⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠂⠀⠀⢷⢠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠐⡆⠀⠀⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠄⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠂⠈⡗⠀⢼⠀⣼⡿⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠃⠀⠀⢸⡇⠀⠐⠀⠀⠀⠀⢹⡇⢲⠾⠀⣧⠃⡆⠀⡆⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠠⣸⡏⣟⠂⠴⡏⢀⠂⢸⡷⣸⢴⠠⠀⠀⠀⠀⠄⠀⠀⠐⠁⠀⠄⠀⠂⠄⠀⠀⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡩⠀⠀⢆⡀⣰⣿⠀⠀⠀⠀⠀⠀⢸⣿⣯⠞⡼⠀⡘⢹⣸⣿⣷⠟⢔⡂⠀⠁⠉⠀⠀⠀⠀⠀⢀⣀⠨⠄⢀⠀⡀⠀⠀⠀⠀⠀⢈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⡢⡤⡄⣿⡄⠀⠀⠀⠀⠀⣼⣿⢟⢱⢣⡰⡔⣼⣿⣿⠿⣪⡀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠨⠀⠂⠀⠀⠀⣄⠀⢑⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⢐⠆⠄⢻⣞⣫⡇⢀⠆⣰⠀⣠⣿⡿⣟⣳⣸⣿⣾⡻⠯⠖⠒⠿⠟⡿⠉⠉⠉⠙⠳⢮⣆⠍⡀⠲⠀⠀⠀⠀⠀⠀⠀⠈⠀⢌⢿⣂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠞⣧⡢⣿⣫⣿⢸⣸⢸⣼⣿⡿⣺⢿⡾⠟⢋⡅⢀⣌⣀⣠⠔⡀⡈⠁⠄⠀⠀⡄⠈⠙⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⢩⣭⣻⣷⣿⡄⢿⣻⢿⡿⡪⠛⢫⠈⣰⢄⡉⢽⣷⣿⣿⣿⣆⠹⠢⠈⡄⢀⣵⡆⠀⡯⣿⣷⣽⣦⡐⠀⠀⠀⠐⠀⠀⠀⠀⢻⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡻⡿⣿⣿⣿⣿⣾⣿⠿⠈⢔⣱⢹⣰⢂⡛⣿⣿⢿⣝⢯⣾⡆⠉⣥⣼⣾⡯⡜⢰⢿⣿⡿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠠⢸⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠿⡿⢿⠏⠇⠀⢰⣄⡞⣿⢸⢻⣿⡜⣿⣭⣏⠈⢰⡗⢀⣯⣿⢟⣽⡿⢋⢿⣯⡿⣫⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣫⣵⣽⡂⡅⢸⣿⡧⣿⣗⡾⢟⡥⡵⢝⣵⢖⣻⣟⣿⣿⢯⢽⣟⢡⡼⠫⢀⠜⣿⢿⣿⣿⣿⣬⠇⠀⠀⠀⡀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⡼⣟⣷⣯⢱⡇⣿⣿⣯⣿⡏⢻⠈⣧⡲⢰⣇⣻⣿⣯⡿⢿⣽⣿⣿⡯⠇⡐⢑⣹⣴⣾⢿⣿⣿⠏⠀⢹⢐⠀⡄⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢱⡼⣿⣽⣿⣿⡿⢸⣷⣿⣿⡿⣿⣷⠿⢜⢽⣷⡟⣿⢛⣻⢷⠸⠛⣛⣻⣁⣀⡉⠁⠐⠉⢢⣴⠿⠋⠁⠀⠀⠀⠗⣲⣶⣿⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⣴⡟⣵⣿⣾⣿⣿⡧⣿⡿⢿⣟⣿⡿⣯⡀⣿⣾⣿⣧⣿⣎⡙⢂⠀⣐⣻⣿⣿⣿⣿⣿⡧⠮⢍⠀⠀⠀⠀⢀⣀⣼⣶⣿⣿⡟⡎⣗⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡁⡏⣿⣿⣷⡏⣷⣿⣾⣿⡶⣿⡇⠛⣥⢸⣿⢹⣻⡿⡵⠭⠤⠴⠾⠿⣿⣿⣿⣿⣫⢅⠐⠀⢌⠳⣴⡀⠀⣉⣴⣿⣵⣻⣿⠁⢿⡉⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡀⠦⠀⣿⠥⢧⣿⢸⢸⠓⠁⢩⢈⢯⡆⡮⣿⡼⠱⠘⣏⢿⢟⡿⢠⣤⣽⣿⣿⣿⣷⣶⢭⢿⠽⣎⠜⠀⠀⠀⢄⢿⣶⢿⣿⢉⢌⠃⠁⠀⣼⢡⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠐⡜⡄⠸⢟⢽⣾⣾⡀⣫⣳⡠⢹⣌⡷⢟⡕⠛⢜⠂⢉⢪⠁⡀⠨⡗⠻⣿⣾⢎⠐⠀⠀⠀⠙⠳⣹⡺⣄⣄⠈⠙⣎⢧⠁⡠⢡⠜⠁⢢⡿⠸⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣯⣲⡜⣶⣝⢿⣿⣾⣯⡑⠾⢿⠇⠐⠉⠀⠀⠁⡖⠱⢖⡚⠂⠬⣦⡉⠈⣽⠿⣆⣀⠀⠀⠀⠈⢗⢶⢭⠻⣍⣿⣎⣯⠃⢘⣤⡚⣹⠃⡄⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣟⢷⡷⢫⢷⡯⡑⠌⠉⢑⡅⡀⠁⠀⠀⠀⠂⠁⠀⠀⠀⢏⠫⠬⢝⣦⣮⠧⣄⠉⠚⠿⣶⣤⣠⢊⠧⣁⠈⠻⣿⡞⡄⣾⣶⣾⠃⣰⡝⣚⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣨⣯⡪⠁⠉⡠⢀⡀⡠⢞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢗⢯⣱⠢⢄⡀⢷⣿⣿⡲⣾⣰⠤⡈⠻⣶⣿⣷⠇⣹⣇⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣮⢾⣣⣿⡴⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢶⣭⣅⢯⢿⣿⣦⡙⢿⡐⣠⢝⣿⣿⣾⣿⡾⢻⡜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⡿⢛⢿⡛⠩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⡻⢻⣿⣿⣯⣶⡝⡖⣽⣙⣻⣿⠋⠀⠈⡳⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⠚⠓⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢹⣞⣿⣿⣿⣼⡝⡾⣆⢱⡀⠀⠂⠫⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⣿⠿⠛⠉⠉⠀⠀⠀⠀⠈⠟⣮⠿⣿⣿⣷⡊⢿⣏⢳⣀⢀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⢿⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⡿⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡼⣿⣿⣯⣿⣯⡐⡞⠌⢧⡘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠋⠉⢀⣤⡦⣶⣖⣿⣟⣗⣦⠀⠀⠀⠀⠸⠹⣻⣿⣮⣿⡥⢙⠐⡸⠇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣽⡟⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⢾⣿⠟⠀⢀⣾⣿⡽⣿⣟⣿⣻⡯⣛⡋⠀⠀⠀⠀⠀⠑⣿⡛⢿⣾⣷⣋⡅⠀⠺⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⢿⠹⣿⣷⡀⠐⠀⠀⡠⣀⡀⡀⡀⠀⠀⠀⠀⠐⠉⠂⢼⣮⢟⡿⠟⠙⢿⣟⡿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠸⠿⢌⢫⢿⡄⢼⡂⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠘⣇⢻⣿⣷⣷⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠒⠺⢋⢽⣿⡿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠣⡹⣧⠀⢧⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠹⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠑⡌⢿⡆⠌⣷⢰⢣⠤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡇⠀⠀⠰⡀⠘⢿⢿⣿⣿⣿⠋⠫⡿⡧⣿⢿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠡⡀⠈⠁⣿⡄⡸⡆⠸⣪⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣣⠀⠀⠀⠀⠄⠀⠳⡹⡿⣿⣷⣿⣽⠾⠁⠀⠸⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⣷⡰⢻⡆⢫⠀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡄⠀⠀⠀⠀⠳⡄⠘⢭⡟⡄⠆⠀⠀⠀⠀⠀⢫⢵⡄⣀⡄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠳⡎⣷⠋⣷⠢⡐⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠈⠆⠀⠰⣵⡀⠀⠀⠀⠀⠀⠸⣾⣿⠁⠠⡧⠳⠉⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢻⡄⢛⣹⢣⢻⡀⣽⡔⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⡆⠀⠀⠀⠀⠀⠀⠀⠑⠈⠛⢄⠀⠀⠀⠀⠀⢟⣿⣿⣿⣻⠷⠶⣾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠈⢷⠀⣮⡏⣽⡭⡰⡐⢅⠖⢁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⢳⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘⠇⢠⠟⣹⠃⠐⡤⢄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢗⠀⠀⠈⣀⠤⠀⠒⠒⠉⠉⠉⠩⢶⣄⠀⠀⠈⠙⠛⠿⠉⢙⣠⣴⣶⣶⣶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠴⡼⠀⠀⠀⠀⠀⠀⠀⠘⣹⢸⠀⠐⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡌⢄⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣀⣾⣿⣿⣿⣻⣽⣛⢥⣠⣠⠄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠆⠸⠘⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡈⠿⣿⣫⣿⠻⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣎⠩⡙⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣤⣤⣤⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠐⡆⠀⠀⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠄⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠂⠈⡗⠀⢼⠀⣼⡿⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠃⠀⠀⢸⡇⠀⠐⠀⠀⠀⠀⢹⡇⢲⠾⠀⣧⠃⡆⠀⡆⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠠⣸⡏⣟⠂⠴⡏⢀⠂⢸⡷⣸⢴⠠⠀⠀⠀⠀⠄⠀⠀⠐⠁⠀⠄⠀⠂⠄⠀⠀⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡩⠀⠀⢆⡀⣰⣿⠀⠀⠀⠀⠀⠀⢸⣿⣯⠞⡼⠀⡘⢹⣸⣿⣷⠟⢔⡂⠀⠁⠉⠀⠀⠀⠀⠀⢀⣀⠨⠄⢀⠀⡀⠀⠀⠀⠀⠀⢈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⡢⡤⡄⣿⡄⠀⠀⠀⠀⠀⣼⣿⢟⢱⢣⡰⡔⣼⣿⣿⠿⣪⡀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠨⠀⠂⠀⠀⠀⣄⠀⢑⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⢐⠆⠄⢻⣞⣫⡇⢀⠆⣰⠀⣠⣿⡿⣟⣳⣸⣿⣾⡻⠯⠖⠒⠿⠟⡿⠉⠉⠉⠙⠳⢮⣆⠍⡀⠲⠀⠀⠀⠀⠀⠀⠀⠈⠀⢌⢿⣂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠞⣧⡢⣿⣫⣿⢸⣸⢸⣼⣿⡿⣺⢿⡾⠟⢋⡅⢀⣌⣀⣠⠔⡀⡈⠁⠄⠀⠀⡄⠈⠙⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⢩⣭⣻⣷⣿⡄⢿⣻⢿⡿⡪⠛⢫⠈⣰⢄⡉⢽⣷⣿⣿⣿⣆⠹⠢⠈⡄⢀⣵⡆⠀⡯⣿⣷⣽⣦⡐⠀⠀⠀⠐⠀⠀⠀⠀⢻⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡻⡿⣿⣿⣿⣿⣾⣿⠿⠈⢔⣱⢹⣰⢂⡛⣿⣿⢿⣝⢯⣾⡆⠉⣥⣼⣾⡯⡜⢰⢿⣿⡿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠠⢸⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠿⡿⢿⠏⠇⠀⢰⣄⡞⣿⢸⢻⣿⡜⣿⣭⣏⠈⢰⡗⢀⣯⣿⢟⣽⡿⢋⢿⣯⡿⣫⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣫⣵⣽⡂⡅⢸⣿⡧⣿⣗⡾⢟⡥⡵⢝⣵⢖⣻⣟⣿⣿⢯⢽⣟⢡⡼⠫⢀⠜⣿⢿⣿⣿⣿⣬⠇⠀⠀⠀⡀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⡼⣟⣷⣯⢱⡇⣿⣿⣯⣿⡏⢻⠈⣧⡲⢰⣇⣻⣿⣯⡿⢿⣽⣿⣿⡯⠇⡐⢑⣹⣴⣾⢿⣿⣿⠏⠀⢹⢐⠀⡄⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢱⡼⣿⣽⣿⣿⡿⢸⣷⣿⣿⡿⣿⣷⠿⢜⢽⣷⡟⣿⢛⣻⢷⠸⠛⣛⣻⣁⣀⡉⠁⠐⠉⢢⣴⠿⠋⠁⠀⠀⠀⠗⣲⣶⣿⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⣴⡟⣵⣿⣾⣿⣿⡧⣿⡿⢿⣟⣿⡿⣯⡀⣿⣾⣿⣧⣿⣎⡙⢂⠀⣐⣻⣿⣿⣿⣿⣿⡧⠮⢍⠀⠀⠀⠀⢀⣀⣼⣶⣿⣿⡟⡎⣗⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡁⡏⣿⣿⣷⡏⣷⣿⣾⣿⡶⣿⡇⠛⣥⢸⣿⢹⣻⡿⡵⠭⠤⠴⠾⠿⣿⣿⣿⣿⣫⢅⠐⠀⢌⠳⣴⡀⠀⣉⣴⣿⣵⣻⣿⠁⢿⡉⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡀⠦⠀⣿⠥⢧⣿⢸⢸⠓⠁⢩⢈⢯⡆⡮⣿⡼⠱⠘⣏⢿⢟⡿⢠⣤⣽⣿⣿⣿⣷⣶⢭⢿⠽⣎⠜⠀⠀⠀⢄⢿⣶⢿⣿⢉⢌⠃⠁⠀⣼⢡⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠐⡜⡄⠸⢟⢽⣾⣾⡀⣫⣳⡠⢹⣌⡷⢟⡕⠛⢜⠂⢉⢪⠁⡀⠨⡗⠻⣿⣾⢎⠐⠀⠀⠀⠙⠳⣹⡺⣄⣄⠈⠙⣎⢧⠁⡠⢡⠜⠁⢢⡿⠸⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣯⣲⡜⣶⣝⢿⣿⣾⣯⡑⠾⢿⠇⠐⠉⠀⠀⠁⡖⠱⢖⡚⠂⠬⣦⡉⠈⣽⠿⣆⣀⠀⠀⠀⠈⢗⢶⢭⠻⣍⣿⣎⣯⠃⢘⣤⡚⣹⠃⡄⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣟⢷⡷⢫⢷⡯⡑⠌⠉⢑⡅⡀⠁⠀⠀⠀⠂⠁⠀⠀⠀⢏⠫⠬⢝⣦⣮⠧⣄⠉⠚⠿⣶⣤⣠⢊⠧⣁⠈⠻⣿⡞⡄⣾⣶⣾⠃⣰⡝⣚⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣨⣯⡪⠁⠉⡠⢀⡀⡠⢞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢗⢯⣱⠢⢄⡀⢷⣿⣿⡲⣾⣰⠤⡈⠻⣶⣿⣷⠇⣹⣇⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣮⢾⣣⣿⡴⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢶⣭⣅⢯⢿⣿⣦⡙⢿⡐⣠⢝⣿⣿⣾⣿⡾⢻⡜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⡿⢛⢿⡛⠩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⡻⢻⣿⣿⣯⣶⡝⡖⣽⣙⣻⣿⠋⠀⠈⡳⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⠚⠓⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢹⣞⣿⣿⣿⣼⡝⡾⣆⢱⡀⠀⠂⠫⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⣿⠿⠛⠉⠉⠀⠀⠀⠀⠈⠟⣮⠿⣿⣿⣷⡊⢿⣏⢳⣀⢀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⢿⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⡿⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡼⣿⣿⣯⣿⣯⡐⡞⠌⢧⡘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠋⠉⢀⣤⡦⣶⣖⣿⣟⣗⣦⠀⠀⠀⠀⠸⠹⣻⣿⣮⣿⡥⢙⠐⡸⠇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣽⡟⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⢾⣿⠟⠀⢀⣾⣿⡽⣿⣟⣿⣻⡯⣛⡋⠀⠀⠀⠀⠀⠑⣿⡛⢿⣾⣷⣋⡅⠀⠺⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⢿⠹⣿⣷⡀⠐⠀⠀⡠⣀⡀⡀⡀⠀⠀⠀⠀⠐⠉⠂⢼⣮⢟⡿⠟⠙⢿⣟⡿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠸⠿⢌⢫⢿⡄⢼⡂⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠘⣇⢻⣿⣷⣷⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠒⠺⢋⢽⣿⡿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠣⡹⣧⠀⢧⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠹⡄⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠑⡌⢿⡆⠌⣷⢰⢣⠤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡇⠀⠀⠰⡀⠘⢿⢿⣿⣿⣿⠋⠫⡿⡧⣿⢿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠡⡀⠈⠁⣿⡄⡸⡆⠸⣪⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣣⠀⠀⠀⠀⠄⠀⠳⡹⡿⣿⣷⣿⣽⠾⠁⠀⠸⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⣷⡰⢻⡆⢫⠀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡄⠀⠀⠀⠀⠳⡄⠘⢭⡟⡄⠆⠀⠀⠀⠀⠀⢫⢵⡄⣀⡄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠳⡎⣷⠋⣷⠢⡐⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠈⠆⠀⠰⣵⡀⠀⠀⠀⠀⠀⠸⣾⣿⠁⠠⡧⠳⠉⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢻⡄⢛⣹⢣⢻⡀⣽⡔⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⡆⠀⠀⠀⠀⠀⠀⠀⠑⠈⠛⢄⠀⠀⠀⠀⠀⢟⣿⣿⣿⣻⠷⠶⣾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠈⢷⠀⣮⡏⣽⡭⡰⡐⢅⠖⢁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⢳⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘⠇⢠⠟⣹⠃⠐⡤⢄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢗⠀⠀⠈⣀⠤⠀⠒⠒⠉⠉⠉⠩⢶⣄⠀⠀⠈⠙⠛⠿⠉⢙⣠⣴⣶⣶⣶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠴⡼⠀⠀⠀⠀⠀⠀⠀⠘⣹⢸⠀⠐⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡌⢄⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣀⣾⣿⣿⣿⣻⣽⣛⢥⣠⣠⠄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠆⠸⠘⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡈⠿⣿⣫⣿⠻⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣎⠩⡙⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣤⣤⣤⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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