⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠟⠛⠛⠛⠛⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡄⠀⠀⠀⠀⠀⠀⣠⡔⠒⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡃⠀⡄⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡆⠀⠀⠀⠀⢰⡛⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⡠⢢⢠⡠⡿⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢻⢿⡄⠀⠀⠀⠈⣶⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠉⠀⢀⡝⡽⠃⣄⡟⠃⠀⡄⢠⢒⠀⠀⡀⠀⢸⡇⠀⠀⢀⡁⠣⠘⠀⠀⢀⣆⠀⡟⣿⠀⠀⠀⠀⢸⢩⡶⣤⡀⠀⠀⠀⠈⢗⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢀⢎⣾⠳⠐⣽⡅⠀⠀⠀⠈⣩⠧⠀⣇⠐⣿⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠹⡄⢸⢹⡇⠀⠀⡶⠤⠏⢗⢌⢿⡄⠀⠀⠀⢸⡷⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣞⣾⢸⠃⢸⣏⠁⠀⠀⢀⣼⠋⢀⣼⢛⣾⡇⢟⡇⠀⡇⠀⠀⢀⠀⠀⠀⠈⢹⡜⡞⣿⠀⠀⠀⠀⠀⠀⠙⠳⠃⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⣸⣾⡞⣼⡠⣾⡟⠀⢀⣠⡟⠁⣰⢿⠏⣷⣟⣀⠘⢿⠀⣿⠀⠀⢸⡄⠀⢤⡀⠀⠙⢧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣋⡁⣤⠀⠀⠀⢀⣿⡝⠚⠛⠰⠿⠡⠴⡿⠏⡴⠟⠡⠯⠼⠋⠀⠉⠉⢹⠀⣿⢸⢀⠘⣷⠀⡘⡟⠒⠤⠤⢽⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢩⡿⢫⡏⠀⢠⠀⢸⡿⡁⣠⣤⣄⡛⢶⠀⠀⠀⠀⠀⠀⣫⣥⣤⣤⣀⠀⠈⠱⢿⢸⠀⠀⣟⣄⠿⣣⣇⠀⠀⠈⣿⣟⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠁⢸⠀⠀⡞⣎⢸⣧⣿⢿⣋⠉⢿⣦⠀⠀⠀⠀⠀⢾⡿⠅⡀⡙⣟⢿⣦⠄⡸⣿⠁⢨⢿⣿⠀⠋⢸⠀⠀⠀⢸⣾⣷⣌⣹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡇⠰⣼⣦⠀⡇⢸⣎⣇⣇⢰⡚⠿⠿⡇⠀⠀⠀⠀⠀⠀⣗⡛⠟⢉⢹⠀⣿⠋⢡⠷⠀⡎⣾⠉⠀⠀⢸⡆⠀⢠⣆⣯⠭⢿⡄⠈⢿⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⣰⣿⣯⣢⡇⠀⣻⣿⠀⣮⡳⠤⠽⠃⠀⠀⠀⠀⠀⠀⠙⠷⠤⠤⠟⡀⠀⢀⡞⢃⡜⢁⣯⠀⠀⢀⡼⠀⣠⢿⡿⠁⠻⣭⣿⡀⠘⡟⠻⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⢛⣻⣽⡿⠖⠛⠉⢹⡄⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠞⠀⣠⣟⣤⠾⠶⠚⡟⠀⣠⡾⠗⠛⠃⠈⠀⠀⠀⠹⣽⣯⠉⠹⡆⠈⡏⠛⠻⣶⣦⠀ ⢀⣴⣿⠿⠛⢿⣺⢵⣦⡀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⡤⠖⠦⠤⠀⠀⢈⣠⡴⠚⠋⠁⠀⠀⠀⣸⣧⡾⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣃⠀⣧⣀⣿⣤⣀⣸⣿⡇ ⠸⣿⣿⠽⠖⣂⣉⠻⢿⣿⣲⣀⣤⡾⠟⠛⠷⢶⣦⣤⣤⣤⣤⣤⣴⣞⡋⠀⠀⠀⠀⠀⠀⠀⠀⣙⣵⣾⣿⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠙⠛⠁ ⠀⠈⠛⠛⠛⠻⣿⠶⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠛⠿⣯⣟⡷⣄⡀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⡾⣣⠆⣀⠈⠹⣺⣵⣛⣶⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢾⣯⣴⠿⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀