⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣻⠟⠋⠈⡡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⣴⠏⠁⠀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⣲⠋⠀⠀⠀⣀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠚⠋⠉⠀⢀⣹⡛⠺⣷⡦⢤⣤⡾⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠁⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠙⠳⣦⡤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⢀⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠐⠋⠀⣀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠉⠳⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡯⠀⠀⢀⠞⠁⢀⣠⣴⣖⣾⣯⣭⣿⣶⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⢶⣦⣤⣤⣿⣟⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⡴⢋⣤⣶⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣲⠟⣴⠋⠽⠿⠶⠿⠶⠶⠖⠀⠀⠀⠀⠀⠤⠤⠤⢤⣤⣤⣤⣄⣀⣀⣈⣙⢻⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠛⠋⠉⢀⡤⠀⣼⣫⠟⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠉⠙⠛⠿⣿⣃⣀⠉⠛⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⣀⠄⣠⠾⠋⢀⣼⡿⠃⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣠⣾⡿⣟⣁⠀⠀⠀⠀⠉⠉⠉⠉⢰⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⣴⠚⠉⠀⠀⠀⠀⢀⣠⠞⣱⠞⠁⠀⢀⣾⠟⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣷⡦⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⢠⡴⣰⠃⠀⠀⠀⣾⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⢸⡷⣧⠀⠀⠀⣼⢃⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⠩⠰⣾⠀⠀⡈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠘⣆⠀⠀⠀⢸⣿⠃⠀⠀⣸⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⠀⠘⣛⣻⢻⡇⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⣿⡆⠀⣠⡏⣼⣿⣿⣿⣿⣿⣿⣿⠻⡟⣩⡆⠙⠿⠮⢕⣊⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⡀⠀⡾⢱⣿⣿⣿⣿⣿⣿⣿⣿⣆⡐⣿⣿⣿⡿⢛⣃⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠘⡇⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣌⣥⣴⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢳⡾⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣀⣠⣴⣶⣶⣾⣿⠿⠿⣿⡟⢿⢻⡿⣯⢻⡍⠉⠹⡏⠙⣿⡄⠘⣇⠀⠀⠀⢻⣿⠹⣿⡆⠀⠀⢻⣿⣿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣤⣶⣾⣿⣿⡻⣏⠉⠀⠀⠀⠀⠀⠘⢷⡘⣏⣷⠘⣧⠹⡄⠀⢿⠀⠈⣷⣤⢿⡖⠚⠛⠙⣿⡉⢻⣿⠛⠃⠸⣿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⣿⣿⣿⣿⣿⢛⣵⣿⣿⠟⠋⣿⠘⣧⣷⢻⡄⠀⠀⠀⠀⠀⠀⠈⢷⣿⣸⣇⠘⢧⠀⠀⢸⡷⠋⠉⢷⡸⡏⡇⠀⠀⣿⣟⣈⣿⡀⠀⠀⣿⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣷⣿⡿⠉⣿⠀⠀⢹⣇⠹⡿⡆⢷⡀⠀⠀⠀⠈⠃⠀⠘⣿⣧⢿⡆⠘⣧⠀⢈⣷⢳⠀⠘⣧⣿⣽⣴⣶⣿⣿⣿⣿⣷⣶⣶⣿⣶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⣿⠀⠀⠈⣿⡄⢿⢻⡈⢷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⡆⠸⡆⠈⣿⡼⡆⠀⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠉⠛⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⠁⣿⠲⢸⠀⠀⠀⠸⣷⠈⣧⢷⠈⣷⡀⠀⠀⠀⠀⣄⠀⢹⣿⣧⣷⠆⢹⣄⢸⡇⣇⢀⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⡄⢠⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⠀⢿⠀⠘⣇⠀⠀⠀⣿⣧⠘⣾⣧⢈⣷⡶⠺⣇⠀⠘⠆⠈⢿⣎⢿⡿⡆⢿⣼⣷⣿⠀⠿⠋⠀⠹⣿⣿⣿⣿⠟⢟⡇⡼⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡆⠀⢿⠀⠀⠀⠘⣿⣦⠙⣿⣿⡙⣿⢦⡘⣆⠀⠀⢀⡈⢷⣜⣿⢻⠘⢿⡿⠋⠀⠀⠀⠀⠀⠹⣿⠋⣉⣤⣾⢿⡇⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣧⠀⢸⣧⠀⠀⠀⢹⣟⣷⠻⣿⣷⢹⡎⢳⣌⢧⡀⠈⢳⣼⣿⣯⠘⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢠⣇⣿⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⣿⡄⠀⠀⠀⣿⡟⣧⠹⣿⣶⣿⣿⣿⣿⣿⣿⣯⡩⠭⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠸⣿⡀⠀⠀⠟⢻⣬⣴⣿⣿⡿⠻⣿⣿⣷⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⡾⢻⡆⠀⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⣿⣷⠀⠀⠀⡈⢷⣿⣿⡟⡄⠀⢹⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠉⠀⢸⡇⠀⠀⠀⠀ ⣖⠂⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣷⣤⡀⣻⣌⣿⣿⣿⣄⠀⠀⠻⣿⡿⠏⢉⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣰ ⣽⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣷⣿⣿⣿⣿⣿⠿⠿⠷⠄⠀⠈⢛⡶⠋⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⢸⠀⠀⠀⣴⠇ ⢷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⠀⠈⢿⣿⣿⣿⣿⠿⣿⣿⣦⡀⠀⠀⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⢠⣿⠀⠀⠀⣼⣼⠀⣾⡏⠀ ⠛⢿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⣿⣧⣻⣿⣷⣼⢿⡎⠻⣿⡀⠉⠻⣿⣿⣆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡏⠁⠀⣠⡾⠁⠀⠀⠀⣿⣿⢰⣿⠀⠀ ⠀⣸⡷⠖⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣧⠀⡿⠻⢿⣿⡏⢿⡻⣿⡄⠈⢿⡀⠀⠀⠻⣿⣧⡀⢀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⡏⣿⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣯⠁⠀⠀⢻⣿⣜⣿⣾⡻⣦⡀⠻⣄⠀⠀⠈⠻⣿⣦⡈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⣿⡟⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣿⡙⣾⡏⢻⣿⢿⣶⣼⣧⡦⠀⠀⠈⠳⣝⣿⣶⣶⣶⡦⠤⣤⡤⣤⠤⠤⠤⠤⣶⢶⣶⣿⣿⣿⠀⣿⣻⣷⣾⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⣿⣿⣿⣿⣆⠀⠀⠹⡇⢘⣷⠀⠹⣆⠈⣍⠀⢻⡄⠀⠀⠀⠹⣿⣿⣻⡏⣷⠀⠀⢠⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⢠⡇⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⣧⠈⣿⠀⣸⢿⣦⠙⣦⠀⢻⡄⠀⠀⠀⠘⢿⣿⡇⣿⠀⠀⠸⠁⠀⠀⠀⣸⣿⣿⣿⣿⡟⣰⣿⣿⣿⣤⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⠀⢻⠀⢿⣷⣯⣿⢹⣷⡈⢷⡈⣷⣀⠀⠀⠀⠈⢿⡇⣿⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣿⣿⣾⢳⣿⡿⣿⡿⠿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣸⡄⠘⣿⣿⣿⣸⣿⣿⡄⠹⢿⣏⢷⡀⣤⡀⠘⣿⡏⠀⡤⠀⠸⡟⠀⣾⡿⣯⢻⣿⣿⣣⣿⠀⢸⠏⢀⣀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⡟⢸⡏⣇⢹⣿⣆⠀⢻⡀⠙⢿⣷⠀⢹⣇⡼⣧⣧⣼⢃⣼⣿⠁⢻⣼⣿⣿⣿⡿⠀⢸⣇⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⡄⠈⣧⣿⣇⠹⡄⠹⣿⢷⡈⣧⠀⠀⡝⡇⢸⣿⢱⠟⣹⣯⣾⣿⠇⠤⠬⣿⣿⣿⣿⣛⠳⣬⣿⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⢾⣿⣿⣿⣿⣿⡿⣿⡀⠸⣿⣿⠀⠹⣄⠘⣧⣷⢸⡄⠀⡇⢻⢸⣿⠏⣴⣿⡿⢹⡏⠀⠀⠀⢸⠇⢿⣿⣿⣿⠞⠋⠀⠐⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢿⣿⣿⠛⠛⢁⣾⣷⡀⠹⣿⣇⠀⠙⣦⢹⣿⡦⢷⠀⢸⡼⣸⠏⣸⣿⣟⠀⢸⡿⠀⠀⠀⢸⡇⠈⣿⡿⠋⢀⡀⠘⠷⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠻⣿⣤⣀⣾⣿⣿⠟⣆⠹⣿⡆⠀⠈⢳⣹⣿⣾⡆⣾⢣⣿⣴⢿⠇⣿⣿⣿⣿⠓⠒⠶⢾⣷⠟⠉⠁⢸⣿⣿⠟⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⣇⡀⠀⠀⠀⠙⠻⢽⣻⣿⣿⡄⠈⠳⢿⣻⣦⡀⠀⠙⣿⣿⠻⡇⣼⣿⠃⣼⠀⣸⣿⣿⣿⠀⠀⠀⣼⠏⢠⡀⠀⠀⠙⠿⣴⠃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠓⠢⢤⠀⠀⠀⠈⠉⠛⣿⣤⠀⠀⠉⠛⢿⠓⠚⠛⣿⣿⣿⡟⠁⣰⠇⠀⣻⣿⣿⣏⣤⣤⣼⡇⠀⠀⠙⢦⡀⠀⠀⠙⣶⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⢷⣀⡀⠀⠈⢳⡀⠀⢸⣹⣿⢁⣴⡋⠀⣰⡏⠻⣟⢛⠛⠛⢻⣷⣀⠀⠀⠀⢙⢦⣄⠺⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣿⣦⡀⠀⢻⡄⢸⠃⢿⢸⡏⢿⣤⠟⠀⠀⠈⠫⣉⢷⣼⠸⣟⣷⣦⡀⠀⠀⠙⢷⡿⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⣟⣷⡍⠳⢦⣿⡞⠀⣸⣿⣰⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⢹⣽⡈⢘⣿⡶⣄⠀⣴⡿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⡄⠙⠻⢿⣦⣄⠀⣷⣀⣟⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣾⢻⡛⠋⠁⠀⠈⠳⠮⣿⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠘⣷⡀⠀⠠⣄⠙⣷⣿⣿⠟⢁⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣯⣷⣄⡀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠙⢷⡀⠀⠘⣦⢹⣿⣏⢠⣿⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⢿⣧⡉⢛⣲⣤⡴⠚⢉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣻⣄⠀⢳⡀⠀⠈⢇⢹⣹⣿⣿⡇⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠙⣿⣯⣩⣤⣴⠞⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣧⡀⠹⣆⠀⠘⣿⣿⡼⡿⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣳⡙⠷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⣿⠿⣿⣦⣌⠳⣴⢿⡟⠘⡷⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⡃⠘⠇⠈⠙⢻⣟⡁⣼⣣⣾⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣆⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣷⡀⠠⡄⠀⠀⠹⣿⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡙⢷⡀⠰⡄⠀⠀⢸⠃⠀⣨⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡙⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⠦⣿⣄⢹⡀⠀⢸⣰⠟⠁⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⣧⡀⢽⣦⣷⠀⣸⡿⠀⢠⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⢿⡘⢲⣿⣿⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⣠⡟⣿⣳⡏⠀⢠⣿⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⠀⠀⠀⠀⠀⠀⡟⣴⣿⠟⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠸⣦⣀⡀⣀⣠⣴⣷⣿⠁⠀⣠⣿⣞⡷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠘⢧⡹⢿⣉⣩⣿⣻⠟⠁⢀⣴⡿⠿⢟⣴⡿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢤⣽⠶⠿⠷⠋⠁⢀⣰⣿⡯⢄⣤⢿⣿⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⠿⠿⠿⠴⠾⢿⠯⠥⠶⠛⢫⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢲⡶⠿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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