Bunnies Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠐⠿⢿⣿⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⣰⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣹⣾⣷⣷⣷⣾⣿⣶⣶⣄⣽⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠀⠀⠘⢿⣿⣿⠻⢿⠛⣿⣿⣿⠟⠁⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⣿⣿⣦⣄⣶⣿⣿⣷⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠻⢿⣾⣷⡿⠋⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⣠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣤⣶⣾⣿⣿⣷⣶⣴⣶⣾⣿⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠛⠃⠁⠀⠀⠀⠉⠛⠛⠿⠿⠿⠙⠃⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠑⡄⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⠀⡀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⣷⣶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡉⢟⠟⣷⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣷⡦⠀⣀⡀
⠀⠀⠀⠀⢂⠀⡄⠀⠀⠀⡆⠀⠀⢠⢎⣠⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣯⣤⣀⡸⠃
⠀⠀⠈⠀⠀⠀⠄⠀⡄⠀⠑⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⢿⡟⠛⠛⠿⢿⣿⣿⣿⠟⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⣠⣢⣴⠶⣶⣿⣿⣿⣿⠟⣫⣏⣁⠂⠙⣏⣿⣿⣶⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠁⠰⡀⠀⢰⠁⠀⠀⣼⣿⣿⣿⣟⣯⣍⠁⢹⡿⠀⠀⢸⠛⠟⣿⡷⢸⠃⠀⡐⠸⢁⠄⠀⡀⠀⠀⣀⠥⣌⣉⡉
⠀⠀⠀⠀⠁⠨⠀⢣⡀⠸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⡎⢀⡤⢺⣷⣼⢻⢃⡎⢀⠔⠁⠘⢁⣠⡠⠈⠙⠀⠃⢀⡠⢀⡠⠄
⠀⠀⠀⠀⠐⢤⠀⠀⢡⠀⢣⠀⣾⣿⣿⣿⠟⠋⣁⣀⠉⠻⣿⣿⠃⠓⠝⠿⠁⣸⡷⠃⠠⠂⠠⢉⠄⠀⢀⠔⠁⠀⡴⠀⠉
⠀⠀⠀⠀⠀⠀⠙⣀⣨⢀⠈⢠⣿⣿⢟⣡⣶⣾⣿⣿⣷⠀⣿⣷⣷⠞⠀⠀⢰⡏⠀⠰⢁⠴⢈⡡⠖⠋⠀⠀⠀⠀⠀⠶⠶⣄
⠀⠀⠀⠀⠈⠁⠈⠁⠸⣹⣿⣼⣿⢷⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡧⠀⠀⣾⡇⠀⠰⠀⠠⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠉⢀⠀⢫⣿⠇⣼⣿⣿⡿⢳⠀⠀⣿⡇⠀⠀⡀⠠⣜⢁⡁⠈⠁⢌⡉⠒⢁⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠔⠀⠀⠒⠀⢰⣿⣿⠏⠀⠸⡀⠀⢛⠀⠀⠀⠀⠀⠙⠣⠙⠂⠤⠀⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢛⢃⡰⣾⣤⣶⣾⠁⠀⢠⣿⣿⣵⠿⠷⠓⢷⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠾⠿⠿⠿⠟⠓⠛⠉⢦⠀⠀⢁⢣⣼⣾⣷⣦⣾⣿⣄⡄⣀
⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣏⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠴⠛⠖⠊⠉⠛⠛⠋⠛⠋⠉⠈⠈⠙⠉⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⡿⡇⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣾⣧⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢸⣿⣿⣿⣇⢀⣄⢀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣞⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠉⠉⠛⠋⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⣾⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠻⢻⣿⡿⣷⡆⠀⠙⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠋⠀⢈⡁⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⢿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠈⠀⣠⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠑⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢀⠀⣤⠆⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣵⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⢿⣄⣀⡀⠠⠼⠟⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⣀⡀⠀⢠⣄⠀⢠⣤⠀⠀⣠⣠⡄⠀⠀⠀⢴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠄⠲⣶⠄
⠀⠀⣰⣓⣲⠀⢻⠈⢧⣼⣿⠀⢸⣏⠀⣻⠂⣴⡖⠚⠛⣿⠟⠳⢶⣶⡀⠀⢸⢿⣿⡅⠀⠀⠂⢀⣴⢭⣲⡚⠛⢛⣶
⠀⡘⣿⠈⠀⠀⠈⢧⣼⠿⢿⣤⡈⠉⠛⠉⠀⠀⠉⠉⠙⡿⢸⣿⠯⠟⢋⠀⠈⠙⠂⠀⠀⡟⢂⠺⠿⠧⠇⡟⠉⠉⣁⣄
⠸⠎⢛⣾⠀⠀⠀⠸⢳⣿⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣀⣀⣠⣬⣶⡆⠀⠀⠀⠀⠈⠀⢀⠀⠀⢔⠛⢟⠋⠙⠏⠄
⠀⠀⠈⠁⡶⣢⣤⣤⡀⠈⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⠸⠈⠻⠟⠋⠈⡿⢻⡶⠀⠀⠀⠀⣀⠀⠀⡀⠀⠘⠃⣇⢰⣿⡟
⠀⠀⠀⠸⣼⣿⡟⢿⣍⠛⠻⠇⠀⠀⠀⣴⢶⠀⣀⡀⢠⣀⡀⠀⣀⣀⣇⣸⠇⠀⠀⠀⠀⢿⣷⣔⠁⠺⠍⠶⠥⠭⠽⠁
⠀⠀⠀⠀⢻⣿⠇⢾⡿⢀⡀⢄⠀⠀⢸⠃⣸⣿⡿⠁⠘⠛⠋⠉⠛⠋⠙⠛⠀⣀⡀⠀⠀⢈⣹⣿⢦⣤⡶⠚⢋⣻⠃
⠀⠀⠀⠀⠈⠁⠈⠉⠁⠉⠁⠁⠀⢀⣦⣭⣍⠉⢀⠀⠀⣰⡾⣏⠷⣄⠀⢰⢤⡿⠁⡀⢀⣾⣿⢱⣶⡘⢿⠋⠉
⠀⠀⣠⡲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣫⢇⡀⠀⠀⢿⣭⢻⣹⡇⠀⠈⠡⣭⠆⠀⠈⢏⠩⠈⠉⢀⣐⣀⡀⢤
⠀⠘⠟⠋⢁⠀⠀⠀⠀⠀⢸⣷⡆⠔⣄⣀⣀⣘⠿⠋⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣞⢋⣿⢿⣿⣎⡀
⠀⠀⠀⠐⢫⣤⣺⡄⠀⠀⢶⣾⠑⣶⠈⠙⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣦⢄⠀⠀⠀⠀⠀⠀⢣⠀⠛⣿⣧⢸⣿⡿
⠀⠀⠀⠸⠯⢀⡀⠀⠀⠀⠘⡷⠿⡛⣤⠔⣿⠟⡄⠀⠀⠀⡨⢭⡆⠀⠛⠿⡷⠀⠀⡀⠀⠀⠓⠘⠓⠘⠓⠂⠘⠃
⠀⢠⢶⠀⢐⣓⣺⡀⢫⣇⣤⠀⠀⠉⠁⠈⠁⠀⠀⠀⡴⣬⠙⠟⠉⣤⡄⠀⠀⠀⢈⣷⡄⣀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠢⡄
⠀⣤⡾⢦⣤⠈⠁⠀⣜⡍⠛⠀⠀⢰⣶⣄⡀⠀⠸⡷⣾⠀⠀⣆⠄⢑⣧⣲⡄⠀⢠⣛⣻⠻⣾⡟⠁⠀⠀⠑⠔⣿⣿⢌
⠀⠈⠁⠈⠁⠀⠀⠀⠈⠀⠀⢿⣉⠉⢓⡦⠘⠄⠀⠀⠛⠃⠠⠂⠀⠺⠷⠀⢠⣶⡄⠀⠀⠘⠇⠀⢀⣾⡆⠀⠐⠄⠄⠁
⠀⠀⠀⠀⣀⠀⠀⣴⡾⣿⠟⠀⠈⠙⠣⣟⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡴⠛⡟⠀⠀⢸⣿⡇⢀⡤⠶⣦
⠀⣠⣾⣿⣿⡿⣛⡛⣿⣤⠀⠀⠀⠀⡀⠈⠉⠩⢄⡨⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⣿⡤⠞⠁⢀⠄⣾⠿⢿⣯⡤⠖⠁
⠀⠀⠉⠁⢘⠉⠿⠧⠼⢿⡇⠀⠀⠀⠻⣷⣶⣶⢆⠀⠀⠀⠀⠀⠀⡾⠻⠧⣿⣇⠽⡆⠀⠀⡌⣼⣿⣿⡶⠛⠂
⠀⠸⣷⣶⣶⡦⣀⣀⣀⠐⠁⠀⠀⢸⣤⡙⡟⣡⣴⠆⠀⠀⢀⢿⣦⣼⣍⣀⠀⣀⣠⠁⠀⠀⠱⠄⡂⢀⣀⣴⣤⣤⣻⠂
⠀⢲⣿⣿⠹⣷⡄⠉⠉⠄⠀⠀⠀⡐⡙⠛⠗⠛⠋⣆⠀⠀⠸⣾⠛⡏⠀⠙⠛⠿⢿⡄⠀⠀⠀⢸⠛⠉⢡⣾⢫⣿⣿⡜
⠀⠈⡿⠛⣘⣿⢓⣤⢘⠄⠀⠀⠀⣧⣅⢀⣀⢀⣠⣏⠀⠀⠀⢻⣀⣇⣀⡀⠀⢀⣠⠃⠀⠀⠀⢠⠢⣤⢸⣿⡘⠿⡿
⣀⣀⣠⣀⣄⣀⢀⡀⣀⠀⢀⡀⢀⡉⢉⡀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠉⠛⠋⠉⠛⠛⠀⠀⠀⠀⠀⢀⣠⣄⣀⡁⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣷⣮⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠈⣿⣿⣿⢹⡀⠀⠀⠀⠀⣰⣿⣿⠋⠰⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠐⣿⣿⡿⠈⡧⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⢻⣿⡇⢸⣇⠀⠀⣾⣿⣿⣿⠀⡏⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⢸⣿⢇⣾⣿⠀⢰⣿⣿⣿⡟⠼⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣿⣼⣿⡿⢧⡾⠿⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⠴⣶⣾⣿⣦⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣶⡄⢰⣉⠿⣿⢿⡃⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⡇⣸⣿⠀⣨⣾⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠁⢈⣁⣠⣤⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⠻⢿⡿⢿⠙⡿⠳⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⠳⣾⠆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣔⢘⠠⠄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣓⣶⣿⡃⠀⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡅⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠛⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⣿⡿⣿⠿⠿⡟⣿⠿⠏⠁
⠀⠀⠀⠀⠀⢠⣤⣠⣾⣿⡿⠋⠀⠈⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⠇⠀⠀⠀⠈⠻⢻⣧⣾⣿⣿⣿⣿⣟⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⣿⢇⠠⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣗⣄⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⠜⣱⣴⣖⣀⣿⣶⣴⣦⣤⣤⣄⣠⡎⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠘⠂⢾⣿⣿⣿⣉⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⡉⢛⣅⡀⢄⣤⠖
⠀⠀⠀⠀⠲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠻⣿⣿⣿⣿⣿⡟⠋⠀⠁⣿⣿⣿⣿⣿⣿⣴⣶⡟⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⣿⣿⣿⣿⣿⣾⡂⠀⣿⣿⣿⣿⣿⣿⣿⠏⡘⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣧⣆⣰⣇⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣄⠹⣻⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣾⣿⣾⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠛⠛⠛⠛⢿⣿⣿⡿⢿⠟⠙⠿⠿⠿⠉⠃⠀⠉⡅⠿⣿⠙⠟⠻⠿⠿⠟⠛⠃⠛⠏⠉⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠶⢶⠶⣄⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⠀⠀⠀⠈⠳⣤⡀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠈⢻⣮⣿⣦⣄⡙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠹⣷⡿⣿⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⢻⣿⣌⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣤⣀⣈⣿⣿⣿⡿⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣏⠉⢀⠤⣴⢄⠉⠻⣤⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⠟⠀⢿⣾⣿⣮⡇⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠉⠀⠈⠉⠉⠙⠓⠶⣤⣴⣶⣢⣾⣿⠿⣯⠀⠀⠀⠉⠉⠉⠁⠹⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣻⢿⣭⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣈⣁⠀⣀⠀⢠⣴⠠⠚⢀⠄⢹⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡿⠳⠖⠅⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⡤⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢀⠘⢻⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣧⡾⠀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡷⠃⠈⠚⠶⣄⡠⢴⠆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡄⡴⠀⠀⠀⣼⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣶⠁⠀⠀⠀⢸⣷⠋⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⢀⡼⠿⣳⣄⠀⠀⣁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⡤⠀⠀⢐⡟⣿⡷⣏⣱⡃⠀⠀⠀⠀⠀⣠⣾⣷⣆⡵⣣⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠦⢴⣜⢄⠘⢻⣾⢟⡥⠂⠀⣸⣶⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠛⠶⢋⣀⣬⡾⠋⠀⠴⠾⠛⠛⠻⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⠿⠟⠉⠻⣿⣿⣼⠱
⠀⠀⠀⠀⠀⢐⡀⠀⠶⠉⣈⠀⠀⠀⠀⠀⠀⠀⣤⠱⡼⢿⣿⠿⠷⠀⠀⠀⠲⡉⣅⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠁⠈⠀⠀⠐⠐⠲⠆⠓⠐⠚⠚⠊⠋⠀⠀⠓⠤⢚⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣁⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠻⣷⣄⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣇⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠐⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠃⠀⠉⠻⠻⠟⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⢟⣿⣿⣿⣿⡇⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢀⠀⡸⠿⠟⠹⣇⣀⣠⠧⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⠀⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠐⠢⣥⠠⡀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠌⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠙⡇⠰⡀⠀⠀⠀⠀⠰⢀⡏⢰⡆⣰⣿
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠌⠀⠀⠀⠀⡁⠀⣵⠀⠀⠀⡐⢣⣿⠄⢻⣀⣽⣿
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠉⠈⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⣇⠱⡄⠀⠰⡅⠀⢹⡆⠀⠀⣃⣼⡁⠀⣶⡞⣁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣵⣦⣶⠃⢀⣿⣷⠀⢸⣿⡿⢇⠀⡿⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣝⡿⢠⠞⠉⠀⠀⠈⠀⠁⠙⢦⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡝⠱⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⣻⣿⢷⡆⢀⣶⡄⠤⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇⠠⠀⡶⠟⠁⠀⠀⢸⣿⡇⠀⠀⠠⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣠⡔⠂⠀⠀⢀⡖⠀⠘⠻⠃⠀⠀⣲⣾⣧⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠏⠃⠀⠀⠀⡜⠀⠀⠀⡦⠀⠀⣈⡉⠡⠌⢹⠇⠀⢈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⡸⠁⠀⠐⠁⢄⡀⢄⡀⠙⠂⠸⡇⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⠅⠀⠞⠀⠀⠀⠀⠀⠙⣿⣦⣆⠚⠀⠀⠀⠈⢛⠛⠁⡰⠃⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣤⣀⠀⠀⠀⠼⠀⠀⠀⢰⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⢳⣆⣤⣴⡶⢤⣤⠶⠋⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠓⠈⠁⠉⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠤⠤⣴⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⢰⣠⣄⣠⣿⡀⠀⠀⠀⣸⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⡤⡀⠀⠀⣿⣿⣦⣤⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠺⠶⠾⠷⣟⠀⠀⠀⠀⠉⢿⠀⠀⡿⣿⣇⢠⡄⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠰⠀⠲⢦⣿⠀⠀⠀⠀⠈⠙⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡾⠃⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠹⣿⣅⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⣀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣉⣙⣏⣛⣛⣿⣯⠈⠻⣿⣿⡏⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⠀⡀⢠⣼⣿⣷⡀⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⣾⣿⣿⣿⣿⣿⢿⣿⡇⠘⠁⠀⠙⣿⣿⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⠿⠗⠼⠄⠙⠿⣿⣿⡿⠀⢡⣴⣿⡶⠈⠉⠿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣿⣵⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠿⣿⣿⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠀⠀⠀⠀⠀⠐⣿⣿⠉⠀⠀⠀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠙⡟⡯⠙⠿⢣⣶⣦⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠠⣧⣼⡶⠂⢠⣾⣿⣿⣁⠀⠀⠀⠰⠆⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠘⣷⣄⣘⣏⣀⣴⣿⣿⠿⠉⡛⠛⢿⣿⣶⣄⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠻⢿⣿⣿⣿⡿⠿⠗⠃⠀⠀⠀⠘⢫⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⢉⠉⣉⠀⠐⠂⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⡄⠰⣶⣴⣶⣿⣿⢷⡖⠔⠀⠒⠂⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⢻⡄⠛⠾⣿⣿⣿⣿⡽⣯⡿⣦⡡⣀⣠⣤⣤⣬⠓⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠟⢉⡉⣥⣼⣾⣷⣿⣷⡝⣼⢻⠛⠉⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡾⠟⢿⠟⣿⣿⠛⠷⢽⣿⣟⣷⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠂⠙⣿⣮⢳⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⢿⣻⣧⢿⣶⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⢿⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣎⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠸⠃⠻⣆⠀⠀⠀⠀⠀⠀⠀⣠⠔⡉⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠀⢰⢨⡆⠀⠀⠀⠀⣠⠞⡵⠋⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢾⢈⣷⠀⠀⣠⠎⠈⣼⢣⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠸⣶⠎⣸⣿⠀⣰⡧⠀⢰⣿⠟⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠶⠋⠐⠿⠿⠴⠿⣾⡆⠺⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠄⠁⠐⠘⠃⠀⠀⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣠⣦⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠃⠀⠀⡁⠀⠀⣀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣛⣿⢠⠀⣠⡄⠀⣀⠄⠀⠐⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠛⡀⢲⡈⠻⠁⠒⠙⠀⠾⠂⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠐⠁⠁⠘⠻⠻⠦⣄⣠⡰⢆⣀⡤⢞⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠄⠀⠀⠀⠶⠆⠀⠀⠀⠀⠙⠛⠙⠉⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣠⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠟⠻⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠂⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢸⣯⠀⠻⠀⠀⠇⢀⣠⠀⠀⢀⠈⠁⢀⣴⠃⠀⠀⢀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⢰⣶⢏⣻⣦⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡲⢾⡿⠁⠀⠀⣿⡏⠺⠿⢿⣧⠀⢀⢀⣿⡧⠀⠲⠖⠾⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⣮⣤⣾⡧⢤⠈⠀⣿⣿⣿⣿⣧⣯⠀⡀⢘⣿⣿⣴⡞⠹⡄⢀⢸⡀
⠊⠀⡀⠀⠀⠀⠀⠀⠁⠀⠘⠹⢿⢤⣤⣤⡾⠃⠀⠀⠀⠈⠿⠦⠴⠌⠻⠇⠈⠙⠛⠛⠚⠓⠛
⠀⡀⠀⠂⡀
⠀⠃⠂⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢻⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⢡⠀⠀⠀⠀⠀⡰⠸⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢡⠀⠀⠀⡎⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢸⢸⠀⠀⢀⡇⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡥⠀⠀⠀⠀⢾⡀⠀⢸⡃⠀⡇⠀⠀⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⡇⡇⠀⢸⣧⡀⡇⣀⣼⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣷⣼⢻⣗⡒⠸⢷⡟⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⠉⠛⠙⠂⠀⠁⠑⠌⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠁⠀⠀⠅⠀⠀⠀⠀⠰⠷⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡢⠀⠀⢀⠀⠀⠀⢻⣿⣽⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠭⠉⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠠⠀⢨⡄⣀⠀⡀⠀⠂⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⡁⢄⣇⣀⠈⠙⠦⠞⠁⠀⢀⡧⠀⠒⣶⡗⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⣀⡠⠔⠢⢄⡠⢈⣤⣠⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⠦⠴⠶⠒⠛⠉⠉⠁

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠻⣎⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢫⡞⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⣿⡄⠝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠃⡾⠐⠈⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡇⠐⢌⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⢀⡟⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣽⢀⠀⢻⣆⠀⠀⠀⠀⠀⢀⠞⠁⡀⢰⡆⠀⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⣸⢠⠀⠀⠘⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡄⠑⠀⠙⣧⠀⠀⠀⠀⣇⠌⠀⠄⢺⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⡇⠀⠀⠙⢼⡄⠀⠀⢸⡇⠀⠀⠀⢉⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣇⢘⣤⡞⡾⢧⠴⠴⠼⠟⢿⣾⡄⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⠻⢡⣶⣀⠘⠀⠀⠀⠀⠨⢻⡴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠻⠏⡄⠿⠀⡗⢀⠀⣾⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢾⡆⠀⠘⠇⠘⣦⠀⡿⠀⢿⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠯⢱⡾⠱⠿⠆⠀⠈⠛⠀⣼⢗⠸⣁⠈⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣤⠆⢸⣷⠀⡀⣀⡤⢰⡇⠀⢿⣿⠀⠩⢷⣦⡀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠁⣠⠟⠁⣴⠓⠁⠀⠀⠁⢀⡈⠑⢶⡆⠀⠘⣷⠘⣍⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠀⢀⣶⠟⠀⠀⠧⠞⠀⠘⠳⣄⠀⠃⠀⠀⢨⠁⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⢀⣾⠇⠀⠀⢀⡙⠊⠀⠀⠀⠻⣧⡤⠄⣸⠟⠠⠄⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⣛⣋⠀⠀⠀⠀⠈⡁⠀⠀⠀⢰⣦⡴⠾⠉⠀⢸⠂⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣇⣐⣀⣊⣍⣀⣀⣰⣾⡟⢃⠀⠐⣄⠘⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠉⠟⣏⣿⢻⣿⠿⡿⠿⣿⡏⠏⠀⠀⠂⠀⠠⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠠⠂⠀⠛⠃⢠⡄⠀⠀⢰⡍⠀⠀⢠⠀⠀⠀⢰⡇⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠀⣡⢂⡠⠀⣡⠆⢰⡎⢳⠨⣴⠈⠂⠀⣄⠰⣦⠲⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⠘⢁⠉⣀⡴⠋⡂⠈⡁⠇⠐⠈⢆⠀⢬⣇⠀⢘⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣎⠹⠿⢏⣄⣼⣧⡼⢧⡄⣤⣴⠺⠃⣃⢀⣾⡞⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠐⢷⣴⣌⠉⠟⠁⠈⠙⢋⣡⣶⡞⠉⣿⠛⣗⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠛⠙⠛⣷⣤⣴⣿⡟⢉⠈⠀⣸⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⣄⣤⣤⡄⢿⣿⣿⣥⡥⠿⡄⢠⣿⣧⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⣀⠀⣾⣿⣿⣧⠀⠀⢀⢈⣿⡿⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠛⠛⠛⠛⠛⠛⠳⠀⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡶⣶⣾⣖⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣷⣾⣭⣝⣿⣲⢤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⣷⢶⡬⡿⠹⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣴⡶⡤⢴⣾⣼⣄⡈⣴⣶⡾⣒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣷⣦⡖⠚⠙⠉⡍⠛⠉⠒⠒⠒⠶⡶⠚⠛⣃⢇⢠⠀⣰⣧⣿⣿⠏⡿⠋⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠛⡁⢸⣽⣇⡠⣷⣿⣷⡠⣄⣴⣷⣄⢀⣠⡬⣦⢳⣿⣿⣿⠏⣼⣁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠛⢿⣿⣾⣦⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠤⣲⣿⣿⢣⣾⠿⠿⠟⠛⠛⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡟⠀⢄⠀⢸⣿⣿⣿⠿⠗⠲⠭⣉⣙⠛⠻⠿⠛⣧⣴⣿⣻⣷⣷⣶⣦⢤⣄⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⣿⣋⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⣿⣦⡀
⠀⠀⠀⠀⢀⣠⢄⡽⢋⣿⣶⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗
⠀⠀⣶⣪⣷⠾⠋⣠⣿⡿⠁
⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠰⠾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡴⠁⣤⠶⠦⠄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢰⠀⣸⠈⡟⠦⠀⠈⠉
⠀⠀⠀⠀⢠⣿⠃⠁⡀⠀⠀⡘⠙⣷⡀⠀⠀⠀⠀⢲⠀⠀⠀⠀⡇⠀⠀⢀⡠⠈⠁⠀⣟⠶⣿⠀⢸⡷⣺⡀
⠀⠀⠀⠀⢸⣿⠀⡟⠈⣍⢍⢹⡦⢹⣷⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠺⢧⣤⣼⣦⣭⣤⡿⢏⡞⢿⡆⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠰⢆⠙⠄⠀⠘⠀⠠⠟⠃⡀
⠀⠀⠀⢀⠰⠉⠀⠀⠙⠀⠁⠁⠂⠁⠈⢧⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠎⠉⠢⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡠⠊⠉⢆⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⠑⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡐⠁⠀⠀⠘⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠱⡀⠈⡆⠀⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⠀⠀⠀⠀⠀⢃⠀⢠⠀⠀⠀⠀⠀⢠⠀⢀⠃⠀⠀⠀⠀⢐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠄⠀⠀⠀⠀⠈⡄⠀⡆⠀⠀⠀⠀⡆⠀⡌⠀⠀⠀⠀⠀⠌⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⢄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢢⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠑⢄⣀⠤⠒⠞⢉⡉⠉⣉⡒⠦⢄⣀⠔⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠊⠀⠀⠈⠤⢠⠌⠀⢘⠖⠁⠀⠈⠒⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢔⣊⡀⠀⠀⠀⠉⠀⠉⠀⠀⣈⣒⠄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠞⣽⣿⡏⢑⡄⠀⠀⠀⠀⣴⣿⣏⠁⡙⢆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡀⢿⣿⣿⣭⡇⠀⠀⠀⠀⣿⣿⣿⣧⠅⡸⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣑⠢⠉⠩⠊⠀⢠⠀⢠⠀⠈⠊⠉⠥⢒⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠪⣀⣀⡈⠆⠀⠀⠀⢀⠽⢅⠀⠀⠀⠀⢎⣀⣀⡨⠂⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠐⠒⠂⠉


⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣿⣿⣿⣛⣿⣟⣛⣻⣟⣟⣻⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠁⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⣇⡀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢤⢀⣸⠒⠈⠀⠀⠀⡆
⠀⠐⠂⢀⠀⠐⢯⠄⠄⢄⡂⢀⠙⠤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠋⡀⢔⡪⠤⠠⡽⠂⠀⡀⠒⠂
⠀⠀⠐⠚⠂⠀⠋⠀⠀⠀⠉⠒⠬⠂⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠐⠥⠒⠉⠀⠀⠀⠙⠀⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠔⠀⠁⠉⠀⠐⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣀⠀⠀⠀⠀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠹⢿⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⢸⠀⢀⢀⣴⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⣴⢢⠘⠃⠀⡙⠥⣿⢂⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢺⡿⠀⠀⠀⠹⠀⢟⡀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡝⠁⠁⠀⠀⢀⠇⡆⢸⢃⠄⠈⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡹⠁⠀⠀⠀⠀⣼⠀⢡⠂⠎⠌⠙⢿⡀
⠀⠀⠀⠀⠀⠀⢀⠄⢁⠞⠀⡀⠀⠹⠀⠀⠀⠀⢀⡌⡆⠀⡘⠀⠘⠰⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⣀⠀⢠⣄⣠⣟⢾⢰⢀⣀⠧⠂⠁⠀⠂⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⣠⠀⠐⠠⢠⠰⠄⠈⠀⠸⠋⠘⠿⠙⠛⠉⠀⠄⠄⡠⠀⠀⠀⠈⠂⠰⠁
⠀⠀⠀⠀⢀⢠⠃⠀⠀⡄⠀⠂⢩⠆⢠⠁⠀⠀⠀⠀⠀⠀⢠⡀⠄⢄⠠
⠀⠀⠀⠀⠈⣼⠀⠀⠀⠡⠬⢄⠚⡴⠈⢁⡀⠀⠀⠀⠀⠀⢠⡔⢒⠢⠆⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡹⣋⠞⠡⠊⠀⠀⠐⠀⠀⠀⠐⠐⠆⠂⠤⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡡⠆⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣦⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠳⠀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢣⣼⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⣿⣏⣥⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠼⡿⢿⣷⡦⣍⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣷⣄⠢⢥⣿⠆
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠠⣤
⠀⠀⠀⠀⠈⢂⠀⣦⠀⠀⠀⠀⡃⠀⠀⠀⣰⢇⣠⡤⠀⠀⠀⠀⢁⣀⣀⣠⣄⣀⣁⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⠛
⠀⠀⠀⠃⠀⠀⠀⡄⠀⢀⡄⠀⠛⢆⠀⠀⠄⠀⠀⣰⣾⣶⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢿⣿⣿⣿⣿⡿⠻⡟⠉⠉
⠀⠀⠀⠀⠀⠉⠁⢠⠀⠀⡁⠀⠀⡸⣀⣤⡴⣂⣦⣾⣿⣿⣿⣿⠿⠿⠓⠤⠈⠻⠖⢶⢶⣶⣌⠙⢿⡟⠁⠀⠃⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠠⠀⠀⠀⠆⢰⡀⠸⠁⢀⠜⠉⠋⠁⡠⣿⣿⣿⣿⡿⠹⠶⢾⠉⢿⠗⠀⠐⠀⣾⣿⣮⢯⣧⠈⡇⠀⠀⠀⢠⠆⢀⠀⠀⠀⠞⠀⠀⠐⠀⠠⠶⠖⠂
⠀⠀⠀⠀⠀⡀⠀⠀⢧⠁⠀⢸⠀⠀⠀⢰⣿⣿⣿⣿⣿⣢⣿⣷⡄⢠⣻⠇⠠⠀⡀⢁⠀⣬⣾⡏⢰⠃⠀⢠⠂⢡⡤⠋⠀⠠⠤⢄⠀⡰⠚⠙⠲⠶⠂
⠀⠀⠀⠀⠀⠀⠈⠆⠈⠣⠀⠘⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣴⡞⣸⣻⣷⣏⡻⢠⡏⢀⠔⠁⠀⠈⣀⣰⠶⠂⠀⠀⡁⠃⢀⠤⠆⣠⠐⠒
⠀⠀⠀⠀⠈⠐⢢⡀⠀⠀⢡⠀⢱⡀⢸⣿⣿⣿⣿⠟⠋⢁⣤⣄⠈⠙⢿⣿⡿⠡⠓⡽⠛⠏⠁⣼⠷⠃⢀⠴⠀⠠⢉⡴⠂⠀⣠⠖⠁⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣸⡀⠀⠁⣼⣿⣿⠟⣁⣴⣶⣿⣿⣿⣷⡀⢸⣿⣼⣲⡞⠀⠀⠀⣼⡟⠀⠀⠎⢀⠴⠀⣩⠴⠒⠛⠦⠤⠄⠀⠁⠠⢶⣶⣤
⠀⠀⠀⠀⠀⠀⠂⡠⠚⠀⣸⢺⣷⣄⣿⣿⢡⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣮⠀⠀⢀⣿⡇⠀⠀⡔⠁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣻⠿⠛⠉⠹⢻⣿⡿⢀⣾⣿⣿⣿⣟⡀⠀⢸⣿⡇⠀⡀⠀⠀⠀⡠⠶⠠⠉⠲⠀⠀⠶⢖⡲
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣿⣿⡿⢻⠙⡄⠀⡞⠀⠀⡟⠛⠁⣾⣿⣿⣿⠋⢸⡄⠀⠸⣿⠃⠀⠀⠐⠐⠙⢷⡐⢶⡆⠄⠀⠑⠆⠐⠀⠐⠂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣿⠡⠈⣀⠀⠎⢁⡄⠈⠁⠀⣸⣿⣿⣟⣁⠀⠘⣇⠀⠀⡝⢀⠀⠀⠀⠀⠀⠈⠙⠀⠈⠀⠁⠀⠈⠃⠴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢙⡋⣄⠳⣿⣶⣾⣿⡧⠀⠀⢠⣿⣿⣧⡿⠟⠛⠛⡹⡄⠀⠀⣀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣿⣿⣿⣿⣿⣟⣿⠣⠂⡀⠿⠿⠿⠿⠿⠿⠶⠛⠋⢩⡄⠀⠈⠉⠙⣤⣾⣿⣷⣶⣴⣿⣧⠀⡄⢀
⠀⠀⠀⠀⠀⢈⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡽⢷⣤⠜⠃⠻⠿⠿⠟⠿⠟⠉⠋⠘⠀⠻⠻⠣⠂
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠛⠋⠉⠈⠁⠛⠛⠻⠿⠿⠶⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠒⠒⠒⠒⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⣑⡾⠟⠉⠉⠉⠉⠻⣷⣊⣀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠸⡒⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⢒⠗
⠀⠀⠀⠀⠀⠀⠀⣨⠗⠀⠈⠦⢴⣾⡿⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⢿⣶⡦⠴⠁⠀⠺⣁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉⠉⠗⢶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⢾⡉⠉⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣃⣸⠀⠀⠉⠙⠓⠒⠦⠤⠤⠤⠒⠚⠋⠉⠀⠀⣇⢘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⠤⠤⠤⠤⠔⠐⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠀⠁⠒⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⢰⠒⠲⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠖⠒⡆
⠀⠀⠀⣤⣒⠂⢻⠀⠀⢱⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠢⠤⢄⣀⠀⠀⡞⠀⠀⡟⠐⣒⣤
⠀⠀⠀⠀⡼⠁⠈⢷⣶⣦⣓⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣚⣴⣶⡾⠁⠈⢧
⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠙⠃


⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⣰⠎⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠳⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠖⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠱⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⠎⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢣⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡞⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⣧⣼⠦⠶⠶⠶⠶⠶⠶⠶⣧⣼⠁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠤⠤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠤⢤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡆⠀⠘⠋⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⠃⠀⢠⣯⡀
⠀⣀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠙⠂⠤⠔⠊⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠑⠂⠤⠒⠋⠀⠙⠳⣄⠀⠀⠀⠀⠀⣀
⠀⠈⠙⠠⣀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣅⣀⣀⣀⣀⣨⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣠⠔⠋⠁
⠠⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤
⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠭⠭⠤⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀
⠀⠔⠛⠁⠀⠹⡄⠀⠀⠀⠀⢀⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⡀⠀⠀⠀⠀⢠⠇⠀⠀⠛⠠
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⡉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠉⠛⠦⣄
⠀⠀⠀⠀⣀⣠⠞⠁⢀⡴⠛⠋⢩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠙⠻⢦⡀⠈⠳⣄⣀
⠀⢠⡴⠋⠁⠀⠀⠀⢸⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡗⠀⠀⠀⠈⠙⢦⡀
⠀⢿⣀⡴⠚⣿⡀⠐⢯⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡽⠂⢀⣿⡓⢦⣀⡿
⠀⠀⠉⠓⠛⠀⠛⠶⠞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠳⠶⠛⠀⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠁⣲⠶⠒⠒⠶⣖⠈⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣹⡄⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢠⣯⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡴⠊⠉⠉⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠉⠉⠙⢦⡄
⠀⠀⠀⠀⠀⠀⣯⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡽
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⡕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢾⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⡆⢈⣣⠀⠀⠀⠀⠀⠀⣠⡞⣡⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⠀⠈⠙⢧⠀⠀⠀⢀⡼⠋⠰⠃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠸⡄⠀⣠⠾⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠃⣠⠓⡻⠃⠐⠛⠾⣄⠈⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠹⠃⠀⠁⠰⢀⠘⠰⡂⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣄⠀⡀⢴⣶⡄⢸⠄⠀⢡⡄⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡃⠀⠘⠛⡁⠁⠸⠿⠇⠀⠀⢠⠈⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠨⠁⠀⠀⠀⠀⡴⠂⠀⡀⠴⠀⢠⡄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠢⡯⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣤⣄⡹⢆⠀⠀⣀⡀⠀⢀⡤⠀⢀⠤⠄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠩⠙⢻⠶⠾⠗⢣⣦⣦⣤⣷⣶⣿⡟⠃⣄⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⡀⠂⠀⢀⡴⠁⣌⡉⢛⠙⢿⡻⣙⠀⠀⢾⣿⠃⠹⠗⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠘⢷⣶⠄⠂⠛⠉⡅⠀⠰⠀⢣⠀⡙⢦⣄⠈⠀⢽⠃⠀⠢⠁⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡠⢈⠤⢶⠂⠀⠈⣠⣶⠆⣀⡐⢄⠈⢄⠰⠆⠀⢠⡄⠤⠙⠊⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠊⠀⠄⠪⠟⠙⠉⠀⠬⠙⠒⠷⠀⡍⠁⠐⣈⣡⡃⠀⡀⠄⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⣱⣢⢆⣀⡀⠰⡴⠃⠀⡎⣎⣶⣼⡅⠀⡂⢠⢸⠁⠤⡏⢀⡀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⢋⠸⠿⣿⣤⣿⣿⣴⠁⡁⠈⠋⠄⠸⢉⡇⣈⣐⠂⠙⠆⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣤⣦⣌⠈⠀⠀⢻⣦⣷⣤⠶⢶⡂⢸⠃⡁⠋⡄⠄⠠⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡁⣴⡾⠛⣟⠙⢴⡞⠀⡸⠃⠀⠀⠉⠘⠂⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠛⢿⣿⠿⣷⠆⠈⠀⠆⠠⠏⠁⠢⠀⠀⠀⠀⢢⣾⠏⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⣿⠀⠰⡄⠆⠀⠀⢸⣀⠀⢠⠀⣀⣀⣠⣼⡋⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣧⣤⣄⣼⡟⠀⢀⣷⣠⠀⣀⢾⣿⡷⠛⠛⠉⠉⢨⣇⠹⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢁⡖⠀⢀⣈⣿⠇⠀⢸⡏⢀⢠⣀⢈⢻⣤⣄⣴⣤⣦⠞⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⠀⠀⠈⠻⠿⠿⠿⠟⠀⠀⠀⠁

⣶⣶⠶⠾⠟⠛⠛⠛⠛⠳⣝⣿⣼⢸⠇⣿⠀⣿⠀⣿⠁⣿⠇⣿
⣦⣤⣤⣶⣶⠿⠿⠿⠻⠷⣜⡇⡇⣾⢰⡏⣸⡇⢸⡏⢰⡟⢠⡟
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢷⢣⡇⣾⢁⡿⢀⣿⢀⣿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⢡⡏⣸⠇⣼⠇⣸⡏⣸⡏⠀⠀⠀⢀⣀⠤⣄⠲⣮⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⢸⠇⣿⢠⡿⢠⣿⠀⡿⢥⣶⣽⡪⡕⣎⢳⡌⢷⡈⢿⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡸⡸⣇⢿⡘⣧⣸⢿⣚⠭⢿⣛⣻⣿⡼⡜⡆⢿⡘⣷⠘⣷⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠽⠿⠿⣟⡫⠵⣚⡭⢖⣫⡭⢖⣒⣻⠵⢷⢹⡘⣧⠹⣧⠸⣧⠘⣷⡀⠀⠀⢀⣀⣀⠤⣤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⡭⠭⠵⣚⣩⠵⢚⣩⠴⢚⣩⡵⠖⠛⢻⢿⣧⡙⢧⡙⢷⣌⠳⣌⡻⢔⣪⠽⠶⠮⡝⡌⢧⢳⡜⢮⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣒⣛⣋⣭⠴⢚⣩⡴⠞⠋⠁⠀⠀⠀⠈⣿⡼⡼⡶⢋⣗⠾⣛⠵⢚⣭⠶⠞⠛⠓⢾⢹⢸⡆⢿⠈⣧⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣇⣿⡭⠗⣋⡵⠞⣋⣤⡶⠿⠛⠛⢾⢸⡈⣇⢸⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣸⡖⣋⣩⡴⠞⠋⣁⣤⣶⠾⠿⠷⣼⡇⣿⠘⣧⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣉⣥⣴⠶⠟⠋⣁⣠⣤⣶⣦⣼⡇⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣴⡶⠿⠛⠋⠉⠀⢨⢹⢇⢸⡇⢻⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⡈⣷⠘⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣛⢌⢧⣘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠚⣛⣩⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠛⠋⢁⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣾⠿⠛⠁

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⡀⠀⠀⡄⠐⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣷⣴⠀⠀⣼⣷⣶⣶⣯⣀⣄⣴⣦⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⡖⠋⠀⠀⠀⢈⡁⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠠⡎⠀⠀⠀⠀⣵⠄⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣷⠀⠀⠀⠀⠀⠃⣿⠀⢇⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠉⠀⠈⠀⠀⠃⠀⠉⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⡰⠀⠀⠀⢼⡧⠀⠀⠀⡄⠀⣿⡂⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣽⡄⢂⠀⢀⡐⣼⡷⣂⡀⢀⠃⣰⣿⣷⠀⠀⠀⠖⠀⠀⠀⠘⡉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠝⡶⢆⣀⡀⠉⠛⠛⠉⢀⣄⡴⣿⣿⡿⠀⠀⠀⠆⠀⠀⠀⠀⢣⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⡇⠀⠀⠀⠣⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⡃⠀⢀⣰⣴⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠁⠀⣾⣿⣷⡧⠄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠿⣄⡀⠀⣀⣀⣠⠶⠟⢋⣶⣩⣧⣾⣿⡯⠬⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠀⣼⡿⢻⠏⠉⠁⠀⣰⡿⠿⠿⠿⢏⠏⣰⠂⠰⢆⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠴⠤⠴⠋⠀⠦⠴⠤⠼⠴⠋⠀⠀⠀⠀⠛⠒⠛⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⢲⣞⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣤⠞⠉⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⡾⠟⢋⠩⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣤⣴⣶⠿⠟⡋⣃⡈⠐⢂⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⢀⣀⣤⣶⡿⠷⠜⠋⠡⠀⠈⠀⠀⠘⢷⡄⠈⢂⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⠿⢛⠉⠁⠒⠙⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⢆⣀⣠⣤⡶⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣦⠸⢛⣩⢥⡲⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢀⡶⠿⣛⠫⢭⣤⠶⣾⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣤⣶⡾⠿⣛⣭⣿⡶⠿⣞⣗⣥⠬⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡐⢨⣿⣷⣾⣿⣏⡦⠽⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠾⠟⠛⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠛⠛⠦⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⠳⣼⣦⣀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠹⣿⣿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⠛⠁⢤⣉⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⡀⠀⠀⢀⠨⣿⣿⡟⠀⢷⣿⣾⢰⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠀⠀⠀⠀⠀⠈⠙⣿⣿⣟⣻⠟⠂⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠲⣆⣂⣀⠀⣠⡤⠤⡀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⡿⠋⠓⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣾⣟⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⣿⠇
⠀⠀⠀⠀⠀⠀⢨⣿⣿⠖⠈⠺⢆⡠⡤⠀⠀⠀⡀⠀⠀⠀⠀⣀⡄⠀⠀⡾⡻
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠄⠀⠘⣿⣥⡴⢴⠊⠀⠀⠀⢀⣴⡛⣿⢄⣠⣶⠃
⠀⠀⠀⠀⢠⣀⡀⠹⣿⣿⣫⠀⢠⣿⣿⣷⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢛⡤⠼⠛⠁⠒⠛⠛⠻⣿⣿⣇⠀⠀⡰⣿⠿⠛⠙⢿⣿⡟
⠀⠀⠀⠀⠢⠀⠁⠀⠀⠀⠀⠤⠄⠇⠑⠙⠛⠋⠀⢄⠈⠄⠂⠀⠀⢀⡑⠄⢠⠲⠶⠄⠠⢀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⣤⣤⣄⣀
⣿⣽⣿⡿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⣀⣠⣤⣴⢶⢾⣿⣻⣿⣷⣿⣿⣶⣶⣤⣄⡀
⣮⣽⣟⣿⡏⣿⣟⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣤⣀
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⢯⢏⢛⣡⣴⣶⣶⣤⣤⣽⣿⣿⣿⣷⣤⣀
⡛⠿⠿⣿⣿⣻⠿⡿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣲⡦⣀⣁⣭⢷⣾⣿⣿⣿⣿⣋⣿⣿⣿⠌⢟⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣾⣿⣷⣼⣗⡿⣿⣿⡿⣿⡑⠖⣊⢝⢿⠅⣿⣾⣥⣤⡰⣿⣿⡻⣿⣿⡿⢛⠻⢇⣀⣼⣿⣿⣿⣿⣿⣦⣀
⠟⢛⣫⣿⡭⠽⣛⣞⣵⣿⣿⣿⣷⣵⣾⡧⣺⣿⣿⣷⣿⣿⣿⣗⠈⠛⠛⠶⢒⠂⢀⣤⣠⣾⡿⣿⣿⣻⡿⣿⣿⣿⣷
⠉⠉⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⢃⠿⣯⣴⣿
⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡜⠁⢈⠀⠈⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠳⠟⠛⠋⣽⣿⣿⡻⢻⡞⠐⢁⠄⡀⠰⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⠙⠻⠟⠿⣾⣏⣀⣤⡖⣰⢏⣿⡾⣿⣿⣾⣵⣟⣯⣾⡞⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣃⣀⡀⠀⢀⡠⠉⠀⠒⠂⠋⠀⢠⣱⠿⠻⠛⠟⠟⠛⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣚⣿⢉⣔⣀⡀⣀⠀⣠⣤⣰⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣻⡿⣿⡟⠛⠀⠁
⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡂⣹⡿⣿⢽⣛⠛⣐⡉⡨⠛⢳⣸⠀⠀⠈
⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣤⣭⣷⡈⢩⠙⠀⠀⠠⣄⣭⠄⠀⠂
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠿⡗⠀⠀⠒⠂⠀⠠⣷⡏
⣿⣿⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣝⠀⠀⠀⠀⢀⣦⣽⠁
⣿⣿⣿⠩⣿⣳⡻⣉⣛⢛⠻⠿⣏⡿⣿⣿⣿⣿⡻⢯⢣⡄⠀⢀⣿⡿⠋
⣿⣿⣯⣽⣨⠟⠳⠤⡤⢤⡄⠀⢸⡧⠑⢿⣿⣿⣧⡀⢶⠄⠂⣾⣿
⣿⣿⣿⢿⣮⠻⣆⢴⢐⢀⣡⢻⡈⠙⠀⢺⣿⣿⡟⡛⠁⢠⣴⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢰⠀⠀⠀⠀⠀⠀⡀⠉⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢃⡀⠠⢀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠆⠈⠙⠲⣄⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣰⠏⠀⠐⠀⠀⠀⠀⠀⠙⢢⡀⠎⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠃⢈⡿⠷⠀⣀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡛⢦⡀⠂⢄⠀⡤⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢿⡀⠀⠙⢦⡙⠢⡀⠀⠀⣠⠎⠠⠊⠀⠀⠈⠓⢤⣑⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⠀⡙⢦⡀⠀⠉⠒⢄⣀⡴⠃⠀⠀⣀⠀⠀⠀⠀⠄⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠈⠋⢻⠀⡉⠢⣄⠀⠀⠻⠶⢄⠀⠀⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠔⠉⢂⡀⠈⠉⢹⣠⠞⠳⣤⡁⠀⠀⠑⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠄⠠⠀⡵⢢⡀⠈⠡⣴⡾⢧⡈⠓⠦⣄⡀⠘⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠞⣡⠏⡉⣄⡀⠈⠀⡸⠀⢀⣄⣀⣉⡙⠁⡟⠛
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠆⢘⠸⡟⠙⠋⠈⢁⡜⠱⠦⣷
⠀⠀⠀⠀⠀⠀⣬⡁⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⡁⢅⠆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⢀⠄
⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣿⢆⢠⣿⣶⣇⡀⠂⡀⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣄⡀⢈⠐⢿⣿⣿⣿⣷⡀⠀⡀⢤⢄⠀⢀⣠⣾⣷⣄⠀⠀⠐⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⠀⡀⠀⠀⣎⣠⣤⣢⣽⣿⣿⣿⣿⣿⣼⣿⣞⣿⣰⣶⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⢀⠀⢢⠀⢀⡊
⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠐⠀⠀⠀⢳⣄⣸⣷⣻⣿⢋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡄⠀⡀⠀⣆⡘⠂⡆⣷⡾
⠀⠧⡞⠀⠀⠀⠀⠀⠀⢢⠈⢷⣅⠀⣛⢌⢢⣧⣌⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⣼⡇⣦⣸⣇⣰⣿⣿⣧⣶
⠀⠸⡧⠀⣄⠰⡀⠑⢠⢸⣾⣼⣿⣿⣿⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⢿⣏⡆
⠀⠀⠉⠀⠀⠀⠉⠀⠀⠙⠃⠋⠻⠛⠘⠙⠁⠉⠁⠃⠈⠙⠋⠃⠙⠛⠙⠛⡟⠏⠉⠁⢻⡟⠘⠛⠏⠙⠉⠙⠛⠈⠛⠋⠙⠁⠉⠉⠙⠁⠁⠈⠛⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠻⣦⠀⠀⢀⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢃⣴⠟⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢹⡇⢀⣀⣀⠀⠈⣷⠀⠀⠀⠾⠃⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣸⡷⠛⠉⣽⠂⠀⠹⣆⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⡾⠋⠀⠀⣴⠏⠀⠀⠀⠹⣦⡀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣰⡟⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠈⠳⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠷⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢁⣀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠻⠿⠃⠀⠀⠀⠀⠈⠛⠉⠉⠉⠙⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣶⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣠⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠇⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣤⣿⣷⣦⣤⣴⠶⠶⠛⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠺⡷⠿⠟⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡇⡀⠀⠀⠀⠲⣦⣄
⠀⠀⠀⠀⣿⡆⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡞⠀⠀⡄⠈⣿⣯⣦⠀⠀⠀⢾⣶⣤⣴⡿⠋⠈⠻⢦⣤⣤⣤⡿⠟
⠀⠀⠀⠀⢿⡟⠀⠃⡘⠱⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣾⠀⠀⠀⢿⠀⢸⡿⡌⡆⠀⠀⠀⠉⠉⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠒⠂⢶⡄
⠀⠀⠀⠀⠘⣿⣄⡀⠠⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⢸⠀⢸⡇⣇⠁⠀⠀⠀⢰⣁⡀⢀⣠⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⢠⠠⢊⡄⠀⠀⡰⠁⠀⠀⠀⠀⠠⡇⢽⠀⠀⠀⠀⠈⠀⢸⣧⣿⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠸⣧⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠖⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠈⡏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠈⠱⠎⡀⢡⠆⠀⠀⠀⢄⢠⡆⠀⠀⠀⠀⡟⢰⡟⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣐⣶⠧⠐⢲⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣈⢳⡄⠈⠀⠀⠀⢸⡌⣿⣦⠀⠀⢸⣷⣾⣿⡟⠀⠀⠀⠀⠀⢀⡂⠈⣽⠟⢻⣿⡿⠦⢴⣾⣏⢀⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣈⡒⠀⠀⠸⣧⣹⣿⣧⡄⣸⣿⣿⡿⠁⠀⠀⣠⣤⡀⠈⣙⣿⠇⠴⣾⣿⣦⣶⣦⣿⣿⠄⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⢿⣿⣿⣧⣿⣿⠟⠀⠀⣤⣀⡀⣼⣿⣿⣍⣥⣴⣾⣟⣿⠩⢿⣿⣯⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣄⠓⠒⠒⠒⢢⡐⠶⠒⠒⢲⡌⠉⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⢿⣶⣻⣶⣶⣽⣿⡿⠿⠿⠿⠛⠛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠬⣿⠠⣤⠤⠤⢼⡅⢠⡤⡤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠠⣀⠀⠀⠀⠀⠁⠀⡀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⠀⠀⠀⠀⢺⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠠⠂⠀⠐⠁⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣏⣤⣄⠠⣄⣸⣇⣤⣀⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡⣿⠈⠉⠁⠠⣽⡆⠉⠉⠴⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⣀⡈⢿⣆⣤⣀⣄⣿⣧⣤⣤⡄⢬⠞⣦⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡎⠀⠘⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣛⣛⣛⣐⣰⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠇⠠⣄⡽⠁⠀⠀⣠⣄⡀⠀⢈⡛⠛⠛⠛⠓⠈⠹⠗⠂⣀⣄⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣞⣉⣿⣿⣿⣿⣶⣶⣶⣿⣿⡇⠠⣄⡀⣍⡁⠛⠷⠦⡹⣿⣛⠛⠛⠶⠶⢶⣤⣤⡤⣼⡿⣿⣧⡀⢀⣤⣴⣶
⠀⠀⢀⣿⣦⡀⣄⢀⣀⣿⣦⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠮⡛⠶⢿⣛⠲⣤⣀⣀⠉⠁⠐⠒⠐⢛⡋⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⠛
⠀⢀⠊⠁⠊⠛⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠢⡀⠙⠳⣴⠛⠛⠛⠛⠶⣶⣤⣄⡀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣷⣆
⠀⠠⡼⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠑⠀⡈⠻⠦⣠⣴⣶⣶⣿⣽⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠁

⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠰⣶⣿⢿⣶⠆⠀⠀⠀⠀⣶⣶⡿⢿⣴⣶⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⣄⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⣼⣯⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣼⣅
⠀⠀⠠⡶⣀⡀⠀⢀⣤⠴⠖⠒⠲⠶⠶⣮⣭⣳⣀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⣈⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⢀⣠
⠀⠖⠔⠁⠠⠁⣰⡯⠖⠒⠒⠒⠶⢤⣄⣀⠀⠉⡿⠛⠻⠶⠶⠶⠾⠛⠋⠀⣠⣿⣧⣶⣿⠃⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⣰⣿⠛⢿⣟
⠼⠚⠀⢀⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⢦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣥⣤⠴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⢻⣶⠞⠿⠃
⠀⠠⠀⠈⡀⢂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⢀⡀⠁⠀⠀⠀⠀⢠⠚⠉⠉⠁⠉⠙⢿⣆⠉⠉⠙⣛⠛⣿⠲⠶⠶⠶⠾⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣆⠀⣤⣿⣛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣠⡾⠋⠉⠓⠀⠙⢋⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠛⠚⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣆⠀⢻⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⠀⠈⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⢸⡀⠁⠀⠀⡼⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠱⢸⡇⡀⠀⠀⣥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⢼⠀⡁⠈⢿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣀⡀⠹⣆⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⢻⣷⣦⣠⡌⢿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣴⡇⠿⣿⣟⠘⢓⣾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠱⠟⠋⠛⠻⣏⠁⠀⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣠⣠⠶⠀⠀⢰⡤⠿⠶⠤⢤⠤⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣯⣾⣿⠃⢘⣠⡶⣄⢀⠤⠖⠋⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⣥⣀⡛⠛⠋⠁⠀⢠⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠋⣘⠯⠁⡰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢄⠀⠂⠠⠄⠘⠂⠲⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣸⣇⢈⠁⠀⠀⠰⡆⠀⠀⠀⠂⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢻⣿⡈⠀⠀⠁⠠⣿⠀⠀⢀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⣻⢷⡄⢿⡁⠀⠠⠀⠀⣿⣿⣁⠀⠀⠀⠘⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠈⣥⠋⠀⢷⡈⢷⠔⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢈⣶⡀⠀⠁⠘⣤⠴⠂⠀⣿⡿⢳⢠⡜⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⢻⡄⠀⠀⢹⡁⠀⠀⡋⠀⠀⡇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠉⣀⣤⠌⢀⡀⠀⠁⠀⠀⠀⠀⠀⢏⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡵⣶⠇⡠⡴⠞⠑⣰⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⣠⣾⡴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠃⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⠖⢤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠘⣆⠈⠀⠱⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡄⠜⠳⠤⡤⢼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣠⠀⠀⠈⢁⠁⠀⠑⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠊⠁⠀⠀⠀⠐⠪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡦⠀⠀⡄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣉⠔⢀⣈⠟⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡃⠂⠑⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⠀⠀⠀⣨⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⡀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠈⠲⠎⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠐⠄⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⢀⡈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⠉⠐⣄⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠘⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⠀⢀⡵⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡦⣤⡉⡻⠤⢀⣀⣉⣉⡉⣀⣀⡠⢆⠀⠀⠀⡄⡈⠀⠀⡤⠤⡠⣄⠰⡠⠄
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠩⠛⠁⠁⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⠀⠀⠨⠤⠀⠀⠀⢀⠀⣄⠀⠀⠐⠂⢘⣔⡀
⠀⠀⠀⠀⠀⢠⣠⣔⡌⠀⠀⠀⠀⢀⠄⠀⠀⣀⢠⠄⠧⠀⠀⠀⠱⠤⠀⣄⣀⡠⠄⠰⠐⠀⠃⠀⠀⠀⠀⠈⣋⠒⠲⠄
⠀⠀⠀⠀⢀⢲⡆⠉⠀⠀⠀⣠⠒⠁⠀⠠⣀⢘⠁⠀⠀⠉⣇⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢈⠃
⠀⠀⠀⢠⢌⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠣⡁
⠀⠀⠀⠀⠀⠉⠀⠁⠀⠐⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⠤⠤⠄⠐⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣉⡉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠋⠁⡹⠀⢸⠂
⠀⠀⠀⣠⠴⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠃⢀⡞⢁⡴⠋
⠀⢀⡞⠁⡤⠶⠦⣄⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⡾⠀⡞⢠⣤⡀
⠀⠈⣧⠘⢧⣀⠀⠀⠙⢢⡈⠳⣄⢀⡤⠴⢒⠛⠛⠛⠛⠒⠳⢤⣧⣤⣍⡛
⠀⠀⠈⠓⠤⣌⡙⠲⣄⡀⢙⡆⠈⠁⣠⡾⠛⠀⠀⠀⠀⠀⣰⠋⣠⣤⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠉⠳⣄⠉⠉⠀⠀⢀⡥⢒⡯⣕⣲⣄⠀⠀⣿⣖⣿⣴⣿⣲⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⢠⢾⣦⡿⠷⢿⠆⠀⣈⠳⠤⡤⠤⠞⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⣿⣋⣁⣀⡴⠋⢰⡏⠉⡷⠠⠀⠐⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡟⢧⠈⠉⠁⢀⠀⠤⠉⣿⡧⣤⣤⠵⢦⣀⣤⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠷⠞⠀⢐⣤⣤⣀⡤⢾⡅⠷⢸⠀⠀⠀⢀⡀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡀⠀⢀⣼⠀⠀⠀⠀⠀⠓⠒⠋⠀⠀⠀⢸⠻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠑⠦⠤⠤⠖⠃⠐⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠰⡄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠓⠤⠖⢦⢀⡠⠇⠀⢀⡇
⠀⠀⠀⠀⠀⣀⡤⠶⠶⢤⣀⡏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⢦⠀⢀⠐⢿⡸⢤⠔⢀⠈⡇
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡬⠷⠞⠃⠈⠓⠚⠛⠓⠦⣄⡀⢠⠞⠓⡞⠉⣷⢤⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢳⡏⢹⠎⢱⡄⠀⠀⢠⠀⠀⠀⠀⠀⠉⠻⠀⠈⠁⠀⢁⡼⠁
⠀⠀⠀⠀⠘⢦⣀⣀⣀⣀⡤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠈⠁⠈⠀⡼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⠶⠛⠓⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠖⠶⢤⣄
⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⣾⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡤⡄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠰⠶⠆⠀⠀⠀⠀⠰⣦⠀⠀⠀⢹⡀
⠀⠀⠀⢰⠇⠀⠀⣰⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⡄⠀⠀⣷
⠀⠀⠀⡾⠀⠀⣰⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣹⠃⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢻⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠹⡄⠀⢸⡆
⠀⠀⢀⡇⠀⢰⠇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠃⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢹⡄⠀⣇
⠀⠀⢸⠇⢀⡟⠀⣼⡀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⠤⠀⠀⠀⠀⠀⠀⡞⣇⠀⢷⡀⢹⡄
⠀⠀⡿⠀⡼⠁⣰⢃⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧⡈⢷⡀⢷
⠀⢸⠃⣼⢃⡼⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠋⢉⡗⠀⠀⠀⠀⢿⡉⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠙⣌⢷⡸⡇
⠀⣾⣰⣣⠏⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣤⣶⣶⡿⠖⢳⡆⢰⡞⠺⢿⣷⣲⣶⣦⠄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢳⣷⣷
⠀⣿⡿⠃⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠈⠉⠉⢁⣠⠴⠋⠀⠀⠙⠶⣤⣀⡉⠉⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢿
⠀⠛⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠴⠶⣤⡀⠀⠀⠀⢻
⠀⠀⠀⢸⠀⠀⠀⢠⠞⠉⠉⠙⠳⡄⠀⠀⠀⠀⠀⢿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠛⠀⠀⠀⢸⢀⣤
⠀⠐⡦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠳⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡟
⠀⠀⢧⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣞⣀⣄⠀⠀⠀⠀⠀⠀⢀⣤⣬⣷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡼⠃
⠀⠀⠈⠳⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⢤⣴⡋⢉⣡⡼⠁⠀⠀⠀⠀⠀⠈⠷⣤⣀⢹⡶⠖⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⠀⣠⠟⠉
⠀⠀⠀⠀⠀⠈⠳⣴⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣨⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⣀⣤⣤⣀⣀⡀⠀⠀⢀⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠶⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠁⠀⣿⠤⡀⡆⠀⠀⠀⠀⢀⣧⢄⠀⡇⣶⡄⢸⡤⠄
⠀⠀⠀⠀⠀⠀⢸⠶⠶⢾⡶⠶⠶⡷⠖⠷⡇⠀⠀⠀⠀⢸⡷⠶⠶⣷⠷⠶⢮⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠷⠈⡟⠁⠀⡇⠀⠀⠀⠀⢸⡇⠉⠀⡿⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⡟⠛⠉⡞⡛⠛⢳⣛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢸⡇⣚⣀⣇⣁⣂⢸⢋⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⡟⣭⠁⣙⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⣶⣶⣤⡶⠒⠃⠀⠀⠀⠀⣯⠭⠤⡭⠭⠤⣥⡤⠤⢼
⠀⢰⡀⠂⢀⣀⣤⣶⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡠⠀⢳⠀⠀⢸⠀⠀⣠⣔⠂⠁⢀⣀⣀
⠀⠖⠛⠋⠉⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡗⠒⠒⡖⠒⠒⣾⠒⠒⢺⠀⠀⠈⠙⠳⠾⠯⠙⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣁⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠘⡇⢀⣀⡃⠀⠀⣻⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣿⣷⡤⠤⠽⣶⣶⠒⠛
⠀⠀⢀⣀⠀⣶⣦⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⢀⣠⡄⠀⠶⡀⣀⣹⠶⣶⡔⠀⠀⠀⠀⠘⣷⣰⣤⣤⠬⣃⠶⣶⠛⠣
⠀⠐⢿⣿⣿⣿⣿⣦⣭⣟⣛⠉⢛⡳⢐⣻⣅⡈⠻⣤⡒⠂⠈⢳⠄⣤⡜⠋⠪⣟⢀⣀⣀⠛⠋⠉⠈
⠀⠀⠀⠈⠛⢿⣯⡉⠽⠿⣿⣿⡵⠖⠉⠀⠛⠂⠀⠙⣿⣾⣝⠃⣀⣙⣆⣴⣶⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠫⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣙⣺⢏⣛⠿⡿⣿⣟⣫⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣮⣿⣿⣿⣿⣿⣿⠟⡲⠃
⠀⠀⠀⠀⣀⠴⣻⣷⣤⡤⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠉
⣠⡴⠶⠟⡡⢾⣷⣮⣭⣤⣾⣿⣿⠿⣟⣛⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⡀
⢛⣲⡞⣭⡴⠋⠁⠀⠉⠙⠛⠛⠛⠉⠁⠀⠈⠉⠁⠒⠒⠫⠭⠭⠻⠽⣿⣻⣟⣻⣿⣿⣿⣿⣟⣛⠿⠟⢲⣤⣤
⠚⠉⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⣷⣦⣤⣀
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠠⠤⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡐⠀⠄⠀⡦⠢⠀⡀⠀⠀⠀⡇⠀⠀⠀⠁⠔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⡀⠀⡀⠀⠱⠆⣤⢧⠀⠀⢀⢣⣀⣴⠀⠀⠒⠒⠊⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠐⠄⠀⠀⠀⠂⠀⠀⠂⣀⠩⠁⠀⠀⠀⠄⠑⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠄⠲⣤⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡖⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⠀⢠⠮⠀⠀⢻⠷⡆⣂⡆⠸⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠙⣄⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⣾⡩⠀⠀⠀⠀⠊⠁⠀⠈⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⢆⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⠈⠉
⠀⠀⢰⠻⢗⢤⡀⠀⠀⠀⠀⠱⡈⠣⡀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠘⡆⠀⠙⠮⡓⢄⡀⠀⠀⠘⢄⠙⢄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠹⡄⠀⠀⠈⠳⣝⠢⣀⠀⠈⠢⡈⠳⣄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠑⢌⠳⣄⠀⠈⢢⡈⠳⣄⠀⣀⠤⠴⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠳⣌⠳⣄⠀⢙⢄⠈⠙⠄⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⢧⡈⠲⡉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠷⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⡞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠒⠐⠠⠁⠈⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣴⡇
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⡱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⢠⡀⣠⣄⢀⣤⡀⣠⣄⢠⡀⠀⣠⡀⣤⣤⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣿⣼⢿⡇⣿⣾⠈⠃⡇⣿⢸⡇⠀⡿⣇⢸⡇⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠇⡿⢸⠟⣧⡿⢺⣴⠇⣧⡿⢸⣥⣴⠗⢿⢸⡇⢸⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⠤⠤⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠄⠈⠀⡽⢇⡠⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡂⠀⠀⠀⠈⠉⠉⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠤⠀⠀⠀⠀⠄⠀⠀⡰⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⡞⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢩⠔⠒⠞⡰⠁⢠⣟⠁⠀⠠⠤⠤⣄⢀⣰⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡴⠁⢠⠇⠀⠉⠁⠒⠐⠊⠀⠠⢙⠥⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡖⠀⠀⠓⠂⠤⠼⠁⠀⡿⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡀⠀⠀⠀⠁⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠒⠦⢤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠠⠤⠤⣄⣀⣀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠢⡴⠓⠶⠉⠲⠚⢦⠔⢆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠓⢃⠀⠡⠀⢠⠀⠀⠀⡆⠀⠀⠀⡌⠀⡘⠚⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠺⡀⠈⢆⠀⢂⠀⠀⠀⠀⢐⢀⡀⢀⠁⠐⠀⠐⠀⡠⠁⢀⠗⢦
⠀⠀⠀⠀⠀⢰⠚⠣⠀⠈⠂⠀⠂⣀⠄⠚⠀⠉⠀⠀⠀⠈⠉⠑⠲⢄⡐⠀⠐⠁⡠⠞⠓⡆
⠀⠀⠀⠀⣚⠉⠑⠄⡀⠑⢀⠐⠊⠀⡠⠄⠒⠉⠁⠀⠀⠉⠐⠂⠄⡀⠈⠓⢄⠈⠀⠠⠊⠉⣓
⠀⠀⠀⣺⠁⠁⠂⠄⠈⠠⠊⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⡁⠠⠐⠈⠈⣕
⠀⠀⢸⡁⠈⠑⠂⠀⡨⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠱⡄⠐⠊⠁⢈⡇
⠀⠀⣏⠈⠁⠀⠐⢠⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⠀⠈⠁⣹
⠀⠰⡉⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠁⢉⠆
⠀⠰⡋⠉⠉⣁⠀⢩⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⣉⠉⠉⢙⠆
⠀⠀⡏⠉⢀⡀⠀⠴⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⠈⢹
⠀⠀⢸⠉⢀⣀⠀⠀⢳⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠤⣀⡀⠉⡇
⠀⠀⠀⣝⠁⣀⠤⠂⠁⠱⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠐⠤⣀⠈⣫
⠀⠀⠀⠀⢽⣀⡠⠐⠁⡠⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢄⠈⠂⢄⣀⡫
⠀⠀⠀⠀⢠⠿⣀⡠⠊⢀⠔⠀⠈⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠋⠀⠢⡀⠑⢄⡀⡍⢣
⠀⠀⠀⡰⢃⠊⠀⠣⢤⠃⢀⠌⠀⠌⠀⠂⠀⠁⢸⠈⠁⠈⡀⠠⠀⢡⠀⠡⡀⠘⡦⠜⠀⠈⠂⠱⡀
⠀⠀⡜⢠⠂⠀⠀⠀⠈⠉⠻⡀⡜⠀⡰⠀⠸⠀⠀⠀⡇⠀⠁⠀⠇⠀⢣⢀⡜⠉⠁⠀⠀⠀⠀⠡⠘⠄
⠀⡈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠱⠤⠣⣀⠦⣀⡤⢀⡔⠤⠎⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⡀
⢰⠁⠄⠀⠀⢀⣀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠄⢀⠜⠁⠘⢆⠈⢀⠀⠀⠀⠀⠀⢠⠤⠤⣄⣀⠀⠀⠀⠂⠐
⣌⣠⠤⠒⠋⠁⠀⠀⠀⠈⡇⠀⠀⠀⢀⠂⢠⠋⠀⠀⠀⠀⢣⡀⢂⠀⠀⠀⠀⡟⠀⠀⠀⠀⠉⠑⠒⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠌⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠂⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡞

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣠⣤⣶⣶⣶⣦⣭⣙⠿⣿⣿⣿⣿⡿⢟⣛⣉⣉⣉⣉⡙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⡛⠛⠿⣿⡏⠈⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣷⡄⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠘⠋⠁⢠⣾⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠈⠙⠉⠀⠀⠀⠀⠀⢀⣠⣾⣿⡃⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠹⣿⣿⠟⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠹⢣⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⡀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣟⡁⠀⣀⣾⣿⣿⣀⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠛⠋⠉⠉⠛⠓⠦⣄⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⢴⣤⣄⠀⢸⣷⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠈⢿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢠⣿⣧⣴⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣷⣶⣶⣿⣿⣿⣿⣿⡿⠟⠁⠀⢼⣿⣿⣿⣿⣿⣄⠀⢀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣆⠀⠀⣰⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠙⣇⡾⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣽⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠙⢿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠠⣾⣿⠿⠋⠀⠐⠿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠀⡘⠡⠉⠁⠁⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣯⣻⣆⠀⠀⠠⠁⠀⠀⡀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠅⠘⠟⢧⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠠⢤⣤⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⡥⣄⡉⠻⣧⠡⢀⣀⣐⣲⣾⣿⣿⣿⠶⢿⣷⠶⠾⠛⠛⠛⠛⠉⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠙⠳⠧⣘⣏⢻⣆⢣⣟⠋⠉⠉⠁⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠓⠤⣀⠀⠀⠙⢻⣆⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠐⠬⠉⠳⢮⣭⣿⡎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣤⠤⠶⠤⢄⣈⡄
⠀⠀⠀⠀⠀⣿⣿⣝⡷⢄⠀⠀⠀⠄⣒⡮⠝⠒⠻⢝⡜⣧⠀⠠⠶⠚⣛⣛⣛⣷⡮⠤⠶⠖⣒⣊⣉⣭⡭⠽⣁⠄⢄⡀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⢠⣒⠉⠀⠀⠀⠀⠀⠀⡽⠾⢟⣫⣭⠭⠭⠴⠶⣒⠶⠿⠿⠩⣉⠀⠀⠀⠀⣀⠐⠀⣞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣯⡻⢦⡀⠀⠀⣀⠤⠐⠂⡀⢷⠀⠀⣴⠺⣄⠒⠲⠈⠀⠀⠈⠑⢄⠀⣞⠁⠀⠀⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⢀⡀⠠⡀⠈⡁⠸⠀⠀⢿⣿⣎⡳⣄⠀⠀⢀⣨⡔⣾⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠘⡃⠀⠚⠀⠀⠀⢠⡄⠀⠙⢿⣿⣦⣄⠁⣰⣆⡠⣺⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠟⠁⠸⢿⣷⣮⢡⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⢄⠀⠀⠠⠊⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢠⠀⠀⡀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣘⣀⣀⣃⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⡞⠊⠉⠀⢀⠀⠀⣀⠉⠉⠒⢧⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⠇⠀⢇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⠃⢀⣠⠔⡚⡁⠀⠀⠀⡝⡒⢤⣀⠘⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠔⠁⠐⠁⣸⠼⠧⠅⢀⣀⠀⠿⠧⠼⠀⠁⠘⢦⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠑⠒⢺⠁⠀⠀⠀⡀⠤⠄⢀⡀⠀⠀⠀⣤⠀⠤⠄⣀⢀⣀⣈⣲⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡏⠉⢉⣏⡁⠀⠀⠀⠈⠁⡖⠉⠁⠀⠀⠀⠉⣹⣀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣎⣁⠨⠑⣀⡀⠤⠀⠒⠑⠒⢤⠄⠀⣀⢖⣁⣀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⡠⠒⠉⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⠀⠀⠀⣀⠀⢀⡰⠁⠀⠸⡀⠀⠀⡀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠒⠈⠁⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡤⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⡀⢰⠁⠀⠀⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀⣀⠤⠴⠖⠚⠃⠉⠉⠉⠉⠻⣄⣀⡀⢀⣧⡖⠉⠉⠉⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣦⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡈⢇⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⢰⠁⠀⠀⠖⠛⠲⠀⠀⠀⡀⠀⠀⠀⠰⠚⠓⠀⠀⠀⠀⣀⡀⣯⢨⡄⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⣁⣿⠀⢀⡀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢵⠒⣂⣿⠤⣇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢹⠤⢾⣆⡀⠀⠀⠀⠀⠀⢀⢠⣷⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢻⠂⢸⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡏⠈⠢⢄⡀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⢀⣠⣴⣊⡀⠀⢸⠀⠈⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡰⠀⣠⡖⠉⠛⠓⢦⡤⢄⣀⡀⠤⡴⠖⡛⠉⠁⠇⠀⠀⠈⠙⠢⣷⡀⢱⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠸⢁⠞⠁⡄⠀⠀⠈⢆⠈⢦⡀⢀⠎⠀⢰⠁⠀⢠⠄⠀⠀⠉⢣⠀⠈⣧⡀⢇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡇⣰⠃⠀⠀⠙⢄⠠⡐⣼⠀⠀⠙⠎⠀⠀⣆⢆⢀⠎⠀⠀⠀⠀⠈⠂⠀⠀⠱⡈⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠞⠘⠀⠀⠀⠀⠈⠣⣵⠏⠀⠀⠀⠀⠀⠀⠹⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⠽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠧⠄⠀⠈⠑⠤⡀⠀⠀⣠⠖⠁⠀⠛⠒⠒⠒⠠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⢄⡀⠀⠀⠀⣀⡠⠤⠤⠜⠓⠚⠓⠖⠂⠤⠤⢄⣀⣈⣳⣵⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠛⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡜⣧⣆⠀⢸⣿⢁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⠀⣸⡏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⡏⣧⢘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣭⣿⣉⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣗⣩⡿⣛⣿⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢃⡟⣰⣻⠟⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡀⢠⠟⠑⠀⡰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⣲⣴⣿⡿⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⣿⣿⣇⠤⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡋⢵⠈⢄⠀⠅⠀⠂⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⣿⠼⡆⠈⠈⢀⣭⣐⣤⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢻⢽⣷⠀⠀⡈⣿⡿⠿⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠻⡌⣿⣷⡈⢰⣿⠇⠀⢀⠄⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣷⣬⣿⡗⠈⠁⠀⣰⠟⠀⠀⠀⠹⡆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⣿⠁⣾⣷⣦⣿⣆⠻⣶⡄⠛⠜⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠇⠀⠃⠘⢻⣿⣿⠻⢿⣆⢹⣧⣀⣤⣶⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡆⠀⠄⠀⠛⣿⡆⠀⠈⠀⠙⣿⣟⣛⣁⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡇⠀⣇⣤⣤⡽⣛⠀⠀⠀⠀⢯⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢂⣼⣛⣀⣀⠉⠉⠙⠙⠧⠓⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏
⠀⠀⢀⣠⠴⠶⠚⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿
⠄⠀⠀⠉⠛⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠃
⠈⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡷⠐⠛⠛⠉⠉⠉⠈⠛⠶⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢤⣤⠽⠿⠿⠿⠿⠿⠿⠟⢛⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠛⢿⣿⠟⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⣠⣦⣄⡀⠀⠀⠀⣀⣠⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠲⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠁⢸⣿⠿⢿⣿⣿⣿⠟⠛⠟⠁⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄⠀⠁⠨⡟⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠸⣷⡀⠀⢰⡇⠀⠀⠀⠀⢠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⣿⣇⠀⣾⠁⠀⠀⠀⣠⡟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⢸⣿⡆⠀⠀⠀⢸⣿⣶⣿⠀⠀⠀⢀⣿⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⣿⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣆⣠⣤⣿⣿⡇⠀⠀⠀⢹⣿⡟⠀⠀⠀⢸⣿⣦⣤⣀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⢀⣿⡇⣰⡄⣀⣸⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢸⣥⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠈⢡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢠⣄⣐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣴⣿⡿⠚
⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣍⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠙⢿⣷⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠻⣿⡄⠻⣆⠀⠀⠀⠀⠀⢀⡾⠁⣾⠇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⢶⣿⡇⠀⢻⡆⠀⠀⠀⠀⣼⡇⢸⡏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠹⣆⠀⢬⣿⠀⠀⠀⢰⣿⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣌⣿⡄⠀⠀⣾⣿⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⢇⣸⣿⣵⣶⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢛⣿⣿⣿⣿⣿⣿⠌⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⢹⣿⡟⠁⠋⡿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠎⢿⡄⠀⠀⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣹⡄⠀⢠⠀⢸⡆⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣌⣿⢃⡀⠀⠀⣀⢛⡇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⣿⣿⠀⠙⢿⡿⠃⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣻⣿⣿⣦⣀⣤⡧⢠⣤⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⢿⣿⣿⣿⣿⡿⠟⠋⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠰⠛⠃⠉⠚⠛⠙⠟⠈⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⠄⠀⠀⠀⣠⠞⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⠎⠀⠀⢀⡴⠁⠀⠀⠀⠀⡼⠁⠀⢠⠂⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡎⠀⢀⡴⣋⣠⠤⠶⠒⠒⢺⠁⠀⢠⠃⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡘⠀⢠⠾⠋⠉⠀⠀⠀⠠⠶⢯⠀⠀⢡⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣴⣛⠶⠄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣖⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠓⢲⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡴⠚⠓⠀⠀⠀⣀⡀⠘⢲⠤⣤⣤⠞⠀⠀⠀⣀⠀⠀⠈⡗⠒⢒⡟⠁⢀⡀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⢒⡂⠀⠈⣆⠀⣠⠇⠀⠀⠈⡿⠃⠀⠀⢱⠀⠘⡆⠀⣐⠂⢀⡟⢁⡤⢄
⠀⠀⠀⠀⢠⠖⡲⠀⠈⠓⢆⠀⠀⠀⠀⢰⠁⠀⢣⠀⠀⠀⠐⠛⠀⠀⠀⡞⠀⠰⡃⠀⠀⢀⡞⠀⠀⠑⠶⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠑⠦⣄⡀⢨⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢙⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠿⠤⢤⣤⣄⣀⣤⣤⡤⠼⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠄⠒⠒⠂⠀⠤⠤⠤⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣠⢞⣽⡿⠋⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢯⣿⠃
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣷⣿⠟⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃
⠀⠀⠰⠑⠒⠀⠀⠐⠀⠀⠀⠠⠤⠤⠤⠀⣾⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣿⣿⠃
⠀⠀⡧⢀⠒⠒⠒⠒⠒⠒⠶⠆⡄⠤⡤⠄⠙⠛⢋⡈⣉⣉⣉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠶⣾⣿⣿⣿⣿⣿⠃
⠀⠀⢷⠈⠀⠀⠀⠘⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠈⠈⠁⠀⠉⠉⠙⠀⠀⠠⣻⣿⣿⣿⣿⠃
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢀
⠀⠀⠀⠧⣤⣠⣀⣀⣀⣀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡟⠉⠁⠔⢿⣤⠤⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⣒⣾⠚⢣⠦⠦⠤⣤⣤⣤⡤⠖⢁⣇⣄⣀⣤⡿⠃⢠⣤⣾⡋⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠉⠀⠀⠑⢦⣀⣀⣀⡰⢁⠔⢁⠀⠠⠾⢅⡀⠀⠀⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⣼⣿⣿⡿⠓⢇⠀⠀⠀⠀⢤⣀⣵⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠑⠲⣤⣬⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣄⣠⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡫⣠⣾⡟⠀⠀⢻⣷⣄⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⠿⢿⣿⣿⣿⣛⣛⣻⣭⣷⢾⣫⣾⣿⠏⠀⠀⠀⠀⠹⣿⣷⣝⡷⣾⣭⣟⣛⣛⣿⣿⣿⡿⠿⢿⡄
⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⡿⠿⣟⣫⣭⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣭⣝⣻⠿⢿⣿⣿⣿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈