⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⠤⠤⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠯⠋⢁⡠⠖⠀⠀⠀⠀⣀⣠⣬⣝⠫⠗⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣀⡀⢀⡴⠋⠀⠀⠀⢀⡤⡺⢡⠀⠀⠀⠀⠀⠚⡷⣌⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⣤⠿⡻⣷⣾⡀⠀⠀⠀⡠⠋⠀⢓⠏⠉⠤⡀⠀⠀⠀⠱⡈⡳⠝⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠸⣅⠎⢆⢗⣩⠞⠁⠀⠀⡔⢁⠎⠀⠈⢃⠀⢀⢻⠉⠂⠤⠂⣿⠘⡄⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣧⣨⣤⣉⡇⠀⠀⠀⡰⢡⠂⠀⠀⠀⠀⠁⣼⢸⠀⠀⠀⠀⡄⡖⠁⠀⢠⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡍⠀⣠⡏⠀⠀⠀⢰⢣⠁⠀⠀⠤⠤⢤⡼⢽⡀⠑⠄⠀⠔⠀⣷⠀⠀⠀⢇⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢄⠀⠀⠀⢰⡇⠀⠀⠀⠃⠀⣿⠁⠀⠀⠀⣮⠃⠀⣠⠞⠀⣠⠎⠀⡎⠀⠀⠀⠀⠠⣤⣿⡆⠀⠀⠘⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠀⢸⠀⠀⠀⠀⠀⢰⡸⠀⠀⠀⠀⣇⡤⢾⠯⢴⣋⣁⠀⢠⠃⠀⠀⠀⣀⠀⡼⠘⡗⢄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣠⣿⣿⣿⣿⣿⡿⢶⡝⢾⣀⣀⠤⢴⣣⠞⠁⠀⡇⢰⠂⠀⠁⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⡀⠀⠀⠀⣞⠕⡇⠀⠀⠀⠹⢳⡿⡏⠙⠻⣿⠀⠀⠀⠀⠀⠀⢨⣿⣯⣴⡸⠵⣻⠀⡸⠀⢸⢱⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⢄⢸⡇⠀⠀⠀⡏⢙⢃⠀⠀⡇⠀⡟⢆⡕⠾⣄⡜⠀⠀⠀⠀⠀⢠⡟⣿⣿⡟⢿⣯⣏⡴⠁⢀⡞⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⡳⣌⢸⠀⠀⠘⣄⢱⡀⢨⠹⠉⠀⠀⠀⠀⠀⠀⣸⣆⠇⠙⡇⢀⡿⣿⢃⣠⢾⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⢸⡿⡇⠀⠀⠈⣗⠻⠂⠁⠁⠀⠀⠀⠀⠀⡀⠀⠑⢾⠞⠀⢸⣁⣉⡭⠧⠼⠶⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠹⡄⣦⡀⠸⣦⣄⣠⠴⠒⠊⠉⠑⠚⠓⠒⠒⠒⠚⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⢀⠔⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣸⠀⣠⣽⣛⢟⡶⠛⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡹⣴⠋⠁⢀⡞⡆⢸⠀⡇⠘⠀⣼⣾⣷⣾⣶⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣺⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢀⠀⣷⠃⠀⠀⢸⡤⣧⠼⣤⠸⣖⣃⣨⣿⣿⣿⣿⣿⣷⣪⡉⢙⣻⠿⢶⣿⡿⠿⠿⠿⠒⠿⣞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⢰⣿⠀⠀⠀⠀⢹⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣻⣷⣦⣤⣔⠀⡋⠳⣄⠀⠀⠀⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢿⠀⠀⡄⠃⢸⢸⠀⠀⣠⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣀⣈⢳⠀⠀⠀⠀⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⡌⠘⡆⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⠧⡼⠀⠀⠀⡔⠁⠀⠀⠀ ⠀⢄⠀⠀⢀⡇⠈⡄⠀⠀⠀⡇⠀⡇⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠉⠙⢗⠲⠬⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠟⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠑⢄⣸⠀⠀⢁⠀⡄⠀⡇⠀⢹⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠳⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⠜⠂⠀⠀⠀⠀ ⢽⠶⠄⢈⡇⠀⠀⠈⣴⡇⠀⢇⠀⣿⣿⣿⣿⣿⡿⠁⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠈⠐⠿⣄⠀⠀⠀⠀⠙⠿⣟⠁⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠭⣢⣼⠀⠀⡄⠀⠘⢹⡀⢸⡀⠙⣿⣿⣿⡿⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⡊⠁⠀⠉⠙⠛⠢⢤⣀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⢸⡇⠀⠀⢸⠳⣄⢧⡀⢻⣿⣿⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠙⠲⢼⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡀⢸⢷⡀⠀⢸⡀⠈⠉⠉⣸⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀ ⠀⠠⡄⠀⢧⡸⡎⢷⡀⠀⣧⡀⠀⠀⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⡰⠁⢀⢤⠉⠛⣦⠙⠶⣽⠟⡶⢤⣼⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢠⠁⠀⠎⠀⣀⠀⠘⡑⡄⡈⠣⡙⠳⣄⣧⠞⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⢇⣶⡼⠀⠀⠛⢀⠀⠇⠈⠱⣤⢑⡴⠋⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠙⡇⠀⠀⡐⠚⠇⢸⠀⠀⢠⠟⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡇ ⠀⠀⠀⠀⠈⠲⡀⠸⡜⠀⢀⣯⣤⣤⣤⣄⣀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡀⠀⢱ ⠄⠀⠀⠀⠀⠀⠈⠆⢠⡶⠋⠀⠀⠀⠀⠈⠉⠛⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣔⡲⠖⠒⠀⢀⣜⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃ ⠂⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣙⠲⣤⣑⡤⢀⣀⠀⠀⠀⠀⢀⣀⣤⡶⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢬⣿⣍⠙⡚⠛⠛⠛⢛⣿⠯⠛⠙⠚⢿⣶⣤⣀⣀⠀⣀⣀⣀⣀⣀⣤⠤⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣯⣷⡶⠋⠁⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣤⣾⣿⣿⡟⡋⠉⠀⠀⠈⣿⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡇⢠⣶⣿⣿⠟⠉⠀⢧⣘⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢀⣀⣀⣤⣴⣶⣶⣋⣿⣿⣿⡿⠿⠿⠛⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠿⠟⠛⠋⠹⡃⠃⠀⠀⠀⠀⠀⣽⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀