⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡖⣶⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⡻⢧⣛⣮⢳⢧⣻⢼⡳⣝⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣻⢳⣝⣮⢽⣫⢗⡾⣹⡞⣵⣫⢽⡞⣵⢏⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣿⢻⡭⣗⢯⣳⠾⣜⣧⣛⣮⢽⣣⣟⣮⣳⢏⣾⡹⣞⣳⡭⣟⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⣯⢷⣹⢞⡽⣎⢿⣱⢾⣱⡾⣯⣷⢿⣾⢯⣟⣾⣳⣟⡶⣽⡺⣽⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠙⣾⣱⡻⣞⡽⣎⢷⣫⢷⣻⢯⣟⣻⣞⣯⠿⣽⣳⡫⠿⣳⣟⣧⢷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠤⡀⠀⠀⡠⠒⠉⢠⣧⠀⠀⠀⠀⠀⠈⢷⡽⣎⢷⡹⣧⢏⣿⡳⣟⣾⢳⣯⣞⡿⣳⢯⣷⡄⠀⡨⠛⡫⠁⠉⠐⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠈⡦⠊⠀⠀⢀⠇⠸⣆⠀⠀⠀⠀⠀⠀⠙⠿⣎⡿⣜⢯⣶⣻⡽⣞⡿⢶⣯⣻⣽⣛⣾⡽⢠⠃⠜⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡘⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣳⣞⣳⠿⣽⣞⣿⣺⣵⣳⣿⠚⢄⠸⡴⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠚⠓⠉⠉⠉⠈⢧⠘⡄⠑⢄⣀⠀⠀⡀⠜⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠪⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢀⠀⠀⠈⡄⣇⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡀⡧⠀⠀⡀⢀⠀⣿⡄⠀⠀⠀⠀⡞⡆⣀⠵⢭⣗⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡐⠀⠀⠀⢰⠆⣯⠑⢄⠐⠄⠈⡷⡇⠀⠀⠀⠀⡗⠃⠓⠚⢤⠤⠭⠆⡈⡙⠒⠒⠒⣦⡒⣭⣀⡦⢻⢉⠄⢹⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⡘⢃⢠⠤⢤⣈⣷⡘⢆⡩⠲⡔⡿⡇⠀⠀⠀⢀⣁⣤⣽⣄⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣤⣼⣷⣼⡰⠀⢸⣌⡼⠄⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡜⢈⠘⢆⠊⠐⠒⠉⠽⣒⠳⠦⣿⡇⠀⠀⠲⣿⡛⠉⣿⢹⡻⢿⠟⠗⠀⠀⠀⠀⠀⢿⣿⢻⡝⡇⣹⡿⠀⠈⠞⢁⠜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡜⣀⠣⠀⠱⣄⠈⠂⠠⢀⠁⠑⢾⠇⠀⠀⡄⠈⠉⢸⠇⢿⡟⡮⡇⠀⠀⠀⠀⠀⠀⢸⠾⢻⡟⡏⢹⢰⠀⢀⡠⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⢰⠁⡆⡀⠀⢈⢷⡀⠀⠀⢱⡀⢾⣶⡆⠀⡷⠀⠀⢸⡀⠈⠰⢸⠀⠀⠀⠀⠀⠀⠀⢸⡶⠈⢸⠇⠈⢿⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣎⠱⡰⡘⠀⠀⢁⢹⡲⢔⣡⡹⠺⣾⢀⠀⡿⣄⠀⠀⠑⠢⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠊⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣇⢣⠱⡈⠵⠀⠀⢢⡇⠀⣟⡗⠤⣘⣏⠆⡇⢯⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠜⡰⣾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⢣⠱⡄⢂⠀⠠⢳⠀⡟⣾⠀⠀⠘⣖⡧⠬⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⢻⢀⣾⡅⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠲⣅⡸⠈⠀⠀⢿⠀⡇⢿⡇⠀⠀⢈⣿⣞⢿⣻⢿⣿⣿⣶⣶⣦⣤⣤⣶⣖⠊⠁⠀⠀⣼⡾⡯⣗⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⡸⠀⠹⠀⠀⢸⠀⢣⡸⠁⠀⡐⠁⠈⠛⠓⠫⠾⢶⣧⣻⡼⡿⣿⣿⠿⢽⡷⠐⠄⠀⣿⠀⢹⠘⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠧⣀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣧⣾⣷⣦⣾⠦⠀⠈⢢⢻⣠⢠⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠠⠒⠈⡟⠎⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢀⡿⣶⣶⣤⣤⣀⣀⣀⣘⣿⣙⣈⣁⣹⣦⣤⣖⠁⠘⣿⡌⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠖⠁⠀⠀⣴⢛⡜⠀⠀⠀⠀⢀⠇⠀⠘⢆⣀⣠⠾⣽⣛⡶⣭⢗⣯⣿⡿⡿⢿⠿⡇⠐⠂⠙⣯⢻⡽⣲⣄⡀⢳⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠞⠁⠀⠀⢀⡴⡣⡟⡜⠀⠀⠀⠀⡜⠀⠀⠀⠀⠙⣾⣽⣏⡷⠽⠮⠿⠶⠿⢿⣿⣫⢟⡇⠀⠀⠀⠸⣟⡼⣳⡭⣟⡶⣿⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⡜⠀⠀⠀⠴⠟⠊⢠⢇⠁⢀⠌⣄⡜⠀⠀⠀⠐⠄⡀⠸⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⡇⠀⠀⠀⠀⢹⣳⢧⣻⢼⣹⢳⡟⣦⣀⠸⡀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⣠⠧⠁⣠⣶⣾⠋⠀⠀⠀⠀⠀⠀⠈⠢⣇⢀⡠⢴⣶⡶⢶⠒⠒⠢⣼⣯⡇⠀⠀⠀⠀⠘⡧⠿⠼⠗⠛⠓⠋⠉⠁⠙⢗⣄⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣀⠔⢉⡠⢔⠅⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢘⠒⠓⣄⠀⠀⠑⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠁⠀⠀⠀⠀⠀
⢧⠄⠐⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⣩⠊⠒⢗⠀⠃⠓⠠⢤⠔⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀
⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠒⠒⠒⠒⠲⣖⣻⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠉⠈⠁⠉⠈⠁⠉⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀