Biology Emojis & Symbols

⠸⠿⠿⡀⠀⠀⣶⡆⢀⡴⢺⣧⣭⡁⢳⣿⡏⠀⠀⠿⠀⠀⠀⠈⠛⠛⠉⠀⠙⠛⠋⠁⠈⠛⠒⠋⠀⠉⠛⠚⠃⠈⠓⠒⠂
⠀⣠⣤⢸⣶⣦⢀⡄⢸⣇⣨⣏⣈⣁⣈⣉⣁⡀⠀⠀⠀⠀⠰⠃⠘⣦⡞⠁⢱⡴⠁⠙⣦⡞⠀⢳⡞⠀⠙⣶⠋⠀⢷⠎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠈⢫⡌⠛⠋⠀⠀⣼⣿⣿⣿⣾⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢸⣷⠀⠀⣿⡇⠀⢸⣧⠀⠀⣿⡄⠀⣸⣇⠀⢀⢿⡄⠀⡀⢠⣤⣀⢀⡖
⠾⡿⠈⢱⣿⡆⠀⠘⣏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠋⠈⠀⠘⡅⠙⢀⠋⠈⠀⠈⠀⠙⠀⠁⠈⠀⠈⠀⠙⠈⠁⠸⣿⣿⣿⣿
⠐⠀⠀⠀⠈⠀⠀⠀⢈⠀⠀⠀⣀⣀⣀⢈⣁⠀⠀⠀⠀⠀⢀⠀⠘⠃⠀⠘⠁⠠⡄⢠⣵⣤⣼⣤⣄⡖⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⡋⠀⠠⠛⠿⡿⠟
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⣧⠀⠀⠀⠀⠠⠤⡀⠀⠈⠃⠰⢤⣠⣾⡿⡿⠻⢿⣷⣼⣷⣴⢂⣀⠀⣴⣶⣧⡀⢠⡆⢠⡀⢰⢰⠂⠠⠰
⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣯⢿⣿⢾⠀⠀⠀⠀⠀⢀⡁⠀⠃⠀⢀⢰⣿⣿⣿⡆⣰⣿⣮⢛⢿⣿⡇⠀⠀⠹⠿⠟⠀⠘⠇⠈⠁⠾⠿⢷⣶
⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠀⢀⠴⠶⠟⠫⡅⠀⢘⡷⠈⢭⣟⣻⣿⡟⢻⣿⣟⣶⣾⣿⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠰⢶
⣭⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡆⠠⣀⡀⢀⣀⡴⠀⠈⠀⠐⠊⣻⣿⣿⠾⣿⣿⣿⣿⣥⡼⠧⠀⠀⠈⠀⠀⠀⠀⠁⠀⠐⡞⠆⠀⠀⣈
⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣀⡜⠃⢠⠾⠛⠛⠓⠄⠀⠉⣂⠀⠈⠁⡹⠿⠿⣿⣿⠿⡟⠫⠀⠀⠀⠐⡂⠐⠦⠶⠛⠛⠂⠀⠉⠓⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠈⢳⡄⠠⣀⠀⣀⣀⡤⠀⠀⠀⠂⠀⢀⡁⠀⠀⠘⠈⠀⠘⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⠆⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣄⠀⠀⣸⠇⠠⠞⠛⠋⠓⠦⠀⠂⠀⣴⡶⢀⠀⠀⠀⣰⣶⣶⡀⠀⠀⢐⣾⠿⣿⣿⠿⠟⠋⠉⠀⣀⠛⠛⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠟⠓⢧⡀⠐⢦⣄⣠⡤⠖⠀⠀⠀⠠⠀⠘⠁⠀⠂⠙⠿⠟⠀⠀⠀⠉⠉⣉⣉⣀⡀⠀⣀⡄⠀⠙⢻⡷⠸⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢸⡇⠰⠚⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠂⢰⣦⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠁⠀⠀⠺⠇⠀⠗⠀⣁
⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠀⣀⣈⠀⠐⠤⠄⠀⠀⠀⠚⠃⠀⠀⡤⠀⠀⣴⣶⠆⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⣄⢀⠀⠄⠀⠐⠐⠂⠸⣿
⠀⠉⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠘⠛⠐⢿⣿⠲⠿⠀⣤⣤⡀⢘⣿⣿⣿⣇⣶⡆⠀⠉⠉⠁⢨⣿⣿⣿⣿⢶⠀⠀⠀⠰⡀⠀⠀⠑
⠀⠀⠂⠤⠄⣚⠳⣼⡑⢞⣿⠀⠀⠀⠀⠀⣀⠸⠷⠀⠛⣿⣇⠘⠿⠿⠇⠛⣿⠄⠘⠛⢀⡀⠹⣿⣿⣿⡿⡟⠀⠠⠀⠀⠈⠀⠀⠈⠀⠠⠴⠤⣄⠐
⠀⣴⡄⠀⠀⠀⢠⡿⢙⣫⡞⠀⢀⠀⠀⣿⣿⡗⠀⠀⣴⣿⣟⣤⣤⣄⡀⠀⢀⣰⢤⠀⠈⠁⣠⡈⠉⠛⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⢐⡀⠐⠀⠀⠇
⠄⢸⡇⠀⠀⢀⡘⣰⡾⣼⠇⠀⢈⠀⠿⠇⣽⣄⢸⣟⡸⠋⢿⠿⣯⡟⢤⠀⠀⢼⣻⠸⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠳⢽⠽⠃⠈⠉⠁⠘⠟⠀⣾⠁⠸⣿⣿⡀⠀⠁⠀⠙⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠒⠀⠀⠀⢸⡇⠻
⠑⡀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⡆⠀⠀⢻⣿⣷⡀⣶⠦⣾⡿⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠺⠇
⠀⡆⠀⣉⠙⠛⠀⣀⠀⠀⢀⣾⢯⣿⣿⣷⣿⣧⠐⠈⢿⣿⣿⣟⢛⣁⡀⠀⠀⣴⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠸⣿⠇⠀⠄⣡⣴⣶⣷⣶⣤⡀⠆
⠘⡇⠈⠙⠃⢰⡆⠙⠀⠀⢸⣿⣿⣅⡸⢻⡿⣿⠠⠀⢠⣿⣏⣿⣽⡍⣿⣀⡀⠀⢀⠈⠀⠠⡆⠀⣾⣿⠆⢀⣤⡀⠠⠀⣼⣟⣹⣿⣿⣯⣽⣷⡌⠄
⠰⡇⠸⠿⠀⠘⠃⠘⣇⠀⠀⠛⢿⣭⣿⣿⣿⠟⠄⠀⢾⣿⣿⣿⣿⣟⠛⠻⠿⣀⡀⠀⣠⡀⠀⠀⣨⣇⠀⢀⣉⠀⠐⠰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐
⠀⣁⡠⠤⢄⣀⡤⢤⣍⠀⠀⠀⠀⠀⠙⠉⠈⠀⢠⣄⠀⣬⣉⡛⠻⠿⣿⠇⠸⣿⣿⡦⢈⣹⠿⠚⢿⡿⠃⠺⠿⠇⠈⠁⠻⣿⣽⣿⣿⣿⣵⡿⠁⠁
⣼⣿⠾⣧⣤⢩⡞⡯⢴⢩⠽⣖⠀⠀⠀⠀⢠⣤⠀⠙⠀⢀⡈⠉⠀⠀⠀⠀⠀⠈⠉⠐⠀⠉⠀⠀⣾⡆⠀⠘⠃⠸⠿⠀⠂⡈⠛⠛⡟⠛⠋⡀⠂⣠⣶
⡱⣿⣮⣗⡣⠒⠽⠣⠘⢜⣗⢾⠜⢀⣄⣤⣿⠃⠰⠇⢠⡟⠁⠘⠉⠉⢳⣤⠛⠉⠙⢲⡴⠛⠉⢳⣤⠞⠉⠙⠳⣴⠛⠋⠃⠀⠈⠀⠁⠈⠀⠀⠀⣯⠿
⢠⣦⣄⠀⠠⠶⠶⠆⠀⠀⠀⢠⣄⣼⣿⣿⣿⠀⠀⣄⠀⣤⠆⠀⠀⠀⣠⣏⡀⠀⢀⣼⣃⠀⠀⢀⣿⡀⠀⠀⣨⣇⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠹⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣶⣶⡿⠿⠟
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣛⣫⣭⣷⠶⠛⠁
⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠛⠛⠛⠋⠉⠁
⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣤⣤⡄⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡤⠟⠉⠉⠁⠓⠶⠶⠦⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠂
⠀⢸⣿⣿⣿⣿⡿⠋⠁⠀⠈⠉⠻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂⢠⠆
⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⣿⣿⣷⣄⡀⠀⠀⣀⣴⣿⣿⡇⠀⠈⠋⠉⠉⠉⠉⠉⠉⠋⠙⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠢⠤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠰⡂⠀⠐⠚⡠⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⡈⠀⠀⠠⠀⠀⣀⣱⠮⢀⠀⠓⠘⠓⠃⠀⠀⡀⢌⡃⠠⡆
⠀⠀⠀⠓⠓⠀⠀⠀⠠⠀⠢⢨⠀⠀⠀⢀⠀⠉⠀⠐⠸⡁⢐⠀⠁⠊⠀⠀⠀⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⠌⠀⢁⠂⠃⢸⡓⠃⠰⣀⠇
⠀⠀⠘⠀⠇⠀⠐⢀⠶⠀⠀⠈⠀⠀⢀⠀⠀⠀⠄⢀⠠⡤⠀⠠⠀⠀⠄⠀⡆⠀⢴⠀⢉⠀⠐⠀⠀⠀⠀⢄⠠⠁⠈⠄⠠⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠔⡀⠢⠀⠂⠀⠀⠄⠀⠠⠀⠀⠄⠈⠈⣠⣀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢀⣀⠀⢀⠠⡁⢈⠆⢄⠀⠤⣄⠀⠀⢔⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⢴⠆⡄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠦⠘⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⣱⠀⠀⠀⠀⢀⠈⠠⠄⠈⢷⠀⠢⡤⠃
⠀⠀⠀⢾⡐⠁⠙⢀⡇⠀⠀⠖⠂⡀⠀⢐⡛⠆⠐⠶⣆⣶⡄⠀⠮⠆⠀⠌⣀⢂⡂⠀⠔⠢⠀⠸⠭⠭⠿⠿⠽⠇⠀⠌⠉⠈⢀⠅⠀⠀⠀⠐
⠀⠀⡀⠀⣅⡋⣀⠁⠁⠁⠀⠈⠀⠀⣲⢢⡀⠀⠀⠧⣍⠴⠀⠠⣄⠄⠑⠀⢻⠀⠈⠀⠀⠀⠀⠀⠉⠈⠚⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉
⠀⢀⠤⢌⠉⢠⠈⠉⠀⠠⠀⠀⠀⠀⠠⣉⠀⢻⠒⡄⢠⠀⠈⣡⢀⡐⠂⠠⠃⠀⠀⠀⠄⠀⡄⠁⠀⣤⠀⣴⡶⢿⠂⡀⢠⡀⠄⡀⠈⠉⣂⠈
⠀⡇⣀⠈⠀⠈⡀⠀⠀⠈⠁⠀⠀⣦⡄⠉⡀⠈⠒⠁⠀⠈⠃⠀⠀⠁⠤⠆⠀⠠⠀⠂⠀⠂⡄⠀⠘⠓⠛⣂⡅⠂⠀⠀⢀⢌⠉⢋⡀⠁⠄⠈
⠀⠑⠤⠜⠀⠀⠀⡀⠐⠀⠀⢀⠤⠤⠤⠀⠫⠀⠀⠀⠀⠰⢆⠀⢀⠀⠘⠂⠀⠜⣁⠀⢿⠆⠠⣛⠃⠰⠊⠁⣀⠋⡁⢀⣠⡃⣀⢀⠋⠤⢰⡄⠆
⠀⠀⣰⡆⠀⢀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠀⠠⡦⠀⠐⠀⠀⠀⢠⠀⠁⡠⠒⠢⡀⢀⠠⠢⡀⠀⠀⠀⠤⠀⣿⠀⠶⠀⡀⠀⣀⢄
⠀⠀⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠄⠀⠀⠀⠈⠀⠒⠉⠀⠀⠀⠀⠱⠄⢤⠃⠘⢈⠌⠀⡡⠀⢀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠃
⠀⢀⡀⣠⠀⠀⠄⠄⠂⠀⠠⠴⡏⠲⢀⠔⠁⠐⠄⠀⢠⠒⢸⣿⠷⠾⡀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠐⠀⠂⠀⢀⡞⠀⠀⡀⠀⠀⠀⠰⠁
⠀⠑⠸⠈⠈⠆⠀⠀⠀⠠⠀⠀⠇⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢟⡠⠀⠂⡄⠀⢬⣽⠀⣄⡠⠨⠀⡀⠐⢀⣁⠀⠂⠀⠂⠀⠁⡀
⠀⠒⢤⠈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠈⠀⠄⠀⢨⠾⡀⠀⠀⠀⡀⠀⠀⢸⠀⠐⠉⠁⠀⠀⣉⢀⠀⢈⡉⣍⠀⠂⠘⠄⡃⠉⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠈⠀⠐⠊⠀⠀⠂⠐⠀⠀⠀⠈⠀⠀⠑⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠲⡀⠈⡀⢀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⣀⣀⣠⣔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣤⣴⣿⣿⠃⠀⠀⠀⠈⢰⡇⣄⣀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣠⣤⠴⢿⣈⣿⡟⠉⠻⢿⡄⠀⠀⠠⡆⢸⣷⣿⠉⠈⣿⣿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣯⠑⢛⡁⠂⠈⢻⣿⣷⠀⠀⡀⠀⢀⣤⡀⣷⣿⠿⣛⡆⣸⡿⢿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⢿⣿⣧⢠⣿⠀⠀⡿⠀⢉⡟⠀⠏⣸⣿⣄⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠡⠹⠆⠀⠀⠈⠀⠀⠘⢻⣿⣾⣧⠀⠰⢷⡄⠸⠷⠠⠂⢁⣾⣯⡿⠛⠿⠿⠿⢇⣤⣄
⠀⠀⠀⠀⠀⣀⣸⣤⣤⣄⡀⣠⠂⠀⠘⢿⣭⢿⣿⣷⠀⠀⣿⠀⠀⠀⠀⠀⠘⡿⠛⠁⠀⠀⠂⢀⣿⠹⠙⢷⡀
⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠁⠈⣀⠉⢿⣾⣿⣿⡀⠀⡽⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⢀⡴⠻⠁⠀⠀⠀⠁
⠀⠀⠀⠘⢷⠶⠦⠤⠂⠄⠀⠀⢂⣄⡈⠻⣾⣿⣿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠪
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⣻⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡈⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠰⣶⣬⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣷⢆⠄⠀⠀⠀⠀⠀⡐⢋
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣄⠀⠀⢠⣦⣰⣾⣴⢂⡤⠶⠦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⣀⣤⣀⣀⣀⣤⡶⠶⠖⠛⠛⠻⣿⣿⣧⣄⡀⠉⠉⠻⣿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⣾⠙⠛⠻⠿⠿⠿⠿⠛⠉⠀⠐⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⡄⠀⣶⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⢀⣤⡴⢊⡿⢳⣼⡟⣹⠟⡀⢹⡄⠀⢼⣁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣦⣤⣠⠤⠄⠀⠀⢀⣍⣸⡿⠋⢀⣬⣿⣷⡿⠟⡃⢸⣷⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠟⠉⠀⠀⣶⠋⠋⠀⣠⡾⠃⢸⡟⣆⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠇⠀⠀⠀⡰⠃⠀⠀⡄⠉⠀⠀⣿⠀⠘⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣼⠁⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⡠⠠⠠⡄⠀⠄⠀⠉⠀⠒⠂⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⡀⡀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠚⠀⠀⡀⠠⡄⠀⠁⠈⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠈⠁⠉⠉⠀⠑⠤⠂⠀⠀⠀⠀⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡂⠄⠀⠀⠀⠀⢐⣓⣒⣛⣒⣒⣳⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⢄⠀⢀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⡩⠘⠁⠄⡒⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠂⠠⠀⠀⠀⠀⠺⠂⠀⠀⠀⠈⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⡄⠛⠂
⠀⠀⠀⢠⢅⣠⠀⠀⠀⠀⠛⢠⡶⣆⠀⢶⠆⠀⡴⠶⣦⠀⣴⠀⠀⢀⡴⠲⣦⠀⣠⠖⠶⠄⠐⣆⠀⣴⠀⠀⠈⠢⠤⠚
⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢸⡷⣯⠀⢸⠀⢸⡇⠀⢸⠄⣿⠀⠀⢸⡇⠀⣹⠀⡿⠀⠰⡤⠀⠘⣾⠃⠀⠀⠠⠀⠠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠧⠞⠀⠾⠆⠈⠷⠶⠛⠀⠻⠶⠶⠈⠷⠶⠛⠀⠻⠶⠾⠃⠀⠰⠏⠀⠀⠀⠁⡀⠁⡀⠈⠁
⠀⠀⠀⠀⠐⠠⡁⠀⡀⠈⠀⠠⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠐⢀⢀⡘⠀⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠀⢼⠒⠂⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠠⢄⠀⠎⠀⠀⠄⠠
⠀⠀⠀⠀⠈⠠⢀⠀⠂⠀⡀⠀⢀⠔⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⢤⠀⠀⠀⠀⠰⠂⠀⠀⠀⡘⠀⠈⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠆⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠦⠀⠀⠀⢶⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠖⠀⠆⢀⡄⠐⡠⠀⡄⠀⣐⠀⠠⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠉⠐⠀⠀⠰⠒⠀⠀⠀⠰⡐⠒⠀⠰⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⣄⠀⠀⠀⠴⠂⠨⢦⡀⠀⠀⠀⠀⠁⠁⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⡤⠒⣆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⡀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠃⠦⠉⠀⠰⠟⠛⠋⠁⠀⠀⠀⠀⠄⣀⠂⠀⠰⠊⠀⢀⢀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠀⠁⠰⠰⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠀⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠁⠀⠞⠀⠀⠀⠓⡀⠀⠀⠀⠀⠐⢺⡆⠀⠀⠀⠀⠚⠻⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⡀⡀⠀⢠⠆⠀⠀⠘⠀⠀⠄⢀⡀⢄⠀⠀⠀⠀⠀⠀⣴⣃
⠀⠀⣠⠀⠀⠀⢀⣀⠈⠋⠀⠀⡄⠀⠀⠀⢬⡻⣄⠔⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢶⡇⡘⣏
⠀⠀⠃⠀⣀⠈⠐⠀⠀⢀⠀⠉⠀⠀⠀⡐⢉⠥⠂⠠⠆⠀⠀⠀⣠⣀⠀⠀⠀⠀⠆⠀⢠⠀⢈⣩⣵⣵⠇
⠀⣸⠀⠀⠛⠀⠀⣀⠐⠈⠀⠄⠀⠀⢀⡁⠊⢀⡛⡀⠠⠆⠀⠘⠑⠀⠀⠀⡦⠀⠀⠀⠈⠀⠀⠀⠹⡏
⠀⣼⠀⠀⠀⠐⠀⠁⢀⡀⢀⠀⠐⠂⢣⡞⠄⣼⠃⢹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡄⠄⡀
⠀⠦⠀⡿⠇⠀⠀⠀⡀⠀⠌⠁⠀⢇⠁⢀⡾⡟⢎⡎⠀⠀⣀⡰⠄⠊⡷⠀⠀⠀⠈⠀⠂⠀⠀⠀⠰⢠⠁
⠀⣴⡔⢳⣦⣀⠀⠀⠐⠤⠀⠀⢀⠈⠣⡾⠈⠠⠌⠀⠀⠁⠻⢯⠆⠀⠁⠈⢀⣀⠈⠓⠒⣂⣸⡧⠄
⠀⠀⠀⠀⢋⠁⠀⢀⡀⠤⢒⡖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠏⠀⢰⠋⠁⠀⡇
⠲⣄⢠⡞⠀⠀⠀⢀⠖⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢠⠆⠀⠀⣀⣤⣼⡤⠴⠊⠀⠼⣆
⢰⡿⣆⡔⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⢈⡀⠀⠀⠀⠀⠁⡆⠀⠀⠀⣇⠀⣸⠇⠀⢀⠀⠀⠛
⠀⠙⡏⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⡒⠁⠀⠀⠀⡄⡀⠖⠀⠀⣰⠚⢻⡍⠁⠀⢰⣶⠧⠶⣄
⠀⢀⡄⠀⡀⠐⢀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠀⠨⠄⠀⠀⢑⠈⠀⢀⣻⠤⠞⠁⡀⠈⠉⡇⠀⠀⢉⠃
⠀⠘⠏⠀⠱⡀⠀⠀⠖⠀⠀⠒⠚⠉⠉⠉⠁⠀⣀⣀⣴⣶⡶⠆⠀⢀⣯⠟⠀⠀⠢⢏⠀⠀⠑⠧⡐⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢠⣄⣠⡀⠂⣴⢄⣺⡫⢛⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀⠒⢀⣿⡟⠛⠏⣅⠨⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂⠡⠃⠘⠾⠀⠃⣀⢌⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠓⠄
⠀⠀⠀⠀⠀⠆⠄⠠⠀⡄⡌⠀⠂⠀⢀⡨⠁⠧⠀⠠⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⣠⣘⠻⠀⠀⠠
⠀⠀⠀⠀⠀⢷⢈⠂⠠⠈⠀⠀⣤⠐⠌⠱⠆⠀⠀⠀⠀⢄⠀⠀⠈⡠⠈⠃⡅⢷⢠⠈⡄⢁⠢⠂
⠀⠀⠀⠀⠀⡉⠴⢆⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣄⠈⢷⣄⠀⠘⣅⢎⠛⣿⡠⠖⣖⠂⠜⠁
⠀⠀⠀⠀⢠⠀⠄⡐⢦⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠁⠰⡌⠢⣚⠀⡈⠺⢷⡞⠁⠠⠀⠠⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠂⠬⠀⠀⠀⠀⠈⢶⡤⢀⡀⠀⠀⢀⡈⠠⠉⢤⡈⠀⡄⠛⣐⣈⣘⣐⣆⠴⠚⠁
⠀⠀⠀⠂⠀⠉⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠱⠏⠲⠂⠀⠀⠘⠄⠘⡄⠀⠨⢠⣌⠀⣈
⠀⠀⠀⠀⠀⢈⠀⠂⡤⠀⡀⠀⠀⠢⠄⠀⢀⠀⠀⠄⠢⢄⠀⢀⠀⠔⢰⠀⠉⠍⠀⡈⠀⢛⠉⠟⠒⠂
⠀⠀⠀⡀⢀⡄⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠐⠤⡈⣀⠏⠀⡀⠀⠀⠒⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⢂⡐⠙⠀⢁⠀⡀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠁⡋⠀⠄⠄⢀⠀⠠⢠
⠀⠀⠄⠀⢀⠈⠡⠀⢀⡜⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠄⠈⠈⠀⠀⡀⠀⠀⠀⢀⡀⠤⠆⠐
⠀⠀⠠⠀⠠⠐⡂⠐⢀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⠘⠀⠀⠁⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠆
⠀⠀⠀⠀⠀⡀⠁⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⢀⠀⠰⠂⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠁⠀⡆⠀⠀⠄⠁
⠀⠀⠀⠐⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠐⠀⢈
⠀⠀⠀⠠⠀⠀⠀⢸⠀⢇⢀⡀⠠⠔⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠹⣄⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⢈⠀⠀⠀⠡⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠁⠘⠀⠀⡀⠑⢀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠚⠀⡀⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣎⣥⣶⣶⣮⣿⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⠋⠀⢈⣿⡿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⢁⡀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⡔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠊⠀⠈⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠁⠀⠠⠈⠀⣠⣤⣦⣀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣧⠄⠀⠀⠡⠼⣿⣿⣿⣿⣷⣬⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣽⣿⡍⢀⠀⠀⠀⠠⠄⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣀⣻⢤⣀⡐⣻⣿⠋⠀⠀⠐⠈⠐⠀⢀⡀⠀⠙⠻⣿⣿⣿
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡽⢟⡩⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠈⠻⣿
⠀⠲⣴⣤⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣤⣿⠿⠿⣾⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠉⠒⠶⠦⢔⢀⣂⣀⠄⠈⢁⡈⠉⠩⠻⠃⠀⡠⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡥⢔⡈⠀⠀⠠⡉⠀⡠⠚
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣻⠷⠚⠋⣰⠻⢅⠎⠀⡤⠄⣦
⠀⠀⠀⣀⣠⣾⡿⠟⠋⠁⠀⠀⢰⣟⣿⡇⠀⠀⠑⣖⠌⡆
⣷⣶⣬⡏⠉⠁⠀⠀⠀⠀⠀⠀⣿⣤⠟⠀⠀⠀⠀⠙⠲⢿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿

⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⠀⡠⠋⠊⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡠⠋
⡰⠋⠀⠀⠠⠔⣒⠒⠐⠄⠀⠀⠀⠀⠀⠀⠰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⢠⠔⣒⠒⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⢀⢾⣿⠶⠋
⠀⠀⠀⠀⠁⠠⣴⠄⠀⠀⠑⢄⠀⠀⠀⠀⠠⡠⢄⡀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠐⠁⠀⣴⠄⠀⠀⠁⠀⠀⠀⠀⠀⠘⡠⢄⡀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠙⢷⣾⡇⠀⠈
⡀⠀⠀⠀⠀⠈⠳⣄⣀⠐⢾⡰⣼⠀⠀⢀⠤⠒⠒⠉⠉⠉⠁⠀⠐⠤⡀⠀⠀⠀⠀⠀⠲⣄⣀⠐⢾⡴⡱⠀⠀⢀⠠⠂⠒⠉⠉⠉⠉⠀⠐
⠈⠢⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠁⠀⠀⢀⡀⠂⠄⠄⠤⢀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⢠⠃⠀⡀⢀⡀⠂⠤⠄⠤⢀
⠦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣯⠉⠁⠀⠀⠀⠀⠘⠢⣀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣯⠁⠁
⠲⡘⡂⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠲⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠳⣄⡀
⣿⠟⠛⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠶⠶⣶⣿⠟⠟⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠷⠶
⢀⣀⢌⣳⠋⠀⠀⠀⢀⠀⠠⠤⣤⣀⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣳⠋⠀⠀⠀⢀⠀⠤⠤⢤⣀⡀⠀⠀⠀⢀
⠭⠞⠋⠁⠀⢀⠔⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠉⠐⠢⠤⠬⠬⠬⠭⠖⠋⠁⠀⢀⠄⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠈⠐⠢⠤⠬⠤
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣹⠏⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢹⠇⠆⠈⡻
⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⡠⠋⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⡠⠫⠊⠀⢰⠏
⠀⠀⠀⠀⠄⢀⢾⣿⠶⠋⠀⠀⢀⡰⠃⠀⠀⡠⠒⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⢰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⡠⠒⠀⠀⠒⠄⡀
⠀⠀⠀⠰⡴⢄⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⢰⠁⠀⣴⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡰⢌⡀⠁⠀⢀⣀⠴⠊⠀⠀⠀⠀⠁⠀⣴⠆⠀⠀⠐⢄
⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⡄⠀⢠⠀⠈⢂⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠙⣿⣶⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡆
⠀⠀⢀⠄⠐⠚⠉⠁⠀⠉⠁⠒⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢐⣿⡴⡧⠀⠀⢀⠤⠒⠚⠉⠁⠀⠁⠀⠀⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢈⣮⡴
⠀⢠⠃⠀⠀⢀⡂⠒⠠⠄⠄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠓⠉⠀⠀⢀⠃⠀⠀⢀⡐⠒⠢⠄⠤⠀⠀⠈⠒⡀⠀⠀⠀⠀⠀⠉⠙⠓⠉
⠀⡆⠀⠀⠐⣿⠁⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣯⠈⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦
⠀⠠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠰⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠳⣌⢦⠀⣃
⠀⠀⠱⡀⠀⠀⠀⠀⠉⠓⠳⠶⢶⣿⠟⠛⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠛⠳⠶⢶⣿⠟⠓⢀⣸
⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡣⠃⠀⠀⠀⣀⠤⠀⠤⣄⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⡳⠋⠀⠀⠀⣀⠤⠀⠤
⡀⢛⡧⠀⠀⠀⠈⠒⠲⠤⠬⠬⠭⠽⠞⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀⡀⠌⢛⣦⠀⠀⠀⠈⠐⠲⠤⠤⠬⠬⠽⠚⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀
⠃⢈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣹⣇⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⢨⠽⠂⠀⠀⠀⠀⡝⠐⠀⠀⣠⠁
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠈⠂⡀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⡀⠀⠀⠠⠨⠈⠀⠀⠀⠀⠀⡀⠡⠮⠠⠀⡀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠧⠈⠀⠐⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢸⡀⠊⠀⠂⢸⠀⠀⢄⠠⠀⠀⠀⠀⢠
⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠈⠶⠠⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠀⢈⠠⠠⠘⠈⠀⠀⠀⠀⠀⠈⠂⠀⡆
⠀⠰⠰⠀⠀⠴⡆⣠⣄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠯⠭⢭⠭⠭⠭⠀⠀⠀⠀⠚⠁⡈⠑⠂⠀⠀⠀⠠⠁⠄
⠀⠀⠀⠀⠀⢆⣘⡠⠄⠀⠀⠐⠁⠐⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠄⠅⠐⠀⢀
⠀⡰⠒⠢⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⣶⠄⢠⡴⢦⡀⢰⠀⠀⢀⡴⢶⡄⠀⡴⠶⡄⠀⣦⠀⣴⠀⠀⠀⠀⠠⠁⠀⠈⡆⠒
⠀⠀⢀⠀⠆⠆⠸⠆⠃⠀⢸⡷⣇⠀⣿⠀⣿⠀⢸⡇⢸⠀⠀⢸⡇⠀⣿⢸⡇⠀⣦⠄⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠘⠷⠋⠐⠛⠂⠘⠶⠚⠁⠘⠓⠒⠈⠳⠞⠃⠈⠳⠶⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⣼⣃⣘⠿⠃⡋⠀⠀⠀⢀⠁⠀⠂
⠀⠘⠃⠀⠁⠀⠸⠂⠀⠀⠀⠐⠇⠀⠀⠀⢄⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⡀⡄⠀⠀⢀⡠⠔⠀⣠⠀⠀⠀⠁⠀⠀⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠐⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠃⠂⠇⠁⠑⠀⠀⠐⡂⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠨⠀⠀⠀⠀⢀⢀⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠄⡀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡐⠀⠃⡀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⠀⢈⠐⠁⠀⠸⣀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡀⠀⠂⠀⠄⡐⠀⢂
⠀⠀⠀⠀⠀⡴⠁⠀⠠⠄⠀⠀⠀⠈⠸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠁⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠹⠃⠀⡐⠄⠈⠁⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⢰⠄⡀⠀⠀⠀⠀⣀⢄⡄⠀⣶⠂⠀⠀⠀⢠⡔⣶⠆⠀⠀⡠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⡀⠀⠀⣤⣈⡃⠐⠛⢘⣣⡌⠀⠀⠙⣦⡀⣿⣿⡍⡤⡟⠀⠀⣜⠦⣹⣿
⠀⠀⠀⠀⠀⠀⠀⢿⢘⠻⣷⣄⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠂⠉⠞⠁⢤⣤⣹⣶⣧⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣰⣾⣥⣾⣤⣀⣀⠀⠀⠀⠀⠀⠠⣤⠤⠄⠀⣀⠠⢦⠐⢺⣶⣽⣿⡟⠏⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⢩⣄⠙⢿⣿⣏⣶⣄⠀⠀⠀⠁⠀⠀⠘⢦⣄⣶⣿⡻⠿⠟⡊⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣰⠂⠉⠉⠉⣉⣉⠁⠀⠠⢤⠤⢤⠄⠀⠀⣀⣀⠘⠻⠿⠛⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢧⣴⡔⠁⠀⣴⣶⠀⢻⣦⠽⣦⡀⠀⠀⡀⢀⣴⠿⢹⡟⢐⣿⣦⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣽⣆⠀⢿⣮⡑⢪⣆⢠⣴⡑⢈⣰⣿⠀⢸⡿⣿⣇⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⠿⠟⠀⠰⣇⠄⣀⠹⣿⡗⠀⣤⣸⡆⠀⣸⠗⣿⣿⡀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡀⢾⣉⡀⠠⢘⡀⠀⠙⣶⡟⠀⠉⠀⢼⣦⠋⠀⠀⣿⢠⣿⡿⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠃⠈⠛⢧⡤⣘⠁⢀⡼⠃⠀⠀⣀⠀⠀⠛⢆⠀⠸⠿⠚⠋⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠸⣿⣧⣄⣀⠀⠁⣰⣦⣄⡀⠀⠀⢀⣤⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣀⣠⣶⣿⣿⡟⠃⠀⠀⠀⠲⠶⢤⡙⣷⠀⢸⣋⢿⣿⣦⣤⣿⣿⣟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⢈⣀⡀⡀⠀⠁⠀⠀⣹⣲⣿⣿⢿⢿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠟⠙⠃⣿⣿⣿⠇⠀⣶⣦⣄⠀⠀⠀⠀⠀⢀⡀⠀⠸⢿⣿⠇⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⡈⠋⠁⣀⠀⢸⡾⣿⣷⣤⣄⣲⣿⣛⠏⠀⣶⣀⡀⠶⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠾⠛⠋⠀⣼⣿⣧⠈⠙⠻⠋⠿⠩⢿⡿⠇⣀⣼⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢤⡾⠉⠈⣀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣰⡿⢟⡗⣿⠁⢘⠃⠀⠐⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⢰⣍⣻⣿⣷⣦⠀⠀⢠⣾⢟⡹⣾⣻⣯⡏⠠⠎⠈⠀⢐⣄⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠀⠀⠀⣰⣾⣿⡿⣿⣿⡿⠀⠀⢿⣫⣾⡷⠟⠿⣛⣧⠀⠀⠀⠀⠈⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣶⣶⣾⣿⣿⣿⡙⠳⠄⠀⢀⠀⠤⣤⣤⣤⠄⢈⣉⣿⣿⣯⣳⡶⢦⡤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⣿⣿⡆⢠⣾⣭⠽⠾⠉⠉⠀⡴⠟⠻⢌⣛⣍⣭⣿⣶⣾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠀⠉⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠂⡀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠄⠀⡼⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠸⠄⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⠈
⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠒⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠆⢱⠀⠀⠀⣀⡴⡄⠠⠀⣀⠤⣀⠀⢀⠀⠀⠀⡀⠀⢀⡀⡀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠃⠈⠀⡘⠀⠀⠀⠀⠉⣤⢺⠁⠀⣸⠁⢨⠥⠀⣠⠃⡇⢸⠈⠩⡍⠀⠀⢹⠀⠀⠀⡆⠀⠞
⠀⠐⠒⠂⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠘⠉⠐⠃⠐⠚⠀⠋⠐⠁⠁⠚⠁⠒⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠂⠀⠈⠙⠋⠀⠿⠧⠽⠟⠟⠿⠉⠿⠯⠤⠤⠷⠾⠾⠿⠀⠈⠁⠀⢖⠀⢆⠀⠲⠀⠠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⢀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⠀⠀⣀⡀
⠀⠀⠀⢘⡁⢈⠀⢀⠒⠀⠀⠄⠀⠀⠀⠀⣠⣾⣽⣿⣷⣤⣀⠀⢻⡏⠀⣄⢿⠆⠈⢐⣘⣓⡀⠐⠀⢸⣟⠛⣦
⠀⠀⠀⠈⠀⠜⠀⣤⢢⢤⠐⠀⠃⠈⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣤⡀⠠⢤⣷⠀⠡⣉⠧⠹⠟⡀⠀⠀⢻⣶⡿
⠀⠀⠀⠀⠀⠀⢠⣟⡞⢖⠣⢯⡃⠀⠀⡀⠈⠻⣿⣽⣯⣴⣺⣭⣿⣿⣷⠀⠀⠀⢀⢻⣀⠀⡴⢹⣯
⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣾⢧⡄⢠⠀⢷⣤⣶⠠⢍⣉⠛⠻⣷⣿⣿⡿⠁⠀⠀⢹⠛⠉⣘⢒⢺⣿
⠀⠀⠀⠀⠀⠀⠨⠑⢿⣤⡼⣧⢂⠁⠀⠈⠳⠥⣄⣀⡐⡱⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠏⢈⢉⣿⠀⠀⠀⣀⣀
⠀⠀⠀⡀⠐⢆⠀⠙⠂⠉⠀⠈⠁⠀⢀⣀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⢾⣿⣧⣹⡄⠀⢀⡿⣿
⠀⠀⠀⠨⠙⣦⡱⢄⠀⣤⡀⠀⠀⠀⣾⠋⣉⠙⡘⣿⠀⠀⠀⠠⢰⠀⡜⠀⠀⠀⠀⠈⢈⢺⣿⣿⢿⣇⠀⢸⣿⡟
⠀⠀⠀⠉⠲⢶⡻⣦⣲⡈⠉⡀⠀⠀⠹⣾⡿⠏⢛⣋⡀⠀⠀⠀⠘⡇⠃⠀⠀⠀⠀⠀⠈⢌⢿⣿⣿⣿⠁⠀⠉
⠀⠀⠀⢀⣠⠤⣬⣷⣽⢛⢷⣶⢯⣖⠀⢠⡶⢿⠘⣿⣿⠆⠀⠀⢀⠘⢶⠀⠀⠀⠀⠀⠀⠀⠑⠝⠛⠡
⠀⠀⠀⠘⠃⡎⣴⠛⠿⢞⣬⠻⣿⣟⣥⠀⢿⣄⣶⠻⠿⠃⠀⠈⠀⠀⢈⠀⣧⡄
⠀⠀⠀⠀⣀⠈⢋⡎⡙⣤⣿⣧⢿⣿⣿⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠐⠛⡁⠀⠀⠀⠀⣡⣶⣶⣶⡅
⠀⠀⠀⢾⡟⣧⠈⠟⡻⡏⠡⠏⠀⠈⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⠄⠐⠀⠀⠀⠀⠀⢿⣟⣿⣿⣯
⠀⠀⠀⢸⣇⡿⠀⣏⠋⠋⠀⢀⠴⠄⠒⢂⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠀⠀⠀⠀⠈⠀⠿⠾⢿⣿
⠀⠀⠀⠸⠿⠃⠀⠃⠀⠀⠀⡏⠀⠀⠉⣈⠄⠀⠀⠀⠀⠀⠀⠀⣀⠚⠁⠙⢒⢂⠀⠀⠀⠀⠀⢈⢄⡀⣉⠘
⠀⠀⠀⠀⢀⠖⠛⠓⣄⠀⠀⡇⠀⠀⠀⠈⠘⢂⠁⢀⠀⠀⠖⠊⠀⠀⡀⠀⢀⡆⠀⠀⢀⣀⡀⠀⠈⡠⠄
⠀⠀⠀⠀⡎⠀⠐⠂⠀⢑⡀⠈⢀⠀⢀⡀⠘⢅⠃⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣯⠏
⠀⠀⠀⠀⡧⠀⠀⠂⠀⢤⠃⣜⠛⠛⠋⠉⢗⡄⠈⠛⠳⡄⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠁⢀⠀⡴⣀⢀⡀
⠀⠀⠀⠀⡀⡇⠀⠰⢄⠎⠀⠯⢦⣿⣿⢶⠆⠀⠀⠀⠀⠈⠀⠀⠀⠖⠉⠳⣄⡈⠛⣲⡾⠗⢂⣞⣛⣋⠁
⠀⠀⠀⠀⡇⠀⠆⠐⣸⠀⣠⣄⣠⣄⠀⠀⠀⠀⣤⣤⢴⢦⡴⢾⠇⣤⣤⡀⠈⠉⠉⢁⡴⠛⠁⠘⢻⠿⠇⣀⡄
⠀⠀⠀⢠⡇⠠⠀⢠⠇⠐⣷⡟⠳⠿⡞⣧⠀⣞⠻⣧⢏⣻⣶⡾⣆⣧⣨⡇⠀⢀⠞⢁⡠⠞⢃⡘⠃⠀⣰⣿⣷
⠀⠀⠀⠀⠑⠾⠖⠁⠀⠈⠫⣿⡛⣶⠟⣯⠀⢿⡴⠏⠾⣾⣏⢳⣽⠎⠉⠀⢠⠋⡀⢸⠀⠀⠈⠥⠄⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢉⠿⡿⠀⠀⠀⠀⠛⠃⠉⠉⠉⠀⠀⠀⠀⠘⠂⡁⢾⠀⣀⠀⠀⠀⠀⠙⠟⠃
⠀⠀⠀⢀⣴⡜⠻⣿⣀⠀⠀⣤⡀⢶⢶⡟⢻⣀⠀⠀⠄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌
⠀⠀⠀⢸⣟⡠⢠⡜⠛⠁⠀⠉⢱⡞⢿⣹⣿⣿⠃⠀⠁⠉⡳⠦⢬⣦⣤⡴⠀⠀⢠⠀⠀⠰⠂⡠
⠀⠀⠀⠀⠘⠶⠿⢃⣰⡿⣂⠀⠈⠻⠟⠻⠶⠛⠀⠀⠀⠄⠠⠶⠲⠺⠛⢙⡀⠸⠛⠒⠦⠀⠺⠖⠂
⠀⠀⠀⠀⠀⠀⠸⠟⠃⠙⠛⠀⠀⠀⠀⠀⠀⠐⠤⠎⠁⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⢠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢸⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⡇⡏⠃⠋⠁⡀⠀⠀⠀⠀⠀⣇⠀⣶⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠃
⠀⠀⢸⢀⣂⣀⠀⠐⠂⠀⠀⠀⠀⡏⠉⡏⡏⠉⠉⠉⡇⠀⠀⠀⠀⠀⡇⢠⣀⣂⠀⠀⠀⠀⠀⠀⠀⡥⠊⠀⠑⢀
⠀⠀⢸⣀⣙⣋⠀⣤⣤⠀⠀⠀⠀⡧⠦⠇⠧⠆⠤⠦⡇⠀⠀⠀⠀⠀⣇⣈⣙⣁⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣾⡿
⠀⠀⠈⠉⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⡀
⠀⠀⠀⠀⢸⡇⠀⢘⡇⠀⠀⠀⢀⡤⠒⠒⠒⠒⠒⢤⡀⠀⠀⠀⠀⢸⣀⡇⠀⢸⠀⠀⠀⠀⠀⠀⣞⣁⠴⠆⣌⢣
⠀⠀⠀⣠⡼⠛⠒⠋⠀⠀⠀⠀⠘⠇⣀⠐⠉⠂⣀⠜⠃⠀⠀⠀⠀⢸⣿⡇⣷⣾⠀⠀⠀⠀⠀⠈⡇⢨⡅⢠⡌⡸
⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠻⠟⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠚⠁


⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢂⡀
⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢴⡿⢽⡀⠀⠀⠀⠀⠀⠀⡀⠡⣿⣮⠄⢀
⠀⠀⣀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣐⣲⣶⣾⣁⠀⠀⠀⠀⠀⠀⠀⡉⢝⠻⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠾⠄⠉⠃⠶⠀⠀⠀⠀⠀⠠⢠⠐⠀⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⠓⠰⠈⠁⣒⠂⠀⠀⠀⠀⠀⠀⣎⣀⣣⠀⠀⠀⠀⠀⠀⠀⢠⣤⣧
⠀⠀⠻⣷⠿⠁⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠐⠁⡂⠁⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠀⠀⠉⠀⢀⡀⠀⠶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣀⡀⠀⠀⠀⢰⡀⡄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡤⢖⣇⠀⠀⠀⠀⣠⠀⠀⠀⠀⠐⠁⠀⠘⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐
⣴⣿⠃⠀⠀⠀⠀⠀⠀⢠⢞⡁⠀⠀⢸⠇⠀⠀⠀⠻⠙⡞⠨⣂⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠃⠀⠈⠉
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢀⠤⠄⠃⢰⠀⠀⠀⠀⠀⣾⣿⠀⢠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠻⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⢸⡆⠀⣤⠄⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⣼⣿⠋⠀⣸⡃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⠉⢀
⠀⠀⠀⠀⠀⠀⠀⣄⣶⡘⠟⠁⠀⠨⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⠀⠀⠈⠀⠀⠚⠀⠙⠀⢀⡄⠀⠀⠀⠀⠈
⢣⠀⠀⠀⠀⠀⠀⠀⠙⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡀
⡼⠃⠘⣦⡀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠠⡀⢄⠄⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠰
⠃⡶⠠⠭⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡆⢘⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⡁⠀⢀⠶
⢲⣒⣷⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠰⡁⠀⢰
⡄⣛⡻⠀⠁⠁⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠈⠀⠄⠀⣀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈
⠀⠋⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠔⠃⠀⠀⠀⠀⢁⡀⠀⠀⠘⠠⡄⠀⠀⢌⣁⠠⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⡀⠶⠠⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡀⠀⠀⠈⠀⠀⠈⠙⠀⢠⠆⠀⠻⣄⠐⠀⠈⠃⢀⠀⡇⠀⢀⠀⢀⡀⠀⡀⣸⣷⠖⣁⣀⠉
⢃⠀⡄⠀⠀⠀⠀⠀⢀⠁⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣸⠳⢦⣀⠄⠀⢠⡇⠒⠋⠀⠀⠁⠀⠀⣭⠉⠀⠈⠠⣵
⠘⠀⠁⠂⢠⠀⠀⠀⠀⢀⣠⠌⠀⠀⠀⡄⠀⡙⠀⠀⠘⣄⣦⡐⢀⡆⠀⠀⠀⠲⣀⠃⠐⠀⠉⢢⣀⡞⠀⠀⠀⡀⠈⠐⠀⠀⢧⣄⠀⠀⠀⠀⠅
⠀⠀⠐⠦⣼⣀⣀⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢴⠋⠉⠄⠀⠀⠀⠤⡄⠈⠂⠠⠀⠀⠀⠸⠁⠀⠀⠀⠠⠤⠐⠀⠀⠀⠉⠀⠚⠃
⠀⠀⠀⠀⡏⠀⠈⠉⠛⣆⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⣀⠀⠀⠀⠀⠀⠀⢦⣀⠀⢀⣠
⠀⢀⡄⠀⠳⣀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠈⣁⡐⠓⠀⠀⠀⠀⠀⠳⡀⠂⣀
⠀⡾⠀⠀⠀⠈⠛⠲⠤⡿⠤⢤⣤⡀⠀⠀⠀⠘⡦⠀⠀⠁⢈⡧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠣⡄⡿⢺⠛
⠘⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠡⡄⠈⠀⠀⠀⠀⠀⠢⡀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠈⡷⠉
⠀⠀⠀⠀⢰⣂⡀⠀⠀⠛⠶⢤⣴⣇⣀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠇
⢠⣞⠉⠓⠺⣿⣿⠀⠀⠀⠀⢰⡏⠀⠉⢷⠀⠀⠀⠀⠒⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢀⣶
⠘⠁⠀⠀⠀⢠⡉⠂⠁⠀⠀⠈⠣⣄⡀⣼⠀⠀⠀⠈⠠⠄⢁⠀⠀⠀⠴⠀⠀⠀⠀⢌⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠈⣿
⣐⢄⠀⠀⣠⣨⠃⠀⠀⠠⡀⠀⠀⠀⠉⣿⠒⢦⠀⠀⠁⢀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠤⠦⠀⠄⢤⣀⣀⡀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⡀⠄⠘⠁⠀⠀⠀⠠⠇⠋⠀⠀⠀⠈⠳⢾⣀⠀⠀⠀⠉⠛⠛⠻⠟⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠄⠁⠀⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠰⡆⠀⠁⠀⠐⢷
⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣆⣨⣅⣀⣀⣀⣁⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢀⣔⣉⠑⣤
⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡸⢫⢽⢯⢺
⠀⠀⠀⠀⠀⠀⡃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢾⠀⢠⡊⠔⢢⣀⣼⢊⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢢
⠀⠀⠀⠀⡠⠞⢿⡖⡶⢅⣠⢄⠀⣀⡀⠀⠀⠀⠀⠈⡶⢡⣆⡸⢒⡈⢆⣿⣁⡷⡤⣤⡆⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⣦⡀
⠀⠀⠀⠀⣇⠈⠻⠷⠄⢧⠘⠚⣾⡿⢃⢖⠒⡄⠀⠀⠐⣺⡏⠃⠘⡗⠈⢯⠍⠇⡤⠄⢰⠀⢀⠀⠀⠀⠀⠀⢠⠵⠒⠟⠇⣼⠋⠑⡄
⠀⠀⠀⢀⠿⠳⣤⣤⡄⢀⣵⣾⣏⡷⠬⠅⡊⠤⠤⠄⠒⠻⣁⡾⢿⣷⡒⡶⢲⡂⣷⡤⠼⠀⠀⠉⢢⡄⠀⢠⠃⡄⢃⠙⠀⢫⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠂⢹⡉⠙⡞⢩⣷⠾⠧⡔⣡⡆⢲⡼⠦⠟⠋⠒⣎⣁⡀⠿⠹⡁⠉⡳⣇⢀⠤⠤⣠⣿⣤⣖⣛⠶⠻⢴⠶⠦⠴⢤⡀⠸⣿
⠀⠀⠀⢳⡶⠖⢞⠧⢠⢫⡟⠁⢰⡟⠱⠠⢵⠆⠀⡔⠀⢺⠀⠏⠁⠙⣌⣠⠿⡌⢝⠂⣹⡴⣖⠛⠫⣇⣠⣓⡶⣶⠃⠀⠀⠀⠀⠀⢠⢿⡄
⠀⠀⠀⠀⣿⠆⣌⠀⡖⣾⠀⠀⠀⠉⠑⠛⠼⢴⣼⣣⣲⣉⣬⣎⣼⢣⣿⣤⣦⣴⣮⠼⠽⠿⠏⠀⠀⣨⢿⡉⠀⠈⡏⠩⠯⢋⠉⠉⠉⠂⠰⡀
⠀⠀⠀⢠⠏⠀⠈⠙⣹⠇⠈⠢⠄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⢻⢾⣷⠀⠀⠲⠀⠸⡀⠀⠐⠀⠁⠀⠱⡀
⠀⠀⠀⢸⣦⠤⢤⣿⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⢀⣀⡀⣀⢤⢤⠤⠖⠊⢁⠁⣋⠷⡋⣼⡇⠀⡆⠔⠂⡾⠒⣄⡀⠀⠀⠀⣘⠄
⠀⠀⢀⠎⢺⡄⣾⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡⠀⢂⠀⠀⠈⠀⠂⡀⣘⣺⠥⣣⣿⠀⠙⠀⢠⣿⡄⢹⠍⢹⠫⢹⠇
⠀⠀⠈⢢⡃⢰⣖⣿⣾⡟⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⠐⠀⢥⠞⣺⢴⣿⠀⠐⠂⣸⢿⣣⠤⠆⠀⠀⡞
⠀⠀⠀⡄⠉⠏⣿⣟⡟⠀⢰⠀⠀⢩⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠉⢎⠌⠀⢀⠂⡚⣡⢦⣫⡏⠀⢂⢀⡿⠀⣿⡀⠘⡀⠀⠱⡀
⠀⠀⢀⠓⠺⢱⣮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⡇⢸⠆⠀⠊⡰⠡⠓⠪⣟⠃⠐⠀⢸⡇⠀⢹⣟⠋⢿⠀⢀⡷
⠀⠀⣄⣀⣯⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡟⢡⠏⠀⠀⠀⣁⢋⣙⣾⡟⢀⡂⠛⣿⠁⠀⠸⣿⡴⠼⣾⠿⢷
⠀⠰⠈⠹⠒⠻⣿⠟⠒⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠋⠀⠀⠀⠐⢛⣊⢿⠎⠀⠨⣤⢨⡏⠀⠀⠀⣿⡇⠀⢃⣀⣠⠆
⠀⠑⢢⠇⢙⣟⣺⠀⠰⣥⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠀⠀⠀⡩⣥⣶⠊⠀⠀⠀⠀⣼⠁⠀⠀⠀⠸⣿⠉⠈⡄
⠰⠀⠄⠀⣾⣩⣇⡀⠠⡎⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠁⠀⠀⢠⠑⠂⣯⢦⡀⠀⠀⢀⢿⡆⠦⢁
⠦⠼⠶⡖⠲⠍⠉⠁⠀⢈⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⢐⡷⠁⠀⠀⠀⠀⢆⡀⢸⡇⠀⡘⣕⢮⡀⠹⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢼⠁⠀⠀⠀⠀⠘⠀⠀⣿⠗⠚⠉⠀⠈⠙⠛⣿⡈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣠⡥⠴⠒⠉⢈⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠩⡏⠀⠀⠀⠀⠀⡌⠙⢸⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠬⡇⠀⠀⠀⠀⠰⢠⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠤⠇⠀⠀⠀⣀⡄⠀⢰⣷⣤⣤⡤⠤⣤⣄⣀⣀⣀⣿⡎⠁⢃⣀⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠉⠉⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢀⡴⠋⢀⣀⡠⣤⡤⠤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠈⠉⠳⢄⡀⠰⠃⠀⠀⠀⠀⢠⢋⡤⠚⠉⠁⠀⠀⠀⢀⡠⠤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⠴⠊⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠁⠀⠈⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠤⣀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠐⠒⠒⠒⠀⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠘⠻⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣈⢁⣠⠤⣄⠀⠀⠀⠀⠀⡸⠃⠀⡤⠤⠚⠙⢦⠀⠀⠀⠀⠀⢠⠎⠘⠂⢤⡀⠀⠸⡄⠀⠀⠀⠙⢏⡉⠑⢦⣇
⡀⡄⠀⠀⠈⠀⠀⠀⢔⡢⠀⠀⠛⠁⡠⠖⠉⠀⠀⠀⠀⣴⠁⣠⠊⠀⣀⣄⣤⣈⠇⠀⠀⠀⠀⣏⣠⣠⣄⡀⠙⢆⠀⡁⠀⠀⠀⠀⠀⠙⢄⠀⠉
⠙⠃⠀⠀⣎⢹⠆⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⡆⣼⡵⢊⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡙⠦⣥⢹⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⣤⠁⠀⠆⠀⠀⠀⠀⠘⢇⣀⣀⠞⠑⢦⡀⢰⠃⠀⢰⡁⢠⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣶⡄⢈⠆⠀⠈⣆⠀⡠⠊⢳⡤⠀⠼
⠀⠀⢀⠖⠉⠈⠉⠐⢢⠀⠀⠀⠀⠀⠀⢨⠀⢤⣀⡿⠚⠀⠀⠀⠉⠉⠉⡵⠊⠉⠑⣤⠤⣤⠖⠉⠉⢲⡉⠉⠁⠀⠀⠀⠀⢹⣠⠖⢸⡇
⠀⠀⡠⢿⣏⣿⠛⣻⢧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢱⠦⡴⠖⠃⠀⠈⠓⠦⡴⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣟⠢⠤⣿⡔⠁⠀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢈⡻⣆⠀⠀⠀⠀⠀⢠⣷⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸
⠀⠀⣯⣉⣈⣿⡍⢻⠀⣇⠀⠀⠀⠀⠀⠀⢧⡀⢀⣸⡄⠀⠀⠀⢀⡴⠊⠁⡤⠊⢑⠖⠒⠶⠊⠓⠄⠀⠉⠒⢄⠀⠀⠀⠀⠟⠢⠴⠋
⠀⠀⢹⡦⠿⠤⠴⠦⢧⠈⠻⡦⣀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡎⠀⣀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣄⡀⠀⢈⡇⠀⠀⡜
⠀⣰⠃⠀⠀⠀⠀⠀⠀⢣⠀⠇⠀⠉⠓⠲⠶⠤⠤⠤⠤⢷⡀⠈⠓⠋⠘⠤⠞⢭⣷⡔⠉⠒⣋⣩⡟⠃⠈⠉⠁⠀⠀⡼⠁
⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⢀⠾⡀
⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣤⢉⡒⠤⣀⣀⣀⣀⣀⣀⣀⡤⠔⣊⣤⠒⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠳⠦⠠⠤⠄⠤⠤⠠⠴⠖⠒⠒⠊⠉⠁⠙⡀⠁⠀⠀⠈⠙⢌⡃⠸⠁⠀⣸⠅⢻⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⠦⣀⠀⠈⢻⠇⢀⠞⠁⠀⡈⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠑⢄⠀⣆⠇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠱⡿⠀⠀⠀⢀⠜⠓⢤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⣏⠀⠀⠀⠙⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠲⢶⡛⢽⣆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⠒⠒⠶⠶⠶⠒⠲⡏⠈⠙⠉⠁⢹⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠋⡆⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠇⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠀⡰⠀⢠⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⢳⢠⠋⠀⠀⠀⢱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⡄⡀⡀⠀⣀⠀⣀⠀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢸⡗⠂⣽⡇⣰⠿⣆⣿⣧⣾⡇⠀⠀⣿⠀⢠⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠁⠉⠁⠀⠈⠉⠈⠈⠁⠀⠀⣿⠀⡿⠳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⢰⡟⠛⢻⠀⣿⢸⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠸⠧⠤⠾⠀⣿⡿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣤⣤⣤⠀⣿⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡇⠀⣸⠀⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⠁⠈⠉⠉⠉⢠⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⡟⠋⢻⠸⣇⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠷⠶⠾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠁⠁⠁⠁

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⠀⢀⠄⠒⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀
⠀⠀⠀⣎⠀⠑⡎⠀⠀⠀⠠⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠕⠈⠀⠉⠪⡱⡀
⠀⠀⡖⠈⠙⠂⢇⢀⡠⠀⠀⢀⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠀⠀⠁⡃
⠀⠀⠑⠒⠒⠈⡹⡇⠀⠀⠀⢀⠄⠢⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⢄⡀⠀⠀⡠⡣⠃
⠀⠀⠀⠀⠀⠘⢻⠀⡌⢹⠀⡘⠀⠀⣱⣤⠀⠈⠋⠁⢀⠤⢄⣀⠤⡀⠀⠀⠀⠀⠀⠑⢲⠄⠆⠊
⠀⠀⠀⠀⠀⠀⠈⠒⠀⡦⠐⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⢮⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠐⠤⠠⢄⢄⣀⢄⠀⠀⠀⢘⡄⠀⡀⢠⡇⣀⡀⣠⠤⢤⠎⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠟⢺⣘⠀⠀⡆⠀⠁⠀⠋⠑⠊⠙⣸⣯⣿⣿⠇⠈⠀⢸⢠⠖⠢⢷⣺⡄⠒⢄⠀⠘⢗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠑⠒⡷⣀⢀⢸⡄⠀⠀⢠⣡⡿⢿⣄⣦⡀⢀⣼⠇⠀⠀⠀⠀⠂⠀⠀⣆⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠠⠃⠀⠀⢸⠈⠂⠂⠹⠈⠙⠛⢩⠇⠀⡾⠁⢇⠀⠀⠠⡠⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠂⠀⠀⢀⠌⠀⠀⢀⠄⠈⡾⠃⢠⠋⣣⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⢀⣀⠤⠤⢀⡀⠀⡔⠀⢠⠗⠉⢰⠀⠈⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠉⠃⠤⠃⠀⠀⠀⠢⠂⠀⠦⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠴⠃⣠⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢑⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣴⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣠⣴⡿⠟⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠋⠀⣠⣾⠟⠉⡶⡾⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣿⣷⣾⣿⠿⠢⠞⠁⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀⡼⢋⣙⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣷⣄⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣆⠀⠀⢜⣋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣶⣯⡻⣇⣶⣾⣷⡀⠀⠀⠀⠀⣀⠴⠟⣫⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢺⣇⣀⣿⢷⡲⣶⣶⣶⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠈⣷⡌⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢹⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣧⣤⣤⣼⣷⣼⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢿⣟⣻⣶⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠠⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣾⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣷⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣯⣿⣽⣟⣿⣻⣿⣿⣟⣯⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⠛⠀⠉⠉⠉⠉⠛⠒⠂⠐⠒⠚⠋⠉⠉⠉⠉⠐⠲⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⣦⣼⣄⣠⡤⠴⠶⠤⣀⣀⣠⣤⣤⣀⣀⠤⠤⠤⠤⣄⣀⣀⢀⣤⡾⠋⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣿⠉⠀⠀⠀⠀⠀⢈⡏⠁⠀⠉⢹⠏⠀⠀⠀⠀⠀⠈⣿⠿⡿⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⡟⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⢸⡄⠘⠛⢤⣤⡤⠛⠃⠀⠀⠀⠀⠀⠈⠛⠦⣤⡤⠞⠋⠀⢸⡇⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡀⠀⠀⠀⠀⢀⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠉⠛⠛⠋⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⣍⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⢧⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣷⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⠾⠛⠉⠉⢁⡿⠁⣾⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣷⠘⣇⠈⠉⠉⠐⠲⣦⣠⣄
⠀⠀⠀⠀⠀⢠⠞⠋⢀⡜⠁⠀⠀⠀⠀⣿⠀⢸⡇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠐⠃⠀⢻⡄⠹⣇⠀⠀⠀⠀⠈⢳⡄⠙⠳⡄
⠀⠀⠀⠀⠠⡇⠀⠀⣾⠀⠀⠀⠀⠀⣼⠃⢠⡟⠀⠀⠀⠈⣤⠀⠀⠀⠀⣀⠂⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠄
⠀⠀⠀⠀⣀⠃⠀⠀⡇⠀⠀⠀⠀⠀⣿⣧⣸⡇⠀⠀⠀⠀⠈⢶⡀⠀⣠⠋⠀⠀⠀⢸⡇⢀⣽⣧⠀⠀⠀⠀⠀⠈⡆⠀⠘
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣤⣄⡀⠀⠀⠀⢣⠞⠁⠀⠀⢀⣠⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾
⠀⠀⠀⢀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘⡄
⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿
⠀⠀⢠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⡀
⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⡁⠀⠀⠀⠀⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⡄
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢦⡀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠶⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠛⢤⣄⣀⡀⠀⠀⠀⣀⡸⠦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⢸⠉⠉⢲⡶⠈⠉⠀⠀⠀⠈⠉⠑⠶⠶⢦⡄⢀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠰⠶⠶⠶⠖⠠⣤⡝⢷⠖⠶⠖⠀⠉⢉⡀
⠀⠀⢸⠀⣴⠋⠀⠀⠀⣀⢀⡀⠀⠤⠤⠤⠤⠼⠓⠀⠉⠉⠙⠛⠋⠉⠁⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⣦⣶⠀⠀⠀⠀⢸⡇
⠀⠀⠸⠀⠙⢧⣤⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣄⣤⣤⣀⣠⡄⠀⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠤⠤⠄⠘⠛⠛⠛⠛⠋⠠⠤⠤⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠈⠳⣤⣤⣤⣤⡀⠐⠶⠶⠒⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠲⡶⠒⠆⢠⣤⣤⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⡀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠈⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⠃⠀⠀⠀⠰⡶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣶⣶⣶⣿⣷⣶⣶⣶⣶⣤⣴⢶⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⢠⡗⣼⠙⢿⡴⣻⡿⣿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢉⠁⡄⠈⢁⣀⣀⠈⡤⠤⢀⡠⡄⢁⣌⢁⡀⠀⠀⠀⣿⢸⡂⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠈⡇⢻⣧⣿⡿⢿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣶⢻⠉⠸⡟⢃⣴⣤⣄⣬⡌⡟⠉⡈⢢⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⡇⢸⠙⣿⡳⣞⡯⣵⢷⣿⣷⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⡟⢆⠀⡅⠛⠾⠤⣼⡄⢣⡿⠁⢿⡏⠸⢇⠀⣥⠈⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⣿⣿⡄⠀⠀⠀⠀⡗⣿⠀⠹⣇⣨⣹⣟⣻⣿⣿⣿⣦⡀⠀⠀⠀⠙⠿⠋⣳⠙⢶⣤⠙⢠⡀⢾⠙⣤⠛⣤⣶⢈⣘⡆⢸⠗⠟⣡⠀⠠⣿⣿⡀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠿⣿⢿⣭⢆⠈⢛⠿⣷⡀⠀⠀⠁⣾⠛⣿⣤⡄⡃⠀⠈⠻⢷⣷⢿⠘⢿⡿⢈⣛⣷⣘⡷⢚⣥⠀⠀⣿⣼⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠂⠱⣎⠹⠿⣷⡄⣲⠈⠻⣄⡀⠰⠋⠲⠉⠝⣛⠷⡒⠰⠃⣰⠃⠾⠴⢤⣤⣿⣛⠿⠿⠆⠈⣆⡄⠀⣿⣹⡃⠀⠀⠀⣿⣿
⣿⣿⡀⠀⠀⠀⠀⡇⣿⠀⠀⢀⣧⠀⠹⣷⡀⢈⡛⢹⣦⣴⣽⣿⠀⣨⡙⠓⢢⠝⠲⡝⣷⣤⣿⣰⣦⣤⣤⡤⣭⣏⠀⠀⠀⠀⣀⣴⠞⡋⢿⣇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⢸⣟⠃⠀⠘⢿⣾⣽⣿⣿⣿⣿⢿⣷⣌⠁⠀⣧⠀⠀⣦⣀⡸⡆⠉⢰⣧⣌⠀⢸⢸⡇⣠⣶⣿⠏⠑⣮⠟⢠⡿⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⢰⡷⣿⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⡿⣷⣄⢻⣿⣦⠀⢏⠀⠀⢿⡉⠙⡁⢶⡈⡉⠛⠶⠞⢫⣼⣿⣿⣿⠶⣦⣠⣶⣿⡅⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣩⠹⣿⣿⣷⣿⣿⣷⡈⠠⡁⠺⠃⠀⠻⠈⠉⠁⠀⠀⣴⣿⣿⣿⡿⣿⣶⣹⣿⣿⣿⠃⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⢀⣤⣶⣾⣿⣷⣤⡈⢻⡖⣿⣿⡋⣿⣿⣿⣻⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⠏⣹⣿⣻⣿⠏⣿⢹⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⣰⣿⣿⣿⣏⣿⣿⣿⣿⣮⢿⣿⢞⣿⣿⣿⣿⠿⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⣼⠿⣡⡾⠂⣩⣿⣿⠏⠀⣿⣸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣿⣻⣿⣯⡿⢿⣟⣷⣝⣧⠛⡿⣿⣿⣶⣿⣿⠿⢋⣱⣾⢻⣦⡀⢀⡀⣀⣾⣿⠶⣟⠻⡁⠈⣹⠏⠀⠀⣿⢰⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣻⣿⣭⣻⣾⣧⠛⣴⣿⡿⢿⣶⣿⣹⣿⣍⠀⣤⠋⣼⣿⣧⣼⡾⣿⣿⣟⣴⡟⢀⡄⠀⡄⣰⡟⠀⠀⠀⣿⢸⡆⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⢠⣾⣿⣿⣿⡟⣿⣿⣷⣿⣷⣴⡿⠿⢿⣿⣿⣿⣿⡀⣠⣾⡿⣣⣾⢟⡋⣼⡿⠋⢀⣿⠀⠚⡁⣿⠃⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣷⣿⣾⣷⣫⣿⣉⡼⣻⣯⣿⣿⣿⣿⣾⣧⣿⠉⠉⠉⢿⣾⣿⡏⣠⡿⣱⣿⣿⡟⠀⢀⣾⣏⣠⣿⠆⣿⡀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣏⣿⣿⣿⣿⢁⠋⣴⣛⣿⣿⣷⣿⣻⣿⣟⢿⡄⠀⠄⠀⣿⡇⢰⣿⣷⣿⣿⡏⢙⡀⣰⡟⢻⣿⠭⣷⣿⣇⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣷⠈⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣯⡹⣷⣟⣷⣶⣿⣿⠀⣻⣿⣿⣿⠛⣰⣎⠡⣿⢷⡈⡏⠀⢀⣿⣿⡄⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⠛⠛⣯⣵⣛⣿⣿⡿⠿⢿⣷⣟⣵⣻⡇⠀⢣⣼⣧⣿⡀⠋⠀⣣⣼⡏⣿⣇⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⡟⢿⣥⣽⣷⣖⣫⡭⠛⣿⣿⣷⣶⣿⣅⣿⣿⡟⠄⠀⠀⠈⢿⣿⣿⠁⣻⣾⡥⠿⠻⠄⣀⠼⣻⡟⢱⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠸⣿⣻⢤⣿⣾⣿⡻⢿⣴⣏⣏⣿⣿⣿⣟⣻⣷⣾⣷⣦⣤⣤⡶⢸⣿⠻⡾⠣⡼⠀⣂⣠⣶⠟⣴⢋⣴⡇⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣵⣾⣛⣿⣿⣿⡿⢿⣏⠹⣯⠀⡈⢉⣿⡟⠓⢸⣿⡄⠀⠂⠐⢚⠋⠙⠁⠰⣷⣋⣽⣧⣿⣾⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡟⣿⠛⣯⢿⣿⡿⠻⠻⠿⣿⣿⣷⣾⣿⣷⣿⣿⣿⠟⣱⠃⣴⠀⠛⣿⣦⣽⣶⣩⣅⣠⠄⠒⣛⣿⠿⣛⣼⣿⣆⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⠀⡟⣿⠀⠙⠿⣿⣿⠀⢂⠰⢀⡻⣿⣿⠟⠉⣿⢻⣿⠀⠉⠀⠹⠀⢀⠸⣿⣿⣿⣩⣾⣛⣶⣛⣫⣿⣶⢛⣿⣿⣿⣷⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠙⠻⣴⣿⣲⣞⢣⣿⣟⣿⡇⣻⢁⣿⠆⡀⠀⡀⡇⢨⣷⣎⣻⢟⣹⡿⠛⢿⣟⣿⣧⣼⣿⣿⣿⣿⣛⣿⢾⡆⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⠙⠻⣿⡞⠹⣿⣿⣿⣿⣿⡿⠸⡇⠄⡙⢿⣷⣿⣻⣿⣿⢋⣷⠏⡀⢟⣻⣿⣿⣿⣿⣏⢾⣿⣿⢘⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣽⣿⣿⣟⣿⣇⠀⣷⣄⣈⣿⣿⠇⣿⣿⣤⣿⣿⣤⣿⣾⣿⣿⡿⣿⣿⣽⣦⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠛⠀⢀⡀⠀⣀⣀⠀⠀⣀⡹⢿⣿⣭⣿⣦⣸⣿⣿⣽⣿⢺⡿⢣⣿⢃⣨⣿⣿⣿⣿⣿⣶⠉⣾⣿⣿⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠠⠆⡰⣯⡿⠀⣻⣯⠛⢛⣿⠸⠾⠋⠤⠀⠙⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡝⢻⣿⣽⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣷⣿⠀⣙⣛⣀⠙⣯⣁⠈⣀⡈⣁⣿⣚⡃⠀⠀⠀⠀⠀⠛⣿⣏⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⢻⣇⡸⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠉⠙⣿⣤⣯⣈⡿⣿⠿⠟⣣⣿⠱⠆⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣿⢟⣷⣿⣏⣿⣟⡽⣧⣀⣄⢻⣿⣷⠘⣿⣸⡀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⢀⣿⣿⠀⠀⠘⠋⠀⠈⠉⠀⠘⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣻⣾⣿⣷⣹⣾⢻⣼⢿⣿⡜⣿⣿⣿⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢉⣿⣧⡝⢿⣻⣾⣷⣟⣿⣿⣿⣿⣿⢸⠀⠀⠀⢠⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣿⣾⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣼⣿⣹⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣿⣿⣿⣿⣷⣿⢿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡻⣿⣿⣸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⣥⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣄⣀⣀⣀⣤⣤⣤⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣭⡿⣿⠀⠀⠀⠸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠿⠶⠿⠤⠶⠿⠷⠶⠶⠿⠿⠿⠿⠶⠶⠶⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠾⠷⠾⠿⠶⠶⠶⠿⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡈⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⣆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠈⠉⠩⠍⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠘⠃⠒⠺⠿⠀⠫⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠺⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⠑⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⢀⠀⠀⠀⠀⠀⠈⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡐⠁⢀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡠⢄⠀⠠⣄⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠉⠆⠀⠀⠀⠀⠀⠠⠊⠉⡆⢔⠋⠀⠀⠈⠂⠃⠑⢄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠣⠃⡁⠤⠀⠀⠀⠀⠀⠀⠀⠅⠀⣠⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠛⠒⢄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣄⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠹⡄⢀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⠄⠀⠀⣈⠥⠊
⠀⠀⠀⠸⣤⠐⢰⡆⡰⠁⠀⠀⠙⢲⣶⡖⠸⣶⡞⠀⠀⠀⠀⠀⢈⣣⣉⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠏⠀⠀⠙⡅⠀⠀⠀⢀⡌⠉⡥⣁⢩⠩⠀⠀⠀⠀⠀⠈⠁⠌⣍⢀⢀⠔⠉⣀⣉⠀⠐⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠣⠀⣑⡂⠉⣓⣀⠈⢉⣁⠀⠀⠀⠀⠸⣏⠁⠀⢁⣀⣀⡀⠀⠉⢀⡠⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣆⢰⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣁⡂⠀⠐⠀⠙⠓⠊⠀⠛⠂⠈⠉⠉⠉⠉⠈⠉⠉⠀⠀⠘⣩⡟
⠀⠀⠀⠀⢀⣀⡀⠀⣀⢀⣀⠀⠀⢀⣀⡼⡅⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠻⠇
⠀⠀⠀⠀⠜⡟⠠⢿⠃⠀⠀⠀⠀⠀⠛⣦⠁⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠒⠛⠛⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠆
⠀⠀⢀⢀⣧⣴⣴⣦⣶⣶⣶⣶⣶⣶⣾⡍⣿⣦⡆⢸⣤⣀⣀⣀⣤⣴⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⠀⡻⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠓⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠲⠀⠀⠐⠐⠐⠐⠀⠀⠂⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠂⠁⠘⠀⠀⠃⠘

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠂⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠀⠀⡼⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⢸⡄⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⡀⠈
⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠒⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⣀⡤⡀⠀⠀⣀⠄⡀⠀⢀⠀⠀⠀⡀⠀⠀⡀⣀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠙⠀⠀⠀⠁⠘⠀⡈⠀⠀⠀⡀⠉⣤⠸⠁⠁⣸⠁⢈⠩⠀⣀⠃⡇⢸⠉⠉⡭⠄⠀⢹⠀⠀⠀⣆⠀⠶⠈
⠀⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠐⠉⠐⠃⠀⠚⠀⠋⠐⠁⠀⠚⠁⠒⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠈⠈⠙⠛⠉⠿⠯⠽⠿⠟⠯⠡⠮⠤⠤⠤⠶⠶⠶⠿⠀⠨⠁⠀⢖⠀⠄⠀⡰⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⡤⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⠶⠒⠛⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⡀⠉⠀⠀⠀⠀⠈⠳⣄⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⡆⠀⠀⠠⣄⠀⠀⠀⠈⢳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⡤⠻⣦⡀⠀⠈⠻⣦⡀⠀⠀⢳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣶⣿⣿⣶⣴⠆⠈⢳⡄⠀⠘⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⡿⠙⠛⢋⠙⣦⠀⠈⣧⠀⠀⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣴⣷⣶⡄⠌⠀⠘⣇⠀⣿⠀⢸⠀⢀⠞⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠁⠀⠀⠀⣿⠀⣿⠀⢸⡆⠈⠧⡴⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴⣦⡤⠀⠀⣿⠀⢿⠀⡨⠿⢄⡀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢇⠀⣠⣿⡇⠀⢰⡁⡀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠏⢷⡀⠈⠙⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡛⠃⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠙⠲⡶⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⣀⠚⣴⣾⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⢹⠀⠀⣀⠀⠀⠀⢀⣀⣴⣶⡡⠀⣀⢀⡠⢞⣡⠟⠁⠈⠻⣄⠀⠀⠀⠀⠀⢀⠞⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣦⣦⠞⠋⢀⣀⣀⠀⢸⣧⣘⢓⡒⣧⢸⠖⠞⢡⡀⠀⠀⠀⠙⢦⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠸⣙⣦⣀⣀⢸⡟⢷⠻⡏⠹⡋⠉⢣⠞⢣⡀⠈⢷⡀⠀⠀⠀⠈⢷⡀⠀⡟⠻⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣀⣴⣛⣯⡓⠬⠉⣹⣀⠈⣴⠻⢄⣙⠂⠈⠹⡦⣻⢄⠀⠙⢦⡀⠀⠀⠈⢷⠀⣇⠘⠀⠀⢸
⠀⠀⠀⠀⠀⣠⡴⠋⠁⡠⠊⠀⠛⠹⡟⠻⠁⠈⠉⠉⠂⣹⠏⣠⠞⣹⠷⡀⠈⠃⠎⠀⠀⠀⠙⣦⠀⠀⠈⠀⣿⣘⠀⢀⡞
⠀⠀⣀⡴⠞⠁⠀⠀⠚⠒⠒⠂⣀⣀⣀⣀⣈⣉⣉⣀⣌⣥⡞⢁⡜⠁⠀⠙⡄⠀⠀⠀⠀⣠⠞⠀⠀⢀⡼⠁⣿⣿⣴⣿⠇
⠠⠾⠧⠶⠶⠶⠞⠛⠛⠛⣋⣉⣉⣭⣭⣭⣭⢤⣤⡤⠤⢾⣷⡏⠀⠀⠀⠀⠸⣆⠀⠀⡰⠃⠀⢀⣴⡟⠀⠀⢿⣟⠁⣿
⠤⠶⠶⠖⠲⣿⡟⠉⠉⠉⠁⠀⢸⣿⡁⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⡄⣰⢁⣠⡶⠋⣸⣧⠀⠀⠀⣟⠀⣿
⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⣿⡇⠀⠀⣾⣧⠀⠀⠀⠀⢀⣾⠉⠉⠻⡿⠶⠛⠉⢻⣧⠀⢠⡏⢠⡏
⠀⠀⠀⠀⢤⠈⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢿⡟⢀⣀⡤⠄⠘⠛⣶⢦⣤⠇⠀⠀⠀⠀⠙⣧⢸⡇⢸⡇
⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⣠⣶⡟⣻⣿⡷⠤⡠⠔⠁⢀⣠⠄⠀⠀⠀⠀⠀⣹⢸⡇⢸⡇
⠀⠀⠀⠀⢸⠀⣷⣀⣀⣀⡀⠀⢠⠤⠤⠤⠤⠰⣿⡷⠊⠀⠙⣷⡎⣁⠿⠦⣀⣴⡏⢡⠞⡀⠀⠀⠀⠀⣰⠋⢹⠋⣽⡇
⠀⠀⠀⠀⢸⡆⢿⠤⠤⠤⢸⡃⣻⡴⣆⠀⠀⠘⡏⡇⠀⠀⠀⣠⡿⡅⢶⠀⠈⡀⣵⡎⢀⠃⠀⡇⠀⢸⣃⣀⣸⣃⡾⠁
⠀⠀⠀⠀⢠⡇⢸⠀⣬⠋⠀⠉⠉⠀⠈⢷⡀⠀⡃⡇⠀⣰⠞⠉⠋⠀⡄⠰⠀⠻⢿⣧⣼⠀⠀⣿⠀⢸⡍⠉⣿⣿⡇
⠀⠀⠀⠀⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠘⣧⠀⡇⣿⣼⠁⠀⠀⠀⠘⠂⠀⣀⡤⠒⣽⣿⣧⣀⣿⣆⣼⠿⣿⢁⣿⠃
⠀⠀⠀⠀⠀⣷⢸⢸⣇⣴⠶⡶⠶⠶⢶⣶⣿⠀⡇⡷⢿⡀⠀⠀⠀⠈⠙⣇⠀⠀⠀⢸⡏⠀⠉⢹⡏⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⣿⢸⢸⡟⡋⠉⠉⠛⠛⠉⢻⢹⡇⡇⡇⠀⠙⢦⡀⠀⠀⠀⠈⢆⠀⠀⢸⡇⠀⠀⢸⡃⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⣿⣾⣷⣧⠿⠤⠤⠤⠤⠤⠬⠦⠿⠿⣿⠷⡄⠀⠙⢦⣀⠀⠀⠈⢷⣄⣸⣧⣀⣀⣼⣁⣀⣀⣿⠸⡿
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠙⠳⣄⠀⠈⢣⣿⣷⡠⠤⣷⠠⠴⠀⣿⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⣶⠀⣸⢸⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⡟⠳⠄⣿⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⢸⢻⡆⠘⣷⡰⣿⣿⣖⣽⡆⢀⡿⠀⡿⢸⠃⠀⠀⠀⠀⠀⠰⠶⣿⣧⡀⠈⣶⣄⠿⠀⡀⢸⠇⣶⣿⡗
⠀⠀⠀⠀⡀⠸⠀⢿⣄⠘⢧⣓⣚⣙⣚⣡⠞⣡⠞⢡⣾⢠⠖⣒⣶⠀⠀⠀⠘⣿⡿⣣⠀⣿⣿⡆⠉⣉⣛⣴⢿⡟⠁
⠀⢺⡟⠛⢿⣈⣛⣛⣛⣷⣤⣀⣈⢁⣈⣴⣾⣥⠶⣩⣤⣼⣿⡿⠿⠀⠀⢰⣷⣿⡓⠻⣧⣿⡟⢻⣏⣉⣉⣧⣾⡇
⠀⠈⠛⠛⠛⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⣿⣾⣿⠏⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣷⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⡿⠿⡛⠛⢻⠻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢂⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡘⣯⣦⣴⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⢛⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡏⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣻⣿⣿⣿⠟⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣿⣿⣿⡷⠶⠶⢒⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠛⣿⠿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠿⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢐⡆⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡆⠙⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⣸⣿⣿⣿⣿⠃⠇⣴⢹⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣹⡄⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⢹⣗⣿⣿⣿⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢐⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⠏⠀⢀⣀⣾⣼⣿⣿⣿⣋⡷⠰⣞⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣸⣟⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⣾⠁⢀⠹⣾⣿⡿⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠸⣿⡆⠀⠙⢿⣿⠒⠛⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡅⣸⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⣀⣹⣿⣷⣾⣿⡈⢷⡄⢀⣀⣥⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⢂⡿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⡹⣷⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢏⣰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠃⠈⠿⣶⡂
⠀⠀⠀⠀⢀⣀⣀⣾⣟⣧⠞⣻⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠘⢿⡿⠟⠋⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣎⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠲⠼⡿⠿⠦⣤⡇⡀⠀⣉⣙⡋
⠀⠀⠀⠀⠀⠀⡿⢟⣋⠠⠀⠺⠀⠀⠀⠀⢂⡠⠋⠀⠀⠈⣄
⠀⠀⠀⠀⣀⣀⣿⡿⠁⠀⠀⠇⠀⢀⡄⠀⢸⠁⡄⠀⠀⢠⠁⠈⠒⠄⡀
⠀⠀⠀⢘⠰⠂⢹⣷⠀⠀⠀⠘⢆⠀⠁⢀⡜⠢⠤⠤⠔⠁⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠈⠠⠐⡆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢪⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⡳⠬⠱⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢉⠿⠿⣅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠀⠀⠀⠀⠀⠀⢀⡤⠻⢤⣴⣉⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠁⠀⢑⡂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠘⣦⠤⠋⢧⠤⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡆⣿⣀⣀⣨⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠤⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠄⠊⠀⡸⠛⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⣀⣀⣸⠀⢀⠠⠒⠁⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁⢍⡙⠳⠤⢄⡠⠀⣀⠀⢀⠘⢦⣀⣀⠛⠦⠞⠙⠊⡁⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠈⠒⢤⣀⠤⠀⠀⠀⠁⢀⡜⠀⠈⠳⢀⣤⠚⠁
⠀⠀⠀⠀⠀⢀⢐⢁⠄⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠀⠀⠭⠖⠐⠋⢀⣿
⠀⠀⠀⠀⠀⠃⠈⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠰⢄⢈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠘⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⢰⠒⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠘⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣦⡀⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣀⣠⣄⣵⣤⣾⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠙⠛⠛⠛⠛⠛⠛⠛⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡴⠚⠋⠙⠙⠛⠛⠳⠶⣬⡄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⢀⠔⣻⢠⡤⡄⣴⢢⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠸⠶⢻⢸⣄⡟⢿⡼⢰⣫⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢸⡇⠀⠀⠀⠀⣸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇⠀⠹⡁⠀⠀⠂⠉⠀⠀⠀⢰⠀⠀⢸⢹⠀⠀⠰⠶⠋⣀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣇⠀⠀⠱⣄⠀⠀⠀⠀⢀⡰⠃⠀⢠⠿⠋⠀⠀⠀⠀⠀⣿⠀⣀⠀⡀⢀⢸⣇⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠙⠒⠒⠒⠉⢀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⢻⠀⡀⡇⢸⡏⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠿⣶⣶⠶⠖⣲⠛⢻⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⣇⡀⠘⠛⠀⢧⡘⠃⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⢲⠏⠋⠉⠉⠁⠀⠀⢳⣶⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⣀⠀⠀⡞⠓⠒⠒⠒⠒⠒⠊⠉⢷⠀⣀⠽⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣌⠀⠈⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠙⢲⡾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢹⡶⠚⠉⠀⢳⡀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢷⡀⠀⠀⠀⠱⣼⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣰⢇⡄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣸⣷⣴⠶⣶⢴⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⣿⣾⡻⠚⠲⠶⠶⠶⣶⣤⣤⣤⣤⡴⠖⣛⣩⣍⣂⣦⣽⣿⣿⡀⠀⢀⠇
⠀⠀⠀⣤⣤⣤⣤⣤⣼⣤⠯⢭⣭⡭⣽⣶⣶⣾⣿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠯⠷⠶⠾⠶⠶⠶⠶⠶⣶
⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣼
⠀⠀⠀⠉⠉⠉⢻⡍⠁⠙⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⡄⢨⠃⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢄⠄⠠⠀⠀⠀⣀
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠚⠈⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⢠⣴⣦⡀
⠀⠀⠀⠀⡀⠐⠛⠛⣀⠀⠀⠀⠀⡼⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠲⠎⢉⡈⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⢣⡈⣥⠛⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⠀⠄
⠀⠀⠀⡀⠰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣄⣀⠠⣿⠧⠀⠀⠀⠀⠇⠀⠀⠂
⠀⠠⠄⠀⠌⡹⠉⣀⠀⠀⠀⠠⠀⢀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠉⠋⢠⡆⠀⣤⡄
⠀⠀⠀⠈⢀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡀⠀⢀⠀⠀⠀⠐⢿⢾⠀⠉⣀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣉⢓⢠⠀⠀⠀⠀⠀⠸⠠⠚⠿⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠫⠆⠒⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⠀⠙⣆⠹⣄⠀⠀⠀⠀⡄⠀⢀⠀⠀⠁⠀⠀⠀⠀⠈
⠈⠀⠀⢠⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠘⠁⠖
⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠐⠀⢄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⡿⠡⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠛⠀⠀⠀⢀⠄⠀⠀⠀⢹⠀⠀⠀⠀⢀⣀⠀⠠⠤⢤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠉⠀⡉⠀⠀⠀⠀⢈⡀⠁
⢰⠂⠀⠀⢠⠖⠒⠒⠃⠀⠀⢀⣤⣤⠀⠀⠀⠀⠆⠀⠀⠀⠱⠈⠁⡈⠀⠀⠀⠾⠷⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀
⢸⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠄⢀⡀⠀⠄⠈⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠉⣀⣠⣄⠀⠒
⠀⠳⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰
⠀⠀⠈⠙⠒⠶⠤⠂⠀⠀⠀⠐⠠⠾⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠛⠛⢦⡀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠈⠛⢦⡀⣰⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢹⡿⠟⣻⣿⢿⣿⡟⢡⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣷⢿⡏⢘⢩⣧⣸⢿⣿⣿⡟⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢻⣿⣼⣷⣽⣯⣿⠏⠈⢿⣿⠇⠘⣿⣿⣿⣿⣶
⢠⣾⠶⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⢻⠀⢠⣿⣿⣿⣿⣿⣷⡀
⢸⣿⠀⣿⣿⣷⡀⠀⠉⠻⣿⣿⣿⡇⢸⣇⠀⣴⢸⣿⣿⣿⣿⣿⣿⣷⡀
⠈⠹⠀⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⠘⣿⣤⣿⢸⣿⢿⣿⠿⢿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠛⢿⣿⣿⣷⠀⠀⠈⣿⣿⣿⡀⣿⣿⣿⢸⣿⠦⣶⣶⣾⠿⠿⠛⢋⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠻⢿⣷⡀⠀⠘⢿⣿⡇⢹⣿⣿⡀⣿⠇⣶⣶⣿⣶⣿⡇⣿⣿⡟⣩⣆⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢈⣿⣇⣸⣿⣿⣿⣿⠁⣈⣙⣩⣿⣿⡇⣿⣿⡇⣈⣩⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⢿⣿⣿⣿⠀⢹⣿⠟⢛⣿⣿⣿⣿⣤⣼⣿⢱⣿⣿⣈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣿⡿⠀⢸⡟⠀⢸⡟⣀⠈⣿⠏⡙⠻⢿⣿⡟⠻⠿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢰⡆⢠⡄⢸⡗⣿⢠⡏⢸⣿⣿⡆⢻⡇⣶⣶⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣧⣼⡇⢸⡇⠃⣼⠃⣈⠙⣉⣰⣿⠁⣿⠟⣡⠟⢩⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣾⣿⣿⢇⣼⣇⣠⡿⢠⣿⣷⠘⣿⡟⢠⣄⣼⡇⢠⣿⡏⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠛⠿⣿⣿⣿⣿⣿⣿⠃⢈⣻⣯⡀⣿⡇⢸⣿⣿⠃⡛⠛⢠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠘⣿⣿⣿⡿⠿⣾⣿⣿⣿⣿⣿⢀⣼⣿⡏⣸⣿⣷⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣼⣿⡏⢠⣶⣤⠹⣿⣿⣿⠿⠛⣿⣿⣤⣿⣿⣿⣨⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣧⢻⣿⣿⣇⢿⡏⢀⣤⣄⠘⣿⠀⣴⣿⣿⠿⠋⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⡿⠀⠙⣿⡄⢿⣿⣿⠘⣿⡜⣿⣿⣾⣿⠀⣿⠋⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⣾⣿⠃⠀⠀⢹⣧⠈⢿⠋⢰⣿⣿⡈⢿⣿⣿⠀⣿⠀⢴⣿⣿⣿⣷⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⠀⣿⣿⠀⠀⠀⠀⢿⣷⣦⣀⡟⢿⣿⡇⢸⣿⡟⢠⣿⣦⡀⠙⢿⣿⣧⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣿⣿⣇⠸⠟⠃⣨⣿⠁⣸⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠈⠙⢿⣿⣦⣴⣿⣿⡏⠀⣿⡿⣿⣿⣿⣿⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠘⢿⡿⠟⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡄⠀⢀⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⠀⠀⠀⠻⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⣄⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡌⣡⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠨⣽⣇⠀⣠⣴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠶⠦⣄⢀⠘⣄⠀⢰⣏⣿⠀⠀⠀⠀⠀⢟⣿⡀⠉⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠢⠤⣤⠤⠀⠀⠀⠀⠀⠀⢻⣦⣠⡾⢟⣁⡘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠉⣯⠀⣄⣤
⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡟⠃⠈⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⢻⡞⠑⣵⠒⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣘⣆⠀⠀⠀⠀⠀⠰⢻⠯⡄⠀⠀⢠⢪⣦⠞⠻⠛⠛⠋⢀⢰⡇⠠⠀⣄
⠀⠀⠀⠀⠀⠀⢸⣟⢛⣧⠀⢰⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⢇⠀⠀⠀⡠⠾⢽⣦⠤⡀⠠⠲⠋⠋⠀⠀⠀⠀⠀⠀⠈⠂⠞⢀⣣⣴
⠀⠀⠀⠀⠀⠀⢘⣓⣛⣷⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠈⠁⠀⠉⠀⡀⠄⠠⡤⠀⢀⣼⡿⢷⡿⣿⢿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⢘⣯⣶⣺⡁⠀⠀⠀⠀⠀⠀⡇⠠⠀⡰⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⣤⣤⡶⢿⠔⠀⠀⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡈⠙⢿⣿⠀⠀⠀⠀⠀⠈⠐⠂⠤⠞⠋⠉⠐⠀⠂⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠙⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠀⢀⠏⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠇⠮⠞⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡔⢓⡒⠛⠑⢀⠀⢠⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⠐⠐⠈⠳⣤⣒⡊⠀⠻⣇⠈⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⢤⡄⣶⢂⢶⢦⡀⠀⠁⠀⠰⢨⠀⠊⢾⠁⠀⠉⠳⢼⡜⣆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡯⢩⡉⣸⠑⡭⠀⡆⣠⢨⢰⡍⠂⠀⠀⠀⠈⢁⠀⠇⠀⢉⣭⠤⢄⢈⡴⠃⢚⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠤⠖⠛⠟⠒⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣋⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣭⣭⣿⣯⣽⣽

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⡟⢨⠰⠂⠀⣠⠶⠾⠟⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠞⠀⠀⠀⠀⠀⠀⠈⡇⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡌
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠶⠀⡀⡀⠠⠛⠘⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⣠⠄⠀⠈⢀⡀⠀⠀⠀⠀⠠⡀⠀⣧⠀⠀⠀⠀⠀⢠⣡⡄⠉⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⢣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠄⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⣠⠀⠀⠀⠀⢀⠀⠀⢠⡆⠀⠀⠐⠃⠀⡠⠀⢐⢀⠄⠀⠀⠀⠀⠀⠀⠀⣤⡇⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠞⠂⠀⢠⠀⠀⠀⠀⣄⠻⣏⢀⠔⠁⠀⢀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠠⠒⠀⠀⢀⣴⡇⡘⣟⠃
⠀⠀⠌⠀⠀⠀⠒⠨⠉⠀⠀⠀⠀⠞⠁⠀⠀⡠⠚⢋⠀⠀⢀⠄⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠦⠚⣣⣓⡉⢑
⠀⢰⠂⠀⢰⡆⠀⠀⠀⢀⢈⠀⠀⠀⠠⠀⠀⠇⡰⠋⠠⡄⠈⠀⡀⠀⢀⢞⠑⢂⠀⢀⡀⠀⠁⠀⠀⠁⠀⠐⠛⣿⡾⡀⠎
⠀⢸⠂⠀⠀⠀⠀⠀⠶⠀⠀⠀⠁⠀⠀⣀⠀⣆⠁⠀⣶⠰⣄⠘⠁⠀⡈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⢮⠂⢀⣀⠈⠉⠁⠀⠠⠤⠀⣇⡀⢸⠂⡱⠧⠂⣾⡇⢠⠿⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠸⠆⠃⡄
⠀⠚⠀⢸⠛⢀⠀⠀⠀⣁⠀⠀⠈⠀⠈⢇⠁⠂⡜⠱⠹⣺⠃⢀⠄⣄⡜⠂⠀⢸⠃⢀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠘⠰
⠀⣴⡦⠛⣶⢤⡀⠀⠀⠐⠤⠀⠀⠀⢀⠈⠣⡾⠀⡄⠆⠁⠀⠈⠡⢻⢻⠵⠀⠀⠀⠈⡀⣀⠀⠉⠒⢒⣁⣸⡤⠆
⠀⠀⠁⠀⠸⡛⠁⠀⠀⡀⢡⠒⢲⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡞⠉⠀⢘⡇
⢤⡀⠀⣠⠇⠁⠀⠂⠉⣩⠖⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠀⣰⠀⠀⠀⠀⣀⣸⣇⣀⡤⠞⠀⡸⡖
⢨⣜⡜⠃⡠⠀⠀⠠⠈⠀⢀⠀⢀⠀⠀⠀⠐⠠⠀⠀⠀⠊⠀⠀⠀⠉⠁⠂⢤⠃⠀⠀⠀⡞⠉⠉⣯⠀⠀⠀⠀⠀⠿
⠘⠯⣥⠋⠁⠀⠀⠀⠉⠀⡀⠀⠀⡀⠀⠀⠀⠀⠤⣀⡠⠒⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣠⣷⡤⠞⠃⠀⣀⣲⢀⣀
⠀⠀⠁⠀⠀⠀⠂⠀⠠⠁⡀⠈⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⡀⠒⠀⠂⠄⠉⠀⠀⠀⡏⠀⢈⡇⠀⠀⣀⡿⠟⠙⠋⢷⣄
⠀⠀⣶⠀⢠⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⣀⣈⡁⠁⠀⠀⠐⠄⠀⠈⠀⠁⠀⢀⡤⣷⠒⠉⠀⣄⠀⠀⢸⢂⠀⠀⣠⠁
⠀⠀⠏⠀⠀⢣⡀⠀⠀⠮⠂⠐⠊⠋⠉⠁⠀⠀⠀⠀⢀⣀⣴⣶⡾⠿⠖⠀⠀⣸⠴⠋⠀⠀⠒⠿⠀⠀⠀⠙⠧⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣻⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⢻⣿⡾⢿⡿⣿⣿⣿⣿⣿⡿⠁⠆⢸⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⡄⠀⢸⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣾⣁⡞⠁⣻⣿⡿⢡⡷⢀⡇⣿⣿⣿⡧⠀⠀⠀⠸⣿⣿⡇⠀⠀⢾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⢿⣇⣠⡇⣿⣿⡏⢀⣾⠃⢻⣿⣿⡇⡀⠀⠀⠀⣿⡿⠀⢰⠆⠺⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠘⢻⣷⠊⣿⡃⣼⣟⠀⠘⣿⣿⡇⢻⡀⠀⠀⣿⡇⠀⡈⠀⣤⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⢆⠀⠈⣿⢧⣿⣧⡿⠋⠀⣤⢻⣿⡇⢸⡃⠀⠀⡿⠀⠀⠀⢠⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡌⠰⠀⢾⣿⡙⠉⠀⠀⢈⡟⢸⣿⣷⠘⣇⠀⣾⡇⢰⡆⠀⢸⣿⣿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣇⣤⢳⣜⣿⣿⠶⠦⢀⣼⠳⠒⣿⣿⠀⠈⢄⣿⠃⢸⠁⠀⣿⣿⣿⡿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⢥⡙⠿⣿⣿⣿⣦⣀⣾⣿⣧⣼⡏⢻⡆⠀⠸⡟⠀⡿⠀⣸⡷⣾⣿⡗⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣇⠔⣯⡒⠠⠉⠛⢿⣿⢿⣿⢹⣿⡇⢸⣿⠀⠀⠀⠀⠁⢠⣿⡿⢿⣿⠁⢿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠹⣿⣿⠂⠘⣧⢀⠀⠐⠠⢸⣎⣷⣿⣿⡟⢸⣿⡆⠀⠀⠈⠀⣾⣯⡟⣾⢫⡎⢸
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢘⣿⡇⠀⠹⣷⡓⠀⣱⣼⣿⣿⣿⡏⠀⢸⣿⠀⠀⢠⠄⣸⡿⢶⢼⣿⡿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸⣿⣷⠀⠀⠈⢿⣦⡈⣿⣿⣿⡿⠀⠀⣾⣿⠀⠀⠀⢀⣿⡷⠾⢼⣿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⣸⡟⢷⣿⣿⣿⡇⠀⠀⣿⣿⠀⢀⠀⣼⣿⣴⠾⣿⡟⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠀⢐⣿⠇⣸⣿⣿⣿⡇⠀⢠⣿⣿⡀⠄⣰⣿⣿⠃⣸⣿⡻⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⢸⣿⢠⣿⠟⣿⣿⠃⠀⢸⣿⣿⡇⣰⠿⣿⣇⢀⡇⠈⣿⡄⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣀⣿⣧⣿⠃⠀⣿⣿⡄⠀⠸⠟⠏⣰⠏⢠⣿⣿⡾⢃⠀⡏⢹⣦⠈⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⣿⣿⣾⠇⠀⠀⣿⣿⡇⢀⣴⢊⣼⣿⡄⠀⣿⣿⣿⣼⡀⡁⢘⡏⢣⡀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⣿⣿⣷⣿⣱⣾⣿⣿⣷⡀⢹⣿⣿⣿⢿⣿⣬⣃⠸⡷⢤⠀⠀⣆
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⠁⢀⢆⣼⡏⢹⡟⣸⣿⣷⣼⣿⣿⣷⡀⢿⣿⣿⣦⠙⣯⣻⣤⡿⢈⠿⡄⠘⠄
⠀⢀⣾⣿⣿⢿⣿⡿⠏⠙⣀⣿⣿⣿⡟⢠⣿⣾⠿⡇⣾⢃⣿⣿⣿⡇⢻⣿⣿⣷⡌⠻⣿⣿⣷⣦⡙⢿⣷⣿⡆⣃⡄⠂
⣴⣿⣿⡟⣱⣿⣿⡇⡀⠀⢻⣿⣿⣿⣷⡟⢻⠃⣼⣿⣿⢸⣿⢹⣿⡇⠀⢿⣿⣿⣿⣆⠈⠉⠻⡻⢿⣦⣽⣿⠘⣿⣧⣤
⣿⠋⡏⣴⣿⣿⠋⢻⣇⠀⢸⣷⣿⣿⡿⢀⣿⡄⣿⠻⣿⡆⣿⡄⣿⡃⠀⠈⣿⣿⣿⣿⣷⣄⠀⠈⠲⡈⠻⣿⡀⠆⢉⠉⠉
⡋⠀⣼⣿⣿⡇⠀⠀⠟⠀⣿⡿⣿⣿⡃⠘⠁⣴⣿⣷⣿⣷⣾⣷⣸⣧⣀⠀⠘⢿⣿⣿⣿⣿⣦⠀⡀⡉⢦⠙⢿⣿⠺⡏⠳⣄
⠁⣴⣿⣿⣿⠷⠄⠀⠀⢀⣿⠇⣿⣿⠋⠀⣰⡟⢸⡏⢹⣿⣿⣿⣿⡍⢷⡤⣤⣜⣿⣿⣿⣿⣿⢷⡌⡜⢤⢣⠈⢿⣇⠘⠃⠘⠫⠑
⣹⣿⣿⣿⣿⠀⠀⠁⠠⣎⠹⣇⢹⡿⠳⠞⢻⡇⢸⣇⢀⣿⣿⣿⣿⣧⡈⢷⣀⠈⠉⠻⣿⣿⣿⣿⡿⣼⣂⢧⠇⠘⣿⣿⣇⠀⠦⠙⣧⡆
⣿⣿⡿⠁⢻⡇⠀⠀⠀⠈⢦⣼⣿⡇⠀⠀⢸⣇⣾⣿⣾⠿⢹⣿⣿⣷⡀⢠⡹⣷⣄⠀⠙⣿⣿⣿⣿⣿⢫⡜⣴⠀⢻⡄⠉⠳⣦⠀⢈⣻⠆⡀
⣿⣿⠃⠀⠈⣷⠀⠀⠀⠀⡈⠻⣷⣿⡇⠀⠟⣿⣿⠛⣏⣰⣿⡿⢿⣿⣿⣄⣹⣿⣿⣶⣄⠙⣿⣿⣿⣿⡟⣤⠛⡄⢸⠉⣲⡤⠬⢷⡀⠉⠀⠉⠢⡀
⣿⡏⠀⠀⠀⢹⡆⠀⠀⠀⠃⠀⢿⣾⡁⢸⣷⡿⣃⣘⡿⠿⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⠀⡇⠘⠋⠀⡈⠳⡄⢻⣦⣦⣀⣤⣤⢦⣀
⣿⠀⠀⠀⠀⠀⢷⠀⠀⢀⡀⠀⢸⣿⠁⣾⡿⢡⣿⠛⠀⠀⠀⣿⡎⠹⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⡇⠀⠀⢸⣦⣾⣿⣶⣼⣿⠀⠉⢤⠀⠉⢦⡘⠋⠂
⡇⠀⠀⠀⠀⠀⠘⣧⣴⣿⣿⣶⣿⣿⣾⣿⣷⣾⣿⠀⠀⠀⢰⣿⡦⣀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⢸⣿⡿⣿⣿⣿⣿⣿⣤⡀⠀⢰⡆⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⡿⠟⢋⣥⣾⡏⢩⣿⣿⠀⠀⠀⣾⢯⣛⣽⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⣿⡿⣷⣏⠻⣿⣿⣿⡉⠳⣄⣼⣇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡤⢀⣾⣿⣧⠙⣿⣿⣽⠀⠀⢀⣿⡶⢉⣬⣿⣿⡇⠀⠻⢿⣿⣧⣼⣿⣿⣿⣿⡇⣸⣿⠀⢸⣿⣧⡙⢿⣿⣿⣦⣙⣯⠀⢂
⠀⠀⠀⠀⠀⠀⢀⣼⡃⠈⢠⣾⣿⠿⣿⡴⣿⠇⣿⣄⣠⣿⣯⣿⣿⣿⣏⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⠀⢠⡘⢿⣿⣦⡙⢿⣿⣿⣿⣇⠀⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⣿⣿⣴⢿⣿⣿⣰⣿⣻⣿⣿⣿⠟⢻⣿⠏⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⣻⣿⠉⢿⠀⢸⣧⠀⠙⢿⣿⣦⡈⢿⣿⣿⣠⠉⠢⡀
⠲⣤⡀⠀⠀⢠⣿⣿⣧⣸⣿⣿⢻⡿⣯⣿⣿⣿⣿⣿⣿⡏⠀⣠⣾⠋⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⡏⠹⣿⡀⢸⠀⢠⢹⣧⠀⠀⠙⢿⣿⡌⣿⣿⣉⠓⡄⠈⠷
⠐⠺⠿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠈⢻⣯⣀⣿⣷⣾⣿⢻⡾⣠⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⣿⡿⣿⠀⡀⠀⠙⢷⣄⠀⠀⠉⢻⡼⣿⣿⣏⠳⣄⢀
⠟⣿⣿⠟⠉⠛⢿⣿⣿⡷⣿⣿⣿⣿⢏⡟⠀⢈⠻⣿⠛⣿⡿⠁⢸⣇⡿⠀⠀⠀⢸⣿⣿⣿⡿⠁⠸⣿⣷⠻⣧⡘⠈⠛⠳⢶⣤⣿⡷⣀⠀⠀⢷⣻⣿⣿⡀⠀⠉
⡜⢡⡏⠀⠀⠀⣾⡞⠟⢀⣿⣟⣸⡿⢦⡄⢀⠘⡆⢽⣤⣿⠁⠀⠀⣿⣇⠀⠀⠀⠞⣿⣿⣿⠇⠀⢀⢹⣿⠀⠛⣿⡄⠀⠀⠀⠈⢻⣆⠈⠙⢆⠘⣧⢿⣿⣧
⣠⡿⠀⠀⢀⡾⠟⡿⠀⣾⣿⣿⠇⡷⢸⠃⢺⠀⣷⣾⣿⠇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⣿⣷⠀⢹⣿⢶⣤⣀⣀⣀⣿⣄⠀⠀⠀⢿⡝⣿⣿⣷⣤
⠟⠀⢀⡴⣻⣷⣄⠃⣼⣿⣿⡌⢠⡘⣿⠀⣼⢰⣿⢹⣿⠀⠀⠀⠀⢹⣿⣆⣀⣠⣶⣿⣿⣯⡀⠀⠀⠀⣾⣿⡀⠸⣿⣧⡈⢻⣿⠿⠿⠟⠓⠆⢤⣤⣵⣌⠛⢿⣿
⠀⠀⠈⣴⠟⢿⣿⣾⣿⣿⣿⣄⣸⣅⡿⠀⣼⣾⣿⠘⣿⠀⠀⠀⠀⣼⣿⡏⠉⣹⣿⣿⡿⠉⣹⣷⣶⣷⣿⣿⣧⠐⣿⣿⣿⣤⡙⡄⠀⠀⠀⠀⠀⠈⠉⠋⠑⢦⡈
⠠⢀⣾⠏⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣧⣾⣿⢻⣿⣴⡿⠿⠶⠶⢿⣿⣿⣷⣾⣿⣿⡿⠿⣿⣿⢻⡏⠉⠉⣿⡏⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⠟⠁⠀⠀⠀⠘⣿⣿⣧⣼⣿⣿⣿⠛⣿⣧⠾⠟⠉⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⡟⠁⠀⠈⠻⣾⠇⠀⠀⣿⡷⣆⠈⢿⣿⣿⣿⣿⣮⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠿⣧⠞⠉⠁⠀⡆⠀⠀⠀⠀⠀⠀⢀⡇⡸⣿⡟⠀⠀⠀⠀⠀⢹⡆⠀⢀⣿⡇⠈⠳⡀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣄

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠀⢠⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⡀⢀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠠⡀
⠀⠴⡀⠀⠀⠀⠈⠉⠀⠁⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⣴⠩⢷⣄⠻⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⡋⢸⠊⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣷⣤⣈⠁⣀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣙⠫⢄⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⡟⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠉⠟⡙⠑⠶⡄
⠀⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣸⠃⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁
⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠻⠖⠋⡀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢖⣦⡀⠀⠀⠀⠈⠉
⠀⠀⠉⠀⢠⠂⠀⢰⠇⠀⠆⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣤⣄⣀⣃⣀⡒⠀⠀⠀⠀⠀⣾⡇⢠⢺⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⣛⢋⡆⠁⠀⠀⠀⣿⠃⠨⣭⠁⡆⠀⠀⠀⢀⡐⠀⣩⣿⣇
⠀⠀⠐⠧⣆⡖⢂⣀⡀⣠⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠑⢸⡟⡼⠀⠀⠀⡰⠂⠥⢐⢣⣿⡇
⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠙⠛⢿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠙⠏⠉⠈⠁⠀⠀⠸⣗⠔⣁⣼⡼⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⣀⡀⠀⠙⠙⠙⠛⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⣆⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠤⣀⠄
⠀⠀⠀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠂⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⠞⢠⡖⡌⢻⠡⠤⡴⢰⡀
⠀⠀⠀⠇⢸⡄⢀⡖⢦⠀⠀⠀⠀⠀⠀⠀⠀⢡⠦⢤⡀⡀⠀⠀⠀⠠⢤⣠⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡽⢧⣼⣛⣾⣯⣽⣾⢹⡲⠿⡄
⠀⡴⠲⢶⣤⣷⣎⣰⠃⠀⠀⠀⠀⠀⠀⠀⢽⡸⡄⣸⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⠭⡿⠻⡿⣛⢻⡟⡙⡶⠆⣾⣧
⠀⠻⢤⣬⠿⡟⢫⣼⣉⠓⢦⡀⠀⠀⠀⢸⠉⡇⣳⡏⠀⠀⠀⠀⠀⠀⠐⠒⣖⠂⠀⠀⠀⠶⠀⠀⠈⠀⠁⠁⠀⠀⠈⢃⡥⢡⡿⢿⣿⠟⠱⣦⠙⡯⠁
⠀⠀⠀⠀⠀⠻⣄⣳⢉⣷⣤⡿⠀⠀⠀⠈⣠⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣩⠦⠀⢠⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠮⣆⠀⢄⠱⠂⢐⣁⠞⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠛⢧⣽⠀⠀⠀⠀⠀⠁⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⡀⡰⠤⠀⢄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠈⠁⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢰⡆⠙⠀⠰⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠘⠒⣀⠐⠄⢀⠄⠀⠐⢦⡤⢘⠢⣀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢳⠀⣄⠄⡸⠀⠄
⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠸⠀⠰⡀⠀⠀⠁⠀⠂⠀⢼⢠⣼⣅⡌⢀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡘⠃⡉⠊
⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠄⠀⠀⡃⢈⡛⠂⠀⡖⠃⣨⠁⠈⢣⠈⠁⠀⠀⠀⠀⠀⢈⠴⠾⡂⢖⣿⡇⠐⠢⣀
⠀⠠⡐⡉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠙⠀⠀⠀⠀⠈⢄⠠⢀⠡⣀⠄⠀⡁⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠏⠉⠏⠀⠀⢈⠁⠈
⠀⠀⠀⠛⠑⠃⡂⠀⠃⠀⠀⠀⡀⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠡⠄⠳⡀⠀⠀⠈⢲⠃⠰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠙⠁⢖⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢟⠀⡀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄



⠀⠀⠀⠀⢀⣀⣀⣤⣴⣤⣤⣄⣠⣤⣤⣤⣤⣤⣀⣠⠀⠀⠀⠀⠠⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣃⡀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠈⢁⣀⡀⠀⠀⠈⣿⣿⣿⣷⣤⣴⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠈⣿⣿⣿⡁⠤⠄⡀⠈⠉⠙⠾⠀⠀⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣀⣀⣀⣼⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠈⠀⠠⡐⠀⠀⢙⣿⣿⣿⣿⣿⣇⣐⣸⣿⣿⣿⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈
⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⡀⠀⠀⠁⣀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⢋⢀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⠛⡅⠀⠉⠙⢿⣿⣿⣷⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢄⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠢⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣦⣤⣄⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⢠⡀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠰⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠘⠀⠠⠀⠠⠄

⠀⠀⣾⣿⣯⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣏⣿⣷⡆
⠀⠀⢿⣿⣿⣿⣿⢿⣿⡏⣿⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣲⣿⡯⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠈⢿⣟⣿⣿⣛⣻⣷⣿⣿⣿⣿⣗⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣴⣾⣿⣭⠿⣿⣿⣏⣻⣿⣻⣿⡟⠁
⠀⠀⠀⠀⠻⣿⣏⣿⣟⠉⠙⠛⢿⣟⠛⠛⢿⣦⣄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠊⣠⣾⡿⠿⢿⣿⠟⠛⠙⢛⣿⣿⣻⣿⠏
⠀⠀⠀⠀⠀⢹⣿⣷⡿⠓⠛⠛⠛⠿⠷⣤⣀⠉⠻⣷⣌⠀⠄⠀⢀⡤⠊⣠⣾⠟⢉⣢⣶⠿⠟⠛⠻⠛⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣷⡦⠶⠶⠶⠶⠶⠛⠛⠓⢶⣮⣻⣦⣈⣷⣇⢠⢾⣿⣵⠿⠛⠛⠛⠳⠶⠶⠶⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⣀⣠⣤⣠⣀⣀⣀⣤⣤⣮⣿⣿⣿⣿⣿⣯⣾⣯⣥⣤⣤⣤⣤⣤⣤⣀⣐⣂⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⣿⠛⠛⠿⠿⢿⣿⣭⠽⢿⣿⣿⣿⣿⣷⠿⠯⣽⣿⣿⡿⠿⠿⠿⢿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣡⡤⠶⠒⢛⣿⠋⠀⢠⡿⣻⣿⣿⣿⣟⣷⡀⠀⠙⢿⡶⠶⣤⣄⣈⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⢁⣠⠴⢟⠟⠁⣀⣴⠏⢠⢯⠿⣿⡿⡟⣎⠙⢦⣄⠈⠙⣶⢦⣌⠩⣛⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢙⣽⣿⡖⡋⢀⡴⢿⡶⠟⣿⠁⣰⠏⠸⠈⣿⡗⢼⡘⣎⢎⢿⣿⢶⣿⢦⣌⠛⠶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣴⠋⢠⡟⠀⣼⠋⣰⡏⢀⡇⠀⣿⡇⠘⣇⠹⣎⢎⢿⣤⢻⡄⡝⢷⣱⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣴⣰⣯⣼⣿⣧⡿⠀⠀⢿⡇⠀⠹⡀⣿⡼⡎⣷⣃⣿⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⢾⣯⣷⣼⡇⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⡀⠈⠉⠀⣠⣴⣲⢿⡄⠀⠀⠀⠊⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⡖⣾⡏⡿⣿⣽⣽⡇⠀⠀⠀⠘⣟⡮⡷⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⣀⡤⣆⢄⠀⠀⠀⠐⠢⢄⠀⡐
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⢻⣻⣟⡧⣏⡄⣽⡇⠀⠀⠀⠀⢹⡾⣿⠟⠀⠀⠀⠉⠒⠂⠀⢌⠀⠁⠀⣿⣹⡳⣻⣹⣯⠷⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⢹⣿⠿⠿⠛⠋⢀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠸⣧⣳⣷⠷⠟⠚
⣶⠀⠀⢁⠀⠀⠠⠄⠀⠀⠀⢠⣿⣿⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⢄⣀⠀⠀⢸⣿⣿⣷⠀⠀⠀⢀⣀⣀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⡟⡗
⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠈⠀⣘⢻⠃⠈⣿⣷⡿⠀⢤⣾⣿⣿⣿⣗⡀⠀⢀⣤⠶⣴⢄⠀⠀⠀⠘⣿⣯⡇⣷
⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣤⣴⡶⢧⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⡂⠍⢀⡞⠀⠀⠁⠁⠀⠀⠀⢻⣿⠿⠛⠁⠀⠐⣟⢙⢖⣿⠗⠀⠀⠀⠀⠀⠙⠙⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡞⢭⣿⡆⠀⠀⠀⠀⠀⠀⡸⠉⠷⣦⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠈⡿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⠀⠀⠀⢠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣳⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⡄⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠻⠯⣷⣿⠿
⢠⠀⠀⠀⠀⠀⣀⡀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣴⣯⣷⣄⠀⢀⡠⢞⠷⣗⠀⠀⠀⢀⣬⣍⡛⠃⠀⠀⠀⠠⣾⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣆
⢹⠀⠀⢀⣴⣾⣿⣷⣌⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡘⢿⣅⡷⠋⠁⠀⠀⣼⣿⣿⣿⣷⣶⠀⠀⠈⢾⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⠀⢸⣁⣉
⢸⠀⠀⠙⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠃⠀⠉⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢀⣄⠀⠀⠉⠻⣷⠟⠀⠀⢀⠀⠀⡀⠀⠀⠀⢸
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⢀⣌⡛⠁⠀⠀⢰⣾⣿⣿⠀⢰⣏⡿⣿⣿⣿⠏⢰⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢷⣜⣥⣶⡀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠈⣯⣿⣿⠄⠀⠉⠙⠛⠛⠁⠀⠀⠙⢿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣤⢿⣤⠀⠀⠀⠀⣀⣀
⡇⠀⠀⠀⠀⠀⣠⣾⢯⠣⡱⣝⢿⡶⢋⣢⠀⠀⠀⠈⠛⠿⣿⣿⠟⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣤⡤⡶⣶⡀⢸⠧⠆⣸⠀⠀⢸⣿⣿⣿
⠋⢀⠀⠀⠀⠸⣿⢮⡳⡑⣝⢮⣢⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣤⣶⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⡟⡼⢱⢣⣇⠈⠑⠚⠃⠀⠀⠈⠿⠿⠛
⢠⣾⣿⣦⣄⠀⠈⠳⣽⣌⣮⠿⠋⣀⣄⣤⡀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡄⠀⣀⣴⢦⠀⠀⠀⠀⠙⠻⠟⠛⠋⠉⠀⠀⠀⠀⠀⣤⣤⣶⣶⣧
⠈⢿⣿⣿⣿⠏⠀⠀⠙⠟⠁⠀⠀⢿⣿⣼⡇⠀⠀⡀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡜⣏⡧⡪⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠘⠿⠟⠛⠉⠀⠈⢢⠞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣢⣤⡀⠀⠀⠀⠀⠀⢀⡟⠳⠒⣢⣤⠀⠀⠀⠀⣤⣶⡞⣿⢸⡇⠀⠀⣾⣿⣿⣷⣆⠀⢀⣶⣿⣷⡄⠀⠁⠀⠀⠀⢀⣠⣴⣶⣦⡄⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⢀
⡽⣿⡵⠀⠀⠀⠀⠀⣸⠐⠉⠐⢠⡇⠀⠀⠀⢰⣷⣿⣿⣿⣿⣷⠀⠀⠙⠛⠿⣿⠏⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣛⡄⠀⠀⠄⠀⠀⠀⠀⢀⣴⣿
⡾⠋⠀⠀⠀⠀⠀⢰⠷⣦⣄⣂⡜⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻
⠀⢀⣀⣀⣀⣀⠀⠈⠐⠲⠇⠈⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣠⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⡀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢶⡗⢸⠇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠷⠛⠛⠃⠀⣴⡞⠉⠄⠀⠀⢳⡞⢳⠀⠀⠀⣶⣾⣿⣿⣿⠀⠀⠰⠀⠀⠐⣾⣿⣻⣷⣦⣄⡀
⠀⠀⠛⠚⠓⠛⠀⢰⣶⣾⣿⣷⡄⠀⣀⣲⢤⣄⣀⣀⣾⣷⣄⠀⠀⠀⠈⡀⠈⠀⠈⠀⠘⣏⣀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣷⣻⣷⣳⣻⢯⡟⣄
⠀⠀⢀⣀⣀⡀⠀⠈⣿⣿⠿⠿⠿⠀⢹⣏⠣⡈⡟⠻⣿⣿⣿⡇⠀⠀⠀⢱⣦⣠⠤⠖⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠷⣿⣣⣯⢧⣿⢻⡗
⣿⣿⣿⡟⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠙⠍⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠷⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣭⡙
⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡳⢤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⡾⢲⡖⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣠⡿⡇⠀⠀⠀⠀⠀⠈⠻⢿⣿⡁⠀⠀⠀⠀⠀⠿⠼⠥⠿⠇⠀⠀⠀⠀⠀⠀⠀⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⣥⣾⣧⣬⣤⡄⠠⣤⠀⡀⠀⢰⠀⠀⠀⡡⠤⠁⠀⠀⠐
⠀⠀⠳⡀⠀⠀⠀⢀⣴⠋⢳⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⢱⡄⠀⠀⠀⠀⠀⠀⣀⠘⢺⠿⢣⡜⠿⡖⠃⣀⠀⠀⠀⠀⠀⠢⡠⣆⠀⠀⢀⣠
⠀⠀⠀⠀⡘⠂⠂⣈⢻⡄⣼⢋⡀⠀⠐⡂⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠛⡿⠋⠉⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠉⢁⠸⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠑⣄⡳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⢀⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢄⣀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠆⡀⠑⢦⢠⠖⠁⠰⠄⠀⠀⠀⠀⠀⡀⢡⠌⠉⠁⡎⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠙⣗⢸⡏⠁⠀⠀⠀⠉⠐⠂⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡡⢬⡇⠀⣿⠤⣅⠀⠀⠀⠀⠀⠀⠈⠴⠈⠹⠁⠶⠒⠁⠀⠀⠈⠂⠀⠀⠀⡀⠀⣯⢸⡃⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢇⠈⠳⢤⠛⠈⢃⠴⠋⣀⠆⠀⠀⠀⠀⢠⠀⠛⠂⠛⠀⢤⠀⠀⠀⠀⠀⠀⢹⣏⢇⣀⡘⣏⣀⣠⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⠂⠂⠀⡉⠀⠒⠒⠁⠀⠀⠀⠀⠀⠄⠈⠓⠐⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⡛⢟⠻⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠒⠲⠤⠐⣄⣧⣥⡔⠡⠤⠒⠂⠀⠀⠀⠀⠀⡆⠀⠀⡥⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⣶⡐⠙⡆
⠀⠀⠀⠀⠀⠀⠐⢻⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠔⠛⠢⣈⠆⠀⠀⠀⠀⢀⠘⣇⠀⠀⢰⡤⣴⠀⠀⢀⡟⢀⠀⠀⠀⠀⠀⣹⣇⢀⡇
⠀⠀⠀⠀⠀⠀⡠⡖⠋⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠦⠤⠏⠀⠀⠀⠀⠀⠀⠀⢼⡄⢀⣻⣿⣿⢒⡀⣼⠁⠀⠀⠀⠀⠀⠀⣿⣷⣾
⠀⠀⠀⠀⠀⠌⠐⢇⠀⢀⠟⠀⠣⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠸⠐⣄⠀⠀⠀⠀⡌⠸⣇⠀⠙⢿⠿⠋⢀⣿⠞⡄⠀⠀⠀⠀⠀⢸⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢀⢴⡄⠈⠀⠀⠀⠀⠐⢀⠘⡦⠀⠈⠀⠠⡞⢀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠂⡀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡽⠤⡧⠬⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠤⠐⠂⢆⡇⠀⠀⠀⠀⢤⡀⠀⠒⠒⠀⢀⡤
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⡾⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠴⠖⠢⠔⢣⠤⠀⠀⠀⢰⠒⠇⢹⠋⠉⠉⠸⠐⡆
⠀⠀⠀⢀⠄⠁⠀⠀⠁⠀⠀⠊⢃⠀⠀⠀⠀⠀⠀⡆⡠⠊⠤⠆⠤⠄⠢⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⣄⠀⢠⡕⠀⣠
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⢠⠀⡀⠀⠹⠁⠨⠖⠀⠐⠲⠀⠹⠅⠀⣀⢠⠀⠀⠀⠀⠃⡀⠀⢈⠀⠀⠀⠀⠀⠢⡀⢦⠂⠐⡄⢀⠔
⠀⠀⠀⠀⠀⠀⢙⠒⠶⠚⡘⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⡀⡀
⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢰⠉⢀⡹⠀⠀⢠⠊⠉⠙⢄⠀⠹⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠘⡄⠀⠀⠈⢆⠀⠀⠀⠀⢨
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠘⢦⣀⠠⠊⠀⠀⠸⠄⠂
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠐⠒⠒
⠀⠀⠀⢠⡄⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡠⠄⠀⠈⠠⠠⢢⠄⡄
⠀⠀⠀⠈⠙⠚⠁⠀⠠⠂⠀⠰⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡇⠀⠄⠀⠀⠀⠀⠘
⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠄⠤⠀⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠛⠁⢀⠁
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠄⠢⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠰⠁⠀⠠⡀⠀⠈⠀⠀⠀⡠⠔⠒⠊⡅⠀⣠⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠖⠊⠁⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣅⣼⣦⡀⠀⠀⠀⠀⠀⠀⢸⣦⠀⣸⣿⠀⠀⢈⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⡟⠀⢠⡿⢻⡇⠀⣤⠀⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⡉⠉⠉⣙⠳⣆
⠀⠀⠀⠀⠀⠠⣤⣙⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠘⠁⠘⠇⠀⣿⣼⠃⠀⠀⠀⠙⢿⣿⠿⠟⠻⠁⢀⠀⠁⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠲⠭⣻⡖⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣧⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⣁⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣵⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠈⠻⡇⠀⠀⠐⠋⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠿⠷⠾⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣴⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣏⠳⣝⢦⡀⠀⠀⠀⠀⣿⡛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡇⠀⠀⠀⣤⡈⠻⣦⠀⢿⣿⣿⠃⢠⡾⠋⣠⡄
⠀⠀⠀⠀⠀⠀⠀⡴⢍⠻⡉⣿⡟⠿⠶⠷⠶⠀⠀⠀⣿⣉⣉⣽⣿⣿⠷⠶⣿⣿⣿⡿⠿⢿⡇⠀⠀⠀⠈⠻⣆⠈⢷⣄⠀⢀⣴⠏⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠢⡑⢌⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⢾⣿⣿⣿⣿⣷⣶⣶⣟⣛⣿⡇⠀⠀⠀⠀⠀⠙⢷⡄⢙⠀⢘⠁⣴⠟⠁
⠀⠀⢀⣠⣤⣀⣀⣿⡖⢌⠢⣙⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠫⡙⢟⠻⣿⠶⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⣿⣿⣿⣿⣿⣿⣶⣾⠛⠛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣹⡅
⠀⠀⠀⠀⠀⠉⠢⡑⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇


⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣴⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠠⠥⠤
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢲
⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⢈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂⠀⠑⠄⠀⢸⠀⢸⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣬⠒⢪⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡄⠀⣨⠇⠀⠀⠀⠀⣤⣤⣬⣤⣤⠀⠌⠀⠄⢣⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠁⠀⠀⠀⠀⠀⠘⠻⠿⠟⠃⣼⣶⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠄⠒⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣼⣿⣤
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢠⡄⠀⠄⠀⣀⠀⠀⠀⠈⠹⣿⠉
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢳⡀⠈⠀⠄⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣐⣿⣠⠊
⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠡⠃⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠀⠘⠤⢤⠆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢀⠀⠀⠰⣄⠄⠀⠀⠀⢀⡀
⠀⠀⠀⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠈⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠰⣶⡾⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠘⡋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢙⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢀⡾⠁⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠸⣧⠀⠀⠀⠀⠻⠃
⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡌⣆⠴⣉⠀⢳⢸⠀⢠⠋⢀⡇⢸⠀⠀⠈⠁⠰⠀⠐⢦⡀⠛⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠃⠀⠀⠀⢀⢃⠇⠰⣉⠀⡆⣾⠀⢸⠀⡤⣣⠸⢀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠠⠒⠋⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⢤⡤⠀⠘⠟
⠀⠀⠔⠊⠁⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⡂
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠐⢸⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢀⡀⠀⠀⢤⣀⢠⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠟⠀⠀⠀⠀⣴⣶⣦⠀⠀⠰⠍⠄⠴⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠢⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠁
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⡔⠀⠲⢄⠀⠂⠉⠀⠀⠀⡀⠀⡀⢂⠀⠀⠀⠀⠀⠀⠀⠰⡁⢀⠀⠀⡀⠀⠖
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠘⣆⠀⠀⠀⢀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠿⢀⠃⣀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⡀⠀⠀⠘⠘⠆⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠶⠀⠀⠈⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣠⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⣄
⣴⡗⠀⠀⠈⠃⠀⡠⡖⠀⠀⡏⠀⠀⠰⢦⠎⢢⠀⠀⠈⣁⠀⠀⠀⡑⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⠇⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠠⠂⠁⢶⠀⠀⠀⣲⣿⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠉⠀⠀⠀⠀⠀⢀⢴⡜⠃⢰⡂⠀⠀⠀⠀⠈⠀⠀⢰⣿⠃⠐⠇⠀⡠⠠⠀⠀⠀⠀⡀⠀⠄
⣆⠀⠀⠀⠀⠈⠛⠶⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠠⠄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡌⠀⣧⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⢀⠠⢀⡀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⣘⣣⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠠⠀⢐
⠸⣾⠍⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠐⢀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠁⠀⠀⠨⠀⠈
⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⣠⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠈⢠⡀⠀⠨⣀⠀⠒⠀⠀⠀⠀⠀⠀⢀⠀⡀
⡄⠃⠚⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠉⠀⡇⠀⢱⣄⡀⠈⠐⢸⢀⠰⠀⠠⠀⠀⠿⠟⠠⠠
⠐⠘⠀⢀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠇⠀⠈⣡⡠⢀⡀⠀⠈⢄⠸⠠⠙⠢⡀⡼⠀⠀⠀⠀⠄⠰⣅⠀⠀⠈⠃
⠀⠀⠢⣿⣀⣀⡁⠉⠀⢀⠀⠀⠀⠀⠀⠂⠜⠉⠈⠀⠀⠠⠀⠁⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃
⠀⠀⠀⡇⠀⠀⠉⡆⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠠⠄⣀⠀⠀⠀⠓⡀⠀⠐
⠀⡎⠀⠈⠲⠤⣀⣇⣀⣀⠀⠀⠀⢢⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠄⠀⠀⠀⢠⠠⠴⡖
⠘⠀⠀⠀⠀⠀⢸⡁⠀⠈⡄⠀⠀⠀⢤⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⠊⠁
⢀⣀⣄⣨⣤⡄⠀⠙⠒⡾⠦⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠜⠃⠀⠈⠛⠧⠂⠀⠘⢇⡀⢸⠀⠀⠀⢀⠐⠀⠀⢀⡄⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢺⡇
⡠⡀⠀⣀⡝⠀⠀⢄⠀⠀⠈⢹⡒⡄⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠠⠄⠀⠄⢀⣀⠀⠀⠀⡀⠀⠂⠀⠀⠈
⠀⠀⠂⠈⠀⠀⠀⠘⠉⠀⠀⢀⠙⠧⠄⠀⠀⠉⠉⠙⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⢐⡂⠀⠀⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⢄⠈⠠⠟⣹⠯⠫⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠃⠠⠿⠀⠉⠠⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⠈⠃⢈⠀⠆⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠈
⠀⠀⠀⠀⠀⠀⡆⠡⠐⠀⢴⠆⠀⠁⠀⢦⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⡀⠊⢦⡍⠆⠀⠐
⠀⠀⠀⠀⠀⠀⢻⠐⡀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠘⢆⠀⠀⠨⡠⠈⣳⣙⠆⠀⢊⡀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⠆⠈⠿⡆⡀⠱⣊⣴⢛⣦⠁⠒⠀⡁
⠀⠀⠀⠀⠀⢀⠀⠀⠠⠈⠠⠀⠀⠁⠀⢄⡀⠀⠀⠀⠀⠂⠑⠌⠰⠄⠀⢌⠉⣣⣈⠈⣀⡀⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣁⠀⠀⠀⠀⠀⠙⣁⡔⠀⡀⠀⠐⡀⠃⣈⠁⢀⡛⠀⠂⠲⠖⠐⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠉⠄⠀⠀⠈⠒⠲⠀⡰⠡⠳⠆⠰⠄⢤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠠⠀⠃⠀⠂⠠⠀⠉⠀⠀⠐⠄⠈⠀⠁⠀⠀⠀⠄⢠⠂⠀⠀⠀⠆⠄
⠀⠀⠀⠀⠂⠀⠅⠀⢴⠀⠄⠀⠀⠀⠀⠀⢀⠀⠴⠀⠀⠀⠀⠈⠑⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠀⢈⠠⠀⠀⠘⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠤⠄⠀⠂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠁⠀⠆⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠁⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠠⠈⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠠⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠩⡈⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢡⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣤⣀⣀⣠⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢀⣀⣤⣴⡾⠿⠋⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠷⠿⠿⠟⢛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣉⣙⡛⠛⠿⠿⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣠⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⢿⣆⡀⠀⠀⣠⡿⠿⠿⠿⠿⢿⣆⡀⠀⠀⣠⣿⠃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⢷⣶⣶⣶⠗⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣟⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⣦⣿⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣇⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠛⠛⠛⠛⠛⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣈⣿⣆⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠛⠛⠛⢿⡆⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⣟⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⢻⣿⢶⣦⣄⠀⠀⠀⠀⠹⣷⡀⠀⠀⠘⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⢸⣿⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣸⡏⠀⠈⠻⣷⡄⠀⠀⠀⠘⢿⣦⣤⣴⢿⣷⣸⣿
⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠙⠿⣷⣤⣿⣿⡏
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠻⠷⣶⣤⣄⡀⠈⢿⣷⠶⠶⠶⠾⣶⣿⠃⠀⣠⣤⣴⡾⠿⠃⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠇⠀⠈⢻⣦⠀⠀⣰⡿⠁⠀⠘⣿⡉⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣤⡀⠀⢀⣀⣀⣀⣀⣨⣿
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣶⠀⣼⣟⠀⠀⠀⠀⠻⣧⣴⡟⠁⠀⠀⠀⢸⣧⠀⣴⡆⠀⢸⣿⠉⠉⠉⠉⣿⡇⠀⢹⡇⠀⠀⠀⢨⣧
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠛⢷⣦⡀⠀⠀⢹⣿⠀⠀⢀⣤⣾⠟⠁⠀⠘⣿⡄⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣯⣠⣶⠟⠋⠀⠀⠀⠀⠀⢸⣷⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣧⣼⣿⠀⠀⠀⠀⣿⣧⣤⣾⡇⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⣶⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⣿⡏⠉⢻⡇⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠀⠀⠀⠀⠶⣶⠆⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢼⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣿⠇⠀⢸⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋⠀⠀⠈⠻⢷⣶⣶⠟⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣿⠁⢸⣿⠀⠀⠀⠀⠶⠾⠆⢸⣿⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⢤⣤⣴⣟⣤⣤⣶⣶⣶⣶⣾⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣟⣧⣤
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⣿⣼⣾⣇⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⢠⣷⢠⣾⡇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡠⢿⠟⠉⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢸⣻⣾⣿⡏⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣶⣦⣴⣶⡶⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣁⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠙⣿⣶⡄⣿⡀⢰⢸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣿⡿⢄
⠀⠀⠀⠀⢀⠴⠛⢀⣴⣿⣿⣿⣿⣧⣼⣦⣷⡄⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⣿⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠹⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠰⢷⣤⣿⣿⡿⡆⠁
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠛⠋⠉⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡈⠻⠿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⢰⠀⡄⠀⣿⠀⠀⠀⢣⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣦⣷⣶⣿⣶⣷⣴⠇⣸⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣤⣄⣀⣀⠀⠈⠦⠠⣄⡀⠙⢦⡟⣋⣙⣿⣿⣿⣿⠶⠃⣀⡴⠰⠀⠉⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⡠⠐⠋⠁⠁⠀⠈⠉⠛⠛⠲⠤⠌⣹⣶⢤⣀⣀⣉⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣖⣋⡩⠭⠛⠛⠒⠀⠐⠀⠂⠈⠑⠢⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠀⠐⠲⠖⠚⠛⢲⠟⠽⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠿⠶⠤⣤⠄⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣠⢴⠏⠀⠄⠀⣼⡇⢠⣿⣿⣿⡌⢿⠁⣙⢿⡉⢹⣦⣀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⡼⢀⡄⠀⠘⠁⣭⣿⣿⣿⣿⣿⣦⡀⠘⠆⢁⢹⡇⠈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⠀⠀⣀⣿⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢜⣶⣇⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⣿⡾⢻⡏⢿⣿⣷⣿⣿⣿⣿⣿⠟⢹⣦⣿⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠙⢿⣿⣿⣿⠟⠋⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣻⠿⢿⡁⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠿⢛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠶⣿⣡⣚⡷⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠿⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣤⡶⣾⣿⣿⠶⣦⣄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠎⠹⠃⣤⡄⠀⢀⣤⡀⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣘⠀⡀⠀⢼⠆⠀⡀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡿⣴⢿⣦⢸⢠⣾⠷⡜⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠺⣦⠀⠀⠀⢾⡷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⣆⠘⡟⢰⢈⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⠐⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⠀⠹⠾⠞⠁⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠂⠠⠈⠈⡄⠀⢤⠀⠀⢀⠀⡀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⢀⠨⠶⠥⠄⠈⠂⠑⠀⡀⢀⠄⢈⠀⠴
⠀⠀⢈⠁⠃⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠈⠀⠁⠢⠀⠁⠁⠁⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠐⣀⢀⠂⠂⠰⢑⡁⢐⡴
⠀⠀⠈⠀⠁⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡒⠀⡀⠀⠀⠐⠐⠐⠀⠸⠀⣀⠀⠀⠀⠀⠀⠂⠐⢂⢀⠒⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠂⠀⠂⠢⠀⠲⢦⡀⠐⡥⢄
⠀⠈⠀⡄⢀⠀⡀⠀⠀⠘⢃⢂⠀⠈⢀⣄⠀⠀⣀⠀⠀⠀⢀⣁⠓⠈⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢥⡤⡄⠀⢰⠄⢀⠀⠀⠛⠀⠑⠊
⠀⠀⡀⠓⠀⠄⠠⠼⠀⠀⠈⠀⠀⢀⠐⠀⠁⢨⠙⡞⡛⠀⠈⠈⠀⡂⢠⠁⠂⠀⠊⠁⠀⠛⡏⠏⠭⠉⠁⠀⠁⠀⠀⠐⠐⠀⢀
⠀⠀⠀⠠⠖⠐⠦⠀⠀⠀⠀⠀⠀⢐⠴⠀⢠⠀⠑⠊⠁⠤⠁⢊⡀⠀⡸⠀⠀⠐⠀⠀⠠⠀⠀⠀⢀⣀⢠⡀⠀⠀⠀⠒⠀⠠⠄⡀
⠀⡎⠉⢣⠀⠇⠀⠀⠀⠥⠀⠀⡀⠈⠶⠀⠪⡨⠀⠂⠤⠐⠁⠃⢀⣈⠀⠀⠀⠀⠁⠈⠀⠀⢼⡥⣞⠛⡘⠁⠂⠈⠂⠴⡆⠠⠀⠂
⠀⢄⠂⡴⠀⠀⠀⢀⠀⠀⠀⠀⠘⠃⠀⠆⠀⠀⠀⠀⣤⠀⠀⠀⠠⠌⠀⠸⠂⠀⣤⠀⠂⢴⡀⡠⠔⠊⠤⠄⠀⠐⠍⠀⠐⠄⠀⡀⢀
⠀⠀⣀⠀⠀⠀⠐⠆⠀⠀⠀⠉⠁⠀⠀⠀⠤⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⠀⠂⢀⠈⢀⠈⠀⡀⡀⠀⠀⠀⢀⡐⢿⠂⣀⠀⠀⠉⢙
⠀⠀⣏⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠄⠀⠀⠈⠀⠀⠠⠔⠀⠘⠀⠀⢃⠀⠠⠀⠀⢀⠐⠐⠀⠀⠀⠀⢹⠀⠀⠀⠁⠀⠑⠁
⠀⢀⠀⠀⠐⠀⠀⠠⠀⠀⡄⣤⢠⠀⡀⠂⠀⠀⠀⡀⠄⢶⣲⣤⠂⠀⠀⠀⠀⠄⠀⠙⡀⠀⠀⠈⠈⠀⡰⠁⠀⠈⠀⠀⠀⠠
⠐⠪⢬⠐⠲⠀⠀⠀⠀⠀⠀⡆⠀⠐⠠⠂⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠴⣂⠀⠀⡀⢠⣒⡆⢀⠀⠀⠁⠀⠀⠠⠂⠄
⠀⠤⡀⢃⠂⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠀⠀⠄⠀⢰⣖⠀⠀⠀⠀⠀⠀⠸⠁⠐⠈⠁⠀⠀⡁⡀⠁⡒⢀⠁⠂⠘⠄⠀⠃⠀⠰⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐⠈⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣷⣶⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠇
⠀⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣰⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⠄⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠘⠁⠶⣶⣶⣶⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⢠⡴⠶⠶⡤⠀⠀⠀⠀⠀⠀⠠⠀⣀⣤⣀⠈⠻⣿⣿⡇
⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠃⠀⣿⡿⠁
⣿⡿⠁⠈⢻⣿⣷⣄⣀⠀⠀⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⣿⠇
⢹⣧⠀⠀⠀⠙⣅⠉⠛⠿⣿⣿⠀⢰⣦⡄⠀⠸⠿⠿⣿⣿⠀⢰⣦⡀⠀⣶⣾⠋
⠘⣿⡀⠀⠀⠀⠀⠈⠀⠤⣀⠁⠄⠀⠉⠁⠀⠀⠀⠀⠠⠈⡀⠈⠛⠀⣀⡀⢠⡁
⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠤⠀⠀⠀⠀⢀⠀⠀⠴⠖⠚⠉⠀⠘⠁
⠀⠀⠘⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡤⠂⡰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⡞⠻⢣⣴⡃⠀⠀⠀⠀⠀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢿⣤⠛⠀⠀⠈⠀⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠂⠄⠀⠘⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠖⠐⠀⠓⠀⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣆⠀⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠇⠀⠓⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠀⠀⠀⠀⠀⠁⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠒
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢄⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠀⠀⠀⠦⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡽⠶⠀⠀⠀⠀⠀⠀⠀⠰⢦⠐⠾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣸⣦⠄⠀⠀⠀⠀⠠⠀⡶⠧⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⢠⠀⠁⣸
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠺⣦⡄⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⢰⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⣀⣴⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠒⣷⠀⠀⠀⢰⣿⡄⠀⠀⢠⣏⢳⣄⠘⠀⠀⠀⠀⠀⢀⣀⣴⠋⡄⠀⢰⠀⠀⠀⢿⣇⠉⢀⣤
⠀⠀⠀⢀⡀⡠⠗⠀⠀⠀⢭⠀⢹⠀⠀⠀⢸⣏⡧⠀⠀⠈⢻⣿⣯⠈⠀⠀⡀⢤⠘⢋⡘⢃⢹⡇⠀⢸⠀⠀⠀⣈⡿⠆⠀⢧⠖⣆⠀⣀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢩⢕⣸⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢻⣆⢠⠀⠠⡛⢎⠀⢯⣀⠘⡄⠇⠀⢸⠀⠀⢀⣿⠄⠀⢀⣶⠞⠛⠛⠃⢰⠃⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣒⠾⠀⠀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠙⢺⠀⠀⠀⠉⠀⠘⠁⠆⠀⠀⠀⢸⠀⠀⠉⠙⠚⠂⠈⠀⣀⠀⣠⣤⣤⣬⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⡶⠏⠀⠉


⣶⡶⠶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠑

⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⣹⠟⠲⣄⠀⠉⠠⠀⠀⢠⢄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣷⠜⠋⠘⠠⠘⠳⢅⣢⢝⣦⣸⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠀⢂⣲⣞⣁⡤⠀⠀⠀⠀⠀⠈⢳⣌⣷⣿⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡿⢡⠞⠁⠀⠀⠀⠉⠀⠚⠙⠉⠀⠀⠉⢿⡙⢷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡽⣿⣿⠄⠀⠀⠁⣤⢤⠀⠀⠶⠈⠛⠀⠀⠀⠈⠛⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠟⢘⡛⣿⡀⣀⠀⠀⠈⠲⡀⠆⠀⠀⢀⣄⢀⡀⠀⠰⢿⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣀⢸⡗⠈⠉⠃⠁⠠⠟⠂⠀⠉⠐⠁⠈⢀⠠⣻⡞⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢣⡄⠀⡔⠀⠆⠈⠣⡄⠐⣀⠀⣤⡤⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠙⣧⠀⠀⠀⠀⠀⠀⢀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠻⠦⠀⠀⣤⣼⠛⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢦⠀⠰⠎⣀⠉⠁⠀⠀⠀⠀⢀⡄⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⣦⠀⢈⡀⣠⡀⢠⡄⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⢤⣖⠀⣤⡄⢐⣚⡥⠬⢯⣉⠉⠑⢾⣧⡴⣦⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡦⠂⠀⠠⠈⣙⣿⠋⠰⠛⢿⡿⠃⠀⡙⠲⠤⡀⠈⠷⢫⣉⡀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⠀⢐⣿⢿⣿⣧⠤⢀⢀⡀⢴⣁⡤⠄⠋⠡⢤⣃⠈⠻⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⠋⠀⠀⠈⢉⡀⠀⠀⠀⠉⠁⠀⠀⢉⣳⣆⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠄⠠⠄⠞⠻⡏⠦⠀⠛⠛⠆⠠⠈⠈⡩⢿⠟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢛⠀⣠⣤⡀⠀⢀⠀⢀⣀⠤⠀⣀⡀⠺⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡇⠚⣿⠛⠋⠀⠀⠉⠉⠁⠀⠀⠀⠈⣡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⡞⠋⢠⡀⠀⠀⡀⢹⢯⣟⠔⠚⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠈⠁⣠⠏⢀⠴⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣤⠿⢤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣦⡀⡀⠻⣘⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⣐⠀⠀⠚⠛⣮⣀⠈⡚⠁⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⣰⠏⢽⣻⠂⡤⠋⠹⠂⢰⡕⢮⣙⠡⢀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠙⠾⠛⣴⣤
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⡴⣠⠖⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⢠
⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⣀⠉⠅⢁⢀⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠘⠐
⠀⠀⠀⡀⠒⠀⠀⠀⡴⠞⠃⠀⠀⡈⡛⡅⠻⠄⠀⠀⠀⣀⠔⠀⠠⡀⠀⢀⣠⢶⡷⡟⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠃⠀⠀⠀⠀⠳⠀⠀⠀⠀⢻⣿⡁⠘⠣⣄⠀⠒⠁⠀⠀⡠⠒⠉⠋⠙⡗⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡟⠙⢄⡃⠀⠈⠏⢀⡀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠠⠤⠾⠇⠀⠀⠉⠳⣦⡀⠈⠑⠣⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡔⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠇⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⠒⣂⠠⡀⠀⠉⠂⠰⠁⠀⠀⢀⠀⢊⠠⠀⢀⠄⠳⢄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢏⠀⠀⠂⣈⢾⣆⠐⠀⠀⢧⠀⠀⡀⠀⡀⠐⠰⠀⠠⣔⢀⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠋⠀⠀⠜⠲⢔⣄⠀⢤⣾⣖⣀⣤⡾⠋⠹⣄⠀⠈⠙⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⡲⠄⢸⠀⠀⠈⠙⠻⣬⠠⠼⡧⠋⠀⠀⢸⣇⠱⣶⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⡀⠓⣦⣤⣤⢄⣸⠀⢸⣟⣥⣤⣤⣪⣷⣞⡐⠁⠀⠐⡂⠀⠉⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠫⠁⠃⠀⠉⠙⠙⣆⣽⣿⠛⠉⠁⠄⠘⡕⠨⠀⠀⠀⠁⠡⢀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⡂⠀⠀⠀⡀⠛⢣⢳⢩⢆⠐⠀⠂⠘⡆⠰⠀⠀⠀⠈⠀⠀⠑⢄⢀⠅⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢧⢤⡤⢀⠠⠁⠸⡼⠀⠣⢑⢄⣐⡊⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡅⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢎⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⢻⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠁⠀⠀⠀⠘⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠈⠀⠀⠀⠀⠀⡭⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢆⠠⠘⠀⢈⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠑⢂⠀⡆⢰⠀⡄⢠⠆⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡁⠀⠀⠂⠀⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠌⢂⣰⡶⠗⠓⠺⣷⣡⠤⠢⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠠⠀⠀⡈⣠⠠⠀⠀⢢⢠⠉⠁⠀⠀⠀⠘⠶⠤⠒⢣⠐⠀⢀⡔⠈⢉⡎⠃⠀⠀⠀⠀⠘⡉⠀⠀⠐⠀⡃⡀⡀⣰⢯⠀⠀⠀⠀⡅
⠀⠀⠀⢈⣄⢀⠀⠄⢈⡀⠀⣣⣰⣮⠉⠁⠀⠀⠀⠀⠀⢹⡿⠒⣀⡠⢹⠥⢸⡶⢫⡧⠀⠀⠄⠀⠂⠁⡀⠄⠀⠀⠀⠢⠤⣉⠃⣸⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠉⢔⣷⠬⣬⠖⣻⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⣿⣟⣀⢴⠾⠋⠉⠁⠀⠀⠀⠒⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠈⠁⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣌⡉⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡈⠲⠞⣁⠉⢢⣄⠠⠀⢀⠀⢰⣦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡸⠛⠁⠀⠀⠀⠀⠉⢳⡔⠨⡿⣬⣟⣠⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣴⣠⠀⡤⠋⠄⠤⠃⡄⠀⣀⢀⡀⠀⠙⠦⡝⢧⣉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⣷⣿⡃⠎⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⣦⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡶⣹⣿⡗⠀⠀⠀⠐⢆⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣃⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠀⡏⠸⣇⠀⣀⣀⠀⠀⠑⠈⠁⠀⣀⠀⠆⢀⠀⠀⣐⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡽⠟⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢰⣂⠀⠒⠀⠀⠀⠣⠀⠠⠄⠀⠴⠖⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠹⣆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡘⠻⠄⠀⠀⢶⣌⠉⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢆⠀⠲⠣⣀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣤⠀⣄⡀⣤⠀⠀⡀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡂⢀⡤⠀⢀⣻⠠⠘⢪⡁⠉⠐⢾⣥⡴⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⠐⠀⠀⠀⢈⣹⡞⠁⠘⠻⢿⠓⠁⠀⠙⠲⠤⠀⠈⠷⠿⣈⠀⠰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠂⠀⣸⡟⢿⡟⠀⠀⠀⠀⠀⢪⣤⡤⠀⠈⠠⢤⡃⠈⠻⣦⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠟⠁⠀⠀⠈⠛⠀⠀⠀⠘⠉⠀⠀⠀⠉⣳⣄⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣀⠠⡄⠠⠆⢽⠃⡤⠐⠻⠶⠤⠤⠄⠃⣩⢿⡿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠃⠀⣤⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠾⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢿⡾⠟⠁⠀⠀⠉⠀⠈⠁⠀⠀⠉⢁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠜⠃⣀⠀⠀⠀⠐⣰⡔⢲⡀⠔⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡀⠹⠊⢐⠆⠁⡤⠺⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣸⡏⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡉⠀⠁⠆⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠉⠨⢿⡦⡄⠀⠚⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠀⠀⢸⠥⣶⡆⠀⠀⠿⢦⡀⢀⢀⡘⠷⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠟⠋⠈⠁⠀⠀⠀⠈⠒⣹⣖⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠒⠀⠰⠟⠰⠋⠸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠙⠀⠀⣠⣴⠀⠈⠀⢢⡼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡟⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢴⠀⠀⠀⠀⢬⠉⠁⠀⠀⢠⣤⡜⠀⣅⠀⠀⠀⡠⠀⠀⠀⠀⡤⠤⡴⢾⣹⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡿⡇⢀⠁⠐⠤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣌⠀⠘⠠⣅⠀⠘⠀⠤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠦⣄⠚⠋⠉⠀⠀⠀⠈⠙⢣⠄⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀
⠀⢀⣤⣶⣦⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢦⠈⠀⠂⢀⠔
⠀⣾⣿⣾⣿⡧⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⢹⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢱⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣤⣻⣄⠈⢯⢾⣎⠇
⠘⣯⡽⣞⠿⣶⡸⡀⠀⢀⡴⠀⠀⠀⠀⢰⣿⣿⡁⠇⠀⢀⡼⠁⠀⠀⠰⠀⢠⠀⠀⡆⠀⢠⠞⠀⠀⠀⠀⣰⣿⡟⢿⡇⠀⠀⠈⠉⢡
⠀⠱⣿⡽⣞⡱⣧⣇⣠⠎⠀⠀⠀⠀⠀⣸⣿⣾⣯⡘⣠⠞⠀⠀⠀⠀⠀⠐⠺⡇⠀⢹⡶⠋⠀⠀⠀⠀⣰⣍⢻⢻⣐⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠹⣿⣯⣷⣷⢼⠁⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⡃⢻⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢧⠀⠀⠀⠀⠀⣯⣭⣛⡛⢠⡀⡮⠀⠀⠀⠀⢡
⠀⠀⠀⠘⢿⣿⣿⡼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⣦⣴⡉⡱⠷⣻⠇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠙⠿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⠿⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠠⠄
⠀⠀⢀⣀⠀⠀⠀⠁⠐⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠠⠘⠃⠀⠈⠀⠁⠀⠀⢄⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠀⠃⠀⠨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⡐⠐⠄⠀⢀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠊⠀⠀⠀⠀⠀⢈⠈⡃⠀⠀⠀⠀⠁⠀⠙⢷⠀⠅⠅
⠀⠀⠸⠄⠁⢁⠠⠀⠀⠂⠀⠀⠀⠉⠀⢐⢣⠶⠄⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⢓⢚⢚⡛⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠴⠀⠦⠀⠀⠀⠀⠀⠘⠠⠀⠄⠈⠒⠊⠠⠐⢀⡀⠀⠇⠀⠐⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠐⠀⠠⠄⠀⠄
⠀⠊⠉⠀⠀⠀⠀⠀⠄⠀⢀⡀⠒⠀⠢⠄⠀⠠⠀⠁⠂⢀⡀⠀⠀⠀⠀⠈⠀⠀⠧⠼⢛⠈⠁⠀⢉⠀⠦
⠀⠂⠠⠂⠀⠀⠀⠀⠀⢀⠀⠁⠀⠃⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠀⠶⠀⢐⠦⠠⠒⠁⠐⠂⢀⡑⠁⠈⠂⠀⣄

⠀⢀⠆⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠆⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡇⠐
⠀⠈⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠄⠀⠇
⠠⠐⡐⠠⡀⠀⠀⠀⠈⠈⠁⠁⠆⠀⠀⠀⠀⠉⠐⠚⠉⠂⠀⢀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠠
⠀⠀⡁⠠⠀⠀⠀⠀⠀⠀⠐⠰⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠊⠀⠐⠂⠈⠘⠀⠐⠀⠀⠂⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⠁

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢂⢐⠞⠂⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⡀⢈⡄⡀⠀⢀⠀⠀⠀⠀⠀⣊⣀⢀⠀⠠
⠀⠘⠓⠀⠀⠈⢐⣁⠀⠀⠀⠀⠀⠀⣲⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣦⡾⡉⡹⡓⠒⠁⠀⠀⢠⠆⠈⣹⠟⠷⡄⠊
⠀⠰⢹⡄⠀⠀⠀⠉⡧⠀⠀⠀⠐⠀⢣⢺⠃⡏⠀⠀⠀⠀⠀⠀⠚⠁⢠⣾⢋⡔⠘⠐⠊⠀⢠⡀⡘⠁⣠⡀⣠⠡
⠀⠀⠹⢄⠀⣀⠀⠄⠁⠀⠀⠀⠀⠠⠊⢹⠡⠁⠀⠀⠀⠀⠀⠊⠁⠀⠚⠕⠂⣸⠀⠀⠀⠠⠚⠀⠁⢀⡈⠀⡤
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠠⠀⡤⡼⠀⠈⠈⠄⠀⠒⠁⠀⠀⠀⠐⠀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⢈⣉⠑⢨⡚⠠⠄⢐⠀⠀⠀⠀⢸⠀⠠⡀⠀⠀⣡⢜⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⢀⣈
⠀⠀⡔⠉⠇⠀⡡⠝⡠⡍⠁⠑⠀⠀⠀⢸⠀⠀⠁⠀⠀⢦⠈⠆⠑⠌⠀⠀⠀⠀⠠⠀⠀⠀⠤⡚⠈⢀⣤⡀⢀⢠⠄
⠀⠘⠀⠀⠀⠤⠔⣾⠸⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠠⠶⡦⠤⠀⠀⡀⠀⠉⠰⢸⠀⣈⣭⣀⢀
⠀⠀⠀⠀⠀⠠⠔⠁⢀⠀⠀⠀⣰⠀⢰⡴⢻⡆⠪⡁⢠⣞⡹⢠⡎⠀⢸⠇⠰⣉⠂⠀⠁⠄⢰⣾⣛⣭⠾⠯⡲⡀
⠀⠀⠀⠀⠀⠂⠀⠰⠁⠀⠀⡄⢿⡠⢺⠀⢸⡠⢄⣸⠾⢧⡤⠚⢧⡤⠾⠤⢄⣨⡇⠀⠀⠀⠁⡇⠡⢶⣺⠁⠇
⠀⠀⠀⠀⠀⠀⢀⠰⣀⠀⠰⠀⠀⠀⢀⠀⡇⡀⢀⢀⢀⠀⡀⡇⢸⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡉⠁
⠀⠀⠈⠂⢀⡲⠊⠌⢶⠈⠀⠈⠀⠀⠸⠄⠇⠃⠘⠹⠰⠛⠆⠧⠸⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢶⣀⠊
⠀⠁⠀⠉⠀⠁⠂⠀⠼⡁⠂⠒⠀⠈⢠⢤⠤⡤⢀⠀⢀⠀⠀⠀⢀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠐⠀⢽⣿⡅
⠀⡀⠄⠂⠁⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⠒⢩⣥⣄⣩⠇⠀⠁⠞⢦⠼⠧⣄⣤⠤⢄⡀⠀⠀⠀⢀⢚⣘⡶⡀
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠠⣎⣠⠀⠑⡌⠉⠆⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠁⡠⠃⢰⣶⡺⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⢁⣆⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⣴⣆⣠⠂⠀⠀⠀⠀⢠⢼⡖⣄⣈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⡤⠀⡏⠊⠀⠀⠀⣠⡄⠀⠀⠀⠈⣋⠉⠉⡇⢀⡀⠀⠄⣀⣀⣧⠙⢦⣌⣀⡐⣁⠀⠠
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠁⠀⠘⢢⣀⡯⠂⠀⠀⠈⠰⢼⠀⠠⡎⠁⠀⠀⠀⠀⠀⠸⠇⠴⠉⠁⠙⠈⠂
⠀⠀⠐⠦⠄⡀⠀⡀⠑⢢⡀⠀⠀⠀⠀⡐⡻⣿⡅⠐⠀⠀⠀⠂⢂⠀⠀⠙⡤⠀⡀⠀⠀⠀⠠⠤⠤⢠⣧
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠢⣉⠄⠀⠤⠀⠸⡴⠋⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⡀⠸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈

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

⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠐⠀⠠⢀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄
⠀⠐⠐⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠗⠀⢠⠇
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢦
⠀⠀⠀⠁⠀⠄⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠁⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡎⢱⠀⠀⢀⣠⡄⠀⣀⡠⢀⡀⣀⠀⠀⢀⠀⠀⣀⣀⡀⠘⡂
⠀⠀⠀⢲⠀⠘⠀⠀⠈⠀⠀⠌⠀⠀⠀⠈⣠⠼⢁⣀⡇⠀⠕⠀⣄⢸⠠⢁⡀⢟⠀⠈⡇⠀⠀⠦⠀⠃⠁
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠀⣀⣈⢀⣁⣀⣈⣀⣁⣀⣀⣈⢀⣉⣁⣀⡇⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠈⠉⠈⠉⠉⠉⠈⠉⠉⢉⠉⠉⠉⠁⠀⠀⡀⠃⠈⠀⠘⠀⠈⠈
⠀⠐⠀⠀⠀⠠⠀⠀⠀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠰⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠄⠡⠤⠤⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠄⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠙⠿⣯⠛⢿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⠁⠀⠀⠴⠒⠒⠀⠀⠀⠀⠀⠀⠰⠒⠍⠛⢻⠏
⠀⢸⠿⠿⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⡇⠀⠀⠈⠓⢤⡀⠸⠁⠹⠂⠀⠀⢀⠀⠀⠾⠉⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠱⣄⡀⠀⠀⠀⠙⢦⡤⠤⠤⠤⠤⠤⠧⠤⠤⠤⡤⠒⣻⠀⠀⠀⠀⢀⣤⡀⠈⢿⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠈⢷⣄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠙⠻⠧⠀⠀⠀⣾⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠻⡑⢤⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⠰⠿⢶⡦⠀⠀⠀⡼⠁⠠⠤⡌⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠈⣱⠬⣶⣤⣀⣀⣀⣀⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢀⣀⠀⠉⠀⠀⠈⠀⠀⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⡠⠴⣅⠈⠉⠉⠉⠉⠉⢹⡭⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠠⠶⢄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡴⠋⠉⠉⠳⡍⠑⠒⠒⠒⠊⣽⠟⠒⢾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠐⠂⠀⠀⠀⢀⣤⠀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⠀⠀⠀⠀⠀⢹⠀⣀⠤⠤⠴⡟⠀⠀⢠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢰⡟⠦⢍⡓⢤⡀⠀⠘⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃
⠀⠀⡆⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⢹⠀⠀⢰⠀⠘⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠂⡀⠻⣑⠢⣍⡿⠁⠀⠀⠀⠀⠀⠀⣰⠿⠛⠻⢿⣿⣿⡇
⠀⠀⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣠⠎⠀⠀⢸⡤⠴⡇⢀⡔⠉⠀⠀⢾⣀⠀⠀⠀⠀⠈⠢⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿
⠀⠀⢧⣠⠠⠤⠴⠋⠰⣄⢀⣰⣿⠃⠀⠀⠀⢸⠀⠀⠙⠉⣇⠀⠀⠀⠀⠀⠈⡝⢀⠔⠊⠉⠣⣍⠒⠦⠄⣀⣀⣀⣀⣀⣀⣤⣄⣀⣤⣾⡿⠁
⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠏⠘⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡳⠦⠤⠤⠤⠞⡰⠃⠀⠀⠀⠀⠀⢉⡽⠶⢽⡿⣿⣿⣿⣿⣿⣿⣿⡷⠋
⠀⠀⢸⠀⢦⡀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⡗⠤⠴⠒⠁⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣿⣿⣿⣿⣿⣏⠉⠉
⠀⠀⠸⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣤⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢧⠄⢀⣀⣀⣀⣀⣀⢠⣤⠤⠤⠔⠒⠈⣳⡴⠚⠉⢁⣠⣽⡆⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⣠⠞⠁⢀⣴⠞⠋⠁⠀⠹⣄⣀⣀⡠⠴⠒⠉⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡁⢀⣴⠟⠁⠀⠀⠀⣤⠶⠛⠀⠙⡄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⡏
⠀⠀⠀⢻⣀⠈⠛⠳⣄⠀⠀⣴⣶⣶⡒⢣⡙⣾⠁⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⣡⣀⡠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⠀⠀⠀⠀⠀⠉⠉⠛⠛⡇⠀⠻⣿⣿⣿⣶⠚⢏⠳⢤⡀⣀⣴⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡇⠀⠀⠈⢿⣿⣿⣷⣤⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣴⠚⢉⣡⡴⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢷⣀⣸⠁⠀⢱⡖⠒⠒⠒⠘⠻⣍⣻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⣹⠀⠣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⡀⣀⠈⣾⣺⠀⡴⠃⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠀⠀⠀⠎⠀⢀⠆⠀⠄⠐⠒⠚⢳⡀⢀⠠⠄⠤
⠀⠀⢯⠾⣨⠌⠀⠁⢀⠀⠀⠀⠀⡀⠀⠁⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⢀⠠⠀⡀⠀⠀⡣⠦⡐⢀⠂
⠀⠀⠀⠁⠉⣠⠄⠈⠣⠟⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠆⡥⠀⠌⠠⠜⠋⠀⢐⠜⣠⡀
⠀⠀⠶⠀⠉⠀⠀⠄⡄⡄⠀⠀⡀⠀⡀⢠⡦⣔⠀⠀⠴⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠂⠁⠚⠒⠀⠈⣶⠓⡤
⠀⠀⠀⠐⠀⠀⠀⣶⣼⡗⠀⠀⠀⠈⠀⡁⠒⠁⣠⠀⠀⠀⠀⠀⣀⢤⣄⠻⠏⠀⡴⠆⡀⠑⠒⠰⣖⢄⠀⠀⡄
⠀⠀⠠⢉⠀⠀⠀⠉⡋⠁⠀⠀⠀⠀⢈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠈⠠⠘⢓⠂⣁⡄⠀⣀⡀⠀⠀⠐
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⢂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠖⣤⡁⠀⠀⠉
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠈⠈⠁⠀⠠⠄
⠀⠰⢆⠀⣀⠀⠀⢀⣠⠀⢀⠀⠀⣀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠂⠀⠀⠀⠐⢀⠀⡡⠄⠀⠅⠀⠐⠀⡜⣦⡀
⠀⠘⠐⢀⣿⣷⣿⠿⣷⠀⠘⢳⡤⠜⠤⠀⠀⠁⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⢱⣊
⠀⠀⠀⠀⠉⠓⠒⠋⠉⠄⠀⢄⠀⣠⢄⣀⡀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠁⠻⡊
⠀⠀⢠⠴⡀⠀⠀⠁⠨⠂⢀⡦⠀⡁⠘⠒⠁⠋⡇⠀⠁⠀⠀⠊⠀⢠⠊⠙⢦⠀⢀⢀⠀⠀⠄⠐⠛⣋⢐⠀⢾⣕
⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠁⠐⠉⠓⠒⠒⠎⠀⠀⠐⠒⠄⠀⠀⠸⠆⣤⠟⢀⣜⣹⣖⠀⠀⠁⠘⠃⣀⠔⠠⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿