⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣿⠁⠀⣀⡀⠤⠤⡀⠄⠤⠤⠀⡀⠂⠤⢀⣀⠀⠀⣿⢷⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⣾⣿⣿⠲⣉⠖⠨⣉⠔⢀⠀⠂⠀⠄⢀⠐⠀⠀⠀⠉⠢⣼⣿⡿⣜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡉⢹⣷⡟⢺⡿⢄⡃⠄⢠⠣⣜⠔⠁⠂⡈⠀⠄⠂⢀⠀⠁⠀⠀⠀⠀⠙⠧⢹⡞⣿⣐⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣓⠭⣿⣿⣷⣿⣣⢷⡘⢆⠡⢚⢤⠢⣍⡐⠀⠠⠈⠸⠀⠀⠐⠈⠀⠀⠄⠀⡀⠠⣿⣿⢹⢷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⢌⡳⣿⣿⣿⣿⣯⢷⡙⡎⠴⢩⡸⣳⡖⡡⠀⠐⢀⣻⣇⠌⠀⠠⠐⠀⠀⡀⠀⠄⢸⣿⣮⠳⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⡀⣟⣻⢿⣿⣿⣟⣮⣝⢮⣓⢧⣳⢿⢧⡁⠄⠂⠀⡟⢿⣆⡐⠀⠠⠀⠂⠀⡀⠄⠺⣽⣿⡑⠌⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⢸⢧⢻⣼⣿⣿⣿⢾⣽⣳⣝⡞⠁⢸⡷⣈⠆⠀⠂⡇⠈⠻⣷⣭⢖⠢⠀⠁⢀⠀⡱⣻⣿⡇⠈⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡀⣿⢎⠲⣿⣿⣿⣿⡿⣷⣛⡞⠉⠒⢌⡷⣥⢊⠄⠐⡇⠠⠔⠛⣿⣿⡱⢈⠀⠄⠠⡱⣿⣽⣿⠀⠠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢸⣧⢏⡳⣿⣿⣿⣿⣿⣳⡟⠀⠀⠀⠀⢹⡧⣏⡒⢀⡇⠀⠀⠀⠈⢿⣿⣆⠂⡌⣐⢳⣿⣟⣿⡆⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡑⠠⠁⣿⢧⣏⣼⣿⣿⣿⣿⣳⡿⣰⠟⠛⢲⡄⠀⢻⣧⣛⠤⡇⢠⠶⠓⠲⡄⠹⣿⣇⢲⣡⢻⣯⣿⢿⣷⠀⠀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⡈⠄⣼⣟⡳⢮⠼⢿⣿⣿⣿⣳⣧⠹⣄⣀⣰⠇⠀⠀⠙⠿⣧⣃⠹⣄⡀⣠⠇⠀⢻⣿⣳⡜⡿⣿⣽⣿⣿⡆⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⡑⢈⢰⣿⢞⡽⢣⠇⠸⣿⣿⣷⣿⣿⣆⣉⡉⠁⠀⠀⠀⠀⠀⠉⠻⠀⠈⠉⡁⠀⠀⣼⢚⣷⣿⠃⢹⡷⣿⣿⣿⡄⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠄⢢⣿⣛⣮⡝⣽⠀⠀⢹⣿⣿⣿⣿⠀⣒⢋⡆⠀⢰⣤⢤⢤⣠⠀⠀⢰⢒⢢⠡⣨⢧⣫⣿⠃⠀⠘⣿⢿⣿⣿⣷⠀⠀⠄⠐⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⣈⠁⣀⣾⣯⢟⡶⣙⡆⠀⠀⠀⠙⣿⣧⡙⢷⣤⣶⣗⡦⣿⣞⣯⢾⡽⡀⠀⠀⣓⣤⡾⣏⡞⠉⠁⠀⠀⠀⣿⡿⣿⣿⣿⣧⠀⢀⠂⠱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⡓⠄⠀⣼⣟⡾⣝⠾⣱⠃⠀⠀⠀⠀⠈⠻⣹⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡷⢿⠹⣿⣱⡙⡊⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⣿⣿⡆⠀⠠⠀⢃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡿⠠⠈⢠⣿⡻⣾⣋⠿⣃⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠿⢿⣷⠄⢈⣡⢠⠀⢀⢌⠈⠀⠈⠉⠸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠠⠀⠈⡀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⡅⠃⠀⣼⢷⡻⣵⢫⡳⢭⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠀⣼⢃⠻⣦⠊⠑⢣⠀⠘⢆⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣾⣿⣿⣿⣿⡆⠁⡀⠁⢱⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡆⠀⢡⡟⢧⣛⡼⢣⣝⢣⡆⠀⠀⠀⠀⠀⣀⣼⠁⣀⣴⣏⠢⠐⣿⠄⠠⣏⠐⢂⠘⡄⠈⠓⡀⠀⠀⠀⠀⠀⠀⣯⢷⡿⣿⣿⣿⣿⣿⠀⠀⠌⢀⢃⠀⠀
⠀⠀⠀⣾⣿⣿⠁⠀⢸⢏⡳⡜⣜⢣⢎⠧⡇⠀⠀⢀⣤⣾⣿⣿⣷⠞⢸⣿⢠⢃⡇⠀⡀⢡⠉⠉⠀⣷⣀⣴⣷⡀⠀⠀⠀⠀⠀⣯⢟⡽⣯⣿⣿⣿⣿⡄⢃⠀⢂⠘⡄⠀
⠀⠀⢸⣿⣿⣿⠀⠀⡺⢌⠳⡩⢌⠣⢎⣜⣇⢴⣾⣟⣿⣿⣿⡿⠁⠀⣿⣿⣎⢿⠁⠄⠀⡘⡁⠀⠀⡇⢿⣿⣿⣷⣄⠀⠀⠀⠀⣧⠻⣜⢷⣻⢾⡿⣿⡗⣌⢒⠠⠌⣰
⠀⠀⣿⣿⣿⣿⡀⠀⠳⢌⢣⡑⢎⡱⢊⡝⣾⣿⣾⣿⣿⡿⠋⠀⠀⢠⣿⡗⢮⡟⠻⠀⠂⠀⠇⠀⠀⢰⠘⣿⣿⣟⣽⣷⣄⠀⢰⢂⠯⡜⣡⠏⣭⢹⣹⣟⡼⡆⡘⠰⡠
⠀⠀⣿⣿⣿⣿⡇⠀⢩⣘⣢⠜⠬⠖⠛⣋⢨⢿⣿⡿⠋⠀⠀⠀⢀⣾⡿⣙⢲⡃⠠⠐⠀⠁⢸⠄⠀⠀⢣⠘⣿⣿⣿⣷⣽⣷⣼⠘⢪⡕⣣⠞⡴⢣⣿⣟⡾⡅⢎⠥⡱
⠀⠀⢻⣿⠷⡈⡿⠈⠉⠀⢀⣀⣤⡴⢾⡷⡎⠉⠋⠀⠀⠀⠀⠀⣾⣿⡰⠁⠂⠉⡲⢄⡬⡂⠁⠀⠀⢀⣤⡆⠸⣿⣿⣿⡏⢁⢝⡬⢡⠘⣥⠻⣍⢷⣻⣾⡿⡜⣬⢳⣽
⢀⣄⠂⠁⡀⠙⣀⣤⠴⡚⠭⠓⡜⡸⢱⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⢼⣽⣿⣿⣯⠦⢀⣴⣵⣮⡻⣄⠙⠿⠉⠉⠉⠁⠀⣇⠚⡤⢛⣬⢳⣟⣿⣿⣿⣼⣻⠆
⠈⢿⠧⠷⠾⣿⣿⢌⡣⢘⠠⠁⠌⢡⡛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢬⣉⣉⡙⠛⠛⠻⠛⠛⠛⠚⢋⣉⡠⠘⠙⠂⠀⠀⠀⠀⠀⠀⢡⡹⣰⢋⡾⣽⣾⣿⣿⣿⡾⠃⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢷⣌⠣⢌⠡⠌⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣈⡏⠉⠉⣿⣉⣀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣱⢯⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠦⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣶⣶⠃⠀⠀⣿⣿⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣼⣿⠀⠀⠀⢻⣿⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡿⠀⠀⠀⢸⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡇⠀⠀⠀⠈⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀