⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣖⣚⠻⢟⡳⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡻⢿⣞⣺⣿⣷⡊⣟⣮⣺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⡿⠆⢶⣽⣝⣻⣦⣷⡮⠢⣹⣻⡌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡸⣾⣿⠿⣶⣽⣿⣟⠎⠙⡌⢦⣹⢦⣰⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣷⡇⠀⢫⣿⣿⣯⠁⢣⡘⢧⢿⡷⡟⢳⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⡿⡇⠀⣀⣳⣿⣿⢿⡎⢿⢸⡿⣇⡬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⣧⢿⣶⠉⠉⠙⠟⠀⠙⠈⠈⠑⠗⠚⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠌⢗⢫⣁⣤⠤⠀⠀⠀⠀⣠⡶⣋⡴⢞⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⣲⠶⡉⠉⢉⣩⢷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡼⢻⠷⠯⠀⠀⢀⣠⣾⣿⠟⠉⣴⠛⣿⣯⠵⣤⣀⣀⣀⣀⠀⠀⠀⠀
⠀⣴⣶⣷⠶⠋⠁⠀⣀⣣⠤⢻⠉⠁⠀⣈⡄⠀⠀⠀⠀⠀⣰⠛⡻⣿⣧⣿⣷⠤⢤⡒⣩⠷⠛⢿⣷⡼⠋⢸⣟⡿⠛⠉⢙⠻⣟⣞⠃⠀⠀⠀
⢰⣵⣲⢝⣧⠖⠊⠉⠀⢸⢀⣬⠗⢊⣡⣤⣃⣀⡀⠀⣀⣾⣿⣿⣯⣽⣿⣿⠋⣰⣿⣟⠯⣉⡉⢈⡿⠁⢠⣿⠋⠔⢊⠵⠚⠁⠘⠽⢦⡀⠀⠀
⠸⡤⣿⠼⣿⠀⡠⠴⠚⣉⢠⣾⠟⢻⡀⠼⠉⢻⡄⠹⣭⡉⠀⠀⠈⠻⣯⢳⣺⢿⠹⠟⠛⠉⣡⣟⣿⣿⣿⣷⣿⣾⠗⠀⠀⠀⠀⠀⠀⠘⣇⠀
⠀⣇⣯⡇⣱⡠⠧⠒⠉⣰⠾⣷⠀⢠⠵⢦⣤⡾⠻⣦⠸⠀⠀⠀⠀⠀⣿⣼⢸⡎⢣⠀⠀⢰⡿⣿⣿⣿⣿⣿⢞⡡⠔⠁⣀⣀⠀⠀⠀⠀⠸⡄
⠀⠈⠉⢉⣹⣤⣖⠚⠺⣻⢶⡿⣀⣉⡦⢼⠳⡂⠀⢹⡷⡀⠀⠀⢀⠀⣿⣿⣿⠁⠀⢆⢀⡿⠛⠛⣿⡿⣿⡿⣋⣤⠶⠛⠋⠉⠉⠁⠀⠀⡠⡇
⠀⠀⣞⣭⡹⣿⡏⣇⠴⠭⠞⠋⡟⠀⠀⠺⠤⣈⣲⣾⡱⢷⢶⠤⣼⡼⢹⣿⣿⠀⠀⢀⣾⣷⣶⣶⡟⣷⣿⡾⠋⠁⠀⣠⣤⣤⣀⣀⡲⠯⢠⠃
⠀⠀⠻⠯⠴⠛⢹⡌⠑⠒⠠⣼⡸⣉⣁⡀⠒⣲⠄⢠⠒⣺⣸⠀⠀⢹⠼⣿⢿⠀⠀⣼⡿⠶⣿⢻⢳⣿⣿⠶⣚⠷⣾⣗⣚⣐⣒⣈⡀⢀⡎⠀
⠀⠀⠀⠀⠀⠀⠘⣎⠒⢤⣴⡗⠙⠛⠯⢍⡉⠋⢀⡎⣠⡿⠃⠀⠀⡞⠀⣼⡄⢀⣆⡿⠁⣰⢣⢻⠘⣿⡟⢉⣠⡤⠤⢄⡀⠀⠀⠀⠀⣼⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣱⣞⡞⠯⢷⣶⣦⣄⠼⣠⠏⣴⠟⠁⠀⢀⡜⠀⡼⠁⠈⠲⣿⡃⢠⢃⣶⣿⣶⣿⣛⣛⣗⣒⣲⠶⣅⡀⠀⠀⣸⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⠙⠦⣄⠀⢹⣀⣾⡯⢾⡁⠀⢀⡤⠋⠀⡴⠁⠀⠀⠀⠀⠉⠓⢮⣸⡟⣿⠟⠉⠀⠈⠉⠙⠻⢷⣝⢦⣀⢣⡇⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠴⠽⠿⠟⠁⠀⠀⠈⠻⢅⣀⣤⠊⠐⠢⢀⡀⠀⠀⠀⠀⠀⠈⠙⠪⠄⣀⠀⠀⠀⠀⠀⠀⠙⢷⣻⡼⢻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠢⡀⠠⢄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⢻⠇⣣⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠿⡢⢄⡀⠀⠉⠒⠂⠄⠀⠀⠀⠱⡀⠀⢰⢡⠃⡼⣿⢿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢤⡀⠈⠢⢌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢧⠧⠴⢽⡻⣼⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠀⠀⠀⠀⠀⠱⣦⡀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⢒⣋⣉⣓⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠒⢲⡦⠙⠢⡰⢄⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠉⠀⠀⠀⣸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣴⣛⣂⠈⠑⠯⣒⠦⠤⠀⠀⠀⡰⠁⠀⠀⠀⣠⠴⠒⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠆⠀⠀⠀⠀⢀⡞⠉⠀⠤⠊⣡⡶⣛⣭⣵⠶⠖⠉⠉⢹⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣓⣲⣒⡒⠒⣒⣒⡶⢲⣖⣖⠛⠓⠻⠭⠤⠤⣀⣠⣠⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠉⠉⢹⣸⣽⠿⢿⣿⣶⣿⠋⠉⠉⠉⠐⠒⠒⠢⠤⢿⢿⣻⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡟⠉⠀⠘⣿⡇⣯⣸⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢳⢿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⠋⡷⠚⢻⠛⣷⠶⠿⢿⣥⣹⠀⠐⠒⠂⠀⠀⠠⠤⠤⢼⠈⠀⠀⠘⠅⣇⠀⠀⠀⠀

⣿⣿⠿⠿⠿⠿⣿⣷⣂⠄⠄⠄⠄⠄⠄⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡾⠯⠉⠉⠉⠉⠚⠑⠄⡀⠄⠄⠄⠄⠄⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⠄⠉⠻⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⠎⠄⠄⣀⡀⠄⠄⠄⠄⠄⠄⠄⠘⠋⠉⠉⠉⠉⠭
⡀⠄⠄⠄⠄⠄⠄⠄⠄⡇⠄⣠⣾⣳⠁⠄⠄⢺⡆⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⣿⣷⡦⠄⠄⠄⠄⠄⢠⠃⢰⣿⣯⣿⡁⢔⡒⣶⣯⡄⢀⢄⡄⠄⠄⠄⠄⠄⣀
⠓⠄⠄⠄⠄⠄⠸⠄⢀⣤⢘⣿⣿⣷⣷⣿⠛⣾⣿⣿⣆⠾⣷⠄⠄⠄⠄⢀⣀
⠄⠄⠄⠄⠄⠄⠄⠑⢘⣿⢰⡟⣿⣿⣷⣫⣭⣿⣾⣿⣿⣴⠏⠄⠄⢀⣺⣿⣿
⣿⣿⣿⣿⣷⠶⠄⠄⠄⠹⣮⣹⡘⠛⠿⣫⣾⣿⣿⣿⡇⠑⢤⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣤⣤⣤⣤⣀⣀⡹⣿⣿⣷⣯⣽⣿⣿⡿⣋⣴⡀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⢿⣿⡿⠋⡒⣾⣿⣧⢰⢿⣿⣿⣿⣿⣿