⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣷⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣼⣟⠀⠀⢀⣾⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣖⣾⡏⠀⠀⢾⣏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣿⣿⣿⠀⠀⣼⡿⣆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⢻⡿⢿⣶⣾⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⢫⡼⢳⣿⣿⣻⣵⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣿⢹⡟⢿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣾⣧⣝⣦⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡤⢠⣄⣵⣤⣿⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢇⡇⠀⠀⠀⠀⠀⠀⣀⡶⠷⣿⣿⣿⠷⣎⡸⠷⣾⣷⣾⢶⣏⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⡼⠀⠀⠀⠀⠀⠀⠘⣩⢏⣿⣶⣭⣂⢿⣿⡿⢋⣶⣶⠖⢾⣿⣝⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⣱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⣻⢷⣮⣕⡙⠿⠿⠿⠶⠟⣛⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⣱⢿⣵⣶⣦⠀⠀⠀⠀⠀⠘⣿⣿⣛⢣⣇⠿⣿⣿⡿⢻⣿⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⡱⣟⣞⣩⢿⣟⡀⠀⠀⠀⠀⣜⣿⣿⢯⠀⠈⠙⠼⣋⠴⣣⣿⣿⣿⣧⣿⢏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡖⠀⠀⠀⠀⠀ ⢠⡱⡙⠈⠸⣺⣵⣻⢿⣢⣄⣀⣶⢹⣿⣏⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡶⠄⣀⠀⣠⠶⣿⢿⣣⡧⠀⠀⠀⠀⠀ ⡰⣱⠃⠀⠀⠈⠀⠃⠉⠂⠀⠒⠂⠚⠀⠉⠀⠀⠀⠀⢨⣿⣿⣿⢿⣿⣿⣿⣿⣛⠛⠷⠎⠉⠉⠁⠙⠚⠃⠁⠀⠀⠀⠀⠀⠀ ⡷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⢾⣿⡎⣿⣿⣿⣿⣷⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣞⣽⣻⣿⣿⢸⣿⣿⣿⣿⡇⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⡴⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⢿⣹⠾⣽⣿⣿⡐⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣕⢣⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣿⣿⡽⣻⣿⣿⣿⡇⣿⣿⣿⣿⣿⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⡝⣢⢓⡤⢠⠤⡀⣀⢠⣤⣤⣶⣿⣿⢸⣿⣷⢻⣽⣿⣿⣿⡇⢻⣿⣿⣿⣿⡇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠓⠼⠣⢝⣲⡱⠎⠶⠍⢛⣽⡎⣼⣿⣞⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣵⢯⠗⣿⣿⢾⣿⣿⣿⣿⢿⣿⢸⣿⣿⠃⠙⢿⡎⣿⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣾⢯⣿⢰⣿⣿⣿⣿⣿⡿⣯⡿⢹⠘⣿⣧⣄⡀⠀⣿⣌⢯⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣹⣾⡝⣾⡽⣿⣿⣿⢯⢿⢕⡖⢋⢧⠹⣿⣿⣿⣾⣿⣿⣷⣝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⣷⣳⣿⣿⣽⡳⣟⣿⣿⣯⢟⣷⠧⠂⢠⠹⣷⣌⠻⣿⣿⣿⠀⠉⠙⢳⣵⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣿⠱⣯⣿⣿⣞⡽⣽⣿⣿⣿⣟⠯⠈⠀⠀⢧⡙⣾⢷⣤⣙⠿⣷⣶⣤⣠⣿⣿⣶⣔⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢠⣞⡏⣿⣿⢸⢷⣿⣿⢾⣽⣿⣿⣿⡳⣫⡃⠀⠀⠀⠐⡻⣮⣟⣾⢻⣷⣮⣙⢿⣿⣿⡇⡩⠛⠿⢦⣂⠀⠀ ⠀⠀⠀⠀⠀⠖⣸⣯⢱⣿⣿⣎⣿⣿⣿⣿⣿⣿⣻⢎⣵⡟⠁⠀⠀⠀⠀⢰⡝⢟⡾⣯⣿⣿⡿⣷⣜⠻⣷⣥⣍⣢⠅⣿⣧⠂ ⠀⠀⠀⠀⠀⠘⢼⡏⠼⣿⣿⣿⣿⣿⣿⣿⣻⢗⣵⣿⠿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠭⢩⣾⢷⡻⢓⢋⣵⣌⠻⢿⣿⣿⣿⣿⠸ ⠀⠀⠀⠀⠀⣏⡰⡈⠶⣿⣿⣿⡿⣿⣹⡾⣱⣿⣷⠿⠆⠀⠀⠀⠀⠀⠀⢸⠉⢷⢈⠹⢏⡁⠆⣷⣿⡿⡿⠹⠰⠆⡉⠿⣿⠁ ⠀⠀⠀⠀⠀⢹⣿⣷⣷⣾⣿⣿⣿⣷⣿⡿⣟⡿⠞⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢊⡑⠢⢬⠿⠿⢝⡳⠉⠀⠀⠀⠀⠀⠂⠄ ⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⢿⣻⣞⠶⢋⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⢱⡷⣾⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢯⣛⠿⠿⡶⠈⠈⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⢯⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡻⣿⣧⢿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣶⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⡶⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠟⡿⣿⣷⣧⡀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣯⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠟⡿⡷⡄⠀⠀⠀ ⠀⢸⣿⡿⣗⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠯⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀