⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡟⣆⠀⠀⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣶⣶⣶⣶⣶⣶⣶⡖⣾⣿⠀⠀⠀⠀⢸⡇⠈⢣⣀⣠⠤⠖⣾⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣀⡤⠼⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣀⣄⣀⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠈⣻⣿⠀⠻⠯⣄⣀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣴⣿⣿⣟⠉⠁⢹⣇⠀⠀⢸⣿⡇⠀⠀⣠⡴⠶⢦⣾⠀⠀⢸⣇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠶⣤⣀⠀⠀⠈⠁⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠈⢹⠀⠀⢀⣀⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⣸⠆⢸⣿⠛⣻⡿⢓⣾⡿⢾⣷⣦⣼⣿⣧⡴⠚⠉⠀⢠⣤⣽⡀⠀⣸⣿⣄⠀⣠⣍⠁⠀⠀⣀⣤⠞⠁⠀⠀⠈⠋⠉⠉⠛⠉⠁⠀⠙⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢸⠀⣠⠏⠀⠈⠉⠓⠿⠆⠀⠀⢀⡠⠖⢻⣗⣿⡉⠞⣽⣳⣿⣿⣤⣾⣿⣿⡿⠋⠁⠀⠀⠀⣀⡾⠶⠦⠭⣭⣛⣙⣟⠷⠬⠭⣤⣴⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢶⢤⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡼⠁⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠙⠒⠺⢿⣿⣿⣿⣷⣿⡟⣀⣿⣿⣿⣿⠷⠀⠀⣀⣶⡿⢿⡇⠀⠀⠀⠀⠀⠀⠈⣛⣯⢷⠶⠶⣮⣭⡭⠭⠭⠭⠽⣿⣷⣾⢿⡻⢾⣾⣿⣧⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢤⡀⠈⠻⣿⡿⣿⣿⣿⣿⣿⣿⣋⡤⠴⠒⠒⢋⣽⡿⣉⣀⣀⡀⠀⠀⣠⣾⡵⡾⢫⡆⣸⡃⠘⣿⣷⣤⣖⣋⡁⠀⠘⣏⠛⠯⠟⢹⣦⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⠀⠀⠀⣦⠤⠤⠏⠈⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠛⠷⣄⣙⣧⣀⣨⠽⠿⠛⠉⠀⠀⡞⠀⣠⠟⡸⡽⠓⠒⠲⠤⣠⣼⢿⣥⣾⢡⣿⣷⢫⣿⠀⢸⠸⣿⣆⢻⣏⣉⣙⠛⢦⣤⡄⢸⣦⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠸⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡤⠖⠁⠀⠀⠀⠀⠀⢸⣿⡤⠒⠲⢤⡀⣴⡖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⣿⣸⣼⢻⣏⢹⣷⣿⣿⡀⣶⡄⣿⣿⣿⠛⠓⠶⢶⣼⡿⠟⠒⢷⣇⠀⠹⣦⣀⠀⠀⠀⠀⠀⣀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠴⢦⣸⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣰⠛⢦⡀⠹⡏⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⡞⠁⠀⠀⠀⠀⠀⢿⡇⣿⡛⢻⣿⣿⣿⠿⢼⣧⣷⣇⣿⣿⠿⠇⠐⠢⡼⢽⣇⡤⠶⠦⣿⡆⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣀⡀⠁⠀⣇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡇⠀⢠⣀⠀⠀⠀⠘⡷⣿⠇⣈⡀⠀⠀⠀⣼⣿⣼⣿⣿⣿⡛⢶⣶⢲⠧⣾⠁⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣫⠿⠻⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠒⠒⠋⠉⠉⠉⠉⠁⠘⣦⠿⠭⠟⠀⢀⣠⣿⣿⣿⣟⣹⣇⡼⢻⣿⠓⢿⡆⠀⠀⠀⠀⢸⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠋⠉⠀⠀⢀⡇⣰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠉⠁⢀⡠⠞⣹⢿⣳⡿⢿⣷⣶⣒⣺⣿⣿⠿⠛⠉⠉⢀⣀⡴⠛⠉⢀⣺⡀⢀⣀⡀⠀⠘⡇⢀⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⠇⠀⠀⠀⣤⣶⢿⠟⠏⠉⠀⠀⣀⣀⣀⣀⣸⠷⠃⠘⢿⣧⠀⡴⢶⣤⣄⣀⠀⠀⣠⠞⠀⠀⠀⣼⣥⡤⢤⣴⣏⡴⠚⣿⣿⡿⢿⣾⢉⣽⠋⣘⡟⠁⣠⣾⣿⠭⠽⡾⣷⠛⢩⠉⠉⠻⣭⣶⣯⠀⠀⣿⣿⣷⠶⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣠⠴⠚⠉⠉⢁⣠⣤⡶⠖⠂⣀⡴⣾⠈⠳⣄⠀⠀⠙⠿⣝⠶⣅⣄⣀⢀⣠⣿⣶⣒⣶⠟⠋⢠⣾⣿⣿⡆⠀⠉⠉⢉⣭⣿⡷⣋⡵⠛⠁⢀⡼⠁⠈⣠⠏⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⣻⡆⠀⠀⠀ ⢰⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠻⠇⢀⣀⡿⠋⠁⠀⠀⢠⠖⢫⠞⠉⣠⠴⠋⢁⣴⡇⠀⠀⠈⠓⠦⣤⡴⢋⡿⣿⣦⣿⣉⢹⣋⡼⠋⠁⠀⣼⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⠿⠋⠁⠀⠀⢠⢾⠇⢀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀ ⢸⣄⠀⠀⠀⠀⠀⠀⠀⠈⣥⣤⣼⣽⣿⣅⠀⠀⠀⢰⠋⠀⠿⠖⠋⠁⢀⡴⣻⠟⡇⠀⠀⠀⣰⠞⠁⣠⠏⠀⠀⣠⠤⠼⠿⢧⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣰⠋⢸⣴⡋⠀⣀⣴⣖⣒⣶⠚⠋⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⢦⣀⡀⠀⠀⠀⣿⢱⠃⠀⢳⣤⠤⠖⡇⠀⢰⣃⡴⠂⠀⢻⠀⠀⣠⠖⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡼⠻⣄⠀⢳⡒⠿⣭⣠⡤⠬⣅⡀⠀⠀⠀⠀⣀⣤⠾⣿⡏⠀⠀⠀⠀⠀ ⢸⣋⣿⡟⢷⣄⠀⠀⠀⢀⣿⣿⣿⠿⣿⣿⡋⣇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠲⠤⢿⣤⡀⠀⠀⠀⠀⠸⣆⣞⠀⢀⣴⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠒⠚⠀⠀⠈⠙⠚⠷⢯⣅⣠⠄⠀⠀⠉⠳⣶⣼⣿⣃⠉⠀⣿⣇⣀⣀⣀⣀⣀ ⢸⣽⣿⡇⠀⠉⠉⠉⠉⠉⠉⠁⠀⣰⠋⠁⠳⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠉⠛⠶⢤⣠⣖⣛⣮⣹⣿⣇⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣄⣸⣿⣿⣿⣿⣤⠄⢠ ⢸⣿⣿⣿⣿⣿⡶⢦⣤⣄⡀⠀⢰⡇⠀⡀⠀⠈⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⢈⡭⠭⢭⣉⣻⣿⣿⣦⡀⠀⠀⣄⢾⣽⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⢤⣤⡤⠤⠔⠒⠒⣖⠒⠒⠓⠒⠒⠶⢤⣤⣤⣽⡟⠛⠛⠋⠁⠉⠀⠙ ⢸⣿⣿⣿⣿⣿⡇⢸⣿⡏⠙⣷⣤⣿⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⠟⠂⠀⠹⢤⣹⣏⠹⣿⣿⣦⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⣾⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣿⣾⣿⣿⡇⣼⣿⣧⣠⣿⠟⣻⢏⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⡉⠁⠉⠻⣿⣿⣟⡛⢟⣿⣿⣿⣿⡿⠶⠒⠲⠦⢤⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠛⠿⠻⠿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣇⡿⠿⢋⡽⠛⡿⡅⠀⢳⡈⠳⣌⠻⣦⣄⡀⠀⠀⠀⢀⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣉⠉⠛⢿⠒⠦⣹⣯⡟⠻⣷⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⣿⣿⣿⠟⠁⠀⠀⢺⡀⠀⠹⣟⠒⠦⠷⠀⠘⡆⠈⠉⠋⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠺⢤⣀⣘⡎⠙⣦⣿⣿⣿⡇⠀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⡠⠤⠤⠤⠤⢤⡀⠀⠀⠀⣾⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⢠⣤⣬⣿⡇⠀⠀⠀⠀⠀⢳⡀⠀⠈⠳⠤⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠴⠒⠒⠒⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠴⠚⠀⠀⣀⣤⠶⠾⣽⡧⠴⠒⢛⡿⠞⠓⠶⠶⢶⣤⣄⡀⠈⠙⣳⣦⣤⣤⣴⣶⣾⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⠀⠀⠀⣀⣠⠴⢾⠉⢸⠟⠷⣶⣒⣀⡤⠔⠚⠉⣀⣠⠴⠒⠋⢁⣠⠴⠚⠁⠀⢠⠖⢿⣀⠀⠀⠀⠀⠀⢈⡟⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣿⣿⡿⠿⠟⠛⠛⠛⢻⣦⠀⠀⠀ ⢸⣿⡿⠗⠒⢻⠉⠉⡆⠀⢸⠀⠘⠦⣄⡀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡤⠖⢻⡅⠀⠀⣠⡴⠋⠀⠀⠈⠙⠲⣤⡤⣀⣸⡴⠃⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠵⢄⡀⠀⠀⢣⠸⡄⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿ ⠀⠸⢿⡄⠀⠘⡆⠀⢳⠀⠈⠃⡀⠠⣇⠉⠉⢷⠒⠒⠒⠚⠉⠛⠉⢻⡀⠈⣿⣤⠞⠋⠀⠀⠀⠀⠀⢀⣀⣀⣙⣦⣿⠓⠦⣄⡀⠀⠙⢿⡿⢿⣿⣿⣿⣿⡟⣆⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠙⢦⡀⠀⠀⢱⠀⠀⠀⣠⣤⣶⡞⠋⠀⠀⠀ ⠀⠀⠀⠹⣾⠀⢧⠀⠈⡄⠀⠀⠀⢠⠿⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣟⠉⠙⠛⠛⢦⡀⠀⠙⢦⣀⣿⠋⠋⢧⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⣧⣤⣿⣿⣿⣿⣿⣶⣶⣶⣶ ⠀⠀⠀⠀⠹⣆⠸⡄⠀⢳⠀⠀⠀⡼⠀⢹⡀⠀⠹⡄⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⣼⠻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣻⡏⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠹⣆⢳⠀⠈⢧⠀⠀⣇⠀⠀⢳⡀⠀⢳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣰⡟⠀⢧⠀⠀⣠⠴⠒⠋⠉⣉⠙⠛⠿⢶⣦⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡋⠉⠉⠉⠀⠀⠘⢻ ⠀⠀⠀⠀⠀⠀⠹⡌⣇⠀⢈⣇⠀⠸⡄⠀⠀⢷⡀⠀⢳⣀⣴⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣁⣴⠞⢹⠇⠀⣿⡶⠋⠁⠀⠀⠀⠰⡏⣹⡂⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢻⡼⣟⠋⢸⣆⠀⠹⡄⠀⠀⢳⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣾⣟⣁⣠⠾⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢹⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠓⢾⣽⣦⣀⠹⡤⠖⢺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⠞⢹⠋⠀⢀⣀⣀⣀⣀⣀⠀⠀⠘⠛⠒⠲⠿⠭⠽⢷⣦⡀⠀⠀⠀⠀⠀⠹⣶⠃⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⠀⠈⢧⠀⠙⣄⠀⢻⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠞⠁⠀⣯⣴⣾⡿⣿⣍⠀⠈⠉⠩⡿⠷⠶⢤⣄⠀⠀⠀⠀⠈⠙⠳⣄⠀⠸⡿⠀⠈⢻⣻⡅⠀⢻⣆⠀⠀⢠⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁ ⠀⠀⠀⠀⢠⣤⣤⣤⡀⠸⡄⠈⢳⡀⠈⢧⣀⣸⡷⠋⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⠻⣏⣀⣿⣿⠀⣀⣠⡴⠃⠀⠀⠀⠈⢳⡀⠀⢰⣾⠄⠀⠀⠙⢦⡀⠀⠀⠀⠹⡿⠚⠉⢿⡆⠀⢀⣷⠉⠁⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⣞⣀⣀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⣶⣷⠀⠀⢙⣦⢾⣿⠟⠁⠀⠀⠀⣨⠟⠉⠓⠦⣤⣀⣴⠃⠀⢀⣀⡤⠤⠤⠴⠿⠟⠛⠛⠋⠉⣀⡤⣄⠀⠀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⣄⠀⠙⢦⠀⠀⠀⢹⡿⣄⠘⡿⡔⠻⠖⢦⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠞⢀⡿⠁⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⣠⡿⠟⠿⠶⠋⣠⠞⠁⠀⠀⠀⣠⠞⣋⠀⠀⠀⠀⠀⠉⠁⣠⡾⠟⠉⠀⠀⣶⣿⡋⠀⠀⠀⠀⠀⣧⣴⡾⠛⠛⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⣿⣷⣄⠘⡆⠀⢸⢿⣧⣏⠳⢄⡀⠀⠀⠈⠟⡀⢠⣤⣤⠀⠀⠀⠀⠀⢠⡾⠷⠶⠶⠠ ⢀⣾⣿⣿⣾⡇⠀⠐⠋⠀⠀⠀⣠⠞⠁⠀⠀⣀⣴⣾⠟⠋⠁⠀⠁⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠶⠤⠤⠬⠥⠤⠤⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⡆⢙⣿⣿⣿⡇⠀⢻⢶⠀⠐⠀⠁⠀⡏⠻⣆⣀⣠⠴⣺⠏⠀⠀⠀⠀⢀ ⠀⢿⠻⣿⡏⢿⣤⣀⡀⢀⡴⠊⠀⠀⣀⣴⣾⣿⣿⡃⠀⠈⠁⠀⠀⠀⠀⠀⠘⣏⠀⣾⠻⢞⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣤⣀⢹⣿⣾⣿⣧⣾⣿⣭⣿⣿⡀⠈⠏⠀⠀⠀⠀⣀⡇⠀⠈⠉⠀⡰⠃⠀⠀⠀⠀⠀⠠ ⠀⠸⣆⠀⠳⠌⠙⠛⠛⠉⠀⣀⣠⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⢯⡉⠉⠙⠛⠿⣬⡿⠿⠿⠷⣦⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⢿⣿⣿⣿⣿⡿⠃⠈⠙⢿⣇⠀⠀⠀⢴⣚⣉⡁⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠐ ⠀⠀⠘⢷⣄⡀⠀⠀⠀⣠⣴⠿⣫⣿⣿⡿⠀⠀⠀⠀⠀⢀⣄⣤⣶⣾⢀⣠⣶⣾⠇⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠓⡶⠀⠙⢿⣭⣿⡇⠀⠀⠀⠀⣽⠷⣄⠀⠀⠀⠀⠉⢹⠀⠀⡴⠤⢤⣙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡿⣄⠀⣼⠟⠁⣀⡿⣿⠿⠿⣶⣤⣄⣤⣶⣾⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣬⡟⠲⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣸⡷⠒⠿⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⢀⣴⣾⡳⢦⡄⠀⠀⢸⣀⡞⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢾⡿⠋⣠⠞⠁⠀⠈⠳⣄⠀⠀⣉⡿⠟⠉⢸⣿⡿⠛⠉⠀⠀⠀⠀⣀⣤⣴⠞⠋⠁⠀⠀⣴⣿⣿⠉⠙⠳⣼⡿⣿⣿⣿⠟⢋⣈⡿⣄⡬⠭⣿⣷⣶⣤⣀⠀⠈⣧⠀⠀⠀⠀⣠⣾⣿⣮⢷⣿⣽⣦⣀⡼⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣄⠀⠀⠈⠙⠚⠁⠀⠀⢿⣿⠃⠀⠀⠀⠀⣀⣤⣚⣻⠏⠀⠀⣀⣠⡴⣿⣿⠟⣿⠀⠀⠀⡏⢸⣿⠟⠁⠀⣸⠿⠃⠀⣤⢞⣩⠿⠛⠋⠉⠳⣦⠈⣦⣴⣴⣾⢻⣿⣿⢻⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⣀⣴⠃⠀⠀⠀⠹⠛⠃⠀⠀⠀⠀⢀⣀⠀⢿⣿⣄⣀⣀⣠⡾⠟⠻⢿⣷⣤⣰⣾⣿⡏⣠⡿⠋⠀⣿⠀⠀⢸⡇⣼⠃⠀⢠⣾⠏⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⡛⠙⢷⡛⢿⣾⡿⡿⣟⣿⣏⣹⣦⠀⠀⢀⣄⠀⣤⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠋⠀⠀⠀⣼⣿⡿⣿⣷⡄⢠⣴⣮⡙⠛⠛⠻⢷⡿⠁⠀⠀⣿⠀⠀⣸⣷⣼⡄⢀⡘⣿⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠈⣷⠶⡄⢳⡌⢻⣷⡽⣿⠟⢻⡿⠋⠀⠃⠈⠋⢀⣿⣿⣶⣦⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⣿⣿⡾⠋⣠⣿⣯⠙⠿⠁⠀⠀⠀⡼⠁⠀⠀⢰⣇⢠⠖⣻⣿⣿⣿⠋⠳⣿⣤⡏⠀⠀⢠⡞⠴⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣳⡀⠹⣄⣹⠞⢁⣴⣿⠇⠀⠀⣠⣾⣿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⣿⠛⠚⠻⣿⣿⣿⣦⣴⠟⠻⣧⡤⣼⣍⡀⠀⠀⠀⠀⢢⣀⡟⠀⠀⠀⠙⢿⣿⣿⣦⠈⠉⠉⠉⢹⠀⠀⠙⠋⠉⡇⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠿⠟⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣿⣸⢦⡀⠀⠘⣿⡟⠛⠳⠤⢤⣬⡧⠇⠀⠙⠲⢤⣀⣀⣀⣉⣀⣠⡤⠶⠚⠉⠁⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢸⣏⠁⢀⣧⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀