⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⣰⠋⠈⠀⢀⣴⡻⡜⣮⣷⠸⡜⡆⢻⡀⠀⠘⣯⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣍⣀⣈⣉⣽⠇⣶⣟⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢿⡅⠀⠀⠀⠀⣰⠏⠀⠀⠀⣼⠳⣷⡹⠜⣮⣧⢻⣻⡌⣷⠀⠀⢿⠀⠀⠀⣴⠟⣀⡤⠔⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⠃⠰⣶⠚⢿⣬⣿⡀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣷⠟⣠⣴⡿⢻⡁⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⡀⠀⢻⣧⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⡿⠉⠀⢸⡇⠀⠀⠀⠀⡟⠀⠀⠀⢸⠇⠀⠀⠈⠳⢼⣘⠆⣷⢷⢻⣧⠀⢸⡀⣠⣾⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡟⠀⠀⠈⠳⢦⣽⠯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠿⣤⡾⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⢹⡀⠀⠻⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣰⣿⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⡁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⠹⡆⢸⡿⠋⠁⠀⠀⠀⠀⣀⣀⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⣠⣀⡀⠀⠀⠀⠀⢀⡤⣴⠟⣍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⠀⠈⠻⢦⡄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢤⣴⠏⠁⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢾⣁⣤⣤⢴⣶⢿⣛⣯⠭⠒⣛⣻⣭⣽⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣀⣈⣷⠀⠀⣠⠾⣽⣼⢯⣤⠈⡿⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣿⣉⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢷⡀⠻⡄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⠤⣤⡀⠘⣇⠀⠀⠀⠈⠉⠀⠚⢿⣾⡭⣔⣒⣿⠭⠥⠖⠒⠒⠚⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣩⠟⠀⠀⣿⣄⠉⣿⣤⣿⣾⠃⠀⠀⠀⠀⠀⠀⢼⡁⠙⠃⣽⠋⠰⡋⠀⠀ ⠀⠀⠀⠀⠐⠈⢷⠀⠀⠀⠈⣧⠀⢻⡄⢷⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⢷⡀⠀⢸⣆⣀⠀⠀⠘⣇⠀⠈⠛⠿⣄⠀⠀⠀⠀⠀⠀⠈⠙⠙⠓⠒⠒⠛⠛⠛⠛⠛⠒⠒⠒⡶⢷⡀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣿⢿⣶⡤⣾⠛⣿⡿⠋⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠈⠳⣤⡾⠋⠀⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⣆⠀⣹⡿⠃⠀⠳⣌⠻⣦⡀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢦⡈⢷⡀⠀⡟⠋⠛⢮⣄⠙⣦⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⢀⡇⠈⣷⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿⢸⠛⢧⣄⣀⡟⠀⠀⠀⠀⣞⣶⣶⣶⣶⣶⣽⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢤⡀⠀⠻⡄⠀⠀⠘⣶⡿⠀⣠⣤⣄⠙⣦⠈⢳⡄⠀⠀⠀⠀⠀⠛⠶⣶⣶⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣦⣧⣼⠉⠻⢴⣄⠉⠳⣜⣷⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣴⠋⣼⠀⠀⢸⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣿⠐⠉⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠈⠛⠦⣽⣦⠀⢀⣿⠀⢰⣿⣿⣿⣧⠈⢷⡀⢿⡄⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣯⣀⠀⠀⠀⠙⢦⣈⠻⣧⡀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢰⡇⠀⣠⢯⣧⠀⠀⠀⠀⣷⠀⠀⠀⢀⠀⢸⠀⠀⣤⣶⣶⡄⠀⠀⢀⣠⣤⣸⣿⣷⣾⠛⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠃⠀⣿⣿⠻⢟⡿⣷⡀⢷⠀⢿⡄⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠛⠲⣤⡀⠀⠈⠳⣌⢳⡄⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣰⢫⠏⣿⠀⠀⠀⠀⢿⠀⠀⠀⡾⠀⣿⣄⣤⢿⣦⡾⠃⠀⠰⣏⡻⠟⠿⢺⡃⠀⠷⠲⣧⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⡏⠀⣾⠃⠙⣷⠘⣇⠈⣷⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠙⢦⣄⠀⠈⢧⡙⣦⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠏⠀⣾⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⣿⠈⢈⣽⠏⠀⠀⠀⠀⠈⠙⠓⢲⢾⣇⣀⣀⣽⠿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣀ ⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⠇⠀⣿⠀⣠⣽⡇⠹⣦⡼⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠉⠳⣄⠀⠹⣌⢳⡀⠀⠀⠘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⡾⢹⠀⠀⠀⠀⣾⠀⠀⢰⠃⢠⡟⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⣫⣥⣞⢙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⡇⠀⣿⠋⠀⠀⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠚⣳⣄⡈⠂⠹⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⠁⢸⠀⠀⠀⢀⡟⠀⠀⡿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠿⠝⣫⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⠀⠀⡇⠐⠁⠀⠀⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠛⠶⣤⡀⠀⠀⢠⡶⠛⠙⣿⠻⣦⣀⡹⣆⠀⠀⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⠀⠀⡾⠀⠀⣼⢃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣼⣯⣿⠏⠀⠀⠀⠀⠀⠘ ⣆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣇⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡛⠻⣿⣦⣄⣀⠀⠀⠩⠛⠦⣼⣗⠀⢀⣾⠀⢘⣿⣧⡙⣦⣤⡾⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⠃⠀⠀⣼⠃⢀⡾⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠺⣯⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⢿⣠⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠉⠙⠛⠿⣦⣤⡒⠀⠀⠉⠳⣏⠁⣠⣿⡭⠿⢿⣿⣏⡀⣠⠀⢠⡞⠀⢀⣀⣀⣤⣤⣤⣸⡇⢠⡟⠀⢀⣼⢁⣴⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⡛⢦⣌⣻⡏⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠛⠶⢤⣄⡀⠀⠀⠈⣿⣤⠀⠀⠀⠀⡜⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠈⠙⠋⠀⠀⠀⠀⠛⠳⣿⣿⣶⣿⣿⣯⣭⣭⣤⣀⣀⢼⣿⢀⡿⠀⣠⡾⣁⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣀⠙⠛⢤⣉⣿⠀⠀⠀⠀⠀⢀⣴⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠦⣬⣻⣿⡦⡀⠀⠀⠙⠛⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣤⠤⡄⠀⠀⠀⠀⢀⠀⢸⢯⡾⣿⡆⠀⠀⣼⣋⡽⠻⣟⡾⢀⣴⣿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⢦⡔⠘⣿⡿⠀⠀⠀⠀⢰⡶⠞⠉⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⠀⠀⠀⠠⢽⣍⠛⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⢀⣾⢷⣸⣿⣧⡾⠁⠀⣼⠟⠉⣠⣾⣿⣵⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⡆⠀⠀⠀⠈⠙⢾⣯⣠⡾⠏⠀⠀⠀⣀⣀⡘⠳⢤⣴⠟⣁⡀⠀⠀⠀⣀⡀⠀⠀ ⠀⠰⣼⡻⢶⣄⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣹⣷⣀⠀⠀⠀⣹⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⢯⡻⣄⠙⠶⣄⡼⠃⢠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⠛⢾⢫⡆⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣶⠒⢦⡀⣩⠖⢢⣤⡰⣏⡽⢦⣠⠿⣍⠋⠀⠀ ⠀⠀⠈⣛⡶⢤⣍⡉⠛⠓⠂⠙⠓⠶⣭⣛⣲⣾⣿⣿⣿⠷⣦⣼⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠈⠳⡙⢷⡄⠉⠀⣤⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⡉⣧⣀⣵⠇⢻⡄⠀⢁⡤⠼⠈⠀⠀ ⠀⠀⢠⣄⣀⣀⡀⠉⠛⠓⠦⢤⣤⣀⣀⣼⣿⣿⡿⠛⠁⠀⠙⢿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠸⣿⠉⠛⠛⣷⣦⠟⢷⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣤⣤⣤⣿⣉⣤⠄⠀⠀⠻⣦⣸⣀⡁⠀⠀⠀ ⠀⠀⣠⡄⠀⠹⣭⣝⠓⠲⢤⣄⡀⠀⣽⣿⠟⠉⠀⠀⠀⠀⣠⣼⠿⠦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠶⠾⢿⣦⡀⠀⠀⠿⠶⠒⠛⠉⠀⠀⢀⡿⠀⠀⠀⠀⣠⠖⠲⣄⣠⠖⠲⣤⡀⠀⠀⠀⠀⠀⣤⡤⢤⣠⡤⣤⡀⠀⠀⠀⠀⢠⡥⣼⠋⢻⣡⡟⠉⠀⠀⠀⠀⠀⠀⠉⠹⢧⣼⣧⣤ ⠀⠀⢺⣷⠛⣍⣷⡌⡷⣴⠏⠀⢩⣿⡿⠋⠀⠀⠀⠀⣰⢟⠛⠉⠩⡍⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⣸⡇⠀⠀⠀⠀⠀⢿⡀⠐⣿⠀⣸⡇⠀⠀⠀⠀⠸⢧⣅⣀⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⣿⣘⣙⣼⢗⡚⠁⠀⣰⣿⠟⠀⠀⠀⠀⠀⠘⣿⠀⢀⠀⠀⠛⣦⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢧⣄⣀⠀⠀⠀⣾⡿⠟⠁⠀⠀⠀⠀⠀⣸⡟⠃⠀⠀⠀⠀⠻⣄⣀⣀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠻⣤⣸⡟⢿⣄⠀⠀⠀⠀⠠⠤⢬⡙⠁⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠙⠋⠉⠙⠉⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠃⠀⠀⠘⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣀⣤⣤⣾⢭⣌⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣁⣠⠖⠛⢦⠀⣦⣾⠭⣷⣙⣀⠀⠴⣲⣶⣿⠿⣷⡆⠀⠀⠀⢀⣤⠦⣦ ⠀⠀⣠⣤⣴⠛⡆⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣖⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠐⣯⢰⣷⡉⢀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢡⡟⠳⠚⣩⠇⣿⡇⠀⠛⠛⢻⣻⢄⢿⣁⠛⠁⣿⠇⠀⠀⢰⡟⠀⠀⠈ ⠀⠀⣹⣯⣜⣿⣟⡶⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣋⠁⠈⠉⠉⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠙⣿⡏⣩⣟⣠⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠈⢿⡋⣠⣖⣿⡟⠀⣿⣧⢀⣀⣤⠾⠋⣿⡆⠛⠻⠿⠛⠀⠀⠀⢿⠁⠀⠀⠀ ⠀⠀⠀⠀⢨⠿⣷⡄⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣤⣾⠇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⣀⡀⠀⠀⢀⣈⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⢐⣷⡛⣿⠇⠀⠀⠛⠛⠛⠛⠁⠀⠈⠛⠻⣿⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⣠⡤⠾⢷⠃⠀⢀ ⠀⠀⠀⠀⠀⢤⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢻⣿⣿⣧⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣴⠟⠛⠲⢤⣄⠀⢰⠋⠁⠉⢷⠞⠁⠈⢻⡆⠀⠀⠀⠀⠀⠠⣿⠉⠟⠇⢹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢨ ⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⠀⠙⢿⣿⣿⣦⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⠛⠉⢩⡉⠉⠙⣧⢻⡄⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠻⣦⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠋⢻⡇⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠶⣤⣄⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⣏⠀⠀⠙⠻⣿⣿⣦⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⢻⡄⠀⠀⠈⠛⡆⠀⣹⠀⠻⣆⠀⠀⠀⢀⡼⣃⣤⣄⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣀⣾⣇⠀⠀⠀⠀⠀⠀⣿⠋⠙⣶⠋⢻⡄⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣧⢻⡄⠀⠀⠀⠈⠙⠻⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⢸⣇⠀⢧⣀⣠⠆⣦⡿⠀⠀⠈⠳⣤⡴⠿⣼⠁⠀⠘⣷⠀⢠⡶⠛⠲⣦⠀⠀⠀⢀⣀⣴⢿⠻⣦⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⡙⣧⢀⣀⡀⠀⠀⠻⣦⠀⢻⣤⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⣆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⣤⣤⣤⣤⣤⠶⠞⢻⣿⣧⡇⠀⠀⠈⣟⠓⠲⠶⠖⠛⠋⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⢀⣠⣿⣆⣿⣰⣤⠀⠹⢗⠓⣶⡏⣼⡟⠈⠉⣿⣀⡈⣽⣍⠛⣽⠀⡇⠀⠀⠀⠙⠉⠈⠙⣦⠀⠀⠈⠻⡼⠇⠹⠗⠀⠀ ⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⡄⢻⣄⡄⠀⠀⠠⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠘⠻⣏⡽⣧⣀⣻⡄⠀⢈⢇⣴⣿⣿⢩⣗⢰⣿⠀⠹⠁⢨⠟⣡⠀⣷⠀⠀⠀⠀⠀⠀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣦⣄⡠⢀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⡄⠙⣷⣦⠀⠀⠈⢧⡙⠶⢤⣄⡀⠀⠀⠀⠀⠀⣠⢿⡏⠈⣿⡇⠀⠀⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠿⠁⠐⢹⣯⠀⣀⣠⣴⠾⠋⠁⠉⠉⠉⠉⠈⢷⣄⣴⡿⠟⠋⠀⢹⣆⣀⣀⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣗⡄⣄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠈⢿⡄⠈⠻⣷⣄⠀⠀⢻⣄⠀⠈⠙⠛⠛⠓⠛⠛⢹⢸⠃⠀⡿⣿⠀⠀⠀⠈⣧⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠛⣫⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠞⢳⡀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⠶⠶⠶⢦⣤⣤⣤⣤⣄⣀⠄⠀⣄⡀⠀⣼⣿⣿⣿⣄⠀⢿⡄⠀⠙⢿⣷⣀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⣿⢻⡄⠀⠀⠀⢻⡄⠀⠀⠈⢻⣶⣄⠀⠀⢀⣠⡾⠋⠉⠻⣴⢛⡭⠛⣧⠞⣿⡇⠲⣿⡆⠀⠀⠀⠀⠀⠀⠸⣧⣤⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣄⠀⠀⠀⠈⠉⠿⣿⡛⠒⠶⠶⣿⣿⣿⣿⣿⣦⠀⢻⡄⠀⠀⠙⢿⣧⡀⠈⢷⡀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣿⠈⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠉⠻⠿⣶⣿⡿⠓⢶⣤⠀⠀⠀⢹⣼⣿⣷⡜⣲⢄⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⡀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠈⠉⠛⠛⠿⣷⣤⣿⣄⠀⠀⠀⢛⢷⡤⠈⢻⡄⠀⠀⠀⠀⢸⡇⠀⠀⣿⡆⠘⣧⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠛⢧⣀⡼⢉⣿⠦⠀⢠⡿⠋⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⡀⠀⠛⣶⡄⠙⢦⡀⠀⠀⠀⠇⠀⠀⠠⣷⡄⢻⡄⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣠⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣡⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢓⢤⡤⠼⡗⠛⠲⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣴⣿⣦⡤⡙⢦⡀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠹⣿⠳⣤⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠶⢦⠀⠀⠀⠀⠀⠀⢿⣤⢼⣤⡈⠘⠳⣤⣀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣴⣝⣳⣤⣀⠀⠀⣼⣆⠀⠘⣧⠀⠀⠀⠀⠽⣧⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠙⢾⣯⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠙⣾⡴⢿⣻⣦⡴⠟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣯⣉⡛⠉⣿⡄⠀⢹⡆⠀⠀⠀⠈⠛⢷⡄⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠸⣯⣿⣶⣲⣯⣤⣬⡇⠀⠀⠀⠀⠀⠀⠈⠛⠟⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀