⢄⠀⡀⠔⠁⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠤⠚⠓⣀⠴⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣰⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢂⠏⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⣀⠀⠀ ⠑⢦⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡁⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢐ ⠈⠉⠀⠀⢀⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠂⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠊⢹⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠐⢮⡁ ⠀⠀⠀⢀⠊⢀⡔⢫⠃⠀⠀⠀⠀⠀⠄⡜⢸⠰⡇⠀⢰⢀⠃⠀⠀⠀⠀⠀⠀⢸⠀⡈⢃⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠈ ⠀⠀⠀⡜⢠⠊⠀⠘⠄⠀⠀⠀⠠⠎⣰⡜⢸⢣⠇⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡂⣀⣇⣈⣆⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢦⡈⢆⠀⠀ ⢀⠇⠀⢹⠁⠀⠀⠀⠀⠀⠀⠰⠁⣰⣹⣶⣾⢾⡶⣀⡸⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠉⠉⡏⢶⣀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡎⢎⡆⠀ ⠁⠀⠀⠘⠀⠀⠀⠀⠀⢀⠔⢁⡚⣹⠁⠀⠘⠀⡅⠀⠸⡇⠀⠀⠀⠀⠀⠀⢰⠀⠆⠀⠀⠀⠱⠀⠈⠙⠀⠈⠢⡀⠀⠀⠀⢀⠃⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠊⣴⢏⣠⣤⣤⣤⣇⠀⠀⢧⠀⠀⠀⠀⢀⢀⠃⡘⠀⣠⣤⣤⣤⣵⣀⠀⠀⠀⠀⠉⠢⡀⠀⠁⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⡠⢐⠥⠛⠁⡠⢾⡷⠛⠋⠀⠀⢀⣘⣝⠂⠈⠀⠀⠀⣠⡾⠃⡜⢠⠞⠋⠀⢰⣤⡄⠙⢿⣆⠀⠳⠢⢀⠈⠢⡀⠀⠀⠀⠀ ⡀⠀⠤⠶⠛⡻⠃⢀⢤⠮⡫⠊⠀⠀⠀⠀⠀⢸⠀⣿⠀⢲⢀⣤⣾⠏⢠⠎⠀⠀⠀⠀⠀⣿⡏⠅⠀⠀⡙⢄⠀⠱⡄⠁⠢⠌⣢⣀⠀⠀ ⢈⠖⠄⣠⣊⠤⠊⡁⠤⡊⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⡤⢼⢊⣋⢼⠆⠙⠀⠀⠀⠀⠀⠀⢻⣇⡖⠀⠀⠈⠢⢍⠢⡈⠢⣀⠀⠀⠀⠀⢀ ⠂⠀⠈⠁⠀⡔⠁⠀⠀⢸⢸⠀⠹⣷⣤⣄⣀⠈⠓⠋⠉⠙⣀⡤⢼⠤⣤⣸⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣤⡄⠈⠑⠻⣦⣑⣠⣀⠀⠀ ⠀⠀⣀⠀⢸⠀⠀⠉⢦⡎⢣⡆⡼⢻⢟⢻⠝⡡⢀⠀⣖⠉⠁⡀⣸⣀⣀⣀⣀⣨⠂⠠⡠⣉⠞⡻⢿⠿⡛⢡⢄⢀⠔⠀⠘⡇⠀⠰⣄⠀ ⠀⠀⠀⢉⠼⡀⠀⠀⠰⠣⡈⢿⡴⠁⡠⢏⠖⡠⠪⠀⠄⠉⠉⢩⠹⠁⠸⠀⠀⠀⠠⢊⠔⠁⢂⡕⠁⡐⡁⠸⠰⠫⠀⠀⣼⠇⠀⢠⠀⠈ ⠀⠀⠴⣁⠀⠐⠢⣄⡀⠀⠈⠺⣷⡜⡴⡡⢎⠀⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠦⠜⡳⠊⠠⠜⠄⠀⡎⠀⢀⣠⠞⣃⡄⢀⠎⠀⠀ ⠀⠀⠀⠀⠉⠒⠠⠄⠀⠁⠒⠒⠸⣯⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡇⡀⠔⠉⠀⡧⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠤⣄⠰⠀⠀⠔⠛⠷⣄⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠉⠀⡔⡂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠵⠞⠛⠉⠀⢶⠁⠀⠀⠀⠈⠓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⡎⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣲⣤⣀⡀⣤⣶⡿⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣾⣿⣿⣿⠿⢁⣾⠏⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠔⠊⣀⡿⠟⢋⡠⠖⠉⠀⠀⠀⠀⣿⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠉⠀⠀⠀⢁⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⢀⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⠀⠐⠢⠄⢀⣀⡰⣎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠷⣶⡇⠴⠒⠈⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠭⢁⣂⣀⡀⡀⠤⢤⣤⣼⠭⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣲⡲⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠠⠤⠤⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠡⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⢤⡤⠒⠁⠀⠀⠉⠁⠘⠯⢁⡒⠢⠤⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢹⠀⢀⡠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡧⣜⠉⠒⢠⡀⠀⠀⠀⠀⠀⠈⣆⢼⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢ ⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠇⠈⠑⠢⣀⠀⠀⠀⠀⠀⠊⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿ ⠀⠀⠀⠀⠫⡻⡵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⠀⠑⡌⠢⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡝⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣆⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⡟⣆⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⢰⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢁⢸⠳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⡀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠸⢸⣠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⢧⡇⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⢸⣼⠁⠇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣦⠀⠀