⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠐⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠸⡇⠀⠐⠈⠀⡀⠁⠠⠈⠀ ⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡧⠀⠂⠀⠄⠀⠐⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠂⠀⠈⢀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⡇⠀⣿⠂⠀⣀⣀⣀⣀⢰⣄⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿⠄⠀⠐⠈⠀⠀⡀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⡇⠀⠀⠀⠀⠀⣿⡃⠀⠠⠐⠈⠀⢀⠠⠀ ⠤⠄⠠⠀⠄⠠⠤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡿⣟⠳⢿⠛⢻⡿⠿⠾⢷⣿⣾⣳⢿⡿⣷⣾⡇⠀⠀⠀⠀⠀⣿⡂⠀⢀⠀⠄⠂⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣼⡏⠀⠉⠀⠀⢻⣤⣀⡴⠚⠉⢙⠻⣿⣿⡽⣿⢿⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⡀⠠⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠘⢷⣒⠒⣦⡤⠞⠓⢿⡀⠀⠀⠙⠉⢻⠻⣿⣯⣿⣿⣤⡄⠀⠀⠀⣿⡇⠀⢀⠀⠀⠄⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡆⣰⠏⠀⠀⠀⠀⠙⠦⣭⡝⠉⠀⠀⠀⠀⣿⠲⣤⡀⣠⠿⣄⠙⣿⣿⣿⣿⡁⠀⠀⠀⢹⡇⠀⠀⠀⠂⠀⠠⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣼⠇⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠰⡶⠶⠿⠯⠽⣛⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⢻⡇⠀⠈⠀⠐⠀⡀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣱⠏⠀⠀⠀⠀⠀⠀⠀⠾⡧⠴⠺⣿⣍⡉⠲⣄⠀⠈⠧⠀⠀⠀⠉⠙⠷⣇⣻⡆⠁⠀⢈⢻⡇⠀⠀⠁⠠⠀⠀⡀⠄ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⢸⡇⠀⠈⠀⠀⡄⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠀⠀⠀⠀⠀⠀⠠⣸⡇⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⢀⠈⠀⢀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣜⣀⣀⣀⣀⣀⣈⣴⣟⡁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⡀⠈⠀⠀⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠉⠉⠉⠉⠉⠉⠀⢿⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠄⠀⡀⠁⢀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠄⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⠀⠂⠀⠐⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⣷⠀⠀⠀⠀⢀⣀⣴⡏⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣠⡤⠤⠶⠾⠧⣤⡐⠀⠀⢸⡇⠀⠄⠈⠀⠄⠀⡀⠁ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡟⣿⠀⠀⠀⣴⠞⠋⠉⠉⠙⢦⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⡷⠋⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀⢸⣧⠀⠀⠐⠀⠠⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢿⠀⠀⠀⠛⠛⠒⣦⡄⠀⠀⠈⠓⠒⠲⠾⢿⣿⣿⣿⣿⡿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡯⠀⠀⠂⠀⠄⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⢹⡄⠈⢧⡀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠐⠀⠠⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢣⠀⠈⠳⣄⠀⠀⢻⡄⠀⠀⢀⣷⠀⠀⠀⠀⠀⣰⣄⣁⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠀⠀⠁⠀⠂ ⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠠⠐⢂⡼⠋⠀⠀⠀⠀⠘⢧⠀⠀⠈⠳⣄⠀⠈⠙⠛⠉⠈⠳⢤⣀⣤⠶⠋⠀⢉⡽⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠸⡇⠀⠂⠈⢀⠈⠀⡀ ⠀⠀⠀⠀⠀⠀⣽⠀⢀⠀⠐⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣨⠗⢦⡀⠀⠀⣀⣤⠶⠋⠁⠀⠀⣠⠞⠀⠀⠀⣀⡤⠖⠋⠉⠉⠁⠉⠉⠒⠦⣄⡀⠀⣿⠀⠀⠐⠀⠀⠄⠀ ⠀⠀⢀⣤⠤⠤⢾⠀⠂⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡴⠃⠀⠈⣧⡴⠿⢯⡀⠀⠀⠀⣀⡼⠃⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣿⠀⠐⠀⠠⠈⠀⠀ ⣀⡞⠋⠀⠀⠀⢼⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⠁⢀⣤⠞⠃⠀⠀⣦⠞⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠑⢤⠙⡄⠀⠐⠀⠀⠂⠁ ⠟⠀⠀⠀⠀⠀⢺⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⡿⠀⠀⢠⠿⠒⠉⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⣠⡶⠚⠉⠉⠁⠈⠉⠉⠓⠢⣄⡀⠹⣯⠀⠐⠈⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠃⠀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢻⡄⠀⠐⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⠀⠀⠀⠂⠈⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠁⠀⠁⠀⠂ ⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠁⠀⠁⠀ ⣀⣤⣤⣤⣤⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⠠⠁⠈⠀ ⠉⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢿⡄⠀⡀⠀⢀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⢻⣆⠀⠐⠀⠀⡀ ⠀⠀⢠⣤⣤⣄⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢸⣧⠂⠀⠠⣦⣀⠀⠀⢹⡆⠀⠐⠀⠀ ⠀⠀⢾⡃⣧⣼⡇⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠁⠅⠀⢀⡀⠉⠳⠶⣿⠁⠀⠂⠈⠀ ⠀⠀⠘⠿⠿⠟⠀⠀⠀⢼⣿⣧⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⣸⣇⠀⠀⠀⣿⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡷⣦⣄⣀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣔⠀⠀⠀⢠⡟⢻⡄⠀⠠⢿⡆⠀⠁⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⡛⡿⣹⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣩⡗⠒⠒⠒⠒⠒⠋⢩⣿⣿⢟⡻⢷⣄⠴⠋⡄⠈⢷⡀⠘⣽⠁⠀⠀⠂⠀ ⠒⠂⠠⠴⠶⠦⠶⠶⠖⠛⠹⣷⣘⡱⢦⢹⡙⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣧⡀⠀⠀⠀⢀⣤⡾⣛⠤⣣⠎⡽⣻⡄⠀⢷⡀⠈⠙⣿⠃⠀⠈⢀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢓⢎⢧⡚⠵⢲⢌⡣⣝⡹⣛⠻⠿⢿⢿⣿⣿⣿⡸⢿⡿⢿⠿⠿⡟⢿⢻⢿⣿⣟⠻⣭⠱⣌⠳⡴⢩⢖⡹⣷⣄⡀⣹⡶⠞⠃⠀⢀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡚⢦⡍⣛⡜⢦⠳⢤⠣⣍⠧⣙⠎⡖⢦⠱⢎⡱⢣⠞⣥⢋⡵⢪⢝⣊⠶⡩⢿⣿⡴⢫⢜⢣⡝⢎⠶⣑⢎⠹⢛⡿⠀⠀⠀⠠⠀⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣖⡸⣡⢚⠦⣙⠦⣓⠜⡜⣆⢛⠼⣌⡓⢎⡱⢣⡙⠦⣍⠲⣍⠲⡌⣇⡓⢣⢎⠿⣷⣊⠶⡸⣉⠶⡩⢎⡕⣫⡇⠀⡀⠁⠀⠄⠂⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣥⢎⢳⣘⠲⣉⢞⡸⢔⡋⡖⢦⡙⢎⡱⢣⡹⢜⢢⠏⡴⢋⡴⢊⡜⣣⠎⢧⡛⣿⡜⣥⣙⠲⣙⢬⢚⣽⡇⠀⠀⢀⠂⠀⠀⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣥⡎⡝⣘⠦⣙⠦⣙⡜⢢⡝⢪⡑⠧⣜⢪⡱⢎⡱⢋⡴⢋⡼⢰⡙⢦⡹⢜⣿⡰⢌⡳⣉⢮⡑⢾⠃⠀⠠⠀⢀⠈⠀⠄⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣧⣚⣥⢚⡴⡘⢧⣘⢣⠹⡜⢢⡓⠼⡌⡵⢋⡴⢋⡴⢣⡙⢦⡙⢮⡜⣧⢋⠖⡭⢦⣙⢻⠀⠠⠀⠠⠀⠀⠄⠀⡀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⢲⣍⠶⣌⢣⡝⡸⢥⡙⢎⡕⢎⡵⢊⡵⣊⢥⡙⢦⢛⠲⣜⡇⢮⡙⢦⠓⣬⢓⠀⠀⠠⠀⠐⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣎⢳⣚⢻⣙⠲⡜⡱⢎⡜⣣⠜⣎⢲⡉⣖⡡⢎⡱⢎⠭⣓⡼⣙⠦⣙⢆⠻⣤⢋⠀⠀⠄⠀⠂⠈⠀⠐⠈⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡓⡬⣃⢮⠱⢎⡵⢣⡞⡴⢫⠖⣧⠳⢦⡝⣬⢓⣎⡻⣴⡛⣬⠣⣍⢎⠳⣌⠇⠀⠠⠀⠠⠐⠀⠁⠀⠂⠀