Vine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⡀⠠⠄⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢠⣄⠀⠀⠀⠀⠈⢀⠉⠢⣄⠀⠀⠀⠀⠀⠀⢀⢀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⣠⣴⠀⠀⠀⠀⠿⠓⠀⢀⠿⣶⡜⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠒⠂⠒⠖⠟⠓⠦⣀⠀⠀⠉⠀⠂
⠀⠀⠀⢀⠀⣿⠟⠉⠀⠀⠀⠟⠋⠁⣰⣶⡀⠀⣀⠤⢜⡉⠰⠛⠀⡀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⡁⠊⠀⢀⠀⠉⠲⢄⣀
⠀⠀⣤⠀⠀⠀⠀⠠⣴⡞⠀⠀⠀⠀⠨⢿⠀⠀⠓⢾⠎⡅⠀⠐⠢⠆⠒⠁⠒⠐⠃⠁⠀⠀⠀⠀⠁⠀⢰⣿⣴⠄⠀⠀⠉⠑⠶⡄
⡀⠼⠛⠀⠀⠀⠀⠀⡀⢁⠀⠀⢀⡀⠀⠄⠠⠔⠈⠓⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⢸⡀⣨⠀⠉⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠍⣄⠀⠌⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣄⠀⣀⢀⠈⠀⣀⢶⡳⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃⠀⣀⠒⠀⠀⢲⣻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⢈⣵⡎⠷⠈⠉⠬⠇⠁⠈⢦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⣤⡄⠂⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣄⣰⣾⠁⠀⡀⣀⠈⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠮⠀⠁⠀⢠⣿⡶⠧
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠟⠻⠁⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⢠⣤⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⣀⣰⡆
⠀⠀⠀⠀⠀⠰⡶⠂⠀⠘⠟⠃⠀⠠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣴⡤⠄⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⣷⣦⠄⠁
⠀⠀⠀⠀⠀⠀⠰⣾⠁⠀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠁⠐⠲⣾⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷
⠀⠀⠀⠀⠀⢠⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠛

⠁⠀⠀⠀⠀⠀⠀⣤⣤⡀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⢠⣶⣦⡘⢿⣿⡆⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠈⣶⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛
⡦⣴⣶⠄⠀⠀⠀⠙⠛⠋⠀⢀⣶⣶⠀⠀⢠⣤⣤⡰⠿⠿⠀⠀⠉⠉⠁⠀⠀⠀⣴⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠁⠀⠀⠀⠀⣠⣤⡀
⠁⠈⠁⠀⠀⢀⣤⣄⠀⠀⠀⠀⠉⠀⣤⣦⡄⠙⠉⠁⠀⢰⣦⡀⠀⢻⣷⡄⠀⠀⠀⣀⣄⡃⠀⣀⣤⣀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠘⠛⠋⠀⠀⢀⣠⣤⡄
⣠⣶⣶⠀⠀⠙⠛⠃⠀⠀⠀⠀⣀⡀⠈⠉⠁⠀⢶⣷⡆⠈⠛⠛⠁⠀⠉⠁⠀⠀⠀⠛⠛⠁⠀⠙⠛⠛⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁
⠉⠉⠁⣠⣴⣶⠄⢀⣴⡀⠀⠾⡿⠃⠀⣴⣾⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢴⣶⠆⠀⠀⠈⠛⠁⠀⢀⣴⣶⡆⠀⠀⠀⢀⣤⣶⠄
⠀⠀⠀⠈⠉⠁⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀⡀⠀⠘⠿⠿⠂⠀⠀⠀⠐⠿⠟⢀⣀⠁⠀⢀⣴⣶⡶⠀⠀⠈⠉⠉⠀⠀⠀⠀⠿⠛⠁
⢾⣿⡗⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣶⣶⡄⠘⠛⠋⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠂⠀⠀⢉⡉⠀⠀⠀⠀⢰⣾⠦⣾⡷⠀⠀⠀⠀⠘⢿⣷⠄
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⣴⣿⠟⠀⠀⣤⣶⣄⠀⠀⠀⠀⢾⡿⠃⢠⣾⡷⠂⠀⠀⠀⠀⠀⠀⢠⣶⣦⠄
⠈⠻⠟⠀⢀⡀⠀⢿⡷⠀⠀⠸⣿⡷⠀⠀⠀⠀⠙⠋⠙⢿⠷⠀⣠⣤⡀⠀⠀⠀⠈⠉⢉⣥⣤⡀⠀⠀⠀⣠⣤⡄⠀⠀⠀⢠⣶⣷⠆⠀⠀⠉⠁⠀⣠⣤
⣴⡄⠀⠀⢸⣿⣆⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣴⣶⣶⠄⠀⠀⠘⠛⠋⠀⣀⣤⣤⠀⠀⠀⠙⠋⠁⠀⠀⠀⠛⠋⠀⢀⣀⡀⠀⠀⠀⠀⣴⣶⡶⠀⠀⠛⠋
⠛⠃⠀⠀⠀⠈⠁⠀⠀⠙⠋⢵⣾⡶⠀⠀⠀⠈⠉⠀⠿⡿⠀⠀⠀⣤⡀⠙⠛⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠛⠿⠟⠀⢀⡀⠀⠀⠉
⠀⠀⠀⠀⢀⣀⡀⠀⢀⣴⣶⠆⣀⡀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠈⢿⠇⠀⠀⠀⠉⠋⢁⣠⣄⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠰⠿⠿⠁⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠛⠟⠃⠀⠀⠉⠁⠈⠻⠿⠂⠀⠀⠀⠈⠁⠈⣦⣄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⢴⣶⣦⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠋⠀⠀⠀⠸⣿⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣾⡿⡂⠉⠀⠀⠀⠈⠻⠃⠀⢠⣤⣄⠰⢿⠗
⠀⠀⠀⢠⣾⣿⠆⠀⠀⠉⢉⣀⠀⠀⢀⣀⡀⠀⠀⠺⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣥⣤⣀⠀⠀⠀⠀⠀⣷⣶⣄⠀⢠⣶⡀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠿⠿⠃⠀⠛⠿⠟⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠓⠀⠀⠀⠀⠈⠉⠉⠀⠘⠋⠀⠀⠀⠀⠰⣶⣶⡄
⠀⠀⣀⡀⠀⠙⢿⠷⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠘⠛⠃⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠆⠀⠁
⠀⠺⠿⠿⠀⠀⠀⠀⠀⠠⣿⠗⠀⠈⠉⠀⠀⣠⣶⣶⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠄
⠀⠀⠠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠻⣿⠆⠀⠀⠛⠉⠁⠀⠀⠀⢠⣶⣤⣶⡶⠀⠀⠀⠀⢠⣶⣶⠀⠀⢠⣴⣤⡰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠷
⣶⣶⡄⠈⠉⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣾⣿⠇⢀⣶⣶⠄⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⣤⣦⡄⠉⠉⠁⠀⠀⠀⠀⠀⢾⣿⠷⠂⠀⠀⣠⣤⡀
⠀⠁⠀⠀⠸⣿⡆⠀⠀⠉⠛⢛⣁⣄⠀⠀⠀⠀⣠⣬⡍⠁⠀⠀⢀⣴⣶⡦⠀⠀⠀⠀⠀⣀⡰⠈⠉⠁⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣿⡆
⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠉⠉⠀⣤⣶⡦⠀⠾⠿⠃⠀⣴⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⠿⠷⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀⡀⠀⠀⠀⠀⢠⣤⣄⠈⠉⠉⠰⣾⡷
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠐⠻⠟⠀⠀⠀⠰⣿⣿⠃⠀⠀⠀⣴⣦⠴⣶⣶⡄⠈⠛⠁⠘⠿⠿⠀⠀⠀⡀⠈⠙⠛⠀⢀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⣤⣶⣤⠀⠀⢀⣄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠰⠿⠿⠃⠀⠀⠀⠀⠉⠁⢣⣤⡀
⠀⠀⠀⢀⣤⣄⡀⠀⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠉⠉⠀⠀⠘⠿⠇⠀⠀⢰⣷⡶⢿⡷⠀⠀⠀⠀⠉⠋⠙⠿⠿⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠰⠿⠟⣃⣀⡀⠀⠀⠀⠈⠈⣶⣦⡀⠀⢠⣦⡀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣴⣾⡶⠂⠀⠀⠀⠀⠀⠈⠛⠿⠛⠀⠰⣿⡷
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠙⠿⠿⠧⠀⠀⠀⠀⠈⠛⠋⠀⠘⠛⠁⠀⠀⠀⠙⠋⢵⣾⡶⠀⠀⠀⠈⠁⠀⠿⡿⠀⠠⢾⣿⠟⠀⠀⠀⠀⢀⣀
⣤⠀⠀⠀⠙⠛⠉⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆⣀⣀⠀⠀⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠻⠟⠀⠀⢀
⣿⣶⣶⣶⣶⡶⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣷⣶⣿⣿⣾⣿⣿⣷⣶⣶⣶⣿⣿⣾⣶⣶⣶⣶⣶⢶⠾⢿⠿⠷⣶⡶⠶⠾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣠⣷⡤⣺⣁⣌⢉⡴⠎⠙⠂⣱⣴⣿⣿⢷⣄⠀⠄⠀⠀⠀⠀⠀⠀⢤⣴⠖⢂
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣜⣍⠂⣠⣊⠤⡾⢿⣿⣿⡿⠻⠾⢲⣿⡭⡛⣗⡠⣉⠀⠀⡤⡙⢆⠀⣀⡄⠀⠀⠰⠛⠙⢲⡶⠂⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣽⣋⠽⠟⠮⡥⠀⠛⠻⡿⠓⠒⠒⠚⢖⢳⡸⠔⠋⠉⠉⠛⢿⣿⣿⣿⠿⡷⠾⠷⠤⣤⡊⠀⡀
⠀⠀⠀⢀⣀⣠⣀⣀⣀⡴⣿⡁⠔⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠙⠃⠀⠀⠀⢰⣿⣿⠟⠋⠳⠶⠀⠀⠁⢠⣽⣷⣤⡐⡆
⠀⠀⠐⠉⠀⢀⠄⠀⣨⡯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠘⠀⠀⠀⠀⠀⣽⣿⣿⣷⡧⢤⣀⣀
⠀⠀⠀⠀⢰⣾⡗⢾⣏⢝⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠙⠳⣏⡟⠠
⠀⠀⠀⠀⠀⠀⠠⣘⡋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⣂⣤⠄⣴⠀⠀⢀⡀⠀⠀⢀⣴⠆⢠⡆⠀⣤⡄
⠀⠀⠀⠀⠀⣦⠀⢀⡀⠀⠺⣂⠤⣄⢂⡉⢊⡗⠐⠋⢿⡣⠤⢵⡁⡈⣀⠾⢦⣤⡤⣉⠡⠴⢔⡉⢉⣂⢲⡙⢋⡀⣠⠤⣐⠷⠀⢀⡀⠀⣠
⠀⠀⢈⡿⡀⠑⣐⠾⠑⡤⠈⢩⠔⣰⢊⡷⠌⠁⠈⣩⡭⣦⠀⠾⢁⣍⠉⠉⠉⣡⠜⣤⠀⠀⣴⢯⣍⠁⠈⠁⠖⣀⣆⠲⠌⠁⢤⡊⠷⣂⠈⢀⢿⡃
⠀⠀⢉⠑⣍⠉⠨⣮⡍⠁⠈⠀⠀⠋⠈⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠁⠙⠀⠀⠀⠈⢉⣵⠅⠉⣡⠒⡉
⠀⢀⠉⣆⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⣠⠉⡀
⠀⢈⠀⠀⠸⠧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠃⠀⠀⡀
⠀⠈⡙⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⠘⢛⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⢀⡉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢈⡀
⠀⠀⠀⠙⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉
⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡆
⠀⠀⠀⢰⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆




⣿⣿⣿⢷⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣷⣴⣾⣦⣾⣶⣿⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢮⡏⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⣄⠷
⠀⠐⠒⠲⠶⢶⡖⡉⣠⠤⣤⢤⣤⢤⣤⣄⡀⠀⢀⣠⣤⠤⠾⢷⠶⠒⠒⠒⠶⠴⠶⠖⢀⣤⣴⣶⣼⡟⠈⠀⠀⠈⠻⠀⠐⢶⡦⢠⠔⠒⡊⠁
⠀⢀⠀⠒⠛⣦⠏⠙⠿⠂⡀⢀⠙⠀⡤⠾⠋⢉⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⠿⢄⠀⠀⠃⠠⠀⢀⠀⠚⠁⠀⢾⣿⣇
⠀⣉⠓⡃⢄⠹⡆⠐⠂⡘⠣⣸⣧⡖⠀⢰⣾⣿⣿⣿⣿⣄⠙⠓⠛⠚⣷⠛⠋⠉⢉⣿⣿⣿⣿⡯⠀⢀⣀⡤⢆⡀⠀⠀⠀⠁⠀⠀⠀⠐⠃⠈⠁
⠉⢁⣀⣀⡿⠷⡟⠋⣐⣤⣴⣿⡿⠒⠶⠶⣿⣿⣿⣿⣿⡯⢐⠀⠀⠀⣻⣁⣀⣀⣼⣿⣿⠿⠛⠒⠋⠉⠁⠀⠈⠀⢦⡄⠀⣆⠠⡀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⢶⠜⠁⠘⢿⣿⣿⡿⠀⠀⠀⠀⠿⠿⣿⣿⣿⠀⠈⢉⣙⣿⡉⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣿⣰⠃⠀⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠇⠀⠀⠀⠀⠸⠿⣿⣿⡄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠈⠓⣤⠀⠀⠀⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠘⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⢧⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⠾⢦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠉⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣯⠁⢠⣼⢩⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⣿⠁⠈⢷⡧⠜⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡏⢸⡗⠀⠈⣧⠀⢰⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⠂⠊⠉⣷⠊⢡⠙⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⡇⠀⣰⠊⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⡇⢀⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡉⠁⠉⠱⢚⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢠⠆⡘⣷⡼⠋⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⢠⠟⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⢷⡋⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡾⠀⠀⣼⣆⠺⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣰⡆⠛⢿⡧⠀⠀⠹⣧⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡷⢶⡾⢯⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡄⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡔⠁⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⡏⢻⣷⣾⣇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢻⣿⣿⣿⣗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠙⣿⣿⣿⡟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣆⣴⡁⠀⢨⣿⣿⡺⢇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠛⣩⡁⠘⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠛⠂⡀⠀⣸⠋⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡤⢆⡜⠁⠀⡟⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠸⣧⣀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⢸⡾⠋⠀⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣼⣤⣤⣤⣧⣤⣤
⣿⣿⣿⠟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⢀⣴⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁⣌⠁⢈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠉⠁⠀⠀⠀⠀⢇⣀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢡⡀⣠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⠁⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠁
⠀⠀⠀⠀⡠⠔⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⠀⠀⠀⠸⡀⠀⠀⣦⣄
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠒⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠁⠑⠀⠈⠻⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⡀
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠟⣻⡯⠄⠀⠀⠀⠙⢿⣆⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⢳⡀⣠⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠄⠈⠉⠉⡀⠀⠀⠀⠀⢈⣿⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣼⠁⠋⠿⠃
⠀⠀⠀⠀⠀⠀⣠⣠⡀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠠⠿⠋⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠟⠋
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣛⣻⠛⠛⠛⠋⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠷⠂⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⣴⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣲⣦⡀⠀⣿⡇⠀⢰⣿⣿⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⢸⣿⣧
⠀⠺⠇⠀⢀⣀⢰⡦⠀⠀⠀⠠⣶⡶⠂⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠻⠀⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠈⠛⠈
⣶⣶⣶⣤⣌⣉⣀⣀⣀⣀⠀⢈⣉⣀⣀⣤⣤⣶⠿⠛⠁⢿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣦⡀⠀⠀⠀⢸⣦⣄
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠸⢿⡿⠂⠀⠀⠀⠀⠀⠀⠰⠦⠤⣤⣴
⠘⠗⠊⠈⠛⠋⠉⠉⠉⣁⠀⠀⠀⠀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣷⣶⣶⣶⣦⣤⣶⣶⣶⣶⡿⠿⠛⠁
⠀⠻⣧⣶⠟⠘⠿⠀⠈⠛⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⣯⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣆⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣯⣭⣿⣿⣭⣽⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠦⣀⠀⣀⣀⠀⠰⣾⣷⡄⠀⢀⣺⣿⣧⣶⣄⣠⣴⣤⡀⠀⠀⢹⣿⡧⣤⣤⠾⣿⣶⣄⣴⣦⢀⣀⡀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⢠⣶⣿⣷⣾⡄⠘⢿⣿⢿⡟⢰⣶⣿⡏⣽⣿⣿⣿⡆⠛⠛⠙⠿⠿⠿⠟⠨⣿⡿⠿⢇⠙⠟⠀⠀⠁⠘⠿⠃⠿⠿⠟⠁⢀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠈⡋⢊⡁⠈⠀⠀⠀⠁⠀⠀⠈⢉⣭⡴⠉⡹⠄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣿⣷⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡏⠉⠁
⠀⠀⠀⠀⠀⢸⣷⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣿⣿⢃⠴⠑⣶⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡙⠛⠛⠟⠁⠀⠀⠀⠀⣀⣀⣄⢾⣿⡟⠇
⠀⠀⠀⠀⠀⠉⠡⣿⡏⡉⢉⠁⠀⠀⠀⢠⣋⡛⠀⠀⠀⠀⢈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣶⠏⠀⣀⣀⣼⠿⠋⠀⢠⣾⡿⠟⣛⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠠⣿⡄⣀⣠⣤⡿⠿⠷⡀⠀⠀⠀⠘⠛⢋⣛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣠⣾⣿⡏⠀⠀⠀⠀⣤⡌⠀⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠋⠀⠈⢛⣋⡁⠀⠀⠀⠀⠀⠀⢸⣦⠙⠛⢉⣦⡄⠀⠀⠀⢰⣦⣶⠆⠀⠊⠀⢂⠀⠀⠀⠀⠈⠃⣀⠀⢸⣿⡿⠂
⠀⠀⠀⠀⠀⠀⣠⠉⠻⠿⠃⠀⠀⣠⡟⠛⠂⠀⠀⠀⠀⣠⣾⡏⠀⠀⠈⠻⠋⠀⣴⡞⠛⠛⠁⢀⣿⣦⠀⢠⣥⡀⠀⠀⠀⡿⠟⠀⠘⠉⢰⡶
⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⣹⡿⠀⠀⠀⣇⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠰⢶⠂⠀⢰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣾⣆⠀⠀⢀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠚⠿⡏⠀⠹⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣟⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⢧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠇⠀⣨⠤
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⢠⠊⠀⠀⢀⣄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠃⠀⠀⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠘⢢⡄⠀⠀⢸⠀⠀⠀⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢈⠞⠋⠉⠙⡆⠀⠀⠀⡎⠛⠉⠀⠀⠀⠀⠀⢀⡀⠤⢀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠱⡀⠠⢄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡼⢦⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣣⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⡀⠀⠙⢢⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⠄⠀⠀⢧
⠀⠀⠀⠀⣴⣾⣿⣿⣿⡌⠑⠒⢾⠷⠿⠿⠿⠿⠶⢦⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⣿⣿⣿⠟⠥⠤⢴⠇⠀⠀⣀⣬⣐⠀⠀⠈⠉⠀⠀⠀⠀⠜⢸⡇⠀⠀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠁⠀⠀⠀⠀⠀⠠⡄⠀⠀⢴⠀⢸⠃⢠⠞⠁⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣶⣌⠀⠋⠀⠆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠐⠁⠀⠀⢾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⠏⠻⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣄⣪⣷⣦⣀⡉⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠓⠲⠤⠤⠤⠴⠋

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

⠀⠀⠀⠀⠀⠀⠀⡠⠖⠲⣄⢀⣀⡴⠆⠀⠠⣄⡠⢆⡠⠒⠀⣘⠐⠦⡀
⠀⠀⠀⠀⡆⡀⠠⠃⠀⠀⢸⠷⠋⢱⠁⠀⠀⠈⠙⠈⠙⠷⣶⣯⢤⣴⣤⣁⣐⠄⢀⢠⡀⣠⠊⠀⠧⠤⡀
⠀⠀⠀⢀⡖⠋⠁⠀⠀⢠⠎⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠉⠁⠒⠉⠀⠀⠙⣄⠁⢉⡶⡄⠀⠐⢇
⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣀⣀⡤⠢⠤⣰⠛⠠⠤⢤⣤⣀⢠⡔⠉⠈⠑⣤⠓⣆⠉⠑⠜⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢀⣀⠴⠒⠓⠫⣉⠈⢤⡄⠀⠸⢄⠀⠀⠀⠀⢈⡟⠉⡑⢋⠽⢿⢂⠈⠿⣄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣧⢀⣀⢀⣔⡿⠋⠁⠀⠀⠁⠀⠈⠻⣶⢡⣄⢀⡈⣵⠂⢀⡔⠁⢹⢘⡅⠀⠔⢺⣟⠣⢦⣀⣰⠂⢠⡄⠀⠤⣄⠀⡠⠊⠉⠂⢢
⠀⠀⠀⢀⣿⠚⠿⣎⢰⠃⠀⠀⠀⠣⠀⠀⢠⠎⠈⡆⠀⠀⢀⠜⡢⢎⠤⣦⣹⣤⣟⣳⠀⠓⠘⢄⠘⠦⠹⣶⣅⠀⠈⠐⠜⢾⣞⠀⠀⠀⠈⢳
⠀⠀⠀⠀⡁⢀⠄⢁⠏⠀⠀⠀⢀⣀⠇⠠⠆⠀⠀⠸⡀⠀⡤⠿⠀⢘⡻⣦⡼⣦⣬⣛⡞⡧⠤⣴⠋⢼⠁⢈⣎⠀⠀⠆⠀⠚⠀⠓⠤⠀⢰⠁
⠀⠀⠀⠀⡇⢸⢠⡋⠀⠀⠀⠐⣷⠬⠺⣤⡀⠀⠀⡤⡶⢎⠀⡇⠀⣎⣹⣥⣦⣬⣥⣽⣿⣥⠊⠁⠈⠑⠒⠁⠈⡀⠀⠃⠀⢘⠀⠀⠘⠀⢸
⠀⠀⠀⢠⠇⡀⠀⢹⠆⠀⠀⢴⣷⠴⢿⣤⣗⠶⣼⡥⠳⠾⠷⠇⠀⠈⢭⣈⡚⣧⣼⠶⠛⢆⠲⡀⠀⠀⠀⠀⠀⠨⣀⢄⠀⠠⡄⠀⣀⢀⠏
⠀⠀⠀⢸⠀⡇⣰⠁⠀⠀⠀⠀⢾⣤⡿⣧⣼⢶⣲⠀⠢⠡⠀⠀⠀⠀⢸⣭⠷⢤⣶⠋⡠⠊⠠⠄⠀⠀⠀⠀⠀⠀⠸⡈⠳⡄⣠⠞⠀⠛
⠀⠀⠀⢸⠀⡇⡟⠀⠀⠀⠀⠸⢶⠾⠶⡛⣷⣾⡥⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠂⠀⠀⠙⡒⠀⠠⠖⠈⠒⠦⠤⠤⢄⣧⣀⣈⡀⢀⠐⠓⡲⡄
⠀⣀⠀⢸⢀⢠⠇⠀⠀⠀⠀⠀⠈⢻⠾⣿⢧⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠩⠹⡿⢌⡁⠀⠱⡀
⠙⡗⠱⡄⢸⣼⠀⠀⠀⠀⠀⠀⠀⠹⠶⠳⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠀⠇⠰⠀⠁⠢⠀⣡
⠀⠫⣗⠀⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠈⢣⠀⠀⣀⡩
⠀⠀⢱⠴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢀⣀⡠⠀⠀⠀⠀⠀⠀⢀⢟⢧⣤⡀⠀⠀⢀⡅
⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⢀⠀⠀⠀⢠⡴⠧⠵⣼⣿⣫⣵⢦⣼⢂
⠀⠀⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⡅⠈⠉⠙⠌⠒⠮⡆
⠀⠀⠀⢿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⠀⠄⠀⢹⠀⠻
⠀⠀⠀⢸⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠋⠉⣦⣤⣀⠁⣘
⠀⠀⠀⠸⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⢠⠃⡠⠀⠒⠂⠻⣮⢨⡑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠔⢰⠋⠉⠉⠈⠁⠀⠀⢄⡜⣹⠢⠥⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠎⠡⣽⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠔⠛⠁⡏⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠠⠌

⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡀⠁⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠂⠀⠀⣦⣄⠀⠀⠁⣠⣆
⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢀⢲⣆⡀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠦⢀⠀⠈⣡⣶
⠀⠀⠀⠀⠀⠀⣄⢯⠐⠂⠘⠬⠩⠘⠀⣰⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⠎⠄⠀⠀⡉⠁⠀⠲⣶
⠀⠀⠀⠠⠀⠀⠀⠀⢠⡄⠀⠀⡀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠿⠓
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⢼⡇⠀⠀⠀⠀⡰⠀⠀⠀⠀⠂⣭⠠⠀⠘⣶⡈⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠙⠂⠀⠀⠈⠀⠀⠀⠰⠷⠀⠀⠒⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠶⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠠⢀⡀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢴⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢀⠐⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠡⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⠁⣐⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢛⣠⣤⠀⠀⠀⠀⠸⣬⣄⣼⢟⣽⣿⡇⣿⣧⣴⡶
⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣿⣿⣿⡷⠀⠀⠙⠛⣷⣠⠀⠠⠶⢾⣿⢷⡞⣽⡾⢿⣿⣿⡟
⠀⢼⡇⣶⡄⡀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣦⣀⣿⡟⠛⣩⣯⣤⡀⣰⣶⣾⠇⢸⣿⣧⣤⡄⢴⡞⠃⠐⣿⠛⢧⣾⠿⢩⣧⣤⡶⠂
⠠⠾⣿⠘⢿⣇⣘⠿⣿⡀⠀⠀⢠⣿⢏⣽⣿⡟⢃⠀⢿⠃⠙⠃⢀⣹⠀⠀⠀⠉⣽⡏⠀⠘⢿⣦⠀⠛⢰⣾⣷⡄⠈⢿⣷
⠀⠀⠀⠀⠻⡯⠉⠻⢿⣿⣿⣷⣾⠿⠿⠿⠇⠘⢿⣷⣦⠀⠀⠠⠬⢿⡆⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⢠⡾⠉⠽⢿⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢹⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡿⠟⠛⠀⠀⠁⠊⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣰⡆⠀⠀⠀⠀⠰⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠂⡻⠇⠀⠀⠀⠀⠀⠀⠉⠀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣷⡆⠀⠀⢐⣶⣦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⢀⠀⣁⡀⠀⠀⠺⢿⣷⣾⣿⣿⡄⡴⠀⠀⠉⠛⢀⣴⣿⡏⢰⣧⣀⣴⠶⠶⠀⠀⠀⠀⢀⠉⠀⠀⣦⢀
⠀⠀⠈⠻⣿⣷⢀⣀⡿⢿⣯⣽⣿⣿⠃⠀⠀⡴⣲⡿⡿⠿⠿⣤⣿⢁⣀⣤⣰⣶⣾⣷⣶⡆⠁⠦⢀⣿⠖⠀⠀⠀⠀⡐
⠀⠀⠀⢰⣶⣬⣿⣿⡷⠋⠈⠙⠛⣻⠄⠀⠀⢰⢿⡇⠀⠀⢀⡬⠿⠉⠀⠈⠙⢿⣿⣿⡿⠄⣠⣴⣾⣿⣤⣠⣀⠀⠈⠀⠄⠀⠃
⠀⠀⠀⣈⣽⠿⣿⠿⠓⠀⠀⠈⠸⠃⣿⣆⠀⠀⠈⠁⠀⠀⠋⠀⠀⠀⠀⠀⠰⠾⠀⡿⠀⠰⠻⢿⡿⠿⡟⠛⢿⡇
⠀⠀⠀⠉⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡀⢀⡀⠀⠀⠀⣀⡀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⣀⠀⣀⠘⣂⣠⡮⠤⢠⣀⡀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠐⠴⢄⠙⢠⢹⡯⡀⠀⡠⢬⣉⣳⠀⠀⠀⠀⢱⣲⠾⠟⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠂⢀⣬⠉⣩⠟⠧⠿⠿⠝⠯⠨⡆⠀⠀⡰⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣵⢠⠾⠷⣿⣋⡴⠦⠼⣷⠚⢧⢸⡀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡠⠴⠒⣄⣰⠚⠁⠈⠙⢆⠀⠀⠀⠀⡄⠀⠀⢰⡉⠷⣿⢿⠛⢳⣯⠟⠈⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠑⢞⠁⠀⡇⢴⢋⠄⡀⢱⠀⠀⠀⠡⢤⠰⣯⣍⣴⠅⠚⠀⠀⠀⢠⣮⡤⠋⣠⠄⢚⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠈⠀⠱⣔⡁⣶⢅⠀⣄⠼⠛⠿⢶⣤⡀⠉⠙⠟⠁⠀⢀⡠⣰⡶⠞⠉⣵⠉⠀⠈⣃⣄⣀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠂⠘⡏⠛⠺⡏⠁⠀⠀⠀⠀⠈⠙⠻⢶⡾⠶⠖⡛⠋⠉⠠⠐⠲⣇⢀⡴⠋⠁⠀⠉⣠⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠃⠄⠡⢰⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢀⡀⠀⢀⠌⠲⠒⠉⠻⢶⠊⠡⢤⡤⠋
⠀⠀⠀⠀⠀⣀⠀⠂⠤⡀⠀⠀⣸⠖⠒⠄⠀⠔⠊⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⡇⠈⡀⢰
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⣦⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣁⡠⣻⠁⡼⠂⠹⣄⣀⣨⠂⠐⡁⣠⠾⠋⠞⡦⠟
⠀⠀⠀⠐⢄⢀⣀⢀⣀⣠⠏⠈⠑⣄⠀⠀⠀⠀⢀⣀⡆⠉⡇⣠⡞⢉⡟⠛⣦⠽⢦⠀⢬⠀⢄⡀⠀⠳⡀⠀⠓⢀⡧
⠀⠀⠀⠀⠀⡱⠀⠉⠐⡏⠓⠀⢀⠈⣢⠀⠀⢀⠋⠀⣄⢢⡿⠋⢣⣪⣦⣰⡏⠀⡾⣀⡟⣄⢎⠁⣽⠀⠉⠐⠺⠞
⠀⠀⠀⠀⠀⠀⢠⠜⢻⠁⡠⣄⠀⢸⡁⠀⢠⠚⢶⡾⠏⠀⣿⣐⣿⠁⢨⡏⣰⡎⠛⣿⠛⠟⠛⡖⢿
⠀⠀⠀⠀⠀⠳⠀⠐⠘⠊⠀⢺⠉⢈⣀⠀⠈⠲⢻⠀⣷⡾⢿⡟⠛⡷⠽⡶⠿⣥⣮⣥⡀⣷⠀⡇⢸⡇⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⢀⠤⠉⠉⠐⠂⢼⠖⠉⠀⠉⢰⡀⠀⠻⢻⣄⣸⣆⠾⣧⣰⣆⣤⡎⢰⠸⠀⠚⠀⢹⠉⠔⢂⢀⡀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠁⠀⠐⠊⠉⠰⠛⠲⠀⠀⠁⢀⡀⠀⠀⠀⢰⠚⣿⠃⢈⣏⠉⡟⠉⣦⢘⡶⠛⢷⠯⣀⣇⡁⠁⠁⠀⡄⠀⡘
⠀⠀⠀⠀⠀⠘⠀⡀⠀⣠⠰⠳⣤⠸⣆⠐⠉⠀⠀⠀⠀⠸⣠⣿⠦⣭⠷⣼⡷⣤⡿⢾⠗⢬⡽⡠⠚⠛⠇⢄⣀⡜⠠⠾⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡⠠⢀⣹⣤⣀⡅⠀⠀⠀⠀⠀⠀⠉⠩⣤⣿⣀⣿⡀⠸⠤⢰⠀⠀⢠⠁⠐⠁⠀⢠⠇⡶⠦⣅⢠⡜⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⣠⠁⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢳⠋⢱⠞⠲⠋⠀⠀⠈⠄⠠⡀⠐⠃⡜⠁⠀⠨⣷⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⠞⣶⢾⢀⡴⠀⠀⠀⠀⠘⢦⣤⡀⣠⠄⠢⠀⠰⠁⠑⢄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡇⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⡿⢿⡿⠿⠿⠿⣦⡀⠀⠀⢠⣿⣿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⣭⢷⡻⣠⠟⠀⠀⠀⠀⠀⠹⡄⠀⢸⣿⣿
⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⣸⣿⡿
⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡇
⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣶⣶⣶⣶⡤⠄⠀⠀⠀⠀⠀⢀⣿⣿⣷⠾⠛⠋⠉⠉⠉⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⢹⣿⡆⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⣿⣿⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣷⣶⣶⣦⣬⣭⣙⡛⠿⣶
⣿⣦⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣾
⠉⠉⠛⢦⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⢿⣻⠛⣹⠏
⠀⠀⠀⠈⢧⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢟⡯⣪⠞⠁
⠀⠀⠀⠀⠘⣇⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣼⣿⣟⣀⣤⡴⠶⠶⠶⠶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⢀⣠⣶⣞⣻⣭⣿⣿⡿⠟⠛⠃
⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⡴⠟⠛⠛⠻⠟⠛⠛⠉
⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣠⠃
⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢻⣿⣰⠃
⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⣛⣛⠛⠿⠷⢶⣦⣄⡀⢸⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣶⣬⣝⣻⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿
⡷⣿⠿⢶⣾⠿⣶⠶⢶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣷⣾⣾⣿⣷⣿⣷⣶⣿⣿⢾⣿⣶⣾⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⠄⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡙⠓⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⡉⣹⣦⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠳⢤⣈⡁⣼⣿⠟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⡆⠀⠈⣭⣭⣤⣄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⢹⡀⠀⠙⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣈⣴⣿⣇⣀⣀⣤⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⡄⠀⠀⠀⠀⠀⠀⢠⡤⠴⠶⠤⢤⣼⢀⣤⣾⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⡞⠲⢤⡀⠀⢀⡟⠀⡄⠀⣷⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⣠⣤⣼⣿⣿⣿⣿⣿⣟⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⡇⠀⠀⠙⢦⡘⡇⠀⠀⠀⣸⡴⠙⡄⠀⠀⠀⡀⠀⠙⠾⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⡇⠀⠁⡀⠀⢧⠹⢤⣄⡴⢻⣤⠃⡗⣠⣾⣿⣿⠀⠀⠀⠀⠀⢀⣼⣿⠋⠙⢿⣿⣿⣿⣿⡿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠙⣦⡀⠀⢀⡞⠀⢀⣼⣿⣿⣿⣿⣠⣿⣿⣿⠇⠀⢀⣀⣤⣾⣿⣿⣿⣿⣷⡄⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠻⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠈⠉⠙⠛⠿⢷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠲⢦⣄⠙⠻⢿⣿⣿⣿⣶⣤⣀⣀⡠⠄⣆⣐⣂⣝⣉⣉⣉⣉⣉⣉⢉⠙⠛⠳⢶⣤⣀
⠤⣤⣤⣤⣀⣀⣀⠀⠉⠻⣶⣤⡈⠙⠿⣽⡻⢿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠈⠛⠶⣄
⠀⠀⠉⠙⠻⢿⣿⣭⣒⠒⠠⠙⢿⣤⡀⠀⠙⠳⣏⠁⠋⠈⠁⠘⠁⠐⠩⠋⠿⠻⠿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⡈⠉⠒⢅⡀⠈⠀⠄⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⡈⠈⠻⢿⣿⣿⣿⣿⣿⣶⣤⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⠉⠉⠙⠲⢬⠆⠄⢠⠗⢀⢀⠐⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⡈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⡀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⠻⣿⡿⠏⠋⡿⠀⣠⣷⣦⣄⠉⢻⣿⣿⣿⣿⣿⣿⣦⡈⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡆⠄⠀⠀⠀⠀⠀⠀⠓⢠⠀⡈⠉⠉⠀⣀⣴⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⠦⠀⠀⠀⠀⠀⠀⠀⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣓⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠳⠀⠀⠀⠀⠀⠂⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⡟⡷⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠦⠀⢠⠐⢄⠀⠀⠀⠀⠁⠚⣿⣿⣿⣿⣿⣿⣧⢐⡆⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⡀⢦⠁⠈⠀⠀⠀⠀⠀⠀⢉⡛⣛⠻⢿⡯⠉⠐⣃⠁⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢤⡁⠘⠳⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⢀⠈⠃⠉⢁⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⠁⠸⠆⢀⠀⠀⠦⠀⠀⠂⠀⠠⣄⠀⢠⡀⠐⠀⠀⠐⠀⡀⠈⠛⢿⢿⢿⠻⡿⠿⢿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠑⠀⠀⠙⠀⢀⠀⢀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠉⠀⢁⡀⠀⢤⡀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀⠀⣤⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠂⠉⠠⠉⠐⠋⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠈⡑⠀⠀⠀⠀⢀⠑⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣄⠀⠀⣀⠀⠀⠀⠁⡄⠀⠀⠉⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠆⠂⠀⠙⠢⡀⠀⠀⠻⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⢠⣄⠀⠈⠀⠀⡁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣄⠀⢿⡀⠀⠑⢦⡙⠆⠀⠢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⡁⠀⠀⠂⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠄⠹⡆⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣴⣿⣀⠀⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⡆⠃⠀⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠓⠤⡀⠀⠘⡴⢠⡞⠀⢀⠤⠒⠊⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣤⢄⣀⣀⢬⢶⣤⢿⠻⣴⣪⣅⡂⠤⠤⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠉⠉⣉⢿⣿⣄⣠⣿⣷⡖⡒⠒⠀⠈⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠔⠒⡨⠋⢠⠃⢃⠈⠢⡉⠑⠢⠤⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⣜⠀⢸⣄⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎⣿⠀⠀⣿⡄⠈⢿⣧⡀⠀⢱⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠋⠘⠏⣤⣴⣿⣧⠀⠸⠙⠓⠀⠀⣿⠪⡙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢴⣿⠿⠛⠉⣰⣿⡄⠀⠀⠻⢟⠻⣿⡀⠀⣇⢀⣤⡀⢸⡇⢱⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣠⡟⠛⠁⠀⠀⠀⢸⠀⢿⣧⠀⣿⡿⠿⠃⠘⠃⣾⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣽⣻⠋⣷⠀⠀⠀⠀⢠⣿⣦⣬⠛⠈⣿⡷⡀⠀⠀⠀⢹⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⢼⡇⠀⠀⢠⣿⢻⠻⠟⠁⠀⢹⣧⣧⠀⠀⠀⠀⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⠀⠀⣿⠏⢸⡷⣄⠀⠀⠙⠿⢻⣇⠀⠀⠀⠀⠉⠀⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⢠⣴⣾⣧⠹⣷⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣫⣿⡆⠙⠇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠓⠄⠀⠀⠀⠀⢀⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠛⠲⠄⡀⠈⠳⣆⡀⠙⠛⢁⣤⠆⠀⠀⠀⠀⠀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⣀⠀⣤⣤⡾⢁⣀⣀⣀⠐⠶⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠲⠆⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠉⠉⠛⠉⠀⠀⠀⠀⣠⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⣴⠆⠀⢀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠾⠣⡴⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠆⣠⠀⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣿⡄⠀⢀
⠀⠀⠀⠠⢴⣶⠟⠿⢷⡆⠉⠙⣶⡋⠀⢻⡿⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢹⣇⠀⠛⠛⠂
⠀⠀⠀⠀⣀⣩⣶⣦⣼⣿⣦⢀⣿⣷⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠉⠘⣿⡀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⢹⠉⠙⣿⣯⣨⣿⡿⠉⠙⣿⠀⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⠟⠉⠉⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣿⠀⡄⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠘⠃⠰⣿⢷⣦⣤⣾⣿⡿⠛⠀⢸⡏⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡀⠀⠀⢸⣿⡆⠀⣶⡄⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠷⣀⠶⠶⢤⣾⡇⠀⢠⡞⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢇⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⡠⠊⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡷⠀⠸⠃⠀⠈⢿⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⡀⠛⠁⣿⣇⣐⠟⠀⠀⠀⢀⠀⠀⢨⣿⡄⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠟⠀⠀⠀⣿⡏⠀⠀⠀⠀⠘⠄⠀⠸⣿⣧⡀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠾⠉⢹⠀⠀⠀⠀⠀⢸⡇⠀⠘⢋⠑⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⡇⠀⢲
⠀⠀⠀⠀⠀⠀⠐⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⢠⡀⠙⠀⠀⠀⠀⠀⣺⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠉⡄⠉⠙⠻⠶⣄⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⣼⡗⠀⠀⠀⠀⠀⣶⣿⠁⠀⠐⠷
⠀⠀⠀⠀⠀⠀⠀⢂⣼⢧⡀⠀⠀⠈⢣⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢨⣿⠀⠀⠀⣠⣴⠟⠉⠉⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⡄⠀⠀⠘⠛⠠⠤⣀⠀⠀⣄⡀⠀⣾⡇⠛⡀⠀⠀⣸⡇⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶
⠀⠀⠀⠀⠀⢀⠶⣾⣿⡄⠘⢿⣦⠶⠶⣦⡀⠀⠙⠷⣆⠙⠿⢦⣿⣇⣠⠋⢀⡴⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠹⡄⠈⣿⡟⢿⣆⠙⢢⡀⢿⣿⠶⣤⡀⠈⢡⡄⠀⠉⠉⠁⠐⠈⠀⣰⡏⠁
⠀⠀⡀⠀⢻⣦⣴⣶⠻⣧⠀⠻⣷⠀⢀⡘⠃⡀⠈⣿⠷⠀⢁⡀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⣀⣀⠀⣿⠀⢸⣷⡸⠷⢶⣄⠀⠈⢳⡜⠁⠀⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⢶⣄⠀⢀⡀⠀⠀⠀⠠⠦
⠀⢀⠙⠻⣷⠉⢶⣿⣿⡇⠀⣸⡿⠷⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠹⠷⡀⠁⠀⣀⡀⣤⡀
⠀⠀⢀⣼⣿⣀⣀⡘⢻⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠘⢿⣆⠀⠀⠀⠈⠁⠘⠓⢠⣤⡄
⠀⠀⠘⠋⠈⠛⡿⠷⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠘⠃⡀⠀⠀⠀⠘⣷⡄⣀⢀⣀⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⣼⣅⠀⠇⠀⠀⣿⡄⠙⢋⣉⠉⠙⠃⠀⣤⠀⠀⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣰⠟⠀⠀⠀⠈⢿⣆⠀⡼⠇⠈⣧⠀⠈⠋⠐⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⣆⣠⣶⠋⠀⠀⠀⠀⠀⠈⢿⡄⠀⡀⠀⠀⠀⠀⠸⡇⠀⠀⠲⣆⠀⢴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢸⠀⠀⠀⠀⠛⠻⠆⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠁⠀⢠⣄⠀⠀⠀⠂⠀⠀⣀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠀⠀⠀⠀⠀⠣⣤⣤⡀⣠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠐⠀⣉⠀⠀⠤⠀⠀⢴⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣀⡀⠀⣠⡼⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠁⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⢀⣶⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⣿⠋⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⣤⣀⣀⠀⠀⣰⡟⠀⠀⠀⣸⡿⠀⣸⠏⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⠉⠉⠉⠉⠂⣴⣏⠀⠀⠀⠀⢻⡄⠀⢿⣾⡿⠉⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟⣿⠛⠛⠋⢁⣄⣀⣀⣤⡞⠉⠉⠀⠀⠀⠀⢸⡇⠀⣿⣿⠀⠀⠀⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠦⠛⠋⠀⠀⠀⠀⠾⠟⠋⢨⣧⠀⠀⠘⠀⠀⠀⠸⣧⠀⠀⣻⣷⣾⡛⠻⠇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡶⠀⢀⣠⡆⠉⠀⠀⢀⠀⠘⠟⠀⢀⡀⠈⠀⠀⠀⢠⣄⠀⠈⣿⡙⢿⣀⡰⠋⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⢁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠸⡇⢸⡅⠀⠀⠀⠀⠈⠛⣷⡀⠈⣧⣸⡏⠀⠀⠸⠻⣷⣶⣦⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣻⠟⠁⠀⠀⠀⢴⡄⠀⠀⠀⠀⠸⠇⠈⠁⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠻⣧⣈⣠⣴⣿⣀⣿⡇⠠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠆⠀⠂⠉⠁⢰⡿⠈⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢿⣄⠀⠈⠙⠛⠴⠿⢿⡏⠁⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠁⠀⠀⠲⣶⡆⠒⠟⠛⠉⠙⣡⣼⣿⣶⣤⣤⣤⣤⡀⠈⠙⣦⡄⠐⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⣶⡶⢿⣿⣟⠙⢿⣧⣿⣿⣍⡛⢃⣀⣀⠙⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣸⣿⡇⠀⠛⠉⠃⠈⢿⣦⠈⣿⡟⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠻⣧⣴⠋⢻⣶⢰⠿⢻⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⢙⠛⣤⠀⢩⣾⣧⡠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠳⣿⣷⡎⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣀⣽⣿⣴⣷⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣼⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣤⣄⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣤⣀⣈⣁⣠⣄⣠⣄⣀⣠⣤⣀⣀⣠⣤⣤⣤⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⡿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣉⣉⣉⣉⣉⣭⣉⣹⣇⣀⣉⣈⣯⣉⣁⣈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣤⣾⣦⣴⣴⣶⣶⣶⣾⣿⣿⣦⣤⣤⣤⣶⣤⣤⣤⣤⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢼⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠟⠏⣁⠰⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⣤⣿⣾⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⣰⣿⡿⠀⠀⠀⠀⠀⢀⣀⣠⠀⢀⡀⠀⣤⠼⠧⢪⣶⣿⣾⠛⠇⠐⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢱⣿⠟⠀⠀⣠⠀⠀⣄⣭⠟⣣⠶⠜⠀⠀⠀⡄⢄⣾⣿⣿⣧⣠⡶⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢸⣿⡂⠀⢀⠋⠀⠸⢿⣯⢖⡹⠇⠀⠀⠀⠀⢃⣾⣿⣿⣿⣿⣿⡃⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⣿⣯⠲⣏⠀⠀⠀⣻⠹⣋⡃⠀⠀⢀⣾⣷⣟⢿⣿⡛⠛⠻⠀⠠⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣷⠾⣿⣿⣳⡭⠀⠀⠀⠈⠇⡈⠁⠀⢀⣴⣵⣼⣿⡺⠏⡉⠐⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣟⣿⠋⣹⣿⣹⡷⣄⠠⠀⣠⠀⣷⠀⠀⠺⣿⣿⣿⣿⣄⢢⢀⡀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⣯⡝⢻⣅⣴⡄⢰⠀⠿⢾⣿⢾⡤⣚⣿⣿⣿⣿⡧⠈⠛⠡⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣽⡿⣷⣟⣿⣿⣿⡇⠦⢰⢸⡧⠏⢷⣿⣿⣿⣿⣿⢷⡌⠁⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣋⣿⣯⣷⡿⣿⣹⡿⣾⣧⠀⠀⠀⢶⣿⡀⢻⣿⣿⣿⡿⠆⠀⠀⣠⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣟⢿⣅⣿⣿⣿⣼⣿⢻⣯⣆⣉⠘⠋⡭⠷⠚⢿⣿⣿⣿⠆⠀⣼⡿⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣧⣼⠿⣯⣼⣿⣋⣹⠟⣯⡉⠴⠾⠛⢚⡃⠸⣿⣿⣯⡴⢀⡿⢅⣿⣡⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⣿⠿⣹⢧⣬⡿⠾⣯⠽⣿⠇⣼⣿⠿⣀⡛⢀⣛⠛⣋⠀⢹⣿⣿⣧⣸⣿⣾⠋⢽⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣟⣿⣟⢧⣿⠛⣿⢶⣷⣶⡿⢛⣾⣿⣄⠈⣉⣙⢿⡆⢸⣿⣿⣿⣿⡿⠃⠠⣿⠃
⠀⠀⠀⠀⠙⣿⣶⣶⣦⣄⠀⠀⠀⠀⢻⣿⣹⣿⣿⣿⣿⣷⣶⣻⣧⣾⣿⣿⡟⡈⠋⠡⣿⡖⡦⠀⣿⡿⢿⡟⠀⢀⣼⣿⠀⠀⠀⢀
⠀⠴⠟⠛⠛⠋⠉⠉⠉⠛⢦⣀⡀⠀⢸⣿⣿⣾⣧⣿⣷⣾⣿⡿⣿⠿⡟⢿⡟⣿⣉⣹⠿⣛⡧⢠⡿⣃⣾⠀⠀⣶⣾⣿⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠆⣸⣿⣻⡿⣩⡿⣿⣾⣯⣤⣼⣞⣿⠀⢉⣤⣉⣹⢟⣏⢁⣼⣿⣿⠁⠀⢰⣏⣿⠋⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⢈⡁⣿⣧⣶⣿⣷⡿⢻⣿⣿⣿⢿⣥⣾⣿⣿⣆⣹⣏⡙⢉⣿⡏⣿⠀⠀⠺⣿⡟⠀⠀⢘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⡀⠈⠁⢹⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣟⣩⣽⣧⡤⣿⢉⣴⠟⢀⢿⠀⠀⣾⠿⠁⠀⠀⠈⡋⠁⠀⣴
⠀⠀⠀⠀⣸⣦⡞⠁⠀⠀⠀⠀⢸⡶⠂⠈⢿⣿⣿⣽⣯⣹⣿⣹⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣯⠀⢿⡴⠀⠀⣹⡆⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⢀⡠⣤⣾⣅⠀⢸⣿⣿⡻⠿⣻⠟⢿⡿⣿⢛⣿⣙⣿⣿⡃⢾⣿⠇⢸⣄⡁⠀⢠⡄⠀⠀⣠⡄⣁
⠀⠀⠀⠀⠈⠀⠀⣴⠏⠀⠈⠛⢿⡏⠛⢷⡆⢿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⡇⠀⠙⠇⠀⡼⢀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⢲⣾⣧⠘⠀⠀⣸⢟⣿⡟⣿⡟⢿⣿⣿⣿⣿⣿⣯⣭⣾⣿⣿⠃⠀⠀⠀⠀⠀⢈⡀⢻⣘⠂⢸
⠀⠀⠀⢀⣶⣾⠏⠀⠘⠀⡄⢸⣿⣿⡄⣠⣼⡇⠘⣿⣷⣼⣿⣿⣿⣿⣍⣽⣇⣿⠶⢾⣿⣿⣟⠀⠀⠀⡀⠀⠚⡀⠉⣿⠀⠚⣧⠀⣀
⠀⠀⢰⡿⠟⠋⠀⠀⠁⣀⠀⠀⣿⣿⠇⢀⣿⣧⣶⡙⣿⣷⣤⣿⣿⣿⣿⣿⣿⡿⠰⣿⣿⣿⣿⠁⠀⠀⠁⠀⢸⣧⠀⠃⠀⠈⠛⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡖⡤⠉⠁⠈⣾⣿⣆⡉⠵⠈⢛⣿⣭⣾⣷⣾⣿⣿⠀⣀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠁⠀⠀⠉⢰⣿⡟⢻⣷⡶⠶⢞⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣰⣿⣿⣟⠋⠉⠠⢴⠏⢘⣿⣿⣽⣿⣿⣿⡿⢟⣽⣧⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⣰⣾⠟⢉⢩⣍⠁⡀⠀⠀⡶⠈⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡷⠙⣿⣧⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠀⠀⠈⣀⣧⠊⠁⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⡍⢀⢏⡰⣅⣸⣮⣿⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡾⣷⠿⠿⠟⠙⢧⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⠃⠐⠓⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢹⣿⣯⣥⣴⣦⣶⣶⣿⣾⡇⠀⠀⠤⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⠇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⠟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇


⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠤⠤⢤⣀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⣤⣀⡤⠤⠀⠀⠤⢀
⠀⠀⠀⠐⣡⡶⠚⣩⣴⠾⠿⣿⣬⡙⢿⣿⣷⡀⠀⠀⠀⣴⣿⡿⢋⣤⡾⠿⠿⠷⢶⣄⠙⢶⣄⠑⡄
⠀⠀⠀⢰⠏⢠⡞⢉⣴⠶⠶⢶⣌⠻⣦⠙⣿⣷⣤⣤⢼⣿⡏⣰⡟⣡⡶⠟⠛⠷⣦⡉⢷⡀⠹⡆⠸
⠀⠀⢀⢸⠀⣿⠀⣿⢡⣾⢷⡆⢹⡇⢹⡇⢻⣿⠟⠻⣾⣿⠀⣿⠀⣿⠁⡾⢻⣷⢸⣧⠘⡇⠀⡇⠰
⠀⠀⠈⣾⡀⢿⡀⢿⣄⠻⣦⣴⠾⢃⣾⠃⣼⠏⠀⠀⠘⣿⡆⢻⣆⠙⠷⡶⠾⢃⣼⠇⣸⠇⢰⣧⠎
⠀⠀⠀⠈⢷⡈⢿⣄⡙⠷⢶⣶⠶⠟⣡⣾⠏⠀⠀⠀⠀⠈⢿⣦⣙⠻⠶⠶⠾⠛⣡⣾⠏⣰⣿⠋
⠀⠀⠀⠀⠀⠹⢦⣍⡛⠷⠶⠶⠾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣟⠻⠷⠶⠾⠛⣋⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢿⣿⡿⠟⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⡿⢿⣿⣿⣿⡿⢿⣿⣿⣏⠻⣿⣿⣿⢿⣿⡻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡇⢠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟
⢿⣿⡛⣿⣿⣿⣿⣿⣿⡟⠛⠋⠙⡻⣷⣯⣄⠻⠿⢸⣿⡿⠛⠉⠛⠛⢉⣿⡿⣇⣤⣭⣍⠻⠿⢳⣿⣿⣿⡟⢻⣿⣟⣿⣿⠿⠿
⣴⣿⡿⣩⣯⢹⣧⠙⠛⢻⣷⣤⣾⡇⠈⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⠿⠃⣿⣮⠙⠋⠀⠀⠀⠙⠁⢀⣤⣶⢿⣿⣿⣿⡧
⠛⠃⢸⣿⡿⢻⣿⡇⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠻⣿⠇
⠀⠀⠀⠉⣀⣬⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡟
⠀⠀⢠⣿⣿⣿⣾⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠇⢻⣿⣦
⠀⠀⠈⠛⢻⣿⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣩⣄⡈⠻⠿
⠀⠀⢀⣴⣾⡏⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⣿⡆
⠀⠀⠻⢿⣋⣀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣦⡀
⠀⢰⣿⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠈⠀⠀⠻⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠛⠁⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⡠
⠀⢀⠀⠄⠀⠀⠆⠀⠀⠀⢀⡀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟
⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠀⠀⠈⠙⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠁⠂⠈⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⢀⡄⠘⠀⢐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠘⠀⠠⠄⢀⡾⠁⠀⠈⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠐⢏⣡⡄⠤⠡⣀⡀⠀⠐⡀⠀⠀⠀⠀⠀⠐⠀⠂⠀⣾⠠⠀⠀⠀⠠⡀⠀⠀⣤⡞⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⡏⠂⠒⠤⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⣾⠀⠀⠤⣁⠐⠈
⠀⠀⠀⠀⠀⠀⠂⠘⠘⣧⠀⠀⠀⠈⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠈⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠐⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠠⠀⠀⠀⢠⡕⣦⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣸⠇⡙⠁⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣀
⠀⠀⠠⢀⡅⠰⠛⡟⠀⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣆⠀⢀⠀⠁⡀⠀⠈
⠀⠀⠀⠈⠡⠄⠈⠀⠃⡐⠖⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡖⠻⣤⣡⠉⠃⠙⢁⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠘⢩⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⢤⢘⠳⣏⠀⢙⠉⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⠘⠑⠒⠒⠀⠀⠀⠀⠒⠀⠈⢠⣆⣄⢠⣏⠴⣀⡖⠀⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠉⠀⠋⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⡀⠠⠔⠀⠀⠀⠒⠆⡀
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠉⠀⠀⢃⠂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⢢⡀
⠀⠀⠀⠀⠀⠓⠠⡄⠀⠀⠀⠀⠠⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠛⠀⣠⡄⠁⠞⠟⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢛⠁⢀⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⣾⣆⣠⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡃⠀⠈⠁⠰
⠀⠀⠀⠐⢀⠠⡄⠄⠀⠀⠀⠀⠈⠛⠳⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠄
⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠋⠂⠀⠀⢠⠝⢷⣄⠀⠀⠀⠠⢈⡐⡀⠀⠀⠄⠐⢠⠀⠀⠈⠀⠀⢄⠀⠀⢀⠀⠀⠀⠀⣛⠀⠀⠀⠒⠁
⠀⠀⠀⠈⣉⠀⠀⠈⠄⢠⡑⠀⠀⠀⠄⠈⠀⡀⠀⠈⠂⠀⢀⠀⠠⠀⡀⡀⠀⠀⠀⣀⢁⠀⠀⢐⡆⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢡⣥⠀⠀⠀⡾⢹⠳⠄⠀⠀⠇⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⡁⠀⠀⢀⣀⠀⠀⠀⠈⡍⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠃⡴⠀⠀⠀⠀⢦⠀⠀⠀⠀⠰⠀⠀⠂⠀⠈⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⢺⡂⠀⠀⢉⠁
⠀⠀⠀⠀⢤⠀⠄⠀⠀⢫⠟⠀⡄⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⠠⠀⠁⠌⠀⠀⠀⠠⢠⠀⠀⠀⠀⠰⢇⡀⠀⠈⡉
⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠀⠈⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠐⠘⠂⠀⠀⠀⠀⠸⠖⠀⠀⢡⠁
⠀⠀⢀⣙⠓⠀⠀⠠⠀⠈⠃⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠄⠀⠀⠀⢉⢈⠀⠀⠀⠀⠚⡂⠀⠀⠆
⠀⠀⠀⣁⠀⠀⠀⡄⢐⡇⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⢈⡇⠀⠀⠰
⠀⠀⣠⣀⠀⠀⠀⠀⠸⢷⠀⠀⠀⠀⠀⠤⠐⠋⡀⠀⠀⠀⠘⢄⠀⠀⠀⠂⢁⠈⠀⠀⠤⠀⠀⠀⠀⠀⠰⠷⠀⠀⠴⠄
⠀⠀⠠⡆⠄⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠄⠞⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠄⠀⠀⠀⢀⡃⠀⠀⢠
⠀⠀⠠⠴⠀⠀⠀⠄⠹⠦⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠠⠅⠀⠀⡄
⠀⠀⠀⢀⡀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠐⠈⣄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠐⠠⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠐⠀⠀⠀⠀⠀⡎⠙⢷⢄⠀⠀⠀⠂⠸⢄⠀⠀⠀⠀⠈⠀⠁⠀⠀⠂⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠒⡈⠀⠀⠀⠘⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠈⠀⡁⠀⠀⠀⠄⠀⠸⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⣰⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⢠⣤⣠⣾⣆⣀⡀⠀⠀⠰⠾⢩⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⣰⠖
⠘⢻⣷⣦⠀⠀⠀⠀⢀⣶⣤⡄⠀⠀⠀⢠⡀⠀⣀⠀⠀⠀⠀⠀⠉⢋⣹⣿⡟⢁⣀⣠⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠛⣿⣧⣄⠀⠀⠀⣼⣧⣾⡏⠀⠀⠀⠀⠀⠀⢺⠏⠛⠛⢰⣿⣏⣤⡀⠀⢀⣽⣇⣾⠋⠀⠀⢀⣴⣆⣀⡀
⠀⠀⠀⠀⢀⣄⠀⣀⠀⠉⠀⠉⠀⢀⡀⠀⠛⠁⠁⠀⠀⠀⢀⣠⣶⣤⡄⠀⠀⠀⠈⠋⠈⠁⠀⠈⠙⠟⠉⠁⠀⠙⠿⢛⣿⡿⠃
⠀⠀⠀⠀⠈⠛⣿⣿⡁⠀⠀⢶⣴⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⢉⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠟⠂
⠀⠀⠀⡴⠟⣿⣿⠿⠓⠀⠀⠀⢡⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠿⠃⠉⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢾⣿⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣶
⠀⣰⣶⢴⠂⠀⢶⣦⣿⣿⣶⣤⠀⠋⠉⠁⠀⣴⣄⡀⠀⠀⠀⠀⢹⡿⣤⠀⠀⠀⠀⢀⣦⣀⡀⠀⠀⠀⠀⠀⢸⣆⣀⣀⠀⢠⣄
⠈⢻⡿⢶⠀⠀⠀⢀⣤⣿⣿⡁⠀⠀⠀⠀⢻⣟⢻⣇⠀⠀⠀⠀⠀⣦⣨⡀⠀⠀⠈⢻⡟⢿⣅⠀⠀⠀⠀⢀⣈⢹⣿⣏⠘⢿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⢀⣶⣇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣶⣼⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠿⠿⠂⠋⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣤⠀⢈⠳⡀⢧
⡄⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠤⠏⣡⣴⠇⠀⢡⠈
⢧⡀⠀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠟⠁⠙⢧⡙⠉⣀⠀⢠⢸⡞
⠸⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⠬⠙⠛⢇
⠃⡴⠁⡦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈
⢀⠟⠋⠁⢠⠞⠇⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠈⢆
⠁⠀⠀⢀⣤⣄⠀⠀⠀⠀⢱⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠈⠓⠶⠺⠄
⢀⠀⠀⠈⠀⢸⠀⠀⠠⠀⠈⠀⡠⠊⣄⠀⠀⠀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠚⠙⡀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠉⠉⠀⠀⠀⢇⠀⡐⠀⠀⢹⡄⠀⢀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠈⠈
⣀⠀⠒⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⢣⡅⠀⠈⣀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣴⠃⠀⠀⠀⠀⢀⠄⠀⣼⣷⠀⡄⠀⠀⠀⠀⠀⠑
⣏⠀⠀⠀⠀⢀⠀⠘⠆⠀⡈⠰⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠂⠀⠀⣁⠀⡈⢉⠀⠀⢸⠇⠀⠙⠁⢰⠇
⣿⣧⣄⡀⠀⢀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠳⡏⣜⡆⠉⠀⢙⡎⠀⠀⣼⣇⠀⠇⠰⣿⠂⠀⠀⠢⡀
⠀⠀⢁⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠂⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠃⠀⡄⠛⢠⣤⠀⡿⡗⠀⡃⠀⡛⠀⠀⠀⠀⠸⡀⢠
⠀⠀⠀⠦⠌⠀⠀⠀⠀⠀⠀⠀⢆⡄⠀⠀⠶⠆⠀⠀⢀⠀⠀⣠⡄⠀⠀⠉⠜⠃⠀⠇⠀⠰⣼⠀⠀⠃⠀⣇⠘⠉⠀⠀⠀⠀⠀⡀⢀
⠀⠐⠊⢀⠄⠀⠀⠀⠀⠀⠀⢠⢈⠀⠀⣠⡀⠀⠀⢠⠀⠀⠀⠉⠄⠀⠀⠀⠙⠣⡄⡄⠀⣠⠇⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠚⠀⠀⠁⠂⠀⠀⠈⠀⠀⡀⠀⢠⡄⠀⢐⠄⠀⠰⠀⡸⠁⠀⠀⠀⠀⠶⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠠⠀⠀⠖⠀⠀⠀⠀⠀⠀⡄⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⠈⣦⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢙⢀⠄⠀⠀⢀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠆⠀⠀⠀⠸⣄⠹⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠒⣈⠀⣤⠄⢀⡄⠀⣀⣄⠀⢀⠁⠄⠘⠋⠉⢉⣉⣅⡀⣀⠀⢀⡀⠀⠆⠀⡀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⡄⠀⣄⣀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣘⣉⡑⠋⠘⠉⠁⠉⢡⠀⠀⠀⠀⠀⠀⠀⠈⠕⠒⠒⢙⠂⣘⡒⢀⠐⠚⡂⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣺⣷⡿⠅⠿⠇⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠉⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣴⢷⡦⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠁⠀⠀⢐⣻⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠄⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⠁⠀⠀⡀⠹⡿⣟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⠿⠋⠠⡀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠟⣃⣰⠂⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠇⠃⠃⠈⠰⠃⠆⠀⠀⠀⡿⠦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢀⣘⡐⠓⣤⠀⠀⠀⠀⠀⢀⠀⢹⣄⣀⠂⠀⢰⠟⢷⣄⠀⠀⠀⢠⠟⠿⢶⡀⠀⠀⠀⠀⠁
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢳⡞⠈⣀⡀⠀⠀⠀⠈⠁⣀⣺⣐⡀⠀⠐⠀⠀⠹⠂⠀⢰⡂⠀⢀⠀⢘⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⣼⠧⣌⠡⡀⠀⠀⠀⠀⠈⠙⠛⠙⠃⠀⣸⠀⣄⡀⠀⠀⢸⣟⠛⣫⡉⡀⠀⠀⠀⠃⠠⠤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣌⣳⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⠐⢚⠐⠂⠀⠀⣟⡰⢖⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡾⢠⢴⠶⡤⡤⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⢬⣹⣧⡍⠀⠀⠚⠛⠓⠛⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠐⠂⠐⠦⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠶⠶⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠛⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⢘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⡇⢀⡜⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠘⡇⠐⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣌⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠈⠐⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⣿⢀⢤⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⣏⠉⠀⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣿⠀⡇⠀⣿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⡠⠤⠺⠋⠃⡶⠿⣧⡄⠀⣿⠀⠀⢠⠊⠹⠖⣉⣉⡉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠀⠀⠀⣰⠀⠀⠹⣷⡀⣿⠀⠀⢁⡴⠚⠉⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⣐⠀⠤⠀⠂⠈⠄⠀⠁⠀⠀⠀⡏⢻⣿⡀⣴⠃⣀⠀⠀⠚⢫⡍
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣽⣿⣇⠀⠀⠁⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠒⢻⠋⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⢀⠄⠀⡇⠀⢸⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢬⣤⣄⠎⠀⠸⠇⣀⣾⡟⣡⣴⣤⣈⣀⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⣠⠌⠀⠀⠀⠴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠶⠂⠀⠀⠘


⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣀⠃
⠀⠀⠀⠂⠀⠀⡰⢶⣤⣴⣶⣶⡀⠐⢷⣍⠁⠀⠉⠛⢻⣄⣀⣤⡐⠶⠆⡤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⢰⡄
⠀⠀⠀⠀⠀⢈⢡⡾⠹⣿⣿⣿⣿⡖⠠⢉⣀⡀⠤⢚⣿⣿⡿⢻⡿⠄⠀⠀⢀⣤⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠐⣤⡈⢿⣿⣿⠇⠀⠀⠘⠃⠰⣿⣿⣿⣧⠘⠀⠀⠳⣄⠀⠈⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣦⡔⠁
⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷⠈⢻⠇⠀⠀⠀⠀⢰⡀⠉⣼⣿⡇⠀⣀⣴⢆⡈⣦⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡶⠉⢁
⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣘⡾⣿⣷⡀⠛⣿⣿⣿⣿⣥⠀⠐⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⠀⣞⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠀⠘⣿⡇⠀⠈⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠘⠻⠟⠡⣽⣿⣶⣇⡝⢻⣗⡀⣇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉⠉⠈⡇⡸⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣰⣦⠦⢄⠹⡗⠀⠀⣟⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠁⠈⣾⣿⡞⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⢷⡆⠀⠀⡼⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠃⠀⠀⢰⣦⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⣿⡀⡀⠀⣴⡄⠀⠀⣠⣴⣶⣶⣿⣾⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣠⣤⠀⠀⠀⠀⠀⠀⡿⠆⢠⣾⢿⣿⣷⣴⠛⢀⣴⣾⣿⣿⠟⣿⣿⣿⣯⣤⣤⣤⡀
⠀⠀⠀⠂⠀⠀⠀⠀⢚⣺⣿⣿⣿⣧⣀⡀⠀⠀⠀⢀⡇⠀⠈⠉⠛⠻⣿⠁⢤⢻⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠴⠀⠁⢀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣵⡀⠀⠀⠀⡇⠀⠀⠀⠰⠟⠁⠀⠈⢻⠈⠻⣿⣟⣶⣿⣿⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢐⠂⠀⠀⢸⣿⣿⣿⣿⣻⣿⣿⣇⠉⠐⠲⣧⠀⠀⠀⠀⠀⠀⠀⣰⡏⠁⠀⠀⠉⠉⠙⠛⠀⠀⠉⠉⠉⠉⠉⠙⠂
⠀⠠⠾⠀⠃⠀⢀⣴⣿⠟⢏⠀⠀⣈⠙⢻⣷⠀⠀⠀⢻⣆⡀⠀⣠⣶⠀⣦⣾⣟
⠀⠀⢠⠀⠀⠀⠈⠁⠈⢠⣾⡄⠀⠀⠈⠙⣿⡀⠀⠀⠘⡏⠀⠀⣿⣿⣖⣿⣇
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠞⢹⡧⠐⣤⣀⣠⣿⠇⠀⠀⠀⢷⠀⢀⠉⠘⣿⡿⠃
⠀⠀⠀⠀⠀⠰⠀⢠⣾⣶⢺⡇⠀⢀⡛⠿⠏⠀⠀⠀⠀⠘⣇⠸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡤⣻⣦⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠐⠓⣺⣿⣿⣧⡄⠂⠉⠻⣿⣿⡙⢯⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠠⣶⠞⢀⣾⣿⣿⣿⣿⣿⣿⡦⢜⠿⠿⢶⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠚⣥⣾⠿⣿⣿⣿⣷⠺⠶⠄⠈⠙⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣶⣿⣿⣿⣿⡿⢿⣾⡇⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⣧⠀⠀⠀⠀⠀⠀⢀⠋⢘⣿⣿⣿⣟⣿⣿⣟⣻⣿⠄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡠⠶⣤⣤⡀⠀⠀⢀⣤⡄⢀⡤⠚⠉⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠎⠀⠘⠃⠈⠿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣿⣿⣦⢠⣾⣟⣃⣌⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠐⡄⡦⠀⠀⠀⠀⠀⠀⠈⠻⠥⠿⠿⣷
⠀⠀⠀⠀⠂⠀⠀⣀⡠⡦⢝⠛⢻⡟⣿⣿⣯⣍⡿⠃⠀⠀⠀⠀⠀⠈⡆⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⢃⣀⣸⣄⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣷⠀⢠⠃
⠠⠞⠃⠐⠂⠀⠠⠀⣀⣶⣿⣿⣿⣿⠟⣿⣿⣿⣿⣦⣮⡀⠀⠀⠀⠀⢸⣠⠬⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣏⣃⣉⠩⣿⠛⠛⠈⠻⡄⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣯⣻⣿⣿⣯⣿⢶⠛⠚⠀⠀⠀⠈⠢⠀⠐⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠁⢹⣾⣿⣿⣿⡙⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣿⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢋⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢸⢂⣿⠁⢀⡤⡄⢰⣅⠀⠠⣤⡠⣤⢠⡄⢀⣠⢄⠀⣤⣄⢘⡃⣀⣀⣀⡀⣛⠀⣀⣠⣄⠀⣀⢀⡀
⠀⠀⠀⣤⠀⠀⢀⣾⡿⠀⠘⠘⣿⠠⣟⠀⠃⠀⠻⣧⢠⡟⢰⡏⢸⡇⢸⡇⠊⠀⢰⡏⣿⠁⢀⣔⡉⢰⡏⢠⡿⢰⡏⣼⠃⣼⠇
⠀⠀⠀⣀⣀⣴⠿⠋⠀⠀⠁⠀⠹⣧⠉⠁⠀⠀⡠⠏⠈⠁⠈⠀⠈⠉⠀⠉⠀⠀⠘⠆⠈⠅⠉⠈⠙⢿⡭⣤⣁⠀⠉⠀⢁⡟
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠠⠔⠋⠀⠀⣀⡤⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣷⡀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⣾⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠒⠋⠁

⠀⣴⣶⡶⠒
⡞⠉
⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠗
⠀⠀⣠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣏⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠂⠀⠀⠤⠙⠿⠇⠀⠀⠀⢀⣤⡀
⣤⠒⢤⡀⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠙⢿⣿⠟⠁⢠⣤⣤⣶⡾
⣶⠀⠀⠱⡀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠁⢠⣴⣿⠛⠁⠙⡃
⢠⠀⠀⠀⠁⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠉⠙⠀⠀⠀⣺
⢸⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⢀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡿⠙⣿⡟⠁⠀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⣶⣶⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⣿⠀⠀⡀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠈⠁⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⢀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣠⣵⡆⠀⠀⣤⣶⣶⠀⠀⠀⠀⠀⣠⣶⣶⠆⠀⠀⣹
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠙⠿⣿⠀⠀⠈⠻⢿⡆⠀⠀⠀⠘⣿⣿⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣠⣤⡀⠀⣶⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠀⠀⢀⣾⣿⡿⠃⠘⠿⣿⣿⡀⢻⠿⠃
⠀⠀⠀⠀⠀⠀⢠⠁⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣼⣿⠁⠀⠀⣰⣆⡀⠈⠡
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠈⢹⣿⣿⡄⠀⠠⣿⠟⠃⠀⠀⣀⠀⠀⣤⣤⣴⡜
⠀⠀⢠⣤⣤⣦⠹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣸⣿⡷⠈⠀⠀⠀⣰⣷⣄⠘⠀⠈⠙⠛⠿⢧
⠀⠀⣿⣿⣿⡟⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠤⠉⠙⠛⠃⠀⠀⠀⠻⣷⡾
⠀⠀⠸⣿⡿⠁⠀⠀⢹⡀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢠⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈
⠀⠀⠀⠛⠁⠀⠀⢀⣠⣵⣤⣾⣿⣿⠷⠀⠀⠀⠀⠘⡉⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⢠⡄⠀⠀⠐⠂⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢀⣀⣀⣾⣿⠈⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠲⠂⠤⢀⠀⠀⢠⣿⣿⡗⠀⢸⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣶⣄⡀⠀⣹⣦⣼⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⠛⠉⠸⣿⣿⠛⠛⢻⣟⠋⠙⢃⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⢻⡿⠀⣰⣿⡿⠂⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡒⠀⠆⠀⠐⠂⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢭⣷⠛⠀⣀⣉⣹⡁⢐⣀⣀⡀⢀⠤⠄⣼⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⢉⣭⣹⣭⣉⣋⡷⢤⡼⠄⠀⢿⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡼⠁⠐⠀⠶⣿⣼⣿⣵⠟⠀⠀⠉⠲⣄⣼⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⡇⠂⠀⠀⠀⠙⣿⣷⡋⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠠⠀⠀⠐⠀⠹⠿⠁⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠁⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠁⠀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠖⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠈⠠⠂⠁⠰⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠰⠐⠀⠀⠄⠄⠀⠀⠀⠀⠀⢧⠂⡠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠠⡀⠀⠀⢨⠗⠒⠀⣶⠂⠀⠈⠈⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠀⠑⠒⠊⠁⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⡀⠐⡋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡁
⠀⠀⠀⠀⠀⠀⡀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡄⠚⠐⡂⠀⣄⠖⠀⠛⠣⠄⠰⠀⡽⠁⠀⠋⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠍⠀⠀⠀⠐⠂⣥⠠⠤⠠⠤⠖⠀⠀⠃⠀⢀⡰⢆⠀⡛⢀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢥⡈⠁⠶⣀⠀⢀⡀⠖⠀⠰⠦⢠⠄⠀⠀⠀⠰⠂⢀⡀⠀⠀⠀⠂⠀⠰⠂
⠀⠀⠀⠀⣀⠀⣤⠀⠘⡼⠂⠌⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⢨⡄⠈⠁⠰⠶⠀⢀⡚
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁⠀⠀⠀⠀⠀⠈⠁

⠉⠿⠃⠉⠀⠁⠀⠀⠈⠈⠀⠁⠀⠀⠈⠀⠘⠑⣻⡟⠙⢿⣿⡿⢫⠋⠀⠀⠐⠁⠀⠛⢉⡁⡀⠻⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⠁⠄⠙⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⠁⢈⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠰⡂⢤⡄⡀⠀⠀⠀⡀⠀⠀⠐⡆⢤⠆⠏⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠜⠋⢀⣄⠳⠐⠃⠈⠀⠀⠀⠀⠀⠀⠊⠰
⠀⠀⡀⠤⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠁⢨⡄⠐⠴⠘⠀⠁
⠀⠀⢪⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠂
⠆⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠀⠈⠋⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⠀⠀⣁⡄⠰⡆
⡀⠀⠀⠀⠘⠄⢀⣀⠠⠐⠃⠀⠀⠀⠀⠀⠀⠰⢋⠾⠁⢀⠀⠀⠀⢀⢴⠞⠉⠀⢠⠔⢉⡀⠀⠀⠀⠀⡀
⠋⢨⡄⠐⠴⠌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣎⣴⣾⢢⣴⠟⠁⠀⠀⠀⠀⠐⠁⠀⠀⢀⠈⠛⠃
⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⠀⣬⡇⢃⠄⠙⠀⠀⠀⠀⠀⠀⠠⠄⠈⢿⠀⡀⠃
⣤⣴⣆⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⢀⣀⡀⣩⣥⣼⣷⢤⣤⣑⠇⡀⠀⡄⠀⠀⠰⡇⠴⠸⠉⠁⠀⠀⣀⢀
⣿⣿⣿⣾⣤⣤⣾⣿⣿⣯⠖⣠⡾⣋⣽⣿⣌⢼⣐⣰⢀⣼⣷⠿⢏⢀⣄⠳⠘⠃⠁⠀⠀⠀⠀⠀⠸⢻⠻
⣿⣿⣿⣿⣿⣿⣿⣿⠟⡶⣃⣿⢞⣫⣵⠿⣿⣞⡛⢛⣿⡾⣿⠾⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣻⣿⣿⣿⣿⣟⣅⡪⠝⠹⢟⣛⣩⣶⣦⣿⣯⣷⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⠃
⣿⣿⣿⣿⣿⣿⡿⢉⣶⣶⣶⣿⣿⣿⣟⣿⣻⣿⣾⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠐⣼⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⢿⢋⢻⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣤⠴⠊⢀⣤⡀⠡⣵⣦⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢘⡇⡇⡸⢸⣾⣿⣿⣿⣿⣷⣴⣴⣿⣿⣫⠕⠀⡴⢛⣵⢾⣗⣄⣷⣬⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣸⢣⢧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢊⡀⢞⣋⡴⠞⢳⣿⣬⢙⣿

⠀⠀⠀⣆⠀⠀⠀⢠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢉⠂⠀⠀⠀⠀⠀⠀⡄⠀⢁⡇⠀⠀⠀⠀⡰⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⣸⢃⡄⠀⠀⠀⠀⠠⡎⠁⠙⠻⡆⠀⠀⠀⠀⢀⡄
⢀⡀⢠⣄⣹⡆⠀⠀⠀⠀⠀⠉⠢⡀⣁⠀⠀⠀⠀⢣⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢠⡌⠀⠘⠀⠀⣴⠀⠀⢧⡀⢠⡶⠃⠀⢀⡠⠆⣘⡇⠀⣠⠎
⠑⠀⠲⠀⠉⠉⡑⠀⡲⢶⡶⠒⠒⠛⠛⠛⠲⠤⠄⠀⠉⣁⠀⠀⠀⢻⡂⠀⠀⠀⠀⠀⢀⡘⣺⡧⠞⠁⠀⠤⡈⣀⣴⢊⣀⣀⣀⡠⡴⢿⣂⣈⣉⣥⠏⠃
⠀⠀⠀⠀⠀⠀⡹⡇⠀⠀⠀⣀⠄⣒⠠⠴⠛⠂⡀⠷⠂⡨⢆⡀⠀⠈⠱⡇⢀⠄⠤⣄⠀⢹⠇⠀⢀⠄⣳⠞⠋⠉⠃⢤⣈⡉⠋⠡⠤⡀⠉⢻⣤⠤⠤⣀⣀
⠀⠀⠀⡠⠆⠛⡀⠁⠀⢀⡀⠧⠐⣃⠄⠐⠲⠁⠀⡀⠀⠀⠉⠲⡄⣴⠃⠀⠛⢤⡤⠉⠰⢞⢀⡴⠐⠓⠉⠀⣀⠀⠄⠀⠑⢌⢠⡀⠘⠂⢹⡂⠀⠉⠊⠉⠁
⠀⠀⠀⢧⡀⣠⠇⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠀⠀⠉⠀⠚⠳⣄⡀⠀⢀⠀⠀⠀⠀⡀⢤⣊⠺⠗⠲⠶⠿⣥⠀⠒⠤⢈⣂⠀⠉⠁⠀⡴⠋⠉⠓⣄
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠁⢀⡄⠐⠐⣻⣟⡉⠈⠻⣆⢀⡀⢀⠂⠉⠀⢠⡆⢀⣠⡖⠀⠀⢲⣍⠦⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⢉⢤⡉⠀⠈⢡⠀⠀⠘⢁⣾⡛⠙⠒⠒⠚⠛⠒⠊⠁⠀⠀⠀⠉⠒⠁⠀⠀⠀⠀⠀⠈⠓⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢣⡘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠀⠀⠊⣠⠙⡉⠑⡄⠀⠀⠀⢦⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠴⣥⠆⠴⠚⠶⡀⠀⠀⠀⠀⠀⡠⠁⣼⠏⠀⠀⢂⠘⡄⠀⠰⠈⢀⡼⡇⠀⢠⡀⠀⠔⢻⠰⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠄⢴⠁⡰⠊⠉⠈⢻⠁⡎⠀⠀⡒⢄⠀⠆⠸⡄⠃⣸⢏⡴⠃⠀⠌⠑⢀⣄⡤⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣤⣄⡀⢠⠈⠣⣤⣤⢴⠏⢸⠀⠐⠀⠀⢾⡁⢸⠀⢹⣤⠛⠋⠀⠀⣀⠀⣼⡆⣄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠐⢶⠄⣉⣙⡙⠲⠶⣤⡤⠤⠀⢈⣹⣦⡄⠀⠀⠀⢸⠀⠀⠠⠀⠀⠑⢮⠀⠸⡇⠀⠀⠴⠋⠉⠉⠀⠀⠀⣴⣏⡠⣶⠎⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⠲⠖⠤⣀⠒⠋⠀⠀⠉⢦⢠⡀⢸⢀⣌⠠⠀⠀⠀⠀⡄⠰⡇⢀⠘⠆⣤⠰⠦⣤⡤⠛⠀⠚⠓⠀⢰⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠘⠂⠈⠀⢰⡄⠀⠀⢸⣄⠐⠀⠒⠀⠀⢨⠖⢿⠁⠀⠀⠀⡠⠀⠀⡇⠀⠓⠀⠐⠁⠀⠀⠀⡠⠚⠋⠑⢞⠙⢶⣯⣤⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⢻⠇⠀⠀⠀⡇⠀⠀⠆⢸⠀⠀⠐⠀⠀⠄⠁⠂⠀⡇⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⢀⢱⠄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⠾⠃⠀⠀⢠⠘⡀⠀⠀⠃⠀⠰⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠘⠦⣠⠶⠋⢶⣣⡀⠑⢔⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⠈⡄⠡⡀⠂⠤⠼⠁⡠⠈⠓⠚⠉⠍⠁⠁⠦⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢂⠈⢀⡨⠋⠉⠛⠳⠀⠉⠦⣀⠀⠘⠁⢈⡀⠤⠤⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣤⠀⠉⠠⡀⠀⠀⠀⠀⣱⠶⠁⠸⣤⠞⠉⣅⠀⠀⢠⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠲⠒⠠⠀⠀⠀⢎⠀⠀⠘⡇⠀⠀⡀⠀⢀⠄⠊⠁⣀⣼⡏⠙⠢⡀⠙⢣⡄⠊⢀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⡄⠀⠘⠦⣀⡾⢀⡴⠟⠀⠀⢀⠀⠀⠾⡉⠀⠙⢆⠀⠐⢄⠀⠘⠀⠋⣷⠀⠀⡠⠞⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣴⡬⢠⣄⣠⠿⡄⠈⠀⠀⢀⠃⠸⠐⡎⢠⡇⠀⠄⠀⢆⠀⠈⢆⠀⠀⠿⣿⠀⢀⣛⠸⠁⠀⠀⠀⢀⣄⠀⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠘⢴⣄⠀⡈⠀⣴⠀⣏⡀⠁⠈⠀⠁⠜⡀⠀⢸⠀⠀⠐⡿⡤⠚⠉⠀⠀⠀⠀⣴⠉⠤⠤⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠙⢀⣄⠀⠀⠙⠗⢚⡁⠀⡀⠀⣄⢻⣬⠃⠀⢛⢰⠟⠀⠘⠢⠀⠀⡆⡇⠀⢸⠀⣠⣬⣤⣾⡉⠉⠙⠛⠛⠛⠂⠀⣴⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡀⠫⠛⠤⠒⢖⡀⡤⠅⢉⡄⠀⠉⠉⡆⠀⣮⠃⠀⠀⠈⠄⣾⢰⠂⡇⠀⠈⡴⠋⠀⠀⣀⠙⡒⠠⡀⠀⠀⣠⠊⠉⠙⣦⠶⠶⠶⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⢀⡅⠀⠄⣼⣟⠐⢤⢀⡅⠀⢛⡄⠐⠓⢄⣀⣈⣿⠀⠇⠀⢻⠀⠀⠀⡎⠁⠀⠀⠠⠶⠶⣄⠱⢄⠙⣀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠞⠋⠠⠁⣴⠈⣇⢱⠀⠁⠲⣄⠀⠰⣄⠀⡉⠀⠈⢫⠚⠀⢀⡟⠀⠀⠀⠣⢀⡀⣀⡸⠀⠀⠸⡆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⡼⠃⠀⠀⠹⣄⠀⠀⠹⡇⠀⣀⠎⠀⣀⣾⢶⠃⠤⡁⠲⠄⠉⠈⠳⠜⣃⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⣠⠟⠀⢀⣖⠋⠀⠀⡛⠂⡀⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⡤⡔⠊⠉⠀⣠⣴⠟⠉⠳⡄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⡴⠞⠉⠉⠳⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⠁⠀⠀⠀⢣⠃⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣼⠀⠀⠀⠀⠀⡇⠀⠀⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠆⠀⠀⠀⡰⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⣧⠀⢀⠄⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⢁⣟⠠⠊⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣨⠷⠊⠁⢀⢰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠉⠉⠀⢀⣤⣶⣆⡂⠈⠛⠐⠶⠦⠤⠴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠶⠛⠛⠋⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠁⠰⢂⣄⡰⠲⠄⠀⣀⠀⡄⠠⠒⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠈⠑⣤⠂⣲⣍⠃⣠⣄⠀⢈⣀⣀⣴⣼⠃
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⢻⣿⣿⡿⠿⠿⠿⢟⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⠿⠿⠛⠻⠿⢿⣿⣏⣩⠉⠻⠃
⠀⠀⠀⠀⢠⠂⠀⠀⠀⣰⣿⣿⣿⣿⣯⣿⡓⠏⠰⢇⠶⡤⠀⠈⠟⠫⠄⠻⣿⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣯⣄
⠀⠀⠀⠀⠎⠁⠀⠀⣼⣿⣿⣿⣿⠉⡨⠀⠁⠀⣄⢦⡀⢀⣀⡀⠀⠀⠀⠠⡟⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠂
⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⠿⡯⠀⠀⣭⣷⣦⣿⣾⣷⣿⣿⣿⣿⣶⡦⢀⡀⠂⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⡆
⠀⢀⡴⠆⠀⠀⢀⣿⣿⣿⣏⠀⠃⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠷⣄⠀⢜⢻⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣷⠀⠄⣀⡀
⠠⣏⣿⠅⠀⠀⢸⣿⣿⣽⣿⣾⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡃⠀⡼⢻⣧⣿⣷⣦⣤⣤⣶⡾⢫⡟⠹⠷⠸⣿⣷⡆
⠀⣾⣿⡀⠀⠀⢸⣿⣿⣿⢟⡁⢀⣾⣿⣿⣿⡿⠛⢛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⢿⠞⣱⣿⣿⡏⠀⠀⠀⠿⣿⠟⠁⠀⠀⠀⠀⠁
⠀⣿⣿⡆⠀⠀⠘⣿⣿⣧⡈⠇⠀⡸⣿⣿⣟⣹⡄⠻⠀⠈⣿⣿⣿⣿⣿⣿⠈⠀⣻⣤⣿⣿⣿⡇⠀⠀⣠⡉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢺⣿⣿⡄⠀⠀⠸⣿⣿⣿⣄⢠⡀⢉⡿⣿⣿⣠⠀⠀⠠⠿⣻⣿⣿⡿⠇⣼⣽⣿⣯⣿⣿⡟⠀⣾⣿⣿⣿⣦⣤⢠⣄⣀⢐⡿⢳⠄
⠀⠀⠈⣿⢓⡀⠀⠀⠙⣿⣿⣿⣶⣁⠟⠘⢛⣻⡟⡶⠹⣷⠀⢸⢶⡭⠷⠶⣷⣿⡿⠿⣿⡿⠃⠀⠻⢿⡿⠿⣿⡁⠈⠋⠉⠀⣠⠎
⠀⢸⣿⣷⣿⣷⡆⠀⠀⠈⠿⣻⠿⠏⠀⠀⠈⡄⢨⢃⣀⡀⢀⡤⠈⢷⣶⣀⣠⣭⣿⠀⠠⠀⠉⠐⡤⠂⠀⢼⠃⠈⣀⣤⠴⠚⠁
⠀⣸⣿⣿⣿⣿⠟⠁⠀⢐⠾⢿⠴⡿⠃⠀⠀⢟⠃⠸⡍⢣⡾⡇⠀⢸⣏⣃⠈⠋⠀⢀⡀⠀⠀⠀⠀⢀⡀⣠⡴⠋
⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣇⢺⡇⠀⠀⢸⣿⣧⡀⠀⠀⠀⠉⠉⠀⠀⣠⠋⡜⢻⡶⠚⡛⢻⡆⠀⠂
⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⠞⠀⢂⠀⠀⢠⣿⣿⣇⠀⠻⢾⡇⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⠋⠘⠷⠋⢀⣠⣧⣜⠁⠀⡆⢀
⠀⢰⠟⠋⠉⠛⢿⣿⣿⠋⠀⠀⠁⠀⢤⣾⣿⣿⣿⠀⠀⢸⠃⠀⠀⢿⣿⣿⣷⡄⠀⠈⠀⠄⠀⣇⢸⡆⠀⢸⣯⠴⣟⢹⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⢀⢼⡄⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠀⡇⠀⣀⡤⠖⣿⠟⠒⢦⡀⠄
⠀⢀⣀⠀⠀⣀⣴⡿⠀⠀⠀⣠⣾⣿⣿⡿⠟⠻⣇⡰⢢⣿⣦⣳⠀⣼⡛⠿⣿⣿⣧⠀⠀⠀⢲⡄⠸⠇⣼⢿⠴⠞⢃⠀⠀⠀⠙⣦
⠀⢈⣿⣿⣿⣿⣿⡇⠀⣀⣾⠿⠟⠩⠟⠀⠀⣸⣫⠝⠿⣛⠿⠛⠊⠉⠃⠑⠀⠘⢻⡄⠀⠀⡷⢹⣄⠰⡇⢠⡄⠀⢸⠀⠀⠀⠀⣿
⠀⠀⣹⡿⣿⡿⢻⣿⣄⣼⠃⠀⠀⠀⠀⢀⢀⣿⣟⣾⣷⣼⣦⢤⠔⢾⡇⠀⠀⠀⠀⢳⠀⡾⣡⡈⠻⣆⠙⠛⠃⠀⢸⡂⠀⠀⠀⣿
⠀⠀⣿⣿⢿⡧⠉⣻⠟⣿⢀⡤⡶⠛⠫⢄⡌⢻⣿⣿⣿⣿⣿⣿⣾⣭⡀⠀⠀⠀⠀⢸⡿⠀⢽⡆⣽⢻⣆⠀⠀⠀⢸⡄⠀⢀⣼⠇
⠀⠀⢿⢯⣏⠡⠤⠻⠄⣿⣾⣼⡁⢀⣤⡈⠀⠀⠁⠀⠉⠉⢯⠿⠿⠿⠉⠲⣄⡀⢀⣿⡧⣃⠀⠙⡈⢧⠝⡄⠀⠀⠘⣇⣴⠟⠃
⠀⠀⡿⢿⣽⢦⡾⠁⡄⣿⣿⣿⣇⠈⠛⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡷⣶⢶⣴⣧⡶⢶⡶⠶⠚⠛⡏
⠀⢸⠃⠜⠃⢂⠁⠀⠆⢽⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡧⡃⠄⠀⢄⠀⠛⢸⠀⠀⠀⡇
⠀⢸⠀⣦⠒⢀⠆⣠⣀⢸⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡅⠁⢀⠤⠀⠀⠀⠊⠀⠀⠀⡇
⠀⢸⠀⠀⢀⠃⠰⣌⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠳⣤⠹⡄⠂⠀⠃⠀⠀⠀⣷
⠀⠘⡄⠀⠠⡁⠠⣎⠓⣵⣼⡿⢻⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⡟⣭⣿⣿⡿⠁⡄⠀⠀⠀⢰⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠄⠀⠁⡀⣙⣀⠼⡛⠿⠿⠧⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣏⠻⣧⠛⢑⡠⠤⠀⠀⢂⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠐⣤⡀⠑⢹⣝⣧⡰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣧⣍⠀⣰⠃⠀⠀⠀⠀⠁⢸⡗
⠀⠀⠀⠀⠈⠳⡀⠠⠛⠛⢿⣟⣧⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠜⠁⠀⠀⠀⠀⠀⠀⢸⣧⠇
⠀⠀⠀⠀⠀⠀⠑⢦⡓⠀⠈⣿⣷⣿⣿⣿⣿⣿⠟⠋⠙⠀⠀⠉⠙⠻⣿⣿⡟⠻⠄⠀⡩⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠭⠉⠓⠂⠙⢿⠏⠀⠀⠐⠒⣀⠄⠀⠀⢹⣿⣤⠄⠉⠁⠀⠀⠠⠤⠄⠀⠠⠴⠠⠤⠤⠤⠤⠤⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⣤⣰⣄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠩⢒⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⡈⠄⠬⠖⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣄⠀⠀⠀⠈⠊⠁⠊⠁
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡾⠢⢄⠀⠸⠄⠀⢀⣠⡀⠄⠀⠀⢀⣀⣠⡤⠄
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠃⣑⣞⡡⠂⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢃⣰⠀⠀⠀⠈⠺⣭⣄⠈⠀⠀⠉⠙⠿⢧⡀
⠀⠀⠨⢵⣆⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⣾⡟⠄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡐⠠⠫⡴⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢙⠁⠀⠀⠐⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣊⣠⣀
⠀⠀⠀⠀⠉⠑⠆⡀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠶⣤⡀⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠈⠙⠻⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⣀⣠⡴⡻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠄⠒⠚⠓⠶⠀⠀⣀⣤⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠁⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⡼⠁⠀⠀⠀⠤⣤⣄⡀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⢀⠄⠊⠀⠀⠀⠀⠂⠀⠀⠉⠛⣿⣿⣀⣼⠿⠀⠀⠀⠀⢀⣴⠾⠃⠠⠀⢈⣿⡿⠤⢰⠿⠂
⠀⠀⠀⡀⠀⢠⣿⣿⠃⠀⠀⢠⡶⠛⣶⡿⠀⣸⣿⠞⢻⣦⢸⣿⠀⢰⣿⠂⢾⣷⠀⣠⠟⣵⠞⢳⣾⠇⢸⣿⠀⠀⣶⡗⠀⣾⡖⢻⣷⠀⣠⡾⠛⣾⡗
⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣿⠃⢠⣿⠃⢀⣿⠇⠀⣾⠟⢻⡇⠀⣿⡏⠀⣸⣿⣰⠃⢸⡏⠀⣼⡟⠀⣸⣟⠀⢸⣿⠁⢸⣿⠁⣾⡏⢰⣿⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠙⠓⠋⠛⠒⣸⡿⠃⠐⠋⠀⠸⣧⠀⠙⠓⠚⠀⠻⠏⠀⠈⠛⠚⠙⠓⠂⠈⠻⠆⠊⠛⠂⠛⠋⠀⠙⠓⠈⠛⠓⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⢀⣠⠴⢃⣿⡇⢀⠤⠶⠆⠀⠙⠦⠀⠀⠔⠃⠀⠀⠀⣀⣠⡤⠶⠒⢂⠍⠂⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠤⢤⣤⣤⡤⠴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠐⠋⢢⡀⠤⠤⠤⢄⣈⣿⣷⣤⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠈⠢⡀⠀⢠⠀⠀⠱⣤⠀⠩⠄⠐⢲⣤⣘⣿⣦⠀⠀⠀⢨⠉⠉⠻⣇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢼⠁⣀⠀⠈⠆⡂⠀⠀⠀⢻⣿⣿⣿⠆⠀⠀⠈⠁⠀⠀⠈⠁⠢⡀
⠀⠀⠀⣤⡀⠀⢠⣶⣶⠆⡾⠟⠁⠀⠘⡇⠀⠀⠀⠀⢿⣿⡟⠀⢀⠀⠀⠀⠸⢦⡄⠀⠀⣑⣀⠶⢧⡄
⠀⠀⣠⣿⣷⣠⣾⣿⡿⣾⠈⠂⠀⢷⠀⠁⠀⠀⠀⠀⠞⠉⠀⠘⠏⠀⠀⠀⠀⠒⠁⠀⢰⠏⠀⠀⠈
⠀⠀⠛⠛⠛⢧⡻⠀⢀⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠯⠀⡄⠀⠀⡀
⠀⠀⠀⢀⣴⣾⣇⢠⢃⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡰⣹⣆
⠀⠀⠀⣾⣿⣿⣿⡟⠡⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠸⡏
⠀⠀⠀⣿⠿⡟⢹⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠠⢣⠄⡇⡆⠰
⠀⠀⠀⠈⠁⣃⡇⠀⠐⡇
⠀⠀⠀⢀⣴⣁⣴⣟⣀⠱⡀
⠀⠀⢠⣾⣿⡿⠛⠁⠁⠀⠘⠤⡠
⠀⠀⣸⣿⠟⠀⣴⠂⠀⠀⠀⠂⠀⣀⣀
⠀⠀⠙⠁⠀⠀⠉⠠⣀⣤⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣢⢀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠈⠒⠄⠤⠤⡀⠀⠈⠁⠠⣓⣰⡢⣄⠄⠀⠀⢀⣚⣲⣄⢠⡀⠀⠀⠀⣀⡄⡄⢛⡉⠀⠀⠀⠀⠋⠀⠄
⠀⠀⠰⠁⢠⡜⡿⠛⡆⠉⢐⣶⢉⠸⠟⢹⠍⢉⣽⣏⠹⢷⠱⠈⡆⢶⣟⡉⠀⢧⡝⡀⢹⣾⠉⠉⢩⠿⢹⠃⢲⣖⠻⡯⡠⠀⠀⢠
⠀⠀⠀⠐⠪⠔⠁⠈⠁⠀⠘⠃⠀⠐⠶⣧⡤⡜⣿⠇⠐⠠⠀⢠⠃⡜⠉⠜⣡⡄⡀⠀⠙⡿⠀⠀⢪⠄⠎⠀⠘⠏⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠐⠀⠈⠀⠀⠀⢀⢜⡾⠁⠀⢭⠃⠰⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢨⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠥⠾⢿⣷⣿⡿⡿⠤⢤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠀⢺⢧⠀⠀⢀⣀⠀⠀⠀⠐⣶⡶⠀⠀⢾⡇⠀⠀⠀⣰⣶⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⡄⣸⣿⡿⠀⠀⠀⠀⠚⠁⠀⡄⠀⠀⠀⣀⠀⠈⡟⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣾⣾⣿⡙⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣿⣿⣀⣰⣁⡴⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠁⠈⢧⡀⠀⠠⣾⣦⠀⠀⠀⠘⠘⠄⠙⠛⠋⠸⣿⡿⢳⣁
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⢢⣿⣿⣷⠄⠀⠀⠀⠀⠈⢄⠠⠀⠀⣿⠁⠸⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⣎⠉⠳⣤⣦⣼⣷⣄⠀⢀⣀⣦⣤⣤⡏⠀⣤⣰
⠀⠀⠐⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣞⣄⠀⣻⣛⢿⡀⠀⢰⣾⣿⣿⡿⢯⣿⣶⣿⣿
⠣⡀⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠛⣏⡇⠈⠢⡀⢤⠞⠀⠀⢸⣿⣿⣝⠉
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠳⣏⢠⣦⣴⢈⣷⣶⣦⣄⢸⡛⣿⣮⠐
⠀⡀⢴⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⠂⠀⠈⠢⣍⠛⠷⣾⣿⣿⣯⣸⣷⣹⢿⣴
⠀⠀⠀⠀⠈⠢⣀⢦⠀⠀⠀⠀⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡷⢤⣾⣻⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣦⡄⠈⠑⠤⡀⠀⠠⢴⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⡀⠀⠛⠻⠃⠀⠈⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠐⡿⡏⠙⠀⠀⠀⠈⣑⡂⢄⣈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣻⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⡛⢓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠀⠀⠉⠉⠐⠒⠒⠸⠿⠤⠤⠤⠤⠤⠤⠤⠀⢀⣀⣀⣐⣺⠿⣿⣷⣿⣿⣿⣇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣤⡀⠀⠀⠀⠀⢠⣦⡀⠀⢀⣄⠀⣀⣩⣛⡿⢿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠏⠁⠀⠀⠀⠀⠛⠛⠁⠀⢨⣿⣿⣿⣿⣿⡤⣤⣿⣿⣿⣿⣾⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣀⣈⣟⣻⣀⣉⣛⣮
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⢛⠂⠀⢰⡆⠀⣠⡀⠀⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⣠⡀⠈⠀⠀⠉⠁⠀⠀⠸⠓⠀⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠙⠁⠀⠠⠄⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠀⠀⠀⢈⡃⠀⠀⢠⣄⠀⠀⠀⢬⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌⢛⠃⠀⠀⢠⣄⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⣀⠀⠈⢴⠠⠀⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⠀⠀⠋⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠾⡠
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠛⠀⠀⠐⠦⠀⠀⠢⠶⠣⠀⠀⡀⠀⠀⢰⡆⠀⠀⠀⠀⣠⣀⠁⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠄⢠⡔⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣠⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠁⠁⠈⠁⠀⡀⠁⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠦⣀⠀⣀⣀⠀⠰⣾⣷⡄⠀⢀⣺⣿⣧⣶⣄⣠⣴⣤⡀⠀⠀⢹⣿⡷⣤⣤⠾⣿⣶⣦⣴⣦⢀⣀⡀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⢠⣶⣿⣷⣾⡄⠈⢿⣿⢿⡟⢰⣶⣿⡏⣽⣿⢿⣿⡆⠛⠛⠙⠿⠿⠿⠟⠨⣿⡿⠿⢇⠙⠟⠀⠀⠁⠘⠿⠋⠾⠿⠟⠀⢀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠈⡋⢈⣁⠈⠀⠀⠀⠉⠀⠀⠈⢉⣭⡴⠊⠱⠄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣿⣷⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡏⠉
⠀⠀⠀⠀⠀⢸⣷⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣿⣿⢃⠰⠑⣶⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠛⠟⠁⠀⠀⠀⠀⣠⣀⣄⢺⣿⠟⠇
⠀⠀⠀⠀⠀⠉⠡⣿⡏⠉⠉⠁⠀⠀⠀⢠⣋⡛⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣶⠇⠀⣀⣀⣼⠿⠋⠀⢠⣾⡿⠟⡛⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⣿⡄⣀⣠⣤⡿⠿⠷⡀⠀⠀⠀⠘⠛⢋⣛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠟⢠⣾⣿⡏⠀⠀⠀⠀⣤⡌⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠛⠀⠈⠋⣉⡁⠀⠀⠀⠀⠀⠀⢸⣦⠘⠛⢉⣢⡄⠀⠀⠀⢰⣦⣶⠆⢀⠈⠀⢀⠀⠀⠀⠀⠈⠃⣀⠀⢸⣿⡿⠂
⠀⠀⠀⠀⠀⠀⣠⠀⠛⠿⠓⠀⠀⢠⡟⠛⠂⠀⠀⠀⠀⣠⣾⣏⠀⠀⠈⠻⠋⠀⢰⠟⠛⠛⠁⠀⣿⣦⠀⢠⣥⡀⠀⠀⠀⡿⠟⠀⠈⠉⢰⡶
⠀⠀⠀⠀⠀⠀⠙⢋⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⣹⡿⠀⠀⠀⣃⠀⠀⠀⣀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠰⢶⠂⠀⢰⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣾⣆⠀⠀⠀⣴⣶⠎⠀⠀⠀⠀⠀⠀⠀⠚⠻⡏⠀⠸⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣟⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠀⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⢯⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⠻⣿⣿⣦⡘⣿⣧⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣏⣿⣿⣿⣻⣾⣾⣧⠻⣿⣿⣷⣾⣿⣿⣴⠟⣴⣿⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⢿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠉⣩⣿⠿⣫⣿⣿⣿⡿⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⣿⣿⣿⡿⠉⠀⢤⠀⣀⠀⠤⠾⣿⣷⣿⣿⣿⠏⠘⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣴⠛⣠⣄⣠⣇⠀⠀⠀⠲⣭⡻⣆⣰⣿⡿⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⡾⢁⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠈⠿⣛⣴⣿⣿⣿⡿⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⢘⣣⠞⠈⠙⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠀⠀⣾⠋⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠇⠀⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡿⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⣀⣀⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣷⣬⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠺⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡖⢿⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⣰⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣤⣤⠀⠀⠀⠀⠀⠀⠉⣿⣟⡁⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠙⠀⠀⠀⠀⠀⠀⢀⣠⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠢⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⡄⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠵⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⣢⠀⢈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠨⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠤⠂⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠐⠂⠀⠠⡙⣄⣀⣠⣤⠤⠶⢒⣚⣩⡭⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢎⠆⠀⢀⠀⠁⠀⠸⣧⠖⣖⡪⠭⢝⠒⠎⡙⠩⢙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⣷⠀⠀⠀⠈⠔⠀⠣⢃⣿⣍⣒⣠⣥⡶⠞⠲⣞⣛⣉⣭⠥⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⣞⣦⣑⣈⣠⣤⠤⡶⠋⠁⠀⠙⢧⠏⠀⠀⠀⠈⢏⠀⠀⠀⢸⠀⠀⠀⠀⡔⠓⣶⠋⠙⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⢬⣭⣭⠭⠴⠒⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡴⠒⢇⠀⢧⡀⡸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢄⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠴⠀⢀⡀⠐⠃⠀⢀⡎⠀⠀⠀⢸⠀⠀⠳⣄⠀⠉⠲⠀⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡜⠑⢄⣀⡤⠊⠀⠀⠀⠀⢸⠀⠀⠀⠘⢦⠀⠀⣀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⡾⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⢸⣀⣀⡤⠚⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠈⠑⠢⠄⣀⣀⣀⣀⣀⠠⠤⠒⠁⠀⠀⠀⠀⢸⣅⣀⠤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡠⠖⠋⢉⣁⣠⣤⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⠞⠀⣠⠚⠁⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡏⠀⢰⠁⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⠞⠁⠀⠈⡧⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣰⠃⢀⣤⣄⠀⠙⢦⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢠⢤⠀⢲⠘⠀⠀⠀⠀⢀⣸
⣇⢀⡼⢸⠈⠓⠒⠋⠀⠀⠀⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⣄⠧⠀⠃⠚⣀⣃⣬⡥⠶⠖⠚⠛⠉⠉
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⡇⠀⢀⣀⣀⣤⡤⠴⠶⠚⠛⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⠃⢠⡞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠘⣿⣷⣤⡀⠛⠁⣤⡤⢤⣄⢀⣤⢖⡄⣾⡇⣰⡏⢠⣿⠀⣦⢠⡯⠀⣤⠴⣦⠀⣠⠀⣿⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⢨⡿⠀⣸⣿⣿⠓⠋⢰⡟⠀⣿⠀⣼⠇⢤⡿⣼⠇⢸⡏⢸⡏⣼⡇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣸⡧⠴⠋⠀⠻⠦⠀⢹⡇⢸⣟⠀⠹⠤⠞⠁⠻⠄⠿⠁⠻⠇⠻⠧⠋⢧⡀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⢿⠀⠊⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠴⠋⠁⠼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⢀⣀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⠉⠀⠉⢉⠉⣉⡁⠈⠉⢉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠈⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢰⣉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣦⠀⣄⠩⡀⠌⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣇⠀⢹⡆⢁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢸⡀⠁⢸⡷⢤⣿⢸⠆⢴
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⢹⣇⠈⢿⣿⣿⣿⢾⣿⠾⢁⠴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠤⣀⡄⠀⠀⠀⠀⢀⠲⢀⠸⣿⡄⠈⠙⢹⣿⣾⣿⠀⠄⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⣤⠐⠀⠁⠐⣀⠀⠈⠁⠀⠀⠿⣷⣦⡀⠐⠫⣿⣏⣠⡾⠓⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠠⠈⣠⢤⠈⢣⡀⢀⠀⠈⠁⣀⠆⠉⠆⠀⠋⠉⠻⣧⣀⣼⠏⠀⠀⠀⠀⢀⣼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⡀⠈⠀⠙⢯⡐⢀⡄⠉⣦⠀⠖⡀⠀⢠⡀⠈⣿⠁⠀⠀⠀⠀⠀⣼⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⠉⠂⠉⢁⠤⠝⢋⡴⢿⣿⣿⣷⣧⣄⡈⠁⢰⡏⠀⠀⠀⠀⠀⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡣⣀⠁⠋⠴⠶⣍⡹⣿⣿⣿⣿⣿⣿⣥⠀⢸⠃⠀⢠⣴⣮⣵⡋⠠⠐⠒⠀⠉⠉⠁⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣉⠴⠂⠀⠀⠈⡿⢿⡿⠿⣿⣿⣿⡟⠀⣿⠀⣠⣿⠛⠝⠃⠀⠠⡆⠀⠀⢀⠔⠀⢀⣶⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠲⢄⡉⠁⢀⣀⣘⣿⣿⣿⡿⠟⢦⣀⣿⡌⠛⠉⠀⠠⣀⠂⠀⠀⣀⡗⠁⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠘⠋⠉⠙⠛⠋⠉⠀⠀⠀⠘⣿⡇⠀⠀⡠⢐⡎⠀⢀⡾⠃⠔⢠⠖⠉⢀⠀⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⡇⣈⠀⠠⠾⠀⣠⠾⠁⠀⠀⠠⠄⠀⠘⠇
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢀⣧⣿⣠⡷⠘⠙⠁⣀⡴⠖⠀⢀⡀⠀⠿
⠀⠀⠀⠀⠀⠀⢸⠷⣀⠀⠀⠀⠀⠈⠻⣽⣟⣿⣄⣀⡀⢀⡀⠀⠀⠀⠀⢿⡀⢠⣿⣿⡿⡷⠊⠉⡙⠃⠀⣠⡄⠚⢣⡔
⠀⠀⠀⠀⠀⠀⠘⠃⡉⠛⣉⠃⢠⣤⠖⠊⢿⡷⣿⢿⣿⣿⣿⣷⣿⢇⡀⠸⣧⣸⣿⣯⣭⡕⢻⣸⡓⠞⠃⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⢀⡆⠈⢦⡀⠤⠲⣤⡀⠀⠀⢠⣈⠈⣍⠙⠿⠉⠉⠉⠉⠙⢿⣿⠀⠀⠐⠈⠏⣥⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠑⣴⠂⠆⠙⢾⠁⠰⠈⠳⡇⢠⡀⠈⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⢀⡀⣤⡀⢄⡀⣠
⠀⠀⠀⠀⠀⠀⢸⡄⢂⠹⠈⠉⣶⣄⠀⡘⠓⣀⠨⠀⠙⢧⡈⠀⠘⢇⠡⠀⠀⠈⠿⡄⢠⡄⠈⠀⠀⢻⠛⣿⡟⢀⠄
⠀⠀⠀⠀⠀⠀⠈⣤⡠⢦⡈⠦⠠⠈⠿⢧⣄⣸⣧⣀⣰⡾⢳⣴⣄⣸⣷⡶⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣍⣹⠻⠶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⠑⠲⠀⠀⠀⠸⣁⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣇⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠸⣿⣭⣖⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣈⢣⡠⠤⡤⠖⠚⣽⡿⣿⣟⣯⣉⠉⠛⢻⣿⠿⣿⠤⠴⠔⢿⠣⠀⠀⠀⠀⢠⡞⣿⣇⡘⠛⢳⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠙⣲⣤⣴⣻⣿⣰⣿⣯⣸⡷⠔⠃⠀⡠⢠⠋⠀⠀⠀⠸⡆⡀⠀⠀⠀⠀⣿⡏⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠹⠻⣾⢟⣻⣿⣿⡿⠁⣀⠶⢊⡔⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢘⣧⣟⠁⡄⣰⣆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠛⠷⠞⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⢛⠀⠀⢀⣾⡝⢻⣧⣽⣋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⢀⣤⡄⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣀⣴⣿⠏⠀⠿⢿⣦⣉⠻
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣣⣤⡟⠛⠛⠋⠉⠉⠓⠒⢲⣯⣉⣉⣲⣦⣤⣤⣀⣠⣴⣶⡁⡨⠟⠋⠀⠀⠀⢺⣅⠙⣭⡥
⠀⠀⠀⠀⠀⠀⣰⣿⠟⠹⠟⡽⠻⣦⡀⠀⠀⠀⠐⠈⠙⢫⡷⠈⠉⠉⠛⠛⠛⠛⠛⠋⡽⠷⠄⠀⠀⠀⠀⠠⣿⢷⡉⠄
⠀⠀⠀⠀⠀⣼⢹⡟⠀⠆⠘⠀⠀⠀⠛⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠄⠀⢀⣾⡄
⠀⠀⠀⠀⠀⣿⣤⣴⣶⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠒⣶⣄⣀⣀⠒⠒⠒⠀⢠⣄⠈⡟⣳⣄
⠀⠀⠀⠀⢸⣿⡏⠠⠄⢀⣀⣤⣴⠶⡶⠞⠛⢙⣛⣟⣻⣟⠛⠛⠲⠶⠖⠛⠛⠛⢿⡟⢋⡈⠀⠀⠚⠛⠻⠀⠘⣍⠿
⠀⠀⠀⠀⢸⠋⣁⠒⠲⣄⠉⠉⠙⠛⠛⠈⢉⣿⣿⠿⠥⢤⣤⣄⠀⠀⠀⠂⢈⠰⡾⠄⣈⠤⣤⠀⠀⠀⠀⠀⠀⠛⣻⡆
⠀⠀⠀⠀⠀⠀⠈⠿⡦⣍⠳⠀⠀⠀⠀⡴⠏⢸⠛⣦⠀⠀⠀⠉⡆⠀⠀⣀⠤⡶⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠶⠴⠶⠴⠶⠶⠞⠀⠚⠀⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡟⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢆⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠤⣿⣶⣺⣡⣬⢩⠔⣋⣈⣀⡴⢾⣿⡿⠷⣀⡀⠀⠀⠀⠀⠀⠀⢢⣴⠞⠠
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠶⣗⣅⣠⣮⣔⡲⠻⣿⣿⣿⠛⠚⠻⣿⢿⡙⣧⠒⣄⡀⣠⣊⣱⡀⣠⣤⡀⠀⡘⠉⠉⢳⡞⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠴⠛⠛⠕⠀⠉⠉⠟⠉⠉⠒⠚⣯⢷⣸⡘⠀⠁⠉⢙⣿⣿⣿⣛⠿⠚⠛⠒⠶⣍⡀
⠀⠀⢀⡠⠤⠲⠤⠤⢤⡻⠧⠘⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⡆⠈⠀⠀⠀⠀⣿⣿⢟⠉⠸⠛⠀⠀⠈⠰⣾⣿⣶⣜⠇⠐
⠀⠀⠀⠀⠀⣠⡀⢠⣾⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⡿⠿⠿⠇⠳⡤⢤⡀
⠀⠀⠀⠀⠼⣿⣍⢿⡄⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠁⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⠤⠒⣈⡵⠁⢠⡌⣣⡦⠞⠀⠀⠀⠀⠀⣀⣀⣀⣤⣔⣂⠀⠀⠈⠁⠌⠉⡘⠏⠰⠟⢢⡀
⠀⠀⠲⠶⣤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠂⣿⠀⠀⣰⣊⣥⣴⠾⠋⠀⠰⢀⡷⠋⢚⡣⠔⠚⠈⠙⢿⣓⡀⢤⣄⠀⠀⠀⠀⠀⠒⠠⣀⠉⠈⠂⠓⠚⠛
⠀⠀⠀⠘⠢⣉⠻⣦⠀⠀⢸⡇⠀⠀⠀⡟⡠⠊⠉⠉⠀⠀⠀⠀⠀⣸⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠛⢏⠲⡤⠀⠲⢄⠀⠀⠀⠀⠈⠗⠠⣤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠷⢀⢸⡇⠀⠀⣼⡟⠁⠀⢠⡦⠀⠀⢀⡰⠞⠁⠀⠀⠀⢀⣀⣨⣭⣤⠶⠞⠀⠀⠈⠛⠘⠿⠛⣧⠀⠀⠀⡀⡷⡀⠘⣄⠀⠉
⠀⠀⠀⠚⢙⠛⠛⠓⠲⠾⠿⠁⠀⠀⡟⡠⢂⣥⠞⠁⢀⠔⠈⢀⣠⣄⠀⡘⠛⠉⠉⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣠⠁⠠⠇⠀⠹⠗⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠇⠖⠋⠁⠀⡴⢃⡤⠒⠉⠀⠈⢷⣌⠑⢤⠀⠀⠀⠹⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢠⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⠀⠀⠀⠀⣨⠔⠉⠀⠀⠀⠀⠀⠀⠉⠻⠦⣀⣄⠀⠀⠹⣆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢸⠓⠰
⠀⠀⠀⠀⠀⠘⣌⠉⠢⡤⠀⠀⠈⣷⠀⠀⢀⡾⠁⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡠⢺⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠱⠎⠠⢆⠀⠀⠙⠀⠀⡾⠁⡠⢚⣅⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠧
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⣑⡄⠀⠀⣼⠠⣃⡶⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠛⣦⠀⡿⠎⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣝⠦⣀⠀⡀⠀⠀⠀⠀⠀⠠⠊⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢻⣿⣦⡇⠀⣰⡇⠀⢠⣁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⢀⠀⡇⢀⠞⠁
⠀⠀⠀⠀⠀⠠⣶⢤⣛⠀⣶⠀⠀⠀⡷⠘⢠⡗⠁⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠰⣶⢉⠱⢦⠸⠗⠀⠃⠀⣿⢂⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⣶⠙⢧⠀⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣴⢄⠀⠸⡇⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⠂⣷⢄⠓⠀⢀⠰⢆⠿⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⢀⣽⡆⠈⢁⣛⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠞⠉⠁⢀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⠀⠀⠀⠀⢶⡀⠈⣴⠀⠀⡠⣎⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢷⣄⠀⠀⡌⣷⠀⠹⠀⢼⣴⣯⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣷⠀⡄⢹⡆⠀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠼⣧⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣛⠓⠲⢶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣀⣀⣤⠶⢤⠄⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢉⠁⠀⠄⢿⠟⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠜⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠑⠦⠀⠀⠀⠈⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠙⠙⠓⢳⠛⠢⡀⠀⠈⠀⢀⠀⠁⠰⡴⠁⢠⡤⣾⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠐⠃⠀⠔⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⠤⣀⡠⣠⡀⠀⠀⣈⡏⠠⠀⠀⢀⡇⠀⠀⠀⣄⡟
⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠳⠀⠀⠌⢣⠀⠀⠐⣈⠇
⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠁⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣓⣐⠠⡀⢀⠀⠐⠀⠀⢠⠀⢄⠀⠀⠀⠀⠀⢦⣀⠈⠑⢀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠈⢣⠀⠁⠀⠀⠀⠂⠀⠀⠛⠴⣨⠁⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠁⠠⠀⠀⠱⡄⠠⢈⣧⣀⣴⠀⠀⠀⠀⣿⢁⠉⠀⠱⣠⢣⣴⡞⢀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⢀⢱⠀⠀⢀⣻⠟⠀⠀⠀⠀⢿⣧⠃⠀⣰⣇⠘⠋⠁⢀⡤⠶⠋⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠆⠈⠙⠉⠉⠤⠃⠀⠀⢹⣀⠤⠞⠓⠒⠒⠦⢄⣀⣀⣨⠧⠊⠀⠀⠁⠒⠚⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠆⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠇⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⡰⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⠟⠀⢸⡗⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⢠⡜⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⠀⢸⣷⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⠖⠉⠁⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⠀⠈⣿⠀⠀⠀⣠⠛⢀⠀⠀⡰⠂⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣶⠀⣀⡀⣿⠦⠤⠔⠋⠀⠈⣀⠾⠉⠘⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢱⡆⠋⡀⠐⠀⡀⢠⠀⠀⣸⠏⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠈⣷⠆⡀⢻⡀⠜⠋⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣿⠀⠹⣦⡿⠗⠀⢤⡄⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⣠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⢄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⢃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠈⠁⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣾⣿⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠶⠀⣿⠀⠀⠀⠀⠀⡰⠏⠁⠀⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣴⠀⠀⣿⠀⠀⠀⠀⡼⠃⠀⠀⠆⢀⡰⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⡿⠀⠀⣿⠀⠀⢀⠶⡁⠀⠀⠀⢰⡏⠀⣀⠀⠂⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⠃⠀⠀⣿⠀⢠⠎⢀⡄⠀⠀⣠⠿⠈⠁⠀⠀⠀⠀⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⢀⠀⠀⣿⠀⡇⠀⠀⣧⠀⢠⡁⠀⢠⠐⠿⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⠀⠀⣿⡷⠀⠀⠀⠋⡰⠋⠉⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠃⠀⠀⠀⣿⡄⣄⡀⠀⣠⠃⠠⠤⠐⠂⢀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⠀⠀⣿⣅⣉⡓⢶⡉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⢹⠀⠀⣿⠁⡈⢣⠟⠀⠳⣄⠀⢠⡌
⠀⣀⣤⡴⠿⠛⠛⠚⠉⠉⠉⠉⠓⠖⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣿⡀⢳⡄⠀⠁⡄⢨⠀⢸⠇
⣾⣋⣀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⣿⣧⠈⠁⠀⠀⢰⣾⣀⠟
⢿⡉⠉⠀⠒⠂⢤⣄⣀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠈⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⣿⡇⡀⠀⠀⠀⠘⣿⡟
⠸⣷⠀⠀⠀⢀⣠⣌⡙⠿⠶⢀⡀⠈⡀⠀⠀⣠⠀⠀⣀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⡟⠀⠀⠀⠀⠈⠀⣀⡀
⠀⢸⣧⠀⠀⠀⠉⠀⠀⠀⢀⣀⠈⠛⢧⣀⠀⠀⡀⠀⢹⠀⠀⠀⠀⠛⠀⠙⠛⠛⣦⠀⠀⠀⢸⠀⠀⣿⠀⡇⠀⠀⠀⢀⡤⠛⡿⠷⣄
⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣨⡷⢦⡄⠀⢻⠀⠀⠀⠀⠀⡀⠀⣴⠎⠁⠀⠀⠀⢸⠀⠀⣿⠀⠁⠀⠀⣴⠋⠀⠀⡇⠀⠉⢶⡀
⠀⠀⠀⠀⠈⠳⣄⡀⠉⠀⠴⠴⠞⠛⠉⠀⠀⠀⠈⠛⢷⣄⠀⠠⣄⡁⠄⠛⠀⠀⠀⠀⠀⠀⢸⠀⢾⠇⢴⠀⢀⡞⠀⡆⠀⠀⠃⠀⣠⠀⢇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⢠⠀⢰⡏⠀⠀⠃⠀⠀⠀⠀⠸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄⣉⣀⠀⠉⠁⠉⠀⣀⠁⠛⠶⡳⢆⠀⠀⠀⠀⠀⠀⠀⣼⠆⣰⡏⠀⡏⢠⠀⠀⠸⠀⠺⠀⠰⠀⠀⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⣄⠀⠘⡏⠀⠀⠀⠐⢎⣤⠀⠀⠀⠀⠀⣰⠉⡶⢻⡇⢀⠀⠀⢠⠀⠀⠐⣣⡄⠁⠀⣀⠃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠃⢰⡆⠀⠀⠈⢡⠆⠀⠀⢀⡞⢡⡾⠀⣾⡇⢸⡄⠀⠈⡄⠀⢸⠛⠀⠀⣠⠋⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⡇⠀⠀⠀⠀⠈⡼⢇⣀⠟⠠⠎⠁⠀⣼⣧⠈⠃⠀⠀⠀⢆⡈⠀⢀⡐⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠳⡜⢿⠀⠆⠀⠀⠀⣿⣿⠀⠠⠆⠀⠀⢘⣁⠔⠈⠀⠀⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣶⠀⠀⠀⠀⣿⣿⠀⠀⢴⠀⠀⠘⠃⠀⠀⢀⠔⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠑⢠⡇⠀⣤⠾⠁⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡿⠃⠀⠀⠢⡀⠸⠟⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢶⠀⠘⣤⠞⠁⠀⠀⢀⣠⡄⠻⣄⠠⠖⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⡀⢸⠋⠀⠀⠂⠀⠉⠀⣿⠀⠏⠰⣀⠙⢆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⡰⠆⣤⣤⣤⠄⠀⠀⢸⣇⠀⠀⠙⠤⢈⣠⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⢻⠖⠋⢸⡇⠀⠀⢀⣼⠇⠀⠀⠀⠀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⠀⢙⣿⡇⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⣿⣷⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢈⠿⠇⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣧⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡏⣠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⢉⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⡴⠛⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⠿⣁⠀⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡷⠀⠈⠛⠛⠃

⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⢀⣤⣄⠀⠀⣴⣆⣀⢀⣀⡀⠀⠀⣶⣆⣀⣠⣤⣄⣀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⣴⣾⣿⡏⠸⣷⠿⠇⣴⣿⢻⣾⢿⡯⠛⠛⠻⠿⠿⠲⣿⠿⣃⠻⠃⠉⠉⠿⠻⠿⠗⠀⣿⣷⣦⡀
⠀⠀⠀⠀⣭⣨⣄⠀⠀⠀⠀⠀⢨⣷⠎⢙⡀⠁⠀⠀⠀⠀⠀⠀⠁⠰⠿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣨⣿⠁
⠀⠀⠀⠀⠟⣿⡟⠓⠀⠀⠀⢸⡿⠋⠈⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣤⡶⠀⣠⣾⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠙⠀⣿⠄⣤⣤⠿⠷⠀⠀⠀⠚⢋⣟⠀⠀⠀⠀⠀⠈⠛⠠⡾⠏⠀⠀⠀⣤⠁⠸⣿⣀
⠀⠀⠀⠀⠀⠰⣶⣏⠀⠈⣶⡄⠀⠀⠀⠀⣸⠃⠉⢸⡧⠀⣀⢼⡿⠋⣀⡀⠀⠀⠀⠀⢠⣴⠀⠿⢋⡀
⠀⠀⠀⠀⠘⠆⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⠉⠰⠀⠀⢠⠂⠉⠀⠀⠀⠛⣧⠈⣿⠆⠀⠀⠁⠀⠀⣨⡅
⠀⠀⠀⠀⠀⠘⠇⠀⣺⡤⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠰⣿⡄⠀⠠⢶⡄⠀⠀⠀⠀⠀⠚⠿⠀⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠈⢣⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤