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