⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢛⣖⡶⠤⠤⠤⠴⠚⡽⠋⠙⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠴⢋⣠⡿⠯⠤⠀⢀⣠⡶⢾⣴⢶⣤⢤⣌⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠒⠒⢲⡶⠛⠒⢂⣶⠶⠦⢻⣥⡶⣶⠮⠓⠿⠶⠷⠜⢧⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⡿⠀⢀⣰⡿⠅⠤⡐⢛⣿⠟⠈⢷⣄⠀⠀⠀⠀⢀⣙⣷⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⣤⣥⠞⠉⢀⡴⣫⠏⡰⠋⠈⠀⠀⡴⠛⢧⣀⠀⠀⢺⢡⠊⠈⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣞⡧⢾⡽⢺⡧⠤⠤⣞⡼⠁⢸⡇⣶⣶⣤⣾⠇⠀⠀⠉⠉⠉⢽⣯⡀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣾⡤⠟⠀⢀⣼⣿⣿⣴⠗⠻⡌⢻⣿⣿⣷⠆⠀⣀⣀⣀⣀⡿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢲⣿⡟⠉⢹⡽⡇⣽⢠⡴⠃⣼⠏⠉⠁⠀⣾⣿⣿⡿⡽⢳⣣⠏⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣫⡾⢸⡗⠋⢉⣿⣿⣘⣏⣷⢠⠏⠀⠀⠰⢶⣸⠈⠀⢰⣇⣸⡅⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡞⠀⣠⠿⣆⢤⣿⠋⣿⣿⠻⠁⠘⣷⣤⣀⣉⡙⠛⠁⣰⡟⠉⣨⠟⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⢸⡇⣠⡬⣿⣟⢾⡿⠛⢦⡀⠀⠈⠛⢮⣉⣿⢶⣾⠛⡇⢸⠁⠀⠀⠀⣠⡾⠋⠉⠛⠒⠒⠂⠀⠀⠀⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡾⠁⠀⣷⡏⠉⠀⣧⠀⢿⣦⣄⠀⢘⣶⠀⡾⠁⣼⡷⠛⠀⠀⢀⣴⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⣴⣞⠛⢳⡄⠙⣋⣀⣀⣀⣾⠁⠀⠀⣿⠀⠀⠙⠻⢷⣿⣿⣼⠁⠀⠛⠁⠀⠀⠀⣿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠉⠳⣄⠹⣏⠉⠉⢹⡉⠀⠀⠀⠀⢿⠆⠀⠀⠀⡾⠀⠀⠁⠀⠀⠀⠀⠀⣤⣶⠿⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⢰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⣆⠀⠠⢷⣄⣀⡀⠀⠸⡄⠀⠀⢼⢳⣦⡀⠀⠀⣠⣤⠶⠚⠉⢡⠀⣧⠀⢸⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⢻⣄⡀⠀⠹⣎⠉⠙⠁⠐⠦⠤⠌⠁⣿⣝⣶⣏⢻⡳⣄⠀⠀⣸⠀⢻⠀⢸⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠻⣷⡀⠀⠈⠻⣦⣀⡀⠀⠀⢀⡼⠋⢹⠉⠈⢻⣧⠹⣆⠀⡟⠀⢸⡇⣼⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⢻⢷⡀⠀⠀⠈⠻⢯⣝⣋⡉⢀⣠⡾⠀⠀⠀⣿⣆⣹⣆⡇⠀⠀⡇⡿⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⢻⡆⠀⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⢀⡾⡟⠀⠈⡇⠙⣦⣀⠀⠀⠀⡀⣉⠉⣉⣁⠀⠀⠀⢀⡏⠘⣦⢹⡅⠀⢀⣿⢃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢛⣖⡶⠤⠤⠤⠴⠚⡽⠋⠙⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠴⢋⣠⡿⠯⠤⠀⢀⣠⡶⢾⣴⢶⣤⢤⣌⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠒⠒⢲⡶⠛⠒⢂⣶⠶⠦⢻⣥⡶⣶⠮⠓⠿⠶⠷⠜⢧⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⡿⠀⢀⣰⡿⠅⠤⡐⢛⣿⠟⠈⢷⣄⠀⠀⠀⠀⢀⣙⣷⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⣤⣥⠞⠉⢀⡴⣫⠏⡰⠋⠈⠀⠀⡴⠛⢧⣀⠀⠀⢺⢡⠊⠈⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣞⡧⢾⡽⢺⡧⠤⠤⣞⡼⠁⢸⡇⣶⣶⣤⣾⠇⠀⠀⠉⠉⠉⢽⣯⡀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣾⡤⠟⠀⢀⣼⣿⣿⣴⠗⠻⡌⢻⣿⣿⣷⠆⠀⣀⣀⣀⣀⡿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢲⣿⡟⠉⢹⡽⡇⣽⢠⡴⠃⣼⠏⠉⠁⠀⣾⣿⣿⡿⡽⢳⣣⠏⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣫⡾⢸⡗⠋⢉⣿⣿⣘⣏⣷⢠⠏⠀⠀⠰⢶⣸⠈⠀⢰⣇⣸⡅⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡞⠀⣠⠿⣆⢤⣿⠋⣿⣿⠻⠁⠘⣷⣤⣀⣉⡙⠛⠁⣰⡟⠉⣨⠟⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⢸⡇⣠⡬⣿⣟⢾⡿⠛⢦⡀⠀⠈⠛⢮⣉⣿⢶⣾⠛⡇⢸⠁⠀⠀⠀⣠⡾⠋⠉⠛⠒⠒⠂⠀⠀⠀⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡾⠁⠀⣷⡏⠉⠀⣧⠀⢿⣦⣄⠀⢘⣶⠀⡾⠁⣼⡷⠛⠀⠀⢀⣴⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⣀⣤⡤⠤⠤⣴⣞⠛⢳⡄⠙⣋⣀⣀⣀⣾⠁⠀⠀⣿⠀⠀⠙⠻⢷⣿⣿⣼⠁⠀⠛⠁⠀⠀⠀⣿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠉⠳⣄⠹⣏⠉⠉⢹⡉⠀⠀⠀⠀⢿⠆⠀⠀⠀⡾⠀⠀⠁⠀⠀⠀⠀⠀⣤⣶⠿⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⢰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⣆⠀⠠⢷⣄⣀⡀⠀⠸⡄⠀⠀⢼⢳⣦⡀⠀⠀⣠⣤⠶⠚⠉⢡⠀⣧⠀⢸⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⢻⣄⡀⠀⠹⣎⠉⠙⠁⠐⠦⠤⠌⠁⣿⣝⣶⣏⢻⡳⣄⠀⠀⣸⠀⢻⠀⢸⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠻⣷⡀⠀⠈⠻⣦⣀⡀⠀⠀⢀⡼⠋⢹⠉⠈⢻⣧⠹⣆⠀⡟⠀⢸⡇⣼⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⢻⢷⡀⠀⠀⠈⠻⢯⣝⣋⡉⢀⣠⡾⠀⠀⠀⣿⣆⣹⣆⡇⠀⠀⡇⡿⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⢻⡆⠀⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⢀⡾⡟⠀⠈⡇⠙⣦⣀⠀⠀⠀⡀⣉⠉⣉⣁⠀⠀⠀⢀⡏⠘⣦⢹⡅⠀⢀⣿⢃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀