⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⣿⡎⠷⢤⣀⠀⠀⠰⣔⣺⣭⣶⣲⣤⣄⡀⠀⠀⢠⢧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⢠⣧⢻⠓⠀⡄⠙⠿⣶⣞⠡⠞⠁⠀⠀⠉⠣⡝⢦⡀⢸⣌⣇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡼⠉⢀⣼⡟⠀⠀⠀⢰⣟⢀⡽⢇⠀⢷⡀⠰⡟⢫⠣⣦⡄⣠⣤⣤⣴⣌⠀⢹⡟⣹⣾⣿⣟⡲⢦⣸⢃⠀⣀⣤⡴⡛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⡟⢵⡾⢻⣻⠗⠀⠀⠀⠘⣻⠋⠀⡄⠳⡈⣷⣴⠿⣿⡴⡌⠻⣿⣿⣿⠏⡿⠃⠘⠃⠀⠀⢀⣀⣈⠳⡜⣾⣷⡿⠛⠉⠩⠙⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣿⡟⢁⡾⢡⢿⡇⠀⠀⠀⢀⡴⢃⢶⡯⡇⠀⢹⣸⠏⠀⠈⠻⣿⡤⠈⠙⠛⠚⢁⣠⠆⢠⢦⣶⣿⣿⣿⡗⠀⢸⡿⠚⠁⠀⠰⣄⡀⠐⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⣴⣿⠁⣸⡇⣘⣾⠁⠀⠀⣴⠋⢹⡏⣴⢲⠇⠀⣿⠏⠀⠀⠀⠀⠈⣿⣶⣶⣶⣶⣿⣿⣈⠳⡞⢿⣿⣿⡶⠃⢠⡿⠀⢠⣶⣿⣷⣮⣿⡆⢸ ⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠛⠃⠀⢹⡇⣿⣸⠀⠀⠀⡇⠀⢈⣇⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⠀⢹⣿⣧⣄⠀⢀⣠⣤⣴⣿⡾⠷⣾⣿⡿⢟⡕⣿⡃⠘ ⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⢹⠀⠀⠀⢧⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⡴⡛⠚⠛⠻⠿⣿⣿⡟⠉⠹⣿⣄⠈⠉⠛⠛⠽⣿⣿⡯ ⠀⠠⠚⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣧⢏⡇⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠃⠀⠀⠳⢽⣷⣤⡴⣛⣉⡙⢯⠻⢷⡄⣿⣿⣿⣿⣿⣿⡿⣿⡟⠃ ⠀⠀⠀⠀⢠⣄⠠⠴⠤⠶⠦⣤⣤⡀⣀⣴⡾⠛⣧⠸⡎⣅⠀⠀⠀⠀⢸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠂⠀⣉⠙⠿⣿⣿⣿⣿⣿⣤⠵⠃⠈⢡⣿⣿⣿⣶⡼⡿⠀ ⠀⠀⢠⣾⣿⣯⠤⠤⣤⣤⣤⣤⣏⢿⣟⠋⠁⠀⢼⣇⢹⡼⡄⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠈⠳⢦⠬⠭⣭⣽⢟⡽⡿⠀⠀⣙⣿⣷⡿⠋⠰⡇⠀ ⠀⠀⣸⡟⠉⠀⠀⠀⠀⠀⠀⠈⠛⣷⣿⢷⡄⠀⠀⣸⣆⢹⣧⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠽⠛⢋⡶⡁⢠⣿⣿⣿⣏⠁⠀⠀⠁⠀ ⡠⠞⢳⣼⣾⣷⣶⣷⣤⡀⠀⠀⠀⢸⣿⣯⣿⣶⡄⠘⣿⣄⠹⣷⡀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣜⣷⣿⡛⠀⠚⣆⠀⢠⠃⠀ ⠃⢸⠟⠛⠛⠛⠛⠿⣿⣿⣄⠀⠀⠀⣺⣿⣷⡙⡇⠀⠘⣿⣿⡛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢽⣛⣷⢭⣖⣄⡘⣇⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣆⠀⠀⠀⢹⣿⣇⢽⡀⠀⠀⠙⢷⣌⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠽⠲⠼⠧⠏⠀⠈⠙⠻⢾⡏⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⣹⡄⢀⠀⠐⢻⣿⡀⡇⠀⠀⠀⠀⠛⢷⣌⠻⣶⣄⠀⠀⠀⠀⠀⠀⠐⢤⣈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣠⣤⡴⠀⠀⠀⠀⢀⣾⠀⢸⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣌⢧⡻⡏⠀⠀⠀⢻⡇⡇⠀⢠⣶⡆⠀⠀⠙⢱⣮⣙⢷⣦⣀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠿⣽⡃⠀⠀⠀⣠⣾⢿⡇⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡾⣦⣧⡄⠀⠀⢸⣷⡇⣀⣾⡟⠃⠀⠀⠀⠀⠙⠛⢛⠮⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢁⢠⠿⣺⣿⣁⣼⣇⣸⠀ ⠂⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠓⢳⣽⣷⠀⣰⡾⠉⣩⣿⡗⠃⠀⠀⢀⠀⠀⠀⡶⣵⣯⣤⣿⣿⣿⣿⡯⣗⡤⣀⠀⠀⠈⠛⢍⡒⠤⣄⣀⠀⠀⠀⣀⡤⢋⣠⣾⣿⣿⢟⣏⣾⣇⠀ ⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⢿⣧⣿⠟⠡⠾⠋⠚⠀⣴⡦⠶⢾⠀⠀⠘⡇⣯⣿⡛⣻⣿⣿⣿⣧⡀⠙⢳⣽⣶⡤⢄⣀⣈⠉⠒⠐⢛⣛⣩⣥⠾⣿⣿⣿⣿⣿⠠⣿⢡⡏⠀ ⠀⠀⠀⠀⠀⢻⡑⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣷⡶⠤⠴⠛⠉⠀⠀⠹⣧⠄⣀⣻⣿⣿⢇⣻⣿⣯⡿⢁⡧⣤⣿⠟⠻⠿⠿⠾⣿⣿⣶⡾⠿⠟⡻⣿⡀⣿⣿⣿⣿⣿⠙⣿⡟⢣⠀ ⠀⠀⠀⠀⠀⠸⣳⡦⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠟⠿⠿⠿⠟⠉⣤⡾⢠⣿⡅⠀⠀⠀⠀⠀⠻⠽⠟⠑⠀⠀⠀⠘⡇⠈⡏⠉⠉⠀⢰⣦⡷⢹⡆ ⠀⠀⠀⠀⣤⣴⣿⠿⠀⠀⠀⠀⠀⣀⣤⣿⡇⠀⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⠀⣠⢄⣾⣿⠃⢸⡇ ⠀⠀⠀⠛⣣⣄⡧⢀⣲⡤⢤⣴⠚⠋⠉⣿⠁⠀⠀⠸⣷⣄⢄⣤⣴⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⣿⠇⣀⣴⣶⢀⠀⠀⣤⠺⣤⣤⠀⠀⠀⣾⡇⠙⡏⡄⣿⣿⣿⣛⠠⣼⠁ ⠀⠀⠀⠐⠋⠻⠟⠛⠚⠛⠙⠒⠛⠉⠁⠉⠉⠓⠦⣤⡙⢿⣿⣮⣭⣟⣁⣚⣛⣷⣤⣤⣴⡾⣯⣓⣒⣾⣷⣮⡿⠿⠽⠏⠐⠒⠚⠋⠁⠀⠤⠤⣴⣿⡇⢣⡿⠟⠟⠉⠸⣯⠸⡟⠀ ⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣻⣟⢛⣛⢛⠟⣡⣾⣿⠇⠉⠀⠤⢄⣀⣉⡙⢲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠳⣄⠀⠀⠈⣿⣾⠇⠀ ⠘⡀⠐⢱⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣛⣚⣿⣾⢀⣼⡾⣻⠀⠉⠁⠤⢀⣀⣈⡉⢻⣿⡀⠀⠀⠀⠰⠯⢱⠞⠛⠀⠀⠀⠀⠙⣷⣜⢿⣶⡀⢩⣿⡄⠀ ⠀⢘⡼⠘⢿⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⣶⠶⢿⣇⣾⣿⠀⢸⢦⡉⠁⠤⣤⣀⣉⢛⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡹⣿⠈⢻⡇⠀ ⠀⠘⢦⣄⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣾⣟⡛⢿⣿⣇⠾⣿⣤⣾⢳⣈⣱⣶⣦⣝⣟⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣞⢿⡄⢹⠀ ⠀⠀⠀⠈⠛⠛⠢⣄⡙⠚⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠽⣥⣄⣨⡿⠦⢽⣿⠟⠛⠛⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⡱⡜⡇ ⠀⠀⠀⠀⠀⠀⠀⣨⠽⢻⡶⠶⡖⢤⣤⡤⠤⠴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⡇ ⠀⠀⠀⠀⣀⣴⡞⣁⡴⠋⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢾