⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠈⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⡾⢄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣤⣤⢤⠀⠀⠀⠀⠻⣖⠒⠫⢭⣛⡛⠷⢶⣺⢤⣀⠀⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀ ⡷⠿⢟⣛⡭⠵⠖⠛⠉⠁⠀⠀⠀⠀⠀⠈⢙⣦⠤⠴⠛⠙⠲⣤⣙⡒⠭⣓⡢⢴⣶⠦⣬⡽⣦⣄⡀⠀⠀⠀⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢀⡠⣰⠏⠁⠀⠉⡓⠦⣍⡒⠮⣙⠻⢯⣲⡳⣿⢷⡶⣫⠤⠼⣷⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀ ⣀⢸⣿⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⠋⣠⠇⢠⠇⢠⠞⠀⠀⣠⡌⠓⠢⣍⡒⢬⣱⣌⠛⢿⣀⡴⣒⣘⡒⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀ ⢳⣿⣯⣿⢻⣽⣆⠀⠀⠀⠀⠀⠀⡰⠋⢠⠂⢲⡏⢸⣸⠀⣮⢠⠏⠀⢀⡾⠹⠟⡆⠈⣆⠉⢶⢬⣙⠿⣜⡛⣇⠀⠀⠉⠺⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⢦⣿⣿⣿⣎⣿⣿⠀⠀⣀⣀⠀⢸⠁⢠⠃⢀⣧⡷⡿⡇⣸⡃⡌⠀⠀⡞⠤⣄⡀⡇⢠⢻⠀⢸⠀⢨⠓⢤⡙⠺⡖⠒⠒⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣻⢞⣉⠀⣀⡽⢸⢸⢿⠀⣼⠃⢰⣇⢷⢻⡁⠇⠀⡼⠀⠀⠀⢹⢧⡼⢸⠀⢰⠀⠀⡇⣆⢫⠳⡇⠀⠀⠀⢯⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⣤⣾⣿⣿⣿⣿⣿⡏⠨⣊⠁⠀⢈⣿⣸⠀⣼⣲⣦⣦⠈⠚⠿⣶⡀⡇⢀⡀⠀⢘⡜⠙⣾⠀⠈⠰⢁⣇⢸⡈⡆⠃⠀⠀⠀⠈⠇⢳⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣏⡝⣿⣿⣿⣿⢷⠒⠚⠀⠀⢈⣿⡿⣆⡟⠉⡍⠉⠃⠀⠀⠀⠀⠴⠾⢷⣯⣷⢄⢠⠏⡰⢰⠃⣼⡞⣸⢳⣱⢰⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⠹⢿⡿⣿⣿⣿⣞⡄⠀⠀⢠⠎⠘⠳⡞⢳⣴⣢⠀⠀⣀⣀⡀⠀⠀⠀⢆⠈⠙⢿⡞⣰⣵⢃⣾⣋⡴⣿⡀⡿⡿⡄⡀⠀⠀⠀⠀⠸⡆⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠓⢛⡡⣿⣿⢿⣿⣻⠀⠀⢀⠠⣷⡄⢧⠈⢉⣈⡁⠟⠂⠠⠬⠵⣄⠀⠾⣏⡇⡼⣰⡷⡡⠛⠊⠁⢀⣈⢿⣶⣇⣽⡛⣻⠣⠦⣄⡀⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⠊⣡⢔⣿⣿⣿⣿⣿⣧⠀⠈⢦⣈⢉⠞⠋⡹⢰⣻⢳⠀⠀⠀⠀⢸⠀⠀⠈⠉⣩⠟⢫⠀⢀⡴⠚⣉⡀⠀⠘⢇⠀⣧⠃⠀⠀⢨⣹⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢒⣩⣴⡟⡿⣿⣿⠛⠉⠀⠀⠀⠀⣨⢏⠀⢰⢣⢿⢇⣟⠂⠀⠀⠠⠎⠀⠀⠀⣰⠃⠀⡎⡴⢁⡤⠊⠁⠀⠀⠀⢸⠼⢼⢀⣤⠞⠋⠈⣏⠓⢦⡘⡃⠴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⣿⣿⣧⣿⣻⣿⣧⠀⠀⠀⡰⢏⡩⠽⢀⠇⡮⡝⡼⡼⡽⠒⢶⣤⡖⠒⠋⣉⣼⣇⠀⡟⡴⠋⠀⣀⠠⣖⠔⢀⡜⢸⠸⣋⣁⠀⠀⠀⢹⠀⠀⠻⣅⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⣶⠀⢻⣿⠿⠛⠉⠀⠀⢰⡇⢸⠃⠀⡞⣸⡹⡹⢱⢀⡇⠀⠀⣑⣧⠖⢺⠏⠁⠘⡄⡀⠲⡶⠟⠒⣉⡤⠔⢯⡀⣸⡔⣸⠉⠻⢤⣀⠈⡀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⡇⠀⣼⡿⠃⠀⠀⠀⣰⠛⠧⣜⡿⢷⣶⡿⠷⢷⣿⣄⣈⠉⠻⣷⠓⣿⢿⠀⠀⠀⢹⠃⠀⠀⢡⠌⢳⠀⠀⠀⣷⢟⣴⡃⣀⣀⣠⠼⠿⠁⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣆⣠⢷⠳⡄⠀⡴⠖⢧⡀⠀⠀⢉⡟⠁⡜⢀⠎⣼⠀⢈⣉⣉⠽⣄⣸⠾⠓⠀⠀⣼⣇⣀⠴⠋⢀⡾⠀⠀⠀⡇⠈⡰⠙⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡗⠘⡄⢘⣾⡁⠀⠀⠈⠓⠢⢾⣀⠐⡥⠊⣠⣼⠦⣄⣤⠴⠚⣾⠁⢀⡠⢄⡺⠤⢤⣤⠤⠔⠋⠀⠀⠀⠀⡇⢠⠃⠀⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀ ⢀⡜⣉⡀⡇⡏⠀⢇⠀⠀⠀⠀⢀⡞⠙⢯⣄⠀⠀⠘⣶⠃⠸⠀⢸⠙⣄⡭⠊⠁⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢹⣡⠴⠊⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⠏⠀⠀⠴⣿⠐⠀⠈⣦⠀⠀⢠⠎⢣⡀⠀⠱⡇⠀⣰⠃⠀⡆⠀⣦⠞⠁⠉⠐⣲⣞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣠⠤⠒⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀ ⢸⠀⠀⠀⡇⡇⠀⠀⠈⠧⢠⡇⠀⠀⡼⠓⠀⡠⠟⡿⠀⠀⡇⢸⠙⣆⡴⠾⢍⠀⣰⣞⡉⠀⡄⠰⡀⣄⣀⡠⠾⣷⣉⠤⠤⠤⠶⠭⠭⠿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⡜⠀⠀⠀⣧⠈⠑⠢⠀⣀⡞⠀⠀⠸⡄⠀⢰⠃⠀⣹⣦⣄⡀⢸⡓⡶⢛⡆⠈⣯⡟⠁⠉⢲⢃⣀⣹⡌⢧⣠⠜⠓⠶⠤⣄⡀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⡠⣯⠙⠚⠉⠉⠀⠀⠀⠀⠀⡽⠦⡤⠀⣴⠛⡉⠓⠓⠚⢹⢧⠈⠉⢹⠇⠀⠀⠀⠛⢊⣾⣤⡧⢬⡇⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠘⢹⣤⠴⢶⢄⠀⠀⠀⠘⡆⠀ ⣀⣤⡶⠃⠻⣄⠀⠀⠀⠀⡴⠖⣒⠾⠀⡼⠀⢀⣰⠒⡇⠀⠀⠀⢸⠀⡵⠂⡞⠀⠀⠀⠀⠀⡼⠵⠗⠒⠚⠁⠀⠀⠀⠀⠀⢰⢦⠀⠈⢦⡠⠖⢢⡄⠀⠹⣠⡞⠋⡭⠩⢕⡄⢻⡀ ⠈⠁⠀⠀⢀⡟⢢⡀⠀⢸⠁⢀⣙⣷⣛⣧⣀⣘⣿⢧⡇⠀⠀⠀⣨⡞⡠⣰⠇⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢇⡧⠐⣚⡶⡄⣠⠧⠤⠄⠀⢹⠠⠥⢄⡀⠓⡌⡇ ⢦⡀⢀⡴⢋⡠⠔⠉⠓⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠻⢷⠀⠀⣰⣯⣾⡵⡟⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠴⠁⢀⣼⢍⡶⣻⣔⣤⣀⠀⠀⠀⠁⡰⠚⠉⠛⡇⢸ ⢊⡽⢉⠴⠋⠀⠀⠀⠀⣠⠤⠖⢋⣉⡤⠤⠤⠀⠀⠀⠀⢧⠀⢠⡏⠛⣺⠁⠀⠀⢀⡼⠁⠀⢸⠀⠀⠀⠀⡆⣠⠤⣶⠟⢢⣠⠞⠉⣰⠬⡬⠤⠤⠤⢬⣁⠀⠀⢸⡁⠀⠠⣰⠃⠘ ⠁⠀⡎⠀⠀⠀⠀⣀⡼⠡⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠁⢠⠃⠀⣀⣀⣞⣀⣀⢀⡾⠚⠋⠙⣒⣯⣄⡞⠉⠉⠉⢉⡴⠋⠀⠀⠘⠀⠀⢀⠔⠉⠉⣆⠀⢣⣀⣞⡝⠀⢠