Qiqi Text Art

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣀⣀⣈⠐⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⣁⣴⣶⣿⣿⣿⣿⣿⣿⣷⣮⣕⠤⡀⠀⠀⠀ ⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣕⢦⠀ ⢀⣾⣿⣿⣿⣿⣿⠟⠛⠋⠉⢹⠛⠛⠛⠿⣿⣿⡏⡟⢹⠀ ⣿⣿⣿⣿⠟⢻⠏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⣿⡥⠊⠀ ⠘⢽⡟⠁⣠⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⣦⠀⢠⡀⠡⠀⠀ ⢀⠎⠀⢠⠃⠀⠀⠀⣰⠁⠀⢠⠀⠀⡰⠋⢯⠀⣿⠀⢡⠀ ⢸⠀⢠⠇⠀⠀⠀⣀⠃⢰⣆⠸⡤⠞⠁⠀⣞⡶⠋⢀⢸⡀ ⡜⣀⡎⠀⠀⠀⢰⣿⣶⡤⠇⠉⠁⣶⣶⠶⡟⢠⠀⣪⠞⠀ ⠐⠼⣀⠀⠀⠐⡟⠩⠍⠀⠀⠀⠀⠑⠂⢰⠁⣡⠚⠁⠀⠀ ⠀⠀⠀⠁⠪⢟⠳⣄⠀⠀⠀⠀⠀⢀⣴⢏⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠠⣙⠟⣶⣶⣴⠚⠉⠉⢿⣿⣇⢆⠀⠀⠀ ⠀⠀⠀⠀⡤⣒⣨⡟⢿⡟⠁⠀⠀⠀⠀⢘⠟⠘⣿⢇⠀⠀

⠀⠀⠐⠀⠐⠂⠀⣼⠷⢧⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⡿⠚⠋⠁⢀⣴⣾⠗⣡⠶⠛⣠⡴⠞⣉⣔⣚⠲⢦⣄⡈⠓⢶⡜⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⣶⣶⣶⣶ ⠀⠀⠈⢲⠖⠀⠀⠀⢀⣀⡽⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⢀⣴⣾⠟⠋⣠⠞⠁⢀⡶⠻⣷⡼⢯⣬⡿⢋⣴⣮⡙⢶⡞⠁⣩⡏⠀⠀⠀⠀⣠⣴⣶⡿⠛⠉⠀⠙⢿⣿⣿⣿⣿ ⠀⠀⠀⣏⠀⠀⡆⠀⢨⡿⠀⠀⠀⠀⢠⣾⠿⠙⠉⠀⠀⣠⣾⠟⠉⠀⢠⡾⠃⠀⣠⠏⢀⣼⣏⢙⣶⣀⡀⠙⢷⣬⠇⠈⢁⣴⠏⠀⠀⣠⡶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿ ⠀⠀⠀⠙⠓⠚⠋⠛⠋⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣠⠾⠋⠁⠀⢀⡴⠋⠀⢠⡾⠧⠴⣿⣁⣽⠟⠧⣬⣽⡷⠶⠀⣀⣴⡟⠁⢀⡴⢟⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿ ⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢀⡾⠋⠀⠀⠀⣠⠟⠁⠀⣰⣏⣤⣀⣰⠏⠙⣳⢦⣴⡿⠃⠀⣠⣾⡿⠋⢀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡺⠿⠛⠙⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⠋⠀⢀⣾⢿⡟⠁⠉⠉⠠⣞⠉⠀⠈⠃⣀⣾⡿⠋⢀⣴⢟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⢠⡾⠁⠀⣠⣿⣇⡈⣙⣶⢀⣀⡀⢙⣷⠀⢀⣴⡿⠋⠀⣠⠿⡿⠋⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠁⢀⡾⣿⠀⠀⠀⠀⠀ ⢴⣶⡶⠶⠚⠋⠁⠀⠀⢀⣀⣤⣶⠛⠀⠀⠀⠀⠀⣰⠟⠀⢀⣴⡟⠁⠙⠻⣿⣿⣿⠏⠻⠟⠉⣰⣿⠟⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣾⡅⣿⠀⠀⠀⠀⠀ ⠈⠙⠛⠓⠒⠒⠒⠚⠛⠉⣱⡟⠁⠀⠀⠀⠀⢀⣼⠋⠀⣠⣿⣏⠀⠘⢻⣾⣿⣝⠛⠷⠆⢠⣾⡟⠁⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣴⡿⠟⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⡞⠁⣠⣾⠿⠉⠛⠷⢴⣿⠓⠉⠉⠀⠀⣴⣿⠏⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠻⢭⣟⣶⣴⡟⠉⠀⠀⢻⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⠲⢄⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣰⡟⢀⣴⠟⠉⠀⠀⠀⠀⠀⠈⠙⢷⣶⣤⣾⡿⠁⠀⡴⠋⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⢀⣤⠖⠋⠛⢿⣶⣄⠀⢸⣿⢠⡴⠊⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⣰⣿⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⢀⣾⠇⠀⠀⢀⠀⠀⣠⡏⠀⢀⣀⣤⣶⡞⠉⠀⠀⠀⠀⠀⠈⠻⢷⣼⣿⠋⠀⡠⠒⠒ ⠈⢢⠀⠀⠀⠀⢰⣿⣏⠀⠀⡀⠠⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⣿⣿⠀⠀⢠⣾⠀⢰⠿⢿⣛⠉⠠⠴⠒⠛⠛⠛⠲⣄⠀⠀⠀⠀⠀⣿⠁⠀⠈⢀⣤⣾ ⠀⠬⢀⠀⠀⠀⣿⣿⡇⠀⣸⠁⠀⡇⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢠⠟⣿⣿⠀⠀⣿⣿⠀⡏⠀⠀⠈⢉⣻⣿⣿⣿⣿⣿⣦⡈⠳⣄⠀⠀⢠⡇⠀⠀⠀⡛⠁⢸ ⢀⢀⠸⠀⠀⣾⣿⣿⠀⠠⣿⡆⢰⠁⠀⠀⢨⡝⠷⣤⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⠏⠀⢹⣿⠀⣸⠏⢹⣸⡃⠀⠋⠉⠉⠉⢉⣿⣿⠿⢿⣿⣿⣶⡙⢦⡀⢸⡇⣀⡇⠀⠃⠀⣸ ⠀⠀⠀⠀⠠⣿⣿⣿⠀⢰⣿⡇⠈⠀⠀⠀⣸⠀⢠⡏⠙⣷⣦⡀⠀⠀⠀⠈⠀⣰⠏⠀⠀⠈⢿⠀⣿⠀⠀⢻⡇⠀⠀⠀⠀⣴⣿⣿⣿⣧⠀⠈⡟⢿⣿⣮⡻⣾⣿⠐⠘⣄⠸⣾⠋ ⠀⠀⠀⠀⣠⣿⣿⡇⢠⡟⢹⡇⣿⠀⠀⠀⢿⠀⢸⣷⡀⣿⣉⡽⣷⣦⣄⡀⣰⠋⠀⠀⠀⠀⠈⢷⣿⡀⠀⠀⠙⠀⠀⠀⡾⠛⢻⣏⣿⣧⠀⠀⣿⠈⠹⣿⣿⣿⡈⢧⡀⠘⠳⠶⠚ ⠀⢠⡶⠛⠛⠿⣿⡇⣞⣀⣘⣧⣿⡀⠀⠀⢸⡀⣿⣿⣿⣿⠘⠋⠉⠻⠽⠛⠃⣠⡤⠄⠀⠀⠀⠀⠙⠛⠇⠀⠀⠀⠀⢰⠃⠀⣾⣿⣿⠿⠷⠴⣿⠀⠀⢸⣿⣿⣿⠿⠿⠷⠤⠤⠶ ⠀⢸⡀⠀⠀⠀⢘⡿⠛⠁⠙⢿⣽⡇⠀⠀⠘⣿⣿⣿⠻⣿⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠛⠻⢿⡃⠀⠀⢀⡿⠀⢀⡼⠻⣿⣿⣦⠀⠀⠀⠀⢀ ⢠⡬⠿⣶⣴⣶⣾⣧⠀⠀⠀⠘⣿⣿⡄⠀⠀⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣔⣲⣤⠙⠂⣀⣈⣽⠆⣠⠞⠁⢠⡞⠀⠀⣿⣿⣿⣷⣄⢀⡴⠋ ⢀⠀⠀⠀⠈⠙⠿⢿⣷⣄⠀⠀⢻⣿⣿⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣷⡭⣽⣶⡦⠍⠉⠉⠁⣤⣴⠋⠤⠴⠖⠛⠉⣻⠏⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣴⡿⣟⣿⣇⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠚⠭⢵⣒⠩⠉⠀⣠⠶⠋⠀⠀⠀⠀⢀⣠⠞⠁⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣿⣦⠈⣿⣿⣿⣿⣿⣏⣙⠛⠛⠛⢻⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⡤⠖⠋⠁⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⢼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣿⡿⠋⣠⠿⣿⣍⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠤⠤⠤⢶⣾⣿⣟⡯⠓⠀⠀⠀⢠⡏⠀⠀⠀⠀ ⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣴⣿⢀⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣝⠓⠒⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠋⠀⠀⣴⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡄⡐⠀⠀⠀⠈⣿⣿⣼⣿⠿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣶⢾⣻⠟⠋⠀⠀⠀⠀⢨⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣾⠳⠃⠀⠀⠀⠀⣽⡿⣿⣇⢀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠋⠁⠀⠀⠀⠀⢀⣴⡿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣻⡿⠁⠀⣶⣦⣤⣀⡐⢹⣿⢸⠛⠛⠛⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢿⣿⠟⠋⠙⢿⣿⠸⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣯⣦⣄⡀⠀⠀⠀⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣧⣤⣀⣀⠀⠀⠈⢿⣦⡀⠀⠈⢿⣇⢹⡀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠛⠢⣶⣾⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠋⠀⠈⠙⠓⢦⡘⣿⣿⣄⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⡄

⠀⠀⠀⠁⠀⢈⣿⡿⠋⠁⠀⢰⣿⣶⣾⣿⣿⣿⣽⣿⡷⠷⠶⠞⠛⠛⠻⠿⣿⣧⣤⡄⣉⢿⣿⣿⣷⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠋⠀⠀⢠⣾⠟⠀⠀⠀⠀⣿⠿⢿⣿⣿⠿⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢿⠿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀ ⠀⢠⣤⣤⡿⠃⠀⠀⠀⠀⠀⣿⣾⠿⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⡀⠲⡉⠻⣿⣇⣤⣶⣶⣶⣤⡘⣿⣷⡀⠀⠀⠀ ⣶⣿⣼⣿⣡⣴⣾⣿⣿⣿⡷⠛⠁⠀⠀⠀⣠⡇⠀⢀⡤⡶⠂⠀⠀⠀⠀⠀⢀⠇⠀⠀⡇⠀⠱⡀⠈⢻⣿⣿⣯⣿⣿⣿⣿⠏⠁⠀⠀⠀ ⣯⣭⣿⣿⣿⡏⠉⣹⣿⡿⠤⠤⠤⠤⠤⠾⠓⠩⠔⠁⡰⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⠀⠣⠀⠀⠉⢹⣿⣭⣙⠛⠁⠀⠀⠀⠀⠀ ⢆⣺⣿⣿⣿⣿⣿⡟⠁⢱⠀⠀⠀⠀⠀⢀⣄⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡇⠀⠀⣀⣀⡀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⡿⠋⠀⢀⠀⡇⠀⣿⣿⡇⢸⣿⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⠃⢀⠎⠹⡀⡎⠀⣀⠈⠳⡀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⠟⠀⠀⢀⡘⠁⢠⠀⠸⣿⣿⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⠧⠤⠤⢽⡀⠀⡟⢷⣄⠹⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠒⠋⢉⡀⠀⠀⠀⡼⠁⠀⢸⠀⠀⢻⣿⠀⠿⠋⠀⠀⡄⠀⠀⠀⠀⢀⣾⠋⠀⣀⡀⠀⠀⢧⠈⠱⢼⡇⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢉⠟⠀⠀⣀⡜⠀⠀⠀⣼⠆⠀⠀⣁⡀⢠⣤⠀⠀⡆⠀⠀⠀⣠⢻⠗⣶⣿⠿⢿⣯⣄⠈⣧⡀⠀⠐⢀⠇⢤⣼⡀⠀⠀⠀⠀⠀⠀⠀ ⠡⣫⣴⡾⠟⡻⠀⠀⣠⠊⡼⠀⠀⠀⠹⠗⠘⠋⠀⠀⢡⠄⠀⣰⣭⡞⠉⠁⣠⠔⠲⢌⠻⣷⣼⡌⢳⠖⠁⠀⠰⠂⠇⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⠉⠀⠿⠁⢀⡔⠁⢨⣃⠤⠒⠊⠉⠑⠒⠲⣄⠀⡎⠀⡜⠁⠙⠇⠀⠀⢻⡘⠟⣸⠀⠘⣿⣄⠎⣠⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⢻⣆⠀⠀⣾⠿⣿⣖⣋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠑⢧⡜⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠠⠖⢛⣏⣼⠟⢁⣀⣠⣤⣤⣷⡤⠄⠀⠀⠀⠀ ⡄⠀⢿⡀⠀⣿⢀⣿⠀⠀⠀⠀⡏⠙⠢⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⠋⠀⠋⢩⣽⡿⠋⢨⡷⣀⠀⠀⠀⠀ ⢷⡄⠸⣧⠀⠻⣿⠃⠀⠀⠀⠀⣅⠀⠀⠈⠢⣄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢩⣿⣃⣴⠾⢆⣼⡟⠁⠀⢸⢣⣯⠳⣄⠀⠀ ⠀⠻⣯⣿⣆⣄⠀⠀⠀⠀⠀⢰⡏⢆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣉⠤⣾⠟⠉⠀⢠⣿⣿⠀⠀⢠⡏⠀⣿⠀⡏⠁⠃ ⣆⠀⣿⣿⣿⣿⡀⠀⠀⣷⡀⠈⢇⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣴⣿⣿⡟⠀⢠⠏⠀⢰⢸⢀⠇⠀⠀ ⣿⣦⣹⣫⣿⣿⣷⠀⠀⢻⠟⠢⣈⣦⡀⣿⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⡿⠁⢀⡴⠊⢙⣿⡿⢁⠔⠁⠀⢠⠃⣸⡼⠴⠀⠐ ⣟⣐⣽⣷⣿⣿⡟⠷⣤⣬⠷⣴⣻⠪⡽⠛⠛⠛⢿⣷⣒⢤⣀⣀⣠⣤⣶⠋⢠⣿⠟⡠⠔⠉⢲⠒⠭⠾⣲⡟⠀⣠⣼⠵⠚⠋⠀⠀⠀⠀ ⣿⢻⣿⣿⣻⠿⠯⢉⣀⡈⠢⣄⣹⠟⠛⠢⢄⠀⢸⠉⠛⣷⣄⣴⡿⠛⠛⡷⢾⠒⠉⠀⠀⠀⠀⣇⣠⡶⣿⡧⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣯⣤⣿⠋⠁⠀⠠⠤⡀⢱⠀⣾⠁⠀⠀⠀⠀⢻⣍⡣⣴⢾⣿⣟⢢⣤⣠⢽⣺⢦⣀⠴⠗⠲⢶⡇⠀⠀⠙⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⢯⡴⠒⣦⣄⠀⠁⠘⣾⣻⣀⠀⠀⠀⠀⢸⠛⢭⣳⣓⣲⣛⣿⡋⠀⠁⠀⢰⠋⠀⠀⠀⠀⠱⣤⡆⠀⢸⡇⠀⠰⠶⠶⠇⠂⢀⡀⠀ ⢸⠀⠸⢧⠀⠘⣏⢦⣼⣾⣿⣿⣟⡧⢶⡤⣴⡋⠀⠀⣧⠼⣿⠿⣿⣇⠀⠀⠀⢸⡀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠧⠼⠃⠀⢸⣶⣿⡿⠿⡿⠋⠀⠈⠁⠀⠹⡛⠉⢀⣠⣿⣧⡀⠀⠈⠉⠉⠉⣳⠤⠼⠓⠶⣿⡇⣠⠀⠀⣷⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡟⣷⣤⣀⡇⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⠟⢻⣿⣦⣀⣀⢀⡰⠁⠀⠀⠀⠀⠈⢿⣇⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀

⢠⠀⠀⣸⠟⠁⢠⣿⣿⣿⣿⠟⠛⠓⠉⠉⠛⠳⢶⣬⣿⣿⡄⠀⠙⢿⣄⠀⠀ ⢀⢤⡼⠁⣀⣀⢸⡷⠛⠁⡘⠀⠀⠀⠀⠀⠀⠰⠀⡆⢍⠻⣧⣴⣶⣤⣻⣦⠀ ⣟⣿⣷⡟⢻⡿⣋⡀⠀⠴⠃⠔⡘⠁⠀⠀⠀⡆⠀⠇⠈⠄⠘⢻⡟⡻⠟⠁⠀ ⢠⣿⣿⡿⠋⠘⡀⣀⣀⣴⡄⠀⡇⠀⠀⠀⢀⠁⡼⡀⠄⠠⢄⠀⠹⡟⠀⠀⠀ ⢸⡻⠟⠂⢠⠃⠇⠸⣿⢸⡇⠀⠁⠀⠀⠀⣜⠬⠤⠵⢀⡷⡄⠂⠀⠇⠀⠀⠀ ⡒⡲⠀⢀⠊⠀⡠⠀⢛⠈⡁⠀⡆⠀⢀⢼⢵⣶⣶⡀⢢⠈⠃⡀⣀⡄⠀⠀⠀ ⣬⠶⢫⠃⢀⠊⠆⡀⠘⠁⠉⠀⠓⠠⠻⡎⠀⣶⡔⡙⢾⢊⠊⠀⠀⢃⠀⠀⠀ ⠙⣆⠀⡶⢷⠞⠁⢀⡀⠀⠈⠑⠧⠁⠀⠀⠀⠓⠈⠠⢚⣧⢟⣀⢤⣬⡤⠄⠀ ⣆⢸⡀⢧⡏⠀⠀⡂⠈⠢⣀⠀⠃⠀⠀⠀⠀⠀⠀⡠⣳⣃⡤⢸⠟⠁⡯⡦⡀ ⡈⣷⣧⡆⠀⢠⠀⡏⢄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⢒⠏⠁⣴⣿⠀⡰⠁⠇⡏ ⡷⢽⢽⣿⡄⢸⡑⣔⣄⣷⣤⣀⠀⠀⠀⠀⣀⢤⡲⠃⡠⢊⢿⢃⠔⢀⢜⡠⠕ ⡷⣿⣿⢿⣛⠛⢍⣻⠷⢅⠈⡟⢿⣒⣶⠿⡧⡾⠐⠁⠈⣀⡭⡏⠴⠋⠁⠀⠀ ⣷⡾⡉⡀⠂⠸⣰⠁⠀⠀⢹⡵⠶⢻⣵⠆⠞⠓⠔⠃⠒⠇⡀⠱⡄⢀⣀⡀⠀ ⠉⠘⡄⠹⡢⣶⣿⡿⢶⠤⣆⣈⠯⢿⠿⠆⣀⣸⡀⢀⠀⣸⠃⠀⣇⠀⠀⠀⠈ ⠁⠋⠁⠀⠿⣏⣹⠀⠀⠀⠘⣤⣴⠿⣷⣄⡀⢠⠋⠉⠉⠹⡎⠀⡿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣼⠁⠀⠀⠉⢢⣄⡉⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣶⣶⣿⠿⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⣏⣠⣴⠾⠛⠁⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⡿⠉⣿⡀⠀⠀⢿⠱⡀⠀⠀⠀⢀⠀⢠⠄⢸⠀⡇⠀⢸⠋⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⡟⠀⠀⢹⡇⠀⠀⠘⣠⡧⢒⡁⠀⠁⣠⠏⢠⠇⠀⠁⡰⠃⠀⠀⠀⠀⢀⡴⣪⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⠁⠀⠀⠸⡇⠀⠀⣰⣥⠛⠁⠀⠀⡰⠃⢠⠋⠀⢱⣀⣇⠀⠀⠀⠀⠀⠈⢻⢿⡿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⢧⢀⡔⡛⠁⠀⠀⠀⣼⠁⢠⡧⢴⣄⠈⢯⠙⠦⠀⠀⠀⠀⠀⠁⠘⣇⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠀⠀⢨⠏⡐⠀⠀⠀⠀⠠⠃⢀⣏⢳⣴⣊⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⡰⢁⠜⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣟⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠑⠋⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠏⢰⣸⡋⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⡌⠀⡆⢠⠁⢀⡠⠤⠐⠒⢎⠉⢫⢠⣾⡟⠙⡄⠀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⢠⠁⠀⣄⠞⠊⠁⠀⠀⠀⠀⠀⠳⡄⢻⣿⡇⠀⠈⠓⠠⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀ ⢀⠎⠀⣰⣯⠀⠀⢧⡀⠀⠀⠀⠀⠀⠈⠸⢿⣟⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⠀⠘⠀⠀⠀⠀⠀⠀⠒⠛⠒⢶⠀⠀⠀ ⡣⠤⠊⠁⢻⠀⢠⢸⣧⠀⠀⠘⣆⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣳⠏⠉⠉⠉⢳⣶⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠘⡇⠸⣦⣧⣇⠀⢠⠈⢧⡀⠀⠀⠀⣀⠀⠀⠉⠙⠒⢒⣲⠶⠋⠁⠀⠀⢀⡼⠁⠀⣶⡿⠭⢍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣇⠙⣿⣆⠀⢣⡀⠙⢆⠀⠀⠀⠈⠑⠲⣶⡚⡩⠭⠭⡽⠲⣾⣭⣿⠀⠀⠚⠁⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀ ⠀⠀⠀⠀⠀⠀⠑⢼⣆⠈⢿⣆⠈⢿⡒⠤⠽⣦⣄⡀⠀⠀⠈⠛⠦⣀⠀⢸⣄⣸⣏⡇⠀⠀⠀⠐⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢀⠿⣗⣌⢣⡀⠀⠀⠀⠉⢳⠲⢷⡶⠤⠄⠉⠹⣿⡻⢿⡇⠀⠀⠀⠀⣠⠖⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠛⢷⡑⣄⣠⠴⠶⠿⠿⢿⡁⠀⠀⠀⢀⣸⣿⣿⡀⠀⠀⠀⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠈⢻⡿⢄⡀⠀⠀⠈⢳⣄⣤⣴⠃⠀⠀⠀⠉⠢⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⡿⠋⡍⠀⠀⠀⠀⠀⢀⠙⣆⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⠀⠀⠀⠠⣿⠀⠀⠀⠀⢠⣾⣿⠆⢀⣧⣄⡀⠀⠀⠀⡜⢀⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⣿⣤⣆⣀⣠⠾⠿⢻⣧⡿⠿⣿⣿⣆⠀⢠⠁⡞⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠀⢀⣀⣿⡿⠟⠻⣿⠀⠀⠀⣻⠀⠀⠘⣿⣿⣇⠘⡸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⡽⠋⠉⠸⡄⠀⠀⠙⢧⡀⠀⣇⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣤⡤⠤⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢔⡇⣀⣤⡴⠊⠀⠀⠀⠀⣇⠀⠀⠀⠀⠉⢦⣿⣦⣀⣀⣼⣿⣿⢿⣤⡀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢙⣶⠄⠀⠀⠀

⠀⠀⢸⠀⠀⣶⠀⠀⢸⣿⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⢀⡭⠔⠒⠀⠀⠀⣤⡤⠒⠈⠁⠀⠀⠙⠒⠠⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣼⣿⣿⣿⣧⢦⣸⢸⡇⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠁⠀⢠⢾⣋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢗⡤⠖⠋⠁⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡟⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣴⢏⡯⠟⠁⠀⢀⣤⠊⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠪⠉⠉⠈⢿⣿⣿⢃⣤⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⡏⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣠⠴⠛⠁⢀⡴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⢀⡤⣞⠏⠊⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠚⠉⠙⠋⠀⠀⠀⢀⡜⠁⠀⠀⠀⣠⠞⠁⠀⠀⣠⠞⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠖⡩⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⠞⠁⠀⠀⢀⡜⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⣠⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠝⠀⠈⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠞⠁⠀⠀⢀⡼⠁⠀⠀⠀⢠⠞⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣞⣡⠋⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠋⣉⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡴⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠙⠭⠭⣉⣁⣀⣀⣀⡠⠤⢴⡾⠋⠀⠀⠀⠀⢀⡾⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠘⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢠⠎⠀⣠⡾⠁⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠀⢀⠞⠁⠀⠀⠀⠀⠀⣤⠤⠤⣖⡢⠤⣀⢀⡤⠞⠉⠸⡇⡇⠀⠀⠀⢨⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣰⠋⢀⡴⠋⠀⠀⠀⠉⠑⠢⣤⡀⠀⣠⡿⠃⠀⣰⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⣠⠴⠻⣲⣄⠀⠀⣷⠁⢀⡤⠖⢾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⣴⣣⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡟⠀⢀⣾⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⣀⡤⠖⠋⠁⠀⠀⠈⠙⢷⣀⣿⡶⠋⢀⡤⠶⡇⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢠⣾⠏⠀⠀⣰⠂⢀⡾⠴⠖⠚⠋⠉⠴⠒⠒⠤⡀⠀⠀⠀⠀⠈⡿⠀⠐⠋⢀⣴⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣏⠀⠀⡞⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⠟⣿⠀⠀⣠⣿⡀⡞⠀⠀⠉⠛⣻⣿⣿⣿⣷⣦⡈⠣⡀⠀⠀⢸⠇⠀⠀⡖⠋⠀⡇⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⢠⡿⡹⠀⠀⡇⠀⠀⠀⠀⠀⡍⠢⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠏⠀⢻⠀⢀⡟⠘⣇⡇⠀⠈⠉⠉⠉⣻⣿⠯⠿⢷⣽⣦⡘⢦⡀⢸⡀⢠⡀⢹⡀⣠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⡷⠀⣸⣿⠀⠀⠀⠀⢰⡇⢠⡇⢹⣶⣄⡀⠀⠀⠀⠀⣠⠇⠀⠀⠘⣆⢸⠀⠀⠸⣇⠀⠀⠀⢀⡾⣿⡿⣷⠄⠀⢙⢿⣿⣎⢳⣾⣇⠀⢳⡈⣿⠛⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣿⣎⡇⢰⠏⢧⠘⡀⠀⠀⢸⡇⢸⣷⢸⡇⠀⠉⠓⢦⣄⡰⠋⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⠁⠀⢠⠞⠉⣡⣉⣹⡄⠀⣼⠀⠙⢿⣿⣧⠘⢦⡀⠙⠒⠛⡇⠀⠀⠀⠀ ⠀⠀⡖⠉⠉⠙⢿⣀⣯⡤⣼⡆⡇⠀⠀⠘⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⢸⣀⠠⠰⣿⠃⠙⠓⢻⠀⠀⢸⣿⣿⡟⠓⠛⠛⠛⠛⡇⠀⠀⠀⠀ ⡀⠀⢣⡀⢀⠀⢠⠟⠀⠀⠈⢳⣷⠀⠀⠀⡇⣿⣿⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠉⠧⡀⠀⢀⡟⠀⣠⠏⠘⣿⣿⣄⠀⠀⠀⣠⠗⠒⠒⠒⠠ ⠒⠀⠈⠙⠛⠿⣷⡄⡀⠀⠀⠘⣿⡀⠀⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠴⠧⠔⠋⢀⡴⠃⢀⣀⡿⠻⠟⠳⣤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⡀⢠⣿⢧⠀⠀⠀⣿⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠀⠈⠉⠀⢀⡴⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢽⡞⣾⠀⠀⣿⠀⢈⣷⣶⠖⠀⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⢀⣠⠶⠋⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⠀⢻⣰⠋⢙⠿⣖⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣍⣀⣀⣀⣠⣤⣴⡾⠛⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣅⣴⡃⠀⠪⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⣀⠀⣧⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣕⠒⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⢳⣌⣷⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣧⡿⠟⠉⠉⠉⠉⢹⣟⢿⣯⣉⣡⣾⣿⣿⣿⣶⣶⣶⣶⣶⢖⡫⠏⠁⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣆⣀⣀⡀⠀⠀⠸⣵⣾⣿⣿⣿⡿⠟⠋⠁⠀⣀⣴⠿⠕⠁⠀⠀⠀⠀⢀⣠⠞⠛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⣀⠋⡼⡍⠉⠉⠳⣶⣾⢿⣿⡿⡿⣿⠏⠀⢀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣏⡉⠀⠈⢷⡇⢻⠀⠀⠀⣿⣟⢱⣬⡧⠴⠛⠒⠊⠉⠁⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠴⠖⠢⢤⣀⠀⣈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⠶⠶⠤⣀⡀⢹⡷⣄⠀⠘⢿⣬⣇⣀⣠⡿⣿⣿⣿⢯⣽⣟⡶⠶⢶⡶⠖⣲⡿⠟⣩⠿⠛⢿⠟⠁⠀⠀⠀⠀⠀⢹⣇⢽⢧⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣙⢷⣄⣀⠀⠀⠀⠙⢦⡹⣼⡀⠀⠈⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣸⡿⠿⢃⡗⠀⠀⢀⣼⡁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⠿⣏⡈⠧⡀⠀⣀⠴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠿⠊⠉⠛⠛⠻⢦⣄⠀⠀⠙⠿⣧⠀⠀⢹⣟⣿⠟⡿⣿⣿⣦⣿⠁⠀⢍⡛⠛⡦⠄⠀⡿⠃⠀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠋⢀⣿⠿⢤⡇⠈⠀⠀⠀

⠀⢠⠀⠘⣑⠀⠀⢀⣴⠟⢋⣡⠖⡫⢊⢴⡩⡺⣑⡪⡱⢻⠀⠀⣠⡤⠞⠻⣿⣿ ⠀⠐⠘⠒⠃⢀⡔⠋⢀⠔⠋⡠⠊⡰⢥⣾⠾⣶⠬⣁⡔⣡⡴⠛⠁⠀⠀⠀⣸⣿ ⠀⠀⠀⢀⡠⠊⠀⡀⠁⢀⠔⢁⠾⣋⠊⢜⠉⢣⡾⢋⡼⠋⠀⠀⢀⠠⠖⡋⠁⠘ ⠶⢒⣊⡁⠤⡴⠋⠀⢠⠊⣠⠋⣙⡿⣟⢊⡴⢋⠔⠋⠀⠀⠀⠈⠀⢀⣼⠁⠀⠀ ⠀⠄⠀⢀⡜⠀⠀⡰⣡⠞⠉⠓⠫⣅⣠⠟⡠⠊⠀⠀⠔⠉⠙⣋⠶⣍⠀⡆⡠⠤ ⠀⠀⠀⣾⠁⠀⣔⠋⠁⠀⠀⠀⠀⣰⠃⣴⠃⣠⢀⢮⡔⠲⠯⠤⡀⠀⠑⠏⠀⣨ ⠈⠆⢸⡟⢰⡄⠀⢱⢢⣀⠀⠀⠠⠃⠜⢹⢀⠻⡌⠐⠒⣻⣿⠿⣮⣢⣸⠠⠈⣸ ⠀⣀⣿⡇⠞⣷⠀⢸⢸⣼⢷⢦⣄⠌⠀⠀⠺⡀⠑⠀⡐⢻⣿⡀⡏⢻⣿⣣⡑⢑ ⢘⣄⣈⡟⠉⢻⡄⠘⣾⠛⠀⠀⠀⠊⠀⠀⠀⠀⢀⣀⠓⠛⢇⢀⠃⡜⢿⣦⡀⡠ ⠀⠀⠉⠛⢦⣸⣿⡀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠮⠉⡱⠊⠐⢉⠝⡝⠁ ⠀⠀⠀⠀⠀⠈⠛⢷⣼⢟⢿⡉⠉⠇⠀⠀⠀⠀⠀⠐⠶⠂⠁⣤⣴⠞⠁⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣾⣿⣆⠀⠀⠀⠑⢆⡀⠤⠀⠒⠊⠉⠀⢀⡠⢺⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠈⣿⡽⠓⠒⢲⣶⣶⣿⣶⣦⣤⣤⡶⠚⠉⢀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠟⠁⣦⠤⣿⠟⠓⣴⣾⣿⣿⣿⡿⠟⠋⠁⢀⣠⣔⠉⠈⡆⠀ ⠀⠀⠀⠀⠀⢶⡷⠠⠄⣹⣄⠘⣾⣤⣾⣿⣿⣿⣦⢤⣴⣶⣾⣿⠋⠉⠉⠐⣾⡄

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣛⣭⡷⢛⢫⡉⢦⡑⢎⡔⡃⣿⢨⡙⢷⣌⠦⡱⢌⢆⠣⡜⡰⢩⠛⢿⡿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⡻⢿⣩⣶⣗⡼⢟⡡⢎⡱⢢⡙⢤⡉⠖⣌⣱⠏⡔⡌⢆⢻⢿⣤⢋⠬⡱⢌⡱⢣⠙⣆⠲⢌⡙⠿⣿⡻⢿ ⣿⣿⣿⣟⣿⣿⣿⣿⢿⣭⢾⣛⢫⣷⡿⢋⡜⢢⡑⢎⡔⢣⠜⣢⠙⡜⣰⣏⢚⠰⡘⡌⢆⡊⢿⣮⡒⢱⠊⡔⢣⠍⡴⢉⠦⣙⠒⣮⡛⢾ ⣿⣿⣿⢿⡿⣫⣿⢟⣯⢞⣿⡼⣿⠏⡔⢣⠜⣡⠚⡴⣈⢇⡚⢤⢋⡼⢏⠰⢌⠣⡑⠜⢢⠑⣦⣿⣞⣿⣿⡾⣷⣮⡴⡉⢖⡡⢋⡔⢻⡔ ⠛⣿⣿⣯⣿⢟⣭⡿⢖⣻⢏⡾⢃⠞⣨⢃⠞⣄⠫⢔⣢⣾⣘⡴⢏⡱⣊⣑⣊⠴⡉⢎⡡⠎⣿⣎⢿⡻⣯⣷⣧⢻⣽⡜⢢⡑⢣⠜⣡⢹ ⢐⣼⡿⣹⢧⣾⢫⡿⣻⢏⡿⢡⢋⡜⢤⢃⠞⢤⢋⢲⢿⠩⡵⠾⢛⢋⠭⢩⡙⠢⢍⡒⠴⡉⡜⢻⣾⣵⣫⢽⣛⢧⣿⢇⠣⡜⣡⠚⡤⢃ ⣼⢏⣾⢿⣫⠷⡻⣽⢣⣾⣡⢃⠎⡜⢢⢍⡚⡤⢋⡜⢻⡶⣈⠕⡊⢬⠘⣡⣬⢑⠢⡑⢦⡷⣜⠢⡌⡙⠻⣷⠿⢟⡋⢆⠳⡘⢤⢋⠴⣉ ⢳⢾⠟⡽⢖⡿⣲⢯⣾⡵⠷⣎⡚⢬⢡⠒⣼⡿⣴⠨⡍⢷⡌⢆⡙⡰⠟⣫⣷⢞⣛⣛⣛⣛⣭⣛⣳⠾⢧⣼⡇⢎⡜⢌⠣⣍⠲⢌⠲⡡ ⡿⣯⣾⢞⡻⢱⡏⣾⢳⡄⢣⡙⣳⣧⣊⡵⣈⣷⡉⠷⢮⣭⣻⣷⡈⣴⣿⡿⠗⢋⣽⠻⣍⠯⣙⠿⣍⠛⠓⣿⣿⠖⡸⢌⠣⢆⡹⢌⢣⡑ ⢟⣡⢗⢪⣔⣿⣸⡟⢢⣾⣴⣼⣭⣭⣭⣿⣴⣌⡻⣎⣒⡤⠧⠭⠴⠿⠕⠀⠀⣾⢣⢏⡴⢣⣍⣾⣹⡆⢠⢖⣻⢌⡱⢊⡕⣊⠔⣊⠦⡑ ⢎⣿⡾⣻⢯⡗⣼⢻⢠⣾⣦⢷⡟⣛⠟⣦⡉⠉⠉⢀⠀⡀⢂⠐⠠⢀⠂⠄⡀⠘⠛⠋⠉⠉⢉⠀⠡⢀⠂⠄⣿⢢⡑⢣⠜⡤⢋⡔⢣⠱ ⢻⣃⢶⡏⣾⢼⣏⢣⣿⠋⢠⡟⡜⣌⢞⣱⡿⠆⢀⠲⠄⡐⠠⢈⠐⠠⠈⡐⠠⢁⠂⠡⢈⠐⠠⢈⠐⠠⢈⣰⢏⣦⡿⢢⡙⡔⢣⡘⢥⢃ ⣏⠴⡛⣼⣷⣾⢹⣞⡇⠀⠸⣿⣼⠞⠋⡁⠄⡐⢀⠂⡐⢀⠡⠀⠌⡀⠡⠐⡀⢂⠈⡐⠠⢈⠐⠠⢈⣤⣶⠿⠋⢡⡟⢤⠓⡬⡑⡜⢢⢃ ⣬⣶⠿⣋⠕⡢⠥⣟⣉⡷⠚⢉⠠⢀⠂⡐⠠⠐⡀⢂⠐⡀⠂⡁⠂⠄⡁⢂⠐⡀⠂⠄⡁⠂⠌⡐⢈⠁⡀⠠⠐⢸⡏⢦⡙⠴⡑⣌⠣⢎ ⡟⠤⡓⡌⢎⡑⢣⠹⢮⣀⠐⡀⠂⠄⠂⠄⡁⢂⠐⣀⣤⣤⣥⠴⠶⢀⠐⡀⠂⠄⡁⢂⠐⢈⠠⠐⢀⠂⠄⠡⢈⢸⡗⢢⢍⠲⢡⠎⡱⢊ ⣌⢣⠱⡘⢆⡹⢧⣙⠢⣍⠛⡶⢬⣔⠈⡐⢀⠂⠄⠋⢁⠀⠠⢀⠂⠄⢂⠠⢁⠂⡐⠠⠈⠄⠂⠌⡀⠂⠌⡐⠀⣾⢡⢃⢎⡱⢃⢎⡱⢃ ⢆⢣⢣⢙⠢⣅⢻⡽⣿⡛⠓⠛⢋⠁⡐⢀⠂⢈⠐⠈⠄⡈⠐⠠⢈⠐⠠⠐⡀⢂⠐⠠⠁⠌⡐⠠⢀⠁⠂⠄⢱⡏⢦⡉⢖⡘⡌⢦⡑⢣ ⠎⣆⠣⢎⡱⢌⡚⣧⠜⣧⠀⡁⠂⡐⢀⠂⠄⠂⠌⡐⠠⢀⠁⠂⠄⡈⠐⠠⠐⠠⢈⠐⠈⠄⡐⢀⠂⠌⡐⠈⣾⡑⢦⢉⠦⡱⡘⢆⡙⢆ ⢚⠤⣋⠦⡑⢎⡔⢻⡌⡽⣦⠀⠡⢀⠂⡐⠈⡐⠠⢀⠡⠀⠌⡐⠠⢀⠁⢂⠁⠂⠄⡈⠐⠠⠐⠠⢈⠐⡀⣹⢇⡜⢢⠍⣲⡇⡙⢦⢉⢾ ⣿⢢⡑⢦⢙⠢⡜⡡⢿⡰⡙⣷⣆⠠⠐⢀⠡⢀⠁⠂⠄⡁⠂⠄⡁⢂⠈⠄⡈⠐⠠⢀⠁⢂⠁⠂⠄⢂⢠⣟⠢⡜⣡⣾⣿⢣⡙⢢⢭⡾ ⢻⣄⠳⡌⢎⡱⢌⡱⢊⢷⡕⢢⡙⢷⣌⣀⠂⠄⡈⠐⠠⢀⠁⢂⠐⠠⢈⠐⠠⢁⠂⠄⡈⠄⡈⠐⡈⢤⡟⣡⢳⡾⣏⣻⠏⡴⢡⣳⡿⢡ ⡹⣧⡓⡜⢢⡑⢎⠴⣉⠎⣻⣦⢙⠢⣍⠛⡾⣤⣄⡁⠂⠄⡈⠄⡈⠐⠠⢈⠐⠠⠈⠄⡐⠠⢀⠡⣰⣿⣱⣾⠯⠶⣾⣽⣷⣘⣼⣟⣥⣿ ⢲⠹⣷⣌⠣⡜⣌⠲⢡⣞⣠⠙⣷⣧⣌⠳⡘⢤⠫⢝⡛⡷⢶⣤⣄⡁⠂⠄⡈⠄⡁⠂⢐⣀⣢⣼⣟⣿⡟⢤⡴⣞⣵⣿⣼⠿⢻⣿⡿⢛ ⣇⡹⡘⢿⣿⣶⣈⢇⠣⡜⣯⡳⠶⣬⡿⣦⣙⣢⣙⣺⣿⡷⣶⣠⢛⣇⠈⡐⢠⣴⠶⣛⣻⣿⢿⡟⣿⢻⣷⢾⡟⠫⡁⠤⢀⢂⠂⢸⣿⣶ ⡱⢒⣍⠲⢤⣉⠛⡷⣧⣶⣡⣛⣷⣦⠱⣌⢫⡙⡭⢩⢍⡱⢊⢛⣿⣿⣿⣶⣿⣡⣾⣻⣳⡽⣎⢿⣏⡿⠋⠀⠄⢃⢒⣠⣥⣦⣬⠾⠻⣿

⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣀⠦⠚⠀⠀⠄⡁⠈⢀⠈⡔⠠⠈⠀⠠⠐⠈⠀⠀⣀⣾⢃⡈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠃⡀⠀⠄⠐⠀⡀⠡⠆⠈⠠⠁⢀⠀⠁⡀⠀⣀⣾⠋⠁⡀⠙⠂⡐⠊⣀⢉⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠇⠀⠀⠀⠀ ⠐⡀⠆⢚⠄⠃⠨⢀⠀⠰⡁⠠⠀⠀⠀⣠⣴⠟⢁⠴⠋⡀⠁⠉⠙⠳⣤⣀⠀⢀⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠐⠀⠂⢀⠣⠀⠀⠀⠀⠐⠡⠀⢀⣠⣾⠛⢀⡔⠋⡀⢀⡁⠘⠰⢀⡠⢀⡿⠦⣾⠃⠀⠀⠈⠛⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠆⠀⡠⠄⠒⠂⢂⣥⡾⠋⣠⡖⠉⣠⠒⠠⣈⠀⠌⠑⠀⣤⠟⠁⣼⠇⠀⠠⠀⢠⡇⠀⠹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⡉⣤⠖⠁⢀⣠⡶⠟⣁⡴⠞⠁⡀⠉⢠⠐⠆⢁⣈⠖⢡⡾⠋⠀⣼⠋⠀⠐⠂⢠⣿⠁⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢁⣴⠏⠰⣶⣛⠡⠰⠞⠋⢀⡀⠐⡐⣂⢠⠀⡉⣀⠈⣴⠟⠀⢠⡾⠃⢀⠐⠀⢀⣾⡇⠀⠐⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠋⠀⣠⣼⣿⣷⣦⣄⡀⠀⠈⠁⠉⢄⡀⡁⠈⣠⡞⠃⢀⣴⠟⠀⠀⠄⠀⣠⡿⢻⡇⠀⠈⡀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣷⡶⠟⠋⠉⣿⠄⠉⠙⠻⢷⣦⣄⡀⠀⠀⣠⠿⠃⠀⣠⠾⠁⠀⠠⠈⢀⣶⠛⠀⢸⡇⠀⠀⡀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠁⠀⠀⠀⠀⣿⠆⢀⠂⠄⢀⣼⡏⠙⠻⢶⣼⣠⡴⠟⠉⠀⠀⢀⣠⡾⠋⠁⠀⠀⢸⡇⠀⠐⠀⢄⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣤⣇⣠⡀⠀⠶⣾⣇⠀⠀⠂⢠⣿⠀⠀⠄⠀⣼⠋⠀⠀⣀⣠⣴⠞⠉⠀⠀⠀⠀⠀⢸⣇⣠⣤⣄⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⢿⣿⣿⣿⣿⣧⢻⣆⠀⠁⢸⣿⣧⠀⠀⢠⣿⣤⣶⠿⠛⠉⠰⣶⣦⣄⠀⠀⠀⣠⡿⠉⠉⣷⠙⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡘⠦⣌⡙⢻⣿⣿⣦⡹⢷⣄⢸⡇⠻⣧⣀⢸⡯⠁⠀⠀⠀⠀⠀⠈⠳⣽⣦⠀⣸⡏⢴⡤⢿⣿⢀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣬⡓⡤⣙⣲⡯⠛⠿⠏⠀⠙⠛⠁⠀⠀⠙⠶⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡟⢀⢺⣇⣼⡟⣨⣿⠃⠀⣠⣤⣄⡀⠀⠀⠀⠀ ⠀⠈⠛⠻⠟⠉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⣤⠀⠀⠀⠀⠀⠀⣾⠇⠠⢸⣿⡿⢀⣿⣯⣶⡾⠿⠿⠿⠿⠿⠶⣶⡀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣶⣶⣦⠀⠀⠀⢀⣴⠟⣷⣅⣸⣿⣷⣿⣿⣿⣿⠀⣴⡾⠞⡷⠷⣆⠸⣷ ⣷⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣉⢛⡛⢿⣿⣿⣯⡁⣢⡾⠃⣼⣾⣿⣿⣿⣿⢿⣟⣾⣿⢸⣿⣰⣿⣿⣷⡹⣇⣿ ⣿⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⡱⡌⢦⣉⣶⠟⢻⣿⣿⠋⠀⡔⣺⣿⣿⣻⢾⣭⣿⣾⣷⣿⣚⣿⣿⣿⡿⣟⡿⣡⣿ ⣿⣇⢈⣹⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠩⢁⣂⣾⠟⠀⢰⠁⡄⣿⣿⣿⡿⣿⣟⣯⣷⣟⣿⣇⡛⢿⠻⡟⢯⡱⢣⡿ ⣿⣟⣿⠉⠉⢻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠐⠀⠂⠀⠀⠙⣿⣯⡀⠄⣩⠄⢲⣾⣿⣿⣿⣿⣿⡿⣿⢿⣾⣿⣿⡿⡟⣟⣻⠷⣻⣿⡇ ⣻⣿⣿⣶⣴⡿⠉⠈⠙⣿⣿⣿⣿⣶⣤⣤⣄⣤⣤⣤⠿⠛⣤⡴⠚⣁⣂⣼⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣿⣿⣷⣝⣻⣿⢿⣱⣿⠇ ⡝⣼⢻⣿⡿⣇⠀⠀⣀⣿⡏⠛⠻⡿⣿⣿⡿⠟⠋⠄⣂⣱⣾⠿⢿⢿⡟⠁⠈⢿⣿⣟⠀⠀⡌⣿⣿⢿⣟⣿⠿⠿⢷⠾⠿⠛⠁⠀ ⣸⡏⣿⣻⣟⣻⠿⣿⣛⣿⠁⠀⠀⠀⠘⢿⣶⣬⣶⣷⠾⠛⠁⠀⠀⠸⣧⢀⢮⣿⣿⣿⣶⣧⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣙⠶⣿⡏⢿⣶⡟⠋⠀⠀⠀⠀⠀⢈⢩⣜⠡⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣏⠰⢨⠄⠁⢹⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⢿⣿⣿⣿⣆⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠹⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⢟⡆⢠⠞⠀⠀⠀⢀⠜⠀⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠳⡀⠘⢿⣿⣿⣆⠀ ⠿⠛⠉⠀⠈⡿⠋⠀⠀⠀⢠⠊⠀⡜⢠⠎⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠹⢿⣿⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⠠⠃⠀⡸⢀⠏⠀⠀⠀⠀⠀⣠⠞⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠈⡎⢆ ⠀⠀⠀⢀⠇⠀⠀⠀⢠⠃⠀⢰⢁⡎⠀⠀⠀⠀⣠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣇⠀⠀⠀⠀⠈ ⠀⠀⠀⡜⠀⠀⠀⢀⠇⠀⠀⡎⣼⠃⠀⠀⢠⠊⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⢀⡎⠀⠀⢠⢰⠇⠀⠀⡰⠃⠀⠀⠉⠉⠉⠹⡏⠑⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡇⠀⢻⠀⠀⠀⠀⠀ ⠀⡰⠧⢄⣀⠀⠈⠀⠀⠀⠈⡞⠀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⢀⠏⠀⣧⠀⣾⠀⠀⠀⠀⠀ ⣼⡁⠀⠀⠀⠉⠒⠤⣀⡀⠀⠇⢠⣀⣀⣽⣶⣷⣤⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠜⠀⠀⡉⢓⡾⡀⠀⢸⠀⠏⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣺⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠈⢇⠸⡄⠀⠀⠀⢀⣜⣠⠊⠀⡠⠊⢠⠎⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀ ⠙⡦⣄⡀⠀⠀⣀⣀⠤⠴⣾⣿⠃⣼⣿⣿⣿⣿⣿⡏⢹⠻⣷⡂⠘⡌⣇⠀⠀⢠⣾⠋⠁⣠⠞⢁⠔⠁⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀ ⡄⢧⠀⠈⡏⠉⠀⠀⠀⠀⢻⡟⢸⠁⠀⣾⣿⣿⡻⣷⣾⠀⠘⠇⠀⠘⢸⠀⣰⡿⣡⢴⣿⣿⣶⣿⣿⣿⣿⣦⣀⣀⣿⠀⠠⠀⠀⠀⠀⠀ ⠀⠸⡀⠀⢹⡀⠘⢆⠀⠀⠈⠏⢸⠀⠀⠙⠛⠋⠉⣼⡏⠀⠀⠀⠀⠀⠈⠋⠙⠉⠀⠘⣻⣿⣿⣿⣭⠀⠙⣿⣆⢠⠇⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⢇⠀⠸⣧⠀⠈⠢⡀⠀⠘⡄⠳⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡗⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈ ⣶⠤⣌⣆⠀⢻⣆⠀⠀⠙⢶⣦⣘⠄⠙⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠘⢿⡿⠉⡹⠁⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⠀⠀⠀⠘⣿⣧⡀⠀⠈⡇⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⢁⡴⠁⠀⡸⢋⡠⠒⠀⢀⡀⠀⠀⠀⠀⠀ ⢸⠉⢳⡄⠀⠀⠘⣿⠻⢦⣀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠯⠄⠐⢻⡟⠉⠀⢀⡠⠊⣀⠔⠛⠀⠀⠀ ⣘⡄⠀⡏⢦⣄⠀⠘⣄⠘⣿⡙⠺⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⠋⠀⠈⣻⣿⠖⠻⡋⠀⢈⣥⣤⣴ ⠛⡇⠀⠀⠀⣿⠉⠑⠻⡦⢼⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠋⠉⠙⣇⠀⠀⠘⢦⣿⣿⠋⠙ ⠀⢳⠀⠀⠀⠸⡆⠀⠀⢣⠀⢿⡀⠙⠳⢤⡀⠀⠀⠀⠀⠀⡅⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣇⠀⠀⢹⡀⠀⢶⣿⣿⡟⠁⠀ ⠀⠘⡆⠀⡇⠀⠉⠀⠀⠈⢇⠘⡏⠢⢄⡀⠉⠳⣤⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠃⠀⢿⡄⠀⠈⡷⠀⣾⣿⣿⠁⡀⠀ ⠀⠀⢹⡀⢸⡀⠀⠀⠀⠀⠈⢣⣱⡄⠀⠈⠲⣄⠈⢿⣷⣶⡤⠤⢤⡴⠒⠖⣶⣶⣿⠉⠉⢹⡀⠀⠀⠀⠘⡇⠀⠀⢳⢰⣿⣿⣿⠀⠁⠀ ⠂⠀⠀⢳⡀⢳⣄⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠑⢦⣿⡿⠃⠀⢈⣏⣠⡏⢀⠛⣿⣆⠀⠀⢇⠀⠀⢸⠂⠇⠀⠀⢸⣾⣿⣿⠃⠀⡄⠀ ⠀⠀⠀⠐⠻⠆⢫⡑⢤⡐⢤⣀⠀⠀⠙⠳⢤⣀⠀⠀⢻⡄⠀⠀⢸⢟⣽⠁⠀⠀⠀⣿⣧⡀⢸⣦⠀⢸⠀⢰⠀⠀⣸⣿⣿⡿⠠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠚⣳⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠞⠉⠀⠀⣠⣤⣄⣠⣤⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⡀⣀⣤⠊⣱⣾⣿⣿⣿⣿⣼⣿⣯⣓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠫⣴⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢈⠵⠒⠋⠉⠀⣠⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⠙⢦⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⠀⣀⡤⠒⢹⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢻⣿⣿⣄⠐⠻⣦⡀⠀⠀⠀⠀⣟⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣤⠴⠊⠁⠀⠐⡇⠀⠀⠀⠀⠀⠀⢀⡴⠻⣄⠀⠀⠈⠻⣿⣦⡀⠙⣷⡄⠀⠀⠀⢸⢙⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡸⢃⣠⣤⣀⡀⠀⠹⣸⡄⠀⣠⣀⠴⠋⠁⠂⠘⣆⠀⠀⢀⠹⣿⣯⡀⣿⣿⢀⢀⣰⣾⠜⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡇⠘⠉⠀⠉⠻⡆⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢦⡀⡇⠀⣿⣿⣿⣿⣿⣿⡾⢾⣅⢀⢿⠁ ⠀⠀⠀⠀⠀⠀⣠⠤⢖⠖⠉⣨⠃⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢴⠖⠒⠲⢦⡀⠀⢹⠃⠀⣿⣿⣿⣿⣿⣿⣿⡟⢻⢶⠏⠀ ⠀⠀⠀⠀⠀⠀⣈⠵⡻⠖⢢⠏⠀⠀⠀⠀⠀⠀⢸⠃⠀⠉⠉⠒⢄⡀⠀⠀⠀⠀⠈⠛⢀⡞⠀⢸⣿⣿⣿⣿⣿⣿⣏⣧⣿⡿⢦⡀ ⠀⠀⠀⠀⠀⠀⢿⣠⠟⠓⣾⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠠⠀⣠⠎⣠⣴⢿⣿⣿⣿⣿⣿⣧⢿⣿⢻⣁⡼⠃ ⠀⠀⠀⢀⣀⣠⣼⡁⡠⠚⣁⣼⣆⡀⠀⠀⠀⠀⠘⡄⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡀⣹⣛⣩⣾⣿⡟⣿⣿⣿⣿⣷⣿⠿⠛⠉⠀⠀ ⠀⠀⠀⣿⠀⢀⡤⡿⢡⡾⠉⠀⠈⢷⣖⠄⠀⠀⠀⠈⠂⠘⠁⠀⠀⠀⠀⠀⢠⣿⣍⣉⣩⡿⣻⣿⡿⢷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢻⣿⡅⠳⣎⠀⠀⠀⢀⣼⣿⣷⠦⣄⣀⡀⠀⠀⡀⠀⠀⠀⣀⡀⢾⣧⣩⣿⡿⡿⠛⢿⣿⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠷⣀⠈⠓⡤⢤⣾⣃⣼⣯⡄⠉⠉⣉⣳⣖⢒⣿⠿⣿⣿⣶⢾⠋⠁⣿⠀⢷⣤⣾⣿⣿⣏⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣽⣶⣿⣶⣲⢏⠛⠉⢿⣷⣄⢒⣿⡟⢿⣿⣿⣾⣿⣿⣧⣶⣶⣾⣿⡄⠘⠛⣿⡿⠋⠉⢉⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⢛⣉⣡⡆⠈⠛⢯⣝⡾⣜⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⡏⠁⠈⣿⣄⣠⠏⠈⠀⣀⠘⣆⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢩⣷⠿⠀⡀⡙⠲⠤⣄⣈⢻⣮⡙⠛⠿⠿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⢯⣠⠾⣡⠾⡒⠚⢁⡾⠀⠀⠀⠀⠀⠀ ⢠⡤⡴⠴⠚⠋⠳⡄⠈⣿⠀⠀⢰⠃⠀⠙⢷⣄⠀⠒⡟⠛⢿⣿⡟⣿⣿⣿⣿⣿⣿⣧⣼⣿⡛⠓⠒⠚⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⢏⠀⠀⠀⠀⠀⠀⠑⣤⣸⠀⠀⠘⠢⢄⣀⠀⠙⢷⣶⠟⣶⠛⣻⣧⣿⠈⣉⣿⣿⠓⢂⣴⠃⠙⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢦⠀⠀⠀⠀⣀⣤⠏⣾⡀⠀⠀⢀⡀⠀⠙⡄⠀⠀⠀⣿⣇⣩⣉⠉⠛⣻⣿⣧⡀⠀⠀⠀⢀⡇⠀⢠⢀⣄⡀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠋⠉⠉⠀⠀⠉⠀⠉⠒⢊⡿⠃⠀⠀⠹⡄⠀⠀⢀⡈⠉⠉⠉⠋⢻⠳⠼⠛⠛⣶⡾⢿⡀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⡄⠀⠈⠉⠉⢉⣙⣓⠦⠤⠤⣼⠀⠀⠀⠀⣸⡇⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠔⠊⢀⣀⡽⣼⠦⡞⠁⠀⠀⠀⠀⠛⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⠞⠛⠋⠀⢸⠓⠛⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⠖⠚⠛⠛⠿⠓⠒⠒⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⠟⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⣘⣋⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⢳⣄⢿⠀⠀⠀⠀⠀⠠⠟ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣶⣿⡿⠿⠿⣶⣦⡀⠀⠀⢰⣿⡷⠺⢿⣷⠆⠈⠛⠁⠠⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⠞⠓⠓⠶⠦⢤⣄⣀⣀⣀⣀⣀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠈⠻⣦⡄⢸⢿⠁⠀⠀⠈⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣸⠃⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⡁⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢆⡀⠀⡼⠀⠀⠀⣠⡾⠛⠻⠿⠿⠿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣧⠀⠀⠀⠀⠈⢿⡆⠀⠀⣀⣀⣀⣀⣤ ⠦⢬⣉⣐⣷⡶⠶⠟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣆⠀⠀⠀⠀⢸⣷⠀⠀⠙⣿⡿⠛⠛ ⠀⠀⠀⢨⡏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠈⣯⢷⣄⠀⠀⢠⣿⣀⣀⣠⣼⠟⠀⠀ ⠀⠀⠀⢸⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢳⠿⣷⣝⠷⡤⢾⡿⣿⡟⢺⣿⠀⠀⠀ ⠂⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⣿⣿⣿⣯⣳⣸⣧⠈⠁⢰⣿⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢹⡿⣿⢯⣍⠉⡟⠀⠀⢈⡇⠀⠀⠀ ⣶⡆⠠⢰⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣜⢧⡀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⡇⡇⠈⠹⢿⠁⣠⣼⣿⠀⠀⠀⠀ ⠿⠷⠠⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⡼⣷⡇⠀⠀⠀⠀⠀⠀⣇⠸⡏⠳⢽⣦⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⡇⣧⣤⣴⣾⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣸⡟⠀⢿⢇⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣹⠿⣦⣀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢰⠟⠀⠀⠘⣼⠀⠀⠀⠀⠀⣠⡿⡇⣧⡴⠛⠁⠀⠀⠉⠃⢈⣇⣆⠀⠀⠀⠀⠀⠀⣏⣁⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣠⠟⢦⣄⠀⠀⣿⡀⠀⠀⠀⢈⣿⠏⠻⠅⣀⡤⠖⣢⣤⣶⣾⣿⢿⣿⠀⠀⠀⠀⠈⡇⣿⠁⣠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠋⢀⣀⡀⠉⠉⢻⣷⠀⠀⠀⢸⡟⠀⠂⠀⣻⣾⣿⠟⠋⠉⠉⠻⣶⣿⠀⠀⠀⠀⠀⣱⣿⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣾⠄⡀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣷⣾⣿⣯⣭⣿⡆⠀⠹⠟⠀⠀⠀⠈⠉⢿⡿⡬⣧⡄⠀⠀⠘⡟⢰⡄⠀⠀⢸⣽⣿⡾⠿⣿⣿⡿⠷⠦⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⠀⢳⠀⠀⠀⠀⠀⠀⣿⠉⢹⣏⡀⠀⡄⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠀⠀⠀⢰⣧⡟⡇⠀⢠⢿⡿⣿⠉⠀⠀⠀⠉⠉⠲⠦⣌⡉⠓⢦⣄⠀ ⠀⠀⠀⠀⠀⠹⡦⣿⡔⣿⡆⠐⡄⠀⠀⠀⠸⡄⠀⢿⣿⣃⣙⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠿⢻⢡⣇⠴⠋⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡘⢷ ⠀⠀⠀⠀⠀⠀⠙⠃⣷⣯⣻⣄⢻⡄⠀⠀⠹⣿⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡟⠁⠀⠀⠀⠀⠟⣿⣳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠈⢻⣷⣟⣦⣤⣀⣘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠤⠤⠤⠤⠄⠀⠀⠠⠀⠀⠀⠀⢻⣽⠙⠉⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⠤⠖⠋⠁⠀⠀⠀⣀⣤⢞⣿⣿⡟⠀⢀⡀⣀⣀⣴⠿⠟⠛⠛⠛⠛⠲⣖⢾⣽⣆⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⠀⠀⠀⠀⠀⢩⣻⡶⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣾⠋⠀⠘⢿⣿⣡⡴⠞⣋⣭⠥⣰⠶⢖⣲⣶⠯⠿⢛⢛⠛⣿⣿⣀⡴⠋⠀ ⠠⠀⠄⠀⠀⠀⠀⠀⠀⣤⠞⠁⢀⡿⠀⠀⠀⠀⠀⢸⣿⠹⣾⣆⠀⠉⢿⣿⣿⠿⣿⣿⣿⡿⠋⢠⡾⠑⠀⣢⣾⣿⡽⠖⣛⠉⣀⡤⢶⣺⡭⠿⠒⠋⠉⠉⠉⠉⠁⣿⡿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⠀⣠⣿⠷⠶⠚⠉⠉⠉⠉⠉⠉⠉⠙⠓⠶⢷⣎⣀⠀⠈⠙⢿⣤⡶⠋⢠⣴⣿⣿⣏⣴⣿⡿⠟⣩⡵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣫⠶⠋⢁⣀⡶⢖⣁⣀⣀⣀⣈⣩⣍⣉⣉⣽⡟⣶⣤⣉⠻⢦⡤⠶⠞⣻⣾⣿⣿⡿⣿⡿⣟⡥⠖⠉⠁⠀⠀⠀⠀⣀⢀⡀⣰⣴⣿⡅⢠⣿⣷⣄⠀⢸⡆⠀ ⣀⠀⠀⡀⠀⠀⢸⠃⡇⢠⣾⠿⠾⠯⠽⠒⠒⠒⠒⠒⠢⠀⠀⠀⠉⠙⠛⠻⠿⢿⣷⣿⣦⣴⣿⣿⢋⣤⣾⠟⠛⠁⠀⠀⣠⢀⣀⣤⡼⣷⣿⡿⠿⠛⠋⠋⠀⠈⣿⣼⣊⠛⠀⢷⡀ ⠉⠀⠀⠁⠀⠀⠀⣴⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠉⠉⠉⣿⠉⠀⢀⣠⠴⣄⣴⣽⣟⢿⡿⠛⠉⣀⠀⣀⣀⡤⣧⣀⣰⣿⣿⣿⣷⣄⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣹⠀⠀⠈⣧⣴⡿⣿⠋⠉⣀⠰⣄⡶⢻⣼⣟⢿⡿⡋⠙⠛⢻⣿⣿⣿⣿⠇⢐

⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠀⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠁⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⡈⢁⣦⣄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠈ ⠀⠀⢀⠎⣠⣾⣇⠀⢀⠤⠒⠋⠙⠓⠒⠒⠚⡉⠀⠀⠑⠄⠀⠠⡎⠛⠻⡄⠀⠀ ⠀⠀⡌⢠⠋⠉⠉⠉⠁⡀⠀⠀⠀⠀⢰⠀⠀⠘⡄⠀⠀⠈⢢⡇⡀⠀⠀⢙⡀⠀ ⠤⠴⠧⠇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⡧⡀⠀⠘⡄⠀⠀⠀⠱⣣⠀⠀⣸⠇⠀ ⠀⢸⠘⠀⠀⠀⡎⢠⠃⡆⠀⠀⠀⠀⢸⣡⠊⠢⣄⢩⠀⠀⠀⠀⢋⠛⠛⠋⣰⠀ ⠀⠘⡇⠀⠀⠀⢇⠃⣡⣧⣆⠀⢠⡇⢞⡝⠋⠉⠻⣹⠆⠀⠀⠀⠸⢤⠤⣴⡇⠀ ⠀⠀⠇⠆⠀⠀⣿⢋⠋⠈⠹⢄⠄⠎⠀⢣⣄⠀⡠⢻⠀⠀⠀⣠⢃⣤⣾⠟⠁⠀ ⠀⠀⠰⣇⠀⠰⣉⠈⠤⣄⠔⠀⠀⠀⠀⠀⠀⠉⠁⣤⠀⡠⢘⡿⠿⠯⠥⢤⣀⡀ ⠀⠀⠀⠀⠑⠦⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠊⠀⠈⣟⢍⠐⠢⠀⠀⠙ ⠂⠀⠀⢀⠄⠂⠀⠘⡤⣀⠀⠀⠀⠑⠀⠀⠀⡀⡴⠁⠘⠀⠀⡌⢳⢄⠀⠀⠀⠀ ⠀⠀⢠⡡⠁⣰⡀⠀⠳⢩⠛⠿⣷⡆⠐⠈⠁⣠⣡⣇⠃⣠⡷⠗⣮⣆⢋⢶⠆⠀ ⠀⠀⠘⠤⢀⡑⠛⣢⣤⠷⠓⠂⣤⣉⣓⡶⠾⠿⠥⠾⡟⠉⠀⢠⣟⡟⠑⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⡑⡩⠛⠦⡄⠀⠁⠀⠀⠀⠀⠀⠀⣔⢳⠢⠀⣜⡏⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠰⢸⠀⠀⠂⠘⡄⠘⠒⠀⠀⠀⠉⡹⠅⠂⠁⣱⡟⠀⠀⠀⠀⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠄⠚⢉⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⡤⠔⣵⣿⣿⣷⣿⣷⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡢⠝⠚⠉⠉⠉⠙⠛⠿⣿⣿⡗⢄⡀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠜⣈⡠⠒⢨⠁⠀⠀⠀⢀⠄⠈⠻⣿⡄⠳⡄⠀⠀⡷⡀ ⠀⠀⠀⠀⠀⠀⠀⣜⢰⢡⠤⣀⠈⢴⢀⣄⠔⠃⠊⢆⠀⠈⢿⣄⣿⣄⣠⡧⣿ ⠀⠀⠀⠀⢀⠤⡄⢻⠃⠀⠀⠈⠁⠀⠀⠀⢠⠤⢤⡀⠱⠇⣼⣿⣿⣿⡽⣧⡎ ⠀⠀⠀⠀⡨⢚⣒⡇⠀⠀⠀⠸⠀⠈⠑⡀⠀⠀⠀⢉⠜⣠⣿⣿⣿⡿⣵⡿⢳ ⠀⠀⢀⡀⢼⡁⢐⡱⡀⠀⠀⠘⡀⠀⠐⠁⠀⠀⣀⣲⣺⣿⣿⣿⣿⣿⠿⠛⠁ ⠀⠀⠸⢤⡖⣵⠋⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⢠⡗⣦⣾⢿⣯⣻⣿⠇⠀⠀⠀ ⠀⠀⠀⠘⠧⡈⡲⢤⣯⣿⡇⢉⣱⣖⣶⣺⣿⠶⢉⣏⢰⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⡠⢖⣋⡝⠻⣦⣌⣿⣶⣿⣽⣿⣿⣿⡿⡟⠙⣆⡸⠋⢀⢪⢂⠀⠀⠀ ⠀⠀⣀⡸⢇⠠⡌⠒⡌⠻⣍⠙⢻⣿⣿⣿⣿⣿⣿⡟⣷⣖⣑⣏⡩⠌⠀⠀⠀ ⠰⡉⠀⠀⠈⢢⡁⠀⠣⠄⣈⠳⠾⣶⢻⣼⣉⣿⡟⠋⠏⢲⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠤⠄⠒⠣⠓⠤⣴⠆⠈⠄⠀⠙⠲⠦⠼⡿⡳⠤⡤⣞⠀⠐⠦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢂⠈⢉⠉⢥⠒⢠⠇⠀⢀⣇⣈⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠒⠊⠹⠃⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⡿⠃⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡷⢋⡠⠂⢀⠒⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢸⠁⡌⠀⡔⠙⢧⡇⠀⠀ ⠀⠀⠀⠀⠀⣰⠵⠁⠀⡀⠀⠀⡄⠀⢀⡄⠊⠁⠀⠀⠈⡆⠰⡀⠱⡄⢸⣳⣶⡀ ⠀⠀⠀⠀⣰⡻⠆⠀⠀⡴⢄⠀⡗⠊⠀⠈⠓⠄⠀⠀⠀⠙⢄⢰⠚⠉⣉⢿⠛⠁ ⠀⠀⠀⡰⢻⢀⠈⣆⡀⡇⠀⠑⠳⣂⠒⠄⡀⠀⠀⠀⠀⠀⢸⠉⠋⢣⡿⢞⡃⠖ ⠀⠀⡰⠁⢸⢸⣦⡇⠉⠁⠀⠀⡰⢛⡿⢿⣦⣅⠀⠀⠀⠀⢸⠂⠀⡠⠈⢧⠷⣬ ⡠⠊⠀⠀⢨⠘⢼⠇⠀⠀⠀⠀⠀⣼⢿⣔⡌⣟⢷⣤⡀⠀⣌⣠⢾⠂⠀⠈⠉⣇ ⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⢷⣀⣀⡵⠋⠀⣿⣄⠘⢈⠇⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⡡⠂⠀⠀⠀⠀⣠⢺⡝ ⠀⠀⠀⢸⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠀⡇⠾⢋ ⠀⠀⠀⠈⡾⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⣀⠀⢐⣡⢴⡏⠒⠋ ⠀⠀⠀⢀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠚⢻⣷⡶⠛⡫⠋⠝⡄⠀⠀ ⠀⠀⠀⠘⠀⢈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⣰⢿⣾⠀⡇⠀⠀ ⠛⢶⡤⠃⠀⠘⡏⠫⢝⣶⣶⣲⣤⣤⣤⣶⣶⣶⣿⠟⠁⢠⡎⠉⣾⣿⡆⠘⡀⠀ ⠄⠈⢿⡄⠀⠀⣧⡱⠤⠱⣉⡀⣻⡯⢿⡿⠋⢡⠊⢀⢔⠉⠐⣿⣿⣿⣷⠀⠀⠂

⠀⠀⡠⠊⠀⢀⠔⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣿⣦⣡⣀⣠⣾⣿⣿⣿ ⠀⡰⠁⠀⠀⡌⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣷⣽⣿⣿⣿⣾⣿ ⡐⠀⠀⠀⢸⠁⠀⢀⠜⢸⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠈⠚⠛⠛⠛⠛⢉⣾⣿⣿ ⠁⡘⠀⠀⣿⠀⣰⡋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡗⢄⠀⡀⠀⠀⠀⠐⣛⣿⣿⣿ ⢀⠃⢀⣀⡿⠞⠋⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⣇⣈⣣⡈⠁⠀⠉⠉⠀⠈⢿⣿ ⠉⠉⠀⠀⢀⠀⠀⢠⠞⠀⢇⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢳⡀⢸⡀⠀⡄⠀⢸⢿ ⢹⠢⡤⠖⠁⢀⠔⠁⠀⢠⢌⣎⡄⠀⠀⠀⠀⢸⣠⣰⣠⣤⣣⢸⢳⢠⠃⠀⡜⡼ ⣜⡋⡤⠴⢺⠁⣰⡾⠇⠘⠻⣏⢺⣄⠀⠈⠄⡄⠟⠉⠀⠉⠻⠋⢸⡎⠀⠰⢡⢁ ⠀⡽⡄⠀⠀⢣⠉⠀⠀⠀⠀⠀⠀⠙⠢⢤⣘⢇⠀⠀⠀⠀⠀⢀⡜⠀⡠⡣⠃⡎ ⠼⠠⠜⢦⡀⠳⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠮⢤⢞⠞⠁⡀⡇ ⠀⠀⠛⠁⠘⣵⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢗⠝⢆⢰⠉⠁ ⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠛⠒⠃⠀⠀⠀⠀ ⠀⠀⢠⣄⣀⣀⣀⣀⣀⢉⣳⣤⣀⡀⠀⠀⢀⣀⠤⠒⢹⢓⣚⣤⣴⣶⢲⣾⠇⠀ ⠀⠀⠀⠻⣾⢿⣿⣿⣶⣾⣿⣿⣿⠫⠓⢛⡩⢐⣠⢞⣭⣾⣿⣿⢿⣱⡿⠋⠀⠀

⠀⠀⢀⣿⣿⠃⢀⡆⠳⡄⠀⠀⠀⠀⣓⠦⠍⠻⣷⣤⣀⠀⢀⣀⢀⣄⣀⣶⣶⣤⣤⣶⣤⡘⣿⣿⣶⡄⠀⠀⠀⠀⠀⠙⡿⢄⠀⠀⠀⠀ ⠀⢠⣿⣿⠇⢀⣾⣿⡄⢹⠀⢠⣾⠟⠁⠀⠀⠀⠀⠉⠙⠲⠿⣿⡿⠿⠛⠛⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⡇⢸⣇⠀⠀⠀ ⣰⣿⣿⠋⢀⣾⣿⣿⣿⣼⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣦⠀⠀⠀⡇⢸⣿⡄⠀⠀ ⣿⡙⠁⣠⣾⣿⣿⣿⣿⡿⠁⢀⠄⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢿⣿⣿⣧⠀⠀⡇⢸⡏⡇⠀⠀ ⣿⣷⣤⣴⣿⣿⣿⣿⣿⠀⡴⠃⠀⠀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠙⣿⣿⣧⠀⢀⠘⡇⠃⠀⠀ ⠿⠿⠿⠿⠿⠛⠋⢡⢿⠟⠀⠀⠀⡜⠀⡜⡰⠁⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠻⣿⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡌⠀⡸⡰⠁⠀⠀⠀⣠⠞⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⢻⢣⠨⡀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡜⠀⢰⢡⠇⠀⠀⡠⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣹⠀⠀⠘⡈⢯⠙⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡸⠀⠀⡎⡟⠀⢀⡜⠁⠀⠀⠐⢺⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⣼⠀⠀⠀⠇⢸⣀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠮⣄⡀⠀⠀⠀⠀⢹⠁⠠⢎⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡎⢸⡀⣿⠀⢀⠄⠀⠈⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⡯⠀⠀⠈⠑⠢⠤⣀⡇⢠⣤⣬⣷⣶⣤⡀⠀⠀⢇⠀⡀⠀⠀⠀⢠⠃⡜⠁⣈⢑⡾⢄⠀⡇⡏⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀ ⣠⣤⣴⡖⠻⣇⠀⠀⠀⠀⠀⠀⢀⣩⡽⣿⣿⣿⣿⣿⢿⣷⡄⠘⡄⡇⠀⠀⣠⡧⠈⢀⠜⢁⠎⠀⠀⠀⣷⠀⢠⠇⠀⠀⠀⠃⠀⠀⠀⠀ ⣿⣿⣿⠛⢆⢸⠙⠢⡄⠒⠒⠉⠹⣿⢁⠛⢛⣿⣿⣿⣤⡏⢻⡀⠹⢹⠀⣴⠟⣠⣶⣯⣴⣧⣤⣄⠀⢠⡏⢀⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⡿⢄⠻⡆⠈⠃⡇⠀⢇⠀⢄⠀⠀⢿⢸⠀⠘⠿⠟⢠⣿⠀⠀⠀⠀⠘⠛⠛⠉⠸⣿⣿⣿⡏⠙⣿⣏⣹⢁⠞⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀ ⡹⢻⠓⣌⡒⠄⢰⠀⢸⡄⠈⢢⡀⠈⢆⢣⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⡿⣿⠇⢸⣿⠃⠋⠀⢀⠇⠀⡌⠀⠀⠀⠀⠀⠀ ⣷⠶⡆⣄⡈⣗⠒⠃⠈⣿⡄⠀⠙⡧⢤⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠛⢁⠎⠀⣾⠃⡀⠀⠀⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⡿⠻⡿⢦⠀⠀⠸⣿⢦⡀⠹⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣴⡋⢠⣴⠷⠊⠀⡠⠊⣠⢮⠑⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡖⣃⠀⠷⣄⠀⠹⡄⢹⡶⢽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢴⣮⠴⡞⠓⢂⣶⣿⣥⣤⣤⣤⣤⣤ ⠀⠀⢀⣏⠝⢻⠀⠀⠸⡏⠒⠻⠼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠉⠉⢲⡖⠈⠹⡇⠀⠙⣴⣿⡟⠛⠛⠉⠛⠋⠉⠛ ⠀⠀⠟⠁⠀⠘⡆⠀⠀⠱⠀⠀⢅⢹⣄⠉⠳⢄⡀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⢀⡾⢳⠀⠀⢣⠀⢰⣿⣿⠉⠀⠀⠉⢀⠀⠁⣠ ⢄⠀⠀⠀⠀⠀⢳⠀⡆⠀⠀⠀⠘⣄⢫⠙⠢⢄⠙⢶⣤⣀⠀⠀⠀⢀⣀⣀⣠⠤⢤⡖⠉⠀⠘⡇⠀⢸⠠⣼⣿⡇⠠⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠈⢆⠸⣄⠀⠀⠀⠈⢻⣆⠀⠈⠑⢄⣹⣿⠉⠈⣿⢀⠄⠹⢿⡄⠀⢣⠀⠀⠀⢣⠀⠀⣷⣿⣿⠃⠀⠐⠀⠀⠐⠀⣼⡿ ⠀⠀⠀⠀⡀⠀⠀⠈⠳⣽⡳⣄⣠⣀⠀⠉⠳⢤⣀⠀⢹⣅⠀⢀⣿⣿⠀⠀⠈⣿⣄⠘⡄⠀⡆⢸⠀⠀⣿⣿⡯⠄⠀⠀⠀⠀⠠⣰⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡹⠿⠓⠊⠉⠁⠀⠈⠢⠸⠀⠒⠂⠄⡀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠴⠊⣡⠔⠂⠀⠀⠀⠀⠀⠀⠀⠊⠱⡀⠀⠀⠈⠲⡶⠶⠿⢄ ⠀⠀⠀⠀⠀⢀⠊⠀⡰⠁⠀⢠⠂⢠⠂⠀⠀⠠⠁⠀⠀⢡⠀⠀⠀⠀⠘⣿⠶⠶ ⠀⠀⠀⠀⢀⠂⠀⠠⠁⠀⢀⠃⠀⠞⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠈⠀⢱⣤⣄ ⠀⠀⠀⠄⠁⠀⢀⠃⠀⣠⣊⠀⠘⠡⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬ ⣀⠀⡠⠢⠀⠀⡌⠀⡸⠁⡇⠈⠈⡘⡗⡀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠠⢡⠁⠀⢀⣀⣢⣥⡔⠇⠀⠀⢡⠐⢌⢢⣁⣿⠉⠢⣰⠀⠀⠀⠀⠀⠀⠀⠈ ⢠⠑⡇⠀⠀⠀⡌⡇⡾⣿⡎⢧⠀⢀⡵⡴⣷⣬⣻⡀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠐ ⢺⠀⡇⠀⢸⡀⢳⠁⠐⠘⣰⣀⣕⠅⠊⢰⢻⢷⣿⣯⡌⠀⠀⡠⠀⠀⡀⠀⢃⠀ ⠀⢡⢣⡄⢸⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⢊⠌⠀⠀⡐⠁⡀⠠⠣⣄⠈⢂ ⠀⠘⢹⣷⡌⡏⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠠⠊⠀⡐⢡⠃⠀⠱⡁⡂ ⠀⢰⢸⡟⢹⣿⠢⠈⠠⡀⠀⠀⠀⠀⠠⠔⣡⠴⠊⢀⢄⣠⢎⠀⢁⡶⠀⠀⠈⠃ ⢀⠸⠤⠯⠾⡇⡆⠀⠀⠈⢤⣀⣀⡠⢰⡺⠓⠂⠊⢌⡪⠒⡃⠄⣾⡥⠤⡠⠂⠀ ⠂⠀⠀⠀⠀⠈⢳⠄⢀⣤⡻⢿⣿⢡⡏⠀⡆⢀⠠⢺⣣⠾⠿⣦⣤⣤⠎⣔⣁⡀ ⠀⠂⠀⠐⠂⠘⠃⠴⢱⠃⡠⠔⢣⠳⠀⣼⠖⠁⠀⢸⡿⣾⡿⣹⢿⡏⣼⡾⢛⣁

⠀⠀⠠⡗⠁⠀⠀⣠⣴⠭⠐⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⣻⣿⣶⢿⠀⠀ ⠀⢀⣀⠎⠀⠠⠊⠈⡠⠒⡠⠊⠀⠀⠀⠀⠀⠀⡀⢀⣠⠖⠋⠀⠈⢻⣾⠀⠀ ⠀⠀⠀⢀⠔⠁⡠⠊⢀⠔⠠⠊⠀⠀⠀⠀⡠⢊⠔⠁⠀⠀⢀⣠⠴⠀⢻⠀⠀ ⠠⠄⠂⢁⡠⠊⠀⠠⠂⡐⠁⠀⠀⠀⡠⠊⠐⠉⠁⠀⠀⠀⠁⣰⡇⠀⢸⠀⠀ ⠀⠀⠀⡔⠀⠀⡐⡡⠎⠀⠄⡀⢀⠞⠡⠊⠀⢀⠔⠒⠒⡠⣒⠉⡇⣀⢸⠀⠀ ⠀⠀⡼⠀⢀⡔⠊⠀⠀⠀⠀⢀⠊⣰⠁⡀⢠⠡⠄⠢⠅⡀⠈⠓⠏⠐⣸⠀⠀ ⠀⢰⡇⢰⠀⠈⠂⢄⡀⠀⠀⠂⡜⢹⢠⢳⡇⠐⢚⣿⠿⣮⡢⣸⠠⢨⣸⠀⠀ ⠀⢼⢇⠚⠀⠀⡇⣧⡏⠐⠠⠌⠀⠈⠺⡀⠁⢀⠊⢹⢅⡄⠹⣯⣢⣑⣻⠀⠀ ⠦⣄⡋⠉⢻⠀⢰⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡀⢂⠜⢻⣦⣀⠜⠂⠒ ⠀⠀⠉⠢⢼⣦⠀⡏⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢈⡠⠂⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠢⣟⡜⢯⡉⠀⠀⠀⢀⠀⠀⠉⠓⣒⠲⠚⠁⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣜⣄⣀⣀⣈⣑⣍⡉⠀⠀⠀⣀⠠⠊⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣫⠠⣀⣸⣾⣾⠟⠋⡩⠟⠃⠀⢀⠔⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣀⡀⠘⣍⠑⣟⠀⢸⣭⣇⣓⣂⣁⣀⢤⣴⡾⠓⠀⢤⢧⠀⠀⠀ ⠀⠀⠀⣦⠵⠦⢄⠀⠳⡄⠸⣿⢿⣿⡿⢺⠧⠃⠠⠃⢸⠀⠀⠀⠸⣯⣱⠀⠊

⠼⣷⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠸⡆⠀⠐⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠹⣠⡰⡾⡋⠀⠀⢀⠔⠀⠐⠈⠠⠈⠁⡊⠳⡄⠈⠀⠐⠄⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⣳⠛⠁⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⢆⠀⠠⠈⢂⠀⠀⠀⠀⠀ ⠀⠀⠰⡇⠠⠊⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠂⠀⢃⠀⢂⠀⠀⠀⠀ ⠀⠀⠀⣷⠃⢀⡠⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣇⢀⠈⡔⠀⠀⠆⠈⡄⠀⠀⠀ ⠀⠀⠚⠁⢹⠁⣧⠁⠀⠌⠀⡜⠀⠀⢠⡐⠀⠀⡹⢦⠆⠘⡆⠀⠀⠀⠰⠀⠀⠀ ⠀⠰⢧⠀⢨⠀⡇⠀⠌⡱⢮⡁⡀⢠⡧⠁⢤⡴⠔⠉⢊⠄⢱⠀⠀⠀⠀⠆⠀⠀ ⠀⠀⠘⠈⡞⠀⡇⡜⠊⣀⢊⣀⡀⠝⢁⠄⠈⣤⣤⣄⣌⢎⣄⠀⠘⠀⡆⠀⠀⠀ ⠀⠀⠀⢠⠠⠀⢨⣒⡾⣯⣽⣿⠻⠉⠀⠀⠐⢻⣿⣶⡏⢳⣅⣄⠃⠀⣇⠀⠡⡀ ⡀⠀⠀⠸⠀⠀⠈⣏⠂⠱⣚⡣⠀⡄⠀⠀⠀⠈⠿⠥⠂⡙⡼⠂⢀⠀⡟⢦⠀⠉ ⠃⠀⢀⢠⡧⡰⡀⡈⠢⢀⡀⣀⣤⠰⣶⠈⠉⠉⠀⠒⠒⠏⣀⡐⠇⢀⣷⠄⠑⡄ ⠀⠀⠮⡜⠰⠀⣷⡬⣉⡩⠊⠀⣿⡆⠹⣇⠀⠀⠀⠀⠀⠀⠀⠙⢮⡎⠑⠄⠑⢔ ⠒⠲⢶⡲⠀⠡⠹⣿⣿⣄⣀⣀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⢆⠀

⠛⠛⠛⠛⠛⠛⠛⠛⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⣀⣤⣶⠞⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⡆⠀⠀⠀⠀⠼ ⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⠿⠿⠶⣄⠀⠀⢰⣿⠿⢷⡾⠀⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⣀⡴⠞⠉⠉⠛⠒⠶⠤⠤⣤⣤⠶⠛⠉⠀⠀⠀⠀⠈⠳⣆⣸⣇⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀ ⢦⠀⠀⣺⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣳⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⢀ ⢄⣙⣀⣧⣴⠶⡾⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢸⡇⠀⠸⣶⠾⠿ ⠀⠀⢀⡏⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣿⣧⡀⠀⢸⣇⣠⣤⡾⠃⠀ ⠀⠀⢸⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⣿⣷⣽⣖⣻⡛⠟⠙⡇⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⣿⣿⣛⠛⡇⠀⠘⡇⠀⠀ ⣦⡄⠀⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⠀⠘⣿⡁⠙⢾⢀⣰⣿⠁⠀⠀ ⠛⠃⠀⣧⡇⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣾⠟⡇⠀⠀⠀⠀⠘⡆⡏⠙⢿⣦⡀⠀⢱⠀⠀⠀⠀⠀⠈⣧⠀⣿⣷⣶⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠃⠀⢿⠀⠀⠀⠀⢀⣷⡇⢀⡴⠋⠙⠦⠈⡇⡀⠀⠀⠀⠀⢻⠒⠛⢻⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⢧⡀⠀⢸⡆⠀⠀⠀⣾⠿⠟⢁⡠⢀⣀⣤⣶⣿⡟⠀⠀⠀⠰⢸⠃⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣇⡰⠁⣀⢀⣉⣙⣷⠀⠀⣰⡏⠐⠀⣹⣿⡟⡋⠉⠙⢷⡇⠀⠀⠀⢀⣿⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⠃⡄⠀⠀⠀⠀⢿⠿⣿⠿⠿⠷⣶⡾⠂⠀⠋⠀⠀⠀⠀⢻⣗⠓⠆⠀⠈⣇⣴⠀⠀⣾⣿⡟⠛⠻⠿⣙⡒⠦⢤⣀⠀⠀ ⠀⠀⠀⠀⢧⢸⣇⣧⠀⡀⠀⠀⠸⡄⢹⣶⠄⢶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⣼⢿⣻⣀⠜⠉⢹⡄⠀⠀⠀⠀⠈⠑⠢⣌⠑⢤ ⠀⠀⠀⠀⠈⠻⣿⣟⣦⠹⡄⠀⠘⣷⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠘⢷⡦⣄⠀⠀⠀⠀⠀⠀⠙⣮ ⠀⠀⠀⠀⠀⠀⠈⠃⠉⢿⣿⣶⣄⣈⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡤⠂⠀⠀⠀⣀⣴⣿⠁⠀⠀⠀⢸⣿⣿⣷⣄⡀⠀⢀⡀⠀⠀⡽ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠉⠓⢦⣀⡀⠀⠀⠀⠀⠉⠑⠉⠁⠀⢀⣠⡴⠚⢻⣿⠇⣀⡤⠴⢒⣛⣉⣁⣠⣤⣽⣿⣿⣷⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⡇⠀⠀⠀⠀⣿⡷⣽⡉⠛⣶⣶⣶⣶⣶⣶⠞⢩⠿⠀⣠⣼⣿⡯⠗⠚⣉⣤⣽⡶⠯⠙⠓⠒⠒⢸⣿⣟⠁⠀ ⠀⠀⠀⠀⠀⢀⣞⡅⣠⡾⠷⠒⠂⠀⠈⣉⣁⣙⣓⠒⠿⣇⡀⠈⠛⢧⣔⢋⣤⣾⣿⣽⣷⠿⣛⠿⠓⠉⠀⠀⠀⠀⠀⠀⠀⡟⠛⠻⡄⠀ ⠀⠀⠀⠀⠀⣿⡿⠋⣡⣤⣾⣥⣤⣤⣤⡔⠢⠤⠼⣿⣷⣶⣭⣶⣖⠈⣹⣿⠟⢿⣿⡿⠗⠋⠀⠀⠀⢠⢠⣤⣤⣶⣿⠆⢸⡿⣶⣄⢧⠀ ⠆⠀⠀⠀⠀⢋⣧⠜⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢙⣿⡿⠿⠟⠻⡾⠛⠁⣀⡀⣀⣶⣶⣾⠿⠛⠋⠉⢀⣤⠀⣸⣿⣷⣄⠘⢦ ⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⢀⡇⠀⠘⣧⡿⣿⠋⢉⠠⣀⠾⣶⡿⣿⠟⠛⠻⣿⣿⣿⡧⠀

⠈⢃⠢⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⣤⣤⣧⣦⣤⣄⡀⠀⠀⠀⠀⢢⠀⠀⠐⡄ ⠀⠀⡆⠀⣇⠀⠀⢈⣷⣶⡿⣟⣷⣻⣞⡶⣟⡶⣭⣟⠷⣦⣀⣠⠂⠀⢀⢠⠓ ⠀⠀⠤⣀⢸⡴⠾⣟⣿⢾⣽⣻⣞⡷⣯⣿⣽⣿⣿⣿⡿⢟⣋⣁⡀⡌⣀⠊⠈ ⠀⠀⠈⣶⠋⡐⠆⣹⣾⣟⣾⠷⠛⠋⠉⠉⠉⠉⠉⣉⠙⠳⢾⣶⣿⡎⠁⠀⠀ ⠀⠀⢰⡇⠤⢁⣾⣯⡿⠋⠀⠀⠀⠈⡜⠀⠀⠀⠀⠈⢧⡀⠀⠉⠻⣷⠀⠀⠀ ⠀⠀⠘⣷⣮⣽⣻⡟⠀⠀⠀⢀⡟⠀⡇⠀⠀⠈⠀⠀⠈⣷⢆⠀⠀⠘⢧⠀⠀ ⠀⠀⠀⣿⣟⣿⣿⠀⠀⡀⠀⣾⣠⢐⡥⠖⠋⡀⠡⠀⠚⡿⣜⡆⠠⠀⢌⣧⠀ ⠀⠀⠀⠸⣿⣿⣿⡀⠀⡀⢰⡟⠁⣩⣾⣧⣶⠀⠁⢨⣤⣏⢸⡇⢀⠁⢸⣿⠀ ⠀⠀⠀⠀⢻⣿⡽⣶⡄⠀⢸⣿⡿⢹⣿⣧⡏⠑⢤⣸⣿⣿⢷⡇⢀⠊⣼⠏⠀ ⠀⠀⠀⣠⠾⢶⣦⣤⣿⣦⣌⣉⠓⠚⠯⠿⠃⠀⠀⢻⣿⠏⣾⣓⣤⡾⠃⠀⠀ ⠀⣰⠞⣁⣼⠯⣼⡉⠑⠶⡮⣍⠁⠀⠀⢸⡟⣳⡶⠀⠀⠈⣻⠏⠻⣆⠀⠀⠀ ⣴⠋⠐⣾⢣⢏⡖⣷⡀⠄⠙⠪⣟⡷⢶⣦⣯⣭⣤⣴⠖⡻⣝⡆⠡⠈⢷⡀⠀ ⡣⢸⠰⣧⢋⡞⣼⣿⣷⣌⠀⣥⠞⠀⢐⣾⡏⢭⠙⣾⣔⠀⠜⣿⠀⡄⣧⡧⠀ ⠀⠲⠾⢧⣯⡜⣿⣿⣿⣿⠿⣿⣿⣶⣷⠿⣌⣒⣼⢾⣷⣶⣶⣾⣆⡼⠃⠀⠀ ⠀⠀⠀⠀⠈⢛⣿⣿⣿⡇⠀⠀⠀⠉⢻⣶⡟⠹⣷⣎⠉⠉⠉⠉⢻⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡢⡀⠀⠈⠆⢀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠛⢕⢄⠀⠸⡇⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⡀⢠⠃⡄⠀⠀⠀⣀⣀⣤⠖⡊⡙⠀⠀⠀⠑⢕⠀⢫⡻⣦⡀ ⠀⠀⠀⠀⠀⠀⣰⢠⠃⢀⢼⡀⠐⠀⢠⠇⠀⢠⣱⠁⣀⣀⡀⡠⠀⠁⢺⠈⠐⠂ ⠀⠀⠆⠀⠀⢩⡷⠉⠁⠁⠈⡇⡄⢠⡿⠀⠀⡰⣳⣿⣿⣿⣟⢳⢶⣥⣼⠀⠀⠀ ⠀⡷⠀⠀⢠⠋⠀⣠⣤⣐⡀⡧⢀⢏⠂⡠⠊⠀⠉⠸⣻⢯⡷⠲⡇⣻⡍⡀⠀⠀ ⠘⡘⢄⡠⠓⣲⣾⣿⣿⣭⡿⠔⠡⠆⠊⠀⠀⠀⠀⠀⠪⣒⡠⠐⡩⢫⠝⠀⡄⠀ ⠀⠰⣢⢁⣼⡟⢹⡋⣏⡗⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⡺⠁⣠⢾⠳⠀ ⠄⠀⠘⢏⠙⠷⡈⠁⡈⢀⡠⠁⢀⠒⡄⠀⠀⠀⠀⠀⠀⠀⢸⡚⠈⡿⠃⢠⡲⢇ ⠈⠢⣀⠀⠳⡢⠍⢉⡐⠂⠀⢀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡰⠁⠀⣆⡯⣹ ⡀⠠⡈⠛⠔⠢⡵⡂⠁⠁⠒⠁⠀⡄⣠⠂⡁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡏⠉⠈ ⡧⡄⠙⢦⡄⢀⣀⢑⣭⣒⠖⠦⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⠀⠀⠀ ⣷⠶⠢⠈⣻⡢⡈⡤⠐⠈⠉⠐⠺⡗⡀⠀⠀⠀⠀⠀⠀⣰⣹⠀⢸⠉⠘⠹⠀⠀ ⠸⠀⠀⠀⢸⠀⣿⠁⠠⠤⠀⣀⠀⠐⣷⣀⣀⠀⠀⠠⠲⡟⡿⢋⠉⠢⠀⠀⢆⠀ ⠀⠀⢀⢴⡷⠋⠀⠀⠀⠀⠀⠀⠈⠢⡿⠂⠀⠀⠀⠀⠀⠃⡿⠊⠀⡠⠔⠈⠁⠀

⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣶⣤⣄ ⠉⢹⠛⠛⠉⠁⡄⢘⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠉⠛ ⠀⡎⢸⠀⠀⢰⠀⡜⢧⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀ ⢠⣇⢘⠀⢀⣸⢴⠥⠬⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢱⡀⢰ ⡎⢹⢸⠈⠁⢸⡞⠀⠀⠈⢦⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠧⢴⢁⡀⢳⡀ ⠃⠈⢿⣤⣤⣼⣷⣒⣂⠤⠀⠳⣼⡘⣆⠀⠀⠀⠀⠀⠀⠀⢀⢾⢠⠇⠀⠈⠐⢳ ⣲⣾⠿⣿⠿⢿⣿⣿⠛⡿⢷⠀⠈⠓⠼⣆⠀⠀⠀⠀⢀⡴⢧⣶⣾⣶⣤⠄⠀⠀ ⠫⠵⠚⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠘⡄⣀⡠⠖⠛⢻⣿⣿⣿⣿⣛⡿⢿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠤⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡤⢄⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣤⢙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⢿⣿⣻⣻⣟⣿⣟⡻⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⡿⢿⡛⣷⡿⣶⣭⣛⠽⢛⠷⡻⢿⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣟⡹⢣⡿⠛⣤⣹⣷⢫⡟⢯⣛⡵⣫⢽⣻⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⣀⣴⣶⣶⣦⣶⣿⣿⢿⣿⣽⣿⣳⢯⡷⣿⣧⣵⣾⣿⣾⣷⣯⣷⣽⣚⣵⢫⢶⣹⢿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀ ⣤⣾⠿⣡⣯⣽⣿⣿⣿⣿⣿⣿⣿⣳⣯⣿⣽⣿⣿⣿⢿⣟⣯⣿⡽⣯⣟⣿⣻⣿⣾⡏⡜⣧⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⣿⠃⣰⣿⢯⣿⣿⣻⣿⢿⣯⣿⣟⣿⣿⣿⣿⣿⣽⣾⣿⣻⣽⡾⠿⢛⡋⢭⡉⣍⠛⢿⡔⢻⡥⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⣿⣏⡯⣿⢿⣽⣿⡿⣟⣯⣿⣿⣿⣿⣿⣿⡿⢟⢫⡑⣆⣶⣭⠶⢟⡋⠁⢀⠀⠀⢻⣏⢷⣦⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡾⣿⣟⣯⣿⣟⣿⣿⣿⣿⡿⡿⣛⢫⣱⡼⡼⠶⠛⠉⠁⠀⠀⠀⠛⢶⣄⠈⠀⠀⠹⣮⢷⡓⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠀⠈⢿⣽⡿⣾⣟⣿⣿⡿⢏⣶⠋⠑⠉⠀⣿⡀⠀⠀⠀⡀⠀⠀⠁⠀⢂⠀⣉⢷⣥⠀⠀⠈⢷⣯⢱⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣧⣄⠀⠙⠻⠿⠿⢛⣫⡴⢣⠇⠀⡘⠀⢸⡏⢷⡀⠀⠂⠀⠐⠀⠂⢠⣴⢛⣉⣦⣹⣧⠀⠡⠀⠹⣯⣿⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠿⣾⣷⣧⣾⣧⣿⠑⡧⠀⡐⠈⣄⣿⣀⠠⢿⣶⣄⡀⠌⢀⠐⣼⣧⣾⣿⣿⣿⢿⡄⠠⠀⣿⡏⠛⠻⠾⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⡈⢷⠀⠀⠈⣿⡇⠀⢰⣶⣶⣿⣿⣶⣷⣶⣿⠀⢿⣿⡿⣿⠉⣇⡇⢰⣿⡿⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⣿⢿⣟⣿⡔⣫⡄⠀⠀⢹⣿⣾⣿⣿⣿⣽⡇⠀⠀⠁⠀⠀⠈⠁⠄⢀⢐⣼⣇⡾⠻⡿⠟⠿⢿⣛⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⢼⣧⠀⠡⡈⠻⣿⡘⠿⠛⣻⠃⠀⠀⠀⠀⠁⠀⠀⠌⠀⢘⣿⡟⠁⠀⠸⡀⠀⠄⠉⠳⢯⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣻⣿⠟⠤⣋⠿⣷⡀⠹⢦⣝⢿⣂⡉⠁⠀⠠⠀⠄⠠⠐⠀⠀⠀⢠⣾⣿⠃⠀⢈⠁⠆⡀⠀⠄⠀⠀⠙⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢿⠟⡡⢎⡱⣜⣮⣿⣿⡿⢯⣭⣿⣭⣓⣤⣀⠀⠀⠀⠀⠀⢀⣠⡾⣿⣿⣟⡶⣿⣻⣶⣧⠰⠄⠒⠈⢓⡀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣯⣼⣵⣿⣿⣿⢟⢯⡿⣗⢈⠒⢮⢼⡿⣙⠻⢟⡿⢿⣟⣿⡻⣍⣣⣽⣿⣭⣷⣿⣯⠿⠃⠀⠀⠒⠠⢀⢹⣾⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⢫⡕⢺⢎⢿⡹⢄⠂⢀⣬⣿⢿⣿⢾⣵⣾⠾⠟⠛⠉⠉⠀⠀⢈⣉⣅⠀⠀⣶⣿⡇⠀⠁⠄⠀⢿⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⢣⠳⡈⢿⡘⢾⣿⣼⣾⣿⣯⣿⣧⣿⣿⠃⠀⡀⠀⣬⣥⣄⠐⠀⠸⣿⣿⣷⣤⢹⣿⣷⡀⠈⠐⡀⠈⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣟⣾⡿⢡⠂⢥⡿⠛⠛⠉⠁⠈⠻⣿⢻⣛⣻⣧⣤⠀⠀⢈⣿⣿⣿⣦⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⠐⠠⠀⠘⠆⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⢧⡇⢣⡉⠌⣿⠀⠀⠌⡐⢀⠀⢿⣿⣿⠟⣿⣿⡇⠀⢸⣿⣿⢻⣿⣷⡄⠘⣿⣿⡄⠛⢿⣿⣿⠄⠈⠠⠁⠀⠸⠆⠀ ⠀⠀⠀⠀⠀⣿⣾⡲⡝⣦⡱⠨⣼⣇⠀⠐⠀⠄⠀⠘⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡿⣿⣿⣦⣿⠿⠟⠂⠀⠉⠀⠀⠠⠁⠈⠄⠀⠹⣆ ⠀⠀⠀⠀⠀⢹⣾⡷⣯⣽⣏⢷⣪⣿⣀⠈⠄⠂⠀⡀⣹⣿⣷⣤⣿⣿⡇⢸⣿⣿⡁⠀⠉⠉⠀⠁⠀⣄⠠⡄⠀⠠⠐⠀⠀⠁⡀⠠⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠋⠀⣈⡉⠩⠉⠉⠉⠉⠛⠀⠀⠀⣄⣀⠀⠀⠈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢤⣤⣤⠤⢤⡤⣤⠤⠤⠤⣦⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠩⠖⢧⡤⠤⣌⠑⠦⣤⣤⣤⣤⠤⣤⡤⣤⡤⠄⠀ ⠀⠀⠀⠀⠀⠙⣷⡖⣻⡀⠉⠁⣠⠖⠉⠉⠑⠢⢦⣠⣶⣾⣭⣿⣿⣿⣿⣯⣵⡦⡤⣤⣀⠀⠈⠲⡺⢦⠈⢎⠻⢿⣍⠀⢀⣹⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣷⣉⠁⢠⠞⠁⠀⠀⢀⣤⠞⠋⠁⠀⠉⠙⠛⠛⣛⠛⠙⠉⠉⠉⠉⠛⢿⣶⣄⠙⢌⠣⠈⠂⣸⢿⣧⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣤⡴⠃⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⡄⠙⢿⣧⠈⢆⢣⠈⢹⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡹⠁⠀⠀⢀⣼⠋⠀⠀⠀⠀⢀⠔⣀⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢻⣧⠈⢾⡦⣌⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢃⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⣃⠞⠓⢻⠉⡁⠂⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢻⠀⢸⡇⣸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣞⣸⡇⠀⠀⢰⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡸⢳⠣⣧⠀⠀⠸⡆⠸⣴⠩⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣿⣿⣀⠀⣼⡇⠀⠀⠀⠀⡸⣅⣤⣶⣶⣶⣿⣷⡀⠀⢠⠀⠀⣰⢃⠏⠀⠈⠿⠀⠀⡇⠀⠓⠨⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⡄⢇⠀⠀⣷⡟⢉⣾⣿⣧⣽⡄⠈⠙⠛⠐⠺⠟⣃⣤⣄⡀⢹⠀⠀⡇⠈⠀⢑⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠛⢋⡇⠈⠺⣷⣤⣹⠃⠘⡇⠙⣋⡸⠁⠀⠀⠀⠀⠀⢠⣿⣟⢻⢿⣾⠀⠀⡇⠸⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣾⣻⣥⣄⣀⠄⣼⠃⠀⠀⡘⠹⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⡏⢸⠟⢰⣰⣧⠃⣴⠦⠘⢿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠉⠁⠘⣿⣿⣿⠛⠀⠀⠀⢃⡆⠀⠀⠀⠀⠀⠀⣤⣤⣤⠤⣄⡀⠀⠀⠉⠋⠀⢁⣴⠟⡟⠏⡘⠙⠒⠇⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠀⠀⠀⠀⠹⣿⣿⡀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠟⠓⠠⢌⠁⢻⠆⠀⠀⠀⠀⡸⠀⢠⣇⠀⠈⠀⠰⠆⠀⢻⣄⠀⠀⠀⠀ ⢀⣼⣿⣇⢀⣀⠀⠀⢀⡸⠿⣧⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⡰⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀ ⠁⣿⣿⡿⠛⣿⣷⠖⡉⠀⠀⢻⣦⡀⠀⠀⠀⠻⣿⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡼⠁⠀⢠⣾⡇⣰⣿⣶⣄⣦⣄⢂⡀⠀⠻⣆⠀ ⠀⢻⣿⡇⠀⢹⡯⠎⠀⢀⠎⠀⡱⢌⣲⣤⣤⣤⣞⡀⠀⠉⠑⢲⣤⣄⣠⢤⣤⣖⣋⠟⠀⠀⢀⣼⠃⢷⣿⣿⣿⡟⠛⣿⣿⡿⠀⠀⣿⡓ ⠀⠀⠈⣿⠀⢸⡏⠀⠀⠈⠀⢰⣃⡾⠓⠉⠀⠀⠀⠈⠉⠂⢄⡀⠏⠉⠳⣔⠯⣁⡀⣀⣀⣴⠿⠃⡰⣡⣿⣿⣿⠁⠀⣿⠁⢠⣤⠀⣹⠀ ⠀⠀⠀⢹⡆⠘⢿⡀⠀⢠⠾⠋⠛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡀⠀⠈⢷⣦⡉⠉⠙⠳⡖⠉⠀⠌⣿⣿⣿⠀⠀⣿⠀⠀⠉⠀⠛⠀ ⡄⠀⠀⠈⡄⠀⠀⠑⣴⠏⠀⠀⠀⢸⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠑⡄⠀⠘⣿⣿⠳⢄⣀⢻⠀⠀⢲⠾⠉⠙⠀⠈⠿⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⣤⣧⠀⠀⢰⡿⠀⠀⠀⠀⠀⣿⡟⢻⡆⠙⢦⡉⠒⠢⢤⣠⠤⠸⢄⣰⡿⢿⡀⢸⡏⠀⠀⠀⡿⠀⣀⣤⠀⢀⡾⠟⠂⠀⠀⠀⠀ ⣇⠀⢸⠁⣿⡄⢰⣻⢧⡤⠶⢤⡀⠀⣿⡿⢸⡇⠀⠀⠙⠢⣄⡜⠀⠀⠀⠀⢻⣷⣼⣿⠈⢳⠀⠀⢸⣧⠞⣹⢃⣀⣾⠋⠁⠀⠀⠀⠀⠀ ⠸⠀⠘⠖⠙⣧⣸⣣⠲⠵⣤⠌⠙⢾⣿⣧⣼⠇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣸⣿⣿⠃⠀⢸⣆⠀⠛⠁⢰⠇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢻⡝⠁⠠⠒⣷⡀⠀⣾⣿⣿⡿⠀⠀⠀⣀⡤⠶⢿⣯⣓⠒⢉⣿⣿⣿⣤⣾⠟⢻⠀⠀⠀⠘⠁⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠳⣄⠀⠀⠀⠺⢆⣿⣿⣿⠁⠀⣰⠞⠉⠀⢀⡀⢈⠁⠐⠋⠉⢿⡿⠋⠁⠀⠀⣇⠀⢀⡤⠒⢋⡉⢢⢄⠀⠀⠀⠀⠀⠀

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⠀⠈⠫⡐⠤⡀⠀⠀⡇⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣔⣉⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⠱⠀⠈⠢⢄⡃⠀⠀⠀⠀⣬⡄⠀⠀⢀⣠⣴⣶⢿⢿⡻⣟⡻⣟⣻⢻⡟⣿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⣸⠆ ⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠂⠀⠀⣧⣶⣿⡿⣟⣯⣟⣾⢯⡿⣽⣻⡽⣞⣷⣻⣬⢷⣩⢟⡻⢿⣦⣄⡀⢀⣄⠊⠀⠀⢀⠈⠀⣌⢃ ⠀⠀⠀⠀⢱⠀⠀⠠⡗⡠⢄⣠⣴⡿⣿⣟⣷⣻⣟⡾⣽⢯⡿⣽⣳⢯⡿⣽⣞⣷⣯⣟⣯⡿⣽⣧⣛⣿⡿⠛⠁⠠⢀⡐⠠⠂⡰⠑⡇ ⠀⠀⠀⠀⢸⠂⢆⢠⣳⡾⠟⠛⢿⣧⢻⣿⣞⡷⣯⢿⡽⣯⣟⡷⣯⣿⣽⣷⣿⣿⣿⣿⣿⣿⡿⢟⡻⢍⡤⣄⣄⣂⣀⣀⢄⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⢄⡿⠋⠠⡌⡔⡈⣿⢺⣿⢾⡽⣯⣿⣽⡷⠿⠟⠛⠛⠋⠉⠉⠉⠛⠋⠙⠙⠻⢿⣼⣧⣾⣴⣮⣶⣵⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠡⢈⡒⡐⠠⣱⡿⣺⣿⣯⡿⠟⠋⠁⠠⠐⠠⢀⡠⠀⠐⠀⠀⠀⠀⠰⢦⡀⠀⠀⠉⠻⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠠⣡⠂⡔⢠⣿⣿⢣⣿⡿⠋⠀⠁⠀⠠⠁⠠⠀⢸⠀⠀⠀⠈⠀⠁⠀⠀⠈⢿⡄⠀⠐⠀⠀⠙⢻⣿⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣄⢢⡔⣿⡿⣯⣿⠋⠀⠀⢀⠈⠀⠀⣤⠀⠀⡟⠀⠀⠀⠀⠐⠀⠂⠀⠀⠈⢻⣄⡀⠀⠐⠀⠀⠙⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣶⣷⡾⢿⣽⡿⠁⠀⡀⠈⠀⠀⠀⣰⠏⠀⠀⡏⠀⠀⠁⠈⠀⠈⠀⠀⠂⠀⠘⣿⠙⣦⠀⠀⠀⢀⠈⢻⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⠇⠀⠀⡐⠀⡀⠀⢰⡟⠀⢀⠜⢃⣠⣴⠾⠛⠠⠀⠡⠀⠀⠰⢶⣿⡄⢻⡆⠀⠈⡀⠂⠀⣻⣇⠀⠀ ⠀⠀⠈⠀⠀⠀⢿⣿⣞⣷⣿⣿⠀⠀⠀⠐⡀⠀⠀⣿⣣⡞⢁⣶⠿⣹⠀⠠⢀⠐⡀⢃⠀⠢⠀⠀⣯⢻⣎⣿⠀⠀⢂⠀⠘⡄⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⢿⣿⣃⠀⠈⠄⠀⠄⢸⣿⠏⠀⠈⣁⣦⣿⣦⣹⡆⢀⠐⠂⠈⣁⣂⣵⣃⠀⣿⣿⠀⢀⠂⠄⠂⣿⣸⡇⠄ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣯⠄⠀⠌⢀⠠⣸⡇⣆⣴⣾⣿⣿⣿⡟⢻⡟⢧⠀⡀⠁⣾⣿⠿⣿⣷⡌⣿⠀⠄⣈⢂⢂⣿⡿⠁⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⣆⠀⠄⠀⢼⣧⣿⡟⠁⣿⣿⣿⣿⣾⠇⠀⠑⠢⣴⣿⣿⣷⣿⡾⣷⣿⠀⠐⠠⢂⣼⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⣤⣄⣀⡈⠿⣷⣄⡠⠈⠍⠙⠷⣤⢿⣯⣿⣿⡟⠀⠀⠀⠀⢸⣿⢿⣿⡟⣣⣿⠿⠠⢈⣴⣻⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⠋⢁⣽⡿⢿⣭⣿⣛⡛⢟⠻⢶⣬⣦⡄⠀⠀⠉⠉⠉⣀⣀⣀⠀⢀⠀⠙⠛⠛⠁⣹⣾⣾⣷⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠋⠀⢰⣾⢏⡜⡲⣇⠀⠉⠻⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⢰⣿⢋⢟⣻⡿⠁⠀⠀⠀⠈⠛⣹⡟⠉⠻⢷⣄⠀⠀⠀⠀⠀ ⠀⢀⣾⠟⠠⢘⣰⣿⢋⠮⣜⡱⣿⡄⠀⡀⠈⠚⢶⣹⢻⣶⣤⣀⡀⠀⠀⣻⠿⠶⠛⠁⠀⠀⣀⣰⣴⢾⡛⣆⠡⢂⠈⠻⣧⠀⠀⠀⠀ ⠀⣾⠃⢀⠠⢠⣿⢣⢏⡝⢦⢳⣹⣿⡀⠠⠑⠌⡀⠘⢣⢎⣽⡿⢛⣛⣛⣷⣾⣷⣷⣶⢾⣿⠏⣉⠛⢷⣽⢸⡀⠘⡀⠀⡙⣷⡀⠀⠀ ⠸⠇⢀⣸⠀⣾⡇⣏⠞⡼⢣⣷⣿⣿⣿⣆⠈⠀⠂⢁⣠⡿⠃⠀⠀⠤⣭⣿⢛⣋⡉⠻⣷⡳⠒⠄⢀⡈⢻⣷⠆⢀⠃⡐⣶⠘⣧⠀⠀ ⠐⠊⠁⡎⠀⣿⡞⣬⣋⢗⡣⣿⣿⣿⣿⣿⣷⣄⣠⣾⣋⣀⡀⢀⠤⢞⣿⠟⣠⢣⠙⠰⡘⣿⡛⠦⠀⠈⠁⢻⡇⠀⠱⢀⣿⠟⠋⠀⠀ ⠀⠀⠘⠷⠾⢿⣷⣦⣙⢮⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⢿⣎⣔⡡⢎⢧⡷⣿⣿⣾⣿⣿⣷⣾⣿⢀⣧⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⠉⠛⠻⢿⣿⣏⣀⣽⣛⠛⣿⣟⡁⣿⠿⠿⠿⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⣷⣿⣯⣿⣗⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠃⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢨⡗⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⢀⣠⣴⣿⣲⣏⣉⡓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⣰⢃⠜⠋⠿⠿⢿⣷⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⡻⢻⠷⣄⡀⢠⣶⣿⡿⠀⣹⡶⠋⠁⠀⠀⠀⠀⠀⠀⢀⣉⠭⠝⠛⠋⠳⣄⡀⠀⠀⠀⠀⢀⣠⠊⠉ ⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡏⠀⠾⢤⣾⠀⢘⣶⣾⣿⡿⣶⡿⠋⠀⠀⠀⠀⣀⡤⠔⠒⣉⣡⣤⣶⣀⠀⠀⠀⠀⠉⠉⠛⠋⠉⢻⣿⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠤⡀⠘⢿⣇⡼⠟⠋⢀⡼⠟⠁⠀⣀⠤⠒⢋⡁⠤⠶⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣀⣈⣿⣇⣀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣬⣁⣠⣉⡩⠶⠒⠉⢀⡤⠒⢉⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣤⣤⣬⣭⣭⣉⣉⠻⣯ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⠴⠊⣁⠤⠊⠁⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⢀⣠⠔⢊⡡⠐⠉⠀⠀⠀⣀⣠⣴⡞⠁⠈⢿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⣋⠴⠊⠁⠀⢀⣠⣴⣶⣿⣿⣿⣿⠃⢀⡀⠘⣿⠟⠛⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⣀⡤⠔⣊⠉⠔⢊⣉⣀⣤⣴⡶⣿⣿⣿⣿⣿⣿⣿⠿⢸⠀⠀⠙⠒⠾⢷⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⠤⠔⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠒⠛⠛⣻⣿⣿⣿⣿⣿⠿⠳⣟⠉⠉⢹⠀⠀⢸⣆⢸⠀⠀⠀⠀⠀⠀⠙⢷⣧⡰⣼⣿⣿⣿⣿⣟⠻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠛⢡⣿⣿⣿⠀⠀⢸⢮⣤⣀⠉⠛⠛⢿⣿⠀⠀⠀⠀⣀⣤⡶⠂⢹⣿⣿⣿⣿⢿⣿⣿⣷⡘⢟⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⣿⣿⣿⢿⣆⠀⢸⠀⠈⠙⢻⣦⡄⠀⠙⠂⠀⣰⣾⠛⠁⠀⠀⡜⢈⠟⢿⡏⠀⠙⢿⣿⣿⣎⢣⡙⢧⡀⠀ ⠀⠀⠀⠀⢀⠜⠀⠀⠀⢠⣿⣿⣿⠻⠀⣿⣦⣀⣧⠒⠚⠋⠉⠀⠀⠀⠀⠀⠈⠙⠛⠶⠤⣀⠇⡜⢠⡟⠀⠀⠀⠀⠙⢿⣿⣷⡱⡀⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠀⢠⣿⣿⣿⠟⡇⠀⢻⣿⢫⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⠁⣾⠙⢯⡉⠉⠒⢤⡀⠈⠻⣿⣷⠀⠘ ⢀⣴⢧⠀⠀⠀⢀⣠⣿⣿⣿⠃⠀⣧⡀⠈⣷⢸⣷⣄⠀⠀⠀⢀⡤⠒⠄⠀⠀⠀⠀⣀⣼⣿⣏⣴⡟⣲⣼⠀⠀⠀⠀⠈⠑⢤⡈⢿⣇⠀ ⢾⢋⠏⠀⠀⢠⣿⣿⣿⡿⠃⠀⠀⢸⣷⡄⣿⠉⣿⣿⣿⣶⣤⣿⣀⣀⣀⣀⡤⣶⣿⣿⣿⡿⣽⣿⠀⠀⠙⢆⠀⡀⠀⠀⠀⠀⠘⡆⠙⡄ ⠁⡜⠀⠀⢀⣿⣿⣿⡟⠁⣀⣀⣀⣸⣿⣿⣿⡄⠹⣿⠏⣡⣾⠡⡝⠻⠛⢉⣴⣿⣿⣿⣇⡼⣿⡿⠀⠀⠀⢸⠀⢸⢠⣀⡀⠀⢠⠇⠀⢱ ⡼⡱⢀⣤⣼⣿⣿⠋⡇⠀⢸⡏⠉⢽⠈⠫⠿⢿⣦⢩⣾⣿⣿⡧⣿⣍⣹⣿⣿⡿⠟⢙⣫⣾⡟⠁⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀⢸⠀⠀⠈ ⢣⣿⣿⣿⣿⡿⠁⠀⡇⠀⢸⠀⠀⢿⠒⠒⠒⠿⠁⢸⣿⣿⣿⣷⡍⠉⣌⠻⡛⠛⠛⠉⠁⠀⠈⠹⠒⠒⠒⣿⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀ ⣼⣿⣿⣿⠟⠀⠀⠀⠃⠀⢸⠀⢀⣿⠀⠀⠀⣠⣾⣍⡛⢿⣿⣿⣿⠀⢈⣲⠬⠓⠤⢄⣠⠲⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸⣀⡾⣿⣀⢴⣪⣴⡏⢇⣬⡳⣜⢿⡟⢳⠁⠀⢀⣴⣶⣤⣼⣷⠬⣷⣤⣀⣰⠿⣧⠀⠀⠀⡇⠀⢸⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸⠛⢿⣿⣿⣿⣿⠿⢿⣾⣇⢑⡌⣆⣻⣾⣶⣶⣿⡿⠟⠂⠺⡟⢀⣀⣼⣷⣶⣶⡀⠀⠀⠀⡇⠀⢸⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⢸⠀⣼⣿⣿⠹⣿⠀⢀⠟⠉⠉⢀⡟⡝⢸⡿⠛⠁⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣷⡀⠀⠀⣇⠀⢸⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⢸⣼⣿⣿⣿⡀⢈⡿⠃⠀⠀⠀⢸⣿⣃⡜⢧⡀⠀⠀⠀⢀⣾⣿⠟⠉⢁⣾⣿⣿⣿⣷⡄⠀⣿⠀⠸⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⡤⢼⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠒⠒⠲⠦⢤⣀⡈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⡠⠖⠋⠉⠀⠈⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠒⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⢻⡀⠐⢳⡀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠀⠀⠀⠀⢳⡀⠀⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⣾⠁⠀⣾⠋⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣸⣶⣖⣒⣒⠒⠛⢄⡏⢣⡀⠘⣷⡀⠀⠀⠀⣸⡿⢀⡼⠁⠀⠐⢚⣩⣭⣭⣽⣿⣆⠀⠀⠀⠀⣳⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠲⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠀⠱⢄⠘⣿⣄⠀⢠⣿⠳⠋⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠋⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⣠⣿⡿⢻⣿⣟⣛⣻⣿⣿⣿⡌⠑⠀⠀⠈⠑⠧⠹⢗⣚⡟⠀⢀⠀⠚⢹⣻⠟⠻⣿⣿⣿⣿⣿⣿⠻⣿⣷⣄⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⣷⣿⡟⠁⡟⠁⣹⣛⣉⡋⠉⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⡼⠀⠀⠘⣿⣦⣴⣯⣬⡝⠛⠛⣿⡇⠘⢿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠸⡟⣿⠀⠀⡟⠋⢹⣿⣿⣷⠋⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠄⢏⠀⠸⣿⣿⣿⠛⠛⢿⡇⠀⢸⡿⡟⠀⠀⠀ ⠀⠰⣄⠀⠀⢹⠘⠀⠀⢣⡀⠈⠛⠛⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠸⡄⠀⠉⠛⠉⠀⠀⡼⠀⠀⡜⢰⠃⠀⠀⠀ ⠀⠀⠹⣷⣄⠀⢣⠀⠀⠀⠱⣄⡀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠔⣁⡠⠊⣰⠏⠀⣠⠂⠀ ⣆⠀⠀⠘⢝⡯⣄⠷⡄⠀⠐⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠉⠉⠀⠖⣡⡶⠚⠁⠀⠀ ⠈⠳⣄⡀⠀⠙⠲⣽⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣋⡀⠀⣀⢠⣠ ⠀⠀⠈⠉⠉⠙⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣸⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣿⠉⠀ ⠀⠀⠀⠀⠀⠀⢿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠀⠀⠈⠘⢫⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⡏⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣤⠤⠤⠴⣺⡥⠶⢤⣤⡤⢤⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢸⠁⠀⠀ ⠀⠀⠀⠀⢱⠀⠈⣇⠀⠀⠈⢓⡴⢖⣽⣶⠞⢉⣷⡄⠀⠀⠀⠀⠀⣠⡤⠾⠟⠀⠀⠀⠈⠀⠀⣽⣆⠀⠀⢀⣠⣶⣽⠃⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⢻⢄⡀⢠⠏⠀⢸⡟⠁⣠⣾⣿⡿⠖⢦⡄⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣿⣿⣿⣆⠀⠀⡇⠀⢸⠀ ⠀⠀⠀⠀⠀⠸⡀⠈⡇⢩⡏⠆⠀⠀⠀⠘⠛⠛⠋⠀⣴⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠃⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠙⣄⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡷⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠤⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢠⠎⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣤⣀⣀⢀⣀⣤⣶⠿⠛⠉⠉⠢⡀⠀⠀⠀⠀⠀⡠⢖⣒⣺⣖⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⣼⣿⣿⣷⣄⠀⡀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢠⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡞⡜⠁⠀⠈⠻⣷⠀⠀⡀⠀ ⠀⠀⠀⠀⡎⠀⣸⠟⠉⠙⠛⠛⠛⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠱⡄⢸⢱⠁⠀⠀⠀⠀⢻⢧⠀⠀⠀ ⠀⠀⠀⢸⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠘⢾⡌⡆⠀⠀⠀⠀⠈⣿⠀⠠⠀ ⠠⠀⠤⣯⠬⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢷⣷⡀⠀⠀⠀⢀⣿⡇⠀⠀ ⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⢀⠆⠀⢠⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⡳⣄⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⣷⣝⡦⢤⡤⣾⠏⢹⠀⠀ ⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⡾⠀⢰⡃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⡎⢀⣈⣑⣦⣄⣿⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠉⠉⠀⠀⣼⡆⠀ ⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⡇⢠⠃⠈⠒⢼⣸⡀⠀⠀⠀⢸⡇⢰⡿⣫⡾⠛⠛⠛⠻⡝⢻⣷⡀⠀⠀⠀⠀⠀⢀⣧⣀⣀⣀⣀⣴⡿⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⣎⣠⣤⣯⡽⣿⣷⡀⠀⢀⠏⢃⠆⠐⢻⠀⠀⠀⠀⠀⢹⣼⠘⠇⠀⠀⠀⠀⠀⣸⠠⠤⠀⣠⣿⣿⠇⠀⠀ ⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⣿⡿⠋⡞⠁⠀⠀⠹⣷⡀⡜⢰⠏⠀⠀⠹⣤⣀⠀⠀⢀⡼⢹⠀⠁⠀⠀⠀⠀⣴⠇⢀⣠⣾⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⣇⣦⠀⠀⠀⠀⢻⠃⠘⡅⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠉⠙⠳⠖⠛⠀⡼⡀⠀⠀⠀⣠⣾⣿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡄⠀⠀⠘⣼⡀⠀⠙⠒⢦⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣠⠞⢁⣿⠟⠛⠛⠛⠛⠓⠶⢦⣤⣀⠀ ⠀⠀⠀⠀⠀⠁⠙⠢⣰⣀⠘⢷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠊⠁⠀⠊⢹⡷⡞⠒⠦⠤⣀⠀⠀⠈⠙⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⠀⠀⠀⠘⣷⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⢀⡤⠒⡇⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⣤⡞⡀⠀⡆⠀⠀⠀⢀⡇⢻⡷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⢁⠔⠀⣇⡀⠀⠀⢸⡇⢿⠷⣶⣦⣤⣤⣄⡀⢀⣀⠠⠤⠒⠉⠁⡼⠀⡇⢰⠀⠀⢠⡆⣼⣀⣤⣷⠈⢧⢢⣄⡢⡀⠀⠀ ⠀⠀⠀⠀⣾⠶⠃⠀⢠⣿⣤⠀⠀⠀⢳⡘⣆⠈⠙⠻⣏⣻⡇⠀⠀⠀⠀⠀⢀⣾⣤⠾⣇⡌⠀⣠⣿⠿⠛⠁⣿⣾⣷⡌⢆⠻⡏⠒⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠛⢩⣿⠧⣄⠀⠀⣷⣾⡧⢤⣀⡀⠉⠛⠳⠦⣤⣤⣶⣿⣿⢋⣠⣿⣿⣿⠟⠁⠀⠀⢰⣿⢿⣿⠟⢾⡤⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠢⠴⠁⡇⢀⡿⣿⣿⡏⠀⠀⠀⠀⢻⠗⠒⠤⠴⠞⠛⠛⠛⠉⠁⠀⠉⢻⠃⠀⠀⠀⠀⣼⣿⡾⠋⠀⠀⢱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠜⠻⠷⡦⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣋⡶⠒⡄⠀⢠⢯⡟⠁⠀⠀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡴⠃⠀⠀⠀⠈⠳⡄⠀⠈⣆⣀⣀⣀⣀⡤⠤⠤⠤⠤⢾⠚⢀⠉⠢⠘⣆⣾⣿⠋⠀⠀⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠘⣇⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠓⠆⠈⠀⠀⢀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣰⡿⢁⣆⢣⠀⣠⡨⠒⠙⠳⢄⣠⣤⣦⡶⠶⣶⣦⣽⣿⣦⡀⠀⠀⠙⢆⠀⠀ ⣴⡿⢁⣾⣿⣮⡴⠋⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠈⢻⢿⣿⡄⠀⠀⢸⡄⠀ ⣷⣀⣾⣿⣿⡏⡠⠂⢀⠀⠠⠂⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠧⠻⣿⡆⢰⢸⠃⠀ ⠛⠛⠛⠋⠹⡏⠀⠠⢁⠢⠁⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠿⠸⢸⡀⠀ ⠀⠀⠀⠀⠰⠀⢠⠁⣄⠃⢀⠔⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠰⢳⢺⠀⠀ ⠀⠀⠀⢠⡃⠀⠂⠀⡌⢠⠂⠀⠁⢹⠐⠀⠀⠀⠀⠀⠀⢠⢻⢸⠀⡀⠈⡜⠀⠀ ⠀⠀⣠⠇⠀⠁⠂⠤⢱⣤⣷⣦⣄⠈⡄⡀⠀⠠⠣⢉⢅⠂⠈⠘⢠⠁⠀⠀⠀⠀ ⡿⣿⢢⠑⢠⠤⠐⠲⡏⠛⣿⣿⣹⢣⠐⠇⣰⣋⣴⣵⣥⡀⢠⠃⠆⡄⠀⠀⠀⠀ ⠧⣜⢄⠙⠀⡆⠂⠀⠏⡄⠉⢱⠇⠀⠀⠈⠉⢈⢿⣿⡌⢻⡜⠊⢠⠁⠄⠀⠀⠀ ⠗⢇⢌⡖⠃⢹⡄⠑⡨⠌⠉⠀⠀⠀⠀⠀⠀⢨⠘⡣⠁⢞⠀⢀⠀⡜⠀⠀⠀⠀ ⠀⠈⣧⡏⠦⡀⢋⢳⢵⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠝⠡⡔⠥⠊⣠⣇⣀⣀⣀ ⠀⡸⠛⢁⠀⢫⠉⡌⡗⠄⡀⠀⠀⠀⢲⠀⠀⠀⠀⠉⣭⠉⠇⢈⣾⠯⠉⠍⠉⠉ ⠀⠀⠀⠘⡀⡀⠀⠐⡩⠒⢌⠲⣄⣀⣀⠀⢀⡤⢔⠊⢈⡄⢸⢼⣿⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠱⣵⢄⢀⠈⠣⣀⡉⢞⠁⢸⡎⠈⢳⡀⡄⠸⠁⠀⣿⣇⠀⠀⠂⢰⡏

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡽⠋⠁⢀⠋⠉⣉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢽⡒⢦⣀⠊⠉⠉⢉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠙⢿⣿⡿⠋⣩⡿⠋⣹⢯⠉⠉⠉⣯⠷⣄⡀⠀⡄⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠉⠙⠯⣉⠙⠳⡀⠈⣛⢻⣟⣯⡯⣿⠉⠹⢻⡟⣿⡟⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⢍⣧⣀⠀⠀⢀⡴⠋⠁⠀⠀⠈⠛⠚⢦⣴⣿⠥⣶⣶⣿⣿⣿⣿⣿⣿⣶⣜⣓⡶⢦⡤⣄⣀⠀⠈⢻⡑⢷⡀⠘⡦⡙⢓⣿⣄⡀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠔⢋⡀⢀⡴⠋⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠈⠙⠓⠩⠭⠿⠿⢻⠯⠉⠉⠉⠉⠛⠛⠛⠻⣿⣽⣄⡀⠙⣄⠹⡄⠐⢧⠐⡿⣿⣇⣼⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⣠⡞⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠻⣿⣿⣆⠘⢧⠸⡄⠚⢰⣴⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⠏⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⢻⣿⣆⠈⣦⢹⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⡏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢹⣿⡄⠘⡾⡷⠾⣄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣾⠃⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣰⢃⡴⠓⠚⢻⠉⡙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢻⡇⠀⢳⡇⢀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⢀⣿⡆⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢠⣳⠋⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢴⣏⢣⠀⠀⠀⠘⡇⠀⢸⠁⡞⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣷⣸⣿⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣀⣀⡈⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡜⠈⠙⣧⢣⠀⠀⢹⠀⠘⣿⠐⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⠀⣰⣿⡅⠀⡀⠀⠀⠀⢸⠳⣴⣾⠿⣿⣟⡿⣿⠿⠷⡀⡀⢀⡆⠀⢀⣴⠇⡴⠁⠀⠀⢸⢹⠀⠀⢸⠀⢀⠏⢀⢢⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣿⣿⣷⡀⢳⡀⠀⠀⣾⣾⠟⢁⣾⣿⣿⣧⣸⡆⠀⠈⠙⠾⠤⠶⠿⠿⠟⣀⣀⣀⡀⠈⢸⠀⠀⢸⠀⢸⠀⢈⠫⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⠿⠿⢿⡇⠙⢦⡳⣄⠀⢹⢻⠀⢸⡟⠹⠿⠏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⣟⢿⣆⡟⠀⠀⢸⠀⣸⠀⠀⠑⣼⡹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡞⠛⠉⠀⠀⠀⣼⡇⠀⠀⠙⡻⢽⠚⠃⠀⠀⠳⢤⣴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣷⣼⠘⣿⡇⠀⠄⣸⢀⡇⢠⡀⠀⣸⣷⣽⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡻⣭⣭⣷⣶⣴⣒⡒⢴⡛⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⢉⠟⢠⠟⠁⣸⣰⣿⡿⢀⣾⡟⢆⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡼⠋⠁⠀⠀⢿⣿⣿⣿⡟⠇⠀⠀⠀⠘⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡶⠶⠤⣀⡀⠀⠀⠀⠉⠉⠉⠀⠃⣰⣾⠗⣿⠿⣀⠿⠉⣓⠷⠇⠨⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⢇⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠯⢍⣉⠙⠓⠭⣳⡄⠀⠀⠀⠀⠀⢰⡇⠀⢠⣿⠀⠈⠳⠄⠀⣴⠀⠀⡾⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠙⢦⣀⡞⠀⠀⠀⠀⠀⠀⡞⠀⠀⡸⡿⢈⠁⠀⠀⠄⠀⠀⠀⡰⣮⣷⣄⠀⠀⠀⠀ ⣠⢾⣿⣿⣧⣠⣄⣤⡀⠀⢀⣤⠚⠋⢷⣇⠀⠀⠀⠀⠀⠹⣟⣦⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣧⡇⠘⠳⡀⠀⠀⠀⠀⠀⠁⠈⠉⢻⣷⡀⠀⠀ ⠀⢸⣿⡿⡶⠟⢻⣿⣯⡶⢋⡄⠀⠀⡈⡞⢦⠀⠀⠀⠀⠀⠙⣿⣹⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢸⢻⡇⠀⣿⣿⣿⣤⣸⣦⣄⢛⣄⠀⠀⠑⣷⡄⠀ ⠀⢼⣿⣿⡇⠀⠘⣿⣟⡴⠋⠀⠀⡜⠁⠘⣦⡙⢶⣀⣀⣀⣀⣨⡟⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⣀⣀⣠⡴⠖⣫⠟⠀⠀⠀⢀⣷⠏⣧⣿⣿⣿⣿⣿⡻⢷⣿⣿⣿⣿⠀⠀⢻⣿⠦ ⠀⠀⠙⠻⣧⠀⠀⣿⡼⠁⠀⠀⡼⠀⠀⢰⠇⣨⣗⡻⠝⠛⠛⠙⠛⠲⠤⣄⡀⠀⠈⢿⠿⢿⣏⠉⣽⠷⠖⠛⠁⠀⠀⠀⣠⣿⠏⢀⡜⢻⣿⣿⣿⡇⠀⢠⣿⠿⠙⠃⠀⠀⢸⢻⠀ ⠀⠀⠀⠀⣟⡄⠀⣇⣇⠀⠀⠀⠁⠀⣀⣯⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⢸⠀⠀⠈⠳⣌⠳⠤⣄⣠⣤⣔⡻⠝⠁⣠⠜⢴⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠾⣷⠀⢸⣸⠀ ⠀⠀⠀⠀⢸⣷⠀⠙⣿⡆⠀⠀⣰⡿⠋⠉⠙⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣇⠀⠀⠀⠹⣷⣦⡈⠉⠉⠉⠱⡞⠏⠁⠀⡇⢹⣿⣿⢿⡇⠀⠸⣹⠀⠀⠀⠁⠀⢸⠚⠀ ⡀⠀⠀⠀⠈⡇⠀⠀⠈⠹⣄⣼⡏⠀⠀⠀⠀⢹⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢻⣿⣿⡷⣤⡀⠀⢿⡆⠀⠀⢦⣶⡟⠉⢩⠁⠀⠊⣿⠀⠀⠀⠀⠀⠸⠀⠀ ⠃⠀⠀⠀⠀⠷⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⡌⠻⣍⠓⠦⢄⡀⠀⠀⠀⠀⠈⢷⡀⠀⢸⣿⣿⡇⠀⢻⡶⠞⠁⠀⠀⣴⡇⠀⠀⠠⠀⠀⠀⣨⣴⣄⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢀⡾⣿⡇⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢻⢸⡇⢸⡇⠀⠈⠳⣤⡀⠈⠙⠓⡶⠚⠋⠉⠳⣄⣿⡟⢉⡇⢀⢱⣧⠀⠀⠀⢀⣿⠁⣠⢴⣿⠁⠀⣴⣟⡋⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣾⠁⣿⣧⠀⢸⣯⡿⣦⡶⠒⠲⣤⠀⠀⣸⢸⡇⣠⣿⠀⠀⠀⠀⠙⢦⣤⡎⠀⠀⠀⠀⠀⠈⣿⣿⣸⣧⡟⠀⢹⠀⠀⠀⢸⣯⠞⠁⣼⢃⣀⣸⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠻⣦⠟⣿⡇⢸⡟⡠⣤⣳⡀⣠⠛⢷⣼⣿⣿⡄⣿⡟⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⢸⣇⠀⠀⠾⠁⠀⣾⠇⠈⣹⡏⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⢿⡾⠁⢀⣈⣿⠁⠀⠀⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣀⣽⣷⠤⣀⣀⠴⢾⣿⣿⣿⡇⠀⣠⣾⣿⡇⠀⠀⠀⠀⣿⠀⠰⣯⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠀⠀⠀⠀⠀⣿⠈⠀⠐⠃⢠⠚⢷⡄⢀⣿⣿⣿⣿⡟⠀⠀⠀⣀⣤⠾⠋⠉⠙⠿⣶⠤⠀⣠⣾⣿⣾⣿⢷⣻⠟⠋⠀⢧⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠘⢦⠀⠀⠀⠀⠘⠚⣎⣿⣿⣿⣟⠀⠀⣠⣾⠋⣀⠀⠀⢀⣀⣈⡀⠀⠘⡛⠀⠈⣿⣿⠋⠁⠀⠀⠀⢘⣄⢀⠀⡠⠖⠛⠁⣀⠈⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⢉⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⡶⠁⠀⢀⣠⣴⠒⠚⠉⠉⠉⠉⠉⠃⣒⣤⡀⠀⠀⠀⣀⡀⢠⡣⠀⠀⠰ ⠀⠀⡘⠀⠀⣠⣿⣿⡇⣀⠤⠀⠤⠄⢀⣀⡠⠞⠋⠉⠑⢤⣸⡋⠙⢄⠀⠀⠀⠀ ⠢⢀⣃⣀⡜⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠘⡆⠀⣀⣠ ⠈⢹⠉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢹⣦⡀⣿⣤⡝⠀ ⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠐⡀⢸⣿⡴⠧⠁⡇⠀ ⣶⡚⣸⠀⠀⠀⠀⢠⠀⢀⣷⠀⠀⠀⠌⡿⣄⠀⠠⠀⠀⠀⢱⠀⣯⣙⣧⣾⠃⠀ ⠀⠀⢣⠀⠀⠀⠀⠜⠀⡜⠘⡆⠀⠀⣴⣇⠜⠑⠀⣃⡀⠀⠀⣗⢛⣿⣿⡏⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⣇⠜⡑⣂⣷⠀⢰⠋⢁⣮⠶⠚⢯⠀⠀⢈⣧⣾⣿⠟⠀⠀⠀ ⠀⠀⢀⢫⡆⠀⠀⢹⢻⣛⣛⡾⠀⠁⠀⠀⠹⠭⠀⢨⣼⢀⠼⡏⠉⠛⠡⢒⠠⡀ ⠀⠀⠈⠺⡿⡴⡀⠸⡆⠑⠈⠀⠀⠀⠀⠀⠀⠀⠈⢈⡟⠁⠀⣳⣤⠀⠀⠀⠈⢪ ⠀⠀⠀⠀⠀⢘⡟⠓⠢⣀⡀⠀⠀⠂⠄⠊⠁⣀⠴⣾⢁⡄⠤⣟⣛⣓⣦⣴⠀⡜ ⠀⠀⠀⢀⠔⢁⣇⠀⠀⠿⠾⣉⡷⠒⢶⣞⡹⣃⡶⣟⡯⢬⠲⠛⠋⠉⠈⡾⢯⠀ ⠀⠀⠀⣿⢃⣥⣶⠤⠤⢙⠭⠷⢾⣵⣖⣺⡾⣻⡿⠟⠈⠀⣀⣤⡴⠶⠰⣷⠌⡄ ⠁⠁⠀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⢹⠁⢰⡶⡞⠛⣉⢤⣤⡶⠼⣿⣷⠘

⠀⠀⠀⢀⣴⠟⡿⠋⠀⣴⡏⠀⠈⢢⡀⠀⠀⠐⠠⠄⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠔⠉⠉⠳⡀⠀⢈⣶⣃⡜⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⠞⠀⠀⡞⠁⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠮⠄⠀⠄⠒⠂⠘⠉⣩⠽⠻⡉⢦⠀⠀⠀ ⢦⣰⣿⣿⠃⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢴⣾⡭⠳⡄⠀⠙⡄⠳⡀⠀ ⢠⣿⣿⠃⠀⡼⡇⢠⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠒⠂⠉⠁⠀⠀⠙⡄⠀⠈⢆⣸⠂ ⠀⣿⡏⠀⣼⠁⠀⢸⡇⢀⠀⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠉⠒⠒⠒⢒⡒⠲⡋⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡀⠁ ⠜⢹⠁⢰⡏⠀⡄⠀⠀⠈⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠑⢄⣹⣖⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⡄ ⢀⡎⠀⢿⠁⠀⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⡄⠀⠀⠀⠀⢀⣾⠯⡘⡷⣝⢦⣡⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘ ⣿⠃⠘⠀⠀⠀⡇⠀⠀⠀⠀⢠⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⣄⡀⢀⠖⡱⠁⠀⠙⣷⡀⠑⢼⡀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢘⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⢠⠈⢆⠀⢱⡼⢳⠾⣀⡀⠀⠀⢈⣧⣀⣀⡇⠀⠀⠀⠀⢸⡄⠀⠀⢠⠀⡀ ⠀⠀⠀⠀⠀⠀⡇⢄⠀⠀⠀⡎⠀⠀⠈⢜⢆⠀⠀⠀⠀⠀⠀⠳⡈⣷⣞⣷⢃⢴⣮⣿⣿⣿⡿⠛⢻⣿⢇⠀⠀⠀⠀⡆⡇⠀⠀⠘⠀⡇ ⠠⠀⠀⠀⠀⠀⣇⠸⡙⡛⠲⣷⣦⠤⣀⣈⠫⣣⡀⠀⠀⠀⠀⠀⠘⢍⣏⠻⢿⣿⣿⣿⣿⠾⢿⡄⠀⡟⢸⠀⠀⠀⢠⢰⠀⠀⠀⡆⢸⠀ ⠀⠀⠀⠀⠀⠀⢹⣦⣣⡱⡄⡇⠈⠉⢒⠀⣭⣹⠟⣶⡤⣀⠀⠀⠀⠈⠻⣆⠘⠁⢻⠿⢿⡧⠀⠃⠀⠁⡟⠀⠀⢀⡞⢸⣧⠀⢰⣇⡎⠀ ⠀⠀⠀⡀⠀⠀⠀⢇⠈⠓⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⠦⣍⡑⠦⠤⢀⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠞⣇⣟⠿⣤⣿⠟⠀⢀ ⠀⠀⠀⢧⠀⠀⠀⠘⣦⣾⣿⠛⠉⣿⣿⣿⣿⢶⡏⠀⠀⡰⢋⡠⠤⠤⠤⠏⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⣀⣴⠟⠀⢿⣿⠀⡱⠃⢀⠀⠘ ⠀⠀⠀⠘⡄⠀⠀⠀⠈⢆⢻⣧⡀⢻⣙⡻⠟⠘⠃⠀⠀⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢠⠋⠀⠀⠀⢀⡔⠁⡠⢉⠀⠀ ⢸⠀⡇⠀⢹⡀⡄⠀⠐⠤⣑⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡠⠊⠀⠈⠀⠀ ⠈⡆⣿⡄⠘⣷⣜⢆⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⣀⡀⠠⠚⠇⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠎⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⠙⢄⢹⡏⠳⣷⣤⣀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⡴⣊⠡⠤⠒⠉⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⡃⢰⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠦⠀⠙⠓⠀⠈⠛⠿⡝⢯⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⠏⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⣴⢿⣷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢀⣀⡠⠖⠁⠀⠀⠀⣰⡿⠋⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣟⠒⣤⣀⡀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⣴⣯⣭⡙⢿⣿⣿⣿⣿⣄⣀⣀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣭⠛⠻⢶⣶⡾⠟⠁⠀⠀⢰⣾⣿⣿⣿⣿⣯⣟⢿⣿⡇⢠⠁⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⡙⣿⣿⣿⣿⡲⣦⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠃⠀⢸⠀⠀

⠀⠀⠀⢀⣾⣿⡿⠁⠀⡇⠘⣦⠀⠀⠀⠀⠀⠀⠓⣢⣤⠝⠻⣿⣶⣄⢀⠀⠀⡠⡠⣠⢄⢄⣀⣢⣢⣦⣄⣔⣤⡢⡠⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⠃⠀⣼⣿⡄⠈⣧⠀⠀⢀⣴⣦⠞⠁⠀⠀⠀⠀⠙⠻⠷⣇⣬⢼⣾⣴⣿⣻⣿⠿⠿⠿⠿⠿⢿⣟⣿⣷⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡼⠀⣿⡄⠀⠀⠀⠀ ⠀⣠⣿⣿⡿⠃⠀⣼⣿⣿⣿⡄⢸⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠮⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡇⠀⣿⢷⠀⠀⠀⠀ ⣼⣿⢻⠟⠁⠀⣼⣿⣿⣿⣿⣿⣾⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⡄⠀⠀⠀⢧⠀⢹⡸⡇⠀⠀⠀ ⣿⡇⠋⠀⣠⢾⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⢿⣿⣿⣿⣆⠀⠀⢸⠀⣿⡇⣧⠀⠀⠀ ⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣯⠀⣠⠞⠁⠀⠀⢀⠔⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠈⠻⣿⣿⣿⡄⠀⢸⠀⢻⡇⠸⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣽⣿⡴⠁⠀⠀⠀⢠⠊⢀⡔⢠⠞⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆⠀⠙⢿⣿⣳⠀⠈⡇⢸⡇⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢧⡟⠀⠀⠀⠀⣰⠃⢀⡼⢠⠟⠀⠀⠀⠀⠀⢀⣴⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠹⡿⡄⠀⡇⠸⣄⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡸⠃⠀⡸⢁⡏⠀⠀⠀⠀⢀⡴⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀⠀⢇⢱⡄⣧⡀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣰⠃⠀⢰⢃⣾⠁⠀⠀⢀⡴⠋⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡀⢻⡍⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⢠⠇⠀⠀⡜⣼⠇⠀⠀⣠⠋⠀⣠⡤⠤⠤⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⣿⠀⠀⠀⠀⣇⠈⡇⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠋⠀⠀⠀⣧⡏⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠸⡇⠀⣹⠀⠀⢀⠀⠈⠀⢷⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠉⠒⠦⢤⣀⠀⠀⠀⠀⣸⠁⠀⠊⠲⣄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡰⠦⠤⣄⡀⣰⠃⠀⢷⠀⣿⠀⠀⡸⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠖⠀⠀⠀⠀⠈⠙⠲⠤⣄⣇⣰⣷⣤⣶⣿⣿⣿⣦⣤⡀⠀⠀⢳⠀⣤⠀⠀⠀⠀⠀⡰⠃⡼⠁⢀⣤⠀⡸⠓⢤⠀⢸⢰⠃⠀⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⣀⣀⣠⣴⡾⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⠿⣿⣿⣿⣿⣿⣿⢿⣿⣦⠀⠈⣇⢻⡀⠀⠀⠀⣼⡥⠈⠀⣠⠞⢁⡼⠁⠀⠀⠀⢸⡸⠀⠀⡞⠀⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠛⢦⠀⣏⠓⢦⣤⣤⡤⠴⠒⠋⢹⣿⠇⣸⠻⠻⣿⣿⣿⣿⠀⣻⠻⣷⠀⠘⡎⡇⠀⢀⣾⠟⢁⣴⡾⢁⣴⣯⣤⣄⠀⠀⠀⣼⠇⠀⡼⠁⢀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⣿⣋⠻⣿⠀⠈⢧⢸⡄⠀⢳⠀⠀⠀⠀⠀⠈⣿⠀⡇⠀⢴⣿⣿⡏⠙⢿⡏⠀⠙⠂⠀⠈⢳⣴⣿⡯⠖⣻⣿⣿⣿⣿⠿⠻⣿⣷⠤⢤⡟⠀⡴⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣩⣦⡙⢧⡀⠀⠈⣇⠀⠸⣇⠀⠳⡄⠀⠀⢱⡀⢧⠀⠀⠉⠉⠀⢸⡿⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢩⣿⣿⣿⣿⣦⣀⠘⣿⣧⣼⢃⠞⠁⠀⢰⠇⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀ ⡤⠋⣿⠙⠦⣉⡓⠄⠸⡀⠀⢻⡄⠀⠙⢆⡀⡀⢳⡌⣇⡀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⣿⠿⣿⡏⠀⣸⣿⠃⠈⠀⠀⠀⡎⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⢾⡀⣄⡀⢻⡛⠲⠷⠄⠸⣻⡄⠀⠀⠱⡬⣦⣙⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠻⡛⢠⠟⠀⡰⣿⠃⢀⡀⠀⠀⠘⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠈⣧⣏⣿⢿⡷⡄⠀⠀⠀⢻⣿⣦⠀⠀⢻⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⣀⣤⠎⠀⣠⢞⣡⠖⠋⠀⣠⠞⠀⣠⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⣄⡼⡇⠙⣦⡀⠀⠈⢿⡈⠻⣦⣄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠀⠉⣹⠏⠀⢀⣠⠞⢁⣠⢞⣉⣉⣠⣬⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣬⣿⣅⡇⠀⠋⠻⣦⣄⡈⢳⡀⢸⣮⠙⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣴⣚⢁⣀⣈⣽⡷⠊⠻⣍⠁⢠⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶ ⠀⠀⠀⢨⣫⠴⠛⣧⠀⠀⠀⢹⡌⠉⠛⢛⠞⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠉⠹⣷⠀⠀⠈⢦⣿⣿⡋⠉⠋⢉⡉⠙⠉⠉⠉⠋ ⠀⠀⣠⠟⠁⠀⠀⢹⡄⠀⠀⠀⢧⠀⠀⠸⡄⢹⣄⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡆⠀⠀⢻⡄⠀⢲⣿⣿⡏⠉⠀⡀⠈⠁⢀⠀⠉⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢆⠀⠈⠀⠀⠀⠻⡀⢯⠓⠦⣄⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁⠀⣷⠀⠀⠘⡇⡀⣾⣿⣿⠃⣀⠀⠁⢀⡀⠈⠀⣀⢀⣿ ⠁⠆⠀⠀⠀⠀⠀⠀⠸⡆⠘⡆⠀⠀⠀⠀⠀⠹⣌⢧⠀⠀⠙⢦⣀⠙⣿⣷⣶⠶⠶⢶⡶⠶⠖⢲⣾⡏⠉⠁⢷⠀⠀⠀⢰⢸⡄⠀⠀⢷⢸⣿⣿⣯⡀⠀⠀⡀⠀⠀⢀⠀⠀⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣄⠸⣦⡀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠉⠳⣬⣿⡟⠀⠀⢸⣟⣔⡁⠈⠛⣿⣄⠀⠈⡇⠀⠀⢸⠀⣇⠀⠀⢸⣾⣿⣿⠁⠀⡄⠀⠀⢠⡄⠀⠀⣴⣿⠏ ⠂⠀⠀⠀⠂⣀⠀⠀⠀⠀⠚⢧⣷⡙⠦⣈⢦⣄⠀⠀⠉⠛⠦⣄⣀⠀⢘⣧⡀⠀⠀⣿⣫⡯⠀⠀⠀⠘⡿⣆⠀⢳⡄⠀⣸⠀⢸⠀⠀⢸⣿⣿⡟⠤⠄⠀⠀⠄⠀⠀⠠⢰⣿⡿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⡆⠀⠀⠀⠀⠀⠐⢼⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠈⠂⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⣰⠠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡏⡙⡆⠀⠀⢁⠆⠄⣀⠀⠀ ⡀⠀⠀⢡⠈⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⠀⡇⠀⢠⠃⣀⡴⡏⡄⠀ ⠈⠐⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⡄⠀⡰⠀⠀⢴⣿⡇⢳⣇⠀ ⠰⣒⠈⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠔⠁⢠⣄⡷⠚⠁⠀⠀⠈⠟⠁⢸⠟⡀ ⠀⠀⠌⢉⣀⣁⡤⠤⠚⡖⠒⣖⣨⣤⣶⣿⣿⠉⠉⠁⠀⠀⠀⢀⠀⠀⢸⠰⠁ ⠀⠀⠀⡌⡌⡀⢃⢸⠀⠀⢠⡉⠻⠾⠯⠭⠜⠀⠀⠀⠀⠀⠀⠀⠇⢀⡾⠀⠀ ⠀⠀⣰⡰⠑⢔⡪⡀⠄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡌⠴⡆⠀ ⠀⢠⣏⢀⡫⠉⠈⢁⠀⡀⢠⢳⣄⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠃⡐⠀⠀⡇⠀ ⠀⢉⠔⠃⢀⠀⡎⠛⠀⠇⠘⢸⠁⠈⠀⠒⠀⠤⠀⢀⣀⣀⠀⡰⠠⣔⣀⣇⠀ ⠀⠀⠀⠀⠨⡉⠑⠀⠇⠘⣠⢸⡦⢤⣤⡤⠄⡀⢠⡏⠀⠀⠀⠀⠀⠝⡻⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⡄⢿⣀⠙⠙⠽⢿⡿⣟⣷⡀⠀⠀⠀⢠⢬⠇⠀

⠀⠀⠀⠀⢀⡀⣀⢀⣠⠊⠠⠄⠈⠁⠉⠁⠀⠠⡤⣀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⡔⡇⠁⡠⠊⠑⢒⡤⢴⣦⣶⣶⣦⣆⣤⣄⡁⢚⢆⢊⠻⣇⢈⡽⠃⠀ ⠀⠀⠀⠀⣗⣢⠊⠀⢀⠔⠉⠀⠀⠈⡩⠂⠀⠀⠀⠈⠻⣦⡱⣡⠑⣽⡟⠀⠀⠀ ⠀⠀⠀⠀⣎⠃⠀⢠⠋⠀⠀⠠⣢⢺⠅⠀⠀⠀⠀⠀⡀⠈⢧⢱⠒⡽⠀⠀⠀⠀ ⠀⠀⠀⢰⢹⡀⠀⡇⠀⠀⢠⠏⠀⠸⣆⠀⠀⠀⢠⠲⠥⠀⠸⠀⡌⡅⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣰⣧⢀⠀⣬⠞⣽⣟⡏⠂⠼⠤⠦⣁⡀⡅⠀⠀⠑⢶⠀⠀⠀⠀ ⠀⠀⢀⣰⡟⠋⠉⡇⠑⡳⠜⠀⠭⠥⠃⠀⠀⠀⡼⣯⠿⡇⢀⡸⣀⢹⣧⠀⠀⠀ ⠀⠀⡔⠋⠙⣿⡞⠀⠀⢷⠀⠀⠀⢀⣤⠤⡄⡀⠐⠊⢈⠴⡟⢑⠑⠂⢫⠀⠀⠀ ⢀⣾⠃⡀⠀⠹⢷⠀⠀⠸⣄⠀⠀⠘⠀⠁⢢⠃⠀⠀⡜⢠⡇⠀⠀⠁⠘⠴⡄⠀ ⢸⣿⠋⣿⡪⠀⠈⢗⢄⠀⢙⡇⠠⢀⡀⠀⠀⣀⢠⠞⠀⣸⣧⣿⣷⣶⣤⡄⠹⣄ ⠀⠙⡆⣾⠀⠘⢀⣣⠟⠉⠉⠉⠐⠠⣉⠙⢜⠍⣁⣠⠴⡃⢪⣿⡟⢐⡏⢥⠀⡇ ⠀⠀⠃⠈⠣⡔⠁⠈⣿⣦⣄⡀⠀⠀⠈⢀⠀⢿⡦⢄⣩⠀⢡⠟⠇⠀⡇⠀⠀⠀ ⡄⢠⢲⠀⣸⢃⣀⠀⢸⡏⡇⠑⢍⠐⠖⠂⠢⣾⣣⡸⡀⠀⣏⢠⠇⣠⠟⠀⠀⠀ ⠃⠘⠚⣆⡯⠹⡤⠓⣾⣧⡇⠀⠀⠙⣄⠀⢀⣿⡟⢀⣧⠐⠁⡞⢸⡉⠀⠀⠀⠀ ⠂⠀⠀⡿⠀⠁⠱⢴⣿⡟⠀⡤⠂⠉⠙⠂⠔⢻⡷⠋⠉⡀⢀⠠⠐⢄⠀⠀⠀⠀

⠀⢀⣴⡻⠁⡜⠁⠈⠢⠀⠀⠂⠠⠄⠀⠀⠀⠀⠀⠀⡀⠔⣁⣀⠄⠼⣮⢆⠀⠀ ⢤⣾⠏⢀⠈⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠦⠣⡀⠡⠢⡀ ⢸⡟⢠⠉⢰⠀⢰⠄⠀⠀⠀⠀⠈⠱⠒⠠⠤⢤⠤⡄⠒⢲⠉⠀⠀⠀⠑⡀⢱⠃ ⢊⠁⡎⠐⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢑⡼⣄⢄⠆⠀⠀⠀⠀⠰⠀⠠ ⠞⠘⠁⢸⠀⠀⠀⠙⡀⠀⠀⠀⠀⠈⡄⢡⢀⢔⠝⠈⠲⠑⠹⠀⠀⠀⡄⠀⠇⠀ ⠀⠀⠀⢸⠀⠀⢠⠀⠐⣠⠀⠀⠀⠐⠌⣤⡦⢫⣶⣶⣶⠷⣶⡀⠀⢠⠃⠀⠀⠠ ⠀⠀⠀⠸⡘⣉⢻⠲⠂⡨⢷⣄⡀⠀⠈⠻⡙⠟⣿⣿⡛⠄⠏⠇⠀⡘⣇⠀⡆⠇ ⠀⠀⠀⠀⢋⢓⣿⣶⣶⣾⡧⡌⠛⠅⠢⠤⠙⠄⠀⠈⠀⠀⢰⠀⡠⣧⡛⣴⢏⠀ ⠀⡆⠇⠀⠈⢛⢯⡀⣿⡿⠹⠀⢰⠔⠈⠉⠁⠀⠀⠀⠀⠠⠗⡺⠁⠙⢡⢂⢜⠀ ⢀⢃⠘⡔⡀⠐⢽⠥⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠀⠠⢊⠔⠁⠀⠀ ⠈⢦⠢⣿⠪⣦⣀⣑⣄⠀⠀⠀⢀⣔⠮⠑⠂⠉⠀⢰⠀⠀⠀⢠⣃⠏⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠁⠑⠄⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⡘⠀⠀⣠⣇⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠁⠀⠀⠐⠈⠀⣠⡾⢁⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣢⣄⣀⡀⢀⣠⠞⠋⢠⣾⣝⢿⣿⣷⢄⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢺⣿⣿⢬⢉⠉⠁⢀⣴⣿⣿⣿⣷⣯⡏⠀⠀⠀

⡠⠁⠀⠀⠀⣠⣾⢟⣽⠟⠉⢀⣾⡏⠁⠈⠙⢦⠀⠀⠀⠀⠐⠤⣤⣈⠁⠒⠀⠀⠀⠀⠤⠄⠤⠄⠀⠀⠀⠒⠈⠁⠁⠀⠀⠀⢀⡴⠋⠉⠉⢢⡀⠀⠀⠑⣦⠟⢀⡞⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⣴⣿⢁⡼⠁⠀⢀⡾⠉⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⣀⣀⣀⣹⠦⠔⠛⢓⣺⡟⢦⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣴⡞⠉⠀⠱⡄⠱⣄⠀⠀⠀ ⠳⣤⣿⣿⣿⠃⠀⢀⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠶⠿⣯⡤⠖⢻⡆⠀⠀⠙⣄⠈⢧⡀⠀ ⠀⣿⣿⣿⠇⠀⢠⡟⡇⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠚⠉⠁⠀⠀⠀⠙⡄⠀⠀⠘⣆⠠⡽⠆ ⠀⢿⣿⡟⠀⢀⡞⠀⠁⢰⣤⠀⠀⠀⢿⢳⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠓⠒⠦⢤⣤⣤⣤⣤⣤⣤⣤⠶⠒⠚⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠘⡅⠓⠀ ⠀⡼⢿⠁⠀⣾⠇⠀⢸⠨⠻⠘⣇⡄⠸⡎⢧⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠙⡆⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠱⡄⠀ ⠞⢠⡏⠀⢸⡿⠀⠀⡇⠀⠀⠀⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⣼⣏⠁⢀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⣄ ⠀⣸⠁⠀⣧⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣴⡿⢇⠘⡷⣄⡳⢤⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘ ⢲⡇⠀⢰⠹⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⢸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⠀⠀⠀⠀⡴⢋⡜⠁⠀⢳⣹⡄⠙⢦⡙⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡆⠀⠀⠀ ⠋⠇⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⡆⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⡗⠢⣤⠊⣡⠏⠀⠀⠀⠀⠙⣷⠀⠀⠙⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠸⡄⠀⢹⡞⠁⡽⠳⢦⣄⣀⣀⣀⣀⣸⣧⣤⣄⣼⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⢰⠃⠀⠀⠀⢱⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⣶⡋⢧⡞⢀⡴⣫⢴⣾⣿⣿⢿⠿⠿⢿⣿⣹⡀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⢸⠀⢸⠑ ⠀⡀⠀⠀⠀⠀⠀⠀⡇⠸⡝⢶⠦⣤⣼⣄⣀⡀⠀⠀⠙⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⢻⡛⢿⣾⣽⣾⣿⣿⣿⣿⣭⣿⣆⠀⠀⣿⠇⡇⠀⠀⠀⠀⢸⠁⡇⠀⠀⠀⣼⠀⢸⠀ ⠐⠃⠀⠀⠀⠀⠀⠀⣿⡀⢳⠘⡄⠈⢹⠒⠺⢭⣙⠒⠒⠬⠯⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⢣⡳⡀⠉⣽⠋⣿⣿⣿⣿⡍⠙⢻⠀⠀⠿⢠⡇⠀⠀⠀⠀⡞⢀⣇⠀⠀⢀⡏⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢦⣧⡙⣆⢸⡀⢀⣀⣀⣉⣑⣒⡦⠟⠉⣿⣗⠦⣄⡀⠀⠀⠀⠀⠙⢿⡄⠁⠀⠹⡏⠛⠾⠿⠒⠉⠀⠀⠀⢸⠀⠀⠀⠀⣰⠃⢸⣾⡄⠀⡼⣧⡼⠁⠀ ⠀⠁⠀⠀⡄⠀⠀⠀⠀⢻⠀⠉⠳⣯⣳⣿⣿⣶⣺⣿⣿⣿⣷⣦⡀⠈⠙⠳⣤⣈⣙⠶⠦⢄⣀⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡼⢻⢠⡏⡏⢣⣰⣳⠟⠁⠀⢀ ⢀⠀⠀⠀⣧⠀⠀⠀⠀⠈⣧⣀⣼⣿⣿⠟⠋⣿⣿⣻⣿⣿⣭⣼⠙⠀⠀⢀⡴⠋⠀⣀⣀⣀⣀⣹⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣠⣾⠃⢸⣾⣾⡃⠘⣱⠃⠀⡇⠀⡸ ⢸⠀⢰⠀⢸⡀⠀⠀⠀⠀⠘⣿⠹⣿⣧⠀⠀⣿⣯⣘⣿⣿⢀⣿⠀⠀⠀⢸⣠⠼⠋⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠔⢫⡿⠁⠀⠀⠛⠛⠁⣰⠃⠀⡴⡇⠠⠀ ⢸⠀⢸⠀⠈⣧⠀⠀⠀⠀⠀⠈⢧⡙⣿⣣⡀⠹⠦⠔⠚⠉⠈⠁⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠟⠁⠀⠀⠀⠀⣀⡾⠁⣠⠎⠀⡕⠁⠀ ⢸⡀⢸⡀⠀⠈⣆⠸⡄⠀⠀⠑⢤⣙⡺⣝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣠⡾⠁⠀⠀⠁⠀⠀ ⠀⡇⠀⣷⡀⠀⣟⢦⠹⣄⠀⠀⠀⠙⣯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠀⠀⡩⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⡇⢣⡀⢸⣿⠳⣌⡳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣀⡤⠖⠛⠒⠊⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⠀⠙⣄⢻⡆⠈⠻⣮⣷⣦⣄⣀⣈⣛⣦⡄⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠧⠀⠈⠙⠛⠀⠀⠈⠓⠿⢭⠙⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣾⠋⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⣾⣿⣠⣟⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢀⣼⣿⠃⣿⡏⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠤⠴⠚⠁⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡽⢳⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⣰⣟⣛⣋⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣦⣿⡻⠿⣶⣦⣤⣀⣀⣴⣿⡿⠋⠀⠀⠀⣄⣼⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⢿⠋⠙⠖⢉⡝⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡦⡀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⠻⡞⢀⠎⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣧⡌⣻⣿⣿⣿⣿⣝⠻⣷⣀⣀⡀⠀⠀⢀⠀⣀⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⢸⠀⠀⠀

⠀⠀⠀⠀⢰⣶⣶⣤⢔⠞⡼⣭⣥⠢⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡿⠛⢺⠢⠄⣴⡾⢁⡷⠂⠀⠀⠀⣀⠠⠔⠚⠓⢄⣀⣀⣀⣠⠀ ⠀⠀⣤⣶⣾⣿⣁⡉⢿⣄⠿⠛⡽⠋⢀⠠⢔⡂⠥⣶⣾⣷⣦⣤⣄⣀⣀⣀⣿⡀ ⠀⠀⠙⣿⣿⣿⣿⡦⠽⠈⠃⡁⠔⡪⠔⠈⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⡆⠌⠻ ⠀⠀⠀⠈⠛⠛⠋⢀⡠⢔⠨⠂⠁⣀⣠⣴⠈⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⢀⠠⠐⠮⢑⣈⣠⣴⣶⣿⣿⡿⡃⠐⠤⢿⡁⠈⢻⣿⣿⣿⣿⣁⠤⠀⠀ ⠀⠀⠀⠂⠉⣽⡿⣿⣿⠋⢫⡍⠣⠠⣧⡅⠀⠀⠀⣈⢳⣵⣿⣿⣿⡝⢷⡄⠀⠀ ⠀⠀⠀⠠⠊⠀⣰⣿⡿⡄⢠⠉⢓⣦⠀⠓⠀⣴⡋⠁⠸⠙⢻⠉⠻⢿⣮⢊⠢⠀ ⠀⢀⠔⠁⠀⣰⣿⡿⠁⢿⢖⠏⠀⠀⠀⠀⠀⠀⠉⢉⣦⢡⠧⡀⠠⢄⠙⢷⣦⠠ ⣰⡓⠀⢀⣴⣿⠏⠀⣦⢸⢼⣦⣄⣀⠔⠐⠀⢀⣠⣾⣯⡞⠱⡇⠀⠀⠈⠢⡙⡄ ⢡⡁⢀⣿⣿⠋⢀⣠⣿⣿⡌⢿⣩⣝⢝⣛⣋⣾⣿⡯⣺⡇⠀⠘⠈⠠⡤⠀⠇⠰ ⢷⣴⣿⡟⠁⠀⠞⠀⣧⠭⠝⢳⣿⣿⡝⢒⢻⠿⠕⠚⠙⠤⠤⢴⠀⠀⢹⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⣰⡇⡀⣴⢏⠽⡻⣿⡠⠑⢃⣒⢰⣢⣀⠀⣘⡀⠀⢸⠀⠀⠀ ⣿⣏⡇⠀⢸⠀⠘⢳⡿⣾⠿⢮⣝⡔⣹⢶⣤⠿⠋⢹⣃⣩⣿⣷⡁⠀⢀⠀⠀⠀ ⣿⣿⡇⠀⢀⠀⣆⣾⣿⠘⡢⠊⠀⢸⡏⠼⡁⠀⠀⣸⡿⠛⣹⣿⣷⡀⢸⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⢀⣠⣤⣿⢒⣒⡒⠒⠒⠦⣄⠀⠀⢀⠀⠀⢀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⡖⠋⣵⠏⢻⡿⠿⣿⣿⣷⣶⡌⠳⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣠⢾⣇⠜⠁⠀⠈⠉⢉⣩⣽⡇⠀⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣈⣙⣳⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠟⢋⠝⢡⡏⢻⡮⢅⠁⢾⣿⣿⣿⠃⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠛⠋⠁⠀⠹⢦⣄⡀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠠⠯⣤⡜⡇⠀⠈⣦⣥⣼⣿⣿⣧⡴⣻⠋⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠋⣁⣠⣤⡔⠚⠉⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠸⣷⣷⠀⣼⣿⡿⠟⠉⢡⣾⡾⠁⠀⠀⠀⢀⣠⠴⠚⠉⢁⣤⣤⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡒⠑⠦⣀⣈⡻⣷⣏⣁⠀⣀⡴⠞⠁⠀⢀⣠⠴⠊⠉⣀⠴⠖⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⢿⣿⣷⢶ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣤⠴⠖⠋⠁⠀⣀⡴⠞⠉⣀⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣦⣤⣀⡈⠻⣦ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣠⠴⠚⢁⣠⠔⠛⠁⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⠴⠋⢁⡤⠖⠉⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⢹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⣀⣤⠖⢋⣡⠴⠊⠁⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⡟⢻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢋⣉⡠⠖⠉⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡿⣿⠀⠀⣄⠀⠈⢿⡏⠉⠉⠀⠳⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⠠⠴ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢋⠡⠶⠚⠉⢁⣀⣠⢤⣶⡿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠇⡟⠀⠀⠈⠛⠷⠮⢿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠤⠖⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢊⣁⣤⡶⠾⠧⢶⣶⣾⣿⣿⣿⡿⣿⣿⣷⢿⠿⠛⠛⢻⠉⠉⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⢦⠀⢦⡹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢙⣿⣿⣧⡏⠁⠈⢻⡂⠤⠀⠘⢧⣄⣰⣜⣷⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⢻⣷⣌⢻⣽⣿⣿⣿⣿⣿⣧⡈⢻⡿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠁⢀⣾⣿⣿⢹⡇⠀⠀⢸⠛⠿⣶⣦⣀⠀⠁⠉⠙⣿⣿⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⢸⡿⣿⣿⣿⢽⣓⢿⣿⣿⣿⣷⣄⠹⣝⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣾⣿⣿⣿⢸⣿⡄⠀⠸⡄⠀⠈⠙⠻⢷⣶⡄⠀⠈⠻⠆⠀⢀⣶⡿⠛⠉⠀⠀⠀⢸⠃⢸⠏⢻⣼⠀⠀⠙⢿⣿⣿⣿⣦⡘⣆⠙⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣾⣿⣿⣿⢻⠀⢹⣿⡄⠀⢷⢠⣤⠴⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣀⠀⡞⠀⡞⢀⣼⠃⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⢇⠀⠈⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣏⡇⠀⢸⣿⣿⢷⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣳⢃⣼⠁⢸⡿⣤⠤⠤⢤⣀⡀⠀⠈⠻⣿⣿⣮⢧⡀⠀⣠ ⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠁⡇⠀⠈⢻⣿⠸⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢠⣿⠀⢉⣶⠂⠀⠀⠉⠲⢤⡀⠈⠻⣿⣿⣇⠀⠉ ⢀⡴⣪⢠⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠀⠀⡇⢀⠀⠘⣿⠀⣿⣦⣀⠀⠀⠀⠀⠀⣶⠖⠲⠖⠂⠀⠈⠁⠀⠀⣠⣾⣟⡿⣱⣼⡏⣛⢦⡏⠀⠀⠀⠀⠀⠀⠉⠲⣄⡈⠻⣿⡄⠀ ⣨⡾⢡⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠀⠀⠀⢹⢸⡄⠀⣿⠚⣿⣿⣿⣷⣦⣄⣠⣾⠃⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣽⢣⣿⣿⠀⠈⠛⢿⡀⠀⠆⠀⠀⠀⠀⠀⠀⠹⡆⠘⢿⠀ ⡞⢡⡞⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⡿⣿⣦⣿⠀⠹⣿⣿⡿⠿⢋⣹⠟⡻⣷⡒⣶⠿⠟⣹⣿⣿⣿⣿⠇⢫⣿⣿⣿⠀⠀⠀⠀⢳⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇ ⠀⡞⢠⠀⠀⠀⣾⣿⣿⣿⣿⠅⠀⢤⣤⣤⣤⣾⠻⣿⣿⣿⣧⠀⠸⣿⢇⣴⣿⣧⠀⣧⣀⣙⣁⣀⣴⣿⣿⣿⣿⣿⣵⢏⣽⣿⠏⠀⠀⠀⠀⢸⠀⠀⠅⠶⢶⡶⠀⠀⢰⠇⠀⠀⢹ ⣸⢱⠏⣠⣶⣴⣿⣿⣿⠏⢸⠀⠀⢸⣿⠀⠀⢾⡄⠙⠪⠻⢿⣷⣴⢡⣾⣿⣿⣿⡇⣿⣯⣉⣿⣿⣿⣿⡿⠟⠩⣚⣵⣿⡟⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⠏⣿⣾⣿⣿⣿⣿⡿⠃⠀⢸⠀⠀⢸⡇⠀⠀⣾⡶⠶⠶⠶⣚⣫⠅⣿⣿⣿⣿⣿⣷⡌⠋⢱⡉⢻⡿⠿⠿⠿⠛⠋⠁⠀⠊⠝⣒⣶⠶⠶⣖⣻⠂⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⣸⠀⠀⢸⡇⠀⠀⣾⠈⠉⠀⠀⠀⠀⡤⠿⣿⣿⣿⣿⣿⣿⡀⠈⠿⣄⡙⢦⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⣾⣿⣿⡏⣿⡏⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⣸⢼⠀⠀⠀⣀⠴⣻⢷⠲⢤⣙⠻⣿⣿⣿⣧⢀⡤⠴⠛⠃⠈⠙⠓⠶⢾⣙⠦⣄⠀⠀⠀⠀⢰⢳⡀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⣰⡿⢾⣄⡴⢚⣥⣶⣷⡘⣧⣤⡌⠳⣌⢻⣿⠉⢻⠀⠀⠀⣰⣾⣿⣶⣤⣾⣿⡶⢮⣓⠦⣤⣤⣿⠽⢑⡆⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⢀⡿⢵⣶⣯⣽⣾⣿⣿⣿⣿⣷⣸⡇⠙⢦⠘⣆⢹⡗⡿⣤⣤⣴⡿⣟⣯⠭⠁⢽⣿⠀⠀⢈⣩⣶⣶⣶⣾⡁⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⣼⣿⣯⡻⣿⣿⠀⠈⠙⣿⠟⠶⠟⠁⣿⢘⠞⣹⣿⣿⠷⠋⠁⠀⠀⠀⢀⣷⣶⣾⣿⣿⣿⢟⣿⣿⣷⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⡇⠀⠀⢸⠇⢰⣿⣿⣿⡄⠓⠿⣄⣀⡞⠁⠀⠀⠀⢸⣏⣜⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⡿⢹⣿⣿⣿⣿⣧⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⡇⠀⠀⢸⣤⣿⣿⣿⣿⣇⠀⣀⡽⠋⠀⠀⠀⠀⠀⣞⣧⣊⣠⠛⣦⣄⠀⠀⠀⠀⠀⣠⣿⣯⠞⠉⠀⢀⣾⣿⣿⣿⣿⣿⣧⡀⠀⢸⡇⠀⢸⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⠤⣄⣀⠀⠀⠠⠿⠿⠿⢿⣶⣶⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠒⢄⠀⠈⡽⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠱⣀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠹⣧⢹⡿⢿⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠹⣷⣣⠀⠀⠀⠠⡀⠀⠹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⣵⣀⡇⠀⠀⠀⠀ ⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⢹⠀⠀⠀⠀⠀⠀⢺⣷⡱⡀⠈⢦⡘⢄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⠁⠀⠀⠀⠀ ⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣯⠀⠸⡄⠀⠀⠀⠀⡠⠊⠉⢙⣿⣄⣠⢽⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡿⠀⠀⠀⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⢀⣇⠀⠀⣠⣮⣁⣴⣾⣿⡋⠙⡇⣤⢽⣷⣦⣙⠿⣿⣿⢿⣿⣿⡀⡀⢻⡇⠀⠀⠀⠀⠀ ⡿⠟⠁⠀⠀⠀⠀⠀⣠⢿⢼⣿⣿⣿⣿⣿⣿⣼⣿⡀⠈⠁⠉⠛⢻⡌⢩⣱⡀⠀⢸⠀⣏⡍⠙⣿⠟⡏⢠⣿⣿⣷⣷⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⣼⠛⡟⠿⠟⣿⣿⣟⡻⣷⡀⠀⠀⠀⠈⣅⣈⠿⠓⠀⢸⠀⢻⡇⠀⣸⡖⢡⣾⣿⣿⣿⣿⣧⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠁⠀⠀⣸⢹⣿⣿⢘⣾⠛⢿⣟⣷⠈⠓⠄⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⣾⣿⢀⣿⣷⣿⣿⣿⠇⢻⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢿⣿⣭⡙⠄⠘⣍⠟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣇⣾⠿⣧⣾⡿⢿⠻⣿⠋⠀⠸⣿⣟⣉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠸⠻⣿⣷⠀⠈⠀⠀⠀⢠⡶⠁⠀⠑⢆⠀⠀⠠⠞⢹⡏⣴⣿⡿⠳⣿⣄⠱⣤⠀⠀⢳⠻⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠊⠀⠈⠛⢻⣿⢀⡄⠉⣿⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠆⠀⠀⠀⡟⣼⣿⣿⡇⢠⠋⠘⠳⣅⠀⠀⠀⢣⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠃⡄⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣷⡿⠟⢼⡇⣼⣿⣿⣷⣾⣄⠀⠀⠀⠣⡘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⢳⣿⣿⣿⣿⡦⣄⠀⠀⠀⠀⠢⢄⠤⠃⠀⢀⣿⡿⠀⣠⣿⣴⣿⣿⣿⣿⣿⠿⠓⠒⠒⠒⠬⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟⢣⢸⣿⣿⣿⣿⣷⡀⠉⠑⠢⠄⣀⡀⢀⣠⣴⡟⡟⢀⣼⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠡⠒⡟⠀⢸⠘⣿⣿⡻⣿⣿⣷⠀⠀⠀⠀⠀⠈⣡⣾⣿⣿⣇⣾⣿⣿⣿⣿⡟⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⡿⣯⡙⣷⣿⣿⣇⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⣀⣠⣦⣌⣓⣤⣤⣤⣤⠀⠀⠀⠀⠉⢄ ⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠇⣃⣼⡻⢿⣿⡿⣿⡀⠀⢀⣿⣿⡿⠗⠋⣉⣀⣤⢗⡫⠟⠻⠿⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠⢶⡿⠃⠀⠙⣆⢻⠁⠃⠃⠀⡼⠛⡿⠁⠠⢎⣠⡾⠗⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣺⣟⠦⠼⠦⠀⠀⠀⢸⣸⣿⣿⣶⣶⣾⣛⣇⣄⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⣛⠛⠛⠛⠻⠿⠻⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣿⢿⢿⣿⣿⣶⣤⣀⡀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣟⣻⣷⣿⣶⣦⣤⠂⢍⢹⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⢻⡻⠿⡿⠛⢿⣿⣿⣿⣿⣿⣿⡇⠈⡊⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⢻⡧⠀⠔⢄⢘⣾⣿⣿⣿⣿⣅⣦⠃⠀⠀ ⣴⣾⠁⠀⠀⠀⣠⣿⣿⡏⢸⠀⠀⢀⠔⢉⣳⡨⢦⡑⢿⣿⣿⣿⡿⢻⣿⠀⠀⠀ ⡿⠇⠀⠀⠀⣰⢹⣿⣿⣷⣸⡆⠐⠙⢾⡛⢢⠀⠏⢛⠓⡿⡟⣹⣷⣆⢹⠀⠀⠀ ⠀⠀⠀⠠⠊⢸⢯⡏⣋⢿⣯⡻⢄⠀⠈⠆⠋⠁⡀⢹⡄⣿⣵⣿⣿⣿⣾⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡜⣿⣝⠄⠿⠃⠀⡠⢀⠀⠀⢀⣡⢿⣵⢟⠿⠟⠀⣿⣏⠀⠀⠀ ⠀⠀⠠⠐⠛⢟⡇⡉⢻⡄⠀⠀⠸⠀⠀⠡⠀⠀⣏⣾⡟⠹⠣⢝⠀⠐⡹⡆⠀⠀ ⠀⠀⠀⠀⢀⣾⣟⢁⣸⣷⡀⠀⠀⠠⡀⢠⠀⢰⡾⢋⣇⣾⣿⣿⣦⡀⣐⢴⠀⠀ ⠀⠀⠀⠀⡈⢙⠟⢸⣿⣿⣧⠁⠂⠠⠈⡠⣴⡛⣡⣾⣿⣿⠟⠋⠀⠀⠀⠈⢃⠀ ⠀⠀⠀⠀⠈⢸⠀⡌⢿⢺⣿⣧⠀⠀⣤⣾⣿⣷⣿⠟⠛⢁⣔⣢⣀⣀⣀⠀⠈⢂ ⠀⠀⠀⠀⠤⠊⢀⣣⠜⢝⢿⠻⠄⢰⢿⠟⡨⣡⡺⠙⠙⠛⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠤⠇⠀⢈⣼⣶⣶⣷⣢⣤⡾⠋⠀⠀⠀⠀⠀⠆⠀⠀⠀⣾⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣦⣍⣉⠉⣞⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⡿⢗⠲⠭⣶⣿⣄⠀ ⠀⠀⠀⠀⠠⢪⠏⡉⠉⣢⠀⢀⠀⠀⠀⠀⠀⠀⣈⠦⡢⠑⠈⠀⠀⠀⠈⠛⠿⣿ ⠀⠀⠀⡰⢡⣁⠔⢈⢵⠁⠪⡑⢥⣀⣤⡼⢗⠌⠂⠁⠀⢀⠠⠄⠒⠀⠀⠀⣠⣼ ⣰⣦⣤⠡⢪⢄⠀⡶⠃⡬⠑⠈⡡⡐⠕⠈⠀⠀⢀⣤⣮⣄⡀⠀⠀⠀⠀⠘⠓⢤ ⠛⠛⣻⡄⠘⢊⢂⣣⠊⢀⢔⠜⠈⠀⠀⢀⣠⣆⠉⠀⠈⣧⣈⠔⠀⠀⠀⠀⠀⢠ ⠢⠀⠉⢹⣶⠔⢒⢅⠠⠊⠀⠀⠀⡠⠂⠁⠈⢿⢦⡀⢀⠙⢄⣳⡀⠀⠀⠀⣰⣿ ⡀⠢⡤⡊⢎⠎⠂⠁⠀⢀⣤⣶⣿⣧⡄⠤⡒⣀⣑⢽⠁⢷⡟⢗⠳⠀⣀⣠⠿⠛ ⡠⡐⠕⠈⠀⢀⣠⡔⡞⣻⢧⣽⡝⢝⢧⠘⣿⢿⠈⢻⡇⣻⠃⢹⢄⠉⠃⢄⠀⠀ ⢉⡀⡤⠶⠌⠀⣿⣇⣿⡃⠸⠏⠃⠀⠀⠀⠀⠀⢀⢞⡇⡏⠀⠘⠀⠈⠂⠄⠀⠀ ⣯⡀⠘⠂⡉⠀⠉⣿⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣨⣎⣇⣷⠀⠀⣦⠄⠀⠀⠀⠀ ⣙⣣⣀⠈⠢⡉⠁⢿⣧⢿⡅⠢⠄⡀⠀⠀⡠⠚⡏⢉⠟⠹⠀⠀⠋⠦⠄⠀⠀⠀ ⠈⣾⠀⠀⡘⣜⡀⢸⡇⡻⡌⢀⣠⣼⣭⣫⢴⠶⢿⣿⣿⣦⡇⠀⢰⡀⠀⠀⠀⠀ ⠀⢰⠈⢁⠟⠇⠃⢸⡇⡿⣸⣿⣿⡿⠇⢀⣤⣶⣿⣿⣿⡟⠋⠁⡐⢦⠈⠀⠀⠀ ⠀⢸⠈⠉⠦⠀⠀⢸⣣⠓⢿⣿⣿⣧⣶⣿⣿⣿⡿⠟⠋⠀⢀⢪⠊⠀⢡⠀⠀⠀ ⠀⠀⠡⡀⠀⠑⢄⢸⡰⡀⢈⢛⠟⠔⠋⠫⢉⠘⠱⢶⠐⠪⠑⠒⠉⠴⠢⡆⠀⠀

⠀⠀⠀⠀⠇⠀⢸⡷⠒⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⠬⠒⠀⠀⢀⠦⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣽⣿⣿⣷⣤⣧⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠛⢢⠀⠀⠀⠀⢀⡴⣿⠟⠋⠁⡀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⢿⣿⣿⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠎⠀⠀⠀⡴⠏⠉⠁⢀⡤⠞⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣤⠾⠛⠀⠀⠀⠀⠹⣷⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠀⠀⣠⠎⠀⠀⢀⠔⠉⠀⢀⠜⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡴⠺⠛⠁⠀⠀⠀⠀⠀⢀⡀⠘⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⡴⠋⠀⠀⡠⠋⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⡿⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠁⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⣀⠤⠒⠁⠀⢀⡤⠊⠀⠀⢀⡜⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠚⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⣼⡆⠀⠀⠀⡇⠀⠀⠀ ⠐⠤⠭⠭⠤⠤⠤⠄⡶⠋⠀⠀⠀⢠⠎⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠃⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⡰⠃⣠⠞⠁⠢⠤⣀⠀⠀⠀⣴⠏⠀⡰⠃⠀⠀⠀⢀⠔⠀⠒⠓⠒⣢⣴⠉⠀⢸⡇⠀⢀⣀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣼⡡⠞⠁⠀⠀⠀⠀⠀⠉⠂⡼⠃⢀⠞⠀⠀⠀⠀⡴⠁⠀⢀⣀⠴⠊⠁⠉⠻⣆⢸⣧⠞⢁⡠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⠠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⣿⠀⠀⡄⠀⡼⠴⡒⠊⡉⠐⠒⠠⣀⠀⠀⠀⢹⠃⠀⢁⡰⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⢠⠃⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠸⠁⣰⠛⣿⠀⣰⢧⣼⠀⠠⠤⠽⢿⣿⣿⣷⣌⠳⡀⠀⡆⠀⠀⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠀⣼⡄⠀⠀⠀⡆⢈⡗⣤⣀⠀⠀⠀⠀⡰⠃⠀⢻⠀⡇⠘⢿⠀⠀⠀⣠⣾⣿⡍⠉⠻⣷⣜⢦⣧⠀⢇⢱⡾⡇⠀⠀⠀ ⠀⠀⠀⣀⣿⡗⢰⠋⡇⠂⠀⠀⡇⢸⣇⡟⠈⠙⠢⢄⡴⠁⠀⠀⠀⠳⣇⠀⠈⠁⠀⡰⠉⠈⣙⣇⠀⡄⠈⢻⣿⣍⢣⣈⠓⠓⡇⠀⠀⠀ ⠀⢠⠀⠀⠉⢧⠷⠒⢷⣆⠀⠀⢃⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣧⠀⢴⡟⠈⠉⡇⠀⣸⢿⣿⡉⠉⠉⠉⣇⠀⠀⡀ ⠀⠀⠳⢴⣤⡍⠀⠀⠈⣿⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣹⣀⠜⠁⡴⠁⢘⣿⣷⣄⣠⠞⠁⠀⠀⠈ ⠀⠀⠀⠀⠈⠙⠳⢄⣀⣿⣇⠀⠀⣿⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠈⠉⣠⠖⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣇⠀⣿⣀⣽⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠁⠀⢀⣠⡴⠊⠁⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣼⢋⡔⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⣒⠿⠛⠉⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣀⠨⡝⢆⠀⠀⠀⠀⠀⠈⠻⡒⠢⠤⠤⠐⠒⠊⠁⠀⠀⠀⠀⠀⣠⠔⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣮⣷⠄⣀⣀⣀⣀⣀⠈⢷⣦⣄⣀⠀⠀⠀⢀⣀⡀⠤⠊⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡏⠁⠀⠀⠀⣾⣹⣷⣶⣿⣿⠿⠛⠛⣻⣿⠋⠉⠀⠀⠀⢀⡴⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⡘⢷⡟⠉⠛⢤⣶⣾⣿⢿⡿⠋⢀⣀⠤⠚⠉⠀⠀⠀⢀⣠⠖⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⢹⣄⠀⠈⣿⢹⡀⠀⢸⣯⣴⣿⣞⣛⠉⠉⠀⠀⣀⣀⣤⣶⣾⣿⠗⠚⠒⠢⢄⡼⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡋⠉⠁⠒⢄⢻⣣⠀⠘⣿⣷⣶⣿⣿⣿⣿⣟⣻⣿⡟⡏⠙⠋⣡⠞⠉⡽⠁⠀⠀⠀⠀⠀⣷⠟⢆⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠳⢦⡀⠀⠙⠿⣆⠀⢸⣿⣿⣿⣿⣿⣽⠋⠙⣛⠺⠥⠀⡸⠃⠀⣀⡇⠀⠀⠀⠀⠀⠐⢹⡿⢦⡇⠀⠀⠀