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