Inactive Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠈⠉⠉⠉⠉⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⢷⣤⣤⣴⠞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡄⠀⠠⣶⣶⡆⠀⢀⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⠁⠀⣼⣿⣿⣿⣿⠟⣩⣴⠶⠿⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⡀⢠⣿⣿⣿⣿⠋⣼⠏⢀⣄⠀⠀⣠⣄⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⡇⣾⣿⣿⣿⡏⢸⡏⠀⠈⢻⣷⣾⡿⠋⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣇⠀⣠⣾⡿⠻⣷⣄⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠂⠻⣦⡈⠉⠀⠀⠈⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⡀⢀⣀⢀⣀⠀⡀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠳⡇⡾⢧⢪⣨⠀⡇⢸⠹⡞⢸⣒

⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⣿⣆⢸⡆⠀⣼⣷⠀⢀⡾⠛⠓⠀⠛⣿⠛⠀⣿⠈⣷⠀⣾⠀⣿⣛⠛⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⣿⠘⢿⠇⣸⠟⠻⣧⠈⢧⣤⡤⠀⠀⣿⠀⠀⣿⠀⠸⣿⠃⠀⣿⣭⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⠇⠀⠀⣀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⡀⠀⠀⢀⣔⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⢳⡦⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⡏⠀⠀⠀⠀⠀⢀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⠘⣄⡤⠔⠒⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠐⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠶⠄⠙⠛⠛⠋⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⠙⣷⡀⠀⠀⠀⢻⣆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠀⠈⢷⡄⠀⠀⠀⢻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣬⣿⡄⠀⠀⠀⠹⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⡏⠉⠉⠀⠀⠀⠀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣶⠶⠶⠶⠾⠿⠷⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛




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

⠀⠀⠀⣠⡾⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⡄
⠀⠀⠀⣿⠀⠀⢠⣤⠀⢠⣤⡄⠀⢠⣤⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⢀⣴⣦⣄⡀⠀⣤⣤⣤⣤⣤⠀⠀⣤⠀⠠⣤⠀⠀⢀⣤⠄⢠⣤⣤⣤⣤⡄⠀⢸⣿
⠀⠀⠀⣿⠀⠀⢸⣯⠀⢸⣿⢿⣦⠐⣿⠀⠀⢀⣾⠟⣿⡄⠀⠀⣴⡟⠁⠀⠉⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⠀⠀⢻⣧⠀⣼⡟⠀⢰⣿⣤⣄⠀⠀⠀⢸⣏
⠀⠀⠀⣿⠀⠀⢸⣿⠀⢸⣿⠀⠻⣿⣿⠀⠀⣼⡿⠶⢿⣿⡀⠀⢻⣧⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠈⣿⣶⡿⠀⠀⢸⣿⠉⠉⠀⠀⠀⢸⣧
⠀⠀⠀⣿⠀⠀⠘⠛⠀⠘⠛⠀⠀⠙⠛⠀⠘⠛⠀⠀⠀⠙⠓⠀⠀⠉⠻⠟⠋⠁⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠀⠘⠛⠃⠀⠀⠘⠛⠛⠛⠛⠃⠀⢸⡟
⠀⠀⠀⠻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠁⠀⠀⠉⠀⠈⠈⠀⠀⠁⠀⠈⠈⠉⠀⠈⠉⠁⠉⠁⠉⠁⠈⠈⠁⠉⠁⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡾⠛⢿⣿⡿⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣦⠀⠉⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⢀⣤⡀⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣦⣰⢀⣶⡀⡖⠲⠐⣶⠂⡆⣆⡰⢰⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠛⠘⠉⠃⠓⠚⠀⠛⠀⠃⠘⠃⠘⠒


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢤⣤⣤⣤⢤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠉⠩⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⠀⠀⣤⡀⠀⠀⠠⣤⣾⣦⡤⠀⠀⠀⣠⡄⠀⠐⢕⢦⡀
⠀⠀⠀⠀⠀⠀⢠⢞⠁⠀⠀⠘⢾⣿⣿⠓⠀⠀⢸⠟⢻⠀⠀⠐⢿⣿⣿⠟⠀⠀⠀⢙⢦
⠀⠀⠀⠀⠀⡰⠓⠁⠀⣠⠄⠀⠚⠉⠛⠀⢀⠀⠀⠀⠄⠀⢀⠀⠘⠋⠙⠂⠀⣴⡀⠀⠁⠱⡀
⠀⠀⠀⠀⣸⠁⠀⠈⢻⣿⣶⠟⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠘⢿⣿⣿⠋⠀⠀⢹⡄
⠀⠀⠀⢰⡁⠀⠀⠀⠘⠉⠙⠃⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠛⠉⠙⠀⠀⠀⠐⣷
⠀⡞⠉⣉⠉⠉⠉⠉⢉⡉⠉⠉⣉⠉⠉⠉⠉⣉⣉⠉⠉⣉⣉⣉⡉⢉⡉⢉⣉⠉⠉⣉⠉⣉⣉⣉⡉⠙⡆
⠀⡇⠀⣿⠀⢸⡿⣆⢸⡇⠀⠰⠿⣇⠀⠀⣬⠉⠙⠃⠀⠉⣽⠉⠁⠀⡟⠀⢹⡄⣰⡏⠀⣿⣭⠉⠁⠀⡇
⠀⡇⠀⣿⠀⢸⡇⠸⣿⡇⢠⡼⠳⢿⣆⠀⢻⣄⣠⡄⠀⠀⣿⠀⠀⢰⡇⠀⠈⣷⡍⠀⠀⣿⣀⣀⡀⠀⡇
⠀⢧⣀⣉⣀⣈⣁⣀⣈⣁⣈⣁⣀⣀⣉⣀⣀⣉⣉⣀⣀⣀⣉⣀⣀⣈⣁⣀⣀⣈⣁⣀⣀⣉⣉⣉⣁⣠⠇
⠀⠀⠀⠸⡦⠀⠀⠀⢠⣀⣠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⣤⣀⣠⠀⠀⠀⠠⡾
⠀⠀⠀⠀⠹⡠⠀⢀⣼⢿⣿⣦⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⢠⣾⣿⣿⣄⠀⠀⡹⠁
⠀⠀⠀⠀⠀⠹⡅⡀⠀⠀⠁⠀⢤⣄⣤⠀⠀⠁⠐⠂⠐⠀⠁⠀⢠⣄⣤⡄⠀⠻⠁⠀⠀⡽⠁
⠀⠀⠀⠀⠀⠀⠘⢮⡢⡀⠀⢠⣾⣼⣿⠆⠀⠀⢹⣶⣾⠁⠀⠠⣾⣿⡿⠦⠀⠀⡠⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣆⠀⠀⠛⠁⠀⠀⠐⠛⢿⠟⠓⠀⠀⠀⠘⠃⢀⢀⡮⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢤⣠⡀⠀⡀⠀⠈⠀⠀⡀⢀⣀⣠⠬⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠤⠤⠤⠴⠤⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠰⠞⠛⠉⣉⡁⣠⣤⢠⣦⠄⣴⡄⢠⣦⢀⣤⠀⣈⡉⠉⠛⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⡁⢠⣦⠄⠻⠆⠛⣃⣈⣉⡀⠉⠀⠡⠥⠬⠉⣈⣉⠀⠛⠃⠾⠗⢤⣦⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢠⣦⠘⠻⢀⡠⠄⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠬⣁⠸⠓⢠⣦⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⠰⠿⠊⡩⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⡉⠲⢷⢀⡈⠳⣄
⠀⠀⠀⠀⠀⣠⠟⢀⣈⠛⢃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠛⢋⣀⠘⢧⡀
⠀⠀⠀⠀⣰⠋⣠⣈⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠛⣡⡀⢳⡀
⠀⠀⠀⢰⠇⣀⣙⠃⡜⠀⠀⠀⠀⠀⠐⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠘⡄⠛⣁⡀⢷
⠀⠀⠀⡿⠀⣙⠋⢸⠀⣶⡄⢰⣦⡀⠀⣴⡆⠀⠀⣴⣶⡀⠀⠀⢠⣴⣶⣶⣄⢠⣶⣆⣴⣶⡆⢰⡆⢰⣶⡀⠀⢠⣶⠀⣶⣶⣶⣦⡆⢸⠀⢛⡁⠸⡇
⠀⠀⠀⡇⠈⠟⠁⡆⠀⣿⡇⢸⡿⢿⣆⣿⡇⠀⣰⣿⢻⣷⡀⠀⣿⡇⠀⠈⠁⠀⠀⢸⡿⠀⠀⢸⡇⠀⢻⣧⢠⣿⠇⠀⣿⣶⣶⠀⠀⠀⡆⠛⠇⠀⡇
⠀⠀⠀⣧⠐⠿⠂⢠⠀⣿⡁⢸⣿⠈⠻⣿⡇⣰⣿⠛⠛⢻⣷⠀⢻⣧⣤⣴⡦⠀⠀⢸⣷⠀⠀⢸⡇⠀⠀⢿⣽⡏⠀⠠⣿⣤⣤⣄⡀⢠⠁⠺⠗⢠⡇
⠀⠀⠀⢻⡀⢾⡖⠘⡄⠉⠀⠈⠁⠀⠀⠈⠁⠉⠁⠀⠀⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠁⡜⠐⣾⠆⣸⠃
⠀⠀⠀⠈⢧⠀⢶⡖⠐⢄⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⠜⠀⣴⡆⢠⠏
⠀⠀⠀⠀⠈⢧⡀⢲⡷⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢰⣷⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠳⣄⠐⠿⠆⣈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⡀⠾⠗⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡘⠛⢡⣦⠀⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠈⢠⣦⠙⠛⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣌⡉⠸⠿⢠⣤⠄⣉⠐⠒⠦⠠⠤⠄⢀⣀⣀⣀⣀⠀⠤⠤⠤⠖⠒⢈⠁⣤⣀⠸⠿⠈⣉⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⣉⠈⠛⠃⢾⡖⢴⣦⢠⣦⠄⣤⡄⣴⠦⢠⣦⠔⣾⠂⠛⠃⣈⣁⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠦⣤⣬⣄⣉⣀⣉⣁⣈⣀⣬⣤⡤⠶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠘⢿⣿⣃⣀⣀⡀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣈⣹⡋⣿⣿⡟⠉
⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠙⠢⢄⡀
⠀⠀⠀⠠⣞⣁⣀⡀⠀⠀⠀⢀⢠⣤⣤⡤⢤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣽⡆
⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⡟⣛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⣴⣾⣷⣀⣀⣀⣀⡄⠀⠀⠀⠀⢠⠸⠻⠿⢟⢿⠟⠆⡈⢣⠀⠀⠀⣀⢰⡾⢿⡷⢖⣴⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠛⢋⣷⠤⠀⠀⠀⡌⠀⠸⠀⡌⠰⡀⠀⢠⣸⡀⠀⠀⠗⠇⠛⢶⢶⣾⠟⠋
⠀⠀⠀⠀⠀⠴⢶⣶⣦⣽⣿⣿⣿⣶⣦⣤⣺⣤⣴⣶⣤⠶⣴⣷⣤⣤⣟⣧⣤⣤⣤⣤⣾⣴⣿⡿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⢤⣤⣖⣒⣶⣮⣭⣭⣿⣿⣶⣶⣿⣶⣶⣿⣯⣭⣭⣴⣶⣒⣲⣤⠤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢰⢸⣯⣭⣿⣷⣶⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⣾⣿⣭⠽⡗⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢲⣤⠀⡆⠀⣰⣦⠀⢀⡔⠒⠆⠐⢶⠒⠂⣶⠰⡄⢀⡖⢰⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢸⠈⠻⡇⢰⠛⠚⢧⠘⢧⣤⠄⠀⢸⠀⠀⡿⠀⠻⡾⠁⢸⣭⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣐⣲⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⣖⣂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠛⠻⠭⠽⠿⣛⣛⣻⢿⣿⠿⢿⣿⣿⣿⡿⠿⣿⡿⣛⣛⣛⠿⠭⠭⠙⠓⠒⠒⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠛⠉⠉⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⠶⠒⠒⠲⠶⣄⡈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢰⠏⣠⣤⡶⣟⡳⢦⡈⢳⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣼⠀⣧⠘⢧⣄⣻⡼⣷⢸⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠏⠀⠈⠓⠶⣤⡼⠷⠃⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣤⡤⠤⢤⣤⣘⡇⠀⠀⠀⠀⠀⢷⠀⠀⠙⣶⠀⠀⠀⠈⠉⠀⠀⢠⠏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠈⢧⡀⠀⠸⣤⣤⡀⠀⠀⠀⠀⢾⠀⠀⢠⠟⠳⣄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⢳⡀⠀⠀⠈⠳⣄⡀⠀⠀⠛⠀⠀⠀⠀⠘⣀⡴⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⣿⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠙⠓⠦⠤⢤⠤⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⣘⣦⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⡴⠞⠁⣀⡴⠋⠀⠳⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⣀⣀⡀⠈⠙⠳⣄
⠀⠀⠀⠀⢸⡆⣠⠴⢛⣩⡤⠖⠛⠁⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡴⠞⠉⠉⠉⠉⠙⠶⡄⠈⠳⡄
⠀⠀⠀⠀⠈⣷⡷⠚⣩⠴⠶⠶⠄⠀⠀⠴⠶⠶⢦⡀⠈⢿⡃⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣼⠁⠀⢠⠶⢶⡄⠀⠀⢹⡄⠀⢹⡄
⠀⠀⠀⠀⣼⠛⠀⠀⠡⠶⣾⠶⠀⠀⠀⠠⢶⣷⠦⠁⠀⡈⢻⡄⠀⠀⠀⢀⣀⣀⣸⣇⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢠⡾⠃⠀⠀⢸⡇⠀⠀⣷
⠀⠀⠀⠀⠸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡁⠀⠀⠀⢈⡀⠀⠀⠀⣼⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠙⢻⡀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⣿⠀⠀⠀⠈⠀⠀⠀⣸⠃⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⠶⠶⡆⠀⠀⠀⠀⢿⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⣀⠀⠁⠀⠀⠁⢀⣠⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠀⠀⠀⠀⢈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⠳⢤⣀⣠⠴⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠈⢹⡷⠲⠶⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡼⠁⠀⣠⡴⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠘⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡞⠁⠀⠀⠀⢀⣙⣛⣂⣤⣤⣤⣴⠆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣆⣲⣾⣛⣋⣩⣭⣾⡿⠟⢋⡿⠁⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠉⠉⠹⡇⢶⣏⠁⠀⣴⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠹⡶⠋⠙⠚⠁⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣠⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠷⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢰⡆⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠐⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠠⠾⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣾⠋⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣰⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡌⠛⠶⠞⠋⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⢻⣆⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⠹⣆⠀⠀⠀⠹⣆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣍⠉⠉⠉⠉⠉⢉⡍⠉⠉⠉⠉⠁⠀⠹⣧⠀⠀⠀⠹⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡤⠾⠧⠀⠀⠀⠙⣧⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⣀⣀⣴⣟⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢰⠆⠀⠉⠛⠋⠛⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⣾⠇⠀⠀⠀⠀⠀⠻⢶⠾⠃⠀⠀⠀⠀⠀⠸⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠉⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡎⠂⣾⡁⢸⠤⣤⠖⢂
⠀⠀⢀⠴⠒⠂⠠⢀⡀⢀⠔⠁⢀⡤⠖⠒⢤⠀⢹⠀⠀⠀⠀⣀⠉⢳⡼⠀⢸⣷⣀⠓⣇⠀⠀⠊⠠⠁
⠀⢠⡏⠀⣀⣀⣀⠀⠈⠃⠀⡰⠋⠀⠀⠀⠈⡇⢸⡇⠀⡠⢼⣄⠑⠌⠑⠂⠀⡿⣷⠀⠈⡄⠀⠀⢦
⠀⢸⡀⠐⡅⠀⠈⠉⢻⠀⠰⠁⡄⠀⠀⠀⢰⠁⢸⠇⠀⠑⢦⡙⠇⠀⠀⠀⠀⠐⡽⠄⠀⠀⠀⠀⠈⡄
⠀⠈⣇⠀⠰⡀⠀⠀⠘⡄⠀⢠⡀⠀⠀⠀⡌⠀⣸⠀⠀⠀⠀⠉⢢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠘⢆⠀⠹⣄⢠⠖⠀⣠⡂⠉⠒⢄⡰⠁⢠⠇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡆
⠀⠀⠀⠈⠳⡀⠈⠁⠀⡴⠁⠈⠢⡀⠀⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠘⢆⣠⠊⠑⠢⠤⠖⠉⢂⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢀⡠⠄⠲⠊⠉⠉⠉⠩⠉⠉⠛⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡴⠊⠉⠉⠉⠉⠉⠉⠉⠑⠒⠤⣀⡀
⠀⠀⢠⠏⠉⠈⠉⠈⠉⠁⠁⠈⠉⠉⠉⠈⠉⠁⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⢨⠧⢀⠄⠀⠀⠀⢀⠀⠀⣀⠀⢀⡀⣀⣀⠀⠀⢺⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠠⠤⠀⠀⠀⠈⢧
⠀⠠⡚⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠀⠀⠀⢹⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠧⡄⢀⡠⠬⡈⢀⡀⠀⠀⠁⣀⣁⢈⣐⠀⣠⠌⣹⠋⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠑⠤⣀⣀⣀⠀⠀⡀⠀⠊⠀⠀⢀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠁⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰⠦⠶⠴⠆⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠆⠀⠀⣀⣀⡀⠀⠠
⠀⣠⣴⣾⠟⣿⡇⠀⠀⠀⠈⠀⠀⠆⠀⠑⠒⠚⠂⠚⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐
⠀⣿⣬⡼⠶⠛⠃⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢀⣠⣞⡇⠈⠀⠫⠩⠥⠼⠃⡀⠀⣶⣳⠐⠂
⠀⠉⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠔⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣣⠟⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠘⠋
⠀⢀⠀⠀⠀⢀⡀⠀⠀⣰⣂⣂⣲⣀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⢸⠟⢁⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠻⠭⠿⠭⠝⠇⠀⠰⡏⣋⣹⣷⣽⠇⠀⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠁⠐⠀⢀⠀⠀⠀⢀⠀⠀⠦⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠩⢐⠀⠀⢨⠀⠀⠀⠀⠸
⠀⠀⠴⠀⠀⠀⣈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⢨⣲⠀⢨⠀⠀⢄⣀⠈
⠀⠠⠀⠀⠀⠀⢀⣈⠔⠀⠀⠀⢰⡶⠶⠄⠀⠀⠀⠀⠀⢠⡤⣤⣤⠀⠀⠀⠁⠀⠈⣤⡤⠆⠀⠀⠀⠀⠀⠈⠐⠀⠐⠌
⠀⠀⠀⠀⠀⠁⢉⠄⠐⠀⠀⠀⣼⣇⠀⠲⠤⠤⠄⠀⠤⠘⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣽⣉⣁⣄⣀⣀⣀⣀⣀⣁⣀⣀⣙⠀⠀⠀⠀⠀⠀⡈⢲⣠⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⡏⣠⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠤⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢿⡟⠃⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⡶⡢⡀⠀⠁⠂⠐⠒⠀⠀⢀⢀⠀⠀⠀⡀⡀⡀⠀⣰⠖⠀⠒⠀⠐⠐
⠀⠈⠀⠀⠀⠝⠂⠀⠀⠀⠀⠀⠀⡎⣭⢉⣑⢂⣜⣣⡥⠏⠀⡄⡀⠀⠀⠘⠀⠛⠘⠀⠂⠀⠃⠓⠃⣼⡏
⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠛⠾⠿⠿⠛⠋⣽⣀⣠⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⣀⠀⣀⣀⣀⣐⣒⣀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢡⠐⡴⣆⠀⠍⠠⢂⢠⠀⠀⠀⠀⠀⠀⠀⠇⠇⠀⠄⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⡂⡤⡒⠂⠀⠂⠄⠀⢂⢢⠀⠂⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠤
⠀⠀⠀⠀⢠⡀⠤⠀⠀⠀⠀⠀⣀⠁⠀⠁⠁⠀⠁⠀⠀⠁⢀⡀⠀⠈⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠓⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠶⢶⡄⠆
⠀⠀⠀⠠⢠⠀⠀⡠⠀⠀⠀⠀⠀⠀⣾⣿⣭⣽⣽⣽⣿⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠂
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⡀⢀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠐⠀⠀⠁⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠛⠒⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢀⣭⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣀⠴⠋⢸⡇⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠒⠛⠒⠛⠐⠉⠀⠀⠀⢸⡇⠀⠀⠘⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠣⢤⣄⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠴⠯⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣤⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⡟⠀⠀⣇⠀⢀⢀⠔⠚⣷⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣞⠺⣦⣘⡇⠀⢸⡇⠀⠀⠹⢶⡾⠋⠀⠀⢸⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢻⡞⢵⣯⣟⢦⣸⡇⣀⡀⠤⢤⣄⣀⣀⢀⣿⣷⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⣿⣎⡷⣮⣭⡀⠀⠀⠙⢿⣷⠟⣫⣭⠏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⠤⠖⠒⠒⠒⠲⠤⠀⠀⡃⢸⣿⣧⣿⠈⡟⢦⣄⣀⣀⣴⢻⠿⣋⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣿⣿⣿⣾⣧⣼⣇⣼⣥⣿⢏⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠲⣧⠀⠸⡆⠀⠀⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⡟⡜⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⠀⠀⢷⣴⣶⠴⢿⡆⣟⣸⢿⣿⣿⢯⡿⡘⠀⠀⠈⠉
⠀⠀⣀⣤⠶⠶⠛⠛⠛⢻⡆⠀⠀⣆⠀⠈⡆⠀⢸⢻⣍⠙⠹⣇⣿⠃⣾⣿⢻⣼⢳⠁
⢠⡞⠉⠀⢀⣠⣴⣶⣶⣶⣿⣀⣀⣮⣲⣄⣵⠀⠀⡞⢉⣓⣶⡏⠿⣿⣧⣧⣾⢏⡾⣦
⣾⠠⡁⠀⢿⣿⣿⣿⡿⠋⠉⠘⣷⣤⠙⠶⡽⡆⠀⠸⡏⣉⠉⢻⠦⣌⣉⣉⡠⢾⣁⡟
⠸⣆⠨⠀⠀⠉⠙⠛⠶⢶⡆⠀⠹⣿⠀⢀⣇⡇⠀⠀⢻⢻⣆⣈⣇⣀⣿⡇⠀⢸⡏
⠀⠈⠙⠲⠦⣤⣀⣁⣁⡀⠙⠳⠞⢉⣳⣿⣉⣿⠀⠀⣸⢧⣭⡿⠛⠿⣾⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⢿⠉⢉⡟⣻⠋⢁⣠⣩⡏⠀⢰⡇⣸⣿⠀⣾⣿⠞⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⣰⡇⠠⣿⣿⠉⠀⢀⡾⠻⣿⣿⠀⢻⣧⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢿⣧⣀⠙⠛⠓⣚⡽⠃⠀⠈⠛⠧⣬⣽⡯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⡀⢠⠀⠀⢄⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠠⠐⠀⣀⢡⡀⠆⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⡄⠀⠸⠀⠔⠘⠘⠊⠄⠀⠉⠀⠀⠡⠀⠀⠀⠀⠀⡀⡀⣧⡄⣧⡗⡠⡐⠳⡘⠆⡅⠄⣦⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⠁⠀⠀⠀⠀⠀⠁⠆⠋⣁⠘⡰⢇⠉⠆⠙⢸⠀⠄⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠾⣄⣅⠣⠈⣤⠆⣻⡼⢢⡄⢠⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⡀⢠⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠴⠥⡌⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣷⠀⠀⠀⠀⢸⠀⠐⠠⠄⠀⠔⣠⠀⡄⣶⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠀⠐⠲⠶⠶⠞⠴⠟
⠀⠀⠀⡈⠓⠠⠤⢄⠀⣀⣀⣀⠀⠀⠰⠞⠃⣈⣾⠀⠀⠀⠀⠀⢇⠀⠁⠀⠁⠈⠉⠉⠁⠒⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⡖⠒⢤⣀⡀⢀⡀⠀⠀⠀⠀⢀⡄⠉⠭⣲⠆⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢠⠉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣰
⠀⠀⠀⡗⢦⡈⠉⡀⠀⠀⠁⠈⠉⠊⠉⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⢀⠘⠷⠤⠀⠀⠀⠠⠴⠔⠒⠀⡠⠖⠁⠀⠀⠀⠀⠀⡄⠈⡀⠀⠀⠄⣄⠀⠠⠃⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠠⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠃⠂⠘⠂⠒⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠄⣠⣄⠐⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⠙⠲⠄⠀⠢⠴⠀⠀⢫⣙⢃⠀⠑⠒⠶⠆⠀⠀⠢⠐⣦⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠋
⠀⠀⠀⠀⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠂⠈⠠⠔⠠⠄⠩⠗⠠⠔⠰⠒⢠⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠊⠀⠒
⠀⠀⠀⠀⠀⠀⠉⠾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠐⠁⠀⠀⠀⠠⠘⠁⠀⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠖⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠖⠛⣏⠉⠙⣇⣀⣀⣷⣤⠴⠿⣦⡀
⠀⠀⢀⣀⣤⢶⡞⠛⢻⠁⠀⢹⣀⣤⠼⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠙⣦⡀
⢰⡟⠋⢯⠀⢀⣧⣤⠼⠗⠛⠋⠁⠀⠀⠀⠀⠀⡀⣄⠰⣄⠀⠀⠀⠀⠈⠻⣄
⠈⣷⡴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠉⠈⠂⢀⣀⡤⠴⠒⠛⣦
⢰⠿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠸⣆
⣿⠀⣿⠈⢳⡄⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣿⠀⠸⡇⠀⢻⣄⡠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣿⠀⠀⢿⠀⠀⢷⠀⢠⠞⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣧
⢸⡄⠀⠸⡇⠀⠘⣧⠀⠚⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡀⢹⡄
⠈⣧⠀⠀⢿⡀⠀⢹⡆⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⣤⠀⣿⣁⠀⢷⡀
⠀⢹⡆⠀⠘⣇⠀⠀⢿⡀⠀⣟⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠏⠁⠈⣿⣦⠀⢉⡇⠘⣧
⠀⠀⢷⠀⠀⢻⡄⠀⠈⣧⠀⠈⠓⢦⣄⠀⠀⢀⡀⠀⣼⠋⢹⣆⠘⠷⠤⠆⠈⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠸⣇⠀⠈⣷⠀⠀⠸⡆⠀⠀⠀⠉⢷⢹⡏⠻⣆⠻⠦⠾⠙⠀⠀⠀⣀⣠⠴⠒⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢻⡀⠀⢸⡆⠀⠀⢻⡀⠀⠀⠀⣸⠇⠓⠀⠙⠀⢀⣀⡤⠖⠚⠉⠁⠀⢀⡀⢠⠀⠀⠀⠈⣧
⠀⠀⠀⠈⣧⠀⠀⢻⡀⠀⠈⣧⠀⠈⠛⠉⠀⠠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢸⠇⠀⠀⠸⡆
⠀⠀⠀⠀⢸⡆⠀⠈⣧⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠹⡇
⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡆⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⡀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⣷⠀⠘⣧⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠸⣇⠀⢻⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⡖⠛⣏⢁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢻⡄⢸⡇⠀⣓⢌⠑⠆⠀⠀⠀⣀⣀⣤⢶⡞⠛⠹⡅⢀⣠⣷⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣷⢸⡇⠀⠈⢁⣠⣤⢶⠞⠛⠙⣇⠀⢀⣧⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡤⢶⡟⠙⡇⠀⠀⣧⣠⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣷⠴⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡂⢄⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠠⠆⢩⠁⠀⠀⠀⢠⣴⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⢀⠈⡄⠀⠀⠀⠠⢠⣉⣩⠝⠀⣤⠤⠛⠂⡀
⠀⠀⠀⠈⠃⠁⠀⠀⠀⠗⠀⠁⠀⠀⠀⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠻⣶⣦⣟⣀⣴⡾⠃⠀⠀⠤⠾⢖⡽⠇⠀⠌⠇⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃

⠀⢀⣤⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣡
⠀⠈⢯⣽⣿⠏⣹⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣤⡁⣤⠀⣴⡀⢠⡤⣄⢠⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢫⠸⠀⣾⣿⡏
⠀⠀⠈⢻⠙⠛⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡷⣿⠻⣿⣰⠿⢷⠻⣤⡤⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢹⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢺⢿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⡀
⠀⠀⠀⠀⠈⠁⣀⣀⢤⣶⣀⠀⠀⠂⢀⡤⠀⠐⢯⠿⠀⠶⡆⠀⠀⠀⠘⠛⠈⠉⠉⠃⡀⠈⠓⠢⠬⠅⠀⠀⠠⠄⠐⠀⡀
⠀⠀⠀⠀⢸⠯⠛⢟⠋⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠀⣠⣤
⠀⠀⠀⠀⠘⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠄⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢘⡃⠃⠙⠈
⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣠⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣍⣀⣀⣩⡄
⠀⠀⠀⠂⠀⠓⠒⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢀⡉⣤⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢂⣠⡶⠂⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢰⠀⢀⣾⣿⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⢸⣧⣾⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⡻⣿⡿⣏⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡸⠀⠀⢰⡁⠀⠀⠀⠤⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢐⣶⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣯⣿⠗⢢⡾⣿⡿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣤⣶⡶⢖⡒⠲⠾⠶⠶⠚⠛⢏⠀⠀⠸⣽⡿⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠛⢛⠿⠿⠒⢋⣙⣓⣶⣄⣀⣀⣐⣛⣗⣶⡤⠋⣨⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣵⣤⣤⣄⡀⠀⠀⠀⠼⠿⠿⠿⠿⠤⠭⠭⠭⠭⠽⠿⠗⠊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠩⡾⡏⣿⠁⢴⣦⠀⠀⢠⠴⠶⠒⠂⠀⠀⠀⣶⣶⣶⢠⣴⣿⠃
⠀⠀⠀⠀⠒⢪⡄⠀⠀⡸⢿⡟⠋⠁⢈⣓⣶⠃⣰⣆⡀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠈⠚⣭⣶⣿⡾⣼⣿⣤⠀⣼⡿⠁⣰⣷⣶⣶⣦⡀⠀⢀⣴⣿⣯⣭⣭⣭⣭⣭⡁
⠀⠀⠀⠀⠐⠀⢿⣿⣿⣾⡟⢹⡏⠀⣿⡇⢠⣿⡿⠿⠿⢿⣷⣄⣛⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⡻⠁⣨⡿⡇⠀⡠⣤⣠⣤⣄⣀⡀⣈⠉⠉⠉⠉⠉⠉⠉⢠⠀⠀⠀⠀⢀⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⣞⠻⠅⠱⠀⠀⠛⠻⠿⠿⣿⣿⣿⣿⡓⠒⠒⠀⠀⠀⠘⣠⢿⡟⠐⠛⠻⠻⠻⠻⣆
⠀⠀⠀⠀⣀⣀⢰⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⢤⣬⡾⣇⣂⠀⠀⠀⠀⠀⣄⠸⠶⣄
⠀⠀⠀⠀⠚⠛⠛⠒⠒⠀⠀⠀⠈⠉⠉⠛⠀⠀⠀⡀⢠⠴⠲⢂⠀⠀⠀⠀⠠⣦⡆⠀⠀⠀⠈⠉⠲⠃⠈⠁⠉⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡄⢠⣶⡀⠘⡤⠠⢴⡂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠁

⠀⠀⠀⠀⠀⢀⡀⢀⠠⠄⢀
⠀⠀⠀⡀⠀⠀⠀⡀⠀⠠⠀⢉⠑⢆⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡁⠀⢁⠀⢀⠀⢠⡀⠠⠀⠈⠁⢆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠢
⠀⠀⠀⠘⠀⠈⠀⠀⡀⠠⠀⠐⠄⠁⡀⢨⡀⠀⠀⠀⣄⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠸⢀⠈⠀⢀⣀⢀⣠⠊⠓⢀⠀⠜⠁⠀⠀⠀⠈⠂⢀⡀⠁⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠈⠀⠉⠀⠉⢄⡀⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⢄⡂⠐⣈⣖⡓⢼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉
⠀⠀⠐⠀⠀⠒⠀⣱⠠⢆⡡⢉⣡⡀⠃⡴⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠁⠈⠀⠈⡉⠂⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⢈⠂⠀⡘⠁⠀⠀⠹⠄⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠼⠄⣀⣀⡠⡀⠀⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠈⠉⢀⠣⡀⠀⠒⠂⠀⠀⠀⠃⠠⠆⠀⣠⣬⡄⠀⢥⣶⠆⡞
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣅⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠁⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠔⣀⡀⢈⣙⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠺⠶⠷⠶⠤⠿⠤⠀⠔⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⢈⠕⢢⡀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢡⠀⠀⠀⡀⠀⠐⢹⠄⠀⠀⠀⠀⠀⠀⡠⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠢⠀⠀⡄⠀⠂⠁⠀⠀⠀⠀⠀⠀⢰⠐⣐⠨⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⣴⣶⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣶⣾⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⣟⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡾⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⢀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠓⠋⠙⠻⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘⢻⣿⣿⡻⣿⠇⢠⠀⠀⠀⠀⢰⣿⣿⢿⡇⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠉⢙⣟⣳⡖⠃⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠘⠿⠿⠛⠁
⠀⠀⠀⠀⡀⠴⠾⡇⠀⢀⣀⣿⡶⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⢶⣀⣼⡿⠋⠀⠀⠀⠀⠤⠀⠀⠀⣀
⠀⠀⠀⠀⢧⣀⣤⠟⠀⣟⠉⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⢼⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢀⠰⠆
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠛⠁⠀⠀⠀⠀⠀⠀⣠⣶⡇⠋⠈⠈⠷⠈⠁⣶⣶⠆⠀⠀⠘⠉⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⢇⠘⠀⠀⢷⡄⢡⣿⡿⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣮⡟⠀⣾⣯⣸⣿⣿⣇⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠹⣿⠀⢰⠏⣠⣾⣯⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡸⠃⠠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠁⠀⢀⡸⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⢈⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣶⢲⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣾⡿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣦⣄⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢶⡄⠀⠀⠀⠀⠀⠀⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠷⢿⡆⠀⠀⠀⠀⠀⠉⣿⣿⢻⡿⢿⣿⠿⣿⡟⣿⣿⣿⢟⣿⣿⣿⠿⣻⣿⣿⣿⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⡓⣿⣿⠀⣞⣿⣿⣿⢳⣟⣾⣿⣿⣶⣿⣿⣿⠏⣠⠃
⠀⠀⠀⠀⠀⠀⡀⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣽⣧⣴⣿⡇⠀⣼⢿⡹⢇⣀⠟⣿⣿⣿⣿⣿⣿⡧⠀⠁
⠀⠀⠀⠀⠀⣿⣤⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣻⣿⣿⡄⣾⣿⣾⡟⣰⣟⣾⡿⣼⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣤⣿⣿⣹⣿⡟⠉⠉⠉⠛⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣼⠿⠿⠋⠸⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⡘⠓⠒⠒⠒⢰⣿⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠚⢣⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢘⡇⠒⠒⠀⠀⠀⠀⠀⠀⠈⣠⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⢀⠤⠊⣾⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠈⠉⣐⣢⣂⠁⠀⢀⠞⠚⢁⣴⠿⠿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠐⠉⠓⠒⠘⢧⠥⠼⠚⠁⠀⢰⢟⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⠀⠀⠀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡡⠒⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡢⡐⠀⡰⠁⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠧⡄⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠴⡁⢠⠃⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢾⡲⠤⡀⠈⢀⠐⠒⠒⠤⠀⠀⢀⠴⢊⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠺⡗⠔⠁⠀⠀⢑⠄⠀⠀⠀⠊⢀⠔⠁⠀⡀⠀⠰⠈⠣⢄⡀⠀⠀⠀⢀⠃
⠀⠀⠀⡠⢴⠭⠶⣠⢒⣄⠄⡠⠀⠀⠀⠀⠀⢦⡓⠤⣴⠀⠈⠙⣉⠞⠁⠒⠁⠀⠀⢠⠁⠀⠀⣀⠠⠒⣿⠋⠐⠂⠊
⠀⠀⠀⠊⠀⠀⠐⠁⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⢩⡀⠄⡾⠉⡆⠀⠀⠀⠀⠀⠘⡤⣶⠒⠃⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡴⢡⡴⠁⣀⠉⠅⠀⠒⠒⠒⠁⣀⡠⠤⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢗⠈⠣⠘⣦⡷⠔⠐⠒⠒⢪⠭⢠⣤⣶⠂⠀⠀⠉
⢀⢀⣀⠀⡀⠀⠀⠀⠀⣀⢤⠀⠮⣛⡚⣶⠀⠀⠀⠄⢸⡄⣤⠥⣠⡀⠀⠀⣀⣀⣀⡶⢸⡤⠔⢲⡄
⠙⠣⣌⠭⠂⠀⠒⠐⢺⠧⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠛⠈⠉⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⡄
⠀⠁⠀⠀⠀⢈⠀⠀⠀⠀⡄⠀⠠⠀⠰⠟⠛⠚⠆⠀⠀⠀⠀⠠⠅⠀⡤⠈⠀⠐⠤⠀⠀⠀⠀⠀⠠⠆⠁
⠀⣤⣶⢿⢻⣻⠀⠀⠀⠀⠉⠑⠚⠀⠘⠛⠛⠃⠛⠀⠀⠀⠎⠀⠀⡀⠈⠀⢀⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠠⡶
⠀⣿⡮⠿⠛⠛⠀⠀⡈⠁⠀⠀⠀⠀⠀⣀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⣠⡶⣿⡇⠁⠉⠃⢻⠿⠋⠀⠀⣼⣽⡀⠂
⠀⠁⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠰⠀⠇⠐⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⠾⠋⠀⠀⠀⠈⠛⠄⠀⠀⠀⠉⠉⠀⠐
⠀⣤⣀⣀⣀⣠⠀⠀⢠⣯⣿⣿⢧⡄⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠘⠁⠴⠄⠀⠀⠂⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰
⠀⠉⠚⠛⠒⠹⠀⠀⠻⣽⣷⣿⣿⠟⠀⠀⠀⠚⠉⠀⠁⠀⠀⠠⡀⠀⢀⠠⠀⠀⢀⠀⠀⢀⢤⡀⠀⠀⡄⠀⠀⠀⢈
⠀⠀⠀⠀⢀⠤⠰⠀⠂⠄⠀⠀⠠⠐⠀⠂⠄⠀⠀⠠⠂⠀⠉⠐⠀⠦⠀⠀⠀⠄⠂⠄⡀⠀⠣⠅⠀⠰⠀⠀⠀⠀⠘
⠀⠀⠉⢀⠀⠄⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠄⠀⢀⡀⠀⠈⠭⠂⠰⣲⠉⢑⢠
⠀⠘⠐⠀⠠⠀⠴⠞⡈⠀⠀⢨⡿⠉⢙⠀⠀⠀⠀⠀⢸⠛⢿⣿⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠁⠉⡀
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠸⡿⠤⠈⠉⠉⠉⠀⠉⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠜⡑⠐⠀⠖⠀⠤⠠⠤⠠⠄⠐⡇
⠀⠀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠘⠓⠖⠚⠒⠒⠒⠒⠒⠶⠳⠒⠂⠀⠀⢀⡀⠀⠐⠀⠳⠋⠀⠀⢄⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⣾⣥⠋⢀⠀⠀⠆⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⡄⠀⡀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⣀⠠
⠀⠠⠀⠀⢀⣿⠡⠐⠀⠀⠀⠃⢠⢳⠻⠛⡝⠫⢯⠖⡷⠀⡃⠀⠀⠀⢐⠰⡆⠄⢠⠀⢸⠰⡸⢀⣾⠋
⠀⠠⡄⢠⠀⠠⠀⠄⠀⢠⠀⡀⠹⣭⣶⣾⣶⠿⢟⣋⣁⠀⡇⠂⠒⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠅⠦⠀⠀⠤⠴⠤⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⢃⠠⣭⡢⠖⡲⣠⡆⡆⠀⠀⠀⠀⠀⠀⢌⣒⠀⢱⢱
⠀⠋⠉⠉⠉⠉⠉⠉⠉⠓⠀⢀⠠⢀⠠⢄⠀⡤⠀⠐⠤⢄⠈⠄⠙⠛⠐⠛⠒⢁⠃⡀⠀⠀⠐⠂⠄⢀⡀⠁⠀⣀
⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠈⠈⠀⠈⠊⠀⠑⠑⠀⠊⠈⠀⠀⠐⠄⣀⡠⠒⠁⠨⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠌⠈⠤⠀⠀⠀⠀⠈⠉⠁⢀⣀⣀⣀⣀⡀⠀⠈⠁⠀⠧⠀⠀⡀⢴⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⡤⣤⣄⡄
⠀⠀⠀⢄⡀⢀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣟⣽⣻⣭⣿⠀⠀⠀⠀⡄⠁⠀⠁⠐⠀⠀⠀⠀⡀⠀⠀⡀⡎⠛⠶⠞⠃⠂
⠀⡀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⢀⠄⠀⡀⢀⣛⠃⢰⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠀⠀⢀⡅
⠀⠣⠤⠤⠤⠤⠤⠤⠤⠽⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠃⠀⠀⠄⠀⠄⠊⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠤⠖⠒⠢⣤⠤⠐⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠔⠋⠁⠀⠩⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠒⠉⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢠⠎⠁⠊⣀⣀⡀⢠⣤⡀⠀⢀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⣄
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⡇⠀⢸⠀⠙⡆⣾⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠞⡀⠀⠀⠐⠚⠓⠂⠸⠶⠚⠀⠙⠒⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⡴⠲⡄⢠⠶⢤⡀⡤⠤⡀⢠⠀⠀⡤⠤⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠀⢈⡿⡁⠀⡼⢸⠀⠀⡇⡇⠀⡼⢸⠀⠀⡷⠆⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⠉⠉⠉⠀⠙⠋⠀⠈⠓⠚⠀⠛⠉⠀⠈⠉⠀⠉⠉⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⡼⢦⡀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠒⠹⡀⢠⠂⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠒⢶⡙⣟⡆⠀⢀⡠⠀⣀⣀⣀⠉⢰⡜⢕⣿⣿⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣧⢸⢸⣇⣿⠛⠚⠛⠓⠉⣤⡀⢬⠉⠙⢿⡾⣹⣩⣽⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢆⣛⣴⣧⠞⠰⠈⠑⠈⠛⠻⠦⣕⠠⡀⠑⢿⣏⣥⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⠛⠋⡑⠊⣀⠴⣀⡠⢒⣃⣀⣬⣓⠤⡔⠠⠹⡟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣤⣮⠷⠟⠉⠻⣄⠀⠈⢱⣄⣉⣀⣀⠈⢦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⠀⠀⣴⣶⣦⡈⠁⠀⢀⣴⣿⣯⡉⠀⠈⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⢸⠃⠉⢹⡇⠀⠀⢸⡈⠛⠋⡇⠀⠀⡟⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⠀⠀⢧⣤⠾⠁⠀⠀⠘⠳⢤⠾⠃⠀⠀⣷⣏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠜⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠈⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣧⣼⠿⠉⣀⡀⠀⡀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⡼⢲⠀⢠⣾⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡇⠀⠀⠀⡠⠃⠁⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠗⠠⣀⠀⢀⡠⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡐⠀⠀⠀⠀⢩⢹⣤⣀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⡇⠀⠀⠓⣠⠋⠊⠻⣧⠱⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠀⠀⠀⠙⢇⠀⣽⡀⢀⡔⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⡿⠀⠀⠀⠄⢐⠀⠀⠀⠀⢸⣾⣿⣇⣬⠀⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⠳⠄⠀⠀⠄⠀⠀⢀⣼⣿⣿⣿⣿⣷⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⣤⣥⣦⢰⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡿⠟⠃⠀⠀⠉⠉⠉⠁⠀⠉⣦⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣧⠠⢀⣠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠉⠛⠛⠛⣻⠁⠀⢻⣯⣝⣻⣿⣿⣿⡿⣆⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠂⠀⢠⡶⣾⣯⡀⠀⠸⣿⣷⣤⣿⣽⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠀⢉⠀⠀⠀⣩⠆⠐⣿⣿⣯⣿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣟⠛⠛⠛⠛⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣮⣍⡛⢶⣄⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠘⣧⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⡻⢦⣤⣀⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⣭⣙⡛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡙⠻⠟⣉⡄⢠⣉⠻⠟⣋⣿⣿⣿⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⠛⠛⠛⠛⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣟⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣠⠤⠒⠂⢼⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠑⠦⠤⣤⡯⠤⠖⠁⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣤⣤⣀⣀⣤⣤⡴⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠤⠤⣀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⡀⠀⢠⠀⠀⠁⠀⢀⠀⠀⠉⠲⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀⠤⠀⠀⠉⠀⠘⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠤⠤⣤⣄⣠⣤⣤⣀⣠⣤⣤⣤⣀⣀⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠳⢶⣤⣭⣿⣍⣀⣀⣀⣠⣴⢦⣤⣤⡶⠂⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡀⠉⠉⠉⠉⠉⠉⠁⣉⣠⣴⠖⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⣿⡀⠀⠉⠉⠛⠓⠚⠛⠛⠛⠉⠁⢀⣠⠄⠀⠀⠀⠈⠻⠷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⠶⠞⠋⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣠⠤⠒⠛⠋⠉⠉⠉⠉⠛⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣁⣀⣀⣀⠠⢤⣤⣄⣀⣀⡀⠀⠀⠀⣸⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣀⣈⣙⠛⠛⠛⠉⠻⢶⣄⡈⠉⠉⠁⠀⠀⢠⣿⣿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢶⣶⣤⣈⠉⠛⠿⣷⣦⣄⠀⠀⠉⠻⠷⠄⠀⠀⢀⣾⣿⠇
⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⣴⠟⠁⠘⠳⢦⣄⡉⠛⠿⢷⣦⣄⡉⠛⠿⣶⣄⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠈⡙⠷⣤⣀⠈⠙⠻⢷⣦⠈⠙⠋⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣴⣿⣯⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢁⣾⡿⠛⠿⢿⣿⢷⣶⣤⠠⣄⡙⠒⡁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡤⠀⠀⠀⢸⣿⠀⠀⠀⡐⢻⣟⣿⣥⡈⠰⠀⠀⠹⣓⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⣿⣧⠀⠀⡴⢀⣬⣿⣿⣿⠟⠠⣄⢤⣀⣤⣤⣄⣜⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⠀⠀⣧⢰⣿⣿⣶⣾⣿⣿⣿⣿⡿⠃⢈⢞⣥⣾⠿⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⠟⠋⠁⣠⣿⣿⡟⠀⢠⣡⠿⠋⠀⢄⣙⣷⣶⡝⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠂⠀⢤⡀⢸⣠⣤⣿⢿⣿⠏⠀⢠⢟⣵⠂⠀⠀⠈⠉⢿⣿⣿⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠈⠀⠀⠠⡑⠾⣿⣿⣿⣿⠏⠁⠀⢠⣾⣿⠀⠀⠀⠀⠀⣺⣿⣿⡇⣿
⠀⢠⣀⠒⠄⠀⠠⠄⠀⠉⠀⠀⠰⠀⠀⠀⠈⢘⣯⡿⠟⠁⠀⠠⠄⡜⢿⣿⣿⣆⠀⠀⣶⣿⣿⣿⢡⣿⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠁⣀⠀⠀⠀⢠⣀⠀⣴⣇⣌⠓⠲⢦⣍⡓⣶⣿⣿⠟⣣⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠙⠂⠐⠀⠉⠙⢿⡇⣼⣿⣿⣿⠟⠉⠱⣤⡀⠈⠻⣦⣭⡥⠞⣡⣿⣿⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠬⠀⠀⠀⠀⠀⡀⠀⠻⢣⣿⣿⠟⠁⠀⠀⠀⠘⣿⣆⢠⣿⣯⠔⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⡀⠀⢠⣴⠏⠁⡠⠀⠈⠿⠷⠢⠀⠘⣷⣄⠈⣿⣿⣿⡿⣫⡾⢸⣿⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⣾⣯⠀⡄⠀⠀⠀⣠⣴⣶⣶⠀⣿⣿⡖⣿⢟⣩⣾⣿⢣⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⢛⡀⠀⠰⡄⠠⣿⣿⣿⣿⣼⣿⡿⣗⣥⣿⣿⣿⢏⣾⢿⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣼⡿⠿⢿⣿⣿⣿⣷⣶⣿⣿⣍⣭⣴⣾⡿⢿⣿⣿⣿⣾⣷⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠹⣿⡿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣯⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⢻⣷⢙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⡿⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠟⠉⣠⣾⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⡇⠀⠀⣾⣿⣿⠃⠀⠀⣀⣀⣀⣤⣤⣴⣾⢿⣿⡧⠙⢿⣿⣟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠉⠁⢀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣿⣿⣿⣿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣯⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣏⢀⣀⠀⠀⢀⣀⣠⣴⣶⠟⠋⠁⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⠀⠇⣼⣿⣿⣿⣿⣿⠟⢻⡟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣿⣻⠉⠏⠭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡏⡇⠈⠻⣄⠠⠦⠀⡄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠐⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣿⣿⣿⣿⠟⠁⠀⠈⠙⢿⣿⣿⣧⡀⠀⢀⣠⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠋⠁

⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠌⠀⢀⠀⡀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠁⠑⡖⢀⡃⠀⠀⠀⠀⠀⠀⠀⠓⣤⠈⠢⡀⠀⠀⠀⠀⠀⠀⢈⡌⡛⢰⠺⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢳⠊⠑
⠀⢠⠔⢂⡁⠀⢸⡐⢢⠀⠀⠀⠀⠀⢰⠃⠀⠠⠈⠚⡃⠀⠀⠀⠀⠀⠀⣼⠉⢂⠌⢂⠐⡀⠀⠀⠀⠀⠀⠘⠚⠧⠿⠓⡇⠀⠀⠀⠀⠀⠀⢠⣂⡥⠞⠕⠀⡀
⠀⠀⠢⡀⠀⠀⠀⢄⠔⠀⠀⠀⠀⠀⠈⢈⠈⠀⡀⡁⠁⠀⠀⠀⠀⠀⢀⣨⢧⠜⠊⠢⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠈⣠⠛⠀⠀⣀⠔
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉

⠀⠀⡿⠉⠉⣉⠉⠉⠇⠀⠀⠀⠀⠀⠀⢀⡄⠠⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠳⡄⠀⠀⠀⠀⠠⠊⠁⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢱⡀
⠀⠀⠀⠐⠥⠤⢬⠂⢀⠀⠀⠀⠀⠀⢀⠊⠀⠔⠙⠅⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢦⢹⠁⠁⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠰⢎⠀⠀⠀⠀⠀⠀⣠⠪⢌⠽⡞⡆
⠀⠀⠀⠠⠁⠀⡈⠀⠈⠀⠀⠀⠀⠀⠘⢉⠉⠉⢉⠏⠀⠀⠀⠀⠀⠀⡀⢸⣌⣳⠥⠃⠀⠀⠀⠀⠀⠀⢸⠙⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡂⢀⡑⢁⡣⠊⠁
⠀⠀⠴⠀⠄⠉⠄⠀⠇⠀⠀⠀⠀⠀⠀⠠⠼⠯⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠢

⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡠⢀⣠⣄
⠀⠀⠈⡕⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠐⣴⣉⣰⣀⣁⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⡠⠠⠀⠀⠀⠀⠩⡈⠒⠤⠤⠒⢁⠍⠁⠀⠀⠀⢠⠘⣟⠕⠊⠉⠉⠣
⠀⠀⠀⠈⡄⠄⠅⡅⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡐⣗⢺⢺⡊⠱⠁⠀⠀⠀⠀⠀⠈⠐⡗⢰⡇⠁⠀⠀⠀⠀⠀⠘⢔⠂⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠓⠖⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡰⣇⠵⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⡠⠊
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠰⡄⠃⠐⠀⠂⡼⠀⠀⠀⠀⠀⠀⠀⢀⡄⠰⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠐⡄⠀⠀⠀⠀⠀⢠⠧⠾⠿⠼⡆⠀⠀⠀⠀⠀⠀⡰⠴⡄⢠⣂⢣
⠀⠠⠧⠀⠼⠀⠾⠧⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⢀⠔⡎⢓⡠⠈⠁⠀⠀⠀⠀⠀⢰⠂⠤⠤⠀⡇⠀⠀⠀⠀⠀⠀⣇⠤⡀⠡⠀⠀⡅
⠀⠀⢘⣀⠒⢒⣚⠀⠁⠀⠀⠀⠀⠀⠀⠀⡅⠠⠈⠇⠀⠀⠀⠀⠀⠀⢔⠁⠈⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⢀⡀⡇⠀⠀⠀⠀⠀⠀⡄⠁⠀⠠⠤⠤⠄
⠀⠈⠙⠞⠁⠙⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠐⠁⠀⠀⠀⠀⠀⠀⠣⠤⠄⠠⠤⠤⠂

⠀⠀⠀⠀⠀⡀⠄⠤⡀⠀⢀⠄⠀⠐⢒⠒⠤⡀⢠⢄⢀⠒⠂⠐⠀⠐⢦⠀⣀⠀⢀⣤⡶⠶⣀⠄
⠀⠀⠀⠀⢰⠁⠀⠀⢸⡐⠁⠘⢀⠤⠨⡁⡄⠑⠘⠉⠀⠍⢣⠲⠢⢴⡞⠀⠓⠀⣺⡿⡯⠑⣶⡇⡁
⠀⠀⠀⠀⠀⠑⠀⠔⠃⢃⠀⡄⠈⢄⠀⡐⠀⡐⢠⠁⢉⠈⢐⠈⡼⢮⠤⡀⣄⠀⣿⣯⣚⣎⣿⣷⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢠⠈⢆⠀⠠⠀⠀⢚⠐⠁⠸⣀⡒⢠⠏⠀⡇⠀⠀⠸⣸⠀⠙⠛⠓⡿⠟⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⢁⡀⠀⠈⠀⠀⠤⡄⠀⠀⡀⡀⠈⠮⠶⠴⠮⠟⠀⢖⠀⠀⡇⢰⠓⠇
⠀⠀⠀⠀⠀⡡⠴⠖⠒⠦⣤⠘⠀⠀⠀⠀⠀⠀⡗⠒⡌⠣⡀⠡⠀⣂⣆⠀⣤⠠⢠⡄⠀⠇⠈⠈
⠀⠀⠀⠀⠘⠆⠀⠀⠈⠀⠇⠸⡉⠥⢀⡁⠄⣀⡃⡰⢰⠀⠈⠁⣏⣀⣉⣉⣁⢈⣧⣶⠘⠄⢀⢄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⠁⠁⢣⠀⠀⠀⠀⡜⠁⠐⢁⠀⢀⡀⠙⠉⠋⡉⠉⠉⠛⠁⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠤⠠⠀⡀⡀⠉⠀⢀⡅⡆⣄⠀⡴⠤⠤⢤⣭⢀⠁⣦⠑⠂⡍⠑⠀⠀⡤⠤⢄
⠀⠀⠀⠀⠀⢴⡀⢰⠢⠀⠀⠒⠁⠀⠀⢥⠼⢿⣼⠀⠑⠢⠀⠐⠁⡈⡀⣄⠀⡘⠁⡜⠀⠀⣟⣻⠁
⠀⠀⠀⠀⠀⠑⠀⢐⠉⢄⠀⠶⢧⣈⠐⢌⠑⠉⢠⡂⠐⠒⠀⠐⣂⠀⠑⠄⠀⠡⢊⢄⠀⠀⡃⢰
⠀⠀⠀⠀⠀⠀⢱⠀⡁⢠⠠⠈⠢⣉⠛⣦⠆⠀⢀⠀⠀⠉⠉⠁⢸⡒⠢⠀⢠⠊⠉⡷⠃⠀⡇⢨
⠀⠀⠀⠀⠀⠂⠘⠀⠃⠁⢐⠍⠵⠀⡠⡀⠀⠀⠸⠀⠀⠀⠀⠀⣠⣬⡠⠠⡊⠀⢈⠁⠀⠀⠯⠽⠄
⠀⠀⠀⠀⠐⣧⣴⣦⣆⣇⣈⡒⠀⠊⠀⠈⠢⠠⠀⠑⠠⠤⠤⠐⠁⠀⠀⠀⡌⠲⡁⠀⠀⡠⡄⢤
⠀⠀⠀⠀⠀⠇⠀⠀⣀⡃⡆⡅⠀⢁⣈⡀⣨⠤⢄⠀⠈⠚⠋⠟⢋⠂⣰⠁⣋⢉⣋⡂⠀⠈⣿⡊
⠀⠀⠀⠀⠀⢈⠉⠘⠉⠟⠒⠀⢸⠀⠀⠀⡁⢐⣼⡇⠆⡞⡇⠷⢾⠀⠇⢀⠀⠀⡈⡑⢀⠎⠀⠱⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠉⠁⠉⠉⠈⠀⠀⠐⠙⠑⠛⠈⠀⠈⠒⠄⠀⠐⠁⠈⠂⠠⠬⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢉⡉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣸⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⣠⠾⠛⠳⣆⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣤⡾⠋⠀⠀⠀⠀⠐⣏⠀⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣤⣤⣤⣤⡙⠷⠶⠶⠋⠐⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⢿⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠹⣆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡌⢷⡀⠀⠀⠹⣦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⡍⠉⠉⠉⠉⠉⣭⠉⠉⠉⠁⠀⠈⢻⡄⠀⠀⠘⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡴⠶⠿⠀⠀⠀⠘⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⡤⠄⣤⣤⣾⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣯⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠸⣇⣠⡿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠒⠉⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⡖⠀⠠⢄⡀⢀⠀⠂⠙⡏⠀⠀⠀⠠⠫⠋⠀⠀⠀⠀⠀⢠⠛⠒⠀⠉⠁⠀⠛⠋⠇
⠀⢰⡥⠒⠂⠠⠤⣀⣀⠙⢆⠀⠀⠀⠀⠀⠈⠒⠤⣂⢀⣀⣀⡠⠀⠀⠀⠀⢠⢁⠄⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⢀⢰
⠀⢸⢠⠀⣁⠀⠘⠁⠀⠢⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡹⡅⠀⠀⠀⠀⠀⢁⠈⡰⠀⠀⠐⠁⠀⠐⠀⠂⡈⢀⠡⡀⠀⢠⡘
⠀⠈⠒⠠⠁⠅⠀⠉⠃⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⡅⡔⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠆⡂⠐⠀⠀⠁⠠⠙⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⣀⠞⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡀⠀⠀⠀⠟⠀⠀⠀⠠⠬⠅⠊
⠀⠀⠀⢈⡒⠲⠿⣐⠀⠄⡀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⢖⡈⣠⠀⠐⡌⠑⠠⣄⡱⡄⠀⠈⠀⠉⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈
⠀⠀⠀⠈⢣⠑⢄⠈⠳⡀⠈⡢⠃⠀⠀⠀⠀⡀⠠⠤⠴⠀⠒⠂⠀⠈⠉⢉⡉⠀⠐⠒⢀⠀⠀⠀⠀⠀⠔⠈⠠⡈⠂
⠀⠀⠀⠈⡀⠱⡄⠑⡀⠈⠉⠀⠀⠀⠀⠎⠀⠀⣴⠂⠀⡴⢠⡖⣰⡆⠀⡜⣧⠀⠀⠀⢈⠀⠀⠀⠀⠀⡠⠄⠂⠐⠉⢄
⠀⠀⠀⠀⠹⡀⠸⢀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⣼⠟⠓⠈⠁⠈⠁⢀⡉⠉⠀⠀⠀⣨⠀⠀⠀⠐⠀⠀⢀⠀⠂⠀⠘⠮⠨⠃
⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠈⠁⠀⠀⡀⠀⡀⠀⡀⢰⡄⡤⣀⢠⡖⣺⣧⡆⢌⡶⢀⠇⠀⠀⡄⠀⠀⠀⢬⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢡⠀⣹⠞⠛⢾⠜⠓⠿⠈⠉⠈⠋⠉⠀⡠⠊⠀⠀⠀⠀⠁⠁⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢔⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀⣄
⠀⠀⠀⠀⠘⠀⠀⠀⢀⢄⠄⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠌⡀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢤⡆⢄⣀⢄⢤⡎⡄
⠀⠀⡐⠁⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠡⠀⢐⠀⠀⠀⠀⠀⠠⠌⠏⠀⡄⠀⠊⠀⠈⠁⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠖⠂⠀⠂⠀⠀⠀⠀⢈⡠⠁⠀⠐⠋⠁⠠⠀⠀⠀⠀⠀⠀⠪⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡠⠒⢒⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢄
⠀⢘⢀⠎⣀⢨⠏⢲⠨⡈⢆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡌⢀⠂⠙⢓⡄⠀⡃⠢
⠀⠈⢌⠲⡄⠠⣖⠫⣀⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕⠀⠀⠀⠀⠐⡠⠈⠀⠀⠈⠁⠀⠀⠀⡆⢀⣤⡴⠟⠡⣠⠗⠀⡅
⠀⠀⠈⠣⢍⠢⠬⢓⡣⠞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⢔⠊⢉⡠⠎
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣤⡀
⠀⠀⠀⠀⠀⠞⡄⠫⠐⠃⠀⠀⠀⠀⠀⣠⠾⠉⢁⣤⣌⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣶⣶
⠀⠀⠀⢀⣦⣧⣵⡠⢲⠀⠀⠀⠀⠀⠀⢇⣀⣚⣉⣀⣉⣀⡻⠆⠀⠀⠀⠀⠀⢀⣴⣿⡺⡿⣽⡏
⠀⠀⠀⢸⣿⠛⠿⣿⣿⠂⠀⠀⠀⠀⠀⣿⠉⣉⣉⣉⡉⠉⡿⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢿⣿⠓
⠀⠀⣰⣿⣿⣿⣶⣿⠁⠀⠀⠀⠀⠀⠀⢸⡆⠛⠛⠛⠋⢸⡇⠀⠀⠀⠀⠀⠀⢸⣯⣉⣙⣻⡏
⠀⠀⠉⠉⠻⠿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠀⠀⣠⠴⢶⠶⢤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠘⢀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣨⣵⣶⡄
⠀⠀⢰⡟⠀⡤⢀⣩⣷⠀⠀⠀⠀⠀⠘⠦⢤⣀⠀⠀⠀⣀⢼⠃⠀⠀⠀⠀⣠⣮⣵⡾⠿⠛⠉⠉⢿⠁
⠀⠀⠘⢿⡂⢴⡋⠦⠤⠀⠀⠀⠀⠀⠀⣘⣿⣮⣕⠶⣪⣷⣿⠇⠀⠀⠀⠘⢿⣿⠁⠀⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣟⡽⠋⠁⠀⠀⠀⠀⠀⠀⠘⠲⠴⠚⠋⠁

⠀⠀⠀⠰⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠶⣶⣬⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡶⣄⣿⢸⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⣀⣼⣿⣿⡦⠙⠁⠀⠀⠀⠀⠀⠰⡚⡇⠇⠻⢸⡇⡏⠀⠀⠀⠀⠀⠀⢀⡶⠶⠾⠶⠶⡆
⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠘⡆⢀⣤⡄⢀⡇
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠏⠙⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⡿⢿⠃
⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠁⢸
⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿