⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠓⠒⠥⣄⠀⢈⣉⣷⣶⣦⣽⣶⣤⠔⠚⠋⠉⠉⠛⢿⡿⢴⣿⣲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠈⠳⣦⡀⠀⢀⣠⡴⠞⠻⠿⠦⢤⣄⡀⠀⠀⠈⠉⠓⠶⣤⣀⡀⠈⢳⡄⠀⠈⢷⣵⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣀⡤⠤⠦⣤⣄⣨⣿⣞⣉⣀⣀⣀⣀⣀⠀⠀⠀⠉⠙⠶⣄⠀⢦⣄⠈⠹⣶⣄⣬⣿⣄⠀⠈⣷⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠖⠛⠉⢀⣴⠞⠛⠁⠀⠞⠋⠉⢻⣶⠤⣄⣀⡉⠉⠛⠒⠤⠄⠀⠈⠻⣦⡈⢳⡀⠹⠙⢷⣄⠉⠛⠲⣾⣸⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠙⠻⣷⡦⣤⣀⠀⠀⠀⠀⠈⠙⢦⣻⡆⠀⠀⠙⣷⡦⠠⢼⡈⠙⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠁⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠳⣌⠙⠿⣶⣄⠀⠀⠀⢈⣿⣿⡀⠀⠀⢸⣧⠀⢸⡇⠀⢸⡟⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⢷⣄⠈⠻⣷⣦⡴⠟⠁⠘⣧⠀⠀⣾⣿⣦⣼⣿⠀⠀⣷⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠿⡿⠀⠀⠀⡀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣆⠀⠊⢻⣄⠀⠀⠀⢹⣆⣼⣳⣿⡿⣄⠙⢷⡀⡿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⠃⠀⠀⢀⣾⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠹⣦⠀⠀⣠⡟⣵⡟⣹⣿⠸⡄⢸⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⠏⠀⠀⠀⣼⣿⠃⠀⠀⠀⡟⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡄⢹⡇⠀⠀⠀⢹⣧⠾⣫⡾⠋⣴⡟⣿⠀⠀⢀⣿⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⢸⠀⠀⠀⢰⡟⣿⠀⠀⠀⣸⠃⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣷⠈⣿⣤⡴⠖⣫⣵⡾⠏⢀⣴⣿⠃⣿⣇⣠⡞⠋⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⣿⠀⠀⠀⢸⣇⣿⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣿⡀⣿⣷⣶⡿⠿⡫⠀⣠⣾⣿⢻⣆⣯⠹⣏⠀⣰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣿⡀⠀⠀⣸⣇⣿⠀⠀⠀⣿⡆⣄⠀⠀⣿⡄⢸⡄⠀⠀⢹⣟⣇⠀⠀⠀⠀⢹⡇⡟⢹⣦⠖⠋⣠⡾⣫⡿⡇⢸⣿⣿⠀⣿⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⣿⡏⠟⠛⠛⠻⠿⢦⣤⣼⡿⢷⣿⡤⣤⣿⣧⣘⣧⡀⣀⣬⣿⣿⠦⠤⣤⡤⠻⣧⡇⠀⢻⣴⠞⣫⣴⠟⠀⡇⣾⣿⠀⢠⣿⡽⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡃⣿⣧⣐⣢⣤⣤⣄⡀⠙⢾⡀⠀⠈⢧⣄⠛⠮⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠙⠳⣟⠀⠀⢸⣧⣾⣿⡏⠀⢀⣷⣿⣇⣀⣼⣻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡀⣻⡇⠈⣽⣿⢦⡀⠛⡆⠀⠀⠈⠁⠀⠀⢀⣴⣾⣿⣿⣿⢿⡶⢶⣦⣈⠙⠆⠀⢸⡿⢻⣿⠃⠀⢸⣿⠏⠉⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠉⠉⠉⠉⠻⣿⡆⢷⠀⠀⠀⠀⠀⠠⢿⣋⣠⡿⠿⠿⣿⣇⣰⡿⠷⠆⠀⠀⢸⢁⣼⠿⠶⠶⣿⡏⣀⡴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠄⠀⠀⠀⣠⠟⠳⣄⠀⠀⠀⣠⠄⢀⡤⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⢠⡏⣼⡟⠀⠀⠀⢸⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢾⠋⠁⠀⠀⠈⢣⡀⠜⠁⡰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⡟⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠈⣧⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣄⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢞⣹⠉⡇⠀⠀⣯⣿⡿⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣆⠀⠀⠀⠀⠈⢿⡒⣶⢶⣶⣶⠶⠶⠾⠛⠳⢷⡴⣿⠏⠀⠀⠀⠀⠹⡜⢷⢾⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠈⠻⣽⣆⠀⠀⠀⠀⠀⢀⣀⡼⠟⠁⠀⠀⠀⠀⢀⡼⣷⡜⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣯⢮⣷⣄⠀⠀⠀⠀⠈⢭⣓⠒⠒⠒⠚⣉⡡⠒⠀⠀⠀⠀⢀⡴⠋⠀⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⠄⢚⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣏⣿⣕⣦⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣠⠖⠋⠀⠐⢶⡿⠋⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠲⢾⣾⢸⠀⠙⠾⣗⣦⡀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠀⠀⠀⣠⡞⠉⢀⣾⡏⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣃⠼⠏⠀⠀⠀⠀⠙⠺⣗⣶⣶⡖⠋⠉⠀⠀⠀⢀⣠⢴⠞⠉⣠⣴⣿⣿⣿⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣤⣴⣚⣿⣷⠻⣧⣄⣠⡤⡶⠾⠛⣙⣤⣴⣿⣿⣿⣿⣿⣿⡿⣝⣦⡀⠀⠀⢀⣠⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡯⠓⠋⠉⠀⠀⠀⠉⣻⣄⡁⠁⢁⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠑⢿⣶⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⠀⣀⣤⠴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣁⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⣠⠤⠒⢶⡉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣛⣹⣿⠟⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⣉⡡⠶⠋⠁⠀⠀⠀⢀⠞⠀⢀⡴⡞⢿⡈⠣⠀⢀⣀⡀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣾⣿⣿⣋⡿⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣡⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⢠⡞⣀⣶⡏⢠⡇⢠⣼⡀⠀⣾⣿⣿⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢠⡇⢀⡾⠁⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠟⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡴⡏⢸⠁⠀⢡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿