Tiramisu Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢬⡱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣷⣤⢭⣾⠷⣿⣧⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣿⣓⣶⡦⢤⣄⣀⡀⠈⠉⠉⢻⣟⠉⠀⣀⣤⣴⣾⣿⣤⣄⣀
⠀⠀⠀⠀⣀⠴⠚⠉⠁⡀⠀⣀⠀⠉⠉⠛⠒⠿⠯⢿⣗⣶⣾⣿⣿⡿⠟⠛⠋⠉⣀⠀⠀⠈⠉⠓⠦⢄
⠀⠀⠀⠊⠀⠀⠀⠐⠉⠀⠀⢯⣙⣓⢶⢦⣤⣀⡀⠀⠈⠉⢹⡏⠁⢀⣠⣴⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠾⣭⣽⣲⠶⣾⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠷⣄⣹⠶⣦⢤⣀⡁⠀⠂⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⢀⠴⢾⠯⣝⠛⡤⢤⣩⠈⠉⡷⢤⣉⡙⠒⢮⡀⡠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⣀⠤⠶⠿⣵⡄⠀⠀⠛⠛⢲⣦⣼⣒⢢⣤⡀⠀⢹⠆⣨⣴⡿⠫⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⣀⠤⠶⠿⢤⠂⠀⠀⠈⠉⠛⣻⣦⣀⣈⣀⠀⠉⠻⠆⣛⣤⣶⡟⠋⢀⣀⣤⡏⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⢸⣤⣀⡀⠤⡊⠉⠛⠛⣿⣄⣀⣀⠈⠉⠉⡿⢂⣠⣴⣾⠟⠋⢀⣠⣶⣿⡿⣟⡅⠀⠂⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠉⠛⠿⣳⣦⣄⣀⠀⠁⠀⠉⣿⠄⣀⣤⡾⢟⡋⠉⢑⣵⣿⡿⠟⠉⣀⣤⣾⣿⣆⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⣄⣀⠀⠀⠉⠙⠛⠿⢷⣮⣥⣴⣾⠟⠋⠁⣀⣴⣾⣿⠏⠁⢀⣤⣾⣿⡿⠋⠙⠻⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⢰⠉⠛⠯⣿⣶⠤⣄⣀⠀⠈⠹⣁⣬⣥⣿⣾⡿⠿⠉⣠⣤⣾⣿⠟⠋⠁⠀⠀⠀⢀⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠐⢄⣧⣄⣀⠀⠁⠙⠓⠧⢽⡶⣾⣾⢿⠛⠋⢉⣠⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠙⠷⣭⣟⢂⣢⣀⡀⠀⠈⣻⠁⣀⣠⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠛⠻⠿⣿⣞⣶⣶⣿⣿⠿⠋⠁⠀⠀⠀⣀⣀⠤⠤⠒⠉⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⡏⠀⠀⠀⣀⣼⣽⣿⣶⣶⣶⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⠿⠿⢿⣿⢿⣿⣿⣿⣾⣿⣿⠿⠟⠛⠟⠛⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠙⠀⠀⣀⣀⡐⠂⡶⠍⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢩⣀⣀⣉⠶⣊⠉⠉⢓⡀⠒⠓⠢⣄⡀⠋⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠐⠒⠚⠉⠀⠉⠁⠀⢀⣤⣴⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⡉⠓⠒⠒⠒⠦⢄⣀⣀⣀⠀⠀⢀⡤⠞⠋⣩⠏⠀⠀⠈⠀⠀⠀⠶
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠶⠶⠶⢦⣬⣭⣿⣧⡴⠶⠛⠿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣭⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢹⠋⣸⢠⣏⠇⢠⡇⢠⡇⣰⠁⡎⠸⡙⢸⠁⡇
⠀⠀⠀⠀⠘⠀⠇⠸⠙⠠⠓⠇⠸⠘⠸⠠⠇⠦⠇⠸⠼




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⢶⡶⡟⠻⠟⠁⠹⠿⠾⠉⠛⠳⡶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⣿⣽⠇⠡⡤⠀⠀⠈⠤⠤⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠹⠖⠦⢤⣤⣀⡀⠀⣀⡀⠃⠀⠀⠀⣀⣠⣤⡶⠷⠟⠛⠛⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡦⢤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠻⠿⣶⡾⠟⠛⠉⠉⠉⠁⠠⠀⠀⠀⢀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠉⢹⣦⣤⡤⣤⣀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣤⠤⢤⣴⡿⠛⠽⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠉⠓⠒⠦⠤⠼⢿⡄⠀⠀⠀⠉⠓⢶⠶⠒⠲⣶⡏⠁⣀⠁⠀⣿⠷⠶⠶⠺⡷⠦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⣤⣀⡀⠀⠀⠀⠀⠙⠲⠦⣄⡀⠀⢀⠀⠀⢀⡼⠓⠶⠒⠚⠉⠀⠀⠀⣀⣴⡟⠛⠂⠀⠀⠁⢠
⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠘⠳⢬⣿⣶⡤⢤⡀⠀⠀⠀⠀⠉⠉⠚⠓⠊⠉⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⠁⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀⠀⠀⠀⠈⠉⠛⠲⢾⣧⣒⣰⢤⡀⠀⠀⢀⣀⣤⠴⠞⢋⣫⠿⠟⠛⠉⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠠⠀⠀⣀⠀⠀⠉⠙⠻⠿⢯⣼⣯⣯⠶⠚⠉⠉⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⠸⠉⠀⠀⢂⣦⣼⣷⡿⠶⣦⣄⡄⠠⠄
⠀⠀⠀⠀⠀⠀⢀⣀⠂⠀⣴⣪⣟⠉⢀⣨⣿⢷⢦⢤⣤⣤⣿⡻⠊⡓⡴⢠⡿⣧⣤⣀⣶⢤⠄
⠀⠀⠀⠀⢀⡔⠋⠉⢴⡖⠊⠉⠁⠐⣧⡏⠈⠀⠁⠀⠂⣀⣬⠿⡤⢤⣴⡏⠀⠀⠀⠙⠯⠁
⠀⠀⠀⢀⡾⠷⠶⣤⣾⡇⠀⠀⠀⠈⠹⣿⡯⣉⡀⢙⣿⣯⠀⠀⠀⠀⠉⠎
⠀⠀⠀⠈⠀⠀⠀⠈⠙⠋⠒⠒⢤⣤⣼⣯⠟⠀⠀⠈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠆
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠄⣴⡆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠺⡡⠴⣓⠚⣸⣹⡟⣿⡆
⠀⠀⠀⠻⣼⣿⡰⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⣼⣦⡜⠰⣂⣯⣴⣼⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠙⠻⢷⣮⡉⡓⢐⣂⢲⡄⠀⠒⠀⠙⡈⠀⣀⢋⡶⣣⣮⣷⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣶⣍⡼⡆⣀⣐⢶⢠⣤⡶⠶⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠀⠈⠻⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⡭⠟⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠯⡐⠒⠒⠒⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⢱⣀⣦⣧⣴⠠⠆⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠘⡿⣶⡄⠀⠀⠀⠀⠙⡀⠉⣄⣷⠞⢉⢢⠀⠆⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣧⠀⠙⠢⣄⠀⠀⠁⠘⠉⣄⢠⡀⠘⠛⠀⠀⠀⠀⠀⢀⣤⠞⣷⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠉⠲⢄⡀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⣮⣱⢄⠀⠀⠀⠉⠲⢤⣀⡀⠀⣀⣤⠖⠋⠀⠀⣀⣤⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠙⠛⠿⠷⣤⡄⣀⠀⠀⠈⢹⡋⠉⠀⠀⢀⣠⣾⡿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠻⣷⣿⣦⣄⢰⣃⣠⣶⣯⠟⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠈⠑⠙⠻⢾⡿⠟⠋⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢻⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⢸⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠈⠳⣝⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⣸⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⡑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢬⣁⣁⡐⠒⠒⠒⠒⠒⠂⠒⠂⠀⠀⠀⣀⣀⣀⠤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⢋⣉⣹⠛⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣚⠉⠍⠁⠀⠀⣼⠁⠰⠉⢳⠀⠀⠀⠀⠉⢓⣲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠝⠢⢤⣀⡀⠹⣄⣀⣠⠾⠀⣁⣠⠴⠚⠉⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠓⠢⣄⡀⠀⠉⠓⠦⣤⠤⠖⢉⠀⠐⣀⡦⠒⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⠤⣄⠀⠉⠙⠒⢬⣀⣸⣀⣠⠔⠋⠉⠁⢀⡤⠴⣺
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⣿⠉⠙⠪⣕⡒⠦⣄⡀⠀⢹⠁⠀⣀⡤⠖⣚⡭⠚⠩⢹⠦⣄⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢻⣙⠲⢥⣠⠉⠛⠲⢍⣒⣺⣒⣊⠵⠊⠩⢁⣠⠴⢚⡹⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠙⠒⢬⣙⠲⠬⣄⡀⢹⠙⣀⡬⠴⢚⡩⠔⠊⠉⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣈⣻⣋⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⣄⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣠⠤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁




⠀⢀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⣉⣉⣩⠋⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡒⠋⠍⠉⠀⠐⠀⡜⠁⠰⠏⢱⡄⠀⠁⠀⠈⠍⠓⢲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠉⠙⢦⣀⡀⠂⠀⢧⡀⠀⠀⣸⠃⠀⠀⢀⣠⠖⠋⢉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⠧⣄⠠⠈⠛⠙⠲⢤⣉⠙⢉⣁⡴⠚⠉⠩⠀⢄⡤⠴⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⠙⠒⠦⢤⣀⠀⠈⢹⠉⠁⢀⣡⠤⠖⠚⠉⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢭⣉⡳⣄⡀⠀⠀⠈⠑⠾⢾⠶⠖⠋⠀⠀⠀⣀⡴⣚⣩⠵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⣧⣀⠀⡙⠢⢭⣉⡓⠦⣀⠀⢸⠀⢀⣠⠖⣋⣩⡥⠞⠁⠀⣁⡟⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠧⣌⡙⠲⢤⣂⠐⠉⠓⠮⣍⣹⣍⣭⠴⡋⠁⢒⣠⠴⠒⣋⡥⠇⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⣙⠲⠤⣄⡂⢸⠀⣀⣤⠤⠖⣋⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣉⢻⠋⣁⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⣀⣀⣠⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢻⡆⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀⠤⠄⢶⡿⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⡁⠀⠀⠀⣠⠀⣿⣂⣄⣀⣤⡄⢀⣾⠁⠀⠰⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠈⢻⣆⢸⣷⡟⢠⡿⣿⡏⣿⡿⢀⣾⠃⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣶⡾⠋⠘⠛⢷⠟⠁⠿⠴⠿⠶⠋⠻⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⢿⠋⣉⠉⣉⠉⡁⠀⠀⠀⠀⠻⣎⣱⠇⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠋⠀⣿⣿⠇⠀⠀⠀⠀⠀⠙⠋⠀⣠⣤⠂⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣠⠟⡇⢰⠞⣆⣿⢹⣟⣷⣆⢀⣿⡇⣧⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠙⠶⠋⢰⡇⢿⡾⣿⠿⠘⠛⠟⠛⣛⣹⡇⠘⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠐⠞⠉⠉⠀⢀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠠⠴⠀⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⣡⠤⠶⠛⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⣄⡀⢠⠆⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠠⣀⡞⠁⠙⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡄⣀⠀⢤⣠⡞⠓⠉⠷⣄⣀⣀⣦⠘⠋⠙⠃⠀⢀⡀⠈⠃
⠀⠀⠀⡄⠀⠀⠀⠀⡉⠀⠀⠙⡓⠀⠀⠀⠁⣿⡶⠆⠹⠤⣄⠀⠠⣄⡼⠋⠙⠒⠀⢀⢀⡷⠸⠇⢀⡶⣶⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢊⣿⠿⠃⣧⣀⣄⣀⣄⠈⣯⠀⣠⣾⣏⡷⠁⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⡟⠓⠒⠲⢤⣄⠀⡀⠀⠀⠈⠁⠀⠀⠀⢸⣽⣿⣿⣧⣿⣾⣛⡷⠉⠀⠀⢀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣲⡆⠘⠻⢷⡄⠀⢀⡀⠉⠳⠶⢦⡄⢀⡀⠀⠈⣿⣿⣿⣿⣿⡟⠋⠀⠀⢔⣰⡿⠁
⠀⠀⠀⠀⠀⠀⢣⣄⠀⠙⠛⠋⠐⠟⢁⣴⡄⠊⠁⠰⣤⣤⣤⣤⣌⠙⢶⣴⣿⠛⠻⢿⡏⢀⡴⢮⣶⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠄⠀⠛⠛⠃⠀⠀⠐⠦⣀⣈⠙⠻⣾⣿⣧⣟⢋⣡⡿⢗⣩⣾⠟⠉⣀⠀⠀⣠⡰⠯⠜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⠀⠀⠀⠀⢘⣛⣿⣿⠉⠉⠛⢿⣶⣿⠟⠁⠀⠲⠀⠉⠉⢠⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠐⠉⠤⠂⣩⠉⣁⣈⠋⣽⣿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠰⠛⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⠛⠀⠛⠙⠃⠀⣀⣠⡄⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠁⠀⠀⠈⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣛⣟⣛⣟⣻⣛⣷⣙⣛⣻⣛⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢰⣶⣧⣠
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣩⣛⣩⡴⠤⠉⠈⠀⠈⢿⡃⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠹⣿⣮⡄⡀⠐⣾⡤⡤⠈⢮⡢
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⢮⣵⡂⠘⢭⠀⠀⠨⣿⣿⣧⢄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⠻⢧⣤⠑⠀⢀⣤⣟⠫⠛⠊⡅
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠳⣄⠑⢄⡀⠀⠙⣷⣷⠞⠋⠁⠀⢁⣠⡆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣄⠙⢦⡀⢘⠀⠀⣀⠴⠚⢉⣠⠆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⣄⠈⠻⠒⠉⣡⡴⠚⠉
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠔⠂⠒⠒⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⠉⠉⠛⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⣤⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⢀⣹⣿⡄⠀⠀⠀⠀⣠⢤⣶⣿⣿⣋⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⢀⣰⣾⣿⣽⠷⠿⣿⣿⣿⣯⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢉⠉⠙⠉⠛⠿⠟⠹⠭⠿⠿⠋⠉⠉⠍⠑⠓⠈⠩⠯⠽⠟⠫⣷⣾⠩⢴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣀⣀⣤⣈⣀⣀⣤⣀⡀⠀⢤⡀⠀⠀⡀⣀⣠⣄⣀⠀⢀⠀⠀⠀⢀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠋⢛⣿⣿⢛⣿⡭⠏⠓⠀⠀⢲⡰⠾⣷⣤⣨⠎⢀⡀⠀⠼⠀⠄⢼⣎⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠴⠦⠼⠿⠶⠛⠒⠒⠒⠾⠲⠶⠆⠙⠀⠩⠥⡄⠠⠺⠷⠶⠣⣤⠠⠤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠶⢖⣮⡇⠠⣶⡦⠔⠒⠲⠶⠶⣟⣲⣆⣤⣄⠠⠐⠀⠀⠰⢘⣟⠲⢶⣶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠒⡞⠙⠳⢒⣁⡁⣽⣤⣅⠀⠾⠛⠛⢿⠻⣟⢂⡀⠛⠛⠰⣭⠙⢵⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠄⠰⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠲⠀⢲⠲⠂⠄⢰⠄⠀⡶⠀⡄⠀⡄⠀⠆⢠⡀⠂⠐⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠤⠀⣿⠀⠀⠈⠸⡆⠀⠆⠀⠅⠀⠄⠠⠄⠠⠉⠡⠀⠇⠰⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⢀⡀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠈⠓⠛⠚⠛⠛⠒⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠤⢆⠀⠀⠀⢀⡀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢤⡄⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⢌⣭⣖⣂⡚⠓⠒⣚⣡⠴⠁⠀⠀⠀⢀⣀⣠⣤⠤⠛⠛⠻
⠀⠀⠀⢰⠟⠓⠒⠒⠒⠶⠀⠤⠤⢤⡤⠤⣤⣄⣀⣁⡀⣈⣉⣉⣩⣭⣶⣾⡿⠛⠻⠟⠋⠁⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡤⠄⠛⢹
⠀⠀⠀⠘⠢⡀⢀⠄⠒⠲⣤⡀⠀⠀⢠⠴⠒⠀⠠⡀⠀⠀⠀⢀⣀⣃⣀⣠⠀⠀⠒⠈⠁⠀⠀⠀⣀⣠⡴⠾
⠀⠀⠀⠀⡄⢸⡀⠀⠀⠀⠰⣷⠀⠀⠆⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⡟⢋⠉⢉⣠⣤⠖⠴⠟⠛⠉
⠀⠀⠀⠀⠟⠉⠑⠒⠲⠒⠚⠛⠀⠈⠲⠶⠶⠶⠶⠾⠃⠀⠶⢴⡶⣿⠿⠚⠛⠉⠁⠀⠀⠀⠀⠐⣃⣀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣴⣶⠿⠞⠛⠉
⠀⠀⠀⠀⠈⠂⠓⠒⠶⠶⠷⠶⠦⠔⠒⠶⠤⠤⢭⣭⣭⣄⣀⠀⢀⣸⡿⠳⠖⠋⠉





⠀⢀⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠶⠖⠒⠛⠏⣉⡉⢉⠉⠉⢱⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⣭⠭⡙⢁⡄⢠⣄⢠⡖⣶⠻⢴⠇⣛⣳⢸⣠⠇⠃⠀⠀⠀⠀⣠⣶⡶⠿⠛⠻⠿⠛⠛⠻⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢷⠀⠇⢹⠀⠺⠽⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠗⠠⠀⢠⣶⣶⣿⣿⣀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠿⣦⣤⣈⣉⣙⣃⣀⣀⣤⡼⠟⠋
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡔
⠀⠀⠀⠉⠓⠒⠀⠀⡀⠀⠀⠀⠀⢄⡀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠙⠿⣿⡶⢦⣶⣶⢶⣖⣶⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⠇⢀⣀⣄⠀⠀⢀⠀⣀⣀⠨⠄⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣟⣿⡿⠿⢿⣿⡿⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⣅⡀⠀⠀⠀⠀⢀⣀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣦⣭⣉⣩⣥⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣽⣵⣖⣾⣿⣯⣻⠷⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⢿⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠉⠉⠉⠉⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⣠⠄⢤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢲⠀⣀⣼⣤⣤⣴⣧⣤⣤⣇⣀⣈⡃⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣡⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣲⣿⣿⣿⣿⣏⣻⠟⡻⢓⡭⠤⠄⣠⣿⣿⣿⣿⣿⣿⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣶⣿⣿⣷⣤⣴⣾⣤⡀⢀⣠⣆⡀⠀⠀⠀⠀⠁⠙⣿⢿⣿⣿⣿⣿⣈⣤⣾⣿⣷⣾⣿⣿⣿⣿⣿⠿⣿⠀⠄
⠀⠀⠀⠀⠀⣄⣰⣾⣛⣿⣿⠿⢿⡿⠻⣿⣿⣾⣿⠿⣿⣷⠿⠛⠃⠀⠀⡀⠀⠀⠀⠀⢹⠟⠻⢿⣿⠿⢿⣿⣿⠿⣿⡟⠛⠻⡇⠀⠸⠀⢀
⠀⠀⠀⠠⠾⠷⣽⣿⣿⣭⡷⣶⣶⣶⣟⢿⣷⣾⡶⠖⠺⢃⡠⢶⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠁⠀⠈⠇⠀⠀⠃⣠⣾⣿⣿
⠀⠀⠀⠀⣄⣀⠘⠋⠀⠉⠛⢿⠟⠻⣿⠿⠛⠋⢀⠤⠒⣡⠤⠚⠀⠀⠀⠻⢿⣿⣦⣄⣀⠀⠀⢰⠀⣠⣤⣼⣄⡀⠀⣂⣀⣠⣿⣉⣽⣿⡏
⠀⠀⠀⠀⣀⣸⠇⡞⠓⠲⣤⢀⣄⡀⠀⣀⠴⠊⣁⠤⢊⡥⢖⡇⠀⠀⠀⠀⠀⠝⠻⢿⣿⣿⣿⣿⣶⡞⣧⣤⣭⣍⣷⣿⣭⣽⡿⠥⠾⠟
⠀⠀⠀⠀⢌⣉⠀⠛⠲⠴⠏⢬⡀⠈⠉⣀⠴⢊⡥⠒⣁⡴⠛⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠉⢹⠙⠳⢿⣭⡭⣽⣿⡿⢹⣟⢷⣄
⠀⠀⠀⠀⢠⣈⡇⣖⠓⠒⡆⡤⢤⣉⣉⡥⠚⣉⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⣄⠀⠀⠀⠀⢸⠀⠀⠀⠸⢠⡿⣸⡇⠀⠙⣷⣝⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠳⠧⢤⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⣀⣸⡀⠀⠀⣰⣿⣷⡏⠦⠤⠀⠈⠙⠻⢿⡿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠾⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠂⠒⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣤⣶⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣶⠖⠁⠀⢀⢶⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠟⠛⠛⠻⠳⠳⠿⠿⠶⠿⠿⣾⣿⣿⣾⣿⡟⠁⠀⢀⣴⡿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⣀⢔⣿⠏⣡⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠤⠤⣤⣤⣤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣶⡿⣡⡞⢁⡼⡡⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⡏⠉⠉⠉⠉⠉⣿⡟⠁⢠⢞⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢈⡉⢈⣉⠉⠛⠋⠉⠁⠀⠐⠶⠟⠛⠀⠀⠄⠠⠔⢻⣤⡞⢡⠎
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⣿⠀⠒⠀⠂⠒⣤⠖⠂⠤⠶⠤⢤⣿⢃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠉⠉⠒⠂⠂⠀⠀⠛⠄⠀⠀⠤⠤⠼⠟⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⡏⠀⠀⠀⢀⣽⣿⣶⣶⣶⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡾⢿⡿⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⡿⠻⠿⠛⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⠀⠀⣀⣀⡰⠒⣶⠉⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣯⣁⣈⣉⢶⣚⡋⠙⣒⡄⠒⠒⠢⣄⣀⠋⢁⡴⠓⠋⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡍⠈⠉⠀⠀⠈⠉⠉⠉⠙⠒⠗⠺⠋⠋⠉⠁⠀⢀⣤⣤⣈⠅⣉⢸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠛⠉⠓⠦⠶⠲⠦⣀⣀⣀⡀⠀⠀⢁⡤⠖⠛⣋⠟⠁⠈⠙⠁⠈⠀⠶⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠲⠶⠶⠤⣥⣤⣭⣭⣷⣏⣤⠶⠿⣿⠀⠀⠀⠘⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⣠⠠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⠂⠀⠀⠳⠬⠀⠠⡴⠬⠠⡈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠒⠒⣺⠁⠈⡇⠀⠀⠀⠃⠈⡸⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠚⢁⡟⠠⠚⣡⠆⢰⢂⢆⢧⠏⠀⠐⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠸⠀⠀⠐⢍⡀⠈⠈⣠⢀⠀⠀⢠⠄⠄⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡔⡩⢄⠀⠀⠀⡏⡏⣀⠀⡟⢠⢠⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⠃⠀⠀⠀⠸⠸⠸⠅⠖⠃⠋⣾⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣉⡈⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠐⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⢀⡸⠃⢸⠀⠀⠾⠆⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣹⡀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⢔⣢⣤⣄⠀⢠⠘⣶⡙⣉⣉⣬⠛⠷⣌⣃⣰⢬⠄⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠉⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠟⢠⣅⢲⣟⣴⣿⠯⠿⠿⣿⢿⡷⠦⠬⣾⠿⣤⡆⠀⠀⠀⠀⠀⣾⣾⣰⡾⢂⣀⣼⢓⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣄⣄⣶⣾⡇
⠀⠾⠿⢟⠸⠃⠆⢸⡆⠀⣸⣿⣿⠈⢸⢿⣾⢝⡟⡝⠛⢛⣷⣿⡖⠂⣿⠂⠀⠀⠀⢰⡟⠯⠿⠿⠚⠃⢹⣮⣧⠀⠀⠀⠀⠘⠀⠻⠿⢛⣿⣻⣯⡟⡇
⠀⣠⣍⢩⣃⠀⠀⢻⡗⢠⡼⣿⠏⠀⠀⠸⠿⠘⡇⢃⠀⠙⠛⠒⠃⠀⡏⠀⠀⠀⠀⠸⣶⠀⠀⣾⠆⠀⠀⣿⠀⠀⢠⡤⠤⣖⠀⠀⠈⢿⣿⣻⡞⢺⡇
⠀⣸⣋⣯⣭⢶⡖⢸⠇⠀⣼⣷⢶⣿⣬⣥⣤⣴⣷⡧⣀⣠⣭⣠⣤⣄⠹⣏⠈⡟⣻⣴⣋⠀⢀⡘⢲⣤⠄⡁⣘⡧⣦⣻⣶⣟⠀⠰⣼⣭⢸⢿⢠⠾⠁
⠀⠉⠏⢸⠁⢈⠣⢸⢦⢂⢲⣴⡎⡀⣠⣄⣤⣤⡄⡍⠽⣶⡇⠤⠈⠹⣿⢻⠎⠩⠿⣷⣎⣛⣀⡀⣀⡉⣉⡧⠬⢠⣽⣷⣞⠹⣀⠀⢘⣏⡄⠉⠀⢺⠂
⠀⡂⣿⣼⠇⠼⠶⢸⡏⢸⢸⣿⡇⠀⢸⣿⣼⣿⡂⡇⢸⣿⡃⠀⠀⠀⣤⠀⠐⠀⡈⠒⢯⢹⠋⠀⠀⠉⠪⠈⠀⢸⣿⡿⡿⢼⡇⠀⣼⣿⣿⠁⣃⢻⠂
⠀⣻⠒⡟⣰⢎⣶⢈⣃⢸⢨⣿⡇⠀⢸⠇⣶⢸⡇⡃⢸⠯⡇⣀⠀⡆⣿⡴⢢⣘⡛⡄⣿⢸⣤⠀⠀⠀⢈⣀⠀⢸⢻⣿⣿⠙⠏⠘⢿⢿⣿⠰⢿⠟⡃
⠀⢛⣾⢡⣟⣫⣏⡐⡃⣾⣞⣻⣟⣿⣿⢻⣯⣯⣿⣽⣾⣦⣷⣿⣾⡿⣿⣛⢻⣿⣶⣶⣾⣄⠼⣔⣠⠉⣽⣿⣷⣮⡬⢩⣿⣄⠶⡿⡬⠭⠛⠖⠤⢥⠄
⠀⠀⣇⠀⣯⢿⣅⢻⡇⠉⣉⢻⡻⠿⠿⠺⠷⠛⠛⠛⠛⠂⠉⠉⠉⠀⠀⠉⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠀⠓⠀⠀⠙⠃⠉⠑⠃⠀⠀⠘⠃⠀⠚⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠈⠦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⡀⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⣿⠀⢸⠆⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⢈⠀⣀⠀⠀⣠⣤⣤⣤⡤⠀⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⡄⠒⠀⠀⠚⠀⠀⢰⠀⠈⢉⢉⠉⢠⣺⢠⠀⠀⠚⠉⠀⠀⠀⢀⠀⠀⠀⠥⠒⠂⢀⢉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠆⠆⠀⠈⠉⠈⢸⡬⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⡀⣿⣷⣷⠀⢤⠀⠀⢀⢀⣠⠀⢄⠀⡈⠀⠀⠀⠀⠀⠐⠀⠀⣠⡄⠤⠄⠀⠶⡶⠿⠈⠈
⠀⠀⠀⠀⢐⠠⠀⠐⣿⣿⣧⠀⢈⠒⠋⠈⠙⠃⠀⠤⠙⠷⣦⣀⣄⣀⠀⣆⠀⠀⣏⡁⠈⠀⠀⣤⣤⣴
⣀⣀⣀⡀⣀⣀⡀⠀⠈⢹⣿⠄⠀⣠⣾⣿⣿⣦⣜⠡⡀⠀⠸⡟⠈⢤⣠⣁⠀⣴⠍⠁⠀⠀⡄⠉⠉⣭⠈
⣭⡩⠨⢾⢯⠇⠀⠀⠀⢸⡟⠀⠀⣿⣿⣿⣿⣿⣿⣷⣽⠲⠲⠒⠄⠄⣀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⣿
⢶⠂⣤⢺⡞⠋⠀⠀⡀⢸⢇⣀⣀⠛⠻⡿⠏⠍⡁⢿⣿⣿⣿⣦⡀⠀⠀⠁⠸⠷⢦⣄⣀⣤⠀⠀⠀⡷
⣋⣉⣹⣏⣥⠀⠀⠀⢀⣼⣰⣿⡏⠀⠁⠀⡀⠢⣷⣼⡁⠹⢿⣿⣿⣦⡀⠀⠀⠄⠀⠀⠉⠋⠀⠷⢦⡧⣀
⢩⡂⣑⡚⣯⠤⠀⢰⣾⣿⡿⢿⡇⠀⠄⠀⠁⠀⢻⣿⣷⡄⠀⠙⣿⣿⣿⡦⣄⡀

⠀⠀⠀⠀⠀⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⣠⡆
⢀⢀⣹⢀⡅⠀⠀⠀⡀⢀⣠
⠐⠞⠀⣸⡄⠰⠀⣇⢃⣾⣟⢀⣦⡦⢤⠀⢄⢀
⡇⣾⢺⣹⡗⣿⠀⠀⢸⣿⣧⣟⣿⠀⠀⡀⠀⢠⠉⢠⠀⢇⡄⠀⠀⠀⢛⠒⠀⠀⡀
⠙⠇⠸⢿⣿⣿⠀⢀⠤⢿⣟⡿⣿⠀⠐⡇⢄⠀⠀⢸⣇⣄⡇⣦⠀⣀⣜⡇⠐⢪⡀
⠀⢠⣿⣯⣿⠛⢀⢸⣶⣿⣿⢿⣿⣿⣠⣧⣘⣤⣼⣿⣿⣿⣿⣿⣧⣤⣰⡇⣦⢾⢂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀
⠺⢧⣿⣿⣿⢦⣀⣸⣿⣿⣿⠻⠿⣷⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠙⣾⣿⣿⢷⣸⣼⡧⡤⡀⠧⣾⣇⠀⠀⠈⢠⡀⣤⡀⢀
⠀⠀⠀⢉⡜⢉⡉⠉⠉⢉⣿⠀⠀⣿⡿⣋⣀⣈⡙⠃⠀⠀⢹⣿⣿⠿⣻⣿⠈⡻⠿⠿⠹⡽⢶⣿⣿⣶⣷⣬⣼⣷⣿⣶⣾⣤
⠀⠀⠀⠈⡅⠨⠀⠰⢠⠀⠹⠠⠀⢽⣯⣋⣋⡉⠃⠀⡀⠀⠈⠛⠛⢻⣿⡇⡀⠘⠛⠛⠿⣤⠠⡄⣼⠛⣿⠿⣿⣿⡭⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠚⠛⠀⠆⠆⠀⠀⠀⠀⠀⠀⠂⢸⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣷⠁⡘⣿⡄⠀⠂
⠠⣤⢤⣤⢤⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠐⠀⠀⠋⠀⠘⠋⠁⠀⠠⠀⠀⠠⠘⠃⠁⠈⣀⡏⠤⠠⢿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⡶⠛⠀⢒⡒⡒⠒⠾⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠁⡳⠀⡗⠀⡸⢴⣄⠀⡏⢸⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠁⠀⢠⠀⣤⡤⢀⠐⢻⡯⡀⣩⢰⡿⠀⠐⢦⡀⢠⠖⣤⠄⠀⠤⡖
⠀⠀⢀⣠⣾⣯⡟⣦⠖⣶⣡⡾⣿⣃⡄⠀⠦⢰⡄⡾⢀⣴⢶⠇⢸⠀⠘⠁⠀⣿⢀⠀⠀⠀⠸⠁⣮⣾⡇⢠⣀
⠀⠀⠈⣿⣿⣛⡉⠿⣟⠓⢋⣻⢿⡷⠄⠀⡱⣤⣧⠾⡋⠐⠛⠗⣤⠀⢠⠠⠀⣰⡀⠀⠴⠀⢀⢺⡿⣸⠇⣿⣿
⠀⠀⠀⢲⡀⢰⡆⠀⣠⡀⣠⣘⣸⠶⠗⠀⣴⠟⣠⣘⠁⠀⠀⠀⢹⠀⢀⢨⠀⣿⠃⠀⠀⣁⢼⢸⡇⣿⠀⠓⠙
⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠈⣭⣅⡔⡏⡀⠡⠾⠋⡛⢇⠿⡷⠂⠈⠀⢈⣀⡀⢉⢠⣶⣀⣿⢸⣸⡇⣽⠀⢾⣷
⠀⠀⠀⢰⡶⠦⠀⠀⠠⣤⡘⠛⠋⠛⠈⠇⠀⡀⡞⠛⠋⠈⠀⠀⢸⡂⢀⠀⠃⢈⠀⢀⠉⠉⣿⠟⠁⠆⠀⠈⠋
⠀⠀⠀⠘⢡⠎⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠋⠈⠰⠘⠁⣀⠰⢀⠘⠃⠋⠀⠀⠈⢠⣼⣍⠀⣵⣶⢄⠘⡇⢰⣶⠄
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠀⣠⣬⠄⣦⠘⠖⠒⣥⣬⡘⣯⣥⢠⣦⢴⡆⣾⡶⠀⠀⠀⠉⢹⣾⠀⡇⠘⠛
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠤⠄⣤⡿⠀⠇⢰⢻⣳⡿⢸⡇⣿⣿⢸⣿⣿⣇⠻⠇⢀⣀⠀⢰⢸⠿⠀⠇⣠⣠
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣿⠨⠉⠁⠀⠶⣯⠥⠄⣟⣋⣉⠀⢰⠀⠈⢁⡬⠸⣀⠰⠄⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣳⡇⡇⡂⠀⠀⣿⢉⡟⠁⠀⠐⠤⠠⠧⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠈⠈⡇⢣⠍⠀⠀⠙⠘⠋⠀⠑⡀⠀⠀⠠⣊⣩⠇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠂⠀⠀⠴⠶⠖⠁⠀⠀⠀⢰⠑⢦⣤⡄
⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢾⣀⢸⠿⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠡⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡺⠆⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠰⠐⠘⠊⠂⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠰⢄⠀⢀⢄⠠⠂⡤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠘⠘⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⣀⡸⠀⠀⠀⠀⠀⠀⠀⢎⡀⡱⠀⢀⣄
⠀⠀⠀⠀⠀⠀⡃⠈⡄⠀⠖⠲⠀⠀⢀⠴⡄⠀⠀⢠⠀⠄⠀⡌⠀⡂
⠀⠀⠀⠀⠀⠀⡭⢭⠀⠀⠀⢸⠀⠀⠨⣀⠸⠀⠀⠐⠀⠀⠀⢨⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢰⠀⢦⠀⠀⠸⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠊⠉⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠠⠒⠒⠀⢸⠉⠉⢹⠀⢘⠉⠉⠙⠀⠒⠂⢆⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠸⠀⠀⠈⠉⠁⠀⢐⠀⡇⠈⠢⡀⠀⠀⢀⣤⣤⣒⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠷⢀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸⠀⣨⠀⠀⠀⠀⠀⠀⠘⠒⠃⢀⠴⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠂⡞⠅
⠀⠀⠀⡂⠀⠁⠒⠀⠤⠤⠀⣀⣀⣀⣈⣉⣁⣀⣀⣀⡀⠠⠤⠄⠐⠊⠁⠀⡇⠀⠀⠰⠆⠀⠀⠀⠤⠤⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠐⠒⡏⠄
⠀⠀⠀⣉⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢈⠀⠀⠀⢐⠒⠂⠀⠠⠤⠤⠤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⠀⠈⠉⠒⠠⠤⢀⣈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈⢉⣀⠠⠤⠒⠈⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠁⡏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⠤⠄⠄⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆
⠀⠀⠀⠈⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠒⠒⠒⠒⠒⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣄⠤⢀⡤⠠⢄⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⢒⡠⠶⠺⣦⠴⠦⣴⠳⠶⢄⠀⠩⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⡠⠊⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠑⣄⠈⠢⡱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀
⠀⠀⠀⢠⠃⡔⠁⠀⢀⠃⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠑⡘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢀⠆⡜⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠐⡈⠆⠀⠀⠰⡁⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢁⠇
⠀⠀⠎⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠐⡈⠄⠀⠀⠋⢲⡐⠢⠤⠬⣉⣉⠈⠉⠀⠁⣉⣀⣀⡉⣁⠠⠀⢐⡴⠙⠆
⠀⠈⡶⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡀⠀⠀⠰⡆⠀⠀⠁⠦⠌⣁⠐⠂⠀⠄⠀⠠⠨⠤⠀⠀⠠⠀⠀⠒⣈⣁⣰⠋
⠀⢰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠈⠒⠤⡉⢈⡁⠀⠐⠒⠀⠀⠀⠈⠉⢉⣀⣁⠤⠒⠁
⠀⠈⠒⠀⠄⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⠂⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠉⠂⠤⢀⣀⠠⠔⠊⠁⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⢦⠀⠀⠀⠀⢀⠠⠉⢦⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢅⣀⡼⠁⠀⠀⠀⠈⠢⠴⠛⠀⠀⠀⠀⠐⣄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠇⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡀⠀⢈⢼⡇
⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠃⠀⢣⣾⠟⠶⠶⢄⡀
⠀⠀⠀⣀⡴⠛⠁⠀⠈⠠⣵⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠀⠐⠈⠀⠀⠀⠀⠀⠈⠤⠒⠛⠁⠀⠀⠀⠀⠉⠳⣄
⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠛⠄⠄⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠒⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⢸⠃⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠶⠒⠒⠒⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠉⡀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡖⠀⠀⠀⠁⢂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠂⠀⢁⠀⠀⢻
⠀⠀⠀⣧⣼⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣠⠚
⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣤
⠀⠀⠀⢘⠣⠀⠀⠂⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣠⣿
⠀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡀⠀⠀⠀⢀⠠⠤⠀⠤⢀⠀⠀⠀⠀⠀⠀⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣏
⠀⠀⠀⠀⠁⣆⣀⡀⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠏⠉
⠀⠀⠀⠀⠀⠈⠃⠰⣄⠘⠻⠢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠞⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠢⢤⣌⣉⠉⠁⠒⠲⠦⠤⣄⣀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠉⠉⠋⠉⠁⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣉⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣏⣉⣩⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡖⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⣀
⠀⠸⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠁
⠀⠀⠂⠀⠀⠀⡤⢤⡄⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠰⠶⠚⠙⠛⠑⢦⠀⠀⠆⠀⠐⠦⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⡀⠀⠀⠀⠀⠁⠐⠋⠰⡄⠀⠀⠄⠐⠇⠘⡄⠀⠀⠛⠛⠻⠿⠚⠋⠂⠁⠀⠀⠐⠃⠀⠀⠀⠀⠚⣇⡄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠁⠀⠀⠁⠐⠁⠀⠀⠀⠰⠢⠴⠤⠤⠤⠤⠄⠀⠀⠘⠇⠀⠀⠐⠀⠀⠋⠠⣄⠄
⠀⠀⡠⠄⠀⠀⠀⠀⠈⠉⠢⠄
⠀⠀⠒⠒⡖⠖⠐⠀⠒⠖⠰⠶⠂⠀⠀⠀⠀⠀⠀⢰⠫⠄⠀⠀⠀⠀⢀⠐⠆⠙⠾⠞⠿⠹⠯⠄
⠀⠒⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠛⠲⠄⠀⠀⠚⡂⠀⠐⢚⠚⠖⠒⠐⠀⠚⠂⠀⠀⠄⠐⠀⠀⠠⠖⠂
⠀⠀⠒⠀⠂⠀⠴⠄⠶⠆⠰⠶⠀⠀⠀⠐⡤⠃⢈⣉⣋⣛⠆⠀⢀⣄⠠⠄⢐⡂⣀⣐⠀⠈
⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⣀⡀⡄⠀⠀⠀⠄⠀⢠⣤⣭⣍⠁⠀⠨⢿⢩⣤⢭⣥⣫⠽⠢⠀⢈⠃⠇
⠀⠀⠬⠅⠐⠜⣻⣇⣏⠻⢲⢤⡀⠀⠀⠀⠀⠀⠶⠶⢤⣬⠀⠀⠀⠈⠀⠀⠼⠁⠸⠀⠀⠀⠈
⠀⢀⣈⣤⡤⠞⠁⠀⠠⠵⣤⣌⣂⠀⠀⠀⠀⠠⠖⠶⠶⠶⠀⠀⠀⠀⠤⠄⠀⠀⢀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠁⠓⠂⠀⠀⠀⠀⠀⠃⠐⠈⠈⠉⠉
⠀⠀⠘⠒⠒⠒⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠤⠀⠤⠠⠠⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡇⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠃⣾⠟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠀⠉⠻⣄⠀⠈⠉⢉⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⠀⠀⠴⠀⠀⠙⣦⡀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠤⠀⠘⢡⠄⠉⣁⠀⢸⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠀⠱⣆⠀⠘⠀⣥⣠⣟⣀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠛⠛⠛⠉⠉⠉⠓⠶⠶⠛⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⣠⣶⠛⢳⡄⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣠⡴⢦⠀⠀⠀⠀⠀⠀⢠⡞⠁⠘⠷⠞⠁⢺⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣼⠃⠀⢸⡆⠀⠀⠀⠀⣰⢿⡇⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠟⣿⠀⠀⠀⣿⠶⣤⣤⠞⠃⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⣀⣴⡟⢳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠋⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠉⣧⠈⣇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠉⢿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡇⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢹⠀⠀⢸⡎⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠶⠶⠖⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢐⡒⠒⠐⢒⣂⠀⡂⠀⠀⠀⠀⠘⢟⡙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠈⠁⣠⣄⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⣿⣥⡷⠛⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⢦⠀⠀⠀⠀⠀⣀⡄⠠⠀⠉⢀⣠⡴⠛⡁⠀⠐⠀⠀⣤⡄⠀⠒⠀⠨⠄⠀⡂⠀⣤⡄⠀⡴⠀⠐⠂⠘⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣲⣦⠿⠋⠀⠀⣄⠑⡀⢻⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠧⠀⠇⠇⠀⣠⠀⠰⠀⠠⠄⠀⠆⠀⠸
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⢢⡇⢸⠀⡯⠰⠇⠈⣠⠤⠄⠠⠀⠀⠀⣀⡀⠀⠀⣆⣒⠀⠐⣷⡀⣔⠀⣲⠀⠀⡀⠀⣒
⠀⠀⠀⠀⠀⠠⠤⠴⠄⠄⠀⠘⠙⠛⣛⡛⠓⠛⣀⡰⠔⠋⠀⠀⠠⡀⠤⠼⠛⠁⠐⠀⠋⣉⠁⠀⠈⠉⠛⠀⠿⡀⢘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠄⢀⡡⣶⠆⠓⠦⠐⠒⠂⠀⠾⠖⠂⠐⡃⠄⠄⠀⠀⠃⠀⠒⠐⠒⠐⠀⠂⢀⣺⠇⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠉⣴⣿⣦⠈⠀⣾⣿⡄⠁⡀⠀⣄⢀⠀⠀⠀⢸⣅⣾⡧⠈⣄⣾⢣⠈⢡⡄⠀⣤
⠀⠀⠀⠀⢠⣶⡦⠀⢀⣄⣴⡀⠤⣠⠾⠇⢀⣿⠿⠛⣀⢌⣙⣉⠐⣠⠏⠘⠛⠛⠷⣇⡾⠮⠄⠿⠧⣼⡀⣧⡘⠀⠸⠷⠀⠛
⠀⠀⠀⠀⡼⣿⣤⣀⣬⡍⠤⠍⣠⣠⣄⣠⢌⣡⣤⣤⣿⣷⣷⣷⣾⣥⣧⡀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠙⠋⠛⠛⠋⡍⠛⠛⠚⠚⠋⠉⠋⠉⠉⠉⠁

⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤
⣿⡟⢻⢿⣿⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠀⠐⠆⠀⠀⠀⢐⠁⠀⠈⣡⠕⠀⠀⠀⠸⢏⣙⡆⠀⠀⠀⠀⠀⢠⡆⠤⠀⠀⢤⠀⠀⠀⢀⡠⠜⠿⢦
⠀⠀⣈⠙⠓⣾⣛⣷⠀⢰⣿⡿⢿⣂⣸⡄⠀⠀⡀⠀⠀⠀⣸⣄⠀⠀⠠⣷⣦⣽⣷⢆⣰⡆⠀⠀⠀⣾⡟⠒⠚⠈⢰
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠰⢸⢸⣿⢯⡇⠀⠃⠀⠀⠹⠿⠀⠀⠻⠆⢄⡤⠀⢸⡷⣦⡄⠀⣼
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠊⠁⠀⠐⠀⠀⢀⣀⡀⠀⢠⣤⣤⡤⠀⢸⣄⣈⡁⠀⣈
⠀⠀⠀⠀⢀⢀⠀⠤⢀⡢⠀⠀⠀⢠⣾⣛⣛⡿⠞⠀⠀⠀⠀⠀⠀⠀⠤⡅⠈⠧⠺⠖⠶⠶⠶⠖⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣟⡶⣶⢤⣌⡀⠀⠀⠐⠀⠤⢍⣙⣷⠀⠀⠠⠔⠀⠀⣤⣶⣢⠀⠀⠀⠀⠀⢀⣚⣁⠚⠻⢶⢂⣰⠄
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⡟⠀⠀⠯⣉⡓⠢⢤⣙⠀⠀⠁⠀⠀⠀⡠⣾⡏⠀⠀⠀⣄⡀⣉⣉⠉⢀⢠⠼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠑⠺⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠙⠂⠐
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠠⣴⢆⢠⢦⡀
⠀⠀⠀⠀⠀⠁⡈⢲⡟⣧
⠀⠀⠀⠀⠀⠀⠘⢿⡶⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠐⠓⠂⠒⠒⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡚⢰⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⡇⣄⣷⣤⣼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⣶⣸⡆⠀⠀⠀⠀⠀⢸⡇⠀⡄⢠⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢱⡾⣿⣄⣀⣀⣀⣀⡀⢃⡀⣅⣸⠀⡇⠀⠀⠀⠀⢀⣠⠤⣒⣭⠴⡟⠪⣴⣄
⢀⣄⣼⣀⣀⡀⣀⡀⠀⠀⠀⠀⢿⣿⣿⡉⠈⠉⢩⠁⠹⠋⣭⠉⢉⡉⠉⢤⣐⣾⠦⠶⣯⡥⠙⠓⠁⠃⠛⡉⢶⣷⣄⣄⡀
⠈⠏⠁⠄⠈⣀⣿⡇⠀⠀⠀⠀⠀⠹⢹⣷⠲⣶⠞⠒⠒⠒⡇⠀⠸⠒⠉⢞⡿⠷⠓⣨⣤⡀⠈⠋⣩⣍⡁⠟⣍⣥⢿⡋⡄⠀⢰⡀
⠀⠀⠀⠀⠀⢸⣉⠁⠀⠀⠆⠀⠀⠀⠘⠃⠀⠉⠀⠀⣰⠆⠖⠒⠀⣀⡛⠘⠒⡐⠋⣓⣛⠃⠒⠁⡙⢲⡷⠎⣛⠻⠀⢥⠈⢉⣾⢥
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⡏⡏⠀⡀⡅⠀⣉⣿⠀⠀⢹⣹⠸⡇⠀⣏⡇⠀⠀⣒⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣠⠀⠀⠀⠀⠤⠀⠠⠳⠃⠠⠤⡠⠄⠙⢛⠀⢤⠸⠿⢴⡯⠤⠗⠥⠄⠀⢿⠧⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠓⢠⠼⠿⣀⠀⡤⠄⣤⣤⣤⣤⣤⣤⡄⣧⣤⣄⣠⣤⣀⣄⣠⣼⣧⣡⣄⣀⣠⣤⣀⣀⣀⡠⣤⡀⠠⠔⡃⠘⡄⠤⣛
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⢸⣶⣤⡉⠘⠛⠚⠒⣼⣶⣽⣿⠭⣽⠏⠉⠂⣹⣿⡿⣧⣶⣦⠌⠈⠉⠉⠙⠧⠘⢲⣍⠘⣁⠹⣀⢣⣼
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠐⠀⠀⢨⣭⡿⠀⢀⡴⠶⢶⣿⣦⣿⠸⡶⡇⠄⣰⡾⣿⣿⡇⢩⠙⣹⠇⣰⣿⣯⡇⠀⢠⣧⡂⣺⣿⣴⣦⡏
⠀⠀⠀⠀⠀⣀⡀⠀⠠⣸⡆⠀⠉⡇⠇⢠⢶⣾⡄⢈⡟⡣⠀⢸⣿⣻⣿⡇⣮⢿⠀⡇⣿⡇⣿⣷⣿⣿⣇⠸⡇⣿⠀⣻⣿⣿⡇⢀⠀⠂⣀⠙⡉⠉⢿⡇
⠀⣉⠉⠹⠀⠿⠿⡿⠧⢀⡁⠀⠀⠇⢀⣴⣋⣩⡇⠘⣿⡆⢀⢸⡋⣿⣿⡇⢧⡟⠀⢃⡿⡣⢿⢿⢿⣫⡏⠀⠁⠻⠄⣿⣟⣿⡇⣺⢈⣲⡿⠿⠙⣀⢾⢧⡦
⠈⠛⣲⣦⡄⠀⠀⠃⠀⠀⠀⠀⠀⠄⠰⡿⠾⠿⠧⠼⠨⣼⠃⢸⣿⣿⣿⠇⣿⠇⠀⢄⡘⢿⠚⠻⠛⠚⠁⠄⠄⠚⠒⠘⠉⢉⠀⣚⠁⠤⠄⠀⣿⢿⣿⣾⡆
⠀⠀⢸⣽⠁⠀⠀⠀⠀⢈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠐⠂⠀⠉⠀⢛⠉⠇⠇⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠀⢀⡀⡀⠀⢀⣄⢄⠀⣀⠀⢀⣄⣠⣀⣀⠀⢀⡄⢠
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⣻⠛⠉⠟⠙⠖⠛⠃⠀⠃⠈⠒⠋⠋⠀⠛⠀⠳⠊⠷⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡤⢦⡀⠀⠀⣠⠄⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣠⢎⡴⣰⢃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠳⠚⠚⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠉⠐⠢⣀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠂⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠐⠦⠀⠀⢦⠀⠀⠀⠸⠀⠀⠀⠀⢨⢀⡈⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢛⠀⠐⠛⠛⠓⠄⠐⣄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠚⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⠂⠀⠀⠀⢸⡆⠀⠀⢈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠤⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠰⡀⠀⢠⣴⡶⣿⣦⣤⡀⠀⠀⢸⡆⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡐⠐⠀⠀⠀⠀⠙⠁⠈⠁⠀⡠⠂⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣤⡤⠄⠈⠀⡠⠊⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⡔⢒⣿⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢑⠲⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢈⢄⡄⠁⠀⠈⠓⠒⠲⠌⠤⠵⠀⠰⠎⣰⠇⡀⢀⡄⡝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠊⠀⠀⠀⠃⠀⠀⠀⠀⠐⠆⠀⠀⣀⡏⠀⠋⡼⠈⠀⠀⠀⢘⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣿⣱⠀⡰⠇⣿⡇⠀⢀⣘⢂⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠏⠏⣏⡼⢸⠱⡋⢀⠀⠀⠉⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⣿⠁⡀⠀⢇⠀⡄⢠⣦⠀⠐⠀⠀⠂⢈⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠀⠈⠑⠰⡿⠁⡀⠀⣆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡇⢣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠁⡀⠀⠀⠀⢀⠉⠇⣂⠘⠂⠉⠂
⠀⠞⠀⠀⠀⠀⠀⠐⠣⡀⠇⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⢰⠁⠀⠀⢀⠂⠀⠀⠈⠉
⠀⠃⠁⠀⠀⡠⠊⢀⠂⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠘
⠀⠈⢦⠀⠔⠀⣠⠠⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠂⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣛⣿⣛⣿

⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀
⠀⠀⢀⠚⠁⠀⠀⡄⠀⢀⠀⠰⠀⠀⠀⠁⠀⠀⠘⠖⠀⠰⠂⠀⢀⡀⠀⠀⠀⡀⠘⠀⠀⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠠⢠⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠚⠁⠀⠀⠀⠀⠀⢆⠀⠀⢀⠄⠀⠀⠀⠂⠀⠀⢀⣠⣤⡀⠀⢀
⠀⠀⠀⠀⠑⠢⢄⠀⠀⠀⠐⠀⠒⢊⣁⠀⢀⡀⡀⠀⢀⠀⢀⡀⡀⡀⠀⠀⠀⠘⠉⠉⠁⣄⠛⠦⠄
⠀⠀⠀⠸⠦⠄⠀⠁⠀⠀⠀⠀⢠⢸⣯⡇⣼⣇⣧⡞⢸⡤⢸⣀⠗⣇⠄⣤⠄⠀⠀⠀⠄⡈⠀⠀⠓
⠀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠀⠘⠘⡇⡷⠇⡇⠏⢣⢸⠀⢸⠙⡄⢸⠀⠿⠄⠀⠀⠀⠓⠊⠃⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠤⣀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠁⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⠈
⠀⠀⠀⢀⣀⡈⠀⠀⠀⠄⠀⠀⠀⠈⢠⠂⠀⠀⠀⠄⠐⠀⠀⡀⠉⠐⠂⠤⠄⠀⠠⠄
⠀⠀⠐⠋⠐⠛⠉⠿⢶⠖⢒⡤⠤⣀⠀⠀⠴⠉⠃⠁⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠂⠀⠠⠀⠈⠀⠀⠀⠤⠀⠤⠤⠄⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⣶⠧⣤⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠋⠘⠁⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⠗⠰⠷⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡅⢰⡏⢘⣿⡟⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣉⡿⠯⠥⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠿⠛⠋⠁⠀⠀⣉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠂⠀⠀⠀⢙⡂⠊⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣈⠉⣸⣓⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠀⠀⡀⢀⡁⢤⣀⡀⠠⠀⠲⠐⣶⠴⠄⠀⠀⣿⣒⠒⣮⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⣶⡆⠊⣁⠀⠀⠀⠀⠉⠀⠀⠠⠐⠂⡔⠂⣦⠄⠐⠁⠛⠛⠊⡹⣧⣐⡀⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⣿⣖⠁⠀⠀⠓⢀⠤⢬⣠⣤⣄⣤⣁⣀⣁⠄⡐⠂⠐⠼⠄⡀⠺⢻⡏⣿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠶⠛⢛⣃⢒⣀⣋⣩⢭⣭⣭⣤⣽⣾⣶⣦⣶⣮⡵⢶⣿⣂⣒⡢⠾⢿⠓⣦⣨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣣⣾⡿⠻⠟⣿⡿⠋⠉⠀⠻⣮⣉⣻⣿⣣⣤⣰⣿⣟⡋⠀⠰⣦⡙⢿⣿⡏⠙⣶⢅⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣻⠍⢹⡷⢔⡲⣿⢟⠋⠛⠛⠉⠛⠛⡟⠻⡟⠀⠘⠋⠻⡍⠁⠀⠀⠱⣴⣾⣧⠄⠈⢋⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠐⢈⣇⣀⣀⡱⢀⢀⣀⣈⣤⣤⡄⠦⠤⢷⠠⠶⠀⠄⠀⡀⠙⠀⢀⡀⡏⣿⠀⠑⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡀⢸⡟⣂⠀⡅⠉⠜⣿⣿⣿⣿⠀⠀⠀⠀⠒⠀⠀⠀⠀⣿⣿⣿⡇⠈⠁⣿⠙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠠⣇⣽⣧⣄⣷⠈⠀⠄⢰⠀⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⢨⣿⣿⣿⣇⠀⠀⢿⠀⣳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⡛⠀⣠⣤⣤⣀⣿⣿⣿⣿⠀⡆⠀⣿⣦⡄⢀⠀⠈⣿⣿⣿⣟⠀⠀⢸⡄⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⡿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣤⣤⠈⣀⣀⠈⠀⠉⠉⠀⠀⢸⣦⠻⣀
⠀⠀⠀⠀⣠⣤⣶⣾⣿⣟⣶⣿⣫⣟⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣧⣶⣶⣿⣿⣳⣿⣠⠤
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⠛⠛⠛⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⣿⠉⠉⠉⢹⠁⠀⠈⠇⠀⠁⠀⠠⡄⣾⢹⡿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠘⡇⠀⠈⠒⠀⠀⠀⣲⠀⢿⢸⠃⢱⠀⠊⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠸⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣴⠀⠛⢧⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⠄⠀⠀⠀⠙⢆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡂⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣦⠀⠀⠀⠀⡸⠿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠀⠰⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⠀⠀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣷⡄⠀⠀⠀⠆⠀⠀⣿⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠈⣿⠀⠀⣇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡇⠀⠀⠀⠂⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⡀⠀⣯⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡺⣿⡇⢀⡘⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⣿⠀⣿⡇⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠆⢸⠁⠈⣀⠇⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⠀⣿⡇⢰⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⠀⡄⣡⡅⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣿⢿⠋⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣼⣄⣶⣼⡟⣿⣷⡄⠀⠀⣀⢀⠀⣀⠀⠀⢰⣾⣿⣿⠀⣿⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⣭⠷⠟⠋⠉⠁⠀⠀⢀⣿⣾⡆⣛⣀⣀⢨⣷⢿⣿⣠⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⣿⡿⣥⣬⣭⣝⣩⣥⣤⡍⣴⣿⡷⠂⠀⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣈⣙⣁⣨⣬⡍⠉⢉⣉⣉⣉⣀⣉⣍⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣟⣢⣿⣇⣿⣿⣿⣿⣿⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣻⣿⣿⣿⣻⣿⣿⣿⡿⣿⣿⣛⣿⣿⣿⣟⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣿⠙⢎⣿⡏⠀⠀⠙⣿⡿⠛⠻⣿⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣿⣆⡘⣿⣇⠀⠀⠀⣿⡇⠀⣠⣿⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣤⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣼⣛⣿⣿⣿⣿⣿⠏⠂⢀⣿⢡⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠀⠙⠃⠀⠀⠘⠃⠀⠀⠉⠉⠉⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣌⣉⣉⣛⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠷⠀⢰⡀⣴⠀⢠⣨⠁⢁⡨⠀⠀⠠⢀⠀⢠⠤⠔⢘⣒⣐⣒⣚⣫⠠⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠔⠈⠰⠘⢛⡀⠯⢤⡈⠵⢭⡈⠜⣧⠸⠷⠤⣠⠁⡉⠈⠙⠀⠉⠡⠀⠀⠴⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠄⠘⠇⠙⠒⠛⠓⠙⠋⡑⢚⣯⡥⢼⣭⡭⠑⠒⠚⠀⣀⡀⠛⠒⠒⠔⠂⠔⠐⠀⠦⠄⠀⡀⠀⣸⠀⠀⣷⠀⢸⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⠆⠁⣰⣇⠁⠀⠀⢀⠒⠘⠛⡛⡐⢠⡄⠄⠠⡄⠛⠂⣠⣼⣦⣇⡐⠎⠁⠀⠉
⠀⠀⠀⠀⠀⢀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠻⢿⠀⠀⠈⣿⠀⠀⠄⣼⠉⣅⣥⣼⣿⣿⣷⣿⣿⣿⣿⣛⣿⣿⣿⣿⡟⢛⡂⠀⣉⠀⠈⡅
⠀⠀⠀⠀⠀⢸⠀⠄⠈⠀⢀⠀⠁⠀⠀⢉⡈⠉⠉⠠⡏⠉⠀⠀⢸⠀⠈⣀⢆⣰⡆⡄⠉⢉⢉⡙⠛⣛⠛⠿⠿⠇⣸⡇⠀⡿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊⢈⠈⢉⠁⠀⠀⠘⠈⠁⠀⠀⠀⠃⢸⠀⠂⠁⠀⡉⠀⠨⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⢉⣘⠙⠰⣶⠀⠒⠒⢁⡀⠤⠤⢤⣇⣇⣀⣰⣤⡄⠘⠀⢸⠀⠉⠀⠿⠀⢠⠐⣀⠀⡀⢈⠀⠀⡆⠀⠲⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠟⠓⠛⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠘⠻⢿⠒⠶⣶⣶⣦⣤⣌⣀⣿⠀⠇⠈⡀⠀⠃⢸⡞⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠌⠀⠒⠚⠦⢘⣿⡏⠛⡷⡶⠶⣶⣼⣇⣠⣶⢶⣲⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⣀⣀⣀⠀⠀⠀⢰⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠈⠉⠀⠃⠁⠀⠀⠉⠋⠽⠛⠻⠿⠟⠳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠛⠿⠿⠿⡿⣾⡓⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⢲⡀⠠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⢹⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢢⠠⠀⠀⠀⠀⠀⢈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠒⢠⠄⠀⠀⠈⠉⠀⠀⣀⠀⠀⠀⠀⠈⢀⡵⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠤⠀⢀⠐⣤⠛⠄⠀⠀⠀⠀⣄⠀⠨⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⣤⢤⠀⢀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡂⠚⠋⡤⠉⡉⠭⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠐⠶⠂⠐⡊⠈⡤⠙⠶⠾⠛⠇⣙⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⢀⢀⣀⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠀⠀⠀⠤⠈⠀⠀⠙⣱⢰⢀⠀⠺⢧⠀⠀⠀⠀⠀⢀⡶⠋⠀⠑⠆⠌⠳⣤⣤⠗⠋⡉⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣠⡁⠈⣆⠀⠀⠀⢠⢾⠀⠀⠀⠤⠀⠈⢤⡄⠂⣀⠀⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢛⡀⠀⠑⠒⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠵⠃⢀⠀⠀⠀⠀⠦⠀⠀⠠⠿⠀⢬⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⠥⠠⡄⠀⠀⣉⠁⠖⠈⠉⠙⠛⠶⠂⠄⡠⢀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠒⠠⠄⢀⣈⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠀⠊⠁⠉⠓⠲⠀⠀⣀⠀⠀⠂⠈⠤⡀⠐⠀⠁⠑⠂⠶⢦⣀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⢡⡈⠰⠤⣄⢠⣄⠀⠀⠀⠀⠈⠓⠒⠀⠀⠐⠋⠀⠈⣀⠉⠀⠄⠉⠀⠀⠠⠈⢃⠰⠢⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠁⠁⠀⢀⠈⠀⠘⢯⡄⠀⡉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⢤⣀⣀⢤⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢁⣈⣀⡀⠈⠗⠄⠀⠠⠘⠔⠂⠈⣘⠳⠈⠉⢽⡲⠖⠠⢀⣀⣀⠀⠀⠀⠈⠉⠉⠛⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠢⠤⠄⠀⠉⠦⠀⠓⠈⠄⠀⠀⠀⠁⠈⠐⠲⠀⠀⢍⠛⠛⠛⣦⣀⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠄⢀⡀⠀⠐⠂⠈⢂⠀⠦⠀⠈⠀⡀⠀⠠⠘⠍⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠠⢤⣁⣀⡀⠀⠀⠘⠀⠤⣐⠒⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠤⣬⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢈⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠈⠲⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠈⢢⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⣠⠀⠈⠹⠀⠤⠒⠀⠀⢰⣤⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠣⡀⢻⡀⠞⠁⡀⠐⣤⣤⡀⠀⠀⢀⣾⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⢁⠾⠁⢺⢨⠉⣀⣴⣶⣿⠏⢸⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠿⣿⠿⠟⠛⠉⠀⢈⣀⡈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠰⠘⢹⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠒⠀⠀⠀⢀⠀⠐⠁⡐⠈⠂⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠂⠉⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⡐⢩⠀⠀⠀⢸⠀⠀⢀⠀⠀⠘⡀⠀⢀⠀⠀⠀⢐⠶⣿⡛⠊⠁⠈⠉⠉⠉⠁⠂⠁⠀⣀⣄
⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠈⡀⠀⢬⠳⣦⡀⠹⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⢀⣀⡀⠀⢀⡀⡐⠋⠉
⠀⠀⠀⠌⠀⠀⠀⡇⢀⠀⠀⢁⠀⡀⠑⠌⠙⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢈⡀⢀⡾
⠀⠀⢸⠀⠀⠀⠀⠃⠂⠀⠆⠀⢑⠌⠖⠀⠀⠀⠈⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢄⠈⣁
⠀⠀⠘⠀⠀⠀⠀⠀⡠⢲⡖⢚⡭⢲⡀⠀⠑⢦⣀⠀⠐⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡀
⠀⠰⠡⡤⠄⠒⠖⠁⠀⠋⡠⠋⠀⠈⠀⠘⠀⠀⠉⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠌⡁
⠀⠀⠀⠣⣀⡀⠀⢀⠤⠊

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂
⠀⠀⠀⢀⠀⠀⢀⠂⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⡳⣄
⠀⠀⠀⡡⠀⡉⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠈⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣥⣭⡆
⠀⠀⠀⣥⠀⠀⠂⡍⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⣢⠒⠉⢀⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡘⠉⠈⠁⢠
⠀⠀⡏⠈⠓⠒⠛⠟⠓⠂⠒⠋⠈⢻⠀⠀⠀⠀⠀⣨⣶⡇⢧⡼⠈⢼⡌⣿⠀⠀⠀⠀⠀⠀⠀⢻⠃⠴⠒⠀⠈⠀⢸⡉
⠀⠀⣥⣄⡀⣠⢀⡀⡀⣠⣀⢠⡴⠊⠀⠀⠀⠀⠐⣉⠉⠈⠁⠀⠀⣀⣁⢉⡁⠀⠀⠀⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠈⠉⠉⠈⠁⠈⠀⠀⠀⢀⠀⠀⠀⠀⠴⠛⠤⠄⠀⠀⠀⠩⠽⡿⠷⠀⠀⠀⠀⠄⠋⠉⠀⠀⠀⠀⠀⠀⠙⠂⠉
⠀⠀⠁⠶⠐⠦⠀⠀⠀⠀⠖⠀⢴⠊⠀⠀⠀⠠⣄⡀⣀⠀⠀⢀⠀⠀⡈⢁⣠⠄⠀⠀⠀⢠⣀⣀⡠⠄⣀⠀⠀⠀⠀⣤⠄⠞
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⠈⠉⠈⠈⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠣⣤⢀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡃⠀⠀⢸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⢣⡀
⠀⠀⠀⠀⣨⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⡆⠀⠀⠀⣴⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⣿⡀
⠀⠀⠀⠀⣡⣀⠄⠉⠈⠑⢂⠀⠀⠀⠀⠀⠀⠀⠚⢧⣸⣅⠀⠳⠾⢯⣏⡀⠈⠂⠀⠀⠀⠀⠀⠈⠁⠁⠐⡛⠋⠉⠀⠈⠆
⠀⠀⠀⠔⠪⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠦⢤⣀⣠⣄⣤⡠⠴⢧⡀
⠀⠀⠴⢀⠉⠄⠤⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⡠⠀⠀⡇⡄⠀⠐⠀⠁⠰⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠘⠄⠀⠴
⠀⠀⢀⡀⠀⣠⠒⠀⠀⢀⠀⢀⠀⣉⠀⠀⠀⠰⠾⠶⢤⡄⢀⣀⣀⡀⣠⣤⣤⡶⠀⠀⠀⢠⣀⠀⣆⠀⠀⠀⠂⠀⠀⠸
⠀⠀⠹⠉⠁⠀⠉⠀⠈⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠃⠀⠀⠀⠈⠉⠈⠉⠁⠀⠊⠑⠀⠀⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠥⢴⡆⠠⠤⠤⢀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⣀⢀⡀⣀⣀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⢠⠈⠀⠠⠀⠀⠀⢀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠈⠀⢈⠀⠀⠀⠀⣽⣉⡛⠓⠛⠓⠒⠚⠛⠛⢀⢛⣫
⠀⠀⣖⠒⠂⠄⣀⣠⢀⠤⠤⠄⠐⢉⠅⠀⠀⠀⠰⣤⣤⠄⠀⠀⠀⠐⠲⡖⠣⠀⠀⠀⠀⣭⣭⡉⠛⣛⣛⣛⡛⢚⣛⣩⣭⡏
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠉⠉⠉⠀⡀⢠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡀⣠⣿⡿⢰⣿⡇⠀⢠⣿⣷⠀⢠⣿⣿⡀⢀⣾⣿⡇⢀⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⢸⣿⡇⠀⢸⣿⡇⢀⣾⣿⣿⣧⣾⣿⣿⡇⢸⣿⡿⢃⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣇⢀⣾⣿⠃⣼⣿⠏⣿⣿⡿⢻⣿⡇⠘⣫⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠻⣿⣿⡿⠃⠰⣿⡟⠀⠘⠛⠁⠘⣿⡗⢈⣭⣉⣉⣉⠉⠁
⠀⠀⠀⠀⠀⠀⣶⣿⣶⣄⠛⠋⢰⣷⣆⠀⣠⣶⡄⣤⣦⠀⠀⣴⣦⠀⠀⢠⣤⡄⠀⠙⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢓⣀⠀⢻⣿⣶⣿⡟⠁⣿⣿⠀⠀⣿⣿⠀⢠⣿⣿⣧⠀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⠟⠀⠀⣿⣿⡏⠀⠀⣿⣿⠀⢸⣿⡟⢀⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⢋⣴⣿⠀⣿⣿⡇⠀⠀⢿⣿⣤⣿⣿⢁⣾⣿⠃⢸⣿⡿⠋⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠹⠿⠁⠀⠀⠈⠻⠿⠟⠁⠘⠿⠃⠀⠀⠉⠁⠀⢹⣿⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣭⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⣀⠀⠀⢠⡅⠐⠀⠉⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠑⢤⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⣛⡆⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡢⡀⠱⡀⠁⠀⠀⠀⠀⠀⠀⢀⢔⣫⣵⠊⢁⢁⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡀⢔⡬⠒⠉⢁⠸⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡥⠚⠁⠀⠀⠀⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⢆⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢆⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢁⠊
⠀⠀⢀⠄⣒⠃⣿⣶⣤⠄⡪⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠶⠁⠀⠀⠀⠐
⢔⣪⣿⣛⣽⡿⢞⣩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⢈⠕⠉
⠀⠈⠉⠻⣵⠚⠅⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠠⠂⠁
⠀⠀⠀⠀⢱⠆⣆⠠⠊⠁
⠀⠀⠀⠠⠌⠊
⠀⠀⠀⠀⠀⢠⠀⠀⡠⠠⡀⡠⡢⠀⠀⡰⠂⠀⢀⢄⠀⠀⡀⠀⢀⠐⢀⠀⠀⡀⡀⡀⢀⢀⢀⢀⠀⢀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠒⠈⠉⠁⢀⣈⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠿⠋⣉⣭⠶⠛⣋⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⠉⠛⢛⠟⠛⠭⢠⡄
⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⣢⣀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠓⠒⠦⢤⣄⡀
⠀⠀⢀⠴⠊⠉⠀⢔⣮⡅⠻⢮⣿⣿⣿⡶⢤⣤⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣌⣬⣵⢦⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣭⠵⠶⠛⠋⣉⣉⣿⠿⠿⢿⣯⣯⣷⣒⣶⣧⣄⣀⣀⣿⠛⠉⠁
⠀⠀⠈⠢⢄⡀⠀⠈⠐⠀⠀⢴⣿⠿⠖⠒⠛⣩⣽⣛⡥⠴⠟⠛⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣰⣦⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠟⠁⣠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡇⠀⢘⠀⣸⣿⠐⣸⡗⠀⠀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡀⠻⠏⣸⡟⠀⠀⣀⠀⠀⠒⠶⢶⡆
⠀⠀⠀⠀⠀⠐⠚⢶⡄⠀⠀⠀⢠⣦⠀⠰⠙⢷⣄⠀⠘⣷⠀⡘⠓⠀⠀⢻⠀⠀⢴⡟⠁⠰⣦
⠀⠀⠀⠀⠁⠀⠀⢸⣿⠀⠀⠀⣾⡏⠀⣀⢂⡈⠿⠆⠀⠈⠉⠠⠀⠂⠐⠂⢄⠀⠹⠄⠄⠀⢿⡆
⠀⠀⠀⠀⣆⠀⠀⣾⡇⠀⠀⣶⣽⡀⠀⢻⡌⠛⠂⠀⠀⢠⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠈⠛⠂⣿⡇⠀⠀⠙⣿⠉⠀⠈⢧⡀⠀⠀⠀⠈⠓⠚⠛⠁⠀⠠⠂⠀⠀⠀⠀⠀⣿⠃
⠀⠀⢰⣶⣦⡄⠀⠘⠧⠠⠀⠀⢹⡇⠀⠀⠀⠉⡀⠀⠀⠀⠄⠀⠐⠀⠠⠀⠀⡄⠀⠀⠀⣼⠏
⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⡀⠸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣠⣴⠇⠀⢀⡼⠋
⠀⠀⠸⡿⠃⣴⡞⠀⠀⠐⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡈⣁⣠⠴⠋
⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣶⣶⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣷⣿⣯⣥⠄
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠽⢿⣿⣿⣥⠄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⣀⣹⣶⣦⣿⣿⣿⣟⡥
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣾⡞⠁⢹⣿⣿⣿⣯⢾⠏
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠴⢿⣾⠞⣯⢻⣸⣧⣯⣤⠄
⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢤⣰⣿⢻⣀⣰⣿⣋⠙⣿⣿⢿⣿⡿⠆
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢁⣏⣓⣿⣿⣿⣿⠛⢾⡿⠴⣿⠋⣩⠽⣇
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠳⢾⣍⡿⠛⢿⣽⣿⣌⣿⡛⠙⣧⣾⣷⣤⠈
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⡷⢋⣹⣯⡤⠿⢶⠤⣿⡙⠛⣿⢧⢞⣙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡏⣸⣿⡁⡞⢽⠳⡍⢳⣸⡄⢸⡝⢦⢸⣟⣉⠉⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠻⣿⣴⠻⣄⡙⣷⣮⠷⢛⡫⠋⡇⢸⠀⢨⢿⡁⣠⣾⡅⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡏⠙⠒⡾⠻⣄⠈⠫⣭⣭⣟⣋⡤⣾⣴⠋⡰⠋⢀⣿⢁⣀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⡞⢆⢀⡄⣈⠉⢳⣙⣤⣹⣇⠀⢻⡓⠲⠾⠶⠤⠴⠚⢁⡼⠋⢀⣤⠿⣿⠈⣉⣠⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠶⣷⣿⣸⣇⣿⢶⣋⣉⠤⢬⡟⠓⣤⣉⣓⣲⣶⡦⠴⠒⠛⢒⣫⢿⣯⣅⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠒⠶⢿⣿⣿⡛⠛⢉⢩⣿⡿⠂⢲⠞⢳⠤⠽⠓⢤⣤⣤⣔⣋⣁⣀⣁⣈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠛⣹⠿⣿⠗⣺⣿⢻⡇⠀⠉⠀⣀⣠⠴⣾⡉⠉⠗⣨⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣰⠃⢈⡵⢿⣨⡷⠛⢛⣯⠤⠶⠛⠁⠉⠳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠋⠀⠘⠉

⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⡃⠀⠀⠠⠀⠈⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣰⢦
⠀⠀⠀⠰⠀⠂⠀⠀⠐⠀⠄⢠⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢇⠀⠉⢀⣇
⠀⠀⠀⠀⢣⠀⢰⠉⠂⠚⠀⠀⠃⠔⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠉⠉⠁⠈⠣⡀
⠀⠀⠀⠀⠀⢆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⡴⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢔⠞⠝⠀⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠃⡌⠀⠀⠣⡈⠁⠒⢽⢄⡠⡀⣀⡀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⣤⠁⠀⠃⠀⡇⠀⠀⠀⠘⡄⠀⠀⠣⢕⠁⡇⠓⢖⠊⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠈⠩⠀⡸⠆⣀⢃⠀⠐⣄⠀⠀⢀⣄⣀⠴⣗⢤⠭⠑⢆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠬⠉⡾⠥⢓⣄⡠⠢⣉⠔⠫⣉⠜⢅⠔⢀⣀⢴⡤⠵⢤⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⢹⠒⠆⠨⠇⠀⢠⠀⠀⡄⠀⠰⠀⢠⡡⠔⠈⠉⠀⠀⠀⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡆⠘⡀⠸⠀⠈⡀⠀⠄⠀⡄⢀⠊⠀⢀⠀⢠⠦⣔⡑⠤⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣘⠀⢀⡀⢸⡤⠓⠠⣇⠀⠃⠀⠀⠀⠇⡆⠠⠀⡀⠱⡋⠀⠀⠀⡈⠃⠀⢀⡀⢐
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠀⠈⠂⠀⠁⠀⠀⢸⡀⠐⠀⠀⡐⠀⣧⠲⠠⢄⠀⠈⠙⠉⠁⠀⠀⡠⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠇⣀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠓⠊⠑⠤⠊⠉⠈⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⠒⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣴⣾⣷⠀⠀⠀⠀⣿⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥
⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⢰⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢸⣿⣿⡇⠀⢴⣤⡄⠀⢸⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⡄
⠀⠀⠀⠀⢸⣿⣿⡗⠠⣾⣿⣷⠄⠙⠀⢸⣯⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⢹⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠟
⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⢹⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⣠
⠀⠀⠀⠀⣻⣿⣿⡇⠀⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⡄⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠛⠀⠘
⠀⠀⠀⠀⢹⣿⣿⡃⢀⣿⣿⡟⠀⠀⢸⠀⡆⠀⢸⣷⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⣤
⠀⠀⠀⠀⢾⣿⣿⠁⢈⣿⣿⡇⠀⠀⣿⢸⣿⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠀⠀⠀⠀⠀⢀⢰
⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⠀⣷⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣸⣿⣿⠀⠸⣿⣿⡇⠀⠀⣿⢸⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣹⣿
⠀⠀⠀⠀⣼⣿⣿⣤⢤⣿⣿⡇⠀⠀⣿⣸⡇⠀⠀⢀⠆⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣁⣾⣟⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠋⣉⠀⠀⠀⣀⠋⠈⠁⠀⠀⠀⠀⠀⣴⠄⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠇⢁⡟⠀⠀⠀⢿⠀⣀⡄⠀⠀⠀⠀⠠⠤⡾⠗⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿
⠀⠀⠀⠀⢸⣿⡿⠀⢻⡅⢰⡀⠀⠀⣨⣿⠅⠀⣄⠀⢀⠷⢶⠄⡀⠀⠐⠀⠀⠀⣀⡁⠀⢈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠿⠟⠀⠀⢀
⠀⠀⠀⠠⠶⠟⠋⠙⠀⠀⠀⠁⠀⠁⣿⡾⣷⣄⢈⣀⠶⠀⠳⠈⠋⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡐⣿⡇⠹⡇⣬⡋⠀⠀⠀⠈⠀⠀⠒⠀⠶⠂⠀⠀⠰⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠟⢉⠁⠿⠇⠀⢃⡿⠁⠀⠀⠀⠀⠀⣠⣦⣤⠘⠃⠐⠂⣠⣤⣽⣗⠘⠒⠂⣧⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣰⠆⣠⢸⡇⠘⠂⠀⡀⠶⠚⣀⡠⠒⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠁⢰⡆⠀⠐⠂⠀⠀⠸⣧
⠀⠀⠀⣴⠀⠀⠀⠀⢀⣄⠀⠀⠠⡄⢸⡃⢽⠀⠇⢀⠰⠛⢁⣔⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⡔⠛⠓⠂⠀⢸⡇⠀⡤⠀⠀⠀⠀⠁
⠀⠀⠀⣿⠀⠀⠀⠀⢸⠗⠂⠉⢰⡇⢸⡇⢾⠀⡆⠀⣠⣶⣿⣧⠞⠋⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⢹⣆⠸⠃⠀⠀⠀⠀⢸⡷⢰⡏⠀⠀⠀⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡃⠘⢨⣿⣰⣿⢡⣿⣣⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣻⣿⠃⠂⠀⠀⠺⡇⠨⠄⠸⠟⣾⣷⡆⣿⡄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⣁⡄⢨⣿⣽⠦⠀⠛⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⣴⣶⣶⠀⠀⠃⠘⣿⣻⣿⣿⠄
⠀⠀⠀⣿⠀⠀⠀⠀⣴⣤⡤⠄⣼⠆⠐⠋⠋⣨⣿⡶⣰⡈⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⡟⠾⠋⠙⠇⠀⠀⠀⠐⣼⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠛⠶⠀⠶⠀⢘⣰⣶⣟⡿⠉⣷⣿⣿⣄⠉⠰⢂⣤⡀⠀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣀⠱⣀⡄⠀⠀⠀⣀⠀⡌⢻⡟
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠻⣿⠃⣰⣿⣿⣿⣿⡷⣦⢟⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢻⡿⣏⢀⣽⣧⠀⠀⣸⡋⡌⠉⠉⠋⠀⢀
⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⡐⠂⠁⢀⣴⠃⢠⣟⠙⢿⣿⣿⣿⢷⣾⣿⡟⠛⡛⢻⡿⠷⡾⢿⣿⣧⢤⠘⢷⣧⠞⢻⣿⡇⢠⡿⣥⣆⣠⣄⣀⠲⠆
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠐⢸⣿⣾⣿⣿⢿⡥⠶⣼⣿⡴⠏⠁⣠⣴⣾⣟⣿⢛⣡⡟⣳⣼⣭⣶⣿⣿⣷⣾⠠⢈⣮⣠⣌⠛⠊
⠀⠀⠀⠘⠀⠀⠀⠀⠐⡒⠒⠀⠀⠼⢀⣄⣠⢛⣾⡇⢛⡿⠻⣆⣸⡌⣤⠄⠒⠀⠀⠙⠯⠉⠁⠛⠽⠋⠛⣟⡿⠀⢉⣘⣿⣻⣆⢉⠈⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⣠⠿⣿⢃⠟⠁⣰⠉⠲⢶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⢷⣾⣤⡀⠋⠿⣿⣿⣿⣦⢰⣤⠦⠈⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡦⠀⠀⠿⣿⠇⣿⠀⣂⣼⣆⠐⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⣴⣿⣯⠁⠈⢳⣾⣿⣿⣿⣧⡘⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠁⠆⢠⣴⣧⣼⠡⣦⠁⠚⠷⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢹⣿⡿⣾⣿⡟⣠⣿⣿⣿⣿⣯⢻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢌⣼⡿⢹⣿⣿⣦⢀⠰⣶⠶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢸⣿⣿⡏⢰⡟⢻⢿⣿⣿⣿⣿⡄⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣾⠟⠁⠛⠩⠾⠿⠏⠀⠛⠺⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠻⠿⠿⠇⠋⠉⠉⠈⠛⠿⠟⠛⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⢀⠘⠂⠀⠀⠐⠀⣈⡭⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⢐⣢⡄⠀⠀⠀⠐⠀⢠
⢀⠀⠀⠀⣙⡀⠈⠀⠀⠀⠂⠀⠀⠀⠃⠀⠈⠀⠁⠀⠀⠀⠀⢚⡩⣥⡶⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⣒⡀
⠙⠛⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠀⠀⢀⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣉⠀⠐⠤⢐⡀⢠⡆⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠉⠛⠓⠲⠾⠭⠦⠀⠀⠘⠤⢄⣀⣀⡇
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⢀
⠀⠀⠘⠀⠀⢈⡁⠀⠩⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣟⣿⣿⡂⠀⢦
⠀⠀⠁⠀⠸⠋⠙⢛⠛⢤⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠘⠛⠉⠁⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣮⣆⣠⠤⡎⠀⢀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠄⠀⡇⠀⠀⠀⠈⢉⢲⠄⠀⠒⠠⠰⠖⠁⠀⠀⠀⠀⣠⠀⡀⠀⠄⠀⢀⠀⠀⠀⠐⡀⢸⠀⠀⠒⠀⠈⠆
⠀⠀⠀⣷⣀⣀⣀⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠢⢌⣉⠙⠰⠂⠦⢤⡀⠀⠀⠉⢺⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣀⡍⠠⠄⣀⣉⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠱⠂⠀⠉⢕⣒⡒⠡⢬⠀⠀⠀⠀⠱⠶⠶⠶⠒⠛⠉
⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠴⠬⣄⣉⣡⡏

⠀⢀⠔⠀⠉⠉⠑⠒⢄⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠈⠉⠀⠒⢄⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠐⠢⡀
⡰⠁⢰⡱⠀⠀⢎⡡⠀⢣⠀⠀⠀⢀⠊⠀⠀⡦⠀⢠⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠃⠠⣤⠄⠀⢤⡤⠀⠱⡀⠀⠀⠀⡜⠀⡞⠒⡄⢰⠒⠢⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⠀⡀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢰⠀⠀⠈⠉⠀⠀⠉⠁
⢡⠐⣇⠀⠀⠀⠀⡠⠓⡐⠀⠀⠀⠘⡄⠣⣀⣤⣤⣤⣄⡔⢀⠇⠀⠀⠀⠀⠀⠀⠸⡀⠀⢤⣤⠄⠀⠀⠀⢠⠃⠀⠀⠀⢆⠀⢀⣴⣿⣿⣆
⠀⢹⣿⣟⠂⠐⢈⠠⠊⠀⠀⠀⠀⠀⠈⠢⢈⣙⠛⠛⣉⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣘⠚⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠓⢌⡙⠟⣿⣉⠠⠊
⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⡠⠂⠁⠀⠀⠈⠑⢢⡀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⡔⠊⠁⠀⠀⠉⠑⢄
⡜⠀⠠⠤⠀⠀⠠⠄⠀⠱⠀⠀⠀⢠⠃⠀⠒⠂⠀⠀⠒⠀⠈⡆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠃⠀⠪⠀⠀⠘⡄⠀⠀⠀⠎⠀⠐⠃⠀⠀⠚
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠸
⠰⡀⠢⡀⠀⢰⣿⡦⢂⡜⠀⠀⠀⠈⢆⢰⣄⡀⠀⠀⡠⠆⡠⠃⠀⠀⠀⠀⠀⠀⠘⢄⠀⠓⠤⠒⠤⠒⠀⡰⠁⠀⠀⠀⢣⡀⢐⡶⡖⠒⠒⠂⢀
⠀⠈⠂⠄⣉⣉⠡⠔⠊⠀⠀⠀⠀⠀⠀⢿⡿⠍⣉⡁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⣀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠑⠢⠝⣁⣀⠠⠔⠁

⠀⠀⢀⡀⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⢀⡀
⢀⠔⠁⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⡠⠊⡀⡀⠀⢀⢀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⠢
⡌⠀⠀⠁⠀⠀⠈⣡⠀⠘⡀⠀⠀⢰⠁⠀⠓⠂⠀⠀⠒⠁⠀⠇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⠃⠀⠐⠒⠀⠀⠒⠂
⠇⢀⡀⢀⣀⠀⠀⠀⣀⢀⠃⠀⠀⢠⠀⢀⡀⣀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠈⡀
⠘⢄⠑⠾⣿⣀⡠⠖⢡⠎⠀⠀⠀⠀⠣⡈⠢⢼⣿⣧⠤⢋⡔⠁⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠠⠛⠄⠀⢀⠜⠀⠀⠀⠀⠑⡄⠀⠈⠻⠟⠁⠀⡠
⠀⠀⠑⠒⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠈⠒⠂⠉⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠀⠐⠊



⠀⠀⠀⠀⠀⢦⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣷⠃⠀⡇⠀⣶⠀⡟⠉⡗⠉⡇⠀⡏⠉⡖⠉⡇⠸⡄⣰⠀⠀⠀⡞⠉⢶⠀⡗⠉⠀⠀⢸⠈⢧⣸⠀⣰⠉⠹⡄⢹⠉
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠳⠤⠟⠀⠇⠀⠇⠀⠃⠀⠇⠀⠇⠀⠇⠀⢹⠃⠀⠀⠀⠳⠤⠞⠀⠃⠀⠀⠀⠸⠀⠀⠙⠀⠘⠦⠜⠁⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⣤⣾⡟⠁⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠤⣄⠠⣀⣀⡀⠀⢀⣀⣤⣶⣦⢀⣤⣶⡿⠟⢱⠟⣉⡅⠀⠀⢀⣰⡷⠛⠫⠀⢰⡗⠆⠚⠷⠾⢿⣿⣿⣿⡿⠿⠿⠿⠻⠛⠛⠉
⠀⠀⠀⠀⠀⠐⠃⠰⠞⠛⠛⠛⠛⠛⠋⠈⠙⠒⠋⠐⠒⠲⢶⡾⠋⠈⠣⠴⠿⠙⠁⠀⠂⠊⠛⠛⠞⠀⣠⣆⡀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢀⡤⠀⢀⠀⢀⡀⠐⠀⠛⠒⠀⠀⠀⢒⣀⣀⡀⠀⠀⠀⠀⠖⠒⠈⠁⣠⣩⠠⡄⣶⢶⣦⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠉⠠⡒⢀⠐⠀⠀⠸⢟⠛⠛⠋⠁⠁⠀⠀⠴⠒⠋⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡇⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠉⠻⠧⠧⠬⠄⣀⠀⢀⣀⠀⣦⣀⣤⢤⡶⣿⢸⡗⠀⠰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⠛⠁⢨⡇⣿⡼⡛⣼⡶⢿⡆⠀⠀⠀⠀⠀⠀⢀⣄⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢹⣿⣿⣿⠽⠙⢾⣷⣿⣇⠒⣿⡇⠸⠧⠀⢀⡀⢀⣤⣤⣴⣿⣧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠤⠠⡀⢀⠀⡀⢀⠀⣀⣴⣴⣻⣭⣭⣵⣶⣿⣿⣿⣿⣟⣹⢛⢰⣴⣾⣿⣿⣿⣿⡿⢿⢚⠃⠚⠿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠙⣿⠉⣹⠉⠀⣽⠀⣀⡠⠔⠚⣁⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⣿⡄⠀⣿⠋⠁⣀⣾⣗⠄⢙⠳⠦⣄⣁⠐⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⣿⡇⠀⣿⡗⠀⠈⠑⠋⠙⠛⢷⣶⠀⠉⠛⣶⣀⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣟⠀⣿⣟⠀⠀⠀⠀⠀⠀⡆⢹⡆⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⣤⠤⢴⠤⠿⠤⠌⠁⣀⣿⣿⠄⠀⠤⠤⠀⠴⠁⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠒⠀⣁⢀⠀⣿⣿⡗⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡬⢻⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠊⠀⠀⠀⠠⡀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡿⣹⣿⠯⣧⢀⠀⠀⠀⠀⠲⠄⠀⢀⠀⠀⡀⠀⠀⠘⠀⡀⠀⡀⠀⠐⡤⠀⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠷⠟⢷⣤⣿⣻⣴⣇⠹⠀⠀⠀⠀⡀⠀⠈⠁⠀⠐⠮⠀⢀⢵⠒⢠⠀⠁⠀⠀⠃⠀⡰⡄
⠀⠀⠀⠂⠀⠀⠀⠀⡈⠉⠰⠢⠉⢁⡁⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢄⠠⢬⡄⣨⣄⢃⢤⠅⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠀⡤⠂⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⠆⠘⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⠀⡈⠀⠍⠀⣂⠈⠂⠀⠀⡀⠀⠘⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⠈⠐⠂⠀⠈⠙⠊⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⠀⡆⢀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⢤⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠐⡃⡓⠾⠛⢫⡇⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⢀⢀⣀⠀⠀⠂⠀⢀⠀⠀⠀⠐⠀⠀⠈⠠⠘⠀⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠃⡀⠀⡄⡌⢿⣜⡟⠓⠀⠀⠀⠀⠀⠁⣀⣼⣏⣁⡾⡿⢽⣤⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠐⠻⡀⠁⢀
⠀⠀⠀⠀⠀⣤⣬⣿⣴⣶⣶⣁⣀⡀⠀⠀⠀⠘⡏⠉⣎⠈⠀⠁⠀⢀⠁⢠⣿⣿⣾⣿⣿⣿⡏⣝⠂⠀⠀⠀⢀⠀⠀⢀⠀⠹⠊⠀⠀⠀⢘⠮⠛⠋
⠀⠀⠀⠰⣻⣿⣿⣿⣿⣽⣧⣿⣿⢿⠂⠀⠀⠀⠈⠉⠉⡀⠀⠈⢢⠊⠀⠈⣧⣼⣿⡟⣻⣯⢳⡾⠃⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⠀⠐⣺⡙⠆⠁
⠀⠀⠀⠀⠙⢃⠛⠻⢿⠭⠛⢿⠏⠁⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠸⠀⠀⠀⠙⠟⣿⣻⣷⣿⢶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣿⣥⠽⠬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠻⢶⣴⠿⢿⣄⠀⠀⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣶⣦⣶⡞⠁⠀⠀⢈⣷⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠋⠉⠻⢿⣧⣬⣁⣠⣼⣿⠁⢀⣀⣸⡃
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠴⠉⠩⠭⢌⢻⣿⣿⡿⢿⡉⢉⣿⣃
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠒⠖⠃⠀⠀⠀⠀⠀⠁⣗⣀⣶⡆⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣸⠂⠀⠀⠀⠀⠀⠠⣿⠅⣿⠇⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠤⠤⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣆⠀⠀⠀⠀⠀⢀⣽⣸⡟⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⠴⢒⣾⡷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣤⡙⣿⣿⣤⣤⣀⣴⣿⣿⣿⣵⠿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠋⠁⠒⠻⡿⠿⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⣿⣿⣿⣿⣿⣿⠿⠛⠑⠉⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⣄⡀⠀⣾⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⡗⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣗⢶⡖⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣴⣷⡄⢛⣿⣿⣿⣖⣦⣼⣀⡀⠀⠀⢹⠀⠀⠀⣥⣾⡗⠆⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠿⢟⠛⠉⣉⣤⣶⣛⣻⡿⣿⠿⢿⣿⣿⣶⣦⣤⡏⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠎⣸⢀⣆⠠⣤⣀⡀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⣀⠙⠉⠁⠀⠐⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⣴⣯⣀⢨⣦⢈⣁⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢿⣖⠲⣶⡤⣀⡈⠛⠛⣩⣟⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠺⠾⢇⣀⣿⣶⡙⢦⠛⣿⡶⢆⠉⠉⠁⠀⡈⠳⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠁⠀⠀⠀⠀⠀⠀⠙⢀⣬⣏⣆⣀⡠⠥⣦⠷⣦⡄⢠⠀⠀⢽⡇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣁⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣨⣟⣁⡙⣿⣳⢶⣿⢻⠘⠀⠀⢸⡇⠠⡅⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣭⣿⠛⠿⢾⣿⣦⣭⡿⢀⡁⣰⣿⣿⣿⣧⣌⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣂⣾⣿⣿⡶⠶⣞⣿⠷⠉⢙⣲⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠈⠀⠸⠿⣓⡲⠶⠶⠾⠟⠻⠉⠉⢠⣶⡿⠿⠷⠞⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠄⣀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢆⠀⠀⠓⠒⠀⠰⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠠⢄⡀⠀⡁⠒⠀⠖⣐⠀⢀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠐⠠⡅⠀⡁⠓⠀⠲⢬⠀⢀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠘⢂⢴⢄⣠⠐⡏⢹⡦⡖⠠⣆⣠⢈⣅⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠒⢳⣶⠿⠻⡀⢻⠛⢄⣸⠛⣋⠚⠛⠓⠰⡟⠻⠠⡿⠿⣯⠻⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢦⣿⠊⠉⢀⠈⡋⠀⢦⣼⠀⠈⠁⠀⢈⠲⡃⠀⡂⢲⡶⢾⣅⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⢴⣶⡑⣔⣤⣿⡁⣀⢤⣠⣤⣄⢬⣶⣽⠶⠿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡶⠀⣠⡄⠀⠀⠀⠈⠉⠉⠁⠉⠋⠉⠁⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠇⠆⢰⠂⠀⢀⡶⡀⠀⣴⢦⠀⢰⠄⠀⠀⣿⡷⠀⣤⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⡧⠘⢀⡟⡀⢠⠀⡏⠂⠠⠟⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠜⠀⠀⠀⡃⠀⠀⠀⠘⠛⠀⡇⠀⠀⢀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⢀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠛⡛⢀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠊⡉⠙⠢⣄
⠀⠀⠀⠀⠀⢀⠔⠚⠉⠁⢀⠀⠂⢈⠀⢠⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⢰⠁⠀⠆⠀⠂⠀⠠⠄⠈⠀⠀⢀⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠃
⠀⠀⠀⠀⢇⠀⠄⠀⠠⠆⠀⠄⠀⠰⠂⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣩⣯⡢⡀
⠀⠀⠀⠀⠘⡆⠀⠆⠀⠀⠀⠠⠄⢀⡤⢤⡀⠀⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠊⣹⡇⠀⠙⠀⢀⡇
⠀⠀⠀⠀⠀⢸⡀⠠⠀⡠⠤⣀⢀⡼⠀⠀⠱⡀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠛⠦⠔⠤⠎⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠁⠠⠄⠈⢀⠁⠀⠂⠀⠘⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⢆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⣀⣴⢶⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⢴⠞⡽⠁⣿⡀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠊⡴⠃⡜⠀⠀⢷⠘⠦⢼⡀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡞⠀⠸⠁⠀⠀⠈⠢⡀⠀⠈⠑⢦⡷⣤⠖⡆⢀⣤⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠁⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⣈⡱⠃⢸⠤⠷⣆⠒⠛⣣⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⠤⠴⡞⠉⠉⣿⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⢅⠑⠂⠺⣄⢀⣈⣳⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⡄⢠⠃⠑⠦⠤⠧⣀⠀⢘⣦⣀⠀⣀⡤⠛⠒⠒⠋⢹⠎⠳⣏⠉⠉⠳⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠵⠐⠸⠿⠭⢍⡲⢄⣠⠖⠲⡄⡨⠛⢦⣀⡤⠒⢦⡰⠒⢄⣀⠴⣦⡤⠶⠳⣖⢢⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠂⡴⠚⢳⠤⣤⡈⣈⣣⠀⠀⢨⠀⠀⠀⡍⠀⠀⢠⠀⠀⢸⠁⣀⠷⠛⠊⠉⢉⠉⡉⠉⢑⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡀⠀⡆⠀⢹⡄⠀⠘⡄⠀⠀⡇⠀⠀⣾⠀⠀⡾⠊⢁⠀⠁⠂⠀⠀⢀⡤⡀⠀⠀⠠⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢇⠀⢹⠀⠀⢧⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡞⠁⠤⠀⠄⣀⣀⣎⣓⡋⢀⣉⡒⣄⠐⠀⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡞⠀⠀⠀⣀⣘⣄⡤⠓⠢⢜⡄⠀⢸⠀⠀⠀⠀⢀⠃⡸⠀⡄⠠⠀⠀⢧⠊⠁⠀⠀⠀⠀⢉⠇⢘⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⠹⠷⠉⠉⠻⡀⠀⠙⠂⠀⠀⠈⣷⠀⠀⡆⠀⠠⠀⢸⠀⣇⢀⡀⠀⣈⠀⠆⡙⠒⡦⠐⠒⠚⡁⠐⠀⢠⠏⠙⢲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠗⠒⠲⠶⠶⠶⠒⠒⠒⠚⢳⡘⠊⠈⢦⠀⢀⣀⡀⠂⠈⣠⣀⣀⠖⠊⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⡴⢥⣀⡀⢀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠑⠉⠀⠙⠢⠞⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⣀⣀⡠⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠛⠎⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠛⠒⠀⠐⠠⡈⠲⠄⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠁⠀⠀⢈⢠⣀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣏⡉⠉⣀⠀⠘⣇⠄⠀⠉⠀⢤⡀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣰⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠙⠊⣱⠶⠚⢻⡦⠀⢧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠒⠀⠀⠃⠦⢀⠀⠐⠀⠀⠛⠳⠂⠀⠀⣾⡅⠀⠀⢡⣴⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠈⠻⠦⢀⡀⠀⠆⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠂⠀⡀⠀⣼⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠓⠀⠀⠀⠀⠈⠁⠀⠁⠠⠘⠁⣤⣶⡿⠟⠀⠀⠀⠒⠂⠀⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠠⠤⠀⠀⠀⠒⠆⠠⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠃⠐⠴⠖⠋⠀⠀⠀⠀⠞⠛⠉⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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