⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡴⢤⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⠛⠙⠟⠀⠛⣙⡿⠿⢿⣆⡖⡎⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡻⠗⠚⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠘⢻⡆⢀⣀⣄⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠙⠂⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠙⠹⠝⠋⠁⠛⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⠀⠀⣰⡾⠛⠉⠉⠉⠀⠀⠀⠐⢿⣿⠟⠀⠀⠀⢀⣴⣴⣄⠀⠀⠀⠀⠉⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣶⣀⣐⣏⠁⠐⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡴⣌⣿⡿⠛⠀⠀⠀⠀⠀⠀⠉⢡⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣖⠞⣿⠶⠒⠓⠈⠘⠁⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡯⠛⠋⠻⣧⢶⣤⠀⠀⠀⠀⠀⠀⢀⣺⡅⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢦⣤⣼⠍⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡟⠛⠦⡿⠟⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡋⠁⢠⣶⣶⠀⢀⣤⣶⣤⣀⣀⣀⡉⠁⠀⠀⠀⠀⠀⠀⡶⡞⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠍⠀⠙⠿⠟⠀⠚⢉⣤⣄⠁⠁⠀⠀⠀⠀⠀⡤⣼⡽⠙⠓⠀⠀⠛⠋⢳⠦⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⣷⠀⠀⠀⠘⠻⢗⣆⠀⠀⠀⠀⠀⠀ ⢰⡞⠃⠀⠀⠀⠀⠀⠀⠀⠻⢯⠏⠀⠀⠀⠀⠀⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠄⠀⠀⣀⣀⡀⠀⠀⣀⠀⠀⠛⠞⠋⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀ ⠸⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠀⠀⠀⠀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠀⣠⣼⣹⠇⠿⠦⡟⠹⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⠀⠀⠀⠀⠀ ⢀⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⣠⣤⣤⡾⠃⠑⢓⣆⣀⣀⠀⠀⠀⠀⠀⠀⢠⡦⡽⢾⣡⡄⠀⠀⠀⠀⠚⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⡯⣤⡴⠒⡆⠀⠀ ⢀⡿⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⢷⣄⠀ ⠘⠒⣻⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠠⣄⠀⣄⡀⠀⡀⠀⠀⢷⠤⠿⠉⠁⠀ ⠀⠀⠙⠚⠛⠳⠶⠶⣆⣠⣦⣠⡄⢀⣠⠀⢀⣀⠀⢀⠀⠀⢀⠀⢀⠀⠀⢠⠀⣀⠀⠐⣶⢶⣆⣾⣀⣀⡖⠒⢦⣄⣴⠖⠋⠳⠾⠏⠉⠉⠉⠉⠉⠙⠒⠟⠲⠶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠘⠛⠛⠓⠚⠛⠒⠚⠓⠛⠉⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡴⢤⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⠛⠙⠟⠀⠛⣙⡿⠿⢿⣆⡖⡎⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡻⠗⠚⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠘⢻⡆⢀⣀⣄⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠙⠂⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠙⠹⠝⠋⠁⠛⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⠀⠀⣰⡾⠛⠉⠉⠉⠀⠀⠀⠐⢿⣿⠟⠀⠀⠀⢀⣴⣴⣄⠀⠀⠀⠀⠉⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣶⣀⣐⣏⠁⠐⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡴⣌⣿⡿⠛⠀⠀⠀⠀⠀⠀⠉⢡⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣖⠞⣿⠶⠒⠓⠈⠘⠁⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡯⠛⠋⠻⣧⢶⣤⠀⠀⠀⠀⠀⠀⢀⣺⡅⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢦⣤⣼⠍⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡟⠛⠦⡿⠟⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡋⠁⢠⣶⣶⠀⢀⣤⣶⣤⣀⣀⣀⡉⠁⠀⠀⠀⠀⠀⠀⡶⡞⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠍⠀⠙⠿⠟⠀⠚⢉⣤⣄⠁⠁⠀⠀⠀⠀⠀⡤⣼⡽⠙⠓⠀⠀⠛⠋⢳⠦⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡿⣷⠀⠀⠀⠘⠻⢗⣆⠀⠀⠀⠀⠀⠀ ⢰⡞⠃⠀⠀⠀⠀⠀⠀⠀⠻⢯⠏⠀⠀⠀⠀⠀⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠄⠀⠀⣀⣀⡀⠀⠀⣀⠀⠀⠛⠞⠋⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀ ⠸⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠀⠀⠀⠀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠀⣠⣼⣹⠇⠿⠦⡟⠹⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⠀⠀⠀⠀⠀ ⢀⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⣠⣤⣤⡾⠃⠑⢓⣆⣀⣀⠀⠀⠀⠀⠀⠀⢠⡦⡽⢾⣡⡄⠀⠀⠀⠀⠚⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⡯⣤⡴⠒⡆⠀⠀ ⢀⡿⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⢷⣄⠀ ⠘⠒⣻⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠠⣄⠀⣄⡀⠀⡀⠀⠀⢷⠤⠿⠉⠁⠀ ⠀⠀⠙⠚⠛⠳⠶⠶⣆⣠⣦⣠⡄⢀⣠⠀⢀⣀⠀⢀⠀⠀⢀⠀⢀⠀⠀⢠⠀⣀⠀⠐⣶⢶⣆⣾⣀⣀⡖⠒⢦⣄⣴⠖⠋⠳⠾⠏⠉⠉⠉⠉⠉⠙⠒⠟⠲⠶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠘⠛⠛⠓⠚⠛⠒⠚⠓⠛⠉⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿