Peel Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠁⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⡠⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠁⠀⠀⣤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠊⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⢀⡠⠀⠄⠒⠀⠉⠉⠀⣀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⣠⡞⠛⠀⢀⠤⠴⠶⠾⠶⠿⠷⠶⠒⠒⠒⠓⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⣿⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠲⠤⢤⣄⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠢⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠉⠀⠉⠉⠐⠒⠤⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣺⣯⣛⣿⣉⣛⣽⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠑⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠻⠃⠐⠀⠀⠠⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣠⣤⣄⣀⣠⣄⣀⣀⠀⢰⣿⣿⣿⡄⠀⠀⠀⢸⠁⠐⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⢸⡇⣪⡱⡎⣧⢸⢁⢳⢰⡡⡎⣿⡇⠸⣿⣿⣿⣧⠀⠀⠀⢸⠠⠀⠀⠀⠹⢀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠛⠛⠋⠋⠉⠁⠋⠉⠁⠀⠻⣿⣿⣿⡗⠀⠀⠸⠄⠠⠾⠔⠒⠊⠉⡀
⠀⠀⠀⠀⠀⠠⠴⣦⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡇⣀⠀⠀⠀⠀⠀⣀⣀⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠃⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠥⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠑⠠⠤⠤⠼⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠋⠉⠁⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⢀⣿⡇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⢀⣾⡿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⢀⣾⡿⠁⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⢀⣾⡟⠁⠀⢠⣿⡏⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⡀⠀⠀⠀⣰⣿⠇⠀⢀⡈⠉⠀⠀⠀⠺⣿⣧⠀⢀⣠⣴⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠉⠛⠿⣿⣶⣾⣿⠋⢀⣴⣿⠃⠀⠀⢀⣾⡇⢹⣿⣿⠿⠟⠋⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⣴⣿⠟⢁⣴⣿⠟⠁⠀⠀⣠⣿⠟⠀⠈⣿⣇⠀⣠⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠿⢋⣡⣶⡿⠟⠁⠀⠀⣠⣾⣿⣿⠀⠀⠀⠘⢿⣿⡿⠋
⠀⠀⠀⠀⣴⣶⣦⣤⣤⣤⣴⣶⣾⣿⣿⣿⣭⣶⣾⠿⠛⠉⠀⠀⣀⣤⣾⣿⠋⠈⢿⣷⡀⠀⠀⠈⠛⢿⣷⣦⣤⣤⣤⣶⣿⣦
⠀⠀⠀⠀⠘⢿⣿⣍⣛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣀⣀⣠⣤⣶⣿⠿⠛⠙⠻⣿⣶⣤⣹⣿⣦⣄⠀⠀⠀⠈⠉⠙⠛⠋⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣷⣶⣿⣿⡿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣿⣶⣶⣤⣤⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⡄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢠⡇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣾⠀⢸⡟
⠀⠀⠀⠀⠀⣿⣋⠙⠶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣷⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⠈⠙⠛⠋⠉⠉⠙⠛⠷⢶⣤⣄⣀⣀⣀⣠⣤⣾⠇⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⣿⣶⡶⠶⠾⠛⠛⠉⢉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠴⠶⠶⢤⣤⣀⠀⠀⠀⠈⠉⠉⠉⢉⡥⢾⡿⠀⠀⠀⠀⠀⠀⢀⡿⢻⢹⡀⠹⣧⠀⢀⣠⠔⣪⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⠴⢞⣿⣲⡿⠁⠀⠀⠀⠀⠀⠀⣼⠓⠾⣧⢳⡀⠙⣿⣵⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢛⣿⠟⠁⠰⣤⡀⠀⠀⠀⣼⠇⠀⠀⠈⢧⡙⢄⡈⠛⠿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠈⠁⢀⡾⠃⠀⠀⠀⠀⠀⠙⠳⢿⣷⣦⣄⣀⠀⠀⠀⠀⣀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⡶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢉⣉⣉⡀⠀⠀⣀⣀⣀⠤⠤⠴⠖⣒⣩⠭⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠾⠭⠭⠴⠶⠒⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣉⣳⠇⠀⠀⣼⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⠞⢁⡠⢤⠬⣦⢤⡴⠧⡤⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠸⠴⠋⡠⠋⠀⠀⠀⡼⡆⠘⡆⠈
⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⡜⠁⡇⢀⠇
⠀⠀⠀⠀⢰⡁⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⢀⡀⣠⠔⠋⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢴⠉⠉⠁⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜
⠀⠀⠀⠀⠀⢠⠖⠋⢉⣑⢮⠀⢀⣠⡋⣉⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠱⡀
⠀⠀⠀⠀⠠⡇⡠⠊⣡⠋⠉⠉⠉⣦⠉⢣⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠉⣠⠖⠁⠀⠀⠀⡰⠉⡇⠀⡇⠀⠀⠀⠀⠀⢯⣉⠉⣉⠜⠁⠀⢀⡇⠀⢹⡒⠒⠚⡳
⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⣀⠜⠁⠐⣅⠜⠁⠀⠀⠀⢀⡠⠴⠚⠉⠁⠀⢀⡠⠋⠹⡄⠀⠙⠺⠭⣀⡀
⠀⠀⠀⠸⡉⣠⠖⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠤⠖⠚⠉⠀⠀⠀⠈⠓⠢⠤⠤⠴⠃
⠀⠀⠀⠀⠈

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

⠀⠀⠀⢀⡠⠔⠂⠒⠢⢤⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⣰⠋⠀⠀⢀⡂⠀⠀⠘⡄⠀⡠⡤⣄⢸⡄⠀⠀⠀⠀⠀⣰⡇⠒⠀⠋⠐⠀⢀
⠀⠀⡇⠀⢈⠀⣴⣷⢾⡒⠀⡻⠀⠀⠀⠋⠀⣤⠀⠀⠄⠀⠀⣿⣧⣀⠀⠀⠀⣠⠟⠄⠀⠀⠀⣠⢤⠄
⠀⠀⢧⠈⠀⡛⠁⠐⠒⠀⢀⠂⠀⠀⠀⠀⠀⠀⢰⠆⢘⠁⠀⠘⢿⡀⢗⠐⢾⣧⠷⠖⠀⠀⣠⠏⠿⠤⠊
⠀⠀⠀⠑⠤⣘⣀⠀⣀⡠⠋⠀⠀⠀⢈⠔⣿⠂⠀⡀⠿⠶⠃⠀⠀⠈⠉⠉⠈⠻⠤⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⠁⠝⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣤⣴⡴⣗⢢⡷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢴⠆⠀⢀⢶⠀⠀⠞⢫⡋⢿⣜⡿⠀⠹⠛⠓⠀⠀⣀
⠀⠀⠀⠀⠀⠲⠀⠋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠏⠀⠀⠀⠈⠀⠒⠡⠃⠚⠂⠀⠀⢸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⣤⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢭⢃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⡤⢣⠀⢸⡋⣄
⠀⠈⠐⠂⠓⠀⢀⠁⠁⢭⠜⢂⠗⠚⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠲⢀⠄
⠀⠀⠘⠐⠁⠀⠈⠁⠀⠉⠀⠀⠀⠀⡀⡀⠠⠂⠰⠦⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠁⠀⠂⠀⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣊⡌⣭⢀⠥⠦⢀⠌⢀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠤⠶⠖⠂⠠⠄⠀⡈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⡀⣆⣉⣠⠆⠀⠒⠒⠈⠠⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠄⠀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠃⢀⣀⣠⣀⣀⠀⠀⠐⠁⠈⠁⠀⠃⠀⠀⣀⠤⢄⡁⠀⠀⠀⠀⠩⠄
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢂⣂⣀
⢰⠉⢀⡰⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⣠⠀⢲⣗⣱⡨⢅⠒⡈⡁⢢⠀⠀⠈⠀⢀⠀⠀⢀⣸⢌⠒⠄
⠸⠀⡁⡮⡀⠀⠖⠀⠀⢂⠀⠀⠐⠁⠐⢲⠇⢠⠄⠰⠀⠱⡍⠁⠨⠀⠀⠀⠀⠩⡧⣀⠐⢝⣦⣶⢧⠀⣀
⠀⠀⠈⠁⠒⠀⢀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢍⢉⡁⠈⣉⡀⠀⠀⠀⠀⠀⡀⠈⠙⠛⠁⠀⠀⢩⣛⠉⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢠⡴⠛⠉⠁⠀⠉⠉⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣤⡶⠶⠶⣤⣄⠀⣿⢠⣴⡾⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣠⣤⣭⣿⣿⡏⠀⠙⢶⣄⠀⠀⠉⠻⠶⣤⣄⣀⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⢦⡀⠀⠙⠳⣦⣀⠀⠀⠀⠉⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠉⠛⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡟⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⠶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⣿⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠸⣇⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢤⡔⠲⠞⠛⠉⠍⠉⢃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡖⠒⠒⢒⠉⠁⠀⢀⠔⡀⠀⡄⠻⠆⢀⠀⠀⠁⣑⣐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⢤⠀⠀⢠⠄⠀⠀⠃⠀⢀⠀⠀⠀⠑⢦⣀⡀⢙⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠁⢠⡤⡶⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠘⠻⡌⠋⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⣄⠁⢘⠃⠀⠀⢀⡌⠄⠀⠀⠱⣆⠀⠀⡀⡠⠂⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠈⠢⠀⠐⠄⣠⡼⠃⠀⠀⠁⢀⠈⠢⠤⠋⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣨⢔⣄⣀⠀⠈⠀⠀⠐⠊⠁⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠂⠒⠤⡀⠀⠀⡠⠊⠀⣀⡠⣭⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡺⠃⠉⠑⠢⡀⠀⠹⡀⡐⠁⢀⡞⠁⢡⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⢐⡉⠉⠑⢄⠀⢹⡄⠀⢱⠁⠀⢸⡇⠀⠸⢄⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠔⡆⢸⡉⢢⠀⠘⠀⠀⠄⠀⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣧⣜⠀⡸⠀⠸⠂⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠓⠚⠛⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄
⠀⠀⢸⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⡄
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠙⠋⠁⣠⣿⣿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⢠⠖⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠉⠀⢠⣄⡐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠉⠒⠀⠠
⠀⠀⡴⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⢦⠀⠀⠀⠀⠀⠈⠂⠄⠈⠈⠟⣤⡂⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⡦⠀⠀⠀⠀⠀⠁⠐⠈⡀⠠⠀⠀⠈⠁
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⢈⠗⠠⠀⠀⠢⡀⠀⠀⠀⠐
⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⡄⠀⡈⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰
⠀⠀⠀⢱⠀⠀⢰⠉⣭⡉⣭⡉⣩⡍⢉⣭⢩⣩⣉⢉⣭⢙⡆⠀⡌⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⣀⠌⠈⡠
⠀⠀⠀⢸⠀⠀⢸⠀⡇⣿⣷⠃⡇⠀⢸⣹⢸⣿⣻⢸⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠁
⠀⠀⠀⠘⡄⠀⠈⡄⠳⠃⠇⠇⠻⠗⠚⠸⠸⠘⠻⠘⠾⢠⠃⢰⠁⠀⠀⠀⠔⠁⢀⠀⠂⡀⠀⠀⠑⠀⠈⠀⠀⠀⠀⠀⠀⠊⠠⠂⠈
⠀⠀⠀⠀⡇⠀⠀⠑⠒⠒⠒⠒⠒⠂⠠⠠⠒⠒⠒⠒⠒⠋⠀⢸⠀⠀⠀⠀⢀⠄⠁⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠿⠻⢗⣦⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠆⡀⠀⠈⠛⠀⠀⡉⠐
⠀⠀⠀⣀⡼⡦⣀⠀⠀⠀⢐⣧⠼⠀⠀⠘⠤⡌⠀⠀⠀⣀⣤⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⡀⠀⠀⠀⠀⠈⠅
⠀⠀⢐⡇⠀⠀⢸⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇⠀⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠺⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⢘⣇⣀⣀⣸⠀⠀⠀⠈⠻⢷⢴⡊⣷⠮⠋⠀⠀⠀⣇⣀⣀⣸⡇⠀⠀⠢⡉⢄⠅⢈⠂⠠⠀⢠⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠄
⠀⠀⠘⣇⣀⣀⣸⠓⠒⠠⠤⠤⢀⣀⣈⡁⠠⠤⠄⠒⠘⣇⣀⣀⣸⠇⠀⠀⠀⠀⠐⠠⢀⠀⠠⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠄⠀⠀⠰⠞
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠹⠄⠍⠙⢳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣰⣀⢠⣠⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⣉⠝⠳⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⣷⣼⣟⣶⢭⣿⣦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⠭⠒⣉⡴⢃⢃⠈⠀⠃⠉⠛⢦⣙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠘⠀⠀⢀⡼⠁⠀⠀⠀⠃⠀⠀⠲⡄⠀⠁⡀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢀⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠣⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠂⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠻⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡋⠀⠀⠉⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢀⡏⠈⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⣠⠾⡇
⠀⠀⠀⠀⢀⡼⠋⢷⠀⠀⠀⠙⠦⣄⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠁⠀⢹
⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠐⠋⠉⣧
⠀⠀⠀⠈⠛⠛⠳⠦⢤⣬⣷⣦⣤⣤⣀⠀⣀⡐⠀⢀⣀⣐⣀⣀⣤⢴⣞⣩⣤⣄⣀⣤⣤⣤⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⣥⣤⣤⣤⣤⣽⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⡴⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⢹⠀⠀⢸⢹⡆⠀⢰⣿⡇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⢸⣿⣿⠀⢸⣿⣿⠁⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡸⡇⠀⢸⢸⡇⠀⢸⢸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⡇⡇⠀⢸⢸⡇⠀⣾⢸⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠈⣿⣿⠀⢸⣿⡏⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡇⣷⠀⢸⢸⡇⠀⡏⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⠀⢸⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢹⠀⢸⢸⡇⢠⡇⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢻⣿⠀⢸⣿⠇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⢸⡀⢸⢸⡇⢸⢳⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⠀⢸⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡞⡇⢸⢸⡇⢸⢸⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⠁⠈⠋⠀⠈⠋⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠒⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡱⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢏⣳⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠀⠀⠀⠀⢰⠁⢀⣤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠴⠒⠒⠢⡤⠊⠁⣇⡠⡴⠒⢦⠀⠀⡏⢏⠀⡴⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣⡠⠒⠒⠃⠀⢀⣠⣎⣀⠀⠀⡇⠀⣇⠀⢈⠷⠒⠛⢆⠙⠚⠛⠹⡀⠀⠈⡢
⠀⠀⠀⠀⠀⢣⠀⣰⠁⠀⠙⠒⢤⡀⠰⠉⠀⠀⠈⠑⢄⣙⡯⠤⠴⠊⠴⠚⠉⠙⠢⡀⠀⢀⣇⣀⡘⠁⠀⠀⣔⢦⡀
⠀⠀⠀⠀⠀⡏⢰⠃⠀⠀⠀⠀⠀⢱⣀⣀⡀⠀⠀⠀⠘⠀⠀⡶⣄⠀⠀⠀⠀⠀⠀⠛⠚⠛⠶⠀⢹⣦⠖⠚⢹⡋
⠀⠀⠀⠀⣀⠜⠉⠉⠉⠉⠉⠲⠖⠉⠁⠀⠨⠕⠒⠒⠒⢤⡜⠈⢞⢯⠀⠀⠀⠀⢀⣄⣀⣤⣄⢀⣼⣁⣀⡀⢀⡇
⠀⠀⢀⠞⠁⢀⠴⠒⠂⠀⠀⠀⣀⠤⢄⠐⠋⠳⡀⠀⠀⠀⠹⠖⠉⠋⠀⠀⠀⠀⢀⣧⣄⣀⡇⠉⠀⠀⠀⠉⠻⠙⠒⡄
⠀⠀⢎⣀⣔⡡⠤⢞⠉⠉⢑⣦⣀⣀⣈⣓⡒⠚⠀⠀⠀⣀⠤⠴⠒⠒⠒⠲⠤⢄⡀⠀⠀⠈⢃⡤⠊⠉⠒⠒⠒⠒⠋
⠀⠀⠀⠉⠀⠀⠀⠀⠑⠚⠉⠀⠀⠀⠀⠀⠈⠉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡾⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠷⠶⠤⣬⠇⠀⠀⠀⣸⠗⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠤⣦⠬⣷⣤⣤⡲⠯⣤⡖⠲⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡰⠋⠀⡴⠃⠀⠀⠀⠀⣹⣆⠀⠹⡄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⠞⠁⠀⠀⠀⠀⣰⠃⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⡴⠃⠀⣾⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠚⢀⡀⠀⢀⣀⠴⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠴⠋⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠛⠲⠴⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣀⣉⡟⠀⠀⠀⠀⣿⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇⠠⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⣈⣙⢧⠀⣀⣀⣸⡃⣀⣀⣈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢰⠃⢀⡴⠋⢉⡟⠉⠙⠋⠉⠳⣌⠉⠳⡄⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠘⠶⠋⠀⡰⠋⠀⠀⠀⠀⠀⣸⢻⡄⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⢚⡿⠁⠀⠀⢸⠇⠀⢸⡦⣤⣠⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡴⠁⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣤⠴⠋⠀⠀⠀⢀⠿⡆⠀⠀⢣⣀⠀⣀⡤⠏
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠸⣧⠴⠃⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠉⠀⠀⠀⠀⢀⡴⠋⠀⠳⣄⠀⠀⠉⠛⠧⢤⣀⡀
⠀⠀⠀⠀⠰⡛⠉⢀⡤⢤⣤⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣀⣀⣀⣤⠤⠴⠚⠉⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⡤⠇
⠀⠀⠀⠀⠀⠙⠖⠋

⠀⢀⠤⠂⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⡞⢇⣀⣤⠤⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⢠⠔⠋⠀⠐⣷⣶⠒⠒⠒⠂⢀⣩⡿⠷⠒⠁
⡇⠀⠙⠦⣀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠂⠘⠤⣄⠀⢶⠿⠟⠒⠂⠉⠉
⡇⠀⠀⠀⠈⠙⠺⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠚⠉⣉⣩⡭⠥⠭⠭⠭⣉⣑⡒⠢⠄
⡇⠀⠐⠤⡀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⠟⠉⣿⢹⡇⠀⠀⣀⠤⠔⠊⠁⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠈⠑⠲⢄
⢻⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠉⠓⠲⠤⣀⣀⠀⠀⢠⢎⡞⠁⠀⠀⣿⠈⣇⠔⠊⠁⠀⣠⡴⠚⠉⠀⢀⣠⡤⠶⠒⠒⠛⠛⠒⠒⠒⠲⠦⠤⣄⣀⡀
⠈⢧⡀⠀⠀⠀⠀⠈⠙⠓⠦⣄⣀⠀⠀⠀⠀⠈⠉⠒⡎⡜⠀⠀⠀⠀⡏⠀⢿⣀⣤⠖⠋⠁⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠐
⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠤⣤⣴⠀⠇⠀⠀⠀⠀⡇⠀⠸⡏⠁⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⣀⡠⢿⢰⠀⠀⠀⠀⠀⡇⠀⠀⢿⡃⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠀⢸⠈⡆⠀⠀⠀⠀⡇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⢧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠈⠑⠢⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣀⣀⣀⣀⣠⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⠓⢾
⠀⠀⠀⠀⠀⠘⠚⠒⠠⣄⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠓⠤⢀⡀⣠⠜⠀⠀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⡇⠀⠀⢧⡀
⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠄⠘⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠔⢃⠀⠀⠈⢎⠉⠒⠒⠂⠀⠒⠒⠒⠀⢀⠆
⠀⠀⠀⠣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠈⢄⠀⠀⠀⠑⠄⣀⣀⣀⣀⣤⡶⠾⠅
⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⠄⣀⣀⣀⣀⣀⡀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⠤⠄⠐⠊


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠲⢦⣄
⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⠟⠙⠷⣦
⠀⠀⠀⢀⡾⠷⣤⣴⡾⠋⠀⠀⢠⣿
⠀⠀⠀⠘⣧⠀⠀⢸⣇⣀⣠⣶⡏⢿⡄
⠀⠀⠀⠀⢸⡟⢻⠋⣡⢿⠁⢸⡇⠈⢿⡄
⠀⠀⠀⠀⣸⠃⣼⢰⣿⣾⡆⠀⢿⡀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣰⠏⠀⡇⣼⡃⣿⢷⠀⠈⢷⣆⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠚⠛⠛⠋⠉⠉⢹⣿⣦
⠀⠀⢰⡏⠀⢸⠃⢹⣆⡿⢸⡄⠀⠀⠹⣧⡀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣻⡟
⠀⢠⡟⠀⠀⣸⠀⠈⣿⠇⠈⡇⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⣠⢊⣽⠃
⠀⣸⠃⠀⠀⢻⠀⠀⢹⣇⠀⢹⡀⠀⠀⠀⠀⠙⢿⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠀⠀⠀⠜⣡⡾⠃
⠀⣿⠀⠀⠀⢸⠀⠀⠀⢿⡀⠀⢧⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣧⣤⣀⢀⡀⡀⢀⣀⣤⣤⣶⠖⣋⣩⣀⣠⣤⣄⣄⣀⣴⡾⠋
⠀⣿⠀⠀⠀⠈⡆⠀⠀⠘⣷⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠛⠷⣤
⠀⢻⡄⠀⠀⠀⠹⡀⠀⠀⠘⣧⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡆
⠀⠸⣧⠀⠀⠀⠀⢳⡀⠀⠀⠘⢷⣄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠊⠉⠉⢁⣼⠃
⠀⠀⢻⣆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠙⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠊⠉⠀⠀⠀⢀⣠⣤⠾⠋
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠋
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠉⠛⠳⠶⡦⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⢾⣿⣟⠋⠉
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠐⣀⣨⡴⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⣠⠔⣱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣶⣶⣤⣤⣤⣤⣶⣶⡶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⢀⡠⢔⡒⠬⠭⠭⠥⣒⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⢠⢖⠥⡪⠕⠲⡟⠿⠿⣻⠒⠪⣑⢬⡢⡀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣟⣿⣟⣿⣶⣾⣿⣿⣿⢿⡶⣄
⠀⠀⠀⡰⡱⣣⠊⠀⠀⡠⢒⠶⢶⡒⡄⠀⠀⠑⡕⠌⢆⠀⠀⠀⠀⣰⣫⣿⣿⣿⣿⣫⣿⣿⡿⣿⣿⣿⣷⣝⣿⣦
⠀⠀⢰⢱⢱⠁⠀⠀⠀⠁⢨⠀⢀⡅⡇⠀⠀⠀⠘⡌⡌⡄⠀⠀⢰⢷⣷⣿⣿⣿⣿⢿⣻⣿⡿⣿⣿⣿⣿⣿⣟⣟⣇
⠀⠀⡄⠌⡆⠀⠀⠈⢢⢸⢠⢙⡣⡄⡇⡜⠀⠀⠀⠁⠁⡅⠀⠀⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿
⠀⠀⢁⢣⢇⠀⠀⠀⢸⠸⡈⠓⠛⢡⠁⡇⠀⠀⠀⡄⡄⡇⠀⠀⢻⢿⣿⣿⣿⣿⣿⡿⣷⣿⣾⣯⣇⣿⣿⣿⣿⣿⣿
⠀⠀⠘⡜⡜⣄⠀⠀⡇⡎⠈⠉⠉⠀⡡⢰⠀⠀⡰⢡⢱⠁⠀⠀⠘⣟⣿⣿⣙⣛⣛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠘⢜⢎⠢⡀⠑⠬⣒⡒⢒⣊⠵⠃⣀⢔⡕⡡⠃⠀⠀⠀⠀⠘⢯⣿⣽⣿⣬⣷⣭⣭⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠓⢝⡪⢕⡒⠤⠤⠤⠤⣒⡪⢔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣷⣯⣿⣿⣿⣻⣿⣽⣟⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠩⠭⠭⠅⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁

⣿⣿⣿⠟⠛⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠷⠤⠤⠤⠤⠤⠴⠧⢤⠤⠀⣠⣠⣤⡀⣭⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿
⠿⢷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠄⠀⠘⠂⠀⠀⠀⠠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢠⣄⡐⡆
⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⢶⣾⣿⣿⣛⣿⣷⣿⣦⣄⣤⡀
⢀⣴⣾⣿⣿⣷⣂⢀⣠⣾⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⢋⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠈⠹⣿⣿⣿⡿⠉⣭⣿⣿⣿⣿⣿⡟⡛⡏⠀⠀⠀⠀⠀⡠⣾⣷⣿⣟⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠈⠉⠀⣰⣿⣿⣻⣿⣿⣿⣿⣟⣛⡃⠀⠀⠀⣠⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣾⣷⣿⣿⣿⣿⣿⠿⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥
⢶⣄⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡗⣾⣿⣿⣟⠁⢸⣶⣾⡟⣿⣿⣿⣿⣿⣏⣋⠻⣽⠥⢜⣿⣿⣿⣿⠿⠛
⠈⢻⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⣽⣿⠋⠉⠋⠹⢿⡟⠀⠈⠉⠈⠁⠀⠀⠀⢿⣿⣷⣿⣿⣶⠄⠈⠻⣟⠛⠙⠆
⠀⢿⡿⠛⠿⢿⣿⣿⣿⣿⣆⣰⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠐⣶⢢⣤⣾⣿⣶⣴⣴⣶⣶⣾⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣄⡠⡼⢰⢳⣶⣶⣤⣤⣍⣉⠐⣄⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣅⣿⣽⣿⣿⣿⣿⣭⣝⣛⣈⡉⣻⣿⠷⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠻⣿⣿⣿⣯⣿⠿⠿⠿⢷⣿⣷⡎⣾⣿⠏⠉⢁⠙⠀⠀⠀⣠⡀⢂⠸⣾⠀⢸⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠙⠹⠀⢤⣶⣶⣾⣿⡿⠛⠁⠀⠉⠀⠁⢀⡉⠛⣾⣶⣮⣟⢾⣷⠙⠦⣾⣷⠂⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⣤⣶⣷⣶⣾⣿⠟⠿⡷⣦⣤⡀⠉⢻⣯⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣮⣿⣿⣿⣿⡟⠻⠿⡿⠏⠀⣠⣶⣿⣿⡤⠘⢉⣿⣷⣤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠖⣠⠤⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡿⣿⣿⣿⡇⢠⣾⣿⣿⣣⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠾⣿⣿⠿⠿⢿⠿⠛⠻⠉⠉⠙⠹⠏⠈⠿⠟⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⡂⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠨
⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠳⠀⠄⠀⠀⢀⡠⠀⠈⠂⠀⠉⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠈⠘⢂⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⡀⣀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠐⠀⠀⠐⠂
⠀⠀⠀⠀⠁⠀⡁⠀⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠈⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠓⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠠⠀⠀⠄⠀⠈⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⣿⠗⢰⡿⠛⠚⠂⢸⠛⢷⡄⢀⣴⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠈⡿⠶⠖⠀⢸⣦⡾⠃⣾⡇⠀⠀⢸⡇⠀⠀⠐⠠⠀⠀⠀⠄⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⡀⠎⠀⠀⠣⠤⠴⠀⠀⠀⠀⢰⣿⣤⣤⣤⠀⣧⣤⣤⡄⢸⠈⠻⡄⠘⠷⣤⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢠⡄⠀⣤⡄⠀⢠⡤⢦⡄⠤⢤⣤⢤⠄⣴⠶⠶⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣀⠀⣼⠃⣼⠏⢿⡀⠘⠷⢤⣀⠀⠀⣿⠀⠀⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣴⠿⣶⡟⢠⡿⠤⢼⣇⢠⣄⣠⡿⠀⠀⣿⠀⠀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣂⡄⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠁⠀⠀⠁⠀⠉⠉⠀⠀⠈⠉⠀⠀⠉⠉⡉⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⢀⠔⠂⡄⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⠀⠀⠀⠄⠀⠐⠀⠀⡈⠀⠀⠀⠀⢄⠀⠀⠀⠐
⠀⠀⠐⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢸⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠀⠈⠓⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠀⠀⠀⠀⣀⠘⠀⠀⠨⠁⢆⠀⠀⠀⡀⠀⠐⡰⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠤⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠀⢐⠒⣀⠀⠀⠚⠁⠀⠡⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣀⣀⡀⡀⡀⡠⠛⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠀⢀⡀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡
⠀⠀⠀⠀⠠⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠤⠀⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠢⠀⠔⡥
⠀⠀⠆⠀⠀⠀⠀⢀⠄⠋⠁⠂⠖⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡍⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⠀⠠⠊
⠀⠀⠐⠂⠄⡀⠐⠣⠄⡠⠊⡁⠀⠀⠀⠀⠀⠀⠁⠄⠀⢴⡀⠔⢀⠄⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠈⠁⠂⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠁

⠀⠀⠀⢾⠓⢄⡀
⠀⠀⠀⢸⡧⣠⣙⣦⡀
⠀⠀⠀⠀⡇⠬⠁⢹
⠀⠀⠀⢠⣧⡇⠀⢺
⠀⠀⠀⣼⡿⠀⠀⢰
⠀⠀⣰⡏⠁⡀⠀⠘⡀
⠀⣰⠋⠀⠀⠈⢻⠉⠱⣄
⢀⡏⠀⠀⠀⠀⠀⣆⠀⠘⣆
⢸⠁⠀⠀⠀⠀⠀⢹⠐⠀⡙⣆
⢸⠀⢲⠀⠀⠀⠀⠈⡇⠐⠀⠜⣆
⠘⡇⠈⡇⠀⠀⠀⠀⠘⡄⠀⠈⠘⣆
⠀⢷⠀⢹⣆⠀⠀⠀⠀⠘⡄⠀⠀⠈⢧
⠀⠘⣆⠀⠙⡢⠀⠀⠀⠀⠈⢄⠀⠀⠀⠱⡀
⠀⠀⠸⡄⠀⠈⡌⠖⡠⠀⠀⠀⠢⡀⠀⠀⠈⠂⡀
⠀⠀⠀⠘⣆⠀⠘⣿⡷⡤⠁⠀⠀⠘⠦⡀⠀⠀⢙⠦⣀
⠀⠀⠀⠀⠈⢢⡀⠈⢜⣎⠈⢢⠀⠀⠀⠈⠢⣀⠀⠑⠪⠉⠒⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣇⠛⠀⠂⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠈⠉⠐⠂⠠⠤⠀⠀⠠⠀⢀⣤⣤⣤⠤⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠚⡂⢜⣷⠀⠀⠀⠀⠀⠐⠫⠀⣠⠠⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣽⡯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠙⠀⣤⢀⢀⢤⢠⠀⠀⠀⠀⠠⠆⠀⠉⠉⠉⠀⠀⠒⠒⠒⠒⠀⠀⠀⠉⠉⠁⠀⠀⡀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠈⠙⣦⡟⡜⣂⠀⣇⡆⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣢⡶⠓⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣈⡑⠿⢽⣻⣴⣭⣷⢳⢂⢿⣦⢓⣗⣒⣰⣽⢽⣼⠾⠛⣊⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠬⣌⣈⣋⣛⣘⣛⣉⣫⡭⠥⠴⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢉⣩⠭⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⠖⠉⠀⡰⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢀⡴⠁⠀⢀⡜⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡞⠀⠀⢀⡞⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡜⠀⠀⠀⡞⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⡿⠀⢸⠁⠀⠀⣸⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠉⠳⣤⡇⠀⡏⠀⠀⢀⡇⢠⠇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⣴⠞⠛⠛⠻⢶⣄⢹⡇⢰⡇⠀⠀⢸⠁⢸⡟⠉⣨⣽⣤⡤⣤⣄⣀
⠀⠀⠀⠀⠀⢠⡏⠀⣴⠟⠁⠀⠀⠀⣠⠾⠻⠿⣇⣸⡀⠀⠀⣸⠀⢹⣤⣴⣶⣦⣤⣀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⡾⠀⣰⠏⠀⠀⠀⣠⠞⠁⡰⢁⠄⣠⠟⠛⠳⣄⣿⡴⠋⢡⠏⠀⠀⠈⢿⠛⠶⣤⣄⠀⠈⠙⢦⡀
⠀⠀⠀⠀⣸⠃⢰⡟⠀⠀⠀⢰⠏⢀⡜⢠⠏⢰⡏⠀⠀⠀⢸⣿⠁⢠⠟⡷⢦⣄⣀⠀⠳⡄⠀⠉⠛⢦⣄⡀⠹⣆
⠀⠀⠀⣰⠋⣠⡿⠁⠀⠀⠀⣿⠀⡼⠀⡼⠀⣽⡇⠀⠀⠀⠀⣿⠀⠈⠀⣿⠀⠀⠉⠙⢦⣸⣦⡀⠀⠀⠈⠛⢦⡌⢷⡀
⠀⢀⡾⢃⣴⠟⠀⠀⠀⠀⠀⡏⠀⡇⠀⡇⠀⣿⡇⠀⠀⠀⠀⢹⡀⠀⠀⢹⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢹⣌⣧
⠀⢸⠇⣾⠃⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⡇⠀⡿⢳⠀⠀⠀⠀⠈⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⢳⠀⡇⠀⡇⠘⡆⠀⠀⠀⠀⢷⠀⠀⠀⢻⡄
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⡆⣇⢸⡇⠀⢳⡀⠀⠀⠀⠸⡆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣽⣿⣸⡇⠀⠈⣧⠀⠀⠀⠀⢷⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠘⣏⠀⠀⠀⠘⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠘⢧⡀⠀⠀⢣⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠈⢀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣯⢀⡁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢡⡏⠘⢇⠰⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠃⠀⠀⢸⠀⠀⠀⡄⠀⠒⠔⠢⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠆⠀⠀⠀⠸⡀⠀⠀⢸⣄⠈⠃⠈⠢⣄
⠀⠀⠀⠀⠘⠀⠘⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⡉⢆⠀⠀⠀⠀⠀⠢⣄
⠀⢠⠀⠀⠀⢃⠀⠱⠀⠀⠘⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠐⠷⣄⠀⠑⢄⠙⢦⡀⡀⠀⠀⠀⠈⠐⠂⠄⠐⢆
⠀⠈⢀⠀⠀⠈⢂⠀⠑⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⡀⠀⠀⠀⠐⠄⠈⠳⣄⠀⠐⠦⣉⠛⢶⣦⣤⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠠⡀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡕⢄⠀⠀⠀⠀⠁⠀⠘⠢⡀⠀⠀⠁⠒⠀⠈⡙⢦⡀⠒⣒⠂⢐⡠⠟
⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠢⢀⡄⠀⠀⠀⠀⢀⣠⠆⠀⠀⠈⠢⣑⠂⠀⠀⠀⠀⠀⢠⣿⠒⣄⠀⠀⠀⠀⠈⢰⠏⠛⠋⠉

⠀⣀⠴⠒⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠒⠒⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠟
⡞⢧⣀⣠⠴⠖⠒⠋⠉⠉⠉⠀⠀⠀⠀⢠⠔⠋⠀⠘⣷⣶⠒⠒⠒⠂⢀⣩⡿⠷⠒⠉
⡇⠀⠙⠦⣀⠀⠀⢀⣀⣠⡤⠤⠶⠒⠒⠚⠤⣄⠀⣶⠿⠟⠒⠒⠉⠉
⡇⠀⠀⠀⠈⠙⠺⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠛⠉⣉⣩⣭⠭⠭⠭⢭⣉⣑⡒⠢⠤
⡇⠀⠐⢤⡀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⠟⠉⣿⢹⡇⠀⠀⣀⡤⠖⠊⠁⠀⣀⡤⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠀⠑⠲⢄
⢻⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠙⠲⠤⣀⣀⠀⠀⢠⢎⡞⠁⠀⠀⣿⠈⣧⠔⠊⠁⠀⣠⡴⠞⠋⠁⢀⣠⡤⠶⠒⠚⠛⠛⠒⠒⠒⠶⠦⠤⣄⣀⡀
⠈⢧⡀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⠀⠀⠀⠀⠉⠙⠒⡎⡜⠀⠀⠀⠀⡏⠀⢿⣀⣤⠶⠋⠁⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠐
⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠤⣤⣴⠀⡇⠀⠀⠀⠀⡇⠀⠸⣏⠁⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⣀⡤⢿⢸⠀⠀⠀⠀⠀⡇⠀⠀⢿⡓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⢸⠘⡇⠀⠀⠀⠀⡇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⢷⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠈⠑⠢⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣀⣀⣀⣀⣠⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⣧⡞⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⠦⣙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡤⠒⡟⠀⠀⠀⠀⠀⠀⠣⠀⡰⢺⠟⠉⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡴⠋⠉⠈⠉⢳⠖⠉⠀⢸⣣⠴⣶⠋⠉⠳⡄⠀⠀⣇⠸⣄⠀⢞⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢧⢀⠴⠒⠒⠚⠀⠀⠀⢀⣔⣁⠀⠀⠀⢸⠀⠀⢧⠀⠀⠀⡧⠔⠚⠉⢢⠈⠙⠚⠛⠉⢹⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡼⠀⠈⠛⠦⣄⡀⠀⠀⡠⠊⠁⠀⠈⠙⠲⣄⠈⠳⣖⣋⣁⣀⠴⢁⡠⠴⠒⠲⢧⡀⠀⠀⠀⢸⡇⠀⠀⢰⠁⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⢀⡼⠀⡼⠁⠀⠀⠀⠀⠀⠙⢦⠀⠁⠀⠀⠀⠀⠀⠀⠈⣷⠒⠋⢉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠘⣆⣀⣀⣸⠋⠛⠓⣄⠀⠀⠀⣠⠓⣮⠟
⠀⠀⠀⠀⠀⠀⢸⡀⣰⣇⣀⣀⣀⡀⠀⠀⠀⢀⣧⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡿⡝⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠑⠀⠀⢸⡖⠉⠉⠁⠸⡅
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠀⠈⠙⠲⠞⠉⠀⠀⠀⠀⠤⠒⠋⠉⠓⠲⢤⡜⠁⠙⣜⢧⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣤⣄⠀⢀⣎⣀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⡴⠋⠁⠀⣀⡤⠤⠄⠀⠀⠀⠀⠀⢀⡀⠀⢠⠖⠲⣄⠀⠀⠀⠀⠀⠹⡤⠴⠚⠿⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⠉⡇⠖⠉⠉⠉⠉⠉⠓⢾⠳⠤⣄
⠀⠀⠀⡜⠀⠀⣠⠞⠁⢀⡤⠤⠶⢄⣀⠀⠊⠉⠈⠳⣄⠀⢀⡼⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠒⠋⠉⠙⠺⡇⠀⢀⡠⠤⣄⣀⠀⢀⣀⣀⠼
⠀⠀⠀⢧⣤⣾⠥⠒⠛⠛⢄⠀⠀⣠⡤⠧⠤⠤⠤⠤⠤⢭⣉⡀⠀⠀⣀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠉⠙⠲⠤⣄⣀⣀⣀⣀⡤⠔⠋⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⢀⣠⣴⢤⡀
⠀⠀⠀⠀⠀⡼⢩⣿⣎⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⢶⣶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⡟⣩⣏⠛⢧⣀⣀⣠⡤⠶⠒⠋⣉⣡⣤⢶⣞⣻⠿⠿⠛⢋⣉⣩⣭⠁⠀⠀⠀⠀⠀⠀⣴⡒⠤⣀
⠀⠀⠀⠀⠀⡇⣿⣿⡆⠲⢽⣿⠷⣒⣶⣿⣿⠭⠷⠚⠋⢉⣀⣤⣶⣾⠿⠛⠉⢩⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠑⢦
⠀⠀⠀⢀⣾⠇⠻⣿⡇⠀⠀⠉⠙⠓⠶⢶⣶⣶⣶⣶⣿⣿⠿⠛⠋⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⢢⠱⡄
⠀⠀⠀⢸⣿⠀⠀⠙⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢡⡈⢄
⠀⠀⠀⠸⣿⠀⠀⠀⠙⣮⣝⠶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⢿⣛⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣧⠀⢣⠈⢧⣴⣷⣦
⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⢿⣿⣶⣾⣭⣭⣽⣿⣿⣽⣿⣿⡿⢟⣛⣿⠟⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⣿⣿⣿⣧⡀⣧⡼⠋⠉⠺⡆
⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠈⠻⢿⣿⣿⣫⣉⣩⣭⣡⡶⠾⠛⠉⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⡰⢁⠴⣪⡗⢰⣶⣭⣿⣿⣤⡀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠊⣾⠉⠁⢸⠃⢹⣿⠁⠉⣷⡀⠀⠀⣧
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠻⠿⣶⣦⣤⣤⣤⣠⣠⣤⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⠀⢻⣰⠀⡼⠀⣿⡟⠀⢀⡏⣷⡀⠀⢸
⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⣰⣶⡆⠀⠀⢿⣿⠀⠈⠛⢰⠇⢠⡏⠁⠀⣸⠡⠟⢣⡀⢈⡇
⠀⠀⠀⠀⠀⣼⡶⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣥⡾⠟⢹⠃⠀⠀⢸⣿⠀⠀⠀⡜⢠⡟⠀⠀⢠⠏⠀⠀⠀⠳⡴⣧
⠀⠀⠀⠀⠀⢻⡿⠷⣤⣀⠈⠛⠲⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⠶⠋⢁⣴⠟⠋⠀⣰⠃⠀⠀⠀⠀⣿⠀⠀⠀⣧⣾⠀⠀⣠⠟⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠘⢧⡀⠈⠙⠻⢦⣄⡀⠈⠉⠛⠛⠛⠋⠉⢁⣀⣤⡾⠋⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⣿⠦⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠶⠛⠛⠉⠁⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠉⠒⠳⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⣠⠀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠚⡡⠂⢠⠃⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠴⣊⣠⠴⠃⠀⠀⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡴⡵⠋⠁⠀⣠⢀⠤⠊⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⢀⢞⠎⠀⠀⢀⡜⡕⠁⢀⠁⠀⢰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠔⠊⠁⠀⢀⡰⢋⠎⠀⠀⢀⠎⡸⠀⠀⡘⠀⠀⢘⠀⡇
⠀⠀⠀⠀⠀⣀⣀⡠⠔⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⡰⠃⠀⠀⢠⠎⢠⠃⠀⠀⡇⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠰⡇⠀⠐⠒⠈⠉⠉⠉⠉⠉⠉⠘⠋⠉⠀⠀⡠⠊⠀⠀⠀⡴⠃⠀⡎⠀⠀⣸⠁⠀⠀⠸⢀⠃
⠀⠀⠀⠀⠀⢸⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⢀⡴⠊⠀⠀⡸⠀⠀⢠⠇⠀⠀⢀⡇⢸
⠀⠀⠀⠀⠀⠈⢄⠀⠉⠒⣠⡤⠠⠤⠤⠒⠊⠁⠀⠀⠀⡠⠖⠁⠀⠀⠀⡰⠁⠀⢀⠎⠀⠀⠀⡸⢀⠇
⠀⠀⠀⠀⠀⠀⠈⢢⡤⠊⠀⠀⠀⣀⣀⣀⣀⠤⠔⠒⠉⠀⠀⠀⠀⣠⠎⠀⠀⢀⠎⠀⠀⠀⢀⠇⡜
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⡰⠃⠀⠀⠀⢀⡎⡰⠁
⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⢀⡠⠊⠀⠀⠀⠀⢀⠎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⣀⠙⠢⠄⣀⢀⣠⠤⠒⠒⠉⠁⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⢀⡴⢃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⠤⠊⠀⢀⣠⣤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠢⠤⠤⠄⣀⠠⠤⠤⠒⢊⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠀⠐⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⣜⠒⠒⠒⠒⠀⢐⣀⣾⠃⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢿⡞⠋⠁⠀⠀⠀⠀⠈⠈⠁⠉⠙⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣒⡿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠇⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠨⠰⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡐⠀⠀⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠷⠌⠀⠙⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠂⢛⣩⣴⣶⣥⡀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠠⠸⠄⠴⡀⠠⣬⡤⠀⠠⠀⠀⢤⠄⡠⠄⢒⡠⢴⣞⠩⡛⠿⡭⢪⠭⢯⡛⠶⣆⠶
⠀⠀⠀⠀⠀⠀⠐⠂⡤⠐⠠⣴⡟⢗⡤⣤⣀⠈⠃⣤⡖⢻⣛⣲⣩⠷⢻⣇⣵⠗⢼⡃⣩⠎⢷⣯⡖
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠾⢿⣿⣷⣦⣁⣛⠿⣷⣄⣼⡇⣿⣿⣿⣿⣶⣰⣿⠈⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡝⠀⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⣶⠑⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠛⡆⢻⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⠞⠉⠀⣿⢠⠇⠀⢷⡀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⢵⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⢹⡎⠀⠀⠀⠳⡄⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⢸
⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠘⢆⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⡄⠀⠀⣀⣀⣀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠉⠓⠒⠲⠶⠤⠤⠤⢶⠧⠀⠹⣏⠉⠉⠉⠉⠉⠉⠉⣧
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⢲⠃⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⠷⣏⡉
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⢩⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠚⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠙⢦⣀⣀⣀⣀⣠⣀⣀⣠⣤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⢾⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⢤⣤⠤⠤⠴⠒⠛⠉⠁




⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣉⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠄⠀⠤⠄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⡠⢰⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢

⠀⠀⠊⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠁⠀⠃⣁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠔⠄
⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠢⡀⠠
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠁⠂⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄
⠀⡀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠉
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠄⣀⠀⠀⠀⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠂⢄⠀⠀⠀⡀⠤⠤⢠⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⢀⣀
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⣠⠟⠻⢦⣄
⠀⠀⠀⠀⣰⣿⣅⣀⣠⡾⠋⠀⠀⢀⡿
⠀⠀⠀⠀⣿⠀⠉⠉⣻⡀⠀⢀⣴⠟⣿⡀
⠀⠀⠀⠀⠙⣶⣤⡴⠟⣻⡞⠛⢹⡀⠹⣧
⠀⠀⠀⠀⢀⡗⢀⡇⣰⣯⣷⠀⠸⣧⠀⠹⣷⣄
⠀⠀⠀⠀⣸⠇⢸⠃⣿⢻⣿⡆⠀⠻⣆⡀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⠴⠶⢶⣶⣄
⠀⠀⠀⣸⠏⠀⡾⠠⣿⢸⡇⣧⠀⠀⠙⣷⡀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠉⠉⠁⠀⠀⠀⠀⠀⢈⣿⣿⡆
⠀⠀⣰⠏⠀⢀⡇⠀⣿⣾⡇⢹⡀⠀⠀⠈⢿⣇⡀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣴⣶⠶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢉⡴⡿
⠀⢠⡟⠀⠀⢸⡇⠀⠸⣿⠠⠘⡇⠀⠀⠀⠀⠹⣷⣄⡀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⡴⢋⣾⠃
⠀⣸⡇⠀⠀⢸⡇⠀⠀⢻⡎⠀⢻⡀⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⢊⣵⡿⠃
⠀⣿⠀⠀⠀⠀⡇⠀⠀⠘⣧⠄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣤⣠⣀⣀⣂⣤⣴⣤⣾⣟⣋⣥⣦⣤⣤⣴⣤⣤⣤⣶⣟⠋
⠀⣿⡀⠀⠀⠀⢻⠀⠀⠀⠹⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢶⡄
⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠹⣆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷
⠀⠘⣿⠀⠀⠀⠀⠘⣆⠀⠀⠀⠙⢷⡀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠉⠉⠁⣨⠇
⠀⠀⢹⣧⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠖⠛⠉⠀⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠍⠉⠋⢋⠉⡙⠩⠉⠑⢀⣀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣤⣀⣀⣀⣠⣤⠤⠤⠤⠖⠒⠚⢉⡽⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢉⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣠⠖⠋⠀⠀⠀⠀⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⡠⠄⣀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⢔⣽⠟⠛⢦⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⢜⠕⡽⠃⠀⠀⠈⠳⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⢣⢊⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠛⠉⠛⠒⠦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠥⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠤⠒⣒⣒⡐⠤⣀⠀⣸⠀⠀⣀⠀⢤⣤⡤⠤⠤⠤⠶⠊⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠁⢊⡞⠉⠀⠉⠳⡌⢣⡇⡴⡩⠔⠒⠒⠲⠬⢕⡂⢄⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠘⣇⠀⠀⠀⠀⢹⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣍⢦⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠼⠀⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣦⣣⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⠂⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣠⠞⠁⢷⢃⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡜⠀⠀⠀⢀⡀⠤⢒⣉⡤⠖⠋⠁⠀⠀⠸⣯⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⢛⢤⠔⣫⡭⠷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠛



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣴⢷⣾⣶⣶⣤⣀⣠⣴⣽⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠁⠐⠢⡀⠀⠀⠀⠀⠀⠀⠙⣿⣖⡢⢄⣀⠀⢀⣀⣤⣾⣄
⠀⠀⠀⠈⢋⣶⣿⣶⡿⡻⢿⣿⣿⢷⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⢄⠀⠈⠢⡀⠀⠀⠀⠀⠀⢻⣿⡿⠷⠒⠛⠉⠉⠉⠉⠛⠇
⠀⠀⠀⠘⣾⣷⣎⢙⢷⣌⠀⠛⠓⣻⣥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠙⠇⠀⡇⠀⣀⡀⢠⡤⠠⡄⠃
⠀⠀⠀⠀⠈⠛⢿⡈⠀⠻⠿⢉⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣄⠀⠈⣲⣅⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣖⣇⠀⠀⠀⢸⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠟⢿⣿⣏⣠⣄⣀⣸⡿⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡛⡄⠀⠀⠀⠀⠀⠀⠀⡧⣮⠴⢞⡿⡯⢶⡆⠈⠀⠈⡄⠘⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢹⣄⠀⠀⠀⠀⠀⠀⠉⠁⢀⣼⠟⣁⣿⣿⠀⠀⠀⠁⠀⠈⠻⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠉⣗⠦⡀⠀⠀⠀⠀⣠⢞⣫⣶⣾⣿⣷⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⠁⣄⢽⣆⠀⢠⣾⣱⠋⠙⠛⠋⢀⡇⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⠀⠈⠁⠑⠕⢦⡈⠀⠀⠀⠀⠀⠸⣇⡠⠖⠁⣀⡴⡚⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣧⠀⠀⠀⢠⠀⠀⠰⡨⠑⠲⠦⠤⠤⠤⠤⠴⡒⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⣵⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠂⢀⡟
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣭⣿⣮⣧⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⢀⡴⡻⣻⢋⡼⢻⡟⣹⡇⠀⠀⠀⠀⠀⠈⠙⠲⢴⣤⣄⣀⣀⣀⡀⠀⠠⣤⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⡠⢧⡀
⠀⠀⠀⠀⣿⢞⡴⣿⡾⠁⣼⠃⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⡼⠁⠗⡇⠀⠀⢀⣀⠄
⠀⠀⠀⢈⣿⣾⡥⢫⣁⣰⣇⣰⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣵⡄⠛⢋⣴⣾⣄⢷⣒⡂⠌⠰
⠀⠀⠀⠈⠋⠛⠐⠻⠩⠺⠏⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠤⠄⠨⠤⠄⠂⠁⠀⠈⠁⠀⠈⠉⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⠷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠴⠋⠀⠀⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠴⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⡀⠔⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣠⡂⠹⣄⠀⠀⠈⢻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢶⣌⢦⡀⠀⠀⠈⠛⢿⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣝⢦⡀⠀⠀⠀⠠⠊⠉⠉⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁
⡇⠘⣄⠀⠀⢀⡀⠀⠠⠤⠤⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠘⢦⣽⣶⣦⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣩⡀⢸⡿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠐⣃⡇⢸⡇⠈⠀⠀⠀⠠⠢⠄⠐⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠄⠡⠤⢀⡄⠀⠀⠀⠀⠀⠀⠦⠀⠉⣤⣼⠷⣶⣦⣀⠀⠀⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠤⠀⢀⠀⠀⠀⠸⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠻⣿⢸⣿⣝⣿⣿⣦⡀⠀⢙⣦⣿⡇⠀⠒⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣦⡆⢹⣾⣿⣧⡌⣿⣿⣇⠀⠀⠀⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠆⠀⠀⠀⠀⠀⣀⠀⢿⡇⢸⣿⠛⢿⣅⣿⣿⣿⣽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⢼⣗⢸⣿⡀⠀⠙⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠖⠀⠸⡆⠀⠀⠀⠀⠀⢀⠆⠀⣨⡼⢸⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⢾⣿⡇⠀⠀⢀⠀⠠⣦⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠿⣿⣿⣾⠟⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡁⠀⠀⢳⣤⡀
⠀⠀⠀⠀⢀⠀⣀⣤⣤⠴⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠤⡢⠾⣿⣄⠀⠈⡴⢬
⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⣚⣿⣷⣶⡶⠀⠀⠀⢀⠀⠀⡏⠀⠀⣐⣿⣿⠇⠀⢠⠀⠀⠀⠀⠀⠐⣡⠎⠁⠀⠈⢻⣆⠀⢠⡌
⠀⠀⠀⠀⠀⣼⣿⣷⣦⣤⣤⣶⣿⣿⡿⠋⠀⠀⠀⠀⢸⡄⠀⠀⡀⢾⣿⣿⡿⠀⢰⡄⠀⠀⠀⠀⣪⡞⠁⠀⠀⠀⠀⠀⠙⣇⠀⠽
⠀⠠⠶⠚⠛⠃⠀⡀⠀⠀⠈⠉⠉⠡⠶⡦⢄⠀⠀⠀⠈⣧⠀⠀⠈⠛⢩⣿⠃⠀⢸⡇⠀⢀⣤⣴⠏⠀⠐⢤⠀⠀⠀⠀⠀⠈⣿⣤⠄
⠀⠀⠀⠀⢧⠘⢠⡇⠀⢀⠏⠀⠀⠀⢤⡶⣾⣿⣿⣶⣀⢺⡆⠀⠀⠀⢸⡏⠀⠀⣾⡇⢀⣾⡿⠁⣠⡤⠒⠈⣷⣷⠀⠀⠀⠊⠈⢷⡀
⠀⢀⣼⣧⣾⣷⣼⣷⣄⣄⣜⠁⢀⠀⠀⠀⠋⠀⠀⠈⢻⣿⣇⠀⠀⠀⣼⠅⠀⢠⣿⠁⣾⡿⣁⡾⠩⣤⢂⡀⠀⢀⡴⠁⠀⠀⠀⠀⠳
⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣿⣾⣦⡀⠀⠀⠀⣿⠸⣷⣄⠀⣿⡇⠀⣼⣟⣾⠟⣰⠏⢰⡶⠼⢿⣿⢴⡎⠀⠄⠀⠂⢠⠄
⠐⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⣦⣀⣼⣴⣿⣿⠳⣾⣇⠀⠁⣾⣯⣴⡏⣠⠉⠁⣀⣽⣯⠁⣀⠀⣠⣤⡴
⠀⠀⠛⠻⣿⣿⣿⣿⣻⣿⠿⠗⠀⠝⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⠻⣿⠿⣾⣿⣿⣿⣿⠧⣤⣾⣿⣵⣿⣶⢶⣠⣿⠋
⠀⠀⠀⠠⠛⢿⣿⣿⣿⣦⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣾⣾⣦⣷⣦⣿⣄⢻⣠⣿⣟⣳⣶⣿⣙⣂⣁⣀⣍⣩⣍⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢁⡀⠀⢌⣉⣩⣥⠍⣩⠉⣙⢻⠀⢻⣿⣽⡏⢸⡿⡿⢟⣻⣿⣿⣿⣿⣿⣿⢿⣟⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠩⣉⠅⠂⠹⠛⠯⢿⠅⠛⠿⠛⠷⠐⠇⠁⠉⠈⠙⠉⠉⠉⠀⠀⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢀⣾⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⡾⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⣿⣀⣀⣀⣤⠶⠛⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⡉⠉⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣧⠤⠴⠖⠛⠉
⠀⠀⢻⣧⠈⠛⢷⣤⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠹⣷⣄⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣷⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠘⢷⡀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠶⠶⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣤⣤⣶⠾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠈⠉⠉⢉⣡⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠶⠶⠾⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠈⠑⢤⡀⠀⠀⠀⣀⠔⠈⣀⠔⠊
⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠔⠀⠀⠀⠀⠀⣇⡠⠔⠉⣀⠔⠊
⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⡠⠔⠁⡠⠔⠉⠑⠖⠊
⡠⠂⠀⠀⠠⠶⠀⠀⠀⡠⠔⠉⢀⠔⠊
⡇⠑⠤⡀⠀⠀⠀⠐⠉⢀⠤⠊⠁
⠑⣄⠀⠈⡆⠀⢀⠤⠊⠁
⣤⣬⣵⣶⣶⣪⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢠⣦⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⣐⠒⠀⠀⢠⡀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢠⡜⠀⠀⢹⣀⠀⠘⠂⣤⠀⠀⠀⠀⠀⠀⡀⠙⠲⠖⠁⠈⠑⢤⠔⠂⠙⠊⢻
⠀⠀⠀⠀⠀⠀⠀⣄⣠⠋⠀⠈⠂⣀⡞⠉⢳⠀⠀⠘⡆⠀⠀⠀⠀⡋⠁⠀⠖⠀⠀⡀⠈⠈⠑⢀⠀⠨⢦⡗⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⡐⠳⢿⠀⠀⢀⣷⡤⠚⠁⠀⠀⠀⠰⠄⡒⠋⠉⠀⢠⣥⡀⢀⣀⠤⠟⠁⢀⣿⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢷⡀⠀⠀⢧⠐⠉⢻⣀⣠⡄⠀⠀⠀⠀⠱⠙⠒⢤⠖⠈⠀⠈⡋⠁⠀⠘⡗⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡇⠈⠢⣄⡿⠀⢀⡞⠋⣉⠀⠀⠀⠀⠀⠀⠐⢷⠒⠲⢀⠀⠀⡳⠤⠴⣾⠁⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣤⡟⢫⣤⡞⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢧⠠⠸⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⠀⣸⣾⣶⣷⣴⢄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠉⠉⣁⠈⠉⠉⠀⢤⡀⠀⠀⠀⠀⠀⢀⡜⢰⢰⠟⢉⡍⣽⢿⣄⣀⡈⠲⡈⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠁⠶⠴⠺⣥⡤⠒⠟⠓⢮⣵⡄⠀⠀⠀⠀⠘⡅⠢⠁⠰⠿⠛⢋⣝⡛⠛⠛⠀⢃⡆⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠃⠀⠀⢈⡠⠀⠀⣸⡥⢲⣯⡀⠀⠀⠀⠀⡘⠀⢰⠂⠀⠀⠈⠈⠁⠀⠀⠢⠈⡴⠀⠄
⠀⠀⠀⠀⠀⠀⠐⢆⡾⠋⠁⠀⢤⡴⠛⠓⠲⠏⠀⣰⠛⣼⡄⠀⠀⠀⠀⡘⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⢀⡠
⠀⠀⠀⠀⠀⢀⣀⣸⠁⠂⣀⢀⣴⡄⠀⠀⣠⠊⠉⣥⠴⡟⠀⠀⠀⠀⠀⠈⠐⠒⢂⠀⠀⠀⠀⠀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⣿⠁⠀⠀⢸⣯⣤⢴⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢉⠉⠠⣶⡃⠀⣠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡤⣖⣍⡆
⠙⡿⣷⡝⢄
⠀⠐⡈⡗⠈⢢⡀
⠀⠀⢰⠺⡄⡀⠉⠒⠦⢄⡀
⠀⠀⠀⠉⡜⡆⢆⠀⠀⠔⡉⢢⡀
⠀⠀⠀⠀⡥⠸⡀⠀⠀⠀⠘⢦⡑⣄
⠀⠀⢰⠀⡊⠀⠃⠁⠀⠀⠀⠀⢒⠌⢢⡀
⠀⠀⢸⠀⡀⠀⠀⢢⠀⠀⠀⠀⠀⠈⢆⠙⢄
⠀⠀⠀⡆⢁⡀⠀⠠⠣⡀⠀⠀⠀⠀⠀⠉⢂⠳⡄
⠀⠀⠀⠘⡌⠥⣂⠀⠁⢙⣆⠀⠀⠀⠀⠀⠀⠱⢈⠲⣄
⠀⠀⠀⠀⠘⢌⠱⡄⠀⠀⠒⣳⣄⠀⠀⠀⠀⠀⠀⠑⠈⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠢⡨⢭⠉⠤⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠀⡀⣀⡀⠀⠀⠐⠚⠉⠀⠀⠀⠈⢹⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡐⣭⠭⠄⠀⠀⢛⠢⣀⠒⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠔⠘⢀⣠⠖⢊⡻⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡘⢁⡀⢒⡀⠈⠐⠫⢦⢄⣈⠐⠑⠐⠔⠠⠠⠠⠠⢢⠠⠂⠁⣀⣠⡶⠞⡍⡄⠧⢈⠜⠁
⠀⠂⢐⠠⢐⠀⡴⠄⣂⠄⣀⠬⣢⢄⠲⠤⠭⠤⢀⠀⠈⠚⠉⢒⠶⡠⣤⢤⢤⢤⠤⠴⡖⡏⡍⡆⢆⢃⠤⢀⠔⠁
⠀⠀⠀⠈⠁⠉⠒⡩⠔⡈⠔⡪⢐⡩⠙⡢⣌⡩⢕⣒⠬⢐⡠⢔⠤⡠⠐⢄⠔⡠⡡⡱⡑⡰⡰⠑⣘⠬⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠁⠂⠥⢊⠅⢋⠝⡢⢌⡐⣀⠁⠈⠀⠄⡡⢊⢔⣔⣘⣠⠅⠖⠩⠊⢀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠐⠑⠉⠋⠛⠙⠹⠻⠻⠫⠂⠔⠕⠡⠪⠔⠕⠤⠨⠂⠔⡤⠠⠨⠢⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢉⣩⠭⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⠖⠉⠀⡰⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢀⡴⠁⠀⢀⡜⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡞⠀⠀⢀⡞⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡜⠀⠀⠀⡞⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣿⠀⢸⠁⠀⠀⣸⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠁⠀⠀⠀⠉⠳⣤⡇⠀⡏⠀⠀⢀⡇⢠⠇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⣴⠞⠛⠛⠻⢶⣄⢹⡇⢰⠇⠀⠀⢸⠁⢸⡟⠉⣨⣽⣤⡤⣤⣄⣀
⠀⠀⠀⠀⠀⢠⡏⠀⣴⠟⠁⠀⠀⢀⣠⠾⠻⠿⣇⣸⡀⠀⠀⣸⠀⢹⣤⣴⣶⣦⣤⣀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⡾⠀⣰⠏⠀⠀⠀⣠⠟⠁⡐⢁⠄⣠⠟⠛⠳⣄⣿⡴⠋⢡⠏⠀⠀⠈⢿⠛⠶⣤⣄⠀⠈⠙⢦⡀
⠀⠀⠀⠀⣸⠃⢰⡟⠀⠀⠀⢰⠏⢀⡜⢠⠏⢰⡏⠀⠀⠀⢸⣿⠁⢠⠟⡷⢦⣄⣀⠀⠳⡄⠀⠉⠛⢶⣄⡀⠹⣆
⠀⠀⠀⣰⠋⣠⡿⠁⠀⠀⠀⣿⠀⡼⠀⡼⠀⣽⡇⠀⠀⠀⠈⣿⠀⠈⠀⣿⠀⠀⠉⠙⢦⣹⣦⡀⠀⠀⠈⠛⢦⡌⢷⡀
⠀⢀⡾⢃⣴⠟⠀⠀⠀⠀⠀⡏⠀⡇⠀⡇⠀⣿⡇⠀⠀⠀⠀⢹⡀⠀⠀⢹⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢹⣌⣧
⠀⢸⡇⣾⠃⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⡇⠀⡟⢳⠀⠀⠀⠀⠈⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⢳⠀⡇⠀⡗⠘⡆⠀⠀⠀⠀⢷⠀⠀⠀⢻⡄
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⡆⣇⢸⡇⠀⢳⡀⠀⠀⠀⠸⡆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⣿⣸⡇⠀⠈⣧⠀⠀⠀⠀⢷⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠘⣏⠀⠀⠀⠘⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠘⣧⡀⠀⠀⢣⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠈⢀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠗⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠂⠓⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠤⠤⣀⡠⠖⡙⢀⣠⠤⡀⠃⠰⢛⠉⡙⣦
⠀⠀⠀⠀⠀⠀⠀⡟⣄⡠⠀⠜⠀⠀⣠⣊⠀⠀⡏⠁⡁⠀⢱⠤⠚⢌⠒⠷⠚⢇⠀⠀⢆
⠀⠀⠀⠀⠰⠀⡰⠁⠈⠒⠤⡀⠰⠋⠀⠀⠉⢢⣘⡮⠥⠔⠣⠒⠂⠘⠢⡀⠀⣸⢀⡀⠃⠀⢀⣖⣄
⠀⠀⠀⠀⢎⣠⣃⣀⣀⠀⠀⢘⣄⣀⣀⠀⠀⠀⠁⢀⣖⣄⣀⠀⠀⠀⠀⠓⠈⠓⠀⠈⡦⠒⠋⢜⠁
⠀⠀⠀⡠⠞⠁⠀⠀⠀⠉⠚⠁⠀⠀⣐⠉⠉⠉⠒⢎⢈⣫⡆⠀⠀⠀⠠⡶⠲⢶⢀⠼⠤⠤⢄⣸⡀
⠀⠀⡜⠀⡠⠊⣁⠤⠤⣀⠐⠂⠲⣌⣀⡱⠀⠀⠀⠈⢁⣀⣀⣀⠀⠀⠰⠓⠒⢾⠀⣀⠤⣀⣀⣁⣀⠇
⠀⠀⠓⠚⠊⠉⠑⢄⠤⠚⠓⠒⠒⠒⠂⠤⠤⠤⠒⠉⠁⠀⠀⠀⠉⠑⠒⠤⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⣶⣶⣶⣤⡠⠤⠤⠶⠒⠒⠊⠉⠁⠂⠀⠸⠮⠷⠤⠤⠤⠤⢄⡤⠒⠒⡒⠒⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠲⠧⠴⣾⠿⠿⠷⠻⠟⠂⠀⠀⠀⠀⠀⠀⣠⠖⢉⣽⣿⣷⣦⣀⡀⠀⢀⣀⣠⣥⡴⠖⣻⣿⣽⣅
⠀⠀⠀⠀⠀⢀⣀⡤⢯⣇⣛⡛⠐⠒⠒⠲⠶⠦⠤⢤⣄⢀⣀⣀⠀⠀⠧⢹⣿⣿⣞⣹⢽⢷⢛⠋⣏⣏⣸⣴⠶⣛⣯⡴⢶⠛⡆
⠀⠀⠀⠀⠀⡟⣙⠑⠲⠶⠤⠤⢭⣛⣐⣒⠶⠶⠤⠤⠤⣤⣈⡉⠉⠉⢉⢉⢋⣋⣇⣦⡶⠾⠾⣟⣋⣭⢶⠚⡋⣙⢰⣤⣾⡟⠁
⠀⠀⠀⠀⠀⠱⣤⣤⣤⣀⣀⡀⠀⠀⠀⠉⠉⠙⠛⠒⠲⠶⠦⢭⢽⣟⣋⣋⣩⣭⢽⠶⠞⡟⠹⢩⢁⣇⣬⡼⣷⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⢾⠖⠱⠋⠜⢋⡟⢃⠶⠶⡤⣤⣤⣀⣀⣀⠀⠀⠀⢀⢀⠃⡆⣌⢸⣠⣥⢷⣞⣿⡿⣫⢎⡧⣿⢟⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠘⠐⣠⠆⠀⠀⠀⠁⠀⠉⠀⠋⠰⠋⠜⢩⠟⣹⠛⡿⢻⣿⢻⣽⣟⡴⡣⠞⣹⣽⠗⡱⣺⣽⣿⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠘⢾⠊⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⣁⡟⢠⣿⣋⢞⡵⣇⣿⣧⣺⢟⣽⣿⠟⣱⡏
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡇⣸⣟⡵⢋⠜⣯⣿⠟⡡⢊⡜⣡⢞⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⡿⢋⠔⡡⢊⡴⣡⠞⡴⢋⠜⡡⢋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡟⠐⠋⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⡴⣣⠞⡱⢋⠔⡡⢊⡴⢫⠞⡠⢋⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⣀⡤⠴⠠⠞⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣋⠔⣡⢎⡴⣫⠞⡱⢋⡴⣡⢞⡴⢋⡶
⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⡴⠋⠁⣠⠤⠖⣶⣀⠴⢃⡴⡛⢦⡀⠀⠀⠀⢸⣃⠞⡡⢊⠔⡡⠞⣠⢊⠜⡡⢊⡴⢣⡿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡇⢠⠞⠁⠀⠀⠙⠁⠀⠘⢦⡉⠐⢵⡀⠀⠀⢸⡥⢊⡔⣡⠞⣡⢞⡵⣡⠞⣰⠋⡴⢡⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡇⠀⠀⢸⡴⢋⠔⢁⠜⡡⢋⡴⢡⠞⣡⠎⡰⢋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠖⠤⢄⣀⠀⠀⠀⠀⠀⠀⢸⠀⢐⡇⠀⠀⢸⡴⢃⠔⣡⠎⡠⢋⡴⢁⡴⣡⢞⡴⢋⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠏⠀⠀⢴⠋⠁⠀⠀⠀⠸⡟⠋⠀⣸⠁⠀⠀⢸⡖⢁⠜⣡⠞⣡⠋⣠⢋⡔⣡⠎⣠⢾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠙⢦⠀⡈⠓⠲⠶⢲⡄⣰⠀⠀⠐⣇⠀⠀⠀⢸⡴⢃⡔⢁⠞⢁⠞⡵⢋⡜⢁⠜⡡⢻⠀⢀⡠⠴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠳⣌⣓⠠⡆⣆⣺⠈⠉⠙⠓⠚⠃⠀⠀⢸⡴⠋⡴⢋⡴⢣⠞⣴⠏⡴⣫⠞⡵⣻⣤⡞⠀⣠⣶⣾⣿⣄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠎⣠⢏⡤⢀⡖⣠⣞⡴⣣⡎⡴⢻⣿⣁⢠⣿⣿⣿⡷⣿⠄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠜⣡⢏⣤⣫⠄⣤⢋⡴⣡⢄⣤⢮⣅⡀⣤⣥⣼⣿⡷⣿⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⢋⠜⢁⢞⡵⢃⠞⣡⢞⡴⣡⢞⣴⣿⡏⡅⣿⣹⠏⡼⣛⡟⣈⣀⣒⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡸⢋⡴⢡⠎⡰⢋⠜⡱⢋⡜⡡⢫⠎⣽⡷⢆⣻⣝⣻⣿⠯⠭⠭⠭⠭⠭⠭⠭⠭⠤
⠀⠀⠀⠀⠀⠀⢸⢰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣶⢊⡴⢡⠞⡱⣫⠎⣠⢋⠜⡱⢣⣾⣿⣝⢫⣭⣟⣉⣉⣀⣀⣐⣓⣒⣛⣛⣛⡛⠛
⠀⠀⠀⠀⠀⠀⠘⠦⣤⣘⠸⠲⠢⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣷⢋⡴⢫⠞⡴⢁⡜⣡⢫⠞⣱⣷⡟⠓⠒⠒⠒⠒⠀⠒⠢⠤⠤⠤⠴⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⣧⢊⡴⣣⠎⣠⢋⠜⣡⣷⣾⡯⠬⠭⠭⠭⠭⠭⢭⣭⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⠤⣄⣀⠐⠤⢕⡂⡷⢋⠔⣁⣞⡱⠿⠯⠭⠭⠭⠭⠉⠉⣁⣒⣒⡓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠳⠿⠾⠯⢉⣐⣒⣒⣓⠒⠒⠒⢒⠲⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⠷⠶⠶⠶⠶⠶⠶⠶⠶⠴⠴⠶⠶⠶⠦⠤⠶⠴⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠦⠮⠁⠦⠈⠱⡇⠀⠼⠴⠷⠾⠥⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢎⠤⠤⠠⠀⠠⠦⡶⡴⣢⢴⡀⡶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⣶⡦⢤⣀
⠀⠀⠀⠀⠀⢠⡏⢸⠀⠈⢧⡙⢦⡉⠓⢦⡀
⠀⠀⠀⠀⠀⡞⠀⣿⠀⠀⠈⢷⠀⠙⢦⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠦⠤⠴⢶⣦⡀
⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠘⣇⠀⠀⠙⢦⡀⠀⠀⠉⠛⠒⠶⠤⣤⣄⣀⣀⣀⣀⣀⣤⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠘⡇⠀⠸⣇⠀⠀⠀⠹⡄⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢷⠀⠀⢿⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠄⠂⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢸⡄⠀⠈⣷⡀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠯⢭⣭⣉⣀⣀⣀⣀⣀⣤⣤⣤⣄⣠⡴⠋
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢷⡀⠀⠀⠀⠈⢯⡙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠻⣄⠀⠀⠀⠀⠙⢦⡀⠈⠉⠛⠒⠦⠤⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠈⠉⠓⠲⠶⣶⣚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣙⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣞⢉⣭⣿⣷⣶⣦⣤⣤⣖⣊⣙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⢄⠇⠀⡏⢾⠟⠩⠋⠑⢠⢈⠍⢙⠛⠺⣷⣤⠏⠀⢘⣑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠉⡜⠀⠀⡇⡎⠠⠀⠀⢸⠀⡇⠀⠇⠀⢀⠹⢻⠀⠀⢸⡈⢂⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠁⡆⡇⠀⠀⡇⡇⢠⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⡷⠀⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⠀⡇⡇⠀⠀⡇⡇⠀⠀⢈⡜⠀⠀⠀⡀⠀⠀⡀⡎⠀⠀⢰⠉⠀⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⠀⢣⠸⡀⠀⢸⠔⣂⣶⢻⠁⡇⣛⢸⡳⣆⠆⡀⡇⠀⣠⠃⠀⠀⠈⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⢢⠙⣄⡞⠀⠁⠂⠀⠈⠀⠂⠂⠑⠛⠋⡻⣇⡔⢁⠄⠀⠀⡄⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠁⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⣇⠎
⠀⠀⠀⠀⢀⣴⠶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⠤⡀
⠀⠀⠀⡠⡻⠁⡈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠛⢮⠢⡀
⠀⠀⡰⣱⠁⢀⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠑⡑⡄
⠀⠰⠱⠉⠈⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠄⡈⠐⡱⡀
⢀⢢⡦⡀⣤⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⠸⡀⢡⢡
⡎⡞⠇⠑⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⢀⢇⢃
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠆⠈⠜⡌
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠠⣀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢄⠑⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠈⢆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⠈⡆⠈⠄⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡌⣾⠀⠘⠀⠀⠀⣷⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⠳⣹⠀⠀⠁⠀⡄⢸⠌⣠⣐⣒⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠒⢈⠿⢀⠀⠀⠀⣧⡼⠞⠧⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠔⣡⠖⡖⢜⢶⣾⠋⢳⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠌⠜⣿⠀⠃⠀⣾⠃⠀⣸⣧⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡰⣰⠃⡐⠀⢰⠃⠀⣰⠇⠈⢀⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡔⡱⠁⠈⠀⡀⠁⢀⡼⠃⢠⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡯⠂⠀⢀⠔⠀⣰⠟⠁⣠⠏⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣠⠤⠒⣁⡴⠚⠁⢀⡼⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠖⠋⠁⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡿⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣩⣩⣿⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣯⠀⠀⢿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠘⠛⢿⠟⠀⠁⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣤⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣥
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣛⣩⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢺⠉⠛⣓⠒⠲⣶⡶⠶⣶⣶⠲⣶⣿⠛⣿⠅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⡁⢈⣻⡁⢀⣟⡃⠀⣿⣋⠀⣻⣏⠀⣹⠛⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣿⣇⠀⣿⡇⠀⣿⡇⢀⣿⣧⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣭⣉⣛⣛⣛⣚⣛⣛⣋⣩⣥⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡉⠑⢄⠈⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠞⡩⢀⡾⠟⣿⠆⡈⢳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⣋⣁
⠣⡑⢀⠑⢄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⡠⠊⢀⡴⠋⠀⠰⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠁⠘⢿
⠑⠭⣦⡁⠈⢢⡷⠀⠰⣶⡄⠀⠀⠀⠀⠀⠀⣀⢀⣠⠔⣉⣠⠶⠋⠀⠀⠀⡄⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠈⠸⠇⠀⠀⠈⢻⣿⡟⣶⣄⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⡟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠢⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠉⠐⠒⠒⠒⠈⠉⢀⣼⡿⠋
⣰⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣸⠏⠀⠀⠀⣰⡏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠶⠶⠞⠛⠉
⠇⠀⠈⣆⠀⠀⠀⠀⠀⡠⢂⣀⠜⢁⣰⠏⠀⠀⠀⠀⡏⢰⠀⠘⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄
⠀⠀⠀⣿⡤⢤⡀⠀⠘⠻⠿⣷⠾⠟⠁⠀⠀⠀⠀⠀⣷⠀⠆⠐⠘⡎⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⡀⠀⣰⡟⠐⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⢄⠑⠿⣾⡇⢀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠈
⣷⣾⣟⠑⢦⡀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠻⣄⣼⡷⠦⠤⢼⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡴⠟
⢈⡼⠃⢱⠈⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠂⠤⠤⠽⢻⣿⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠁⠀⢁⠜
⠋⠀⠀⢀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠖⠋⢙⢻⣦⣤⣀⣀⣠⠟⠀⠀⣠⡾⣿⡿⢶⠀⠀⠀⠀⠈⠀⡠⠔⢁⣤
⠀⠀⢀⣮⡾⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣀⣀⡴⠃⠀⠀⠀⠀⠀⢀⣾⠃⡰⠋⠠⠁⠀⠀⠀⠳⠶⠯⠴⠚⠋⠁
⠀⠀⠘⠉⠀⠀⢀⣶⢿⣿⠛⠉⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠇
⠀⠀⠀⢠⣴⡶⠾⠿⠯⠉⠉⠉⠀⠒⠠⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢣⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⠇⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣷⣤⣧
⠒⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠡⣄⠀⠀⠀⠀⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠷⣦⣄⠀⠀⠀⣴⠟⠛
⡶⢋⣉⣉⣉⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣰⣇⡢⡀
⣴⣭⡀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⢆⠀⠀⢰⡟⡩⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠙⢻
⣿⣆⣙⣳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣊⣿⣁⣸⣄⣴⣿⣇⣀⣀⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣘⣦⣤⣄⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠜⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⢆⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠘⢍⠑⠒⠒⠀⠤⠤⠄⠒⠒⠒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠘⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⣀⡠⠚⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⣀⡠⠔⠁⠀⡇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠘⠪⠭⠭⠭⢭⠤⠒⠤⠤⠤⠊⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄⠀⠀⠀⠑⠤⠤⠤⠤⢄⡀
⠀⠀⠀⡤⣀⣀⣀⠤⠚⠁⣀⣄⡀⠀⠀⠀⠀⠀⡸⠀⠣⡀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⡠⠤⠤⠬⠵
⠀⠀⠀⠉⠒⠒⠒⠒⠒⠉⠀⠀⠈⠁⠒⠒⠒⠊⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡀⢀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⡄⠀⠀⠀⢀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣴⣶⣽⣏⣻⣿⣿⣿⣻⣯⣭⣭⣿⣾⣿⠀⠀⢀⣾⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣆⡀⣤⣤⣴⣾⣿⢮⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣏⢀⣴⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣝⣛⣿⣿⣿⣿⡿⠉⣽⣿⣿⣿⣿⣯⣶⣶⣿⣿⡿⢋⣿⣿⣿⣿⣿⣻⡧⣽⣿⣿⣿⣿⣟⣿⣏⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⠻⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣭⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠃⣀⣤⣄⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣭⣭⣬⣭⡿⠿⡿⣻⣏⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣗
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠿⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠿⠻⣶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⣀⡤⠔⠒⠒⠢⣄⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⣠⠞⢉⡤⠒⠒⠲⣄⠈⢷⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⡜⢁⡴⠋⠀⠀⠀⠀⠈⣇⠀⡇⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⡾⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⢸⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⢀⡌⢰⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⢸⡇⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠆⢸⡇⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢃⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡇⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⡀⢧⡀⠀⠀⠀⠀⠀⢀⡾⢁⡞⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡀⠻⡌⠳⣤⣀⣀⣠⡴⠋⣴⠋⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⡀⠙⠲⣌⣉⣉⣁⣤⠞⠁⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠿⠛⠻⠿⢯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣿⣇⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⢿⣩⣛⡓⣂⣉⣹⠿⣷⠶⠾⠶⠛⠷⠲⠾⡶⠾⠛⠷⠶⠞⠿⣷⣶⣤⣤⣀⣀⣠⣴⣾⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡟⠺⣿⣿⡟⢋⢛⣉⠛⠉⠰⠉⠠⡀⠒⠁⠀⠐⡐⠋⠐⠀⠀⠀⠀⠀⠀⢤⠁⢉⠛⢻⣿⡉⢾⡙⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣍⡒⠒⠶⢻⣯⣭⡙⠷⠾⣧⣌⣶⣤⣥⣤⣤⣤⣥⣤⣤⣤⣤⣤⣄⣤⣭⣤⣴⣔⠿⠲⣿⣧⣾⣵⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠛⠛⠿⠶⢶⣶⣤⣭⣭⣭⣍⣥⣤⣼⣿⣿⡧⠶⠆⠰⠲⠶⣟⣰⣧⣤⣤⣬⣭⣿⣷⠿⠿⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡉⠛⠳⠦⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠛⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠻⠶⣦⣄⣈⣍⠉⠙⠛⠛⠛⠒⠒⠂⢤⠤⠤⠤⠤⣤⠤⠤⠤⡤⠤⠒⠛⠛⠉⢉⣉⣰⡶⠞⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠀⠀⠉⠉⠛⠛⠛⠛⠿⢦⣶⣶⡶⣦⡶⣤⣤⣢⣤⣦⡴⣦⢶⣤⣶⡶⠝⠛⠛⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⡙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠻⢷⣄⣈⡉⠑⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠋⢁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⡈⠙⠳⢶⣦⣄⣀⡈⠉⠑⠒⠶⠶⠶⠶⠤⠠⠤⠤⠤⠤⠶⠖⠚⠉⢁⠀⣤⣤⡾⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠷⣶⣦⣴⣦⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠷⠛⠋⠉⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣠⡿⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣴⠟⠋
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠶⠿⠛⠉
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠇

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⢺⣿⣿⣿⢿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠸⣿⣝⢿⣯⣷⣿⣟⣦⣄⡀
⢸⣿⣿⣿⣼⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠈⠻⣯⡟⠷⠿⡾⢻⡾⣽⡶⣄⡀
⣺⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⢹⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⢸⣿⣿⣿⣿⡟⣛⢳⢻⣚⢻⣛⢻⡟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣀⣀
⢸⣿⣿⣿⣿⡇⣩⣼⢸⠇⣿⠇⣿⢃⠚⣿⣿⣿⡇⠀⠀⠀⡀⠤⣢⣅⠶⠯⡿⣛⡲⢾⣬⣤⣔⣂⠤⡀⠀⠀⢀⣀⣠⣿⣿⣢⣴⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣽⡉⣿⢉⣷⠺⣯⢵⣎⣭⠘⢃⣩⠞⠀⠀⣀⠙⠛⠋⢶⣿⡿⠛⣃⣠⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⢫⡉⠛⠳⠾⢷⣤⣬⣭⣠⡶⢿⠃⠀⠀⠸⢻⡷⣦⣴⣶⣦⣀⣾⡿⡻⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠒⠤⠄⠀⢀⠉⠽⠛⠊⠁⠀⠀⠀⠀⠀⠀⠁⠛⠫⠟⠛⠝
⢸⣿⣿⣿⣿⡿⠷⢛⣩⣝⣛⡿⠿⠧⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣦⡀
⢹⡿⠿⠛⣭⣤⠛⣛⠼⡿⣝⣋⡻⠿⣶⢶⣿⣭⣝⡒⠲⡄⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣤⣄⣀⡀
⢺⢆⣘⡛⠹⣿⠟⣻⡷⠶⢌⣩⣶⣾⣿⣑⠶⠖⠉⣡⡏⠀⠀⠀⠈⠙⢿⣦⡄⢀⣴⣤⠀⠀⠀⠀⠀⢠⣦⣤⣦⣦⣼⣽⣿⡿⡿⢶⣦⣤⣀
⣸⣌⣟⠻⠶⢾⣦⣩⣥⠚⢿⡷⢛⣿⣶⠿⠋⢛⣛⠉⠀⠀⠀⠀⠀⠀⠈⣛⣿⣿⣟⣋⡳⣄⠀⠀⠀⣸⠣⣿⣿⣻⣷⣿⣼⣹⣓⡷⡶⠀⡿
⢹⣿⣿⣧⣀⠀⠈⠉⢹⣿⣦⣤⣬⣯⣁⣰⣶⠿⡁⠀⠀⠀⠀⠀⠀⠀⢾⠋⣴⣷⣜⣿⣧⢸⡇⠀⢠⣯⣚⡻⠟⡿⣿⣷⣿⣿⣹⣿⡇⣸⠃
⢸⣿⣿⣿⣿⣿⣶⣤⣤⣤⣭⣿⡻⠿⡿⢟⣥⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⡹⣿⡇⡁⠀⠀⠉⠉⠛⠳⠶⢦⣬⣝⣋⠛⠿⢃⡟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡙⠻⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠾⠁
⢯⣭⣭⣭⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣷⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢀⢉⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠐⠀⠉⠐⠛⢰⡏⣹⡟⢲⡶⣤⡤⠒⠉⠘⠀⠀⠀⡀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠃⠉⠀⠀⠀⠀⠀⠨⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⡛⠉⠀⣀⣀⠤⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠉⠍⠤⢄⡀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠈⠃⠀⠀⠀⢀⣀⣀⣐⣒⣦⡤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⡀⠠⣀⠀⠠⠘⠂⠀⢴⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡤⠖⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠌⠀⢀⣀⣠⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⢁⣀⣀⣀⣀⣀⡀⠰⡟⠦⣄⣀⠀⢀⣠⠖⠁⢐⠁⠀⢠⠇⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠤⠤⣄⡉⠙⠛⠒⠂⠈⠉⠉⠀⠠⣀⢾⡀⠀⢸⡒⠊⠑⠛⠉⠓⠢⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⠤⠤⠔⠒⠉⠉⠁⠀⠑⠢⠬⣥⠤⠤⠒⠒⠒⠲⠬⠭⠽⠩⠭⠇
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢿⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⣋⡴⠋⠀⠀⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠁⠀⠀⠀⢀⣠⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⡀⠤⠚⠋⠁⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢀⣠⠄⠚⠁⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣔⠈⢱⣄⠀⠀⠀⠘⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣦⡙⢦⡀⠀⠀⠀⠉⠻⢿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡹⣦⡀⠀⠀⠀⠀⠉⢉⠟⠛⠻⠷⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⠳⣄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⡇⠐⢇⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠑⢄⢸⣧⣤⣄⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠁
⠀⠈⠛⠛⠛⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⣤⣤⣤⣶⣶⠿⠿⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣶⣶⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣦⣀⡀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣴⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠻⢿⣿⣟⠉⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠰⢿⠛⢉⣻⣵⡿
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⡀⠀⠀⢀⣼⣿⣿⣿⣋⣉⣹⣿⣿⣿⡄⠀⠀⣷⣦⣤⣤⣴⣿⣿⡟⠀⠀⠠⣤⣤⡄⠀⠀⠀⠉⠉⠁⣀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡄⠽⡟⠃⣿⣿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣽⠻⠀⠀⠀⠀⠀⢘⣿⠆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⢿⣦⣤⠀⢀⣼⣧⣬⡷⠃
⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⡏⠉
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⣿⣷⣶⠃
⠀⠀⠘⣽⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⢺⣶⣶⣶⡿⢺⠀⠀⠀⠀⠀⢀⣀⣀⡄⠉⠀⠚⠛⠿⠏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⢿⣿⣆⣁⠀⠀⣴⣧⣼⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⠛⠉⠙⠛⠉⣇⠀⠀⠀⠀⠀⢸⠸⢿⣿⣿⠿⢸⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠘⢿⡿⠿⠋
⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢚⢛⠿⣿⣿⡿⣛⢛⠀⠀⠀⠀⢹⣤⣤⣤⣄⣠⣤⣤⣤⡯
⠀⠀⠀⣿⣿⠟⠻⣿⡟⠀⠀⠀⢖⣺⢸⡇⣿⢸⡇⣿⢸⣒⠆⠀⠀⠀⣤⣀⣀⣉⢉⣁⣀⣤⠄⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣿⡏⢿⠟⣹⡇⠀⠀⠀⠀⢹⢸⡇⣿⢸⡇⣿⢸⠁⠀⠀⠀⠀⣀⣀⡁⠉⠉⠉⣁⣀⠀⠀⠀⠀⢹⣶⣾⣻⣶⡟⣷⣾⢻⣶⣾⠁
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⢸⡇⣿⢸⡇⣿⢸⠀⠀⠀⠀⠀⢠⣍⣉⣉⢙⢉⣉⡍⠀⠀⠀⠀⢸⣿⡿⢿⣿⡇⣿⣿⢸⣿⣿
⠀⠀⢰⣽⣿⣿⣿⣿⣧⡆⠀⠀⠀⠘⡾⢇⣿⣸⣇⠿⡞⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠈⠈⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣘⠭⢁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣎⣿⠀⠀⠙⠟⠲⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠀⠀⠀⠈⡦⠄⠀⠀⠀⠀⠉⠛⠡⡀⡔⠁⠀⠀⠀⢀⣦⡀⠀⠈⢢⡤⠐⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠱⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢸⣷⣀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢀⡀⢸⣿⣿⣽⣆⣀⣾⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⡀
⠀⠀⠀⠀⠀⠤⠄⠀⠀⣀⠀⠀⢀⣑⣾⡇⠒⠀⣸⣿⣿⣿⡻⢛⡟⠏⠁⠀⡀⠀⠀⠀⣆⣴⠁⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠉⠍⣽⣽⣶⡾⡻⠛⠋⠁⠀⠈⠀⠀⠰⠿⠃⠀⠀⣰⣿⣥⣴⡾⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠴⠚⠋⠉

⠀⠀⠀⢀⣤⠶⢒⣦⡀
⠀⠀⠀⢸⠏⠉⢹⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠸⣤⠲⣊⠀⢯⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠁⠀⠀⢘⡆
⠀⠀⠀⠀⡇⠀⡙⡆⠘⢧⠀⠉⠉⠉⠓⠒⠒⠦⠤⠤⠤⠴⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⡇⠀⢧⢹⡀⠁⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠴⠃
⠀⠀⠀⡼⠁⠀⠘⣼⠁⠀⠀⠀⠈⡳⢤⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣢⣬⡖⠚⠉
⠀⠀⢸⠇⠀⠀⠀⡈⢧⠀⠀⠀⠀⠈⠢⠉⠓⠦⣭⣥⣤⣴⣖⣒⣛⣉⣥⠤⠴⠛⠚⠋⠉⠉⠉⠳⣆
⠀⠀⠈⣆⠀⠀⠀⠀⠌⢧⡀⠀⠀⠀⠀⠀⠁⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⠁⣰⠋
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠢⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠉⠉⠉⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠈⠢⠈⠙⠒⠦⢤⣄⣀⣀⣀⣀⡤⠤⠴⠶⠦⢤⡤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠤⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⣤⣤⣤⡤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⢀⣀⠠⠔⠚⠋⠉⠉⠉⠉⠁⠐⠒⠀⠤⢀
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠
⠀⢀⡴⠃
⢀⡎⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⣜⠀⢀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⡟⠀⠈⠓⢀⡁⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠹⣀⡔⠉⠁⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠁⠇⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠎⠀⠂⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣴⣶⣶⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿