⠀⠀⠀⢠⡏⡜⠀⣇⠈⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢪⣝⡣⣄⣠⠇⠘⡎⣷⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⡇⠀⠘⡖⠒⠒⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠓⠛⠳⣝⢦⡀⢷⢹⡆⠀⠀⠀⠀
⠀⠀⠀⣿⡴⡇⠀⠀⠙⡄⠀⠀⠀⠙⠳⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤⠤⢫⠿⠖⢶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠁⠀⠀⠀⣰⠁⠳⡝⢎⢸⡇⠀⠀
⠀⠀⠀⣿⠀⡇⠀⡤⠞⠙⢆⠀⠀⠀⠀⠙⢮⡉⠛⢳⣶⡴⠞⠛⠉⠉⠀⠀⠀⢈⣀⠀⠀⣀⡁⠀⠀⠀⠉⠉⠛⠷⣦⣤⠶⠞⢛⡽⠋⠀⠀⠀⠀⡴⠉⠧⢤⠘⣎⢣⡇⠀⠀
⠀⠀⠀⣿⠀⣇⡔⠁⠀⢸⡉⠳⡄⠀⠀⠀⠀⣹⡾⠛⠁⠀⠀⠀⠀⠀⣠⠴⢊⡵⢒⢷⠞⠒⠚⠑⠦⡀⠀⠀⠀⠀⠀⠉⠻⣶⣏⠀⠀⠀⠀⢀⡾⢛⡆⠀⠘⢦⡸⡌⣇⠀⠀
⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢧⠀⠈⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣠⣞⡡⢚⠏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠋⠀⡼⠀⠀⠀⠀⡇⢧⢸⠀⠀⠀⠀
⠀⠀⠀⢸⡄⣯⠀⠀⠀⠀⠈⢧⡀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⠂⡼⢡⠟⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢀⡼⠁⠀⠀⠀⠀⡽⢸⢸⠀⠀⠀⠀
⠀⠀⣦⡸⣧⠃⠀⠀⠀⠀⠀⣏⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⡇⡏⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣳⠀⠀⠀⠀⠀⢹⣼⢸⣤⠀⠀⠀
⠀⠀⣿⠙⢿⣆⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠻⠄⠀⠀⢳⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣰⡟⡼⣿⠀⠀⠀
⠀⠀⠘⢷⡀⠈⣆⣀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠻⡑⠷⢄⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣰⣹⢳⣿⠃⠀⠀⠀
⠀⠀⣤⠤⠟⠃⠀⠈⠲⣾⠃⠀⠀⠀⠀⢀⠎⢀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣉⣒⣢⠄⠀⠀⠀⣿⠀⠀⡠⢲⠿⠛⣇⠀⠀⠀⠀⠈⢿⡴⠉⡰⡳⠯⠥⣤⠀⠀
⠀⠀⠈⠓⠶⠤⠶⡆⢸⡏⠀⠀⠀⠀⠀⡎⠀⢸⣀⣤⣴⣶⣾⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣶⣶⣧⣯⣸⡇⠘⡄⠀⠀⠀⠀⠘⣷⣾⡿⠥⠴⠞⠉⠀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⣸⡴⠞⢻⣏⠉⠁⠀⠘⣷⡸⡄⠀⣤⠀⠀⠀⠀⠀⡛⡤⡀⠀⠀⠀⠀⡜⢸⠀⡾⡹⣝⢯⠻⡶⣽⡀⠀⠀⣀⣴⢿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠞⢻⡇⠀⠀⠀⠀⢾⡏⠀⠀⠈⡟⡄⠀⠀⠀⢳⡱⡙⣄⢇⠳⣄⢸⠳⣄⣇⠈⢿⣦⣀⣠⣼⢡⣇⠔⠡⠗⡟⡷⠻⠾⠧⡿⠶⠛⠋⠀⠈⣿⠲⣄⡀⠀⠀
⣀⣠⠤⠴⠚⠁⠀⣿⠁⠀⠀⠀⠀⢸⢣⠀⢀⣤⣷⣾⡿⣿⣷⣶⣷⣝⣌⠘⢆⠈⠛⢦⠀⠙⠒⠦⢌⣓⢶⣷⣿⣷⣶⣶⣾⣤⣇⡀⠀⣠⢿⠀⠀⠀⠀⠀⢻⡆⠈⠙⢲
⠀⢤⣀⣀⠀⠀⢠⣿⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⡿⣿⡋⢙⣿⣿⣿⣷⠑⢬⣣⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡁⣻⣿⢿⣿⣿⣿⣿⣟⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⢀⣠⣷⣿⣿⣿⠟⣡⠞⢉⣿⣻⣿⣿⣎⠁⠀⠀⠈⠉⠓⠒⠒⠒⠊⠉⠈⢩⣾⣿⣧⣿⡉⠳⣌⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⢸⡷⣄⠀⠢
⠛⠒⣲⡶⠞⠁⠀⣿⠀⠀⡄⠸⣿⣿⣿⣿⠁⢰⣛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⡆⢨⣿⣿⣿⡿⠋⠀⠀⠀⣸⠧⣈⠻⣶⡶
⠖⠋⠁⠀⣀⣠⠴⢿⠀⢠⠸⡄⠈⢹⣿⡿⠀⢸⡟⣙⠻⢿⡛⡽⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣍⢻⠛⡻⠟⠋⢹⡗⠈⠿⠟⡞⠀⢀⡄⢠⠀⣿⠦⣌⣑⠒⠙
⠛⠛⠛⠉⠉⣿⠀⢸⡇⠘⡄⢳⢠⠀⢧⠀⠀⠘⠓⠧⡣⣀⣈⡀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢿⢆⣉⣀⡀⡠⠘⠋⠀⠀⡸⠁⡄⡜⢀⠇⢰⡏⢠⡏⠉⠙⠓
⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⢱⠀⢧⠳⡀⠳⣄⠀⠈⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠰⠋⠀⢀⡴⠁⠼⠑⡱⡟⣤⣿⠃⠈⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢣⢈⡃⠙⢤⡈⠳⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣖⢉⣀⡠⠞⣋⣰⢹⠙⣿⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡏⠀⣰⡟⣠⣶⣤⣀⠙⠶⣦⡬⠽⠦⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣤⡶⢞⣵⣣⣾⡀⢿⠀⠀⢹⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣼⠃⠚⠛⢛⡟⢰⠋⠉⠙⡟⠛⢿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢻⢻⠋⢯⠈⣿⢾⣷⡄⠈⣷⠀⠀⠀⠀
⠀⠀⠀⣰⠇⠀⢀⡞⡼⠁⣾⠀⠀⠀⡇⠀⠀⡩⠛⠻⢶⣦⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣴⡶⠟⠋⣤⠀⠸⡌⣇⡘⣆⠘⢆⠸⡄⠀⠘⣧⠀
⠀⠀⣴⠏⠀⢠⣞⡞⢁⡼⡏⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀⠈⠉⠉⠉⣩⣽⣿⣶⣶⡶⢶⣒⣶⣿⣿⣿⣭⠉⠉⠉⠉⠀⠀⠀⠸⡸⡆⠀⡇⢱⡇⠸⡷⣌⡳⡹⣄⠀⠘⢷
⣴⠟⠁⠀⣰⣿⣫⠴⠋⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⣀⣤⣤⣶⣶⣶⣾⣧⠈⠙⢻⡟⣻⢿⡟⠛⡇⡏⠁⢸⣷⣶⣶⣦⣤⣄⡀⠀⡇⢷⠀⡇⠈⣇⡄⡇⠀⠉⢻⠻⣧⡀
⠤⠤⠴⣾⡟⠉⠀⠀⠀⡄⣇⠀⡀⠀⢷⠀⠀⣰⡾⠛⠉⣸⠀⠀⠀⠈⢹⠦⣄⣸⣿⣟⢷⣋⣀⣇⣧⣞⢫⠀⠀⠀⠐⡏⠙⢻⣦⠀⠸⣾⠁⠀⣿⣷⢷⠀⠀⠘⠄⠘⣿⠷⠶⠶⠞⠀⠀⣸⡟⠀⠀⠀⠀⠰⠁⢹⠀⢣⢀⠸⡄⣸⡟⠁⠀⡰⠃⠀⠀⠀⠀⡼⠖⠉⠈⠉⠉⠉⠉⢹⢛⣛⡮⠙⣆⠀⠀⠀⠹⡀⠀⢻⣇⠀⡟⠀⢰⣯⣿⠈⢧⠀⠀⠀⠀
⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠘⡇⣲⡘⣆⠻⡿⠕⠒⠋⠀⡴⠀⠀⣀⠜⠁⠀⠀⢀⡤⠊⡉⡑⠺⠁⠈⡇⠀⠈⢦⡀⠀⢰⠙⢦⣸⣿⡜⢠⢀⣿⣸⡏⠀⠀⠃⠀⠀⠀⠀⢹
⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠳⣌⢢⡙⣄⠀⢀⣰⠗⠒⠊⠁⠀⠀⢀⡴⠋⠀⠀⢷⠃⠀⡇⢸⣧⡀⠀⠀⠈⠑⠚⣇⠀⣠⠞⣠⢣⡾⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⠛⠛⠚⣳⣻⡏⠀⠀⠀⠀⠀⢠⣋⠀⠀⠀⠀⢸⠀⠀⣿⣿⡇⠑⠀⠀⠀⠀⠀⢹⣟⠓⠺⠷⣏⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡰⠃⣿⡴⡆⠀⢀⡄⠀⠀⠀⠙⠢⣀⠀⠀⠀⢐⡿⠿⡇⠀⠀⢀⡀⠀⢰⢦⣿⠀⠀⠀⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧