⠻⣤⡀⠀⠉⠲⣄⡀⠈⠙⠓⠒⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⡆⠀⠀⣤⡹⢶⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⢤⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠻⣄⠀⠀⠉⠳⢦⣁⡀⠀⠀⠀⠀⠑⠲⢤⡀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡖⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠓⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢹⠀⠀⢻⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⠰⣿⣛⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢠⠟⠀⠀⠀⢸⠀⠀⠀⢿⡆⠹⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⣶⢦⣭⣿⠿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡞⣠⠎⠀⠀⠀⢀⡏⠀⠀⠀⠈⠑⠀⠱⡟⢦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡷⠶⠏⢙⣲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⠋⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢷⣶⠛⠷⠶⢀⡼⢠⠇⠀⠀⠀⠀⠀⡞⠀⠀⣰⠀⠀⠀⠀⣠⠞⣡⡾⠁⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡿⠛⠀⠀⠀⠀⣼⠇⣾⠀⠀⠀⣰⠀⢰⠃⠀⢀⡇⠀⢀⡴⠊⣠⢾⠟⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣶⣶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⢠⡏⢀⠇⠀⢠⠀⡏⠀⢸⠀⠀⣾⠠⠀⣉⡴⠞⡡⢋⡴⠁⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠼⠁⢸⠃⠀⠀⢠⢣
⠀⠀⠀⠀⠀⠉⠛⠳⣶⣤⠄⠀⠀⠀⠀⠀⠀⣼⡇⢸⠀⠀⡿⠀⠀⠀⡇⣤⠾⠇⡶⠚⠉⣠⣞⣡⠊⠁⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣠⢃⠆⠀⠀⣼⢸
⠀⠀⠀⠀⠀⡐⢿⣿⣷⣦⡀⠀⠀⠀⢀⣴⢇⣿⠀⢸⠀⠀⣇⠀⠀⠀⡇⠀⠀⣰⠃⣠⣾⡟⠋⠀⢀⡤⠖⣋⡴⠎⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣾⣷⠋⠀⠀⠀⡿⢸
⠀⠀⠀⠈⠻⣿⣛⠉⠀⠀⠠⠤⠴⠶⡾⢫⢸⣿⠀⢸⠀⠀⢻⠀⠀⢰⡇⢠⣼⣿⡟⠁⡼⠀⠀⢛⡫⠶⠛⢥⣀⣀⠀⠀⣠⠖⢁⣴⡾⠁⢠⣾⠟⠁⠀⢀⠆⢰⢧⢿
⠀⠀⠀⠀⠠⣤⣿⣟⡛⠀⠀⠀⠠⠞⠁⣿⣸⣿⢀⡄⠀⠀⠘⠀⠀⠈⡇⠀⡿⣿⣣⢠⠇⠀⠀⠀⠀⢀⣤⢞⣁⢤⣽⣻⣷⣫⢷⡿⢴⣾⣻⠛⠀⣠⢦⡞⢠⣾⠏⡞
⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⠀⠀⠀⠀⠉⣿⣿⡜⣇⠀⠀⠄⠀⠀⠀⢳⠀⢹⢻⣿⣾⢰⠀⣰⣶⣴⣿⣿⣯⣽⣽⣿⣿⣯⣅⣛⣴⣿⠟⠅⣠⡞⣡⢏⣴⣾⡏⢀⡇
⠀⠀⠀⠐⢾⣯⣤⣤⣤⣶⢂⣴⠀⣰⠁⢀⣿⠘⡇⢻⡀⠀⠈⠀⠀⠀⠘⡆⠀⣎⣿⡟⢠⣾⣿⣿⡏⠉⠉⡟⠀⠀⠉⢻⣿⣿⣷⢟⣩⣴⣾⠏⣶⣿⣿⠛⡽⢡⡾⠀
⠀⠀⠀⠀⣤⣶⣾⠛⠛⠋⠹⠃⣰⢏⣠⠾⢿⡄⠘⠈⣧⠀⠀⠀⠀⢄⠀⢹⡄⠈⠸⣿⣿⠃⠀⢸⣷⡀⠀⣇⠀⠀⣀⡼⠛⠏⠉⠛⠉⠛⠉⣲⣿⣿⣷⣾⣵⢿⠃⠀
⠀⠀⠀⠀⠀⠉⠛⠛⢻⣷⠗⠾⠛⠿⠁⠀⢾⣇⢳⡀⠘⢧⠀⠂⠀⠈⣆⠀⢱⡀⠀⠘⢿⣧⣄⣀⠈⠛⠶⠾⢦⣄⣷⣤⡞⠀⠀⠀⠀⡀⢠⢿⠛⠹⣿⢿⠶⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣠⣤⣄⣠⠀⠀⠈⢿⡘⣇⠀⠘⢷⣄⠀⠀⠘⣧⠀⠃⠀⠰⡈⢿⡄⠙⠛⠶⢤⣀⠀⠀⣄⡀⠉⢧⠀⠀⠀⣷⠈⣿⣤⣾⡟⠈⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⣿⡶⠀⠀⠸⣧⠹⣆⠀⠀⠙⢷⣄⠀⠘⢷⣄⠀⠀⠹⣶⣿⠶⠦⠶⠶⠛⠛⠂⠀⠙⠦⠜⠃⠀⠀⠸⣤⡘⢦⣥⡇⠀⢇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣠⣴⠆⠹⣧⠻⣆⠀⠀⠀⠉⠳⣤⡀⠙⢷⡀⠀⠹⣎⠓⠄⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡃⡇⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⢋⣽⢃⣠⡇⠙⣷⣿⣦⠀⠀⠀⠀⠀⠙⢶⣦⣙⢶⣀⠘⢿⡍⢉⣩⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢳⡇⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣛⡛⠉⠁⣿⣿⣞⣿⣿⣷⣄⠻⣦⠀⠀⢤⡈⠙⠻⢿⣷⣄⡹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠉⠛⠓⠲⠿⣥⣿⣿⣿⣿⣿⣦⡌⠳⣄⠀⠹⣶⡄⠀⠻⣿⠻⠶⣤⣀⠀⠀⠘⠛⠒⠒⠒⠒⠒⠒⠀⠀⡼⢃⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠌⠳⣔⣦⡢⣄⠀⠀⠉⠙⣿⣿⣿⣿⣿⣦⡝⣷⡄⠘⣿⡄⠀⠘⣧⡈⠛⠫⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡞⡼⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡈⠻⣟⢮⣷⡀⠀⠀⢁⡉⠉⠛⡟⢿⣿⣾⣿⣄⠘⣿⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡾⠏⢀⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡻⣦⡈⢷⡙⢿⣦⡀⠀⢳⡀⠀⠀⠀⠈⣟⢿⣿⣆⢹⡇⠀⣸⡿⣶⣄⡀⠀⠀⠀⠀⠀⣰⢃⣼⠧⠾⠋⠀⠀⡸⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⣀⣼⠋⠀⠈⢻⣾⣷⡄⠛⠦⣦⡀⢷⡀⠘⡄⠀⢹⡀⠙⢿⡄⣷⠀⣾⣷⣿⣿⠟⢻⣶⣤⣤⡤⠴⠛⣹⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠀⣀⣠⡿⠁⠀⠀⠀⠀⢻⣿⣿⣷⣄⢘⢿⣤⢧⠀⢳⡀⠀⡇⠀⠘⣷⢹⡀⣇⣿⣿⡋⠀⣼⠈⠀⠀⠀⠀⢠⡏⡀⢠⣀⡾⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⢉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣾⣿⣿⣧⢈⣧⠀⢹⠀⠀⢻⣸⣧⣿⣿⡇⠁⣢⡟⠀⠀⠀⠀⢀⣾⠟⢁⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣄⠄⠋⠀⠁⠙⡂⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡄⠘⣷⠀⢸⣿⡟⠙⣿⡇⢈⣿⡇⠀⠀⠀⠀⠈⢁⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠦⠀⣀⠛⠉⠀⠀⠀⠀⢀⠉⠀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⢿⠀⡿⢛⡁⣸⠉⠳⣾⣿⡘⠦⣄⣀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠤⠿⠃⠀⠜⢀⠒⠀⢠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠟⣸⠃⠀⠸⣿⣿⣿⣶⣤⣙⡳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠻⣤⡀⠀⠉⠲⣄⡀⠈⠙⠓⠒⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡆⠀⠀⣤⡹⢶⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⢤⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣄⠀⠀⠉⠳⢦⣁⡀⠀⠀⠀⠀⠑⠲⢤⡀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡖⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠓⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢹⠀⠀⢻⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⠰⣿⣛⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢠⠟⠀⠀⠀⢸⠀⠀⠀⢿⡆⠹⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⣶⢦⣭⣿⠿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡞⣠⠎⠀⠀⠀⢀⡏⠀⠀⠀⠈⠑⠀⠱⡟⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡷⠶⠏⢙⣲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⠋⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢷⣶⠛⠷⠶⢀⡼⢠⠇⠀⠀⠀⠀⠀⡞⠀⠀⣰⠀⠀⠀⠀⣠⠞⣡⡾⠁⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡿⠛⠀⠀⠀⠀⣼⠇⣾⠀⠀⠀⣰⠀⢰⠃⠀⢀⡇⠀⢀⡴⠊⣠⢾⠟⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⡸⠀⡼⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⣶⣶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⢠⡏⢀⠇⠀⢠⠀⡏⠀⢸⠀⠀⣾⠠⠀⣉⡴⠞⡡⢋⡴⠁⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠼⠁⢸⠃⠀⠀⢠⢣ ⠀⠀⠀⠀⠀⠉⠛⠳⣶⣤⠄⠀⠀⠀⠀⠀⠀⣼⡇⢸⠀⠀⡿⠀⠀⠀⡇⣤⠾⠇⡶⠚⠉⣠⣞⣡⠊⠁⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣠⢃⠆⠀⠀⣼⢸ ⠀⠀⠀⠀⠀⡐⢿⣿⣷⣦⡀⠀⠀⠀⢀⣴⢇⣿⠀⢸⠀⠀⣇⠀⠀⠀⡇⠀⠀⣰⠃⣠⣾⡟⠋⠀⢀⡤⠖⣋⡴⠎⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣾⣷⠋⠀⠀⠀⡿⢸ ⠀⠀⠀⠈⠻⣿⣛⠉⠀⠀⠠⠤⠴⠶⡾⢫⢸⣿⠀⢸⠀⠀⢻⠀⠀⢰⡇⢠⣼⣿⡟⠁⡼⠀⠀⢛⡫⠶⠛⢥⣀⣀⠀⠀⣠⠖⢁⣴⡾⠁⢠⣾⠟⠁⠀⢀⠆⢰⢧⢿ ⠀⠀⠀⠀⠠⣤⣿⣟⡛⠀⠀⠀⠠⠞⠁⣿⣸⣿⢀⡄⠀⠀⠘⠀⠀⠈⡇⠀⡿⣿⣣⢠⠇⠀⠀⠀⠀⢀⣤⢞⣁⢤⣽⣻⣷⣫⢷⡿⢴⣾⣻⠛⠀⣠⢦⡞⢠⣾⠏⡞ ⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⠀⠀⠀⠀⠉⣿⣿⡜⣇⠀⠀⠄⠀⠀⠀⢳⠀⢹⢻⣿⣾⢰⠀⣰⣶⣴⣿⣿⣯⣽⣽⣿⣿⣯⣅⣛⣴⣿⠟⠅⣠⡞⣡⢏⣴⣾⡏⢀⡇ ⠀⠀⠀⠐⢾⣯⣤⣤⣤⣶⢂⣴⠀⣰⠁⢀⣿⠘⡇⢻⡀⠀⠈⠀⠀⠀⠘⡆⠀⣎⣿⡟⢠⣾⣿⣿⡏⠉⠉⡟⠀⠀⠉⢻⣿⣿⣷⢟⣩⣴⣾⠏⣶⣿⣿⠛⡽⢡⡾⠀ ⠀⠀⠀⠀⣤⣶⣾⠛⠛⠋⠹⠃⣰⢏⣠⠾⢿⡄⠘⠈⣧⠀⠀⠀⠀⢄⠀⢹⡄⠈⠸⣿⣿⠃⠀⢸⣷⡀⠀⣇⠀⠀⣀⡼⠛⠏⠉⠛⠉⠛⠉⣲⣿⣿⣷⣾⣵⢿⠃⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⢻⣷⠗⠾⠛⠿⠁⠀⢾⣇⢳⡀⠘⢧⠀⠂⠀⠈⣆⠀⢱⡀⠀⠘⢿⣧⣄⣀⠈⠛⠶⠾⢦⣄⣷⣤⡞⠀⠀⠀⠀⡀⢠⢿⠛⠹⣿⢿⠶⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣠⣤⣄⣠⠀⠀⠈⢿⡘⣇⠀⠘⢷⣄⠀⠀⠘⣧⠀⠃⠀⠰⡈⢿⡄⠙⠛⠶⢤⣀⠀⠀⣄⡀⠉⢧⠀⠀⠀⣷⠈⣿⣤⣾⡟⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⣿⡶⠀⠀⠸⣧⠹⣆⠀⠀⠙⢷⣄⠀⠘⢷⣄⠀⠀⠹⣶⣿⠶⠦⠶⠶⠛⠛⠂⠀⠙⠦⠜⠃⠀⠀⠸⣤⡘⢦⣥⡇⠀⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣠⣴⠆⠹⣧⠻⣆⠀⠀⠀⠉⠳⣤⡀⠙⢷⡀⠀⠹⣎⠓⠄⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡃⡇⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⢋⣽⢃⣠⡇⠙⣷⣿⣦⠀⠀⠀⠀⠀⠙⢶⣦⣙⢶⣀⠘⢿⡍⢉⣩⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢳⡇⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣛⡛⠉⠁⣿⣿⣞⣿⣿⣷⣄⠻⣦⠀⠀⢤⡈⠙⠻⢿⣷⣄⡹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠉⠛⠓⠲⠿⣥⣿⣿⣿⣿⣿⣦⡌⠳⣄⠀⠹⣶⡄⠀⠻⣿⠻⠶⣤⣀⠀⠀⠘⠛⠒⠒⠒⠒⠒⠒⠀⠀⡼⢃⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠌⠳⣔⣦⡢⣄⠀⠀⠉⠙⣿⣿⣿⣿⣿⣦⡝⣷⡄⠘⣿⡄⠀⠘⣧⡈⠛⠫⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡞⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡈⠻⣟⢮⣷⡀⠀⠀⢁⡉⠉⠛⡟⢿⣿⣾⣿⣄⠘⣿⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡾⠏⢀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡻⣦⡈⢷⡙⢿⣦⡀⠀⢳⡀⠀⠀⠀⠈⣟⢿⣿⣆⢹⡇⠀⣸⡿⣶⣄⡀⠀⠀⠀⠀⠀⣰⢃⣼⠧⠾⠋⠀⠀⡸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⣀⣼⠋⠀⠈⢻⣾⣷⡄⠛⠦⣦⡀⢷⡀⠘⡄⠀⢹⡀⠙⢿⡄⣷⠀⣾⣷⣿⣿⠟⢻⣶⣤⣤⡤⠴⠛⣹⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠀⣀⣠⡿⠁⠀⠀⠀⠀⢻⣿⣿⣷⣄⢘⢿⣤⢧⠀⢳⡀⠀⡇⠀⠘⣷⢹⡀⣇⣿⣿⡋⠀⣼⠈⠀⠀⠀⠀⢠⡏⡀⢠⣀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⢉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣾⣿⣿⣧⢈⣧⠀⢹⠀⠀⢻⣸⣧⣿⣿⡇⠁⣢⡟⠀⠀⠀⠀⢀⣾⠟⢁⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣄⠄⠋⠀⠁⠙⡂⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡄⠘⣷⠀⢸⣿⡟⠙⣿⡇⢈⣿⡇⠀⠀⠀⠀⠈⢁⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠦⠀⣀⠛⠉⠀⠀⠀⠀⢀⠉⠀⣀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⢿⠀⡿⢛⡁⣸⠉⠳⣾⣿⡘⠦⣄⣀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠤⠿⠃⠀⠜⢀⠒⠀⢠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠟⣸⠃⠀⠸⣿⣿⣿⣶⣤⣙⡳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀