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