⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠉⠀⡀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⢀⣤⣤⣤⡤⣤⠀⠁⠀⠰⠁⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠠⠀⠀⠀⢡⠜⠁⠀⠀⠀⠀⠀⠙⠗⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣆⠀⠀⢄⠡⠈⠉⠐⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣠⣄⡒⠊ ⠔⠋⠁⠀⠀⠀⠐⠺⠿⣛⣃⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⣼⣶⣥⣔⣉⣿⢃⠂⠀⠀⠀⠁⠀⠀⠀⢀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⢀⢀⠀⠀⠐⠰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠁⠠⠄⠒⠀⠀⢐⣭⠊⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣣⣰⣧⠀⢿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢤⣿⣿⡿⢋⣡⠄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⠀⣅⠀⠀⠀⠀⠀⠋⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠂⠀⠀⠀⠈⠀⠀⠀⠱⣤⣅⡀⠹⠇⠀⢀⠀⠀⠀⠀⢀⣀⣠⣤⠠⠼⠟⣓⠀⣄⠀⠈⠂⠲⣾⣿⣿⣿⣿⣶⣶⠦⢀⣄⣀⠀⠀⠀⠆⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡌⠻⣿⣧⣄⠠⣤⣴⣶⣶⣾⠿⠟⣛⣉⣤⣤⣥⡶⠀⢒⣒⣀⡄⠀⠈⠉⠉⠁⠶⠶⠤⠤⣈⠙⠻⢷⢀⣜⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⢶⣤⣭⣛⣘⡛⠋⠥⠶⠾⠿⠿⠛⠋⣉⣀⣤⣶⠿⢛⣩⠶⢛⣁⣤⣴⣶⣾⣿⣿⣿⣦⣤⣄⣠⠀⡛⠿⣿ ⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠛⠳⠮⢙⡻⠿⣿⣿⣶⣤⣀⠉⠛⠿⠿⠿⠟⠋⠁⣀⣠⣴⡾⠿⠟⣛⣩⢭⣤⣀⡀⠈⠉⢭⣉⠛⠛⠳⠱⣦ ⢿⣶⡄⠀⠀⠀⠀⠀⠑⠶⣌⠙⠳⣮⣴⣒⠡⢄⠀⢉⡛⠿⢛⣋⣤⣤⠴⠖⠚⣋⣭⣥⣤⣤⣶⣶⣶⢆⣴⣬⠉⠉⠀⠠⡄⠘⠂⣠⣿⣦⣦ ⢸⣿⣿⣷⡀⠀⠠⢤⣤⣄⢤⣤⣤⣤⣍⡛⠿⢎⢿⣿⠿⠿⢛⣋⡭⠖⣨⡴⣿⣿⡿⠿⠿⠿⠿⠿⠃⠛⠻⠿⣿⣷⣦⣀⡁⠠⣾⣿⣿⡿⠟ ⢸⣿⣿⣿⣷⣤⡀⠀⠀⠈⠈⠉⠛⣛⣛⠻⠛⠠⠤⣶⣾⠿⠋⠁⠀⢀⣀⣀⣠⠤⠶⠿⠿⠛⠛⠛⠛⠉⠁⠀⢀⠉⠟⠻⠷⣶⣤⡀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡷⠖⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠙⠻⣷⢰⣾ ⡼⢿⢟⣛⢩⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠉⣸⣿ ⣾⣿⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⡀⠀⠀⠈⣼⣿⡿⠃⠂⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⡖⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡆⠀⠀⣰⡿⠁⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⠿⠛⢋ ⣿⣿⣿⣿⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⡄⠈⣤⣿⡿ ⣿⣿⣿⡏⠀⡈⠀⢀⡆⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢉⠍⠘⠂⠻⠝ ⣿⣿⣿⡇⠀⠁⠀⣿⠀⢰⠀⠀⢠⠀⣄⢻⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⢀⣤⠟⠿⣋⢀⠀⠀⠀⠀⠀⠿⡄⠈⠂⠀⠀⠀⠀