Girls night out Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣶⣤⡀⠀⠀⣀⣤⣄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠸⠜⠛⠡⠹⠈⠛⠻⠞⠋⠁⠻⠻⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⢿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⡗⢀⣐⠀⣘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠃⢸⣿⣿⣿⣿⣄⡙⠿⢣⣾⣿⣦⣉⠻⣿
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠰⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⡿⠿⢋⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠇⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀
⠀⠀⠀⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡇
⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢙⣿⣀⡀⠀⠀⣀⣺⠀⠀⣀⣀⠀⠙⣿⠀⠀⣿⣿⣿⣿⠋⠀⣀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⢿⠿⠃⠀⣽⠀⠀⣿⣿⣿⣷⡀⠈⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣀⡀⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⣤⣴⣿⠀⠀⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⠿⠃⠀⣾⠿⠗⠀⠘⠿⢿⠀⠀⣤⡀⠈⠻⣿⠀⠀⠿⠿⠿⣿⠋⠻⠿⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⣾⣿⣤⣤⣤⣤⣤⣼⣀⣀⣿⣿⣦⣠⣾⣤⣤⣄⣤⣤⣿⣶⣤⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠰⣶⠧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠓⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢘⡗
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠟⠻⡟⠛⠛⠛⠛⠻⣿⣿⡿⠿⠻⠿⣿⣿⠛⢻⣿⣿⡿⠛⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⠀⠀⣧⣤⡀⠀⣤⣤⣿⠋⠀⣠⣤⣀⣼⡯⠀⢸⣿⣿⡇⠀⢸⣤⣄⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⠀⠙⣿⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣸⡿⠛⠛⠛⣧⠀⠘⠛⠛⠃⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣧⠀⠈⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⢻⣧⣤⡄⠀⣷⠀⢠⣦⣤⡄⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣷⡄⠀⠀⡏⠉⠁⠀⠉⠙⣿⣄⠀⠙⠋⠀⣰⡏⠀⢸⣿⣿⡇⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⡛⠛⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣾⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠙⡇
⠀⠀⠀⠀⠙⠚⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁
⠀⠀⠀⠀⡤⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⡤⠠⡤
⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⢿⣿⣿⡿⠿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣀⠀⠈⢻⡇⠀⢸⣿⣿⡇⠀⣧⣀⡀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⣿⣿⣷⠀⠈⣧⠀⢸⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⠀⠀⣿⠀⢸⣿⣿⠀⢀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠛⠛⠁⠀⣼⣿⣆⠀⠛⠋⠀⣼⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⣄
⠀⠀⠈⢿⣧⣴⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡿⡿⢿⡿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣴⣿⠂
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁


⣿⠛⠛⣿⢿⠿⢿⠿⠿⢿⡿⠿⠷⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⢿

⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠘⠀⠠⠄⢤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⣠⡀⠀⠤⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠁


⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢰⣶⡀⠀⢠⡤⣤⣦⡶
⠀⠀⠀⠀⠸⣿⣷⣠⣄⣠⣀⠀⣀⡾⢿⣼⣤⣿⣏⠄⠀⠀⠀⠀⣰⣿⣿⠀⠠⣴⣆⢀⡀⣸⢻⣶⣄⠀⠀⢀⡀⠸⣷⣛⣧⠀⢀⣼⠻⣇⡀⣾⣤⣬⣛⣿⣦
⠀⠀⠀⢀⣾⣿⣵⣷⣿⠛⠛⠿⣿⢛⣿⣾⣘⣿⡿⢷⠀⠀⠀⣳⣿⣿⢿⣤⣴⣿⡿⣉⣱⣿⡿⣿⣯⣀⣤⠠⣧⣺⣿⣿⣾⣀⠸⣿⣿⣿⡇⢹⠗⣻⡿⣿⣿
⠀⠀⠀⢨⣿⣷⣿⣿⣿⣧⣀⣁⣈⣿⢹⣟⣿⣿⣗⣾⠀⠀⢠⣿⣶⣷⣟⣿⢿⡿⢷⣷⡏⢻⣷⣿⣶⣏⠉⢨⣷⣿⣿⣿⣾⣿⠿⣿⣿⣿⢿⣿⠄⣿⣷⣿⣵
⠀⠀⢰⣫⣻⢿⡛⢷⣾⡿⣾⡟⢤⣿⣿⣽⣽⣿⣾⣿⠃⠀⠈⣯⣿⣿⣯⣛⣿⣿⣿⡿⡇⣴⢿⡏⣍⣁⠀⢈⣭⣟⣍⣩⠉⣍⢸⣿⣿⣿⣿⣿⢰⣿⣿⣿⡟
⠀⠀⢸⡿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⡻⢿⣿⣿⠿⢿⠀⠀⠀⣿⠉⠉⢉⡟⣻⠉⠿⡧⡇⡇⢰⣏⠋⣉⢈⣛⡉⢉⣉⣉⠀⣿⢸⣿⣿⣿⠉⣿⠘⣿⣿⣿⡇
⠀⠀⢸⠀⢸⣰⣿⣿⡯⡝⠿⡿⡷⢺⠀⢈⠁⢨⠘⠀⡆⠀⠀⣇⠀⣀⣹⣿⣏⣤⣠⡇⡇⢿⠋⠿⠀⣯⣛⠙⣷⣿⣿⣿⣒⣫⠈⣿⣭⣿⣤⣿⠀⢻⣹⣿⠁
⠀⠀⢸⠀⣸⣻⣿⠿⣿⣿⣻⣷⣷⣼⣀⣸⠖⢸⠐⡄⠃⠀⠀⡏⠉⠉⠉⢛⣿⡋⢉⣇⡇⢛⠀⠀⣀⣼⡇⠀⡇⠉⣿⣿⣁⣸⢀⣿⣼⠃⠀⢹⠀⠈⣽⠟
⠀⠀⡌⠀⣩⠀⠇⠀⢠⠤⠨⣷⡧⢼⠍⠙⠉⢹⠀⠁⠰⠀⢰⠇⠀⠀⠰⢿⠷⠿⠿⠏⠀⠈⠀⠀⠁⠉⠀⠀⠒⠒⠟⠻⠓⠂⠈⠛⠛⠀⠀⠸⠀⠿⠿⠏
⠀⠀⠃⠀⠋⠀⠀⠀⠈⠀⠀⠀⠁⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠠⡀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⡐⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣀⠔⠊⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣷⣄⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⣴⡦⣤⡀⢀⣠⣤⣴⣿⣿⠋⢀⣤⡀⠀⠠⣶⡄⠄⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⡄⢰⡟⢸⣿⣿⠀⠀⢦⠘⠿⠃⢘⠀⣾⣿⡏⠀⠀⠀⠀⠈⠀⢸⣿⣿⢠⡿⢹⣿⣦⠀⠉⡟⠛⢾⣿⣿⠾⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⡴⠟⢸⣿⣧⡿⠀⣿⣿⡟⠀⡀⢀⣿⣷⡄⠀⢠⣿⣿⠁⠀⣼⣿⣆⠀⠀⢸⣿⣿⣾⠁⣿⣿⣿⠈⢻⡇⠀⣿⣿⡟⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⠃⢰⣿⣿⠃⠀⢠⡾⣿⣿⠁⢈⡼⢿⣿⡄⣰⢻⣿⣿⣀⣤⢾⣿⣿⠇⢀⣿⣿⡇⠀⣸⠇⠀⣿⣿⡇⠀⣢⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠿⠀⡘⣿⣿⠀⣴⠟⠀⠻⣿⣧⠛⠁⠈⠛⠟⢃⣸⣿⣿⠉⠀⠘⢿⡏⠀⢸⣿⣿⠀⣠⣟⠀⢀⠸⣿⣇⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠠⠘⠀⠘⠿⠟⠁⠀⠀⠐⠊⠁⠀⠀⠀⢀⠴⠛⢹⣿⡟⠀⠀⠀⠀⠁⠀⠀⠻⣿⡠⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⢠⠋⠁⣀⣀⠀⠘⠀⣀⣰⠃⠼⣠⡄⠀⠀⢠⡟⣆⢰⠃⡐⢀⡀⢰⡂⢀⣼⣤⠀⠀⡞⠉⠉⢳⠀⠀⢠⣼⡄⠀⠸⠃
⠀⠀⠻⣄⣠⠽⠉⠸⠴⠏⠁⠻⠤⠀⠬⠇⠀⠀⠾⠀⠘⠟⠘⠁⠻⡟⠿⠙⠴⠳⠤⠀⠈⠣⠤⠴⠟⠳⠾⠴⠧⠤⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠶⠆




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣼⣿⢣⡿⠀⠀⠀⠀⠀⠀⣸⡏⣿⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢠⣿⣷⡿⣁⣀⣶⡦⢀⣤⣤⣿⣧⠇⣷⣶⣦⡆⣰⣾⣿⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠋⣾⣿⢻⣿⣇⣾⡿⢫⣿⡏⠀⠻⣿⠟⢹⣿⡿⢋⣴⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢸⣿⡇⣸⣿⣿⣿⣇⡼⢿⣧⠀⠀⡆⠀⠸⣿⡴⠛⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢷⣄⠛⠟⠁⠈⠁⠉⠉⠀⠀⠀⠀⣀⣇⡀⠀⢠⣶⡶⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⣾⡏⣼⣿⠇⠀⠙⢷⣤⡀⠀⠀⢀⣼⣿⠆⠦⣄⣀⠀⢀⣀⡈⢿⣦⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠙⠻⢿⣾⣿⡿⠋⣄⢀⠀⠈⠉⠉⠁⠀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠸⠹⡾⣸⢰⠉⣝⢸⠶⣧⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⣀⣉⣉⣈⣀⣠⡤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣦
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⣀⠀⠀⢰⣶⠀⠀⠀⠀⠀⢠⣥⣼⣿⣿⣿⡟⠀⠀⠀⠀⢠⣤⣾⣿⣶⣦⣄⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⣀⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⣠⣻⣀⣤⣤⠀⠀⣿⣿⣿⣿⣿⣿⣇⢸⣿⡀⠀⢻⣿⣿⣿⣿⣿⠿⣿⣦⡀
⢀⣴⡿⠋⠁⢹⣿⣿⣿⣿⣿⢀⡴⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⣼⠁⠁⠀⠙⠛⢧⡀⢻⣿⣿⣿⣿⢻⡏⠈⠋⠹⣄⢸⣿⣿⣿⣿⠏⠀⠀⠙⢻
⠺⣿⣄⠀⠀⢸⣿⣿⣿⣿⣷⡾⠁⠀⠀⠀⠀⢸⡟⢸⣿⣿⡏⣿⣾⠃⠀⠀⠀⠀⠀⠈⢻⣼⣿⣿⣿⣿⡸⡇⠀⠀⠀⠹⣾⣿⢻⣿⣿⣇⠀⢀⣴⠿
⠀⠀⠙⠳⣄⣾⣿⣿⣿⡜⠋⠀⠀⠀⠀⠀⠀⣸⢃⣾⣿⣿⡇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⢸⣿⣿⣿⣷⣞⠁
⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⢿⣿⠃
⠀⠀⠀⠀⠉⣿⣿⠉⠉⠉⠉⢹⣿⡇⠀⠀⠉⠉⢸⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢿⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠃⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢸⣷⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠘⠁⢀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠠⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢤⡘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠘⠻⢿⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⡓⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡍⢽⠃⠤⠀⠂⠀⠀⣿⣿⢿⣿⣿⣿⡇⠀⠀⠷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⢁⡊⠀⠀⠠⠖⠀⠀⠙⣿⣿⣿⢿⣿⡅⠀⠲⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠙⠸⣿⡇⠀⠀⠁⠀⠀⠀⠼⠁⢀⢸⣿⣷⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⡈⡿⠿⡿⢻⠇⠀⣠⣴⡏⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⣘⣿⣿⠇⠀⠠⣤⠀⠀⣦⡿⡇⠀⣔⢿⣇⢤⣌⠻⣿⠀⠈⣇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⢿⣿⠃⠀⠀⠀⠃⠀⡆⠿⢠⣄⣰⡾⠀⠀⠀⠙⢳⣄⠀⠀⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⠀⠀⣀⠀⠀⣰⣶⠂⠘⠉⠀⠀⠀⣀⠀⠀⠀⠙⢿⣶⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣍⡓⢶⠛⡟⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣇⣌⣉⣉⡤⠆⠀⢰⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢧⣤⣽⣥⠶⠇⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠘⣶⢶⣦⣺⡇⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣟⣿⡾⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣖⠆⢚⡇⠀⠀⢻⢛⣛⣫⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠉⠛⠋⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣦⣄⢄⠀⠀⠀⠀⠀⢸⠿⣤⣀⢠⣼⣯⣿⠿⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠙⠻⠇

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⢠⣿⣿⣷⣄⠀⠀⢠⣿⣿⡆⠀⠀⠀⢠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣟⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⢇⣄⠘⢿⣿⣿⣿⠆⠀⣿⣿⣿⠁⡀⠀⠀⠈⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡄⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⠀⢰⣿⣿⣿⣷⡿⠲⢴⣶⣿⣿⣿⣷
⠀⠀⠀⣴⣦⢀⣿⣿⣿⣧⡤⠤⠲⣶⣽⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡀⠋⢻⣿⣿⣿⣇⣀⡀⠩⣿⣿⣿⣿⡇
⠀⠀⠀⢿⣿⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣴⣿⠟⠛⠀⠀⠀⢸⣿⠿⣿⣿⠿⣿⠛⠛⠃⠰⠛⠧⣿⣿⣿⣿⣿⣿⡟⠿⠿⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⢀⣿⠀⣿⠃⠀⠈⢷⣤⡄⠀⢀⣼⣿⠁⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⡀⠀⠀⠀⢀⣼⣿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⠆⠀⢈⡟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠁⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠐⡀⠀⠀⠲⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡛⠲
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠠⠠⠈⠁⠀⠀⢰⡇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢄⠪⠤⠀⠀⠀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⡠⠜⠃⠀⠀⠀⢈⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠒⠂⡞⡌⠀⠀⠀⠺⡁⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠏⡉⠋⠀⠀⢉⠔⠃⠀⠀⡄⠀⠀⠆⠀⠀⢸⠀⠀⠀⠀⣀⣀⣶⡕⠒⠈⠀⠉⠉⠉⢢⠀⠈⠲⠒⠋
⠀⠀⠀⠃⠀⠀⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠶⠻⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠒⠓⠒⣲⠂
⠀⠀⠀⠀⡠⡦⠊⢃⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰⣀⡤⠀⠀⢀⡴⠚⢁⡀⠀⠈⠉⠀⠃
⠀⠀⠀⠰⠏⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣁⠀⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡏⠀⠀⠀⠀⠀⠀⠀⠰⢇⡀⠀⠀⠰⣘⣆⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠊⠀⠰⡀⠀⠀⠀⠀⠀⣠⠒⢻⠀⠀⠀⠤⠤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡄⠀⠀⠀⡴⠁⢰⠋⢀⠀⢀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠸⡀⣠⠊⠀⣠⠇⠀⠀⠀⢸⠀⠀⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠟⠁⡠⠊⠈⢣⠀⠀⠀⠀⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡠⠊⠀⠀⠀⣈⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢌⣀⠐⠆⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠏⣤⠘⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢠⠀⣠⠞⠀⠀⠂⣰⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⢶⣿⡄⡀⠀⠀⢿⡀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣮⠁⠀⠀⢀⡿⠀⠀⠀⢀⡈⠗⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡄⠀⣇⠷⣤⠀⠀⠨⠀⠀⠀⠀⠸⠁⣀⣁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⣾⣟⣏⢲⣿⠐⠄⠰⠀⠀⠀⠀⢠⠠⡤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢠⡟⢟⠙⠛⣅⡿⠀⠀⠀⢦⠀⠀⣰⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢸⡇⠀⠀⠀⢨⡄⣤⡿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢸⡇⠀⠀⠀⣈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢁⣤⠬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢰⡶⠈⡄⠪⠛⡃⣙⠀⢠⡀⠀⠀⠀⠄⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡠⡁⣶⠑⡏⠡⡘⢋⠿⢐⠙⠞⠳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠌⠀⢴⡮⠺⠇⠚⠁⠋⠠⠋⢁⡰⠦⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⡀⣴⠤⡄⠀⠁⣩⡿⠳⣦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠊⠀⠢⠀⠀⡀⠙⠛⠳⢶⡀⠀⠸⠟⣅⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠁⢸⡷⢴⡶⣤⠙⣶⡛⠀⢀⡄⠈⠃⠀⠀⢠⠄⣴⡆⠽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠆⠀⠰⢟⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⣿⣿⡀⠈⠀⢠⠀⠀⣰⢿⡜⢿⣀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⡀⠈⠃⣀⠀⠀⠠⢠⠀⠀⠀⠀⡘⠁⠿⠛⠉⠉⠓⠴⣠⢞⣥⣾⣿⣾⣿⣷⠀⠀⠓
⠀⠀⠀⠀⢀⣔⣡⠄⠀⠀⠐⣄⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠳⣷⢶⡾⡰⠆⠀⠀⠀⠀⠀⠀⣤⣛⡟⠀⠉⠈⠉⠉⠀⣤⠊
⠀⠀⠀⠀⠻⠿⠛⠀⠀⠰⣶⡌⠀⠰⠊⠀⠀⠼⠃⠐⠁⠀⣠⠋⠀⢀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⢀⠸⠆
⠀⠀⠀⠀⣄⠀⠀⣀⢠⠶⠋⠀⠀⢴⠄⠀⠀⠀⠀⠀⢡⡶⠀⣠⠶⠉⠁⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡀⠀⠀⡿⠃
⠀⠀⠀⠀⢸⣉⣋⡹⠏⠀⠀⠀⠀⠘⢧⣀⣁⠂⠀⢠⡘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⡀⢡⠟⠀⣀⡠⠟⠁
⠀⠀⠀⠀⠀⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⢨⠹⢳⣦⣨⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡤⠚⢩⣵⣦⢰
⠀⠀⠀⠰⠀⠚⠉⠉⠉⢠⣄⠀⠀⢀⠰⠏⢙⣁⡉⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⢀⡅⢨⣿⠼⢦⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⢤⣉⡷⠾⣯⣼⡷⣤⡜⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠆⠛⣋⣙⠳⠻⠷⠄⠡⠂⠈⡙⠂
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠛⠲⠚⠋⡁⣐⠂⠨⠷⢴⡋⠙⠂⠙⠙⡶⠄⠀⠀⠀⠀⠀⠀⠀⣼⡆⠁⠀⠁⠉⠉⠀⠁⠀⠀⠀⠃⠀⠁⠘
⠀⠀⠀⣀⣤⠄⣎⡀⠉⢙⡂⡴⠚⣂⠐⠛⢲⠾⡀⠀⠀⢂⠤⣤⣐⣀⣼⠀⠀⠀⠀⠀⢀⡴⠂⠉⠠⠆⠀⠀⠠⠀⠠⠄⠀⣀⡀⢠⠁
⠀⠠⠂⠉⠀⡰⠀⣑⠟⢈⠁⠆⠘⠁⢶⡎⠀⠃⢁⡀⡤⠉⣧⢘⣀⡅⠸⠀⠀⠀⠀⢀⠢⠄⣸⠀⠠⠤⠤⠤⠤⠤⠤⠤
⠰⠀⡀⠀⣰⠃⣔⠉⠖⠉⠀⠀⠛⠂⠒⠠⠠⣆⠀⣄⠁⠀⢀⡜⢿⠌⢀⠦⠀⠀⠀⡜⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⢀⠀⡙⠲⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠷⠚⠂⢿⠤⠶⠌⠀⠈⠂⠰⠁
⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠡⠤⠤⠤⢀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⣄⠀⣠⠄⠒⠂⠀⠀⠐⠒⠒⠈⠉⠀⠀⠀⢡⠀⢀⠖⢉⠤⠄⣉⡑⡄
⠀⠀⠀⠀⠀⢀⠤⠊⠀⢀⣤⠶⠒⠂⠘⡖⢂⠀⠀⠀⣀⣠⣀⠀⢀⡤⠶⠤⣄⠀⢸⠀⢸⠀⠇⠀⡠⠚⣉⢝⠠⢄
⠀⠀⡠⠔⠊⠁⠀⣀⠀⠸⠀⢀⣤⠤⠄⠘⡌⡄⠀⠚⠁⠀⠈⠁⠈⠀⣀⣀⡀⠀⢨⠔⠁⡸⠀⠀⢧⡞⣊⠥⠒⠉
⠀⢎⠀⠀⠀⣰⠟⠉⠁⠀⠀⠸⠁⠀⢀⡀⠘⣷⠀⢠⠶⠛⠓⠄⠀⠘⠉⠉⠉⠀⡖⠒⠊
⠀⠈⠢⡀⠀⠃⠀⣴⠞⠃⠀⠀⡀⣠⠎⢱⠀⢹⢃⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠈⡶⢄⠀⠁⠀⠀⣀⡭⠞⠁⠀⠸⠀⢸⠈⢆⠀⣠⢶⣒⠛⠿⠟⠻⠄⠸
⠀⠀⠀⢠⠀⠎⠑⠤⡀⠙⠤⣀⣀⣀⠔⠁⠀⡌⠀⠈⢦⡉⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠈⣼⡀⠀⠀⠈⠒⠤⠤⢀⣀⣀⡠⠔⠁⠀⠀⠀⠉⠢⣀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠈⠫⣁⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣈⠆
⠀⠀⠀⠀⢐⣉⡁⠬⠄⠒⠊
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⣄⣤⣀⡤⢤⠀⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣯⡈⠛⣦⣉⣣⠘⣇⣼⢳⠈⠒⣉⡿⠴⢟⣒⣒⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⣓⣾⣿⣿⠈⠧⣈⠭⣤⣙⣻⡾⠛⣛⡥⠖⠛⠉⠛⠣⠍⠙⡚⠭⢷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⣿⣿⡿⣫⢟⣻⣿⣶⣦⣼⣿⡿⢋⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢶⠱⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣾⠛⣭⣭⣭⣗⣓⠿⣿⣿⣿⣿⠟⣡⠶⢛⣡⣤⠦⠄⠀⠀⠀⠀⣤⣤⡀⠈⠻⣈⠷⢸⡿⣄
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣰⣟⣻⠿⣭⣿⣿⣷⡌⣿⣿⢏⡜⠁⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⡀⠈⠉⢦⠓⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣚⡡⠖⠉⠉⠉⠉⠛⢿⣿⣫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⢆⠀⣿
⠀⠀⠀⠀⠀⢀⡴⠻⠋⠈⠳⢄⣤⣤⣴⣶⣤⡿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡀⢣⣿
⠀⠀⠀⠀⠀⠀⣿⠓⠲⠴⢚⣿⠿⣿⣿⣿⡿⣹⣁⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⡄⠉⢁⣼⡟
⠀⠀⠀⠀⠀⢀⣘⣦⣠⣾⢻⣸⡇⡏⢸⣿⣿⠉⠈⠓⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠟⠛⠁
⠀⠀⠀⠀⠀⢯⣿⢁⣿⣿⣿⣿⣧⣿⣿⢳⠇⠀⠀⠀⠀⣀⡀⠀⠀⠈⠍⠁⠀⣀⣠⣤⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⡼⢿⣿⢿⣿⢿⡟⢿⣿⢿⡿⠖⠢⠄⠈⠉⠉⠁⢀⣀⣤⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⣧⠀⣿⡆⢻⡌⣷⣼⣏⣾⣋⣀⡤⣰⣦⣤⡶⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠹⠤⣿⣽⣾⣷⣿⣫⣿⣿⡷⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡀⠀⢀⢀⡀⣀⣵⣺⣣⢒⡒⡢⢀⣀⣯⣿⣭⣽⣽⣟⣫⣽⣿⣶⣶⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⢚⣉⣦⣖⣍⣯⣸⣳⣦⣦⣶⣎⣴⣽⠉⢉⣯⡭⠀⠉⠀⠉⠉⠉⠁⢩⠀⢻⡿⡟⢁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⣿⣿⣿⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⢳⠇⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⣷⡂⡡⠄⢀⡀
⠀⠀⠀⠀⢀⣄⣶⣶⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠹⣷⡃⠘⠊
⠀⠀⠀⠀⠰⣻⢿⣿⣿⣿⠁⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⢲⣞⣥
⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣸⡇⠀⢰⣾⣶⣶⣶⣶⣶⣶⣶⣿⣷⠀⣿⡆⠀⣺⣿⣏⣻⣒⢀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⠁⠀⢀⣤⡀⠀⠀⠀⢹⣿⣿⣿⣿⢹⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠁⠀⣻⣿⣿⣿⡇
⠀⠀⠀⠀⢐⣺⣿⣿⡇⠀⠀⠀⠘⠀⢀⠀⢰⣴⡅⠈⣿⣿⢸⣿⣟⡄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⢀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⡨⡿⣿⣿⠀⣤⠀⠀⠀⠀⠁⠀⠀⠀⣥⠀⢿⣿⣇⢻⣿⣷⡹⣻⣿⣿⣿⣿⣿⣿⣿⣟⣼⣏⡼⣰⣿⣿⣿⣿⣾⠂
⠀⠀⠀⢼⣭⣿⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⠠⠚⠯⣄⣨⣿⣿⣯⡿⣿⣿⣷⣾⣿⠛⢻⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⢛⢟⣴⠕
⠀⠀⠠⣴⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⠻⣷⣿⣓⣐⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⡩⠶⠄
⠀⠀⢴⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⡿⢿⣿⣿⣿⣭⣛⠻⣿⡿⠿⢛⣟⣽⣿⣿⣿⣿⣿⣿⣿⣻⢏⡑⠉
⠀⢠⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡀⠐⠘⠁⠈⢻⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠐
⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠠⠡⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠃⠀⠌⠀⠀⠀⠀⠀⠀⢿⣻⡉⠻⣿⣿⣿⣏⠀⠳⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣅
⠀⢼⣿⣿⣿⡇⠆⠒⡄⠀⠀⠀⠀⠀⠁⠸⡗⣠⠤⠀⡀⠀⠀⠀⠀⡘⣠⡾⢻⠉⣿⣇⣽⣶⣶⣿⠭⢉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⣾⣿⣿⣿⠏⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢋⡇⠀⠀⡁⠀⠀⠀⣞⠀⣻⣧⣈⣀⣿⣿⠘⠻⡇⠀⠀⠀⠡⣴⡿⢻⡏⠙⠻⣿⣿⣿⣿⣿⣧⡀
⠀⣿⣿⣿⡟⠀⠀⠜⠁⠀⠀⠀⠀⠀⠲⠀⠈⠀⠀⠠⢶⠀⠀⢸⣧⣿⣷⣿⠿⣧⣾⣿⣶⣶⣿⠦⠤⣤⣶⣾⡇⠈⠃⣀⡀⣿⣿⣿⣿⣿⣿⣷⣀
⠀⣿⣿⣿⠏⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠈⣿⠖⠉⡀⠈⠀⠀⠀⠙⣿⢿⣿⣧⣻⣿⣿⡇⣿⢁⣁⢀⡽⠟⢻⣹⣷⡜⠻⡇⠈⢻⠿⠉⠙⢿⣿⣿⣶⣆
⠀⣽⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡟⠀⠀⠻⡆⠀⠀⠀⢀⣻⣿⣿⣿⣿⣟⣿⣜⣿⣶⣿⣿⠀⢡⣤⠛⠛⢇⠀⠐⢠⣿⠋⠉⠀⣼⠛⠛⠿⡿⣷
⠀⠹⠿⠿⠷⢦⢤⣤⣀⣀⡀⢀⠀⢀⣤⣽⡇⠀⠀⠀⠁⢀⣀⣀⣨⣿⣿⣿⡿⣿⠇⣿⡿⣿⣿⣿⣿⡄⡇⠘⠄⠀⢸⣖⠶⢶⠉⠇⠀⠀⣟⠒⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⡛⠟⠛⠋⠙⡛⠛⠉⣉⣁⣯⠞⠻⣾⣿⣍⣝⢯⣿⣿⣿⣿⣦⣤⣤⣾⣿⡿⡿⣷⢦⡴⢾⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣒⣶⣒⣒⣒⣒⡒⢰⣶⣿⣿⣍⡀⠓⢋⣶⣷⣐⠞⠳⠞⠛⣛⣿⠾⠁⠙⠛⠻⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠈⠉⠉⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈

⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦
⢸⣿⡿⠻⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⢣⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠙⢦⠀⠀⢸⣿
⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣀⣀⣞⢲⣶⣶⣶⣶⣶⣾⠟⠢⣀⠀⢸⣶⣶⣾⣿
⢸⣿⣿⡿⠋⠉⠙⢿⣿⠛⠛⠻⢿⣿⣿⠿⠛⠿⣿⣿⣿⠟⠉⠉⣹⣿⣿⠉⠉⠉⠉⣿⡟⠉⠀⠙⢻⣿⣷⣄⡈⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣧⠤⠤⠤⠼⡇⠀⠀⠀⢸⠿⠧⠤⠤⠤⠼⣿⣏⠀⠀⠘⡕⢨⡧⠤⠤⠤⠼⢿⡀⠀⠀⠀⢀⣿⣿⣛⡻⠿⠿⣿⣿⣿⣿
⣸⣿⣅⡠⠤⠤⠴⠂⠱⢤⢤⡤⠊⡔⠉⠉⠉⠉⣲⣨⣿⣿⣿⣛⣷⡊⡰⠒⠒⠒⢒⣤⣕⣀⣀⣀⣺⣩⠒⠒⠒⠒⠒⣆⣹⣿⣉
⡧⠤⣁⠉⡆⠀⢰⠊⣉⣉⣉⣙⣒⠒⠢⡀⠀⡎⢡⠤⠤⠤⠤⠤⠤⣍⠙⠆⠀⡎⠁⣀⡀⠤⠤⠤⢄⠈⢱⠀⠀⡰⠉⣠⠤⠤⡼
⡇⠀⢸⠀⡇⠀⡇⢰⠁⠀⠀⠀⠀⢹⠀⡇⠀⣇⢰⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⠇⢸⠁⠀⠀⠀⠀⠀⡇⡸⠀⠀⢇⢸⡁⠀⠀⢣
⠑⢄⣸⣀⣯⣷⣷⣈⡆⠀⠀⠀⠀⡎⢸⠀⠀⠸⡀⢇⠀⠀⠀⠀⢠⠃⣾⡆⠐⣾⣈⣆⡀⠀⠀⠀⡰⢡⠃⠀⠀⠘⡄⢣⠀⣀⠼
⣶⣶⡶⣷⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢠
⠀⠀⠀⣆⣀⠈⠀⠀⢈⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣧⣀⣀⣀⣛⣀⡼⡀
⠀⠀⠀⢿⣿⡟⠀⠘⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⣶⠀⢠⣶⣶⣿⠂⠀⠸⡇⠀⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠈⢿⣿⠄⢸⣿⠟⠀⠀⠀⢿⡞⠒⠲⠶⠶⠶⠶⠶⠖⠒⠒⠉⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⢰⣿⡿⠃⠀⠀⠀⠳⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠣⠽⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠐⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠃⠀⠦⣈⣀⣈⡠⠞⣁⠀⢸⡇⠀⠀⠀⠨⣅⣀⣀⡠⠽⢡⠀⠀⠀⣿⠀⠘⠀⠀⠀⡷⡍⣁⣀⣩⡵⠀⢹⠀⠸⠀⠀⠸⢯⣀⣀⣈⡭⣇
⠀⠀⠀⡆⡀⣾⠀⠰⠀⠀⠈⢀⢸⠇⠀⠠⣦⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⡇⠀⠘⠔⠀⠀⣇⠂⠀⠀⠀⠁⠀⢸⠀⠀⠠⣤⠀⠘⢸⠃⠀⠀⠉
⠤⠤⠀⠤⠧⡿⡤⠤⠼⠀⠤⠼⠼⣤⣤⣤⢤⣥⠤⡼⠧⠄⠠⠤⠴⠤⢠⡧⠄⠄⠠⠼⣶⠿⠤⠴⠧⠠⠤⠦⠼⣤⣤⡤⠼⢤⠤⡼⠤⠄⠤⠤⠧⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⣀⢴⡄⠀⢀⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣧⠼⢿⡛⠋⣽⣿⣿⣿⣿⢛⠛⣲⣶⡴⠟⢾⡇⠀⠈⢛⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⣾⠯⠙⠀⣇⠀⠀⠙⠚⠁⢻⢱⣿⣟⡍⠛⢩⢟⠀⠀⣨⠿⠛⣿⣭⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣲⣴⡟⠿⠏⠀⣺⢶⡞⠋⣠⠖⢯⡲⣀⣸⣿⣿⡷⠶⠶⠿⠾⠶⠾⠷⣤⣤⣴⣴⣿⣿⡽⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠻⣷⣽⣶⡞⠋⡹⣷⣣⢙⣷⣿⡿⠛⠋⣍⣙⢲⠂⠀⠄⠘⠃⣤⠀⠙⠛⠒⡾⢭⣛⠿⣿⣦⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡄⠀⢿⣿⣿⣝⣦⣐⣿⠿⠛⠙⠿⠃⡀⠀⠶⠾⠍⠀⠀⠆⠀⣤⠀⠀⠛⡇⠠⡍⠛⠾⣝⠲⣝⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣁⣀⡿⣀⡎⡼⣻⣿⡿⢋⠁⠀⠀⠀⢰⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠤⠈⢁⠈⠓⢮⠻⣆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡆⠀⠊⠉⠚⠛⣇⣷⣿⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⢀⠀⠌⠳⡜⣧⡀
⠀⠀⠀⠀⠀⠀⡾⢿⠿⢀⡿⢹⣄⣤⣤⣖⣴⠟⠛⠻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠐⣾⣼⣤⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠦⣤⡿⠟⣻⣷⣤⣤⣿⡁⠀⠈⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢠⠀⠀⠀⡀⡌⠀⠀⠀⠘⠉⠉⢁⣠⡴⠞⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡟⠉⠀⠹⢿⣾⣿⠟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⡀⠀⠀⣤⠀⣀⣬⡶⠞⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡧⣶⣲⣿⣿⣾⣿⣟⡤⠀⠀⠀⠀⠀⠈⠀⠀⠐⠍⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⠀⠀⠋⣀⣼⠶⠛⠋⠁
⠀⠀⠀⢀⡴⣫⣷⣿⣿⣿⠿⣿⣿⣿⡞⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⢀⣠⣤⠶⠛⠉
⠀⠀⢠⣟⣾⣿⡿⠛⣡⡶⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠾⠀⠀⠠⠀⠀⢠⠀⢀⣠⣴⢾⣯⣡⡴⠞⠛⠉
⠀⠀⠈⠿⣯⠿⢤⣠⣘⠿⣿⢯⡇⠘⠟⠀⡤⠀⠀⠀⠀⣄⣀⠀⠐⠃⢁⣠⠴⠚⣉⣤⡿⠟⠋⠁
⠀⠀⣠⣖⡲⡄⢰⠋⣡⠶⣿⢸⢡⡄⠀⡶⠀⠀⠀⠀⣰⡓⡾⡄⠀⠚⣉⣤⠶⠛⠉⠁
⠀⠀⢧⣙⠛⣁⡼⢏⠁⢀⣿⢸⠺⠀⠀⠀⢀⠀⢀⠀⠌⢙⣩⣴⠶⠛⠉
⠀⠀⠀⠈⠉⠉⠀⡼⢰⢯⣿⣼⣆⢀⡀⠀⢈⣌⣨⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⢰⣳⣎⢿⣿⣷⢿⣼⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠉⠉⠙⠛⠻⠿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠦⣤⣤⣸⣷⣤⣀⣀⣀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠛⢛⢿⠏⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠆⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠐⠀⠺⢽⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⣀⠀⠀⠀⠀⣄⡶⡀⢠⣀⠙⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠛⠋⢉⡙⠿⣿⢿⣿⣿⣿⡀⣤⠀⣰⣿⣿⣷⣿⣿⠿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢘⢿⠁⣤⠴⠒⢋⣉⣩⣝⡳⣝⣿⢿⢷⡜⠢⣿⣿⡷⢛⣁⣘⠢⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠃⣨⣤⠶⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠀⡿⠿⣿⣿⠿⠟⡁⠒⠀⠀⠀⠀⠈⢻⣿⡿⠟⠛⣻⡏
⠀⠀⠀⠀⠀⣴⠟⠟⠓⠄⠙⡀⠀⠈⡆⠀⠀⡀⠄⠊⠀⣠⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡛⠿⣿⣧
⠀⠀⠀⠀⠀⢿⣇⠀⠀⢠⠀⠃⠀⢀⠧⠀⠀⠀⡀⠴⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡵⡤⡸⣿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⢀⣠⠔⢁⡠⠔⠂⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⣀⣀⠀⠀⢸⣷⡸⣿⣿⡇
⠀⠀⠀⠀⣼⣉⠙⠧⡀⢸⡿⢁⡔⠉⡗⡀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⣿⣿⣦⣼⣿⣿⣻⣿
⠀⠀⠀⣼⡟⡟⠓⠄⠘⢌⡇⣼⣀⣠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢿⣿⡟⣿⣿⡏
⠀⠀⠀⢰⣵⣇⠀⠀⠐⠪⡿⣛⣿⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣴⣋⣍⠳⡶⣻⣯⣠⡉⢷⣽⠟
⠀⠀⠀⠘⣿⣿⠀⠀⠀⢰⠳⣾⣷⣄⠈⢆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠿⠛⠛⠉⠛⢿⣾⠛⠿⣿⢟⡿⠁
⠀⠀⠀⠀⢹⣻⣦⠀⠀⢸⠀⠘⡿⣿⣷⠈⢢⡀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢤⣀⣀⣀⣘⣿⣤⣾⣿⣼⠃
⠀⠀⠀⠀⠘⣿⡽⣄⠀⡀⠃⢁⡇⢿⣧⢠⡀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠿⣿⡿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢾⣷⣤⣿⡤⠞⠀⠘⣿⢦⣕⢤⡀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢷⣿⠉⠁⠀⠀⠈⠛⠷⣦⣤⣄⣀⠀⠀⠀⠀⡀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠒

⣞⣟⣉⣉⣉⣉⣉⠉⠉⠉⠙⣶⣶⡄
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣛⣙⣿⣻⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣟⠋⢹⣏⠉⢉⣿⠳⣮⣛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣿⠀⣼⠃⣠⠞⠛⣯⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠤⠤⠼⠦⠼⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠧⠿⠶⠧⠾⣧⣤⡴⠛⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢦⣄⣀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡞⠁⠙⣿⣦⡈⠙⢻⡿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡴⠋⠀⠀⠀⠈⢧⣙⣶⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠎⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⣿⣿⣿⣿⡿⠋⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠛⠛⠛⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⠀⠀⣿⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠉⠀⠀⢹⡀⢀⣿⠀⠀⠉⠉⠉⠙⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣄⣀⣀⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠎⢀⡴⠀⣠⠏⡀⠀⢄⣀⠒⠦⠤⣄⣀⣀⣀⡤⠤⠀⠀⢀⣀⡠⠤⠀⠙⣆⠀⢢⡀⠑⢄⡀
⠀⠀⠀⠀⣀⠴⠋⣀⡴⠋⣠⡞⠁⠀⠉⠲⢤⣀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⢀⣠⠴⠊⠁⠈⠳⣄⠙⠦⣀⠙⠦⣄
⠀⠀⠀⠀⠀⠠⢚⣡⡴⢾⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣤⣤⣤⡤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠈⡗⢦⣌⣓⠆
⠀⠀⠖⠒⠚⠋⠉⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠙⠛⠒⠒
⠀⠀⠀⠀⠀⠀⢰⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡀⠀⡆
⠀⠀⠀⢰⠀⡸⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢧⠀⡇
⠀⠀⠀⡘⡰⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢧⢡
⠀⢀⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⡀
⢀⢛⠩⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⡍⡙
⢸⢸⠀⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⠀⡇
⢸⢸⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⠀⡇
⢸⠀⠀⢁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠸⠀⠁
⠈⠀⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⠀⢨⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠒⠳⡆⠀⠀⠠⠀⠀⠀⡠⠐⠁⠀⠉⠉⢂⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣇⡟⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⢿⡆⠀⠀⣿⠇⠀⢀⣴⠋⠀⠀⠀⠀⠀⡴⠋⠀⢠⠄⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⢠⠟⠀⠀⡈⢷⣄⢈⣀⡀⠀⠏⢠⣧⣾⠃⠀⠔⠊⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠂⠘
⠀⠀⣠⠏⠀⠀⠀⠈⠀⠙⢮⠉⠉⠀⠸⣸⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠻⠤⠤⠀⠀⠀⠀⣀⡀⢀⡀⠠⠞⠛⣷⣧⡶⠾⠛⠛⠒⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠔⠒⠉⠀⣀⣴⣶⢂⡴⠃⠀⡠⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠀⡄⡄⠀⡄⠀⠀⢠⠀⡄
⠀⠀⣎⡀⠀⠀⢠⣾⣿⣿⢱⣿⠁⠀⠀⠀⠘⡄⠳⣄⠈⠉⠙⠒⠒⠠⢤⣄⡠⠀⠀⠀⠀⠈⠀⠈⠀⠁⠈⠀⠁⠀⠀⠈⠀⠃
⠀⠀⠉⢻⡄⠀⢻⣿⣿⡇⡿⢹⢀⠀⢠⠀⠀⢻⠀⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣼⠇⠀⢸⣿⣿⣷⣡⣿⣿⠀⠀⠆⠀⢸⠆⠁⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠸⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⢷⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡦⠀⠀⠀⠀⡄⠀⡀⢀⠀⠀⣀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⣻⣿⣛⣿⣿⡄⣧⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠱⠀⠙⠄⠓⠀⠀⠸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣫⡿⠿⢿⣮⡸⣧⢿⠀⠀⠀⠀⠀⠀⠐⢶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣼⠁⠀⠀⠀⠹⣷⡄⠈⡀⠠⣴⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡇⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡇⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠁⠀⠀⠀⠀⠀⠀⠸⣿⢷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⢠⠖⠉⢹⣿⣓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⠀⡔⠁⠀⠀⣻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡜⠀⠀⢀⣼⣿⣿⣿⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠐⠋⠀⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠠⠅⠀⣠⠄⡂⠀⠀⠀⠅⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⡃⠘⠀⠘⣛⣛⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣉⣉⣉⣉⣉⡅⠠⠂⢸⣿⣿⠇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠈⠁⢠⡆⣼⣿⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠆⠨⣤⠄⣀⣴⣪⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣌⢛⠋⣡⠎⠙⡽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢴⠃⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠀⠀⣀⣼⣿⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⠋⢹⡏⠐⠛⠉⡿⠿⠧⣤⣄⣰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣞⣹⡂⣀⢀⡀⠀⢸⡇⠀⣇⠀⢸⡇⢀⠀⠀⠀⠠⠀⠈⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⣠⣾⣿⢛⣿⡿⠿⣾⣿⣽⣦⣯⣼⣇⣿⣿⠀⣿⣿⡈⠀⠀⠀⠀⠀⠀⡀⠈⠹⣷⠜⠛⢦⣾⣄⡤⡄
⠀⠀⠀⢀⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣿⡿⡧⢱⣟⠇⠀⠀⢐⣦⡀⠀⣀⠀⢸⣿⡟⠲⣾⠁⢻⡌⢶⠚⠀⠀⡀
⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣶⡿⢻⣾⣿⠟⣿⣋⠏⠃⢆⠀⠀⠀⠟⠒⠶⠆⢀⣡⣂⣠⣤⡼⠛⢏⡉⠿⠉⣹⡟⢢⣼⡷⠒⢡⣾⡅
⠀⠈⠛⠻⣿⣿⣿⣿⣹⣿⣼⣿⣶⣿⣿⣿⡏⠋⣐⣶⣨⣤⡀⠈⠛⠛⣙⣿⣿⣿⡟⠁⠉⣿⣿⠈⠁⣄⣸⡉⣳⡋⢻⣷⢦⣾⡿⠁
⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣦⣿⣬⣄⣁⣀⣀⡐⣀⣉⣉⣰⡟⠹⣿⣿⣿⣿⡷⠠⣾⣿⣿⣦⣤⣷⣾⣭⣿⣯⣽⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠉⠛⠃⠉⠉⠉⢩⢀⠁⠉⠩⠤⠖⠌⠻⠄⠰⠶⠂⠲⠛⠛⠛⠏⠡⠤⢿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠙⡟⢼⣑⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⢀⠨⣷⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠈⠐⣲⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢀⣠⣶⠾⢀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⢀⣤⡾⠟⢉⡶⣶⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠊⢉⣉⢰⣄⠠⠀⠀⠀⢀⡾⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢠⠙⠟⠉⢀⣉⢻⡇⠀⣀⠀⠀⣼⠃⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⣹⣆⣙⣓⣰⣍⠹⡷⠶⠞⢹⣦⣼⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠃⠀⠟⢻⣍⣏⠂⣤⠀⠀⠀⠉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢭⡶⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⢀⡿⡀
⠀⠀⢿⡶⠤⡀⠀⠀⠀⠀⡿⢦⣄⡥⢠⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡞⡱⣡⣶⣦⡀
⠀⠀⠈⠓⠀⠀⠀⠐⠀⠚⠁⠀⠙⠛⠻⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣠⡴⢋⣾⣿⡿⠿⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣰⡿⢛⣡⣖⣯⣍⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⡾⢋⣴⡿⠟⢿⡿⣃⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢂⠟⣥⢊⡴⢋⣾⠟⠉⣀⣤⡾⣿⣏⠉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠔⠋⣿⠃⢚⡴⠁⣫⣴⠾⠋⠁⠀⠋⢸⡇⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣄⠀⠀⣿⣶⠟⣠⡾⠛⠁⠀⠀⠀⠀⠀⣾⢷⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣡⡀⠀⠀⢉⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⣏⠉⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣦⣄⠀⠀⠀⡾⣁⢶⡇⢹⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⣹⣃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣶⣦⠀⠙⠬⣾⡷⠋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣷⡏⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⡷⠎⢠⡄⢰⣷⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡞⠙⠂
⠀⠀⠀⠀⠀⢰⠖⠀⠑⣪⡻⠿⡟⠃⠀⠀⠀⠘⣫⢏⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⣤⠂
⠀⠀⠀⠀⠀⠘⣧⡘⢛⠻⢿⣆⠹⣤⣄⣤⣴⠞⠃⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⣶⣶⣤⣀⠀⠈⠙⢯⣴⡄⢨⡳⡄⠉⠁⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⢷⣾⣿⣿⣶⣦⣤⣤⣴⣿⡙⠲⣤⣭⣬⠗⣼⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠉⠉⠛⠉⠛⠛⠛⠃⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡤⠤⢄⡀⢀⡠⢎⠉⠳⣄⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠈⢳⢤⡤⠃⡠⠴⡌⠭⠀⠈⠂⠀⢈⠭⣓⣂⣚⢳⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠉⠉⢆⠀⠀⢦⠃⠀⠘⡀⣀⣱⠰⡶⠧⠴⢊⡵⠮⢭⢤⣍⣿⢀⠎⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠲⠤⣀⠀⢦⡱⣀⠮⠁⠀⣊⣉⠭⢵⣿⣭⠥⠤⠽⢊⣉⣠⠤⢾⠋⠉⠑⢤⣀⣠⢷⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣇⠀⠀⢲⠤⠞⣓⡩⠭⠭⠝⣒⣦⣀⣹⡀⣁⣠⠤⠔⠚⠛⢛⣛⣛⣛⣛⣒⠲⠦⢄⡀⠀⢃⠄⢀⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠤⠤⢩⠖⣡⣶⠋⣠⡂⠤⠔⡺⠉⢉⡥⠖⠉⢁⣠⠴⠒⠚⠉⠉⠁⠀⠀⠀⠉⠉⠙⠒⠮⣕⡺⡀⠁⠈⠉⡧
⠀⠀⠀⠀⢀⡖⠉⢱⠀⠙⠲⢡⢞⣥⣶⠦⢤⣛⡏⢈⡱⠚⠁⣠⠴⣚⠥⠂⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠲⢍⠻⣦⡀⠘⢑
⠀⠀⠀⠀⠀⡇⢀⡴⣒⣤⢣⣣⠟⠋⠘⡄⠀⢜⡵⠋⢀⡴⢋⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢷⡔⠋
⠀⠀⠀⣠⠚⠉⡰⡪⠃⣟⢿⣧⠀⠀⡠⣇⡴⠋⢀⠔⢩⠞⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷
⠀⠀⠀⢇⠀⡰⠃⠀⣸⡟⢀⡾⣖⠊⢠⠎⢀⡴⠃⠔⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⣸⠙⠁⢅⠮⠊⡠⢪⡄⠀⡴⠃⣠⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢰⠃⢠⡌⡆⠠⡪⡾⠛⠃⡜⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⢀⡏⠀⢾⡀⠀⡇⡇⠳⢄⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤
⠀⡼⠀⠖⠀⢨⠂⢄⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠁
⢠⠇⡆⠠⣀⡴⠒⢲⠁⡼⢀⡞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠤⢒⣊⠭⠐⣂⡥⠴⠒⠉⠁
⣸⢰⠉⡀⢀⠀⠐⠊⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣊⠥⠖⠊⠉
⡇⠘⢀⠀⠘⢰⠄⡰⠁⣰⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀
⡇⡇⠈⠓⢚⣜⡼⠁⣰⠃⠀⠀⢀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠉⢻⡏⠉⠀⣸⣧⠀⠀⣴⠟⠋⠙⠁⣴⠟⠉⠛⢷⡄⢼⡏⠉⠋
⢻⡿⣌⣩⠥⠊⢀⣜⣡⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣯⣼⣇⠀⣿⡀⠀⠀⠐⣿⠀⠀⠀⢸⡇⠈⠙⠻⣦
⠀⠙⠒⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠠⠟⠀⠀⠹⠆⠘⠻⠶⠶⠆⠙⠳⠶⠶⠋⠀⠲⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⣐⠀⠀⠀⢀⠀⢠⠂⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠤⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⠄⠀⠈⢄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠢⠀⠀⢂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠐⠄⠀⠀⠑⢄⠀⠁⢀⠀⠢⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠢⢄⠀⠑⢄⠀⠢⡀⠡⠀⢂⠀⠄⠀⠀⠀⠈⠠⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⠑⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠢⠤⠤⠄⣾⣄⣤⣤⢤⠦⡤⠴⡼⠇⠀⢀⠀⠀⠀⠀⠀⢸⠀⠐⠖⠰⠤⠴⠤⠦⠂⠒⠒⠚⡅⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢣⠀⠀⠀⠀⢻⡳⠤⣤⣠⣄⣤⣀⣄⣤⣠⡤⣠⠤⡔⡆⠀⠈⠀⠐⠂⠀⠀⠘⠓⠆⢤⠀⠀⡘⠇⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⡜⣧⠀⠀⠁⠈⡒⠉⠠⠀⠀⠐⢌⠲⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠰⠀⡄
⠀⢀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠠⠤⣼⣧⡀⠈⠀⠁⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⢀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⣀⣠⠬⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⡇⠀⠈⠐⠂
⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⢦⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⢀⡀⠀⣨⠤⠀⠈⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠁⠉⠉⡁⠀⠐⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠶⠿⠛⠛⠛⠛⠛⠛⠿⠶⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣀⣠⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣄⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⠃
⠀⠀⠀⠀⠀⠀⡌⣁⣈⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣟⣿⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡷
⠀⠀⠀⠀⠀⠀⠈⣹⣿⡉⣀⣈⠿⠿⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢟⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢒⣒⣒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣍
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠘⣍⣉⣏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿
⠀⠀⠀⠀⠀⠀⣧⡉⠐⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⣬⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠖⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠈⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣃⣠⡄
⠀⠀⠀⠀⠶⣿⡄⢈⣏⠰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠙⠋⠁

⣿⠿⠿⠿⠿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣛⣿⣟⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⣋⣩⣵⣶⣦⣤⣾⠏⠁⣉⣭⣭⣵⣶⣿⣿⣿⣿⣭⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢡⣴⣾⡿⠛⢻⣿⠋⢉⣡⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣀⣴⣿⣧⣌⣡⣤⣾⠟⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢀⣾⡟⠛⠀⠉⣹⡿⠉⢡⣾⠟⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣿⣟⠁⠀⣠⣤⣿⠇⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡿⠀⣠⣿⠿⠿⢿⣿⠁⠀⣼⡟⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠁⠀⢀⣼⡿⠀⣼⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⢠⣿⠁⣾⡟⠀⠀⣿⡏⢀⣾⡟⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣠⣿⠇⠀⣀⣿⣇⣾⡟⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⣠⡀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢰⣿⢉⣾⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣼⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢰⠂⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⡆
⠀⠀⠀⠀⠀⢸⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠘⡄
⠀⠀⠀⠀⠀⢰⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣴⠃
⠀⠀⠀⠀⠀⢼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⢀⣠⣧⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣼⡅⢛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⡆
⠀⠀⢀⣿⢱⣿⣿⢻⣿⣿⣿⡄⠀⠀⠀⣼⠃⣿⡇⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠟⢁⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠊⢹⡆⡀
⠀⠀⢸⡏⢸⣿⣿⣸⣿⣿⡟⡇⠀⠀⠀⣿⣄⣿⠇⢤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⣾⣦⣼⣷⣧
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠄⠀⠀⠀⠀⠛⣿⣿⡄⠀⠀⠀⠀⠀⣼⢳⣿⣷⢸⣿⣿⣇
⠀⠀⠸⠇⠘⠛⠛⠻⠟⠿⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣸⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⣸⠃⢸⣿⣿⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣤⣀⣿⣀⣤⣿⣿⣿⡤⠀⠀⠀⡿⠀⢸⣿⣿⢈⣹⣿⣿⣧
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⡟⢸⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣶⣶⣤⣤⣤⣤⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠀⠛⠛⠃⠒⠛⠛⠛⠛
⠀⠀⢸⡇⢸⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢸⣿⣿⣾⣿⣿⣿⣿⠀⠀⢶⣤⣤⢀⣀⣀⣀⣀⣀⣤⣤⣵⠂
⠀⠀⢸⡇⣺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣾⣿⣿⣠⣿⣿⣿⣿⠀⠀⢸⣿⡃⠀⢙⣟⡓⠀⢹⣿⣿⣿
⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⣀⣿⣥⣀⣸⣿⣿⡇
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠘⠷⣶⣤⣤⣤⣤⣤⣤⣶⠾⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠁⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠂⠐⠈⠁



⠀⠀⡀
⠀⠀⠀⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠡


⠀⠀⠈⠀⠀⠂⢀
⠀⠀⠀⠀⣀⣀⡸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⣀⣀⡀
⠀⠀⠘⠋⠃⠀⠀⠀⠀⠲⠠⠖⠐⠀⠄⠄⠒⠺⢛⣿⠟⠛⠛⢿⡛⠛⠒⠠⠄⠖⠒⠐⠂⠐⠀⠀⡀⠠⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⡄⡀⠈⠉⠀⠀⠀⣄⣾⠁⠀⠀⠀⠈⢱⣄⠆⠀⠀⠈⠉⠀⡀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⡆⣠⡍⠀⠈⠉⠀⠈⠉⠀⠘⣤⢀⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠛⠒⠒⠶⠶⠦⠤⠴⠶⠶⠒⠓⠚⠒⠤
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⡀⠀⠀⠀⢠⠀⣥⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣧⣄⣷⣶⠀⠀⠀⠀⠀⠁⠐⠂⠜⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠑⠒⣿⠀⠀⠀⠀⠀⠆⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠀⠀⠀⠀⢰⠀⠀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠀⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠦⠈⠾⠃⠀⠀⠀⠀⠀⠣⠀⠠⠾⠃⠀⠀⠀⠸⠆⠀⠶⠃⠀⠀⠀⠀⠠⠄⠠⠶⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠴⠟

⠀⠀⠀⠀⣀⡀⠀⢠⣰⢄⡀⠀⠀⠀⡤⠄⠀⠠⠀⢤⠀⠀⢠⠂⠐⠒⠂⢲⡄⠀⠀⣠⡤⢀⠀⣤⣤⣄
⠀⠀⠀⠀⠹⡄⠀⠈⢹⠟⠀⠀⠀⠀⢂⠀⠀⠀⠀⠘⠀⠀⠀⢂⠀⠀⢀⠞⠀⠀⠀⠣⠀⠀⠀⠀⠀⠉⠀⠀⢠⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠙⢻⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡟
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠀⠀⠀⠐⠋

⠀⠀⠀⠀⣀⡀⠤⠄⠀⢀⡀⠀⠀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢏⠀⡀⢀⡀⢻⡇⠀⠀⠀⠘⠓⠛⠛⢛⡗⠀⠀⠀⠂⠀⠈⠀⡶⠀⠀⠀⠀⠃⠀⠀⢹⡇⠀⠀⠀⠐⠗⢒⣆⣰⠛⣿
⠀⠀⠀⠀⠘⡀⠀⣀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⢄⡋⢿⢛⡇⣿
⠀⠀⠀⠀⠀⢟⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⢀⠐⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⢀⡁⠀⠒⠊⠀⡁
⠀⠀⠀⠀⠀⠘⠃⠀⠚⠃⠀⠀⠀⠀⠀⠙⠀⠒⠛⠀⠀⠀⠀⠘⠀⠐⠛⠁⠀⠀⠀⠀⠀⠂⠀⠚⠀⠀⠀⠀⠈⠓⠂⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠤⠤⠴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠆⠀⠒⠛⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣶⣶⡟⠒⠀⠀⡀⠀⠀⠀⣴⢯⠘⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⠟⠣⠄⢂⠀⠄⠀⠀⠀⠾⣞⣾⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢈⣙⠧⠻⣀⠀⠀⣿⣷⡆⠀⠀⠀⠀⣌⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⣸⡿⠿⢤⡄⣡⢐⣿⣿⣿⡀⠀⠀⠀⠀⠈⢈⣁⠁
⠀⠀⠀⠀⠀⠀⢀⣷⠾⠿⡁⠉⠀⢹⣶⠂⢹⣿⣽⣏⠀⠁⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⣾⠻⠆⠀⢷⡎⠐⠛⠫⣴⣿⣟⠁⢭⣤⡃⠀⢸⠋⠀⠀⠀⠀⢀⣠⣶⡿⠈⢀
⠀⠰⠐⠀⣦⠛⠁⢹⣄⢸⣿⠧⠀⠠⣤⡿⡧⣭⡤⠓⢩⢧⠀⠀⠀⠀⠀⠀⠐⠛⠉⡅⠂⠀⠀⠀⠀⢲⠒⠀⠂
⠀⠀⠀⠀⡇⠁⠀⠉⠙⢻⠉⠓⢶⠈⢈⡏⠉⠉⠁⠀⢸⠀⠘⠖⠀⡄⠤⠀⠀⠢⢠⡄⣰⣷⣶⣤⣄⡘⠈⠁
⣀⣂⣒⣛⢓⣒⣒⣐⠒⠚⠒⣒⣒⣒⣚⣓⣀⣒⣒⡂⣖⣀⣀⡐⣚⣓⣒⣓⡐⠚⠚⠒⣓⣛⣛⣛⣓⣀⣒⣒⣂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢢⠰⠀⡆⠦⠰⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡆⢰⢠⠆⡄⠴
⠀⠀⠈⠀⠀⠆⡆⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠨⠘⠀⠅⡇
⠀⠀⠠⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠁⠀⠃
⢀⣠⠂⠄⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⢄
⠀⣿⣿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⡻⣻
⠀⠘⡠⢂⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠐⡙⢾
⠀⡀⡀⠈⡌⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⠃⢀⣸
⠀⠉⠘⡂⢄⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⢐⠆⠘
⣈⣉⠉⠦⠮⣀⡀⠲⠖⠩⡉⡱⠶⠀⠠⡀⡶⠊⠉⢉⣲⡆⠀⠀⢰⣖⠈⠉⠑⢦⣀⠀⠀⠶⢆⢉⠉⠲⠤⢄⢀⠱⠶⠨⣉
⠈⠁⢲⡔⠀⠉⠁⠀⢢⡄⠉⠁⠀⠐⣤⠉⠁⠀⠀⠲⡟⠀⠀⠀⠀⢻⡄⠀⠀⠈⠙⣤⠂⠀⠈⠉⠲⡔⠀⠈⠉⠀⢢⡄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣁⠈⢨⡇⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠠⠐⢸⡇⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠖⠂⣡⣼⡇⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⣡⡴⠋⠁⢸⡇⠀⠀⠐⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢔⡼⡫⠆⠀⠀⢸⠁⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣤⠎⠈⠀⠀⠀⠀⡾⠀⠀⢄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠋⠀⠀⠀⠀⠀⢠⡇⠀⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⢀⡟⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣰⠇⠀⠀⠀⠀⠀⣴⢻⢁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠅⠀⢀⡟⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⠏⠀⠀⠀⠀⢀⡾⠁⣾⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡡⠂⡀⢠⡞⠀⠀⠀⠀⠀⠢⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡟⠀⠀⠀⠀⢀⡾⠓⣼⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⢄⠀⡾⠁⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⡿⠁⣠⡟⠀⠀⠀⠀⠀⣼⠉⣰⠟⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⡃⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⢀⡴⠶⠶⠿⠋⢻⡿⠃⢨⣏⡘⠀⠀⠀⠀⢠⡇⣰⡟⠀⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢠⣴⡏⠀⠀⠀⠀⠀⠀⠠⠃⢀
⠀⣰⠛⠅⠒⠀⢀⠠⠞⠳⠟⢋⠉⠉⠙⠋⠛⠓⠺⣷⢫⡇⠀⢸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⢔⡵⢫⡞⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿
⢰⡗⠀⠀⠀⠀⢉⡀⢠⠎⠁⠀⠀⠀⠀⠀⠀⢀⡤⠞⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣰⠟⠊⣸⠃⠀⠀⠀⠀⢠⣴⠞⠋⣾⠏
⣿⢀⠀⣶⡾⠟⠋⠉⠻⡆⠀⠀⢀⡠⢀⡶⣺⠏⠀⠘⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡴⠃⠀⢠⠏⠀⠀⠀⠀⣠⣿⣷⢀⢡⡟
⠹⣷⡾⠇⠀⠀⠀⠀⠀⣽⡦⣤⣄⡈⠉⣰⢇⣤⠾⠟⠉⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⢀⡾⠁⠀⢀⡟⠀⠀⠀⣠⡾⠋⠈⣿⠈⢸⠃
⠀⢾⠃⠀⠀⠀⠀⠀⠀⠘⣷⣄⣈⣁⣼⡿⠟⠁⠀⠀⠀⠀⠀⠟⠟⣶⣄⣤⣴⡾⢛⠕⠁⠀⠀⠀⠀⢀⡞⠀⠀⢠⡞⠀⠀⢀⡴⠋⠀⠀⠀⣿⡀⢺
⠀⠘⢦⣤⣤⣤⣴⣶⣤⣤⠴⠶⣾⣿⠋⠀⠀⠀⢠⠝⠓⢶⣤⣞⣛⣛⡛⠋⠉⠀⠅⠀⠀⠀⠀⠀⣠⠟⠀⠀⣠⠟⠀⠀⢠⠟⠀⠀⠀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡶⠛⣲⢀⡖⠁⢄⠀⠀⠀⠈⠻⠶⠶⢮⣀⣀⠀⠀⢐⡶⠋⠀⣠⡞⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢿⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠖⠚⣹⠟⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⢀⣌⣹⡶⠖⠋⢀⣠⠞⠋⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠀⠀⣸⠃⠀⣤⠀⠀⠀⠀⢀⣠⡽⣶⠚⠻⠭⢥⣤⡤⠶⠋⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⠤⢿⡄⠀⢿⣄⣤⢶⠞⠋⣠⠾⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠦⣤⣬⣂⣈⣻⡄⠘⠉⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣄⣀⣠⠿⠷⠶⠶⠶⠶⠶⠦⠤⠬⢭⣭⣭⣤⣶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠿⣭⡾⣿⠛⠛⣻⠶⢦⣍⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣭⠿⠶⠒⠶⠶⢬⣟⡛⢿⣤⣄⣭⠿⣤⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠈⠀⣀⣁⣀⣤⣀⣈⡙⠷⣄⡘⢧⣤⡀⠻⣎⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⣀⣤⣶⣛⣽⡿⢶⡴⣬⣍⣙⠳⢦⡙⠷⣼⡷⢦⡉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣻⣯⣥⣬⣭⣍⣳⠶⢾⡏⠈⠙⣻⣆⡙⢦⡨⠙⢾⣷⡾⠇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠁⠀⠀⡀⠀⠈⠉⠓⢦⣝⡋⢿⣉⡈⠹⣦⢻⡞⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠠⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠛⢦⣍⣿⣄⡘⠻⣿⡀
⠀⠀⠀⠀⠀⢀⡿⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠈⠻⢮⣿⣤⣿⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠐⠀⠀⠃⠀⠐⠂⠀⠠⠀⠀⠀⠀⣀⣤⠴⠟⠋⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠰⠀⠀⠀⠄⠀⠠⠄⠀⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡄⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁






⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⢀⠄⡀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠻⣄⠈⠁⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠿⠛⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⢰
⠀⠀⠴⢲⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠤⠴⠶⠚⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠤⠤⠄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⢀⠀⠐⢦⡀⣀⢸⠀⠀⠀⠀⠀⠃⣠⠖⠉⠀⣀⢀⣀⠀⠀⠢⡄⣠
⠀⢠⡇⠀⣀⠀⠤⠤⠄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢰⠋⢧⡀⠀⠀⠀⠀⠀⠀⠉⣀⡼⢺⠀⠀⠀⠀⠀⠀⠳⠄⡀⠀⠀⠀⠀⠗⠠⢀⣷⡏
⠀⢸⣷⠋⡀⠛⠀⠀⢂⡴⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠛⠓⠒⠒⠒⠚⠋⠉⠀⡾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠤⣐⣽⠟
⠀⠈⢿⡋⠃⠜⠀⠒⠒⠈⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠦⣌⣙⠒⠚⠛⣋⣡⢄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠶⠲⠶⡛⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢭⣭⣭⣽⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠐⠂⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⡸⡄
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⣀⡀⠀⠠⠚⠁⠁⠀⠮⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠦
⠘⠁⣬⠁⠀⠀⠀⠀⠀⠀⠘⠮⣏⠄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠚⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠔⡁⠈⠃
⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠤⠴⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠲⠤⠤⠤⠴⠖⠒⠒⠚⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢰⠚⠉⠉⢀⡄⠂⠐⠒⠒⢤⡠⠐⠂⠉⠉⠀⡈⠉⠘⠳⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣒⠉⣀⣀⣠⢚⡁⠤⠶⠁⠀⠀⠠⠤⣤⡎⠀⠠⢒⠉⡁⠉⠉⠛⠳⠄⠀⠁⡙⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠄⠊⡀⣄⢀⡠⠈⠁⢀⣠⠠⠄⠀⣀⣀⣀⠀⢈⡟⠁⠀⠉⠃⠀⠀⠀⠀⠐⠺⡦⠜⠀⠀⠛⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠁⠀⡴⠱⠋⠀⠠⠉⠀⣠⢚⠷⠒⠆⡂⣹⠃⠀⠀⠉⠉⣀⡠⠴⠒⠂⠀⠀⠈⠉⠁⠀⠒⠂⠄⣀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⢀⠜⢰⠁⠀⠀⠀⡧⠁⢀⠀⠀⣠⡈⠷⠀⠀⠀⠈⠑⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠂⢄⠙⡄
⠀⠀⠀⠀⠀⢀⠎⠀⢺⠀⠀⣰⠃⢸⠀⡈⠀⠘⡠⠲⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾
⠀⠀⠀⠀⢀⡌⠀⡖⠉⡖⠈⠁⠀⠀⢂⡇⠀⠇⡇⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡼⠀⡔⢀⣼⣇⣀⡀⠀⠀⠈⢁⠀⡇⡃⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⢰⠁⠠⠋⠀⠀⠀⠀⠀⠀⣠⠛⠉⠀⠋⢀⠌⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⢀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⢀⡐⠂⠀⠀⠀⢰⠁⠉⠁⠀⣠⠊⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⣈⠀⠀⣠⠞⠁⢀⠜⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠸⡀⠐⢄⡀⢀⡔⣃⡴⠚⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡾
⠀⠀⠀⠀⢳⢄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⠠⠄⠤⠴⠶⠶⠶⠶⠶⠖⠚⠁
⠀⠀⠀⠀⠈⢦⡈⠀⠈⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠶⠒⠚⠉⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⠿⠛⡿⠿⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣞⣛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢚⣉⠛⣉⡻⡾⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⢿⣇⠟⣸⠿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣶⣾⡛⣷⣶⣶⣖⣾⡿⠻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⢂⣬⢉⢩⣝⣶⢻⡿⠋⣿⡟⢷⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢪⡿⣿⠸⢸⠟⠁⠈⠁⠀⠸⣧⣸⣿⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⡏⣽⣶⡶⠂⠀⠀⠀⠀⣤⣤⣼⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡁⣤⣀⠀⡙⢋⠡⣍⣻⣋⡍⠁⠀⠀⠀⠀⠀⠀⠈⢰⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠂⡾⢿⡿⢿⡜⠃⡿⢿⡿⢿⠘⠣⡿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⣯⢹⣶⣶⣶⣶⡏⢽⣶⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⠍⠉⣭⣳⣞⣩⠍⡉⣭⣻⣟⣭⢉⠩⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⠻⠿⡿⢿⡜⠃⡿⢿⡿⢿⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣲⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠹⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⣿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿
⣻⣿⣿⣿⣽⣟⠾⣭⣭⡿⢟⣿⣟⠶⣿⣽⡷⣿⣿⣿⣻⣿⣿⣿⣽⣟⠾⣭⣭⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠯⣭⣯⢿⣿⣟⢮⣭⣭⣿⢟⣿⣿⢿⣿⣿⣿
⢾⣿⣿⠿⡋⢙⠿⣳⣶⣻⢿⡋⣛⢟⣿⣾⡻⠟⠉⠻⢷⣿⣿⠿⠋⠙⠿⣳⣶⣺⠿⠋⠻⢟⣾⣿⡿⠟⠉⠻⢿⣿⣿⠿⡋⢙⡿⣶⣶⡾⢟⡉⣻⢟⣶⣾⣻
⣷⢰⣿⣿⡇⣾⣿⢰⣿⢰⣿⢠⡿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠘⣿⡐⣿⡐⣿⡇⢹⣿⣷⠀⣿
⡏⢸⣿⣿⢁⣿⡇⣾⡇⣾⠇⣼⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⣇⢻⣇⢻⣇⢻⣿⠸⣿⣿⡄⣿
⡇⣸⣿⡟⣸⣿⢰⡿⣰⡟⣸⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⡌⣿⡜⣿⡘⣿⡆⣿⣿⡇⢻
⠃⣿⣿⢁⣿⢇⣿⢣⡿⢡⡟⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢿⡜⣷⡹⣧⢹⣷⠸⣿⣧⢸
⢸⣿⡏⣼⠏⣾⢣⡿⣱⠟⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢻⡜⣷⡹⣧⢻⣇⢻⣿⡘
⣾⡟⣼⢏⡾⣣⡟⣵⠯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡻⣌⢷⡽⣧⢻⣎⢿⣇
⣟⣼⣫⣞⡵⣫⣾⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡻⣾⢷⡻⣎⢿
⣾⣿⡿⣫⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣷⢿⣾⣿
⣛⡹⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣝⣛
⣭⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣽
⣿⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿
⣹⣽⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣹⢿⢿
⣇⣧⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⡟⡿⣾
⣿⢸⡸⡞⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⢱⢇⣿
⣿⡎⡇⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡟⣼⢸⡿
⢿⡇⣿⢹⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢹⡇⡏⣾⡇
⢸⣿⢸⢸⡟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⢸⡇⣿⡇
⢸⣿⢸⣇⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣸⢠⣿⢰
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⡾⠋⠡⠁⢈⢹⠆⠀⠀⠀⠀⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⡇⢻⣿
⠀⠀⢰⡦⠤⠴⢶⡆⠀⠀⡘⠀⠈⠈⠉⠙⢇⠀⠀⠀⠀⠀⠀⣩⣗⡢⢀⡝⣈⠔⠲⣄⠀⠀⣿⣿⣨⠇⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⢸⡇⠂⠺⢻⡇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⠾⠀⣠⡶⢻⡃⠸⣿⠟⠺⠄⠀⡏⠛⠸⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠘⣇⠀⠀⣸⠁⠀⠸⣄⡀⠀⠀⣀⣀⣸⠃⠀⠀⢠⡏⡀⠚⠿⠁⠘⣿⣶⢿⣁⠌⠀⠀⡄⢸⢸⠀⠀⠀⠀⠀⠀⣠⣧⣼⣿⣄
⠀⠀⠀⠙⢷⣾⠃⠀⠀⠀⠙⠷⠶⣶⣾⡿⠋⠀⠀⠀⠸⠏⠀⠀⠀⠀⠒⠈⢳⠴⠋⠀⠀⠀⡅⢸⠠⠀⠀⠀⠀⢀⡾⠋⢉⣿⣿⡟⣳⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⢀⠒⢋⣦⡀⠀⠀⠀⠀⣠⡴⢴⡦⢔⠀⠀⠀⠀⡇⣿⠘⡀⠀⠀⠀⢸⠁⠀⣼⣿⣿⡇⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠢⢾⠉⢙⠇⠀⠀⢤⣐⢃⠎⢹⡖⠁⠀⠀⣸⠷⢿⠔⢧⠀⠀⠀⢸⠀⠀⠻⠿⣿⡗⠛⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹⡆⢱⡞⢀⠀⠀⢰⣇⠀⢠⠀⠈⣆⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠰⢿⣭⣷⠂⠀⠀⠀⠀⠀⠠⣤⡄⠀⠁⠀⠈⠀⠀⠀⢠⣯⣿⡆⢸⡇⠀⢹⣆⠀⢸⠀⠀⠀⠀⣙⠀⠀⣿
⠀⠀⠀⠘⠯⠿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣠⠀⣚⣫⡽⣧⡆⡀⠀⠀⠀⠀⣸⣿⣇⣙⣿⡏⠀⠈⣿⠀⢸⠀⠀⠀⠀⢩⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⠴⣚⡿⡬⢇⣰⡼⡵⢫⠇⠀⠀⠀⣿⡿⠉⠀⢸⡏⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡄⢐⡆⠀⠠⠼⠃⠀⠀⠀⠀⢰⣟⣺⣽⡫⢞⣸⢛⣿⣉⣻⢤⣟⢷⣀⠀⠀⠀⣿⣇⠀⠀⢸⡇⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣩⠗⢣⣎⣸⣶⣾⣉⣻⡷⣦⣉⣗⣆⠮⣭⡶⠀⠀⣿⣿⠦⣤⣼⡇⠀⠀⣿⠀⢸⡇⠀⢺⣿⣿⡟⣿⢷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣛⡶⠷⠳⢲⡳⢾⢭⠷⣿⣧⡶⠏⢿⣭⡮⢽⣒⡿⠿⠧⠀⣿⣿⣠⣴⣾⡷⣄⣰⣿⠀⢸⡇⠀⢸⣿⣿⣇⢿⣿
⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠁⠀⠮⠗⠑⠚⠣⣇⣶⣷⠞⠛⠙⠻⠦⠀⠀⢿⣿⣿⣿⣼⡇⠈⢻⣿⠀⢸⣇⣀⣸⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠒⠛⠉⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⡿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡻⠊⠁⠀⠀⠀⢹⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠏⠀⠀⠀⠀⠀⠀⢸⢣⠃⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠁⠀⠀⠀⠀⠀⠀⢀⣞⠎⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣫⠟⠛⠻⢿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠞⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢸⡇⠀⠀⠀⠀⠈⠺⡳⣄⠀⠀⠀⠀⠀⠀⠀⢠⢿⠋⠀⠀⠀⠀⠀⠀⠀⣰⢯⠋⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠸⡌⡇⠀⠀⠀⠀⠀⠀⠈⢪⠳⡀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣷⠃⠀⠀⠀⠀⠀⠀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢳⠹⡄⠀⠀⠀⠀⠀⠀⠀⠱⠝⣆⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣼⡏⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢣⡹⡄⠀⠀⠀⠀⠀⠀⠀⠘⣌⢧⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⢧⡇
⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠀⠀⠀⠀⢳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠈⢎⢿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢀⣾⣿⠟⣡⡞
⠀⠀⠀⠀⠀⠀⠀⡏⣿⡆⠀⠀⠀⠀⠀⠱⡜⣆⠀⠀⠀⠀⠀⠀⠀⠈⢮⢧⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢀⣴⣿⠟⡡⢾⠏
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣄⠀⠀⠀⠀⠀⠙⣞⣧⠀⠀⠀⠀⠀⠀⠀⠈⢏⣆⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⣠⣿⡿⣫⠊⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢿⠹⣿⣿⣦⠀⠀⠀⠀⠀⠘⡞⣧⠀⠀⠀⠀⠀⠀⠀⠈⡜⣆⠀⠀⢠⣿⣿⠇⠀⠀⣰⣿⢟⣾⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣿⣿⣷⡄⠀⠀⠀⠀⢹⡘⣇⠀⠀⠀⠀⠀⠀⠀⠘⡜⡄⢠⣿⣿⠏⠀⠀⣼⣿⢫⣾⣿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠻⣿⣿⣦⡀⠀⠀⠀⢣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠰⡘⣿⣿⡟⠀⠀⣸⣿⢣⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣌⢿⣿⣿⣄⠀⠀⠈⣧⢿⡄⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⠀⠀⣰⣿⢃⣿⣿⣿⡏⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⣷⡙⣿⣿⣆⠀⠀⠸⡞⣿⡀⠀⠀⠀⠀⠀⠀⠀⠱⡸⣆⢠⣿⣏⣾⣿⣿⣿⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⢹⠀⢻⣿⣎⢿⣿⣆⠀⠀⢻⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢿⣿⣸⠡⣿⣿⣿⠃⢸⠁
⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠈⡇⢸⣿⣿⣮⢿⣿⡄⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢻⡏⠀⣿⣿⣿⠀⢸
⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣿⣿⣿⣏⢿⣿⡀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⣄⣿⣿⣿⠀⣼
⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣏⢿⣧⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⠀⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⣿⣿⣿⣿⡌⣿⣆⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢤⡇⠀⠀⣀⣀⡀
⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⢹⡼⣿⡄⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠷⠟⠋⠉⠁⠀⠈⠙⠢⣄⡀
⠘⡅⠈⠉⠙⠒⠲⠤⣤⣄⣀⣀⣀⣇⢸⣿⣿⣿⡇⠈⣿⣿⣿⡄⠀⠀⠀⠀⠈⠛⠿⠷⣤⣤⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀
⠀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠘⣿⣿⣿⡏⠉⢹⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡇⠀⠀⣷⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⠀⠀⠀⢸⠀⣿⣿⣿⡇⠀⠀⢸⡆⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣤⣸⡆⡇⠹⣿⡇⠀⠀⠀⣧⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⡇⢇⠀⠘⣧⠤⠤⠀⢹⡄⠀⠀⠀⠀⠈⠛⠿⢿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⡀⢀⣀⣀⣠⠤⠤⠔⠒⠚⠉⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢰⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣀⣸⡇⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣉⣿⣹⣭⣿⣱⣍⣭⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣯⣵⣯⣭⣽⣿⣿⣭⣭⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡔⠂⠐⡄⠀⠀⣿⡣⠄⠙⠀⠈⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢘⣃⡀⡀⠀⠀⢘⣖⣟⡠⠂⠀⠀⣿⡠⢄⠀⠲⢘⠀⠀⠀⠀⠀⠻⣷⠄⢀⡉⠁⠟
⠀⠀⠀⠀⢸⣥⣅⢛⣄⠀⠈⣼⠋⠀⠀⠀⠀⢸⠟⢢⠒⠂⠈⠀⠀⠀⠀⠀⠀⠘⣷⠄⡒⠊
⠀⠀⠀⠀⠀⣿⡯⠉⢩⡙⠡⠸⠀⠀⠀⠀⠀⢿⣦⠿⠰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢹⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⠓⢄⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡦⢠⠛⢸⠀⠀⠀⠀⠀⠀⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠢⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠖⠀⠁⣄⠁⠈
⠀⠀⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠐⣠⠶⣌⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣾⣦⠤⠦⣻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣭⡏⠀⠩⠃
⠀⠀⠀⠀⠀⠀⠘⠛⠿⢀⡀⠀⠀⠀⠀⠀⠀⣯⣁⠌⠂⠒⢙⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣧⢄⠀⢀⢘⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢁⢨⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⡀⠀⠀⠀⠀⣿⠟⠶⠄⠛⠛⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢺⡄⠀⢠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣰⡖⠀⠀⢀⣄
⠀⠀⠀⠀⢿⡄⠀⠘⢧⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⢠⠾⡄⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣠⠟⠁⠀⣀
⠀⠀⢀⠀⠀⠙⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⣀⠀⠀⡰⠁⠈⠢⣀⡰⠃⠀⠹⣄⣀⠔⠋⠁⠸⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡾⠋
⠀⠀⠻⢷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠖⠁⠀⠀⠀⠈⠀⠀⠀⣀⣈⣀⢀⠀⠀⠀⣇⡀⠔⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡴
⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠉⠐⢒⣤⠼⠤⠄⢆⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⢸⠀⠀⠀⠈⣀⡀⠤⠤⠷⠤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠉⠀⠀⠀⢀⣀⠤⢦⡀⢸⠀⠊⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⣀⣀⣸⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣭⠃⠀⠀⠀⡤⠤⢄⡀⠀⠘
⠀⣀⠠⠔⠚⠉⠁⠀⠀⠈⣧⠺⠀⡆⠀⠀⠀⣦⠀⠀⠈⣆⠀⠀⢰⠃⠀⠀⠀⡴⠉⠀⢠⠀⠀⢺⠏⠀⠀⠀⡤⠒⠦⡀⠀⠀⠈⣆⠀⢀⣾⠁⠀⠀⠈⢳⠄
⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⢆⠁⠀⠀⠀⠿⠆⠀⠀⠘⡆⠀⣿⠀⠀⠀⠀⢷⠛⠒⠚⢠⠇⢽⠀⠀⠀⠼⠠⣄⠀⢹⠀⠀⠀⢹⡖⢩⠃⠀⠀⠀⢀⠎
⠘⣆⠀⠀⣀⠀⠀⠀⢻⣁⠀⠈⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡟⣆⠀⠀⠀⠀⠉⠉⠙⡏⠀⢻⠀⠀⠀⠇⠀⠈⣆⠜⠀⠀⠀⡾⢠⠃⠀⠀⠀⢠⠃
⠀⠘⠾⢋⡈⡆⠀⠀⠀⢇⢑⠀⠀⡇⠀⠀⠀⢰⡞⢷⡀⠀⠀⠸⣇⠈⠳⣄⠀⠀⠀⠀⠀⢧⠀⠘⡆⠀⠀⠈⠒⠚⠁⠀⠀⠀⡰⢣⡏⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠉⢘⡄⠀⠀⠸⡆⡆⠀⢠⠀⠀⠀⠀⢮⠈⣷⣀⣠⠤⠼⡄⠀⠈⠙⠒⠶⠖⢒⣏⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⣤⠾⣳⣉⣑⠒⡤⠊⠙⡲
⠀⢠⡔⠒⠉⠁⢱⠀⠀⠀⢻⡘⠄⢸⣀⡠⠤⠚⡃⡁⠱⣄⣀⣀⣼⣷⡶⢶⣮⣧⢒⣓⣾⣦⡷⣤⣀⡀⠉⠉⠉⠋⡋⠝⠁⠾⡏⠀⠀⠙⣄⡴⠊
⠀⠀⠈⠲⣄⠀⠘⣇⢀⡠⠔⠛⢱⡀⠁⣀⡀⢤⣿⡿⠻⠍⢉⣍⠑⠣⡔⢉⡬⣷⣄⣴⣛⣶⣦⠤⡛⠳⢶⡐⠂⠉⠀⠀⢸⠀⠈⠲⡶⠚⠛⠤⣄
⠀⠀⠀⠀⢀⠵⠀⠈⠁⠐⠀⠐⡠⢤⣖⣩⣵⣾⣶⡿⠶⠶⠶⠶⠶⠦⣷⣎⡐⠁⢤⣮⣙⡯⣶⠶⠻⣶⣤⣌⠽⣦⡀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠙⣲⠆
⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⢠⣲⣷⠟⠋⠉⠀⠠⠀⠀⠔⠰⠂⠀⠀⢀⠙⠊⠍⢻⢦⣄⠠⠄⠨⣇⢰⡵⢟⠉⡖⢈⢿⡷⣄⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠈⠐⠒⠤⣀⠀⠀⠀⣠⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⡁⠉⠳⣦⡒⢉⢠⣸⣏⣀⠙⡇⠘⣿⢬⡳⣄⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⡠⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠪⠻⢦⡈⠛⣤⡙⣛⠟⢮⡉⢑⡙⢮⣧⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢪⠻⣮⠁⠙⣆⣠⣴⣹⠉⢱⠊⢯⠳⡄⣀⡤⠖⠊⠁
⠀⠀⠀⠃⠠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢌⢳⣏⡾⠀⣉⣹⢛⡿⠻⡏⢣⢻⣅
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠢⠹⣦⠘⣭⠐⠊⡃⣠⢦⡾⡆⢻⣑⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠣⠘⣧⠲⢈⠟⢋⠩⠀⠸⢿⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡘⣷⡄⡀⢨⠀⠀⣀⣾⢸⡇
⠀⠛⠀⠀⠈⠛⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢌⡻⣤⣠⣴⣮⡿⢣⣾⠃
⠀⠴⠂⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠛⠛⠓⠒⠲⠶⠶⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⣒⣺⣉⣥⡶⠟⠁⠀⠀⠀⠀⠀⠙
⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⠋⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀
⠀⠘⠁⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠸⡄⠀⠀⣠⠖⠄⠀⠀⠀⣠⠆⡀⠀⠀⠀⡜⠑⢦⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠋
⠀⠀⠠⡾⠋⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠋⠀⠀⠈⢆⢀⠔⠁⠀⠙⢦⡀⢰⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡾⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠰⡆⠀⢸⡄⠀⠘⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⡜⠻⠄
⠀⠀⠀⠀⠠⠔⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⣴⡴⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠸⢀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⡼⡿⠿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠸⢰⣿⡿⣿⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠄⠒⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⠟⠏⠈⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣤⣯⠤⡀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣰⠃
⠀⠀⠀⠀⢀⡙⠻⠿⠷⠾⠿⣫⡄⠀⠀⠀⠀⠀⠀⠈⠲⢼⡷⠀⠀⠀⢠⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⢤⠇
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣁⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠂⠒⠚⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠢⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠛⣿⡿⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠲⠤⡌⣉⠀⡤⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⣼⡄⠀⠀⠘⠙⠓⠒⠒⣒⣲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺⣿⣧⡠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢻⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣷⣂⡀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⠧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣿⣷⣦⠀⣡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥
⠀⠀⠀⠀⠀⢀⣿⣻⣛⡓⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠲⠤⠭⠭⠙⠂⠈⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⠟⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣛⠿⢿⣿⣿⣿⣯⣭⡵⠶⢛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣄⠀⢤⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣉⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠶⠒⠋⠐⠒⠂⣨⡿⠷⠖⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠶⠶⠶⠶⠶⠖⠛⠛⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢄⢠⡄⢠⣤⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠁⠀⣶⡾⢠⠀⠀⠀⠶⣆⣱⠿⠈⢛⢱⡄⡠⠀⠾⠋⡋⢁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠄⠀⣠⡙⠋⠀⢀⢉⠑⠋⢁⠬⠂⠂⠄⠀⠀⠉⠙⠲⢨⣿⡁⣾⡘⠛⡀⣾⡥⠀⠀⡐⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⡟⢿⠈⣿⣧⠢⣬⡡⠀⠀⠃⠤⠀⠀⠀⠀⠋⠙⣉⠁⣀⡨⡏⢠⣤⡄⢘⠀⠈⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠫⢬⡄⣥⡴⢇⠨⣤⣶⣄⠻⠄⠛⠆⢀⠀⠀⠀⠈⠑⠅⢁⠇⠟⣡⢉⢀⢄⣀⣀⣀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠡⣀⠀⣘⠀⡟⠁⣎⢥⣤⣤⡼⢟⡆⠀⠀⣄⠀⠀⠙⠣⣄⡘⣒⡀⠯⣨⣿⣧⣚⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⣍⠏⢻⣅⣇⠻⢁⠋⠉⠓⠈⠡⣀⠀⢹⣇⠀⠀⠀⠉⠻⡏⡿⠋⠁⡉⣌⢃⢭⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡟⣯⠉⣦⣔⢻⣶⡠⡔⢂⡿⡔⠘⣿⣆⠀⠀⠀⠀⠙⣿⣄⠀⢀⡍⢁⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢭⣘⣏⠂⠀⠠⠠⣿⠫⣾⣷⡀⠹⣿⣔⠀⠀⠀⠀⠀⠹⠛⢿⣴⡿⠷⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠠⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⢿⠿⢷⣄⣐⡠⠄⣤⠐⠻⣷⠄⣿⣿⣶⡄⠀⠀⠀⠈⠢⣼⣯⠀⢦⣤⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡞⠉⢿⣷⡶⣷⠾⣿⣿⡀⢸⣿⣿⣿⣁⠀⢀⠀⠀⠙⠙⣾⣷⡶⠆⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣼⣯⡁⢠⣄⣈⠻⣇⠀⠀⠉⠛⠿⢿⣶⣦⣤⣀⣳⡄⣿⣵⣔⣗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠛⠻⠿⣶⣤⣄⡀⠀⠀⠀⠈⠨⢽⣧⣶⣯⣅⠀⢻⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠮⣏⠉⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣦⣤⣽⣄⢹⣿⣻⡀⢸⡛
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣝⡿⠛⠇⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣤⠴⠛

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣿⠉⠉⢹⠉⠉⢹⡏⠉⢹⡏⠉⠉⡏⠉⠉⡏⠉⠉⣿⠉⠉⣿⠉⠉⢹⠉⠉⢹⡋⠉⢹⡏⠉⢹⡏⠉⠉⡏⠉⠉⣿
⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⣿
⠀⠀⣿⠀⠀⢸⣀⣀⣸⡇⠀⢸⣇⣀⣀⡇⠀⠀⣇⣀⣀⣿⠀⠀⣿⣀⣀⣸⠀⠀⢸⣃⣀⣸⡇⠀⢸⣇⣀⣀⡇⠀⠀⣿
⠀⠀⢻⣄⣀⣼⠋⠉⠹⣇⣀⣸⠏⠉⠙⣧⣀⣠⡟⠉⠉⢿⣀⣀⡿⠉⠉⢻⣄⣀⣼⠋⠉⠹⣇⣀⣸⠏⠉⠙⣧⣀⣠⡟
⠀⠀⣾⠈⠉⣦⠀⠀⠀⠈⢉⡅⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢨⡉⠁⠀⠀⠀⣴⠉⠁⣷
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⣿⠀⠀⡇⠀⡖⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢲⠀⢸⠀⠀⣿
⠀⠀⣿⠀⢸⡇⢠⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡄⢸⡇⠀⣿
⠀⠀⣿⠀⣼⠁⣼⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣧⠈⣧⠀⣿
⠀⠀⣿⢀⡟⢰⠏⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠹⡆⢻⡀⣿
⠀⠀⣿⣸⢣⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣜⣇⣿
⠀⠀⣿⣉⣉⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣿
⠀⠀⣿⠀⣧⢿⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡿⣼⠀⣿
⠀⠀⣿⠀⢹⡎⢷⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡾⢱⡏⠀⣿
⠀⠀⣿⠀⠈⡇⢸⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⡇⢸⠁⠀⣿
⠀⠀⣿⠀⠀⡇⠈⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠁⢸⠀⠀⣿
⠀⠀⣿⣀⣀⣃⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣘⣀⣀⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣶⡶⣶⢎⡠⢌⣳⣍⠛⠻⣭⣉⣿⡶⠂⠀⣠⠴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⢤⣬⣭⣿⣶⣬⣭⣍⣙⣻⠧⠤⠶⠶⣮⠿⠟⣛⠩⠉⠈⠛⢷⡇⢸⡷⠳⣄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢠⣤⣀⡀⢀⣀⣾⠵⢚⣩⠵⠚⣹⡶⢞⣛⣭⣤⣤⣤⡴⠚⣩⣴⡞⢉⣉⡛⢿⣍⣁⣨⡇⣾⠞⣩⣟⣷⣶⣶⣾⣿⣃⣀⣀⣠⣤
⠀⠀⠀⠀⠧⢤⣭⣉⣙⣳⣾⠿⠶⠯⠽⠥⠾⢭⣁⣊⡥⠚⢁⣴⠿⠽⢿⡶⠋⢹⡙⢿⣿⠟⢰⢳⣧⣾⣿⣿⡿⠿⠿⣒⣒⡒⢂⡴⠋
⠀⠀⠀⠀⠀⣰⠟⠉⠁⠀⠀⠈⠉⠉⠉⠁⠒⠂⠒⠬⠭⣝⠻⠿⣿⣶⠋⠀⠀⠀⢯⠀⢈⡇⡾⢸⢷⣿⠁⣶⠶⠚⣩⠽⢻⣷⡾⠤⠤⠤⠤⣤⣀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢍⡛⠦⣄⡀⠈⣧⢸⣧⢇⣼⣞⡁⢸⣧⣖⣋⣤⣤⣾⣷⣿⣞⢶⠲⠦⠴⠋
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣙⠷⣿⣻⠃⠀⠀⠉⠉⢙⣛⠶⣮⣿⡟⠛⠛⠛⠛⠛⠓⠒⠒⠶⡄
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠛⢶⡒⠒⠒⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡶⠶⠇
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⢦⣀⢄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡄
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣇
⠀⠘⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿
⠀⠀⠀⠈⠉⠙⠛⠲⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡹⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⢌⠻⣿⣿⣿⣿⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⣦⣤⣀⣀⠂⠈⠛⠟⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠘⣿⣿⣿⡖⠒⠒⠲⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⣹⣿⣿⣿⣷⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣶⣾⣿⣿⡿⠟⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣽⣽⡿⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠛⠉⠉⠉⠉⣼⣿⣿⡿⠀⠀⠀⠀⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣄⡀⠀⣀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⡠⠤⠒⢶⠖⢳⡄⡠⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠑⡄⠀⠀⢨⠀⢎⠀⠀⢠⠏⢠⢊⠞⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠘⡄⠀⠘⡄⢸⠀⠀⠸⣀⡷⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣀⣠⣄⣀⠀⢹⠀⣰⠁⢸⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⢟⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠲⢄⡠⠴⢺⠁⠀⠀⠀⠀⣠⡶⠖⠒⠀⠈⠀⠀⣠⡶⠶⠖⠀⠘⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠀⠑⢤⡚⠣⡀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣤⠞⠋⠀⠀⠀⠙⢦⡑⣄⠀⠀⠀⢠⡾⠛⠙⠁⠀⠀⢀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠃⠀⠀⣴⠞⠋⠀⠀⠙⢮⡦⡀⠀⠋⠀⠀⠀⠀⠀⠒⣋⣤⠔⣛⡻⠆⠀⡇
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⠀⠐⡏⠀⠀⠀⣰⢄⠀⠑⣞⢦⡀⠀⠀⠀⢀⡴⢟⡭⠖⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠒⠦⣄
⠀⠀⠀⡴⠃⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⢀⢀⡏⠀⢣⠀⠘⡄⠙⢦⡀⠀⢿⠞⠁⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡴⠻⡀⠹⡄⠀⠀⠀⠀⠑⡄
⠀⢀⠎⠀⠀⠀⠀⡟⠀⠀⣠⡶⠒⠀⠀⢀⢄⡾⠁⠀⠀⡆⠀⠰⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡘⠀⠀⠹⡄⠙⣄⠀⠀⠀⠀⢸
⠀⠘⢄⠀⠀⠀⠀⠇⠀⠀⣿⠁⠀⠀⠀⣡⠞⠁⠀⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠁⠀⠀⠀⠀⣠⣖⠉⡆⠀⠀⠘⣄⠘⢆⠀⠀⠀⡸
⠀⠀⠀⠉⠒⠤⣄⣀⡀⠀⠁⠀⠀⢠⣞⣁⣀⣀⣀⠴⠃⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠈⢆⠘⢆⠀⠀⠈⢦⠈⠳⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠉⣑⠂⠤⢄⣀⣀⠈⠀⠈⣀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⢢⣈⣳⣀⣀⣀⡳⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡀⡿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⣀⠀⠀⠀⠀⠀⣀⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⣄⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡤⢚⣥⡮⡓⢄⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠤⠤⠀⣈⣣⠀⠀⠀⠀⠀⢀⡠⢎⠀⡠⢒⢥⡺⣟⠥⣊⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⡩⠋⠀⠀⢀⡠⠖⠉⠀⠈⢦⠻⣅⠛⣊⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠁⡠⠖⠉⠀⠀⣠⠴⠉⠀⠀⠀⢀⡠⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠋⠀⠀⣀⠴⠊⠙⢄⠱⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁


⣿⢿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣄⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄⠀⢀⡀
⠀⠀⠀⠲⡀⠘⠆⠀⠁⠀⠀⠈⠀⠀⠀⠀⢠⢄⠀⠀⡠⢢⠀⠀⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⠞⠀⣠
⠀⠠⣄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠁⠀⠑⠂⠀⠀⠳⠀⠁⠀⢱⠀⡠⠔⡆⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀
⠀⣀⠈⠁⠀⠀⠀⠀⢰⠒⢠⡤⠤⠤⡀⠀⠀⠀⢀⡠⠒⠀⠀⠀⡆⠀⠈⣁⠠⠤⠧⢄⡀⣀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⡀⠤⠔⠒⣆⡀⠈⠀⠀⠀⠀⠐⡀⠀⢀⠎⠀⠀⣠⠄⢠⠃⣠⠞⠁⠀⣀⠀⠀⠙⢇⠀⠀⡴⠐⠠⢀⢈
⢔⠊⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⢹⠄⠀⠱⡀⢸⠀⠀⠀⡿⠀⠎⡰⡟⠀⠀⡼⢁⠙⡆⠀⠈⡤⡺⠁⠀⠀⡘
⠈⡄⣀⣄⠀⠀⢫⡀⠘⢷⠀⠀⠀⣀⠀⠀⢣⡜⢆⠀⠀⠈⠀⢹⠁⢣⠀⠀⠀⢈⡦⠁⠀⢰⣳⠃⠀⠀⠜
⠀⠈⠑⠒⠆⠀⠈⡖⡀⢸⠀⠀⠘⡏⢧⠀⢀⣳⠈⠓⠤⣄⣀⣬⠆⠘⢄⠀⠀⠀⠀⢀⣠⡯⠧⢀⡠⠮⡀
⠀⢤⠒⠂⠙⡀⠀⠱⡣⠈⣄⠠⠔⢙⠘⣏⣠⣼⣷⣶⣶⡤⣤⣾⣴⢤⣀⠉⠒⠒⠺⠋⣹⡋⠉⢒⡠⠚
⠀⠀⠀⠢⡀⠣⠔⡚⢉⠆⢀⠤⣰⣻⣟⣃⣵⣉⣱⡉⢺⠷⡶⣽⣿⣲⣝⡛⠬⡁⠀⠘⠅⣈⠛⠉⠑⠢⢄⡀
⠀⢀⡠⠊⠀⠀⠀⢀⣤⡴⠟⠛⠋⠉⠉⠩⠉⠉⠙⠻⠳⢮⣁⠊⠉⣏⣸⡟⢻⠙⣶⣄⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠉⠒⠠⠄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠳⣖⠩⣤⡧⣌⣃⣸⠷⣷⣄⠀⠀⠣⣄
⠀⠀⠀⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠳⣤⠓⢬⠋⡱⡄⢊⢻⣧⠀⢀⡨⠗
⠀⠀⠚⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠳⣺⠉⣉⢟⡿⠺⢣⢿⡁
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡹⣎⡓⢬⣥⠖⢺⡏⣯⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⣦⠀⠐⠂⢀⡿⣿
⠀⠁⠀⠈⠓⠦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⣤⡶⢟⣱⠇⠀⠀⠀⣀
⠀⠉⡀⠀⠀⠀⠀⠀⠀⢨⠀⠉⡉⠍⠉⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⢲⠶⠶⠶⣶⠚⠛⠋⠁⠀⠀⠠⣀⠈
⠀⠘⠁⣠⠄⠀⠀⠀⠀⠀⠂⠉⠀⢸⠀⢀⠴⠀⠀⠀⡠⢀⠀⠀⠰⠓⢄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠃
⠀⠀⠚⠁⣠⠖⠀⢠⠀⠀⠀⠀⠀⠈⠖⠁⠀⠀⠢⠈⠀⠀⠑⢤⠃⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠘⣆⠀⠳⠄
⠀⠀⠀⠀⠉⠀⠐⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⣠⡞⢁⣼
⠀⠀⠀⠀⣼⠏⢀⣾⡿⢧
⠀⠀⠀⢰⡏⠀⣼⣿⠃⠈⢆
⠀⠀⠀⣿⣷⣴⣿⡟⠀⠀⠈⠂
⠀⠀⠀⠹⣿⣿⣿⣿⣄⠀⠀⠀⠠⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠘⣾⣿⡿⣿⣿⣿⣦⡀⠀⠱⡀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠘⣿⣿⣮⡛⢿⣿⣿⣆⠀⠑⡄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡙⢿⣿⣷⡄⠈⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠘⣿⣿⠟⠁⠙⢮⡻⣿⣿⣶⣦⣄⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⠻⣜⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⣯⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠑⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣠⠜⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠉⠛⠛⠦⠀⠙⠛⠿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣞⣛⣛⣭⣭⣭⣉⡙⢿⣮⣲
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠶⠤⠤⠤⠶⠶⠶⠶⠶⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⣠⣴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⣹⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠸⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡝⢿⣷⡦⠀⠀⠉⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡧⠀⠙⢷⣦⣤⡀⠀⠀⠙⢿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⣽⣿⣿⣦⣀⠀⠈⢿⣿⣿⣿⣷⣦⣤⣄⣀⡀⢸⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣸⣿⣿⣿⣿⣿⣦⣀⠀⠈⠛⢿⣿⣿⣿⣿⡟⠀⠀⠤⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⢻⣿⠛⠛⠛⠻⣿⣿⣷⡀⠀⠈⢻⣿⣿⣿⡁⠃⣘⠁⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⢿⣿⣿⣿⡀⢽⠂⢤⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠂⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠘⣿⣿⣿⣇⣷⣄⡋⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⣿⣿⣿⠛⣿⣿⠖⠂⡬⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢹⣿⣇⣀⣿⠻⣦⣼⠆⠠⠅⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠘⣿⣿⣧⠀⠀⠙⣿⠁⢸⠇⠘⢋⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⢸⣿⣿⣷⣄⡀⠈⠛⢷⡖⠈⡿⠀⠩⣅⢲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢾⣿⣿⣿⣿⣿⣿⣷⣦⣍⣛⣿⣾⣤⣿⣅⣠⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⣀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠴⠦⠄⠀⠀⠀⠀⠁⠀⡟⠀⠀⠸⠀⠀⠀⠀⠒⠒⠒⠒⠒⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠋⠁⠀⢀⣠⠴⠒⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⣤⣄⡀⠀⢀⣀⡀⠀⠉⠛⠻⣦⡀
⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠞⠋⠀⠀⠀⢀⣀⣤⣶⠿⢃
⠀⢀⠙⠳⣶⣶⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠾⣿⠟⠛⠉⠀⠀⠈
⠀⠈⠉⢉⠱⠿⢤⣭⣉⣉⣙⠛⢛⣛⢛⠓⠛⠛⠋⠀⠀⣓⠒⣛⠛⠛⠛⠛⠛⠋⣉⠉⠉⠉⠁⢀⡄⠀⠀⠀⠈⠀⠀⠀⢀⣀⡠⠄
⠀⠀⠀⣾⠀⣀⠀⠂⠈⠉⠉⠘⠛⠛⠛⠛⠋⠉⠁⢀⠛⠉⠉⠉⠀⠀⠀⠀⠔⠊⠉⠑⠀⠀⠀⠀⣀⣀⣤⣤⡤⠶⠚⠛⠋⢹
⠀⠀⠀⠸⠀⠈⠙⠛⠓⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠾⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⢀⢸⡇
⠀⠀⠀⠀⠀⣿⣎⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠀⠀⠀⠀⠀⣠⡴⠶⠾⠶⢤⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⢻⡏⠓⠤⠄⠀⢀⡎⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠈⠀⠀⢐⡒⣤⠶⢷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠖⠒⠒⠉⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠀⠈⠃⠌⠉⣉⠝⠋⠉⠉⠉⣉⡉⠉⠙⠛⠒⢤⡀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡼⠃⠀⠀⠤⠀⠀⠈⠉⢄⡀⠀⠀⠀⠉⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠸⠀⠀⠀⣧⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣤⣤⡤⠐⠂⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠀⠀⠀⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢀⡠⠤⠐⠛⠀⣀⣉⠤⠤⠤⠤⡴⠒⠓⠀⠀⠀⠠⠠⠀⠈⢁⡈⠁⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⢾⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣄⣀⠀⠈⠛⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠘⠷⣤⣤⣀⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠦⠤⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠤⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠒⠂⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢁⣀⣤⠤⢴⣖⣿⣿⣟⠛⠙⠛⠛⠛⠻⠿⣻⣷⣶⣶⣦⣤⣤⣀⣈⠁⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⣤⣶⣿⠭⠥⠒⣋⣴⢡⣿⣿⣿⣟⡒⠒⠒⠒⠊⠉⠭⣿⣿⡙⠛⡇⠙⣿⡻⠿⠷⢦⣤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣠⣾⣿⣿⣏⡙⠛⣛⡫⠝⡡⠻⣿⣯⡫⣈⠉⠑⠒⠂⠈⢑⡿⢟⣿⣷⣄⠙⠦⣈⠉⠙⠛⢋⣹⣿⡄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⣰⣿⢿⣷⣼⣯⣬⣭⣥⡔⠋⠀⠀⠙⢿⣷⠄⣈⣉⠉⠂⠈⡡⠴⣿⠟⠁⠀⠙⠦⢄⣉⠉⠉⢈⣁⣽⣿⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡯⣿⢺⠇⠀⣄⠐⢸⠟⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠀⠀⠰⠒⠊⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⣯⣿⠛⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡟⢻⠏⣿⠀⠻⢻
⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⡗⢄⠀⢀⡿⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⡇⢸⠀⠈⡇⠀⡇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃⢸⠀⡿⠀⠂⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠇⣿⠀⢸⡇⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢠⠀⢠⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⢿⠀⣿⠀⣼⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⢸⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⣿⢀⡿⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⡄⠈⡀⢸⣸
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⢠⡟⢸⡇⢰⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⢸⠁⣼⢀⡏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⢱⠘⡇⣦⢻⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣾⢀⡇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡀⣇⢹⣼⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣷⣾⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⢺⣟⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢿⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢸⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⣷⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⡀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠋⠉⠁⠈⠁⠈⠉⠉⠋⠉⠉⠙⠉⠁⠉⠁⠉⠉⠉⠸⠀⠀⣸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⢠⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣿⣿⠀⡄
⠀⠀⠀⠀⠀⠤⠠⢦⠼⠿⠘⠛⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠙⢻⣤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⡀⢐⠀⠀⠀⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠠⠤⠀⣀⡀⠀⠀⠀⣀⣤⣌⠁
⠀⠀⠀⢀⠀⠀⠾⣦⣤⡤⠈⣿⠁⠀⠀⠧⠈⠓⠈⣿⣾⠀⢸⣾⠁⠀⣦⣰⡆⠀⢁⣄⣠⠀⠀⢙⡋⠉
⠀⠀⠀⠈⠁⠀⠀⠘⠟⠀⠰⣿⡆⠀⢸⣿⣿⡇⠀⢻⡿⠆⠀⣿⠀⠀⡿⢽⡇⢀⣿⣿⣿⣷⠀⠯⡿
⠀⠀⠀⠠⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠈⠿⠿⠁⠀⠀⠀⠀⠀⠛⠀⠀⠿⠿⠇⠀⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣀⣀⣀⢰⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡇⠀⣾⣿⡇⢸⣿⡏⢡⣤⣤⠉⠠⠖⣶⣿⠆
⠀⠈⠿⡿⠞⢸⣿⣿⠘⠰⣶⡦⠂⢸⠂⢠⡀⠠⡄⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⠃⢸⣿⣿⠀⠀⣯⡆⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⠐⠀⠈⠉⠉⠀⠻⠿⠟⠃⠀⠛⠛⠃⠀⠈⠀⠈⠛⠛⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣼⠟⠰⠶⠶⠶⠆⠦⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠐⣿⣿⠇⠿⠿⠿⠿⠇⠺⠀⠀⠀⠀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠁⡄⢠⡄⠀⠄⠀⢸⣇
⠀⠀⠈⠁⠀⣿⣿⣿⣿⡷⢸⠇⣤⣤⡄⣿⣿⠀⣶⣶⡂⠀⢰⠀⠀⠀⡇⢸⡇⠀⠀⢀⣯⣹⠀⢤⣤⣤⠄
⠀⠀⠀⠀⠐⠾⠿⠿⠷⠇⠸⠀⠙⠛⠁⣿⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⢸⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠋⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠠⠄⠤⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡜⠁⠉⠁⠀⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢠⢤⠄⠂⠀⠀⠀⠀⠀⠂⠀⠀⠠⡀⢤
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⠀⠀⠀⠸⣶⣤⣤⣤⣆⣀⣀⣀⣐⣒⣒⣀⣀⣀⣀⣾⣼⣿
⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⢿⣿⣿⡏⠛⠋⠉⠉⠿⠩⠭⠉⠉⠈⣽⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠑⡣⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣷⣴⣇⠀⠀⠀⠁⠀⠀⠐⣰⡟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⡛⠆⠀⠀⢀⠀⢶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣧⣵⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⡷
⠀⠀⠀⠀⠀⢀⡀⠂⢠⠊⠇⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡄⢀⣡⡐⢀
⠀⠀⠀⠀⠘⠶⣽⣶⣊⣝⣶⡀⠈⣁⣒⣂⣭⡴⠂⠀⠀⠀⠀⠀⠐⠦⣀⢀⣉⠀⠀⠀⠀⢀⣀⣁⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⢒⠔⢀⡤⠀⣉⠀⢀⠈⢉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⠀⡀⢆⡴⢁⠔⠁⣀⣤⠵⠖⢂⣈⣉⡋⣛⣁⣒⣀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢁⡠⠐⣘⣃⡔⢡⢎⡴⡡⢊⢐⡩⢴⣺⠿⠟⠻⠽⠉⠉⠉⠉⠩⠽⠗⣒⠯⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢠⣬⡖⠉⠈⡌⡰⠡⢎⣴⢔⣫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠩⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋⠤⣶⠞⠲⠂⣌⢢⡜⡐⣽⡶⣫⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠑⢂⠀⣀⣤⣀⠀⠀⡼⢡⡟⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡏⡀⠔⡊⢈⠁⠀⠝⢈⠳⡾⢫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠀⡕⠚⠁⢆⠀⢚⠶⢁⠞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠓⡆⢀⠁⣘⢁⡤⠚⡠⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢰⡀⢨⠔⠿⠉⠀⡰⣡⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⢈⡔⢋⠠⠚⢃⡜⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢖⣒⡫⠭⠴⠒⣚⣃⣭⣤⠴⠶⠖⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢠⠛⠂⠀⢚⠔⠁⠔⢣⢎⡼⠁⠀⠀⠀⠀⠀⠀⢀⠠⠤⢒⣋⠥⠔⢒⣉⣩⡤⠶⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⡸⠂⠀⢠⣀⡠⠚⣠⢋⡞⠁⠀⠀⠀⠀⠀⠀⠈⠀⣐⣈⣥⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠐⠂⢩⠋⡔⣡⠏⠀⠀⡀⠤⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢶⢤⣉⡳⢎⠜⠁⣀⣠⡭⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠶⠷⠚⠋⠉




⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⢀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⡆⠀⣀⣴⡿⣟⡉⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡿⢫⣾⣿⣿⣦⡀⢰⣿⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⣠⣶⣮⣿⣿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣭⣄⣀⣀⣀⣰⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣠⣤⣶⣶⡽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢹⣿⣇⣤⢸⣿⣿⣦⣤⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⠏
⠀⢀⣴⣾⠟⠛⠉⠁⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⢀⣠⣿⣿⡾⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣉⣻⣿⡟
⢰⣿⠋⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⠿⣿⣿⣶⣾⣿⣿⢟⣾⠀⠀⠈⣿⣟⣁⡀⠀⠀⠈⢻⣿⣿⣿⣿⢿⣤⣄⣀
⠘⠿⣷⣶⣶⠾⠿⠛⠛⠛⠻⢿⣦⡀⠀⠉⠙⠛⠉⠁⠈⢿⣧⡀⠀⠘⣿⣿⣿⣷⣦⣄⡀⣿⣿⠿⠃⠀⠉⠙⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠈⠻⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣠⣴⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣤⣤⣴⡖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢠⠅⠁⢠⠤⢐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡐⠉⢢⠢⠰⠈⢀⡠⠓⢌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠰⠤⠄⠤⠥⠉⠐⣡⠊⠀⠀⡊⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠮⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠈⠉⣰⣂⡴⡄⢦⠠⠬⠴⡅⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠒⠚⠆⠋⠍⠁⠐⡏⠢⢠⠀⡐⣠
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⣇⠠⠔⣉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠗⠒⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⡇⡠⢄⣀⣀⡀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⢀⠠⠐⠈⠉⠉⠒⠢⠤⠐⠊⠁⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠇⠀⠀⢠⠁⡀⠔⠂⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⣘⠠⠀⠀⠀⢄⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠡⠀⠀⠀⠀⠠⢹⠀⢠⡀⠀⠀⠑⢄⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠑⠀⠀⠁⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⠀⠀⠀⠀⢀⠄⠁⠂⠌⣶⡀⠀⠀⠀⠰⢸⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠂⠀⡀⠢⢀⠀⡉⠀⠀⠀⠀⠁⠀⢀⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡆⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠒⠐⠁⠀⠀⠀⠀⠀⠀⢰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢦⣙⠲⠤⠤⣤⣤⣤⠤⠤⠐⣊⡡⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠉⠒⠒⠒⠂⠒⠒⠂⠉⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠤⠤⠐⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣋⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⡿⣿⢿⡿⣿⣿⡿⣿⡿⣿⢿⣿⢿⣿⢿⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡿
⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣾⣿⣾⣿⣿⣾⣿⣿⣷⣿⣾⣷⣿⣿⣷⣿⣷⣿⣶⣿⣾⣿⣾⣿⣿⣿⣾⣿⣷⣿⣷⣿⣷⣿⣷⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠬⠽⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⣛⣛⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣓⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣤⣴⣶⣶⣦⣭⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿
⣿⡿⣿⣸⣾⢸⢫⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⢸⣾⢸⡿⣿
⣿⣧⡇⣯⣇⡟⣼⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⡏⠟⡏⠿⢻⢻⢹⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⢷⢸⡇⡟⡏⡇⣿
⣿⣿⢷⣹⣹⢱⣿⣱⣿⣿⣿⣿⣿⣿⡿⣿⢻⠃⡇⢸⠀⡇⠀⡇⠀⢸⠸⠘⡇⠃⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⡜⣇⣧⣇⣇⣿⣿
⣿⣿⡿⣿⢧⣿⣷⣿⣿⣿⣿⣿⣿⡿⠇⢻⢸⠀⠃⠘⠀⠁⠀⠀⠀⠘⠀⠀⠃⠀⠀⢸⢸⡏⣿⣿⣿⣿⣿⣿⣿⣽⣽⣹⢿⢹⣿
⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⡿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⣿
⣿⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣧⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠃⠚⠘⠐⠃⠘⠚⠃⠃⠃⠘⠘⠐⠚⠂⠃⠛⠘⠀⠃⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣼⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⣀⣀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠖⠒⢈⡠⠂⠠⠤⣀⠤⠐⠐⠀⠀⠚⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠍⠀⢠⡪⠤⠒⠂⠀⠒⠢⠴⣁⡠⢂⣩⠉⠉⠓⠆⠀⢩⡲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠈⠔⠂⠖⠀⣠⣔⡂⠀⣶⠒⠂⠤⠜⠀⣀⡀⠀⠀⠤⠈⠙⠋⡀⠀⠉⢡
⠀⠀⠀⠀⠀⡠⠪⠀⠉⠁⡆⠀⠀⢀⡘⠮⠀⠈⠑⠂⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠄⠀⠈⠁⠢⠈⢣⡀
⠀⠀⠀⠀⡐⠁⣀⢀⡠⠃⠣⠀⠀⣀⠘⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢇
⠀⠀⠀⠰⠁⡊⢠⠁⠀⠀⠀⢦⠀⠘⠀⢀⡀⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⢀⠃⠼⠂⠉⠉⠉⠀⡰⠚⠀⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢡
⠀⠀⠘⠀⠀⠀⠀⠀⢀⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠉⠀⠀⠀⠇⠀⢀⡔⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢰⠀⢄⠀⢀⠴⣀⠤⠉⡠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠳⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠤⠴⠶⠶⠦⠶⠚⠁
⠀⠀⠀⠈⠢⣀⣈⡀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠄

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢄⣀⡠⠂⠂⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠊⠁⠀⣰⣐⡂⣀⠀⠀⠀⡀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢖⢉⢡⡄⠀⠄⣉⠢⣜⠀⠋⠀⢂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⠈⠂⠐⢄⠀⢠⣄⣀⣀⣴⣷⣶⣿⣿⣧⣍⢙⣷⣶⣮⣅⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⣢⠊⠤⣾⣶⢦⣯⣭⣻⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻⡀⠶⠾⠿⢿⣶⣀⣽⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⣀⠀⠀⠀⡐⡩⢀⠉⢯⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢣⢀⣴⢰⡱⠀⠌⢉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⢟⣵⡂⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡉⡯⢶⡟⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⣴⡟⣏⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⢘⠉⠐⠀⠀⢻⣷⡈⡘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⠉⠉⣿⣿⠇⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡝⢻⠀⠁⢀⢀⡰⡢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢾⡇⣄⠄⡈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⢻⡝⢆
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢻⡌⢳⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⣄⠻⣄
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢻⣆⠙⣦
⠀⠀⠀⠸⣿⠀⡀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢷⡀
⠀⠀⠀⠀⣿⡀⠈⠳⣄⠀⠀⠀⠀⠀⢻⣧⠈⠻⣄
⠀⠀⠀⠀⢸⣇⠀⠀⠈⢳⡀⠀⠀⠀⠀⠹⣧⡀⠙⣧
⠀⠀⠀⠀⠈⣿⡀⠀⢠⡶⠛⢦⡀⠀⠀⠀⠹⣷⡀⠘⣷⡀
⠀⠀⠀⠀⠀⢻⡇⠀⣿⠀⠀⠀⠙⢦⡀⠀⠀⠸⣿⡄⠘⢷⡀
⠀⠀⠀⠀⠀⢸⣿⠀⡿⠀⠀⠀⠀⠈⠻⣆⠀⠀⠘⢿⣆⠈⢷⣄
⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠈⠻⣷⡀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣿⢠⡗⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠙⣿⣦⣀⠈⠉⠛⠛⠛⠛⠛⢲⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠙⠻⠿⣶⣤⣤⣤⡴⠾⠟⠁⠉⢉⣿⣦
⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣹⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠶⣶⣶⣶⣶⣶⠶⠿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣿⣷
⠀⢰⠂⠀⠀⠀⠀⠀⠻⣿⠀⠀⠄⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⢰⠆⠀⠀⠀⠀⠐⠰⣶⡿
⠀⠘⢦⡀⠀⠀⠀⢀⡴⠋⠀⠀⠈⢄⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⣀⡈⡸⠃⠀⠈⢧⣀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠉⠻⠶⠞⠋⠀⠀⠀⠀⠀⠈⢳⣾⠟⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠻⡿⡟⠁⠀⠀⠀⠀⠉⠛⠶⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢈⠀⢀⣤⡈⡁⠁⢃⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⢿⠃⠙⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡄⠀⠁⠀⣨
⠀⠀⢀⠀⠀⠒⠓⠠⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠦⠾⢿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠠⢀
⠀⠀⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡏⠩⣍⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢓⡿⠋⠁⠀⠀⠈⢳⠜⣧⡄⣀⢤⡔⠶⡖⠊⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠁⠐⠀⠀⠀⠀⠀⢧⠾⠷⠟⠓⠛⠉⠉⠻⡤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⡿⠿⠔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠺⢳⣿⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠐⣿⣿⠀⡄⠹⢶⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠘⠣⢤⣁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⣀⣀⠈⠳⣜
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡀⠆⠀⠀⡍⡇⡇⡀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠂⠇⠀⠀⠀⠀⠁⠇⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⡀⡀⣀⣠⣀⣀⣤⢀⣦⣴⢤⣦⣶⣶⣾⢾⣳⣖⣙⣿⠡⢍⡢⠀⠀⠸⠀⢰⢮⠰⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢟⣄⣤⣦⣴⣶⣷⣻⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⢤⣀⠅⡘⠹⠸⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠉⠙⠻⠛⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣑⠾⣢⡄⠰⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠟⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⣶⣽⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠰⠶⠠⠖⠀⠀⠒⣚⣘⣂⣉⣀⣋⡿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⡈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⡀⠀⢀
⠀⠀⠀⠀⠀⢠⠠⠂⡄⠀⠀⢀⠀⠀⠀⠠⠉⢁⡶⠂⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠰⠈⠆⠀⠀⠐⢀⠂⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠂⢃⠀⠀⠈⣀⠀⠀⠐⢄⠘⠋⠀⠀⠀⠀⠀⠂⠀⠀⢱⠀⠒⠀⠀⠸⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠞⠀⣴⠁⠀⠀⠀⠈⠓⢄⠀⠀⢀⡤⠂⠀⠀⠀⠀⡀⢁⢠⡀⠄⢀⠀⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠁⠠⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠈⠀⠠⠀⠂⢰⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘