⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠻⠷⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠟⠋⠁⠀⣀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⡀⠀⢼⡆⠈⣿⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠒⢲⣶⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⢠⣤⢺⡇⠀⠘⢿⡄⢸⣧⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣼⠇⢠⡿⠑⢲⣤⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠀⠀⣷⡈⠻⣧⣀⣠⣆⠸⣷⠉⢻⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⢸⡏⢠⣾⠃⣰⡟⠁⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢴⣦⡀⠘⢷⣄⠙⢋⡀⣻⡆⠹⠂⠈⣁⣠⠤⠴⠶⠶⠶⠶⠶⠦⢤⣄⣈⠉⠙⠟⠠⣾⡁⣼⠟⠀⠀⠀⢀⣴⡶⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠏⠀⢠⣄⠀⠙⠻⣦⡈⠻⣦⡈⠟⢉⣡⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⠀⠙⠋⣼⣏⢀⣴⡿⠋⣠⡷⢤⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⣤⡏⠛⢿⠿⣦⡈⠻⡞⠉⣡⡔⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠹⠟⢉⣴⡿⠋⣀⣤⣷⠄⠘⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠁⠀⠀⠙⠻⢷⣾⡀⠈⣿⠆⣠⠞⠁⠀⠈⢻⣿⡆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡆⠀⠀⠘⢷⡄⠀⠻⣅⣤⡾⠛⠉⠀⠀⠀⠈⢿⡆⠀⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢁⡴⠋⢀⣠⣴⣶⡾⣿⡇⣩⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⢦⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀ ⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢈⣽⣿⣥⣴⣿⣿⡾⠷⠦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣾⣿⡷⠶⠶⢿⣶⡆⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀ ⠀⢸⡏⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡟⠀⠘⠿⠿⢿⣿⣍⣼⠃⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⡇⠀ ⠀⣿⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⣰⣿⠏⠻⣿⡄⠘⣿⣆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠗⠀⠀⠀⠘⣿⡀ ⢠⡿⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡇⠀⠀⠀⢰⣿⣯⣶⡿⠟⠃⠀⠈⢿⣷⣿⣆⠀⢀⣴⣶⣦⣄⠀⠀⠈⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢿⡇ ⢸⡇⠀⠀⠀⠀⠿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠻⢿⡿⠀⠈⣧⠈⠿⣶⠗⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⣀⠇⠀⢠⡦⢈⠝⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢁⡀⡿⣦⠀⢠⣲⡆⠀⠀⠀⠀⢀⡴⢺⠀⠀⠈⢉⠏⠀⡰⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⢾⠿⠥⠿⠤⢼⣇⡽⢤⣠⠤⠐⠋⠀⠈⣆⠀⣠⡋⢠⠎⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⡇ ⠀⣿⡄⠀⠀⠀⠀⢷⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠜⠑⠢⢤⣀⢀⡠⠔⠋⢻⡄⠙⠿⠏⠀⠀⣠⣼⡆⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣴⠀⠀⠀⠀⢠⣿⠁ ⠀⢸⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠘⠆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣀⣤⣾⣿⣏⢹⡄⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀ ⠀⠈⢿⡄⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠘⠛⠳⣶⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡜⠁⠀⠀⠀⢠⠆⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠘⣷⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⠞⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣾⠇⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣧⡞⠁⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠭⠉⠉⠉⠉⠥⢔⣯⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⢤⣄⠀⠉⠉⠛⠒⠒⠶⠶⠖⠒⠒⠛⠉⢉⠀⢀⡴⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣼⡏⢀⣿⠁⣶⡆⢀⡴⠀⣴⠀⣴⡤⠔⢻⡆⠘⣷⡄⠘⢿⣆⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠼⠟⠉⠐⣾⡟⠀⣼⡏⠀⣿⡵⠋⠀⠀⣿⡄⢸⣧⠀⠘⣿⡄⠘⣿⡄⢈⣻⣷⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⢸⣿⠁⣰⡿⠁⢸⣿⢿⣦⠀⠀⣿⡇⠀⣿⠀⠀⢻⣧⠀⠹⠟⠋⠁⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⣦⣄⣀⠀⠛⠃⠀⠿⠇⠀⢻⣧⠀⣿⠇⠀⡿⠟⠛⠛⠋⠀⢀⣠⣴⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣦⣤⣤⣄⣀⣁⣀⣀⣀⣠⣤⣤⣴⡶⠾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀