Cute kitty Emojis & Symbols

⠀⠀⠀⠀⢰⡿⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢶⡄
⠀⠀⠀⠀⣾⠇⠑⢦⡉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢉⡤⠂⢸⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⡀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣰⣋⠀⠀⠈⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠩⣭⣿⣄⠀⠀⠙⠷⣦⣤⡶⢶⣶⡾⠛⠛⣿⣷⡶⢶⣶⣦⣤⡶⠟⠁⠀⣠⣮⠤⠖⠒⠀⠀⣿
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠰⠤⢬⣷⠀⠀⠀⠈⠀⠀⠈⢿⣷⠀⠀⣿⡟⠀⣾⠁⠀⠈⠀⠀⢀⡼⢭⡷⠶⠛⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠒⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠋⠀⠀⢠⣿
⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣾⠃⠀⠀⠀⣰⢞⣿⣿⣿⠁⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠀⢘⣿⣟⢶⡀⠀⠀⠀⢻⡆
⠀⠀⠀⢸⡏⣀⣠⠀⢸⠃⣼⣿⣿⣿⣷⣶⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣿⣿⣿⡄⢷⠀⢠⣀⣈⣿
⠀⠀⠀⣼⣿⡿⠃⠀⢸⡀⢻⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⠁⣼⠀⠀⠹⣿⣿⡆
⠀⠀⠀⢻⣿⣀⡀⠀⠈⢷⡀⠻⢿⣿⣿⣿⠿⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⢿⣿⣿⣿⠿⢁⣴⠃⠀⢀⣀⣨⣿⡇
⠀⠀⠀⠸⣿⠿⠿⠛⠀⠀⠉⠳⠦⠤⠤⠴⠖⠋⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⠓⠶⠤⠤⠴⠖⠋⠁⠀⠈⠻⠿⢿⣿⠁
⠀⠀⠀⠀⢻⣆⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⡀⣀⣾⠃
⢀⡠⠤⠒⠚⠻⣿⣍⠀⢉⣉⠉⣭⠉⠈⠉⠀⠀⠀⠀⡀⠀⢀⣿⣄⠀⢀⡀⠀⠀⠀⠈⠉⠀⡀⠀⣉⣉⠉⢀⣼⡿⠛⠒⠒⠤⠤⣀
⠀⠀⠀⠀⢀⡠⡜⠿⢿⣦⣀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠉⠛⠉⠀⠈⠙⠋⠀⠀⠀⠀⠀⠒⢄⡀⠀⢀⣠⣼⠿⠻⢠⢄⡀
⠀⠀⠀⠊⠁⠀⠀⢀⡠⠟⢛⣿⣾⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⡟⠻⢄⡀⠀⠀⠀⠈⠁⢀⣴⠾⠶⣦⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣾⠃⠀⠈⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠿⠛⠋⠉⠀⠈⢿⡄⠀⠙⢦⡀⠀⠀⠀⢸⣇⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⡄⠀⠀⠁⠀⠀⠀⠀⢿⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣾⠋⠻⠿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢻⡆⠀⠀⠀⢀⣾⣧⡀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢸⡿⠀⠀⠘⣷⠀⣀⣴⠋⠀⠻⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠰⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠛⢻⣿⣦⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢻⡆⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⣀⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⡷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⣿⡄⢀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⠀⣿⣄⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣬⣧⣸⣄⣸⣀⣀⣿⣦⣤⣤⣤⣤⣤⣴⣾⣄⣀⣸⣀⣼⣰⣧⡼⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠘⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢻⡦⣄⠀⠀⠀⠀⠀⡴⠛⠛⠢⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠑⢆⢻⡈⠳⣄⠀⢀⡜⠀⠀⠀⠀⢉⠀⠀⢀⡠⠴⠒⠒⢢⡀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠢⡈⢻⡇⠀⠈⢧⣜⠀⠀⠀⢀⠖⠉⠀⡒⠉⠀⠀⠀⠀⢸⠖⠋
⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠹⢀⣁⣀⠀⠠⡝⢦⣄⠀⢸⣄⠀⠞⠉⠉⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠸⢀⣀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠰⢷⡀⠀⠀⣠⠖⠋⠉⠀⠀⣀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠎⠁⠀⠀⣠⠖⠉⠀⠀⠀⠀⢸
⣤⠀⠀⡀⢀⣀⠴⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⠴⠚⠀⠀⠀⠀⣼⠁
⡏⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⡏⣠⠖⠈⠁⠀⠀⢀⣿
⠰⡄⠀⠀⠀⠀⠾⡿⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢀⡼⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠐⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⣱⠁
⠀⢂⠀⠀⢀⡀⠀⢣⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣽⣷⣦⢆⣀⠀⠀⠀⠀⠈⢦⡄⠄⠚⠁⡰⠃
⠀⠈⢷⠒⠢⢬⣑⠢⣌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠜⠁⢰⡆⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠀⠄
⠀⠀⠀⢷⡤⠶⠬⠵⣫⡗⠀⢠⠤⡀⠀⠀⠀⠀⠀⣀⣨⣥⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⡀
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠣⣀⠀⡋⠁⠀⠀⠀⢰⡖⡐⠒⠲⠶⢤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠉⠓⠶⠤⠤⠔⠛⠣⢌⡉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⠛⠦⢄⡀⠀⠀⠀⠀⠀⢀⡤⠆⠸⠦⣀⠀⣀⡠⠤⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣻⠋⠀⠑⢤⣀⣈⠉⠀⠒⢢⡞⠁⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠉⠉⠛⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⡼⠟⠋⠉⠁⠀⠈⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢮
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⢄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣟⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡤⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠰⠋⠀⠀⠀⠑⣆⠀⠀⠀⠀⢀⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⣐⠃⠀⢀⡠⠈⡇⠀⠀⠀⠀⠀⣼⠁⢠⠄⠀⠈⡆⠀⣀⠴⠋⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢀⠘⡆⠚⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣹⣀⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠳⡄
⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢻
⠀⠀⠀⠀⢰⠃⠀⠀⠙⢦⡀⠀⢀⣀⡤⠤⠶⠶⠒⠺⠤⢀⡀⠀⠀⢸
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡹⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⡀⣼
⠀⠀⠀⠀⠈⣇⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠱⡇
⠀⠀⠀⠀⠀⠹⡄⡜⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⢈⠢⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠁⢀⣤⠀⠄⠀⠀⠀⠀⠀⢝⠿⠛⡠⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢿⡿⠃⠀⠀⣀⢠⣄⠀⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠐⠐⠈⠀⠀⠙⢛⠁⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠀⢀⣠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⢤⣤⡀⠀⠤⠤⠄⠒⠊⠁⠀⠈⢳⡀⠀⠀⠀⠀⣠⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣧⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠸⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡇⠀⣰⠇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠸⡀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣧⠖⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⠶⢠⣇⠀⠀⡅⠀⠀⠀⡘⠀⠀⠀⢸⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣤⣇⣀⣀⣰⠁⠀⠀⠀⣇⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠚⠛⠉⠉

⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⡀⠀⢀⣠⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⢀⠋⡠⠚⠃⢠⡈⠎⡠⠹⡏⠀⠃⠐⣌⡁⠠⠂⠀⠀⡢⡀⣀⡀⣠⣃⠀⠀⠀⠑⠀⣄⠀⢠⠀⢠⠛⠀⠀⠀⠃⠀⠘⠇
⠀⠐⡀⠄⠀⢏⠈⡟⢠⠅⠀⠅⠀⠘⢤⡇⠀⠀⠀⠀⠄⠀⡀⠀⢀⡀⠈⡄⠀⠀⠠⡀⠀⠐⠀⠀⡸⠀⠀⠀⠀⡢⢤⠴⢁⠄⣀
⠀⠀⠈⠒⠒⠉⠀⠠⠂⠀⠀⠊⠀⠀⠀⠃⠂⠀⠀⠀⠡⡀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠈⠐⠀⠀⠊⠁⠀⠀⠀⢠⠀⠀⠀⡏⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⠠⠆⠀⠀⠀⠀⠉⠀⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠐⠃
⠀⠀⠀⡤⠴⡄⠀⠀⢴⠛⠆⠲⣷⠀⣀⡀⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠒⠒⡲⠃⠀⣀
⠀⠀⠀⠧⠀⣼⠀⠀⠀⠀⢀⣀⠀⠤⣤⡥⠀⠀⠀⠀⠀⠀⠄⠀⠰⠆⠀⠀⠀⠀⢱⡀⢠⠚⠂⠠⣴⠋⠀⠀⠀⠞⠒⠀⠀⠐⡇
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢦⡄⠀⠀⠀⠀⠀⠀⠀⠛⠁⡄⡴⢢⣤⠀⠀⠀⠀⠐⠆⠀⢄⢠⠃
⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠐⠳⠀⠀⠀⠀⠒⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⣺⠀⠀⡇⠀⢸⠄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠸⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠠⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠒⠀⢐⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⢤⠰⠀⠀⠠⡅⠖⠀⢸⠀⠀⢨⡔⠁⠀⠀⠀⠸⠁⠈⠁
⠀⠀⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⣁⠠⠠⠄⠀⠠⣈⡀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠃⠇⠀⠀⠈⡇⠀⠀⠀⠀⢸⣀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣶⡆⠀⣤⣦⠈⠁⠀⠀⠠⠤⠄⠄⠄⠀⠃⠀⠀⠀⢠⠀⠀⠉⠠⡜⠀⠀⠀⠀⠀⠀⠬⠩
⠀⠀⠀⢔⣚⣛⣛⣒⣲⠀⠀⠀⠄⠉⠁⠄⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⠷⢀⡠⠀⠀⠀⠀⠀⢣⣠⠀⠀⠇
⠀⠀⠀⠀⢸⡽⣿⡇⠀⠀⠀⠀⠀⠀⡉⡉⢹⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡀⢸⡄⢌⡧⠄⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⡶⠀⠒⢼⠀⠀⠀⠸⢂⡀⠀⠀⠀⠀⠀⠒⠂⢄⠀⠀⠀⠀⠀⠰⠄⠠
⠀⠀⠀⠷⢄⡉⠉⡄⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠄⠰⠆⢆⠀⠀⠀⠀⠁⢄⡐⠂⠀⠀⢀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠈⠐⠒⠀⠐⠃⠀⠊⠁⠉⡆
⠀⠀⡴⠀⠀⠀⠀⠛⠋⠁⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠀⠀⢔⠆
⠀⠀⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡤⠒⢉⠆⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠼⠦⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠈⢒⡞⠤⠒⣁⡤⠄⣺⠃⠀⠀⠀⠀⠠⠆⢴⠀⠀⠀⠀⠀⠐⢫⠵⠆⠀⠆⠧⡀
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠶⠀⢾⠀⠀⠀⠀⠀⢸⡀⠀⢰⣱⡏⢁⣏⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⢸⢐⢠⡄⠀⠀⣌⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠠⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡰⠃⢀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠓⠋⠉⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠐⢛⠶⠦⣀⣀⡤⠤⣄⠀⢀⣀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠞⢧
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠐⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣸⡀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⢆
⠀⠀⠀⠀⠀⠀⠀⡇⠙⢦⣀⣀⣠⠔⠋⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⣸⠃⠀⠀⠀⡞⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠦⠤⣀⠜⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠉⠲⣤⣀⣀⣀⣀⠀⠀⠀⣀⠴⠒⠒⠲⡾⠁⠀⠀⠀⠈⠣⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⡤⠖⠋⠀⠙⠲⢤⣤⠞⠀⠀⠈⠉⠉⠉⠉⢇⡀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⢤⣀⡀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠄⠀⠀⠀⠂⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠆⠆⠆⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠘⣇
⢠⡶⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠀⠀⢻
⣿⠀⠀⠄⢄⠙⢷⡀⠀⠀⢀⣀⣤⠴⠶⠒⠛⠛⠛⠛⠲⠦⣄⠀⠀⠀⠀⢸⠁
⣿⠀⠈⠀⠀⠐⠄⠹⣦⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣾
⢻⠀⠈⠀⠀⢀⡴⠋⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠶⠶⠄⠀⠹⣴⡏
⠘⣇⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠙⣆
⠀⢹⡆⣸⠁⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣶⣷⡀⡈⠳⠀⠀⠀⢹⡆
⠀⠀⢻⡟⠀⠈⠁⢀⣠⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⡻⢿⡿⠃⢠⠀⠀⠀⠀⢿
⠀⠀⠀⣏⠀⠀⠀⠺⣿⣷⣴⡆⢡⠀⠀⠀⠀⠀⠀⠈⠒⠐⠒⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⠀⠀⠀⠐⣌⠛⠋⣀⠎⠀⠀⣴⣪⣿⠆⠐⢀⠀⠀⠀⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠉⠉⠀⡠⠂⠀⠈⠉⣇⠀⠀⠌⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⠊⠀⠈⠢⠤⠞⠁⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡠⠤⠲⡋⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢸⠃⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢷⡀⠀⠀⠀⢹⡄⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⣠⠟⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠈⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⣥⠾⠋⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣄⣀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⢠⠖⠉⠁⠀⢠⠇⠀⠀⠀⠀⣞⠀⠀⠀⠀⣰⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⢦⣤⣤⣤⣼⣀⢀⠀⣀⣀⣿⣤⣤⠴⠞⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠶⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣛⠀⢴⠂⠀⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠀⢤⡄⠈⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣼⢃⡋⠀⠀⣄⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⠙⠂⠀⠉⢢⠁⣷⠀⢴⠆⣤⠐⢲⡎⢻⣇⠉⠉⠈⠳⢀⠐⢺⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡖⠲⣴⠇⠀⠀⠀⢸⡆⢠⠀⠈⠇⢸⡇⠀⠀⠀⠀⠈⠹⠿⣿⣿⠿⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣟⣡⣾⠛⠁⠀⠀⠀⠀⠈⣇⠸⡇⠀⡆⠘⣧⡁⠀⠀⠀⠄⠀⠀⠀⠙⣤⣤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣙⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⢻⡀⢳⡘⡇⢀⣏⠱⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠃⡀⠇⠄⢀⠉⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⣡⣾⣧⣤⠁⠀⠟⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⣤⣦⣶⣦⣌⠀⠀⠹⠇⢹⠟⠀⠀⣰⠟⣿⣏⡉⢻⣿⠷⠦⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⡏⢈⣹⣿⡝⢦⠀⠀⠈⠀⠀⠀⠀⣇⠘⢿⣿⠇⢸⡟⠀⠀⠀⠀⠈⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⢻⣇⠘⠿⠿⢃⣼⡃⠀⠀⠀⠀⠀⠀⣿⠷⢦⡴⠶⠛⢀⣠⡜⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠤⣄⠀⠙⠛⠶⠚⢋⣩⡏⠀⠀⠀⠀⠀⠀⠘⠓⠲⠲⣶⣿⠿⠿⠺⠿⠿⠶⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⣤⣴⣎⠿⢷⣾⣷⡟⠉⠀⠀⢠⣄⣀⣀⣤⣶⠀⠀⠀⠀⠘⠻⢻⣎⣁⠰⠂⢱⣯⠽⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠄⢙⠉⢋⣉⣉⣶⣶⠿⡷⣀⠀⠀⠀⠈⠉⢯⣭⡽⠁⠀⠀⠀⠀⠁⠤⠀⣹⢇⡀⠐⠀⠀⠀⣼⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠉⢀⣄⣠⠤⢰⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢀⣰⣟⢰⣾⡿⢋⠲⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡖⠂⢉⣥⣤⠊⣉⣶⣔⠂⠐⢀⣀⡀⢤⠞⠛⠛⠛⠖⠐⢶⣶⣶⡿⢻⣿⣿⠁⣤⢾⡛⠫⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠶⠞⠃⠀⠉⠿⣿⣿⣟⢛⡿⣿⣅⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢭⣿⣿⣭⡾⠿⠏⠀⠀⢀⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⠀⠈⠁⠀⠀⠀⡼⠉⢹⣿⣷⣊⡛⠛⣶⣦⣤⠤⣴⣶⣿⣧⣿⡿⠟⠉⠇⠀⠀⣌⡲⣷⠌⠁⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⣤⠀⠀⠀⠊⠁⢰⢏⡀⠈⠛⠙⠾⣿⢏⣼⣿⡿⠟⠟⠛⠁⠀⡤⢀⣾⣶⣿⠾⠇⠀⠀⠀⢠⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣋⡉⠉⠘⠓⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠄⢠⠀⠁⠀⠐⠂⠀⠲⠞⠃⠈⠈⠀⠉⠀⠀⠀⠀⠀⠼⠛⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⠋⠉⠛⢢⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣨⠉⠉⠛⠳⠶⢤⣬⣹⠿⣦⣀⠁⠀⡀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠸⢳⣦⠴⠂⠂⠀⠠⣤⠠⡌⠉⢙⣿⣿⣷⡄⠸⣦⢀⣄⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⣠⣿⡷⠄⠁
⠀⠀⠀⠀⠀⠠⣾⠏⠁⠐⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣿⡻⣿⣿⣿⣤⣾⣿⣶⣀⣼⣷⣶⣶⢶⣵⣶⣦⠘⠻⠗⠦⠶⡶⠟⠿⣧⣦⡀⠦
⠀⠀⠀⠀⠀⠀⣿⠆⢀⠶⠶⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠏⠁⠉⠁⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠳⣄⠀⣀⠈⠙⣿⠂
⠀⠀⠀⠀⠀⠀⢹⣶⣋⣴⡂⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣘⣙⣁⣘⠳⣾⠇
⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡂⠈⣿⣿⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣜⡀⢠⠄⠀⠀⡀⠀⠀⢸⠁⠀⣠⠀⢐⣾⣿⣤⠞⠁⣠⠆⠀⠀⠀⡤⠀⠀⠶⠀⢀⡀⢀⢀⣿⣿⡷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢤⡀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⢈⣿⣿⣿⣧⣼⡏⠀⢀⣠⠟⠁⠀⠀⣸⣷⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⢹⣤⣠⣿⣦⡿⠾⠛⠋⠁⠈⠙⠛⠛⠻⠿⠿⠷⠶⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁


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

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠓⠰⢂⠀⣠⠛⢪⠐⠠⢀⠀⠀⠀⠀⠄⠠⠀⡤⠀⣤⣀⠀⠀⢀⠀⠀⠀⠐⡄⢀⢍⡵⠖⠐⠀⠉⠀⠒⠶⢮⢅⠀⢰
⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠏⠀⢠⢑⠀⠀⠀⠀⡁⠀⠂⠀⠀⠀⠈⠁⠘⠡⡀⠀⡀⠀⡇⡐⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢆⡾
⠀⠀⠟⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠺⠀⠀⠸⣀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⢸⠁⠀⣄⡀⠀⠁⠀⠀⠀⣀⡠⠀⠘⠁
⠀⠀⠀⠰⢿⣯⣽⡆⠀⠀⢸⣯⣽⣿⠆⠀⠀⠀⠀⠙⢨⣷⡒⣦⠀⠀⢀⡔⢲⣦⡀⠃⠀⠀⢸⢰⢿⣿⣽⣆⠀⠀⠀⣾⣯⣽⢳
⠀⠀⠠⠀⠑⠙⠛⠃⠀⠀⠘⠛⠛⠈⠀⡀⠀⠀⢀⠄⠈⠻⣿⣿⠀⠀⠸⡿⢿⠟⠁⢀⠀⠀⢸⠀⠊⢾⣿⠏⠀⡀⠀⠳⡿⠋⠈⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⢀⠀⠈⠉⡋⠉⠀⠡⣠⡆⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⢐⠒⠲⠒⡖⠒⡉⡝⠁⠂
⠀⠀⠀⠀⠀⠒⠂⠀⠀⠁⠀⠀⠆⠁⠀⠀⠀⠀⠀⢔⠄⢀⠞⠀⠀⠠⠂⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⢀⢰⠃⢀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⢄⠲⠀⠀⠀⡀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢘⠀⢡⠀⢉⠀⠎⠀⡟⠁
⠀⠀⠀⠀⠀⠈⠀⠐⠂⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠓⠒⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣭⣫⣬⣭⣯⣭⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⢿⣿⣿⣷⣄⠀⢀⣀⣀⣀⣼⣿⣿⣿⠋⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠉⣿⣿⣦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣾⣿⣿⣿⣿⣦⠠⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⣴⢲⡄⠈⠻⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⢿⣌⠉⠉⠁⠀⠀⠀⠰⢄⡩⠯⣤⠔⠀⠀⠀⠉⠉⢉⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠄⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⠇⠀⠀⣤⠀⠀⠀⣠⡿⠁⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⣿⠀⢀⣴⠏⠀⠀⠀⠸⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢿⣴⠟⢁⣦⠀⠀⠀⠀⢹⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣾⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠘⣧⠀⣼⡇⠀⠀⠀⢸⡏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⡄⣿⠀⠀⠀⠀⣿⣱⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠆⠲⢤⣤⡄⠀⢘⣷⠀⠀⠀⣿⣧⣿⠀⠀⠀⠘⣿⢾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⡃⢀⡆⢠⡿⣻⣯⠄⡄⢠⡿⠀⠸⣧⣴⣄⣹⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠘⠻⠾⠷⠛⠁⠀⠀⠀⠉⠉⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⣶⣶⣶⣶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠭⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣶⣤⣤⣼⣿⡹⡆⣀⣠⣦⠀⡀⡀⣴⣾⠏⠦⢠⣴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⠿⠟⠛⢈⡻⡄⢉⣿⣨⣱⣾⣿⢰⣟⣻⠗⣲⣶⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢿⠻⠀⢈⡅⠈⠂⢠⣽⣮⣛⡿⠀⢨⢸⡦⢉⢻⣗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠠⢸⠀⣯⣿⣿⣼⢷⡆⢹⠃⡼⢶⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠦⠿⡋⢹⡌⠗⢾⡀⠈⢹⢇⡽⠘⣣⡥⣭⣤⣵⡔⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠃⠀⠈⠙⠿⢿⣷⠛⣇⠀⠈⣼⣇⣿⢬⣥⣯⣼⡭⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠂⠀⠀⠐⠋⣿⡿⣿⠀⠀⢽⣿⣿⡿⣿⣯⣷⠤⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠘⠋⠈⠙⠴⣶⡿⢿⢿⣿⣌⠛⠷⢶⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⡀⠀⠀⠀⠀⣀⣋⠀⠀⠀⠛⢉⣿⣾⣿⣿⣳⣿⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⢲⣄⡀⠀⠀⠈⠉⠁⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠻⣶⣦⣤⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣿⣿⣿⣿⡿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡟⢠⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡝⠁⢿⣿⣿⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⢀⣿⡟⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠿⠿⢿⣇⣼⣾⠿⠿⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣠⣾⡛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⢶⣦⡄
⠀⠀⠀⠀⢀⣿⠀⠙⣄⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠉⠀⠀⠀⣠⠎⠈⣿⡀
⠀⠀⠀⠀⢸⡿⠀⠀⠈⢧⡀⠀⠀⠈⠻⣦⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡰⠋⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⢳⡀⠀⢀⡤⠾⠛⠋⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠛⠓⠶⣤⡀⠀⣠⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡆⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠻⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡶⠚⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⡴⠞⠛⠳⢦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠓⠀⠀⠀⠙⣿⠃⠀⠀⢰⠏⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸
⠉⠙⠛⠓⠶⢦⣿⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣄⡀⠀⣠⠿⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣀⣿⠤⠶⠶⡾⠓⠒⠒⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢹⡏⠙⠂⡠⠐⠀⠀⠐⠀⠀⠀⠈⡏⠉⠁⠀⠈⠉⢙⡇⠀⠀⠄⠒⠐⠀⠀⠀⠀⠀⠉⢰⡟⠀⠀⣸⠃⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠊⠉⠉⠉⢺⠁⠀⠀⢄⠀⠀⠀⠀⢰⠀⠀⢀⡿⠁⠀⠀⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⣀⡼⢿⣏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣿⣥⡀⠀⠀⣿⠀⠀⠀⢰⡏
⠀⠀⠀⢀⡴⠚⠁⠀⠀⠉⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠈⠙⠷⣤⣿⠀⠀⠀⣾
⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠀⠀⠀⠻⣦⠀⠀⠀⠀⢀⡟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢤⡀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣠⠞⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠎⢠⠄⠀⠀⡾⠀⡀⠀⡀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠾⠤⠔⠚⠳⣼⣀⣾⣀⣠⡴⠿⣀⣀⣀⣀⣀⣑⣒⣚⣩⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠁⠑⠠⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡠⠊⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠑⡄⠀⠀⠑⠒⠒⠂⢲⣶⠂⠒⠊⠀⠀⢀⠜⠀⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠟⠀⠛⠀⠀⠀⠀⢠⣦⠘⣿⠀⣴⠄⠀⠀⠈⠉⠸⣧⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠛⠠⠏⠀⠀⠀⠀⠀⠀⠈⠚⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⡠⣞⢿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⢻⣿⣿⠠⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣍⡀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢀⠀⢀⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠬⠙⠻⠟⠀⠀⠐⢄⡰⠀⠀⠙⠋⠉⠐⠁⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⡠⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠤⠊⠀⠂
⠀⠀⠀⠀⢨⢐⡀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢺⡀
⠀⠀⠀⠀⠃⡌⣋⠐⡁⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠈⠓⢬⣀⡈⠉⠉⢁⣀⡡⠔⠉⠀⠀⢘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⢢⠀⡀
⠀⠀⠀⢀⡀⣈⢁⢋⠐⠹⠀⠀⠀⠀⠀⠀⡐⠀⢢⠀⠀⠀⢲⠀⠈⡏⡏⠀⠀⡇⠀⠀⠀⡠⠚⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡑⣐⢻⡐⡅
⠀⠀⠀⠀⡑⠀⠘⠆⡧⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠑⠢⢀⠀⠑⠊⠉⠉⠀⠚⣁⠤⠒⠈⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠱⢈⣯⠅⣤
⠀⠀⠀⠀⠑⢄⠑⢬⠆⠀⠀⢀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⢉⠥⠐⡢
⠀⠀⠀⠀⠀⠀⠑⠤⡔⢀⠎⠸⠀⠀⠌⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣡⡐⠀⠒⠤⢀⠀⠀⡃⢀⢠⢸⠁⠄⠊
⠀⠀⠀⠀⠀⠀⢠⠀⢀⢻⢀⠃⠀⡼⠋⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⢟⠢⡀⠰⠛⢳⡄⢣⠀⡇⣆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠡⡈⠘⡁⠀⢠⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡀⢱⠀⠀⠀⠸⠀⠲⠀⡡⠔⠁
⠀⠀⠀⠀⠈⠓⠨⢁⠻⢆⡱⢰⡌⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡇⡸⠀⠀⠀⠀⣤⠧⢮⡀⠐⢂⡨⠒
⠀⠀⠀⠠⠀⠀⡀⡠⠏⠈⠕⠃⣸⣄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣴⠔⠁⠀⠀⠀⢸⢀⠄⠊⠙⡉
⠀⠀⠀⠈⠂⣤⠜⡇⠀⡂⠀⠁⠈⢆⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⣀⠊⠀⠀⠀⠀⣰⡏⠒⠀⠄⠒⡆⠂⠉⡩
⠀⠀⠀⠀⠀⠃⠒⢣⣠⣁⠁⢀⣠⠞⠉⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠀⠀⠈⠑⢄⠀⡠⠾⠔⠓⠣⠤⠦⢎⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⢱⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⢸⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⣠⡀⠤⠧⣀⠀⡀⢀⡰⠁⠀⠙⣤⠀⡀⢠⡸⠂⠤⢀⣇⠀⠧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⡠⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠒⠀⠈⣿⣶⣿⡏⠉⠉⠉⣿⣿⣿⣄⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣑⠀⣰⣿⣿⣿⣿⠇⠀⠀⠀⢙⣿⣿⣿⣷⣄⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣃⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣆⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡻⣷⣼⣿⡄⠀⠀⠀⣾⣷⣼⡿⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠒⠣⣄⢠⡄⠓⠛⠛⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⠀⠀⠀⡴⠚⠉⠉⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⠓⠒⠂⠀⠀⠀⣀⣤⣶⣾⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠐⠲⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠙⠲⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡀⢀⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⠆⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⣿⡿⠋⢪⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠁⠀⢹⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠚⠉⠉⠀⠀⠈⠙⠛⠒⠒⠶⠶⠶⠶⠒⠒⠒⠶⠶⠖⠋⠉⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠉⠉⠉⠀⠀⠀⠀⠁⠄⠠⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⠀⠐⠆⠀⠀⢣⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⡆⠀⠀⠀⠐⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠄⠈
⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠐⠖⠀⠀⣀⡀⢀⠠⠐⠋⠀⠀⠀⠀⠀⠠⠀⠀⡔⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⡠⠤⣀⠂
⠀⠀⡐⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢐⡰⠒⠀⠁⠀⠄⠀⠀⠀⠢⢄⡈⠀⢀⣀⡠⠊⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠐⠒⡒⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⡠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠊⠀⠠⠄⠐⠂⢐⠆⢀⠠⠗⠀⠐⠒⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠄⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠙⠓⠂⠀⠀⠀⢀⡄⠀⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠉⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠀⠀⠀⠤⠤⠤⠌⠀⠀⠤⠄⠀⠤⠤⠀⠂⠂⠩
⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠲⠶⠒⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠶⠖⠋

⠀⠀⠀⠀⠀⠀⣼⠟⠳⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠾⠛⣧
⠀⠀⠀⠀⠀⢠⡟⠀⣠⣤⣀⠈⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣠⣄⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⣀⣤⡄⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠉⠛⠲⣤⡀⠈⠻⣦⣀⣤⠴⠶⣿⣿⡏⠉⠁⢹⣿⣿⡏⠈⠉⢹⣿⣿⠶⠦⣤⣀⣴⠟⠁⢀⣤⠖⠛⠉⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣾⠁⢰⡿⠀⠀⠀⠀⠀⠙⠦⡀⠈⠉⠀⠀⠀⠈⢿⡇⠀⠀⠈⣿⣿⠁⠀⠀⢸⡿⠁⠀⠀⠀⠉⠁⢀⠴⠉⠀⠀⠀⠀⠀⢿⡆⠈⣷
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢹⡏⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⢹⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⡏
⠀⠀⠀⠀⠀⠸⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣠⣯⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣀⠈⣻⣟⠁⣀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣽⣄⣀⣀⡀
⠀⠀⠈⠉⠉⠹⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣦⣄⡀⠀⣿
⠀⠀⠀⠀⠀⢀⠼⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡧⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠳⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠶⠞⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠲⠶⢤⡀⠀⠀⠀⠀⣀⣀⣘⣷⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣃⣀⣀⠀⠀⠀⠀⢀⡤⠶⠖⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠉⠛⠂⠀⠀⠀⢻⡟⠀⠀⠀⠐⠛⠉⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡄⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠙⢿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣿⣿⣿⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⠋⢰⠿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⣴⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠶⢷⣶⣶⢾⠿⠿⠾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⠶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣉⡯⠀⢀⣿⣿⣿⣿⠟⠁⠙⡿⢩⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠛⠙⢿⠿⠇⠰⢾⠿⠿⠟⠁⠀⢀⣀⠁⠀⢙⣻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣶⣿⣄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣴⣏
⠀⠀⠀⠀⠘⢿⣶⣭⣀⣁⣀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠉⠙⠛⠋⠙⣿⣿⣿⠟⠛⠇⠹⠿⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⣉⣉⣹⣭⣿⣿⣯⠀⠀⢀⡀⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣟⣛⣿⣿⠋⣹⣿⣿⣿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠟⣩⣿⣿⣷⡄⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⣹⣿⡟⠙⠋⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⣤⣶⣶⣶⣾⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣤⣴⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠖

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢣⡙⢄⠀⠈⢻⡛⠛⠛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⡀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⡃⣇⠀⠀⠘⣧⠀⣀⠄⠀⠀⠀⠀⠀⠀⠁⠑⠀⠤⠤⣤⣤⣴⣶⡿⠉⠀⣹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⡅⡇⣠⣔⠒⠛⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⣠⣾⡿⠉⠋
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡆⠀⢩⣞⣅⡀⡀⢤⠠⠀⠀⡀⢀⣴⣶⡿⠟⠁⠀⣠⣾⣿⣿⢣
⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⠹⣿⠯⠐⠚⠛⠛⠟⠛⡷⠿⢷⣾⣿⡿⠛⠁⠀⠀⣠⣾⣿⣿⣿⡟⣾
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⠀⠀⣀⡀⣔⠀⠀⠀⠀⠀⠁⢀⢀⣀⢀⣴⣶⣿⣿⣿⣿⣿⠃⠨
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣟⣒⠀⢀⠀⠀⢠⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⢏⢄⡇
⠀⠀⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢛⣉⣙⠛⠛⠛⣛⠋⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⢿⡼⠁
⠀⠀⠀⠼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣷⡶⠦⠾⠿⠶⠷⠳⠤⠴⠤⢤⣤⣴⠷⠋⢵⡟
⠀⠀⠀⠘⠻⠻⠿⣿⣿⡟⣿⣿⣿⣿⣷⣄⡀⠹⣶⣤⣴⣤⣤⣄⣄⣠⣤⣤⣤⣤⠤⢤⣀⡀⣼⠛⠓⠚⠓⠒⠛⠛⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⣿⣿⣦⣌⠛⠛⣟⠿⠿⠛⠿⠻⠿⢿⣶⣶⣤⣬⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠤⢠⠄⢠⣄⣀⣀⠀⢀⡁⣁⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠉⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡿⣼⣿⣿⣷⣴⣶⣦⣤⣤⣄⣀⡀⣸⡿⡙⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⣿⣿⣿⣿⣷⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣴⡌⣿⡟⠀⠀⢘⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠻⠷⠭⠓⠋⠠⠤⡄⢇⢾⠆⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠁⢀⠈⠙⠻⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣈⡀⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠈⣩⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⠗⠀⠉⠉⠛⠋⠉⠁⠀⡴⢿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣠⠤⢤⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⡇⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣀⣠⢀⡀⣀⡥⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠠⣸⡅⠀⡸⠀⠀⠠⠤⠤⠤⠤⠤⠄⠒⠚⠉⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⣠⣤⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠙⠟⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⣿⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⡿
⠀⠀⠀⠀⠀⠸⡆⠈⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠙⢷⣤⣠⣤⣴⣶⣶⣶⣶⣶⠾⠛⠁⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣤⡀⠀⠀⠙⠟⠋⠀⠀⣴⣻⣿⡆⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠛⢛⡛⠳⢦⡀
⠀⠀⠀⠀⢀⣸⣇⣤⡤⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⢻⣿⡆⠀⠀⠀⠀⠉⠉⠙⠛⢻⡟⠒⠂⠀⢸⡇⢸⡏⠙⢷⡀⣿
⠀⠀⠘⠛⠋⠉⢧⠀⣀⣤⡤⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠶⠤⣤⣤⣾⣀⠀⠀⠀⠀⠻⠶⠃⢀⣼⠁⣿
⠀⠀⠀⠀⠀⣀⣼⢿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⢿⣀⢉⡥⠶⠦⣤⣤⣤⡴⣟⡁⣰⡟
⠀⠀⠀⠀⠾⠋⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⢶⣤⣤⣴⠟⠀⠀⢀⣠⡴⠚⠁⣼⣿⣿⣄⣠⣤⣤⣀⣀⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⣤⣄⣀⣀⣠⣤⡤⠶⠚⠋⠁⠀⠀⠀⢻⣿⣿⣿⣯⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡤⠶⠶⢤⣤⣤⣄⡀⠀⠀⠀⢀⣴⠞⠳⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢠⡞⠁⠀⠀⠀⠀⢸⡅⠈⣷⡀⠀⣠⡟⠁⠀⠀⣷⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠻⠾⠋⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⣤⡤⠴⢦⣤⡤⠶⣀⣤⢶
⠀⠀⠀⢰⠾⢭⣤⣤⠖⣉⣁⣤⢖⣉⣠⣶⡿⠁⡠⢾
⠀⠀⠀⢸⠀⢰⣯⣿⠀⠂⠀⣇⠀⠀⢸⣿⢣⠄⢠⣿
⠀⠀⠀⡞⠀⠀⡆⢸⠐⠒⠂⡗⠀⠺⢹⡏⠂⠀⠀⢽⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⠀⣀⠀⣻⠀⠀⠀⡇⠀⡀⢸⡇⠀⠀⢂⣾⠀⢀⡠⠤⠒⠊⠁⠀⠀⠀⠀⠀⢉⡩⠝⢛⣢
⠀⠀⠀⡇⠀⠈⠀⣽⠀⠛⠀⡇⠈⠛⢸⡏⠘⡣⢻⣗⣈⣁⣀⣀⣀⣀⣀⣀⣀⣠⠔⢊⠁⡤⣾⡿⣋⣀⡀
⣰⢀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡇⠀⠈⢸⡇⠀⣩⣅⣿⣀⣀⣁⣉⣉⣉⠉⠉⠉⣻⣿⣿⣟⣛⠉⣠⣴⣿⠃
⠀⠁⢀⣇⠁⠐⡟⡟⠀⠐⠂⡇⠒⠚⢺⡇⠀⣇⠀⠈⢉⡉⠉⠉⠉⢉⡍⠉⠉⠉⠁⠘⠀⠀⣽⢛⣿⣿⡶
⠀⠀⠒⡇⠈⠈⠟⡏⠀⠀⠆⡇⠀⢐⢸⠁⠀⡞⠙⠓⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠗⠾⠷⠶⢿⣿⡿⡏⠀⠀⣀
⠀⠀⠀⣇⠀⠘⣇⡿⠀⠙⡅⡇⠀⠩⢸⣇⣴⣇⣄⣀⣤⣄⣀⣀⣀⣈⣁⣀⣀⣨⣀⣄⣀⣀⣸⣇⣴⣿⡷⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠛⠋⠀⠀⠀⠀⣤⣤⣀⡀⠀⠀⠀⣤⡖⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣹⣿⣶⣶⣾⣧⣄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣆⠀⠀⠀⠀⣿⣿⡹⢗⡇⠀⣋⠷⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⣹⣿⣿⠟⢃⣀⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡦⠀⠀⠠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢿⣿⣯⡁⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠀⠀⢸⣿⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⢼⡿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣦⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⣿⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⢻⣿⢋⡀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠿⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⢉⡩⠐⡀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⡀⠬⣉⠃⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⠔⠋⠀⠀⠀⠀⠀⠠⣀⣤⠾⠦⣤⡤⠀⠀⠀⠀⠀⠈⠲⣄⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄





⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣻⣿⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡴⠂⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡀
⠀⠀⠀⠀⠠⠈⠁⢀⠀⠀⠀⠀⠀⠄⠠⡤⠄⢤⡤⢠⡄⠶⠀⠛⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠡⣤⠀⠈⡄⠀⠀⠀⡧⠔⠒⠗⠒⠒⠳⠼⠧⠤⢀⣥⣿⣦⠀⢴⠆⠀⠀⢠⣶⣄⠀⠀⠿⠀⠀⠀⠀⠐⠠⠄⡀
⠀⠀⠀⠀⠀⡩⠋⣑⣷⡀⠀⠀⠁⠤⡴⠃⠂⠂⠁⠀⠀⠀⠀⠀⠉⠫⡀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⢠⣿⣷⠀⣶⠀⠈⠐⢄
⠀⠀⠀⠀⠠⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢶⠄⠀⠀⢰⡦⠀⠀⠈⠛⠋⠀⠀⠀⣠⣤⠀⠐⢄
⠀⠀⠀⠀⠸⠟⠐⣶⣾⠁⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣿⠃⠀⡀⠁
⠀⠀⠀⠀⣀⣀⡠⠛⠋⠀⠑⠄⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⢀⣠⡜⠀⣿⣿⠂⢀⣄⠀⢠⣾⣦⠀⠀⠛⠁⠀⠀⢀⣄⠀⠀⠘⠋
⠀⢀⣒⠁⣶⠀⠀⠀⠀⠀⠀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠈⣥⢀⡈⠁⠀⢈⡉⢀⠈⠿⠏⠀⣀⠀⠀⢀⣤⠀⠉⠐⠀⣤⠈⡀⠀⡀⢀
⠀⢿⣿⡇⠀⠀⠄⠀⠀⠀⠛⡤⠇⣀⣀⣀⠀⣀⣀⣀⡀⢀⠀⠀⢀⠀⠰⡎⠉⠁⠉⠀⠀⡀⠝⠒⠄⠀⠛⠀⠀⢿⣿⠇⣴⠁⠀⢈⡤⠚⢈⣵⣦⠀⣨⡄⢀
⡆⠈⠛⠡⣦⠀⠐⡀⠲⠀⠀⠈⠐⡆⠠⠄⢀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠒⠲⣤⠦⠀⢠⣾⠀⠀⢀⢀⡠⠀⠀⠠⢤⣥⣴⠁⠀⢀⠋⢴⠆⠘⢿⠟⠀⠈
⠇⠿⠂⢰⣿⣧⢠⡀⠀⠁⠀⠀⠀⠈⢠⠀⢠⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⢠⠟⠁⠰⢲⠟⠉⠁⣿⡄⠀⠀⢠⣤⡀⠀⣠⡄⠀⣰⣶⡄
⠀⢄⠀⠈⠛⠃⠈⢁⡀⢀⠀⠀⠀⠀⣨⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣬⠏⠀⠀⠀⣿⣧⢀⠀⢻⣿⠇⠈⠀⡀⠀⠹⠿⠃
⠀⠀⠈⠐⠀⡄⠠⣿⣿⡆⠀⢀⡈⢁⣸⠠⢥⢀⠑⠢⣀⠀⠀⠀⠀⢠⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢩⣿⣾⢰⡆⠀⠀⠀⣿⣿⡄⠀⣦⡠
⠀⠀⠀⠀⠀⢘⠀⣉⠉⠙⣦⡙⠁⠀⠊⠀⠉⢚⣴⣶⡄⠱⠆⠀⠀⢲⡗⢦⠅⣀⠀⠀⠀⠀⠀⣀⣀⡠⡧⠴⠐⠂⠈⣿⣿⣍⠀⣠⣤⠀⠀⠙⠋⡶⠈⠉
⠀⠀⠀⠀⠀⢸⠀⠛⠀⢸⣿⡇⠀⣶⢼⣶⠂⠀⠹⠿⠇⢠⣾⣷⣀⣀⡀⣰⣶⣦⠉⠿⠀⠉⠈⢿⡿⣀⠀⢰⣿⣷⠀⠛⠋⣶⠀⢿⣿⠇⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠉⣁⠚⠛⠃⠠⠤⠊⠈⠂⢺⡇⠀⠀⣴⣦⡀⠀⠟⠀⠘⠿⠋⠀⠀⠰⡷⠀⠀⠀⠛⠁⠈⠻⠋⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠄⠒⣁⠀⠀⢸⡏⣿⡀⡄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠆⠜⠛⠛⠿⠥⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣉⠶⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠉⠇⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣭⠒⡋⢱⠀⠀⠀⠀⠘⠁⠀⡙⣥⠸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⢀⠼⠄⠀⠀⠀⠈⢦⡀⠀⠀⣀⣤⠤⠤⠤⣄⣤⠀⠀⠀⢠⠃⠀⢀⣘⠃⡌⢳⠀⠀⠀⡞⠁⠘⠟⠀⢒⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠯⠶⠼⠅⣅⣠⠋⠀⠈⠉⠃⠸⠀⠀⠈⠛⠀⠔⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣛⢙⠉⠀⢻⡰⠂⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠸⠤⠄⠀⣠⠶⠋
⠀⢀⣀⣤⡼⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⡠⠔⡏⠨⠇⠀⠀⡖⢨⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⢡⠁⡄⠁⠀⠀⠀⠀⠀⠀⡀
⢀⣼⠀⠀⠀⠀⠀⢀⣀⣀⠀⠺⢤⡀⠀⣌⣀⣀⡂⠈⠅⠀⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⢨⠆⠀⠀⠀⠀⠀⡼⠁
⠛⠢⠤⠖⠉⠙⠛⠃⠀⡠⠤⢤⠴⠛⠋⠉⠁⠈⠹⡄⢙⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠃⠀⠀⠀⢰⠋
⠀⠀⠀⠀⡀⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠆⠀⠀⠀⡜
⠀⠀⠀⢮⡁⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣠⠤⠤⣶⠫⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢐⣊⠤⡀
⠀⠀⠀⠀⠻⠤⠶⠚⠛⠚⠋⠀⠉⠁⠀⠀⠀⠀⠈⠙⠣⢿⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠀⠀⠀⠙⠚⢢⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠲⠖⠓⠲⠶⠤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣳
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣲⣞⣛⣶⣴⣙⣓⣒⣋⣉⣉⣈⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢁⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⢵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠚⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠞⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⡷⠆⠀⠀⡀
⠀⠀⠀⠈⡟⠀⠤⣀⡀⠉⠉⠙⠒⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠚⠳⣦⣀⣠⣴⠶⠿⠯⠑⠒⠂⠀⠀⠀⢡
⠀⠀⠀⠀⡇⠀⠀⠀⠉⠙⠲⠦⣄⣀⠀⠀⠀⠀⠉⠉⣓⣒⣶⠤⢤⣄⣹⣄⣤⠶⢿⡏⠁
⠀⠀⠀⣀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣠⣤⣟⡛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠐⢀⣠⣯⣿⠗
⢰⡿⠁⠉⠙⠛⠶⠬⣝⣳⣦⣤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠔⠒⣒⣈⣩⠥⠤⠔⠒⠒⠉⠉⠉⠀⠀⡟
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣬⣤⣶⠶⣞⣛⣛⣭⣭⡵⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠙⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠛⠋
⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡤⠶⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠦⣤⣄⣴⠄⣀⣀⣀⣤⠤⠶⠗⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠶⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡤⠖⠚⠓⣆⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⠒⢲⠀⠀⡟
⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠀⠀⠈⠉⠙⠒⡶⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡦⣏⠀⢰⠇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⢠⠏
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣇⢈⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠳⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢻⣦⣠⡦⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠻⠟⠁⠀⠀⠋⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠙⢦⡀⠀⠀⠀⠀⠀⠾⣽⠂⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣾⡇⠀⠀⠈⠇⠀⠀⠀⠐⠦⠴⠋⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣟⠉⠛⠒⢒⣲⠤⠀⠀⠀⠀⠀⠀⠀⢲⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠳⡀⣀⠀⠀⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠟⠉⠙⣦⠿⡄⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⣇⠀⠸⡇⠳⣄
⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣁⣀⣀⡤⠞⠻⠤⠴⠳⣄⠀⠀⠀⠀⠀⠀⢀⡼⠻⡄⠀⢸⡄⠀⡇⠀⢼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠹⣟⡒⠀⠀⠀⠈⠉⣣⣱⣄⢠⡇⣰⣇⣀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠋⠁⠀⠈⠉⠈⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠟⠛⢉⣡⣤⣿⡿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠛⠛⠉⢁⣠⣤⣶⡿⠿⠛⠉⣁⣤⣾⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⢀⣀⣤⣴⣶⡿⠟⠋⠉⣀⣠⣴⣶⣿⣿⠿⠛⠛⠉⣉⣡⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠟⠛⠋⠉⠀⢀⣠⣤⣴⣾⠿⠟⠋⠉⣀⣠⣴⣶⡿⠿⠛⠋⠉⢀⣀⣤⣴⣶⣿⣿⣿⣿⠿⠿⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⣀⣠⣴⣶⣿⠿⠛⠋⠁⣀⣠⣴⣾⠿⠟⠛⠉⠀⣀⣠⣤⣶⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣠⣴⣶⡿⠟⠛⠉⠁⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠋⢁⣀⣤⣴⡾⠿⠛⠉⠁⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢰⣿⣿⠉⠁⠀⠀⣀⣠⣤⣶⣿⡿⠿⠛⠋⣁⣀⣤⣶⠾⠟⠛⢉⣁⣠⣤⣶⣾⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⣶⣶⣾⣿⣿⠿⠛⢋⣡⣤⣶⣾⣿⣟⣋⣩⣤⣶⣶⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣾⣿⠋⠉⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠏
⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠟⠛⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⡿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⠛⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡿⠛⠋⠁
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣠⣴⣶⣿⣿⣿⠿⠟⠋⠉
⠙⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠙⢿⣿⣷⣶⣦⣴⣶⣶⣶⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡤⢄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡤⠤⣤⣄⣀⣠⣤⣤⣭⣭⣭⣤⣤⣿⣟⣛⡶⠂⣀⣿⣿⣿⣿⣿⡿⢻⣷⡾
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢯⣭⣭⣛⣻⣿⣿⣿⢇⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡀⠠⠤⢤⣴⣶⣶⠶⠒⠒⠒⠒⢛⣓⣫⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠗⠃
⠀⠀⠀⠀⠀⠀⣴⣮⣴⠒⣒⣴⣶⣿⣿⣿⣿⣿⣶⣶⢶⠀⠀⠀⣉⣽⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡶⢾⡉⣹⣿⢿⣿⣿⣿⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠛⢛⣻⣿⣯⣽⣯⣽⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡿⢫⣿⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠻⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠸⡀⡀⡘⢆⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣤⠀⢤⡸⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⢿⡿⠿⢿⣿⣷⣶⣶⣶⣶⣶⢶⣶⡶⠿⠤⢤⣭⣭⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣷⣷⣶⢷⣶⣿⣿⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠒
⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠄⠉⠉⠋⠹⠿⠂⠙⢹⡿⠛⠉⠉⠻⠟⠛⠛⠛⠛⠛⠛⣻⣛⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣊⣉⣉⣉⣉⣉⣉⣍⢩⡭⣿⣿⣿⣿⡘⣧
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣤⣛⣂⣠⣿⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣛⣛⣫⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣽⣯⣭⣭⣿⠿⠿⡟⢻⡿⠟⠋⢉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠛⠿⢿⣿⡉⠉⢈⣙⣿⣍⣉⣉⠁⠈⠁⠀⠀⠀⡀⣀⣸⣧⠀⠀⠸⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⣂⣤⣤⣤⣭⣭⣭⣅⣛⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣀⣐⣿⣿⣷⣄⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⡼⠛⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⡟⠀⠈⢻⣦⠀⠀⠀⣀⣀⣀⣠⡶⠛⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣷⣦⣤
⠀⠀⠀⣼⣇⣴⣾⣿⣿⠀⠀⢠⣿⣿⣿⣿⣷⣤⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿
⠀⠀⢠⣿⡟⢉⡙⣿⠇⠀⠀⢸⡿⢋⣙⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟
⠀⠀⣸⣿⡀⢿⣿⠉⠀⠀⠀⠸⡇⢾⣿⡆⣿⣿⣿⣿⣿⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠉⠁⠀⠀⠠⠴⠀⠀⠀⠀⠑⠈⠉⠀⠉⠉⠙⠛⠿⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣄⢠⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠉⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠉⠁
⠀⠀⣼⠷⢦⣄⡀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡀⠀⠀⠀⠀⠀⢀⢤⡠⠄⠤⢄⠀⠀⢠⢊⠋
⠀⠀⠀⠀⠀⠈⠛⢗⢄⠀⠀⡇⠀⢱⠀⡀⠤⣀⠀⠀⠀⠀⠀⣏⣉⠉⡇⠀⠀⠀⠀⠰⡅⠀⠑⣴⡄⠀⠑⡴⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡕⢤⡃⡠⢼⠉⠀⠀⠀⢑⠖⠢⢄⣸⡀⣩⡧⠧⠒⠊⠉⠒⡎⠀⠀⢀⣩⠉⣶⠎⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⢌⡐⠪⢅⣢⡎⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠺⠵⣴⣝⣢⣁⠔⠁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠑⠤⣈⡏⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠉⠐⠂⠀⠤⠦⠤⠤⠤⠤⠒⠂⠉⢛⠉⠉⢹⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠤⠄⠐⠂⠉⡠⠃⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣀⣸
⠀⠒⠒⠂⠒⠂⠒⠒⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛

⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠘⢿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⣠⣤⠤⠤⠤⢤⣀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠈⣷⠜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣟⡛⠂⢼⣿⡏⠀⠀⠀⠀⣀⡈⠙⠛⠁
⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⢠⡆⠦⣾⠿⡄⠀⠀⠀⣾⡽⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣩⡌⠀⢉⣉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢋⠀⠀⠁⠀⣁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⢈⡃⠉⠘⠋⢁⡠⠂⠀⠀⠀⠀⠀⠀⠈⢌⣀⣁⡈⠀⣽⠀⠈⠲⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠐⡟⠀⠀⡜⠠⠁
⠀⠀⠀⣀⣾⣽⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⡟⠻⢟⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⡀⠤⣷⠦⠒⣶⣆⠀⠀⠀⠀⠀⠀⠑⠊⠀⠂⠂
⠀⠀⠀⠈⠓⣶⣼⣿⣧⣤⣤⣤⣤⣤⣤⡜⡴⣷⣍⢱⠖⣿⣿⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⡤⣤⣀⣀
⠀⠀⠀⠀⠈⠈⠙⡷⡋⢃⡿⡿⢿⣿⣿⣿⣿⡜⡁⠀⢀⡜⣛⣿⠀⠀⣠⣴⠚⠛⠀⠛⠁⢀⣄⢀⡠⢘⠻⠿⠒⠘⡄
⠀⠀⠀⠀⢲⡄⠀⠁⠈⠁⡜⠉⠸⠛⠿⡿⣿⠿⣾⢷⠟⠛⠉⠁⢀⣞⠁⠁⠀⠀⠀⠀⠀⠀⠈⡏⠩⣹⡟⠀⠀⠀⣙⣢
⠀⠀⠀⠀⠈⣃⠀⠀⠀⣆⠈⠀⠒⠒⢋⡑⠃⢠⡔⠉⠀⠀⠀⠀⠈⠻⣶⣴⣶⡀⠀⣀⡀⢀⡐⠃⢠⡌⠂⠀⠦⣠⢸⣿⣧⡀
⠀⠀⠀⠀⠀⢃⡀⠠⠞⠰⡀⠀⠀⠀⠘⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠫⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⠈⠉
⠀⠀⠀⠀⠀⠈⠧⠀⠝⠀⠁⠀⠀⠀⠀⠀⠄⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠒⠒⠂⠉⠉⠩⠐⠒⠒⠢⠤⠤⣤⣀⣀⣀
⠀⠀⠀⠀⢀⣀⣤⠤⠐⠒⠒⠈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉⠉⠛⠒⠒⠶⠦⠤⣤⣀⣀⣀
⠀⠀⠀⠀⡎⡀⠀⠉⠉⠒⠒⠲⠤⢤⣄⣀⣀⠀⠀⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠬⢿⡟⠁
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁⠀⠀⣼
⠀⠀⠀⠀⠱⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⠶⢤⡴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣠⣄
⠀⠀⠀⠴⣴⣖⡛⠛⠉⠓⠒⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣀⣀⣀⠀⠀⠀⠀⢀⣤⣶⠾⠟⣋⣁⡠⠭⠽⠗⠲⡀
⠀⠀⠀⠀⢹⠉⠉⠛⠲⠦⣄⣀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠈⢻⣷⣤⡶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⣀⣀⣉⣩⡿⠷⠶⠶⣦⣤⣿⣤⡶⠿⠛⡿⠇
⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡞⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣀⣠⣽⠿⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⠖⣲⣿⣓⡶
⣰⡿⠛⠻⠾⢷⣤⣍⣻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠒⠒⣋⣉⣭⣥⡴⠶⠶⠛⠛⠛⢹⡏
⣿⠃⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣶⣤⣀⡀⢠⠏⣌⠀⠀⢀⣀⣀⣤⣴⠶⠶⠒⢛⣋⣉⣭⣥⡴⠶⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣾⣟⣋⣩⣭⣤⣶⡶⠾⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀
⠀⠛⠿⢶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡶⠶⠞⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣄⣀⠀⣀⣆⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠾⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣯⣵⡶⠶⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⡽⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠿⢶⣔⣒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡦⣽⣿⣿⣦⠂⠀⠀⣠⢘⠋⠿⣢⠀⠈⠀⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣿⣿⠗⣉⠥⣓⢀⠁⠘⣇⠀⠁⠀⠀⡘⠋⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠟⣂⣻⠄⢉⠀⠀⠈⣩⣾⣿⣶⠒⠶⠇⣄⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⡿⢿⣧⠀⡄⠀⠀⣻⣧⡭⠋⠘⠂⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⠸⠂⠁⣒⣿⠗⠀⠀⡘⠁⠀⠀⠤⠀⠀⢶⣞⣟⡉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣶⣾⡩⢋⣠⠇⢸⣤⣤⡏⠀⠀⠀⡀⣠⣾⠞⡻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⢿⣿⣿⣶⠀⠀⠙⣧⠀⠀⢀⣨⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣷⣾⣿⣿⣿⣿⣶⠛⠉⠀⠈⣹⣿⣿⣯⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⣴⡿⡿⢳⣯⣉⣩⣿⡿⣿⢷⣿⣿⢿⣟⢛⠋⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣔⣿⡿⢻⢦⣬⠘⠁⠺⣧⡀⠢⠰⠛⠁⠈⠉⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠒⣒⠋⠈⠀⠀⠀⠈⠰⠣⣦⡿⠃⠀⠀⠀⠀⠀⡀⠀⠁⠔⠃⠀⠠⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⠆⠀⠀⠠⠠⣤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠄⠖⠤
⠀⠀⠀⠀⠀⠀⠠⣾⡿⠟⠁⠀⠀⠀⢠⣌⠉⠦⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢩⡟⠀⠀⢀⣠⣄⣀⣀⠀⡀⡔⠆⠈⠲⣆⠀⢼⠀⠀⠀⠈⡅⢀⡄⢹⡀
⠀⠀⠀⠀⠀⠀⣺⠓⠛⠙⠋⠙⠉⠉⠙⢷⣾⣤⣀⡄⢠⠙⣧⡀⠂⡀⠀⠀⣿⣰⣀⣾⣹
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⣾⣇⡀⣦⢸⡏⡃⠀⢻⡀⡀⣾⡿⠟⠉⠉⠁⠂
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠴⡈⠙⠻⢿⣿⣿⣿⠁⣿⢀⢸⣡⣿⠋⢅⡀
⠀⠀⠀⠀⠀⠀⠉⠡⠂⠀⠀⠀⠁⠀⠈⡠⠂⠀⠀⠀⠉⠁⠀⠁⠛⠛⠹⢧⣼⣾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠙⢟⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡟⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣠⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢠⠀⠀⠀⠀⢠⡀⠀⠀⠈⠙⢿⣶⣆⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣸⡀⢀⣬⢀⣸⠃⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⡅⣦⡍⠆⠀⠀⠀⢂
⣠⠔⠀⠉⠈⠁⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠀⠉⠒⠀⠀⠀⠀⠈
⠣⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⣴⡆⠄⠀⠀⡜⠀⠄
⠀⠑⡀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠁⠙⠁⠀⠀⠈⠃
⠀⠀⠘⡄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢀⠔⠒⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠉⠓⡀⠀⠀⠸⠀⡀⡇⢄⢀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠄⠁⠈⢑⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠈⠀⠐
⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠤⠀⠀⠠⠄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠈⠐⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⢠⢈⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⣀⣀⡤⣊⡁
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠈⠀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠉⠉⠁⠈⠐⠂⠤⠤⠼
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣶⣦⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠶⠖⠒⠒⠂⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢈⠐⠦⣍⣛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣉⡓⠦⣌⣙⠒⠌⠉⠛⠷⣦⣄⠀⠀⠀⣀⣠⡤⠴⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠬⣅⡒⠬⣕⡂⠌⠙⠒⠄⠀⠀⠀⠙⢷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⠲⢭⣑⠲⠬⣑⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠒⠒⠛⠛⠶⣤⣌⣀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠛⠛⠓⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠾⠿⠷⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣄⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢩⡿⣍⠿⣯⣉⣉⣉⣉⣉⣁⣤⣤⣤⣤⣴⠶⠶⠟⠛⠛⠋⠉⠁⠀⠀⠀⢀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⠀⠹⣆⢸⡏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⠀⠀⣀⣀⣘⣿⣧⣶⣶⣶⡶⠶⠶⠶⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⢀⣠⣴⠶⠞⠛⠉⢉⣿⣴⠟⠛⠉⠉⠉⠉⢙⣛⣛⣛⠛⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣦
⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠭⠭⠍⠉⢓⣒⣒⣒⣒⣒⣒⣒⡂⠀⠀⠀⠀⠀⢉⡿⣥⣀
⣸⠏⠀⠀⠀⠒⠤⣀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠤⠤⠤⣀⣀⣀⣀⣀⡒⠒⠒⠒⠶⠶⠶⠍⠁⠀⠀⠀⢸⠁⠀⠉⠓⠦⣄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⢀⠀⣀⣈⡉⠉⠙⠛⠛⠛⠒⠒⠒⠒⠒⠒⠢⠤⠭⠭⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢈⣙⣷⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣭⣭⣭⣍⣛⣛⣛⣛⣷⣶⣶⣶⣶⣤⣤⣤⡤⠤⠀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠈⠳⡶⠶⠛⠛⢹⡏⠉
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣍⡉⠉⠉⠉⠉⠉⠉⠉⠛⠛⣛⣛⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⠀⠀⣸
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠶⠛⠉⠉⢁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠤⠤⠀⠂⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠶⢒⣛⣋⣩⣭⣤⠴⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣙⣮⣍⣁⣀⠀⠀⢈⣉⣉⣭⣤⠤⠶⠶⠞⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢁⣀⣈⡉⣀⣶⢤⡐⠦⡤⠤⠤⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⣨⣿⢭⠳⣤⡼⠀⢙⣷⠀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠤⠀⠠⠒⠎⠀⠤⠤⠠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⠁⠈⠐⠳⣌⣑⣦⠪⡾⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠂⠀⠀⠀⢠⠀⠄⢸⠀⠫⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠀⠀⠈⡿⠀⡐⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⣁⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⠀⠤⠀⠀⠀⡠⡿⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⢠⣀⣀⣀⣀⣀⣈⢸⠀⠰⢸⡇⠀⠀⠀⠀⢠⡤⣤⣤⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⢀⢀⡣⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣄⣶⡂⠐⠀⠀⠀⠀⠀⠘⠀⢀⣺⡇⠀⣠⠔⢈⢉⣁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣠⠿⠵⠶⠶⠇⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠒⠓⠛⠓⠒⣶⡴⢶⣶⠒⠒⠓⠛⠒⠛⠊⠀⠀⠀⠑⡍⠀⠀⠀⠀⠐⠀⠀⠀⢀⠴⠊⠁⠄⡀⠀⠀⠀⠀⡴⡀
⠀⠀⠀⠀⠀⠀⢼⢇⣰⣂⣀⣀⣘⣉⣉⣉⣉⣉⢓⣒⣲⣶⣶⣖⡆⠔⠲⡀⠀⡀⠀⠀⠀⠐⠂⠌⢀⡖⠁⠀⣀⡀⠀⠀⠆⠀⠀⡞⢈⡅
⠀⠀⠀⠀⢀⠀⡈⣆⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢄⡇⠙⢞⠁⠠⢣⡀⠀⠀⠀⣀⣂⣈⡁⠀⣊⡀⣱⠀⠀⠰⢀⠈⠀⠸⠁
⠀⠀⠀⠀⠹⡭⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠁⣦⡀⠀⠀⣇⠀⠉⠁⠈⠀⠀⠀⠈⠣⡀⠀⠉⠁⡀⠠⠚⠁⢀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⡇⠘⠛⠉⠉⠑⠒⠴⠤⠤⠤⠤⠤⠤⠾⠢⠤⠤⡶⠥⠟⠒⠋⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⠀⠀⠀⢊⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡃⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣀⣄⣀⣴⣶⣦⣴⣶⠶⠲⡶⢲⣀⣸⣨⡗⣷⣷⣷⠤⢦⣤⠤⠤⢤⡬⢬⣤⣤⣤⣤⣀⣀⣥⣥⣼⠶⠶⢶⠾⠃⠈⠑⠂⠉⠀⠄⠒⠀⠂

⠀⠀⠀⠀⣰⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⣾⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡇
⠀⠀⢀⣿⣃⠀⢻⣿⣿⣦⣺⣾⣿⣿⣶⣶⣶⣿⣿⡿⣿⡟
⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⣻⢿⣿⣿⣿⣿⡿⢿⢻⣿⡇
⠀⠀⠀⣹⣿⣿⣿⣿⣿⣦⣥⣾⣿⣿⣿⣿⣧⣬⣼⣿⣧⡀
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⡈⢁⠈⠉⠉⢽⠿⢏⡫⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣥⠉⠀⢀⠀⠈⠰⢀⠀⠀⢁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣌⡪⢠⣄⠀⠁⠀⠀⢀⠀⠣⡈⢻⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣏⣿⣀⢀⡘⣆⣶⣦⣀⢙⣲⠤⣠⡘⢷⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⠿⠉⠉⠠⢁⢹⣺⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠃⠚⠋⠀⠀⠀⠀⠈⠓⠋⣻⡿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡳⣪⠀⠀⢀⠀⠆⠀⢤⠐⠄⢌⣷⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠧⢖⡀⠀⠀⢀⠀⠀⠉⠀⢀⢨⣿⣿⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠤⠌⠁⠀⠀⠀⠀⠀⠀⡆⠎⢂⡹⢿⡇⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣂⣀⢐⠀⠀⠀⠀⠑⠀⡀⠐⣠⣁⠀⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣧⠸⠀⠀⠀⠦⡀⠀⠀⠀⠘⠋⠁⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣂⢀⠀⠘⠀⠀⠈⢺⣀⡠⣘⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣭⠟⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡘⣸⢀⠤⠀⠀⠰⢿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⣿⣿⣭⣉⣻⢟⣻⣿⣿⠿⠿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣦⣭⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣀⡼⠀⠙⠀⠀⢀⣀⣀⣀⣤⡤⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠂⠁⠀⠀⢰⡟⠑⠉⠉⢠⠖⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢥⡴⣲⣦⡀⠀⠀⠈⠀⠀⠀⠛⡜⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠢⡘⡰⠿⢟⠇⠀⠀⠀⠀⠀⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⠈⡉⠁⠀⠀⠀⠀⠀⠰⣾⡿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠁⠀⠀⠈⠙⠉⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⢀⡶⠋⠉⠢⡀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⣻⠀⠀⣀⠀⠀⠀⠈⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⢤⠕⠂⠀⠈⣀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠐⠠⠤⢄⡿⠁⠀⣠⠆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⠀⠀⠈⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣄⣀⡀⠀⠀⢀⡄⢀⡀⢀⠀⠀⠀⢀⡰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⢹⣇⠀⠀⢻⢿⣿⣿⣿⣿⡆⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⡀⠀⣸⢘⣿⣿⣿⣿⣷⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠋⠀⠛⠙⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠂⠀⠈⠀⠠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠠⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⢹⠄⠤⢀⠄⢳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠿⠄⠤⠀⠀⠓⢃⠀⣸⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⢆⠐⠂⠘⠚⢤⣤⠠⠤⠔⠁⠘⣧⠯⠀⢹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢺⣧⠘⣄⡀⠀⠀⣠⡿⠀⠀⡘⣿⢠
⠀⠀⠀⠀⠀⢀⣴⠻⣷⣄⠈⠻⢷⡘⣿⡼⢋⣭⡆⠀⢰⡇⣿⡄
⠀⠀⠀⠀⠀⣿⡹⣧⡙⣿⡟⠀⠀⠉⠀⠑⠿⣿⡇⠀⢼⣇⢸⡇⠆
⠀⠀⠀⠀⠀⢿⣱⡜⣷⡌⢿⣷⣄⠀⠀⠀⠀⠀⠁⠀⠘⢿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄
⠀⠀⠀⠀⠀⠈⢿⣽⣮⢿⣆⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡈⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠻⣾⠷⣻⣧⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠆⠀⠀⠀⠈⠀⠀⠈⠀⠀⠒⠀⡖⠠⠠⢴⠐⠂⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡟⣝⢷⣌⢻⡄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠑⠤⣤⣤⣤⠼⢦⡀⠈⣤⣶⣆⣠⣞⣁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣻⣿⣦⠻⡀⠀⢀⡾⠁⠀⠀⢀⣤⣴⣮⣥⣤⣤⣤⣄⣀⡀⠀⠀⠀⠘⠛⠿⠀⣷⣦⣤⡜⣻⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣷⣷⣠⣾⡿⢷⡶⢿⣿⣿⣿⣯⣭⣽⣿⣛⣛⡿⠿⠷⣶⣤⣬⣽⡛⢾⣿⠠⠛⠉⠉⠙⠒⠤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠿⠾⠷⡾⣧⡼⠿⢼⣿⣸⣿⢸⣷⠉⣾⡏⣻⣟⣛⠷⣶⣶⠙⡿⠃⠈⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡄⢰⡶⠂⠀⢰⡿⡵⢞⡪⠓⠋⠁⠀⠀⠀⠀⠀⡀⢉⠉⠓⠛⠣⠿⣇⣽⡏⡸⠟⠁⠀⠀⠀⠠⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⣸⡥⠊⡡⢤⠇⣢⡀⢀⣰⠀⠠⠙⠙⠉⠑⠀⠀⠀⠀⣸⡟⠉⠀⠀⢀⡠⢀⡥⠚⠁⠀⠀⡄⠀⠆
⠀⠀⠀⠀⢀⡸⠀⢀⡀⢶⠸⠟⠏⡾⢠⢗⡀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢌⠟⠀⠀⡀⢔⡡⠞⠁⠀⠀⠀⠀⠀⠊⠀⠁⠶⡄
⠀⠀⠀⢆⠈⠀⠙⠨⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⡶⣀⠐⣞⢀⡠⢊⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠛⠳⡌⠛⠛⠹⢸⡿⣫⣞⢡⡄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣩⠞⠋⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⣦⣤⣤⣦⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⡀⠀⠀⠀⢀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣿⣿⢿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠸⢇⣿⣿⣏⠻⢃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠈⢙⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠉⠉⠳⣄⠀⠀⢀⣤⣄⠀⣀⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡆⠀⡀⠀⠀⢀⠀⢰⠘⡇⠀⢸⡇⠈⠋⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡇⠘⠋⠀⠀⠛⠀⣿⣠⠇⠀⢸⡇⢠⣤⠀⠀⣤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠻⠗⠀⣠⡏⠀⠀⠀⠀⢷⡀⠀⠘⠃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠙⠓⠶⠖⠚⠉⣷⠀⠀⠀⠀⢠⠟⠲⠶⠶⠖⠋⠙⢳⡄
⠀⠀⠀⠀⠀⣼⣇⢠⡏⠀⠀⡄⠀⣀⣀⣀⡀⠀⣿⠀⠀⠀⠀⢸⠀⠀⣀⣀⠀⠀⡀⠀⠹⡄⠀⣰⠶⡄
⠀⠀⠀⠀⠀⣿⠘⣾⠀⠀⠀⡇⠀⠀⢹⠉⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⢻⠀⡿⠀⡇
⠀⠀⠀⠀⠀⠸⣆⠋⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⡇⠀⠀⢸⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠙⠒⠒⠋⠓⠒⠚⠁⠀⠀⠀⠀⠈⠓⠒⠛⠙⠒⠚⠛⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠒⠒⠂⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢂⢀⣀⡈⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠘⠁⠶⠾⣿⣿⣿⡆⠀⢠⣿⣿⣿⡿⠿⠓⠈⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣀⠈⠛⠛⠁⠒⠀⠙⠛⠛⠀⣠⣴⣾⣿⣿⣷⡄⠀⠀⣠⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⡀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡇⣠⣞⣩⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠻⠿⠿⠿⠿⠿⠿⠛⠟⠛⠛⠛⠛⠀⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⣀⣀⣀⡀⠠⡆⢀⣀⣀⣀⣀⡀⠀⠀⣿⠀⣀⣀⣀⡀⠀⠀⢠⢀⠀⣀⣄⣀⣀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡍⠛⠉⢿⣟⣛⣋⠉⠉⠙⠛⠛⠛⠉⠉⠉⣿⡍⠙⠛⠚⠛⠯⡽⠟⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⠛⠻⠶⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⠀⢷⡐⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⣖⣒⣒⣚⣻⣯⣭⣭⡍⣩⣤⣤⣭⣵⣶⣒⣒⣲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣾⣿⣿⣿⠿⡿⢿⡿⣿⡿⣿⢷⡏⠀⠤⠤⠤⠤⠭⢩⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡏⣜⠸⢿⢸⠇⠾⡀⡿⢱⣿⢸⠁⠠⠄⠀⠈⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣷⣾⣤⣾⣤⣦⣴⣧⣴⣮⣿⢸⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⡤⠤⠼⣿⣯⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣾⣧⣀⣭⣭⣭⣭⣭⣭⡭⠿⣂⡀
⠀⠀⠀⠀⠀⢠⣟⡭⣭⣥⣀⣒⣒⣀⣀⠤⠤⠤⠈⠉⠉⣙⡋⠉⠙⢛⣉⡉⠭⠭⢭⣀⣀⣒⣦⡤⠽⠿⢷⠟⠃
⠀⠀⠀⠀⠀⢸⢸⣇⡂⠀⠐⠀⠈⠩⠍⠉⠙⠛⠛⣒⡒⠒⢂⡤⠤⠖⠒⠺⠿⠯⠉⠉⠀⠀⠀⠀⠀⡀⢸⡀
⠀⠀⠀⠀⠀⠸⣏⣓⣒⡒⠂⠀⠭⠥⣄⣀⣠⣤⠤⠤⣤⣄⢼⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⣂⣀⣠⣥⣥⣼⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣷⣶⣶⡾⢁⠐⣶⢶⣒⡩⠙⣲⢤⣈⣩⣤⣴⣶⣶⣿⣿⣿⣯⣽⠿⠶⠞⠛⠋⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡿⠹⠏⣿⣿⢡⠁⠀⠀⠀⠀⠩⢓⡦⣍⡺⢽⣻⣿⣿⡟⠉⠉⠁⠀⠀⠀⠅⢀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣼⣧⣾⣿⠃⠂⣠⣴⣦⢠⣠⣀⡀⠈⠑⠫⢗⡾⣝⢮⡟⣦⠀⠀⠒⠀⢀⣀⡠⠤⣖⣚⣿⠆
⠀⠀⠀⠀⣀⣠⣤⣶⠛⠻⠿⠿⣿⠏⠌⠀⠉⠈⠈⠈⠘⠹⠔⡀⠀⠀⠐⢰⠃⡠⢱⣯⡴⣾⣾⣿⣽⠶⠞⢛⣋⣽⣷⣤⣄
⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣴⡏⡈⠀⠀⠀⠛⠷⣦⡆⡀⠘⢿⠁⠀⢠⠇⢸⢣⡿⠿⠟⠛⣉⣥⣴⢶⣾⣿⣿⠿⣟⣻⡽
⣾⣿⣷⣶⣦⣬⣍⣙⣛⡻⢿⡟⡐⣥⡁⠀⠈⠈⠓⠂⣉⠛⠀⠀⠀⢀⡏⢠⢇⣾⣥⣶⣾⣿⣿⣿⠾⣟⣫⡽⠶⠛⠩⣸⣧
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠁⠘⠿⣦⣷⣄⡀⣀⠀⢠⡀⠀⠀⡞⠀⡞⣾⢿⣿⣿⣛⣩⡵⠞⠛⠉⢁⡠⠴⣒⣯⠽⠚
⠀⠀⠉⠉⠙⢛⣿⡿⠿⣿⢃⠃⠀⠀⢠⣄⣹⡟⠿⣿⣤⣄⡀⠀⡜⠀⡜⣼⣿⣭⣽⣿⠍⣀⡠⠴⣒⣩⣵⣾⡛⠉
⠀⠀⠐⢾⣿⣿⣿⣯⣽⠇⠂⠀⠀⠦⠀⠉⠛⠷⠤⡀⠉⠁⠀⣼⠁⣸⣰⣿⣿⣿⣿⣿⣭⣵⡶⠟⣋⠉⢺⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠈⠙⠻⠿⣿⡈⠀⠀⠀⠙⡲⢍⠐⠤⣀⠀⠀⢀⢰⠇⢀⢧⣿⠦⠤⡭⠿⠛⠉⠀⢀⡡⢐⣀⠼⢿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠉⠃⠀⠁⠀⠀⠀⢢⡟⠀⣞⣾⣏⡀⠀⢫⠀⠀⣀⠬⠖⣊⣭⣶⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣻⣦⡴⠶⠶⢦⣀⠀⣾⣀⣘⣼⣿⣦⣬⣉⡉⢛⣩⣴⡾⠿⠛⠉⠁
⠀⠀⠀⢀⣀⣤⡤⠴⠖⠚⠛⠉⢉⡀⡀⡀⣀⣠⣀⡌⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⢠⡞⠉⣁⠀⠀⢀⠀⣀⣦⡰⠼⠋⠉⠉⠙⠁⡀⢄⣠⣀⠀⠙⠻⢿⣏⡁
⠀⣿⢀⠑⠢⡁⠀⡈⠃⠉⠁⠀⠀⣄⢦⣰⠬⠷⠽⠚⠋⠉⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⣿⠸⢞⣠⢈⠐⢄⡀⠀⠀⠸⠒⠋⠁⠀⠀⠀⠤⢄⡲⠤⠴⠖⠒⠋⠀⠀⠀⠀⣙⠳⣄
⠀⠈⠷⣌⡙⢻⣶⠀⠈⠢⢈⠂⠀⠀⠀⠀⠐⠂⠉⠠⠖⠒⢉⠀⡤⠤⢐⣒⣨⡥⢴⡶⠃
⠀⠀⠀⠈⠻⢦⡀⠸⢴⣤⣀⠑⠠⡑⠀⠀⠀⠠⠄⣒⣈⣥⡤⠶⠚⠛⠩⠉⡀⠂⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠈⠳⡏⠀⠈⢠⠃⣴⠚⠋⡉⠡⠄⢀⠀⠀⠀⠀⢈⡡⠤⠞⣹⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠘⠃⡞⣸⡯⠉⠀⠀⣀⠠⠤⠐⣒⣢⣭⡴⠶⠞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣇⠹⠗⣒⣨⣥⡴⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠛⢷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⣏⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣇⠀⠈⢿⣿⣶⣶⣶⣶⣶⣯⣿⠉⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠐⠀⢂⣻⣿⣿⣿⣿⣿⣿⣿⣥⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⣾⠿⠛⠓⠈⠋⠛⠙⢿⠿⠿⣿⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⢀⣤⣦⣄⠀⠀⠀⢠⣶⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠁⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⢹⡟⣋⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠟⠀⢀⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠠⡀⠀⠈⠙⠲⣖⣉⣉⣽⢟⣉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣯⣏⣽⣟⣿⣟⢯⡩⢿⣿⣯⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣏⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣷⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⢿⠛
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡿⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠓⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣰
⠀⣼⣿⣿⣧⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠿⠻⡄⠀⠀⠀⠹⣆⢠
⠀⢹⣿⣿⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⠀⠀⠙⠀⡄
⢰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣤⡀⠀⠀⠀⢀⣠⣦⣤⠄
⠈⠛⠻⠿⠿⠿⠟⢻⠿⠿⠶⠤⢀⣀⣀⣀⣀⠀⢠⠤⠶⠶⠛⠛⠉⠙⠓⠒⠒⠛⠛⠋⠉⠛⠙⠋⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠙⠛⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⣿⡆⠀⠀⠀⠀⠐⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⡿⠋⠀⣠⣴⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠉⠛⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣷⣄⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣿⣯⡀⠀⠙⢿⣿⣿⡆⠀⠈⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦
⣾⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢀⣴⣿⣿⣿⣧
⠙⣿⣦⠀⠐⢶⣾⠂⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⣤⣴⡾⠟⠀⠀⠘⠛⠉⣀⣼⣿⡆
⠀⠈⠻⣷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⣤⣤⣀⡀
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⡷⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⠿⣿⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣶⣤⣤⣶⠟⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠋⠀⠀⠸⠟⠁⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⣿⣷
⠀⠀⠀⠀⠀⠹⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠋⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣏⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠁⠀⠀⠀⠀⠉⠉⠁⡀⠀⣿⣿⠃⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣷⣤⣶⣿⣤⣾⣷⣴⣿⣿⣷⣾⣿⣿⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⡟⠋⠀⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟

⠀⢀
⠀⠈⠃
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠂
⠀⡀
⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣦⠆⠀⠐⠀⠀⠀⠤⠤⠀⡀
⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠈⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡃
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠄
⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣄⣿⠤⠇⠀⠑⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣬⡀
⠀⠨⠊⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠘⠀⠰⠂⠀⠀⠀⠀⠠⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣰⣶⣀⣄⣤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⢰⣿⣿⣾⣿⣦⣠⡄⠀⢲⠀⠒⠂⠀⠚⠳⠀⠀⠀⠀⠒⠂⠶⠆⠀⠀⠈⠈⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠀⢨⣃⡀⠂
⠀⠀⣿⣿⠻⠁⣾⡿⠁⠀⢹⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠙⣿⡦⠐⡟⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⡤⠄⠈⡉⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠀⠠⠄
⠀⠀⠀⢟⡛⠛⢛⣳⠶⠶⠾⠆⠀⢀⠔⠁⠀⠀⠈⠉⠁⠀⡧⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠈⠀⢀⠂⠀⠀⠀⠀⠀⠀⠤⠔⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠹⣿⣷⣦⣶⣤⣤⡖⠰⡟⠀⠀⠀⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠀⢹⢿⣿⠄⠤⠤⠭⠹⣟⠀⠀⠀⠀⠺⣙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡟⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠠⠠⠤⠀⡤⠤⠀⠶⠤⠀⠤⠤⡤⠄⠤⠄⠄⠦⠤⠤⠀⠤⠤⠠⠦⠤⠰⠤⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠰⠲⠀⠂⠀⠆⠰⠂⠐⠂⠂⠰⠆⠀⠀⠖⠔⠀⠐⠀⠃⠤⠲⠂⠐
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿