Lashes Emojis & Symbols

⠀⡸⢦⡴⡇⠀⠀⢀⡷⡤⢾⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⣀⣀⣴⠀⠀⠀⠀⢶⣤⣤⠆⠀⠀⠢⣤⣤⠶
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠑⠒⠃⠀⠀⠀⠓⠒⠁⠀⠀⠀⠘⠳⠶⠃⠀⠀⠈⠲⠖⠃⠀⠀⠀⠀⠻⠷⠶⠋⠀⠀⠹⠶⠾⠗
⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⣀⠀⠀⠀⣀⠀⠀⡀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⢀⠀⢀⣀
⠀⠈⠉⠋⠁⠀⠀⠀⠉⠋⠁⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠉⠋⠁
⠀⠶⣤⣤⠄⠀⠀⠰⣤⣤⠶⠀⠀⠀⠦⣀⣠⠖⠀⠀⠐⢄⣀⡴⠂⠀⠀⠀⢶⣤⣤⠄⠀⠀⠢⣤⣤⡶
⠀⠀⠀⠀⡀
⠀⠘⠳⠾⠃⠀⠀⠈⠳⠶⠛⠀⠀⠀⠛⠲⠚⠃⠀⠀⠈⠓⠲⠚⠁⠀⠀⠀⠛⠶⠶⠃⠀⠀⠑⠶⠶⠋
⠀⢀⡀⠀⣀⠀⠀⢀⠀⢀⣀⠀⠀⠀⢀⡀⠀⣀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⣤⣀⣀⡤⠀⠀⢤⣀⣀⣄
⠀⠈⠙⠛⠁⠀⠀⠈⠙⠛⠁⠀⠀⠀⠉⠙⠛⠁⠀⠀⠈⠙⠙⠉⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠙⠉⠁
⠀⠠⣄⣀⡴⠀⠀⠲⣄⣠⠄⠀⠀⠀⠠⢄⣀⠄⠀⠀⠠⣀⣀⠄⠀⠀⠀⠀⢴⣤⣤⠄⠀⠀⢠⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠰⢤⡤⠖⠀⠀⠐⢤⣤⠶⠀⠀⠀⠴⣤⣤⠄⠀⠀⠠⢤⣤⠶⠀⠀⠀⠀⠶⣤⡴⠖⠀⠀⠲⢤⡤⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⢿⣿⣿⣾⣿⣿⣿⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⢿⣿⣷⣿⣿⡿⠿⠿⢿⣶⣦⣤⣀
⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠛⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠛⠑⠙⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢙⣶⣶⣴⣤⣤⣤⣤⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣤⣤⣤⣤⣴⣴⣶⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⡿⠛⢏⠙⣿⡿⠛⡷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢾⠋⢻⣿⠏⡹⠛⢿⣿⡿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⠶⠤⠴⠾⠤⠄⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠠⠦⠷⠦⠤⠶⠷⠞⠛⠉

⠀⠀⠀⠒⣺⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣗⠒
⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠅
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠛⠻⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠟⠛⠈⠈⠀⠁


⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠒⣲⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣖⠒
⠀⠀⠀⠀⠀⢊⣿⣿⣿⣷⣦⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⣴⣾⣿⣿⣯⡐
⠀⠀⠀⠀⠀⠀⠐⣛⢻⣿⣿⣿⣿⣿⡟⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠐⢿⣟⣿⢻⣿⣿⣿⣿⣿⡟⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠹⠟⠏⠓⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠚⠹⠻⠏⠁⠈⠂⠈



⠀⠀⠀⠀⠠⣤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⠄
⠀⠀⠀⠀⠀⠈⠽⢿⣿⣿⣷⣶⣶⣶⣶⡿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠹⣿⢿⣶⣶⣶⣶⣾⣿⣿⡿⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠙⠋⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠙⠋⠉⠙⠋⠃


⡀⣀⡀⠀⢀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠙⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⠟⠁⠀⠀⢀⡀⣠⡄⡀
⠀⠀⠀⢠⣾⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠻⠋⠁⠀⣀⣸⣴⣿⣿⣿⣿⣿⣿⣾⣤⣠
⠀⠀⠀⢿⠋⠉⠉⠛⠿⠿⢿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠏⠁⠘⢿⣷⠿⢿⣤⣿⣿⠋
⠀⠀⠰⣾⣿⣿⣿⡿⠟⠛⣿⣿⣹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠗⠠⡰⠣⠈⠻⠉
⠀⠀⠀⠙⠛⢿⣿⣤⣀⣠⣭⡿⠟⠓⠉
⠀⠀⠀⠀⠀⠀⠙⠟⠛⠈⠊

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⢰⠟⠛⠻⢿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢀⣠⣼⣦⣠⣠⣀⠀⠉⠛⠻⠿⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠟⠻⢿⣿⣦⡀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣆
⠀⠀⠸⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣆⣴⣤⣼⣼⣶⣦⣴⣄⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠈⠙⠛⣿⡁⠀⠀⢿⣿⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠹⠳⢄⡤⢈⡛⠿⠋⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠟⢻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠈⢯⣿⣿⡷⠃⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢠⠀⡄⣤⠰⡘⣿⠟⠿⠿⠿⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠉⠛⠿⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠲⠤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣉⣉⣩⣭⣶⣾⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣉⣡⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣥⣴⡾⠿⢛⣡⣾⡿⣫⣿⡟⣽⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠷⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣀⣤⡶⠿⠋⣡⣾⠿⠋⣰⡿⠃⣾⡟⢸⣿⢻⡿⢻⡏⢿⡿⣯⠻⣎⠻⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠟⠋⠁⣠⡾⠋⠀⣸⡟⠀⣾⠇⣸⠇⢸⡇⢸⡇⢹⡄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠞⠋⠀⡼⠋⢠⠟⠀⡼⠁⠘⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠠⠀⡄⠀⠀⡆⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⢀⠀⣿⢸⡆⢰⡇⡅⣸⠃⡇⣾⡧⣾⢀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡜⣇⠠⣸⡶⣏⣿⣬⣿⣼⣷⣿⣿⢰⣱⡟⣸⣧⣾⣿⢧⣤⢶⡾⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠹⣦⠬⢿⣧⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣿⣿⣟⣽⣿⣷⣟⣶⣫⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠢⣤⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⢋⣤⠟⣁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣼⣿⣿⣿⣿⣿⣿⠟⠛⠙⢉⢁⣸⣤⣤⣃⠜⣩⠻⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢟⣩⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠀⢸⣿⠀⠀⠀⢀⣿⠛⠛⠋⢙⣷⠁⠀⢨⣿⣷⠀⠐⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡿⠖⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⠟⠁⠀⠀⠀⠀⠸⣿⠉⠉⠉⣹⣿⣧⡀⢀⣼⡿⠷⠄⠘⣿⠏⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣴⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢻⣧⣔⡩⢖⡽⠛⠻⠟⢻⡁⠀⠀⣰⠟⠀⠠⠴⢶⣶⣷⣾⣿⡿⠻⠷⠭⠉⠁
⠀⠀⠀⠀⠀⠐⠫⠥⠀⠙⢶⣦⣤⣄⣀⠀⠀⣄⣤⣤⠙⢿⣾⣩⠆⠀⠀⠀⠀⢿⣠⡴⣋⣠⣤⣴⣾⣿⠿⠿⣍⠉⠲⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠉⢻⢿⣿⣾⣶⣶⣦⣤⣽⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⢿⡟⠗⠉⠁⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠙⠉⠉⠉⢻⠙⣯⠙⠃⠘⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁








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

⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⢿⣷⣦⣄
⠀⠀⠀⠠⠞⠋⠉⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⢿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣀⣀⣠⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⡿⣿⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⣀⡴⠟⠋⠉⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠈⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣼⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣿⣿⠿⢻⣿⢿⣽⡿⣿⡟⠿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠟⣿⡿⣭⣿⢿⣿⠙⠿⣿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣄⠈⢿⣄⣉⣡⡾⠃⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠻⣧⣍⣁⣴⠏⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠿⠿⠿⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠺⠿⠿⠗⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠁⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠁⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠉⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣤⣤⣀⣀⣀⣀⣀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⢿⣿⣿⣿⣿⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⣀⠴⠟⠋⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠟⠛⠉⠉⠉⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⣠⣠⣠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⣿⣿⣿⣿⣿⣖⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠀⣿⡙⠟⣹⡇⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⢿⣙⠛⣹⠇⢀⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠮⠿⠿⠯⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠿⠿⠷⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⠿⠟⠛⠛⠛⠛⠛⠷⢦⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣶⣶⣾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣶⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣿⣿⠿⡿⠿⢿⣦⡀
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⣀⣠⣤⣶⡾⠿⠟⠛⠛⠿⢶⣄⡀
⠀⠀⠐⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠁
⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⡿⠿⠟⠛⠛⠛⠳⠶⠤⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⣠⣶⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠦⡀

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⣷⣦⣄⡀⠀⠀⠀⣠⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣽⢻⣶⣿⣷⣦⡍⠙⠻⠿⠿⠟⢛⣛⣛⣃⡒⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⢿⠉⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠆⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢛⠶⠤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣤⡶⠶⠛⠿⣿⣿⣷⠀⠈⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠄⠀⠀⢰⣌⠉⠉⠀⢠⠀⠀⠀⠘⣿⣿⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⠀⠀⠀⣾⡟⣧⡀⠀⠸⣧⡀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠹⣿⣦⣄⡻⣿⣦⣀⠀⢁⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⠻⣿⡿⣾⣝⠿⣿⣖⢿⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⣾⣿⣿⣦⠈⢳⡄⠀⣿⣿⠈⡿⠀⠀⠙⡇⣿⣧⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡀⠈⠉⠉⠁⢠⠘⣿⣦⣿⠋⠀⠁⣠⣴⡾⠁⣿⠏⢀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠒⠊⠀⠀⣿⣿⠃⡄⣴⣿⣿⡟⢁⡾⠃⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⢿⡿⣿⣿⠀⢸⢁⣾⡿⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⣰⣿⠏⠻⣿⣿⣌⠻⣆⠈⢾⡏⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠔⢱⣿⠀⠀⠈⢻⣿⡷⣌⣷⡈⠛⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡰⠀⠀⠀⠀⣴⣯⠀⣿⣿⡀⠀⠀⢀⣿⠇⠨⣿⣧⠀⠘⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⣆⠈⠙⠻⢦⣠⠞⠁⠀⣴⣿⣯⠎⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⢀⣼⡿⢇⡴⠛⠉⣾⣿⣦⡀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⣼⡏⢠⡏⠀⠀⠀⠹⢿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡏⠈⠻⢾⡇⠀⠀⢀⠄⠎⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢿⡀⠀⠸⣷⡀⠀⠘⢆⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⠻⡀⢀⣿⡿⠀⠀⠀⠉⢶⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⡴⠞⠋⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢀⡤⣄⣠⡤⢠⡄⣤⢠⣤⠤⡤⢠⠤⡄⡄⢀⡤⣄⣠⠤⠄⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠘⠦⠞⠸⠟⠺⠛⠻⠸⠿⠀⠇⠙⠶⠋⠷⠜⠷⠞⠙⠾⠃⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⡇⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣠⠤⠴⢻⣇⣀⣀⣀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣰⠀⣿⠈⠈⢸⡇⠉⠉⣹⠀⣧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠉⠁⢿⠀⠘⣆⠡⢸⡇⠀⣠⠏⠀⡛⠈⠉⠛⠲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣸⠶⠖⠚⣷⢾⡷⣾⠛⠲⢤⣇⠀⠀⠀⠀⠀⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⢻⡏⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢁⣤⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣬⣤⣄⣀⢠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣣⠴⠒⠛⠶⡇⢸⡇⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡧⠀⠛⠒⠒⠒⠒⠛⢸⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠶⠖⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠙⣆⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠸⠇⠀⠀⠀⠀⣠⢤⡟⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣘⣾⣭⣭⣭⣤⣤⡐⠀⠀⠀⠀⠀⢃⠀⠀⣀⣾⡷⠊⠀⠀⢀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣓⣒⣒⣒⣺⣇⢻⡀⠀⠀⠀⠀⢈⢧⠀⠈⡃⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏⠀⠘⢦⣷⡤⠤⠠⠶⠛⣸⠀⠀⠙⠲⠤⡤⢤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠚⠉⠉⠉⠉⠑⡄⠀⢀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠋⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⡧⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣉⣙⡛⠂⠤⠄⠀⠀⠻⠿⠁⣦⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡙⠉⡹⢻⣿⡷⠃⢢⣤⢶⣶⣭⡟⢿⡿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠘⠟⠁⠀⠀⢻⣦⠉⣿⡇⠀⠹⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳

⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⣿⠀⢹⣿⣿⢿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠁⣰⣿⣿⣿⣿⣷⣦⣌⣿⣻⣻⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⡾⠻⠛⣩⡿⢿⣿⣿⣿⣯⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡇⠀⢀⡟⡰⠶⢾⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⡖⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠳⣔⠞⠁⠈⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣾⠟⠛⠛⠻⢿⣿⣿⣟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢻⣦⣄⠀⠀⠀⠙⣏⢿⣷⣤⡀⣌⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠉⠃⠀⠀⢀⡿⢀⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠞⠗⠛⢻⣿⣿⡿⠟⠛⠿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠘⢆⡶⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⢷⠀⠘⣿⣿⣿⣿⣿⡿⣿⠟⠛⠛⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠈⡷⡀⠀⠘⣄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢻⠻⣿⠀⠘⠦⠀⢀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢀⠀⠈⢦⢀⠈⠑⠒⢀⣤⣤⣤⣤⣤⣤⣀⣀⡀⠘⢦⡣⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠬⠀⠀⠀⠉⠀⠀⠀⠸⠿⠿⢿⢿⢿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣶⢶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⢀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⢸⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠋⠁⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣴⣎⡔
⠀⠀⠠⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠐⣾⣿⣿⣿⣿⡟⠉⠙⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⣿⣿⠟⠉⠉⠀⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⠏
⠀⠒⠶⠿⠿⠟⠋⣽⣷⠀⠀⢸⣿⡟⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡏⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠻⣿⣿⡾⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢾⣷⣤⣤⣀⣀⣀⣀⣤⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣴⣶⡾⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢸⠈⠛⠻⠿⠿⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⢠⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠶⢤⣄
⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠟⠉⠁⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢀⠀⡀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢬⣶⣿⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣿⣿⠟⠛⠛⠋⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⡿⠉⠉⠁
⠀⠠⠤⣾⣿⡿⠟⠋⣿⣇⠀⠀⢸⣿⡽⢿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡇⠀⠀⠀⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠻⣿⣾⣶⡿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⣼⣧⣄⣀⣀⣀⣀⣀⣨⣽⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣤⣶⠷⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⠿⠛⠙⠉
⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⣿⣿⣷⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣆
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠘⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣤⣤⣤⣤⣄⣠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣿⠿⢿⣿⣿⠿⢿⣿⡟⠿⣿⣿⣿⣿⣿⣯⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⣿⣯⠀⠸⢿⣷⠆⠀⢹⡿⠀⠈⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⣿⣄⠀⠈⠁⠀⣤⡿⠃⠀⠀⢀⠜⣽⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠈⠛⠻⠶⠶⠞⠋⠀⠀⠀⣀⠥⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠂⠄⠤⠠⠂⠐⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢀⣤⠾⠿⠿⠿⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠿⠿⠿⢦⣄
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠈⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⢀⣀⣀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠈⠙⢿⡁⢿⣙⣋⡿⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⣯⣛⣹⢇⣨⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢀⣤⠾⠿⠿⠿⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠿⠿⠿⢦⣄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠟⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢶⣶⣦⣄⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⣀⣤⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠿⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣦⣤⣄
⠀⠀⠀⢀⣴⠟⠋⠉⠉⠙⠛⠛⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠛⠋⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⢠⣀⣴⣿⣶⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⢶⣶⣦⣶⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠈⢯⣛⣃⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠻⣝⣛⣸⠃⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂

⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀
⠀⠀⠀⠐⠋⠉⠀⠀⠉⠉⠙⠗⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠺⠋⠉⠉⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠐⠛⠉⠙⠛⠿⠙⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠛⠿⠙⠋⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⣿⣿⢿⣯⠀⠀⠀⣀⣠⢄⡉⣍⣛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣪⣵⠞⠁⠘⡍⢸⡏⠀⠀⠀⠘⠾⣿⣿⣿⣿⣿⣦⣝⢿⣦⡀
⠀⠀⠀⣠⣶⣿⠿⣿⣿⣿⣿⡏⠀⡆⡆⠘⢦⡁⢄⠀⠀⠀⠀⠈⠻⣿⡌⢻⣆⠙⢿⣿⣿⣆
⠀⠀⠰⢫⠏⣠⡿⠻⠛⣫⣿⣧⠀⠈⢹⣄⣠⠈⠙⠷⣤⡀⢄⢠⡀⠙⣿⡆⠙⡆⠀⠹⣿⣿⣧⡀
⠀⠀⠀⢸⠀⣿⢀⣠⠞⠉⢿⣿⣦⣦⠀⠙⠻⣿⣧⠰⣦⡙⢾⣧⢱⡄⠘⣿⡀⠈⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠈⠻⣏⠻⣷⣦⣀⠀⠉⠻⢮⣿⣦⡹⣧⢻⡄⢹⣧⠰⡄⠘⣆⢻⣿⣿⢷
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣉⣹⣿⠷⣶⣤⡈⠙⢷⣿⣾⣷⠈⣿⡀⣿⡄⢻⡌⣿⣿⣎⠃
⠀⠀⠀⠀⠀⠀⠐⣛⡲⠀⠀⠀⠐⠛⣩⣥⣤⣤⣄⣤⠉⠻⣦⡀⢻⣿⣿⠀⢿⡇⣿⣇⢸⣷⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠘⠉⠹⠷⠀⠀⠀⠀⠃⠘⠛⠘⠋⠀⠀⠀⠸⣷⠀⣿⣿⠀⣿⣿⣿⣿⣼⢻⡿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣿⣿⠀⣿⢸⡇⢻⡏⠈⠇⣿⣿⡇⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣾⣰⣿⡇⢰⡏⠈⠀⠸⢡⡄⣸⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡾⢡⢾⡿⣿⡿⢀⣿⠁⠀⢀⠀⣼⣰⢯⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⣸⠁⣿⠸⣹⣿⠃⣼⡏⣸⠀⣾⣰⣿⢋⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠋⠀⠀⢠⡏⠀⡇⢠⣿⡏⣸⡿⣰⢇⣼⣿⠟⣡⡿⣹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⣿⣰⡿⣱⣿⣾⠟⢃⣼⠋⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣼⣿⣿⣷⣿⠟⠁⠔⠋⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⠿⠋⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣹⣿⠇⢀⡀⠀⢀⠔⣡⢟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⣸⣧⢱⣿⣶⣿⣔⡴⢋⡼⢋⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⡇⠘⣷⣿⣿⡿⢋⣴⠟⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠎⠻⣿⣷⡟⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣾⣶⡜⢻⣷⠏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣧⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⢿⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢰⢸⡇⢀⢠⣼⢀⡇⢸⢠⡆⣶⡀⢠⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣆⢷⡈⣇⣿⣼⣼⣼⣿⣷⣸⣿⣷⣿⣿⣾⣿⣶⣼⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣶⡞⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⠿⠿⢻⠟⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⡟⠀⢠⣄⣠⣿⣿⣿⣿⣿⣇⠙⢿⣿⣿⣮⣴⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣄⠀⠀⠀⠀⠀⣿⠀⢸⣾⣿⣿⣿⣿⣿⣿⡇⠀⣾⠉⠻⣿⣯⣥⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣋⡽⢷⣄⡀⠀⠀⠘⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⣰⠇⠀⠀⠈⠻⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠖⣋⡽⢟⣦⣄⡀⠀⠢⣄⣀⠀⠉⢀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡴⠋⡴⢋⡽⢳⠶⣤⣬⣉⣉⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠁⠏⢰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣠⠀⡀⣠⢐⢄⡮⢀⡤⠰⠀⠀⡆⠀⡞⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠣⣸⠐⠏⠁⠸⠅⢾⠀⠯⠰⠇⠿⠸⠇⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠄⠰⠀⠀⠀⠀⠀⠠⠀⠀⠐

⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣀
⠀⠀⠀⠔⠛⠉⠉⠁⠀⠀⠉⠙⠻⠿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠉⠉⠁⠈⠉⠉⠛⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠉⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠁⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠉⠀⠀⠈⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠉⠁⠈⠉⠙⠲⠄
⠀⠀⠀⢀⡀⢀⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⠀⢀
⠀⠀⠀⠢⢭⣽⣿⣿⣿⣶⣤⣤⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣭⡥⠄
⠀⠀⠀⠀⠀⠛⠿⠟⣿⣿⣿⣿⣿⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⡟⠿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⠉

⣶⡶⢶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢉⣙⠛⠳⢦⡀⠀⠀⠀⠀⠀⢀⡴⠾⠛⣉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⠿⣿⣿⣷⣦⠈⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⣀⣁⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠛⠙⠂⠙⠂⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠋⠉⠛⠒⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⠳⠀⠀⠀⠀⠘⠛⠉⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡿⠟⢟⢿⡷⠄⠀⠀⠀⠀⠀⡰⢿⡿⠿⠿⠿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣈⣉⡛⠓⠆⠀⠀⠀⠀⠠⠶⠛⠋⢉⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢻⡟⣿⠆⠀⠀⠀⠀⠀⠀⠀⡶⠿⡿⣿⡿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠉⠉⠉⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠂⠀⠀⠀⠀⠈⠉⠁⢠⣴⣴⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⠛⢉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⠈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⣤⠶⠿⠿⠿⠿⣿⣶⣶⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⠿⠿⠿⠿⠶⣤⣄
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⡴⠞⢛⠻⣿⣏⠿⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢛⠿⣹⣿⠟⡛⠳⢦⣤
⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⢦⡉⣁⡴⢁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⢦⣈⣉⡴⢁⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣾⣿⣿⣶⣾⣿⣿⣿⣿⢿⠾⣟⣯⣭⠶⢶⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⣿⣿⣿⣿⣿⢿⠿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣰⣴⡟⣼⠹⠛⠛⠋⠁
⠀⠀⠀⠀⢠⢸⣿⡟⠃
⠀⠀⠀⠀⢸⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣀⣴⣄⣠⣤⣀⣄⣄⣔⣀⣀⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣷⣿⣿⣿⡿⣿⡿⠿⡿⠿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣬⡿⠟⠋⠹⡀⠈⠿⣷⠿⠃⢀⠇⠀⣠⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠋⠀⠀⠀⠀⠑⠤⣀⣀⣠⣴⣧⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠤⡤⠤⠄⠖⠒⡎⠫⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⣴⡿⠻⢷⠆⣰⡾⠟⢿⣦⠀⣾⡟⠻⠆⢸⣿⣷⠀⣼⣿⡇⢾⡿⠛⠟⠘⠿⣿⠟⠃⣴⡿⠻⢷⣦⠰⣿⠀⠀⢠⣶⠟⠻⣶⡄⣠⣾⠟⠿⠦⠙⣷⣀⣼⠟
⠀⣿⡄⠀⣀⡀⣿⣇⠀⢀⣿⠇⣙⠻⢿⣶⢸⣿⢻⣿⡟⣿⡇⣿⡟⠛⠛⠀⠀⣿⠀⠘⣿⡀⠀⣸⣿⢈⣿⠀⠀⢸⣧⠀⠀⣼⡇⢿⣇⠰⢿⣷⠀⠘⣿⡏
⠀⠈⠛⠛⠛⠁⠈⠛⠛⠛⠋⠀⠛⠛⠛⠋⠘⠛⠀⠛⠀⠛⠃⠛⠛⠛⠛⠀⠀⠛⠀⠀⠈⠛⠛⠛⠁⠘⠛⠛⠛⠀⠙⠛⠛⠋⠀⠈⠛⠛⠛⠋⠀⠀⠛⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠶⠶⠶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⣰⡄⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⢀⣠⣴⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢀⣿⠿⠿⠛⠋⠁⠀⣿⣿⣶⣤⣀⣀⣀⣀⣤⡄⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⠀⠺⠆⠰⠶⠀⣿⡇⠀⠉⠛⠛⠛⠋⢹⡇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢸⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢿⡇⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣿⠷⠿⠛⠃⢸⡏⠀⠀⠀⢻⣇⠀⠶⠆⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢸⡇⠘⠻⠿⢷⣦⣾⣇⡀⢀⡀
⠀⠀⠀⠀⢀⣾⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠈⢿⣦⠀⠰⡶⠀⣿⡇⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠉⠙⠛⢿⣧⣄⣀
⠀⠀⠰⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢀⣻⣷⣄⡀⠀⣿⡇⠀⠀⣠⣴⣟⠁⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣶⠾⠿⠛⠛⠙⣿⠿⠷⣿⣷⠾⢿⣿⠉⠛⠻⠿⢶⣶⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷
⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣇⣀⣼⠟⠀⠀⠀⠀⠀⠈⠙⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆
⠀⠘⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⣼⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠿⠿⠿⢶⣶⣤⣀⠀⣾⠟⠛
⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⣀⣤⣤⣶⣿⣥⣄⣰⡿⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠈⠁⢀⣴⡿⠛⠉⠁⠀⠈⠉⠛⠿⣧⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⣶⡷⢶⣦⠀⠀⠀⣾⣯⣤⣤⣄⣤⣤⣤⣤⣤⣤⣸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠈⢿⡆
⣿⠆⠀⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠸⣿
⣿⣶⣶⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⠿⠿⠆⠀⣿⡇
⠘⣿⡄⠈⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⡟⠁⠀⠀⠀⠀⣿⡆
⠀⠘⣿⡄⠀⠹⣷⡀⣠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⣿⠇⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠘⢿⣄⠀⢻⣷⣿⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⡀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠰⣾⣿⠛⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⢿⣆⣼⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢰⣦⣾⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠰⣿⡾⠿
⠀⠀⠀⠀⠈⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠻⣿⡀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢹⣧⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠹⣷⡀⠘⢿⡄⠀⠀⠀⠀⠀⢀⣀⣴⡾⢿⡇⢸⣿⠀⠀⠀⠀⠹⢷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠙⠻⠶⠿⠿⠿⠿⠛⠛⠀⠛⠻⠏⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⡿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣷⣤⣤⣾⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣐⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣠⣶⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠠⠖⠛⠉⠉⠉⠉⠉⠛⠛⠛⠋⠛⠟⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠟⠟⠋⠛⠛⠛⠋⠉⠉⠉⠉⠙⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⢄⢀⠀⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⢀⠄⠀⢀
⠀⠀⠀⠀⠀⠺⢿⣷⣮⣿⣿⣶⢿⡞⣿⣿⣷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢷⣿⣿⡟⣾⢷⣾⣿⣯⣶⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢤⣀⣣⣙⠛⣋⣈⣀⣈⣙⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣞⣉⣀⣘⣈⡛⢛⣡⣃⣠⠼⠛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡤⠴⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡀⠀⢢⣈⣷⡚⡅⢢⠀⣀⠀⡀⢆⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠹⣷⣌⢢⣔⠙⣌⣿⣞⢆⢳⡹⣧⣳⡘⣾⣾⣼⡄⡆⡆⡀⠀⡅⢠⠁
⠀⠀⠀⠀⢄⡀⠀⠈⠻⢦⣄⡀⢀⠑⠢⣝⣿⣷⣮⣓⣮⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣷⣷⣿⣆⡇⡿⢠⢆⡔⡀
⠀⠀⠀⠀⠀⠙⢷⣦⣤⣀⣈⣙⠛⠿⣶⣦⣭⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⢉⣽⠿⢿⣿⣿⣿⣿⣿⣿⣇⣾⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣰⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣏⠛⠻⢿⣴
⠀⠀⠀⠀⠀⠙⠲⠶⢶⣤⣤⣤⣶⣶⡾⠿⠛⠋⣁⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡁⠀⠀⠀⠀⠀⠀⠘⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⡶⠟⠁⠀⠀⠀⠀⠀⠀⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠿⠻⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⡗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⡤⠶⠚⠋⠉⠉⢸⢠⠃⠀⠀⠀⠀⠈⠉⣹⢛⡗⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡋⠁⢀⠀⠀⢰⡇⣤⢸⢸⡀⢰⠂⡄⢀⡆⢠⡏⢸⠃⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢸⣬⣇⢀⢸⡀⣇⢸⣇⣽⢸⣼⡇⣸⢠⠇⣼⢇⡾⣄⡟⢀⠀⢀⠄⠀⠀⠀⠉⠲⣄⣰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠁⣼⣆⢰⣻⣿⣬⣷⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣾⣟⡿⡹⣿⡵⢃⣴⠋⠀⣠⡾⠁⠀⢀⣼⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣴⣾⠏⢀⣠⢞⡿⠃⣠⠈⠳⡄
⠀⠀⠀⠀⠀⣠⡴⠒⠀⠀⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⠟⣋⣹⣿⣿⣭⣭⣵⣾⣭⣤⢞⡥⠞⢁⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠳⠶⠶⠦⠤⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣦⠖⣡⠄⠀⠀⠀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠻⣿⣿⣿⣶⣿⣥⣔⣁⣀⣴⠞⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣡⠴⣛⡥⠖⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⣛⣛⣋⣀⣠⣤⣤⠤⠦⠒⠀⠀⠀⠈⠻⣿⣿⣵⣖⣿⣯⢶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠂⢀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⠢⠀⠈⠉⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠆⠀⠀⠐⠀⡄⢄⢀⠀⢆⠰⠘⢆⠢⠙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣷⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠙⠉⠉⠀⠀⠀⠙⠛⢿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⡿⠛⠋⠀⠀⠀⠉⠉⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⡿⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡤⣖⣃⣠⣽⣈⡃⡲⣄⠀⠉⠙⠻⠐⠀⠀⠀⠀⠀⠀⠈⠟⠋⠉⠁⡠⢖⣘⣁⣦⣄⣘⣲⢤⣀⢀
⠀⠀⠀⠀⠀⠀⠐⢤⣲⣿⣷⣿⣿⣿⣶⣦⣾⣼⣻⢦⡱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⠼⣟⣥⣶⣵⣷⣿⣿⣷⣿⣿⣊⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣟⠙⣏⠫⣿⠟⡏⠉⠳⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣷⠞⠉⢿⠻⣿⠍⡻⢉⣿⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣷⡬⣷⡒⣋⣀⠤⠶⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⠦⠤⣀⣙⢒⣮⢵⣿⡟⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢄⣠⣤⣄⣄⣀
⠀⠀⠀⠀⠤⠒⠒⠛⠋⠉⠙⠛⠿⠛⠿⢿⡿⠷⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠾⢟⡿⠿⠛⠿⠛⠋⠉⠙⠛⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠏

⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⠞
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠛⠛⢿⣿⠟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠻⢿⣿⠛⡛⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠷⠬⠥⠴⠥⠄⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠠⠬⠦⠬⠥⠾⠶⠚⠋⠁

⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣷⣦⣀
⠀⠀⠠⠚⠉⠀⠀⠀⠀⠈⠉⠛⠛⠿⢟⣣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⣞⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠉⠓⠄

⠀⠀⠀⢀⠀⠀⣠⣔⣂⣩⣩⣭⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⣭⣍⣉⣐⣢⣄⠀⠀⡀
⠀⠀⠀⠈⠛⠿⠿⠛⢿⠻⡿⢛⠏⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠹⡛⢿⠝⡿⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⣶⡶⠶⢶⣶⣶⣶⠶⠶⣶⣶⣶⡶⠶⢶⣶⣤
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣿⡏⣀⠀⢀⠘⣿⢁⠀⠀⡈⢿⠏⡀⠀⢀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣧⡀⠀⢀⣰⣿⣄⠀⠀⣠⣿⣧⡀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⠛⢛⠛⠛⢛⡛⠛⡛⠛⠛⡛⠛⢛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣸⡀⠀⣘⣃⣀⣇⠀⢀⣟⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⣾⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠁⠀⠈⢻⡟⠃⠀⠀⠛⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠘⣇⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣠⠏⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⣀⠴⠚⠋⠉⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⡿⠿⠛⠉⠉⠀⠀⠈⠉⠙⠳⢤⣀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠻⢿⡄⠀⠀⠀⠀⢠⣿⡟⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡀⡀⢂⢄⢰⡀⠀⣷⢀⣄⡆⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⢠⢠⣀⡀⣶⠀⢀⡆⡀⡐⠀⢀
⠀⠀⠀⠢⡐⢜⣾⣦⡻⣿⣷⣶⣿⣾⣿⣿⣾⣣⢎⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡱⣼⣿⣿⣿⣷⣿⣤⣾⣿⢟⣵⣳⣣⢂⡄
⠀⠀⠀⠲⢭⣲⣭⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣯⣶⣫⠔
⠀⠀⠀⠉⠲⠿⢿⡿⠋⠁⢻⣿⣿⣿⣿⣿⣿⠃⠈⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠘⣿⣿⣿⣿⣿⣿⡿⠈⠙⢿⡿⠿⠖⠋
⠀⠀⠀⠀⠠⢚⡭⢛⣦⣄⡈⠻⢿⣿⣿⠟⣁⣠⡴⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⡘⠿⣿⣿⣿⠟⢁⣠⣴⡿⢍⠳⠄
⠀⠀⠀⠀⠀⠈⠰⢫⣾⢿⢻⢿⣷⣶⡿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣷⣶⣶⡿⡿⡿⣿⡙⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠑⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣶⣦⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣴⠉⠙⠂⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⠶⠀⠀⠈⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣖⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⣼⣯⡿⠛⠉⠉⠛⢯⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢸⡷⡟⠀⠀⠀⠀⠀⠈⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠇⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠂⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣙⣿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⣀⣀⣀⠸⣭⣿⣽⣯⣽⣯⣿⣭⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⣸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣀⡀⠀⠻⠿⠶⢠⣶⡶⠦



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀
⠀⠀⠐⢋⡤⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠱⣌⠑
⠀⠀⠀⠁⣠⠞⢡⠎⢙⠲⠦⢤⣀⣀⣀⣀⣀⡠⠤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣄⣀⣀⣀⣀⣠⠤⡴⢚⡉⢦⠘⠦⡀⠁
⠀⠀⠀⠀⠀⠠⠋⢠⠏⢠⠇⢰⠃⣾⠀⡆⢰⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢰⠆⡆⠸⡆⢺⠀⢷⠈⢣⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠋⠀⠇⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢃⠀⠃⠀⠃⠀⠁







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⡠⠶⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠳⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⣒⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣖⡂
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠿⠿⣷⣄⡀
⠀⠀⠀⠀⠠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣠
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣶⣶⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⡿⣿⡿⡿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠟⠟⠿⠻⠿⡟⠿⠓⠈⠁




⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣂⣯⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠛⠻⢦⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠉⠉⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣶⣤⣤⣀⣀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣿⣿⢿⡿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⢿⠿⣿⣿⣿⢿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣾⣿⣿⣶⣾⣿⣿⣿⣿⠿⠾⣛⣯⣭⠶⢶⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⣿⢟⣿⣿⣿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⢀⣠⣴⡟⣼⠑⠛⠛⠋
⠀⠀⠀⠀⢠⢸⣿⡟⠃
⠀⠀⠀⠀⢸⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⣴⣄⣠⣤⣀⣄⣄⣄⣀⣀⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣷⣿⣿⣿⡿⣿⡿⠿⡿⠿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣬⡿⠟⠋⠹⡀⠈⠿⣷⡿⠃⢀⠇⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠝⠋⠀⠀⠀⠀⠑⠤⣀⣀⣠⣴⣯⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠤⡤⠤⠄⠖⠒⡎⠫⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⡤⠀⢠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠙⠘⢉⠁⠈⡉⠀⢀⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⢠⢸⡀⣼⣶⣰⣷⣷⣾⣷⣿⣤⣵⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣜⢦⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠛⠛⢉⡏⠁⠈⢻⣿⣿⣿⣿⢿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣿⣿⣿⠀⣿⠻⣿⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣺⠿⣦⣀⠀⠀⠃⠀⠻⢿⣿⣿⠿⠃⣰⠃⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠝⣻⢷⣦⣄⡐⠢⢤⣤⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠊⡴⢹⢫⠟⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡣⠈⠀⠀⠀⡀⢀⡎⢀⢀⠀⣀⠀⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠇⡞⠼⠈⠸⠰⡃⠆⠴⠸⠸⠇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⡿⠟⠛⠛⠉⠉⠙⠻⠿⢦
⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠛⠓⠄⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉
⠀⢼⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠉
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡿⣿⠻⠿⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⡿⠿⠿⠷⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠋⠘⠃⠀⠀⠀⠀⠁
⠀⢀⣴⣶⣾⣿⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣄⣴⣿⣿⣿⠟⠛⠛⠉
⠀⠈⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠟⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠛⠢
⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠟⠛⠛⠉⠉⠉⠉⠙⠓⠢⠄⠀⠀⠀⢠⣾⣿⠿⠟⠛⠉⠉
⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠈⠉⠛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣆⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠁⠈⠉⠻⣿⣿⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠖⠋⠀⣀⣤⣴⣶⣶⣶⣄⠈⢿⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⡾⠋⠁⣠⣴⣿⣿⠿⠛⠉⠁⠀⠈⠀⠀⠈⠠⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣫⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠄⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⡀⠀⠈⠙⠳⠄⠀⠀⠀⠚⠉⠀⠀⣠⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⢼⣦⣤⣀⣀⠈⠀⠀⠀⠠⣤⣴⣾⠿⠂⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡆⠀⢡⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⢀⠆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢣⡀⠀⠡⡀⠀⠠⠶⠶⠶⠄⠀⢀⡞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠈⠀⠀⠑⢄⠀⠓⠒⠊⠀⡴⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠑⠠⠤⠔⠉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠿⠿⢿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠿⠿⠿⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠈⠙⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠉⠉⠀⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡖⢻⣻⣿⣶⣦⣧⣼⣴⢦⣦⣢
⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⡶⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣐⠲⠶⣞⣽⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢯⡀⠿⠿⢃⡇⠀⣹⣿⣿⡛⠁
⠀⠀⠀⠀⠙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⡟⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣝⣒⣚⣭⡴⠾⠟⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣩⠿⣿⣿⣿⢿⠟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣼⣾⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⡀⠀⠀⠀⠀⢰⠀⣰⠀⠀⠀⡄⠀⡀⠀⠀⢰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡾⡿⠿⣿⠿⡿⣿⣷⣾⣧⣿⢀⣿⢀⡆⣸⠃⣼⢡⡇⢠⡟⣠⠏⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⡧⢠⠇⣰⢏⡼⣱⣧⣿⡟⣽⢿⣿⣷⣾⣵⡟⣼⢏⡾⣠⣿⣵⠏⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⢿⣿⣿⣿⣿⠟⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢻⣿⠋⠀⠠⣼⣿⣿⣿⣿⠂⢈⣿⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡿⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⢿⣄⠀⠀⠿⡿⡿⠟⠃⠀⣼⠇⠀⠀⠀⣠⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⠻⣷⣤⣆⣀⢀⣄⣤⠿⠋⠀⢀⣤⣾⣿⣿⠿⣿⡛⠶⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠒⠒⠒⠶⠤⢤⣄⣀⣉⣙⣛⣛⣉⣁⣤⣴⣾⣿⢿⡟⢯⠉⠓⠀⠙⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⡇⠘⠀⠇⠈





⣿⣏⢹⡟⠻⣿⣛⠟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⣠⡾⠿⠛⠛⠿⠿⢿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⡿⠿⠿⠛⠛⠿⢷⣄
⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣤⣤⣀⣤⣠⣄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣄⣤⣀⣤⣤⣶⣄⡀
⠀⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣀⡀
⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡿⢿⡿⢿⣏⢉⣿⢿⠿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⣿⣿⡏⢙⣿⣿⡿⢿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠉⠻⠿⣿⣅⡀⠀⠃⠀⠙⠋⠀⠈⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠁⠀⠙⠋⠀⠈⠀⢀⣨⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣾⣿⠿⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠿⣿⣶⣷⣿⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣶⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⡀⠀⣸⢣⣄⣀⢀⠆⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣸⡄⣶⢠⡟⣼⢃⣴⢇⣸⣿⣷⣶⣿⣿⣽⣿⣿⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢷⣽⣷⣿⣿⣿⣿⣿⣿⣷⣟⣌⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣼⡿⠋⢻⠛⢧⣼⡿⠻⡟⠙⠻⣿⣶⣮⣭⣽⣿⣛⠥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠏⢀⣀⣈⠳⣄⣀⣠⢞⣡⣴⡾⢏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠋⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡄⢠⠄⣠⠄⢸⠇⢀⡄⡤⢠⡆⢀⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠘⠇⣿⠀⠯⠀⢹⠀⠙⠈⠇⠀⣷⠸⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⢰⠋⣳⠰⢯⡃⣿⣦⣿⢸⡯⠅⢹⡏⢰⠋⢳⢸⡇⠀⡞⢙⡆⡞⢩⡃⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠛⠋⠘⠛⠁⠉⠀⠉⠘⠛⠃⠈⠁⠈⠛⠋⠈⠛⠃⠙⠛⠁⠙⠛⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠉⠙⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣠⡄⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣤⠤⠤⠶⠒⠊⠁⠙⢦⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⡇⢠⢖⢦⡀⢠⢖⣦⡀⣯⣻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⡇⡇⠘⠮⠞⡤⠘⠪⠞⠁⡏⡹⠈⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠀⠀⢻⢻⡘⠟⠀⠙⠂⠘⠟⢠⢟⠇⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢢⡀⠀⠀⠀⠀⠀⠑⠷⣌⠀⠉⠁⢈⡱⠟⠋⠀⠀⠀⠀⣀⣠⣬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠉⠀⠀⣠⡤⣤⡴⢊⣹⠛⣗⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⡄⠀⠀⠀⢶⡶⠶⠶⠶⣷⠀⠀⠀⠀⢀⢞⡧⣉⠓⠶⡭⠚⢣⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⡇⠀⠀⢀⠞⠈⠉⠉⠉⠙⣆⠀⠀⢠⣿⣋⠴⣫⣷⡀⠀⠀⠈⢿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⡇⠀⠀⢸⠛⠛⣻⢿⡛⠛⢻⠀⠲⣞⣩⠝⠿⣝⡇⠱⢤⠀⠀⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠶⡇⠀⠀⢸⠀⠀⢧⣤⠇⠀⢸⠀⠀⠈⣠⠎⠀⠀⠈⠳⠤⢤⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠷⠀⠀⢸⠀⠐⣖⠲⡖⠀⢸⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢸⣉⣉⣉⣉⣉⣉⣻⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠤⣀⠶⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⣠⣤⣠⣤⠴⠃⠚⠉⠁⠈⠁⠉⠁⠀⠉⠀⠢⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣶⣼⣾⣷⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⠀⠀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣽⣛⣩⣽⣭⣭⣽⣿⣿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣐⣿⣿⣻⣽⣾⣿⡿⠿⣿⣟⣿⣿⡿⣿⣿⣷⣾⣿⣷⣷⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣍⣿⠟⢻⣿⣟⣠⣷⣿⣿⣿⠁⠀⣸⣍⠻⣿⣿⣿⣼⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢐⣿⣥⣿⠁⠀⢼⣿⣿⣿⣿⣿⣿⣿⣷⠶⣿⣟⢸⠃⢹⣿⣿⣿⣿⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣩⣿⣿⣷⡈⣀⢹⣿⣿⢾⣿⣿⠿⣿⣿⣿⣿⠍⣼⠁⢐⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣁⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣣⣴⣿⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣽⣿⣿⣾⣿⣿⣿⡿⣟⠫⠋⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣴⣤⣄⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠋⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢠⡞⢁⣿⠟⢿⣇⠙⣿⣿⣿⣿⠿⠊⠀⠀⠀⠀⣿⣿⣿⢫⣶⠃⢠⡄⠈⣷⡄⠀⠀⠀⣉⣭⣿⣿⣿
⠀⠀⠀⠑⢦⣿⣿⣿⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⡃⠀⠀⠰⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠋⠘⠀⠁⠑⠘
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠉⠙⠛⠿⣷⠄⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⢙⣛⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⣋⠝⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠀⠐⠀⠄⢰⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⡠⠾⠛⠛⠛⠿⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠿⠟⠛⠛⠛⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠠⣼⣿⠟⢻⣿⣿⢿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⢿⣿⢿⠛⢻⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠌⠢⠵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠵⠶⠥⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠀⠀⢀⣼⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢧⡀⠀⠀⠀⣠⡾⠋⣠⣿⣿⣿⣿⣿⣿⡿⣻⣿⡿⠀⠙⣿⣝⢷⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠠⣉⠓⠒⠛⢉⣠⣾⣿⣿⣿⣿⣿⠿⣫⣾⣿⠟⠀⠀⠀⠈⢿⣷⡙⣧⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠙⠛⠛⠫⣵⣿⣿⠿⢟⣫⣵⣾⡿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣷⠘⣇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣶⣿⣻⣭⣶⣿⠟⠛⠉⠙⠂⠀⠀⠀⠚⠉⠉⠉⢉⣿⣿⠀⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⢿⣿⣿⡇⠛⠷⠶⠒⠀⠀⠀⠀⠐⠲⠶⠟⣻⣿⡿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠟⣡⣾⡟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣾⣿⣿⢁⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣼⢃⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⣾⠃⣿⣿⢸⣿⣿⣷⡄⠀⠀⢖⠻⠛⠲⠀⠀⢰⣿⢸⡇⢾⣅⠀⣹⡏⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣿⣿⢸⣿⣿⣿⣿⣦⡀⠈⠉⠉⠀⣠⠔⠙⣿⣾⣿⣌⠻⠿⠛⠁⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠸⣿⠘⣿⣿⣿⣿⣿⣿⡗⠲⠖⠊⠁⠀⠀⠹⣿⣿⣿⣷⣶⣤⣶⣾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠹⣧⢻⣿⣿⣝⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣛⡭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣦⡀⠈⠳⣿⣿⣿⣦⣈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠹⣿⣿⣶⣤⣈⠙⠿⣿⣿⣷⣄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠙⠻⢿⣿⣿⣷⢮⣙⢿⣿⣷⣄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⠻⢿⣮⠳⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠋⠉⠁⠀⠙⣷⢹⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⣼⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠦⣀⣀⣀⣴⠟⣡⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠮⠵⠶⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⣿⡿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⢿⣿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠈⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢀⣴⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⡿⣿⣿⣿⣞⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⣴⣻⣻⣾⣿⡿⢿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⣶⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠹⠿⠦⠀⠀⠀⠀⠼⠿⠏⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠁⠀⠀⠀⠉⠙⠻⢿⢿⣿⣿⣿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣷⣿⣿⣿⡿⡿⠟⠋⠉⠀⠀⠀⠈⠉⠛⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⢿⡟⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢻⡿⠟⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠿⠿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⠿⠿⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢯⣽⡤⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢠⣿⠽⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣷⣶⣦⣴⣤⣤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣤⣤⣤⣴⣶⣷⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⠟⢿⠿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⡿⠻⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣴⣶⡄⠀⠹⣧⠀⢶⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣧⠀⣿⣿⣧⣿⠀⢻⣆⢸⠀⠻⢿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠋⠙⠚⠋⠁⠸⣿⣿⡿⠀⠈⠙⡄⢠⠃⠀⠙⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠀⠉⠀⢠⣾⠗⠐⠡⠈⠐⠀⠹⠿⠇⠀⠀⠀⠐⡀⠀⠀⢀⣴⣿⡿⠿⠛⣠⡄
⠀⠀⠀⠀⠀⡞⠀⠀⣴⡿⠋⣠⡴⠚⠉⢀⡀⣴⣺⣦⠀⠑⣄⠀⠀⢰⠀⣾⣿⡟⠀⣀⣭⣥⣤⣤⣀
⠀⠀⠀⠀⢸⠃⠀⡸⠟⠁⠀⠈⣠⡴⠞⠋⠁⠘⣷⣻⣧⠀⠘⠃⠀⣿⢰⣿⠋⠀⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠠⠿⢀⡞⠁⠀⠀⠐⠿⠛⠁⠀⢠⣄⠀⠘⢻⣿⠂⠀⠀⣀⣿⠈⠁⠀⠀⠘⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠐⣃⠶⠉⢠⡦⠀⣀⣀⣤⣤⣴⣶⣿⣿⡆⠀⠀⠘⣧⠀⠀⣸⣿⡀⠀⣧⠠⠤⠌⠛⠿⠿⠛⣁
⠀⠀⠀⠀⠄⢠⡿⢡⣾⣿⣿⣿⣿⠿⠋⢡⡌⠁⢸⡿⣧⠈⢧⠀⠻⠿⡷⠀⠛⠀⣀⠤⢠⣄⢀⣼⣟⣴⠆
⠀⠀⠀⢀⢤⣾⠁⠈⠻⠿⣿⣟⠁⠀⢠⠏⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⣼⣿⣾⣿⣿⣿⣿⡁
⠀⠀⠀⠃⣿⠏⠀⢀⠀⠀⠹⣿⣷⠀⠀⠀⣰⣿⠇⠀⢻⠀⠐⢀⠖⣈⠜⠁⢀⣶⡀⢠⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⢀⣿⠏⢀⡴⠁⠀⠀⠀⠹⣿⡆⠀⣰⣿⠏⢠⣤⠈⠀⠀⠨⠉⠃⠀⣦⠀⠻⣇⠙⢿⣿⣿⠟⣫⣄
⠀⠀⠘⠋⣠⡞⠀⣠⣾⣇⠀⠀⠙⠃⢀⡟⠉⢠⡿⢃⡀⠀⠀⣤⡐⢢⡀⢻⣇⠀⢻⠀⠀⠉⠁⣴⣿⠏⠁
⠀⠀⠀⠰⢿⠇⠚⣿⣏⠉⠓⢀⡾⢣⠏⣀⡀⠚⠁⢼⠉⢢⠀⠈⢿⣆⠈⠀⢿⡄⠘⠀⠌⠱⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣄⠁⠀⠃⣄⠈⠉⠑⠀⠈⣆⠀⢇⠀⠀⠙⢷⣄⠘⣷⠀⠀⠐⣠⡿⠳
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠇⡸⣶⣽⣷⡀⣶⡆⠀⠘⣴⣾⡀⢀⠀⠈⠻⣆⠘⣧⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⢀⣻⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣧⠀⠙⢦⣀⠘⢷⣽⡆⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣧⠀⡾⠹⣿⣆⠀⠀⠹⡷⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠁⣼⡇⠀⢻⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄⢀⣄⣨⣤⠤⢤⠤⠤⣴⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢀⣸⡄⢳⡀⢻⡍⣧⢠⢷⢠⣸⠀⠀⣿⠀⢰⠀⠈⡙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡴⠚⣿⡘⢧⡘⣷⣈⣿⣿⣷⣾⣾⣿⡇⣴⣿⣴⣿⢀⣰⡇⣀⡠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣸⢾⣉⢳⣷⣝⣿⣌⢿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣽⣿⣿⣷⣿⣣⡾⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣠⢾⡳⣤⡛⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣾⠻⣦⣍⡺⢿⣶⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠙⠓⠮⠅
⠀⠀⠀⠀⠀⠀⠠⣔⢤⣀⡿⣦⣝⣾⣿⣿⣷⣾⣿⣿⣿⠟⠁⣼⣿⣿⣿⡿⠛⠋⠉⣉⣽⣿⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣯⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⠤⠖⢋⡉
⠀⠀⠀⠀⠀⠲⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⢢⠒⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⡿⠿⠟⠛⠉⠀⠀⡀⢤⡓⠆⠉
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠛⠁⠀⠐⠒⠒⠒⠒⠛⠛⠉⠉⠉⠀⣀⠀⠀⢄⠀⠦⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⡴⢂⠖⠄⠄⠀⠀⢠⠆⡐⠆⠀⠎⠉⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠛⠉⠉⠉⠉⠉⠙⠒⠒⠦⣤⣀⠀⠀⠀⠀⠈⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠙⠓⠶⠶⠶⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠔⠂
⠀⠀⠀⠀⠐⠲⠶⠶⠾⠿⠛⣛⣽⣿⠟⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡚
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠞⠛⢋⣩⣴⠿⢛⣵⡿⢋⣼⡟⣸⡿⢻⡿⣿⢿⣿⣿⣿⡿⣿⠿⣍⠛⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⣠⠶⠟⠉⣠⡾⠋⢠⡿⠁⣿⠃⣿⢸⡿⢸⡇⢿⠈⠳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠰⠋⠀⡼⠋⣸⠃⢸⠃⠘⠁⠈

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣷⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⢀⡴⠟⠋⠉⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠈⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠄

⠀⠀⠀⠀⠀⠠⢶⣾⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⢀⣀⣠⣴⣾⣶⡆
⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉



⣿⣿⢟⠿⢛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⠀⢀⣀⠐⠈⠀⢀⠀⠀⡀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⢸⠉⠁⠀⠀⢙⠀⠀⠀⠀⢀⠄⠠⢯
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠤⠤⠂⠚⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⣀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠲⣄
⠀⠀⢸⠀⠀⡠⠤⠀⠤⣀⠀⠀⣠⠄⠠⡄⢀⠔⠒⢤⢈⠀⠀⠀⠀⠀⠀⠀⠘⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢸⠀⠎⠀⠀⠀⠀⠀⠣⠀⢇⠀⠀⡸⠸⡀⠀⣠⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣄
⠀⠀⢸⠰⠀⠀⠀⠀⠀⠀⠀⡇⢀⠝⠭⡀⢀⠌⠫⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⡀⠀⠀⠈⠄⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⢸⠀⢇⠀⠀⠀⠀⠀⢠⠃⣇⠀⠀⡐⢨⡀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀⠂
⠀⠀⢸⠀⠀⠑⠤⠤⠤⠔⠁⠀⠈⠁⠉⠀⠀⠉⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⢀⠀⠀⡀⠀⢀⣄
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠱⡀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⢤⢤⣤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⢅⠀⠀⠑⡄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠚⠀⠄⠓⠠
⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠢⡀⠀⠀⠠⢀⠅⠀⡀⡂⠀⠀⣹⠀⢠⠊⠁⠀⠈⠑⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠘⢆⠀⠀⠀⡠⠀⢀⠍⠀⢸⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠊⠀⠀⢀⠤⢄⠙⠒⠊⠓⠐⠈⠀⠀⠈⠳⠤⡀⠤⠔⠁⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠤⠄⢀⠀⠀⠈⠀⠈⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠅⠀⠀⡄⠀⠀⠃⠀⠀⠀⢀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⣷⣇⣦⣶⣿⣿⣷⣿⡯⣷⠶⣓⣫⣥⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣞⣿⢿⣿⣿⣿⢿⢿⡿⠟⠋⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢠⡀⣴⢣⠟⠞⠵⠻⠋⠉⠁
⠀⠀⠀⠀⢀⢰⣾⣿⠯⠈
⠀⠀⠀⠀⢸⠘⠋⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⣀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⣶⣶⣶⣷⣿⣷⣿⣿⣾⣶⣿⣷⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢴⣶⣾⠿⡟⠛⢹⣿⣭⣿⠍⠉⡏⠉⠛⢛⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠟⠉⠀⠀⠱⣄⠀⠙⠛⠁⢀⠜⣀⡤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⣑⣒⡶⡾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠃⠀⠀⠐⠛⠛⠋⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⣠⣴⠿⠟⠛⠿⠿⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠿⠿⠛⠿⠷⣦⣀
⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⡀⣤⣶⣶⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣶⣆⡄
⠀⠀⠀⠀⠀⠐⢿⣿⠟⢹⡟⢿⠟⣿⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣿⠻⠿⢻⡏⠙⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣻⣶⣾⡃⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣷⣶⣿⠴⠞⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢒⠂⠠⢀⢀⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⠁⠁⠀⠍⠉⠻⣿⣿⣿⣿⣿⣮⣲⣼⡳⣿⣶⣤⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠟⠿⢿⢿⢮⣿⣻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠙⠊⠻⠿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⣠⣤⣾⣿⣿⣾⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿⢿⡏⠁⠐⢿⣿⣿⡇⠐⡿⠀⠀⠀⠉⠛⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣛⡛⠉⠀⠀⢳⡀⠀⠀⠀⠁⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠠⠀⠈⠉⠒⠒⠐⠞⠁⠒⠒⠒⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⡀⠀⠀⠀⠀⣇⡇⡆⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⣷⣆⣴⢠⡤⢼⡧⣧⣤⣤⣰⣰⣿⢰⣡⢃⢀⡇⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢘⣼⡷⣖⡂⠉⣿⣿⣤⣾⣇⣾⣇⣿⣿⣏⣾⣼⣯⣿⢿⣦⣼⣣⣮⡆⡠⠀⠀⠀⠀⡔⡀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡴⠚⢧⡳⣿⣻⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⢟⣵⢿⣿⣷⣡⡆⡔⡔⣸⠟⡼⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⢑⣦⠚⠁⡙⢎⣦⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣫⣾⣿⣯⣾⡾⣯⢞⡜⡱⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⢦⣾⣳⣕⢶⣬⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡿⣪⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣀⣺⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣴⡫⣽⣿⣻⣿⣿⡿⠛⠁⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⠀⠀⠀⠈⣹⠟⠿⢿⣿⠿⠿⠟⠚⠉
⠀⠀⠀⠀⠀⠀⠠⣼⣉⣛⣛⣻⣿⣿⠛⠀⠀⠀⢿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣿⣿⢿⣧⣾⡟⠀⠀⠠⠚⠁⠀⣠⠤⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠧⢭⣭⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣿⡯⠖⠋⠁⢀⣤⣄⡒⠢⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠚⠀⣀⣀⣀⣀⣤⡤⠄⠙⠻⠿⠿⠿⠿⠷⠛⠛⠋⠉⠀⣀⡀⠠⢔⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠰⠒⠋⠉⡠⢠⢀⠄⡠⢀⠄⠀⠀⠀⣀⠀⠀⢀⣀⠀⠐⠫⡑⠍⠦
⠀⠀⠀⠀⠀⠀⣠⣮⠖⠉⠀⠀⠀⠀⠀⠁⠀⠸⠱⠃⠸⠀⡤⢳⠙⠀⠘⡄⠈⠻⠣
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘