⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣶⠟⢿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⢀⣜⠲⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣎⢲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠤⠀⠀⢀⠀⡸⠆⡇⢻⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡍⣾⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⢀⣜⣀⣀⣈⡉⠁⠀⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣬⡏⢈⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⠔⠉⠁⠀⠀⠀⠨⠫⡤⠉⡷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣥⠘⠈⢄⢣⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠐⠁⠀⠀⠀⠀⣠⣎⠀⢀⡀⣌⠐⡾⠧⠝⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣦⡀⠈⢂⢂⠀⠀⠀⠀⠀⠀⠀⡟⠀⠄⢠⢄⠀⠀⠠⠊⠁⠀⠉⢻⡆⠠⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⠬⢻⣱⡈⠓⢦⣀⢆⢐⠀⠀⢠⠀⢠⠇⡜⠀⠀⠊⢀⠄⠀⣀⢀⠀⠀⢸⠣⠄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠳⢂⢄⠙⢎⠎⠄⠀⠀⠀⢸⢰⠃⠀⠀⡴⢁⠔⠊⠀⢈⡀⢀⡌⠛⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⢮⣆⣁⠀⣈⠈⠂⢠⠀⢸⡜⡘⢀⡞⠐⡡⠔⠈⠁⠀⡠⠁⣸⡶⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣿⡘⣂⣉⢿⡄⠙⡄⢸⡇⢣⣾⠗⠀⠀⣀⣤⣖⣭⡴⠾⠁⠃⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⡄⢝⢻⣮⠻⠎⠷⡾⢁⣤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡤⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠑⡙⢷⣷⣄⢈⢉⣁⡈⠉⠉⠉⠉⠙⠻⣖⣲⣦⣄⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣩⡛⡄⣎⢻⣮⡳⣮⡉⠛⠂⠭⣛⡛⠫⠤⢤⣧⣸⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⢰⠀⢹⡄⠹⣿⣦⡙⢦⡀⠀⢀⠬⣁⠒⠤⣤⣟⠙⡆⠀⡇⠀⠀⣴⠉⠙⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⢸⡆⢸⡀⠀⡱⠉⠻⡆⠹⣷⢤⣁⣈⣆⡀⣀⣽⣏⠳⣤⠃⠀⠀⠉⠀⣠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠟⠒⢼⣼⢠⢃⠃⢧⡰⣥⡀⠙⠦⠮⡿⣳⠕⠦⣧⠦⣟⡄⢀⡀⠤⠔⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣦⡇⠀⠀⠀⠟⣜⠀⡆⣗⠇⠈⢷⡄⠀⢀⣤⠶⠊⠉⠀⠀⠀⠹⣆⠙⠲⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣁⠼⠀⠀⠀⠀⠈⢿⢧⣴⢺⠄⠀⢨⣷⡴⢛⠴⡄⠒⠄⠀⠀⠀⠀⠈⢷⡀⣽⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢿⡎⠀⢀⣿⡟⠀⠘⢄⠸⠀⠆⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⠑⡀⠀⠀⠈⢿⢀⣾⡿⠃⠀⠀⢸⢀⠌⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⠃⠀⠀⢀⣤⡻⣛⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣀⠀⠀⠀⠀⠀⠀⢠⠊⣀⣤⣶⠿⠋⠀⠈⠑⢶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢀⠙⡄⠀⠀⢀⣴⣿⠿⠛⢹⡋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡇⠇⣠⣾⣿⠟⠁⠀⠀⣀⣉⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⣿⠟⠁⠀⠀⠀⢰⠁⣆⡅⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⢀⣼⣿⣿⠏⠀⠀⣀⡀⠀⠈⢦⡀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡉⠑⠲⢄⢂⣾⣿⣿⡏⢀⡄⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠒⠂⠚⠸⢟⣿⣟⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠁⠀⠀⠈⠹⡌⠁⠀⠉⠁⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣐⠁⠀⠀⠀⠀⠰⡀⠘⠀⠀⡐⠀⠀⢸⢀⡖⠂⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠔⠋⠉⠀⠀⠉⢙⠲⣤⣀⠙⢤⢡⢠⣡⣴⠴⢂⠨⠀⡎⠌⠌⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⣀⠀⠀⢀⠄⠁⠀⠩⠯⣩⡦⢬⠞⢋⣀⣂⠤⠖⠂⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠒⠋⠀⠀⢰⠀⠐⠊⠁⠐⠉⠀⢸⣶⣾⡿⠏⠋⢭⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠓⠠⠄⡀⠀⡀⠐⠁⡎⣧⠹⣀⠀⠀⠀⠈⠀⢰⠀⢀⡀⠠⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠊⡩⠟⠋⣧⠋⠀⠀⠃⠘⠄⠈⡀⠤⡀⠀⢀⡴⠂⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠃⢀⡠⠄⠊⠀⠱⡀⠀⠀⠀⢀⢴⡄⠀⠈⠂⡬⠁⡠⢀⠀⠀⠀⠀⠱⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠔⠁⠀⠀⠀⠀⠀⠑⠂⠉⠉⠈⢻⣿⠆⠠⢸⠀⢰⣱⠃⠀⠀⠀⢰⡏⡥⠐⠂⢉⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⠤⠐⠂⠀⠀⡀⠃⢸⣟⡠⠀⢀⣤⣾⣧⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀
⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⡰⠋⠈⢠⠁⠀⠀⠀⡈⠅⠭⡕⠪⣿⣅⠘⠅⠀⠀⠈⢧⠀⠀⠀⠀⠄⠁⠉⠒⢄⢀⣀⠀⠀⢸⠟⡐⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⢣⡀⠀⠘⠤⡀⣀⢀⣠⡴⠂⡰⣾⣿⡇⠣⡒⠢⣀⠀⠀⠙⠀⡄⠀⢀⠀⠀⠀⠘⡄⠀⠑⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠟⠏⠁⠆⠠⠞⢞⠁⡏⠘⢤⠀⠀⠀⠁⠀⠰⠀⣇⠀⠘⠦⣸⢀⠆⡰⠀⢀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⡐⠀⠀⢸⢌⢐⢣⠀⠈⠧⢤⣠⢄⠒⠁⠀⠈⠉⠮⢁⢻⣇⠴⢃⣴⣶⣀⡁⠐⠒⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡀⠀⣾⡘⠈⠈⠂⠀⠀⠘⠗⠿⠿⣷⣶⠚⠀⠂⢀⣾⢣⣴⣯⠉⠒⠀⠒⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⡆⡇⠙⡰⢄⢀⡠⠤⠜⠀⠀⠀⠀⠀⢅⠀⠐⠁⠎⠸⣟⢓⠌⠂⢄⠀⣀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢌⡂⠀⠱⡘⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠒⢲⡄⡀⠀⠠⠘⡌⠆⠀⠀⢻⣖⠢⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠔⠁⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠰⡐⠉⠀⠀⠐⡰⠁⠈⢲⡇⠀⠀⠀⠀⢀⢬⠀⢳⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢆⠀⠀⠀⠀⠀⢀⠞⡄⠀⠀⠀⠀⠈⠐⠒⠒⠀⠁⠀⠀⢸⡷⡦⣀⣀⡔⠀⠀⠑⡌⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⢣⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠧⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⢀⠇⡌⢠⣼⠇⠀⠀⠀⠀⠀⣠⢞⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢧⡘⡆⠀⠁⠀⠀⠀⢀⣤⠞⠁⠘⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⣶⣶⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠟⠛⠉⢹⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠰⡄⠀⠀⠀⢸⡀⠈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀