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