⠀⠀⣼⠇⢸⠇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠙⣆⢰⠇⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠃⣰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⢫⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⠀⣡⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣷⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⢻⣧⠀⠀⡸⢀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⣀⡀⢀⣴⡟⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢺⠁⢸⠄⠀⠈⢆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⠀⢠⠇⡜⠀⠀⠀⡰⣃⣀⣀⣀⣀⣰⣟⣁⣤⡶⠾⠛⠋⠉⠉⠉⠙⠒⠦⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⡆⠀⠀⠈⢷⡀⠀⠀⠀⢈⣿⡤⠼⣞⣷⠴⠒⠋⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠠⢤⣤⣤⣤⣤⠤⠤⣄⣀⣀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⢀⣠⠇⠀⠀⠀⠀⣳⠀⣠⠶⢋⣥⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡃⠀⠀⠀⣸⠏⠛⠻⠿⠆⠀⠀⠀⠀⠀⠀
⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⡴⣡⠞⠁⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣧⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡞⢀⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡿⢷⣀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡋⢠⠄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀
⠀⣿⠀⣀⣠⣤⣄⡘⡆⠀⠀⢰⡃⠀⠀⠀⠀⠀⢉⡏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡆⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀
⠀⢿⡾⠋⠁⢀⣩⣽⣿⡄⠀⢸⠁⠀⠀⠀⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠹⡵⡄⠀⠀⢠⡷⠀⠀⠀⠀⠀
⠀⠈⠀⠀⣰⡿⠉⠀⠀⣹⣦⡉⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⡄⠀⠀⢳⡀⠰⡄⠀⠹⡜⡄⣠⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡿⠁⠀⢀⣴⠟⠙⢿⣦⣀⠀⠀⠀⢀⢠⠇⠀⢠⠃⠀⠀⠀⠀⢸⠁⠀⢸⠁⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣷⡀⠀⠀⢳⠀⠹⡄⠀⢳⢹⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⡇⠀⣠⡿⠃⠀⠀⣾⠃⢹⠳⢦⣄⠎⠸⠦⢄⣏⣀⡀⠀⠀⠀⡜⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡏⣇⠀⠀⠈⡇⠀⢳⡀⢈⣟⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⣰⡟⠁⠀⣠⡿⠻⠀⢸⣄⣨⠏⢠⠂⠀⠀⠀⢠⣏⣉⠙⠓⠓⠒⠲⠇⠀⠼⠤⠤⠤⠤⣤⠤⠤⠧⠤⠤⠤⠗⠘⠶⠒⠲⡞⠚⢫⠉⠉⠓⢿⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⢷⡟⠀⠀⢀⡿⠀⣼⠀⢀⣏⠎⠀⡜⠀⠀⠀⠀⢸⣲⠮⠭⢭⣙⣒⡒⠒⠦⠤⠤⠤⣤⡴⢋⣀⣀⣀⣀⣠⣤⡤⠤⢤⣤⡴⢷⠀⠀⠳⡀⠰⣄⠈⠉⠛⠓⢒⣻⠟
⠀⠀⠀⢹⣿⠁⠀⠀⢸⡇⢰⣿⡆⢸⡏⠀⣰⡇⠀⠀⠀⠀⢸⠛⠛⢻⡿⡿⢾⡿⣿⣿⣶⣶⣶⡾⠁⣾⣶⣶⣶⣶⣶⣶⣮⣭⣭⣭⣶⣿⢇⠀⠀⠙⡄⠙⢿⡛⠿⠟⠛⠁⠀
⠀⠀⠀⠘⠛⠀⠀⠀⠸⣧⣿⠛⣷⡞⠀⢠⠃⡇⠀⠀⠀⠀⢸⣄⡀⠀⠳⢽⣲⣴⣺⠽⠁⣠⢾⠞⢀⣷⡀⠘⣟⢯⣙⣋⣽⡽⠁⢀⣼⣤⡸⡄⠀⠀⠘⡄⠈⢻⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢀⡿⠀⠀⣾⠀⡇⠀⠀⠀⠀⢸⠛⠛⠷⢦⣤⣤⣥⣤⠶⠛⠵⣁⠤⠤⢯⡻⣦⣌⡙⠒⠒⢉⣠⣴⠿⣿⣄⠀⣧⠀⠀⠀⢸⡀⠀⢿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡅⢇⢱⠀⠀⠀⠀⠸⡗⠢⠤⠤⠤⠤⠤⠔⠒⠉⠁⠀⠀⠀⢸⣰⠋⠙⠯⣉⡉⠉⢹⡶⠔⡇⢀⡼⠹⡀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⣷⠈⢫⡆⠀⠀⠀⠀⣇⠀⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠹⡀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⢻⣧⡀⠙⡄⠀⠀⠀⢸⣆⠀⠀⠑⢦⡉⠓⢲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣰⣿⣆⠀⡇⢰⠁⠀⠀⠀⡀⠀⣸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢹⣇⠹⣷⡄⠘⣄⠀⠀⠀⢿⣷⣦⣀⠀⠉⠓⠪⢤⣀⡰⠋⠉⢉⣝⡲⠾⠋⠁⢀⣠⣾⡁⡟⣿⡀⡇⡜⠀⠀⠀⢀⠇⣰⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢿⡄⠈⠻⣦⠘⡆⠀⠀⠘⣿⠿⣿⣟⣶⣦⣄⡀⠀⠀⠉⠉⠁⠀⠀⣀⣤⡶⠟⠉⢸⡇⡇⢹⡇⣷⠃⠀⠀⢀⣮⡾⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣮⢿⣆⠀⠙⣷⡘⠀⠀⠀⣿⡄⢈⣭⣿⠛⢾⣿⡿⣶⣶⣶⣶⠾⠛⠋⠁⠀⠀⠀⢸⣧⣷⢸⡷⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⠸⣷⠀⠀⠀⢹⣾⠟⠉⣿⠀⠀⠈⠻⢿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠘⣿⣯⡿⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢻⡇⠀⠀⢸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠉⠻⣿⠈⠙⠻⢶⣤⡀⠀⠀⠋⣾⠃⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⡶⠶⠟⠛⣿⠀⠀⡿⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣶⣤⣀⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠉⢯⠉⠉⠉⠉⠉⢹⠁⠀⠀⣰⢻⠀⢰⠃⠈⠓⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣻⡿⠋⠻⡄⣿⣧⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⢇⠀⠀⠀⠀⡞⠀⠀⣰⠃⢸⢀⠇⠀⠀⢠⣇⠀⠉⢑⠒⠂⠀⠀⠀⠀⠬⣧⠒⠒⠊⠉⠀⠙⣆⠀⠹⣧⢻⡉⠉⠉⠉⠉⡟⠛⠻⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣆⠀⠀⢰⠇⠀⣰⠃⠀⢼⡞⠀⠀⠀⢼⡈⠉⠑⠺⣆⠀⠀⠀⡤⠶⠒⢹⡄⠀⠀⠀⠀⠀⠘⣦⠀⠈⠈⣧⠀⠀⠀⢠⠃⠀⠀⢻⡄⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣘⣆⣠⣾⣀⣠⣏⣀⣀⣞⣀⣀⣀⣀⣈⣳⣄⣀⣀⣘⣀⣀⣀⣀⣀⣀⣾⣃⣀⣀⣀⣀⣀⣀⣈⣧⣀⣀⣸⣆⣀⣀⣞⣀⣀⣀⣸⣧⠀⠀

⠀⠀⣼⠇⢸⠇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠙⣆⢰⠇⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠃⣰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⢫⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⠀⣡⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⣷⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⢻⣧⠀⠀⡸⢀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⣀⡀⢀⣴⡟⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⠁⢸⠄⠀⠈⢆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⠀⢠⠇⡜⠀⠀⠀⡰⣃⣀⣀⣀⣀⣰⣟⣁⣤⡶⠾⠛⠋⠉⠉⠉⠙⠒⠦⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⡆⠀⠀⠈⢷⡀⠀⠀⠀⢈⣿⡤⠼⣞⣷⠴⠒⠋⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠠⢤⣤⣤⣤⣤⠤⠤⣄⣀⣀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⢀⣠⠇⠀⠀⠀⠀⣳⠀⣠⠶⢋⣥⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡃⠀⠀⠀⣸⠏⠛⠻⠿⠆⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⡴⣡⠞⠁⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡞⢀⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡿⢷⣀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡋⢠⠄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀ ⠀⣿⠀⣀⣠⣤⣄⡘⡆⠀⠀⢰⡃⠀⠀⠀⠀⠀⢉⡏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡆⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀ ⠀⢿⡾⠋⠁⢀⣩⣽⣿⡄⠀⢸⠁⠀⠀⠀⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠹⡵⡄⠀⠀⢠⡷⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⣰⡿⠉⠀⠀⣹⣦⡉⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⡄⠀⠀⢳⡀⠰⡄⠀⠹⡜⡄⣠⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⢀⣴⠟⠙⢿⣦⣀⠀⠀⠀⢀⢠⠇⠀⢠⠃⠀⠀⠀⠀⢸⠁⠀⢸⠁⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣷⡀⠀⠀⢳⠀⠹⡄⠀⢳⢹⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡇⠀⣠⡿⠃⠀⠀⣾⠃⢹⠳⢦⣄⠎⠸⠦⢄⣏⣀⡀⠀⠀⠀⡜⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡏⣇⠀⠀⠈⡇⠀⢳⡀⢈⣟⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣰⡟⠁⠀⣠⡿⠻⠀⢸⣄⣨⠏⢠⠂⠀⠀⠀⢠⣏⣉⠙⠓⠓⠒⠲⠇⠀⠼⠤⠤⠤⠤⣤⠤⠤⠧⠤⠤⠤⠗⠘⠶⠒⠲⡞⠚⢫⠉⠉⠓⢿⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢷⡟⠀⠀⢀⡿⠀⣼⠀⢀⣏⠎⠀⡜⠀⠀⠀⠀⢸⣲⠮⠭⢭⣙⣒⡒⠒⠦⠤⠤⠤⣤⡴⢋⣀⣀⣀⣀⣠⣤⡤⠤⢤⣤⡴⢷⠀⠀⠳⡀⠰⣄⠈⠉⠛⠓⢒⣻⠟ ⠀⠀⠀⢹⣿⠁⠀⠀⢸⡇⢰⣿⡆⢸⡏⠀⣰⡇⠀⠀⠀⠀⢸⠛⠛⢻⡿⡿⢾⡿⣿⣿⣶⣶⣶⡾⠁⣾⣶⣶⣶⣶⣶⣶⣮⣭⣭⣭⣶⣿⢇⠀⠀⠙⡄⠙⢿⡛⠿⠟⠛⠁⠀ ⠀⠀⠀⠘⠛⠀⠀⠀⠸⣧⣿⠛⣷⡞⠀⢠⠃⡇⠀⠀⠀⠀⢸⣄⡀⠀⠳⢽⣲⣴⣺⠽⠁⣠⢾⠞⢀⣷⡀⠘⣟⢯⣙⣋⣽⡽⠁⢀⣼⣤⡸⡄⠀⠀⠘⡄⠈⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢀⡿⠀⠀⣾⠀⡇⠀⠀⠀⠀⢸⠛⠛⠷⢦⣤⣤⣥⣤⠶⠛⠵⣁⠤⠤⢯⡻⣦⣌⡙⠒⠒⢉⣠⣴⠿⣿⣄⠀⣧⠀⠀⠀⢸⡀⠀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡅⢇⢱⠀⠀⠀⠀⠸⡗⠢⠤⠤⠤⠤⠤⠔⠒⠉⠁⠀⠀⠀⢸⣰⠋⠙⠯⣉⡉⠉⢹⡶⠔⡇⢀⡼⠹⡀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⣷⠈⢫⡆⠀⠀⠀⠀⣇⠀⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠹⡀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⢻⣧⡀⠙⡄⠀⠀⠀⢸⣆⠀⠀⠑⢦⡉⠓⢲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣰⣿⣆⠀⡇⢰⠁⠀⠀⠀⡀⠀⣸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢹⣇⠹⣷⡄⠘⣄⠀⠀⠀⢿⣷⣦⣀⠀⠉⠓⠪⢤⣀⡰⠋⠉⢉⣝⡲⠾⠋⠁⢀⣠⣾⡁⡟⣿⡀⡇⡜⠀⠀⠀⢀⠇⣰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢿⡄⠈⠻⣦⠘⡆⠀⠀⠘⣿⠿⣿⣟⣶⣦⣄⡀⠀⠀⠉⠉⠁⠀⠀⣀⣤⡶⠟⠉⢸⡇⡇⢹⡇⣷⠃⠀⠀⢀⣮⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣮⢿⣆⠀⠙⣷⡘⠀⠀⠀⣿⡄⢈⣭⣿⠛⢾⣿⡿⣶⣶⣶⣶⠾⠛⠋⠁⠀⠀⠀⢸⣧⣷⢸⡷⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⠸⣷⠀⠀⠀⢹⣾⠟⠉⣿⠀⠀⠈⠻⢿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠘⣿⣯⡿⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢻⡇⠀⠀⢸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠉⠻⣿⠈⠙⠻⢶⣤⡀⠀⠀⠋⣾⠃⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⡶⠶⠟⠛⣿⠀⠀⡿⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣶⣤⣀⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠉⢯⠉⠉⠉⠉⠉⢹⠁⠀⠀⣰⢻⠀⢰⠃⠈⠓⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣻⡿⠋⠻⡄⣿⣧⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⢇⠀⠀⠀⠀⡞⠀⠀⣰⠃⢸⢀⠇⠀⠀⢠⣇⠀⠉⢑⠒⠂⠀⠀⠀⠀⠬⣧⠒⠒⠊⠉⠀⠙⣆⠀⠹⣧⢻⡉⠉⠉⠉⠉⡟⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣆⠀⠀⢰⠇⠀⣰⠃⠀⢼⡞⠀⠀⠀⢼⡈⠉⠑⠺⣆⠀⠀⠀⡤⠶⠒⢹⡄⠀⠀⠀⠀⠀⠘⣦⠀⠈⠈⣧⠀⠀⠀⢠⠃⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣘⣆⣠⣾⣀⣠⣏⣀⣀⣞⣀⣀⣀⣀⣈⣳⣄⣀⣀⣘⣀⣀⣀⣀⣀⣀⣾⣃⣀⣀⣀⣀⣀⣀⣈⣧⣀⣀⣸⣆⣀⣀⣞⣀⣀⣀⣸⣧⠀⠀