⠀⢀⡀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠤⠐⠂⠈⠉⠉⠁⠉⠈⠀⠉⠈⠁⠉⠀⠉⠈⠉⠀⠒⠀⠤⠤⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⢸⠀⠀⠀⢶⣄⡠⠤⠤⠒⠒⠒⠂⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⡀⡄⣀⣀⠀⠀⢨
⠸⡆⠀⠀⠈⡇⠈⠁⠀⠀⠓⢦⣀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⣀⠤⠔⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠑⠒⠒⠤⠤⠐⠒⠊⠉⠀⠀⠀⠀⡤⣄⡀⣐⣴⡿⠋⠀
⠀⠱⡀⠀⠀⠘⡄⠀⢠⡀⠄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡛⢡⠐⣹⣏⠁⢀⡇⠀⠀⠀⡎⠀
⠀⠀⢳⠀⠀⠀⠘⣤⡈⢣⠘⣴⢻⣾⣤⣰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣯⣶⣿⣿⢡⢆⡙⠄⠻⠶⠞⡇⠀⠀⢘⠀⠀
⠀⠀⠀⢣⠀⠀⠀⣿⠀⢂⠹⣾⣯⢿⣿⣿⣆⠀⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣷⣯⣷⠌⢂⠀⠀⣰⠃⠀⠀⢸⠀⠀
⠀⠀⠀⠘⡄⠀⠀⠸⣇⠠⠘⢸⣿⣿⣿⠻⣯⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⢿⣿⣿⡏⡜⠀⠀⣼⠏⠀⠀⠀⡜⠀⠀
⠀⠀⠀⠀⢣⠀⠀⠀⢻⡄⣱⣾⠟⠋⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠉⠙⠿⣷⣌⣠⠏⠀⠀⠀⡸⠁⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠀⠀⠈⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣀⣤⣶⣦⣤⡀⠀⠉⢻⡟⠀⠀⠀⡰⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠸⣄⠀⠀⢀⠀⠀⠀⢰⣿⣽⣿⣿⣿⣿⣿⣷⣤⠢⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣲⢇⣶⣿⣿⣿⣿⣿⣾⣿⠀⢠⡾⠀⠀⠀⢰⠃⠀⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⢻⣼⠟⠂⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂⡜⢀⠂⠀⠀⠀⠀⠀⠀⠠⠈⣄⡞⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⠃⠀⠀⢠⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠹⣤⠀⠄⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠐⢂⠈⠄⠀⠀⠀⠀⠈⠠⠑⢨⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⠀⠀⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⣇⠀⠀⢀⠈⢻⣿⠿⣿⣿⣿⣿⣫⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠂⣾⣿⣿⣿⣿⠿⣿⣻⠟⢁⣼⠏⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣻⠐⠈⠄⡨⠄⡌⢛⠶⠦⠷⠿⠛⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠡⠉⠀⠉⠛⠛⢛⣛⣡⡶⢯⡏⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⡇⠘⡈⠰⣀⢣⠘⡤⢢⠑⡰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⠈⠀⠐⢈⠡⢩⣷⠟⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⡇⠰⢈⠡⢂⠦⢩⠔⡡⢊⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠋⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡼⢃⠐⠌⢢⠍⣎⠱⣊⠱⡌⡘⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢫⣽⠃⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡼⠁⢈⠐⡈⢆⡉⢆⠳⡌⡓⢬⠑⡌⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⡤⢐⠈⣆⣿⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣸⢃⠐⠀⠂⠌⢠⠘⡌⡓⢬⡑⢎⡒⠄⢡⠠⢁⠢⠄⡀⢀⠠⣴⡲⢦⡲⢶⡼⣿⣶⢰⡟⢡⡌⢦⡹⣾⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡴⢃⠄⠀⠌⠐⠈⠄⢊⡐⢉⠆⡙⠦⣉⠞⣠⠢⢡⢆⠱⣈⠦⣁⠛⣿⣳⣿⣯⣿⠟⣥⢧⣚⣥⢺⣽⠓⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡰⠁⠀⠀⢀⡾⣑⠈⠀⢈⠠⢁⠢⠌⡄⢌⠢⢌⢡⠓⣬⢚⡤⣛⡴⢪⢵⣘⢦⡝⣺⢴⣻⣿⣿⢣⣟⡞⣧⠿⣜⣿⡎⢧⣹⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡰⠁⠀⠀⢠⢟⠰⠁⠀⠀⠀⠐⡈⠰⠩⢜⢢⠳⡌⢦⡝⢦⣋⠶⣣⢻⡝⣮⡝⣶⣹⢷⣫⣟⡿⣞⡿⣾⡽⣯⢿⣽⢺⡝⢦⡹⡇⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠁⠀⠀⢠⠏⠰⠁⠀⠀⠀⠀⠐⠀⠡⢁⠊⡄⢣⠘⣅⠚⡤⢋⢞⡱⢧⣛⢶⡻⣵⣻⣞⣷⣫⢿⣽⣻⢷⣻⣯⣟⡾⣻⢼⢣⡱⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠇⠀⠀⢀⡾⣸⠁⠀⠀⠀⠀⠀⠀⡀⠁⢂⠐⡈⢄⠣⢄⠋⡴⢉⠦⣙⠶⣹⢞⡽⣳⡽⣞⡾⣽⣻⢾⣽⣻⡽⣾⡽⣳⢏⣟⢦⡑⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⠀⠀⠀⣼⢣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠂⡐⠠⠒⣈⠒⡌⡱⢊⡥⢫⡕⣫⢞⡵⣻⣝⣻⢷⣯⣟⡾⣳⢟⣧⢿⡹⣞⢼⡣⢞⡸⡇⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⠀⢈⡯⠽⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠂⠠⢀⠡⠒⣀⠣⢌⡑⠣⡜⡡⢞⡱⢎⡷⣣⢯⣛⡾⣳⠾⣽⡝⣾⢣⣏⢷⡹⣆⠟⡤⢓⣷⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠇⠀⠀⢸⡿⠆⠀⠀⠀⠀⠀⠀⠀⢈⠀⠠⠁⢂⠐⠠⢁⠂⢅⠢⠌⡱⢐⠱⢌⠲⡍⠶⣭⢳⣏⢷⣫⢟⡵⣻⣜⡳⣎⢷⠳⣭⢚⣥⢃⢿⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠠⠐⠀⠠⠐⠠⠀⠌⢂⠡⠈⠄⢂⠂⠡⠈⠆⡌⡱⣘⠳⣌⠷⣪⠷⣹⢎⡷⣳⢎⡷⣹⢎⡟⡴⢫⡜⢪⡜⣷⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀