⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣾⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢟⣯⣳⠽⣞⡽⢮⣽⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡽⣺⢧⣏⡿⣹⣞⣻⣾⡟⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣧⣿⡽⣳⢏⣾⡹⣗⣾⣵⣟⠾⣽⣹⣿⢀⣴⣶⣶⣦⣠⣴⣾⡿⡿⣟⡿⢿⡿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⣲⢟⣿⢧⣟⣮⣿⢿⡿⢿⣾⣿⣷⣭⣿⡿⢯⣳⣽⣿⡻⣝⣧⠿⣵⡻⣼⢻⣼⢳⣮⢽⡻⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⣫⡷⡿⢯⣿⢿⣹⢾⣹⢞⣯⠶⣏⣾⢻⣿⡽⣯⡿⡽⣖⢿⣹⣎⢿⣱⡟⣵⡻⢮⣷⡹⣞⣳⡽⣞⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣽⣽⣿⠛⣾⢹⡞⣽⢺⣧⣿⢹⣮⡗⣯⣿⣿⡝⢻⣼⡏⣶⡏⡟⣮⣽⢳⢻⣽⢲⡟⣽⡎⣷⡏⡞⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⡳⣿⣯⢟⣧⣟⣳⢯⣳⢾⣱⡟⣮⡽⣞⡽⣳⢯⡻⣵⣛⣧⢿⣹⡝⣾⣹⡞⣧⡟⡾⣵⢻⡵⣻⡝⡿⣿⡆⠀ ⠀⠀⢀⣤⣤⣀⠀⠀⢻⣷⡽⣿⢧⡟⣶⠽⣮⢗⣯⢞⣧⢿⣱⡟⣼⡳⣏⣷⣻⣵⣿⠾⠷⣿⣾⣷⣧⣿⣱⡻⣝⡾⣭⢷⣫⡽⣽⣻⡇⠀ ⠀⢠⡿⠁⠌⠻⣿⣿⠿⣿⣞⣿⣟⡾⣭⢟⡾⣹⢮⡟⣼⢧⣻⣼⣳⣿⠟⢋⠙⢿⠀⡐⠠⠀⢼⡄⢹⣟⠷⣿⣧⢟⡞⣧⣟⡼⢧⣿⣿⠀ ⢀⣿⢃⡰⠈⠄⡈⢿⣿⣝⣿⣾⣿⣽⣞⢯⣝⢯⣳⢻⣝⣞⣳⣾⠏⡁⡐⠂⢄⠊⡐⠠⠑⡈⢘⣇⠄⢻⡆⠙⢿⣾⣹⣳⢞⣽⢫⣾⡇⠀ ⢼⡿⢀⡧⢈⠐⡀⢊⢿⣿⡿⠁⠨⢿⣿⣮⣛⡾⣭⢟⡾⣼⡿⠡⠠⡁⠰⢁⠢⢀⠡⢁⠒⡀⠢⢻⡄⢚⣿⠀⠘⣷⣻⡼⣏⣾⢫⣿⠇⠀ ⢽⡇⠸⡇⠠⡁⠰⢀⠚⡟⠠⠘⠠⢀⠊⠻⢿⣾⣵⡻⣞⣽⠁⢡⠂⠌⡐⠂⠄⣵⣾⣿⣲⠶⣷⡿⠁⣌⣿⠀⠀⣿⠷⣽⡺⣵⣻⡟⠀⠀ ⢸⣧⠁⣿⡀⠁⠆⡁⢂⠁⠂⠥⠘⠠⠌⠄⡂⢈⠉⠛⠛⢛⠈⡄⢈⠒⠠⢁⣾⠋⠈⣿⣿⣳⣌⠹⣶⠟⣇⡾⠀⣸⣟⡧⢿⣱⡿⠀⢀⣷ ⣿⣿⡀⠜⣧⠁⢢⡔⠠⢈⠴⣠⣅⣢⠌⢠⠁⠆⠌⢂⡁⠢⡐⠈⠤⢨⢁⣿⠃⠀⢀⣿⣿⣷⡹⣆⠘⢿⣟⠁⠀⣿⢾⡹⣏⡿⠁⣠⣾⡏ ⣿⡟⣧⠐⢸⣧⠹⣷⣡⣶⡿⠛⠙⢻⣿⣶⣌⠌⢂⠂⠤⠁⠄⡁⠊⡔⢸⣿⣀⣠⡿⠉⣿⣿⡇⣹⡀⠀⣿⡆⠀⣿⢯⣝⣿⣥⡾⣟⣿⠃ ⢿⣿⣽⣆⡉⣯⣄⠩⣽⣿⠁⠀⠀⢸⣿⣿⣿⣿⡢⠌⡄⠃⢌⠠⡁⠌⢸⣿⣿⣿⣿⣾⣿⣿⠃⢸⠇⠀⠽⣷⠀⢻⣟⡾⣝⡾⣱⡿⠃⠀ ⢸⣿⣻⢿⣷⣍⡽⠿⣿⣿⡀⠀⢀⣾⠉⣹⣿⣿⣷⡏⡠⢁⢂⠐⡠⢁⠺⣿⣿⣿⣿⣿⣿⠏⣀⠈⠀⢀⡷⣿⡄⠈⠛⠿⠾⠟⠋⠀⠀⠀ ⠸⣿⣯⡻⣽⢿⣝⡛⠛⢯⡻⣶⣿⣿⣿⣿⣿⣿⣿⣷⠠⡁⢂⠌⡐⣀⠂⣙⣏⠛⠟⠛⢉⢠⡼⠃⠀⢰⣟⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⡿⣎⣯⢟⣿⡄⠈⢷⢩⠿⣿⣿⣿⣿⣿⠟⣻⡇⢐⠂⠌⡐⢀⠂⢌⡹⡆⠙⠛⠚⠋⠀⠀⠀⣸⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣜⡯⣿⣷⣣⠈⠓⠀⢀⡍⠛⠋⠍⠰⣹⣷⡆⢈⠰⣤⠶⠛⢋⠁⡹⣄⠀⠀⠀⠀⠀⣰⠋⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣷⢯⣿⣿⣷⣀⠀⠚⠦⢬⡴⠼⠛⠓⣿⢃⠐⠠⣄⠠⢁⠂⠼⡀⠌⠱⠲⠤⠖⠋⡁⢢⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣟⡧⢿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⢀⡟⢀⠸⢀⠛⠄⡀⠜⡀⢸⠇⡀⠃⠄⡘⠄⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣟⣮⡽⣏⢿⣾⣿⡉⠲⣤⣀⣀⣀⣠⠞⢀⠂⣰⣄⠈⠄⠡⠂⢄⡿⠐⡈⡁⢂⠅⣲⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢞⡶⢯⡽⢾⣱⢿⣿⣦⣄⠈⡉⢉⠠⡐⢈⠐⡀⢉⠳⠾⡤⠷⠋⡁⠆⠡⢐⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣯⡟⣞⡯⣽⣫⡽⢮⣳⢟⡿⣷⡶⣄⣂⠄⠡⠂⠅⠢⠐⠠⠐⠠⢁⣰⣬⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣝⣳⡽⣣⢷⡻⣝⣧⢿⣹⡗⣿⢿⣯⣿⣶⡷⣾⣴⣷⣶⡷⠿⠛⢋⠡⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣾⡵⣻⢭⡷⣫⡽⢮⣳⢧⣟⡞⣧⡟⣼⣫⢿⣦⠀⠤⡀⠄⠢⠑⠂⠄⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣟⣷⣿⣼⣷⢿⣟⣧⠿⣼⣹⢧⡟⣧⢯⣻⣿⡐⢐⡈⠄⠃⠌⡁⢆⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣾⣵⣛⣮⢿⣟⡮⣟⡵⢯⡾⣹⠾⣭⡿⢃⠁⢂⠐⡈⢁⠂⠡⢈⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀