⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠿⠫⠀⠀⠀⠀⠻⠟⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⢸⣅⣷⣆⣇⣧⣾⠰⣧⢶⣴⡜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⢻⢻⢝⠛⣿⢷⣶⣄⢸⠐⠲⡀⠀⡂⠐⠀⣒⡐⠒⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠍⣿⠌⣢⠀⠀⠀⢹⠉⠻⣦⣀⡂⠀⠀⠀⠀⠀⠂⠀⠀⢐⡇⠀⢠⡴⣦⠠⣦⢤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⢂⡤⠀⠀⢲⣿⢻⠰⢰⠛⠸⠟⠀⠀⠀⠉⠀⡶⠈⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢰⢻⣿⢣⣺⢺⡇⠀⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢣⢤⡴⠛⠉⠉⢁⣼⡟⠚⡇⠾⢠⡀⡀⠀⠀⠀⢐⠄⠀⠚⡀⠻⣦⠀⠀⠀⠀⢀⣀⣀⣸⡇⠀⠸⠬⠭⠭⠬⠼⠃⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⠷⠋⠀⠀⠀⢀⡼⠇⠀⠰⠁⠀⢿⠃⠀⢀⠀⠀⠐⠀⢅⣌⡤⢠⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⣰⣄⢰⠚⠠⣸⠄⠀⠀⠀⣤⣵⢟⢨⣟⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⣶⢹⣄⣏⣹⡰⠀⠀⠐⡬⡞⡷⣷⡟⡋⠻⣅⣸⠂⠀⠀⠀⣀⢀⣀⢀⢰⣿⣏⠉⠙⢆⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣏⢫⡏⢻⣩⠁⠄⠀⠀⢠⠁⠃⠉⣔⠢⡀⣽⣫⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠣⣿⣧⠀⠀⠁⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣉⠺⢸⠃⠀⠐⠄⠈⠀⢀⡾⢈⣹⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣃⡀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡶⡍⠿⡤⠡⠀⠀⠀⠀⢒⡿⣟⣙⡅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀
⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠈⠛⠦⣤⣤⠀⣜⡿⢟⣺⣰⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠇⠀
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡄⠀⠀⠀⠀⠉⡍⣡⢠⡽⡋⢠⣛⠙⢉⠁⠰⢂⠖⣲⡐⠶⠒⠶⠒⣽⣻⣏⡽⣍⡁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠠⢸⠟⠛⠀⠠⣾⠟⠭⠤⠬⠙⠓⠨⠤⠝⠶⠖⠒⠊⢤⡤⠤⠄⠘⢃⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡴⠛⠀⠀⠑⠀⠳⣷⣄⡀⠀⠀⠀⠈⣛⡦⡂⠀⠀⠐⠾⠤⣤⣀⣀⠀⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣟⠒⠷⣾⡻⠉⣇⣄⢀⣠⣬⢓⠄⣽⣺⣿⡿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠚⠟⢻⠀⠀⠀⠀⠀⠂⢀⠀⠀⠠⠀⢀⡓⡔⠤⣀⢠⠙⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⢀⣼⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡖⠋⠃⠈⠀⠀⠀⡠⢀⢀⣠⠀⣶⣉⠀⢀⣦⣄⢠⣷⣒⣦⣀⡉⢉⣓⡧⠾⠢⠄⠄⠀⠀⢂⠄⠉⠀⠀⠀
⠀⠀⣠⣤⠖⡖⡂⠐⠲⣦⣄⡀⢀⡤⠖⠛⠛⠋⠈⢁⠀⡀⠀⠀⢰⠄⠘⣰⣿⠷⠋⠁⠀⠀⠉⠉⠉⠉⠉⠉⠝⠤⠂⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀
⠀⠐⣿⡈⠄⠃⢓⢦⠘⠐⢉⢙⠛⠓⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⢰⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡤⠕⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠎⠀⠀⠀
⠀⠀⢹⢞⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢰⠆⠀⠀⠘⣷⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣦⡠⠴⡤⣄⣠⡴⠶⣍⠀⠘⠦⠠⠤⠤
⠀⣀⢸⣟⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡈⢀⣸⡶⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠴⠖⠚⠙⠓⠒⠚⠛⠛⠒⠂⠋⠓⢧⡀⠦⢤⠀
⠀⠀⠀⢻⠒⠀⠀⠀⠀⢀⣀⣀⠀⡠⣶⠀⢰⡴⣛⣡⣤⠤⠴⠒⠒⠒⠒⠉⠉⠉⠈⠀⢀⡀⣀⣀⣀⣤⠤⠬⠆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⣀⡤⠗⠒⠈⠤
⢤⠴⣦⣬⣧⡀⠀⠀⠀⠹⣿⣈⣭⠿⠟⠚⠁⠉⣀⣀⣀⡤⠤⠤⠔⠒⠚⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡞⠥⠤⣈⣒⣤⠤
⠸⠀⠐⠠⠘⢿⣦⣄⣀⣠⠟⠉⠀⠀⠀⢠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢐⠂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠈⠑⠒⠠⠤⣌⣉
⡏⣆⠤⠀⠁⠀⢉⡻⠻⢡⠦⠀⠀⠀⠀⠈⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠢⠀⠠⠤⠤⠤⠤⠤⠄⠀⠒⠒⠀⠀⠈⠉
⠁⠀⠀⡀⠀⠀⠀⠀⠄⣿⢦⠀⠁⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⣤⡤⠤⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀