Spongebobhouse Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣶⡶⠲⠶⣶⡶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢠⣾⣿⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣦⠀⠀⢹⣿⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⡟⠀⠀⢀⡠⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠹⣧⠀⠀⢻⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⡿⠁⠀⡠⠊⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠙⢧⡀⠀⢿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡠⠊⣠⣾⡟⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠈⠻⣄⠀⢿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⠋⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⡀⠙⢦⡀⢻⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⣿⣿⣁⣤⣶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠻⣄⠙⢿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡿⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡛⠋⠁⠀⠠⠄⠀⣻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⢻⠟⢀⡠⠄⠊⠀⠀⠰⣽⢇⣿⡇⢾⣻⡯⣿⣿⣿⣿⣿⣯⢶⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣫⠶⠊⠁⠀⠀⠀⠀⠀⢺⣿⣾⣟⣵⣾⣵⡾⣿⣿⣿⣿⣿⣿⣿⣹⣆⠀⠀⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢶⣿⡟⠁⠀⠀⠀⢰⠇⠀⠀⠀⠰⢿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢆⠀⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣽⣿⡿⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠿⣼⠅⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘⣽⣿⠻⣿⣭⣻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣏⣿⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠋⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⣼⣿⠁⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣣⡟⠁⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⣇⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣧⡖⠀⣴⣯⡶⠛⠳⣼⢿⣆⠀⠀⠀⠀⠀⢠⡀⠺⣏⡽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⡆⠸⣇⣿⡀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠀⢻⣝⠻⣤⠶⢛⣿⠏⠀⠀⠀⠀⠀⣀⣴⡿⢯⡿⣿⣾⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠋⠀⠈⠂⠙⠻⠿⠞⠋⡡⠀⠁⠀⠀⠀⠸⣿⡟⣻⣷⣿⣷⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣷⠀⠀⠀⠁⠄⢀⠄⠁⠀⠀⠀⠀⣀⡠⠴⠿⣧⣿⣟⣻⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠛⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡠⣮⣤⠶⠷⠶⣦⡜⢿⣷⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢧⣦⣀⠀⠀⠀⠀⠀⠀⠀⣎⣱⢏⣼⠟⠋⠉⠢⣻⡆⢹⣇⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⢯⡆⠀⢀⠀⠀⠀⢺⠉⣿⣼⠃⠀⠀⠀⠀⢻⣿⠃⣿⣝⣾⣿⣿⣿⠁⠀⢻⣿⣿⣿⣿⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣦⣷⠀⢸⡇⠀⠀⢸⠀⡟⡟⠀⠀⣦⠀⠀⣸⣿⡇⣿⣼⣙⣿⣿⣿⣦⣄⣸⣿⣿⣿⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣻⣿⡄⠘⠃⠀⠀⣼⠀⣿⣯⠘⣿⣿⣿⣟⣻⣼⠃⣿⣎⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣽⣾⣿⣧⡀⢀⣴⣿⠈⣏⡷⠘⠛⣿⡿⠟⣿⢸⡇⣿⣬⡿⣼⣿⣿⣿⣿⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠨⣿⣿⣿⣿⣿⣿⠏⠄⠿⠀⢟⣧⠐⡈⠂⠘⠀⢹⣼⡇⣿⠿⢡⢹⣿⣿⣿⣿⣿⣿⣿⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠻⣿⣟⡘⠋⢰⡆⢚⠀⣸⠿⣤⣤⣄⣠⣀⠼⣿⠃⣉⠀⣫⣯⠹⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠁⠘⣩⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⠛⠉⠉⠃⠛⠋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣱⢀⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⢠⣅⠀⣀⣀⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⢁⡾⠘⣧⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⢀⣀⣀⣀⡀⡀⣄⢠⣠⣤⣤⣤⣠⣒⣶⣦⣦⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠞⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣶⣤⠉⠁⠀⠀⠀⠀⠙⣽⢽⣾⣮⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣴⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⡶⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⢹⣿⣿⢇⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣦⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣼⣿⣿⣿⠇
⣿⣿⣏⠭⠋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣄⣻⣿⢿⣿⣿⣿⢿⣿⣧⣀⡀⡀⡀⠀⠀⠀⣠⡟⠋⠉⣹⣿⣯⠀⢀⣴⡄
⣿⣯⡘⠀⠀⣀⣸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⡀⠀⠘⣴⣿⣿⣷⣿⣿⣿⣶⣾⣿⣶
⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⢿⣿⢣⡀⠊⠀⣻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇
⣠⣤⣤⣤⣤⣤⣼⣿⣿⡿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⢿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠿⡿⠿⣿⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⢀
⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⣼⣿⣿⣿⣧
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠄⢉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⣠⡤⠶⠶⠶⠶⣖⠲⠶⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⢀⡀⠀⠀⠙⠦⣀⠀⠈⠉⢳⣤⡀⠀⠀⠀⠀⠀⠀⠸⠃⠋⠙⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠑⢤⡀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⣦⣖⠉⠀⠙⣦⣤⠀⠀⠀⠀⠰⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠙⠢⣀⠈⠻⡀⠀⠀⠀⠀⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢠⣲⠀⠀⠀⠀⠈⠢⢄⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢽⡆⠀⠀⠀⣧⠄⣘
⠀⠀⠀⠀⠀⠀⢀⡾⢇⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⣀⠔⠛⠦⡀⠀⠀⠀⠀⠀⠰⠟⠀⠀⡠⠀⢹⡤⠠⢀⡇⠀⠀⡄
⠀⠀⠀⠀⠀⢠⠏⠀⢀⠟⠣⣀⣚⡀⠈⠑⣦⡠⠊⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⣁⡔⠊⣷⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢀⡟⠀⢠⠋⢀⠞⠉⠑⢬⣦⠟⢹⡄⠀⠀⠀⣠⡀⠀⠀⠀⠈⠓⢤⡀⠀⡠⠞⠁⠁⠉⠙⣗⠒⠒⠀⠁
⠀⠀⠀⠰⡿⠁⠀⢸⠀⢸⠀⢀⡴⢪⣟⠢⣼⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠜⠛⢤⡀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢠⠇⠀⠀⠈⢦⣊⠷⠛⠚⠁⣠⠔⠉⠓⢤⡀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠈⠑⠢⣄⠀⠈⡇
⠀⠀⠀⣾⠀⠀⠀⡠⠞⠉⠐⠒⠂⠉⠁⠀⠀⠀⠀⠈⠲⢄⠀⡠⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠦⣷
⠀⠀⢰⠏⢲⣤⠋⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣀⠔⠛⠢⣄⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠛⠁⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⡆
⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⣠⠖⠁⠀⢀⣇
⠀⢀⡇⠀⣦⠀⠀⠀⠀⠀⠈⢑⣤⠖⠉⠀⢀⡀⠀⠀⠀⠀⠰⡗⠀⠀⠀⠀⠀⠀⠈⢳⣤⠊⠁⠀⠀⠀⢸⡟
⠀⢸⠃⠀⠉⠀⠀⠀⠀⣠⠔⠋⢀⡱⢾⣉⣉⣉⡙⠦⡀⠀⣀⣀⡀⠀⠀⠀⢀⡠⠖⠁⠀⠙⠦⣀⠀⠀⢸⠁
⠀⢸⣄⠀⠀⠀⠀⡠⠚⠁⠀⢀⠎⢠⠞⠉⠳⣄⠙⢆⡸⠋⠁⠀⠉⢲⣤⠖⠉⠀⠀⠀⠀⠀⠀⠈⠓⢤⣼
⠀⢸⠈⠳⣄⡴⠋⠀⠀⠀⠀⡎⢠⠇⠀⠀⠀⠀⠑⣾⡀⠀⢀⣠⠔⠋⣧⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⡏
⠀⠸⣆⠴⠋⠳⣄⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⢰⠃⣙⣶⣞⡓⢤⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠈⠑⢄⠀⢸⠀⡆⠀⠀⠀⠀⣀⣴⠚⠋⣼⣟⣿⣆⡁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠑⣾⠀⡇⠀⢀⡤⠚⠁⢰⠀⣶⡜⡚⣋⡤⠉⢺⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⢸⢙⣷⡚⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠀⠙⠢⣄⠀⢀⡴⠊⠁⣰⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠂⠙⠤⠷⠽⠦⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀⣸⠤⠤⠄⣠⠟⠷⡂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠛⠋⠉⠉⠛⢯⣉⠉⠉⠛⠛⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢦⣀⠀⠀⠀⠀⠸⡽⠂⠀⠀⠀⠀⠀⠈⠙⢦⣀⡴⠚⠁⠈⠳⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠑⠦⣄⠀⠀⠘⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢰⣋⡗⠀⠀⠀⠀⠀⠈⠙⢦⣄⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣼⣧⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠿⠀⠀⠀⡀⠀⢹⣆⣠⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⣦⣔⠋⠉⣭⠉⠙⠒⢦⡀⠀⢀⡴⠚⠁⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⡤⢿⡅⠀⠈⠉
⠀⠀⠀⠀⠀⣼⠁⠀⢀⡼⣃⠈⣳⢶⡒⠦⣄⠀⣀⣹⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⣸⠶⢉⣀⣼⣷⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⠇⠀⢀⡞⠀⢡⠞⠁⠀⠙⠲⣼⡶⠋⠁⣧⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢀⡴⠋⠁⠀⠀⠀⠀⠹⣏⠉⠉⠉⠉
⠀⠀⠠⣾⡿⠀⠀⢸⡇⠀⣿⠀⠀⠀⣠⠞⣽⡓⢦⣠⠏⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠻⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣽⠁⠀⠀⠀⢧⡠⠜⢧⣤⣎⡥⠞⠁⠉⣠⠟⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠸⡇
⠀⠀⢠⡇⠀⠀⠀⠀⠀⣹⠶⣏⣀⣀⣛⣠⡴⠞⠁⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⣿
⠀⠀⣾⡀⠀⠀⢀⣠⠞⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠳⣾
⠀⢰⡏⠙⣦⣴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣸⠳⠞⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⡿⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣿
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣿⡄
⢸⠃⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡞⠉⠀⠀⠀⠀⠀⠈⡿⠁
⣸⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢙⣦⡖⠚⠋⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠉⠲⣄⠀⠀⠀⠀⢀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⡴⠋⢀⡽⠶⣞⠛⠓⢦⡈⠙⣦⡴⠒⠒⠒⠦⣄⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⢸⡇
⣿⢦⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡼⠁⣠⠏⠀⠀⠈⠳⢤⡀⢳⡴⠋⠀⠀⠀⠀⠀⣈⣷⠚⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠓⣾
⣿⠀⠙⢦⣠⠖⠉⠀⠀⠀⠀⠀⣸⠃⢠⡏⠀⠀⠀⠀⠀⠀⠙⣾⡁⠀⠀⠀⣀⡤⠞⠁⢸⡀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠀⠀⠀⣿
⢻⠀⣠⠞⠙⢦⡀⠀⠀⠀⠀⠀⡟⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠘⢲⣤⠾⠫⣆⡀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢸⡏⠁⠀⠀⠀⠙⠶⣄⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⠋⢽⣿⣷⣦⡙⠞⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⡟⠀⠀⠀⠀⢀⣠⠖⢻⠀⢨⠘⡟⠧⡾⣭⠳⣬⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⠀⡇⠀⠀⣠⠴⠋⠁⠀⢸⠀⠼⡣⠬⠋⢩⡤⡞⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⡟
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣧⡖⠋⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⣷⠈⠙⠲⣄⡀⠀⠀⣀⡴⠚⠁⠀⣼⠃
⠀⠈⠉⠉⠒⠒⠒⠲⠤⠤⠤⠼⣗⠋⣯⣙⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣙⣦⣾⡡⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳⣄⣀⣀⣀⣀⣀⣀⣀⡴⠋⠉⠉⠁⠠⠟⠁⠈⠓

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢱⠻⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢻⡁⡈⡼⢡⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⡇⠃⠁⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠬⡞⠓⠵⢅⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠣⡄⠀⠀⠓⠤⠀⡸⡄⡠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠰⢀⠀⠃⠤⠀⡀⠊⠁⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢢⡔⢛⡕⠢⡀⠈⠁⡠⠊⢸⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⢿⣿⡶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢀⠦⠘⢠⡀⠀⡐⠢⢀⡶⣾⠀⠀⠀⠀⠀⣠⣿⣿⡛⠋⠉⠉⠸⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡈⠀⠦⣠⣾⠛⢻⣢⠈⠛⣻⠁⠀⠉⠐⠀⠻⣿⣿⣷⣶⣶⣶⣶⣷⣶⣾⣿
⠀⣠⠴⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠢⣤⣻⠿⣹⠒⣿⡤⣀⡏⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⢦⠴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠻⠤⠴⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⢀⢀⠄⢠⢀⢀⡀⣀⢀⡠⢀⠀⠀⡀⡀⢀⣀⣀⡄⣀⠀⢠⢀⢀⡀⠀⠀⡠⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣠⠖⣉⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⢶⣶⣶⣾⣷⣠⣞⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣏⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⢉⣁⡶⣿⣿⣟⣿⣟⠓⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠛⠁⡇⠀⠀⠀⠀⠀⠀⠴⣊⠁⠀⠀⠀⢢⡉⠻⣎⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⡇⠀⠀⠀⠀⡠⠀⠠⠴⠿⠿⠶⠂⣨⣿⡟⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⡸⠁⠀⠀⠀⠀⢂⣠⣞⠉⠶⢿⣷⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢨⡀⡀⠀⢠⠃⠀⠀⠀⠀⡠⠞⢳⡙⠀⣸⠟⠻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠺⠊⠂⠀⢀⣒⣓⣁⣀⣸⠀⣰⣿⡆⠀⡠⠀⠀⣱⣾⣷⡿⠗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢸⣀⡇⠒⠀⠈⠉⠉⠁⠈⣄⠀⠀⢀⣹⠀⣿⣿⣿⠀⢱⣤⡾⡿⢿⣿⡆⢰⣏⠉⠉⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⢉⡋⢟⠀⠘⠉⠀⠰⢆⢉⣴⣻⣿⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠂⠒⠀⠂⠀⠀⠐⠀⠒⠀⠐⠀⠀⠐⠒⠀⠀⠐⠀⠐⠐⠐⠀⠐⠀⠀⠀⠐⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢛⣴⡾⠛⣋⣙⣹⣿⣿⣤⣴⠾⠛⡓⠻⢶⣤⠀⢆⠀⠀⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⡛⣼⣿⣿⣿⣿⣿⡿⢉⣴⣾⣿⣷⠀⢹⣿⣷⠀⠃⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⢾⣿⣿⣿⣿⡿⣾⠃⢼⣿⣿⣟⣿⠇⢰⣿⣿⠀⠒⠀⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⣹⠦⣖⣟⣟⣿⣿⣿⣆⣬⣿⡿⠛⠃⣤⣾⣿⡿⠀⠷⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣴⢋⡿⣿⢿⡟⠻⣿⣿⣿⣷⣶⠊⠉⠉⠉⠁⠀⠀⢰⣿⣿⣿⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠉⠛⠃⠛⠙⠁⢠⡻⢿⣿⠿⢟⣢⣾⠃⢀⠖⢀⡴⣿⣿⣿⢹⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⣀⠀⢸⣶⣤⣤⣄⣀⣀⣤⣼⣦⣶⣾⣿⣿⠃⠀⠁⠀⠘⣿⠷⣟⠷⢾⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣇⠐⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⡿⣀⣄⠀⢀⣼⡹⢧⣷⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠿⠿⠋⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠿⠛⠁⠙⣿⣿⣯⡿⣿⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⣾⣇⠐⢻⣿⣿⣿⣻⡿⢟⢋⣽⠟⠁⢀⣤⣤⠀⠀⢈⣿⣿⡩⢇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠁⢤⣴⠋⠛⠿⠿⠿⠟⠛⠁⠀⠀⣿⣿⡿⣇⣠⣿⣿⡟⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠾⢿⣶⣶⣮⣽⣿⣶⣶⣤⣤⣤⠤⠀⠀⠀⠹⡏⠀⠀⣿⣿⣿⠃⠀⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⣐⣂⣟⡳⠿⠿⢿⣿⣿⢿⡛⢲⣶⣤⣤⣶⣇⣀⡀⣸⣿⣿⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣯⢿⣿⣿⣿⣿⣧⣤⣍⣉⣁⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣇⣼⣇⣸⠉⢻⣿⣿⣿⠻⠛⠃⠉⣿⣿⣿⣷⡶⢶⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⣻⡟⢻⣿⣷⡿⣿⣥⣇⣀⣀⡀⠀⠀⠨⠃⠁⣨⣿⣿⡿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠁⠈⢹⠛⡃⠀⠟⣿⡿⠟⠿⣶⡾⢧⣤⣤⣼⣧⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠑⠀⠈⢹⠁⢤⣄⠁⠇⡔⢻⠋⠇⠛⣟⠉⠘⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣼⠀⠀⠀⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠷⠀⠀⠈⡃⠄⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⡄⢾⠀⠀⠛⢈⡰⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢣⠈⠀⠀⠀⠘⠁⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠢⡀⢦⡇⠀⠞⠀⠐⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⡉⠁⠍⠉⠒⣄⠀⠀⠀⢸⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠢⠀⠀⠀⡀⠈⠁⠀⠙⣇⠀⠘⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠘⠀⠀⠈⠰⢈⠀⠀⠀⠄⠀⡘⣦⢠⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠊⠀⠁⡀⠒⠀⢀⠀⠁⠠⠀⠀⠀⠀⠢⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀⠀⠄⠂⠢⠀⠀⠀⠀⡀⠀⠉⠂⢀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⣀⠐⠉⠀⡁⠀⠀⠀⠀⠤⠈⠀⠀⠀⠄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢆⠀⠀⢀⠀⠐⠀⠀⠀⡀⠲⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⢀⢀⠄⠀⠠⢠⣾⣿⣧⠀⠈⠁⠄⠀⠀⡀⠀⠁⢸⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠌⢥⠈⠀⡆⢀⠀⠂⣿⣿⣿⡏⣄⣤⠠⢀⠀⠀⠈⠀⡤⡟⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⠘⠁⣀⢑⡀⣿⣿⣿⡇⠊⠛⠄⠀⣠⠂⠠⠈⠠⡋⡈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⣀⣃⣴⠃⠿⠿⠿⢷⣀⣀⣀⡈⠀⡌⡰⠚⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢁⣝⡶⣉⠀⣉⠒⡙⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠠⣀⣄⡃⠀⠐⣿⡖⠊⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⣁⣠⡂⠐⠲⡝⢛⡐⠠⠀⠩⢂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠁⢒⠊⠠⠄⢠⡀⠈⠘⠅⣂⣄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢍⣈⣑⠄⠈⠀⠠⠄⠀⠀⠆⣀⣀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠀⡔⠀⠈⠢⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊

⠀⠀⣤⣴⣤⣄
⠀⣾⣿⣿⣿⣿⡆
⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢤⢄⡠⣤⣄⡀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠁⠉⠉⠉⠉⢹⠀⠀⠀⠀⠸⡓⠙⡀⠀⠁⠁⠈⠈⠽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⣈⠦⠀⠀⠀⠠⠀⠀⢴⡑⡏⡇
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢀⠀⠙⢣⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣶⣀⣤⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⣸⠐⠐⡆⠀⠈⠀⠀⠀⠈⠀⠀⠈⣇
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣟⣛⠁⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⡇⠺⠤⠖⠀⠀⠀⠈⠀⠀⠀⠘⠀⢸
⠀⢀⣾⠿⣷⣄⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⡇⠀⠀⠀⠄⠀⠀⡀⠀⠀⢸⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣽
⠀⢸⣧⣴⣿⣿⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣏⠀⠀⠀⠆⠠⠈⠀⠀⠀⠨⢠⣅⡞
⠀⠈⢿⣿⡿⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡀⠄⠀⠀⠀⠀⠀⠁⠰⠊⠈⢰⠃
⠀⢠⣴⣶⣶⣄⠀⠀⠉⠉⠉⠐⠒⠒⠒⠒⠉⠉⠉⠀⠀⠉⠉⠁⠙⠓⠓⠛⠛⠒⠒⠉⠁⠀⠀⠉⠒⠒⠒⠒⠒⠒⠶⠖⠒⠒⠋
⠀⢺⣿⣿⣿⣿
⠀⠀⠙⠛⠉⠁

⠀⠀⠐⠧⠿⠲⠡⠖⠶⠧⠼⠆⠗⠮⠱⠿⠀⠺⠺⠆⠾⠖⠁⠖⠀⠾⠔⠾⠮⠕⠰⠾⠞⠲⠒⠙⠸⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⠟⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠲⢀⣛⣤⣿⡇⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣆⠀⠸⣿⣿⣿⣷⡿⣿⢿⣿⡇⡤⠞⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠲⠙⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠄⠠⡄⢠⠀⡤⢠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣯⣿⣭⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠋⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⠺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠆⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡄⠀⠀⠠⠀⠂⠀⠀⠀⣴⣿⣿⣿⣿⣷⣾⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⡠⠀⢀⠄⠄⠎⢀⠈⠀⠀⠀⠇⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴
⠀⠀⠀⠀⠀⢄⡢⡀⠀⡀⠐⠂⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⠟
⠀⠀⠀⠀⠀⠈⠋⠈⠢⠐⢶⣤⣄⣰⣤⡀⢐⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠲⠞⠄⣙⠛⣙⣉⠅⣈⡡⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠈⠀⠀⠒⠪⠄⠰⣀⠏⠠⢴⣎⣿⣿⣿⠿⠀⠀⠀⠀⠀⣿⢿⣿⡿⠿⢿⣿⠿⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⢶⣶⣶⡿⠟⣋⠙⡛⠀⠀⠀⠀⠀⠀⠛⠀⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⢆⠘⠋⠁⢰⡏⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠀⠸⠷⠆

⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠂⠀⠐⠀⠆⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠄⠀⠀⠀⠀⠀⢂⠈⠡⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠢⠴⠂⠀⠀⠀⠀⠀⠀⠶⠰⠄⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠉⠉⠀⠀⠄⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠄⢀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢐⠀⠀⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣥⣴⣶⣶⣶⣶⣤⣌⡛⢿⣷⡀
⠀⠀⠀⢰⣿⣿⡿⠛⠛⠻⢿⣿⣿⡿⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⢀⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⣣
⠀⠀⢘⠋⡎⠉⠀⠀⠀⣦⠀⠀⠀⠀⢰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠚⡉⠀⠀⡀⡀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠆⠀⢀⠀⠀⠀⠘⣲⠺⠂⠀⠀⠀⠀⠀⣸⡇⠘⠂⠻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠈⠡⠀⠋⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠰⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠑⢄⠙⠻⢿⣷⠀⢰⣿⠿⠛⢉⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠒⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⢀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠸⠿⠗⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠮⣹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠐⠀⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⠀⠀⠐⠲⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠴⠈⠄
⠀⠀⠀⠀⣠⠀⡠⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⢁⣠⠼⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⡄⠀⠀⠀⠀⠴⢿⣆⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡿⠤⠠⠀⠄⠀⠀⠈⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢈⢁⡤⢏⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠃⠀⠀⠈⠳⢄⠠⠤⠄⠆⠀⢂⡈⠁⢢⡀⠈⢧⡀⠀⡀⠠⣀⠁⡀⠀⠡⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠁⢈⠀⠀⠀⣂⢀⠂⠀⠀⠀⠒⠦⡀⠀⠀⠀⠀⠑⡌⢀⠊⠀⠀⠈⠀⣀⣀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⢀⠂⠐⡰⠇⠄⠀⠀⠈⠱⡀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢰⠀⠀⠀⡠⠤⠀⠠⣄⠑⢆⠀⠰
⠰⣄⡆⠀⠀⡅⠀⠀⠀⢀⡤⡄⠀⢤⡄⠀⠀⠀⠀⠀⡆⠀⠀⠚⡅⠀⠀⡄⠀⠀⠀⡄⠀⠀⠰⠘⠲⠠⠄⠉⠀⢸⠀⡘
⠚⠻⣿⠋⠀⠁⠀⠀⠀⠀⣤⡄⠀⣄⡌⠀⠀⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⢊⡀⠀⢰⢤⡀⠈⢠⣀⠀⠉⡡⠀⠀⠃⡐
⠀⠀⠈⠳⠦⠴⡀⠀⠀⠈⠘⠀⠐⠒⠀⠄⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠿⠀⢰⣦⣤⡼⠁⡀⢡⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠤⢒⣿⠀⠀⠀⠀⢠⢷⠀⠀⠡⢄⠀⡠⠄⢀⣼⣿⣾⢇⠀⠘⠒⠊⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⣵⣤⡄⠀⠈⠋⠑⢀⡤⢄⡠⢴⣋⣿⠀⠀⠀⠀⣀⠀⠀⠀⣠⠋⢀⣨⠦⢀⣀⣀⡠⢒⡏⣀
⠀⠀⠐⢦⣤⣀⣻⠀⠉⠉⠒⠦⢖⠒⠉⡇⠀⠀⠀⠞⠟⠓⠂⠰⡎⡼⠁⠒⠈⠀⠰⠯⠥⠤⣤⡄⠀⢳⠈⠳⠟⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡟⢧⣰⡇⠀⠀⠀⠀⠀⠀⠀⣠⠿⠴⠶⢲⡆⠀⠀⠀⣀⣴⠟⠁⠀⠈⠷⠤⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣥⣤⡀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⢀⢤⠊⠀⠩⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⠀⢀⠀⠀⣠⠐⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠹⡨⠄⠉⠁⠀⠀⠀⠄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡀
⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠃⠌⠠⠀⠀⣀⣀⣀⢠⡀⠀⠤⠆⢒⠀⠀⠀⠀⠔⡀⠌⠀⠀⠁⠘
⠀⠀⠀⢀⡌⡄⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⡠⠁⠐⠤⠀⠀⠀⠂⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⠀⠊⠐⠠⡀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠘⠀⠀⢂⣠⡀⢠⣀⠂⠀⢸⠀⡐⠀⠀⠄⠀⠀⢀⠈⢂
⠀⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⢩⣆⠀⠀⣶⡙⠀⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢃⠀⠀⡀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠉⠁⢀⡃⠐⢤⠄⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠆⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠑⢤⣀⣀⣀⣀⠴⢋⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣾⡏⠉⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠶⣤⣌⣙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢧⣤⣈⠙⠲⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⠀⣠⠞⡩⠟⣳⡶⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣯⣼⢁⡞⢁⡜⢑⣷⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⣿⣄⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠲⣤⠋⣦⢶⡄⠀⠀⢀⣀⡤⠄⣝⠻⢿⠛⢃⡞⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡬⢧⣙⣷⣿⣦⣧⣼⠋⡡⢞⣩⠴⣖⣻⣭⣽⡤⠬⣼⠀⠐⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⢰⡓⠀⢽⣿⣿⣽⣽⡿⡼⢱⣿⣟⣯⠽⢶⣒⣛⣗⣓⡏⠀⠀⠀⠀⢬⡳⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠐⠯⣥⣽⠟⡿⣿⢿⡇⡇⣼⣿⣿⣿⣿⣭⠽⠶⡗⠖⣷⣦⣤⣐⣬⣷⣽⢢⣿
⠀⠀⠀⠀⠀⠀⠰⠋⠲⣳⠋⢹⣧⠶⣾⣻⣿⣎⠺⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⡾⠿⢟⣫⣴⣿⣿⣆
⠀⠀⠀⠀⡖⠒⠦⣇⠀⢹⡀⣼⡇⠀⢻⣿⣟⢿⣟⠦⣤⣀⣀⠀⠠⠤⠤⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⡀⢠⢄⢀⣄
⠀⠀⡤⠶⠮⢦⣤⣿⣿⣿⣿⣿⣷⡿⣿⣷⣍⠳⠮⣙⠒⠬⠉⠉⠛⠛⣛⣛⣭⡭⠷⢾⣿⣿⣿⣿⣿⣷⡈⣻⣌⣯⣼⠚⣓
⠀⠀⣙⠶⠤⣼⣿⣿⣟⣴⣶⣾⣿⣧⢿⣷⣬⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖⣚⣻⣽⣿⣿⣯⢞⡿⣸⣿⣟⣿⣿⣿⣉⡽
⠀⠈⢣⡤⠤⠤⣿⣿⣿⣿⣿⣿⣿⠻⡼⣿⣷⣭⣓⠂⠀⠀⠀⠀⠀⠀⠐⠒⢛⣛⣩⣭⣿⣿⣿⣿⣿⢃⡩⣿⣿⣿⣿⡿⢅⡭⠂
⠀⠀⠻⢤⡤⠔⠚⢻⠟⠉⡟⠙⡄⢙⣶⣿⣿⣷⣭⣙⡒⠀⠀⠀⠀⠈⣉⣉⣭⣭⣴⣾⣿⣿⣿⣿⣿⣏⣤⠊⣹⢻⡏⢲⠤⠗
⠀⠀⠀⠸⠷⠶⣞⣁⣠⣾⣧⣠⣿⣾⣿⣿⣿⣿⣿⣾⣭⣙⡒⠒⠶⠤⠴⠶⠶⢶⣿⣿⣿⣿⣿⣿⣛⣻⣿⣶⣿⣤⣑⠞
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣻⣿⣾⣭⣝⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⣛⣒⣒⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠭⠭⠭⠭⠭⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⢛⣛⣛⣛⣛⣛⣛⣛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠛⠛⠛⠛⠛⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣄⢄⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣨⣭⣿⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⡠⠔⠋⠀⡇⠀⢰⠒⠒⠒⠒⢻⠆⠀⢸⡇⠀⠀⠀⠀⠀⠒⣺⠽⣿⠟⠛⠻⢿⣿⣿⣿⡀
⠀⢰⠚⢁⣀⣀⣀⣀⡇⠀⠈⠉⠉⠉⠉⠁⠀⠀⢸⢹⠀⠀⠀⠀⠀⣀⣀⡰⢁⠈⠂⠀⢸⣿⣿⡿⠁
⠀⣼⠀⠠⠤⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢧⣀⡀⠸⠀⠀⠀⠸⠛⣿⠁
⠀⡏⠀⠰⠶⠤⠤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠖⠟⠀⣀⢴⣤⡄⣪⡵⡧⠤⠤⠤⣀
⠀⡇⠀⠘⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠘⡟⠺⢯⠃⡞⢱⢟⣿⡾⠁⠀⡀⠀⠀⠑⢆
⠀⣧⠀⠈⠉⠉⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠉⣲⡜⣆⠀⠀⠈⣾⡽⠀⠀⣧⡄⠀⠀⠈⣇
⠀⢹⠀⠀⢰⡶⢰⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢠⠞⠻⠿⣿⣷⣲⣻⣿⡤⠀⣸⡿⠀⠀⠀⠀⡿
⠀⠈⠓⠦⢄⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠀⠀⠘⢀⣴⡟⢀⣀⣠⣴⡚⢱
⠀⠀⠀⣀⣀⣤⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⠃⠤⢤⣾⢧⣄⣀⡤⠶⠛⠛⠛⠛⠛⠋⠉⠀⠀⡇
⠀⣰⠞⣉⣁⣀⣀⣀⣹⣤⣤⣤⣤⣤⣤⣤⣶⣶⡿⡄⠀⠀⠀⢣⠀⠠⣠⡇⠀⠀⡀⠘⠲⣤⣀⣀⡀⢀⣀⣀⣠⡼⠓
⠀⢹⡀⢯⣤⣤⠤⠤⠤⠤⣤⣤⣤⠤⠤⠤⣤⣤⠤⠇⠀⠀⠀⠈⢧⡀⠀⢳⡀⠀⠈⠙⠛⠻⡉⠉⠉⠉⠉⠀⠀⠀⣀
⠀⠈⡇⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢀⣠⣽⠶⣤⣽⣦⡀⠀⠀⠀⠘⢿⣟⣛⣛⣩⣭⣽⣿
⠚⠛⠁⠀⣸⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣼⡀⠀⢀⡴⠚⠻⠿⠿⢛⣡⠤⢶⣿⣷⣤⣤⣤⣤⠟⣟⢛⡇⢸⠁⢀
⠀⠀⠀⢸⣗⣲⣱⠀⠀⠀⠀⠀⠀⠀⠰⡷⣋⢇⡇⠀⠘⠿⣶⣶⠶⢯⡵⠞⠛⠛⠿⠿⠋⣈⣉⣀⠴⠋⠉⠀⠈⠛⠉

⠄⢣⡶⢶⡀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠙⠆⢣⣾⢻⡄⠀⠀⣼⢿⣧⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡘
⠀⠈⢓⡚⠁⠀⠀⢙⡟⠃⠀⠀⠀⠀⠀⣾⣿⣷⣛⣛⠁⠀⠀⢈⡟⠃⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠐⠋⠀⢠⣤⡐⣯⣀⡆⠀⠀⠀⠀⠀⠈⠙⠁⠋⢀⢂⣤⣄⢻⣀⡶⣠⣤⡀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠻⣤⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠾⠀⠀⠀⢿⡌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠐⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢷⢰⠼⠾⠝⢋⡉⠉⠉⢉⢉⢣⠉⠉⠉⠙⠁
⠀⠀⠀⠈⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣗⣧⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠹⠻⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⠒⠂⠀⣤⠀⠀⠀⠀⠀⠤⠄⣀⠀⠀⠀⠤⠂⠠⡄⠀⠀⠀⠀⠀⠀⣸⢷⣒⠒⠒⠒⠒⠒⢺⡇
⠀⠀⠀⠀⢀⠟⠛⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠄⠀⠀⠀⠞⠀⠀⠀⠄⠠⣽⣏⠀⠀⠀⠀⠀⢀⠸⠇
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⠦⠄⠈
⠀⠀⠀⠘⠀⠀⠀⣲⣂⠀⠀⠀⠀⠀⢀⣠⣰⣄⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀
⠀⠀⠀⠀⠃⠀⠀⠘⠷⡥⢰⡆⠀⠀⠐⢿⣄⡸⠆⠀⠀⠀⠀⠀⠐⠿⠟⠃⠀⠈⠀⠀⡈⣆⡀⠀⠀⠀⠸⣿⡿⢷⠤⠄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⡼⠁⠀⠀⠀⠉⣼⠑⡯⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣀⠘⠈⠁⠀⡀⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡠⠤⠴⠧⠄⣀⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠞⡡⠔⠀⠘⣟⠀⢢⣍⠺⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠔⢀⣁⢀⣉⣛⡑⠠⢀⠀⠐⡑⡼⠁⡷⢌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠒⠲⠀⠀⠐⠡⡊⠀⠀⠀⡄⡁⠉⠑⠢⣄⠀⢬⡃⢠⡧⠜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠒⠀⠀⠃⠀⠀⠀⠀⠀⢡⠡⠀⠀⠀⠀⠙⣦⡑⢏⠈⠈⠀⠀⠖⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢃⢣⡀⠄⠂⡜⠁⡟⢢⠑⡀⢀⡙⢢⠔⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣓⣋⣀⣐⡂⠤⣄⡀⠑⡑⢄⠜⢀⡜⠀⠀⢱⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⠊⠉⠈⢆⠀⠉⠁⠂⢍⡓⠾⡛⢤⡾⣀⠀⠀⠀⡇⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈⢌⣦⣠⡴⠒⠚⠳⢶⡈⠺⡏⠢⠍⣁⡉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡄⠀⢀⡼⠓⠢⢍⡓⢤⡀⠀⢹⡑⢌⠢⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣘⡾⠖⠋⠀⠀⠀⠀⠈⠲⣝⢦⣸⠇⠀⠣⡘⡄⢀⡆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢦⢹⡀⠀⠀⠐⠘⡄⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⢾⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⡀⠐⡡⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠙⢦⡀⠀⣠⠞⠁⠀⠀⡰⠃⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠙⠺⣯⢋⠄⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣳⠴⠋⠀⠐⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⢠⡷⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⣤⣾⣷⣶⣾⣟⣁
⠀⠀⠀⠀⠀⢀⠠⠔⠃⢀⣀⠇⠀⠀⠀⠀⠀⠊⠟⠣⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⡀⠉⠏⠿⠿⠿⠿⠿⢄
⠀⠀⠀⠠⡀⠌⢀⠀⢈⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠐⠂⠸⢯⣿⠚⢲⣖⣒⡖⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⣀⠀⢀⡄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠛⣄⠀⠉⢧⣤⠖⠉⠀⠀⠀⠀⠶⢭⠏⠁⠓⠀⠀⠀⠀⠀⠚⠛⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⢀⠀⠘⢄⠀⠈⢳⡀⠀⡇
⠀⠀⠀⢀⡀⡰⠿⠿⠃⠀⠀⠈⠱⡀⠈⠣⡀⠀⢻⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⠄⠠⡀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢦⣜⣆⡀⢹⣦⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⡠⠚⣠⣶⢳⣶⣧⣤⣤⣤⠤⢬⣥⡵⠶⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣾⠁⡟⢸⠿⡿⠁⠀⠈⠀⠀⢿⡂⠀⠈⢃
⠀⠀⠀⠀⠀⢠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣏⠀⠁⡞⠐⢀⣀⣬⣤⣀⣀⢸⣇⢀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡶⠘⠛⠋⠋⠁⠀⠀⠀⠀⠀⠈⠉⠲⣄⡄⡆⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡾⠶⠀⠀⠠⣤⣀⡀⠀⠀⠀⣀⡀⠀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠂⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠐⢀⡇⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⡅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡂⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣄⡰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣷⣶⡶⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⢀⢁⢙⣶⢰⣎⡄⠀⠀⠀⠀⠀⡠⠤⠐⠀⠀⠀⢀⣽⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡣⠀⠉⠉⠉⠉⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠻⢝⡻⠷⢶⡶⠴⣶⣴⣦⣶⣶⣦⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠉⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⣠⠞⠩⢀⡤⠶⣾⣷⠶⣄⠀⠀⠀⠀⠀⢀⠀⠌⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡾⠁⠀⣰⠋⠀⠀⠈⠻⣷⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⣼⠃⠀⠀⠀⠀⠀⠘⣿⡌⢧⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡄⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⢰⣦⡀⠀⠀⣿⢸⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠈⣧⠀⠀⠀⢸⣿⡝⢦⡀⠏⢸⠇⡁⠀⡁⠀⠀⠐⠀⢸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⠀⣸⠘⣷⡀⢹⡇⢹⠀⠈⡊⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠹⣎⣡⠙⢦⡀⡟⣶⣿⣧⣼⠀⠸⡆⠀⠀⢆⡀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠐⡆⠀⡀⠀⠀⠀⠀⠀⠈⣻⣷⣤⣉⣓⣟⣉⣵⡇⠀⠀⢧⠀⡓⠒⠒⡄⠀⣀⡀⠀⠀⠀⠀⠙⢀
⠀⠀⣰⣇⠈⡏⠀⠀⠀⡐⠈⠀⣤⣇⠼⣟⣿⣯⣿⡋⡜⠀⠀⠀⠘⣆⠀⠀⠀⡇⠉⣄⠙⠋⠐⠒⠲⠄⠤
⠐⢠⠇⠸⡄⣇⠥⡀⠇⣘⠀⠐⠿⠿⣽⣧⣟⡗⣏⠟⠁⠀⠀⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⣌⡉
⣠⡏⠀⠀⢹⡇⠃⠐⠀⠄⠾⠂⢼⡆⣼⣙⡮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡁⠀⠀⠉⠈⠒⠂
⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠃⠈⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⢂⡡
⠈⠓⠤⠔⠊⠀⠀⠀⠀⠀⠐⠆⠠⡶⠖⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢶⣤⡼⢃⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣀⣀⣡⣤⣔⣀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢧⣼⣿⣿⣿⣿⣧⣼⡿⠿⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⢾⣿⣿⠿⠟⠻⠿⡿⠍⠛⠛⠛⠓⠚⠒⠛⠛⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣀
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⣿⣿⣿⣓⣂⣋⣁⣀⣠⡤⠤⠤
⠈⠉⠉⠉⠉⠉⠉⢉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢨⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠠⠤⠤⠤⠤⠤⠀⠄⠀⠖⠒⠿⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠒⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠲⠮⠵⠶⠦⠤⠄⠀⠀⠈⠀⠤⠤⠶⠶⠶
⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⡀⢀⠀⠀⢤⣄⣤⡄⠀⣤⣤⣤⣤⣤
⣾⣿⣶⣶⣷⣶⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⡀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⡛⢛⣻⢿⠿⢿⣿⣿⣿⡿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣯⣿⡖⠀⠈⠙⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠛⠻⠛⠛⠛⠉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⢤⣀⣌⢱⢛⢹⣻⢻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⠚⣻⠿⠿⠶⡶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣛⢛⣿⣾⣿⣶⣤⣙⢲⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠤⠄⣈⣐⣛⡻⠿⢿⣿⡿⣟⣛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠤⣤⣤⢤⣤⣤⣤⣀⣦⣤⣍⡛⠛⣿⣿⣿⣿⣿⣿⡿⠾⠏⠙⠿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⠿⠟⣩⡿⣻⣿⣿⣿⣯⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠹⠋⠉⠉⣿⣦⣘⠛⣋⣉⣉⠁⠘⢶⣶⣮⣷⣶⣭⣍⣙⡛⣿⣿⣿⣟⣙⣋⡻⠿⣿⣿⣭⣿⣿⣋⣉⣭⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠾⠿⠿⠛⠛⠉⠛⠛⠛⢿⣿⣿⣿⣯⣽⣭⣁⡀⠀⢀⣹⢿⣿⣿⣿⣿⣷⣦⣬⣭⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣤⣶⡶⣿⣷⣤⣭⣭⣤⣄⣀⠀⠀⠀⣠⣤⣶⣤⣭⣭⣭⣭⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡿⠀⢠⣿⡟⢀⣴⡶⢲⡆⣾⡶⠛⣿⡇⣿⠏⣀⡿⠃⠀⣼⣷⠀⠀⣴⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢱⣿⠇⢠⣿⣿⢃⣿⡟⢀⣾⢳⣿⣵⠞⠉⢠⣿⣿⠉⠀⠀⢸⣿⠃⣠⢾⣿⠇
⠀⠀⠀⢠⣤⠀⢀⡾⠁⣾⡿⢠⡏⣿⡏⠘⣿⡛⣋⡴⣻⡟⢿⡀⠀⢸⡿⣿⠀⠀⢸⡎⠛⠛⠃⣾⡟
⠀⠀⠀⠸⣯⡠⠟⠀⠀⢿⣷⠏⢸⣿⠃⠀⡈⠉⠉⠀⣿⡇⠘⣇⠀⠺⠇⠘⢦⣤⡼⢣⡤⠀⣼⡿⢡⣎⡗
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⠿⣤⠾⠁⠀⠀⠀⠉⠁⠀⠘⠳⠤⠾⠀⠀⠀⠀⢿⣀⣼⡿⠁⣞⡷⣞⠄
⠀⠀⠀⠀⢀⡴⢻⣿⠀⠀⣿⡇⠀⢀⣠⣴⠖⠛⣷⠰⣿⡇⢀⣴⠞⠓⣦⡀⠀⣶⡆⢀⣭⣭⣤⣤⣤⣤⣶⣶⡦
⠀⠀⠀⢰⠟⠀⢸⣿⠠⠾⠻⣤⣶⠋⣿⣿⠀⣠⡿⢡⣤⠀⣿⡏⠀⠀⠛⠃⠀⣿⣇⡤⣤⡀⠀⠀⣿⡇
⠀⠀⠀⣿⠀⠀⢸⣿⠀⣠⠞⠙⣿⡄⣿⡷⡞⠁⠀⢸⣿⠀⣿⡇⠠⠶⣶⡶⠂⣿⡏⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠈⠀⠀⢸⣿⣰⠏⠀⢀⣿⠇⣿⡇⢻⡄⠀⠸⠿⠀⠻⣧⣀⣰⣿⠇⠀⣿⡇⠀⣿⠃⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢻⣀⣀⣼⠟⠀⣿⡇⠀⠻⣤⣀⣠⠆⠀⠈⡇⠘⠿⠂⠀⣿⡇⠘⣿⣠⡷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠦⠠⠁⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠓⡄⠀⠀⠀⠀⠀⠀⢀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠖⠀⠀⠀⠀⠀⠀⠀⢘⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡓⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⢀⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡁⠠⠤⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠄⠀⠘⠀⡀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠄⡰⠊⠉⠀⠀⠀⠀⠀⠉⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠁⠈⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡔⠁⡜⠀⠀⢀⠔⠈⠉⠀⠒⠂⠤⠤⢀⣀⠈⠑⢄⠀⠀⠀⠀⠀⠢⡉⠒⠤⠀⠁⠀⠄⡇
⠀⠀⠀⠀⠀⡸⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⢆⠀⠀⠀⠠⠀⠈⠢⢄⠠⠀⢀⠀⠑⠒⠒⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠀⠀⠀⡟⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠋⠻⠤⠀⠢⢄
⠀⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠉⠁⣀⣀⠠⠔⠁⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠈⠑⢒⠒⡀⠉⠉⠁⠀⠀⠀⠂⣠⠋⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠘⢦⡀⠱⣀⠀⠀⠈⠀⠈⢀⡀⠠⠤⠄⠒⠶⠍⢏⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢃⣀⣑⠬⣐⠒⠈⢀⠠⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠌⣉⠄⠉⠉⠉⠉⠀⠀⠀⠀⠆⠂⠀⠀⠀⠘⡀⠀⠀⠀⠂⠒⠂⠄⠂⠤⠖⠐⠂⠀⢀⡴⠙⠚⠡⠀⡀
⠀⠀⠀⠀⡀⠄⡌⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣀⠀⠄⠀⠀⠂⠀⠀⠀⠁⠀⠰⠄⠉⢁⠀⠀⡸⠀⡇⠀⠀⠀⠠⠄⣀
⠀⠄⠂⠉⠀⠂⠚⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠐⠀⠈⢀⠂⠠⠅⠊⢀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡂⠔⠂⠀⠑⠤⠄⠐⠊⠀⡀⠘⠀⠁⠕⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠚⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⡠⠄⠀⡀

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠀⠀⠐⠢⡀
⠀⠀⠀⠀⢀⠼⣁⠈⠐⠒⠒⠒⢒⠉⡸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢄
⠀⠀⠀⠀⣼⡀⠀⠈⠉⠁⠀⢸⣿⣯⠠⢞⡄⠀⠀⠀⠀⣀⣀⡀⠀⡾⢟⣛⣆⠠⠔⠈⡩⠃⠀⠀⠀⠀⠀⢀⠀⠀⡰⡃⠀⠀⠀⢈⠄⡀⠀⡀
⠀⠀⠀⠀⣧⣈⠉⠓⠒⠂⠀⣿⣿⣿⠔⢊⡇⠀⠀⠀⠸⠄⣀⣈⣸⠿⣛⣋⣙⡤⠴⠚⠐⠠⡀⠀⠀⠀⡠⠂⠀⠀⢱⡱⠀⠀⠠⢂⠎⠀⠀⠘⡄
⠀⠀⠀⠀⠷⣄⡉⠉⠉⠉⣉⣿⣿⣟⢊⣡⠃⠀⠀⠀⣠⠔⠒⠂⢹⡿⢛⣉⣙⠧⣀⠀⠀⣀⠆⠀⠀⠀⢱⡀⠀⠀⡠⢃⠒⠂⠒⢌⢢⡀⠀⢀⠂
⠀⠀⠀⠀⠘⣦⣀⡉⠉⠁⣀⠬⠟⠋⡡⠃⠀⠀⢀⠎⠠⠂⢀⠀⠁⠙⢧⣀⠼⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢓⣂⢈⡱⡁⠀⠀⠀⢨⠆⡠⠤⢥
⠀⠀⠀⠀⠀⠈⢷⡲⠭⠤⠄⠔⢒⡼⠁⠀⠀⠀⠐⠄⠀⠔⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠱⡙⠆⠄⠔⠃⡔⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠆⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡰⢁⠂⠀⠉⢆⢣⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠒⠐⠁⡎⠀⠀⠀⢈⠎⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⡀⡔⠁⠅⢀⠀⠀⠀⠀⠀⢠⠓⡄⠀⠀⠀⠀⠘⠦⠤⠤⠂
⠀⠀⠀⠀⠀⠀⢰⠠⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣂⡀⢱⠀⡴⠊⢁⠇⠀⠀⠀⠀⡇⢀⠆
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⡁⢨⠨⠀⠊⠉⠁⠢⠀⠀⠀⠈⠁⠀⠀⢀⠤⠀⠒⠂⠀⠐⠒⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⣀⡉⠭⠭⠅⢐⡀⠀⠀⠀⠀⡠⠊⠁⢀⠆⠀⠈⠙⡖⠒⠁⠀⠀⠀⠀⠀⠀⢰⡅⢀⣀⣀⣀⡀⠀⠠⢾⠔⢁
⠀⠀⠀⢀⡀⠠⠊⡠⠔⠂⠉⠀⠀⠀⢀⠠⠈⡇⠀⠀⠀⢰⠀⢀⠔⡏⠀⡼⣀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠠⠊⡁⠀⠀⠀⠀⠀⠀⢀⠉⣩⠁
⠀⠀⠀⣅⠈⠻⡎⠀⠀⠀⠀⠀⠒⠈⢁⠀⢀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠧⠒⠦⠚⠦⠈⠢⠀⠈⢰
⠀⠀⠀⠙⢦⡀⠱⣄⠈⡉⢉⡀⢰⠄⠘⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣅⠈⠉⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⡀⠀⠀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢤⠮⠄⠴⠶⠶⠶⠶⠶⠶⠶⠶⠾⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠞⠀⠀⢡⡀⠀⠀⠀⡠⠒⠈⠁⠀⠀⠸⡐⠀⠀⠀⡀⠀⠀⡀⢀⠀⢐⡘⠀⠀⠀⠀⠉⠒⢤⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⢒⠲⢤⡀
⠀⠀⠀⡴⠁⢰⢀⡄⠀⠳⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠁⠀⠀⠈⠁⢀⡏⠀⠀⠀⠀⠀⠀⣀⢴⠀⠀⠀⢀⠴⢋⣄⠒⡔⢱⢨⣁⠀⠙⡄
⠀⠀⡸⢠⠀⠸⠛⠔⠈⠀⠱⡄⠀⢆⠈⠐⠒⠐⠆⠄⠰⡆⠄⠠⠀⠀⠀⠀⠀⣸⠀⡤⠄⠀⠀⠒⠈⢀⠆⠀⠀⡴⠁⠀⠨⠿⠆⠱⠂⠃⠁⡆⠀⢰
⠀⠀⡇⡌⣀⣰⣀⣠⣦⣠⠆⢱⠀⠈⡆⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⠀⡠⠀⢀⠁⠀⠁⠀⠀⠀⠀⠀⡎⠀⠀⡞⢰⡆⡁⢀⠒⡆⠘⣦⣼⢼⡡⢀⠇
⠀⠀⡇⠷⠱⠞⢋⠿⠃⣾⡀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠣⡀⠈⠁⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠸⠀⠆⢁⠘⠟⠚⠞⠋⠙⠀⢀⡴⠋
⠀⠀⠘⢄⠀⢰⠁⢀⡰⠃⠀⡜⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠉⡲⠶⠚⠁⠀⠀⡀⠀⠀⠀⠀⠰⠁⠀⠰⠃⠀⠀⠨⠤⠤⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠑⠠⢍⣁⣀⠤⠊⠀⠀⠀⠀⠀⣱⠀⠀⠀⠃⠈⠁⠹⠇⢀⡭⠉⠉⠙⠁⠐⠂⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⢉⣩⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⢀⣤⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⢀⣴⡿⠛⠉⠀⠀⠀⠀⣀⣠⣤⣤⠶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⣠⠟⠁⠀⠀⠀⣠⡴⠞⠋⠉⠁⢀⣠⠞⠋⢀⣤⣾⣿⣿⡿⢿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⣰⠋⠀⠀⣠⣴⠟⠉⠀⠀⢀⡠⠖⢋⣠⣴⣾⣿⢟⣩⣾⠟⠀⠘⣿⣿⣎⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢰⠃⠀⣠⣾⡟⠁⢀⣠⣔⣮⣵⣶⣿⣿⡿⢟⣫⣴⡿⠛⠁⠀⠀⠀⣿⣿⣹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠃⢀⣼⣿⣯⣶⣾⣿⣿⣿⣿⣟⣻⣭⣷⣾⠿⠛⠉⠀⣴⠶⠖⠢⠀⣿⣿⡏⢸⡇
⠀⠀⠀⣀⣀⡀⠀⣿⡇⠀⠀⣾⣿⣿⣿⣿⡟⠙⠛⠛⣛⡛⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⣿⣿⡇⠘⠀⡀
⠀⡰⢋⣀⡀⠉⠀⠸⣇⠀⢰⣿⣿⣿⣿⣿⡏⠳⡶⠛⡿⣿⣷⡄⠀⠀⠀⠀⠀⢠⡾⣿⣿⠻⣶⣿⣿⠇⠀⢠⠇
⠀⠀⡊⠀⠁⠀⠀⠀⠹⡄⢸⣿⢿⣿⣿⣿⡇⠀⠙⠄⣳⣟⠋⠀⠀⠀⠀⠀⠀⠈⢒⣿⡛⠐⢹⣿⣿⠀⢀⡾⠀⠀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣿⡌⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢀⡾⠁⠀⢸⡀⣀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⠺⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣼⣿⠏⡰⢫⠇⠀⠀⠘⠛⠃⠀⠀⢸
⠀⠀⢀⠴⠊⠁⢀⣀⡀⠀⠀⠢⡙⣆⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠈⣀⡈⠁⠀⠀⣠⣾⡿⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⢰⣏⠀⠀⠀⠀⠀⠉⠓⢄⠀⠘⠜⠄⠀⢸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⣀⣴⣾⡿⠋⠀⠀⣠⠏⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠈⠁⣠⠤⠒⠀⠀⠀⠀⠀⢳⠀⠐⠀⠀⣼⣿⡇⣿⣿⡿⠀⠈⠉⠛⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⢀⡀⠀⠢⢄⣀⣀⡠
⠀⣠⠎⢁⡴⠚⠁⠀⡀⠀⠀⠀⠃⠀⠀⢠⣿⣿⡇⣿⣿⠃⠀⠀⠀⢸⡟⢸⣿⠁⠀⠀⠀⠀⣤⡀⡴⢻⣇⣀⠀⠀⠀⠁
⢰⠃⠀⣾⠁⠀⠀⠚⠃⠀⠀⠀⠀⠀⢠⣾⣿⡿⢰⡿⠁⠀⠀⠀⠀⢻⣇⠀⠙⢦⠀⠀⠀⠀⠣⢘⡀⢋⡉⠉⠳⣄
⡟⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⣾⠁⠀⠈⠂⠀⠀⠘⢿⡄⠀⠀⠀⠀⣠⢒⣡⢚⠛⢄⠲⢤⡤⠞⠃
⣇⠀⠀⠀⠙⠻⢶⣶⣶⣶⣾⣿⣿⠿⠛⠁⠀⢠⡇⠀⠀⠀⢰⠀⠀⠀⠀⠻⣦⠀⠀⠀⠉⣽⠁⠉⢸⡄⠀⠀⢷
⠘⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀⣠⠞⠙⢦⣀⠸
⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⠟⠁⠀⠀⠀⠈⠓⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⢧⡀
⣠⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣉⣢⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠌⠉⠉⠉⠪⢢⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠌⠀⠀⠀⠀⠀⠡⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠸⢁⠀⡠⡄⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⣠⠀⢤⠲⡏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠂⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⠸⠖⠒⠒⠒⠒⠒⠒⠶⠞⠀⠀⠀⠈⣥⡛⡟⡛
⠀⠀⠀⠀⠀⠀⠰⡟⢢⠤⢄⠀⠛⢤⡀⣀⣀⣀⣀⡠⠂⠀⢸⠁⠀⠀⠈⡇⡗⠲⠶⢶⢠⣤⣤⣄⣀⣀⣤⣶⠘⠓⠒⠒⠒⣤⠾⠿⣏⡛
⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⠜⠁⠂⣤⡀⢁⡅⠀⢠⡀⠀⢀⠸⠶⠶⠶⠶⠇⡇⠀⠀⣾⡌⣿⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠐⣴⠁⠀⢀⣀⣀⡀⠀⠘⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣈⠉⠈⣅
⠀⠀⠀⢠⠀⠀⠚⠁⠀⠀⠈⠉⠈⠙⠉⠂⠐⠂⠂⠀⠓⠐⠓⠀⠀⠀⠀⠘⠃⠛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⡀⢸⡇⠀⠀⢹⠄
⠀⠀⠀⠀⢹⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⢻⡟⠛⡟⠛⣟⠛⣿⠛⣻⠛⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡄⢀⡖⠓⠒⠒⠚⢲
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⡇⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢁⠀⡀⠀⠀⠈⢀⠀⣲
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⡇⠀⢸⠀⡇⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⡀⢸⠉⢰⡖⠘⣿⠒⣶⠂⡒⡎⢳⠀⢸⡇⠀⣧⠀⣸⣠⣧⣤⣷⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠄⠀⠠⠦⠀⠀⠠⠄⠀⠶⠇
⠀⠀⠀⠀⠀⡃⠨⠄⠸⡇⠀⠷⠀⢿⠀⠅⠇⠸⠀⠸⢧⡤⠿⠠⠼⡿⠓⠂⠛⢻⡿⠶⠤⣤⠠⠤⠤⠤⠤⠠⠄⠐⠒
⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡃⠀⠀⠀⠀⠀⠀⠀⣺⢴⣶⣶⠿⢶⣿⣷⣶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠐⠦⠾⠤⠤⠴⠴⣏⠀⠀⠉⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠴⠤⠶⠖⠚⠋⠉

⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡞⠀⠐⣀⣀⠀⢄⠀⠰
⠀⠀⠀⠀⠀⣄⣠⣷⠎⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⣀
⠄⠀⠀⠠⡀⢀⠁⠀⢀⠄⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⡀⢤⡀⠀⠀⠀⠍⢻⠁⢀⡴⢃⣀⠈⠃⠐⠀⣠⣤⡘
⠉⠉⠘⠀⠀⠀⢘⢘⠀⠊⠀⢴⣆⣤⠠⢠⣖⣿⣿⡓
⠀⠠⠇⠀⠀⠀⣰⢣⠀⠀⠴⡶⢟⣠⡶⠟⠋⠉⢉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠓
⠃⢘⡜⠁⢠⢠⣿⡴⡒⠂⡾⣿⠟⠁⠀⣠⠖⠓⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢸
⢀⡏⠀⠠⢃⡾⠑⠃⢁⡞⣰⠏⠀⠀⢠⠁⠀⣤⡼⠀⠀⠈⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠆⠀⡆
⣸⠃⠀⢀⡞⠁⡀⢀⡞⣄⡇⠀⠀⠀⠈⡄⠈⠓⠒⠂⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣴⣆⡀⠀⠃
⡇⠀⠀⠔⢊⠐⠀⠾⠣⡈⣧⠀⠀⠀⠀⠈⠂⢀⢤⡴⡶⣦⠀⢀⡀⠀⠺⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠂⠿⠀⠀⠀⠀⠀⠙⡣
⠇⠀⠀⢀⡏⠀⠀⠃⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⣠⡤⠤⢀⠈⠉⠃⢾⡧⠾⠤⠀⡀⠀⠀⠊⣿⠇⡀⠘
⣦⠰⡁⠸⠁⠀⠀⡅⡄⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⣩⠅⠀⠑⠀⠱⣆⡔⠀⠀⠀⠀⠀⠉⠢⡄⠀⠈⠒⠁⠤⡀
⡟⠁⢇⠎⠀⠀⠀⢧⠀⠀⠀⢀⠙⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠴⠶⠋⠉⠈⠡⣞⠁⠀⣺⠀⠀⠀⠀⠀⠠⡶⢀⡼⠈⠂⠀⠀⡀⠈
⡇⠀⠀⠀⠀⡄⠀⢰⣌⠢⠀⠀⠉⠐⠈⠑⢤⣄⣀⠀⠀⠀⣀⣤⠤⠶⠊⠀⠀⠀⠀⠀⠀⠀⠈⣤⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣷⠀⡀⠀⠀⠁⡄⠘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠂⠀⠀⠀⠀⠀⠀⡠⠒⠂⠂⠔⢘⠃⠀⠀⡀
⠹⠗⠀⠀⠀⠀⠀⠠⠀⠙⢦⣈⡁⠀⠀⡀⠀⠀⠘⠢⢤⣀⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠒⢢⡈⣄⠀⠀⠀⢈⢀⡀⠀⠀⠀⠀⠀⣀⡤⠄⢀
⠀⠒⠀⠀⠀⠐⡀⠀⠅⠀⠃⠙⠶⣀⣈⠢⠐⠒⠐⢀⡰⠊⠀⠀⠀⡠⢚⠕⠀⠀⠀⠠⠀⠀⠻⢼⡇⠀⠀⠀⠹⢄⠀⠀⠀⠂⠨⠥⡀⠀⠀⠐⠤
⡀⠀⢦⠈⠀⠀⢁⠀⡄⠀⠑⢄⠐⠈⠙⠷⠶⡶⢦⡤⡤⢄⡶⠊⠁⠄⠀⠀⠀⠀⠀⣀⠤⠀⠈⢛⢷⠀⠠⠀⠀⠀⠉⠀⠀⠠⠤⣤⠤⠄
⠀⠈⠐⣷⡀⠀⠠⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠞⢀⠊⠀⠀⠉⠀⠀⠀⠀⠀⢀⠠⠐⠚⠺⢦⠀⠀⠀⠀⢀⣀⡳⠠⠐⠂⠀⠘⠢
⠀⠀⠀⠘⢷⣜⠀⠀⠀⠀⠄⠂⠐⠀⠀⠁⠒⠈⠁⠀⠈⠀⠀⠀⠀⠀⠐⠈⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠘⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⣈⡉⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⢫⠒⠒⠰⠶⠖⠂⠀⠀⠒⣄
⠒⠀⠀⢄⠀⠀⠈⠛⢤⡀⠘⢆⠂⠑⢀⠀⠠⠤⣀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠒⠀⠀⠀⢸
⠀⠀⠀⠀⠑⡐⠆⣀⠀⢉⡲⠮⣷⣦⣤⣬⣕⡢⠤⠍⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠲⣿⠀⠀⠋
⠀⠈⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐
⡿⢿⠿⠿⡿⡻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⢿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⣿⠏⠀⠀⠀⣴⣾⣿⣦⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣿⡏⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠸⠿⠿⠛⢀⠶⠄⠘⢿⣉⠀⠀⠀⠀⠀⢠⠃⠀⣿⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣼⡿⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠈⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠀⠐⡡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠋⠀⢀⣤⠟⠀⠹⣿⣿⣿⣶⣶⣶⠆⠀⣰⠀⢀⡷⠀⢸⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣶⠿⠋⠉⣿
⠀⠀⠀⠀⢀⣠⣿⡋⠉⠀⢠⣾⣿⣄⣀⣠⣀⡙⠻⠿⠿⣿⣿⣦⣤⣿⣤⣼⣿⣤⣾⣿⡋⠀⢀⣀⣠⡾⠿⣦⡀⠀⠀⠀⠀⠀⣴⡿⣿⠀⠀⠀⠀⠀⣰⡟
⠀⢀⣴⠾⠛⠉⠉⠉⠻⣆⣸⡟⠀⠉⠉⠙⠛⢿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⡿⠿⠿⣧⠀⠘⢷⣦⣤⣤⣤⣰⣿⠀⠘⠷⠶⣶⡶⠟⠋
⠀⣾⡇⠀⢀⣤⣤⡀⣀⣿⠟⠁⠀⠀⠀⢠⡄⠀⠙⢷⣿⣟⠛⠛⠛⠻⣿⡟⠹⣿⣛⣉⣀⣀⣠⣤⣶⣿⣶⣦⡄⠉⠁⢨⡿⠟⠃⠀⣠⣶⡾⠟⠀⠴⠂⠄
⠀⠈⠛⠛⠋⠉⠈⠙⡛⠁⡀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⠿⠿⠷⠶⣾⣿⠃⠀⣿⡛⠉⠉⠉⢉⣉⣉⣿⠇⠹⣿⣀⣴⣿⣦⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠀⠀⢠⠀⠻⢷⣦⣤⣄⣠⣤⣴⣿⠀⢸⣿⣟⡛⠛⠻⠿⣿⣿⡁⢀⠆⠙⠛⠋⠀⠹⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⣉⣽⣿⡄⢸⣿⡛⠿⣿⣷⣶⣤⣽⣿⢠⡇⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠟⢋⣩⣿⣷⣿⣿⣿⣦⣄⡙⢿⣯⡉⠀⠈⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣯⣴⡾⠿⣿⣿⣁⣠⣿⣿⡿⠿⢿⣷⣿⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠿⢿⣶⣤⣶⠟⠙⠷⣦⡤⡈⠙⣿⠟⢁⣤⣶⠟⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⣦⡀⠀⠀⠈⢀⣀⡀⣠⡿⠀⠀⣠⣿⠀⠈⢻⣇⠀⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠁⢸⣿⣤⣤⣾⠿⠛⠛⢿⣤⣴⠾⠋⠙⠷⣦⣤⣿⣦⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⠻⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠈⢻⣧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠈⠙⢻⣦⣤⣄⡀⠀⠀⠀⠘⠟⠀⠀⠀⠀⣿⡷⠾⢿⣷⣾⡏⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠛⣿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢈⣩⣿⠆⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⠃⢰⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣾⠟⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⢷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣤⣄⡀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢳⡄⠈⢹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣧⣀⠀⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠿⠛

⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠈⣿⠀⢸⡇⠀⢠⡤⠖⢒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⣀⣉⣉⣉⣭⣭⣤⣤⣬⣽⡛⢳⠀⠀⣀⡀⣀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⢇⡼⠋⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡇⢸⡏⠀⠈⣷⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠈⠳⠤⠔⠃⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣄⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⠀⣹⠃⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠒⠊⠁⠀⠀⡇
⠀⠀⠀⣿⠀⢸⣇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠈⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⠉⠙⢣⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠻⠤⠤⠟⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡄⢀⣤⠤⣤⣄⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⡏⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⢖⣋⣀⣼⠁⠸⣇⠀⣀⡟⠀⠀⣿
⠀⠀⠀⢹⠀⠀⣿⠀⠘⠓⠒⠒⠒⠒⠛⠒⠛⠛⠛⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⣸⣿
⠀⠀⠀⠈⢻⣷⡿⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⢳⣶⣿⣿⠟⠛⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⢸⡟⠁⠏⠹⣿⣄⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠀⠀⢿⠉⠁⡏
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠁⠈⠉⠙⠛⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢀⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⣾⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢡⡉⢯⠀⡇⢀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠛⠃⡰⢸⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠈⢷⣍⣈⡳⢿⣌⢣⡘⡔⡆⢲⠀⡇⡜⢀⡀⢐⡴⠋⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀
⠀⠀⠀⠀⠀⠈⠉⠀⢀⣿⡧⠙⡀⠁⢘⣨⣤⡒⠉⠛⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠉⠉⠉⠁⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠾⠁⠀⠉⠀⠀⠀⠀⠀⠉⠛⠛⡛⣥⡀
⠀⠀⠀⠀⢀⡤⠞⣽⠃⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠻⣆
⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠈⡇⠀⠀⠀⠀⠸⣦⣀⣤⠤⠖⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⡽
⠀⠀⠀⠀⠛⠦⠄⢻⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢷⠚⠻⢶⡀⠀⡟⠀⠰⡀⠀⠓⠦⠤⣤⠤⠤⠤⠤⠤⠤⠞⢯⡉⠉
⠀⠀⠀⠀⠀⠀⡾⠛⠛⠓⠶⠖⠒⠚⠃⠹⡇⠀⠀⢹⠀⠀⣸⠃⠀⠳⣄⡣⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠿⠖⢒⢙⡶⡟⠁⠀⢀⣰⡞⠛⠛⠛⢷⣦⣄⣀⣀⣀⣀⣀⣀⣠⣴⢋⣀⣀⡀
⠀⠀⠀⠒⠀⠀⠈⠍⠛⠛⠛⠛⠿⠿⠿⠅⠻⢿⣸⠗⠛⠁⠀⠀⠀⢀⣘⡛⣒⡚⣒⣂⣉⡉⠛⠉⠉⠉⠉⠁⠀⠨⠭⠭⢥⣤⢄
⠒⠒⠀⠀⠀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⣉⣁⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠡⠈⠠⠭⠭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣀⣠⠴⠶⠶⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡀⢀⡤⠖⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⠟⠹⣶⠋⠀⠀⠀⠻⣄⠀⢀⠀⠀⢠⡴⢰⣾⣇⡼⢧
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⢠⣌⠳⠖⠋⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⢀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠟⠀⠀⠀⢹⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠸⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠛⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢷⣿⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠙⠿⠁⠀⠀⢀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢻⣆⠀⠀⠀⠀⠰⣤⡀⢀⣠⡄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⢳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⢷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠀⢠⣀⠀⢉⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣾⣇⠀⠀⢿⣷⣤⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠉⠉⠛⢳⡶⠤⠶⠚⠛⠉⠀⠀⠘⣏⠀⠴⠤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⠤⠚⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠃⠀⠀⣿⡉⣹⠏⠉⠉⠉⠉⢁⣀⠀⣼⠿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠏⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⡏⢉⣿⣿⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⢋⡴⠲⡄⠀⠀⣠⠖⠲⡄⠀⠀⠀⠉⠊⢹⡟⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⠈⠳⠞⠃⠀⠀⠛⣤⠾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⣄⠀⠘⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⠋⢙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡴⠇⠀⠀⠀⢳⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⡀⠀⠀⠙⠓⠋⠀⠀⠀⢠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡸⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⡷⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠉⠉⠀⠀⠀⠺⣅⣿
⠀⠀⠀⠀⠀⠀⢸⡿⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠿⠀⠀⠀⠀⠀⠀⢀⣀⢼⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠙⣿⡽⣟⠓⣂⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⠾⣿⠛⠊⢳
⠀⠀⠀⠀⢠⡎⠀⠀⢰⡟⠀⡏⠀⠀⠀⠀⠈⠘⡿⢻⡄⠈⠉⠉⠉⠛⠛⢻⣿⠹⠉⢻⠀⢹⠀⠀⠘⡆
⠀⠀⠀⠀⠘⢧⣄⡀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢃⢸⡇⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠹⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⣀⣠⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠿⠶⠶⠶⠶⠾⠿⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⣠⡀⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⠁⠀⠈⣻⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣺⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡜⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⣨⠟⠛⠷⣤⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣅⣀⣀⢀⣀⣈⣉⣉⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⣿⠿⠿⡿⠿⠿⢏⠹⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⡟⣻⣛⠛⠛⠛⣛⡛⣛⢻⣿⣿⠛⠛⠛⠿⠿⠟⢻⠛⠛⠻⣿
⣿⣷⣿⣶⣶⣷⣾⣶⣾⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⢐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠈⠐⠢⠄⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠄⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⡀⢀⠀⠀⠉⠐⠂⠀⣀
⠀⠀⠀⠀⠃⠁⠀⠀⠀⢐⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡤⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠤⠄⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⣤⢬⠽⢭⠂⣠⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄⡀
⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⡠⠀⠉⠉⠑⠢⠤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠲⠄⣠⠀⢉⠏⠀⠀⠀⢠⠐⢲⡆⠀⠀⠀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣸⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠒⠀⡂⠐⢀⠜⠁⠀⠀⠀⠀⠀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡎⠀⡀⠀⡀⠈⠀⢿⠁⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⡐⠀⠀⡎⢀⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡀⠖⠂⠐⠾⢡⡊⣀⣀⣀⣀⠀⠀⢀⡀⠀⠤⣭⡖⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⠤⢒⠡⠶⠙⡿⠶⢖⢤⠞⠛⠨⠲⠤⡑⢬⡈⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⡄⠁⠁⡄⠸⡍⠛⠙⠃⠛⠓⠚⠁⢨⠀⠀⠀⠀⠀⠈⡐⠤⡀⠀⠀⢘⠉⢳⣠⣄⡀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⡔⠒⣇⡀⠯⠂⠒⣰⣤⠖⠁⠀⠀⠑⢄⠀⠀⠀⠀⠢⠀⠀⠑⠢⢄⣀⠉⠐⣯⠛⠻⢅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠑⢀⡠⠄⢖⠈⠀⠉⠑⡄⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠁⠀⠀⠤⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠙⠄⠀⠘⢤⠀⠐⠂⠀⠀⠀⠸⠀⠀⡀⠤⠤⠈⢶⣄⠀⠀⠀⠀⠑⢄⠀⠁⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠑⠢⠤⣀⣀⣀⡜⠚⠀⢀⠀⠀⡀⠌⠀⠑⠤⡀⠀⠀⠀⠑⢄⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠬⠖⠀⠀⠀⠀⠙⠦⠤⠤⠤⠴⠒⠒⠂⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⣀⡄⠀⠀⠀⡆⠀⠀⠠⠃⠀⢀⠀⠀⠀⠟⢀⠁⠀⠈⢀⣤⡀⠀⠀⢘⣀⡀⠀⠐⠃⠀⠀⠀⠀⠀⠊⡀⠀⠠
⣀⢠⠠⢄⡀⠀⢸⠃⢠⠩⣄⡀⡄⠥⡀⠀⠡⡏⢀⡌⢄⣀⣤⠤⢅⠀⠀⣼⠀⡄⠡⣀⡠⡠⠤⡀⠈⢡⠃⢠⠉
⢙⡉⠀⣼⠤⠐⢂⠀⠬⠀⠈⡋⠀⢠⠥⠄⠒⡀⠤⠁⠀⢉⠁⠀⡬⠄⠐⠀⠠⠄⠀⠉⡉⠀⣴⠥⠀⠂⠀⠬
⠀⢰⠤⠷⠀⠂⡼⠀⠀⡤⠀⠀⣦⠼⠄⠀⠠⠂⠀⢦⠄⠀⣸⡴⠇⠐⠀⠖⠀⠰⡤⠀⢰⣤⠾⠀⠂⡸⠂⠀⡦
⠀⠠⠀⠀⠉⠐⢳⢃⡀⢲⠀⠀⠅⠀⠈⠀⠛⠏⣀⠐⡆⠀⠨⠀⠀⠁⠘⠾⢀⡑⢷⢀⠠⠅⠀⠉⠐⠳⠇⡀⢺

⠀⠠⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡠
⠀⠀⢆⠀⢠⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣀⠼⠂⠉⡥⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠀⢀⢆
⠀⠀⠈⡄⠀⠂⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀⠇⠀⡀⠤⢾⠁⢀⡤⠞⢁⠀⠀⢀⠠⠌⠒⠀⠀⡊⠲⢘⠋⠀⠀⠀⠈
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠄⠂⠀⠀⠀⠀⠀⠇⠐⠺⢄⠀⢠⠟⠁⠀⠀⠏⠀⠀⠀⠀⠈⠀⡠⡀⠀⠀⠀⡀⠄⢀
⠀⠀⠀⠀⢱⡀⢀⣀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡀⠣
⠀⠀⠀⠀⡀⠋⠁⠀⠚⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡗⣀⠄⠒⠉⣉⣱⡄⠀⠀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠹⣡⠔⠈⠁⣀⣄⣱⠀⠀⠀⠀⠇⠀⠸⠀⡆⠀⠀⢸⠀⠀⡇⠀⡸⠀⠀⠾⠀⢸⠀⠀⠀⢍⠀⠚⠿⠇⠀⠀⠀⠀⠐⠈⡀
⠀⠀⠀⠀⠀⠩⣤⠊⠁⠀⠀⡸⠀⠀⠀⢰⠀⠀⡆⠀⠣⠀⠀⠸⠀⠀⡇⠀⠑⠀⠀⠀⠀⠸⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠤⠚
⠀⠀⠀⠀⠀⠀⠈⢦⠄⠐⠊⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⡶⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈
⠀⠀⠔⣠⠀⠁⠀⠘⠀⠀⠀⠀⠈⠉⠀⠀⠬⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠉⠈⢢⠀⠀⢠⠐⠀⠀⠀⠐⠀⠂⢀⠄
⠀⠄⠐⡸⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠽⠤⠴⢼⣶⣶⠾⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠠⠐⢡⠀⠠⠁⠀⠤⠀⠠⠀⠠⠄⠀⠲
⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠘⠞⠀⠈⠀⢀⠶⠣⠔⠲⣦⡄⠜⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠁⠀⠀⠀⠀⠐⠂
⠀⠀⠄⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⠄
⠀⠆⢁⠀⠈⠀⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠀⠀⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠄⢀⠑⠀⠐⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠄⠀⠀⠐⠂⠀⠀⠀⠐⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠉⠄⠑⠄⠮⠀⠁⠀⡀⢈⠀⠀⠀⠁⠀⠀⠀⠈⢷⡂⣠⠠⠀⠀⣂⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⣾⠏⣀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠞⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣄⣀⣀⠀⢻⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣿⣀⣿⣤⡟⠿⠁⢼⡟⠛⠛⣧⣀⣿⣆⠀⠀⠀⠀⢵
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣃⣼⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡂⢠⠟⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⠄⠀⢸⠃
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⡄⢀⡎
⠀⠀⠀⠀⠀⢹⣸⣇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠆⣸⠃
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋
⠀⠀⠀⠀⠀⠀⢹⣆⠹⣦⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣠⡾⠃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠼⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣦⣤⣄⣀⡀⠀⠀⢀⣀⣠⣤⠞⠛⣿⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠙⢿⣄⠈⠉⠙⠛⠚⠉⠉⠁⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠛⠿⠶⢶⣤⣀⣀⣀⣤⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣠⡛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠶⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠶⣦⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢾⡷⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣧⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⡀⢠⣴⠀⢶⣾⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣦⣾⡿⠿⠛⠉⠁⣿⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⢻⡃⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠄⢦⣤⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠶⠶⠶⢶⣤⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⣤⠚⠛⠛⠛⠛⢳⣄⣼⠋⠁⠀⠀⠀⠀⠈⠙⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢾⣧⣄⠀⠀⠀⠀⠀⠀⣨⣿⣤⣤⣀⣤⣤⣤⡤⠶⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣿⣶⣶⣾⡛⠾⠉⠈⠙⠛⠋⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠲⠙⠓⠉⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠉⡻⠛⠲⢤⡀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⡎⠀⢀⣀⣀⣀⠤⣤⣤⠤⢂⣁⣀⡀⠀⠹⡄⢠⠦⠀⠀⠠⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⢉⣉⠀⣤⣤⡄⠀⠀⠀⣤⡀⠀⣉⡑⠂⡗⠀⠋⠀⡀⠀⠑⠨⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡚⢡⣿⣿⣿⣷⣶⣤⡄⢠⣤⣶⣾⣿⣿⣿⡆⠙⡄⠀⠞⣡⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠻⣿⣿⣽⣿⡿⠀⠀⢿⣿⣯⣿⣿⠟⠠⢚⣷⠀⠀⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡐⣚⠁⠈⠛⠛⠛⠑⠛⠚⠊⠛⠛⠋⠁⠀⣐⠃⡼⢂⡠⠀⠀⠀⠀⠀⠮⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢧⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠⠏⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⠞⢉⠉⠒⠤⡙⢦⣄⣀⣀⠀⠀⠀⣀⣀⣤⠞⠁⠀⠀⠀⠊⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⡍⠀⡀⠀⠀⠀⠈⣦⠤⠽⢿⣉⣉⣹⠿⠷⠦⢤⠀⡀⠤⢄⠄⡀⠀⠀⠀⢀⠀⠤⠤⠒⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⠤⠄⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⠉⠉⠁⠀⠀⠀⡞⠘⠀⠠⠀⢀⠈⠆⠀⠀⠀⠳⣤⡀⠀⠀⠐⠴⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠐⠁⠠⠒⢄⠀⠀⣸⡀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠠⢹⣦⣌⠛⠿⠶⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠰⠀⠀⠀⠁⠐⠙⡇⠀⠀⢀⠘⠄⠀⠀⢠⡇⢀⠀⠀⠀⠂⠀⠀⠀⠁⠌⢉⡙⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣄⠤⢤⣿⣄⣀⡴⠛⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠀⠀⢀⠢⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠘⠁⠀⠀⠀⠀⠉⠑⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⣿⠃⠉⠁⠀⢬⠀⠀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠊⣾⠁⠈⠉⠉⠉⠉⠀⠀⠘⣿⣿⣉⠀⠀⠀⢀⡴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡷⠀⠀⠀⢠⣴⠀⠀⠀⠀⢿⠈⠻⢃⠂⠤⠞⠁⠀⠀⠤⠀⠴
⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢸⢹⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡂⠀⠀⠄⡀⠀⠈
⠀⠀⠀⠀⢸⠀⢀⠀⠈⠐⠄⣸⡆⠀⠀⠀⠀⠀⢀⣠⠊⣿⠀⠀⠀⠀⣾⠘⡆⠀⠀⠀⠀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢄⣸⣀⣀⣨⠉⠑⠉⠉⠀⠀⠉⡇⠀⠀⠖⠋⠀⢧⣤⡀⠤⠄⡞⠅⠀⠀⠀⠁⠘⠁⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠈⠻⠤⣄⣠⠶⣹⠋⠉⣹⠉⡁⠀⠰⠀⠀⣠⣖⣠⠀⡄⠀⠀⠀⠀⠀⠀⠄⣴⡒⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠈⠠⠴⠃⠠⠁⠀⠀⢀⣴⢋⡽⠁⠀⠀⠀⠀⠀⠀⡲⠘⠻⠶⠻⢦⣄⠀⠀⠃⠉⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣷⡏⠀⠀⠀⠀⡀⠀⡜⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⡆⠀⠀⠀⠐⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠣⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠂⡠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣷⣦⣤⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠈⠹⠛⢩⣿⣿⣿⣿⣿⣿⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢈⠋⠁⢸⣿⠻⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⢨⠀⢠⢫⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠿⠤⠖⠒⠇⠀⢀⣀⣸⡇⠘⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⡠⢀⣤⣤⣤⣄⣀⣀⣀⣀⣀⣸⡇⢀⠀⠚⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠹⣷
⠀⠀⠀⣴⢿⣿⠙⠋⠿⠸⡟⡛⢿⠟⠉⠁⠀⡿⠋⠁⢀⡤⣄⡠⠀⠀⢀⣤⣶⠟⠉⣀⣠⣄⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠃⢀⣀⣀⡀⠡⣧⣄⡀⠠⣴⡾⠃⣰⡶⠺⣇⠯⣀⣀⡾⠛⠋⠀⠀⢀⣈⣿⣿⣿⠖⠒⠀⣀⡀
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠛⠀⠈⢿⣧⣀⠈⠑⠈⠙⠋⠉⠀⠀⣀⡀⠈⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣴⠿⠛⠙⠳⣤⣤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣠⠎⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠖⠂⠀⢀⡜⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠒⡆⠀⠘⢧⡶⠟⠉⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠘⠗⠁⠀⠀⠀⠀⠀⣤⠀⠊⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿⠀⠀⠀⠀⠀⠀⢊⡨⠐⠒⢦⠀⠀⠀⠀⠀⠀⡰⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠴⢒⢿⣄⠘⡄⠀⣠⣾⣾⣿⣷⣤⢔⢾⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣉⡉⠀⠀⣼⣿⣿⣿⣟⢯⠎⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⠟⡧⠰⠯⢄⡀⠀⢀⣠⠤⢠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢣⠞⠑⣧⠀⠀⠙⢾⡋⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣿⠟⣵⣋⡤⠶⠛⠳⣤⣀⣠⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⢢⡼⠋⠉⠉⡹⢫⣞⡠⢿⣶⡒⠒⠒⠀⠩⢩⡤⢀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⠞⠀⠀⢀⡞⡵⠁⠙⡄⠀⠉⠻⣷⣄⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣧⠀⠹⣆⡠⣴⣫⠞⠀⠀⠀⡇⠀⢀⣤⣾⣿⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣠⠴⠛⠉⠁⠀⠀⠀⠀⠈⠳⣤⠏⡐⢸⡃⠀⠀⢀⡞⠀⠀⢻⣿⣿⠟⠙⠋
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢔⣵⠏⠁⠀⢠⠏⠀⢠⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠋⠁⠀⠀⡴⠃⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⠀⠀⢀⣼⠁⠀⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⠤⢤⣤⣏⠟⠀⠀⠀⠀⠰⠿⠛⠛⡟⠉⠉⣿⡏⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠇⠀⠀⠀⢀⠔⡁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⠰⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠢⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠀⢷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡠⠊⡀⠀⠈⠢⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡿⠀⠸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠤⠴⠚⢁⡠⠀⣈⠔⠊⠀⡤⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢒⣉⡥⢔⡉⠄⣀⠔⣉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠤⣚⣩⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠄⠀⠀⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠢⢀⠀⡁⠀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⢷⡤⣀⠀⠀⠀⠀⠀⠐⢄⡀⢠⣹⣥⣔⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡶⣦⢳⣱⣿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠁⠀⠀⠏⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣿⣮⡷⠉⠁⠐⢆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡃⣿⢿⣿⡿⣃⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢀⡜⠀⡄⠐⢇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⣄⠀⣭⡈⠀⣰⡈⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠛⠃
⠀⠀⠀⢀⣀⠀⢈⣀⠁⢉⡀⠉⣁⡉⢉⣩⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠉⠁
⠀⠀⢠⡋⠉⠁⠁⢉⡀⠉⣹⠚⠉⢓⠋⢉⡋⠁⠀⠀⠀⣠⣼⠾⣏⠙⣧⠈⣧⢈⣠⠤⠔⠚⠉⠉
⠀⠀⠈⠇⠙⠈⡃⠉⠛⠐⠊⠑⠘⠛⠃⢘⠋⠀⠀⠀⠀⡏⢹⡆⢹⣆⢽⣶⣾⡿⠃
⠀⠀⠀⠘⠃⡈⠛⠆⠛⠛⠀⠞⠛⢆⠘⠀⠶⠀⠀⠀⠀⠸⣿⣿⣷⣿⣾⣿⠛⠁
⠀⠀⠀⠈⠳⠶⡄⠜⠶⠤⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⠨⡝⠃⠀⣚⠠⠌⢹⡻⠦⣥⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡀⠈⢘⠷⢤⣀⣈⣵⡒⠜⢃⡴⠋⣛⣻⣿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠀⠀⠈⠐⠯⢁⠵⠔⣩⡿⠙⠈⠉⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢶⣴⠀⢳⢉⣶⢻⡇⢠⡴⠖⠚⠩
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⣀⠀⠀⠐⢀⣺⣖⢂⣸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣦⡙⠛⠟⠀⢸⡏⠀⠀⣠⢤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢉⠛⠳⠛⠛⢻⡯⡹⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡤⡼⠧⠤⠞⠛⠉⡇
⠀⠀⠀⠀⠀⠤⠀⠐⣷⠀⠁⠀⠒⢄⢚⡄⣿⡝⠯⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣄⠠⢀⡀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠝⠻⣦⡵⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡛⠊⠿⢶⣥⠴⡧⠤⠆⠂⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠓⠀⠀⡠⠀⠳⡟⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠅⠀⠀⠈⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣦⡇⢀⢓⣶⣾⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⡤⠀⡶⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠂⠰⠢⠠⠁⠐⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⠰⠀⡃⡄⠀⠐⠀⠠⠄⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡔⢀⠋⡇⡈⠀⠀⠐⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⢰⠼⠌⣍⠖⠃⠀⢀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⠠⠀⠠⠀⡐⠠⠀⠀⠀⣠⢌⣷⢎⠁⡉⢈⡮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⣈⢤
⠀⠀⠀⠀⡀⠀⢀⠀⢀⡲⣞⣁⠀⡡⠀⢀⢘⠀⠀⠀⠈⣡⠧⠑⣿⢮⣀⣙⠳⢷⣝⢄⠀⠀⢀⡠⠄⡀⠀⢀⢈⡀⡘⣾⡇⠄⠈⡡⢛⣀⠂⠀⠤⡀
⠀⠀⠀⢰⢲⠞⣁⡓⠏⡔⢿⣿⡿⠟⡊⢁⣠⠜⢦⠠⣬⣟⡣⠒⠉⠁⠉⠉⠳⣦⡙⠃⠙⠲⣷⣼⣷⡶⠛⣡⣤⠫⣉⣜⣗⣶⣶⣛⣾⠿⣖⣒⣋⣳⡶
⠀⠀⠀⣜⣛⡥⠥⠒⠒⠚⡳⠮⠝⣍⡉⠛⢫⢀⣕⣰⡼⠎⠀⠘⣧⣟⣦⣃⣣⢘⣐⣤⡴⠮⣿⠛⠿⠛⠻⠿⣟⡟⠿⡿⠟⢛⣃⣾⣷⣟⣿⣿⣷⣶⡍
⠀⠀⠀⢘⠂⠋⢉⣙⠑⢦⡙⠭⡒⢬⡛⠛⠲⣛⠋⣍⡴⡋⠠⣞⡲⠃⠻⣶⢿⣿⡞⠥⠤⣙⣾⢦⠶⠶⠦⡶⠶⠽⠷⠴⠿⡿⠿⠿⢿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⢨⣤⠤⠞⠉⠻⡶⣭⣝⢾⣆⢹⡓⠂⠺⠯⠴⠦⠖⣊⡥⠍⢳⣖⣛⣋⡉⠓⠦⣰⣬⣿⡷⠷⢶⡶⠷⣾⣾⣶⣶⣶⡶⠶⢶⠾⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⣀⠔⠙⢦⣑⢲⢖⢲⡈⠛⠾⠧⣶⡖⠒⠚⡋⠁⠂⠀⠳⠭⠷⠤⠘⠲⠦⠼⣿⣧⠴⣚⠥⠒⠱⢤⡉⠉⢉⡿⠊⠉⢠⣙⠑⢲⣈⢀⡠
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠈⠁⠀⠙⠙⠐⠒⠚⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠩⠙⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⢠⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠀⠀⠀⠁⠠⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠐⠖⠀⠀⠈⠢⡀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠃⢀⠀⢢⠀⠀⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠠⡀⠀⡠⠁⠀⠐⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⢊⠀⠉⡁⠀⠘⠢⢄⠀⠑⢄⠀⠀⠀⣀⡠⠔⠒⠒
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠑⢄⠶⡀⠀⠀⠀⠉⠦⡀⠑⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠀⠂⠀⠀⠀⠘⠂⠠⠄⠠⠤⠀⣀⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠁⠁
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⢐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠰⠀⠀⠀⠀⠠⠐⠀⠀⠘⠂⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⡂⢀⣀⠀⢀⠀⠀⡀⢲⠀⢸⡆⣀⢠⠀⠀⠄
⠄⠒⠀⠀⠀⠈⣶⣀⠀⢠⠤⠀⠀⠀⠇⠈⣤⡆⠴⠀⠈⠁⠐⠛⠿⢋⠓⠆⠅⡆⢥⣀⠡⠁
⣶⡔⠰⡂⡀⠀⠈⠉⠀⠀⠀⠀⠀⠰⠖⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⢦⣍⡑⠆⠛⠒⠈⠁⠀⣄⣀
⠉⠛⠒⠛⠋⠀⠀⠀⠒⠶⢖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠙⠷⠶⣦⣤⣴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣳⣶⣤⣄⣀⣀⣐⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⠂⠀⠀⠀⠀⠀⠀⠀⡀⢸⡿⣲⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢀⡀⠀⠀⠀⠀⣜⢣⡘⠛⠊⠀⡷⠲⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠼⠁⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⣤⠙⠉⠀⢠⠄⠦⢸⠫⣿⣧⣴⠦⠂⠇⣾⠚⠂⣀⠀⠀⠀⠀⠀⡠⢶⠀⠁⢀⠀⠀⠤⠄⠀⠄⠒⠂⠈⢀⡼⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠀⠁⠀⠘⢘⠀⠀⢿⣄⠉⠙⢲⡦⠰⡆⢈⢩⡩⢼⠀⠀⠀⠀⠊⠐⠛⠁⠰⠤⣀⠀⠂⠀⠀⠀⣀⣀⣴⣿⣧⣄⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠈⡏⢠⠚⠟⢶⣎⣭⡃⣬⠬⠄⣶⢳⠻⠁⠀⠀⠸⠀⠀⢀⡀⠀⠀⢀⠟⠁⡈⠉⠹⠟⢿⣿⠋⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣧⣤⣀⡔⣀⣼⠁⠖⢃⣚⣓⣈⢫⠡⢂⡀⠀⠀⠀⠀⠀⢀⣡⠶⣶⡎⠀⡠⠇⠀⣄⠀⠈⢨⠀⠀⠀⠀⠈⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠓⠟⠰⣿⣿⡟⠐⠀⡉⣩⣥⡌⠆⠖⢨⠇⠀⠀⠴⣢⣴⣯⡜⢀⢦⠴⠋⠀⠊⠀⠈⠙⢲⢯⣘⠀⠀⠸⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠁⠴⠌⠋⠀⣆⡀⢠⠸⠻⠀⠀⠀⠀⠁⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠓⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠀⠀⠠⠍⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢻⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠦⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⢉⡶⢀⠀⠀⠀⡀⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠉⠀⠠⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠂⠁⠐⠠⠾⠀⠀⠀⠐⠀⠈⠻⠷⣦⡄⢀⡀⠀⠀⠀⠀⠀⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⢢⠂
⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠳⢤⡀⠈⠙⠢⢄⣘⠓⠂⠀⣿⣀⡀⠀⠀⡀⠀⢀⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣦⣀⠠⠤⢤⢂⠆⠂⠐⠐⢢⡀⠀⠈⠀⠀⡴⢠⠀⠂
⠀⠀⠀⠀⠀⠉⠓⠀⢠⠀⣿⣿⢿⣶⣬⣿⣧⣴⣦⣹⡶⠾⠟⠾⢦⡄⠀⠀⠀⠀⢀⡀⠀⠀⣄⠀⠀⠈⠓⣶⣆⣼⠄⣰⠁⠀⠄⠀⠹⠀⠀⠈⠀⢠⠁
⠀⠀⠀⠀⢀⡤⠀⢈⣠⣾⣿⣿⢄⠀⣀⡀⠰⠿⠗⢤⣀⣀⡀⠀⠰⡄⠀⠀⠀⢀⣀⡿⠀⠶⠛⠀⠀⠀⠀⢸⠿⣿⢠⡷⠀⡜⠀⢠⠁⢉
⠀⠀⠀⠰⠋⠀⣀⡿⠋⢹⣿⡿⠚⠉⠉⠀⠀⠀⠀⠈⠣⠼⠟⠛⠻⣿⠃⠀⠀⠘⢷⡜⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⡷⠘⣿⣠⣿⡀⣼
⠀⠀⠀⠀⠒⠛⠉⣰⢃⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠚⠁⠛⠛⠁⡀
⠀⠀⠀⠀⠀⠀⢠⠃⢸⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⠙⠇
⠀⠀⠀⠀⠀⠀⡄⠀⠸⠸⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⡯⠋⠛⠁⡠⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢴⡇⠉⣰⣶⠆⠀⢸⣻⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡀⢰⣤⠀⠘⠏⠋⠀⢘⣬⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠈⣻⡆⢀⣀⡈⣰⡶⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠈⠀⠀⠀⠀⠀⡐⠀⠐⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠂⠤⠤⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡴⠟⠛⣢⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣉⣰⢸⢁⢎⢜⢃⡾⠣⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⢸⡅⣪⣣⠾⢃⡸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⡇⠸⢼⡧⠇⢀⢞⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠂⣤⠀⠀⠀⠀⠀⠀⠀⠈⣀⡅⣰⣿⢏⢀⠒⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠈⡉⠂⠀⠀⠀⠀⠀⠀⣶⣊⡀⣋⢪⢡⡷⢱⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⣠⣥⣌⠛⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠄⣰⣷⡷⠀⠀⠀⠀⠀⠀⢠⣭⣤⠆⣗⢀⡝⡱⣻⢿⣿⡅
⠀⠀⠀⠀⢀⡼⢭⣴⠟⠛⢁⢀⡀⢀⠀⠀⠀⠀⠀⠈⠀⣠⠀⢸⣽⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⡇⠴⢰⢡⠟⣽⣿
⠀⠀⠀⣰⣿⣿⣿⣛⣖⠚⣁⣀⣠⡭⡜⠀⠀⠀⢀⣤⣶⠖⠎⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣿⡇⢠⣃⣋⣰⣿⣿⣀⣀
⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠷⠧⠤⠶⠿⠿⠋⠁⠄⠸⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠢⠊⠓⠰⠾⠯⣝⣻⢠⣽⠟⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⡶⠶⢦⣤⣤⣾⣿⣶⣤⣤⠶⠶⢦⡄
⠀⠀⠀⠻⣤⣤⣤⣤⣴⣶⢶⣶⣤⣤⣤⣤⣼⠏
⠀⠀⠀⠀⠀⠁⢀⣠⣤⣿⣤⣿⣤⣀⡀
⠀⠀⣀⣀⣀⡾⠋⠁⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⢸⡏⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠛⠳⠶⣤⡀
⠀⢸⣇⣀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢻⡄
⠀⠈⠉⠉⠉⠷⣄⣀⣀⣀⣀⣀⣀⣀⣴⠟⠙⠛⢷⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣻⣄⣀⣄⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠹⠟⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢛⢙⡛⡛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣉⣉⣉⣉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⢨⢬⣥⡥⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⡟⠀⢀⡴⠛⠙⢷⣴⠞⠳⣆⠀⠀⢠⡶⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡄⠀⠉⠁⢀⡴⣋⣤⣤⣴⣏⠁⢀⣴⣯⡀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⣰⠞⠋⠛⣫⣤⣀⠀⠉⠛⠋⠛⣿⣿⠀⠘⠷⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣸⣧⡾⢻⡾⠛⢾⣇⠀⠙⢷⣴⠛⠛⢦⡘⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⢻⣇⠘⣧⣀⠀⠙⢷⣄⠀⠙⢷⣄⠀⠙⢦⣄⠛⢶⡄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢹⡿⠁⣼⠋⠛⢦⡀⠀⠙⢷⣄⠀⠙⢷⣄⠀⠙⢧⣈⣿
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⣇⠀⠹⣦⡀⠀⠙⢦⡀⠀⠙⢷⣄⠀⠙⢷⣄⠀⠙⢿⡄
⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠛⠉⠳⣶⠈⠻⣦⡀⠀⠙⢦⡄⠀⠙⢷⣄⠀⠉⠀⠀⠀⠙⢦⣄
⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠈⠻⣦⡀⠀⠙⢶⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⢶⣌⡻⣦⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⢋⡵⠛⠛⠛⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠁⠀⠈⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠙⢷⣄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠙⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡴⠋
⣶⣤⣶⣤⣦⣦⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣼⣿⣴⣦⣴⣦⣤
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀
⠀⠀⠀⠱⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠐⠁
⠀⠀⠀⠀⠁⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀
⠀⠀⠈⠆⠀⠀⠤⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡖
⠀⠀⠀⠀⠀⠀⢂⠁⠀⡰⠃⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⡄⠀⠀⡀⠀⠠⡀⢩⠀⠀⢠⠀⠀⢀⡘⠁⠀⠒⠂⠀⠀⠀⠀⠠⠀⢖⠀⠴⢀⡀⠀⠀⠀⠀⠀⠀⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠂⢰⡇⠀⠀⠓⣮⠒⠀⠘⣧⡄⠈⢅⢀⡀⠲⣆⣒⡆⠀⢠⠊⣤⠈⠀⠂⣈⠀⢋⠁⠀⠀⡀⠀⠾⠂⠀⡄⠀⠀⠀⠀⣀⠀⠀⠼⠶⠧⣄⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠚⠛⠀⠀⠖⠛⠁⠘⠚⠞⠃⠈⠀⠈⠈⠀⠈⠓⠀⠀⠀⠀⠀⠚⠂⠀⠀⠚⠃⠀⠁⠐⠚⠋⠀⠀⠀⠐⠚⠀⠈⠀⠰⠖⠛⠁

⣿⣿⣿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣶⣴⣧⣾⣯⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣸⣿⣿⣿⣿⣿⢿⣿⡏⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⣿⣿⣿⣿⠃⠸⡿⣅⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⢸⣿⣿⣿⣿⠋⠰⠁⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⣀⣤⠄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⣿⠛⢿⣿⣿⣿⣿⣥⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠈⠃⠀⠀⠉⠉⠻⢿⣿⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠖
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣶⠄
⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣾⣿⣿⠷
⣷⣶⣶⣾⣿⣿⣦⣤⣤⣴⣯⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠟⠟⠉⠙⠋⠙⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠟⠃⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⢀⡛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠂⠇⠉⠀⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⣥⠈⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢲⡿⢟⢉⣿⣿⢿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣼⣿⣿⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⠟⢀⡀⣖⠠⣅⠾⠡⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡆⠀⠄⢀⠼⣧⣨⣿⢍⣥⣦⠛⢠⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣦⡰⣿⣽⣦⢀⣄⢠⠄⠀⠀⢰⣄⡰⠇⢠⣼⢊⣳⠿⠉⠑⢲⣬⣿⣬⣿⣿⣿⣿⣿⣿⣶⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣇⣼⣛⣤⣄⡀⢠⣞⠋⠀⣾⠁⢜⣃⣠⣶⣶⣿⠿⣿⣼⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣻⣿⣧⣨⠋⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣤⢀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣉⣁⣤⣤⣤⣀⣉⡙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣿⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣼⣿⡿⠿⠛⠉⠈⠛⠻⠿⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⢿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠀⠉⠃⠈⠃⢹⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢋⠅⡀
⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠈⠁⠀⢀
⠀⠀⠀⠀⡕⢢⠙⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢱⠿⠠⠂⠀⢀⠀⠀⠀⠀⢒⡶⢶⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⡗⠚⢾⡔
⠀⠀⠀⠀⠠⢈⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠃⠀⠀⠆⠀⠁⢄⢀⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠁⡙⠿⣷⣦⣤⣄⠀⢀⣴⣶⣾⡿⠟⢉⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠁⠂⣀⠉⠙⠋⠀⠜⠙⠋⠀⢠⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⡐⢂⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢹⣶⡄⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠃⠀⠀⠘⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢡⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⣀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⠀⠥
⠀⠀⠀⠄⡀⠑⠂⠀⠌⠀⠀⠠⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠂⠂
⠀⠀⠈⠁⠜⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⣀⣶⠟⢻⣆⣀⣀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⢰⡟⠁⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠙⣷
⠀⠀⠈⢿⣤⣤⣤⣤⣴⡶⠶⢶⣶⠿⢷⣶⠶⠶⣶⣤⣤⣤⣤⣴⠟
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣟⠀⢈⣿⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠶⣦⣄
⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⣾⠟⠛⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠷⠶⠶⣦⣤⣀
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠈⠉⠻⢶⣄
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠿⠷⠶⠶⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠛⠛⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣀⣄⣀⣤⣀⣤⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⢩⣯⢹⡏⢹⡏⣽⡍⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠉⢻⣦⣁⢀⡀⢨⡀⣨⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢠⣿⠋⠘⠃⠘⠃⠙⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡶⠟⠹⠗⠸⠇⠸⠇⠿⠂⠿⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢠⡆⢠⡄⣴⠄⣶⠀⠀⠀⣸⡟⠉⠉⢻⣆
⠀⠀⠀⠀⢀⣴⠾⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⡶⠟⠛⠛⠻⢶⣤⣠⣀⣤⡀⠀⠀⠹⣧⣀⣀⣼⠏
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠙⠻⠋⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠙⢷⣄⠀⠈⠉⠋⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣠⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀
⠀⠀⠀⠀⠘⢷⣄⣀⢀⣀⣴⡟⠁⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡟⠁⠈⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠘⣷⣄⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣧⣤⣀⡀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢷⣶⡟⠉⠉⠙⢷⣄⠀⠀⠀⠀⠈⠛⠷⠶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠈⠻⣦⡀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣠⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠈⠻⢷⣄⠀⠀⠀⣠⣶⢶⠶⠟⠋⠁⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠈⠻⣷⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠈⠙⢶⣤⣤⣤⣤⣤⣤⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⠶⠶⠶⠾⠿⠿⠿⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣶⣶⣦⣶⣶⣦⣤⣤⣤⣤⣦⣶⣤⣶⣴⣤⣤⣤⣤⣴⣶⣶⣶⣤⣶⣴⣤⣤⣤⣤⣤⣤⣴
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡡⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠡⠀⠀⢸⣯⣿⡇
⠀⠀⠀⠿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠶⠷
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠂⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⣿⠛⠛⠛⣿⠀⠄⠁⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⣿⡀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠠⠀⠀⠀⠛⠋⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣨⣠⣤⣍⢥⠀⠐⠐⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡄⠀⠀⡄⠀⠈
⠀⠀⠀⠁⣠⣤⣤⣀⡀⠀⠀⠓⠊⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠇
⠀⠀⠀⠀⠋⠉⢙⣿⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⢀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⡟⡛⣛⡛⣻⠿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣀⣴⣷⢟⢢⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣤⠌⢀⣄⠑⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠊⠀⠠⠀⠓⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⠦⠤⡞⢓⣈⠀⠀⠀⠀⠀⠀⠀⠀⡞⡄⠀⡈⢀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠐⠀⠁⠀⠐⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⠤⠤⠀⠀⡺⠒⢀⡾⠁⠀⠂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠊⢀⣀⣀⣨⣡⡠⡠⠿⠀⠀⠈⠰⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠃
⠀⠀⠀⠀⠀⠵⡶⡆⠀⠀⠀⠀⠀⣻⣶⣦⣤⣤⣾⣿⣶⢿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠳⡌⡤⣤⣤⣄⢀⢀⣀⡀⣀⢠⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠧⠴⡆⠴⠀⠀⣿⡅⠐⠀⠀⢐⠀⣸⠏⢀⠐⠂⠠⡄⠢⠀⠁⡄⠃⡠⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠲⠶⡴⠶⠐⠶⠲⠶⠆⠴⠶⠅⠀⠈⠢⣘⠄⠂⠠⠅⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠉⠁⠈⠀⠉⠐⠑⠻⠖⠚⠓⠛⠒⠚⠓⠛⠒⠚⠲⠓⠲⠶⠟⠢⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄⢄⡀⠀⠐⢄⠀⢆⠀⠀⠀⠀⠀⠀⡄⠀⢦⠰⢄⠰⠀⡆⠆⡀⠄⠠⡀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣄⣀⡀
⠀⠀⡠⣾⣷⡀⠀⠀⢠⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠐⢋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡿⠓⣀⠀⠀⣬⣇
⠀⠀⢈⣼⣷⣄⣿⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⣽⡇⠀⣼⣿⠀⡀
⠀⠀⣼⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣽⣅⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⡇⠉⠉⠉⠉⠉⠉⠁
⠀⠸⢧⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠖⣩⣿⣿⠀⠀⠀⠀⠀⠀⠐⢣⣿⣿⣿⡄
⠀⠠⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⣿⡿⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡿⠿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠻⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⢠⣾⣦⣄⣀⡠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣯⣀⣀⡀⠀⠀⠀⠀⡐
⡇⢸⣿⣇⣉⡉⠉⠉⣿⡋⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⡍⠻⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⠐⠚⠛⠓⢺⡟⠛⠓⠒
⠥⠬⢿⠿⠿⣿⣆⢰⠃⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⠆⠇⣠⣶⣇⠐⣶⣶⣶⡶⠀⠀⠀⢸⣀⣻⣿⣿⣿⣆⠀⡏⢱
⠀⢀⠎⢂⠀⠈⢿⡏⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⠘⣧⠀⢸⣍⠛⠛⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠠⢣⠀⠈⠻⣿⠁⠀⡇
⠀⠀⠀⠈⠀⠀⠼⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠂⠘⠿⠗⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⢠⠇⠀⠀⢸⡄
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠀⠀⠐⠐⠀⠀⠀⠀⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣤⡄⠀⣨⢁⠀⢀⣴⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠀⠀⢦⣤⣺⡿⢧⣾⣇⠈⢿⣿⣿⡆⣿⣤⡄⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⡀⢀⣼⣿⠟⠻⢎⢻⡏⠀⢸⣿⣿⣿⣹⣿⣋⣿⣦⠔⡅⠀⠁⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠻⠿⠉⠀⠀⠌⢇⠀⠀⣯⠉⡿⠛⡿⢿⣿⣿⣿⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠘⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠉⠀⠁⠀⠁⠸⣿⣿⣿⡿⠁⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⡈⣸⢀⡿⣸⣿⣷⣤⡤⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⣠⣤⣆⣴⣿⡿⠛⠋⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣸⣥⣿⣿⣿⣿⣇⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢟⠉⠉⠉⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢀⠏⠀⣸⣿⣿⣿⣿⣿⣿⣿⡾⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣄⣀⣄⣀⣠⡟⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠻⠋⢷⣿⣿⣷⣤⡿⠁
⠀⠀⠀⠀⠀⢀⣠⡤⠶⠓⠀⠛⠉⠉⠉⣭⠉⠈⡙⠿⠛⠛⠳⠶⠆⠀⠤⢶⠶⠀⢀⣠⣭⡿⠃⠀⡀⠀⠀⣠⣦⣀⣴⠋⣀⡼⠋⠹⣿⡟
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠩⠤⠤⠥⠤⠀⠀⠙⠻⠤⣀⣀⠀⠸⢿⠇⠀⠀⢀⡻⠋⢁⣤⠊⠀⠘⠋⠘⣫⡯⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⣶⠶⠒⠚⠛⠛⠛⠒⠀⠤⣀⣀⡀⠀⠀⠀⠀⠶⠚⠁⠤⠀⠀⠉⠰⠶⠛⢋⣡⢾⣫⣴⣮⣤⣀⣬⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠑⠂⠀⠀⠀⠀⠤⠈⠉⠉⠁⠀⠀⠀⠴⠚⠛⠉⣿⣿⣿⡿⠋⠙⠛⠿⠿⡿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢀⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢤⣤⣤⠋⢠⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⠷⠴⣢⣄⠱⣷⣴⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣚⠋⠶⣦⣝⢿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠞⠉⠐⢿⣦⣈⢿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⢙⡿⣯⣿⠋⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠦⣀⣈⣢⠟⡫⠕⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠈⠍⠁⠜⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣦⠠⠤⠤⠤⠤⠤⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⢂⣩⣀⣲⡤⢶⠴⠀⢀⠰⣶⠶⠴⠄⢀⣀⣀⣀⠀⠉⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠴⣟⣹⣇⣘⣠⠧⠬⣧⠀⠈⡐⣧⡤⠤⠤⠤⣤⣄⡀⠉⠢⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣶⢮⣋⣉⠩⢔⣀⠀⠀⠀⣀⣉⣈⣂⣀⣀⣀⠀⠀⣉⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣭⣀⠀⢉⡁⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠈⠀⢰⡈⠉⠀⡄⠐⣃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣿⡻⢿⠀⣶⡃⠀⠀⠀⢠⣶⡆⢲⡏⢦⡀⢂⡘⣇⢈⣀⡥⡆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠨⢀⡇⠀⠘⠋⢪⡇⠀⠀⠂⢨⠟⡻⠻⠻⠚⠟⠛⡋⡙⠁⠃⠇⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⡻⠀⠀⠀⠀⢠⠀⠀⢀⠁⢸⡇⠄⢂⢃⠀⡀⠠⠠⠀⠀⡘⢠⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⢀⣠⣆⠠⡴⣅⣼⣷⣶⣶⣤⡀⠀⢢⡆⣼⢠⠇⡼⣰⣇⣶⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠰⠿⠋⠉⠓⠶⠟⢿⢀⡀⡈⠿⠓⠀⠀⠘⢁⡿⢰⠇⡿⣾⢹⢰⡻⣆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⢀⣾⠇⢀⣀⣤⣤⣤⠀⣴⣿⣬⣧⣠⡄⢈⣥⡄⠀⠸⠃⣽⢸⡷⠻⢿⣼⣧⢻⣆
⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⣜⡋⠀⠉⠁⠐⠂⠀⢸⡏⠉⡛⠛⠉⠀⠀⠛⠛⠀⠀⠘⠃⠛⠁⠀⠈⣻⣿⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⢧⣈⣽⣭⣅⣼⣿⣿⣿⡿⣿⡆⢀⡾⠣⢴⡾⡿⠀⢠⢴⢿⠶⣷⡄⢹⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡜⣃⠠⠔⢹⠿⣷⣝⣿⢷⠻⠃⠁⣠⠂⡘⡜⠀⠀⢘⠘⢀⠷⣈⡁⠾⠀⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠰⡉⢆⠶⠻⠷⠸⢋⢾⠈⡤⠁⡐⢁⣲⠍⠀⠀⠀⢀⠃⡈⡀⢁⠁⡆⠁⠰⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⠦⠀⠁⠀⠀⠀⠔⢡⡿⠃⠀⠠⢁⠂⠘⠰⢡⠁⠄⡘⠰⠀⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠈⠊⢭⠴⠶⠖⣂⣀⣀⣰⠟⠀⠀⢀⠂⠄⠀⠀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠠⠁⠀⠀⡐⡀⢀⢎⠎⡰⢁⠎⣀⠊
⠀⠀⠀⠀⠀⠀⠐⠢⠐⠂⠀⠊⠑⣤⣈⠀⠕⢨⠔⡠⠂⢂⠐⠀⡡⡁⢁⠌⠔⠜⠀⠂⠎⠈⣁⣤⠞⢡⠂⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢀⠠⢂⠄⢉⡰⠛⡰⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⢤⠴⠐⢞⠝⢡⠞⡠⢊⠐⢁⠔⡡⢊⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢡⠒⢁⠔⢉⠔⢊⡠⠊⡠⠊⡁⠈⡡⠈⡠⢊⠔⢠⠂⡠⢁⠔⡡⢊⡔⢁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠐⠁⠎⠀⠊⠐⠁⠐⠁⠊⠀⠁⠈⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁