⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡌⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⡲⠔⢒⣄⠀⠀⠀⠀⠀⣀⣀⡯⠘⢄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣤⣤⡖⢋⡝⣠⠟⡚⢱⡷⣤⡴⠉⠐⡀⠋⠿⠩⠦⡀⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣻⢿⠏⡜⠎⣰⢵⡱⠃⢖⠳⢹⠃⠀⠀⠱⣄⠰⣦⢍⠑⣡⣡⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢟⠉⡾⣋⢘⠞⠋⣐⣐⢼⡀⡐⠀⡅⣿⡖⠀⣰⢇⡀⠉⡧⠀⢺⣼⢾⠒⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢾⠇⣠⠋⣾⢠⡇⡰⡘⠿⠿⠋⢡⡮⣴⣇⣟⣦⠟⡿⣿⠃⡇⣰⠀⡀⡄⡘⣴⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠾⢮⠎⡸⡙⣸⣧⡷⣇⢴⣤⣀⠍⣝⢣⣿⢿⡟⢀⠀⡀⠀⠉⠱⣴⡻⠧⠁⣽⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣢⢮⣴⣷⣵⡳⡆⣇⠈⠛⣋⣔⡿⠛⡟⢄⢣⣀⠺⠃⠀⡠⠊⢱⣷⡜⠋⠀⠀⠀⠀⠀⢀⠔⣉⣤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⣎⠞⠝⠀⠘⡭⠉⢹⠜⠛⠁⣠⡄⢀⠿⠶⠵⢶⠾⢣⠃⠈⢗⢄⠀⠀⠀⠀⠀⠰⢡⡞⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣜⣼⢃⣸⠀⠀⢀⡇⠀⠀⠀⠀⢸⠯⣿⢽⠆⠀⠀⠀⢠⣶⠀⠀⢠⠀⡗⡄⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠀⢃⠃⠀⣼⣷⡀⠀⠀⠀⡸⠀⡇⠈⡄⠀⠀⠀⣀⣏⡇⠀⡌⣂⡇⡵⡀⠀⠀⢃⠘⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠈⠀⠀⣿⣿⣧⣀⠤⠐⢁⢴⡓⢄⡈⠐⠤⣀⣽⠩⡇⠀⢸⣿⢧⣁⣃⠀⠀⠈⡄⠘⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⣜⠟⠉⠀⡠⠒⣝⡿⡳⢿⡎⠂⢄⠀⠙⢖⢵⠀⠘⣿⢸⡿⣿⠀⠀⠀⠈⢄⠘⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠋⣀⣴⣛⣷⡐⠈⡘⢹⡆⠸⡀⠀⢹⣢⣀⠙⠀⢀⣿⣇⢻⡇⠀⠀⠀⠀⠈⢂⠈⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣾⣿⠗⣾⣯⣳⠞⠁⠀⠛⠦⣤⠉⣘⢏⢀⠑⠠⠸⠇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠿⢿⣝⠄⠀⠀⠀⠀⠈⠑⠂⠬⡆⡀⠀⠀⠈⡢⢈⡢⡀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⡀⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⢱⢇⡔⠂⠉⠉⠉⠉⠘⠒⢄⠀⠀⠀⡸⠀⡄
⠀⠀⢀⣴⠿⠿⣛⢛⠿⠿⢿⣿⣿⣿⡿⢰⣿⣷⡝⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣒⠊⣀⠔⠁
⢀⣴⣭⣶⣿⣿⡿⣯⠉⠁⠒⠨⣙⠻⣷⣾⣿⡟⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡉⠉⠀⠒⠤⡀⠀⠀⠀⠀⣧⠯⡁⠀⠀
⢸⣿⣿⣿⡿⢡⠁⠙⣷⡀⠀⠀⠀⠑⢺⡟⡉⣧⣿⠏⠉⠀⠀⠀⠀⠀⢀⣠⢞⡿⡇⠱⡄⠀⠀⠀⠈⠢⡀⠀⡰⡏⠀⢱⠀⠀
⢸⡇⠙⠿⣇⠘⡀⠀⠈⢷⣄⠀⠀⠀⠈⠳⡕⠏⠀⠀⠀⠀⠀⠀⠀⠀⢾⠖⣺⠁⣇⣠⠟⢠⣀⣀⠀⣀⢵⠊⡼⠀⣀⡠⡆⠀
⠈⣧⠀⠀⠻⣦⣕⣄⠀⠀⠹⣦⡀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣏⡹⠚⢻⠭⢤⢲⢀⢀⢀⣰⠾⠂⠉⠀⠰⣻⠀
⠀⠘⡇⠀⠈⠀⠉⠘⡉⢹⠁⠘⣷⣄⡀⠀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠎⠓⢉⠧⠓⣞⣇⣝⣼⢁⢀⠑⠂⠒⠒⠻⠋⠀
⠀⠀⣿⡀⠀⠀⠀⠀⠡⡈⢄⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠶⡍⠀⠀⢬⠃⢀⠋⢼⣼⢏⣝⡞⡪⡄⢔⣹⠀⠀⠀
⠀⠀⢹⣿⣶⣤⣄⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⡙⠀⠀⣼⠃⠀⣘⢮⣳⠹⠁⠓⢩⡤⠓⣓⡏⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢧⣷⡆⣾⣗⣶⢢⡿⣟⣗⣷⢶⣀⣷⣱⣦⣶⠁⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⡎⠛⣿⠛⠛⣻⣟⢿⢹⡇⠘⢋⢿⠛⠛⢛⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⠀⣰⠆⢀⢜⡞⠁⠀⠸⠀⢀⢮⠃⠀⣴⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠄⠀⡏⢡⣙⣀⡾⡿⠀⠀⠀⠀⢀⢮⠃⢀⢼⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠙⠿⠟⠋⠁⠀⠀⠑⠊⠥⠊⠓⠁⠀⠀⠀⠐⠨⠧⠄⠚⠃⠀⠀⠀⠀