Bio decoration Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠟⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢠⣾⢛⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠐⠂⢲⣿⠏⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⠜⣴⠟⠁⡹⠀⠰⣬⣀⠀⠀⢠⡞⠉⡿⠀⠀⣼⠋⠁⠀⣿⠀⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⡏⣼⡏⠀⢸⡇⠀⢀⠀⣹⠀⢠⡟⠀⢀⡇⠀⢸⠇⠀⠀⢠⡿⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⣾⠃⢠⠇⠀⣿⠀⣸⠃⠀⣾⠀⢠⣿⠊⠀⠠⢸⡇⠠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠁⠀⢸⡿⠀⠻⠦⠞⠙⠛⠁⠀⠀⠻⠆⠋⠒⠊⠉⠐⠃⠙⠂⠀⠁⠀⠀⠀⠀⠀⣀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠛⢻⡟⠓⠒⠒⠲⠲⠶⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⡤⠤⠶⠶⠖⠚⠋⠉⠁⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠀⠀⡝⠂⠀⠀⢀⠠⠄⠀⠀⣠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣀⡠⠊⠀⠀⠀⠇⠀⢆⡠⠊⠀⠀⠀⠠⠁⠀⠀⠈⠁⠀⠀⠀⠀⢰⡆⠀⠀⠠⠐⠆⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠼⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠙⡀⠀⠃⠀⠘⠀⠀⢈⠙⢤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠁⠈⠁⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠦⣄⡀⠀⠀⣀⡤⡔⠎⠂⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡒⢄⣀⡀⢄⠺⠞⠟⡢⢀⣀⠀⡰⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠨⠑⢈⡀⠄⠋⠀⠀⠀⠀⠀⠙⠦⡈⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡡⢐⡩⠄⠂⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢⠀⠐



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⠤⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠀⠀⢀⡦⢤⡎⡴⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⣆⠃⠀⠀⠀⠀⠀⠀⣤⠆⣚⠑⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠰⠗⠐⠀⣹⠃⠀⠄⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢰⡟⢳⡄⠠⠀⠀⢸⡇⠀⠀⠀⠀⠈⠀⠘⠤⠃⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣳⢸⣴⠛⣾⣧⡟⣧⡼⣻⣶⢸⡆⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠦⠤⠘⠓⠚⠉⠘⠘⠚⠙⠋⠓⠋⢙⣿⠘⠛⡇⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣵⠴⠳⠀⠀⠀⠐⠺⣄⠀⠀⠀⠀⠀⠀⠀⠛⠋⠠⠞⠁⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠀⠀⠀⠀⠀⠳⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠿⢆⡀⠐⠇⠀⠀⠀⠀⠰⠛⣖⠻⣿⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠛⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠹⠧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣴⣣⡞⢁⡴⠀⠀⠀⠀⠀⢠⡞⠁⠀⣴⣷⠀⠈⠻⡄⠀⠀⠀⠀⠀⢠⢎⠁⠰⡇⡦⠀⢁⢆
⠀⠀⠀⠀⢠⣾⡿⠷⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡜⡽⢋⡾⠋⠀⠀⠀⠀⠀⠀⣾⠰⠾⢶⠉⠁⠘⢿⡆⢹⠀⠀⠀⠀⠀⢣⠈⢁⡂⡇⠆⣂⠉⢠
⠀⠀⠀⣠⣤⣬⣥⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣴⢋⣠⠔⠂⠀⠀⠀⠀⠀⢹⡀⢠⣶⡄⢠⣶⣤⠀⡾⠀⠀⠀⠀⠀⢃⡸⠀⣁⡇⣂⡁⠰⡠
⠀⠀⢀⣤⣬⣿⣿⣿⣯⣤⣤⡀⠀⠀⠀⠀⠀⠛⣾⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣉⠁⠀⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⣈⠇⣁⡤
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⣄⣠⣿⣿⣄⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⠄⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⢲⡄⣸⡇⠀⣧⡟
⠀⠀⠀⡀⢸⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠁⠙⣄⠀⠀⣡⢄⡰⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠈⢻⣿⠁⢠⣿⡄⢠⢀⡀
⠀⠀⠀⠀⢙⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⢋⠀⠀⣩⣉⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣧⠈⠈⠁⢸⡾⠁
⠀⠀⠀⠀⠎⠘⠿⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠈⡋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠙⠇⠀⠀⡾⢿


⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⢤⡄⠛⠃⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢠⢶⡄
⠀⠀⠀⣠⡄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⢨⠉⡅⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠻⠃⠀⠘⠟⠀⠀⠀⠀⠀⠀⢻⠙⠲⠠⣶⣶⣦⡄⠀⣸⠀⠀⠀⠀⠀⢀⣀⠀⢐⡛⡿⢿⠯⠀⠀⠀⠀⠀⠀⠠⣿⠴⣷⣶⣾⠄⢸⠂⡇
⠀⠀⠀⠀⠀⠾⠆⣠⡐⠿⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⠙⠛⢿⣇⡴⠋⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣈⣉⣁⣀⣾⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⣠⡼⠻⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠚⠃⣀
⠀⠀⢀⡞⣿⠻⣆⢻⠄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡁⠀⢴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢈⣄⢸⣦⣾⢉⡔⡀
⠀⠀⠘⢧⣙⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠈⠛⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⣠⢿⣿⣿⢣⡀⠼⠆
⠀⠀⠀⢀⣹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠘⡋⠻⠀⣐
⠀⠀⠀⠈⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣤⣉⠀⠈⠦⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⣙⠟⠡⢈⣱⣄⠐⠀⣄⡀⣼⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡤⠛⢁⠄⠀⠀⠀⠀⠹⣏⠸⣳⣾⣥⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣠⣿⠄⡰⠎⠐⠀⠉⠂⠀⠤⠠⠄⠀⠘⠓⡟⠦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⡔⠃⠀⠀⣀⠀⡀⠀⣀⠀⠶⠀⠀⠀⠹⢦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠋⡿⢻⡁⠀⠀⠀⠉⠢⠀⠄⠀⠀⠀⡀⠀⠀⠀⣠⡆⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠘⡷⠐⠒⠂⠀⢠⡴⠄⠀⠒⠈⠁⠒⠀⠠⣦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⣤⠀⠠⠄⠀⠀⢆⡀⢀⡀⢀⣀⡄⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠙⢶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠻⠆⠀⠀⣤⣔⠛⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠰⠦⣀⠉⠁⠀⠀⠀⠀⢀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣦⡀⢨⡀⣠⠀⢀⡀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⣴⡀⣠⠆⣐⣘⣃⠌⢫⡍⠉⠐⠿⣧⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡎⠀⠀⠀⢨⣽⢏⡀⠋⠻⠟⠁⠀⡈⠓⠦⣀⠘⠛⡧⣌⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⢀⣼⠛⣿⠗⠀⠀⣀⡀⠰⠶⢖⣀⠂⠐⢮⣅⡈⢻⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢨⣄⠀⢀⣀⡀⠀⠀⠀⡨⣿⣄⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⠆⠘⠂⠋⠘⠃⠓⠀⠉⠙⠋⠉⠀⣠⠚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⢠⣤⣴⡷⠀⠀⠤⠀⠠⠄⠁⠀⡴⠌⣡⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣈⣽⠋⠀⠀⠀⠀⢀⡀⣄⠀⣠⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠐⡶⠂⣤⠒⢘⣳⣎⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣶⠁⡀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣞⠁⠉⢤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⣻⣷⣀⠀⠲⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠇⠀⠀⣾⢤⣴⠀⠀⠿⠶⡄⢀⠄⡘⠷⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡬⠛⠁⠁⠀⠀⠀⠈⠓⣽⣦⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢼⡇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠠⡀
⠀⠀⠀⠀⠀⢀⡄⠁⠉⠀⠐⢋⠸⠁⢘⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠢⠄
⠀⠀⠀⡀⠆⠁⠁⠀⢴⢾⠀⠀⠀⠙⢯⠸⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣤⢼⡇
⠀⠀⠀⠃⠀⠀⠀⠘⠆⠀⠀⠀⠘⣿⡎⠘⠆⡀⠀⠐⠀⠀⠀⢀⠙⠐⠛⠻⡟⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠋⢃⡒⠀⠈⠅⢀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⣠⠴⠿⠀⠀⠈⠳⢤⣄⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠞⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠠⠠⠆⠀⠀⠈⠀⢠⠀⠰⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠂⠀⠀⢀⠀⢀⡀
⢀⣶⠀⠀⠀⠸⠂⠂⢀⣄⠀⠀⢸⡇⠀⠀⢀⣴⣩⢣⠀⠀⠀⠐⠂⠀⠀⠀⠁⢀⠀⠫⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⣿⡟⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠘⠁⠀⢀⣈⠅⢡⠈⠂⠀⠀⣠⣾⠀⢀⠀⠐
⢯⠁⠀⠀⠀⠀⠀⠂⠀⠀⣇⠀⣀⠀⠀⠈⠀⠀⠘⠄⠀⠀⢠⣾⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⣀⣤⠺⠗⠁⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠁⠀⠉⠀⠠⠊⠑⠀⢀⡀⠀⠠⠀⠈
⣣⠀⡀⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠒⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡎⡀⢹⣦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡢⢂⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠄
⣐⣃⡜⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠄⠀⠘
⡘⠾⡟⠢⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠋⠀⠄⠀⠂⠀⠉
⠁⠓⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠀⠀⠐⠀⠀⠀⠘⢀⠀⠈⠀⠒⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀⠀⠀⠀⠀⠀⠘⠂⠀⠆⠀⢳⡄⠀⠉⠃⢀⠐⡄⠀⠀⠀⠀⠀⡀⣶⡦⢄⣀⠐
⢃⢠⡄⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⢀⡇⠀⢀⢤⠀⠀⠀⠀⠀⠳⠀⢀⡟⠳⢄⡀⠀⢰⠀⠊⠁⠀⠁⠀⠀⡍⠁⠀⠀⠵
⠈⠀⠀⢠⡄⠀⢀⣀⡤⠔⠀⠀⠀⠄⠀⠁⠀⢈⠤⣷⡍⠼⠀⠀⠀⠑⢤⠁⠁⠀⠑⢤⠏⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⡀
⠀⠀⠈⢺⠇⠤⠤⣄⠀⠀⠠⣤⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁
⠀⠀⠀⠸⡀⠀⠀⠈⡇⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠶⠀⢄⠀⠀⠀⠈⢖⠀⡔⠋
⠀⡞⠁⠀⠙⠲⢤⣀⣇⣀⣀⠀⠀⠀⠀⢦⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠢⡀⣶⢴⠆
⠸⠇⠀⠀⠀⠀⠀⢸⡁⠀⠈⢃⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡷⠊
⠀⠀⠀⠠⣂⣀⠀⠈⠓⠦⢤⣧⣄⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢃
⢰⠏⠉⠃⠿⣿⠀⠀⠀⠀⣟⠀⠈⣷⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠐⡆⠁⠀⠀⠀⠈⠒⠤⣿⣀⠀⠀⠀⠂⠀⠀⠀⠒⠁⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛
⠚⠐⠀⠐⠔⠁⠀⠀⢱⠠⠀⠀⠀⠻⣌⡇⠀⠀⠐⠲⠿⣶⣶⣄⣀⡀⠀⠀⠉⠁⠁⠈⠒⠲⠢⠄⠀⠐⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡅⠀⠂⠀⢤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣄⣨⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢼⠀⡶⠆⠀⠀⠀⠀⠀⠀⣀⡈⢁⣈⢁⠈⠁⣀⠀⠀⠀⠀⠀⡇⠠⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉
⠀⠀⢸⢠⣀⣠⠀⠈⠀⠀⠀⠀⣿⠉⠉⠉⠈⠈⠀⣿⠀⠀⠀⠀⠀⡇⣤⣀⡄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈⢢
⠀⠀⣼⣀⣉⣁⢰⣶⡆⠀⠀⠀⠿⠒⠂⠒⠂⠐⠂⠿⠀⠀⠀⠀⢀⣇⣈⣉⡀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟


⠀⠀⠀⠀⢠⠶⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠲⠀⠖⡆⠀⠀⠀⠀⠀⠀⡠⠖⡒⠤⡀
⠀⠀⠀⠀⢸⣄⣀⡼⠀⠀⠀⠀⡖⠉⠉⡩⡉⠉⢱⡄⠀⠀⠀⠀⢰⣴⠀⣀⡇⠀⠀⠀⠀⠀⡜⠴⠜⠃⢶⢸
⠀⠀⣠⡶⠋⠀⠁⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠰⣔⠇⠘⢓⠜
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⣶⡎⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢂⣠⣤⢂
⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣀⡽⠀⠀⠀⠀⠀⠀⠈⠀⢻⢿⠃⠘
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠉⠘⠂


⠀⠀⠀⣤⠈⠛⢫⣄⠀⠀⠀⠀⠀⢀⡨⠄⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢙⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡐⠠⠄⠃⠎⠀⠀⠀⠀⠀⠀⢀⣂⣈⡄⠀⠀⠀⠀⠀⠀⠀⣄⣿⡀
⠀⠀⠷⣶⠾⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠋⡒⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣠⣿⣄⡀

⠀⠀⠀⠀⠆⣄⠀⠀⠀⢀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠂⡀⠂⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⡄⠄⠀⡼⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠆⠡⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⢸⡄⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢣⡀⠈
⠀⠀⠀⠠⠀⠐⠠⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠄⠚⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠓⠀⠀⠈⢠⠀⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⠇⢱⠀⠀⠀⣀⣴⡄⠀⠄⣀⠤⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀
⠀⠀⢀⠐⡄⠀⠙⠀⠀⠀⠃⠘⠀⡞⠀⠀⠀⠀⠉⣤⢻⠁⠀⣸⠀⢩⠭⠀⣠⠂⡇⢸⢈⡁⡭⠀⠀⢹⠀⠀⠐⣆⠀⠿⠈⠀⢀
⠀⠘⠒⠚⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠘⠉⠑⠃⠁⠚⠀⠋⠐⠁⠁⠚⠁⠚⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠉⠙⠛⠀⠿⠯⠝⠿⠟⠟⠩⠿⠷⠧⠼⠷⠾⠾⠿⠀⠺⠁⠀⢖⠀⢆⠀⠶⠀⠠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⡀
⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢆⡀⢀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣠⢠⠀⣾⠁⢹⠂⠀⠀⠀⠈⢠⣿⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢤⡀
⠀⠀⠠⢼⠋⠀⠙⣗⠉⠉⠉⠀⠀⠀⠀⠐⠀⠛⢛⣧⣴⠀⠀⠀⠀⠀⠀⠀⠐⢀⢰⣦⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⣤⣒⡤⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢿⢁⡀⠀⠀⠀⠀⠐⠁⡀⠀⠙⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢠⣥⣤⡐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢈⣶⠸⠟⣥⡷⠀⠀⠀⠀⠀⠆⣣⣔⣒⠆
⠀⠀⠀⠀⠈⠻⢛⣧⣦⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠮⠀⡀⠨⢶⠆⠄⠀⠀⠀⠀⣿⠻⠿⠆⠀⢱⡆
⠀⠀⠀⠀⠁⠀⠨⠙⡛⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣳⣄⠻⣦⠀⠀⠀⠀⠀⠁⡁⠁⠀⠈⡀⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⠄⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠐⠂⢊⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⢠⡀⠄⠁⠀⠀⠀⠀⠀⣄⡷⣿⣹⣨⣿⢾⡀⠀⠀⠀⠀⠈⣁⡀⠥⠰
⠀⠀⠀⠀⠀⠳⡡⠊⠐⢀⡀⠀⠀⠀⠀⠀⢾⡘⠇⠋⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⣼⣺⣿⣵⠀⠀⠀⠀⢀⡄⢤⡤⠂⠀⢰
⠀⠀⠠⠪⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣷⣟⣧⣠⣭⣬⡉⠀⠀⠀⠠⢯⣽⠑⠛⢤⣠⠞⠷⠦
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⢤⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋⢩⡿⢷⡀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠀⠀⠀⡀⢾⡿⠿⠿⣿⣿⡇⠀⠀⠀⠀⢸⣤⣌⣿⣿⣧⣈⡇⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠂
⠀⠀⠀⠹⣿⣧⣀⠀⢀⡿⠁⠀⠀⠀⠀⠘⢿⣀⣹⣇⣀⡹⠃⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠈⠙⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑

⠀⠀⠀⠀⢸⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠔⢒⣚⠒⢄⠀⠀⠀⠀⠀⠠⣄⢰⠀⢰⡴
⠀⠀⠈⠈⣄⢀⡩⠄⣐⡀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡧⠶⡜⠃⠲⡎⡇⠀⠀⠀⠀⠀⠹⣾⠀⡼⡇⢀⣀
⠀⠀⠀⠈⠀⢈⠤⣀⠴⠤⠀⠀⠀⠀⠀⠻⣟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠇⠰⠷⣠⠃⠀⠀⠀⠀⠀⢠⡟⣧⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠁⠁


⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⢴⣶⣤⠀⢾⣶⡄⠀⠀⠀⠀⠀⣶⠖⠲⠲⠰⠺⠐⢶⡆⠀⠀⠀⠀⠀⢰⢿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠉⠁
⠀⠀⠈⠻⠿⣀⡀⠉⠑⠂⠀⠀⠀⠀⣿⣀⣀⢈⣀⢘⣀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡃⠐⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠈⠉⠈⠉⠘⠁⠀⠀⠀⠀⠀⠸⣶⣾⡾⠀⠀⠀⠀⠀⠀⠀⠙⠇


⠀⠀⠀⠀⣀⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶
⠀⠀⢠⣾⣿⣿⢰⣿⣷⡀⠀⠀⠀⠀⠐⡇⢀⠛⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙
⠀⠀⣾⣿⣿⠇⢸⣿⣿⡇⠀⠀⠀⠀⠀⡇⠲⣶⠇⢀⠀⡀⠀⠀⠀⠀⠀⠀⣨⡙⠀⡹⠃⠀⠀⠀⠀⠀⠀⢠⣶⣶⣈⣴⣶⡆
⠀⠀⠘⠛⠁⠀⠘⠿⠿⠃⠀⠀⠀⠀⠰⠷⠶⠶⠦⠸⠿⠗⠀⠀⠀⠀⠀⠰⠶⢿⠿⣭⠴⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿


⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀
⠀⠀⠀⣿⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣺⡠⠤⣠⡇⠀⠀⠀⠀⠀⠀⠀⠘⣀⣦⣔⣋⠀⠀⠀⠀⠀⠀⠰⡏⠀⣹⠀⠈⡏
⠀⠀⣼⢏⣾⡇⣷⡀⠀⠀⠀⠀⠀⠀⠋⢹⡛⣈⢻⠍⠃⠀⠀⠀⠀⠀⠘⠀⠜⣿⡿⠤⠘⠂⠀⠀⠀⠀⠀⠉⣟⠁⢠⠏⠙⣦
⠀⠀⠈⠺⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠽⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠈⠓⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠀⠐⠈⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡦⢀⢃⠄⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⢠⠀⠐
⠀⠀⠀⠀⠀⠀⡠⢖⡝⠶⠆⠀⠀⠀⠘⡈⠐⠀⠀⠀⠈⠁⠃⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⢿⠀⠀⠀⠀⠀⠁⢀⣄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⠁⠀⠰⠀⠀⠀⢨⠀⠂⢀⡞⢐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠋⠳⡁
⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄⡔⠉⠡⠂⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⡊⠀⠀⠈⠇⠀⠀⠀⠐⠃⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⡠
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠲⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠤
⠀⠀⠀⠀⠀⣤⠘⠀⠀⠠⠘⢀⠀⠀⠀⠀⠘⡀⠀⠄⠀⠀⠘⠀⠀⠀⠀⡀⠠⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡤⠐⠀⠊⠉⠀⠀⢴⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⠷⠡⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠍⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣤⣇⠠⣦⠀⠈⠀⠀⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢃⠥⡤⣅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈⡀⠓⠀⠁⠀⠀⢠⡀⠉⠀⠀⠀⠀⠀⠀⠐⠈⠐
⠀⠀⢀⣠⠄⡀⢀⠀⠀⡰⠠⠈⠀⠀⠀⠒⠀⠐⠀⠀⢰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠃⠊⠀⠀⢬⡰⠢⠤⠖⠂⠀⠠⠀⠀⠀⠤⠀⠑
⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠂⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠘⠂⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢄⠙⠂⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢽⠛
⠀⠠⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠘⡤
⠀⡀⠀⠀⠀⠀⡤⠁⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠄⢠⠂⡲⠊⠀⠀⠐⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠀⠀⡎⠈
⠀⠈⠀⠀⢀⣰⡇⢄⢀⡀⠀⠀⠀⠐⠂⣁⣀⣀⣀⣀⣬⣈⣋⣀⣀⣀⣀⣈⣁⣁⣀⣠⣀⣀⣀⣈⣀⣀⣀⣁⡀⠀⢠⠂⠃⠀⠀⠔⠀⠁⠀⠀⠀⢱⡔
⠀⠀⣰⢮⡙⠅⡇⠉⢉⡁⠐⠄⠀⠀⢸⣿⣿⣿⣿⣿⡿⡿⡿⢿⣿⢿⡿⠿⢿⡿⢿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⢰⠉⠈
⣀⣀⣧⣲⣝⣶⣃⣀⣀⣀⣁⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣶⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⡘⣆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⡉⡉⢋⣸⣏⣨⢃⢳⢰⡆⡇⢽⣁⣸⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢫⢾⡻⡍⡗⠛⠋⠁⠉⠉⠉⠀⢸⣿⣿⣿⢿⠿⡿⠿⠿⣿⣿⠿⠿⣿⠿⠿⣿⢿⠿⢿⠿⠿⠿⡿⣿⣿⣿⠋⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⡏⢉
⢀⣀⣏⢢⡙⣦⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢀⠼⣏
⠙⠧⢸⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠰⠀⠀⠀⠀⠀⣀⠀⠀⠒⠠⠁⠓⠀⠀⢀⠀⠢⠀⠀⠉⠀⠀⠀⠈⠤⣸
⠀⢀⢞⠀⠀⠀⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠖⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠰⠄⠈⡀⢀⢄⢀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠘⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠁⠀⡀⢀⠀⠀⠀⠀⠉⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠁⢀
⠀⠀⠄⡈⠃⠐⠀⠠⡠⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠂⠁⢀⠀⠰⠀⠀⠀⠀⡀⠐⠆⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⣰⠄⠀⠀⢠⠃⠀⠀⠀⠀⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⣀⡹
⠀⠀⠀⠀⠀⠀⠘⢶⠊⠁⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠔⢒⡨⠅⠺
⠀⠀⠀⠀⠀⠀⠀⠐⠃⡔⠊⠉⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣀⠐⠆⠓⠒⠒⠒⠠⠤⠤⠐⠉⠀⠀⠀⠀⠀⠀⠙⠤⣀
⠀⠀⠀⠀⠀⡀⠄⠂⠀⠈⢣⠘⡄⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢈⣅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⠄⠀⠀⠉⠘⠒⠢⡄
⠀⠀⢀⡴⠊⢀⠄⠂⠀⠐⠀⢇⠰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠃⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⠊⢠⠊⠀⠀⠀⡠⠊⢀⠼⢆⣣⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇
⢀⠂⡰⠁⠀⠀⢀⠊⢠⠊⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠀⢠⢤⣹⠟⠳⠒⢇⡀⠀⠀⣸⠀⠀⠀⠀⠐⠢
⡈⢀⠁⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆⠀⠀⣤⢺⠼⠁⠀⠀⠀⠀⠢⠄⠀⢨⠂
⡇⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⠀⠐⣀⡀⠄⠐⠀⠉⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⢀⠜
⢣⠀⢆⠀⠀⠀⠘⢄⠘⢄⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⡀⢼⠀⠀⠀⢢⠚⠀⠀⡀⢀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡠⠁
⠈⢆⠘⡆⠀⠀⠀⠈⡆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠓⠮⠅⠐⠉⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠦⠐⠲⠠⠖⠊⠀⠀⠀⠀⠀⠀⡜
⠀⠈⡄⠈⠢⠤⠔⠊⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠆⠆⠀⠀⠀⠀⢃
⠀⠀⠈⡄⠀⠀⡴⡫⠄⢌⠐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠐⠃⠈⠙⠐⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠁⠀⠀⡀⠅⠀⢀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡀⠀⠀⣠⠖⠐⠢⡤⣤⠤⠾⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠭⠅⠊⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠇⠀⡰⠁⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠒⠒⠒⠊⠀⠐⠃⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠬⠭⠭⠭⠥⢀⠀⠀⠀⠀⢠⠀⠈⠀⡰⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠛⠦⠴⠊
⠀⠀⠀⠠⣀⣘
⠀⠀⠀⠀⡀⠚⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⢚⠂⡁⠶⠀⠀⣠⣤⡴⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢨⠃
⠀⠀⠐⠁⠈⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢐⣂⠀⣤⠈⠃⠀⠀⡰⠆⠴⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢈
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠃⠛⠈⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡚⡂⠐⠒⠚⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠀⣰⠊⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠒⢾⡇⠀⠀⠀⠀⠀⠀⢚⢿⡀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠘⠃⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠈⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆⠈⠀⠀⠠⠤⠀⠀⠀⠀⠀⠇⠀⢂⠰⠁⠀⠀⠀⠠⠀⢹⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⢠⠄⠀⠀⠀⢀⢀⠀⠀⢀⣶⠀⠀⠀⠀⠁⠀⢠⠤⡀⣌⡁⢄⠀⠀⠀⠀⠀⠀⠀⢀⢤⡟⢠
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠲⠓⠀⠀⢤⠀⠀⠀⠀⢀⣄⢻⡏⠀⡠⠊⡀⠀⠀⠈⠀⠀⠀⠐⠀⠐⠊⠀⠘⠠⠐⠀⠀⠀⣠⣶⡃⠘⣾⠛
⠀⠀⢸⠋⠀⠀⠀⠔⢒⡒⠒⠀⠀⠀⠡⠴⠃⠀⠀⠀⣠⠜⢎⢉⠁⠐⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠟⢇⠿⣸⠛
⠀⠀⡠⠀⠀⣢⡄⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⢨⠀⢠⠚⢉⡀⠈⠃⠀⠀⠀⠀⡴⠳⢄⠀⠀⠀⠠⠈⠁⠀⠀⢹⠀⠀⠤⢶⣿⣽⡏⢜
⠀⢰⠇⠀⠀⠘⠁⠀⠀⣠⡀⠁⠈⠀⠢⠀⠀⠀⠀⣠⠐⠃⠀⣌⠣⡀⠀⠾⠀⠀⠈⡈⠁⠁⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣧⠑
⠀⢈⠇⠀⠀⠀⠠⠤⠄⠈⠀⠀⠀⠀⠀⠀⢰⠖⠡⣠⠛⣄⢸⡟⠈⢻⠄⠀⠀⠀⠂⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⡀⣄
⠀⢘⠁⠀⣲⣦⠀⠀⠀⠀⠀⠛⠁⠘⠶⠄⠸⡎⠴⠁⠁⣠⡿⣧⢸⡙⠀⠀⠀⠀⢀⡀⢠⢺⣇⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠈⢁⠀⠸
⠀⠈⠁⢀⣏⠁⢀⠀⠀⠀⠰⠌⠀⡁⢈⠀⠀⠱⡄⠀⣳⢋⠚⠈⣴⠃⠀⣖⠐⣴⣯⡏⠀⠘⡏⠀⡄⠀⠐⠠⣀⡀⠠⢀⠀⣄⠀⠘⠘⠇
⠀⢺⣿⡈⠹⠗⣦⡠⠀⠀⠈⠓⠖⠀⠀⠀⡠⠀⠙⢶⡏⠀⠄⡒⠁⠀⠀⠀⠌⠝⢳⠚⠀⠀⠀⠀⢉⣀⣀⠀⠈⠉⣉⣁⣀⣿⠴⠂
⠀⠀⠀⠀⠂⠛⡉⠀⠀⠀⢀⠈⣥⠒⢲⠃⠀⠀⠀⠀⠁⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠏⠀⢀⡾⠉⠀⠀⢸
⢤⡀⠀⢀⣴⠂⠁⠠⠐⠈⢉⡵⠖⠋⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠀⣀⠀⢠⡄⠀⠁⠀⠀⠀⠘⣇⢀⣠⡴⠎⠀⡸⡆
⢘⣙⢆⠾⠁⡀⠀⠀⢀⠠⠋⠀⠀⠀⡄⠀⠁⠀⠀⠠⣀⠀⠁⠀⠔⠁⠀⠀⠘⠓⠂⠄⣈⡙⠀⠀⠀⢀⡞⠛⠛⢻⠉⠁⠀⠀⠀⠁⣿⡀
⠸⣿⣻⣰⠟⠁⠀⠀⠀⠔⢀⠀⠅⠀⠌⠀⠀⠀⠀⠀⠀⡀⠀⢀⡰⣀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠘⣆⣀⣠⡿⠀⠀⠠⣄⠀⠀⠈
⠀⠈⢹⠁⠀⠀⠀⡐⠈⠀⠀⠐⠀⠆⠠⠂⠀⠀⠀⠀⠀⠈⢑⠉⠀⠀⣁⡀⢀⠀⠁⠶⠑⠀⠀⢠⡞⠛⢻⡍⠀⠀⠀⢰⣷⡾⡴⠲⣦⡀
⠀⠀⢈⠀⠀⡀⠀⠄⠀⢈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠜⠀⠀⢘⡀⠀⠀⠄⠡⡄⠂⠀⠀⢸⣅⣀⡼⠃⠀⠀⠑⠞⣫⠁⠀⠀⠙⠳
⠀⠀⢿⡇⠀⢣⡀⠀⠑⠀⢀⡀⠀⠀⢀⣀⣤⠤⠤⠴⠶⠄⠀⠀⠀⠀⠉⣁⣀⣀⠐⠈⠀⠀⡶⢺⡏⠁⠀⠀⢻⠆⠀⠀⢯⣠⠀⣀⣰⡇
⠀⠀⠘⠀⠀⠀⠳⡀⠀⠀⠈⠂⠀⠉⠁⠁⠀⢀⠀⠀⠀⠀⠀⠠⠤⠶⠿⠿⠟⠛⠉⠀⢀⣼⡟⠋⠀⠀⠀⠉⠚⠄⠀⠀⠀⠉⠓⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢐⢀⠀⠀⠀⢀⡀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢁⠘⠐⠈⠀⢀⠔⠁⠀⢀⠋⠉⠁⠁⠁⢲⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠊⠀⠒⠒⠁⠀⣀⣹⠒⢲⡏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⡄⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠔⠛⠶⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠾⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠐⣿⠃⢀⣠⡈⠁⡀⠀⠤⣴⡀⠀⠀⠀⠀⡰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠃⠀⠈⠙⠁⠈⠁⢀⡴⣅⠀⠀⠠⠀⢘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⣿⠛⠛⣦⠀⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠸⣄⡼⠃⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠾⢿⣄⢠⡄⢀⣤⣄⢸⡇⢠⣤⣄⠀⣠⢦⡄⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⢸⡇⣿⠁⢹⣾⡇⣿⠀⣻⢴⡏⣸⡇⣿⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣀⠐⠿⠶⠛⠛⠁⠘⠇⠙⠷⠛⠘⠇⠙⠶⠋⠈⠛⣻⡇⠙⠛⢹⡇
⠀⠀⠀⢀⡴⠉⠛⣲⣄⠀⠙⠤⠇⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣽⠃⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠑⣡⡴⠞
⠀⢀⡠⢋⣴⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠁⢳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠉
⠀⠀⣠⡾⠋⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣘
⠀⠸⠏⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠲⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⣤⣾⣿⡆⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠿⡤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢾⠀⠉⠻⠁⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡇⠀⠀⠈⠛⠛⠣⣄
⠀⠀⠀⠀⠀⣠⠀⠀⠙⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣦⣤⠀⠀⣽
⠀⠀⢀⡀⡸⠋⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠨⢙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠈⠀⠀⠀⠠⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⣶⣶⣦⣶⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⠀⠀⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠢⢄⡈⠙⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢀⠔⠋⠉⠒⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⡅⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠑⠲⠤⣀⡀⡰⠻⡶⢄⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡼⠁⠀⠘⡌⠣⡀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⠴⠋⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⢉⡆⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠛⠛⠛⡿⠃⠀⠀⠀⢠⠃⢰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡽⠒⠒⠒⠒⣅⣀⣀⣀⡠⠋⢠⠇⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⠤⠒⠉⣀⠔⠁⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⡶⠀⠀⠓⠂⠤⠤⠐⠚⠒⠊⠉⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⢶⣶⣶⣦⣤⣶⣶⣔⣶⠶⠶⠶⠶⠟⠛⠋

⠀⠀⠀⢰⡀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠆⠀⠀⠀⠀⠄⢠⠀⡀⠀⡄⢸⢀⢏⣾⢇⢻⣼⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⢠⣼⣧⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⢂⠀⠘⠸⢹⠇⡀⠚⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣄⠀⠸⣿⣯⢆⠙⠹⣄⠀⢀⠀⢀⠀⠀⠀⠀⢰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢀⠀⠏⠃⠁⠀⠀⠀⠁⠀⠀⢰⣿⠿⠶⠄⠴⠖⣶⠀⠀⢀⠃⠀⠀⣴
⣿⠐⠆⡹⣿⣾⣇⢣⠸⣂⣄⡿⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣦⠀⠀⠀⠀⠀⢤⣶⣦⣄⣧⠀⣀⡀⣀⠞⠁⠀⠀⠈⢧⡠⣼⣿
⣿⡆⠣⡄⠙⣿⣿⡞⣧⡘⣌⠴⢖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠀⠀⠀⠀⠀⠀⣿⠄⠀⣹⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢳⣸⣿
⣿⣿⣦⡈⢦⡈⢿⣿⣦⡄⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣏⠀⢀⣱⣿⡴⢀⡴⣊⠀⠀⠀⡌⠀⢀⡿⠀⠀⠀⠀⣄⠀⠀⢀⡆⠀⠀⠙⣿
⣿⣿⣿⣷⣎⢿⣷⣿⡷⢾⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠆⠈⠁⠃⠀⠀⠀⢸⣥⠞⠋⠀⠀⠈⠁⠶⠟⠉⠀⠘⠛⠏⠁⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⣤⡶⠤⢼⣆⠖⠀⠾⡍
⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⡅⣾⣣⠂⣀⢠⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠒⠻⢆⠠⠙⠛
⠸⣯⡻⣿⣿⣿⣿⡻⢿⣿⣟⡁⢳⡝⠂⠽⢿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣦⣤⣤⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠛⠀⢀⠀⠀⠀⠀⢀⡀
⠜⠘⢿⣮⣻⣿⣽⡿⣴⠊⢿⣷⢿⡏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠹⡿⠉⣿⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⢙⣿⣿⣿⣁⡈⠆⠘⡿⢘⣷⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⡰⢇⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠠⠿
⠂⠀⠐⠉⠀⠘⢿⣧⡙⣿⢿⢆⣼⣿⠇⢠⡟⠁⠀⠀⠀⠀⠠⠄⢸⣟⣿⡋⠒⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣷⠀⠀⠠
⠀⠀⠀⠴⣣⠀⠀⠙⢻⣦⢳⡚⣶⣿⣿⣁⡴⢞⠉⠀⠀⠀⠀⢠⢋⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⠻⣿⣿⣯⠞⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣀⠶⡀⡀⣄⣀⠀⠙⢷⡝⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⡴⠀⠀⣿⣦⡀⠀⠀⠠⠖⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣄⡠⠄
⠀⠀⠀⠈⣿⣷⡄⠺⠋⠉⠀⠀⠀⠻⠉⠀⠈⠇⣴⣄⡆⣠⣶⠞⠀⠀⢸⠿⠟⢁⠠⠆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡏⠀⣀⠀⢠
⠀⠀⠀⠀⢻⣷⡘⢿⣆⠀⠀⠈⢀⣀⠀⢠⠴⢗⣿⣾⡿⢡⣿⣤⡀⢀⣼⡤⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢨⣿⣡⡠⢟⣀⡤⠤⠤⠆
⠀⢠⣤⠀⠘⠿⠆⠀⠘⠳⠀⠰⣯⣿⣿⣿⣿⣯⣷⡜⠃⣀⣄⣼⡟⠚⠁⣡⠤⣄⡙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠘⢿⣿⠯⡽⡆⠀⡆
⢀⡘⠙⠀⠀⠀⠀⠀⣀⣴⣦⣼⣿⣿⣿⡏⣹⡏⢸⣧⣸⡿⣷⣤⡽⠶⢾⡱⠷⣄⡁⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⠀⢈⣶⣤⣷⡄
⢺⣿⠗⠀⠀⠀⡀⢀⡹⣿⣿⢿⣾⣿⣧⠠⣾⣷⣯⣽⣿⣳⣿⣿⣧⣾⣿⣷⡶⡟⠇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠸⣆⡞⠛⠏⠰⣷
⠀⠈⠀⠀⠀⠀⠉⢰⡾⠛⠳⠿⣏⣿⣥⡔⠛⣿⣦⣾⡛⣷⠂⣿⣿⣿⣿⠯⣷⡀⢠⡃⠀⠸⣶⠴⠂⠀⠰⠷⠐⠃⠁⠐⠃⠆⠀⠀⠁⠀⠀⢣⡅⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣘⢿⣯⠳⣾⣍⣭⣤⣿⣿⣷⢬⣙⠟⢻⣽⣿⣁⠀⡿⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠀⣴⣿
⠀⢀⠀⠄⠀⠀⠰⠤⣤⣀⣀⠀⠉⠀⠻⣄⢉⣹⣿⡟⣻⣛⣋⣤⣙⣦⡀⠙⠋⠈⠀⠀⠀⠀⠀⠀⣠⣴⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣯⡀⠙⠋⠁
⠀⠀⠀⠀⠀⠄⠀⢀⡀⠉⠍⠻⡓⠈⣠⠼⣟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀⢀⣤⣤⣦⠘⠙⠻⡾⠋⠀⠀⠀⠀⠘⠶⣦⣶⣾⣶⣤⡀⣿⠀⠀⣂⡖
⡠⡇⠀⠠⢀⡄⠀⠀⠀⢀⣰⡿⠋⠀⣡⠞⠉⠀⡴⢿⠟⠉⠉⠉⠉⠉⠈⠂⠀⢀⡐⣿⣿⣿⣿⣇⠀⠀⠀⣦⣤⡤⠄⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⡀⠀⡇
⠀⠀⠀⠀⠚⠐⠀⠀⣠⣿⠟⠀⠀⠐⠁⠀⠀⠞⠁⠉⠀⣔⠀⠀⠀⠀⠀⠠⠀⠀⣁⣸⣿⡟⣿⡟⠀⠀⣼⣿⣭⣤⣄⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⢦⠁
⠀⠨⠀⠂⠀⠀⢀⣰⠟⣱⡇⠀⠀⠀⠀⡀⠀⢄⣀⡀⡰⠏⠀⠀⣁⠀⠀⠀⠀⠀⠉⠻⠁⢸⡏⠁⠀⡿⡀⠀⠉⠉⠉⠉⠉⠉⠒⠀⠀⠀⠘⢏⠁⠱⣼
⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢍⡹⠁⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡌⠀⠀⠀⢷⣌⡱⠀⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⢂⠀⢹⣄
⠀⠀⠀⠀⠀⣤⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠀⢠⣾⡔⢠⣾⢻⡌⢷⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⣈⣻⣦⣾⠀⣴⠆⠀⠀⠀⠀⠀⠀⣴⣶⣾⣗⣺⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣸⣉⣹⠿⣍⣹⡇
⠀⠀⢸⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢻⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣷⣷⣿⣟⠋
⠀⠀⢸⣿⣿⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢳⡞⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠟
⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⡀
⠀⠀⠀⢸⣿⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⡳⠆⣿⠲⢚⣫⣄
⠀⠀⠀⢸⣿⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣮⣙⣛⣋⣿⣙⣛⣩⣵⡦
⠀⠀⢠⣿⣿⣷⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢿⣿⠟⠀⠀⠀⠀⠀⠸⣿⣭⣭⡥⣷⢬⣭⣭⣿⠆
⠀⢠⣟⣉⣉⣉⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣿⣇⢀⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠶⠶⣟⣿⣻⠶⠗
⠀⠘⠻⠿⠿⠿⠛⠁⠘⠋⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠉⠛


⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⣴⣿⡿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠖⢋⣁⠉⣧⠀⠀⠀⢠⣿⣿⣿⣿⣳⣶⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⡺⢗⣿⣿⡇⠀⠀⠀⠀⠀⠀⣇⠀⢠⣤⡄⠉⢰⠏⠀⠀⠀⠀⠛⠋⢳⣾⢹⣿⢹⣶⠋⠙⠃
⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣽⠀⠈⠋⢡⠀⢸⡆⠀⠀⠀⠀⠀⠀⣾⡙⣻⣿⡛⢙⡦
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠖⠛⠲⠶⠚⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠈⠙⠋


⠀⠀⠀⣴⣿⣿⣷⠀⣺⣟⠂⠀⠀⠀⠀⠀⠀⢀⣤⣰⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀
⠀⠀⠀⢻⣿⣿⣿⢈⡿⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⢰⣿⣿⣿⠘⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠻⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠙⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠠⢲⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣯⣷⡄⢠⡩⠻⠃⠀⠀⠀⣠⠔⠚⠉⠀⠀⠙⠬⠱⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠿⢥⣆⡀⠀⠀⢀⢴⣞⠉⢠⣐⡀⠀⣿⠉⢺⣤⠏⣀⠀⢀⡠⠋
⠀⠀⠀⠀⠈⡳⠉⠀⣢⡄⠀⠀⠸⡀⠀⡈⠀⡇⢷⠳⡄⣰⠿⠟⠅⢀⣄⡙⠙⣶⣿⡠⣾⠏⠘⠁⠀⠀⠁⠀⠤⠀⠲⠲⡽⠈
⠀⠀⠀⠀⠀⠙⠁⠀⡉⢉⢢⠀⠀⢣⠀⣧⠀⡇⢸⠀⢸⣿⡀⣀⠤⢴⡛⢿⣷⣿⣿⣿⣿⠴⢃⣠⠊⠀⠀⠀⠀⢰⠢⠦⡶⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⣹⡃⠀⡈⣧⣼⣀⠧⣾⠄⣯⡟⠓⠋⠹⠭⣭⣭⣨⣿⣿⣿⣇⡀⠈⠀⠀⠀⠀⠀⢈⠼⠷⣿⣻⣿⡿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⣨⣍⢶⣬⣾⣯⠟⠲⢿⡏⠋⠀⡄⠐⣀⠀⠲⣶⢾⠿⣿⣿⢻⣓⣋⠩⠂⠀⠀⠘⠋⢍⡿⠋⠉⠀⠀⠈⠂⣶⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⣽⣽⠋⠙⢳⡀⢸⣷⢸⡆⢣⠀⠘⠁⠐⢹⡯⢶⡟⠋⠙⢉⠉⣠⠀⠀⠀⠀⡆⡸⡇⠁⢀⣤⢊⠠⠎⡍⡽⢀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣘⠿⠶⡒⠻⣿⣿⣽⣿⡔⢻⣦⡀⣀⠀⠀⠱⣸⢷⣄⣶⡏⠐⣁⠀⠃⠌⢀⣼⣰⣿⣤⠞⠛⣍⡠⠞⣼⠃⠈⢾⡇
⠀⠀⠀⠀⠀⠀⡶⡦⢀⣠⣄⣾⡃⢀⠶⠶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠌⣭⠎⣹⣼⢿⣷⣿⣎⢚⡡⠂⠀⠀⠀⠀⠙⢯⣠⣤⣼⣯⢶⡿⠃⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⣤⠴⠻⠛⠻⠉⠀⠀⡱⢒⣫⠿⣿⣿⢧⣀⡀⠀⠠⠦⣄⣠⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⢀⣠⣾⠿⣡⠭⠄⠚⠟⠀⠀⢀⣀⠀⠀⠀⣌⠃
⠀⠀⠀⠀⠀⢀⡟⠱⠂⠀⠀⠰⢤⣰⡛⠙⠋⠁⠚⠫⢨⠜⠁⠀⠀⠀⠀⠒⠭⣙⡿⣻⡿⠿⠃⠤⣤⣶⣶⢻⢿⡆⠀⠠⠖⠀⠀⠀⠂⠀⠸⠋⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠐⠀⢀⡅⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠁⠀⠁⣀⡘⠁⠁⠙⠀⠀⠀⠀⠙⢷⠀⢤⢳⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣁⠀⠦⣀⣀⠀⠦⠀⠀⡀⠀⠀⠀⠀⡔⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠈⠀⠐⠀⠀⠂⠀⠀⠦⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠉⠡⠀⣀⠨⢧⣜⣿⣄⣀⠀⠀⠀⠤⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠲⠄⠘⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢉⠓⢂⣈⣉⣼⣿⣿⣿⣿⢵⡤⠠⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⣑⠦⣀⠀⠀⠀⠘⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢄⠿⣏⠈⠙⢛⡿⣿⣿⡿⣿⣆⡅⠈⠁⠀⠀⠀⠐⠀⠀⠂⢤⣄⣤⢴⣾⣧⣤⡴⠾⠥⠈⣆⣀⠑⠢⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡱⠀⠀⠀⠈⠰⣾⣷⡯⠏⣝⢀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠘⠰⠈⠉⠺⡿⣿⡿⠙⠋⠁⠀⠀⠙⣌⠑⠲⠤⣬⠭⢄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⠌⠀⢈⡍⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠙⠚⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡀⠈⣷⣀⡀⠀⡈⠐⢲⠖⠒⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡀⡼⠛⢏⣿⣾⡇⠈⡿⠈⠀⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡮⢞⠵⠋⠀⠀⠈⢻⣿⡇⢠⠇⠀⡴⠛⢀⠠⡀⠀⠀⠀⠀⢀⠔⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⢹⠀⣾⣀⡼⣣⣤⡤⠰⠆⠀⠂⠠⠐⠉⠀⠦⢶⠑⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡅⣫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡎⠀⠰⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠇⢠⠁⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠒⠀⠀⠀⡄⠀⠀⠀⡠⡋⠀⢠⣁⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣠⠋⠀⠀⠀⡀⠀⠀⠀⢠⣮⡄⠛⣀⠀⢠⣷⠞⠁⠈⠪⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣦⣄⣈⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⣀⠀⣀⠠⠚⠟⠁⠀⠋⠉⠛⠉⠛⠿⠦⠌⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡐⠁⢸⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⣥⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠀⠀⣼⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢿⣻⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⢰⡏⠀⢠⡇⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡀⠀⢸⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠇⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠈⣦⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠙⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠠⣸⠃⠀⠀⢀⢀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⡄⠀⣿⢦⠀⠀⠀⠀⠀⠀⠀⠈⢇⠜⠁⠀⠀⠀⢀⡌⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢹⡜⠳⣀⡀⢀⡠⠀⠀⠘⠁⠀⠀⠀⠀⠀⢿⡿⠫⢔⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡴⡸⣼⠃⠀⣇⣴⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⢆⠗⣎⢀⣄⣿⡉⡁⠈⠧⠜⣀⠀⠀⢀⣤⣠⡶⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢮⠔⢹⣟⣟⢁⠈⠈⢋⣑⠟⣁⠽⠭⠩⠤⠿⠾⠻⠙⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇⡄⠞⢻⠀⠃⠀⠀⠈⠁⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠁⠛⠃

⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡸⠃⠊⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⠀⠀⠀⠀⡸⠃
⢠⠞⠁⠀⠀⢀⠤⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⣶⣤⠶⠊⠀⠀⠀⢠⠞⠀⠀⠀⣀⠤⠰⠖⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣼⣷⣤⡶⠊
⠁⠀⠀⠀⠐⠁⢀⢉⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡃⢀⠘⠨⠉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⢰⠁⡀⢉⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡆⣀⠘⠈⠉⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⢿⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⠦⠱⠢⠀⡀⠰⠄⠊⠁⠀⠀⠀⠀⠀⢠⠀⠀⢿⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠘⠪⠱⠂⢀⡀⠠⠒⠊⠁
⠀⠀⠀⠀⠘⡄⠀⠈⢧⣀⠀⣦⠀⠂⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⢇⣄⠀⣆⠀⠂⢡
⠀⠀⠀⠀⠀⠘⢄⠀⠈⠻⠿⠿⡣⢐⢸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠻⠿⠿⡃⢀⡀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⣄⠀⠀⠀⠀⠀⠀⠓⢦⣄⡠⢙⠧⢞⡼⠀⠀⠀⡠⠒⠊⠉⠁⠀⠀⠀⠀⠉⠐⠢⣀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡈⢹⠧⢖⡴⠀⠀⠀⡠⠒⠂⠉⠀⠀⠀⠀⠀⠉⠐
⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⠉⠀⠀⠀⠎⠀⠀⡀⠀⠠⠂⠆⠤⠠⠄⢀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⢀⠊⠀⠀⡠⠀⠀⠂⠄⠔⢠⠤⢀
⢤⡀⠀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢴⣟⠉⠁⠀⠀⠀⠀⠀⠲⢦⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢰⣏⠉⠉
⢤⡙⢦⠀⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠐⢤⡙⢦⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠹⢦⡀
⣤⣿⡾⠆⢘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠉⠲⢤⣤⣄⣀⣄⣤⣿⣶⡆⠐⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠉⠳⠤⣤⣄⣠
⠛⠉⠀⣠⢂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠈⣠⢲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣠⠴⣖⡤⠋⠀⠀⠀⢀⠤⠒⠀⠒⠚⠶⢴⣦⡀⠀⠀⠉⠢⢄⡀⠀⠀⠀⣀⢀⢀⣠⠴⣒⡥⠋⠀⠀⠀⢀⠤⠒⠈⠒⠒⠲⡶⣦⡀⠀⠀⠀⠢⢄⡀⠀⠠⠀⣀
⠒⠋⠉⠀⠀⠀⢠⠚⠁⠀⠀⠀⣀⣤⡄⠆⠘⣻⡄⠀⠀⠀⠀⠈⠉⠒⠒⠶⠦⠒⠒⠋⠉⠀⠀⠀⣠⠒⠁⠀⠀⠀⡀⣤⡄⠂⠑⡿⡄⠀⠀⠀⠀⠈⠉⠒⠒⠶⠶
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⣿⠇⠂⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣿⠇⠃⠀⣍⠇
⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⡸⠃⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡼⠣⠋⠀⠀⡞
⠀⠀⠀⠀⢀⠀⠀⣼⣶⣤⠶⠋⠀⠀⠀⢠⠞⠀⠀⠀⢀⠤⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⣶⣤⠶⠋⠀⠀⠀⢠⠞⠁⠀⠀⣀⠤⠀⠀⠤⢄
⠀⠀⠀⠀⡄⣀⠘⠈⠋⠁⠀⠀⠀⣀⠔⠁⠀⠀⠀⠰⠁⠀⢀⡀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⢄⠙⠈⠋⠁⠀⠀⠀⣠⠔⠁⠀⠀⠀⠰⠁⠀⢀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠈⠪⢕⣂⣀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⠪⢕⣂⣀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⡀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢧⣀⡀⣂⠐⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢧⣀⢀⣆⠐
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠻⠿⢿⣣⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠈⠻⠿⡿⡃⢰
⠀⠀⢀⡠⠀⠉⠈⠁⠀⠀⠀⠀⠈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠙⢦⣀⡄⢽⠧⢚⡶⠀⠀⠀⡠⠒⠉⠙⠈⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠑⢦⣄⡄⢹⠧⢒
⠀⠀⡎⠀⠀⡀⢀⠒⠒⠆⠤⠠⠤⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⢀⠊⠀⠀⡀⢀⡒⠂⠒⠤⠠⠄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉
⠀⢸⠀⠀⠀⠴⣏⠉⠁⠀⠀⠀⠀⠀⠹⢦⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠰⣏⠉⠁⠀⠀⠀⠀⠀⠱⢦⡀⠀⡵⡄
⠀⠘⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠒⢠⡙⢧⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠐⢦⡙⢦⠀⠘⡄
⠀⠀⠣⡀⠀⠀⠀⠀⠉⠓⠦⣤⣤⣠⣤⣴⣿⣾⡆⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣠⣤⣴⣿⣾⠃⠘⣷
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⣠⢂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⣠⢒⡎
⠖⣦⡀⠀⠀⠉⠢⢀⣀⠀⠀⠀⣀⢀⣀⣠⠔⣸⡵⠋⠀⠀⠀⣀⠤⠐⠒⠘⠋⠷⠶⣦⡀⠀⠀⠉⠢⢄⣀⠀⠀⠀⡀⣀⢀⣤⠔⣪⡵⠋⠀⠀⠀⢀⠤⠒⠒⠀⠙
⡄⠈⣻⠀⠀⠀⠀⠀⠈⠙⠓⠲⠒⠒⠲⠚⠋⠉⠀⠀⠀⡠⠊⠁⠀⠀⠀⢠⣤⡄⠂⠉⣿⡄⠀⠀⠀⠀⠈⠙⠓⠲⠖⠒⠲⠚⠋⠉⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⣤
⠃⢀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⠀⢀⣿⣃⠂⠀⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⠀⠀⠀⠀⢀⣾
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠦⠦⠶⠰⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡿⢿⣧⠀⠀⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠙⠛⠛⢫⡄⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⣠⠴⠤⣄⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⡠⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⣶⡋⠀⠀⠀⠀⠀⢸⠁⣸⣇⠈⡇⠀⠀⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠳⣬⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠸⠤⠼⠀⠀⠀⠀⠀⠈⠳⢤⡤⠞⠁⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠾


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⣴⣾⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣿⡀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠰⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣴⣤⡄⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⠀⢠⣶⡆⢰⣶⡄⠀⠀⠀⠀⠀⣿⣿⡗⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠘⠿⠇⠸⠿⠃⠀⠀⠀⠐⠂⠈⠛⠁⠁⠀⠀⠀⠀⠘⠿⠿⠿⠋



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⠶⠶⠶⢶⣾⡶⣶⣶

⠀⠀⠀⠂⠀⠀⠀⠀⢠⣄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣤⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣴⣾⠋⠇⠳⢠⠏⢭⢿⣄⠄⠒⣀⠀⠦⠀⠀⢀⠀⠀⡀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⠜⠛⠻⢒⡖⠲⠻⢷⣀⠒
⠀⠀⠀⢠⡐⢄⣶⠉⠙⠷⣼⣜⡅⠀⠈⠙⡦⣌⡠⠖⢫⡡⠀⠁⠔⠀⣀⠀⢸⢴⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠛⠶⣼⣜⠄⠀⠀⢠⣉⠅
⠀⠀⠀⡀⢹⣷⣈⢆⠀⠀⠈⣙⣣⣀⠄⢘⡱⠉⠀⢰⣾⣁⠠⡀⠁⡀⣥⡀⢨⢰⣿⠁⠠⠀⠀⠁⠄⠀⡘⢷⣞⡙⣄⠀⠀⠀⣩⣶⣤⣒⢨⢎⡄
⠀⠀⠀⠠⠀⢿⣿⣿⣓⡁⣞⠭⠼⢛⣳⠎⠁⠙⠲⣜⣝⣦⣶⢷⠀⠰⣿⡇⠈⣼⣿⠀⠀⠀⠀⠀⣀⡤⢓⠈⣿⣷⣮⢓⣃⣾⠫⠔⢛⣽⠃
⠀⠀⠀⢢⡄⠘⡼⠔⠋⢻⣷⣄⡠⣪⠃⠀⠀⠀⠀⡘⠩⢒⣲⣼⣧⠀⢻⠀⠀⣿⠋⣰⣶⣶⠂⠘⡁⠐⢤⡂⠸⡉⠀⠝⢻⣷⣤⡐⠹⠁
⠀⠀⠀⢴⣿⣄⠸⢌⣠⣔⡽⣿⣿⣷⣄⡀⠀⠀⢀⣁⢉⣀⠉⣼⣿⡆⠀⠀⠀⠁⠐⢋⡩⠽⠗⠿⠿⣤⣬⣿⣄⡡⣔⣀⣄⡙⣿⣿⡷⣤⡄
⠀⠀⠀⢠⡟⢷⣀⡨⠍⢁⡈⠬⢿⢀⠈⠃⠀⡍⢈⢉⣯⣭⣛⣍⠻⣷⠀⠈⠁⠹⢆⡞⠛⢦⣄⠀⠀⠀⢈⡿⢷⣀⣈⠏⢀⠀⠬⢿⢅⢀⣂
⠀⠀⠀⠘⠀⠂⠁⠀⠈⠀⢀⠀⢰⠀⠁⡀⠀⠃⠘⠙⣻⣿⣿⣿⡷⠈⠁⠀⢢⠠⢀⣬⣀⣀⣬⠟⣠⢀⠼⠁⠘⠉⠀⠈⠀⢀⠀⠠⠀⠁⡀⠀⡇
⠀⠀⠀⢀⠀⡐⢀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢠⠀⠟⠛⠛⠛⠻⠛⠁⠀⠀⠓⢈⡴⡯⠼⡏⠉⠀⢁⡈⣵⡄⠂⠀⠂⠀⠀⠀⠁⠀⠀⠃⠀⢠⠠
⠀⠀⠀⠘⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠤⠤⠄⠀⠠⠀⡀⠀⠔⠧⠄⠠⠀⢈⣦⣊⣥⠞⢋⠞⠑⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠰⢰⠀⠁⡠⠁⠀⡠⠡⠊⣀⠀⠂⠀⠐⢦⡰⠿⠿⢿⡧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⢈⠀⢀⠠⠀⢀⠔⣤⢇⣔⠠⣄⣀⢠⢬⢏⠒⠦⣄⡊⠀⠈⢃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠂⠀⠀⢻
⠀⠀⠀⠐⣄⡤⢀⠀⠀⠐⢀⠀⠀⠈⢆⢻⠸⠈⠰⠄⢁⠄⡈⠸⣿⡆⠀⠙⡆⠀⠀⢀⡀⠀⠁⠀⠀⠀⠑⢄⡤⠀⠀⠀⠀⢀⠀⠀⠈⢄⢸⠸
⠀⠀⠀⢸⡟⠘⢦⡀⠀⠐⠁⠀⠐⠀⢘⢻⡇⠀⣶⢀⠂⢰⣶⣦⣝⡧⠤⠚⠋⠲⣴⡶⢶⣤⣀⠐⠀⣠⣶⡿⠰⢧⡀⠔⠀⠀⠀⠀⠄⠸⢻⣷
⠀⠀⠀⢘⠁⠀⠀⡈⠒⠄⣀⠀⠐⠀⢸⡌⣇⠀⣿⠇⢀⣶⣮⠍⠉⢁⠀⠀⠀⠀⠘⡏⠀⠙⣤⣷⠞⣿⢟⠃⠀⠀⣈⠒⠄⣀⠀⠐⠀⢰⡄⣿
⠀⠀⠀⠀⣠⣠⡞⠀⢻⣶⣏⠩⠙⠛⠠⢄⣿⠀⠏⠀⣼⣧⣈⠋⠁⠚⠀⠀⠀⠀⢀⣸⣴⣾⠟⠈⠁⢀⠃⣠⣠⡞⠁⢺⣶⣞⠋⠉⠛⠀⢤⣿
⠀⠀⠀⢰⣿⣿⣿⡟⢻⣒⣫⣧⡢⢎⢠⠖⠈⠀⠀⢰⣿⣏⣛⣭⡭⠉⠃⢃⠀⠈⠉⠉⡿⠑⠲⠶⡤⠃⢰⣿⣿⣿⡿⢻⣄⣫⣧⡂⢞⣀⠞
⠀⠀⠀⣾⡿⠛⠀⢷⢈⢂⠀⠐⠚⣠⡑⢄⣠⠀⠓⣾⠏⣴⣿⣟⣛⠛⠓⠀⠀⠀⠀⠁⠙⠒⠀⠠⠒⠦⣾⣿⠿⠁⢻⠰⣂⠀⠒⠚⣢⡁⢤⠠⠄
⠀⠀⠀⠟⠀⠅⠀⡈⢈⢽⡋⠓⡭⣉⣹⣦⡑⠴⠃⠀⠘⠻⠿⠿⠷⠶⢾⠈⡄⠐⠁⢀⠀⠀⠄⠀⠀⣼⠟⠁⠄⠀⠈⢃⠽⡏⠓⡭⢍⣍⡦⡙⠔
⠀⠀⠀⢀⠀⠐⠀⣜⠷⣔⠺⣄⠀⢀⢀⣀⣩⣄⠐⡀⠀⠄⠈⢀⣉⡀⢀⠀⠗⠃⠀⠀⢀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣔⢿⣗⡻⢦⠀⠀⣀⣠⣬⠦
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⡀⣿⠁⣞⠙⣧⠀⢰⡏⠙⢰⠋⢻⡔⢯⣍⢸⣷⣼⡇⢸⡭⠍⢹⡏⠈⡟⢰⡏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠛⠂⠙⠚⠁⠀⠈⠛⠛⠈⠓⠋⠈⠓⠋⠘⠃⠀⠃⠘⠓⠂⠘⠃⠐⠛⠈⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢴⠄⠘⠃⢀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣋⠭⠭⣍⡓⢒⠲⡄⠻⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡵⠋⠀⢀⡠⢤⠌⠹⡇⣇⠀⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⢸⠁⣸⣏⣻⡴⠟⢲⠆⢱⢹⠀⣿⣸⡃⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⢸⠸⡌⠓⠦⢽⣾⡥⠋⠀⡜⣸⠀⡏⠈⡇⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⣷⡙⢦⣀⠀⠃⢀⣠⢞⡵⠃⢸⣁⡀⢸⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⠦⠛⠒⠮⠭⠭⠭⠖⠋⠀⠀⠈⠓⠒⠋⠀⠀⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠈⠳⠀⢀⢰⣆⠀⠀⢀⡴⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡾⣛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢦⡼⣰⡞⢢⡝⣾⠥⠀⢾⣙⡶⢻⠂⠀⠀⠀⢸⡇⠀⣶⣒⡦⠀⣷⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢚⣻⣉⠛⠁⢐⣿⣂⠀⠸⣅⣳⣻⠀⠀⠀⠀⢸⣇⣒⣒⣒⣒⣀⠿⣭⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢹⠀⠀⣿⢹⢽⠀⠀⣿⡟⣗⠀⠀⠀⠀⢸⡇⢀⡤⠤⣽⠁⣀⣋⣀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢻⠀⠀⣾⢻⢻⠀⠀⣿⠇⢿⠀⠀⠀⢀⢸⡇⠸⣄⣀⣿⢈⣓⣒⣚⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣾⢸⢸⣒⣒⣿⢸⢽⣒⣒⣿⡟⣷⣲⡆⡴⠋⢸⡇⠤⠈⠉⣿⠀⢀⣂⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠘⢸⠀⠀⣿⠘⢽⠀⠀⣿⠃⣯⢸⠁⠀⠀⢸⡧⠭⠤⠤⣿⠀⠀⣦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣓⣋⣉⣉⣙⣒⣋⣉⣉⣙⣒⣋⣙⡇⠀⠀⠈⠓⠒⠒⠒⢿⣀⣀⣋⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⢀⡀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡠⠮⠤⠛⠉⠑⠒⠈⠀⠈⠉⠁⠀⠀⠂⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠸⠃⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⣸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢀⡬⠤⠦⠤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣄⠀⠀⢀⠶⠀⠀⠁⠄⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠖⡋⣶⣷⡄⠁⠁⠀⠀⠀⠈⠃⠘⠠⠄⠀⠀⠀⠀⠀⢹⡐⠃⠀⠊⠀⠀⠀⢀⣄⠀⠀⠀⠰⠀⠈⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠋⠘⠉⠀⠀⠁⠀⡀⠀⠀⠘⠃⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡎⡇⠱⠀⠀⠀⠀⠈⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⢀⠃⠀⠀⣀⠀⠈⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠠⠀⢀⡀⠐⠁⠀⠀⢠⠀⡄⠀⠀⠀⡋⠀⢠⠂⠄⢠⠟⠐⣆⠈⠁⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠆⠹⣦⡄
⠀⠀⠀⠀⢀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠈⠁⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⢃⠈⢀⢀⡴⢻⡄⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⡽⠛⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠅⠀⠘⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠋⠀⠁⠠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠠⠀⠁
⠀⠀⠀⢸⠀⠀⠀⠄⠈⢻⠀⠀⠁⠀⢠⡤⠶⠂⠀⠀⠀⠀⠀⠶⠀⠀⠀⠈⠃⢀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠆⠀⡃⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠸⠀⠀⠀⠐⠐⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠄⠂⠀⠀⠄⠠⠒⠚⠋⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⡴⠀⡀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡜⠁⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⣴⠁⠀⠈⠀⠀⠀⠠⠊⠀⡀
⠀⠀⠀⠀⠀⢄⣀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⣴⣾⣤⠤⣄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠈⢠⡀⡀⠀⠀⠀⢀⡂⢄⠀⢀⠀⠀⠀⠂⢛⡉⠀⠀⠘⠃⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠃⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡓⠀⠀⠀⠀⠀⠼⠀⠁⢤⠀⠀⠀⠀⠀⠀⠘⠄⡄⠀⠠⠅⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⢠⡀⢤⠂⠀⠄⠠⢄⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠀⠀⠀⠀⣀⡀⢴⣉⠰⠊⠃⠊⠀⠀⠉⡥⠄⠀⠀⠀⠀⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢐⡀⢆⡴⣠⠃⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠡⢛⠙⡆⠔⠀⠀⠀⠀⠄⠀⢤⠀⠀⢀⠀⠂⠀⠀⠀⠈⠀⣀⣾⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠖⠊⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣏⡋⠀⠀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⠀⠀⢄⠠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠗⣶⢿⡄⠷⣿⡄⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠧⣘⣃⣀⣙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠋⠩⠷⠉⠶

⠀⠀⢀⢠⢀⠀⢀⠀⢀⠀⠀⣀⣀⠀⠀⡤⡀⠀⡀⢀⣀⢀⢀⢀⣀⣀⣀⠀⠀⠠⠄⠀⠀⠀⠀⢀⣤⡀⠠
⠀⠊⠄⣜⠀⠁⠘⠁⠘⠢⠀⣉⣉⡇⢂⠀⠈⠀⢢⡊⣓⢻⡌⠀⢿⠿⡿⢠⡈⢰⣿⣦⣶⠀⢰⣿⢸⣿⡆
⠀⠀⢀⠀⠀⠀⡀⠀⢀⠀⠀⠉⠉⠀⠐⠈⠁⠀⠶⠺⠜⠺⠧⠀⣤⠀⡤⠀⠀⠀⠈⠙⠋⠀⣈⣻⣿⣟⣙
⠀⢒⡚⢀⣁⠀⠀⠀⠀⡀⠀⠀⣤⣆⡀⡳⠇⠖⠀⠂⠀⠀⠀⠄⢀⣤⣀⠀⠂⡀⠀⣠⠀⠀⣿⣿⣿⣿⣿
⠀⢇⣼⣷⣠⢀⠀⠁⠀⠠⠀⠀⠀⠈⠁⡁⡄⡇⣾⣿⣿⣷⠄⠀⣾⠶⢿⠄⢠⣿⠛⣿⣧⠀⠀⠂⠀⠒
⠀⠀⡙⡋⠁⠀⠀⠀⠠⠀⢀⣀⠀⠀⣀⣀⣀⢑⠐⠭⠭⠕⠊⠀⡯⠤⢼⡀⠤⠀⠀⠡⠄⠀⠀⠀⡄
⠀⠐⢀⠄⢒⠂⠄⠀⣤⡄⠀⠋⠀⣊⠉⠉⢹⠈⠀⠁⡀⠉⠄⠀⠂⠀⠀⠀⠀⠘⠛⠏⠀⠀⠀⠐⡇⠀⠘
⠀⠀⠈⠁⠙⠀⠀⠀⠀⢀⣼⠈⠁⠈⡀⠤⠘⠀⠡⠚⠁⠐⠀⠁⠁⢸⡇⠈⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⢸⠆⢾⠭⢿⠀⠀⠈⢿⣇⠀⠀⡀⢀⠀⠀⠤⠴⠒⠂⠄⠂⠄⣤⣤⡄⢻⠓⣶⣀⡀⠓⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⡘⠋⡀⠀⠀⠈⠀⠀⢀⣠⣤⣀⣤⡀⠀⡃⠉⡇⠀⠀⠠⠦⠀⠀⠀⠀⢸⣿⡇
⠀⣠⣤⣶⣤⣄⠐⣠⣴⣶⣶⡀⠀⠀⠀⠈⠀⢰⠉⠹⠿⠇⠉⠹⠀⠋⠉⠃⠓⠆⢀⣶⣦⣤⠀⠀⢸⣿⡇
⠀⡷⣄⠀⠀⢸⠐⠻⣿⣿⣿⣷⢦⢰⣄⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠸⢿⣿⡟⠀⠀⣸⣿⡇
⠀⡇⠀⠀⡀⣸⠀⠀⠨⠈⠄⠀⢀⡈⢿⠋⠉⠓⠀⠀⢠⣒⠀⠐⢄⡂⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡛⠛⡃
⠀⢧⡀⠀⠈⠵⡀⢬⠇⠁⠀⠐⣬⡓⠐⠰⠟⠋⠀⠠⣟⣛⣉⣂⣘⡋⠀⠀⠀⠘⠀⠀⠀⣶⣀⡄
⠀⣤⣤⣤⣤⢠⠀⠈⠀⠀⠀⠀⠙⠃⠀⡀⠀⢉⡉⠀⢽⣯⣭⣩⣿⠀⠀⠀⠀⡀⠀⠄⠀⢉⠙⠓
⠀⠿⠻⠿⠿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠴⡧⠶⢦⡀⠋⣉⢉⠂⣠⠤⣤⠤⣤⠀⠀⠀⡠⠀⠀⠀⡠
⠀⣬⣤⣤⣤⠄⠉⠁⠈⠁⠀⠀⠀⠀⠐⣿⢹⣟⣿⣻⠿⠄⢐⡨⠀⣙⣛⢃⢐⡁⠀⢀⠐⠄⠐⠨⠄⠐
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢸⠀⢀⣿⠀⠀⢀⠤⠀⣀⠔⢃⠤⠀⠆⡀⠂⠂⠸⠐⠀⠀⠐
⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢸⠀⠀⣿⠀⢠⠄⠈⠀⣠⠄⠛⠂⠀⠄⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠤⠀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣶⣡⠴⠀⠑⠠⣁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠖⠋⢙⠤⠤⠀⠠⠀⠨⠁⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠈⢉⠒⠒⠀⠀⠀⠀⠐⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠤⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠉⠉⠀⠀⢈⡆⠀⠀⠀⢅⡀⡄⠀⡀⠀⠀⠀⠀⠰⠀⠠⠄⠒⠂⠒⠆⡁⠀⠀⠀⠈⣘⣉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠓⠂⠐⠛⠐⠠⠄⠒⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠤⠤⠄⠠⠤⠤⠤⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣐⣁⠀⠀⣀⣈⣉⠉⠀⠀⠀⠢⢀⢘⡂⡸⠓⢛⡖⠒⠄⠉⠀⠀⠰⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠓⠒⠒⠒⠒⠒⠚⠒⠂⠀⡘⠀⠘⡈⠉⠙⠳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠃⠀⠐⠒⠒⠒⠀⠉⠀⡄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⡤⠀⠀⠀⠀⡄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠊⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠖⠠⠃
⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⠀⠀⢀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⠀⢺⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢔⠀⠇⠀⠀⠀⠀⠀⠈⠁⠲⠛⠀⠀⠀⠁⠀⠢⢄
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⣀⡀⡄⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠦⠀⡤⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠴⠦⠴⠶⠶⠂⠑⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⠈

⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡴⢶⣶⡄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠾⠿⠷⡄⠀⠀⠀⠠⠀⠀⡀⠀⠀⢰⣷⣶
⠀⡄⢀⡄⠀⠀⠀⠀⠀⠠⣶⣎⡉⡇⡓⢒⠷⣄⠐⢀⢤⣆⠐⠱⠀⡀⠀⣠⢀⡴⠀⠀⠀⠀⠀⠀⠰⣿⣭⡄⣫⡍⠻⠻⢦⡀⡡⢴⣣⠀⢀⠂⣠⢸⣿⣿
⢈⢱⡏⠀⠀⠀⠀⠀⣄⡠⠇⠨⠛⠿⠃⠀⢁⢄⠙⠁⣼⠃⢀⠐⠈⣅⠀⢣⣿⠀⠀⠀⠀⠀⠰⣤⠼⡁⠀⠙⠛⢃⢀⠀⡢⠋⠀⣼⠃⢠⠀⠀⣬⢸⣿⣿
⠈⣾⡇⠀⠀⠀⠀⡰⠘⣷⣌⡤⠀⡴⢚⡷⡤⠃⠲⢄⣫⣢⣼⡄⢰⣿⠀⢸⣧⠀⠀⠀⠀⣠⠇⢸⣷⣴⠤⢠⠞⠫⠗⠜⠁⠒⠤⣽⣶⡾⣇⠀⣿⢸⣿⣿
⠀⡿⢁⣦⡆⠐⠉⢄⡀⠩⠛⠱⣷⣅⠀⡼⠃⠀⠀⠌⢉⠨⡱⣷⠀⠿⠀⣿⠃⣴⣶⠒⠉⠠⣄⠀⢝⠭⠺⣷⣅⡀⡞⠁⠀⠀⢠⡍⢒⣞⣿⡄⠹⠸⣿⣿
⠀⡠⠚⡻⠷⠶⢧⣤⣷⡀⢠⠀⡈⢿⣷⣦⡀⠀⠀⢘⡁⣋⢢⣿⡇⠀⠀⡀⠘⡉⠽⠲⠿⢦⣬⣧⠀⠄⣀⡜⢿⣿⣦⡀⠀⢀⢀⣉⣩⡀⣿⣧⠀⢰⣿⣿
⠀⠣⣘⠛⢦⡀⠆⠈⡿⢧⣀⠛⢁⠀⢿⠅⠉⠀⠄⢈⣙⣙⣭⡙⢷⠀⠀⠘⢦⠋⠳⣄⢈⠀⢨⠿⣄⡈⠋⠀⠈⢿⠀⠁⡀⠅⣈⣽⣯⣍⣍⠻⡀⢸⣿⣿
⢀⠀⣰⣀⣤⡞⢑⠤⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⠀⢉⣉⣿⣿⣿⠈⢁⠀⠔⡠⣇⣤⠴⠃⡢⠘⠀⠉⠀⠈⢀⠀⠀⠈⢀⠀⠁⠏⣉⣽⣿⣿⠂⢉⣸⣿⣿
⠀⠚⠓⢇⠀⠀⢈⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠀⠉⠉⠉⠉⠁⠀⠈⠁⠼⠳⠺⡀⢀⡤⣼⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠀⠋⠉⠉⠉⠁⠀⠀⢹⣿⣿
⠐⠂⠀⣠⣦⡴⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠀⢀⣶⣤⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢺⣿⣿
⠀⢨⣞⡛⠛⠗⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠁⠀⠄⠃⠀⠀⠀⠀⣶⡛⠛⠛⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠅⢸⣿⣿
⠐⠚⠀⠉⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⡀⠠⠀⠚⢾⡉⠲⡤⠒⢁⠉⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢠⠂⠞⢶⡅⠒⣼⣿⣿
⠤⡄⣀⣂⠀⠀⠀⢀⣴⢪⠀⠀⠀⢂⠀⠀⢦⣇⠀⡃⠐⢀⣀⡺⡇⢀⡴⢤⢀⡂⠀⠀⠀⠀⣀⡶⢁⠀⠀⠀⠀⠀⠀⢤⣇⠀⡋⠠⢀⢀⠘⢇⠀⣸⣿⣿
⠀⠘⡷⠉⠟⣤⣤⣿⠏⠀⠑⠄⠀⠀⠀⠀⡀⣿⢸⣷⠁⣸⠻⠛⠎⠁⠀⠈⢿⠌⢻⢂⣄⣴⣿⠁⠈⠂⢁⠀⠀⠀⠀⡈⣿⢸⣷⠁⣘⣛⠿⠶⠉⢸⣿⣿
⠀⠀⢨⣠⣾⠋⠒⠱⢀⢀⡞⢠⣤⡲⠶⠦⠉⢸⠸⠏⢰⣏⠿⠆⠤⠀⠀⠀⠈⣄⣴⡿⠣⠊⠇⠀⣠⠖⢤⣐⢦⠤⢄⠃⣹⠘⡏⢠⡟⠷⠤⠠⠀⢸⣿⣿
⠀⠘⠋⣿⠣⢤⡴⠀⣼⣿⣷⠾⣛⣳⡂⡄⢠⠋⠀⠀⣾⡟⢂⠰⠲⠀⠀⠠⠞⢻⡟⠠⣄⠈⢠⣿⣿⣶⢿⢛⣦⢀⠄⣨⠛⠀⠀⣼⡿⢶⡴⠶⠂⢸⣿⣿
⠀⠀⠋⠐⠀⠀⠐⢴⣿⠿⠹⡐⡉⠀⠥⣈⠡⡀⠀⢰⡟⣹⣿⣷⠶⠆⠀⠀⠐⠉⠂⠀⠈⢤⣼⣿⡏⢷⠘⠉⠨⠥⠈⢋⠀⠀⢤⡿⢫⣿⣶⡶⠦⢸⣿⣿
⡀⠂⠀⠂⠀⠀⢀⡾⠁⠀⠀⢁⠽⠘⠪⠉⡵⡈⠰⠂⠈⠻⠿⠿⠶⠆⠀⠀⠀⠀⠀⠄⠀⢰⡟⠁⠀⠈⢊⢗⠒⢙⣛⣦⠁⠴⠊⠀⠿⡿⠷⠶⡄⢸⣿⣿
⢉⠁⠀⠀⠀⢀⠞⠀⠀⠀⢰⡻⢤⠳⠀⠀⠠⠮⢄⠀⠀⠀⠀⢬⠄⠀⢈⠅⠀⠀⠀⠀⣠⠏⠀⠀⠀⢔⢷⡂⢦⠀⠉⣊⣅⡄⠂⠀⠀⠀⢀⡁⠐⢘⣿⣿
⠘⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠻⠌⠳⠾⠆⠔⠂⠀⠄⠀⠐⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠈⢧⠙⢦⣶⡄⠤⠄⠌⠄⠀⠰⠀⠀⢀⠀⠸⣿⠿

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⠃⠀⠀⠀⠰⡶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣶⣶⣶⣿⣷⣶⣶⣶⣶⣤⣴⢶⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⢠⡗⣼⠙⢿⡴⣻⡿⣿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢉⠁⡄⠈⢁⣀⣀⠈⡤⠤⢀⡠⡄⢁⣌⢁⡀⠀⠀⠀⣿⢸⡂⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠈⡇⢻⣧⣿⡿⢿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣶⢻⠉⠸⡟⢃⣴⣤⣄⣬⡌⡟⠉⡈⢢⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⡇⢸⠙⣿⡳⣞⡯⣵⢷⣿⣷⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⡟⢆⠀⡅⠛⠾⠤⣼⡄⢣⡿⠁⢿⡏⠸⢇⠀⣥⠈⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⣿⣿⡄⠀⠀⠀⠀⡗⣿⠀⠹⣇⣨⣹⣟⣻⣿⣿⣿⣦⡀⠀⠀⠀⠙⠿⠋⣳⠙⢶⣤⠙⢠⡀⢾⠙⣤⠛⣤⣶⢈⣘⡆⢸⠗⠟⣡⠀⠠⣿⣿⡀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠿⣿⢿⣭⢆⠈⢛⠿⣷⡀⠀⠀⠁⣾⠛⣿⣤⡄⡃⠀⠈⠻⢷⣷⢿⠘⢿⡿⢈⣛⣷⣘⡷⢚⣥⠀⠀⣿⣼⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⠘⠂⠱⣎⠹⠿⣷⡄⣲⠈⠻⣄⡀⠰⠋⠲⠉⠝⣛⠷⡒⠰⠃⣰⠃⠾⠴⢤⣤⣿⣛⠿⠿⠆⠈⣆⡄⠀⣿⣹⡃⠀⠀⠀⣿⣿
⣿⣿⡀⠀⠀⠀⠀⡇⣿⠀⠀⢀⣧⠀⠹⣷⡀⢈⡛⢹⣦⣴⣽⣿⠀⣨⡙⠓⢢⠝⠲⡝⣷⣤⣿⣰⣦⣤⣤⡤⣭⣏⠀⠀⠀⠀⣀⣴⠞⡋⢿⣇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⢸⣟⠃⠀⠘⢿⣾⣽⣿⣿⣿⣿⢿⣷⣌⠁⠀⣧⠀⠀⣦⣀⡸⡆⠉⢰⣧⣌⠀⢸⢸⡇⣠⣶⣿⠏⠑⣮⠟⢠⡿⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⢰⡷⣿⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⡿⣷⣄⢻⣿⣦⠀⢏⠀⠀⢿⡉⠙⡁⢶⡈⡉⠛⠶⠞⢫⣼⣿⣿⣿⠶⣦⣠⣶⣿⡅⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣩⠹⣿⣿⣷⣿⣿⣷⡈⠠⡁⠺⠃⠀⠻⠈⠉⠁⠀⠀⣴⣿⣿⣿⡿⣿⣶⣹⣿⣿⣿⠃⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⢀⣤⣶⣾⣿⣷⣤⡈⢻⡖⣿⣿⡋⣿⣿⣿⣻⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⠏⣹⣿⣻⣿⠏⣿⢹⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⣰⣿⣿⣿⣏⣿⣿⣿⣿⣮⢿⣿⢞⣿⣿⣿⣿⠿⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⣼⠿⣡⡾⠂⣩⣿⣿⠏⠀⣿⣸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣿⣻⣿⣯⡿⢿⣟⣷⣝⣧⠛⡿⣿⣿⣶⣿⣿⠿⢋⣱⣾⢻⣦⡀⢀⡀⣀⣾⣿⠶⣟⠻⡁⠈⣹⠏⠀⠀⣿⢰⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⠀⠀⣻⣿⣭⣻⣾⣧⠛⣴⣿⡿⢿⣶⣿⣹⣿⣍⠀⣤⠋⣼⣿⣧⣼⡾⣿⣿⣟⣴⡟⢀⡄⠀⡄⣰⡟⠀⠀⠀⣿⢸⡆⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡇⣿⢠⣾⣿⣿⣿⡟⣿⣿⣷⣿⣷⣴⡿⠿⢿⣿⣿⣿⣿⡀⣠⣾⡿⣣⣾⢟⡋⣼⡿⠋⢀⣿⠀⠚⡁⣿⠃⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣷⣿⣾⣷⣫⣿⣉⡼⣻⣯⣿⣿⣿⣿⣾⣧⣿⠉⠉⠉⢿⣾⣿⡏⣠⡿⣱⣿⣿⡟⠀⢀⣾⣏⣠⣿⠆⣿⡀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣏⣿⣿⣿⣿⢁⠋⣴⣛⣿⣿⣷⣿⣻⣿⣟⢿⡄⠀⠄⠀⣿⡇⢰⣿⣷⣿⣿⡏⢙⡀⣰⡟⢻⣿⠭⣷⣿⣇⠀⠀⠀⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣷⠈⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣯⡹⣷⣟⣷⣶⣿⣿⠀⣻⣿⣿⣿⠛⣰⣎⠡⣿⢷⡈⡏⠀⢀⣿⣿⡄⠀⠀⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⠛⠛⣯⣵⣛⣿⣿⡿⠿⢿⣷⣟⣵⣻⡇⠀⢣⣼⣧⣿⡀⠋⠀⣣⣼⡏⣿⣇⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⡟⢿⣥⣽⣷⣖⣫⡭⠛⣿⣿⣷⣶⣿⣅⣿⣿⡟⠄⠀⠀⠈⢿⣿⣿⠁⣻⣾⡥⠿⠻⠄⣀⠼⣻⡟⢱⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠸⣿⣻⢤⣿⣾⣿⡻⢿⣴⣏⣏⣿⣿⣿⣟⣻⣷⣾⣷⣦⣤⣤⡶⢸⣿⠻⡾⠣⡼⠀⣂⣠⣶⠟⣴⢋⣴⡇⣿⣿⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣵⣾⣛⣿⣿⣿⡿⢿⣏⠹⣯⠀⡈⢉⣿⡟⠓⢸⣿⡄⠀⠂⠐⢚⠋⠙⠁⠰⣷⣋⣽⣧⣿⣾⠀⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⡟⣿⠛⣯⢿⣿⡿⠻⠻⠿⣿⣿⣷⣾⣿⣷⣿⣿⣿⠟⣱⠃⣴⠀⠛⣿⣦⣽⣶⣩⣅⣠⠄⠒⣛⣿⠿⣛⣼⣿⣆⠀⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣧⠀⠀⠀⠀⡟⣿⠀⠙⠿⣿⣿⠀⢂⠰⢀⡻⣿⣿⠟⠉⣿⢻⣿⠀⠉⠀⠹⠀⢀⠸⣿⣿⣿⣩⣾⣛⣶⣛⣫⣿⣶⢛⣿⣿⣿⣷⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠙⠻⣴⣿⣲⣞⢣⣿⣟⣿⡇⣻⢁⣿⠆⡀⠀⡀⡇⢨⣷⣎⣻⢟⣹⡿⠛⢿⣟⣿⣧⣼⣿⣿⣿⣿⣛⣿⢾⡆⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⠙⠻⣿⡞⠹⣿⣿⣿⣿⣿⡿⠸⡇⠄⡙⢿⣷⣿⣻⣿⣿⢋⣷⠏⡀⢟⣻⣿⣿⣿⣿⣏⢾⣿⣿⢘⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣽⣿⣿⣟⣿⣇⠀⣷⣄⣈⣿⣿⠇⣿⣿⣤⣿⣿⣤⣿⣾⣿⣿⡿⣿⣿⣽⣦⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠀⠀⠛⠀⢀⡀⠀⣀⣀⠀⠀⣀⡹⢿⣿⣭⣿⣦⣸⣿⣿⣽⣿⢺⡿⢣⣿⢃⣨⣿⣿⣿⣿⣿⣶⠉⣾⣿⣿⣿⣿⢸⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡇⣿⠠⠆⡰⣯⡿⠀⣻⣯⠛⢛⣿⠸⠾⠋⠤⠀⠙⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡝⢻⣿⣽⣿⢸⡇⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣷⣿⠀⣙⣛⣀⠙⣯⣁⠈⣀⡈⣁⣿⣚⡃⠀⠀⠀⠀⠀⠛⣿⣏⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⢻⣇⡸⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠉⠙⣿⣤⣯⣈⡿⣿⠿⠟⣣⣿⠱⠆⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣿⢟⣷⣿⣏⣿⣟⡽⣧⣀⣄⢻⣿⣷⠘⣿⣸⡀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⢀⣿⣿⠀⠀⠘⠋⠀⠈⠉⠀⠘⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣻⣾⣿⣷⣹⣾⢻⣼⢿⣿⡜⣿⣿⣿⣿⣿⢸⠁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢉⣿⣧⡝⢿⣻⣾⣷⣟⣿⣿⣿⣿⣿⢸⠀⠀⠀⢠⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣿⣾⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣼⣿⣹⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣿⣿⣿⣿⣷⣿⢿⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⡀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡻⣿⣿⣸⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣿⣿⣥⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣄⣀⣀⣀⣤⣤⣤⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣭⡿⣿⠀⠀⠀⠸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠿⠶⠿⠤⠶⠿⠷⠶⠶⠿⠿⠿⠿⠶⠶⠶⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠾⠷⠾⠿⠶⠶⠶⠿⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠶⣄⠈⠁⠀⢈⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣿⠀⠘⣧⠞⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣇⠀⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠂⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢂⣴⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⣿⢸⣶⡄⢤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢧⣶⠶⠛⢷⣼⣿⡏⠀⠙⠻⠆⠀⠀⠀⣿⢠⣿⣿⡇⠀⣰⣿⣧⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠙⢡⣈⠀⠈⢻⣿⣷⠀⠀⣀⠀⠀⣶⡆⣹⣾⡟⢫⡽⣠⡿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠈⠀⠈⠀⠀⠀⢿⣿⣧⢸⡿⠁⠀⡼⠂⠀⣾⠀⠘⢠⣿⣷⣤⣤⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⢠⡄⠌⠓⠀⠀⠀⠀⠀⣀⠈⣻⣿⣿⣧⠀⠐⢻⡦⠘⠻⠂⠊⠀⣴⣿⣷⠟⠛⠿⠟⠿⣧⣴⣄⡀
⠀⠀⠀⠀⠀⣀⣬⣧⣤⡤⡤⢀⣜⠀⡀⠘⣿⡍⢻⣿⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⠟⠋⠀⠀⡀⠈⣠⣿⠙⠈⠷⡄
⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠡⣀⠈⢿⣿⣿⣿⡄⠀⣸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⢀⡴⠫⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠳⡶⠶⠦⠔⠠⠀⠀⠀⢠⣄⡀⠻⣞⣿⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠣
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣍⣿⣿⣿⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⣦⣤⣒⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⡆⡀⠀⠀⠀⠀⠀⢀⠼⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣮⣀⣀⠀⠀⠀⣠⣈⣴⣧⡴⢂⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣇⣀⢀⣀⠀⠀⢀⣀⣤⠦⠤⠿⠿⠿⣿⣿⣷⣀⠀⠉⠛⠻⢿⣷⠿⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠿⠿⣿⣿⣿⣿⡿⠿⠋⠁⠡⠀⢀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣄⠀⠠⡇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠠⠀⡀⠠⠀⠀⠈⠀⠀⠀⢀⣠⡴⣶⡾⣉⣿⠟⣿⠆⠘⣧⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⢶⣤⣤⣀⠀⠀⣀⡀⠀⠀⠀⠒⢙⣿⡶⠉⡐⣿⣯⣼⣧⠾⠀⣿⣇⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣶⡿⠞⡏⠀⣀⡿⢻⠋⠉⢀⣾⠀⣿⢿⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡜⠁⠀⠀⠀⣼⠁⠀⢀⠰⠋⠀⢀⡿⠀⢣⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠞⠀⠀⢀⡾⠀⠀⠀⠸⡇⠀⠈⠇⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⣼⠇⠀⠀⠀⠀⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠇


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠋⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢮⣿⠓⢦⡀⠉⠠⡀⠀⣤⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡽⠊⠁⠁⠈⠙⠳⡴⢹⣧⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣆⢀⡬⠭⠄⠒⡀⢀⣀⡄⠀⠙⠦⡿⣯⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣇⠚⠀⠀⣀⠀⠀⢀⡀⠤⠄⠀⠀⠳⣌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢳⡟⡏⠀⠀⠀⠙⠤⠀⠀⠀⠀⢀⠀⠀⠀⣸⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⡀⢹⠜⠓⠂⠀⢠⠷⠀⠐⠂⠋⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⢠⠀⠠⠀⠀⠀⢶⠀⣂⠀⣤⡤⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢻⣀⠀⠀⠀⠀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠓⠀⠐⠶⣏⠁⠈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡘⠑⠦⠀⠀⠀⠀⠀⠰⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀⡄⠀⣀⢈⢽⠟⢠⡷⠔⠇⣠⡇⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢘⣳⡾⠃⠾⣾⣿⠅⠙⠦⣄⡈⠻⡯⣟⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠠⠀⢠⣿⢷⣯⣤⢀⢁⠀⣌⣀⠤⠜⠢⣴⡋⠻⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡛⠁⠀⠈⢉⡀⠀⠀⠈⠁⠀⠈⢙⣶⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡆⠀⠆⠚⠛⠏⠒⠘⠛⠓⠒⠀⣁⠟⡟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡉⣥⣴⣷⠄⠀⠴⠀⠄⠒⠀⠴⠌⡣⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⡹⠇⠀⠀⠀⠀⣠⢠⣄⡠⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡈⠷⠀⡔⠃⡩⠿⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡿⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣧⡀⡈⠲⣲⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⡀⠀⢀⡄⣀⠘⠛⣯⣀⠉⠋⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⢀⡼⠑⡿⠇⠒⠉⠙⠀⢾⣹⣬⠐⠠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣾⢡⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣶⡀⢀
⠀⠀⠀⠀⠀⢀⠂⠐⠂⠀⠟⠴⠉⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠁⠠⢄
⠀⠀⠀⠠⠀⠉⠀⣠⣴⠂⠀⠀⠶⡿⢯⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣼⡏
⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠀⢲⣿⠃⡾⢄⡀⠠⠂⠀⠀⡨⠃⠚⠛⡾⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⢄⡂⠀⠻⢠⡀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⣣⢄⠤⠖⠃⠀⠀⠙⠲⢦⡀⠁⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⠀⢼
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣀
⠀⠀⠀⠀⠀⣼⠋⢩⡍⠉⢳⠀⠀⠀⣠⡇⣧⡀⠀⠀⠀⣘⣿⡖⢁⣴⠇⠀⠀⢀⠌⠈⠙⠂⠀⠀⠀⠀⠐⣤⣶⠀⠀⠀⢸⣧⣸⣿⡇
⠀⠀⠀⠀⠀⢃⠂⠠⠰⣀⡾⠀⠀⢰⡇⠀⠁⡷⠀⠀⣠⠟⢛⡵⠛⠁⠀⠀⠀⠈⢀⣀⡀⠀⠄⠀⠀⢀⠀⣿⣿⡿⠀⠀⢸⣿⠛⢿⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠁⠀⠐⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠛⠟⠟⠀⠀⠈⠙⠃⠞

⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠤⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣞⠉⠉⠁⡝⢷⠀⠀⠀⢸⠁⠀⠐⠈⢻⡄⠀⠀⢠⡟⠁⢴⡄⠀⣅⠀⠀⠀⠐⠀⢀⡄⠀⠁⠀⠀⠀⢰⠏⠀⠀⡄⠈⡆
⠀⠀⠀⠀⠀⢼⣦⣄⣈⣥⡞⠀⠀⠀⠸⣦⣀⣀⣀⣠⠃⠀⠀⠈⢄⣈⠛⣋⣴⠏⠀⠀⠀⢠⣀⡈⠁⢀⠎⠀⠀⠀⠘⣀⡀⠘⣑⣼⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁

⠀⠀⠀⠀⠀⢠⣤⠖⢠⡀⠀⢠⣶⣶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⢀⣠⡤⢀⡀⠀⠀⠀⣠⣴⣶⣤⣄
⠀⠀⠀⠀⠀⣿⣿⣦⣾⠇⠀⠚⢩⠴⠀⠄⠀⡀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⣰⠿⡄⠀⠀⠀⣿⣿⡀⢼⡷⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠀⣿⠁⣽⡟⠀⠀⠀⣀⣂⣡⣤⣾⠇⠀⠀⠀⠠⠤⠤⠾⠂⠀⠀⣼⡇⠀⣽⣄⠀⠀⠀⠻⣷⣶⡖⠀⠀⠀⠤⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⣠⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⡠⠞⢉⣤⣴⣶⣾⣿⣶⣬⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢀⡀
⠀⣼⣯⣾⣯⣹⡿⡿⣿⣿⣿⣿⣿⣝⡆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠟⠸⡣⠔⠀⠀⠀⠀⠤⠉⢷⡀
⠀⢸⣿⣿⣿⣾⣶⣿⣾⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⢴⡿⠷⠶⠀⠘⠀⠀⠀⠀⠀⣰⠀⡀⣴⣧
⠀⢸⣿⣿⣿⡿⢿⣿⣿⢫⢾⣿⣿⣿⡟⠀⠀⢀⡴⢩⡞⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣦⡀
⠀⠀⠹⣯⡻⢿⣿⣿⣿⣾⣿⡿⠟⠿⠃⠀⣴⠃⠈⣸⠧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠶⠖⠀⠉⠀⠉⢇⡀⠔
⠀⠀⠀⠈⠛⠖⢒⠛⣻⣭⠥⠐⠁⠀⢀⠚⢁⣷⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣅⣀⣴⠃⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⠿⠏⠛⠛⠋⠀⡉⠉⢩⣀⡀⠀⢀⡀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁⠀⠰⠂⠀⠒⠀⠙⠓⠀⠉⠉⠀⠠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⢶⣿⡇
⠠⣠⡄⢀⠀⠸⠟⠁⠀⠀⠀⠀⠀⢀⣠⣦⣾⠋⠀⠀⠀⠀⠀⠀⠙⢢⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠸⡿⣥
⠀⡵⣕⠘⠄⠀⠀⠀⠀⠀⠀⢀⠸⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⠃⣿⡆
⠀⠉⡄⠁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣿⡛⠿⣧⠀⠰⢻⢸
⠀⠢⣑⠀⠀⠀⠀⠀⠀⠀⡇⣠⠜⠂⠀⠀⣀⣀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣧⡀⠀⠀⡠⠋⢷⡀⠈⠇⠀⠨⠀⠄
⠀⠐⡄⠀⢀⡀⠀⠀⠁⠀⣷⠇⠠⠁⠀⠀⡏⡯⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠉⠀⠀⠀⠀⠈⠻⡄⢀⠀⠀⠣⣸⡄
⠀⠀⠉⣖⣒⡀⠁⠀⠀⠴⠁⠀⢀⠈⣄⠀⠐⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠙⠋⢁⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠠⠀⠠⢄⡈⣷⣤⣀⣀⣀⣿⡏
⠀⠀⠀⠒⢒⡿⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣿⡟⠛⠛⣿⣛⣋⡀⠂⡀
⠀⠀⠀⠀⠀⠃⠤⠄⠀⠶⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠿⠻⠛⠉⠃⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⡀⠀⠀⠘⢳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠓⠒⠒⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣶⠀⠀⠀⠀⢰⠋⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⣠⡴⠒⠲⢦⡶⠋⠸⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠒⠒⣿⠒⠒
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⠶⠋⠀⠀⠀⠀⠀⠻⢶⣿⡶⠿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢧⣀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠤⠀⠀⠀⠀⠀⠀⠀⠿⠉⠻⠆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⢶⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠲⣦⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣞⠀⢸⠋⠙⣧⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⡟⠀⣿⠋⢹⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡀⢸⠀⠀⣿⠈⠋⢻⠛⠃⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⡟⠀⢸⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢥⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⠀⠀⢸⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⢾⣷⡄⠀⠀⠀⠀⠀⠀⢿⣆⢸⣿⠀⠀⣰⣿⡁⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⡷⠶⠦⣤⣄
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⢰⠟⢹⡇⢰⡇⣰⠆⠀⠀⢾⣿⣿⣿⣿⣿⠿⠋⠠⠄⠀⠰⠌⠳
⠀⠀⠀⠀⠀⢛⡶⣤⣀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄⠀⠀⠈⠁⢈⣿⠋⠀⠀⠀⠀⠙⠛⠋⠉⠱⣄⠤⠀⠀⠖⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠉⠰⠿⢔⣺⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢿⡄⠀⠀⢠⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠪⡑⣄⠀⠀⠀⠀⢰⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣷⠀⠀⠀⣀⡀⢷⣄⠀⣿⣿⡿⠀⣰⠟⢀⡀
⠀⠀⠀⠀⠀⠀⢠⢬⡹⣍⢿⡿⠷⠶⠧⠤⠀⠀⢸⣟⣛⣻⣿⣿⡯⠿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠈⠿⣄⠙⢶⡀⠉⣠⡶⢉⣰⠟⠁
⠀⠀⠀⠀⠀⠀⢸⡒⢝⢮⡙⣇⠀⠀⠀⠀⠀⠀⢸⡷⠶⢾⣿⣿⣿⣿⣷⣶⣾⣛⣻⣿⠀⠀⠀⠀⠀⠙⢷⡌⣋⠀⣋⢠⡾⠃
⠀⠀⣠⣤⣤⣄⣸⣿⠢⡑⢍⠏⠀⠀⠀⠀⠀⠀⢸⣿⣭⣽⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠈⢦⡹⣍⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⣒⣺⣿⣿⣿⣿⣷⣶⣾⣉⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠈⠪⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠉⠉
⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⢸⣿⣏⡢⠔⣙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣤⠀⠀⣳⠀⠀⠀⠀⣄⣀⣐⣀⣀⢀⠎⢄⠡⠀⣸⣿
⠀⠀⠀⠀⠀⢸⣿⣯⣴⣦⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠧⠚⠁⠀⠀⠀⠀⠘⠿⡿⠿⠃⣼⣴⣶⣦⣇⠈⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠒⠤⢤⣀⡀⠀⠀⠀⠀⣠⣶⣿⣿⡧⣿⣿⣷⣦⡀⠀⠀⠀⠀⣀⣠⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⢱⣾⣶⢹⣯⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⢈⡿⣿⣮⣛⣫⡾⣿⡏⠀⠀⠀⠀⠀⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⢶⣶⣤⣀⠀⠀⢰⠀⠀⢀⣠⣴⣶⢶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣦⢍⣛⠿⣷⡀⢸⠀⣰⡿⢟⣋⢥⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣟⣤⣝⢸⢘⣥⣜⣿⣿⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⢸⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢠⣾⣷⡄⢀⣀⠀⣴⣿⣷⡄⢀⣀⠀⣴⣿⣦⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢺⣿⣿⡿⣿⣿⢹⡟⣿⣿⣿⢹⣿⡿⣿⣿⣿⢺⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣝⣫⣵⣿⣿⣎⢷⣽⣿⢟⣾⣿⣷⣭⣛⣥⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠟⠥⠇⠺⠼⠻⠧


⣏⣈⣯⣯⣟⣯⣿⣹⣽⣿⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣛⣟⣜⢳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡞⠋⣩⠉⠙⢿⣧⣽⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⠻⣦⡀⠠⠀⠀⠈⠡⢘⡁⠄⠙⠻⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⡀⢀⡔⠒⠰⠂⠀⡠⢾⣿⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠟⠿⣿⣿⡋⠀⡀⢴⣼⠿⠛⠋⠉⠹⣿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡆⢈⠟⠈⠀⢀⠻⣤⠃⠀⢀⠀⣄⢘⠁⠆⡜⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⡺⠀⢸⠛⣄⠸⣏⢸⣎⢺⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠠⡄⢿⠑⢿⡕⠬⣿⣽⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠈⢀⡘⠳⡄⣻⣄⣻⣮⣽⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠴⡶⠹⣦⡀⠻⣿⣏⣺⣿⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣄⣠⣴⣷⣄⣿⢻⣶⣿⠙⣿⣻⢟⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡍⣿⡿⠿⣥⡾⠹⣷⣴⣿⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⣷⠟⠛⢾⣼⠷⣎⠻⢽⣿⣾⣼⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣼⢟⣄⣀⣾⢻⠛⠿⢿⣵⣶⣭⣻⣿⣟⠻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢹⡟⠛⠠⢄⠀⠉⠛⢿⣿⣷⣬⣵⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣶⣂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡼⠛⣿⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢢⣧⢸⣿⣇⣿⣏⣿⢻⣿⡗⠯⡂⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠡⢹⡿⠋⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠐⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢰⠉⣉⠉⠉⠉⠑⠆⠀⢰⠒⠒⠀⠐⠀⠀⡖⢩⠭⢍⣐⠒⢤⡀⠀⠀⡔⠉⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠈⠉⠉⣨⠃⢀⠞⠀⠀⢸⠀⠊⠉⠉⠀⠀⡇⢸⠀⠀⠈⡇⠀⠱⠀⢰⠀⡜⠉⢳⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠊⠀⠀⠀⠿⠀⠤⠤⣄⠀⠀⡇⠸⠤⠄⠚⠁⡠⠃⠀⡄⠀⠁⠀⠀⡆⢸
⠀⠀⠀⠀⠀⢀⡜⠀⡰⠁⠀⠀⠀⠀⡇⢀⠤⠤⠜⠀⠀⠃⠀⢰⠒⠂⠉⠀⠀⠀⡇⢸⠀⠀⢀⠃⢸
⠀⠀⠀⠀⢀⠞⠀⣴⣁⣀⣀⡀⠀⠀⡇⢸⡀⠀⠀⠀⢀⠀⣤⠀⠱⡀⠀⠀⠀⠀⢃⠀⢆⣀⠜⠀⡈
⠀⠀⠀⠀⣎⣀⣀⣀⣀⣀⣀⡇⠀⠠⣁⣀⣉⣀⡇⠀⢸⣀⡇⢣⣀⣱⡄⠀⠀⠀⠈⢦⡀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢞⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⢠⠋⠉⠳⠀⠀⠀⠠⠊⢀⣀⡀⠑⡄⠀⡋⠉⠁⠀⠀⠀⠀⠀⡀⡁⠀⡜⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠸⡀⠘⡆⠀⠀⣠⢤⡀⠀⠀⢸⠀⠰⠀⠀⠆⠀⠀⠀⡇⠀⠀⡇⢰⠃⠀⠈⠉⠀⠀⠉⠉⠉⢹⠀⡇⠀⠀⠀⠀⠀⡇⠀⡏⠉⠉⠁
⠀⠀⠀⠀⠀⢃⠀⢧⠀⡘⢁⡄⢹⠀⠀⢸⠀⠇⠀⠀⠀⡘⠁⠀⡇⠀⠀⠣⡀⠙⠒⠒⢦⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡇⠀⣅⣀⣄
⠀⠀⠀⠀⠀⠸⡄⠸⣠⠃⡞⢹⠀⡇⠀⡆⢸⠀⠀⠸⠀⡇⠀⠀⡆⠀⠀⠀⠈⠉⠉⠳⠀⠇⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⡇⠀⡤⠤⠴
⠀⠀⠀⠀⠀⠀⢇⠀⠉⡸⠀⠈⡄⢳⢠⠀⡜⠀⠀⡇⠀⠁⠊⠀⠁⠀⢠⢄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡀⢠⠃⠀⠀⢣⠀⠉⣠⠃⠀⠀⠁⢰⠉⡇⠀⡆⠀⢡⠈⠢⠤⠤⠊⡠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⠃⠀⠓⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠓⠂⠀⠙⠒⠁⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⢀⣴⢾⠿⠟⢫⣭⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢸⠠⢞⣁⡛⢾⣿⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠻⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⣛⠻⢿⣷⢦⡀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣵⣶⣶⣦⢊⡻⣆⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠶⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⢰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣹⡷⢠⡐⢶⣿⣷⣌⠻⣿⣿⡇⢿⣿⣷⣦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⠛⣴⣿⢣⣿⣿⡷⣹⣿⣿⣷⣌⢿⣿⣶⣍⡛⣫⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢇⣾⣿⡟⣵⣿⣿⣿⣿⢃⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣬⡻⢿⣷⢹⣿⣿⣿⢏⣾⣿⣿⣿⣷⣝⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠛⠂⠙⠘⠟⠛⠉⠈⠉⠛⠛⠛⠻⠿⠀⠙⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⡆⡖⢲⣴⠒⢰⣴⡆⣶⡀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠉⠈⠉⠈⠈⠉⠁⠁⠁⠁


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

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠟⠋⠐⡄⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⣿⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣄⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⠻⢿⣿⣿⣿⣿⡿⠟⠀⠀⠈⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠷⣼⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⣶⣿⡻⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣟⣛⣛⣛⣛⣻⣇⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡀⠀⣼⡆⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠹⣿⣿⣿⣿⠟⠉⠘⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⢀⣾⣿⣿⣿⠿⠷⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⣿⡁⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣿⣷⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⢸⣿⣿⡶⢶⣦⣄⠀⠀⢾⣿⣷⡄⢀⣴⣾⡿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣧⣾⣿⣧⣀⡀⢸⣿⣿⡀⢸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⣹⣿⡿⢸⣿⣿⡇⠸⣿⣿⣧⣠⣾⣿⠟
⠀⠀⠀⠀⠀⢸⣿⣿⡿⠶⠟⠛⠉⠀⠘⠛⠛⠃⠀⠈⠉⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⣀⠀⣀⣀⠉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣷⢸⣟⠡⣟⣹⡦⣿⣹⡇⢻⣆⣿⡇⢿⣀⡀⠸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠉⠀⠈⠉⠀⠈⠉⠁⠀⠉⠉⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⡀⡀
⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢰⠉⢀⡹⠀⠀⢠⠊⠉⠙⢄⠀⠹⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠘⡄⠀⠀⠈⢆⠀⠀⠀⠀⢨
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠘⢦⣀⠠⠊⠀⠀⠸⠄⠂
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠐⠒⠒
⠀⠀⠀⢠⡄⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡠⠄⠀⠈⠠⠠⢢⠄⡄
⠀⠀⠀⠈⠙⠚⠁⠀⠠⠂⠀⠰⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡇⠀⠄⠀⠀⠀⠀⠘
⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠄⠤⠀⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠛⠁⢀⠁
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠄⠢⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠰⠁⠀⠠⡀⠀⠈⠀⠀⠀⡠⠔⠒⠊⡅⠀⣠⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠖⠊⠁⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠁
⠀⠀⠰⠙⢄⠀⡇⡂⢵⠁⡟⢡⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⢸⣿⣗⣿⢰⡟⣷
⠀⠀⠂⠀⡀⡥⠧⠤⠮⠶⠭⠦⠴⠥⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣀⣘⣛⣋⣙⣈⣛⣋⣀⡀
⠀⠀⠈⠀⠉⠂⠏⢸⡖⢁⢳⠈⡌⠂⢸⠙⠀⠁⠀⠀⠀⠀⠀⠉⠀⣿⡇⢐⡏⣴⡟⢡⠌⣿⡏⣷⣿⣧
⠀⠀⠀⠀⠀⠇⢓⣒⣁⡒⠋⠑⠒⠁⠟⠢⡀⠄⠀⠀⠀⠀⠀⠀⠀⠻⠷⡶⢷⠶⠾⠶⠶⠿⠇⠙⢿⠇
⠀⠀⠀⠀⢀⠔⠁⠀⠚⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣥
⠀⠀⠀⠀⠀⠁⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠙⠿⢇⠀⠀⣶⠆⢠⡖⣿⣬⡁⢳⣿⠁⠀⠹⠂⠀⠀⠙⠛⠉⠀⠉⠛⠉⡀⠙⠚⠉⢀⠙⡛⢉⠈⠑⠒⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣶⡆⣿⣿⠤⠆⢸⣧⣿⡤⣤⡤⣤⣤⠀⠀⠀⠀⠚⠀⢹⡞⠁⢹⡎⠀⢱⡎⠀⢹⠃⠀⢳⡏⠀⢻⠃⠀⢷⡀⠀⠀⠀⠀⠀⠘
⣠⣄⠶⣈⡁⠀⢠⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠳⡀⡘⢧⠀⡘⠳⡀⡜⠧⠀⠜⢣⠀⠜⠇⠀⠞⠧⠠⠆⢼⣷⣤⣾
⠉⠁⠀⠛⠋⠀⠘⠓⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠶⠀⠠⠄⢀⠀⢙⣀⣰⢀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢸⢿⣿⣿
⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣿⣾⡆⠀⠀⠀⢀⡀⠀⠀⠖⠠⣀⣨⣶⣿⢿⣿⣏⣻⣄⡄⢀⠀⣠⣤⣄⠀⡄⢀⠀⣠⡤⢉⡀
⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⡇⠀⠀⠀⠀⢈⠁⠐⠀⢀⢰⣿⣿⣆⢐⣾⣿⠛⣿⡗⠉⠀⠻⠿⠋⠀⠷⠘⠡⠼⡶⣤⡀
⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠅⠀⠴⠒⠛⠫⠄⢀⡳⠈⢼⣟⣿⡟⡙⣿⣟⣶⡿⣟⠒⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠶
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⢦⣄⣤⡴⠂⠀⡀⠘⢁⠽⣿⣟⣿⣿⣿⣿⡶⠛⠀⠀⠀⠀⠀⣀⣀⠀⠈⣝⡂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠶⠶⡉⠀⠋⠉⠈⠉⠂⠀⠐⠀⠀⠠⠋⠋⢻⠻⠛⣇⠁⠀⠀⠈⠀⠉⠉⣉⣉⣥⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⡄⠀⠀⣽⠀⣱⠶⠶⢞⡁⠀⠀⣀⡀⠐⠀⡀⢀⣤⣄⠀⠀⠀⣠⣤⣴⣶⣿⠿⠿⠛⠁⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠶⠴⡁⠀⢄⡀⢀⣠⠄⠀⠀⢉⠁⠐⠀⠀⠘⢿⠿⠀⠀⠐⠚⢐⠛⢁⠀⠀⣀⠀⠛⣴⡄⣶⣷
⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣹⠀⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣄⠀⠀⠀⠀⠙⠛⠋⠀⠉⠁⠀⠶⠆⠰⠎⢉
⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⣠⡁⢀⠢⠄⠀⠀⣀⣋⣀⡀⠤⠀⢰⣶⡆⠀⣤⣤⣀⡀⠀⠀⠀⠀⠠⠀⡄⠄⠀⠒⠐⠀⠿
⠀⠀⠀⠀⢀⡀⢠⣖⣦⡀⠀⠉⠘⠿⠟⣛⠃⢶⣦⠀⣽⣿⣿⣧⣿⠂⣀⡉⠀⢸⣿⣿⣿⣿⠄⠀⠀⠠⠀⠀⠈
⠀⣈⠉⠁⠠⠌⣿⢎⢿⡃⠀⠀⠀⣤⣤⠛⠀⠈⣿⡧⠈⠙⠉⠈⠛⠀⠈⠀⠦⠈⠻⢿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠘⢀
⠀⣿⠀⠀⠀⢸⢋⣔⣿⠀⠐⠀⣤⠛⣛⠠⣶⢹⡟⣿⣿⢿⣆⠀⠐⡪⠝⡄⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠐⠌
⠁⠉⠀⠀⠀⢯⣻⡿⠃⠒⠂⠠⠦⢈⡟⠁⣿⣿⠀⠙⠊⠙⠊⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⣦⠸
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠀⠀⢹⣿⣇⢠⡶⢴⡶⠃⠀⠈⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠏
⢀⡆⣀⡉⠛⠀⣀⠀⠀⣴⣿⡿⢿⣿⣿⡔⠀⢻⣿⣿⣏⣩⣄⠀⠠⠦⠀⠀⠀⠁⠈⢀⡀⠀⠘⠿⠇⠐⢀⣴⣶⣷⣶⣄⠐
⠈⡇⣀⡉⢸⡇⢉⡀⠀⢿⣿⣧⣌⣽⣻⡇⠂⢰⣿⣿⣿⣷⣽⣤⡄⠀⠀⠀⠀⠃⠀⢿⠟⠀⣴⠄⠐⢠⣿⣭⣿⣿⣷⣿⣷⠐
⠸⠁⠙⠁⠀⠁⠈⠇⠀⠀⠙⠓⢿⠟⠏⠀⠀⠙⠿⢿⣿⣿⣤⡍⢡⣤⣄⠰⢦⣤⣠⣾⣦⢠⣶⡄⠠⠘⣿⡿⣿⣿⣿⣻⡿⠨
⣠⣶⣽⣉⠶⣯⣍⣓⢤⡤⠀⠀⡀⠀⢀⠀⠳⠀⠛⠲⠂⠈⠉⠁⠈⠻⠟⠁⠺⠉⢀⣽⡁⠠⡍⢡⣦⠀⠙⠿⣿⣿⡿⠟⠡⠀⣀
⣩⣷⣸⢝⡹⠷⠇⠋⣲⣬⡴⠀⣀⣠⡿⠁⣤⢀⡾⠀⠶⠒⢢⣀⠖⠒⠢⣤⠴⠒⢦⣉⠶⠒⠦⣤⠴⠲⠊⠀⠀⠂⠐⠈⠀⢼⢻
⢠⣭⡀⠁⠤⠴⠆⠀⠈⠁⣄⣸⣿⣿⡇⠀⣤⠈⣤⠆⠀⠀⢀⣟⠀⠀⢀⣟⠀⠀⢈⣏⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣠⢠⣾⢀⡄
⠀⠀⠀⠀⠀⢠⡦⠀⡀⠀⡜⠛⠀⠀⠀⢰⡇⢿⣇⡞⢀
⠀⠀⠀⠀⠀⠋⢤⠀⠛⣾⡟⠆⠀⠀⠀⢸⣃⣇⢸⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⡧⠀⠀⠀⠀⠘⡋⠉⠻⣣⣾⣀⡀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡇⠀⠀⠀⠀⠀⠁⠀⢠⠈⠹⠿⠃⠀⠀⠀⠀⡠⠊⠁⣀⠴⠂
⠀⠀⠀⡤⢀⡀⣿⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⢀⣼⠋
⠀⠀⠀⠀⣀⠙⡷⣴⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣤⡐⠀⠀⢠⣼⠉
⠀⠀⠀⢱⠋⣼⣿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠝⠛⠙⠀⠀⠈⠊⢅⣀⣀⣠⠤⠐⠀⠀⠂
⠀⠀⠀⠘⣰⡟⢻⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⡵⠂⠀⠀⠀⢤⣤⣤⣬⣿⣿⣧⣀⠀⠀⠀⠈
⠀⠀⠀⢰⡏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣏⣹⠛⢿⠷⠤⠄⠀⠀⢀⠠
⠀⠀⠀⢸⢷⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⡠⠐⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡇⠀⡜⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠢⣀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⡃⠀⡃⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⣽⠾⠧⠇⠀⠀⠀⠀⠀⠀⣶⣥⡒⠂⡐⢾⣶⢄⣀
⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠛⠛⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢸⠀⠀⠛⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠉⣴⣯⡆⠀⠀⠀⠀⠀⠰⣀⠿⣿⣦⡟⡂⢴⠈⠖
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠂⠋⠈⠁⠀⠄⠱⠈⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠤⡀⠈⠁⠀⠀⠀⣠⠱⢦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠁⠀⠀⠀⠀⠀⠸⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠆⡶⢴⡡⠄⣠⠔⠁⠀⠀⠀⠇⢀⠀⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠂⠁⠑⢄⠀⠀⡀⠀⣠⣤⠤⢤⠀⠀⠀⠀⢀⣀⡀⢓
⠀⠀⢰⠦⣂⠕⠄⠄⠳⡞⠁⠸⠃⠀⠀⢀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠲⠀⠠⠀⠀⢁⠀⢰⡄⠀⠂⠁⡄⠀⠀⠀⠀⢧⢀⠔⠊⠁⠀⠃⠀⠁
⠀⠀⠈⢾⠛⢴⡺⠀⢀⣀⠰⣄⡀⠀⠐⠀⠠⠄⢠⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⢠⣄⠁⠀⡡⠎⠓⡈⡀⠍⠀⣀⠁
⠀⠀⠀⠀⠉⠀⢀⣤⠀⠀⠙⠾⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠼⢢⡆⢀⡞⠀⢤⠙⠉⠁⠎⣷⠞⣡⡄
⠀⠀⢰⣆⠀⠚⠉⠀⠀⡄⣀⢀⡄⠀⠀⢄⠀⠀⠁⢀⣤⣈⡠⠀⠀⢐⣤⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠀⠠⠀⠀⠸⠤⠔⠠⣗⣦⠠⠌⢁⣴⢿⢄⡄
⠀⠀⠈⠀⠠⠍⠀⠀⢀⣧⡻⣾⡁⠀⠠⠈⠀⠘⠁⠸⢋⡴⠃⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠒⢰⣿⠆⠀⢀⣀⡀⠀⠦⣥⣀⣠⣄⡀⠀⠈⠂⠀⠈⠁
⠀⠀⠀⠠⣄⡐⠀⠀⠸⢿⣵⡿⠀⠀⠀⠀⠀⠀⠠⢤⡤⠀⠀⠺⠀⠀⠀⠀⠀⠀⠠⣤⣹⣿⠄⣉⠀⢠⢟⣙⠠⡆⠀⠀⠀⠙⠳⠛⠂⠀⢀⡇⠠
⠀⠀⠀⠢⢀⠀⡁⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠐⢈⠡⡌⠠⡤⡴⠀⢀⣀⡀⢠⠀⠀⠊⡀
⠀⠀⠀⠐⠂⠀⠁⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⠢⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢈⡷⢢⣦⡁
⠀⠀⠐⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠇⠷⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠉⢀⠄⠀⠑⠜⠂⠀⠀⢀⠀⡠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⣀⠀⠀⠀⠀⠐⣁⠘⠀⠇⠀⠄⢀⠆⠐⠂⠀⠃⢠⡄
⠀⠀⡉⠆⠀⢦⣄⢀⣀⣠⡴⠆⠀⢠⡄⠀⠀⡆⠈⠉⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠁⠐⠁⠐⠖⡀⠂⠈⠀⠀⠂⡀⠂⠀⠀⡇⢬⡶
⠀⠀⡇⠘⢀⣾⣟⣿⡿⠿⣿⡇⠀⠊⠭⠧⠤⠈⠐⠀⠐⠠⠄⠠⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠃⢀⠃⠀⠀⠀⠈⠀⠀⠀⠠⠤⠠⡄⠁⠈⠂⣘⢯⡁
⠀⠀⠀⠈⠀⠈⠛⠶⠖⠛⠉⢡⡄⢀⣄⠀⠀⢢⠄⣀⡐⠀⠒⠀⠀⠀⠈⠁⡆⠤⠄⠀⠀⠤⠄⠠⠀⠀⠀⢠⠀⠀⡰⡀⠀⢀⠠⠀⡆⠐⠁⠻⣦⡕
⠀⠀⠠⣀⣀⠀⢀⠀⠀⠂⠀⡣⠀⠀⡄⠁⠸⠃⠺⣍⡵⠠⠖⡆⠀⠰⠀⠂⡆⠀⠒⠀⢀⡤⠒⢶⣄⠀⠀⠀⠉⠉⠁⠀⠀⢤⣦⡾⠆⠠⠀⣠⡿⡄
⠀⠀⠀⠉⠉⠒⣄⠀⠀⠀⠀⠁⠀⠑⠞⠀⡸⢤⣄⡀⢀⣀⣸⠇⠀⢀⣀⣠⡄⣀⠀⠀⢺⡆⠀⢀⣿⠄⠀⡦⡖⣀⡀⠏⠰⠄⢃⣶⠀⠞⢀⠈⢫⠅
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠣⠀⠀⠀⠀⠋⠃⠀⠉⠀⠈⠓⠾⠟⠋⠠⠥⠤⠾⠯⠀⠀⠀⠀⠠⠉⢠⠔⠃⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣾⣿⣷⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⣠⠠⡒⣒⣒⣒⣒⡢⠀⠀⠀⠀⠀⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠤⠴⠡⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⢀⠄⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠁⡎⠀⢠⠀⠑⠀⠈⠉⠀⠉⠉⠈⠉⢁⠴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⡀⠁⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⢷⠶⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⡀⠀⠀⠂⠶⠼⠲⠁⣤⠟⠀⠀⠀⠀⠀⠀⠀⠐⠤⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣾⠇⠠⠀⠄⡠⣀⢤⣤⡤⡭⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡦⢚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢀⣤⡄⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⠀⠘⠛⠃⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠛⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⡿⠏⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⣾⠿⣫⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣙⠿⡷⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠺⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠓⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣴⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣭⣭⣽⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣭⣶⡶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⠻⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣤⣤⣤⣴⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⠀⠀⢠⡆⢠⡟⠑⡄⣴⠏⠙⡆⠿⢷⡎⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⠀⠀⠀⢹⡇⢸⣇⣠⠁⢿⣇⡼⠁⢠⡿⢱⣳⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⣀⡈⠁⠀⠉⠁⠀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⣿⣷⡞⠋⠉⠉⠉⠙⣦⡀⠀⠀⢹⣿⣧⠀⠀⠀⢀⣴⠟⠁⢿⣿⣷⡄⠀⠀⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⢸⣿⡇⠀⠀⢀⣀⣴⣿⠃⠀⠀⢸⣿⣿⠀⠀⣰⣿⡏⠀⠀⠀⠀⠙⣿⡀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠸⣿⣷⣾⣿⣿⡿⢿⣁⠀⠀⠀⢸⣿⣿⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⣿⡟⠋⠉⠁⠀⠀⠈⣿⡄⠀⢸⣿⣿⡇⠈⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⣿⣷⢀⣀⡀⠀⢀⣠⣿⠇⠀⠸⣿⣿⡇⠀⢻⣿⣇⠀⠀⠀⠀⠀⠸⠀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⢿⡿⢻⣿⣿⣿⡿⠿⢋⠀⠀⠀⠻⠿⠇⠀⠀⠙⢿⣦⣄⣀⣠⠔⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢂⡀⠄⠀⠀⠀⠀⣰⢂⠆⠀⠈⠁⠀⠀⠀⢠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠄⠀⢸⠁⣩⠤⣤⡶⠐⣶⠆⡏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠐⣿⢣⠙⠐⠁⠁⠈⠈⠀⡇⢀⠄⠀⠀⠀⣠⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢁⡜⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣷⣶⣬⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠛⠿⣿⣿⣿⠿⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⠀⠀⠀⠀⡤⢀⣀⡀
⠀⠈⣈⣤⣤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣨⡝⢆⢀⡀⠀⠀⢠⡆⠀⠀⢈⣄⡀
⠀⠀⠉⠀⠰⠷⠄⠀⠀⠀⠈⠙⡏⢀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡈⠩⢓⡏⡈⠀⠀⠀⢠⡀⠀⠕
⠀⠀⠀⢈⣵⡆⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠀⠀⠀⠀⠡⠀⡀⠀⠈⠐⢩⢠⣶⠀⠉⠁⠀⠀⠀⠘⠃⠂⠒
⠀⠀⢈⡧⠄⣠⡔⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⡎⡔⠀⠀⣁⣤⠄⢅⠉⠁⠀⠀⠀⠀⠰⢢⠀⡀⠙⠷
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⡀⠀⡿⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠈⣽⣶⠃⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨
⠀⠀⢀⠱⢟⣛⠀⠀⠀⠀⠈⣱⡀⠀⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⢈⣻⡩⢊⠁⠄⠀⠀⠀⠠⡀⠠⠒
⠀⠀⠈⣇⠀⠉⡤⠀⢀⣶⣿⡿⠅⠀⠀⠉⠉⢀⠀⠰⠀⠆⡂⠀⠀⡰⠀⠾⢿⡿⠀⠀⠀⠀⠀⠉⠂⠀⢀⠈
⠀⠀⠀⢹⣶⡟⠁⠀⠘⢛⣿⣿⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳⠀⠀⠀⢰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣌⡤⢀
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⡄⠀⠀⠀⠀⠀⢱⡁⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣌⡉⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡈⠲⠞⣁⠉⢢⣄⠠⠀⢀⠀⢰⣦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡸⠛⠁⠀⠀⠀⠀⠉⢳⡔⠨⡿⣬⣟⣠⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣴⣠⠀⡤⠋⠄⠤⠃⡄⠀⣀⢀⡀⠀⠙⠦⡝⢧⣉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⣷⣿⡃⠎⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⣦⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡶⣹⣿⡗⠀⠀⠀⠐⢆⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣃⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠀⡏⠸⣇⠀⣀⣀⠀⠀⠑⠈⠁⠀⣀⠀⠆⢀⠀⠀⣐⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡽⠟⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢰⣂⠀⠒⠀⠀⠀⠣⠀⠠⠄⠀⠴⠖⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠹⣆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡘⠻⠄⠀⠀⢶⣌⠉⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢆⠀⠲⠣⣀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣤⠀⣄⡀⣤⠀⠀⡀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡂⢀⡤⠀⢀⣻⠠⠘⢪⡁⠉⠐⢾⣥⡴⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⠐⠀⠀⠀⢈⣹⡞⠁⠘⠻⢿⠓⠁⠀⠙⠲⠤⠀⠈⠷⠿⣈⠀⠰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠂⠀⣸⡟⢿⡟⠀⠀⠀⠀⠀⢪⣤⡤⠀⠈⠠⢤⡃⠈⠻⣦⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠟⠁⠀⠀⠈⠛⠀⠀⠀⠘⠉⠀⠀⠀⠉⣳⣄⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣀⠠⡄⠠⠆⢽⠃⡤⠐⠻⠶⠤⠤⠄⠃⣩⢿⡿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠃⠀⣤⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠾⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢿⡾⠟⠁⠀⠀⠉⠀⠈⠁⠀⠀⠉⢁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠜⠃⣀⠀⠀⠀⠐⣰⡔⢲⡀⠔⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡀⠹⠊⢐⠆⠁⡤⠺⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣸⡏⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡉⠀⠁⠆⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠉⠨⢿⡦⡄⠀⠚⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠀⠀⢸⠥⣶⡆⠀⠀⠿⢦⡀⢀⢀⡘⠷⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠟⠋⠈⠁⠀⠀⠀⠈⠒⣹⣖⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠒⠀⠰⠟⠰⠋⠸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠙⠀⠀⣠⣴⠀⠈⠀⢢⡼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡟⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢴⠀⠀⠀⠀⢬⠉⠁⠀⠀⢠⣤⡜⠀⣅⠀⠀⠀⡠⠀⠀⠀⠀⡤⠤⡴⢾⣹⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡿⡇⢀⠁⠐⠤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣌⠀⠘⠠⣅⠀⠘⠀⠤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠦⣄⠚⠋⠉⠀⠀⠀⠈⠙⢣⠄⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢰⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠙⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⣴⣀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠳⣤⠀⡀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡘⠷⣧⣴⡂⣀⠻⡇⠀⠀⠀⠀⠘⠠⡀⠀⠘⠶⢦⣴⣿⡧⠔⠁⠀⠀⢳⣸⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠻⣥⣈⣻⣿⣿⡾⠀⢠⠤⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣗⠀⠀⠀⠀⢹⣿⣃⡠⠉⠙⠋
⠀⠀⠀⠀⠀⢠⢁⡤⠴⠆⠶⠶⠿⣿⠿⣿⣧⡠⣷⠀⢀⠀⠀⠁⠀⣠⣤⠶⠋⠀⠀⠛⢆⡀⠀⣤⣾⣿⢻⣍⢛⠠⢄
⠀⠀⠀⠀⠀⠈⠈⠒⠤⠀⢀⣤⠤⠾⣄⠀⠉⠧⢿⣄⡽⠒⠀⠂⠀⠑⢆⠀⠀⠀⠀⠀⠈⠁⠀⠘⠿⠿⠏⠉⠙⠷⠬⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣟⢠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡄⡄
⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢣⠈⣄⠀⠀⠀⡞⠀⡄
⠀⠀⠀⠀⠁⢀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣼⡀
⠀⠀⣀⠀⠀⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⢨⣀⣴⣿⠷⣠⠀⣠⠔
⠀⠈⠀⠀⣀⠀⠀⢧⠀⠀⠀⠀⠐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⢀⣄⠤⣙⣿⣿⣿⣷⣶⡈⠀⠀⠂
⠀⢀⡠⠜⠁⠀⠀⠼⡖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡇⣆⡏⠀⡀⠀⠀⠀⠐⠂⠀⠉⠿⡿⠟⠿⠿⣿⡂
⠀⠸⠀⠀⣄⠍⠀⠀⠉⠀⡀⠀⠀⠲⠄⠀⠀⠀⢀⡃⢀⠹⣿⣠⣨⣾⡶⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠁⠀⠀⢀⠀⢁⠉⠚⠉⠀⠀⠀⠀⠀⠰⢄⡪⣤⣰⢳⣿⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⠈⣑⢿⡻⡘⣿⣗⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡇⠀⢸⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⣿⠇⢇⠘⢻⣃⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⡀
⠀⠀⠀⠀⣤⡀⠆⠸⠀⢐⡤⠂⢐⠀⠀⠀⠀⠀⠠⠄⠉⠙⢳⠄⢧⡘⡵⢊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⣸⣿⣰⠁⡠
⠀⠀⠂⠀⠨⣍⠳⡟⢤⣠⣦⠄⠚⠚⠀⠘⠁⠀⠀⠀⠄⠚⣉⡥⠄⢣⣘⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⣿⣇⠎
⠀⠀⠀⠀⢢⣝⣦⣶⠈⣿⣡⣴⣷⡶⠂⢀⠀⡀⠀⠀⠀⠈⠐⠚⠿⠶⣛⠅⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢈⣻⣷⣿⠃
⠠⠀⠀⠀⠀⢉⡽⠿⠿⣿⡿⠑⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠬⢝⣿⡏
⠀⠀⠀⠀⠀⠨⣀⠀⠠⡿⠛⣦⣤⣴⣶⣍⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠴⠾⢿⡦⠂
⠀⠀⠀⠀⠀⠀⣦⠀⠀⣏⠉⣡⠋⠯⠙⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣥⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠒⠒⠢⡀⠀⠀⠀⠀⣀⠐⠀⠀⢀⣀⡀⢀⠀⢀⡀⡀⣀⠀⠀⠀⠀⣚⢋⣉⠁
⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠬⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡄⠂⠉⠒⡄⠀⠀⠀⡠⠖⠚⠲⡄⠀⠐⢶⣇⠙⠃⠀⠀⠀⠀⠀⠰⣏⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠤⠘⠁⠀⠀⠀⡇⠀⠀⠀⠘⣆⠀⠀⠋⠁⠀⠀⠠⠀⠀⠀⠀⣀⣀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⠂⠀⡐⠀⠀⢠⡖⠒⢲⡄
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣀⠴⠃⠀⠀⠀⠢⠤⠂⠀⠀⠀⠠⠭⠭⠭⠄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⢠⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣾⣻⡆
⠀⠀⠀⠀⠀⠐⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁
⠀⠀⠀⠀⠀⠶⠆⠀⣸⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠀⠀⠀⠁⠔⠂⠀⠀⠅⠸⠀⠉⡆⠃⡄⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢈⠉⠛⠚⠁⠀⠀⠀⠒⠀⠀⠸⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠓⠲⠶⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠂⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉
⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠀⠀⠀⠠⠊⠀⠈⠋⠈⠙⣆⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠲⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⢀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠉⣄⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢀⠀⢈⠁⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠐⢀⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠠⠀⠀⠃⠀⠠⠄⠀⠀⠘⠦⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠐⣶⣤⡄⠀⠀⣀⢰⡶⣾⣶⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⢀⣆⡀
⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⡀⢿⣼⢟⣿⣛⡆⠀⣤⢹⣼⣿⣿⡩⠄⣠⣴⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⡿⡃⠀⠀⠐⢿⣷⡄
⠀⠀⠀⠀⠀⠲⣿⠂⠀⠀⠀⠀⠻⣾⣫⣾⠿⢦⠀⢰⣸⣿⣿⣽⣿⡗⠀⣿⣿⣿⣿⣿⣷⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣯⣴⡶⠂⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⢯⠷⠀⠀⠀⠉⠙⠿⠟⠃⠀⠀⠻⢿⣿⣧⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠙⣿⡓⠀⠀⠀⠠⣾⣿⡇
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡡⠄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠹⢿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⢠⣿⠂⠀⠀⠀⠀⢀⡴⡛⠈⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⡀⣄⣀⠀⠀⢠⣄⠀⠀⠀⠀⣀
⠀⠀⠸⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣿⡟⢁⣴⡿⠀⠀⢀⠎⡀⠁⠀⡀⠄⠀⢸⣿⡆⠀⠉⠀⠠⣉⣻⡥⢆⡀⠘⣿⣷⠀⣠⣾⣿⠀⠀⠀⢀
⠀⠀⢻⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⢬⣷⡿⣋⣤⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⢐⠲⠶⣽⠋⠩⠀⠀⠈⠛⠃⣿⣿⠟
⠀⠀⠻⣿⣿⣿⡗⠀⣤⣤⠀⣼⣷⠀⣠⣤⠸⠿⡶⠦⣿⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠀⠀⠠⠭⢭⣯⠴⠞⣋⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠁
⠀⠀⠈⢿⣿⠆⠀⠀⡻⣿⣷⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠘⠀⠀⡀⠀⠀⢠⠀⠐⣻⡭⠀⠠⣤⣀⡒⣶⣚⣯⠗
⠀⠀⢠⣀⠀⠀⠀⠘⠿⠿⣿⣿⣿⡷⠿⠷⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠐⢢⡤⠙⠀⠄⠀⠀⠀⢻⡯⠀⠲⠦⣤⣄⣋⣡⠴⠚
⠀⠀⠸⣿⣿⣦⠀⠀⠀⠰⠿⠛⠻⠿⠀⣴⣄⢠⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠂⠐⠠⠀⠀⠀⠁⠀⠑⠶⢦⣄⣉⣴⠾⠋⠀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⢰⠀⠀⠀⣬⣽⠿⡇⠀⠀⠀⠀⠀⠀⣾⡆⠾⠡⡤⠆⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠁⠀⠀⠀⠛⠏
⠀⠀⠀⠀⠈⠉⠁⠀⢠⡀⣴⠀⢁⣀⣠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣦⡘⠳⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡀⠀⢰⣴⡀⠀⣄⠀⠀⣶⡧
⠀⠀⠀⠀⠀⣀⠸⣆⢸⠇⣯⣴⣿⡉⠁⠀⠀⢀⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠛⠀⢼⣯⠄⠈⠉⠀⠀⠿⢀⡀⠈⠁⠀⢠⡐⣴⢃
⠀⠀⠀⠀⢦⡙⢦⠻⣼⣿⠯⠄⠀⢀⢠⣶⠶⠘⣿⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡙⠶⣋⣤⠄⠀⠀⠲⣝⣗⣫⣔
⠀⠀⠀⠳⣮⡻⣦⣍⣛⡛⠁⠀⠠⢜⠛⠁⣀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⡇⠀⢠⣛⠯⢈⠥⠶⡂⠀⣈⡻⢮⡭⢟⡋
⠀⠀⠐⠲⣞⣿⡓⢦⡄⠀⠀⠀⠀⠀⣶⡿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡿⠇⠀⠀⢭⣍⡀⢚⡋⠁⠀⠠⣭⣹⣛⡭
⠀⠀⠀⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠱⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣤⣭⣥⣦⣭⣷⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣤⣀⣀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⣶⡏⣿⣿⣿⣿⠛⠛⣡⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣤⣤⣝⣾⣧⣈⠀⠿⠾⠀⢠⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣧⠙⢻⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢧⡀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡟⠿⣿⣷⣄⠀⠉⠛⠻⠿⠿⣿⢻⣷⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⣀⠸⠿⣿⣿⣿⣿⣦⣶⣿⣿⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢰⣿⠿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢄⣨⡄⠴⠛⠁⠈⠃⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣻⣿⡖⣶⣿⣶⠠⢄⣀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠰⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣦⣴⣿⣿⣿⣿⡿⣦⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡿⠃⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡿⠿⣿⡿⠿⠻⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣦⠛⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣙⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣤⡴⠂⣤⣤⠀⡀⠀⠤⣤⣘⣻⣄⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣀⡀⠀⠸⠏⢤⠀⢰⣯⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⣀⠉⠉⠉⠛⠛⠛⠛⠓⠀⠀⠘⠛⠚⠛⠛⠿⠿⢿⣦⠳⡄⠀⠀⠀⢀⣥⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠄⠠⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⡀⣀⠈⣾⣺⠀⡴⠃⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠀⠀⠀⠎⠀⢀⠆⠀⠄⠐⠒⠚⢳⡀⢀⠠⠄⠤
⠀⠀⢯⠾⣨⠌⠀⠁⢀⠀⠀⠀⠀⡀⠀⠁⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⢀⠠⠀⡀⠀⠀⡣⠦⡐⢀⠂
⠀⠀⠀⠁⠉⣠⠄⠈⠣⠟⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠆⡥⠀⠌⠠⠜⠋⠀⢐⠜⣠⡀
⠀⠀⠶⠀⠉⠀⠀⠄⡄⡄⠀⠀⡀⠀⡀⢠⡦⣔⠀⠀⠴⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠂⠁⠚⠒⠀⠈⣶⠓⡤
⠀⠀⠀⠐⠀⠀⠀⣶⣼⡗⠀⠀⠀⠈⠀⡁⠒⠁⣠⠀⠀⠀⠀⠀⣀⢤⣄⠻⠏⠀⡴⠆⡀⠑⠒⠰⣖⢄⠀⠀⡄
⠀⠀⠠⢉⠀⠀⠀⠉⡋⠁⠀⠀⠀⠀⢈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠈⠠⠘⢓⠂⣁⡄⠀⣀⡀⠀⠀⠐
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⢂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠖⣤⡁⠀⠀⠉
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠈⠈⠁⠀⠠⠄
⠀⠰⢆⠀⣀⠀⠀⢀⣠⠀⢀⠀⠀⣀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠂⠀⠀⠀⠐⢀⠀⡡⠄⠀⠅⠀⠐⠀⡜⣦⡀
⠀⠘⠐⢀⣿⣷⣿⠿⣷⠀⠘⢳⡤⠜⠤⠀⠀⠁⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⢱⣊
⠀⠀⠀⠀⠉⠓⠒⠋⠉⠄⠀⢄⠀⣠⢄⣀⡀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠁⠻⡊
⠀⠀⢠⠴⡀⠀⠀⠁⠨⠂⢀⡦⠀⡁⠘⠒⠁⠋⡇⠀⠁⠀⠀⠊⠀⢠⠊⠙⢦⠀⢀⢀⠀⠀⠄⠐⠛⣋⢐⠀⢾⣕
⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠁⠐⠉⠓⠒⠒⠎⠀⠀⠐⠒⠄⠀⠀⠸⠆⣤⠟⢀⣜⣹⣖⠀⠀⠁⠘⠃⣀⠔⠠⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⡦⢴⢴⢄⠴⣴⡦⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⡠⡤⢀⠀⣤⢄⡀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⣽⣿⣗⠀⢸⠀⢄⡮⣛⡇⠀⠀⠀⠀⠀⢸⣾⢿⣿⢧⣳⣽⢠⣟⡞⣷⡏⡿⡇⠀⠀⠀⠀⣼⡻⠤⠽⠷⢾⣿⠴⠿⠥⠴⣟⡀
⠀⠀⠀⠀⠀⢹⣖⠍⠀⢸⠁⢐⣭⣶⡂⠀⠀⠀⠀⠀⢸⡜⡜⣟⢯⣻⣿⣿⣯⡞⡽⣱⣱⠆⠀⠀⠀⠀⣿⠅⠀⠉⠍⢹⣿⠉⠩⠥⠬⢽⡇
⠀⠀⠀⠀⠀⢿⣛⡫⠁⢸⡄⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡝⣌⢳⡙⣿⣿⣫⢞⡵⢣⢿⠃⠀⠀⠀⠀⣿⡛⣛⣛⣒⣻⣿⣛⣛⣛⡓⣻⡇
⠀⠀⠀⠀⠀⣿⣿⣓⠂⢸⡇⣐⣿⣿⡃⠀⠀⠀⠀⠀⢨⢳⡹⣌⢳⣽⣿⣿⣣⢞⣵⢋⢎⠂⠀⠀⠀⠀⣿⠄⠀⠠⠤⢾⣿⠤⠤⠤⠄⢽⡇
⠀⠀⠀⠀⠀⣲⣿⠿⠗⢸⡇⠾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣧⣳⣌⢷⣽⣿⣿⣫⠟⣡⢟⣾⠇⠀⠀⠀⠀⣿⡍⠉⠩⠭⢽⣿⢭⣭⠍⢩⣽⡇
⠀⠀⠀⠀⠀⣸⡷⢏⠁⢸⡇⠨⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⠳⣽⣦⡙⢿⡿⣡⣾⣿⢋⢾⠇⠀⠀⠀⠀⣿⣄⣒⣒⣒⣚⣿⣒⣒⣒⣒⣺⡇
⠀⠀⠀⠀⠀⣻⠽⡣⠂⢸⠀⢔⣽⣿⠃⠀⠀⠀⠀⠀⠀⢧⠳⣬⡳⣽⣿⣿⡵⣛⣵⢏⡞⡀⠀⠀⠀⠀⣿⣒⠲⠶⠶⢺⣿⠒⠒⠒⢒⣺⡇
⠀⠀⠀⠀⠀⣼⣭⡶⠀⢸⠂⢨⣒⣿⡇⠀⠀⠀⠀⠀⢸⡘⠷⢮⣽⣿⣿⣿⣞⣯⠵⠟⣡⡇⠀⠀⠀⠀⣿⠧⠤⠭⠭⢭⣿⠭⠭⠭⠴⢿⡃
⠀⠀⠀⠀⠀⣾⣿⣡⣀⡸⣠⣤⣝⣿⡅⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠻⢿⡿⠖⠒⠚⠻⠟⠁⠀⠀⠀⠀⠛⠁⠀⠀⠈⠸⠿⠘⠛⠁⠈⠙⠃
⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠈⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠋⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⢒⠂⠐⣓⠸⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣧⡀⠂⠀⢀⣾⣿⣿⠇⠀⡀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣠⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢹⣿⣿⣿⢴⠂⠰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⠁⠄⡀⣲⣼⣿⣿⣶⣤⣤⣼⣿⣿⣟⡾⠋⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠴⢦⣴⣿⣿⡹⣿⣾⣿⢿⣿⣿⣿⣿⣿⣄⠴⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠟⠉⠉⠛⠛⢿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣄⣀⣀⣠⣶⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣩⣵⣾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⡄⠀⣶⣿⠀⠀⣤⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣿⡿⠃⠀⣿⣿⠀⣼⣿⡟⠁⠉⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⠛⢻⣿⣦⠀⣿⣿⠀⢿⣿⣧⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⢿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣶⣿⠿⠋⠀⣿⣿⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡈⢿⣿⠟⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡷⠀⠙⠷⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⡿⠟⠛⠿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣦⣤⡀⠀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢠⣤⣴⡿⠃⠀⣠⣤⣤⣿⠃⠀⣠⣤⡀⠈⢻⣿⣿⣿⠀⣨⣿⣦⠘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢀⣀⣸⣇⠀⠘⣿⣿⣿⣯⠀⠀⣿⣿⠇⠀⢸⣿⣿⣿⠀⢿⣿⣿⣧⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⠉⠉⣿⣄⠀⠈⠉⠉⣿⣆⡀⠈⠉⠀⣠⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣩⣍⡉⢩⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣟⣛⣭⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠁

⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠀⠐⢛⠒⠂⠒⠀⢲⠀⡛⠁⠍⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠠⡄⠐⠒⠒⠂
⠐⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡆⠀⡆⠁⣀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢠⢶⠴⢫⠽⠯⠉⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢀⡀⠙⠈⢀⣀⣀⠘⠁⣠⢀⠀⠀⠀⠀⠀⠠
⣠⡆⠀⠨⢤⡄⠀⠊⠠⠤⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠸⣿⣿⡿⣤⡄⠐⠉⠄⠀⠤⠀⠴⠦⠀⠀⡿⣿⣷
⢬⠏⠀⢀⢉⡉⢁⠶⠆⠤⠀⡤⠬⢛⠀⠂⠀⠤⠟⠀⢤⠈⣀⠶⠀⣼⣿⢻⡟⠁⠀⠛⠂⠐⠀⠈⠂⠀⠀⢶⣴⣤⠿
⠄⢠⠀⢠⢠⣖⢳⡌⠉⠉⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⣁⡈⠠⠀⠀⠾⠀⠘⠂⢀⠀⠀⠀⢀⠄⠄⠀⠀⢀⣘⣿⣿⣿
⠲⠚⠂⡀⠛⣱⠄⡐⠀⠀⠀⠂⠠⠃⠀⡀⠀⠀⢄⠀⠿⠟⠀⠘⠁⠀⠄⠂⠰⠈⠠⠐⠂⠉⠈⠙⠥⠄⠀⠀⠙⠿⠿
⠀⠉⠁⠁⢨⣉⢀⣆⣄⠀⠐⠉⠁⠀⠀⠁⠀⠀⠈⠐⠀⢤⡀⠤⠄⠁⠤⠄⠀⠀⠀⠤⠥⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠚⠀⢘⠋⡿⣴⡧⠀⠀⠀⠐⠀⠀⠃⠀⠀⠉⠀⣶⡖⢀⣚⣋⣀⠂⠀⣃⣐⡂⠐⠂⠀⠙⠛⢛⣋⣈⡁
⠉⢡⡄⠀⢀⠘⣳⣚⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠢⠀⢠⠀⠐⠡⣤⠤⠀⠴⠶⠀⠀⠀⣤⣤⣴⣎⡀⠤⠔⠋⠀⠆⢶
⠉⠘⠁⠀⣉⠉⠉⠉⠁⣀⣀⡀⢀⠀⠀⠀⠁⠀⢀⣀⣘⡁⠄⠘⢙⡉⠈⠈⠀⡀⠀⠒⠛⣺⢏⣁⣀⣀⡄⠀⣀⠀⠈
⠐⠒⠺⣾⣭⡗⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠂⢸⣿⣿⣷⠿⠀⠿⠟⠀⠀⠀⠀⡂⠀⠀⠠⠠⠤⠀⠀⠢⠀⢈⡀
⠀⠀⣰⡟⣱⣗⡀⠈⢘⠈⠁⣀⠀⠀⠀⣀⠀⢀⠄⠉⢁⠀⠤⠄⠃⠐⠂⠉⠀⠊⠀⠐⠒⠀⠈⠂⠀⠀⠀⢠⡩⢉⡆
⢢⠀⠘⠋⠃⠀⠀⠀⠀⠉⣀⣄⠀⡀⠠⠸⠀⢂⣀⠴⠟⠀⡒⠃⠶⠀⠼⠁⠀⠀⠀⠄⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⢀
⣾⠠⢀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠈⢉⣠⠤⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠹
⡞⢀⣀⢡⣉⠀⢀⡀⠀⠀⠀⢙⣉⡀⡆⠀⠀⠒⠒⢳⡀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸
⡇⠐⠊⠈⠟⠀⠏⢀⠘⠂⠀⠼⣿⣿⣷⠄⠰⠡⠈⠡⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⡒⠦⠐⢐⣤⣦⡌⠁⠀⡉⠈⠟⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠁⠀⠀⣠⣤⣄⠀⠂
⠓⠡⠚⠁⠊⠉⠙⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⣸⡃⠀⢸⣿⣽⣿⠇⠀⠀⣠⠄⢤⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⡒⠀⠀⢀⣀⣠⠀⠛⠃⠀⠀⠙⠛⠋⠀⠀⠐⣅⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢖⠂⠤⠀⠀⠀⠀⠀⠀⠀⠟⠒⠀⠀⠀⠀⠀⠀⠂⡰⠀⠐⠂⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⣀⠠
⠋⠘⠆⠄⠋⠈⠀⡠⠂⠉⠉⢉⠏⠑⠒⠒⠒⠡⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠈⠀⣀⡀⡀⠀⠀⠀⡀⠀⠀⠉⠀⢁
⠈⠁⢀⠠⠤⠤⡼⢀⢀⣀⡀⠊⠀⠀⢶⣤⣠⣤⠏⢠⡞⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⡀⠴⠿⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁
⠀⠀⠁⠀⢀⠜⠀⠀⠀⠀⠀⠀⣠⣶⣾⣄⣤⣿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⠀⠑⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⢿⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠟⠀⢉⡀⠉⠃⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢨⠁⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠄⢠⣷⠄⠀⠀⠀⠛⠁⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠹⣄⠜
⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⢾⡷⠀⠲⠆⠀⠀⡟⠛⠀⠀⠀⠀⠠⠚⠙⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⠚⠓⣆⠀⠀⠀⠀⠰⢄⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⠏⠉⢹⣷⠀⠀⣤⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠦⠴⠃⠀⠀⠀⠀⠀⠀⠽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠶⠿⢷⣄⠀⣶⠀⣤⣶⣄⢸⣿⢀⣴⣦⡀⠀⣴⢶⡄⣶⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡇⠀⠀⢀⣿⠀⣿⢸⡏⠀⣿⣾⣯⣾⠃⠸⣿⢼⡇⣸⣇⢿⡆⣸⣿⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠠⣿⣧⣶⠶⠟⠉⠀⣿⠘⢷⣶⠟⢸⡿⠹⣷⣾⠏⠸⢷⢿⣿⠘⢷⠟⣿⡇
⠀⠀⢀⡀⠀⣠⠖⠤⡄⡀⠙⠉⢎⠙⣦⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⡏⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⡔⢀⣀⡤
⠀⠀⠀⢀⠞⢡⣦⣤⠶⠿⢦⠀⠈⠉⠁⠀⠐⠦⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠟⠁⠀⣴⠾⠃⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣿⠟⠋
⠀⠀⠴⠋⣴⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢿⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⠀⠀⣠⣾⠟⠀⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠈⠿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⢦⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣾⣲⣄⣤⣶⣿⣿⡆⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠼⢧⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣾⡄⠉⠻⣿⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠁⠀⠀⠠⠀⠀⠠⠀⠠⠀⠀⠀⠐⠐⠂⠀⠘⡇⠀⠀⠀⠸⠶⡶⡆⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⡀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠀⠀⢸⠇
⠀⠀⢀⣠⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⣤⣴⡏
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠒⠀⠐⢊⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠀⠠⠀⠀⠴⠿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣶⣶⣶⣶⣤⣤⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠄

⢱⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠑⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠁⠀⠀⠹⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠸⣄⠀⠀⠱⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠉⠢⣄
⠀⠸⣇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠡⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠘⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠀⢒⠆⠙⣦
⡅⠀⠀⠀⠀⠀⠻⣄⠈⣆⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⠈⠀⠀⠀⠀⠀⠂
⠘⢦⠀⠀⠀⠀⠀⠹⣆⠘⡄⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠊⠁⠀⠀⠔
⠀⠀⠳⡀⠀⠀⠀⠀⠘⢆⠹⠀⠀⡂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠿⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀
⠐⠀⠀⢀⠀⠀⠈⢧⡀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠁⠠⠌⢷⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⢀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⡌⣿⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠪⣷⡟⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠠⡀⠀⠀⠀⠀⠈⠠⡀⠀⢹⡇⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢸⡇⠐⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣟⠉⣿⣻⣛⣛⣛⣟⣛⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣟⣛⣛⣻