⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⢛⠛⠛⠻⠿⢿⣉⡛⠻⢿⣿⣿⣷⣄⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣄⠀⠀⠀⠀⠉⠑⠢⢌⡛⢿⣿⣿⣦⡏⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡻⣿⣿⣷⡄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠙⠋⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⡈⠐⠠⡀⠀⠀⠀⠀⠀⠈⠺⣽⣿⣿⠖⣄⠑⡤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⢣⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠘⣿⣷⡀⠈⠢⡀⠀⠑⠤⣀⠀⠀⠀⠐⢌⢻⣇⡠⠟⠊⢰⠓⢄⣀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢁⠃⡆⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡐⣿⡟⠀⠀⠀⠐⡄⠀⠀⠈⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⡸⢊⡽⡫⠍⠩⠭⡺
⣖⢀⠀⠀⢠⣿⣿⣿⣿⠋⠔⢺⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢏⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⢴⣿⠋⣠⠖⠒⠲⣌
⡏⣿⣷⠀⣾⣿⣿⡿⢁⠄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠢⣧⡀⠀⠀⠀⠀⢈⢳⠤⠤⠀⣠⡄⢠⠤⠤⠒⠊⠙⢿⣿⡼⢁⡤⠤⢄⡈
⡇⠩⢁⢼⣿⣿⡿⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡈⠉⠀⠀⠈⠳⡀⡀⠀⠠⢸⠣⢃⠀⠀⠁⠀⠀⠈⠀⠄⡀⠀⠈⠻⣟⢞⠀⠀⣀⡱
⣡⢡⠎⣿⣿⣿⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⡽⣿⣿⣿⣮⠳⠀⠀⠀⠀⢳⡇⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⠀⠁⠂⠈⠐⣦⣀⢸⠈⣆⠀⢀⡞
⢡⠃⠀⣿⣿⡏⢰⠀⠀⠀⠀⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠸⣜⢻⢹⠉⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠀⠋⠉⠀⠀
⠛⡆⣄⣿⡿⠁⠀⢀⠀⠀⠀⠇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠒⠒⢶⠗⠁⡸⠀⠀⠀⠀⠀⠴⠗⢷⠀⡸⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠠⠒⠁⠀⠀⠀⠀⠀⣸
⡷⣼⣹⣿⠃⠀⠀⠙⢁⡄⢠⠀⠀⡹⡀⠀⠀⠀⠀⠀⣀⡀⠤⠍⠉⠁⠀⣀⡤⣾⣅⠀⠀⠀⢠⠆⠀⠀⡸⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠏
⠀⠈⠻⡿⠀⠀⠀⠀⠘⣷⡈⣆⠀⠃⢹⠀⠹⣶⣶⣿⣾⣭⣛⠃⠀⠀⠉⠈⠙⠻⠮⣷⣤⣀⡜⠘⡆⠁⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠌⠓⠶
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⣿⣿⣶⣼⡆⠁⢉⡻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠾⢤⣀⣀⣀⣀⣤⣤⣒⣲⣍⣓⠲⠂⠀⠀⠀⠀⠀⢀⣠⣴⡦⠤⠖⢒⡯
⠀⠀⠀⡇⡄⠀⠀⠀⠀⢸⡀⠹⠿⠿⠟⠘⣄⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⡩⠟⠛⢒⣿⣶⣿⣿⠙⡏⡍⠖⠒⠒⠊⠉⡏⠈⢿⣿⡿⠛⠻⠾
⠀⠀⠀⣧⠃⠀⠀⠀⠀⠏⡇⠀⠀⠀⠀⠀⠘⣦⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠫⡹⣄⠀⠀⠀⠀⡎⣀⣴⣾⣿⣷⠿⠿⢿⠇⣱⠀⠀⠀⠀⠀⠀⢃⠀⢸⡁⠀⠀⠀⠀
⠀⠀⠀⢸⠈⡄⠀⠀⡘⠀⠱⠀⠀⠀⠀⠀⠀⢿⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠰⠋⠀⠈⠿⣿⣇⠀⢀⠜⠔⠂⡇⠀⠀⠀⠀⠀⡎⡆⠀⢣⠀⠀⠀⠀
⠀⢀⢀⣸⠀⠀⢄⣰⠀⠀⠀⢣⠀⠀⠀⠐⢄⠘⣆⡠⠞⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢒⡲⠂⠀⠀⠈⠉⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⢠⠿⡇⠀⠈⡆⠀⠀⠀
⠀⢔⣄⠔⢀⡠⢼⢹⠤⣀⠀⠸⠀⠀⠀⠀⠀⠑⢿⡀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⢀⡨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⠄⠀⠀⠀⢀⠎⢰⠃⠀⠀⢸⠀⠀⠀
⠤⠚⠋⠉⠀⠀⠈⡌⡆⠈⠀⠀⢇⢻⠦⡀⠀⠀⠀⠩⣖⢶⡖⠉⣁⡨⢿⣽⣀⠹⣖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠎⠀⠀⠀⢀⠮⠴⠃⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⣳⠀⢠⠀⠈⠪⣆⠈⢲⠠⢄⣀⣮⢣⣶⣾⣿⣿⠟⠋⢻⡉⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡴⠋⠀⢀⠤⡆⡎⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢇⢸⢣⠀⠀⠈⠛⠦⣥⡀⠐⠛⢟⠯⠁⠙⠿⢦⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⡰⠋⠀⠀⠙⠃⠀⠀⠀⠀⡄⢰⢁⣠⠔⠒
⠀⠀⢠⠳⡀⠀⠀⠀⢸⠈⢢⢃⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣸⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡔⠁⡔⠀⠀⠀⠀⠀⠀⠀⣰⣵⡋⣹⠃⠀⠀
⠀⠂⣸⡀⠙⠖⠠⢤⠏⠀⠀⢙⢟⣯⣦⡀⠀⠀⠀⠀⠀⠐⢠⢔⣝⣦⣄⣀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⡞⠀⠌⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢳⣿⠀⠀⠀
⠀⠀⠙⢗⡀⠀⠄⠊⣀⡠⠔⠋⠀⠸⡀⢿⢦⣀⠀⠐⠒⠈⠐⠉⠀⠀⠀⢀⡼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢤⠁⡌⠀⠀⠀⠀⠀⠀⡰⠋⠀⠠⠀⣸⣿⡀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⡋⠉⠱⡘⡌⠑⢭⡒⠠⠤⠄⣠⣔⠒⠒⠁⠉⠓⠦⠤⣤⣤⣤⠤⠴⢲⡖⠒⠋⠁⢙⣾⡀⠀⠀⠀⠀⢀⠀⣰⣷⣿⢿⡆⠀⠀⠻⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢄⠀⠈⠑⠤⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⠞⠶⣾⠒⣶⠋⢀⢣⠀⠀⠀⢠⡟⢀⣿⣽⣛⠀⠡⠄⠠⠀⣷⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠤⣤⡤⠤⠌⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⡀⠘⠤⢧⣤⣶⣾⣇⠀⠀⠛⣇⠸⡏⠙⢮⠹⢿⣿⣿⣿⣁⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⣸⠟⠋⠋⠙⣆⠀⠀⠈⠂⢿⡄⠈⠳⣄⠁⢹⡿⢋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠈⠆⢿⣀⣀⣀⣈⡿⡗⢤⡀⠀⠀⠙⠢⡀⠈⢳⣼⣵⣾⣿⣿