⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣠⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠁⠾⠭⠯⢍⣀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣠⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⣠⠼⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⢿⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣶⣄⡀⠨⣿⠃⡎⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣶⣿⠊⡇⠀⣀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⡇⠀⠀⠀⣀⡠⠞⠀⠀⠀⢠⠿⢦⣀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⢻⠃⠀⡇⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣙⣹⢄⠀⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠗⠢⣤⣀⣤⡇⠀⠀⠀⠀⠀⠀⠰⠚⠋⢹⠋⠉⢙⣻⡶⠦⠀⠀⠀⠀⠀⠀⣴⣾⣟⡉⠀⢸⡏⡆⠀⣷⠤⠤⢤⣤⣀⡀
⠀⣀⡤⠴⠒⠒⠒⠓⠚⠒⠒⠒⠋⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⡻⠽⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⡍⠓⠾⠇⠹⡄⢸⠀⠀⠀⠀⠀⡷
⣏⠁⠀⠀⠀⠀⠀⠒⠒⠒⠢⠤⢤⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢰⡄⠀⢧⢸⠀⠀⠀⢠⠞⠁
⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⠀⠀⠀⠀⢀⣀⣤⣄⣀⣀⡀⢀⣀⣀⣀⡀⢷⠀⠹⡄⣸⢸⠀⣠⠞⠁⠀⠀
⠀⠀⠈⠓⠲⣤⣀⡀⠀⠀⠀⠀⠙⠚⠙⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⡆⠀⠀⢠⣾⣯⣄⣀⣀⣀⣀⣉⣉⣩⣤⣿⠇⠀⢨⡇⣧⢯⣸⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⡈⣿⣿⣿⣶⠶⡦⠴⠰⡇⠀⠀⠀⠀⠀⠀⡰⢸⢀⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠸⡇⣟⠀⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⣝⢿⣿⣿⠂⢳⡀⠀⠇⠀⠀⠀⠀⠀⣠⠇⣸⢸⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⢰⣇⠏⣰⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢿⠃⠀⠳⣬⠃⠀⠀⠀⠀⣰⠋⠀⣇⠘⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⣸⢏⢜⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣧⡀⠀⣠⡞⠁⠀⠀⡀⠀⡗⠀⢹⡉⠛⠿⠿⠿⠿⠿⠛⢋⣡⠾⠋⠀⣀⠴⠋⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠘⢟⠀⠀⠙⢷⠶⣄⡳⢠⡇⠀⠀⠉⠲⢤⣤⣤⠤⠴⠞⠉⠀⣀⡤⠞⡥⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣸⡃⠀⠀⠈⣷⠀⠙⡄⠁⠀⠀⠀⠀⠀⢀⣀⣠⡤⢶⠞⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢠⡟⣧⠀⠀⠀⣼⡻⢹⣷⣤⣀⣀⣀⣀⣰⣯⣍⣀⡰⡿⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣠⡿⣄⡘⡳⣄⠰⢿⡘⢺⡿⣿⣿⣿⣿⣿⣿⠂⢀⠉⠙⢷⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣀⡴⠛⠃⣒⣹⠛⢺⡀⠀⢻⣿⡀⠀⠀⠀⠀⠸⠿⣷⡄⠃⠷⠋⣿⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⢁⣠⣤⢶⣏⠠⣀⢀⢔⢤⢖⠼⣇⠀⠀⡧⡻⣦⠀⠀⠀⠀⠀⢿⢻⡄⠝⢼⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⠕⢕⢖⢑⢔⣛⠷⢯⣕⣑⠥⠖⡦⡪⣧⣤⣯⡂⡠⠻⣄⠀⠀⠀⢸⣞⡇⠀⢄⢷⡀⣸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢺⡕⡕⡕⡕⣵⣮⡕⣮⡍⡝⠛⠓⣶⣾⢸⡇⠀⢻⢢⢠⠘⣧⠀⠀⠀⣷⡇⡔⡕⣽⡗⢻⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣧⢟⣫⢪⡠⣪⠋⣼⠆⣐⢂⡺⣢⠊⢠⢝⡝⣇⠀⢸⣗⡝⢒⡝⢷⡀⢠⣿⣹⣤⡟⢹⠃⢸⡯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡧⣹⣬⠪⡖⡪⣮⣾⣏⣷⡎⣽⢢⣾⣁⣗⠗⠙⣦⢾⡄⣿⣷⣄⣆⢻⣼⣷⡟⢡⡦⣾⣆⣸⢳⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠟⠯⣻⣺⡯⡻⣞⡻⢟⡶⢫⡯⣻⢺⢍⡻⣢⢱⡇⠀⢻⣼⡇⠾⢹⣿⣿⣇⠚⣮⣴⡏⠘⣯⠰⠡⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣟⢞⠼⡡⡫⡢⡺⡱⡄⡠⢓⡮⡹⡣⡻⢊⣝⣗⢘⡇⠀⠈⣷⢁⣴⣿⣿⡿⣿⣿⡈⢾⠃⠀⢸⡺⣻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⢕⢕⢩⠪⡪⡢⡪⡪⡂⣨⣒⡪⡠⣪⠲⡂⢕⢕⢕⣇⠀⠀⠸⣤⣿⣿⣿⠁⢿⣿⣿⣾⠀⠀⢸⡧⠤⠊⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀