Bunny ear Emojis & Symbols

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣴⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢳⡀⠀⠀⠀⠀⣰⠋⠉⠓⢤
⠀⠀⠀⢠⡇⠀⣶⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⡆⠀⡇⠀⠀⠀⠀⡏⠀⣶⣄⠀⠱⣄
⠀⠀⠀⢸⠀⢸⣿⣿⣧⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⣿⣿⣷⠀⢻⠀⠀⠀⢠⡇⠀⣿⣿⣷⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣉⣑⠢⣄
⠀⠀⠀⢸⠀⢸⣿⣿⣿⣷⡀⠹⡄⠀⠀⠀⠀⠀⡼⠀⣰⣿⣿⣿⡟⠀⣼⠀⠀⠀⠈⡇⠀⣿⣿⣿⣿⡄⠘⡆⠀⠀⠀⠀⠀⢠⠋⢾⣿⡿⠟⠑⠈⠳⡄
⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣧⠀⢱⠀⠀⠀⠀⢸⠁⢰⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⣇⠀⢿⣿⣿⣿⣷⠀⢸⡄⠀⠀⠀⢀⡇⠿⣦⡁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢷⠀⢹⣿⣿⣿⣿⡄⠘⡇⠀⠀⠀⡇⠀⣾⣿⣿⣿⣿⠁⢰⠃⠀⠀⠀⠀⢹⡀⠸⣿⣿⣿⣿⡇⠀⣇⠀⠀⠀⣼⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠘⡆⠀⢿⣿⣿⣿⡇⠀⣧⠀⠀⢸⠇⠀⣿⣿⣿⣿⠇⢀⡏⠀⠀⠀⠀⠀⠈⢇⠀⢻⣿⣿⣿⣷⠀⢻⠀⠀⠀⡇⠀⣿⣿⣿⣿⣷⣦⡀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠸⡄⠈⢿⣿⣿⣇⣀⣿⣀⣀⣸⣀⣸⣿⣿⣿⠏⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢻⣿⣿⣿⣾⣾⣀⣀⣠⣷⣷⣿⣿⣿⠟⠀⡹⠙⠢⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣆⣠⣿⣿⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣇⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣾⣿⣿⠿⠟⠛⠛⠛⠛⠻⠿⣿⣿⣿⣶⡞⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣼⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣄
⠀⠀⠀⠀⢰⣿⡟⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⢿⣿⡀⠀⠀⠀⠀⢸⣿⡏⠈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⣸⣿⡏⠻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠈⣿⣷⠀⠀⠀⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⣿⣿⠀⠀⢠⣿⡟⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⣿⣿⠀⠀⢰⣿⡟⠀⠀⠀⣰⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣠⣤⣿⣿⣷⣿⣾⣿⣷⣤⣀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣠⣤⣿⣿⣷⠿⣾⣿⣷⣤⣀⣴⣿⡟⠀⠈⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣯
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡀
⠀⠀⠘⠈⡲⢤⡀⠀⠀⠀⠀⠀⠀⣠⢖⡯⠈⢰⠃
⠀⠀⠀⠀⢻⣣⡈⠓⢦⠀⠀⠀⡼⢁⣾⢁⢀⡟
⠀⠀⠀⠀⠀⢳⡑⡄⠀⠁⠤⠀⠀⠸⠟⢡⠎
⠀⠀⠀⠀⠀⠀⠙⡇⠆⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣹⢄⡀⠀⠀⠀⠀⡜⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠸⠁⠈⣱⠀⠀⠀⠐⣄⢸⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⢀⠄⣰⢳⠇⠀⣤⠠⡄⠘⠇⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣞⠀⢸⢀⠀⠀⠀⠁⠀⢠⣸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡿⠀⠈⠛⠀⠛⠋⠉⠛⠉⠳⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣆⢰⡀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⠀⠀⠀⠀⠐⢤⣿⠃
⠀⠀⠀⠀⠀⣀⡮⠈⠀⣹⠇⠐⣀⠟⠁⠀⢀⣴⡆⠀⠀⠀⣀⣠⣎⠀⠀⠀⠀⠀⠻⣿⡀
⠀⠀⠀⢀⣾⡁⣀⣠⣾⠋⠀⡠⠿⠀⠀⣰⣿⣷⢶⣤⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠳⠶⠶⠚⠛⠃⠀⠀⠈⠛⠓⠒⠒⠛⠛⠛⠛⠃⠈⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠱⡄⠀⠀⠆⡇⠀⠀⡀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡀⡙⠄⠄⠀⠀⠐⡈⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠸⡀⠹⠀⠀⢀⠇⠀⠀⡑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠾⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠀⠀⢣⠰⠀⡀⠠⠀⠐
⠀⠀⠀⠀⠳⡀⠀⡄⠈⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠠⠀⠀⠓⠚⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠻⢿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⢀⣸⠰⠀⠀⠀⠀⠀⠀⠈⠂⠨⠤⠀⠀⠀⠀⠀⠀⠀⢦⠞⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⢰⢂⡄⠀⢁⠉⢉⠁⢀⡀⠀⢰⡖⠂⠀⣀⢸⠋⠀⡄⠀⠀⠀⠀⠀⠈⠓⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠹⡖⠋⢸⠟⡿⠋⢨⠃⠀⢸⡗⠰⠧⠱⣼⡺⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠹⠀⠘⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢄⠠⠀⢀⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠰⡼⣶⠂⠀⠀⠀⠀⡀⢲⢠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠫⠍⠈
⠀⠀⠀⢀⠲⡀⠀⠘⠒⠚⠀⢀⠀⠀⠀⠈⣏⠉⠀⠀⠠⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢸⠀⠘⡄⠀⠀⠀⠔⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠃⠸⡄⠀⡀⠀⡄⠀⠀⠀⢀⠓⢦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢆⠀⠃⢀⡀⠌⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠢⠀⠀⠀⠀⠀⠀⢨⠀⠀⠃⠀⠀⡔⠀⡄
⠀⠀⠀⠀⠈⠃⠘⠋⠛⠀⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠢⠀⠘⠋⠻⠂⠔⠁

⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⡐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠠⡄
⠀⠀⠇⠈⣧⠀⠀⠀⢀⡾⠁⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠚⢤⡀⢢⠀⠀⠀⠀⣠⡀⢠⡀⠀⡘⠀⠘⠢⠽
⠀⠀⢠⠀⣽⡆⠀⢀⣾⠁⣰⠃⠀⠀⠀⠀⠀⠀⢸⠀⢸⢀⡎⠈⠁⠀⠀⢀⡄⠔⠃⠈⡇⢀⠇⢀⠆
⠀⠀⠀⠑⠼⣧⣀⣸⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⡸⡄⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠔⠁
⠀⠀⠀⠀⠚⠉⠀⠀⠉⠂

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⠙⡀⠀⠀⠀⠀⠀⡜⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⡀⠀⠀⢰⠛⢦⠀⠀⠀⠀⢠⢶
⠀⠀⢀⠃⠀⠰⠀⠀⠀⠀⠐⠀⠈⡆⠀⠀⠀⡴⠚⠉⣶⠀⢰⠁⣄⡀⢹⠀⠀⢸⠀⢸⡆⠀⠀⠀⡿⢸
⠀⠀⣸⠀⠀⠀⡇⠀⠀⢀⡇⠀⠀⡷⠀⠀⡞⠁⣠⠎⡇⠀⡆⢀⠎⠈⠁⠀⠀⠸⡄⢠⢹⠀⠀⢸⠁⣼
⠀⠀⠸⣆⠀⠀⣿⠀⠀⠸⡇⠀⠀⠃⠀⠀⠑⠊⠈⢇⢰⠐⠠⠋⠀⠀⠀⠀⠀⠀⢧⠈⠞⣆⠀⣯⣠⠇
⠀⠀⠀⠁⡣⡀⠉⠀⠀⠀⣄⡐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠉⠀⠋⠁
⠀⠀⠀⠀⠑⠹⠇⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⡀⠀⠀⠀⢀⣤⣶⡄⠀⠴⠃⠀⡏⢸⡄⠀⠀⡴⣺⠋⡟
⠀⠀⣀⢒⡀⠀⣶⡄⠀⡀⢀⡀⠀⠀⢰⣃⠾⠀⣿⠀⠀⠀⡾⠉⣸⠃⠀⠀⠀⠸⡇⢸⡇⠀⣾⡽⢡⠞
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢃⡻⡆⠀⠸⠃⢀⠟⠀⠀⠀⠀⠀⢳⡸⡇⢸⢟⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠂⠡⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠸⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢰⣇⡠⡪⢳⡄⠀⠀⣿⠀⠀⣿⠀⠀⢀⡴⣻⣿⣦⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡯⢊⠔⠁⢹⡄⠀⢿⡄⠀⣿⠀⠀⣾⣳⠟⠝⢹⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣷⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⣯⣷⢷⣺⣿⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠸⣧⠔⠠⠂⢹⡆⢸⡇⠀⣿⠀⣿⣻⣵⣯⣿⠇⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡙⣷⡀⠀⠸⣇⢸⣧⠀⣿⢰⣿⣿⣿⣽⢏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡸⣿⣄⣼⣿⣼⣿⣤⣿⣾⣿⣿⣿⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡆⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⣿⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡴⠃⠀⣠⣾⣿⣿⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣾⣿⣿⣿⡏⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⣿⣿⣿⣿⠟⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣰⣿⣿⣿⣿⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⣼⣷⣄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⣿⣿⣿⠟⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⣿⣧⠀⠹⡄⠀⠀⠀⠀⠀⠀⡟⢀⣿⣿⣿⠋⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠻⢿⣿⣿⣧⠀⢹⡀⠀⠀⠀⠀⢰⠃⣸⣿⡿⠃⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡟⠳⣄⠉⠻⣿⣇⠀⢧⠀⠀⠀⠀⢸⠀⣿⡿⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠁⠀⠈⠳⡄⠙⠿⠀⠸⡄⠀⠀⠀⣿⠀⠙⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣰⠃⠀⠀⠀⠀⠘⣆⣠⣴⡾⠿⠛⠛⠛⠻⠷⢶⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⠋⣀⠀⠀⡘⠛⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⣾⣦⠀⠀⣰⣿⡄⠀⠀⠀⣴⢦⡀
⠀⠀⠀⠀⣾⣿⡿⡄⠀⠀⣰⠋⢸⡇⠀⠀⠀⣿⣿⣇⢠⣿⣿⡇⠀⠀⠀⡏⠈⢧⠀⠀⢀⣶⣶⣦
⠀⠀⠀⠀⣿⢿⡀⢹⡀⢠⠇⢠⠞⠀⠀⠀⠀⢻⣿⣿⢸⣿⡿⠁⠀⠀⠀⠹⡄⢸⠀⢠⠏⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢄⣇⣸⡰⠋⠀⠀⠀⠀⠀⠀⢻⣿⣸⡿⠁⠀⠀⠀⠀⠀⠹⣸⣀⣎⡴⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠙⠂⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠂⠀⠀⠀⠀⠀⠚⠉⠉⠉⠓

⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣤⣤⣄⠀⠀⢀⣤⣤⡀⠀⠀⢰⡿⢦⠀⠀⠀⡴⢿⡄
⠀⠀⠀⢸⣿⡿⢻⡀⠀⢠⠟⢿⣿⡇⠀⣼⢹⣿⣿⡆⠀⣿⣿⣿⢹⡀⠀⠸⡇⠈⣇⠀⣸⠁⢸⠃
⠀⠀⠀⠸⠟⢳⡀⢧⠀⡞⢀⠞⠿⠃⠀⠙⠉⢻⣿⣧⢸⣿⡿⠉⠛⠀⠀⠀⠹⡄⢹⠀⡇⣠⠏
⠀⠀⠀⠀⠀⠀⢙⣼⢤⣧⡋⠀⠀⠀⠀⠀⠀⠀⣹⣿⢼⣿⡁⠀⠀⠀⠀⠀⠀⢘⣼⢤⣷⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⢀⣾⣿⣦⡀
⠀⠀⢀⣾⡟⠉⠻⣿⣄
⠀⢀⣾⡟⠀⠀⠀⠙⢿⣷⡄
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠹⣿⣦
⢰⣿⡇⠀⠀⠀⣦⡀⠀⠀⠈⢿⣷⡀
⣸⣿⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠻⣿⣄
⣿⡿⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀
⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠋⠉⠛⠛⠛⠿⢿⣷⣦⣀
⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣧⡀
⢻⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠸⣿⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢿⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠘⣿⣆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠹⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢻⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢻⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠻⣿⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⣽⣿⣿⣦⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠘⣿⣿⣿⣿⣿⣿⠀⢠⣿⡇⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⣿⣿⣿⣿⡟⠁⢀⣾⡿⠁⠈⠙⢿⣷⣤⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠘⢿⣿⣿⣿⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡀⠸⣿⣿⣿⣿⡟⠀⣠⣿⡟⠀⠀⠀⠀⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠈⢻⣿⣿⡇⢀⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⣿⣿⣿⠏⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠙⠛⠁⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠙⠛⠁⣠⣾⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⢰⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⣧⠀⠀⠀⢹⠀⠀⠀⢸⢀⠀⢸⠀⠀⠀⡏⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⠘⡆⠀⢆⠈⠆⠀⡇⠈⢸⠀⡈⢠⠃⠸⠀⢀⠀⣰⠋⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡀⠳⡄⠘⢆⠘⠀⠘⡀⠀⠀⠇⠀⢸⠀⠀⡘⢠⣶⢦⡉⡰⠃⢀⠄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢦⡀⠘⢦⠘⠀⠈⢆⠀⠀⠁⠀⠀⢠⠀⠘⠀⠀⠁⣾⠃⣸⡇⠁⣠⠋⡠⠋⠀⡀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠑⢤⡙⠀⠀⠓⡀⠀⠈⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢸⣿⡴⠛⠀⠐⠁⠀⠀⠰⠊⣠⢖⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠑⠄⡀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⢸⣿⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠈⠛⠲⢤⣀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⣰⠏⠠⠒⠉⢸⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⣧⠀⠀⢀⣼⠏⠀⠀⠀⡀⢸⣿⠐⢁⣀⠤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⣏⢸⣿⣧⡿⠈⠳⠶⠋⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⢀⣤⣴⠆⠀⠀⣰⣿⡶⡟⢰⣿⡇⠀⣿⠀⠙⠛⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣉⣁⣀⣤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣼⣧⠀⢀⣿⣿⠀⣿⠈⠻⡷⠼⠃⠀⠀⠀⠀⢹⡇⠀⣤⡀⠀⠀⠀⠀⢀⢸⡿⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢰⣿⡇⢀⣿⣿⣆⡾⢿⣿⢀⡿⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⣧⣼⣻⠇⠀⠀⠀⠰⡄⢠⡄⠀⢀⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⠃⣿⣿⡃⠈⣙⠛⠁⠀⠀⠀⠀⠀⣸⣿⢻⡄⣿⣿⣿⠟⠀⠀⠀⠀⢸⡇⠘⠷⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠙⠛⠁⠀⣼⣿⣇⠀⣿⣧⠀⢀⣀⠀⣤⠀⣿⡯⠀⢰⡿⣿⡟⣷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⠀⣸⠏⣿⣿⠀⢸⣿⡀⢸⣿⡀⣾⠀⢹⣿⣠⡞⠁⢿⣧⠘⣿⡄⠀⣸⠇⠀⠉⠒⠦⠄⠀⠀⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠄⢀⡠⢠⡟⠀⣿⣿⠀⢸⣿⡇⠸⣿⡇⣿⣇⡾⠁⠀⠀⠀⠀⠀⠀⠈⠻⠶⠏⠠⢄⡀⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⣡⠖⠉⠀⣾⢀⠄⢸⣿⠀⠸⣿⣇⣼⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⢄⠙⠂⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⣀⠔⢰⡏⠀⠀⣼⡏⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠑⢆⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⡇⡔⢠⡟⠁⡀⢠⠈⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⢀⠘⣆⠀⠱⣄⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣈⠳⠴⠋⠀⡜⢀⠏⠀⡄⢸⠀⢀⠀⡄⠀⠀⢃⠀⢀⠈⣆⠀⢳⡈⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⡼⠁⠈⠀⢰⠀⠟⠀⢸⠀⡇⠀⣆⠘⡀⠀⢆⠈⠀⠀⢳⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡏⠀⠀⠀⣾⠀⠀⠀⢹⠀⠀⠀⠸⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠃⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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







⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠘⣯⠉⣉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⣄
⠀⠀⠀⠀⠀⠀⠘⣆⢙⠛⠷⣬⡛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡀⠈⠻⣮⡻⣄⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠳⣜⢧⡀⠀⠀⠀⢀⣼⡣⢾⡇⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠈⠊⢳⡀⠀⠀⣼⠋⠀⠈⠛⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠀⠈⠁⢠⡁⠀⠀⢣⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠑⠞⠁⠀⠀⠈⠲⠀⠉⠲⣄⠀⠱⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠶⠈⠠⡆⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠃⠀⠤⠀⠀⣴⣿⣛⣛⣻⣶⡇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡀⠀⠀⠙⢿⠟⠉⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠆⡀⠀⢱⠀⠠⠄
⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣧⡀⠀⠀⠉⢙⠀⠀⢀⠒⠒⠒⠀⠀⠀⣰⣷⣶⣶⣤⣤⡄⠀⠈⢶⠎⠀⠰
⠀⣠⣶⣾⣿⠿⠟⠛⠛⠉⠉⢙⣳⣤⣄⡀⠀⠀⠈⠀⠀⠀⢀⣤⡞⠉⠉⠉⠙⢛⠟⠁⢀⠀⠘⠄⢀⠘
⣾⣿⣿⣿⣧⣤⣠⠞⣛⢦⡤⠿⠁⠀⠈⠙⠛⠀⠀⠀⠀⠛⠉⠀⠙⣆⠈⡠⠚⠁⢀⣴⣯⣽⣦⣤⣼⡇
⠙⢿⣿⣿⣿⣿⣇⣘⢠⠁⠀⣶⣶⣶⣶⣦⣴⣦⣴⣤⣶⣴⣶⣶⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠈⠙⠛⠿⠿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⢒⡶⢶⠀⠂⠙⠀⢠⠁⠀⠀⠈⠈⢡⠀⢀⡆⠐⠀⢠⣆⢀⣢⡀
⠀⠀⠀⠀⠀⠀⠚⠋⠀⠰⠂⠀⠀⢨⣤⣼⣇⡀⠀⠀⠀⠱⡆⠀⠀⠀⢸⢀⡋⠈⠁⠉⠉⠉⠙⠁⠳⡀
⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⢰⡴⣊⡁⠀⠀⢀⠙⢶⡀⠀⠀⣇⠀⠈⠀⢾⡠⠙⠳⠲⠶⠶⠀⠀⠀⠀⢧⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡎⠘⠿⠇⠴⠘⢿⠇⠀⣧⡬⣄⣯⣥⣤⣤⣬⣄⡀⠁⠀⠠⢐⠀⠀⠀⠀⠈⣧⠀⡀
⠀⠀⠀⠀⠠⠆⢠⠀⠀⠘⣇⡀⣀⣤⣀⣀⣄⣀⣠⢿⣶⣾⣟⡶⠿⢰⢣⣸⣷⣤⣀⣾⡿⢃⠀⠀⠀⠠⠿⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡾⢹⠅⢠⣿⣡⡾⢹⣔⡂⢹⣿⠿⠶⠷⢾⣼⣿⠟⣬⢻⣿⣷⣿⠿⠛⠛⠒⠶⡶⢶⠀⠉
⠀⠀⠀⠀⡠⣠⣸⠃⠀⠐⣿⡊⠀⠀⢘⡿⢁⢳⣦⡟⠉⣀⡀⠂⢀⡀⠘⣿⣿⡁⢛⣽⡿⢧⣀⠈⠀⠀⢠⠁⢾
⠀⠀⠤⠦⢁⣙⣻⣤⠀⠱⠄⢨⣴⣋⣿⠻⢶⠌⣾⠀⠀⣿⡇⠀⣼⣿⠀⢸⠉⢛⡿⠿⠿⠞⠿⠦⣔⠂⠀⠄⡉
⠀⠀⢾⡁⢋⡀⠃⢀⣄⠀⠀⢀⠀⠙⣿⠿⢶⣴⣿⠀⠘⣿⠇⠀⣿⡟⠀⣾⣵⠋⣠⣬⡀⠀⠀⠀⠀⠙⢶⡈⠑
⠀⠀⠈⠁⡞⠀⠀⠀⠉⠀⢸⣿⣿⠀⠈⣴⢾⡟⠟⣦⣀⠉⠀⠀⠉⢀⡼⢋⡏⠀⢿⣾⠟⠀⠀⣀⢤⣔⠂⢳
⠀⠀⠀⠀⢇⠀⣾⣿⡆⠰⠀⠉⠁⣤⠼⠿⠿⣿⠰⢨⢽⡷⡤⢦⡶⠋⢀⡼⠷⢄⠀⠀⠘⠷⠂⠿⣿⠟⠀⣼
⠀⠀⠀⠀⠈⢀⠉⠉⢀⠀⢀⠠⠒⠁⣶⠀⢠⡈⠙⡖⠊⠀⠀⡀⠀⢀⠟⠀⣠⣾⡿⠆⢄⣀⣀⣀⣀⣤⣾⣇⠀⡀
⠀⠀⠀⡠⠠⠤⣟⣦⡈⠉⠀⠛⣀⠀⠁⠃⠛⠁⠘⣅⡀⣬⠰⣷⣻⣆⣀⣴⡿⠿⠥⠤⠾⣯⡿⠛⣟⢡⣤⠌⡗⠀⡀
⠀⠀⢰⠀⠰⠆⠀⠀⣬⠉⣦⣤⣥⣶⡶⠄⠠⠀⠾⢯⣤⠗⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣆⣻⣬⣭⣴⠏⠉⠝
⠀⠫⠚⠁⠀⠀⠀⠁⠀⠀⢿⣻⣿⠋⣴⡆⠀⠰⣷⡤⠛⠚⢺⣦⣄⠀⠀⡀⠠⠤⠤⠤⣴⣧⡶⠛⣿⠛⠿⠧⢤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠠⢦⠀⢀⡄⡘⠀⠀⠀⠀⢳⡿⣆⠀⢴⣶⣶⠀⣼⣟⣻⡷⢤⣁⡔⢧⠄⠈⢣⡀
⠀⠀⢠⡱⠢⣤⣤⣤⣴⣾⠟⠛⠛⠒⠚⠈⠹⢶⠁⠀⠈⠀⠀⠘⣿⣿⢆⡀⠉⢁⣰⣿⠟⠛⠓⠶⣏⠀⠠⠀⠀⠤⡇
⠀⠀⠠⠀⣆⡉⣿⠿⣟⡙⠀⠀⠂⠁⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⣷⠎⠀⠉⢛⣿⣿⡟⠀⠀⠀⠀⠈⠛⢦⡘⠂⢀
⠀⠀⠀⡎⠀⠉⠻⣄⡸⣷⠠⠂⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⢸⢧⣿⣿⡲⣀⠐⠆⠀⠀⠀⣭⣶⠉
⠀⠀⢀⡵⢤⣀⡀⠈⢠⢻⠘⠂⠀⠀⠀⠀⠀⠀⠐⢥⣿⢿⣽⣭⠀⠀⠀⠀⢸⣿⣿⣿⡶⣿⠷⣤⡀⢀⣜⡔⠁
⠀⠀⠈⠣⣤⠋⢀⠀⠠⠛⠂⢠⣤⣤⡤⠄⠠⣴⣶⣜⠿⣾⣿⣻⠀⠀⠀⠀⠈⢿⣸⣿⠉⣿⠛⣦⣭⡌⢛⡀
⠀⠀⠀⡞⠁⠀⠈⡔⠁⠀⣴⢯⣽⡿⢁⣀⡀⢻⣿⠟⠂⠻⣼⣿⡂⠀⠀⠀⠀⠀⠻⡉⠘⢿⡚⢿⢧⣷⢈⡁
⠀⠀⢀⣾⣦⣤⠮⣄⣠⠞⠁⠀⠙⣇⢿⣿⣿⡏⠁⠀⠈⠰⠋⡙⠛⡀⠀⠀⠀⠀⠲⠈⣦⡄⢹⡜⡆⠈⢿
⠀⠀⠈⡏⠙⠻⣷⣌⡏⢰⣷⠠⣿⠹⢆⡉⡕⠉⠀⣀⠀⠀⣾⣟⠆⠈⠀⡀⠒⠀⠀⡰⠃⠀⢸⣷⡇⠀⠋
⠀⠀⠀⢃⠀⠀⠘⢿⠁⠈⠋⠀⠋⠀⣿⢵⡞⠀⢾⣟⡗⠀⣈⠉⠀⠀⣀⣟⣿⠛⠉⢠⡄⠀⡏⠈⡆
⠀⠀⠀⠀⠑⠠⠀⠼⢧⡀⠀⠀⠀⠠⠁⠘⠧⡀⠀⠀⠀⠀⠈⠀⡠⠞⠀⢉⣑⢢⣄⣉⠉⡜⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠠⠀⠀⠀⢙⠒⠛⠢⢤⠤⠞⠁⠀⠘⠉⠋⠠⠌⠉⠛⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⢶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⢀⣼⠏⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠋⠀⣠⣴⠶⠶⠿⠿⠿⠛⠋⠁⠀⠀⠀⣠⠟⠁⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣽⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⢰⣶⡶⠿⢿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣆⠘⠁⠀⠀⠀⠈⠳⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣽⣏⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣤⠀⡄⢀⡤⣄⠀⣄⣤⠠⣄⣠⠄⠀⣠⢤⡄⢀⣤⡀⠠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⢿⣤⠇⠸⣧⡤⠀⡟⢧⠀⢹⡏⠀⠀⢿⣤⡄⣼⠿⣧⠀⣿


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

⠀⠀⠀⠀⠀⢀⠠⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠘⢂⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠈⠁⣂⡀⠀⠀⠀⠀⠀⢊⢆
⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠑⠄⠀⠠⠤⠄⠀⢠⠊⠀⠀⠀⢀⠂⠈⠚⠀⠑⠄
⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠈⢡⣀⣀⣀⣀⣠⠉⠀⡆⠀⠀⠀⠀⡀⠈⠀⠀⠈⠀⢸⠀⠀⠀⠀⠘⠠⠤⠤⠤⠄⠐⡄
⠀⠀⠀⠀⠈⡇⠔⠛⠪⠌⡖⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠀⡀⠁⠀⠀⢩
⠀⠀⠀⠀⠀⠰⠂⣈⠐⠸⠀⠀⠀⠀⠀⠑⢀⠉⠀⠀⠈⠁⡠⠯⠅⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠱⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠣⠤⠄⠤⠴
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠠⠐⠃⠀⠐⢄⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡠⠄⠊⠈⢂⠀⠀⠀⠀⠀⠆⠀⠉⠉⠀⠰⡄⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⡄⣀⡀⢀⡀⢄⡎⠀⠀⠀⠀⡠⠰⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠇⠖⠈⠀⠀⠈⠢
⠀⠀⠀⠀⠀⢀⠀⠔⡈⠀⣯⢢⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡑⠄⠀⠀⢀⠔⠈⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢂⠀⠀⠀⠀⡰⠅⠊⠀⠀⠅⠀⠀⠈⠀⠀⠈⠀⠀⢀⠂⠀⠀⠀⠈⠀⠀⠁⠀⡇⠂⠀⠀⠀⠁⡠⣀⠀⠀⠀⠂⠢⣀⠄⣀
⠀⠀⠀⠀⠀⢀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠐⠀⠉⠑⠀⠒⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠙⠂⠤⠀⠁⠀⠀⠁⠀⠠⠂
⠀⠀⠀⠀⠀⠘⣁⢀⠅⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠀⠤⠐⠂⠀⠀⠀⠀⠐⠠⠄⠀⠄⠊
⠀⠀⠀⠀⠀⠰⣁⣜⠐

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠦⣤⣀
⠀⠀⠀⠀⣠⠞⠉⠀⣀⣀⣀⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⢀⣀⣠⣀⣀⠀⠉⠻⣦
⠀⠀⠀⠈⠁⠀⣴⠟⠁⠀⠀⠀⠉⠳⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣠⡾⠉⠁⠀⠈⠉⠻⣦⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠄⠘⡆⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠈⣷
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡆⢹⡆⠀⢹⡆
⠀⠀⠀⠀⠈⣇⣀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠉⠙⠓⠒⠒⠲⣦⠀⠀⢱⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠙⠓⠒⠒⠒⢦⡀⠀⠹⣿⡀⣸⡇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢻⠃⣼⠁
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡟⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡆⠀⠀⠀⠀⠀⡼⠀⠀⣼⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⡴⠋⠀⠀⢠⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠁⠀⠀⢀⡴⠚⠁⠀⢀⠇⢸⡏
⠀⠀⠀⠀⣼⡏⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⠖⠛⠉⠀⠀⠀⠀⠈⢀⡿⠁
⠀⠀⠀⠀⠘⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠒⠠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠴⠖⠋

⠀⠀⠀⠀⠀⡠⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡄⣠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢱⣬⣴⡟⢁⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠢⡀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠤⢚⡏⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠄⠐⡀⠀⠀⠈⠢⠀⠢⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⢁⠠⠐⠀⠉⠀⢀⠅⠀⠅
⠀⠀⠀⠀⠀⠀⠈⢄⠘⠄⠀⠀⠀⠑⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠀⠁⠀⠀⡀⠔⢈⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠢⠀⠀⠀⠈⠄⠰⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⢀⠊⠠⠊⠀⠀⢀⠔⢈⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠑⠄⠀⠀⠈⢂⠡⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⡠⠁⠔⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠢⡀⠀⠀⠄⢁⠀⠂⠀⠀⠀⠀⠘⠀⡰⢁⠌⠀⢀⠔⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⢄⠀⠈⠄⢦⠀⠀⠀⠀⠀⠀⡴⢁⠂⠀⡠⠃⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡑⡄⠰⠆⣀⠀⠀⠀⠀⢀⣠⡂⢀⠌⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠼⠀⠀⠁⠀⠀⠰⣄⣀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠊⠀⠀⠁⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠁⠁⠒⠠⢀⡀⠀⢠⠄⠊⠁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢲⡅⠀⠀⣹⢥⠄⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠟⠠⢖⠙⡂⠀⠠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠌⠀⢸⠈⡄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡘⠀⠠⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠳⣄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣠⠞⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⠳⣄⠀⠀⠈⢷⠀⠀⠀⠀⡼⠁⠀⠀⢠⡞⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠻⣷⣄⣀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠙⢦⠀⠀⠘⣧⠀⠀⣼⠃⠀⠀⣴⠋⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⣆⣰⡏⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠛⠛⠛⠛⠿⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠛⣥⣄⣀⣬⠛⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⢿⣶⣄⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⢠⣤⣄⠈⠻⣷⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠈⠉⠻⣷⡀⠘⢧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⣀⡀⠀⠀⠀⠘⣷⠀⠈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠙⠛⢶⣄⠀⠀⢹⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠳⣄⠀⠀⠙⢆⠀⡼⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡈⠀⠀⠀⠈⠀⠁⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⠉⠛⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⣠⠴⠦⢤⣀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡴⠞⠁⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⡾⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠑⠛⡇⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠐⠶⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠈⣿⡤⠔⠀⣈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠙⠿⠿⠒⠢⢤⣤⣽⣿⣿⣾⣛⣿⡦⢀⣼⣿⡆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣂⠈⢀⣩⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣇⡔⠀⢀⠠⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡟⢛⠤⣀⣄⣈⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣅⣈⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠻⠿⠟⠀⠀⠘⢿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠪⠻⣧⠠⠀⠀⠀⠠⢆⣈⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠄⠀⡜⢢⠀⠀⠀⠙⠻⢩⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠄⠀⠘⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⡃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⠀⠁⠘⣷⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣿⣿⡿⠇⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠙⡄⠀⠿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡏⡂⠀⠀⠈⠻⢇⡀⠘⢀⡿⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠢⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠑⢤⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡳⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢊⣿⣿⣿⠷⢶⣦⣀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢱⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣾⠟⠋⠁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢾⡿⠿⢿⣿⣟⢿⣿⣿⣿⡟⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢍⠙⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢸⡟⢻⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⠏⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣼⣿⣿⣿⠂⠀⠀⠀⠀⢼⠁⠀⢻⡄⠀⠀⠀⢀⣴⣿⣿⣶⡄
⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠹⡆⠀⠀⢰⠏⠀⢀⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣇⠀⠈⣇⠀⠀⢠⡞⠉⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⠟⠻⣄⠀⢿⠀⠀⡿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠐⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⢠⡟⠀⣠⡾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⢸⣆⣰⡇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣟⣀⡼⢠⠾⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠳⢤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠳⢤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⢠⡾⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⢧⠀⠀⠀⠀⣿⠁⠘⣷⠀⠀⠀⢠⡟⠁⢹⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠋⠹⣆⠀⠀⠀⡾⠉⢻⣿⣿⡇⠀⠀⣾⠀⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣟⢘⡇⠀⠀⠀⢹⡄⠀⠸⣇⠀⠀⡿⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢿⣿⢿⣄⠀⢻⡀⠀⣸⠃⠀⣴⢿⣿⠇⠀⠀⠻⠛⠉⢿⣿⣿⣇⠀⣿⣿⣿⡟⠉⠻⠃⠀⠀⠀⠀⢻⡄⠀⢿⠀⢸⡇⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠙⢦⠘⡇⠀⡟⢠⡞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⠀⢸⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠿⠷⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠶⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠾⠷⠾⢾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣼⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⢿⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⡏⠸⡇⠀⠀⣠⣶⡟⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠀⠀⣿⢠⡞⠁⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⣷⡄⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡏⠀⠀⣿⠏⣀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⢀⠎⠀⠀⠈⢻⡄⠀⢀⡾⣻⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⡇⠀⢀⣿⣾⣇⣩⡄⣠⡴⠚⠉⠙⠻⢦⠀⡌⢀⡠⢤⡀⠀⣷⢠⡟⠀⡏⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠦⣿⠀⢸⠹⣿⣿⣿⡇⣟⠀⠀⠀⠀⠀⠀⣷⢠⣿⣤⣼⣿⡆⢹⠏⠀⣸⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣇⣼⣦⡝⠿⠛⡱⠹⣇⠀⠀⠀⢀⣶⠟⢼⣿⣿⣿⡿⠀⡾⠀⣰⠃⢰⡶⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣷⣆⣉⣀⣀⣈⣳⣶⣖⣛⠁⢈⡶⠿⢯⣉⠤⣾⣷⠾⣥⣤⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⡈⠀⠈⠳⡦⡤⠀⠀⠀⠀⠀⠙⢳⣖⣖⣶⣻⠾⠁⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠉⠀⠀⢰⠇⡇⠀⢀⡤⠀⠀⠀⢨⡟⠉⡟⠀⢀⣰⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡞⠀⣃⠀⠻⣷⠀⠀⠀⣀⠀⠀⢿⠀⠈⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣤⡿⠖⠋⠹⣆⠀⠹⠇⠀⠀⠈⢦⡉⠛⢷⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠉⠛⢶⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⠓⠤⢀⣀⣀⣀⣠⣒⡁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣉⡀⠀⠀⠀⢀⣠⡤⠟⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⣀⣀⣄⣀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠓⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⠑⠦⣀⡀⣸⡇⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣰⠋⠀⠈⢻⡆⠀⠀⠀⠉⣿⠓⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⡠⠃⢀⠔⠒⢦⡀⠀⣿⠀⠀⠀⠀⣷⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠉⠀⠈⠁⠀⠀⢺⣴⠀⠘⡇⡠⢻⣿⡀⠀⠀⡟⠀⣼⠃⢀⣿⡆⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣴⡆⠀⠀⠀⠀⣸⣿⣒⡺⠋⠀⢸⣏⠙⠓⣾⠓⠋⢿⣧⠞⠙⣿⣄⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⠔⠁⢉⣉⡀⠀⠀⠈⠻⠶⠞⠁⠀⠀⠀⠀⢀⠀⠈⠛⠷⠦⠤⠔⠁
⠀⠀⠀⢀⠴⠒⠛⠛⠛⠛⠛⠛⠓⢻⡟⠋⠉⠀⢠⡞⠉⠀⠙⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⡏⢀⣤⡀
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢠⡿⠀⠀⠀⢀⠏⠀⠀⠀⠀⣰⠏⠉⢹⠀⣾⡗⠁⣾⠁⠀⠀⠀⠀⣀⣀⡀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠑⣾⡧⠤⠄⠒⣡⠀⠀⣾⠀⠀⣿⠀⠀⠀⢠⣿⣷⣞⣁⡀⠀⢀⠔⠋⠁⠈⢻⡆
⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⡇⠀⠀⢰⣿⠀⢰⣿⠀⢰⢿⣦⣤⠴⠃⠸⠇⠀⠈⢙⠿⣧⣤⣀⣀⣠⠞⠁
⠀⠀⠀⠙⠷⣶⣤⣤⡴⠖⠋⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⡸⣿⣤⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠔⠒⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠘⠀⠄
⠀⠠⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠈⠉⠐⠄⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀
⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⠀⠀⠀⠀⠠⡀⢀⠄⠂⠈⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⢄⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠃⢄⡀⠀⠀⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡄⠀⠖⡠⢠⡀⠀⠀⠀⡀⢠⡀⠦⠀⡆⠀⠀⠸⠀⠒⣡⢀⡀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⠀⠀⠀⢸⠀⠔⣀⢀⡀⠀⠀⠀⠀⢀⡀⢅
⠀⠀⠀⠀⠀⠸⣿⣿⡟⢀⣀⠘⣿⣿⡿⠀⠀⠁⠀⠀⠀⠀⠘⢿⣾⡿⠀⠀⠀⣶⣰⣦⠘⠀⡆⠀⠀⠀⠀⠀⠀⠐⣿⣾⡿⠀⠀⠀⣿⣴⣿⠀⠀⠁
⠀⠀⠀⠀⠰⠶⠂⠉⠀⠘⠛⠁⠈⠁⠰⠶⠀⠀⠀⠀⠀⠺⠛⠀⠉⠀⠲⠾⠀⠻⠿⢛⠀⠀⠁⠀⠀⠀⠀⠀⠰⡶⠊⠉⠁⠸⠿⠃⠉⠛⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠐⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⡀⢀⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠢⠀⣠⢠⠄⠤⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡁⡇⢸⠁⣀⡈
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠔⣈⡤⠀⠀⠀⢤⣁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡦⠠⡄⠃⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠀⢄⢄⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢡⣴⡔⠀⢢⣦⡌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⡿⢿⣿⣿⡟⠿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠙⠻⣿⣷⣦⣍⣙⡒⠾⢭⣤⣈⡙⠲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣝⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣍⣙⠓⠲⢮⣭⣳⢮⣷⣵⡝⣿⣿⣿⣿⣿⣿⣿⣿⣦⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⢷⣒⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠓⠂⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⠈⠀⠹⣿⣿⣿⣿⣿⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⠿⠋⢁⠀⣀⣀⣀⡀⢀⡠⠤⠒⠉⠁⠙⣿⣿⣿⣿⣧⡐⢀⣿⣿⣿⣿⣿⣷⡁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⡶⠿⠗⠀⣠⠊⠉⠀⠉⠻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⡞⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣷⠬⢄⣀⢠⣀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣀⡼⡟⢺⢋⠳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⢃⠀⡇⠀⠙⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠈⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡇⡿⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢠⠉⠉⠑⡄⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣏⠄⠀⠀⠈⢆⢈⡤⠴⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡟⣦⠀⠀⠀⠀⠡⡄⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢿⣿⣿⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠘⣷⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢸⠻⣿⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠈⢿⣄⠀⠀⠀⠀⠈⠂⠀⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣠⣤⣤⣈⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⢊⣡⣤⣤⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠑⢄⠀⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣿⣿⣿⠏⠐⠈⠉⠁⠀⠀⠉⠉⠐⠈⢿⣿⣿⣿⠇⡘⠀⠀⠀⠠⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡫⠋⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⠌⠫⡛⢀⠃⠀⠀⡆⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠑⡋⣿⢿⡅⠄⠀⠀⠀⠀⡊⡿⣿⡍⡗⠁⠐⡆⠀⠀⡠⠃⢄⠆⠄⠄⡀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠈⠉⠈⢀⣤⣤⣤⣄⠈⠈⠉⠈⠀⠀⠀⢠⠀⡐⠀⠀⠀⠉⠘⠁⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢁⣀⠈⠥⢰⠁⠙⢿⠟⠁⢳⠨⠍⢁⡈⠉⠀⠸⠠⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢁⠠⠒⠉⠹⠀⢀⠜⢄⠀⡸⠉⠐⠢⡀⠉⢀⠃⠁⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡁⠀⠀⠀⠀⠙⠢⠤⠤⠚⠀⠀⠀⠀⠀⣰⡇⠘⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡟⡷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⠃⠃⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠑⠻⠾⠭⠿⢿⣿⣿⠿⠿⠿⠟⠛⠉⠢⡀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢄⠀⠀⠀⠀⠀⠈⢦⣀⣠⣮⣐⢄⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠂⠀⠑⠄⣠⡀⣀⣠⣿⣿⣿⣿⣿⣷⡑⡀⠀⠀⠠⠂⠉⠑⢄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⢂⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⠊⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⡠⠄⠂⠀⠐⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠠⡀⠠
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣨⠻⣿⣿⣿⣿⣿⣿⣿⣿⢫⡁⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡂⣂⣂⡣⠗⠓⠱⢍⠻⠿⣿⡿⠿⢛⠵⠁⠒⠦⣆⡆⡄⣄⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⣄⠑⢀⣀⣠⠤⠤⠤⠤⣄⣀⡀⠊⣠⣾⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣾⣿⣷⡀⠣⠀⠀⠀⠀⠀⠀⡼⢁⣼⣿⣧⣾⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢻⣿⣿⣧⣠⣷⣾⣿⣿⣷⣾⣄⣸⣿⣿⡟⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠁⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠑⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠊⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢴⣽⢉⡉⠁⢀⠀⠀⠈⠉⢉⠉⣯⣤⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⢹⣯⢰⣿⡄⠀⠀⠀⠀⢀⣷⡶⣿⡏⣶⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⣼⡿⠈⠛⠣⠀⠀⠀⠀⠼⠛⠃⢾⣧⣿⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠙⢧⡀⠀⡀⠀⠐⠊⠀⢀⠀⠀⡼⠋⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠅⠰⠇⠀⣀⣽⣷⣦⣔⠋⠙⣺⣤⣾⣯⣄⠀⡸⠆⠸⡄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣲⣽⣿⣿⣿⣧⠙⠻⠿⣻⣿⣿⣿⣿⣿⣆⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡎⣩⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣏⢉⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⢀⡤⠖⣛⣋⣛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣛⣙⣛⠲⢤⡀
⠀⣰⢋⡴⠋⠉⠀⠈⢻⡄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢠⡟⠁⠈⠉⠛⢦⡙⣆
⢰⠃⡾⠀⠀⠀⠀⠀⠀⣷⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣿⠀⠀⠀⠀⠀⠀⢷⠸
⣿⢸⡇⠀⠀⠀⠀⣀⣠⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣄⣀⠀⠀⠀⠀⢸⡇
⣏⢸⠀⠀⢀⡴⢛⣩⠞⣃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⠷⣍⡛⢦⡀⠀⠈⡇
⣿⢸⡆⠀⢸⠀⠠⠖⠋⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠲⠄⠀⡇⠀⢰⡇
⠹⡄⢷⡀⠈⠳⣤⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡤⠞⠁⢀⡾⢠
⠀⠹⣆⠻⣦⡀⠈⢧⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⡾⠁⢀⣴⠏⣰⠏
⠀⠀⠈⢷⡀⠙⢦⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⡴⠋⢡⡾⠁
⠀⠀⠀⠀⠙⣦⡀⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⢀⣴⠋
⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⡴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⣤⣖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣌⣿⣯⣟⣹⣬⣿⣷⣿⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⠿⠛⠻⠻⠿⠿⠿⠿⣿⣿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢶⣶⣦⣀⣀⣠⣶⣶⣖⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⣻⣿⣿⡏⣒⡀⣿⣿⣿⣿⣿⣿⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡹⠟⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⡇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⣅⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣍⣁⠲⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣆⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣦⣀⠀⣰⣟⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⣀⣴⣶⣄⡈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠟⠉⢹⣦⡘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⣄⡀⠈⣿⣷⠘⣇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣿⣿⣿⡟⠛⢷⡄⢹⣿⢀⣿⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣝⣿⣿⣿⠀⠀⠁⢸⡟⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠓⠙⠀⠀⠀⡼⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠖⠒⠂⠀⠀⢀⠠⢊⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠂⠀⠀⠀⣡⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣴⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣦⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡦⠀⢀⣠⡾⠛⠛⠒⠒⠒⠚⡛⣦⣄⠲⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠒⠿⢶⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⢠⠚⠁⡄⠸⣇⠀⡀⠀⠀⠀⠀⠀⡠⠀⠐⠋⠀⠘⠁⠚⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄
⠀⠀⠀⠀⠀⠈⠄⡄⠰⠀⢛⣼⠀⠀⠀⠤⠂⠉⠀⢀⡀⢀⣀⣐⣄⣠⠀⠀⠈⠉⠻⠷⠀⠀⠀⢀⣀⣀⣀⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠾⣦⡳⡀⡟⠀⠀⠀⠀⢀⢴⠀⡀⠙⠿⢿⣿⣿⣽⣝⣢⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⢀⠠⠟⠿⣿⣿⠀⣴⠋⠀⡂⠀⠈⠉⠲⣶⣤⡝⠋⠃⠀⠹⠗⠒⠢⡀⠀⣀⣤⡶⢦⣤⣞
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣇⢸⠇⣴⡹⠁⠄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣇⣀⣉⡿⠛⠐⣼⣿⠛⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠎⠉⠉⢿⠀⠀⠀⠉⣤⣷⠀⠈
⠀⠀⠀⠀⠀⠰⡀⢆⠀⠀⢀⠀⡋⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣀⡴⠞⠡⠄⠀⠀⠠⠀⠀⠀⠀⣠⢏
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣄⣈⢳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠁⢸⠂
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠈⠉⢿⡏⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢿⡆⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠶⠐⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡟⠀⢑⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⡀⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣤⣰⡿⠀⠀⠀⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⢁⠬⠁⠌⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣁⢰⣧⡞⠂⢤⠀⠈⠀⠀⠀⠀⠐⠖⠆⢸⡷⠋⣠⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢯⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢲⣄⡈⠳⣏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⢉⢻⣶⠿⠀⣀⣷
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠲⢿⡇⡀⠘⡟⠀⠀⠀⠀⠀⢹⣧⣾⠁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡒⣾⣿⣀⣶⡇⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠻⠿⠋⡕⠀⠀⠀⠀⢀⠐⠉⡒⠖⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢲⣆⠁⠑⣄⠀⠀⣾⡠⢠⣇⠨⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠆⠀⢻⡆⠀⣿⢃⣾⠃⢸⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⡸⡄⠈⠟⠀⢹⣾⡏⢠⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣀⢷⡁⠀⢸⠀⠈⣽⡁⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠏⠿⡀⢸⠀⠀⠙⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣛⣛⣹⣯⣩⣉⣿⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣴⣶⣿⣷⣶⣤⣀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣻⡿⢋⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾⣿⡿⠟⡱⠋⠁⢋⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣉⣉⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⣾⣿⡿⠁⠀⠀⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣀⣠⣄⣠⣵⣶⣶⣶⣾⡿⠿⠟⠋⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣏⠁⠀⠀⢀⣦⡽⠛⠛⣩⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣬⠋⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⢀⡴⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠃⠀⠀⢰⡇⠀⠀⢰⣿⡿⠛⠋⠀⠀⣀⠤⢘⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⠀⠀⠀⢈⠄⠀⠐⠛⠁⡀⠀⢀⣀⣠⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡂⠀⠀⠀⠘⣰⣿⠿⠉⠉⠉⠛⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⡆⠀⠀⠈⣷⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢻⡀⠀⠀⠈⢧⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣿⣀⡀⠀⠀⠉⠠⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⢿⣿⣦⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠙⢿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠂⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⠤⢤⣤⡤⠴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠶⣄
⠀⠀⠀⠀⣰⠟⠀⠀⡀⠀⠀⠈⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢰⠏⠀⠀⠀⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢳⡀
⠀⠀⠀⢷⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⢸⡄⠀⠀⢸⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⣤⡾⠋⡇⠀⠀⠀⡟
⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢹⡀⠀⠈⡀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⡇⠀⠀⡼
⠀⠀⠀⠀⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢰⡇⠀⢠⠇
⠀⠀⠀⠀⠀⢸⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣠⣼⣿⣶⣶⣶⣶⣶⣶⣾⣇⡀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼
⠀⠀⠀⠀⠀⠀⣧⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠸⡄⢸⡄⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢳⠀⡇⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢰⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡧⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢸⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣤⣰⣀⣀⣤⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⣤⡀⠄⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⡤⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠙⢦⣤⣶⠁⠀⠀⠀⠀⠉⣶⣤⠖⠉⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡅⠀⠀⠀⠀⣀⡀⢨⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠔⠋⠀⣀⣴⡾⠿⠻⣿⣆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣠⡞⠉⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣾⣿⣶⣦⠀⠀⢴⣒⣁⢸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⣿⣿⠋⠉⠀⠁⠀⠈⠉⠁⠠⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⡄⠀⠀⠄⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣍⠀⠰⣟⡳⠆⠀⣠⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢷⣄⣀⣀⡤⠚⣿⣿⣿⡿⣿⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⡆⠙⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠙⢉⣿⠙⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢻⣯⠉⠁⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠑⠀⠀⡈⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠐⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠇⠴⠃⢳⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣿⡇⠀⠀⠄⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠟⠀⣄⣼⡿⢿⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⣢⡿⣿⣧⣰⠀⠸⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠒⠀⢹⠟⠁⢈⣿⣿⣷⣶⣶⣾⣷⣶⣶⣾⣿⣿⡋⠈⠻⡟⠀⢘⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢆⠀⢸⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⡇⠀⡰⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠃⠘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁⠀⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠛⠻⠿⠛⠉⠉⠉⠉⠉⠉⠙⠻⠿⠋⠁⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠒⢶⣦⡈⣰⣏⠐⢦⣀
⠀⠀⠀⠀⣤⣼⣭⣿⣤⣌⣩⣾⣷⣆⠀⠀⠀⠀⠄⣅⣂⠀⠉⣿⢿⣾⣿⣶⣌⣷⡄
⠀⠀⠀⢰⣿⣿⣛⢙⣿⣿⡿⢶⠾⢵⣦⡴⠚⢓⣨⣟⣦⣹⣦⡙⣮⢻⡿⣿⣿⢻⣿⡄
⠀⠰⠀⣴⣿⣿⣟⣂⣀⢉⢽⣮⣽⣛⠋⠂⠀⠐⠠⣾⣿⣿⣯⣿⣎⣧⣱⠘⢿⣷⠃
⠀⡇⠘⢿⢳⣬⣍⢡⣼⠓⣩⠞⠁⡀⠙⠃⣠⣿⣶⣶⣬⣙⢧⡲⣬⠻⣿⠆⢲⡝
⠀⢡⠀⣦⣵⣮⣭⣥⡾⢠⠞⡠⠈⠀⠀⠀⣿⡏⠁⠈⠙⠻⣿⣿⡜⣧⣽⠗⡋
⠀⠀⠀⠙⠂⢀⣖⣣⣴⣯⠎⠀⠀⠀⠀⠀⠿⠈⣀⢀⠀⢀⣀⡉⠻⣦⢿⣦⠁
⠀⠀⠀⠀⠀⠈⡽⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣸⣿⣷⠄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⡅⠰⠛⠛⠛⠛⠃⠀⠀⠈⣿⣿⣿⡿⢿⣿⠟⢻⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠸⢾⠃⠀⣴⡿⢿⣿⠢⠀⠀⠀⠻⣷⣿⠿⢿⡋⠀⢸⡏⡛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⣆⠀⠀⠀⠀⠀⠙⠀⢨⠀⢑⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⠆⠀⠀⠀⣠⠏⠀⠈⠁⠸⡀⠀⢀⢀⡀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀⣤⠿⠃⠐⣄⠀⠀⠀⠁⠀⠀⠚⠁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠠⣴⣿⣷⡷⠻⠉⠀⣠⡾⡀⠈⡄⠀⠀⠀⠀⢀⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡄⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⡼⠋⠀⠈⠳⢤⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠒⠶⠶⣤⣀
⠀⠀⠀⣠⠞⠉⠀⠀⢀⣀⡀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⢀⣀⡤⢄⣀⡀⠀⠙⢳⣄
⠀⢀⡾⠁⠀⡠⠒⠉⠁⠀⠈⠙⢢⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡴⠉⠀⠀⠀⠀⠉⠳⡄⠀⠹⣆
⠀⣸⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀
⠀⣿⠀⢰⠁⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⡷⠀⢸⠇
⠀⢻⡀⠈⡆⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡇⠀⣾
⠀⠘⣧⠀⢱⠀⠀⠀⡰⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢹⡀⠀⠀⡼⠀⢰⠇
⠀⠀⠹⣆⠀⢣⠀⠀⢣⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠀⠀⢀⡼⠀⠀⠴⠁⢠⡟
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⠒⠒⠉⠒⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠉⠉⠉⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠙⠷⢤⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

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

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣷⣽⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣷⣿⣷⣮⣿⣷⣿⣿⣿⣶⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠛⠿⠿⠿⠿⠿⠟⠋⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⣷⣤⣀⡀⠀⢀⣀⣤⣾⡿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠷⢢⣭⣉⠛⠛⣛⣛⣉⣥⠐⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⠁⢀⣄⣿⡼⠁⠀⠀⠙⣯⣿⣿⣤⡀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣛⣁⣀⣠⣴⠟⣾⡏⠀⢀⣀⡀⠀⠈⢿⣿⣷⢳⡀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⢻⡄⠀⠘⠻⠃⠀⠀⢸⣿⡟⠈⠻⢷⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⡀⠌⠀⢄⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠛⠉⠀⠀⠀⠀⠈⠙⠻⠯




⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠳⠀⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠁⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⣤⣀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⠻⣦⠀⢀⣀⠀⠸⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⣿⡄⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣀⠀⠈⣷⡀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢨⣿⡯⠀⠀⢀⣿⣇⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣹⡇⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢠⣿⣿⡏⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⢻⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⢸⣿⡿⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⣇⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⡏⣿⣿⣿⠁⠀⠀⣿⠃⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⣿⠀⠀⢺⣿⣿⣻⣿⣠⠀⣠⣿⣿⢯⡉⠀⠀⠀⣿⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⡆⠀⣼⠟⠁⠀⠀⠀⠀⠈⠈⠁⠀⠈⠐⢤⠀⠃⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⡀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣆⠀⠀⠀⠐⠈⠓⠉⠉⠉⠙⠻⣄⠀⠀⣸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣠⡏⠀⠈⠛⠃⢄⠀⠀⠀⠀⠀⠀⠉⠀⠈⣄⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠀⣿⢱⠃⠀⠀⠀⢬⣳⣞⡠⠂⠀⠀⠀⠀⠀⠸⠃⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀⣴⣷⡖⠺⣷⡀⠀⠀⣈⣏⡀⠀⠀⡀⠀⠀⣴⣶⣀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠞⣛⣿⣷⡀⠘⠋⠻⡟⢿⣿⠁⠛⠻⠇⠰⣶⣿⡿⠿⠃⢀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⠛⢟⣿⡿⠢⠀⠴⠒⠛⠛⠛⠂⠶⠀⠀⠘⣯⡽⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣠⣿⣏⡾⠦⠄⠀⠀⢀⢀⣀⡀⠀⠀⠀⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⠏⠑⠹⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠰⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⣼⠃⠀⠀⣀⣿⠋⢿⣿⣿⡿⣮⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠐⠀⠰⣎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠀⣸⡀⢰⢇⣄⡍⣡⠉⡏⢁⣼⠛⣿⣿⣿⣿⠿⣿⣿⡇⠀⠆⠀⣴⠀⠀⠀⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠁⠀⠀⠈⣿⡛⠙⠛⠁⢸⡧⢀⡷⠙⠋⢹⣷⡟⠙⠃⠀⢰⡦⣠⡐⢷⣦⡀⠀⠁⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠚⣭⣶⣿⣷⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣴⣾⣿⣷⡀⠈⣿⣿⣿⡇⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⣛⢉⣩⣭⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢛⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣤⠀⢀⣠⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠛⢛⣉⣉⣭⣬⣽⣿⣦⣀⣀⣀⣴⣿⣿⡿⣣⣾⣿⡿⢋⣿⣟⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣟⣵⣿⣿⡟⢠⣿⣿⣿⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣬⡙⢿⣿⣿⣿⣿⠿⠛⢛⣉⣉⣉⣩⣭⣥⣤⣶⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢛⣉⣥⣴⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣶⣦⣬⡙⠿⣿⣿⣿⣿⣦⡹⣿⠿⠛⠻⠛⠛⠛⢛⣋⣥⣶⣿⣿⣿⣿⣿⣿⣷⣤⣬⣉⠁⣁⣴⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣛⣉⠽⣟⣫⣴⣾⣿⠋⣾⣿⣿⡇⣴⣄
⠀⠀⢀⣴⣦⣄⣈⡙⠻⢿⣿⣿⣿⣦⡙⢿⣿⣟⠻⠛⠻⠿⠿⠿⢛⣫⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⢸⣿⣿⡟⢠⣿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣶⣤⡙⠿⣿⡿⢻⣾⣷⡾⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⣛⣯⣥⣤⣴⣷⣿⣟⣋⣠⣴⣿⣿⣿⢁⣿⣿⡿
⢀⣙⣙⠛⠛⠛⢿⣿⣿⣿⢿⣷⣾⡆⣷⣿⣿⣴⣷⣿⠛⣿⣿⣿⣎⢻⣿⣿⣦⠀⠉⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⠟⢡⣾⣿⣿⠇
⣿⣿⡿⠿⠛⢛⣛⠟⣽⢃⣿⣿⣿⡇⢹⣿⣿⣷⣹⣿⡇⢹⣿⣿⣿⣆⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢧⣴⣿⣿⡿⠋
⠋⣡⣴⣾⣿⣿⢋⣾⡇⢸⣿⣿⣿⡇⢸⣿⡟⢿⣿⣿⣿⡈⢿⣿⣿⣿⣇⢹⣿⣿⡇⠀⠀⠀⠀⠠⡄⠘⠛⠁
⣿⣿⣿⣿⠟⣵⣿⣿⡇⢸⣿⣿⣿⠇⣾⣿⣇⠸⣿⣿⣿⣷⠈⣿⣿⠿⠟⠀⠉
⣿⣿⠟⢡⣾⣿⣿⡿⢀⣿⣿⡿⢣⣾⣿⣿⣿⠀⠿⠿⠟⠛⠁
⠟⢁⣴⣿⣿⡿⠏⣴⣿⣿⣿⠇⠘⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠾⠟⠛⠛⠛⠛⠿⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⡸⠛⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⡠⠋⠀⠀⠀⣀⡴⠓⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡞⠁⠀⠀⢀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠹⣷
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⣠⠏⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢹⣇
⠀⢰⡿⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⣰⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢿⡀
⠀⣿⠇⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡾⣿⣷⠀⠀⠀⠀⠀⢸⡇
⢸⡟⠀⠀⠀⢀⣾⠋⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠈⠠⠤⠤⠤⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣧
⣿⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⠋⠄
⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣿⠇⠀⠀⠀⠀⠀⡼
⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠋⠉⠉⠉⠉⠛⠛⢻⣿⡟⠀⠀⠀⠀⠀⢰⠇
⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢠⡟
⢻⣇⠀⠀⠀⢿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⢀⡾
⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⢀⠞
⠘⣿⡄⠀⠀⠀⣧⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡴⠋
⠀⢻⣇⠀⠀⠀⠘⡄⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⢀⣴⠎
⠀⠘⣿⡀⠀⠀⠀⢣⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢿⣷⣄
⠀⠀⢹⣧⠀⠀⠀⠘⣆⠀⠀⢳⡀⠀⠀⢸⡄⠀⠀⠘⠤⣀⣀⣀⣀⣤⣤⠶⠚⠋⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢻⣆⠀⠀⠀⢹⡆⠀⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡀⠀⠸⡆⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⢷⡀⠀⠻⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠱⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠃⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣄⣀⣀⣀⣀⣠⣴⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡐⠐⢶⠄⠦⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠈⠡⡗⢤⢳⠄⣤⣱⠉⢨⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢹⣲⠇⠊⠀⠀⣼⣷⣦⣚⣙⡁⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡖⣸⣤⡾⠎⠀⠀⠀⠙⢯⣟⡟⣷⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠉⠁⣶⠆⠀⠀⣶⡆⠁⢸⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⢀⠄⠛⠳⣤⠴⡋⠗⢀⣼⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠗⡄⠇⠀⠀⠘⠀⠀⠁⠀⠘⢿⣷⣜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠁⡄⢸⠀⠀⠀⠀⠀⢰⠀⡄⣎⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣏⠀⢄⠀⣸⠀⠀⠀⠀⠀⠸⡁⠀⠏⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠎⢈⠁⠀⠄⠀⠀⢀⠀⠉⠀⢲⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠛⠃⠀⠂⠀⠀⠐⠀⠄⠀⠀⠘⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠣⢀⣀⣀⣀⠀⠠⠤⠔⠓⠒⠒⠐⠒⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢛⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠤⠶⠄⠀⠀⡠⢊⣵⣿⣿⠷⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⣱⣶⣯⡉⠳⢦⣀⣠⣤⠴⠶⠖⠚⠛⠓⠻⠷⠿⣿⣿⣋⢸⢸⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⢙⠹⣿⣿⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡇⠀⣠⠄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡰⠂⠘⠛⠓⠶⣍⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⢤⡀⠀⠀⠀⠈⢷⡶⡟⠛⠲⣤⡈⠻⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢀⡴⠞⠛⠓⢦⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠉⠃⠀⠀⠀⠀⣷⢰⠀⠀⢀⢹⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠇⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡷⠷⢸⣶⡇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⡿⡷⠿⠆⢺⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣾⠀⠀⠀⠀⢸⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠓⣶⠆⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣴⠟⣹⣿⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢮⣛⢶⣬⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣋⣥⣪⢕⣿⠇⠀⠀⠀⠀⢰⡇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣼⢫⡑⠮⣷⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣾⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠓⠦⣭⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⡿⢴⣶⣿⡟⠛⢫⡍⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⡷⣻⣿⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠠⠖⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢛⠿⣿⣻⣿⠿⠁⣩⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠿⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡏⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⣾⣷⣀⠀⠀⠀⠀⠀⠐⠏⢀⡾⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢋⢿⡆⠀⠀⠀⠀⠀⠈⢿⡄⣼⠟⠉⠉⠉⠉⠀⡀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠈⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⣦⣰⠀⠀⡀⠐⣀⣼⠻⣆⡀⠀⠀⣒⣢⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠈⠉⠛⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⣀⠈⠑⢦⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡄⡀⢁⣀⡀⢸⣯⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠈⠁⡍⣰⠚⠁⠀⢱⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠞⠀⡧⠀⠀⢀⡸⠋⣯⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢐⡨⠤⠴⠒⠋⠀⣰⣷⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠙⠠⣀⠀⠀⣀⣴⠊⠁⢀⣀⣤⣶⢾⡿⠛⡛⡋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡀⠀⠈⠉⠉⠉⠙⠛⠻⠛⠛⠉⠁⣄⣴⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢁⢻⠘⡗⢲⠲⡖⢷⠶⡶⢿⠛⡟⣻⣹⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠘⡆⣧⠸⡄⣇⢸⠀⡇⣿⢸⣇⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢰⣿⣼⡀⣧⣿⣿⣤⣧⣿⣿⣾⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠁


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

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⢻⡄⠀⠀⢸⠀⠀⠀⢿⣤⣤⢤⣤⡀⠙⠶⣶⣦⠀⠶⢋⡼⠀⢀⣤⠤⣤⡀⠀⣠⠴⠶⠶⠾⢿⡙⠓⠲⠶⠴⠞⠀⠀⠘⣧⠀⠀⠀⡇
⠞⠋⠀⠀⠀⠈⡆⠀⠀⠈⠁⣠⠶⢤⣵⠀⠀⠀⠙⠶⠒⢿⣀⡾⢋⡤⠆⡼⠃⢰⡇⢀⡀⢰⣤⡟⢷⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣀⣿⣤⠾⠻⣄⣠⣤⣤⡀⠀⠀⢻⠿⠷⠶⠛⠁⠀⠸⣶⠟⠛⠃⠀⠀⠘⢧⣤⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⣇
⢴⡖⢶⡆⠀⠀⠈⠙⠉⠉⠁⢙⡄⠀⠀⠉⠁⠀⢀⡿⠀⠀⠀⣷⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⣶⠀⠀⠀⠈
⠊⢻⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⣀⣤⡴⠏⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠙⣧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣁⣀⡿⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣶⠄⢸⡟⢢⣾⡆⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠰⣿⣧⣽⣾⡗⢿⡿⢻⣿⡛⢯⠗⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡄⢀⡄
⠒⠀⠀⠀⠀⣴⢳⣄⣷⣿⢾⠙⣿⡆⠱⠟⠈⠛⠙⠟⠁⠀⠀⢀⣀⢸⠏⠷⠒⣲⠆⠀⠀⢀⣀⣀⣀⣀⣈⣂⣤⣢⣀⠒⠂⠀⠀⠀⢠⡞⣆
⠀⠀⠀⣾⢷⣸⣿⡯⣄⠙⠾⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠄⣀⠘⣧⡀⠀⢰⢫⣽⡍⢉⡩⣭⣉⠉⠉⠙⢇⠀⠀⢰⡟⣦⣿⣿
⠀⠀⠀⢨⣿⠣⡜⠓⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠉⠑⠛⠃⠀⠸⡌⠉⢱⡏⡽⠳⡍⣧⠀⠀⢻⠀⠀⠀⣼⡟⢤⠙
⡇⠀⠀⠀⠈⠓⠛⠀⠀⠀⢠⡖⣴⠋⢱⠀⢀⡤⢤⣄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⡇⠀⠘⢧⣛⣛⣥⠏⠀⠀⢻⠀⠀⠀⠀⠙⠚⠃
⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⠳⣤⣰⠏⢰⡏⣀⢠⠀⠉⠛⠤⠤⠤⠺⡇⠀⠀⠀⠀⠀⠰⣦⣀⣤⣤⡬⢭⡤⠤⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢉⠳⣄⣁⣀⠼⡇⠉⠉⠀⠀⠀⡀⣤⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠛⠛⠀⢩⡽⠛⠛⠛⢦⣀⠶⣴⠦⠟⢋⡵⠋⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⡀⠀⠀⣠⠞⠛⢳⡄⠀⠀⠀⠀⠀⢀⠟
⠀⠀⢀⣀⡤⠞⢁⠀⠀⠀⢠⠀⡏⠀⠀⠀⠀⠀⠉⢻⡟⠲⢾⠋⠀⠀⠀⠀⣠⣤⣹⣾⣁⠀⣴⠋⠙⠳⠾⠁⠀⠀⢸⡇⠀⠀⣀⣠⠴⠋⡀
⠀⠀⠈⢧⣀⠀⢷⠶⢶⠟⢚⣷⠁⡀⠀⠀⠀⠀⠘⠻⠟⠠⠞⠻⠀⠀⠀⠀⣬⣏⣿⠯⠛⠀⠘⢦⣀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠹⣦⡀⠰⡷
⠀⠀⠀⠀⠉⠛⠓⠶⠄⢾⠋⠹⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢌⡻⠿⠾⠗⠀⠀⠀⠉⠛⠶⣤⣴⣋⠀⠀⠀⠀⠀⠀⠙⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⢠⣦⢙⣿⣏⣶⠄⠀⠀⠀⠀⠀⠀⠴⠋⠁
⣠⡶⠛⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢆⣿⠿⣟⢶⡹⣆⠀⠀⠘⣻⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣆⣠⠞⠋⠉⢻⡆
⢟⠀⢰⣤⡿⠀⢀⣀⡀⠀⠀⠀⠀⠀⢺⡀⢿⣝⠛⠻⠇⣛⠸⡀⠀⠘⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠛⠁⣾⠻⡇⠀⣦⣸⠏⠀⣀
⠘⣷⠚⠁⠀⢰⠋⠀⠙⣦⠀⠀⠀⠀⠀⢿⡀⠈⠻⠦⠴⣿⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣉⡀⠀⠀⠀⣸⠃⠀⢻⡶⠋⠀⠀⡾⠁
⢀⣸⠆⠀⠀⢸⡀⠀⠀⢹⠶⠶⠒⠶⣄⠈⠛⠻⣷⠒⠛⣡⠞⢀⣤⠶⠒⢶⡄⠀⡴⠛⠛⠛⠛⢻⡄⠈⠙⠛⠙⠃⠀⠀⢀⡷⠀⠀⠀⣧
⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⠛⢲⣾⠀⠀⠀⠈⠙⠉⠻⣤⣏⣠⠞⣡⠞⠀⢸⠇⣰⣄⡼⠶⠏⢻⡀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠸⣆⣤⣤⡤⣿⠶⠋⠙⣧⠴⠶⠶⣄⠀⠀⠙⡏⠉⠛⠁⠀⠀⠘⠟⠁⠈⠁⠀⠀⠈⠳⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⣺⣯⣹⠇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠻⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣿
⠁⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣤⣤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠶⠞⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠶⣤⣤⠟⠀⠀⠀⠀⣄⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢰⢻⡀⣸⣯⣲⣽⣇⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋
⠀⠀⠀⠀⠀⠀⡀⠀⡞⣷⣈⣷⣷⠻⡿⣏⢹⣟⣹⣻⡍⠳⠋⠀⠀⢀⡿⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠦⠠⠆⠀⠀⠀⠀⠀⠀⢀⡀
⠉⠀⠀⢀⡀⢿⣹⣦⠿⣿⢫⡘⢿⠗⠈⠛⠀⠉⠀⠉⠀⠀⠀⢠⣤⡼⠃⠙⢉⡽⠃⠀⠀⣠⣤⣤⣤⣤⣤⣥⣶⣷⣦⡉⠀⠀⠀⣀⠰⣏⣧
⠀⠀⠀⢿⣹⡾⢿⡟⣦⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⢢⣤⣌⣷⡄⠀⢸⠹⣾⡇⣠⢔⡒⣤⡀⠀⠈⣃⠀⠀⠸⢏⣷⠿⣟
⡂⠀⠀⠸⢿⣕⣆⠉⠁⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠈⠉⠁⠀⢸⡆⠀⢸⡇⣏⣙⡆⣿⠀⠀⣽⠀⠀⠠⠟⣯⣲⡌
⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡏⠛⠁⡸⠀⣴⠖⠚⠲⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠻⠭⠭⠞⠃⠀⢀⣹⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣙⠢⡼⠃⢸⡇⢤⣴⠀⠀⠉⠛⠒⠛⢙⡇⠀⠀⠀⠀⠀⠈⠷⠴⠖⠒⠒⠒⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⣠⠙⣦⢤⣤⣛⣧⠀⠀⡀⠀⠀⣤⣳⠄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⣀⡞⠁⠀⠉⠁⠀⢰⠞⠉⠉⠉⠳⢤⣻⡾⠛⢋⣡⠞⠁⠀⠀⠀⠀⣴⢳⡄⠀⠀⣀⢀⡀⢀⡾⠋⠉⢹⡆⠀⠀⠀⠀⠀⣰⠋
⠀⠀⢠⡶⠚⠋⡠⠀⠀⣀⣰⣀⡇⠀⠀⠀⠀⠀⢀⣹⣏⠙⢯⣁⠀⠀⠀⠀⠶⣶⣼⣿⣤⠀⢾⡁⠈⠉⠛⠀⠀⠀⣸⠃⠀⠀⣶⠔⠛⢁⡄
⠀⠀⠀⠛⢦⣀⡛⠛⠛⣉⡱⢿⣀⡄⠀⠀⠀⠀⠀⠙⠋⠐⠋⠉⠀⠀⠀⠀⢾⣤⣿⢛⡉⠀⠈⠳⢤⣀⠀⠀⢀⡴⠋⠀⠀⠀⠘⠷⣄⣘⠟
⠀⠀⠀⠀⠀⠉⠉⠛⠋⣻⣁⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣟⣛⠛⠃⠀⠀⠀⠀⠉⠛⣲⠾⠥⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⢀⣀⣠⣀⡀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⣀⣴⣄⡲⣄⠀⠀⠀⢸⡷⣨⡿⠷⠿⠂⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣴⠟⠁⠀⣌⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣻⣿⣻⣯⡿⣌⢣⠀⠀⢀⡽⠿⣛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⢾⣧⡾⠋⠀⢠⡹⠇
⢫⡄⢸⡶⠋⠀⣤⠶⣄⠀⠀⠀⠀⠀⠹⣄⠻⠦⣄⠙⠁⣭⠘⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠁⢀⡿⠘⣧⠀⣷⠾⠁⢀⡴
⠈⢿⠁⠀⠀⢸⠁⠀⠈⣷⠀⠀⠀⠀⠀⠻⣤⣀⣈⠛⣙⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⠶⢤⣀⣀⣀⡼⠁⠀⠸⣏⠁⠀⠀⡟
⣠⠾⠃⠀⠀⠸⡄⠀⠀⠘⠛⠋⣉⠛⢦⠀⠀⠙⠷⣏⣡⣴⠋⣠⠞⢋⡉⢹⠆⢠⡟⠁⠀⢀⠀⣽⣆⠀⠀⠀⠈⠁⠀⣀⡴⠟⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣿⠉⣹⢿⡀⠀⠀⠀⠀⠀⠘⢷⣷⣼⣋⡴⠋⠀⢸⣅⡼⢦⡞⠛⠁⠹⡆⠀⣀⡴⠶⠛⠁⠀⠀⠀⠀⠀⠘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⠄⡀⣄⠍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠒⠉⣂⡬⣁⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡴⢊⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⠀⠀⡴⡫⠊⢁⠄⠠⢄⠀⠀⢀⠔⠉⠲⠀⠀⠀⠀⠀⠀⣎⡉⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⡜⡁⢠⡞⡔⠀⢀⡤⠀⠀⠀⢣⠀⡎⠀⠀⠐⠥⢀⠀⠀⠀⠀⠰⠀⢭⠤⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡾⡸⢠⡓⡜⠀⠐⠀⠀⠈⠢⣀⠀⣣⠅⢠⠎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⡐⠀⡼⠳⠁⡞⠜⠀⠀⠐⢄⡀⠀⡀⠘⢣⣽⣷⢃⣀⣢⠔⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠁⢰⡷⠃⢰⢍⠂⠀⠀⠀⠀⠀⡉⢭⠓⢿⢿⡿⢟⡉⡉⠉⠑⢆⠀⠀⠀⣘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⣼⣠⠀⢸⠪⠀⠀⠀⠀⢠⠊⠀⠈⠶⠉⢸⡗⠆⠙⠑⠀⢀⡼⠀⠀⣰⠃⢠⠆⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠆⠀⢯⣼⠀⢰⢽⠀⠀⠀⠀⠈⠢⠤⠄⠀⠀⡘⢃⠀⠀⠀⠀⡅⠀⠀⣰⠓⢀⠿⡔⠀⡜⠁
⠀⠀⠀⠀⠀⠰⡆⠀⢸⠙⡆⠈⣟⡆⠀⠀⠀⠀⠀⠀⠘⠂⠒⠁⠈⢳⣤⠔⠊⠀⢀⡜⠃⣠⠟⡩⠀⣼⡙
⠀⠀⠀⠀⠀⠀⣧⠀⠘⣷⠚⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡑⢄⡠⠋⢀⣴⢋⠟⢀⡜⡬⠁
⠀⠀⠀⠀⠀⠀⢈⡀⠀⣈⠀⠈⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠊⠀⣴⣿⡷⠃⢠⣾⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠗⠾⡀⠐⢤⡀⠀⠀⠀⠈⠲⠄⡀⠀⣀⣀⡠⠔⠀⢁⣠⣶⠚⡲⠋⢀⡴⣿⣾⣷⡶⠶⣲
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠢⡀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠾⠛⣉⠕⠋⠀⡠⡛⡥⠋⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠒⢄⡈⢙⠲⠦⣀⡀⠀⠀⠀⠀⠀⠓⠉⠀⣀⠰⢫⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣠⠈⠑⠢⠤⢀⣨⣇⡄⠀⢀⣀⡤⠔⣋⣥⣖⠉⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠓⠮⢦⣠⣠⡻⠲⠗⣚⣙⡡⠜⠚⠁⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠂⠡⠀⠨⠐⡠⢀⠄⡉⢍⠡⡀⠄⡀⢔⠠⣐⠄⡂⠄⡂⠅⡂⢅⡪⠑⠌⠂⠅⠪⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡴⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡇⠀⠀⠀⠀⠀⣰⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⡇⠀⠀⠀⠀⢠⢧⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⡇⠀⠀⠀⢀⣿⠇⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠟⠛⠉⠉⠉⠛⠻⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠛⠃⠀⠘⠛⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠄⣀⠘⡛⠃⣀⠠⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠘⠄⣍⠠⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠛⠒⠒⠒⠛⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣟⠁⢹⠆⠀⠀⠀⠰⡏⠈⣻⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢛⣿⣷⣶⣶⣾⣿⣿⣿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠿⠿⠿⠿⠿⠟⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠁⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⢊⠔⠡⠈⡛⡐⢌⠢⠀⠀⠀⠀⠀⢐⠁⠉⠉⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣈⠘⡢⡀⠀⠀⠠⣄⣀⠅⣀⣃⠨⠈⠦⡀⠀⠀⠀⠀⠌⠉⠋⠒⠋⠁⠈
⠀⠀⠀⠀⠀⢠⠊⣄⠀⠙⠳⠀⠁⠀⠰⠒⠀⠤⠤⠤⠄⠀⠂⠈⡇⠀⠀⠀⢰⠳⢦⠦⠤⠴⡶⠞⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⡀⠀⠀⠀⠀⢃⠀⢤⠀⠀⠀⠰⠆⢰⠀⠀⠀⠀⠀⠂⣈⠁⠀⠀⢁⠐
⠀⠀⠀⠀⢆⣹⢳⡤⠐⠊⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⠊⠉⣂
⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⣴⣾⡄⠀⢠⠅⢀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡌⠀⡡⢄⠀⡀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡛⠉⠀⠀⣬⣀⡈⡒⠉⣴
⠀⠀⠀⠀⠀⠀⠸⠠⠱⠢⠀⠀⠀⠀⠀⠀⢩⣙⠬⠚⠉⠀⣂⠀⠀⠀⢐⠁⠰⠀⣀⠈⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠸⣈⡉⣉⣃⠀⠀⠀⠀⢘⠁⢀⡠⠄⠂⠁⠀⣱⠀⠀⢸⠙⡴⢦⣄⠴⠀⠀⠀⡠⢔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡒⠂⠨⡄⠀⠀⠀⠀⠏⠀⠀⣀⠆⠐⠉⢈⠄⠀⣖⢣⠜⡝⠁⠀⠀⠀⠜⠀⡜⢅⢌⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠚⠁⠀⠀⠀⠀⠈⢎⠀⡀⠄⠐⠊⠁⠀⢰⣏⢦⠋⠀⠀⠀⠀⠀⠂⡡⠣⣊⣣⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠁⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠁⠀⠀⠀⠀⠀⠀⠙⠄⡁⢈⡁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⢜⡰⠦⠤⣤⣄⣀⣀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠑⠘⠋⠀⠀⠀⠀⠀⠀⠈⣉⠙⠃⠀⠀⠀⠀⠀⣀⡤⠴⠒⠲⡤⣀
⠀⠀⠀⠀⠀⣿⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡏⠀⣀⢄⡀⠀⠀⡔⠉⢀⠀⢀⠀⣀⠈⢷⡀
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢠⡤⠀⠀⡀⠀⠀⠀⢉⠒⢠⣿⣀⣀⣁⡼⠇⠀⢸⡃⠀⠀⠄⠀⠑⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⣿⠃⠀⠘⠧⣴⠃⢰⡟⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠕⠀⠀⠑⠄⠔⠁⠀⢠⠃
⠀⠀⠀⣆⡀⠀⠀⢀⣿⠀⣿⢀⣿⡠⢱⡟⠀⣿⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⠀⣀⣀⡴⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠈⠁⠀⠁⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢔⣠⣾⣿⣿⣿⣿⣿⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣁⣥⠖⠛⠛⠛⠿⣿⣿⣿⣿⣿⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⣒⣂⡀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣹⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣆⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⢰⣯⣥⣾⠃⠀⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡿⣿⣿⣿⣿⣧⡀⠀⠈⠈⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠹⣿⣿⣿⣿⣿⣷⡶⠆⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⡄⣈⣛⣛⣛⣛⠻⢫⡄⠀⠼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠟⠉⠙⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣧⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿⣿⣿⣿⣆⠈⣻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣾⠟⠛⠟⠚⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠊⠁⠀⠀⠀⠀⠺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⠛⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠉⠲⣽⡇⠄⠀⠀⠀⠀⠀⠀⢀⡜⢠⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠝⠋⠈⠀⠀⠀⢠⣀⡴⣻⠇⣿⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠠⠂⠀⠀⠀⠀⠘⢿⡿⠸⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡖⢀⣠⠀⠀⠄⠤⠠⠤⠾⠷⢾⣿⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣀⣀⡀⡀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠾⣧⣀⣠⡖⢺⡉⢉⡅⡀⠀⠀⠈⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠸⡿⠟⠀⣿⡏⠈⠱⣄⢬⢃⠂⠠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢳⣀⠀⠀⣠⢳⡆⠠⢿⡟⠀⢰⣿⣿⣿⣄⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⡿⠟⠙⠉⣠⡿⠀⠐⣿⡀⠀⢘⡿⢿⠙⣿⠀⢘⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⡇⢀⡅⠀⠀⠀⢹⣿⣕⢸⡏⠀⠐⠋⣄⣰⣆⡈⢻⠈⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢀⡟⠠⣾⠃⠀⠀⠁⢠⣻⣿⣾⡽⠅⠀⢀⠈⢻⠛⢠⡟⢢⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠸⠗⣰⠃⠀⠀⠀⠀⠀⠰⠟⢿⣿⣴⡁⠀⠉⠛⠂⠀⣠⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⢿⣿⣿⣿⣿⣿⣿⡟⠉⠟⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠸⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠙⢟⠿⠁⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠀⠀⢰⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⠼⣤⣿⣦⠀⠀⠀⠀⢃⡀⣄⡠⣀⣯⡀⡀⠀⠀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⢹⣇⠀⠀⠀⠈⣶⣿⣷⣿⣿⡧⢀⠀⢰⣿⣯⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣀⡀⠀⡀⣿⠀⠀⢀⣤⣿⣿⠿⣿⣿⣿⡧⠀⠸⣿⣿⣶⡜⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⠁⠀⠀⠠⠹⠇⠒⠟⠿⠷⠸⠆⠦⠇

⠀⠀⠀⠀⠀⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣆
⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢤⣶⣾⣿⠿⣿⣿⣿⡄
⠀⠀⠀⠰⣿⣿⡗⡀⢨⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢾⡁⠛⢙⠆⠀⠀⠀⠘⣿⣿⣯⠀⡀⣿⣿⡿
⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⣀⣷⡖⠋⣉⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⢠⡋⡀⠘⣿⢤⡬⠂⢀⣠⡄⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⣠⣶⡶⢶⣼⡟⠀⣀⣀⡀⠀⠀⠀⠉⠑⠚⢹⡄⠀⠀⣼⣿⠀⠀⢸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠀⣼⣿⠏⠀⢀⣿⢃⣾⣿⣏⣻⣄⣠⣾⡿⢷⡀⣸⣇⣤⣤⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢠⣿⣿⡏⠙⣿⣿⡇⠀⣿⣿⣤⣴⣿⠇⣾⣿⠃⠀⢹⣿⣿⡏⠙⢺⡟⣿⣿⠏⢹⣿⠀⠀⠀⢠⣿⣿⣿⠉⢿⣿⣷
⠀⠀⣸⣿⣿⣀⣸⣿⣿⠁⠀⢈⣉⣭⣴⡿⠚⣿⣿⠀⣠⡟⣿⣿⠀⠀⣾⢹⣿⡏⠀⣾⡏⠀⠀⣠⠟⢹⣿⣿⣄⣸⣿⣿⡆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⣾⡿⠋⢁⡿⠁⣀⣙⡛⠛⠋⠀⠻⣿⣦⠞⠁⠘⢿⣷⡴⠛⢷⣤⠾⠋⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⡾⢁⣾⠛⣿⣿⢀⣤⡆⢀⣤⠀⠀⣠⣤⣄⠀⢠⣷⠀⠀⣰⡿⠃⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⠉⢻⣿⣿⠛⠿⠟⠋⠀⣾⠃⢠⣿⠏⢸⣿⠃⢸⣿⠀⣼⡟⢰⣿⠀⣼⡏⢀⡴⠏⠀⠀⢀⣿⣿⡏⠹⣿⣿⣿
⠀⠀⣿⣿⣿⣀⣼⣿⣿⠀⠀⠀⠀⢰⣏⣴⡿⠋⠀⣿⡿⠀⣸⡟⢸⣿⠁⠀⠁⣠⣿⠿⣯⠀⠀⠀⠀⢸⣿⣿⣇⣰⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⡿⠋⠀⠀⢠⣿⣧⣤⣿⣇⣼⣿⠀⢀⣴⣿⡏⠀⣿⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣄⣠⣴⠟⠛⠛⠋⠈⠛⠻⣿⣿⠟⠁⠿⠃⠀⢹⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⣿⣿⣿⡏⠹⣿⣿⣷⡀⠀⠀⠙⠛⠉⠑⠶⢤⠀⠀⢀⣶⡄⠀⠠⠶⠖⠂⠀⠀⠀⠉⠁⣠⣿⣿⣿⠋⢹⣿⣿⡟
⠀⠀⠀⠸⣿⣿⣧⣀⣿⣿⣿⣿⣄⠀⠀⠠⠤⢤⠤⠄⠀⠻⣏⠁⢉⡿⠃⠠⠶⠶⠶⠆⠀⢀⣴⣿⣿⣿⣇⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣠⠴⠂⠀⡷⠖⠾⡇⠐⠲⠦⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⣀⣀⣀⡀⠀⣀⣠⣔⢂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣻⣿⣿⣿⣿⣿⣿⢿⣿⡤⢐⡀⣀⠀⠀⠀⠄⠈⢷⡀⠈⢮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣼⣿⢸⣿⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠙⢷⣾⣧⣠⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣚⣿⡿⣻⣿⣧⡈⢷⣿⣷⣔⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣽⣸⡿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣿⠿⠉⠛⢿⣿⣾⢿⠉⠋⠛⠿⠿⠤⠀⠀⠀⠀⠀⠑⢹⣿⣿⣿⣿⣿⡿⠛⠛⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢛⣹⣿⣿⣧⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣠⣾⣷⡿⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⠿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⣀⣀⠀⠀⠈⠀⣈⡴⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⡏⠛⠑⣲⠚⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄
⠀⠀⠁⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⣼⡇⢸⣿⣧⠙⣿⠃⢸⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⢹⡇⢸⣯⣿⠀⣿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠛⠘⠃⠙⠁⠛⠁⠋⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⣤⡴⠆⣶⢸⡆⢿⣟⠀⣿⢹⡇⢹⣿⡏⢸⡏⣿⢸⣷⣾⢰⡶⠆⠀⢀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣇⠠⠈⣿⠀⢹⣿⡇⢸⡏⠀⣿⢿⡇⠀⣿⠁⢸⣇⣿⢸⣿⣿⣸⠋⠀⠀⠛⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠨⡇⠀⠙⠶⠀⠻⠃⠘⠛⠃⠛⠈⠋⠀⠙⠀⠈⠙⠋⠘⠋⠃⠛⠃⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠦⠒⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⣖⠀⠀⠀⠀⣀⠀⠀⡀⢐⠀⠥⠒⠉⠀⠀⢀⡀⢠⠜⢲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣤⣤⣀⠀⠀⢀⣀⣀⠀⠀⢀⣠⣤⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣤⣄⡈⠙⠛⠛⠉⠉⠉⠙⠛⠋⠁⣠⣤⣄⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠉⠉⠙⠁⢀⣀⣀⡀⠘⠉⠉⠙⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠐⠒⣃⠀⠀⣀⠀⠘⣻⡟⠁⢀⡄⠀⢀⣘⠲⢰⡿⠞⠛⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠁⠀⠀⠈⠛⠛⠋⠙⠛⠋⠀⠀⠀⠉⣡⠟⠀⢀⡀⢀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠁⠀⠲⣼⣧⣼⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢸⠃⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡆⠀⠘⠷⣽⡵⠞⠀⠀⠀⢠⣀⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣤⡴⠶⠒⠲⠶⢦⡀⠀⠀⠉⠙⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣙⣦⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠙⢦⣄⡀⠀⠰⣬⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠛⡟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⡤⠶⠶⣤⡇⠀⠀⠀⠀⠀⠀⢸⣤⠴⠶⠦⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡄⠀⡄⠀⢹⡄⠀⠀⠀⠀⢠⡟⠁⢠⡀⢠⡌⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠷⠶⠷⠶⠟⠛⠳⠶⠶⠚⠛⠻⠶⠾⠷⠾⠷⠟⠁


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

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢴⣾⣿⣿⡄⠈⠂⠙⠛⠀⠀⠐⠀⠀⠀⠀⠎⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠋⡿⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣼
⠀⡠⠒⠃⠀⠒⢀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⢀⣾⣟
⠞⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠉⠉⠤⠤⠤⠄⢀⡴⠒⠒⠒⠠⡀⠀⠀⠈⠃⡀⠀⠀⠀⠄⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⣶⣿⡟⢉
⠂⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⣄⡀⢈⢢⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠐⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢯⣿⣿⢿⣿⣿⣯
⠷⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⡠⠒⠀⠀⠐⢉⣿⡿⠄⠉⠏⠛
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢵⣤⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠈⡟⠒⠠⠀⠀⠀⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠙⠧⠀⢀⠀⠀⠀⠒⠤⢤⣿⣿⣿⡇⠀⣿⣇⣠⣴⢅⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠠⣤⡼⣿⣿⣿⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⢈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠠⠀⠀⠀⠑⠀⢀⡎⠀⠄⠺⠃
⠀⠚⠀⢤⡀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢔⣾⠿⠛⢿⡇⠐⠦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠈⠐⠛⢧⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠄⣀⣀⣀⡀⠤⢰⠞⠋⡠⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠁⠀⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠒⠻⣷⢶⣷⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣀⡄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⢆⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠁⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⢸⣇⣸⣀⣠⣾⠿
⠀⠀⠀⢀⡇⠉⠉⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢱⣄⣆⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣽⣧⣾⣿⣿⡿⠿⠃
⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⡜⠁⠀⠀⢀⣴⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⡁⠀⠀⠀⠐
⠀⠀⠀⡀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢤⣀⠀⠀⠀⠀⢻⣿⣷⣀⣠⡄⠀⣤⣿⣿⠟⢀⡀⠀⠀⠀⠀⠢⡄⢀⠍⠀⠂⠉⠷⣁⠂⠤
⠒⠀⡉⠁⠀⠈⠀⠀⠐⠄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠈⠙⢿⣿⡛⠃⢰⣿⣿⣩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣶⣶⣉⡄⠓⢦⣹⣿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠈⠞⠛⠙⠋⢻⡿⢿⠅⣠⣆⠋⣼⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠴⠦⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣠⠖⠊⠉⠉⠀⠈⠉⠙⠒⢤⡀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣒⣚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⠇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠉⠉⠓⠀⠀⢀⠀⠀⠀⠈⡆⠀⠀⠀⡼⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⡸⠁⠀⠀⣰⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠒⠁⣀⠜⠁⠀⢀⡼⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⣀⠔⠋⠉⠉⠀⠀⠀⡠⠋⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠊⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢤⣤⠤⠴⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠥⡠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠐⠀⠂
⣤⠔⡃⠀⡀⢀⡴⢢⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡈⠛⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡐⠶⢶⡆⢰⠋⠉⠱
⠀⠉⠀⡏⠉⠺⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⠈⠉⠴⠄⠋⠤⢤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⣲⣎⠀⠘⡄
⠀⠀⢀⠙⠦⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⢴⠖⠚⠳⣦⣈⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⣵⠀⡇⠀⣰
⢠⠴⠍⣁⠀⠀⢀⡀⠀⡊⠶⢉⠀⠀⠀⠀⠀⠀⠀⡧⢤⡄⣟⢸⡀⠀⢀⣯⡇⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠉⡏⠉
⠈⠒⠤⠃⠀⠘⠀⠐⠀⠙⠂⠚⠀⠀⠀⠀⠀⠀⠀⢧⡐⠂⠘⠦⣭⣩⣵⣛⣔⣒⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣀⣀⣠⠃



⠀⢰⡒⢏⡾⢽⡾⡗⠹⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠂⠹⠁⡠⠿⠂
⠀⠺⡥⢼⣛⢂⠄⢉⣽⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⣁⡀⠀⠙⠢⢀⣀
⠀⠀⠑⠻⣏⣤⠰⢦⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣂⡐⠒⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠒⢤⠋
⠀⠀⠀⠀⠀⠈⠉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⡀⣄⣀⣄⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⣤⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⠶⢶⡶⠶⠶⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢹⢩⢉⠇
⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣄⣨⡤⠎


⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡠⠤⢄⣈⢁⣀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠔⠒⠒⠒⠒⣒⣦⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀
⠀⢼⠀⠐⠀⠹⡀⠁⠐⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠀⢸⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⢉⣉⠉⢴⣢
⠀⢰⡀⠀⡀⠀⡇⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠘⠾⠃⠀⠀⣸⢒⡋⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢖⡕⠋⣘⠻⡑⡀
⡰⠃⠀⣠⠎⢀⢃⢠⢀⡈⠱⢤⠀⠀⠀⠀⠀⠀⠀⡔⠁⠹⡖⠤⠤⠤⢤⣺⠇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⡸⡀⠛⠋⢠⢧⠃
⠑⠄⠀⠀⠀⠁⠀⠢⣉⡀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠈⠉⠉⠉⠉⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱⠬⠶⠾⠿⠥⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣞⠉⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣄⠀⠀⠀⠀⢀⣴⠶⢶⣄⠀⠀⠀⠉⢷⠏⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠹⣇⠀⠀⢀⣾⠁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡄⠀⣸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⡾⢛⣻⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣟⣡⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠟⢻⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⠛⠻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣾⣷⣤⣤⣤⣄⣼⣿⣤⣤⣤⣤⣴⣿⣶⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠙⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⢀⣶⠞⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣿⠃⣠⣤⡀⠙⣷⠀⠀⠀⠀⠀⣴⠟⠉⠀⠈⠙⣦
⠀⠀⠀⠀⠀⣿⡀⣿⠀⠹⡄⢸⡇⠀⠀⠀⢰⡏⠀⢀⣄⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢹⣇⠸⡆⠀⢻⠀⣧⠀⠀⠀⢸⡇⢰⠏⠉⣻⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢻⡄⢻⡄⢸⡆⣿⠀⠀⠀⢸⡇⣸⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⢷⡀⠀⠀⠀⠀⠀⠀⣰⢟⣉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠻⡈⣷⠀⡇⢿⠀⠀⠀⢸⡇⡟⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠞⢦⠻⣄⠀⠀⠀⠀⡼⢣⠞⠉⣧⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠃⠀⠘⠒⠋⠙⠛⠁⠀⠸⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠀⠐⠃⠉⣾⡋⠛⠐⣶⠈⠈⠓⠋⠈⠃⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⠀⠄⠀⠀⠀⠀⠀⠀⢀⢠⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠃⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⡸⣱⢛⡶⢠
⠀⢀⠰⣖⢲⡻⡄⠀⠀⠐⠋⠉⠓⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⣁⠀⠀⠀⢳⣿⣼⡅⢰
⠀⢱⠀⣽⣬⣷⠇⠠⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠂⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠐⠀⠀⠀⢸⠃⠀⠀⢸
⠀⢸⠀⠀⠀⢿⡀⠀⠒⠀⠀⠀⠀⠦⠚⠳⠴⠂⠀⠀⠀⠉⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠙⠉⠈⠋⠀⠀⠀⠀⠀⠀⢠⠏⡠⠖⠒⣼
⠀⢸⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣻⠀⣧⣀⣠⡟
⠀⠘⣇⠀⠀⠀⠐⣏⠛⠳⢶⡶⢦⡤⢤⠤⣴⠶⠖⠚⢛⣡⠞⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢦⣍⣉⠛⠛⣳⠖⣒⣾⡛⠛⡉⢉⣠⠶⠃⠀⠈⢀⡟
⠀⠀⠘⢦⡀⠀⠀⠈⠛⠲⠶⠤⡜⠐⠒⠒⣻⠧⠴⠖⠋⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠟⠉⠙⠛⢻⣈⣥⡠⠿⠏⠉⠻⣷⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠒⠛⠛⠉⠀⠀⠀⣤⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⢄⠀⣧⠊⠁⠀⢀⡌⠉⠀⢈⣉⠀⣠⠇⠀⠠⠏
⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⣠⠔⠀⠀⠒⠒⣊⣷⡶⣮⡴⠂⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣠⠘⣮⠱⠶⢤⣤⣮⣤⣤⡬⠷⠚⠁⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⢰⠇⠀⠀⡰⠁⠀⠀⠀⢠⣾⠟⢃⡀⠛⣾⠩⡤⢶⡟⢣⠀⠀⠀⠀⠀⠀⠀⠻⣧⠚⢁⢠⡼⠂⢀⣤⡈⢷⣧⡀⠀⠀⠀⠀⠀⠀⠀⢄⠈⣆
⠀⠀⠀⠀⠀⡿⠀⠀⠀⡄⠀⠀⠀⢠⢿⡏⢡⡗⡿⢠⣶⣛⡆⠠⣷⠘⡄⠀⠀⠀⠀⠀⠀⡴⠈⠛⡞⠋⣤⠄⢹⡌⡃⠀⢻⣧⠀⠀⠀⠀⡆⢆⠀⠀⣷⢸⡄
⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⣎⣿⣀⡾⠀⣾⣾⠉⢹⡇⠰⡏⠀⡇⠀⠀⠀⠀⠀⢠⡇⠐⢢⣧⠈⣹⡞⠀⢯⡿⠂⠉⢿⡇⠀⠀⠀⡙⢦⣀⡤⠟⠀⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⡀⠀⢰⣿⠇⠤⠄⠀⠀⠁⠀⠟⣀⣹⠃⢠⡇⠀⠀⠀⠀⠀⢸⡇⠈⡆⣿⡔⠀⠉⠀⠀⢒⢦⠄⢘⣿⠀⠀⢰⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠹⢤⣸⣿⣉⠀⢴⠄⠐⣽⡟⠆⢠⡟⠀⣼⠁⠀⠀⠀⠀⠀⠈⣿⣮⡴⠋⢷⡂⠀⢷⣆⢙⣿⣷⠈⣿⠀⠀⠀⣧⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠈⣿⠀⠤⣼⡂⠼⣿⠋⣈⡿⠁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠘⢷⣀⠛⠏⢀⡉⠅⣺⠏⠀⠀⠀⡿⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⢠⡎⣠⢀⡄⠀⡆⠀⠛⢦⣄⠀⠍⢙⡋⣰⠞⢡⠰⡝⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⡶⢠⠄⠛⣶⣌⣀⣤⣾⣥⣤⣤⣄⣀⡇⠀⡆⢰⣸
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠚⠁⠀⠀⠀⠈⠉⠛⠉⠉⠙⠓⠛⠚⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡿
⠀⠀⠀⠀⠀⣀⡀⠈⠓⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⡼⡁⠤⠒⠒⢒⣶⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠒⠛⠀⢀⡀
⠀⠀⡆⠀⠀⢀⣩⣳⣄⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠊⠀⠀⠠⠴⢚⣉⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⢀⣴⣏⣍⡀⠀⠀⢰
⠀⠀⣇⠀⠐⠁⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠈⢻⡦⠒⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠈⠙⢦⣶⡏⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠙⠀⠀⡟
⠀⠀⢹⡄⠀⠀⢀⡴⠒⠒⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⡈⠉⠙⠓⠶⠇⠁⠀⠀⠀⠀⠀⢠⠟⠒⠲⣄⠀⠀⠀⣸⠃
⠀⠀⠀⢻⡄⠀⠘⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢱⡀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠘⠀⠀⣰⠏
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣖⠳⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠴⢓⡲⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠋⠉⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣀⠀⠀⠀⠀⠉⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠺⡉
⠀⠀⠀⠀⠀⠀⠀⠐⠗⢲⢃⡀⡄⠀⢰⣿⣿⣧⡀⠀⢀⣠⣿⣧⠀⠀⠀⠀⠀⢀⣾⣷⣀⠀⠀⣀⣾⣿⣿⠀⠀⡆⢀⠰⡒⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠓⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⡗⠊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣏⢿⡟⠉⠙⠻⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⠛⠉⠉⢿⡟⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠹⣮⡳⢄⣀⣀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⣀⠴⣋⡾⠃⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠉⠓⠒⠚⠋⠀⠀⡀⣀⡴⢆⡀⢀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠛⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠦⠜⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠔⠋⠉⠉⠛⠒⠶⢤⣄
⠀⠀⠠⠞⠋⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠋⠉⠉⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠴⠶⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⠬⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢀⣀⡤⠤⠤⣤⣀⠀⠀⠀⠀⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣂⣆⢀⣀⠔⠉⠀⠀⠀⠀⠀⠈⠙⢦⣀⣀⣆⣢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣶⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⠟⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⠂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣶⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣿⣿⣿⣿⡿⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠙⣿⣿⣿⣿⣿⡁⢀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢠⣿⣿⠟⠉⠉⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡠⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠀⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡜⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠐⣄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡎
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠑⡄⠀⢣⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡰⠁⠀⠀⡆⠀⠀⢠⠇
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸⡀⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇⠀⠀⢀⠇⠀⠀⡜
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⢱⠀⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⢸⠀⠀⢰⠁
⠀⠀⢸⠀⠀⠀⠀⠀⡴⢣⠀⢇⠀⠀⠈⡆⢱⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⢠⠇
⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⢣⠈⢆⠀⠀⢱⠸⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠘⠀⠀⡎
⠀⠀⠘⡄⠀⢀⠜⠀⠀⠀⠀⢣⡈⢦⠀⠸⠀⡇⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠱⠔⠁⠀⠀⠀⠀⠀⠀⠱⡀⠣⡀⡇⢣⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠃⠸⠀⠀⠀⠀⠈⠁⠀⠇⠀⢀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠩⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠯⠍⠛⠻⢶⣄⣿⢀⢀⠄⠀⠈⠠⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠭⠁⠀⠠⢄⡢⢝⡿⢧⢊⠞⡠⠀⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣅⡂⠀⠭⣓⠬⣓⢽⡣⠋⠊⠔⢁⠔⣩⠇⣠⡴⠶⠖⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠄⢐⡂⢭⠒⠅⠹⠀⠀⠀⠀⣾⢋⡾⠁⠁⠀⠀⠀⠈⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠟⠛⡗⢦⣝⠳⣶⡭⠁⠀⠀⢼⡧⢎⢀⡞⣡⠏⠀⠈⡔⣠⢃⠄⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠄⠀⠀⠀⡈⠢⠉⠛⢦⣉⠳⢦⡐⢼⡧⢫⢏⡴⡁⡠⠀⠀⠐⡱⣣⣎⢔⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⡐⢤⡑⢌⡂⠀⠀⢄⡈⢕⠦⣝⣶⣷⣷⣊⣯⣼⠖⠊⠉⢙⡪⣓⢭⡻⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢀⠨⣕⡮⣑⢤⠄⠈⠲⠶⠶⡶⣲⠾⣿⢿⠧⣍⡂⠀⠀⠠⡑⢍⠪⡑⢍⠢⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⡟⡵⡱⡳⣢⠂⢀⠀⢈⡴⢋⡼⣹⣎⣗⢦⡙⠦⣠⡕⢌⠢⡑⠌⠂⠁⡀⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠜⡼⡱⢱⢣⢣⢇⣦⡞⣠⠞⠀⠁⣿⡤⡅⠙⠲⣌⡻⣦⣠⡀⢄⢠⣰⣌⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠐⠡⠁⠃⠃⠈⣸⢏⣼⠕⡡⠀⢀⠈⡗⠀⠀⠀⣉⠛⢦⡉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⠃⡄⡀⣰⣰⠶⢳⢋⠁⢊⠔⡡⣢⢠⡇⣔⠤⡑⠠⠈⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡟⠉⠀⠀⣿⠥⢀⠵⣪⢞⡵⡳⣫⡪⡑⠬⡑⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⣿⢂⠀⠊⠵⠫⠞⣼⣿⡟⠈⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⠃⠀⠀⠀⠀⠘⢧⣒⡡⢂⣠⡴⠋⠈⠻⢦⣤⣤⠼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠉⠙⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠛⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⣿⣿⡄⠀⠀⠀⣼⣿⡟⠀⠀⠀⢀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⢀⣿⣿⣇⣀⣀⣀⣿⣿⠁⠀⠀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⢋⣝⡁⠛⣆⢛⠙⢿⣄⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⣴⢛⣿⠀⠀⣿⠿⣦⠀⠹⣝⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣾⣿⣤⣴⣿⣦⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⡿⠋⠉⢻⡟⢻⣿⣿⡟⠉⠙⢿⣙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⡾⠟⠻⢿⣿⡄⠀⠀⠀⣿⠋⠈⠻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⡟⠀⠀⠀⠀⢻⣿⣦⣤⣴⡏⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠈⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⣿⡏⠀⣸⣿⡇⠀⠀⠀⠀⣼⣿⠃⠀⢻⣿⣦⠀⠀⢠⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣶⣿⣿⣿⣦⣀⣠⣾⣿⣿⣧⣠⣾⣿⣿⣷⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠉⠙⢿⣿⠟⢿⣿⣿⣿⣿⡿⠛⠛⠛⢿⣟⢉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⡇⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⢿⣄⠀⠀⢀⣿⠿⠛⠿⣿⣿⣇⠀⠀⠀⠀⣰⠋⠁⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣿⣶⣿⠁⠀⠀⠀⠀⢻⣿⣷⣶⣶⣾⠁⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣷⣌⣿⣷⣀⠀⠀⢀⣼⣿⠉⣩⣿⣷⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢍⡙⠻⣟⣿⣿⣿⠟⠛⢙⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡿⣿⣿⣿⣿⣡⣴⣿⣭⣭⡟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⠛⠉⠙⠿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⢶⠀⠀⠰⠾⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡇⢰⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢈⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣝⢻⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⣻⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⣿⣧⡉⠻⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⣀⡶⣶⠄⠀⠆⠀⠀⠀⠀⠈⡎⣹⣿⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣿⣆⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣠⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋