Text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⠘⣿⡟⠀⣸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠛⢛⣣⣛⣤⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠴⠿⠷⣦⠀⠀⠀⡇⢰⠂⠀⢠⢳⠀⠀⢸⣙⠆⠀⢚⣹⠀⠀⢦⡜⠀⠀⠀⣠⣾⡿⠁⣷⣌⡉⠉⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⢻⠷⣦⡀⠃⠐⠂⠀⠊⠈⠃⠀⠘⠀⠀⠀⠊⠀⠀⠀⠘⠀⣀⡀⠀⠻⣿⣇⠀⠻⣿⣿⠟⠁
⠀⠀⠀⠀⢠⣾⠋⢠⣶⣦⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣰⣿⡁⢀⣾⠋⠀⠀⠀⢀⡾⢩⣿⠀⠀⠈⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠷⢶⣿⠟⠁⠀⣼⣟⡀⠀⠀⠀⠈⠛⠉⣽⡟⠉⢡⣾⠃⠀⠀⠀⠀⣼⢁⣼⠏⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣾⠇⢀⣠⡾⠋⣹⡋⠀⣠⡄⠀⠀⢰⣿⠁⢀⣾⢃⠀⠀⢀⣀⣠⣧⡞⢁⣠⣤⡀⢠⣀
⠀⠀⠀⠀⠀⣸⡏⠀⠛⣿⡀⢠⣿⠇⣨⢟⣿⠏⢀⣿⠇⠀⣼⣿⢿⡗⣰⠋⣠⣾⠋⣰⣿⢋⣼⢇⣾⡟⣰⣷
⠀⠀⠀⠀⠀⢻⡇⠀⣠⡿⠀⣾⣏⡴⠃⣼⣏⡴⢻⣿⣠⡴⣿⠃⣿⣃⣷⣾⠟⢿⣄⣿⣿⢻⣿⢾⣿⣵⢏⣿
⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠉⠀⣁⣬⣅⣀⣉⢁⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠉⠉⣩⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣠⡾⠟⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠉⠀⢠⡾⠟





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⣴⣠⢄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠲⢒⣼⢿⣖⣾⣹⣷⢧⢼⠃⡘⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⢶⣳⣯⣿⡛⡷⣤⣍⣯⣉⣷⣞⣷⡾⠼⣅⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢑⣧⡼⢯⡷⣿⡟⢯⣠⣤⣯⣿⣯⣉⣿⣱⣿⣿⣇⣔⣆⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⣷⡾⠿⣿⣉⣶⣿⣿⣯⣿⣿⣿⣿⣭⡿⣿⣿⢿⣹⡷⡞⠋⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⢾⡷⣾⣿⣿⣾⣿⣧⣽⣿⣭⣿⣿⣿⣶⣽⠶⠟⡳⠁⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣗⣶⢶⣿⣿⢿⣿⣿⣿⣿⣿⣹⡿⡿⣟⣷⡿⣡⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣻⣟⢙⣿⢷⣾⣿⣿⣿⣺⡟⣭⠿⡩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⡿⣿⣿⣿⣼⣿⣟⣿⣿⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣥⣿⣿⣿⣯⣶⡎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣻⣯⡿⠿⠇⢚⣽⣿⣧⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠃⠠⠀⠀⢘⣻⠝⠶⠗⠀⠀⠀⠀⡀⡠⠬⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⢊⡏⢄⡲⢢⢿⣤⠊⠣⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢘⣃⠿⠉⢟⣮⡘⢇⠼⣀⡀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠿⢿⡿⣾⣻⣶⡿⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣠⡶⣿⡿⢛⣷⣦⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠿⣶⡟⢀⣾⣃⣼⠗⢀⣾⣧⣴⠶⣦⣤⡶⠾⠿⣯⠁⢠⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣿⣿⡟⠀⣼⠋⢉⡁⠐⠿⣿⡟⠀⠴⣸⠋⠠⠶⢦⡞⠀⣼⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣿⣿⠟⠀⡰⢿⡟⠛⢻⣧⠀⢹⡄⠀⠺⢋⡞⠙⠃⣠⡁⠀⢃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⢀⣴⡁⠈⠻⠶⠿⠃⢀⣾⠛⠷⠿⠛⠻⠶⠟⠋⠻⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠙⢷⣦⣄⣀⣠⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣆⠀⢰⡀⡄⢠⠄⠀⠀⡴⠠⡄⢠⣂⠦⢀⡖⠲⢠⠆⠀⠄⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡄⠀⡀⢀⡔
⠀⠀⠀⠂⠸⡄⠸⠥⠷⠘⢄⠠⠀⠧⠠⠇⠸⠍⡤⠈⠏⠀⠘⠄⠰⠆⠀⠨⠤⠀⠇⠐⠘⠤⠐⠀⠇⠸⠌⠸⠄⢁⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⢸⠀⠞⠀⡎⠀⢰⠁⢰⣤⠋⠀⡆⠀⠀⠺⣆⠸⡇⠐⠣⣸⠀⠀⠀⢀⠀⡀⢐⠀⣀⠄⠐⠀⠠⢄⠤⠀⠀⢄
⠀⠀⠀⠘⠀⠓⠀⠳⠐⠘⠀⠸⠀⠳⠀⠒⠰⠀⠂⠈⠀⠇⠀⠀⠹⠀⠀⠀⠐⠀⠁⣸⠀⠃⠢⠀⠂⠂⠘⠘⠀⠀⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⡇⠀⣽⠀⡅⠂⠰⠀⠈⡇⠘⠠⡇⠀⠂⡅⠀⠰⠈⠠⡇⠈⠀⠀⠀⢠⠀⡖⠆⠠⠒⠀⢰⠂⠠⡂⢘⠂⡀
⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠮⠀⠈⠂⠁⠈⠂⠁⠀⠘⠀⠀⠁⠊⠀⠀⠀⠈⠀⠇⠁⠈⠈⡅⠈⠀⠑⠁⠘⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡄⢠⠀⡀⠀⠀⢀⠀⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠰⠎⢳⠃⢀⠘⢄⠀⠈⡎⠀⢀⠂⢀⠀⠀⠀⠀⠀⠀⢡⠄⠐⡌⡧⠁⠸⠀⠸⡄⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠁⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡃⠀⠀⡠⠁⠀⠀⢧⠀⠀⣸⡀⠀⠑⣦⠀⢸⢰⠀⠀⢠⠁⠀⠀⢮⠀⠘⣠⠃⠀⡆⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠉⠁⠀⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢰⠆⢀⠆⢀⣠⡀⠀⠀⠀⠀⡴⢂⠀⠠⢂⢀⠀⡀⠰⣖⠀⠰⡶⠠⠂⠀⠀⣶⠀⠰⡀
⠀⠀⠀⠀⢇⠀⠤⠀⡄⠀⠦⠀⠠⠀⠀⠙⠀⠈⠉⠀⠧⠼⠧⠄⢡⠸⠾⠔⠁⠠⡿⠂⠀⠔⠁⠺⠆⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣄⠀⠀⠀⠀⡠⣤⠸⣇⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡄⠀⠀⣼⠁⠸⣆⠹⣧⡌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠶⣦⠀⠀⠘⣧⠀⠀⠻⣧⡤⠛⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⢹⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠛⠛⠻⢶⣤⣄⣤⡶⢶⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣠⣤⣄⣀⣀⠉⠉⠀⢀⣿⣴⠟⢙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠰⣿⣉⠉⠉⣹⡟⠀⣴⠿⢿⡿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⠾⠟⠛⠛⠛⠀⠘⠛⠷⠿⠁⢀⣿⠟⠛⠟⠛⡿⠛⠛⠻⣷⡾⠛⠛⠻⣾⠛⢻⡟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢁⣴⠾⣿⡟⠀⢠⡿⠛⣷⠂⠀⣼⠇⠀⡾⠀⢸⠃⢠⡆⠀⡾⠀⣰⠆⠀⡏⠀⣾⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⣧⣴⠟⠀⢀⣾⠃⢸⡏⠀⠀⣿⣆⣀⣡⣀⡉⠀⣘⣁⣴⠆⢀⣉⣀⣶⣆⣀⡁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠉⠁⠀⢠⣾⠃⠀⣿⡃⠀⢸⣿⠉⠛⠉⣿⠁⢰⡟⢻⡿⠀⣼⡟⠋⣡⡿⣿⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⡾⠛⠁⠀⠀⠹⣧⣤⣤⡿⠗⠀⢸⣟⠀⢼⡇⢸⡇⠀⣿⡀⠀⣿⡀⠁⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⠿⠛⠋⠈⠻⠿⠛⠁⠀⠙⠻⠿⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣩⣱⣦⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⣶⣶⣄⠈⢳⣄⠀⠀⠀⢀⡎⢀⣾⠀⣽⣿⠃⠀⡴⢦⣠⠇⢸⣷⡄
⠀⠀⠀⠀⠀⠀⢰⠃⢸⣿⠟⡥⣼⠀⠈⣿⡆⠀⠀⡼⠀⣼⡇⢀⢟⡉⢳⣴⠳⣶⡶⠀⣴⣶⡽⠋⢉⢲⣄
⠀⠀⠀⠀⠀⠀⠸⡄⠘⢿⠔⣱⣿⠀⠀⣿⡟⢲⣴⠃⢰⣿⠀⢠⡾⠀⣾⠏⢠⣿⠇⢠⣿⡟⠀⢠⢟⣽⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣶⣾⡿⢿⠀⢰⠏⣄⠘⡏⠀⣾⡏⠀⣿⠃⠸⢋⡀⠸⢫⠀⢸⠟⡄⠀⣶⡿⣱⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⣼⣿⠀⠁⣸⣿⡟⠶⣿⡷⢶⣿⡷⢶⣿⡷⢶⣾⡿⠶⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⣾⣿⠿⣀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠿⠋⠀⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠙⠓⢦⣀⢀⡞⠁⠈⠹⣦⡀⣀⡤⠖⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠋⠀⠀⣀⠈⠿⠛⢁⡀⠀⣠⣾⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠒⢿⠀⠀⢶⣤⣀⣼⣿⢷⣄⣴⡟⢀⣾⣿⠟⠀⢀⣠⠤⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠛⠓⢦⡀⣿⠀⠀⠀⣼⡇⠀⢸⣿⣙⢛⡏⠀⠈⢻⢀⣿⡿⠁⢀⡴⠋⠀⠀⠀⢀⡄⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⢠⣿⡷⣤⣤⣶⡟⠉⠉⠓⢦⡈⢻⣿⠃⢠⠏⠀⠀⠀⢀⣴⣿⡏⠀⠀⣿⣧
⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⠀⠀⠀⢰⣿⠏⠀⠀⣰⣿⡿⠛⠉⢩⣿⡄⣴⠀⠀⠰⠟⠉⠉⣳⠏⠀⠀⠀⣴⣿⡿⢻⠇⠀⠀⣻⣿⣦⠀⠀⢀⣄⡀
⠀⠀⠀⠀⣼⠁⠀⠀⢠⡏⠀⠀⢠⡿⠃⠀⣠⣾⠿⠿⠇⠀⠀⣸⣿⢿⡿⠀⠀⢀⡤⠀⢠⡏⠀⠀⠀⣼⣿⣏⡀⠘⢶⣤⣾⣿⠟⠁⠀⣠⠏⢀⣿⡆
⠀⠀⠀⠀⡇⠀⠀⢠⣿⡇⠀⠀⠈⠁⠀⠈⢁⠀⠀⠀⠀⠀⠀⠻⠿⢋⠀⠀⢀⣾⣇⠀⠘⠁⠀⠀⠀⠀⠈⣉⣉⠉⠛⢿⣍⠁⢀⣠⠞⠁⢀⣾⣿⠇
⠀⠀⠀⠈⡇⠀⢠⣿⣿⠁⠀⠀⢀⣠⣴⣾⡟⠀⠀⠀⣼⣦⣤⣤⣶⣿⣤⣀⣾⣿⣛⣆⣀⠀⠀⠀⢰⣄⠀⠙⠿⠀⠀⠸⠿⠒⠉⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⢻⣀⣾⣿⢹⡇⠀⠀⠘⣿⡟⡟⠀⠀⠀⠘⣩⡴⠛⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⢸⣿⡻⢶⠆⠀⠀⣤⣤⣤⣤⣴⣿⡿⠛
⠀⠀⠀⠀⠀⠻⣿⠃⠘⡇⠀⠀⠀⢹⣿⡇⠀⠀⣠⣾⠋⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣾⣿⣆⠀⠀⢸⣿⡿⠋⠀⠀⣸⣿⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢿⣟⠿⣿⣿⢃⣠⣴⣶⣾⠿⢛⣩⣵⣾⣿⡿⠟⠛⠙⣦⡀⠈⠉⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣼⣿⡄⠀⠙⠿⠿⠻⣯⣴⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠛⢶⣤⣤⣄⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠀⣸⣇⣀⡀⠀⢀⣀⣀⣠⣤⣤⠀⣠⡤⢤⣤⣄⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣠⡤⣼⣧⡀⠀⢀⣤⠶⠶⣦
⠀⠀⣰⠟⠉⠙⢶⠏⠉⠉⢷⣰⢿⠉⠁⢠⣤⣼⣾⡃⠀⠀⣤⣾⡿⣤⣄⠀⠾⣇⣴⡟⠛⠛⣧⣾⠃⢀⡤⣼⣇⣠⡟⡇⠐⠿⢿
⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⠀⠀⢈⣽⣚⣧⣉⡽⠆⠀⢹⣷⠤⠜⠀⠀⣸⡿⠀⠛⠂⢹⣿⠀⠘⠞⠁⠈⣹⠇⡇⠀⣴⣾
⢠⣿⠇⠀⠀⣤⡀⣠⢦⣀⣀⣸⣾⡀⠀⠈⠉⣹⢹⣀⠀⣀⣠⡾⢿⣀⣀⣀⣴⢡⣇⣠⠗⣄⣘⣏⠓⠶⠾⣆⣿⢻⠀⣇⣀⣀⣸
⣼⠉⠉⠉⠛⣁⡙⢁⣀⡉⢉⣩⣏⣉⣉⣉⣽⢿⣄⣉⣩⡽⠛⣇⣀⣈⣭⡼⢿⣤⣤⠟⠲⠶⠞⠛⠒⠻⢤⣼⠃⠘⠷⠭⠭⠽⠋
⠉⠛⠛⠒⠚⠋⠛⢻⡏⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠂⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⣤⠤⢦⣀⡼⠷⠶⣆⢀⣶⠶⠒⠚⠛⢻⣠⠞⠋⠙⠛⣷⣶⠛⠛⠛⣻⡇⢀⣤⣤⣤⡀⣠⡞⠋⢛⢻⡆⢀⣴⠏⢉⣭⣿
⠀⢀⣾⠀⠀⠀⠛⠀⠀⠀⢻⣾⢹⠀⠀⠺⢿⢻⡟⠦⢤⡀⠛⢿⣎⠛⣳⠀⠉⣷⢻⠁⣤⠀⢿⣿⠀⢴⣹⠛⠳⢾⠃⡇⠈⢉⣿
⠀⣾⡇⠀⠀⠀⠀⢀⡀⠀⠀⢻⢸⠀⠀⠰⠿⢾⢳⠛⠋⠁⠀⣼⡿⠉⠁⠀⢠⢟⠇⠀⣄⠀⢸⡿⣄⣀⣡⠀⣤⣾⠀⡇⠀⠛⢻
⣸⠿⠤⠤⣤⠛⠦⠎⠹⠶⠶⢾⡿⠦⠤⠤⢤⣾⠘⠦⠤⢶⣾⡇⠙⠶⠶⢺⣯⠘⢛⣿⣉⣓⣺⣧⣈⣭⠉⢳⡏⢾⣐⡷⠶⣢⡾
⠿⣤⣤⣀⣠⠶⣦⡴⣶⠦⠶⠞⠳⠶⠶⠶⠋⠙⠳⠶⠚⠋⠈⠓⠶⠖⠛⠉⠙⠛⠛⠁⠉⠉⠁⠀⠀⠈⠙⢻⡇⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⠶⠶⠶⠶⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠙⠷⣄⡀⠀⠀⠘⣯⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠘⢷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢷⠀⠀⠀⣰⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣼⠀⠀⢰⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡏⠀⠀⣼⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠏⠀⠀⢀⡏⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣰⠋⠀⠀⠀⣸⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⣠⠶⢶⡄⠀⠀⠀⣠⠶⠲⢦⡀⠀⠀⢰⡿⠃⠀⠀⠀⠀⣿⠋⠀⠀⠀⣠⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢀⡾⠁⠀⢸⠇⠀⠀⣼⠃⠀⠀⣼⠃⠀⣠⣾⠁⠀⠀⠀⢠⣾⠇⠀⠀⠀⡾⠁⠀⣾⠛⣷⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢫⣧⡟⠀⠀⠀⡿⠀⠀⢰⣇⣠⡴⠞⠁⢀⡴⢋⡟⠀⠀⢀⣴⠋⣿⠀⠀⢀⣼⡇⠀⠀⠈⢳⡿⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣼⡏⠀⠀⠀⢸⡇⠀⢀⡼⣏⠁⠀⢀⡴⠛⠀⢸⡇⢀⣴⠟⠁⠀⣇⢀⣰⠟⠹⣇⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠛⠛⠉⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠋⠁⠀⠀⠉⠛⠛⠁





⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⢶⠶⠶⣶⣶⡶⠶⠶⣶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⢀⣀⣀⡀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⢀⡔⠁⢀⡤⠖⠋⠉⠁⠉⠉⠑⠶⣄⠀⠙⢄⠀⢀⡀⣤⣤⣶⠄⠀⠀⠀⠀⠠⢾⣿⣯⣀⠐⠤⣀
⠀⠀⠀⠀⡎⠀⢠⡞⠙⠆⠀⠀⠀⠀⠀⠀⠒⠺⣧⣀⣼⣷⣿⣿⣼⣿⣿⣠⣤⣤⣾⣿⣿⣿⣿⣽⣿⡇⠀⠾⠂
⠀⠀⠀⢸⠀⢐⣫⣼⣄⣤⣤⣤⣦⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡇
⠀⠀⠀⢸⡐⣿⣿⣿⣿⣿⣭⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⡟⢿⣿⣼⣿⣿⣿⣿⣿⣿⡿⠧⠸⣿⠿⢿⡟
⠀⠀⠀⠀⠈⠈⠛⢻⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡿⣯⢉⢋⣴⣿⣿⣿⣶⡕⠈⠁
⠀⡄⠀⠀⠀⠀⠀⢾⣿⠸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢏⡇⣿⣿⣿⣿⣿⣿⣿⡜
⠀⠘⡄⢠⡄⠀⠀⢸⣿⣀⣨⣿⡧⢿⠟⡛⠋⡉⠀⠀⡀⠈⣛⡛⠉⠀⣀⣈⣇⢿⣿⣿⣿⣿⣿⣿⠱
⠀⠀⠈⠙⠦⡄⢐⣿⠿⠆⠙⠛⠛⠈⠀⠛⢃⡠⠀⠀⢻⠃⠀⠠⣄⡛⠃⠉⠉⠮⣙⠿⠿⠿⣛⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢺⢒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⣿⡇⠀⣠⡟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣟⣀⣠⡟⠀⣠⣤⡀⠀⣴⢏⣄⠀⣰⢟⣀⠁⣤⣶⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⡿⠉⠉⣿⠁⣼⠋⣼⠃⣰⣟⣡⡿⢰⣿⢁⣿⢁⣾⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⠐⣿⡀⠳⠊⠻⢲⡟⠛⠛⢁⡿⠛⠛⠁⠘⠓⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢼⠁⠀⠀⢸⠃⠀⠀⣴⣋⣽⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⢀⡄⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠠⣶⠇
⠀⠀⠀⠀⢀⣤⢶⡶⠒⢦⠀⠒⢛⡛⠒⠒⠶⢤⣼⣯⣴⣟⣁⣀⣠⡿⠀⣾⠃⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠻⢠⣿⣁⣤⡜⢀⣤⡍⢡⣶⡄⠀⣸⠏⣸⢏⣭⣭⢉⣩⣤⣼⠃⠀⣠⡴⣤⠀⢠⡶⢀⡦
⠀⠀⠀⠀⢀⣾⠁⠁⢀⡇⢸⠏⣀⠴⣻⠏⣰⡏⢠⡿⢋⡾⢡⡟⠁⣰⡇⢀⣼⠏⣰⡏⢠⡿⢠⣿⠃
⠀⠀⠀⠀⠸⠷⠶⠶⠋⠀⠙⠛⠁⠈⠛⠋⣿⠀⠘⠁⠈⠓⠈⠛⢋⠉⠛⠋⠘⠋⠘⠋⠈⠛⣹⠇
⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣴⠏⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠶⠶⠶⠦⣤⣤⣾⣧⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣷⠇⠂⠀⠀⠀⠀⠀⠠⣄⣀⣀⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢹⡇⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢻⡆⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢀⡼⠁⠀⠀⠀⢰⣿⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣼⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⣀⣤⣶⣦⡀⠀⠀⠀⣼⣿⣀⡴⠋⠀⣠⠶⠶⠶⣿⡿⠶⣶⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠻⠿⣿⡿⠀⠀⢠⣿⠃⠀⣴⡿⠋⠀⣸⣿⠀⠀⣰⣿⡏⠁⠀⠀⠘⠁⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢠⣿⠃⠀⢀⣾⡟⠀⢸⣿⠁⢀⣴⠋⣿⣠⠞⢹⣿⢀⡴⠛⣿⡆⠀⠀⠀⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣴⠟⣿⡇⠀⣸⠿⠶⠟⠁⢀⣿⠁⠀⢸⣿⠏⠀⣸⣿⠁⠀⠀⣰⣿⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⣿⣇⣴⠃⠀⠀⠀⡴⠋⣿⠀⠀⠘⣿⠀⠀⣿⡏⠀⠀⣴⠋⣿⡇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⡞⠁⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⣤⠞⠁⠀⠘⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢸⠇⠀⠀⠀⠀⠀⠀⣰⡿⠁⢸⠇⠀⢠⣿⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⡞⠀⢀⣀⡀⠀⠀⣰⡿⠀⡠⠋⣀⣠⣿⣇⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣠⠎⠀⣰⡿⠋⣻⠀⢰⣿⠷⠊⠰⠛⢻⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⢰⣿⡧⠞⠋⢠⣾⡟⠀⢀⣠⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢸⣿⡀⠀⣠⣾⣿⠿⡏⠉⠀⣼⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡟⠙⠿⠛⠉⢸⣿⠀⡗⠀⠀⣿⣇⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣴⠟⠀⠀⠀⠀⠀⠘⣿⣴⠇⠀⠀⠘⠿⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⣹⠤⡀
⠀⣀⣴⠄⡀⢀⠀⠄⠀⠂⢀⡀⠀⠀⠀⠀⢠⣤⣤⣬⣷⣿⣷⣾⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠄
⠈⣽⠃⣼⣵⢰⢷⢠⡷⡆⣾⣄⠀⠀⠀⠀⢸⣟⢃⡟⠹⡿⣿⠻⣿⢻⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠂⠐⢧⠜
⠀⠋⠀⢇⡛⡹⣸⠌⡦⣵⠀⠙⠀⠀⠀⠀⢸⣟⣼⣡⣂⣰⣈⣄⣇⡘⣿⡇⠀⠀⠀⠐⣺⠏⡼⣄⣠⣄⣠⣀⢠⠆⠄
⠀⠀⠀⠘⢳⠃⠇⠀⣃⡃⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⢏⠋⣾⢉⢏⣿⣿⡇⠀⠀⠀⠀⠏⠀⢇⡃⡃⡁⢋⠛⠘⠻⠄
⠀⠀⠀⠀⠐⠺⠻⠏⠃⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣻⢹⠁⠿⠸


⣀⣠⡤⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⡦⣠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣤⢄⡄⠀⠀⠁⠂⠄⢀⡀
⢠⡟⢠⡏⡆⣴⣢⢰⣶⡆⣾⡄⠀⠀⠀⠀⢩⡟⢰⡯⡆⡾⣦⣸⢶⢠⣏⡂⠀⠀⠀⠐⣻⠃⡞⣾⣸⢳⢰⡷⡆⣾⡐
⠈⠁⠈⢡⣅⣍⡬⢨⡌⡅⠁⠙⠀⠀⠀⠀⠘⠁⠘⣠⢃⢥⡭⢩⣜⡌⠉⠃⠀⠀⠀⠀⠋⠀⢃⡍⡼⣼⠈⣦⣡⠉⠙
⠀⠀⠀⠘⠼⠘⠃⠘⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠸⠀⠸⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠇⠀⠃⠛

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⢀⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⣹⣿⣠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⣦
⠀⠀⠀⠀⠸⣦⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⢠⣞⣩⡏⠙⢻⡍⠀⢻⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣾⣿
⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢠⣢⠀⠀⢸⡇⣿⣿⣿⠃⠀⠀⣷⠀⠈⣿⣿⣿⠀⠀⠀⡐⣆⠀⠀⣸⠃⢸⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⣿⣿⡆⠀⣼⠁⣿⣿⣿⠀⠀⠀⣿⠀⠀⢹⣿⣿⡄⠀⢰⣿⣿⠀⠀⡟⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⡸⢻⣿⣇⢠⠇⠀⢻⣿⣿⡇⠀⢠⠏⠀⠀⠀⢿⣿⣧⣀⡜⣿⣿⡀⣸⠃⠀⠘⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠈⠻⠿⠋⠀⠀⠀⠛⠿⠷⠶⠋⠀⠀⠀⠀⠈⠻⠿⠟⠀⠘⠿⠿⠃⠀⠀⠰⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀
⠀⠀⠀⠀⢀⡤⠖⠚⢯⢆⠉⠻⣿⡟⠉⠉⠉⠉⢹⠏⠉⢻⡿⠛⠉⠉⠙⠻⣿⠋⠉⣿⣿⠉⠙⠋⠉⠙⠉⠉⠉⣿
⠀⠀⠀⠀⡾⣥⠘⣶⣼⣿⡄⣤⢻⡇⠀⠐⠛⠛⢿⠀⠀⢿⠀⠀⣶⡶⠤⠴⣿⠀⠀⠙⠋⠀⠀⣷⣶⠀⠀⣶⣶⣿
⠀⠀⠀⠀⣿⡕⡽⣿⡿⡏⠱⣙⠈⡇⠀⠀⣶⣶⣾⠀⠀⣸⠀⠀⠻⠷⠀⠀⣿⠀⠀⣶⣦⠀⠀⣿⣿⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠹⠣⡼⢼⡄⠀⠀⠁⣼⣧⣤⣤⣿⣿⣿⣤⣤⣽⣷⣤⣤⣤⣤⣴⣿⣤⣤⣿⣿⣤⣤⣿⣿⣤⣤⣾⣿⣿
⠀⠀⠀⠀⠀⢣⠻⠆⠇⠀⠤⣼⣿⡇⠀⠤⠼⠁⣤⠈⢻⠀⠤⠀⣿⣿⣄⠙⢁⡼⠁⣤⠈⢋⠀⣿⠀⡏⠀⠤⠈⣿
⠀⠀⠀⠀⠀⢸⢈⠴⠀⠉⢷⣿⣿⡇⠀⣶⣾⡀⠛⠀⣼⠀⣤⠘⢿⣿⣿⡀⢸⣧⡀⠛⠀⣼⠀⠛⢀⣧⠀⣄⠘⣿
⠀⠀⠀⠀⠀⢸⠸⠃⠀⠀⢸⣿⣿⡟⠛⠛⠛⠛⣿⠛⢻⡿⠛⠛⠛⠻⣿⠛⢻⣿⠛⠛⠛⠛⠛⠛⢻⠟⠛⠛⠻⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⡇⠀⠚⠃⢀⣿⠀⢸⠀⢠⣶⠦⠐⡇⠀⠈⠉⠀⢸⣶⡆⠀⣾⣿⡀⠈⠓⠲⣿
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣿⣿⡧⠀⢰⡄⠘⢿⠀⢸⡆⠀⠛⠁⢀⡇⠀⢸⣿⠀⢸⣿⡇⠀⣿⣿⠈⠙⠃⠀⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⡔⢉⢭⣽⣦⡀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡔⢡⣶⣿⢶⡀⠙⣦⡀⠀⠀⢀⡎⢀⣾⠀⣿⣿⠁⢀⠖⠦⠼⠀⠿⣧⠀⣀
⠀⠀⠀⠀⠀⠀⡜⠀⣿⡿⢡⢲⡇⠀⢹⣷⠀⠀⡼⠀⣼⡇⠰⢋⠀⣹⡞⢻⣷⡆⢠⣿⡶⠋⢁⡝⣦⡀
⠀⠀⠀⠀⠀⠀⠱⣀⠙⠗⣣⣿⡇⠀⣼⡏⠙⣶⠃⢰⣿⠀⣰⡏⢀⡿⠁⣸⡿⠀⣼⡿⠁⠀⣞⣵⢫⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢻⠇⠀⠟⣴⠀⡟⠀⣿⣯⠀⣿⡀⢘⣵⡀⢛⣤⠀⠟⣱⡀⠸⠿⣡⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⣿⠀⠀⣸⣿⠏⠙⠿⠏⠻⠿⠛⠻⠿⠛⠿⠿⠛⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⣼⣿⠋⠧⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄


⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⢀⢈⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⣶⡆⢀⣀⡈⢉⣉⣉⠉⣉⣉⡉⢉⡉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⠀⣿⡗⣿⡇⣿⢼⣿⢸⡏⢸⡇⣿⠀⣿⣿⡇⣿⡇⢠⡄⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠛⠃⠛⠃⠛⠚⠛⢸⣿⠊⠁⣿⠒⠉⠸⣇⡿⠇⠈⠰⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡏⢱⡆⣿⢀⣤⢤⡀⣴⡆⢸⣷⢤⡀⢀⣀⣿⢀⡤⢄⡀⣤⡀⣤
⠀⠀⠀⠀⠀⠀⠀⢿⡏⢹⡧⣿⢸⣿⠈⠁⣿⡇⢸⡇⢸⣷⣿⠀⣿⢨⡗⢺⡇⣿⡂⣿
⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣁⣉⣈⣉⣀⣀⣈⣉⣈⣉⣈⣁⣉⣉⠉⠈⠉⠉⠁⠺⠯⠟
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⠇

⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⣀⣤⣤⣀⣠⣤⣀⡀⣀⣤⣀⣀⣤⣤⣠⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢸⠃⠀⢹⡏⠉⢹⡟⠀⠈⣿⠁⠀⢹⣿⡏⠀⢹⣿⠁⠈⣿⣀⣀⠀⠀⣀⣀⣿⠁⠀⢀⣀⣀⣹
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠀⠀⠘⠛⠃⠀⢸⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠘⠛⠛⡇
⠀⠀⠀⠀⠀⠸⣆⠀⠘⠃⠀⠘⠃⠀⣰⣿⠀⠀⣾⣿⡇⠀⢸⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠸⠻⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠾⠶⠶⠾⠿⠛⠷⠶⠿⠛⠳⠶⠿⠿⠶⠾⠋⠙⠿⠶⠾⠃⠙⠿⠷⠶⠶⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⢛⣛⣛⠻⢷⣤⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⣶⠟⠻⣦
⠀⠀⠀⠀⠀⠀⢠⣿⠋⢀⡾⠉⡽⠟⢃⡀⠁⣀⡀⣹⣇⡀⣠⡶⠿⠿⢶⣦⡾⠛⣡⡄⠀⠀⠀⣼⣟⣀
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡘⠁⣠⣶⠾⣿⡇⠀⣿⠟⠛⡉⢻⡟⠓⣶⡶⠀⡌⠀⡘⠉⣤⡄⠀⣼⠟⡛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⠁⣠⡿⠁⢠⠏⣰⣧⠀⡈⠀⣼⠟⠀⡼⠀⣰⣾⠀⢹⠀⣸⠃⠜⢁⣼⢿⣶
⠀⠀⠀⠀⠀⠀⠀⣾⠛⣤⣸⣿⣴⠟⠁⢠⣾⡀⠉⢁⣼⡇⠀⢩⠀⠀⣇⠀⠃⠊⣀⣾⠀⣇⠀⠛⢋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣉⢉⣀⣠⣴⠟⠙⠛⠟⠛⠉⠛⠟⠛⠿⠶⠟⠻⠟⠟⠛⠙⠿⠿⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⢠⠀⡀⢀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠀⠂⠀⠁⠀⠀⠀⢀⡡
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠁⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⢀⡂⠀⠀⠀⡀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠃⠘⠀⠀⡀⠰⢂⡇⠀⠂⠀⠄⠀⠄⠠⠀⠀⠀⠄⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⢰⡔⢰⠐⡔⢰⠐⡔⠀⠀⠀⠈⠁⠠⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣁
⠀⠤⠠⠀⠀⠀⠀⠸⠄⠄⠀⢸⠀⡀⠈⠈⠀⠈⠈⠈⠈⠀⠀⠀⡇⠀⢰⡆⣠⠀⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠛
⠀⠀⠀⠀⠀⠐⠀⠹⠛⠻⠿⠿⠀⣽⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⡃⠀⠈⠁⠀⣀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠠⠀⠃⠀⠂⠀⠈⠰⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠁⠂⠀⠀⠈⠀⠀⠠⠄⠠⠀⠤⠀⠤⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⢰⡏
⠀⠒⠂⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⡀⠀⢠⣄
⠀⠘⠛⠛⠂⠀⠀⠀⠈⠀⠀⠈⠀⠂⠀⠀⠀⠐⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⣾⣿⣿⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢰⣿⣿⡇⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠁⣿⣿⡟⢠⣾⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⣿⣆⢸⣿⣿⢃⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⡟⢀⣿⣿⡇⠘⠿⠛⣀⡿⠛⠃⢸⣿⣿⠀⣿⣿⡏⣼⣿⣿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢻⣿⣷⢸⣿⣿⠀⣰⣾⣿⢻⣆⢀⠀⣸⣿⡟⠀⣉⣉⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⡏⢸⣿⣿⢠⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠇⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⣿⣿⣿⠘⣿⣿⣷⣿⣿⣿⠀⢿⣿⣷⣾⣿⠟⢸⣿⣿⡏⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠉⠛⠋⠀⠈⠛⠋⠙⠛⠋⠀⠀⠉⠉⠉⠁⠀⠘⠛⠋⠁⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠐⡾⠿⠛⠛⠛⢿⢷⠀⠀⠀⠀⡴⠉⣤⣤⡌⢷⠀⠀⠀⠰⡿⠿⠿⠿⠿⠿⠿⠿⠿⡗
⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢤⡿⣯⡥⣼⡄
⠀⠀⣸⣿⣿⣿⣿⣿⣟⡃⠀⠀⢰⣷⣶⣶⣶⣶⣶⣾⡆⠀⠀⠿⠉⠛⠧⠴⠛⠉⠻⠁⠀⠀⣤⣶⡶⠿⠿⠿⠷⣶⣦
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢀⣀⠀⠀⠀⠐⠯⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⢠⣄⣠⣤⣤⣤⣀⡀⠀⠀⠠⣴⣶⣤⣤⣄⣠⣤⠀⠀⠀⠀⣾⣤⡤⡤⡤⢷⠁⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠁⠈⠉⠉⠛⠋⠁⠀⠀⠀⣻⡛⠛⠛⠛⣿⠄⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⠀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠋⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤
⠀⢠⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⠛⠿⠟⠛⠉⠻⠿⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣾⠿⠿⠟⠛⠋⠉⠉⠙⠇
⠀⠈⢙⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⣤⣾⠿⠿⠿⠿⠛⠀⠀⠈⠙⠻⠿⣿⣿⡿⠿⠛⠁⠀⢀⣴⣶⣶⠿⠿⠟⠛⠋⠙⠓
⠀⠀⠀⢀⣀⣠⣤⣴⡂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⢠⣴⣿⠿⣶⣦⣴⣾⠄⠀⠀⠀⠾⠛⠻⠿⡀⢠⠀⠀⠀⠠⣴⣶⣶⣶⣶⣶⣶⣶⣾⠇
⠀⠀⠿⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠙⠁⠀⠀⠈⠉⠈⠀⠀⠀⠂⠀⠀⠲⠷⠔⢐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠛⠶⠾⠷⠶⠛⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣼⣶
⠀⠀⣤⣤⣴⣶⣶⣿⣿⡃⠀⠀⠀⠘⠛⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠐⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣩⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⡿⠿⠷⣼⠿⢿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⢹⣿⣿⣿⣿⠿⠿⠇⠀⠀⢠⣿⣿⠟⠛⠻⣿⣿⡄⠀⠀⠈⠿⣿⣿⣿⣿⠿⠃⠀⠀⢠⣶⡿⠛⠛⠛⠛⠛⠻⣷⣦
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠟⠉
⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⣿⡿⠋⠻⣿⣿⣿⣷⣄
⢹⣿⣿⣿⣿⡄⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣻⣟⣛⣻⠛⠀⠀⠀⠈⢻⣿⣿⣿⣷⣄
⠀⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⡀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢳⡀
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢶⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⡖⣳
⣿⡀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠜⠿⣱⡟
⠙⢿⣯⠻⢫⢍⢍⢝⠝⠉⡩⡫⢋⠯⠍⠍⠉⡩⢛⠝⡩⠫⡻⢛⢻⡆⠀⠀⠀⠀⠀⠀⠀⣠⢏⠐⠀⢀⡰⠋
⠀⠀⠙⣗⣕⣁⡑⡁⠡⢠⢊⢀⠔⠐⠁⠀⠀⠔⠀⠊⠀⠀⠔⠕⣹⡇⠀⠀⠀⠀⠀⣠⠾⢁⠉⠀⢰⠏
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠚⠒⠒⠶⠶⢼⠃⠀⠀⠀⣠⡞⠋⠀⠀⢠⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡴⣫⠎⠀⢀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⠫⠀⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠃⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢠⣿⡇⠀⠀⠀⠀⠐⣿⡆⠀⠀⠀⢀⣶⠆⠀⠀⠀⠀⣀⣴⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢸⣿⡇⣤⣤⣤⣤⡄⣿⣧⠀⠀⢀⣾⠏⣤⣤⣤⣤⠀⣿⠋⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣾⣿⡇⣿⡇⢀⣀⠀⢸⣿⡄⠀⣼⡟⠀⣿⠁⢀⣈⠀⣿⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣿⡇⣿⡿⠟⠛⠃⠀⣿⣷⣼⣿⠁⠀⣿⡿⠛⠛⠀⣿⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⣿⣿⠃⣿⣇⣀⣠⡀⠀⠸⣿⣿⠃⠀⠀⣿⣃⣀⣤⡀⣿⡇⠀⠻⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⠇⠀⢸⣿⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠛⠈⣿⡇⠀⠀⣰⡿⢡⣶⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠰⣷⣶⠀⣿⠀⢹⣿⡀⢠⣿⠃⢸⣿⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⣽⡟⠀⣿⠀⠘⣿⣷⣿⡏⠀⢸⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⣿⠄⠀⠹⣿⡟⠀⠀⢸⣿⣤⣴⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣀⡀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⢸⡏⠉⠉⢻⣇⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⢸⣧⣤⣶⣿⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⣿⡀⢸⡿⠿⠛⠉⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⣠⣿⣿⡇⢸⡇⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠹⠇⠸⠇⠀⠀⠀⠀⠀⠖




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡾⠈⢧⠀⠀⠀⡞⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⡆⠀⠀⢠⠋⢸⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡏⠙⣆⠀⠀⣿⠀⠸⡆⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇⠀⠀⡞⠀⢸⠇⠀⢠⠞⠙⡆
⠀⠀⠀⠀⠀⠀⣷⠀⠸⡄⠀⢹⠀⠀⣇⠀⢸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⢠⡇⠀⢸⠀⠀⡞⠀⢸⠇
⠀⢀⣀⡀⠀⠀⢸⡀⠀⢳⠀⢸⡄⠀⢸⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⢸⠀⠀⡾⠀⢸⠁⠀⣼⠀⠀⠀⣀⣀
⠀⢸⠀⠙⣄⠀⠈⣇⠀⠈⡇⠀⡇⠀⠸⡆⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⡟⠀⠀⡇⢀⡏⠀⢀⡇⠀⢀⡞⠁⣸
⠀⠈⢧⠀⠈⢦⠀⢸⡀⠀⢹⡀⣷⠀⠀⣇⣼⠀⠀⡇⠀⠀⠀⠀⠀⣠⠴⠲⡄⡴⠲⢤⠀⠀⠀⠀⠀⠈⡇⠀⢸⣀⠇⠀⢸⠃⡸⠀⠀⣸⠀⢠⠏⠀⢠⠇
⠀⠀⠈⢧⠀⠈⢧⠈⡇⠀⠀⢳⡼⠀⠀⠘⠃⠒⠂⢳⠀⠀⠀⠀⡴⠃⢀⡞⠀⠹⡄⠀⠳⡀⠀⠀⠀⢸⠁⠒⠊⠛⠀⠀⠸⡴⠃⠀⢀⡇⣠⠏⠀⣠⠃
⠀⠀⠀⠀⢳⡀⠈⠳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡼⠁⠀⡞⠀⠀⠀⠹⡄⠀⠹⡄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠃⠀⣰⠃
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠊⠀⠀⡸⠁⠀⠀⠀⠀⢹⡀⠀⠘⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠲⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣾⠛⢋⣭⠙⢻⣶⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠸⣇
⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠈⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⣠⣴⠶⠶⠶⠖⠛⠛⠋⠉⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⢇⠀⣇⠀⠀⠀⡀⠀⠀⣰⣆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⡄⢸⠀⠀⠀⠀⠀⣼⣿⣿⢀⠊⠡⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠇⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⣻⣿⡏⠈⠀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠰⢸⠀⠀⡀⠀⢰⢈⡇⠀⠀⢀⠀⠇⠀⠅⢰⣒⣂⣈⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠄⠀⢸⠀⠀⡇⠀⠸⡆⡇⠀⠀⠘⢀⠀⠀⢀⠘⠟⠛⠛⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡄⢈⡠⠀⠁⠀⠀⠀⡇⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠨⠀⡸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠃⠘⠐⠒⠒⠒⠒⠂⠷⠄⠀⢀⣀⡀⠀⣀⡄⡇⠠⠄⠐⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⢶⢄⣴⡄⡖⠂⣧⠆⠀⡶⢄⣤⠀⢀⡀⢀⡀⡀⠀⣀⢠⣤⣮⢧⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣏⠗⠿⠟⠳⠖⠟⠂⠀⠧⢼⡼⠀⠸⡝⡎⠉⣟⢳⢇⡿⢧⠏⠇⢂⠄
⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠄⢰⡖⢲⣖⠀⠐⠂⡒⡒⠶⡆⠀⠌⢁⠈⠁⡉⢈⡌⡥⠀⠐⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣤⣼⡏⠈⣿⣤⣶⠀⠆⡀⠀⡇⠀⠀⠈⠀⠀⠂⠁⠀⠁⠀⠀⠀⢸⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠈⠹⡇⠀⢹⡇⢨⠀⠀⡏⠈⣇⠁⠀⢠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⣰⠇⠀⠀⠳⣬⣠⣠⡇⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⠀⠀⢸⠀⢰⠀⠀⠀⠀⡦⠴⠶⠲⠟
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⢸⡂⠀⠀⣤⠂⠀⠀⠆⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠭⣓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢑⡢⠭⣀⠈⠙⠓⢦⣄⠀⠀⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⢴⣪⠥⣒⠁⠀⠈⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠬⠿⠶⣥⣀⡀⠀⠀⠀⠀⣼⠀⠀⢀⣀⣠⡤⠶⠶⠿⠯⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠿⠗⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⣶⢶⣶⠶⠶⠶⠶⠖⠒⢒⣒⣒⣒⣶⣶⠶⠶⠓⠓⠒⠛⠛⡞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⢳⣸⡟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⣀⠀⠀⠀⠀⠐⠊⠙⢦
⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃⣀⣠⣤⣿⣷⣶⣶⣶⣖⣒⡚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⢀⡴⠞⠛⠉⠁⠀⣿⠟⠉⠀⠀⠀⠀⠐⠋⠭⠭⠭⠭⠭⠍⢉⣛⡛⣛⣛⡒⠒⠒⠒⠲⢶⡾⠓
⣰⠋⠀⠀⠤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣈⠉⠩⠭⠭⠭⠤⠄⠀⠀⠀⣼⠉⠓⠦⣄⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⣀⣀⣉⣉⣉⡀⠐⠒⠒⠒⠠⠍⠉⠉⠉⠀⠀⠀⠀⠀⢇⠀⠀⣀⣀⣹⡷
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣈⣻⠉⠉⢠⠇
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⣠⠴⠖⠒⠛⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸
⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡙⢷⡠⠀⠀⠀⠀⠤⠤⠶⢖⣒⣛⣯⡭⠭⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠃⠙⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠟⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠄⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣗⣤⡄⣠⣄⢠⣤⠤⣀⡴⠆⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⠀⠀⣿⢸⡡⣯⠙⠺⡇⣼⠿⣇⡀⠀⡠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡄⠀⠈⠁⢘⡇⢠⢄⠀⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⡇⣾⢷⣸⡇⣸⠘⡷⣤⡄⠀⠈⠀⢸⡈⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇⠛⠖⠈⠃⠹⠄⠀⢹⡇⠀⢠⡏⢹⠃⣾⠉⡇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣈⠛⠀⠀⠑⠈⠃⠙⠊⠓⠙⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠖⢀⡀⠐⠀⠀⢠⡇⠀⠀⠀⢀⡆⠀⡖⡄⠀⠀⠠⡰⢃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⠘⢦⣀⠀⠀⢸⡇⢰⠂⢰⢸⣧⢰⣧⠀⠀⢠⢶⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠙⠂⠀⢹⡆⠀⠘⡇⠸⠆⣿⣸⡇⢸⡇⠀⠀⠻⣄⠑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⢋⡴⠆⠘⠁⠀⠀⠈⠀⠉⠀⠉⠀⠀⠀⠀⠀⠼⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢢⠔⠉⠙⠆⠀⢸⠁⢆⡀⢀⢀⠀⣀⡀⠀⢀⣀⣀⢀⠀⣀⠀⢀⣼⡸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⡅⠼⡇⣼⢸⡗⢹⠇⠀⣾⠁⣿⢸⡖⣹⢰⠉⣿⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⡀⠀⠀⠀⠀⢸⡇⢀⢅⠘⠃⠀⣈⠃⠀⠈⣃⠉⠀⠀⠙⠈⠁⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡏⡆⠉⠀⡏⠐⣠⠀⠊⠀⠀⠀⠀⣿⠀⡀⠀⠀⠑⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢀⡴⢼⡷⠀⡴⠄⣇⣀⡻⣤⡄⢀⡤⣤⠀⡗⢀⡅⠀⣤⣀⢠⡄⣠⡄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⣸⡅⡸⡇⢸⣇⠀⣏⢘⠇⢸⡇⢾⡀⣾⠠⣯⠀⣇⢰⣇⠑⠺⡇⢸⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠊⠁⠈⠀⠙⠂⠉⠁⠈⠁⠀⠀⠈⠁⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣀⣀⠈⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠸⣇⠀⠀⣤⡶⢶⣦⠀⠀⣿⣇⣾⡟⣼⠃⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⣿⠀⣾⡿⢀⣾⠃⠀⠀⣿⠻⣿⣟⠁⡴⠀⢸⣿⡇⠀⠀⢀⣠⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⢸⡇⣿⣿⡟⠁⢸⣷⣴⡟⠀⠙⠿⠟⠁⠀⠀⠙⠓⢀⡴⠏⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣷⣄⣼⠇⠈⠛⠛⠀⠀⠙⠋⠁⠀⢀⠀⠀⠀⠀⠀⢠⣶⣟⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠉⠉⠁⠀⠀⢀⠀⢰⣦⡤⠄⠀⠀⣾⣿⡆⠀⢰⣦⢸⣿⣿⣦⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠙⠋⠀⠀⢰⣶⡄⠀⢸⡇⢸⣿⡄⠀⠀⠀⢹⣿⣷⠀⣼⣿⡌⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⣀⡈⣿⣿⡀⢸⡇⠸⣿⣇⡀⠀⠀⠈⣿⣿⡾⠃⠙⠃⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⢀⣀⠀⠙⠁⠘⣿⣧⢸⡇⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣾⣿⡇⢀⣤⠀⠹⣿⣿⡇⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⣿⣿⡇⠘⣿⣇⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⢀⣼⣿⣿⣿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠂






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠒⠒⠀⠀⠀⠀⠀⠀⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠢⢭⣙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠒⠦⣌⡉⠒⠦⣍⡛⠷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠤⢍⣓⠦⢌⡙⠲⠤⣀⡀⠀⠀⠙⠻⣦⣄⠠⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⠬⣙⡲⠬⣉⡒⠬⢌⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣙⣳⣦⣍⡓⠂⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠉⠉⠉⠉⠛⠷⢶⣤⣀⣀⠀⠀⢀⣀⣾⠇⢀⣀⣠⣤⣴⠶⠾⠛⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡟⢧⡹⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠸⠀⠈⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⢀⣀⣈⢻⣿⣤⣶⣶⣶⣶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣀⣤⣤⠶⠞⠛⠋⢹⣿⣴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⠶⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣆
⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢛⣛⣒⣒⣒⣒⣒⡒⠲⠶⠶⠤⠤⠤⠭⠭⠭⠍⠉⠉⠉⠉⢉⣿⡉⠉
⢠⡿⠁⠀⠀⠤⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣂⣀⣀⡀⠀⠀⠀⠀⠨⠭⠭⠭⢭⣭⣭⣭⣅⣀⡀⠀⠀⠀⠀⣾⠀⠉⠓⢦⣄⡀
⣿⠁⠀⠀⠀⠀⠀⠈⠉⠂⠀⠘⣿⡀⠀⠀⠀⠀⠒⠒⠂⠤⠤⠤⠤⠤⢤⣤⣭⣍⣉⣉⣉⣙⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠄⠀⠀⠀⣧⠀⠀⠀⠀⠈⠙⠷⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣐⡒⠲⠶⠶⠶⠦⣤⣤⣤⠀⢠⠀⡐⢒⡒⠒⠚⠉⠉⠉⠉⠉⠠⠤⣤⣤⣤⣒⣂⣀⠀⢿⣄⣠⣤⣤⣶⢶⣿⠿⠛
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠻⠶⠶⠾⠷⣬⣤⢦⣥⣥⣬⣥⣤⣿⣿⣿⣿⣷⣦⣄⣀⣐⣒⣲⣶⣖⣂⣈⣹⣯⠉⠀⠀⢰⡇
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⢀⣀⣤⠠⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⣿⠁
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠠⠖⠒⠒⠉⠀⠀⠀⣿
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠒⠂⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡠⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠶⠚⣛⣋⣉⣥⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣌⣛⣬⣑⠒⠀⠀⠀⠀⠒⠊⢉⣉⣉⣩⣭⣤⡴⠶⠶⠚⠛⠛⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⢬⠁⠂⡿⢀⢸⠀⠀⡁⠀⢸⠈⠁⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣀⣀⣇⣁⣠⣈⣀⣿⣇⣄⣸⣠⣄⣃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⣷⠀⠀⠹⢧⣤⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⣶⠚⠛⢳⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢰⡆⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠘⠃⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣴⣦⣤⣤⣶⣤⣤⣶⣤⣤⣤⣿⣷⣠⣤⣤⣤⣤⣤⣤⣄⣿⣄⣤⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⣿⣶⣽⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢴⣶⡄⢠⣶⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠤⡘⠋⠱⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠁⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠖⠋⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⠻⢿⣧⠀⠀⡀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⠀⠚⣧⠀⢹⣶⡎⢀⠆⠀⠀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢡⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢰⡀⣀⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⢶⣤⣄⣀⣀⣼⣿⣿⡄⠀⠀⠀⠀⢸⡯⠁⠀⠀⣇
⠀⠀⠀⠀⡰⠀⠀⠀⠀⣸⣿⡏⠼⣿⣿⣿⣿⣿⣟⡷⡆⠀⠀⠀⠀⢺⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡠⢄⠀⠐⠂
⠀⠀⠀⢠⠇⠀⠀⢀⣰⣿⡿⢘⢱⣿⣿⢿⣿⣿⣿⢸⣷⠀⠀⠀⠀⣸⢿⡄⠀⠀⠈⠓⠒⠒⠛⠉⠉⠉⢹⡁⠀⢼⡿⠃⡂
⠀⠀⠀⢸⠀⠀⠰⢋⠙⠻⢷⣥⣲⣿⡿⣸⣿⣿⡜⣾⣿⠀⠀⠀⠀⣽⠀⢳⣴⠇⠀⠀⠀⠀⢀⣰⣀⣀⣨⡷⠒⠚⠛⠃
⠀⠀⠀⢸⡢⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠁⠀⢉⠙⢿⡀⠀⠀⠀⣿⠀⠀⠻⠦⠤⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠙⠛⠲⠶⠤⣤⣄⣀⡀⠀⣸⠀⠀⠀⣴⠂⣺⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠟⠿⠶⠤⢴⣾⡿⠁⠀⠀⢤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣶⣶⣦⣀⣉⣰⣶⣾⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⢻⣿⢿⣿⣿⣿⣿⣯⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠂⣄⣺⣿⣯⠿⣿⣿⣿⣷⣾⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠀⢸⣿⣿⣿⡟⠀⢻⣿⡿⠷⠶⠦⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠈⠙⢛⡛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢾⣁⣤⢹⡇⠈⠋⠉⠉⠉⠀⠀⣠⣤⣤⡴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠙⠛⠳⠶⣤⣬⣉⣡⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣴⢛⣿⠆⠀⣈⠃⣠⡀⣤⡄⢀⡶⠿⣦⠀⠀⠀⠉⠉⢀⣀⠀⣤⡀⢀⣠⡶⣤⠀⢀⣿⠃⣸⡇
⠀⠀⣼⠃⠀⠀⠀⣸⡿⢰⡿⠀⣹⡷⣾⣧⠾⠋⢠⡾⠛⣳⠀⣾⣟⣠⡙⣿⣻⡏⢀⣿⠀⣼⡏⣠⣿⡇
⠀⠀⣿⠠⣿⣻⣶⣿⢁⣿⣇⣰⡟⠀⢻⣤⡴⠆⣿⠀⢀⣿⢠⣿⢹⣿⣧⡟⠹⣦⡾⠿⠾⠛⠿⠋⣿
⠀⠀⠹⢦⡼⠟⠁⠻⠟⠁⠙⠉⠀⠀⠀⠀⠀⠀⠹⠶⠞⠛⠛⠙⠛⣉⡉⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠛⠛⠛⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤⣤⣤⡴⠄⠀⣿⡀⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠐⠶⠒⠖⠂⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⢀⠙⠋⠉⠛⠀⠀⠀⠀⡀⠁⠀⠐⠐⠀⠊⠈⠉⠉⢀⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠈⠉⠀⣈⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠤⠀⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠠⠔⠆⠂⠀⠀⠀⠀⠀⠰⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠀⠈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠉⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣚⢂⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⣈⣛⡁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⠠⣍⢬⣥⡁⡄⠀⠡⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣍⢨⣥⠄⣤⣡⢤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠦⠄⠖⠒⠐⠦⠲⠶⠔⠦⠄⠀⠐⠰⠦⠄⠀⠀⠀⠀⠀⠀⠀⠢⠴⠶⠴⠒⠦⠐⠖⠂⠒⠴⠶⠢⠴⠤⠔⠶⠒⠠⠄
⠀⠀⣀⣀⡐⠃⠓⣛⣛⢚⠓⠊⣛⣋⢈⡓⢙⡛⢒⡛⠂⡀⠀⠐⠑⠛⠛⠒⡛⠒⣙⣋⡓⡛⠚⣛⢛⠉⠒⢙⣛⡁⠋⠒⣛⡛⢚⠒⠊⣛⣋⢈⡓⣙⡛⢒⡀
⡠⣉⡡⣭⣍⡉⣉⣭⣍⣩⣍⡁⣭⡭⢩⣉⢬⣭⣩⣍⡁⣥⡄⠀⠈⠡⡄⢉⢍⣉⢭⡡⠉⠉⠁⡭⢉⣤⣉⢨⣭⠍⣩⣉⣭⣍⣩⣉⡁⣭⡭⣩⣍⢭⣍⣩⣉
⠴⠤⠐⠶⠆⠄⠤⠶⠦⠴⠦⠔⠶⠖⠰⠦⠲⠦⠤⠦⠄⠶⠖⠴⠦⠴⠶⠤⠀⠄⠂⠀⠀⠀⠀⠶⠤⠰⠦⠰⠶⠆⠴⠤⠶⠦⠴⠤⠔⠶⠒⠴⠦⠲⠦⠴⠦
⣘⠒⢊⣛⡓⠂⠒⣛⣒⢚⡒⢂⣛⣋⢘⡓⣙⣓⢒⡓⠂⣛⣋⠚⠓⢛⣛⠒⡃⠀⠀⢀⡀⡓⠚⣛⠒⣚⠒⢘⣛⡁⢒⠒⣛⡓⢚⠒⢂⣛⡉⢚⡒⣙⡑⢚⡒
⣨⣉⣡⣥⣍⡁⣉⣩⣉⣩⣍⡁⣭⣥⢀⣉⣨⣍⣉⣍⡁⣭⡥⣉⣌⣩⣍⣉⣅⣀⢤⣥⣅⣌⣉⣭⣉⣉⣉⢈⣭⡅⣁⣉⣭⣉⣩⣉⡁⣭⣅⣩⣉⢬⣍⣩⣉

⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⡠⠐⠀⠐⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⢀⡔⡄⠀⡠⠂⡲⢲⠒⠒⠒⠒⡄
⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡱⠃⠀⠀⠀⣎⢸⠀⠀⠀⠀⢸
⠀⠀⡀⠂⠀⠀⠀⠀⢐⠀⠀⠈⠉⠠⡀⠀⡄⠀⠀⠀⢀⡖⡖⠁⠀⠈⠉⡇⠀⠀⠈⠉⠳⡀⢢⡒⠚
⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢘⠀⠀⠀⠠⡃⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢆⢕
⠀⠀⠑⠈⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⢡⡌⠉⣩⣭⣭⣍⢩⣭⠉⢩⣭⢩⣭⣭⣥⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣬⣿⠁⢸⡇⢸⣿⠉⣤⣅⢸⣿⣤⣼⣿⠀⢸⣿⠉⠁
⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⡄⢸⣷⠘⢿⣤⣽⡿⠀⣿⠁⢸⣿⠀⠘⣿
⠀⠀⠀⠉⠂⠀⢀⣄⡆⠀⠀⠀⠀⠀⠁⠀⠀⠁⠚⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⡇⢴⡄⢠⣤⡀⣠⡄⣤⣶⣤⣤⠀⣠⣴⣶⣄⠀⣴⣦⠀⣴⡄⢀⣤⣶⣶⡄⠀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⡇⢸⣷⣼⢿⣇⣿⠃⣿⣷⣼⡟⠠⣿⡇⠀⣿⡇⣿⡿⣧⣿⡇⣾⡏⢠⣤⡄⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⡇⠀⣿⡿⠈⣿⡿⠀⢿⡏⠙⣿⡄⠻⣧⣴⡿⠃⢹⡇⠹⣿⡇⠹⣿⣦⣿⠇
⠀⠀⠀⠀⠑⠒⠐⠶⠒⠒⠒⠒⠂⠐⠒⠐⠒⠒⠂⠐⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠲⢲⠒⠀⠒

⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⡔
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠐⣿⣿⣿⠃⣰⣿⣷⣄⢀⠀⠀⠀⣤⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢟⣾⣿⣿⣿⡶⣻⣭⡍⢣⣿⣶⡄⣴⣿⣿⢟⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠆⠀⠾⣿⣿⣿⣿⠸⣿⠿⢣⣿⠿⠟⠼⣿⣿⡇⢿⡿⠛⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠙⠻⠟⠻⠟⠛⠿⠛⠻⠟⠋⠻⠿⠛⠿⠿⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⠀⠄⠠⠀⠄⠀⠀⠀⠀⠄⠀⠆⠄⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠈⡤⠀⠈⠠⢄⠀⠄⠀⠠⠤⡄⠀⠀⠀⡀⠀⠀⠀⠃⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠆⠀⠀⠀⠒⠘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⣐⣀⣀⣀⣀⣀⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠙⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⡇
⠀⠀⡇⢀⠤⠀⠀⢄⠀⢠⠔⠢⡀⡔⠒⢄⠁⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡸⠃⠀⠀⠀⠀⠁
⠀⠀⡇⡎⠀⠀⠀⠀⢡⠘⢄⠠⠃⠣⡤⠎⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠶⠲⡄
⠀⠀⡇⠇⠀⠀⠀⠀⠸⢰⠁⠉⡄⡋⠈⠁⠀⠀⠀⠀⠀⠀⣋⣈⣁⠀⠀⢀⣀⠈⠀⢠⠀⢠⠀⠀⠀⠘⢄⡀⡠
⠀⠀⡇⠈⠢⢄⡠⠔⠁⠈⠓⠊⠀⠑⠒⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠈⠉⠉⣉⠉⠉⠉⠉⡉⡉⠁⠀⠀⢀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢭⡋⠿⢢⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⡀⠇⡄
⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⢀⠀⠀⣇⠆⠈⢸⠠⠆⡷⠀⡔⠉⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠘⢬⣠⣠⣮⡻⠃⠀⢧⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠠⠈⠀⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢀⠀⠀⡀⠀⡆⠀⠀⠀⢸⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⡇⠇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠀⢡⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⣴⣵⣾⣿⣶⣿⣶⣰⣿⣶⣄⣷⡄⠀⣀⣘⣷⡀⠀⣰⣿⣶⣄⣷⣄⣿⡆⠀⠀⣸⣿⡄⣿⡶⣠⣾⣿⣷⣿⣧
⠀⢸⣿⣿⡟⢡⣤⣤⣀⣿⣿⣷⣿⣿⣷⣼⣿⣿⣿⣧⠀⣿⣿⣷⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢻⣿⣇⣈⣻⣿⣿⣿⣿⡿⣿⣿⣹⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠛⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣧⣀⣀⣄
⠀⠀⠀⠙⠿⣿⣿⣿⡿⠿⣿⠇⠈⠿⣿⣿⡟⠀⠀⠻⢿⡿⣿⠇⠀⠀⠻⢿⡇⠀⠈⠿⣿⠿⢿⡇⠘⠻⣿⣿⣿⣷




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⣀⡀⠀⠀⢀⣀⣤⣀⠀⢀⣀⠀⠀⣀⡀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠙⣿⣧⠀⣿⡇⠀⣰⣿⠟⠛⠋⠀⢸⣿⠀⠀⣿⡇⠘⠛⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⠏⠀⣿⡇⠀⣿⡏⢀⣤⣤⠀⢸⣿⣦⣴⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣷⡄⠀⣿⡇⠀⣿⣇⠈⢹⣿⠀⢸⣿⠉⠉⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣧⠀⣿⣇⠀⠙⢿⣷⣾⣿⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢠⣤⡄⠀⢀⣤⣤⣄⠀⢠⣤⡄⠀⣤⡄⠀⣤⣤⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢸⣿⡇⢰⣿⡏⠙⣿⣇⠘⣿⡇⢠⣿⣷⠀⣿⡏⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣸⣿⡇⣾⣿⠀⠀⣿⣿⠀⣿⣇⢸⡟⣿⢀⣿⠇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠹⣿⣿⡇⢸⣿⡄⠀⣿⡿⠀⢹⣿⣿⠃⢿⣿⣿⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠻⣿⠇⠀⠻⢷⣾⠿⠁⠀⠘⢿⡿⠀⠸⣿⠏⠀⠀⠀⠀⢿⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢯⣿⣿⡿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠛⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣿⡀⣀⣤⡶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣷⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⡾⠿⠿⠿⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢹⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⠶⠶⠾⠿⠿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠸⡏⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣤⡟⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠁⠘⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠶⠾⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠈⠉⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣾⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡆⢠⣤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⣦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠓⠒⠲⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡿⠷⠀⠀⠀⠠⣿⡆⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⡿⠀⠀⠀⣶⡶⠂⠀⢀⣿⣿⣿⡇
⠀⢰⣰⣆⢰⣶⣰⢰⢲⢰⡆⢰⡄⣴⡖⡆⣶⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠁⠀⠀⠀⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠐⠷⠴⠦⠲⠅⠠⠄⠤⠤⢔⢤⠄⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣯⣿⣾⣿⣽⣭⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⣿⣯⣿⣬⣬⣾⣭⣯⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣄⢠⣄⣤⡄⠤⡄⠤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠨⠥⢠⢡⣨⡄⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡒⠲⠒⠒⠒⠀⠐⠉⠉⠉⠉⠀⠉⠀⠀⠀⠈⠙⠋⢲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣀⣀⢀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣈⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢙⡏⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠞⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠋⠉⠉⠉⠚⠉⠙⠉⠩⠍⠩⠭⠉⠉⠛⠛⠙⢛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠓⠒⠒⠒⣶⠶⣶⡞⠛⠛⠛⠒⠒⠒⠒⠛⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠄⡇⠀⣀⡠⠤⢒⠊⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⡢⠤⠖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⣀⣴⣶⡾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠛⠃⠀⣤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢠⡖⣾⠀⠀⣧⠔⣺⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⡳⣠⠖⢦⡇⠙⠓⠺⠷⠀⠉⠋⢇⠔⢲⣄⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠎⠙⠙

⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⡶⠋⠁⠀⠀⠉⠐⢤⠀⠀⠀⠀⢰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠉⠉⠙⡍
⠀⠀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘⠀⠀⠀⠀⡀
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⢣⠀⠀⠀⠀⡁
⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠌⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠄⣀⡀⢀⣀⡰⠕⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠖⠒⠤⠒⠉⠒⠒⠉⠁⠈⠣⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠠⣶⠶⠖⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠐⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠣⢄⡀⢀⡀⣀⣀⣀⡤⠤⣄⡠⠶⢷⠉⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣀⣈⣀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢀⣴⠂⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢞⡁⠀⠀⠈⠖⠢⠖⠲⡄
⠀⠀⠦⣰⠒⠒⠒⠒⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⡀
⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⢰⠛⠁⠀⠹⠱⠊⠉⠑⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡛⣟⠀⠀⠀⠀⠀⠀⠀⣀⣀⡨
⠀⠀⢀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⣙⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠿⢬⠢⠤⠚⠑⠛⠲⠞⠁
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠂⠤⠤⢤⣀⠄⠀⠛⠊
⠀⠀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⣠⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⢄
⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇
⠀⠀⠈⠪⠶⠦⠤⠒⠼⠑⠒⠒⠒⠁⠀⠀⠀⠈⠑⠠⠤⠤⠤⠤⠤⠤⠤⢤⡠⠤⠤⠤⠤⠀⠀⠐⠛⠉

⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⣀⣤⣶⣦⣄
⠀⠀⠀⢸⣿⣿⣿⣿⠟⣹⣿⠀⠀⣸⣿⣿⣿⠟⢉⣷⠀⠀⠀⠀⡀⠀⢀⣴⠆⠀⠀⠀⠀⢀⠀⠀⣠⡶⠀⠀⠀⣀⠀⠀⣠⡾⠂
⠀⠀⠀⢸⣿⣦⡉⣡⣾⣿⣿⠀⠀⢻⣷⡈⢁⣴⣿⣿⠀⠀⠀⠈⠻⣶⠟⠁⠀⠀⠀⠀⠀⠙⢷⡾⠋⠀⠀⠀⠀⠻⣷⡾⠋
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠛⠿⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⢸⣿⡟⠻⡿⠛⣿⣿⠀⠀⢠⣿⠻⣿⠟⢿⣦⠀⠀⠀⠀⢠⡀⢀⣄⠀⠀⠀⠀⠀⢀⣄⠀⣠⠀⠀⠀⠀⢠⣦⡀⣠⡆
⠀⠀⠀⢸⣿⡿⠂⡀⠺⣿⣿⠀⠀⣿⣿⠗⣀⠰⢿⣿⠀⠀⠀⠀⢀⣿⢿⡁⠀⠀⠀⠀⠀⠀⣹⠿⣇⠀⠀⠀⠀⠀⣹⡿⣯⡀
⠀⠀⠀⢸⣿⣷⣾⣿⣶⣿⣿⠀⠀⠘⠿⣶⣿⣷⡿⠋⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠈⠋⠀⠈⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢒⣒⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⣄⣠⠶⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣶⣿⢿⡟⢸⡿⠉⣷⣄⡀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣤⠞⠀⣼⣿⣟⣶⣿⣷⠀⠀⡤⣄⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⠃⢰⣿⣿⠵⠊⣠⣿⣿⣰⣶⠀⣸⣦⡴⠋⣠⣶⢹⣦⡔⠁⣠⣬⠋⢙⣦⡼⠁⣼⣿⠏⢈⣿⡟⠈⣷⣴⠇⣿⡗⠉⣠⡶⢹⣦
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡿⠙⠷⣾⣿⡿⣳⣿⠃⢠⣿⡟⠀⣾⡟⢁⣾⡟⠀⣼⣿⠏⠀⣾⣿⠃⢰⣿⡟⠀⣾⣿⠃⢸⣿⡏⣰⡟⠀⣾⡿⢁⣾⣟⣷⣄
⠀⠀⠀⠀⠀⠀⢹⡀⣿⡇⠀⢀⡤⢊⣼⣿⡏⢀⣿⢯⡄⠠⣵⣾⣿⢟⡄⢰⣿⢏⠀⣸⡿⡁⢀⣿⢏⠀⣼⡟⣵⠀⣾⢟⣴⣿⡇⢠⣵⣾⣿⢏⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣬⣙⣛⣩⣴⣿⡿⠋⠳⣬⣵⣿⡿⢦⣭⣭⣴⣿⡷⣤⣵⣿⣦⣭⣾⣷⣬⣵⣿⣤⣭⣾⣿⢦⣭⣾⡿⠋⠙⢦⣭⣭⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠁⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⢀⠀⢀⠀⡀⡀⡀⢀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠁⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⣉⣍⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠑⠀⢦⡴⡀⠴⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠐⠐⠀⣀⠀⠀⠀⣿⣿⢸⣿⣇⠀⢨⠞⡳⣫⢌⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⣀⣠⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠐⠛⠁⠀⠀⠉⠀⠀⠈⠀⠀⢠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⣨⠏⢷⠏⣿⡂⠀⠀⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⠀⠀⠀⣿⣿⣄⣁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠚⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣤⡶⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⠀⣼⠃⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢏⣼⠃⠀⠀⠀⠈⠁
⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠙⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢲⡶⠀⣤⡄⢀⣀⡀⠰⡶
⠀⠀⠀⠈⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⣀⣀⠛⢁⣀⡀
⠀⠀⠀⠀⠱⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡀
⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠲⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⡶⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⣿⣿⣦⠀⠀⣀⣀⡀⠀⢠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⣻⡟⠏⠀⠀⠀⠈⠛⠿⠀⠀⠘⠛⠀⠀⠸⠟⠁⠀⠀⠀⠀⢦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢹⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⣷⠗⠺⣶⠇⠀⠀⠰⡶⠀⠰⡶⠂⠀⠀⠀⠀⢀⡀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠦⠮
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣴⣴⠂⠀⣀⣀⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⣿⠿⢿⡇⠀⢰⠿⠿⠿⠿⠆
⠀⠀⠀⣶⣶⣶⠄⠀⠈⠉⠉⠁⠀⠀⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢨⡇⠀⠀⢀⣶⣶
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠦⢀⢔⡠⡄⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⡖⢖⣾⣮⠖⡇⣻⣔⢆⢼⠃⠲⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢤⡞⣶⣻⡾⢿⣧⣈⣙⣏⣙⣦⢾⣶⡼⠽⣉⠮⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣀⣶⣻⡽⣟⠿⡋⣀⣩⣟⣿⣏⢹⣿⢹⣷⣶⣏⣠⡄⣳⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢚⣤⣿⣿⡞⢳⣬⣿⣶⣟⣿⣻⣿⣿⣹⣿⣿⣿⣟⢻⣿⡼⢏⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢟⢯⢶⣬⣿⣿⣯⣿⣿⣕⣿⣿⣻⡟⣿⣷⣽⣳⣬⠿⢧⠃⡒⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣭⣯⣼⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣧⣷⣯⣿⢄⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡾⣼⠿⢿⣿⣭⣿⣿⣯⡯⣿⠿⣇⣮⢛⠛⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣿⣇⣿⣾⣿⣿⡞⢙⠉⠉⠸⠇⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣼⣾⣿⣿⡿⢻⣿⣿⣿⣡⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣿⢿⣿⣿⢛⡿⢿⣿⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⡿⡄⠉⠀⠒⣿⣿⢿⣈⡆⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠀⠀⣲⠏⠡⣉⢠⣤⠀⡠⡄⠦⠋⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣢⢺⣤⠷⣯⡮⢹⡏⢠⠋⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢮⣩⣨⢵⣟⣊⣵⡛⣶⠖⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣻⠏⠛⠚⠿⣯⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢸⣿⣿⠿⣿⣿⣦⠀⣿⣿⡇⡄⠀⠀⢰⣿⣿⣿⣿⣤⠀⣾⣿⡿⢿⣿⣷⡀⣸⣿⣿⢄⣾⣿⡟⣦
⠀⠀⠀⢸⣿⣿⣘⣸⣿⡿⡄⣿⣿⡇⡇⠀⠀⢸⣿⡇⣿⣿⡇⢠⣿⣿⣿⠃⠛⣛⡱⣿⣿⣿⣼⣿⡟⣼⠃
⠀⠀⠀⢸⣿⣿⢛⢻⣿⣶⠃⣿⣿⡇⡇⠀⠀⣿⣿⣧⣽⣿⣷⢹⣿⣿⣿⠀⣀⣀⠀⢸⣿⣿⢿⣿⣷⠃
⠀⠀⠀⢸⣿⣿⣬⣼⣿⣿⠀⣿⣿⣧⣥⣤⢠⣿⣿⢻⢹⣿⣿⠀⣿⣿⣯⣴⣿⣿⢣⣿⣿⣿⡜⣿⣿⣧
⠀⠀⠀⠘⠛⢟⢿⡿⠯⠵⠇⠛⠻⠿⡟⠿⠼⠿⠿⠼⠈⠛⢿⠽⠈⠛⢛⣛⣻⡭⠟⠙⠻⡯⠇⠘⠻⠿⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⡀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠙⣿⡆⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠋⠁⢀⣠⣤⠀⢹⣿⣀⣀⣤⣴⣾⠿⢛⣋⣭⣶⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⣠⣾⣿⣿⡄⠀⣿⣿⣿⣫⣥⣶⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⣴⣶⣤⣤⣄⣴⠟⠁⢹⣿⡇⠀⢹⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⢀⡀⠀⠀⠀⠀⢹⣷⠀⠈⠉⠁⠀⠀⢸⣿⣿⠀⠘⣿⣤⣤⣤⣴⣶⣶⣾⠿⠿⠿⠿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠁⢀⣀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣭⣥⣶⣶⣶⣾⠿⠿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠁⢠⡖⠋⣹⠟⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⣿⡟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡗⠚⢻⡶⠀⠀⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠷⠶⠾⠃⠀⢠⣿⣀⣄⣀⣀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢸⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣍⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⠿⣶⣶⣶⣤⣤⣄⠀⠀⠀⠈⠉⠉⠉⠁⠙⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⣠⣾⢿⣶⣶⣶⣤⣤⣤⣀⣀⣀⠀⠈⠛⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣠⣾⡿⠁⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣶⣶⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉