⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡻⣝⢯⡻⣽⣏⢿⡹⣏⢿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢽⡞⣭⢷⣻⢮⢯⣽⡹⣞⡵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣹⣟⣿⠆⠀⠀⠀⠀⠀⢸⣲⣾⣺⣿⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣞⡧⢿⣹⡞⣽⣟⣮⢳⡽⣣⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡧⣉⢽⡟⢻⠆⠀⠀⠀⠀⠀⢸⣿⠈⣿⢳⣟⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡼⣏⣷⣹⣻⡷⣚⣯⣳⠽⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⡩⢾⡇⢸⣃⡀⠀⠀⠀⠀⢸⣿⠀⣿⠘⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡼⣝⡶⣻⣼⡿⣹⡖⣯⢻⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⣱⢻⡇⢸⣟⣿⠀⢸⣿⣿⣿⣿⠀⣿⠀⢿⡆⢹⡄⠀⠀⠶⣤⠤⢄⡀⢀⣤⢶⣠⣴⠶⠂⠀⢼⣻⡵⣻⣼⢳⣽⡟⣵⣫⡽⣳⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠶⣹⡇⢸⡧⢼⣩⣹⣛⣞⣻⣿⠀⣿⠀⢸⣧⠈⣧⠀⢀⣀⣤⡿⣾⣱⣼⣿⣾⣿⣶⣤⣀⠀⢸⡷⣝⣳⢾⣹⢾⣟⡵⣳⡽⣣⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣶⠀⠀⢸⣿⣿⡏⠳⣹⡇⢸⡇⢸⠚⢸⣿⣿⣿⣿⠀⣿⠀⠀⢿⡄⢻⡆⠀⡼⣿⣮⡿⣿⣽⣿⡿⣷⣿⡿⢆⠀⢹⣟⣮⠽⣞⢧⣿⡯⣞⣳⡽⣳⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣄⠀⠀⠀⢀⣱⣤⢾⢣⢠⣟⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣽⡄⠀⢸⣿⣿⡗⠂⠺⣧⣼⣗⣻⠀⢸⣿⣿⣿⣯⠀⣿⠀⠀⢸⣧⣸⣧⢼⠋⢰⣿⣣⣾⣿⣿⣦⣸⣿⠀⠹⡆⣾⣳⢞⣯⠽⣞⢾⣟⡵⣏⡾⣵⣫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠷⣤⣤⡈⣑⣢⠼⠛⠛⡞⡇⢸⠛⠛⠗⢿⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢛⣹⡏⢏⣆⢸⣿⣿⣇⣶⣸⣯⣿⣧⣾⠀⢸⠿⠟⢿⣷⣀⣿⠀⠀⠀⢿⣉⣿⡆⠀⠀⢿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⢹⣧⡟⣮⢟⣭⢿⣏⡾⣝⡾⣱⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡞⠁⠀⠀⢰⢳⢃⣨⠇⡀⠀⠀⠘⢷⣠⠀⠀⠀⠀⠀⠀⣿⣧⣂⠒⡌⢆⣼⣿⠁⠁⠈⠀⠉⠀⠁⠀⢹⣶⣾⣿⢽⣿⣛⣛⣻⠀⠀⠀⠸⣯⣵⣷⡀⠀⠸⣿⣿⣻⣾⡿⣿⠃⠀⠀⠀⢸⡷⣽⣚⢯⣞⣻⣯⢞⣳⡽⣳⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡄⠀⢀⣦⠘⠿⡸⠀⠢⠀⢤⠤⢱⣼⣟⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣸⣟⢶⣫⢟⡼⣽⡷⣫⢷⣹⢧⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣰⢁⠞⠁⠀⠁⢀⡴⡿⠟⢛⣿⣿⡿⣧⠈⠀⠀⠀⢹⠿⠽⠾⣯⣷⡿⠽⠾⠯⠿⠾⠽⠷⠯⠿⠾⠽⠷⠯⠿⠾⠯⠿⠾⠽⠷⠿⠷⠯⠿⠾⠷⠿⠾⠽⠯⠷⠿⢾⣷⣭⡷⠿⠽⢿⠀⢼⣛⣮⢽⢾⣹⣽⡷⣫⢷⣫⢾⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠊⣄⡆⡄⣶⠋⠀⣄⢸⡿⣷⢯⡵⢍⣀⡀⠀⠀⠀⢆⣀⣀⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠟⢃⣀⣠⠃⠀⢺⡽⣎⢿⡺⣵⢾⣟⣵⡻⣼⢳⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣠⣿⠿⣿⠁⠀⠢⠗⠂⠈⠁⠸⡖⠫⢳⠬⠖⡲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡹⣞⡽⣞⣽⣯⢶⡻⣵⢻⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢹⣠⡴⠂⠀⢀⣀⡀⣤⠚⠰⢕⡪⢟⣩⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣝⡧⣟⣞⢾⡷⣫⣗⢯⣳⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠈⣯⢄⡀⠀⠈⠀⢽⠃⠀⠀⠙⠺⠯⠒⠢⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣮⢽⡞⣞⣻⣯⢗⡾⣫⢞⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⢦⣘⡗⡒⠲⠊⠀⠀⠀⠀⢀⠀⠀⠀⠨⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢞⡧⢿⣭⢻⣧⣟⡳⣏⢿⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠥⢀⣀⡀⠀⣀⡴⠁⠀⠀⠀⠀⠈⢻⣇⠘⢆⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢫⣞⠿⣜⣿⡷⣺⢽⣹⢮⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠰⠁⠀⠀⠀⠑⠢⢄⠀⠀⢀⣈⣆⡙⣷⡄⠑⢄⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣛⣮⢿⡹⢾⣷⢫⣟⣼⢫⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠊⢽⠶⣄⡈⠁⠒⠒⢊⡜⡄⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡽⣎⣷⣛⢿⡷⣻⠼⣞⡽⢮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢃⠈⢳⡦⣀⠀⣼⡰⠙⢦⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⢳⣮⢽⣻⣯⢳⡟⣽⢺⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢷⡉⢹⣷⠁⠀⠀⠑⢄⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢞⡽⢮⣳⣻⡷⣫⡽⣞⡽⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠃⠀⠀⠀⠀⢀⣀⣠⣴⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢘⡇⢾⢸⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢾⣹⣏⢷⣽⡷⣫⢷⡝⡾⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠈⠀⠀⣸⠠⢉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠠⡏⣽⢸⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢫⣶⣛⢾⣺⣟⣵⣛⡾⣝⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠢⣁⣌⠹⢦⡀⠀⠻⠟⠀⠀⠀⢀⢴⡳⢤⡾⢣⣼⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣛⣶⢫⣟⣼⡟⣶⢫⣞⢧⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⠃⣇⠈⠢⢄⡉⠒⠀⠀⠐⠒⠊⠁⠀⡇⣸⠀⠀⢹⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡽⣎⡿⣜⣻⣯⢗⣻⡼⣫⣶⣧⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠐⡄⠀⠀⠀⡼⠱⡀⢌⢘⠦⡀⠀⠀⠉⠉⠑⠢⡀⠀⠀⠈⠎⢳⠀⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⢳⡽⣭⣻⣧⢟⡧⣿⣽⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠎⠀⠀⠣⣠⣤⠞⠹⡔⢡⠂⠌⣣⣀⠉⠀⠉⠑⢄⡘⠁⠀⠀⠀⡄⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣜⢯⢾⡱⣿⠯⢾⣽⡟⠛⣿⣿⢿⣿⣿⢾⣿⢿⣗⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠀⠀⠀⠀⠸⡅⠀⠀⠙⣤⡘⣨⠇⠈⠁⠰⡀⢠⠀⠈⢢⠀⠀⠀⢇⢹⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢾⡹⣞⣽⠇⠀⠀⠘⣏⢦⠈⣿⣿⣿⢯⣿⣿⣿⢿⣗⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⡇⡏⠀⠀⠀⠀⠈⠣⠄⣀⡋⠀⠀⠀⢨⢸⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣮⣿⠿⢻⣄⠀⠀⠀⠈⠈⠁⠈⣾⣿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡂⠹⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢫⢱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⢶⠺⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⡔⡛⠫⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣻⡼⣆⠀⠀⠁⠀⠀⠀⠣⠀⣀⣾⣿⣿⣿⣻⣯⢿⣟⣾⡇⡀⠀⠀⠀ ⡶⣖⡶⡶⣶⠶⣶⢾⡄⠀⠁⠀⠀⠀⠀⠀⣷⡶⣶⢶⣾⡚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠮⠛⠱⣇⢆⣱⡟⣶⢶⡶⣶⢶⡶⡶⣶⠶⣶⢶⣶⡶⢶⠞⠉⠉⠉⠈⠁⠉⠉⠉⠑⠒⠲⢶⣶⣶⣶⢾⡷⣿⡿⠗⢄⠀⠀⠀⠀⠀⠐⡻⠿⢯⣟⣿⣿⣿⣿⣿⣿⡇⠀⠁⠂⠄ ⡿⣼⢳⣽⢺⣝⡧⢿⣧⠀⠀⠀⠀⠀⠀⠀⣿⡿⣜⣧⢻⡇⢳⣤⣀⣀⠀⠀⠀⠀⠇⠀⠀⠀⢠⡆⣿⡼⣇⢇⠀⡄⠀⠀⠀⠀⠀⢠⢊⠗⢀⣀⠀⠀⣿⣾⡟⡷⣏⡷⣽⣚⢧⣻⣵⣫⣿⡼⠷⠯⢄⡠⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢇⠸⠉⠫⠟⢁⣀⣀⡀⠑⠢⠤⠔⠬⣙⣴⣫⣾⣿⣿⣿⣿⣿⣿⠇⠀⠉⠒⠀⠀ ⣿⣱⠿⣼⢫⣞⡽⣫⢿⠀⠀⠀⠀⠀⠀⠀⣿⣳⠽⣎⡿⣱⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⡾⢸⣿⣳⣿⡈⢆⣳⡀⠀⠀⣀⢔⠉⠁⣀⠾⣁⣴⣿⡯⣷⠽⠷⣽⠾⠓⣛⢻⡋⠥⠀⢹⡔⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠹⠁⠒⠢⠤⠀⠈⠉⠉⠉⠉⠁⠀⠰⣿⣿⣿⣿⡿⠟⣟⠃⠠⡀⠀⠀⠀⠀ ⣷⣭⣛⣾⣹⣮⣝⣧⣿⡇⠀⠀⠀⠀⠀⠀⣿⣱⣟⣽⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣸⠇⢸⣾⣷⣹⡷⠉⠁⠈⡉⣞⠕⠁⠀⢰⣹⣿⣿⣿⡿⠟⠟⠛⠂⢐⡏⠀⠀⠙⡇⠀⠀⠀⠇⠀⢸⢡⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⡘⠁⠌⡀⢀⠀⠀⠀⠉⠂⠀⠀⠀ ⣯⡝⣯⢻⣭⣛⣯⡿⠿⣯⠀⠀⠀⠀⠀⠀⣿⡝⣯⣿⡇⣇⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢻⠲⠦⠿⠿⢿⣕⣢⣤⡬⠾⠮⠗⠀⣶⣾⣿⣿⠛⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡄⠀⠀⠀⢠⡀⠸⡈⠺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⡴⠀⠀⠀⠈⠐⠢⠀⠀⠀⠀⠀⠀⠀ ⣳⢽⣣⣿⠞⣉⣴⠶⠟⠻⣇⠀⠀⠀⠀⠀⣷⣿⢿⣹⣇⠈⠦⡜⠁⢀⣀⠤⠤⠤⠤⠤⠤⠼⠶⠒⠓⠋⠉⠡⠤⠄⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁⠒⠒⠠⡀⠀⠀⠀⠣⣀⠀⠀⠫⢦⡀⠐⠉⠙⢎⠱⢄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠑⢄⠄⠀⠀⠀⠀⡞⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠚⡹⡏⣴⠋⠀⠀⠀⠀⢻⡆⠀⠀⠀⢠⠀⠉⠋⠓⠛⠓⠚⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠑⡀⠀⠀⠀⠂⠀⠑⢦⢄⣉⡒⠀⠀⠠⢄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣸⡁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡃⣴⠏⠀⠀⠀⠀⠀⠈⡽⡄⠀⠀⠘⣆⣀⠤⠓⠒⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠑⠠⠄⡀⠀⠑⠤⡀⢣⠀⠉⠉⠉⠓⢢⣉⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⣰⠇⡃⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠀⣟⠀⠀⠀⠀⠀⠐⠒⣿⡁⠀⠀⠀⠈⠒⢤⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⢆⠀⠀⠀⠈⢧⠀⠀⠂⠀⠀⢹⣆⡵⢄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢰⠞⠀⢃⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⣿⠠⠄⠀⠀⠀⠀⠀⢹⡀⠀⢀⠀⠀⠐⢄⡑⡄⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⡄⠐⠀⢁⣶⠟⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠈⡀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀ ⠀⠹⣇⠸⣆⠠⠤⠤⠤⠤⠤⢼⡇⢆⠈⡆⠘⣆⣀⣧⠗⠠⠤⣤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣀⠠⠤⠐⠠⢄⣀⡀⠀⣀⣀⠤⠐⠃⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡼⠁⠂⠑⠄⠡⠀⠀⡑⠀⠂⠄⠄⢂⡁⠄⠂⠁⠀⠀⠀ ⡿⣶⢿⣦⠘⢣⣄⡀⠀⠀⠀⠘⢿⡘⣧⠹⣖⠚⣦⡘⢦⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡞⠉⠀⠀⠀⣀⡠⠤⠒⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠄⢀⣀⣤⠈⠉⠀⠀⠀⠀⠄⢠⣿⠁⠀⠀⠀⠀⠀⢐⣀⣀⠤⣒⣁⠤⣲⠏⡁⢀⠀⠀⠀⠁⠢⠄⠠⠐⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣜⢯⣻⣷⣤⡈⣙⡿⣷⣶⢿⣿⣟⣮⣳⣌⢳⣘⣻⣬⣿⢷⣖⠦⠭⣑⣒⣂⣤⡄⠀⢀⠀⠀⠀⠤⡤⣤⣤⣤⡴⠶⢟⠛⠒⠒⠮⢥⠭⢉⡁⠤⠤⢶⠶⠛⠩⡉⠙⠒⠒⣒⢚⠓⠋⠉⠛⠓⠤⠤⠤⣀⣁⣀⣀⣠⡟⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⡴⠋⡰⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀ ⣿⡹⣞⡵⢾⣹⡿⣿⢻⢯⣛⡮⣿⣞⡵⢯⣛⡿⣻⣯⢷⣹⢞⣻⡷⠀⠀⠀⠈⠁⠉⠉⠉⡏⣹⠟⠛⠉⠉⠀⠠⠖⠉⠀⠀⠀⠀⡨⢄⡈⠂⢀⠤⠂⠁⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠠⠒⠊⠁⠈⠒⠢⡀⠀⠀⠀⢸⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⡟⠔⠒⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠈⢍⠀⠀⠀ ⣷⢫⣗⢯⣛⡶⣿⢭⡟⣧⡻⣵⣻⢾⡹⣏⣷⣹⢳⣯⡗⣯⣞⣳⡇⡧⠀⠀⠀⠀⡼⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⠤⢈⠑⠢⢄⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠀⠉⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⠑⠀⠀ ⣯⢟⡼⣏⡷⣫⣯⡗⣯⣳⢽⣣⢿⣏⡷⣏⡶⣏⢿⣧⢟⡶⣭⡿⢁⠃⠀⠀⠀⠸⡇⠀⢠⠇⠒⠈⠁⠀⠀⠀⠈⠉⠢⣠⠞⣀⡰⢉⡦⠤⠈⠀⠀⠈⠑⠒⢯⠠⠔⠒⠒⠒⠚⠈⠉⠉⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀ ⣟⡾⣹⡞⣵⢯⡷⣏⡷⣽⢺⡭⣿⣞⡵⣏⡷⣫⢯⣷⣛⢾⡽⢠⠎⢇⠀⠀⠀⠀⠹⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈⢦⡞⢁⡎⣸⡒⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⡤⠊⢡⠁⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⢳⡽⣫⣞⣯⠷⣽⣚⢯⣳⢿⣺⠵⣏⣷⢫⣟⣧⢟⣾⢃⡏⠀⠈⠂⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⡊⢳⡞⣰⢡⢼⢶⣄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⢀⠄⠀⣸⡜⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣱⢯⣳⢟⡼⣯⡻⣵⣫⢟⣼⣻⣭⢟⣳⢾⣹⢞⣯⡞⣿⢸⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡴⠃⠀⠱⠀⠈⠃⡒⠲⢋⠈⠚⠷⠶⠶⠟⠒⠒⠚⠛⠳⠶⠤⢄⣒⣂⠐⠐⠂⠒⠒⠒⠒⠒⠊⠉⢾⣁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢉⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⢯⣞⡧⢿⣹⡷⣏⠷⣭⢟⡶⣻⢾⡭⣗⢯⢾⣹⡷⣫⣿⡸⠀⠀⠀⠀⢀⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠹⠄⠀⠀⠃⠀⠀⠀⠀⠀⠑⠆⠀⠈⠀⠀⠠⠒⠈⠀⠀⠀⠄⠀⠈⠀⠍⠉⠋⢙⠚⠓⠛⠊⠉⠉⠁⠤⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡁⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠤⠁⠉⠉⠊⠛⠓⠚⢙⠋⠉⠍⠀⠈⠀⠄⠀⠀⠀⠈⠒⠠⠀⠀⠈⠀⠆⠑⠀⠀⠀⠀⠀⠃⠀⠀⠄⠹⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡎⢀⠀⠀⠀⠀⡸⣿⣫⡷⣹⢾⢯⣗⡭⢾⣻⡶⢟⣭⠷⣏⡷⣹⢿⡧⣞⢯⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢉⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣀⣁⢾⠉⠊⠒⠒⠒⠒⠒⠂⠐⠐⣂⣒⢄⠤⠶⠳⠛⠚⠒⠒⠟⠶⠶⠷⠚⠈⢋⠲⡒⠃⠈⠀⠱⠀⠃⡴⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⢀⠀⠀⠀⠀⠀⢸⣿⡞⣯⢞⣹⢾⣳⢟⣭⣻⣼⢟⣫⣵⡻⣯⡼⢟⣳⢯⣱⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠉⠕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⡜⣸⠀⠄⢀⠀⠀⡀⢄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⣄⢶⢼⢡⣰⡞⢳⡊⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡼⠀⠀⠀⠂⠈⠀⡏⢃⣾⢟⣧⣟⢫⣷⣏⠵⣺⢿⣳⢯⣚⣽⠷⣯⣞⣫⡽⢳⣼⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠤⣀⠀⠀⢀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠘⠀⠁⢡⠊⡤⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⠀⡒⣸⡎⢁⡞⢦⠈⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠹⠀⠀⠀⠀⢇⠎⢠⡽⢾⣛⣷⢯⣫⡷⣏⡵⣞⣿⡭⢺⣽⡷⣏⡷⢯⣵⡞⣹⡾⣟ ⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉⠉⠈⠚⠒⠒⠒⠔⠠⢯⠒⠑⠈⠀⠀⠈⠤⡦⢉⡰⣀⠞⣠⠢⠉⠈⠀⠀⠀⠁⠈⠒⠇⢠⠀⡇⠸⠀⠀⠀⠃⢁⡿⣭⡶⢟⣧⢿⣏⡶⣏⡷⣏⢿⣣⢽⣳⣯⡗⣯⣫⡷⣏⡼⢟⣯ ⠀⠀⠑⠈⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠈⠉⠀⠉⠉⠒⠔⡠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⡀⢄⠢⠑⢈⠤⢳⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⡼⠀⠀⠀⠀⡧⡇⣳⣞⣯⡗⣯⢳⣹⣷⣏⡹⢾⣻⣵⡻⣧⡟⢭⣿⡶⣛⢯⣗⢫⣷ ⠀⠀⠀⢍⠈⠧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠒⠔⡟⡰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⢸⠀⠀⠀⡀⠢⠒⠈⠁⠊⠒⠠⠀⠀⠀⠁⠊⠠⠀⠀⠀⠀⠁⠂⠤⢀⠂⡈⢄⡨⠀⠀⠀⠀⠉⠖⠠⠀⠉⠉⠛⠟⣹⡏⠉⠉⠉⠁⠈⠀⠀⠀⡷⣻⢞⣹⢷⣯⣻⡿⣛⢯⡵⣞⣿⡮⣛⢯⢻⣿⡿⣹⢾⡵⣞⡹⣿ ⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀⡰⠋⡴⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⡟⣠⣀⣀⣁⣀⠤⠤⠤⠓⠛⠉⠋⠓⢚⣒⠒⠒⠙⡉⠩⠛⠶⢶⠤⠤⡁⢉⠭⢥⠮⠒⠒⠛⢟⠶⡴⣤⣤⣤⡤⠤⠀⠀⠀⢀⠀⡄⣤⣂⣒⣑⠭⠦⣖⢷⣿⣬⣻⣘⢳⣌⣳⣮⣟⣿⢿⣶⣷⡿⣙⡈⣤⣷⣻⢯⣜⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠐⠠⠄⠢⠁⠀⠀⠀⢀⡁⠏⣲⠤⣁⣒⠤⣀⣀⢐⠀⠀⠀⠀⠀⠁⣿⢠⠄⠀⠀⠀⠀⠉⠈⣤⣀⢀⠄⠀⠀⠀⠀⠀⠉⠉⠈⠀⠉⠒⠤⡠⣀⠀⠀⠀⠉⡞⠴⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠀⠀⢦⡘⣦⠚⣖⠹⣧⡘⢿⠘⠀⠀⠀⡀⣄⢣⠘⣦⢿⣶⡿ ⠀⠀⠀⠁⠂⠄⡁⢂⠄⠄⠂⠀⡑⠀⠀⠡⠄⠑⠂⠁⡼⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢠⠀⠃⠐⠤⣀⣀⠀⡀⣀⢄⠠⠐⠤⠠⣀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⠤⣤⠤⠠⠗⣧⣀⣆⠘⡆⠈⢆⡇⢼⠤⠤⠤⠤⠤⠠⣆⠸⣇⠹⠀ ⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⠘⠀⡀⠈⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠟⣶⢁⠀⠐⡄⠈⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⠀⡄⡑⢄⠐⠀⠀⢀⠀⡀⢹⠀⠀⠀⠀⠀⠄⠠⣿⠀⣿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⢃⠀⠞⢰⠀⠊⠠⠀⠀⠀⠀⠀⠀⠀⢄⡵⣆⢹⠀⠀⠂⠀⠀⢧⠈⠀⠀⠀⢆⠈⠀⠀⣄⠲⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀⠀⢤⠒⠈⠀⠀⠀⡁⣿⠒⠐⠀⠀⠀⠀⠀⣟⠀⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡃⠇⣰⠀⠆⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣉⢢⠓⠉⠉⠉⠀⢣⡀⠤⠑⠀⡀⠄⠠⠑⠀⠀⠀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠤⠒⠓⠤⣀⣆⠘⠀⠀⡄⡽⠈⠀⠀⠀⠀⠀⠏⣴⡃⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡁⣸⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⢄⠠⠀⠀⡒⣉⢄⢦⠑⠀⠂⠀⠀⠀⡀⠑⠀⠀⠀⢋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡉⠚⠓⠛⠓⠋⠉⠀⢠⠀⠀⠀⡆⢻⠀⠀⠀⠀⠋⣴⡏⡹⠚⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⠀⠀⠀⠀⠄⢄⠑⠀⠀⠀⠀⠀⠁⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠈⢄⠱⢎⠙⠉⠐⡀⢦⠫⠀⠀⣀⠣⠀⠀⠀⡀⠠⠒⠒⠁⠉⠀⠈⠁⠀⠀⠀⠀⠀⠄⠤⠡⠉⠋⠓⠒⠶⠼⠤⠤⠤⠤⠤⠤⣀⢀⠁⡜⠦⠈⣇⣹⢿⣿⣷⠀⠀⠀⠀⠀⣇⠻⠟⠶⣴⣉⠞⣿⣣⢽⣳ ⠀⠀⠀⠀⠀⠀⠀⠢⠐⠈⠀⠀⠀⡴⠀⢃⢠⠀⠀⠀⠀⠀⠀⠀⢀⠣⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠺⡈⠸⡀⢠⠀⠀⠀⡄⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠉⠛⣿⣿⣾⣶⠀⠗⠮⠾⡬⣤⣢⣕⢿⠿⠿⠦⠲⢻⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣇⡇⣿⣯⡝⣿⠀⠀⠀⠀⠀⠀⣯⠿⡿⣯⣛⣭⢻⣯⡝⣯ ⠀⠀⠀⠂⠉⠀⠀⠀⢀⡀⠌⠁⡘⠋⠼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢡⢸⠀⠇⠀⠀⠀⡇⠙⠀⠀⡏⢐⠂⠛⠟⠟⡿⣿⣿⣿⣹⢰⠀⠁⠕⣞⡉⠈⠁⠉⡷⣹⣷⣾⢸⠇⣸⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣽⣟⣱⣿⠀⠀⠀⠀⠀⠀⡇⣿⣧⣝⣮⣹⣾⣛⣭⣷ ⠀⠀⠀⠀⡀⠠⠃⣟⠟⡿⣿⣿⣿⣿⠰⠀⠁⠉⠉⠉⠉⠈⠀⠤⠢⠒⠁⠹⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⡔⢹⠀⠥⡋⢻⣛⠓⠾⣽⠷⠽⣷⡯⣿⣴⣁⠾⣀⠁⠉⢔⣀⠀⠀⡀⣳⢆⡈⣿⣳⣿⢸⡾⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠁⣱⡿⣎⠽⣳⣿⠀⠀⠀⠀⠀⠀⠀⢿⣫⡽⣞⢫⣼⠿⣱⣿ ⠀⠀⠒⠉⠀⠇⣿⣿⣿⣿⣿⣿⣾⣫⣴⣙⠬⠔⠤⠢⠑⡀⣀⣀⢁⠟⠫⠉⠸⢇⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡠⢄⠯⠷⡼⣿⣫⣵⣻⢧⣚⣽⡷⣏⡷⡟⣾⣿⠀⠀⣀⢀⠗⢊⢠⠀⠀⠀⠀⠀⡄⠀⢇⣇⡼⣿⡆⢠⠀⠀⠀⠇⠀⠀⠀⠀⣀⣀⣤⢳⡇⢻⣧⣜⡿⣿⠀⠀⠀⠀⠀⠀⠀⣧⢿⡧⣝⢺⣽⢳⣼⡿ ⠄⠂⠁⠀⡇⣿⣿⣿⣿⣿⣿⣟⢯⠿⡻⠐⠀⠀⠀⠀⠀⢄⠗⡿⣿⡷⢾⣶⣶⣶⢶⠲⠒⠑⠉⠉⠉⠁⠈⠉⠉⠉⠞⢶⡶⣶⢶⣶⠶⣶⡶⡶⢶⣶⡶⢶⣶⡟⣱⢆⣇⠱⠛⠮⢔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡚⣾⢶⣶⡶⣷⠀⠀⠀⠀⠀⠁⠀⡄⢾⣶⠶⣶⡶⡶⣖⡶ ⠀⠀⠀⡀⡇⣾⣟⢿⣯⣻⣿⣿⣿⣾⣀⠀⠣⠀⠀⠀⠁⠀⠀⣆⡼⣻⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠫⡛⡔⣠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠺⢶⠀⠄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⢫⠀⠀⠀⡇⠈⠀⠀⠀⠀⡀⠹⡂⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣦⣿⢿⣿⣿⣿⣿⣿⣾⠈⠁⠈⠈⠀⠀⠀⣄⢻⠿⣿⣮⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡅⢸⢨⠀⠀⠀⡋⣀⠄⠣⠈⠀⠀⠀⠀⡏⡇⠘⠀⠀⡀⢻⠀⠀⠀⠀⠀⡇⠟⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⣗⢿⣿⣿⣿⢯⣿⣿⣿⠈⢦⣏⠘⠀⠀⠇⣽⣞⡹⢾⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⢹⢇⠀⠀⠀⢢⠈⠀⢠⡀⠰⠁⠈⠇⣨⡘⣤⠙⠀⠀⡅⠸⠀⠀⠀⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⣗⢿⣿⢾⣿⣿⢿⣿⣿⠛⡟⣽⢾⠯⣿⡱⢾⢯⣜⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⡄⠀⠀⠀⠁⡘⢄⠑⠉⠀⠉⣀⣣⠌⠂⢡⡔⠹⠞⣤⣠⠣⠀⠀⠎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⣿⣿⣽⣿⡧⢟⣧⣻⣭⡽⢳⣼⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⠀⠀⢳⠎⠈⠀⠀⡀⠢⠑⠉⠉⠀⠀⡀⠦⢘⢌⡀⠱⡼⠀⠀⠀⡄⠐⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⣧⣶⣫⡼⣻⢗⣯⣻⣜⡿⣎⡽⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠘⢹⠀⠀⣸⡇⠀⠁⠊⠒⠐⠀⠀⠒⡉⢄⠢⠈⣇⠃⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⢧⣞⢫⣶⡟⣼⣟⢫⣶⣛⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⢸⣼⢣⡾⢤⡳⢴⢀⠀⠀⠀⠟⠻⠀⡀⢦⠹⣌⣁⠢⡇⢀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡶⣝⡾⣛⣵⣟⣺⢾⣛⣶⢫⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⢸⣽⡏⠠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⢉⠠⣸⠀⠀⠈⠀⠀⠀⠀⠀⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣵⡾⡝⢷⣫⡷⣽⢷⣏⣹⢾⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⢸⢾⡇⢘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡫⣴⣠⣀⢀⠀⠀⠀⠀⠃⠎⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣺⡽⣞⡽⣫⡷⣻⣳⢮⡽⢞⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⢄⠑⠀⠀⠁⣷⢹⡉⢷⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡽⢺⣽⡟⢳⣯⣻⢽⣮⢳⣼⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢦⠙⡰⣼⠀⣀⡦⢳⠈⢃⠀⠀⠀⠀⠀⠀⠀⠁⠖⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢮⡽⣞⠼⣻⡷⢿⣛⣷⣎⡽⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⡄⡜⢊⠒⠒⠁⡈⣄⠶⢽⠊⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣟⢫⣼⣟⢫⣷⢾⡹⢿⣮⣛⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⢄⠑⡄⣷⡙⣆⣈⢀⠀⠀⢄⠢⠑⠀⠀⠀⠁⠰⠀⠀⠀⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠷⢮⣹⢽⣺⡷⣿⣜⠿⣞⢫⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠐⠈⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⢆⠘⣇⢻⠈⠀⠀⠀⠀⠁⡴⣀⠀⡀⣀⢀⠥⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⢿⣏⡳⣟⣧⢻⣭⢿⡧⢞⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⠨⠀⠀⠀⢀⠀⠀⠀⠀⠊⠲⡒⡗⣘⢦⠈⠀⠀⠀⠀⠀⠀⠀⠉⠖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⢞⣫⡾⢗⣯⣻⣞⡞⢽⣮⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠢⠒⠯⠺⠙⠀⠀⠃⢽⠀⠈⠀⡀⢄⣯⠈⠀⠀⠀⠁⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠽⣳⢯⣗⣫⡷⢾⣞⣟⡧⣝⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣩⢟⡪⢕⠰⠚⣤⡀⣀⢀⠀⠂⡴⣠⢹⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⢻⣵⡻⢶⣯⣽⣞⡽⣞⡹⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡲⠖⠬⢳⠫⡖⠸⠁⠈⠂⠗⠢⠀⠁⣿⠿⣿⣠⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣭⢳⣼⡻⣵⣟⢾⣵⡺⢿⣎⡽⢺⠀⠃⣠⣀⢃⠟⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠻⣀⣀⢆⠀⠀⠀⡀⣀⢍⡵⢯⣷⡿⢸⣄⠀⠋⣶⡄⡆⣄⠊⣇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣱⢾⣫⢷⣫⡷⣽⣹⢾⢽⣮⣛⢼⠀⢿⠽⠿⡷⣭⣷⢾⠿⠷⠯⠽⠾⠿⠷⠾⠿⠯⠷⠿⠷⠽⠾⠿⠯⠾⠿⠯⠷⠽⠾⠿⠯⠷⠽⠾⠿⠯⠾⠽⡿⣷⣯⠾⠽⠿⢹⠀⠀⠀⠈⣧⡿⣿⣿⢛⠟⡿⡴⢀⠁⠀⠁⠞⢁⣰⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⢧⣹⢷⣫⡷⣽⡼⢟⣫⢶⣟⣸⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⣀⣟⣼⢱⠤⢤⠀⠢⠀⡸⠿⠘⣦⢀⠀⡄⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⣳⡽⣳⢞⣯⣻⣞⢯⣚⣽⡷⢸⠀⠀⠀⠃⣿⡿⣾⣻⣿⣿⠸⠀⡀⣷⣵⣯⠸⠀⠀⠀⣻⣛⣛⣿⢽⣿⣾⣶⢹⠀⠁⠀⠉⠀⠈⠁⠁⣿⣼⢆⡌⠒⣂⣧⣿⠀⠀⠀⠀⠀⠀⣠⢷⠘⠀⠀⡀⠇⣨⢃⢳⢰⠀⠀⠁⡞⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣳⣱⡾⣝⡾⣏⢿⣭⢟⣮⡟⣧⢹⠀⠀⠀⡯⣿⣿⣿⣿⣿⣿⢿⠀⠀⡆⣿⣉⢿⠀⠀⠀⣿⣀⣷⢿⠟⠿⢸⠀⣾⣧⣿⣯⣸⣶⣇⣿⣿⢸⣆⢏⡏⣹⢛⣾⢠⠀⠀⠀⠀⠀⠀⠀⡀⡀⢿⠗⠛⠛⢸⡇⡞⠛⠛⠼⣢⣑⡈⣤⣤⠷⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣫⣵⡾⣏⡵⣟⢾⣞⠽⣯⢞⣳⣾⡆⠹⠀⣿⣸⣦⣿⣿⣾⣣⣿⢰⠋⢼⣧⣸⣧⢸⠀⠀⣿⠀⣯⣿⣿⣿⢸⠀⣻⣗⣼⣧⠺⠂⡗⣿⣿⢸⠀⡄⣽⣿⣷⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡃⣟⢠⢣⢾⣤⣱⢀⠀⠀⠀⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢞⣳⡽⣳⣞⡯⣿⢧⣞⠽⣮⣟⢹⠀⢆⡿⣿⣷⡿⣿⣽⣿⡿⣮⣿⡼⠀⡆⢻⡄⢿⠀⠀⣿⠀⣿⣿⣿⣿⢸⠚⢸⡇⢸⡇⣹⠳⡏⣿⣿⢸⠀⠀⣶⡖⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣟⣣⡽⣳⡵⣟⢾⣹⢾⣳⣝⡷⢸⠀⣀⣤⣶⣿⣾⣿⣼⣱⣾⡿⣤⣀⢀⠀⣧⠈⣧⢸⠀⣿⠀⣿⣻⣞⣛⣹⣩⢼⡧⢸⡇⣹⠶⡏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠈⠀⠀⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢞⣳⡽⣫⣵⡟⣽⢳⣼⣻⡵⣻⢼⠀⠂⠶⣴⣠⢶⣤⢀⡀⢄⠤⣤⠶⠀⠀⡄⢹⡆⢿⠀⣿⠀⣿⣿⣿⣿⢸⠀⣿⣟⢸⡇⢻⣱⡗⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⡄⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣭⢻⣯⡖⣹⡿⣼⣻⡶⣝⡼⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣿⠘⣿⠀⣿⢸⠀⠀⠀⠀⡀⣃⢸⡇⢾⡩⡷⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣎⠽⣳⣯⣚⡷⣻⣹⣷⣏⡼⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣻⣟⢳⣿⠈⣿⢸⠀⠀⠀⠀⠀⠆⢻⡟⢽⣉⡧⣤⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⣯⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣟⣣⡽⢳⣮⣟⣽⡞⣹⢿⡧⣞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡿⣿⣺⣾⣲⢸⠀⠀⠀⠀⠀⠆⣿⣟⣹⣉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡵⣞⡹⣽⢯⢮⣻⢷⣭⡞⢽⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⣷⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⢿⣏⡹⢿⣏⣽⡻⢯⣝⡻⢯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀