Politeness Emojis & Symbols

⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠲⢤⣀
⠀⠀⠀⢠⠞⠁⣀⠀⠀⠀⢀⡀⠈⢳⡀⠀⠀⢀⡞⠁⠀⡀⠀⠀⠀⣀⠈⢳⡀⠀⠀⢀⡞⠁⣀⡀⠀⠀⠀⣀⠈⠳⡄
⠀⠀⢀⡏⠀⠀⠿⠃⠀⠀⠸⠟⠀⠀⢳⠀⠀⡟⠀⠀⠞⠉⠳⠀⠘⠿⠀⠀⢻⠀⠀⡞⠀⠀⣤⠟⠂⠀⠻⢥⠀⠀⢹⡀
⠀⠀⢸⡇⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⢸⠀⠀⡇⠀⢠⡄⠀⠀⠀⠀⢠⡄⠀⢸⠂⠀⡇⠀⠠⣶⠶⠶⠶⠶⣶⡄⠀⢸⡇
⠀⠀⠀⢷⡀⠰⠏⠁⠀⠀⠈⠻⠄⢀⡟⠀⠀⢳⡀⠀⠙⠶⠤⠤⠶⠋⠀⢀⡞⠀⠀⢻⡀⠀⠙⠷⠦⠤⠶⠋⠀⢀⡾
⠀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⠴⠋⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠙⠦⣄
⠀⠀⠀⣰⠃⠀⣤⡄⠀⠀⢠⣤⠀⠙⣆⠀⠀⣰⠋⢀⣤⡀⠀⠀⢀⣤⡀⠙⣆⠀⠀⣰⠋⠀⣤⣤⡄⠀⣤⣤⡄⠘⣦
⠀⠀⢠⡇⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⢸⠀⢀⡇⠀⠈⠛⠁⠀⠀⠈⠛⠁⠀⢸⡀⠀⡏⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⢸⡆
⠀⠀⠈⡇⠀⠘⣧⡀⠀⠀⣀⡼⠃⠀⣸⠀⠀⣇⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣸⠀⠀⣇⠀⠐⢧⣀⠀⠀⢀⣴⠇⠀⢸⠃
⠀⠀⠀⠹⣄⠀⠈⠙⠛⠛⠉⠀⠀⣰⠃⠀⠀⠙⣆⠈⠉⠉⠉⠉⠉⠉⠁⣰⠋⠀⠀⠘⣆⠀⠀⠉⠛⠛⠋⠁⠀⣠⠏
⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠈⠑⠦⣤⣀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⢠⠴⠛⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣾⣭⣄⣈⠉⠑⠦⡀⠀⠀⠀⠀⢀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⣄⡀⠀⠉⠛⠻⢶⣤⡈⢆⠀⡠⠊⠁⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣸⣿⣿⠀⠀⠀⠀⠀⠉⠛⢾⣞⣠⣤⣶⠶⠿⠛⠛⠒⠶⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠒⠒⠒⠶⠶⠦⣤⣀⡀⠀⡼⢏⠛⠟⠋⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠈⠂⠐⠒⠒⠚⠓⠒⠶⠦⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠛⠻⠷⠶⣶⣤⣤⣤⣤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠿⠛⠛⠛⠛⠷⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡿⢻⣆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣷⠀⠀⠀⢀⣿⠁⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⢿⡄⠀⢀⣾⠃⠀⢸⡟⣀⣀⣤⣤⡶⠶⠿⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠘⣷⢀⡾⠃⠀⠀⠛⠛⠋⠉⠁⠀⠀⣀⣠⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⡶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠂⠁⠀⠠⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡧⣶⡆⠀⠀⠀⠅⢤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠊⠀⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠈⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠂⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠢⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠂⠀⠀⠢⠀⠀⠀⢀⣀⡀⣀⣂⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⣀⣀⣁⡀⠁⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛⠛⠁⠀⠀⠁⠀⠁⠀⡀
⠀⠀⠀⠀⠈⠛⠋⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠂⠀⠀⠂⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⢀⡀⣀⠠⠀⠀⠀⠠⠃⠙⠃⠣
⠀⠀⠀⠀⢨⣤⣨⡀⠅⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠈⠠⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠠⠀⠠⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⢀⠀⢀⠠⠀⠀⠀⠠⠂⠀⠀⠢⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡩⠂⠁⠀⠪⠁
⠀⠀⠀⠀⢶⠶⢶⠆⠁⠀⠀⡀⢀⣈⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⣒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠂⠒
⠀⠀⠀⠀⠢⠀⠀⠈⠀⠀⠀⠀⠈⠉⠩⠀⠀⠀⠀⠈⠂⠀⠠⠂⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⠠⠀⠀⠊

⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢙⠂⡀⠀⠀⣀⢈⣉⣉⢀⡀⠀⠀⣠⣞⣉⣙⢦⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠁⠀⠀⡁⣾⡿⣿⠄⠁⠀⠀⡁⠀⠉⠀⠁⠁
⠀⠀⠀⠀⠠⠀⠠⠈⠀⠀⠀⠀⠠⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡉⠂⠀⠀⠢⡁⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⢀⠀⣀⠠⠀⠀⠀⠠⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⢉⣀⠁⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠈⠙⢶⡄
⠀⠀⠀⠀⠀⢰⠏⠀⢰⣶⡄⠀⢴⣶⠀⠀⢻⡀⠀⠀⠀⠀⠀⡾⠁⠀⣴⣦⠀⠀⣶⣦⠀⠙⣇⠀⠀⠀⠀⠀⢰⡏⠀⢠⣶⡆⠀⢰⣶⡄⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢹⡄⠀⣄⡀⠀⠀⠀⣀⡄⠀⣸⠃⠀⠀⠀⠀⠘⣧⠀⠘⠛⠶⣤⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⡆⠀⢀⣤⠖⠒⠶⣄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠻⣄⡀⠙⠓⠒⠛⠉⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠈⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠹⣦⡛⠁⠀⠀⠀⠀⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠞⠋


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⠀⠀⠀⡈⠙⢶⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣁⠀⠀⠀⣀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠀⠀⠸⡇⠀⠀⢻⡀⠀⠀⠀⠀⢀⡿⠀⠀⢈⣻⡶⣿⡉⠀⠀⠘⣧⠀⠀⠀⠀⠀⢰⡏⠀⠸⣿⠃⠀⠸⣿⠇⠀⢹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠋⠁⠀⠈⠙⠀⠀⠀⣿⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⣿⠆⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⣷⠀⠀⢿⡉⠉⠉⣹⠏⠀⢠⡟⠀⠀⠀⠀⠀⠸⡇⠘⢿⡛⠛⠛⠛⢛⣿⠃⣸⠇
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠉⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⠷⣄⡈⠙⠛⠛⠉⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠙⠛⠒⠚⠋⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠖⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠚⠛⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠶⢦⡴⢶⣖⣛⠛⠉⠙⠛⠛⠳⢦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆⠀⠀⠀⠀⠀⠉⢷⡀⢠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣩⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⢣⠠⢤⣤⣤⣄⡀⢻⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⡟⣹⠞⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣄⡀⢿⠀⠀⠙⠾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣾⣥⠟⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠙⣻⣇⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠏⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⣤⡾⠋⣀⣠⣤⠖⠲⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⠉⠉⠉⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⣠⠄⠀⠀⠠⡄⢀⡼⣡⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠻⣦⠱⣴⠃⠀⠀⠀⠀⢹⠏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢴⠤⣤⣤⣀⡀⠀⠀⠀⠀⠈⢳⡉⡄⠀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⢻⡜⡄⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⡀⠀⢿⣰⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡇
⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣀⣀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⢇⢇⡀⠻⠒⠂⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⣿
⠀⠀⠀⠚⢏⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⢀⠀⠛⠒⢤⣀⠀⠈⢷⡀⠸⡘⢻⠆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠉⠓⢿⣍⡉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠓⢦⠘⣧⠀⠇⢸⡄⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⣠⡄⠀⠀⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⡄⢸⠈⡃⠀⠀⣤⠎⠁⠀⠀⢀⢀⠞⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⠐⣦⣀⣀⠀⣤⣀⣰⡶⠛⠛⠉⠀⠙⠷⣄⡀⢳⠀⢰⡇⠀⠀⡀⠀⣸⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡀⣿⠀⠀⠀⠹⣮⠃⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠉⠙⠿⣄⣀⣀⣠⣉⡀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠳⣄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠙⢦⣸⢦⣷⣤⠶⠞⠛⠛⠙⠛⠶⣄⠀⢀⣀⣀⣀⣀⠈⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠉⠉⠉⠉⠉⠛⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠞⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴⠤⣝⣋⠩⣙⣻⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⣴⠒⢦⣄⠀⠀⣰⣿⠀⣿⡀⠿⠃⢀⣼⢿⣔⢇⡦⠞⠁⠀⠀⠀⠀⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⡟⠀⠀⠈⣳⡾⠃⠹⣧⣌⠙⠳⣤⡏⠁⠀⠹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠠⠤⠤⣀⣾⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡴⠶⠤⠶⢤⡀⠀⠀⢀⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠏⠀⣠⡴⢶⠉⠉⠀⢀⡿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣠⡤⠤⠤⠚⠋⠁⢀⡼⠋⠀⠘⠳⢄⣀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠷⢦⣄⣀⣀⣴⠞⠉⢩⠟⠁⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⣠⡶⣿⠖⠴⠶⠛⠛⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⠉⡜⠁⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⣤⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠉⠉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣀⣀⣠⡶⠏⠥⠤⠤⢤⣬⡽⢶⣤⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣀⠀⡴⠘⡄⢀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⢸⠁⢧⢰⠁⠹⡀⠀⣷⠃⢰⣣⠖⠁⡤⠖⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠈⠺⡄⠈⢿⠀⠀⠹⡄⢹⠀⡼⠁⠀⢰⠀⢀⣾⠤⠖⣲⠶
⠀⠀⠀⠀⠀⢠⡀⠀⢃⠀⠉⠒⢤⣙⢦⣸⡄⠠⠀⢻⣼⡾⠁⠀⠀⡼⢀⡞⠁⣠⣞⣁⡀
⠀⠀⠀⠀⠀⠈⢏⠓⠮⣷⡀⠑⢄⠈⠻⣿⣧⣠⣧⣼⣿⣧⣴⣇⣰⣷⣯⠴⠚⠉⠀⢀⣆⣀
⠀⠀⠀⠀⠀⡤⢬⣷⣄⣀⡙⢦⡀⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠔⠈⣀⠔⠁⠀⣀⠵
⠀⠀⠀⠀⠀⠱⣄⡠⠤⠬⠭⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣞⣁⠤⠖⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠊⢄⡀⠀⠀⠤⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠓⠒⠶⢶⣒⠒⠋
⠀⠀⠀⠀⣤⠤⠤⠭⠟⠒⠶⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⣀⡈⠕
⠀⠀⠀⠀⠈⠓⢦⣤⠴⢚⡽⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣭⣉⡉⠉⠀⠙⢆
⠀⠀⠀⠀⠀⢖⡉⢀⠔⠉⠠⠔⠊⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠧⡀⠙⣎⡉⠙⢿⡓⠚
⠀⠀⠀⠀⠀⠀⠉⠁⠀⡠⢤⡶⠋⣡⣾⠃⢸⠛⢻⣿⠟⢿⠋⢻⢿⠦⣄⠈⠂⠈⢻⡲⢤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡼⢁⡇⠀⠂⢠⠏⡟⡆⠈⡀⢸⡌⠳⣌⠑⠢⢄⣀⢳⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠯⠖⠚⡿⠁⢸⠀⠀⡰⡟⠀⣇⠹⡀⠀⢸⠷⡀⠘⡶⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠴⠚⠠⠊⢠⠇⢠⢿⠀⠑⡀⡸⠀⢳⢀⡇⠈⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠁⠸⡆⠞⠀⠁⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⣾⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⣸⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡳⢦⡀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢀⣤⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣦⡀⠀⠀⢀⣠⣤⠤⣤⣤⣀⠘⠁⠀⠀⠀⢀⣤⠾⣋⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⡾⢋⡥⠶⠶⠶⢦⣍⡛⢦⡀⢀⣴⣿⡷⠛⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡴⢋⡴⢖⣚⣒⠶⣬⡻⣆⠻⣆⠉
⠀⠀⠀⠀⠀⠀⠿⣭⣉⣉⣉⡛⠛⠶⠶⢤⣀⠀⠀⡟⣸⢡⡏⡼⣫⠥⣭⡙⣮⢳⡜⣇⢻⡄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⣠⡀⣇⢻⠸⡞⣟⢧⢾⡆⣷⢸⡆⡇⣿⢸⡇⠶⢿⣿⣿⣯⣭⣭⣭⣭⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⡽⣎⢷⣙⢮⣽⣭⠾⢃⡾⣱⢇⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠻⣌⠳⣭⣓⠲⠖⢚⣋⡴⢋⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣦⠀⠈⠳⣌⡛⠦⣭⣍⣉⣩⡥⠞⣋⡴⠋⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⣥⠞⠁⠀⠀⠀⠀⠉⠓⠶⠦⠤⠶⠖⠛⠉⠀⠀⠀⠈⠻⣍⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠠⡶⡄⠀⠀⠀⠀⠈⠙⢦⣉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡟⠀⠀⠀⠀⠀⠀⢷⠹⣄⠀⠀⠀⠀⠀⠀⠉⠳⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⠇⠀⠀⠀⠀⠀⠀⠘⣇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃

⠀⠀⠀⣠⣶⣶⣤⠀⠀⣠⣶⣶⣦⡀⠀⢠⣴⣶⣦⡀⠀⢀⣴⣶⣦⡄⠀⢀⣴⣶⣶⣄⠀⠀⣤⣶⣶⣄⠀⠀⣠⣶⣶⣤⠀⠀⣠⣶⣶⣦⡀⠀⢠⣴⣶⣦⡀
⠀⠀⠐⣿⣾⣷⣿⠇⠀⣿⣾⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⢾⣿⣿⣿⡿⠀⢸⣷⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠰⣿⣾⣷⣿⠇⠀⣿⣿⣿⣿⡇⠀⢻⣷⣿⣾⡇
⠀⠀⠀⠈⠛⠛⠋⠀⠀⠈⠛⠛⠋⠀⠀⠈⠛⠛⠋⠀⠀⠈⠙⠛⠛⠁⠀⠀⠙⠛⠛⠁⠀⠀⠙⠛⠛⠁⠀⠀⠉⠛⠛⠉⠀⠀⠈⠛⠛⠋⠀⠀⠀⠛⠛⠋
⠀⠀⠀⣤⣶⣶⣦⠀⠀⣠⣶⣶⣦⡀⠀⢠⣶⣶⣦⡀⠀⢠⣴⣶⣶⡄⠀⢀⣴⣶⣶⣄⠀⢀⣴⣶⣶⣄⠀⠀⣤⣶⣶⣦⠀⠀⣠⣶⣶⣦⡀⠀⢠⣶⣶⣦⡀
⠀⠀⠐⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⢻⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⠀⠸⣿⣿⣷⣿⠀⠘⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡇⠀⢿⣿⣿⣾⡇
⠀⠀⠀⠈⠛⠛⠉⠀⠀⠈⠙⠛⠋⠀⠀⠈⠙⠛⠋⠀⠀⠀⠙⠛⠋⠁⠀⠀⠙⠛⠛⠁⠀⠀⠉⠛⠛⠁⠀⠀⠈⠛⠛⠉⠀⠀⠈⠛⠛⠉⠀⠀⠀⠙⠛⠋
⠀⠀⠀⣴⢿⡿⣦⡀⠀⣴⣾⣿⣶⡄⠀⣠⣾⣿⣷⡄⠀⢠⡾⣿⢷⣄⠀⢠⡶⣿⣷⣆⠀⢀⣴⣿⣿⣦⠀⠀⣴⣿⣿⣦⡀⠀⣴⣾⣿⣶⡀⠀⢠⡾⣿⢦⡀
⠀⠀⠀⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⠇⠀⢷⣿⣿⣿⡇⠀⢻⣿⣿⣿⡟⠀⠸⣿⣿⣿⡿⠀⠸⣿⣿⣿⣽⠀⠘⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⠇⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠉⠋⠁⠀⠀⠀⠉⠋⠉⠀⠀⠀⠉⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠋⠁⠀⠀⢈⡙⠋⡁⠀⠀⠈⡉⠋⡁⠀⠀⠀⠉⠛⠉
⠀⠀⠀⣾⢿⣿⣷⡀⠀⣴⣿⣿⣷⡄⠀⣴⣿⣿⣷⡄⠀⣰⡿⣿⣿⣆⠀⢠⣾⣿⣿⣦⠀⢠⣾⣿⣿⣦⠀⠀⣾⢻⡟⣷⡀⠀⣴⢿⣿⣷⡄⠀⢰⡿⣿⢷⡄
⠀⠀⠈⢿⣿⣿⣿⠃⠀⢿⣿⣿⣿⠇⠀⢻⣿⣿⣿⠇⠀⠹⣿⣿⣿⠟⠀⠸⣿⣿⣿⡿⠀⠘⣿⣽⣯⡿⠀⠈⢿⣿⣿⣿⠃⠀⢿⣿⣿⣿⠇⠀⠸⣿⣿⡿⠃
⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⢉⣉⠁⠀⠀⠀⢈⣉⡁⠀⠀⠀⢈⣉⡁⠀⠀⠀⠈⣉⡉⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⢉⣉⠁⠀⠀⠀⢀⣉
⠀⠀⢀⣾⣻⣟⣷⡄⠀⣾⣻⣿⣻⡆⠀⣴⣟⣿⣻⡆⠀⣰⣟⣿⣻⣦⠀⢰⣟⣿⣿⣧⠀⢠⣾⣿⣿⣷⠀⢀⣾⣿⣿⣷⡄⠀⣾⣿⣿⣿⡄⠀⣼⣟⣿⣻⡆
⠀⠀⠀⢿⣿⣿⡿⠃⠀⠻⣿⣿⡿⠃⠀⠻⣿⣿⣿⠇⠀⠹⣿⣿⣿⠟⠀⠘⢿⣿⣿⠟⠀⠘⢿⣿⣿⡿⠀⠈⢿⣿⣿⡿⠁⠀⠻⣿⣿⡿⠃⠀⠹⣿⣿⡿⠃
⠀⠀⠀⠀⣀⣀⡀⠄⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⡀
⠀⠀⢀⣿⣿⣿⣿⡄⠀⣾⣿⣿⣿⡆⠀⣾⣿⣿⣽⡇⠀⣼⣟⣿⣻⣧⠀⢰⣿⣿⣻⣷⠀⢰⣿⣿⣿⣿⡀⢠⣿⣻⣿⣿⡄⠀⣾⣹⣏⣹⡆⠀⣼⣟⣿⣻⡆
⠀⠀⠀⠻⣿⣿⠿⠁⠀⠻⢿⣿⠿⠃⠀⠹⢿⣿⡿⠃⠀⠘⢿⣿⡿⠋⠀⠘⢿⣿⡿⠟⠀⠈⠿⣿⣿⠟⠀⠀⠻⣿⣿⠟⠁⠀⠻⣿⣿⡿⠃⠀⠹⢾⣿⡾⠃

⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣄⡧⠀⠀⠀⣀⡀⠠⠀⠀⠠⠀⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡀⠀⠀⠀⢀⠀⠙⠁⡀⠠⣶⣄⠟⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⢿⠆⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢄⠀⠀⢀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⢤⡤⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠸⠉⠀⠀⠀⠀⠀⠾⠁⡤⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠐⠀⠀⠀⠴⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠂⠀⠀⠀⠀⠀⠐⠁⠀⣠⣼⣿⣿⣿⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⡇⣤⡀⠀⢀⠀⠀⢰⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡇⠈⠁⠀⠀⠀⠘⢇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⣶⠿⠰⢆⣤⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⡀⠀⠀⢀⣀⢸⡀⠀⠈⠙⠙⢻⣿⣿⢻⡇⠰⣿⠋⠀⡀⠛⠻⣏⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣸⡷⠀⠀⠀⣻⡷⣿⠿⠃⠀⠀⠀⠀⠀⠛⢸⡅⠄⠀⠀⠀⣀⡀⢠⠿⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⡟⠋⠀⣿⠂⠻⠗⠘⢀⣀⢠⠀⠀⠠⣤⣼⣿⡇⠀⠀⢀⠀⠛⣤⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⣬⣿⡿⡀⠀⠀⠀⢙⣿⡇⠀⢀⡈⠀⠀⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡀⠠⡀⠀⠆⠀⠀⠀⠀⠀⠀⡅⠀⠐⢷⣀⠀⢺⣿⣯⡇⠀⣯⣉⣥⣐⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠛⣦⠀⢀⡀⠀⡀⠂⠀⠀⢈⠀⠀⠀⣿⡆⠰⣞⣿⣿⣾⣿⡛⣿⠀⢋⣍⣿⣿⠛⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⠷⡶⠇⠀⠑⣀⣠⡴⡏⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⠉⠀⢻⡆⠉⠛⠋⠁⠀⢀⣥⠀⠂⠀⡖⣠⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡹⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⣠⣨⡗⠀⣴⣦⣿⠀⠙⣴⠀⣴⣾⣿⣇⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⠀⠀⠀⠀⠀⠀⢀⢀⡘⠀⣀⠀⠀⡈⠁⠀⠈⠱⡆⢺⣿⣿⡿⠀⠀⠁⢠⡿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣋⣼⠂⢀⡄⢠⣤⣾⠉⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣧⣴⠃⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⢀⡙⣽⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠘⣻⣦⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⢤⣤⣄⣄⣿⣿⣶⠟⠁⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⠀⠰⣆⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠰⠍⠁⠐⢶⣤⢤⣿⣿⠿⢿⣿⡛⠉⠉⠀⠀⣶⠀⢠⣌⣿⣥⣿⡿⠟⠋⠉⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣇⡀⢀⡴⠚⠁⠀⠀⠈⠀⠁⢀⠀⠀⡄⠁⠀⣰⠿⣿⠏⠙⠃⢀⣤⠆⠀⠀⣀⠴⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣽⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢸⠷⠟⠀⢀⡀⠑⢀⠉⠠⠀⠶⠋⣁⡴⠖⠋⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣴⣶⣦⣤⣀⣤⣴⠶⣿⣶⣶⣶⣿⣷⠀⠉⠙⣦⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣉⣿⣿⣿⣿⣿⣤⡿⣿⠿⠏⠈⠁⠹⠿⣦⡞⠛⠁⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣏⣿⡿⡿⢿⣷⠀⠀⠸⠃⡀⠀⣼⣀⡀⠰⠦⠀⢁⠀⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣽⣿⣿⠟⠻⣾⡿⠟⠻⣧⣼⠈⠻⣿⣏⢀⣀⣽⣿⣿⣿⣅⠀⣠⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠋⠀⠀⠠⣈⣁⠀⠀⠹⣿⡇⠀⢹⣿⣿⢹⣿⡿⠛⠛⠉⠀⠁⠀⠈⠈⠉⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣦⣀⠈⢷⣶⠾⢯⡄⢸⣷⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠓⢛⣹⣿⣿⣾⣿⠃⢸⡇⠈⣿⠂⢀⣾⣇⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠉⠀⠈⣿⠀⠸⣧⠀⣿⠖⠁⠙⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⠄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢹⣿⣿⣿⡇⠙⣿⢸⠃⠇⠈⢸⡏⣻⡏⣿⢿⣿⣿⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢟⢿⣿⣷⠀⢹⣿⠻⡅⠀⢹⠘⠀⠀⠀⠸⠀⢃⠀⡿⠣⡾⠁⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣎⠳⡀⠂⠫⠃⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠜⡰⠱⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⡉⠻⣯⡂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⣹⠿⣿⢿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠻⣤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⡕⠋⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣍⠻⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⢴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣪⠛⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢉⣿⣿⣿⣿⣿
⣿⣿⣾⣍⡋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣿⣿⣿⣿
⡷⠷⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣞⣿⣿⣿
⣿⣯⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠏⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢛⣻⣿⣿
⣾⣯⢤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠀⠈⠹⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⣿⣿
⣿⡿⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⢠⡀⠀⢹⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣭
⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠘⠀⠈⢳⡄⠀⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢬⣭
⡿⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⣿
⣿⣖⣛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⡶⢶⣮
⣿⣿⡻⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣙⠿⣿
⣿⣮⣡⣀⣄⣤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⣷⣿⣿⣿
⣿⣿⣿⣿⡟⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣽⣻⣿⣿⣿
⣿⣿⣿⣿⣾⣛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣉⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾⡣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⢢⣀⢵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⢀⣠⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⣰⠇⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠐⡀⣄⣆⢰⣄⠰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⡿⡕⠀⣼⠀⣴⣧⢎⡄⢸⢠⡄⣇⠀⡀⡈⠀⠀⣿⡄⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣹⣾⣿⣿⡄⣾⣼⣧⣿⡆⣷⣾⣇⡰⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠄⣀⣼⣿⣷⠞⠛⠲⢿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡞⠉⠋⠀⠀⢀⡴⠦⡶⠆
⠀⡀⣰⠋⠀⣠⡄⠐⢲⣷⣦⠀⠀⢳⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢸⣟⢰⠇⠈⠓⡀
⢀⣷⠃⠀⣄⣿⣝⣷⣶⡁⣿⣽⠀⠀⢻⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠋⢹⣿⣤⣛⣾⡃
⢸⡇⠀⠀⠹⣿⣛⠏⠈⠀⣄⠃⡰⡶⠋⠉⢱⠇⠀⠀⠀⠀⠀⠀⢠⠙⢦⣀⠀⠀⠀⣀⣈⣿⡷⣽⠛⡇
⠀⢷⠆⠙⣦⠈⠙⠛⠄⠠⡤⣶⠏⢸⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⣦⠀⠀⠀⠈⠿⠆
⠀⠈⠀⠛⠁⣀⣀⠐⢄⣨⠇⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣿⡀⠀⠀⠀⠀⢀⠀⠀⣀⣴⡄
⠀⠀⠀⠠⡈⠛⠠⡄⠉⠀⢠⠀⠀⠈⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⣿⠉⠀⠀⢀⠀⣴⡃⠀⢿⡽⡀⠹⠂
⠀⠀⠀⠀⣹⣦⡴⣿⣄⠀⢁⠀⠀⢠⣾⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠛⠁⠀⠴⣦⠛⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠁⠐⠋⡉⠁⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢋⣠⠀⠀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⣠⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣿⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡶⠦⣤⣄⣛⣁⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣧⣙⣿⠀⠀⠀⠰⠋⠀⠀⡀
⠀⠀⠀⠀⣹⡾⡇⠀⠋⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⣼⣿⣿⣿⡇⠀⠀⠀⠿⠶⣢⣿⣄⠀⡀
⠀⠀⠀⠀⢨⠟⡠⣷⢖⣼⡷⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣿⡝⠋⠹⣆⢀⣤⣤⡼⠋⠀⠀⠉⠁
⠀⠀⠀⣰⠃⣾⢃⠻⣿⣿⡟⢷⣤⠀⠀⢀⢀⢄⠀⠀⠀⠀⠀⠀⠈⢫⠟⠓⠢⠀⠘⠛⠻⠟
⡀⢀⠠⠋⢝⡻⠈⢇⡈⢻⣷⣤⣿⠀⠀⠀⢿⡙⡇⠀⠀⣠⣤⠀⡟⣿⣠⡀⠀⠀⠀⠘⠁⠄
⠈⠉⠀⠀⠈⠀⢀⡺⠃⢀⢻⣿⣌⢧⠀⠀⢀⢻⡇⠀⠀⢛⠖⣠⡇⢿⡟⠛⣀
⠀⠀⠀⠀⠀⠀⣮⠀⢠⣶⣿⣿⣿⢀⠀⢀⡼⢫⠃⠀⠀⠘⣄⣇⠁⣼⣡⢸⠏⠀⠀⠀⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠻⣷⠷⢿⣿⣿⣿⢆⣀⣤⡿⠋⠀⠀⠀⠀⠈⢺⡤⢿⠗⢉⣦⣤⣄⣠⣶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣥⣶⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⡾⠋⠛⣷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣠⣄⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡄⠻⠧⠛⢁⣾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣛⣉⣉⣁⣀⣀⣀⣉⣉⣉⣙⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⢻⡏⠛⠷⢦⣤⣀⡀⠀⠈⣿⢋⡭⠥⢄⠀⡀⠈⠉⠉⣉⣉⡉⣿⣁⣀⣤⣤⠴⠶⠞⠛⠋⢉⡿⠀⠀⠀⢀⣤⣦
⠀⠀⠀⢀⣀⣤⣤⣿⠀⠀⠀⠀⠉⠛⠻⢾⡏⡆⠀⠀⠘⠈⡇⠉⡇⠈⠀⠀⠈⡿⡏⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⣷⣿
⣠⣾⣆⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠇⠀⠀⠀⠁⡇⠀⡇⠀⠀⠀⠀⢇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣄⡀
⠉⠛⠛⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠈⠀⡇⠀⠃⡆⠀⠀⠀⠘⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠃
⠀⠀⢀⣤⡴⠾⠛⠀⠀⠀⠀⠀⠀⠀⢰⠇⡂⠀⠀⠀⠀⠀⡇⠀⡆⡇⠀⠀⠀⠀⠇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⠀⠀⠀⠀⠀⡇⡇⠀⡇⡇⠀⠀⠀⠀⠸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⢀⣹⡧⠀⠀⠀⠀⠀⠀⢰⠇⡆⠀⠀⠀⠀⢠⠇⡄⠀⡇⡇⠀⠀⠀⠀⠀⡇⢻⡄⠀⠀⠀⠀⠀⠀⠰⣿⣀
⠀⠀⢠⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⡞⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠰⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡦
⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⣸⢣⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⢿⡆⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⣹⡷⠀⠀⠀⢠⠏⡎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⣠⣶⠛⠁⠀⠀⠀⠀⣾⢠⣁⠀⠀⠀⠀⠀⠀⡂⡸⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⢸⠄⣿⠄⠀⠀⠈⠻⣦⡄
⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠹⡄⢀⣉⠉⠑⠒⠀⠒⠀⠓⠠⠤⠃⠘⠦⠤⠴⠒⠚⣉⣁⠀⡿⠀⠀⠀⣀⡴⠟⠁
⣀⣠⣤⣤⡄⠀⠀⠙⣷⠄⠀⠀⠹⡼⡄⠀⠉⠉⠉⡆⠀⡖⠒⠒⡆⡰⠒⠉⠉⠀⠀⢀⡌⡼⠁⠀⠀⠺⣯⡀⠀⠀⢾⣿⣿⡆
⢻⣏⣼⠏⠀⢀⣤⠞⠁⠀⠀⠀⠀⢻⡱⡀⠀⠀⠀⢰⠀⡇⠀⠀⠃⡇⠀⠀⠀⠀⢀⠎⡼⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⠁
⠈⠋⠁⠀⠀⠛⠛⠛⠛⢿⡆⠀⠀⠀⣷⠱⣀⣀⠀⢸⠀⣇⠀⡘⢰⣀⣀⠀⠀⡠⢂⡼⠁⠀⠀⠀⢠⣶⠶⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⠶⠛⠻⣷⣤⠬⠭⠍⠀⢈⣉⣀⣀⣀⣀⣀⣀⣀⣾⣁⠀⠀⠀⣠⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣅⣀⣀⡀⠀⠀⢀⣀⣀⣀⣬⣿⠏⠁⠈⠛⠶⣤⡏⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⣉⣉⣉⣉⣉⣥⡼⠃

⢠⠂⠉⠉⠁⠢⠀⠀⢀⠔⠈⠉⠁⠢⡀⠀⠀⠔⠈⠉⠁⠂⡀⠀⠀⡔⠂⠉⠁⠐⢄⠀⠀⡠⠂⠉⠉⠐⢀
⡇⣘⠃⠀⠛⡀⠁⠀⠄⠀⠓⠀⠚⠀⠀⠀⠈⢀⠛⠀⠚⣀⠀⠀⠠⡔⠛⡂⡞⠛⣪⠀⠀⠀⠚⠀⠀⠓
⠡⡙⠾⣾⠖⡡⠃⠀⠐⠀⠀⠀⠀⡠⠂⠀⠘⢌⠶⣷⠷⢃⠌⠀⠀⢎⠉⠠⠌⢉⠔⠀⠀⠢⡀⠺⠗⢀⡔
⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠁
⢀⠔⠀⠁⠐⢄⠀⠀⢀⠔⠂⠁⠐⠠⠀⠀⠀⡄⠂⠈⠐⠢⡀⠀⠀⡠⠂⠈⠀⠲⠂⠀⠀⠠⠒⠀⠁⠒⢄
⡆⠀⠀⠀⠀⠀⠃⠀⡄⠈⣤⠀⠀⠀⠁⠀⠘⠀⠂⠀⠰⠂⠐⠀⢸⠀⠚⠂⠘⠓⠒⠀⠀⠁⠰⠆⠀⠀⠈
⠣⡀⠠⠤⠀⡠⠃⠀⠰⡀⠠⠤⠄⢀⠂⠀⠘⡘⢿⣦⡿⢏⠌⠀⠈⢌⢿⣧⣿⢎⠜⠀⠀⢆⠀⠀⠂⠀⡠
⠀⠈⠀⠀⠈⠀⠀⠀⠀⠈⠐⠀⠊⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠐⠈
⢀⡄⠂⠐⠂⢄⠀⠀⠀⠠⠒⠀⠒⢄⠀⠀⠀⡠⠒⠀⠒⠠⡀⠀⠀⣠⡔⠀⠐⠢⡀⠀⠀⢀⠔⠂⠐⠂
⣤⢂⢢⠠⢂⢢⡃⠀⡈⠀⢦⠀⡷⠀⠁⠀⢘⠀⠶⠀⡰⠄⢐⠀⢰⠁⠰⣄⡀⠀⢈⠀⠀⠁⠘⠃⢘⠃⠈
⢫⠂⠊⠈⠂⢊⠃⠀⠩⡶⡁⠶⢈⢦⠅⠀⠘⡵⣁⠀⢈⢰⡍⠀⠈⣵⢎⠀⢀⡱⡭⠀⠀⢥⢎⠀⠀⡱⡮
⠀⠉⠂⠀⠊⠁⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠈⠐⠀⠐⠉⠀⠀⠀⠀⠑⠀⠐⠈⠀⠀⠀⠀⠁⠂⠁⠊
⠀⠠⠐⠒⠠⢀⠀⠀⠀⡠⠐⠒⠀⢄⠀⠀⠀⡠⠒⠀⠐⠠⡀⠀⠀⢀⠄⠒⠂⠤⡀⠀⠀⢀⠄⠒⠒⠠⡀
⡌⣴⣶⢰⣶⣮⠂⠀⡈⠀⢄⠀⢠⠀⠃⠀⠘⠀⠄⢰⠱⡱⠐⠀⢰⢁⣤⡀⢠⣤⢐⠀⠀⠁⢀⠂⠐⣀⠈
⢃⠉⡁⠀⡉⢁⠆⠀⢡⠀⠀⢠⠰⠑⢲⠀⠐⡀⠤⠤⢤⠄⠔⠀⠘⡤⢍⣀⣈⠭⡴⠀⠀⠄⠈⣠⢄⠁⢠
⠀⠑⠂⠄⠐⠁⠀⠀⠀⠁⠂⠤⠐⠉⠁⠀⠀⠈⠑⠤⠜⠁⠀⠀⠀⠈⠒⠨⠀⠊⠀⠀⠀⠈⠐⠠⠄⠂⠁
⠀⡠⠄⠀⠤⡀⠀⠀⠀⡀⠄⠀⠠⣀⠀⠀⠀⡠⠐⠀⠐⠤⡀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⢀⠤⠀⠠⢄
⡌⢀⡀⠀⣀⠈⠆⠀⠘⣤⣤⠀⣤⣤⠂⠀⢐⠔⡑⡄⠜⡒⢑⠀⢠⡇⣀⢠⣄⡀⢷⠀⢠⠁⢀⡀⠀⠀⠑
⢃⠈⢁⣀⠉⢀⠄⠀⢁⠈⣉⣀⣉⠁⡄⠀⠰⡑⠐⣁⣑⠒⡔⠀⠘⡑⢂⡁⣈⠒⠩⠀⠘⡀⠈⠀⡄⡔⠒
⠀⠐⠀⠄⠐⠊⠀⠀⠀⠑⠨⠉⠅⠊⠀⠀⠀⠈⠒⠒⠚⠻⡄⠀⠀⠈⠂⠉⠁⠒⠁⠀⠀⠈⠂⠤⠡⠚⠊
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡶⣆⣠⡴⣦⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣤⡷⢦⣀⡾⠁⣼⠋⠀⢸⠀⣿⠖⡷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣦⣄⣿⠀⡈⣧⠀⠙⢧⣾⠃⠀⠀⣼⡾⠁⢠⡿⠋⣿⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣦⡐⢽⡌⠛⢦⣱⣿⠀⢀⠈⣿⠀⡀⣸⡟⡀⣴⠋⠀⠀⡟⠉⢉⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠉⠉⠛⠻⣄⢀⠙⢿⣧⠸⣆⣿⢠⣇⣿⣵⣾⠁⠀⠀⢀⡷⠞⠋⠉⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡉⠉⠓⠦⣤⡀⡈⢿⡳⣤⣻⣦⣿⣿⣿⣿⣿⣿⣧⢀⡜⢀⣞⣀⣀⣠⣾⣋⡉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠦⣄⡀⠀⣿⣿⣴⣿⣿⣯⢽⢽⣺⣷⣟⣟⢿⣿⣫⠶⢛⡉⠉⠉⠉⣩⣟⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⡀⠀⠈⠉⠛⣛⣿⣿⢯⣿⣬⣽⣮⡯⣷⣗⡯⣯⣿⣗⣊⣁⣀⣤⠴⠛⠁⠀⢈⡭⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠛⠛⢛⣻⣿⣿⣿⣳⡿⣽⣲⣻⣟⣿⣯⣟⣿⡻⣿⣿⡿⠿⢿⣶⡶⠶⠶⢯⣄
⠀⠀⠀⠀⠀⠀⠈⣛⣶⠶⠖⠚⢋⣩⣿⣿⣿⣷⣞⣟⢛⡜⣿⢯⣷⣿⣻⡾⣹⣿⣿⣒⡒⠂⣈⣻⣷⢦⣀⣼⠛
⠀⠀⠀⠀⠀⠀⠀⣩⠟⠛⢛⡿⠋⠀⣀⣀⣤⣿⣿⣽⣟⡾⡯⣟⣟⣯⣿⣿⡏⠀⠘⣷⣾⡋⠉⠀⣀⡤⣿⡯⠿⠆
⠀⠀⠀⠀⠀⠀⠚⠓⠒⣶⠟⠒⢛⣉⣭⠟⠉⢁⣸⣏⠙⠻⣷⣿⣿⣟⠉⠉⢳⣾⠿⠿⣤⣉⠛⢿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡞⠋⢩⡟⠁⠀⠉⠁⠀⢙⣷⡶⢿⠋⢻⢻⣿⡶⠦⠿⣗⠒⠦⡈⠛⣦⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⠋⠉⣙⣛⣛⣿⡏⠸⠁⣿⠀⢸⢸⡇⠳⣄⠀⢿⣤⣤⣤⣤⣬⣟⠋⠁
⢠⣤⣤⣤⠤⠤⠶⠶⠶⠤⠤⢭⣿⣍⣉⠉⠉⠀⠈⢧⡀⠀⣿⠀⠎⢸⠗⢦⣌⠀⠸⡆⠀⠀⠀⠀⠉
⠀⠙⢦⡀⠀⠙⠛⠒⠶⢦⣤⣄⣀⠈⡍⠛⠶⣄⡀⠈⠛⠶⣿⠀⠀⣾⠀⠀⠈⠙⠓⠿
⠀⠀⠀⠙⢦⣄⠀⠀⠀⠉⠉⠉⠙⠛⢷⣦⣀⠈⢳⡄⠀⠀⠘⣦⣀⣿
⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠛⠉⠉⠉⠈⠙⢷⣄⢻⣄⠀⠀⣿⠻⣿⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⢛⡛⠛⠛⠓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⣀⣨⣿⠟⢧⡀⢸⠀⢻⠀⠀⠀⣰⠟⠁⠀⠀⣠⣞⣩⣤⠤⠴⠤⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠙⢷⣄⠻⣾⠃⢸⡆⠀⢰⠏⠀⣠⣴⡞⠋⠉⠛⠓⠂⠀⠀⠀⠀⢀⣠⡤⠶⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠙⠀⢸⣇⣤⣿⡴⠟⠁⠈⠉⠙⠒⠂⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⠋⣡⡿⠷⢦⣄⣀⡀⠀⠀⣀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⡴⠋⠀⠀⠀⠈⠉⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠛⠿⠛⡿⠻⡿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠊⠳⠄⠀⠀⠀⠀⠲⠉⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⠙⠀⡫⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣉⡡⠀⠈⠒⠀⠁⠐⠠⠂⠀⠀⢀⠈⠈⠈⠊⠁⠠⡉⣩⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠒⠒⠚⠈⠉⣀⡀⠀⣀⣀⠀⠈⠉⠀⠇⠒⠐⠁
⠀⠀⠀⠀⠀⢠⠀⠠⠄⠄⠄⠆⠠⠠⠀⢤⠀⠀⠰⠀⠀⠀⠀⠀⢠⠂⢀⠀⠀⠀⠀⠠⠒⠈⠈⠁⠐⠄⠄
⠀⠀⠀⠀⠀⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠌⠐⠀⠀⠒⠀⠀⠈⠁⠀⠀⠈⠈⡁⡀⠀⢀⢈⠈⠁⠀⠈⠈
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢧⡁⢀⠽⠠⠀⠀⢔⠒⠒⠒⡊⢠⢧⢰⢿⡈⡒⠒⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠀⠈⠶⡬⡉⡣⢲⡤⢏⡞⠀⢇⠳⢼⡲⡜⡁⡤⠎⠀⠀⠠⠄⠀⠤
⠀⠀⠀⠄⠠⠃⠂⠀⠀⢄⡀⢀⠠⠀⠀⠀⠣⠐⣀⠀⠀⠑⠒⠈⣡⢔⣀⡀⢀⢠⢭⠴⠀⠀⠀⠀⠰⠮⡭⢀⡀⡀⣐⢠⡈⠐⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢍⠉⠁⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⣄⣀⣠⠄⣴⠀⠀⢀⣀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢉⢼⠩⡧⡘⡡⠀⢀⣸⡈⢦⠀⠀⢸⣻⡇⠀⠀⢸⢟⡇⠀⠀⡰⠃⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢸⠀⡇⡛⠁⠀⢸⡀⠳⡀⠱⡀⠀⣿⣟⣠⣆⣻⣿⠄⠀⠜⠀⡜⢁⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⡵⠀⠀⠀⢣⠙⢆⠙⠢⡀⢠⡙⠙⠃⠘⠛⢙⡠⢈⡄⠊⡠⠊⡼
⠀⠀⠀⠀⠠⣶⣀⠈⢂⠀⠀⠌⠁⣠⡶⠄⠀⠀⠀⠀⠀⠀⢀⠸⢲⠥⢴⡛⠀⠄⣗⠦⠤⣽⣏⠛⡈⠳⡄⢠⡖⢁⠗⣩⣮⠤⠤⢺⠁
⠀⠀⠀⠰⠲⣌⢉⢷⡶⠂⠲⣶⡾⠉⣰⠾⠀⠀⠀⠀⠀⠀⣤⡴⣹⠇⠸⢧⠣⠶⠈⢟⠒⣚⠣⣄⠘⡀⡽⢻⡀⡪⢀⠬⣓⠒⣺⠁
⠀⠀⢀⣀⡀⡘⠻⡖⠁⠀⠀⠘⠾⠋⢁⢀⣠⠀⠀⠀⠀⠠⡤⠖⢹⠂⠀⣧⠙⠲⠂⠀⠉⠣⢖⣁⡍⢲⡁⢈⡗⢸⣈⣒⠄⠋
⠀⠀⢸⠀⠈⠙⠒⡗⠀⠀⠀⠀⢓⠚⠋⠀⠈⡀⠀⠀⠤⠀⣀⡠⠋⠀⠀⠈⠓⣠⠤⣹⡄⠀⠀⠀⠈⠉⡀⠀⠈⠉
⠀⠀⠳⢆⢤⢇⡐⡏⠀⠀⠀⠀⢟⣂⡤⠤⠰⠃⠀⠀⠙⠉⠈⠀⠀⠀⣠⠞⢉⠍⡓⢀⢦⠀⠶⡆⢒⡩⡉⠳⣄
⠀⠀⠠⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡰⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡜⠁⠐⢅⠒⠤⢏⢨⠀⡑⠁⠥⠒⡈⠃⠈⡑⡄
⠀⠀⠈⢱⡊⣯⠀⠀⠀⠀⠀⠀⠀⢠⣿⢱⠈⠀⠀⠀⠀⠀⠀⠀⠰⡠⢃⠸⡼⠐⠢⣀⠍⠀⠈⣇⡔⠂⢣⠜⢘⢄⡠
⠀⠀⠀⢻⡟⢋⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⡃⠀⠀⠀⣀⠤⠂⣡⠔⡀⠀⡀⠀⡌⢠⠀⠀⠀⠀⠀⢇⢰⡀⢀⠀⢀⠲⣄⠐⠤⣀⡀
⠀⠀⠀⠈⠓⠬⢧⠀⠀⠀⠀⠀⠀⡾⠴⠋⠁⠀⠺⠩⢤⡶⢛⣡⠞⣡⢾⣁⠜⠑⠋⠀⠀⠀⠀⠀⠈⠊⠑⣄⡷⢄⠳⣬⣙⠶⡤⠌⠵

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠐⠀⠀⠂⠘⡆⠀⠀⠀⠀⠀⣸⠁⡀⠀⢀⠀⢳⠀⠀⠀⠀⠀⠀⡞⢐⠂⠀⠘⠈⣇⠀⠀⠀⠀⠀⢠⠋⢨⠀⠀⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠘⣄⠈⠓⠚⠁⢠⠇⠀⠀⠀⠀⠀⢹⡀⢁⠤⡌⠁⡼⠀⠀⠀⠀⠀⠀⢧⠘⠶⠶⠞⢀⡏⠀⠀⠀⠀⠀⠸⣄⠀⠰⠆⠰⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠂⠐⠈⢳⡀⠀⠀⠀⠀⠀⢠⠋⠐⠀⠐⠙⢧⠀⠀⠀⠀⠀⠀⡴⠻⠆⠀⠾⠙⡄⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠻⢿⡃
⠀⠀⠀⠀⠀⠀⢸⡀⠡⢀⠀⠜⢀⡇⠀⠀⠀⠀⠀⢺⡈⠀⢀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡇⠂⠀⠂⢀⠂⡗⠀⠀⠀⠀⠀⢸⡀⠐⠂⠐⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠘⡿⣇⣀⣀⡵⠋⠀⠀⠀⠀⠀⠀⠙⢦⣀⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⢤⣐⣂⡤⠎



⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⢰⣶⣋⣉⣉⣳⡦⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢙⢦⡀⠀⠀⠀⠀⠀⣘⡴⠺⠉⠉⠗⢆⣃
⠀⠀⠀⠀⠀⠀⢸⠁⣀⡀⢀⣀⠈⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⡏⢐⣀⢁⣀⡀⡇⠀⠀⠀⠀⠀⢹⠁⣆⣀⣀⣰⠈⡏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠠⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⣄⠐⠤⠐⣠⠞⠀⠀⠀⠀⠀⠀⠳⡌⢙⡿⠿⠳⠃⠀⠀⠀⠀⠀⠘⢧⣘⠛⠉⣁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉


⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⣸⢁⠁⠀⠈⠀⢳⠀⠀⠀⠀⠀⠀⡞⠐⠂⠀⠘⠈⡇⠀⠀⠀⠀⠀⢰⠋⡈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠘⣄⣄⠈⠉⠀⢠⠇⠀⠀⠀⠀⠀⢹⡀⢠⡤⡤⠀⡼⠀⠀⠀⠀⠀⠀⢧⠈⠒⠒⠊⢁⡏⠀⠀⠀⠀⠀⠘⡄⠙⠒⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠦⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠋⢠⠀⢀⠆⠀⢹⠁⠀⡠⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠓⠦⣴⠁⠙⢢⡆⠀⠀⠘⣦⠎⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠓⡄⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣰⠔⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢃⠀⠀⠀⠈⡄⢰⠀⠀⠀⠋⠀⠀⠀⡰⠁⠀⢠⠃⠀⢀⡠⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠠⡒⠉⠉⠉⠳⡡⡀⠀⠀⢸⠀⢣⠀⠀⢰⠀⢀⡞⠀⠀⡰⠁⢀⠴⠋⠈⠁⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣈⡢⣀⠀⠀⠘⢌⡢⡀⣀⡳⠰⠷⠖⠈⡗⠛⢇⡴⠊⡠⠊⠁
⠀⠀⠀⠀⠀⣠⠔⠉⠁⠀⠀⠑⠢⢄⡀⢹⠛⠉⠀⠀⠈⠀⠀⠀⠀⠀⠰⣴⢁⣤⠶⠒⠒⠚⠉⡨⠁
⠀⠀⠀⢀⣚⠢⢤⡤⢀⣀⡀⠀⠒⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡏⣀⣀⡀⠀⢀⡔⠉⠂
⠀⠀⠀⠘⡀⠉⠁⠀⠀⠀⠈⠙⠒⠚⡧⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⣹⠉⠀⠀⠈⡱⠛⢍⠑⠢⠥
⠀⠀⠀⠀⠈⠑⠢⣀⣀⠠⠤⠀⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⣯⣠⠤⠖⠉⠲⡄
⠀⠀⠀⠀⠀⠀⣴⡾⠒⠂⠈⠉⠉⣉⡭⡷⣠⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠑⢄⡀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⣼⠟⠀⠀⢀⡠⠖⣉⡤⠚⠋⢉⡽⠖⠶⣤⠴⣴⠖⢇⠀⠀⠀⠈⡻⠙⡁⠀⠐⠒
⠀⠀⠀⠀⠀⡋⢀⡤⡖⠉⡠⢊⠍⠀⠀⣠⠋⠀⢀⡾⠁⠀⠁⠀⢸⠉⠉⠉⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠛⠁⢰⣧⠋⢀⠎⠀⢠⠊⡇⠀⢀⠏⠆⠀⠀⠸⠀⠈⡧⣀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠸⠀⡰⠁⠀⢹⠀⡈⠀⠘⡀⠀⢠⠀⠀⢃⠀⠉⠑⠀⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠰⠁⠄⢠⠋⢦⡇⠀⠀⡜⢢⠘⡧⡀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠁⠀⠀⠱⡀⡸⠀⠀⠉⠁⠈⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⢹⣿⢹⡏⣿⡏⣿⠙⣿⢹⡏⢻⡏⣿⠙⣿⢹⡏⢻⡏⣿⠛⣿⢹⡟⢻⡏⣿⠛⣿⢹⡟⢻⡏⣿⠛⣿⢹⡟⢹⡏⣿⠛⣿⢹⡟
⣿⢸⣿⢸⡇⣽⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⣼⡷⠟⠛⠛⠶⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⢿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⣀⣿⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠿⣤⣿⢸⡇
⣿⢸⣿⢸⡇⢿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⣸⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇
⣿⢸⣿⢸⡇⣾⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⡇
⣿⢸⣿⢸⡇⢻⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⡇
⣿⢸⣿⢸⡇⣸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⢸⡇
⣿⢸⣿⢸⡇⣿⡇⣿⠀⣿⢸⡇⢸⣇⡿⣄⣿⣼⣧⣼⣇⣿⣀⣿⣸⡇⢸⡕⣶⠚⣿⢦⣀⣀⣀⣠⠔⣷⢲⡶⢶⡟⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⣿⡇⣿⢠⣿⡸⠓⠁⠀⡈⠭⣭⣭⣿⣿⣿⣛⠳⠶⢟⠻⠿⠧⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⣿⡇⣿⡴⠋⠀⣀⡴⠖⠚⠛⠛⠻⢿⣿⡻⢍⠩⡑⠄⠀⠀⠀⠈⠙⠻⣸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⢿⣧⠏⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣟⢦⡀⡈⠀⠀⠀⠀⠠⠀⠀⠘⢧⣸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⡹⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡌⢄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡗⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡘⢄⠘⢮⣳⡀⠀⠀⠀⠀⠀⢰⣼⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⠈⠀⠀⠈⣼⣠⣤⣤⣤⠀⠀⠀⠘⠛⢉⣁⣀⡀⠉⠁⠱⣦⣽⣿⡄⢐⡀⠀⠀⠈⣿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⡟⠀⠀⠀⣰⣿⣀⣤⢦⣄⠁⠀⠀⠀⠰⠋⣹⣍⣻⠇⠀⠀⠈⠦⡽⣷⣈⡇⠀⠀⠀⢿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⡇⠀⠀⢠⣿⣿⠛⠥⠭⠖⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠁⡏⣿⡇⢀⡀⠀⡎⠳⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢄⠀⢸⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠹⢇⢘⣇⠀⢷⡀⠙⢦⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡧⡄⣷⣇⠀⠀⠀⠀⠲⠄⠐⠂⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⣦⣀⠉⠉⣙⠂⠕⣄⢀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⢸⡟⢸⡄⠀⠀⢠⠀⡰⠄⠁⢀⠀⠀⣠⣤⠑⠀⠀⠀⠀⠀⣿⣹⢿⣿⣦⣌⠱⡄⢹⡆⣿⢿⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⠜⠀⠆⣽⢆⠀⠃⠶⠦⠅⠠⠀⠂⠀⠁⠀⠀⠀⠀⠀⢀⣼⡇⡏⠀⢏⠁⠈⠀⣿⢠⣿⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⣇⠀⡈⠰⢣⢸⣷⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣧⠡⡑⣌⡓⣶⣾⣯⣿⠉⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⢦⡀⠀⣿⡾⣿⣟⣳⣄⡀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⣿⠳⠭⣿⣿⡿⢿⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⢸⣿⢸⡇⣺⡟⣦⣈⢌⣺⣧⣽⡏⣿⢐⣤⢲⡞⢿⡁⠀⠀⠀⠀⠀⠀⡟⠀⣠⣿⣾⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇
⣿⣼⣿⣸⣇⣼⣇⣿⣠⣿⣹⣯⣽⣇⣿⣤⣿⣸⣧⣼⣿⡄⠀⠀⠀⠀⣰⣧⣾⣿⣿⣿⣧⣼⣇⣿⣤⣿⣸⣧⣸⣇⣿⣤⣿⣸⣧

⠀⠀⠀⠀⠀⡐⡶⠶⢰⠒⠀⠀⠀⠀⡔⡖⡖⣲⢢⠀⠀⠀⠀⢶⡖⠆⡶⢂⠀⠀⠀⢠⢲⠲⢂⡖⠄
⠀⠀⠀⠀⠀⡇⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⡠⠠⡀⠈⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡔⡇⠘⠀⠐⢸⢢⠀⠀⡐⡀⢺⢄⠓⢸⢢⠀⢠⢺⠀⠂⠀⠂⣐⡀⠀⢠⢺⠐⡀⢐⠀⡗⡄
⠀⠀⠀⠀⠀⠱⡀⠐⢁⠌⠀⠀⠀⠀⠣⡐⠤⢀⠎⠀⠀⠀⠈⢆⠉⠉⡡⠃⠀⠀⠀⠈⢜⠒⠒⡳⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠠⡶⣶⢢⠤⠀⠀⠀⠀⡔⡖⡖⣢⢤⠀⠀⠀⠀⢴⡖⡖⡦⢄⠀⠀⠀⢀⢶⢲⠖⡤⠄
⠀⠀⠀⠀⠀⡇⠁⠀⠈⠀⠀⠀⠀⠀⠀⡁⠀⡁⢸⠀⠀⠀⢰⠈⠠⠠⠁⠀⠀⠀⠀⠘⠈⠀⠀⠁
⠀⠀⠀⠀⡤⡇⠴⣀⡶⢰⢤⠀⢀⠴⡀⡦⠀⡦⢸⢤⠀⢠⢼⠠⠆⡠⠆⠰⢄⠀⢠⢼⠠⠄⠠⠄⡧⡄
⠀⠀⠀⠀⠈⠡⡸⠿⠟⡜⠁⠀⠀⠉⢃⠰⠶⢆⠎⠁⠀⠀⠉⢆⠘⠇⢠⠋⠁⠀⠀⠙⡄⠐⠀⡠⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠈⠁⠈

⣿⡟⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣦⣧⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀
⠀⡐⠡⠀⠈⢣⠀⣔⠥⣀⢌⡂⠀⠊⡀⢀⠉⠄⢠⢪⡤⢤⡕⡀⡐⠁⠀⠀⢡⠀⡜⢡⠀⡌⢂⢀⠊⠀⠀⠙⡄
⠀⠡⡐⠖⠖⡘⠀⢢⡉⠈⢈⠔⠈⢄⠢⠶⢂⠆⠘⡔⠧⠼⡢⠃⠡⡀⠒⠂⡸⠀⢃⠒⠙⢆⠌⠈⢄⠲⠰⢂⠃
⠀⠀⠈⣉⠁⠀⠀⠀⠈⣉⠁⠀⠀⠀⢉⡉⠀⠀⠀⠀⢉⡉⠀⠀⠀⠈⢉⠉⠀⠀⠀⠈⣉⠁⠀⠀⠀⢉⡉
⠀⡐⢉⠀⡈⢢⠀⢔⣁⣀⢌⠂⠀⠊⣁⢀⡑⠄⢠⠊⡀⢀⠑⡄⡰⢉⠀⢈⢢⠀⠔⣥⣠⣬⢂⢀⠊⡁⢀⠑⡄
⠀⢣⡰⣖⠖⡰⠀⢂⠙⠭⢊⡔⠈⢄⢶⡲⢂⠆⠘⡀⠀⠆⢀⠃⠡⡀⠒⠂⡰⠀⢃⠀⠸⢁⠌⠘⢄⠒⠲⢧⠇
⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁
⠀⡰⠉⠀⠉⢢⠀⡔⢉⠀⡉⢂⠀⠎⣁⢈⡑⡄⢠⢊⡁⢈⡑⡀⠠⠊⠀⠉⢢⠀⡔⢉⠀⡉⢆⢀⠞⠁⠈⠑⡄
⠀⢣⠠⠤⠖⡸⠀⢇⠀⠰⠀⡐⠸⡇⠶⠲⢊⠗⠘⣼⠷⠿⣧⠃⠡⡰⠆⠦⡸⠐⢟⠐⠐⠀⡿⠘⡄⠁⠄⢀⠆
⠀⠀⠉⠀⠉⠀⠀⠀⠉⠀⠉⠀⠀⠀⠁⠀⠁⠀⠀⠈⠁⠈⠁⠀⠀⠈⠀⠈⠀⠀⠀⠉⠀⠉⠀⠀⠈⠁⠈⠁
⠀⠠⠊⠉⠁⢢⠀⡐⢉⠉⡑⢆⠀⠔⠉⠉⠑⡄⢀⠂⠉⠉⠠⡀⠠⢊⡉⣉⢢⠀⡔⢉⠉⡑⢄⠀⠔⠉⠉⠑⡄
⠀⢃⠐⣶⠆⡸⠀⢟⠨⠲⠅⡿⠀⡀⠠⠂⢀⠄⠸⡀⠅⠨⢀⠃⢣⡈⠒⠃⠐⠀⠇⠶⠲⠆⡼⠸⡗⢶⣲⢖⡷
⠀⠀⠁⠒⠈⠀⠀⠀⠁⠒⠈⠀⠀⠈⠑⠂⠉⠀⠀⠈⠐⠂⠁⠀⠀⠁⠒⠊⠀⠀⠀⠐⠛⠋⠀⠀⠈⠛⠛⠉
⠀⠠⠊⠉⠁⢂⠀⡔⠈⠉⠑⣤⠀⠔⡉⢉⠐⡄⢀⢖⡉⢉⡢⡀⠠⠊⠉⠁⢢⠀⡐⢈⠉⡑⠄⠀⢔⡉⢉⡐⡀
⠀⢃⠠⠀⠤⡸⠀⢇⠴⠴⠄⡙⠀⡀⢄⣠⠄⠄⠸⡑⠪⠕⢃⠇⢂⠨⣀⡠⢸⠀⢇⠨⣤⠅⡘⠘⡘⠨⠕⠊⠇
⠀⠀⠑⠒⠊⠁⠀⠈⠐⠒⠈⠀⠀⠈⠐⠒⠈⠀⠀⠈⠒⠒⠁⠀⠀⠁⠒⠂⠁⠀⠈⠑⠒⠊⠀⠀⠈⠐⠒⠉
⠀⡠⢊⠀⡑⣤⡀⡠⠊⠈⠐⠄⠀⡔⠈⠈⠲⡀⢀⠔⠀⠁⢢⡀⠠⠂⠁⠑⢦⠀⡠⠊⠈⠐⠄⠀⠔⠈⠈⠲⡀
⠀⢇⠓⠋⠒⡹⠁⠆⠈⠀⠁⡠⠐⡀⢭⢬⠅⡄⠨⠀⠀⡄⢨⠝⢃⠈⠅⠍⢸⠀⡇⠨⠤⠅⡘⠘⡀⠥⢤⣆⡇
⠀⠀⠑⠀⠂⠁⠀⠈⠐⠐⠊⠁⠀⠈⠒⠐⠊⠀⠀⠁⠒⠒⠁⠀⠀⠑⠂⠒⠁⠀⠈⠒⠒⠊⠀⠀⠈⠂⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠶⠶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠶⠶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⣸⡿⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⢿⡿⠂⠀⠀⠀⠀⠈⣿⡆⠀⠀⣾⡏⠀⠀⠀⠀⠀⠺⣿⠇⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢻⣧⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣾⡏⠀⠈⣿⡆⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠉⠙⠻⢷⣄⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠈⢿⣆⠀⠀⠀⠘⠿⣦⣄⣀⠀⢀⣀⣠⣴⠟⠁⠀⠀⠀⣼⡿⠀⠀⠀⠸⣿⡄⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⣾⠏
⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠙⢿⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣶⣶⣤⣤⣶⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣦⣤⣴⣶⣶⠿⠟⠉

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⢶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⢀⠇⢨⡍⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⡄⠓⢄⠀⠣⠤⢴⠤⠬⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡆⢀⡖⢊⡴⡳⢤⠈⣆⡀⠀⠀⠸⢲⣽⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣤⣤⡀⠈⠁⠘⡧⣦⢱⢁⠴⠃⣼⢉⠆⠀⠳⣿⡯⠊⠀⠀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⢀⠸⣄⢀⡝⠀⢀⠤⣰⡏⠉⠘⠦⢾⠣⣀⠇⠀⠀⠇⠀⠀⠀⠀⢨⣿⣼⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⢾⣧⠈⢃⡀⢀⡧⢠⠟⢉⠗⠀⢀⠴⣦⠖⢦⠀⠀⣼⠀⢀⠀⢀⠼⢿⣿⣝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢷⠿⠋⠲⣼⡇⡋⣠⠼⡁⢸⠀⠀⢈⠆⠾⠄⢏⢠⡀⣧⣴⣿⣔⡅⠀⠀⠈⠊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢷⠜⠸⣠⣤⢾⡣⡈⢴⡢⢬⡙⡄⠀⢧⡠⢶⠦⠴⠉⢿⣿⣿⣟⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢧⣱⡥⢱⠘⢎⢯⠽⠁⠰⠀⡖⢄⢸⣠⠤⡄⢈⠟⠛⠋⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡴⠁⠈⡵⠋⠱⣄⣽⣴⣟⡀⡇⠑⢌⣿⠧⠊⢀⠎⣀⣴⣾⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡤⣀⣴⠋⠓⠛⣾⣧⢱⢻⣦⣷⡺⢢⠞⠋⡹⣯⢻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡴⡖⢢⠛⠿⢯⠘⡄⢹⠁⡴⠁⠀⠀⢧⠋⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠜⠓⠒⠒⢧⡇⣺⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠈⠀⡀⠀⠀⠀⣀⡤⠄⢀⣰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠀⠀⢪⠤⢴⠍⠀⢀⣼⡁⠀⠀⣼⠃⢐⣳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⢠⠂⠂⠀⡋⠀⣈⢻⡿⠖⠛⠛⢳⣦⣾⣿⡇⢳⠀⣠⠆⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠘⢀⣧⢀⡄⠀⠀⠀⠉⠀⠇⠀⠃⠶⣬⣿⢟⣿⡟⠀⠲⠁⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣯⠈⠄⠀⣿⡆⠎⠀⣰⠀⣾⣦⣾⣿⣿⡿⢆⠀⠀⠀⡠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣥⢼⡄⠈⣻⠄⠀⠀⠀⠀⣿⣿⣿⢾⣿⢨⡿⣢⠄⠘⠑⣠⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠘⠳⠤⠇⠀⠈⢱⠀⡔⠀⠑⠁⣸⣿⣿⣾⡟⠀⠀⠀⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⠀⠎⠀⠀⠀⡄⠸⣧⠀⠘⢋⠿⣼⣿⠇⠀⠂⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠀⠀⠀⣄⣧⠀⠉⢄⣤⣯⣤⠸⠃⠀⠐⢡⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠄⢄⠆⠀⠀⠘⠙⢧⠀⠈⠠⣸⡿⠁⣀⠀⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢅⠀⠰⠦⠄⢴⣤⣢⣄⣠⢿⠅⣀⠄⠈⠄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢀⠀⠀⠀⡩⠋⣉⣸⠅⠈⡀⢄⡾⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⣠⡈⣆⠀⠀⡤⠾⠋⠀⠀⢤⡤⠎⡀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⡀⠈⠈⠉⠁⠀⣀⣀⡴⠟⠋⣠⡔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢑⢖⠒⣛⢚⣿⠏⠃⣠⡴⣠⠍⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠚⣇⠀⠄⢈⠤⠟⠉⠁⠀⠀⠀⠀⠁⠔⠐⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⠊⠁⠀⠀⠀⠀⢀⠴⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⢇⣁⣶⠒⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢑⠁⠀⢄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠸⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢘⠠⠀⠀⠄⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠴⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢀⡀⠀⠥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⢏⣤⠶⡉⠄⡄⢰⡄⠠⠆⠀⣀⣘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⠴⠞⠀⠀⠂⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣌⣠⠉⣌⠀⢟⠉⣥⠄⡀⡤⠠⣁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠺⠷⠆⠀⢈⠀⠟⠀⠀⠀⠄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⠟⠐⢟⢒⣮⡛⣤⠴⠅⠈⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠒⠭⠁⣰⣆⠀⡾⠂⠁⢰⠀⣀⢀⣤⢣⣄⡴⠖⠀⠀⠀⠀⠀⠀⠊⠀⢁⠷⡁⠙⠘⠋⠀⠀⠈⠁
⠀⠀⠀⣀⠀⣄⠀⠀⣀⠰⢄⡀⠀⠈⠃⠹⣧⠀⠀⢹⡧⠉⡮⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠉⠔⠃⡈⢣⣤⠁⡀⠀⢀⡀⣿⠂⠁⠸⠏⠈⠑⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠷⠞⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢙⣿⠀⠀⠈⠱⣿⠀⣄⠀⠂⢹⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣧⡖⠓
⠀⠀⠀⠄⡸⠰⠆⠴⠆⠀⠄⡏⠁⠀⠀⠐⣿⣧⢽⣿⣇⢐⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠊
⠀⠀⠀⠀⠁⠀⠀⠐⠴⢈⣿⣧⣀⣤⠀⠀⣿⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠐⠋⠉⠉⠀⠒⠙⠵⠶⢶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⢤⠀⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡑⠒⠀⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⠀⠀⢀⣀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⣦⣷⠈⠋⣷⢀⡄⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠁⠀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⢕⣰⡞⠂⠈⣣⣄⡀⢇⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⢀⢪⣍⡼⣦⠟⢙⣻⠗⠈⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⣨⣿⣌⠳⠂⠛⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⡀⢀⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⡄⠰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠦⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠄⠀⠀⡾⡆⣐⡀⠺⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢠⡐⠂⢰⠐⠄⢠⠀⡆⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣐⠀⡀⠀⢱⣎⣈⠐⠡⣀⡨⡅⠀⠉⠠⡀⢀⠴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠠⡆⠀⡂⠙⣏⡥⢀⠛⢿⢏⠀⠃⣤⡀⣿⡏⡄⠧⢀⢀⠁⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢠⠀⣜⣠⢾⠛⡏⢫⠿⣦⣼⠒⡿⣠⡁⠀⠷⣷⠂⠜⡠⠁⠖⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣠⢉⣽⡈⢛⣶⣬⣏⠘⢁⣍⠿⢻⣿⡴⠛⢻⣿⡅⡲⢎⣽⣇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢘⡟⢃⣞⣱⣧⣿⣵⣾⣷⣞⣿⣿⣽⡤⣿⣬⣤⣤⠜⢃⡈⡛⠂⠊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠚⢆⠈⣋⣀⡍⢫⣯⣽⡍⠥⣿⣿⣿⣿⣿⣷⣿⣞⣷⣾⣿⢂⣻⣶⣎⡹⡇⢀⢦⡆⠁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠹⠀⢠⣿⠈⡙⠘⣬⣿⣷⣶⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⢻⣏⣻⡓⢻⠮⣨⣁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⢗⣁⣈⢓⣻⣿⣿⣿⣯⠿⣾⣷⣾⣯⣈⣿⣿⡶⣟⣻⡿⣿⠛⢫⣶⡄⢞⠣⢙⠁⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡈⢠⡏⠉⣴⣡⣽⣯⣷⣮⣿⣴⣯⣿⣿⣿⣿⣿⣟⣛⣿⣿⠟⡿⣋⣿⣵⣦⢎⠟⣈⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⡴⢣⡍⢟⣲⠼⣿⠿⣿⣯⣾⣿⣿⣿⣟⣺⣿⣿⣇⡟⠸⣧⡟⢬⠉⢁⡀⠤⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⢊⠋⠉⠷⣬⣿⢶⣸⣻⡿⣿⣿⠻⣿⣿⢛⣽⣿⣛⣿⡅⠿⣞⢃⠁⣸⣻⠃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢂⢃⡀⢽⣯⣀⢾⣽⢮⣤⡤⣿⣿⡟⣿⢹⣿⡷⣼⣿⣟⠻⠟⢟⡰⠅⠱⠒⠊⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌⡙⠳⠆⡸⠚⠫⠙⢻⣾⢗⣾⠟⣟⠱⢦⡽⢻⢷⣬⡸⢋⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠠⠓⠃⠒⠉⣼⣠⣥⡴⢦⠐⣀⣼⢿⡐⢻⣯⡴⣤⠐⠴⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⠠⠒⡀⠉⢻⠳⠛⠊⢁⡱⠥⠚⠙⠂⡁⠀⠀⢀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠋⠁⡀⠁⡀⠈⠴⢆⢉⡆⠹⠄⠋⠒⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠤⠄⠂⠐⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀



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

⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⣠⣽⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⡯⡀
⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠵
⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠈⢩⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠋⠟⠋⠉⠻⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⡿⠟⠉⠻⠏⠳⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣼⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⣿⣿⣿⣿⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⣿⣿⣿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠠⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡺⢭⠿⢛⣻⠿⠯⣅⣶⣭⡛⣓⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣉⣉⣩⠽⠟⠋⠉⠀⠀⠀⠀⠈⠉⠙⠒⠓⢄⢻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠈⠣⣙⣏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠅⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀⣹⠘⢳⡀⠀⠀⠀⠈⢻⡈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡰⣠⠏⣀⡀⠀⠀⠀⠀⠀⠀⡵⠀⠉⠘⠦⡜⢦⡄⠓⠦⣤⣤⡀⠀⢧⣱⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡖⠁⣠⠇⠙⡹⠒⠢⣄⣠⠤⠭⣒⣦⠋⠐⠳⣼⠀⠀⠀⠀⢀⠇⣀⠈⣏⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡆⡇⠀⠹⢄⡚⠁⠋⡁⡎⠁⣂⢑⠜⠁⣀⠀⠀⣨⣤⣤⣀⡴⠿⢏⣉⠗⣸⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⡇⡔⠋⠋⡉⠷⣀⠀⡳⡀⡂⠊⢾⣹⣴⡂⠎⢻⣄⢸⡥⠄⠀⠀⣹⢠⢇⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠖⠧⣇⠀⣠⠀⣀⠉⠀⠀⠠⠀⡠⠓⠚⣿⠭⣆⢀⠈⠙⣄⣀⡀⢀⣉⡉⢭⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣀⣠⣷⣿⡰⠃⠀⠀⠀⠀⡖⠀⠀⠀⠀⠙⢻⡯⣈⠎⢀⠔⠚⠛⠁⠄⠫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠤⣐⠀⠀⢀⡎⠁⠀⠀⠀⣼⠋⠡⡑⡀⠀⠀⢀⡌⠭⢽⠀⡄⠎⠉⠆⢨⢨⡄⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⡔⠉⡖⡀⠈⡁⠦⠂⠉⠀⠳⡤⡴⡜⠁⠙⠺⡅⠐⢈⠘⢢⡑⠒⢊⡠⢣⠀⠈⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⡄⠣⠄⠰⢡⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢈⠄⠀⠠⡤⠊⠉⢣⠀⢙⠈⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣴⡏⠜⠂⠲⠓⢠⣜⣄⠀⡠⢎⢀⠀⠀⣠⠴⣉⢌⠋⢠⠓⢋⢠⠈⠀⠩⠀⡷⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠈⡇⠈⡐⠈⠒⠁⢅⠀⠈⠀⡈⠀⠀⠋⢠⢹⢻⢫⠕⠨⠀⠀⠀⠉⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⠀⠀⠀⢁⠨⠄⠀⢀⠀⠀⠀⠈⢙⠈⢡⠤⠐⠁⠀⢐⡈⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡂⠀⠠⣠⠃⠀⠉⠀⠀⠀⠑⠁⠀⠀⠀⠀⠄⠂⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠀⠀⠀⠀⠁⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⠠⠄⠀⠀⠀⠈⠅⠀⣀⡤⠤⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠙⠛⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡎⣽⠹⠏⣹⠊⠂⠀⠀⠀⠀⢠⢎⡟⢹⠉⣷⠙⡆⠀⠀⠀⠀⢰⢫⡏⠽⢉⡗⠱⠀⠀⠀⠀⠀⡰⣹⠏⡏⢩⡎⢳
⠀⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⣀⠀⡄⠀⠀⠀⠀⢸⠀⠁⠀⠀⠁⠀⡇⠀⠀⠀⠀⡌⠈⢀⡀⣀⠁⢸⠀⠀⠀⠀⠀⡇⠈⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡄⢰⡂⠀⣀⠀⣇⡀⠀⠀⢀⣸⠀⣐⠄⢰⣀⢀⣃⠀⠀⠀⢀⣃⠀⡁⠀⢀⡁⢸⣀⠀⠀⠀⣀⡇⢀⡈⠈⢃⠀⣼⡀
⠀⠀⠀⠀⠀⠸⠬⡇⠀⠀⢀⡈⢀⠧⠜⠀⠀⠣⢼⡀⢨⠛⢢⠀⢸⠥⠇⠀⠐⠧⢽⠀⣀⣀⣀⠀⣸⠤⠃⠀⠘⠤⢇⢠⠔⠒⠢⡀⡯⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⣀⠜⠀⠀⠀⠀⠀⠀⠣⡈⠢⠚⣠⠎⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⢌⠊⠉⢛⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡏⡾⠐⠇⢼⠉⠃⠀⠀⠀⠀⢠⠣⡟⠸⠀⡿⠉⡆⠀⠀⠀⠀⢸⢱⠇⠺⠠⡏⠙⠀⠀⠀⠀⠀⡜⢼⠇⠏⢰⠏⢹
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⣀⠀⠀⡀⠀⡇⠀⠀⠀⠀⡄⠀⠠⠂⠢⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣸⡆⣤⡆⠐⣥⠀⣧⣀⠀⠀⣀⣼⠀⢤⠀⠠⣄⢠⣥⡀⠀⠀⣀⣥⢠⢤⠀⠤⡄⢸⣄⡀⠀⢀⣠⡇⢠⡄⠀⣠⡄⣾⣀
⠀⠀⠀⠀⠀⠙⠒⡇⢰⣾⣿⣦⢀⠗⠊⠀⠀⠑⠺⡄⢙⡤⣤⡁⢸⠒⠋⠀⠈⠓⢺⠀⠀⣾⠀⠀⡼⠒⠁⠀⠈⠒⢣⠀⠀⡠⠄⠀⡗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⣉⣉⡡⠊⠀⠀⠀⠀⠀⠀⠑⢌⡉⣉⡴⠃⠀⠀⠀⠀⠀⠀⠳⣄⣈⣀⠜⠁⠀⠀⠀⠀⠀⠈⠢⣀⢀⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡌⠀⣚⠋⠋⠀⣀⡨⣶⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠠⠶⠀⠄⣤⠶⠉⠀⠀⠀⡕⠰⡁⠈⡁⠀⠀⠈⢢⡅⠐⢤
⠀⠀⠀⠠⢠⡄⠐⠠⠠⠈⠙⠁⠄⠀⠀⠀⢰⣤⠄⠁⠌⠈⠉⠭⠀⠀⠀⠀⡍⠀⠀⠠⠀⠀⠀⢰⡄⠀⠀⢳⡦⢘⠀⠀⡀⠀⠀⢐⡀⠀⣄⡄
⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⠀⢁⡄⠀⠀⠈⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠁⠀⢀⠀⠤⠔⠀⠄⠀⠀⠘
⠀⠀⠀⠀⠀⣀⣠⠍⠁⠤⠬⠴⠞⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⢁⡀⢙⠲⣀⣖⠀⠀⠀⠀⠀⢂⠀⣠⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠
⠀⠀⠀⠀⠀⣴⠀⠀⡀⠈⠁⠈⠻⠀⠀⠀⠸⠄⠈⠀⠁⡁⠁⠿⠀⠀⠀⠀⢠⠂⠀⠀⠀⠈⠁⣤⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠉⠀⢀
⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠀⠈⠠⠀⠀⠀⠵⠀⠀⠀⠐⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠀⠀⠀⠀⠀⠈⠰⠞⠁⡠⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⡠⠀⠀⠀⠀⠀⠠⠇⠴⠄⠉⠀⠴⠤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠁⠐⡀⠀⠀⠀⠀⠐⠀⡁⠈⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⠆⠀⠀⠀⢀⣡⣖⣲⣠⣢⡆
⠀⠀⠀⠀⠀⠀⣶⠀⣁⠀⠀⠄⠐⣧⡀⠀⠀⣀⠀⡀⠀⠀⡈⠐⡄⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠘⠇⠐⠀⠐⠋⠙⠻⠟
⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠀⠐⠀⠐⠀⠀⣗⠀⠀⠀⠀⢈⠀⠁⠄⠈⠀⢀⠄⠀⠀⠀⠀⠀⠠⣀⠄⠀⠠⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡨⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠤⠀⢀⠁⠀⠀⠀⠀⠀⠂⡀⠀⠈⠀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⣄⣀⠀⠙⠂⠀⠀⠀⠠⠀⢄⣀⣀⣀⠀⠀⠀⠀⠀⣤⠀⠀⠒⠀⠐⢠⠀⡄⠀⠀⠀⡄⡖⣀⠆⡄⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠸⠾⡁⠀⠈⠀⠀⢉⢁⡠⠀⠀⠀⡝⢋⠀⠉⠩⠁⠡⠆⡄⠀⠀⠙⠀⠯⠀⠠⠌⠈⡶⠇⠀⠀⠀⠁⠀⠡⠀⠈⠂⠛⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠈⠀⣀⣀⣀⠀⠀⠇⠀⠀⠀⠀⠒⡀⠀⡠⠄⠀⡘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠈⠉⢁⡀⠜⠀⠀⠀⠀⠀⠀⠐⠀⠩⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠤⠉⣠⠀⠀⠀⠀⠀⠠⠒⠀⢈⠀⠈⠳⡀⠀⠀⠀⠀⢀⡀⢤⢀⡀⡀⢀⠀⠀⢐⠁⢈⠽⠃⠨⠔⠢⡙
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠈⣆⡗⠀⠀⠀⠃⠀⠀⠀⢈⠈⢑⢒⠀⠀⠀⢠⠾⠂⠀⠈⠁⠀⢋⠀⠀⠈⢰⠀⠀⠀⠀⠀⠰⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠘⡋⠀⢂⠀⠒⠀⠈⣄⠀⠀⠀⠙⡀⠀⣀⢀⡆⠀⠀⠀⠀⠐⢤⠃⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⠒⠀⠀⡠⠂⠀⠀⠀⠀⠀⡀⠂⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠐⠀⣀⠙⣁⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠀⡄⢀⠇⢰⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡀⠀⠂⠠
⠀⠀⠀⠀⢀⠑⠀⡣⠸⡸⠀⠎⠈⠈⣠⠄⠀⠀⠀⠀⠀⠊⠀⣀⠑⠄⠄⠀⢈⠀⠀⠂⠀⠀⠀⢠⡀⠀⠛⠁⣀⡀⠀⡠⠊⢁
⠀⠀⠀⠀⠀⠉⠒⢬⡤⠋⠉⠑⢶⠊⠠⠔⠚⠉⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠧⠀⠁⡔⠁⠀⠀⠑⡈⠁
⠀⠀⠀⠈⠀⠩⠄⠲⣇⠀⠀⠀⢀⠒⠒⠒⠒⠀⠀⢀⠏⠀⠐⠀⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠀⢠⠀⢢⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠠⠔⠚⢉⡌⡲⠄⠐⢯⡉⠒⠄⠀⠀⠀⠀⠀⠈⣰⠂⠀⠐⠀⠈⠠⣀⢀⠀⠀⠀⠈⢄⠈⠃⠠⠉⠀⡈⠄⠀⡀
⠀⠀⠀⠀⠐⠉⠐⡋⢀⡏⠀⠰⠀⠱⣄⠰⠄⠀⠀⠀⠀⠀⢇⠀⠈⠈⢦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡈⠀⠗⠳⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠈⢁⣀⡈⠀⠀⠀⡀⠃⢀⡀⠃⠁⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠠⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠈⣠⣄⠁⠀⠀⠀⠈⢁⣄⠈⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠁⢠⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢆⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠲⠶⠖⠲⠶⠆⠀⠀⠠⠆⠀⠔⠀⠀⠀⠁⠈⠂⠀⠄⠀⠀⠀⢸⠄⠀⡧⠀⠀⠀⠘⠾⠂⠻⠗
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠘⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠘⢧⢄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠁⠀⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠬⣯⠁⠀⠰⠂⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠛⠀⠠⢦⡔⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣀⡀⢨⠍⠙⠔⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣐⣸⠂⡘⢛⣡⡀⠉⠐⠆⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⢀⠾⡒⠙⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠡⠆⣴⠃⠀⠯⢼⠗⠀⠀⢀⡀⠀⠸⢶⣄⡙⢦⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣳⣶⠀⠀⠀⠀⠸⣆⣱⡿⣺⣧⡼⢃⡨⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠺⠓⣤⣶⣼⡾⢿⣿⡯⢿⣖⣿⣿⣦⡠⠀⠀⠀⠠⠕⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⢀⣐⣭⠈⠑⣿⣼⣿⣗⠀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣽⣗⣠⢫⡟⢡⣀⣀⣿⣿⣿⣿⣟⠀⠤⡀⠀⠀⠢⠔⠐⠀⠀⢀⡠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣧⣀⣿⣿⣿⣿⡿⠿⠉⠀⠀⠈⠢⠒⠄⠀⡀⠠⠐⡑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⠟⠛⠈⣾⢛⡛⠹⢦⠀⠀⠀⠀⠀⠀⠀⠃⠁⢀⠠⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠜⡙⠀⠀⠀⠩⣤⡀⣀⡻⠆⠀⠀⠀⢀⡀⠀⠈⢀⠀⠀⠀⠰⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠟⠁⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⢀⠀⡤⠣⠆⠀⠜⠀⠀⠀⠀⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠠⠀⡐⠀⠀⠠⠃⠀⠀⠸⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣿⠌⡌⣷
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⢠⣿⣿⢣⡼⣿⢈⣧⠘⣷
⠀⠀⢠⣄⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠂⠀⠀⢠⢳⣜⣧⠀⠀⣠⣿⣿⠟⣸⡇⣿⢸⣷⢲⠈⠃
⠀⠀⠉⡀⠀⠀⠀⠀⠦⡐⠐⠂⡀⠀⠀⠰⢊⣰⢃⠀⠀⠀⠘⣷⠻⠎⣡⣴⣿⡿⡃⣴⡘⢁⠏⢸⣿⢸⡆⢰⡄
⠀⢀⠁⠁⠀⠀⠈⠘⠀⢣⡠⠀⡞⠢⠄⣀⡀⠀⠀⠀⠁⠀⢿⣿⣿⡷⠿⢟⢻⣾⣷⡙⢡⣿⢠⢲⣏⠸⡇⣧⠁
⠀⠟⢐⠀⠀⠀⠈⠘⠀⠀⠀⠔⠁⡜⠀⠄⠈⠎⠒⠀⠀⠀⠀⢫⣶⣾⡏⣿⠿⡷⠉⣴⣼⣿⢸⢻⣿⢦⣌⢹⡀
⠀⡆⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⢤⠴⠣⠀⠀⠀⠀⠀⠘⣣⣙⢃⡌⣴⢰⣿⣻⠆⡟⣾⣻⣿⢸⣿⠘⡇
⠐⠁⣤⠀⢨⠀⢠⠀⢡⡰⡀⡄⠠⠀⢧⠈⠂⠣⠀⠀⠀⠀⠀⠀⠫⠏⣿⢣⣿⢸⡇⡿⡐⢰⣿⢹⣿⢸⣿⠀⣧
⠀⢠⠹⠀⠀⠀⢨⠀⠀⠀⠛⠱⡧⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠸⢹⠸⢡⡄⣿⠈⣿⣼⡏⣿⣿⢀⢹
⠀⡣⠈⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣻⠇⣿⢰⡏⣿⠇⣿⡋⣾⡌
⠀⠀⢠⠃⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠘⢱⡟⠀⢿⠇⢫⡄
⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡄⡾⠁⠆⠘⠀⠈⡃
⠀⠀⠂⠀⡜⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡇⠀⡾⠀⠀⡼⡀⡁
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⣡⠀⡇⢽⡇
⠀⠀⠀⠈⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⡏⣴⡆⠻
⠀⠀⠀⡀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢃⣼⡟⣰⡟⠀⠰
⠀⠀⠘⠀⠀⠀⡀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣾⠟⢠⠟⣴⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⢀⠠⣾⣿⠘⣿⡇
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣽⣿⠸⣿⣿⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠏⡠⢐⡆⢄⠹⡆⠀⠀⠀⠀⠀⣸⠁⠀⠑⠁⠀⢷⠀⠀⠀⠀⠀⠀⡞⢤⣀⠀⣠⠌⡇⠀⠀⠀⠀⠀⢰⡃⠀⠂⠐⠂⡙⡄
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠁⣠⠇⠀⠀⠀⠀⠀⢹⡀⠀⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⢧⠀⠁⠀⡥⢠⡇⠀⠀⠀⠀⠀⠸⣄⠀⣤⡄⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠾⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠚⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠑⠂⠐⠈⢳⡀⠀⠀⠀⠀⠀⢠⡈⣁⠖⢎⠉⣰⠀⠀⠀⠀⠀⠀⡴⠋⠂⠀⠸⠙⡄⠀⠀⠀⠀⠀⢀⡞⣁⠀⠀⣈⢳⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠻⣿⠿⠿⢀⡇⠀⠀⠀⠀⠀⢺⡀⣁⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠀⠀⡗⠀⠀⠀⠀⠀⢸⡄⢉⣥⣬⡁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⢤⣐⣂⡴⠞⠀⠀⠀⠀⠀⠀⠘⠡⣤⣀⣀⡴⢋⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠱⢭⡀⢀⡭⠞



⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⣠⢞⡉⠉⢙⢢⡀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠉⠓⣆
⠀⠀⠀⠀⠀⠀⢸⠁⢨⡤⠤⡅⠈⡇⠀⠀⠀⠀⠀⣸⠶⠆⡘⠁⠠⢸⠀⠀⠀⠀⠀⠀⡇⠀⣄⣀⣄⠀⣧⠀⠀⠀⠀⠀⢸⣁⣙⣃⣘⣋⣈⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⣄⠀⠓⠶⣂⠞⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠘⢟⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉


⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡖⠲⣤⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠈⠠⡔⠉⠙⡄⠀⠀⠀⠀⠀⣸⠟⣉⠉⢈⡛⢷⠀⠀⠀⠀⠀⠀⡞⠁⠆⠆⠤⠈⣇⠀⠀⠀⠀⠀⢠⠇⠘⠇⠸⠇⠸⡄
⠀⠀⠀⠀⠀⠀⠘⣆⠠⠤⠤⠌⢠⠇⠀⠀⠀⠀⠀⢿⡀⠀⣀⡀⠀⣼⠀⠀⠀⠀⠀⠀⢷⠂⠤⠀⠀⢀⡏⠀⠀⠀⠀⠀⠘⡆⢢⣄⣠⡔⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣻⣷⣦⣽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠓⠶⣿⣿⣟⣿⣿⣿⣿⣿⣦⣤⡀⠀⢀⠠⢀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣷⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣦⢸⣷⣤⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⢿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠿⠛⠀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⢻⣿⣿⣷⣿⣦⣀⠀⠀⣸⣿⣿⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⢿⣿⣿⡤⠀⣼⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣨⠏⠀⣿⣿⣅⢀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣰⣿⣿⣿⣿⣇⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡟⠙⠁⠀⢹⣿⣿⣿⣿⣿⠀⠀⠹⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠴⠶⠷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠍⠀⠒⠀⢉⣙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⠀⢀
⠀⠀⠀⠀⢰⢁⢂⠐⢀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣘⣀⡀⠐
⠀⠀⠀⠉⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠉⢠⣶⣿⠛⢃⠅
⠀⠀⠀⠀⠀⠀⠐⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣐⠐⠂⡀⡀⠀⢀⠁⡈⢿⠯⡁⢘⡙⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠤⠀⠀⠀⠀⠄⠤⣀⣨⣤⣤⣄⡁⠘⢄⠀⠁⠱⠠⠌⠋⠿⣇
⠀⠀⠀⠀⠀⡀⠀⢻⡀⠈⢀⣀⡁⠀⢈⡄⠢⡾⣽⣿⣷⣿⣷⠬⠨⡂⠀⠀⠀⠀⠀⠀⢻⠀⢀⡀⠀⠀⡀
⠀⢀⠐⠀⠀⡒⠀⣸⠁⠀⠀⠀⠀⠀⠀⠂⡸⢿⣿⣿⣿⣿⣿⠀⡀⠄⠀⠀⠀⠀⠄⠀⠘⡶⠁⠐⠠⠀⠂
⠀⠀⠈⠉⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠂⡤⠔⠟⠛⠛⠉⠀⠱⠀⠀⠠⢀⣀⡀⠌⠀⣰⡇
⠀⠀⠀⠀⠀⠠⠀⢸⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⢠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠂⠀⠀⠀⡀⠀⠀⠀⠠⡂⠀⠇⠀⡢
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⡿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣴⠖⢀⠉⢀⠀⣀⢀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣄⠀⠨⣿⣿⣧⣙⣱⣶⡆⢾⣿⠀⡵⠀⠀⠀⠛⠀⠀⢀⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⢁⡄⠀⠿⠷⠀⠽⣿⠃⢀⣴⣿⠏⢀⠀⠈⠀⢀⣮⡄⢀⣼⠔⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠂⢀⡺⠛⠉⠀⠀⠈⠔⠞⢉⠁⠰⠿⢣⣤⠀⢚⣭⣵⣿⣟⣵⣶⡿⢋⠀⠸⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠟⢟⠻⠿⢻⡾⠆⣠⣿⣿⠿⠀⠀⠏⠰⠾⢿⣿⣯⣿⣿⠟⠀⡼⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡤⠀⠀⠈⠁⠀⠀⠀⠀⠐⣄⣠⡟⣿⡗⠓⠨⠄⠀⠀⠂⠀⠙⠿⣻⣿⠀⠚⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⣙⠇⠀⠀⠙⢈⢛⣻⡗⠀⣀⣉⣯⣷⣤⢡⡶⢴⡷⠢⠆⠀⠀⠀⠀⢐⡿⠁⣰⣦⢦⣤⢄⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠌⠁⠀⣀⠿⠀⣯⠽⡿⢩⠋⠀⢶⠉⣤⣽⣋⠀⣀⡀⠀⠀⠀⣺⣯⣤⠀⢣⠈⠲⣷⡿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡀⠢⠣⠰⡜⡫⠉⠦⡴⠁⣰⣧⣿⣿⡦⠸⣷⡄⠀⠀⠙⢿⣿⣆⠼⡆⠰⣿⡘⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⣀⠀⣀⡀⣰⣧⠈⠐⠢⢞⣿⢿⣿⣾⣧⣤⣭⣴⠶⠀⠀⢠⣞⣉⣀⣳⣴⣤⠉⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠻⠀⠂⠀⠁⣈⡠⡄⠀⠀⣙⣴⣿⠿⠷⢿⣷⢛⣉⠶⠊⠈⣿⣿⣿⣿⠷⣿⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠈⠂⡘⠃⢈⣱⠎⠐⠂⢁⠈⣠⣴⣴⣷⣡⣿⣿⣟⣣⠀⠀⣤⣤⠀⠀⠀⢰⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠁⡴⠄⠁⢀⣘⠋⢀⠀⢦⡤⣿⠛⠛⠻⠻⠿⢿⣾⡛⠃⠀⢠⣿⣿⡧⠰⠄⠘⠵⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠔⠋⠀⠀⠀⠀⠐⢤⣥⠌⣿⡏⠀⠀⣄⣀⣀⠀⠛⠁⠰⡶⠀⠠⡄⢹⣿⣿⡄⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠅⠙⠶⠦⠶⠂⠀⠀⢨⡟⠀⠀⠐⢿⣿⣿⣷⣎⣩⣿⣄⠀⢢⡀⠈⠙⠿⡃⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣧⠀⠀⠀⢁⡀⠘⠢⠀⠉⠻⣿⡿⡟⢤⣾⡷⡘⠀⢀⣱⡄⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠀⠈⠂⠀⣬⠘⠛⣀⡄⠀⡀⠈⡁⠀⠀⠀⣿⠀⠑⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡤⠀⠘⠃⣀⠓⢶⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠿⣦⣄⠀⠀⠀⣠⣴⣿⠿⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣼⡟⠋⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣤⠶⣾⣿⠃⠀⠀⠈⠛⠶⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠋⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡠⠄⠄⠤⠠⠠⠠⠄⠤⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢍⠁⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠃⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡶⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡤⠠⣄⡜⠋⠹⡀⠀⠀⢠⡆⢀⠦⣄⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢇⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⠷⡄⠀⠀⢀⡇⠀⢳⡀⠀⣰⠃⢸⡀⠀⠀⠀⣀⠀⠀⠀⢀⡖⠲⡆
⢀⡠⠊⠁⠀⠀⠀⠀⠁⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⢦⡀⡼⠀⠀⠀⠻⡴⠃⠀⠈⡇⠀⣠⠞⡻⠰⡖⠂⠋⠀⠀⠻⢠⣤
⠉⠒⠠⣤⠀⠀⢀⢀⣀⡀⠠⠖⠋⠀⠀⠀⠀⠀⣟⠒⠦⣄⡀⢸⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⡇⠀⢈⠆⠀⠀⠀⠂⣾
⠀⠀⠀⢸⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣄⣀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣸⣤⣴⡷⠤⡤⠟
⠀⠀⠀⠀⣧⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠃⠀⢈⠻⡀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⣹⠛⢦⡀⠀⠀⠀⠘⠛⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡴⠤⣄⠀⠀⠀⢰⡖⠒⠛⠳⡆⢠⡤⠐⠋⠀⠀⡠⢶⣉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⢄⠀⠀⠀⠀⣴⣃
⠀⠀⠀⠀⠀⡜⠀⠀⠽⠦⢤⣤⡀⠙⠢⣄⠀⠛⠚⠁⠀⠀⠀⡜⠁⠀⠈⠉⠒⠤⣤⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠉⠒⠒⢤⣤
⠀⠀⢶⡐⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣈⣳⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⡦⠀⠀⢀⡀⠀⠀⠸⣞⠉⠉⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⡸⠁⠰⣎⠁⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⠓⣻
⠀⠀⠀⠀⣇⣀⡠⠞⠉⠉⠘⠚⠉⠑⢤⡀⠀⠀⠀⢀⠇⠒⠀⠀⠤⠤⠀⣀⠀⠀⠀⣃⠀⠠⠔⠊⠁⠀⠀⠀⠀⠰⠁⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⠛⠢⡄⢀⣀⣨
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠶⠒⠒⠋⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣀⣉⡶⠀⠀⠀⠀⣧⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⢛⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠋⠀⣠⠔⠉⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⡰⢻⣄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡞⠉⠳⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⠉⠓⢄⠑⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡶⠦⠿⢦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⣀⣀⠀⠉⠂⢵⣼⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⣄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠙⡄⠀⣸⣠⡟⠲⠛⠁⠀⠀⠀⠀⡴⠋⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠁⢈⠉⠉⠉⠁⠀⢠⣦⠀⠀⠀⠀⠀⠀⠑⡄⠀⣷⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⢍⡁⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠉⣇⠀⠀⢀⡴⠋⠸⡆⠀⠀⢀⣶⡀⠀⠈⢦⣿⣮⣀⠀⠀⠀⢸⡟⠒⠦⢤⣀⠹⡄⢀⢀⠀⠀⠀⠀⠀⠀⢸⣀⡶⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⠏⠀⠀⠀⢳⡀⢀⡞⠀⢳⡀⠀⣼⠋⠀⠈⠛⠲⢤⣘⡆⠀⠀⠀⠈⠙⢋⠏⠈⢳⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠠⠤⠄⠚⠀⠀⠀⠛⠒⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢠⣀⠀⢁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠊⠀⠀⠀⠀⠀⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⣀⡔⠁⠉⠳⠾⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠟⠒⠤⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤
⠀⠈⠙⡦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠈⠀⢀⠰⠂
⠀⠀⠀⠈⠀⢠⠉⠓⠶⠠⢄⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠐⠪⠀⠢⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠠⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⣠⡧⣿⡄⠀⠀⠀⡘⠰⠁⠀⠀⠀⠀⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠄⢹⡷⠁⢁⠘⢥⣶⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢷⡁⠀⠀⢰⡝⠒⠀⡀⠀⢀⠐⠀⠀⠂⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡠⠀⠀⠠⠀⢈⡖⠀⠀⡏⠀⡈⠁⠠⢀⢳⡨⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢁⠘⠀⡌⠙⠒⠀⠀⠀⢰⡀⠀⠀⠑⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣿⡌⢸⠀⡇⠰⠀⠀⠀⠀⠀⠓⣼⠀⢰⠒⠲⠅⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠛⢹⠀⠀⣇⠀⠀⠀⠀⣀⣀⠀⠈⣕⢺⡧⠀⠀⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡦⠴⠖⠀⠉⠁⠀⠀⡀⠤⡀⢄⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⡧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⠚⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣧⠀⠀⠐⢄⠀⠀⠀⠀⠀⠃⠀⠐⡘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈⠳⡄⠀⠀⣼⣀⡤⠀⢷⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠤⠂⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠤⡀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣤⣤⣤⣤⡀⣳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣠⣿⣷⣸⣿⢹⣿⣽⢿⣏⣉⣀⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⡿⠿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠛⣿⠛⢻⡟⠀⠉⠀⢰⣫⡿⢋⣤⣤⣉⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⣧⣄⣀⣸⣿⡛⠓⠙⠛⠻⣿⣿⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠛⣿⣧⣴⣿⣿⣿⣿⣿⣿⣦⣤⣄⢀⡀⠉⠙⣿⠀⠀⠀⣀⣿⠆⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⣿⣿⣿⣿⡿⢹⢿⡇⢹⠿⣿⠟⡛⣿⠀⣀⠀⢀⣶⠋⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⡆⣿⢿⣿⣿⣠⣿⣸⣿⣼⡟⠀⠘⠻⠛⢿⣿⠇⣠⠇⠀⠀⠀⠀⠀⠘⣧⣤⡄
⠀⠀⠀⠀⠀⢠⣤⡀⠙⠿⣦⡀⠀⢀⣿⣿⢹⣧⣾⣿⣿⡿⠛⡛⢩⡀⠈⠣⣀⠀⢸⣿⡄⢻⠀⣇⠀⠀⠀⠀⢸⡏⠜⢋⠤⡀
⠀⠀⠀⠀⣶⣾⡻⣿⣦⣤⢙⣿⣀⡾⠟⠷⣾⣟⠻⣫⣴⠀⠸⠃⠀⠈⠀⠀⠀⠘⣿⡿⣷⠘⠋⠋⠀⠀⡃⢀⠟⠁⠀⠀⠀⠁
⠀⠀⢀⡀⠈⠛⢧⡄⠉⢧⣽⡝⢡⣤⣶⣷⡌⣿⣿⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡽⢛⠛⠷⣤⣀⠴⠋
⠀⠀⠋⠙⢿⣦⣀⣈⣉⣢⣌⣻⣶⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠈⠁⠙⣿⣴⣿⣻⣷⠌⣥⠀⡃⠀⠀⠀⢀⣀
⠀⠀⠀⠰⠚⣛⣛⣛⣋⣭⢾⣷⣿⣿⣿⣿⢿⡙⠷⣶⣦⡶⠁⠀⠀⠀⠀⠀⠙⠻⡟⢻⣿⣿⣿⣿⡿⢧⣭⡁⠀⠀⠀⠈⠉
⠀⠀⠈⢥⣄⠿⢻⠙⠋⣠⠟⣩⡞⠉⠻⣿⣮⠙⢦⡄⠙⢠⡄⣀⠀⠀⠀⠀⠀⠙⠛⢻⣾⡿⢹⣿⡻⣮⠁
⠀⠀⠀⠀⠿⣿⣷⡶⠀⣴⠾⠋⣀⣾⡆⠻⣿⡦⠀⠀⣀⣤⣤⣹⢧⣠⣄⠀⠀⡀⠀⣸⣿⠁⠀⠈⠁⠈⠁⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠿⣿⣿⢿⣦⣴⡆⠀⣿⠿⠛⣿⠏⢸⣿⣿⣄⣀⡁⠉⠀⠙⠶⠦⠤⠤⣤⡀⠀⣤⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠐⠿⣯⠏⠀⢿⣿⡁⠀⠉⠀⢸⣿⠀⠀⠛⢿⣿⣿⣿⠿⣿⣶⣶⣿⣷⣦⣴⣶⣶⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⢿⣷⡄⠀⠀⢈⡇⠀⠀⠀⠎⠉⠛⠉⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⣿⣿⢻⣏⣽⢦⣄⡀⠀⠁⠀⣠⣾⣿⣿⣿⣿⣌⠻⣧⡉⠻⣿⣿⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠹⢿⣿⡷⣿⣥⣿⣧⣿⠇⠀⠂⠀⠉⢉⣿⣿⣿⣿⣿⣷⣽⣿⣦⡈⣻⡦⠠⣿⣿⣯⣝⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠳⣦⣤⣴⣿⣿⣿⣿⣿⢿⣤⡄⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣶⣯⣛⣿⣿⣶⣶⣶⡶⠟⠻⠿⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡻⠟⡹⣿⣿⣿⡏⠛⠻⠆⠀⠀⠀⠀⠀⠈⣀⣸⣿⣿⣿⣯⣤⣹⣯⣿⣿⠆⢰⣶⡶⠶⠞⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠵⣶⠋⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠿⢿⣿⣟⣻⣿⣿⣿⡿⢛⣛⣁⠴⠖⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⠤⣄⣈⣿⣿⡷⠀⠀⠀⠀⠺⠀⠀⠀⡾⠁⣿⣿⣿⣿⡿⠿⠿⡿⠏⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡱⠟⠀⠀⠀⠀⢀⠀⠀⢀⡾⠀⠀⠿⠛⠉⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣣⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠘⡇⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠸⡇⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⣶⣶⠲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⡙⠉⡋⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡶⠀⠀⠀⠀⠙⠐⠋⠀⠀⠘⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁


⠀⠀⠀⠀⢀⠀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣭⣭⣽⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠑⠀⠀⠀⢠⠊⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠀⡀⠀⠀⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⣁⠄⣅⠀⠀⠀⠀⠀⠈⠀⠈⣤⣜⠀⠀⠀⢠⠀⠀⠀⡄⠁⠀⠀⡀⠄⠀⠀⠠
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠈⠀⠔⠀⠀⠀⠈⠀⢁⣀⠈⠀⠀⠀⠀⠀⠢⠀⠀⠝⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⡰⢀⡀⢀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⢧⠔⠾⠀⠀⠀⠀⠀⠙⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠢⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠄⠀⠀⠀⠀⡠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠠⠀⡆⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⢀⠁⠀⠀⠀⠀⡂⠀⠀⡜⠀⠆⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠘⢀⠀⠀⠀⡠⠁⠀⠀⠠⠀⠐⠃⢀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠁⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠊⠁⠀⠀⠢⠀⠀⠀⠀⢉⡀⢀⠈⠂⠀⠀⢠⠊⡀⠀⡄⠐⡄⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⢀⢊⣁⠀⣤⡕⠀⠀⠀⠠⠀⡀⠀⡀
⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠈⢥⣀⡼⠀⡀
⠀⠈⠒⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠔⠀⠀⠀⠀⠈⠂⠄⠠⠄⠀⠀⠀⠀⠀⠀⠉⠠⠊⠀⠀⠀⠈
⠀⠀⡠⠄⠀⠠⡀⠀⠀⠀⢠⠔⠂⠒⠢⡀⠀⠀⠀⠀⠔⠒⠢⢀⠀⠀⠀⠀⡠⠖⠂⢄⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠂
⠀⠘⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠰⠁⠄⠀⠐⠈⡇⠀⠀⠞⠀⠄⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⢠
⠀⠀⣄⠀⠂⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠆⢀⠔⠀⠀⠐⡄⠀⠀⠀⠀⠁⠀⠀⠡⡀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠒

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠔⠋⠀⠙⢦⠀⠀⠀⡉⠀⢡⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⡁⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢀⡀⠀⠀⠀⢀⡤⠄⠠⡀
⠀⠀⠀⠀⠀⢠⠖⠁⠈⠓⠀⠀⠀⠕⠲⠠⠤⡄⠀⠀⠀⠀⠀⠉⠃⠀⠀⠊⠀⠀⠀⠘⠀⠀⠤⣤⡤⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⠆⠀⠦⠀⠀⠀⢀⡔⠒⠐⢦
⠀⠀⠀⠀⠀⠢⠄⠶⠋⠀⠀⠀⣀⢀⠀⣀⡀⠀⠀⠠⠤⡄⠰⠿⠀⠀⠀⠀⠀⠀⢀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⣠⣀⢀⡤⡀⠀⠀⢀⠴⠂⠲⠀⠀⠀⠀⢀⣤⠀⣄⡀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠔⠋⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠


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

⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢤⡄⢀⠈⣤⡈⡑⠃⣨⢐⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡤⢢⡤⠬⣿⣿⣿⣚⣉⡼⢙⣣⢖⣇⡒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠠⣄⡓⣎⡳⣷⣬⢻⣿⣽⣿⣿⢾⠟⢻⣆⡹⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢸⠤⢧⢵⣿⢿⣳⣾⣿⣿⣿⣛⣿⣶⠾⢟⣼⣗⠶⢷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠱⢴⢶⣼⣼⣿⠿⣿⣿⣯⣬⣿⣝⣿⣿⡿⣧⣭⢽⡄⣿⡥⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠞⣭⣿⢷⣿⣿⣿⣻⣿⣿⣽⣟⣿⣿⣿⣿⣿⣾⣷⣶⠏⢀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠛⣿⠻⣿⣏⣿⣯⣿⣿⣻⣯⣿⣽⣿⣟⣟⣷⡿⣿⣏⣩⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡘⣀⡏⣹⣿⣌⣼⣯⣽⢷⡾⣯⣻⣽⣿⣿⣯⢿⣷⢩⣻⡿⢪⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠑⠙⣿⣾⣿⢭⣭⣻⣿⢿⣿⣧⢿⡿⣿⣽⣻⣾⣎⡱⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⠀⡛⢢⡟⢻⣽⣉⣿⡗⣷⣫⢷⣟⣏⡻⠎⣙⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⠒⢻⡦⣻⣯⣿⡝⣿⢋⡈⠽⠁⢹⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡀⠈⢘⣺⢓⢣⠈⡳⠘⠉⠟⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣸⡟⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋
⠀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⢀⣿⠃⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⣀⣤⣤⣶⣶⠶⠾⠿⠿⣿⡿⠂⠀⠀⠀⠀⣀⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠈⢿⠿⠟⠋⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⢠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣴⡦⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⣶⠿⠛⠿⣷⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

⠀⠀⠀⠀⠀⠀⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠚⠓⣶⡼⢿⣾⣷⣾⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⠏⠀⠀⠀⡰⣿⠃⢋⣴⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⣠⠋⠀⠀⢺⡂⠁⠀⠐⠛⠛⠛⠿⠛⠶⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢽⠀⠀⡁⠀⠠⢔⣾⡅⠀⢀⣻⣛⣻⡟⡟⢛⡟⠉⠉⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⡾⠏⠀⡇⠀⢀⡼⣻⢸⣷⣦⣽⣏⢙⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣇⠐⠡⣰⡇⠻⠛⣧⡈⣻⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⢀⣠⣤⣆⣀⣨⣿⣿⣧⠶⢻⣿⣿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠲⢶⡿⠟⠛⢉⣽⠟⠉⠁⢈⣿⡿⠛⣧⣠⣼⡿⠿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠋⠌⣿⠂⢤⣾⡟⠊⠁⢉⣿⢻⡗⢂⡾⣻⡟⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⢀⣁⣈⣆⠔⠋⠀⠀⢠⣿⣿⣿⣴⠪⣭⣬⡙⢦⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢚⣿⣿⣏⣀⠀⣠⣟⣯⡿⠋⠁⢚⣃⣨⣤⣤⣤⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣥⣽⣿⣿⣿⡿⠿⠿⠿⠿⠿⠻⠛⠛⠋⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⡀⠀⠑⠄⢀⡀⠀⠀⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⢄⢦⠤⠤⡠⠚⠉⠑⣄⠤⠎⠁⠀⠈⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⢣⠀⠀⢁⡀⠀⠀⠴⠒⠢⡂⠀⠑⢀⠀⢅⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠲⡀⠀⠀⠂⠀⢀⠼⢀⠀⠇⠀⠀⠜⠀⠀⠀⡸⠛⠀⠰⠀⢀⠇⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠑⡤⠤⢤⡤⠊⠀⠠⠐⠀⠀⠀⠀⡉⠀⠰⣗⣄⠀⣁⡰⠈⠀⠈⠀⠲
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀⠀⠀⢱⣀⣄⡕⠐⡆⠈⠂⡄⢠⠀⠦⠀⢀⠂⠊⠀⠁⠘⠃⠆⡀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣶⠀⠁⡀⠐⠘⢿⡁⠀⢀⣈⠣⡼⣀⡹⠀⠀⠀⠀⠠⠄⡀⠀⢦⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣀⠃⠀⠄⠰⠆⠨⣍⢉⠽⠌⠀⠀⠁⢳⠀⠀⠀⠀⠀⠀⠁⠀⠐⢥⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠐⠀⣠⢻⣃⠀⠈⠈⠀⠼⣇⡀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢀⠐⠠⡆⠈⠙⣾⡠⠦⡝⠋⠀⣹⠤⢄⡠⣤⣀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⡀⠀⠀⠀⠱⡆⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠀⠀⠿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⢸⡒⠟⢀⠤⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⣰⠻⡙⡐⡌⠙⠒⠒⡏⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⡄⢀⠁⢳⢠⠆⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠈⡎⠌⣇⢫⠀⠀⠑⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠻⣹⠐⡜⢎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠈⣷⣿⣿⣷⣿⡴⠂⠀⠀⢀⠼⡽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠷⢦⣄⡀⢿⣷⣾⣿⣿⣿⣿⣷⣴⣶⡤⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣂⡀⠑⠲⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⠿⠟⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣭⣤⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡨⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠿⠉⠀⢀⠔⠫⠟⣿⣿⠿⣿⡟⣿⣿⡏⠛⣗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠲⣿⠃⠀⠀⣴⡟⠀⢸⣧⠀⠈⠻⢇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠁⠀⠀⠻⢃⠀⣾⡀⠱⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠘⠀⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣸⡇⠀⠀⣀⠀⠙⣿⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⣿⣿⣧⡀⠊⠀⠀⠠⣝⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣉⡆⠙⠟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠃⠀⠐⢠⣬⣿⣦⢲⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⠟⠲⢄⡀⠙⠛⠋⢸⡟⡆⠀⠀⢀⣴⣾⢿⢿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠲⢄⠀⢸⣧⡇⠀⠀⣬⣿⣷⣦⣄⢀⠙⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠁⢸⡏⠀⠀⠀⠛⠻⢿⣉⡙⠫⣦⣄⡰⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡝⠛⠛⠛⠓⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡻⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣦⣿⣤⠿⠷⠺⠷⠿⣶⣼⣿⠀⢀⣀⣀⠀⠀⠀⠀⠀⠙⠻⢶⣟⣿⣿⣷⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠋⠁⠀⠀⠀⠀⠀⠀⠈⢹⣿⠐⢬⡍⠛⣷⣆⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠶⠀⠰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⠀⠀⠀⢣⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡶⡀⠀⠀⠀⢨⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣼⣿⣷⡄⠈⢷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠆⠳⣝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⣄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣠⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣤⡀⠀⢀⣄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠀⠈⢁⡄⠀⡄⠀⠀⠀⠀⢿⠀⠀⠈⠁⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠉⣀⣀⡀⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠑⠲⠶⠶⠖⠋⠀⣼⠃⠀⠀⠀⠀⠸⣆⠀⠀⠀⠚⠛⠁⠀⢠⡟⠀⠀⠀⠀⠀⠹⣆⠀⠊⠁⠀⠈⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠆⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⠄⠀⢤⡂⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⡢⠀⠀⣔⠀⠀⢻⡄⠀⠀⠀⠀⢸⠃⠀⠈⠋⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢠⣶⣶⣦⠀⠀⢠⡏⠀⠀⠀⠀⠸⡇⠀⠀⣀⣄⣀⢄⡀⠀⣼⠁⠀⠀⠀⠀⠸⡆⠀⢲⣶⣶⣶⣶⡆⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠛⠛⠋⢀⣠⠞⠁⠀⠀⠀⠀⠀⠻⣦⡈⠁⠀⠁⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠹⣆⡀⠉⠛⠛⠉⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠛⢶⡄⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⣄⠀⠀⣤⡄⠀⢻⡆⠀⠀⠀⠀⣾⠁⠀⣴⡄⠀⠠⡦⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃⠠⠖⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⣴⣶⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠄⢠
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠋⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⡆⠀⠀⢿⣿⡿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠹⣄⠈⠒⠶⠶⠶⠚⠉⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠃⠀⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣇⢄⢀⣡⣤⣤⣤⣷⣀⡅⣴⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠢⠀⠀⠀⠈⠲⣬⣿⣿⣯⣿⣿⡯⣿⣿⣿⣿⡀⡀⠄
⠀⠀⠀⠈⡤⠀⠤⠀⠀⠀⠀⣀⠀⠀⠢⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⡹⣿⣷⡄⡀
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣯⢠⠔⠚⠁⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢯⣽⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡟⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣙⠂⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠊⢀⠿⣿⣾⣿⣿⣾⣿⡿⢿⠛⠀⠀⠉⠑⠀⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠈⠈⢸⠏⠉⠛⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡰⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠀⢄
⠀⠀⠀⠀⠀⠀⠐⠁⠠⢤⠀⠀⠠⠀⠈⡆⠀⠀⠀⡰⠀⡀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⡄⠈⠢⠀⠀⠀⡆⠀⢀⡀⠀⢀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠈⡁⠀⢨
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠤⠔⠁⡠⠁⠀⠀⠀⢁⠀⠀⠄⡀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠠⡀⠙⠒⠀⠒⠁⠀⠎⠀⠀⠀⠡⡀⠘⠿⠿⠟⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠐⠉⠀⠀⠀⠀⠀⠀⠒⠀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠉⠉⠐⢀⠀⠀⠀⠀⠀⡠⠂⠁⠈⠈⠉⠢⡀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠣⠀⠀⠀⠸⠁⠀⠆⠀⠀⠶⠀⠘⡄⠀⠀⠀⠀⡇⠀⢴⠄⠀⠰⡆⠀⢡⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣀⡉⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠈⡇⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠦⠤⠃⠀⡠⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠘⢄⡀⠙⠟⠁⠀⡠⠂⠀⠀⠀⠐⢄⠀⠀⠑⠊⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠈⠁⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡰⠄⠀⠄⠀⠀⠃⠀⠀⠀⡏⠀⠐⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⠀⠀⡌⠀⠠⠄⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠠⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡤⠒⠦⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⢠⣤⣤⡄⠀⠀⠘⠀⠀⠀⠇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠁⠈⠀⢀⠔⠁⠀⠀⠀⠈⠢⣄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠈⠁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣯⣭⣥⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠔⠊⠉⠉⠐⢤⡀⠀⠀⣠⠔⠈⠉⠉⠒⢄⠀⠀⠀⡠⠒⠉⠉⠁⠢⣄⠀⠀⢀⡄⠂⠉⠉⠑⠢⡀⠀⠀⢀⡐⠂⠉⠉⣰⢤⡀⠀⠀⣠⠖⠈⠉⠉⠒⢄
⢠⠇⢠⡄⠀⠀⢤⡄⠱⠀⢰⠁⠀⠲⠂⠀⠶⠀⢣⠀⡜⠀⠶⠀⠀⠐⠖⠈⢂⠀⡎⠀⠠⠦⠀⠀⠤⠈⡄⠀⠏⠀⠈⠋⠀⠈⠀⢱⠀⢰⠁⠴⠄⠀⠀⠶
⢨⡀⢠⡀⠀⠀⢀⡄⢀⠃⢠⠀⠀⠀⣀⣀⡀⠀⢸⠀⠇⠀⠀⠐⠒⠒⠂⠀⡸⠀⡆⠀⣀⡀⠀⣀⣀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⢀⣀⣀
⠀⠳⣀⠉⠒⠒⢉⡠⠊⠀⠈⠢⣀⠈⠀⠀⢈⡤⠃⠀⠘⢆⡀⠀⠀⠀⣀⠔⠁⠀⠐⢄⡀⠈⠉⠀⣠⠜⠀⠀⠘⠢⢄⢠⣤⣶⠗⠁⠀⠈⠢⣀⠘⠤⠜⢀⡴
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⣠⠒⠉⠀⠈⠉⠢⡀⠀⠀⡠⠊⠉⠀⠈⠑⢢⡀⠀⢀⡔⠊⠁⠀⠉⠑⢄⠀⠀⢀⠔⣉⠁⠀⢉⡒⢄⠀⠀⣠⠞⠉⠀⠈⠉⠢⡀⠀⠀⡠⠊⠉⠀⠈⠙⢦
⢰⠃⠰⠆⠀⠀⠒⠀⠸⠀⢸⠀⠐⠇⠀⠰⠆⠀⢱⠀⡎⠠⠄⠀⠀⠤⠀⠀⢣⠀⠆⢀⣉⣀⣀⣈⡁⠈⠆⢠⠃⠐⠖⠀⠀⠲⠂⠸⠀⢸⠀⠺⠂⠀⠀⠻
⠨⡄⠀⠀⠀⢀⡜⠀⢠⠁⢨⠀⠀⠀⣾⡆⠀⠀⠸⠀⢇⠀⠀⠀⠀⠀⡠⠀⡘⠀⡆⣿⣿⣿⣿⣿⣿⠇⠄⠘⡄⠀⠀⢠⣔⣢⠀⢠⠀⢸
⠀⠑⢄⣈⠉⠁⣀⠔⠃⠀⠀⠳⢄⡀⠻⢃⡀⠔⠁⠀⠈⠢⣀⠀⠐⢊⡠⠜⠀⠀⠘⠬⣛⠻⠿⣛⡩⠊⠀⠀⠑⢄⣀⠀⢀⣀⠴⠃⠀⠀⠳⢄⡀⠀⢀⡠⠔
⠀⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⠀⠀⠀⠀⠀⢀⡀⡈⢀⠀⠀⠀⠀⠀⠀⢀⢈⠁⣀⠀⠀⠀⠀⠀⠀⣀⢈⢀⡀⠀⠀⠀⠀⠀⠀⣀⢉⢀⡀
⠀⡠⠊⢠⡄⢠⡌⠑⡄⠀⠀⡔⠉⠀⠀⠀⠈⠲⡀⠀⢀⠖⠁⠀⠀⠀⠉⢢⡀⠀⢠⠊⣡⡀⠀⣤⡑⢄⠀⠀⡠⠊⠀⠀⠀⠈⠑⣄⠀⠀⡔⠹⠆⠀⠠⠎⠢
⢐⣷⣄⡀⠀⢀⣀⣴⣾⠀⠸⠀⠀⠀⠶⠀⠐⠒⢰⠀⡎⠀⠀⠚⠀⠀⠒⠀⢡⠀⠇⠀⠀⠀⠀⠀⠀⠀⠆⢰⠁⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣷⣶⣤⣶⣾⣿
⠀⡿⣿⣿⣿⣿⣿⣿⡿⠀⠰⡀⢔⠢⠤⠤⠄⠀⡸⠀⢣⠀⠠⠐⠒⠒⠒⠒⡌⠀⢇⠀⠀⠀⠀⠀⠀⢀⠆⠘⡄⢄⠉⠀⠀⠉⡴⢰⠀⠸⢻⣿⣿⣿⣿⣿⣿
⠀⠘⠫⢟⣿⣿⠻⠟⠁⠀⠀⠑⠤⣀⣀⣀⠠⠊⠀⠀⠀⠓⠄⣀⣀⡀⠴⠊⠀⠀⠈⠢⢄⣀⣉⡠⠔⠃⠀⠀⠈⠢⢉⣁⣉⠩⠔⠁⠀⠀⠑⠽⣛⣿⣟⠿⠋
⠀⠀⢀⡀⠤⠤⣀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⢀⡠⠤⠤⢀⠀⠀⠀⠀⠀⢀⠠⠤⠤⣀
⠀⡔⠁⠠⠄⠰⠄⠑⢄⠀⢀⠖⠁⠀⠀⠀⠀⠑⡄⠀⢠⠎⠀⠀⠀⠀⠈⠳⡀⠀⡠⠊⢀⡀⠀⠴⠈⢢⠀⠀⡴⠁⠀⠀⠀⠀⠑⢄⠀⢀⠔⢁⠀⠀⠀⣀⠑
⠸⡁⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠉⠁⠀⠈⠁⢸⠀⡇⠀⢠⠄⠀⠀⠤⠀⢱⠀⠇⠀⠀⠀⢠⣾⠃⠀⠃⢸⠁⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⢉⣁⠀⢀⡉⡀
⠀⡜⢄⠀⠀⠀⢀⡠⡰⠀⠰⡀⠀⠀⠀⠊⠉⠀⡜⠀⢣⡀⠀⠠⠄⠢⠄⢀⠎⠀⢃⠀⠀⠀⣿⣿⡤⢠⠂⠈⡆⠈⠁⠀⠀⠁⠀⡰⠀⠸⡀⢗⡚⠿⠗⣒⢓
⠀⠈⠂⠌⢁⡈⠥⠊⠀⠀⠀⠘⠢⠄⣀⠠⠔⠊⠀⠀⠀⠑⠦⠀⢀⠠⠔⠋⠀⠀⠀⠓⠤⢀⣨⠍⠛⠃⠀⠀⠘⠲⢤⣿⣧⠴⠚⠁⠀⠀⠙⠶⣤⣤⣤⠶⠊
⠀⠀⣀⠤⠐⠠⠤⡀⠀⠀⠀⠀⡀⠤⠒⠠⢄⡀⠀⠀⠀⠀⡠⠄⠒⠤⢄⠀⠀⠀⠀⢀⠠⠔⠲⠄⣀⠀⠀⠀⠀⡀⠐⠒⠂⠀⣀⠀⠀⠀⢀⣠⠴⠶⣦⣤⡀
⢀⡜⠁⠠⠄⠀⠠⠌⢢⠀⢠⠊⠀⢀⡀⠀⢀⡙⢄⠀⢠⠃⢘⣁⣀⣘⠀⠑⡄⠀⡰⠁⢀⠀⠀⢠⡌⠳⠀⠀⠏⠁⠀⠀⠺⠂⠈⢣⠀⢠⠏⠀⠶⠀⠉⣁⣙
⠨⠀⠀⢄⠀⠀⢀⠄⠈⡄⠘⠀⠀⠈⠁⠀⠈⠁⢸⠀⡇⣴⣿⣿⣿⣿⣷⡄⢸⠀⡃⠀⠉⠁⠀⠀⠀⠀⡅⢰⠀⠶⠀⠀⠀⠀⡆⢈⠀⢸⠀⢀⠔⠊⠉
⠀⢆⠀⠀⠉⠉⠁⢀⡜⠀⠘⡄⠀⠀⠀⠀⠨⢇⠌⠀⠡⡻⣿⣿⣿⣿⡿⢣⠂⠀⢣⠀⢀⣀⣀⠀⠀⡠⠃⠀⢧⠀⠠⠤⠤⠚⢀⠜⠀⠘⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠑⠠⠤⠤⠐⠉⠀⠀⠀⠈⠓⠤⠤⠤⠒⠁⠀⠀⠀⠈⠒⠬⠭⠅⠒⠁⠀⠀⠀⠙⠢⠤⠄⠔⠊⠀⠀⠀⠀⠑⠢⠤⠤⠒⠁⠀⠀⠀⠈⠒⠤⠠⠤⠒⠁
⠀⠀⡠⠔⠒⠒⠤⣄⠀⠀⠀⢀⡠⠔⠒⠒⠤⡀⠀⠀⠀⢀⠤⠐⢒⡦⢄⡀⠀⠀⠀⣀⠔⠒⠒⠢⢄⠀⠀⠀⠀⡠⠄⠒⠒⣢⣄⠀⠀⠀⢀⡤⠖⠒⠂⠤⡀
⢀⡎⠀⣤⠀⠀⣤⠈⢣⠀⢠⠋⢠⡄⠀⠀⣤⠈⢆⠀⡰⠁⠀⠶⠀⠁⠀⠘⠄⠀⡜⠁⡀⠀⠀⠀⡀⠱⡀⠀⠎⠀⠀⠿⠀⠉⠈⢣⠀⢠⠋⣠⡀⠀⠀⣀⠈
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⠀⠀⠀⣀⠤⡄⠀⢸⠀⡇⠀⠀⠀⠀⢀⣶⡀⢸⠀⡁⠀⠋⠀⠀⢈⡋⡀⠅⢸⠀⠀⠀⠀⠀⠀⣤⣀⠀⢸⠀⠀⠤⠤⠤
⠈⢧⠀⠀⠰⠶⠀⢀⠜⠀⠘⢄⠀⠈⠉⠈⠁⢀⠎⠀⠰⡀⠀⠀⠀⠘⠛⡣⠃⠀⠣⡐⠤⣀⣀⡤⠜⡱⠁⠀⢧⡀⠀⠀⠀⠀⢑⠏⠀⠘⢄⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣾⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛
⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠚⢿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⡿⠖⠂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠘⠃⢰⡆⠀⠀⢀
⠀⠀⠀⠀⠀⣷⣤⣤⡤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠹⠁⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⠀⠻⠁
⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠠⣾⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢴⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⡴⠀⠛⠃⠀⠀⠀⠀⣠⣶⣄⠀⠀⣰⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⠀⡹⢿
⠀⠀⠀⠀⣀⣠⣾⣷⣤⣀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⢾⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠛⠿⠄
⠀⠀⠀⠀⠉⠛⢿⣿⠟⠉⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠰⠆
⠀⠀⠀⠀⠐⠆⠈⠁⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠗⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣴⠃
⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢤⣤
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⣡⡄⠀⠀⠚⠛
⠀⠀⠀⠀⠀⣤⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠛⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⠶
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁


⣿⣷⣶⣾⣶⡷⢾⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⡶⢷⠾⠿⠿⠿⣷⣶⠿⡶⠶⠶⠾⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡄⠀⠸⣇⠀⠀⣧⠇⠀⠀⠀⢀⡞⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠹⡹⡀⠀⣿⡄⠀⠛⢀⡆⠀⢠⣿⠁⠀⣠⣾⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠘⠿⡀⠙⠇⠀⣧⢧⠀⠀⣼⡇⢠⢯⠇⠀⣜⡵⠁⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠰⣆⠀⢻⢸⡄⠀⠿⢠⠏⡾⠀⠘⢋⡤⠀⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠈⠻⣟⡲⢦⣄⡀⠀⠀⠈⠻⣗⠦⣀⠈⠀⣸⣤⠷⠤⣤⣏⣼⠁⠀⠴⠟⠁⣀⣠⣴⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢭⣷⣤⡀⠀⠈⠑⢮⣹⠞⠁⠀⠀⠀⠀⠈⠙⢦⣀⣤⠶⣛⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡴⠋⠁⠀⠀⢀⣀⡠⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠿⠿⠿⢾⣿⣟⣛⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⠤⠤⣤⣌⡙⠒⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠦⣍⡉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⡭⠋⣹⣦⡀⠀⠀⠀⠀⢀⣠⠞⠛⠲⠦⣍⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠒⠋⠁⠀⣴⢋⡴⠋⠛⠒⢲⡟⢻⡀⠘⣗⢄⡀⠀⠈⠉⠛⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⠏⠀⢀⡄⠀⠀⢳⡈⣇⠀⠘⢦⡑⣄⠀⠀⢤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⣠⣿⠞⠁⠀⢠⢿⠃⠀⡄⠈⢧⢻⡀⠀⠀⠙⠾⣆⠀⠀⠈⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣴⠟⠁⠀⠀⠀⣿⠋⠀⠀⣿⡀⠈⣿⡇⠀⠀⢲⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠘⣿⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠆
⡀⠀⢠⠂⡇⠀⠀⢀
⡝⢀⢇⣇⢣⠀⢀⠎⢦
⠀⢺⢸⣿⣸⠀⡼⠸⠂⠳⡀⠀⠀⡴⡇⠀⡠⡎
⠀⠈⢺⣿⠃⠀⢡⠀⡀⠀⠹⣀⠞⠀⣧⠞⠀⠁⢀
⡀⠀⠈⡏⠀⠀⠀⡄⢻⣤⣶⠋⠀⠀⣯⣼⠀⡇⡸⠄⠀⠀⡔
⠀⢀⣸⠁⠀⠀⠆⢣⢸⡿⠁⠀⠀⠀⣿⣯⢀⡽⠁⡱⠊⢰⠁⢀⡤
⢀⢸⠏⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣼⡷⢋⡴⠋⠀⠀⣿⡊⢠⢀⠰⠂⠀⣠⠂
⢸⡼⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⡴⠋⠀⠀⠀⢠⡿⠗⠋⠀⠀⡥⠎⡅
⠸⣷⢸⠀⠀⠀⠀⣄⣷⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⡷⡹⠁⠀⢀
⣟⣿⣼⣦⣸⢂⣰⣿⣧⠀⢀⡃⠀⣼⡄⡠⠀⠀⠀⣼⣤⠄⠄⣀⡠⠞⠛⠁⣠⢖⠥⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡕⡡⡠⢡⣾⡿⠟⢛⡉⠀⠀⠀⣠⢞⣑⡁
⢿⣿⣫⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣕⡴⣋⡥⢔⣠⠔⠀⠀⢀⡞⡉⢉⡌⠀⠰⠊
⣟⣎⣳⡗⣿⣿⣟⣏⣥⣿⢿⣿⣿⣿⣿⣿⣿⡿⢚⠉⠀⠀⣀⡴⠛⠛⠂⠉⢉⠬⠋⠁
⣾⣿⣿⣿⣿⣿⣶⡷⣯⣞⣿⢺⢿⣿⣿⣿⠿⠟⣋⣡⣴⣾⣧⣀⣀⣀⣤⣾⣁⣀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣭⣾⣿⣿⣿⡟⣛⣩⠍⠉⠉⠉⠉⢁⣀⡈⠉⠉⠉⣉⣩⣭⠖⢊⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡷⣿⣿⣿⣿⣿⣛⣃⡩⠍⢀⡈⠄⠀⣀⣴⡾⠖⠂⠔⠂⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣿⣻⢿⣿⣿⠿⠿⠧⠒⢒⣈⣡⣤⣶⣉⣉⣉⠒⠚⠤⠆⠒⠒⡨⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣯⡼⣹⣿⣿⣷⣶⣾⣿⣿⡢⠬⠍⣙⠓⠶⣔⣒⣂⣀⠤⠒⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣹⣿⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⢟⣽⣿⢿⣿⣿⣻⣿⣛⣿⣿⣿⣾⣿⣿⣿⣿⣿
⡋⠿⣍⡻⡭⣟⢻⣾⣯⣿⣿⣫⡼⢟⡻⣿⢤⢸⣉⣛⠿⡿⣟⣋⢿⡵⢿⡘⣿⢿⡃⣽⡟⢻⠻⣟⠟⠯⢻⣿⣿⣤⣽⡍⡙
⠙⣟⠿⢙⠖⠸⢭⡷⠛⠃⢛⠟⡷⠛⣧⠽⢲⣏⣧⣿⣇⠻⣭⠻⠚⠷⠧⠓⢃⡾⡻⣿⠌⠧⡇⡹⡛⠄⣜⣹⣷⣶⣿⣧⠛
⠀⠉⠂⠁⠄⠀⠘⠀⠀⠚⠉⠀⠀⠀⠡⠆⠀⠋⠀⠃⠀⠡⠎⠃⠉⢀⠀⠆⠀⠀⠒⠁⠀⡀⠁⠂⠋⠉⡀⠁⠀⠀⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣤
⠀⢀⠠⠀⡖⠀⠀⠄⠀⢠⢀⣠⠄⣰⡄⠀⡀⢀⠀⠀⢰⠈⡂⠀⠀⠀⠀⣀⢰⣄⠄⠀⢀⡅⡀⢄⡁⢀⠘⠀⠀⡀⠀⠀⡠
⢲⣼⣅⣤⡧⡤⠴⡷⣶⠌⢿⣣⡤⢥⣬⣡⡽⣍⡖⠻⣏⡷⣇⣶⠢⣄⡛⡃⠈⣶⣤⣇⢺⠟⡋⠋⣭⠔⢪⣊⢦⣶⣙⠓⢖
⡁⣒⣻⣷⣷⣾⣰⣿⣿⣿⣟⢿⣱⣺⣟⢿⣌⣍⡳⣮⡘⢿⣿⣛⠿⠟⢿⣈⣹⢈⣿⣥⣿⡌⡟⣿⣆⢶⣶⣧⣯⣼⣿⣴⡿
⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣳⣾⣿⣿⣯⣿⣿⣿⣿⣴⣿⣿⣯⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⡀⠄⠀⠤⠀⢀⣠⣶⢀⡈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢁⠈⠰⠁⠉⡰⢰⠂⣠⣤⣷⠀⠨⠁⠁⠶⣤⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠁⣻⠷⠈⡰⠃⠄⢃⣡⣀⠀⣰⣷⢺⣿⣴⣩⣄⠐⡋⢸⡕⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⣠⠄⠑⠦⡹⣶⠀⣂⣀⣐⡆⠀⠉⠟⣘⢻⣿⠚⢿⣏⣿⣼⢷⣉⠃⡥
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⢀⠀⣶⠛⠂⠁⠛⣧⣹⣯⠙⠙⣧⠔⡆⠀⠱⣿⡸⠄⠋⠻⠂⢾⡿⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠡⢊⡁⠀⠀⣸⡲⣿⣿⡯⠁⠀⣅⠀⠰⡀⠀⢸⡗⠐⠦⡄⠀⣀⠂⠘⡁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠠⠋⣹⣿⣧⣄⠺⢁⢅⡆⣀⠁⢢⠸⣧⡔⠂⢸⠆⠁⣀⠂⠄⠹⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠓⡀⠒⠄⠴⠋⣜⣻⣏⠰⠈⢉⠄⡙⣂⠙⠇⠁⠐⠀⣬⠤⠼⣩⡧⡈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⡀⠀⠁⠀⢘⡄⢱⡤⠀⢶⠋⠀⠛⢋⠁⣾⣷⡶⠒⡃⠀⠈⣅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⢹⡆⠲⠒⣸⣧⠺⠷⡤⣎⠀⢲⡄⢀⠛⠙⣿⢧⣀⡼⠟⠀⠈⠲⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠏⢱⣄⠰⢏⡿⠆⣀⠀⡿⠛⣯⠀⡄⠠⠲⣿⣽⡅⠐⢿⣶⣌⠛⢈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠣⠄⣼⠀⢠⡎⢀⣂⠁⠁⣥⢨⡍⣈⠁⠀⠀⡸⢿⣧⠀⠀⠁⡠⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠐⠞⣷⠛⠋⣱⡶⠇⠈⢸⡇⠐⢈⠈⣴⢞⡁⠀⠚⠀⢀⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⣻⣿⠡⢛⡘⣡⣤⣁⣠⢘⣷⣶⡈⢲⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠈⠀⠙⢿⣧⣿⠚⢿⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⡎⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣇⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⢃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠅⣿⠇⣿⠸⣆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡤⠘⠃⠜⠃⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈



⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠿⠷⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠶⠶⣤⡀
⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⣸⡏⠀⠠⣾⣷⠀⠀⢰⣿⡦⠀⠈⣿⡀⠀⢀⣿⠁⠀⢼⣿⡆⠀⠀⣾⣿⠄⠀⢹⣇⠀⠀⣸⡟⠀⠠⣾⣷⠀⠀⢰⣿⡦⠀⠈⣿⡀
⠀⠀⣿⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⢸⡇⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠉⣁⣤⣤⣄⡉⠁⠀⠀⢸⡇
⠀⠀⣿⡀⠀⢷⡀⠀⠀⠀⠀⠀⣸⠇⠀⣼⡇⠀⢸⣧⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣿⠀⠀⣿⡄⠀⢠⡾⠋⠉⠉⠉⠛⣦⠀⠀⣸⡇
⠀⠀⠘⣷⡀⠈⠻⣶⣤⣤⣴⡾⠋⠀⣴⡟⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠘⣷⡀⠟⠀⠀⠀⠀⠀⠀⠘⠇⣰⡟
⠀⠀⠀⠈⠻⣦⣄⣀⡀⠀⣀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠙⢷⣦⣀⣀⠀⢀⣀⣠⣶⠟⠁⠀⠀⠀⠀⠈⠻⣶⣄⣀⡀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁




⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡗⠀⢸⣿⣿⣿⠀⢹⢈⡇⠀⠀⠀⠀⡆⠀⠀⢸⣿⣿⣿⣿⣿⣯⣉⣿⡿⣿⣿⣿⣟⡋⠁⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢰⣿⣿⣿⣿⣿⣿⣷⢸⡇
⣿⣿⣧⠀⠈⣿⣿⣿⠀⣾⡾⢣⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣏⣹⡏⣿⠉⠁⠀⠙⠓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣾⣿⣿⣿⢸⣿⣿⣿⠀⡇
⣿⣿⡏⠀⡀⣿⣿⣿⠀⣼⡇⠛⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣬⠹⠿⣿⠇⢹⡦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⡟⣼⣿⣿⣿⢀⡏
⠹⣿⡇⠀⢹⣿⣿⣿⡀⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣟⣥⣤⣄⢿⠀⣶⡀⣀⠀⠀⠀⠀⠀⠀⢠⣴⡄⢀⣀⣀⣤⣤⣺⣿⣿⡇⠈⣿⢿⣿⣷⡇
⠃⣿⡁⠀⢸⣿⣿⣿⡃⣿⡷⠀⠀⠀⠀⠀⠃⠀⠀⠺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣹⠇⡄⣿⢸⣿⢹⡇
⠀⣿⡇⠀⢸⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⡘⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣯⣥⣾⣿⣿⣿⣯⢸⣦⣡⡏⢸⣿⢸⡇
⠀⡿⠃⠀⠘⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⢰⣿⡅⠹⣿⣿⣿⣿⣯⣉⣀⣰⣿⣿⣿⣿⣿⣿⡗⠘⣿⡿⠿⢯⣉⣉⣽⣿⣿⣿⣿⢰⣿⣿⡇⢸⡏⠈⡇
⠀⡇⠀⠀⠀⣿⣿⣿⣼⣿⡅⠀⠀⠀⠀⠀⢰⠀⢠⠀⣿⣿⣷⡶⠛⠉⠁⠷⠾⢷⡷⠶⠿⢟⡋⣹⣿⣿⡿⠀⢿⣿⠛⠿⣤⣬⣭⡟⣻⣿⣿⢸⣿⢿⡇⠈⡇⠀⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣿⣿⡟⠀⠘⢿⣆⠀⠀⠉⠁⢺⣿⣿⡟⢘⣿⣼⡇⢠⡆
⢸⡆⠀⠀⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡶⢞⡛⢿⣿⡋⠀⠀⢸⡿⣿⣦⣀⠀⢸⣿⣿⡇⣸⣻⣿⡏⠘⡇⢸⠂
⠸⣅⠀⠀⠀⣿⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡟⠀⢀⣐⣶⣿⣿⢛⣩⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⢿⣿⣆⣽⡿⣿⡇⣼⣿⣿⣧⠀⠇⣼
⢠⣿⠄⠀⠀⣿⡏⢿⡇⣿⣿⠀⠀⠀⠀⠀⢸⠀⢻⡇⢹⣿⣿⠧⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⢿⠀⡆⣿
⢸⡿⠀⠀⠀⣿⡇⣨⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⣿⣿⡆⠷⢣⣿⣿⣿⡿⠿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣻⣿⢸⠆⠁⣿
⢰⣏⠀⠀⠀⢺⣧⢹⡇⢸⡇⠀⠀⠀⠀⠀⢘⠀⢸⡄⣸⣿⣿⣿⣾⡘⣟⢻⣿⣿⣿⣿⣏⣹⠋⢛⠉⡏⠙⡏⢿⣹⣿⣿⣿⡿⣻⣿⣖⣯⢀⣿⣿⣿⢀⣧⠀⣿
⢸⣿⡄⠀⠀⢸⣿⢾⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⣿⣴⣿⣿⣿⣿⣿⣷⡙⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢃⣯⡨⣿⣻⣿⣾⣿⠀⣿
⢸⣿⡇⠀⠀⢸⣿⢸⡇⢸⣿⠀⠀⠀⠀⠀⢸⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣌⠸⡿⣿⣎⣩⣙⣋⣯⣯⣽⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣼⠇⠿⣿⢻⣿⣿⣿⠀⡟
⠸⣿⡇⠀⠀⢸⡇⢸⡇⢸⡟⠀⠀⠀⠀⠀⠘⡂⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣌⠻⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢠⠄⣿⢸⣿⣟⣟⠀⡇
⠀⣿⡇⠀⠀⢸⡇⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣜⣿⣿⡿⣿⣿⢿⣿⣏⣿⣿⣿⣿⣿⣿⡟⣿⣸⠘⣿⢸⣿⣿⢿⣳⡇
⢸⣿⡇⠀⠀⢨⡇⢸⡇⢸⢿⠀⠀⠀⠀⠀⢠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣋⠁⣀⣼⣧⣽⣿⣿⣿⣿⣿⣿⡷⠠⣿⣿⠛⣿⢸⡟⢸⢸⢻⡇
⢸⣿⡇⠀⠀⢸⡇⢸⡇⠘⠸⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⣿⢸⣿⣼⡇⠘⢸⢺⡇
⣼⣿⡇⠀⠀⢸⡇⠸⣇⠀⣱⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣟⣿⣷⣸⣶⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠦⠀⢚⠀⢨⠀⢾⢃⢀⠈⠀⠀⢲⡆⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠘⢇⠈⠃⠀⠀⠀⠀⣀⢀⠀⢈⣿⣷⠀⢀⣼⠿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⠴⠂⠁⠀⣀⡀⣠⣴⠼⠛⠁⢠⣼⡟⠋⢠⡄⢹⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠶⡶⠿⠿⠛⠋⣉⣀⣠⣴⣾⣿⡏⣿⡄⠸⢧⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠂⣿⣿⣵⣶⣴⣶⣶⣦⣿⠿⠿⠿⣿⣭⡉⠀⢈⣁⣄⡹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣷⠟⢀⣈⣽⣿⡛⠉⢹⣯⣵⡄⣼⡟⠉⠉⠣⡀⠈⠉⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⣬⡶⠃⠘⡋⠉⢻⣤⠞⠋⢿⠁⠈⢻⠷⢤⡀⠹⣿⡅⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠛⠁⠤⠼⣇⡀⢻⠿⠆⠀⢩⡰⣄⣼⣿⣜⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠠⡆⠰⡇⠋⠾⠻⡏⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢶⣶⡀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠷⠶⣦⣤⡘⣳⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣋⣼⣷⣶⣶⣦⡤⠭⠭⢥⣀⠀⢨⣿⠀⠀⠀⠀⢣⡞⠉⣀⠄⢊⣠⣶⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣋⡉⠝⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⡇⠀⢠⣾⣿⣿⣷⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⣼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠂⣀⠀⡀⢀⣼⠟⠁⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⣠⡿⠟⠛⠛⢿⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠞⠝⠁⠀⠀⠀⠀⠘⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣁⣠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⢿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢰⡀⠀⢸⠀⠀⣴⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢠⠠⢀
⠀⠀⠀⠀⠀⠢⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠃⠀⢈⠀⠀⠁⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠
⠀⠀⠀⠀⠈⠡⢠⠨⠁⠀⠀⠀⠀⠘⠀⢤⣄⠀⠀⢠⡀⠀⢿⠀⢀⣤⠀⠀⣀⣤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠘⠠⠞⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠙⠛⠉⡀⢀⢀⡉⠛⠛⠁⠈⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠖⠀⠀⢰⠟⠁⣼⠀⠙⢦⠀⠀⠒⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠙⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢰⠃⠀⢸⠀⠀⢷⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢈⠀⠀⠀⠂
⠀⠀⠀⠀⢄⠈⠂⠘⠀⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠢⠀⠰⢄⠸⢀⡴⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡘⠇⠸⠁⣀⡄
⠀⠀⠀⠒⠀⠒⢂⠀⢀⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠭⠀⠀⣍⡁
⠀⠀⠀⠊⢀⠐⠃⠸⠀⠓⢀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠃⠳⠀⠁⠁
⠀⠀⠀⠀⠁⠠⠂⢰⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠄⠠⢤⡀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⢀⣤⠀⠤⡀⠀⠀⠀⠀⠀⡤⠄⠠⡀
⠀⠀⠀⠀⠀⡃⠂⠀⠂⡧⠀⠀⠀⠀⣿⣤⣤⣥⣷⠀⠀⠀⠀⡎⠛⣁⠀⢸⠀⠀⠀⠀⢜⠐⠚⠐⡘
⠀⠀⠀⠀⠀⠱⠤⡠⠴⠃⠀⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠘⠤⠤⠤⠊⠀⠀⠀⠀⠘⠦⢌⠤⠟


⠀⠀⠀⠀⠀⡔⠉⠉⠑⡄⠀⠀⠀⠀⡶⣯⠭⡽⢆⠀⠀⠀⠀⡰⠪⠉⠙⢢⠀⠀⠀⠀⢠⠪⠉⠩⢢
⠀⠀⠀⠀⠀⣄⠠⡅⠀⡍⠀⠀⠀⠀⢇⠈⠀⠁⡼⠀⠀⠀⠀⢇⢶⣶⡶⡸⠀⠀⠀⠀⢱⠰⠶⠶⣢⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠙⠒⠊⠁⠀⠀⠀⠀⠀⠉⠒⠊⠁

⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⣀⠤⢄⡀
⠀⠀⠀⠀⠀⠃⠀⠂⠀⠇⠀⠀⠀⠀⡎⠀⠀⠀⢱⠀⠀⠀⠀⡟⠛⠛⠛⢻⠀⠀⠀⠀⣸⠳⠄⠴⠛⡀
⠀⠀⠀⠀⠀⠣⣈⣉⡠⠃⠀⠀⠀⠀⠳⣙⣒⡣⠎⠀⠀⠀⠀⢇⣲⡟⠓⠘⠁⠀⠀⠀⠙⢤⣘⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⡐⡶⣶⣖⡀⠀⠀⠀⠀⡠⢖⠓⡲⡄⠀⠀⠀⠀⢠⠒⠚⠒⢄⠀⠀⠀⠀⢠⢖⡊⣒⢆
⠀⠀⠀⠀⠀⡍⠈⡅⠉⡅⠀⠀⠀⠀⡇⣀⣀⣁⡸⠀⠀⠀⠀⣇⠈⠀⠉⢸⠀⠀⠀⠀⢢⣸⠒⢸⣀⠂
⠀⠀⠀⠀⠀⠈⠂⠀⠊⠀⠀⠀⠀⠀⠈⠒⠀⠚⠁⠀⠀⠀⠀⠀⠐⠂⠒⠁⠀⠀⠀⠀⠀⠛⠂⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠈⠳⠌⠰⠁⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠘⡧⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠂⠀⠀⠀⠀⠂⡰⠒⠀⡁⠁⠀⠀⢀⠀⠀⠈⠀⠀⠘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠄⢈⣰⣋⠁⠀⠁⠀⠀⠀⠀⠠⡀⠐⠀⠠⠈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢈⠧⠄⠀⠄⠀⢰⠁⠀⠠⠀⢈⢠⡀⠀⠀⠘⢀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠒⠀⢆⠈⢙⠡⢀⣠⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠤⣿⣇⠀⠀⠀⠀⠁⠉⠀⠀⠘⢀⠤⣀⠀⠀⠀⠂⠀⠀⠀⡀⡾⠁⠈⢀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠉⠲⡀⠀⠁⠠⠀⠁⠐⠁⠀⠈⢺⡄⢀⣀⠀⠀⠀⡿⠂⠈⣀⠀⠈
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠖⠒⠲⠾⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠠⠀⢄⡀⠁⠀⠀⠀⠸⠁⠈⠱⣆⠀⠀⠀⠀⠀⠀⠤⠠⠷⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠉⠳⡄⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⢰⣠⠤⡋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⢄⡀⠀⠀⠈⡀⠀⠀⠀⠰⠂⠠⠄⠀⠀⠒⠉⠙
⠀⠀⠀⠀⠀⠀⠂⠰⠉⠄⠀⠀⠀⠀⠀⠀⢀⠈⠙⢙⣆⢀⠢
⠀⠀⠀⠀⠀⢀⠈⠄⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣾⡅
⠀⠀⠀⢀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⠀⠀⠀⠐⠂

⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⢻⡇⠀⠀⠀⠀⣼⠁⠙⠲⠦⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⡇⠀⠀⠀⢰⠇⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⣄⠀⠀⠀⠀⠳⡄⠀⠘⡇⠀⠀⠀⡾⣷⣶⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⡗⣀⠀⠀⠀⠹⣄⠀⡇⠀⠀⢸⠃⠀⣩⠋⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢥⣄⡀⢸⡇⡿⠳⣄⠀⣀⠼⠶⠓⠶⠦⢯⣀⡜⠁⠀⠀⠀⢀⣠⠴⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠉⠙⠓⠧⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠉⢳⡄⢀⣠⠖⠋⠁⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠒⠦⢤⣀⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⣀⣀⣀⣤⠤⠤⠶⠾⠓
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠋⠉⠉⠉⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣄⠀⠉⢉⣽⡷⠒⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⠀⠀⣠⠞⠙⢲⣤⣄⣀⣀⣤⡴⢾⠁⠀⠈⠓⢦⣾⡟⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡔⠁⠀⠀⡾⠀⢠⡇⠀⠈⡇⠀⠳⡄⠀⠀⠀⠘⠦⣀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡴⠋⠀⠀⠀⣼⠃⠀⢸⠃⠀⠀⢻⠀⠀⠙⣆⠀⠀⠀⠀⠈⠳⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠋⠀⠀⠀⠀⣸⣧⠤⠴⠾⠀⠀⠀⠸⡆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣰⠚⠛⠉⠉⣹⠀⠀⠀⠀⣷⠀⠀⢀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⢦⣿⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡆⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⣆⢀
⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⢰⣦⣺⣞⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣟⣿⣢⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣻⣿⣷⣄⡀⠀⣀⣴⣿⣿⣻⣿⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⠋⠀⠈⠊⠀⠈⢻⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠟⣿⡿⣿⣦⡀⠀⠀⠀⣠⣾⡿⣿⡿⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣠⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠐⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⠀⠈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⢀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⣰⠛⠁⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢰⠁⢀⠐⠻⣿⣿⣦⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐⠚⢿⣿⣶⡄⠈⠇⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⣾⡀⢀⣾⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⣸⣿⣿⣿⠀⠘⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⡴⠛⠛⠶⣄⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⣠⠶⠛⠛⢦⡀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⣾⠀⠀⠀⠀⣹⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣏⠀⠀⠀⠀⣷⠀⢰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠘⢧⣄⣠⡴⠋⠀⠀⠀⠀⠀⠀⠈⢿⣟⠛⠶⠶⠶⠛⣻⡿⠁⠀⠀⠀⠀⠀⠙⢦⣄⣠⡼⠃⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠁⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡆⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣾⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⣠⣾⡇⠀⠀⠁⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⠹⣦⡀⠀⠀⣠⡿⣧⣀⣠⡾⠋⠸⣧⣀⣀⣠⠄⠀⢀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠁⠀⠀⢻⡟⠶⠾⠛⠀⠈⠉⠁⠀⠀⠀⠈⠉⢻⡇⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣀⣼⠇⠀⣀⣤⠶⠖⠛⠛⠲⠶⣤⡀⠀⠈⠻⠶⠶⠶⠶⣲⡿⠋⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⠀⣸⡇⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⢰⡟⠀⠀⠀⠚⣉⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣟⠛⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠘⢧⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⢀⡿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡟⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣷⡀⠀⠈⠙⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣾⡃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢈⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢠⡾⠋⠉⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⢀⣼⡀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠀⢠⡾⠻⢧⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢹⠄⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠀⠀⣠⣟⣤⡴⠶⠲⢦⡀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣤⣀⠀⢸⡆⠀⠀⠄⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠸⠷⠶⣦⠀⣴⠟⠉⠙⠿⠁⠀⠉⠻⢦⣷⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⡇⠀⠀⢠⡆⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⠀⠀⠀⠺⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⠻⣩⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣲⠇⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⠀⠀⠀⠀⠂⠳⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠈⠹⣀⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢰⡂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠠⡀⢻⡄⠀⠀⠰⡄⠃⠀⠀⠀⠀⠀⠀⠈⠹⠷⡄⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣶⠀⠀⢀⡧⠀⠄⠠⠄⢀⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠒⢂⠀⠛⢊⡄⠟⠉⠀⠠⣆⣟⣡⠞⠀⠴⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⠀⡀⠀⠀⣳⣌⡉⠉⠒⣄⢀⣤⡼⢉⣬⣧⣈⣉⠚⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢲⠞⠛⠀⠈⠀⠀⠈⠉⠉⠀⠤⣈⣍⠹⣦⣄⣦⣌⠁⢰⣦⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣢⡈⠐⢁⠀⠜⢻⠷⡂⢺⡿⠟⠐⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣽⣷⣶⡄⠀⠘⠀⠓⠀⠣⠤⠁⠀⠀⠀⠀⠀⢴⠊⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠂⠐⠀⡠⠘⡷⠀⠀⠀⠉⠀⢿⣿⠿⠛⡳⠀⠀⠑⠳⡄⠀⠀⠀⢂⠀⠀⠀⠀⠘⣤⣴⢛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢡⠎⣠⣄⠃⠀⠀⡀⣠⡆⠀⠀⣄⠀⠿⠀⠀⠀⠠⣫⠤⡀⠀⠀⠀⠀⠀⠀⠁⢿⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠼⣜⠑⠆⠀⢸⡧⢿⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢦⠙⢄⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⠿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣆⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢤⣒⣐⣐⣴⣶⣛⣀⣁⡘⠄⠄
⠀⠀⠀⠀⠀⢸⣏⠙⡯⣉⠩⣍⠏⠉⢉⠙⠉⠉⠉⠋⠛⠈⠋⠇⠑⠿⡍⢙⠑⡿⠩⠹⠃⢿⣇
⠀⠀⠀⠀⠈⢼⡞⠛⠓⠀⢙⠙⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⢈⠈⣡⠀⠀⡀⠀⠀⠀⣄⣸⢇⠁
⠀⠀⠀⠀⠐⢸⡏⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⢠⠈⠀⠁⠈⠀⠤⠤⣼⡿⠂⠁
⠀⠀⠀⠀⠐⢺⡏⠨⢥⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠼⠆⡢⣜⠀⠤⡆⠀⠀⠤⠀⢸⡇⠘
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠐⠈⠀⠂⢘⡂⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⣟⡜⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠃⠀⠈⠓⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⠀⢸⡇⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠒⠀⠐⠨⠀⠀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠠⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠠⢜⡀⠀⠀⠂⠸⠇
⠀⠀⠀⢀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡀⠀⠈⠙⢹⡇
⠀⠀⠀⠀⠐⠸⡇⠢⡄⠁⠀⠀⠀⠀⠠⠀⠀⠀⠄⡀⠀⠀⠲⢂⠀⢀⢀⡠⠀⠀⠂⠀⠈⣸⡿
⠀⠀⠀⢠⣤⢰⡃⠀⠀⣤⠀⡦⠂⠈⠀⠒⠀⠐⠐⠃⣄⠀⢀⠀⠀⠀⠀⡀⠀⠤⠠⢧⠂⣸⡇
⠀⠀⠀⠀⠀⠼⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⣈⠤⠄⠀⠀⠀⠀⠁⠀⠀⢔⡨⣆⣻⡆
⠀⠀⠀⠀⠂⣸⣧⣤⣤⡠⡊⠐⠸⠎⠃⠀⠚⠂⠤⠨⢇⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢍⢹⡇
⠀⠀⠀⠀⠀⢸⣇⣁⣡⣅⣀⣠⢄⢀⢤⣀⣲⠂⣈⣄⣀⣁⣰⢂⣀⣀⡀⣀⢀⣉⢹⣼⣩⣽⡆
⠀⠀⠀⠀⠰⠤⣁⠙⠉⠩⠉⠁⠈⠉⠉⠉⠉⠈⠉⠉⠙⠉⠙⠙⠋⠉⠓⠉⠋⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠘⠛⠻⣿⣿⠿⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠠⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⣿⣿⡿⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣴⣶⡚⠭⠡⠃⠒⠂⠄⡀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢒⣚⣭⠴⢒⣋⠉⣁⠽⣬⣼⣅⣒⠀⠀⠀⡁⠀⢀⣾⡿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⣶⣲⡿⠿⡿⠿⢟⣛⡿⢷⣶⣚⣩⠶⢋⡵⢊⡕⣠⢟⣦⣁⢛⢸⠁⠠⣾⣿⣿⣾⣿⣿⠷⣒⡦
⠀⢀⡠⢔⣒⡩⠽⢚⡊⠥⠐⣀⡡⠴⢛⣫⡽⠖⣫⠔⢋⡽⡋⠿⣐⣯⣞⡵⣋⣴⡟⣿⠸⡀⠀⢿⣥⡟⣯⣡⣤⡾⠋
⢓⡞⡚⡩⠠⠖⣊⣉⡤⠔⣛⠉⠀⢔⠋⢁⢐⡋⠀⠖⠫⡠⢊⠔⢉⡤⠙⣟⣥⡞⢁⠘⢻⡟⢃⣛⣿⣯⣿⣿⠃⠀⢄
⠀⠉⠀⠋⠉⠈⠀⠈⠈⠉⠀⠈⠁⠀⠀⠈⠉⠀⠉⠁⠀⠁⠈⠈⠃⠀⢀⠀⠒⠚⣏⣼⣼⢴⣿⣯⣼⡥⣸⠃⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡊⠄⡴⣱⠞⣵⣿⠟⣹⠿⢿⡓⠁⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠜⢡⠞⡵⢅⡜⠁⣈⡝⢇⣰⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠓⠒⡶⣖⡥⠄⠀⠉⠉⣻⣿⡲⡤⣦⣼⡵⠵⠞⢛⣣⣼⣯⠞⠓⡿⠀⠐⣀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠔⢊⠁⠀⠁⠀⠀⠀⠀⢀⢙⡿⣃⠂⢁⠨⠁⠀⢁⣾⣏⡉⠁⠪⣤⣝⡞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣾⠟⠡⠐⠁⠰⢡⢠⢤⣄⠌⢡⣬⠛⠛⢛⡁⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢞⠩⢊⠞⢁⣴⣥⠤⠚⣠⠪⡠⡠⢫⠔⠀⣀⢠⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣤⠅⠪⠳⠊⠅⠈⠳⠄⠀⠉⠓⠛⠋⠁⠀⢞⡵⠎⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠁⠀⠠⠀⠀⠀⠔⠉⠼⠡⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⡀⢈⡥⠶⠊⡁⠄⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⠫⠝⠻⢀⡤⠊⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡁⠀⠀⣀⡔⠈⠒⠤⢀⣀⡠⠄⠒⠀⠚⠋⠠⡤⠤⡀⠏⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⠑⠢⠀⠀⠈⢉⠥⠀⣄⣀⢀⡀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⢤⣀⣈⠀⣂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠉⢱⠀⡌⠉⠉⠁⢀⣠⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⣐⡊⠅⠈⠑⠇⠀⢀⣀⠠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠀⢒⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡀⠀⡄⠀⢀⠀⢀⣀⠀⢀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠑⠃⠀⠃⠀⠋⠂⠘⠙⠀⠈⠀⠑⠂⠐⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⣄⠀⠀⠻⠀⠀⠀⠀⠀⠀⣾⣠⠀⣀⣤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠀⠉⠀⡀⠀⠀⠀⡉⠁⠀⠀⠀⠀⢀⣿⣦⡿⠟⠰⢛⢡⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠈⢐⡏⠁⠀⠀⠀⡁⢀⣀⠀⠀⢾⢿⣿⡍⠀⣦⣼⠟⠈⢻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠻⣄⠀⢀⡀⠛⠁⠀⠀⠐⡾⠃⠈⠛⠻⠶⠮⢡⠶⡿⣿⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠢⣀⠀⠀⠂⣠⣤⣄⣣⠠⢔⡒⢳⣆⡠⠆⠈⠽⣿⣿⡻⡥⢘⡿⢚⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣠⡙⠁⠀⣴⣿⣿⣿⠏⠐⠀⠘⢀⡎⠀⠲⠖⠀⠀⡈⢀⠀⣾⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢸⣆⣄⡀⠀⠈⠣⡄⠠⠀⢉⠟⠋⣍⠈⢢⢁⠴⠿⠉⠀⣀⡀⣄⠈⠀⠠⠆⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⣉⣿⢠⡹⣤⠁⡶⡀⠂⠈⠃⠠⡀⢠⠆⠀⠀⠀⠔⠀⣥⣿⠂⠀⠀⣰⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⢠⠞⠙⠡⠤⠙⢤⣴⠑⠙⠲⡁⢤⣀⣅⠀⠁⣸⡏⠀⢈⠼⣿⣿⠺⠀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠀⣩⡤⠀⠾⠈⠁⠈⠁⠄⠑⢤⣴⣿⣿⣿⣷⡄⠘⣧⠀⣀⢧⠅⠊⡀⠀⠐⠘⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⡆⠀⠘⠷⠂⠀⢠⠀⠘⢯⣻⡿⠿⠃⠀⠈⢷⠍⡉⠁⠀⠀⠀⣈⡀⠀⣠⢐⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⢀⡆⢀⠀⠈⠃⠀⠀⠀⠀⠤⡠⠤⠀⠄⠂⠠⠘⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠂⠀⠀⠀⠘⠃⠁⡀⢀⣀⠀⡤⣘⠀⠊⠀⢐⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⠀⠈⠉⠉⣄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠎⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠐⢛⡻⡆⠀⠈⢻⡀⠒⣀⢲⡀⠈⠀⠘⠀⠀⠺⢙⣒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠒⠀⠀⣉⠎⠀⣠⠠⣌⡁⠀⠀⠀⠎⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠰⢫⡀⠈⠻⠄
⠘⠀⠘⠀⠐⠂⠀⠁⠘⠂⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠘⠂⠘⠂⠘⠃⠀⠀⠈⠂⠘⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⡠⠐⠀⠐⠀⡀⠀⠀⠀⢀⠔⠂⠐⠢⡀⠀⠀⠀⠀⠄⠒⠀⠂⢄⠀⠀⠀⠀⡠⠐⠀⠐⠠⠀⠀⠀⠀⢀⠐⠂⠐⠢⡀⠀⠀⠀⢀⠄⠒⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠁⠐⠀⠐⠀⢘⠀⠀⠀⠈⠀⢐⣀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠂⠀⠁⠀⠀⠀⠃⣀⣂⣀⣀⠘⠀⠀⠀⠀⢀⣂⣀⣂
⠀⠀⠀⠀⢄⠂⠀⠔⠀⠂⠀⠀⠀⠢⡑⠀⠀⢂⠌⠀⠀⠀⠀⠌⠀⠀⠈⠠⠁⠀⠀⠈⢄⠀⠀⠀⡠⠀⠀⠀⠀⠣⡻⠋⠙⢏⠜⠀⠀⠀⠀⠈⠻⠿⠛⡠
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠔⠁⠀⠀⠁⠄⠀⠀⠀⡐⠁⠀⠀⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠠⡀⠀⠀⢀⠆⠀⠀⠀⠑⡀⠀⠀⠀⣰⣀⡀⣀⣀⣆⠀⠀⠀⠠⠂⠀⠀⠀⠢
⠀⠀⠀⠀⠀⣀⣀⣁⡀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢠⠀⠀⠀⠀⢀⠄⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠁⠀⡀⠀⠀⠀⡛⠛⠋⠙⠛⢛⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠙⠿⠛⠕⠁⠀⠀⠀⠐⠤⠀⠀⠀⠂⠀⠀⠀⠀⠢⠀⠀⠠⠈⠀⠀⠀⠀⠂⠀⠀⠀⠔⠁⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠀⠀⠈⠢⠁⠀⠈⠊

⠀⠀⠀⠀⢀⠠⠀⠤⡀⠀⠀⠀⠀⠀⡀⠄⠠⢄⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⡠⠄⠠⢀⠀⠀⠀⠀⠀⢢⠤⠤⠤⡆
⠀⠀⠀⠀⠁⠀⠀⠠⠀⠂⠀⠀⠀⠎⠀⡀⠀⠀⠡⠀⠀⠀⠐⠀⠠⠀⠀⠈⠄⠀⠀⠠⠁⠠⠀⠀⠈⠂⠀⠀⠀⠎⢴⡦⢴⡆⠱⠀⠀⠀⠐⠀⠠⠀⠀⠈
⠀⠀⠀⠀⡀⢶⣶⣶⠆⠀⠀⠀⠀⢄⠀⢠⡄⠀⡐⠀⠀⠀⠠⠐⠶⠿⠶⢀⠂⠀⠀⠰⡀⠔⠀⠐⢄⠄⠀⠀⠀⢄⠀⠀⠀⠀⡰⠀⠀⠀⢀⠠⠀⠀⠠⢀
⠀⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠁⠒⠀⠂⠁⠀⠀⠀⠀⠈⠐⠀⠒⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠁⠂⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠂⠀⠐⠠⡀⠀⠀⠀⠠⠀⠀⠀⠂⡀⠀⠀⠀⢀⠄⠀⠀⠐⢄⠀⠀⠀⠀⡀⠂⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠂⠁⠀⠀⠀⢉⠖⠂⠀⠐⢎⠁
⠀⠀⠀⠀⢠⣭⣤⣬⣥⠀⠀⠀⠀⠁⠀⠘⠀⠀⢸⠀⠀⠀⠈⠀⢀⠀⠀⠀⠃⠀⠀⠈⠀⠰⠀⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠦⠀⠆
⠀⠀⠀⠀⠠⠙⠀⠘⡡⠂⠀⠀⠀⠡⡚⠿⠿⢃⠌⠀⠀⠀⠘⢄⠀⠀⠀⠀⠁⠀⠀⠈⠄⢻⣿⡿⠣⠀⠀⠀⠀⠡⠀⠀⠀⢀⠌⠀⠀⠀⠐⢈⠂⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠊⢀⠀⠀⠑⠄⠀⠀⠀⡔⠁⡀⠀⡈⢂⠀⠀⠀⠠⠈⠀⠀⠀⠐⡀⠀⠀⢀⠂⠀⠀⠀⠗⡄⠀⠀⠀⡔⢰⣤⣤⡄⢦⠀⠀⠀⠰⠫⠤⡀⠬⠳⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⡈⠁⢠⠀⠀⠀⢀⠰⠀⣀⠀⠀⠄⠀⠀⢀⠀⣈⣤⣄⡀⡀⠀⠀⠀⡄⣾⠿⢿⡇⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠑⠤⠀⠠⠀⠀⠀⠀⠀⠘⠢⠄⠠⠄⠁⠀⠀⠀⠈⠂⠄⠀⠤⠊⠀⠀⠀⠀⠑⠬⠉⠩⠐⠀⠀⠀⠀⠀⠨⠔⠪⠕⠁⠀⠀⠀⠈⠂⠄⠀⠤⠊

⠀⠀⠀⠀⢀⠤⠀⠠⢀⠀⠀⠀⠀⠀⠠⠀⠠⢀⠀⠀⠀⠀⠒⡤⠠⠀⠤⡔⠂⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠠⢄⠀⠀⠀⠀⠀⡀⠄⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠄⠠⠀⠱⠀⠀⠀⠘⠀⠠⠀⠄⠘⠇⠀⠀⠐⠁⠠⠀⠠⠀⠂⠀⠀⠀⠊⠒⡦⠔⠶⠑⠀⠀⠀⠈⠐⠒⠖⠒⠈
⠀⠀⠀⠀⡀⠀⠀⠠⢂⠄⠀⠀⠀⢆⠑⠀⢤⠆⡐⠀⠀⠀⠠⡀⠀⠄⠀⢀⠃⠀⠀⠐⡀⠀⠀⠀⢀⠆⠀⠀⠀⢂⠐⠐⠒⠂⡐⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠈⠐⠀⠂⠁⠀⠀⠀⠀⠀⠁⠂⠐⠈⠀⠀⠀⠀⠀⠈⠂⠀⠂⠁