⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡴⠒⠚⠛⠉⠉⠉⠛⠻⢿⣕⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠻⣌⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⢋⠀⠀⠀⠀⠀⠀⢸⡀⡧⣀⠀⠀⠀⠀⡟⠅⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⣰⣳⠇⠀⠘⠀⠀⠀⠀⢸⣇⣷⠾⠓⠢⢄⡀⢻⠃⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠞⣸⠀⠀⡇⠀⠀⠀⠀⣾⡿⢣⣖⣶⣶⠀⠹⣎⢻⡅⠀⠀⠀⠙⠻⠶⠒⡆⠀ ⠀⡇⠀⠀⠇⠀⠀⠀⡼⠋⠁⡇⢻⠟⠃⠀⢠⠁⢡⣃⠀⠀⠀⠀⢀⡠⠜⠁⠀ ⠀⠇⠀⣴⠀⢰⣶⣾⣇⡀⠀⠀⠀⠀⠀⠀⢠⢧⡬⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⢀⠎⡼⢀⡾⣯⠜⠛⠹⠄⢀⣀⠀⠀⢀⣏⣤⠥⠬⠖⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠜⠋⠁⢣⢸⠦⣠⣀⡈⡧⡄⢀⣴⣿⣤⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠺⡄⠀⡱⠁⠐⢪⣿⢿⠏⠁⠀⠀⠠⣲⠟⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢶⠃⠀⣠⣾⡟⠁⠀⠀⠀⠀⣼⠁⠀⠀⠈⠳⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⢳⣾⣿⠋⠀⠀⠀⠀⠀⢸⣿⣤⣀⠀⠀⠀⠀⠑⣄⠀ ⠀⠀⠀⠀⠀⢠⠊⠀⣇⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⡉⠑⢤⡴⠦⠀⠈⡆ ⠀⠀⠀⠀⣰⠁⠀⠀⢸⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠋⠀⠀⡠⠊⠁

⢯⡀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠙⣾⠃⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠉⢠⠞⠁⠀⣼⠁⠀⠀⠀⠀ ⢀⢻⠀⠀⢠⠟⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠀⠀⠚⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣶⡲⠒⠒⠚⠉⣩⡶⠋⠀⠰⠃⠀⠀⣰⠃⠀⠀⠀⣠⠁ ⣾⡀⢰⣰⠏⣠⠞⠁⠀⢰⠟⢦⣄⢀⣿⡀⠀⠘⢧⠀⠀⠀⠀⠈⠻⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠉⠑⠲⠿⣍⣁⡀⠀⠀⠀⠀⢀⣰⣏⣠⣴⠖⢫⡿⠀ ⠙⣧⡼⣁⡼⠁⠀⠀⠀⣼⠀⢀⣿⣿⣿⣇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⠳⣌⠛⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⠤⣀⣀⣀⠀⠈⠙⢛⣛⡒⠶⠞⣛⡶⠞⢁⣴⡟⠀⠀ ⢀⣿⣿⡿⠁⣤⠀⠀⠀⣿⠀⢸⠿⡟⠿⣿⡆⠀⢦⠈⢿⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠙⠛⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠈⠉⠛⠚⠯⣭⣛⣛⡿⠶⠶⠿⠯⠭⠤⢴⡿⠛⠁⠀⠀ ⣾⣿⡟⢀⣰⠃⠀⠀⠀⣿⠀⢸⠀⠀⠀⠹⣿⡀⠈⣦⠈⢿⠳⣤⡀⠀⠀⠀⠀⠈⠳⣤⣽⠶⣭⣉⣹⣾⣝⠛⠛⠷⢶⣶⣠⠤⣤⣤⣤⣀⣀⣉⣉⣉⣉⣉⣤⣤⣖⣻⡇⡀⠀⠀⠀ ⣧⠟⠁⣼⡏⠀⠀⠀⠀⣿⠀⣸⡦⢦⡀⠀⠘⣧⠀⢹⣷⡀⢳⡈⠙⠳⣤⣀⠀⣠⢶⣫⠿⠾⣍⡈⠙⠲⢭⣷⡄⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⠒⠀⣀⣴⠞⠋⠉⢉⠉⠉⠉⡇⠀⠀ ⣿⠀⠀⣿⠇⠀⠀⠀⠀⣿⡀⣿⠟⠶⣝⣦⡀⠈⢧⠈⢷⠻⣄⠹⣆⠀⠀⢈⣿⠿⠯⢤⣀⣀⣈⠙⢿⣶⣤⣈⡻⡟⠲⠶⠦⣤⣤⣤⣴⣶⣾⠟⠋⠉⢀⣠⠴⢺⡏⠀⢀⣾⠇⠀⠀ ⢿⠀⠀⣿⠀⠀⢿⠀⠀⢻⡇⢻⠀⢀⠀⠙⠻⣆⠈⣆⠘⣧⠈⠻⢜⣦⣴⠟⠀⠀⠀⢀⣀⣠⣽⣿⠿⠟⠿⣿⣿⢟⡛⢶⡖⠚⠛⠉⠀⢸⣇⠀⣠⡞⠉⠀⠀⠞⠀⢀⡾⠃⠀⠀⠀ ⣼⣇⠀⢻⠀⠀⢸⡀⠀⢸⣹⣼⠀⣿⣿⣦⡀⠈⢳⡜⢦⠹⣆⠀⠀⠙⠻⣦⣀⢀⣴⣿⡿⣿⡟⠻⣆⠀⠀⠈⣿⣧⠀⠀⣇⠀⠀⠀⠀⠀⢿⡴⠋⣿⠆⠀⠀⠀⣰⠟⠓⠦⠶⠶⢶ ⠈⣿⡆⠘⡆⠀⢸⡇⠀⠈⡏⢿⡄⣿⠏⣽⣿⣦⠀⠃⠈⠳⣽⣄⠀⠀⠀⠀⠉⠛⣿⣿⣷⣿⣿⠀⢹⡄⠀⠀⢹⡟⠀⠀⢻⠀⠀⠀⠀⠀⠘⡇⢠⠏⠀⠀⢠⡞⠻⠿⢶⡶⢾⡿⠛ ⡆⣿⣿⡄⢹⡀⠸⣷⠀⠀⢹⣼⣿⡟⠀⣬⣼⣿⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⢸⠹⣿⣿⠀⢈⡇⠀⠀⣸⠀⠀⠀⢸⡇⡆⠀⠀⢳⠀⢻⠛⠀⠀⣴⣏⡠⠤⠤⣶⠖⠋⠀⠀ ⢻⠟⣿⣷⡀⢣⠀⣿⣇⠀⠀⢳⣯⣇⠀⢹⠙⣿⣿⡆⠀⠀⠀⠀⠙⠿⣄⡀⠀⠀⠀⠈⣧⣈⠁⣀⡼⣀⡀⠀⠀⣀⡄⢀⣼⢡⡇⠀⠀⠘⣧⢸⣄⣴⣿⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀ ⡞⢰⣯⠻⣿⣄⠀⠸⣿⣷⡀⠀⢻⡞⣦⠘⣧⠘⠛⣿⠄⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠉⠛⠛⠛⠋⠁⣠⣴⣫⢵⠾⠛⣻⣾⡇⠀⠀⠀⢹⡟⡿⠷⣬⣽⣲⣤⣤⣄⣤⣤⠆⠀⠀ ⢷⣼⠌⣷⠈⠻⢦⡀⢻⣿⣿⣦⡀⢻⡌⠑⠻⠶⠾⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⢀⣿⠿⡇⠀⠀⠀⠀⣿⣷⠀⠀⠀⠈⢉⣩⣴⠟⠁⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⠀⠻⣼⣿⣿⡏⢿⣷⣽⣦⡤⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣼⠃⢈⡇⠀⠀⢰⢰⣿⡏⠉⠉⣉⣭⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠈⠙⢿⡇⠉⣧⠉⠉⠛⠲⠆⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠋⢡⠀⠀⠀⠀⠘⠁⠀⢸⡇⠀⠀⡾⣼⢿⡟⢿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠸⣆⠀⠀⠀⠀⠀⠈⠳⠆⠀⠀⠀⠀⣀⣠⠤⠔⠛⠉⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣼⡇⠀⢠⣇⡟⠚⠿⠿⠧⢤⣤⠄⠀⠀⠀⠀⢸⡇⠅ ⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠙⣆⡀⠀⠀⠀⠀⢶⣦⠤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣠⠟⢹⠀⠀⣼⡿⠙⠛⠒⣶⡖⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀ ⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣦⡏⠳⣤⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠲⠤⡞⠀⠀⣠⣾⠋⠀⢸⠀⣼⣿⠃⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣧⠀⠀⣿⡇⠀⠈⠻⣦⣄⠀⠀⠈⢧⡀⠀⠀⣠⡶⠒⣶⠏⠁⠀⠀⠀⢀⡇⢀⣴⠟⠁⠀⠀⣿⡾⢡⣿⠶⠖⠲⣦⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⠀⣿⡇⠀⠀⠀⠀⠉⠻⢦⣄⠀⠻⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣵⠟⠁⠀⠀⠀⠀⡿⠀⠸⢹⡄⠀⣿⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣌⠧⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⣿⠀⢸⣷⠙⠻⢦⣄⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⣄⣤⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢷⣿⠀⢸⡿⠀⠀⠀⠈⠛⠲⢦⣄⡀⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣿⣦⠤⠤⢤⡤⠤⢶⣶⣶⣀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⣿⡏⠀⠀⣼⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢻⡇⣰⡿⠉⢀⣼⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣾⠃⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⣾⣡⡿⠃⠀⣼⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⣿⡟⠁⠀⣼⡏⠀⣼⠏⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⡞⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢠⣿⠋⠀⠀⢰⣿⠁⣸⠃⠀⠀⠀⠈⠉⠛⠛⠿⣿⠏⠀⠁⠀⢀⣜⢁⣀⣤⡤⠄⠒⠒⠀⠀⠀⠀⢀⣼⠋⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠸⣿⡀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣠⢯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠙⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠋⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢛⠿⠲⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⠉⣠⠞⠁⣠⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⡀⠀⠻⢛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⡦⣼⣯⣵⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣀⢀⡘⣿⡇⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠉⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠉⠻⣿⣿⣿⣿⣧⣠⣶⠄ ⢰⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⠁⠀ ⢸⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⢻⡃⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠛⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠛⠛⠿⠿⠿⣿⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣤⠞⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠉⠉⢀⡴⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡼⠋⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣠⠻⣆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⣰⠋⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠔⠁⠀⠀⠀⠀⠠⠞⠁⣰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢠⡆⠀⠀⠀⢀⠀⠀⢀⡴⠋⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⢀⡴⢃⣠⡶⠋⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⢰⠏⢀⠀⠀⠀⣴⠋⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢴⣶⣿⠟⢋⡿⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀ ⠀⠀⣀⣤⣿⣤⣼⡀⠀⢠⡏⠀⠀⠀⢤⣴⣲⣺⣿⣯⠷⠛⠛⠉⠁⠀⢀⣾⣧⠶⠛⣉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠃⠀⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⣿⣿⣿⡆⠀ ⠀⠀⣿⣿⣭⣀⣨⣧⣤⣾⠷⢶⣶⣾⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣉⠡⠴⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢠⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⣿⣿⣿⣇⠀ ⠀⠀⢻⡇⠀⠀⠀⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠘⢿⣧⠀⠀⠀⠀⣼⠇⠀⠀⢀⣾⣿⣿⣿⣿⠀ ⠀⠀⠈⣧⡀⠀⣠⣿⠏⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⡀⠀⠀⢀⡏⠀⠀⣚⣫⣼⣿⣿⣿⣷⡄ ⠀⠀⠀⠸⣧⣴⡿⢋⠀⠀⠈⠻⠿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁⠀⠀⣸⡇⠀⠀⣼⠶⠟⠉⠉⠀⠀⠀⢀⣄⡿⠁ ⠀⠀⢀⣴⣾⠟⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⢀⣿⠁⠀⠀⣿⠠⠀⠀⠀⠀⠀⠐⢢⡾⠁⠀ ⠀⣠⣿⡟⠃⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣼⡇⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀ ⢀⣿⣿⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⣀⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡏⠀⠀⣿⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀ ⠰⠹⣿⣇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉⠈⠻⠷⣶⣶⣶⣶⣶⡶⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⣿⠀⠀⠀⡿⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠹⣿⣦⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣾⠃⠀⠀⠸⡇⢀⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣸⠏⠀⢰⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣶⣭⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⡟⠀⠀⡟⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠿⣿⣷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣶⣿⡇⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢠⡟⠉⠛⠛⠛⠻⠿⠶⠦⣤⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⡿⠿⠛⠋⠁⠘⣷⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠃⠀⠀⠀⠀⠀⢀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠈⣿⣍⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣴⣿⡏⠉⠉⠛⠓⠲⠶⠶⠶⠶⠾⢟⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡟⠋⡙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣽⡗⠈⢉⣿⣧⣀⣀⣤⣴⣾⡟⠻⠏⠉⠹⠑⠛⢱⣶⣿⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣿⡟⠀⠀⠘⢿⣟⠛⢻⣯⡿⠋⠉⠀⠀⠀⠀⠀⢀⣼⠟⣡⣾⠟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣿⠃⠀⠀⠀⠘⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣁⠸⣣⡿⠋⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡟⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢠⣿⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡟⣿⠟⠉⣉⡨⠽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠋⣩⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣸⣇⡯⡴⠊⢡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⢂⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠉⠁⣀⡽⢟⣏⠀⡙⢦⡀⠀⠉⠉⠓⠲⣶⡶⠶⠶⠶⣶⠶⠶⠿⠟⠛⠁⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⣸⣿⡆⠹⣆⡙⢦⣄⡀⠀⠀⢀⣩⠿⠒⠶⠶⢶⣂⣀⡀⠀⢀⣀⡠⢤⡝⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣣⠖⢻⣿⣿⣿⣦⡙⣟⠲⢽⣯⣱⣶⣿⣴⣿⠶⣶⣄⣤⠤⢶⠞⠛⣩⣴⠒⢀⣧⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠟⣧⢿⠀⠘⣿⣿⠁⠀⠙⠮⣧⡀⠽⠟⢻⣿⣿⢿⠀⢸⠋⢻⣄⠈⢣⡘⣧⣯⠀⡼⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣸⣧⠀⢿⣷⣴⣶⣤⡤⠀⠉⠲⠀⠈⠛⢻⡾⠀⠚⠀⠀⢻⣧⡀⢻⡿⢋⡾⢳⣤⣬⣵⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⢻⣧⡘⣿⣼⣿⣿⣿⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⡘⣷⡞⠁⠀⠈⠓⣦⣤⣯⣁⣀⡼⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣬⣿⣷⣾⣿⢷⡿⠟⠠⣷⠀⠀⠀⠀⣀⠤⠒⢻⡆⠀⠀⢹⣿⡄⢹⣷⣤⣴⣖⣋⠍⢿⢉⠙⢿⣦⡀⠰⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣍⠿⢿⡿⣿⢻⡆⠀⠀⠀⠉⢁⡠⠔⠊⠀⠀⠀⠀⡇⠀⠀⢸⣿⠳⣸⣄⣠⠝⠋⠀⢠⡟⠚⠓⢦⠌⠑⠚⠦⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣸⠀⢷⠀⠀⠀⢲⡏⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡏⢸⡷⣿⣿⣦⡤⠔⠀⢸⠗⠶⣶⢬⠧⠀⠀⢀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣼⠳⣄⠀⠀⠙⠢⣀⠀⠀⠀⣠⠞⠀⣠⡟⠀⠀⣿⠺⠿⠦⠤⠀⠀⠹⣗⢦⣈⡇⠀⠑⢤⣼⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⠀⠀⠙⠲⢤⣀⣀⠉⠓⠋⠁⣀⣼⡿⠁⠀⠀⢿⣷⣦⡀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣘⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣾⣿⡿⠁⠀⠀⠀⠈⢿⣿⣿⣟⠋⠉⠉⠉⠙⣿⣿⣶⠚⠁⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⡉⠀⠀⠀⠀⠀⠀⠈⣻⢻⣿⣧⠀⠀⠀⠀⢻⣿⡛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠒⠲⢷⣶⡒⢶⣤⡞⠁⠀⠀⠙⢦⣄⠀⠀⠀⣠⢴⡽⠃⠀⣿⣧⠀⠀⠀⢸⣿⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠙⠻⣶⣤⣤⣤⣤⡬⢷⣦⣄⢻⣿⠀⠀⢀⣷⣧⠀⠀⢀⣸⡟⠀⠀⢸⣿⡦⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣤⣀⠀⠉⠉⠉⠉⠢⣷⣄⠈⡿⡄⢀⣾⣿⡻⡄⠀⠀⣿⣀⣴⠖⠋⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠈⠛⣲⣷⣷⣿⢿⣿⣷⣿⡶⠞⠋⢁⣏⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣾⠟⢋⣼⡷⠞⠋⠉⢸⠇⠀⠀⡜⢹⡀⠀⠀⠳⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠛⠁⠀⠀⠀⠀⠸⡇⠀⠀⣇⠀⠙⠢⣤⡴⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠸⣄⡴⠞⣉⡤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠰⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣷⠾⠛⠋⠙⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⢀⣠⣾⡿⢛⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⠚⠉⣉⣵⣾⡿⠟⠉⠹⣯⣿⣛⣿⠗⠒⠶⢤⣄⡀⠀⠀⢀⣤⣀⣠⠴⠛⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡿⠟⠛⣿⣶⣀⣠⣴⣿⣿⣯⠁⠀⠀⠀⠀⠀⠉⠳⠚⠋⠉⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡤⠿⠟⣻⣋⣉⣉⣀⠈⢷⡀⢀⣀⣀⢀⡴⠻⣦⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣿⣶⣶⣶⣿⣿⣷⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⣀⣠⠤⠖⠛⠉⠉⠉⠉⠙⠛⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣶⠒⠒⠒⠒⠒⠛⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⣄⠀⠀⠀⠀⠀⠀⠢⢤⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢶⣈⠁⠲⠤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠛⠒⠲⢤⣀⠈⠀⠀⠀⠙⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢷⣄⣀⡨⠗⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⢃⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠘⣧⠀⠀ ⠀⠀⠀⠀⣼⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡄⠀ ⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠁⢠⠏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡇⠀ ⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠈⠁⠀⠀⠀⣰⢿⡀⠀⠑⢄⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠱⣄⣤⣾⣿⠿⠿⠦⠀⠀⠀⠀⢸⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⡶⠿⠛⢻⡀⠀⠘⢦⡀⠀⠀⠀⠀⢸⠀⢀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠴⠁⠀⣩⠅⠀⠀⠀⠀⠙⢦⡀⠀⠙⢆⠀⠀⠀⣼⠛⠉⠀⠀ ⣥⣀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⠞⠁⢀⡤⠊⠁⠀⠀⠈⠒⠀⢀⢀⣙⢢⡄⠀⠑⠂⢠⡇⠀⠈⠀⠀ ⢸⢯⠉⠻⣖⠒⢢⡤⠤⠄⠀⠀⠀⣀⣠⣤⣄⣀⣚⡁⢀⣠⠴⣛⡥⠔⠊⠁⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠈⠳⣤⡀⡞⢻⡀⠀⢀⠆ ⠈⠈⠳⡄⠈⣳⠊⠀⠀⠀⠀⢰⡿⠟⢛⣛⠛⠛⠛⠛⠻⢧⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠛⠉⠉⠉⠛⠛⡿⣶⡆⡀⣼⠛⡁⢸⠁⣀⠜⠀ ⠀⠀⠀⢹⡿⠓⠒⣶⠒⣶⠛⡿⠅⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠃⢀⡇⢸⠋⠀⠀⠀ ⠀⠀⠀⠈⠻⣆⠀⠙⢤⠇⠀⡏⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡎⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⡞⠀⠀⢿⡄⡀⠀⠀⠀⠘⣿⡷⢬⣭⣭⣭⣍⣉⣉⡉⠀⠒⠒⠒⣲⣶⡆⠀⠀⠀⠀⢠⣿⠀⢸⠁⢠⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⠻⣮⠢⣄⠀⠀⠘⢷⡷⠛⠉⠉⠉⠉⠉⠉⠛⠻⣝⣻⣿⠟⠀⠀⠀⢀⣴⣿⣿⡄⠞⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡿⠀⠘⣿⡮⣁⠦⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠁⠀⣠⣤⡶⠋⢱⠿⠛⡇⠀⢠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡾⠃⠀⠠⠹⣷⠞⠻⢦⣄⣀⡀⠈⠛⠒⠤⠔⠒⠛⢁⠀⣀⣴⣿⣿⣧⣲⣤⡸⠀⠀⢧⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⣰⠟⠁⠀⠀⠀⣤⡟⠀⠀⠀⠀⠙⣿⠉⣙⠒⠒⠒⠒⠒⢻⡿⠛⠁⠀⠀⠈⠙⣿⣇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⢸⠋⣷⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠈⠉⠉⠉⢩⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⣿⠉⠉⠉⠒⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠉⠁⣀⣀⠀⠀⠉⠑⠢⡟⠄⢸⣠⠤⠀⠤⣤⠀⠀⠀ ⠀⣶⠒⠒⠉⠁⠀⣠⠔⠂⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠉⠈⠁⠉⠒⠪⣄⠀⠀⠀ ⠀⢇⠉⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠈⢢⡤⠚⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀ ⢫⡉⠁⠀⠀⠀⣠⣾⠟⠛⠛⠀⠀⢀⠤⡞⠀⠀⠀⠀⠰⠶⣶⣶⡄⠀⠀⠀⠀⢃ ⠈⠫⣔⠢⠤⢀⠟⠀⠀⠀⠠⠀⠂⢁⡜⠁⠀⠀⣀⣤⡶⢧⠈⢻⣿⠀⠀⠀⠀⢸ ⠀⠀⠈⠑⡦⠤⠤⠤⠤⠤⠒⠒⣩⣋⣀⠤⠖⠛⢉⠥⠊⠺⣧⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠀⡴⣿⠿⠿⠿⠿⣶⣄⠀⠀⠼⠔⣈⣠⣤⣤⣄⣈⠛⠷⣤⣀⠀⠀⢸ ⠀⠀⢰⢸⠀⢁⣿⣶⣶⣶⣤⣼⠹⠀⠀⠀⠘⣹⠉⠙⠛⠛⠿⣿⣆⠀⢸⠀⠀⠘ ⠀⠀⢸⢸⠀⠀⠈⠻⢿⣿⠿⠓⠁⠀⠀⠀⠠⢻⣿⣿⣷⣶⣶⡾⠌⠀⢸⠀⠀⡄ ⠀⠀⠸⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠿⠿⠿⠟⠁⠀⠀⡆⠀⠀⡇ ⠀⠀⠀⢣⡠⠳⣄⠀⠀⠀⠀⠈⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠙⠵⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⡮⢷⠛⡀⢠⠞⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢯⠑⠒⠒⠤⢴⡶⠶⠚⣿⣭⠋⠁⠀⠁⠀⠓⠁⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⡡⠞⠁⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠒⠂⠤⠤⠤⠄⢀⣈⣒⣤⣔⣋⣀⣀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀

⠀⠐⣺⠟⠉⢀⣾⠃⠀⠀⠀⠀⡾⠃⠀⢠⠞⣾⠁⢀⡇⠀⢹⡀⠀⠀⠀⠀⠀⣸⠈⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣆⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⣀⠀⠀⠀⠀⢄ ⢀⡾⠁⣠⠞⡟⡏⠀⠀⠀⠀⢰⠃⠀⢀⣏⣼⢿⠀⢸⡇⠀⠀⣷⠀⣇⠀⠀⠀⢸⣦⠈⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠀⠄ ⠋⣠⡾⠃⡸⠀⠁⠀⠀⠀⢠⡏⠀⢀⠞⡼⠋⢻⡇⢸⡇⠀⠀⠘⡆⠹⡀⠀⠀⠘⡾⡀⠀⢿⣦⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠈⣧⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀ ⠞⡝⠁⢀⡇⠀⠀⠀⠠⢄⣸⠃⠀⡼⡼⠁⠀⠈⣇⠈⠀⠀⠀⠀⢱⠀⢧⠀⠀⠀⢿⢧⠀⠀⠙⢧⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⡆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⡼⠁⠀⡾⠀⠀⠀⠀⠀⠀⢹⠿⣲⣿⡁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢧⠘⣇⠀⠀⠈⣞⣆⠀⠀⠀⠳⡀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⢹⠲⡀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⡼⠀⣹⢷⣍⠳⣤⡀⠈⣿⡆⠀⠀⠀⠀⠈⣆⠘⡄⠀⠀⢻⡽⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠈⢧⠙⣄⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠘⠀⠀⠀⠀⣼⠀⠀⡇⢠⣇⣀⡙⢦⡀⠙⢧⣹⡇⠀⠀⠀⠀⠀⢹⡆⣵⡀⠀⠸⣿⣱⡄⠀⠀⠀⠘⣦⠀⠀⠀⠀⢿⣎⢦⠀⠀⠀⠈⠀⠉⢦⠀⠀⠈⠳⢤⡀⠀⠀⢢⡀⠀ ⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⡼⣿⣾⣭⣙⠻⣦⡘⣿⣷⠀⠀⠀⠀⠀⠀⢻⠹⣷⠀⠀⢻⣱⣿⣆⠀⠀⠀⠈⢳⡀⠀⠀⠈⢟⡎⠳⡀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠉⠓⠦⢤⣬⣤ ⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⡇⣿⣿⠋⠛⣿⣮⣻⣽⣯⠳⠀⠀⠀⠀⠀⠘⡄⡟⢦⠀⠈⡇⠻⣿⢧⡀⠀⠀⠀⢳⡄⠀⠀⠘⠘⣆⠙⢆⠀⠀⠀⠀⠀⢻⣟⠿⠦⣤⡤⠤⠤⠤⠖ ⡇⠀⠀⠀⠀⠀⠀⢸⡽⣆⠸⡇⣿⡇⠀⠀⣿⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣧⡇⠈⠧⡀⢹⠀⠻⣇⠻⣄⠀⠀⠀⠹⡄⠀⠀⠀⠘⣆⠈⢳⡀⠀⠀⠀⠀⢹⡛⠦⣌⡙⢦⡀⠀⢢ ⣧⠀⠀⠀⠀⠀⠀⢸⡇⠘⣄⢿⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⠃⠀⠀⠹⣌⢇⠀⠹⣆⠈⢦⡀⠠⡀⠹⣆⠀⢀⠀⠘⣆⠀⢱⣄⠀⠀⠀⠀⢳⡀⠈⠙⠶⣷⣄⠈ ⢻⠀⠀⠀⠀⠀⠀⠀⣿⡄⠘⣎⣿⡇⠀⠀⡏⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⢿⡄⠀⠘⣆⠀⠱⡄⠱⣄⠘⢦⠈⢧⠀⠘⡄⠀⢻⢦⠀⣄⠀⠀⢳⡀⠀⠀⠘⣟⠧ ⠀⠇⠀⠀⠀⠀⢠⡆⢹⣧⠀⢸⠿⣿⣄⠀⣿⠈⢉⣿⡟⣿⡿⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⢤⣠⣿⣖⣯⡼⠷⠶⠿⢶⠛⣷⡌⢧⡘⣦⠀⠈⠀⠀⢳⣤⠈⢧⠀⠈⢷⡄⠀⠀⠘⢦ ⠀⢀⠀⠀⠀⠀⡞⡸⢹⠟⡆⠸⡆⠙⢧⡀⠻⣷⣘⣉⣳⣻⢿⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠛⠛⠛⠻⠒⠒⠒⠒⠒⠒⢷⡾⣿⢾⣯⢿⣦⣤⣠⠀⠈⢯⣧⡀⢳⡀⠈⢿⣄⡀⠀⠀ ⠀⠀⡆⠀⠀⣼⣹⢃⡎⠀⣿⡄⣷⠀⠀⠙⠲⢤⣍⣛⠛⢉⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠙⣞⡄⠙⢦⢹⣆⠉⣧⠀⠈⣾⣷⡄⠱⡄⠘⣿⣷⣄⠀ ⠀⠀⠁⠀⢰⣿⡇⣼⠁⠀⢻⢻⡜⡆⠀⠀⠀⠀⠀⣨⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢏⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠈⢷⠀⠈⢻⣿⣆⠘⡆⠀⢹⣷⠙⣦⠹⣆⠙⣿⡛⠛ ⠀⠀⡆⢠⡿⣿⣸⢷⢀⡞⡞⠈⢻⣵⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠋⠛⠛⠻⠿⠦⢬⣉⢿⣇⠀⠈⣿⡿⣦⢱⡀⠀⢿⡄⢹⠷⣜⣦⡙⣿⡀ ⠀⢰⣧⠏⠀⡏⣷⠃⡼⠁⣷⠀⠀⠹⣧⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡍⠀⢿⠃⠈⣿⣳⠀⠘⡇⣸⠀⠈⣮⢿⣌⠙ ⣠⠞⠁⠀⠀⣿⢃⣾⠇⠀⢿⡆⠀⠀⠈⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⠿⢀⣾⠏⢻⡇⠀⢹⣿⣿⣿⡇⠈⢯⠓ ⠁⠀⠀⠀⣰⣿⢫⣿⠀⠀⠸⣷⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢲⡏⢀⣞⡟⠀⠈⣿⡀⢸⣿⡿⠋⠀⠀⠈⢧ ⠦⣄⣠⠞⠁⠟⢸⡏⠀⠀⠀⡿⣷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠏⡼⠀⠀⢠⣿⣇⢸⡏⠛⠲⠶⠶⠒⠉ ⠀⠀⠈⠙⢲⡦⣼⡁⠀⠀⠀⡇⠝⣷⡀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣾⠃⡼⠁⠀⣠⣾⣸⢻⡸⣷⠀⠀⠀⣀⡤⠾ ⠀⠀⠀⠀⠘⠁⠀⠙⢳⣤⣀⡃⠀⢘⢷⣄⠀⠀⠀⠈⠳⢭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⣽⢃⡜⠁⢀⡞⣽⣇⢧⣿⣇⣿⢺⠟⠋⠀⠀⠀ ⠤⠤⣤⣀⠀⠀⠀⠀⠸⠦⣌⣙⣲⣾⠀⠹⣦⠀⠀⠀⠀⠀⠻⠭⣝⣒⡢⠭⠭⢒⣒⣦⡄⡀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠏⠀⢠⠏⣰⣽⣟⡎⠸⣽⡧⢿⡀⠀⠀⠀⠀ ⡆⠀⠀⠉⠳⢦⣤⣤⣀⣀⣀⣩⣿⡜⠀⠀⠈⢦⡀⠀⠀⠀⠀⣀⠀⠈⠉⠉⠑⠒⠛⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⣰⠃⣜⣿⢯⣾⠀⠀⡌⠀⠀⢳⡀⠀⠀⠠ ⢳⡀⠀⠀⠀⠸⣤⣿⠀⠀⢸⣧⣿⠃⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠳⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⡇⠀⣰⠇⢸⣾⣿⠏⠉⣧⡀⠀⠀⠀⠈⢿⣳⣄⠀ ⠀⢱⡀⠀⠀⠀⣿⣿⠀⠀⢸⠹⠋⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⢰⣿⠀⢠⠏⣰⢏⡾⡏⣰⣄⢹⡿⣦⣀⠀⠀⢈⢏⠛⠦ ⠀⠀⠹⣄⠀⣀⣿⠿⠚⠋⠙⠛⠲⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠛⠁⠀⠀⠀⣴⣿⡏⠀⢚⡴⠓⠋⠀⣷⣿⣟⣆⠹⣌⠫⠓⢤⣈⢾⣧⠀ ⠀⠀⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⢘⣇⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⠃⣿⡇⣤⡾⠁⠀⠀⠀⢿⣿⢻⣏⠳⣜⣿⡲⢶⣬⣍⣛⣧ ⠂⢀⣞⡟⠀⠀⠀⠀⠀⠀⣠⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡏⠀⢻⣇⡿⠁⠀⠀⠀⠀⠈⣿⠀⠹⣆⠀⠉⠙⠒⠂⠈⠉⠉ ⢷⠟⠀⠀⠀⠀⢀⣠⠶⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠀⠀⣠⡴⠚⠋⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠀⠀⠀⠨⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣦⣠⡤⠤⠴⠒⠶⠤⡀ ⣀⡤⢞⠁⠀⠀⠀⠀⠀⠀⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⣞⣿⣭⡤⠶⡓⠚⠛⠛⠓⠀⠀

⠁⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣁⣀⣸⣿⣿⣶⠗⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠴⠛⠉⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠃⢀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠁⠀⠀⠀⠀⡠⠋⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⠊⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⠤⠾⠧⠤⣴⣶⡯⠵⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀ ⠳⢄⡀⠀⠀⠉⢶⡶⠬⠭⢒⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢦⠤⠔⠒⠉⠉⠁⣀⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣄⠀⠀⠈⢿⣦⣤⣤⣠⣄⣈⠑⢦⣄⡀⠠⡀⠱⡀⢣⠀⣀⣠⡴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠈⢿⣿⣏⠉⠉⠛⠻⣶⣽⣿⣄⠘⣄⠹⣦⣿⠿⠝⣊⡽⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⡆⠀⡇⢀⠀⠀⠘⡜⣿⡄⠀⡴⢋⡟⠉⢻⣿⣆⠸⡄⢹⣿⡶⠞⠛⠉⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⢰⠁⠀⣿⠀⢇⠀⠀⠱⠘⣷⣼⡡⢣⠋⣽⣟⠙⠈⢣⣇⠀⣿⣇⠀⠀⠀⠀⢀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⢀⡟⠀⡄⡟⢠⠘⣧⠀⠀⢇⣸⣿⠁⠈⣸⣿⣿⣧⡀⠀⣿⣠⢿⠹⠀⠀⠀⢠⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀ ⡞⠀⠀⡇⣹⠃⠀⣿⣧⠀⣸⡏⢻⡆⠀⣿⠛⢧⠟⠿⢷⣾⣿⢸⠀⠀⠀⠀⠀⠀⠀⠈⠒⢦⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠹⡀⠀ ⠇⠀⠀⡇⣿⠀⠀⡟⣿⣷⡃⠠⣸⣿⣀⣿⣤⣤⠬⠟⠛⢋⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠛⣄ ⠀⠀⢰⠃⣿⡇⠀⡇⢹⡇⢳⠀⢻⡛⣿⡉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢙⡆⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠐⡌ ⠀⠀⣼⢸⠹⣷⠀⢱⠸⣧⢸⣧⡀⣇⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⢎⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿ ⢦⣀⢻⡟⢆⠹⡆⢸⠀⢻⡄⢧⡳⣽⠷⣦⣭⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠛⠉⠀⠀⠈⠓⢔⠻⣶⣶⣿⣂⣘⣿⠦⢀ ⠀⠉⠛⢧⡈⢆⢻⡄⡇⠈⢿⡈⣿⣿⣧⠀⠨⢭⣬⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠟⠻⣿⠹⠿⠊⠉ ⠀⠀⠀⠀⠈⠛⢧⣻⣷⡀⠘⣷⡘⡟⠿⣦⣀⠀⠈⠉⠛⠢⠤⢤⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⣘⣷⡘⢄⠀⠙⠻⢶⡤⣤⣤⡄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢀⣠⠴⣶⣶⣖⣒⣒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣖⣤⠄⣀⣀⣀⡈⠭⢖⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢫⡟⠁⠀⣠⠴⣛⣴⣾⣿⣿⣿⣾⣶ ⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡤⠤⣤⣄⣀⣈⡙⠿⣦⣄⠀⠀⣀⠴⠊⠁⠀⠿⣤⣠⠞⣡⠾⠟⠛⡿⢛⣥⠍⢙⡛ ⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡈⠙⠢⣽⠿⠿⠿⢟⡋⠀⠀⠀⠀⠀⠀⠈⠙⢯⡀⣀⠴⣋⡴⠛⠁⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⢸⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠶⠮⣷⡄⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀ ⠀⣷⣄⠀⠀⠀⠈⡇⠈⣆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢷⡤⣄⣈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣎⠑⢄⠀⠀⢇⠀⠸⡀⠀⠀⠀⠀⡰⡇⠀⣀⣤⠆⠀⠀⠀⠀⠙⢶⣮⣍⡑⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⠋⣨⢷⠀⠑⣄⢸⡀⠀⡇⠀⡠⢀⣜⣠⠗⢈⡴⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠶⢮⣽⣒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠱⡢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠔⠒⠒⠀⠉⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀ ⠐⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣰⠀ ⢀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⠎⠀ ⠀⠙⢦⠀⢀⠀⠀⠠⠤⠤⠤⠄⠀⠀⢰⡤⠤⠾⠥⠼⣄⠀⠀⠀⠀⠀⠱⠀⠀ ⠀⠀⣠⠕⡊⠀⡏⢲⣶⣶⡶⢂⠉⠉⠤⣤⣤⣤⠤⠤⢌⠓⢤⠄⢠⣀⠀⠃⠀ ⠀⠀⠘⠆⡇⠀⡇⡌⠛⠛⢀⠜⠀⠀⠣⡙⠛⠛⠀⡠⠊⠀⢠⠀⢸⠒⠊⡹⠃ ⠀⠀⠀⠀⢀⠀⣇⠈⠑⠪⠋⢄⡀⠀⠀⠹⡐⠒⠉⠀⠀⠀⠘⡄⢸⠒⠏⠀⠀ ⠀⠀⠀⠀⠘⡀⣿⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⢸⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⢋⡏⡷⠤⣀⡉⠀⠀⠀⠀⢀⣀⣠⠤⠒⠉⡐⠳⣸⡈⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡀⠠⠐⠐⡈⢉⠝⢫⠉⠁⠀⠈⣧⢄⠀⠁⠀⠁⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠋⠀⣰⢉⠀⠀⠀⢠⢱⠢⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣐⣳⣒⣂⣺⣖⣒⣤⢫⢆⠀⡠⡡⠃⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠈⠉⠉⠉⠉⠉⠁⡸⣶⣇⡓⠚⡔⡖⡃⠀⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⣿⠤⢄⠉⠀⠈⢢⠁⠀⠀⠀⢰⠀⠀⠀⠀

⠁⡰⠊⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⡿⠚⠁⠀⢀⣧⣼⣿⣴⣶⡶⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠙⠛⠛⠛⠛⠛⣋⣽⠿⠋⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠖⠋⠁⠀⠀⠀⢴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⢀⣀⣤⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠒⢀⣀⡤⠶⠷⠤⠤⢤⣴⣾⣋⡤⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠀⠐⢦⣤⣄⣉⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⠀⣀⣤⠤⠶⠛⠛⠉⠁⣠⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⣄⠀⠀⠀⠀⢹⣯⡉⠉⠉⠑⠒⠿⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⣄⠈⢯⠉⠀⠀⠀⠀⠀⣀⣴⢞⣟⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⠀⠹⣿⣶⣶⣥⣄⣶⣤⣀⡀⠙⢷⢦⡀⠀⠳⣄⠘⢇⠈⢣⠀⣀⣠⣶⠾⣫⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣻⣿⣿⠉⠉⠛⠛⠻⢷⣦⣹⣾⢦⡀⠘⣆⠈⣷⣌⢿⣞⡯⠔⢛⣭⠞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡆⠀⣷⠄⠀⠀⠀⠈⢧⠳⡽⡆⠀⠀⢀⡴⢚⡿⠛⢾⣿⣵⡀⠹⡆⠘⡞⣾⣧⣤⣶⠯⠗⠚⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⢸⡀⢰⡀⠀⠀⠘⡆⢹⣿⡀⢠⠏⣠⢻⣦⣤⣬⡿⣯⠻⡄⢳⠀⢹⢿⣏⠉⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⢸⠇⠀⢷⡀⠀⠀⠹⡀⠻⣷⣏⡼⠃⡞⢀⣿⣿⡀⠈⠀⠹⣼⡄⢈⣿⢼⠀⠀⠀⠀⠀⠀⣰⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⣼⠃⠀⡀⢸⠀⡄⠘⣷⡀⠀⠀⢧⢀⣿⣟⠀⠸⠀⣼⣿⣷⣿⣆⠀⠀⢹⡇⢸⢻⡜⠆⠀⠀⠀⠀⣸⠃⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆⠀⠀⠀ ⣼⠃⠀⠀⡇⢘⡴⠁⠀⢹⣷⡀⠀⢘⣿⠻⣿⡀⠀⢸⣿⠻⣇⣻⢿⣿⢦⣨⣿⡸⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠘⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⡟⠀⠀⠀⡇⢸⡇⠀⠀⢸⣿⣷⡀⡾⠹⠀⣷⢧⠀⢸⡟⠀⠈⠁⢼⣭⣭⣽⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⡀⠀⠀⠀⠀⠀⢿⣆⠀ ⠇⠀⠀⠀⡇⣾⣇⠀⠀⢸⢱⣷⢿⡅⠀⢣⣿⣞⣇⣼⣷⣶⠶⠖⠒⠋⠉⠀⡞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣅⠀⠀⠀⠀⠈⠏⢦ ⠀⠀⠀⢸⠃⣿⣿⠀⠀⢸⠘⣿⡀⢻⡄⠈⢿⡘⢿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠸⡌ ⠀⠀⠀⣿⢴⠛⣿⡇⠀⢸⠀⢻⡇⠀⣿⡀⠈⡇⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⠏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣳ ⡀⠀⢠⢻⢸⡀⢹⣷⠀⠸⡄⢸⣿⠀⣿⢻⡎⢷⣤⣀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣰⣧⠖⠋⠈⠙⢦⣄⠀⣠⣄⡀⢀⣠⣤⠀⢠⣤⡀⠀⠉ ⠻⢤⣜⢸⡇⠻⡄⢹⣇⠀⡇⠀⢿⢢⠘⣷⡽⣞⡗⠻⢵⣶⣭⣷⣄⣀⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠳⣍⣛⣿⢟⣾⣯⣤⣬⣿⡞⣊⣥ ⠀⠀⠉⠻⢷⣄⠳⡄⢻⣆⢱⠀⠈⢿⣆⢹⡿⣾⣿⡄⠠⠤⢤⣤⣴⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢳⠟⠓⣽⣧⢸⣿⠊⠉⠢ ⠀⠀⠀⠀⠀⠉⠳⢿⣦⢻⣾⣇⠀⠸⣿⡄⢻⡾⣿⣷⡀⠀⠀⠉⠉⠻⠿⢭⣉⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠽⣿⣆⠀⠙⣿⡄⢳⡀⠉⠻⣷⢤⣀⣀⠀⠀⠀⠀⢀⣉⡭⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢜⣿⣄⣓⠤⠀⠈⠐⠒⠻⠟⠳⠶⣾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠃⠀⠀⠀⠀⣠⠴⠋⣹⣿⣷⡶⠦⣶⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣽⡖⣦⣤⣤⣄⣀⣀⡀⠀⠭⣽⡒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢡⡿⠁⠀⠀⣠⡴⠟⣑⣶⣾⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⣄⣀⣀⣉⣉⡀⠀⠈⠙⠾⣿⣦⡀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⣿⡇⡀⣠⠾⢋⣰⣾⡿⠿⢿⡿⠟⣉⣉⠙⠻⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣈⠉⠛⠿⣯⣟⠲⠶⠤⣹⣿⠳⣤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠙⠿⣧⡶⠛⠁⠀⢀⡴⢋⣠⣾⠟⠉⠁⠚⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⢄⣀⡈⠻⢟⠛⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡤⠞⣋⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⢸⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡛⠛⠛⠦⣿⡖⠒⠒⠒⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠒⠒⠚⠛⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢦⡀⠀⠀⠀⠀⠈⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠛⢏⠛⢆⡀⠀⠀⠀⢻⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣮⣍⡓⠲⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡨⢧⡀⠙⢦⠀⠀⢸⡀⠀⠈⡇⠀⠀⠀⠀⠀⣰⠇⡇⢀⡤⢖⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⣉⡛⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠩⠛⢀⡼⠫⡀⠀⠱⣄⠀⣇⠀⠀⡇⠀⢠⡔⣀⡼⣁⡼⠛⢁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠿⢶⣬⣛⡛⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣰⣯⠞⠉⠀⠀⢸⣟⠀⢠⡟⠉⠉⠉⠉⢻⡄⠀⠀⠀⢻⢹⡍⢦⣀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠉⠲⣄⠀ ⠀⠀⠀⣠⣾⡿⡁⠀⠀⠀⠀⣿⣿⠀⢸⣃⣀⣀⠀⠀⠀⢷⡀⠀⢸⡈⣇⢻⡌⠻⣷⣤⣀⠀⠈⠳⡄⠀⠀⠀⠀⠰⡄⠀⢈⢯⡓⠦⣌⠀ ⠀⠀⠈⢡⠞⡴⠁⠀⠀⠀⠀⡿⢸⠀⢸⡭⠗⠘⢷⣄⠀⠈⣧⠀⠘⣧⢹⣄⠹⣄⠀⢻⡛⠷⠶⠤⠹⣆⠀⠀⠀⠀⠙⡄⠈⣧⣝⣄⠈⠑ ⠀⠀⢠⢏⣾⡇⠀⠀⠀⠀⠀⡇⢸⡄⠈⠀⠀⠀⠀⠙⢦⡀⠘⣇⠀⡏⢧⣿⢦⡈⠀⠀⠹⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⠘⣆⠘⣎⠙⢷⡄ ⠀⢀⣯⡞⢸⡇⠀⠀⠀⠀⠀⡇⠘⣷⣴⣼⣿⠷⣶⣦⡀⠉⠀⠘⣆⢻⠘⣿⣇⣹⣦⡀⠀⠹⣧⡀⠀⠀⠈⢷⣄⠀⠀⠀⠈⢷⡜⣆⠀⠙ ⠀⣼⣿⡏⢹⡇⠀⢸⢧⠀⠀⠀⠀⢿⣿⡟⠁⠀⠈⢻⣿⠄⠀⠀⠘⢿⣇⠈⢿⣧⠈⠳⣄⠀⢹⣿⣦⡀⠀⠀⢻⣗⢄⠀⠀⠀⠻⣿⣆⠀ ⠀⡿⠀⢳⡀⢻⡀⢸⣞⣆⠀⠀⠀⠘⣿⠧⠀⢀⡞⠻⡿⡷⠀⠀⠀⠀⠹⣄⠀⠙⢧⣠⡿⢛⣦⣿⡛⢿⣦⡀⠀⠙⢿⢷⣦⡀⠀⠈⠻⣦ ⠠⠃⠀⠀⠙⢦⣳⢸⡟⣿⣧⡀⠀⡄⢹⡆⠀⢸⢠⣶⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢁⡎⠀⢹⡷⢄⣙⣷⣦⣄⡈⠓⢿⡛⠒⣦⣤⠈ ⠀⠀⠀⠀⠀⠀⠙⣾⣇⡿⣿⡙⣦⣌⣾⣧⠀⣾⣜⣫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢸⣱⡿⢺⠇⠀⣹⢿⡇⠈⡟⠛⠺⣿⡿⢭⣳⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⣡⠈⠳⣸⡏⠙⠻⣷⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛⠀⠀⠁⣸⠁⣼⠃⠀⣄⢿⠒⢈⡥⠚ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⡏⠀⠀⢈⡇⠀⠀⠈⢻⡆⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⠏⠀⠀⣟⣾⡖⠋⠀⠀ ⠀⠀⠀⠀⠀⠠⠟⠁⢸⡇⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⡿⠀⠀⣰⡏⠙⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡇⠀⣿⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣿⡇⠀⢀⣧⡇⡀⠨⣷⣂⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢻⡀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⣿⠀⠀⣾⣿⠁⢹⣦⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠸⣇⠘⢷⡙⢷⣄⠀⠀⠐⣶⡒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇⢠⢿⡏⠀⣼⢡⣏⠀⠈⡇⠙⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣦⢹⡇⠈⠳⡀⠙⢷⣄⠀⠀⠉⠉⠙⠛⠁⠀⠀⠀⣠⡴⢛⡵⠋⣠⣿⠿⡇⣸⠃⠀⢿⠳⣄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⠴⠋⠁⣠⠎⠀⠞⠋⡹⢠⣧⣿⣇⠀⠸⡀⠹⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠟⠁⠀⢀⠞⠁⠀⠀⠀⠀⢳⡞⢹⣿⢿⣷⣄⣳⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⣹⣿⠁⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢸⠃⠈⣿⠀⠉⠋⠙⠳⡄⢀⣠⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣯⣥⣤⣈⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⣛⠛⠉⠉⠉⠉⠛⠛⠶⠯⣽⣖⣶⢤⣀⡀⠀⠀⠀⢸⡀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⡩⠃⠀⣺⡊⣉⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣽⣷⡀⠀⠸⣇⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠶⠊⢠⣤⣴⣾⠿⠿⠿⢿⣿⣿⣿⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠂⢀⣴⣿⡿⢷⡶⠶⢶⠶⣯⣨⣇⠈⠙⢿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⠒⣦⣿⣿⠋⠋⠀⠈⠀⠀⠀⠀⠀⠀⠛⣹⠶⣶⢻⣷⣛⠋⡀⠀⠀⠀⠀⣀⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡾⠾⢯⣭⣏⡛⠓⠲⢦⣿⡿⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣤⡤⠴⠞⠋⢁⣀⡤⠴⠶⠶⠂⠀⠀⠉⠻⠶⠤⠈⠻⣄⣌⢻⣐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⡴⠒⠋⢀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠉⢳⣄⢀⠈⠿⣾⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠿⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⠹⣿⣿⣧⠘⣿⠋⠙⠿⢿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠸⣶⣄⠀⠀⠀⠀⠀⢀⣴⠟⢋⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡷⣽⣿⡌⣷⣟⡀⠀⣨⣽⣯⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⣿⡇⠀⠀⠈⠛⣻⣿⣧⠟⠁⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠉⠀⠀⠀⠀⠀⠚⠽⠟⠋⠉⠈⠉⢳⣄⠈⠙⠶⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⢱⣼⣿⣇⣠⠤⢴⣾⡿⠟⠁⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡁⠤⣙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣷⢤⣄⢸⡿⠋⠁⠈⠛⣿⣵⣶⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⡄⠀⠀⠀⠈⢮⢿⣦⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠁⢀⣿⡟⠀⢀⣀⣠⣼⣻⣽⡁⠀⠀⠀⣠⡴⢋⣤⠞⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢯⠀⠀⠀⠀⠀⠢⣦⡄⠀⠳⡄⠀⠹⣎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⠁⣰⣾⣽⣯⣤⣤⣈⠿⠿⠿⣿⠃⢀⣤⣾⠿⢚⣿⠋⣠⡟⠀⠀⠀⠀⠀⠀⠀⣠⡞⡇⠘⠀⠀⠀⠀⠀⠀⠘⣟⣆⠀⠙⡄⠄⣿⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠹⣿⣿⣿⣿⣧⡀⠈⢻⡿⣇⣴⠏⣠⠿⠁⠀⢠⣿⣧⠞⡿⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣿⡇⠀⠀⠘⡆⠀⠀⠀⢸⣟⡜⢆⠙⣸⡿⣹⠷⢿⣧⣀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⢹⡿⠛⠿⣍⠛⠂⠀⣷⣾⡿⣿⡯⢀⣠⣶⣿⣿⡏⢰⠇⠀⠀⠀⢀⣠⣾⣋⠀⠀⠀⣿⢿⡀⠰⣄⣿⠀⠀⠀⠠⣿⣦⣌⡀⣿⣷⡇⠀⠀⠈⠛⢧⡀⠀⠀⠀ ⠀⠈⢻⣸⡄⡇⣀⣠⠼⠷⡄⠀⣿⠐⠶⠿⣿⣿⣿⣿⣧⣌⠁⣿⢀⡞⠀⢰⣿⡟⠛⠛⢛⡿⠿⣶⣤⣷⡄⢿⢿⣄⠀⠀⢦⣽⡀⠀⣷⡿⠋⠀⠀⠠⢄⣤⣤⣽⣦⠀⠀ ⠀⣠⣴⣿⣷⡟⠋⣦⡀⠀⢻⣴⠃⠀⠀⠀⠛⢿⣿⡅⣿⣿⣷⣿⣾⠁⣰⠟⣾⣿⣿⣶⣦⣕⠀⠈⠙⣿⡟⠾⣿⣿⣳⣦⣿⡿⠽⠿⠟⠷⣥⠀⠀⠐⢶⣿⣧⣴⡝⠀⠀ ⢸⢟⣩⣿⡿⠀⠀⣇⢳⡀⠛⠁⠀⠀⠀⠀⠀⡾⢻⣧⠙⠻⢿⠛⣻⡷⠃⠀⠀⢸⣿⣯⡄⢹⡷⠆⠀⢹⡇⠀⣾⣿⣿⣿⡟⠋⠉⠀⣀⡴⠟⠀⠀⠀⢠⣿⠟⠉⠀⠀⠀ ⢀⣿⡿⠟⠁⠀⠀⠙⠮⠷⠀⠀⠀⠀⠀⠀⣼⠇⠘⡇⠀⠀⠃⠐⠋⠀⠀⠀⠠⣌⠻⠿⠦⠈⠀⠀⠀⢸⡇⠀⢹⣿⣾⣋⣒⣭⣶⠚⠿⣄⣴⣤⣄⣴⡾⠟⠀⠀⠀⠀⠀ ⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣿⡿⣅⣀⡙⢳⣤⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⣿⣿⢀⣶⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢿⡄⠀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠋⣇⢠⠀⣽⣽⣷⣽⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⢸⠙⠮⢷⡀⠀⠀⠀⠀⣀⣤⠴⠖⠋⢉⡴⠃⢠⣿⡟⢠⡿⣹⡿⡾⢷⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣧⢸⣻⡿⣿⣯⣛⣶⣿⠉⠅⠀⠀⣀⡰⠋⠀⠀⡾⠋⣟⣼⠹⡟⣟⠗⣶⠈⠙⠉⠻⠿⢷⣶⣦⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠈⣿⣿⣿⣷⣽⣿⣿⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⡿⡷⠀⠀⣿⠈⢻⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠉⠀⠀⠀⢀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢡⡞⠁⢠⠀⠀⠈⣿⣿⡏⢸⣿⣿⣦⣤⣤⣅⢠⠀⠀⠀⠀⣠⡾⠁⠀⣀⠀⠀⠀⢸⡇⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿ ⠀⠀⠀⠀⠀⠀⣠⣶⠞⠉⠀⠀⠘⠁⠀⢸⡀⠀⠀⠻⣿⡀⠀⣿⣿⠓⠦⣄⣉⠙⠲⠀⠀⡰⠿⠛⠉⠉⠁⠀⠀⠀⣸⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋ ⠀⠀⠀⠀⠀⠀⠻⣿⠛⠦⠀⠀⠀⠀⠀⠸⠇⡆⠀⠀⢿⡇⠀⣿⣿⡄⡈⠙⠺⠍⠓⣒⣒⡒⠒⠒⠲⠶⠦⠤⠴⢶⡏⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢸⣷⠀⢹⡟⣿⡿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠛⠂⠒⣒⣠⡾⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡤⠀⠀⠸⣧⠀⠉⢷⡀⠀⣤⠖⠚⠒⠒⠚⠉⠉⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⣸⡏⠀⠀⠀⠀⠸⣇⣤⣿⡄⠹⣷⣀⡈⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣇⡀⠀⠀⠀⠀⣿⡍⢘⣷⣽⡟⠙⣿⠀⣠⠖⠴⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⣸⣿⣼⠋⢸⣧⣰⣾⠀⠀⠀⢀⠀⠒⠲⡹⣆⢀⣀⠤⠤⠒⣋⡭⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠆⠼⣿⣿⣿⡄⠠⡄⢀⣬⢽⣦⣻⢈⠷⠖⠒⠛⠉⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠶⠶⠶⠦⢤⣤⣀⡀⠀⠀⣼⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡟⠣⡀⠀⣧⣀⣤⠴⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⡤⠤⠒⠊⠉⠀⠀⠀⢀⣀⠤⠔⠒⠒⠛⠛⠛⠓⠒⠦⠄⠀⠀⠀⠀⠈⠙⠒⠤⠤⠿⠯⠽⠶⣤⣀⣴⠚⠋⠀⠀⠀⠀⠀ ⠀⠀⣿⡉⠁⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠑⠒⠒⠒⠒⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀ ⠀⠀⠹⡆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⠙⠶⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀ ⣶⡤⠶⠒⠋⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠸⣧⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠙⢯⡑⠢⠤⣀⣀⠀⠀⣿⠋⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁⢀⡾⠃⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠙⢶⣄⡀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠈⠀⢀⣀⣤⣴⣶⠟⠁⠀⠀⠀⣀⣤⣶⡿⠟⢋⡉⣙⣧⡀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢸⢻⡗⠶⠶⠤⠤⠤⠤⠶⠶⠚⠛⠋⠉⣀⣾⣃⣀⣤⡤⢶⠟⠋⠉⠀⣠⠔⠋⠀⠘⣿⣷⡄⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⡾⣼⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣦⣀⠉⠉⠉⠁⠀⢀⡞⣀⡠⠖⠋⠀⠀⠀⠀⠀⠈⠻⢿⣶⣞⡁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢠⣷⡟⠀⢸⠛⢻⡏⠉⠉⠉⠉⠉⠛⠻⣿⣷⡄⠀⠀⠀⠞⠉⢁⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⣄⠀⠉⠛⠷⣶⣄⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣸⢸⡇⠀⠐⡄⢿⣿⣿⣶⣶⣦⣤⣤⣤⣿⠉⡏⠀⠀⠀⠀⠀⠺⠛⡿⠋⠙⠛⠛⠛⠿⠿⣿⣿⣿⣆⠀⠀⠀⣿⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⡟⢸⡇⠀⠀⠙⠼⣿⣿⣿⣿⣿⣿⣿⣿⠏⡼⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣄⣀⣀⣀⣀⠀⠈⣿⢻⡆⠀⠀⣿⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⡇⠈⣇⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠟⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠜⠀⠀⠀⣿⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⢷⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠸⡆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠹⣄⣠⡾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⣫⣿⡇⠀⠀⢀⣰⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣞⣿⠶⢛⡽⠉⣇⠀⢀⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠻⡟⠓⠶⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⡿⢿⡿⠟⠿⠤⠴⠋⠀⠀⠸⡴⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠉⠙⠫⠭⣍⡉⠀⣨⠿⠿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠋⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⢾⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠲⠶⠦⠤⠤⣤⣤⣉⣿⣖⣋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣶⣶⣾⣥⣄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣤⣴⠶⣶⣿⠟⣻⡭⠟⠲⣦⣀⣀⣠⡞⠓⠮⢭⣝⡻⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠉⣠⠾⣫⠴⠛⠉⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠈⠙⠳⣭⡻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢀⣼⣯⠞⠁⠀⠀⠀⠀⠀⠀⢘⣹⣿⠏⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢀⣀⠀⠀⠀⠀⢀⡴⣾⡟⢠⡿⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⣻⣾⣿⣾⣽⣦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠈⠉⠒⠂⢤⠋⢠⣿⣱⠟⠀⠀⠀⠢⠄⡀⠀⣠⢞⡽⠉⠈⠁⠋⠘⠁⠀⠑⢏⠲⢄⡀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿ ⣀⡠⠄⠀⠀⠀⢇⣾⡿⠁⠀⢰⠀⠀⠀⠀⣠⠞⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⢦⣀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣿ ⢡⠀⠀⠀⠠⠔⢻⣿⡀⡀⢠⣿⣄⠀⣠⣾⢷⣶⣾⣤⣤⣤⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠾⣷⡄⢠⡷⠢⣼⣿⠛⠉⠑⠠⣀⠤⠊⣿ ⠀⠢⠐⠁⠀⠀⣾⠋⣿⣆⠈⠸⣏⠀⣻⢡⣴⢾⣿⣿⣿⣿⢆⠀⠀⠀⠀⢠⣿⣿⣿⠿⡷⣦⡄⡇⠀⣽⠃⣴⣿⠁⠀⠀⠀⢠⠀⠀⠠⣿ ⠀⠀⠀⠀⠀⢠⡿⠀⣿⣿⣷⣄⢹⡄⣯⡿⠁⠘⣿⣿⣾⡟⢏⣆⠀⠀⠀⠸⢹⣿⣿⣿⠁⠈⢿⡇⡼⣣⠞⣿⣿⣄⡀⠀⠀⠀⢀⠀⠀⣿ ⠀⠄⠂⢉⣠⣼⡧⠶⠛⠉⢹⠈⠻⢿⣿⣇⠀⠀⢻⣿⡿⠃⠈⣿⡆⠀⠀⠀⠀⠻⣿⠏⠀⠀⣸⠟⣿⣁⢀⣇⣈⡉⠛⠻⠶⣦⣤⣀⠁⣿ ⠀⣴⣾⠛⠉⡡⠤⠔⠒⠊⢹⡆⢀⠘⢧⠘⠳⠀⠀⠀⠀⠀⠀⠹⣷⡶⠀⠀⠀⠀⠀⠀⠀⠚⠁⣼⠟⣡⢿⠁⠈⠉⠉⠒⠢⢀⣉⣽⠇⣿ ⠀⠈⠉⠻⠷⣶⣄⣀⠀⠀⠀⣧⠈⣧⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⡼⠁⡾⠀⠀⣀⣠⣶⡾⢿⡋⠀⠀⣿ ⢀⠎⠐⠒⠒⠢⢿⣎⠙⣷⣶⣼⣆⠈⢻⠺⣄⠀⠀⠀⢲⣶⣶⣭⣭⣭⣽⣶⣶⡆⠀⠀⠀⢼⡟⣹⢁⣴⣷⣾⣿⣿⡉⠀⠀⠀⠈⠑⠢⣿ ⠂⠀⠀⠀⡀⠀⠀⢿⡄⠘⣿⣿⣿⣿⣾⡇⠘⢦⠀⠀⠈⢻⡟⠛⠛⠛⠛⢻⡟⠀⠀⠀⢠⠞⠀⣿⣿⡿⣛⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿ ⠢⡀⠀⠀⠀⠱⠀⠘⣿⠀⢸⣿⣿⣿⡇⢙⣦⡀⠱⣄⠀⠀⠛⠶⣤⣤⡶⠟⠀⠀⢀⠴⠋⣠⢾⣹⡟⢧⣸⡏⠀⣀⣀⣀⣀⣀⠤⠤⠤⣿ ⠀⠀⠀⢠⣴⣶⢶⣾⣿⡇⠈⢻⣿⣿⣿⣿⣦⠙⢲⣬⣙⠦⣄⣀⠀⠀⠀⣀⠤⣚⣡⢴⡏⢡⣾⣻⡏⣳⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⡇⣼⣾⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣷⣾⣿⡍⠉⠀⠉⠉⠘⠉⠁⠉⢹⣷⣿⣿⣯⣤⣙⢲⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣀⠤⠤⢼⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⣟⢸⣿⣿⣿⣿⣿⣤⡼⠟⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⣿⣸⣿⡿⠟⠛⠉⠁⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⣿ ⠀⢀⣠⣼⠿⣯⡁⠀⠀⠀⢀⣤⣶⣿⣿⣿⠏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⠉⣿⡀⠀⠀⠀⣿ ⡶⠛⠉⠀⠀⠀⠙⣦⣴⣿⣿⣿⣿⣿⣿⣿⣾⡿⠙⠛⠛⠻⠿⠿⠿⠿⣿⠟⣵⣦⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⠋⠙⠷⣦⣀⣿ ⡄⠀⠀⢤⠴⠚⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣾⡛⢾⣿⣅⣰⣯⢙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠙⣿ ⢧⠀⠀⠈⠑⢄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⠻⣿⡿⢁⣾⡿⠁⠸⣿⣿⣿⣿⣿⣿⣥⠃⠀⠀⠀⠀⠀⣿ ⠈⢣⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣌⣰⣿⠟⠀⠀⠀⢿⣿⣿⡿⣫⡟⠁⠀⠀⠀⠀⠀⢠⣿ ⣧⡈⢧⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣼⠏⠀⠀⠀⠀⠀⠀⣠⠟⣿ ⡟⢷⡀⠳⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⢀⣼⠋⢰⣿ ⣿⡌⢷⡄⠘⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⠀⡠⠊⣠⡿⠁⢠⣿⠃ ⠹⣿⣄⢻⣆⠘⢆⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣉⣉⣛⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠜⠁⣴⠏⠀⢠⣿⠏⠀ ⠀⠘⢿⣦⡹⣧⠈⢆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠛⠛⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡾⠃⢀⣴⣿⠃⠀⠀ ⠀⠀⠈⠻⣿⣾⡇⠈⢧⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣶⣶⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⡇⣠⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣄⠀⠑⠠⠖⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣈⣉⣉⣉⣉⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣾⣿⡛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠻⠃⠀⠀⠀⠃⢀⣭⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣄⣉⠁⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠁⠀⠀⠀⠀⡀⠉⠐⠢⠌⢢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⢉⠐⠤⡀⠀⠀⠀ ⡀⠏⢀⠔⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢋⣂⠀⠀ ⠰⡀⠀⠀⠀⠀⠀⡔⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⢛⡆⠀ ⠀⠡⡀⠀⠀⠀⠺⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠈⢆⠀⠀⠈⡇⠀ ⠀⠀⣐⢆⠀⠀⡰⠁⠴⠿⠶⢦⡄⠀⡄⠀⣀⠠⢔⣾⠿⠶⠦⠀⢢⢰⠀⣸⡀ ⠀⠀⠱⡈⠁⢸⠀⠀⣠⢴⣶⣶⣌⠓⠉⠁⠀⠔⣩⣴⣶⡦⣄⠀⠀⠘⠈⠡⠁ ⠀⠀⠀⢱⠆⢸⠀⠸⡁⢸⣿⣿⠇⠱⡀⠀⠀⡔⠁⣿⣿⡷⠈⠇⢰⠀⣆⠃⠀ ⠀⠀⠀⡌⠀⡌⡆⠀⠈⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⡌⢀⡏⠀⠀ ⠀⠀⠀⡀⡔⢀⠋⢄⠀⠀⠀⠀⢤⣤⣀⣑⣁⣠⣤⠆⠀⠀⢀⡜⢀⡼⠀⠀⠀ ⠀⠀⠀⠉⠀⠐⠒⠒⠓⡤⣀⠀⠈⠛⠿⠿⠿⠟⠁⠀⣀⡔⠊⠒⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣒⢒⣊⠏⠀⠐⠒⠒⠂⣞⡋⠐⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⡊⠁⠀⠈⣶⡀⠀⠀⣀⣴⠞⠋⠀⠉⠙⠲⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⢞⠁⠀⠀⠀⡞⡗⡎⣿⣤⠾⠋⡔⡖⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀ ⠀⠀⠚⠁⠀⠀⠀⠀⠓⠃⠱⠙⠋⠓⠊⠛⠁⠃⠃⠀⠘⠂⠀⠐⠒⠛⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠚⠛⠛⠒⠚⠃⠻⠶⠶⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⡴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠋⠀⠀⠀⢀⠞⠀⢳⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠐⠁⠀⠀⠀⠀⠋⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⡄⠀⠀⠀⠀⠀⣠⠞⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀ ⠀⠀⠀⢀⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇⠀⠠⢂⣠⠞⠁⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀ ⠀⠀⠀⡾⢀⡀⠀⢰⠋⠁⠀⠀⣀⣀⣀⣤⣴⣶⠾⠟⢋⣿⢀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣧⠀ ⠀⢴⣾⡟⢛⣇⣠⣯⣀⣤⣴⣿⠟⠛⠋⠉⠁⠀⠀⠀⠚⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢀⠀⠀⠀⠀⠀⡜⠀⠀⣿⣿⣿⠀ ⠀⠸⡏⠉⠉⣿⣿⢁⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠈⢿⡆⠀⠀⠀⡼⠁⠀⣠⣿⣿⣿⠆ ⠀⠀⢳⠀⣠⡿⠁⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⣧⠀⠀⢠⣁⣠⡬⠵⠿⠿⠿⡦ ⠀⠀⢈⣿⠟⡵⠀⠀⠈⠙⠛⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠃⠀⠀⣿⠀⠀⡾⠉⠀⠀⠀⠀⢐⡼⠁ ⠀⣴⡿⠋⡜⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢰⡇⠀⠀⠀⠀⣠⡾⠁⠀ ⠸⣿⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣤⣾⣦⡀⠀⠀⠀⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⠁⠀⠀⢀⣴⣿⠁⠀⠀ ⠀⢻⣧⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⢫⡟⠀⠀⡟⠀⢀⣴⣿⣿⡟⠀⠀⠀ ⠀⠀⠙⢿⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡿⠀⢠⠀⢿⣾⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣸⠁⠀⠇⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣍⠛⢻⡷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠿⢿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⡼⠁⠀⠀⠀⠉⢉⣩⡏⠀⠀⠀⠀⠒⣖⠒⠛⠛⠛⠋⠉⠀⠀⠀⠘⡇⢀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⣶⡟⠉⠛⠒⠶⠶⠦⠶⢿⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠷⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⡀⠀⠀⢀⣠⣤⣶⠿⣛⣁⠍⣻⣦⣀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢷⡿⠁⠐⣿⣷⣶⣾⣿⠿⠀⠁⠀⠁⠀⣼⠟⣡⡿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣼⠇⠀⠀⠘⣷⡾⠋⠁⠀⠀⠀⠀⢀⠰⣿⡟⠉⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣰⡏⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣇⣀⣀⣀⣀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠉⠉⠉⠉⠉⠉⢉⣭⠿⢙⡋⠩⠭⠭⠭⠭⠉⣙⠋⠭⣉⠉⠉⠛⢭⡉⠉⠉⢹ ⡇⠀⠀⠀⠀⠀⣴⠫⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡑⠢⡀⠀⠈⠳⡀⢸ ⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠘⢄⠀⠀⠙⣾ ⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢢⠀⠀⣿ ⣇⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠹⣆⠆⠀⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⢹⢸⠀⣿ ⡗⠦⣄⣀⠀⢀⢠⣴⣶⡄⠀⠀⠀⣀⡴⠊⣀⣴⡾⠿⠷⣜⢆⠀⠀⠀⢘⢸⡀⣿ ⡇⠀⠀⠀⣼⣁⠀⣀⠤⣽⠦⡐⢋⡋⠤⠞⢋⠥⣶⢤⡀⠀⠠⠑⢄⠀⡸⢸⣰⣼ ⡇⠀⠀⠀⠀⡸⡰⠁⢰⣏⣷⠀⠀⠀⠀⢠⠃⠀⣿⣀⣸⢂⠀⠀⠸⠀⠯⡒⠀⣿ ⡇⠀⠀⠀⡴⠁⡇⠢⢀⣿⠟⠁⠀⠀⠀⠙⠄⣀⠹⣿⠏⠘⢠⠠⠁⠘⡔⣡⠺⣿ ⡇⠀⠀⡜⠀⠀⢡⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠁⠀⢀⠏⠁⡇⣿ ⡇⠀⢠⠁⠀⢀⡔⢦⡀⠀⠀⠀⢈⡁⠤⠤⠄⠀⠀⢀⠔⣱⠀⠀⣀⠎⠀⡸⢠⣿ ⡇⠀⠘⠒⠊⠁⠀⠀⠹⢶⣤⣀⣀⠀⠀⣀⣠⢤⡤⣒⣭⢤⡠⠔⠁⠀⢠⢣⠋⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣈⠭⠻⠔⠂⡠⠓⠒⠤⢀⡑⣄⠀⠀⣾⠃⠀⢹ ⣇⣀⣀⣀⣀⣀⣀⣀⣀⣄⣴⣇⣄⣀⣸⣭⣽⣤⣠⣤⣤⣤⣼⣱⣵⣲⣧⣄⣀⣼

⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤ ⠘⣿⣿⣿⣷⣦⣄⣀⠀⢠⠔⠀⢀⡼⠿⠿⢆⠀⠀⠲⣄⠀⣀⣠⣴⣾⣿⣿⣿⠇ ⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⠀⢀⣾⣷⡀⢀⣾⣷⡀⠀⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀ ⠀⠀⣤⣤⣶⣶⣶⣶⣶⣿⣆⠈⠉⠉⠉⠉⠉⠉⠉⢠⣿⣶⣶⣶⣶⣶⣤⣤⠀⠀ ⠀⠀⠘⣿⡿⠟⠛⠉⣡⣿⣿⣷⣤⠀⢠⣆⠀⣤⣶⣿⣿⣬⡉⠛⠻⠿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣿⣿⠛⢠⣿⣿⡄⠛⢿⣿⡘⢿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⠏⠀⣸⣿⡇⢀⠻⣿⣿⠟⣀⠸⣿⣇⠀⠙⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠁⣿⣿⠀⠻⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠉⠙⠓⠀⠘⠏⠀⠘⠟⠉⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣶⣦⣼⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⡟⣹⡟⣴⢻⣷⠘⠿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠐⢋⣴⣋⣯⣽⣷⣦⣤⠤⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣒⡻⠟⣿⣨⣿⠉⠉⠐⣲⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⡤⣢⢹⠉⣣⣠⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣦⣤⣤⣬⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⢿⣡⡆⡤⣭⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⣿⣷⣅⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠏⠙⠿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠃⠀⠀⠀⠈⠙⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣄⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠸⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡏ ⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢀⣴⡟⠀⠀⠀⠀⢠⣟⠛⠛⠛⠛⠛⠛⣣⡀⠀⠀⠀⠀⠹⣷⡀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣿⣿⡇⠀⠼⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠷⠀⢰⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢁⣹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⡿⠃⢀⣾⣿⣿⣿⡄⠀⠿⣿⣿⣿⣿⣯⠈⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⡏⠀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡆⠀⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠁⠀⠀⣾⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢿⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣸⣿⣿⣿⡇⠀⢠⣤⡀⠉⢻⣿⣿⣿⠋⠀⣠⣄⠀⠘⣿⣿⣿⣧⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⢠⣿⣿⠃⠀⢸⣿⣿⣿⠀⠈⢿⣿⣇⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⠂⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠿⠿⠿⣿⣿⡆⠀⠀⠈⢿⣿⠃⠀⠀⠰⣿⣿⠿⠿⠿⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⡠⠤⣷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠦⣈⠥⢂⠈⠉⠀⣀⠋⣌⡲⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢦⡀⠀⣠⡔⠍⠊⠀⠀⢀⡀⠀⠉⣾⣿⠾⡀⠿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⠈⡾⠧⣴⣞⠉⠀⢀⠔⠊⠀⠀⠀⠀⡆⠀⠀⠈⢱⣌⣽⠇⠀⠀⠀⠀ ⠀⣼⢁⣿⣁⢠⣾⡇⣀⡔⡵⣢⠀⠀⠀⢀⡜⠀⠀⠐⢦⠰⡈⡏⣀⡄⠀⠀⠀ ⢸⠈⡿⢿⠦⢹⣶⣕⣡⣼⡟⠇⠀⣀⣔⠁⡿⡀⣡⠀⢘⣎⣸⡿⠙⠢⡀⠀⠀ ⢀⣽⡖⣎⢑⠜⠉⠙⣿⣷⣾⣞⡘⢿⣬⣏⠛⡷⢿⣦⣴⡷⠿⡇⠀⣾⡼⠂⠀ ⢸⡟⠁⠑⠇⠀⠀⢰⠹⠀⠃⠋⠀⠘⠛⠈⠁⠀⠸⣿⡱⢔⠪⠤⠴⠟⠀⠀⠀ ⠘⢡⠀⠀⠀⠀⠀⣿⡄⣧⡀⠀⠀⠀⠀⠀⣀⢼⠀⣿⣺⠇⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⢀⣱⢨⣽⣤⣠⠄⠒⠨⠊⡼⣥⣿⢟⠲⠦⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢠⣿⣿⡿⠈⡄⠀⠀⢠⠑⠛⢀⢃⠀⠀⠀⠀⠉⠓⣦⠀ ⠀⠀⢀⣤⠒⠑⠁⡆⠈⢿⢸⡿⣔⣒⠀⠠⠃⠒⠀⢸⠘⠀⠀⠀⠀⠀⠀⡸⠁ ⠀⠀⠀⠑⢄⠀⠀⢱⠀⢸⠈⠿⡶⠅⠀⣀⣒⡈⠩⠃⡘⠀⠀⠀⠀⡠⠊⠀⠀ ⠀⠀⠀⠀⠀⠑⠤⡎⠀⠈⡧⢦⣷⢌⢚⢁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠼⠎⣱⣾⢀⢀⣄⡵⠔⠢⠘⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣠⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠋⠉⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⠀⠀⠀⠀⢿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢃⣠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢰⣿⡿⢋⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠻⢿⣿⣿⣿⣿⣶⣄⣿⣶⡌⢿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⢠⣶⣶⡤ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⣿⣿⣿⣿⠀⠀⠀⠀ ⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀ ⢸⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⣠⣖⡁⠤⠐⠒⠀⠐⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠹⢍⠩⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡶⠤⠤⠄⣁⠀⠀⠑⡄⠀⠀ ⠀⠀⠀⡰⣳⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⢄⠀⠘⡄⠀ ⠀⠀⣰⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠈⢣⠀⢰⠀ ⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⣜⠈⢂⠀⠀⠀⠀⠈⡇⠈⡀ ⠀⠀⠀⠀⠀⠸⠿⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⢠⠎⣀⣷⡶⠟⢛⠂⠀⠀⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⢁⠪⠁⡀⠈⠢⡀⠡⡀⠀⡖⠊⠁ ⢳⠒⢤⠤⡀⡀⠀⠀⣀⣀⣀⡔⢀⡠⣖⠡⠂⠁⠀⢀⣀⣀⡀⠈⠢⣈⠰⣇⠀⠀ ⠀⠑⣄⡏⣀⣀⣠⡟⠭⠉⠉⠉⠙⠀⠀⠀⠀⠀⠊⠉⠉⠉⠙⠳⠂⡜⠁⠩⠔⠁ ⠀⠀⠹⢄⠐⡌⢸⠀⠀⠀⢀⣀⢀⣀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠃⡀⠀⠀ ⠀⠀⠀⠀⡹⠁⠈⡧⡀⡀⠈⢿⡵⠒⠒⠒⠲⠶⣶⣿⠏⠀⢀⣴⣇⠈⢀⠇⠀⠀ ⠀⠀⠀⢰⠁⠀⡸⠁⢹⣶⣄⡀⠑⠤⢀⣀⠀⠤⠚⢁⣴⡖⡉⡞⢹⢀⠎⠀⠀⠀ ⠀⠀⠀⠈⣆⡜⠁⠀⣠⡇⠀⠉⢱⡂⠒⠒⠒⢲⡞⠉⠉⠙⣿⡀⠐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠁⡇⠀⠀⠀⠣⠂⠠⢤⠋⠀⠀⠀⠀⣠⢾⠆⠀⠀⠀⠀⠀

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⠀⠀⣠⡾⠊⠀⢠⣧⢀⠏⠉⠈⢱⠀⢠⢋⢏⢢⡀⠀⠳⡄⠀⠀⠀⠁⠢⡄⡑⠄ ⠀⠘⣕⡍⠀⠀⢸⢹⢸⠌⠙⢦⠀⢇⠈⣏⣎⢂⠙⡗⠒⠈⢆⠀⠀⠡⡀⠮⣎⠑ ⠀⣜⢾⠀⠀⠀⢸⢸⣼⣠⣤⣄⠑⠈⢆⠏⢾⣣⡀⠈⣆⠀⠈⢣⡀⠀⠐⢜⠌⠳ ⢰⠿⡉⡆⢸⠆⠀⠀⣿⡇⢀⣹⣗⠀⠈⠻⡈⢳⡈⣢⡘⡷⣄⠀⠹⣦⡀⠈⠻⣄ ⠘⠀⠑⢜⣼⢻⣆⡠⡸⡄⠘⣴⡏⠀⠀⠀⠁⠀⢹⢣⢋⢹⢌⣳⡤⣈⡹⣒⣠⠌ ⠀⠀⠀⠀⢹⢎⠳⣹⠺⢷⡙⠚⠁⠀⠀⠀⠀⠀⠈⠸⠿⠏⠀⢫⢀⠇⢈⡯⢕⡣ ⠀⠀⠀⢀⠞⡝⠀⠨⡀⠀⠙⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡚⠀⣸⢾⠁⠀ ⠀⠀⠀⠀⠀⢃⡀⣦⢳⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢉⣼⠃⢠⡝⡀⡷⠤ ⠀⠀⠀⠀⠀⠘⣧⢸⢸⡟⢦⡀⠀⣤⠤⢀⠀⠀⠀⠀⢀⣴⢡⡟⢀⢿⡃⢹⠳⠀ ⠀⠀⠀⠀⠀⠀⠙⠣⣿⠈⠂⠙⢦⠀⠈⠉⠁⢀⡠⢚⠕⡡⢿⢃⣎⠀⡟⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠉⢲⣶⠞⠁⡠⠋⠀⠀⢱⠋⡿⣦⣰⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣼⣃⣐⡊⠀⠀⠀⠀⠘⠀⡇⠀⠀⣩⠔⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡔⢚⡩⢉⠉⠉⠉⠐⠛⠣⢶⡤⣄⠀⢡⢠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠕⣩⡤⠾⠾⣿⡶⢯⣄⠀⠀⠀⠀⠈⠹⣦⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⢥⣴⡞⠟⠙⠉⠉⠁⠲⣤⢹⣧⡤⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀