Nz Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⡟⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣃⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⡽⡿⣿⢠⣭⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠋⢠⢿⣼⣿⣿⢉⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣾⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢻⣿⣿⡿⠿⠿⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠀⠀⢀⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣶⣿⢿⣍⢿⣷⣦⣤⣈⡿⠻⠿⣦⣤⣌⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⡀⢠⠠
⠀⠀⠀⠀⠀⠤⠈⠉⠤⠅⠀⠀⠀⠀⠀⡈⠁⠲⠅⠀⡤⠄⠠
⠀⠀⠂⠈⠉⠁⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠐⠚⠁⠀⠛⠂
⠀⠀⠀⣀⡰⠶⠤⢤⣄⡀⠀⡄⢀⠀⠀⠠⢠⢄⣠⠠⠀⡄
⠀⠀⠐⠛⠻⠌⠂⣀⡲⠐⣢⡌⢁⣀⠀⠰⡴⠤⣭⢔⡨⣖⡚⡶⠂⡠
⠀⠀⠀⠀⠀⠁⠐⠞⣃⡀⣛⣿⠗⠀⣖⡈⢑⠒⢀⡀⣀⠀⠀⠠⠂
⠀⠀⠀⠂⠑⢛⣛⣛⣻⣿⣵⡴⢶⢦⣼⣮⠏⡤⣙⣁⣼⣻⣧⣒⣦⣀⡀
⠀⠀⠀⠀⢀⠉⠉⢹⠁⠘⠟⠃⠙⢸⣯⠛⠉⠙⠛⠙⠻⢉⡻⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠀⠀⢠⠀⠀⢀⠀⣆⠄⠤⠠⠠⡠⠀⠄
⠀⠀⠀⠀⠮⢾⠁⡟⠁⠃⠀⠸⢉⠸⣇⡀⢠⠄⠄⠘⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠂⠊⠁⠀⠈⠀⠉⠂⠘⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠃⠀⠰⠀⠀⠐⢲⡶⠠⢰⡿⠓⠖⠚⠐⡒⠒⡔⠒⡒⢣
⠀⠀⠀⠀⠀⢁⡇⠀⠀⠁⠊⠂⠀⢰⡷⠀⠐⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠼⠁⠀⣀⠆⠀⠰⠀⢸⡇⡁⢈⡁⠀⠸⠀⠀⠀⠀⢀⠬
⠀⠀⠀⠀⠸⠊⢐⠘⠁⠀⠀⠀⢀⣘⠧⠤⠤⢄⠤⠤⠄⠀⠓⠈
⠀⠀⠀⠀⠀⠉⠙⠀⠌⠀⡤⠁⠀⣼⡅⡄⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠷⠄⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⣿⣿⡷⠚⠀⠀⠀⠀⠀⠀⡔⢁⠀⠛⢨⣿⠶⠶⠶⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⣻⣼⡸⢋⡀⠀⠀⠀⠀⠀⢀⡤⠞⠀⠈⢱⣧⠼⠃⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⢿⣟⣿⡿⠃⠀⢀⡠⠀⠊⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⣧⠀⢸⠛⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⢠⠎⠀⣠⢴⣃⣀⣀⠤⠔⠂⣀⡴⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣷⠏⣠⣞⣽⣿⣿⠿⠿⠿⠛⠛⠉⠀⣠⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⡏⠀⢉⡾⠟⠁⣠⣿⢛⣀⣠⣤⠖⠋⠁⠀⠀⠀⠀⠘⣿⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠁⢀⠎⠀⣀⠾⠛⢿⡟⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⣿⣦⢋⠀⣼⠏⠀⠀⠸⣇⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⢃⠏⡼⣛⣀⣀⣀⣀⣹⣢⣤⣘⢳⣄⣀⠀⠀⠀⠀⣸⣡⡾⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠈⢠⠁⠉⠉⠀⠘⠃⠀⠈⠛⠉⠝⠚⠛⠋⠀⠲⠖⠛⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠰⠢⢦⢦⣤⣤⣶⣦⠶⠾⠶⠶⢶⣶⣶⣶⣴⣴⣦⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⡾⠯⣉⣉⠙⠲⢦⡤⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠙⢦⠀⠀⠈⠉⠒⢌⠂⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠈⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣤⣀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⢀⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣠⣴⣀⡀⠠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⡁⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠙⠛⠛⠻⠿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣦⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⠖⠒⠒⠒⠲⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⢸
⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⡾⠛⠇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢳⢶⣤⣤⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠂⠀⠙⠹⣧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢹⡆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡦⠀⠀⠘⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠙⢻⣿⠀⢹⠆⢰⣦⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⠶⢾⡏⢿⡆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⢿⡁⠀⠈⠁⠈⣇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢻⢀⣀⡀⠀⠀⣀⠀⠶⢦⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠆⠀⠈⠙⠒⠊⠁⠀⠂⠠⠄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡄
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡞⠀⠀⠀⠀⠀⠀⡄⢀⠠⠀⠀⠀⢀⡐⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡰⠒⣶⡜⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢳⠀⠂⠐⠀⠀⠀⡶⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠃⠀⠂⠀⠀⠀⠀⠀⠀⢼⠀⠀⠘⠀⠀⣸⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡾⠁⢀⠀⣀⣀⡀⠀⣶⠀⣠⠏⠀⠀⠀⢰⠆⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠠⠀⠙⠉⠀⠀⣾⣿⣧⣠⠀⠀⣤
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⠋⠈⠀⠈⠃⠀⠂⠀⣿⠈⠉⠹⠶⠞⠁
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠈⠀⢀⠀⡠⠂⠀⠀⣰⠛
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⠏⡆⠀⡤⠀⠄⠁⠀⢀⡞⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢟⣄⠀⠀⣶⠄⠀⠀⣠⡞⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⣋⠰⡎⠽⠀⣜⠂⠀⢠⣞⡉
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢟⠁⡚⠈⠀⠃⡶⠛⠁⢀⠀⣈⣙⡃⠉⠈⠁
⢸⡄⠀⠀⠀⠀⠀⠀⠠⣷⠚⠻⣯⠶⡯⠀⠉⠇⢀⡔⠀⢠⣴⠿⠛⠫⠽⠗
⢸⡇⠀⠀⠀⠀⠀⣠⣼⡟⠀⠠⠟⣂⡴⠊⠁⠀⠄⠀⢰⡟
⢸⡇⠀⠀⠀⣀⣶⡏⢈⡖⢁⠠⠶⠉⠀⠀⠀⣄⠀⠀⣼⡁⠀⠀⠁⠾⠤⠄⠐⠆⠐⠸⠀⠇
⢘⠀⠀⠀⣠⣿⣯⠄⢀⠙⠉⠀⣀⠀⠘⠆⠀⠈⠀⣸⡟⠁⠈
⢸⡇⠀⢀⣿⣿⠍⢀⡋⠐⢶⢀⠋⠀⠀⠀⠀⢀⣴⣿⡗⢠⣤⣤
⢸⡇⠀⠾⣿⡧⠒⢌⠛⠂⠀⡎⠀⠀⠀⠀⢀⣾⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⣤⣤⣄⣤⢠⡄⣰⢠⡆⢰⡄
⢸⠃⠀⠀⠘⠛⠓⠛⢻⣶⣦⣡⣄⠀⣀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠈⠀⠀⠁
⢸⠀⠀⠀⠀⠀⠀⠀⢹⠅⢸⡇⠉⠽⠋⠩⡄
⢸⠀⠀⠀⠀⠀⠀⠰⣯⠰⠛⠛
⢸⡀
⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⣭⣉⠛⣓⠲⢤⡀
⠀⠀⠀⠀⠈⠻⣿⡳⠶⠶⣤⡤⠤⠴⠶⠖⠛⢉⣁⠀⣉⣵⠶⢾⠛⠋⠉⠙⠛⡻⣶⣄⠀⠀⢀⡴⠤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡶⢤⣄⣀⣀⣐⣤⣤⡴⠞⢋⠟⠀⡰⠃⠀⣠⡴⠚⠉⠉⠉⠛⢷⣴⡏⠁⠀⢬⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡀⠀⠔⠈⠀⠐⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⢶⣻⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣼⣇⣠⡟⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠛⠆⠀⠉⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⢀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣟⣿⣛⣿⣟⣻⣟⣦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⡍⣿⠻⣛⠿⣿⠻⣟⠻⣿⡟⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣮⣿⣯⣷⣶⠟⢻⣿⠘⣿⣧⣙⢿⠪⣻⡷⣿⢳⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣣⣼⣿⣿⣵⠾⢛⣿⣷⣞⣉⣓⢿⣷⣍⠛⠓⠌⣣⣘⢾⡿⢯⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣽⣿⣯⣽⠿⠿⣭⣥⣸⣷⠭⣵⣬⣿⢄⡘⢷⣝⠊⠚⡷⣎⢿⣿⣶⣤⣴⣆⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣽⣿⣿⣟⣛⣃⣉⣉⣛⣶⣿⣷⣦⣍⣤⣓⣤⡈⢩⣛⠷⣾⡋⢳⣯⡨⢂⣲⣿⣿⣿⣿⣷⣶⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣽⡾⠟⣹⠿⠿⠛⠻⡿⣿⣈⣩⣮⠁⢁⣘⢻⡻⠿⢿⠙⠃⢎⣸⠿⠟⠻⣿⣾⣶⣟⡰⢀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣯⣿⣯⣿⣷⣶⠛⠓⡶⢲⣭⣿⣛⡛⢛⣷⠏⠃⠘⣻⣤⣿⣬⣂⣉⣳⣄⣬⠀⠰⠶⠀⡿⢿⣿⡴⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣷⣾⣻⣽⠷⠶⣶⡶⢮⣤⣂⠰⣾⠒⠶⠢⢽⣟⡳⢶⣾⣟⡻⣛⣶⡦⠀⡀⢦⠾⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣧⣴⣾⣫⣭⠆⠀⢲⣏⡈⠀⠁⠒⠛⢿⣿⣯⣮⣙⠳⣷⣌⢂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣻⡿⣤⣤⣴⣶⣷⣴⣯⢇⣸⣶⠿⠖⠟⠛⠙⠉⠙⠟⠉⠉⠑⢦⡀⢰⡀
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣝⣿⣉⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢿⡄
⠀⠀⠀⠀⠀⠀⣀⠁⢀⠘⣤⣤⠈⠀⠉⢛⠛⠏⠻⠻⠿⣻⣿⣿⣿⣿⢿⡹⣿⡻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢷⡀
⠀⠀⠀⠀⠀⠰⢬⡳⢤⠀⠸⢹⠇⣦⣿⣦⣦⠀⠠⣤⡀⠻⣽⣿⣻⣿⡟⢿⠈⠃⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠠⠴⢦⡀⠁⠀⠀⢰⡟⢹⠛⡇⠀⡄⠘⢉⠐⠤⢻⠋⢹⠀⠀⠄⠀⠀⠀⣡⠴⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠱
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⢄⠀⠙⣼⣿⢿⣄⠰⣦⣉⠻⢿⣿⠀⠈⢴⣷⣄⣤⠀⡀⣀⢠⣶⠖⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡿⠀⠀⠈⢴⡈⢙⠓⠲⠫⠂⠀⣀⡙⠛⠛⠿⠿⠢⣄⣀⡀⢘⠛⠓⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⡄⠐⠂⠁⠀⠀⠄⢀⡠⠷⣄⠈⠻⠲⠗⠺⢶⠉⠄⠁⠈⠛⠀⠰⠂⣀⠒⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠊⠉⠀⠀⠀⠑⠮⣴⠐⠁⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠿⠿⠛⠛⠛⠉⢁⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠂⠀⠀⢀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠊⡉⠀⡤⠀⠀⠀⣲⣦⣴⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⢁⠀⠈⢠⣬⠀⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡶⠖⠄⣀⡐⠁⠀⠁⡖⢡⣎⢄⡰⠃⠀⠂⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⡶⣷⡞⠁⠉⠡⣮⢔⡫⣕⡠⣻⠟⠁⠀⠀⠈⠀⠂⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠙⢋⣀⣤⣴⣿⣷⣾⣭⡵⠋⠀⠀⠀⠀⠀⠀⢄⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡡⠶⠀⠳⠬⣿⣿⣯⣿⣿⣿⡏⠉⡀⠀⠀⠀⠀⠀⢐⣵⠛⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣶⣶⠿⠶⠾⡶⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⢀⠐⡶⠛⠀⠀⡠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠤⠞⠍⠿⠠⣷⠾⡄⡀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠞⠛⠛⠛⣦⡴⢊⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⣼⣯⣵⣿⠃
⠀⠀⠀⠀⠀⠀⣀⠔⠮⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢀⠠⣪⠾⠋⠉⠃
⠀⠀⠀⣀⢔⡪⢖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣦⣶⠋⠁
⢀⣴⣿⢟⠟⣨⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⠿⣿⠿⠟⠉
⠈⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⢠⣶⡶⠶⢆⡔⢴⢶⣦⠄⠀⠀⠀⠀⠀⣀⣄⣄⡄⡄⣤⠠⡄⣤⢀⣄⡀⠀⠀⠀⠀⢀⡀⢀⡀⠀⣤⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢨⡿⢿⡄⢸⡇⠠⣟⢭⠀⠀⠀⠀⠀⠀⣿⢹⣿⣳⣷⣿⣼⡷⣹⣿⣿⠇⠀⠀⠀⠠⣼⡓⢒⣛⣛⣿⣛⣛⡓⢚⣯⡄
⠀⠀⠀⠀⢀⣻⣕⢄⢸⡇⣠⢶⣿⡀⠀⠀⠀⠀⠀⣯⢏⢿⡱⣽⣿⣿⡟⡱⣣⢳⡇⠀⠀⠀⢘⣟⣂⣀⣐⣐⣿⣂⣐⣒⣒⣻⡃
⠀⠀⠀⠀⢸⣿⣭⡀⢸⡇⠠⣿⣿⡆⠀⠀⠀⠀⢀⢿⢯⠳⣝⣞⣿⣿⢞⡵⣣⢿⠇⠀⠀⠀⠀⡿⠤⠤⠤⠴⣿⠆⠤⠤⠤⢿⠅
⠀⠀⠀⠀⠘⣻⣷⣆⢸⡇⣲⣷⣷⠂⠀⠀⠀⠀⠀⣎⣮⠳⣝⣾⣿⣯⢏⡼⢣⢏⡆⠀⠀⠀⠨⣯⠤⠤⠭⠭⣿⡭⠭⠭⠥⣽⠇
⠀⠀⠀⠀⠐⣿⣯⠍⢸⡇⢩⣿⣯⠅⠀⠀⠀⠀⢠⣏⢮⣷⣝⢿⣿⡷⢋⣴⣫⢻⡇⠀⠀⠀⢠⣟⠁⠈⡉⠩⣿⣍⣉⠁⠙⣿⡄
⠀⠀⠀⠀⠸⢿⡶⠠⢸⡇⢤⣻⣿⠅⠀⠀⠀⠀⠀⢯⢦⡙⢿⡷⣿⣵⣫⢞⣱⢻⢃⠀⠀⠀⠠⣿⢖⣐⣒⣒⣿⡓⠒⢒⡒⣽⡇
⠀⠀⠀⠀⢈⣟⣪⡀⢸⡇⢘⠯⣿⡀⠀⠀⠀⠀⢸⡘⢧⣝⣷⣿⣿⣯⢶⣛⣵⠏⡜⠀⠀⠀⠀⣿⣇⣐⣒⣒⣿⣒⣒⡒⣸⣿⠃
⠀⠀⠀⠀⢐⣿⣟⣄⡸⡇⣨⣻⣿⡃⠀⠀⠀⠀⠈⠻⠶⠶⠿⠿⣿⡿⠭⠵⠶⠿⠇⠀⠀⠀⠘⠛⠂⠀⠒⠒⣿⠒⠒⠒⠒⠛⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡀⠀⢀⢀⡀⣀⣵⣺⣣⢒⡒⡢⢀⣀⣯⣿⣭⣽⣽⣟⣫⣽⣿⣶⣶⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⢚⣉⣦⣖⣍⣯⣸⣳⣦⣦⣶⣎⣴⣽⠉⢉⣯⡭⠀⠉⠀⠉⠉⠉⠁⢩⠀⢻⡿⡟⢁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⣿⣿⣿⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⢳⠇⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⣷⡂⡡⠄⢀⡀
⠀⠀⠀⠀⢀⣄⣶⣶⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠹⣷⡃⠘⠊
⠀⠀⠀⠀⠰⣻⢿⣿⣿⣿⠁⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⢲⣞⣥
⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣸⡇⠀⢰⣾⣶⣶⣶⣶⣶⣶⣶⣿⣷⠀⣿⡆⠀⣺⣿⣏⣻⣒⢀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⠁⠀⢀⣤⡀⠀⠀⠀⢹⣿⣿⣿⣿⢹⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠁⠀⣻⣿⣿⣿⡇
⠀⠀⠀⠀⢐⣺⣿⣿⡇⠀⠀⠀⠘⠀⢀⠀⢰⣴⡅⠈⣿⣿⢸⣿⣟⡄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⢀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⡨⡿⣿⣿⠀⣤⠀⠀⠀⠀⠁⠀⠀⠀⣥⠀⢿⣿⣇⢻⣿⣷⡹⣻⣿⣿⣿⣿⣿⣿⣿⣟⣼⣏⡼⣰⣿⣿⣿⣿⣾⠂
⠀⠀⠀⢼⣭⣿⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⠠⠚⠯⣄⣨⣿⣿⣯⡿⣿⣿⣷⣾⣿⠛⢻⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⢛⢟⣴⠕
⠀⠀⠠⣴⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⠻⣷⣿⣓⣐⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⡩⠶⠄
⠀⠀⢴⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⡿⢿⣿⣿⣿⣭⣛⠻⣿⡿⠿⢛⣟⣽⣿⣿⣿⣿⣿⣿⣿⣻⢏⡑⠉
⠀⢠⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡀⠐⠘⠁⠈⢻⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠐
⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠠⠡⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠃⠀⠌⠀⠀⠀⠀⠀⠀⢿⣻⡉⠻⣿⣿⣿⣏⠀⠳⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣅
⠀⢼⣿⣿⣿⡇⠆⠒⡄⠀⠀⠀⠀⠀⠁⠸⡗⣠⠤⠀⡀⠀⠀⠀⠀⡘⣠⡾⢻⠉⣿⣇⣽⣶⣶⣿⠭⢉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⣾⣿⣿⣿⠏⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢋⡇⠀⠀⡁⠀⠀⠀⣞⠀⣻⣧⣈⣀⣿⣿⠘⠻⡇⠀⠀⠀⠡⣴⡿⢻⡏⠙⠻⣿⣿⣿⣿⣿⣧⡀
⠀⣿⣿⣿⡟⠀⠀⠜⠁⠀⠀⠀⠀⠀⠲⠀⠈⠀⠀⠠⢶⠀⠀⢸⣧⣿⣷⣿⠿⣧⣾⣿⣶⣶⣿⠦⠤⣤⣶⣾⡇⠈⠃⣀⡀⣿⣿⣿⣿⣿⣿⣷⣀
⠀⣿⣿⣿⠏⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠈⣿⠖⠉⡀⠈⠀⠀⠀⠙⣿⢿⣿⣧⣻⣿⣿⡇⣿⢁⣁⢀⡽⠟⢻⣹⣷⡜⠻⡇⠈⢻⠿⠉⠙⢿⣿⣿⣶⣆
⠀⣽⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡟⠀⠀⠻⡆⠀⠀⠀⢀⣻⣿⣿⣿⣿⣟⣿⣜⣿⣶⣿⣿⠀⢡⣤⠛⠛⢇⠀⠐⢠⣿⠋⠉⠀⣼⠛⠛⠿⡿⣷
⠀⠹⠿⠿⠷⢦⢤⣤⣀⣀⡀⢀⠀⢀⣤⣽⡇⠀⠀⠀⠁⢀⣀⣀⣨⣿⣿⣿⡿⣿⠇⣿⡿⣿⣿⣿⣿⡄⡇⠘⠄⠀⢸⣖⠶⢶⠉⠇⠀⠀⣟⠒⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⡛⠟⠛⠋⠙⡛⠛⠉⣉⣁⣯⠞⠻⣾⣿⣍⣝⢯⣿⣿⣿⣿⣦⣤⣤⣾⣿⡿⡿⣷⢦⡴⢾⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣒⣶⣒⣒⣒⣒⡒⢰⣶⣿⣿⣍⡀⠓⢋⣶⣷⣐⠞⠳⠞⠛⣛⣿⠾⠁⠙⠛⠻⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠈⠉⠉⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠴⠖⠒⠂⠉⠉⠉⢉⣁⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠂⠼⠤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⢤⣄⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠔⣀⣬⡁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⡀⢿⣷⠇⡖⠲⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢘⣉⢉⡰⠃⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁⡠⢊⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢈⡠⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠔⢁⣠⠴⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡇
⠀⠀⠀⠀⠀⠀⢀⠊⢀⢔⡡⠖⠉⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣣⢠⡇
⠀⠀⠀⠀⢀⡔⢁⢔⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠻⡾⠁
⠀⠀⠀⢠⠊⡀⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡢⠈⡀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡼⠁⠀⠁
⠀⠀⠠⠁⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠁⢸⠋
⠀⠠⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⣤⣀⣀⣀⠈⢧⡀⠀⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠶⣤⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡏⠈⠉⠙⠛⠛⠓⢤⣷⠒⣾⠛⠛⠉
⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢒⣊⡉⠍⠉⠈⠒⠋⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠝⠋⠁⢀⡠⠔⠂⠀⠀⣀⣀⡀⠘⡆⠀⠀⣀⣀⠤⠤⠃⠀⠈⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢤⣤⡴⠊⠁⠀⣀⡤⠖⠋⠁⠀⠈⢛⠥⠒⢉⣁⣤⣤⠤⠀⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠷⠖⠛⢉⡤⠚⠁⠀⣀⡴⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣀⣠⠴⠚⡽⠁⣠⡴⠋

⣷⡀⠀⠫⠙⠁⠰⠏⣿⣿⡗⠀⣄⡿⠦⢀⣤⠠⣽⣶⡖⣿⡟⠙⠘⢷⡦⠀⢠⢇⣦⡄⠀⠀⢴⣄
⠻⣷⡀⢠⠀⣠⣐⣹⠇⠈⣿⣸⣯⠇⠀⠀⢀⠀⠨⣽⣱⠋⠀⠀⠀⡮⠑⣄⠈⠸⢧⡅⢴⣦⠤⢿⡄⠀⢀⡀
⡀⠹⣷⠐⠂⣉⣬⣱⠄⠒⢈⡡⣞⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠁⠀⠀⠐⡌⠳⠂⠈⠇⢼⣧⡳⣄⣿⣦⠀⠙⢦
⢿⣦⡘⠆⠁⠀⠛⠁⠀⠆⠘⠁⠀⠀⠀⠀⠀⣠⢠⡤⣱⠍⠀⠀⠀⠀⠈⣽⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⣗⠀⠄
⠀⠉⢻⣦⣂⠀⠒⠀⠀⡀⣠⣤⠀⣨⣅⡰⠤⠉⠓⠋⠁⠀⠀⠄⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡝⠇⠦
⠀⠀⡶⠈⠻⠝⣯⡈⢁⡇⠓⠀⢠⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡆⢦
⠀⠀⢀⣀⠠⠔⠶⣶⢈⣫⠷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠀⠀⠀⠀⠀⠀⣀⣁⠹⠿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⠀⠀⠀⠀⠀⠀⢚⣲⣿⣶⡆⣿⣿
⠀⠈⠃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢡⡐⠀⠀⠀⠀⠈⣿⣿⠟⢴⣿⡟
⠀⠈⠀⠀⠱⠄⣀⡀⢹⣶⣀⢀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡀⠀⠐⠀⠉⢀⠀⠀⠀⠀⠈⠙⠁⣼⣿⣷
⠀⢘⢆⠀⢀⡀⠀⠙⠪⡗⣿⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠲⠀⠀⠀⢶⣼⣿⣿
⠀⢸⠜⠓⠀⠛⠚⠶⠀⠀⠁⠀⠀⠀⣀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢻⣿⣽
⠀⠀⣦⣤⣶⡶⠖⠛⣉⠍⡺⠲⠆⠀⠀⠀⢠⣤⡄⣤⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠚⠁⠀⢱⠀⠀⢀⣼⡏⢿
⡇⠀⠛⠉⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⣀⣶⣤⣝⠃⠀⠀⠀⠀⣀⣀⣠⣇⠀⠀⠀⠄⠀⠀⠀⣼⠀⢶⣿⣿⠱⣿
⣥⡄⠂⡀⠀⠚⠁⢠⣦⡏⠀⠀⠀⠀⠀⠐⢧⣍⡀⠀⠀⠴⠚⡉⠉⠋⠉⠛⠢⠀⠀⠀⣠⣴⣿⠀⢸⣿⣏⡾⡛
⣷⣾⣷⣏⠀⠀⣾⢸⢷⠀⣀⠀⠀⠀⠀⢐⣿⣟⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠻⣿⠀⠘⣡⣾⣦⣆
⣿⣿⣿⣿⣃⠀⠻⢺⢸⣰⣿⠀⠀⠀⠀⠉⠹⡇⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠢⠀⠀⣹⠀⠠⡟⣿⠙⠉
⣿⣿⣿⡿⣿⣧⡀⣾⢸⣿⡯⡄⠀⠀⠀⠀⡀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉
⣿⡻⣿⣿⣾⡏⠓⠜⢸⣽⠂⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⣾⣂⣀⣦⣧
⣿⡇⠹⣿⣿⣷⠀⠀⢈⠟⡀⢠⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⡇⠉⣿⠿⠳⣤
⢹⠁⠀⠈⢻⢿⡄⠀⠀⢹⢱⠸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⡅⠀⣿⣷⣤⢛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢠
⠀⠀⠀⣆⣀⠈⠀⠀⢈⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣧⣀⣀⣀⣛⣀⡼⡀
⠀⠀⠀⢿⣿⡟⠀⠘⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⣶⠀⢠⣶⣶⣿⠂⠀⠸⡇⠀⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠈⢿⣿⠄⢸⣿⠟⠀⠀⠀⢿⡞⠒⠲⠶⠶⠶⠶⠶⠖⠒⠒⠉⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⢰⣿⡿⠃⠀⠀⠀⠳⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠣⠽⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠐⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠃⠀⠦⣈⣀⣈⡠⠞⣁⠀⢸⡇⠀⠀⠀⠨⣅⣀⣀⡠⠽⢡⠀⠀⠀⣿⠀⠘⠀⠀⠀⡷⡍⣁⣀⣩⡵⠀⢹⠀⠸⠀⠀⠸⢯⣀⣀⣈⡭⣇
⠀⠀⠀⡆⡀⣾⠀⠰⠀⠀⠈⢀⢸⠇⠀⠠⣦⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⡇⠀⠘⠔⠀⠀⣇⠂⠀⠀⠀⠁⠀⢸⠀⠀⠠⣤⠀⠘⢸⠃⠀⠀⠉
⠤⠤⠀⠤⠧⡿⡤⠤⠼⠀⠤⠼⠼⣤⣤⣤⢤⣥⠤⡼⠧⠄⠠⠤⠴⠤⢠⡧⠄⠄⠠⠼⣶⠿⠤⠴⠧⠠⠤⠦⠼⣤⣤⡤⠼⢤⠤⡼⠤⠄⠤⠤⠧⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠐⢠⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡢⢄⣀⠀⠀⠀⠘⢑⣠⠔⠓⢀⠀⣀⠴⠀⠀⠀⠁⡺⡞⣳⠄
⠀⠈⠢⠴⠈⠇⠀⠀⢀⡄⠀⠀⢰⠀⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠓⠻⣙⣻⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠐⢀⠇⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠭⣦⡄
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠡⡀⠀⠄⠘⠠⠒⠂⢄⠀⠀⢰⡀⠣⡬⢺⡀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⡔⠀⠀⠀⠀⠙⠋⠁⠀⠑⠀⠀⠀⠀⠀⠐⢤⡤⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠷⠂

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠠⣤⡁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠦⠐⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠊⠁⠒⠦⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠄⠀⠀⠀⠀⠀⠐⠳⠤⢴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠚⠈⠁

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣀⣤⡀⠀⡀⢀⡆⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⢸⡹⠁⠀⠀⠔⠋⠠⠄⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠈⢈⢃⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠁⠂
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⡀⠀⡀⠴⠀⠀⡠⠰⠂⠀⠀⠀⡀⠀⠠⠒⣀⡠⢲⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⡶⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣠⡄
⠀⢀⠚⡁⠐⠀⢨⠀⠜⠀⠲⠀⠀⢀⠟⢡⠮⠐⣉⠠⠊⠁⠀⢀⠀⢀⡆⡞⣠⠦⠋⠀⠀⠤⡠⠘⠀⠀⠈⡆⢀⠐⠛⠂⠑⣄⠠⠀⠆⢀⠔⢱⢀⡀⠴⠃
⠀⢀⠀⢣⠀⠀⢰⠮⠀⠰⠥⠤⣀⣁⠀⠀⠀⠀⣤⠀⢰⡇⠀⡏⢀⠎⣠⠿⠇⠒⠛⢀⠘⠀⠀⠀⡇⠀⢌⡠⠊⠃⠀⠀⠀⠠⠛⠟⣠⣄⡀⠁⠄⠐⠁⢀⠤⠀⠤
⠀⠀⣀⣠⣆⡤⠆⠀⠀⠀⠀⠠⠐⠁⠀⠀⡆⠀⡏⠀⣹⠁⠀⠀⣼⡿⠅⠒⠚⠁⠀⡂⠑⠀⠓⠆⠃⠋⠀⢀⠔⢁⠖⠠⠾⠐⡠⢈⠄⠊⠉⠚⠦⡀⠀⠀⠔⠀⢀
⠀⠐⡉⢀⠀⠉⠒⠀⠤⢤⠄⢠⠀⠀⡇⠀⠇⢸⠀⢈⡈⢠⣷⣞⠡⢄⡐⠲⠖⠂⠰⢈⠂⠠⠄⡀⢁⢠⠂⠐⠀⠁⠀⠀⡀⣤⠊⢡⢂⠠⠒⡁⠄⠘⡳⢎⠐⢈⠍
⠐⠈⠀⡠⠈⠀⠀⠀⠀⢠⡆⢸⡇⠀⠇⢸⠀⢸⡄⣼⣴⣛⠉⠀⠀⠀⣠⠤⠄⠀⠡⡀⠁⠀⠀⠀⠀⠄⡀⠀⠀⣀⠄⠊⠘⡀⠀⠸⠃⠀⢊⠄⠀⡠⢀⠸⠶⠁
⠀⠀⢘⠑⠀⠀⢀⠀⠀⠀⠇⢈⠃⠀⠀⢸⡆⠸⣷⣭⣉⡁⠀⠈⣉⣀⣀⠀⠀⠀⠂⠀⠉⠉⠱⠐⠚⠀⠈⠈⠁⠀⠀⢀⡐⠀⠀⠀⠀⠘⠃⠀⢸⠖⠀⠀⠈
⠀⠂⠸⠀⢣⡄⢸⡄⠀⠀⣦⠀⡠⠀⣇⠸⠣⢮⣤⠤⠤⠄⢀⣉⣈⠉⠉⠀⠀⠀⠃⡀⢀⡀⠤⠀⢄⠐⡀⠶⠀⠂⠀⡁⠴⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⡚⡀⠂⢄
⠰⢀⠂⠸⠀⢇⠸⠃⠀⠀⢹⠀⣿⢐⠉⠂⠀⠀⠀⠀⠀⠀⠀⠉⢉⡁⠤⢄⠀⠀⠀⢤⠀⡀⢀⠠⠊⠀⠟⠂⠠⠀⠠⠐⠁⡠⠂⠁⠀⠀⢢⠀⠀⠢⠀⠇⠈⢢⣀
⠀⠻⡤⠃⠀⠘⠀⡎⠀⠀⡸⢂⡑⣉⠛⠋⠁⠒⠠⣤⣀⡀⠀⢠⡞⠒⣆⠊⠙⠤⡀⠀⠑⠀⠀⠀⠔⠁⠀⠁⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢸⠀⢀⠔⠀⠀⠒⠊⠅
⠀⠀⠀⠀⠀⢸⠀⣇⠀⢪⣤⣉⣉⠉⠛⠁⠁⠲⣤⣄⠀⠁⠠⠶⢰⣤⠈⠓⠈⠀⡁⠀⠀⠀⠀⠀⠀⡀⠘⠰⠀⠀⡰⠅⠀⠤⢀⣀⠀⠀⠈⣤⠀⡠⠊⠀⠈⠢⡀
⠀⠀⠀⠀⠀⡸⢖⡡⠺⠶⠶⢄⠨⢅⣀⠙⠒⠶⠀⢀⣤⣯⡡⠛⡦⠈⡇⢠⡄⠈⠁⣀⠀⢀⡀⠠⢚⠁⠨⠄⠀⣌⠠⠀⠀⠀⠀⠀⠈⠀⣉⠛⢟⠂⠀⠀⠀⠂⣄
⠀⠀⠀⠀⢊⠔⠉⠛⠋⠂⠐⠢⢬⣁⣈⠙⠃⠀⠀⢀⢠⠌⢹⠀⠘⠇⠁⢀⡶⠀⠈⠋⢰⠈⣠⠔⠁⡀⠀⠀⡨⢀⠀⣠⡤⠀⠀⠒⠀⠝⠃⠀⠀⢢⡀
⠀⠆⡠⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠉⠁⠀⠈⣀⠀⢞⠀⠀⠀⠀⢠⢰⠀⣼⢃⣈⡡⠋⠀⠀⠃⡠⠀⠀⠀⠀⠀⡠⠂⠀⢠⠀⠀⢸⠃⠀⢀⠎
⠀⠈⠀⠀⠀⠀⡠⠐⠆⡐⠁⠀⠀⠌⢃⠀⠀⠀⠀⠀⢠⠄⠘⢁⠀⠌⢄⠘⠈⠀⢀⣴⠎⠀⢀⡀⠠⡆⠀⠠⡆⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⡄⠀⠄⠀⡤⠁
⠀⠀⠀⠀⠀⠁⠀⠀⡀⢡⠀⠀⡐⠀⠈⡆⠀⠀⠀⡀⠘⢃⠠⠈⢂⠐⠀⠆⢰⣥⠊⠉⠀⠐⠂⠀⠐⠀⢀⡀⢡⠠⠀⠐⠠⠋⠀⠀⠀⠀⠀⠀⢠⠄⠋⠀⡠⢄
⠀⠀⢀⢦⠀⠄⠀⠀⠑⠄⠁⡐⢀⠂⠂⠀⠀⠀⠘⠅⠐⡀⠀⠡⠀⠀⣡⣾⠬⠈⡐⠠⢈⠐⠂⡶⠠⢊⠘⠃⠀⠄⠀⠐⠁⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⢈⠀⡘
⠀⠀⡀⠀⠢⡀⠁⢢⠀⢀⠌⠀⡀⠀⠀⡉⠰⡆⠘⡈⢂⠐⡀⠆⣶⣦⣠⠤⢁⡀⠀⣁⢠⣀⠁⠰⢁⡎⡠⠀⠀⠘⠚⠀⠀⠀⠉⠀⠀⠀⠀⠈⡉⢀⠀⡬⢝⠁⡰
⠀⠀⠠⠀⠀⠈⠁⢉⠔⠁⠀⠀⡈⠐⠂⠀⠀⢌⠢⠈⢆⠱⠘⠿⡥⠄⢀⠈⠐⠈⠄⠠⠤⠀⢀⡷⠨⠔⠀⡀⠀⢤⠂⠊⠉⠁⠐⢢⠀⠀⠀⢠⡀⢉⠙⣤⠐⠉⡤
⠀⠀⠀⠈⣐⡶⠎⠀⢎⠑⢄⠀⠀⢈⠇⠀⠟⢄⠡⠐⡀⣷⡧⠄⠤⢁⠀⠄⡁⠒⡶⠀⠀⠒⠁⠀⣠⠰⠋⠀⠀⢸⠀⠀⠀⢀⡴⠋⢁⠀⠀⠀⠢⠠⠳⠀⠠⠡⢤
⠀⠒⠊⠉⠀⠀⠐⠄⠀⠑⠠⣁⠀⠁⠀⠀⠈⠢⡀⠀⣷⣥⠤⠀⢀⠀⠨⢐⣀⠴⠆⠀⠀⡠⠠⣊⠀⠀⠡⠀⠀⠈⢁⣰⠞⠉⠀⠀⡀⠀⠀⠏⠀⠂⠀⠛⠀⠀⠊
⠀⠀⠀⠀⠀⠐⠉⠢⠈⠉⠉⠀⠀⠀⠒⡂⠀⠀⠈⢿⣥⠤⠄⠁⠀⡀⠉⠚⠁⠀⠄⠒⠁⠀⠀⠘⣆⠀⠀⢀⣤⠴⢏⡀⠀⠀⠀⡘⠀⠀⠀⠈⠐⢚⣦⠔⠀⠒⡲
⠀⠀⠀⠀⠀⠄⠀⠀⠰⠀⠀⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠒⢊⠵⠀⠸⡀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠴⠛⠁⠠⡀⠀⠁⠒⠞⠀⠀⠀⠀⠀⠒⠁⠀⠑⠀⠂
⠀⠇⠀⠒⢄⠡⡀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢳⡀⠀⠀⠈⣄⣄⠔⠟⠁⠀⠀⠀⠀⠉⠒⡄⢈⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀
⠀⠐⢀⡀⠀⠁⠐⠀⠠⠀⠀⠀⠠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⢀⡔⠎⠊⠁⠀⠀⠑⢄⠀⠀⠀⡠⠊⣴⣿⣿⣿⣟⣿⡛⣿⢿⣿⢻⣿⣿⣿⣦
⠀⠀⠀⠈⣐⠀⠄⣙⠆⠃⠤⠤⠂⠁⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠰⢐⠩⠂⠉⡀⠀⠐⣆⠀⠀⠀⠀⢁⠖⠈⠀⢸⣿⣿⣿⣿⠿⣿⡶⣿⣿⣿⠿⣿⠿⣿⣿
⠀⠀⠘⢄⠀⢀⡀⠹⣶⢠⠜⠒⠢⠤⢄⠐⠀⠈⠀⠀⢀⠠⠀⠈⠤⠀⠈⠀⠀⠀⠀⠀⡀⠀⠈⠓⡄⠀⠊⠀⠀⠀⠀⢸⣿⡇⣿⣷⢸⣿⠁⢻⠸⢸⠸⣿⠸⣿⣿
⠀⠀⠀⠀⠀⠀⡠⡼⠉⡀⠑⠔⢀⠀⠀⠈⠑⠄⠐⠡⠐⠂⠁⠀⡈⠀⡀⠀⠀⠀⠀⠀⠈⠤⠔⠊⠀⣀⡤⠀⣠⠀⠀⠸⣿⣷⢸⣿⢸⡿⣨⠸⡄⣼⢰⣿⡧⢹⣿
⠀⠀⠀⢀⠠⠄⠊⠀⠀⠱⡀⢘⠀⠀⠂⠤⠤⠘⠂⠐⡇⠤⠤⠤⣜⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠔⢁⠤⠐⢊⠑⠀⠀⠀⠹⣿⣶⣿⣶⣷⣿⣷⣷⣿⣶⣿⣶⣿⠏
⠀⠀⠂⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠶⠎⠁⠒⠈⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠋⢡⣴⣶⣷⣾⠿⡿⣿⣄⣬⣭⣓⠲⢤⣀
⠀⠀⠀⠀⢀⡾⢰⣿⣿⣷⣿⣽⣿⣿⣟⣿⣿⣿⣿⣵⣿⣷⣮⡕⠢⣀
⠀⠀⠀⠀⣼⣿⡈⠿⠿⣿⣿⣿⣾⣿⣿⣏⠀⢀⣽⣟⣽⣿⢿⣿⣷⡈⠳⡀
⠀⠀⠀⢠⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⡛⠻⠻⢾⣯⣿⡃⢳
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣬⡙⠛⠹⣿⣿⣿⣿⠍⢁⣺⣿⣆⡅⠀⠈⠙⢧⡼
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣬⣿⣿⠟⠀⠀⡀⠀⢀⣱⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠀⠀⠀⣠⣶⣿⣿⣿⣿⣴⠖⠀⣉⣻⣶⣃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣞⣂⣭⠀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠠⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠙⢊⣙⡛⢿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠁⠈⠛⣋⠈⠀⡿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⡀⣠⣏⠐⠀⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠯⠉⠻⢿⣿⣿⣿⣧⠚⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠻⣿⣽⣾⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠋⠉⢉⠉⠙⠛⠙⢿⣿⣗⡀⢀⠀⠀⠻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⡀⡀⠀⠁⣠⣌⢻⣿⣿⣿⢏⡙⢂⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⣿⣅⢶⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣦⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡜⣿⣿⣿⣿⠛⢿⣿⣿⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡿⠱⢢⣌⢿⣧⠉⠀⠈⢹⣿⡟⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣤⠄⠙⢻⣿⣿⡄⠀⠀⢸⣿⠿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠋⠛⠃⠀⠀⠀⠈⢹⣇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⠊⣳⡖⠌⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⡹⡁⡀⠀⠀⠀⠀⢠⡈⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡞⢠⠀⠀⡄⠀⢬⢿⣿⠀⠸⣦⡄⣠⣸⣾⣿⣽⣾⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣾⣶⢠⣾⣾⡄⣾⣋⣯⣼⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢯⡿⡞⣾⡁⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣧⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣧⣽⣿⣯⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠋⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⢿⠟⢽⡿⢯⠛⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣰⡦⠀⣀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠠⠅⠀⣠⠄⡂⠀⠀⠀⠅⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⡃⠘⠀⠘⣛⣛⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣉⣉⣉⣉⣉⡅⠠⠂⢸⣿⣿⠇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠈⠁⢠⡆⣼⣿⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠆⠨⣤⠄⣀⣴⣪⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣌⢛⠋⣡⠎⠙⡽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢴⠃⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠀⠀⣀⣼⣿⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⠋⢹⡏⠐⠛⠉⡿⠿⠧⣤⣄⣰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣞⣹⡂⣀⢀⡀⠀⢸⡇⠀⣇⠀⢸⡇⢀⠀⠀⠀⠠⠀⠈⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⣠⣾⣿⢛⣿⡿⠿⣾⣿⣽⣦⣯⣼⣇⣿⣿⠀⣿⣿⡈⠀⠀⠀⠀⠀⠀⡀⠈⠹⣷⠜⠛⢦⣾⣄⡤⡄
⠀⠀⠀⢀⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣿⡿⡧⢱⣟⠇⠀⠀⢐⣦⡀⠀⣀⠀⢸⣿⡟⠲⣾⠁⢻⡌⢶⠚⠀⠀⡀
⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣶⡿⢻⣾⣿⠟⣿⣋⠏⠃⢆⠀⠀⠀⠟⠒⠶⠆⢀⣡⣂⣠⣤⡼⠛⢏⡉⠿⠉⣹⡟⢢⣼⡷⠒⢡⣾⡅
⠀⠈⠛⠻⣿⣿⣿⣿⣹⣿⣼⣿⣶⣿⣿⣿⡏⠋⣐⣶⣨⣤⡀⠈⠛⠛⣙⣿⣿⣿⡟⠁⠉⣿⣿⠈⠁⣄⣸⡉⣳⡋⢻⣷⢦⣾⡿⠁
⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣦⣿⣬⣄⣁⣀⣀⡐⣀⣉⣉⣰⡟⠹⣿⣿⣿⣿⡷⠠⣾⣿⣿⣦⣤⣷⣾⣭⣿⣯⣽⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠉⠛⠃⠉⠉⠉⢩⢀⠁⠉⠩⠤⠖⠌⠻⠄⠰⠶⠂⠲⠛⠛⠛⠏⠡⠤⢿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡔⡞⠓⣶⡄⠀⠀⠀⠀⠀⢀⠎⠀⢱⠀⠀⠀⠀⠀⠀⠀⡴⠉⠙⡄⠀⠀⠀⠀⠀⢀⣔⣲⠛⠛⣷⡀
⠀⢰⠁⠈⠈⠉⠁⠘⡄⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠱⡀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠀⢱
⠀⠘⡄⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠣⡀⠀⢀⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡜
⠀⠀⠈⠢⠤⠤⠴⠁⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠈⠚⠙⠚⠉⠁⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⢀⣴⠾⠷⢢⡄⠀⠀⠀⠀⡠⠊⠉⠾⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⡨⠛⢦⡀⠀⠀⠀⠀⣶⣿⣿⣿⡅
⠀⠀⣞⡂⡅⢘⠹⣸⡅⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠀⠀⠀⣠⡾⡿⣷⣄
⠀⠈⣖⠅⡁⢀⢒⢼⠆⠀⠀⠘⣄⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣀⢀⠤⠊⠀⢀⠇⠀⠀⠀⠀⣟⣝⢾⡳⣿
⠀⠀⠛⡯⣄⣀⡧⠋⠀⠀⠀⠀⠈⠑⠲⠤⠴⠊⠀⠀⠀⠀⠘⣅⣀⣀⣨⠴⠋⠀⠀⠀⠀⠀⠹⣵⣳⣻⠏
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⡰⠋⠙⠉⠉⢆⠀⠀⠀⠀⠀⢀⡠⢤⣀⡀⠀⠀⠀⠀⠀⢀⡠⠦⣧⣤⡀⠀⠀⠀⠀⡴⢋⠁⠈⢉⢙⢦
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⡆⠀⠀⠀⢀⡞⠃⡐⠀⠁⢹⡀⠀⠀⠸⠐⠀⠀⠀⢀⠐⠈⡇
⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⠇⠀⠀⠀⢸⡇⠉⠁⠀⠸⢸⠁⠀⠀⢠⠀⠠⠀⠀⠀⠠⢠⡇
⠀⠀⠀⡇⠀⢀⡰⠃⠀⠀⠀⠀⠀⠈⠓⠒⠒⠁⠀⠀⠀⠀⠈⠻⣴⣀⣀⣠⠎⠀⠀⠀⠈⠢⣁⡀⢀⣀⡴⠏
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠸⠃⢢⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⢴⣶⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀
⠀⠀⠀⠀⠈⡂⠈⠆⠀⠀⠀⠀⡠⠚⢉⠃⣭⠷⣄⠀⠀⠀⣀⡴⠹⠁⠐⢁⠤⡏⠀⠀⠀⠀⢠⣖⣟⣲⣋⡇
⠀⠀⠀⠀⢀⡎⠀⡁⠀⠀⠀⢸⠷⠓⢀⠗⠀⠐⢮⡆⠀⠀⠇⣁⠤⢲⠀⠀⡾⠁⠀⠀⠀⡤⢯⠒⢯⠤⣧⢼
⠀⠀⡠⠒⠁⢀⠔⠁⠀⠀⠀⠈⢄⢛⠨⠆⢠⡉⡴⠀⠀⠀⢇⠀⠀⠎⢒⠞⠋⠀⠀⠀⠀⢳⠞⡶⢻⣲⠏⠁
⠀⠀⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠒⠉⠀⠀⠀⠀⠀⠉⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠤⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⠄⠀⠈⢄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠢⠀⠀⢂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠐⠄⠀⠀⠑⢄⠀⠁⢀⠀⠢⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠢⢄⠀⠑⢄⠀⠢⡀⠡⠀⢂⠀⠄⠀⠀⠀⠈⠠⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⠑⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠢⠤⠤⠄⣾⣄⣤⣤⢤⠦⡤⠴⡼⠇⠀⢀⠀⠀⠀⠀⠀⢸⠀⠐⠖⠰⠤⠴⠤⠦⠂⠒⠒⠚⡅⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢣⠀⠀⠀⠀⢻⡳⠤⣤⣠⣄⣤⣀⣄⣤⣠⡤⣠⠤⡔⡆⠀⠈⠀⠐⠂⠀⠀⠘⠓⠆⢤⠀⠀⡘⠇⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⡜⣧⠀⠀⠁⠈⡒⠉⠠⠀⠀⠐⢌⠲⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠰⠀⡄
⠀⢀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠠⠤⣼⣧⡀⠈⠀⠁⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⢀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⣀⣠⠬⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⡇⠀⠈⠐⠂
⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⢦⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⢀⡀⠀⣨⠤⠀⠈⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠁⠉⠉⡁⠀⠐⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠶⠿⠛⠛⠛⠛⠛⠛⠿⠶⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣀⣠⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣴⣿⣵⣿⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢛⡿⣻⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣻⣄⠁⢀⡩⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠋⠁⠀⢈⣿⠁⠰⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠬⠁⡙⣭⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡰⠷⠆⣰⣞⣷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠀⣀⣼⠳⣶⡻⢮⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢠⠀⠸⣿⣿⢄⠛⣬⣙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡐⠃⠀⢸⣿⢠⡈⢻⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣀⣠⡞⠃⠀⢠⣿⣿⣷⣼⣻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣥⣀⣀⡀⣀⡘⣯⡄⢉⣻⡗⠠⣾⣿⣿⣝⢷⡼⠋⠀⠀⠀⠀⠀⠈⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢿⣿⢉⠘⠛⠛⠻⣿⣿⣿⣿⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣦⣠⣿⣿⡠⡀⡄⠀⠀⠈⠻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠆⠛⠉⠉⠀⠉⠛⠻⠉⠻⣥⣡⡀⠀⠀⠀⠀⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⣀⡀⠤⠒⠉⣀⣤⣔⣾⣾⣷⣦⡌⠡⣄⢘⠅⠀⡄⣥⡁⠑⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠁⠈⠀⢰⣦⣴⡒⢘⡷⣺⣿⡿⠛⠉⠀⠀⠘⣿⣿⣿⣠⣼⡧⢀⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠘⡿⣇⢀⣀⣴⣤⡶⢿⢿⣿⣿⣧⣿⠞⠋⠀⠀⠀⠀⠀⠀⠨⣷⠙⠛⣳⠼⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣷⣠⣸⢾⡇⡛⡽⣿⣿⣾⣝⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣉⢿⣾⣾⣽⣾⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠋⠉⠁

⢀⡴⠀⠀⠀⠀⢀⠔⠀⠀⠀⠘⠁⡄⠀⠠⡌⠀⠀⠀⠀⠀⠀⢠⣄⡔⠅⠀⠀⠀⠑⠈⠀⠰⣄⠙⠂⠀⠀⢠⠁⠀⢀⢤⣤
⢨⡦⢀⣀⡀⠀⠋⠀⠄⠀⡄⠀⢘⢁⠀⢰⣄⠀⠀⠀⠀⣀⡠⠾⠋⠀⠀⠀⠀⠀⣈⠀⠘⡆⠈⠀⠀⢀⡄⠈⠵⡒⠙⢌⠛
⠈⠋⠈⠉⠈⠀⠊⠐⠀⠀⠀⢀⡾⣀⡠⠀⠉⡄⠀⠀⠊⠁⣀⠀⠀⠀⢤⣄⡄⠰⠋⠀⠂⢀⠀⠐⢂⡀⡀⠀⠀⠀⠀⣄⣀
⠀⡈⠀⠀⠀⠀⠀⠂⠀⢀⡤⠶⠂⢽⠃⠜⠶⣅⡒⡀⠀⠘⠏⣢⡶⡸⡗⠨⣿⡓⠒⠀⢠⡤⠚⠁⠈⠑⢙⠳⠍⠀⠀⡎⡉
⡐⡂⠀⠀⠀⠀⠀⠀⠟⠀⠀⠰⠚⠊⠁⠀⢦⡈⠛⠀⠀⠀⠚⣡⠆⠀⠑⠦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠶
⠀⠁⠃⠀⠀⠀⠹⣦⠀⠀⠀⠀⢊⡀⠀⠳⠀⠁⠀⠀⠀⠀⠀⠀⠸⠀⠈⡁⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡴
⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⠄⠀⠀⠀⣙⣈⣛⠤⠀⠀⠼⠟⣥⠀⠀⢠⠊⡀⠀⠀⠈
⣆⠀⢳⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠣⠀⠈⣁⠀⣀⠀⠀⢠⣽⣿⠟⣃⣘⠀⡄⣱⠈⢧⣄⠀⠀⠉⢠⣾⡄
⠈⠐⠻⡇⢀⡎⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠀⢀⡀⠉⠀⠀⠐⠂⠀⢠⡶⠟⢫⡤⠹⣟⠰⠙⠋⠲⠶⣄⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡀⣀⠀⣴⠦⢐⣬⡀⣀⡀⡀⠈⠃⠀⠀⠀⠀⠀⢠⡵⠘⠀⠀⠙⠶⠀⠀⠀⢀⣀⠀⠸⠇
⠀⡄⢻⣿⠿⠳⠆⠀⠴⣺⠘⢧⣮⠢⡭⣇⣀⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣠⠆⠀⠈⢷⠀⠀⠀⡀⠈⡿⠂⠀⠈⠁
⠺⠡⠀⠉⠙⠀⠀⠀⠐⠁⡾⠋⣠⠅⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⢀⡀⠀⠁⠐⠃⠀⠀⠚⣠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠀⠀⠀⠀⠈⠁⠢⠴⣤⣀⣀⣀⠀⠀⠀⠘⠋⠀⠀⡀⠀⠻⡀
⢀⡆⠀⢀⣤⣼⡆⠑⠂⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠈⣃⣝⢦⡛⡤⠤⠈⠀⠀⠐⠛
⡞⠀⠀⠉⣉⠁⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⣤⣤⠂⠀⠀⡀⢴⣧⡀⠀⠀⠌⣱⠞⢉⡀⠁⠉⠘⡓
⠀⠀⠀⠋⢁⡀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⢀⣿⡿⠁⢶⠄⡯⣼⣀⡓⠀⠀⠀⠀⠋⠀⠞⠁⣴⠀⠀⢉⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠚⠀⠀⡈⠁⠀⠀⠀⠈⠣⠀⠀⠈⠴⠛⢁⡍⠃⠀⠰⣄⠉⠀⠀⢀⡀⠀⠀⠀⠀⠉⡠⠄⠈⠓
⣆⣷⠀⡞⢐⠂⠀⢹⠀⠀⠀⠀⠀⠠⠀⢰⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣭⠷⠀⠸⡀⡜⢤⠀⠀⠀⠀⠘⠧⠤⠄⡀
⠈⡟⠰⠄⠈⠁⢦⣈⠀⠀⠀⠀⠀⠀⣀⣬⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠶⠂⠁⠀⢦⡀⠀⠀⠀⠀⠀⡀
⡞⠀⠀⠀⠀⠀⣈⠻⠆⠀⠀⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠁⠀⠀⣀⡀⠀⢱⣄
⡐⡀⢀⡅⡴⣠⠘⣿⠅⠀⢀⡴⠶⠒⠀⣤⣴⣶⡃⠀⠠⠚⠸⢄⠛⢥⡀⣊⣀⡀⡀⠀⠀⠀⡄⠀⠐⠀⡒⠀⠀⢾⠡⠠⠄
⢁⣤⠹⠐⢈⡙⠶⠌⠀⠀⠈⢔⡠⡀⣷⠆⣙⡿⠶⠄⠀⠡⠀⣀⠀⠀⠙⢒⣺⣿⠟⣂⡀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠰⠞
⢈⡴⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣋⠑⠸⢡⣈⠀⠀⠀⠀⠀⠀⠈⠳⠂⠉⡩⠽⠷⠈⣟⢂⢳⣤⡀⠤⠀⠐⢮

⠀⠀⠀⠀⠀⡠⠒⠉⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢀⠔⠦⣀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀
⠀⠀⠀⠀⢠⡟⠁⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⣾⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠐⢄⠈⣧⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠈⢳⡿⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡀⠀⠀⡀⠀⢀⣀⣉⣿⡶⠦⣤⣤⣿⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡤⠚⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉⠒⠦⢤⣤⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠴⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⡶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⠻⠿⠀⣹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠐⠻⠿⠯⠉⠻⢧⣄⠀⠀⠀⠀⠀⠂⠀⠀⠤⠠⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠛⠛⠶⡄⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣄⣀⠀⠐⠂⡈⠀⢀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣶⣦⣅⣀⣲⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋⠙⠻⢿⣿⣿⣿⣿⣿⡆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠤⠖⠛⠁⠋⠀⠀⣀⣀⡴⠞⠃⠈⠙⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠉⠁⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠈⢄⢀⠘⠁⠀⠀⠀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⡤⠊⠁⠠⠊⠁⠀⠀⢄⠀⠀⠀⠀⡀⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠔⠋⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⣾⡀⠀⠀⡆⠀⢀⠄⣿⡖⢡⣶⠇⡀⠁⡀⠀⠀⠀⣾⡏⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠹⠗⠀⠉⠁⠀⠀⡀⠀⠀⠀⢉⠙⢊⠛⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠴⠶⠟⠀⠠⠃⠀⠰⡀⠘⠿⠟⠠⠈⠠⢀⠂⠀⠀⠀⠙⠿⠓
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢀⠄⠠⠠⠄⠐⠐⠀⠀⠀⡀⠀⠐⠀⠀⠀⣀⠈⠀⠠
⠀⠀⠀⠐⠀⠀⠀⠘⣤⡄⠘⢻⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⣦⡄⢀⣀
⠀⠀⠀⠰⠀⠀⠀⠀⣿⠿⠀⠈⠉⠀⠀⠀⢠⠀⠀⠀⠀⠐⣿⡆⠀⣿⠇⠀⠀⠀⠀⠀⠾⠿⠁⣼⡿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⣶⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⠀⡄⢰⠀⠀⣀⣀⣀⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠴⠾⠛⢀⠜⠀⠀⡄⠀⠈⠛⠉⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠁⠀⠀⠀⠈⠂⡀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⢰⠂⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⡆
⠀⠀⠀⠀⠀⢸⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠘⡄
⠀⠀⠀⠀⠀⢰⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣴⠃
⠀⠀⠀⠀⠀⢼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⢀⣠⣧⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣼⡅⢛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⡆
⠀⠀⢀⣿⢱⣿⣿⢻⣿⣿⣿⡄⠀⠀⠀⣼⠃⣿⡇⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠟⢁⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠊⢹⡆⡀
⠀⠀⢸⡏⢸⣿⣿⣸⣿⣿⡟⡇⠀⠀⠀⣿⣄⣿⠇⢤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⣾⣦⣼⣷⣧
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠄⠀⠀⠀⠀⠛⣿⣿⡄⠀⠀⠀⠀⠀⣼⢳⣿⣷⢸⣿⣿⣇
⠀⠀⠸⠇⠘⠛⠛⠻⠟⠿⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣸⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⣸⠃⢸⣿⣿⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣤⣀⣿⣀⣤⣿⣿⣿⡤⠀⠀⠀⡿⠀⢸⣿⣿⢈⣹⣿⣿⣧
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⡟⢸⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣶⣶⣤⣤⣤⣤⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠀⠛⠛⠃⠒⠛⠛⠛⠛
⠀⠀⢸⡇⢸⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢸⣿⣿⣾⣿⣿⣿⣿⠀⠀⢶⣤⣤⢀⣀⣀⣀⣀⣀⣤⣤⣵⠂
⠀⠀⢸⡇⣺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣾⣿⣿⣠⣿⣿⣿⣿⠀⠀⢸⣿⡃⠀⢙⣟⡓⠀⢹⣿⣿⣿
⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⣀⣿⣥⣀⣸⣿⣿⡇
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠘⠷⣶⣤⣤⣤⣤⣤⣤⣶⠾⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢃⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠘⣿⡤⠄⠤⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⢀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡥⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠆⠀⢳⡆⠀⠀⢐⠓⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠨⠛⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⣹⡁⠤⠈⠀⣠⠄
⠀⠀⠀⠀⠠⣄⠀⠀⠀⢷⡀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⣸⡗⠂⠄
⠀⠀⠀⠀⠀⠁⠐⠃⠠⢀⣏⠀⠂⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡷⠒⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠀⣀⠀⠠⢸⡀⡀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠑⢀⡀⠸⣧⠈⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⢤⠞⣿⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⠀⠀⠀⠀⠠⠠⠶⢲⠦⠶⠶⠇⠰⠳⠴⠶⠶⠴⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⠀⠀⠀⡁⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡷⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠀⠄⠰⡤
⠀⠀⠀⠈⠓⠀⠑⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⢠⣼⠃⠀⠀⡀⠀⡘⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠲⠄
⠀⠀⠈⠐⠀⠀⠈⢸⣇⡜⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⡀⠉⠑⣾⣄⣠⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠠⠤⠄⠲⠼⢾⡿⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣰⠞⠂⠀⠀⠀⠀⠀⠀⠀⡉⠀⠁⠀⢀⡹⠷⣤⡆⠀⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠠⠀⢠⣼⡟⠂⠀⠈⠀⠄⠀⠀⠀⠀⠈⠀⡀⠀⠀⡀⠑⠉⠉⠿⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢤⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡷⣾⠟⠉⢣⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢾⡿⣯⣏⣀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠈⡏⠸⠟⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢀⣄⣴⡏⣾⣷⣴⢤⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠀⠟⠀⠋⠈⢱⡈⣱⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣌⢻⡷⠞⠢⠄⢀⣸⠇⢹⢇⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⠛⣿⣿⡈⠃⠀⠀⠀⠀⠀⠀⠈⢈⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠛⣡⣞⣿⢿⣷⠀⢿⠀⠀⢀⣦⠀⢀⠋⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡘⠷⢸⡟⠸⠟⢹⣿⠿⠀⠀⠀⠀⢸⡟⠘⠛⡀⢘⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠼⠛⢇⣉⣥⠆⠀⠀⠀⠀⠈⠀⢡⣾⡇⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡤⠀⣠⡴⢯⡼⠇⢀⣀⣙⠀⠀⠀⢀⡼⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣤⠀⠿⠁⣼⢟⣾⣿⣿⠀⣜⠉⠁⢰⡆⠀⠀⣠⡿⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⣡⡟⠸⠇⣠⣾⣿⣿⣿⠀⠟⠋⠀⠠⡤⠄⠀⠉⠁⠘⢿⣿⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠻⢠⣾⣴⣿⣿⣿⣿⠃⣸⠖⠂⠀⠀⠀⠀⠰⢀⡄⠀⢶⡟⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢸⡷⢠⣼⡿⣿⣿⣿⡏⣸⣟⡛⠁⣰⠀⠈⢹⡄⠄⠀⢆⣈⠳⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠘⠁⢈⠻⣷⣿⣿⣿⣿⡟⡟⠉⠀⠈⠀⠀⠀⣤⡄⢀⣸⠇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣦⠀⠈⢱⡞⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠈⠉⠀⣼⡁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣏⠘⡿⣾⣤⣿⣿⣭⣾⣿⡿⠖⠀⠂⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⡜
⠀⠀⠀⠀⠀⠀⢠⣿⣹⡶⠃⠙⣿⣿⣿⣿⣿⣿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⡏⢩⣥⢀⡀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠟⠧⠘⣿⣼⡇⣿⣿⣿⣿⣿⠉⠋⠀⠀⠛⠠⠀⣠⠋⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢠⠀⣀⡸⠃⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⢀⡄⠁⠀⠀⣰⠏
⠀⠀⠀⠀⣸⣿⣍⠀⣹⠇⣼⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣴⠋⠀⠀⠀⠰⠋
⠀⠀⠀⢰⣿⣿⠃⠀⣿⣾⣿⣿⣿⣿⣿⡿⢀⡀⢀⣶⣿⠟⠀⣠⣷⠘
⠀⠀⠀⠸⠛⠁⠀⡄⣿⣿⣿⣿⣿⣿⣏⡿⠟⣻⣿⠁⣿⣯⣾⠟⡿⠀⢀
⠀⠀⠀⠀⠀⠀⠰⢁⣿⣿⣿⣿⣿⣳⠏⡀⢠⣿⠷⢀⣈⠛⠓⣶⣷⣤⣀⣀⠁⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⢍⢤⡛⢹⡤⣶⡏⠉⢉⠉⢉⢙⡁⠈⡏⢉⠉⠍⠉⠛
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢀⡜⣀⠀⠉⢰⣿⡇⠀⠀⠁⢸⡎⠁⠁⠁⢹⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣹⣿⣼⣿⠀⠀⠀⢿⡇⢰⣀⡇⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢀⣿⣿⣿⡿⠀⠀⠀⢸⡇⠈⢿⠃⠘⣿⢠⠀⠀⢸⡀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⣿⣿⢿⣿⠇⠀⠈⠀⠘⣧⠀⣸⠁⢰⣿⡇⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⣾⡏⠀⣼⡟⠡⣬⡟⠀⠀⣸⠇⢀⣿⠀⠁⠀⣸⢹⡇⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢀⡿⠀⣸⣿⠃⣴⠃⠁⠀⣸⡏⠀⡼⢿⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢸⡇⠀⣿⡏⡸⣏⠀⠀⠀⢻⣿⣶⣧⣼⠀⠰⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣼⠀⣰⡟⢠⠃⠈⠀⠀⠀⠈⣿⠁⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠘⠀⠾⣧⢆⠀⠀⠀⠀⠀⠐⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠒⠶⠦⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃
⣦⣴⣶⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣭⣭⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣷⣶⣤⣤⣤⣤⣤⡄⢀⣥⠠⠶⠯⠅⢸⣿⣿⣿⣿⣿⡇⠀⠒⠒⠒⠂⠀⠀⠀⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡄⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣠⣐⣀⡀⠀⠀⣠⢤⠤⠴⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⢸
⣬⣤⣤⡄⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⣶⣿⣧⣼⣿⣿⣷⡀⡀⣠⠃⠦⢶⢀⣀⣂⣿⣿⣿⢸
⣿⣿⣿⡇⣸⣿⣿⣿⣿⣷⣶⣶⣦⣌⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡰⣟⣔⣋⡃⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⡿⠿⠿⠿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠾⠿⠿⣿⣿⣿⣿⣿
⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠡⠨⠤⠄⠤⡠⠤⣄⢤⡰⣄⣀⣠⣤⣄⣀⣄⣀⣠⣀⣤⣤⣤⣤⣄⣐⣖
⠀⠀⢁⡀⣤⣤⠤⠤⣀⠀⣀⡀⠄⠀⣀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠤⠤⠴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠆⠀⠒⠛⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣶⣶⡟⠒⠀⠀⡀⠀⠀⠀⣴⢯⠘⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⠟⠣⠄⢂⠀⠄⠀⠀⠀⠾⣞⣾⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢈⣙⠧⠻⣀⠀⠀⣿⣷⡆⠀⠀⠀⠀⣌⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⣸⡿⠿⢤⡄⣡⢐⣿⣿⣿⡀⠀⠀⠀⠀⠈⢈⣁⠁
⠀⠀⠀⠀⠀⠀⢀⣷⠾⠿⡁⠉⠀⢹⣶⠂⢹⣿⣽⣏⠀⠁⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⣾⠻⠆⠀⢷⡎⠐⠛⠫⣴⣿⣟⠁⢭⣤⡃⠀⢸⠋⠀⠀⠀⠀⢀⣠⣶⡿⠈⢀
⠀⠰⠐⠀⣦⠛⠁⢹⣄⢸⣿⠧⠀⠠⣤⡿⡧⣭⡤⠓⢩⢧⠀⠀⠀⠀⠀⠀⠐⠛⠉⡅⠂⠀⠀⠀⠀⢲⠒⠀⠂
⠀⠀⠀⠀⡇⠁⠀⠉⠙⢻⠉⠓⢶⠈⢈⡏⠉⠉⠁⠀⢸⠀⠘⠖⠀⡄⠤⠀⠀⠢⢠⡄⣰⣷⣶⣤⣄⡘⠈⠁
⣀⣂⣒⣛⢓⣒⣒⣐⠒⠚⠒⣒⣒⣒⣚⣓⣀⣒⣒⡂⣖⣀⣀⡐⣚⣓⣒⣓⡐⠚⠚⠒⣓⣛⣛⣛⣓⣀⣒⣒⣂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠲⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⢶⣤⠀⠀⠀⡀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠀⠀⠉⠉⠛⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢈⠌⡈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡂
⠀⡀⠀⠀⠀⠀⠀⠀⠈⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣧⠴⠘
⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠐⠅⡐⠠⡀⠀⠀⠀⢀⠀⡳⠋
⠙⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣢⡤⢤⡋⠈
⠀⠀⠀⠙⠲⠲⣖⣠⡤⠤⠤⠤⠤⣤⠋⠙⡻⣿⣿⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣴
⠀⣀⣀⣀⢰⠟⠁⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⢹⡟⠀⠀⠀⠀⠈⢰⣦⣄⡀⢀⣀⡀⡀⠁
⡠⠊⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⡀⣀⠀⠀⠐⠊⠣⡀⠉⠉⠉⠉⢣⠟
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠈⣄⠀⣬⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣀⠄⢀⡔⠉⡼⠁⢀⣀⣀⢤⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡆⣄⣤⡶⣾⣷⡄⠁⠁⠀⠀⠉⢸⡀⠀⢦⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣿⡿⡟⠦⠿⡔⠋⣿⠁⢠⣜⢀⣠⣥⡼⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣿⠹⠟⠀⠀⡃⢱⡄⢆⠂⠟⢟⠤⠼⠛⠚⠋⠉
⣀⣤⣤⡀⠠⠤⢀⣀⠀⠀⣈⡅⢀⣶⣦⣀⠀⡴⠟⠐⢟⣮⣁⣌⡟⠀⠈⡄
⠈⠍⠉⢁⠖⠐⠉⠉⠀⠉⠉⠩⢾⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿⠋⢻⡀⠀⣷⠲⢤⣄⣀⡀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣰⠀⠂⣜⠄⠀⠀⠀⠀⢠⡾⠑⡄⠘⣇⠀⠈⠀⠀⠀⠀⠉⠁⠈⢙⣦⠐⠈
⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⠶⠁⠀⣐⠟⠀⠀⠀⠀⢴⠏⠀⠀⠑⡄⠹⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⣈⡄⢀⡀⠀⠀⣰⠇⠆⠀⠀⣶⠀⠀⠀⣠⡦⠂⠀⠀⠀⠀⠈⠄⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢻⡇⠀⠀⠠⠂⠄⠀⡂⠀⢠⢇⠠⠐⣠⠏⡧⣀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⣤⠸⠀⠀⠀⣶⣦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠃⠀⠀⠀⠀⣠⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⢀⣠⣤⡖⣾⠐⠶⠦
⠀⢀⠊⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⠋⠁⢡⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒
⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠈⡠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠑⠂⠐⠂
⡿⠀⡇⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠂⠉⠉
⡀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠓
⠐⠀⢠⡄⠢⣀⠀⠋⠉⠀⠀⠐⠒⠲⠤⠖⠾⠁⠀⠀⠀⠀⡀⠀⢈⡀⢠⠆⠀⢠⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣬⣯⣔⠀⠉⣀⣀⣀⣒⣚⣻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠒⠙⠹
⠀⠀⠈⠂⢿⠿⣿⣿⣿⣿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀⠀⠄⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⢀⠀⠀⠙⠻⣟⣙⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⡁⠀⢀⠀⠹⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠴⠄⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡄⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣴⣦⡐⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣤⠀⡀
⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣦⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢧⠈⢻⢣⡔
⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠠⡀⠀⠄⠀⠀⠀⠀⠿⠛⠃⠀⡠⠴⠈⠃⠀⠀⠀⠀⢄⠈⠄⡀⠀⠇⠀⠀⠀⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣠⢾⠡⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⠈⠀⠀⠀⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠀⣯⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢼⣳⣶⣿⡿⠟⡳⠶⠶⠦⢀⣀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁
⠀⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⡶⠄⡀⠀⠀⠀⠀⠰
⠀⠈⠑⠠⢤⡴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠵⣄⠁
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⡓⠀⠀⠀⠀⠀⠀⢀⠄⠔⠁⢀⠀⠐⡠⠞⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠸⠷⠁⠀⠀⠀⠀⠀⠀⠌⠀⢠⢋⢆⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠒⠀⠀⠀⠀⢼⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠎⠀⡔⢀
⠀⠀⠀⠀⠐⢢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠠⢃⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠇⣰⣿⣏⠉⠙⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠋⠁⠾⠿⢿⣿⣦⣄⣀⣉⢉⣁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣛⠻⣷⣶⠀⣼⣿⣿⡿⠋⢀⣠⣤⣤⣀⠀⠙⢿⣿⡿⠋⠉⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢿⠿⣷⠘⣿⢸⣿⣿⡟⢠⣾⠟⢉⣭⠉⢻⣷⠀⠈⠟⠀⠀⢀⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣻⢷⣤⠾⢋⣰⣿⠘⣿⣿⠀⣿⡏⠀⣿⣏⣀⣸⡿⠀⢰⡀⢀⣾⠟⠻⣷⡜
⠀⠀⠀⠀⠀⠀⣰⣿⣛⠋⠉⠀⠈⠛⠿⣿⣧⠙⣿⠈⣿⣧⠀⠈⠛⠛⠛⠁⢀⣾⣧⡈⢿⣿⠇⣹⣿
⠀⠀⠀⠀⠀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⠂⠹⣿⣷⣤⣀⣀⣠⣴⣿⣿⠻⠿⠦⣤⣶⣿⡏
⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠟⡁⣾⠟⣦⠈⣿⠏
⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢻⣬⣵⠀⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠽⠛⣉⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣻⠿⠋⠁

⠀⠀⢀⠄⡀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠻⣄⠈⠁⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠿⠛⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⢰
⠀⠀⠴⢲⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠤⠴⠶⠚⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠤⠤⠄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⢀⠀⠐⢦⡀⣀⢸⠀⠀⠀⠀⠀⠃⣠⠖⠉⠀⣀⢀⣀⠀⠀⠢⡄⣠
⠀⢠⡇⠀⣀⠀⠤⠤⠄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢰⠋⢧⡀⠀⠀⠀⠀⠀⠀⠉⣀⡼⢺⠀⠀⠀⠀⠀⠀⠳⠄⡀⠀⠀⠀⠀⠗⠠⢀⣷⡏
⠀⢸⣷⠋⡀⠛⠀⠀⢂⡴⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠛⠓⠒⠒⠒⠚⠋⠉⠀⡾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠤⣐⣽⠟
⠀⠈⢿⡋⠃⠜⠀⠒⠒⠈⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠦⣌⣙⠒⠚⠛⣋⣡⢄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠶⠲⠶⡛⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢭⣭⣭⣽⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠐⠂⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⡸⡄
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⣀⡀⠀⠠⠚⠁⠁⠀⠮⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠦
⠘⠁⣬⠁⠀⠀⠀⠀⠀⠀⠘⠮⣏⠄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠚⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠔⡁⠈⠃
⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠤⠴⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣤⣤⣒⣠⣤⣤⣶⣖⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣴⠟⣡⡶⠿⠿⢛⣩⠵⠚⠉⣉⣡⣤⣴⣾⣿⣍⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣠⢞⡵⠋⠁⢀⣀⠼⠉⣀⠤⠚⠛⠉⠉⣁⣀⣀⠀⠉⢉⣛⢻⣇⣒⣢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠱⠁⢨⠀⢀⣊⡥⠤⠒⠚⠁⠀⠐⠒⠲⠾⠭⣉⣉⣁⣒⣂⠈⠙⠛⠺⢭⡑⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡠⠃⢀⡴⡣⠒⠉⠀⠉⠉⠉⠙⠛⠛⠉⠒⠒⠶⠤⠤⠤⣉⣉⡉⠛⠢⣤⡀⠀⢚⡷⣶⣞⠛
⠀⠀⠀⠀⠀⠀⠀⡀⣠⡤⠀⣤⣤⣤⣀⣀⡀⣀⣰⠿⠋⠀⢀⠟⠀⡁⠤⠴⠖⠒⣒⠀⠈⠀⠀⠀⠀⠒⣒⣒⡒⠲⠀⡀⠉⠁⠀⡀⢉⠒⠀⠙⠦⣉⠳⣄
⠀⠀⠀⠀⣠⣴⡞⡼⣣⢂⡼⢋⣴⠖⠉⠁⠈⠋⢀⠒⢒⡚⠁⠀⢀⡴⠒⠒⠉⠉⠉⣀⣀⡀⠒⠒⠶⠦⣤⣀⣀⣀⡀⠉⠁⡀⠢⢍⠛⢷⣄⠠⡐⢮⡳⣌⠳⡀
⠀⠀⢀⣴⣿⡏⠐⣱⠃⠊⠀⠛⠕⠊⠁⠀⢐⣲⡶⠞⠋⠁⠀⡀⠀⢩⣐⡒⠄⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠵⣦⣄⠀⠀⠈⠑⢄⡙⠢⡀⠙⢷⡄⠙⢎⠳⣽⣄
⠀⠀⢸⣿⡋⠁⣀⢃⣠⢤⡄⠀⠀⠠⢈⣉⡭⢍⡈⠁⠶⠞⠛⢂⣀⠀⠈⠉⠛⠃⠤⢄⡀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠉⢢⡈⠲⡆⠹⢦⠈⢳⣌⢎
⠀⠀⣼⠹⡇⠀⠀⠘⣷⣶⠄⠀⠀⠀⠀⢀⠀⢠⡤⠵⠖⣂⣀⡀⠈⠉⠁⡒⠢⢀⠀⠠⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠠⡀⠈⠀⠀⠀⣀⢻⣄⠸⠀⠀⡆⢺⣿⣦
⠀⠀⣿⡀⠿⠀⣤⣠⠈⠋⠴⠂⠀⠀⠤⠀⠀⠀⠙⠲⣬⢍⣈⠉⠙⠂⠀⠉⠉⠛⠤⡀⠙⢦⡀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠙⢦⣄⠀⠀⠈⠙⢿⣇⠀⢳⣿⡀⢻⡟
⠀⠀⠘⣇⣠⢠⡀⠙⠡⠀⠀⡀⠴⠒⠒⠢⢄⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⣄⡀⠀⠀⠈⠑⠢⠝⢦⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⢧⡀⢠⠀⠀⢻⡄⢸⡿⠇⠀⣷
⠀⠀⠀⣻⠏⡜⢀⣏⠀⣤⡀⠀⠐⠲⣆⠈⠒⠤⣄⠀⠉⠒⠂⠤⣀⠀⠀⠀⠉⠳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡀⠀⠀⢀⡀⢳⠀⡄⠀⠈⠁⠈⠇⢱⡀⢸
⠀⠀⢠⠇⣸⠀⡼⠃⢰⣶⢄⣀⡙⢆⢰⠀⠐⠄⠀⠙⠲⠤⠀⠀⠀⠉⠒⠦⠈⠐⠒⠽⠶⢤⣄⠀⠀⠀⠀⢤⡀⠈⠳⣝⢆⠀⢤⢳⡈⡆⡇⠀⠀⡇⠘⠀⢸⡇⣼
⠀⠀⡟⢠⠏⡜⠁⠀⠉⠈⠁⠉⠻⣦⡱⣷⠀⠀⢠⠀⠀⢆⠘⢆⠈⠓⠤⡕⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡑⡄⠀⠈⢎⢃⠈⢧⠆⢱⠀⠀⠀⡇⠀⠀⢸⡇⡍
⠀⢸⠃⠊⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣇⡀⠘⡄⢣⠀⢈⢦⡀⠑⢤⡀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⢠⡀⠀⠘⢜⠀⠀⠈⠀⠀⢸⡇⠀⠀⢀⠞⠀⣠⢦⣾⠁
⠀⣾⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⣌⢧⠀⢢⡀⠀⠀⠈⠉⠀⠀⠈⠓⠒⠒⠈⠳⡄⠀⠳⠐⡆⠈⠀⠀⠀⡰⠃⣼⠁⠀⡴⠃⠀⣰⠃⣿⠇
⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⢊⠈⢳⡀⠱⣄⠠⣀⠲⢌⠑⠢⠄⠀⣀⢣⡀⠈⠀⠀⢀⠇⠀⠀⠀⡰⢁⠞⠁⠀⠊⠀⡀⡰⢃⣼⠏
⢸⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠳⣄⠁⣀⠈⠙⠦⠉⠒⠷⠦⣄⡀⠈⡆⠁⠀⠀⠀⠈⠀⠀⠀⡜⠰⠃⠀⣠⠀⠀⣴⠟⢡⠾⠃
⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣳⣦⣀⠀⡀⠀⠀⠀⠈⠀⠃⠀⠀⡄⣸⠃⣠⢄⠀⠀⠀⣠⡞⢁⣠⣾⢏⡰⠁
⣾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⢖⣬⡿⣽⣷⣕⡔⢄⣀⡄⠀⠰⢃⡴⢡⠎⢀⡔⣰⣯⡶⣻⠟⠁⠈
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣞⢮⢇⢻⠀⠐⢋⠴⠋⣠⣢⣾⢿⠏⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣬⣾⠇⠀⢁⣠⣞⣼⠿⡯⡿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡿⣆⣦⣿⣿⣀⣤⣴⣧⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⡿⢻⣿⠛⢸⢻⡟⠋
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡿⡟⢸⣿⣷⠛⠬⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⢰⣾⣏⡿⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢶⣤⢤⣄⣴⡟⡻⢈⣿⠻⡷⠝⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠽⠶⣤⡾⠿⣏⠉⠈⠁⢀⣿⠦⠤⠐⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙⣣⠟⠋⣠⠤⣤⠄⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣷⣒⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⡟⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄⢰⠉⠉⠁⡆⣿⡃⡼⠶⠶⢧⡰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣆⣄⠀⡏⠉⠈⢸⠀⠀⠀⡇⣿⡁⡇⠀⠀⠈⡗⠒⠒⢲⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠁⡇⠀⠀⢸⠀⠀⠀⠁⢉⠀⠃⠀⠀⠀⠁⠀⠀⢸⢰⠓⠚⡆
⠀⠀⠀⠀⠀⡖⠒⠒⠂⡇⠀⣿⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠡⡔⠒⠒⠒
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⠀⠀⡇⠀⠀⢸⠀⠀⠀⠁⣿⡄⡇⠀⠀⠀⠀⠀⠀⢸⢸⢈⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⢸⢸⠈⡀⠀⡇
⠀⠀⠀⠀⢀⣃⣀⣀⣀⣃⣀⣛⣀⣀⣃⢀⠀⠘⠀⠀⠀⠀⠛⠃⠃⠀⠀⠀⠀⠀⢀⠘⠘⠀⠀⣀⣃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⣢⣤⡤⠤⢀⡀⢠⣠⣬⣭⠭⣭⡤⡌⢩⡍⣭⡄⣤⡄⣄⠠⠤⣤⣀⣀⣀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠉⠈⠭⠭⣁⡥⠤⠍⠉⠁⠉⠁⠀⠉⠉⠉

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠁⠀⠀⠑⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡆⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⠀⠀⠀⠀⠐⣶⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠐⠒⠤⠄⠀⠒⢢⠽⠛⠉⠙⠁⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠈⠉
⠀⠀⠀⠀⠃⠀⠀⠀⠑⢦⡀⠀⠀⠀⠎⠑⢶⣿⣤⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠚⠀⢶⣬⣇⠘⣡⠚⠛⠚⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡶⢾⡀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠀⣠⢻⡮⠿⢩⣄⡤⣤⣈⡿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢄⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⢀⢀⡼⠃⡀⢶⣶⡌⢀⠌⠉⠀⠈⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⡀⢲⣶⡀⠊⠱⠐⠄⠑
⠀⠀⠀⠀⠀⣀⣀⡀⠲⠶⠛⠻⢥⡀⠒⢤⠌⠣⠛⢀⣀⣀⣀⠈⠻⠇⠠⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠠⢀⣴⠷⢿⣡⠾⠀⠐⠰⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⣼⡼⢠⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢢⣤⣤⣤⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠎⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠒⠂⠀⠈⠁⠾⠀⠐⠀⠀⢀⣰⡆⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢷⡀⠀⠐⠠⢄⣠⡀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠶⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⠐⡖⢀⠀⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⠀⠒⠢⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡐⠛⠚⠏⠩⣿⣆⡤⠘⣋⣈⣭⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠁⠈⠁⠀⠀⢀⡀⢘⣷⣞⢣⣾⡯⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠙⣯⡀⢀⣼⠓⠀⣐⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣥⡿⡟⠧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢡⡤⢤⣗⢆⣜⠁⠀⢈⡉⣦⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⢀⠀⠀⡤⠄⢂⣈⢁⣨⡧⠄⠟⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠺⠿⠀⠀⠀⣏⠀⠱⣶⡘⠈⠀⢸⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡉⠲⡶⣀⡴⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠑⢂⠀⢀⠦⠤⠐⠁⠀⠀⠈⠁⠀⢐⠈⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠐⢶⠃⣾⡿⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠁⠀⠋⠙⠢⢀⡀⠀⠀⠀⠤⠛⠂⠀⠄⠀⠀⠀⠐
⠀⠀⣀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⣉⡻⠿⠿⠿⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣬⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣷⣽⣮⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⣠⣤⣶⣹⣿⣽⣿⣿⣿⣿⣽⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣛⢿⡙⠢⠙⣆
⠀⠀⠀⢀⣴⣿⣽⣿⣟⡿⣟⣯⣽⣿⣿⣿⣹⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⡲⣝⢧⠑⢈⡀⣟⡄
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣾⣟⣾⣦⣵⣶⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣟⣿⣿⣿⣾⠿⣫⣽⢿⣦⣄⣀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⠓⠗⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣯⣿⣿⢾⣗⢻⣿⣿⣿⣿⣿⣿⣟⡛⠃⠹⣿⢿⣿⡷⠆⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣮⣤⣆⣈⠁
⠀⠀⠀⠀⠀⠒⠲⠶⢶⣤⣤⣄⣀⣤⣄⣄⠟⠿⣿⡿⢟⡉⣙⣛⡛⡻⢿⣿⣿⣿⣟⣿⣿⣿⣿⡏⠁⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⢧⣞⢿⡾⢿⣾⡻⣷⠌⠐⡝⢿⣿⣿⣿⡿⣿⡿⠉⠑⠻⠷⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣆⣨⣿⣿⠿⣶⡼⠀⠘⢿⠛⢟⠉⣀⡤⠤⠄⠐⠂⠛⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠨⢟⣊⢯⣰⠄⢀⣼⣄⣄⣹⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⠿⠋⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠬⠋⠐⢂⡀⠀⣀⣠⣆⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣰⠋⠁⠀⠀⣤⣤⣤⣤⣶⣿⣦⠀⠀⠀⠀⢀⡀⠀⠙⢻⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠄⠀⠀⣼⣇⠀⠀⠀⠙⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠊⣿⣶⡾⣿⣿⠿⣿⠽⠯⠅⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣗⣀⣈⣀⡄⠀⠁
⠀⠀⠀⠀⠀⢀⠒⠛⣻⣷⣶⣿⡏⠑⠛⠙⠙⠉⡉⡀⣴⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⠿⣿⣿⣿⡉⣽⣏⣁⣤⡀
⠀⠀⠀⠀⠀⠐⣤⣴⣿⣻⣿⣿⣷⡀⠀⣤⠶⠾⢻⣿⣿⣶⣤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣸⣿⡙⠗⠿⣿⣿⣯⡗⠂⣀
⠀⠀⠀⠀⠀⠀⠘⢧⠚⢧⣾⠟⢻⣙⣶⣯⢻⣼⣿⣿⣿⣿⢷⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠹⡍⠀⣄⣉⣹⣿⣿⣿⣶⣿⡷⠄
⠀⠀⠀⠀⢨⣵⣾⣾⣶⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⡋⢀⣤⣭⡟⠻⣿⣷⣄⣀⣀⣴⡄⠀⢁⣀⣥⣤⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠿⣿⣿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣾⠿⠿⠛⠛⠛⠛⠛⠒⠻⠿⠿⠿⠟⠻⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣾⣿⣿⣷⣴⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢂⣿⣿⠿⠿⣿⣿⠃⢼⣿⡿⣛⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⢠⣦⣽⣷⣭⣾⣿⣿⣷⠄⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⢿⣿⣿⣿⡄⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠀⠀⠀⠙⠛⠛⠻⠰⠛⠿⠛⠁⡈⠂⠙⢿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠏⠰⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣹⣿⣷⣦⣀⠀⠀⠀⢀⣀⣴⣿⣿⣿⠀⠀⠹⣿⣿⣄⡀⠀⠀⠀⠀⠀⣠⣄⢀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⠿⠾⠿⠿⡿⠿⠿⠿⠃⠀⠀⠀⠘⣿⣿⣿⣷⠾⢶⣶⣿⠿⠿⠿⠟⠁
⠀⠠⠴⠶⠶⠶⠾⠿⠿⣿⣿⣿⣿⣿⣴⣴⣶⣶⣶⣦⣦⣶⣶⣦⣴⣦⣤⣤⣤⣤⣤⣼⣤⣦⣤⣠⣼⣶⣶⣶⣶⣶⣶⣶⡷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⣯⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠋
⣿⣷⣆⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣷⣦⣄⡀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣶⣦⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡙⠿⠿⣿⣿⣿⡿⠿⠋⠙⠻⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠈⠓⠂⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣭⣿⠁⠀⠀⣀⣀⣀⣉⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣄⣠⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠈⢳⡤⣀⠀⠀⡞⢹⣷⣶⣄⣀⠀⠀⠀⠀⠈⢳⣄⠀⣩⣽⣿⣿⣿⣿⣿⣟⣋⣉⣤⣤⣴⣦⡀⠸⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡑⡼⠃⠀⠛⢿⣿⣿⣶⣄⢀⣰⣶⣶⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⢻⣷⣤⣬⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡆⠀⢀⣠⣬⠿⠿⠿⠻⠟⠉⠛⣿⣿⣿⣿⣿⣿⣿⡿⢻⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣮⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡟⠻⠛⠋⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣋⡁⣀⣠⣤⣶⣾⠶⠿⢿⡯⣁⣀⣀⡁⡀⢀⣠⣤⡄⣀⣀⣠⣆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⣸⣿⡿⠟⠉⠁⠀⠀⠀⠀⠙⠋⠉⣹⢛⣟⠛⠣⡈⢑⣄⠀⠈⢮⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠷⠁⢠⡿⣾⣨⣦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡄⠀⣀⣀⣀⠀⣿⠂⢰⣶⣶⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿
⠀⠀⠀⠀⠀⣀⣀⡀⢸⣿⠀⢰⣶⡆⢀⣀⣀⡀⣀⣿⣿⣿⣇⣰⣿⣿⣿⡆⢻⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⣿⣿⡇⣸⣿⡀⢸⣿⣧⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⢸⠀⢸⣿⣿⢠⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⡄⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⡀⠀⠀⣀⠀⠀⣀⣀⣀⠀⢀⡀⠀⣀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠙⣧⠀⠀⣿⠀⠀⣿⠀⣾⠋⠉⠉⠀⢸⣇⣼⡋⠀⠀⣿⠀⠀⠀⢠⡟⢷⡀⠀⢸⠷⣄⢸⡇⠀⢹⡏⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠛⠻⠆⠀⠻⠦⠴⠏⠀⠙⠶⠤⠶⠀⠸⠟⠉⠷⠆⠀⠿⠶⠶⠠⠿⠒⠛⠷⠀⠸⠀⠘⠿⠇⠀⠸⠷⠶⠟



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⡾⠋⠡⠁⢈⢹⠆⠀⠀⠀⠀⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⡇⢻⣿
⠀⠀⢰⡦⠤⠴⢶⡆⠀⠀⡘⠀⠈⠈⠉⠙⢇⠀⠀⠀⠀⠀⠀⣩⣗⡢⢀⡝⣈⠔⠲⣄⠀⠀⣿⣿⣨⠇⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⢸⡇⠂⠺⢻⡇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⠾⠀⣠⡶⢻⡃⠸⣿⠟⠺⠄⠀⡏⠛⠸⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠘⣇⠀⠀⣸⠁⠀⠸⣄⡀⠀⠀⣀⣀⣸⠃⠀⠀⢠⡏⡀⠚⠿⠁⠘⣿⣶⢿⣁⠌⠀⠀⡄⢸⢸⠀⠀⠀⠀⠀⠀⣠⣧⣼⣿⣄
⠀⠀⠀⠙⢷⣾⠃⠀⠀⠀⠙⠷⠶⣶⣾⡿⠋⠀⠀⠀⠸⠏⠀⠀⠀⠀⠒⠈⢳⠴⠋⠀⠀⠀⡅⢸⠠⠀⠀⠀⠀⢀⡾⠋⢉⣿⣿⡟⣳⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⢀⠒⢋⣦⡀⠀⠀⠀⠀⣠⡴⢴⡦⢔⠀⠀⠀⠀⡇⣿⠘⡀⠀⠀⠀⢸⠁⠀⣼⣿⣿⡇⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠢⢾⠉⢙⠇⠀⠀⢤⣐⢃⠎⢹⡖⠁⠀⠀⣸⠷⢿⠔⢧⠀⠀⠀⢸⠀⠀⠻⠿⣿⡗⠛⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹⡆⢱⡞⢀⠀⠀⢰⣇⠀⢠⠀⠈⣆⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠰⢿⣭⣷⠂⠀⠀⠀⠀⠀⠠⣤⡄⠀⠁⠀⠈⠀⠀⠀⢠⣯⣿⡆⢸⡇⠀⢹⣆⠀⢸⠀⠀⠀⠀⣙⠀⠀⣿
⠀⠀⠀⠘⠯⠿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣠⠀⣚⣫⡽⣧⡆⡀⠀⠀⠀⠀⣸⣿⣇⣙⣿⡏⠀⠈⣿⠀⢸⠀⠀⠀⠀⢩⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⠴⣚⡿⡬⢇⣰⡼⡵⢫⠇⠀⠀⠀⣿⡿⠉⠀⢸⡏⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡄⢐⡆⠀⠠⠼⠃⠀⠀⠀⠀⢰⣟⣺⣽⡫⢞⣸⢛⣿⣉⣻⢤⣟⢷⣀⠀⠀⠀⣿⣇⠀⠀⢸⡇⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣩⠗⢣⣎⣸⣶⣾⣉⣻⡷⣦⣉⣗⣆⠮⣭⡶⠀⠀⣿⣿⠦⣤⣼⡇⠀⠀⣿⠀⢸⡇⠀⢺⣿⣿⡟⣿⢷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣛⡶⠷⠳⢲⡳⢾⢭⠷⣿⣧⡶⠏⢿⣭⡮⢽⣒⡿⠿⠧⠀⣿⣿⣠⣴⣾⡷⣄⣰⣿⠀⢸⡇⠀⢸⣿⣿⣇⢿⣿
⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠁⠀⠮⠗⠑⠚⠣⣇⣶⣷⠞⠛⠙⠻⠦⠀⠀⢿⣿⣿⣿⣼⡇⠈⢻⣿⠀⢸⣇⣀⣸⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠒⠛⠉⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢰⡆⠀⠀⢈⣧⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠛⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⣛⣹⡀⠀⠀⠀⠀⠀⠀⢣⠀⣀⠔⡫⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⢀⣴⡾⠕⠒⠉⠉⠁⠀⠉⠳⠶⣦⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇
⠀⠀⠀⠠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣟⠲⣄⠀⠀⠀⢦⣄⣀⣀⣈⣻⣷⣶⣶⣿⣿⣿⣷⣶⣦⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡀⠈⠑⠦⣄⡀⢻⡻⢿⣿⣿⣿⣯⡉⠉⠀⠀⠀⠉⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠓⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠸⠗⠴⠶⠶⢶⣶⣶⡏⠙⢿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⠀⠀⢸⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠇⠀⠀⣼⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡀⠀⠀⢰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣺⣭⣕⠒⣶⣻⣭⣕⠒⠒⠋⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠶⠒⠒⠚⠻⠷⠒⠒⠓⠒⠒⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⡇⢠⣴⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣿⡇⠸⣿⠁⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⠀⢸⣿⣿⣿⣿⡇⠀⣀⣀⣀⠀⢸⣿⣿⣿⣿⠀⢀⣀⣀⡀⠀⢰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣿⣿⣿⣿⡇⢠⣤⣤⣤⡄⣿⣿⣿⣿⡇⠀⣿⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⣾⣿⣿⣷⠀⢸⣿⣿⣿
⠀⠀⠀⣞⡆⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⠀⣿⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⣴⣾⣿⣿⣶⡄⢸⣿⣿⣿⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⠀⣿⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⢰⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣰⣿⣿⣿⣿⣧⣼⣿⣿⣿⡇⣿⣿⣿⣿⣷⣸⣿⡀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠋⡀
⠀⠀⠀⠀⣼⣯⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣿⣿⡇⠀⠀⠀⠀⠀⡼⠉⠉⠉⠉⠈⢳
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣥⣾⣿⡿⠁⠀⠀⠀⠀⠀⢳⠀⠐⠂⠂⠀⡸
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠞⠁


⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡇⠀⢀⡀⠀⠀⠀⠀⠀⢰⣦⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣤⠂⠁⠀⠀⠀⠀⠀⣴⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠛⣆⣽⡆
⠀⠀⠀⢼⣿⣿⡟⡻⠿⠿⠇⠀⠀⠀⠀⠀⢾⣿⣿⡿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⢋⣁⠐⢢⠀⠀⠀⠀⠀⢐⠻⣤⣺⣾⣿⡿
⠀⠀⠀⠀⠙⠻⠿⢷⡟⣶⠲⣯⠆⠀⠀⠀⠘⢿⣿⣿⣶⠖⡴⣦⣠⠆⠀⠀⠀⠀⠙⠻⠟⢦⣤⣭⣴⡿⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣷⠏⣀⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢼⣿⣿⡿⣟⣿⣿⣀⣤⡀⠀⠀⠀⠀⠀⣾⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣠⣠⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⠛⠁⠀⠀⠀⠀⠀⣿⣧⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣙⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⢾⣿⣿⣷⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣾⢟⣽⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢧
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⣇⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣼⣾⣦
⠀⠀⠀⠀⠀⠀⠻⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⣇⠀⠀⡏⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⢠⠀⠀⢿⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⡄⠀⠀⠇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠸⡄⠀⠘⠀⠀⠇⢠⡆
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠻⠄⠀⠘⠀⠀⠀⠀⡇⢸⡇
⠀⢀⡀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣷⣼⡇
⠀⣾⣿⣦⣀⠀⠀⠱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣼⣿⣿⣿⡇
⠀⠙⠷⠀⠉⠁⠀⠀⠀⠉⠙⠛⠢⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢐⠄⣿⣿⣿⣿⣿⣿⡇
⠀⣠⣄⡀⠀⠀⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣬⣄⣻⣿⣶⣤⢶⣄⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⢀⡀⢛⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠐⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠴⠶⣦⣬⠭⠀⢻⣿⣟⠛⠑⢲⣤⣀⠀⠈⠉⠁⠂⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛
⠀⠀⠀⠀⣴⣶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠉⠀⠀⠉⣷⣶⡄⢈⣉⠿⣿⡚⠓⠂⠀⠀⠒⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄
⠀⠀⠀⠀⠈⠉⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠒⠊⠉⠚⠋⠉⣉⣥⡄⣠⣼⣿⡙⢦⡙⢦⣴⣤⡽⠷⣶⣿⣿⣿⣿⠟⠀⠖⢀⣴⣧⣤⣤⣿⣿⣿⣶⣤⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠸⠟⠉⠉⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⢀⡸⠟⢱⢞⣹⠟⣿⣶⠚⣷⠚⣧⢁⡀⣤⠈⠿⣿⣿⣀⠀⣀⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡤⠤⠀⠀⠀⠀⢀⠠⠚⠉⠀⣀⢤⠟⢃⣼⣟⠟⣧⣛⠠⢀⣻⣿⣥⣄⣀⣉⠈⠵⣦⠉⠻⣏⣹⣝⣻⣈⡉⠛⠛⣿⣿⡿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⡤⠖⠋⠁⠀⢀⡴⠚⠁⠀⠀⠈⢧⡟⢰⣿⡟⠀⢠⣴⣿⣿⠿⠫⠉⠁⠀⠘⠋⣤⡀⠀⠙⠿⠟⠁⢠⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⢀⣤⡞⠋⠀⠀⠀⠠⠀⢀⢾⡃⢿⣿⡗⠀⠈⣙⣿⠟⠀⠀⠀⠀⠂⠀⠘⠉⠁⠐⣠⡄⠒⢠⣾⡿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠁⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠘⠿⣿⡎⢆⢙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠸⠛⠛⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⢀⣠⠄⠀⠀⡀⠀⠀⡀⠀⠀⡤⢻⡟⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠀⢀⡴⠀⠀⢀⠁⠀⠀⠃⢹⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⢠⡎⠀⠀⢸⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣼⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢀⣿⡂⠀⠀⣠⣶⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡄⢸⣿⣏⣅⠀⠀⠐⠀⠀⢠⠞⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⡿⣧⣿⠀⠀⠀⢠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣆⣼⠋⠀⠘⣿⢀⡤⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⣼⣿⣿⣯⣿⣇⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢠⠾⠋⣿⣿⣿⡿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠰⠀⠀⡀⠙⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠶⢋⡄⣤⠃⠀⢀⠀⠀⠀⠀⡅⡀⢠⣰⡆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠸⠛⠀⠠⠟⠀⠠⣦⢠⣿⡿⠰⠋⠛⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡄⠀⢀⣀⣀⠀⣿⠀⣴⣶⣶⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣿⣿⡇
⠀⠀⠀⠀⢀⣀⣀⠀⣾⣷⠀⣶⣶⠀⣀⣀⡀⢀⣼⣿⣿⡇⣰⣿⣿⣿⡆⢻⠀⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⡄
⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⡀⣿⣿⣼⣿⣿⣿⢸⣿⣿⣿⣧⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣠⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⢸⣿⣿⣿⣿⣿⣇⣀
⠀⠀⣤⣤⣼⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠈⠛⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣟⣿⣿⣿⣿⣿⢻⡟
⠀⠀⠉⠉⢹⣿⣿⠸⢿⡿⠟⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⣿⣿⣿⣿⡟⢻⠋⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠈⠉⠉⠀⢸⡇⠀⠻⠿⠈⠉⠉⠉⠈⢻⣿⣿⡇⠙⢿⣿⣿⠇⣸⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠉⠉⠉⠉⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⢶⠄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠁⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣆⣿⠱⢃⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠶⠟⠙⠻⠋⡡⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢔⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠁⠀⠀⠀⠀⠀⠀⠐⡄⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⡀⠀⠀⢠⠀⡸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⡷⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⠀⡇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡲⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠘⡡⠶⣥⣀⡀⢴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣇⢀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⣠⢚⢔⡵⠊⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⠋⠉⠙⠻⣿⣿⣧⣤⡀⣀⣀⡶⠃
⠀⠀⠀⠀⢔⣵⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠈⠉⠀⠀⢸⠋⡿⠉⠀⠀⠀⠀⠀⠀⠘⡏⣿⠁⠁
⠀⠀⢠⣦⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟
⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢷
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⢞⡒⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣲⣴⡾⠉⠃⠰⡁⠀⠀⠀⠀⢠⠟⠒⠚⡏⢠⠴⠌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡠⠞⠻⡆⢧⠀⠀⠀⠀⠀⠀⠀⢠⣇⠏⠀⠀⠐⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠑⢾⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⠿⢛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⢈⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⡿⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖



⠀⠀⠀⠀⠀⢠⠄⢀

⡀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⠦⢀⣴⠘⣁⣬⠥⠀⣤⠀⠀⢀⣁⠀⠀⠀⢠⠀⠀⠄⠀⠀⢸⣿
⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠀⠓⢄⣺⣿⡈⠁⠠⢊⡰⠀⠀⠐⣾⠁⠀⠠⠶⠦⠄⠀⢀⣴⢸⣿⡿
⣇⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢠⠄⡎⠀⢀⣴⣶⢿⣿⣿⣿⠀⢾⢃⡄⠀⠠⢿⠓⠀⠀⠀⠀⠀⢠⠘⢻⠈⣿⠶
⣿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣴⠃⠸⠁⠀⣾⠟⢁⣿⣿⣿⣿⡷⠴⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠉⣁
⣿⣶⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⡏⠻⣿⠀⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⣟⣫
⣿⠟⢰⡄⣿⣹⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠀⠅⠀⠏⠂⠀⡆⠢⠀⡇⠀⠀⠀⠀⠀⣾⣧⢀⣸⠀⣟⣿
⣏⢸⣿⣷⣿⡇⣿⣿⡇⠀⠠⢤⢾⢦⡄⠚⠀⠀⠀⠀⠀⢀⡂⠠⢓⠓⠀⠄⠀⠀⣥⠀⠀⠀⠀⢸⣿⢻⠤⣼⠀⠙⠋
⣿⣿⣿⣿⣿⣇⣿⣿⣿⣦⡀⢀⡈⠏⠃⠀⠄⠠⠀⠀⠀⠈⠀⠀⠁⠸⠀⠀⠀⠠⣿⡀⠀⠀⢠⢀⡷⢠⠀⠾⠀⣈⠃
⠟⣫⣾⣿⣿⣇⣿⢿⣿⣟⣥⣖⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠇⡱⠀⣿⠀⠀⣸⠧⠀⢀⢠⡴⠗⣚⣒⡟⠈⢹
⣾⣿⠋⣿⣿⣷⢹⡮⢿⣿⡿⡿⠀⠀⠀⠀⠀⡆⢀⣀⠀⡄⠀⠀⠐⡷⠀⣯⡔⣆⣋⠢⡄⠌⣆⢠⢄⡐⠱⠤⠬⣞
⣿⠓⠢⣽⣿⣿⢸⣿⠈⣵⣶⣿⡆⠀⠀⠈⣤⡇⠈⣥⣤⣁⠛⢢⣄⠑⢠⣧⣧⢱⢶⣷⢿⡀⠐⠚⠋⡀⢦⠀⠀⡀
⠖⠀⣴⣿⣿⣹⡏⢿⣆⠘⣿⣿⣿⡀⠰⣗⢿⣟⣯⠀⠈⠙⣻⣦⣿⡇⡈⠻⣷⣾⣾⢿⣧⠈⣀⠀⠀⠀⠸⠋⠀⠀⢄
⠀⢀⣿⡿⣷⣿⡇⠘⢷⠆⠀⠉⠓⠀⠀⠛⣷⢟⣭⡅⠀⠓⠛⢹⣰⠃⡟⢶⠻⡻⣿⣟⣳⡾⡿⢀⣀⡀⠀⠀⠀⠀⠈
⠀⠸⣿⢠⣿⣿⣇⠀⠀⣸⣶⣦⠀⠀⠀⠀⠙⣕⣢⡘⢿⡆⢂⡀⠛⢰⣩⣷⣿⣷⠖⢹⠓⣵⣿⣿⠟⡓⠀⠀⠀⠀⠐
⣧⢰⡟⢿⡿⣾⣯⣷⣸⣿⠻⠟⠃⠄⠀⠀⣠⣿⣯⣝⢄⣷⣾⣿⠀⢨⣻⣿⣿⠁⠀⠀⠀⢻⡛⠉⢀⠃⠀⠀⠀⠐⠄
⣻⣬⣷⣄⢠⣟⣹⣿⣟⣿⣦⣀⠀⠀⣠⣼⢏⣩⣸⣿⡾⣿⣿⣀⣀⣀⣧⡉⢉⠀⣀⠀⣀⣈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⣤⣲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣳⣶⠟⠻⢿⣿⡾⠓⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⣾⣷⣶⣶⠆⣽⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⡇⠸⣯⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⢸⡶⢿⣟⣾⣧⣤⠀⠹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⣿⠾⣿⣽⣿⢿⣿⣯⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣵⣮⣔⣋⣵⣛⡵⠛⠷⠏⠀⠀⠂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡵⢋⡵⣪⢔⣫⡽⣟⡽⠆⠶⠣⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⢾⡯⣾⣿⡿⠷⠿⡷⠶⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⢀⡘⢁⠀⠐⠋⠁
⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠁⡄
⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣆⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠀⠤⠀⠄
⠀⠀⢰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠶⠶⠾⠙⠛⠻⠟⠷⠶⠷⠿⠖⠾⠃
⠀⠀⠈

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠉⠉⠈⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⣈⡄⠄⠀⢺⡿⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠁⢀⣀⠔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠄⠊⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠉⠀⠀⢄
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢨⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢢⡀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣠⣄⣀⣀⣀⢀⢀⣀⠀⢀⠰⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⣇⠀⠀⠀⠘⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠸⠀⠀⠀⠀⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡇⠀⠀⠀⠈⠇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢤⡀⠀⢠⠈⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠀⠀⠀⢁⠀⣠⠀⠀⠀⠀⠀⠈⠀⡎⠠⠄⠀⠀⠦⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⡠⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠈⢆⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣮⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠱⣶⠇⠀⠀⠹⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⡀⠀⢁⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐⢄⠈⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡈⠃⠙⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠐⠦⠀⠓⠀⠙⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠂⠀⢂⠀⢠⣿⣼
⠀⠀⠀⠀⠀⠀⠡⠀⠢⠀⠄⠀⠀⠀⠤⣀⠀⠀⠀⠘⢄⠃⠀⠀⠀⢡⠀⢠⠐⡙⠀⠀⢸⠿⡇⡀
⠀⠀⠀⠀⠀⠱⣔⠊⠦⠄⢀⡑⠂⠀⠀⠀⠀⠐⠀⣳⠀⠃⠀⠀⠘⡆⠱⡀⠐⠃⠀⠀⠀⠀⠁⠡⡀
⠀⠀⠀⠀⠀⠀⢈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠂⠀⡐⠀⠄⢱⣄⠐⠓⠀⠀⠀⠀⠀⠀⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣢⠤⠄⠀⠀⠀⠀⠀⠂⠉⠀⡠⡖⠀⠌⠀⠀⠀⠙⡄⢠⡾⠀⠀⠀⠀⠸⠷⢀⣻
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⡐⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⢰⡧⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠔⠐⠂⠀⢀⠄⠀⠀⠸⠀⠀⠀⠂⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠂⠀⠂⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣀⠀⣄⠀⢠⢀⢀⡌⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠠⢄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⠀⠀⠀⣀⣠⡷⠤⡀⠀⠀⠀⠀⢃⠈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢂⡠⠔⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠏⠘⡆⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠔⠒⢋⠩⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣚⠇
⠀⠀⠀⢋⠀⠀⠊⢔⠊⠡⠔⠀⠠⢊⠔
⠀⠀⠀⠀⠀⠀⠁⢀⡤⠔⢚⠡⠐⠁
⠀⠄

⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣤⡶⠀⠂⠀⣄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣨⡷⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⡀⠀⠀⢹⢡⠙⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡙⢂⡆⠀⠄⠀⠀⠂⠈⠠⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⣾⠃⠄⠀⠀⠀⠂⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣳⣀⣹⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣵⢧⠋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣛⠛⠛⡂⠀⣀⣀⣤⣾⣿⣿⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⣀⠛⠛⠉⠀⠀⠿⡿⣿⡏⢍⡊⠼⢽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⠧⠻⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣄⠰⡱⡑⣕⢮⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣶⠔⠔⣱⢲⢿⢸⢹⠈⢢⣤⢀⡆⠈⠁⠓⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⢪⢦⢃⣇⣎⣄⢤⠖⠉⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡈⠀⢄⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠑⠋⠊⠉

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣛⣛⣽⣷⠿⣙⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣴⣶⣿⠟⣻⣻⡻⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣾⡿⢿⣿⣿⣾⣿⡇⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢿⣿⣿⣿⣿⣿⣷⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣤⢤⡀⠙⢧⣼⣧⣴⣒⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣁⠀⠉⠛⠛⠛⠋⠉⢀⣿⣷⠓⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣰⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⡀⠀⣀⣄⣠⣾⡃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡟⠛⠿⠙⠇⣿⣿⡿⠻⡟⣷⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⢸⠀⡇⣴⣾⠀⠀⠸⢣⢷⣿⣿⡛⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠲⢾⠰⠇⠋⠈⠀⠀⠀⠀⠈⠘⢻⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⣿⣿⣿⡽⣷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣿⣿⣿⣿⣿⣿⣧⣛⢀⠀⠁⠀⠐⢄⠀⣠⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣮⣻⣿⣿⣿⣿⣿⣿⣾⣆⣤⣾⣷⣮⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣷⣿⣿⣟⢉⣉⣉⣉⣉⣭⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠟⠿⠛⠿⠟⠛⠿⠿⠓⠂





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⠟⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣛⠿⢿⣿⣿⣿⣯⣭⡵⠶⢛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣄⠀⢤⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣉⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠶⠒⠋⠐⠒⠂⣨⡿⠷⠖⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠶⠶⠶⠶⠶⠖⠛⠛⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠂⢴⣶⣿⣻⣭⠽⡒⠁⠨⠍⠉⠱⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠹⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⠣⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠂⠘⢳⣄
⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⢠⢖⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠁⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⠀⠙⠙⣣
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠃⢈⢿⠇⠀⠀⠀⠀⠼⣠⣿⣶⣴⢀⣈⡀⢀⠀⠀⠈⠀⠒⠂⠀⠰⠀⠀⠀⢉⣰⡀
⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠴⢏⡁⠀⣄⡂⠀⠙⢿⡿⣝⠣⠀⠀⠀⠀⠀⠀⠀⠤⢀⠠⠀⠀⡀⠀⢀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠂⠄⠁⡸⠶⣤⣈⠳⣄⠈⢫⡞⠗⠀⠂⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠓⠾⡆
⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⣰⡾⠊⣹⣷⣦⡑⢄⠑⢄⠀⠀⢄⣉⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠄⢶⡇
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⣸⣿⣿⢙⣶⣄⠈⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠈⢈⡿⣷⣄⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠃⠀⡞⠢⡀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢰⣀⠂⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⢿⣿⣾⣤⣤⣤⣀⣠⡀⠐⣀⡀⡂⠈⠀⠀⠁⠀⠀⠀⠀⢈⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣿⠽⣻⣟⡿⣿⣿⣿⠙⠚⢦⣤⠀⠀⠀⢀⠀⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⡾⠷⢧⣾⠋⠀⠀⠀⠙⠿⣦⣄⣦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢫⡈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠛⠚⣋⣉⣡⣠⡤⠂⣰⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠴⠒⢋⠔⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠉⠉⠉⠁⠀⠐⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠑⠒⠒⠒⠋⣽⢀⡼⠋⠑⠶⣍⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠀⠀⠀⠀⠀⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣭⣽⣿⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣽⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⢠⠟⢡⡀⠀⠀⡀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠀⢀⣾⡄⠀⣰⠇⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣜⠀⠀⢀⠹⣿⣁⠀⣿⠀⢀⣼⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⢿⡄⠱⡄⠀⣿⣿⢠⡟⢀⣾⠇⣸⣏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠛⣿⣦⠀⠀⢿⣿⡇⢠⠟⢠⠚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣆⠻⡇⠀⠀⢰⣿⡰⠇⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣄⡲⣦⣈⣑⠉⢿⣄⠂⠀⣸⣿⡇⢀⣴⡿⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢳⣌⠛⣷⣤⡟⠀⠠⠋⣸⣷⣾⠟⣣⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣄⣈⣻⠿⣿⣮⡛⠀⠀⢠⣿⡟⠁⣾⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣿⣆⠸⠉⢿⣆⠀⣹⠏⢀⣴⣃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣽⣿⣇⠀⠘⠛⣿⣁⣰⡝⠛⠉⣡⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠀⠀⠛⣿⡁⣠⠾⣿⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡛⣿⣷⣀⠰⠛⣿⣤⢎⣹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣻⣧⣉⣫⣿⣦⣾⣿⡛⠾⠛⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣿⣯⣭⢉⣿⠉⣿⣷⣄⣹⣷⣶⢢⣽⣏⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣴⠋⢻⡄⣼⡟⠙⢷⣿⠁⢈⡿⠟⢿⣀⢈⡿⠻⡝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⣿⠃⠁⣸⠷⣿⠀⠁⢰⡿⠤⣾⡇⠘⠀⣿⣬⣇⠈⢘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠈⣧⣼⡇⠠⢸⣇⣠⡟⠀⠀⠈⣷⣀⣶⠁⠀⢻⣄⣸⠃⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠹⡇⣶⢃⠘⣷⠀⣼⠃⡉⢳⡄⠀⢠⡟⠉⠹⣧⠀⣸⠏⢹⡆⢰⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⣠⠿⢿⠀⢰⡿⠾⣿⠀⠁⢺⠷⠶⣿⠀⠘⠐⣿⠴⣷⠀⠀⣿⣿⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣷⡏⠂⣼⣤⣿⠀⠂⢹⣦⣤⡿⠀⠂⢸⣧⣤⣾⡃⠠⢸⣇⣸⡇⢸⣇⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣢⡟⡀⢹⡄⢠⣞⠁⠈⣷⣀⣀⣼⠃⠀⠙⣵⠂⡼⠋⠹⢇⢰⡉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡿⠙⣇⠀⣼⠛⠛⣯⠀⠀⣾⠋⠉⠿⠀⠀⢀⡿⠲⣷⠀⢀⡾⢷⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣼⡇⠃⣽⣴⣏⠐⠂⢸⣦⣼⣏⠈⠁⢸⣧⣤⣾⠀⠀⢸⣇⣸⠇⢸⣇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣻⣱⡏⡄⢹⣂⣠⡏⢠⠀⢿⣅⣠⣾⠃⡀⢹⡆⠀⡜⢉⢹⡆⡸⢋⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⣿⠙⣇⠀⣼⠋⠙⣧⠀⠀⣾⠋⠉⢿⣀⠀⢰⠟⠺⣧⠀⢸⡿⣷⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣏⠁⣿⡤⣿⠀⠀⢸⣧⣼⡇⠀⠀⢸⣧⣤⡿⠀⠀⣿⣤⣿⠐⣽⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣂⡛⠄⢸⣆⣐⡟⠀⠀⢹⡄⣰⡎⠡⠈⢷⡀⣰⠏⠀⢿⡀⢏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠉⣿⠄⣨⠋⡉⢿⡀⠀⣼⠋⠙⣧⠀⢠⡟⠉⢻⡄⢀⡞⠻⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣬⠗⠻⣆⠁⣸⠗⠚⢧⠀⢐⡿⠒⢿⡆⠀⣼⠷⣾⢈⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⡻⠖⢿⡀⠁⣸⠷⣿⡀⠀⣸⡷⢴⡏⠀⣨⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣷⣀⢈⣿⠴⣯⠀⣨⣷⣼⣇⠀⣠⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠿⣿⡿⢿⣿⣿⠿⠿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠈
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀
⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠒⠈
⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡃⠀⠐
⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠃⠂⠃⠀⣀
⠀⠀⠀⠈⣿⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠙⣿⣧⠀⠀⠠⡄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣶⠯⢀⠀⠀⠀⢀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢿⣯⢤⡄⢷⢀⣄⡞⣂⣠⣤⣄⣴⡶⠋⠁⠀⠀⠀⠑⠂⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠻⣿⡧⣤⣿⣾⣿⣿⣯⣭⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢸⠛⡟⠉⠈⠹⡿⢟⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠹⡌⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠏⡀⠀⠀⠀⠀⢸⡈⠢⡀
⠀⠀⠀⠀⠀⣠⣔⠥⢤⣙⡒⣲⣶⠄⠁⠹⣄⡦⣭⣭⣽⣶⣤
⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣽⣿⣿⣿

⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤
⠀⠀⠔⠀⠀⠀⠀⠀⢀⣴⣿⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣻⢖⢲⢶⢶⢶⢶⣾⣿⣿
⠀⣀⠀⠀⠀⠀⠀⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡛⠛⠛⠓⠒⠒⠒⠚⠛⠋⠁
⠀⠏⠀⠀⠀⢐⡿⠛⠋⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⣤⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⡆⠐⠀⠀⠀⣈⣠⠀⡴⠀⡴⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠉⠃
⠀⠁⠀⠀⠁⠀⠀⠀⠀⢀⠆⠠⠔⠃⠀⠀⠀⡋⢱⠸⡄⠱⡀⠹⡀⢇⢸⠀⡎⢵⠂⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠘⢀⣩⣀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠈⠀⠸⠘⠆⠃⠺⣶⣤⡄
⠀⠀⠀⠀⠀⣀⠀⠚⠋⠀⢉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠙
⠀⠀⠀⠀⠚⠅⠀⠀⣀⣠⣤⣤⣄⣶⣦⣤⣷⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠙⠁⡠⠖⠋⠉⠋⠉⠁⠉⡟⠉⠉⠻⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠂⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⢠⢖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡀
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣐⢀⡀⠀⠤⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⣰⣷⣴⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⣦⠀⠀⠀⠀⣿⣿⣿⣷⣿⣷⡀⣠⡄⠀⠀⠀⢸⣿⡇⣀⣿⠀⠀⢀⣀⠀⢠⣄⣠⣤⣤⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣦
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⢰⡷⣦⣄⣀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠈⣿⣮⣻⣿⣷⣄⣼⣿⢟⣵⣿⡟⠁
⠀⠀⠀⠀⠘⣿⣿⣾⢻⣿⢽⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠙⠿⠏⢫⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣠⣴⣦⢶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⣮⡻⣿⠿⢿⣷⡀
⠀⠀⠀⠀⢀⣀⣀⣿⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣩⣟⡛⠛⣠⡀
⠀⠀⠀⠀⠀⠉⠛⢿⡆⢀⡤⠀⠈⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢩⣼⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣺⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣦⣤⡀⢀⣤
⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⡿⠛⠉⠉⠙⣿⣿⣿⠀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⡆⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢟⣟⢿⣽⣟⣷⣿⣿
⠀⠀⠀⠀⢀⣾⡟⠉⠀⣾⠋⠀⠀⠀⠀⠀⢻⣿⡿⠀⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⡈⠛⠛⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣯⡿⣿⡿⣾⣿⣿⣿
⠀⠀⠀⢠⣿⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣠⣼⣿⣧⠠⣌⠻⣿⣿⣿⣿⣿⢸⠀⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣷⣿⣾⣧⠙⠿⠟⠃
⠀⠀⠀⣼⣿⣷⠀⠀⠀⢻⠀⠀⢀⣀⣀⡀⠀⠈⢻⣿⣿⣿⠀⣿⣦⠈⠻⣿⣿⣿⠘⣇⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠟⠀⣦
⠀⠀⠀⣿⡏⢿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠹⣿⠿⠀⣼⣿⣧⠀⡘⢿⣿⠀⢻⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⠄
⠀⠀⠀⢹⣷⠀⠙⢧⡀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣴⣿⣿⣿⡇⢹⣆⠹⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢠⢿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠁⣼⣿⡆⢠⠸⣦⣈⢉⣀⣶⣄⠀⠀⠀⣀⣀⣤⠖⠀⠀⠀⠀⠀⣠⡾⠃
⠀⢀⡴⠋⠀⠻⣦⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠠⢾⣿⣿⡗⢸⣧⡙⠿⠿⠉⠻⢿⣿⣾⣽⣟⣋⣁⣀⣀⣀⣤⣴⡾⠟⠁
⠀⠉⠀⠀⠀⠀⠘⠳⣄⡀⠀⣿⣿⣿⡿⣿⣯⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢫⣥⣾⣿⣿⣶⣶⡄⠀⠀⠈⠉⠛⠛⠻⠿⠿⢿⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢘⡛⢿⣶⣿⣿⣮⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡽⣿⣻⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⡏⣿⣯⡻⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢹⣿⣷⡘⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⠈⣿⣿⣿⡌⢳⡝⣷⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⡌⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡆⠸⣿⣿⣷⡀⢻⣎⢿⣷⣄⠀⠀⠀⠀⢿⣯⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡘⣷⡀⠹⣿⣿⣧⠀⢿⣆⠻⣿⢷⣄⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡇⢻⣧⡀⠙⢿⣿⠀⠘⣿⡆⠹⣧⡙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⡄⠹⣷⣄⠀⠁⠀⠀⣿⣿⠀⢹⣷⠈⢿⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠻⠀⠙⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢸⣿⣿⣦
⠀⡄⠀⠀⢸⣿⣿⢸⣿⡀⢀⡀⠀⠀⢸⣿⢀⣿⠀⠀⠀⢀⣀⣀⣠⣨⣿⣿⡀⣴⣾⣿⣿⣿
⠀⣿⣾⣆⣼⣿⣿⢸⣿⣿⣿⣧⣦⣴⣿⣿⣿⣯⣸⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣴⣆
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢸⣿⡀⢸⣦⡀⣿⡏⠀⣾⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠹⣶⣦⣿⣷⣤⣿⣿⣿⣷⣼⣿⣧⣾⡟⠀⣤⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣼⣿⡿⠟⠛⠋⠉⠉⠙⠛⠿⣿⣿⣧⣾⣷⣀⣴⣾⠟⠁
⠀⠀⠀⠒⠶⢶⣤⣤⣀⠀⠙⠾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⡿⠀⢀⣀⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣩⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⠤
⠀⠀⠒⠛⠛⠛⠛⠛⠛⢛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⠛⠛⠻⠿⠷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠓⠂
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⢸⣿⠟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠻⢿⣦⣄
⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠋⢁⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⢦⠀⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢻⡟⠀⣿⡿⣿⣿⠻⣿⡿⣿⣧⠈⢻⣷⡀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠀⣸⣿⠁⠉⡏⠀⣿⣇⠀⠘⠂⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣷⣶⣬⣽⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣌⠹⠗⢿⣟⣿⣿⡿⠛⠃⠉⠙⢿⣿⣿⣿⣿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠓⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣮⣭⣵⡏⠀⠀⠀⣀⣄⢀⣀⣠⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣤⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⣠⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⣸⠞⣶⣤⣄⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠉⢛⣻⣿⣿⣿⣿⣿⣿⠿⠟⠛⣉⣀⣠⣄⡀⠀⣶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡅⢄⣠⡟⠀⠻⣿⣿⣿⣷⣄⡀⠀⠀⣠⣤⣙⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠿⠟⠛⢿⣷⡄⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⡁⠀⠀⠈⠙⠻⣿⣿⣿⣦⣾⡿⢿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣮⣝⡲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣄⣤⣶⣿⡟⠉⠉⠙⠉⠉⠀⣠⣸⣿⣿⣿⣿⡿⠟⠛⠛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢯⠈⠋⠈⠀⠀⢀⡀⣰⣾⣾⡿⠿⠿⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢯⣄⣠⣤⣴⣿⡿⠿⠛⠛⠻⣿⣢⣤⣤⣤⣀⣀⣠⣴⢶⣶⠠⠤⠤⣾⢥⣀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡿⣩⠯⠉⠓⣄⠈⣷⡄⠄⡈⠢⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⠷⠁⠀⣿⢸⣇⣽⣦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠘⢃⣀⣉⠀⠰⠇⠀⠀⠀⠀⠀⠀⣄⠹⣇⠹⠀⠀⡜⢀⡀
⠀⠀⠀⠀⠀⡀⣄⣴⠟⢯⡓⣄⠀⠀⠀⠀⠀⠀⠙⠁⡄⠀⡀⠀⡀⠀⠀⠶⠂⠀⠀⠀⠲⠀⠁⢈⣤⣤⣄⠐⣡⡴⡆
⠀⠀⠀⠀⠀⢀⠸⡧⣸⣅⣼⣇⠀⠀⠀⠀⠀⠛⠃⠰⠀⠢⣀⣀⡡⠄⠁⠠⡤⠀⠀⠨⠭⠄⠀⣿⣿⣿⣿⡇⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠛⠏⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠶⠒⣡⠌⠛⠛⠋⠀⢌⡙⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠺⠃⠀⡆⢰⠀⠘⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⠄⠸⡄⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢃⣀⠃⢠⠆
⠀⠀⠀⠐⠶⣄⠢⠄⠐⠈⡔⢀⣤⡄⠀⠀⠀⠀⠀⢠⠿⣟⣛⡛⠿⣷⡀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣦⡀⠤
⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠠⠄⠀⢤⠄⠀⠀⠀⠀⢿⣜⢾⣜⣟⡶⣿⠁⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡇⠤⠄
⠀⠀⠀⠙⠋⠁⠔⡀⠄⣀⠢⠘⠲⠄⠀⠀⠀⠀⠀⠈⠮⣯⣿⣿⡵⠃⠀⠀⠀⠁⠀⠀⠐⠂⡘⠿⣿⣿⣯⠟⠡⢄
⠀⠀⠀⠀⠚⠁⡸⠁⠀⠘⡄⠐⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣠⠆
⠀⠀⠀⠀⢠⣀⢻⠢⡸⠣⠞⣏⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣤⣀⣹⠟⠀⠀⠀⠀⠑⠧⢤⣤⣤⠀⠀⠀⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠍⠫⣝⢦
⠀⠀⠀⠀⠈⣲⠄⠀⠀⠀⠀⠀⠺⣍⣀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢆⢞⣻⣾⣿
⠀⠀⠀⠒⠛⣡⣟⣀⠀⠀⠀⠀⣏⠈⠁⠀⠀⠀⠀⠀⠈⠢⣈⣋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠧⣂⠥⣕⣵⠏
⠀⠀⠀⠀⠘⠉⠀⡶⠉⣦⠲⡏⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣷⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⣀⢀⣿⣿⣿⣶⣶⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⣶⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣤⣼⣇⣴⣦⠀⠀⠀⢀⣀⣠⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⡆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣸⣿⣿⣷⣶⣶⣤⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣶⣼⣿⣿⣿⣿⣦⣿⣿⣦⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇
⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣸⣿⣿⣿⣿⣿⣀⣀⣀⣤⣀⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢻⡿⢿⡿⠿⣿⣿⡎⠻⢿⠟⠛⣻⡷⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⠿⢿⢿⣿⣿⣿
⣿⣿⣿⣷⠸⠘⢿⠉⠉⠀⠀⠀⡤⡈⠉⠞⠃⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠸⣿⡿⣿⡶⠄⣌⡹⠷⠌⠁⠀⠀⠿⢿⢿⠛⢟⣻⣿⣿⣿⣾⡟⠈⠱⠀⠀⠀⠁⠉⠉
⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⢱⣆⠀⣤⠉⣡⡤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠘⠛⠀⠁⠞⠉⠁⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡄⠀⢀⠀⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈