⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⣉⣉⡉⡐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⣉⣉⣁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣠⣴⣒⢆⢌⣆⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡰⡎⣱⣒⢦⡁⡀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣊⡠⠀⣁⣽⣶⣺⣿⣧⡪⡎⠄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢠⢳⢗⣼⣿⣷⡚⠧⣉⠔⢄⣱⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣐⡿⢋⡸⣾⣿⣿⠟⠋⣩⣿⣿⠾⡈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⡀⢠⣾⣿⣍⠙⠻⢷⣿⣷⣮⡋⢟⣂⡀⠀⠀⠀⠀ ⠀⠀⡔⠉⢀⣴⣟⢾⡿⠟⢁⣤⡾⢿⣿⡟⡃⠠⢂⡸⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠠⠔⣨⢿⣟⠚⣵⣠⡀⠹⢿⡿⡝⢧⡀⠉⢢⠀⠀⠀ ⠀⠀⠀⢠⠟⠐⢡⣿⣥⣶⡿⠋⣤⣶⣿⣿⣌⣦⠀⠑⠳⡀⠀⣁⡂⣄⠀⡀⠀⠀⢀⠠⢀⢀⠄⣂⠀⢀⠜⠁⠀⢺⣫⣿⣗⢿⡤⠙⢿⣶⣬⣷⡄⠢⠹⢄⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⢠⣿⣯⣾⣿⢂⣠⣼⣿⣟⠏⣉⣹⣔⠀⠀⠈⠁⠀⠀⠀⢀⡔⠀⠀⢨⠀⠀⠀⠀⠀⠈⠁⠀⢀⣣⣍⣉⠽⣿⣧⣥⣀⠐⣿⢿⣿⣿⡄⠀⠉⠆⠀⠀⠀ ⠀⢠⠏⠀⢠⣿⢿⡟⢩⢳⣿⣹⣿⣿⣟⣳⣿⣻⡇⣭⠥⢆⣀⠀⢀⡤⡞⠀⠀⠀⠀⢳⣕⠤⣀⣀⣀⡴⠺⣍⣙⣙⣟⣦⣿⣿⣿⣷⣿⡟⡎⢻⡽⣿⡀⠀⡘⡄⠀⠀ ⠀⠎⠀⠀⣸⣏⢿⣁⣘⡍⢰⣿⠏⢸⣿⣿⡷⣿⣿⠕⢻⣭⠯⡏⣩⡴⡇⠀⠀⠀⠀⣸⢦⣍⣹⠭⣠⠛⢩⣿⣿⣻⣿⣿⡿⣇⠹⣿⣆⢩⡡⣘⡇⡽⣧⠀⠱⢹⠀⠀ ⠸⠀⠀⠀⡟⡍⣿⣿⣏⡇⣿⣿⡤⣿⣯⣿⣿⡿⣥⣶⡿⠗⠘⢹⡪⡾⢻⠀⠀⠀⢠⢟⠶⣵⠙⡄⠸⣷⣆⣼⢿⣾⣿⣯⢽⣿⣆⣻⣿⢸⣷⢿⣧⠸⡭⠀⠀⠀⠇⠀ ⡆⠀⠀⠀⣿⢱⣟⡏⠛⡘⡿⡂⢰⡟⠿⣿⣿⣿⣿⣿⣷⣾⣾⣼⣿⡷⡿⠀⠀⠀⠈⣾⣼⡟⣶⣾⣷⣾⣿⣽⣿⣿⣷⡿⠿⣻⡆⢤⣿⢃⠃⢸⣿⣣⣷⠀⠀⠀⢸⠀ ⠃⠀⠀⢸⣾⣿⡟⢣⣠⣗⢳⠈⢻⠿⠄⡷⢈⣿⣼⣿⣼⡾⣽⢿⡇⡎⠁⠀⠀⠀⠀⠋⡉⣸⢿⣭⢾⣤⣶⣯⣧⣼⠁⢁⠸⠷⣿⠉⡝⣹⡆⡼⢿⣇⣜⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⢻⢻⡧⠀⠙⣧⠈⣷⡞⣧⡀⣿⣤⣿⣷⡙⣿⣷⡤⣼⣴⠃⠀⠀⠀⠀⠀⠀⠡⣶⠧⣤⣿⡟⠘⣻⣾⣟⣄⣾⠀⣼⢧⣼⠃⣼⠋⠀⣸⡟⡟⠀⠀⠀⢸⡇ ⢀⠀⠀⠀⢾⣇⣳⡀⠠⣻⣧⢹⢷⣿⣟⠿⣽⡙⢻⣿⢏⠙⠻⠧⡉⡀⠀⠀⠀⠀⠀⠀⢀⢋⡿⠛⠉⢵⣾⡏⢁⣴⡾⠟⣻⣿⡾⡏⣰⣟⠄⠀⡿⣸⡷⠀⠀⠀⢸⡇ ⣾⡄⠀⠀⢨⣿⣿⣣⠸⣿⣿⢟⠁⢻⣿⣤⣿⣯⣾⣟⡷⢯⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡁⢣⡿⠥⣾⡏⣔⣽⣯⣶⣼⣾⡟⠀⣻⣿⣻⠃⣸⣿⢿⡇⠀⠀⢀⣸⠁ ⡇⣧⠀⠀⠀⣷⣵⡌⠘⢷⣿⣿⣷⣔⣿⣿⣟⠿⣿⣿⣝⡂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢱⣡⣿⡿⠫⣾⣿⣷⣿⣤⣾⣿⣿⢻⠁⣈⣾⣾⠁⠀⠀⣸⢻⠀ ⢰⢹⡇⠘⣷⢸⣿⣟⣄⠸⣻⣿⣶⣿⣿⣿⣟⢄⡀⠙⣯⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠟⡽⠋⢀⠀⣶⡿⣿⣿⣿⣿⣣⣿⠇⣮⣿⣿⡏⣰⠄⢀⠿⡄⠀ ⠈⣎⣿⡄⠈⣧⣿⢟⡘⣷⣿⣵⠸⣿⣿⢡⣻⣿⡿⡷⢷⣵⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣮⡿⠶⣻⣿⢛⡆⣻⣿⡿⠀⣼⣿⣾⢃⢻⡿⣼⠃⠀⣾⢣⠁⠀ ⠀⢰⣿⣻⠀⠘⣿⡏⢇⠈⡻⣦⡄⣘⣿⣷⢟⠉⠿⢿⣦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⢟⠛⠕⢿⣿⣾⡿⢁⣢⣴⣟⠃⡸⣹⣷⠋⠀⣸⡏⡆⠀⠀ ⠀⠀⢹⣿⣆⠀⢸⣿⣿⡵⡌⠹⣿⣾⣿⡫⣳⣕⣦⣄⡸⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠋⡀⢠⣤⢾⣿⣿⣷⣵⣿⡟⠠⢾⣽⠟⡏⠀⣰⣿⡜⠀⠀⠀ ⠀⠀⠀⢛⢻⢦⡈⣿⣿⣟⣆⣐⣿⣿⣝⢿⣏⠮⡛⣻⠿⢷⣭⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢫⣆⠥⣶⠛⠕⢻⡿⢫⣿⣿⢏⢀⣴⣫⣾⣽⠁⣠⣾⡿⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⢃⠆⣿⣩⢿⣿⣿⣿⣿⣿⣷⣝⠇⢈⠲⡳⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢚⠅⠀⠰⣫⣽⣿⣏⡾⣿⣿⣿⣿⣿⡞⠋⣿⢣⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡐⡤⢽⣿⢿⣽⢿⢿⣿⣿⣿⡿⣷⣧⡒⢌⢯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣋⣐⢔⣾⡿⣿⣿⣻⣿⣯⡿⡿⣿⢿⢢⠀⣇⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣡⣾⣿⣿⣾⡅⢿⣿⡿⣿⣻⡿⣿⡙⣿⢷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡬⡿⢫⡿⢿⣿⣿⢫⣿⠎⣼⣟⣿⣿⣿⣰⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣧⡹⡏⢿⣿⣌⢣⢳⣼⣿⣿⣎⣧⠈⣆⠈⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠁⡜⠀⢰⣵⣺⣿⢇⠎⡔⣰⣿⣯⢻⡿⢷⣻⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡎⢷⠙⡘⡿⡏⠀⠋⢿⢿⣿⣞⣡⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡞⣻⡷⡷⡟⠀⠀⡿⣿⠃⠈⣏⢳⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠘⣡⠐⠸⡙⡀⠀⠘⣇⠻⣾⣧⡑⠐⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠂⠈⣰⣟⡳⢰⡁⠀⢸⣱⡇⠀⣘⠆⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠆⠀⢳⣽⢆⢠⢽⠻⠸⢟⣷⠀⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡼⡿⠃⠀⣏⡆⢴⡿⡟⠀⢠⡏⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡿⠀⢘⡎⣟⣀⣽⡇⠃⠈⣫⣾⣲⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢢⡾⣽⠁⠀⢸⢀⠀⡾⢹⡁⠀⢮⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢫⢧⠻⣿⡸⡂⠹⡧⢀⠄⢹⡈⢳⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⠂⡇⢀⡈⣼⠎⢠⢇⣿⠀⣴⡌⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡘⣟⣿⣳⢗⣸⣧⠙⡀⠀⣧⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣠⠁⠌⠇⣸⡅⣾⣾⣿⣸⠏⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇⣿⢞⡾⡞⢛⢿⠀⠐⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠈⠀⡟⡇⣷⡞⣷⣿⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⢹⡾⡗⣷⣪⢿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣹⣇⠻⡘⣿⡟⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⢸⡇⡇⢸⣟⣯⡆⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣙⡀⠀⣾⣡⡇⢰⢹⡇⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⡶⢹⡆⢳⢦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢱⠹⢸⡆⠓⠈⣸⡇⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⢸⡇⠀⡀⣿⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠃⠈⣴⡆⠘⢺⡇⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⢸⡇⠀⡷⡟⠠⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡆⢿⢹⠀⢻⢇⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⢰⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⢸⣿⢰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠼⡃⠸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠃⢸⡏⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢠⠀⢴⠃⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⣟⠀⡆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣠⢟⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡻⡄⢃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣧⠎⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢹⣾⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠁⡘⡙⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠐⢹⣣⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⢠⡝⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⢫⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢡⠀⠀⠀⠀⠀⠀⠀ ⡠⠄⠀⠔⠂⣰⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣢⠀⢢⠀⠀⢄⠀ ⢃⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⢄⠀⠀⡸⠀ ⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀