⠀⠀⢀⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢭⣻⢭⡳⣞⡽ ⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣠⢫⡞⡵⢯⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⣹⢳⣏ ⠀⠀⠀⣆⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣷⣻⡅⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢀ ⠀⠀⢀⣿⣿⣦⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠌⣾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⢀⣼⢷⣿⠀⠀⣠⣇⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞ ⠀⠀⠠⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣬⢬⠀⠀⠂⠿⠞⣳⡄⠀⠀⠀⠀⠀⢀⣽⡗⢠⠵⠏⠛⠚⠛⣰⣋⣛⣙⣷⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⢏ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⠏⠛⠃⠋⠓⠲⢄⠨⣄⢀⠀⠀⠀⢸⡯⢄⣤⠖⠚⠉⡉⢉⠁⡙⠚⠽⣾⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢖⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡠⣒⣦⣵⠎⠒⠔⡀⠑⣿⢌⠰⢀⠀⢬⣟⣿⠀⢄⣮⠓⡈⠐⢲⣾⣴⣂⠈⠳⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⣀⠁⠀⢹⣄⣿⢯⡿⣖⣄⠸⣾⢷⣳⣿⣯⡄⠀⠀⠀⣿⣿⣿⣧⡈⣏⣤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢹⢮ ⠀⠀⠀⡄⢀⢂⣦⠀⢠⣶⣶⡶⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⡏⠉⠀⠀⢸⣿⢯⣟⡿⣯⢿⡴⣮⢿⣽⣿⣇⡀⠀⠀⢀⣿⣿⣽⣿⡇⣽⡫⠀⠀⠀⠀⠘⡀⠀⠀⠀⠐⢀⣟⣦⣘⣯ ⠀⠀⠀⣦⣿⣾⣷⢸⣾⠟⠉⠀⠀⠀⢰⠆⠀⠈⠄⢿⣿⣿⣿⣷⣦⣶⣿⣿⣻⢾⣽⣟⣯⡿⣽⣻⡞⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⢐⡯⠂⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠈⠚⠑⢋⡾ ⠀⠀⠐⣿⣿⣿⠟⢀⠀⡀⠀⠀⠀⠀⠈⢷⣌⠀⣶⣴⣭⣭⣽⣻⢿⣭⣭⢷⣻⠯⠁⠹⣾⡽⣷⣻⢾⣬⣟⣛⣛⣛⣛⣛⣯⣍⣶⣯⠂⠀⠀⠀⠀⣠⡘⠀⠀⠀⠀⠀⠀⢀⡴⣯⣽ ⠀⠀⠐⣿⣿⣿⣴⢎⣴⠁⡀⠀⠀⠀⠀⠈⢿⣆⢯⡿⢽⣯⣟⡿⢾⣽⣻⣞⡿⡆⣴⣦⣿⣳⢯⡿⣾⣽⣻⣽⢯⡿⣽⣻⡽⠿⣽⣻⢀⠀⠀⠀⣠⡟⠃⠀⠀⠀⣀⢠⡴⣞⡷⣯⢟ ⠀⠀⢈⣿⣿⣿⡿⣼⡏⣰⠃⠀⠀⠀⠀⠀⠀⢻⣘⣿⣿⣿⣯⣞⡯⡷⣯⢿⡽⣧⣿⢾⣳⣯⢿⣽⣳⢯⣷⢿⣻⡽⢷⢯⣗⡾⡽⣋⠬⢦⣴⢾⡳⠋⠀⠀⠀⠀⠈⡿⣼⢭⣗⢯⣟ ⠀⠀⠠⣿⣿⣿⣿⣿⣷⠿⠐⠀⠀⠀⠀⠀⠀⠀⠉⣟⡾⣯⣧⢼⣯⢿⡽⣿⣻⣽⣾⣻⣽⢾⣟⡾⣽⣻⡽⣿⣽⢿⡽⣯⣟⣦⣲⣟⡞⡖⠏⠉⠀⠀⠀⠀⠀⠀⠀⡽⣧⣟⢾⡽⣺ ⠀⠀⠐⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⡿⣯⣟⣾⢯⡿⣷⣟⡷⣯⢷⣿⣻⢾⣽⣯⣷⣟⡿⣾⣻⣽⡷⣯⣥⡿⡞⠁⠀⠀⠀⢽⡲⣄⠀⢰⣄⠀⣽⢣⣟⡾⣹⢣ ⠀⠀⠈⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⣴⡝⡿⣷⣻⣞⡿⣽⣤⣤⢤⣍⣽⣤⣤⢤⣤⢤⣬⢿⣽⣻⣽⣾⣻⢷⣯⡟⠁⠀⡄⠀⠀⠘⢷⠯⣷⣰⢎⡷⣜⡳⣎⠷⣭⢫ ⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⠄⠀⠀⠀⠿⠛⠊⠻⣷⢯⣟⣷⣻⣞⣿⣽⣞⡷⣯⣟⣾⢯⣟⡿⣞⣿⣞⡷⣯⠿⠈⡄⡦⠀⣙⡳⣖⢶⣪⢖⣶⣛⣾⡱⣞⡵⣫⢻⣜⣫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣾⡷⣯⣟⣾⢷⣻⣽⢷⣻⣞⡿⣞⣿⡽⣞⣯⠿⠉⢢⠀⢞⡷⣕⡮⣝⣻⢎⣷⢫⣶⣛⢶⡻⣜⢾⡱⢯⡞⣶ ⠀⠀⠀⡄⣠⢀⣤⣠⣤⣠⡄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀⠀⠈⠻⣽⢾⣯⡿⣽⣾⣻⢷⣯⣟⡿⣾⠽⠋⢁⠔⡨⠱⢨⠸⡽⣞⡵⣏⢷⣫⢞⡷⣹⢮⡳⣝⣮⣳⢻⣽⣚⢶ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⠇⡁⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡨⢂⠤⠀⠆⢈⠙⠾⡽⣷⣏⣿⣻⠾⠙⠃⡁⢀⠆⣡⢊⠔⣾⠀⢘⡳⣝⡞⣭⡞⣵⢫⡞⣽⢫⡗⣯⢶⣫⣟⡶⣯⢟ ⠀⠀⠐⣿⣿⣿⣿⣿⣿⣧⡾⣠⡏⢀⠆⠀⠀⠀⠀⡄⠆⠈⢠⠀⠀⠀⠀⠶⣌⠄⡠⠈⠉⠀⠁⠀⠀⠠⡛⣄⠊⣰⡯⠀⣿⠀⢠⡟⣵⠻⣼⡹⢮⡟⡼⢧⡻⣼⢏⡿⣞⡽⣽⢯⣟ ⠀⠀⠈⣿⡿⠿⠿⢿⣿⣿⣿⣿⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣽⣳⣄⠃⠤⡀⡀⠀⡀⢆⠩⣮⢾⣯⠇⢸⣯⢤⡀⠙⠸⢛⢶⡹⢧⣫⡝⣧⠿⣭⢿⣹⡽⣽⢯⠿⣼ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠛⢿⣯⣥⠄⠀⠀⠀⠀⠈⠘⠋⠀⠀⠀⠀⠁⣰⣯⢿⣽⡷⣄⡱⠐⡠⠑⣨⣼⣯⣟⣾⢁⡿⣞⣯⡿⣽⣶⣄⠈⠩⠓⢇⠿⣬⠻⣜⢧⣏⢷⡻⠾⣝⠶