⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠁⢀⠤⠊⠀⠀⣀⣖⠨⠂⢀⠀⠀⠀⠀⠀⠲⠉⢢⣀⠀⠑⢄⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠜⡡⠀⡠⠂⠀⠀⣠⡾⠊⠀⠀⢠⢪⠃⠀⠀⠀⠘⡄⠀⠣⡑⢷⡄⠀⠐⢄⠀⢀⢽⣦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⢃⠔⢁⠌⠀⡀⢀⡴⠋⡠⠊⠀⢠⢣⠃⠀⠀⠀⠀⠀⠹⡄⠀⠐⠀⡹⢂⠀⠈⢢⢸⠺⣣⢱⠈⢄⡠⠒⠉⠉⠐⠢⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⡠⠃⠠⠃⠀⡜⢀⡞⢀⢎⠂⠀⠀⠃⠎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢁⢣⠀⠀⠻⡀⢻⢸⠃⢸⠁⠀⣠⢴⠎⠉⢉⢳⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⠌⠀⡰⠁⠀⡜⢀⠎⢠⢢⠃⢀⠀⡼⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠃⠀⠀⡇⠀⣸⠀⡞⢃⢮⣱⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠂⡔⠰⠁⠀⡘⠀⡎⢀⢆⠆⢀⠆⢠⠇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡄⠰⠸⡸⡀⠀⠸⣀⣹⣀⡧⣵⡭⡅⠩⠕⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠃⠆⢀⠃⠀⠀⠁⠘⠀⡌⡌⠀⡼⠀⣾⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠃⠀⡇⠃⠇⠀⠀⢿⣿⣿⡖⠁⢣⣷⠀⠠⠼⢧⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠎⡜⠀⡎⠀⠀⡘⢀⡇⢸⢷⠃⢸⡇⢠⠿⢈⡇⠀⠀⠀⠀⠀⢠⠀⠘⢠⢢⠀⠀⢀⠀⢃⢸⢰⠀⠀⡜⣸⣼⡛⢤⡀⣾⠀⠀⠀⢨⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡜⢠⠀⢰⠁⠀⠀⠇⣼⢀⡷⢸⠀⣾⡇⣸⢠⢸⡇⣇⠀⠀⠀⢀⡔⠀⡄⢸⠸⠀⠀⢸⠀⠀⠈⡞⡀⠀⠀⠿⣿⣽⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠁⡌⠀⡎⠀⠀⠀⢸⡙⢸⢣⣏⢰⣿⠁⣧⣼⢸⢇⡿⠀⠀⠀⡘⡗⠀⣷⢸⠀⡇⠀⢸⠀⣰⠀⡇⡇⠀⡸⠀⣿⡎⣿⡢⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡎⠀⠃⠀⠁⠀⠀⠀⡀⡇⣾⢸⢹⢸⡟⢜⠀⢀⣾⢼⢁⡆⠀⢀⢵⢁⢸⡏⢎⢠⡇⢀⣿⢠⣩⠇⡇⠃⠀⡇⢸⢹⣷⣯⢫⠁⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠁⣸⠀⢸⠀⠀⠀⠀⢿⢸⠿⣄⠘⣼⠤⢯⢤⣃⠹⠈⣼⠸⢀⢎⡿⣜⠏⡟⠀⡼⢡⢸⣾⣨⠟⡆⡇⠃⠀⠈⢾⣿⣯⣞⡈⡈⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⢿⠀⣜⠀⠀⠇⠀⣼⢤⣶⡿⣿⣿⣿⣿⣶⣭⠇⠃⠹⣧⡨⢫⠗⢊⡼⢚⣹⣧⣼⣾⣤⡟⢸⣲⡅⡇⠀⠀⠀⢯⠘⣽⠘⢇⢧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⢸⠀⣼⠀⢰⠀⠀⣿⠻⡏⠀⠿⡿⢿⡿⣿⠙⠀⠀⠀⠀⠁⠀⠀⠀⠾⢻⣿⣮⡟⣿⠛⢿⣿⢻⡇⡇⠀⠀⢏⠀⣆⠈⢷⢄⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠇⢨⢸⠀⠉⠀⠀⠀⠀⡏⠀⠈⠂⠈⢧⢬⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠛⣩⡟⠀⡼⠋⢹⣇⠁⠀⡸⠸⠀⢹⣆⠀⢫⠙⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢨⠰⣼⠀⡆⡄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⠀⠉⠀⠀⣸⠹⠀⠀⠃⠀⠀⠈⣏⣆⠀⢣⣿⠲⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠏⠀⣧⢡⢰⢰⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡀⠀⡘⢠⠀⠀⢰⠸⣼⡀⣼⡧⠜⠃⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡎⢰⡇⢿⡈⡞⠘⡄⡞⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡣⡆⡇⠀⠇⡎⠀⠀⢾⢠⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠒⠠⠤⠀⣀⣀⠀⠈⠻⠘⡽⠈⣧⠱⠁⢁⢡⠃⠰⡄⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡫⢴⢱⠁⢸⣰⠀⠀⠀⠇⠇⢠⠎⣇⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢷⣿⢧⠹⡆⢣⡘⣼⣼⡀⠘⢦⡀⠀⠀⠀⠀⠈⠂⠤⠀⠠⠕⠋⠀⠀⠀⠀⠀⠀⡴⠁⠀⣬⡆⢀⣯⢃⠃⣴⣼⡞⣠⠗⠃⠀⠀⠀⠉⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡳⢽⡄⠱⡀⠻⣵⡄⢠⠙⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡊⠀⡄⣰⡟⢀⣾⣏⠎⣾⣽⣿⣔⣁⠀⠀⠀⢀⡀⠀⣰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠀⠙⠢⣱⣜⠬⡮⠰⠕⠊⢋⠑⡦⣀⠀⠀⠀⠀⠀⣀⠤⠒⡾⣗⡾⠣⠮⢪⡝⣡⣿⣿⠾⠭⠮⠭⠄⢀⡀⠀⠀⠀⣀⠀⠤⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠐⠳⣕⠤⠄⠀⠀⠘⡜⠀⠀⠉⠒⠒⠂⠉⠀⠀⢠⠃⠀⠉⠒⣰⣿⣾⡻⠋⠁⠀⠀⠀⠀⠀⢀⡜⠽⠂⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢈⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠤⢀⠀⠀⠀⠐⠉⠀⡸⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⢤⡀⠀⠀⣧⠀⠀⠀⠀⢠⠃⢀⠤⠊⠁⣀⡼⢋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡬⣲⣖⠈⠀⠀⠀⣴⠏⣔⡠⠄⠒⠉⠠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀
⠀⠀⠁⠈⠉⠙⠫⡉⠍⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⣜⠀⠀⡴⠟⡁⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠉⠒⡀⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣰⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⡄⠙⠢⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠇⠎⢔⠁⣌⡶⠀⠤⠤⠤⠤⠠⠄⠌⠕⠒⠚⢤
⠀⠀⠀⠀⠀⠠⠤⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⢀⠜⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡎⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠈⠉