⠀⠀⠽⢆⣷⠏⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠶⣞⣛⣺⡀⢀⣤⣰⣧⣤⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⢠⣞⡉⠉⠘⠷⠻⣆⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠚⠁⠙⣧⠀⢀⡴⠛⠻⣆⣠⣄⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀ ⢀⡦⣧⣾⣍⠉⢹⣷⣀⣄⣿⠬⠿⣷⣦⣀⣤⡤⠟⠉⠻⠶⢶⡶⠶⠟⠋⠙⠿⢶⣤⣄⡶⠿⠋⠙⠷⠶⠶⠶⠾⠛⠉⠻⢷⣦⣤⣴⠾⠟⠙⠻⠶⢶⡶⠶⠿⠋⠙⠻⢶⣤⣄⠀⠀ ⠀⠁⠈⠁⢸⡇⣼⠙⠋⠈⠁⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠛⢿⡇⠻⢤⣀⡀⠀⣀⣀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡷⣄⢺⠯⠤⠤⠤⢤⣄⠀⣨⡇⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠋⠁⠈⠋⠉⠿⠷⣶⡀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠈⠋⠀⠀⠀⠀⠀⢸⣆⡏⡇⣿⠀⠀⠀⠀⠀⠀⣴⠟⠁⣀⡴⠒⠦⢤⡀⠀⠀⠙⠻⣶⠶⠟⠉⠛⠛⠛⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣄⠀⠀⢰⣟⠙⣦⣸⠿⣇⡇⣿⠀⠀⠀⠀⠀⢠⡟⠀⢸⡉⢀⣰⣤⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣉⣉⠉⠉⢿⣟⣛⣭⡄⠨⡇⣿⠀⠀⠀⠀⠀⢸⡇⠀⠰⣏⠀⠛⠛⣄⡿⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠙⠒⢦⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣧⢠⡟⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢼⣷⡆⢺⡃⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣴⣋⣶⣄⣰⣟⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠸⣇⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⢄⣌⠈⣠⠾⠁⠀⣼⠀⠀⠀⠀⠀⠀⣠⣤⣿⢉⣿⣋⡽⣋⣸⠀⠀⠀⠀ ⠀⠀⠐⠊⠉⠁⠀⣈⣙⠒⠒⠒⠒⡇⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡤⠤⣄⣀⡺⣷⣦⣦⣷⠀⠀⠀⠀⠈⠉⠁⠀⠀⣾⠇⠀⠀⠀⠀⢠⣴⣿⣽⡋⣻⠷⠛⠳⣻⠟⠀⠀⠀⠀ ⠀⠀⠚⠁⠀⠀⠀⠀⠙⣷⡾⠛⠛⡇⣿⠤⠤⢤⠀⠀⠀⣿⡀⠀⢸⠃⣀⣠⣼⣿⡿⣾⣷⣼⣷⣤⠤⣤⡀⠀⠀⠀⣰⡾⠃⠀⠀⠀⠀⠀⠘⢷⣼⠲⡙⠿⣷⡿⣿⣷⡄⠀⠀⠀⠀ ⠀⢰⡄⠀⠀⠀⠀⠀⢀⣿⡇⠀⠠⡇⣿⠀⠀⢸⡇⠀⠀⢸⣇⠀⠸⣤⠈⠛⢸⡄⠀⠺⠇⢉⣿⠶⠖⢒⡛⠀⠀⢀⡿⠀⠀⠀⠀⣀⡀⠀⠀⢨⣿⣞⣯⣿⡿⣷⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠙⢶⠤⠤⠤⠤⠾⠉⠷⠤⢤⡇⣿⣀⣀⣘⣷⠀⠀⣠⡿⣧⣀⠈⠉⠉⠉⠉⠒⠶⣴⢟⣵⠞⠛⠋⠛⢲⣦⣼⠇⠀⠀⠀⡞⠉⢙⡄⠀⠘⢿⣍⣿⣿⣻⣿⣿⠿⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⢹⡄⣴⠀⠀⠀⠒⣦⠀⡇⣿⠉⠀⣿⠁⠀⣾⠋⠀⠈⠙⠷⣤⣀⢀⡀⠀⠀⠉⣼⠍⠀⠀⠀⠀⠀⠹⣇⠀⠀⡴⠻⡟⢒⣋⠀⠀⠀⠀⠀⣿⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⢺⣷⡇⠒⣲⣤⠀⣹⠀⡇⣿⠀⠀⣿⠠⣾⠁⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⡤⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠉⠉⠹⣅⣸⠀⠀⠀⠀⣠⡿⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⢨⣥⣬⠗⡳⣤⡨⣼⠶⠛⠀⡇⣿⠀⠀⢻⠐⡟⠀⠀⠀⠀⠀⠀⠠⣼⣿⠿⣿⡇⠀⢻⡆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡀⠀⢀⠉⠉⢑⡄⠀⢠⡿⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⢀⡼⣷⡴⣿⡿⣆⣰⠟⠒⠒⠚⡇⣿⠀⠀⢸⣠⣯⡀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡀⠀⠀⠀⢿⣄⡀⢀⠀⢀⣤⠾⠁⠸⣧⠀⠀⠀⠀⣼⠃⠀⠈⣿⡀⠀⠀⠀⢠⣿⣴⠶⠛⠋⠑ ⠠⢾⣃⡈⠛⠦⡀⣿⢿⠀⠀⣀⣤⣧⣿⡀⠀⢸⣿⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⣶⠚⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠛⠓⠛⠒⠛⠛⠒⠒⠒⠚⠛⠛⠛⣻⡿⠿⠁⠀⠀⠀⠀ ⠀⠈⠙⠙⠒⠒⢶⣏⠘⣷⣾⠋⠀⠀⠙⠛⠛⠻⣿⡶⠾⠷⠶⠆⠀⠀⠀⠀⠠⠾⠷⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠞⠋⠛⣶⣶⣶⠟⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡛⢛⣛⣛⣛⣛⣻⣛⢛⣻⣿⣿⡿⣿⡿⣿⣿⣛⣻⣛⣿⣛⣛⣿⣿⣟⣛⡿⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡝⠛⠈⠛⠋⠛⣿⢸⠛⠀⠛⣁⣛⣃⠛⠛⢿⠛⡏⠛⠃⠙⠋⠀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀