⠀⠀⢸⡇⣼⠂⡇⡞⣰⠃⠐⡟⡸⣿⠀⠻⣼⠏⠀⠀⠀⠀⠀⠀⠀⣠⢏⡾⣪⠟⠁⠀⠀⠀⠻⣷⡄⠙⢦⠀⠀⠀⠁⠀⠀⠀⠈⢿⣆⡼⠟⢽⡇⣇⡇⠇⣇⠀⠀⢸⠘⣸⠀
⠀⠀⢸⣷⡏⠀⡇⢷⠃⣴⣾⡇⡇⡿⡄⣼⠯⡛⠁⢀⠀⠀⠀⠀⣰⣟⢞⠝⠁⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠳⡀⠀⠀⠀⠀⠀⡀⣨⣿⣄⠀⡻⡼⡸⣿⢸⢻⠀⠀⠸⠀⢻⠀
⢠⢾⣼⣟⡾⠘⢹⠏⣸⣹⣿⠇⡇⠹⣯⡟⠀⠘⠣⣼⠠⣀⡀⣼⣿⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢳⠀⠀⠀⠀⢄⠹⣆⠙⢿⣴⡵⢁⢿⢿⢸⢾⠀⠀⡇⠀⣼
⢸⢀⣷⢿⠁⠀⢸⠀⡇⣿⣿⣾⣧⢰⣹⠃⠀⠀⢀⡇⠑⠄⡴⢻⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣣⣀⣧⢀⡠⡎⠈⢆⠘⢇⠘⣵⣀⢞⣾⣿⢸⡜⢰⢠⡇⠀⣿
⠸⣮⣿⣧⠀⠀⢸⠀⠀⢻⣿⣏⣿⣌⡟⠀⠀⠀⢸⠀⠀⣼⠁⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣷⡝⣇⠈⢣⠀⠈⠀⠈⣆⢫⣎⢾⣯⢿⡸⣷⠈⣸⢠⠀⣿⢻
⣸⣾⣿⢹⡄⠠⢸⠀⠀⡏⣿⡼⡼⣾⠃⠀⢀⣠⡯⠒⣾⢫⢷⣮⠇⠀⠈⠙⠶⠀⠀⠀⠀⠀⠀⠶⠋⠁⠀⠀⠘⡽⡽⡍⠒⣦⢄⡀⠀⠘⡞⣵⡿⡸⣿⣷⡝⢠⠏⡎⢠
⣻⣿⣿⠘⣷⡀⢾⠀⠀⣧⢻⡇⢳⡿⡠⠒⠉⢠⡇⣰⢧⠋⣾⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⣷⡀⠨⡆⠈⠑⢤⣹⢟⡴⢱⡟⡜⣇⣾⠸⠁⡜⢳
⠇⣏⣿⡆⢇⢣⣸⠀⠀⣿⣸⣻⢰⡏⠀⠀⠀⢸⣇⣏⠏⠀⣏⡇⠒⠶⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠶⠒⠀⠀⠹⡜⢧⠀⣷⠀⠀⠀⠈⢸⣇⣾⢳⢡⣻⣏⠄⣰⠃⢈
⠀⠁⠁⢳⢸⣇⢻⡄⠀⣯⣿⣿⣾⡇⠀⠀⠀⡸⡿⡞⠀⢰⠳⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⡜⣇⢹⡇⠀⠀⠀⠘⣏⣾⡃⢀⣯⣻⢠⣏⢄⣼⢻
⡀⠀⠀⠈⡏⢸⢸⡇⡆⣹⠽⣿⣿⠀⠀⠀⠀⣇⢷⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠙⡾⣷⠀⠀⠀⠀⣿⣬⣧⣸⠻⡇⡼⠀⢨⠏⠈⢳
⡇⠀⠀⢰⠃⠸⣸⢇⠃⣧⢶⢮⣯⢀⣀⣀⣀⣿⣬⣤⣤⣿⣭⣉⡻⢦⡀⠀⠀⠉⠀⠀⣀⠤⣀⠤⣂⢤⡴⠟⣋⣭⣭⣥⣤⣧⣼⣷⣀⣀⣰⠀⢻⠉⣽⣿⠈⢥⢇⡰⠛
⢧⠀⠀⣾⡀⠀⢸⣞⢤⣿⠸⣾⣿⠀⠈⠩⠽⡟⠣⠽⣿⡿⠿⠿⣿⡷⢯⠒⢋⡡⣔⠬⣓⠭⠒⣉⠤⡴⠾⣻⠿⠿⢭⣽⢿⡤⡟⠿⡍⠁⠀⠀⢸⣷⣿⢸⠀⢸⠋⢠⠃
⠣⣷⣄⣹⡠⣴⠿⠚⠁⣿⣒⣻⠈⠀⠀⠀⣀⠧⢒⡩⢼⣏⠥⠒⢉⡠⢔⡪⢗⡩⠖⣉⡤⠒⣉⠤⢒⡩⠔⢋⣁⠤⠒⠉⠁⣀⠼⡔⢗⣀⡠⠔⢺⡏⠀⠩⢶⣼⣄⡀
⢀⡧⡶⠝⠉⠀⠀⠀⠀⠘⣵⣀⡀⣀⠀⠉⠤⢚⡡⢔⡿⢀⠤⢒⠭⢊⠥⠚⣡⠔⢊⣡⠴⣫⠕⠊⣁⠤⠒⠉⠀⣀⠤⠒⠉⣀⠤⢗⢹⣁⠤⡆⢸⡇⠀⠀⠀⠈⠉⠛⢶
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⡇⡆⠀⠈⡇⢀⣾⢋⠥⢊⡥⠚⣡⠔⢋⡠⢶⡋⠁⠀⠈⢑⡍⠀⢀⡠⠔⠋⢁⡠⠔⠊⣁⠤⠺⣹⠤⠒⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⠀⣿⢳⣡⠀⠀⣧⡮⠛⠡⠚⣁⠔⢋⡠⠖⠭⠊⠁⣬⡯⡖⠉⠉⠐⠊⠁⠀⠀⠚⠁⣠⠔⢊⡡⠔⣺⣽⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⣏⠏⣿⢀⡀⡿⠁⠀⠀⠀⠁⠐⠉⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡰⡽⢹⠀⠀⠀⣆⡇⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⡜⠀⢏⠘⣇⣿⣆⠀⢀⢇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱⡝⠀⢸⠀⠀⠀⢻⣼⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⠀⢸⠀⢻⣸⠳⣷⡀⠛⠀⠘⡆⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣠⠞⠁⣜⠟⠁⠀⡸⠀⠀⠀⢸⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣹⠀⠀⠀⠐⡍⣆⡈⣯⣦⡀⠀⠈⠀⠀⡠⠋⠉⠈⠉⠒⠒⠒⠉⠉⠑⢾⡁⠠⡏⠀⣮⢿⠤⠔⢊⡇⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⢡⠋⡆⠀⠀⠀⠸⣱⢹⣿⠻⣷⣄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⡔⠁⡜⡀⠀⡸⢀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿⠀⠀⢃⠀⠠⡀⠀⡷⣿⡇⠀⠀⠳⣿⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠏⠀⠀⡇⡇⢰⣟⠇⠀⠀⠀⣧⢧⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⠀⡸⡀⠸⣧⡆⢸⢹⣧⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣧⣧⢣⣽⡎⠀⢀⢺⣟⠎⠀⠀⠀⢠⣼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⢷⢠⠀⠇⢟⡄⢫⣞⡄⣿⡟⣷⣄⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠏⣾⣽⡀⠀⢸⢏⢎⡀⠀⢀⣠⣼⠃⣠⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠘⢦⣀⠸⣸⡜⣌⢞⡵⡘⣅⠈⠻⣯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⡟⠀⡱⢹⡇⢀⣴⣻⣽⣿⢃⣾⢿⡿⣾⣫⣷⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠉⠛⠱⡽⡌⢮⢷⡘⢷⠙⠦⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣿⠀⢠⣃⢸⡇⢈⠏⣿⣷⣿⣿⢿⣿⡟⠛⠛⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢇⠀⠀⠀⠘⢿⣦⣍⢷⡈⢧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⢠⣿⢸⢸⡇⢸⠀⠘⢋⣿⡇⠀⠘⠃⠀⠀⠀⠀⢀⡞⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⡀⠀⠀⠀⠀⠉⢹⡟⢿⣮⡣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⢿⡇⣾⣿⢸⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⢸⡇⠀⠙⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣃⣼⡇⠘⢿⣾⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⡠⡔⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⣿⡇⠀⠀⢹⢧⢸⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣼⢰⢹⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣠⡳⠁⣧⠀⠀⠞⠘⡿⣀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡘⢎⢆⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀