⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢁⠬⠃⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣠⣀⡤⠒⠊⠉⠉⠉⠁⠀⠒⠄⡀⠐⢣⡜⣿⠀⢱⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⢋⡽⠊⢦⠄⠀⢤⠈⣢⡀⠀⠀⠀⠑⠚⡔⠡⠄⢀⠍⢐⠶⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣍⡁⠀⠛⢏⠆⣰⣫⣥⣀⣞⠻⣝⣏⡢⡐⣞⣄⣨⢃⠀⣘⠥⡨⢅⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣢⣖⣙⣦⣄⡀⡓⢄⡈⣻⢋⣿⣦⣙⠛⣹⣿⠋⢰⡼⢃⣿⠋⢪⠤⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡔⠔⡩⡬⢿⢻⢼⣆⡑⢳⢉⠙⣿⣗⡟⢻⡇⠀⠀⠰⠡⠓⠨⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠸⢇⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⠟⡾⢧⠗⣸⣡⡏⡿⠀⠀⠉⣻⠛⠛⣹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢞⠒⠤⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢨⠾⢺⣽⡴⡏⠶⠀⡸⢃⡿⣽⣽⣀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⠀⠀⠘⣧⠛⠛⢴⡱⠋⠀⢀⣶⣛⣁⣀⠀⠔⠊⠁⢀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠢⠀⠀⠀⠀⠀⠀ ⠠⣶⣶⣶⣶⣶⣶⢲⣶⣴⣢⡤⣤⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⣄⣴⣶⡦⡴⢪⡿⣿⠈⠉⠀⣠⣾⣫⣵⣖⡻⠭⠄⠒⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢯⡺⠭⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⣸⣿⣽⣿⣿⢿⡿⣯⣷⡟⣿⣿⢻⣏⣿⠀⠘⣖⠒⢯⡻⣭⣸⣿⢻⣟⠄⠛⢸⠃⣀⠤⢾⠿⣿⠿⠛⢲⡶⢆⣀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣁⣃⣁⡯⢫⢹⠙⣇⣿⡿⢞⣿⠿⢄⢀⠟⢬⡑⢹⣦⣿⣿⠹⣷⣶⣤⣶⣿⣷⣿⣿⣿⣫⠀⢠⠀⠹⢄⠁⠉⠒⠲⢶⠟⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⢿⣿⣿⠋⠉⠒⠓⠞⡹⢛⠟⢳⣷⠏⠀⡸⣤⣼⣻⣆⢌⠳⣜⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⣠⡟⠀⢈⣈⢧⡀⠀⠰⠊⢧⠄⠀⠀⠀⠀⠀⠀⠐⢀⣤⠆⢤⣀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡾⣂⡱⠿⣴⢈⠉⡉⡛⡻⣿⡿⣿⣯⣿⣿⣿⣿⣾⣯⠏⡊⠔⢀⠀⠚⠁⠱⢈⡦⡀⢡⠟⠀⠀⠀⠀⢀⡀⠀⠀⠈⠳⢥⣪⡗⠀⡀⡤⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠉⠘⠚⠚⠛⠛⣿⣿⣿⣟⡽⢿⣿⠿⢿⣟⣠⠮⠄⢐⡉⠉⠃⣸⠁⣷⠊⠀⠀⠀⢀⡰⡱⡮⠃⠀⠀⠀⠈⠣⡀⢀⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢉⢻⣿⠿⠋⠀⣸⠾⣦⣤⢄⡀⠈⠷⠀⣾⠀⣹⣧⣄⠀⠀⠑⡟⠈⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠘⠚⣊⠆⢿⠁⠀⣶⠏⡇⠄⠉⠣⡀⠑⢆⢸⡩⣧⣿⣹⣿⡧⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢻⡿⠛⠙⠦⠄⠤⣈⣇⡱⡇⠀⠃⠈⢄⠂⠨⡀⢀⣼⣭⣿⣿⣼⣿⡿⠀⠉⠂⠁⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⣰⡟⠀⠀⠀⠀⠄⠀⠈⠉⠛⠻⡦⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⣸⣿⣽⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⣌⣱⣶⣶⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠨⣿⢻⣻⣴⣰⠀⠀⢆⠀⠐⡀⠀⠀⠀⠈⢺⣃⠐⡏⠘⡟⢍⢙⣹⣿⠽⠿⠻⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠻⢏⢻⣇⡀⡄⠡⢀⠀⠀⠀⠠⡀⢸⡎⠀⡇⠀⠘⡤⡉⠁⠛⠣⣄⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⣧⣌⢢⡐⢄⠀⠀⠀⠉⠪⡇⠀⢣⠀⠀⠀⠀⠀⠐⢆⠐⣄⡀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⣿⣿⣻⣿⣿⢿⣿⣿⢷⡻⢆⣁⠄⠀⠀⠀⢺⢀⠂⡇⠀⠀⠀⠀⠀⠈⠂⢶⣹⣁⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⢻⣟⣿⣿⣿⢿⢿⣿⣿⣿⣿⣧⠀⠁⠠⢀⡀⢸⣗⠐⠞⠒⡀⠀⠀⠀⠀⣀⠜⠋⣀⡄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠍⠶⠳⠟⠻⠯⠘⠉⠈⠉⠉⠉⠉⠈⠒⠒⠚⠙⠛⠋⠂⠤⠀⢯⢉⢁⠀⣙⠯⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀