⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠐⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⢀⡀⠀⠀⠀⠾⠾⣶⣤⣙⢷⡌⣿⠀⠀⢀⣠⣴⠶⠾⠛⠶⠳⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣾⣻⡿⠀⠀⠀⠀⠀⠀⠈⣙⣷⣽⣼⣤⡾⠛⠉⠀⠀⠀⢀⣀⣀⣤⣤⣤⣭⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⠞⠉⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣤⡾⠟⣛⣭⡿⠿⠟⣛⣛⣻⣿⣷⡄⠀⠀⠘⢿⣷⣿⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣛⠀⠸⢻⣿⣿⡿⠀⠀⠀⠁⢀⣹⣷⣬⣭⣄⡰⠚⠛⣉⣩⣽⢿⣿⣿⠀⠀⠀⠀⠙⢺⡽⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣀⣴⡿⣿⠂⠀⠀⠀⠀⣠⣾⣿⣻⣿⣿⡟⠀⠀⠈⠉⠋⠁⠀⡀⣮⡾⠛⠉⠁⠀⠀⠉⠛⣷⡜⢉⣭⣴⣿⠟⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣷⣻⢯⣿⡟⠀⠀⠀⠀⣴⡿⠛⠿⢻⠿⣿⢿⡴⣿⠛⠛⢶⣤⣰⡿⠋⠀⠀⠀⠄⠀⠈⠀⠈⠉⣿⣾⣿⠿⢷⣻⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⣽⣻⣾⠁⠀⠀⠀⣰⣿⡗⡄⠀⠀⠀⢠⡟⡀⠈⢀⣸⠂⣻⠟⠀⠀⠀⠌⠀⢀⠈⠀⠐⠀⡀⢽⡏⠙⢳⣌⠀⠦⠶⠶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢯⣷⠀⠀⠀⢰⣿⡿⣼⢣⡄⠀⠀⢸⣿⣬⣰⣯⠅⢰⡏⠀⠀⠐⠀⠀⡀⠀⠀⠂⠀⠄⠀⣾⡇⠀⠈⢿⡆⠰⠾⣛⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣏⣿⣦⠄⠀⠀⢈⣵⠟⠀⠀⡾⠉⠻⢶⣤⣀⠁⠀⠐⠀⠁⠈⠀⣤⣿⠁⠀⠀⢸⣿⣬⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣿⣿⣯⣿⡈⠀⠀⢠⣿⠁⠀⠀⢀⡇⠀⠀⠀⠻⣿⣷⣄⠈⠀⡀⠐⣰⣿⠃⠀⠀⠄⢸⣿⣷⣤⣤⣤⣀⠀⠀⣾⢿⣷⣀⣾⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠙⣿⣆⠀⢸⡇⠀⠀⠀⠐⢷⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣰⡿⠃⠀⠀⠂⢀⣿⣿⣿⣝⡳⣦⣍⠀⠈⢻⣟⡾⣿⣽⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠠⠀⠀⠂⠐⠀⠄⠀⠄⠘⣿⣤⠘⣿⡀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⢻⣶⠟⠁⠀⠀⠁⢀⣼⠟⣿⣿⠀⠻⣆⠙⠃⠀⠀⠈⠛⠷⡯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠈⣠⣤⣶⣿⣾⣷⡶⠶⠀⠠⠀⣿⣏⠀⠈⠿⣦⡀⠀⠀⠀⠙⢶⣤⣤⣤⡴⠞⠻⣿⣄⠀⠀⠠⣀⣿⠋⢠⣿⡟⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣰⣿⡿⠛⠟⠻⠛⠁⠀⠀⠀⢠⡿⢿⣧⣀⠀⠉⠻⢶⣤⣀⣀⡈⢳⣄⠈⢳⡄⠀⠀⢻⡄⣠⡶⠛⢉⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣿⢿⣅⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠛⠿⣯⠀⢠⣿⠟⠋⠛⠛⠻⣿⡛⠛⠛⠒⠖⠒⠛⠉⠀⡴⠀⣀⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⡿⠁⠀⠂⠀⠈⠀⢀⠀⠄⠀⠄⠀⠀⠀⠀⢸⢿⣄⠀⠀⢀⠀⠘⢿⣄⠀⠀⠀⣀⣠⠾⣟⣁⣄⣴⠏⠀⢀⣤⣤⣄⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠟⠈⠁⠀⠀⠀⠀⠂⢀⠀⠀⠀⡀⠠⠈⠀⠐⠀⠈⠈⢛⣻⡶⣤⡀⠀⢸⡟⠛⠛⢛⣭⣷⣴⣾⣿⠟⠁⠀⠀⢻⣯⣟⣽⣆⣴⡿⣯⢿⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣖⠀⠀⠀⠂⠀⠈⠀⠀⠄⠀⠌⠀⢀⠀⠠⠀⠈⠀⢨⣴⠟⠋⠙⠳⡟⠀⢸⣿⣶⣄⣺⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⣷⣟⡾⣿⢯⡿⣽⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣧⠀⠀⠀⠂⠀⠁⠐⠀⠂⠀⡐⠀⢀⠀⠂⢀⢠⣿⣁⣠⣄⡄⠀⠀⠀⠘⠁⠹⣿⣿⣋⢉⠻⣧⡀⠀⠀⠀⠀⠀⠸⣯⢿⡽⣯⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠿⠀⠀⠀⠐⠀⠁⠠⠀⠂⠀⠁⠀⠄⠀⠀⠐⢀⣼⠟⠋⠁⠀⠀⢀⠀⠐⠀⠂⢀⠀⠉⠉⠉⠀⠈⢿⡄⠀⠀⠀⠀⠀⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⢀⠂⠀⠄⠂⠀⠐⠀⠁⠐⠀⡀⢈⠀⠀⢾⣏⠀⠀⠠⠀⣀⠀⡀⠀⠀⠄⠀⠀⠄⠀⠠⠀⠠⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣶⣶⡶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠠⠀⠀⠄⠁⠀⠐⠈⠀⠠⠀⠀⠀⠄⠈⠿⣶⣤⣴⡶⢿⡅⠀⠈⣠⣼⣿⣶⣶⣤⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⡿⣿⣿⡟⠃⠀⠈⢿⣿⣷⣦⣄⠀⠀⠀⢀⣼⣿⣿⡄⠀⠂⠀⠠⠈⠀⠄⠂⠁⡀⠁⠀⠂⠀⠀⠀⠁⠀⠀⠈⠻⠿⠟⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣇⠀⠈⠁⠀⠀⡀⠂⠀⠿⠿⠟⠻⠛⢶⣾⣿⣿⡟⢿⣿⡄⠁⠀⠀⠙⢧⡀⠠⠀⠀⠀⠁⠀⡁⠀⠁⠀⠈⠀⠐⠀⠀⢀⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣣⠀⠀⠀⠀⠀⠠⠀⢠⣴⣦⣄⡀⠀⠈⠙⠛⠁⢸⣿⣿⡄⠀⡀⠀⠘⣷⡀⠐⠀⠁⠠⠀⢀⣴⣠⡆⠀⠈⠀⢀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⠙⠀⠀⠀⠀⠠⠀⢰⡿⠁⠀⠉⠻⣮⣔⠀⠀⣀⣼⡿⠋⣷⡀⠀⠄⠀⠘⢿⠷⠶⣤⣤⣤⣿⡷⠋⠀⠀⠠⣰⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡟⣦⠀⣶⠀⣧⠀⣖⠀⣿⡇⠀⠀⠀⠀⠀⠙⠛⠻⠛⠉⠀⠀⢸⣇⠀⠀⠐⠀⠘⣷⠀⠀⢈⣽⠟⠀⠀⠐⣈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⡄⣿⡀⣿⢀⣯⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠈⠀⠀⢼⡇⢠⡿⠃⠀⠀⠈⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣇⣿⣮⣷⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠠⠀⠂⣸⡇⣿⠁⠀⠀⡀⠂⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠐⠀⣴⡿⠁⠘⣷⡀⠀⠄⠀⠀⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣁⣴⡾⠿⠛⠛⠟⠷⠶⢦⣬⣿⣧⡀⠀⠂⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣴⡟⣥⠞⠀⠀⡀⠀⢀⠀⠀⡀⠉⠛⠻⣶⣴⠷⣦⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢰⣿⡾⠁⠀⠀⢀⣠⡾⠋⠀⠀⠀⢀⠠⠀⠀⠙⠳⡄⠛⠀⠈⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠛⠁⠀⢀⠀⠸⣿⠃⠀⠀⠂⢰⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⢝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⢀⠀⠀⠂⠀⠀⠀⢿⣧⡀⠁⠀⢸⣇⠠⠀⡐⠀⠀⠀⣠⣾⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⠐⠀⡀⠂⠀⠀⠄⠀⠂⠁⡀⠀⠙⠻⠷⠿⠿⢿⣤⣀⣀⣠⣬⣾⡟⠻⣦⣤⣠⣤⡿⣇⠀⠀⡈⠀⠂⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⢶⣤⣤⣤⣠⣤⣤⣤⣴⣶⡄⠀⠀⠂⠀⠀⢤⡀⠀⠉⠙⠋⠉⠁⠀⣿⡀⠈⠉⠉⣹⡆⠙⢿⣄⡀⠀⠂⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣮⣄⣠⣄⣴⣾⣇⠀⠀⠂⠀⠀⠂⢀⣿⠁⠀⠀⢠⣿⠃⣀⣾⠋⠻⠶⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠻⣧⣒⠀⠁⢀⣠⣾⠷⣶⣶⣾⣿⣷⣾⣿⣿⣿⣷⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀