣧⠀⠀⠀⣾⠏⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣠⣿⠃⠀⠀⠻⣷⣤⣾⠟⠀⠀⠘⣿⣄⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣛⡁⠀⠀⠀⢠⣬⣭⣥⡄⠀⠀⠀⢈⣛⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠀⠀⠀⢸⣿⠉⣿⡇⠀⠀⠀⣿⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣀⣀⣸⣿⠀⣿⣇⣀⣀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡇⢸⣿⠛⠛⠛⢻⣿⣀⣿⡟⠛⠛⠛⣿⡇⢸⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡉⠀⠿⠿⠿⠿⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠿⠿⠿⠿⠀⢉⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣾⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⢿⣧⠀⠈⠉⢉⣿⣏⠉⠉⠉⠉⠉⣻⣿⡉⠉⠁⠀⣼⡿⣷⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠿⣶⣶⠿⠋⠻⣷⣤⣤⣤⣾⠟⠙⠿⣶⣶⠿⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠉⠛⠻⠿⢶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠿⠟⠛⠉⠀⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⣿⣶⣶⣤⣤⣤⣄⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣠⣤⣤⣤⣶⣶⣿⠛⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣿⣧⠀⠀⠉⠉⠉⠉⣿⡟⠛⠛⠛⠛⠛⠛⠛⢻⣿⠉⠉⠉⠉⠀⠀⣼⣿⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠉⢻⣧⣀⠀⠀⢀⣴⡿⣷⡀⠀⠀⠀⠀⠀⣠⣿⢿⣦⡀⠀⠀⣀⣼⡟⠉⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠈⠻⢷⣦⣤⣴⡾⠟⠁⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉

⠀⠀⠀⣦⠀⣴⠀⢀⣦⠀⢠⣶⣦⡄⣴⣶⣤⢰⣆⢀⣶⠀⠀⢰⡶⢶⡄⢰⡄⣶⣶⣄⠴⣶⡶⠆⣶⠀⣴⡄⣶⢶⣄⠀⢠⣦⢰⣆⢀⣶
⠀⠀⠀⣿⠶⣿⠀⣾⣻⣧⢸⣧⣼⠇⣿⣧⡿⠀⢻⣿⠃⠀⠀⢸⡷⢾⡇⢸⡇⣿⣤⡿⠀⢸⡇⠀⣿⠶⣿⡇⣿⠀⣿⢂⣿⣻⣆⢻⣿⠃
⠀⠀⠀⠛⠀⠛⠘⠋⠉⠛⠘⠋⠁⠀⠛⠋⠀⠀⠈⠛⠀⠀⠀⠘⠛⠛⠃⠘⠃⠛⠉⠛⠀⠘⠃⠀⠛⠀⠛⠃⠛⠛⠋⠘⠋⠉⠛⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡇⠀⠀⡼⢦⠀⠀⠀⢰⡆⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⡎⢹⡀⠀⠧⠬⠇⠀⠀⣏⠘⡆⠀⢠⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠀⠀⠀⠳⣞⠀⠀⢸⣻⠀⠀⠀⢈⣻⡁⠀⠀⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⠀⠀⠀⢸⢹⠀⠀⢸⣿⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⣠⠤⢸⣼⡀⠒⢺⣿⠒⠒⠒⠈⣿⡇⠒⠲⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⣿⡅⠀⠀⢸⣿⡇⠀⠀⠉⠀⠀⠀⠀⡏⡇⠀⠀⠉⠁⣀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣉⣡⡤⠴⠒⠋⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⠤⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⢀⡏⠀⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠁⠀⠀⠹⣄⠀⠀⠀⠀⣠⠞⠁⠀⠈⢳⡀⠀⢀⡼⠁⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⠀⠀⠀⠈⠓⠦⠴⠚⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⡤⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠙⠓⠲⠤⠤⢤⣄⣀⣀⣀⣀⣀⣤⡤⠤⠶⠒⠋⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⣤⢠⡄⢠⡀⢀⣠⡀⠀⣀⢠⡀⢀⠀⠀⠀⣠⢤⡀⢀⢀⣠⣀⢠⣤⠄⣤⢠⡄⡤⣄⠀⣴⢠⡀⢠⠄
⠀⠀⠀⣿⢼⡇⣾⡇⢸⡤⠞⣸⣉⠇⢳⠏⠀⠀⠀⡧⣴⠃⢸⢸⣇⡼⠀⣿⠀⣿⢾⠁⡇⣸⢠⣿⡇⢱⠏
⠀⠀⠀⠋⠘⠰⠋⠓⠸⠀⠀⡟⠀⠠⠏⠀⠀⠀⠀⠷⠞⠁⠸⠘⠋⠳⠄⠛⠀⠃⠈⠀⠋⠁⠚⠀⠡⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢷⠀⠀⠀⠀⠀⠀⡟⠈⣷⠀⠀⠀⠀⠀⠀⢰⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠀⠀⠀⠀⠀⠘⣇⣀⡿⠀⠀⠀⠀⠀⠀⢸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⡀⠀⠀⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⡄⠀⠀⣿⠀⠀⠀⣼⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠿⠶⠶⠾⠿⠿⠷⠶⠶⠿⠶⠶⠶⠿⠿⠿⠶⠶⠾⠷⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣴⠶⢦⡀⠀⣴⠶⣦⠀⠀⢠⡟⠉⠻⣆⠀⣼⠏⢿⡀⠀⡿⠙⣧⠀⢰⡿⣆⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠃⠀⢸⡇⢀⡿⠀⢸⡇⠀⣼⠁⠀⠀⠙⠶⠏⠀⢸⡇⢸⡇⠀⠘⠷⠾⠃⠙⢧⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⠞⠁⠀⠀⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡀⣀⢀⣀⢀⣀⣀⢀⡀⢠⣀⢰⢀⣀⣄⣠⣀⢀⣠⢀⣀⢀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠓⠟⢹⠾⢻⠿⠋⡿⠁⠘⠞⠛⠛⠁⠳⠛⠘⠙⠾⠒⠟⢸⠏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⣀⢠⡀⢀⢀⠀⡀⡀⢀⡀⡄⢀⢠⡄⣀⡀⡤⣀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠘⠁⠀⠁⠁⠈⠁⠁⠀⠈⠀⠉⠀⠁⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⠀⣠⠤⠼⣤⠏⠘⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠘⡄⠀⢈⠑⠢⠀⡠⡊⠀⠀⠀⠙⣴⣰⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠨⡙⣢⠵⠄⠀⠑⣀⠞⡄⠀⠀⠀⢀⠁⡘⣧⠤⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢼⠁⢈⡴⠆⠰⢇⠀⠐⠀⠘⢀⢤⡒⠂⢼⣿⡙⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠙⡿⠾⠷⠿⡄⠉⠈⢫⣌⣁⣨⣥⣾⡀⠀⠁⣼⠇⠉⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠫⣁⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠈⠓⠂⠉⠓⠚⠛⠓⠊⠀⠀⠀⠊⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠱⡀⠀⡼⠛⠉⠙⢳⠀⠀⢠⡶⠛⠉⠙⢏⠁⢠⠞⠉⠙⣦⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠿⣖⡲⡇⢰⣇⡀⠀⠀⡈⠀⠀⢾⡀⠀⠀⠀⣸⠀⢸⣤⣤⠶⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡇⢸⠟⠋⠉⠉⠙⠤⠤⠞⠙⠛⠋⠩⢽⠀⢸⠒⠚⠉⣻⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡁⠂⣴⢁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣀⣤⣴⣿⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡀⠀⠀⠑⠶⠞⠋⠉⠉⠉⠀⠀⠒⠒⠂⠈⠉⢻⣻⡄⠘⢯⠟⠛⠉⠉⣾⡟⠻⢶⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠫⠻⢕⣿⣿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⣧⣀⣸⣀⣠⡴⠟⣻⢿⣧⠀⠀⠛⢦
⠀⠀⠀⠀⠀⡞⠁⠀⢰⣿⣟⠊⡠⠤⣌⠉⠑⠒⠒⠲⠶⠦⠤⠤⠤⠤⠶⠶⠖⠛⠛⠛⠉⣉⡠⠴⠊⠕⢋⡟⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⣇⠀⠀⠈⠻⣙⡏⠀⠀⣸⡄⠀⠈⠓⠀⠀⠀⠀⠀⠤⠤⠤⠐⠒⠒⠊⢉⣽⠒⠲⣤⣠⠶⠋⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠘⢮⡢⡀⠀⠈⠙⠒⢶⠟⠛⠲⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡈⠉⠁⢰⣷⡀⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠺⢕⣠⢄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠙⠲⢛⣛⣭⣔⣮⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⣲⣤⣄⣤⡤⠤⠤⠤⠤⠤⠀⢴⣀⣀⣀⣤⡬⠽⠟⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⢠⠐⠈⡁⠁⠉⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⠀⠀⢫⠀⠀⠀⠠⠌⠀⠈⠀⠀⠀⠀⢂⠐⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢏⠀⠀⠀⠀⡀⠀⠓⠳⠢⡀⠀⠀⠀⠐⠆⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⠄⠀⠀⠀⢀⠀⡐⠃⠉⠂⠀⠽⡃⠀⠀⠀⠀⠀⡀⠠⢆⠰⠀⠈⠀⠀⠐⠁⡘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠦⣁⡇⠘⣠⣀⠀⡌⣅⠀⡀⠘⠀⠇⢀⠀⢠⠂⠘⠀⠀⠈⠀⡇⠈⠐⡎⠀⠀⠀⢊⠀⡀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⢀⣁⠉⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠁⠀⠀⠀⠉⣐⠴⠂⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠊⠁⠤⠨⠀⠀⠀⠀⠀⠂⠀⠀⠀⠅⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠊⠉⠁⣲⢄⡀
⠀⠀⠠⠀⠃⠑⠂⢠⡠⠚⠗⠂⢐⢲⠀⠀⠐⠒⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⡤⢠⠀⠤⣶⣶⠄⠀⠰⠁⢁⡨⠂⠀⡁⢡
⠀⢀⡀⠄⠀⠀⠚⠆⡐⠁⠀⠀⠈⣚⠄⠀⠀⠀⠀⢀⡆⠙⢲⠀⠀⠀⠀⡎⠀⠎⠐⢠⡀⠀⠀⠀⠀⠈⠀⠀⡤⠈⢱⡈
⠀⠀⠀⠠⣠⠌⠼⡀⠳⡄⠄⠀⡜⠁⠀⠀⠤⢠⡚⢁⠛⢆⡀⠑⠊⠑⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠂⠃⠀⠀⠀⠀⠰⡊⠀⡰⠆⢚⡙⠁⠐⠀⠈⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⢠⠄⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⠠⡂⠀⢠⠄⠀⠀⡀⠤⡄⠠⠄⡀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⢠⠀⣀⣀⢀⡀⣀⡀
⠀⡔⠃⢀⠌⡑⠄⠀⡈⠆⡀⢠⢲⠐⠃⠀⢘⣃⡄⠰⠈⠁⣾⠈⣰⠃⢄⠀⣿⢁⡽⣈⠇⢨⡇⣯⡋⣿⡇⡠⠂⠐⢄⡀⠤⢌⡀⠥⠄⣀⠄⠀⠠
⠀⢐⠀⠀⢈⢌⡄⠈⡥⠔⢀⠸⠐⠚⠀⠘⠌⢤⠠⢀⠬⡲⠍⠹⣤⡀⠤⠁⠻⠿⠿⣿⣿⡿⠿⠿⠿⠛⠀⠃⠰⢤⠸⢁⣰⡀⠑⣠⣀⠙⠀⣦⡄
⠀⠢⠸⢀⠂⠈⢥⠢⣒⢐⠈⠀⢘⠌⠊⠐⠤⠄⠊⠀⢨⡄⠃⢀⠘⠁⠀⡰⢄⢀⠀⠀⠛⠁⡘⡂⠀⢠⠄⠡⢈⣁⠠⠈⠒⢁⡌⠓⠉⡰⢀⣉⡁
⠀⠀⢀⠶⠀⡀⠤⢀⠀⠠⡢⠠⢊⢍⠢⠀⠀⢐⡄⠀⠉⡀⢀⠃⢀⠔⠈⠁⠁⠀⢰⠀⠀⢠⢜⠦⠀⢠⣜⠀⠀⠁⠀⠈⠒⠁⠈⠑⠋⠀⠈⠁
⠀⠔⠱⢆⠈⠁⠆⡐⡠⢒⣓⢔⠀⢡⠄⡇⡠⢚⠢⡀⠀⠀⠀⠀⣻⡈⠀⠤⠈⠀⢈⠓⢠⢸⠀⢸⠀⡧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢄⠃⠂⠄⠐⡰⠀⠅⣉⣈⢈⠘⠀⠊⠀⠰⠀⡰⠀⠰⠒⡂⠪⣈⠒⠒⢐⣀⠩⠄⠐⠁⢸⠀⢸⠀⢃⢈⡇⠠⠰⢆⠀⠸⠝⠀⠀⢉⠟⢄
⠀⠀⠈⠁⠀⠀⠀⢀⡂⠥⠥⠮⠀⠉⡝⠀⠂⠤⠄⠁⠀⠱⠁⠀⠀⠀⠀⣀⢸⡆⠄⠀⠀⠘⠂⠊⠀⣆⠠⠅⠀⠀⠁⠠⠀⠠⠀⠀⡖⡀⠈⠄
⢀⠄⠀⠠⡄⡀⠊⠀⣈⡢⠐⢙⠗⢖⠒⢒⠶⠒⠒⠒⠶⠒⠐⡲⠫⡀⠀⡄⠈⠁⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡄⠀⢠⠀⠀⠸⠁⢁⠂⡈⠄
⢘⣠⣤⣤⢸⠙⡀⣾⣿⣿⠁⠀⠀⠈⢧⠎⡀⠐⢄⠌⠀⠙⠴⠃⠀⠀⠲⠀⠀⡂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡐⠈⠑⠈⢱⠀⡇⣀⢀⠁⠀⠸
⠈⣿⣿⣿⠏⠀⠈⠚⠛⠫⣇⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢀⠠⠤⢐⠶⠒⠶⠤⢤⣀⠐⡀⠀⠀⠀⡸⠉⠀⠂⠱⣑⠀⡀⡄⠀⠀⠀⠀⢀
⠀⠈⢩⠉⠀⠀⠀⢀⠄⠀⢈⠷⡠⢀⣀⣸⢄⣀⠀⠀⠀⢠⡇⠀⠀⠀⠐⢠⠀⡄⢈⠀⢗⡈⠲⠒⠊⠀⠀⠀⠀⠀⠳⡀⠐⠁⠀⠄⠀⠘⠋
⠀⡀⢼⠤⡀⠀⠠⠃⠀⠁⡌⠈⠀⡁⠀⠈⠀⠀⢘⠀⠀⡖⠀⠰⠒⠐⠔⠠⠂⡇⢨⠀⠁⠂⠀⠀⡄⠀⠀⢀⠜⠀⠀⠑⠀⠀⠀⢄⠸⠄⠀⡠
⠀⠀⠈⠀⡀⡀⢨⠀⠀⠀⣨⠀⡎⠐⡠⡀⠀⠀⠔⢱⠀⠳⠀⢂⠀⢁⢀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠋⠈⢀⠒⠐⢂⠀⠀⠀⠂⠐⢄⠈⢄⡀
⠠⠤⠀⢰⠻⡀⠐⡄⠀⠀⡖⢀⣃⠋⠀⠂⠐⠂⢈⢘⠀⠈⠖⡔⠀⠀⠉⠈⠁⠀⠉⣄⠖⠀⢀⠀⠀⣀⣀⣘⠁⠀⠉⣄⣀⣀⠂⠀⢀⣀⡀⠁⡀
⠀⠆⢀⠋⠀⠱⠀⠡⢀⢀⠃⢎⠣⢌⡀⠀⠀⣀⠠⢜⡁⠀⠀⠈⠀⠓⠐⠒⠒⣉⣀⠀⠀⠀⠟⠂⠘⢿⡟⠁⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠐
⠀⠀⡞⠀⠀⠀⢣⠀⠉⠀⣀⣠⣁⠀⡔⠀⠀⠒⠐⢉⡀⢤⡔⢀⠀⠀⢀⠐⠨⠂⢀⠄⣉⢀⣠⡀⠀⡊⡅⠐⠀⠀⠐⠀⢸⠢⠀⠔⠒⠉⠉⣉⠢
⠀⢸⡀⡀⢀⡀⡀⡇⠀⣸⠀⠈⠁⠈⠋⢁⠀⠀⣠⠊⠄⠐⢀⢀⡀⡀⠐⡮⠥⣐⡥⠊⠀⠈⠚⠡⠀⠀⠁⣀⠀⠀⢀⣠⠁⠀⢠⡀⠙⠁⡂⠡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡄⠂⡂⡂⢨⠀⡰⠃⠀⠀⠂⣈⠜⠃⠀⠀⠡⠀⠀⢃⠀⢀⠄⠀⢖⠦⠀⣨⣀⣽⣼⣧⣠⡇⠀⠀⠁⠂⠀⠐⠀⠁
⠀⠀⠀⠘⠻⢃⡀⠀⠐⠦⠘⠐⡀⠂⠀⡈⠸⣥⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠑⠂⠬⠔⠁⠰⡷⢀⣀⣀⣈⣉⢙⣛⡋⠉⠁⢀⣀⡀⠀⣀⠠⢿⠂
⠀⣴⠋⢲⡶⣃⡱⢀⠀⠀⢀⢀⠀⠀⠀⢀⡀⠀⠀⠀⡸⠖⠉⠉⣣⡴⠒⠒⠀⠀⠀⠠⠀⠀⠁⢀⠇⠀⠞⠈⠀⠀⡅⡏⢉⠉⠈
⠀⡖⠝⠋⠉⣑⢡⠨⠁⢂⠀⡀⠀⠀⠰⡈⠈⠐⠀⢨⣑⠢⠤⢀⣀⠇⡀⠀⢠⠀⠀⠀⠘⠄⠀⠘⠋⠑⠇⠰⠐⠠⠃⠷⠛⠦⠀⠖⠀⠒
⠀⣀⠀⠨⠁⠀⠠⢨⠀⣠⣀⠀⠀⢀⠀⢓⢵⠃⠀⠀⢀⡀⠐⠀⠞⡰⠙⡄⠈⢱⠀⠀⡀⠀⢤⠀⢤⠀⡤⠀⠀⢀⢀⠀⢀⢀⢠⢀⡤⠀⢀
⠀⠈⠢⢴⠀⠤⠒⠊⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢣⡈⠁⡜⠀⠘⡐⠓⠒⡺⠀⠀⡀⠀⢈⠃⢸⠐⠐⠂⠀⢨⠅⠀⣨⠌⠀⠂⠀⠀⡀
⠀⠔⠒⠂⠀⠀⠐⠂⠠⢠⠣⠀⠀⠀⠀⠀⠃⠇⠀⠣⠀⠀⠐⠀⠀⠀⢙⠀⠀⡄⠀⠀⠀⢀⠈⠀⠀⠀⡀⠈⡀⣉⢀⡀⢁⠀⠈⠁⣀⡀⢀⡀⣀
⠀⠀⠀⠸⠉⠇⠀⡠⢀⠀⠀⠁⠀⠀⡄⠀⢀⣀⢀⣀⣀⣀⣀⣀⢬⠼⢆⢢⡰⠀⠀⢨⠀⡀⠀⢀⡃⡇⠀⠘⠁⢘⠂⢰⠀⠈⠂⠠⠡⠄⠀⡂⠁
⠀⠓⠀⠀⠀⠀⠀⠋⠀⠈⠒⠀⠈⠉⠀⠀⠘⠀⠈⠒⠒⠒⠒⠒⠒⠐⠀⠀⠀⠀⠉⠀⠁⠘⠁⠙⠀⠃⠀⠃⠀⠈⠀⠈⠈⠈⠁⠀⠀⠈⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⣈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡁⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠓⠯⠵⠚⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠉⢹⡟⠲⣖⠛⡏⠉⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢰⠋⠓⠲⠤⠾⡏⠢⣄⢹⡷⠤⠖⠚⠑⡆⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡤⠤⠞⠀⠀⠀⠀⠀⢟⠦⠀⣸⠀⠀⠀⠀⠀⠳⠤⢤⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠒⠒⢦⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⡴⠒⠒⠁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣄⡀⠀⠀⠸⣀⣠⠤⠶⢄⠀⠀⠀⠀⡠⠶⠤⣄⣀⠇⠀⠀⢀⣠⠟⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣧⠀⠀⠙⠲⠦⣄⣀⣀⠀⠀⠈⠓⠦⠴⠚⠁⠀⠀⣀⣀⣤⠴⠖⠋⠀⠀⣸⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣟⠓⠚⠳⡄⠀⠀⠈⠉⠉⠙⠛⠛⠒⠒⠛⠛⠋⠉⠉⠁⠀⠀⢠⠞⠓⠚⣻⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢿⡀⠀⠀⠹⣄⣠⠞⠳⡄⠀⠀⢀⡤⢤⡀⠀⠀⢠⠞⠳⣄⣠⠏⠀⠀⢀⡿⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠁⠀⠀⠳⣤⣤⠞⠀⠀⠳⣤⣤⠞⠀⠀⠈⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⡏⢷⡀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠋⠁⠀⠀⠀⠀⢠⡾⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡟⠶⠴⠞⢲⡄⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠶⠶⠖⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⢠⡖⠳⠦⠶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢻⡄⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢠⡟⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠹⣄⣰⠏⠀⠈⣧⠀⠀⠀⠀⣴⠚⠛⣦⠀⠀⠀⠀⣼⠁⠀⠹⣆⣤⠏⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⡼⠃⠀⠀⠘⢧⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⠌⠙⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠆⠞⢤⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠙⢂⢀⡖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠡⠀⠁⠀⠀⠀⢀⣀⡀⢄⠠⠤⡠⣤⠒⠲⡖⠂⣼⡃⢠⢤⠆⠤⣤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡁⢮⡽⣽⠵⣈⡓⢡⢶⢑⢇⡈⠊⠱⢎⢒⣃⠮⢜⣛⡍⠌⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠀⠀⢡⠀⣴⣡⠇⣈⡗⢡⠲⠑⠮⢟⡃⡰⡗⢿⡺⢈⡛⠧⠊⢰⢢⠓⡧⡀⢎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠆⠀⠀⠀⠡⣇⡤⡘⠒⡡⡑⠃⡐⡲⢧⡫⡈⡗⢄⠤⠘⣬⢲⢢⠈⣚⠀⣉⠚⡠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⡌⢱⠉⡉⡚⢠⢻⢡⢴⢭⠋⢫⡁⣚⠦⢝⡡⡯⠮⠼⢦⢠⣄⡭⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⢀⠂⠀⠀⠄⠙⢹⠀⣶⢥⡇⢸⡼⡁⢸⠀⠈⠑⠁⠀⠘⣬⠃⡶⢫⣸⢸⢸⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡠⠁⠀⠀⡐⠀⠀⢸⡄⠈⠉⠀⢸⠋⢯⣿⠀⠀⠀⠀⠀⠀⠉⠒⠁⢸⡐⢸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡠⠈⠀⠀⠀⡐⠀⠀⠀⠀⢣⡀⠀⠀⢸⠸⣵⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠈⢣⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡠⠀⠁⠀⠀⡀⠔⠈⠀⠀⠈⠶⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠠⠄⠂⢁⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠠⠘⢷⠐⠲⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣖⡐⠂⠀⠉⠀⠀⠀⠀⢀⡀⠠⠀⠂⠈⠀⢀⠠⠘⠀⢈⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠀⠀⠀⡀⠀⠀⢀⠄⠦⠴⠊⠉⠉


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

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠲⡦⠀⠀⠂⠤⠠⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠄⠀⠀⠀⠀⢦⣤⡶⠆
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠁⠀⡀⢢⡢⠀⠈⠀⢠⡀⠀⠾⠓⠆⠀⢰⠸⠁⠀⠀⡀⠀⠀⠀⢀⠰⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣅⠀⠀⠀⠀⢁⡼⠀⠁⣼⠁⠀⠀⠀⠄⢷⣄⠀⠀⣀⣴⡟⠀⠀⢠⠜⠁⠀⠀⠀⠀⠊⠀⠀⠀⡄⡘⠀⠀⠀⢀⠠⠘
⠀⢀⠠⠆⠀⠀⠀⢀⡷⡤⢠⣈⡀⠒⠖⠒⠛⠀⠀⢠⠇⢠⠀⠀⠆⠘⠢⡉⠙⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣧⡇⠀⢀⢀
⠀⡁⠀⠀⠈⠄⢀⣤⣠⣴⣾⣿⡿⠒⠀⠀⠀⠀⠀⡾⠀⠈⠀⠀⠀⠀⠦⠀⠱⡖⡲⠲⣶⠂⡀⠀⠀⠀⠀⠀⡙⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠣⠄
⠀⠁⠤⠤⠞⠀⠸⣿⠿⠿⠛⢉⠑⠁⠀⠠⠆⢠⡄⢠⡄⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⢀⠉⠀⠲⡀⢠⡀⠀⠀⣓⡀⠀⠁⠀⠀⠀⠀⠀⠸⠀⠘⣧⠀⢻
⠀⢀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠦⡀⠀⢐⠎⠁⠀⡈⠀⠀⠀⠀⠠⠬⠐⠀⠀⢠⡀⣤⡀⠀⠀⠀⣄⡁
⠢⠈⠥⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣄⣀⠀⠃⠀⠀⠀⡀⠀⠰⠞⠒⣆⠳⡄⠀⠀⠀⡠⠄⣤⡀⠀⠀⠀⡛⠀⠀⣞⠸⡃⠕⢸
⠀⠃⠀⡼⠻⣦⠀⠀⠀⠀⢂⠲⠙⠶⠠⠁⠉⠀⡀⠀⠠⠀⠀⢂⠀⠀⠀⠈⢧⠙⠆⢠⠊⠀⠀⣿⠇⠀⣤⣤⠀⠀⠀⢰⠀⠁⠈⢨⠀⢀⠄⠀⠀⠃
⠀⠀⠰⠛⡁⠘⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠠⠄⠀⠀⠈⠓⠒⠃⠀⠀⢠⡿⠀⠀⣉⣉⡇⠀⠀⠐⠄⡣⣠⠞⠀⠘⠀⠠
⠀⠀⠀⠀⠤⠄⢧⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠂⠀⠀⠀⢤⢨⠄⢲⢚⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⣤⠄⠀⠄⠀⠀⠀⠀⠄⢁⣲⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠂⡀⠀⢸⢐⠀⡠⠴⡕⢾⡄⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋
⠀⠀⠐⠀⠀⠀⠀⠙⠓⠛⠀⠀⢂⠀⠀⠀⠀⠀⠘⠧⠀⠘⢨⠈⠳⠊⢀⣸⠃⢀⠆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠐
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⣟⠋⠁⠀⠂⠀⢀⡿⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠰⣶⣶⣴⣶⡦
⠀⢠⡄⠘⠃⠀⠀⠰⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣽⠀⢠⡃⠀⣠⡾⠁⠀⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⡆⠀⢀⡀
⠀⠈⣗⣄⠀⠀⠀⠀⢫⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⣠⣄⠓⠒⠋⠀⠀⠁⠚⠛⠁⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠘⠒⠒⠒⠚⠀⠟⢻⣿⣿⣦
⠀⠀⢋⡈⣳⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⡎⠙⠏⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠤⠄⠀⠀⠋⠈⠉⡀
⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⢰⣲⠆⢠⠀⠐⢶⣯⠈⠛⠁⢀⣀⠄⠀⠤⠚⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢃⠀⠀⠀⠠⠂⠁⠢⠀⠀⠀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠙⠀⠘⠉⡀⠈⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣫⡇⠀⠃⠀⠀⣠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⢀⣀⡀⠀⣶⣖⠄⠐⠒⠂⠈⣁⠠⠼⠀⠀⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠂⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠠⠂⡀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⣠⡀⠀⠀⢀⠄⠒⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠂⠄⠀⠐⠚⠙⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠘⣀⡀⠀⠀⠈⢀
⠀⠉⢁⠰⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠂⠀⣸⣷⠟⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣷⣿⠀⠀⠸⣭⣡⠴⣼⠁
⠀⠉⠀⠊⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠠⠤⣤⠄⣄⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡏
⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠆⢰⠀⠀⢠⣋⡴⠃⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⣠⢲⢓⢀⡀⠀⠀⠴
⠈⢠⣴⣦⡀⠀⠀⠀⠀⠂⢀⡀⠒⠂⠉⢁⡀⠀⠀⠀⠈⠀⠀⢢⡄⠀⠀⠄⢀⠀⠘⡄⠀⠀⢠⠃⢰⠆⢀⠔⠲⠀⠀⠀⢹⢀⢂⠀⠃⠀⠀⠀⠀⠡
⠀⠘⣏⣼⠇⠀⠐⠠⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠘⢢⠀⠉⠀⠄⠁⠈⠀⠘⠇⠀⠀⠁⠀⣤⡶⢾⡿⠿⢿⠀⠀⠰⠒⠣⠼⠃⠠⠶⠤⣤⣤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠤⠤⠚⠁⢴⡒⢪⣹⡇⠀⠀⠀⠀⠀⠠⠜⠀⠲⢿⡟⠀⠀⠀⠘⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⢘⠖⠲⠘⠳⠚
⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⢁⠀⠂⠐⠁⣠⠦⠀⠐⠀⠀⠀⠀⣧⠀⠀⠇⢀⣟⢟⠣⠀⠀⠀⠁⢀⠀⠐⡂
⠀⠈⠈⠁⠀⠠⠂⠚⠉⠀⠀⠀⠀⠀⠀⠬⠱⠤⢀⠀⠀⡠⣦⠀⠀⠘⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⢀⣨⡤⡄⠒⠀⢀⡀
⠀⠀⠀⠀⢀⣤⠤⠀⠐⢠⠀⠀⠀⡄⠀⠀⠏⠊⣹⢇⢼⠉⢉⡇⠀⠀⠉⠁⢠⣶⣶⠀⠀⠩⣤⡤⣧⠀⠀⠠⠀⠀⠈⠑⠠⠆⡰⠔⠃⠀⠻⣿⣾⣿
⠀⠀⠀⠀⠈⢿⡀⠀⡠⠋⠀⠀⠀⠀⠈⠀⠀⠀⠍⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢄⣁⠤⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣁⣴⣁⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣿⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠿⠟⠛⠛⠛⠉⢉⣉⣽⡿⠿⠿⣿⣭⣭⣭⡙⠛⠛⠛⠿⠷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⢀⣀⡀⠀⢰⡿⠟⠛⣿⠋⠀⠀⠀⠈⢻⡇⠙⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⢰⡟⠛⠻⣶⣾⠇⠀⠘⣿⡀⠀⠀⠀⠀⣸⡟⠀⠿⠷⠿⠿⠿⠿⠷⢶⣦⣄⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢀⡀⠙⢿⣦⣤⣤⣾⠟⠁⠀⠀⣴⡾⢶⣦⣄⠀⠀⠈⣻⡇⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⢰⣿⡋⠁⠀⠀⢸⡟⢻⣧⠀⠀⢩⣿⠶⣶⣄⠀⠀⢻⣆⠀⠈⠙⠻⠶⠾⠟⠁⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⣿⡋⠛⢷⣦⣄⣀⠀⠀⠙⠻⢷⣶⣤⣾⠇⠀⢿⣆⣀⣼⡇⠀⠈⠻⢷⣤⣼⡿⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋⣻⡇
⠀⠀⠀⠀⠀⢹⣷⡀⠀⠈⠙⠛⠿⠷⣶⣦⣤⣤⣀⣀⣀⣀⡈⠙⠛⠋⠀⠀⠀⢀⣀⣈⣁⣀⣤⣤⣶⡶⠾⠟⠋⠉⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⣿⡋⠻⢷⣤⣀⡀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⣴⠿⠋⣿⡇
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠈⠙⠻⠷⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⡾⠿⠛⠉⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⣿⡟⠻⣶⣤⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣠⣴⡾⠛⣿⡆
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠉⠛⠻⠷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡶⠿⠛⠋⠁⠀⣠⣿⠃
⠀⠀⠀⠀⠀⣾⠟⠿⣦⣄⡀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⣀⣤⡾⠟⢿⡆
⠀⠀⠀⠀⠀⢻⣧⠀⠈⠙⠛⠿⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠾⠟⠛⠉⠀⢠⣿⠃
⠀⠀⠀⠀⠀⣾⠟⢿⣦⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠷⠶⠶⠶⠾⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⣀⣤⣾⠟⢿⡆
⠀⠀⠀⢀⣤⣿⣇⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡶⠿⠛⠉⠀⢀⣿⣧⣄
⠀⣠⡾⠟⠉⣼⡟⢷⣤⣀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⢀⣠⣴⠟⣿⡌⠙⠿⣦⡀
⣼⡟⠀⠀⠀⢿⣇⠀⠉⠛⠿⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠾⠟⠋⠁⢀⣿⠇⠀⠀⠘⣿
⢿⣆⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⢀⣾
⠈⠻⣷⣄⡀⠀⠀⠀⠉⠛⠷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋⠁⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠈⠉⠙⠛⠻⠿⠷⠶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⡶⠶⠿⠿⠛⠛⠉⠉⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⡶⠾⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠊⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢆⣀⢀⠈⠀⠀⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠤⠂⠀⠀⠀⢭⡄⠀⠀⠀⠈⣻⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠆⠀⠀⠀⠀⡃⡄⠀⠀⠀⠀⠌⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢂⠀⠀⠀⠀⡃⠆⠀⠀⠀⠀⠂⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠶⠖⠀⠃⠛⠀⠀⠀⠘⠙⠉⠉⠉⠛⠛⠉⠉⠙⠉⠁⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠘⠒⠲⢤⡄⠋⠀⠉⠂⠀⠠⠚⠀⠈⠀⠑⠂⠐⠊⠀⠉⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠤⠤⣀⡀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠠⢄⡀⠀⢀⡠⠖⠛⠛⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡖⠒⠒⠢⢌⡉⠐⠂⠉⠉⣀⡤⠖⠒⠂⠤⠈⢉⣁⡤⠔⠒⢲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣇⣀⢀⣀⣀⣈⡁⣘⣛⣋⡉⢀⠀⢀⣀⣀⣀⣀⣁⣀⣀⣀⣠⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣀⡀⠀⣀⠀⣀⠀⠀⠀⢀⣤⣀⡀⢀⣠⣀⠀⣀⣀⠀⠀⢀⣠⣄⣀⢀⣠⣄⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠖⠋⠁⠀⠁⠈⠀⠁⠉⠙⠚⠛⠉⠀⠈⠀⠈⠀⠀⠈⠀⠈⠀⠈⠈⠁⠀⠉⠈⠁⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠈⠱⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⠊⠉⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢘⠁⠘⡆⠀⠀⠀⠀⠘⠶⠎⠁⠀⠀⠀⠀⢰⡉⠉⡂⠀⠀⠀⠀⠀⠓⠖⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣈⣑⠊⢁⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣙⣊⡁⠀⢀⣠⠤⢄⡀⠀⢀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣏⣁⣀⣈⣙⡉⢀⢀⣈⡓⠞⣉⣀⣀⣠⣬⣽⣭⣤⣤⣤⣬⣷⢭⠤⠤⠤⠈⠿⠃⠤⠤⠼⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⢀⡤⣀⣀⡴⣄⠀⠀⠈⢩⡭⠤⣄⡀⢀⣠⠖⢀⡀⢀⡰⠆⠖⠒⢦⣀⣠⢤⠴⠦⠤⠴⠓⠤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠈⠑⠒⠒⠉⠀⠀⠀⠉⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠤⠤⢄⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡴⠆⠤⣀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣁⡤⠲⢄⡉⠲⠤⠔⠚⠉⣀⠤⣈⠓⢤⣀⡀⣀⣠⡴⠊⢁⣀⡈⠳⢤⡤⠞⠁⣠⠴⠢⣄⡑⠞⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠉⠓⠶⠴⠒⠋⠁⠀⠈⠑⠦⢌⣉⣉⣀⡠⠞⠋⠀⠉⠛⠒⠶⠚⠋⠁⠀⠀⠀⠉⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⡀⠀⢀⣀⣼⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⣁⡉⠉⠛⠋⣉⣀⠈⠙⠛⢋⣉⠉⠙⠳⠞⠋⠉⠉⠙⠳⠶⠋⢉⣭⡉⠛⠛⠉⣉⠉⠛⠋⣁⠤⡀⠈⠳⡄
⠀⠀⠀⠀⠀⢰⣖⣚⣒⣚⣓⣛⣒⣒⣚⣓⣚⣓⣒⣚⣓⣒⣛⣒⣒⣒⣛⣛⣛⣒⣒⣒⣒⣛⣒⣛⣒⣒⣛⣛⣛⣒⣚⣓⣒⣚⣓⣒⣛⣲⡆
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠰⢶⡤⠀⣤⡄⣤⠀⠐⣠⣀⠤⣄⣀⠤⠀⠄⠀⠤⠤⡤⢤⠠⠤⠄⣶⣄⣢⣴⢄⣰⡖⠶⠶⠒⠒⠒⢒⣲⣶⣶⡶⢶⣶⠶
⠈⡈⡡⠀⠠⠁⠢⠄⠜⣠⠴⢫⠥⡀⠉⠺⣩⢈⢳⣃⠜⡀⠀⠀⠈⠋⠁⠐⠚⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢰⠟⠻⠋⣴
⠀⡤⣠⠒⠉⠉⠉⠓⢤⠁⠈⠉⠁⢣⡀⠈⠐⠀⡰⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠍⣩
⠀⢧⠃⠀⠀⠀⠀⠀⢘⡦⡀⠀⠀⢀⠉⠒⠒⠎⠑⠁⠀⠀⠀⢨⢧⢻⢀⡈⢰⢴⡧⠇⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⢋⡏⣿
⠀⡿⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⢠⣶⢰⠉⡎⠀⢸⠁⠀⠀⠀⢀⣀⡀⠀⢀⡘⠒⢹
⠈⡇⠂⠀⠀⠀⠀⡼⠁⡰⢳⠀⠀⡸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣁⣁⡈⠉⠘⣀⣁⠀⠈⠀⠀⠀⠀⢎⠀⠈⢲⠋⢹⠀⢸
⠀⠞⠆⣄⣠⠴⠊⠀⡰⠃⡜⢀⠰⠁⠀⠀⠡⢦⠈⣷⣤⠀⡐⣶⠁⢹⣄⡀⠉⢃⢦⡑⡄⠀⠀⣠⠀⠬⢦⡀⠀⢀⠎⡀⠼
⠀⠀⡅⢺⠓⡤⠀⠔⠁⢠⢯⠏⠀⠀⠀⠀⠀⠋⢖⠡⡌⠀⡽⠊⢰⢸⡔⢽⠀⠸⢀⠃⡇⡹⠆⢸⣀⢀⠀⢙⠶⠊⢟⡬⠂
⠀⠈⡢⠸⣄⠀⠀⠀⢠⠓⠋⠀⠀⠀⠀⠀⣄⠗⡨⢠⡇⠰⠇⠀⠼⠸⠗⠸⣀⡗⣋⠞⠸⢧⣾⣼⣾⢸⡀⠘⠄⣀⡠⢣⢷
⢸⡄⡠⠸⠈⠃⡶⠊⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣴⣏⠁⣠⣯⠎⠸⠆⠀⠀⠀⠀⢺
⠈⣿⠡⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠚⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡳⠀⠠⠓⠀⠀⠀⠀⢸
⠀⣇⠂⡞⠛⠚⠶⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠙⡇⠀⡔⠀⠀⠀⠀⢰
⠰⣹⢰⡇⠀⠀⠀⠈⢳⡥⠦⣄⣠⠤⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡈⣿⠀⠘⠇⢠⢈⡆⠀⠘
⠀⠛⡉⠣⣎⣉⠭⢽⣾⠀⠀⣏⣀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣀⠈⣉⠀⢀⠠⢄⠀⢀⠤⡬⢀⠋
⠀⠈⠐⠀⡇⣏⠉⠉⠛⠓⣾⠓⠛⢷⠢⠬⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠘⠲⠃⢰⠤⣬⠂
⠀⠠⠐⠚⡛⣿⠀⠀⢀⠀⣿⠀⠀⠼⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢅⡂
⠀⠀⠀⠀⠁⡿⠀⠀⢸⠀⡏⠀⠀⠇⠀⣎⣩⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠛⠋⠭⠭⠭⠭⠭⠉⠛⠃⢈
⠀⠀⡆⠀⢠⡇⠀⠀⢈⢀⡇⠀⢸⠠⡄⠀⠀⣀⡈⠉⠛⠛⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⣡
⠀⡀⢘⢾⠋⣇⠀⠀⠀⢸⠁⠀⣈⢀⠃⢰⢰⠃⠙⠉⠓⠄⠒⠑⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⢸⡁
⠀⠀⠜⠒⠢⠭⠿⢿⣿⠛⠒⣒⠉⠸⠤⠬⠥⠤⠤⠀⣀⣀⣀⣀⡧⣀⠀⣀⠀⠀⠀⠀⢜⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢣
⠠⠀⠚⢿⠥⡤⠤⡤⠶⠶⣶⢖⡟⠉⣓⠠⠼⠿⠷⠶⠶⠶⠶⢒⡠⡿⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠁⠊⠙⠈⠀⠈⠃⠃⠊⠘⠘⠲⠊⠘⠀⠀⠒⠋⠟⠙⠂⠓⠈⠀⠓⠖⠀⠀⠲⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁⠒⠒⠂⠒⠋
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡹⠃⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠥⠭⣭⣉⡆⠀⠀⠀⠀⠚⠶⠆⠀⠀⠀⠀⠓⢤⣀⣧⡇⠀⡀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠢⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠞⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠜⠉⠁⢀⠤⠼⡆
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠳⡤⠊⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠁⠀⣰⣷⡀⠀⠸⣷⣀⣠⠼⠁⣀⡀⠀⠀⢻⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⢤⣀⣠⠏
⠀⠀⠀⢼⠉⠑⠖⠁⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⢳⡀⠀⢿⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠸⣽⡆
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⡆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠁⠸⠏⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣴⡏⠙⠳⡄⠀⠀⢸⡇⠀⢰⣾⠙⠳⡄⠈⠉⢹⡏⠁⢀⣀⠀⠀⡀⢸⡇⠀⠙⡄⠀⠀⠀⠀⢶⡄⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⠴⠃⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠸⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣿⠉⠉⠲⡄⠀⣿⠀⠀⢸⡟⠳⣄⠀⠀⠀⣼⡇⠀⣼⡷⠦⢼⠇⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡞⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠿⠖⠋⠀⣼⠯⠤⡇⠀⠀⢹⡇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⡀⠀⠀⢴⠏⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠳⠊⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡇⠙⡖⠦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣸⣄⣧⠤⠔⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡭⠤⠔⠲⣚⣉⠽⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢡⠀⢣⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⣀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠽⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⡱⢰⡄⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡇⢰⢳⠘⡇⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠘⣾⢸⣿⢸⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⢸⣠⡿⣤⣿⢤⠜⡄⠤⠢⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠁⠀⠈⠟⠀⠉⠀⠛⠀⠋⠀⠀⠀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⡤⠤⠄⠀⠤⠀⠒⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⡤⠤⢤⠤⠢⠔⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢉⣀⡉⠉⠈⢁⣂⣀⣉⡠⠤⠬⠄⠒⠓⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣉⣉⣀⣀⣀⣀⣀⠤⣀⣀⡠⠤⠤⠚⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠒⠒⠉⠒⠉⠉⠑⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠦⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⢾⣉⠉⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠠⠐⣞⡒⠒⠤⢬⣭⣍⣉⡉⠉⣭⡭⠤⠤⠔⣒⣋⠥⢞⡩⠗⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠈⠓⠒⠂⠉⠉⠛⠓⠒⠒⠒⠒⠚⠛⠋⠉⠉⣉⣀⣠⠤⠤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⣆⠀⠀⠈⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠖⠁⠀⠀⣰⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢸⡆⠀⠀⡗⠒⢺⠀⠀⠀⠀⢀⡞⢳⡀⠀⠀⠀⠀⡶⠶⢲⠀⠀⢰⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡞⠀⠀⢳⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠒⢻⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠙⠶⠶⠋⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡟⠒⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢰⠲⠖⡆⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢀⣀⣠⡇⠀⢸⡤⠤⠤⠤⢾⠀⠀⡷⠤⠤⠤⢤⡇⠀⢸⣄⣀⡀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⡃⠀⢸⠉⠀⠈⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⠁⠀⠉⡇⠀⢸⡧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⢰⡇⠀⢸⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⡇⠀⢸⡇⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠢⣄⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣠⠔⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠒⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠒⠒⠲⠶⠦⠤⠤⠤⠶⠶⠒⠒⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣼⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣧
⠀⠀⠀⠀⠀⠀⢹⢤⣀⠈⠉⠓⠲⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠖⠚⠉⠁⢀⡤⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠲⠤⣤⣀⡀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣤⠤⠖⠊⠉⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠲⠶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⢤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡿⢿⠿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠈⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⢄⡄⠀⠉⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠴⠀⠄⠈⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣉⢨⢁⣀⡀⠀⠘⠄⠀⠀⠀⠌⠀⠀⡃⡆⠀⠠⠀⠐⠀⢒
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢔⢤⠀⠐
⠀⠀⠀⠀⠀⢁⡹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⢀⡨⢃⠇⡈⠛⠛⠀⠀⠁⠐⠊⠀⠠⡀⠆
⠀⠀⠈⠀⠀⢒⠀⣄⠀⠀⠀⠚⠀⠀⠀⠠⢚⠧⠀⠣⠤⠦⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠅⠀⠁
⠀⠀⠀⠈⠀⠀⠡⠌⠄⠂⠁⠀⠀⠀⠄⠁⢠⡤⠟⠒⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠠⠤⠤⠤⠤⠤⠀⠐⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠔⠚⠉
⣿⣿⡷⠾⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣷
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢴⠟⠻⠿⣿⣶⣤⢸⡞⣇⠀⠀⠀⠉⠁⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠒⠴⣄⣀⢙⣿⣿⣻⠏⠀⢀⡀⠄⠈⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡤⠔⢁⣠⣶⣿⣿⣿⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣆⣠⠀⢀⣀⠀⠀⠀⠀⠀⣤⣩⣰⣾⣿⣿⣿⠿⢋⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠻⢷⣿⣿⣷⡄⢀⣀⣴⣿⣿⣿⣿⣿⡏⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣻⣤⣤⣄⣉⠉⠃⠸⠿⢓⣿⡿⠟⢋⣤⣾⣿⣿⡿⠛⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⢟⡟⡹⢿⣿⣇⣰⣦⣤⣤⣷⣿⣿⣿⣿⠿⢃⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣀⠙⠚⠚⢿⣯⣻⣿⢿⣿⣿⡿⠟⣡⣵⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣮⠽⣽⣷⠶⣤⣤⣀⠈⠙⠛⣛⣉⣠⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣛⣽⡗⣭⣿⣶⣾⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢭⣇⣻⣟⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣿⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⡿⠛⠛⠉⠉⢠⣶⣿⣷⣦⠀⢠⣄⠙⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡟⠉⡉⠙⠿⠇⢸⣿⣟⠀⣿⣿⣿⣿⣿⡇⢘⣿⠀⠙⠛⠛⠛⠛⠻⠿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣇⠘⢿⣷⣦⣴⣿⣿⣿⡄⠙⢿⣿⣿⠟⠁⣼⣿⣶⡶⠞⠻⢿⣿⣶⣶⣤⡈⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⣀⣹⣿⣿⡟⠋⠙⢿⣶⣤⣤⠤⠴⠾⣿⣿⣿⠀⢰⣶⣤⡈⠙⠻⠟⠃⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣀⠙⠻⢿⣿⣿⣿⣧⡈⠛⠿⢿⣿⠇⢸⣧⠀⣿⣿⡏⢠⣶⣤⡈⠻⣿⡧⠈⣿⣿⣿⣷⣶⣶⣾⣿⠿⠛⢁⡀
⠀⠀⠀⠀⠀⢿⣿⣦⣄⣈⠙⠛⠿⠿⣷⣶⣤⣤⣴⣿⣿⣦⡈⠉⣀⣼⣿⣿⣿⣦⣤⣤⣴⣿⣿⡿⠿⠟⠛⢉⣀⣤⣾⣿⠇
⠀⠀⠀⠀⠀⣀⠙⠿⣿⣿⣿⣷⣶⣤⣤⣄⣈⣉⣉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⢉⣉⣉⣀⣤⣤⣴⣶⣿⣿⣿⡿⠟⢁⡀
⠀⠀⠀⠀⠀⢿⣷⣦⣄⡉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣁⣤⣶⣿⠇
⠀⠀⠀⠀⠀⡀⠙⢿⣿⣿⣿⣶⣦⣤⣄⣈⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⣉⣉⣀⣤⣤⣶⣾⣿⣿⣿⠟⠁⡀
⠀⠀⠀⠀⠀⢿⣷⣤⣈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢉⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣶⣤⣄⣈⣉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠋⢉⣉⣀⣤⣴⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⣿⣶⣄⡉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⣁⣤⣾⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣤⣈⣉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⢉⣉⣠⣤⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣿⣦⣄⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⣤⣾⡇
⠀⠀⠀⣀⠀⠘⠿⣿⣿⣷⣦⣤⣄⣉⡉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⣉⣁⣤⣤⣶⣿⣿⡿⠟⠀⢀⡀
⢀⣴⣾⣿⠀⣶⣤⣈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠛⢉⣠⣴⡆⢸⣿⣷⣄
⣾⣿⣿⣿⣆⠘⢿⣿⣿⣶⣤⣄⣉⡉⠙⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠉⣉⣁⣤⣴⣾⣿⣿⠟⢀⣾⣿⣿⣿
⠙⢿⣿⣿⣿⣷⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⣁⣴⣿⣿⣿⣿⠟
⠀⠀⠙⠻⢿⣿⣿⣿⣷⣦⣤⣈⡉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠉⣁⣠⣤⣶⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡀⠀⠀⡀⠀⢌⡀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⢘⢧⠀⠃⡐⠢⡀⣋⡤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠉⠀⠨⠌⢿⡉⣿⠓⠦⢯⣠⠶⠛⠀⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⢙⠀⠀⠀⡀⡀⠒⠢⢿⡚⣓⣬⣤⣑⣜⠁⠈⣠⡄⠒⠀⠄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠁⠀⠀⠀⢀⠸⡄⣨⠖⢉⣉⠁⡱⠚⠋⢉⡄⢩⠈⠙⣆⠛⠤⡈⡑⠀⢂⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠱⠁⠀⠀⠀⠀⠀⠀⣀⠽⠫⠀⠐⠒⢲⣷⠪⢆⡀⠈⠊⠄⠂⠘⠷⣄⠑⡠⠔⠉⠁⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰⡄⠀⠀⠀⠀⠀⣼⠇⠑⠀⠈⢁⢀⣀⣼⣷⡒⢤⠀⣠⠀⠖⣠⣐⡾⡁⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡨⡷⢄⡀⠀⠀⠈⠺⠛⠛⠋⠉⠉⠀⠉⠀⠈⠙⠓⠚⠛⠉⠉⠁⠈⠀⠀⠀⡀⠀⠰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣙⠂⠫⡉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⣁⣀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡼⡀⢢⢘⡇⢠⡖⣄⠀⢀⡠⠤⢄⣀⡀⠀⠀⠀⡩⠭⢁⣀⣠⡀⠀⢠⠎⢀⠞⢲⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠡⠑⠈⢃⠓⠞⠀⠈⠛⠁⠊⠉⠢⠉⠹⣄⠀⡜⠠⡰⠋⠙⣦⠀⠀⠁⠀⡼⠀⠀⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢠⠀⠌⢧⠀⠀⠀⠀⠀⠀⡐⠀⢦⠀⠀⠉⠀⡐⠀⢀⠀⣨⢷⡄⠀⣼⠃⠀⠘⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⠘⠀⠁⠀⠑⢠⠀⠀⠈⠀⡇⠁⠀⢢⠀⢀⠄⢀⠐⢸⠰⠇⠀⢹⣰⡇⢐⠰⠆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢡⡀⣣⡠⠄⠀⣿⠀⠀⠀⠀⡟⠀⠀⠠⢣⡇⠀⠐⠀⡘⡀⠰⡀⠀⡿⢁⠒⣀⠠⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡑⠄⠉⠒⠚⠹⣂⡈⢀⠂⢳⠀⠂⠀⡼⣇⠀⠐⠀⠀⠱⠀⣀⡴⠁⠈⠋⡀⠄⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣀⠠⠢⠀⢀⠉⠉⠉⠛⠢⠐⠀⠀⠈⠛⠀⠉⠀⠈⠈⠁⠀⢤⢀⣁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⣀⠂⠘⠔⠀⠄⢠⠀⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢆⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⣠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⠀⠀⠀⠀⠐⣇⠀⢨⠇⠀⠀⠀⠀⢸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⣖⡋⠀⠀⠀⠀⢀⡬⠖⣋⠀⠀⠀⠀⠀⢈⣣⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⠚⢻⠀⠀⠀⠀⢸⣍⡉⢹⡇⠀⠀⠀⠀⣻⠒⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⠉⢹⠀⠀⠀⠀⢸⠀⠈⠙⡇⠀⠀⠀⠀⣻⠉⠒⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⢸⠀⠀⠀⠀⢸⠦⣀⠐⡇⠀⠀⠀⠀⣼⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠉⢹⠀⠀⠀⠀⢸⠀⠈⠙⡇⠀⠀⠀⠀⢺⠈⠓⢾
⠀⠀⠀⠀⡴⠒⠒⢄⠀⣠⠤⠤⠾⣗⢤⣼⠆⠒⠒⠢⣼⢋⡶⠒⠓⠒⢤⠀⡠⠿⠦⣄⣼⣀⠤⠖⠤⣄⢀⠤⠤⣄
⠀⠀⠀⠰⡀⠀⠀⠀⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⠿⠁⠀⠀⠀⠸⠃⠀⠀⢸
⠀⠀⠀⠀⢳⠤⣄⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢠⢦⣀⣀⣠⡎
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠒⠒⠋⠉⠙⠒⠢⠴⠒⠋⠈⠳⢤⣄⡤⠔⠉⠳⠤⠤⠞⠉⠑⠒⠒⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡰⠚⠛⠲⢼⣀⡴⠚⠋⠉⠛⠲⡄⣀⡤⠶⠖⠒⠶⢄⠀⢀⡴⠖⠒⠒⠲⢤⠀⣠⠤⠶⠤⣄⠀⣠⠴⠶⠶⠦⣄⣧⡤⠦⢤
⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠷⠋⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠸⠋
⠙⢶⡤⣄⡀⣠⣄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡰⢦⣀⣀⣀⣴
⠀⢸⠀⠀⠀⠀⠀⠉⠛⠓⠚⠛⠉⠉⠛⠒⠶⠶⠖⠚⠉⠉⠳⠤⣤⣤⠤⠖⠉⠓⠦⠤⠴⠚⠁⠙⠒⠒⠚⠁⠀⠈⠁⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⢀⠼⠤⢄⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢀⡠⠤⠤⣀⡀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣠
⡎⠀⠀⠀⠈⢣⠞⠉⠀⠀⠀⠉⠲⠞⠁⠀⠀⠀⠀⠙⣦⠞⠁⠀⠀⠀⠀⠙⣶⠋⠀⠀⠈⠳⣤⠎⠁⠀⠀⠈⢱⡞⠁⠀⠈
⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠
⠀⠀⠈⠉⠉⠉⠙⠒⠤⠤⠤⠤⠒⠓⠦⢄⣀⣀⣠⠤⠒⠒⢦⡀⠀⠀⢀⡠⠞⢦⣀⣀⣀⡴⠛⠢⠤⠤⠴⠋⠈⠑⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⢈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⢲⡖⠒⢦⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠘⣦⠤⢤⣀⠤⠤⠼⣄⡤⠦⠤⢄⡠⠦⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡄⠀⢰⡇⢠⠀⢻⠀⠐⠃⢈⡇⠀⠒⠀⡷⣄⠉⢁⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠿⣧⣀⣸⡀⡴⡆⠘⡆⠀⣖⠋⣇⠀⢰⢚⢁⣸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠠⣏⢩⡏⠩⠙⣏⠉⣹⠉⠏⢻⠉⡙⡿⢉⢹⡌⢋⡹⠂
⠀⠀⠀⠀⠀⠀⠀⣇⣀⣘⣠⣏⣨⣇⣀⣸⠜⣆⣿⣰⣆⣼⣀⣡⢇⡴⣄⡿⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⡿⠿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣶⠄⠀⢰⡶⠀⠀⣶⠆⠀⠀⠀⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⡀
⠀⠀⠀⠀⠀⣀⣤⣴⣾⠟⠋⠀⠀⠸⠗⠀⠀⠿⠃⠀⠸⠟⠀⠀⠻⠇⠀⠐⠿⠀⠀⠺⠇⠀⠈⠻⣿⣦⣄
⠀⣀⣴⣶⣿⠿⠛⠉⠀⠀⣀⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⣀⠀⠀⣀⡀⠀⢀⣀⠀⠀⣀⡀⠀⠀⣀⠀⠙⢿⣷⣤⡀
⣼⣿⠛⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠋⠀⠀⠛⠁⠀⠘⠋⠀⠀⠙⠃⠀⠈⠛⠀⠀⠙⠃⠀⠈⠛⠀⠀⠀⠈⠛⢿⣷⣤⡀
⣿⣧⠀⠀⠀⠀⢠⣤⠀⢀⣤⡀⠀⢠⣄⠀⠀⣤⡄⠀⢠⣤⠀⠀⣤⡄⠀⢠⣤⠀⠀⣠⡄⠀⢀⣤⠀⠀⣤⡄⠀⠀⠈⢻⣷
⠹⣿⣦⡀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⣠⣿
⠀⠈⠻⢿⣶⣤⣄⣀⠀⠠⣶⠄⠀⢰⡦⠀⠀⣶⠄⠀⢰⡶⠀⠀⣶⠆⠀⠰⣶⠀⠀⢶⡆⠀⠠⣶⠀⠀⠀⠀⠀⣠⣶⡿⠏
⠀⠀⠀⠀⠉⠙⠛⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣦⣤⣤⣤⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠿⠿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠛⠋⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣶⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⣲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣠⢿
⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣤⠦⣄⠀⠀⠀⢸⡟⢁⢼⡆⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⢿⠀⠀⣹⣀⣀⣀⣀⣀⣀⣘⣧⣤⣼⣇⣀⣀⣸⣧⣁⣈⣇⣀⣀⣀⠀⠀⠀⢸⡇⠀⣸⠂⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⢀⣤⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠶⠶⠦⠤⢾⣄⣀⣿
⡾⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻
⠹⣦⣤⡤⠞⠳⣄⠀⠀⠀⠀⣀⡾⢧⡀⠀⠀⠀⠀⢀⣠⡴⠻⣆⠀⠀⠀⠀⠀⠀⢀⡴⠻⡆⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢠
⠀⢸⡅⠀⠀⠀⠙⠳⠶⠶⠚⠁⠀⠀⠙⠛⠓⠚⠛⠉⠁⠀⠀⠙⠲⠦⠤⠤⠶⠞⠋⠀⠀⠹⣦⣀⣀⣀⣠⡴⠋⠙⠷⣤⣄⣀⣤⣴⠋
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⢿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⣷⠦⠤⣭⣭⣉⣉⣓⡒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⣒⣿⠁
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉⡿
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠸⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿
⠀⠀⠀⠀⠀⢿⠒⠲⠬⠭⣝⣓⣒⣒⣒⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⢒⣛⣋⣭⠭⠽⢿⡏
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠸⡏⠉⠙⠛⠓⠒⠲⠶⠶⠦⠤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠶⠶⠶⠖⠚⠛⠋⠉⢩⡏
⠀⠀⠀⠀⠀⣀⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢧⡀
⠀⠀⠀⠀⠸⣏⠀⠈⠙⠲⠶⠶⠤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠶⠖⠛⠋⠉⣀⡼⠃
⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⣤⣀⣀⣀⡀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠉⢉⣉⣁⣀⣤⣤⠤⠶⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠓⠲⢤⡈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢼⢱⡀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⣀⠀⠈⢣⠀⠀⣹⠦⢿
⠀⠀⠀⠀⠀⠀⠀⡼⠚⠀⠀⠀⢀⡀⠸⣁⣀⡀⠀⠀⠀⠀⠀⠙⠢⠤⠴⠦⣄⢰⠃⠀⠀⣀⣈⣉⡿⠥⠖⠋⠁⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⢯⣈⡉⠁⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⢻⠈⡏⠉⠉⠉⠀⠀⠀⠀⣀⣠⢴⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡞⣿⠇⠀⠀⡠⠤⠭⢷⣶⣶⣤⣤⣤⣤⣤⣤⡤⠤⢤⠤⠬⠿⠥⠤⠶⢖⣒⣒⣋⡭⠵⠚⠉⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠸⡗⣇⠀⠀⠀⠓⠤⣄⡀⠀⠀⠉⢉⡽⠯⡍⠉⠉⠉⠉⣹⠿⢯⠉⠉⠉⠉⠉⠀⠀⢀⣀⡤⠴⠋⢸⡇
⠀⠀⠀⠀⠀⠀⣰⢳⡼⠃⠀⠀⠀⣠⠖⠛⠒⠒⠒⣾⠦⠤⠭⠤⠤⠤⠤⠥⠤⠬⣥⠤⠶⠖⠒⠚⠋⠉⠀⠀⠀⣠⠞⣧
⠀⠀⠀⠀⠀⠀⢻⠸⣀⠀⠀⢀⣀⢹⣄⣀⣀⠀⠘⠛⠁⠀⠀⠰⣤⡴⠆⠀⠀⠘⠛⠁⠀⠀⠀⢀⣀⣠⣤⡶⠞⠁⢀⡏
⠀⠀⠀⠀⠀⠀⣼⢳⣌⣳⠀⢳⠬⠭⣤⣀⣈⣉⣉⣉⣛⣛⣛⣒⣒⣒⣒⣒⣒⣒⣛⣿⠿⠽⠟⠛⠛⠉⠁⠀⣀⣴⠏⢧
⠀⠀⠀⠀⠀⠀⢧⠀⠙⢿⡀⣾⠤⢤⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⣖⣺⠭⠟⠉⠀⡼
⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠉⠉⠙⠓⠒⠒⠻⠿⠯⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠓⠚⠛⠉⠉⠁⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢒⣠⣦⠖⢊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠛⣿⢻⡮⢵⡟⢻⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣸⠲⣽⡇⢸⣸⣇⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠸⠔⠉⠈⠲⡭⠷⢣⣹⡀⣶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⢿⢷⡶⣤⣤⣤⣼⣤⣶⢘⢛⡦⡡⡥⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⡇⡇⡇⣿⢸⢸⢸⢸⡇⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⢸⢸⡇⡧⠃⡇⣿⢸⢸⢸⡘⠣⡇⡇⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡉⢸⡜⠃⠀⠀⠀⠛⠼⠸⠊⠁⠀⠐⠧⠋⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡜⡙⢂⡽⠷⣼⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⢾⢹⣹⣿⣿⣿⡏⡏⡏⡏⣿⣿⣹⢸⢸⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⡇⣿⣿⡸⠈⠀⠘⢸⣿⡇⡇⡇⣧⠟⠀⠙⣼⢸⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠓⠛⠉⠀⠀⠀⠀⠀⠙⠃⠇⠛⠁⠀⠀⠀⠈⠚⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠻⣷⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⠿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢷⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣠⢦⠈⡇⠀⠀⠀⢠⣿⡀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⠿⠀⠀⠀⠀⠀⠳⠤⠼⠃⠀⠀⠀⡼⣦⢷⠀⠀⣼⣩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⢳⠀⠀⢸⡘⣳⠀⠀⠀⠀⠀⡶⢻⠀⠀⠀⠀⢳⡶⠋⠀⠀⢿⣥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡽⠃⠀⠀⢉⣥⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢸⢹⡇⠀⠀⢰⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⢸⣸⡆⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⣾⢸⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡏⡿⠀⠀⠀⢸⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢷⡇⠀⠀⠀⢸⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠚⠓⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠛⠒⠚⠛⠛⠓⠚⠓⠒⠒⠒⠚⠓⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⡖⠳⡆⠀⠀⠀⠀⣞⠛⣦⠀⠀⠀⠀⢠⡖⢲⡄⠀⠀⠀⢰⡞⢳⡄⠀⠀⢀⡖⢲⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠙⠛⣡⠴⠒⠦⣀⠙⠛⢁⡴⠖⢦⡀⠈⠓⠚⢁⡤⠶⣄⠈⠛⠋⢀⡴⠓⢦⣙⠋⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠒⠚⠁⢰⡛⣦⠈⠓⠖⠋⣴⢲⡄⠓⠦⠤⠶⠋⣴⠶⡌⠳⠶⠖⠋⢰⠒⣦⠈⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣙⣛⣁⣀⣀⣀⣀⣀⣙⣚⣁⣀⣀⣀⣀⣈⣙⣁⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢰⣏⣉⣀⣉⣉⣩⣭⣭⣭⣥⣤⣤⣄⣀⣈⣉⣉⣭⣭⣭⣥⣤⣤⣄⣀⣀⣉⣭⣭⣭⣭⣽
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣤⣀⠀⢤⠀⢀⣀⣀⠀⠀⡄⠀⢀⣤⢤⣀⠀⣤⠀⠀⣠⣤⣀⠀⢤⠀⠀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡀⠈⠓⠦⠶⠋⣀⠈⠳⢤⣤⠴⠋⠀⡀⠈⠳⠤⠴⠋⠁⣄⠈⠳⠤⠶⠛⠉⡍⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⠤⠤⠤⣼
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⠤⠤⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠦⠤⠤⠤⡤⠤⠤⠤⠤⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠶⣄⠀⠀⠀⣠⠶⣦⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⢠⠶⢦⠀⠀⠀⢀⡤⢤⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠳⠤⠏⠀⠀⠀⠙⠦⠞⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠘⠦⠞⠀⠀⠀⠘⠧⠴⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀
⠀⣰⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⡇⠀⠀⢸⡃⠉⠙⠲⠦⠤⣄⣀⣤⡤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀
⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠦⠴⠖⠒⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠙⠒⠦⠤⠤⠴⠒⠛⠙⠛⠓⠒⠒⠶⢤⣈⡇
⢰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡏⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡇⠀⠀⠀⣿⠑⠲⠖⠚⠉⠓⠲⠤⣄⣠⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⣇⠀⠀⠀⢸⠛⠒⠒⠓⠢⠤⣤⣤⠤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠙⡄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⣤⣤⠤⠤⠤⣀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠲⠦⣄⣀⣀⣀⣀⡤⠤⠶⠦⢤⣀⢀⣀⠤⠖⠲⠶⠖⢺

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢠⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⢠⣾⡇⠀⢀⣠⡆⠀⢠⣿⠀⠀⢀⣠⡀⠀⠀⢠⡀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣻⠁⠀⠀⠀⣹⡏⠀⠀⠀⢨⠇⠀⠀⠀⠈⣏⠁⠀⢘⠟⠁⠀⠘⣿⠀⠀⠙⣟⠁⠀⠀⠻⣿⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣡⠆⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠘⢦⠀⠀⠀⣟⠀⠀⠀⣿⠀⠀⠀⢰⡧⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠘⢃⡄⠀⠀⠀⣽⡇⠀⠀⠀⢀⣴⠀⠀⠀⢨⢿⠀⠀⢠⠔⠀⠀⠀⣬⠀⠀⠀⣿⠀⠀⠀⢼⡷⠀⠀⠀⢀⣽
⠀⠀⠀⠀⠀⠀⠰⢏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠁⠀⠀⠀⢐⣿⠀⠀⠰⣄⠀⠀⠀⣾⠀⠀⠀⣿⠁⠀⠀⣼⡧⠀⠀⠀⢬⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⡶⠀⠀⠀⠸⣿⠀⠀⢀⣤⠀⠀⠀⣎⠀⠀⠀⣿⠁⠀⠀⢼⡧⠀⠀⠀⣨⠟
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⠀⠀⢈⠁⠀⠀⠠⣏⠀⠀⠀⣿⠄⠀⠀⢾⡇⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⡴⠞⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⠀⠀⠀⠘⣿⠀⠀⠀⣉⠀⠀⢠⡟⠀⠀⠀⣿⡇⠀⠀⢸⡧⠀⠀⠀⣞⠁
⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠀⠀⠘⠉⠀⠀⠘⠛⠀⠀⠀⠛⠃⠀⠀⠘⠃⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣆⠀⠀⠀⢀⣆⠀⠀⣠⡆⠀⠀⣰⡄⠀⠀⡀⠀⠀⠀⠀⢰⡄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠠⢾⡿⠀⠀⠀⠀⢿⠟⠀⠀⠀⢺⠏⠀⠀⢻⠃⠀⠐⣿⠇⠀⠘⣿⡆⠀⠀⠀⣿⠇⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⢠⡷⠀⠀⠀⢠⢟⠀⠀⠀⠀⣚⡂⠀⠀⢘⡇⠀⢀⣅⠀⠀⠀⣾⠀⠀⠀⠀⢪⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⢒⠀⠀⠀⠰⢋⠀⠀⠀⠀⡐⠁⠀⠀⢨⢂⠀⢈⣉⠀⠀⠀⣻⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⠀⠘⢋⠀⠀⠀⠐⣋⠀⠀⠀⠀⡑⡁⠀⠀⠰⣃⠀⠈⣉⠀⠀⠀⢿⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⢈⣥⠀⠀⠀⠘⢋⠀⠀⠀⠀⡐⡀⠀⠀⢘⡥⠀⠀⠛⠁⠀⠀⢾⠀⠀⠀⠀⣵⡆
⠀⠀⠀⠀⠀⠀⠈⣼⠀⠀⠀⠀⠈⠵⠀⠀⠀⠐⢋⠀⠀⠀⠀⠤⡁⠀⠀⢈⡄⠀⠀⠛⠃⠀⠀⣿⡇⠀⠀⠀⣾⠅
⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠘⡿⠁⠀⠀⠰⢛⠀⠀⠀⠀⠦⡁⠀⠀⢐⡃⠀⠀⠛⠃⠀⠀⢿⡅⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠙⠁⠀⠀⠈⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢺⠀⠀⣴⢺⠄⠀⣰⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⠀⠀⣼⣻⠀⠀⢸⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⠀⠀⣾⣽⠀⠀⢸⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢾⠀⠀⢿⢾⠀⠀⢸⠾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡿⠿⠤⠤⠶⠿⠦⠤⠼⠾⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⢀⡀⠀⢀⢀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡎⠉⡆⠐⡆⡇⠇⠸⠁⢸⢸⠘⠀⠃⠀⡆⡊⣀⡶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢇⡡⠈⠀⡆⠈⡄⠃⣨⢸⠀⢣⠀⠢⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⢀⠠⠤⠤⠵⠖⠀⠒⠀⠒⠠⠼⠤⢀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠉⢱⢠⠲⠰⠁⡇⢰⠁⢸⢘⠈⡆⠘⠀⢱⠠⢲⠀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠁⠀⢸⠈⡄⠉⢀⠃⠘⠀⢊⠀⡄⠇⢰⠀⠠⡰⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠇⠀⠀⠉⠀⠀⠘⠤⠴⠀⠈⠉⢰⠀⠀⡆⠀⠀⠀⠸⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⡔⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⢀⠟⢢⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⢈⣐⠂⠈⠩⠬⠉⠀⠀⢀⣀⣀⡀⠀⠀⠉⠭⠭⠁⠐⣂⡁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡞⠉⠙⠀⠂⠰⣀⠀⠁⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⢀⡀⠀⠀⠈⠀⡭⠅⢒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠀⡄⣀⣠⠔⡅⠀⠙⡦⠀⠀⡀⢀⠀⠀⠀⠀⠈⠉⠙⠻⠓⠓⢲⠺⡟⠻⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⢁⠸⣆⢡⡰⡿⣂⠒⢴⠃⠀⢐⣤⠙⠛⠁⠀⠆⠀⣠⡀⠀⠈⠀⠀⢈⡀⠀⢀⢠⣀⡰⢶⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣌⡀⣽⠋⠘⣧⡉⣀⣼⣦⣀⣸⣿⣧⣤⣄⣤⢠⡀⡄⠀⢢⣦⣠⣤⣿⣥⣼⠷⢶⡿⣿⡿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢈⠍⠉⠀⠚⠋⠉⠉⠁⠀⠀⠈⠁⠈⠉⠉⠁⠚⠁⢙⣤⠸⠐⠉⠁⠀⠀⠀⠀⠈⢀⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣙⣿⠀⠀⠀⠀⠀⠀⢰⠀⣿⣿⣆⢴⢤⠀⠀⠀⠀⢋⣫⠷⢂⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠀⠒⠉⠋⠈⠁⣻⠆⠋⠛⠁⠀⠀⡀⠈⢣⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡂⠀⠀⣳⣶⣦⠀⠀⠀⢀⣸⣷⣶⠦⠀⠒⡴⠆⠐⣛⣿⠀⣽⡷⢎⠀⠀⠀⠀⠀⠀⢰⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⢀⣀⣹⣋⣀⡉⠉⢁⣁⣀⣾⠇⠈⠉⠁⣀⣉⠉⣡⡀⣤⡖⡋⠀⠀⠀⠀⣠⣴⡇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣽⣧⣀⡀⠀⠀⢀⣨⣯⡟⠀⣀⠉⠁⣀⣀⣠⡾⠃⢾⡛⣦⣤⣤⣶⣿⣿⣿⡗⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⡞⠋⠈⠉⠉⠉⠉⣉⣼⠟⠉⠉⣉⣠⠬⠤⠄⠀⢸⣿⣡⢗⠚⠙⠛⠻⠿⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠘⠚⣻⡧⢤⣤⣄⣀⣀⣀⣈⣿⠀⠀⢀⣠⣀⣤⣶⡿⠇⠀⠋⣡⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⡿⣶⣎⢅⣀⡀⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⢀⣀⣨⣷⢶⣞⡋⠛⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣦⣤⣁⣀⣉⣉⣉⣉⣈⣉⣉⢉⣁⣤⣤⣤⣿⠾⣈⡁⣠⣿⡖⠃⢘⣶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⢹⡏⠛⠻⠛⠿⠶⠾⢃⠔⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠤⠄⠐⠒⠋⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣧⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠐⠲⢤⡀⠀⠀⠀⠀⢀⠴⡛⠋⠻⣾⢁⠀⣱⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠈⣆⠀⠀⢀⠈⡑⠄⢀⠔⡁⠀⢁⡀⠀⠘⣾⣠⡿⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠢⣅⠻⢢⣹⣄⠀⠀⠳⣀⡸⢃⡈⠠⠀⠀⠀⠈⠁⠘⢧⣤⡀⠈⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠂⠈⡟⠡⠤⢂⣱⡀⢀⡞⢠⠀⢠⠀⠠⠆⢀⣡⠤⠅⣘⣷⡶⢶⣊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣷⣄⣣⣐⣲⡞⠙⠤⠤⡝⠄⠤⠀⠠⠄⢰⡏⠙⠢⠰⢈⣟⠻⠦⠗⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣁⣀⡠⠭⠙⠛⠛⠉⢳⣄⡀⣐⣡⠷⠤⢶⡶⠶⠿⢧⣀⠀⡠⢞⣝⠀⣄⠀⠀⠀⠀⢈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠉⠣⢄⡀⠄⠀⠀⠀⠀⢈⣉⡉⠁⠀⠀⠀⠀⠈⠉⠀⠉⠉⠛⠉⠉⠋⠁⡀⠀⠐⠚⠍⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⣦⠀⠀⣨⠟⠛⠙⠛⠳⠄⠀⠀⢠⣶⠟⠛⠙⠛⣟⠉⠁⣠⠞⠉⠙⢳⡄⠀⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣶⢤⣄⣸⠀⢀⣿⠀⠀⠀⠀⢰⠀⠀⢸⣾⠁⠀⠀⠀⠀⢸⡄⠀⣏⠀⣀⣠⣼⡇⠐⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠒⢸⠀⢸⣿⣖⡒⠶⠤⢾⡀⠀⠘⣼⣦⣤⣤⣤⡴⢾⡇⠀⡟⣛⣫⡭⢾⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠈⠀⠙⠒⠛⠁⠀⠀⠐⠒⠒⢺⡇⠀⡏⠁⠀⠀⢠⡇⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠧⣌⠑⢲⠟⢠⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣧⡤⣴⣶⣿⣇⠠⢈⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣇⠀⠀⠀⠈⠦⠴⠟⠋⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠚⠛⠋⠭⢽⡇⠀⠹⣯⠽⠚⠋⠉⠙⣾⡟⠺⢽⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⣪⢵⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠚⠛⠛⢻⣟⠄⠀⢸⠀⠀⣀⣤⣾⠿⣿⣶⡀⠈⠈⡙⣦
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁⠈⣴⣿⣿⡳⠌⠉⠓⠲⠤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣿⣷⣶⠿⠾⠛⠋⣁⡤⢞⡵⢻⡇⠀⠀⠀⠜⣧
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠸⣿⡻⣦⣡⠖⠋⢱⡄⠀⠀⢀⣀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣀⡤⠤⠒⠋⠁⠐⠉⣠⡞⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⢧⣸⡁⢀⠀⣠⣿⠀⠀⠀⠈⠁⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠁⣠⣾⠉⠉⢷⢦⡴⠞⠉⠀⠀⠀⡠⣫⣾⠇
⠀⠀⠀⠀⠀⠀⠈⠳⡕⢄⡀⠀⠀⠈⠙⠒⢶⣾⠛⠓⠶⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣯⠈⠉⠉⠁⣺⣶⠀⠀⠀⢀⣭⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍⡲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠈⠳⣦⡶⠾⠟⣛⡡⢴⣺⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⢽⣒⣦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⣒⣺⣭⠷⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠯⠭⠭⠭⢭⣍⣉⣉⣉⣭⣭⣭⡭⠭⠤⠴⠶⠖⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢎⢈⠆⠀⠀⠀⠀⠀⠠⡁⡸⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣱⠀⠰⠲⠀⠀⢀⠶⡄⠀⠀⡆⠦⠀⢎⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢸⢸⠀⠀⠘⠤⠆⠀⠀⡇⠐⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣉⠉⠀⠀⠈⡀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠘⣀⣀⣸⠈⣇⢀⣀⡇⢀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠊⠈⠑⠀⠐⠊⠈⠒⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⡇⠈⠁⠹⡰⠁⠀⢸⠀⡅⠀⠀⣇⡜⠈⢹⠀⡇⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠈⠈⠈⠁⠀⠀⠁⠈⠁⠀⠈⠀⠉⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⢇⡀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⢸⣠⠇⠀⣱
⠀⠀⠀⠀⠀⠀⠀⣧⠠⠊⠙⠢⢀⡀⠴⠊⠑⠤⢀⠠⠔⠉⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠠⠄⣀⡀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⣀⡠⠄⠊⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⢘⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⣻
⠀⠀⠀⡇⠀⡠⠛⢄⠀⠀⠀⣠⠞⢦⠀⠀⠀⢀⠜⠣⡀⠀⠀⠀⡴⠳⡄⠀⡇⠀⠀⠀⠀⠈⠉⠒⠆⠤⠍⣁⣀⡒⠒⠒⠒⠒⠒⢒⣂⣀⡉⠥⠤⠒⠊⢩
⠀⠀⠀⡗⠉⠀⠀⠀⠁⠒⠊⠁⠀⠀⠉⠒⠊⠁⠀⠀⠈⠐⠒⠉⠀⠀⠈⠑⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠒⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠐⠊
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡔⢂⣢⠴⠯⠭⠶⠮⠤⠼⠶⠭⠭⠦⣴⣒⢢⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣄⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣣⣌⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢱⡄⠒⠢⣀⡠⠤⡀⢀⣀⡀⢀⠠⠤⣀⠔⠒⠢⡎⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠤⠚⣄⠀⢀⣏⠀⠀⢸⠁⠀⠈⣇⠀⠀⢸⡄⠀⢀⠗⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠓⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⢎⠀⠈⠑⠒⠉⠑⠐⠊⠉⠐⠒⠁⠀⡰⢄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠍⠉⠩⠥⠭⠬⠉⠉⣇⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠀⠀⠑⢄⡀⠀⣀⠔⠉⠢⣄⠀⢀⡠⠊⠀⠀⠈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠍⣑⠂⠤⠤⠀⣁⣀⣀⣀⣀⣀⣉⠈⠤⠤⠐⢂⡩⠔⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠄⠀⠐⠒⠒⠂⠀⠉⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡘⢄⣀⠀⠉⠁⠒⠒⠂⠀⠀⠀⠀⠀⠐⠒⠒⠈⠉⠀⢀⡠⢃⠇
⠀⠀⠀⠀⠈⠀⠈⠈⠁⠁⠀⠐⠒⠒⠒⠒⠪⠭⠭⠍⠉⣉⣉⣉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠮⣍⣀⡒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⣂⣩⡥⠖⠁
⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⢶⡶⠶⠶⡶⠒⠛⠛⠋⠉
⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡀⠀⠀⠁⠉⠀⠉⠉⠉⠀⠒⠒⠒⠒⠒⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠀⣇⠀⣠⠀⠈⠉⠒⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠚⠛⠋⠁