⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠙⠛⠿⣶⡄
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠁⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⣸⣿⡇
⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣴⣾⡿⠋
⠀⠀⠀⣷⣤⣤⣼⣿⢰⣄⠀⠀⣠⡆⠀⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣾⠀⠉⠉⠁⡇    
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣤⣤⣤⣇
⠀⢀⣾⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⣿⠇
⢠⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢳
⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾
⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢧
⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼
⢀⣴⣿⠿⠛⠿⣿⠧⢄⠀⠀⠀⢀⡼
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⢻⣿⠀⠀⠀⠀⠀⠀⢀⡴⠁⡠⠁
⠀⠹⣷⡀⢀⡤⠖⠉⣀⠔⠁
⠀⢀⣿⣿⢁⡤⠖⠉
⠀⠧⢼⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠓⢲⣶⡤
⠀⠀⠀⠀⢀⡴⠚⠁⠁⠁⠁⣁⠵⠛⠉⠁
⠀⠀⢀⣴⠁⠁⠁⠁⠁⢁⡞⠁
⠀⢠⡞⠁⠁⠁⠁⠁⢁⠏⠀⠀
⢀⡾⠁⠁⠁⠁⠁⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀ ⠀⢠
⣼⠁⠁⠁⠁⠁⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡄⣰⣿
⣿⠁⠁⠁⠁⠁⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏
⣿⠁⠁⠁⠁⠁⠁⢻⡄⠀⠀⠀⣴⠿⢿⣆⠀⢀⣴⣿⣿⣿⣿⠃
⢻⠁⠁⠁⠁⠁⠁⠉⣷⡀⠀⠀⣿⠀⠾⠏⣴⣿⣿⣿⣿⣿⡟
⠈⢧⠁⠁⠁⠁⠁⠁⠉⠷⣄⠀⠹⡄⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠘⢆⠁⠁⠁⠁⠁⠁⠁⠉⠳⣄⠹⣦⡀⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⢳⡁⠁⠁⠁⠁⠁⠁⠁⠉⠙⠶⡿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠉⠳⣅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⣁⡥⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠳⢧⣥⣥⣥⡥⠥⠵⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⡀
⠀⠀⠀⣴⡿⠟⠷⠆⣠⠋⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣠⣾⡿ ㅤㅤ
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠏⡆⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡟⢦⡀⠇⠀⠀⣀⠞⠀⠀⠘⡀⢀⡠⠚⣉⠤⠂⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⡇⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠘⢧⠔⣉⠤⠒⠒⠉⠉⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣤⠶⠶⢶⡄⠀⠀⠀⠀⢹⡆
⠀⣀⠤⠒⠒⢺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢸⠀⡿⠀⡀⠀⣀⡟⠀⠀⠀⠀⢸⡇
⠈⠀⠀⣠⠴⠚⢯⡀⠐⠒⠚⠉⠀⢶⠂⠀⣀⠜⠀⢿⡀⠉⠚⠉⠀⠀⠀⠀⣠⠟
⠀⠠⠊⠀⠀⠀⠀⠙⠂⣴⠒⠒⣲⢔⠉⠉⣹⣞⣉⣈⠿⢦⣀⣀⣀⣠⡴⠟

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