⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢴⡲⡼⡯⣿⡾⠉⠉⠩⢖⠖⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠝⠉⠀⠁⠌⠈⠀⡈⣧⠌⠀⠀⠁⠮⠀⠉⠙⢛⠕⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡻⣱⠥⠀⠄⣠⢸⡶⡆⠘⢗⣇⣤⢄⡴⣄⢤⣢⢀⠀⡀⠐⠃⠓⠵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣷⡰⠰⣷⠞⢺⢔⣚⢾⣿⠳⣞⢦⣆⣶⢾⣻⣻⣫⡵⣏⠀⠀⡁⠀⢀⠄⡙⢼⣧⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⣷⣑⢓⣯⢯⣦⣪⡽⣵⣿⣴⣷⢝⣾⣕⡻⣻⣿⣿⡾⣻⣷⣓⣿⡏⡒⣿⠾⡘⣘⠹⣿⣄⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣅⠋⢫⣺⣿⢞⣟⣿⣻⣟⣿⡯⣯⣳⣿⣽⣟⣛⢞⣿⡫⡯⣿⣶⣿⣾⣿⣿⡿⣺⣾⣦⢔⡋⡞⠝⣎⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠫⣤⡮⣯⡎⡻⣻⣟⣟⣟⣼⣯⣿⣻⣯⣽⣺⣾⣿⣟⡻⣻⣝⢿⣟⣿⣟⣿⣷⣿⣿⣕⣟⠟⣀⡄⠀⡈⢼⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣲⣧⠿⣣⣾⢿⠿⠹⣾⣟⣿⣽⢟⣟⣿⠵⢻⡟⣭⣽⣵⡻⢿⠿⣷⣿⣾⣯⣾⣯⣽⣿⣷⣮⡍⠠⡕⡈⠉⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⡋⢀⣵⣿⣝⡿⠂⠀⢫⣿⣿⢯⣿⣽⢷⣷⣽⠯⣜⢫⣞⣠⡦⠸⣡⡿⡟⣿⣿⣫⢿⣯⣯⣿⣨⢺⣢⡗⢣⣣⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡜⡑⣟⣯⢇⣿⠃⠀⠀⠈⢿⣾⡿⣿⣿⣷⢿⣕⢸⣯⡧⡏⣺⡏⠈⡐⡫⢻⡿⣎⡯⣿⣿⣶⢷⣣⢷⡫⡗⣷⠸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣸⡻⢫⣥⣯⣀⣀⡀⠀⠀⠙⠯⣿⣟⣗⢻⢿⣿⡹⣏⢍⠉⠻⠃⠐⣻⡝⣟⠹⣿⣞⡬⣿⡾⡶⣹⢘⠃⠸⢰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢽⣢⢾⠋⠉⢿⠙⠛⠻⠿⠿⢿⣷⡏⠛⠛⠢⠷⠿⠾⠗⠵⢶⣐⣤⣺⣚⣑⢻⠻⢿⢿⡿⣳⢹⣯⣧⡒⠳⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⢸⡟⣾⣿⡏⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠊⠀⠈⠁⠀⢠⡇⠀⢙⣿⣷⠓⡳⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠻⣾⡽⣿⡄⠀⠀⢧⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢠⡞⠀⠀⢠⣿⢁⢸⠏⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⠒⡇⢏⢞⣿⡝⠂⠀⠻⢦⣤⣴⠞⠀⠀⠀⠀⠀gyaru⠀⠀⠀⠀⠀⠹⢦⣶⠲⠛⠀⠀⢠⣿⡇⢠⡻⠉⢹⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠈⠰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠁⢠⠃⠀⠘⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢆⠀⠈⠺⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠀⣠⠃⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⠢⡀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡟⠁⣠⠖⠁⠀⠀⠀⢰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠢⣐⢦⣀⠈⠙⠿⣶⣶⣦⣤⣤⡤⠤⣤⣄⣄⣀⣤⡤⢶⡲⢶⣿⣿⢿⣏⣴⣯⡃⠀⠀⠀⠀⣜⡎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣔⣾⣿⣶⣿⣶⣤⣌⣻⣷⡿⣫⢔⠭⢛⡶⢮⢿⣿⣿⣿⣿⣷⣟⣵⡿⣿⣿⣿⣷⣤⠀⠀⣼⡞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡀⠀⠀⠀⠀⡅⢿⣿⣿⣿⠿⠻⣀⠈⠙⢄⠃⠱⠫⡢⡝⡌⢸⠻⢿⣷⡎⡼⠛⣿⣿⣿⣟⣿⡿⠈⣇⣼⢯⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⡀⠀⠀⠀⠱⣄⣹⠏⠀⠀⠀⣾⣿⠿⠀⠑⠴⣊⢹⢩⠺⠶⠷⠛⠋⡇⠀⢠⣿⣿⣿⠟⠋⠀⢰⠛⡇⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⡼⠃⠀⠀⠀⣰⠉⠻⣄⠀⢀⠔⠁⢸⢸⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⡏⠒⠊⠁⣌⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠹⣧⢀⠜⠁⠀⠀⠀⢠⡇⠀⠀⠈⠙⠁⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⡰⡽⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠋⠀⠀⠀⠀⠀⡾⣿⡦⠤⢤⣤⣤⣤⣤⣴⣿⣶⣤⣤⣄⣀⠄⣼⣿⣿⣿⣿⡇⢀⣰⡿⠁⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⠀⣆⣧⣝⣷⠀⠀⣻⣟⣿⣿⡛⠛⠛⣿⣿⣿⡿⣾⣿⣿⣿⡿⠛⠃⣡⣿⠁⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠝⣾⠉⠉⠀⠀⠀⠸⡗⠀⢀⣸⣿⣿⡇⠀⢸⣿⣟⢹⣿⣿⣿⠿⠟⠁⠀⠙⢳⣽⠀⡘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣸⠶⣼⣿⠇⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⢻⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⠀