Dairy farm Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢰⣿⢋⣴⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣄
⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⣾⣿⣧
⠀⠀⠀⠀⠀⠸⡇⣿⢹⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⡇⠟⠀⢻⣏⠀⡠⠀⠉⡉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⠆⠀⠀⠈⠛⠂⠸⣿⣿⣿⣿⡿⠋⢸⣿⣿⣿⡿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠐⠃⢸⡟⠛⠉⠀⠈⢻⣿⣿⣿⣿⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⢼⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠇
⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢘⢡⡆
⠀⠀⠀⠀⠀⠙⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣤⢤⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣶⡮⠓⣶⣶⣶⡶⣀⠐⣶⡖⠀⠀⣀⣻⡟⠁⠀⢾⡿⠀⠀⠀⠀⠀⢀⣾⠀⡌⣍⣛⣿⣍
⠀⠀⠀⠀⠘⢯⡄⠛⠃⡉⠉⠬⠻⠀⠃⠃⡀⠀⠠⠬⠄⠀⠈⠠⠤⠀⠄⠀⠀⠀⣾⠏⢀⠰⠀⠈⠱⠙⡆⡄
⠀⠀⠀⠀⠰⠌⢮⠀⠙⠛⠓⢻⣠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⠀⣀⡀⢀⣀⡀⣀⡀
⠀⠀⠀⠀⢀⠀⢄⢀⠀⠀⠀⠈⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣦⣀⣀⣠⢤⣴⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠘⣿⠃⠀⠀⠀⠀⢸⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⣅⢀⣾⣿⣿⡛⠟⡁⠀⠀⠨⣿⠂⠀⢢⣆⡀
⠀⠀⠀⠀⠀⢐⣰⣆⣠⣤⣄⣀⠀⡀⠩⠿⠿⢿⠶⢶⢦⣤⡿⡄⠀⢀⠠⢀⠀⠠⠀⠀⠀⠀⠹⠀⠺⠁⠀⠹⢿⣿⣿⡏⣷⣶⣷⣶⣶⣾⣏⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⢈⣋⢧⡼⠦⠆⠀⠀⣠⡶⢮⣐⠾⢾⣟⣓⠧⠤⣤⣭⣦⣾⣿⣇⢀⣀⣀⣠⡀⠀⠠⣶⣧⣬⡅⣻⡟⠉⢀⠈⢚⡏⠀⢾⣦⣄⡄
⠀⠀⠀⠀⠐⡄⠀⠾⠉⠃⡄⠀⠀⠀⢸⠀⠀⠀⢉⢀⡞⠁⠀⡖⠀⠌⠻⣿⣿⣿⣾⣿⠀⣴⣷⢿⣾⣿⣿⣿⣷⣆⣿⣿⡧⠀⠸⡎⢠⣷⡈⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠣⠀⠀⣤⣀⡁⣸⣧⣀⣶⠁⢾⠀⢤⡄⣉⣆⡠⡄⣼⣯⣇⡏⠀⢀⣪⡾⠶⣿⡿⣿⣯⣽⣿⣿⣿⣿⣶⣶⣦⣿⣿⣿⢽⣿⣿⣽⣿⣶
⠀⠀⠀⠀⠠⣀⠀⢀⣀⣤⣴⠎⡽⣿⣿⡏⣿⠋⢠⣶⣤⣤⠞⠟⠿⠻⣷⡟⠿⠋⠀⠂⠘⠋⠁⠰⠷⣶⣶⠾⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⡟⢯⢽⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣶⣿⣿⣏⢸⢇⣄⣼⣿⠋⡀⠀⠀⠀⠀⣸⣿⠀⢳⠀⢰⣶⣶⣦⣶⣾⣿⣿⣝⡉⠻⠽⢿⣿⣿⣿⣁⣙⣿⡿⢠⣿⣻⣿⣿⣿⣿⣇
⠀⠀⠀⠐⣲⣿⣿⣟⣉⢀⠹⣟⣿⣿⣿⡞⣾⣿⡍⢁⣴⠏⣶⡴⣶⣾⢿⡟⣼⣿⣿⡀⣘⣻⣿⣿⣿⣿⡩⠛⠛⠒⢀⡀⠈⠹⠻⢿⣿⢿⣷⣶⣿⣟⣿⣯⣿⢿⡛
⠀⠀⠀⠈⠛⠓⠈⠙⠛⠛⠾⠙⠻⠯⠿⢧⣿⠿⣧⣼⡟⠓⠾⠃⢹⣟⣛⣿⣿⣻⡟⢷⣿⣿⣿⣿⣿⣿⣋⢰⣀⠀⢀⠀⢀⠀⢸⡟⢷⣾⣿⣯⣶⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢀⣀⣾⣿⣯⣿⣶⣄⠀⠀⠀⠀⢀⣀⠀⠉⠉⠀⠶⠀⠀⠈⣭⠤⢉⣉⣉⠀⠀⠈⠙⠻⠿⢿⣿⣷⣿⣾⣿⣼⣿⠗⢮⢻⣄⣤⣤⡴⠾⠾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠈⠉⠙⠚⠓⠛⠛⠒⠂⠀⠀⠀⠀⠁⠉⠉⠉⠒⠒⠒⠐⠒⠉⠛⠛⠻⢿⣿⣿⣿⣾⣿⠟⠁⠀⠀⠒⠃

⠀⠀⠀⠸⡛⠛⠛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣀⠀⣠⣤⠀⠀⠀⠀⠀⢠⡒⣒⣒⡒⣒⡆
⠀⠀⠀⡰⠁⠀⠀⠡⡀⠀⠀⠀⢀⣤⡤⠤⠤⢤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣛⣿⣿⣦⣿⣏⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⣾⣽
⠀⠀⠀⠇⢀⣠⣀⠀⠁⠀⠀⠀⢸⢺⣿⢶⣶⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⢻⣿⣿⢻⣿⠀⠀⠀⠀⡀⢀⣀⣀⡀⢸⣿⣿
⠀⠀⠀⠈⠹⠿⠟⠁⠀⠀⠀⠀⠉⢸⣿⣿⡿⠧⣤⢼⢻⣿⣷⠀⠀⠀⢰⣷⣿⣿⣯⣷⣽⣿⣿⣼⣟⡀⠀⠀⠀⠄⠻⠿⠿⠟⢸⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠲⠄⠀⠀⠇⠿⠀⠻⠇⠀⠀⠀⠸⣗⣒⣒⣒⣒⣒⣒⣒⣒⣺⡧⠀⠀⠀⡅⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⣠⠴⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⢠⡦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣻⣿⣿⣠
⠀⢀⡞⠀⠀⣀⡀⠀⠘⡆⠀⠀⠀⠠⣿⠿⠟⠉⠙⢿⣿⡆⢸⡇⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣻⣯⣾⣿⣽⣿⡃
⠀⠸⣷⣿⣾⣿⣿⣶⣶⣿⠀⠀⠀⠀⣿⡷⠀⠀⠀⠐⢿⡇⠘⣧⠀⠀⠀⢸⣿⣹⣿⢿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠈⢉⣾⣿⣿⣿⣿⡛
⠀⢘⣿⣿⣛⣿⣟⣻⣿⣟⠀⠀⠀⠀⣿⣷⣶⣄⣠⣶⣿⡇⢰⡇⠀⠀⢠⣿⠇⣿⢹⡇⠈⠉⣵⢹⡇⢸⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿
⠀⠈⠳⠶⠿⠶⠾⠷⠶⠋⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠁⠸⠇⠀⠀⠀⠀⠀⠻⠈⠇⠀⠀⠻⠸⠃⠀⠿⠀⠀⠀⠀⠀⠉⠛⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠰⣦⣄⣀⠀⠀⠀⣠⣾⣿⡯⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⣄
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣘⣿⢷⣿⣿⡿⣋⣽⣻⢿⡃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣶⣦⡀⠀⠀⠀⢀⣞⠞⠁⠀⠈⢧
⠀⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿⡿⢻⣿⣾⡏⣿⣿⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠻⠿⡟⠁⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣭⢺⡇⠀⠀⠀⠞⢸⣿⡻⠿⢿⣿⢟⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠁⠳⠆⠀⠀⠀⠀⠀⠘⠻⠷⠿⣿⠟⠋⠙⠛⠘⠃⠀⠀⠀⠀⢸⠉⠧⠀⠀⡷⠿⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⡠⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⣶
⠀⢀⢔⠢⣄⠀⠀⣤⠂⢄⠀⠀⠀⠀⣴⣿⣽⣛⡿⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡿⡿⣿⡇
⣀⣞⣃⣀⣈⣄⣌⣃⣀⣈⣆⡀⠀⠘⠿⢽⣿⣿⣿⣿⣾⣯⣟⣿⠆⠀⠀⠀⠸⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣯⢯⡿⡽⣯⣿
⠈⣿⣿⣿⣿⠟⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⠼⠏⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⠇⠀⠀⠀⠀⠀⣸⣯⢯⡿⡽⣯⣿
⠀⠘⠛⠛⠛⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⣷⣿⣿⡆⠀⠀⠀⠀⢀⣿⣯⣯⣿⣽⣯⣿

⠀⠀⠀⠀⢀⡀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡠⣄
⠀⠀⠀⠁⠂⠚⠈⢰⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠐⢈⠀⠊⠁⠈⠳⣤
⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡲⠂⠀⠀⠀⠀⠀⠔⠀⢰⠀⠀⠀⡤⠈⢳⡀
⠀⠀⠀⠀⠀⡘⡄⠀⠂⠀⠀⠀⠀⠠⠒⠠⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠀⠀⠉⠀⠈⣷
⠀⠀⠀⢈⣙⣍⡠⠀⠀⠀⠀⡄⠀⠶⠛⢀⠃⠀⠀⢀⡞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠴⠀⠠⠀⠀⠀⠠⠀⠀⠉⠀⢸⠆
⠀⠀⠀⠀⠀⢩⠁⣔⢀⠀⠀⠁⢀⠆⠘⠁⠀⠀⠀⠈⠀⠀⠀⠀⠸⠋⠉⠉⠈⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠖⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⡈⡀⠀⠠⠆⢀⠠⠀⠀⠀⠀⢀⠀⢀⡀⠄⢠⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⡀⠄⠀⠙⠀⠀⠁⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠺⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⢽
⠀⠀⠀⠀⡈⠰⠀⠀⠀⠀⠲⢼⠆⠁⠀⠀⠀⢀⢴⠀⠀⠀⠀⢀⢰⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡄⠈⡦⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢄⠈⢦
⠀⠀⠀⠀⢰⠀⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠲⠿⣀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⢱⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⡀⠀⠀⠀⠠⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠀⣠⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⢸⠀⡗⠀⢠⡴⠁⠀⠀⢨⠀⠀⢀⢀⣤⣄⣤⠶⠶⠾⠶⠆⠀⠀⣷⠟⠁⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⢹⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠀⣠⠿⣤⢀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⠀⠀⠘
⠀⠀⠀⠀⡃⠈⠀⡞⡄⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠃⠀⠀⠀⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣶⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠄⠁⡄⢀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠁⢡⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡏⠀⠀⠰⡄⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠂⠀⠐⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠓⡲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣤⣤⣤⣮⣽⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢧⢩⣭⡍⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣷⣯⡠⠀⠀⢘⣠⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠈⠁⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣷⡾⢋⣠⠼⢻⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣊⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠈⠿⠊⠝⠂⣴⡿⡫⠀⠹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠉⢉⣏⣏⣉⣙⣛⠀⠀⣴⠚⣛⣉⠉⠉⠉⢳⡆⠀⠀⠀⢸⣿⢁⡄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠀⣿⣙⠓⠒⠒⠒⠈⠹⣿⣿⣿⣿⣿⣇⣸⡆⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠬⡭⢭⠉⢁⣾⠁⠡⡀⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⡆⠀⡀⠀⢀⡀⣠⡷⠀⠀⡞⠿⣤⣤⡑⣄⢀⡀⠠⢒⣪⣥⣾⣿⣿⣿⣿⡷⠄⠐⠄⢠⡏
⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠻⡟⠀⠀⠀⡇⠀⠀⣲⠇⠈⠙⠷⠚⠉⠁⢻⣿⣿⣿⣿⣿⠥⣄⡈⠓⢾⡇
⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣷⣤⣀⠀⠳⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠋⠀⠀⠀⠙⢷⣼⠇
⠀⠀⠀⠀⠰⠶⠶⢿⣿⣿⣿⣿⣭⣉⠁⠀⣿⠀⠀⠀⠐⢿⣋⡉⠛⠲⠚⠋⠁⠀⠀⠀⠠⣀⣴⠚⠋
⠀⠀⠀⠀⠀⠈⠉⣭⣭⣛⣛⣛⣛⠛⠛⠀⣿⠀⠀⠘⣏⠉⠁⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠭⠭⠁⠀⢿⡀⠀⠀⠘⢧⣄⣡⡤⢞⣩⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠚⠛⠩⠿⠿⠛⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣂⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠋⠀⠉⡇
⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠉⢉⠀⠀⠀⠀⠀⠀⣏⡗⢀⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠋⠂⠀⠀⡞⠋⡆
⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⢀⢤⣞⠀⠀⠀⠀⢀⣴⣿⡇⠈⠐⠀⠁⠁⠀⠑⡄⠀⠀⠀⠀⢹⠖⠲⠦⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠁⠀⠔⠁⠀⠀⠙⠛⢻⣿⠀⠀⠀⢀⣿⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢰⠀⠀⠀⠀⣀⠈⠁⢀
⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⠀⣰⣸⡟⠀⠀⠀⢸⣿⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠛⠀⠀⠀⠀⠀⠙⠻⢥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⠀⠺⡟

⣶⣶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⢰⡿⠃⠄⠀⠀⠀⠐⡱⠛⠸⡇⢐⢉⣄
⠀⠀⠀⠀⠀⠘⠀⠀⠠⡀⠀⠀⣘⠁⡀⢀⠋⣉⢠⠀⠀⠀⠀⠀⡶⠒⠀⠀⠒⠚⠒⢢⡀⠀⠒⠀⠂
⠀⠠⠄⠀⠐⠸⠲⠂⠀⠀⠀⠀⠉⠨⠿⠿⣄⠉⢸⠀⢠⠀⠀⠀⠸⡃⠈⠉⠁⠀⠒⠛⠁⠑
⠀⠀⠀⠀⣀⡀⢄⠄⠀⠀⠀⠀⠠⣱⡀⠀⠀⠀⠸⡀⢈⠀⣧⣠⡴⠃
⣤⣤⣥⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⣄⣤⡀⠀⠀⠀⠀⠀⣀⡤⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⢤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠼⡋⠉⠁⢿⣿⣷⣶⡖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢁⣠⡭⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣠⠋⠘⠛⢀⡀⠰⣦⡄⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⣾⠘⣾⡆
⠀⠀⠀⠀⢠⣾⠥⠀⠀⢀⣺⣥⣼⣿⡿⠀⠀⠀⢀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣸⠇⢰⣿⣧
⠀⠀⠀⠀⠀⠛⠶⠶⠾⠿⠛⠛⠙⢿⣷⣄⣀⣰⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⡿⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡄⠀⡀⠀⠀⢈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣤⣤⡀⠀⠀⠀⣾⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣶⣶⣶⣿⣫⣤⣤⣶⣾⡿⠛⢿⡀⠀⠀⢻⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⢸⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣄⠀⠀⠹⣄⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡀⣸⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⢧⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⣿⡟⠁⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢻⠀⠀⣇⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⡟⠀⢀⡇⢹⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⡀⠀⣠⣞⣠⡞⠀⢠⣿⣀⡟⠀⢀⣠⣀⡤⣆⠀⠀⣠⣞⣡⡿⠀⢀⣼⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠛⠛⠛⠀⠀⠛⠛⠛⠃⠐⠛⠛⠛⠛⠛⠂⠀⠛⠛⠛⠁⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⣿⠉⠉⠉⠙⠓⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣷⣶⠶⠦⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣟⠛⠛⠛⠛⠓⠒⠒⠀⠠⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣟⠉⠉⠉⠉⠉⠛⠛⠛⠃⠀⠀⢀⣀⡀
⠀⠀⠀⣦⠀⠀⠀⣀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠿⣆⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰
⠀⠤⠒⢿⠚⠛⠋⢻⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠀⠀⠀⠀⠘⠟⠛⠛⠿⣶⠶⠶⠶⠶⡿⠶⠒⠒⡿
⠀⠀⠀⢼⠤⠤⠒⠚⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⣧⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠶⠦⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⣠⣤⢐⠆⠀⢤⡶⠤
⠀⠀⠀⠀⠶⣿⣿⣾⣶⣶⣶⣶⢶⣖⠆
⠀⠀⠀⠀⣶⣌⣞⣋⠉⠉⠀⠉⢉⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⣠⣀⣰⡄⡀⠠⣀
⠀⠀⠀⠀⣿⡟⠉⠉⠙⠏⠉⠀⠐⣿⡇⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠹⠗⠚⠛⠛⠚⠛
⠀⠀⠀⠀⢹⢷⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⡤⠀⠀⡀⠀⠀⠀⡍⠉⠉⠉
⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠛⠣⠚⠆⠀⠁⠈⡒⠠⠀⡄⠀⢀⡐⡀⢀⡄
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢤⠐⣴⠀⠠⠉⠤⠃⠀⠈⡳⣿⠛⠃
⠀⠀⠀⠀⢸⣿⠇⠀⡈⠄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡐⠉⠓⠂⠀⠀⠀⠀⠀⠀⠎⠇⠛⠈
⠀⠀⠠⠀⠈⠛⠳⠷⠧⠤⠀⠤⠖⠊⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⡠⠚⢉⣉⠉⠉⠉⠉⠉⠉⣵⣶⣖⣒⣊⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⡀
⠊⢀⣴⣿⣿⣷⣴⣶⣴⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠉⠲⣄⡀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠛⠀⠀⠀⣠⣴⣿⣿⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄
⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣄
⡷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⡇⠀⠹⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠃⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀⢤⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⠁⠀⠀⠀⠀⢰⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⠛⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠛⣉⠤⠒⠛⡋⠠⡀⢸⣿⣿⠿⣿⡏⠀⡋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⣌⣦⡀⠀⠀⢸⣿⠁⠀⠀⢠⠃⠀⠀⠒⠠⣀⠀⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⠒⠀⠂⠈⣇⠀⠀⠀⡇⠀⠈⢺⡿⠉⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠹⠃⠘⡛⠉⣿⡟⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡄⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⡄⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣷⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡜⠀⠀⠀⠀⢆⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⢡⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠈⡆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢂⠀⠀⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⡨⠆⠀⠀⠀⠀⠀⡇⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡀⣨
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⢀⣈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠰⣿⣟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⠀⠈⠙⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⠃⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⢉⠃⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠠⡿⠋⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠛⠋⠀⠀⠀⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠘⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣾⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⣯⣍⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣅
⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⣿⣿⠋⠹⣿⡟⢫⣿⣿⣿⠛⢛⣿⣿⣿⣿⢻⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⡀
⠀⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⢻⣷⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⠾⠿⡿⣿⣿⣿⣿⣿⣿⣿⡻⢏⡛⠝⠛⠛⠛⠛⠯⠛
⠀⠀⢀⠂⠠⠀⠀⠀⣿⣿⡇⢹⣿⠙⠛⡣⠀⠸⢿⣿⣿⣿⣟⣿⣿⣿⣫⣟⣡⣴⣦⣀⣿⣿⠿⣿⡟⠿⡿⠃⠁
⠀⠀⠈⠆⠠⠀⠀⠀⣿⡏⢧⠀⠈⠲⠂⠙⠂⢤⣄⢠⣤⣿⢿⣿⡟⠿⠋⢿⡟⠙⠿⣿⣿⣿⠀⠛⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡉⠀⢄
⠀⠀⠐⠀⠀⠀⠀⠀⣿⣥⣷⠀⣠⣶⠖⠒⠲⣦⣌⠻⣿⣃⠈⠉⠡⠆⠀⠀⠀⠴⣦⣿⡿⡟⢊⠁⠀⠀⠀⡀⠀⠈⣗⠟⠦⠐⣾⣄⠀⠀⠈⠅⠤⠤⠄
⠀⠂⠀⠀⠀⠀⠀⢰⣧⠏⢁⣾⢿⡟⠿⢶⠊⠉⠉⠓⠮⠽⠶⠶⠶⠖⠒⠉⠉⢹⣿⣿⣿⠁⠼⠗⠀⠀⠀⠀⠀⠀⠦⠄⢈⣤⡄⠉⢸⠾⡄⠠⠘⠷⠞
⢠⠀⠀⠀⢀⡀⠀⢸⡇⡐⠉⣿⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠐⠀⠘⣟⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡄⠰⠀⢀⠈⡇⡆
⠀⠤⠄⠀⠀⠀⠀⢸⠉⠄⠀⠘⡏⠀⠀⠂⠀⠀⢸⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠿⡁⠘⣿⠀⠄⠄⠀⠀⢀⣴⡆⠀⠀⡦⠀⠀⢤⠘⠀⠃
⠀⠀⠀⣄⢘⢦⣤⡼⠀⠂⠒⠂⢀⠀⠀⠀⠀⠀⠰⠒⠙⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠈⠉⠉⠀⠀⠀⠉⢉⠁⣀⣐⣃⡐⣤⠀⠀⣀
⢠⣿⠿⢿⣿⣿⣟⣻⠄⡛⠿⠷⠶⡿⣠⠀⡀⠀⠀⠀⠐⢂⡈⠁⠄⠔⢺⣓⣶⣶⣶⣂⣐⠀⠀⡀⠀⠐⠋⠀⠀⢀⣉⣽⣿⣿⣿⣷⣼⣿⣇⣤⣄⣀⡀
⠀⠀⠀⠀⠄⠀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠈⠛⠙⣩⣍⡉⠉⠙⠟⠉⠛⠟⠛⠁
⠀⠀⠈⠉⠀⠀⠀⢀⡀⢀⡠⠶⢶⣦⠄⡤⠀⠀⠀⠀⠀⠐⠎⡅⣤⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣴⣶⣶⠦⠤⢀⠥⠰⠤⢶⣖⠒⠦⠼⣂⠉
⣶⣾⣷⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣿⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣾⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠛⠿⠿⠟⠀⠀⠻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠻⠿⠿⠛⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⣄⠀⣤⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⣴⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠛⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⣠⡄⠛⢿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⠛⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠈⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⢿⣿⣶⣶⣶⣶⣿⡿⠃⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣠⣿⣿⣿⣿⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠟⠛⠿⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢦⣬⣿⣤⡼⠳⣿⠄⠄⠀⢀⠀⠤⠤⠤⢤⣀⣀⣀⣀⡀⠀⠀⠄⠤⠤⠤⠄⠠⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠉⢀⡴⠶⠀⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀
⠀⠀⠀⠀⠀⢀⣧⠌⠀⣀⣴⡿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣇
⠀⠀⠀⠀⠀⠃⣀⣀⠈⠛⠿⣷⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡃⡏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢿⣎⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣼⡇⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣯⣆⠀⠀⢠⣿⡏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⡰⢠⣾⣷⣿⣶⣾⣶⣷⣾⣿⣿⣿⣿⣆⠀⠈⣿⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⢰⡏⠉⠉⠉⠙⠛⠛⠛⠛⠋⠙⠿⣿⣿⣧⡀⠈⣷⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠹⡄⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠿⠇⣾⡾⠀⣄⡠⠤⠤⠀⠀⢠⡤⠄⠠⠷⠟⣁⠀⢰⣶⠏⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠓⠒⠀⠀⠀⠐⠒⠒⠒⠐⠒⠀⠀⠂⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⣦⡄
⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⡰⠁⠀⠀⠀⠈⣄⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⠛⠿⠟⣿⣿⣷⡀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⢸⣿⣿⣿⣿⣯⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣷⣦⣀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣄⢰⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣥⣄⣠⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢽⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠈⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠸⣿⠏⢿⣿⠇⣿⣿⣿⣿⡿⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⢷⠹⠏⠉⠻⡟⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢻⣿⣿⣿⡇⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡁⠀⠀⢸⡇⣾⣿⣿⣿⣿⣦⣤⣀⣀⣠⣄⣠⣴⣷⣦⣄⠙⢿⣿⡇⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣠⣴⣿⣿⣿⡟⠀⠉⠉⠛⠛⠛⠻⣿⣿⣿⣿⡇⠙⢧⠀⠀⠃⠀⠀⠙⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠸⡧⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠋⠀⠀⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣧⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣷⣴⣿⣄⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣿⠀⡀⠀⠀⣼⣆⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣄⣤⡀⠀⠀⠀⠀⢀⣀⡤⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⡋⠉⠁⠻⣿⣷⣶⡖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢁⣠⡍⠁⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡴⠋⠘⠛⢀⡀⢸⣶⡄⠀⠀⠀⠀⠀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⣾⠘⣾⡆
⠀⠀⠀⠀⢰⣾⠥⠀⠀⢠⣺⣥⣾⣿⡿⠀⠀⠀⢀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣸⠇⣰⣿⣷
⠀⠀⠀⠀⠀⠙⠶⠶⠿⠟⠛⠛⠉⢿⣿⣤⣀⣰⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⡟⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄⢀⡀⠀⠀⢈⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣤⣤⡀⠀⠀⠀⣾⣏⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣶⣿⣿⣫⣤⣴⣶⣿⠿⠛⠿⡄⠀⠀⢻⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⢸⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⡿⠿⠻⣷⣄⡀⠀⢹⣄⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡁⣸⣿⡿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⢳⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⡟⠁⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢻⠀⠀⣧⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢱⡟⠀⢀⡇⢹⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣀⡀⠀⣠⣏⣠⡞⠀⢠⣿⣤⡟⠀⢠⣰⣀⡴⣆⠀⠀⣠⣞⣤⡿⠀⢀⣾⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠀⠛⠛⠛⠀⠀⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠁⠀⠘⠛⠛⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣿⣿⣷⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢀⣴⢶⣦⡀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣶⣶⣾⣿⡆⠀⠀⠀⠸⣗⣶⣿⣿⡆⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⣤⠀⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠋⠁⠀⠀⠀⢀⣾⣿⣆⠀⠈⠻⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢹⡀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠒⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡸⣷⡄⠀⠀⠀⠀⠀⠸⣿⡿⠋⠙⢻⣿⣿⡿⠋⠉⠙⠿⣿⡿⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢀⠌
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⣿⡇⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠂
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢾⡿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⡐⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⢀⠀⠀⠘⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢀⠀⢀⣀⡠⠐⠃⠀⠀⠀⠀⠀⠁⠐⠂⠤⠀⣀⡀⠀⠀⠠⢄⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⣀⣀⣀⣀⣙⡓⠄⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣈⣳⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣈⣓⠲⠶⠶⠖⠒
⣶⣶⠾⠷⠒⠀⠒⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢤⠠⠀⠀⠠⠤⠤⠤⠠⠤⠄⣀⠀⠬⠁⡀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣸⣇⠀⡐⠀⣀⣀⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⣀⣀⡀⠩⢴⡤⠤⢤⡀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠠
⠖⠚⠛⠋⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠘⠓⠦⠔⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠁⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⡀⣀⠤⠴⠒⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠈⠙⠛⣛⡋⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⣀⣀⡄⠤⠖⠒⠒⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢰⣾⣿⡿⠀⣾⣿⣿⣧⠀⠀⢀⣀⠠⠅⠒⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠀⠾⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⠶⣶⡎⠓⠰⣶⣶⣶⠖⠴⣁⣀⣠⣤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠋⠉⢩⣭⣥⣍⣉⡉⠳⣖⠢⠀⢠⡄⠈⠛⠁⠀⠀⠘⡿⢫⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⡿⠀⠈⠁⠀⠘⠋⠀⠀⠸⠿⠀⠀⢩⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠱⣿⠇⠀⢠⣴⣾⣿⣷⠀⠀⠘⠛⠛⠀⠀⠀⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢊⡠⠄⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⣴⣶⣿⠀⠀⠺⡦⠀⠀⠀⠀⢰⣯⠑⠈
⠀⠀⠀⠀⡠⠒⠁⠀⢢⡀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⢀⡀⠀⠀⠀⠀⠈⢁
⠀⠀⠰⠿⡄⠀⠀⠀⠈⠃⠀⠀⠀⠈⠁⠀⠀⣴⣶⣦⣴⣿⣿⣿⣿⣿⣄⠀⠈⠫⣓⡲⠖⠀⠉⢀⠔
⠀⠀⠄⢠⠇⠀⠀⠀⢰⣠⣦⢠⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠿⢿⣿⡿⠏⠀⠂⢢⠄⠤⠀⠒⠉
⠀⠀⠈⠃⠀⠀⠀⠀⢸⣿⣿⢈⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⡀⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁⠈⢀⣠⣀⠒⡸⡉⡙⠁⠐⠒⠒⠀⢻⣷⡀⠸⠂⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠘⠛⠁⠸⠘⣄⠨⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠤⢆⠀⠀⠀⠀⢂⠈⠁⠆⠀⠀⠀⠀⡧⠀⠢⡀⠑⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⢉⣉⣱⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠤⣬⣭⣭⣭⣥⢤⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⢩⢩⠍⡍⠉⢩⣽⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⢈⣷⣿⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⣼⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣼⠃⢀⠄⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢘⣰⡇⠀⠀⠴⠦⠤⠔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠠⢤⣬⡤⠤⠐⠒⠦⢤⣀⠀⠀⠀⠀⢠⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣻⣦⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⠒⠶⠶⠒⠒⠒⠺⠾⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸
⡤⠔⣒⣒⣒⣒⣒⣒⣒⣂⣐⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢱⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣁⠀⠤⠂⠈⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡔⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⡄⠀⠀⠀⠀⠀⠀⡄⠐⠄⠀⠹⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⣸
⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢱⡄⡇⠃⠀⢸⠀⠀⠀⠀⠇⠀⢀⠟
⠀⢸⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢣⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠂⢳⣷⣾⣶⠸⠽⠥⠤⠒⠒⡉⠁⣀⢒⡀⢢
⠀⠘⡄⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠈⡆⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠠⡈⠉⠋⡻⠹⢟⣳⡍⢳
⠀⠀⠈⠉⠛⠛⢒⠏⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠦⠍⣾⠋⢿⡦⠠⣿⢻⡏
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠧⠄⠹⢶⠻⠛⣹⡯⠉
⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⡤⠒⣀⣀⣀⢈⡷⠔⠒⠉⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣠⣀⡁⠤⠄⠐⠀⠄⠊
⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠟⠀⠀⠀⠹⠿⠿⢿⣿⣿⣿⣿⣷⣶⣦⡈⠪⡃⠀⠁⠀⠙⠋⡹⠂
⠀⠀⡔⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢶⣽⠻⠿⠿⠿⣿⣿⣿⣿⠁⠘⠃⢀⠀⡁
⠀⠀⢹⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠿⠟⠛⡀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⡸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠀⠈⣠⣀⠗
⠀⠀⠀⢁⢻⣷⠀⠀⠀⣠⡀⠡⡰⣿⣿⣿⣿⣿⣿⣋⣤⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡎⣿⡀⠀⠀⣿⡷⠀⠈⡻⢿⣿⣿⣿⣿⣿⣧⣬⡉⠀⠐⠁⠀⠀⢀⠆⠀⠀⠄
⠀⠀⠀⢰⡇⣿⡇⠀⠸⣿⠁⣀⠐⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠉⠋⡀⠀⠀⡜⠈⠁
⠀⠀⠀⣾⠇⣿⠀⢀⣴⠇⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⢰⠏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠐⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠫⠀⢂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐
⠀⠀⠀⠀⠁⠁⠀⠀⠐⠂⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡴⠶⢶⠶⠶⢶⠖⠚⢿⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠈⡇⠀⠀⢸⡀⣀⣈⣇⣀⣼⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⠶⠾⠛⠛⠛⠛⠛⠉⠉⣉⣥⣤⣤⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠽⢧⡀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠈⣷⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⠵⠊⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠸⣿⣧⣤⣴⠏⠀⠀⠀⠀⠈⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠉⠉⢀⣀⣤⡴⠶⠟⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠷⠶⠦⣤⣤⣤⣤⣤⣄⣀⣀⣀⡙⣦⡀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠴⠖⠒⠒⠒⠚⠉⠁⣿
⠀⠀⠀⠀⢸⣟⠛⠛⠛⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⠦⢤⣤⣤⣤⠤⠴⠖⠒⠒⠶⠦⣄⣀⢀⣟⢀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠉⠙⠛⠳⢾⣷⣻⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣧⣤⣤⣤⣤⣦⠾⣦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⣶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣹⣧⣿⣟⣉⣉⣉⡉⠉⠙⠛⠓⠛⠛⠛⣿⡟⢷⡄⠀⠀⠀⠀⢸⡇⠀⣾⠷⡶⢷⡈⣥⢸⡇⠸⠟⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⡛⣿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⣿⢻⠃⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠸⠇⠉⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠘⣧⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠋⠉⠉⠉⠛⠓⠲⠶⠶⠶⠶⠶⠒⠒⠒⠲⡇⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠶⡄⠀⣰⠃⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⠲⡄⠀⠀⣀⣼⡧⣄⠀⠀⡟⠀⠀⠙⠚⠁⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠙⠤⠴⠁⣸⠃⠈⠳⠚⠁⠀⠀⠀⠀⠀⠆⣀⣥⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢱⡏⠙⠳⠶⣤⣄⡀⣿⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣑⠢⠤⣤⣄⣀⣀⣀⣀⣠⠤⢚⣱⠟⠀⠀⠀⠀⠀⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠞⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠁⠁⠀⠀⠀⠀⠉⠈⠁⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣄
⠀⢿⢿⣦⡇⠀⠀⠀⠀⢠⣶⣾⣷⢄⣀⠀⠀⠀⠄⠀⢀⡀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣏⠀⠀⠀⠠⠦⡐⢿⣾⠋⠀⠈⠙⠻⡀⠀⠀⠀⠀⠐⠖⠚⠻⠟⠛⠇⠀⠀⠀⠈⠀⠀⠀⠰⠶⠶⠶⠦⠑⠺⠾⣷⣮⡂⡀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⢸⣧⣶⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣗
⠀⠀⢦⣈⡤⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⣄⠀⠀⡆⠘⣿
⠀⠀⠙⠿⠿⠶⠿⣿⣿⣿⡞⢹⣿⣿⣿⣿⡏⠀⠀⠀⠐⣦⣀⣄⡀⠀⠀⠄⢀⡀⠀⢠⠀⠀⠀⠀⠀⣼⣿⡾⡣⠊⢿⣷⣿⣇⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣇⣀⠙⣿⣿⣿⢆⣴⣾⡆⠀⠈⢿⣿⣷⣤⣸⣾⣼⣧⣤⣿⣇⣾⣤⢠⣾⣿⣿⣿⣜⢄⡀⠊⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠛⢿⣻⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣦⣂⣤⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠠⢸⣿⣿⣿⣧⡈⣻⠟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⣀⣈⣛⢿⣿⣿⣿⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣄⣄⢿⣿⣸⣿⣿⣏⣀⣜⣿⣿⣿⣿⣿⣿⣿⣿⡟⡉⢘⡩⠙⠉⢿⣭⣏⣹⡾⣿⡟⠛⢿⣮⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⢭⣶⣿⣿⣿⢧⠉⠁⠀⠈⠉⠉⠛⠛⠻⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⢳⣤⣿⡿⣀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣮⠀⠀⠹⣿⣇⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⠀⠀⠀⠀⢹⣿⡷⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠁⠀⠀⠀⠀⠀⣟⠣⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣯⡝⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡡⠀⠀⠀⠀⠀⠀⠀⠓⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠰⡟⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡊⣉⣉⠐⠒⠤⠄⣀⠀⠀⣒⠆⢀⣀⣀⣀⡀⠀⠀⠀⢀⠀⠀⠨⠉⠉⣩
⠀⠀⠀⠀⠀⠀⡀⢴⣬⢀⣩⡡⠀⠀⣀⠀⡜⠣⠐⠘⡆⠀⢀⠇⢤⡄⠀⢠⠆⠀⠢⠊⢀⠔⠈⠉⠈⠉⠂⢄
⠀⠀⠀⡠⣔⢈⠠⠄⠠⡴⢏⣀⠀⠈⠁⠊⠀⠤⠀⠀⠇⢠⠥⠬⠴⠯⢤⠥⠬⡄⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⡋⠉⠲⠊⠢⠀⠘⠤⢸⠄⡇⠀⠀⠀⠀⠀⠀⠘⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠊⠀⠀⠢⠘
⠀⠀⠁⡄⠈⠈⠁⠀⠀⠀⠐⠠⠃⣄⡴⠶⠤⠐⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⢰⠀⠀⢀⡀⠄⠀⠐⠁⠉⠁⠀⠀⠀⡎⠈⠈⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⢉⣀⠀⠠⠤⠀⠀⠀⠀⠤⠄⠀⣀⡈⠢⠊⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠉⣉⣐⣆⣒⡂⠀⠀⠀⠀⠁⣁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠤⠤⠤⠤⠥⠤⠬⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢥⠰⣿⠇⠀⠀⠀⠀⠀⠈⠐⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⢶⣴⣆⢰⣶⠀⡇
⠀⠀⠀⠀⠠⠀⣀⠀⢀⠀⠀⠑⢄⠀⠀⣀⠀⡥⠊⠀⡑⢘⠀⠀⠀⠀⢀⠀⠀⠀⠸⡀⢦⠄⠀⠤⠌⠤⠠⠠⠇⡠
⠀⠀⠀⠠⠁⠀⠀⠀⠹⠉⠈⠈⠉⠙⢄⠀⢠⠥⡀⡐⠀⠘⠒⠒⠒⠒⠚⠒⠒⠂⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠈
⠀⠀⢀⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠁⠚⠳⠚⡀⠀⠤⡀⠐⡇⠂⢹⠂⠀⠀⣇⠀⢐⡇⠀⠀⢳⠀⢁⡇
⠀⠀⣆⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠑⠁⠀⣍⠉⠉⡀⠀⠀⣏⠉⠉⡅⠀⠀⣬⠉⠉⡅
⠀⠀⠀⠈⠀⠐⠺⠠⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠠⠀⠀⠀⢠⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠂⠀⠀⠀⠈⠖⠃⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠋⠁⠀⠀⠐⠒⠚⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢰⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠐⠈
⠀⠀⠈⠐⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠂⠁⠀⢐⠚⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠚⢒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠍⡉⠉⠁⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⢂
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁⠀⠀⠀⡟⠂⠀⠀⠀⠒⠒⠲
⠀⠀⢰⣶⡀⠀⠘⣿⡿⣿⣿⡇⢸⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢈⠀⠘⠻⠏⠀⠀⠈⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡆⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠌⠁⠄⠀⠠⠀⠀⠄⠀⠄⠤⠴⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠉⠐⠀⠀⠀⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⡶⠶⠾⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⡶⠶⠿⠿⠟⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡄⠀⢀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⡀⠀⠀⢰⡄⠀⣶⠀⠀⠀⡟⠀⠈⡇⠀⢿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⣸⠁⠀⢹⡀⠀⢀⣧⣀⣤⣷⣴⠾⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠀⠀⣧⣀⣀⣼⣤⡴⠾⠷⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢷⣶⠶⠿⠗⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⢀⣴⠏⠀⠀⠀⢀⣀⣀⣤⣤⡴⠶⠛⠋⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⣠⣾⣡⣴⠶⠞⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄
⣰⡟⠙⠛⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠛⠉⠉⢻⡇
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠶⢦⣤⣀⣀⠻⠄⢀⣀⣠⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣆⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣴⣶⠀⠀⣟⢹⣷⠋⣸⠇⠀⢻⡆
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡶⢶⡀⠀⣰⣧⠀⠸⡏⢻⡸⡇⢸⡇⠀⢹⡄⠁⢰⡏⠀⠀⢸⡇
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠈⢷⣤⡟⠘⣧⠀⣿⠘⡇⣿⠈⣧⠀⢸⡇⢠⣌⠻⣆⠀⠸⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠉⠁⠀⠙⣆⢸⡄⣧⣿⡀⠻⠛⢻⣧⠘⣟⢷⣌⡷⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣤⡀⠀⣶⡀⠹⣼⣧⣹⣿⣧⡴⠶⠾⠿⠶⠟⠀⠉⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢸⡏⢷⣀⣿⠿⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠘⠛⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⣩⣙⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⢦⣭⣛⠳⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⡇⠀⢰⠶⢦⣭⣙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠘⣇⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⣿⡀⠀⠹⢦⣄⡀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⢷⣤⡀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼
⠀⠀⠀⠀⠉⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⢸⣇⣠⣤⡶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣶⡿⠟⠋⠁
⣿⣿⣿⣿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠱⡄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡊⢿⣦⣤⣶⡇⠀⠀⠀⠀⠈⣴⣦⣿⡟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⡄⠈⠀⠀⣀⣈⣼⣯⣿⣿⣧⣦⣦⠀⠀⢀⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⣤⠀⠀⠀⢴⡞⠋⠀⠀⠤⢾⣿⣋⠀⠀⠀⠈⠋⣹⠙⢻⣿⠟⢿⣦⣿⣧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣺⡏⣴⡿⡟⠰⣿⠖⠋⠁⣀⣠⠄⠀⠈⣛⠏⠀⠀⡰⠃⠀⠇⢠⣾⣿⣇⠀⠈⠙⠟⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢿⡿⣿⣵⠃⣼⠿⠃⠀⠀⠈⠁⢀⣴⡄⠁⠀⠀⡞⢀⣠⣼⠀⣼⣿⣿⣿⣷⣦⣤⡀⠀⢀⣄⢁
⠀⠀⠀⠀⠀⠀⢸⡄⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠘⡿⠀⡄⠀⢸⣤⣞⠉⣿⣿⣿⣿⣿⢟⣿⠟⠁⠉⠙⠋⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⢯⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡏⠙⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣿⠿⠛⠛⣾⢣⡿⠁⡆
⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠇⠟⠁⢀⠅
⠀⠀⠀⠀⠀⠀⡸⢻⠀⢸⠏⢻⣿⣿⣿⣷⣶⣦⣴⣬⣿⣇⠀⠀⣼⣧⣤⢈⡄⢀⣆⡴⡏
⠀⠀⠀⠀⠀⣴⡇⣞⠀⡼⠀⢸⢿⣟⢹⡏⠉⠉⠉⠉⠉⢹⠀⠀⡏⠉⢹⡼⢧⣴⠏⢰⠃
⠀⠀⠀⠀⣸⣿⣿⢹⠀⣿⠀⣾⢸⣿⡾⠁⠀⠀⠀⠀⠀⠈⡇⠀⡄⠀⠀⠀⢸⡏⢠⠃
⠀⠀⠀⢠⡿⠉⠹⣿⠠⠇⠀⠹⡎⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠹⡘⡀⠀⠀⠀⠀⠀⠀⠈⣷⢿⠃⠀⠀⠀⢻⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢧⠡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⢀⡏⢀⡀⠀⠀⠀⢸⣄⣵⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡇⠐
⠀⠀⠀⠀⠀⠀⠈⢻⣏⣄⠀⠀⠀⠀⠙⠷⠗⠀⠀⠀⠀⠘⣿⣑⡄⠀⠀⠀⠀⣷⣤⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠉⠛⠛⠋
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⣶⣶⡶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⢿⢸⡄⠀⠀⠀⠀⢸⡏⣯⠉⠉⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⢷⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢿⢸⡀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⢸⠇⡟⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠶⠶⠶⠿⠿⠷⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠾⠿⠿⠷⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⣨⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⡶⠤⣤⠴⠶⠖⠛⣇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠹⣄⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣠⣤⣷⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠙⣆⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠘⢧⡀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠈⢳⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣧
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣠⠶⠛⠉⠙⢦⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣰⠏⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠁⠀⠀⠈⢳⡀⠀⠀⢀⡴⠚⠛⢦⡀⠀⠀⠀⣾⡷⠒⢦⡀⠀⠀⣠⠖⠒⢦⡀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠉⠙⠋⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⣀⡿⠀⠀⠀⠀⠀⠙⠲⠴⠞⠁⠀⠀⠀⣷⠀⠀⢀⣿⠀⠀⣸⠇⠀⠀⣿⠀⠀⠠⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢻⡟⠀⠀⣿⠀⠀⣠⡟⠀⠀⠀⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢠⣾⣷⡄⣠⣴⣄⠀⠀⠀⠀⢰⣷⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢸⣧⠸⠿⠟⢹⣿⠀⠸⠃⠀⢸⡇⠀⢸⣇⣠⣾⠟⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠘⣿⡄⠀⠀⠸⣿⠀⢸⣷⠀⣸⡇⠀⢸⣿⠻⣷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠁⠈⠁⠀⠙⠁⠀⠘⠛⠀⠘⠿⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣤⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⢶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣤⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⢸⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⡇
⠀⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣟⣽⣾⣿⣻⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣿⡇
⠀⣿⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⣿⣿⡄⢀⣾⣿⡇⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⣠⣿⠋⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⣿⡍⣷⣼⠏⣿⡇⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⣿⢿⣧⠀⠀⠀⠀⠀⢸⣿⢼⣿⣿⣿⡇
⠀⣿⠀⠀⠀⠀⢿⠇⠙⠏⠀⣿⠇⠀⣿⡇⠀⣿⣷⣴⣤⡄⣿⡇⠀⠻⣷⡀⠀⠀⠀⢸⢿⣾⣿⣿⣿⡇
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣾⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣶⡷⠾⠧⠤⠤⣤⣀⣀⣀⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⢎⠉⢁⣀⡐⢿⣷⠀⠙⠿⠋⢰⣆⣀⢻⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠉⠀⠀⠀⠀⠀⠰⠿⠀⠁⣄⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠛⠂⠀⠂⠲⠶⠶⣄⠱⠉⠀⠀⠀⠀⠀⠀⢸⣿⢼⡿⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣆⠀⠀⠀⠀⠀⡆⠈⡞⡄⠀⠀⠀⠀⠀⠀⢸⣿⣻⣷⣿⣿⡇
⠀⢸⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠛⠾⠻⠶⠶⠶⠶⠾⠿⠶⠿⢷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⡄⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢸⡇⠀⣠⣾⣿⣶⣶⣶⣿⣿⣷⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣶⣶⣶⣾⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⢸⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⡿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟
⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠏⠀⣀⣇⣀⣧⣠⣧⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡛⠉⠉⠉⠉⠁⣤⠖⠲⣆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡫⠚⠁⠙⣆⠀⠀⠀⠀⢿⣆⣀⡞⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢉⣁⡤⠴⠖⠛⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠛⠛⠛⠓⠒⠲⠶⠿⣦⠖⠛⠉⠁⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡠⠔⠒⠒⠒⠊⢹
⠀⠀⠀⠺⢭⣍⣉⣿⣦⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⠊⠉⠉⠐⠢⠤⣿⠤⠒⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠙⣏⣧⣀⣤⣤⣤⣧⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⢠⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣽⣼⣯⣭⣉⣉⣉⣉⣉⣙⣻⣿⣳⠄⠀⠀⠀⡇⢰⡷⠖⣦⣥⠸⠘⠟⠆⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠈⣧⢿⠉⠉⠉⠉⠉⠉⠉⠉⢹⢹⠀⠀⠀⠀⡇⠈⠁⠀⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡜⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⢤⡀⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠁⠒⠒⠒⠈⠉⠉⡛⣿⡀⠀⠀⠀⡇⠀⠀⡠⠚⢆⣠⠃⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠘⢄⡰⢺⡏⠳⠤⠃⠀⠀⠀⠠⢐⣢⠇
⠀⠀⠀⠀⠀⠀⠀⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢻⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠧⣄⣀⠀⢸⡇⣀⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣗⡤⢄⣀⣀⣀⣀⡠⢔⣱⠃⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠾⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣌⣉⣉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢋⣉⣤⠴⠖⠚⠋⠉⢉⣁⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠭⣭⣷⣦⣄⠈⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡴⠞⢉⣠⠴⠚⠉⠁⣀⣤⠴⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⢻
⠀⠀⠀⢀⡴⠋⢀⡴⠋⠁⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡼
⠀⠀⠀⡞⠀⠀⣾⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⣠⠞⠁
⠀⠀⠀⣧⠀⠀⠹⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠉⠀⣀⡴⠚⠁
⠀⠀⠀⠈⠳⣄⡀⠀⠉⠛⠲⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠚⠛⠉⠉⠀⣀⣠⡴⣶⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠴⠖⠚⠋⠉⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠤⠤⠤⠤⠴⠶⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⠴⢶⡶⠶⠶⡶⠖⢻⡟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⡇⠀⠀⠀⡇⠀⣀⣇⣀⣸⣧⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⡶⠶⠿⠞⠛⠛⠛⠋⠉⢉⣩⣤⣤⡀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⡼⢷⡄⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢻⡆⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡥⠞⠁⠀⠀⠹⣦⡀⠀⠀⠀⠀⠘⢧⣷⣤⣤⠾⠀⠀⠀⠀⠀⢉⣳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠉⠁⣀⣠⣤⠴⠶⠛⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠙⢷⡀⢀⣀⣤⡶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠉⢸⡇
⠀⠀⠀⠀⢰⣟⠛⠛⠲⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣀⣀⣀⣤⠤⠴⠶⠲⠶⠤⣄⣀⠀⣿⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠛⠓⠶⢶⣧⣻⣷⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡘⣧⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⣦⡴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣧⣹⣗⣋⣉⠉⠉⠛⠒⠒⠒⠛⠛⠻⢿⡟⢳⡄⠀⠀⠀⠀⠀⣿⠀⢰⡶⣤⢶⡆⢹⡀⣿⠈⣿⢷⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⡟⣿⠿⠾⠿⠯⠭⠭⠭⠭⠿⠿⠿⠿⢶⢻⡇⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠈⠷⠘⠁⠈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇⠘⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡗⠓⠛⠛⠛⠓⠶⠤⠤⠤⠤⠤⠶⠖⠒⠲⡇⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠴⣄⠀⢀⡎⠀⠈⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠦⣄⠀⠀⢀⣠⡷⢤⠀⠀⢰⠁⠀⠘⠖⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡿⠀⠘⢦⣠⠏⢸⡇⠈⠳⠶⠋⠀⠀⠀⠀⠀⠰⠀⣉⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡟⠛⠳⢦⣤⣀⠀⢸⣇⣠⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡓⠦⢄⣀⣀⡀⠀⠀⠀⣀⣠⠴⣋⡾⠁⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠮⢭⣭⣭⡥⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡐⠀⣐⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣷⡆⠈⠁
⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⠀⢠⠀⠀⠉⠙⢿⣿⣿⣄⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠂
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡇⠀⣌⣿⣿⣿⣿⣿⣿⡏⡠⠊⠓⠂⠒⠀⠘⠃
⠀⠀⠀⠏⢿⣿⡟⠉⠣⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠻⣿⣿⣿⣿⡿⠛⠐
⠀⠀⠀⠀⠘⠹⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⣴⠏⠻⡿⠁⠀⣸⣿⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠁⡆⠀⠀⠠⠤⠤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⢻⡟⠃⡜⠋
⠀⠀⠀⠀⠀⠂⠀⢀⠔⠀⠀⠀⠸⠦⣄⣄⠰⢀⡰⠖⠓⠺⣿⡇⠀⠀⠞⠁
⠀⠀⠀⠀⡞⠀⠀⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡧
⠀⠀⠸⠀⡆⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠒
⠀⠀⠀⠀⠁⠀⠀⠀⢸⠁
⠀⠀⠀⣌⠀⣠⡤⣠⣈⣑⣶⡦⢴⣦⢤⣄⢤⣀⣄⣤⣶⣤⣤⣦⣄⣠⣄⣀⣠⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⠶⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⣩⡿⠋⠈⠙⠛⠿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧
⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⠋⢹⣿
⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠉⠁⠀⠀⠀⢸⣿
⢠⡿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⣤⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢸⡇⠉⠻⢿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣀⣤⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⠀⠀⢠⣿⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⢸⣿⡆⠀⢸⣿⠀⠸⣿⣿⣶⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⢸⣿⡇⠀⣾⣿⠀⠀⠀⣽⡟⠿⠀⣿⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⣼⡟⣧⠀⣿⢿⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⢀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⣿⠁⣿⢸⡏⢸⡇⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣼⡟⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣾⡄⠀⣿⠀⢻⣾⡇⢸⡇⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇⢰⣿⠁⠀⢸⣿⡇
⣿⡇⠀⣿⠀⢸⣿⠀⠈⣧⠀⠀⢹⡇⠀⠀⣿⠀⠀⠀⠀⢸⣧⣿⠇⠀⠀⢸⣿⡇
⣿⡇⠀⠀⠀⠈⠟⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢸⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠀⣿⣿⣧⣄⠀⣿⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⢸⣿⡇
⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠀⣿⡀⠀⢀⠀⢸⡇⢻⡆⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⢸⡇⠘⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⡇⠀⢹⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⡀⠸⣿⣀⣀⣠⣤⣶⣾⡿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠹⡑⡤⠒⠒⠒⢦⣺⠃
⠀⠀⠀⠀⣴⠖⡶⣾⢳⠀⠀⢀⠤⡿⢏⢙⡷⠐⢲⠦⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣠⣤⠄⣀
⠀⠀⠀⠀⠀⠉⠉⣯⠜⠀⠀⡜⠠⡏⠉⠁⠀⠀⠘⠢⢤⡀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⡠⠔⠁⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣊⣉⣉⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣀⣈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⣀⠔⡡⠊⠁⠀⠀⠈⠉⠀⠈⠈⠑⢦⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠐⣵⣀⣤⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠉⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⢦⡀⣀⠤⠤⡄⠀⠀⡠⠒⠉⠉⠒⠠⠤⠤⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠀⠀⢀⠇⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡜⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⢧⠀⠀⠀⠘⣆⣀⣀⣀⣀⣠⣞⣁⣀⣀⡠⠤⠔⠒⠒⠲⡄⠀⠀⠀⠀⢀⠃⡏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠚⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⠀⠀⠀⠘⡄⠀⠀⠀⢸⢰⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣖⠒⠚⠙⡆⠀⠀⢸⠀⠳⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣴⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⢇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠾⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡎⢠⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⢨⡎⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⠁⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠈⣱⡾⠓⢢⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⢄⡴⠋⢀⠏⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⡄⢀⣤⣤⡀⠀⣀⣤⣄⡀⠀⣀⣤⣀⣀⡴⠶⠾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⣉⡉⠀⠀⠀⠙⠛⣁⣀⣀⣀⡀⠀⠠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠉⠙⠉⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢤⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⢀⡾⣦⠀⠀⠀⢰⡟⢷⠀⠀⠀⣿⠹⡇⠀⠀⠀⠀⠀⠀⡞⠹⡇⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⢾⠀⣸⠇⠹⣄⠀⠀⠘⡇⢿⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⣧⣤⠖⠉⣠⠿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠛⠃⠀⠀⢱⡄⠀⠀⠃⠈⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⡾⢳⡀⢠⡞⣧⠈⢷⡄⠀⢳⠀⡇⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⢻⠀⣀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⢸⠃⣤⠁⠀⠹⠟⠀⠈⢷⠈⢷⠀⢸⠀⣿⠀⠀⣿⠀⣾⠀⠀⠀⠀⠀⠀⢸⠀⢻⣷⡈⠱⡀
⣿⠀⠀⠀⠀⠀⠀⡎⢠⠉⠀⠀⠀⠀⠀⠀⠘⢇⠈⡇⢸⡇⠛⠀⠀⣿⠀⠙⠛⠛⠛⠒⠲⢤⠘⠀⢸⠀⢿⡀⠻⡀
⣿⠀⠀⠀⠀⠀⠈⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡦⠈⠿⠗⠀⠀⠙⠷⠤⢤⣤⣤⠴⠶⠃⠀⠿⠂⠀⠈⢳⣤⠗
⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠙⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣤⣤⣭⣽⣿⠟⠛⠛⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⡄
⢀
⢸⡆
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⠀⣧
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢹⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠏
⠀⠀⠙⣿⣶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢠⡄⣤⡄⠴⠶⠶⢶⡶⠲⠖⢉⡿⢛⡿⠟
⠀⠀⠀⠈⠻⣯⠉⢫⡀⠀⠘⢧⠀⠈⠫⠀⠀⠹⠏⠁⠹⠋⠀⠀⠻⠁⠀⠀⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⣠⠞⢋⣾⠋⠁
⠀⠀⠀⠀⠀⠙⠷⣾⣿⣦⣤⣼⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠿⠶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣩⣤⣤⣀⣀⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⠑⠦⢄⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⡗⠤⠴⠋
⠀⠀⠀⠀⠀⣼⣿⣩⣎⣿⣿⠁⠀⠀⠀⣀⣀⠀⠀⡏⠹⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠁⠀⠀⠀⠘⠁⠹⠂⠀⢀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⠈⢻⣿⣿⡶⠤⣀⠀⠀⠀⠀⡠⢊⠝
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠛⠁⠀⠉⠛⠿⠟⠀⠀⠀⠀⢀⣀⡀⠉⠀⠀⠈⠢⡤⠀⠚⠋⠁
⠀⠀⠀⠀⢠⠀⠤⠤⠤⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠘⠀⠀⠀⢠⠆⠀⠀⡄⠈⠉⠒⠠⢄⡠⠁⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠔⠁⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⠤⡤⠤⢔⣚⡁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠇⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠐⠀⠀⠀⠖⠖⠀⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢢⡄⢀⣀⣠⡔⠁⠀⡜⡄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢠⠃⢧⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⢦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡞⠀⠘⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⢿⡿⣿⣿⣿⣿⠏⢩⣼⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣀⣀⡈⠛⠛⠁⢀⣾⣿⣿⣿⣿⠟⠛⠋⠀⠀⠈⠻⣿⡿⠿⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣿⣿⣿⣂⣀⠀⠈⢿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⣴⣦⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⢼⣿⠟⠛⢿⣿⡿⠁⠀⠀⣴⣿⣶⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⣿⣿⣿⣿⡿⠦⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⢿⡟⠁⠀⠉⢳⡀⣀⠀⠀⠀⢀⡠⠤⢤⣄⣠⠀⠀⠀⠀⢀⡙⠳⠆⠑⢶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡾⣤⢤⡠⠤⠞⠉⠉⠉⠉⠉⠁⠀⠀⢸⠈⢹⠀⠀⡸⠒⠁⠙⠲⡁⠐⠞⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢸⢇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠋⢳⠀⡇⠀⠀⠀⠀⠑⢄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⠈⡌⣄⠀⣀⣀⡀⢀⠀⢀⡀⣀⣀⣀⡆⡅⠀⠈⢧⢸⠀⠀⠀⠀⠀⠈⠳⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣷⠿⣿⢿⡿⢿⣿⠿⣿⡼⠟⠿⠿⢿⡿⣷⣿⣷⣶⣦⣦⣤⣤⣶⣴⣶⣤⣭⣽⣴⣶⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠁⠈⠉⠉⠉⠉

⠀⠀⠀⠀⢠⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢
⠀⠀⠀⠀⢿⠀⠙⢤⠖⠒⠛⠛⠓⠒⢤⠞⠁⢸
⠀⠀⣠⣶⣿⣦⡤⠊⠀⠀⠀⠀⠀⠀⠈⢢⣤⣾⣦⣄⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀
⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠒⢤⡀
⣿⣿⣿⣿⡿⠃⣠⣄⠀⠀⠀⠀⠀⢀⣠⡀⠙⣿⣿⣿⣿⣷⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⣶⠶⣤⣄
⠻⠿⠿⡏⠁⠀⠿⠾⠃⠀⠀⠀⠀⠸⢷⠞⠀⠈⠻⡿⡿⠟⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣰⣿⣆⠀⠉⢳⣄
⠀⠀⠀⢳⠀⠀⢀⠔⠊⠉⠉⠉⠉⠑⢦⡀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠙⢷⣄⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠣⡀⡏⠀⢤⡀⠀⠀⣠⠄⠀⢣⠀⣰⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⢀⣠⠷⢾⣿⣿⠿⠂⠀⣀⣤⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⢒⣂⣉⠉⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⢋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠉⠉⠉⠀⡆⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠿⣠⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⢀⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣷⣿⠆⠀⢰⠧⠤⠤⠤⠐⠒⠺⡋⡍⠉⣄⣧⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⣤⣿⣿⣀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠈⣮⣭⣤⣽⣀⣀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠉⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⢻⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠶⠶⠶⠶⠶⠤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠀⣴⠘⠀⠀⠀⠀⠀⡀⠀⡆⠀⣀⣰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡛⠛⠛⠛⠒⠛⠲⠾⠦⠿⣤⣧⣤⣿⣯⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡷⠟⠋⠁⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡿⠟⠉⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣁⡀⠠⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⢳⣄⣀⠤⠴⠖⠚⠉⠉⠀⠄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡠⠤⠔⡒⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⣒⣒⣒⣲⣶⣶⣒⡐⠂⠲⠤⠤⠤⠤⠤⠤⡷⢒⡪⠭⠀⠂⠈⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⡇⠀⢈⣍⠉⢉⡍⠉⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⠀⠘⡿⠀⣼⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠞⠉⣧⠖⢳⠀⢸⠀⢸⡇⠀⠀⣇⣴⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⡏⠀⠈⠀⢸⠀⢸⡇⠀⢠⣿⣧⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠟⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃⠀⠸⠇⠘⣷⣆⠀⢸⠀⡀⢤⣀⡶⠾⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣓⡒⠶⠶⠶⠤⠤⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⡭⣿⠕⠚⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⣢⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠾⠟⠻⠶⠶⠶⠶⠦⠤⠤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡿⠞⠁