Bacteria Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢿⣷⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⠖⣏⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣵⣆⢳⠟⣹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠡⢅⠞⠁⢸⡿⢳⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⢦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠏⠀⠀⠘⢷⡠⡎⣿⠀⠀⠀⠀⠀⣠⣶⢴⣄⠀⠀⠘⠛⠏⠁
⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢹⣳⠆⢿⡗⠀⠀⠘⡟⠊⣁⢩⣿⠆⠀⠀⠀⠀⠀⠀⣠⣀⣰⣆⣀⡀
⠀⠀⠀⠀⣰⢋⠛⡚⣛⢳⣄⠀⠀⠀⠀⠘⠛⢼⠞⠃⠀⠀⠐⣿⣦⢹⡊⣿⡀⠀⠀⣠⣴⡖⠿⢩⣥⢉⡹⢻⡀
⠀⠀⠀⠈⠻⢜⡞⠀⠸⠈⠉⠳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⡹⣯⠀⠀⢴⠿⢢⠰⠎⣃⣨⣍⣵⣾⡇
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠴⠖⠒⢰⡎⢹⡶⣤⣀⠀⠀⠀⠀⠀⡼⣁⠟⣶⣿⡀⠀⠘⢻⠞⠛⠋⠙⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣶⠀⡘⠁⠸⡇⠙⣻⡄⠀⠀⠀⣾⠇⠹⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⠆⢰⠀⣈⡽⠁⠀⠀⣰⡦⠞⠠⣖⣸⡟⠀⣀⣶⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠒⠺⠃⠀⠀⠀⠸⣧⣄⣴⡾⠉⠀⣴⢿⣷⣬⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡴⣶⢾⡗⢲⢖⣶⢤⣤⡀⠀⠀⠀⠀⠈⢀⣀⡶⠝⠓⣬⣽⠉⠀⠀⢀⣴⠷⢶
⠀⠀⠀⠀⠀⠀⠀⠰⣟⢣⠖⣠⡄⠃⣤⠰⢚⠊⠰⣷⠶⠀⠀⣠⡴⣿⠟⠐⢟⣉⣿⠍⠀⠀⢀⡼⣫⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢻⣯⣬⣩⣤⢿⡬⠵⠾⠽⣧⠟⠀⠀⠐⢿⣰⢋⠀⣿⣨⠟⠃⠀⠀⠀⣸⡧⠡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⣴⣦⣦⣀⣀⢀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢨⣥⡹⠟⢿⠧⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣥⡐⠯⡄⠇⠞⠢⠏⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠗⢾⡧⡾⢤⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⢀⠄⠀⠀⡀
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⠀⠈
⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗
⠀⠀⠞⢀⡖⠁⠈⠉⢀⠀⠀⣀⠠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀
⠀⠀⠂⠈⠁⠀⠀⢀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠
⠀⠀⠀⠀⠄⢁⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣠⠆⠲⠒⢿⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠦⠠⢤⣀⠀⠀⠀⠈⠀⠀⣤⡀⠀⠀⠀⠀⠠⠆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣹⠁⠀⠀⠀⠀⠠⠊⠁⠐⠀⠀⠀⠀⠀⠐⠠⠓⣄⠀⠀⠀⠠⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⡀⠀⠈⡄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠀⢈⠀⠠⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢻⣄⣀⡀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠄⠃⠀⢀⠂⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⢀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠀⠀⠀⠀⠀⠃⠀⠄⠀⡱⠊⠀⠀⠀⠀⠐⠀⠀⢀⠀⡀⠀⡀⠤⠄
⠀⠀⠀⠀⠑⠀⠠⠙⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠠⠂⠈⢂⠤⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⣄⡀⠀⠀⠀⠐⠀⣀⢀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠐⠊⠈⡁⡠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⡂
⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠉⠀⠀⠓⠉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠙⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠐⢒⠒⠶⠶⠂⠀⠈⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠐⠦⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⡀⢀⣀⡀⣠⡤⢀⡤⣀⣀⡀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣀⠁⠠⠖⣋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉
⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣷⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢘⣿⣿⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠉⠉⠀⠈⠉⠉⠛⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⣾⣿⣷⠀⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠘⣿⣧⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠸⣿⡟⠋⢁⣀
⠀⠀⠀⠀⣠⣶⣾⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠉⠈⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⢿⣿⠇⠀⠀⠀⠻⣿⣅
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⣄⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠘⠛⠋⠉⢿⣧⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠙⠻⢿⣶⣾⣿⠋⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⣶⣾⣶⣄⠀⠀⠈⠻⣿⣦⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠉⢻⣿⣶⣄⠀⠉⠛⠿⠿⠿⠟⠛⠁⠀⠰⣿⣿⡇⠀⠀⣸⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⣿⣿⠿⠿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣠⣿⡿⠻⢿⣿⣷⣦⣄⣀⣀⡀⢀⣀⣠⣴⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⢀⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡇⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠺⠟
⠀⠀⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⡉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⡅⠀⠀⠙⣴⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⢿⠃⠀⠁⠴⢀⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠐⠀⠀⠀⠔⠄⠀⠀⠀⠒⠀⢻⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠁
⠀⠀⠀⣜⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢂⠤⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠠⠠⠀⠀⠀⠀⠀⠀⠰⡭⠂⠀⠾⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⣐⠲⣮⣈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⡀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢴⠀⠀⠁⣷
⠀⠀⠀⠐⢋⠾⠿⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢲⣀⡆⡲⠟
⠀⠀⠀⡞⠉⣿⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿
⠀⠀⠀⠙⡿⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢘⡓⣿
⠀⠀⠀⠘⣦⣠⣄⡅⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⣏⣏⡹
⠀⠀⠀⠀⠈⠀⠈⣇⢀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠻⣿⠇
⠀⠀⠀⠀⠐⠶⠿⢻⣿⠋⡄⠱⠀⠀⠀⠀⢁⣠⡴⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎
⠀⠀⠀⠀⠀⠤⣀⣤⠏⠄⠈⠀⠀⠀⠀⠀⠀⢃⣀⡼⠗⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢁⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠋⠰⠚⠉⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⣁⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠉⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠰⡄⠒⠒⠠⢤⠀⠀⠀⠀⠀⠀⠀⠐⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀⠀⢀
⠀⠀⠀⢀⠃⠀⠀⠰⠀⠰⠄⢰⠀⠀⠀⠀⠐⢀⠆⠈⠀⠀⠈⢡⠄⠀⠀⠀⠀⢠⢟⡶⡟⢷⡐⠽⡷⡀⠀⠀⠀⠀⠀⠐⠀⠄⠁⠈⠣⡘
⠀⠀⠀⢘⠀⡉⠀⠀⣀⠠⠄⠀⠇⠀⠀⠀⠀⠋⡐⠀⠄⠤⠀⡠⠀⠀⠀⠀⠀⢾⣳⣂⡝⠀⢠⡲⣠⣧⠀⠀⠀⠀⠀⠀⢰⣄⡬⠄⠒⢳
⠀⠀⠀⠘⣄⣁⠐⢀⡐⠀⠄⡛⠀⠀⠀⠀⠀⠁⠙⣀⣀⡄⠴⢄⠀⠀⠀⠀⠀⠈⢉⣾⣿⣯⢤⣇⣰⠏⠀⠀⠀⠀⠀⠀⢸⡧⣄⠈⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠰⠀⠅⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠜⠁⠀⣠⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⡿⠉⣤⠉⠙⢺⣣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⢀⣺⣿⣴⣤⡸⠂⢙⣋⠀⠀⢰⢁⡞⠀⠀⠀⢀⣰⣦⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠲⠀⠈⠉⡿⢿⣿⣵⡺⠾⠙⠁⠀⣆⣾⠀⠀⢀⠴⢛⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠃⠉⠁⠀⠀⠀⠀⠻⠋⠀⠀⠑⠒⠁⠀⠀⢶⡴⡦⣴⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢰⡷⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢶⢧⢠⡉⣽⣿⣏⡀
⠀⠀⠀⠀⠄⠒⡫⠟⠀⠀⠀⠉⠀⠀⠀⠀⠈⠹⢿⠄⠀⢸⣥⠄⠃⠀⠀⠀⠀⠀⠀⠘⠻⡆⢨⣤⠑⣻⣿⣥⠀⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⠈⠙⠉⣀⠀⠀⠀⠀⢰⢻⣧⠘⠛⢶⡤⣶⠛⠃⠀⠀⡜⣺⡏
⠀⠀⠀⠀⠀⢀⡿⠏⡈⣛⣿⡴⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣦⣿⣤⣶⢀⡀⠈⠫⠸⠇⠀⠀⠀⣀⡀⢀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣽⠠⡥⢻⣿⡗⠀⠀⠀⠀⣿⢻⠀⠀⣤⣟⠓⠋⠿⣿⢟⣿⠅⠀⠀⠀⠀⠀⠐⠿⠷⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠶⠎⠋⠉⠀⣄⣶⠄⡽⠠⠀⠀⠀⣷⡦⠙⠡⡶⠈⣾⡄⠀⡰⣶⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣤⣄⢀⣄⠀⠈⠚⠃⠀⠣⠜⠀⠀⠀⠉⠿⠓⣶⡖⠿⠀⠀⣰⣱⠃⠀⠀⠀⠀⠀⢉⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⠉⠀⠀⢠⡄⣤⣠⡄⠈⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⡤⢤⡄⠀⠀⠀⠀⠀⠛⢻⡇⠀⠀⠀⣤⣽⣍⣋⣿⣄⠀⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⣴⣿⣔⢃⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⠁⠆⠹⢠⡯⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣻⢿⡦⡴⠇⠀⠀⡰⠀⠀⠀⠺⡷⠄⠈⠀⠿⢶⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠙⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⣶⡄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⠄⡀
⠀⠀⠀⠀⠀⣴⡄⠉⠁⢀⡃⠂⠈⡋⢁⣶⡄⠀⠀⠀⠐⢀⢶⣦⣶⣶⡄⢂⠀⠀⠀⠀⠄⡢⠆⠔⠔⡠⡀⡀
⠀⠀⠀⠀⣀⠉⡁⠰⠷⣴⠇⣻⠃⣤⡤⡉⣡⡄⠀⠀⠠⠸⠿⣿⣽⣿⠇⡘⠀⠀⣐⠜⠁⠀⠘⠀⢃⠀⠑⢒⢀⠀⠀⠀⠀⠀⠀⣰⠎
⠀⠀⠀⠘⠟⠱⠸⠋⣴⣦⠘⠻⠃⣽⡄⢜⢙⡃⠀⠀⠀⠡⡈⠛⢛⠅⠒⠀⠀⢀⠾⠀⡃⠀⠃⡀⠈⠀⠂⠠⠦⠀⠀⠀⠀⢀⠰⠏
⠀⠀⠀⢰⣷⠁⠘⣛⢠⣦⠐⠿⢃⣬⢁⠀⠿⠇⠀⠀⠀⠀⠀⠁⠁⠀⡀⠀⠀⠀⡢⠀⠄⠼⠀⠀⢀⠀⡄⠠⢑⠀⠀⠀⠠⣮⠃
⠀⠀⠀⠀⢡⣴⠀⢅⠰⠷⠐⢿⠆⠅⠘⣿⠆⠀⠀⠀⠀⠀⠠⠐⠋⠉⠁⢢⠀⠀⠁⢣⢀⠂⠀⢁⠀⠰⠠⠁⠄⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠈⠉⠀⣴⣴⠁⣥⡁⠈⣷⡆⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠈⡁⢂⠠⡠⡘⠃⠉⠀⠀⠀⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠃⠀⠀⠀⢀⡠⠒⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠋⠠⠖⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⣠⣖⡭⣛⡤⠀⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠑⠅⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⡴⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡡⠟⣙⠋⣵⠃⠀⢀⡞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠴⠃⣀⡀⠠⢼⠜⠊⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡀⣀⣈⠫⠾⣋⢾⡛⠃⠁⠀⠀⡨⠇⣁⡘
⠀⠀⠀⠀⠀⠈⠀⠀⡠⠃⠀⢤⡑⠺⡑⡯⠀⠀⠀⠀⠀⡾⢗⣩⢉⣶⠾⠟⠉⠀⠀⠀⠀⡂⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠
⠀⠀⠀⠀⠀⠀⠔⠊⠀⠠⣹⡄⢾⠧⡈⠂⠀⠀⠀⠀⠐⢋⡘⢡⣤⠟⠀⠀⠀⠀⠀⠖⢀⠉⠈⡓⣁⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⠛⡦⣍⠂⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠦⠈⠳⠈⢈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠈⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡑⠲⣄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡀⠀⠀⠀⠀⠀⣤⠀⣀⢠⢘⠁⠀⠀⡀⠀⠀⢀⠤⠦⣄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣰⢱⡞⡧⣹⠀⠀⠀⠀⠀⢀⢔⠱⢇⡂⠓⢆⠈⠁⠀⠀⡌⢘⠐⠂⢱⠀⠀⠀⢰⣾⣦⣀⠀⠀⠀⠀⠀⠐⠲⡒⢦⡁
⠀⠀⠀⠀⠀⠀⠿⣈⢡⡦⣹⠀⠀⠀⠘⠃⢸⡀⠀⠋⢂⠕⡞⡀⠀⠀⠀⢷⠈⡀⠂⠀⡅⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢃⠞
⠀⠀⠀⠀⠀⠀⡷⠿⣤⢹⠏⠀⠀⠀⠀⠀⠀⠙⠢⠬⠥⠈⠀⠁⠀⠀⠀⠘⣆⠁⠐⠠⢇⠀⠀⠀⠁⠙⣿⣷⠀⠀⠀⠀⠀⢸⣻⣄⣀
⠀⠀⠀⠀⢀⡼⢰⡗⢫⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⡄⠂⢸⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⡆
⠀⠀⠀⠀⢸⣵⠆⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡁⠖⢉⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡾
⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢢⡀⠀⠀⠀⡐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠠⠀⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠱⠀⠃⠀⠀⠀⡇⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠔⠃
⠀⠀⠀⠁⢰⠓⢢⠀⠓⠀⠀⠀⠀⠀⠀⠰⠀⡂⠀⠀⠈⠳⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣠⠀⢸
⠀⠀⠘⡶⠋⠀⠀⠑⢄⡀⠀⠀⠀⠀⠔⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⠠⠀⠊⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣌⠀⠸⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠊⠀⠀⠀⠔⠀⠂⠀⠄⠀⠀⠄⢀⠀⠀⠀⠀⡃⢸⠀⠀⠀⠀⡁⠇⠀⠀⠀⠀⠀⢢⡼⢖⠣⠀⠀⠀⠠⠂⠂⠀⠄⠂
⠀⠰⠁⠀⠀⠀⠜⢀⠀⠀⠀⠀⠁⢸⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠇⢸⠃⠀⠀⠀⠀⠀⠀⠈
⠠⠤⠄⠀⠀⠀⢀⠈⠂⠴⠀⠀⠀⠘⠀⡀⠀⠀⠀⠤⠇⢰⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠤
⠈⠁⠐⠀⠀⠤⠠⠂⠀⠀⠁⠊⠀⠸⠀⠁⠀⠀⠀⢲⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠘⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣿⣟⣧⠀⠀⠀⠀⠀⠀⠎⠹⠄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡠⠦⡄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢴⣿⣶⣶⣶⡄⠘⣿⣯⣿⣟⣆⠀⠀⠀⠀⠀⢠⢉⠀⠀⠀⢀⡠⢞⡉⠉⢻⡇⠀⠀⠀⣤⢠⡄⢝⠫⠂⢀⣧⡴⠃⡔⠒⣮⣠⠕
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡀⠀⠸⣾⣏⣿⣻⡄⠀⠀⠀⠨⣁⡼⠀⢀⡴⢋⡄⢀⡀⠀⣼⠇⠀⠀⠀⢠⠤⡈⠁⠀⡠⢿⣤⠇⣀⡉⠉
⠀⠀⢠⣞⣿⣷⣤⡀⠀⠘⢿⣦⠀⠹⣾⢿⣟⣿⠀⠀⠀⠀⠉⢀⡴⡋⣰⡆⡄⠈⢃⡾⠁⠀⠀⠀⠀⢸⠶⣇⡖⠙⡷⠔⠁⢸⣿⣨⡦⢄
⠀⠀⠀⠛⢿⣿⣿⣿⣷⣄⠀⠀⣤⡄⠙⠛⠛⠁⠀⠀⠀⠀⢠⡞⢈⡑⠂⠶⣀⡴⠋⠀⠀⠀⠀⠀⠀⠘⢯⣻⡕⠊⠀⣀⡀⢎⡉⠈⠳⠴⠃
⠀⠀⠀⠀⠀⠉⠻⢷⣿⠟⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣈⣡⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣈⡇⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠘⠂⠀⠁⣤⣤⣦⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⢠⡮⠛⠁⠀⠀⣴⢫⡶⠶⠶⣭⡇⠀⠀⠀⠤⢀⣼⣉⣹⢷⣟⣿⡀⡀⠸⠿⠀⠀⠀⠀⢀⣤⣤⠀⡶⣿⣼⣏⣽⣟⠁⢠⣾⣷⡀
⠀⠀⠀⠀⠀⢀⡣⠃⠀⠀⠀⢀⡽⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣹⣿⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠉⠈⠉⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⢀⡤⠶⣚⣚⣛⣋⣭⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⠛⠻⠉⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣴⣮⣵⡄⠀⢠⡿⢻⣽⢶⣦
⠀⠀⠀⠀⡏⣾⠋⠉⣉⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡘⠁⠀⠘⠇⠀⠀⣶⣾⣷⣆⠠⠀⠀⠀⢠⣼⣿⣤⡿⢷⡀⠀⢻⣿⣿⡾⠉
⠀⠀⠀⠀⠻⣼⠆⠘⠯⣟⣒⣛⠭⠝⠛⠭⠟⠀⠀⠀⠀⠘⢷⣿⠗⠀⠀⠀⠀⠀⠈⢧⣿⣻⠿⢀⠀⠀⠀⠨⣽⣶⣏⢙⣿⡅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠀⠈⠘⠛⠻⠯⠁

⠀⠀⠀⠀⢠⠴⠒⠒⢦⠀⠀⣠⡶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⣠⣤⠀⠴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣄⡀
⠀⠀⠀⢠⡇⠀⠀⢀⡼⠀⢸⡏⠀⢠⠀⠀⠙⣷⡀⠀⠀⠀⢀⣿⡏⠀⠀⠈⠙⡛⠛⠃⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢿⡆
⠀⠀⠀⠘⡇⠀⠀⠸⡀⠀⠈⢻⡄⣤⠀⠀⠆⠘⣧⠀⠀⠀⠈⠛⣡⣶⣾⠿⠽⠟⢀⣴⡿⠋⠀⠀⠀⢀⣠⢴⡶⣶⣦⣤⣀⠈⠙⠋⠋
⠀⠀⠀⠀⠙⠦⠬⠴⠃⠀⣰⠟⢀⠀⠠⠀⠀⠀⣿⠀⠀⠀⠰⣿⠞⣩⣤⣤⣶⡾⠟⡋⠀⠀⠀⠀⠀⣾⣧⣝⣟⣿⣿⢿⣽⡿⣦⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⡀⠀⣀⣠⠀⢸⡇⠀⠀⠀⢀⣄⣀⠉⠉⠉⠀⠀⠘⠛⠻⠟⠀⠀⠀⠹⣯⣿⣿⣳⣾⣾⣿⣻⣿⣧⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠈⠐⠆⠀⠀⣠⡟⠀⠀⠀⠀⠻⠾⣼⣟⡖⣶⢶⢶⢲⣶⣲⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⡿⡿⠿⠊⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠨⠃⠀⠀⠐⠉⠅⣀⠀⠀⠀⠀⠀⢀⠁⠐⠆⠀⠂⢄⠀⠀⠀⠐⢄⠈⠒⠘⢂⠔⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢀⠀⠑⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠊⠄⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠊⠁⠈⠉⠶⡀
⠀⠀⠀⠀⠀⠀⠂⢀⣀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠉⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠘⠃⠚⣊⠁⢺⠀⠑⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡆⠈⠑⢄⠀⠀⠀⠀⠠⠀⠚⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⢄⡐⠩⡠⠀⠀⠱⡀⠀⠀⠀⠋⠘
⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠞⠁⠀⣄⠀⠑⡄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⡀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⢠⠀⠉
⢦⡀⠀⠈⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠨⢀⠀⠀⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠐⠁
⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡅⠆⠀⠐⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠐⡥⠆⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠂⠈⠐
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠁⠀⠀⠰⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢠
⠀⠀⠀⠀⠀⠈⠒⠳⠀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠈⠀⢀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡄⠀⠐⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⡠⠒⠀⡈⢤⡀⠀⠀⡠⠂⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⠔⠊⠀⠀⠀⡴⠉⡠⢦⠄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢧⠀⡇⢌⠀⠀⠀⠀⠈⠈⠐⢉⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠
⠀⠸⠅⢌⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠑⠄
⠀⠒⠈⠉⠀⠁⢀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡈⠀⡀⠂⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠆⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠀⡀⠀⠈⠁⠐⠀⣀⠔

⠠⠀⠂⠐⠠⠀⡀⠀⡔⠂⠒⠠⢀⠀⠀⠠⠠⠤⢀⠀⠀⢀⠤⠠⢄⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡀⠒⢠
⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠀⠄⡀⠀⣀⠠⢄⠀⠠⠃⠀⣬⠀⠀⢀⡃⠀⠀⠋⠀⠀⠀⠠⠀⠀⠀⠃⠃
⠐⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⠐⠊⠀⠀⠀⠠⡀⢀⡀⠃⠀⠀⠀⠘⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⢀⠂⠃⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠗
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠈⠐⣄⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠐⠀⠢⠀⠀⠀⡀⢱⠀⢀⠘⠆⠀⠀⠂
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠘⠀⢰⠀⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠠⠀⠀⠁⠁⠀⠀⠈⠀⠠⠤⠒⠃⠀⠀⠐⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⡤⣴⣶⠿⢿⣶⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠂⠠⠀⢠⡞⡟⡀⠀⠂⠌⢦⢰⠭⠝⣷⣬⣿⠿⣇
⠀⠀⠀⠀⠀⠀⢀⠀⠘⣀⠰⠀⠄⠀⢸⣧⣠⡷⢶⡶⠶⡖⢺⢛⣻⡋⠉⠙⢠⣿⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠘⣇⢈⠇⢠⠁⡻⠻⡞⣇⠰⠷⢈⣃⣸⡿⠀⠀⠀⠀⠀⠀⡀
⢨⠀⠀⠀⠇⠀⠀⠂⣀⠐⠀⠀⠄⠀⠀⠈⠓⠒⠞⠛⠛⠛⠛⠛⠛⠟⠛⠛⠋⠀⠀⠀⠂
⠀⠑⠂⠊⢀⢀⠀⠠⠀⢘⠉⠆⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠭⠸⠂⠛⠂
⢀⣀⠂⡌⠀⠀⠈⡄⠐⠀⠀⠀⠀⠁⠀⠀⡀⢀⠀⠀⠀⢠⠋⢠⠀⠀⠀⠀⠂⠀⣀⣀⡀
⠀⠀⠀⠣⣀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠅⠀⠀⠀⠈⠁⠀⠰⠈⢶⡲⣽⡇⠿⠈
⠀⠀⠂⢀⠀⠀⣀⠄⡀⡀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈
⡀⠈⠨⠀⠂⠀⠂⠀⠁⢀⡄⠀⠀⢀⠤⠄⢄⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⠊⡡⠤⠄⠊⠀⠠⠂⠀⠠⠁⠀⠀⠀⠀⠀⠡⠀⡀⡈
⠈⠂⠍⠀⠠⠠⠂⠂⠀⠁⠀⠑⠈⠀⠀⠀⠈⠤⠀⠂⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⣿⡿⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠖
⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠘⠀⠀⠈⣡
⠀⢀⠇⡠⠂⠐⠂⠀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠃⠀⠀⡠⠁⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢀⠀⠀⠘⠀⢀⡄⠀⠉
⠀⠀⠀⠆⠠⠈⠀⠎⠀⠀⠀⠀⠀⢀⡴⠚⠚⢻⡁⠀⠀⠀⠀⠀⡠⠄⠀⠐⠒⠂⠤⢀⠀⠀⠈⠀⠢⠄⣈⡀⠀⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠸⠁⠀⠀⠀⣠⠁⠀⠁⠀⠠⠀⠀⠀⠈⠳⡀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⡤⠊⠀⠀⠀⠀⢀⠁⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠀⣀⠀⡀⠀⠀⠀⠀⣿⣀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠀⡄⠀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠄⠀⡀⠲⠀⠀⢠⠀⠀⠀⠸⠀⠀⠀⠁⢠
⠀⠀⠀⢄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⢀⠀⠀⠀⡁⠐⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢒⠁⠐⠦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠠⠀⠀⠡⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠄⢠⠈⠀⠁⡀⢀⠀⠄⠀⠀⠀⠀⠠⠐⠂⠀⠐⠀⡀⠀⠀⠀⠐⠈⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠱⢂⠀⠈⠀⠀⠈⠀⠀⢠⠓⡀⠀⠀⣐⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠀⠘⠚⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⡀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠍⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠉⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢨⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠠⠴⣊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⡄⠀⠀⣀
⠀⡀⠀⠂⠀⠰⠄⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠉⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠙⠄⠀⠀⠀⠀⠀⠀⠐⠁⠤⠀⠀⠀⠀⠀⢰⢯⠃⠀⠀⠀⠀⠀⢣⣍⣷⣌⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠊
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠰⢈⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⡾⠀⠀⠀⠀⠀⠈⠲⠖⠂⣥
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠃
⠀⢀⡤⠆⠀⠀⢀⠀⡀⠀⠀⠙⠂⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣰⡟⠶⣄
⠀⠀⠀⠀⠃⠀⡏⠀⠁⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣦⣴⣴⡦⠀⠀⠀⢠⡿⠀⠤⠿⠀⠀⠀⠀⢀⠠⠴⣄
⠀⠀⢤⣠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⡇⠀⣽⢱⠀⠀⠀⡔⣂⠠⣺⡿
⠀⠀⠀⠈⠁⠚⠙⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠛⠿⣿⣿⡿⠛⠁⠀⠀⠀⠳⠘⠃⠁⠀⠀⢧⡴⣂⣵⠿⠃
⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢠⢤⠀⠉⠈⠉⠙⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⣐⡤
⠀⠀⢨⠸⡀⠀⣀⠀⠀⠀⠀⠈⠁⠀⢐⣒⠀⠀⠀⠀⠀⣀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⢸⣕⣼⡧⣻⠇⢡⡄
⢀⡠⢨⣄⣧⡜⡠⠁⠀⠀⠀⠀⠀⢰⢻⠉⡗⠀⠀⠀⠀⠈⠛⠀⠙⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⣏⡻⢿⡿⠿⡏⠓⣬⢬⣷
⠈⠧⢤⠿⡟⢯⣷⡑⢦⡀⠀⠀⠀⠋⣇⣼⠁⠀⠀⠀⠀⠀⠒⣔⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢒⡥⢨⠿⣿⠗⠱⡤⢺⠍
⠀⠀⠀⠀⠹⣤⢇⡽⢦⠏⠀⠀⠀⠰⣽⢿⡄⠀⠀⠀⠀⠀⠀⡜⠂⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⢤⣀⠘⣂⣘⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠙⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡖⠚⠈⠄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠐⠀⡈⢠⠀⠁⠠⠠⣤⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢀⡠⠰⠁
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡃⠠⢀⠀⠉⠀⠀⠠⡇⣴⣇⡍⢀⠀⠀⠀⠀⠀⠐⢦⠞⢈⣑⠁
⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⠀⠐⠀⠈⠀⠍⠉⠐⠋⠰⠁⠀⡁⠀⠀⠀⠀⠀⠀⠜⠛⠂⡿⣿⠉⠑⠤
⠀⠐⢠⢤⡀⠀⠠⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠐⠀⠂⢰⡂⠀⠂⢀⣠⢈⡀⠄⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡈
⠀⠀⠀⠀⠰⠒⢠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⠀⢠⡶⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣷⡤⠿⠶⠿⣤⣴⠏⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢳⣴⢟⡵⠖⠛⠛⠓⠶⣍⠳⣏⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⣿⢟⡵⠋⢛⣠⣤⣄⡀⢳⠈⢳⡜⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⣽⢟⡵⠋⠀⠀⣾⠁⠀⠈⣷⠀⠀⠀⣷⢸⡗⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣽⢟⡵⠋⠀⠀⠀⠀⠙⣦⣤⡴⠏⠀⠀⢀⡿⣸⠷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣼⢟⡵⠋⠀⡴⠀⠀⠀⢠⡟⠉⢻⡄⠀⠶⣦⢞⣵⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠁⣠⢞⣵⠿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠳⢶⡏⣾⠁⣴⠖⠶⣄⠀⠀⣀⠀⠀⠀⠀⣠⢞⣵⠟⢻⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠰⣤⢼⡇⣿⠀⢧⣀⣀⡿⠀⠀⠉⠁⠀⣠⢞⣵⠟⠙⢦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡘⣧⡀⢉⡉⠀⠀⠀⠀⣠⢞⣵⡟⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⣹⣮⡛⠾⣧⣤⣤⡴⢞⣵⣿⡉⠳⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣰⠟⠓⣶⠶⣶⠞⢿⡁⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠾⠃⠀⠿⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡤⡄⠀⠀⢠⣶⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⡀⢀⣤⠀⡀⠀⠀⠄⢐⠠⠄
⠀⠀⠀⡄⠈⢁⠀⠀⠀⢸⡎⠀⠀⣶⠀⠀⠀⢀⠀⢁⣄⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡙⠀⠁⠉⢁⡀⠀⠆⢿⠗⠂⠀⠀⠠⠋⡀⡓
⠀⠀⠀⠠⢈⡀⠐⠀⠀⠸⣿⣄⠀⠏⠀⠀⢠⡂⢰⣿⠏⠀⠀⠈⠛⠶⢶⣤⡀⠠⠺⣆⠀⠀⠀⣠⢠⠄⡠⡌⠁⠀⠀⢿⡿⠒⠀⠀⠀⢀⣃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠁⠉⠁⠐⠀⠀⠃
⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣼⡷⠶⠿⠟⡀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⠰⡐⠁⠀⢠⠴⠂⡄⠀⠀⠀⣘⣿⢿⠀⠀⠀⣠⠄⠀⠀⠠⠄⠀⠧⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢂⠠⢀⠀⡀⠀⢈⡀⠀⠀⡠⠠⠡⣼⡇⣒⠀⠀⣀⠻⠛⠁⠀⠀⠀⠀⠂⠸⠂⠀⠐⠀⠀⢠⣄⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⣞⠇⠀⠀⠂⠈⠁⠢⠊⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢁⠅⢠⠋⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⡄⢴⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⢀⣠⠤⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠆⣠⠀⠀⠠⣠⣄⠂
⠀⠀⠀⢼⢡⠁⠄⠛⡀⠀⠀⣱⣿⣦⢝⣤⡀⠀⢸⣧⣀⣾⠀⠀⡞⠹⡅⢦⠀⠀⠀⠀⢀⠀⠀⠤⠁⠀⣀⠐⣊⠀⠀⠔⣶⡀⠀⠀⣀⠀⠠
⠀⠀⠀⠖⢞⠀⣈⠅⠉⠀⠠⠹⣿⠁⠿⠾⠁⠀⢼⣷⠿⠋⠀⠀⠁⠭⠖⠂⠀⠀⠀⠀⠀⠀⠀⠉⡥⢁⡏⡔⠂⠀⠀⣖⣼⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠋⠚⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠈⠁

⠀⠀⠀⡆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⡖⠂⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲
⠀⠀⠈⡏⠉⡍⢁⠀⠀⢤⠀⠀⠀⠀⠀⣶⠾⠰⠆⡇⠶⠰⠰⢲⡆⠀⠀⠀⠀⠀⠈⡏⢉⠍⢅⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⡠⠀⠸⣀
⠀⠀⠀⡇⠸⣶⡶⠂⠀⠀⡀⠀⠀⠀⠀⣿⠘⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡇⠸⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣀⣀⣀⡇
⠀⠀⢠⣧⣤⣤⣤⡄⢾⡿⡧⠀⠀⠀⠀⠿⠚⠛⠒⠛⠓⠚⠛⠺⠇⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢰⠏⠁⠉⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡇⡉⠈⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⡄⠉⢢⡀
⠀⠀⠀⠀⠀⣸⣦⣄⣤⠟⠀⠀⠀⠀⠀⣏⠀⠀⢠⠦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⣶⡇⣆⣀⡇⠀⠀⠀⠀⠀⠀⢼⠐⠳⠌⠁⠻⠇⡇
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠈⠀⠒⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣄⠺⠆⠸⠗⣠⠃
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣠⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣦⣤⢛⠁
⠀⠀⠀⢠⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⡋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠐⠢⠬⢿⣿⠧⠄⠆
⠀⠀⠠⡜⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣽⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⢡⡉



⠀⠀⠀⢀⣔⠉⠟⠟⣑⡄⠀⠀⠀⠀⠀⠀⡀⠀⡭⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠉⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⠀⠁⠉⣄⠀⠈⠦⣐⣂⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣁⣀⣀⡀⢠⣤⣴⡀⠀⠀⠀⠀⠀⠀⠚⠀⠈⣄⢀⠨⠄⡀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠂
⠀⠀⠈⠻⠿⠛⠀⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢴⠒⡀⢀⣀⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡄⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠊⠉⠑⠢⣀
⠀⠀⠀⠀⣎⠑⡄⢠⠂⠉⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡏⠀⠀⠀⠀⠀⢹⡖
⠀⠀⠀⠀⠈⠉⢸⠁⠀⠀⠀⠀⠀⠀⠀⠐⡴⠭⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣗
⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠈⠒⠊⠙⡄⠀⠀⠀⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢀⡨⡢⠄⠀⢀⣀⠄⠊⠈⠂⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⣠⠮⡀
⠀⠀⠀⠀⠀⠰⣁⣀⠇⠀⠀⠀⠕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⡀⠠⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⢄⣀⣀⡠⠴⡊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠄⠼⠀⠧⠢⢄⡞⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣩⣃⡀⢀⡔⢢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠁⠀⠁⠆⡀
⠀⠀⠀⡔⠤⠏⠀⠀⣀⠀⠀⡤⢄⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄⡰⠊⠀⠉⠉⠉⢴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠙⣱⠀⠀⠘⠊⠀⠀⠈⠉⠀⠀⠈⣉⢹⠀⠀⠀⠀⠀⠀⠀⠘⢤⡛⠠⠒⠄⡐⠀⠂⠸⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⢰⡁⠨⠥⠀⠀⠀⠀⠀⠀⠀⡠⢤⠱⡀⠀⠀⠀⠀⠀⡖⢲⡠⠊⠀⠀⠉⠀⠢⠔⡡⠛⠋⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡤⢗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠜⠀⣑⣹⠀⠀⠀⠀⢨⠇⠊⢈⢂⠊⢀⠀⡴⠢⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⠒
⠀⠀⠀⠈⠋⢝⠀⠀⢀⠸⣈⠽⠀⠀⣠⠤⠞⠀⠁⠀⠀⠀⠀⣸⠀⠢⠌⢨⡠⢂⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⢑⡄⣧⠱⣄⣀⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠸⣥⠖⠶⠶⡆⢖⠁⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠪⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠖⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡇⢸⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡴⠋⠀⢸⢸⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⡇⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣸⠁⠀⠀⢸⠘⢚⡥⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢸⠀⡇⡇⢸⠀⠀⠀⢀⢇⡀⠀⠀⣿⡀⢠⡀⠀⢣⠀⠀⠀⢹⠀⠀⢹⢀⣀⠀⠸⠚⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⡇⢸⢸⠀⡇⡇⢸⠀⠀⠀⢸⢸⠁⠀⢠⡧⡵⣌⡏⢶⢬⣇⠀⢸⠈⡇⠀⠀⡏⠉⡇⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⣀⣧⣸⣇⣇⣸⣸⣀⣇⣇⣸⣀⠀⠀⢸⢸⠀⠀⡾⠰⠀⠈⠉⠀⠆⢹⠀⢸⠀⡇⠀⣠⠕⠸⢵⡒⠒⠚⠉⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡆⢸⡇⠀⠀⠠⠄⠀⠀⢸⡆⢸⢀⡇⠀⠛⠚⠒⠚⠃⠀⢀⣀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠳⡙⣾⠙⢤⡀⠻⠟⢀⡴⢋⡹⣼⡞⠀⠀⠀⠀⠀⠀⠀⢀⡷⠾⢤⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⠸⠬⢷⠀⠀⠀⠀⠀⠈⠳⠞⢦⡏⠑⠊⢹⡤⠚⠓⠙⠀⠀⠀⠀⠀⠀⢠⢴⡏⠀⠀⠀⠹⡽
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡇⢐⣒⣒⡂⢸⠀⠀⠀⠀⠀⣀⣠⡴⢻⠁⠀⠀⣈⣟⠦⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠈⠙⡇⠈⠭⠭⠅⢸⠀⠀⡰⠋⠉⠁⢼⠀⡏⠀⠀⠈⠀⢸⠀⣹⠈⠉⠓⣄⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⣤⡤⢤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠷⠶⢶⠶⠖⠚⠀⠀⡇⠀⠀⢀⡜⠁⡗⠒⠒⠒⠒⢻⠈⢣⡀⠀⠀⢸⠀⠀⠀⡷⠒⠒⠒⠒⠒⠒⠛⠓⠲⡇
⠀⠀⠀⠀⢠⠜⠃⠀⣄⢸⢀⡄⠀⠸⢤⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡏⠀⡘⠀⠀⠀⠘⡃⠀⠀⡇⠀⠀⠠⡏⠉⡆⠀⠀⠀⡇
⠀⠀⠀⠀⢏⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡇⠀⠀⡼⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⢠⠃⣰⠃⠀⡆⠀⠀⡇⠀⠀⡇⠀⣀⣀⣉⣉⣓⣀⡀⠀⡇
⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⢧⠈⡇⠀⠀⡼⢠⠏⠀⠀⡗⠀⠀⢻⠀⠀⡇⠀⠭⠭⠭⠭⠭⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠘⡆⢻⠀⢰⠇⡞⠀⠀⢰⡇⠀⠀⢸⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡀⣸⡀⣀⣀⣸⣸⣆⣜⣼⢀⣀⣀⣸⡀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡇⠉⠈⠁⠉⠉⠈⠁⠉⠁⠁⠉⠁⠉⠉⠉⠉⢹⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠯⠥⢜⣦⣠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣿⡹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣶⠟⠁⠀⠀⢀⡧⣙⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠤⠤⠤⠴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠑⠠⠑⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠠⠀⢐⠀⠂⠀⡠⠀⠁⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠰⢁⠠⠀⠀⠂⠀⢀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠂⠈⠁⠀⡇⠨⠭⠍⠀⠀⠂⠀⠀⠀⠂⠈⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠊⢁⠁⡀⠀⢀⡈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠤⠤⠄⢘⠃⠀⠘⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠈⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠤⠠⠤⠀⠠⠄⠤⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠊⠀⠒⠀⠘⠀⠒⠂⠀⠀⠀⡆⠙⠑⢄⠀⠀⠀⠀⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⢀⡀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⡀⡠⠠⡀⠀⢈⡁⡀⣉⡄⡄⡄⠀⠀⠀⠄⠃⠣⠜⡠⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⡀⠁⡀⠀⠀⠀⠁⠀⠁⠄⠀⢠⡀⠄⠀⠀⠑⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠅⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠒⠒⠁⣇⠈⠀⠀⠀⠀⠀⡀⠀⠑⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠏⠉⢀⣀⡤⢤⠶⠤⢤⣄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠖⣋⠥⠚⠈⠁⠁⠈⠘⠛⠶⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠞⡥⠋⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⣇⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠁⠀⢲⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠃⠀⢄⠿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⣂⣠⠔⠋⠀⡠⣪⠛⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠁⠀⠀⢄⡮⠞⠉⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣠⠞⣳⠲⠤⣤⣀⣀⣀⣀⣤⠤⠔⢚⠉⢁⡸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠂⠀⢀⡠⢺⢀⠖⠉⠑⠲⠤⢦⣼⣄⣥⣰⡤⠦⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠊⠀⢀⡴⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⢋⣠⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⡔⢃⡤⠊⠁
⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⢁⡴⠋
⠀⢀⡴⣉⠀⠀⣠⠞⢁⡴⠋
⠀⢸⠀⠀⠙⡎⣡⠞⠁
⠀⠀⠓⢧⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠢⠀⡀⠀⠀⠀⢀⠇⠈⣆⠀⠀⠀⢀⠀⠔⠈⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣡⠴⠖⠚⠩⠋⠀⠀⠈⠫⠓⠲⠦⣌⡀⠀⠀⠀⠀⠀⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⡀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢄⠀⠀⠀⠈⠳⡀⠀⠀⡠
⠀⠀⠀⠀⠀⡠⠀⠌⣀⡞⠀⠀⠀⠀⢀⠔⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡆⠀⠀⠀⠀⢹⡄⡈⠤⠠⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡴⠃⠀⠀⠀⠀⠀⢧
⠀⠀⡀⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⢣⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⡠
⠀⡆⠘⠐⢒⣒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠅⠈⠅⡀⠸
⠀⠡⠌⠉⠀⠀⠈⠁⣦⢄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠘⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠤⠀⠠⠀⣳⡀⠀⠀⠀⠘⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡘⠀⠀⠀⠀⡼⣑⠠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠳⣄⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠀⠀⠀⢠⡞⠁⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡠⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠐⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⠌⠝⠒⠲⠷⣄⠀⢀⡴⠥⠴⠒⠻⠡⡀⠀⠀⠀⠀⠀⢰⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠘⡄⡜⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⢲⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣧⣀⣼⣭⣯⣭⣭⣯⣽⣭⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣿⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡈⠙⠲⢤⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠋⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢿⠀⠢⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠉⡒⠤⣄⣀⣰⠙⢟⠢⡀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠈⢀⡼⠃⠀⠈⢧⠙⢆⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⢤⣀⡴⠋⠀⠀⠀⠀⠈⡆⠈⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡒⠒⠒⠒⠒⠒⡄⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣲⣒⣶⣒⣖⣲⠇⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣀⣀⣀⣠⠎⠀⠀⠀⠀⣠⠃⢀⠇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⢺⠁⠀⠀⠀⠀⡗⠒⢒⡲⠖⠁⡠⠋⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢉⣁⣠⠴⠊⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠭⠟⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠷⠶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠽⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠐⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡏⠻⠽⠿⢷⡄⠀⠀⠀⠊⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠸⠆⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣗⣜⢃⡚⣜⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠠⠈⠘⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣷⣼⡿⠃⠀⠀⠂⠀⠀⠀⠀⢄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠄
⠀⢀⣞⣷⢾⣿⣿⣷⣟⡦⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⢄
⠀⠈⡼⣿⣽⣿⣿⣿⣯⡶⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡄⠀⠀⠀⠘
⠀⠀⠘⢻⢿⣿⣻⢿⡑⠃⠀⠀⠀⠀⠤⠤⠖⠒⠒⠒⠒⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⢀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠆⠠⢄⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠸⣗⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡆
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⡷⡂⠀⠀⠀⢀⣻⡭⠀⠀⠀⠰⣤⣀⡀⡀⠀⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣤⢀⢐⢎⠟⠃⠀⠀⠀⠀⠈⠉⠛⠛⠶⠾⠾⠿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁

⠀⡀⢠⠀⠄⡀⠀⠀⢀⠤⠤⢀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⠂⠀⠀⠐⠡⠀⠡⠤⠠⣀⠈⠁⠈⢀⡀⠀⢈⠂⠀⡚⠀⠀⠱⠆⠀⠀⠂⠀⠀⠁⠄⠀⠈⡰⠐⠅⠈
⠀⠄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠁⠀⡀⢈⠀⠀⠀⠁⠦⠤⠘⠀⠀⠘⠀⠀⠀⢠⠆⠀⠀⠀⢶⠀⠐
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⢀⠤⠂⠄⠀⠈⠁⠉⠀⠀⠀⠂⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠈⠀⠸⢠⠤⠃⢠⡀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⡆⠀⠈⠣⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠂⢠⠞⠀⠱⠀⡏
⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠠⠠⠀⠀⠀⠁⠀⠀⠁⠀⠄⠤⠖⠁⠀⠀⡄⠀⠈⠋
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⣶⠾⢶⣦⣄⠀⠀⠁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠁⣀⣀⠂⠠⠀⢀⡾⡟⡄⠀⠢⡌⢆⢢⠭⠙⣦⣬⡿⢿⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢣⡨⠁⠠⠀⢸⣧⣠⡷⣶⡶⠾⡖⢺⢛⣻⠩⢉⠃⣈⣇
⠀⠠⠤⠤⡀⠀⠀⠀⠐⠀⠄⠀⠂⠀⠘⣧⢊⠇⢠⠁⡻⢻⡞⣆⠲⢃⢈⣀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⡅⠀⠀⡀⠀⠀⠐⢀⠐⠀⠀⠤⠀⠀⠈⠑⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⢄⠔⠂
⠀⠈⠂⠈⡁⠀⢀⠀⠀⠸⣉⡕⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡮⠞⠚⠃
⠀⢁⠐⠐⠀⠀⠀⠁⠀⠀⠄⠐⠀⠀⠀⠀⡠⠤⠀⠀⠀⠰⠉⡡⠀⠀⠀⠚⠉⣀⢠⡠⡀⠠
⠀⠀⠀⠘⠄⣀⠠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠣⠠⠂⠀⠀⠀⠀⠀⠀⠐⢙⡯⣧⠿⠂⠇⠁⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠄⡀⡀⠐⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠠⠐⠄⠒⠚⠐⠀⠀⠂⠪⡄⠀⠀⡠⠔⠒⢢⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⢀⡒⠀⠀⢐⠀⠀⠁⠀⢀
⠀⠀⢄⡀⠀⠀⠀⠀⡀⠀⠁⢠⢊⠤⠐⠒⢁⠠⠐⠁⣀⠔⠀⠀⠀⠀⠀⠀⠲⢀⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠄⠄⠂⠊⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣣⣤⣶⣶⣶⣶⣶⣶⣤⣄⡸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣦⣤⣀⠀⠀⢀⣤⣾⣿⡿⠟⠛⠋⠉⠉⠙⠛⠻⢿⣿⣶⣄⠀⠀⢀⣴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⢇⣴⣿⡿⠟⠁⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠙⢿⣿⣆⢴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣷⣶⣤⡀⢀⣠⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣋⣵⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⣿⡏⣶⣦⣴⡶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⢿⡿⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⢀⣾⣿⡿⣡⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⢲⣿⣿⠀⠀⠀⣠⣶⣿⣷⣦⠀⠀⠀⣴⣶⡄⠀⠀⠈⠉⠀⠀⠀⣰⣿⣿⠋⠀⠈⠉⠙⠋⠉⠛⠻⣦
⠀⠀⠀⠐⠶⢤⣤⣴⣾⠿⠛⠋⠉⢸⣿⡇⠀⠀⠰⣿⣿⣿⣿⣿⡇⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⣰⣿⡿⣱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠙⢿⣿⡿⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠱⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⢀⣼⣿⡿⠁⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢋⣄⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣝⠿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⣿⡿⠛⠁⠙⢿⣆⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠈⠙⠛⠿⠿⢿⣿⣿⣿⠿⠿⡛⠋⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⣋⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡿⢧⣀⠀⠀⠀⢿⠹⡇⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣠⡖⠏⡑⢯⣀⡞⢉⣷⡄⢀⠞⢿⣾⡀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⢀⣼⠯⡂⠁⠀⠀⠙⢦⡞⠀⠿⠈⢢⢻⡇⢱⠀⠀⠠⡞⠒⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣛⢿⣦⣄
⠀⠀⠀⢠⠟⡂⠅⠀⠀⠀⠀⠀⠈⢛⡀⠁⣠⣚⣚⡏⠉⠀⠀⠀⢇⠀⣠⣇⣶⣴⣷⣿⠁⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣦⡀
⠀⠀⢀⡿⢑⠂⠀⠀⠀⠀⠀⣄⢲⢹⠃⡔⠋⠀⠀⡇⠀⠀⠀⠀⣀⣧⠉⣻⢿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⣿⣻⡽⣿⣦
⠀⠀⢸⠯⠐⠀⠀⠀⠀⡞⡧⠛⠄⠁⠀⡇⠀⠀⠀⠃⠀⣠⣴⠟⣽⣼⢊⡴⣩⠛⠢⣀⠀⠀⠀⠀⠀⣠⡾⢿⣛⠽⠗⠋⠉⠁⠨⡲⢕
⠀⠀⢸⠭⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠀⠰⠖⣩⣿⣿⢠⡿⠀⣫⢖⡁⠜⢴⣚⣦⣠⢴⣲⠿⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠨⡑
⠀⠀⢸⡅⠀⠀⠀⢸⠦⠽⢧⠀⠀⠀⠀⢣⢀⣠⣴⣿⣿⣿⡇⢸⡵⠊⣀⡼⠀⠀⠚⢿⣿⡏⠉⠀⠀⠀⠀⠀⢀⣴⣿⢿⣶⣄
⠀⠀⢈⡧⠖⣒⣶⣬⣯⣉⣚⣷⠀⠀⠀⠘⢿⣿⠿⠟⣿⣿⣧⢊⡤⠊⠁⠀⠀⠀⠀⠀⢻⣷⠒⠒⢶⠒⠒⡞⡿⡈⠁⡀⠙⢮⠇
⠀⠀⡞⢸⣿⣿⡿⣿⢿⣿⣄⣽⣇⣀⣀⣀⠀⠀⠀⠀⣸⣿⠱⠋⠀⠀⠀⠀⢠⣆⠀⠀⣸⣸⠀⠀⠀⠀⠀⣇⣱⠣⡀⢉⣰⠞⢦⡀
⠀⠀⢣⡼⠟⢁⡀⠉⣸⡇⢣⠀⠀⠠⠞⠛⠳⣤⠞⣶⣿⡇⠀⠀⠀⠀⠀⢰⠁⣸⠀⡠⣿⣿⠀⠀⠀⠀⣷⠀⠈⣳⠋⢋⣡⣰⣴⣽⣄
⠀⣴⣿⣟⢳⣌⢀⣠⣿⢃⢸⠀⠀⠀⠀⠀⡾⠓⠚⠉⠉⣇⣀⣀⣤⠔⠒⠉⠉⢀⣠⡿⣟⣽⢶⣒⠒⠒⢿⠀⡴⠃⣠⡎⠳⣄⣀⣀⣀
⣼⣿⣿⡟⠛⢻⣿⣿⣻⠏⠛⠇⠐⡄⠀⠀⢹⠀⠀⢦⣤⡟⠀⣢⢰⠀⣠⣾⢿⡻⠕⠊⣿⣟⣩⡖⠒⢲⣾⠟⢀⣼⣻⠁⠀⣾⣿⡛⠛
⣿⣿⠏⠉⣿⠾⣿⣿⣿⠀⠀⠀⠀⢳⡀⠀⠈⡆⠀⠀⠛⠛⣿⣿⣿⣦⣷⣾⡇⠀⠀⠀⢿⣿⡝⡇⠀⢸⠁⣠⣾⣏⡇⠀⣸⣿⡦⡝⢦
⠸⣿⠀⢸⣿⣷⡼⣿⣿⡆⠀⠀⢀⣿⣿⣋⣥⣷⠖⣶⣶⣿⣿⣿⡿⠿⠛⠓⢻⠀⠀⣠⣿⣿⣷⡁⠀⣸⠾⠛⠋⡽⠀⢠⣿⣗⠭⠂
⠀⢿⠀⠘⣿⣿⣧⣦⣿⣧⣀⡤⠾⠛⠋⠉⠀⡟⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣀⣰⡿⠿⠛⠋⣇⠀⠙⢦⣄⠰⣇⠀⣼⣿⡪⠕⠀⢸
⠀⠘⣷⡶⠿⠿⢷⡿⣿⣉⣹⣀⣠⣤⣴⣶⣿⢟⣶⣷⠤⣄⣀⣀⣀⣀⣀⣀⡸⠏⠀⠑⢄⡀⠀⠈⠙⠛⢿⡿⠀⢳⣝⣿⡳⢮⣀⠀⣿
⠀⢠⣿⣁⣀⣀⣸⣄⣀⣀⣈⣉⣿⣿⣯⣽⣾⣿⣸⣿⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣙⣦⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣷⣭⣻⣿
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⣀⡀
⠀⡀⠀⠀⠀⠊⢸⣆⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢰⣇⠀⠀⠀⣼⡟⣿⠄⠀⠀⠀⠿⡔⠀⠀⠀⠀⢀⢐⣶⣿⡇
⠈⣿⣦⣴⣴⣄⣀⡀⠀⠀⠀⠀⢋⢻⣠⣀⣀⣠⡎⡈⣻⡾
⠀⠈⠈⠚⠟⠋⠉⠀⠀⠀⠀⠀⠀⠙⠽⡿⣧⣩⣿⢷⣛⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠂

⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠡
⠀⠀⠐⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠄⠤⠤⠤⠄⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣈⣥⠄⠖⠚⡘⣡⠷⢯⠋⡘⠰⢲⢂⠬⡍⣁⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣡⠄⢞⢀⠂⠊⠈⠀⢠⠃⠀⢈⡆⠀⠁⠀⠈⠈⠀⠀⠘⠙⠲⢍⡒⢄⡀
⠀⠀⠀⠀⠀⠀⡠⠊⣠⠎⢀⠢⠀⠀⠀⠀⠀⠀⠙⠖⠋⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠁⠙⠢⣌⠢⡀
⠀⠀⠀⠀⠀⠔⠁⠰⠣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⣀⡀⠈⠈⠀⠘⠀⠀⣎⠈⡇⠀⠈⠳⡜⢦⡀
⠀⠀⠀⢀⠎⠠⡀⡑⡐⠀⠑⠊⠀⠉⠀⠀⡠⠒⢉⣠⣀⣀⣀⣀⡠⠓⠀⠀⢄⠈⡂⠀⢸⣀⡄⠀⢠⠀⠙⢆⠳⡀
⠀⠀⠀⡎⢠⠙⢌⠌⠀⠀⠀⠀⢀⡠⠐⠊⢀⡰⠊⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠈⢂⢳⡀
⠀⠀⠘⠠⠏⠢⠂⢀⠘⠃⠀⠀⠎⠀⡰⠋⠁⠀⠀⠘⠃⠀⠀⠘⠀⠀⡖⠄⠀⠀⠀⠰⠀⡀⠀⠸⡄⠈⣆⠀⠈⡄⣧⠂
⠀⠀⠆⡴⠑⠁⠀⠣⠤⠀⠀⢨⠁⠀⡃⠀⠆⠐⠂⢀⣄⣀⠐⠝⠀⢀⡇⠸⠀⠀⢀⣀⣜⠊⠀⠀⢸⠀⢹⠀⠀⢐⢹⢂
⠀⠀⠀⢎⠌⢀⢤⠀⠀⠀⠀⡾⠀⢀⠃⠀⠀⠀⡴⣡⠖⠦⡑⢤⡤⠊⡠⠃⢀⡞⠁⡤⠞⠀⢀⣀⡸⠀⢐⠁⠀⠀⢸⢆⠂
⠀⠀⠀⡃⠀⠀⠁⠘⠃⢠⠜⠀⢀⠚⠀⠀⠀⢰⠁⡇⢎⡑⠭⡒⠒⠊⠁⠀⠈⠦⠎⠀⠀⠀⡇⢠⡤⣤⠎⠠⡄⠐⢸⢃⢂
⠀⠀⡇⢇⠀⠀⢠⡀⠀⠹⡤⠔⠁⠀⠴⠀⠀⠘⣆⠧⣄⡨⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡆⠀⠠⠄⢠⠀⡴⠡⠃
⠀⠀⢡⠹⡄⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠈⠓⠒⠒⠉⠀⠀⠀⠖⠐⡄⠀⠀⢤⠀⠀⡇⢰⠇⢀⠀⠠⠋⢠⡇⠡⠁
⠀⠀⠀⢣⠱⡀⠀⢪⣀⣠⠍⠀⣠⠞⢁⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢰⠃⠀⠐⠒⠀⠸⣄⢼⣤⢈⡥⣾⢁⡾⡴⣡⠃
⠀⠀⠀⠀⠣⡙⢄⠀⠀⠀⠀⢸⠁⣼⠁⠀⠀⠈⠀⡀⠀⡌⠁⠀⠀⠈⠉⠁⠀⠰⠀⠀⠀⠀⠛⠺⠛⢘⣶⢃⣾⡝⡽⡥
⠀⠀⠀⠀⠀⠙⢄⠑⢄⠒⠀⠀⢧⡈⠓⠤⢤⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢁⢎⠌⠌⡘⠁
⠀⠀⠀⠀⠀⠀⠈⠑⣄⠑⠤⡂⠀⠙⠖⠤⠤⣄⡈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢂⡠⠁⡡⠊⣴⢋⢂⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣌⠓⠤⣀⠀⠀⠀⠉⠲⢄⣈⣉⡹⠀⠀⠠⢄⠀⠀⠔⠤⠃⡠⠊⡠⡺⡡⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⢒⠤⣉⠒⠢⢄⣀⡀⠀⠀⠀⠀⠀⠈⢁⡄⠐⠤⠒⡁⢰⢊⠜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠒⢢⠤⣀⣉⢉⡉⣉⣉⢉⡁⣀⠤⠐⠞⡐⠁⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠐⠁⠊⠌⠐⠠⠁⠊⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⣶⣤⡀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠁⠀⠀⠈⠙⠻⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢤⣍⣙⠛⠿⠛⣋⣩⣤⡶⠶⠿⣿⣿⡧
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢠⣶⣦⣬⣉⢋⣩⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⣀⣀⣠⣴⣾⡿⠏⣰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⢠⣴⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠦⣤⣞⠁⠀⠀⣠⠶⠦⣄
⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣥⠤⠀⠀⣠⠤⠤
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⠷⠀⣀⡀⠀⠀⠀⠹⣶⡶⠚
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⢲⡄⠀⠻⠇⠀⡤⢤⠀⠈⠉⠛⢿⣍
⠀⠀⠀⠀⠐⣇⠀⠀⠀⠙⠛⠁⢀⣀⠀⠈⠷⠞⠁⠀⠀⡄⠀⠈⢻⡋⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠙⠶⣄⣁⠀⡄⠀⠈⠛⠀⠀⠀⢀⣤⠀⠀⠋⠀⠀⠈⢷⡶⠚⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⠶⣤⣀⣀⣀⠀⠀⠈⠉⠀⠀⣠⣤⠀⠀⣼⣛⠛⠲⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢠⡏⠉⠻⣯⣷⢶⣦⣀⣶⡃⠀⠟⣁⣠⣿⣍⣉⣭⣄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⡄⠀⠹⡄⢻⣹⡉⠙⢻⡛⠉⠻⠦⠬⣭⣀⠀⠙⠦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠙⣇⠀⠀⠙⢦⣀⡀⠀⠀⠈⠓⢄⠀⠈⠉⠉⠉⠉⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠓⠂

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⡏⡴⠋⠉
⠀⠀⠀⢻⡸⡄
⠀⠀⠀⠀⢣⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠹⡅⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⠹⡄
⠀⠀⠀⠀⠀⡟⢿⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡞⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢱⡘⣧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣆⢰⣆
⠀⠀⠀⠀⠀⠀⢧⢉⣁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠉⠛⣿⣿⣿⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⣀⣾⣿⢸⣿⣤
⠀⠀⠀⢀⣤⣶⣾⣿⣟⡁⢷⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠟⠛⣫⠛⠷⠶⠚⢻⣿⣿⡿⠀⠀⠈⢳⣦⠰⠖⠛⢡⣿⣟⣸⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣬⣇⠀⠀⠀⠀⠀⠀⢸⣀⡘⠛⡸⠁⣇⠸⠗⠀⣼⡙⡿⠁⠀⠀⠀⠸⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠿⣿⣿⣿⣿⣿⠛⠡⠼⡀⠀⠀⠀⠀⠀⠀⠉⢩⠉⢥⡄⠉⠉⠉⠛⣯⠜⠁⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡆⠤⣶⠴⠂⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣉⣁⣤⠞⠁⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⠀⠀⠀⢹⡍⠂⢄⡀⠀⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡤⠦⠤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠁⡼⠀⠀⠁⠀⠙⢦⠀⠙⣄⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠓⠒⠚⠀⠀⢳⣄⣀⡀⠶⣒⣨⡇⢀⣜⠀⡟⠺⢄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇⠀⠀⠘⠂⢰⡄⣿⣿⣿⣿⣿⡟⡔⠁⠀⢹⠃⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⢀⠎⠀⢀⡀⠀⣠⠏⠀⣿⣿⣿⣿⡟⠀⢹⡀⠀⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⡞⠀⠀⢸⡇⡰⠁⠀⠀⣿⣿⣿⡟⠀⠀⣠⠃⣸⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡼⠁⠀⠀⣸⠃⠸⡀⠀⠀⣿⣿⡿⠀⢀⡜⠁⢠⡏⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⠀⠱⡀⠀⣿⣿⠁⣰⠋⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⢀⡞⠀⠀⠀⠀⠱⣘⣿⢇⡼⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⢹⣿⠞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢰⠇⠀⣠⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢀⡼⠃⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣫⠏⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠖⠁⠀⣶⡜⢛⡙⠛⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠄⣜⠃⣤⠠⣿⠟⠀⠀⢀⠖⢲⠀⠀⠀⠀⠀⣀⡀⠀⠀⠑⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣆⠀⠰⠾⢿⣿⣿⡷⣀⣄⡲⣶⠀⠀⡘⢠⡇⠀⠀⠀⣀⡴⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡨⠀⠀⠀⠛⢉⣿⠻⡿⠘⠁⠀⠀⠀⣧⣾⠀⠀⢠⣊⣁⠔⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠿⠺⢯⣿⣧⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠂⣹⠟⠀⠀⠀⢀⣠⣄⡀⠀⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣘⡟⠃⢴⠄⡶⣿⣷⡦
⠀⠀⠀⠀⢔⢈⠩⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠛⡿⠀⠀⣿⣶⡂⡁⠀⠀⠀⠀⠀⠀⠀⠉⢹⣄⠰⡶⠈⣽⣿⠶⠀⠀⡔⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⣀⡀⠀⠀⠀⠀⡛⣿⣆⠙⠉⢶⠶⣶⠋⠉⠀⠀⠰⣉⣿⠁
⠀⠀⠀⠀⠀⠀⣸⠿⢂⡈⣺⣷⡴⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣴⣦⣿⣤⣾⢀⣀⠀⠘⢅⠿⠀⠀⠀⠀⣀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⢨⣇⢠⡅⠻⣿⡗⠀⠀⠀⠀⢸⡿⡇⠀⢀⣄⡟⠞⠋⢿⣻⠟⣿⡍⠀⠀⠀⠀⠀⠀⠐⠿⠷⠖⠚⠛
⠀⠀⠀⠀⠀⠀⠈⠹⠖⣶⠛⠛⠙⠀⣀⣲⡄⢸⡇⡅⠀⠀⠉⣧⡤⠛⠃⣶⠈⣽⣄⠀⢀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⡀⠀⠐⠴⠏⠀⠸⣀⠆⠀⠀⠈⢫⣶⠶⣤⡤⢶⠏⠁⢀⡜⣼⠃⠀⠀⠀⠀⠀⠟⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠚⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢾⠿⠃⠀⠀⢀⠀⣀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠴⡿⣦⠀⠀⠀⢀⣘⣷⠿⡾⣷⡄⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣠⡟⣩⠝⢧⡄⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⢨⡽⠛⡛⢩⡋⡿⠂⢨⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡍⠀⠘⣿⣿⣦⡓⢰⠟⠀⠀⢀⠀⠀⠀⢀⣤⡀⠀⠾⠣⣴⢁⣨⣴⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠻⠙⠋⠁⢠⢢⠎⠀⠀⠀⠀⠻⡍⢆⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣒⠚⠂⠀⠂⠤⠀⠀⠉⠈⠁⠐⣢⡀⠀⢀⣀⢀⡔⢒⠞⠑⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡼⠄⠀⠀⠀⠀⡜⠁⠠⠀⢀⡀⠀⠀⠸⠓⡨⠀⠭⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡠⢞⠓⠊⠀⠀⠀⠀⠀⣸⡵⠟⠁⢑⠢⠄⠑⠂⠜⣁⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⣠⡔⠴⠛⠁⠀⠀⠀⠀⢀⣀⢀⢨⠀⠠⠴⠀⠂⢡⡯⠖⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠥⠤⠚⠪⡢⣀⣄⡄⠀⠚⠔⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⣴⡂⠖⠓⠒⠁⠀⠀⠀⠀⠈⠀⠀⢐⡂⠀⢀⠀⠀⠀⠄⠀⠀⠃⠀⣀⠒⠀⠀⠀⠀⠲⠦⠤⣤⣤⠤⢀⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠒⠏⠀⠀⣆⣆⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠜⠃⠀⠀⢀⠀⠀⠀⠸⠀⠡⠄⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡤⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠂⠛⠉⣣⢤⠨⢀⠀⠀⢠⡆⠂⠀⠀⠐⡄⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠊⠉⠐⠀⠀⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢹⡀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠈⠵⠦⡀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠀⢀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⡅⠀⠀⠀⠀⠒⠁⠀⠀⠘⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠈⠁⠙⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠬⠀⠀⠀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⠀⣀⠤⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⡀⠸⠴⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⣀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⢀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⠒⠂⢀⠀⠀⠀⠑⢆⠀⠑⠀⠀⠀⠀⢐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠁⠀⠀⠀⠀⠀⡁⠈⡀⠐⠀⠀⠈
⠀⠀⠘⠃⠀⠀⠀⠀⠋⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⠠⠀⠀⡀⡀⠀⠀⠀⠐⢠⡀⠀⢀⡀⠁⠀⠀⠐⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⣀⣀⣀⣈⡀⢀⡀⠀⠀⠀⠀⠈⠁⠀⢠⠞⠱⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠆⠀⢠⣾⣶⡀⢀⠁⠀⠐⠐⠀⠉⠉⠉⠉⠉⠀⠰⠀⡀⠀⠄⠉⠀⠀⠈⠓⠊
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠙⠋⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠰⠆⠀⠀⠀⠀⠁⠀⡀⠀⠀⠲⠀⠈⠂⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠄⠀⠀⠀⠀⠀⢤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⣇⣄⠀⠀⠀⠀⠀⠀⠁⠑⠢⡀⠀⠀⠀⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡈⠂⠀⠀⠀⠀⣀⠀⢾⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠁⠢⠀⠈⠄⠉⠁⠀⠀⠈
⠀⠆⠂⠀⢠⠤⠀⡀⢀⠀⠸⠀⠀⠳⣶⣦⣀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⠀⠸⣀⡠⠇⠠⠄⠘⡁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⡤⠰⡤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠶⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠃⠀⠀⠀⠸⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡄⠘⠦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⣀⠀⠀⢻⡐⠀⠀⠀⢀⡏⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠟⠀⠀⠑⠤⠤⠔⠉⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⣀⡀⡠⠂⠀⠀⠀⠀⠀⠀⡤⠀⢀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⣠⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠠⠠⠀⠀⢀⠀⠀⢀⠀⠀⢀
⠀⠀⠁⠀⢀⡀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⡄⠀⠀⠀⣠⠚⠋⠥⠤⠐⠃⠀⠀⠀⠘⢃
⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⣁⠔⠀⠀⠀⠛⠲⠦⢤⣀⣀⠉
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠾⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠊⠀⠀⢠⡄⠀⠀⠐⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⡰⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡀⠀⠀⣔⠀⠀⠠⣿⡷⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠜⠀⠘⠀⠀⢠⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⠇⠰⠀⠈⠁⠀⠀⠀⠂⠒⠀⠀⢠⠂
⠀⠤⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠶⠠⠀⠀⡄⢀⡀⡀⠈
⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠼⠀⠀⢀⣤⠤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠈⢳⠀⠐⠀⠀⡀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢋⣿⡛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣣⠾⠏⠉⠟⢷⡄⢻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⣠⠞⠡⠄⢀⡀⠘⠀⡇⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⣦⢞⡁⠒⠀⠀⠀⠠⣤⡾⢁⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡿⠋⣠⡞⠁⠈⠁⠀⠄⠐⣣⡾⠋⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⠞⠉⣡⠄⢀⠛⠀⣰⡾⢋⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣾⠉⠃⠰⠀⠀⣀⣠⡿⠋⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡇⠀⢷⡘⠃⠰⠆⣠⡾⠋⣻⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣁⣠⣿⣜⠈⠛⣶⡶⠞⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⠏⠉⠀⠀⠀⡟⢳⣦⣭⡤⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠔⠁⠀⠀⠀⢀⡼⠟⠉⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠤⠒⢚⡟⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡜⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠜⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⢧⡁⠀⠀⢀⣾⣿⣷⠀⢰⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠧⠀⠸⣧⡘⣿⣦⠀⠀⠀⠀⠀⠻⠿⠛⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠻⢿⡿⠿⣁⣀⣀⡙⣿⣦⣬⣠⣞⠻⢿⣷⣄⠀⢠⣶⣾⣍⠁
⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠘⣿⣦⠻⡆⢠⡾⢛⣋⣉⢹⣿⡿⠀⢹⣿⣷⣄⠙⣿⡗⠻⣿⣿⣿⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⠿⡿⠟⠀⠀⢠⣼⣿⣷⣄⠈⠐⢛⠋⠁⢿⣿⠇⣀⣬⣿⣿⣿⡆⣹⣏⣄⠹⣿⡇⠀⣾⣿⣿
⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠈⠉⢡⣥⣤⣶⣿⡟⠀⣀⠀⢸⣯⣿⣿⣿⣿⣿⣯⣾⣿⠀⣿⠇⠀⢿⣿⠟
⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⢀⣮⡉⢻⣿⡿⣿⣿⣿⣿⣿⡟⢻⣧⠉⠉⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠛⠁⣀⡀⣤⣄⣘⣓⡂⠀⠀⠀⣸⣿⠇⢼⣿⣿⣿⣿⣿⣿⣯⣶⢿⣧⣶⠶⠶⡌⠽⡻⠦
⠀⠀⠀⠀⠀⠀⢐⣦⣿⣿⣿⣶⣿⣛⡻⠟⢛⣡⡘⣿⣍⡾⣯⡿⣿⣿⠿⠿⠅⠀⠀⣾⡏⣰⣶⠞
⠀⠀⠀⠀⣠⣶⣦⣿⣿⣿⣿⣿⡿⣋⣴⣾⡿⠛⠁⠻⠿⠿⣛⣁⣀⠀⠀⠀⠀⠀⠘⢿⣯⠉⠁⠀⠀⠀⠀⠄⢰⣿⣷⠄
⠀⠀⠀⢸⡿⣛⣿⢿⣿⣿⣿⣿⣷⣍⣩⣥⣄⠀⠀⣠⣤⠘⠛⠛⠿⢿⣦⡀⠀⠀⠀⠈⠛⢺⣷⣄⢀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠈⠛⠛⠉⠞⠩⢻⠿⡟⢋⣤⣿⣿⣿⠇⢸⡿⢿⣷⣽⣿⣷⣦⠙⠇⠀⣠⣤⡀⠀⠈⢿⣿⣷⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠘⢿⣦⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣷⣀⣦⠀⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣶⠀⢠⡴⢃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠲⣦⡀⠀⢹⣦⣤⣿⣶⣿⣴⣏
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠠⣄⠀⠀⠀⠀⠈⠋⠀⢸⣧⣴⠟⠉⠀⠀⠀⠀⠉⠙⢷⣦⣴⠂
⠀⠀⠀⠀⠀⠀⠈⠟⢹⡆⠀⢠⣇⠀⣠⡈⣧⠀⠀⢸⣆⣀⣴⠿⠋⡄⠀⠀⠀⣦⠀⣀⠠⠀⠀⠹⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠿⠛⠛⠛⠻⠿⠷⠶⠿⠛⠋⠁⠀⠀⠀⠀⢠⡄⠉⠀⠘⠀⠀⠀⢠⣿⣉⡀
⠀⠀⠀⠀⠀⡤⠴⢦⣾⠋⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠂⢰⡆⠀⠀⠁⠀⠀⠀⠀⠘⣢⣾⠋⠉⠉
⠀⠀⠀⠀⠈⠳⢦⣼⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠾⠀⣀⠀⠀⠀⠈⠀⠀⠠⠴⠄⠀⢀⣠⣾⠟⠛⠻⠶⠒
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⡿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠲⠾⠛⠻⣦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣠⣾⡟⢿⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣻⡷⢶⣤⣤⣤⣈⣀⣀⣀⣀⣠⣤⣤⣶⠾⠛⣿⠘⢷⣌⡛⠶⠂
⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠋⠀⠸⠛⣯⠈⠉⡉⣹⠏⢻⡉⠀⢸⣇⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠀⠰⢣⡟⠀⠘⣧⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠐⣯⡿⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠤⠀⠀⠀⠀⢜⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠄
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡐⠀⠀⠀⣮⠆
⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⢀⢀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢄⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠩⡀⠃⠀⠀⠀⠘⠀⠀⠀⠀⢉⠳⠀⠑⠢⠁⠀⠀⠠⠁⠀⠀⠀⡌⠱⡀⠀⠂
⠀⠀⠀⠀⠀⢘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠒⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠤⠀⠄⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⡧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⠶⣏⡟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣵⣆⢷⢟⣹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠡⢅⠿⠁⢸⡿⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⢦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠏⠀⠀⠘⢷⡠⡎⣿⠀⠀⠀⠀⠀⣠⣶⢴⣄⠀⠀⠘⠛⠏⠁
⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢹⣳⠆⢿⡗⠀⠀⠘⡿⠊⣁⢩⣿⠆⠀⠀⠀⠀⠀⠀⣠⣀⣰⣆⣀⡀
⠀⠀⠀⠀⣰⢋⠚⡚⢛⢳⣄⠀⠀⠀⠀⠘⠛⢾⠞⠃⠀⠀⠐⣿⣦⢹⡊⣿⡀⠀⠀⣠⣴⡖⠿⢩⣥⢉⡹⢻⡀
⠀⠀⠀⠈⠻⢜⡞⠁⠸⠌⠉⠳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⡹⣯⠀⠀⢴⠿⢢⠰⠎⣃⣨⣍⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠙⣧⡄⠶⠶⠒⢰⡎⢹⡶⣤⣀⠀⠀⠀⠀⠀⡼⣁⠟⣲⣿⡀⠀⠘⢻⠞⠛⠋⠙⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣶⠀⡘⠁⠸⡇⠙⣻⡄⠀⠀⠀⣾⠇⠹⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⠆⢰⠀⣈⡿⠁⠀⠀⣸⡧⠞⠠⣖⣸⡟⠀⣀⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠒⠺⠃⠀⠀⠀⠸⣧⣆⣴⡾⠉⠀⣴⢿⣷⣮⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡶⣴⢾⡗⢲⢖⣶⢤⣤⡀⠀⠀⠀⠀⠈⢀⣀⡶⠝⠓⣬⣽⠉⠀⠀⢀⣴⠷⢶
⠀⠀⠀⠀⠀⠀⠀⠰⣿⢣⠗⣠⡄⠃⣤⠰⢞⠊⡰⣷⠶⠀⠀⣠⡴⣿⠟⡐⢟⣋⣿⠍⠀⠀⢀⡼⣫⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢻⣯⣬⣩⣦⢿⡬⠵⠾⠿⣧⠏⠀⠀⠐⢿⣰⣋⠀⣿⣬⠟⠃⠀⠀⠀⣸⣧⠡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⣴⣦⣦⣀⣀⢀⡀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢨⣭⣹⠟⢿⠧⢴⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣥⡐⠿⡄⠇⠟⠢⠏⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠗⢾⡧⡾⢤⣿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠻⡄⠀⣠⠴⠂⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠴⣾⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡴⡿⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⢃⡴⠚⠙⠲⣤⡀⣾⡟⠀⠀⠀⠀⠀⠹⣆⠀⠚⠉⡉⠈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠙⢯⡿⢦⡀⠀⠀⠀⠀⠙⢧⡀⡿⠙⡟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣿⡄⠀⠀⠀⢀⣀⣭⡇⢀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠦⢤⣽⣷⣿⠤⠖⠚⠉⠉⠀⠙⠛⠓⠞⠷⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠴⠶⠶⠶⢦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⢦⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⠶⢾⣷⣤⣬⣵⣤⣤⣵⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⣙⢦⡀⠀⣠⡟⠀⠀⠶⠖⣻⣿⠟⠓⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠁⣿⠂⢙⡾⠋⠀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡶⠟⠁⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠀⠀⠸⣧⠶⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣄⣤⠶⡿⢲⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣽⣷⣭⡙⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⣈⡝⢿⡀⠙⢿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣇⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣠⣶⣶⠾⠷⠿⠿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡯⠀⣿⠷⢼⡇⢰⠜⠃⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⢹⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠠⣾⣥⣤⣤⣤⡴⠛⣻⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢳⠀⠸⡇⠈⡇⢸⠀⢸⡿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢷⣜⣧⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⢷⠀⣿⢸⠇⢸⣇⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⣄⡈⠻⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠸⡇⢸⡿⠀⠈⣿⢹⣆⣿⣤⢴⣶⡤⠶⣶⣆⢹⣷⠤⢀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠛⠋⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡀⠀⠸⡇⠀⣿⣸⣧⣤⠶⠛⠉⠉⠀⠀⢰⣿⠀⠀⣿⡽⠦⠿⠄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠛⠶⠖⠲⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠃⠀⠀⢿⡤⠼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣀⢹⡗⣶⠶⢆⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣒⣚⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣧⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣉⡚⣣⡇⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠙⠓⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠸⣿⡃⠀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡟⠉⠉⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⡏⠙⣿⠉⢻⣏⣉⣠⡤⠶⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⢿⣆⣠⣿⠀⠘⣏⠉⠀⠀⠀⠀⣿⣤⠤⠤⠴⠶⠶⠶⠖⠚⠛⠛⠛
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⡇⠁⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠂⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣧⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⠤⣤⠼⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠛⢛⣻⣿⣿⣿⠿⠧⠤⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠒⠒⠂⣉⡿⠋⠀⣮⠈⠛⠓⠶⠶⢠⡿
⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⢀⣀⣀⣤⣤⣤⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣀⣤⠴⠶⢿⡷⠻⠛⠒⠒⢠⡄
⠻⣤⣀⣀⣈⠹⣦⣹⣯⣭⡿⠿⠛⠛⠋⠉⠁⠀⠀⠉⠉⠐⠶⠾⠶⠧⠶⠶⠾⠋⠁

⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠹⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⢱⠁⣸⠤⡀⠀⠀⠀⠀⢀⢠⣶⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣠⣤⡀
⠀⠀⠀⠀⠈⠸⣯⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠃⠂⢁⡐⠁⠀⠀⠀⠀⠀⠒⢍⠻⣟⣎⠀⠀⠀⠀⠀⠀⠀⣙⣿⠟⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠈⠈⠻⢑⠄⠀⠀⠀⠀⠈⡞⠏⣠⡌⡤⠄⣈⠆⠀⠀⠀⠀⠀⠀⠀⢡⢹⣻⠈⠀⠀⠀⠀⠀⠀⢻⣿⢾⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢈⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⡄⠂⡈⢐⠂⠄⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣀⣤⠀⠀⠀⠀⠈⠀⢴⡄⠐⠆⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⡀
⠀⠀⠀⠀⡙⡈⢁⠐⢀⢐⡘⡀⠀⠀⠐⠲⢦⡄⠹⠀⠚⢋⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠴⡐⠀⡐⠈⠄⠠⠀⠀⠀⠀⠀⣀⣴⠂⣴⠃⠈⠻⣦⠀⠀⠈⠠⠙⣏⠀⠀⠀⡠⠙⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠆⠡⠐⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠘⡈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⣯⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡮⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠃⣠⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠤⢄⡀
⠀⠀⠀⠀⢸⣛⣿⠉⢹⡆⠀⠀⠀⠀⠀⠐⢄⢀⠘⠀⠞⠃⠀⠀⠀⠀⠀⢠⡶⣿⣛⠁⢰⡿⠀⣴⠆⠀⠀⠀⢰⡆⠠⡸⣀⢀⠓⠂
⠀⠀⠀⠀⠀⠻⣿⣷⣿⡻⣆⠀⠀⠀⢠⠄⠠⠁⠀⠀⠀⢠⡉⠥⠀⠀⠰⠟⠁⠈⠁⢀⣬⣿⡶⠇⠀⠀⠀⠀⠩⣄⢀⠪⠑⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⢼⣺⡷⠈⠀⠀⠀⠀⠋⠈⠑⠂⢠⡀⠐⠈⠐⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠦⠄⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠰⠸⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣈⣱⠀⠀⠀⠀⠀⠀⣲⡾⣿⣿⡷⣶⠀⠀⠀⠀⠀⠀⠰⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡵⢘⡄⢀⠀⠀⡔⡀
⠀⠀⠀⠀⢸⣶⣿⠿⣿⣶⡄⡀⠀⠀⠒⣿⣻⣽⣾⣿⣻⡗⠀⠀⠀⠀⠀⠈⢄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢒⠹⢢⠖⠄⢠⠈⠁
⠀⠀⠀⠀⠙⢿⣿⣄⣼⣿⠁⠀⠀⠀⠀⢹⣯⣿⣻⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣦⡀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠹⢉⠠⡂⡆
⠀⠀⠀⠀⠀⠘⠛⠛⠇⠀⠂⠀⠀⠀⠀⠈⠀⠉⠫⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢮⡐⠂⠀⠀⠀⠀⠀⠢⠕⠀⠀⢤⢉⢦⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠝⠁⠀⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠀⢸⡶⢋⣍⠉⠳⢾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣾⣆⣈⡁⢴⠐⠾⠏⠀⠀⢠⠋⡹⠀⠀⠀⠀⢀⣤⡀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡼⡄⠀⠛⢻⣿⣽⣟⣤⢶⣼⠻⠀⠀⡌⢴⠁⠀⠀⣠⡴⢋⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠂⠀⠀⠈⠁⣼⠉⠛⠉⠁⠀⠀⠀⢷⡿⠀⠀⠸⠥⠔⠁⠀⣠⡄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠋⠙⢞⣿⣶⠛
⠀⠀⠀⠀⢀⣀⠤⣾⠆⠀⠀⠐⠛⠁⠀⠀⠀⠔⣶⣦⠀⠀⣰⠂⡐⠄⠀⠀⠀⠀⠀⠀⠀⣼⣍⠁⢛⡸⣻⣿⣟⠃⠀⠀⢀
⠀⠀⠀⠀⠃⠐⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⠞⠀⠀⠻⠿⠤⠀⠀⠀⠀⠀⠀⣤⣤⠀⣽⣆⣛⢁⣰⠿⠛⠃⠀⡨⣼⡿
⠀⠀⠀⠀⠀⠀⣠⣬⠓⢿⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⠀⣀⠀⠀⠐⢤⠟⣦⠀⠈⠋⠙⠃⠀⠀⠀⠀⠃⠞⠁
⠀⠀⠀⠀⠀⠐⢺⠈⠲⢰⣾⣿⡁⠀⠀⠀⢠⣶⡄⠀⠀⠀⣤⣚⡿⣿⣿⣿⣴⠆⠀⠈⠀⠁⠀⠀⣠⣴⣂⣀⣿⠆
⠀⠀⠀⠀⠀⠀⠚⢧⣛⣀⣿⠿⠄⠀⢀⡀⠀⡏⢹⠀⠀⠿⣗⠁⣤⠍⣚⠱⢿⠃⠀⠀⣀⡀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠀⠔⣲⠟⠀⠃⢸⠀⠀⠠⠿⣏⣀⢀⠛⣠⠿⠇⠀⠜⢹⠃⠀⠀⠀⠀⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠻⠯⠭⠴⠆⠀⠈⠁⠀⠀⠙⠁⠀⠀⠀⠈⠋⠈⠻⠏⠉⠁⠀⣼⣴⠃⠀⠀⠀⠀⠀⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠁⠀⠀⠀⢶⣰⣦⣾⡀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡶⢚⡲⢆⡀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣘⡿⠿⠟⡙⢣⡄⠀⣨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠐⢾⣷⣮⠥⠨⡷⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡽⣀⡘⠀⣋⡾⠂⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⠻⠷⠞⠂⢀⢀⡜⠀⠀⠀⠘⢯⠃⡀⠀⠘⠛⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠀⠐⠠⠀⠀⠀⠀⠉⠛⠚⠒⠒⠒⠂⠀⠄⢀⠄⢀⡀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠉⠉⠐⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂⢐⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠂⠤⠀⠀⠀⠀⢂⠀⠑⢦⣄⣿⠀⢰⣾⠉⠈⠁⠀⠀⠀⢀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢖⠀⠀⠀⠀⠀⠀⠈⠀⠂⣀⣴⡇⠀⠀⠈⠁⠀⠈⠻⠖⠄⠀⢀⡀⠤⠚⠁⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⠀⠀⠀⠂⠀⢐⡟⠑⠲⣄⠀⠈⠉⠁⠀⠄⠈⠛⣧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢀⣤⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠉⡀⠀⠀⠄⠀⠈⠲⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡐⠂⣠⠐⠒⠀⠂⠀⠁⠀⠀⠀⢠⢟⠅⠀⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⡀⠠⠀⠀⢺⡄⠀⠀⠁⡀⠀⠀⠡⠀⣡⡀⣰⠖⠁⠀⠻⢇⣤⣀⡀⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠑⢴⢾⡇⠀⠀⠀⠐⡀⠀⠀⡅⠈⠛⠋⠀⢀⣤⣄⠀⠀⠀⢀⠀⡀⠀⠀⢀⡔⠂⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠀⠀⠄⠀⠀⠀⠀⢀⠑⠗⡾⠇⢀⠀⠀⠀⠋⠁⠘⠺⣄⠀⠃⠀⠀⢱⡀⠩⢣⠀⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⣶⠶⠃⠀⠀⠀⠀⢨⡅⠀⠀⠀⠁⠀⠆⠀⠀⠠⡀⠀⠈⠠⠀⠰⣀⣼⡇⠀⠀⠀⠀⠁⠀⠄⢠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡄⠃⠀⡀⢠⠠⠂⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠄⠀⠀⢠⡀⠀⠀⠠⠂⠩⣴⠀⠀⣀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⠀⠈⠼⣲⠿⠉⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦⠀⢤⠀⣸⡇⠀⠀⠀⠀⠀⢛⠃⠀⠋⠁⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢠⠃⠀⢠⠀⢠⠀⠀⢺⠀⠀⠒⠛⠃⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⡤⠐⠂⠀⠀⠀⠀⠜⠋⠀⠸⡷⡶⠖⠀⢀⠀⢀⡚⠀⢀⡀⠀⢠⠀⠀⠠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣵⣧⣀⣀⢀⠠⠂⠁⠀⠀⡀⠄⠀⠀⠒⢂⡀⠉⠉⠀⠌⠀⠛⡇⢈⢄⣤⠄⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡀⠈⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⡤⣿⠇⠀⠈⠀⢀⣀⠁⠈⠛⠉⠋⠀⠰⡵⢶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠇⣐⣁⠀⣀⣀⠀⠀⠈⠉⠉⠀⠀⠀⠪⣷⣶⠞⠁⠀⢀⠀⠂⠙⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠿⠁⢀⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢼⣇⢀⡤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣄⠀⠀⠀⠀⠀⠀⢀⢴⡟⠀⠈⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠀⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠐⢀⡈⠂⠈⠀⠊⡠⠄⠀⢰⠉⠀⠀⠈⠁⠂⠠⠀⠠⠐⠐⠐⠂⠐⢄⠀⠀⠀⡠⠓⠂⠻⠂⡐⠀⠀⠀⢀⠠⠐⠀⠠⠄⠀⠀⠀⠠⢀⠀⡈⠂⠠⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠓⠒⠂⠂⢄⡀⠀⠀⡀⡀⡄⠄⠀⡀⡴⠀⠀⢠⡄⠀⠀⠀⢈⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⡀⠀⠀⡜⠀⠈⠲
⠀⠠⠐⢀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠆⡠⠤⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⡐⡂⠀⠀⠀⠀⠰⡖
⠀⢀⠀⠁⠀⠄⠀⠂⠀⠀⠀⠀⠀⠅⣀⠂⣀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠘⠀⠂⠃⠁⠀⠀⠠⠄⠀⠀⢸⡀
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢀⠀⠘⠀⠠⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠌⠁⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢈⢀⠀⠄⠀⠂⠀⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠢⠌⠀⢐⠄⠀⠰⠠⢀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠀⠀⠀⠈⠱⡆⠀⠀⠘⡣⡀⠀⠀⢀⠀⠀⠀⡀
⠀⠠⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠉⠀⠀⠀⠀⠈⡄⠀⠀⠀⠄⠈⢅⠀⢰⠀⠈⠁
⠀⠐⢄⠀⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠀⢀⡪⠂⠀⠀⠉⠀⣐⠄⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠈⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⢠⠠⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠠⡀⠰⠲⠓⠀⠀⠀⠀⠆⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦⣤⣀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠅⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣴⡾⠾⠿⠛⠿⠻⡿⠟⠛⢿⣿⣟⠉⠉⢿⣿⣷⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢄⠈⠁⠰⠂⠀⢠⣿⢱⠇⡆⢀⠈⠠⢦⠹⡄⢳⡶⠶⠙⣷⣬⣴⡿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡋⠀⢀⠀⠀⢼⣿⠀⢠⣧⣸⣤⡷⢴⡷⠶⢾⠷⠒⣿⠛⡛⠉⠃⢀⢹⡇⠀⠀⠀⠈⠄⠀⠠⠀⠂⠁⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠉⠉⠁⢠⡀⠀⠀⢸⡟⢛⠻⡏⠈⠻⡀⣶⣶⣦⢸⡆⢉⣉⣄⠁⢶⠀⢸⣾⡗⠀⠀⠐⡀⠀⠀⠁⠈⠀⠠⢀
⠀⢀⠖⠀⠀⠲⡀⠀⠀⠀⠀⠀⠁⠀⠔⠀⠀⠀⠀⠀⠀⠻⣄⠦⠁⠘⣦⣀⣜⢋⣹⣆⣻⡀⠉⣉⣄⣦⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠐
⠀⢊⠀⠀⠀⠀⡀⠀⠀⠄⠐⠀⡀⠰⠀⠐⠀⠤⠀⠀⠀⠀⠈⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠤⡀⠀⠀⠀⠀⠀⠁
⠀⠈⠒⠤⠠⠔⠁⠀⠀⠀⢀⡀⠀⣰⠒⠒⡀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠒⣰⠅⢴⢆⠤
⠀⢠⠄⢄⠀⠠⠐⠀⠀⠢⡀⠀⣀⠀⠲⠐⠁⠀⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⡀⠉⣦⠴⠉
⠀⠣⠀⠜⢐⠁⠀⠀⠀⠀⠡⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⢀⠄⠂⠄⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠤⣤⠤⡀⠀⠄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡺⡉⠹⡀⣏⠒⣌⠂⠁
⠀⠀⠁⢠⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠤⠘⢀⠲⠰⠲⢈⢰⠀⢃⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠄⠄
⠀⡄⢁⠄⠚⠀⠈⠀⠁⠁⠀⠂⠈⠢⣐⠀⠀⠀⢀⡤⠒⠂⠐⡄⠀⠀⠀⢀⠤⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠊⠀⠀⠀⠀⢂⠈⠀⠀⠄⢀⠀⢀⠀⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡂⠀⢠⠔⠁⣀⠀⠤⠔⠀⠀⢀⡠⠀⠀⠀⡘⠀⠀⠠⠀⠀⠀⢀⠀⢁⠀⠀⠀⢀⠑⠀⠀⠀⡀⠄⠀⠀⠠
⠀⠐⡊⢂⠄⠀⠀⠠⠐⣄⢈⠥⠀⠄⠀⠀⢇⡰⠊⠀⠀⠀⠀⡐⠈⠁⣀⡀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠂⠂⠁⠀⠁⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠠⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡴⠶⠶⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠛⠈⠛⠛⠛⠛⠀⠛⠒⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡏⠀⠀⠀⣬⢻⡄⠠⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⠻⣦⡾⠁⣸⠇⠠⡤⠤⠤⠤⠤⠤⣤⠄⢀⣿⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠶⢤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠐⠒⠶⢦⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠞⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣀⣀⣀⣀⢸⡇⠐⠶⠶⠶⠶⠶⠶⠶⠞⢧⣀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀⠀⠀⢀⡼⠁⠐⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⠁⠒⠒⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⠀⠀⠈⢳⡄⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠛⠛⠛⠛⢸⠇⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠧⣶⡄⣶⣠⣶⢄⣶⢰⠆⡖⠂⡗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠉⠀⠉⠈⠉⠈⠀⠉⠁⠁⠁

⣶⣒⡲⠦⣄⠀⠀⠀⠉⠛⠒⠶⠯⠇⠀⠀⠀⠀⠀⠀⠨⢻⡙⣶⠚⠓⠓⠋⠀⠀⠀⣀⣀⠀⠸⣇⠙⡄
⠀⠀⠈⠓⠚⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠘⡧⠀⠀⠀⣠⣶⠾⠛⠹⠀⠀⢻⡀⠙⢆
⠄⠀⠀⠀⠀⢤⣰⡖⣬⡭⢑⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⢿⡴⠞⢿⣉⠀⠀⠈⢿⡈⢙
⠀⠀⢆⣠⠶⢛⢽⣦⠓⣍⠲⣌⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡼⠗⠁⠀⠀⢸⡧⡆⠀⠀⠈⠛⠿
⠀⠀⢀⣰⠼⠞⡆⣷⠀⠀⢦⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⣟⣿⠀⠀⠀⠉⠁⠀⠀⢠⡶⠀⢀⣠⠀⡄⠀⠀⡄⠀⠤⡀
⠲⣄⠀⠀⠀⠀⢧⡟⠀⠀⠀⠀⠀⣀⡴⢛⣠⣞⠸⣿⣾⢶⣶⣾⣤⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢍
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣠⢚⡽⣋⡧⢰⣯⣳⢲⢀⣤⣐⣖⣂⣠
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢰⡟⢐⡴⠁⣾⠃⣽⠀⠈⢻⡆⠸⡟⠙⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⢠⣿⡿⣿⢗⠀⠀⠈⠛⠖⠀⢸⡧⠄⡇⠀⠀⠘⢿⣦⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢻⣄
⣇⡀⠀⢸⣿⣇⠀⡻⠀⠀⠀⠀⠀⠀⢾⣇⣚⡇⠀⠀⠀⠀⢻⡇⣽⣄⠀⠀⠀⡠⢦⡀⠀⠀⠀⠀⠀⠹⣍
⠟⠃⣠⣿⣿⡈⠛⡇⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠈⢿⣤⣾⠀⠀⠰⣿⡌⢿⡄⠀⠀⠴⣶⠻⠹
⣠⣾⣯⣿⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣻⡃⣼⣧⠀⠀⠀⠀⠀⢀
⣍⢍⣾⣏⠉⠴⡆⠀⠀⠀⠀⣀⣴⡷⠾⠿⠶⠶⣶⠶⢶⣦⣴⡶⣦⠄⠀⠀⠀⣿⠁⢈⣿⠀⠀⠀⢀⣴⠟
⠁⠈⣿⡇⠀⠀⡇⠀⠀⠀⠀⣿⣧⠀⣐⠂⣀⣤⣀⣄⣰⣄⣁⡀⣀⡴⠀⠀⢠⡇⠰⢮⣿⠀⠀⢀⣤⠛⠓
⠀⠀⠽⢇⣐⠣⠁⠀⠀⠀⠀⠈⠘⠒⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣾⡁⢃⣼⡟⠀⠀⠈⢳⣖
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠹⣷
⠃⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣇⡆⠀⠀⠀⠀⠀⠀⡰⠫⢃⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠻⣏⢹⠦⣀⡀⠀⢸⡧⠀⠀⠀⠀⠀⠀⢠⢣⣡⣫⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⢳⡄
⠀⠀⠀⠀⠀⠉⠛⢶⣾⡙⠳⠟⣖⡆⠀⠀⠀⠀⠀⠋⣬⣍⣥⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠘⣷⣄⣷
⣏⣉⣯⣿⣏⣯⣿⣽⣽⣿⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠑⠢⢍⣛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠑⠦⣌⣉⠒⠤⡉⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣑⠢⢭⣑⠢⢍⡙⠒⠤⣀⠀⠀⠈⠙⢷⣄⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠓⠮⣍⣒⠦⢍⣓⠢⠄⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣭⣷⣦⣌⣁⠐⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣯⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣄⣠⣤⣴⣟⣁⣤⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢻⣿⢿⣿⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢛⣛⣛⣻⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡜⠘⣯⠉⣿⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠁⠀⠘⢧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⢶⡟⣀⣠⣤⣴⣦⣬⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⢤⣭⣉⣉⣉⣉⣉⣉⣛⣛⣛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⢶⡾⠿
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠒⠒⠤⠬⠭⠭⠭⠭⠭⠍⠉⠁⠀⠀⠀⢠⡟⠳⢤⣀
⣼⠃⠀⠀⠀⠉⠑⠢⠄⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣒⡒⠒⠒⠢⠤⠤⠤⠤⢬⣭⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠄⢀⣀⣀⣀⣀⣈⣉⣉⣉⠉⠉⠉⠉⠉⠉⣛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⣤⣽⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣭⣭⣭⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⡦⠄⠤⠄⠀⠀⠀⠉⠁⣀⣀⠀⠀⠙⣟⠛⠋⠉⠉⡟
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣉⣩⣭⡿⠿⠟⠛⠛⠛⠛⠛⠒⠶⠶⠾⠿⠛⠀⠀⠀⢸⠃
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠛⠉⠁⢀⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠶⠒⣛⣉⣉⣤⡤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣈⡳⣭⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠦⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠦⡀⠀⠀⠀⠀⠀⣠⠔⢲⢰⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⡆⡇⠀⠀⠀⠀⠀⣼⠕⠂⢀⠀⢠⠂⠀⠈⢆⠀⠀⠀⡜⠁⠀⢸⢸⠴⣚⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢸⠀⡇⡇⠀⠀⠀⠀⡸⠁⠀⢠⢇⡴⠃⠲⡀⠀⠘⡄⠀⠀⡇⠀⠀⢸⠔⠊⠁⢀⡇
⠀⠀⠀⠀⠀⠀⡞⢳⢸⠀⢸⠀⡇⡇⠀⠀⠀⢀⠇⢀⡴⣷⢍⠀⠀⡠⣈⢦⠀⠱⡄⠀⢹⠉⡣⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⢀⣧⣸⣼⣠⣼⣄⣧⣇⣤⡀⠀⢺⠊⣏⠀⠐⠆⠀⠀⠰⠀⠀⣳⢄⣹⢀⡼⠃⠯⡖⠒⠊⠁⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣷⡀⠀⣐⣂⠀⢀⠟⡏⢀⡞⠈⠉⠉⠉⠁⠀⡤⡄⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢹⢦⡀⠀⠀⠀⠹⣄⣇⠙⡦⢍⡡⡴⠋⢠⢃⡟⠀⠀⠀⠀⠀⢀⡴⠋⠙⢢⡴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠭⠬⠉⡇⠀⠀⠀⠀⠈⢁⣹⡇⠀⠀⣸⣾⡓⠋⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡴⠚⠉⠓⡇⠀⣛⣛⠀⡇⠀⢀⠔⢺⠉⠉⢣⡈⢲⡞⢁⠇⠈⠙⡶⠦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠰⡁⠀⠀⡀⠳⠤⢤⠤⠄⠇⠀⠆⠀⣸⠀⠀⢘⠑⢻⡟⠋⠃⠀⠀⡇⠀⢹⠀⠀⢸⠖⠖⠖⠒⠲⠚⠳⠲⡇
⠀⠀⠀⢀⠔⠁⠀⢄⣇⡠⠀⠘⢦⠀⠀⢰⠀⠀⢻⠀⠀⠘⠖⠑⣞⠒⠂⠀⠀⡷⠀⠈⡄⠀⢸⠀⠀⠰⣉⣱⠀⠀⠀⡇
⠀⠀⠀⠸⣄⠀⠀⠀⠉⠀⠀⠀⢠⠇⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣧⠀⠀⡇⠀⢸⠀⠤⠤⠤⠬⠤⠄⠀⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣇⣀⡀⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⢳⠀⢸⣀⣉⣉⣉⣉⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠒⠬⣷⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣟⡩⠭⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡞⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣇⠀⣠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢼⣄
⠀⠀⠀⠀⠀⠀⠤⢤⡴⣫⡿⠓⠒⢾⢶⡥⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣳⣯⣻⣦⡤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠺⠛⡏⠀⠀⣀⠜⠓⠚⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠃

⠀⠀⠀⣠⣶⣤⡄⠀⠀⠀⢀⣶⣾⢺⡷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⣾⣿⣷⡄⠀⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⢀⣴⣲⡶⣤
⠀⠀⠐⣇⠙⠃⡧⠀⠀⠀⠀⠴⣷⠚⣿⠅⠀⠀⠀⠰⣯⢯⡧⠀⠀⠀⠀⠀⠩⣍⣉⠀⠀⠀⠀⣴⠚⠛⠛⣿⠀⠀⠀⢈⣭⣭⣭⣭
⠀⠀⠀⠉⠋⠋⠀⠀⠀⠀⠀⠈⠹⠛⠛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣸⣿⡧⠀⠀⠀⢀⣴⣿⣷⣦⠀⠀⠀⢸⣿⣶⡿⠿⠶⠀⠀⠀⣠⣴⣶⡶⢦⠀⠀⠀⢻⣶⠶⣶⠶⠉⠀⠀⢀⡦⣵⠟⡂⠄
⠀⠀⠠⣾⣿⡿⠃⠀⠀⠀⠸⣇⠛⠛⣺⠁⠀⠀⠈⣽⣿⠷⠟⠃⠀⠀⠐⣇⣩⣁⣰⡞⠁⠀⠀⢸⣧⣻⣼⡀⠀⠀⠀⣰⣿⠽⠻⠿⠆
⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠟⠁⠀⠈⠱⠆⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⢀⣶⡿⢻⣆⠀⠀⠀⢀⡴⣴⠚⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⢾⣿⠷⠂⠀⠀⠀⢸⡏⠉⠀⠀⠀⢦⣴⣿⣄⡆⠀⠀⠶⢳⠾⣅
⠀⠀⠘⣏⠀⢀⡿⠀⠀⣀⡤⠛⠋⠀⠀⢠⣤⣤⣴⡿⠀⠀⢐⣲⣾⣿⣷⣾⠀⠀⢠⡟⠁⠀⠀⠀⠐⢲⣿⣿⡷⠂⠀⠀⠀⠈⢧⠁
⠀⠀⠀⠈⠩⠉⠀⠀⠀⠻⠿⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠀⠀⠀⠙⠻⠏⠉⠁⠀⠈⠻⠦⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣏⣿⣯⣧⠀⠀⠀⠀⠀⠘⢉⡇⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⡔⢲⡄⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠿⣿⣿⣿⡇⠀⢿⣷⣿⣯⣆⠀⠀⠀⠀⡐⠀⡇⠀⠀⣠⠔⠫⠄⠈⣿⡆⠀⠀⠰⠱⠆⡪⠑⠁⡨⠷⡞⠰⣉⡹⠦⠜
⠀⠀⠀⣀⣄⡀⠀⠀⠀⣄⡀⠈⢿⢷⣿⣽⡆⠀⠀⠀⠣⠔⠀⣠⠞⡱⠆⢰⡄⣠⠟⠀⠀⠀⢰⠚⡆⢀⣀⡞⢻⡶⣡⡤⣄
⠀⠀⠸⣿⣿⣿⡶⣄⠀⠙⠻⠀⠘⢿⣻⣽⠇⠀⠀⠀⠀⢀⠾⡅⡸⢃⠒⢀⡼⠃⠀⠀⠀⠀⠀⣟⣷⣏⣠⠟⠉⠀⡯⡷⢾⠙⣦
⠀⠀⠀⠈⠻⢿⣿⣻⣿⠄⠀⣾⡇⠀⠉⠀⠀⠀⠀⠀⢀⡏⠰⠆⠀⣩⠶⠋⠀⠀⠀⠀⠀⠀⠀⠙⢽⠧⡄⠀⠒⡄⠒⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⢰⣙

⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠦⠀⠁⡀⣀⣅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣷⣄
⠀⠀⠀⠀⠀⠀⡠⡦⠋⠀⠀⣠⢞⣭⢭⣍⣳⡄⠀⠀⢀⠀⣠⡟⢻⣯⣿⣖⠉⠀⢶⡆⠀⠀⠀⠀⢀⣀⠀⣼⣟⣻⣗⣿⡶⠀⣠⣶⡄
⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⣹⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⣾⣛⣟⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠛⠙⠋⠉⠁⠀⠛⠛⠃
⠀⠀⠀⠀⣀⡼⠶⢶⣒⣒⣋⡵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠹⠛⠿⠋⠀⠙⠀⠠⠀⠀⠀⠀⠀⠈⠁⣠⣦⣤⡀⠀⣤⡿⣿⣶⣦
⠀⠀⠀⢰⡧⡞⠉⢉⡉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⣐⠃⠀⠘⠆⠀⢀⣶⣾⣶⡀⠄⠀⠀⢀⣼⣿⣤⡿⢶⠀⠘⣿⣿⡶⠏
⠀⠀⠀⠀⠣⡷⠀⠻⠽⣒⡛⠭⠛⠛⠫⠇⠀⠀⠀⠀⢿⣾⠿⠀⠀⠀⠀⠀⠘⢷⣿⡿⠃⡄⠀⠀⠘⣽⣷⣏⣹⣿⡅⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠛⠓⠁

⠀⠀⠀⢀⡔⠋⢉⠑⡆⠀⣴⠞⠛⠛⠶⣤⡀⠀⠀⠀⠀⢠⣶⠄⠘⢷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡀
⠀⠀⠀⢸⠈⠀⠀⡔⠁⠘⣧⠀⠒⠀⠄⠈⢷⡀⠀⠀⠀⣾⡟⠀⣀⣀⣤⣍⠉⢁⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿
⠀⠀⠀⠘⣄⠀⠀⣳⠀⠀⣸⠇⠛⠀⠈⠁⢸⡇⠀⠀⠀⣨⣴⡿⠛⠛⢉⣡⣴⡿⠋⠀⠀⠀⢠⡶⢻⣯⣿⣿⣷⢶⣄
⠀⠀⠀⠀⠈⠉⠉⠁⣠⡾⠋⠰⠀⠘⠀⠁⢸⡇⠀⠀⠀⠛⠉⠶⠿⠿⠛⠋⢡⣤⣤⡄⠀⠀⢸⣿⣿⡿⡟⣻⣿⣿⣿⣷⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⢂⡀⠒⠉⢠⡿⠀⠀⠀⢰⣿⣶⢦⣤⣀⣀⣀⣀⣠⡈⠀⠀⠀⠀⠙⠿⣿⣾⣿⣿⣿⣾⠿⠳⡀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠈⠉⠛⠷⠻⠼⠾⠾⠷⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉