⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⡇⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠙⣄⡀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⠄⠀ ⡇⠀⠀⣤⣼⢠⠁⠀⠀⠀⠀⠀⠀⠀⣼⢧⠀⠀⠀⠀⠀⠈⠙⠒⢲⢲⠒⣶⡟⠛⢹⡇⢀⣀⣰⣶⣴⣿⣧⠈⠉⠉⢹⡍⠉⠁⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⠛⢉ ⡷⣶⡦⠾⠃⡼⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⢧⢰⠒⠢⣄⠈⠀⢀⡞⠀⢳⠬⣿⣷⣿⣿⡿⣼⣿⡿⠿⣿⠛⠲⣶⠀⠾⠁⠀⠀⠀⠀⠀⠀⣠⠋⢸⡆⠀⣀⡤⠄⠀⠀⠀⢹⡀⠀⠚ ⡇⠈⢻⣄⠀⡗⠀⠀⠀⠀⠀⠀⠉⠚⠳⣄⠈⢿⣀⡠⢲⠑⠦⠾⡇⠀⣼⠊⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢷⣀⣤⡀⠀⠀⣀⣖⣏⣿⣆⠷⠋⠁⠀⠀⠀⠀⠀⠰⣇⠈⠻ ⡇⠀⠀⡿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣷⣦⣀⡌⠀⠀⠀⣇⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣷⣞⣿⣿⠛⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠀⠉⠉⠉⢉⡏⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⠟⠉⠀⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀ ⡇⠀⠀⠀⢀⠑⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣧⠀⠀⣸⣄⣴⣼⠿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠉⢡⡀⠀ ⡇⠀⠀⢀⣨⣿⠗⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣷⣿⡿⠿⠛⠓⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡚⠉⠉⡳⠴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠿⠻⣦⡘⢷⠀ ⡇⠀⠘⠭⠿⠶⠶⠶⠶⠤⠉⠒⡤⢀⡀⠀⠀⠀⠀⠀⢸⣿⡽⠃⠑⡾⣒⠤⠷⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⢼⣷⠾⠟⠋⠉⡏⠂⠀⠀⣀⡄⢀⡠⠔⠋⢧⡀⠀⠀⠀⠈⠻⣏⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⢀⣉⡱⢦⢄⠀⠀⠈⢀⡅⠤⣘⠀⠀⡽⠓⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢴⠟⢣⣀⣠⣤⡞⢠⣀⣤⠚⡡⠚⣯⣀⣀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢰⠁⡞⠀⠉⠲⢄⡨⡄⡠⠉⠛⡯⢝⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢩⡿⢖⠈⠉⢀⢶⢦⡀⠉⠀⡰⠋⣻⢃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠃⢠⠃⠀⠀⠀⠀⣧⡈⠓⠒⢶⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⣼⢶⠉⢉⡼⣧⠙⠢⣴⡷⠛⠁⠘⣇⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡎⠀⠏⠀⠀⠀⠀⠀⡛⠉⠓⠒⠳⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠀⠀⣞⢧⠞⠉⢧⡀⠀⠀⠸⡆⠀⠀⠀⠀⠙⢦⡀⠀ ⡇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡌⠀⡼⣤⣸⣷⠀⢀⣤⣇⣄⣠⣤⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠱⢴⣺⣛⣶⣹⣦⡀⠈⢳⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠙⢦ ⡇⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⢿⡿⠿⣿⣿⡟⣿⣿⣯⡿⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠘⠛⡻⣿⣷⣿⣿⣿⣷⣾⣇⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢠⡋⠀⢀⡀⠤⠤⠤⠾⠤⢤⡮⣀⡈⢷⣀⠩⠽⠯⠤⠤⢅⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠁⠀⠀⠉⠉⢩⢟⣹⣿⡧⢔⡂⠈⠉⠉⠉⠉⠐⠒⠤ ⡇⢠⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⠴⠊⠉⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠁⠿⠓⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠸⡀⠙⣦⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒ ⡇⠀⠀⠀⠀⠀⠀⣿⣷⣶⠧⢄⣀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠉⠛⠛⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠙⣤⣏⡀⠀⠀⠀⢀⣴⣂⣀⣀⠤⢴⠒⢉⠁⠀⠀ ⡇⠀⠀⠿⣷⣖⠛⠋⢠⠇⠀⠀⠈⠉⠉⠐⠲⠽⢦⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡼⠈⠉⠉⢀⠔⠋⠀⠀⠀⠀⠀⠈⣦⠈⣷⠀⠀ ⡇⠀⠀⠀⠀⠙⠳⠄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠐⠶⣊⣡⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢀⡠⠚⠀⠀⠀⣔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠙⢷⢀ ⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⠀⣇⠀⠀⡼⡄⠀⠀⠀⠀⡀⠀⣠⠏⠀⢠⣠⠚⠁⠀⠀⠀⠀⠀⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠛ ⡇⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢹⠀⠀⠀⠀⠀⠹⡀⢸⠀⠙⢄⡀⠀⠀⠸⠞⠙⢤⡀⢻⠃⠀⠀⠀⠀⠀⠀⢠⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⡇⠀⠀⠀⢠⣖⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡇⠀⠀⠀⠀⠀⠙⠾⡆⠀⠀⠙⠢⡀⢀⠇⠀⠀⠑⠪⢦⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⡇⠀⣀⣠⡴⠿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⢇⡞⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⡇⠀⠉⠚⠛⢶⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠚⠁⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡠⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⣧ ⡇⠀⠀⠀⠀⠈⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠃⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟ ⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠣⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠫ ⡷⢶⣶⣿⡧⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⠒⠢⠤⡆⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⠑⠉⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⡇⠀⠙⢷⣍⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀ ⡇⠀⠀⠀⢩⠊⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⣀⠤⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠳⠤⣀⡀⠀⠳⡀⠀⠀⠀⠀⠀⠘⡆⠀⠘⢆ ⡇⠀⠀⣰⠃⠀⠀⠀⡇⠀⠀⠀⢀⡜⠀⡏⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡗⠀⢇⠀⠀⠀⠀⡗⠀⠀⠈ ⡇⠀⢰⠃⠀⠀⠀⠀⠱⠀⢀⣰⡯⠤⠒⠓⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡖⠓⠒⠂⠼⠥⣀⠀⠀ ⡇⢀⡏⠀⠀⠀⠀⣀⠖⠉⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠉⠢ ⡇⢸⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⡇⠸⡄⠀⡞⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀ ⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀ ⡇⠀⢸⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠸⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⢀⠈⣆⢘⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌ ⡇⠀⢸⠀⠘⣆⢻⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⡇⠀⣸⠀⠀⠈⠣⡹⣦⡳⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠔ ⡇⠀⡇⠀⠈⢷⣄⠈⢫⣝⢜⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣱⠊⠁⠀ ⡇⠸⠀⠀⠀⠀⠙⢶⣜⠍⠙⢷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡽⢋⣽⠀⠀⠀ ⡇⢠⠀⠀⠀⠀⠀⣄⣟⢗⣤⡀⠹⣾⢞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⣽⣿⠾⠋⢹⠀⠀⠀ ⣧⠆⠀⠀⠀⠀⠀⢹⠁⠀⠉⠻⢷⣿⣿⠉⠚⠷⣯⢭⣓⠢⣄⡀⠀⠀⠀⠀⣀⣠⣤⡶⠛⣫⢰⢿⢸⢿⣄⣉⠓⠤⣄⡀⠀⠀⠀⢀⣀⠤⠒⣋⣩⢤⡰⢾⠟⣽⠀⠀⠀⢸⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠹⣿⣵⣦⢤⣀⠈⠙⠚⠋⠻⣿⣿⣿⣿⣿⣭⣥⣤⠾⠋⠀⢹⣾⠀⠈⠉⠛⠻⠶⠶⠾⠿⠷⡾⠉⠙⠒⠋⠁⠀⢀⣮⡼⠋⠀⠀⠀⡼⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢨⠏⠀⠈⠉⠛⠻⠴⠶⠆⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠦⠤⣤⣤⣤⣤⣼⣤⣤⣤⠂⠀⠀⠙⠚⡏⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⡇⠀⠀⠀⠀⡀⠀⢻⣧⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡟⠀⠀⠀ ⡇⢠⠞⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠩⠟⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆⠀⠈⠉⠀⠀⠘⡆⠀⠀⠀⢠⠁⠀⠀⢀ ⣷⠃⠀⢰⠋⠀⠀⣠⠇⠀⠀⠀⠀⡴⠁⠀⠀⠀⡄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⣆⠞⠉⠈ ⡏⠓⠒⠉⠒⠀⠐⠃⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠇⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠈⢣⣄⠀⠀⠈⠑⠂⠐ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠦⠤⠤⠤⠤⠾⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠬⠧⠤⣀⠤⠴⠚⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠚⠴⠤⣀⠤⠧⠬⠤⠤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠤⠤⠾⠤⠤⠤⠤⠦⠧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠐⠂⠑⠈⠀⠀⣄⢣⠈⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠀⠀⠇⠀⠀⠀⠀⠃⡼⣀⠀⠀⠀⠃⠐⠀⠒⠉⠒⠓⡏ ⠈⠉⠞⣆⠈⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡄⠀⠀⠀⠁⡴⠀⠀⠀⠀⠇⣠⠀⠀⠋⢰⠀⠃⣷ ⢀⠀⠀⠁⢠⠀⠀⠀⡆⠘⠀⠀⠉⠈⠀⡆⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠟⠩⠉⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠈⠀⠁⢸⠀⠞⢠⡇ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣧⢻⠀⡀⠀⠀⠀⠀⡇ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⡏⠚⠙⠀⠀⠂⣤⣤⣤⣼⣤⣤⣤⣤⠤⠦⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢹⠆⠶⠴⠻⠛⠉⠈⠀⠏⢨⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡼⠀⠀⠀⠋⡼⣮⢀⠀⠁⠋⠒⠙⠉⡾⠷⠿⠾⠶⠶⠻⠛⠉⠈⠀⣾⢹⠀⠋⠾⣤⣥⣭⣿⣿⣿⣿⣿⠻⠋⠚⠙⠈⣀⢤⣦⣵⣿⠹⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⢸⠀⠀⠀⣽⠟⢾⡰⢤⣩⣋⠒⠤⣀⢀⠀⠀⠀⡀⣄⠤⠓⣉⣄⢿⢸⢿⢰⣫⠛⡶⣤⣠⣀⠀⠀⠀⠀⡀⣄⠢⣓⢭⣯⠷⠚⠉⣿⣿⢷⠻⠉⠀⠁⢹⠀⠀⠀⠀⠀⠆⣧ ⠀⠀⠀⢹⠋⠾⣿⣽⢒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣿⢿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢞⣾⠹⡀⣤⢗⣟⣄⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⣽⢋⡽⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣾⢷⠙⠍⣜⢶⠙⠀⠀⠀⠀⠸⡇ ⠀⠁⠊⣱⢞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⢜⣝⢫⠈⣄⢷⠈⠀⡇⠀⡇ ⠔⣀⠊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡳⣦⡹⠣⠈⠀⠀⣸⠀⡇ ⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣌⢻⣆⠘⠀⢸⠀⡇ ⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢘⣆⠈⢀⠀⡇ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠸⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⢸⠀⡇ ⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇ ⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⡞⠀⡄⠸⡇ ⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠁⡴⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⠀⠁⡴⠀⠀⠀⠁⢸⡇ ⠢⠉⠀⠀⠀⠀⡀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⢀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠀⠀⠀⠀⠉⠖⣀⠀⠀⠀⠀⡏⢀⡇ ⠀⠀⣀⠥⠼⠂⠒⠓⡖⢲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⢀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⠓⠒⠤⡯⣰⢀⠀⠱⠀⠀⠀⠀⠃⢰⠀⡇ ⠈⠀⠀⡗⠀⠀⠀⠀⢇⠀⡗⢤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣤⠀⠀⡏⠀⡜⢀⠀⠀⠀⡇⠀⠀⠀⠃⣰⠀⠀⡇ ⢆⠘⠀⡆⠘⠀⠀⠀⠀⠀⡀⠳⠀⡀⣀⠤⠳⠒⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠞⠤⣀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠊⢩⠀⠀⠀⡇ ⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣍⢷⠙⠀⡇ ⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠉⠑⣰⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡆⠤⠢⠒⠈⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡧⣿⣶⢶⡷ ⠫⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⣠⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⠣⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇ ⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠃⢠⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠐⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠀⠀⠀⠀⡇ ⣧⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡆⠁⠚⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡦⢶⠛⠚⠉⠀⡇ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⡞⢇⢠⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠿⡴⣠⣀⠀⡇ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⡀⢦⠪⠑⠀⠀⠇⢀⡀⠢⠙⠀⠀⡆⠾⠙⠀⠀⠀⠀⠀⡇⠈⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣖⢠⠀⠀⠀⡇ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠁⢠⠀⠀⠀⠀⠀⠀⠃⢻⡀⢤⠙⠞⠸⠀⠀⡀⢄⠙⠀⢸⡀⠹⠀⠀⠀⠀⠀⢹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡟⠀⠀⠀⠀⠀⠀⡇ ⠛⠈⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡇⠀⠀⠀⠀⠀⠁⠚⣠⢠⠀⠏⣠⠀⡀⠀⠀⠀⠀⡄⡼⠀⠀⣇⠀⠀⠀⠀⠀⡇⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⡇ ⢀⢷⠙⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢇⣔⠀⠀⠀⠚⡠⢀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⣡⣊⠶⠐⠀⠀⡄⣳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠄⠳⠙⠀⠀⠀⠀⡇ ⠀⠀⣷⠈⣦⠈⠀⠀⠀⠀⠀⠋⠔⢀⠉⠉⠈⡼⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⢦⠽⠲⠐⠉⠉⠈⠀⠀⠇⢠⠋⠛⣖⣷⠿⠀⠀⡇ ⠀⠀⠁⢉⠒⢴⠤⣀⣀⣂⣴⢀⠀⠀⠀⡀⣏⣤⠙⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠛⠉⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⣀⢄⠧⣶⣷⣿⠀⠀⠀⠀⠀⠀⡇ ⠒⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠜⣦⠙⡀⠸⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠒⠉⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠓⠿⠁⠈⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠉⠊⠴⠑⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⢠⡇ ⠤⠒⠐⠉⠉⠉⠉⠈⡂⢔⡧⣿⣹⢟⢩⠉⠉⠀⠀⠁⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢅⠤⠤⠯⠽⠩⣀⢷⡈⣀⡮⢤⠤⠾⠤⠤⠤⡀⢀⠀⡋⢠⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⣇⣾⣷⣿⣿⣿⣷⣿⡻⠛⠘⠀⣀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⢿⡿⣯⣿⣿⡟⣿⣿⠿⡿⢿⠁⢰⠀⡜⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⡇ ⢦⠙⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⢳⠈⡀⣦⣹⣶⣛⣺⢴⠱⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣴⣤⣠⣄⣇⣤⢀⠀⣷⣸⣤⡼⠀⡌⢀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠀⡇ ⠀⡀⢦⠙⠀⠀⠀⠀⡆⠸⠀⠀⡀⢧⠉⠞⢧⣞⠀⠀⠉⡉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠞⠳⠒⠓⠉⡛⠀⠀⠀⠀⠀⠏⠀⡎⢀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡀⠢⠈⠀⠀⠀⣇⠘⠁⠛⡷⣴⠢⠙⣧⡼⢉⠉⢶⣼⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣷⢶⠒⠓⡈⣧⠀⠀⠀⠀⠃⢠⠃⢠⠀⠀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⢃⣻⠋⡰⠀⠉⡀⢦⢶⢀⠉⠈⢖⡿⢩⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢝⡯⠛⠉⡠⡄⡨⢄⠲⠉⠀⡞⠁⢰⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⣀⣀⣯⠚⡡⠚⣤⣀⢠⡞⣤⣠⣀⢣⠟⢴⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠓⡽⠀⠀⣘⠤⡅⢀⠈⠀⠀⢄⢦⡱⣉⢀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⣏⠻⠈⠀⠀⠀⡀⢧⠋⠔⡠⢀⡄⣀⠀⠀⠂⡏⠉⠋⠟⠾⣷⢼⠣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠾⠷⠤⣒⡾⠑⠃⡽⣿⢸⠀⠀⠀⠀⠀⡀⢀⡤⠒⠉⠤⠶⠶⠶⠶⠿⠭⠘⠀⡇ ⠀⢷⡘⣦⠻⠿⠛⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣏⠴⡳⠉⠉⡚⣔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠓⠛⠿⡿⣿⣷⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠀⠗⣿⣨⢀⠀⠀⡇ ⠀⡀⢡⠉⠝⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⣀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡟⣿⠿⣼⣴⣄⣸⠀⠀⣧⢶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⠑⢀⠀⠀⠀⡇ ⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣁⠀⠉⠟⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡏⢉⠉⠉⠉⠀⣸⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇ ⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢃⠛⣿⣿⣞⣷⣻⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣇⠀⠀⠀⡌⣀⣦⣷⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⡇ ⠻⠈⣇⠰⠀⠀⠀⠀⠀⠁⠋⠷⣆⣿⣏⣖⣀⠀⠀⡀⣤⣀⢷⠙⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠛⠊⣼⠀⡇⠾⠦⠑⢲⡠⣀⢿⠈⣄⠳⠚⠉⠀⠀⠀⠀⠀⠀⡗⠀⣄⢻⠈⡇ ⠚⠀⡀⢹⠀⠀⠀⠄⡤⣀⠀⡆⢸⠋⣠⠀⠀⠀⠀⠀⠀⠁⠾⠀⣶⠲⠛⣿⠿⡿⣿⣼⡿⣿⣿⣷⣿⠬⢳⠀⡞⢀⠀⠈⣄⠢⠒⢰⢧⠈⣇⢀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠾⡦⣶⡷ ⢉⠛⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠀⠀⠀⠀⠀⠁⠉⡍⢹⠉⠉⠈⣧⣿⣴⣶⣰⣀⢀⡇⢹⠛⡟⣶⠒⢲⢲⠒⠙⠈⠀⠀⠀⠀⠀⢧⣼⠀⠀⠀⠀⠀⠀⠀⠁⢠⣼⣤⠀⠀⡇ ⠀⠄⣠⡄⠘⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠋⠴⣠⢀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠙⠀⠃⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⡇ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇