⠀⠀⠀⠀⠀⠀⠚⠁⣀⣀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣾⠞⢁⣀⣠⠤⠤⢤⣀⣀⡀⠀⠀⢰⡖⠒⠲⢦⣌⡳⣿⢥⡀⠈⢻⣶⡎⠀⠀⢀⣴⠟⠉⠀⢠⡟⠀⠀⠀⠀⢠⡟⠀⣾
⣦⣼⡀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⢀⡤⠚⠁⠀⣼⠁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠳⢾⣇⠀⡀⠆⣹⣤⡈⠀⡇⠀⠀⠉⡇⠀⢠⠟⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⣼⠁⢠⡯
⠈⠻⣿⣂⣀⣠⣾⠟⢻⣿⣷⣀⡶⠋⠀⠀⠀⠀⣻⡦⠓⠀⠀⢰⣞⠻⣍⠙⠲⢤⣀⠀⣠⠞⠒⠛⠉⠁⠈⠻⣍⠉⠳⠤⣤⣇⡴⠋⠀⠀⣀⣤⣶⢾⠀⠀⠀⠀⢰⡇⠀⠀
⠀⠀⠈⠻⣿⠟⠁⠀⠀⢿⣿⠏⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣀⣈⠙⠳⠶⠶⣶⣒⡲⣆⠀⠘⢧⡀⠀⠈⢯⣠⠶⣤⣾⣿⣿⣿⢸⠀⠀⠀⠀⣾⠀⠀⡟
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠸⡇⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠉⠓⠦⣤⣀⠀⠈⠉⢻⡆⠀⠀⠳⣄⣠⣶⣅⣀⡈⢿⣿⣿⣿⢸⣀⡀⠀⢠⡟⠀⠀⡇⣿
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢳⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠤⠤⠤⠤⠽⠶⢤⣤⡄⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⣿⠀⠈⣿⣿⠙⣿⣿⣏⠉⠉⠉⠓⠾⢧⣄⣀⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆⣼⠁⠀⠀⠀⢠⠆⠀⣾⠘⠧⠤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡯⠀⠻⡇⠈⣿⣦⡀⢀⠀⠀⠈⠉⠙⠻
⣢⣄⡈⢧⠀⠳⣄⠀⠀⠀⠈⣷⡏⠀⠀⠀⢀⡟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠙⠒⢦⡴⠟⠁⠀⠀⠀⠀⠀⠠⡾⠀⠈⣣⣴⠗⢦⢀⡿⡄⡇⠹⡎⠲⣕⢄⠀⠀⠀⠀
⠈⠙⢿⣮⣳⡀⠸⡆⠀⠀⢀⣻⠃⠀⠀⠀⢸⠃⠀⢸⠀⠀⠀⠀⡀⠀⠀⢀⣬⠷⠤⠤⠖⠋⠀⠀⠀⠀⠀⣀⣤⣤⣴⡇⠀⢰⣿⡟⠀⣼⢿⠁⠀⡇⠀⢳⠀⠈⢦⡁⠀⠀⠀
⠀⠀⠀⢙⡿⢿⣦⣿⠀⠀⣼⢸⠀⠀⠀⠐⡟⠀⠀⡟⠀⠀⠀⠀⣧⠀⠰⣏⣀⣀⣀⣀⣀⣀⡤⠤⠖⠒⠚⢹⣿⠛⣟⡀⢠⣿⡿⠁⣼⣷⡿⠀⢀⡧⠀⠘⡆⠀⠀⠙⠆⠀⠀
⠀⠀⣠⠎⢀⡀⣿⢿⣇⣰⠇⢸⠀⢸⠀⢰⠇⠀⠀⡇⠀⠀⠀⢠⠿⣇⢻⡄⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣠⠟⠉⢦⡈⢻⠛⠻⢧⣴⣿⡿⠁⠀⣾⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀
⠀⢈⡵⢀⠞⣠⣿⢈⣿⠏⠀⣏⠀⢸⠀⢸⠀⠀⠠⡧⠤⠤⣀⣸⡀⠘⢦⡻⡀⠀⠀⠀⠀⠙⢷⣦⣄⡘⠁⠀⠀⠀⠳⣬⣇⠀⠈⣯⠉⠓⠦⣼⠋⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀
⠄⣹⣠⡏⡀⢈⣿⡿⠁⠀⣸⠏⠀⢸⡀⢸⠀⠀⠀⣷⠀⠀⠀⢸⠉⠙⠦⢝⣾⣦⣄⠀⠀⠀⠀⠉⠲⢍⠛⠲⢤⣀⣀⡽⣿⡤⠶⢿⡆⠀⣠⢿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀
⣶⠾⠿⢴⣷⡿⠋⠀⠀⢠⣿⠀⠀⢸⣇⢸⡄⠀⠀⡿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⢀⢀⣤⠴⠛⠀⠀⠀⢀⡴⠖⠀⠀⢀⣿⡟⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⣿⣄⡾⠋⠀⠀⠀⢠⡞⣻⡀⠀⢸⢻⡄⢳⡀⠀⢷⣸⢦⠀⠺⣄⡀⢀⣀⣀⠀⠀⠀⠙⠓⠟⠋⠁⠀⠀⠀⢀⡴⣫⣤⣶⣶⣖⣹⢿⣧⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⠀⠹⡆⠸⣧⠈⢳⡈⢷⡀⢿⡟⢻⡃⣸⣿⠀⢻⡇⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⠀⢀⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠻⣿⣿⣿⣿⣷⣄⠙⣦⣿⣧⠈⢳⡀⢳⣜⣷⡘⣷⣮⣁⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⣿⣟⣿⠀⠀⢸⢸⠓⣾⡃⠀⠀⠀⠀⠀
⠀⢀⡴⠋⠀⠱⢮⣻⣿⣿⣿⣿⣶⣌⡹⣟⣷⡄⠙⢮⡏⠻⣷⡬⢿⡿⢿⡵⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢻⣾⠀⠀⢸⢸⠀⠈⢻⡆⠀⠀⠀⠀
⣴⡿⣦⡄⠀⠀⠀⢻⣻⣿⣟⢻⠛⣿⣻⣿⣏⢿⠶⣄⠙⢦⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠈⣿⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀
⣿⣦⣾⣿⣆⠀⠀⠀⡏⣿⣿⣷⣿⣿⣿⠿⣟⠾⣧⠈⠻⣦⣝⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⠟⣿⣀⠀⠀⢸⠀⠀⣸⢸⡀⠀⣸⠃⠀⠀⠀⠀
⠾⠿⠿⠿⣿⡄⠀⢀⣸⣼⠿⠿⢛⠛⠁⠀⠈⠳⣿⣧⠀⠻⣦⡉⠛⠿⢶⣦⣤⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⡇⠀⠀⣠⣾⣿⡄⢸⠸⡄⠀⢸⠀⢠⡇⣾⠁⢠⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠉⣷⠜⣩⣥⣤⣈⠛⢿⣷⣄⠀⠀⠀⠀⠻⣧⠀⢻⡟⠳⣤⣀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣼⠃⣠⡾⠋⠈⢿⣷⠘⡇⣧⠀⣼⢠⣿⣧⡿⠀⣾⠃⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡾⠗⠋⠁⠀⠀⠉⠳⡀⠙⢿⣷⣄⠀⠀⠀⠹⣧⡀⢻⡄⠀⠉⠓⢦⣄⣀⡀⠈⠻⢦⣄⡴⠞⣡⡴⠋⠀⠀⢠⠽⠻⠀⠇⢻⣤⣟⡿⣹⣿⠃⣸⠏⠀⠀⠀⠀⠀
⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡈⢻⣿⣆⠀⠀⠀⠘⢷⡄⢻⡄⠀⠀⠀⠀⠉⠙⣿⡶⢤⣀⣤⠞⢹⡇⠀⠀⠀⠘⣻⠟⠉⢹⠛⡿⠋⢠⣿⠏⢠⡟⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢙⣿⣄⣀⠀⠀⠈⠻⣄⠻⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⣴⠟⣻⡄⠀⠀⠀⠷⠶⣶⣲⠒⢻⣠⡿⠋⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀
⣓⢦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠐⣀⡉⡉⠑⠀⠀⠈⠳⣝⣷⣀⣀⣀⣓⡀⠀⠤⠾⠛⠁⢀⡟⣷⠀⠈⠀⣖⣾⠟⣿⣦⠈⡟⠀⠀⠚⠀⠀⠀⢀⡀⢀⣀⡴
⠉⠳⣀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠣⡈⠻⣿⣆⠀⠀⠀⠀⠈⠳⢿⣍⣡⠤⢤⡀⠀⠀⠀⢠⡾⠁⠸⡇⠀⠀⣿⡿⣿⣽⢁⡼⢧⡀⠀⠀⣀⠴⠊⣡⢶⠟⠁⠀⠀
⠀⠀⠈⢷⡾⠛⠉⡍⠙⢆⠀⠀⠀⢠⠇⠀⠀⠀⠙⢦⡈⠿⣿⣄⡀⠀⢀⡤⠾⠋⠀⣄⠀⠙⢶⡒⠾⠋⠀⠀⠀⡇⠀⠀⢠⢃⣿⡽⠋⠀⠀⢻⠀⢚⡥⣾⣿⣴⡋⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠛⠶⣧⠀⠘⡷⢶⣶⣼⣤⣤⡀⠀⠀⠀⠱⣤⣸⠿⠿⠛⠉⠀⠀⣠⠾⠽⠷⢦⣀⠙⡆⠀⠀⠀⠀⣇⣴⣶⢏⣾⠟⠀⠀⠀⠀⢸⠞⣿⣿⠟⡏⠉⡿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡇⢸⠛⡇⠸⢻⠉⡷⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠈⠉⠉⠓⠺⠶⠦⣿⡟⢡⡞⠁⠀⠀⠀⠀⠀⢸⠀⡇⣾⡄⠇⠀⡇⠀⠝⠿⣾
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡇⢸⠀⡬⢤⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠒⠒⠒⢛⣶⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡿⣄⣽⡠⡇⠀⡆⡞⣛