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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠴⠴⠤⠤⠤⠤⠶⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠞⠶⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠓⠉⠀⠀⠀⠀⠀⠀⠀⠋⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⠓⠈⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠉⠉⠉⠋⠖⠤⣀⣀⣀⠤⠳⠈⠀⠀⠀⠀⠀⠀⠀⠁⠾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠤⣠⣀⣀⣀⠤⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀ ⠃⠿⠾⠶⣯⣤⣘⣌⡐⣏⣠⠀⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡶⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠈⠀⠀⠀⠀⠀⠀⠜⢁⠈⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣧⠾⠼⠿⠳⠘ ⡿⢸⢆⠤⠁⢠⠤⡈⡞⢀⠀⠀⠀⠋⠔⠤⡄⢤⠳⠉⢸⠀⠀⠀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠈⠀⠀⠀⠀⡏⣶⣠⣀⢀⡀⣀⠢⠘⠀⠀⠀⠀⢷⣣⢞⣬⣹⣳⣿ ⡀⣀⢤⠿⠛⡌⠇⡅⢸⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⣄⢦⠙⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⠉⠞⣀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⡇⢳⢯⣟⡤⣀⣀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠙⢩⠍⡉⠟⡶⣫⣜⢫⡵⡞⠽⣎⠧⣷⢿⣿⡿⡿⠷⢻⣿⢻⠖⠶⡷⣾⣷⢈⠳⢤⠃⡠⠔⡌⠀⠚⠂⢡⡌⠒⢁⣋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣳⣟⢛⣽⠯⣜⡻⣝⢧⠾⣝⢯⡻⢾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⡛⡙⣛⠙⣉⠩⢉⡩⠙⢩⠛⠟⠾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀