Baby pink Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡏⠙⠙⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠗⠾⠛⠓⠖⢻⣿⠿⠿⠟⠹⠋⡁⠰⠀⠰⠆
⠀⣀⠀⣀⣄⠀⠀⣀⣀⢀⣄⠠⢤⢠⣄⣿⣿⠈⣕⣉⣛⢻⠐⠀⠘⠀⠀⠒⢀⣀⡤⣤⡄⢘⠀⠀⣠⡀⠠⠄
⡅⠀⢸⠉⠘⠘⠁⠋⠙⠉⠙⠁⠉⠉⢉⡬⠉⠉⠉⠉⠁⢀⣽⢿⣟⢠⢄⣏⢸⣭⠿⠿⠇⡀⠀⠠⠉⠁⠃⠀⡀
⠀⠂⠀⠀⠁⠀⠀⠀⠐⠀⠂⠀⠀⠁⠈⠁⠀⠀⠀⠴⠤⠶⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣄⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠻⡁⢢⠀⠀⣰⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢨⠉⠲⣄⡀⢸⣿⡏⠀⠀⣠⡤⢧⣠⣽⣿⢀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣸⠀⠀⣬⢿⣿⣿⣶⣼⠇⠁⠘⡿⣿⠿⣫⠋⠀⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⠲⣤⠈⢸⡠⡐⢼⣿⣷⡧⣿⡷⢀⣶⢠⣇⠟⡴⢁⠜⠐⠃
⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⢈⠀⡟⢀⠼⣇⢿⡘⣿⣿⣧⡌⣿⣿⢷⣾⣿⡿⠐⠁⢠⡞⠂⠐⢄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣀⢉⠓⠦⠌⣶⣿⣘⣿⣟⣾⣯⣿⣿⣟⢻⣿⠁⢪⣿⡟⠛⠶⣿⣿⣿⣷⣶⠂⠘⠃
⠀⠀⠀⠀⠶⠿⠿⡙⠫⣛⢶⡶⠿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠳⠿⡂⠲⢆⣩⠟⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠦⣬⣻⣯⣀⠀⢤⣿⣤⣿⣿⣿⣿⣟⣽⣿⣗⠯⣄⢠⣿⣿⣿⣿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⡿⢻⡿⣻⣿⣛⣻⣿⣿⣿⣿⣿⠟⣿⠃⣿⣞⠻⠓⠛⠿⣷⣿⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢉⣾⣽⡿⠟⢦⣤⣾⡿⠛⠿⣿⣿⣿⢟⣿⣷⡀⡿⣍⢳⣤⠂⠀⠻⠃⠐⠉
⠀⠀⠀⠀⠀⠀⠘⠫⣭⠹⠿⢿⣤⣤⣀⡿⠀⣠⠾⣿⣏⠘⣀⢣⣿⣿⣶⣤⡋⠻⠇⠻⣿⣤⡶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⡾⠫⣣⠩⠀⠉⢁⣠⣿⣏⡹⠍⠋⠇⣸⡟⠿⢿⠳⡖⣤⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠣⠚⢿⡶⣴⣷⣻⢻⠏⢛⣿⣶⢀⣦⣿⠛⠂⠤⣄⠹⣼⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⢒⣫⣴⣾⢿⣿⣥⣶⣿⡟⠿⠟⣿⣿⡷⣈⠓⠨⠤⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⢻⡿⠣⠚⠽⠛⢧⡋⣃⣠⡞⠉⣿⣿⠀⠉⠉⡋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠤⠊⠁⠀⠀⠀⠈⠙⠿⠀⠂⢿⣿⡁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⡛⡙⣤⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠖⠃⣤⠙⠀⠀⠀⣠⡀⠀⠀⠀⠉⠁⠀⠀⠀⢋⡰⠌⡃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠘⠃⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠷⢈⢡⡄⠋⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⡶
⠀⠀⠀⠀⠀⠀⣀⢤⢀⣄⠀⠀⠀⠀⠀⠀⠘⠿⠀⢀⡀⠀⠀⠀⠀⠀⠀⢒⡒⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢩⡴⠆⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣈⢸⣫⡡⠆⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⡜⢣⡄⢛
⣀⠀⠀⠀⠀⠛⢠⡄⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⣤⠙⠁
⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠻⠃
⢛⡰⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡁⠦⢉⡄⠀⠀⠀⠀⠀⠀⢠⡄
⢈⢁⡄⠛⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠆⠋⠰⠈⠁
⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣄⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⢤⠲⠆⠓
⡄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠶⢩⡔⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⠀⠀⠀⠀⠈⠛⠀⠀⢰⠆⠶⠲⠘⠃
⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⠜⠃⡀⠶⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁
⣶⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠐⡐⢂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢣⡌⢛⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⢠⠀⠉

⠀⠀⠛⠋⠀⠀⠀⠈⠛⠃⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠃⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠛
⡿⠀⠀⠀⠰⣿⡗⠀⠀⠀⠸⣿⠇⠀⠀⠀⢾⡿⠀⠀⠀⠀⢿⡷⠀⠀⠀⠸⣿⠇⠀⠀⠀⠺⣿⠆
⠀⠀⣴⣦⠀⠀⠀⢠⣶⡄⠀⠀⠀⣠⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣄⠀⠀⠀⢠⣶⡄⠀⠀⠀⣤⣦
⡀⠀⠙⠉⠀⣀⡀⠈⠙⠁⠀⣀⠀⠈⠋⠀⢀⣀⠀⠉⠉⠀⢀⡀⠀⠙⠁⠀⣀⠀⠈⠉⠁⢀⣀⠀⠉⠋
⠿⠀⠀⠀⠘⠿⠗⠀⠀⠀⠸⠿⠃⠀⠀⠀⠻⠿⠀⠀⠀⠀⠿⠟⠀⠀⠀⠘⠿⠇⠀⠀⠀⠸⠿⠃
⠀⠀⣶⣦⠀⠀⠀⢠⣶⡆⠀⠀⠀⢴⣶⡄⠀⠀⠀⣶⣶⠀⠀⠀⢠⣶⡦⠀⠀⠀⢰⣶⡄⠀⠀⠀⣴⣶
⣀⠀⠉⠁⠀⣠⡀⠀⠉⠀⢀⣄⡀⠈⠉⠀⣀⣄⠀⠈⠁⠀⣠⡀⠀⠉⠁⢀⣠⡀⠀⠉⠀⢀⣄⠀⠈⠉
⠟⠀⠀⠀⠈⠻⠋⠀⠀⠀⠘⠿⠃⠀⠀⠀⠻⠟⠀⠀⠀⠀⠻⠟⠀⠀⠀⠘⠿⠃⠀⠀⠀⠙⠟⠁
⠀⠀⣾⡷⠀⠀⠀⢰⣿⡆⠀⠀⠀⢼⣿⠆⠀⠀⠀⣾⣷⠀⠀⠀⠰⣿⡧⠀⠀⠀⢰⣿⡆⠀⠀⠀⢾⣷
⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⢠⣤⡀⠀⠀⠀⣠⣤⠀⠀⠀⠀⣤⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⢠⣤⡀
⠋⠀⠀⠀⠈⠛⠃⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠛⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⠛⠃⠀⠀⠀⠘⠛⠁
⠀⠀⢿⡷⠀⠀⠀⠸⣿⠇⠀⠀⠀⢸⣿⠆⠀⠀⠀⢿⡿⠀⠀⠀⠰⣿⡗⠀⠀⠀⠸⣿⠇⠀⠀⠀⢾⡿
⣦⠀⠀⠀⢀⣴⣄⠀⠀⠀⢠⣶⡄⠀⠀⠀⣴⣦⠀⠀⠀⠀⣴⣦⠀⠀⠀⢠⣶⡄⠀⠀⠀⣠⣦⡀
⠉⠀⣀⡀⠀⠙⠁⠀⣀⠀⠈⠋⠁⢀⣀⠀⠉⠋⠀⢀⡀⠀⠙⠉⠀⣀⡀⠈⠉⠁⠀⣀⠀⠈⠋⠀⢀⣀
⠀⠀⠿⠟⠀⠀⠀⠘⠿⠇⠀⠀⠀⠺⠿⠃⠀⠀⠀⠿⠿⠀⠀⠀⠘⠿⠗⠀⠀⠀⠸⠿⠃⠀⠀⠀⠻⠿
⣶⠀⠀⠀⢠⣶⡆⠀⠀⠀⢰⣶⡄⠀⠀⠀⣴⣶⠀⠀⠀⠀⣶⣦⠀⠀⠀⢠⣶⡆⠀⠀⠀⢴⣶⡄
⠁⠀⣠⡀⠀⠉⠁⢀⣠⡀⠀⠉⠀⢀⣄⠀⠈⠉⠀⣀⣀⠀⠉⠁⠀⣠⡀⠀⠉⠀⢀⣄⡀⠈⠉⠀⣀⣄
⠀⠀⠻⠟⠀⠀⠀⠘⠿⠃⠀⠀⠀⠙⠟⠁⠀⠀⠀⠻⠟⠀⠀⠀⠈⠻⠋⠀⠀⠀⠘⠿⠃⠀⠀⠀⠻⠟
⣷⠀⠀⠀⠰⣿⡇⠀⠀⠀⢰⣿⡆⠀⠀⠀⢾⣷⠀⠀⠀⠀⣾⡷⠀⠀⠀⢰⣿⡆⠀⠀⠀⢸⣿⠆
⠀⠀⣤⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⣠⣤⠀⠀⠀⢀⣤⡄⠀⠀⠀⢠⣤⡀⠀⠀⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⢾⣉⣿
⣿⣿⣶⣟⣋⣉⣿⣿⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣾⣿⡋⢿⣟⡓⠒⣾⣭⢿
⢸⣟⣶⣿⣥⣤⣼⣟⣀⣿⣿⣿⡳⢤⡀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⣠⣞⣩⣿⣿⣛⣷⣾⡋⠉⢻⣿⣹⡿
⠀⠻⣷⣾⣿⣤⣤⣿⡿⠶⠾⠟⠛⠓⠻⢶⣄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡰⠁⠀⢀⣤⠾⠋⠉⠉⡉⠉⠉⠉⢻⡿⠛⣿⣿⡿⠁
⠀⠀⠙⢿⣿⣏⣹⣿⠀⠀⠀⠀⣆⠀⠀⠀⠉⠳⣤⡀⠀⠑⠀⠀⠀⠀⡘⠀⠀⣠⠞⠁⠀⠀⢀⣠⣧⠄⠀⣀⣼⣿⢶⣿⣿
⠀⠀⠀⠘⣿⣿⣽⣿⡷⠂⠀⠉⠉⠑⠦⡀⠀⠀⠈⠻⣄⠀⠀⡄⠀⡘⠀⢠⡾⠃⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⣿⠟⣿⣿⠃
⠀⠀⠀⠀⠸⣿⣯⣽⣇⠀⠀⢀⣀⣤⡤⠷⠄⠀⠀⠀⠈⠳⣄⣸⣴⡀⡴⠋⠀⢀⡀⠀⠚⠛⠓⠶⠶⠀⠠⣴⣟⣻⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠈⢿⣿⡟⢁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣬⣿⣦⣀⣀⣠⣤⣶⣶⣶⣤⣤⣤⣤⣤⣽⣿⣿⣿⣦⣤⣤⣴⣶⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠛⠛⠉⠉⠛⠟⠉⠉⠟⠋⠁⡽⣿⣿⣿⢧⡀⠐⠚⠂⠀⠙⠂⠀⠀⠀⠀⠙⣿⡟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣦⠤⠤⠀⢰⠆⠀⠀⠀⣀⡴⠋⢀⢃⣿⡏⢂⠈⠳⢤⣀⠀⠀⠈⢋⠉⠉⠉⠙⢿⣟⣿⣇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⣠⡎⣀⣠⠴⠞⠁⠀⢠⠆⠘⣿⡗⡀⢧⠀⠀⠈⠛⠲⢦⡄⠷⠄⠀⣀⣀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡶⠀⠈⣩⠌⠉⠀⠀⠀⠀⡠⢁⣼⠁⣿⡇⠸⣄⠑⡄⠀⠈⠀⠀⠈⠐⢄⠀⠉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣤⡞⠁⠀⠀⠀⠀⠀⡐⠀⣾⠃⠀⠙⠁⠀⠹⣇⠈⢀⠀⠀⢀⠀⠀⢀⣿⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣿⣷⣦⣤⣶⣃⣀⡾⠀⣰⠃⠀⠀⠀⠀⠀⠀⠹⣆⠀⢷⣤⣼⢿⣿⣿⣿⣿⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣷⣿⣿⣿⣽⣷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣷⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣍⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣽⣽⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣮⣭⣴⣾⣿⠿⢿⡖⣶⣶⣂⣾⣿⣿⣹⣿⣿⣏⡏⡙⠛⢱⣦⣬⣙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⢉⡄⠘⢓⣿⠛⢿⣿⣷⡾⠁⢹⣿⠙⠻⣥⡔⠉⠉⠻⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣋⣁⡀⢁⣀⣀⡛⠿⠇⠀⣻⣿⠀⠀⠘⣛⣡⣤⣬⠥⢤⣄⣀⡉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢰⣿⣿⣿⣛⣰⣿⣿⣿⣿⣷⡦⣀⣬⣥⣄⠔⣠⣾⡿⢿⣿⣆⠀⢼⣿⣿⡎⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⣿⡟⠛⣿⣿⣿⣯⣭⣿⣷⣿⣿⣿⣿⡄⣿⣷⣶⣾⣎⡿⠀⢸⣿⣏⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠠⣿⡅⠀⠸⣿⣿⣿⣿⠿⢿⠟⠁⠀⠙⢯⠛⠿⠿⠿⠟⠁⠀⣼⣿⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⢿⣿⣤⣄⠈⠉⠉⢀⡴⢿⣀⡀⠀⢀⣬⣷⣄⠀⠀⠀⢰⣾⣿⡟⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣭⣤⠤⠔⠚⠉⠀⠀⠉⠻⣷⡼⠁⠀⠈⠙⢒⣶⣶⣿⣶⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠈⢀⠁⢀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣷⣾⣏⣀⣀⣤⣴⣿⣷⣤⣤⣤⣤⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⣿⡙⠛⠛⠋⠉⠉⠉⠉⢁⣴⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣬⣻⣿⣦⣤⣀⣠⣄⣤⣴⣿⣿⡿⢋⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⠿⠛⢿⠿⠛⠛⠋⣀⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠒⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣇⠀⢀⠀⡀⠀⢠⠖⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣯⣄⡀⣀⠋⠈⢹⡗⠏⡆⠀⠈⠁⣠⣶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿⣿⠋⠁⠠⠆⠨⣴⣾⠃⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠲⣿⠟⡿⠀⠀⠀⠘⡿⠟⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣦⠀⠀⠀⠀⣴⣿⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠘⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⡀⢀⡒⣛⣛⣻⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠿⠛⠛⠉⠁⠀⠈⠉
⠉⣉⣀⠀⠈⠁⠂⠀⠀⠈⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠉⣓
⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⠉⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠠⡖⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡀⠐⠀⠀⣀⢠⢀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⢙⠁⠀⠀⠀⠋⠀⡼⠀⠀⠥⠒⡨⠉⠋⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠉⠉⠉⠉⠁⠀⢀⣿⠀⠀⠀⠀⠀⢠⠉⢉⡀⠀⠀⠠⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠀⣠⣿⡄⠀⡀⠰⢈⡀⠀⠈⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⠃⠀⠰⡀⠀⠀⠀⠒⡀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠉⠉⠉⢹⠛⣟⠉⠀⠀⡄⢱⠀⠀⠡⠀⠰⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢸⣠⠀⢀⠀⠀⢸⠀⢏⠀⣀⣠⠃⠀⢃⡀⠀⡘⠀⡐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢤⠉⠚⠛⠓⣂⠁⠀⠈⣆⠀⢈⣉⡀⠄⠂⠠⠀⡄⠁⢀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣰⠁⠀⠀⠈⠉⠉⡉⠉⢹⣿⡇⠈⢆⠀⠐⠀⠐⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡌⢹⣴⣶⣿⣿⣶⣾⣿⣷⣾⣿⣿⡄⠈⢳⣾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠹⣆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⢿⡏⡇

⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢰⣶⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠿⠛⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣀⣠⣤⢹⣦⡀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡁⠈⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣦⡀⣤⣀⣤⣤⣾⣠⣟⡿⣿⣿⣿⣷⣄⣾⣿⣿⠀⣴⣶⣄⣠⡴⠀⠛⠉⠙⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣗⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢩⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣹⡿⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⡧⠙⠿⣿⡄⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣿⣿⣿⣗⣠⣿⣿⠃⠀⠀⠈⠻⣆⢼⣿⣁⣰⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⠿⡏⠀⠀⠀⣄⠀⠀⠘⢿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⡟⣟⠋⠁⣻⢿⠛⠂⠀⠀⠀⠀⢹⣦⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣰⡟⠉⠻⡷⠶⠙⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⣼⣿⣿⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⣴⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠋⠋⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⡍⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⣿⣿⡏⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢸⣿⠁⠀⠀⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⢀⠀⠀⣠⣤⣤⡀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⢠⡀⠀⠰⣴⠃⠀⠀⠀⠀⠀⠤⠄⠠⠀⠀⢸⣿⣿⣿⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⡼⡿⠿⠸⡃⣀⣠⣈⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⣤⣤⡈⣡
⠀⠀⠀⠈⠀⠰⣾⠻⣷⠿⢇⠙⠂⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠙⠋⠀⠀⣀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠾⠀⠀⢁⡦
⠀⠀⠀⢀⡀⣤⣄⣶⣴⣦⣿⡆⠀⠀⠘⠃⠐⠀⠀⢠⣾⣿⣷⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡴⣿⣿⣿⣿⡷⠾⣷⣄⢠⣾⡿⠀⠀⠀⠀⠈⢠⠟⢀⠀⠀⠀⠀⢀
⠀⠀⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⢸⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⢼⣿⡇⠀⠀⠙⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠹⡿⠆⠀⢸⡿⠃⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠐⠠⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂
⠀⠀⠀⠀⠌⢄⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣠⡄⢠⣄⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠑⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠁⠀⠀⡄⠀⢀⠀⠀⢠⠂⠀⠈⠁⠀⠀⠂⠰⣦⠀⠀⠀⠀⠀⢹⣿⠁⣼⡿⢾⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⢀⣀⠈⠋⣀⣙⠁⣈⠃⢙⣛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠤⠤⠀⠀⢠⠠⡆⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⢠⡀⢀⠀⣆⡠⢀⢸⡟⠀⠀⢸⣿⣇⢸⣿⣏⠺⣿⣅⠛⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠸⠷⠿⠻⠿⠷⠰⠾⠟⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢻⡆⣴⣿⣿⣶⡀⠀⣰⣿⣦⠀⢰⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠋⠀⠀⠀⣠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⡁⣿⣏⠨⣿⡇⢰⣿⠤⣿⡆⢸⣷⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠰⣾⣿⡿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠛⠃⠙⠿⠿⠛⠀⠿⠋⠀⠘⠛⠘⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠠⠉⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠘⠋⠉⠉⠈⠉⠲⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠠⠤⠤⠷⡆⠠⡌⠐⡦⠤⠤⠤⠀⠛
⠀⠀⠀⠀⠀⠀⢀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠋⠀⠀⠈⠛⠊⠛⠛⡃
⠀⠀⠀⠀⠀⣠⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢲⣰
⠀⠀⠀⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⡈⣷⢂⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⣁⣁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣿⣾⣾⣷⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⣡⣀⡄⠀⣴⣿⣆
⠀⠀⣿⣇⣸⣿⢸⣿⣛⢻⣿⡇⠀⣿⣿⠀⢠⣿⡿⣿⡆⣿⡇⠀⠀⠀⠙⠛⡿⠿⠉⠁⠀⠀⠐⢆⠀⣀⠒⠦⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢀⣿⣿⠀⢀⢂
⠀⠀⣿⡟⢻⣿⢿⣿⣿⡹⣿⣧⣤⢿⣿⣤⡜⣿⣄⣿⠇⣛⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢦⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠉⠀⠈⠁⠈⠉⠉⠀⠉⠉⠁⠈⠉⠉⠀⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⡀⠀⠀⠁⢀⡄⠈⠉⠀⣄⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⢀⠀⠄⡀⠀⠀⠀⠀⣦⠀⠀⣀⡀⠙⠁⠀⠒⠆⠀⠋⠁⠀⠐⠋⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠀⡀⠃⠠⠀⢂⠠⠂⠠⠀⡁⠀⠀⠀⠀⠉⠀⠀⠘⠃⢀⣀⣤⠀⠀⠢⡄⠀⢦⣤⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠰⠀⠈⠁⠰⠀⠀⠀⢠⢈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠁⠀⡀⠀⠀⢀⣀⡀⠉⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠀⠀⠀⣀⠢⠐⠀⠀⠀⠀⠀⡇⠀⠉⠁⠀⠀⠣⠀⠙⠖⠀⠀⠉⠀⡀⠀⠀⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠤⠀⠡⠈⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠄⠀⠀⠀⣄⣀⠀⠀⠚⠂⠀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠒⣄⠀⠀⢦⡀⠉⠀⠀⠀⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⢰⡄⠁⠀⠈⠉⠀⣶⠀⠀⠈⠉⢁⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠁⠀⢀⠀⠀⠀⠈⠁⠀⢢⡀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡨⢈⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠁⢀⠀⠀⠈⠙⠁⠀⣦⠀⢀⡉⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠚⠒⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⢀⡀⢀⡷⠀⠀⠘⠛⠀⠀⠀⠀⠀⢀⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠑⠛⡇⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠐⠶⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠈⣿⡤⠔⠀⣈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠙⠿⠿⠒⠢⢤⣤⣽⣿⣿⣾⣛⣿⡦⢀⣼⣿⡆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣂⠈⢀⣩⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣇⡔⠀⢀⠠⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡟⢛⠤⣀⣄⣈⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣅⣈⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠻⠿⠟⠀⠀⠘⢿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠪⠻⣧⠠⠀⠀⠀⠠⢆⣈⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠄⠀⡜⢢⠀⠀⠀⠙⠻⢩⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠄⠀⠘⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⡃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⠀⠁⠘⣷⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣿⣿⡿⠇⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠙⡄⠀⠿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡏⡂⠀⠀⠈⠻⢇⡀⠘⢀⡿⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠢⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠑⢤⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡳⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢊⣿⣿⣿⠷⢶⣦⣀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢱⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣾⠟⠋⠁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢾⡿⠿⢿⣿⣟⢿⣿⣿⣿⡟⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢍⠙⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⡿⢿⣿⣿⡟⠿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠙⠻⣿⣷⣦⣍⣙⡒⠾⢭⣤⣈⡙⠲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣝⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣍⣙⠓⠲⢮⣭⣳⢮⣷⣵⡝⣿⣿⣿⣿⣿⣿⣿⣿⣦⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⢷⣒⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠓⠂⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⠈⠀⠹⣿⣿⣿⣿⣿⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⠿⠋⢁⠀⣀⣀⣀⡀⢀⡠⠤⠒⠉⠁⠙⣿⣿⣿⣿⣧⡐⢀⣿⣿⣿⣿⣿⣷⡁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⡶⠿⠗⠀⣠⠊⠉⠀⠉⠻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⡞⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣷⠬⢄⣀⢠⣀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣀⡼⡟⢺⢋⠳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⢃⠀⡇⠀⠙⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠈⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡇⡿⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢠⠉⠉⠑⡄⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣏⠄⠀⠀⠈⢆⢈⡤⠴⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡟⣦⠀⠀⠀⠀⠡⡄⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢿⣿⣿⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠘⣷⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢸⠻⣿⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠈⢿⣄⠀⠀⠀⠀⠈⠂⠀⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⢀⠀⢀⡼⠈⠱⠎⠁⡌⠸⣏⠀⡿⠃⢆⠉⡲⠉⠀⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡗⠉⡲⠈⠀⠀⠻⡍⢈⡿⠘⡀⠉⠶⠉⡸⣄⠀⣀
⡁⠀⠀⠈⠉⠉⠁⠄⠁⠘⠀⣆⡀⢈⣋⠁⢀⣼⠀⠀⠙⠡⠈⠉⠉⠁⠀⠀⢈⠁⠀⠀⠉⠁⠉⠡⠔⠀⠀⢸⣆⠀⢙⣋⠀⢀⡟⠈⠀⠃⠄⠉⠈⠉
⢃⠀⠀⠀⠀⠀⠀⠀⡱⠒⠀⠩⢷⣾⡉⣷⡫⠁⠀⠒⡆⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⡀⠀⠀⠀⠀⠀⡖⠂⠀⠩⢷⡟⡹⣷⢯⠁⠀⠳⡀⠀⠀⠀⠀⠀⠐
⠂⠀⠁⠀⠀⢠⠀⠀⠷⠀⠀⠈⠉⠀⣀⠀⠉⠀⠀⠰⠇⠀⢠⠄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢤⠀⠀⠖⠀⠀⠈⠉⢀⡀⠈⠉⠀⠀⠴⠇⠀⣠⠀⠀⠐
⢰⡿⡙⠀⠀⣰⠃⠀⠀⠀⠀⠀⢁⠒⡂⠂⡀⠀⠀⠀⠀⠀⠸⣄⠄⠐⢈⢷⡄⣶⡯⠰⠀⢀⣼⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⠀⠀⠀⠀⠀⠀⢰⣀⠀⠜⠼
⠙⠀⠛⡆⠀⠠⠁⠄⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢺⠋⠀⠏⠋⠈⢻⠆⠈⠠⡀⠄⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠄⠠⠈⠀⡞⠃
⢧⣄⠀⠁⠀⠀⡈⠠⠏⠉⠛⠀⠀⠀⠉⠀⠀⠀⠋⠉⠿⠐⠁⠘⡈⠀⢀⣤⡾⣦⡄⠀⠁⠀⠀⡉⠸⠋⠈⠃⠀⠀⠈⠁⠀⠀⠘⠉⠙⠧⠘⠀⠈⡁⠁⢀
⢘⡿⠀⠀⠐⣴⠃⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠒⣴⠃⠀⠘⣿⠁⢹⡟⠀⠀⢢⡜⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢢⡔⠁⠀⠸
⠚⠁⠀⡇⠀⣀⠐⡀⠓⠒⠛⠀⠀⠀⠂⠀⠀⠀⠓⠒⠛⢀⠢⡀⠀⣴⠀⠈⠗⠋⠀⢸⡄⠃⡨⠂⠘⠓⠚⠃⠀⠠⠀⠂⠀⠀⠘⠓⠚⠃⡀⠆⠀⠀⣄
⢻⣤⣛⠁⠀⢦⠂⠀⠀⠀⠀⠀⠂⠀⠻⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠙⢻⣴⡟⣳⣴⣋⠁⠰⢤⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⢢⠶⠀⡙⢣
⠉⠙⠈⠂⠀⠰⠅⠀⣀⠀⠀⠀⠁⠈⠦⠁⠈⠀⠀⢀⡀⠀⠸⡄⠀⠐⠐⢋⠈⢈⠑⠐⠀⠀⠼⠀⠀⣀⠀⠀⠈⠀⠠⠠⠀⠀⠀⠀⣀⡀⠀⢯⠀⠀⠘⠘
⠡⠂⠀⠀⠀⠀⠀⠀⢏⠀⠀⠨⣰⣦⠆⣴⣢⠀⠀⢀⡍⠀⠀⠀⠀⠠⠀⠀⠍⠡⠂⠀⠀⠀⠀⠀⠘⡅⠠⠀⢊⣲⡦⢦⣶⣨⠀⠀⢈⠇⠀⠀⠀⠀⠠
⠇⠀⠀⠀⠀⠁⠀⠀⠊⠁⠀⡶⠂⠙⠚⠋⠓⢦⠀⠉⡁⠀⠀⠀⠀⠀⠀⠠⠸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡶⠊⠛⠚⠉⠲⡆⠀⠉⡃⠄⠀⠀⠀⠀⠈
⠂⠀⠀⠐⠒⠚⡆⠐⠁⢠⠐⠃⢀⣠⣦⣀⠀⠸⠀⠀⠈⠃⢰⠒⠒⠂⠀⠀⠐⠂⠀⠀⠒⠒⢺⠄⠊⠀⠂⠘⡀⢀⣰⣦⡀⠀⠛⠐⠀⡈⠂⡶⠒⠒⠀⠐
⠀⠀⠀⠀⠀⠀⣰⠠⢄⡀⠀⠨⢼⡟⠀⢿⡇⠀⠶⠀⠶⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠱⢿⡏⠸⣿⠸⠀⠢⣀⠇⢲
⠄⠀⠀⠰⠤⠰⠏⠀⡎⠁⠈⡄⠠⠱⠴⠋⠀⢰⠀⠀⠃⠂⠹⠀⠶⠀⠀⠀⠀⠀⠄⠀⠲⠀⠸⠁⠀⠀⠒⠁⡀⠈⠳⠴⠃⠀⡄⠰⠉⡄⠊⠗⠠⠶
⠆⠀⠀⠀⠀⠀⠀⠁⣠⢤⠐⠛⣂⣴⠶⣦⢐⠛⠀⢬⡤⠀⠀⠀⠀⠀⠠⡈⠰⠌⠀⠀⠀⠀⠀⠀⠀⣨⠄⠘⠓⣀⡴⢶⣄⡒⠓⠀⣤⠄⠁⠀⠀⠀⠀⢠
⢄⠀⠂⠀⠀⠀⠀⠀⣎⠀⠀⠘⠜⠋⠒⠛⠾⠀⠀⢀⡃⠀⠀⠀⠀⠀⠁⠀⡣⠀⠀⠂⠀⠀⠀⠀⠠⣁⠀⠂⠀⠚⠃⠊⠻⠼⠀⠀⢨⡂
⢄⣤⢐⠀⠀⢘⠅⠀⠀⠀⠀⠀⠄⣌⠂⠀⠀⠀⠀⠀⠁⠀⢸⠁⠠⢀⡰⣤⡀⣠⡤⠂⠀⠀⢹⠀⠀⠁⠀⠀⠀⠀⠀⠊⡄⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⢢
⠾⠋⠥⡄⠐⢊⠂⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⠈⡓⠀⣠⠬⠙⠧⡞⠩⢥⡄⠐⡃⠀⠀⠁⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⣥⠍
⣄⠀⠀⡃⠀⠈⠲⠅⡦⠀⠤⠀⠀⠀⠆⠀⠀⠀⠤⠠⣶⢨⠆⠠⠐⠘⠀⠀⣠⡀⠀⠘⠇⠀⠀⠢⢠⡤⠠⠄⠀⠘⠀⠆⠀⠀⠠⠄⠠⡆⠡⠊⠀⠂⠃
⠹⣿⠀⠀⢀⢀⠇⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⢀⡇⠈⢰⣿⠏⢿⣷⠀⠀⢀⢠⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠆⠀⢸
⡴⠋⠈⡆⠠⠛⠠⠘⡦⠀⠤⠀⠀⠀⡤⠀⠀⠠⠤⡠⢾⠁⡀⠓⠀⠀⠀⠻⣄⡼⠃⢀⡀⡜⠃⠀⢹⠦⡠⠤⠀⢀⠀⡄⠀⠀⠰⡄⠠⡟⠀⡘⠃⠀⠀⠈
⣤⡀⡴⠇⢀⡊⡀⠂⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠐⠀⣂⠀⠹⢤⢀⣤⣄⢠⠼⠃⢐⢊⠀⠂⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠿⠄
⠼⠿⣱⠀⠀⢹⡀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠠⠀⠀⠀⠀⠀⢸⠁⠀⠐⣈⠿⠣⠺⢯⡰⠀⠀⢹⠀⠀⠀⠀⠀⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠐⡹
⠄⡀⡀⠀⠀⠈⠀⠀⡖⠀⠀⢀⢀⡈⡀⣁⣀⠀⠀⠐⡂⠀⠈⠁⠀⠐⠀⢀⡢⠂⠀⡀⠀⠀⠉⠀⠠⠒⠀⠠⠀⣀⡁⡈⣀⡀⠀⠀⠰⡂⠀⠈
⡄⠀⠀⠀⠀⠂⠀⠀⠘⠤⢀⣀⡜⢿⣤⡟⢌⣀⠈⠴⠣⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠳⠄⢀⣀⡜⢯⣼⠟⣎⣀⠀⠶⠆⠀⠀⠀⠀⠀⠠
⡄⠀⠀⢠⠤⢠⡄⢡⠈⢀⠠⡏⠀⠀⣄⠀⠀⢹⠀⠀⠡⡄⢠⡠⠤⡀⠀⠀⠀⠀⠀⠀⡠⠤⣠⡀⡁⠃⡀⢰⠁⠀⢀⡄⠀⠀⡷⢠⠀⠢⡁⣄⠠⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠠⠰⠾⠛⠷⠆⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠂⠶⠟⠻⠶⠰⠁⠀⠀⠆⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⣤⣖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣌⣿⣯⣟⣹⣬⣿⣷⣿⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⠿⠛⠻⠻⠿⠿⠿⠿⣿⣿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢶⣶⣦⣀⣀⣠⣶⣶⣖⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⣻⣿⣿⡏⣒⡀⣿⣿⣿⣿⣿⣿⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡹⠟⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⡇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⣅⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣍⣁⠲⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣆⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣦⣀⠀⣰⣟⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣀⣰⣿⣿⣿⣿⣦⣀⡴⠏⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⣀⣴⣿⣿⣿⣷⣄⣠⡀⠀⠀⠒⠃
⠈⢹⣿⣿⣿⡻⠋⠉⣿⣿⣿⣿⠁⠀⢙⣿⣿⣿⡟⠁⠈⢻⣿⣿⣧⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠈⢹⣿⣿⣿⠋⠀⠈⣿⣿⣿⣇⠀⠀⢀⣀⣠⣶⡆
⣴⣿⡿⠻⣿⣿⣦⣾⣿⠟⠻⣿⣷⣤⣿⣿⠟⢿⣿⣦⣴⣿⡿⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣦⣴⣿⡿⠻⣿⣿⣤⣾⣿⠟⠻⣿⣷⣤⣿⣿⠟⢿⣿
⣿⣿⡀⠀⣨⣿⣿⣿⠇⡀⠀⣸⢿⣿⣿⣅⠀⢀⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣧⡀⠀⣴⣤⣤⣶⣄⠀⢀⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣧⡀⢀⣼⣿⣿⣿⣅⠀⢀⣿
⠙⢿⣿⣿⠟⠉⠙⠁⠀⡁⠠⠄⠒⠉⠻⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⡿
⣠⣾⡏⠀⠀⠀⠘⠀⠀⠀⢀⡐⠀⠀⠐⠿⠿⢿⣷⣄⣠⣾⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣴⣿⣿⣿⣷
⠋⠉⠁⠀⠀⠘⢦⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⠙⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⠋⣠⠀⠀⠀⠀⡀⢻⡟⢻⣯⣽⣿⡟⠁⠈⢻⣿⣿⣿⡋⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣿⠿⣿⣷⣤⣾⣿⠟⢿⣿⣦⣴⣿⣟⠫⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠺⣿⣵⣶⣿⣦⣴⣿⡿⠻⣿⣷⠆⠘⠟
⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⡿⠀⣼⣿⣿⣿⣅⠀⢀⣿⣿⣿⣿⡄⠐⠀⠆⣠⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⣨⡇⠂⠀⢀
⠀⠀⠀⠀⠸⣿⣿⣿⡧⠀⠀⢀⣠⣤⡀⢀⣼⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⡿⠋⠙⠋⠄⠰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⣯⠁⠠⠀⠁
⠀⠀⢀⣀⠔⠉⠉⠉⠃⠀⠀⠈⠉⠙⣿⡿⣛⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣷⣄⣠⡞⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣿⣿⣷⣄⣠⣾⣿⣿⣿⠃⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠙⠻⢿⣗⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⣿⣿⣿⣧⠀⠀⠀⠒⠃⠀⠀⠀⠀⢻⣿⣿⣿⡋⠀⠈⣿⣿⣿⣿⣡⣤⣿⡆⠀⠀⠁
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠟⠻⣿⣄⣀⣀⡀⠀⢀⣶⣤⣴⣿⡿⠻⣿⣷⣦⣾⣿⠟⠻⣿⣿⣿⣿⣿⣶⢶⣷
⣿⠇⠐⠀⠀⠀⠀⡤⠤⠀⠀⡀⠈⢀⣀⣼⣿⣯⣾⣿⣿⣿⡛⠉⣩⣿⣿⣿⣧⠀⢀⣼⣿⣿⣿⣄⠀⢀⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣇⡀⠀⣼⣿⣿⣿⣿⢻⡦⡿
⡟⢆⡀⠀⠀⣀⡀⠀⠀⠠⠀⠁⢐⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠻⣿⣿⣿⣿⠟⠉⠻⣿⣷⣿⡿⠋⠙⢿⣿⣾⣿⠟⠉⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣾⣿⣿⣿⣯⣁⣧⣠⣱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣰⣿⣿⣿⣿⣤⣀⣴⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣦⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⠙⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⠋⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⢻⣿⡿⠿⠟⠀⠬⠙⠿⣿⣿⠁⠀⠙⣿⣿⣿⡟⠉⠛⢻⣿⣿⣿⠛⠻⣿⣿
⠻⣿⣷⣤⣿⣿⠟⢿⣿⣦⣴⣿⡿⠛⣿⣷⣤⣾⣿⡟⠿⣿⣿⣿⣿⣿⠟⢿⣿⣦⣴⠟⠛⠀⢀⠀⠉⠀⠀⠁⠛⠉⠀⠀⢿⣿⠟⢿⣿⣦⣴⣿⡿⠻⣿⣷⣤⣾⣿
⠀⣸⣿⣿⣿⣅⠀⢀⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣄⠀⢀⣿⡟⠃⠀⠐⠂⠀⠀⠈⠓⠐⠀⠀⠀⠀⠀⢈⣅⠀⢀⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣇
⣾⣿⠟⠙⠻⣿⣷⣿⡿⠋⠙⢿⣿⣾⣿⠟⠉⠻⣿⣿⣿⣿⠟⢹⣿⣿⣷⣿⣿⣆⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⣷⣿⡿⠋⠙⢿⣿⣾⣿⠟⠉⠻⣿
⣿⣿⣄⣀⣴⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣆⣘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣦⣀⣰⣿
⣿⣿⣿⣿⣿⠋⠀⠘⣿⣿⣿⣿⠃⠀⠙⣿⣿⣿⡟⢁⣼⣿⣿⣿⣿⡿⠋⠀⠈⠉⠀⠀⠁⠀⠀⢀⣦⡀⠀⣀⣤⣴⣾⣿⣿⠋⠀⠈⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⡟
⣿⣿⣿⠿⣿⡷⠤⣾⣿⠿⢻⣿⣷⣤⣾⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣴⣿⣿⠿⣿⣿⣤⣾⣿⠿⠿⣿⣷⣤⣿⣿⠟⣿⣿
⣿⠟⠛⠐⠀⠀⠀⠀⠣⡄⠀⣸⣿⣿⣿⣅⠀⢀⣿⣿⣿⣿⡋⠁⣿⣿⠽⠁⠐⡄⠀⠀⠀⠀⠛⢻⣿⣿⣷⣯⣿⣻⣿⣷⣬⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣅⠀⢻⣋
⡀⠀⢀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠋⠉⠿⣿⣷⣿⡿⠋⠙⢿⣿⣾⣿⣿⠏⠀⢀⡁⠀⠀⡀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣷⣿⣿⠟⠉⠻⣿⣷⣾⣿
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⣀⣴⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣦⣀⣠⣀⡀⠀⠀⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣄⣀⣴⣿⠛⠁
⠻⠓⠦⣀⣀⣄⠀⠀⣀⣀⣀⢻⣿⣿⣿⠋⠀⠈⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⡟⠁⠀⢠⣤⣿⣿⠋⠀⠹⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⡟⠁⠈⢻⠿⠛⠙⠋
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣷⣤⣾⣿⡿⢿⣿⣷⣤⣾⣿⠟⢿⣿⣦⣴⣿⡿⠻⣿⣷⣤⣾⣿⡿⢻⣿⣷⣤⣾⣿⠟⢿⣿⣦⣴⡟⢀⠀⠀⣀⠄
⠀⠀⣿⣿⣿⣭⡾⣿⣿⣿⣿⣿⡀⠀⣨⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣅⠀⢀⣿⣿⠿⠋⣀⠀⣨⣿⣿⣿⣇⡀⠀⣸⣿⣿⣿⣅⠀⢀⣿⣿⡟⠅⠠⡀⠘⠁
⠀⢠⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠉⠻⣿⣷⣾⣿⠟⠉⠻⣿⣷⠟⠀⠀⠐⡀⠀⠉⠛⠉⠉⠻⣿⣷⣾⣿⠟⠉⠿⣿⣶⣿⡿⠋⠙⠆⢀
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⠾⡿⢿⠿⣿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠘
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣤⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⣤⡤⢠⣤⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⢀⣄⣤⣄⣀⣀⣀⣀⣀⣤⣴
⢠⣾⠟⠛⠛⠛⢻⣿⡿⠛⠛⣶⠆⠘⣿⣯⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣾⣶⣿⣿⡇⠀⠀⠀⠀⣿⣏⣹⣿⠀⠀⠀⠀⣤⣤⣷⣶⣤⡌⠛⠛⠉⠉

⢿⣇⠀⠀⢀⣤⠘⣿⡟⠀⢀⣿⡆⠰⢿⣷⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡛⢚⣿⣿⡇⠀⠀⠀⠀⣿⣭⣿⡿⠀⠀⠐⢀⣿⣿⣿⣿⣿⡆
⠈⠻⠿⠿⠟⠉⠀⣿⡇⠀⠘⣿⢁⣹⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⡇⠁⠀⠀⠀⣼⣿⠟⣿⡇⠛⠀⡄⠀⣿⣿⢿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠃⢦⣍⣻⣿⠀⠀⢀⣴⣿⣿⣿⣿⡇⢰⣷⡄⠀⣿⡏⠀⢻⠃⠀⠀⠛⠲⣩⣿⣾⡟⠛⠀⠀⠙⠿⠿⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠳⣽⣿⣿⠀⠀⢸⠟⢹⣿⣿⣿⡇⠀⠻⠇⠀⣿⣿⡄⣼⡇⠀⠀⠀⠀⠋⢻⣿⣿⠀⠀⠀⠀⢰⣬⣷⠄⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣶⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡟⡡⠀⠀⠀⠠⣿⣿⣿⣿⡇⠀⠀⠀⠀⣷⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⢸⣿⣿⣤⡆⠀⠀⠀⠀⢿⣿⣿⣿⠄⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣤⡄⠀⠀⠉⠀⠀⠀⠁⣘⢻⣿⣿⡇⠀⠀⠸⠷⣾⡿⠛⠁⠀⠀⠀⠀⠀⠿⣿⣿⣤⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⡟⠀⠀⠀⠀⠾⠃⠀⠀⣀⣂⡀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠤⡼⠃⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣀⠀⠈⢻⣯⣉⠠⡄⠤⠀⢲⣆⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣤⠀⠀⠀⠿⠃⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣴⣏⣽⠀⠀⣠⡄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣾⣿⡇⠀⠀⠀⠀⣽⣧⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢀⠶⠀⠀⢸⡟⠀⠐⠟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣤⡾⣿⡿⡄⠀⠀⠀⢸⣶⣿⣽⠇⠀⠀⠀⠀⣹⣹⣇⣸⡇⠠⠀⠐⣶⣿⣿⣿⣿⣀⡀⠀⡀⢸⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣛⣿⣿⠉⠀⠀⠀⢸⣿⢛⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠐⠀⠀⣿⣿⣿⣿⠈⠁⠤⠁⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⠉⠗⢦⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠐⠀⣿⣿⣿⢿⠀⠀⣀⠀⢸⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠁⢸⣿⣿⠙⢳⠀⠀⠀⠀⠛⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠋⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⢸⣿⣿⣦⡾⠀⢠⡎⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢈⣻⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣆⠻⠿⢣⣟⠀⠀⠀⠀⢸⣿⢿⣿⣇⠀⠉⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⠿⠀⠀⠀⠀⠸⠿⠟⠿⢥
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⣷⣦⡌⠙⠀⠀⠀⠀⢸⣧⣾⣿⣷⠴⠎⠙⠂⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣿⣿⣷⠀⠀⠀⠀⠀⢰⣤⣴⣶⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⣿⣿⣧⣶⠆⠀⠀⠀⢸⣿⣿⣭⡵⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣇⡀⠸⡆⠀⣿⣿⣿⣿⠀⠀⠀⢤⣿⢟⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠄⠉⠉⠁⠐⠀⠀⠀⠀⢨⣯⣿⣿⡇⠀⠐⠫⠠⣿⣿⣿⣿⠏⠁⠀⠀⠀⣿⣿⣿⣿⠿⠛⠀⡴⢱⡆⠉⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠶⣾⣷⣶⠀⠀⠀⠀⢺⣶⣤⣽⡏⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠤⠀⢸⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣷⣿⣏⣿⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⡇⣀⠀⠀⠀⣿⣿⣿⣿⠠⡄⠂⠀⢿⣿⡿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⡟⠻⠇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⣿⣿⡻⣿⠀⠀⠀⠀⠘⠉⠈⠀⠀⠀⠰⠷⠀⠈⢻⣿⣵⡆⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠸⢋⡿⠋⡑
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⠋⠡⠈⠐⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣭⣭⣭⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣦⡖⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⠀⠸⠗⣤⣴⠀⠀⠀⠰⣦⠀⠀⠘⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⢰⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠶⢦⣴⣾⠶⣦⠀⠀⠁⠀⠀⢀⣠⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠿⠿⠿⡿⠀⠀⠀⠀⠨⠱⣶⠶⠤⠀⠀⠀⠀⠤⡾⢿⡿⠇⠀⠀⠀⠠⢿⠿⠿⡿⠀⠀⠀⠀⠸⡿⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢆⠤⢀⡀⠀⠀⣀⣘⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠢⢌⠓⡄⠀⠀⠈⠉⠙⠒⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡄⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠊⠩⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠲⠲⠛⠁⠀⠀⠀⠀⠀⣇⢉⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠦⠄⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣀⡤⠖⠋⠘⣇⠀⠀⠘⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⣶⠲⣟⣉⠁⠀⠀⠀⠀⢹⡀⠀⠀⢧⡀⠀⢳
⠀⠀⠀⠀⠀⠠⡀⠀⠈⠷⣿⠾⠛⠁⠀⠀⠙⠂⠀⢀⡀⠀⠀⠀⠈⠳⣄⡀⢸⡃⠀⠀⠀⠀⣧⠀⠀⢸⠑⣼⠙⠇
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣀⡀⠀⠀⠉⠛⣻⡟⠀⠀⠀⠘⣆⡶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠄⠚⠋⠀⠀⠀⠀⠘⠃⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣦⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡦⠀⢀⣠⡾⠛⠛⠒⠒⠒⠚⡛⣦⣄⠲⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠒⠿⢶⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⢠⠚⠁⡄⠸⣇⠀⡀⠀⠀⠀⠀⠀⡠⠀⠐⠋⠀⠘⠁⠚⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄
⠀⠀⠀⠀⠀⠈⠄⡄⠰⠀⢛⣼⠀⠀⠀⠤⠂⠉⠀⢀⡀⢀⣀⣐⣄⣠⠀⠀⠈⠉⠻⠷⠀⠀⠀⢀⣀⣀⣀⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠾⣦⡳⡀⡟⠀⠀⠀⠀⢀⢴⠀⡀⠙⠿⢿⣿⣿⣽⣝⣢⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⢀⠠⠟⠿⣿⣿⠀⣴⠋⠀⡂⠀⠈⠉⠲⣶⣤⡝⠋⠃⠀⠹⠗⠒⠢⡀⠀⣀⣤⡶⢦⣤⣞
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣇⢸⠇⣴⡹⠁⠄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣇⣀⣉⡿⠛⠐⣼⣿⠛⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠎⠉⠉⢿⠀⠀⠀⠉⣤⣷⠀⠈
⠀⠀⠀⠀⠀⠰⡀⢆⠀⠀⢀⠀⡋⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣀⡴⠞⠡⠄⠀⠀⠠⠀⠀⠀⠀⣠⢏
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣄⣈⢳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠁⢸⠂
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠈⠉⢿⡏⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢿⡆⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠶⠐⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡟⠀⢑⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⡀⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣤⣰⡿⠀⠀⠀⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⢁⠬⠁⠌⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣁⢰⣧⡞⠂⢤⠀⠈⠀⠀⠀⠀⠐⠖⠆⢸⡷⠋⣠⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢯⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢲⣄⡈⠳⣏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⢉⢻⣶⠿⠀⣀⣷
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠲⢿⡇⡀⠘⡟⠀⠀⠀⠀⠀⢹⣧⣾⠁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡒⣾⣿⣀⣶⡇⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠻⠿⠋⡕⠀⠀⠀⠀⢀⠐⠉⡒⠖⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢲⣆⠁⠑⣄⠀⠀⣾⡠⢠⣇⠨⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠆⠀⢻⡆⠀⣿⢃⣾⠃⢸⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⡸⡄⠈⠟⠀⢹⣾⡏⢠⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣀⢷⡁⠀⢸⠀⠈⣽⡁⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠏⠿⡀⢸⠀⠀⠙⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣛⣛⣹⣯⣩⣉⣿⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠒⠂⠉⠉⠛⠛⠛⠛⠂⠒⠒⠒⠒⠦⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⡟⢫⡀
⠀⠀⠢⣄⣀⣊⠁⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⡍⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁⠿⠀⠉⠃
⠀⠀⠀⠀⠀⢸⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡆⢄⠇
⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⢂⠆⠀⠀⠀⠀⠀⢴⣿⣿⣶⣤⣤⣤⣴⠶⠏⠋
⠀⠀⠀⠀⠀⠀⠀⠳⡆⠀⠀⠀⢰⣿⣿⣾⣿⣯⣤⣿⣶⣶⣦⣾⣖⣾⣓⣿⡷⠠⠀⠀⠀⣤⣿⠟⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣿⣿⠏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣄⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡄⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠙⠂
⠀⠀⠀⠤⠤⢤⠄⠀⢈⠿⠗⠦⠴⠀⠛⠛⠖⠶⠂⠦⠄⠀⠀⠐⠲⠆⠀⠒⠂⠂⠛⠂⠘⠦⠤⠤⠄


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠚⣭⣶⣿⣷⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣴⣾⣿⣷⡀⠈⣿⣿⣿⡇⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⣛⢉⣩⣭⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢛⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣤⠀⢀⣠⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠛⢛⣉⣉⣭⣬⣽⣿⣦⣀⣀⣀⣴⣿⣿⡿⣣⣾⣿⡿⢋⣿⣟⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣟⣵⣿⣿⡟⢠⣿⣿⣿⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣬⡙⢿⣿⣿⣿⣿⠿⠛⢛⣉⣉⣉⣩⣭⣥⣤⣶⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢛⣉⣥⣴⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣶⣦⣬⡙⠿⣿⣿⣿⣿⣦⡹⣿⠿⠛⠻⠛⠛⠛⢛⣋⣥⣶⣿⣿⣿⣿⣿⣿⣷⣤⣬⣉⠁⣁⣴⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣛⣉⠽⣟⣫⣴⣾⣿⠋⣾⣿⣿⡇⣴⣄
⠀⠀⢀⣴⣦⣄⣈⡙⠻⢿⣿⣿⣿⣦⡙⢿⣿⣟⠻⠛⠻⠿⠿⠿⢛⣫⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⢸⣿⣿⡟⢠⣿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣶⣤⡙⠿⣿⡿⢻⣾⣷⡾⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⣛⣯⣥⣤⣴⣷⣿⣟⣋⣠⣴⣿⣿⣿⢁⣿⣿⡿
⢀⣙⣙⠛⠛⠛⢿⣿⣿⣿⢿⣷⣾⡆⣷⣿⣿⣴⣷⣿⠛⣿⣿⣿⣎⢻⣿⣿⣦⠀⠉⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⠟⢡⣾⣿⣿⠇
⣿⣿⡿⠿⠛⢛⣛⠟⣽⢃⣿⣿⣿⡇⢹⣿⣿⣷⣹⣿⡇⢹⣿⣿⣿⣆⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢧⣴⣿⣿⡿⠋
⠋⣡⣴⣾⣿⣿⢋⣾⡇⢸⣿⣿⣿⡇⢸⣿⡟⢿⣿⣿⣿⡈⢿⣿⣿⣿⣇⢹⣿⣿⡇⠀⠀⠀⠀⠠⡄⠘⠛⠁
⣿⣿⣿⣿⠟⣵⣿⣿⡇⢸⣿⣿⣿⠇⣾⣿⣇⠸⣿⣿⣿⣷⠈⣿⣿⠿⠟⠀⠉
⣿⣿⠟⢡⣾⣿⣿⡿⢀⣿⣿⡿⢣⣾⣿⣿⣿⠀⠿⠿⠟⠛⠁
⠟⢁⣴⣿⣿⡿⠏⣴⣿⣿⣿⠇⠘⠟⠛⠉⠁

⠀⠐⢀⠀⠂⠐⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⢠⠀⠀⠂⠀⠈⠠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠁⡀⠀⠀⠀⠠⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠴⠀⠁⠀⠄⠠⠀⠀⠀⠈⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⠀⢀
⠘⠀⠀⠂⡀⠁⠀⠂⠈⡀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠐⠀⠉⠀⠂⠀⠐⢀⠀⠀⠀⡈⠀⠄⠠⠀⠀⠀⠐⠀⠀⢀⠀⠂
⠠⠀⠠⠀⠀⠂⠀⠠⠀⠁⠀⠀⠀⠀⡃⠈⠁⠀⢀⠁⠀⠁⠀⠀⠀⠂⠀⠀⠁⠀⡀⠈⠀⡀⠀⠐⠀⠰⠀⠈⠀⡈⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢠⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠄⠀⡁⠀⠀⠠⠁⠒⠈⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠄⠀⠄⠀⠁⠀⡀⠀⡀⠁⡀⠠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⢈⠀⠐⠈⠁⠐⠈⠀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⠀⡄⠠⠀⠂⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠐⠀⠰⠈⠀⠀⠈⠀⠄⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠀⠄⠀⠂⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡁⠘⡀⠐⠀⠐⠀⠁
⠀⠀⠀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢁⠀⠂⠄⠀⠀⠀⠀⠁⠈⠀⠁⠰⠀⠁⠄⠀⠀⠂⡀⠁⡀
⠀⠀⣀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠄⠈⠀⠁⠠⠀⠀⠀⠀⠂⠀⠄⠀⠁⠀⠀⠁⡀⠀⠀⠀⠁⠀⡀⠠⠄⠀⠠⠀⡄⠀⢀
⠈⢀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠐⠀⠀⡉⠀⠈⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠈⠄
⠐⢀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢁
⠀⠀⠀⠀⠉⢀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠈⠀⠄
⠐⠀⠤⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠤⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠄
⠘⣀⠀⢀⠀⢀⠀⠄⠀⠈⠀⠀⠀⠀⠠⠀⢀⠤⠀⠀⡁⢀⡀⢈⠀⠂⠀⠀⡀⠂⠀⠀⠠⠀⠃⠀⠀⠀⠀⡀⠀⠀⠂⠀⠁⠀⠂
⠡⠀⠄⢈⠀⠄⠀⠀⠀⠄⠐⠂⠐⠀⠐⠀⠈⢀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠂⢀⠀⠠⠀⠒⠀⡈⠀⢀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠂⠈⡀⠐⠀⠀⠡⠀⠀⠀⠂⠠⠈⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠂⠀⡁⢀⠀⠠⠀⠀⠂⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠁⠐⠀⠀⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠠⠀⠐
⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠈⠀⠈⠀⠐⠀⠂⡀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠐⠀⠐⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠈⠀⠁⠄⠀⡌⠀⠀⢈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⢀⠈⠀⠁⠀⠄
⠀⠀⠠⠀⠀⡀⠁⠀⠀⠒⠈⠁⠀⠠⠀⠁⠰⠀⠤⠀⠠⠈⠀⠀⠀⠄⠐⠠⠄⠤⢀⠀⠠⠀⢀⠈⠀⠂⠀⠠⠄⠈⠀⠄⠐
⠀⡐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠀⠠⠄⠄⠀⠐⠰⠀⠀⠁⠀⢁⢀⠉⠠⠀⠄⢀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⡄⠈⠁⠐
⠒⠀⠀⠠⠀⠂⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠠⠄⢀
⠀⣀⠀⡀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⡿⠀⠀⠀⠀⠀⠻⣤⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡀⠀⠀⠀⠈⠉
⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠛⠃
⠀⠀⠀⠂⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣀⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣏⡁⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡘⣿⠫⠁⠉⢁⣦⣀⠀⠀⠀⠀⠀⢈⠷⠦⠀⠀⠘⣛⡉⠀⠀⠙⠉⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠓⠚⠀⠀⠀⠀⠈⠉⠁

⣀⣀⣀⡀⠀⣀⣀⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⢀⡀
⣿⣿⠟⠛⠀⠙⢿⣦⣤⢰⣿⣷⣦⡘⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣒⣶⣆⢀⠀⠀⠀⣤⠶⠶⣄⡀⠀⠠⣀⠄
⠿⠃⠀⠀⠀⠀⠈⠹⢏⠀⢉⣿⣿⣟⣤⡀⠀⣴⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⡀⠈⠙⣿⠿⠋⠀⠠⣴⣾⠀⠀⠈⠁⠀⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠛⠛⠉⠉⠙⠃⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠺⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⣿⣧⠀⢀⣶⢀⣦⣼⣇⠀⠙⢰⣷⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⢶⡦⣤⢹⣆⠓⠘⠈⠀⠀⠀⣀⣤⣰⠛⣶⡆
⣿⣧⣶⣿⣿⣿⣿⣿⣿⢶⡦⠸⠋⠀⠀⡀⣤⠀⠃⣤⡟⠑⢂⣀⣤⡖⠀⠀⢀⠀⣹⠳⣆⡈⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠠⠼⠉⢀⡔⣿⣿
⠫⠙⠙⠝⠛⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠻⠂⠐⠏⠙⠉⠀⠀⠀⠈⠰⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⡜⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠂⠀⠀⢠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠛⠃⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠠⠀⠒⠒⠿⠀⠀⠀⠴⣶⠌⠻⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠠⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⣄⠀⠀⠀⠀⢦⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⣿⣿⣏⠉⠛⠿⢛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠘⠏⡀⢠⠄⠀⠀⠀⠠⠾⠟⠀⠀⠀⢠⡄⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠈
⠈⢻⣿⣷⠀⠈⠈⢻⣰⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠀⠀⠠⠶⠀⠀⠀⣤⣴⣶⣿⠇⣺⡽⣿⣂⣀⣠⡄⡄⠀⠀⣿⣿⡇
⡿⢿⠿⢿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡐⠐⢶⠄⠦⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠈⠡⡗⢤⢳⠄⣤⣱⠉⢨⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢹⣲⠇⠊⠀⠀⣼⣷⣦⣚⣙⡁⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡖⣸⣤⡾⠎⠀⠀⠀⠙⢯⣟⡟⣷⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠉⠁⣶⠆⠀⠀⣶⡆⠁⢸⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⢀⠄⠛⠳⣤⠴⡋⠗⢀⣼⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠗⡄⠇⠀⠀⠘⠀⠀⠁⠀⠘⢿⣷⣜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠁⡄⢸⠀⠀⠀⠀⠀⢰⠀⡄⣎⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣏⠀⢄⠀⣸⠀⠀⠀⠀⠀⠸⡁⠀⠏⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠎⢈⠁⠀⠄⠀⠀⢀⠀⠉⠀⢲⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠛⠃⠀⠂⠀⠀⠐⠀⠄⠀⠀⠘⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠣⢀⣀⣀⣀⠀⠠⠤⠔⠓⠒⠒⠐⠒⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠋⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣀⣤⡤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢹⡆⠀⣴⠀⠀⠀⠀⣴⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠈⠉⠱⠶⣄⡀⠀⠸⣷⠀⠘⣧⠀⠀⠀⣿⠀⠀⠀⣾⠁⠀⢸⡇⠀⠀⢀⡴⠾⠉⠁⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⢹⣧⠀⢿⡄⠀⠀⣿⠀⠀⣰⡏⠀⢰⡏⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠙⢿⣿⣇⠈⣿⠀⠀⣿⠀⢀⡿⠃⢠⣾⣱⡟⠋⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⣿⣆⠸⡇⢀⣿⠀⢸⡇⢀⣾⡿⠋⢀⣴⠟⠁
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠀⠙⢷⣆⠈⣿⡾⠛⠛⠉⠉⠉⠁⠾⠟⢁⣴⠟⠁⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣄⡀⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⢀⣤⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠙⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠾⠿⠿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⣤⢤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣤⣤⡤⢤⣶⣶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠛⠉⢁⣬⡿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣌⡉⠙⠻⠷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠋⠁⣀⣠⣶⠟⠛⠁⢀⣼⠛⢷⣶⣶⣴⣶⡚⠻⣦⡀⠈⠛⠷⣦⣄⡀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⠀⢀⡰⠾⠋⠉⠀⠀⢀⣴⠟⠁⢠⡾⠀⣼⡇⠈⢷⡄⠈⠻⣦⡀⠀⠀⠉⠙⠶⢄⡀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⡿⠁⢠⡿⢿⡀⠈⣷⡄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄
⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣠⡿⠀⢀⣿⡇⢸⣿⠀⠈⢿⣄⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢠⡼⣿⡄⠈⠹⢧⡀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠾⠁⣸⡇⢈⠀⠘⠷⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠹⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⣀⣠⣤⡶⠒⠒⠛⠻⠲⠶⠢⣤⣤⣀⠀⠀⠀⠀⠀⠀⣾⡇⢻⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠿⠛⠛⠷⠒⠲⢶⣄⣤⣀
⠀⢠⣶⠋⠉⠀⢁⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠀⠀⠀⣿⡇⣸⠇⠀⠀⠀⢀⣴⡿⠛⠀⢀⠀⠀⠀⠀⡀⠀⠀⢠⡎⠀⠉⠙⢻⡦
⠀⠈⢁⡀⠀⠂⣾⣧⡀⠀⢱⡄⠀⠀⢰⡆⠀⠀⠄⠈⠻⣦⡀⠀⣿⡇⠹⡆⠀⢀⣴⠟⢁⠀⠀⠀⠈⠀⠀⠀⠸⠇⠀⢠⣶⡔⠂⠀⠀⠘⠁
⠀⠀⠈⠠⠄⠛⠁⠀⠈⢛⣿⠷⢄⣀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣄⢸⠃⢠⣇⣰⣿⠁⠀⢸⡇⠀⠠⡇⢀⣀⡴⢿⣞⠛⠀⠀⠙⠃⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠁⠀⠈⠉⣽⠿⢦⣄⣸⡇⠀⠀⡜⢻⣿⡆⢸⣿⡟⠃⠀⠀⣨⣤⣤⠾⢿⡍⠉⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⠛⠃⢠⣿⠀⣻⡇⠸⡏⢰⣦⠀⠚⠛⢧⣀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠋⠁⠀⠀⠰⠊⣉⣤⣿⡇⢸⣿⣄⡉⠒⠀⠀⠀⠉⠲⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣦⣤⣴⣶⡶⠟⠛⠋⠉⠁⣿⡇⠘⡏⠀⠙⠛⠛⠷⢶⣶⣦⣴⡶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠁⠈⠋⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢔⣠⣾⣿⣿⣿⣿⣿⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣁⣥⠖⠛⠛⠛⠿⣿⣿⣿⣿⣿⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⣒⣂⡀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣹⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣆⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⢰⣯⣥⣾⠃⠀⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡿⣿⣿⣿⣿⣧⡀⠀⠈⠈⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠹⣿⣿⣿⣿⣿⣷⡶⠆⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⡄⣈⣛⣛⣛⣛⠻⢫⡄⠀⠼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠟⠉⠙⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣧⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿⣿⣿⣿⣆⠈⣻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣾⠟⠛⠟⠚⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠊⠁⠀⠀⠀⠀⠺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⠛⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠦⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣗⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡤⣌⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠈⣣⠈⠃⠐⠂⠉⠉⠉⠉⠒⠁⠐⠃⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢒⣠⣤⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⢠⣴⢴⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠉⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢤⢴⢶⠃⠀⠀⠀⢐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣬⠄⡄⠀⢠⠀⠤⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠲⠶⢺⡃⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡸⠀⠀⠀⢀⠈⡈⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⡤⠐⢒⣾⣇⣉⣿⣿⣃⣀⣀⣲⡀⠘⡄⠀⠀⠀⠈⢆⡈⠊⠔⠕⠐⢐⡴⠃⣀⠀⠀⢈⡈⠁⠀⢀⣍⠩⢁⣄⢈⣩⣁⣀⣀⣈⠑⣂
⠀⠀⠀⠀⠀⠀⣿⠒⠺⡾⡧⢼⣟⠂⠤⠧⠶⢿⡇⠀⠈⣦⡀⠀⠀⠀⠈⢁⡒⠲⠒⣋⡠⠚⠀⢀⠠⠋⠀⠀⠀⠈⣏⡛⠀⣛⣛⣹⡇⠠⡿⣿
⠀⠀⠀⠀⠀⠀⢾⣍⣹⣟⡗⠲⢿⣉⣐⣛⣛⣻⣧⠀⠀⠂⢙⡢⡀⠀⢀⣀⠈⠉⠉⠀⡀⠀⡀⡀⡀⢸⠀⠀⠀⠀⣶⠄⢨⣭⡭⠷⣯⢉⣯⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠢⣤⢭⣭⠿⠟⠒⠀⠲⣄⡐⡠⠊⠔⠋⣽⣿⡏⠫⠨⠊⠌⠄⠂⠼⠀⢰⠮⠭⢁⣠⡴⡬⣿⣻⣷⢤⢷⠟⠚⠌⠚⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠇⣀⣀⣴⣳⡍⠙⠋⠛⠋⠍⠈⠝⠒⠶⠲⠖⠞⠋⠐⠀⠘⠗⠲⠲⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⢥⠥⠶⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




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

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⣀⣀⣀⡀⠀⣀⣠⣔⢂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣻⣿⣿⣿⣿⣿⣿⢿⣿⡤⢐⡀⣀⠀⠀⠀⠄⠈⢷⡀⠈⢮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣼⣿⢸⣿⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠙⢷⣾⣧⣠⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣚⣿⡿⣻⣿⣧⡈⢷⣿⣷⣔⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣽⣸⡿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣿⠿⠉⠛⢿⣿⣾⢿⠉⠋⠛⠿⠿⠤⠀⠀⠀⠀⠀⠑⢹⣿⣿⣿⣿⣿⡿⠛⠛⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢛⣹⣿⣿⣧⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣠⣾⣷⡿⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⠿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⣀⣀⠀⠀⠈⠀⣈⡴⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⡏⠛⠑⣲⠚⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄
⠀⠀⠁⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⣼⡇⢸⣿⣧⠙⣿⠃⢸⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⢹⡇⢸⣯⣿⠀⣿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠛⠘⠃⠙⠁⠛⠁⠋⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⣤⡴⠆⣶⢸⡆⢿⣟⠀⣿⢹⡇⢹⣿⡏⢸⡏⣿⢸⣷⣾⢰⡶⠆⠀⢀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣇⠠⠈⣿⠀⢹⣿⡇⢸⡏⠀⣿⢿⡇⠀⣿⠁⢸⣇⣿⢸⣿⣿⣸⠋⠀⠀⠛⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠨⡇⠀⠙⠶⠀⠻⠃⠘⠛⠃⠛⠈⠋⠀⠙⠀⠈⠙⠋⠘⠋⠃⠛⠃⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠦⠒⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⣖⠀⠀⠀⠀⣀⠀⠀⡀⢐⠀⠥⠒⠉⠀⠀⢀⡀⢠⠜⢲⡀

⠀⡤⠀⠀⠦⠀⠀⣀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡶⠀⠀⠒⠀⠀⣠⠀⢠⡄⠀⠀⠆⠀⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡦⠀⠀⠂⠀⠀⣄
⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠀⠃⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠠⠄⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡴⠀⠀⠰⠀⠀⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡶⠀⠀⠒⠀⠀⣤⠀⠀⣀
⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠖⠀⠀⠒⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠀⠶⠀⠰⠆⠀⠀⠃⠀⢀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠶
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠺⠂⠀⠰⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠿⠀⠀⠄⠀⠀⠀⠀⡄
⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⢤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣄⠀⠀⡄⠀⠀⡀
⠀⠋⠀⠀⠉⠀⠀⠶⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠛⠀⠘⠃⠀⠀⠁⠀⠠⠶⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠛
⠀⠀⠀⠐⠂⠀⠀⠀⠀⡴⠀⠀⠐⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡶⠀⠀⠒⠀⠀⣤
⠀⡀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠁⠀⠀⠐⠂⠀⢀⡀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠀⠀⠀⠁⠀⠀⠰
⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠒⠀⠀⣤⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠂⠀⠀⣤
⠐⠀⠀⠀⠀⠀⠐⠗⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠇⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⣠⡀⠀⠠⠀⠀⡀⠀⠋⠀⠀⠀⠀⠀⠺⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠀⠀⡀⠀⠋⠀⠀⠀⠀⠀⠿⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠂
⠐⠀⠀⠄⠀⠀⠀⠀⡄⠀⠐⠀⠀⢠⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⡄⠀⠐⠀⠀⡤⠀⠀⡄⠀⠀⠀⢠
⢀⣀⠀⠀⠀⠐⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⠐⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢠⡄⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐
⠀⠀⣹⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⠀⠙⠃⠀⠀⠀⠀⠋⠠⡵⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢤⠄
⠀⠀⢻⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⢀⠀⢀⣀⣀⠀⡀⠓⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣠⠀⠈⠰⠦
⠀⠀⠰⡀⠀⢠⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠨⣿⣿⣿⡿⠿⠟⠻⣿⣿⣦⡄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠐⠄⠃
⣦⠀⠴⠄⠀⠈⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⠀⢀⣄⣀⡌⠀⠙⠛⠁⠀⠀⠀⠁⡀⠀⠀⠠⠀⠀⠁
⣿⠙⠒⣦⠀⠘⠀⠀⣬⠀⠈⠆⠀⠀⠠⠀⠀⠀⣀⡀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠴⠣⠄⠠⠀⠀⠀⠘⠀⢠⠀⠀⠐⠀⢀⠥⢀⠆⠠
⢻⢄⠀⠈⠀⠃⠀⠀⣽⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⣶⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⡇⠀⠀⠄⠄⠀⢀⠀⠀⠀⡤⠇⡉
⠀⢯⣠⡀⠉⠁⠀⠀⣽⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠘⣿⠟⢀⡠⡮⡰⠐⠊⠍⠀⠀⠀⣔⠀⢠⣰⣿⡀⠀⠀⠀⠠⣄⠠⠧⣀⣄⢘⠃
⠃⠉⢀⠙⠄⠰⡄⠀⢺⣁⣸⡀⠀⠀⠀⠀⠀⠀⠤⠀⠙⣇⠬⠴⠁⠸⠂⠀⠀⠀⡞⢡⠈⠒⠀⣯⡣⠀⠀⠀⠁⠀⠨⠶⣌⠉⠄⢀⢴
⠀⣰⠏⢳⡄⠀⠆⠀⣽⠛⣿⣧⢀⡀⠀⠀⠀⠀⡀⡘⢀⠃⠒⠚⢃⣸⠏⣰⢤⣻⠃⣻⠀⣦⢢⣽⠃⠀⣄⠀⠀⠀⠀⠀⠈⠛⢁⠂
⠀⠁⢀⠀⣷⢀⣶⢆⣟⠀⡟⢹⣏⠁⠀⠀⢀⠄⣿⠇⣼⠆⠀⠀⢪⢈⠓⠈⠠⣬⡁⠛⣦⠜⠮⠝⠃⠀⠈⢢⠔⡀⠀⣀⠀⣠⠈⠐⠆
⡰⠄⠀⠓⠮⠋⠖⠀⣼⠰⠉⠙⣽⠳⡄⢀⡌⢠⡟⠀⠠⠓⢦⡆⡠⠈⡀⠀⠀⠀⠀⣾⣼⣷⣄⣠⠀⠐⢰⡰⢰⢰⠐⠣⠠⠘⠂
⠀⢼⣴⣆⣠⡠⡾⠿⣿⠦⠋⢸⣽⠀⢲⠀⢰⡶⡶⠄⡄⠸⣬⢞⣓⢺⡏⠉⠀⡠⠀⠸⣺⣯⡄⡧⠀⢀⣉⡀⣸⡞⡉⠃⠀⠁⠀⠶⡀
⠆⠈⣥⣄⠐⣛⣷⣀⣿⡄⠐⠢⡍⢀⡨⠴⢦⣞⠁⢠⠛⠞⠀⠀⠀⢾⣁⣠⡜⠱⢶⡢⠍⠫⠛⣰⠆⡙⠛⠁⠛⠁⠒⣮⡳⠄⣤⣤⠙
⠻⢎⣿⣿⢡⣬⣭⡙⣿⢛⢀⠀⠸⠀⣷⣶⣾⣿⣷⣷⣴⡎⢀⠀⠶⡟⣵⠞⢆⣿⣺⣀⣗⠘⠋⠽⢨⡅⠠⠀⢠⣄⣠⠬⠁⣹⠘⠓⠷
⡖⠺⣟⠿⠿⢋⣙⣿⠁⡀⠀⢴⡄⢨⣯⣾⠽⠿⢿⣿⠀⠒⠤⠀⠘⣝⡯⢙⠈⢻⢿⢿⠏⠙⣠⠗⠃⢩⠑⢆⣼⠾⢻⣤⣺⣭⠶⣄
⠉⠴⣿⣀⢴⡄⢀⣤⢞⣿⣿⠶⣲⢻⣏⡈⢥⣷⠓⣿⣄⣤⡖⢠⣮⣯⣗⡁⢀⠉⠻⡇⠃⢄⢘⡂⠺⢻⠄⠻⢳⢛⣬⣷⢷⢻⡙⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙⠓⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠳⡌⠳⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⢴⠖⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄⠈⢧⣀⡤⠦⠷⢧⣄⣠⠞⢁⠎⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⠐⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⢁⡄⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢔⡒⠂⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠤⢤⡀⠙⣦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⣠⠤⣄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠀⢸⣷⣞⣹⡄⠀⠀⠀⢾⣿⣸⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⠀⠀⠀⢀⠀⠺⢿⣿⡿⠀⠀⠀⣠⣜⣿⠟⠋⠀⠄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠈⣴⠗⠋⠁⠀⠉⡳⣄⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⡸⠉⡆⠀⢎⣸⠈⡆⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⢄⡙⢋⣡⠦⣤⠥⠜⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠚⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⡏⠀⠔⠊⠉⠉⠙⠲⢽⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠓⠢⠤⠀⠀⠀⠀⠀⠀⠀⠒⣱⠃
⠀⠀⠀⡀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠠⣦⡀⠀⠀⠀⠀⠀⡀⠀⢀⡼⠥⠤⣄
⠀⠀⠀⠱⣜⠬⠼⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢑⢒⢦⡙⢦⡀⠀⠀⠀⡇⢀⠎⠀⡰⢀⡞
⠀⠀⠀⠀⠀⠉⠉⠈⠲⣄⡀⠀⠀⢀⡀⠀⠎⢈⠟⣸⣁⣠⢵⡀⠀⠂⢳⣨⠟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠋⠓⠲⢼⠔⠁⠀⠀⠈⠓⠒⠙⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤
⠀⢨⣿⣿⢟⢿⣿⣧⠀⠀⠀⣰⣞⡛⣳⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠶⢤⠁⠆⠰⠆
⠀⠸⣿⣯⠈⠠⣿⡗⠀⠀⢠⡟⠛⠁⠙⠛⡇⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢿⣤⣬⣇⠁⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⢶⢆⣶⣶⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠤⠤⠤⠆⠀⠀⠂⠀⠉⠉⠈⠉⠈⠀⠀⠀⠠⠄⠀⠤⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠻⡿⠿⠃
⠀⠀⠀⠀⢀⢀⠀⠀⣈⠥⠀⠀⠰⣠⡆⣴⢰⣴⢰⠀⣤⣤⢀⡆⣦⢰⠀⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠐⠻⠳⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠈⠈⡈⡀⣁⡈⡀⡅⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⡄
⠀⠀⢠⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿⡶⣾⣏
⠀⠀⠀⠁⠈⠁⠁⠀⠀⣶⡄⠀⠀⢠⣶⠀⠀⣀⣻⠟⢉⠙⢿⣃⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⠙⢹⣿
⠀⠀⠀⠏⠀⢒⣛⠀⠀⠘⡇⠀⠀⢸⠇⠀⠀⣭⣿⠀⠀⠀⢈⣯⡅⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢹⡷⣶⣶⣿⡍⠁⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣶⣾
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣍⠀⠀⠀⠀⠶⠖⠀⣬⣿⡄⠘⠿⠗⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⣰⠟⠻⣦⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⢻⣦⠀⠸⠇⠀⠀⢹⡇⠀⢠⡾⠉⠙⣷
⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⣿⡀⠀⠀⠹⣧⣶⠀⠀⠀⠈⣷⣴⠏⠀⠀⠀⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢿⠋⠈⠙⠻⣦⣼⣇⠀⠀⠀⠘⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⢸⢀⡴⠞⠋⠀⢙⡇
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠙⢿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⢰⡿⠋⠀⠀⠀⢀⡿⠁
⠀⢀⣠⣤⣤⣄⣈⣻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⣤⣤⣤⣄
⠀⢸⡇⠁⠀⠉⠙⠛⠻⠷⠆⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠉⠁⠀⠀⢸⡇
⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛
⠀⠀⣀⣀⣩⢿⣶⣤⠀⠀⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡿⣉⣀⣀
⡴⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳
⠁⠄⣠⣤⣀⣀⣀⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⠶
⠀⠀⠈⠉⣉⣽⠿⠛⠁⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⢸⣇⠀⠀⠀⣀⣀⣴⡶⠉⠀⠀⠀⠙⠷⣦⣄⣀⣀⣀⣀⣀⣠⠖⠋
⠀⠀⠈⠉⠉⠁⢀⡸⠋⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⢀⣠⣾⠇⠀⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢺⣥⣠⣤⠶⠋⢰⡟⠀⠀⠀⣼⠛⡇⠀⠀⠘⠛⡆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣼⠁⠀⢀⣼⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠠⠿⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⡅
⠀⠀⠀⠀⠀⠀⣀⡤⣤⢤⠤⠰⣶⣤⣄⣀⠀⠀⢨⣿⢀⡃⠀⠀⢀⣀⣴⣶⡶⢤⡤⠶⣤⣀
⠀⠀⠀⣤⠶⠋⠉⠀⠀⠀⠠⠀⠀⠠⠈⠙⢿⣦⣸⣿⢀⣇⣴⡾⠟⠉⠄⠀⠀⠆⠀⠀⠀⠉⠙⠷⣤⡀
⠀⠀⠾⠃⠀⠶⠶⠒⣿⠖⠶⠿⠶⠒⡶⠆⠈⠆⣹⡟⠸⣏⠐⠁⠐⣾⠂⠶⣿⠶⠲⢾⠒⠲⣷⠀⠀⢹⡷
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠐⢀⣠⡴⠀⢉⡄⢀⡏⠀⠠⣄⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠋⠉⠀⠀⢸⣿⢞⡁⠀⠀⠈⠙⠛⠳⠦
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠶⠶⣶⣤⣄⡀⠀⠀⢸⡏⢸⡇⠀⠀⠀⣀⣤⣤⡤⠤⡤⢤⣤⡀
⠀⠀⠀⣠⣶⠟⠉⢀⠀⠀⠠⠀⠀⠀⠈⠛⢷⣦⣸⡏⠸⣇⣠⣶⠟⠋⠈⠁⠀⠀⠀⠀⡀⠉⠛⠶⣤⡀
⠀⠀⢾⡉⠀⣶⠤⠠⠶⠤⠤⣶⠤⠠⣶⠄⢠⠍⣹⡇⢰⣿⠭⡅⠤⣾⠄⠤⣶⠠⠤⠾⠀⠠⣶⠀⠈⢹⡧
⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠠⠁⠀⠐⢀⣠⣬⠞⢹⣇⢸⡟⠳⢦⣄⡈⠂⠀⠈⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠞⠛⠉⠀⠀⢸⡿⢸⡇⠀⠀⠈⠛⠻⠶⠦
⠀⠀⠀⠀⠀⠀⢀⣀⣠⢴⠦⢶⣦⣄⣀⡀⠀⠀⢸⡇⢸⡇⠀⠀⠀⣀⣠⣤⡤⢤⡤⢤⣀⡀
⠀⠀⠀⣀⣴⠟⠉⠉⠁⠀⠠⠀⠈⢉⠉⠻⢷⣤⣸⡇⠀⢁⣠⣴⠟⠋⡉⠁⠀⠄⠀⠀⠉⠉⠒⢦⣄
⠀⠀⣾⠋⠀⣶⠄⠀⣶⠀⠀⣷⡄⠀⣶⠀⠈⠏⣻⡇⢰⣟⢻⡁⠀⣶⠀⢠⣏⠀⠀⣶⠀⠀⣶⠀⠉⢻⡦
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠉⠀⠐⠁⣠⣴⠞⠻⠇⢠⡟⠳⢧⣄⠀⠀⠀⠉⠄⠀⠈⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠖⠛⠋⠁⠀⢸⡆⠀⠃⠀⠀⠙⠛⠛⢶⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣤⣄⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄
⠀⠀⠀⣀⣴⠖⠛⠉⠀⠀⢀⠀⠈⢉⠙⠻⣶⣄⠈⠃⠀⠀⣠⣴⠾⠛⡉⠁⠀⠄⠀⠀⠈⠛⠳⢦⣀
⠀⠀⣴⠏⠀⣶⠄⠀⣤⠀⠀⢷⠤⠀⣶⠀⠘⡍⢻⡇⢠⡟⠿⡅⠠⣶⠀⢤⣾⠀⠀⣤⠀⠤⣴⠀⠈⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠁⣀⣤⠖⢻⡇⠀⠙⠶⣤⣀⠈⠀⠀⠁⠄⠀⠀⠂⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠞⠋⠀⠀⢸⡏⠀⠀⠀⠀⠙⠳⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣴⣶⣤⣶⣴⣶⣶⣦⣴⣤⣤⣶⣶⣶⣶⣶⣶⣦⣴⣶⣦⣴⣶⣶⣦⣤⣦⣴⣶⣤⣶⣶⣶⣶⣶⣶⣶⣤⣶
⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⠆⠀⠀⠃⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣤⣤⣴⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡀⣢⣉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⣿⣿⣿⣿⢿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣆⢢⣲⣶⣠⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⣜⣶⣿⢿⠎⠑⡛⢽⣿⣟⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡔⠃
⡀⠀⠀⠀⠀⢠⣟⡫⠇⠈⡀⠀⡇⠈⠈⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⡀
⢿⠆⠀⠀⠀⣞⣛⣒⠀⠂⡆⠀⡇⠀⢈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠤⠤⠤
⣾⡆⠀⠀⠀⠴⣖⣚⠀⠀⠹⡿⠇⠀⠈⣙⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⢂⢀⡀⠀⠀⠀⠀⠀⠀⣾⣤⣦⣄⠀⢠
⣿⡇⠀⠀⠀⠈⠟⣶⣧⠀⡀⣐⣀⣀⢠⣻⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠒⠻
⡻⠃⠀⠀⠀⠀⠘⠻⣻⣿⣿⣿⣴⣷⣿⠏⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⠀⠒⠒⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣶⣦⠠⣶⣶⣶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⣄⡀⡀⡄
⠀⠀⠰⠖⠂⠀⠀⠀⠒⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠼⠍⠉⢼⢗⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⣀⡿⣿⣿⡂
⠀⠀⠀⠀⠈⠡⠻⠓⡈⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠀⠀⠀⠤⣯⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⣤⣼⣿⢚⣛⡁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢲⡞⠂
⠀⠀⠀⠘⡀⢸⠀⠐⠀⡰⠁⠈⠀⠀⠀⠀⠀⡴⢧⡖⠀⠀⠐⠊⠀⠈⠹⣮⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⠠⠀⢠⣥⡀⠄⢰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿⡷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣿⣿⣤⣾⣆
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⡿⢿⠿⡿⢿⣿⣧⣶⣦
⠀⠀⠀⠈⠁⠙⣿⣿⡅⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⡆⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢀⠠⠀⠛⣿⠃⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⡇⠀⠃⠆⠸⣿⣿⣿⠗
⠀⠀⠀⢸⠛⠰⣶⣶⡆⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠂⠈⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⢷⠇⠀⣿⣿⣿⡶

⢸⡷⢤⣀⣀⣀
⠀⠹⡖⢄⠀⠈⠉⠙⠒⠤⡀
⠀⠀⢧⠀⠑⡄⢀⣀⠤⠄⠘⠒⠒⠲⠤⢄⡀⢀⡠⠔⠒⠒⠒⠒⠒⠲⠤⠤⣖⡆
⠀⠀⢸⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⢀⡠⠔⢢⠟⠋
⠀⠀⢨⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢠⠃
⠀⢠⠇⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⣠⠃
⢠⠞⠊⠉⠉⠐⢦⡀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠥⠤⢤⣀⡀
⡇⢔⡆⠀⡤⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⣀
⠑⢄⡀⠀⠉⢁⡠⠃⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢰⡟⠛⣷⣀
⠀⠀⠹⣍⠉⠁⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣶⠿⠋
⠀⠀⠀⠘⠿⡇⠒⠒⡎⢁⠇⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⠀⠀⠀⠀⠀⠱⣄⣀⡳⢊⣔⣀⣀⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢃⠀⠀⠀⠀⠀⢠⣀⢤⡤⠘⡄⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⢂⠀⠀⠀⢀⡎⢀⡴⢳⠤⢸⡄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⠜⠉⢹⡆⠀⠀⡜⠈⠳⢖⡡⣤⡼⢳⠠⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢒⡾⣋⠌⠉⢹⠁⠀⠀⠀⠈⠳⣖⣡⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠉⠄⠉⠑⢄
⠀⠀⠀⠀⢠⠖⠉⠀⣀⠠⠂⠁⠀⠄⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠇⠀⠈⠀⠈⠀⠀⠂⠀⡀⠀⠰⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣬⡀
⠀⠀⠀⠀⢇⠈⢁⠀⠉⠀⠋⡀⠀⠀⠀⠀⠀⡠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡎⠐⠾⠓⢹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⠀⠁⢠⠋⠉⢆⠀⠰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⠀⠀⡧⣀⣀⣀⠜⢦⡀
⠀⠀⠀⠀⠀⠸⡌⠀⣾⠉⠙⠒⠋⠀⠀⠈⠂⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⠀⡁⠐⠀⠬⠀⠈⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡠⡶⡻⠃⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⣩⠊⡴⠁⠀⣇⠑⠤⣆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠁⢰⠁⠀⠀⠈⢦⡀⠀⠉⠳⣽⢦⡔⢢⢀⣤⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⣠⡎⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣦⣹⠃⢸⠤⠻⢖⠚⠉⡦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠒⡏⠀⢸⣇⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⣠⠣⣈⠒⢛⣦⣀⠠⢵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⢄⣾⠀⠑⠒⠚⠢⠄⣈⠷⠤⠠⡤⠚⠉⠉⠉⠀⠏⠉⠣⡀⠀⠑⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠂⠉⢸⡁⠒⠪⠕⣤⠊⠉⠢⠔⠉⠑⠤⠊⠉⠲⠊⠙⢦⠖⠻⢶⣀⣉⠯⠽⠥⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⠀⡏⠒⢶⠐⠸⡆⠀⠐⡄⠀⠀⡆⠀⠀⡛⠀⠀⣇⡤⠚⡉⠀⠠⠀⠀⠂⠀⠠⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠰⠀⠘⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡼⠃⠀⠂⠀⠀⣠⢄⠴⠛⢤⣀⠀⢁⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⢱⣀⡈⡆⠀⢸⠀⠀⠁⠀⢰⠁⡜⠀⠈⡁⠉⢔⡲⠗⠂⠉⠉⠐⢦⠇⠄⠐⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣧⠄⠠⢔⠂⠘⠿⠁⠀⠈⢷⡀⠀⡆⠀⠀⠀⡸⢠⠅⠈⠀⠀⠂⡈⠣⢄⣀⣀⡀⠤⠊⡀⠀⢠⠲⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠘⡂⠀⠀⠀⠀⠀⢸⠥⠄⠁⠀⠀⠤⠅⠤⠵⡞⠦⠚⢢⠀⠀⠀⠁⠄⠐⢀⠁⢀⠤⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡸⣁⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠓⠒⠉⠑⠤⠔⠉⠁⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠖⠊⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⡀⠤⠔⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠀⠀⠀⠀⣷⠦⣄⣀⣠⣤⣄⡀
⠀⠀⠀⠘⡏⠙⠓⠒⢾⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠸⠄⢀⡠⢼⡄⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⣀⣠⣤⠤⠖⠋⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⠶⡄
⣞⢉⡇⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢯⡰⢁⣶⡆
⢧⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⢸⠋⠓⠺⣏⠀⣀
⠀⠁⠑⠦⢤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣠⠤⢤⣀⣀⣀⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⡀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠙⠲⢤⡀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⢳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡿⣿⣿⣿⣿⣡⣴⣿⣭⣭⡟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⠛⠉⠙⠿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⢶⠀⠀⠰⠾⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡇⢰⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢈⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣝⢻⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⣻⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⣿⣧⡉⠻⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⣀⡶⣶⠄⠀⠆⠀⠀⠀⠀⠈⡎⣹⣿⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣿⣆⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣠⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡌⢻⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣶⣿⣴⣤⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⢹⣿⠟⠿⠇⠀⠈⢻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠁⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣦⣀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡶⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠶⠖⠂⠀⠠⣈⠛⠓⠀⠀⠀⠉⠛⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠐⢦⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⣀⠀⣰⣄⠀⡀⠀⣼⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣯⣴⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠘⠋⠈⢋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣄⣤⣝⠈⠁⠀⠀⠀⠤⣴⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡄⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣪⣠⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⣄⢀⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⡇⢀⠀⢀⠸⠿⠿⠿⠦⠤⠄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠛⠉⠙⠛⠿⠟⢻⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠁⡀⠀⠂⠀⠀⠐⠃⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢠⠢⢈⣶⣤⣤⣤⣦⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⠀⠀⢀⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠐⣄⣶⣤⣂⠤⢄⡀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⢀⠠⠤⢔⣦⡴
⠀⠀⠀⠈⠛⠿⣛⣷⡄⠙⢦⠐⠀⠉⠀⠀⠈⠀⠒⠔⠃⢀⣾⡿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡀⢀⡠⣠⠂⠁
⠀⠀⠀⠀⡀⠘⠿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠈⣼⡇
⠀⠀⠀⠀⢠⠀⠀⠨⢿⠁⢐⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⣿⠅⠀⡀⠀⠀⠀⠀⠀⢠⠃⠀⣀⡀⠀⢿⠠⠘⠁⠀⠐⠀⠀⠀⠀⠒⠤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠺⠀⡻⠃⠀⠀⠀⠀⠀⠀⠘⢿⡚⠟⠂⠀⠊⠀⠀⠀⠀⠀⠀⠼⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⡤⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠃⠘⠁⢐⠀⠀⠀⣴⠘⡀⢀⣀⠀⣀⣠⣤⠀⠀⠐⠒⠠⢤⡤⠔⠂⠀⠀⠀⠀⢸⡆⠀⠀⢠⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠓⣾⣷⡶⠋⠀⢀⡴⠁⢀⠀⠉⣿⣿⣋⠹⠿⣀⣀⣀⡀⠀⠀⠳⠠⣄⣀⣤⠀⠀⢸⣁⣀⣀⣾⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠲⣤⡀⠀⢐⣫⣴⠖⠋⠀⠀⣼⡄⠀⣜⣋⠀⣶⡄⠀⠸⣿⣿⣷⡆⠀⢳⠘⡇⢈⠀⢠⠏⠉⠉⣹⢹⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⣀⠀⠀⠈⠉⣡⠀⠀⠀⢰⣿⠃⠀⠀⠓⠾⣿⢴⣿⣠⣿⣿⣿⠃⠀⠠⠀⡇⠸⠀⡟⠀⠀⣰⣡⠾⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣶⣤⣤⣶⠋⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⢹⣿⠟⠉⢹⢻⡇⠀⠀⠿⠞⠁⠵⠶⠃⠁⠀⠉⠑⠷⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠉⠙⠛⠛⠂⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⠐⠋⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣛⡻⣿⣭⣯⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣗⣿⠁⠀⠀⠀⠀⢀⡀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⢿⣟⣒⣂⠀⠀⣫⣭⣥⣄⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⢻⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⣿⡿⣹⣿⣿⠟⠀⠀⠙⠿⠿⠋⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣰⣿⣟⣿⣧⡀⠀⠲⠶⠂⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⣾⣵⣟⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢳⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣾⢿⢻⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠸⡿⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⠃⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠿⢶⢤⣦⣤⣄⣄⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣾⣿⢃⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣏⣹⣿⢷⣽⣤⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣡⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡄⢿⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠌⢧⣴⣾⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠐⣾⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠀⠈⠻⣧⣼⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⢉⣭⡀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢻⡇⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢺⣦⣤⣄⡀⢐⣚⣿⣿⡟⠋⢱⡄⠀⠀⢀⣾⣿⣿⣿⡿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣧⣤⣤⣴⣾⠟
⠀⠀⠀⢸⣿⣿⣿⡟⢹⣿⣾⡏⠀⠀⠀⠻⣆⠀⣾⣿⣿⣿⣿⡁⠀⢸⡇⠀⢀⣄⢀⣠⣤⣾⣶⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⢠⡹⣿⣿⣼⣿⣾⣿⢶⣶⣄⠀⠀⠙⣦⢹⣿⣿⣿⣿⣷⣶⣾⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⢻⣿⣿⣿⢟⠛⣻⣾⣏⣿⡿⠀⠀⠘⣷⡿⠛⢤⠙⢻⣿⡛⠋⢿⣿⣿⣿⡏⠉⡕⠋⢙⠋
⠀⠀⠀⠀⠀⠙⣿⡷⢾⡶⢏⠁⣹⣧⣿⢦⣄⠀⠉⠠⠀⡚⠀⠀⢿⡿⣤⠛⣿⡿⢏⣳⣤⣤⠈⠀⠈⣀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠙⠳⣶⣾⣿⣿⣿⣿⢧⠈⣿⣾⣿⡆⣙⣁⣼⣧⡜⣋⠀⠸⣯⣠⣿⣿⠛⣿⠆⠀⠦⠀⠾⠿⢿⣿⣷⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⣾⡷⢿⠁⠀⠈⠙⠛⢿⣅⣤⣍⠀⢠⣿⣿⣻⣷⡶⠀⠀⠀⠀⠀⠀⠠⠾⠿⣿⣷⣾⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠀⣽⣇⡤⣤⠀⠀⠄⢾⣆⡘⠙⢿⣿⣄⣸⣿⡛⢿⣿⣷⣆⡀⢠⡆⠀⠀⣀⣤⠖⠛⣿⣿⣿⠄⡁
⠀⠀⠀⠀⠀⢀⣀⠀⣀⣘⣿⢖⣷⣿⣯⠀⢙⢷⣀⣀⣈⠛⠃⠀⣼⠟⣠⣤⣼⣿⡟⣿⠀⠀⠀⠿⠟⢋⣈⣩⠀⡄⠀⣼⣿⣧⣿⠆
⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⡉⠉⠉⠹⠄⠈⠉⠻⠈⢿⡷⠈⠁⠄⢸⣷⣦⡄⡰⠋⠀⠈⠀⠀⠀⠘⣿⣿⣿⡿⠂
⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⡟⣛⣛⣷⣶⣾⣿⣇⣀⣠⣴⣿⣆⡀⠀⢀⡀⠀⠀⠀⠀⠸⡿⠿⠟⠁⠀⠀⠀⣴⣀⠀⣤⣏⣿⣿⣿⡀⡀
⠀⠀⠐⢈⠛⢿⣷⣿⣿⣿⠾⣭⣿⢟⣿⣧⣿⣿⣿⣿⠋⠹⡟⢡⣴⣾⠃⠀⠀⠀⢀⣿⠁⠀⠀⠰⣤⣀⣼⣿⣍⠉⠀⠉⠙⣿⣿⣿⣤⣄⡀
⠀⠀⠀⢻⣷⣿⣿⣿⣿⠛⢶⣿⣿⠶⣀⣽⣿⣿⣿⠋⣀⣄⠀⠈⠛⠏⠙⠀⣤⣤⣾⣿⡀⣀⣀⠀⣰⣿⣿⡿⢟⡁⠀⢀⠰⣿⡿⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⠃⣼⣿⣿⣿⣿⣿⠀⠘⠉⠀⠀⢀⣀⠀⢀⡸⣿⣿⣿⠙⠛⢛⣿⠻⣿⣉⢀⣬⡟⠛⠋⠀⢠⡤⠄⣽⣿⣿⣷⣄
⠀⠀⠀⠀⢴⢌⡀⢭⢵⣙⣿⣷⣷⣾⣿⣿⣿⡿⠙⢿⣧⡀⠙⣿⣿⡟⢲⣬⣶⣿⣍⠉⠀⠀⠙⣿⡀⠀⠛⠀⠛⢳⣆⠀⣀⠀⡄⠀⣸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠦⣠⣼⣿⣿⣿⣾⡟⣿⣿⣿⡁⠀⠀⠀⠉⢉⣾⣿⣿⣬⣙⣻⣿⣿⡿⠀⢀⠀⠰⣿⡿⢶⣿⢶⠆⣠⠌⠛⠇⠠⠀⠀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣠⠿⣿⣿⣿⣿⣻⣷⣬⣿⣿⣧⣠⣴⣿⣷⡾⢿⣿⣿⡻⣿⠟⠉⠈⢁⡀⢀⡄⠂⢺⡿⠟⣻⡷⠲⣿⣶⠃⠀⢠⣦⣤⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢩⣟⣿⠿⠿⣹⣿⣧⢹⣿⣿⣿⣫⣌⠀⠸⣿⣿⣷⠊⢢⣤⣤⠛⠳⡆⠐⢦⣀⠤⠺⣏⠈⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣾⠻⣷⠒⢾⣿⢋⣠⠟⠁⢻⣿⡷⠋⢶⣀⠙⣿⣏⣠⡄⣿⡇⠀⣀⠈⢠⣤⡏⠀⠈⢿⣿⠟⠛⢀⠀⢠⡄⢰⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣆⣽⣻⣿⣤⡄⢠⣿⠄⠀⢈⠁⣾⣿⣿⣿⣠⡏⢁⠀⢁⣶⡈⠹⠇⠀⠀⠼⠛⠀⠀⣈⣴⣿⣶⣴⣿⣿⣿⡏⠛⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡽⣿⣿⣉⡀⢀⣧⣤⣴⠏⠀⣼⣿⣿⣦⠙⠛⠛⣠⡿⠟⢻⡄⢢⠄⠀⠀⠀⠀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣷⠾⣟⣿⣧⠀⡄⢠⣈⡙⢻⣷⣒⠀⠈⠀⠀⠉⠙⠒⠀⠀⣄⠀⢀⡀⠉⣿⣿⣿⣿⣿⣿⣟⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢨⣿⣿⣿⣟⠁⠀⠉⢿⡟⠃⠀⠘⠿⣿⣧⣿⣿⣶⡆⢀⣤⡀⠀⣤⣾⣿⣿⣷⣾⡃⣴⣿⣿⣿⣿⡿⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⣿⣶⣿⣦⣤⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡻⣿⣿⣿⣷⣶⣿⣧⡙⣿⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢠⡜⠹⣿⡿⢻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⠴⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⢀⢠⡟⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠈⠁⠈⢑⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠶⠈⠛⠛⢫⣿⢹⠷⣿⠛⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣧⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠄⢳⣴⣎⠑⢀⠉⢠⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣈⡛⣺⣿⣄⠷⡀⠈⠄⠀⠆⢩⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣉⣽⣿⣿⡥⣶⣷⣦⡴⢾⣿⣥⢍⢼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣹⡇⣊⣶⣦⢿⡿⢻⣟⣉⢁⣄⠀⠛⣿⡎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣻⡟⢸⣿⣍⡰⣶⠾⡻⠇⣻⣅⢿⡷⣠⠄⢻⣧⠈⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣾⣿⠻⣽⣇⠈⢯⣿⣿⣶⣾⣿⣋⡈⣧⡼⢾⠃⣀⣻⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠛⡟⣿⣆⠈⠛⠳⠄⣉⠛⣿⡿⢿⠿⠿⣻⣿⣿⠟⠛⠉⣁⡴⠀⠀⠀⠀⢘⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠁⠶⣿⣿⣄⠀⠀⠀⠀⠉⠛⠲⢤⡄⠒⠛⢋⡥⠖⠛⠉⠉⠀⢀⠜⠁⠀⣼⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡄⠀⠈⠻⣿⠳⠦⠤⣤⣀⣀⣀⣽⡷⠒⠉⠀⠀⠀⢀⣤⣎⣠⣤⣤⢾⠁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠠⣿⣿⣿⠀⡀⢰⣼⣦⣤⣤⣤⡾⠟⢋⡁⣀⣀⣀⣤⣤⠖⣻⠛⠉⡼⠋⠀⠸⠀⠈⣧⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠁⠙⢿⢷⣦⣤⣮⣿⣿⠿⠶⠛⠉⠉⠉⠉⠉⠁⠀⢀⡼⠁⠀⠠⠀⠀⠀⡆⠀⠀⡼⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠀⠤⣚⣿⣫⣽⡎⠁⠀⠀⠀⠀⠀⢀⣀⡠⠾⠋⠀⢀⡴⠀⠀⠀⠀⠀⢀⣼⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣼⣷⣋⣀⡤⠔⠊⠁⠀⠀⣀⣴⡦⠖⠋⠀⢀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣐⠛⠿⠿⠿⠶⢶⣦⡶⢾⢛⡋⠉⠉⠛⠛⠻⠿⠶⠶⠖⠛⠉⠁⠀⠀⣀⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⠟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠁⠀⡍⠙⠏⠁⠀⠲⢦⣶⠶⡖⠒⡲⠞⢻⠛⠉⠹⠏⠀⠂⢳⢠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢨⡇⠘⡀⢰⠄⢠⠀⢠⠀⠀⠧⠀⠀⠀⠘⠃⢸⠃⠇⢸⠁⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣧⣄⣇⢸⡄⠀⠀⠈⡄⠀⢰⠀⠀⠀⢸⠀⢾⠀⠀⡘⢠⡧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⣧⣿⣏⡿⢸⣧⠐⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⡕⠀⠀⣇⣘⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣦⣿⣿⣿⣅⣀⡻⠆⠈⠀⢷⣀⠘⠀⣀⢀⡾⠀⠃⣐⣀⣩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢿⡿⢽⣿⡿⣿⣿⣶⣶⣶⣷⣶⣶⣶⣿⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡚⢿⣿⢿⣿⣽⣟⣛⣻⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠍⠛⠷⠛⠛⠉⠉



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣀⣀⣀⠀⠀⣀⣤⣶⣶⣶⣶⣦⡀
⠀⠉⠙⠻⣿⣾⣿⣿⣗⣼⣿⣯⣭⡝⢷⡄
⠀⠀⢀⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⣦⡀
⠀⣰⣿⣟⣿⣿⣦⣴⣿⣿⣿⣿⣿⣽⠻⣽⣾⣻⣆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣾⣷⢮⡻⣿⣿⣿⠶⣄⡀
⠀⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⡽⣿⣿⣿⣻⡷⠙⠉⠓⢿⣬⣻⣄
⠀⠈⣿⣿⣿⣿⣿⣿⡹⣟⣿⣿⣿⡿⠃⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⢿⣿⣿⣿⣿⣷⡝⢮⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⡌⢻⣷⡀
⠀⠀⠸⣿⣽⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣽⣿⣿⣡
⠀⠀⠀⢿⢻⣿⢿⣽⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠘⣯⣿⡎⢿⣯⢻⣿⡀⠀⢀⣤⠶⠒⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠘⣿⣿⢸⣿⠘⣿⣿⣄⠀⢀⣤⣴⣾⣷⣿⣿⠉⠛⠛⠋⠉⣿⣷⡀⠀⠀⢁
⠀⠀⠀⠀⠀⠹⢿⣧⣻⣆⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⢀⣔⠂⢸⣿⣿⣿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣯⠙⣾⣻⣿⣿⠿⠟⠉⠀⠀⠁⠀⢀⣼⣿⠘⣿⣿⣦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣈⠧⠻⣟⡷⣄⠀⠀⠀⠀⠀⣢⡿⣽⡇⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⣻⣟⠴⠗⠋⠃⠛⠃⠀⠀⠀⢀⡿⢃⣿⣷⢸⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⠋⠀⠀⠀⠀⡄⡀⠀⠀⠀⠈⠁⢾⣿⡿⢯⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠶⣃⣄⣴⠄⠀⠈⠿⣿⣸⠟⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⠟⠐⠲⠶⣤⠄⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⣿⣷⠀⠀⠈⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⡏⠀⠀⠈⠓⠠⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⢠⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⠀⠀⠁⠰⠄
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄

⠀⠀⣠⠶⠚⠛⠶⣄
⠀⠀⡏⢠⠞⢻⡆⢹⡆
⣤⠤⠧⠼⠶⠋⣀⡾⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⢀⣤⣤⣄⣀⡀
⠙⠓⢲⡖⠺⣫⣽⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⣧⠀⠉⠛⠻⣷⣦⣀⣠⣤⣤⣄⣀⠀⣀⣤⣤⠤⠴⠖⣻⡿⢿
⠀⠀⠀⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠉⠙⠛⢩⡴⠶⠶⠶⠛⠉⠀⣼
⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡼⠈⠁⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢀⡼⠃
⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⢯⠀⡴⠶⢦⡀⠀⠀⢀⡤⣄⢸⣀⣀⣠⡟⠁
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠀⠃⠀⠀⠈⠲⣾⣿⡏⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇
⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣠⠞⠉⠙⠲⣄⠸⣿⡀
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⢧⣸⣇⠻⢗⠸⠟⡾⢀⣿⠃
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢳⡀⠀⠠⡀⠀⠉⠛⢿⣋⣩⢏⢠⣾⠟
⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⣼⠓⢄⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠦⣀⣀⣀⡩⢕⣿⡟⠁
⠀⠀⠀⠘⣿⡀⠀⠀⠀⢰⡿⢦⣄⡑⠦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠴⣾⡿⢫⡇
⠀⠀⠀⠀⣨⡷⠀⠀⠀⢸⡿⠋⠉⠉⠛⠻⠷⠦⠤⢤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⡿⠁
⠀⠀⢀⣾⢻⡇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠰⣄⣀⣀⣠⣤⣤⣤⣤⣶⡿⣫⡾⠋
⠀⢀⡜⣳⡘⢧⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠉⢹⢫⠇⠀⠉⠉⣡⡾⠋
⠀⠈⠛⠋⣿⠶⢿⡆⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⢸⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠻⢶⣾⣃⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣼⡟⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣏⣷⡞⠛⢿⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⣿⢳⣀⠀⣶⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣷⣤⣼⠷⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣤⠀⠀⢻⡟⡏⠉⠹⣏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡟⠙⠿⠛⣧⠻⠶⣶⠿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡼⢤⡿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣂⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⢸⢻⣿⢿⣳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⢵⡞⢣⣾⠸⡏⢷⡏⠳⣌⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡱⢮⢀⢠⡖⠙⠁⢀⡿⢸⣧⠐⣿⠀⣿⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠛⠒⣻⣛⣩⡤⠿⠧⠺⠏⢠⣟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⡠⠴⠒⠛⠛⠉⠁⢛⣃⡀⠤⠐⠊⠉⣋⣴⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⢀⣠⣶⣶⣿⠿⠿⠛⠛⣛⣻⡿⢛⣽⠏⣿⣿⡝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣀⡴⠟⠋⠉⣉⢹⠭⠤⠒⢊⣉⣻⣅⠴⢛⡯⢃⣿⣿⣿⢸⣇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡞⠋⠀⣠⠖⠋⠁⢀⣤⠖⠂⠉⠁⠀⢀⣀⣨⡤⠞⣹⣿⠏⣸⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣧⣿⠀⣰⠋⠀⠀⣰⠞⠉⠀⣀⠤⠖⠊⠉⠀⣀⣀⡴⠞⣋⠤⠞⠟⢳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠘⢿⡄⣧⠀⠀⣴⠁⠀⣰⠞⠁⢀⣠⡴⠚⠋⠉⣠⡴⠋⠀⠀⣀⣤⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢤⡀⠀⠉⠚⠧⣄⣿⡀⣼⡏⢀⣴⣿⠁⢀⣀⣤⢾⣿⡏⢛⡿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢆⠉⠉⠊⠓⠰⠤⣍⣉⣙⣛⣻⣛⣻⣟⣿⣵⣾⣴⣾⢿⠿⡟⢻⠏⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⡍⢩⠉⣏⠉⡯⢹⠇⢹⡇⣾⣼⢸⡇⣿⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡗⢸⠀⣸⢁⡏⡇⣸⢧⡏⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⢸⡆⡿⢘⠀⡾⢸⢃⣉⡏⣿⢸⣿⣿⣿⣆⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⡄⢡⠰⢠⠀⡆⢀⠰⠈⡇⡻⣸⢰⡇⣼⣴⢼⢳⣿⣾⣿⣿⣿⣿⣿⣶⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡺⡎⣦⣇⠡⠀⡇⡆⣷⢾⣾⢸⣷⡟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⡿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⢿⣿⣄⣧⣓⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⡏⠻⢿⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉

⠀⠀⠈⣠⡏⠀⠸⡀⣇⡆⠀⡞⠁⠀⢾⢿⡋⢵⣶⣾⣽⡇⢠⠀⡀⠀⠀⠘⠀⠀⢿⢴⢼⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⣍⣁⠀⢀⡙⢿⣇⠀⠈⠀⠀⠤⠤⠬⠅⠀⠉⠁⠀⠀⠈⠴⠚⠀⠆⠀⠀⠈⠐⠚⠀⠀⠀⠡⠼⠀⠀⠀⠾⠿⠏
⠀⠀⠀⠙⠁⠀⢸⢱⢠⠤⠶⠶⠤⣀⡀⠀⢀⣀⠀⠀⠒⠛⠓⠒⠀⠀⠄⠐⠀⠀⠀⠀⢀⡀⢰⠖
⠀⠀⠀⠀⠀⠀⠈⡼⠁⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠠⢀⠀⠈⠀⢀⠀⠀⢀⠀⣀⡀
⠠⢀⡀⠂⠀⠀⠚⠁⠀⠉⠙⠃⠀⠄⠀⠀⢄⠀⠑⠀⠢⠀⢠⠇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⢀⡀⠈⠀⠀⣇⣖⠉⢻⠆
⣀⡀⠀⠀⠀⠈⢧⠳⡈⠦⡀⢿⣿⣷⡄⠐⠀⢡⠀⠀⠀⠁⢸⠀⠀⣠⣲⣦⠀⠀⠀⣠⠀⡖⠋⣤⠀⠀⠀⠹⡸⠶⡣
⣿⡿⠀⠀⢀⠀⠈⠃⠈⠀⠈⠀⠀⠀⠀⠊⡠⠃⢀⠜⠀⠀⠘⡆⠀⠹⠁⠸⠂⢸⣴⢣⡄⠀⠀⠉⠀⠠⡀⠀⠉⠉
⠁⠀⢀⠠⠊⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢷⣴⠄⠀⠋⠀⠀⠀⠂⢠⡄⠀⠳⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⣐⢡⣿⣤⣀⣤⠴⣒⠢⢄⠀⠀⣀⠤⠆⠀⢢⡀⠀⢀⠀⠘⠿⠀⠀⠀⠀⡰⠀⠀⠈⡟⠄⠀⠀⠀⠀⢠⠏⡠
⠀⢀⣀⣠⣤⠀⠀⠙⠉⠉⠲⡄⢨⠤⠊⠐⠉⠀⠀⠀⠀⠀⠱⢰⠀⠀⠀⠀⣠⠂⠀⣰⠇⡤⠐⢄⠈⠈⢦⠀⠀⡰⠁⠜⣴
⠞⠋⠀⠈⠁⠠⢄⡀⠀⠑⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⠲⡄⠀⠸⡇⠀⠀⠙⠁⠀⢰⠏⠐⠁⣐⠄⠀⠀⠀⡆⣰⠁⡘⢸⠋
⠄⠀⠀⠀⣠⡀⣀⡇⠀⠀⢠⣧⠀⠠⠁⠀⣴⠤⠠⣤⠢⠈⠀⠀⡇⠀⠠⠤⠆⡀⠁⢀⣠⠄⣾⠁⠀⠀⠀⠃⠇⠀⠃⡀⡀
⠀⠀⠀⢠⣿⡟⠘⣧⠀⠀⠸⢻⣧⠀⠀⠀⠛⠗⠚⠉⠀⠀⠀⠀⠁⠀⠀⢂⠀⢀⡀⣟⡧⠾⠋⠀⠀⡀⠀⠀⠀⠀⠄⠑⣽
⠀⢰⠀⠀⣿⣇⠀⠘⡇⠀⢰⠈⠙⣆⠀⠠⢀⡀⠀⠀⢀⠞⠁⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⢈⡴⠀⠀⠀⠀⠀⡈⠪
⠀⠸⡄⠈⠘⣿⣳⣶⣧⠀⠀⠀⣀⠈⠂⠀⠀⠀⠀⠠⠀⠄⣀⢠⠴⠶⠞⠛⠉⠙⢻⠇⠀⠀⢈⣠⣥⣤⣄⡀⠂⠀⠀⠈
⠀⠀⠈⠂⠀⠈⠙⠛⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠐⡄⡴⠐⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀
⠀⠀⣢⣀⠀⠀⠀⣀⣀⡴⠀⢀⠈⠉⠀⠀⠀⣴⡟⠀⠂⠀⠠⠄⠀⠀⢀⠈⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⢀⡀⠠⡀⠐⠤⣁
⠀⠀⠈⠉⠛⠲⠤⣈⠉⠀⠁⠞⠀⠤⠂⠀⠀⢀⠰⡄⠀⠀⣸⣇⠀⠞⠁⠁⠀⠀⠘⠁⠀⡴⡡⣠⡤⠾⢿⣫⠃⠈⠀⠀⣈
⣢⣴⡶⣄⠀⡄⠀⠈⠀⢀⠁⠀⢀⡶⠆⠃⠀⣄⠣⠁⠀⠀⣿⡏⠀⠀⠀⠠⠀⠀⠀⠐⢄⡑⠑⠿⠓⠀⠾⠅⡀⠀⠀⡔
⠛⠉⠡⠅⠊⠁⠀⡠⣢⠎⠀⠌⠲⠂⠀⠄⣚⡁⠀⠄⠀⢠⡈⢃⡀⠀⠀⣠⣄⡀⠀⠒⣒⠄⢁⠀⠀⠀⠀⠈⡀⢀⢜⡄⢇
⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠀⠀⠤⢾⡭⠤⠀⣀⣀⠀⢀⣿⠀⠀⠀⠀⠀⢀⠉⠀⠀⢁⠐⠦⢤⠀⠀⠀⣀⠀⠉⠀⠑⣈
⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⢤⢉⠗⠀⠀⠀⠀⢀⠀⠀⠀⡰⣣⠀⡀⢠⣷⠊⠁⠀⠀⠈⠛⠧⣀⡀⠀⠈⠉⠀⠀⠀⠀⣀⡀
⠔⠀⠰⠂⠀⠀⠀⠀⠀⠀⡴⠀⡔⠀⠀⠀⠀⠀⠈⠂⠐⡄⠈⠈⠔⠹⡇⠀⠀⠀⣠⠤⠀⠀⡈⠙⠂⠀⡑⠢⣄⠀⠀⢀