Swinging Emojis & Symbols

⠀⠀⠀⠀⣀⣄⡆
⠀⠀⢀⠚⣫⠘⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡐⠠⡀⢀⠀⠀⠀⠀⠀⣰
⠀⣨⠱⡭⠀⠀⢀⣨⠤⠴⣿⣟⣁⣀⣀⢐⠐⢲⡶⠒⠒⠂⠄⠀⠒⠀⠂⠱⠦⠀⠢⠀⠀⠀⠤⠀⠉⠀⢀⡔⠁
⠑⢿⠻⡑⠈⠉⠉⠀⠀⠀⣯⡇⠀⠀⠉⠉⢉⣿⠗⠲⠤⣤⡐⢀⣀⡄⠀⠀⠀⠀⠀⠠⣄⠀⡀⠀⢠⠖⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠘⡟⢠⣀⣀⠶⠋⠁⠈⠉⠓⠒⢄⡀⠀⠀⠘⢂⡁⢠⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⢚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠛⢒⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⡀⠀⠀⠰⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡊⠉⠀⠠⡅⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠀⠈⠈⢂⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⣀⠀⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣆⠀⢀⠀⠰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠿⠠⠶⢾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠍⠀⢀⡀⢘⣩⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠸⣀⠐⠛⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠒⠛⠢⡷⠗⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⢀⡀⠂⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⢀⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⠀⠀⢀⣀⣀⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⢀⡐⡀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⡔⢀⠇⠀⠊⠱⡶⠔⠲⠕⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⠀⠤⡄⠐⠮⠄⡀⠂⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒⣫⠷⠸⣏⠍⢦
⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢼⢣⡆⢤⣄⣰⣴⣿⠺⣜⢦
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠐⡟⠘⡟⠀⠲⠀⠐⣷⡀⠙⣦⠑⡄
⠀⠀⠀⠀⠀⠀⠷⠠⣄⠀⠀⠀⠹⣖⣹⡦⣀⣒⣦⣻⠒⢶⣏⢳⡜
⠀⠀⠀⠀⠀⠀⠣⡀⢹⡀⠀⢀⠔⢖⠾⡓⠢⢼⡧⡍⠊⣄⡿⠊⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⣦⣳⠿⣦⣆⣽⠫⢃⢌⢀⠄⢹⠀⠀⡠⠜⠓⣿⣉⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⣀⣸⠧⠋⠄⢀⢁⢀⣠⣼⠴⠗⠒⢲⠢⠛⠐⢄⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⣯⡓⢇⣐⣦⡶⡋⢈⠒⠀⠈⡗⠾⢀⡀⠀⠈⢦⠀⠳⡄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣓⣊⠿⢍⣘⢂⣀⣬⠤⠟⠺⠉⢳⡀⠀⠀⡱⢄⠙⠢⣀⣤⡚⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡏⡽⡞⣏⡇⠀⠀⣀⣤⠶⠛⠙⢦⣎⡰⠉⠳⣤⢜⢫⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡑⡼⣝⣤⠶⠛⠉⠀⠀⠀⠀⠀⠈⠛⢦⡀⢌⣇⣾⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⠄

⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⢠⢶⣄
⠀⠀⠀⠀⠀⠸⢦⠘⢟⠒⠳⠴⣇⣀⢀⡠⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠉⢹⠒⠦⣌⡏⣼⠓⠧⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡏⠀⠀⠀⠹⡸⣖⡶⠤⢄⣉⠑⠒⠦⠤⢀⣀⢖⣓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⠭⢽⠇⠀⠀⠀⠉⠑⠒⠢⠤⢼⡘⣏⠚⠳⠴⡋⢣⣀⠀⢠⠎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⢽⠙⠒⠳⡄⠹⣍⣙⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡭⡝⠀⠀⠀⠘⡆⠀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡇⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢼⣺⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⣼⡏⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⡇⠀⢰⡿⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⡇⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⣿⣇⡠⠔⢻⣷⠒⠤⣀⠀⠀⠀⠀⠀⣾⣭⣿⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⢴⣿⠁⠀⠀⠀⠉⠀⠀⠀⠉⠒⠤⣀⠀⣏⡿⣸⡀⠀⠀⠀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣗⠜⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⠧⣷⢧⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⡇⠈⠐⠭⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠀⠘⣮⡗⢤⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢍⡑⠢⢄⡀⠀⠀⠀⡿⡇⠀⠀⡠⢚⠝⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢌⣑⠢⢌⡛⣁⠔⡩⠐⠁⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⠵⠊⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠃

⣿⣿⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⣿
⣿⣿⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⣿
⣿⡟⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢻
⣿⡇⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢸
⣿⡇⠀⡇⠀⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠀⢸⠀⢸
⣿⡇⠀⣿⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⣿⠀⢸
⣿⡇⢸⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⣿⡇⠸
⣿⠀⢸⣿⠀⢸⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢿⣿⣿⣿⣿⣿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⡏⠀⣿⡇
⣿⠀⢸⣿⠀⢸⣿⡇⠈⠙⢶⠄⠀⠀⠀⠶⠋⠁⠀⣾⣿⣿⣿⣿⣿⡄⠈⠛⢶⠀⠀⠄⢠⡴⠛⠁⢡⣿⡇⠀⣿⡇
⣿⠀⢸⣿⠀⢸⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡇⠀⣿⡇
⣿⠀⣾⣿⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⣿⣿
⡏⠀⣿⣿⠀⢸⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠸⢏⣾⣿⣿⣿⣿⣿⣿⣿⡹⠃⠀⠀⠀⠀⠀⠀⠻⢣⣿⣿⡇⠀⣿⣿
⡇⠀⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠠⠄⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿
⡇⠀⣿⣿⡆⢸⣿⣿⣿⠀⠀⠀⣸⣷⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣷⠀⠀⠀⣿⣿⣿⡇⢠⣿⣿
⡇⢀⣿⣿⣷⣾⣿⣿⠏⠀⠀⠀⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄
⠃⢸⣿⣿⣿⣿⣿⣿⣉⠛⠓⣲⣿⣿⣇⠲⠒⢃⣻⣿⣿⣿⣿⣿⣿⣿⣿⡐⠒⠚⣸⣿⠐⠒⠒⢸⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠴⢺⡶⠦⣀⣿⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠃⠀⠈⢹⡄⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⢿⠏⠠⠎⠀⣸⠇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢐⡿⣿⢸⣧⡀⠀⠀⢀⣀⠘⡄⠀⠀⠀⠀⠈⡵
⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⡜⠁⡇⠀⠀⡈⠉⡰⠁⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⢀⠔⡖⠀⠹⡍⠑⠒⣒⡺⣍⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⢀⡤⠤⠶⢮⣥⣶⠁⢰⡲⠃⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⢠⡟⠈⢣
⡰⠋⠀⠀⠀⢈⣿⣟⣋⠉⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⣴⣇⣸⡶⠂
⠑⠤⠤⠔⠚⠋⠉⠉⢯⠀⢹⡀⠀⠀⠀⠀⠀⠀⢿⡤⠾⠈⢻⠟⠉⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣃⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠊⠀⣀⣟⡤⠖⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢷⠀⢀⡀⠀⠀⠐⠸⡶⠞⣁⣤⣞⡿⠭⠐⠒⢄⠀⠀⠀⠈⠑⠢⢤⡀
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠙⣦⣶⣟⣛⡹⢉⣽⡽⢿⠧⡺⠋⠁⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠠⠆⠑⠲⠶⢤⣤⣀⣀⣀⣀⣀⣠⣤
⠀⠀⣠⢞⠕⠒⠂⠉⠓⣦⣽⠞⡏⠁⣖⡭⢥⣀⣀⣠⠇⠀⠀⠀⠀⣠⢮⡀⠀⠀⠀⠈⠳⣖⠶⠾⠤⢤⣀⡀⠀⠀⠀⠙⣉⣩⠝⠋⡩
⢀⣜⣥⣖⠂⠀⠀⢠⠔⠋⠀⢀⡿⢚⠅⠈⠀⠀⠀⠈⠉⠉⠒⠒⠺⠥⢤⣿⣷⣄⠀⢀⠞⠉⠑⠦⣀⡀⠀⢹⠈⣀⡴⡺⠋⣇⠴⠊
⠈⠁⠀⠉⠻⡄⠘⠀⡔⣠⠔⡩⠀⢶⣦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣤⣀⡀⠀⠀⠉⠙⢯⠉⢉⠔⢁⠜
⠀⠀⠀⠀⠀⠹⡘⠀⠘⢧⣊⣀⠀⠀⠈⠈⠉⠘⠛⠛⠰⠲⠦⣤⣤⣤⣀⣀⣄⢀⡴⠋⠀⠀⠉⠑⢦⡀⡐⠁⡴⢋⠔⠋
⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠈⣉⣽⡶⠖⠒⠦⠤⠤⣀⣀⣀⠀⠀⠉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣀⠈⢁⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣐⢦⡄⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣏⣈⣿⡮⠟⢹⣷⣮⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣸⢫⢡⣾⡿⠋⠁⠠⠄⢰⣿⣿⠃
⠀⠀⠀⠀⠀⢠⣾⣇⣿⣿⢁⣾⡆⠀⠀⠀⢹⣿⡉
⠀⠀⠀⠰⢶⣿⣿⡿⠀⣼⠘⠏⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠘⢻⣿⣷⣼⣶⠃⠀⠀⢠⣼⡏
⠀⠀⠀⢠⣴⣿⣿⠛⢿⠁⠘⠃⠀⠀⠀⠀⣄
⠀⠀⠀⠋⠀⠋⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⢙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠰⣾⠋⣀⣾⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡑⠦⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⡅⠠⠀⠀⣺⣿⡏⠀⠙⢷⡀⠀⠀⠀⡀⠀⢀⠜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣻⣦⣶⢿⣾⡿⠇⠀⠀⠀⠙⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠗⢂⠜⢣⣾⢻⡿⠆⠄⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⡀⠂⠀⢘⣿⡎⣿⠀⠀⠀⣀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡾⣡⠄⠀⠀⠈⠑⢿⠀⣦⡸⢿⣍
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⣀⢀⣴⣶⣤⣀⣀⣀⠈⠑⢂⣭⣿⡀
⠀⠀⠀⠀⠀⠀⠔⣹⡷⠊⢹⣿⣿⡿⠛⠻⢿⣿⡄⠀⣈⣿⣽⠃
⠀⠀⠀⠀⡠⠂⣠⠿⠃⠬⡄⣼⣿⠇⠀⠀⠀⠀⠻⠀⠈⢹⣭⡴⠶
⠀⡀⡤⠘⠁⠀⠀⠀⠀⠀⠀⠨⣈⣷⣤⣀⢀⠀⢀⡄⠀⠀⠃
⣷⣤⣀⡤⠀⠀⠀⠀⠀⠀⠘⠓⢦⡽⡿⠿⠿⢏⢻⣿
⠀⠉⠛⢷⣤⡄⠀⢀⣀⣴⡶⠟⠛⠁⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠈⠿⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡿⣂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣠⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢿⠉⢳⣄⣀⡀⣰⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⣏⡉⠛⠲⠾⣤⣄⡀⣠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⠉⢹⡶⠶⢤⣈⣹⡃⡾⠳⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⣸⠁⠀⠀⠈⠹⣇⢷⣤⣄⣀⠉⠙⠓⠶⠤⣄⣀⡀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⡹⣼⡷⣏⠈⠉⠓⠲⠤⣤⣀⣀⠉⠉⠒⢲⡏⣴⣦⣸⡆⠀⢀⣤⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠈⣗⡒⣚⠇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⣇⠹⣄⣉⠙⠓⢻⡀⠙⣦⣀⡀⢠⠟⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣹⣼⠋⠓⠒⠿⡄⠈⢧⣉⡙⠓⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⢸⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⣺⠀⠀⠀⠀⠙⢦⡀⠉⢩⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⠀⢸⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢸⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡀⠀⠀⠀⢀⣞⡾⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⣧⣭⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⡇⠀⠀⠀⢰⣿⠉⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⡇⠀⠀⠀⠀⠀⢸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⠀⣿⡟⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⠀⢸⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⠀⠀⣸⢻⠁⠀⠀⣹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠞⣧⠀⠀⠀⠀⠀⢸⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⠀⢀⡯⣿⠴⠒⠉⠀⢷⣧⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⢺⣿⣿⢽⠃⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣤⢼⢷⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⣼⢰⢿⡸⡆⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡟⢤⡹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⣸⣄⣧⢻⡀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠓⠢⢝⡲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠹⡎⢧⣀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠀⠀⠀⠈⠳⢤⣉⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠀⠀⠀⠹⠟⢈⠵⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡉⠑⠦⣄⡀⠀⠀⠀⠀⡟⣾⠀⠀⠀⣠⠔⣡⠞⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣉⠒⠤⣄⡘⠿⠇⣀⠴⢋⡠⠊⠀⠀⠀⢸⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣉⠓⡞⣡⠔⠉⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠼⠇

⠀⠀⠀⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠡⣠⡆⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛⢀⡄⠈⠰
⠀⠈⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢙⡾⠗⠀⠉
⠀⠒⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠄
⠀⠀⠀⠁⢀⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠈⠀⣀
⠀⠀⠀⣄⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⢀⡤⠀⢀⣧⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⡃⠀⠀⠀⢠⡀⠀⠀⠀⠘⡟⠀⠀⠸⠃⠀⣺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⠀⠀⢠⣸⢧⠀⢀⠀⠀⣠⣦⠀⢀⣼⠇⣁⣀⣠⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠻⣿⣧⣀⣠⡾⠀⠛⠻⢷⣾⣿⡿⠛⠻⢿⣿⣿⡿⠟⠋⠤⢀⡀⠐⣶⣯⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣤⠀⠀⠀⣠⠽⠛⠀⢀⡀⠀⣿⣿⡶⠞⣃⣤⠀⠩⡷⠾⣷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡄⠉⠻⠿⢷⡿⠁⠀⠀⢠⣤⣧⣼⡿⠋⠀⣷⡙⠿⣶⣾⣧⣴⡾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠋⣀⢀⡠⣆⣴⣤⣿⠟⣯⣭⣥⣄⢶⠋⠹⡄⠀⠈⠻⡿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠋⢡⡀⠘⢻⠇⠉⠉⠀⢀⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠘⠁⠀⠀⠀⠀⠀⠀⡿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⠦⣄⣀⠀⣰⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡋⡞⣱⣾⣿⣿⣟⡝⠋⠈⡍⠂⠺⠛⢋⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠏⠀⠐⢀⣿⣿⣿⠧⢀⡠⠘⠀⠀⠀⠀⠘⠟⠋⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣩⠷⠂⠈⡐⠉⢹⣿⢿⠀⠀⠀⢀⣠⡀⣠⣶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣟⢃⢊⠊⣰⣷⣼⣷⣿⡷⣤⡐⣿⢛⣭⣟⣻⣷⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣃⣪⠏⠰⣿⣻⣽⣻⣧⡇⢟⣖⣣⣂⢶⣾⣿⣿⣟⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⣟⣛⣭⣉⡍⣾⣷⢈⡽⡽⠻⠋⢻⡾⡷⢷⣞⠈⠙⠿⣿⣿⢿⣿⣛⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⡿⠽⠌⢷⣿⢷⠿⠝⠡⠉⢣⣿⣿⡛⡛⠃⠀⠀⠀⢸⡥⣘⡏⠁⠈⠠
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣝⡓⠤⡀⠀⠈⠛⠛⠴⣙⣈⣿⣿⡷⠟⠀⠀⠀⠀⠀⠀⠁⠻⠋⠀⠀⠀⠑
⠀⠀⠀⠀⢀⣾⣻⢿⢛⢻⢿⣷⣦⣄⣀⠀⠀⠀⢀⡈⠉⠉⠁⢻⣿⣯⠑⢶⣦⣤⣀⣀⣀⣈⠁⣄⣄
⠀⠀⠀⠀⢨⣟⡏⣼⢆⣎⢏⢋⣎⡟⣽⢿⣷⠶⣦⣔⠆⠀⠠⣦⣽⠏⢘⠖⠋⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠶⢶⠠⢤⢤⣤⡀
⠀⠀⠀⠀⠸⣛⠋⢿⣶⣦⣬⡼⢭⢽⠎⣶⣿⣿⡿⠏⠛⠒⠿⠿⣃⣴⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣤⠶⢶⣶⣤⣀⠀⠀⠛⠉⠀⠁⠘⠂
⠀⠀⠀⠀⢸⣿⣿⣿⠯⣹⡉⢳⣮⣿⣿⡞⣯⠛⣸⣆⠀⠀⠀⢀⣴⣶⡧⠈⠉⠉⠉⣉⣉⠉⣹⡿⠙⢬⣶⣌⠛⢿⠙⣽⣶⣶⣖⠶⠒⢦⣶⣀
⠀⠀⠀⠀⢸⣿⣟⠀⢊⠜⢻⣿⢋⢿⣿⣄⡠⢁⣾⣿⠀⢀⣴⠟⣿⣿⣿⡿⠃⢀⠤⠀⢴⣿⣿⠑⠘⣿⣧⣯⠀⣼⣿⣭⣿⣿⣿⣿⣔⣀⣰⣶⣬⣤⣀
⠀⠀⠀⢠⣿⣿⣿⡏⠁⠀⠀⠸⢿⣿⡏⠙⡔⠸⣿⣿⡄⣾⣯⣭⣽⣯⣿⣽⣭⣿⣿⣿⣿⣿⣿⣦⣘⢷⠿⠟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⢾⡿⣻⡿⠃⠀⠁⠀⢴⣿⣿⣷⠀⡤⠰⡯⣹⡗⠈⠟⣯⢽⢿⠛⠛⠋⠙⠛⠛⠋⠉⠉⠛⠻⠶⠚⠛⠙⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠈⠀⠉⠋⠀⠀⠀⠀⠋⠉⠉⠋⠘⠁⠀⠁⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢰⡾⢶⣦⠀⠀⣀⣤⣄⡀⠀⣀⣤⣴⡶⠿⠛⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⢿⣷⢶⣦⣤⣤⣾⠏⠀⣿⣷⡿⠻⠋⠙⣿⡾⠟⠉⠀⠀⣀⣤⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢠⠎⠀⣼⠇⠀⡿⠋⢹⠋⠀⢠⡿⠁⢠⠀⠀⢰⠏⠀⠀⣠⣴⠿⠟⠛⠛⢉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⣿⣆⣸⠏⠀⠘⠁⠀⠀⠀⢠⡞⠀⢀⠃⠀⢀⡎⠀⠀⡜⠉⣠⠤⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣤⣈⡉⠙⣟⠀⠀⣰⡇⠀⢀⣴⡟⢀⣴⣿⠀⠀⣼⡇⠀⢸⣿⠟⠁⠀⢀⣼⠟
⠀⠀⠀⠀⣰⡿⠋⠀⢠⣿⡟⠁⠀⣿⣆⣰⣿⣷⣴⣿⣿⣿⠿⠿⠿⠷⢦⣿⣷⣤⣈⣀⣀⣠⣴⠿⠋
⠀⠀⠀⢠⣿⠁⠀⢠⣿⠏⠀⠀⣼⣿⣿⡿⠟⠛⠉⠀⠀⢀⣀⣀⣀⣤⣤⣤⣽⡿⠛⠛⠛⠉⠁
⠀⠀⠀⠈⣿⡄⠀⠟⠁⠀⢀⣼⡿⠛⠁⠀⢀⣠⣴⡶⠿⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠘⢿⣦⣀⣀⣴⡟⠁⠀⢀⣠⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⢷⣦⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⣀⣤⣰⣿⣷⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢟⣿⣿⡇⠀⣼⣿⡀⠀⣠⣤⠀⣴⣿⣿⡏⠀⣠⣾⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⠿⠋⠁⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⣼⣿⡿⠁⣼⣿⣿⢀⣾⣿⣇⣼⣿⣿⣿⢁⣾⣿⡿⢡⣿⣿⣿⡏⣼⣿⣿⣿⠟⣁⣤⣶⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠘⠿⠃⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⢷⣿⣿⣿⡟⢸⣿⣿⣷⢣⣾⣿⠟⢛⣽⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣶⣶⣦⡄⢸⣿⣿⣿⡟⢸⣿⣿⣿⣿⠟⠁⣿⣿⠟⠁⢸⣿⣿⣿⠁⣿⣿⣿⡏⠀⠉⣡⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⠀⠀⢉⣼⣿⣿⠘⣿⣿⡿⠀⠀⣿⣿⠟⠁⠀⠀⠛⠃⠀⠀⠘⠿⣿⡇⠀⢹⣿⣿⣧⣤⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⣠⣿⣿⣿⡏⠀⠘⠛⠁⠀⠀⠈⠁⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠉⠙⠛⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⢿⣿⣿⠃⢀⣼⣿⣿⣿⠟⠀⠀⣀⣤⣾⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣴⣿⣿⣿⡿⠋⢀⣤⣾⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠀⣴⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢉⣉⣉⣉⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢻⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⡏⠀⠀⡸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠘⡆⠀⠀⠇⡇⠀⠀⠀⠀⠀⡇⠀⢀⠃⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⢃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⢻⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡘⢀⠇⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⢸⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⠀⡇⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⡸⠀⡇⠈⡇⠀⢸⡇⠀⠀⠀⠀⠀⡧⣴⠄⡼⠀⠀⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢷⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀⡿⣿⠀⡇⠀⠀⠸⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⢸⠀⢹⠀⢸⢄⠀⠀⠀⠀⣀⡇⡇⢠⠁⠀⠀⠀⡇⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠘⡄⠸⣖⠿⠎⠓⠒⠒⠋⠓⠛⠮⣺⡀⠀⠀⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⡇⠀⡦⠤⣀⡐⠀⢀⣀⡀⢤⠀⡤⠃⠀⠀⠀⠘⡄⢸
⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⢳⠀⡇⠀⠀⠈⠉⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠇⠈⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠘⠂⠀⠀⠀⠀⠀⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠛⠀⣀⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣷⣶⣶⣿⣿⣷⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠉⠋⠉⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠱⠦⡵⠀⢘⠋⡙⠀⠀⠁⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠉⠁⠀⢀⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡤⠀⠀⠀⣠⡞⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣧⣀⣀⣠⡴⠞⠁⠟⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⡈⠃⠈⢿⢿⠛⢿⠛⠁⠀⠀⠀⠀⠀⠸⠙⠲⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡿⠀⠀⠒⠀⣴⠊⠀⠀⠀⢶⡄⠀⢠⠇⠀⠀⠈⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠾⠁⠀⠘⠃⠀⠀⠇⡀⠏⣀⡄⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⡄⠀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡰⠀⠄⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣭⣑⠾⣯⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠈⠀⠀⠛⠻⢷⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⡆⠀⠀⠀⠁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⣤⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢈⠂⢀⡀⠢⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⣼⠃⠀⠀⠁⢠⠁⠄⣉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠓⠤⠿⠀⠄⠈⢀⡁⠀⠀⢹⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠸⡄⠀⢈⣥⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣁⣄⠁⠀⠀⣀⠀⠀⣀⣀⣀⣀⣀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⣠⣖⣫⣍⣠⣤⣶⣶⣦⣿⣿⣿⣽⡷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠾⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢾⣷⠷⠶⠶⠞⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⡈⠛⢶⣤⣀⣻⣿⣿⣏⣀⣠⣤⠾⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⣠⣤
⠀⠀⠀⣀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣆⠀⠈⠛⣿⣿⣿⠛⠋⠉⠀⠀⠀⠸⠀⣀⣀⡀⠀⠀⠀⢶⣀⣀⠀⠸⠿⣿⣿⡧⢀⣴⠞⠉
⠀⠀⠀⠙⠳⢦⣬⣿⣿⣟⣁⠀⠀⠀⠈⣻⣿⣟⠁⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣤⣴⡶⠀⠀⠀⠀⠀⣨⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⣾⣿⣿⣿⡏⢿⣷⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⡁⢠⣿⣿⣿⣿⡇⠀⠛⠀⣼⣿⠉⢿⣿⠀⠀⠀⠀⠀⣿⢟⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠛⢿⣿⢿⣿⠟⠗
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⣿⡇⠻⣿⠀⢹⣿⡇⠀⠀⠀⣿⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⠿⣿⡆⠀⠀⠀⠀⠀⢸⣿⠈⣿
⠀⠀⠀⠀⠀⢼⣿⣿⠀⢰⣿⠃⠀⠀⠀⠈⣿⠁⠀⠀⠀⣿⣿⡅⣿⣿⡆⠀⠀⠀⠀⠀⠙⠃⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠈⣿⠀⣿⠂
⠀⠀⠀⠀⠀⠈⣛⣟⠀⢘⣿⠃⠀⠀⠀⢘⣻⠆⠀⠀⠀⠀⠀⠀⣻⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣻
⠀⠀⠀⠀⠀⠸⢿⣿⠀⠈⡿⠀⠀⣀⠀⢀⣯⠀⠀⠀⠀⢘⣶⡂⣿⣿⠃⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⡼⠀⣸
⠀⠀⠀⠀⠀⠀⠈⢿⣇⣰⣿⠁⠸⣧⣤⣼⣾⡃⠀⠀⠀⢻⣟⠀⣹⣿⠀⠀⠀⠀⠀⢤⡉⢴⡿⣿⡿⠗⠀⠀⠀⠀⠀⣀⢰⣷⣀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣼⡀⠀⠻⣿⣿⣿⣇⣴⠏⠀⠨⣻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠿⣾⡿⣍⡁⣀⡀⠀⠀⠀⠀⠈⢿⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠠⠶⣠⣿⣟⠛⠋⠀⠀⠉⣪⣿⣟⠁⠀⠀⠈⣵⣿⣟⠇⠀⠀⠀⠀⠀⠀⢴⣾⣿⣧⠀⠉⠉⠀⠀⠀⢀⣀⣰⣿⣿⣯⡀
⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⡗⠀⠀⠀⠘⠿⠿⡿⠁⢀⣀⣤⢽⣿⣟⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠈⠉⠈⠠⣬⣿⣯⣅⠉⠓⠦⢀
⠀⠀⠀⠀⠀⠈⠙⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⢠⣶⣿⢟⢧⡀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⢛⣻⣯⣽⠿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⣿⣻⣱⣿⡿⠉⣠⣶⣟⣿⣿⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢸⣇⣿⣿⣿⢋⣰⢱⣿⣿⣟⣮⣿⡿⣿⣷⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⢿⣿⣿⣧⣿⣿⣾⣿⣿⣋⣀⣠⣼⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣳⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣟⠿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣯⣄⣀⠈⠙⠛⠋⢀⣠⣴⣄⠀⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⠋⠉⠙⠇⠀⠀⢀⠊⣡⣤⣌⢣⣹⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣵⣿⣿⣷⣤⡿⢥⣿⣾⣿⣿⣿⡆⢿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠉⠙⠻⠿⠟⠟⣀⢈⣻⠿⠿⠿⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⣹⣿⣿⣿⡄⣸⣿⡇⠻⣶⡶⣾⡋⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠉⠉⠉⢭⣿⣿⣹⣿⣮⡍⠉⠛⢓⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠟⠋⠉⠛⠿⠷⠶⠖⠋⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⠻⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⡿⢉⣴⣦⠄⠀⠀⠀⠉⢽⣶⣅⠀⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣸⡇⠈⠙⠛⠀⠀⠀⠀⠀⠘⠛⠁⠀⣿⣯⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⡿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣶⣿⣿⡿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠟⢷⡀⠙⢿⡿⠿⡿⠋⠉⠉⢙⢟⠟⠻⢿⣹⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠓⢠⠂⠀⠀⠑⠪⠭⠽⠛⠋⠀⠀⠀⠹⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠂⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢠⣦⣄⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢈⠏⠓⠒⠂⠤⠤⠤⠤⠔⠒⠒⠚⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢶⠦⢴⣦⣤⣤⡤⠶⢶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⠀⠀⣿⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⢀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡂⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠀⠈⠛⠛⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣼⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠉⠉⠉⠉⠉⢙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡋⠉⠉⠉⠉⠉⣿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢻⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡟⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢸⣿⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣿⡇⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡿⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢸⣿⡀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⢠⣿⡇⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⣿⡇⠀⠀⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⠀⠀⢸⣿⠁⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠒⠂⠤⢤⡴⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠹⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣅⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠖⢮⡀⠈⠙⠲⢄⠀⠀⠀⢀⠔⠁⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠞⠀⠀⡻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⡄⠒⠳⡤⣀⣀⡀⠀⠀⠀⣀⡀⠀⣀⡠⢶⠀⠀⠱⠴⠚⢣⠀⠀⠀⢑⡤⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⣀⠽⠦⡀⠀⠀⠀⠀⠀⡾
⠀⠀⣠⠞⠁⠀⢸⠤⠄⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⡎⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠛⠻⠛⠓⠒⠒⠋⠁⢉⡉⠀⠀⠀⡏⠳⣌⠀⠀⢀⠇
⠀⠀⢹⠋⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠇⠈⠳⣄⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡇⠀⠈⢣⣀⠞⢄
⠀⠀⠓⠤⠲⢖⢽⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢄⣀⣤⣆⣠⠎⠀⠀⠀⠈⢧⠀⢰⡀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⠤⠶⢹⡏⠀⠀⠱⡄
⠀⠀⠀⠀⠘⠋⠀⠳⣄⠀⠑⠒⠚⠀⠀⠀⠀⠀⠀⠀⣀⡥⠊⡸⠀⠀⠀⠀⢀⣬⠆⠀⠑⢄⡀⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⡠⡖⠁⠘⣄⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣢⣄⣀⣀⣀⣀⣠⣤⠔⠚⠑⠢⢄⡧⢿⠀⢀⣦⡸⠀⠀⠀⠀⣀⠬⢵⣦⣤⠤⢤⣤⠔⣲⠮⢥⡒⠓⢄⠀⠙⠦⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⣿⠉⠈⢁⡤⣇⡙⢖⠒⠒⠮⣷⣠⡷⠋⠀⠀⠀⠀⠀⢠⠃⠀⠐⡇⠉⠉⠋⠀⠀⣏⠀⠀⠙⢍⠙⣗⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣰⠏⠀⢠⠮⠀⠈⢱⠀⠑⢦⡀⠈⠻⡁⠀⠀⠀⠀⠀⠀⢸⡀⠀⣴⠃⠀⠀⠀⠀⠀⠻⣄⣀⣀⢼⠀⡏⢡⠜⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠋⠁⠀⠀⢸⠀⠀⠀⠀⠣⡀⠀⠱⡀⠠⠹⡀⠀⠀⠀⠀⠀⠀⢇⢻⡝⠀⠀⠀⠀⠀⠀⢄⠙⠻⡄⠀⡆⠹⢀⣰⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡟⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⣴⠗⡐⠄⢡⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠇⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⡹⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢼⣀⣀⠀⠀⠀⠀⢀⡠⠊⠀⠀⡜⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢥⣀⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠍⠉⠉⠙⢰⣢⢀⡴⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡶⠤⠤⠤⣤⠤⢤⠲⠿⣜⡢⠜⢁⠦⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢆⣠⠤⢄⡀⠀⠈⡷⢫⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⡟⠀⣸⠀⢐⠂⠈⠑⢭⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢹⡤⠊⠀⡴⠡⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡉⠢⣄⡀⢀⡼⢧⡔⢁⡴⠻⡀⠀⠀⠀⢳⠤⠔⠃⠐⠤⣤⣤⣄⡤⡞⢄⠀⠀⠀⡎⠱⣖⡋⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⠖⠉⢇⠀⠈⣳⠆⠀⠹⠉⠀⠙⣧⣀⡠⠃⠀⠀⠀⢠⠂⠀⠀⠀⡜⠁⠀⠀⠀⠉⠢⠉⠒⡺⠀⠉⢙⠀⠰⠀⠀⠀⠀⡾⠀⢀⡀
⠀⠀⠀⠠⠀⡏⠀⠀⠀⠉⠈⠁⠀⠀⢸⠀⠀⠀⢳⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢫⠀⠀⠀⠀⢀⡞⠁⠈⡀⠙⠢
⠀⠀⡂⠀⠀⠹⣄⠀⢀⠀⡀⠀⠀⣠⠇⠀⠀⠀⠀⠙⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠑⠦⠤⠴⠋⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠠⢀⠀⠈⠙⠈⠁⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠉⠁

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

⡎⠁⢢⣄⡀⢀⣀⣀⠲⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⡀⠀⠀⢀⠄⠰
⠷⡲⠾⠟⢷⣦⡿⠯⠖⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢈⣿⣿⣾⣿⣿⣃⣈
⠀⠀⠀⠀⡘⣿⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⡇⠀⠈⠉
⠀⠀⠀⠀⠇⢸⠈⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡽⠁⢿⡇
⠀⠀⠀⠀⠁⢸⡇⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠛⠁⠀⠁⣇
⠀⠀⠀⢠⠀⢠⡇⠀⠈⢊⢦⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣱⠏⠀⠀⠀⡁⣿
⠀⠀⠀⠚⢰⢈⣿⠀⠀⠀⠈⠳⡀⢌⠳⣄⡀⢀⠀⠂⡠⢤⣤⠀⣀⣀⠀⠀⠀⠀⠀⠠⢊⠀⡠⠃⠀⠀⠀⠀⠇⣿
⠀⠀⠀⡆⢸⢲⡞⠀⠀⠀⠀⠀⠙⢦⡠⣬⣍⠸⢀⢶⣄⣠⣏⡾⢱⣎⣡⡤⣴⣻⠵⣣⡏⠀⠁⠀⠀⠀⢀⣠⣤⣿⡄
⠀⠀⠀⣤⢾⡞⡇⠁⠀⠀⠀⠀⠀⠀⠙⢾⣿⣣⣉⠂⣿⣅⡾⢿⣝⣋⣽⡛⠹⣷⠾⠃⠀⠀⠀⠀⠀⠀⠘⢯⡿⣽⡇
⠀⠀⠀⠈⠞⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⡼⣾⠿⣫⠿⡮⡔⢰⣉⠟⠣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⣿⣶⣍⡛⢿⣦⣈⢀⠓⠄⠠⢀⠀⢄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡍⢻⣿⡀⠀⢈⠀⠀⠀⠑
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠋⠀⠀⠀⠈⠆⠠⠈⠂⡈⠑⠂⠄⠀⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠘⣿⣿⠿⣿⣿⣿⠆⠀⠀⠀⣀⡤⠴⠶⠒⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠑⠤
⠀⠀⠀⠀⠀⠹⣿⡞⠉⠻⢿⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠸⣷⣀⠰⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠹⢦⠀⠀⠀⢁⠀⡀⢁⠀⠂⠄⠬⠤
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⡆⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠆⠀⢳⠀⠀⠀⢢⢆⢸⠀⠀⠀⢀⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠈⠒⢄⡀⠀⠀⠀⠀⠈⠃⢐⡁⠀⠀⢃⠀⠀⠀⠙⣼⠀⠀⠀⡜⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠈⠀⠒⠂⠠⠤⠤⠚⣿⣆⠀⠀⠀⠀⠂⠀⠙⡄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠹⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠑⠈⠲
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⣁⠈⠙⣷⣦⠀⠀⠀⠀⠁⠂⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⣠⠖⡀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⢉⠉⠻⠭⣅⠂⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢀⡾⠃⠀⠀⠈⢀⠀⠊
⠀⠀⠀⠀⠀⠀⢡⠐⠀⠁⠀⠀⠀⠈⠓⢄⠠⠙⠿⣷⣦⣀⠀⠀⠀⠀⠈⠻⣧⡀⠈⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠁⡀⠙⢦⡁⠠⠙⣿⣿⣶⣄⡀⠀⢀⠸⢷⣆⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠟⣿⣷⣽⡳⢄⡀⠀⠻⣦⡀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠀⠋⢀⠀⠀⠀⠀⠈⠑⢦⡈⠙⠿⣿⣄⡉⠓⠢⣝⣷⣄⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠄⠐⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡙⠛⣿⣦⠀⠀⠀⠹⣷⠀⠺⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⢀⡴⢿⡇⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⡏⣠⡶⠋⠀⣾⠃⠀⢀⣴⠿⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⣿⡿⠋⠀⢀⣼⣷⣤⠶⠋⢁⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⡞⠁⠀⢠⡿⠋⠀⢀⣴⠟⢁⡿⠁⣠⡶⠛⠉⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣱⡿⠋⠀⢀⣴⣿⠁⣀⠴⠋⠁⣠⡾⠓⠋⠁⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⠋⠀⢀⡴⠛⢡⡿⠚⠁⢀⣠⠾⢿⠀⠀⣀⣴⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠠⠊⠀⣠⠾⠋⠀⣠⣾⡧⠔⠊⠉⠀⣠⡿⠖⠛⠉⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣏⢀⡴⠛⠁⢀⡴⠞⠉⣼⠃⠀⢀⣠⠾⠋⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡠⠋⣸⡋⢀⡤⠞⠉⠀⣠⣾⡥⠴⠞⣏⣁⣠⣴⡶⠿⠿⠛⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⣠⠞⣡⡟⠉⢀⣠⡴⠞⢋⡝⠀⢀⡼⠉⠉⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢩⢷⣊⠄⢈⠴⣳⠞⠋⠁⢀⡴⠟⠒⢚⡿⠤⠤⠴⠶⠶⠿⢻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡴⠃⢺⡁⠀⠔⣪⡏⠤⠴⠚⢛⣷⣠⣴⠿⣁⣀⣀⣠⣤⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠟⡦⠐⣡⠁⢐⣩⣯⣤⣤⠤⢶⡟⣉⡼⢃⠀⠀⠀⠀⠀⠉⢉⣹⡏
⠀⠀⠀⠀⠀⠀⢀⡞⣼⠃⣺⠀⠄⡎⠀⣐⠶⠤⢤⣶⠚⠉⢛⣿⠳⠦⣬⣉⣛⡓⠒⢛⣻⠏
⠀⠀⠀⠀⠀⠀⡾⢸⠃⠐⣂⠠⡬⠥⢭⣋⡱⢖⣋⡉⣙⣾⠛⢣⣄⡀⠀⠈⠉⠛⠿⣿⡅
⠀⠀⠀⠀⠀⠀⣷⠸⡆⠬⣗⣺⡿⢟⠫⡑⠬⣶⣬⡽⠋⢀⣹⡟⠈⠙⢷⣶⣤⣤⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠙⠷⣯⣶⠾⣕⣬⠦⢵⠾⣟⠻⣤⣈⣷⡞⠉⠻⣶⣤⣄⣹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⡷⢬⡉⢦⣦⣳⣬⣷⠾⠛⡅⠙⢦⣀⠈⢳⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⡄⢹⡋⠹⣇⠀⠘⣆⠀⠹⣦⣈⠻⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢦⣳⣄⠹⣧⣀⠹⣦⠀⢻⡟⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠟⠷⣬⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠐⠁⠔⠊⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡑⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⢁⠤⠀⠀⠈⠉⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠦⠀⡀⣀⠀⠀⠀⠀⠀⡀⠋⠀⣠⠕⠁⢀⠠⠐⣀⠄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠀⡆⠁⠒⢄⣀⠨⠃⠀⠈⢀⣀⠊⠀⠀⠀⠀⠸⠀⠀⢐⣧⡞⠉⠐⣀⠥⠐⠊⠁⠠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⡀⢁⢁⠀⠀⠈⠁⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⢠⠀⠀⡠⠂⠊⠃⠀⠀⠡⠄⠀⠀⠀⣠⡁⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢐⠀⠢⠀⠀⠀⢿⡆⠀⠀⡀⠻⠃⠀⠂⠀⠀⠀⠀⡜⠀⡀⠀⠂⠈⠀⢸⣷⠀⠀⠀⠹⠃⠀⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠩⠂⠀⡀⠀⠀⠀⠀⠀⢇⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⢀⣣⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⢄⠀⠀⠀⠀⠁⠤⠚⠀⠀⠜⠀⠀⠀⠀⠀⠘⡜⣄⣴⠖⡀⠀⠀⠀⠀⠈⠒⠀⠀⡠⢋⠏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⢀⣀⡠⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣷⠤⠀⠐⡦⠀⢠⡤⠄⠒⠉⠅⢨⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢃⢱⢰⡯⢛⡒⠚⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠘⠀⠀⠀⠄⠀⠡⠰⣄⢆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⡳⡜⠞⠚⠉⠉⠁⠀⠐⠒⠓⠀⠐⠀⠒⠀⠀⠀⠀⠌⠉⠠⠅⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠢⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⡒⠬⠝
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠐⡖⠶⠤⠤⠄⠤⠤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠀⠀⢰⠄⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠠⡶⠀⡘⠋⢠⡄⠐⠶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⠁⣶⠄⠈⠋⢀⣄⠀⠰⠇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⢠⣄⠀⠿⠀⣈⠁⢰⣦⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠠⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀⠂⠀⠀⠀⠀⡆⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡨⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠦⢤⣀⡃⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠀⡀⠀⠀⠀⠀⠀⠀⠠⠥⠒⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣀⣑⣈⡆⠀⠀⠀⠀⠨⣠⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠐⠤⢌⣈⡀⠀⠀⠀⠀⠀⠐⠄⠆⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⣤⣤⣤⣴⡖⡀⢙⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠙⠻⣿⣿⣹⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⣀⣈⣙⠿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠉⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠹⣿⣿⣶⣦⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢠⣄⡀⠀⠀⠀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡴⠖⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣶⡆⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⠀⣾⢃⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠁⠀⠀⡖⣸⡿⠀⣠⣤⡀⠀⠻⠀⠃⠈⠁⠀⢠⡀⠀⠠⡌
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸⡏⠀⢻⡔⠆⠀⡴⠆⠀⠀⠈⣠⡶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⢸⡇⠀⣠⡾⢛⣷⠀⣰⡟⠀⣰⣿⠘
⠀⠀⠀⠀⠀⠃⠀⢻⣇⠀⠠⡄⠀⠀⣿⡀⠀⣰⣆⠀⠈⠛⣿⠷⣿⡟⢀⣾⠇⢠⣿⢁⡼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢻⡇⢀⡿⣿⠀⠀⠀⣿⠀⣿⣠⠏⣿⢠⡟⢿⠞⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⣄⠀⢸⣿⣸⠃⣿⡄⠀⢰⡏⠀⣻⡧⠀⠙⠋⢀⣠⣴⣾⣿⡿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠈⣿⣿⠀⢿⡇⠀⣼⠃⠀⠀⠐⠀⣠⣶⡿⠛⠉⣹⣿⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⢻⡟⠀⢸⣷⢠⡿⠀⠠⠀⢀⣾⡟⠉⠀⠀⠀⣿⡏⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠈⣿⡄⠀⠀⠀⠈⣿⣼⠇⠀⠀⢠⣿⠋⠀⢠⡄⠀⢸⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣇⡄⠀⠀⠀⠙⠋⠀⠀⢀⣿⣳⠂⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣴⡿⠸⠃⠀⢠⡶⡀⠀⠀⠀⢸⡏⠟⠀⠀⠀⠀⣼⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠟⢡⣿⠘⠃⠀⢺⡇⠀⠀⠀⢀⣼⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⣿⣄⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣿⠏⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣸⣿⣏⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣻⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠛⣛⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢟⣩⠤⡒⠉⠀⢀⣀⣄⣠⣄⡒⢛⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⡿⠿⠿⢿⠿⢿⣿⣿⡿⠀⠀⠈⣩⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣤⣮⢻⣿⡷⣲⣴⡿⢋⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⢪⣿⣿⣿⣿⡾⣫⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⡿⣦⣴⣶⡿⢋⣼⣫⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣄⣀⣀⡀⠀⠈⠛⢻⣟⣾⣿⣿⣷⣾⣿⣿⣯⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣿⣷⠀⣙⣿⣿⡿⣷⣾⣿⢷⣦⠺⣶⣤⣛⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣅⣥⣀⣙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣈⡉⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⢏⢻⡟⠟⠀⠙⠻⢿⣿⣿⣿⢄⠀⣸⣷⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠟⣻⣿⣿⢡⡆⠀⠀⠄⣀⣬⣽⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⡥⣄⣽⣿⣷⣶⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣿⣿⣿⣿⣻⢿⣿⣿⡟⠏⢧⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⠟⣽⣿⣟⠉⡈⣉⣍⣼⣷⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⡿⣽⣿⣿⣿⣿⣿⣿⢿⣅⣸⣿⣿⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⣿⣿⡟⣻⣿⡏⣿⣿⣿⣿⣼⣿⣿⡾⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣣⣯⣾⣿⣿⠿⣿⡟⠋⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠛⠋⠉⠀⠀⠈⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⠛⠉⢻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠨⢿⣿⡷⠶⣛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⣶⡇⠀⠀⠀⠀⠀⠈⠉⠙⢧⣿⡖⠒⠒⠒⠒⠒⠒⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⠟⠁⠀⠀⢸⡅⠧⢄⡀⠀⠀⠀⣀⣀⡈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡜⠁⠀⠀⠀⢠⢰⣿⢀⣀⡁⠄⠀⣬⣁⡄⠀⢿⣛⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠀⠀⠀⠀⠀⡘⠆⢻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⣄⣀⠀⠳⣴⣿⣧⠀⢀⣀⣙⣀⠀⠀⢀⣾⣿⣿⠿⠒⠚⣓⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⠓⠦⠤⣀⡀⠀⠛⠛⠦⢌⡙⠛⢉⠠⠐⠚⢋⣉⠤⠔⠒⠋⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⡆⠀⠀⠀⠈⠉⠓⠒⠤⢄⣤⠤⣤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⡄⣰⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⡇⢀⣠⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣴⡟⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣩⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠻⣿⡫⣹⣿⣻⠣⡙⣄⠀⠀⠀⠀⠀⠀⠀⣛⠉⠙⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⡿⢻⢯⠻⣚⢎⢶⣾⡇⠃⢉⠒⢌⠀⠀⠀⠀⠀⠀⠀⢃⠀⣤⠀⠀⠋⣂⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣽⣽⣿⣷⣷⡑⡑⡡⡓⡄⣹⠇⠐⢌⡛⠨⣆⠀⠀⠀⠀⠀⠀⢸⠀⠈⡶⢜⢲⡸⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠙⠝⠟⠙⢶⡏⠋⢋⠻⠿⠶⢲⠏⠀⣙⣢⣁⣑⠖⢦⣤⣀⣀⠀⠀⢠⣤⠀⣳⣤⠠⠙⠃⢀⣠⣴⣶⠟⢫⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣤⣿⣶⣮⣮⣻⣬⣿⣶⣴⣴⣼⣄⣾⣿⣿⣿⣿⣷⣒⣀⣩⣯⣙⣛⡶⠶⣶⡭⣭⡄⠀⣸⢋⣷⣿⡿⣠⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢠⠶⠖⠒⠢⢄⡀⠀⠀⠀⠀⣀⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣙⣛⣟⣛⣛⣻⣭⣿⣶⣯⠀⣿⠀⠀⡷⢟⣭⣵⣀⣿⣿⡿⠿⣁⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣶⣶⣿⠿⠟⢋⣉⣭⣿⣿⣿⣿⡏⠻⣻⣽⣯⣯⣯⣭⣏⢪⣩⣹⣿⣾⣷⡀⣠⠟⢿⣿⣿⣽⣿⡿⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣋⣩⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡻⣿⡻⣿⡟⢿⠷⠶⠶⠶⠿⡿⣿⣿⣷⣿⣿⣀⣠⣮⣉⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⣘⠓⠒⠚⠻⠛⠋⢩⣿⣿⣿⣿⣿⣿⣿⣿⡿⡙⢯⢿⡌⢷⡜⣿⣆⠀⢢⡈⠀⢀⢒⡌⢂⠀⠱⢠⡝⠿⠹⣿⠿⡿⣤⣀⡀
⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⡜⠀⠀⠀⠈⢉⣻⣿⡿⠿⠿⢿⠧⣤⠈⢟⠽⣎⢻⣎⢿⣥⡡⡻⣆⠠⡢⠹⣦⠱⡀⠀⠚⡄⢀⣬⣧⡑⡈⡹⣿⣧
⠀⠀⠀⣠⠞⠁⠀⢀⣴⢋⣠⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⢸⡃⡙⣿⢄⢢⢿⣷⡙⡷⡻⣖⡙⢌⢧⡑⡔⠜⢅⢐⣷⣤⡙⣦⣿⣏⣻⣌⠈⢍⣻⡆
⠀⠀⢸⡇⠀⠀⢠⣿⠗⠛⠁⠀⠉⠙⠛⠒⠒⠦⠤⢄⣀⠈⠳⣆⢾⣷⣱⣣⡹⣻⣜⢿⣜⢮⡈⠢⠳⡈⠊⢀⣿⣯⠊⢱⣾⣗⠀⢅⣹⡤⠋⠈⣿⡀
⠀⠀⠘⠁⠀⠀⢸⣿⠀⢰⣾⣶⣶⣶⣿⣾⣶⣶⣴⣤⡀⡀⠀⠈⡷⢫⡻⣿⣷⣵⡹⣿⣛⢎⢻⣦⡑⠀⣦⣿⠋⠑⡁⣿⣿⠂⢠⣾⠏⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠸⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣧⢳⠀⠀⣷⡐⡕⡼⣮⣿⣿⣎⠻⡞⡣⠉⡙⣶⡟⠁⠀⠀⣸⣿⠇⢀⡿⣿⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢤⣤⣤⣤⣤⣤⣥⣤⣍⣉⠉⠀⠀⢸⡎⣎⠂⠈⠙⠻⣿⡢⠛⠈⢀⡼⠋⠀⠀⢀⢐⣿⢏⣴⠟⠁⠸⡆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢺⣷⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠘⣿⣣⣾⠁⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢼⠗⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣸⠝⠋⠸⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠻

⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿
⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿
⠛⠋⠀⠘⠛⠁⠀⠛⠋⠀⠈⠛⠁⠀⠙⠋⠀⠈⠛⠁⠀⠙⠋⠀⠈⠛⠁⠀⠙⠛⠀⠈⠛⠃⠀⠙⠛⠀⠈⠛⠃⠀⠙


⠀⠀⠀⠀⠀⢀⣴⡾⠂⣰⣶⠃⢀⣾⡗⠀⣶⡶⠀⢰⣿⠂⠐⣷⡆⠀⢶⣶⠀⢺⣶⡀⠐⣷⣆⠐⢿⣦⡀
⠀⠀⠀⠀⣠⣾⠏⢀⣴⡿⠃⢀⣾⡟⠀⢰⣿⡇⠀⣼⣿⠀⠀⣿⣧⠀⢸⣿⡆⠀⢻⣷⡀⠘⢿⣦⡀⠹⣷⣄
⠀⠀⠀⣼⣿⠁⠀⣾⣿⠁⠀⣾⣿⠁⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠈⣿⣷⠀⠈⣿⣷⠀⠈⣿⣧
⠀⠀⠀⠘⠋⠀⠀⠙⠛⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠛⠋⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠤⡤⠄⡤⢀⡀⠀⠀⣀⡀
⠀⠀⠀⢸⣋⢳⢺⣭⡸⡦⡆⣧⢸⡇⠀⠂⠀⠀⠀⠂⠀⢮⠂⠀⠀⣦⠀⠀⠐⡀⢀⠂⠀⠠⠒⡁⡒⠀⡇⠀⠀⢀⡎⠑⢄⠓⠃
⠀⠀⠀⠈⣏⠘⡿⠦⠟⠃⠛⠉⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⢹⡐⢄⠀⠉⠉⠀⠀⠀⠈⠀⠀⡆⠈⠒⢂⠨⠀⠂⣀⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠁⠀⠀⠠⣄⠐⠶⠀⠢⡀⠁⠀⠤⢡⠜⠁⠉⠉⠘⠷⡉⢉⠂⢈⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⢌⠣⡀⢲⡒⢰⠀⠘⠀⡇⠀⠀⠀⠀⡀⢀⠕⠁⠲⠈⠓⠒⠳
⠀⠀⠀⢀⣠⠄⠀⢀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠁⡀⢀⠀⠀⠑⢻⣄⠃⠀⠀⠀⣤⣇⠀⡀⠔⡠⠒⢁⠄⢉⠔⠉⠀⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⠀⡀⠀⠀⠨⡉⡇⠀⡐⠀⠀⠑⢄⠀⠀⠉⢷⣄⠀⠀⠘⣎⠥⠖⡉⠀⠔⠋⠀⡏⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠰⠁⠀⠀⠈⠀⠁⠠⠅⠂⠀⡉⠀⠀⠒⠀⠀⠈⠳⠀⠀⠈⢎⡡⠀⠂⢄⠉⣀⢳⠀⡤⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠴⠀⠀⠀⠖⠀⠀⡀⠐⡀⠀⢀⢥⡈⠀⠀⠉⡉⠀⢀⠂⠀⠀⢠⢤⠀⢃⠀⠀⠀⠀⠀⠄⠹⠀⡉⢠
⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⠈⠀⢀⠀⠀⠁⠆⠀⡀⢀⠁⢠⠀⠀⠣⠈⠁⠀⠀⣧⣀⢀⠏⠐⢠⠀⠀⣈⡀
⠀⠀⠀⠀⣖⡦⠀⠾⠱⠂⡠⠙⡆⠀⠀⠄⠀⠃⡀⠀⠆⠁⠀⠔⠀⠀⢎⠀⢁⠀⠀⠄⠀⠒⠀⠠⡂⠀⠀⢒⣂⣨⡇⠀⠛⢧
⠀⠀⠀⠀⠀⠀⣠⢃⢎⠬⣁⡁⢃⠀⠀⠘⠀⠠⠊⠀⡤⠀⠂⠐⡄⠀⠀⣂⠠⠄⠰⠉⠢⠀⠀⠠⣉⣉⣉⣉⡀⢤⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡿⢛⠘⡃⠓⠸⣿⠀⠀⠀⡐⠠⠀⠐⠀⠀⠀⠀⠀⡔⠆⠡⠀⠂⢀⡀⠀⠀⠀⠀⣁⣀⣀⠠⠥⠰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡿⢇⠿⢸⠏⣶⡾⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠄⠐⠒⠀⠁⠀⠀⠀⣀⣀⣀⡀⠀⠐⠀⠠⠊⠠⡚⠂⠲⠀⡇
⠀⠀⠀⠀⠀⢸⣶⣒⡆⣱⢒⡤⡕⠀⠀⠀⣀⠈⠉⠀⣀⠀⠀⣤⠴⠶⣶⠚⢹⣏⣋⣉⣭⣥⠵⠗⠀⠀⠀⠀⠀⠐⠥⠄⠔⠀⡇
⠀⠀⠀⠀⠀⣸⣄⠤⡴⢀⢌⣙⡃⠀⠀⠀⠠⢅⠂⠤⣀⠀⠀⠓⠒⠚⠋⠉⠉⠉⠉⠀⣀⠀⠀⠀⠀⡀⠄⠈⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡗⢚⡒⣓⠓⠸⠤⡇⠀⠀⠀⠄⡄⠈⠐⣦⣤⠀⠠⠠⠄⢴⣠⡭⠄⠀⠥⠠⠀⠀⠌⠁⡠⠐⡀⠀⠀⠂⢄⠡
⠀⠀⠀⠀⢰⣏⡏⣹⢠⣊⣑⢲⠁⠀⣴⠀⠈⠨⠶⠁⠤⠤⠬⠂⠀⣊⡉⠉⠑⢤⢔⠕⠁⠀⢈⠀⠌⡐⠁⠔⠀⠠⡑⠄⢃⠈
⠀⠀⠀⠀⢡⢤⡔⣤⢤⠠⣉⣙⠀⠀⡏⠀⠀⠃⢿⡿⠛⣿⣿⠓⡒⣶⣶⠶⣶⡦⠁⠀⠀⠀⣀⠈⢀⠀⡁⠈⠀⡁⠁⣀
⠀⠀⠀⠠⠚⠐⠃⠓⠚⠠⠧⢼⠀⢸⡧⡾⠀⠀⣘⠿⠾⢻⠧⠂⠶⠹⣷⣤⣾⢇⠀⠈⠁⠀⢈⠀⣜⠀⠉⠈⠀⡇⠀⡃
⠀⠀⠀⢠⡊⠆⠊⠂⠊⠂⠊⡎⠀⠈⢠⠇⠀⠀⠀⠈⠉⢋⠰⠆⠶⢸⠒⠂⠀⠂⠀⣖⡆⠀⠙⠀⠉⠀⠛⡀⠈⠉⠀⢁⠀⠑
⠀⠀⠀⢸⠀⠁⠀⢠⠀⡞⠀⡇⠀⠀⠾⠀⠀⠀⠁⠠⠤⡀⠁⠉⠀⠀⣀⠀⠠⠂⠀⠀⠀⠀⠨⠀⡅⡀⠀⠀⠀⢨⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠂

⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⢿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣶⡆⠀⠀⠀⠀⠀⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠉⠁⠀⠀⠀⠀⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢾⣿⣴⣤⣴⣶⣦⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣼⣿⠁
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶
⣿⡇⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⣿⣧⣀⣀⣸⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣄⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣼⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣀⣀⣠
⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⣿⣿⣿⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⢹⣿⣿⡟⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡧⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⢐⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣴⣿⣟⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠩⠑⠀⠀⠀⠀⠀⠀⠀⡸⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⣀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢁⣀⣤⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢉⣀⣤⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠛⢋⣁⣤⣴⣶⣿⣿⠿⠿⠿⠛⠛⢋⣉⣁⣤⣤⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢛⣉⣤⣶⡾⠿⢛⣛⣩⣥⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣩⣶⣿⢟⣫⣵⡶⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⣠⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣏⣾⡿⣻⡷⠟⣋⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢿⣿⠟⣫⣶⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⡈⠻⣫⣵⣶⣶⣾⣷⣶⣶⣶⣤⣤⣤⣈⣉⣉⡉⠙⠛⠛⠛⠛⠛⢋⣡
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣷⡀⠻⣭⣶⣶⣦⣤⣉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣾⣿⣷⡀⠹⠿⡛⠻⠿⢿⣿⣶⣤⡈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⣿⣿⡇⠀⣿⣿⣿⣶⣤⣈⠙⠻⢿⣷⣦⣤⣀⣀⡉⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢰⣿⣿⣿⡇⠀⣭⣍⡙⠻⣿⣿⣷⣦⣄⡈⠙⠛⠛⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣿⣿⣿⣿⠇⠰⠿⣿⣿⣦⡈⠛⠿⢿⣿⣿⡿⠶⠒
⠀⠀⠀⠀⠀⠀⣰⡿⢡⣾⣿⣿⡿⠋⣠⣿⣶⣄⠙⠿⢿⣶⣤⣤⡤
⠀⠀⠀⠀⣠⡾⣋⣴⣿⣿⡿⠛⢡⣶⣮⠻⣿⣿⣷⣦⣤⣤⡄
⠀⠀⡠⠞⠩⠾⠿⠛⠋⠁⠀⠀⠀⠙⠻⠷⠦⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⢘⢠⢖⠆
⠀⠀⠀⠀⡄⢼⡷⠹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⢌⠋⡴⢍⠉⠙⢧⡢⣀⡀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢴⣦⡉⠒⠠⡀⢣⠀⠀⠀⡀⠤⡂⢀⣭⣇⠔⠀⠀⠐⣈⡜
⠀⢈⣫⣙⣌⡇⠀⠃⠀⠐⢈⣡⣤⣤⣯⣿⣋⣉⠁⢀⢀⠒⠒⠒⡖⣿⡴⠒⠒⠒⠦⠤⠤⠤⠒⠒⠒⠢⢝⣶⠦⠀⠑⠤⠀⠀⡀⠄⣑⠤⠀⠈⠁⠀⡐⢰⠜⠁
⠤⣸⢷⠶⡾⡤⠤⠶⠞⠚⠉⠀⠀⠀⢞⠿⡏⠉⠉⠙⠚⠒⠿⠦⣷⣿⣥⣁⡖⢠⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢐⢒⣊⠀⠠⢐⣰⠔⠁
⠀⠉⠟⠊⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⠃⠀⠀⠀⠀⠀⠀⢰⡛⡟⠀⠉⠙⠛⠺⢖⣠⡴⠶⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⠀⠤⠀⢐⢨⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃⣦⣀⣀⢐⡵⠋⠀⠀⠀⠀⠉⠉⠛⠲⣄⣌⠀⠀⠀⠉⡙⠒⠀⡂⢠⡾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⠀⠀⠀⠀⠀⠀⠀⠈⣸⢠⠽⢯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠐⡀⠨⣩⢗⣉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢘⠀⠐⠀⠩⣐⠀⣒⣑⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠀⠀⠀⠀⠀⠀⠀⢈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣽⠀⠤⠌⠥⠀⠄⡲⠖⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡭⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡇⠀⠖⠚⠛⠒⣈⢔⣡⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠠⠭⠍⠉⠅⣒⠩⡂⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣬⠩⠉⠉⠀⢐⡊⠤⡡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⡏⢉⣉⣁⣀⡀⢔⡡⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⢸⠈⠁⠤⠬⢀⠶⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣀⣀⠀⠬⢑⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⢿⣆⣀⡀⠀⠀⠀⣞⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡄⠀⢸⠇⠰⠿⠭⣟⠠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡒⡉⠋⠀⠀⠀⠈⢉⢫⠓⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⢿⠇⠀⠘⡿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⣀⣀⣌⠉⢡⣖⡒⢄⠾⠾⣫⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⠄⠀⠠⠷⠿⠿⠷⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠚⠓⠞⡻⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣴⠆⠀⢶⣶⣶⡶⢶⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡛⠀⠀⢐⠀⠐⢒⡀⠩⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢘⣙⠀⠀⠐⢀⣘⠋⢀⡮⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠡⢐⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠐⢲⡏⠀⣠⡁⣠⡴⠦⠤⠄⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠑⠀⠄⠠⠔⠤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠠⢽⠁⠀⠐⠐⠒⣐⢌⣋⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠀⠀⡀⠈⣿⠀⢀⣘⢛⣀⣡⣀⣀⢤⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠃⠠⣼⠀⢰⠃⠀⠐⠒⡀⠡⢑⡐⠢⣉⠓⠜⢯⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡇⠀⠈⠀⠠⣶⡄⠀⠐⢯⡦⣄⠀⠑⠀⠈⠓⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⢔⣫⣝⢓⣀⠀⣀⠀⠀⠀⠀⠀⢀⠰⠶⠤⢀⠀⠀⣾⣀⡀⠀⢀⠀⣤⣀⠀⣠⠼⠇⢀⣠⠶⠒⠒⠲⢦⡀⠀⢄⠀⠆⣠⠤⠤⠤⡀⣷⠎
⠀⠉⡱⡣⡠⠀⠢⡂⠕⡆⠀⠀⠄⠀⠀⠀⠀⠀⠈⠆⠁⠀⠙⠁⠈⠉⠉⠀⠈⡆⠀⠀⠟⠀⠀⠀⠀⠀⠀⠓⠐⢈⣺⠊⠁⠀⠀⠀⠀⢻⡓
⠀⠠⡉⡉⠀⠀⠀⠀⡀⡰⠀⠺⠀⠄⠀⠀⠀⢀⠆⡘⠄⠐⡁⠀⠀⠀⠀⠀⡄⡘⠀⠚⡀⠂⠀⠀⠀⠀⡐⡠⠁⠘⢋⢀⠀⠀⠀⠀⡔⢀⠁
⠀⠀⠑⢄⡀⠠⠠⡐⠕⠀⠀⠀⠑⠠⣀⣒⣂⡡⠊⠀⠀⠀⠈⠢⠐⣀⣐⠪⠐⠀⠀⠀⠈⠢⢤⣐⣂⠬⠊⠀⠀⠀⠀⠃⢅⡂⢐⡊⠔⠁
⠀⠀⠀⠠⠎⠉⠉⠆⠠⢀⣀⠠⠀⠲⠈⢀⠁⠋⠀⠂⠆⠂⠦⠐⠂⠈⠁⠂⠂⠀⠤⢤⠔⠊⠅⠈⠁⠈⡈⠂⠴⠠⠐⠊⠨⠉⠉⠐⡦⡀
⠀⠀⠈⠀⠁⠀⠀⠈⡄⠀⠀⠀⠀⢸⠂⣒⠐⠃⠀⠀⠀⠀⠀⡰⠀⠀⠀⠈⡄⠀⠀⠀⠀⠘⡤⠠⡤⢤⠄⠀⠀⠀⠀⢀⠃⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⡆⢰⠒⠁⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⡄⠔⠒⠀⠀⠀⠀⠀⠀⠈⡎⢁⠈⠀⠀⠀⠀⠀⠸⠐⡄⠄⠀⠊
⠀⠀⠀⠀⠒⠃⠈⠓⠀⠀⠀⠀⠀⠒⠃⠀⠘⠒⠀⠀⠀⠀⠀⠀⠒⠃⠚⠂⠀⠀⠀⠀⠀⠐⠚⠁⠈⠓⠃⠀⠀⠀⠀⠀⠒⠃⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂
⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠁⠈
⠀⠐⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⠀⠄⠈⢦⡿⠞⠂⠠
⠀⠀⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠤⠀⠀⠀⠀⡩⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠏⠠⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡄⠈⠙⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⣀⠠⠞⠁⠀⢀⠀⠂
⠀⠀⠄⠀⠄⠀⠀⠀⠲⣗⣂⣷⣀⠀⠘⣗⠀⠀⢀⡀⠀⠀⠀⠠⢴⣴⣶⣿⣷⠤⠀⠀⠀⢐⣴⡾⠿⠂⠠⣤⡤⠀⡀
⠀⠐⠀⠀⠀⢀⠀⠀⠀⠉⠁⣤⡈⢷⡄⠋⠁⠀⣠⣧⣀⠀⠀⠀⠈⠁⠻⣿⡄⣀⡞⠀⠄⠺⠟⠒⠢⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠠⠾⢧⣀⣀⣈⣷⣯⢿⡶⢄⡀⣨⢯⣥⣿⣿⣿⣷⣾⠉⠅⢀⣰⠆⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⡶⠒⢀⣈⣛⠿⢻⠟⠛⠿⡖⣈⣄⠮⢿⣫⣿⠉⠿⢿⡿⠳⣤⡈⠉⠀⠀⠀⠀⠠⠀⠤
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠁⢈⣵⡶⢃⡀⠀⣰⣷⣾⣶⣾⣿⣿⣿⡁⠣⡁⠀⢰⡆⣀⠀⠀⠀⠀⣀⠀⢀⠀⡈⠁
⠀⠁⠀⠈⢠⡆⠀⠀⠀⢠⠀⠈⠀⠋⠉⡟⠀⡟⠻⢿⣿⣟⠉⠉⠻⡿⣿⣿⣯⠄⠐⣂⠀⠁⠈⠁⠀⠀⢀
⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⣁⣥⣾⠛⣿⣿⠿⠀⠄⢀⣀⠉⠃⠀⠀⠀⢂⠀⠀⠀⠀⠀⠰⢦⣤⣤⣄
⠀⠀⣶⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠋⠺⢯⠟⠛⠃⠏⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣤⠛⠛⠛⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠏⠉⠉⠉⠉⠉⠉⠉⠹⣿⣶⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣰⣿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⣴⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣈⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣞⣻⣿⣿⣿⣿⣖⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⢳⣿⣿⡿⣿⣿⣿⣿⣿⢟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣫⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⢿⣿⣵⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢟⡛⠝⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠋⠋⠉⠛⠛⠛⠛⠻⢿⣿⣿⣿⠿⠿⣿⣿⣿⡻⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⢟⣩⣿⣿⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡿⠿⣿⣿⣿⣿⣿⣭⣛⣻⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣧⡹⣿⡟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠻⣿⣿⣿⣷⣜⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⠶⠆⠀⠀⠚⠛⠉⠁⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⡆⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢲⣿⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⣿⣿⣿⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣾⣿⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⣿⣽⡟⢿⣿⣟⣉⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⣟⣿⠆⢉⣻⡿⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡷⠆⠀⠂⠀⠀⠀⠀⠀⢰⣄⣾⣿⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⣧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣷⣶⣶⣾⣶⣦⣤⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠈⢉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠛⠫⡉⢢⡉⠢⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡄⢄⠀⡄⠲⡈⠣⠑⢲⠤⡄⠀⣼⠖⠀⠀⠀⡠⢺⠋⢍⠒⠀⠀⠁⠀⠁⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⡀⠣⠘⠀⠁⠀⠄⠈⣏⣥⠾⠃⠀⠀⠀⠀⡔⡏⢀⡀⠀⠀⠀⠀⡀⠀⠀⢸⡱
⠀⠀⠀⠀⠀⠀⠀⢠⠿⡀⠀⠂⠀⠀⠀⢀⡄⠀⡏⢀⣀⠀⠀⠀⠀⠀⠈⢇⠀⠁⡀⠀⠀⢀⡁⠀⠀⡬
⠀⠀⠀⠀⠘⣷⣀⣈⡽⠳⡀⠀⠒⠒⠒⠉⢀⡴⠡⡋⠈⠃⢀⠐⠠⡆⠀⠈⠢⡀⠙⠂⠐⠊⠀⢀⠔⠁⢠⡤⢤
⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠈⢓⢶⡴⠦⣚⣉⣠⠔⠉⠁⠀⠈⠓⠚⠳⢄⣠⢤⡌⠓⡴⢤⣤⠖⠥⣤⠴⠚⢦⡼
⠀⠀⠀⠀⠸⣉⡹⠒⠒⠾⡉⠉⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢤⠀⠀⠀⠀⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣀⣀⣀⠠⢧
⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⠀⠀⠀⠀⠀⢀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⡀⠀⢀⡱⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠒⠒⠒⠲⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠒⠃⠑⠘⡀⣠⣻⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠦⠠⠃
⠀⠀⠀⠀⠀⠀⠰⢏⣈⡹⠃⠀⠰⣛⣃⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⠀⣀⣤⡀
⠀⠀⠀⢀⢀⣄⠀⢴⣔⣾⣆⢸⡟⢛⡀⠀⢯⠉⢿⡜⡡⢠⠟⣦⡀⣤⢆⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡀
⠀⢰⣶⢟⣉⣿⣴⣾⣿⣿⠿⣿⣧⣸⡧⠄⠈⡇⠘⢳⣥⡎⡼⡹⢋⡠⠊⠀⡖⠛⠉⠉⠉⠀⠀⠀⠀⣀⣸⡇
⠀⠀⢉⣋⣽⡟⠟⣘⣋⡧⠤⠬⠯⠭⠌⠀⠀⣧⠀⠀⠉⠙⠓⣱⠃⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠙⡏⠙⠒⠉⠁⠀⠀⠀⠀⢀⠴⠂⠀⠈⠷⢌⣀⣠⠤⡎⠁⣠⣄⡀⢀⠀⡀⠀⢀⣄⣀⠀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⢰⠏⢀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠺⣿⣭⣡⣿⣾⣿⣼⠉⣿⣿⣞⡁⣿⣥
⠀⠀⠀⠀⢀⢴⡆⡔⡟⠀⠀⠘⢦⣼⡴⠋⠀⠀⠀⢠⣤⡄⠀⣤⣤⣴⢿⡇⠃⣿⢿⣤⡿⡏⠙⣿⣿⣤⣤
⠀⠀⠀⠀⠹⠜⠀⠙⠁⠀⠀⠀⠀⠀⠓⠦⠤⠴⠖⠋⠟⠁⠀⠀⠈⠉⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⡀⠀⠀⣠⠤⠖⣚⠛⠋⠭⠍⣁⠒⠂⠄⣀⠀⢀⡠⠄⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⡠⣿⣁⠀⠀⠀⠀⠀⠉⠒⠤⣀⠉⠐⠤⡀⠉⠃⢄⡀⡀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠆⠀⢀⠔⠈⡸⠋⠀⠙⢆⠉⠒⠄⣀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠑⠢⣀⠈⠃⢅⠢⠀⠀⢃
⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠜⠀⠀⡰⠀⠈⢳⣄⡀⠀⠁⠂⠤⠄⣀⠀⠀⠀⠁⠂⠤⠠⠍⣒⣤⠿⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⠀⢀⠌⠀⠀⡴⠁⠀⡀⠁⠈⠙⠅⡂⠤⠄⣀⣀⠈⠉⠀⣒⡒⠴⠶⢋⣨⡄⢚⠇
⠀⠀⠀⠀⠀⡇⢀⡄⠋⠀⠔⠋⣀⠔⠊⠀⠀⠀⠀⠀⠄⠁⠲⠤⠤⠀⠀⠀⠠⠤⠤⣒⠈⠉⢉⢛⡦
⠀⠀⠀⠀⠀⡇⠀⠈⠛⡱⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢋⠈⠆⠀⠀⡇
⠀⠀⠀⠀⢠⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⡇
⠀⠀⠀⢀⠎⠀⠀⠆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠰⠀⠀⠰⡀
⡀⠤⠔⠊⠀⢀⠌⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠱⡀⠀⠑⠤⢀
⠑⠄⠀⠠⠔⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡤⠄⢀⣀⣀⣀⣀⠠⠤⠐⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠢⠄⢀⡀⠀⠀⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡔⠊⠉⠉⠑⢄⠀⠀⠀⠸⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡌⠀⠀⠀⠀⠀⠈⣤⣤⣤⠶⠶⠟⠛⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣦⣴⡆⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠁⠈⡏⠈⠉⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⡏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣄⣤⣁⡠⢤⣤⡒⡦⢻⣟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡠⣄⣰⣄⣴⢰⡄⢧⣼⠃⠀⠀⠘⠀⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠁⠀⠀⠀⠀⠊⠑⠂⡘⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⣀⠠⠋⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠒⠒⠶⠂⠠⠤⠤⠿⣀⠤⠚⠉⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⡀⠀⠀⠀⠀⡼⠤⠤⠤⠶⠒⠒⠋⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡸⠀⠀⠀⠀⠀⠸⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⡰⠃⠀⠀⠀⠀⠀⠀⠳⡀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡰⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠱⡄⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡇⡜⠀⠀⢠⠃⠀⠀⠀⠀⣀⠀⢀⡄⠀⠀⠀⠀⢣⠀⠀⠘⡄⡇⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣶⠑⠀⠀⡆⠀⠀⠀⢀⠔⡇⠀⠈⡗⢄⠀⠀⠀⠀⡆⠀⠰⢱⡇⠀⢣
⠀⠀⠀⠀⠀⠀⢀⠀⡎⠀⠀⢹⡇⠀⢀⣇⣠⠔⠊⠁⡜⠀⠀⠀⠘⡄⠉⠒⢤⣀⡇⠀⠀⣿⠁⠀⠈⡆⢀
⠀⠀⠀⠀⠀⠀⡎⠱⡇⠀⠀⢸⣿⣤⣾⠋⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⢻⣦⣴⣿⠀⠀⠀⡷⠙⡆
⠀⠀⠀⠀⠀⠀⡇⠀⢇⡀⠀⠐⣿⣿⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢹⣿⡏⠀⠀⣀⠇⠀⡇
⠀⠀⠀⠀⠰⠲⡇⠀⠘⣴⡀⣼⡟⡋⡇⠀⢠⠃⠀⠀⣤⠀⠀⠀⢠⡄⠀⠀⢣⠀⠀⡏⡛⣿⣤⣰⡟⠀⠀⡷⠲
⠀⠀⠀⠀⢠⠀⢧⢂⠀⠱⣳⣿⠀⢽⡆⠀⠸⠀⢀⡴⡇⠀⠀⠀⠀⡷⣄⠀⠸⠀⠀⣿⠃⢸⣷⡻⠁⢀⢢⠇⢰
⠀⠀⠀⠀⠸⡀⠘⡜⡄⠀⣱⠿⡀⠘⣷⣄⣰⠷⠋⢠⠁⠀⠀⠀⠀⢱⠈⠳⢷⣀⣴⡟⠀⡸⢷⡁⠀⡜⡜⠀⡼
⠀⠀⠀⢸⠉⢣⡀⠘⢝⣦⣿⠀⢷⣄⣷⢿⡏⠀⢠⠃⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⢷⣇⣴⠇⢸⣧⣾⠝⠀⢠⠋⢹
⠀⠀⠀⠈⣆⠀⢻⣦⠈⣯⠿⡆⠈⢿⠇⣜⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣞⡄⢿⠏⠀⡼⢿⡏⢠⣾⠃⢀⡎
⠀⠀⠀⠀⣘⣦⠀⠙⢷⣿⡀⠹⣤⣿⡆⢿⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⠇⣼⣧⡼⠁⣸⣷⠟⠁⢀⣞⡀
⠀⠀⠀⠀⢣⠈⢷⣄⠘⡿⢧⡀⣿⠻⣇⢸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢀⡿⢻⡇⣰⠿⡟⣀⣴⠏⢠⠃
⠀⠀⠀⠀⠈⢣⡀⠙⢿⢿⡀⢻⣿⡀⠻⣷⡟⢉⡈⢳⠀⠀⠀⠀⠀⢰⠋⣈⠙⣷⡿⠃⣸⣿⠃⣸⣿⠟⠃⣠⠋
⠀⠀⠀⠀⠀⢏⠱⣄⣘⣯⠙⣮⣯⠹⣦⣿⢰⣿⣉⡼⠀⠀⠀⠀⠀⠸⣌⣹⣷⢸⣧⡾⢩⣯⡞⢩⣟⣀⡔⢉⠇
⠀⠀⠀⠀⠀⠈⢦⡈⠙⣿⠷⣈⣿⠳⢼⡏⣼⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⡀⣿⠴⢻⣏⡴⢿⡟⠉⣠⠎
⠀⠀⠀⠀⠀⠀⢏⠙⠦⣾⣦⡈⢻⡓⠾⡇⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠇⣿⠖⣻⠋⣠⣾⡦⠚⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠓⣤⣘⣦⡉⠻⣟⠲⣧⠸⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⢠⡗⢚⡿⠋⣡⣞⣠⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣉⠛⣟⡓⠻⣗⠻⡆⠱⣼⣦⠤⡀⠀⠀⡠⢤⣾⡴⠁⡾⢓⡿⠓⣛⡟⢋⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣛⠛⢯⣹⣦⡈⠻⠆⣸⠀⢸⡀⠾⠋⣠⣾⣩⠟⢛⡺⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠛⠓⠚⠁⠀⠀⠙⠒⠛⠓⠚⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠉⠉⠀⠒⠒⢄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠒⠀⠠⠤⣀⠀⠀⡠⠊⠀⣀⠤⠤⠔⠒⠠⢄⠀⠀⠧⢄
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡂⡠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢣
⠀⠀⠔⢀⡤⠚⠙⠢⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠜⠀⠀⢀⣀⣀⣀⡀⠐⡄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠎
⠀⢀⡤⠀⠀⠀⠀⠀⠣⠀⢀⣀⠀⠀⠀⠀⡇⡈⠀⠃⠉⠉⠀⠀⠀⠉⠉⢳⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣀⡈
⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠉⠒⢤⣀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡮⢎
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡀⠀⢃⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢝⣆⡀⠀⠀⠀⠠⠐⠁⠀⣀⠞⠁⠁
⠰⢆⡀⠈⠢⢀⠀⠂⠤⠤⠖⠀⣀⠔⠁⣠⣤⠠⡀⣈⣦⡀⠀⠐⠁⠺⣅⣀⠀⠀⠀⢀⡜⠀⠙⠲⠤⣤⠬⣥⡔⠊⠁
⠀⠀⠈⢑⠁⡠⠊⠒⠒⠒⠚⢯⠀⠲⠊⠀⢀⣀⣀⣀⠄⠨⠓⠒⠒⠖⡞⠩⡉⣉⡉⠥⡆⣀⡐⠀⠚⠰⣀⠀⠈⢇⢰⠤⢤⣀⣀
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢫⠈⠀⠀⠉⠀⠀⠈⠠⠄⠀⠀⠀⠀⢠⠤⠊⠀⠰⠆⠉⠀⠘⠌⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⣘⠀⠤⠀⢀⡀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆
⠀⠐⢯⠉⠉⠐⠠⠤⠛⢅⢀⠀⢀⠸⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⢉⠂⠀⠀⠉⢀⠈⣉⡠⠔⢓⠇
⠀⠒⠚⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣤⣀⡀⠤⠤⠲⣄⠉⢀⡀⠀⠘⡲⠈⠁⠐⠚⠉⠀⠀⠀⣮⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠳⠏⠀⠢⣤⠃

⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤
⠀⠐⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢹⡟
⠀⠀⢸⠀⠙⢯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢿
⠀⠀⠘⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣷⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣀⡀⠀⣀⠖⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠛⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠙⠶⣼⠃⣴⡦⢤⡝⢳⠀⢀⠀⢀⠀⠀⠳⣼⡆⡼⠟⣻⢟⣤⡄⠀⠀⣴⠧⣄⣾⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣿⡃⣨⣏⣈⣄⠀⣳⡏⣠⢲⡀⣿⠷⢍⣫⣴⣿⠷⡙⣶⡶⣿⠷⡿⢿⡏⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠒⣼⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠹⣿⠟⠛⠸⡾⢿⣴⣿⣦⣽⠶⠆⣿⠉⡿⣿⣟⣿⠛⠀⠻⣷⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⣴⣾⣿⡇
⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠠⠤⠉⡁⠀⠀⠀⠈⠀⣴⣶⢾⣯⣿⣿⣿⣵⣇⢒⣛⣻⠽⣯⣍⣠⣶⠖⢡⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣴⠶⣿⣧⠹⠧⠤⠏⣛⣿⠉⠸⣇⠸⣿⣿⠦⣇⠙⠏⢿⣷⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠈⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠽⠟⠓⢀⣴⠋⢩⣯⣼⡿⠟⠀⣨⣽⠒⣋⡀⠀⠰⣏⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠈⠁⢠⣴⡌⠹⢷⣿⣿⠟⣸⢻⣿⣷⣴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⢶⡌⠛⠁⠀⠀⠀⠀⠸⠋⠀⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢀⡾⠏
⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⢀⣀⠠⡀
⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⡴⢮⠞⠛⠛⠂⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣦⡽⠏⠁⢀⣠⣤⣤⣤⣤⡄⠀⠹⣆⠀⠀⠀⠀⠘⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠏⠉⠀⠀⠀⣠⣾⠟⠋⠉⠀⠀⠀⠀⠀⠘⠷⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠌⠁⠀⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⣧⢸⡦⢻⠆⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢠⡄⣡⠶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣰⣦⣶⡀⠘
⠀⠀⠀⠀⠀⠁⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣾⣿⣡⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⡀⠸⣆⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢆⠙⣤⣾⡿⠿⠛⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢿⡀⠀⣴⡿⠋⣹⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡷⠞⠁⠀⠀⠀⠀⣀⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⣄⣰⡿⠁⠀⣀⣄⣀⣠⣀⡄⠀⠀⠀⠀⠀⠀⡠⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⢿⣧⡀⠀⠀⠈⠁⠀⢀⣼⣿⠿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠐⠁⠀⢸⡇⠐⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠻⣿⣷⣤⣄⠀⠀⢻⣿⣷⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠻⣿⣿⣿⣷⣦⣀⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠃⠀⠙⢿⣿⣿⣿⣿⣶⣦⣤⡀⠀⢀⣠⣶⣄⠀⠀⠀⠀⢀⣤⣾⣿⣷⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡿⠿⠁⠘⠳⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠙⠛⠉⠉⠁⠀⠀⠉⠉⠙⢿⡍⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠠⠂⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣴⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⠠⠼⠧⠴⠟

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡛⠋⣻⡿⢟⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠁⢀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠉⢀⣠⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⠉⠁⣀⣠⣴⠶⠛⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠾⠟⠋⣿⣏⣠⣤⣴⠶⠟⠋⠉⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⢛⣻⡿⠟⠁⠀⢠⣴⠟⠛⠉⠉⠀⠀⢀⣠⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠉⣀⣤⡶⠟⠉⠀⠀⣀⣤⣼⣧⣤⣤⣤⡶⠶⠛⠛⠉⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⠀⣸⡟⠋⠁⠀⠀⠀⢀⣸⣏⠁⠉⠉⠉⠁⢀⣀⣀⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢀⣤⣤⡴⠟⠀⠀⠀⠀⢠⡾⠛⠉⠛⠛⠛⠛⠛⠛⢛⣿⠋⠁
⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣤⣤⣤⣤⣤⣶⠾⠛⠁
⠀⠀⠀⠀⢠⡿⠀⠀⠀⣸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠘⣷⣄⣀⣴⠿⠷⠶⣤⣄⠀⠀⠀⠀⠀⢰⡟⠻⠶⠶⠶⠶⠟⠛⢻⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠹⣷⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⡟⠛⠻⠶⠶⠶⠿⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢘⣿⣤⣀⠀⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢀⣀⣿⡉⠉⠛⠛⠛⠛⠛⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⣾⠋⠉⠛⢶⣤⣤⣀⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⣾⠛⠛⠷⣤⣀⡀⠀⠈⠉⠉⢉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠛⠻⣧⡀⠀⠈⠉⠛⠷⠶⣶⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠛⢷⣤⣀⣀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣴⠿⠋⠉⠉⠁



⣿⠉⠙⡟⡛⠛⡟⠟⠻⣟⠻⡟⠟⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⢸⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⠀⠀⢸⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡀⠀⢸⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⢸⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣦⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⣿⣷⡀⡜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣞⠀⣿⣿⣿⡟⣿⣿⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣿⣿⣿⣇⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⢀⢻⠉⢿⣿⣿⣦⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣠⣘⣀⣨⣿⣿⣿⣿⣦⣀⣼⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⡿⡿⣿⣿⣿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⠤⡤⠀⠀⠢⠄⠀⠀⠀⠠⢦⠄⡀⣀⡤⠐⢂⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⢀⢋⠒⠊⠀⠈⠤⠀⠀⡄⠈⢀⡈⠂
⠀⠀⠀⠀⠠⠀⠁⠐⠐⠋⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⣀⠁⠀⢘⠀⠀⠀⠀⡀⠀⠈⠉⠁⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⣀⡥⢈⠸⣀⠀⠉⡀⣀⠠⠠⠃⠀⠰⢿⣶⣀⡇⠁⠀⠠⠀⣀⠂⠀⢔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡽⢱⣽⡾⣏⠧⣈⠦⡄⡤⠰⠏⠋⢙⣉⠀⡀⠀⣔⠹⣷⠒⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣄⡀⠀⢑⠈⠉⠣⠌⢷⠀⠀⠈⠔⠃⠐⠀⠀⣀⠼⠒⠺⠍⠀⠋⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡀⠀⠈⡄⠀⠀⢂⠔⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⡈⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠛⠁⠛⠀⠃⠘⠁⠀⠀⠀⠀⠣⠐⠢⠖⠀⠐⠀⢀⠀⠈⠈⠋⠒⠙⠞⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⠿⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣤⣦⣤⣀⡉⠙⠛⠿⢶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣰⣿⠁⢿⣿⠛⠻⢶⣤⣄⣀⠉⠙⠛⠿⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⣿⣿⡄⠈⣿⡆⠀⠀⠀⢹⣿⣻⡷⣶⣤⣀⡀⠈⠉⠛⠻⠷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣼⡏⢹⣧⠀⢹⣿⠀⠀⠀⠨⣿⡟⠀⠀⠈⢹⣟⠻⣶⣦⣤⣀⡀⠈⠉⠛⠻⠷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣸⡿⠀⠀⢿⡇⠀⢿⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠃⠀⠉⠙⠛⠿⢶⣦⣤⡀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿⠇⠀⠀⠸⣿⡀⠘⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⡟⠀⠀⠀⠀⢻⣧⠀⢹⣷⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣷⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⡿⠀⠀⠀⠀⠀⠈⣿⡆⠀⢿⣧⠀⣿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢀⣿⢿⡇⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢰⡿⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢸⣷⡀⠘⣿⡄⣿⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣸⡟⠘⣿⡀⠈⣿⣇
⠀⠀⠀⠀⠀⢀⣿⠃⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢹⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣿⠁⠀⢹⣇⠀⠸⣿⡄
⠀⠀⠀⠀⠀⣼⠇⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣼⡏⠀⠀⠀⢿⡆⠀⢻⣷
⠀⠀⠀⠀⣸⡟⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣼⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⡏⠀⢠⣿⠁⠀⠀⠀⠘⣿⡀⠈⣿⣇
⠀⠀⠀⢠⡿⠁⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢫⡾⠿⣝⢷⠀⠀⢀⣿⠀⠀⠀⠀⠀⢰⡿⠀⠀⣼⡇⠀⠀⠀⠀⠀⢹⣇⠀⢸⣿⡄
⠀⠀⢀⣾⠃⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣯⠴⠶⢿⣾⣤⢖⣻⣿⡷⣄⠀⠀⠀⣾⠇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⣷
⠀⠀⣼⡏⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⡇⠀⠀⢠⡟⣱⢿⣍⠉⣷⢸⡆⠀⣸⡟⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣿⡇
⠀⠀⣿⣄⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣷⣦⣀⣸⠁⣿⠀⠈⠛⠿⣾⡁⢀⣿⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢹⣿⡀
⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢀⣇⠀⢀⣠⣴⡿⠇⣼⡏⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠻⣿⠿⠛⠁⠀⢠⣿⠁⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣷⣾⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣴⣶⣥⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣬⣭⣦⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡿⢛⣋⣉⣉⣛⠛⠛⣛⣛⢉⣉⡛⢿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣧⢸⡗⢇⣐⡿⣰⣦⠺⠦⠴⠟⠇⣸⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⣭⣩⣩⢴⣿⣿⣦⣉⣍⣬⣴⣿⣿⣿⣿⣿⡷⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⠾⢺⢿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⡟⠁⣤⣤⣤⣼⡇⠈⣿⣿⣿⡟⢨⣿⣿⠃⠀⢻⣿⣿⠟⠁⣤⣤⣤⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣧⣀⠉⠛⠿⣿⣿⠀⣿⠁⠸⡇⢸⣿⡏⢰⡆⠈⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣶⡄⠈⣿⡄⠀⣶⠀⠁⣿⡿⢀⣉⣉⠀⢸⣧⠀⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣏⣉⣉⣉⣠⣴⣿⣇⣰⣿⣇⣠⣿⣃⣼⣿⣿⣇⣀⣿⣷⣄⣈⣉⣀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣴⡌⠉⠉⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⣿⡇⠀⠀⠀⠸⠿⣀⣀⣀⣀⣀⣀⣀⣀⠿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡇⠀⠀⠀⠀⠀⠀⢀⡰⠿⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⡟⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣉⣉⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠛⠛⠛⠛⠛⠛⠛⠛⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠉⠉⠉⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣾⣿

⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⢸⣇⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠈⠉⠁⣿⠉⠉⣿⠉⠉⠉⠉⠉⠉⠙⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠶⢶⣤⣤⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡿⢦⡀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢠⡟⠁⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⠻⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢹⡇⠀⠘⠷⣤⣀⠀⢿⡀⠀⠀⠀⣿⣤⣴⠾⠛⠁⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⣷⡀⠀⢸⡏⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠙⠃⢸⡇⢀⣠⡾⢋⣿⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣷⡀⣸⠇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣨⣿⠟⠁⠀⣼⠇⠐⠻⠆⠀⠀⠀⠠⠿⠿⢶⣤⣤⣤⣤⣌⣷⠀⠀⠀⢸⣧⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢻⡟⠉⠁⢿⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⡄⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠘⣧⢀⣶⠿⢷⣀⠀⠘⢇⠀⠑⠦⢤⡄⣤⠠⡤⠀⠀⠀⠀⣾⣋⣵⠟⢷⡄⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢀⣿⠀⠀⠰⢦⣄⠀⠀⠀⣿⡀⠀⠀⠹⣾⢷⣤⣾⠉⠓⢲⡆⠿⢲⣦⣠⡀⠀⠀⣤⢠⡤⢾⡇⠛⠋⣿⣤⣾⠃⣰⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠻⠆⠀⢸⡇⠀⠀⠀⠙⢷⣄⣿⡗⠶⣼⡇⠀⠀⠀⠈⣷⠀⢠⡿⠀⠀⠀⢃⡶⠟⠋⢁⣿⡾⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠙⢻⣷⣤⣍⣙⣻⣾⡏⠀⠙⠷⠛⠁⢰⡶⠋⣸⣧⣴⠶⠛⢹⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠀⠈⣿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡀⢀⣤⣤⣾⡷⠶⣶⣶⣶⣶⠾⢧⡀⠀⠀⠀⠀⠀⠀⢿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⣇⣾⠁⠀⠈⣷⣰⡏⠀⠀⢻⡆⠈⢿⡄⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣀⣨⣿⠇⠀⠀⣸⣧⡿⠀⠀⢀⣿⣀⣀⣸⣇⣀⣀⣀⣀⣀⣨⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢩⡿⠀⠀⢠⡿⣽⠃⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠿⣿⠃⠀⠀⣼⣿⡟⠀⠀⢰⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠷⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡾⠋⠛⠳⢾⣿⠟⠙⠛⠶⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠳⠶⣦⣤⡾⠛⠶⢦⣤⣴⠟⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠛⢋⡉⠉⠉⢉⠛⠻⠿⣿⣿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠁⠀⢀⣀⡀⠰⣯⢀⠀⠀⠀⠀⠀⠑⠠⣄⠈⠐⠤⡀⠑⠢⢀⣀⡀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⠏⠁⠀⠙⣆⠈⠐⠤⣀⡀⠀⠀⠀⠑⠢⢀⡀⠑⠢⢀⡙⠻⣆⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⢸⣿⠃⠀⢀⠎⠀⢈⠳⢦⡀⠀⠀⠁⠒⠤⢀⡀⠀⠀⠉⣐⣒⠴⠛⣻⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⡸⠃⢀⡴⠃⢀⠔⠁⠀⠀⠀⠀⠌⣀⠒⠂⠀⠀⠀⠂⠉⢉⠠⠶⠧⣾⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠛⢶⣤⠥⠐⠊⠁⠀⠀⠀⠀⠀⢠⠀⣬⠉⠀⠀⠀⠀⠀⠉⠐⠂⠠⣶⣶⠁⠀⢸⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠃⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠘⣿⣿⣿
⣿⠿⠟⠃⠀⣰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⠘⠿⣿
⣧⣤⣤⣤⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣦⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⠠⠤⠤⠤⠤⠐⠂⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠐⡠⣤⡄⠠⠤⠐⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠜⠁⠀⠀⠈⠢⠀⠀⠀⣉⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣘⠀⠀⠀⠀⠀⠀⠟⠛⠋⠉⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠓⠐⢒⠒⠒⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⣶⢮⣄⢲⣤⣜⣶⢻⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⠤⠴⠧⠶⢸⡌⠗⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠈⠠⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠉⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣤⡀⠀⣀⢈⡎⠀⣀⠤⠒⠈⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⢀⣷⣀⣤⣤⣤⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢺⣿⣿⣟⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠐⠀⣤⣾⣿⣴⣖⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣼⣿⣷⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣇⣿⡿⣿⡼⠄⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡟⠿⢿⠿⠃⠙⠛⠁⠐⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠈⣭⣴⣄⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢄⣀⣀⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠰⠶⢔⠀⠶⡦⢸⠀⢰⣁⢦⢠⢠⡄⡆⣀⣆⢀⣀⡀⣄⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠙⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢰⡤⢄⠀⠀⢀⣀⣴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠀⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠘⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢠⡄⠀⠀⠀⠈⠁⠀⠀⣤⠄⠀⠀⠀⠈⠁⠀⡐⢤⣀⡀⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⡃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣴⣶⡆⠀⠀⡀⠘⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠌⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⡼⠀⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠠⠘⡄⠀⠀⡀⠀⠰⠶⠶⣶⣦⣄⠀⠀⢀⣴⡶⠿⠻⠶⠄⠀⠀⠀⠀⠰⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⣤⠶⠶⢆⡍⠛⠀⠀⠈⠋⣤⠶⠦⢤⡄⢠⠀⢠⡀⣤⣾⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠤⠢⢦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠈⣤⠈⠆⢈⠃⠈⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠗⢒⠀⣴⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠟⠢⣀⣀⣤⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣀⠀⠈⠗⣀⢠⠀⠀⠀⠀⠀⠀⣤⣀⡤⠀⠀⠀⠀⠀⢠⣲⠀⡾⠀⠀⠙⣏⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠁⡒⣢⣀⣀⡼⠟⣶⠛⠤⢉⠋⢀⠀⠀⠀⠀⢀⣀⣈⣄⡀⠀⠀⠀⣠⡇⠀⠰⠂⠀⠀⠀⢸⣄⣄⣤⡀
⠀⠀⠀⠀⠀⠰⠉⠉⠁⠈⠁⠀⠀⠠⢓⢠⠊⠀⠈⣷⡄⠀⠈⠻⢿⣿⡿⠟⠀⢀⡄⡶⠀⠀⡇⠀⠀⠀⠀⢀⠏⠉⠉⠁⢀⠐
⠀⠀⠀⠐⢠⡄⠀⠁⠀⠀⢠⡆⠀⠀⠀⢸⡀⢊⣑⠉⣧⣄⣀⣀⣀⣀⣀⣀⣀⣽⣤⠀⠀⡐⠁⠀⠀⠀⠀⢰⡗⢤⠄
⠀⠀⠠⣘⢧⡄⠀⠀⠀⠀⠙⠋⣀⡀⠀⠀⢉⣿⠉⡸⠇⠀⠀⠈⠈⠉⠉⠉⠁⠀⢅⡀⡺⠞⠀⠀⠀⠀⠀⣼⡠⠂
⠀⠀⠀⠁⠳⢤⣀⠀⠠⠖⠈⠉⠉⠉⠉⠻⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠰⠆⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣰⠏⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡏⠁⠀⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢉⣯⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⣀⣼⣿⡿⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣤⣀⣀⣀⣀⣀⣴⣾⡿⠟⠉
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢄⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠞⠀⡀⠂⠀⣀⠓⠀⠈⢉⠠⢀⠀⠀⠀⠀⠒⠀⠠⠈⠀⠀⠀⠈⠀⠤⠂⠀⠀⠀⠂⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠑⡆⠀⢀⡠⢄⠤⠀⠀⠈⠧⠤⡀⠀⠀⠀⠀⢰⢃⡶⢄⠀⢀⣄⠄⠈⢑⡀⠀⡀⠀⠀⠀⠘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠀⠀⠀⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡞⠲⠶⠶⠀⠀⢙⣈⠀⠀⠠⡀⠉⠉⠈⠉⠲⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⣀⠀⣠⢄⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠰⠖⠄⠒⠖⠐⠒⡆⠀⠀⠀⠀⠀⠁⠀⠀⠺⡤⠤⡞⣉⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠁⠈⠀⠀⠠⣐⢀⡀⢀⠀⠐⠁⣀⠀⠀⠀⠈⠢⠤⠀⠀⠈⢇⢀⠀⠀⠀⡁⣄⠀⠀⠠⠀⠀⠀⠀⠈⠃⠄⠀⠀⢀⠀⠈⠈⠄
⠀⠀⠀⠀⠂⠀⠀⠐⠀⠴⣐⠴⠉⠑⡀⣠⠁⣈⠹⡀⡀⠁⠈⡂⠀⡀⠠⢄⡔⠃⠀⠀⢶⢿⣗⡖⣈⣗⠁⠀⠃⠀⣄⢐⣒⡎⠀⠠⣜⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⠀⠀⠁⠁⢠⡘⢲⠾⣌⠧⢴⡿⢻⠋⠑⡶⣄⣀⣀⡀⣠⠚⠿⠚⠻⠙⠠⠀⠀⠀⢀⠜⠿⣳⣤⢠⣀⣉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⠀⠠⡠⠃⢁⠉⠻⣍⠀⠿⣿⡋⠙⢦⡙⠓⠏⠈⢧⠞⣠⠉⢉⡈⠤⠳⠺⢋⡌⠃⣀⣿⠖⡈⣷⠧⠤⡷⣶⡾⠞⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡰⣦⣌⡀⣀⢈⡆⠀⠀⡑⠐⠐⢿⠀⠀⡠⠀⠞⢉⠡⠀⠒⢂⣀⡠⠔⠛⠉⠓⠧⠀⠀⠅⠀⠀⠀⠈⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠈⠁⠀⠣⡀⠈⠐⢄⠘⠄⠀⠐⠀⠒⣠⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄⠉⠁⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠡⠀⠀⠂⡄⠀⠀⠀⠀⢨⡄⢰⠀⠀⠀⠀⠀⠀⠤⠄⠴⠒⠂⠀⠀⠀⠀⠠⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠄⢠⠀⡁⢢⣷⡀⢀⡀⢀⠀⠀⣁⠇⠀⠀⠀⠀⠈⡥⠐⠄⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣄⠐⠴⡀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠒⡉⠉⠀⠈⠀⠍⢉⢀⠋⡀⠀⠀⠀⠄⠀⠙⠧⠚⠘⠚⠓⠠⠈⠓⠀⠀⡀⠁⠀⣀⢈⠁⠛⠁⠛⠘⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⢀⢰⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠛⣀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⢀⡐⠀⠂⠈⢠⠤⢆
⠀⠀⠀⠀⢀⡀⠐⡏⠀⢠⣶⠖⠒⠀⣀⣀⠀⠀⠈⠟⠁⢲⡄⢹⣾⣆⣠⣄⡄⠀⣀⣠⡄
⠀⠀⠴⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣹⣧⣄⣧⣳⡴⠚⠳⠋⠀⣍⢉⣽⡶⠛⣽⠖⠀⠀⢀
⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠰⣼⣿⠛⠓⣞⢠⣶⣻⡎⢁⡙⢶⠀⠓⡀⠀⠘⣧⡽
⠀⠀⠙⣠⡤⠛⠻⣦⣄⠀⠀⠠⠀⠠⣤⣻⡷⠚⠛⣿⡿⢿⠋⠉⠉⠉⠁⠉⠙⢋⡔⣭⣷⣦⠀⠛⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠉⠛⠀⢀⡀⣼⠂⠉⠉⠉⢆⠉⠈⣷⣆⠘⣶⣦⡀⠀⠀⣁⠘⢧⣾⡟⠃⣼⠂⠀⠀⠐⠼⠟⠂⠀⠠⡀
⠀⠀⠀⠀⠀⣄⠈⠀⠀⢠⣥⣅⢸⣆⠀⡢⣄⠘⡧⠄⠋⠉⠀⠘⠃⠁⠀⠐⠸⡇⣈⠹⠟⣃⠹⡀⢴⣾⣿⡆⡠⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠙⢤⣤⠄⠻⠇⢴⡍⠙⢲⣦⣯⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠈⢻⡇⠀⠘⣋⢁⠈⠋⡹⠟⢀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠍⣳⠊⢈⠙⠛⠉⢢⣀⡾⠁⠀⠀⠀⠑⠿⠃⢶⠄⠉⠀⠀⠀⢸⡟⣀⣿⠗⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣸⡦⡋⢠⡴⠇⠀⠀⠰⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣻⠉⢹⡆⠀⠀⠸⡀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣠⠋⠃⢰⡿⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢡⣼⣷⡧⠘⢠⣀⠀⢻⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠋⠀⣠⡞⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣼⣟⣿⣧⠀⠘⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠞⣴⠇⢀⣿⣿⣧⣤⡠⠶⢤⡄⠀⠀⠀⠀⠈⠈⠁⠀⠒⠦⠀⠀⢀⣀⢈⢲⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡘⠛⠁⠁⠀⣰⢤⣀⢀⡀⢠⣾⠗⠂⠀⠀⢴⢶⣆⠁⠀⠀⠒⢀⣨⠤⡤⠈⠓⠷⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠈⣡⣴⣿⡌⣷⠉⢉⣀⡀⠀⠀⠀⣀⣁⠀⢀⠀⣠⠾⠄⠴⠛
⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⡐⢲⣯⡁⠈⢹⠏⠉⠲⣿⣭⣯⠀⢤⣶⣿⠟⡋⠉⣠⣿⢀⣠⣶⠖⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⠉⠛⠋⠉⠁⠹⡄⠀⠀⠙⠛⢃⠀⢀⣿⣷⡞⠉⠿⣿⣾⢟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠦⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠘⡗⠂⣀⠈⠟⢣⡰⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⣀⡀⠀⠀⠘⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠛⠛⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣤⣶⣾⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣅⠙⢿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠛⢀⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣶⣼⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣧⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣧⣤⣈⣹⣿⣿⣷⣤⣠⣾⣿⣿⣟⣁⣤⣼⣿⣿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢻⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⠉⢀⣾⠟⢁⣿⣿⠃⠀⢻⣿⣇⠹⣿⣆⠈⠉⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣷⣿⣿⠏⠀⠀⠈⢿⣿⣷⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠃

⣀⡀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠢⢠⠀⢀⡀
⠛⠻⣿⣷⢶⣶⣚⠉⠀⠀⣀⠄⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠳⣄⣩⡟⠻⣿⣥⣦⣀⣀⣠⡤⣾⠖⠒⢲⠲⠧⢠⡀⢚⢃⠠⠄⢀⠀⠠
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⡷⠤⣀⣀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠊⠐⠆⠀⠐⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢋⡉⠓⣧⢤⣀⣉⠩⠉⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠖⣀⠽⣀⠀⠈⠐⢆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠛⠛⠛⠛⠛⠛⠛⢿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⠀⣶⠒⠒⢲⣶⡶⠶⠶⠶⠶⠶⣶⣦⠤⠤⠤⣤⣤⣄⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⡀⢹⠀⠀⢸⣟⡇⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⢸⠃⢀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⡟⡇⠸⡇⠀⢸⣯⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡾⠀⢸⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡾⠀⣸⡤⠷⠀⣧⠀⠈⣗⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⡇⠀⣿⣻⠀⢹
⠀⠀⠀⠀⠀⠀⢀⡇⠀⣁⡤⢤⠀⢸⡀⠀⡇⡇⠀⠀⠀⠀⠀⢿⢿⠀⠀⠀⠀⢸⠁⠀⠉⠉⢉⠚⡇
⠀⠀⠀⠀⠀⠀⢸⠁⢸⠇⠀⠘⡇⠘⡇⠀⡇⡇⠀⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⡿⠀⢸⠋⠉⣧⠀⢿
⠀⠀⠀⠀⠀⠀⡾⠀⣸⠀⠀⠀⣇⠀⣧⠀⣯⡇⠀⠀⠀⠀⠀⢸⢾⠀⠀⠀⢠⡇⠀⣿⠀⠀⢸⡄⢸⡄
⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⢻⠀⢹⠀⣿⣿⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⢸⠁⢀⡇⠀⠀⠈⡇⠈⣇
⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⢸⡀⢸⣶⢿⣿⣳⣄⣀⣀⣀⣸⣾⣄⠀⠀⣾⠀⢸⠃⠀⠀⠀⣷⠀⢻
⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⠘⡇⡐⠋⠈⠀⠀⠀⠀⠀⠈⣅⠉⠞⢻⡄⡇⠀⣼⠀⠀⠀⠀⢸⡀⢸⡄
⠀⠀⠀⠀⠀⡟⠀⡾⠀⠀⠀⠀⠀⣇⠀⣶⠶⠦⠤⣤⣀⣀⣁⣀⡤⠴⠋⢸⠇⠀⡏⠀⠀⠀⠀⠘⡇⠈⡇
⠀⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⢻⣤⠿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢠⡇⠀⠀⠀⠀⠀⣷⠀⢿
⠀⠀⠀⠀⠸⣥⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⢹⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠀⠀⠘⠦⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠛⠛⠛⠒⠒⠤⣀
⠀⠀⠀⠀⠀⢀⠤⠐⠒⠀⠀⠀⠒⠒⢤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀
⠀⠀⢀⠤⣊⠔⠂⢀⠤⠒⠁⠀⠀⠀⡘⠇⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⡠⢣⠎⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣀⣀⣀⡤⢤⠖⠂⠀⡀⠀⠀⠀⠀⣀⠀⠈
⠰⢠⠁⠀⠔⠀⠀⠀⠀⠀⠀⠀⡀⢀⡜⠀⢗⢄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠠⠍⣀⡀⠀⠛⢒⡪⠝⢇⣀⠠⠔⠊⢡⠸⡀⠄
⡇⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣠⠏⠀⠀⠀⠣⡑⠌⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠙⠆
⠇⠀⠀⠀⠀⠀⢀⡠⠒⣁⠔⠉⠁⠀⠀⠀⠀⠀⠙⠢⣹⣏⡃⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠
⢸⠀⢀⣀⡀⠬⠄⠒⠉⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠈⡇⡰⠀⣀⡀⣄⠀⠀⠰⢺⠀⠀⠀⢀⡤⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡟
⠀⢣⠸⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠋⢣⠀⡹⣄⢐⡇⠀⠐⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠏⢳
⠀⡖⣷⡄⠀⠀⠀⠛⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⢀⢾⢀⡸⠊⠑⢠⠉⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠐⠠⠒⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁
⠀⠐⢏⠛⣄⠀⠀⠀⠀⠀⠀⠑⠄⠠⠃⠀⠀⢀⠔⡩⠜⠊⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠁
⠀⠀⠀⠁⡟⡶⢤⣀⠀⠀⠀⠀⢀⣀⠠⠔⡸⢹⠉⢂⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣎⠙⢄⣉⠴⢲⣄⠉
⠀⠀⠀⠀⠇⢰⠈⡄⠈⠉⠉⢁⣟⡒⠒⡺⠐⢺⠀⠀⢳⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁⠀⠈⠱⠂⠷⠶⠋⠀⡓⠠⡀
⠀⠀⠀⠀⢇⠀⠀⢁⠀⠀⡠⠛⡌⠋⠛⠤⠐⠣⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠑⠠⠆⠀⡐⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠁⠰⠤⣺⣀⡀⠀⠀⠀⠀⠀⠀⢀⣃⢢⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣀⡰⠀⠀⠠⢾⣀⣀⣤⡀⠄⠠⠀⠀⠀⠉⠲⢤⠀⠐⠒⠒⠓⠠⢀⣀⣅⢠⡟⠈⢉⠫⡀⠀⠄⣿⣆⣑⣤⠴⠉⠒⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⢽⣦⣄⣀⡀⣈⡁⢀⠃⣀⠀⢀⣠⣀⣤⡤⠤⠛⠢⠀⠀⠀⠀⠀⠀⠈⠠⢤⠤⠶⠶⠶⠶⠞⢛⣛⣉⣉⣡⣤⣤⣤⣤⣤⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⢀⣁⣉⣁⣀⣀⣤⡤⠤⠖⢶⡒⠲⠮⠤⠤⠔⠒⠒⡞⠒⠶⠶⠷⠖⣒⡛⠺⠿⠿⢍⠉⠉⠉⠉⠉⢹⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠑⢤⠤⠀⠀⠐⠒⠒⢣⠀⠀⠀⠀⠘⡗⠤⣀⠀⠀⠀⠙⠲⡂⠤⢀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠐⢯⣉⠁⠀⠁⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠑⣤⠂⠀⠀⢡⡀⣀⣱⡤⠀⠄⠀⡦⠤⠄⢼⢸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣠⡀⣦⡀⠀⠀⠀⢀⣀⣀⡀⡤⠔⠒⡛⠒⠒⠀⠉⠉⠀⠁⢙⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⢰⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠩⡀⠈⠙⡁⠀⠀⠀⠷⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡆⠀⠨⣀⡀⣠⠃⢍⠢⢄⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡒⢄⠀⠀⠀⠀⠀⠙⢆⠉⢣⠀⠀⠀⢰⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⢒⠇⠀⠀⠈⠉⠈⠀⠀⠈⠂⢍⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠠⠀⠀⠀⠀⠀⠳⢤⣣⠀⠀⠈⠓⠁