⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣞⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⡯⢟⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣿⡳⢯⣞⣽⣿⣿⣿⢿⡿⠿⢿⣿⣿⡿⣿⣯⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢭⣦⣤⠾⣿⣿⣿⣿⣿⣷⣿⣶⣫⣾⠟⠁⠀⠀⠀⠀⠀⠈⠹⣿⣯⣿⣿⣿⣿⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⣧⣢⣿⣿⣿⣿⣿⣣⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡲⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠳⣦⡀⠀⠀⠀⣤⣶⢶⠶⢶⢦⡀⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣜⣄⢃⠀⠀⠘⠇⣠⣄⣤⣀⢀⡟⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉⠧⠼⠛⠓⢋⠆⠀⠐⠫⢥⡿⢏⡻⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣛⢸⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⣿⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣵⣳⢾⣿⣿⣿⣿⣿⣿⢿⣿⣿⡅⠀⠀⠀⠀⠛⠀⠳⠞⠀⠀⠀⠀⠀⢀⣨⣶⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡹⠅⠘⠩⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡀⠀⢀⣴⣦⣖⣖⣄⡀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢟⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⡀⠈⠽⣿⠻⣹⡿⡳⠀⠀⠀⢀⣾⣿⣿⣿⢿⣻⣿⣿⡯⠍⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠞⠉⠘⣻⣻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢦⡍⡴⠞⠁⠀⢀⠴⣿⣿⣿⣿⣿⣿⣯⣭⣤⡐⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣭⠟⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⡠⠊⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠠⠦⠄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⢉⣁⣢⣄⠿⢿⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⢿⣿⣿⣿⠿⠇⢹⣿⡀⠀⠀⠀⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣠⠕⠊⢁⣾⡿⠁⠀⠙⠛⠿⠿⣏⠀⠙⠻⢷⠶⣶⢞⠪⠟⠛⠉⠀⠀⠉⠀⠈⠁⠒⠀⠈⢿⣷⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠐⢀⠡⢐⡖⠋⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⢀⠀⢀⣀⣀⢀⣀⡀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⡈⠰⠈⢄⢂⠏⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢀⣀⢄⣀⡀⢀⣠⢄⣠⡠⡀⢁⡔⡊⢷⣌⠉⠙⢠⢲⡃⠤⣀⡁⠂⢀⠑⣼⣆⠀⠀⠀⠀⠀⠸⡆⠀⢀⠀⠀⠄⠠⠀⠀ ⢀⠠⢀⡁⢢⠐⡡⢉⠆⣚⠀⠀⠀⠀⢰⣿⡁⠀⡀⡢⠚⠉⣡⢟⠉⠉⠁⡴⠃⢑⣽⡌⠏⣿⢆⡀⠘⢳⡀⠀⠁⣝⢤⡀⠈⠢⡀⠑⢼⣿⡆⠀⠀⠀⠀⠀⢻⡠⢀⠂⣁⠂⠤⣁⠂ ⢀⢂⠢⡘⢄⠣⢔⠣⣘⡍⠀⠀⠀⠀⡿⡟⠐⢋⠀⠀⢠⠾⠋⠀⠀⣴⠊⠀⢀⠍⠣⣽⡄⠀⠒⢧⠀⠀⠙⠂⠀⠀⠑⠵⢄⠀⠀⠄⠀⠻⣿⡀⠀⠀⠀⠀⠘⣧⠂⠥⡐⢌⠒⡄⢂ ⣌⢢⠱⣘⠬⡑⢎⡱⢢⠇⠀⠀⠀⢸⡿⠁⠠⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⢰⠁⠐⣅⠐⠻⢦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡧⠀⠀⠀⠀⠀⣿⡘⢆⡱⢊⡜⣌⠣ ⡜⢢⠓⡜⢲⠙⣦⠓⣽⠀⠀⠀⠀⡟⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡎⠀⣧⠀⡌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡄⠀⠀⠀⠀⣼⡏⡜⢢⡍⢲⡌⢣ ⣓⢎⠧⡝⣎⠵⣊⠶⡏⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⢿⠙⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠸⣯⡱⣋⡜⢣⡚⡥ ⡳⢎⣳⢹⢬⡳⢭⡞⡇⠀⠀⠀⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⣿⠀⠀⠀⠀⠐⢻⣵⢣⠞⣥⢛⡴ ⣝⡳⢮⡝⣶⢫⡗⣾⡁⠀⠀⠀⡵⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢸⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⣏⠀⠀⠀⠀⠀⠘⣷⣏⠾⣰⣋⠶ ⣯⡝⣧⢻⣜⣧⢻⡼⠀⠀⠀⠀⢹⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡆⠀⠀⠀⠀⠀⢹⣏⢾⡱⢎⡳ ⣷⣛⡾⣝⡾⣼⢯⡟⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⠀⠀⠀⠀⠀⠈⣿⣧⢻⡭⣳ ⣷⢯⡿⣽⣽⣳⢯⠃⠀⠀⠀⠀⡻⠃⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣀⠀⠀⠀⠘⣿⢧⡳⢧ ⣿⢯⣟⡷⣯⣟⡟⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⡷⢦⣀⠀⢻⣯⡝⣯ ⣿⣟⣯⣿⢷⣿⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⣀⣰⠞⣈⣳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡡⢛⣦⡹⣷⡹⢶

⢶⡹⣷⡹⣦⢛⡡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⡀⣤⣳⣈⠞⣰⣀⠀⠀⠀⠀⠀⠀⣆⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠀⠁⣿⢷⣿⣯⣟⣿ ⣯⡝⣯⢻⠀⣀⢦⡷⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⡟⣟⣯⡷⣟⢯⣿ ⢧⡳⢧⣿⠘⠀⠀⠀⣀⣦⢳⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠃⡻⠀⠀⠀⠀⠃⢯⣳⣽⣽⡿⢯⣷ ⣳⡭⢻⣧⣿⠈⠀⠀⠀⠀⠀⣧⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⠐⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⢸⠀⠀⠀⡟⢯⣼⡾⣝⡾⣛⣷ ⡳⢎⡱⢾⣏⢹⠀⠀⠀⠀⠀⡆⣿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⡀⢹⠀⠀⠀⠀⡼⢻⣧⣜⢻⣧⡝⣯ ⠶⣋⣰⠾⣏⣷⠘⠀⠀⠀⠀⠀⣏⠀⡀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡵⠀⠀⠀⡁⣾⡗⢫⣶⡝⢮⡳⣝ ⡴⢛⣥⠞⢣⣵⢻⠐⠀⠀⠀⠀⣿⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡃⠀⠀⠀⡇⡞⢭⡳⢬⢹⣳⢎⡳ ⡥⡚⢣⡜⣋⡱⣯⠸⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠙⢿⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠰⠀⠀⠀⡏⠶⣊⠵⣎⡝⠧⢎⣓ ⢣⡌⢲⡍⢢⡜⡏⣼⠀⠀⠀⠀⡄⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⠀⣧⠀⡎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡟⠀⠀⠀⠀⣽⠓⣦⠙⢲⡜⠓⢢⡜ ⠣⣌⡜⢊⡱⢆⡘⣿⠀⠀⠀⠀⠀⡧⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢦⠻⠐⣅⠐⠁⢰⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠠⠁⡿⢸⠀⠀⠀⠇⢢⡱⢎⡑⠬⣘⠱⢢⣌ ⢂⡄⠒⢌⡐⠥⠂⣧⠘⠀⠀⠀⠀⡀⣿⠻⠀⠄⠀⠀⢄⠵⠑⠀⠀⠂⠙⠀⠀⢧⠒⠀⡄⣽⠣⠍⢀⠀⠊⣴⠀⠀⠋⠾⢠⠀⠀⢋⠐⡟⡿⠀⠀⠀⠀⡍⣘⠣⢔⠣⢄⡘⠢⢂⢀ ⠂⣁⠤⠂⣁⠂⢀⡠⢻⠀⠀⠀⠀⠀⡆⣿⢼⠑⡀⠢⠈⡀⢤⣝⠁⠀⡀⢳⠘⡀⢆⣿⠏⡌⣽⢑⠃⡴⠁⠉⠉⢟⣡⠉⠚⡢⡀⠀⡁⣿⢰⠀⠀⠀⠀⣚⠆⢉⡡⠐⢢⡁⢀⠠⢀ ⠀⠀⠠⠄⠀⠀⢀⠀⡆⠸⠀⠀⠀⠀⠀⣆⣼⠑⢀⠂⡁⣀⠤⡃⢲⢠⠙⠉⣌⢷⡊⡔⢁⡀⡠⣠⢄⣠⢀⡀⣀⢄⣀⢀⠀⠀⠀⠁⡿⣼⠀⠀⠀⠀⠏⢂⢄⠈⠰⡈⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠈⠀⠀⠀⠀⠀⣧⡿⠘⠀⠀⡀⣀⢀⣀⣀⢀⠀⢀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣾⢀⠀⠀⠋⡖⢐⠡⢀⠐⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⣷⢿⠈⠀⠒⠁⠈⠀⠉⠀⠀⠉⠛⠟⠪⢞⣶⠶⢷⠻⠙⠀⣏⠿⠿⠛⠙⠀⠁⡿⣾⢁⠊⠕⣠⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠑⠉⠀⠀⠀⡀⣿⢹⠇⠿⣿⣿⣿⢿⠿⣿⣿⢀⠀⠀⠀⠀⠀⠀⡁⣇⣿⣿⣿⣿⣿⢿⠿⣄⣢⣁⢉⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠄⠦⠠⣖⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁⠊⡠⠀⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⣟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡐⣤⣭⣯⣿⣿⣿⣿⣿⣿⠴⢀⠀⠁⠞⡴⡍⢦⠙⡀⣷⣿⣿⣿⣿⣿⣿⣿⣻⣻⠘⠉⠞⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠍⡯⣿⣿⣻⢿⣿⣿⣿⣾⢀⠀⠀⠀⡳⡿⣹⠻⣿⠽⠈⡀⣧⣿⣿⣿⣽⣿⣿⣿⣿⣿⢟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣥⣿⣿⣿⣿⣿⣿⣿⣼⠈⠀⠀⠀⠀⡀⣄⣖⣖⣦⣴⢀⠀⡀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠩⠘⠅⡹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣶⣨⢀⠀⠀⠀⠀⠀⠞⠳⠀⠛⠀⠀⠀⠀⡅⣿⣿⢿⣿⣿⣿⣿⣿⣿⢾⣳⣵⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣴⣿⢀⠀⠀⠀⠀⠀⠀⢄⠈⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⣿⣿⣿⣿⣿⢸⣛⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣷⣿⣿⣿⣿⣿⣿⣿⢀⠀⠋⡻⢏⡿⢥⠫⠐⠀⠆⢋⠓⠛⠼⠧⠉⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⢻⡟⢀⣀⣤⣄⣠⠇⠘⠀⠀⢃⣄⣜⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⢿⡀⢦⢶⠶⢶⣶⣤⠀⠀⠀⡀⣦⠳⠛⡛⣟⣿⣿⣿⣿⣿⣿⣿⡲⢔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣿⣿⣿⣽⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣷⣿⣿⣿⣿⣿⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣽⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣾⣣⣿⣿⣿⣿⣿⣢⣧⠽⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣯⣿⠹⠈⠀⠀⠀⠀⠀⠁⠟⣾⣫⣶⣿⣷⣿⣿⣿⣿⣿⠾⣤⣦⢭⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣯⣿⡿⣿⣿⢿⠿⡿⢿⣿⣿⣿⣽⣞⢯⡳⣿⣿⣾⣼⢀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⢟⡯⣿⣾⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣶⣶⣷⣿⣿⣿⣿⣿⣿⣞⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀