⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣦⣀⣲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠒⣫⡴⢿⢁⣹⣧⣉⣠⣭⣀⡛⠭⠁⠶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣯⢇⡠⠀⠀⣾⣟⣡⣧⣼⣿⣴⡇⠉⠛⣿⡍⡙⢦⡀⠀⠙⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⢋⣴⠷⡧⣄⡶⣲⠏⣰⣿⣿⣿⣿⣾⣿⣷⡀⡟⣷⡵⢄⠻⣶⣄⠀⠑⠦⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠺⠊⣽⠟⢠⠋⢀⣼⠁⣠⣿⣿⣿⣿⣿⣿⡟⠛⠿⣆⣏⡙⢦⡉⠊⢝⠓⢦⣤⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⣠⡾⡿⣠⣇⠄⣸⣯⣴⢿⣿⣹⢧⣰⣤⡾⠃⠀⢀⠏⢿⣧⠀⠙⣆⠀⠁⠀⠉⠚⢞⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣼⣾⣽⠟⣡⢞⡝⡟⠿⣾⣯⠄⠈⠉⠁⠀⢀⡠⠋⠀⠈⡻⣍⣠⡹⣦⣄⠀⢈⣣⣀⢨⠙⠦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠚⣽⢻⡿⠋⠀⣰⡷⠚⣷⡟⣶⣿⣿⡟⠃⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢿⠀⠉⢹⡉⠉⣧⠈⠘⢷⣼⡍⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠚⡦⣾⠿⢛⣀⣴⡟⢠⢃⠜⣹⡿⢟⠽⢠⠄⠀⠀⠀⠈⠁⠀⠀⠀⠸⣀⣀⣼⣡⠀⢰⡕⠀⢻⡇⠸⡆⢿⣿⡸⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣴⣿⣯⣾⡇⢸⠆⣾⡋⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢻⣿⠃⠀⠀⠸⡀⠀⢱⠀⠸⣌⠟⡷⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⡫⠥⣻⢏⣼⣿⡾⣤⣿⣯⠽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣭⢿⣇⢠⠀⠀⠀⡄⠀⠈⡇⠀⢹⡄⣳⢌⢇⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⣤⢄⠴⢖⣻⣧⣎⢸⠧⣠⡄⠀⠀⠀⠈⠑⢦⣄⣀⣀⣰⡼⠛⢋⡉⠀⠈⠉⠉⡒⠄⢒⣶⠇⠀⢠⣸⣆⠈⣷⢿⡏⢳⠁⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠾⣗⠭⡯⢹⣿⢾⠀⡿⢗⠊⢿⡿⣒⠂⢸⠆⠀⠸⣟⡷⢒⠝⠰⣶⡶⢤⣄⣿⣿⠏⣻⠀⠀⣼⣿⠘⠂⣿⣿⣿⡸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢦⣧⠿⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢻⡇⠀⠀⠀⠛⠂⠈⠁⡌⠘⢠⣿⠀⢀⡤⡇⠀⠀⣩⣿⡏⠁⠂⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⣀⣠⡦⣿⠙⣿⣿⣯⠢⢄⡀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡁⠁⠸⣿⢦⠀⠀⢷⠠⣩⣉⡽⣍⣳⠶⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⣾⣏⣽⣁⠀⢹⣿⣿⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢢⠈⠑⠒⠂⠐⠒⠉⠀⠀⠀⢻⣾⠙⢷⣆⠀⠹⣧⣶⢾⠀⠒⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢂⠜⠛⠿⡄⣴⣟⡏⣿⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠶⠖⠂⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⡝⣮⠫⠙⢦⣙⢿⣿⣤⣿⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢀⡰⠀⣹⣿⣿⣿⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣷⣿⣆⠈⢲⡎⢻⣿⠿⢿⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣲⡵⡺⠛⣿⢁⣿⠻⣯⣿⡀⠀⠀⠰⠦⠄⢴⡒⢀⣀⣀⣤⣉⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⡿⠍⠃⣸⣿⠀⠰⣿⢶⣯⡤⣴⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⢒⣶⡟⠠⣞⣤⠿⣟⣿⣟⡛⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⢨⠛⠁⠀⠀⠀⠀⠀⢠⡾⣿⠿⠔⠂⣻⡉⢠⣼⣿⡄⠈⣻⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡋⢰⣷⠿⣯⡀⠻⠻⣷⠉⠄⢷⡀⠀⠀⠀⠀⠀⠁⠙⠂⠀⠉⠁⠀⠀⠀⠀⢀⡴⡿⡧⣾⡿⡀⠀⠘⡃⢀⣿⡿⠷⣾⡯⠟⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠁⡀⠈⣿⣇⣠⣿⠋⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⣿⠀⡇⢣⣸⣇⣸⡄⢠⣻⣿⣿⣿⣾⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠉⠉⢉⠀⠀⠀⠀⢀⠀⠹⣦⠀⠐⠄⣀⡀⣀⣀⣀⡤⠖⠋⠁⢠⠇⢷⣧⣼⣿⣿⣤⣍⣛⣍⣉⣣⡿⢛⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⢆⢀⠢⢀⠈⠆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡃⣺⣿⣿⢹⣿⡿⢿⣿⣏⣭⣼⢀⠎⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠅⠀⠀⠀⠘⡊⢻⣦⡀⠀⠀⠀⠀⢀⡤⠀⣼⣿⣡⠇⠹⣿⠣⡙⠛⠛⠋⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠊⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣂⠆⢄⠀⠠⡀⠠⠀⢳⠙⠲⠦⠴⠖⠋⠀⡼⠫⣿⠃⠀⠀⢟⢆⠐⠃⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠴⠊⠁⠀⠀⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠈⠄⠌⠁⠀⠘⠄⡀⠀⠱⠀⠀⠀⠀⠀⠞⠀⢸⡇⠀⠀⠀⠘⡎⢱⡀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀
⡴⠁⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠐⠀⠀⠆⠀⠀⢱⡀⠀⠀⡸⠀⠀⢸⠇⠀⠀⠀⢠⣻⡀⢹⡀⢂⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⡆⢢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⡀⠸⠀⣀⣀⡤⢖⡖⠁⢣⠀⢠⠃⠀⢀⡏⠀⠀⠀⠀⢸⡼⡇⠀⠇⠈⢇⠀⠀⠀⠀⠈⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡸⠰⢺⡟⢙⠃⠣⠖⣜⠙⢄⠀⡇⠘⠀⢀⡎⠀⠀⠀⠀⢀⣾⣷⠚⡾⠈⠢⡈⢦⠀⠀⠀⠀⠈⢆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠒⠒⠒⠠⢤⠤⢤⡀⠀⠘⠀⠀⢸⡏⠢⡀⠆⣁⠀⠠⠀⠠⠚⠓⢤⣜⠀⠀⠀⠀⣰⡯⣿⣧⠌⠑⢄⠀⢱⠆⠀⠀⠀⠀⠀⠀⢆⠀