BẰNG Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠠⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠳⢄⠀⠀⠌⠀⠘⢷⡀⠀⡀⠈⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⡀⠄⠀⠀⠙⠎⠀⠀⠀⠈⠷⠈⠀⠀⠀⠀⣿⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠂⠀⣾⠇
⠀⠀⠀⠀⠀⠈⢉⠀⠀⠄⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢶⠶⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠹⡄⠀⠀⠀⠸⣆⠀⠀⠀⡼⠁⠀⢀⣠⣀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠞⠃⠀⠂⠀⠀⠿⠆⠀⠀⠁⠀⢀⡀⠀⠋⠀⠀⠀⠀⠀⣰⡿⠋⠉⢀⣀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⡀⠀⠀⠀⣿⠛⠁⠀⠀⠀⢿⠁⠀⠀⠀⢠⡀⠀⠈⠃⠀⠀⠀⢀⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢃⣀⣀⣠⣿⠀⠀⢤⣤⣶⠾⠆⠀⠛⠛⠻⠃⢤⣀⡀⢀⣀⣴⡿⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠛⠉⠉⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠁⠒⠘⠷
⠀⠀⠀⠀⠀⠀⠘⠚⠛⠉⠉⠀⣀⣴⠾⠛⠀⠀⢀⠀⠀⣰⡄⠀⠀⠀⣶⠄⡀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠴⡆⠀⢠⣾⠏⠀⠚⠄⢰⣿⠀⠀⠐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠚⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣽⣿⣯⣽⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞⠙⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⢸⡉⠁⡠⠄⠀⠐⠂⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⡟⠓⢦⡀⠀⢸⡹⠙⢦⡀⠀⢀⡾⠁⠀⠹⣦⣀⡴⣋⣳⠀⠁⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣾⠈⠙⢦⣼⠃⠀⠀⠙⠶⠟⠁⠀⠀⠙⢳⣾⣀⣄⠀⠀⡹⠿⠊⠀⢈⠀⠀⠀⠀⠀⠀⡄⠸⣀
⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣸⠉⡹⠷⣶⠃⠀⡠⢄⣀⡤⣄⠀⠀⣠⠤⣄⠼⠢⣀⡎⠀⠀⠀⠱⠞⢀⣀⡀⡰⠹⡀⢀⠀⠀⠀⠀⢠⠀⢘⡄
⠫⣵⠀⠀⠀⡰⠋⢉⡁⠀⠀⠈⡉⣀⠀⠀⠑⠖⠁⠀⣀⡀⠀⠑⢴⠁⣀⠠⠀⠀⠈⠁⠆⠐⡄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡀⠸⡀
⠀⠀⡠⠏⢉⢁⡊⠁⠀⠀⠀⠀⠒⠀⠐⠠⡀⠀⠉⠁⠀⠈⠢⣀⠀⠀⠁⠀⠀⠐⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠚⠀⠀⠀⠀⠁⡡⠤⡹⡄
⠀⠀⢳⠀⢡⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠈⢆⠀⠐⠀⠀⠀⠈⠉⠙⢄⠀⠀⠀⢆⠀⠀⠊⢰⠂⠀⠀⠒⠒⠀⢀⠅⠀⢁⠘
⠀⠀⠀⢆⠈⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⡀⠀⠈⠀⠀⢰⡄⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⠀⠀⠃⠀⠀⠀⠀⢀⠀⠂⠀⠠⠈
⠀⠀⠀⠸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠮⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠀⡇⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⢘⠀⠀⣀⢀⣀⣠⠖
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⣀⠀⠀⠀⠑⠈⠆⠀⠀⠸⠓⢄⠀⠀⠀⢰⠐⢄⣀⠠⠠⠋⠉⠈⠀⠀⡏⢩⣤
⣠⢄⡀⠀⠘⡆⡄⠀⠀⠀⠰⠝⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠀⠑⡀⠀⢀⠄⠐⠤⠘⠐⠀⢀⡑⠈⠉⠀⢀⣄⠀⠀⣤⠤⠴⠾⠿⠾⠀⠀⠯⠗
⠙⠈⠁⠀⠀⠇⢰⠀⠀⢀⡀⠀⠀⠀⠀⡈⢀⡤⡠⠄⣀⠄⠀⠀⠈⠀⠁⠀⠀⢀⠶⠤⠴⠋⠙⠚⠛⣲⠧⣤⣙⡊⢹
⠀⠀⠀⠀⠀⢸⠈⡄⢀⡄⠡⣀⠤⠔⠋⠀⣀⡀⢀⣠⢄⣀⣸⠉⠲⠒⠉⢉⣉⡉⠀⠀⠀⣰⠦⣄⣀⣿⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠘⠦⣀⠤⠴⣄⣠⣤⡤⠤⣴⡷⠟⣿⡄⠀⠈⢹⡷⣄⡀⢠⡟⠉⠙⠶⣄⣼⠃⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠀⠀⢹⡇⠀⠀⢸⠇⠀⠙⠟⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠗⠀⠀⢀⡀⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠢⣿⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡶⣤⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣼⠃⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⣿⣿⡾⠿⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⣿⢸⠉⠙⠛⠲⢤⡀
⠀⠀⠀⠀⣀⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⣀⡟⠀⢢⣤⠞⠸⠶⠶⣦⣀⡾⠀⢀⣤⣄⣀⡀
⠀⠀⣠⠞⠁⠀⠀⠀⢹⠀⠀⠀⣀⣤⣄⠀⠀⢹⠈⢳⡀⠀⡏⠉⠉⢡⠀⡾⠁⠀⠀⠀⠀⠀⠉⠁⠀⢸⠃⠀⠈⠉⢳⡆
⠀⠀⢻⡄⢰⣒⡄⠀⣾⠀⠀⡟⠁⠀⠘⢧⡀⠘⡇⠀⠻⡄⣇⠀⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡟
⠀⠀⠀⢷⠀⠉⢀⣴⠏⠀⢀⡇⠾⠓⢦⡈⢳⡄⣧⠀⠀⠹⣿⠋⠀⢸⢸⡄⢀⡶⠲⠶⣤⣀⡀⠀⢠⡇⠀⢀⣈⡿
⠀⠀⠀⢸⡶⠛⠛⠛⠳⡶⠾⢧⣄⣀⡤⠽⠂⣹⣿⠀⠀⠀⠙⠀⠐⢺⠀⢳⡘⠷⣤⠀⠀⠈⢹⠆⣸⠦⠀⠀⣼⠁
⠀⠀⠀⢸⣧⠀⢀⣠⣄⣀⠀⠀⠈⢧⢠⣄⡀⠁⠘⢆⠀⣠⠀⠀⠀⢸⡀⠀⠉⠹⠉⠀⣴⢤⡾⠀⣿⣀⠀⣰⠃
⠀⠀⠀⠈⡗⠀⢸⠀⠀⠈⠳⡀⠀⢸⢹⠈⠛⢦⣀⣸⠁⢸⣦⠆⠀⢸⠋⠛⠛⣿⠀⢸⠃⠀⠀⢀⣠⣍⡙⠋
⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⣰⠁⠀⣸⢸⡄⠀⣸⣉⣁⣠⡿⠹⠶⠶⠚⠀⠀⠀⠛⠒⠛⠀⠀⠀⡟⠃⠈⣷
⠀⠀⠀⠀⢻⠀⠘⠓⠚⠋⠁⠀⣠⡧⠼⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁
⠀⠀⠀⠀⢸⣄⣴⣤⣤⣤⡷⠞⠋
⠀⠀⠀⠀⠀⠈⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢳⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢳⡀⠀⠀⠀⢰⣇⠀⠀⠀⠀⡴⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢳⡀⠀⠀⣼⢻⠀⠀⢠⡞⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢳⡀⢀⡏⠸⡇⣰⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢳⣼⠇⠀⡿⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⠀⢿⡆⠀⠀⢻⠀⠀⠀⠀⠀⣸⠁⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠛⠓⠶⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠟⠚⢉⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠶⠶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣴⠾⡿⠀⠀⣠⡀⠀⠀⣿⠷⣦⣄⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⢸⡇⣠⡾⠛⣷⡄⠀⣿⠀⠀⠉⠙⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠈⠻⣆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠈⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⢹⣷⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠘⣿⣄⠀⠀⠈⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠈⠁⠀⠀⠀⠘⣿⣆⠀⠀⢹⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⣿⡇⠀⢸⣿⠀⠀⢀⣴⡿⠿⢿⣦⣠⣄⡀⠀⠘⠿⠿⠿⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠀⠈⠀⠀⠀⠁⠀⠀⠸⠿⠀⠀⠀⠻⠋⠙⣿⣶⣶⣦⣤⣤⣀⡀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣴⡶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⡿⠿⢿⣶⣦⠀⢀⣤⣿⠋⠀⠀⠹⠋⠀⠀⠙⠿⢿⠿⣷⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠉⠀⣀⣤⣴⣤⣄⣀⣀⡀⠀⠀⣼⡟⠉⠉⢉⣩⣿⠿⠋⠁⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⢀⣀⣿⡏⠉⠀⠀⣼⡟⠉⠁⠉⠛⠛⠛⠛⠀⠀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⢀⣠⣴⡾⠿⠛⠙⠻⠿⠀⠀⠉⠁⠀⢀⣀⣀⣤⣤⣶⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠐⠿⠿⠿⢷⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⠿⠿⠛⢋⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⢀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣶⣤⡄⠀⠀⠀⠀⠈⠻⢷⠿⣷⣶⡀⠀⢀⣴⡄⠀⢀⣼⡟⠋⠁⠀⠀⠀⠀⠀⠀⢴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠻⠿⠿⠋⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⣄⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡇⠀⠘⣿⡄⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣿⡇⠀⠀⢻⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠑⢬⢦⡀⠀⠀⠈⠐⠀⡢⠄⡀⠀⣀⣐⣠⡒⠚⡁⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠐⢂⣠⠄⠀⠱⢤⠂⠄⠄⠠⠄⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠢⠖⠉⠀⠀⠀⠈⠙⢅⠐⠂
⠀⠀⠀⠀⠰⠒⡊⠐⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠄⠀⠀⠀⠀⠁⠂
⠀⠀⠀⣠⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠤⠀⠀⠀⡖⢲⠙⠉⠀⠀⣸⢙⠀⠀⢐⡄⠐⠈⠉⠀⠀⠉⠻⡄⠂⠀⠀⠀⠀⠉⢲⣄
⠀⢀⡀⠴⠈⠠⠄⡀⠀⠁⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠻⡄⠄⠀⠨⠃⠀⠀⢀⣀⣀⣀⠸⠃⠆⠀⠀⠀⠀⠀⣘⢃
⠀⠀⠱⠰⠃⠀⢦⣤⠀⠀⠀⡦⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⠀⠀⠀⠂⣀⣀⣀⣀⠤⣄⢠⠀⠀⠀⠀⠀⠀⢣⡞
⠀⠐⢢⠠⡀⠀⠀⡄⠇⠀⠀⠋⠀⠀⠀⡇⢸⠀⠀⣛⡀⠀⠀⢫⠀⠀⢸⢆⠀⠀⠀⠀⠀⢸⡉⡍⠀⠀⠀⠀⠈⡛⢢⠶⠀⠀⠀⢀⠜⣡
⠀⠀⠰⠀⣉⠂⠀⠇⢠⠀⠀⠀⠀⠈⠉⠳⣴⠀⠀⠀⠀⠀⠀⠈⠆⠀⠨⡄⢂⠀⠀⠀⡀⠈⠛⣓⠂⡀⠀⠀⠀⡔⠀⠀⠀⠀⡀⢈⢨⡀
⠀⠀⢄⠀⠸⠃⠀⢰⠸⠀⠀⢀⣄⡀⠀⠀⠘⠀⠀⠠⢤⢄⠀⠀⠀⡀⠀⡙⣄⢂⡀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣄⠡⡀⠄⠀⠠⠁⠀⢳⡆
⠀⠀⠐⣠⠁⠀⠀⢸⣤⡄⠀⠀⠿⠆⠀⠀⢀⡀⠀⠀⢨⡈⣄⠀⢀⠗⠀⠁⠈⠉⠉⠉⠑⠚⠒⠒⠒⠂⠀⠀⠈⠉⠉⠛⠈⠀⠀⠀⢐⠜
⠀⠀⠀⠋⣄⠀⠀⢸⣬⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂
⠀⠀⠉⠣⠈⠢⢀⠀⠁⠁⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡠⠊⠈⠀⠈⠀⡠⠆
⠀⠀⠀⠀⠁⠉⠀⠉⢣⢲⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⢀⠐⠈⠹⠲⡂⢤⠄⢄⡀⠀⢀⠠⠀⢀⠀⠁⠒⠲⠅⠀⠒⠢⠈⠈⠑
⠀⠀⠀⠀⠀⠀⠂⠀⢀⠑⠁⠒⠒⠀⡂⠜⠠⢤⠑⠀⠲⡤⠀⠀⠀⡀⠠⠉⠈⢃⠬⡀⡀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠸⠃⠉⠐⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⣀⣀⣀⣀⢀⡀⡀⠀⠀⠀⢺⣆⣿⣼⣿⣧⣸⣇⣾⣿⣼⣿⣴⣿⢿⡗
⠀⠀⠀⠀⠀⣾⠛⣷⢹⣤⣿⠹⢀⡰⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣯⡿⢿⣿⣿⣻⠃⠀⠀⠀⠈⠿⠏⠿⠟⠟⠙⠛⠋⠛⠻⠋⠃⠿⡭⠁
⠀⠀⠀⠀⠀⠙⠛⠃⠘⠁⠉⠈⠘⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠠⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠔⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⡄⣠⣤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⣠⡤⢰⠆⠀⠀⠀⠀⠀⠀⣰⡟⢻⣾⣿⣶⢿⣿⣏⣲⡆⠿⠀⡄⠀⠀⠀⠀⣴⢶⡄⣿⢸⡇⣾⠋⢸⣇⣿⢹⠇
⠀⠀⠀⠀⢾⣻⣺⣿⣾⠟⠿⢿⣼⠯⠀⠀⠀⠀⠀⠀⠠⡘⠷⠾⠛⠛⠉⠘⠃⠙⠋⠑⠃⡠⠃⠀⠀⠀⠀⠻⠾⠃⠙⠛⠁⠙⠛⠘⠁⠻⠐
⠀⠀⠀⠀⠘⠛⠉⠉⠉⠀⠀⢀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠀⠀⠐⠒⠂⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠾⠷⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣡⣠⡄⠀⠀⠀⠀⣠⡦⣠⡶⣦⣴⠶⣦⣴⠆⢠⡄
⠀⠀⢀⣤⡤⣶⣖⡦⢰⣿⡄⣿⣛⠀⣧⣸⣿⡇⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣾⢻⣾⣷⢿⣿⡃⠀⠀⠀⠀⢿⣤⠿⠦⠞⠛⠶⠟⠿⢶⡛⢠⠃
⠀⠀⢻⣄⣤⢹⡟⠷⠼⠗⠿⠰⠾⠛⠋⠈⠋⠂⠀⠀⠀⠀⠀⢺⣿⣿⠷⠾⠉⠛⠁⠁⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠔⠁
⠀⠀⠀⠉⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⡀⠀⠀⠀⢀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⡶⠆⣶
⠀⠀⠀⠐⣿⣻⢾⣏⣿⣿⡾⣷⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠲⣴⢶⣶⢃⣶⣆⣶⢸⣾⡇⠀⠀⠀⠀⠀⠠⢀⣤⣄⣾⠛⣿⣿⠞⠉⣛⣷⣏
⠀⠀⠀⠀⠹⠃⠀⠉⠉⠈⠁⠉⠛⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠷⠾⠛⠿⠟⠹⠯⠁⢲⠀⠀⠀⠀⠀⢿⣁⣽⠻⠶⠋⠛⠀⠀⠀⡈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠠⠤⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠙⠁⠀⠂⢀⢤⡄⠰⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⢿⡀⣶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢸⡇⣿⠀⠀⠀⠀⠉⠙⢷⡄
⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠰⣄⣠⡾⠇⠹⠶⣶⣶⣧⡀⢀⣾⠁⠀⢀⣤⣀⣀
⠀⢀⣶⠟⠉⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⣆⠀⠀⠀⡟⠛⠛⠛⢻⡆⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⢸⡏⠈⠉⠙⠛⠶⢦
⣴⡿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⡴⠞⠻⣦⡀⠀⠀⢸⡇⠀⠹⣧⡀⠀⣇⠀⠀⠀⠀⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣰
⠹⣷⠀⠰⣟⢻⡆⠀⠰⣿⠁⠀⠀⣿⠁⠀⠀⠀⠘⢿⣄⠀⠀⣷⠀⠀⠘⣷⡀⣿⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢠⡟
⠀⠹⣇⠀⠙⠋⠀⠀⣠⡿⠀⠀⠀⣿⠀⡿⠷⣤⡀⠀⠻⣆⠀⢻⡀⠀⠀⠈⢷⣿⡶⠟⠀⠀⣿⢸⡇⠀⠀⣰⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠐⢲⡿
⠀⠀⢿⣀⣀⣤⣴⣾⣏⣀⠀⠀⢰⡇⠀⡇⠀⠀⠙⢦⡀⠙⣧⣸⡇⠀⠀⠀⠈⢿⡇⠀⢀⣀⣿⠈⣷⠀⢰⡟⠀⠀⠈⠉⠛⠳⢶⣤⠀⠀⣾⠀⠀⠀⠐⢶⣾⠃
⠀⠀⢸⡟⠋⠉⠁⠀⠉⠉⢿⠟⠛⠳⢶⣇⣠⡤⠶⠚⠋⠀⣸⢿⡇⠀⠀⠀⠀⠈⠁⠀⠈⠉⢻⠀⠘⢷⣜⠛⢷⣦⠀⠀⠀⠀⠀⣿⠀⢠⡿⠶⠆⠀⠀⣼⠃
⠀⠀⢸⣇⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢧⠀⣤⡀⠀⠀⠁⠈⢻⡀⠀⠀⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠛⡟⠁⠀⢠⣤⣤⣰⡟⠀⣾⡇⠀⠀⠀⣸⠇
⠀⠀⠸⣿⣉⠀⠰⡏⠉⠉⠛⠶⣄⠀⠀⠀⠸⡇⣿⠛⢷⣄⡀⠀⠀⢹⡆⠀⣿⡀⢀⠀⠀⠀⣿⢶⣦⣤⣤⣤⡅⠀⠀⣾⠁⠈⠉⠁⠀⠉⠛⠳⢶⣴⡟
⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⣿⠀⠀⠈⢻⣦⣠⡞⠀⠀⣿⣷⠋⠁⠀⠀⣿⠀⠀⠀⠉⣽⠃⠀⢰⡏⠀⠀⠀⠀⣀⣤⠶⢶⣄
⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⠀⣰⠇⠀⠀⢰⡇⢿⡀⠀⠀⣼⡇⢉⣀⣀⣠⡿⠸⣧⣶⠶⠿⠛⠀⠀⠀⠀⠛⠛⠛⠿⠃⠀⠀⠀⢰⡟⠳⠀⠀⣹⠄
⠀⠀⠀⢸⡀⠀⠸⠧⠤⠤⠴⠞⠃⠀⠀⢀⣾⣀⣸⡇⠀⠀⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡶⠟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠀⢰⣤⡾⠛⠉⠉
⠀⠀⠀⢘⣇⣀⣼⣷⣤⣤⣤⣼⡷⠿⠋

⠀⠀⠀⠀⠀⠀⠀⣄⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢦⠛⠻⠟⠻⠟⢺⠛⡶⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⣤⣿⣶⣿⣦⣴⢀⢀
⠀⠀⠀⠀⢨⣘⣡⣄⣃⣄⣀⣄⡷⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢠⠄⠀⠁⠀⣼⣸
⠀⠀⠀⠀⠀⡼⠟⢻⡟⠛⠇⠈⠁⠀⠀⢀⣢⣤⣾⣦⣾⣧⣤⣀⢀⡀⠀⠀⢱⣾⢶⣶⢷⣾⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⢹⠀⠉⠈⠠⠺⡇⡇⠀⠀⠈⠀⠈⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⢶⣶⢷⣾⠲⠆⠁⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣀⣰⣄⣴⡆⢀⡀⠀⠀⠀⠀⠈⠁⠈⠏⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⣤⣀⣴
⠀⠀⠀⠤⠚⢋⡏⢩⡏⠉⡏⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠟⠻⡟⠛⠻⢛⣰⢰
⠀⠀⠀⠰⠆⣸⣤⣬⣏⣠⣷⣾⠀⠀⠀⠀⡀⠀⣤⡀⣠⠀⠀⠀⠀⠀⠀⠁⣠⣈⣃⣄⣠⣾⣂⡸⠴
⠀⠀⠀⠀⠀⠛⠉⡿⠉⠙⠂⠀⠀⠀⠀⡄⠻⢻⠛⠛⠛⠓⢛⠂⡆⠀⠀⠀⠸⠟⢹⡟⠙⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡄⣸⣇⣸⡇⣴⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢻⡿⠙⠿⠈⠁
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣰⣷⣴⣿⣀⣤
⠀⠀⢀⠀⡷⢶⡿⢿⡿⡶⡶⣤⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠖⠈⠋⠟⣉⠙⡏⣷⠤
⠀⠀⠀⠀⣁⢸⠁⢸⣇⢰⡇⡜⠀⠀⠀⠀⠰⣶⢾⡷⢾⡷⠴⡆⢤⠀⠀⠀⠛⢼⣤⣷⣤⣴⡇⠷⠄
⠀⠀⠀⠀⢹⠿⢻⡿⠿⣯⠙⡃⠀⠀⠀⠀⠆⠀⠀⠁⢘⠀⠚⡇⡞⠀⠀⠀⠀⠋⠡⠸⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⣿⠾⢷⡚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⢷⠸⣿⣿⡜⠎⢸⠀⣿⣿⣿⣿⡟⡿⢸⠃⢎⣾⣟⡾⢣⡿⢋⡾⣿⣿⠟⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣯⢧⠘⣿⣧⠀⠀⠀⢹⢿⠉⡟⠃⠇⠇⠀⣜⡟⡼⢡⡟⣱⢟⣾⠟⣡⣾⡿⢟
⠻⣿⡿⣿⡿⣝⢿⠙⠃⠀⠈⢎⠂⠘⡿⡄⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠞⠈⠠⢋⡞⡵⠋⢀⣼⡿⣫⡴⢟
⣿⣮⡙⢮⡙⢮⡣⡁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠊⠀⠴⠋⣨⠞⡫⠖⡩
⡳⢿⣻⢦⡈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠕⠈⢐⣬⣶
⡻⠶⢍⡓⠯⣳⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡽⣞⣿
⢭⣓⠢⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣷⣄⣀⣠⡾⢹⣦⣤⣴⢾⡏⠀⠀⠀⠀⠀⠀⢀⡠⣖⡯⠷⢛⣋⡽
⣟⣶⠤⢄⣀⠀⠀⠀⠀⢤⣀⣀⣀⣀⣿⡌⠻⠟⠁⠀⠛⠋⠁⣿⣷⣤⣤⣤⣴⠖⠋⠑⠉⠁⠀⣈⣠⣤⢶
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⡉⠉⡉⠙⡏⠁⠀⢧⠃⠐⡆⠐⡆⠈⡉⠡⡶⠋⣄⠀⠀⠀⠀⠈⠙⠒⣚⣋⣩
⣀⣀⣀⡀⠀⠀⠀⣀⣀⣠⡇⠀⠃⠠⡇⠀⡄⢸⡇⠀⠀⢠⠇⢐⠧⢤⡇⢀⣇⣀⣀⠀⠀⠀⠉⠋⠉⠛⣓
⣿⠿⠿⠟⠉⠉⠉⠉⠙⠛⢿⠀⠸⠀⠀⠀⣄⠀⡇⢸⡀⢸⡄⠘⠀⢸⠃⣼⠛⠉⠉⠉⠀⠀⠀⠒⠲⠶⠶
⣖⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡧⢴⣖⣛⠒⠛⠉⠉⠉⠉⠉⠈⢉⣉⡙⢿⣇⠀⠀⠀⠀⠀⠀⣐⣢⡤⢭⣭
⣵⣖⣂⠄⠀⠀⠀⠀⡠⠴⠛⠛⠙⠻⣿⢀⣠⣤⡀⢀⣤⣤⡀⣿⡟⠛⠛⠛⠳⢤⣀⠀⠀⠀⠀⠈⠉⠙⠛
⡿⢟⠂⠀⣀⠤⡂⠀⠀⠀⠀⠀⠀⢀⣿⠞⠉⠛⢷⣸⠟⠉⠛⠾⣇⠀⠀⠀⠀⠀⠀⠹⣲⣤⣿⣷⣶⣮⣽
⣫⣤⣖⣯⠖⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⡏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠈⢙⢿⣿⣿⣿⣿
⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠐⢝⢮⣲⣍⡻⣿⣿⣿
⠴⣊⠔⣠⢔⡤⣠⠖⡡⠀⣠⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢰⡵⣄⡙⢿⡿⣿⣶⣝⡿
⣚⣵⣿⡿⣫⡾⣣⢞⢄⣴⣷⡃⠀⠀⡜⡆⠀⠀⠀⢀⠀⠀⠀⣀⢹⣷⡀⠀⠠⡈⢻⣮⡿⣦⡙⢮⣿⣿⣿
⣿⡿⣫⡼⢋⡼⣳⣯⣾⣿⡿⢁⠆⣼⢷⠇⢀⢰⢰⢸⢠⠀⢸⣸⡈⣿⣷⣱⡱⡹⣽⣿⣿⣿⣿⣮⡹⣿⣿
⣿⣿⢟⣴⣿⣿⣿⣿⣿⣿⢃⡞⣰⣿⣿⠠⣟⣼⣼⣿⢸⡄⡀⣇⣧⢸⣿⣷⣷⡽⣽⣿⣿⣿⣿⣿⣿⣮⡻

⡽⣿⣿⣧⡻⣎⢿⣿⡞⣟⣿⢿⣧⢿⣿⣿⣿⡇⢿⣿⢿⣿⣿⠈⣿⠘⣿⡿⣿⢸⣿⣿⡿⡼⣼⣿⡟⣼⣿⠏⢠⡟⡱⣿⢏⡾⣱
⣧⡈⠻⣏⢷⡙⣆⠻⣿⡜⠜⡏⠿⡜⣿⡘⡏⠃⠘⠙⠈⠁⠸⠀⠏⠀⡟⠃⠉⠘⠸⢹⠇⢡⢇⡿⠁⣹⡟⢠⠏⢀⡼⢣⢎⣾⡿
⣯⡻⢄⠘⢧⠹⡌⢧⠙⡕⠀⠀⠀⠀⠀⠡⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠘⠀⠀⠟⢀⠏⢀⡞⠁⠁⡴⢋⡴
⣿⣿⣦⠁⠀⠑⠈⠀⠀⠉⡩⠄⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠞⢑⣿⠿
⣲⠍⠫⠳⢄⠀⠈⢲⣄⠀⠀⠑⠀⠀⣷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣄⠠⠤⠀⠂⢛⣉⣍⡉⢠⡴⠶⡟⢸⣿⠾
⠉⠓⠂⠀⠀⠰⠄⠀⠹⣿⣦⡀⠀⠀⢹⣿⠀⠀⢼⣿⡄⣰⠧⠤⠴⠤⢘⣊⣩⣤⡤⠶⣶⡞⢹⡷⠋⢁⡀⣙⣿⠀⢸⠇⣿⣇⠔
⣿⣢⠄⡀⠀⠀⠀⠀⠀⠙⢿⡷⡈⢷⣄⡙⠀⣷⡀⠉⢡⡴⠒⠛⠛⢾⠏⠁⠀⢻⡇⠀⠸⡇⢸⠃⢠⣏⣉⡭⣿⠀⣼⢠⣿⠵⢾
⣯⡉⠁⠀⠀⠐⠀⠀⠀⢰⣘⣿⣷⠈⢿⡝⢦⣿⠻⣦⢸⡇⠀⠶⠀⣼⠀⢸⠀⢸⡇⠀⠀⠀⢸⠀⢸⣏⡅⠀⣿⠴⣏⠸⣿⡈⠄
⠿⢧⣶⣶⣶⣖⠚⠛⠉⣉⣉⣀⣀⣀⣠⣿⣆⠙⠃⠀⢸⡇⠀⣤⡈⢻⠀⠘⠀⠈⡇⠀⣇⠀⢸⣆⠀⠙⢁⣼⣇⣀⡼⢀⣿⢂⠉
⣅⠐⠉⠍⠉⠛⠻⢶⣠⣉⠙⠻⢿⣿⡛⠛⠛⠂⠀⠀⢸⡇⠀⠉⢀⡄⠀⣸⣇⣀⣅⣤⢿⠴⠚⣋⡓⠒⣋⣥⣬⣭⣴⣿⠋⠄⠄
⠧⠄⠀⠀⠀⠀⠀⠀⢀⣨⣵⣶⠄⠈⣹⡷⠄⠀⠀⠀⢸⣧⡤⠶⠛⠛⣋⣉⣉⣉⣥⣴⣤⡶⠟⢫⠹⠛⣛⣯⠵⠘⡈⠄⠀⠀⢤
⠓⠀⠀⠀⠀⢀⠤⡶⠿⠟⠛⠡⠴⠿⠿⠶⣶⠆⠀⠰⠶⠶⠶⠶⠾⣿⠿⠿⠛⠛⠉⠀⠉⠀⠀⠀⠂⠡⠰⡘⡊⠥⠀⠀⠀⠀⣀
⣥⣄⡀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣶⡶⢂⣴⢋⣠⣴⡆⠀⢀⡀⢶⣤⣈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡀⠐⠲⣾
⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠏⣰⣿⠿⠛⠉⢸⣿⣠⡿⠳⣼⣿⠈⠉⠛⠻⢦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣌
⢕⡤⠒⡡⠂⠀⠀⡀⢀⠾⠋⠀⠚⠉⠀⠀⢸⡿⢸⣿⡟⠁⠀⠘⠿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢤⡪
⠋⡠⣪⠎⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠏⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⡈⢦⡱⣄⢻
⣫⣾⢗⢔⠄⡰⣠⠂⢀⠄⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠠⡀⡀⠀⢡⠀⠱⣀⠠⡑⣄⠳⣜⢷
⡿⣵⣿⣯⡾⣵⠃⢠⣾⡟⡠⣠⠇⣾⣴⣧⠀⡰⠀⡀⢠⢰⡄⢠⡄⠀⡄⠀⡆⠀⢸⣷⣇⢀⢷⣼⡄⡈⣧⠀⢻⣷⡱⡜⢧⡙⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡴⠞⠉⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣞⠍⠉⠉⢺⠕⠈⠑⠔⠀⠀⠀⠀⠀⠀⠘⡶⠒⠓⠲⣄
⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠘⠒⠒⢦⡀
⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠃⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣣
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡄⠀⠀⠀⠀⡀⢀⡥⠤⠲⣤⡞⠉⠀⠀⠉⡖⠉⠁⢸⣿
⠀⠀⠀⢸⡄⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣖⠉⠉⠉⠲⣇⠀⠀⢿⣇⠀⣶⣷⣦⣿⠀⠀⢸⣿
⠀⠀⢀⣠⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⡀⠀⠀⠀⠙⠀⠀⠸⣿⡄⡇⢰⡛⠉⢇⠀⠸⣿⡇
⠀⠀⢾⠁⢀⣠⠤⠖⠒⢤⣄⡀⠀⡖⠉⠈⠣⡀⢇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⠺⠟⠀⠘⡄⠀⣿⡷⣄
⠀⠀⡸⠓⠉⠀⣤⡄⠀⠀⣿⣿⡄⣷⠀⢠⡀⠙⢼⡀⠀⠀⢦⡀⠀⠀⠘⣿⣄⣀⣀⣤⣾⠳⣶⣿⠇⠘⡆
⠀⠀⠹⡀⠀⠀⠛⠃⠀⠚⠛⠿⣤⣿⠀⠸⠷⠀⠈⢣⠀⠀⠸⣿⡦⣠⣤⣿⣿⠿⠛⠋⠁⠸⣀⣸⣦⠀⡇
⠀⠀⠀⢱⡀⠀⠀⢠⣤⡄⠀⠀⢹⣿⣆⠀⢀⣀⡀⠘⢶⣾⡿⠿⠇⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠁⣸⠃
⠀⠀⠀⣼⢣⠀⠀⠀⠿⠃⠀⠀⣼⣿⡟⠀⣸⢿⣷⣶⡿⠃⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢀⣀⣠⠞⠁
⠀⠀⠀⡏⠀⢧⠀⠀⠀⣀⣤⣾⣿⢿⣿⡿⠟⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⢷⠀⠈⠶⢶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠓⢤⣤⡤⠊⠉⠁⠀⠠⠀⠀⠀⠀⠠⣔⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣠⠴⠊

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⡀⠀⠀⠀⢀⣤⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣠⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⢻⣿⣿⣿⠿⠛⠛⢻⣿⡿⠋⠉⠀⠈⣿⠛⠉⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⢰⠃⠀⠀⠀⣀⣀⣀⣼⣿⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠻⠀⠀⠀⢸⠀⠀⠀⢰⣿⡿⠿⠿⢿⣧⠀⠀⠀⢸
⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣦⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢿⠀⠀⠀⠸⣿⣤⣤⣴⡿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠈⣦⡀
⠀⠀⠀⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠘⢦⣀⣀⣠⣦⣤⣤⣴⣿⣧⣄⣠⣴⣿⡿⠆
⠀⠀⠀⠀⠹⡇⠀⠀⠀⢰⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣷⡀⠀⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠋⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠘⠤⢤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢻⡀⠀⣀⣀⣠⣤⣴⡁⠀⠀⠀⠀⠀⣸⣿⣿⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⢿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠙⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⣠⠴⣒⣯⣽⣓⢦⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠲⣄⡱⠋⠀⠀⠀⠈⢳⣁⡴⠚⠉⠙⠲⣄⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠘⡆⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢾⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠒⠒⠲⠍⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡥⠼⠂⠀⢀⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣰⢫⠄⠀⠀⠀⣸⠃⠀⠈⣷⠀⣤⠶⠶⣦⠀⢠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠿⢦⣤⡾⠃⢸⡇⠀⢸⠇⢀⣿⠟⢙⡷⠀⣠⣤⣤⡀⠀⢸⠇⠀⠀⢠⠞⢀
⠀⠀⠀⠀⠀⢳⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠻⠄⣼⠃⠀⣸⠇⣼⠋⠀⢠⡟⢀⡿⠀⠀⠀⠘⣆⠈
⠀⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠶⠖⣿⠁⠘⠃⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢠⣷⡂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⡾⠃⠀⠙⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠈⠀⠀⠘⢦⡀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠙⠲⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠉⠉⠋⠉⢬⢧⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⢠⠏⠀⠘⠀⠀⠈⢳⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠲⣤⣴⣺⠽⠂⠙⠦⢤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿



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

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⡠
⠀⢀⠔⠂⠁⠀⠃⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠈⠛⡀⢴⠉⣆⣠⠓⠀⠂⠀⠀⠀⠀⠀⠀⡰⠂⡉⠠⢀⣀⡀⠉⢀⢀⣀
⠀⢀⠀⠐⠀⡖⠀⡆⢐⡇⠆⠋⡠⡞⠀⠀⠀⢀⠴⡁⣢⠛⠛⠟⠛⢡⡁⢣⠃⠀⠀⠀⡴⠧⠠⢌⣾⠉⠛⡅⠉⠉⣈⡄
⠀⠈⠄⠀⢰⠃⢊⢡⣀⣠⣠⣌⠣⡭⠀⢀⠀⢸⢀⠂⣉⣀⣀⣤⣬⣥⠼⢬⠅⠀⠀⢠⢣⡀⠤⠒⣿⠜⣦⠽⡔⠒⠎⠰
⠀⠀⠀⠀⠈⠋⠉⠉⠉⠀⠀⠀⠤⣱⠀⠀⠐⠈⠙⠁⠋⠁⠸⠉⠃⠈⠀⠱⠆⠀⠀⠀⠁⢹⠀⠔⠁⠸⠈⠃⠀⡞
⠀⠀⠀⠀⡄⠀⢀⠀⡀⠀⠀⠆⠂⠁⠀⠀⠀⠀⠀⠆⠁⢢⣀⡀⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣓⠶⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠄⢤⠦⡀⠢⠚⢤⣀⣎⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣀⣴⣄⣀⡀⠀⠀⠀⠠⢀⡠⠀⠤⠠⠄⡀⠈⠣
⠀⠀⡀⢀⣗⡀⠀⠀⢀⡭⠀⠁⡈⠀⡀⠀⠀⠀⢀⠀⠀⣰⠀⠀⠸⠛⠏⠐⠀⠀⠀⢁⠀⢨⠃⠀⠀⠀⠀⠨⣤⢤⠄⡄⡆
⠀⠀⢣⠀⣈⠛⡱⠶⠟⠷⡂⠂⠋⣏⠁⠀⠀⠀⡌⠀⠀⠘⣶⣦⣤⣀⣴⠊⠀⠀⠀⠈⡀⠈⡔⠀⠈⡤⠉⡶⠀⠀⠰⠧⠁
⠀⠀⠉⡽⠀⢂⠁⣀⠚⢄⢥⢴⡖⠊⠀⠀⠀⢠⠊⠠⠀⠾⠐⠐⡡⡜⠀⠀⠀⠀⠀⠀⠀⢀⣇⡵⠦⠕⠶⠞⠚⣾⠛⠋
⠀⠰⠒⠲⣏⣠⠥⢤⠊⠁⠻⠉⠀⠀⠀⠀⠀⢸⢐⣈⣄⣀⡄⢄⡣⠍⠀⠀⠀⠀⠀⠀⣩⡰⡀⠀⡀⠀⡀⣠⠞⠃⠐⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠔⠄⠀⠀⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⠀⠡⡀⠀⠀⠀⠐⠢⡀⣤⠴⢤⠃⠀⠘⡠⣔⡀⠀⠀⠀⠀⢀⠀⠀⠤⠠⢀⠐⡢
⠀⠀⠀⠳⢄⣠⣔⣀⣀⡀⣀⣤⠴⠃⠀⠀⠀⠀⠐⠨⡀⡤⠊⠀⠉⢙⠀⠀⢸⠄⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⢈⠄⢤
⠀⠀⠀⠀⢀⡀⠀⠙⠻⠋⠩⣄⢀⡀⣀⡀⠀⠐⠂⢰⡁⣀⠀⠂⡆⢘⠡⡅⢃⡇⠀⠀⠀⠠⠀⠀⣸⠀⠠⠆⠴⠀⣀⣘
⠀⠀⠀⣀⣀⡗⢦⠀⠤⡒⢒⡍⠃⠁⣧⠀⠀⠀⡠⠰⣓⣈⣤⡄⠤⠬⡥⠲⡖⠑⠀⠀⠀⠄⣀⠀⠲⠚⠓⠉⠋⠉⠋⠉
⠀⢠⠏⠽⠀⣺⡍⢀⣈⠣⠌⠦⠶⠲⢎⠀⠀⠀⠱⠀⡈⠹⢄⣠⠖⢞⠁⡀⡓⠀⠀⠀⠀⠀⠀⠒⡀⣀⠀⠀⠄⠂⢀
⠀⠹⢶⠒⢋⡁⢉⣀⢀⠀⡠⡀⣀⢀⡠⠃⠀⠀⠀⠘⠀⠘⠀⠀⠆⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠄⠀⠀⠀⠀⣀⣀⠀⠀⠸⣀⣠⣤⣤⣀⡀⠀⢰⢲⠶⠶⢖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢆⠔⡪⠓⠋⠉⠙⢣⡤⡊⠁⡠⡲⠟⠻⢷⣌⡀⡄⠀⠈
⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⢀⢄⡲⠖⠛⠓⠣⢄⠎⠀⠀⢀⡋⢹⠉⠑⣘⡘⡘⠀⢀⡀⠀⠹⡁⢃⠀⠸⠘
⠀⠀⠀⠀⠈⠻⡢⣀⢀⢜⠕⠁⡠⡤⣤⡤⡦⡀⡏⠟⠋⠙⣽⠌⠆⠀⢁⠁⠇⠀⠘⠈⡆⠀⠁⠘⡄⠀⡎
⠀⠀⠀⠀⣀⣤⡼⠶⠿⢮⣄⠀⡆⡅⠀⠀⠘⡵⢰⠸⠀⠀⠈⢆⠸⠀⠘⡀⡇⠀⢸⠀⢐⠠⠝⠆⢰⠀⠰⢃⣀⣀⣀⣤⠤⠄
⠀⠀⢰⠪⠋⠁⠀⢀⠀⠀⠙⡵⡇⡇⠀⣀⠀⠱⣹⡄⡆⠀⣀⠀⠳⣇⠀⢡⢡⠀⠀⡘⡄⡀⠀⠘⠀⣣⠼⡸⡒⠉⠁
⠀⠀⠈⠆⢇⠀⠘⡀⢈⠀⠀⡀⡅⠃⠀⢸⠄⠀⠱⠃⢡⠀⠸⠳⡀⠈⠀⠈⡄⡄⠀⠰⡈⡐⠀⢠⠀⢡⠀⠘⢐
⠀⠀⠀⠸⠘⡀⠀⠓⠃⠀⠰⣡⡇⠀⠀⠨⠼⠀⠀⠣⠈⡆⠀⠇⠈⢆⠀⠀⢱⠈⢆⡀⠈⠁⢀⠆⣸⡈⠒⠐⣸⠇
⠀⠀⠀⠀⢃⢣⠀⠀⡤⢄⠀⠀⢣⠀⠀⠀⣀⠠⡀⠀⢣⢡⠀⠐⣹⢆⠳⡀⠰⠚⠢⢌⣀⣈⠡⠊⠀⠀⢀⠜⡝
⠀⠀⠀⠀⠘⠘⠄⠀⢃⢀⠇⠀⢸⠸⠀⠀⡁⢆⠡⡀⠤⠇⠦⠀⠃⡆⠓⠐⠒⠊⠁⠀⢀⠟⠒⠀⠐⣊⠥⠊
⠀⠀⠀⠀⠀⠇⢃⠀⠈⠁⠀⡠⢃⢰⣀⡀⠇⡀⠂⠐⠒⠒⠀⠉⠉⠁⠀⠀⠀⢰⠂⠒⡩⠊⠑⢄⠹⡀
⠀⠀⠀⠀⠀⢸⠘⠄⠒⢂⡉⡔⠻⠤⠄⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠏⠁⠀⠀⠀⠀⠑⢼⡄
⠀⠀⠀⠀⠀⠀⠉⠉⡹⢁⠔⠉⠢⡑⠤⣀⠀⠀⠀⣀⠤⠊⠢⠄⣀⣀⠠⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡣⠂⠀⠀⠀⠈⠒⠤⠌⠉⠡⠔⠚⡄⠀⠖⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠛⠛⠛⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⠈⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⢀⣾⠋⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣼⡇⠀⠀⣤⣤⣀⣀
⠀⠀⢠⣿⣷⣾⣿⣿⣿⣿⣿⣷⡀⠀⣴⣶⣶⣿⣿⣿⣿⡇⠀⢠⣶⣶⣾⡇⠀⢠⣶⣶⣶⡗⠀⠀⣀⣴⣾⣿⣿⣿⣷⣆⠀⣿⣦⣄⣸⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢉⣿⣿⣿⣿⠃
⠀⢠⣿⣿⣿⣿⠋⠀⣽⣿⣿⠋⠀⣼⣿⣿⡿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⣿⡏⢠⣿⣿⣿⣿⡿⠛⠉⠛⠁⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀
⠀⢸⣿⣿⣿⣿⣴⣿⣿⠟⠁⠀⢰⣿⣿⣿⢣⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣧⢸⣿⣿⣿⢣⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣀⡄⠀⢰⣿⣿⣿⠇⠘⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⢀⣿⣿⣿⡟⢸⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣾⣿⣿⣿⠃⠀⣴⣾⣿⣿⣿⣿⡇⠀⣾⣿⣿⡏⠀⠀⢹
⠀⣿⣿⣿⣿⠋⠉⢉⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡏⠀⢠⡿⠿⢿⣿⣿⡿⠀⠘⠛⠻⠟⠀⠀⠀⣸
⢀⣿⣿⣿⣿⣷⣶⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⡟⢿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣧⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⢀⠀⠀⠀⠀⢀⣿
⢸⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣇⣿⣿⣿⡇⠘⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣶⣿⣿⣿⠟⠁⢠⣶⣿⣿⣿⡆⠀⣠⡾⠃
⠾⠿⠿⠿⠟⠋⠁⢸⡇⣾⡿⠿⠿⠟⠀⠸⠿⠟⠛⠛⢹⣿⣿⣿⠃⠀⠸⠿⠟⠛⠁⠀⠈⠻⣿⣿⣿⣿⠿⠛⠁⠀⠀⠻⣿⣿⡿⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⣀⣀⣤⣴⠾⢻⡿⠃⠀⠀⠀⠀⠀⠀⣴⣿⣶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⣴⣟⣀⣀⣀⠀⠀⠀⠀⣼⣯⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢻⡿⠃⠀⠀⠀⢉⣩⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣤⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠾⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⢿⡘⣿⣿⡏⢏⠺⡁⢿⣿⣿⣿⣿⢸⢣⡏⡸⣽⣿⣿⠟⣼⠟⣴⣿⣿⡿⢋⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢯⢳⠈⢿⣿⠀⠀⠁⢸⣿⠻⢸⡏⡟⡘⠀⢱⡿⣱⠋⡼⢫⡾⣵⡿⢋⣴⣿⡿
⡻⣿⡿⣿⡻⣝⢿⠛⠃⠀⠈⠣⠣⠈⢿⡇⠀⠀⠘⠛⠀⠀⠀⠀⠁⠀⡱⠁⠁⠞⡵⢫⠞⠁⣴⣿⢟⣵⠾
⣿⣮⣙⢮⡙⢮⡳⡕⠀⠀⠀⠀⠀⠀⠘⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠁⡠⠞⢁⡵⢛⠵⢊
⡳⢿⣻⢧⣈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠩⠒⠁⣢⣵
⡻⠶⣍⡓⠯⣓⢤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣯⢷⣻
⢭⣓⡢⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣀⣼⠻⣷⣤⣤⠞⣿⠀⠀⠀⠀⠀⠀⠀⣠⢴⣺⡽⠞⣛⣭
⣟⣲⠬⢅⣀⠀⠀⠀⠀⠤⣄⣀⣀⣀⣼⡏⠛⠿⠋⠀⠙⠛⠁⢸⣿⣦⣤⣤⣤⠶⠊⠑⠈⠉⠀⢀⣁⣤⡴
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡎⠉⡉⠙⣿⠁⠀⢱⡆⠀⢶⠀⡶⠀⠉⠉⣴⠛⢁⠀⠀⠀⠀⠀⠩⠓⣒⣛⣋
⣀⣀⣀⡀⠀⠀⠀⣀⣀⣠⣧⠀⠋⠀⢿⠀⡄⠈⡇⠀⠈⠀⡇⠀⡷⠤⣿⠀⣼⣀⣀⡀⠀⠀⠈⠉⠉⠙⣛
⣿⠿⠿⠟⠋⠉⠉⠉⠙⠛⢿⡀⠸⠀⢸⠀⣠⠀⡇⠀⡆⠀⣇⠀⠃⢀⡗⢰⠟⠋⠉⠉⠁⠀⠀⠐⠲⠶⠶
⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢴⣖⣚⠒⠛⠋⠉⠉⠉⠉⠉⢉⣉⣉⠻⣿⡀⠀⠀⠀⠀⠀⣀⣲⣤⠬⣭
⣷⣖⣂⠄⠀⠀⠀⠀⢠⠴⠛⠛⠛⠛⣿⡇⣠⣤⡄⠀⣠⣤⣀⢺⣿⠛⠛⠛⠻⠦⣄⡀⠀⠀⠀⠀⠉⡉⠛
⡿⢟⠒⠉⣀⠤⡂⠀⠀⠀⠀⠀⠀⠀⣿⠞⠋⠙⢿⣸⡟⠉⠙⠻⣷⠀⠀⠀⠀⠀⠀⠩⢗⣮⣼⣿⣶⣾⣭
⣫⣥⣶⣯⠗⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡀⠀⠉⡻⣿⣿⣿⣿
⣿⠟⢋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⡀⠪⡳⣕⣮⣙⢿⣿⣿
⠴⣪⠔⣠⢔⡥⣂⠔⡡⠂⢠⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢐⣝⢦⣈⠺⣿⢿⣷⣮⣻
⣚⣵⣿⡿⣫⡾⣫⢞⡕⣴⣷⡧⠀⠀⣼⡸⠀⠀⠀⢠⠀⠀⠀⢠⠸⣿⡄⠀⡐⣄⠙⣷⣝⣷⣌⢳⣿⣿⣿
⣿⣿⣯⡾⢋⡴⣻⣿⣾⣿⣿⢃⡎⣰⣧⡇⢀⢠⢠⢸⡀⡀⠀⡎⡆⢻⣿⡜⣜⣜⢮⣿⣿⣿⣿⣷⣝⢿⣿
⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⢃⡾⣰⣿⣿⣇⣺⢸⢸⣼⡇⡇⡄⣿⢻⡈⣿⣿⣾⣞⣯⣿⣿⣿⣿⣿⣿⣷⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢆⠀⠀⢀⣀⢤⣤⣤⣄⡄⠀⠧⣒⠦⠧⠶⣶⣤⣀⠀⡏⢹⠛⠋⢳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢢⠔⡭⠊⠉⠀⠈⣉⣳⣴⢭⠀⢀⢔⠝⠛⠛⠻⣷⣴⢸⡀⠀⢸⢸
⠀⠲⣄⠀⠀⠀⠀⠀⠀⣠⢔⡢⠝⠙⠛⠛⠡⢄⡎⠀⠀⡀⣀⡇⢺⠉⠉⡇⣆⠇⡎⠀⢀⣀⠀⠈⢊⠀⠇⠀⠘⡚⡀
⠀⠀⠈⠻⡢⣀⠀⢠⢎⠔⠉⣀⣀⣠⣤⣤⢦⠀⠏⢹⠛⠛⠪⣻⡈⡆⠀⠸⡘⢸⠀⠀⢸⠀⢇⠀⠈⡆⠸⡀⠀⠇⠇
⠀⠀⠀⣀⣈⣦⡵⠧⠎⠀⠀⡇⡏⠁⠀⠀⢣⢣⢸⠘⡀⠀⠀⠱⡄⢹⠀⠀⢇⢸⠀⠀⢸⢠⠘⠖⣒⡣⡀⢣⠀⠸⠸⠀⠀⠀⠀⢀⣀
⡠⢔⠾⠛⠉⠀⠀⠀⠁⢢⢦⡇⢃⠀⠀⠀⠀⢫⢣⡄⢇⠀⠀⠀⠈⢆⣇⠀⠸⡄⡆⠀⠘⡴⡆⠉⠀⠀⢱⠈⣆⣀⡆⣆⠬⠙⠛⠉⠁
⢳⠘⡀⠀⠀⡔⠒⢄⠀⠀⡇⡇⢸⠀⠀⣧⠀⠈⢏⢧⢸⠀⠀⢷⡄⠀⠻⠀⠀⢇⢣⠀⠀⢣⠱⠲⡆⠀⢸⠀⢞⠛⠑⡜⡄
⠈⡆⢣⠀⠀⢃⢀⠜⠀⢀⡇⣦⢸⠀⠀⡏⢆⠀⠈⢎⠀⡇⠀⠘⡈⢂⠀⠀⠀⠘⡌⢆⠀⠀⠣⠤⠃⠀⡸⢠⢸⡀⠀⣰⢰
⠀⠸⠈⡆⠀⠈⠁⠀⠀⠚⢴⡿⢸⠀⠀⠱⠚⠀⠀⠈⣆⢸⠀⠀⢇⢀⠱⡄⠀⠀⢃⠀⠳⣄⠀⠀⢀⡴⢁⠿⣄⣉⣩⣥⡼
⠀⠀⢇⢱⠀⠀⢠⠤⢄⡀⠀⠱⡘⡀⠀⢀⡠⠤⡀⠀⠘⡄⢇⠀⠘⡸⡣⡈⠦⠤⠼⠸⠓⠤⣈⣉⡡⠔⠃⠀⠀⢀⡴⣡⠃
⠀⠀⠸⡈⡆⠀⠘⡄⢀⠇⠀⢀⠼⡇⠀⢸⢠⣆⠱⣀⡀⠼⠸⠤⠤⠇⢧⠙⠒⠒⠒⠋⠁⠀⠀⡸⠑⠒⠒⠒⢚⡡⠔⠁
⠀⠀⠀⡇⢳⠀⠀⠉⠁⠀⢀⠎⠀⡇⠀⢘⠊⡈⠦⠤⠤⠐⠒⠒⠒⠊⠉⠀⠀⠀⠀⢠⠤⠤⠒⡡⠋⠢⡀⢫⡁
⠀⠀⠀⠘⠈⣄⡀⠤⠤⠒⣁⢼⣇⣉⣉⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡖⠂⠉⠀⠀⠀⠈⢢⡱⡀
⠀⠀⠀⠀⠧⠤⠤⠶⠒⢩⠳⡄⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⣠⠞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⢠⠃⡔⠁⠀⠈⠢⣈⠓⠢⠤⠤⠤⠔⢚⡁⠀⠈⠑⠒⠒⢒⣉⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⡧⠊⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠊⠁⢸⠀⢰⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡀⠀⠀⠀⠀⢀⡠⡶⠀⠀⠀⠀⠀⡰⢋⡀
⠀⠀⠀⠀⠀⠀⢄⡀⠠⣄⠀⠀⡦⣀⠀⠀⢰⠓⢄⢰⠇⠀⠳⣤⠔⢧⡴⠋⠀⡇⢀⢠⡀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠹⣆⠑⠢⣼⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠁⢸⣇⡀⠄⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣠⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣍⣉⠉⠀⠀⠀⣿⢀⡷⠀⣰⣿⠀⣼⡆⠀⡖⢀⡴⢦⠀⢀⡀⠈⠙⠒⢤⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠉⡻⠂⠀⠀⣿⠻⡅⢰⣇⣼⠀⡏⢻⣸⡇⣼⠁⠈⠀⣼⠀⢰⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣀⣀⠀⠀⠓⠚⠁⠏⠀⠹⠀⡇⠈⣿⠀⣿⠰⣦⠀⠃⠀⣀⣱⡄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠁⠀⠸⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣼⣠⠖⠋⡇⢀⣴⡀⠀⢀⡄⠀⠀⣄⠀⠀⣠⡀⠀⡗⠶⠦⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣷⠏⠀⢳⡴⠋⢻⠀⡜⠈⠳⠞⠈⠻⢦⠹⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠁⠀⠀⠀⠀⠀⠀⠙⠂⠀⠈






⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⣦⡙⢿⣯⡹⣿⣄⠘⢎⢻⣦⠻⣧⢻⣿⣆⠈⣷⠈⣿⣿⠸⣿⡇⠀⢸⡇⣿⣿⣿⢸⣿⢠⣿⡏⣼⣿⡇⢰⣿⠃⠀⢠⣿⠟⣴⣿⠟⢠⣾⣿⣿⡿⣫⡿⢋
⠀⠈⠙⢦⡙⣿⣌⢻⣧⡀⠣⡹⣷⡹⣧⢻⣿⡄⠸⣇⠸⣿⡆⣿⣿⠀⢸⡇⣿⣿⡏⣼⡟⣸⣿⢡⣿⡿⢠⣿⠃⠀⣠⣿⠋⣼⡿⠃⣴⣿⣿⡿⢋⡴⢋⡴⠋
⠳⢄⠀⠀⠙⢌⠻⣷⡝⢷⡄⠑⡜⢷⡙⣧⢻⣷⡀⢻⡄⢻⣧⢸⣿⡀⠈⡇⣿⣿⡇⣿⡇⣿⡏⣼⣿⠁⣾⠃⠀⢠⠟⠃⣼⠟⢁⣾⣿⡿⢋⡴⢋⠔⠉⢀⣴
⣤⡀⠙⢦⡀⠀⠑⢌⠻⣮⡻⣦⠈⢎⢳⡜⢇⢻⣧⠀⢷⠈⣿⡀⣿⡇⠀⡇⣿⣿⡇⣾⢠⣿⢡⣿⠇⢸⠇⠀⣰⡟⢠⣾⠋⣰⣿⡿⠋⡴⢋⠔⠁⢀⣴⣿⣿
⠙⢿⣦⣀⠙⢦⡀⠀⠁⠈⢷⣌⢷⡀⠣⠻⡌⢧⢻⣧⠘⣇⠰⡇⢹⡇⠀⡇⣿⣿⠀⡟⣸⡇⣼⡟⢠⡏⠀⣰⠏⣠⡟⢁⣾⣿⠏⡠⢊⠔⠁⣠⣾⣿⣿⡿⠋
⣤⡀⠈⠻⢷⣄⠉⠢⣀⠀⠀⠙⢦⡙⣆⠀⠙⢆⢇⢹⡆⠘⡀⠛⠈⣿⠀⠃⣿⣿⢀⡇⣿⢀⣿⠁⡘⠀⣰⠋⣰⠏⣐⣵⠟⡡⢊⠔⠁⣠⣾⣿⣿⠟⢉⠔⠊
⣦⣝⠳⣤⡀⠙⠳⣦⡈⠳⢄⠀⠀⠙⢌⠣⡀⠈⢆⠀⢻⡄⢳⠀⠀⢹⡄⠀⢿⣿⢸⢳⡇⣸⠇⡐⠀⢰⢃⡼⢃⣮⡾⠃⠊⠐⢁⣴⢿⣯⠞⠋⠀⠀⣀⠴⠚
⠍⠛⠿⣦⣍⡳⢤⡈⠙⢦⣀⠑⢄⠀⠀⠁⠙⢄⠀⠁⠀⠻⡈⠇⠀⠀⠃⠀⢸⡇⠈⣸⢠⡏⠀⠀⠠⢡⠞⢀⡵⠋⠀⠀⢀⡴⢛⡵⠛⠁⠀⠀⠔⠈⢀⣠⠴
⠿⢦⣄⣀⠉⠻⢶⣍⡳⢄⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢸⡇⠀⠃⡸⠀⠀⠀⣠⠋⣠⠞⠁⠀⣠⠾⡫⠞⠁⠀⠀⠀⠀⣀⠤⠒⠉
⢷⣦⣬⣙⠻⠶⣤⣈⠙⠳⢬⣀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠈⢠⠁⠀⠀⠐⢀⡼⠁⠀⣠⠞⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡤⠴
⠀⠀⠉⠙⠛⠶⢦⣍⣛⠲⢤⣉⠓⠦⣀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⣁⣠⣤
⣷⣶⣦⣤⣀⣀⠀⠀⠉⠑⠒⠬⣝⡲⠤⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠚⠛⢉⣉⣤
⠨⠭⠍⢙⣛⠙⠛⠛⠲⠦⠤⣀⡀⠈⠁⠂⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢉⣉⠡⠤⠔⠒⣛⣉⣉⣭⣶
⠶⠤⠤⢤⣤⣄⣈⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠒⠚⠛⠙⠋⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠐
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⡉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠶⠶⣶⣤⣤⣤⣄⣀⣀⣀⣉⠉⠉
⣤⣤⣤⠴⠶⠚⠛⠋⠁⠁⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠐⠤⣄⡀⠀⠀⠀⠈⠉⠙⣛⠛⠿⠿⢿⣿
⠁⠀⣀⣀⡤⠤⢒⣈⣥⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢤⣀⠁⡂⠄⡈⠙⠲⠦⣤⣀⡐⠀⠬⢉⣒⠲⠤
⠚⢋⣩⣤⠶⠞⠋⣁⡤⠒⠈⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠓⢮⣑⠦⣍⡒⠤⣀⠉⠛⡻⢶⣦⣄⣉⠙
⠞⠋⢁⣠⡴⠖⠋⠁⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⢦⣈⠳⢦⣝⠳⢮⣙⠲⢤⣅⡂⠭⣛⡿
⡴⠞⠋⠁⠀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⣸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⣄⡉⠻⢦⣍⡻⢶⣬⣙⠳⢦⣬
⠀⣀⣤⣾⠿⠛⠁⠀⠀⠀⡀⠀⠀⣠⠞⢀⠔⠁⠀⠀⣠⠇⠀⢀⢀⡟⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠈⢄⢄⠀⠈⢢⡀⠀⠀⠈⠻⢦⡀⠝⡻⣶⣌⡛⢿⣶⣌
⣿⡿⠋⠁⠀⢀⠀⢊⡤⠊⡀⣪⠞⠁⡰⠃⠀⡠⠀⣰⡏⠀⠀⡌⣸⡇⢀⡇⣷⠀⠀⠀⠀⠀⢣⠀⠀⠈⢮⢢⠀⠀⠑⢄⠀⠀⠀⠈⠙⢷⣌⡲⢝⠻⣷⣬⡙
⠁⠀⠀⣠⠔⣁⡴⢋⡔⣨⢞⠕⣠⠞⠀⠀⡔⠐⣴⡟⠀⠀⣼⡄⣿⠃⢺⡆⣿⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⢷⡳⡀⡀⠈⠳⣄⠀⠀⠀⠈⠺⣿⣦⣝⠦⣝⠿
⢀⡴⠊⣠⠾⢋⡴⣫⠞⡡⢁⡼⠁⠀⢀⠞⢀⣼⡿⠁⠀⣸⣱⣸⣿⡀⡎⡇⣿⢠⠀⢠⠀⡄⠀⠘⡆⠀⠈⢌⢳⡝⣌⢆⠀⠘⢦⡀⠀⠀⠢⡈⠻⣿⣷⣬⡛
⢁⣴⠞⢉⠴⣩⡾⡣⠊⣴⠏⠀⣠⢠⠏⢀⣾⣿⠃⠀⢠⢇⠇⣿⣿⢡⣷⡇⣿⢸⠀⠈⡄⢣⠀⠀⢹⡘⡀⠘⣆⢻⣌⢦⠳⡀⠀⠹⣦⠀⠀⠘⢳⣌⠻⣿⣿
⠟⣡⠞⣣⡾⣫⠎⣡⡞⢁⠄⡴⣱⢋⢢⣾⣿⠇⠀⢀⡿⣼⢸⣷⣿⢸⢹⡇⣿⢸⠀⠀⠇⠘⡄⡀⠀⣷⠱⡀⠘⣇⢻⣎⢳⡙⣌⢂⠈⢳⣄⠀⠀⠘⢷⣌⠻
⣞⣡⣾⣋⣾⣁⣼⣋⣀⣀⣞⣼⣃⣠⣿⣿⣟⣀⣀⣼⣳⣇⣿⣽⣇⣸⣸⣇⣿⣸⣀⣀⣸⣀⣧⣠⣀⣘⣇⣡⣀⣹⣧⣹⣧⣻⣌⣣⣁⣀⣙⣧⣀⣑⣄⣉⣷
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⠑⠠⠀⠈⠛⢦⡀⠈⠣⠀⠘⡆⠀⠀⠀⠀⠀⣿⠀⡏⠀⠀⠀⠀⡞⠁⠀⠀⠀⣠⡶⠟⠁⠀⠀⣠⡴⠟⠋
⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠞⠋⠀⠀⠀⠔⠋⠁⠀⠀⣀
⣀⠈⠉⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣠⠴⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠉⠁
⠶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤
⠶⠶⠦⠤⠤⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⢤⣤
⠀⢀⣀⣀⣠⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠲⢦
⠀⠀⢀⣠⠴⠊⠁⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⡀⠀⠙⠢⣄⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⢹⣿⣿⡇⣿⠇⣿⢸⡿⣿⣿⣿⡟⣼⢟⣿⢟⣼⣿⣿⢏⣾⣿⣿⣿
⣌⠻⢿⣿⣟⢿⣿⣿⣿⡟⣧⠹⣿⣿⣿⣿⡞⣿⢻⡇⢻⠀⡿⢸⣧⣿⣿⡟⢰⠏⣾⠏⣼⣿⠟⣵⣿⣿⣿⣿⣿
⣮⡳⢦⡙⢿⣦⠹⣿⣿⠻⡈⢷⡙⣿⣿⡘⣧⢻⢸⡇⠐⠀⡇⣿⢸⢋⡿⢡⠏⡴⢃⣴⡿⠃⠊⣵⠟⣫⣿⣿⣿
⣿⣿⣶⣝⠢⣙⠳⣄⠙⢷⡄⠀⠳⡈⢿⣧⢹⡘⡏⡇⠀⢠⡇⠏⠏⣸⢃⠏⠀⢁⡞⠁⠀⣠⠞⢁⡾⠟⣻⣿⣿
⣿⣿⡻⣿⣷⠌⠐⢌⠢⠀⠈⠂⠀⠑⠈⠛⠆⠁⠃⠁⠀⠘⠀⠀⠀⠃⠎⠀⣠⠋⠀⠀⠈⠀⠀⢉⣤⣾⣿⣿⡿
⣿⣿⣿⣷⣭⣳⢤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣠⢔⣫⣿⠟⢋⣡⣴
⣶⣬⣙⠛⠿⠿⢷⣮⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠴⢛⣩⠴⢞⣿⣿⣿
⣿⣿⣾⣉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣚⣭⣴⣾⣿⣿⡿⠿
⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠋⠉⠉⠉⣁⡠⣤⣴
⣿⣿⣿⣿⣿⣿⣯⣭⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠶⠶⠿
⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠶⠶⢶
⣶⣶⣒⣒⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣙⣒⡒⠲⠶
⣟⣛⣉⣩⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠙⠻⣿⣿⣿
⠟⣋⣩⣤⠶⢖⣪⠵⠒⠁⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢶⣦⣔⣤⣤⣙⡻
⣛⣋⣭⠶⠛⠉⠀⠀⣀⡴⣊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢭⣿⣿⣿⣾⣭
⢟⣩⣤⠖⠊⢀⡴⢞⣥⠞⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢄⠀⢀⡑⢦⣬⣿⣿⣿⣿
⠟⣋⣤⣤⣾⣫⡶⠋⠁⢀⡔⠁⡀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡀⠈⢢⡀⠠⡑⣄⠙⢦⡻⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢋⣀⣔⣴⠋⢀⠜⡜⣰⠇⠀⢀⣆⣠⠀⠀⢸⡆⢰⠀⠀⠄⢱⡐⣄⠻⣆⠈⡪⡳⣤⣌⡻⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢁⣤⢏⣾⣴⣟⡾⣼⣿⣼⣿⡆⢐⢸⣿⢸⡆⢰⠘⣄⢳⡜⣆⢻⣷⣿⣿⣮⡻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣴⣿⢣⣾⣿⣿⣿⣻⣿⣿⣿⣿⡇⣿⣼⣿⣸⣿⡼⣇⢻⣆⢿⡜⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⣿⣌⣿⣎⣿⣜⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡣⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢣⠑⣄⠀⢰⣄⡀⣀⠞⠁⠉⠹⠄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢦⣸⡆⠈⠓⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣹⠀⠉⠁⠀⠀⡠⠖⠛⠛⠲⢄⡀⠀⠀⠀⠀⣸⠁⠀⣠⣴⠞⠁⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠉⢀⣤⠤⠤⡎⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠉⣼⠁⣀⣠⡤⠖⣋⠔⠉
⠀⣴⠖⠒⠂⡤⠚⠃⢀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢦⡀⠀⠀⠀⠈⠉⠉⠀⢠⠞⠁⢀⣀⣤⠴⠊⠁
⠘⠁⠀⠀⠀⠤⣄⣀⣈⢻⡖⠶⠆⠀⠀⠀⠀⠀⢠⡴⠶⠄⣀⣀⡀⠀⠀⠀⠟⠉⠛⠶⣄⠀⠀⠀⠘⠛⣫⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣍⡁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢾⣀
⠀⡆⠈⠉⠛⠫⢅⣐⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⡆
⠀⠙⠦⣼⠀⠀⠀⠀⠉⢒⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣰⣤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠈⠳⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠉⠁⠀⠀⢰⠦⢤⣀⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⢰⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣠⠇⠀⠀⠀⠀⠀⢀⡀⠀⢧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣠⠤⣄⣀⠀⢀⡀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠳⡀⢹⠉⠢⡘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠗⠉⠀⠀⠋⡝⣠⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣇⠀⠙⢼⡀
⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⣸⡗⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠴⠖⠃⠘⣞⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⠲⠖⠒⠦⠤⠞⠳⠶⠚⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠠⢄⡀⡀⠀⠀⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀⠀⠣⡀⡀⠀⠀⡀⣀⠤⠚⠁⠉⠉⠑⠠⠀⠀⠈⠙⠠⣈⠐⠂⠉⠀⠲⠆⠠
⠀⠀⠀⠠⠄⠂⠀⠀⠀⠉⠀⠀⠈⠀⠀⠒⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠤⠀⠀⠈⡀⠂
⠀⠀⠠⢄⠄⠀⠀⢀⠀⠀⠀⠀⢠⠤⠐⠂⠀⡒⠆⠉⠀⠀⡏⡁⠁⢠⡀⠀⠉⠀⠀⠙⠄⠀⠀⠀⠀⠁⢢⠄
⠀⠤⠐⡡⠐⢂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⢀⠀⠀⠀⠓⡄⠀⠈⠀⠀⠠⠶⠄⠀⡇⠃⠀⠀⠀⠀⠊⢀⡀
⠀⠠⠉⠀⠀⢙⠣⠀⠀⠟⠀⠀⡄⠀⠀⢸⠀⠀⢱⠀⠀⢢⠀⠈⠀⠈⠀⡤⡖⠒⠒⠋⠙⠤⢀⡀⠀⠀⠀⡽
⠀⠀⠁⠑⠀⠘⠀⠀⠀⠀⠀⠒⠣⡆⠀⠈⠁⠀⠀⠃⠀⢸⠠⠀⠀⠀⠀⠳⠒⠀⠀⠀⠀⡅⠀⠀⠀⡀⠠⡈
⠀⠀⠀⠘⠃⠀⡆⡄⠀⢠⣄⠀⠀⢁⠀⠀⢤⠄⠀⠀⡄⠈⠳⣐⣀⢠⠄⠀⠀⠀⠀⢀⢤⢣⡀⠀⠀⠁⠈⢦
⠀⠀⢡⠀⠀⠀⡶⠆⠀⠈⠋⠀⠀⡨⠀⠀⠸⠤⠄⠀⠊⠀⠀⠀⠀⡀⠉⠉⠉⠁⠀⡀⣀⣀⣉⣁⡄⡠⢀⣤
⠀⠠⢄⠐⡀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡀⠒⠐⢂⠂⠂⠘⠃⢋⣿⣬⣭⣴⣾⡉
⠀⠀⠀⠃⠒⠑⠢⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠚⠤⠀⠀⢄⠀⠀⠀⡀⠈⠁⠠⠤⠀⠉⠠⠐⠁⠺⠁
⠀⠀⠀⠀⠀⢀⢀⠁⠁⠐⠂⠀⠐⠀⠄⠀⠓⠄⠀⠀⠀⠀⠁⠑⠤⡀⠄⠀⠄
⠀⠀⠀⠀⠀⠊⠀⠀⠈⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⢠⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡾⠀⢸⠶⡂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡅⠆⢰⠃⡰⡣⠖⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠓⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠰⠦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢄⣀⡀⠀⠀⢀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡄⠀⢐
⠀⠀⠀⠀⠀⠀⠻⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣄
⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠐⠀⠀⠀⠁⠤⡀⠀⠀⠀⠀⠀⠒⠈⠹⠿⠃
⠀⠀⠀⠀⠀⠘⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡟⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠂⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢨⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠈
⠀⠀⠀⠀⠷⠞⠺⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⢤⠥⠶⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠸⣶⡿
⠀⠀⠀⠀⠀⠈⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠂⠁
⢀⡀⠀⠈⠑⠀⡠⣀⠈⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⣠⠄
⠘⣉⠉⠁⠀⠈⠛⣻⠓⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠁⠂⠈⠀⠀⠀⠀⠀⠂
⠀⠉⠀⠀⠀⠒⠀⠄⠀⠀⠀⢀⡋⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠰⠄⠒⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⣤⠆⠀⠒⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃
⠁⠀⠠⣘⠄⠐⠂⠀⠂⠤⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠈⠉⠀⢶⠆⠀⠀⠲⠀⢀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⢀⠀⠀⢠⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄⠀⠀⠀⠀⡀
⣤⣤⣤⣬⣤⣤⣤⣵⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢳⠀⠀⠀⠀⠀⢸⠀⢠⡆⢀⡏⠀⣸⠃⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⡄⠈⢧⠀⠀⠘⡇⢸⠀⢸⠀⣸⠁⣰⠃⢀⡜⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠳⣄⠙⣄⠘⡆⠙⡀⡇⢸⠀⡟⢠⠇⢠⠃⢀⠎⢀⡤⠉⢀⣴⠆⠀⠀⡀
⠀⠀⠀⢠⣄⠀⠀⠀⣤⠀⠑⠀⠈⢦⠘⢆⠸⡀⢧⢰⠸⠀⡇⡜⢠⠃⠀⠀⡰⠋⢀⡴⠋⠀⠀⠀⠊⠁⠀⢀⡄
⠀⠀⠀⠀⠉⠓⠦⣄⡀⠘⠦⣄⠀⢀⠱⡌⢆⠁⠸⡀⠀⢠⠀⢁⠂⠀⢠⠞⣁⠔⠁⣠⠄⠀⢀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠰⠦⣄⣀⠉⠒⠤⣈⠑⢬⡓⢌⠀⠂⠀⠃⠀⠀⠀⠀⠀⠔⡡⠚⣡⠔⠋⣡⠴⠒⠉⢀⣄
⠀⠀⠐⠶⠤⣤⣀⣈⠉⠒⠢⠄⠁⠂⠈⠂⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢂⣁⡤⠴⠒⠛⠉⠉⣀⣀⣀
⠀⠀⠀⠀⣤⣀⣀⣈⣉⣉⡑⠒⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠄⠒⠒⠛⠉⠉⠉
⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠄⠈⠉⠁⠀⠀⠀⠀⠀⢺⣍⡿⠀⠀⠀⠀⠀⠀⠒⡒⠒⠒⠒⠒⠘⠃
⠀⠉⠉⠁⠀⢀⣀⣠⡤⠤⠖⠒⡂⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⣉⣉⠉⠙⠒⠒⠒⠲⠶⠤
⠀⠀⠀⠀⠀⠈⣁⣠⠤⠒⠊⣩⠴⢊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡑⠒⠤⣀⡉⠙⠒⠲⠤⣤
⠀⠀⠠⠆⠚⠋⠁⠀⠰⠆⢉⡠⠒⢁⠔⠁⢀⢀⠆⠀⠀⠘⡀⠐⡀⢄⠠⡀⠠⡈⠐⠤⣀⠉⠓⠲⢤⡀
⠀⠀⠀⢀⡠⠔⠀⠀⣠⠔⠉⣠⠔⢁⠄⢠⠂⡜⠰⠀⠀⡀⡇⢁⠰⡌⢢⡈⠢⡈⠓⢄⡈⠑⠦⣄⡀⠀⠘
⠀⠀⠀⠀⠀⣠⠴⠋⢀⣤⠞⠁⡰⠃⡰⠃⡼⠁⡇⢸⠀⡇⢹⠈⡆⠹⡄⠱⡄⠙⢦⡀⠙⠦⣀⠀⠙⠲⡦
⠀⠀⠀⠀⠚⠁⠀⠀⠀⠁⢀⠞⠀⡴⠁⣐⠃⢸⠀⣸⠀⡇⠸⠇⠸⡄⠹⡄⠘⢦⠀⠙⢦⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⡼⠁⠀⠈⠀⡏⠀⡏⠀⡇⠀⠀⠀⢳⠀⠹⠄⠈⢳⡀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡞⠀⠀⠀⠀⢸⠁⠀⡇⠀⣇⠀⠠⠀⠈⣇⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠚⠉⢡⣿⠟⠉⠉⠛⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠈⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⢻⡶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣶⠛⠃⠀⠀⠘⣶⠛⠁⠀⠀⣀⠀⠀⠀⣀⡀⠀⠁⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠻⠀⠀⠀⠀⠘⠇⠀⠀⠀⣿⠉⠀⠀⠀⠈⢻⠉⠀⠀⠀⢸⡏⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣉⣷⣤⣤⣄⡀⢨⡀⠀⠀⠀⠀⠁⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡆⠀⠙⠶⠂⠀⢠⣤⣿⠿⠿⠿⠛⠋⠀⠉⠁⣿⠿⣾⣿⡀⢴⡿⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡆⠐⠛⣠⠄⠀⠾⠧⣄⢢⠀⢠⠀⢰⢃⣾⣿⣀⣠⡼⠯⠀⠙⠀⠀⣶⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣤⣤⠴⢤⣤⡴⣮⣙⣧⠘⡇⣿⢸⣿⣛⣁⠀⣊⣤⣄⣴⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⣁⣿⡀⢷⢿⡞⣾⠥⣌⣉⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⣩⣶⢾⣧⠀⠘⡇⣼⠶⣶⢉⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢀⡉⠻⢇⣸⣿⣸⣇⣁⣿⡴⢿⡄⠘⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣷⡄⠀⣩⠉⠀⠛⠀⢉⠀⠀⠁⢐⣆⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⡶⠾⠿⡟⠳⣾⡿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠂⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡙⣧⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠏⢸⡇⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣾⡿⠏⠀⠀⠸⣧⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠇⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣤⡀⠀⠀⠀⠀⠀⣠⠎⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠙⠷⣄⡀⢀⡼⠁⠀⠸⡄⢀⣀⣤⣴⠾⠛⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⠶⣤⣀⠀⣼⠇⠀⠀⠀⠠⠶⠿⠛⠛⠉⠉⢹⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⠙⠳⠉⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⡆⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⡅⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⡟⠁⠀⠀⠀⢀⠀⠀⠀⡠⠴⠶⠦⣄⠀⠀⠘⣧⠀⠀⠀⣷⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠉⠁⠀⠁⠀⠀⠀⣾⠁⠀⣀⠊⠀⠀⠀⠀⠈⢳⡄⠀⠸⡇⠀⠀⣿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠐⠊⠳⣄⠀⢹⡀⠀⡏⠀⢠⠞⠉⠙⠲⠾⠓⠀⠀⢷⡀⠀⣿⠀⢸⡀
⠀⠀⠀⠀⠀⠲⣖⠒⠒⠚⠛⠛⢛⣉⡁⠀⠀⡜⠲⣆⢰⠀⠀⠉⠳⣼⡇⠀⣿⢐⡇⠀⠀⣠⡤⠤⠤⠴⢦⠸⡇⠀⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⡏⠉⢉⠳⡄⡇⢠⠈⢿⡇⠈⡷⡄⠈⠃⠀⣿⠘⣇⠀⠀⢸⣄⡀⠀⡄⢸⡆⢹⡤⠟⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⢷⠀⠁⠼⠷⢧⡈⢁⡈⠛⢆⢡⠈⠳⡀⠀⢿⡄⠙⢦⡀⠀⣀⡇⠀⣿⠟⠁⣠⠔⠢⣄⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣸⣇⠀⠠⠀⣨⡇⡏⠻⡦⠾⣿⠀⠀⠉⢦⠜⠿⣦⣄⣉⠉⠉⣀⡴⠁⠀⠀⢿⣶⣢⠞⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢿⣀⣠⡾⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⠀⣀⣠⡴⠞⠊⠁⢲⣄⠀⢀⡴⠟⠀⠀⢦⡀⠀⠀⠀⢀⣴⠏⠀⠈⠈⠑⠒⠦⢤⣄⣀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠙⠗⠉⠀⠀⠀⠀⠈⢳⣄⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠏




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⠀⠀⣰⠀⠀⢠⡖⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠹⡆⠀⠀⠀⠀⣄⠀⢿⠀⠀⣿⠀⢀⡟⠀⢀⡞⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡀⠀⢳⡄⠀⢹⡀⠀⠀⠀⣿⠀⢼⠀⢠⡏⠀⣼⠁⠀⡾⠀⠀⡴⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠻⣄⠀⠻⡄⠀⢻⡀⠛⠃⢸⡀⢼⠀⢸⠃⢠⠏⠀⡼⠁⠀⡼⠁⢀⡌⠋⠀⢀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠈⢧⡀⠹⣄⠈⢧⠀⢿⠘⡇⢸⠀⣼⠀⡾⠀⣼⠁⢀⠞⠀⣴⠟⠀⢀⡴⠛⠉⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠰⢿⣤⡀⠀⠀⠛⠃⣄⠀⠁⠀⠀⠹⣄⠘⣆⠈⡆⢸⡆⠇⢸⠀⡏⢰⠃⡰⠁⠠⠂⣠⠞⠁⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠾
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠈⠳⢦⡀⠀⢠⡈⢣⡘⢆⠘⡀⢧⠀⠸⠀⠃⠎⠠⠁⠀⢀⡴⠁⣠⠞⠁⢀⣴⠆⠀⠀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠐⠶⣤⣀⡀⠈⠙⠲⢤⣀⠙⠲⣄⡙⢦⡑⠌⢢⠀⠸⡀⠀⠸⠐⠠⠁⠀⡠⠋⡠⠊⣀⡤⠞⠉⣀⡤⠶⠋⠁⠀⣀⡀
⠀⠀⠀⣤⣤⣀⣀⠀⠉⠉⠛⠲⠤⣀⡈⠑⠢⢄⡙⠢⡙⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⢊⡤⠚⣉⠤⠖⠉⢁⣀⣤⡴⠶⠚⠛⠁
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠤⠤⣀⣈⠁⠐⠀⠀⠐⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠐⢁⡤⠴⠒⠛⢉⢁⣀⣀⣤⡤⠤⠶⠖⠖⠛⠃
⠀⠀⠀⠀⠀⠶⠶⠶⠶⠤⠤⢤⠤⢤⣤⣈⣉⣀⣀⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠈⠉⠉⠉⢀⠀⢀⡀
⠀⣀⣀⣀⣀⣀⣀⣀⣤⣠⣤⣤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⠇⠀⠀⠀⠀⠈⠉⠉⣉⣉⣉⠉⠉⠉⠉⠁⠉⠁
⠀⠉⠉⠉⠉⠁⠀⢀⡀⣀⣀⣀⣤⠤⠴⠖⠒⣋⠩⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣁⠒⠠⠤⣀⣀⡉⠉⠙⠛⠚⠒⠶⠶⠶⠤⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⣀⣠⠤⠖⠊⣉⡤⠊⡠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣈⠑⠢⢤⣀⠉⠉⠛⠲⠶⢤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠀⣤⠶⠋⣁⠔⠋⡠⠊⠀⠀⢠⠀⠀⠀⠘⡀⠐⡀⠂⠠⡈⠂⢀⠑⠢⢄⡀⠙⠓⠶⣤⣀⠀⠀⠉⠉⠛
⠀⠀⠀⠸⠇⠉⠁⠀⠀⠀⠀⠛⠀⣀⡴⠊⢁⡤⠊⣠⠂⡠⢁⠏⡘⢰⠀⠂⡇⠡⠐⡄⢣⡈⠢⡀⠑⢤⡀⠉⠳⢤⣀⠀⠈⠙⠳⠶
⠀⠀⠀⠀⠀⣀⡤⠂⠁⠀⢀⡤⠞⠁⢀⡴⠋⢀⠔⠁⡜⢁⡞⢀⡁⢸⠀⠆⢻⠀⣇⠹⣄⠙⣄⠈⠢⡀⠈⠳⣄⡀⠈⠛⢦⣄⡀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠁⠀⢀⣠⠞⠋⠀⢀⣴⠏⠁⡰⠋⢀⡞⠀⣼⠁⣼⠀⣾⠀⡆⢸⡆⠘⡄⠙⣄⠈⢧⡀⠙⢦⡀⠈⠙⢦⡀⠀⠈⠙⠶⣤⣤
⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠺⠟⠁⢀⠞⠁⢀⠞⠀⣼⠃⢠⡇⠀⡏⠀⡇⠀⣷⡀⢳⡀⠹⣄⠀⠳⣄⠀⠙⢦⡀⠀⠙⠳⡄⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠏⠀⠰⡆⠀⣼⠀⢠⡇⠀⡇⠀⠛⠁⠀⣧⠀⠹⣆⠀⠙⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠏⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠸⡆⠀⠹⠂⠀⠈⢳⡄⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⠃⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⣿⠀⠀⠶⠀⠀⢻⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢀⠜⠢⠄⢂⣀⢀⡀⠘⠱⠤⠄⢄⠀⢀⠀⠉⠁⠀⣀⣀⢠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⣄⠀⠀⠀⠘⠣⡀⢀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠛⠊⠉⠉⠉⠒⠢⠤⠐⠉⠉⠉⠑⠫⢄⡋⣀⠶⠒⠒⠒⠂⠮⢆⢆⢀⣀
⠀⠀⠀⠀⢀⡀⠀⣀⠔⡀⠤⠀⠀⠩⠥⠐⠒⠈⠣⡉⠄⢥⣈⠉⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⠢⡀
⠀⠀⠀⠀⠀⡋⢁⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⢠⠤⠀⠀⠀⠀⢀⡀⠀⡀⣀⣖⠒⠎⠐⠀⠀⠀⠀⣇⠀⠈
⠀⠀⠀⠠⡄⢠⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡤⢴⠒⠒⠂⠠⣚⠉⠏⠉⠁⠀⢀⢸⠀⡁⠀⠀⢨⣆⠉⠉⠉⠀⠀⠀⠈⠙⢆⠃⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⡀⡠⠆⡎⢠⢄⡀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠅⢨⠀⠀⠀⠀⠹⡀⠠⠀⠀⠀⠀⠱⣇⢰⠀⠀⠸⠃⠀⠀⠀⣀⣀⣀⢀⠨⡞⢸⠀⠀⠀⠀⠀⠀⢀⠋⡀
⠀⠈⠑⡄⡴⠂⠀⣄⣶⡀⠀⠀⠠⢤⠀⠀⠀⢸⠀⢈⠀⠀⡄⠀⠀⠰⡐⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⡠⠈⠉⠉⠁⣀⣀⣇⠈⡀⠀⠀⠃⠀⠀⠀⠑⣄⠗
⠀⠠⢄⠘⡀⠀⠀⠈⡁⢱⠀⠀⠀⠟⠀⠀⠀⣼⠁⡎⠀⠀⡿⡀⠀⠀⠱⡇⠀⠀⢹⢄⠀⠀⠀⠀⠀⠀⢰⡖⢞⠋⠉⠉⠉⠀⠈⠧⠧⢠⠄⠄⠀⠀⠄⢀⡝⣄
⠀⠀⠀⡇⠑⠦⡀⠀⣇⠘⠀⠀⠀⠀⠀⠰⠦⣯⡀⡇⠀⠀⠓⠃⠀⠀⠀⢳⠀⠀⠈⡎⢂⠀⠀⠀⠀⠀⠘⡷⢼⣄⠀⠠⠀⠀⠀⠘⡁⠉⠁⠉⠒⠀⠐⡎⠄⠉
⠀⠀⠠⠃⠀⢧⡀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡷⡀⢂⠀⠀⠀⠆⠀⠈⠐⠂⠄⠂⠀⠀⠀⢼⠀⠀⠀⠀⠀⡇⠀⢦⠓
⠀⠀⠑⠄⢀⠋⠀⠀⠈⡄⡇⠀⠀⢰⣖⢦⠀⠀⠀⢰⠀⠀⠐⢻⠙⡄⠀⠀⠈⡤⠀⣡⠱⣄⣢⡀⣒⡗⢤⡀⠀⠀⠀⠀⠀⠠⠺⣌⣢⣈⣀⢀⠐⠁⠀⠀⠟⢄
⠀⠀⠀⢣⡌⠀⠀⠀⢠⢧⡴⠀⠀⠀⠛⠊⠀⠀⠀⣜⠀⠀⠄⠈⣆⣰⣀⡀⠀⠏⠀⠀⠀⠀⠀⠀⢀⢉⢉⢉⡙⡋⠉⡁⡀⡀⡀⡀⣀⣈⠁⢀⣀⡀⣀⠀⣥⡃
⠀⠀⠀⡈⠐⡀⠀⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⢉⠁⢘⡞⡜⡸⡱⡙⣸⡞⡛⠃⠿⠱⠉⣠⣾⠿⠇
⠀⠀⠉⠒⢄⠘⠦⡀⠀⠉⠈⠁⠁⠉⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠴⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠀⠀⠁⣄⡀⠀⠠⠀⠀⢀⣤⢁⡿⠿⡿⢿⣽⠿⠄
⠀⠀⠀⠀⠘⢈⠖⠂⠑⢶⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠄⠒⢻⣢⠄⣀⣀⣄⠀⠀⠀⠀⢀⡠⠊⢀⢉⠂⠤⢤⡐⡀⠠⠤⡄⠚⠐⠲⠅
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠓⠕⠄⢀⡀⠠⠀⠤⣄⡁⠒⠢⠂⢏⢐⠃⠀⠀⠀⠀⠃⠒⠂⠢⡉⠐⠀⠊⠀⠀⢠⡃⢀
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠬⢇⠀⣀⣀⠀⠀⠒⠈⠀⠈⠙⠀⠀⠀⠙⠀⠀⠀⠀⠂⠨⠀⠀⠀⠊⠉⠦⠊⠉⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠉⠁⠈⠉⠉⠙⠷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⣀⣴⠋⠉⣀⣀⠀⠀⠒⠂⠒⠒⠀⠀⣀⣀⡉⠙⢷⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⢀⣾⡋⠉⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⣴⣻⣏⠁⠀⢠⡂⠀⠀⠀⢰⠀⠀⠀⠀⢦⠀⠀⠀⠀⡆⠀⠀⢹⣿⣷⠀⠀⠀⢀⣿⢹⣷
⠀⠀⠈⢻⣿⣷⣶⣾⣷⣤⣤⣤⣾⣦⣄⣠⣤⣿⣦⣤⣤⣾⣿⣶⣶⣿⡿⠋⠀⢀⣠⡎⢻⡞⢹⣤⡀
⠀⠀⠀⠀⠙⠚⠟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠗⠛⠁⠀⢰⠿⠿⠇⢸⡇⢸⠿⠿⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠼⠓⠺⠗⠻⠟⠉⠋⠙⠟⠓⠷⠚⠧⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠈⠛⠳⠤⠤⢶⣦⣤⣤⣤⣤⣴⡶⠤⠤⠔⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣀⣇⣸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠉⠀⣸⡇⣼⣿⠀⣿⠀⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠋
⠀⠀⠀⠀⠀⠖⠋⠠⠒⠒⠉⠁⣿⠇⣿⣿⡄⣿⡄⠉⠑⠒⠄⠉⠓⡄⠀⠀⠀⠀⠀⡄⡄⠀⡄⡄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠿⠛⠻⡞⠙⠋⠑⡿⠛⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⡇⢣⢀⠇⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⡈⠋⣰⠃
⠀⠀⠀⠀⠀⠈⠉⠙⠷⠶⢶⢿⣄⣠⣄⣀⣦⣠⡾⣷⠶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢳⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⢤⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣀⢀⡤⠶⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠉⠙⠣⡀⠀⠀⠙⢦⠀⠀⠀⠀⣴⠋⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⢼⡑⣆⠀⢸⠇⠀⠏⠀⠀⠀⡤⠒⠂⠀⠀⠀⠀⠏⠙⠢⡀⠀⠀⠄⠠⠀⠉⠀⠀⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡴⠀⡀⠀⠀⠀⠀⠀⡿⠃⠀⣸⠄⠀⠀⠀⠤⠠⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠋⠀⡄⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠁⠀⡀⠀⢀⣼⠅⠀⣰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⠷⢤⣀⣡⠤⢂⣈⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠀⠀⠈⠀⠀⠀⢧⠀⠀⠀⢄⠀⢀⣤⡀⠂⠀⢠⢆⠀⠀⠰⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠀⠙⣿⠘⢹⣶⣶⡏⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠇⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠁⠉⠑⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠲⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠁⡐⠀⠀⢠⠙⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣹⢣
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⡄⢐⠦⠐⠂⠀⠀⣰⠀⡈⠴⠀⠀⠀⠋⠂⠒⡆⠀⠨⠀⠀⡈⡑⢤⡀⠀⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠄⢶⣄⣄⣠⡝⠁⠀⠀⠀⠀⠀⠑⠲⠞⢉⠀⠀⠰⠐⠰⠁⡺⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢿⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⠁⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠈⠀⠀⠀⠀⠀⠀⢨⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⢀⡘⣶⣴⣿⣷⣿⣧⣤⠶⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣶⣄⣴⣇⢀⣀

⠀⠀⠀⠀⡀⠏⢠⠄⠁⣤⠈⠀⠉⠀⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠟⠻⠛⠛⠛⠻⠛⠋⣶⢰⠂
⠀⠀⠀⠀⠀⠚⢦⣶⣷⣤⣶⣤⠶⠦⠟⠙⠀⠀⠀⠘⠀⣀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠘⠃⣠⢀⣄⢀⡟⢼
⠀⠀⠀⠀⠀⠀⠟⠋⢹⡟⠈⠙⠃⠀⠀⠀⠀⠠⢬⣷⠶⣿⠿⢿⠿⣶⠶⢤⡠⣤⠀⠀⠀⣸⠿⠻⣿⠟⢿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠸⠀⡈⠀⠀⠐⢚⡇⡿⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣶⣶⣿⣶⡗⠶⠆⠁⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⢠⣄⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠀⡿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡄⠐
⠀⠀⠀⢀⣠⢽⠿⡿⠛⣿⠟⢲⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣶⣿⣷⠿⢷⣴⠶⢀⢀⡀
⠀⠀⠀⠀⣉⡀⢼⡇⠨⡷⠄⢹⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠉⢠⠄⠁⠐⣀⣅⡐⢺⢨⠁
⠀⠀⠀⠀⡉⢁⣿⠷⣿⡿⢶⣟⠓⠛⠀⠀⠀⠀⠠⣤⣀⣾⣦⣾⣇⣀⣤⠀⠀⠀⠀⠀⠐⢻⣶⣶⣧⣼⣿⡷⠴⠞⠈
⠀⠀⠀⠀⠀⠈⠁⠀⠹⠁⠀⠉⠀⠀⠀⠀⠀⠲⠈⠏⠙⠉⣍⠉⣭⠉⢭⠈⡇⠀⠀⠀⠀⠛⠁⠘⡟⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣠⣄⣸⣿⣰⣿⣀⣯⡐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠹⣿⠋⠻⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣶⣤⣾⡇⣀⣀
⠀⠀⠀⠀⢐⣦⣤⣿⣶⣾⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠻⠟⠻⠛⠛⢿⠛⣧⣀
⠀⠀⠀⠂⠈⠃⢸⠇⢰⣿⠈⣰⡆⣿⠀⠀⠀⠀⠀⢤⣀⣰⣦⣤⣾⣀⣀⣀⠀⠀⠀⠀⠠⣆⣠⠀⣤⡘⢃⣼⠠⣏⠁
⠀⠀⠀⠀⠀⢧⣼⣦⣤⣿⣦⡿⣧⡇⠀⠀⠀⠀⢀⡉⠋⠙⠟⠉⡟⢉⣹⡇⣿⠀⠀⠀⠀⠀⡿⠟⢻⡿⠛⢿⡄⠉⠁
⠀⠀⠀⠀⠀⠿⠋⠹⡿⠉⠛⠇⠀⠂⠀⠀⠀⠀⠈⢁⣄⣠⣤⣀⣆⣐⣀⣇⠏⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⣿⡟⠻⢿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠗⠀⠀⠀⠀⠀⣀⢴⣒⣿⣿⣓⢦⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠲⣄⡱⠋⠀⠀⠀⠈⢳⣑⡴⠚⠉⠙⠲⣄⠀⠲⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠘⡆⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢾⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠒⠒⠲⠍⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡥⠼⠂⠀⢀⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣰⢫⠄⠀⠀⠀⣸⠃⠀⠈⣷⢀⣴⠶⠶⣦⠀⣠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠿⢦⣤⡾⠃⢸⡇⠀⢸⠇⢀⣿⠟⢙⡷⠀⣠⣤⣤⡀⠀⢸⠇⠀⠀⢠⠞⢀
⠀⠀⠀⠀⠀⢳⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠻⠄⢸⠇⠀⣸⠇⣼⠋⠀⢠⡟⢀⡿⠀⠀⠀⠘⣆⠈
⠀⠀⠀⠀⠀⠀⠙⠲⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠶⠖⣿⠁⢘⠃⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢠⣷⡂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⡾⠃⠀⠙⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠈⠀⠀⠘⢦⡀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠙⠲⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠉⠉⠋⠉⢬⢧⠀⠀⠀⠀⠀⢀⢾⡀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠀⠀⠈⢳⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣤⣴⣺⠽⠂⠙⠦⢤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣾⣶⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠟⠋⢋⢿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣠⡾⠛⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠋⠀⠐⢻⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢘⣾⡟⣿⣿⣿⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣴⣿⠟⣄⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠟⠉⢠⣿⡿⠃⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⢀⣀⣴⠟⠁⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠋⣡⣤⡶⠞⠉⠀⠀⠀⠀⠀⣠⣾⣄⠀⢀⣠⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡠⠞⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⡿⣟⣵⡾⠟⠛⠛⠛⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡉⠃⠀⠀⢀⡠⠴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠉⢻⣷⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣀⡠⠴⠞⠻⠏⠋⠻⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⡟⠈⠉⢳⣄⠀⢿⣿⡿⠁⣠⡟⠉⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⢊⣼⣷⣤⣤⣤⣾⣿⣿⣿⣷⣆⠙⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⠀⠈⠘⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⢀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠀⣠⣿⣟⣿⣿⣿⣿⣿⣧⣀⡀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢰⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣈⠐⣀⣂⣨⠘⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠈⢑⡄⡁⣒⣀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠒⠉⠁⠈⠁⠉⠀⠀⠀⠀⠘⡄⣀⢈⢠⡏⡴⡿
⠀⠀⠀⠀⠉⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠐⠋⠉⠉

⠀⠀⢀⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢱⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠘⠏⠙⠉⢘⠠⠄⠂⣦⡄⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠄⠤⣡⢸⡯⠀⠀⠀⠀⠀⠀⠘⡀⡀⢢⣈⣰⠃
⠀⠀⠀⠼⠛⠛⠺⠖⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠒⢤⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⠀⣠⣽⣿⣿⣶⣤⠀⠀⠀⠸⠴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⢻⣿⡿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠘⢿⣿⣀⡀⠀⠀⠀⠀⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠽⠆⠀⠀⠀⣰⡾⠟⠿⠏⠀⠀⠀⠈⠛⠋⠛⠳⣄⠀⠀⠀⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠄⠀⢸⣦⡀⠀⠀⠀⠀⣸⣷⠀⠀⠀⢠⣿⣶⣦⣄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢸⣿⣿⠃⠀⠀⠈⢿⣿⣦⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠙⢿⣿⣧⠀⠈⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⢻⣿⣷⢀⣿⣿⣿⡇⠀⣀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢠⣼⣿⣿⣾⣿⣹⣿⡇⣴⣿⡀⠀⠀⣸⡿⠃⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣿⣿⠿⠛⣦⡀⠀⢸⣿⣿⣿⣉⣿⡟⣿⣿⣻⣿⡇⠀⠐⣿⣦⡀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⣴⡿⠁⠀⠀⢿⣷⠀⠈⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⣄⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣧⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠓⠀⣿⣿⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠘⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⢳⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣯⣿⡟⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡘⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣧⣾⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣷⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣯⣷⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠛⠛⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠛⠁
⠀⠀⠀⠀⠀⢘⣿⣿⣿⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠉⠑⠒⠉⠠⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⢿⣿⠿⠁⠀⠀⠠⠚⠉⠙⠙⠢⠄⠈⡀⠀⠀⠔⠈⠉⠑⠢⠀⠀⠀⠠⣿⣦⡀
⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⠿⡗
⠀⠀⠀⠀⠀⠙⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠠⠤⠄⠴⠂⠀⠀⢤⠂⠀⢠⠴⠿⡆⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⢠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⣀⠀⠀⠀⠀⠀⢾⡘⠧⣀⠀⠀⡠⠞⢰⠀⠀⠀⠀⢠⣤⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣏⠉⠛⠀⠀⠀⠀⠀⢰⣧⣀⡀⠀⣈⣡⣀⡿⠀⠀⠀⢺⡿⠋
⠀⠀⠀⠀⣠⣶⡇⠀⠀⠾⠟⠑⠀⠘⢿⡷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠙⣿⠁⢠⡆⠀⠀⠀⢀⣤⢠⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠈⠙⠈⠷⠀⠀⠠⠟⢡⡠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣱⣾⠿⣿⡮
⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣇⢀⡇⢰⠀⠀⠀⠀⠀⠉⢿⣇⣀⣸⣿⡆
⠀⠀⠀⠀⠀⢄⡀⣹⣼⣼⣴⡡⠀⠀⠀⠀⠀⠘⣆⣿⣿⣧⣿⠇⠀⠀⠀⠀⠀⠙⡻⡿⡟⠓
⠀⠀⠀⠀⠀⠀⣨⣿⠏⠉⠻⣿⠦⠄⠀⠀⠀⠈⠿⠛⠙⠛⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⢹⣿⣿⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣶⣦⢤⡀⣀⣦⡀⣠⣤⡀⢸⣿⣿⠉⠀⠀⠉⢻⣿⣿⡇
⠀⠀⠀⠀⣰⣿⣿⣿⠟⢙⣉⡛⢿⣿⠟⠋⠉⠈⢳⠈⠟⠙⠋⠙⠀⠉⠀⠈⠒⠀⣼⡟⠱⡆⠀⠅⠀⠈⣿⣿⡇
⠀⠀⠀⢀⣿⡟⢿⠟⠁⠐⠿⠓⣼⣿⡀⠀⢀⣀⣰⣦⣀⡀⠀⣄⠀⣈⠁⠐⢀⣼⣿⣧⢀⣀⠀⠀⠀⠀⣿⣈⡇
⠀⠀⠀⢸⣿⠟⡏⠀⠀⠀⠀⣄⣽⣿⡁⠙⠛⠁⢀⣰⠋⠀⠀⠀⠀⠉⣰⣾⣿⣿⣹⣧⣾⣿⡖⠀⠀⣠⠇
⠀⠀⠀⠈⠁⠀⣿⣦⣄⠈⢽⣿⣿⣿⣷⣤⣀⣀⠨⣿⣆⠀⠁⠀⣠⢦⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣯⡀
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⠟⢏⢷⣶⣾⣛⡵⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⡄
⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣦⣈⣼⠟⠉⠁⣠⣀⠜⠛⠯⣿⣿⣿⣿⣿⣿⣿⡟⠂⠙
⠀⠀⠀⠀⠔⡱⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠆⢉⡇⠀⢀⠀⡝⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢈⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣠⣄⡀
⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠂⠀⠀⠀⠀⠀⠀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠈⠙⠑⢒⣒⠲⣺⠟⠒⢢⡽⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣠⠚⠁⠀⡠⠋⠓⠲⠲⠶⣒⡾⢥⡄⠀⡠⠤⠤⣄⡁⠀⠠⣿⡇⠀⠀⣖⡈⠓⢤⣀
⠀⠀⠀⠁⢠⣀⣀⠤⣤⣔⣋⠀⠉⠁⠈⡩⣿⢶⡄⠀⠀⢰⣦⣄⠀⠀⠈⣷⠆⠈⢹⡫⠂⠀⠀⠀⠉⢦⢡⣿⠀⠀⢀⡏⠀⠀⡴⠋⠀⠐
⠀⠀⠀⠀⡼⠑⣧⡉⠀⠀⠀⠘⠲⣄⠜⢐⡇⡆⠈⢢⡀⢸⣷⠀⠙⢄⡀⣿⡆⠀⠈⡀⢀⣤⣖⣢⣐⡈⢹⣿⠀⠀⢘⠀⠀⡌
⣀⠀⣠⡨⠁⠀⠻⣆⡀⠀⠀⣦⠀⠘⡎⣸⢠⠀⢀⡀⠙⢎⣏⡄⠀⠀⠙⢿⡇⠀⠀⢀⣿⣧⠀⠀⠀⠙⣿⣿⠀⠀⡎⠠⠈⡇
⠀⠀⠂⠈⠳⣄⠠⠺⣷⠀⠀⠀⠀⣠⣃⡟⡆⠀⠚⠳⠄⠈⠻⡅⠀⠀⣄⠀⠉⠀⠀⡟⣯⣳⣤⡄⠀⠀⣿⡿⠤⣤⠗⡀⠠⢣⡀
⠀⠀⠀⠀⠀⠘⡄⠀⣷⡆⠀⠀⠀⠀⠈⢣⠃⠀⠀⠀⠀⡀⠀⠙⣄⠀⣟⢷⣄⠀⠀⢀⠈⠀⠋⠀⠀⡰⣿⡇⠀⠈⡿⠷⠊⠉
⠀⠀⠀⠀⠂⢰⠁⢐⣽⡇⠀⠘⠛⠆⠀⠘⠀⢰⡯⠩⠍⢿⡄⠀⠈⢢⠝⠀⢙⡷⠤⡾⠤⠤⠤⠴⠾⠶⠿⠷⡶⢾⠇⡠
⠀⠀⠀⡀⠐⡓⠒⢿⣶⠁⠀⠀⠀⠀⢀⣴⣀⡞⠀⠀⠀⠊⠻⠦⠖⠋⠀⢠⠾⠁⠘⡇⠠⠤⠤⠤⠶⠤⣤⣠⣦⡟⢀⠁
⠀⠀⠀⠀⠀⠀⠑⠀⠈⢶⠒⠒⢂⣉⣁⡀⠉⠀⠀⠀⠀⠀⢀⣀⣀⡀⠰⠃⠀⣀⠔⠛⠛⠓⠓⠥⡀⠀⡁⢉⣛⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠆⠋⠁⠀⠈⠉⠑⠢⡀⡠⠖⠈⠉⠀⠀⠉⠓⢦⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⣼⠋⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠢⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀