Solar eclipse Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡆⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢻⡄⠀⠀⢸⡇⠀⠀⣼⠇⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣧⠀⠀⠘⢗⣀⣀⣘⣁⣀⡀⠟⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠦⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢈⣥⠶⠛⠛⠉⠉⠉⠉⠉⠙⠛⠷⣦⣍⠀⠀⢀⡴⠏⣠⡶⣿⠋⠁⠀⢀⣀⠀⠀⢿⡅⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠛⢶⣤⡀⠀⠀⠈⣡⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠋⣠⣾⣉⣠⡟⠀⠀⠀⣿⣹⡷⠀⠈⠻⣦⣄⣤⣼⠟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠂⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣴⠛⠉⠻⣆⠀⠀⠀⠀⠀⠀⣼⠋⠁⠈⠹⣦⠀⠀⢿⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣠⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⢿⣄⣀⣰⠟⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⣠⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠉⠉⠁⠀⠀⢀⣤⣄⡀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⣟⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣤⡄⠀⠀⠀⠀⠀⠙⠶⠾⠋⠀⠀⠀⠀⠀⠀⣴⠶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠂⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠻⣦⠟⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠶⠟⠉⠀⠀⠀⣠⡜⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⢰⣟⣹⡇⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣨⠙⠷⢦⣤⣄⣀⣀⣀⣀⣤⣴⠶⠛⣉⠀⠀⠙⢷⣄⠙⠻⢦⣤⣀⠀⠀⠀⠉⠉⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡆⠈⠉⣭⠉⠉⢠⣆⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛





⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⡟⠋⠁⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣱⠦
⠀⠀⣿⣿⣿⡿⠋⠀⣠⣶⣿⣷⣶⡄⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣦⣴⣿⣿⣿⣾⣷⡎⢀
⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⣿⣿⣿⣧⡀⠀⠻⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⢐⣹⣿⣿⣿⣿⢿⡟
⠀⠀⣿⣿⣿⣿⣷⣄⠀⠈⠉⠉⠁⠀⢀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠐⠘⠿⣻⠟⠊
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣶⣟⠛⠛⠛⠳⠶⣤⣀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣇⠀⠚⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⠇⠀⠲⠶⣦
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣴⠟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠛⠷⠶⠶⠶⠞⠛⠉⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢳⡀⠀⠀⠘⡇⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠣⠀⠀⡘⠅⠀⠀⡠⠇⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣀⠀⠀⢠⢃⠀⠰⢰⠀⡐⢠⠁⡠⢊⠌⠀⠀⠠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡑⡀⠘⠀⡄⠆⣸⣀⣥⣤⣌⣠⢃⠠⢂⠥⠊⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠐⠒⠲⢄⢄⠀⠰⡘⢄⣣⣾⣿⠟⠋⠁⠀⠀⠀⠈⠒⢡⠐⢂⠡⠌⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠤⣑⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄⠤⠠⠄⠀⢠⡤⠞
⠀⠀⠀⠀⠀⠤⠶⠦⠄⡂⠄⢈⡂⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⠁⣂⠄⣀⣤⠤
⠀⠀⠀⠀⠀⢀⡤⠴⠦⠄⣐⠒⠒⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠌⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⢄⠉⠂⠕⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠀⠀⠒⠂⡩⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⡠⡚⢆⠈⢆⢢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⡊⠅⠐⠈⡔⢉⠟⡛⢻⠲⠒⠒⡁⠁⠐⡈⡀⠀⠑⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⡠⡪⠐⠁⠰⢁⠂⠸⢠⠁⠃⡂⠀⠐⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠏⠀⠀⠀⡑⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢸⡅⠀⠀⠘⡆⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⡛⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⡆⠀⡀⠀⡀⢀⡾⠀⣗⡀⠀⠀⣀⠄⡾⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠸⡆⠙⣄⢸⣾⡁⠐⣿⣲⢁⡴⠁⣾⠁⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣐⣶⣶⣷⣦⣵⣧⣀⣈⡿⠟⠛⠛⠛⠿⣏⡁⢀⣿⡥⠒⢁⡰⠓⠈⢆
⠀⠀⠀⠀⠀⠀⡠⠈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟⠅⠀⠀⠀⠀⠀⠀⠀⠙⢟⠉⠀⣴⠯⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠘⢀⡀⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣞⣛⠛⡃⠀⠛⢛⡛⡂⠈⣿⣾⡓⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡀⠐⠂⢿⣿⣿⣿⣿⣿⣿⣙⣿⣿⡟⠛⠉⠈⠀⠈⠙⠛⠁⠀⣷⠀⠁⣠⣴⠴⠛⠂⢀
⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⠿⢏⡒⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠐⡄⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⠓⠀⠀⠀⣴⣯⣀⠀⢷⡀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢌⡛⠿⣿⣿⣿⡿⠟⣿⠀⢉⣽⣶⡤⠤⢴⣾⣯⡁⠀⣿⠲⣬⡙⣦⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⡈⠉⠁⠀⢠⠟⢠⠟⢰⢿⡄⠀⣿⢱⡀⠹⡄⠹⡇⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠠⠾⠖⠃⠀⠈⠸⢹⡄⣹⠂⠀⠀⠈⠀⠹⠄⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠈⣧⠃⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⠤⣥⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠦⠙⠘⠃⠟⣦⡀
⠀⠀⠀⣴⣿⡇⠛⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠈⠀⠀⠀⠀⠀⠐⢓
⠀⠀⠀⢿⣿⡇⠀⠈⠙⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣠⠀⡀⣀⢠⡹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠆⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⣶⡝⠟⠀⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡔⠃⠈⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⣿⣏⣛⢋⠀⠀⠀⠀⡦⠶⣾⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡀⠀⠀⠠⠄
⠀⠀⠀⠀⢿⣾⡯⣻⠀⠀⠀⠀⠓⠒⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠙⠧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠡⠄⢀⠀⡀⠀⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠒⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠛⠛⠛⠛⠛⠶⣶⣟⠋⠉⠉⠀⠀⠉⠉⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⣠⡶⣦⡀⣾⠛⠛⠛⣷⠀⠀⠀⣰⠟⠛⢛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠁⠀⢸⡇⠻⣤⣤⣤⠿⠀⠀⠀⢿⣄⣀⣿⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⣤⣴⠞⠁⠀⢀⣀⣠⣤⡴⠶⠶⢦⣬⡉⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠠⠶⠶⠶⣾⡇⠀⢀⣠⣄⡀⠀⢰⣟⠉⠉⣀⣤⣤⣄⣀⢈⣿⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡿⠁⠈⣿⠀⠀⠙⠛⠛⠉⠀⠀⣈⣉⡋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⠻⠶⠶⠛⠀⠀⠀⣠⣤⣄⢠⡟⠋⠉⢹⡧⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢀⠀⢹⡆⢻⡌⠻⠶⠶⠟⠁⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠿⣦⡀⠀⣾⠋⠛⠛⠀⣸⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠈⠛⠶⣿⣤⣾⠛⠋⠉⣀⣀⣠⡴⣾⣏⣀⡀⠀⠀⢀⣀⣠⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠛⠛⠛⠉⠉⠁⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⡀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠼⠶⠆⠐⠠⠐⣀⣠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢨⠂⠀⠀⠀⡆⢠⢻⣗⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣰⡡⠀⠀⢀⡏⠀⠀⠀⡘⢀⠆⠀⠹⣔⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠤⠦⣄⠀⠀⠀⢠⡁⠉⢢⢐⢊⠠⠠⠤⠴⢁⡎⠀⠀⠀⠹⡧⠜
⠀⠀⢀⠀⢤⢼⡤⠣⢴⡤⠺⠇⠀⠐⠀⡜⠐⠀⠈⢰⠁⠀⠀⢨⠂⡜⠀⠀⠀⠀⠀⢹⡌⠡
⠀⠀⠀⠁⠠⣭⠇⠀⠈⠀⠠⣐⡲⣤⡴⣅⣀⡀⣠⡁⠁⠀⢀⠆⡼⠀⠀⠀⠀⠀⠀⢸⠿⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣧⡈⠉⠉⠐⠊⠡⠭⠱⠒⠎⡰⡇⠀⠀⠀⠀⠀⠀⢸⡠⢀⣨⠯⠦⠄
⠀⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣄⣤⠶⠚⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⣠⢦⣄⣀⡀
⠀⠀⢠⣶⣶⢴⣿⣿⣿⢶⣶⣦⠀⠀⠀⣾⠀⠀⠈⡇⠀⠀⠀⠀⣿⡟⣿⣿⣿⡄⠀⠀⠰⣯⣯⣞⡾⠉
⠀⠀⠚⢻⠛⠸⠿⡿⠿⠞⢻⠛⠃⠀⠀⡈⠓⠶⠚⢁⠀⠀⠀⠐⠛⢓⡻⠓⠛⠓⠀⠀⢸⣏⣿⣮⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⠀⠘⠀⠀⠀⠀⠤⠤⠤⣶⣶⢢⠀⠀⠀⠀⠉⠛

⠀⠀⠀⢸⣿⢾⣷⢾⡷⠀⠀⠀⠀⡠⠤⠠⠄⡄⠄⠀⠀⠀⠀⢀⣤⠶⠤⣄⠀⠀⠀⢠⣶⣴⣶⣶⣶
⠀⠀⠀⠸⣿⢾⡿⢿⡿⠀⠀⠀⠀⣃⣙⣘⣀⣇⣀⢀⠀⠀⠀⣼⠁⠀⠀⢹⠆⠀⠀⣸⣟⣿⢷⢿⡿
⠀⠀⠀⠸⠿⠻⠿⢻⢿⠛⡆⠀⠀⠄⠧⠼⠤⠧⠬⠠⠀⠀⠀⠈⠷⠤⡴⠛⠀⠀⠀⠛⠿⠿⡹⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⡅⠀⠀⡀⠀⠀⠀⢐⣾⣿⣿⣖⠀⠀⠀⠀⠸⣿⣿⢿⣿⡿⠀⠀⠀⠀⣸⡟
⠀⠀⢀⣀⣀⣀⣀⡜⣀⣀⡰⠀⡀⠀⠀⠀⢻⢿⠿⠃⠀⠀⠀⠀⡷⣿⣿⣾⣿⣷⡄⠀⠀⠀⠿⣿⡟
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⢀⣈⣀⣀⡄⠀⠀⠀⠓⠒⢒⣖⠛⠛⠃⠀⠀⠀⠠⠏
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠁⣤⡆⣤⢄⣤⣴⠀⠀⢰⣿⣿⢾⣿⣷⠀⠀⠀⢘⣾⣾⣾⣞⠀⠀⠀⢸⣿⣿⣿⣻⣿⡀
⠀⠀⠀⠀⢀⣾⢟⣾⢛⣾⡳⠁⠀⠀⢠⣿⣿⣼⣿⣧⠀⠀⠀⠻⣿⣦⣿⡿⠃⠀⠀⣸⣿⣾⣿⣾⣿⡆
⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠁⠀⠀⠀⠨⠛⠛⠘⠛⠫⠀⠀⠀⠈⠙⠹⠙⠉⠀⠀⠀⠉⠹⠥⠿⠼⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠰⡆⠀⠀⢸⠀⠀⢀⡶⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠿⠀⢀⣸⡀⠀⠸⠇⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢙⣤⠶⠛⠛⠉⠉⠉⠙⠛⠶⢦⣜⠁⠀⣠⡾⢃⣴⣾⠛⠉⠁⣀⠀⠀⢿⡉⠙⠳⢦⣀
⠀⠀⠘⠶⣤⣀⠀⠈⣩⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⣫⣾⣏⣤⠟⠀⠀⢸⣏⡿⠀⠈⠳⣤⣤⡴⠟⢷⡄
⠀⠀⠀⠀⠀⠙⠓⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠰⠶⢤⡄⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⢹
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⠀⢹⡇⠀⠀⠀⠀⠰⡏⠀⠀⠀⣿
⠛⠛⠛⠛⠛⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠚⠋⠀⠀⠀⠀⠀⠀⠙⠦⡤⠾⠃
⠀⠀⠀⣀⣀⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣴⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⠉⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣤⣀⠀⠀⠀⠀⠙⠷⠾⠋⠀⠀⠀⠀⠀⣠⠶⣾
⠀⠀⠀⢀⣤⠶⠃⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡘⠷⠟⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣧⡾⠃
⠀⠀⠚⠋⠀⠀⠀⣠⠎⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠱⣄⠙⢦⣄⠀⠀⠀⠀⠀⢿⣽⠇⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠚⠁⠀⢀⡶⠈⠙⣓⠶⠶⠦⠶⠶⢞⠛⠉⢶⡀⠀⠈⠳⠀⠉⠛⠶⢤⣤⣄⣀⣠⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢠⡟⠀⠀⣿⠀⠀⢹⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠁⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢦⡀⠀⠀⢀⠊⣿⡀⠀⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⣦⠤⣾⠀⢱⣷⡤⣤⠊⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠒⢤⣀⣤⣳⣄⡤⠟⠛⠋⣉⣉⣉⣛⣻⣤⣤⣿⣤⡤⠒⠒⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡄⠀⢸⠟⠋⠀⢀⣠⡶⠟⠉⠉⠀⠈⠉⠉⠛⠻⢿⣄⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠤⣼⣻⠷⠁⠀⠀⣴⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣆⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⢨⡏⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⡃⡀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡟⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡟⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠴⠻⢾⡇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠓⠤⡀
⠀⠀⠀⠀⠀⠉⠳⢄⢀⣀⣸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣒⣲⡶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⡇⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⢹⡄⠀⠀⠀⠀⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⢡⡟⠋⠲⡄
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠶⠞⠽⡄⠀⠀⠀⠀⠈⠻⢶⣦⣀⣀⣀⣄⣀⣠⣤⣴⠿⠋⣠⢿⣦⣁⣀⠬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⡛⢦⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⣠⡞⠉⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⢀⡴⣙⣳⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣞⡿⢆⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠀⠨⠃⠀⠀⣿⣻⣿⠚⠛⢻⣟⣿⠁⠀⠹⠀⠀⠈⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣠⠞⠁⠏⢁⠀⠀⢠⠋⠈⢆⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⢦⡴⠁⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣏⠀⠀⢀⡞⡟⠀⢰⣟⠀⠀⠀⣀⣤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡏⣇⠀⠋⢇⠀⣼⠀⢧⠀⡘⢜⠀⣰⠋⡰⠁⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢿⠤⡀⠀⡇⠈⢦⡘⡄⢧⣹⡀⠈⢆⡸⢸⢱⠃⠀⡇⡰⢣⠃⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠱⣑⠲⡘⣦⠀⠈⠻⣄⠹⣧⠀⠘⣿⠄⣿⠀⠀⣧⠃⡜⣠⠚⢁⡴⠋⠀⣀⣀⡀
⠀⠀⠀⠀⣄⠀⠀⠀⠱⡄⠉⠒⠮⢧⣄⠙⠷⣄⠀⠹⠀⠈⡄⠀⠉⠀⢹⠀⠀⡿⢀⣷⠃⠀⡞⢀⠤⣪⠋
⠀⠀⠀⠀⠘⠷⣒⢄⡠⡈⢲⠤⣀⠀⠈⠣⡀⠈⣄⡤⠶⠶⠒⠲⣶⣤⣅⣀⠜⠀⢸⠃⠀⣸⡕⢋⠜⢀⣀⣀⣀⡀
⠀⠀⠀⢷⢤⣀⠈⠓⠒⢌⣁⣉⠚⠉⠢⣀⡷⠋⠁⠀⠀⠀⡔⢋⡄⠀⠄⠹⣷⣖⠁⢀⠔⠛⣠⣧⠞⠉⣀⠤⠚⠛⠓
⠀⠀⠀⠈⠣⣈⠉⠉⠉⠉⠉⠉⠂⢄⡴⠋⠀⠀⠀⠀⢀⡎⣧⠄⢷⠲⣌⠒⠙⢢⠻⣄⢀⡸⠛⠁⢀⡜⢁⡠⡠⣴⠶⠤⠄
⠠⣄⡀⢀⣀⢈⣉⣓⠶⠶⠖⠂⢄⡼⠁⠀⠀⠀⠀⠀⣎⠓⢐⡄⠀⡀⢈⡘⠇⡀⡿⣻⣄⣀⠠⢴⠿⢊⡭⠔⠉⠁
⠀⠀⠙⠓⠚⠥⠒⢤⣶⠶⠤⠄⣸⠃⠀⠀⠀⠀⠀⢰⠈⣀⠀⣀⢨⠁⣀⣠⠀⠔⠀⠉⢿⠀⠀⢠⣒⡪⠤⠖⠶⠤⣀
⠀⠳⣶⠦⠤⠖⠊⠁⠀⣀⡀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡀⠴⠉⢠⠉⠉⡐⢃⠉⠡⢀⡈⢼⠁⠀⠉⠁⢀⣠⠤⠒⠒⠺⠷⡄
⠀⠀⠈⠙⠒⠲⠒⢺⠟⢋⠀⣀⢸⡄⠀⠀⠀⠀⠀⠘⡰⠊⠀⠤⠄⡁⢰⠀⠂⡛⠀⠠⣾⠁⠀⠲⠾⠛⠂⢒⣢⢤⣤⣀
⠀⠀⠀⢀⠤⠔⣩⠥⡶⠋⠁⠀⡀⢷⡀⠀⠀⠀⠀⠀⢷⠃⠄⠖⠀⠉⡄⢐⡀⢖⠜⣰⠋⠢⠴⠦⠶⢮⣍⡉⠀⠉⠀⠉⠓
⠀⠈⠉⠉⠉⢈⡠⠎⠀⣠⣴⠇⠀⡀⠷⣄⠀⠀⠀⠀⠈⢖⠀⠰⠀⡀⡀⢀⠒⢊⡼⠋⠢⢄⣀⣀⣀⣀⣀⣈⠳⣄
⠀⠀⠘⠻⠯⣭⣤⠤⢚⡹⢁⣶⠋⠀⡠⠘⠳⣄⡀⠀⠀⠀⠑⢧⡄⠍⠃⣨⡷⠋⠑⢄⣠⣈⠓⠛⠤⢄⡀⠉⠑⢾⡄
⠀⠀⠀⠀⠀⠀⠀⡠⢎⡴⢻⠃⠀⣼⡇⢀⠎⠀⡹⠛⠲⠶⠶⡶⠿⠟⠋⡅⠀⠑⣄⠀⠈⠛⠫⣍⠒⠒⠭⢶⣄
⠀⠀⠀⠀⢀⣤⠾⠟⠉⣠⠏⠀⡼⢻⢀⡟⠀⢠⢧⠀⣸⠀⠀⣀⠀⣣⠀⠘⢶⣄⠙⠻⡒⠦⣄⡈⢳⡀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠠⢴⣾⠥⠴⠋⢰⠁⡞⡇⠀⢸⢸⠀⣿⡀⠀⢻⡆⠹⣷⣀⠀⠙⣍⠣⣉⢢⠀⠙⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠞⠀⡇⠀⡾⢠⡃⡏⢳⡀⠈⡏⢇⠰⡈⠳⡀⢸⡄⠈⠲⢷⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⢀⣜⡤⠚⠀⠀⡇⠏⠀⡇⢀⡇⠀⣇⣇⠀⢹⣸⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡵⠃⢀⣧⠞⠀⠀⠈⣿⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠘⠁⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠀⠀⠀⠛⠛⠀⢀⣀⣀⣤⣿⣿⣤⣀⣀⡀⠀⠛⠛⠀⠀⠀⠀⠀⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⣀⣤⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣶⣤⡀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣴⣿⣿⠟⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣅⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⢿⣿⣷⣶⣤⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⣤⣶⣾⣿⡿⠃
⠀⠀⠀⠈⠉⠛⠛⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⣀⣤⣄⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⣠⣤⣀
⠀⢠⣶⣿⣿⠿⠛⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣶⣄⠀⠀⣼⣿⡟⠀⠀⠛⠿⣿⣿⣶⡄
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠉⢻⣿⡆⠀⠿⠋⠀⢀⣀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣾⣿⠇⠀⠀⢠⣾⣿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠸⠿⠃⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣾⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⡆⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠸⠆⠀⠀⢠⣇⠀⠀⠀⣸⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠹⢣⠀⠀⠐⠀⠀⢀⠎⡆⠀⢀⢜⠎⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⢄⠀⠀⡇⠇⠀⠇⠀⠀⠎⠘⢀⠔⡡⠊⢀⡠⢔⡹⠃⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢣⠣⡀⢃⠘⣀⣤⣴⣶⠶⠷⠒⠒⠡⡔⢁⠔⠉⣀⣀⡀⢤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⡢⣀⠈⢆⠑⣬⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠑⢎⣁⠤⠒⠊⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠑⢄⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⠒⠒⠀⢀⣠⠶⠚⠁
⠀⠀⠀⠀⠀⠠⠖⠒⠒⠦⣐⠠⢄⣑⣺⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠤⠍⣒⣤⣄⣤⡤⠄
⠀⠀⠀⠀⠀⠀⢀⡤⠴⠆⢀⣒⠒⠒⢺⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡉⠢⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⣉⠩⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡈⠑⠬⣒⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⠭⠥⠤⠄⠒⡹⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡈⠢⡘⣄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⢀⠤⢒⡉⠤⠊⡹⠛⡿⣷⣦⣤⠤⡤⠖⢹⠐⠆⢂⠀⠙⠺⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠉⠀⠀⡠⢊⠤⠊⢠⠁⡜⢨⠀⡆⢠⢨⠀⠘⡌⡄⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⣼⠔⠁⠀⢠⢃⠎⠀⠸⠰⠀⠸⢸⠀⠀⠈⠺⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢰⠃⠀⠀⢠⡆⠀⠀⢻⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠀⠀⠀⠀⢷⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⠁⠀⣀⡀⣸⠃⢀⣀⠀⡀⠀⠀⠰⠊⡿⠈⣷⢀⣀⡀⢀⢀⡀⠀⣀⢸⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⡷⢸⠓⡿⣿⢰⡇⣼⡀⢳⠀⠀⠀⠀⡿⠐⠁⣏⢸⡇⡿⢸⡇⣾⠘⣸⡁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠈⠀⠉⠈⠁⠈⠁⠀⠀⠀⠃⠀⠀⠉⠈⠁⠁⠈⠁⠈⠁⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⠿⠸⠻⡿⠿⢿⠿⠀⠀⡿⠿⢿⠐⡿⠿⡿⠿⡿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣀⣄⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣄⣤⣠⣠⣀⣤⣄⣤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⢀⡀⣀⣀⣁⢀⣿⢁⡀⣀⣀⣀⢸⣿⢀⣀⣀⣀⡀⣀⣀⣈⣿⣀⣀⡀⣀⣀⣀⣿⣆⣀⣀⢀⣀⡀⢘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠋⠙⠉⠉⠉⣿⠏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠙⠉⣿⡋⠉⠉⠉⠉⠋⠙⣿⠉⠉⠉⠉⠉⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠿⠶⠶⠶⠶⠶⠶⢶⡿⠶⠶⠶⠶⠶⠶⣾⡷⠶⠶⠶⠶⠶⠶⠶⠶⢿⡷⠶⠶⠶⠶⠶⠶⢿⡷⠶⠶⠶⠶⠶⠶⠿⣇
⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣼⠟⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⢛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠻⣟⠛⠛⠛⠛⠛⠛⠛⠻⣦
⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠎
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣽⣿⡏⢹⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣴⣹⣿⣯⣿⣯⣯⣿⣿⣽⣿⣿⣆⠀⢠⣶⣶⢶⣶⣦⠀⠀⠀⠈⢹⣿⡇⠈⠁⠀⠀⢀⣶⣶⣶⣶⣦⡀⠀⣴⣄⣼⣿⣿⣯⡿⣿⣿⣿⣯⣿⣆
⠀⠀⢸⣷⣷⣿⣤⣿⣤⣧⣼⣷⣵⣿⣵⣿⡆⠉⠉⠉⡋⠉⠉⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠉⠉⣛⠉⠉⠁⢼⣷⣿⣿⣤⣾⣬⣦⣼⣷⣮⣿⣼⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⠤⢾⣿⡇⠰⠦⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠾⠿⠷⠶⠶⠒⠛⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⠄⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⡇⠀⠀⢀⡜⡟⠀⢀⢾⠁⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡼⢳⠀⠰⡕⠄⠀⡞⠀⣇⠀⢠⢫⠂⢀⡴⠋⡝⠁⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⡧⣀⠀⠀⣇⠈⢧⡀⢧⠑⡄⣧⠀⠸⡄⢹⠈⡇⡞⠀⢸⠁⡠⢫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡀⠉⢮⠣⢄⠹⣄⠀⠙⢶⣆⠙⢾⡆⠀⠸⣾⡀⢳⡇⠀⢸⣠⠇⡣⢀⡴⠚⢋⠽⠋⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠘⣇⠙⠦⣌⣓⣄⠓⠺⣷⡀⠀⠙⡇⠈⠻⠀⠀⠷⠃⢸⡇⠀⢸⡇⢸⣤⠏⠀⣰⠃⠀⡠⡶⠚⠋⠁
⠀⠀⠀⠀⠸⣦⣀⡀⠀⠘⢦⣀⠀⠉⠙⠻⣦⠈⠙⠆⠀⠐⠀⣀⣁⣀⡂⠀⡠⠀⠀⡜⠁⣼⠏⠀⢠⠇⡰⢩⠖⠁
⠀⠀⠀⣄⠀⠈⠒⢮⡒⠒⠤⠬⢝⣲⣤⡀⠀⠣⣀⡼⠖⠛⠉⠉⠉⡩⠝⠟⠗⠦⣎⡀⣀⠋⠀⢀⣾⠋⡰⢊⡤⠶⠒⠲⣦⣄⡀
⠀⠀⠀⠘⣗⠦⣄⣀⣈⣉⣶⣶⣤⠀⠀⠈⣤⠞⠁⠀⠀⠀⠀⢠⡎⠠⡖⢀⢈⡀⠻⡟⢦⣀⠔⠉⢁⣴⡷⠋⠀⣠⠖⠉⠉
⠀⠀⠀⠀⠈⠦⣄⡀⠀⠀⠀⠀⠀⠉⢢⡼⠁⠀⠀⠀⠀⠀⢰⡅⠷⠣⠹⠌⠣⡈⡁⠈⠦⢹⣄⠠⠜⠁⠀⢀⠞⣁⡤⢢⣒⠝⠛⠒
⠐⢦⣀⢀⣀⣀⡠⢍⡭⠛⠛⠛⠐⠢⡼⠁⠀⠀⠀⠀⠀⢠⢁⠉⢘⠄⠀⡀⠈⡄⠙⢀⠰⢮⣽⣄⡀⠤⠾⠕⠉⡤⠔⠁
⠀⠀⠉⠓⠒⠢⠔⢒⣴⠶⠷⠦⠤⢴⡇⠀⠀⠀⠀⠀⠀⠘⢀⡔⠀⣤⠠⠅⢠⣠⠌⠰⠃⠀⡜⣷⠀⠀⢠⣒⡩⠴⠒⠒⠲⢤⣀
⠀⠹⣶⠦⠤⠴⠚⠉⠀⠀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠉⢠⠈⠉⣀⠋⡈⠉⠄⢀⠁⣼⠁⠀⠉⠁⠀⣀⡤⠶⠒⠒⠺⠷⡀
⠀⠀⠀⠙⠲⠦⠤⠖⡺⠛⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⣰⠈⠀⢤⡀⢈⢠⡄⠐⢐⠃⠀⣤⡟⠐⠒⠲⠶⠟⠣⠴⢒⠤⢤⣄⡀
⠀⠀⠀⠀⣀⢤⠜⣉⣥⡴⠛⠉⠁⠀⣳⡀⠀⠀⠀⠀⠀⠘⡴⢢⠁⡤⢀⠚⣂⠀⠀⠠⠤⠔⣸⠓⠄⣠⣔⣢⣖⣉⠒⠉⠉⠉⠉⠙⠢
⠀⠙⠛⠛⠗⠀⠋⣡⠞⠀⢀⣤⡎⠁⠈⣳⡄⠀⠀⠀⠀⠀⠐⡬⢀⢠⡀⠀⠈⠈⢩⠤⠃⣼⠓⢄⠀⠀⠀⠀⠀⠈⠉⠳⣄
⠀⠀⠠⢤⣴⠖⠋⢁⣀⠴⢻⠋⣠⠔⠉⠀⡙⢦⣀⠀⠀⠀⠀⠘⢤⡆⣀⠓⢎⠌⢒⣢⠞⢇⠀⠀⠹⠯⠿⣛⠋⠉⠛⠲⢬⣧
⠀⠀⠀⠀⠈⠉⠉⠉⠁⡖⣁⢴⠏⠀⢀⣎⠀⢀⠝⠓⢦⣤⣀⣀⣀⣙⣣⣬⡤⠞⠋⠑⡀⠀⠙⠻⢷⣖⠲⢌⣩⡳⢄⡀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⡰⡩⠖⢃⡞⠀⢀⣾⠃⣰⠆⠀⢰⠁⠀⢸⠉⠉⠋⠀⢀⠀⠘⣄⣀⠸⣶⣤⣀⠀⠈⠑⢆⠀⠈⠉⠻⣆
⠀⠀⠀⠀⠐⠚⠛⠉⢀⣠⠞⢀⣠⠏⡸⢀⣿⠀⠀⡟⡇⢠⣾⠀⠀⣦⡀⢸⣆⠀⠈⢿⡦⢤⡙⢌⡉⠓⢤⡈⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠚⠉⠀⣨⢇⡟⢸⠀⠀⡏⢣⠈⡿⡄⠀⢹⡧⡀⢻⠳⣄⠀⠙⣆⠓⢲⠱⡀⠀⠱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠏⠀⡼⠀⡼⠃⠺⡀⡇⠹⡄⠀⣇⠸⣌⢣⠈⢳⡀⢹⠀⠀⠉⢻⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⣠⣾⠵⠚⠁⠀⢰⢱⠁⠀⡇⢀⡇⠀⠸⡸⡀⠀⢧⡞⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡟⠀⢠⣧⠎⠀⠀⠀⢹⠇⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠊⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⡀⢀⣄⣀⣀⣠⡀⢀⣄⣀⣀⣠⡀⢀⣤⣠⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠋⠀⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠀⠙⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠗⠀⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⡆⠀⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣽⣿⣿⣯⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣅⣨⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠷



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⣠⢤⢰⢠⣄⣤⠀⢠⢤⢠⣄⣠⣄⣠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠈⠉⠉⠁⠀⠘⠉⠈⠉⠉⠈⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡤⣠⡤⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡁⠂⢀⢲⡀⢄⠸⡰⣠⡰⡰⢀⡄⣰⢂⠠⠂⣩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡞⡍⢁⡎⠆⠈⠀⠀⠀⠑⢈⠛⠋⠀⠁⢀⠁⠈⠀⠆⣆⠉⡛⡆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⡑⠎⠺⠏⠀⣀⢀⡬⠤⠴⠃⡰⣀⠓⠤⠬⣀⢀⠀⠘⠿⠋⠚⣀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⢀⠛⠄⠀⠀⢡⠀⠆⣄⣈⠀⢀⣀⢲⢡⣿⣧⣠⣶⣈⣀⣄⠆⢠⠀⠀⠀⠜⠃⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠩⡲⠘⠀⠀⢣⠒⠃⠠⠿⠈⣱⡌⣁⠀⠀⠀⠀⠀⠉⠙⠳⢿⣿⣧⣤⠓⢢⠃⠀⠀⠠⡪⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢺⠡⠴⣾⠄⠂⠒⠋⡀⠀⢀⡴⠊⠁⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⠻⣏⣀⣀⠐⠂⠀⢼⡶⠤⢹⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡉⠁⠀⢀⠈⢤⡛⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣃⡝⢀⠀⠀⠉⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠄⢀⣀⡸⠀⠘⢁⡸⠁⠀⠀⠀⠒⠒⠦⣄⠀⠀⠀⠐⣤⠖⠒⠂⠒⠄⠀⠀⢿⡟⠁⠰⡀⣀⠀⠴⠾
⠀⠀⠀⠀⠀⠀⠀⠒⢀⠑⠀⠀⢀⡇⠀⠠⢲⠁⠀⠀⠀⣀⢠⣤⢄⠈⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠂⣇⠀⠀⠐⣁
⠀⠀⠀⠀⠀⠀⠀⣫⠐⣩⣌⠀⢉⠠⠼⠂⠙⠀⠀⠀⠀⠀⠘⠛⠀⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡤⢈⠁⢀⣌⡑⢨⡂⠐
⠀⠀⠀⠀⠀⠢⠀⢏⣀⣊⠋⠀⢬⠈⠳⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠋⢨⡀⠈⢻⢢⣊⠇⠠⠈
⠀⠀⠀⠀⠀⠀⠈⠂⠀⡤⠀⠀⣈⡇⠀⠐⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠀⣏⡀⠀⠠⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣖⠆⠈⠀⢹⠀⢠⡌⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡠⠀⢀⡤⠀⠀⠀⠀⢠⣿⣷⠄⢸⠁⠉⠀⢑⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡉⠀⠀⠈⠠⠍⠤⡄⠹⢄⠀⠀⠀⠀⠀⠐⠀⣁⠞⠉⠀⠀⠀⠀⠀⠀⣰⣿⣦⠌⠥⠈⠀⠐⠈⡉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢎⡄⠹⣿⠃⠄⠦⢄⠀⠀⠈⠗⠦⣄⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⢀⠤⠆⠀⢻⠣⠀⣬⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠨⠕⠠⠀⠀⠌⠶⡄⠀⡷⢀⡜⢃⡤⢀⡀⢀⣀⣤⣤⣴⡾⣿⣿⡏⢉⡴⠌⠄⠀⢠⠐⠌⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡴⢆⣀⠀⠈⠀⠂⢁⣈⡀⠀⠀⠶⡌⣿⠏⠈⠛⣉⣀⠉⠂⠈⠀⢀⣀⠱⣊⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡠⣢⣲⣦⠀⠀⠀⢁⠊⠓⠄⠰⠀⠔⠋⢲⠁⠈⠀⢠⣶⣆⡂⡈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠦⣥⠀⢃⠆⢂⢄⡀⢀⠀⢊⣴⣌⠂⢀⠀⣀⢀⠀⢆⠇⢠⡥⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠐⠀⠺⠀⠁⢸⠱⡉⡱⢹⠀⠁⠸⠆⠐⠠⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡙⠉⢛⡡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠊

⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⠿⠻⡿⠛⡿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⡀⠀⢀⡞⠉⠹⠖⢦⡀⠀⠀⠀⠙⣠⠴⠦⣄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⣏⡁⠀⠀⠀⠈⣹⡇⠀⠤⢸⠁⠛⠁⠈⡇⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⠻⣄⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢈⠳⣤⣤⠼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⣠⣽⡦⢾⡉⠙⠲⣄⡀⠀⠀⢀⡤⢤⣀⡀⠉⠀⠰⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠖⠋⠁⢸⠁⢸⠉⠛⠒⠲⠟⠀⠠⣞⣁⣀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⡁⠺⠈⢯⠐⠗⠹⡇⠱⠎⢻⡈⠲⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢷⠒⢒⡚⣗⠒⣒⢻⡖⢒⣚⢷⠒⢒⡺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣻⡆⠀⠈⣧⣤⣤⣼⣦⣬⣤⣷⣤⣤⣼⣧⣤⣤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡉⠉⣧⠀⠀⠘⣆⠐⠂⢹⡄⠒⠊⢧⠀⠒⠸⡆⠐⠂⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⠀⠀⠀⠈⠛⠛⠛⠛⠛⢻⡛⢻⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠤⣾⠧⠾⠦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠸⠶⠾⠶⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⠛⠀⠀⡴⢠⡎⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⢻⣄⡀⣼⢦⡙⣦⢿⡘⣷⣠⢴⠁⡁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣀⣙⠶⣬⣯⡙⣶⣿⢻⠨⠿⠟⠿⠼⢆⡗⣴⢋⣴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⣖⠲⢭⣷⡌⠟⠃⠈⠁⠠⠀⠀⡀⢰⠶⠖⣡⣿⡼⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⠳⠶⢶⣿⣛⠻⣿⣇⡀⢀⣀⡀⠀⠀⠉⠑⠺⣔⡨⠽⢋⣼⢏⡍⣀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣲⣛⡛⢯⢳⣿⣿⣿⣆⣀⢙⢒⠂⠀⠀⠀⠀⠲⡾⠿⢿⣿⠴⣧⡤⠤
⠀⠀⠀⠀⠀⠘⢷⠀⢉⣭⢽⣿⣦⣿⡟⠛⠛⠻⣿⡗⠀⠀⢊⣤⣤⡀⠀⢱⣂⣒⣶⣾⣯⡶⠖⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⣛⣛⢻⣿⣷⠀⠛⠀⠈⢁⡀⠀⠀⠉⠁⠀⠀⠰⣦⣬⣭⣭⠾⣤⡀
⠀⠀⠀⠀⠀⠐⠦⠴⠾⣻⡿⠟⠽⣿⣿⣦⡀⠀⠀⡸⣷⠀⠀⠈⠀⠀⠀⡸⢀⠹⣿⣗⣛⣡⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠒⠚⢻⠖⣿⣷⣿⣿⣿⣇⠀⣀⠀⢛⠀⠀⠀⠀⠀⣴⣍⣦⣳⣬⣭⠯⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠋⣜⣱⡟⣡⣟⣿⣿⣿⣿⣿⣾⣷⡶⣶⡴⠛⢹⡿⠶⠙⣻⠷⠶⢦⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡾⣿⢋⣴⣿⣿⢿⣿⣿⠿⠿⣮⣗⢶⣶⣇⡐⠦⠽⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠟⣡⠟⢼⠡⡏⣧⢸⣿⠁⣶⢾⠷⣍⣿⡟⠶⣍⠉⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢀⠗⠉⢻⡍⣷⠹⣌⠳⡟⠈⠙⣧⠹⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⡸⠃⠞⠀⠀⣤⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠰⠀⠀⠀⠛⠀⡀
⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⠸⢀⠡⣀⡀⣶⣶⡄⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠘⠓⠛⠀⣀⡴⠿⣿⣿⡄⠀⢶⡄⢁⣀⣀⠀⠀⠉⠀⠀⠀⠈⠉⠤⣼⠧⠧⢠⣿⣿⡞⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠙⠛⣿⣷⣶⣶⣶⣀⣈⣿⣿⠧⠤⠶⠶⠂⠀⠀⠀⠄⣀⣀⡋⣼⣿⠿⣏⢈⣋
⠀⠀⠀⠀⠀⡀⠀⡄⠀⠆⠀⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⢀⣀⡠⠀⠄⠀⠄⢀⡀⠀⣀⠀⢀⠉⠙⠛⠾⢿⣿⣿
⠀⠀⠀⠁⣠⡡⣤⡴⣶⡎⣿⡞⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠤⢤⣌⣠⣉⢉⠋⢈⡶⠚⢃⠆⠂⡤⠬⢀⢠⠁⡁⡆⠈⠙
⠀⠀⠀⠀⠘⢧⠈⢳⠀⢳⡀⢱⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠂⠀⠌⠀⣸⠏⠉⠑⠒⠚⡦⠴⠥⡄⣌⣀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⡇⠀⠃⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠢⠤⣄⣀⡌⠀⣰⠏⠀⢀⠂⠀⢠⠀⠀⡘⠀⠀⢸⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡶⠶⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠋⠐⠒⠂⠤⣀⣃⠀⢠⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠿⠉⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠒⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢹⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠹⣖⠦⣅⠈⠀⠀⠡⢀⠀⡇⢸⡿⠁⢸⡇⡄⢀⠀⠈⠀⠀⠀⡠⠔⡾⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠙⣆⡀⠱⣄⢠⠐⣄⡀⣱⡟⠁⠀⣸⠧⡏⡠⡐⠀⠀⡴⠉⠀⡼⠃⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⠀⠀⠀⠀⠀⢻⡧⠀⠘⣧⡀⠰⣿⡟⡀⠀⠀⢻⣴⢃⡷⠁⣀⡾⠁⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⣤⣤⣴⣬⣶⣤⡑⢶⣸⡟⠀⠀⠈⠻⢷⣿⣷⣷⣶⣦⣧⣼⣿⣷⠾⠋⠁⠀⠈⣿⠥⠀⢤⡂⠥⠆⠠⣤⠄⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣉⣴⣶⣿⣿⣻⣿⣿⣿⣷⣬⣿⡰⣄⣠⡶⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠷⣤⡀⣠⢰⡿⢞⠝⠉⠀⣄⣴⠞⠁⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⡴⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⣷⠟⠉⠁⠀⢠⣾⠟⣁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣠⠋⠀⠀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢁⣠⣤⣤⣤⣀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠈⢶⣄⡠⢀⣾⢋⡁⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠰⠃⢀⣀⡀⣿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠄⠉⠉⢍⠀⠀⣈⠍⠉⠁⠈⢍⣉⠀⠈⣿⣾⣛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⡇⠀⢀⣈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⢿⣿⣛⠷⠈⡇⢠⠃⠴⣟⣿⡿⠶⠉⠀⠀⣹⠀⠉⠛⠋⠁⠀⣀⠀⣈⣑⣦⠄⠘⡇
⠀⠀⢰⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⣰⡾⠟⠋⠉⠀⠀⠀⢀⡇
⠀⠀⠀⣿⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣶⣾⣛⠋⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢸⡇⠀⠀⢰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠙⡆⠉⠉⠐⠒⠄⠀⡀⠀⠀⣼
⠀⠀⠀⠀⠱⣄⠀⠘⢿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⢠⣾⣿⣅⣀⠀⠀⢺⣇⠂⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠘⢧⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠛⠛⠻⢶⣄⡀⠀⠀⠁⠀⣀⣠⣴⡶⠟⠉⠈⠈⣿⡷⣄⠀⠙⠳⣄⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣙⠛⠿⣿⣿⣿⣿⡿⠿⠋⢀⣿⠀⠀⢀⣴⡾⢿⣿⢿⠛⠛⠉⢹⣿⠛⠷⣦⡀⠀⠀⣸⡆⠈⠉⠲⠄⠨⠷⠦⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠉⠉⠉⠉⠀⠀⠀⠈⢸⣿⠀⢀⡾⠉⢀⡿⢫⡘⠀⠀⢠⣿⠹⣇⠀⠈⢻⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢰⡟⠀⣠⡞⢁⠀⣠⠇⢸⢳⣄⠀⠘⣿⠆⠣⢁⠀⠀⠙⣄⠈⠸⡇⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⡿⠶⠛⠉⢀⠀⠐⠁⠀⢺⠈⣻⡄⠀⣏⢝⠀⠀⠀⠀⠀⠀⠀⠂⠽⣄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⢰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⣀⣀⡀⠀⠁⠀⣀⣀⣀⣤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢂⢀⣴⡔⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡤⣽⣷⣾⣿⣿⣿⣿⣼⣧⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡠⣽⣿⠿⠋⠉⠀⠀⠀⠉⠻⢿⣿⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢒⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃⢇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠥⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢁⠺⢿⣷⣦⣤⣀⣠⣤⣴⣿⡿⠛⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⣜⠟⡛⢏⠿⣻⡟⡿⡞⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠘⠐⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠐⠉⠁⠁⠂⠈⠉⠉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠉⠉⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡹⣹⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠁⠀⠄⡠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣾⣯⣿⢇⣇⣗⣏⠃⡢⠀⠀⠠⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣷⡄
⠀⣀⠀⠤⢀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣾⡯⣿⣿⡻⣾⢮⣟⣞⡼⠱⡀⠀⠀⠀⠀⠀⠈⠀⡩⢁⠊⣴⠀⠀⢀⣼⠁⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⢟⣖⣿⠏⡵⢊⡜⡭⡩⠓⡚⠠⠤⣀⡀⠀⠀⠀⠀⣸⣿⡍⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢭⡕⢛⡮⠋⠴⣫⠮⠜⠀⡀⡰⢋⡐⠀⢀⣼⠃⠀⣰⠇⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠪⢔⡱⠱⠆⢂⡌⢁⠞⣀⣧⢿⣿⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⢔⡁⣨⡟⠃⠀⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⡆⠀⢀⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢃⠀⠀⡆⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠀⠙⣤⡆⢈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠀⣤⡜⠁⢀⡴⡋
⠀⠀⠀⣀⣀⠀⠀⠰⣄⠠⡘⢦⣉⡳⠮⢿⣾⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣾⠯⠶⣏⣡⠞⡠⢀⡴⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠉⠑⠦⣄⣈⣝⡿⠋⠉⠀⠀⣼⣿⣿⣿⣧⢀⡠⠤⠤⠤⠤⣀⣀⣿⣿⣿⣿⡄⠀⠈⠉⠻⣟⣍⣀⡤⢖⠉⠁
⠀⠀⠀⠀⠀⠀⢘⠢⡴⠋⠀⠀⠀⠀⠀⣿⣶⣿⠿⠋⠀⠀⢀⡰⢀⡄⠀⠈⠛⢿⣟⣿⡇⠀⠀⠀⠀⠈⠳⡴⢚
⠀⠀⠀⠀⠀⠛⠶⣽⠁⠈⠉⠙⠳⡄⠀⣿⣿⠋⢀⣀⣄⣀⠀⠉⠁⠀⣀⣄⣄⠈⢻⣿⡇⠀⡴⠛⠉⠉⠀⢹⡵⠞⠃
⠒⠒⠲⣉⡓⢒⣒⡏⢀⣤⢶⣶⣤⠿⠀⣾⠃⠀⠄⠀⠀⠉⠃⠀⠀⠉⠁⠀⠀⠅⠀⢻⡇⠸⢷⣶⣶⢦⣄⠈⣗⢒⠒⣋⠱⠒⠒
⠀⠀⠀⠀⠈⠑⣸⣷⡀⠙⠚⠓⠋⠀⢸⣿⠀⠀⠤⣤⣤⡤⠀⠀⠀⠠⣤⣤⡤⠄⠀⢨⣿⠀⠈⠓⠛⠚⠁⣰⣿⡐⠉
⠀⠀⠀⠀⠴⠿⠭⢿⠉⠀⠀⠀⠀⡀⣸⣿⡗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡀⡀⠀⠀⠀⠀⢹⠯⠽⠷⠄
⠀⠀⠀⠀⡠⠤⣖⣛⣧⠀⠀⠀⠀⢀⣽⣿⣿⡇⠀⠀⠀⠀⠀⣨⡀⠀⠀⠀⠀⠀⣾⣿⣿⣅⠀⠀⠀⠀⢠⣟⡓⡦⢤⡀
⠀⠀⠀⢸⠋⠉⠉⠉⢚⣷⣄⠀⠀⠀⠸⢿⣿⢿⣦⡀⠀⠀⠐⢭⡅⠀⠀⠀⢀⣼⣿⣿⠿⠂⠀⠀⢀⣴⣟⠊⠙⠉⠉⢻
⠀⠀⠀⠈⠀⠀⠀⠰⠛⢻⣿⡗⣤⣀⣀⣨⣿⣿⣿⠋⠒⠦⠤⠤⠤⠤⠔⠚⢻⣿⣿⣯⣀⣀⣠⡔⣿⣿⠛⠳⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠚⠁⢡⣏⠝⢏⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢯⠟⢌⣇⠁⠙⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⠀⠃⠀⢸⢏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⢿⡀⠀⠃⠀⠀⠈⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣊⣀⣀⣑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣐⠂⢄⠀⡴⡀⡈⠠⢣⡋⢑⠜⠄⢃⠠⠤⠀⡠⠐⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⡞⠋⡝⡄⠜⠐⠁⠨⠢⡑⢿⠿⡪⠔⠁⠈⠂⢃⢰⢫⠝⢳⢦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢇⠓⣷⡷⠰⠁⠠⠐⣄⣀⠆⢂⡀⠰⣀⣠⠂⠄⠀⠄⢾⣶⢚⡸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⣥⠉⠀⠀⠀⠄⡀⠘⠒⠋⠈⠁⢤⡆⣸⣧⠈⣡⡝⠒⠃⣀⠠⠀⠐⠀⠉⣭⠳⠀⣀
⠀⠀⠀⠀⠀⠂⢉⠤⠤⣄⠃⠀⠐⠄⣀⠎⠀⣦⠑⠞⠀⠂⠂⠈⠈⠉⠙⠛⠻⠏⣷⣾⣶⠀⢳⣀⠠⠂⠀⠘⡠⠤⠤⡉⠒
⠀⠀⠀⠀⢠⢠⡾⠉⢹⣤⠀⠀⡠⠜⠀⠀⡈⣁⠤⠚⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠇⠀⠣⢄⠀⠀⣧⡏⢉⢷⡄⡆
⠀⠀⠀⠀⠈⢆⠓⠭⠙⡋⠀⠠⠠⣤⡆⢪⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣧⠄⠄⠀⢙⠋⠭⠚⡠⠁
⠀⠀⠀⠀⠀⡤⢒⠉⠁⡀⢳⠀⣱⡄⢠⠃⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢄⡀⠀⠀⠱⣶⣿⠀⡞⢀⠈⠉⡒⢤⡀
⠀⠀⠀⠀⣀⠨⡁⡀⠐⢠⡉⠀⠠⣐⠃⠀⠀⠈⠁⠀⠀⠈⠳⠆⠀⠀⠀⠾⠋⠀⠀⠀⠀⠁⠀⠀⢻⣄⣀⢙⡤⠂⠀⢈⠍⢀
⠀⠀⡠⢡⠤⡂⢌⠆⠠⠜⠁⣄⡨⡌⠀⠀⠀⠀⠐⢸⣿⠂⠄⠀⠀⠀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠸⣟⣧⠈⠢⢄⠐⡡⣐⠤⡍⢆
⠀⢈⠀⢸⣎⢈⣿⡇⢀⠰⢘⣉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠆⡀⢼⣿⡁⡱⡇⠀⠑
⠀⠀⠱⣘⠒⠅⢊⠌⠐⢢⡀⠋⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⢀⠔⠢⠢⡑⠩⠒⣃⠎
⠀⠀⠀⠀⠁⡐⡁⠁⠠⠘⣅⠀⠐⠩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⠀⣈⠃⠄⠀⢈⢂⠈
⠀⠀⠀⠀⠀⠑⠭⣀⠀⠁⠼⠀⡹⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠒⠀⠀⠀⠀⢀⡞⠛⣟⠀⢧⠈⠀⡀⢥⠚
⠀⠀⠀⠀⢀⠊⡴⣒⣠⣅⠀⡐⠐⠛⠇⢜⠢⡀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠟⠂⢂⠀⣨⣄⣒⢤⠑⡀
⠀⠀⠀⠀⠀⠘⢶⣀⣸⠛⠐⠀⠑⢢⠀⠀⢁⣉⠑⠠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⡿⠇⠀⡔⠊⠀⡂⡛⣇⣀⡾⠃⠇
⠀⠀⠀⠀⠀⠄⣈⠒⠒⠋⡀⠀⠠⠂⠉⢆⠈⠏⡠⢦⠐⠄⠤⢄⠠⣤⣤⠶⣶⡏⡽⢿⠿⠀⡴⠉⠐⠄⠀⢠⠑⠒⠒⣁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢦⡛⣀⠠⠀⠄⠂⠁⢠⠤⡄⢀⡀⠛⠧⠹⠟⢀⡈⣡⠤⡄⠈⠐⠠⠀⠀⣀⢓⡤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡎⡥⡿⡷⠐⠀⠐⠨⠉⠉⢆⠈⠣⠰⠉⠙⠄⠂⢀⠃⢾⠿⢬⢱⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠣⢧⣄⣣⠃⢣⠠⡀⢀⠔⡡⣶⡶⢅⠢⡀⢠⠄⣌⠸⣜⣠⡼⠜⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠭⠄⠊⠀⠺⠁⢁⠐⡜⣄⡨⢢⠂⡈⠀⠆⠀⠑⠠⠭⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢉⠉⠉⡡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⠋⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⢀⢀⠀⢀⡔⢀⡆⣤⢠⠀⢠⠠⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣾⣧⣯⣮⣾⣧⣾⣧⣿⣸⣧⣧⣳⣙⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⣿⠁⠉⢉⠉⢹⠏⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢧⡀⠈⢀⡜⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⡀⠰⣯⣿⣷⠀⠙⠷⣿⣶⡦⠀⠀⢀⡀⢈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⣀⢠⣶⠈⠀⠀⠙⣻⣣⠴⠖⡾⢟⣏⣻⣲⣶⣿⣧⣬⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣦⣤⣤⣾⣷⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠛⠡⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣛⠛⠿⣿⠟⣿⢿⣿⡿⣿⣿⣿⠟⠛⠛⠛⣧⠀⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠉⢰⣿⠀⠘⠁⠀⠉⠁⠀⠀⠀⠀⣿⣷⣤⣀⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣠⣵⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡛⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣻⢶⡿⣿⣿⣿⡧⡀⠀⠀⠀⢀⣷⡀⢀⣾⠃⠙⠿⠳⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡏⢻⣿⣿⣦⣤⣶⣾⠿⠿⢿⣿⠀⠀⠀⠀⠐⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠃⠀⠀⠁⠈⠃⣶⣄⢠⣄⣾⡟⠀⠀⠀⡀⠀⠋⢁⣠⣴⣿⣾⣧⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠈⠳⡝⠛⡛⠉⠀⠀⠀⠀⢘⣿⡫⣿⣿⠟⠛⠛⠻⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣴⣶⡖⢤⣿⣶⣤⣶⡶⢷⣶⡄⠺⢿⠿⠗⠋⣁⣤⣤⣶⣾⣧⣿⢷⠠⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢦⠀⠀⠉⠁⢐⣾⣿⡟⣿⣟⣷⡆⢀⡠⠒⠢⣴⣶⣿⠿⠼⠟⠉⠁⠀⠀⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⡇⣸⣷⣶⢦⣽⣿⣿⣿⣿⣿⣿⡿⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⣻⡇⠹⢿⣄⠙⠿⠛⠛⠛⠋⠉⢱⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡟⠙⣧⠀⠈⢯⡃⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣆⠀⢀⠀⠄⠀⠀⠈⠹⡿⠧⢾⣿⠇⠀⠀⢹⣆⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠻⡿⠟⠛⠉⠉⠁⠀⢀⣠⣤⡄⠀⠐⠀⠀⠀⠘⠟⠁⡄⢾⣏⣹⡏⢱⣿⣏⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣶⣆⢻⠞⢹⠿⠀⠈⠉⠹⡏⠛⠿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠟⠛⢻⡆⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃

⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⣀⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢂⡠
⠀⠀⠀⠈⠀⠀⠈⠉⠩⠈⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⣾⠂⠀⣠⡴⠃⠀⢀⡤⠁⢀⡐⢀⡀⠠⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠂⠍⣹⠎⠳⢤⡄⢶⣃⠀⡠⠋⠀⣠⠕⣠⣌⢂⠀⠀⠀⠀⠈⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⠿⡗⣺⣅⣀⣠⠞⠉⠈⣹⠅⠚⢖⠚⡡⠎⠀⠈⢆⠢⡐⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⢀⠈⠬⣝⡡⡾⡋⠀⣠⠮⠚⠳⡆⠺⣁⣀⡴⣣⠞⠀⢰⣲⡆⠈⠣⡘⢄⠀⠀⢄⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⡘⠓⠚⢧⣀⢠⠞⠁⢀⣴⢉⠞⠁⠀⠀⠈⠽⠇⠀⠀⠘⢌⢦⡠⠎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⠴⣠⣄⡘⠲⠴⡻⡱⠃⠀⣀⣀⠀⠀⠠⢤⠀⠀⣶⠄⢣⣿⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠙⠳⣮⣽⠀⠀⡆⢠⣾⡄⠾⠾⣾⠄⠠⣿⠆⣿⡷⢥⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣮⡙⢢⠀⢀⣀⠀⠀⠄⢸⠀⠀⠀⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⣁⡏⣼⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠚⠀⢸⣿⡈⠆⣀⢸⠀⠀⣀⣀⡀⡀⠀⠐⠉⢉⡥⣔⠀⡿⠀⠐⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⡀⠀⠀⠈⢙⠀⠃⢰⠀⠀⡆⣰⣧⡇⠀⠐⠚⠓⠋⠁⢀⠇⠈⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢘⠀⠃⠀⠀⠀⡇⠁⢸⣃⣀⣀⣀⣤⠤⠴⠾⠖⠛⢘⡠⣤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⣀⠒⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⡦⠗⣹⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣍⡑⠁⠀⠀⠀⠙⡴⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢒⡀⠀⢀⠀⠀⠀⣍⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢓⣤⢊⠀⣀⣔⢳⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠌⢏⠔⠋
⣀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⢀⠃⡈⠀⠀⠀⠀⠀⠀⢒⠄
⠁⠀⠀⠀⠈⠉⠉⠉⠈⠀⠀⠉⠀⠀⠀⠀⠀⢀⡠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⢀⠔⠐⠀⠠⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⣂⠈⠠⠚⠾⢁⠐⠄⠀⠀⠀⠀⠀⠀⠈⢄⠀⣀⣀⢀⣀⣀⣀⠑⠂⠀⠀⠤
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑⢌⢂⠀⠀⠀⠀⠀⢂⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⡀⠀⢀⠠⢪⣠⡗⠀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠐⠉⠀⠀⠁⠀⠐⠒⠂⠉⠐
⠀⠀⠀⠀⠀⠀⢸⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠔⠁
⠀⠀⠀⠀⡠⢊⠔⡟⠓⠤⠤⠁⠐⢠⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠚
⠀⠀⠀⢐⠔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠰⠊⠐⠀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠁⢀⠀⡠⠂⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⡐⠶⠷⢿⠲⡶⢲⠖⠢⠀⠙⡔⠶⡖⢶⠒⡶⠲⠾⢳⡤⠐⢖⠶⡞⢺⠗⠶⠲⡖⢒
⠀⠀⠀⠀⠀⠿⢻⡇⢿⠛⡿⠻⡗⢃⡆⢀⠹⢹⠟⢻⠛⡟⠻⡇⠟⡄⠀⡜⢻⠟⠽⠏⠭⠉⠍⠙
⠀⠀⠀⠀⠸⡞⣺⠓⢻⠚⢻⠚⡟⢺⢀⠀⡟⢻⠓⡻⠓⣿⠚⡿⢻⠇⠀⠛⢺⠓⣿⠓⣿⠚⣷⠒⡇
⠀⠀⠀⠀⠔⠀⠉⠀⠉⠀⡍⠀⠉⠁⠊⠐⠈⠉⠀⠉⠀⡍⠀⠉⠀⠂⠐⠈⠉⠀⠩⠄⠍⠀⠉⠀⠒⡀
⢀⣀⣀⣈⣀⣀⣀⣀⡐⣒⣂⣀⣀⣀⣀⣀⣀⣀⡄⣐⢂⠋⢢⣀⣀⣀⣀⣀⢀⡄⡐⣂⢂⣠⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠇⣀⡀
⠀⠀⠀⠈⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈
⡀⡀⣀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣐⠂⢠⣄⣀⣀⣀⣀⣀⣀⡄⠒⣈⣁⣀⣀⣀⣀⣀⣀⡀⠀⣀⢀⢀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢸⣇⠀⠀⡴⢹⠀⠀⢫⠀⠀⣀⢤⠖⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢠⡇⢇⠀⡟⢄⢰⡁⠸⡀⢘⢨⡀⡜⢁⠎⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⣴⡀⠙⢗⣄⠀⢇⠈⠳⣼⡈⠦⣇⠀⠱⣼⠐⣼⠀⢸⠀⡎⡎⢀⡠⠤⣲⠶
⠀⠀⠀⠀⠀⠀⠀⢹⠙⠦⣈⠢⡘⠮⢷⡄⠀⠻⠆⠻⡄⠀⠿⠂⣿⠀⢈⡏⢰⣡⠋⢀⠎⠀⣠⡴⠖⠂
⠀⠀⠀⠈⢦⣀⡀⠀⠳⣄⡀⠉⠙⠳⡌⠙⠂⠀⣁⣀⣄⣀⣄⣀⠌⠀⡘⠃⣾⠃⠀⡞⡰⢩⠚
⠀⠀⠰⣄⠀⠉⠪⣋⡑⠒⠫⠷⠦⡀⠈⣤⠞⠋⠉⠁⢀⠠⠙⠛⡛⢲⣄⡠⠃⠀⣼⠏⣰⣡⠔⠒⣒⣲⠦⠄
⠀⠀⠀⠹⣝⠒⠒⠒⠚⠛⠳⠄⠀⣰⠋⠀⠀⠀⠀⠠⢦⡀⢧⢤⠰⠌⠫⣱⣖⠁⠀⡾⠋⠀⣠⠊⢁⢀⣠⣀⡀
⠀⡀⠀⠀⠈⢓⠲⣦⢤⡤⠤⢀⡼⠁⠀⠀⠀⠀⠀⠹⠨⣌⠈⠀⠙⠰⡄⢨⡾⣇⠁⢀⣠⣾⠕⣊⡹⠓⠋
⠀⠈⠓⠛⠭⠡⠬⣤⣴⠄⠀⣸⠃⠀⠀⠀⠀⠀⡄⢁⠨⢁⢀⠃⣈⣀⠀⠆⠈⢹⡇⠀⢀⣄⣚⠤⠤⠤⣄⡀
⠀⠲⣦⠤⠤⠒⠋⠀⢀⡀⠀⣸⠀⠀⠀⠀⠀⠀⡀⠩⠈⢠⠈⠃⡘⠃⠋⠅⢀⠡⡇⠀⠈⠉⠀⣀⠤⠖⠒⠻⠦
⠀⠀⠈⠑⠒⠒⣒⠟⢋⣁⡀⢸⡄⠀⠀⠀⠀⠀⠣⠆⠁⠠⠄⡁⠰⠀⠂⠃⠀⢴⠏⠀⠐⠾⠛⡒⢒⣢⣤⣤⡀
⠀⣀⣀⣠⣲⣊⠔⡶⠋⠁⢀⠠⢷⡀⠀⠀⠀⠀⠘⡋⠆⠰⠀⠉⠄⠠⠔⡆⢋⡞⠑⠐⠺⠵⠯⠬⣅⠀⠀⠀⠈
⠀⠀⣈⣉⣀⠤⠊⠀⣠⡾⠃⣀⠄⠻⣄⠀⠀⠀⠀⠘⡀⡐⠂⣄⠄⢄⠋⣠⡏⠈⠢⡤⣤⠤⠤⠤⢄⡑⡄
⠀⠀⠈⠙⠒⠒⠒⢋⠔⣀⡞⠁⢀⡔⠉⡱⠦⣄⣀⠀⠈⠳⢆⣀⣡⠴⠛⡁⠈⠲⣶⣤⠭⣑⣒⢄⠀⠈⠻⠄
⠀⠀⠀⠀⠀⠀⣴⡪⠞⣸⠁⢠⡿⢁⡔⠀⢠⠀⠈⠍⠉⡏⠉⠅⠀⢂⣀⠰⣦⣀⡀⠉⠓⢌⠀⠑⠛⢦
⠀⠀⠀⠀⠚⠋⠉⣠⠔⢁⡠⢋⠜⡸⡇⠀⣜⡇⢰⡆⠀⢷⡄⢾⡄⠀⠹⣧⢤⠱⢌⠙⠢⡈⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⡴⡠⠁⡇⠀⡇⠱⢸⢳⡀⠘⡗⠄⢋⠲⣄⠈⣆⠉⢢⣣⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⡼⣁⠜⠀⢱⢸⠀⢣⠀⡇⠐⡎⡇⠈⣆⡼⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⢸⡆⠀⣸⡴⠁⠀⠙⡷⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠐⠋⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠄⠰⣇⢀⠀⠀⠀⡔⠢⡷⠄⠀⢀⡤⠬⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣈⡠⠀⠀⠤⠜⠁⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⢀⠀⠀⠀⠀⣠⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉
⠀⠀⠀⠀⡠⡰⣅⠀⠀⠈⢙⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣓⠦⠤⠺⡇⠀⡀
⠂⠀⠀⠈⢀⡽⠈⠀⣠⠞⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣈⠉⠁⡠
⠀⠁⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡁⠂⢄⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣀⣀⠠⠤⠤⠴⢿⣥⣄⠀⠀⠀⠀⠀⣠⣶⠗⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢤⡈⠹⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠈⠺⠡⡖⠲⢿⣶⠅⠀⠀⠀⠀⠀⢀⡀⠀⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡽⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠐⠀⠛⣿⠛⠂⡡⠊⠀⠀⠠⠄⠀⢠⠊⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠒⠦⢤⠀⠀⠀⠠⠶⠒⠒⠀⠀⠀⠀⠀⡀⠦⠀⠠⢄⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢐⡀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠄⠀⠀⢉⣙⠢⠀⠀⠀⠠⠚⣛⠂⠀⠀⠀⠀⠀⠇⢸⠀⠀⠋⠽⠻⠖⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠀⠉⠐⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢉⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠈⢐⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⠄⠀⠀⠀⠑⢈⠓⠐⠀⣤⠤⠄
⣠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⠤⠤⠤⠴⠚⣫⠿⡡⣢⠀⠀⠀⠀⠀⠀⠈
⠇⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠐⡘⣿⡆
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣹⣶⠦⠤⠤⢀⣀⡀⠤⠤⠴⣶⣿⠁⠀⠀⠀⠀⠡⠙⠝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠁⠀⠀⠀⠀⠀⠀⠀⢠⢠⣿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠈⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠄⠀⣠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠄⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣼⡃⠀⢠⠎⠑⠜⣇⡰⠈⠹⣤⣠⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⢺⡡⠀⠀⣏⠀⠀⠀⠀⢠⠖⠲⣍
⠀⠀⠋⠙⠻⣍⣀⣙⣃⠘⣆⣀⠀⢀⡠⠀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⢈⠆⠉⠀⠀⠀⠈⠁⢀⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠔⠁⠀⠀⠈⠢⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠡⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⢀⠀⠀⠀⠀⡠⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠀⠀⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠊
⠀⠀⠠⢠⣶⡶⢰⣶⡆⢰⣶⡆⣶⣶⡀⣶⣦⡀⡀⠀⠀⠀⠀⠀⠀⡀⣠⣶⡆⣰⣶⡆⣴⣶⠀⣶⣶⠰⣶⣦⠠
⢀⠄⣴⣿⡟⢡⣿⣿⠃⣿⣿⡇⢸⣿⣷⡘⢿⣷⣌⠂⠀⠀⠀⠀⢊⣴⣿⠟⣰⣿⣿⠀⣿⣿⡇⢻⣿⣧⠙⣿⣷⡄⢄
⠓⠚⠛⠛⠓⢻⠛⠛⠒⠛⠛⠛⠚⠛⢻⠓⠚⠛⠛⠓⠃⠀⠀⠓⠛⠛⠛⠒⢻⠛⠛⠚⠛⠛⠓⠚⠛⢻⠓⠛⠛⠛⠒
⠀⠀⠀⠀⢀⣨⣀⣀⣀⣀⣀⡠⠊⣼⣿⣿⠃⣼⣿⣿⠁⣿⣿⣿⠈⣿⣿⣧⠘⣿⣿⣦⠑⢄⣀⣀⣀⣨⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⠝⢠⣾⣿⡿⠃⣼⣿⣿⡏⢠⣿⣿⣿⠀⢹⣿⣿⣧⠘⢿⣿⣷⡄⠫⡉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠼⠿⠿⠿⠧⠼⡿⠿⠿⠧⠼⠿⠿⠿⠧⠼⠿⠿⢿⠧⠼⠿⠿⠿⠧⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⢠⣾⣿⣶⣤⣤⡀⠀⠀⠀⠀⠰⠆⢀⣠⣅⣀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣼⣿⢛⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠙⠁⣿⣿⣿⣿⣿⣿⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠁⠈⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠻⠿⠿⠟⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠈⠀⠀⠰⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠿⠋⠁⢸⣿⣿⡏⠙⠛⠿⠿⠿⠗⠀⠀⣶⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣰⠶⢲⡖⢶⡖⠶⣒⠶⣶⠶⢶⡖⢶⡶⠶⣲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠸⣆⠈⠉⠀⢷⡀⠉⠁⢹⣆⠈⠉⠈⣧⠀⠉⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢹⡟⠛⣛⡙⣿⠛⢛⣉⢻⡟⠛⣛⡙⣟⠛⢋⣛⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⢻⡀⠀⠀⢻⣄⣀⣀⣸⣧⣀⣀⣀⣷⣀⣀⣀⣹⣆⣀⣀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⢿⡀⠠⡤⠹⡇⠀⢤⠌⣯⠀⢠⡤⢹⡅⠁⢤⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣇⠀⠀⠀⠘⠷⠤⡤⠤⠿⠤⠤⢤⣼⣧⣤⠤⠤⠿⠤⠤⡤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⣤⠀⠀⠀⣸⡇⠀⠀⢀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣷⡀⠀⣿⡆⠀⢀⣿⡇⠀⢠⡟⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⢷⣄⠀⠀⣿⣷⡀⣿⣿⣄⣼⣿⡇⣰⣿⡇⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠈⢿⣷⣦⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣧⣶⣿⠏⠀⣀⣴⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣾⡟⠁⠀⠀⢀⣠⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣦⣤⣼⣿⣿⣿⣿⣿⠟⠋⣉⣥⣤⣬⣭⣙⠻⣿⣿⣿⣿⣿⣿⣤⣤⣶⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠒⠲⠶⢤⣤⣄⣀⣀⣀⡙⠻⣿⣿⣿⣿⠟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⡿⠟⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢛⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠔⠒⠛⠋⠉⠉⠁⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄⡀⠉⠛⠿⠿⠿⠿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣇⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠛⣩⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣍⠛⠻⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣴⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡄⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣾⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⡄⠀⠈⠛⠦⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣼⠏⠀⢠⣿⠏⠀⣿⣿⠀⢿⣿⠁⠙⣿⡇⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⣾⠏⠀⠀⢸⡏⠀⠸⣿⠀⠀⠈⢿⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠸⠁⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠤⡤⢄⣀⠠⠿⡿⠃⣾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⣿⣿⣿⣿⣿⣷⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣻⣶⣶⣷⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠉⠫⡍⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣠⣤⣷⣾⣿⣿⣿⡿⢿⠀⠀⠀⠀⢀⣀⠀⠀⢀⣠⣰⢿⣶⣾⣿⣿⣿⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⣨⢴⢄⠀⠀⣻⣉⣤⣶⣶⣻⡿⢿⣿⢿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣹⡷⣾⣧⣬⣿⣟⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠊⠁⠀⠨⠙⢻⠿⣡⣾⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣓⡔⣠⣶⣾⣶⣅⣘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⢰
⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿
⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⣀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⢸
⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⢹⣿⣿⣿⢸
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣤⣾⣿⣿⣿⢸
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⣿⢸
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠀⠀⢸⣿⣿⣿⠈
⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣄⣸⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⣈⣁⠸⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣎⣳⡄⣿⣿⣿
⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⠇⠘⣿⡽⠃⣿⠛⠿
⠀⡇⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⡝⠛⠉⠛⢩⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⣄⢀⣤⠀⠘⢿⠟⠀⣿⡀⣿
⠀⡆⠛⠛⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠀⢀⡸⣿⣿⣿⣿⣿⣿⣥⡌⠹⢁⠀⠀⢴⠄⠀⣿⡇⣥⢸
⠀⠆⠀⠒⠒⢾⣿⣿⣿⢯⠿⣹⠻⠉⠀⠒⠅⠀⢀⣀⣐⠀⠀⠀⣀⣄⢠⣾⣿⡆⠁⠒⠺⠿⠉⠀⢤⣙⠷⡿⠀⣈⣹⣈⡀⣿⣷⣿⢸
⠀⠂⣤⣤⣤⣸⣿⣿⣷⢿⠁⢿⡿⠿⢢⣼⣷⡟⡁⠹⠐⠋⠙⢈⠋⠏⠉⠉⠀⠀⠀⠙⣾⣧⣤⣶⢸⣧⣤⣴⠻⢿⣿⣿⠟⢿⡇⢁⢸
⠀⠆⢹⡏⠀⢸⣏⣿⣁⡆⠁⢸⡏⠉⠘⣿⣿⠀⠱⢦⣠⣄⣠⢘⠀⡄⢀⠀⠀⠀⠀⢠⣿⡉⠁⣴⢾⣿⣿⡏⠀⠀⡶⡀⠀⢻⣇⠀⢸
⠀⡇⢸⡇⠀⢸⠇⣿⠁⠈⠐⠀⣇⠀⠈⠉⠙⠉⠁⠀⠀⠀⠈⠛⠋⠙⠛⠛⠛⠆⠀⢸⣿⣿⠛⢢⣿⣻⣿⡇⠀⠺⠷⠷⠀⢸⣏⢶
⠀⡇⢸⡇⠀⢸⠄⣿⠃⣅⠸⠂⢿⣇⣻⡇⢠⠀⠀⠀⠀⠀⡄⠲⣶⡀⠀⠀⠀⠄⣤⠿⣽⡯⡀⠘⣿⠀⠹⡇⠀⠀⠀⠀⠀⢸⡿⢿
⠀⡇⢸⡇⠀⢸⠀⣿⠠⡙⡀⠘⣿⣿⣿⡿⠿⠀⠀⣶⡀⠀⠧⢴⣿⡃⠀⠀⠀⠈⠁⣺⡟⠁⠙⠛⠛⣶⣤⡅⢹⠖⣻⠄⠀⢸⣧⣻⢀
⠀⠇⢸⡇⠀⢸⣤⣿⠶⣿⡃⢺⣿⣿⣿⣇⠀⠀⠀⢐⡇⠀⡀⢀⢸⡿⡷⢀⡔⠈⠈⠛⢷⣦⡄⠈⠋⢻⡉⠁⠀⠰⡇⠀⠀⢸⣿⠛⠘
⠀⡇⢸⡇⠀⢸⠁⣿⠀⢸⣿⣿⣿⣿⢿⠃⠀⠀⠀⣼⣧⣾⡇⣈⣸⡇⢀⣿⣧⣸⣄⠀⢸⣿⠿⢆⣷⠚⠋⠀⠀⠀⡟⠀⠀⢸⣿
⠀⡇⢸⡇⠀⢸⠀⣿⠀⠸⣯⣟⡿⠿⢿⡿⠿⡷⠶⠌⢹⡿⠟⠉⠛⣷⣤⣿⣿⡝⢻⣶⣾⣿⠷⠟⠁⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⡄⣾⣧⣀⣸⣴⣿⣆⡨⠛⢉⡠⠀⠈⠛⠛⣿⡆⠀⠸⠇⠀⠠⣀⣼⣿⣿⣿⠟⡿⠧⢤⣿⡇⠀⠐⠻⣿⠀⠀⠀⠀⠀⠀⢀⣿
⠀⡆⠖⠤⠍⣿⣿⣿⠋⢁⠀⣾⣅⠀⣸⣿⣾⣿⠃⢴⣀⡤⣤⣾⣿⣿⡿⣿⣁⣆⣷⣶⣤⣿⡇⠀⠐⣿⣣⣼⣿⣶⠒⡒⣂⢴⣿⣶⣄
⠀⡇⠀⠀⠀⢻⣿⡇⠀⢸⡀⣷⣾⣁⢿⣿⣿⣿⣀⣈⡋⠀⠀⣼⣻⣿⡷⠋⢸⣿⣿⣿⣿⣿⣇⣀⣠⣌⣿⠻⢿⠿⡿⢿⣿⣿⣿⣿⠈
⠀⡇⠀⠀⠀⢿⣿⣷⡀⠀⣿⡾⢿⣿⣾⣧⡔⡿⠀⡙⠉⣀⡠⣇⣿⣿⡿⠄⢸⣿⣿⣿⣿⣿⣿⠿⠛⢿⡏⠀⠉⠉⠉⠉⠉⠉⣿⡇⠘
⠀⡇⠶⣶⠖⣾⣿⠋⣡⣴⣿⢻⣿⣿⣿⠁⢠⠁⠀⠃⠘⠻⣛⣛⣿⣿⠇⠀⢼⣿⣿⣿⣿⣿⣿⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⡃⠀⠈⠙⢿⣛⣥⣾⣿⡡⠚⠁⢿⠏⠀⠀⠀⠈⣻⠉⡙⠉⡛⢽⣏⣀⣀⣈⣿⣿⣿⣿⣿⣿⣧⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⡅⠀⠤⣤⣄⣹⣄⣬⣶⣶⣾⣿⣘⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠂⠻⠿⠿⠿⠿⠟⠛⠻⠿⠟⢛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠂⢠⣤⣤⡄⣌⣉⣠⣀⠀⠀⠉⠉⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣤⣀⣤⣠⣤⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣛⣻⣼
⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⢸⣿⣀⣀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⡛⣛⡛⣛⣛⡛⣛⡛⠛⠛⠛⢛⣛⠛⠛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠳⠳⡤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⡴⢦⣀⡀⢰⣄⣠⡀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡒⠠⠅⣑⡚⠂⠠⠀⠀⠀⠀⠡⠠⠪⠊⠀⠀⠀⠉⠁⠀⠀⠉⠑⠀⠰⡆⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠓⡦⡥⣇⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡀⠺⠌⣉⠑⠒⠤⣪⣂⡀⠐⠀⠀⢀⠄⠇⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠙⠓⠶⣤⣍⣀⡘⠤⠄⡉⢙⠗⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣄⣠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠐⡐⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠇⣙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣀⣦⡀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⣿⣧⠇⠀⠀⠸⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⢦⣀⠀⠀⡠⠎⠁⣀⡀⠠⣤⣦⡂⢷⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⢀⠀⠀⠀⠈⠦⠟⣞⣻⠄⢸⡮⡏⠀⠴⣒⠐⠋⢍⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⡀⠀⠁⠆⢈⣨⣄⠀⣦⢴⠀⣷⣻⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣠⠀⠀⠀⠀⠄⠀⠠⠅⣚⠀⠸⠘⠁⠘⠚⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠁⠀⠀⡀⡀⣀⣠⠤⠚⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠴⠱⠿⠈⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡲⠞⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣂⠤⠖⠚⠒⠂⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⡤⣞⠭⠊⠁⠀⠀⢀⡠⡄⠊⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⢀⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⡩⠘⠠⠀⠀⠀⠀⡠⠋⠀⢧⠄⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⡥⠒⠁⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣉⡤⠖⠁⠀⠀⠀⠀⠀⠀⢀⠰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠙⠉⠀⠀⠀⠀⠀⠀⡠⠀⢀⡠⠔⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠁
⠀⠀⠀⠀⠀⢒⠶⠇⠀⠀⣜⣀⡀⠀⠀⠠⢆⠁⡴⠞⠁⢀⠤⠚⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠈⠠⠌
⠀⠀⠀⠀⠈⠀⠀⢆⠀⠀⠆⠉⠉⢽⣠⠤⠀⠀⠀⡤⠛⠉⠂⡀⡈⠡⠀⠀⠀⠀⠀⠁⠉⠲⠀⠀⠠⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠠
⠀⠀⠀⠀⠠⠀⠀⠈⠑⠒⢀⣤⠖⠋⠀⠀⠉⠂⠀⠀⠪⠁⠀⠫⠠⠄⠀⠀⠀⠀⣀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡤⠶⣄⠠⠚⠁⢀⡀⢠⡄⠀⠀⡀⠀⢀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠆⢹⡤⣊⡈⢿⠂⡊⠐⠀⠀⡄⠀⢀⠀⠀⠀⢀⣮⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠈
⠀⢣⠀⢀⠘⣋⡡⠔⠁⠈⠀⠀⠀⠀⢄⠀⡀⠃⠀⢰⣟⠉⠐⠋⠀⣀⠆⠚⠑⠋⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠐
⠀⠈⡢⣈⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠚⣿⡃⣀⡆⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⢀⡠⠒⡡⠔⠀⢀⡀⠙⣟⢟⢿⣁⠄⠀⠀⠑⠤⠤⠄⠠⠴⠶⠒⠉⠉⠀⠘⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡥⠐⠁⠀⣀⠔⠊⠷⠐⠙⣦⣟⠀⠀⢀⡠⠔⡈⠕⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⢀⣠⣴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠁⠈⡠⠐⠉⠀⠀⠀⠀⢐⣤⡝⣿⣝⠲⠥⣀⠁⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠀⠀⠀⡀⠀⠀⢀⠠⣾⠇⢀⡼⠋⠳⢄⠀⠉⢒⢤⣴⣚⠉⠀⠀⣀⡀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠖⠉⡀⠄⠊⠁⣼⠇⠊⠁⠃⠂⠀⠈⠵⠚⠁⠀⠀⢉⣰⠶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠁⠠⠒⠉⠀⠀⠀⣸⠏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⡇⠀⠀⠀⠀⣰⢿⠃⠀⢀⣾⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢿⢧⡀⠀⠀⡼⠁⣿⠀⠀⢸⢹⡄⠀⠀⣠⠴⣺⠟⠁⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⠈⣧⠀⢈⡇⣇⡀⢰⡇⠀⢻⡀⠀⡞⢺⡁⢀⡾⠁⣰⠋⠀⢰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢿⡧⣄⠀⠀⢹⡀⠈⢷⣀⠳⡄⢹⡀⣇⠀⠈⢳⡀⡽⢠⡇⣾⠀⠀⣿⠀⡴⢫⠞⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⡄⠀⠙⡎⠣⢤⡈⢧⡀⠀⠉⠳⣧⡀⠙⣿⡆⠀⠀⢳⣳⠀⢱⣟⠀⠀⢿⣠⠇⣸⠀⣠⠶⠛⢉⡵⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠙⠦⣄⡘⠲⡄⠑⠶⢿⣦⡀⠀⠈⢿⠂⠙⢿⠀⠀⢸⡿⠀⢸⡟⠀⠀⢸⡇⠐⣅⡼⠁⠀⣰⠋⠀⠀⡴⣶⠾⠛⠃
⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠹⣄⠀⠀⠉⠙⠻⢷⣦⡈⠛⠳⡄⠀⠈⡆⠀⠀⠆⠀⢸⠀⠀⢀⠃⠀⠀⡿⠃⣰⣿⠃⠀⢠⡏⢠⠖⣫⠴⠁
⠀⠀⠀⠀⠀⠀⠻⣗⣒⢦⣀⣤⡈⠙⠶⢤⣀⠀⠀⠈⠣⡀⠀⢸⣀⣤⠷⠶⠞⠓⠲⠻⣶⣶⣮⣀⣀⠜⠀⠀⣹⠃⠀⢀⣾⡴⢋⣠⠇⠀⣀⣀⣀⣀
⠀⠀⠀⠈⣷⣄⠀⠀⠈⠳⠤⢤⡉⠋⠉⠲⠼⠗⠢⡀⠀⣱⡶⠛⠉⠀⠀⠀⠀⢀⠴⢉⡈⡁⢩⠉⢻⣶⣤⠖⠁⠀⢀⣾⠟⠀⣸⣠⠞⠋⠉⢀⣨⡭⠿⠶⠆
⠀⠀⠀⠀⠘⣎⠙⠲⠦⠤⠤⠴⠿⠿⠿⣦⡀⠀⠀⣱⡞⠁⠀⠀⠀⠀⠀⠀⡰⣇⠀⠺⡃⣤⠠⡆⣈⠺⣉⠳⣤⠒⠁⠀⢠⣾⠟⠁⠀⢀⠶⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠓⣴⠋⠀⠀⠀⠀⠀⠀⠀⡼⡄⠿⠛⠎⠿⠈⠱⡄⢀⡀⠀⠗⡙⣦⡤⠴⠊⠁⠀⢀⡴⢋⣀⡴⢒⣒⣫⠟⠛⠛⠒
⠐⢦⣀⡀⠀⣀⡀⢀⣌⣉⡹⠿⠯⠿⠓⠒⠤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⢀⠋⢘⣣⠀⠀⡀⠊⣥⠘⠗⢀⢰⡾⣝⣧⣀⣀⡠⢶⣯⠞⢁⡤⠴⠏
⠀⠀⠉⠻⠯⠦⢭⣁⠤⢌⣠⣤⣶⣄⣀⡀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠠⢈⠁⠀⢈⡃⠀⠠⣀⠂⣸⠆⠀⠉⣿⡅⠀⠀⠀⡤⠖⣚⣠⡤⠤⢤⣄⡀
⠀⢠⣄⣀⡀⡀⢀⣀⡤⠖⠋⠉⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣋⠴⠘⠃⠮⠦⠘⣵⠏⢴⠶⠀⠀⠼⢈⡷⠠⠤⠼⠓⠋⠉⠀⠀⢀⣀⣀⣉⣳⣄
⠀⠀⠙⢯⣍⡉⠉⠁⠀⢀⣀⣤⣴⡖⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⢘⡦⠠⢉⡘⠐⠇⢀⣂⠴⠃⠒⡀⢈⡁⠐⠂⢸⣧⡀⠀⠀⢀⣀⣤⠴⠚⠉⠁⠀⠀⠉⠙⠓
⠀⠀⠀⠀⠈⠙⠛⠛⢛⣉⡟⠉⣉⣀⣀⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⡀⠳⠶⠀⣤⠘⡿⠀⠙⢈⠁⠀⠰⣾⠇⠈⠉⠙⠛⠛⠉⣙⠚⣉⣕⣒⣲⣦⣄
⠀⠀⠀⠀⠀⣠⢤⠼⢉⣭⢤⡾⠟⠉⠀⠀⢀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠹⡞⠢⠅⢰⠆⡘⠙⣡⠀⠒⡀⠴⠤⠜⢠⡟⠲⠤⣠⣖⣒⣖⣊⣉⡉⠁⠀⠉⠀⠀⠉⠓
⠀⠙⠛⠶⠿⠕⠚⠛⠋⣠⠟⠀⠀⢀⣴⠊⠁⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠳⣬⠁⡌⣀⠀⠀⠘⠀⠉⣍⣼⠃⣸⠟⢄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣤⡀
⠀⠀⠀⣀⣀⣠⣤⠴⠛⠁⠀⣠⢴⡿⠋⣀⡠⠒⠉⠙⢧⣄⠀⠀⠀⠀⠀⠀⠱⡄⣡⠉⠰⠦⣔⢀⠦⠤⣀⡼⡏⠀⠀⠈⢷⣲⣶⠶⠶⠒⠒⠶⢤⣌⢳⡄
⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠛⣡⠼⠀⣼⡟⠁⠀⢠⠖⠉⠙⣳⣤⣀⠀⠀⠀⠀⠈⠻⣴⠃⠒⠈⣁⣴⠟⡏⠀⠈⠢⣴⡢⣄⣈⣉⡙⠶⠦⣄⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⡴⢋⡟⠀⠀⣰⣿⠀⠀⡜⠁⠀⡹⠛⠓⢶⠶⠶⣦⠶⠿⡟⠋⠹⠀⠀⠈⢢⡀⠀⠀⠉⠛⠯⣄⠙⠒⠓⢮⣓⣲⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣫⠖⠉⠁⡼⠁⠀⣰⢿⠃⢰⡿⠀⠀⢰⡁⠀⠀⡌⠀⠀⡆⠀⠀⢣⠀⠀⠳⡤⣄⠘⠿⣷⢦⣄⣀⠀⠈⠻⣄⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⣠⠞⠁⣀⡴⠃⡼⢃⡼⡇⠀⠀⣾⢹⠀⣴⣇⠀⠀⢳⣦⠀⢾⣦⠀⠀⠙⢾⡧⠤⡈⠳⣄⠉⠙⢦⡀⢹⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠖⠒⠛⠁⠀⢈⡇⣸⠀⡇⠀⠀⣿⠸⡄⠸⣿⡀⠀⠘⣿⣆⡈⢻⠷⣄⠀⠀⠹⣄⠙⠲⣄⢇⠀⠀⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⡞⠁⢠⡇⠀⣰⠇⢠⡇⢸⠀⢳⡀⠀⢸⡄⢿⠘⢦⠈⠳⣄⠀⢹⡀⠀⠘⠲⣽⡄⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠀⢀⡞⣀⡴⠋⠀⠀⡽⣰⠃⠀⣧⠀⢸⡇⠈⢹⢼⡃⠀⠸⡆⢸⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠴⠟⠛⠉⠀⠀⠀⠈⣧⣷⠀⠀⣿⢀⡞⠀⠀⠈⢳⣳⠀⠀⣿⡟⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢰⡷⠋⠀⠀⠀⠀⢸⡏⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⣤⣤⣄⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⠟⠉⠁⠀⠉⠛⢷⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⢷⣄⠀⠀⠀⠀⢀⣼⠏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⠷⠶⠟⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡍⠉⠉⠉⠛⠛⠛⡟⠻⠿⠿⠿⠿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠘⠁⠀⠀⠀⡆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⢇⠀⠉⠉⠉⠉⠙⠛⣟⠛⠛⠿⠿⠿⠿⣿⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡒⠒⠲⠦⠤⠴⣿⣦⣤⣤⣀⣀⣀⣀⣸⣦⣀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠹⣿⡄
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉⠉⠉⠉⠙⠛⠻⡷⠒⠒⠶⠶⠦⢿⣷⡀
⢿⣿⡟⠛⠛⠛⢷⠶⠶⠶⠶⣤⣤⣤⣤⣿⣿⣿⣧⣀⣀⣀⣀⣀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢻⣷
⠘⣿⣷⡀⢀⣀⢀⣆⠀⠀⠀⠀⠱⡀⠀⠈⢻⣿⣿⣇⠀⠀⠈⠉⠉⠙⢿⠉⠉⠙⠛⠛⠓⠚⢿⡶⠒⠲⠶⠦⠤⠴⣷⣤⠤⣤⣤⣀⣀⣿⣧
⠀⠘⣿⣷⠀⠀⠀⠉⠏⠉⠉⠉⠉⢻⠒⠒⠚⢿⣿⣿⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠹⣿⣷⠐⠀⠠⠼⣦⠄⠤⠤⠀⣧⣀⡀⠈⣿⣿⣿⡖⠒⠒⠒⠶⠴⢿⣦⠤⠤⠤⠤⡤⢤⣬⣷⣄⣀⣀⣀⣀⣀⣨⣧⣀⡀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⢻⣿⣆⠀⠀⠀⠐⡄⠀⠀⠀⠈⢇⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠙⡏⠉⠉⠉⠉⠉⠹⣿⡄
⠀⠀⠀⠀⢻⣿⡏⠉⠈⠉⠻⠋⠁⠀⠀⠛⠗⠒⠒⠻⣿⣿⣧⣤⣀⣀⣀⣀⣀⣷⣄⣀⣀⣀⣀⣀⣀⣘⣆⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠈⢿⣿⡤⠤⠤⠤⢷⡤⠀⠀⠀⣸⣄⣀⣀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠈⠉⠉⠉⠻⡏⠉⠉⠉⠉⠉⠙⢻⡟⠛⠛⠛⠓⠒⢻⣷⡀
⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⢃⠀⠀⠀⠀⠙⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠺⠿⠿⠾⠟⠿⠛⢾⠿⠿⠿⡿⠞⢿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠷⢶⣶⣷⣶⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠿⢿⣟⣻⣿⢛⣛⣿⣷⣶⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⣥⣤⡶⠶⠶⠟⠛⠛⠋⠉⠉