⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⢢⣀⣀⡀⠀⠀⠀⢀⣀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠲⢄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠹⠄⠀⠀⠁⠀⠈⣆⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣤⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⡀⠀⠀⠀⡿⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠀⠀⡇⠀⣏⠢⡀⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⢦⠀⠀⠀⠀⠀⠐⠋⠙⢾⡑⡄⣌⠓⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣈⡧⡀⣸⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢮⡉⠑⣦⢄⣱⡀⠀⠀⠀⠀⠀⠀⣼⢸⣟⣠⠾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠦⣀⠀⢍⠻⣠⠀⠀⠀⠀⠀⠹⠅⠉⠣⣔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠒⠷⣸⠀⠆⠀⠀⣀⠜⡠⠐⢘⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡴⠛⠲⣄⡀⢠⡄⠈⢳⡀⣤⠐⢳⠊⠀⠀⣸⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣇⠀⣸⣫⣠⣴⣇⣠⡤⣷⣿⣤⠇⠀⣠⠞⠹⠀⡴⢃⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⡼⢳⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠉⠁⠁⣠⢿⣧⣤⣿⠂⠀⠹⣿⡿⣾⣝⢦⣴⡇⡜⢀⠎⠀⢠⠀⠀⠀⣤⣿⣀⣿⣰⣁⡈⡆⢄⠀⠀⡰⡃⣄⠀⠀⡀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⠀⢸⣏⠁⣼⣃⢹⢿⣆⠀⣠⣟⡀⠈⢻⡿⢋⣿⠀⣈⠀⠀⢸⠀⠀⠀⣶⠘⣷⠉⢻⡀⠉⠳⡏⠆⠀⡌⠀⡿⡆⠀⣇⡞⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠞⢻⣿⡉⣿⣻⢹⣾⣯⣏⣿⢛⣿⣿⣏⡴⡹⢿⡄⡏⠀⢠⡟⣧⢰⡄⡇⢀⡿⢄⣀⣈⡑⠀⢹⣿⡆⢸⡀⡇⢳⠰⡟⢉⢹⢻⡄⠀⠀⠰⢦⡀⠀⠀
⠀⠀⠀⠙⠷⣥⣝⣽⣿⣀⣹⢹⣯⢻⣿⡏⡜⠚⠋⣿⣧⠇⣷⣧⢼⣯⣿⡉⠉⠛⢷⢶⣴⣶⣶⣮⡇⢱⣸⠷⣰⠸⣿⡡⠓⠀⢻⢻⣞⡄⠀⣸⠀⠁⠀
⠒⠛⠫⢍⠉⢛⠻⣦⢿⣧⢸⡈⠀⣴⣿⣯⣀⣀⡠⢿⣿⡰⣿⡄⢆⣹⡿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠃⠘⠏⠀⢿⡂⠀⢷⣾⣷⣌⣹⣷⣇⣰⡗⠀⠀⠀
⠁⠀⠀⠀⠑⢄⠑⠪⡢⣿⣿⣤⣾⠋⢀⣯⡿⡋⠀⠘⢠⠃⠘⣻⢦⣸⡇⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢹⠃⡀⠀⠀
⠀⣤⣤⣄⡤⠤⣍⠑⠺⢯⣿⣿⣧⣇⣼⣽⡿⣖⡶⣗⣉⣉⣒⣛⣾⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⠃⡀⠀
⣴⡯⠋⡛⡀⣜⣯⠀⠀⠀⢻⣿⣹⠟⠛⢕⣫⠝⢻⣿⠓⠉⠉⠉⡻⢶⣹⡀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠈⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢃⡜⣁⣠
⣿⡁⠠⠁⢧⡼⠋⠉⢹⠞⢉⠄⠸⡄⢠⠞⠁⣦⢀⣿⣷⣶⠛⠫⢍⣲⡞⢷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠚⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⢾⣿⡿⠁
⠈⣷⡀⠘⢾⣗⡠⣜⡟⠈⠒⡤⠚⠳⣇⣠⣾⠯⣉⠙⢟⡳⡿⡞⠛⠚⠓⠾⣷⡄⠀⠀⠀⠛⠻⠶⣦⣦⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⠀⠀
⠀⠘⢷⣶⡋⠀⠨⠂⠱⡤⠋⣅⠄⢀⣸⣿⣿⠞⠁⠐⠎⠛⢯⣷⡀⠀⢀⣀⣿⡙⣦⡀⠀⠀⠀⢠⠤⣀⢈⠘⠉⠉⠀⠀⠀⠀⢀⣤⣾⢏⣙⣁⢤⠀⠀
⠀⠀⠀⠈⢻⣇⠀⠈⡼⠁⠆⢀⣟⣿⣿⠋⠀⠀⠀⠀⠈⢿⡆⢉⣿⣾⣿⣿⡇⠀⠈⠻⣄⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⣀⣤⠖⣫⡏⠱⡄⡥⠦⠞⠀⠀
⠀⠶⠛⢭⣩⠹⠛⢻⣏⠒⢂⠎⣼⠇⣇⡀⠀⡀⠀⠀⠀⣼⠟⢿⣿⣿⡁⢸⢃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⣠⠟⠒⢦⣀⠵⠶⣞⠂⠀
⣠⣖⣋⣉⠉⠙⠲⢿⣦⣧⡾⣶⣇⠀⣿⡷⣗⠀⠀⢀⡼⠃⢀⣼⡇⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⢀⠤⢯⡀⠀⠀⠧⠀⠀⣸⣠⠚
⠁⠀⠀⠐⢿⣦⣤⣤⣿⠋⡀⠹⣿⣴⣿⠟⠿⠷⠖⠋⠁⣀⣸⡟⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡇⠀⢠⣟⠀⠀⠀⢀⣜⠉⠙⢦
⠈⠓⠒⠲⢾⣟⠁⠈⠳⢳⠅⢠⡗⠛⣣⣄⣤⣴⠶⠶⡟⠋⠉⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠐⡎⠀⠊⢀⣱⢶⡇⠉⠓⠂⡀⠲⠁⢱⡀⢘
⠀⣀⣤⣤⣤⡽⠶⠒⠚⠛⠛⠛⠛⠛⠉⠉⠀⠀⠘⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⡀⠀⠀⠀⠀⢘⣦⣖⡯⠗⠛⡟⠦⠖⠊⠑⠤⣄⣾⠗⠋
⣾⠋⠉⢇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⣠⣶⡿⠛⣟⠦⣀⠀⣧⠐⡀⠀⢠⢠⣿⣴⣮⡖