⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠳⣌⡉⠻⣄⠀⠙⡇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⠃⠀⠀⣶⠒⢦⡀⠉⣓⣽⡄⠀⢹⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠒⠚⠛⠛⠉⠙⠛⠓⠒⠛⠦⢌⣻⢦⡀⠘⢧⡀⠙⣾⠋⠀⣻⡀⠸⣆⠀⠀⢀⣀⣀⡀⠉⠑⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⠻⣄⠈⠳⣤⠏⣷⡀⢯⢳⡜⠉⢀⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⠀⠀⠈⠛⢧⣳⣸⠏⠀⢀⡾⣧⣄⣀⡤⠴⠚ ⠀⠀⠀⠀⢠⡶⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⣀⡀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢀⡤⠊⠉⠁⠀⠀⢸⣷⡿⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣠⠟⢀⠖⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢀⠀⢀⡜⠳⢄⢀⠦⠖⠒⢦⡱⡄⠀⠀⠀⠀⠹⣎⠀⠀⠀⠀⠀⠀⣼⠸⣿⣎⠛⢦⡀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⠏⣠⠋⡠⠀⠀⠀⣠⠎⠀⠀⠀⠀⣰⡷⠃⠀⡾⠈⠓⢠⠏⠀⢴⠉⠂⢌⢹⠠⣄⠀⠀⠀⠹⡄⠀⠀⠀⣠⡾⠋⠉⠱⣽⣧⠀⠙⠳ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⣇⠀⠀⠀⠀⡞⣰⢃⠞⠀⢀⡠⡴⠃⠀⠀⠀⢀⡾⠋⠀⣠⢾⠃⠐⢠⡟⠀⠀⡎⠀⠀⠀⠀⡇⣈⠱⣄⢀⠀⢹⡋⠉⠉⢻⡀⠀⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⠀⠀⠀⣸⠱⡷⢃⣤⠞⠁⢰⠃⠀⠀⠀⢀⠞⣠⣶⣟⣁⣸⡀⠀⣾⠃⠀⠀⠇⠀⠀⠀⠀⢸⠈⠓⢌⠻⡆⠀⣇⠀⢀⣨⡿⠿⣯⠉⠙⣒⠷⠿⣍ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣤⢤⣀⣿⠜⣴⠟⠁⣠⠤⡇⠀⠀⠀⢀⠏⡩⠋⠁⠀⠀⢸⢨⠉⡿⠀⠀⢀⠀⠀⠀⢀⠀⢸⠀⠀⠈⠂⢹⠀⢹⢯⠉⠀⠹⡄⠸⣖⣫⠥⠦⠤⠤ ⣄⡀⠀⣠⣴⣾⡿⢿⠀⠀⠀⣾⡤⣬⣽⣛⠀⣡⢤⠞⣴⣻⠀⠀⠀⠀⣾⠞⠁⠀⠀⠀⠀⠘⣇⠀⡇⢀⠀⠸⡀⠀⠀⣯⢤⣸⠀⠀⠀⠀⠈⡇⢸⠘⡆⠀⠀⢳⠀⢻⡤⠶⡖⠤⣄ ⠀⢉⣷⢿⡿⠋⠀⢸⡇⠀⠤⢻⢋⣵⡿⣿⡤⣀⡏⢸⣖⡇⠀⢀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⡇⢸⢀⠀⡇⡆⢀⣿⠀⡟⡧⡀⠀⠀⠀⣇⡞⠀⠹⡀⣀⡬⠧⠞⠳⣤⠇⠰⡹ ⠀⡾⣡⢏⣠⡴⠖⣿⡇⠀⠀⢸⣫⠋⠀⢸⣱⣦⣳⠸⣸⡇⠀⢸⠀⠀⣷⣶⣶⣶⣻⣍⡑⠆⠀⠙⢧⣾⣎⠀⢱⡇⢸⢸⢰⡃⢣⠙⡄⠀⠀⢻⡇⡠⠖⣫⢫⠆⠀⠀⠀⠸⡈⢀⡇ ⠘⢡⢃⡟⠀⠀⠀⠈⠳⣤⣀⡼⠷⣄⠀⠈⣇⠳⡌⢇⢹⠀⠀⢸⣸⡀⡇⠀⠀⠀⠈⠙⠷⡄⠀⠀⠘⣟⠻⢦⡨⣗⣿⣿⣿⣧⣸⠀⠀⠀⠀⢸⠋⠀⡴⢡⠏⠀⠀⠀⠀⠀⢷⣟⣹ ⢠⠞⠋⠀⢴⡄⠀⠀⠀⠙⢦⠀⠀⠉⢙⡷⢺⣧⡘⢮⣻⡄⠀⠸⡇⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣽⣿⡏⢿⣿⡄⠀⠀⠀⣾⢠⠞⠐⠃⠀⠀⠀⠀⠀⠀⠘⢷⡙ ⠏⠀⠀⠀⠀⠻⢦⡀⠀⠀⡼⡇⠀⣠⠞⠁⠈⣿⠻⣄⠘⡇⢸⢀⣿⢹⠳⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠛⣿⣿⠇⣸⣿⡇⠀⡀⠀⣿⡣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷ ⠀⠀⢦⡀⠀⠀⠀⣹⡖⠊⢡⡇⢰⠏⠀⠀⣠⣿⡀⠈⠙⣇⡌⡞⡏⢿⡄⠈⠙⠀⡞⠒⠤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠿⠤⠚⢉⣼⣇⠀⡇⢰⠧⡙⢦⢙⢆⠀⠀⠀⠀⠀⠀⠀⢀⠘ ⠀⠀⠀⠓⣦⠤⠴⠃⠹⡄⢸⡇⢾⡞⣴⠟⡟⡇⢷⣄⠀⢹⡁⠇⡿⣌⠳⠀⠀⠀⢻⡀⠀⠀⠉⡒⣤⡀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠀⡇⣼⡀⢳⡈⣧⢫⣧⠀⠀⠀⠀⠀⡴⠃⢀ ⢷⣤⣠⡤⠂⠙⢦⣤⣤⠟⠉⠀⠈⠙⠁⣸⢯⡿⠀⢹⡏⠓⢷⡀⣇⣼⠳⣄⠀⠀⠀⠈⠒⠢⠤⠟⠋⠀⠀⠀⠀⠀⠀⣰⠟⠊⢹⠀⢰⣇⡇⡇⡄⣇⢸⡀⢹⡆⠀⠀⢀⡞⣁⣴⣂ ⠀⠘⣿⣭⡙⠒⠚⠁⠀⠀⣠⡤⠤⠴⢾⣿⢸⠃⠀⡼⢷⠀⠈⢷⡸⡇⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⢀⡏⢠⢿⣼⢀⢧⡇⢺⢸⢳⢀⡗⠲⣶⠋⠙⢧⠀⢸ ⠘⢄⢇⠳⣝⠳⣤⣤⡴⠞⠁⠀⠀⣠⠏⣞⡏⡄⢀⡇⢸⣦⠀⠐⣷⣿⡀⠀⠀⠀⠙⠲⠶⠶⡶⣲⣾⠋⢉⡟⠁⠀⠀⠀⠀⡼⣠⠎⣾⣿⡸⣴⠀⡏⣸⠞⠻⣷⡀⠈⠻⣄⠈⠳⠘ ⠀⠈⠻⣄⠈⢳⣤⣄⣀⣀⣀⡴⠚⡇⢠⡿⠀⠀⣼⡇⠀⡏⢧⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⢸⢫⢿⡏⣰⠏⠀⠀⠀⠀⢀⣾⠵⠁⣼⢟⣷⠣⠃⣸⢡⡏⣦⡀⠀⠙⠶⣄⡈⠓⠄⠸ ⢷⣀⠀⠘⢦⡀⠳⣄⠀⠘⡆⠀⢠⣧⣿⠃⠀⣸⣻⢀⢸⡟⢎⢣⡀⠀⠈⢷⣀⣀⠀⠀⠀⣿⢾⡆⠙⠳⣄⡀⠠⠴⠞⠋⠁⣠⠞⢁⡞⠁⠀⢠⣣⠋⢹⣹⠋⠀⠀⠀⠀⠁⠀⠀⣰ ⠀⠙⠳⣦⣌⠙⠲⢮⣷⣄⣹⠴⠾⣱⠏⠀⣼⢣⠇⠜⣼⣧⡈⢣⡱⣄⠀⠈⢧⣈⣉⠓⠦⣉⠈⡇⠀⠀⠀⠙⢻⣍⡉⠉⣽⢁⡠⠊⠀⠀⣴⠿⠥⣤⡞⠁⠀⠀⠀⢀⣀⠀⣴⠏⠀ ⠀⠀⠀⢻⠙⠳⣄⠀⠉⠓⠦⠄⣰⠏⠀⠘⠁⡞⠀⢀⡇⠘⣝⢦⡙⢦⡑⢄⠈⢯⠺⢽⣢⡈⠳⡇⠀⠀⠀⢀⠞⡼⢫⣷⡛⢉⡠⠄⣠⢞⣏⢾⣹⠋⠀⠀⠀⠀⠀⠉⣠⠞⠁⠀⠀ ⠀⠀⠀⠘⢧⡀⠈⠁⠀⠀⠀⠐⠃⠀⠀⠀⡼⠁⠀⡼⠀⠀⠈⢦⡟⠶⣝⠢⣙⢮⣧⠀⠙⢮⣾⠁⠀⢀⡴⢋⠞⢠⠟⡄⡿⣧⠖⣻⡵⠋⢹⠈⢿⡀⠀⠀⠀⠀⢠⡾⠻⣷⣄⡀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠳⣄⠏⠳⣌⡓⢬⡇⠀⣰⣃⠤⢒⡩⠖⢁⡴⠫⣀⡟⠀⡹⣆⣿⣇⡴⢻⠆⣸⠙⣦⣄⡀⠀⢻⠀⠀⠈⢳⡝⡆ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣤⠯⠽⠦⢽⣴⣥⣴⣊⣡⠴⣺⠛⣄⢀⡟⢀⣄⡇⢹⣜⡾⡄⠹⣆⡇⠀⡼⠀⠩⢽⠞⠒⢒⡶⠿⢥⠇ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⠙⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣡⣶⠒⢻⢋⣿⣷⣿⣟⠒⣯⣟⡧⣄⣸⠏⠀⠘⣿⠀⠈⢻⡝⢳⡀⠈⢷⣤⡇⠀⠀⡞⠀⢀⡞⠀⣰⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠞⠁⠘⢧⠇⢸⡏⣿⠹⣞⢿⡅⠀⣹⣾⡳⡄⠀⠀⢸⡄⠀⠀⠻⣄⢧⢄⠀⠙⢯⣓⠦⣧⣀⣸⣁⣠⠇⠘⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⠀⠈⢧⢸⢃⡏⣿⢻⣎⢷⡞⠉⠀⠹⣽⡄⠀⠀⣧⠀⠀⠀⠘⣾⡜⠀⠀⠀⠙⠳⣄⠀⠉⠉⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣧⡀⠀⠀⠀⣨⠏⣼⣿⠉⢧⢿⣷⣝⢦⣀⣠⢏⡇⠀⠀⢸⠀⠲⠤⣀⡿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢡