⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂⡠⢆⡑⢀⠦⢑⢈⣴⠜⡀⡔⠢⢑⠎⡴⢡⠎⡴⢡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⢁⠲⡡⢐⢨⢦⣿⠟⡡⠆⣁⣶⠏⠎⠜⠀⠀⠀⠀⠁⠣⠜⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⢼⡏⢠⠓⠠⡍⢦⠛⠁⡎⢀⣶⣿⠿⠟⠋⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⣃⠀⢎⠡⠎⠀⠀⡞⠂⠀⣘⠐⣫⠫⠅⢃⡄⠲⣌⠳⣌⢎⡱⢥⠳⣐⠆⣄⢠⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠈⡎⠵⣊⡄⠀⢙⠆⠀⠀⠁⠀⠠⡌⠃⡥⠅⢊⣄⢚⢥⣈⠓⡈⠞⠘⠦⠛⠬⠙⠠⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢎⡕⢪⡕⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠜⣀⠮⡱⢌⣿⣾⠿⣷⣊⢭⠓⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡚⢬⠎⠁⢠⡚⢵⡒⢦⠤⣀⡀⠀⠀⠀⠀⠀⠀⣴⣬⣶⣤⠀⠀⠀⠀⠁⠈⠈⢀⡀⢤⡐⢦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠁⠂⠀⢠⣗⣵⢆⡞⣡⠛⠴⢉⠒⠂⣄⢀⣠⣾⣿⣿⣿⣿⣷⡜⢢⡓⢮⡱⣋⠶⣙⢦⡙⢦⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⡟⡌⠴⣌⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣂⡳⡉⡞⡜⢦⡙⠮⠀⢠⡶⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠱⣄⠧⢘⡵⢪⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⡭⣡⣶⣶⣿⣿⣿⣿⣿⣦⠙⣦⠹⠁⢠⡿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠠⢎⡳⣌⠳⢈⠶⣩⠀⢠⣿⣿⣿⣿⣿⣿⡿⢣⢉⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠌⠁⢀⢠⡷⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢨⠀⠘⡅⡳⣌⢳⢈⠷⣡⠀⢸⣿⣧⢿⣿⣿⠟⢔⠕⠋⠑⢞⢩⠅⢚⣿⣿⢟⣿⢷⡴⣄⠀⠎⣺⡿⠀⡀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠀⢸⡁⠳⣌⠧⢘⡜⡥⠀⢨⣯⣿⣿⣭⣅⡀⠁⠀⢨⠾⣟⣬⣷⣿⡿⣵⢻⡻⣿⣿⣻⣇⣷⣿⣦⡜⠃⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⢦⠃⡝⣢⢏⠐⡜⡲⠀⠀⠈⠳⢾⡿⣫⣷⣤⣤⣤⣤⣾⣿⣿⢿⣿⡿⠷⠛⠓⢽⢣⡟⣼⣿⡟⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⠃⡼⣑⢎⠀⠼⣱⠀⠀⢀⡀⠀⠰⣿⣟⣷⣿⣿⣿⣿⡿⣳⣿⣿⣥⣶⣵⣶⣶⢿⢃⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠭⣚⠀⠘⡴⢃⠀⠉⠁⠀⢠⡹⣭⣿⣿⣿⡯⣭⡾⠿⠟⠥⣻⠟⠉⠈⠀⠰⡈⢻⣿⡏⢠⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⢙⠆⠀⢱⠋⡀⠀⠀⡤⠰⡸⣽⢽⡿⣿⣟⣶⡀⠀⠀⢀⠀⠀⠀⢀⣴⣿⢻⣦⠙⠁⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⠆⠑⠀⠈⠀⠀⠁⠁⠁⠻⢯⡾⠛⠋⢀⠀⠀⡀⠀⣠⣾⣿⣿⠇⢟⡷⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⠀⠪⡑⣿⣢⣄⠁⠀⠀⡆⠀⠀⢀⣤⣃⢲⣤⠰⠛⠉⢈⠔⠉⣾⠃⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠋⠈⠀⢀⡀⣽⣤⠻⡜⢽⣯⠀⠲⠇⡠⠊⠁⢀⠠⠋⠀⠀⠂⠃⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠯⢳⠙⠋⠁⠀⢠⠙⡀⣦⣢⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⡇⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠑⠁⠻⡏⣶⣵⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠘⢀⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣶⡦⠧⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠜⠉⠂⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢫⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠃⡄⠀⠀⠀⠀⠀⠀⠀⢀⣏⡀⠐⠀⠀⠀⡔⠋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠃⠄⠐⠀⠀⢀⠠⠴⡤⠂⠉⠀⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠈⢑⠀⡤⠐⠂⠀⠀⠀⠀⢀⠀⢂⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⡷⣟⡿⣽