⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣧⢡⣀⣴⠶⠋⠁⠀⢀⠄⣀⡶⠋⠉⢯⣿⡻⣧⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⣟⣷⢿⡁⣠⡶⢋⡰⢋⣴⣿⣧⣤⣠⣻⣿⣷⢹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⡄⢠⠃⣰⠀⡄⡇⣾⡟⣃⢴⣽⣟⡴⢋⡴⠿⠿⢿⣾⣟⢿⣿⡻⣿⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡰⠎⢀⠏⣰⠏⢸⢻⢱⣿⣿⣷⣿⣯⡟⢳⣟⣄⣀⣀⣈⣑⠪⡝⢿⡷⣶⠈⡢⣤⣤⢤⣄⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡿⠁⠀⠀⢀⠘⠀⣠⠋⣠⣿⢀⡧⢃⡿⣻⣷⣿⣿⢏⡌⢻⡙⢒⣀⠤⢴⡶⠛⠓⠚⢷⡟⠤⣄⣭⣍⡻⠤⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠁⠀⠀⠀⠃⣀⠴⠁⡴⢫⠃⠋⣠⣿⡿⢛⣿⡿⣡⣾⣿⢿⡮⢃⡬⢈⣥⠲⢔⣠⠶⠋⠀⠈⠀⡜⠎⠛⢗⡮⡑⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣮⠳⠤⣀⣠⣴⡮⠉⣠⣞⣀⣥⣶⣿⠟⠁⣴⣾⡏⣴⣿⡿⣣⡿⡣⢊⡴⣋⠜⢫⡿⡩⢔⡷⢀⡞⣰⠈⠀⠀⠀⠈⢎⠫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡏⣿⣷⣒⠠⠬⢭⡭⠉⣓⣾⠟⢩⠁⠀⣠⡿⢫⣾⣿⢻⢧⣾⡞⡑⣫⣪⠕⣡⠟⣫⣾⠋⣴⠟⣜⡇⠀⠄⡀⠀⡄⢈⢱⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢎⡤⠊⣟⢻⠛⡛⠓⡂⡝⠀⣠⢾⠃⢘⠟⣵⠏⢹⣷⣿⣾⣏⣼⣿⠟⣡⢾⢁⣾⠟⠁⢀⠋⣤⣿⢩⡄⢰⡽⡄⠱⡈⢧⢻⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢰⡇⣼⡘⣃⣠⣻⣦⣮⢣⣇⡴⣫⡞⠁⠰⣞⣿⣿⡿⢨⣿⢫⣾⣯⣿⣿⣛⠄⡀⣠⣾⣟⠇⢞⡷⣾⡇⣽⢦⢱⡘⡧⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡿⢱⢹⢘⣸⡼⣡⢟⣿⣳⣡⠏⣩⡾⠋⠁⡀⣤⢻⣯⢻⡇⣹⣿⣿⣿⣿⣻⡽⢘⣞⣵⡿⣿⣿⢀⡜⢱⣿⡇⣿⣾⡈⣷⣸⡙⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡿⣷⡵⠡⠋⣵⣿⡿⡟⣿⣿⡇⠀⡇⢹⣎⡟⠏⢷⣿⡿⡿⣉⣹⣿⣾⣿⡛⠿⠿⣿⡇⡾⣰⣿⡿⢰⠏⣧⣷⣹⢯⣇⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢹⢸⡇⣿⠀⠀⣸⣿⡿⣧⣝⡿⠻⡇⢰⣼⡘⣾⣇⡜⡜⡿⠠⣷⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢋⣿⣧⣿⡆⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣧⡜⣿⣇⢿⣧⣴⣿⠋⣷⣴⣟⣘⠠⢿⡈⡟⡇⢱⣻⡵⢰⢹⡀⢍⣿⣽⣿⣫⡿⡿⠻⠿⡿⠛⠁⣼⣿⣥⣼⣿⣿⡟⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡟⣧⡜⣿⡜⣿⡜⣿⣿⣿⡿⣿⣜⢤⡿⣯⢡⠐⠀⡇⠳⠀⠏⢇⠀⠉⠻⢿⣿⣣⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢧⠘⣷⡀⢿⡜⣿⣜⣿⣿⣿⣿⣿⡳⣷⣟⡎⣿⡆⢷⢰⡞⢼⢸⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠿⣯⡏⠉⠀⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢣⠘⣧⣨⣿⣜⣿⡝⣿⣿⣿⣿⣿⠶⣿⡶⢸⣿⢸⠏⢧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠖⠤⣅⡘⣇⡻⣿⣞⣿⣎⢛⣿⣿⠙⠄⢿⣷⣼⣹⡟⡇⢸⠰⡈⡇⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⣐⢇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠺⣥⡌⣿⠞⣿⡏⡟⢹⠁⠀⣾⣾⣯⣏⣟⠁⠸⡀⠃⡇⠀⠀⣤⣀⣀⣀⠀⠙⠖⠋⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡜⡜⣧⣉⣧⣧⠘⠘⣸⣿⣿⣷⣽⣾⡼⣼⢻⣾⠃⠀⠀⠀⠻⣿⣛⠿⣿⠋⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⢣⠀⠃⢈⣿⣿⣀⠂⠸⡿⣿⡯⢷⡻⣽⣿⣾⣻⡀⠀⠀⠀⠀⠈⠭⠝⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⣼⣷⣄⣩⠀⢰⣿⣿⣧⠸⣧⣥⢻⣹⡏⢙⢶⢄⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠚⠤⣀⢄⡀⠀⠀⣞⣞⡴⠑⠞⣯⢹⢠⣷⣻⣯⣿⣾⣹⣶⡘⣿⣠⢪⠇⠀⠉⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠚⠷⢯⣿⡿⠛⠁⠀⣸⠀⠥⢹⣿⡷⢩⢳⣿⣿⡿⣷⣣⢸⡅⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⠀⠇⠀⢀⢿⣿⢡⢣⣿⢷⠛⣧⣿⣿⡇⢷⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠼⣾⣿⡇⠁⣮⢣⡇⣸⡿⢻⣿⣿⡸⣧⣙⣝⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣇⣏⠇⣧⣏⣎⠜⡰⣍⢾⣽⢿⣇⠇⠘⢯⣎⢣⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡴⠀⢰⣾⣿⣦⡿⠋⣜⣰⠋⠊⠻⣿⣸⡘⣼⠀⠀⢻⣆⠑⣄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢾⡀⡠⠋⡿⣟⣟⣷⣼⣞⡇⠈⠲⣄⣿⢻⢿⢹⡇⠀⠈⣿⣄⠈⢢⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠄⠀⢠⠞⣽⠃⠀⠙⠶⣄⠘⢎⠛⢿⡿⢿⣷⣦⣄⣀⣿⣿⣾⣿⠏⢷⠤⣘⣎⣄⠀⡙⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠰⢰⠏⣼⠃⠀⠀⠀⠀⠈⠙⠦⣍⡀⠈⠑⣎⠭⣟⣹⣿⣻⡽⡕⢤⡀⠀⠀⠙⠻⣦⣌⠱⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⢣⠏⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡜⢡⣿⠟⡼⣧⢡⠀⠈⠓⠤⣀⠀⠀⠙⠳⣄⢐⠫⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⡞⣸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⢿⣣⢿⣿⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠁⠙⠙⣢⢍⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⢣⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣏⣮⢹⢻⣿⣀⡀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠏⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⠉⢸⢸⡇⠈⠻⣦⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣇⣼⡿⠀⠀⠀⣿⠏⠻⢮⣒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡻⣧⣽⣿⣿⡁⠀⠀⢰⡿⠀⠀⠀⠉⢿⡊⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠛⠋⢸⣷⡀⢠⣿⠁⠀⠀⠀⠀⠀⠑⢄⢨⠛⢦⣤⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣸⣿⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⠀⢋⡻⣧⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠛⠉⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣀⠻⣪⡻⡳⣄⢀⡏⠀⠀⠀⠀⠀⣤⡶⠚⣯⡿⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠑⠌⠑⣷⣾⡟⠀⠀⣀⣾⡃⣀⢀⣉⣽⡿⣿⣒⣶⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢡⠏�

⠀⠌⡄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣥⠀⠲⠒⠒⠒⠒⠲⠶⠶⢲⢤⣀⡀⠤⠀⠒⠒⠄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠒⠊⠉⡠⠘⣈⠃⠤⣁⣀⠀⠀⠀⠀⠀⠀⠁⢃⡱⡀⠄⠀⠀⠀⠈⠢⡀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⢀⠡⠀⠀⠀⠀⠀⠀⢀⣀⣔⣫⠄⠡⢊⠁⠆⡐⠡⢄⡘⢠⠐⡀⠆⣁⠂⠤⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡀⠃⠆⠀⢀⡤⢒⠋⠍⠨⠄⠬⠑⡂⢩⠐⡡⠑⡂⢄⠃⡌⡐⢢⠐⡈⠒⡌⠢⢤⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀
⠀⠀⠀⠀⠁⢂⢈⡞⠡⡐⠌⡰⠈⡅⢊⡦⢑⠨⠄⢃⠔⠡⡘⢠⠊⡐⡈⢰⢈⠔⠡⢸⣅⢊⢧⡰⣼⡽⣂⠀⠀⡀⠀⠀⠀⠈⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠃⠂⢱⡔⠁⢌⡏⡐⠂⡅⢊⠄⣊⠔⠱⡄⠱⠠⠡⢡⢷⡌⡑⡂⢯⢖⢀⠑⣼⣟⣷⢀⠀⠠⡀⠀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀
⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⢡⠀⢀⣾⠁⠈⠀⢸⢤⣎⠜⡎⠁⢳⡀⠑⠀⠑⠘⣿⡽⣗⠈⡌⣎⢂⢈⢿⣞⡇⠢⠀⢡⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠇⠀⡸⡟⢀⠀⠀⢼⡀⣿⣄⢠⠀⠸⡤⡀⠀⠀⠀⢻⠿⣿⣧⢸⡘⣇⢀⠀⠻⡃⢇⠃⢤⠠⡀⠀⠘⠃⠠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⢀⣢⡟⠤⢀⢻⠀⢠⠀⠀⣾⡇⣧⠘⢯⠂⢈⣷⢉⠀⠠⠘⡌⢇⡈⠛⣷⣧⡙⣷⣄⠀⠈⢢⡘⡀⢆⠡⡄⡘⠀⢄⣈⠢⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡴⢋⠰⠐⢌⡚⠀⡇⠀⠀⡏⢱⢰⠡⡀⠙⣌⠢⢧⢂⠥⡉⠔⠘⡬⠶⢦⠝⠷⡌⢿⣷⡔⠠⡁⠪⣀⠆⢩⠃⠀⠈⡇⢦⡀⠂⡀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠟⠡⠌⣂⠍⡠⡇⡀⡇⠰⠁⡟⡈⣦⢇⡀⢤⠘⢦⠸⡷⡂⡑⢸⠀⢧⣠⣤⣤⣷⣙⣄⠻⣯⡓⠤⣕⣤⣝⡞⡐⠀⡄⣿⠠⠹⡷⣌⢤⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠋⣬⠂⡑⡌⢢⢡⡇⢼⣁⡣⢁⡗⠛⠩⢺⠤⠤⣄⠈⢣⡱⡉⢔⠡⢆⠸⠛⢿⣿⣿⡟⢿⡗⡬⠿⠇⠡⠸⡊⡳⣄⠀⣡⢭⣧⡑⠸⡌⠣⡳⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠣⡸⡇⠸⠐⠏⢠⠎⡇⢼⡇⣗⠠⣇⣴⣶⣿⣿⣷⢶⠍⠀⠁⠹⡤⠃⠚⢀⡖⣮⠿⣉⡇⡼⠃⣷⡆⠆⠔⡡⡊⢢⡀⠳⣟⠠⢸⣇⢽⠉⠄⢹⡱⠀⠀⢂⠀⠀
⠀⠀⠀⡜⡴⢱⡇⡇⠀⠀⣀⠃⣿⡠⣇⠟⡦⣿⠿⣃⡸⣿⣏⡇⠂⠀⠀⠀⠀⠀⠀⠀⢈⠷⠿⢿⠃⠀⠁⠘⣔⠘⡀⢱⣅⠢⠌⠤⠸⣆⢹⠧⢤⡁⣰⣚⠳⠦⠀⢀⠀⠀
⠀⠀⢀⠓⠁⢸⡇⠜⣴⠤⢂⣱⣽⣧⠘⡾⡐⠻⡄⠳⣞⣭⣦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠋⢖⠠⡈⣯⠙⠚⠦⢕⢸⣼⢁⠦⠙⠉⠀⠀⠀⡇⠀⢀⠀
⠀⠀⢨⠇⠀⢸⢹⢘⡏⡐⢢⣿⢻⢈⠋⣿⡄⠀⠘⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠠⢘⠤⠑⢜⣷⠀⠀⠀⠙⠍⠐⠐⣀⣀⡀⣀⠠⠃⠀⠀⠀
⠀⠀⢸⠀⠀⠀⢿⣊⠤⣤⠿⢁⡼⣄⠺⢸⣷⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣌⠆⣈⢳⣤⣀⣎⠗⡾⡍⢡⠰⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠸⠇⣹⡜⠋⡠⢋⠂⢁⡡⢼⣿⠑⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠤⠤⢴⡂⠀⠀⠀⠀⢀⣾⡽⡄⠀⠙⢶⡀⠆⠳⣸⣆⠀⢘⢽⡄⣺⢀⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢈⢃⡝⡵⠇⠒⠁⡠⢺⣻⠙⠚⣄⠀⠀⠀⠀⠀⠀⣾⣩⡥⠐⠂⠛⠻⠀⠀⠀⠀⢠⠞⣁⠖⠱⡀⠀⠈⠛⢮⣡⡈⡻⡄⠁⠈⢧⠏⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢍⡌⢍⠀⠀⠈⠞⡇⠀⠉⠷⣄⠀⠀⠀⠀⠀⠁⠠⢀⡀⠄⠀⠀⠀⢀⡴⠟⠈⢁⡐⠁⢱⡄⠀⢀⠑⢴⠽⣝⠛⣆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠇⠀⠑⠠⣄⡘⠽⡤⠔⠂⠈⠑⠤⣄⠀⡀⠀⠀⢄⡀⠂⠀⠀⡔⠋⡗⢂⢢⢡⠀⠀⠀⠈⠄⠘⣤⡀⠑⠊⣷⡈⢦⠀⠀⠈⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⢏⠤⣀⠀⠘⠀⠀⠀⢀⠞⠁⢹⢓⡲⠤⣄⣀⣀⣄⣫⠔⠾⠧⢤⠸⠁⠁⠀⠀⠀⠈⠦⣌⢯⠓⠦⢄⡙⣾⢣⠀⠌⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⠌⣖⠀⠀⠈⠉⠉⠉⠀⠀⣐⠫⠉⠉⢉⣱⡝⠀⠘⡖⣆⠀⠀⢀⣆⠀⠀⠀⡆⠀⠀⣰⠆⠍⠹⢶⡇⢊⠝⠁⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⢰⠈⠂⠀⠀⠀⠀⠀⠐⠉⣴⠀⠀⠉⢸⡔⠀⠀⣭⣤⣤⣤⣬⠃⠈⠁⢺⡔⠀⢰⢩⡄⢩⡜⢱⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⡌⠄⢀⡠⠤⠐⠀⠀⣠⠚⢧⣂⣠⠖⣍⣳⢢⡽⡗⢆⢎⡮⢣⠉⢲⠀⡤⢋⠃⢮⠂⣬⠾⢥⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢠⠞⠤⠋⢀⡀⠀⠀⠀⢘⣄⠂⠁⡹⢀⠯⠖⡏⣼⢷⠘⢆⠉⠀⠐⢷⡇⠸⢁⠅⢾⠾⠚⠐⠀⠁⠀⠀⠍⠋⠲⠤⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠊⠠⠀⠀⢀⡀⢀⡄⠈⠒⡒⠒⠐⠈⠗⣴⠃⠂⠂⠰⡅⠿⡾⠈⠀⡖⠀⠀⠂⣅⢀⢠⠞⠁⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢙⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⢂⠀⠀⠀⠀⡌⠀⣀⠟⠛⠳⢌⠢⠐⠀⠀⠀⠊⣈⡀⠁⠂⢰⠁⠀⠀⠀⠐⠘⡆⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠈⠼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢰⡠⠒⠁⠀⡀⠂⢀⠈⢂⠂⠀⠀⠀⠁⠋⠙⠶⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡟⠀⠀⠖⠨⠚⠛⠃⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠘⠒⢐⢀⡀⠤⠶⠖⢣⢎⡢⠀⠀⠄⠀⠤⠀⠤⠤⠐⠂⠀⠀⠄⠒⠠⠀⠤⠤⠠⠤⠀⠀⣀⣀⣲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡤⠤⠠⠀⠤⢹⡀⠢⠀⠀⢤⣀⡀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡈⠀⠀⠀⠀⠀⠀⠚⠒⠙⠢⣀⠀⠀