Organelle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢳⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠶⣦⡀⠀⠀⠈⡇⠀⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠘⣿⣤⣼⠃⠀⠀⠀⡇⠀⠊⠀⠀⣯⠀⠁⣀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⠓⢄⠀⠀⠀⠀⠀⠀⢬⠀⢄⡀⠀⠈⠉⠁⠀⠀⠀⣠⡁⢀⠀⡄⠀⠀⠈⠛⢁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢉⣉⡩⠇⠀⠀⣸⣜⢾⢻⣶⣤⠀⠈⠅⠂⠀⠒⠂⠉⢠⢁⣀⣷⢿⡷⠂⠠⣾⠻⣛⠶⠞⢍⣒⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣟⢿⡑⣟⣉⢴⣛⣷⣖⣶⣦⢔⣂⡴⣿⣿⢿⣧⠜⠀⠀⠀⠭⠌⠁⠚⠤⠼⣊⠄
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢻⣮⠙⣸⢹⢚⡼⠿⡟⣲⡷⣭⡴⠿⢿⣿⠉⡹⠋⠀⢀⣤⣤⣤⡀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢸⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠤⠘⠺⡁⠀⠀⠀⢪⠽⠉⠘⣯⠿⠷⠚⠀⢰⣴⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠈⠂⠀⠀⠀⣰⡏
⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡶⢆⠶⣦⢀⠀⠈⠁⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⢈⢩⣿⣿⣿⣿⣿⣿⡿⠿⡀⠀⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠸⣿⡷⡄⠀⠀⠀⠀⣴⡿⠡⠘⠒⠂⠚⠛⠲⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠤⠀⡏⢁⠈⠀⡀⢸⠧⠀⠇⠀⠀⠀⠀⣠⣿⣿⡏
⠀⠀⠀⠀⠹⡟⠈⠃⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠀⠀⠀⠑⠀⠀⠀⠘⠈⠂⠀⠁⠉⠉⠀⠀⠀⢀⠤⠚⣻⣿⡟
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠴⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⠀⣰⣾⠟
⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⢀⣀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠒⠠⠀⣀⣀⠠⠀⠖⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣚⣉⣉⣉⣛⡒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡡⠔⠚⠉⠁⠀⠀⠀⠀⠉⠙⠢⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⡡⠞⠉⠀⠀⣠⠖⠋⠙⢦⠀⢠⡞⠲⣄⠈⠳⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⢒⣉⠤⠒⠉⠀⠀⠀⠀⠀⡇⠀⣞⡆⠈⡇⠈⡇⠀⠈⢣⠀⠹⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣋⣩⠥⠤⠖⠒⠋⠉⠀⣀⠀⠀⢠⠊⠑⣆⠀⢱⡀⠀⠀⣀⣈⠋⠁⠐⠿⠊⣇⠀⢧⢸
⠀⠀⠀⠀⠀⠀⢀⠔⢋⡤⠚⠉⠁⠀⠀⢀⡤⠖⠢⡄⢸⠉⢳⠀⢸⠀⠀⠘⡆⠀⢣⠀⠀⡇⠀⢳⡀⢰⠒⠦⠟⠀⢸⢸⡇
⠀⠀⠀⠀⠀⡴⢡⠞⢁⡠⢤⡀⠀⠀⠀⡏⠀⣠⡄⠙⠋⠀⠈⠣⠜⠀⠀⠀⢳⠀⠘⡆⠀⢹⡀⠀⢳⡈⠑⣆⠀⠀⡼⢸⠁
⠀⠀⠀⢀⡞⣰⠃⢠⠋⠀⠀⠙⡆⠀⠀⣧⠀⠉⠁⠀⠀⠀⢠⠖⡄⢀⠤⢄⠈⠳⠜⠁⣖⡄⢳⠀⠀⢣⣀⡼⠀⢠⠃⡞
⠀⠀⠀⢸⢠⠇⠀⡏⠀⡴⢦⠀⢳⠀⠀⢸⠀⠀⢠⠎⠉⢳⡀⠉⠁⢸⡀⠈⣇⠀⢠⠖⢤⠀⠀⢣⠀⠀⠀⠀⣠⠋⡜
⠀⠀⠀⣿⢸⠀⢸⠁⠀⠈⠁⠀⠸⣄⢀⡸⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⡇⠀⢸⡀⠸⡀⠈⣇⠀⠀⣧⠀⢀⡴⢁⠞
⠀⠀⠀⢸⠘⡆⠘⡇⠀⢀⡠⠴⢤⠀⠉⠀⠀⠀⠸⡆⠀⠀⢹⠀⠀⠀⢧⠀⠀⢇⠀⢳⠀⠈⠓⠚⢁⡴⢋⡴⠃
⠀⠀⠀⠈⢧⠹⡀⠑⠚⠉⠀⣀⠜⢀⠔⠛⡆⠀⠀⢇⠀⠀⠸⡆⠀⠀⢸⠀⠀⠘⠒⠊⠀⢀⣠⠖⣩⠔⠉
⠀⠀⠀⠀⠈⢧⡙⢄⠀⠠⡎⢁⡴⠋⠀⣰⠁⢰⣦⢸⠀⠀⠀⠳⠤⠤⠋⠀⠀⠀⣀⡤⠒⣩⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡑⠦⣉⠉⠀⠀⠀⣇⣀⣀⣠⠞⠀⠀⠀⠀⠀⣀⡠⠴⢒⣉⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠬⣉⡓⠲⠦⠤⠭⠥⠤⠤⠴⠒⢒⣋⣩⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠚⠉⠉⠉

⠀⠄⠀⠀⠄⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠔⠒⠀⠀⠀⠦⠀⠰⠰⠂⠂⠖⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠐⠂⠂
⠐⠒⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠀⠐⠒
⠀⠛⠐⠉⠀⠀⠘⠃⠃⠀⠋⠋⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠉⠀⠈
⠀⠛⠂⠀⠐⠀⠂⠀⠃⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠉⠁
⠀⠉⠀⣁⠀⡈⡁⠉⠀⢈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠁⢈⠀⢈⡉⠀⢁⢀⣀⡀⢀
⠀⡀⠀⠈⠀⢈⠁⠀⡀⠀⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⣀⠀⡀⠀⠀⣀⡀⠈⠉⠁
⠀⡁⠀⢀⡀⣈⡀⠀⡁⡈⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⢀⢈⠀⠀⢈⢀⡀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⣠⠀⠀⢀⠀⢀⡀⢀⡀⠀⢀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⡄⢀⢀⣀⣠⣄⡀
⠀⢠⡀⠀⠀⣀⠀⠀⠀⢠⣀⠤




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠶⠶⣶⣶⣶⣶⣶⠾⣶⣤⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⣤⣾⣟⣵⣦⣷⡶⠷⢿⠟⠷⣿⣯⣴⢷⣿⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣌⡞⠰⣿⠀⠀⠉⠻⣿⠟⣧⣰⠾⠛⠛⠛⠛⠛⡷⠇⠘⠁⠀⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠤⠟⠀⡀⠜⠀⠀⠀⠀⠀⠠⢈⣀⠉⠙⠒⠒⠒⠈⠁⠀⠀⠀⠀⠄⠀⠀⡅⠠⠀⠀⣿⠶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⠒⠈⠀⠀⠀⠀⠀⠀⠀⣾⣯⣷⠄⠀⠀⠀⠀⡀⠀⢀⠀⠀⠈⣤⣶⣦⠀⣀⣀⣀⡈⠀⠀⠀⠌⣠⠆⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠆⠀⠀⠀⠀⢀⡔⠂⠈⠁⢀⣤⣴⣿⣿⣿⣿⣶⣿⣿⣷⣶⣻⢌⠻⡆⠙⣩⢿⡿⠁⣴⣃⣠⡑⠶
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠁⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠈⣿⣿⣿⣿⣿⡆⡖⢙⠀⢨⣮⣧⡓⠚⡀⢿⡷⢀⣤⡀
⠀⠀⠀⠀⠀⡤⠒⠀⠀⠀⡄⠀⡀⠀⢠⢻⡁⠀⣈⢏⠠⡀⠀⢸⠟⢿⣿⣿⣶⣤⣦⣾⣿⣿⣿⣿⠟⣸⡇⠈⠀⠈⣿⣇⣀⣀⠀⡜⠛⣡⣼⣁
⠀⠀⠀⠀⠀⡀⠀⠀⠶⣉⠇⢺⣷⠀⠘⢸⡇⠀⣹⠀⢱⡆⠀⠈⣶⠀⠸⡿⠛⠛⠛⠛⠛⢿⠋⠁⣠⣾⣥⡒⡀⢀⡋⣌⣱⣒⠒⣆⣤⢡⡬⠟⠀⢠
⠀⠀⠀⢀⠀⠀⠀⠐⢂⢹⠀⡰⣏⠀⠀⣽⣿⠀⢸⣆⡀⢡⡄⢠⡸⠦⣀⢀⡀⠀⢠⡄⠀⠀⢀⡞⣩⣷⡷⣮⡽⢢⣽⣿⠟⠛⢱⣤⡠⠀⢀⡘⠶⢻
⠀⠀⠀⢸⡄⠀⠀⣠⢊⠁⡆⠠⡌⠣⣶⣻⡾⠣⠀⠉⢁⡂⠉⠕⠐⠦⣄⣉⠉⠵⢖⣦⣀⣰⡾⢁⣠⣿⣟⣋⣠⠼⠛⠿⣿⡲⢦⣼⡷⠁⠈⠁
⠀⠀⠀⠀⣿⡄⠀⠂⠼⠿⠁⠀⠸⡀⠀⠈⠁⣶⢈⠠⢴⡖⠁⠀⡤⢒⡋⠉⠁⠐⡞⠉⡁⠀⠈⠙⢿⣍⠉⠉⣠⣼⣾⣏⣩⣧⠶⠀⡽⠃
⠀⠀⠀⠀⠸⣷⠀⢀⡀⢀⡀⠀⠀⠙⢦⣀⠀⢻⣮⡵⢮⣭⣄⣸⣇⢿⡇⢀⠀⡒⠀⠀⢃⠀⠂⢠⣤⠀⠈⡘⠛⠉⣠⠈⠉⠁⠀⠀⠰⡄⠀⠀⠐
⠀⠀⠀⠀⠀⢻⡆⠀⠀⠨⠷⠀⠀⠁⠀⠙⠣⣈⡻⡆⡁⠀⠈⠉⣡⡾⠟⢿⣿⠭⣶⠀⠀⠑⢄⠠⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢦⣤⣤⣎⣩⣤⣤⡴⠛⠋⠁⢀⠚⠀⠀⠑⠒⠣⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⢹⡦⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⡠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣠⠀⠤⠤⠄⠀⣀⡤⠀⠀⠀⠀⠠⠀⠂⠆⠀⠀⠂⠰⠐⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠐⠀⠠⡆⡦⠀⠀⠀⠨⣁⠒⠤⡂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠀⠀⠈⠻⠙⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠆⠠⠀⠠⠠⠠⠀⠤⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠃⣠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠳⠄⠀⣠⠚⠁⠀⠀⠀⠀⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠖⡖⠀⠀⢀⡀⣀⠀⠀⠀⡀⠀⠀⡠⢔⠀⠀⠀⠀⢀⠠⠠⠀⠤⠠⠀⠄⠠⠀⠀⠄
⠂⠀⠃⠈⠀⠘⠘⠀⠁⠀⠀⠀⠀⠀⠈⠃⠠⢄⣀⠐⠛⠁⢀⣀⡈⠤⡒⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠄⠄⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠠⣤⠀⢀⠸⠷⠀⠠⡀⠀⠀⣤⠀⠀⠀⠀⢀⡾⠃⠀⠀⠈⠁⠀⠀⠙⠛⠀⠸⣿⡿⠰⠂⠀⠀⠄⠀⠀⢱⢶⣴⡿⢿⣿⣷⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠙⠶⣾⣷⡄⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⡤⠀⠀⢠⣶⠀⡀⠊⠁⠀⠛⠛⢿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢶⠀⠀⢠⡤⢿⣿⡉⠋⠛⣿⡄⠈⠹⢾⠀⠀⠈⠀⠀⣠⣤⡀⠀⠀⡀⠰⡿⣏⡖⠀⠢⡀⠀⠶⠃⠀⠀⠀⣦⡀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⢾⡇⠀⢹⣿⡀⠀⡘⠳⣄⠀⠈⠻⢶⣀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⣨⣷⠀⠈⢥⠄⠀⠀⠀⠀⠀⠉⡀⠈⡏⢻
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⢷⣄⡸⠟⠀⠀⢀⣀⠈⢷⣄⠀⠀⠈⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⣀⠀⠀⠀⠈⢀⠐⠀⠺⢷⣷⢿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⢸⠉⠀⠀⠈⠁⠀⠠⣾⡄⣀⣤⣶⣶⣦⣀⣠⡀⠀⠈⢷⡄⠤⢰⠦⣀⡤⠤⠜⠃⠀⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠈⠉⠀⠐⢬⡀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠠⠀⠀⣼⠃⢀⣟⠻⣿⠿⠂⠀⠀⠀⢿⡀⠀⣀⠉⢳⠚⠐⠛⠀⠀⣲⣶
⠠⣤⡉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⢐⠼⢿⣿⡦⠀⠈⡃⠈⣥⣽
⣤⣄⣙⠓⠦⣉⠳⠤⣄⡀⠀⠀⠐⣿⣿⡆⠀⠤⠴⠂⠀⠀⠀⠀⠀⠙⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠉⠀⠀⠀⠸⣧⠀⠀⠠⠿⠃⠆⡠⣤⡤⠄⢈
⣿⣿⣽⣷⡀⠙⢷⡄⠈⢻⡆⠀⠚⠃⠀⢀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠉⠀⠰⡦⠒⢲⡾⠇⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣿⡤⠸⠧⠐⢄⣲⣾⣇⣠⣶⣨
⣿⣿⣿⣿⣧⠀⠈⣷⡀⢸⠃⠀⠀⠀⠶⠿⠆⠀⢀⡴⢶⡀⠀⠐⢤⡶⠀⡶⢶⡀⢰⡇⢠⡏⠀⠀⣠⢀⡁⠲⠆⠀⠀⠺⠽⠗⢸⣏⣨⣄⠀⢰⡄⢞⣋⠻⣿⣶⣿
⣿⣿⣿⣿⡿⠀⠀⠈⣧⣼⡆⠀⠀⠀⠀⠀⠀⣠⠀⣁⡘⠁⠀⠀⢀⠶⣾⠇⠈⣿⡌⢷⠈⢷⣀⡴⠿⠟⠃⠀⠐⣷⣤⣤⠀⠀⠀⣿⣿⡾⣿⡝⢀⣄⠱⢈⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣄⡀⠀⠸⠶⠛⠀⠀⡈⠀⢸⣤⠟⠙⢧⣤⡼⠀⠰⠂⠀⠉⠁⠀⠀⠀⢹⣿⣷⣿⠶⣼⣿⣿⣤⣭⣿⣿
⣿⡿⠛⠁⠀⠀⠀⢰⣿⠇⣸⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠈⠁⠴⠲⣶⣧⣼⣾⣭⣴⣿⣿⠀⠀⢀⡿⡿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠈⠹⠤⠋⠀⠀⠀⢀⡐⠾⠋⠁⠀⠀⠀⠀⠠⠀⣸⣿⣿⣿⣇⠹⣿⠟⣷⢰⠚⠁⠀⠀⠀⠀⠀⠀⠙⣟⡧⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡀⠀⠀⠰⠏⠀⢀⠀⠀⠀⠀⠘⠁⠀⠀⠂⠀⣄⢠⡀⠀⠰⣯⣿⣿⣿⡿⢛⡿⠛⠁⠙⠀⠀⠀⠀⢀⡶⠀⠀⠀⠈⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠁⠀⠀⠀⠀⠀⢿⣿⡄⠀⠸⠧⣀⣤⣴⣦⡀⠉⠀⠀⠀⠧⣾⣿⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⠀⣠⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠛⠟⠿⣛⣀⢠⠴⡾⠇⢰⣼⣿⣿⠿⢷⡄⣀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⢆⡠⠀⣀⣀⠴⣿⣿⣶⠟⠛⠓⢦⣿⣿⣿⣇⠀⢸⡟⢻⡆⠀⠀⠀⠀⢰⡄⠀⢀⣤⣤⣄⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⡀⠀⠀⠀⠁⠈⣠⠾⠛⢻⠆⠀⠘⠻⠶⣾⠿⠫⠀⠀⠀⢀⣾⣿⣽⣿⣿⣤⡿⢛⣿⣿⣷⣴⣶⡸⣿⡄⠀⢸⣿⣋⣻⣿⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠙⠀⢀⣤⡀⠀⠛⠋⠁⠀⠀⠀⠀⠘⠀⢿⣤⣇⣴⣴⡶⠟⠉⣹⣿⣇⣿⣿⡇⣼⣯⢈⣿⣷⣟⠁⠀⠀⠀⠀⠙⠷⢾⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠤⠭⠉⠁⠀⣠⡶⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠐⠀⢠⣾⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⡧⠀⠀⠀⠀⠺⠃⡙⠻⢿⠏⠀⢻⣿⣿⣤⣼⡏⠉⢁⣤⣤⡀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿
⠰⢦⡤⠀⠰⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠰⡾⣧⣤⣾⠙⣿⠋⣩⣄⣀⡼⣿⡿⣧⣤⣄⠀⠈⠃⠀⠀⢿⣿⣿⣿⡷⣿⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⢀⣤⣿⣿⣿⣿⣶⣦⡀⠀⠂⠀⠐⠀⢀⡘⠛⠻⠇⠈⠙⠛⠛⠉⢀⠀⠀⢹⣿⡿⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟
⠀⠀⢠⣄⠀⠀⠀⠛⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠂⠀⠈⠁⠀⠠⠶⠀⢀⡠⢶⣷⣀⢀⡀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣷⠜⠁⡀
⡆⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣸⣿⣿⣿⣿⣾⣿⣦⣄⠼⠁⣠⣿⣿⡿⠿⢿⣯⣿⣿⣿⣿⣦⣸⠛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠚⠀⠀⢀⡀⢠⡞⠀⠈⠉⣸⣏⣿⣿⣿⣿⠟⠛⠿⠿⠁⠀⣿⡿⠃⠤⣶⡄⢯⣸⢿⣟⣿⣿⠟⣷
⠀⠆⠀⠀⠀⠰⢶⣤⠀⠀⠀⠀⠀⠹⡿⠛⠛⠋⠉⣿⣿⣷⣄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣿⣿⣿⡟⠋⠀⠀⣠⡀⣀⣤⠀⣿⣧⣤⣦⣭⣶⣦⣉⠤⣩⣭⣭⣶⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢹⡆⢴⠦⠀⠹⣿⣿⡿⠀⠀⠰⡆⠀⠀⠐⣠⣤⣾⠿⠟⠉⠀⠀⠀⠀⠉⠁⠀⠀⠐⣿⣿⣏⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⡷⡿⠁⠀⠛⠀⢀⣨⣿⡄⠀⠠⠄⢀⣤⡾⠋⣹⠟⠁⠀⠀⠀⠀⠀⣤⣠⣦⣀⣀⠀⣀⣿⣿⣿⣿⣿⣿⣿⢟⣉⠽⠎⠉⠙⠿
⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⢀⣤⣶⠆⠀⠀⠰⣦⠙⠋⠀⠀⣠⡴⠟⠋⠀⢰⠇⠀⠀⠀⠀⣠⡀⠀⢿⣯⣍⣿⣿⣿⣿⣿⣿⠿⠟⢋⠁⠀⠉⠉⠀⠀⣀⣀⢀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⢀⡟⢡⡟⠀⠀⠀⠀⡈⠀⢰⣤⡔⠋⠀⠀⣀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⠟⠁⠲⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⡿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠀⣾⡆⢼⡇⠀⠀⠈⣻⣥⣴⠿⠛⣀⣠⣴⡟⠋⠀⠀⠀⠀⠀⣶⡦⠀⠀⢀⣀⡀⢰⣿⣿⡿⠁⠀⣄⢡⡚⠂⢁⣴⣶⠂⠀⢸⣿⣿⠉
⠀⠀⣤⣼⣿⣿⣿⣿⣿⠃⠀⠘⠷⠞⠁⢶⣶⣿⣥⣠⣤⣴⣿⡋⠀⠀⢙⡕⠀⠀⠀⠀⠀⠉⠁⢠⡄⣴⣿⣿⣿⡿⢹⣶⣶⣴⣯⠿⣭⠀⠀⠀⡤⠀⠀⢿⣿⣿⢿
⣤⣤⣿⣿⣿⣿⣿⣿⣿⣤⣤⣾⣤⣤⣤⣿⣿⣿⣿⣭⣭⣭⣤⣤⣤⣤⣬⣭⣦⣤⣼⣿⣤⣤⣤⣬⣥⣽⣿⣿⣯⣤⣤⣾⣿⣿⣿⣤⣭⣤⣤⣤⣤⣤⣥⣤⣭⣭⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠒⠚⠓⠐⠚
⠀⠀⠀⠀⠀⠁⠉⠉⣉⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡉⠉⠙⣋⡽⠟⣉⡉⣹⢏⡉⠁
⠀⠀⠀⠀⠀⣦⣀⠀⠀⣾⠻⠒⠞⠖⠀⠀⣴⡄⠀⠀⠀⠀⠙⠃⠀⠈⠴⠂⠉⠹⡐⠈⠶⠉⠁
⠀⠀⠀⠀⠀⠉⠛⠛⠶⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⣴⠀⠀⠀⠀⠀⣀⢄⡁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⣄⡀⠐⢦⣄⠀⠀⠀⠀⢀⣴⢋⣭⣭⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣉⣟⡁⠀⠈⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠾⠿⣿⡟⠉⠳⢶⣏⠀⠀⠀⠈⠙⢱⣏⣻⣿⠇⠀⠀⠘⠷⠷⠿⠿⠿⠿⠷⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣠⡶⡶⢶⣶⠶⠄
⠀⠀⠀⠀⠀⠀⢛⠺⢃⠉⠩⠀⢃⠀⠀⠀⠀⡠⠤⠤⢀⣀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠉⠁⠀⠀⠀⢸⣼⣿⣿⣿⣿⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠈⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠐⠲⣈⡋⠙⠿⠿⡛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠛⠁⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣾⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠒⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡟⠋⠁⠀⠀⠴⣏⠀⠀⠀⠀⠰⠀⢀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣠⣶⣶⣶⣶⣶⠏⠀⠰⠾⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠿⠿⠋⠀⠀⠀⠀⠠⠔⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⢤⣤⠀⠠⣤⠠⡤⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣤⣠⣤⣤⣤⣤⢠⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠿⠿⠧⣤⣄⡂⠄⠀⠀⠀⠀⠀⠉⣀⡈⠉⣉⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⠀⠖⠂⢀⡀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠙⣦⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⢲⠴⠓⠈⠯⠉⠛⣗⠄⠠⣤⠲⢬⠳⣄⠀⠀⠀⠸⡟⠀⠀⠀⠀⠒⠒⠀⠒⠂⠀⠲⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠤⡀⠀⠀⠀⠀⠙⢦⡛⣮⠳⣄⠀⠀⣧⡅⠀⠀⠀⢤⣀⣀⣀⠀⣀⣀⡀
⣀⣀⡀⣀⣀⡀⣀⣀⣀⠀⠀⠀⡆⣿⠀⠀⠀⣴⣴⠒⠁⠀⠀⠀⠀⠀⠦⠀⣤⣦⡀⠀⠙⢎⠻⣿⠆⠀⣟⠃⠀⠀⠀⠤⠤⠤⠤⠤⠤
⠀⠤⢀⠀⡄⢠⣤⣤⠀⠀⠀⠀⣇⣿⠀⠀⢰⡞⡈⠀⠀⠀⠀⠀⠀⠀⢰⠉⢤⡤⢷⣤⣀⠈⢧⠹⠆⠀⡇⠇⠀⠀⠀⡀⠀⢀⡀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠐⠿⠀⡃⠀⠀⠀⠀⠀⠀⠰⠈⠳⠄⠤⢴⡟⣿⣷⠆⠀⠀⢀⡟⡁⠀⠀⠀⣉⣉⠉⣁⣀⣁⣀⣉⣁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢲⣿⣾⣿⡿⠃⠀⠀⢠⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⡀⠀⣹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠻⡟⢡⣖⡂⠀⢀⡇⣦⠀⠀⠀⠓⠒⠒⠚⠀⠈⠁⠀⠒
⠉⠉⠉⠁⠀⠉⠁⠈⠉⠀⠀⠀⠀⣸⡇⠀⠙⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠟⠃⠬⠀⠀⢸⡇⠉⠀⠀⠀⠋⠛⠉⠙⠉⠀⠙⠉⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣽⣧⡘⠠⢀⠀⠀⠀⣀⣤⣶⠗⠛⣯⣳⠀⢰⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⢀⣿⣿⣯⣿⢶⣤⠀⠀⢰⠟⣧⠹⠖⢾⣍⠞⢀⠏⠀⠀⣾⢠
⠀⠀⠀⣄⣀⡀⢀⣀⣀⠀⠀⠀⠈⣿⡀⠀⠀⠙⠿⠿⠟⠛⠉⠁⠀⠈⠓⠾⠶⠖⠋⠁⠀⠈⠀⠀⠀⣿⡈⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠇⠀⠀⠀⠀⣀⣀⠀⢀⣀⣈⣀⣀⣀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠖⠒⢀⣠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤⣄⠏⠰
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠒⠒⠂⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠋⠛
⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⣀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣀⣀⣤⣤⣀⡀⠀⣀⣠⡀⠀⠀⠀⠀⠄⢁⢠⣴⢋⠡⠂⣠⠖⠒⠒⢲⣦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⡴⢋⠔⠁⠀⠀⠚⠊⠑⠚⣀⢁⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢌⡴⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⢷⡄⠀⠀⠀⠈⡀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠁⠀⠀⠀⢠⠂⠀⠀⠀⢀⡴⠃⣰⣶⠀⣸⠇⢁⠀⠀⠀⣷⠀⠀⠀⠐⠂⠀⠂⠘⠓⠃⠀⠛⠛⠒⠚⠓⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠁⠁⠀⠀⣾⡁⠀⠈⠁⢀⡾⠀⣸⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣉⣉⠉⢉⣠⣴⣿⠀⡀⠀⠇⠀⡀⠀⢠⣄⣀⣀⠀⢀⠀⢀⣀⣀⣀⣀⡀
⠀⣀⢀⢀⠀⡀⢀⡀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⢀⢰⣶⡀⠀⠿⠀⣤⣿⡽⢿⣿⣙⢿⣿⠞⠁⠀⠀⠀⠃⠀⠀⠤⠄⠠⠤⠄⠤⠄⠤
⠀⣀⣀⠈⢀⣁⣈⠁⠀⠀⠀⠃⠀⢻⠘⣆⠀⠀⠛⣼⣿⣿⣆⠈⠣⢌⡉⢉⡙⢫⠉⠀⠀⠀⠀⠀⠆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⣆⠸⣆⠀⠈⠙⣿⡿⢿⡟⠀⠘⠋⠘⠁⠓⠀⠀⠀⠀⢀⠌⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣦⠈⢷⡀⠀⠉⠉⠉⠃⠀⠀⡀⠀⠀⠀⠠⠄⠀⡀⠁⠀⡏⠀⠀⠀⠈⠋⠐⠛⠋⠀⠉⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠈⠳⣄⠙⠂⠀⠀⢄⣠⠶⠂⠀⠉⠂⠀⠀⠀⠉⠀⠀⠀⠇⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⠀⢀⠑⠂⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠒⠶⠦⠄⠀⠠⠶⠆⠀⠀⠀⢄⠀⠀⢠⣿⣧⠀⣀⣀⣠⣦⣤⣄⣀⣀⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠰⣿⠗⢿⡿⣿⢹⣿⡯⣿⠛⡟⢿⣼⣿⣿⢿
⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠦⠄⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠁⣤⣤⣰⣗⣾⡇⠀⢿⣆⢸⡿⢠⣤⠀⠀⣿⣏⣿⢶⡟⢠⣦⣄⣤⣤⠀⣾⣧⠀⢠⡿⠛⠛⢀⣤⣤⣰⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠂⠻⠭⠌⠿⠻⠇⠀⠈⠻⠿⠃⠨⠿⠆⠀⠿⠏⠁⠈⠿⠺⠿⠿⠿⠸⠇⠸⠧⠀⠀⠻⠶⠶⠈⠿⠭⠙⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠿⠿⠥⠤⠤⣤⣀⡀⠉⠈⠙⠻⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣭⣙⠶⣄⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣤⣐⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣼⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣿⣿⣿⣿⣿⡿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣠⡿⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⢀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⣼⣿⣿⣿⣹⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⣿⣿⣿⣿⣷⡑⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡝⣛⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠟⠁
⠀⢻⣿⣿⣿⣿⣿⣮⣙⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠘⣿⣿⣿⣿⣿⣿⡟⠻⠶⣭⣿⣟⣛⣟⣛⣻⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⣁⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣐⠂⠀⠀⠂⠄⢁⠠⠤⢶⠲⡀⢠⣤⢤⠤⢄⡀⠀⠀⠤⠐⢀⡄
⠀⠀⠀⠀⠀⠰⣎⠁⠀⣀⠿⠃⢸⣤⣤⢀⣶⣽⠆⡠⢤⠤⣄⡀⠘⠁⠔⢢⡄⢀⡀
⠀⠀⠀⠀⡄⠀⣙⡉⠛⠁⠀⠀⠀⠈⠙⠛⠋⠁⠘⢷⠀⠀⠀⣹⡷⠀⡶⣄⣀⠁⢀⠁⠀⠀⢀
⠀⠀⠀⠀⡇⢰⡟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠋⠁⠻⣉⠀⡙⠓⡄⠐
⠀⠀⠀⠀⡇⢠⡆⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠦⡴⢃⠀⠀⡀
⠀⠀⠀⠀⡇⠀⢙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣦⠀⡇
⠀⠀⠀⠀⡆⢀⠏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠡⣽
⠀⠀⠀⠀⡇⠠⡆⣓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡶⢷
⠀⠀⠀⠀⡇⠠⣥⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶
⠀⠀⠀⠀⡟⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠀⠻⡧
⠀⠀⠀⠀⡆⢸⡏⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣸⡇
⠀⠀⠀⠀⡇⠸⣧⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣅
⠀⠀⠀⠀⡇⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⣹⣤⢠⡄⠀⠀⠆⠁
⠀⠀⠀⠀⡆⠀⣾⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⣤⣭⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡇⠐⡿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟
⠀⠀⠀⠀⠀⠀⣷⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠓⢶⡀
⠀⠀⠀⠀⠀⡀⢈⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠁⢸⠉⠻⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡆⠀⠀⠀⠀⢠⡆⡦
⠀⠀⠀⠀⢠⠀⢸⠆⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠄⠀⢈⣍⣹⡏⠉⠉⠉⠀⠈⠘⠁
⠀⠀⠀⠀⠸⠠⠘⠿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠄⢿⣾⢟⡁⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢼⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⢴⠀⣧⡜⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠰⠖⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠹⠀⡄⠀⠀⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣍⢀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠸⢯⢬⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣿⡆⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⡄⣄
⠀⠀⠀⠀⠀⠀⢠⠆⣼⠛⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⡸⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢻⠄⡙⢛⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠈⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠰⣆⠁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡛⣿⠀⢲
⠀⠀⠀⡀⠀⠁⠀⠀⠄⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⢃⣟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣅⣤⠃⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⣅⢨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣉⠁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣧⣾⡟⠀⣠⣤⣤⣤⡀⠀⠀⣠⡾⠛⠳⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠉⠁⠀⢼⣙⣇⣠⠀⣛⡆⠀⣿⣤⣼⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⢀⡠⠀⠉⠉⠛⠛⠋⢀⠀⠠⠛⠃⡉⢁⣀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡀
⣿⣿⣿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣤⣢⣄⣤⠦⣴⠀⠀⡇⠀⠀⣞⢹⢦⣠⣴⡤⢦⣦⣴⣸⣤⣆⣔⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣀⣀⣀⡀⠀⠀⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⣛⣛⣛⣭⣯⣭⣭⣤⣭⣬⣭⣭⣍⣉⣛⠛⠻⠶⢶⣤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣛⣭⣗⡶⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⡠⠤⠄⣉⠙⠷⣦⡀⠀⠹⡵⡄⠈⠉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⢶⣫⣵⠾⠟⣋⣉⣀⣀⣀⠀⠀⠀⢠⠊⠉⠉⠉⠉⠙⢣⡀⠀⠀⠀⢈⣱⠘⢿⣄⠀⠘⣞⣆⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⣠⡾⣫⣗⠟⠋⠀⠀⣏⡀⠀⠀⠀⠀⠉⣦⠤⣴⡓⠂⠤⠤⠤⠐⢚⠤⣉⣉⣉⠠⠴⡟⠛⢿⡆⠀⠘⡞⡄⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⢀⡾⢫⣾⠟⣁⠠⠤⠤⠼⣁⣨⣭⡁⠀⠈⢉⡟⠀⢸⠉⠁⠐⠒⠒⠈⣉⠆⠀⠤⡤⠒⠚⠓⠒⠒⢿⡄⠀⠹⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⢠⡿⣱⡿⠁⢸⣄⡀⠀⠀⠀⠀⣱⣀⣈⣉⣉⣠⡏⢐⣭⠴⣈⣀⠉⢈⣁⣨⠋⠉⠋⡶⠤⠀⠀⢀⣀⠼⣧⠀⠀⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢠⣿⣼⡟⠀⠀⡣⠤⣀⣈⣉⣉⣁⡼⠤⠄⠠⠤⠰⡏⠀⢸⠢⢄⠀⢀⡀⠤⢾⠀⠀⠀⣗⠂⠠⠤⠤⠤⠖⣿⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣼⣻⡿⠀⠀⠀⡓⠤⠤⠄⠠⠤⠴⡖⠀⠠⠄⠐⠾⠒⠒⠚⠛⠿⢤⡓⠀⠒⢚⡆⠀⢈⠅⣉⣁⡂⠒⢐⣉⣿⠀⠀⢈⡇
⣏⣿⡳⣄⠀⠀⣉⠒⠒⠒⠐⠒⠒⡏⠓⠒⠒⠚⡗⠒⠤⠤⠤⠤⠔⢗⠚⢋⡥⠒⠒⠚⠒⠢⠤⣀⠉⠀⣠⡿⠀⠀⣟⡇
⢹⠻⣿⣾⣵⣦⣧⣍⣑⡒⠒⢐⣢⡭⢖⡴⠐⣾⠍⠒⠒⠒⠒⠒⢊⡻⠐⠙⡗⠢⠤⠤⠤⠤⠤⣿⣃⠼⣿⠇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠣⡈⠙⠻⢷⣯⣭⣛⣻⠿⢶⣶⣧⣤⣌⣉⣱⣶⣉⣉⠁⠀⣀⣩⡇⠀⠀⣟⠐⠒⠠⠤⠤⠒⣏⣀⣠⡟⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠈⠢⣀⠀⠀⠈⠉⠛⠛⠓⠶⠶⢶⣾⣭⣭⣭⣭⣭⣿⣟⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⡉⣩⣤⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠉⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠤⠤⠖⠒⠛⠉⠉

⡞⠉⠁⡧⢤⢸⢀⡤⢄⢠⠄⡤⢤⢠⡄⢄⢸⠀⣠⡄⣤⠄⢶
⠑⠄⠂⠃⠘⠘⠈⠣⠊⠘⠀⠓⠘⢸⠆⠊⠘⠘⠔⠃⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣒⣯⠭⠽⠗⠒⠒⠒⠒⠒⠒⠒⠒⠺⠯⠭⢽⣒⣲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⠽⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠯⣕⡢⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣫⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣝⢦⡀
⠀⠀⠀⠀⠀⣰⢫⠞⠁⠀⡴⠒⠛⠛⠛⠛⠛⠓⠒⢦⡀⡷⠚⠉⠉⠉⠉⠉⠙⢲⡃⠀⡴⠒⠛⠉⠉⠙⠛⠒⢦⠀⠱⣝⢦
⠀⠀⠀⠀⣰⢣⠃⠀⠀⠀⡷⠒⠛⠋⠉⠉⠙⠛⠒⠶⣧⡷⠚⠉⠉⠉⠉⠉⠙⠲⠧⣠⠷⠚⠋⠉⠉⠉⠉⠓⢺⡁⠀⠘⡎
⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⡧⠖⠒⠒⠛⠛⠓⠒⠲⢤⠖⠦⣄⣀⣀⣀⣀⣀⣀⡤⠖⠒⡶⠋⠉⠉⠉⠉⠉⠙⢲⡃⠀⠀⢹
⠀⠀⠀⠀⢻⡘⢄⣀⠀⠀⣇⡀⠀⠀⢀⣀⣀⣀⣀⣸⣇⣠⣤⣭⣭⣭⣭⣥⣤⣄⣀⣀⣧⣀⣀⣀⠀⣀⣀⣀⡼⠁⢀⣠⠏
⠀⠀⠀⠀⠈⢿⠲⠬⢭⣭⣭⣭⣭⠭⠭⠭⠥⠤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⠤⠭⠭⠭⢭⣭⣭⣭⡭⠭⠴⡾
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⡄⣀⣀⡀⠀⠀⠀⠐⠦⠴⠤⠄
⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣌⣉⣀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠴⠄⠤⠀⠀⠀⠀⠐⠰⠶⠤⠄⢤⠦⠤⠤
⢠⣤⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠲⠶⠶⠶⠶⠒⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠤⠀⣒⣈⣩⠥⠤⠤⠄⠒⠐⠀⠠⠬⠍⠭⣁⣒⡂⠠⣤⣁⢠⠁
⠀⠀⠀⠀⠀⠀⡠⠔⣘⠥⠔⣾⣯⣵⣴⣤⠀⠀⠀⠀⢠⣤⣤⡄⣀⣀⣀⡀⠀⠨⠋⠑⠲⣯⣑⠢⣀⠀⠀⠀⠐⠓⠒⠒⠿
⠀⠀⠀⠀⢠⠊⡠⠚⠁⠀⢰⣿⣿⣯⣿⣿⠟⠛⠷⠶⣿⣒⣚⣫⣿⣭⣍⣛⣛⣿⣭⣭⣭⣷⡆⠙⢮⡵⣎
⠀⠀⠀⢀⠃⡜⠀⠀⠀⠀⠸⣿⣿⣭⣭⡿⠶⠶⡶⢾⣛⣛⣛⣻⡟⠸⢏⣩⣽⣿⣿⣿⣿⣿⡠⢒⡁⢱⡘⡄
⠀⠀⠀⠸⡀⡇⠰⠄⢠⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⢸⣯⣭⣭⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡈⠁⢸⡇⡇
⠀⠀⠀⠀⢳⡜⣄⢠⡦⢉⣻⣷⣿⣿⡿⠿⢟⣥⢠⢼⣿⣿⣿⣿⣟⣛⠛⠛⢿⣭⣿⣿⣿⡧⠘⠃⠛⢺⢁⠇
⠀⠀⠀⠀⠀⠑⢌⠳⣄⣼⣿⣿⣿⣿⣿⣇⣤⣍⣸⣿⣿⣿⣿⣷⡷⢈⣤⣶⣶⣿⣿⣿⣷⡄⠀⠀⢠⢎⠜
⠀⠀⠀⠀⠀⠀⠀⠑⣾⣟⠦⣍⠉⠉⢉⡝⠉⣁⢹⣻⣛⣻⣿⡿⡇⢻⣿⣿⣿⡿⠿⢟⠉⠀⣀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠈⠑⠂⠭⣓⡾⠤⣀⣉⡀⠈⠀⣽⠋⠉⢷⠀⠀⣀⣀⠠⠤⠒⣻⡭⠒⠉
⠈⠑⠲⠲⠶⠶⠶⠶⠀⠀⠀⠀⢀⠎⠉⠉⠒⠒⠠⠭⢭⠭⠭⠭⠽⠭⠥⠀⠒⠒⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢄⠤
⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⢤⠴⢤⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⡛⢙⠃⢀⠀⠀⠀⠀⠀⠤⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⣤⢤⡤⠤⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⢀⠀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠈⠉⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣢⣀⢀⣑⣄⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠣
⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂
⡆⡀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⣶⠀⠁⠀⠤⠤⣤⠠⠄⠀⠀⠀⠀⠀⠀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠦⠰
⡇⠁⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠁⠆⠀⠂⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠖⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠀⠀⠀⠁
⠀⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠄⡤⢠⠄⡤
⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⡠⠔⠁
⠀⠀⠈⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⡀⠀⠀⠈⠢⢀⣀⢀⣀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠐⠂⠐⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⣿⣿⡇⢤⠄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠘⠃⠀⠀⠀⡤⠤⣀⣶⣶⡦⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⣿⣿⡇⠼⠄⠀⠀⠀⠸⢢⠆⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠩⢹⡇⠀⣿⠿⠿⠟⠛⠋⠀⠣⣰⣾⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⡷⠤⠴⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⢠⣶⣾⢸⡀⠀⠀⢠⡎⠉⠉⠉⠉⠉⠀⠀⠀⢀⠄⢠⢰⡆⣿⡇
⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⡇⠀⢬⣿⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠛⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣀⣀⣀⣀⣘⣃⣿⡇
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠒⠒⠀⠀⠀⠀⣶⣦⣤⠤⣤⣤⢤⣤⣤⣤⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡓⣿⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠚⠛⠛⠛⠀⠀⠀⠀⣿⣿⣶⡇⠀⠀⢀⣀⣠⣤⠀⠀⠛⠉⠀⠁⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⡶⠆
⠀⠀⠀⠀⠀⢀⣀⠀⣠⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠻⢯⣀⠀⠀⠀⢸⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣀⡊⠓⠲⢻⠀⠀⠀⢸⣷⣿⣾⣿⣿
⠀⠀⠀⠀⢈⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠀⠀⠀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠛⠛⠒⠀⢸⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⢫⠀⠀⠀⠀⠀⢶⣦⣤⣴⡾⠉⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⠻⠟⠿⠟⢃⡀⠀⠀⠀⠛⠘⠳⠁⠠⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠤⠴⠦⠼

⡞⠉⠀⡇⢄⢸⢠⠢⡀⡄⢠⠢⡄⡄⢤⢸⠀⣢⡀⣔⠀⡖
⠑⠒⠀⠃⠘⠘⠘⠒⠁⠃⠘⠒⠁⠗⠊⠘⠘⠒⠃⠂⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠤⠤⠤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⣒⠯⠭⠓⠒⠚⠛⠉⠉⠉⠉⠉⠙⠓⠒⠒⠯⠭⣗⣲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡯⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠒⠯⣓⢤⡀
⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡏⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⢀⣀⣀⣀⣀⣀⡀⠙⢮⡳⡄
⠀⠀⠀⠀⢠⢎⠞⠁⠀⣰⢉⣁⣀⣀⣀⣀⣀⣉⢳⡀⣏⣀⣤⡤⠤⣤⣄⣈⣧⠀⡜⢉⣀⣀⣀⣀⣀⣉⢳⠀⠙⣜⢆
⠀⠀⠀⠀⡏⡞⠀⠀⠀⢸⢉⣀⣀⣀⣀⣀⣀⡈⠙⣒⠋⠀⠀⠀⠀⠀⠀⠈⢙⣒⠋⣁⡤⠤⠤⠤⢤⣈⣹⠀⠀⠘⡜
⠀⠀⠀⠀⡇⣇⠀⠀⠀⣸⠉⠀⠀⠀⠀⠀⠀⠈⢹⡍⠙⠲⠤⠤⠤⠴⠖⠚⠉⠀⣟⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⠇
⠀⠀⠀⠀⢻⣌⡓⠦⠤⠼⠶⠤⠤⠴⠖⠒⢒⣒⣚⣓⣒⣛⣛⣉⣉⣙⣛⣓⣒⣒⣚⡒⠒⠶⠶⠶⠶⠶⠥⠤⠖⣋⣼
⠀⠀⠀⠀⠀⠳⣌⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⢉⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠴⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠤⢊⠀⠂⠒⠒⠬⡑⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⢀⠔⡨⠄⠒⠈⠉⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠐⡀⠇⠀⠀⡀⠖⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⢊⠔⡩⠂⠡⠀⠀⣠⠖⠄⠀⢹⠀⡄⠀⠀⠠⡀⠀⠀⠈⠀⠀⠱⡀⢢⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡐⠁⠠⠊⠀⠀⠀⠀⠀⠣⠀⠀⠴⠉⠐⠇⠀⠀⠐⡄⠀⢁⠂⠀⠀⠀⠀⠀⠁⠡⡀⢆⢀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡈⠀⠁⠀⠀⠀⠐⠀⠘⢇⠐⠈⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⠀⠙⠂⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠇⠘⠀⠀⡛⢉⡖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢰⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡹⡷⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⡁⠀⠰⢠⠆⠀⠀⠀⠀⠕⠀⠁⠀⠀⠄⠠⠀⡀⢢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡀
⠀⠀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠉⣀⠠⠾⡦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠄⠉⠀⢀⠀⠀⠂⠀⠀⠀⠀⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠐⡀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⡈⠠⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠑⠂⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠂⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠂⠂⠀⠂⠀⠄⠐⠀⣤⠀⡆⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⢀⡀⡄⠀⢰⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠊⠀⠀⠀⠉⠣⡀⠀⠡⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠶⠛⠋⠛⠋⠀⢏⠉⢣⡢⡀
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⠈
⠀⠀⠠⠈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⢜⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡢⢀⠀⣀⡀⠀⠀⠉⠢⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⣴⠛⡏⠉⠷⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⣤⢴⠆⠈⠁⠒⡭⠄⠀⠀⠚⠉⠀⠀⡀⠀⢀⡡⠀⠦⠌⢛⠡⠂⠀⠘⣄⢀⠾⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡗⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠊
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢄⠀⡀⠄⡧⠀⠀⠀⠠⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⢀⠔⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠑⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡜⠃⠀⠀⣀⠄⠈⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠂⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠚⠀⡠⠁⠀⠰⠇⠐⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⡄⠀⠀⠀⡀⠀⠄⠀⠀⢠⠀⠀⡠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢠⠀⠠
⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠁⠀⠈⠀⠀⠆⠀⠃⠀⢸⠀⠠⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄⢀⡴⣇⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣴⣾⡀⣆⣠⣦⠖⠀⢸⠀⢠⡄⢒⢫⣴⣷⣿⣅⠀⠀⠀⠀⠀⡀⢦⢎⠃
⠀⠀⢀⣼⢉⣼⣿⠟⠞⢁⣼⣾⡾⢰⠇⠀⠙⢾⠯⡽⣿⡷⢀⢴⢐⣆⡘⣿⣿⡟⡳⠇⠀⠀⠀⠀⡀⡄⠠⠤⠬⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠉⣁⠀⣸⡿⠇⣀⣒⠀⢲⡈⣩⣆⣄⣾⣴⢎⠲⢑⣠⣃⠈⠠⣤⣒⠊⠀⠆⠀⠐⠇
⠀⠀⠀⠀⠀⠀⡂⠀⡀⢡⡄⡠⠨⣱⣏⣯⠁⠀⠀⠀⣀⣶⣿⠦⢅⠀⠄⠋⢩⢤⡯⢤⠀⢉⣀⠆⠤⢤⢲⠆⠂⢀⣴⠂
⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠙⢿⡅⢌⠀⠀⠳⠀⠀⢉⠁⡆⠈⠁⠀⠘⠉⣉⠁⠀⠀⠈⠉⠁⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠘⠑⡞⠒⠓⠻⠘⠛⠐⡶⠀⡟⠉⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⢖⢀⣀⡂⣟⠂⡐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠳⣄
⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢣
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠤⢤⣀⣀⣀⣀⣀⣀⡤⠤⠤⠔⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠾⠢⠞⠖⠇⠀⠆⠀⠎⠖⠦⠀⠽⠷⠪⠞⠣⠰⠆⠣⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⢶⡶⡶⠶⠶⠶⠶⠶⠶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣞⣻⣭⣭⣷⡶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣦⣌⠉⠉⠻⡿⡙⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⣵⡾⠿⠛⠋⠁⠀⠀⠀⢀⡠⠤⠤⠤⠤⣤⡒⠂⠉⠐⠒⠤⡙⢷⣄⠀⠘⢞⢆⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣠⡴⣿⣽⡿⠛⠉⡥⠒⠒⠒⠒⠒⠤⡀⢀⣸⣄⡀⠀⠀⠀⣀⣽⠒⠤⠤⠄⠒⣻⣤⣿⣧⠀⠈⢏⢇⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⣠⡾⣫⣿⠟⠁⠀⠀⢠⠓⠢⠤⠤⠤⠤⠤⡿⠓⢻⠦⠄⠉⠉⠡⠤⠾⣉⠒⠒⢊⣉⡽⠄⣈⣻⣆⠀⠘⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⣴⢟⣼⠟⢡⠒⠋⠉⠉⠉⠓⢿⠓⠒⠀⠒⠒⡇⣀⠜⣀⠀⠤⠤⠤⠐⢺⠤⣈⣽⣉⠀⠀⠀⠀⠈⣿⡄⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⣼⢯⣿⠋⠀⢜⠑⠂⠤⠤⠤⠔⢺⠐⠒⠒⠒⣉⡯⠒⢫⡉⠒⠂⠀⠒⠂⣳⠀⠀⢸⢅⣉⠁⠀⠐⢉⣹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⢰⣟⣿⠃⠀⠀⣎⡉⠘⠒⠒⠒⣚⣯⣉⣉⣈⣉⣨⣁⣀⣷⣬⣵⢀⣖⣈⣉⢽⠀⠀⢸⠒⠤⠬⢉⣩⠥⢼⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⣾⣿⣿⠀⠀⠀⡣⠍⣉⣉⣉⣉⣡⡿⠤⣈⣀⣰⣅⣀⠀⠀⠀⠉⣹⡤⠤⠤⢞⣀⡤⣾⣉⣒⠒⠒⠒⠒⢺⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢻⣿⣷⣕⣤⣀⣗⠢⠤⢀⣀⣀⣐⠣⢄⣀⣀⣼⠦⢄⣉⣉⣉⣉⠤⣗⣒⣶⣅⣀⡀⠀⠀⠀⣙⣶⠄⣰⣻⠇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠘⢎⠙⠿⣿⣿⣻⠿⢶⣶⣶⣒⣚⣏⠙⠒⠤⢭⡤⠤⠤⠤⠠⠤⠴⠃⠀⢘⠤⢀⣉⣉⣉⣉⣩⠗⠋⢩⡟⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠳⣄⠀⠉⠙⠛⠷⠶⣦⣭⣭⣛⣛⣛⣛⡿⠾⠷⠶⠶⠶⠶⠾⣶⠶⣾⣶⣶⣶⡶⠶⠶⠶⠷⠶⠟⣀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠷⠾⠶⠾⠛⠟⠟⠏⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠛⠛⠉⠉⠉

⡔⠉⠁⢸⠤⣄⢸⠀⡤⢤⠀⡤⠄⡠⢤⠀⡤⢤⡀⡇⠠⠤⡀⣠⠤⠠⡦
⠳⣄⡤⠸⠀⠼⠸⠀⢧⡸⠃⠇⠈⢧⡸⠃⡧⡠⠃⠇⠸⡩⠇⢨⡹⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⣖⣒⣒⣒⣛⣛⣓⣒⣒⣒⠶⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣚⣫⠭⠖⠒⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠲⠯⢭⣓⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠮⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⠀⠀⠀⠀⠈⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣝⠦⡀
⠀⠀⠀⠀⠀⠀⣠⢋⡴⠁⠀⢀⡤⠖⠒⠚⠛⠛⠛⠒⠒⠲⢤⡀⢸⡖⠛⠉⠉⠉⠉⠉⠙⠓⢾⠃⠀⣠⠶⠒⠛⠛⠛⠛⠛⠒⠦⡄⠈⠳⡝⢦
⠀⠀⠀⠀⠀⣰⢣⡏⠀⠀⠀⢸⣤⠴⠶⠒⠒⠒⠒⠲⠶⠦⣄⡇⢸⡤⠖⠚⠛⠛⠛⠛⠒⠶⢼⣇⠀⣯⡤⠶⠒⠒⠒⠒⠒⠶⠦⣽⠀⠀⠙⣎⢧
⠀⠀⠀⠀⠀⡇⡾⠀⠀⠀⠀⢸⣁⣠⣤⡤⠤⠤⠤⣤⣤⣀⡀⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⡤⠴⠶⠶⠶⠶⠶⠦⢤⣸⠀⠀⠀⢹⡘
⠀⠀⠀⠀⠈⡇⢧⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠙⠲⠶⠶⠶⠴⠶⠖⠚⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢸⢃
⠀⠀⠀⠀⠀⢷⣌⠳⠤⣤⣀⣘⣦⣤⣠⣤⣤⣤⠤⠤⠤⠤⠶⠷⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠼⠦⠤⠤⣤⣤⣤⣤⣤⣶⣃⣠⡤⠴⢋⣼
⠀⠀⠀⠀⠀⠈⢯⡙⠒⠶⠦⠤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠶⠶⠶⠤⠤⠤⠤⠶⠖⠚⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠴⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠉⠡⠌⡁⠀⣐⠂⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢁⣀⣀⠀⠀⠀⡀⢄⠀⠈⠊⠀⠐⠂⠐⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⡱⠊⠓⠠⠀⠤⠂⠁⠀⢎⠀⡠⠔⠀⢀⠀⡀⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⡀⡨⠂⠢⠄⠀⠁⠀⠀⠁⠑⠄⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘⢅⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠐⠠⢄⣁⠀⢬⡄
⠀⠀⠀⠀⠀⠀⣤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⠉⠁⠐⠐⠃⠂⠤⢀⢁⡀⢀⠀⠀⠀⠀⠀⠀⢁⠄⠘⠒⡀⠀⢢⡀⠠⠤⡀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠐⠂⢁⣀⡀⠸⡀⠀⠀⠐⠀⠀⠠⠂⠀⠀⠡⠌⠀⠁⠐⠃⠀⠠
⠀⠀⠀⠀⠀⢠⠈⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠲⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠁⡅
⠀⠀⠀⠀⠀⠀⡀⠠⡈⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡄⠀⠀⠀⠀⠀⡀⠤⡾⠃⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⢄⠐⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⣐⠣⡀⢀⣀⠐⠒⠊⡘⠁⠀⠸⠄⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠔⠁⠔⠍⠀⠈⠉⢀⠡⠞⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢈⠙⠋⠒⠒⠲⠖⠀⣀⣀⣀⣀⡒⠈⠅⠀⠒⠈⡠⠴⠁⠀⠦⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠤⠤⠤⠤⠤⠀⠐⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡦⠤⠤⠤⠰⠶⠤⠤⠤⠄⢤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠙⠈⠙⠛⠈⠋⠛⠘⠋⠛⠀⠃⠋⠙⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⠀⣤⣀⣀⡀⣀⢀⣀⣀
⠇⠲⠒⠃⠘⠃⠒⠖⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡈⠀⠀⠀⠀⠀⠈⢀⢁⣈⡈⡁
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⡃⠉⠙⠉⠋⠛⠘⠋⠉⠘⠉⠉⠁
⣈⠁⠉⠉⠉⠃⠀⠀⠀⢀⣤⣾⣿⠿⠟⠛⠛⠛⢙⡋⠛⠛⠛⠿⠿⣿⣿⣦⣄
⠈⠙⠚⠚⠓⠚⠚⢃⣴⣿⠟⠉⠀⠀⠀⠀⢀⣠⣤⡀⢀⣤⣤⣄⠀⡀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⣠⣶⣶⣦⣀⡔⣿⣿⣿⣿⣽⣿⣿⣿⢢⣝⣂⣀⠀⠙⢿⡆⢠⠠⠴⠦⠄⠆⠆
⡄⣀⣀⣀⣀⠀⢸⡏⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣁⠀⠈⣿⢀⡀⠀⢀⠀⠀⡀
⠁⠀⠀⠀⠀⠀⠘⣇⠀⠪⣿⣿⣿⣿⣿⣿⣿⡿⡻⢻⣿⣿⣿⣹⣿⣿⣿⣿⣿⠃⢀⠂⠀⠋⠉⠉⠘⠉⠁
⡶⠶⠤⠤⠤⠤⠤⠌⠒⠤⠠⠨⠁⠛⠛⠛⠛⠳⠾⠾⠭⠭⠍⠿⠿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⢀⣀⠀⡀⢠⢀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠁⠁⠈⠉⠈⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢠⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢁⣴⠌⠉⠀⠀⠩⣿⠿⠀⢿⣗⢾⡟⠓⠀⠀⠐⣶⠀⠉⠉⠓⢦⣄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣐⣩⣗⠀⠀⠄⠀⠨⣇⠀⣀⡀⣸⣿⡇⠐⣒⢒⣒⣺⡖⠂⠀⡀⠀⠈⠳⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡴⠛⠛⠛⠓⠦⢤⠀⠀⢹⡗⡓⣀⡀⢸⣿⡯⣀⠒⠒⠒⠺⠧⡀⣀⠗⠀⠠⡆⢱
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⣨⣗⠀⠀⠀⠀⢠⠜⠃⠀⣘⣛⣐⣣⣒⣚⣿⡉⣿⣿⣿⣿⣿⣿⣿⠿⠥⠐⢒⡆⣸
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠥⠿⠒⠸⢠⣄⣿⠄⣰⣿⣿⣿⣿⣿⠁⠀⠸⡆⣿⣿⣿⣿⣿⣿⡇⠙⠃⠀⡼⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠠⠴⡟⢻⠥⢺⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡀⠀⣀⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠐⢀⠀⠠⠼⡇⠈⠓⠸⠿⠻⠛⠛⠓⠂⠒⠒⠛⠛⠛⠛⠟⠙⠛⠉⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⢀⡀⢈⡓⢦⣦⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀
⠀⠀⠀⠀⠀⢀⡠⢔⠂⠀⠄⠀⠀⠀⠂⠀⠀⠉⠢⠑⡀⠀⠀⠀⣠⡤⠀⠀⠀⠤⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⢁⠪⢀⠀⠠⡀⠉⠑⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡩⣫⣵⣤⣀⣠⣄⡀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠐⠁⠐⠁⠀⠀⠀⠸⠀⠀⠔⠃⢆⠀⠀⢂⠀⢃⠀⠀⢈⢨⠀⠁⠊⢡⢄⣐⠟⠋⠀⠀⠀⡤⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠘⠀⠙⢄⠂⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠘⢃⠀⡀⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠠⠤⠀⠀⠀⡠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠆⠀⠀⠀⠘⣿⣇⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢠⢀⡄⠀⡀⠁⠢⢐⠀⠀⠀⠀⠀⠀⠒⠒⠰⠦⠤⠤⣄⡀⠀⠀⠓⠀⠀⠀⠄
⠀⢠⢣⠀⠀⠀⠀⠀⠈⢁⠤⢾⡧⣄⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠉⠀⠀⠀⠀⠀⠀⠀⡐⠐⠏⠃⠀⢹⠁⢰⠋⢢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⣄⡀⠀⢸⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⢰⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢣⡀⠀⡄⠀⠀⠀⠀⠀⠀⢰⣂⣀⠀⢰⠀⢠⡀⡘⠀⠀⠀⠀⢀⠀⠤⠄⠄⠀⠀⠀⠈⠀⠀⠀⠀⢈
⠀⠀⢀⠔⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⡉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠮⠁⠀⡐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠸⡀
⠀⠀⢀⠀⠀⠂⢄⢐⣋⠀⠘⠢⡀⠀⠀⢠⡤⠂⠀⠐⡄⠘⠒⡄⠀⠀⢸⠉⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⡄⠀⠀⠂⠋⣨⢇⣂⡀⠀⠢⡀⢤⠀⠀⣴⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⢠⠑⠂⠀⠤⠴⠇⠀⠀⠈⠐⠄⠈⢀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⢸⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠑⢄⠒⠐⠚⡇⠀⠀⣀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠂⠢⠄⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠈⠓⠤⠀⢀⠺⡤⡤⠟⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡓⠀⠀⢀⠀⠒⠉⠉⠉⠛⠃⢦⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⡀⠀⠀⠘⠛⠁⠀⣠⡦⠀⠀⠀⠀⢀⠉⠀⠀⠙⣇
⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⢠⣿⣾⡀⢀⠀⠀⠀⠀⠠⢀⠄⣿
⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠊⠁⠀⠈⣷⠊⢡⡄⠁⠀⠀⠀⠀⠄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠲⠟⠀⠠⠈⠃⠀⠀⠀⠀⠀⠙⢉⣄⣐⠂⠀⠀⠀⠈⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠠⠠⠤⠠⠄⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡄⠘⠛⠃⠀⠈⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡩⠀⠀⠀⢌⠰⣋⣀⠀⠀⠘⠀⠀⠀⠀⡟⣱⡄⣀⣀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠂⠀⠀⠈⠀⠀⠀⠈⠉⣈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢠⡙⢧⠻⠁⠀⠀⠀⠀⠉⠉⢀⡀⠀⠀⠀⠀⠀⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠂⠀⠀⠀⠀⠀⠀⣠⣦⠿⠗⠀⠀⢰⣷⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠉⠁⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠐⣒⣀⣀⣠⠀⠄⠀⠨⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠹⠏⡆⠠⠞⠉⡉⠁⠀⠈⠐⠄⢠⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠉⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢐⣆⣙⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⠀⢀⠀⠀⠀⠨⢨⡃⠀⠀⠀⡂⠢⠄⠠⠼⠄⠀⢠⠭⠴⠀⠀⠄⠀⠀⠠⠠⠤⠤⠤⠠⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠒⠠⠀⠀⠠⠲⢂⣁⣃⠄⠀⠀⢡⠀⢰⡎⠗⡆⠀⠀⢠⣤⡄
⠂⠀⠤⠀⡄⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡀⠀⠀⣠⣄⠘⠊⠈⠀⠀⠀⢋⠀⠸⠇⡆⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠁⠉⠈⠀⠁⠈
⠀⠀⠠⠤⠠⠀⠠⠠⠠⠀⠀⠀⠂⠀⠀⠀⠠⠇⡀⣇⡇⠀⠰⢧⣽⠇⠀⠀⡀⠈⢵⠂⠀⣤⠸⠁⢠⡤⡄
⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⣄⢙⠌⠁⠀⠀⠀⢬⡁⠀⢀⡄⠀⠰⠅⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⡈⠃⠐⠒⠢⢄⣀⠚⡄⢀⣰⠌⠡⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠰⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣤⡄⠀⢘⠷⠬⠗⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠉⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⢠⠖⠂⢠⢄⠠⢀⠤⡀⡠⢀⢄⢀⡠⡀⡆⠠⡀⡠⠄⡤
⠀⠀⠀⠀⠀⠈⠢⠀⠂⠘⠀⠘⠀⠃⠃⠑⠜⠹⠦⠃⠃⠃⠃⠨⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣒⠯⠽⠓⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠚⠯⠽⣖⡦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡪⠕⠊⠁⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠈⠙⠪⢕⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⡵⠋⢀⣠⠤⠤⠤⠤⠤⢤⣀⠀⣧⠤⠤⠤⠤⠤⠤⣼⠂⠀⣠⠤⠤⠤⠤⠤⣄⠉⠪⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠏⠀⠀⢮⠤⠴⠒⠒⠒⠢⠤⢬⣇⣧⠔⠒⠒⠒⠒⠲⢼⣀⣸⡤⠔⠒⠒⠒⠲⠤⡗⠀⠙⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠀⠀⠀⢫⠴⠒⠒⠒⠒⠒⠲⢤⡬⢤⣀⡀⠀⠀⣀⣀⡤⠴⢧⠖⠒⠛⠛⠛⠒⠲⡞⠀⠀⢹⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⢄⣀⣀⢻⣀⣀⣀⣀⣀⣀⣀⣠⣧⠤⠤⠭⠭⠭⠭⠤⠤⣤⣸⣄⣀⣀⣀⣀⣀⣠⣏⣀⡠⢎⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⠒⠬⠭⠭⠤⠤⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠢⠤⠬⠤⠥⠔⢒⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠔⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣷⣀⣸⣿⣿⣿⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣴⣠⣶⣠⣽⣯⣿⣵⣿⣿⣿⣯⣷⣯⣷⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠴⠶⣶⣶⣶⣶⣴⣶⢄⣴⣟⡋⠽⣭⣭⣿⣿⠁⢛⡻⠛⠟⡛⣿⣟⡟⠻⣿⣿⣿⣟⣍⣙⣛⣛
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢖⣛⣯⠵⢶⠾⢻⠛⡻⠟⡛⠿⠶⠭⣭⣛⣳⣿⣟⡛⠛⠛⠛⠛⠀⠿⠟⠿⢿⣿⠿⣻⡿⠿⠿⠿⠿⠿⠿⠟⠛⣿
⠀⠀⠀⠀⢀⡴⢞⡭⠞⠋⠅⡠⣄⣀⣵⣦⣌⠠⠄⡄⣾⣿⣶⣶⣮⠛⠓⠮⣍⠳⢤⡀⠀⠀⢈⡤⣀⣮⣾⣿⠿⠁⠀⠀⠀⢸⣆⣀⣀⣸⣿
⠀⠀⢀⣴⢛⡵⠋⣠⣈⣀⣴⠾⢿⣿⣭⣯⣿⠛⠻⠿⢿⣯⣭⣿⡟⠛⠛⠛⠉⠛⢯⡉⢯⡉⠘⠛⠻⠟⠛⠟⠂⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⣠⢟⡵⠋⣴⣯⣛⠽⡏⠀⠀⡙⠛⠛⠉⠁⠀⠀⠀⠀⠈⡉⠉⠁⠄⣀⣀⣐⣤⠀⠙⢦⡙⢦⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⢼⣿⣿⣿⣿
⣴⢫⡞⠁⠂⠹⠯⠕⠋⠀⠀⢠⣴⣤⣤⣤⠀⢀⣰⣿⣿⣻⣿⡿⠶⢾⣿⣿⣿⡿⢠⣤⣤⢿⡬⢧⠤⠤⣴⣿⣿⣿⣾⡶⣿⣯⣹⣿⣿⣿⣿
⢳⣜⢦⡒⡀⠈⠀⠀⠀⠀⠀⠨⣿⣿⠟⠽⠖⠋⠉⠻⠟⠛⠛⠁⠀⠠⠉⢉⣩⡀⠀⠀⢄⡼⢡⠟⠀⠀⠀⠀⠀⠀⠇⠸⠀⢠⣽⣿⣿⣿⣿
⠀⠙⢦⡹⣄⠀⣀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀⡀⢀⣠⣴⣶⣿⣿⣿⡆⠀⢀⡞⣡⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠠⠙⢾⣕⢯⣀⢾⣿⣿⣿⣿⠧⣤⣤⣼⣟⠃⣨⣿⣿⠟⠯⠁⠻⠟⠛⠁⢐⡴⢋⠜⠁⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠄⠀⠈⠳⢭⡻⢦⣄⠀⠀⠀⠀⠈⠉⠛⠒⠚⠟⢋⣘⠃⢠⡄⠁⣁⡴⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿
⠀⠀⣀⣤⣀⠀⠀⠀⠉⠓⢮⣝⡓⠦⢤⣀⡀⠀⠀⠀⠠⣙⣻⣿⣷⡶⢟⣩⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣟⣹⣷⡞⠀⠀⠀⠀⠀⠉⠛⠲⠤⢀⣉⢉⣉⣉⣿⣯⣽⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣠⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⣸⣿⣿⠻⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣿⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⡀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡗⠋⠁⠀⠀⠀⠉⠏⠿⠋⠀⠀⢀⡄⢀⠄⠀⠐⢩⡅⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠬⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠣⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⡢⠊⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⠀⠀⠀⠀⠀⠰⣇⡛⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⡿⠽⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠾⠁⠈⠀⠀⠠⠀⠀⠀⠀⠀⠿⣿⣳⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡅⠀⠀⣠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⠀⠀⠀⠸⠀⡀⠀⠀⢀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢠⠀⡄⠀⠀⠀⠙⠠⠄⠀⠀⠂⠄⠒⠈⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢸⠁⠀⠀⠀⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄⠁⠀⠀⠐⠷⠜⣿⡧⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⣐⢀⠏⠀⠐⣴⠀⠴⠁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠠⠄⠐⠡⠀⠀⢀⠂⠈⠈⠀⠒⢚⡟⢧⠀⠀⠀⠀⠀⠀⡠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢢⢀⠘⠲⠼⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠜⠀⠀⠂⢀⠔⠁⡙⢱⣿⠀⠠⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⡐⢸⣿⠆⣄⣠⣶⡄
⠀⠀⠀⡀⠀⢄⡠⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⢀⠔⠁⠀⠈⢉⣸⡗⠀⠠⠀⠠⠌⠀⠀⠀⠃⠀⠀⠀⠀⠼⠋⢯⣅⠊⠁⠀⠜⠛⠋⠙⠂
⠀⠀⠀⠀⢀⣴⡗⠀⡀⠀⠀⠀⠦⠙⠃⠀⠀⠀⠈⠠⠔⠀⠀⠠⠁⠀⢠⠙⠁⠀⠀⠀⢠⠀⠀⠀⣘⠂⠀⠀⠀⠀⠀⠀⠀⠚⠑
⠀⠀⠀⠀⠘⠁⠀⠀⠳⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⣞⠃⠀⠀⠈⠀⠀⠀⠀⠀⢀⠴⠟⠳⣦⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⠀⠀⣿⠀⠐⠺⠷⠶⠄⠀⢰⣀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠖⠂⣠⠉⠀⠀⠀⠀⢶⣾⡿⣷⠆⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢤⡀⠐⠂⠓⠚⠓⠒⠀⠈⠝⠃⠈⠋⠀⠀⠀⠀⠀⠀⠆⢠⠇⠀⢀⠀⠀⠀⢺⣿⠆⠀⠸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⡘⠛⠸⠉⠋⢋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠋⠀⣴⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣃⠈⡳⠤⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣿⡟⢤⡇⢀⠀⠤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣾⡟⠉⠀⢺⡀⠉⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠀⠀⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣬⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠉⠛⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢩⣧⣸⣍⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣠⣋⡠⠞⢀
⠀⠀⠀⠀⠀⠐⠒⠢⣄⠔⠉⢻⣅⢀⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠎⡥⢬⠳⣖⣋⡤⠂⡄
⠀⠀⠀⠀⣀⣀⣀⣴⣁⢀⡤⠊⠈⣻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⣏⢹⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡼⣆⠓⠚⡠⢬⡙⠲⣏⣡⠴
⠀⠀⠀⠘⠉⠀⠙⣆⠉⢹⡁⢠⡞⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⡞⢳⢤⡙⠚⢡⠶⡌⢧⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡟⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡟⢻⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠞⢰⠏⣳⣜⠚⣡⠾⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⣷⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠇⠸⡍⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⡄⠀⠀⣀⣀
⠀⠀⠀⠀⠀⡤⢤⠀⠀⠳⡞⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣇⣀⣸⣇⡼⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠲⢤⣀⣠⠖⠉⠉⢢
⠀⠀⠀⠀⠀⠓⠺⣤⠴⠚⠓⠦⣤⠓⠚⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣀⡴⠋⠉⢀⣤⡉⠳⣤⠞⠁⢹⡆⠀⠀⠀⠀⠀⠀⢧⡀⠒⠀⣠⢤⡀⠘⠃⢰⠃
⠀⠀⠀⣠⢤⡀⣰⠃⠰⣄⠸⠆⠘⣆⢀⡤⣄⠀⠀⠀⠀⠀⠈⠓⠒⣾⠁⢀⡀⠹⠤⠇⠀⢸⡖⠒⠚⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠈⠛⠀⢀⡀⠈⠣⢄⡀
⠀⠀⠀⠑⠚⠉⠹⡄⠠⠎⢱⠄⢠⠏⠉⠳⠋⠀⠀⠀⠀⠀⠀⣠⠤⢾⠀⠻⠽⠀⡖⢢⠀⢸⠧⠤⣄⠀⠀⠀⠀⠀⠀⣾⠁⠸⣭⠆⠈⠁⠀⢇⡼⠂⠤⠀⢱
⠀⠀⠀⠀⠀⡤⣤⠛⠲⢤⡤⠖⠛⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡴⠳⣄⡀⠀⠉⣁⣴⠋⠑⠦⠞⠀⠀⠀⠀⠀⠀⠈⠒⠖⠒⢄⠀⢠⠀⠀⣠⠤⠤⠖⠃
⠀⠀⠀⠀⠀⠳⠚⠀⠀⡴⢧⠀⠀⠓⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹⠉⢉⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠛⠀⠀⠳⠤⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣮⢟⡻⣥⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⡁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠓⠊⠑⠚⢧⢤
⠀⠀⠀⠀⠀⠀⠀⢤⣳⢞⡁⠘⠋⠈⠻⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡭⡍⢳⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠠⡞⠁⡤⠂⠀⣞⠛⢦⡈⢓⡆
⠀⠀⠀⠀⢀⡐⣬⠟⠁⠻⠏⠸⠿⣠⢞⠳⠀⠀⠀⠀⠀⠀⢠⠞⣩⡉⢦⢳⡘⠦⣼⠾⠁⠀⢀⠞⣰⠃⠀⠀⠀⠀⠀⠀⢯⠁⠀⠀⠠⣄⠈⠱⣄⡱⠀⣹⠂
⠀⠀⠀⠀⠠⠽⣇⠿⠇⠸⡷⣠⡾⡍⠂⠀⠀⠀⠀⠀⠀⠀⠘⢆⡑⣷⠸⣍⣉⡓⠺⠦⠖⢚⣡⠔⠁⠀⠀⠀⠀⠀⠀⠐⢧⠀⣏⣹⠆⠀⠀⢀⣈⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠈⡝⣳⣄⣠⢞⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡙⠒⣋⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠁⠀⡔⠀⠘⠾⠁⢴⠛
⠀⠀⠀⢀⣤⡤⠇⠁⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡦⢤⣀⣄⣠⢤⠏⠉
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠈⠉⠑⢢⡀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠉⠑⢦⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠂⠀⠀⠆⠀⢱⠀⠀⠀⠀⢰⠻⣿⣿⠟⢿⣿⡟⢳⠀⠀⠀⠀⢠⠁⠀⠆⠀⠀⠂⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⡀⢀⠀⠀⡸⠀⠀⠀⠀⠰⡀⠀⢀⠀⢀⠀⠀⡼⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠑⠄⡀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠑⠄⡀⠀⢀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠒⢄⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠒⢄⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠄⠀⢣⠀⠀⠀⠀⢠⠃⠰⠢⠀⠠⠲⠀⢣⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⠤⠤⠤⢤⠀⠸⠀⠀⠀⠀⠰⡀⢠⠤⠤⠤⢤⠀⡸⠀⠀⠀⠀⠸⠀⠀⢀⡀⣀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⠒⠒⣁⠔⠁⠀⠀⠀⠀⠀⠑⢄⡑⠒⠒⣁⠔⠁⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠑⠒⢄⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠀⠒⢄⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⡂⠀⠀⡐⠀⢣⠀⠀⠀⠀⢠⠃⠠⠆⠀⠀⠦⠀⢣⠀⠀⠀⠀⢠⠃⠐⡀⠀⠀⡒⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⣀⣀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⢁⡴⠁⠀⠀⠀⠀⠀⠱⢄⠈⠉⠉⢀⡴⠁⠀⠀⠀⠀⠀⠣⣄⠈⠉⠉⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣾⣛⠲⣤⡀
⠀⠀⠀⠀⢠⡶⠋⡍⠉⡍⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⣴⠶⠾⠷⠶⣦⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⢞⣩⣭⡇⡿⢞⡙⢦⣻⡄
⠀⠀⠀⠠⣏⣀⣃⣀⣃⣀⣀⣈⣀⣸⡆⠀⠀⠀⠀⣾⣉⣉⣉⣉⣉⣉⡇⠀⠀⠀⠀⠀⢠⡟⠒⠻⡆⠀⠀⠀⠀⢠⡟⣰⢋⣑⢲⡇⣿⡯⢟⣫⣍
⠀⠀⠀⠀⣯⡤⢤⣤⡤⢤⣤⡤⠤⣽⠇⠀⠀⠀⠀⠈⣯⠈⠉⠉⠉⡿⠀⠀⠀⠀⠀⠀⣼⠛⢶⡀⣿⠀⠀⠀⠀⣾⢰⡇⢯⡽⢺⣥⠵⣚⠛⡇⢻
⠀⠀⠀⠀⢷⠶⣶⠒⠒⠒⠒⣶⡶⣾⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡶⠟⠀⡏⠀⠀⠀⠀⢹⡈⣇⢰⣷⡌⠄⠺⠿⣰⠇⡿
⠀⠀⠀⠀⠘⠳⠾⠷⣄⣠⡾⠿⠶⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡇⠀⠀⠀⠀⠀⠳⣌⠳⢭⣴⣛⣷⠞⣣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠤⠟⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣤⠻⡍⢿⢸⡟⣹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡍⠻⣜⣳
⠀⠀⠀⠈⡏⠛⠛⠾⠿⠗⠛⠛⣿⠀⠀⠀⠀⠀⠀⢠⠶⠮⠶⠵⠶⣦⣀⡀⠀⠀⠀⢠⡞⠋⠠⠈⠠⠈⠤⠉⢳⡄⠀⠀⠀⠀⢀⡞⠠⠀⠄⠠⠈⣿
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡿⢉⡿⠀⠀⠀⠀⠻⡏⠙⡟⠉⢻⡟⢙⡟⠁⠀⠀⠀⠀⣸⣅⠰⠀⢂⣠⠞⠁
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⣀⣸⣇⣀⣀⣀⣠⣟⣉⣀⠀⠀⠀⠀⠀⢳⠀⣷⠀⣸⠃⣼⠁⠀⠀⢀⣤⡴⢃⡼⠓⠛⠋⠁
⠀⠀⠀⠀⠈⢧⣤⣤⣤⣤⣤⡾⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣀⣀⣀⣀⣤⠞⠀⠀⠀⠀⠀⠘⢧⣼⣤⣿⡴⠃⠀⠀⠀⠈⠳⣬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⢉⣳⣄
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠳⣄⠀⠀⠀⠀⣾⣉⣉⣻⣍⣙⣦
⠀⠀⠀⠀⠀⣾⣉⣉⣀⣀⣙⣧⠀⠀⠀⠀⢀⡾⠋⠉⢹⠏⠉⠉⡟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠓⠦⢿⡀⠀⠀⠘⢷⠷⠷⠷⣾⣷⡟⠁
⠀⠀⠀⠀⢾⣡⣀⣀⣄⣀⣠⣨⡇⠀⠀⠀⣼⢦⡤⠤⡤⠤⠤⠤⠤⡤⠤⢤⢼⡄⠀⠀⠀⠀⠀⢀⡴⠛⠳⣄⡀⢸⡇⠀⠀⠀⠘⣧⠶⠛⣁⣼⠁
⠀⠀⠀⠀⢸⡄⠈⡇⠀⣿⠁⣸⠃⠀⠀⠀⣿⣏⣓⠺⣟⣒⡋⣓⣚⣿⢒⣋⣿⡇⠀⠀⠀⢀⡴⠚⢳⡄⠀⠀⠙⣿⠀⠀⠀⠀⠀⢹⡖⢋⣩⡇
⠀⠀⠀⠀⠀⣷⠀⣷⠀⡿⢀⡏⠀⠀⠀⠀⠘⠶⠭⢭⣭⣭⣍⣭⣭⣭⠭⠵⠞⠁⠀⠀⣾⡋⠻⡄⠀⠙⣦⣀⡴⠋⠀⠀⠀⠀⠀⠈⣿⠋⡽
⠀⠀⠀⠀⠀⠘⠷⠿⠶⠷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢻⠛⠶⡦⠀⠀⠀⠀⢀⡾⠳⣄⢀⡴⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⡇⣠⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡞⣽⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⣷⠛⣯⣷⣻⠆⠀⠀⣰⠋⠐⣆⠙⣿⠀⢦⠈⢷⠀⠀⠀⠀⢸⠀⢸⠀⣹⡟⢻⡇⠀⠀⠀⠀⠀⠀⣠⠞⣱⣏⡾⠁⠀⠈⡇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡟⠓⢻⡼⠃⠀⠀⠀⢿⠀⣰⠃⠀⣽⢠⡟⠀⢸⠇⠀⠀⢀⡼⠀⠸⣾⠉⠀⠀⠙⡇⠀⠀⢀⡴⢚⡵⢞⡵⠋⠀⠀⢀⡼⠃
⠀⠀⠀⢰⠋⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠘⢦⡘⢂⣴⢿⡈⠃⣠⠟⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠸⡟⣽⠞⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠳⣄⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠁⠀⠙⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠙⢧⡀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠈⠻⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠾⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠉⠉⠉

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⠶⣶⡶⠶⣶⡶⠶⣶

⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠑⠀⠀⠶⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠢⡙⢆⡀⠉⣉⡀⡀⠩⠀⠰⠂⠙⠀⡰⣰⠀⠠
⠔⠠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢄⡀⠀⠀⡆⠀⠀⠀⠀⠠⢈⠉⠀⠀⢨⡁⠀⠀⡙⠢⡀⠀⠀⠀⢀⡔⠔⣠⢮⡼⠁
⠐⠂⣄⠀⠀⠊⠂⡀⠀⡧⠐⢁⡠⡄⡀⠀⠀⠸⣀⣀⠀⠀⠄⠀⠡⠀⡄⢀⠁⠂⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠖⠋⠑
⠀⢀⠈⠀⠃⠈⢀⢐⠀⠀⠠⠍⠀⡀⢀⠐⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠰⠆⠀⢀⠠⠔⠀⠁⠀⠤⠠⠏⠀⡁⠀⠀⠌⠀⠆⠠
⠀⠀⠀⠐⠈⠀⠁⠨⠀⠀⠀⠀⠀⠶⠅⠠⡨⠀⠀⠀⠀⠀⠠⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠁⠀⠁
⠒⠂⠀⡀⢈⡁⠀⠀⡠⠂⠢⡀⠀⢀⣔⣽⠣⠁⡠⠒⠀⣈⡀⠄⠀⠀⠈⠀⠊⠁⠀⠐⠀⠀⢀⠀⠀⠤⠀⠔⠁⡇⠀⠀⠀⣀⡘
⠀⠀⡀⣉⢠⢀⠀⠐⠀⠀⠀⠃⢠⡵⠋⠄⠁⠀⠁⠆⠣⠀⠈⠁⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⡋⠀⠀⠀⠉
⠈⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠱⣞⡖⠀⡀⡀⠐⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⡀⠄⢀⠄⠀⠄⠄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣒⠒⠂⠀⠀⠀⠀⠀⠌⡀⡟⡁⠀⠀⢈⠆⠀⡀⢁⠁⡀⠀⠀⠀⠐⠊⠀⡀⠀⡀⠀⠐⠂⠜
⠀⠌⠂⡀⠀⠡⠀⠈⠁⠀⠀⠀⠀⠀⠀⠴⠃⡇⠹⠀⠀⠀⠀⠀⠀⢁⠀⡤⢨⠀⠀⠠⣀⠀⠀⣷⡄⠀⠈⠀⠁⠀⠀⠀⠀⠀⣤
⠄⠘⢀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡔⢇⠀⣃⣤⠁⠈⠠⣀⠄⠀⠀⠀⠶⠂⠀⠀⢀⠠⠄⡀⠀⠄⠀⠀⠀⠀⠈⠛⠀⠒⠒⠊⢀⠤
⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠌⠀⠀⠰⠀⣠⠀⠀⠀⠀⠸⠐⠂⠀⠀⠰⠅⡀⡂⢀⢔⠀⠰⠴⠃⡄⠠⠀⠀⠀⠀⠀⢀⠂
⠠⠀⠠⠄⠒⠂⢄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠌⠋⠀⠘⠁⠄⠐⠘⠂⠁⠂⠀⠀⠀⠐⠒⠅⣀⠄⠢⡀⠀⠄⢀⠈⢖⡰⠀⣀⣄
⠀⠅⠰⡂⠢⠄⠀⠅⠀⠀⠰⠀⢀⠔⠁⠀⠀⠤⠤⡞⠁⡀⠀⠀⠀⠀⠀⢃⠁⡄⠀⠠⠊⠀⠀⠀⡗⠀⢀⡌⠀⠉⠀⡀⢀⠀⠂
⠈⠀⠀⠏⠡⠂⠀⠂⠀⣄⡀⠤⠁⠠⢊⡡⡁⠐⠄⠀⠠⣧⠀⠀⠀⠀⢁⡀⢠⠀⠀⠅⠀⠀⢈⠈⠀⠀⢉⠀⠀⠀⠀⡀⠀⠐
⠀⠉⠈⠐⣀⠀⠀⠈⠀⠐⢀⠀⠀⠁⠠⠀⠈⡠⠂⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠑⠊⢀⡎⢀⡀⠃⠀⠐⠀⠒⠀⠀⠀⢀
⠄⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠂⠀⠀⠀⠧⠔⠂⠀⠀⠀⠑⡀⠀⠂⠈⠈⠠⠀⡁⠀⡁⡀⠀⠀⡙⢈⠁⠀⠀⣠⣁
⢉⠂⡄⢊⠐⠁⠀⠀⠀⠀⠀⣀⠊⢀⡀⠀⢠⡠⡠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⡄⢁⠒⠀⠂⠈⢻⣿⠀⠀⠀⠀⠈⠐⠀⠀⠀⠒
⢀⠄⡉⠠⢎⠶⠀⠀⠀⢀⠆⠀⠐⠀⠐⠔⠐⠒⠀⢂⢀⡀⠀⠀⠒⠀⠀⣀⠀⠁⠄⠁⠀⠠⢤⠀⠇⠀⢀⠤
⢈⠀⠆⠀⠆⢺⣡⠧⠔⣸⠀⢀⠀⡀⠆⠀⠀⠀⠀⠸⠀⠉⠀⠀⠒⠉⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠈⠤⠈⢁⢆⡸
⠀⠀⠂⠂⠀⠡⠗⠆⠀⣆⠔⢠⣠⢀⠈⠂⠤⠠⠐⠁⢄⠒⢬⡀⠀⠀⣂⠀⠀⢀⢂⠀⡀⠀⠐⠒⠒⡄⠈⢀⡉⠈⠋⠀⠀⠀⢀
⠂⠄⢀⠆⠀⠀⢀⠀⠀⢀⡴⣲⢏⠂⣠⢠⡄⠐⠀⢤⡠⢀⠀⢈⠓⢊⠰⠁⠂⠡⠈⠈⠀⠀⠀⠀⢸⠀⠀⢉
⠘⠄⠋⠠⠐⠂⠀⠂⠀⠠⠟⠁⠂⠀⠀⠣⡕⣠⠊⠒⢝⡷⡒⠀⠀⠀⡀⠲⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠂⠀⠤⠀⠀⡠
⠀⠀⠁⠀⠀⠀⢀⠐⡀⠀⠂⠄⠀⠀⠀⢐⢻⣅⠅⠀⠀⠙⠙⠂⠀⠀⠁⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛⠊⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠋⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠐⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⡶⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⢀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀⠀⠀⠀⠶⣀⣐⣪⠴⡈⡆⠀⠀⡠⠔⠊⠉⠉⠉⠀⠒⠒⠒⡺
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢤⣄⡀⠀⠀⡇⡇⣠⠊⢀⡠⠄⣒⣂⣤⡀⠤⠄⠊
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢌⢢⠀⡇⡷⠁⣤⠏⢂⡩⠤⠤⣀⠬⠷⠦⣀
⠀⠀⠀⠀⠀⡧⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠀⠀⠀⠀⠀⠈⢆⢳⣷⢁⣺⠵⠾⡅⠀⡠⠊⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⢐⢀⡠⠔⡖⢻⠿⠿⣼⠿⣫⠔⠚⡇⡅⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠉⢆⠀⠀⠀⠀⡇⢰⠋⠀⠀⠣⣈⠒⠤⣳⣊⣹⣆⠀⠳⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢠⠃⠀⠘⡄⠀⠀⠀⣷⡇⠀⠀⠈⠐⠤⡉⠒⠒⠒⠒⠉⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⡇⠀⠀⠀⠰⡀⠀⠀⣇⡥⠔⢄⠢⢄⠀⠀⠉⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠸⠀⠀⠀⠀⠀⣧⠀⢀⠏⣤⡞⠊⡀⠀⠀⡡⠊⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢡⠀⠀⠀⠀⠀⠀⢣⣌⠮⠴⢥⣀⡀⠈⡞⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡎⢠⠁
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢑⢢⣤⡤⢊⢣⣼⡟⠊⠉⣀⣉⡡⠽⡃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡸⠀⡎
⠀⠀⠀⠀⠀⡧⠼⠤⠤⠤⠍⠲⢲⡶⡶⢋⡟⢫⡙⠃⢌⡀⠀⠀⠹⡄⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡰⠁⡜
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠋⡠⠊⡇⠈⡍⠳⢄⡙⢆⠀⠀⡇⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⠜⢁⠜
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠚⢰⠉⠀⠀⢡⠀⡇⠀⠀⠉⠚⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠐⠐⢧⡀⠀⠈⠶⠀⠀⠀⠀⠀⢀⡔⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠉⠳⠦⣆⠀⠀⠶⠒⣉⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⢀⡉⠤⠀⠒⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠒⠀⠄⠁⡀⠂⠠⢀
⠀⠀⠀⠀⢀⠄⢂⠡⠔⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠌⡐⠄⡀
⠀⠀⠀⠀⡡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⠀⡀
⠀⡐⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⠀⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠂
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈
⠸⠀⢠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡜⢰
⠈⡘⢄⠁⡀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠜⡠⠙
⠀⠐⡀⠑⢌⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢂⡡⠊⡠⠁
⠀⠀⠈⠢⢀⠈⠐⠠⢁⠂⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⡈⠄⠂⠁⡠⠊
⠀⠀⠀⠀⠀⠑⠢⢀⠀⠈⠀⠒⠀⠈⠁⡀⠐⠂⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠐⢂⢈⠈⠥⠀⠒⠈⠁⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠠⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠀⠐⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣔⠒⢃⣂⡀⠩⠭⠙⣫⡭⢁⣏⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⠀⠀⠛⣽⡶⠥⠁⠤⠄⠐⠲⠶⢃⡍⠀⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠀⠀⢈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠄⠀⠦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢰⣆⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠡⠀⠀⠀⠀⠀⠀⠀⠉⠀⣤⣤⣷⣾⣿⣷⣾⣿⣵⣮⡅⠄⠂⠀⠀⠁⠘⠁⢄⠀⣬⠹⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣨⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⢠⠀⠀⠀⠀⠴⠀⠀⠐⢸⡀⢴⡄
⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⡄⠀⠀⠀⠀⡄⠙⢿⣿⣷⣾⣿⣿⣿⡿⠟⠋⣸⠀⠀⠀⡹⠇⢠⣀⠀⡠⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⡁⠀⢢⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠁⠀⠙⠁⠠⠴⠋⠀⠀⡀⠀⠀⣼⡶⢀⠂⠂⠃⠡⢄⠈
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠒⠀⠀⢐⠀⠀⠀⠀⠀⠀⢀⠀⠠⣠⠇⢀⣁⠴⠊⢀⠽⠾⣤⢄⡈⡃⠀⠀⠂
⠀⠀⠀⢠⠀⠀⠀⠰⠂⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⢀⠞⠛⠉⠑⠲⣟⠋⠒⠉⣀⠀⡀⢉⠆⠉⠙⡆
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠸⣄⠀⢉⢀⣀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠃⢀⠉⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠘⠄⠀⠀⠠⠇⠀⠀⠀⠈⠃⢈⠻⠄⠀⠀⠀⢀⡼⠒⠐⠌⠀⠄⠀⠐⢄⠀⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠆⠤⢤⠡⠄⠠⠖⠃⠀⠀⡀⡁⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣔⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡰⡩⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⠢⡀⠀⡁⠰⡐⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠎⠑⢌⢢⡇⢸⢃⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣁⡀⠀⣀⠱⡱⠸⡞⡐⠪⡓⠄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠬⡙⣷⢡⡁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠬⣠⠤⠄⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⠳⣄⠀⣀⣠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠙⡯⠗⣚⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⢀⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⣀⣤⣀⡠⠐⠂⢄⠔⠚⠚⠟⠋⠤⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢑⡖⠋⠀⠀⠀⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⡿⠋⠹⣓⠦⢖⣤⡭⣭⠶⣄⢄⣀⠼⡸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⡩⢮⡺⠟⢸⡏⠑⠲⡮⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⢀⠤⢊⠴⠋⠈⠀⡀⣇⠀⠀⠱⡴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠤⠍⠔⠊⠁⠀⠀⠸⠴⠡⠜⠀⠀⠀⠈⠢⠂

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣟⣻⣿⣻⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠐⠂⠒⠒⠓⠂⠁⠒⠘⠈⠚⠀⠒⠈⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⡄⡄⣠⢀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⢀⠠⡀⢂⣀⣸⣠⣤⡦⠴⠶⠞⡚⣛⠛⠉⠉⠛⢷⡡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⣆⣈⣤⡦⠼⠾⠞⠚⠛⢉⠉⡉⡰⢠⠄⠀⠰⠂⠡⠄⠀⠀⠀⡗⠀⢹⡷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢌⣶⢟⡉⠉⠰⠀⠠⠤⠷⠶⣄⣄⢄⠀⢀⠀⠂⡄⠁⠀⠂⣠⠂⠀⠰⠄⠀⠒⢸⡯⠅⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠑⣾⠁⡄⠥⠀⠀⠀⠀⡌⢹⣆⣉⢹⢱⠀⠐⠀⡀⠀⠀⠀⢀⢀⡒⢀⠐⠀⠈⣠⢞⡋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠥⣿⠀⣄⠒⢀⠠⠄⠀⠙⠋⠙⠥⠒⠚⢤⠂⠄⠰⠀⢀⣀⣀⣤⡤⢶⢶⢶⠫⠫⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⢉⠜⢷⣀⠂⠀⠰⠆⢠⣀⣃⣀⣠⣤⡤⠶⠶⠒⢛⠻⠙⠙⠘⠀⠃⠈⢈⣤⡶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠑⠩⢛⠛⠛⡋⠏⠩⠙⠈⠀⠂⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠢⡀⠀⣀
⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⡉⠍
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⠀⢀⠀⢀⠀⢀⠀⣤⠀⢘⡇⠀⢀⠀⢀⠀⠀⠀⢠⡄⠀⣉⠀⡀⠀⢀⠀⠀⠀⡁⠖⠀⠁
⣿⡿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠃⠈⠲⢄⠀⣿⠀⢸⡇⠀⢸⡆⢾⠀⠀⠃⢸⡆⠀⣿⠸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠂⠀⠈⠀⠈⠀⠈⠀⠈⠁⠀⠈⠁⠈⠑⠀⠀⠀⠁⠀⠉⠀⠉⠒⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠀⠀⠿⠀⠀⣟⠀⠈⡇⢠⠁⠀⢹⠄⢻⠀⡇⠀⠣⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠛⠀⠀⠛⠀⠀⠛⠈⠃⠀⠘⠀⢻⠀⠓⠀⠂⠀⠃⠀⠀⠰⣶⣿⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠸⣶⣝⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⡀⣀⣿⣿
⠀⢠⣀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠌⠳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⠂⠀⠈⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⢀⡠⠤⢄⠀⠀⠀⠀⡇⠠⠄⠀⠈⠁⢀⡠⠈⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣳⣤⣞⠀⠀⠀⢳⠀⠀⠀⠘⢦⣀⠀⠄⠀⠀⢀⡼⠁⠀⠀⠀⢀⡴⠋⣉⣀⣠⣤⣤⣤⣭⣭⣉⡓⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠈⢳⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠁⠀⠀⠀⠀⢀⡾⠞⠛⠉⠁⠈⠀⠀⠀⣀⠤⢬⣉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡇⠀⠀⠀⢨⣧⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⢤⣤⣤⣄⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴
⠀⠀⠀⣰⡿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡫⠉⠐⠒⠈⠐⠒⠂⠈⢍⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠜⣅⢀⠀⡀⢀⢀⠀⡀⣀⢂⡡⣰⠌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣭⣥⣿⣿⣿⡿
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢁⣤⡔⢕⢁⣬⡀⠗⣩⣍⠦⢗⣴⡁⡘⠄⢿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⣷⣾⣿⣿⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣟⡵⠋⠀⢙⣒⠋⠈⠓⠞⠁⠉⠛⣋⡈⠙⢶⣔⢸⠀⠀⠀⠀⠀⢀⣴⣿⣖⣋⣩⣯⣿⣷⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠻⠟⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⢠⠚⡇⠀⠀⠀⣾⣷⠀⠀⠀⣤⠀⠀⠀⣾⡆⠀⠀⠀⣼⠓⡀
⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⠶⣬⣦⢷⠀⠀⣤⠈⠁⣠⣤⡤⠤⢤⣤⣄⠀⠠⡤⠀⢀⣯⣞⡵⢦⠀⠀⠀⠀⠀⣠⣤⣤⣴⣧⠤⣤⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣴⠉⠸⠥⢈⡏⢧⡀⠀⠀⠀⠳⣄⡀⠀⣀⣠⠏⠀⠀⠀⣠⠎⣟⠀⡽⠊⢱⡄⠀⠀⢸⠁⠀⠙⠛⠋⠁⠀⢻
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠦⣤⣠⠾⢦⡀⠉⠲⢤⣄⣀⣀⠉⠉⢉⣀⣀⣤⠴⠚⠁⢀⠼⢦⣀⣤⠞⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⠒⠛⠉⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠓⠒⠉⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠉⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡴⠚⡉⢱⠀⠀⢀⠜⠁⣸⠁⠀⠀⠀⠀⠀⠀⢧⣤⣤⣀⣀⣀⣀⣠⣤⣤⡿⠀⠀⠀⠀⠀⢀⣠⡤⠴⢶⣶⡯⣍⠉⠓⠦⣌⠉⠓⢦⡀
⠀⠀⠀⠀⠀⡜⠘⡆⠱⠀⣡⠖⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⣮⡇⠀⠀⠈⡧⠀⠀⣹
⠀⠀⠀⠀⠰⡇⠀⣀⡤⠚⠡⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣠⡾⣄⣀⣄⣠⠇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢰⢯⠀⠀⢠⡖⠁⢀⡟⠁
⠀⠀⠀⠀⠠⡏⠉⠁⢄⠙⠆⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⣒⣺⠀⣿⣒⣲⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⣿⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⢀⣸⠆⣏⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣸⡿⢤⡼⠧⠤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀⠀⠀⠀⠘⣇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢘⣄⣀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠉⠙⠚⠓⠄⣀⡀⠀⠐⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⡴⠊⠉⠉⢁⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣤⣶⡾⡟⠉⢉⡼⠋⠀⡀⣀⣀⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣠⣾⣿⡿⠋⠀⠙⠖⢋⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⠟⠀⠀⠀⠀⠀⠸⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣁⠤⠠⢤⠀⠐⠢⣤⣀⠀⡎⠀⠀⠱⣤⣀⡀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣶⣴⠞⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠙⠒⠄⠀⠈⠳⢄⡠⣴⠋⠈⠉⠛⢿⡟⠉⠙⠻⠛⠛⠛⠉⠛⠁⣉⣀⣴⢞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢷⣄⣀⡀⠀⠀⠀⠀⢀⣀⣴⣤⠶⠶⠿⠉⠉⠁⣀⣨⡵⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠻⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⢄⠀⠈⠉⠀⠉⠋⠙⠛⠉⠛⠁⠀⠀⢀⣀⠠⠐⠒⠋⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢹⡏⣹⠏⠳⢤⠦⡀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠠⠤⠶⠀⠐⠊⠉⠀⠀⠀⠀⢀⣄⣀⣠⣦⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⣽⠀⠀⠀⠀⢉⡶⠛⠂⠤⣤⣄⠀⢀⣀⠀⠀⣀⡀⠀⣠⡄⣠⣴⠟⣻⣿⡿⠟⠿⠟⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢸⡇⠐⣧⢠⡄⠀⠀⠉⠀⠀⠀⠠⠁⢈⡿⠛⢻⠟⠚⢻⠏⠉⠁⠀⠀⠐⠊⠁⢹⣧⠀⢀⡇⠀⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢠⡏⠀⠛⠦⢤⡤⠀⢰⠋⠀⠀⠎⠀⠐⠋⠀⠀⣼⠀⠀⠀⠀⠀⣀⣠⡤⠾⡇⠀⢸⡆⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠁⠀⣿⠀⠀⠠⠋⢀⡴⠁⠀⠀⢠⡀⠀⠀⠀⣠⠎⠀⠁⠂⢒⡾⠋⠁⠀⢀⣰⡇⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢸⡇⠈⣷⠀⢀⠃⠀⠈⠁⠀⠀⡰⠁⣈⠐⠒⠊⠁⠀⠀⠀⠀⡟⠀⠀⠀⠊⠉⢙⠇⠀⠀⠳⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⣇⠰⣿⠀⠈⢧⠀⠀⢀⠀⢈⣠⣎⡀⠀⠀⠀⠀⠀⣀⡤⠶⢳⣄⣀⣀⣀⣀⢘⠇⠀⠀⢸⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⡇⠀⣸⠇⠀⢀⡤⠤⢤⡞⠉⠀⠀⠀⠉⠢⣀⠈⠁⠀⢀⡴⠛⠉⠉⠉⠉⠛⣿⠀⠀⠀⢸⡀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠀⢹⡆⠀⢨⠀⠠⣼⠀⠀⠐⠶⠤⢤⣤⣤⣭⣤⡼⠟⠁⠀⠀⡀⠀⠀⢸⠃⠀⠀⠀⢸⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠘⣆⠘⣧⠀⠀⢦⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠼⠃⠀⠀⠀⡼⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⡀⣾⣠⠤⠊⠀⠀⡼⠉⠓⠦⢤⣤⣤⡤⣤⣤⣤⢶⡆⣀⠀⠑⣴⠟⠀⠀⠀⠀⣸⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣽⣧⣼⠋⠉⠁⠒⠋⠁⠀⠀⡆⠀⠀⢹⡀⠈⣧⠀⢸⡟⠉⠉⢺⡇⠀⠀⠀⠀⣴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⢀⣰⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠻⣦⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⠇⠀⠀⠲⠶⠒⠿⣿⣷⣶⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢠⡾⢷
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢀⣸⡇⢸⡤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀
⠀⠀⠀⣴⠋⢭⣾⣇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡀
⠀⣀⣴⠉⠑⠒⠮⠭⠭⢭⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠖⠚⠉⢧⣄⡀
⣎⡀⠳⠤⢤⣀⣀⣀⣀⡀⠀⣀⣀⠀⣀⠀⠀⣀⣀⣀⣀⡠⠤⠜⠀⣹⡆
⡧⢭⣓⡲⠦⠤⠤⠤⢌⣉⣉⣉⣉⣉⣉⣉⣉⣁⠤⠤⠤⠴⠒⣚⣫⢽⠃
⢸⠀⠀⠉⠉⠑⠒⠒⠒⠒⠲⠶⠶⠶⠖⠖⠒⠒⠒⠒⠊⠉⠉⠁⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠶⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡾
⠀⠸⡇⠀⠀⠀⠈⠉⣉⠙⠓⠒⠒⠒⠒⠒⠒⢚⡉⠉⠉⠀⠀⠀⡇⠀⠀⠀⣠⠴⠶⠦⣄
⠀⠀⡇⠀⠀⠀⠀⣼⠿⣦⠀⠀⠀⠀⠀⠀⢠⡿⢿⡄⠀⠀⠀⣠⣧⠤⠴⢮⣁⣀⣀⡀⠀⠳⣄⣀⣠⠤⣴⡤⠤⠶⠲⠤⠤⣄⡀
⠀⠀⢳⠀⠀⠀⠺⠃⠀⠹⠇⢀⣀⣀⣀⠐⠟⠁⠈⠿⣠⠖⠋⠁⢀⣀⣤⡴⠞⠉⠉⠉⠻⣍⠉⠉⠉⠉⠙⠓⠒⠲⠤⢤⣀⠀⠉⠓⢦⡤⣀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡧⠀⠀⢠⠞⢁⣠⢔⡾⠟⠚⠉⠀⠀⠀⢀⣀⣀⣬⣷⣶⣮⣉⣉⣉⠉⠒⠲⠤⢤⣍⣓⣦⣄⠳⡈⠳⡄
⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⢻⠇⠀⢀⣏⠔⣫⠖⠉⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⣄⡀⠀⠀⠈⠉⠙⠳⡄⣙
⠀⠀⠀⡷⠤⢄⣀⣀⠀⠀⠀⠈⠻⠶⠋⠀⠀⡼⢣⠞⠁⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⣇
⠀⠀⠀⢱⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠋⠉⢹⠁⡏⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠄⣼⠋⠀⠀⠀⠀⠀⠈⢓⢦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⠋⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷⡸⣴
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎
⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠴⠶⠶⠚⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠴⠶⠖⠛⠋⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡀⠀⠀⢰⡋⢉⣩⠗⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠖⢾⣇⠀⠀⢀⠁⠘⡓⠠⠤⣾⡆⣉⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠴⠊⠰⡉⢀⢀⠉⣉⢲⡁⣐⣼⡄⢆⡑⣀⣮⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠌⣂⣠⠗⣚⢌⣦⢸⣿⣘⠶⢛⡸⠷⣺⣭⡬⣦⠥⢋⡙⣣⣬⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠧⣤⡄⢡⣊⣛⣮⣿⣿⣿⣧⣼⢽⣾⣾⣇⡛⣍⠒⠑⣋⡹⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠞⣈⠒⢤⡄⣸⣽⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠛⠯⣿⢈⢥⢤⡜⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠑⣿⣫⣿⣿⣿⡏⡖⠀⣦⢻⣿⣿⠿⡁⣇⢀⠘⡷⠷⡏⠉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⡷⠫⡛⠟⠩⢿⣿⣇⡛⠾⣋⣼⣿⣿⣇⣳⣬⣩⣼⣱⢆⢿⣾⠠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣡⠰⣇⠀⡼⣸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⡯⣿⠁⣚⣣⡇⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠑⢞⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢛⠙⢻⡠⠃⠀⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣉⣦⣽⡼⢛⣛⠿⠿⠿⠿⣹⡅⠷⢴⣸⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⣏⠴⠤⡑⡏⢷⠙⣄⡤⡾⠑⢊⠿⠏⣁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠀⠀⠀⡛⠭⡝⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠊⠀⠑⠂⠁⠀⠤⠄⠀⠀⠐⠐⠒⠂⠀⣀⣀⣧⠀⠀⠈⠉⠈⠀⠀⠫⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢀⠂⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠋⠠⠀⠀⠀⠛⠛⢶⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠑⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⠀⢀⣀⡂⠀⠀⠀⢀⡀⠀⠸⡇⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠉⠀⢀⠨⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠚⠗⠂⡉⢩⣆⠀⠀⠏⠀⠀⠀⠛⠦⣄
⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠠⠞⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠠⢀⢌⡀⠘⢠⠀⠀⠀⣰⣶⠉⣇
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⠰⠊⠁⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡡⣘⠊⠡⠁⠀⠀⠀⠀⠄⠀⠀⠙⠋⢀⡟
⠀⠀⠀⠀⠀⡀⠁⢢⠀⠀⢰⣄⢈⡑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣑⠂⢬⡄⠠⡆⣀⢀⡀⡀⠩⢴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠘⡇⠒⠃⠐⠂⠒⠀⠉⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣤⣤⣤⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣿⣄⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⡿⠛⠋⠙⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣿⣿⡄⠀⠸⠿⠿⠿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⡿⠛⠃⠀⣀⡀⠀⣀⣸⣿⡇⠈⠉⠛⠛⠛⠛⠉⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⡀⠀⣀⣼⣿⣿⣿⣿⠿⠋⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠉⠛⠻⠿⠿⠛⠋⠀⠀⠀⠘⠿⢿⣿⠿⠟⠁⠀⣀⣠⣤⣶⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢠⣿⣿⠁⠀⣾⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⣠⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⠀⠀⢀⣤⣤⣤⣄⣀⣀⣴⣿⣿⠿⠿⠿⣿⣿⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣰⣿⡿⠿⠿⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣡⠶⠒⠒⢍⠙⢢⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢂⡈⠛⠡⡀⠀⠃⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣁⠀⠀⠘⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⢰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠊⠉⠀⠀⠀⡇⢸⠀⠀⠀⠉⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡠⠤⠄⠤⠼⠤⠶⠄⠀⡄⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄⡀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠒⣆⠠⠒⠈⠀⠀⠀⠙⡀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠧⢤⠦⢬⣻⣀⠔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠈⢀⠝⠉⠀⠀⠀⠀⠀⣀⢴⢥⡀⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⡆⠔⢻⣃⠖⠀⠐⠈⠀⠀⡠⠊⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⡠⢄⣠⠤⢸⡬⠲⣢⡶⠶⡾⠅⠠⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢐⠉⠐⠢⠤⢀⠤⠤⠤⠬⠂⠤⠔⠒⠂⡊⠉⡄⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡜⠀⠀⠢⠤⠢⠤⠔⢢⠔⠒⠒⠎⠑⡆⢱⠀⢱⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⢨⠀⢇⠀⢳⠀⢘⠀⡟⠀⢀⠖⡗⢨⠀⢆⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⢸⠀⠏⠀⣘⣄⣈⡠⢳⠤⠼⢴⠇⠨⠀⠌⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠄⠸⠀⣆⡠⠀⠈⡎⠂⢸⣦⣤⠴⢠⠂⢀⠄⠀⡃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⣄⡀⢀⡠⠄⠠⢚⠖⠒⢃⣀⠁⠔⠂⢀⡸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡀⠀⠀⠀⠀⠈⡏⠀⠀⠀⡇⠀⣀⣁⡠⠄⡠⠎⠁⠀⠀⠀⡇⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⣀⠀⠀⠀⠀⠁⠀⠀⠀⠱⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠄⠄⠀⠈⠳⠀⠀⠀⢀⡄⢠⡀⠢⠀⠀⡎⠀⠀⣀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠷⠀⠂⠀⠀⢀⠀⢠⠤⠄⠐⠀⠀⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢯⡥⠀⢀⠆⠀⠑⠀⠠⡀⠈⢢⡁⣶
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⣎⠁⠀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠁⠀⠀⠀⠀⡀⠠⣤⡀⢳⣿
⠀⠀⠀⠀⠀⣀⣈⣀⠒⠒⠁⠀⠀⢀⡄⠠⢀⠀⠀⠲⣚⠀⠇⠀⠀⠘⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡄
⠀⠀⠀⠐⠁⣤⣀⠈⢣⠀⠀⡉⠀⠛⠹⠄⠀⢁⠀⠀⠉⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠉
⠀⠀⠀⠀⠠⣿⣧⠆⢀⠀⠀⠃⣀⠀⠀⠀⠀⠌⠀⠐⠙⢄⠀⠀⠀⠀⠀⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠈⠀⠀⠀⠔⠃⠀⠀⠀⠙⠀⠀⡠⠊⠀⠀⣠⣸⠆⠖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠠⠀⠀⠀⠐⠀⠀⢱⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠚
⠀⠀⠀⠀⠀⠀⠈⠀⠒⢤⣄⡀⠀⠀⠐⠀⠀⠀⠈⠢⣤⣤⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⡄⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢤⣀⡇
⠀⠀⠀⠀⠀⠐⠲⣤⡄⠐⠶⠦⠤⣤⣀⡍⠈⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣘⣦⠀⠀⠀⠀⡆⠀⠀⢰⠀⢙⠁⠀⠀⠄⠘⠀⠀⡦⠀⠂⠀⠈⠃⠀⠠⣀⣠⡶⠀⠀⠄⠁⠀⠀⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣍⡳⡄⠀⠀⡇⠀⠀⠈⠀⢘⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⢀⡀⡀⢸⠀⠀⠀⠀⠈⠀⢠⢀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⡀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠀⠀⠀⠁⠈⠈⠀⠀⠘⠀⠀⠂⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠉⠀⠈⠁⠀⠉⢢⠀⠀⠀⠀⠀⡄⡰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⣇⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣂⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⡀⠀⢸⠀⠀⠆⠀⠀⠈⠺⠏⠁⠄⠀⠀⣠⠤
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁
⠀⠀⠀⠀⡰⠁⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢐⡀⠀⢰⠂⠀⢀⡀⠀⡄⠀⣀⠀⢀⠌⠀⠀⠀⠀⠐⠀⣠⠊⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠠⠀⠈⠁⠀⠀⣵⠊⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠈⠃⠀⡰⠁⠀⠈⢀⠀⠀⠀⠀⠀⠠⠀⠂⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠒⠹⢆⠀⢀⡤⢀⠀⠀⡠
⠀⠀⠀⠀⠻⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠤⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠂⠉⠀⠈⡆⠸⢇⡀⠤⠊⠀⢰⣄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠄⠀⠈⠐⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⣀⣀⣠⣴⠄⠀⠀⠀⠀⠀⢴⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣁⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠰⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡞⠋⠓⠄⠀⠀⠀⣈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⠀⠀⢀⠀⠀⣶⣆⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠙⠂⢀⣤⣄⣠⣼⡷⠀⠹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⡿⠉⠈⠛⣿⣧⠰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⢿⡏⠀⠀⢠⣾⣿⣿⣦⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡇⠀⠀⢿⣿⣽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣸⣇⠀⠀⣴⣏⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⣾⡏⢙⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠤⠶⠿⢿⣿⣿⣿⣿⡇⢘⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣤⣤⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠋⠀⢰⣿⠁⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⡇⠀⣶⡆⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠛⠁⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡜⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⡤⠀⠀⠀⠉⠀⠠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠸⠿⠀⠀⠸⠇⠀⣹⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠉⠀⠀⠀⣀⣀⣤⣤⣤⡴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢀⣤⡀⠀⢠⣼⠟⠿⠁⠻⢿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣇⠈⠛⢁⡀⠘⠟⠀⣀⡀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠸⣿⠀⠘⠛⢷⣄⠀⠻⠃⣰⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠰⠀⠀⠀⠀⠀⠹⢶⣤⣿⡟⠙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣀⣼⣿⣦⠀⠙⢁⣴⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠒⠀⠀⠿⢿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡀⠀⠀⠀⠉⠙⣿⣷⣤⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⢰⣦⠘⠿⠿⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠹⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣿⣿⠿⠿⠿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣰⣿⠿⠁⠀⢠⣴⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠻⣿⡇⠀⢰⣿⣿⠀⠀⠀⠘⠿⠁⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⠉⠀⠀⠀⣿⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⠋⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠿⠃⠀⠀⠀⠛⠀⠀⠂⠀⠛⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠉⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠈⠛⠁⠀⡿⠀⠀⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠚⠀⠀⠀⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣶⡄⠀⠀⠃⠀⣼⡿⠁
⠀⢀⣀⡀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠉⠀⣰⣆⠀⢾⠟⠁
⣠⣿⡿⠋⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠁⢶⣤⠀⠀⠀⠀⠛⠛⠀⠈⠛⠛⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣿⠋
⠛⠛⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⢠⣤⡄⠀⠹⠃⢠⣦⡀⠀⠀⢰⣿⠗⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⡿⠀⠀⣰⣿⠉⢁⣀⣴⣿⣿⣶⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠛⠿⠁⣠⣿⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⢁⣄⡀⠀⠀⠀⣀⣼⣿⡟⠐⠶⢶⣾⣿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣶⣿⡟⠻⣧⣤⡄⠀⣿⣿⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠘⠉⠀⠘⠛⠃⢠⣿⣇⠀⠘⣿⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢹⣿⡀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠘⠿⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣯⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⠿⣿⣏⠉⣱⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠹⠿⣠⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡆⠉⣿⣿⣿⣦⢀⣽⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣤⣄⠀⢸⣿⣧⠈⠉⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣀⣤⡾⠋⠉⠀⠸⢿⣅⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⢰⣶⣶⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣦⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⠉⠹⢿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢠⣾⣷⠀⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠉⠁⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⣀⡀⠁⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣼⠿⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣋⡉⠉⠓⢶⡖⠒⠶⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠸⢥⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠤⢤⡿⠀⠀⠀⠈⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⣎⡶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠸⣤⣽⡀⠀⠀⠀⠀⠀⠀⣀⣉⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢀⣠⠤⠾⡁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠀⠸⣇⡼⠓⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⡴⠋⠀⠀⠀⠙⢦⣀⢀⣠⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠹⢤⡼⠀⠀⠀⢀⡤⣯⣈⡇⠀⠀⠀⠠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠁⣠⢤⡀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⢹⡀⠀⠀⠀⢀⣟⢙⡦⠤⠤⠤⢾⣁⣽⠀⠀⠀⠀⢳⡴⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⡴⠋⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢦⠀⠀⢀⣀⡴⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⢰⡛⢳⣤⣤⣤⡴⠞⠲⠋⠀⠀⣯⣉⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⢰⣀⣀⣀⣀⣀⣀⣙⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠉⠉⣩⠿⠽⠛⢯⢭⡉⠹⠉⢉⡭⠭⣍⠉⠹⠉⣉⣩⣉⡉⠉⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢰⡋⢁⣤⡶⠆⣤⡀⠓⣆⠀⡏⠐⢒⠈⡇⢠⠞⠥⠆⢤⠙⠆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⣏⠀⣬⠁⣴⢢⠈⣷⠀⢿⡀⠘⠶⠲⣚⠀⠸⡄⠦⢙⡀⢀⡀⣸⠁
⠀⢸⡀⠹⡧⢈⣡⣴⠄⠀⡞⠀⡴⠊⣉⠉⠛⢦⠙⠲⠤⠶⢋⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠶
⠀⠀⠹⣤⣄⠈⣉⣀⡴⠛⡅⢸⠁⣌⢡⡆⢻⠄⣇⡰⠖⠲⡌⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠉⠁⣨⠴⠒⢤⡘⢆⠙⠠⠶⠂⣰⠙⣄⠚⢃⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⡌⢇⠃⡳⠈⡟⠲⠒⢊⣁⣤⣈⠉⢉⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠬⠖⠁⠀⣀⢠⠞⢁⣤⠄⣉⠱⣌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡛⡳⡄⢎⠀⡍⢠⡦⠹⡆⢺⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠡⣠⠃⠲⣄⠛⠠⡴⠖⢀⡎⠀⡄⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠤⠤⢤⡈⠒⠢⠖⢴⠉⠆⡠⠤⠔⠤⣍⠛⠲⠶⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠖⣃⢦⠹⡈⠃⠠⠌⢀⡏⢡⡶⠂⢤⡌⢳⡄⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣀⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠃⠥⠎⣰⢃⣀⣐⠂⢹⠄⣶⡐⠿⢂⠛⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⠊⢱⠃⢆⢠⣻⡌⢳⡈⠁⠛⠋⣡⢾
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣊⠙⠒⣌⠀⠸⣜⠉⢇⡰⠃⠐⠉⠙⠊⠉⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠁⡘⢩⡌⢷⠀⡇⠒⣀⠉⢩⠔⢉⡉⢙⠒⣀⠀⣠⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠻⠨⠵⠆⢰⠃⠈⡤⠀⣎⢠⡉⣤⠘⡇⢸⣼⡁⢭⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠒⠚⠁⠞⢡⡈⢓⠻⡌⠓⠴⠖⢀⡾⠀⠑⠒⠋⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣁⡅⠀⠒⠀⠀⠳⣄⡠⠞⢠⡉⠙⠒⠒⠁⠀⣉⠀⠀⠆⠐⠂
⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂⠄⠀⠀⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⢦⣀⠸⠀⠀⠀⣀⠰⠠⠒⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⡀⠻⠏⢀⠂⠈⢂⠠⠈⢢⣰⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠓⢄⠌⢀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠪⣿⡀
⠀⠀⠀⢨⣈⠑⠀⢰⠂⠚⠧⠀⠀⠀⠑⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠘⠛⢁⠂⠈⢰⡤⠀⠠⠀⠀⣩⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢡⠀⠀⠄⠀⠤⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠃
⠀⠀⠀⠀⠀⠀⠲⠤⣀⠀⠠⠀⠀⠑⠶⠦⠋⠀⠀⠀⢀⠀⢀⠁⠀⠀⠀⠀⠀⠒⠐⠓⠀⠄⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⢄⣀⠀⣤⣀⣙⠒⠠⢦⠀⠀⠀⠀⠀⠀⠀⠘⠄⠘⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠉⠳⠦⣧⡀⠀⠰⡄⠀⡆⠐⠀⠀⠀⠂⠀⡆⠀⠀⠑⠀⠤⠴⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠈⠈⠈⠀⡀⠐⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠈⠈⠁⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⢀⠆⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠷⠗⠀⠀⢀⠄⠀⠀⢀
⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀
⠀⠀⠀⠁⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠄⠀⠓⠀⢩⡤⠰⠀⠁⠐⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⡠⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠂⠃
⠀⠀⠁⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢴⡀⠀⡀⠀⠀⡀
⠀⠀⠈⢇⢠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠒⠈⢳⠸⠁⠀⠈⢠⡤⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠄⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣴⠶⠋⠀⠀⠀⠀⢇⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈

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







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠖



⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣤⣀⠀⠀⠀⠀⢧
⠤⡤⠀⠀⠀⣠⠴⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣠⠏⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿⡿⠃⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠉⠀⣤⣤⡀⠀⠀⣇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠶⠆⠒⠶⢤⣀⠀⠈⠀⢀⣤⠴⠚⠁⠀⠰⣄⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⢸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⡴⠋⠙⢦⡀⠀⠀⠈⠛⢦⡀⠀⢀⡀⠀⠀⠀⠀⠈⠓⠶⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⢆⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠀⢀⡶⠀⠀⠀⣀⡀⠀⠀⣠⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣷⡄⠀⠀⠘⠛⠉⠉⠀⣤⡄⠀⠈⢁⠐⣇⠀⠀⡀⠀⠀⢹
⠴⠢⠶⠖⠴⠆⠂⢳⡄⠀⢾⣿⣿⣿⣿⣿⣿⡿⠿⢃⣀⣤⡤⠀⠀⠀⠀⠀⠰⢦⡳⣌⢧⡙⢦⠈⠛⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠉⠉⠉⠉⠁⢀⣴⢾⣋⣥⣤⣤⣄⠀⠀⠀⡄⠀⠀⢳⡜⢦⡻⣌⠳⡄⠀⠀⠀⢧
⠄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣤⠀⠀⠈⣡⣾⣿⣿⣿⣿⣿⣿⣦⣰⡄⠀⠀⠀⠹⣌⢳⡙⣆⢹⡄⠀⠀⠸⡆⠀⠀⠐⠴⠰⠲⡶⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣼⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⢹⠈⣇⠘⠆⠁⢠⣦⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠃⠀⠀⠀⢸⠀⢠⣤⠀⠀⠀⠀⠀⠀⢧
⠐⠃⠁⠒⠃⠓⠓⠓⠓⠀⢻⠀⢿⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣤⠀⠈⠛⢾⣿⡿⣿⠿⠟⠉⠁⠠⡄⣆⢹⡀⢧⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠰⠰⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⣄⠈⠉⠉⠀⠀⣄⡀⠀⣿⢸⡆⡇⠸⡇⠀⠀⣼⠀⠀⠀⣀⣤⣤⠀⠀⡇⠀⠀⠰⠤⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⡀⠈⠉⣛⠛⠁⠰⣌⡉⠋⣁⡞⢀⡇⢠⡇⠀⢰⠇⠀⠀⢺⣿⣿⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢾⠀⠀⠀⠉⢁⠀⠀⠈⣇⢤⠙⢦⡉⠉⠉⢀⡼⠀⡼⠁⢠⡟⠀⠀⠀⣠⣿⡟⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣦⠀⠀⠀⠘⠃⠀⠀⡿⠈⠳⣤⣉⠛⠚⢋⣠⠞⠁⢠⡞⠀⠀⣰⣿⣿⡟⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⠈⠳⠀⠀⠀⢀⣠⠾⠁⠀⣄⠀⠉⠉⠉⠉⢁⡀⠀⠋⠀⠀⠀⠙⠛⠟⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠷⠀⠒⠛⠉⠁⠀⠀⠀⠈⠳⢤⣤⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉