Bumblebee Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣄
⢀⠔⠀⢁⡓⠒⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢸⣆⣀⣠⣤⣤⣄⣰⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠉⢀⡼⠀⠀⡠⢻
⠘⡀⠀⠀⢱⡀⠀⠦⣈⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⢸⣦⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣰⣾⡄⠀⠀⠀⣀⡤⣔⡉⠀⠒⠂⠁⠀⡠⢃⡠⠊⢀⡎
⠀⠸⡄⠀⠀⠙⢦⡀⠀⠀⡀⠀⢸⡀⠁⠒⠤⣀⠀⠈⢿⣿⡆⠀⢠⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⡆⠀⢸⣿⡿⠀⣀⠔⢊⠡⢐⣏⠄⠀⢒⣀⢴⣏⠴⠋⠀⢠⡟
⠀⠀⠳⡀⠀⠀⠀⠈⢳⡒⠤⠤⣤⣉⠳⣤⣀⠈⢙⠲⢤⣙⣿⣷⣼⠋⢩⡀⢀⠀⢀⣀⡀⠀⠉⠳⢤⣾⣿⡴⢊⠔⢊⡠⢴⠫⢤⠶⠛⠉⣀⠼⠃⠀⠀⢀⡞
⠀⠀⠀⠈⢷⠶⠤⠤⠤⠈⢲⠤⣀⡀⠀⠡⡈⠓⠦⢄⣀⠈⠙⠻⣥⣵⣼⣷⣿⣷⣿⣿⣿⣷⣦⣤⡤⠛⣁⡤⠕⡚⣋⠴⣣⣴⡥⠖⡻⠋⠠⠀⢀⣁⣠⠞
⠀⠀⠀⠀⠀⠱⣄⣀⡀⠀⠀⡒⠤⢌⣉⣒⠄⠹⣒⠢⠤⠬⣽⣕⣒⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣖⡯⠵⢞⡿⢋⣀⡬⠶⠷⠶⠛⢀⠶⠛⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⡀⠁⠒⠢⣬⣉⣁⣀⣉⣉⠽⠾⠟⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠬⠭⠥⠤⠭⢤⠴⠭⣤⣤⣶⣥⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠛⠉⠉⠉⣹⣉⢁⡀⠤⢔⣪⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠭⣄⡒⠦⠤⠼⠒⡄⠀⠀⠀⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢰⣃⣀⠤⠤⢚⡩⠔⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢬⡁⠂⠶⠶⠾⠂⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⢀⣀⡤⠴⠚⢉⣤⣾⠏⠀⠀⠋⠉⠟⢻⡿⠟⠛⠟⠋⠛⣟⢿⣷⣦⡉⠛⠲⠤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠸⣿⣿⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠋⣿⣷⣶⣄⣠⣀⣀⣀⣠⣶⣦⣀⣀⣠⣠⣤⣶⣿⣿⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢸⣿⣿⣟⡙⢻⣿⠿⠿⠿⣿⢿⣿⡿⠿⠛⢋⡿⢹⣿⡇⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠿⠁⠙⢾⣦⣻⡆⠀⠀⡀⠀⠀⠂⠀⣠⠟⠁⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠙⠿⢥⣄⣀⣃⣀⣤⠶⠛⠁⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠒⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠈⠑⠀⢀⠀⠀⠀⠀⡀⠀⠀⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⣵⣶⣶⣾⡀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠸⣿⣷⣤⠞⠛⠉⠉⠛⠻⣤⣾⣿⠇⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣄⣀⠙⣿⣥⣾⣿⣿⣿⣿⣷⣾⣿⠋⣀⣠⠤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠿⣿⣿⠿⠛⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⣤⣤⣀⣀⣤⣤⢾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣠⣬⣿⣿⣿⣯⣀⣤⣽⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢫⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠁⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⢳⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⢸⣿⡿⣄⠛⠿⠿⠿⠿⢿⡿⠿⠟⠋⢉⢿⣿⡇⠀⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠹⡀⠀⠐⠀⠠⠄⠐⠒⠀⠀⠎⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⠦⢀⠀⠂⠀⠀⠀⠀⠂⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠹⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠒⠒⠋⠀⣠⣾⣿⣷⣧⡀⠉⠛⠃⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠖⢤⣀⡀⢀⣤⣿⣿⣿⣿⣿⣧⡄⠀⣰⡖⠚⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠋⠉⣙⣉⣙⠛⠻⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡠⠤⠴⡶⣛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠢⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠠⠔⠒⠀⠉⠁⠃⠀⠀⠀⢤⠾⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⡀⣄⠀⠀⠀⠀⠈⠙⠋⠒⢂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⢀⠀⠄⠀⢁⠄⡎⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠰⠈⠡⢍⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠋⢘⣴⣿⡿⠟⠛⠛⠛⠛⠛⢻⠿⣿⣿⣷⣦⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢰⣾⣿⡇⠀⢀⣀⣀⣤⣄⣀⣈⣶⣿⣿⣿⣿⣗⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠁⠻⣿⡉⠁⠀⠀⠀⢀⢩⣿⣿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣶⣤⣾⣦⣷⣿⠟⠁⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢀⣠⣀⣄⡀⠀⠀⡴⠋
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢳⡀⣸⡿⠿⣿⣇⢀⡜⠁
⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⣏⣀⣠⣾⣿⣏⡀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠄⡀⠀⠀⣀⠠⠐⠒⣂⠄⠒⠈⡡⣻⣿⣿⣿⣿⣿⣟⢌⠂⠒⠤⣐⠒⠂⠄⣀⠀⠀⠀⡠⠀⠊
⠀⠀⠀⠀⠈⠂⠾⠁⠒⠈⠀⠀⢀⢴⡾⣿⣿⣧⣬⣭⣭⣴⣿⣿⢷⣦⡀⠀⠈⠀⠂⠈⠧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣉⡴⠋⣴⢿⣿⣄⣀⣀⣀⣠⣿⡟⣦⠙⢦⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⢿⣄⠀⠀⠀⣠⣿⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⠻⠿⠿⠿⠟⠁⠀⠀⢏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡀⠀⠀⡰⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡸⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣷⣦⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣴⠋⠉⠉⠁⠀⠉⠉⠉⠉⠛⠒⠦⣄⣸⣿⣿⣿⣿⣿⣿⣀⡤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⢳⡄
⠀⠀⠀⢻⣄⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠈⠛⢶⣶⣋⡉⠀⠀⠉⠉⠙⣦⢰⣿⣿⣿⣿⣿⣿⣿⣷⢠⡞⠉⠉⠀⠀⠈⣉⣳⣶⠞⠋
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠉⠉⠛⠒⠛⠉⠁⣀⣿⣿⣿⣿⣿⣿⣿⣏⡀⠉⠙⠛⠛⠛⠉⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢤⣤⣤⡤⠶⠒⠋⡽⠿⠿⠿⠿⠿⠿⠿⠿⡍⠓⠲⠦⣤⣤⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣶⣶⣶⣶⣶⣶⣶⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣤⣤⣤⣤⣤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣉⣉⣉⣉⣉⣩⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⢛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠢⡈⢦⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠱⡈⢻⡇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠈⠑⠦⡀⠹⡄⢿⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⠄⢱⡸⣧⠀⢰⡏⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠢⣝⣿⣧⠘⣧⣤⣴⣶⣄⡟⣠⠤⠤⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣮⣿⣿⣿⣦⣀⠉⠻⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣠⣤⣴⡾⣿⣷⣀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣄⠈⢻⡿⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣄⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠿⠿⠟⠛⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠛⢉⣿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠷⠻⣮⡳⣮⡙⡿⠯⠍⢙⠛⠿⣷⢒⡲⠦⢄
⠀⠀⠀⣀⡴⠞⠟⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠈⢏⠀⠈⠑⠒⠀⠀⠙⠒⠒⠀⠀⠉⢸⠇
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⣺⡇⢻⣷⣴⠀⠀⠀⠢⠝⢢⣤⣀⡀⠀⠀⠑⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢄⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⣿⡏⠀⠀⠀⢀⠀⠀⡨⠉⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⡛⣿⣿⡿⠟⠋⢠⣿⠃⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⢀⣴⣿⠏⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⡿⠿⠋⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢆⡀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠂⢄⣰⣆⠔⠀⠀⠀⠀⠞⠉⠉⠀⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠰⡖⠀⣶⣾⣿⣿⣗⡲⠐⡿⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢥⣀⡀⠀⠀⠈⢙⡹⠉⠀⠈⠙⢷⡞⠀⠀⢀⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢲⣄⠀⣿⣾⣤⣤⣦⣴⣶⣿⡤⠖⣋⠟
⠀⠀⠀⠀⠤⠀⠐⠂⠀⠤⠤⣀⠀⣀⣀⣀⣈⠠⠽⠓⣿⣿⣿⣿⣿⣿⣿⣿⠷⢋⣅⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡐⠢⠄⢀⣀⠰⠋⢿⣿⣿⣿⣿⣿⡟⠲⢦⣀⠀⠑⢄⠈⠉⠀⠀⠀⠈⠉⢉⠉⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⣰⠤⠗⠐⠒⠺⠋⠀⠀⣴⣾⣿⣿⣿⣿⣿⣦⠈⢆⠈⢋⡐⠀⠀⣀⡀⠀⠂⠄⠀⠀⠢⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠠⢀⠀⠀⠀⢀⣰⠏⢿⣹⡿⣹⢷⡿⡻⢿⠑⢤⡀⠀⠁⠀⠀⠈⠛⢦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⢄⡤⢶⣿⠟⠠⠀⠀⠁⠐⠂⠂⠀⠀⣀⠼⣍⠳⢄⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠚⠁⢸⣂⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣷⣷⣶⣾⣶⣦⣶⣾⣿⠟⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠻⢿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⣀⠀⠀⠀⠻⣿⡏⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣿⣿⣦⣴⣾⣿⣷⣄⡀⢀⣿⡇⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠋
⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⢸⣿⣿⣿⣿⡿⠿⠿⠓⠨⣿⣧⣤⡄
⠀⠀⠀⢻⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡆⢹⣿⣿⣯⠀⠀⠀⢀⣶⣿⣿⣿⣿⣴⣄⣀⣀⠀⠀⢀⣠⣄⣠⣶⣿⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠠⠤⡠⢶⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣟⣽⣿⣿⡟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡋⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⢀⠤⢺⣿⣿⣿⠟⢿⣿⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⣿⣿
⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⡠⠖⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣀⢹⣼⠃⣌⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣾⣿⣷⣿⣿⡆⣉⡴⠖⠀⣰⣶⡄⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⣦⡉⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⣶⣶⣾
⢿⣿⣾⣿⣿⣿⣿⡯⠃⠀⠀⠘⠋⠀⠀⣀⠀⠀⠀⠀⠀⣀⣙⣲⣚⣁⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠛⠆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢿⣿⣿⣿
⠄⠀⠈⢹⡇⠀⠉⠁⠲⡦⠀⣀⠀⠀⠀⠈⠙⠓⠒⠒⠚⠛⠛⠛⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⣿⣔⢿⣷⠀⠀⠀⠘⣿⣿⠟
⠂⠀⠀⠈⢀⣾⠀⣀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣭⣝⢆⠀⠀⠀⠀⠘⣿⣧⠀⠙⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⣼⡟⠀⢸⠧⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⡟
⠀⠀⠀⠜⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⡿⣏⣉⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⢀⣠⠤⢤⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣃⠀⠻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⢀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠉⢉⣛⣿⡟⠿⠿⠛⠋⣧⣿⡇⠀⠀⠈⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤
⢄⠘⠛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣅⣤⣄⣤⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠊⣡⣾⣶⣾⣿⣯⣯⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣤⣀⡐⠠⠤⣤⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢿⣿⣿⣿⣿⣿⣈⣿⣿⣶⣴⣤⣶⣾⣿⣿⣿⢿⣿⣿⣿⢿⡟⢿⡶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⣉⣙⠻⣿⣿⣿⣿⣿⠿⣿⣷⠀⠉⠉⠻⢧⠳⣝⣷⣦⣈⡉⠛⠓⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡃⢀⣹⡿⠳⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣏⣩⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠒⠲⠶⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣿⣏⠀⠾⣿⣙⣹⣿⣿⢿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠋⠀⠀⠀⠀⠁⣽⣤⡜⠻⠻⢻⠿⠃⠀⠀⠉⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣆⣠⣤⣼⣼⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⡀⠀⢀⣤⣷⣾⣿⣶⣶⡄⠀⠀⡀⣀⣴⡞⠁
⡄⠀⠀⠉⠀⠀⠀⠒⠀⠤⣀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⢀⡼⠿⠛⠛⠛⠻⠻⠿⡀⢰⡿⠛⠁⠀⠀⠀⠀⠀⢀⠠⠔⠂
⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀⠀⢻⡏⠀⢀⣀⣠⣀⣀⣀⠀⠙⣾⠁⠀⠀⠀⠀⡠⠐⠈
⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠬⠀⠀⠀⠀⠸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡧⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠂⠀⢀⣀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠉⠁⠤⠀⠀⢂⠀⣶⣶⣶⣶⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⣶⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⢀⠀⠀⠀⢠⣾⠟⠉⣀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣴⣿⢿⠛⠙⠻⠶⢤⣤⣤⣤⡤⠖⠛⢻⡿⣷⣄⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⣤⡴⠿⠋⠀⣰⣿⡀⣼⣧⣤⣄⣀⠀⡀⠀⠀⠀⣀⣤⣾⡇⠈⣿⡇⠀⠙⠿⣦⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢾⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣍⣛⠛⠛⠻⠛⠛⠛⢛⣹⣿⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢹⣿⣿⣿⠿⠷⠶⠶⠶⠾⠿⢿⣿⠇⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠘⠿⣟⡃⠀⠒⠚⣫⠟⠁⠀⠀⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠋⠁⠀⠀⠀⠀⠉⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠤⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣄⠤⠶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠿⠟⠛⠛⠛⠟⠛⠛⠿⠷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠉⠀⠀⣠⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⣀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣽⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠻⡗⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠊⠀⣸⠟⢠⡖⠈⠙⠉⠉⠉⠉⠙⠉⠛⠛⠉⠙⠋⠁⣦⡀⢻⣄⠀⠑⠤⢀⡀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣿⣷⠀⢀⣀⣀⣠⣤⣄⣠⣤⣀⣀⣀⠀⢠⣿⣇⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠏⢲⣿⣿⣿⢿⠿⠿⠿⢿⣿⣿⣿⣷⠆⢻⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠂⠄⣀⠀⠀⣀⠤⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡴⠋
⢠⣷⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢦⡀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣤⣤⣀⠠⠤⠈⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣴⣦⣄
⢸⣿⣿⣝⢣⣀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠳⣽⣦⡀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡀⠀⠀⢀⣴⣎⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣈⣼⣿⣻⣿
⠘⣿⣿⣿⣾⡍⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣍⣳⣦⣀⣴⣿⠿⠃⠀⠙⣿⣿⣦⣾⣏⣼⠟⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣻⣿⡿
⠀⠘⣿⣿⣿⠛⢧⠀⠀⠀⠀⠑⠀⠠⠀⢀⠀⠀⠑⢦⡉⠛⢿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⡿⢁⡴⠊⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⠁
⠀⠀⠙⢿⣿⣷⣄⡑⠦⠄⠚⠀⠀⠀⠀⠈⠁⠀⠀⢴⣿⣷⣼⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣴⣿⣶⠄⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠐⠀⣹⣿⣿⡿⠋
⠀⠀⠀⠀⠙⠻⣿⣤⣄⣀⡤⠄⠀⠀⠀⢀⠂⠄⠠⢾⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⡷⠶⠤⠀⡤⠷⠤⠄⢀⣀⠀⡸⠷⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣘⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠒⣻⣿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣯⣉⠲⣦⢀⡇⠀⠀⠀⠉⠈⢹⠛⢻⣏⠁
⠀⠀⠀⠀⠀⠀⢰⣿⡀⡀⠀⠀⠀⡄⠀⠀⢠⡴⣸⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡏⠂⠀⡀⠀⠐⠂⠀⠀⠀⢿⣶⣤⣿⡧
⠀⠀⠀⠀⠀⠀⠘⣯⣭⡀⠀⢀⠐⠀⠠⠖⢁⣾⣯⡟⣠⡎⠙⠻⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣦⣹⣿⣷⡄⠉⠀⡀⠀⠰⣄⠈⢠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠈⠀⠀⠀⢠⣾⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢹⣷⡹⣿⣷⡀⠀⠀⠀⠀⠀⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⣹⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⡀⠉⠳⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢠⣿⢻⣿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡎⣻⡇⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠃⠀⠻⣭⣩⣟⣹⣿⣿⣿⣿⣛⣿⣿⡟⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢹⣿⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠟⠛⠋⠀⠀⣿⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣼⠟⠀⠀⠀⠀⠈⠢⡄⠀⠀⢀⡀⠄⠀⠀⠀⠀⢹⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣴⠤⡤⠀⠀⠀⠀⠄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣴⣿⣿⣿⣿⣆⣀⣈⣷⣤⡀⠁⠀⡇⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⣀⣰⡀⠀⢀⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣱⣻⣄⡄⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⢀⣾⣿⣿⣟⡉⢽⣿⣿⣿⣿⢾⡿⢿⣵⣿⣿⣿⣿⣿⡿⢧⣿⣿⣟⠀⠀⠀⠀⠀⠀⡇⠀⠈⣧
⠀⠀⣼⣿⣿⣿⡿⢻⣽⣿⣿⣿⣿⣿⣯⣻⣿⣷⡛⣿⣻⣏⠀⡯⢿⣿⣮⠷⠀⠀⠀⠀⠀⢄⣦⣶⡿⠒⠦⣄⡀
⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⠿⣯⣿⣿⢟⢫⣽⢿⣇⠁⠈⡿⢶⠿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠘⠟⠛⠁⠀⠀⠀⠉
⠀⠀⠈⠛⠛⠣⣾⣟⠉⠉⣾⡟⣴⠏⠀⠀⣽⠈⡇⠂⢀⡈⠀⠀⠑⡷⡉
⠀⠀⠀⠉⣕⠀⠂⢈⣑⣊⣀⡐⠠⠀⠂⡐⢀⠠⠐⠈⠀⠀⠀⠔⠀⠀⠈⢢⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢑⣶⣶⣶⡶⠊⠀⠀⠀⣠⡿⠁
⠀⠀⠐⠈⠉⠁⠉⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠂⠋⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠉⠑⠢⢀⠀⠀⠀⠀⠹⣿⣤⠿⠛⠋⠉⠉⠙⠛⠿⣤⣿⠟⠀⠀⠀⠀⡀⠔⠊⠉⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⡀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⢀⣀⠄⠒⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⢉⣹⣿⣿⣶⣶⣧⣶⣶⣼⣶⣶⣿⣿⣏⣉⠄⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⢀⣴⡿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣦⡀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢰⣿⠟⠃⢉⣉⣉⣉⣥⣶⣶⣬⣉⣉⣉⡁⠙⠻⣿⡆⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢠⣿⠀⠀⠁⠀⠁⠉⠉⠛⠃⠘⠛⠉⠉⠈⠀⠈⠀⠀⣿⡄⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⣼⡟⠀⠀⠆⣀⣀⣀⡀⣀⣠⣄⣀⢀⣀⣀⣀⠶⠀⠀⢻⣧⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⣿⠇⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠸⣿⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⡀⠀⠀⠘⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣴⠃⠀⠀⢀⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣧⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢀⣴⡏⠍⠀⠈⢹⣷⣄⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⡄⢸⣿⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⡠⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣳⠀⠛⣿⣯⣾⣶⣿⣭⣍⡀⠀⠸⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠉⠋⠉⠁⠁⠉⠛⢿⣿⣿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⡄⠀⠀⠀⠀⠀⠀⠐⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⢀⣾⣏⣄⠄⠀⡀⠀⢀⢠⣤⣿⠷⣄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣶⣖⣶⢊⠿⠏⠀⢢⠆⠯⠿⣿⣷⣾⡷⣿⣾⣿⡿⣿⣫⠅⠄⠀⠈⢳⣶⣶⠦⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠃⡤⣶⣶⠛⠉⠍⠁⠛⠋⠁⣳⢶⣖⢤⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠘⢈⢿⠙⠛⡦⣤⠄⡤⠤⠴⠟⠛⠈⡍⠉⡀⠀⠀⠀⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢀⠂⠀⠘⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠌⠀⠠⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⡟⠙⠃⠀⠄⠀⠠⠄⠀⠐⠁⣉⠀⠰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⠋⢰⡀⣀⠀⠀⠀⠀⠀⠀⢠⠰⣿⠀⠀⠙⢮⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⠛⠙⠂⠀⠀⠄⠠⠤⠖⠂⡉⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⣀⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠉⠋⠋⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠞⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢧⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⣃⣀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡅
⠀⠀⠀⣀⢤⡖⢤⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠉⠀⠈⠉⠳⣄⢀⠤⠒⠂⠚⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠤⣄⡀
⠀⠀⡸⢥⠀⠘⣄⡵⠞⢶⠤⢤⣀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠶⣁⠞⠀⣈⠆
⠀⠀⡇⠀⠳⡴⠫⢀⠤⠈⠀⠀⠈⠉⠢⢄⡀⠀⢀⡇⠀⠀⠀⠰⣿⠂⠀⠀⡗⠾⠆⠀⠀⠀⠀⣸⣄⡀⠀⠀⢀⡠⠖⠋⠁⠀⡇⠠⢄⠼⢦⠔⠁⢸
⠀⢰⠙⠀⠀⠁⠀⣀⡠⠞⠀⠀⠀⠀⠀⢀⣽⠞⠋⠙⣄⠀⠀⠀⠀⠀⢀⡴⠣⣀⠀⠀⠀⢀⡴⠁⠈⠙⠳⣖⠉⠀⠀⠀⠀⠀⠙⠤⣀⠀⠈⠀⠀⠚⡄⠀⠠
⠀⢠⠗⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠈⠑⠢⠤⠤⠖⠋⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢡⡤⠀⠀⠀⠸⡄
⢠⡏⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡾⠁⠐⠲⠆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣠⠀⠙⣦⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢳
⣸⠀⠀⠀⠀⠀⠀⢸⠄⠒⠛⢲⡞⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⣰⠃⠀⠀⠘⣗⠛⠛⠒⢴⡇⠀⠀⠀⠀⠀⠸⡆
⡇⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⡾⠀⠀⠀⠀⠈⣇⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡴⠃⠀⠀⠀⠀⢸⡆⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠙⠢⢤⣀⣀⣀⣀⣀⡀⠠⠴⠊⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠐⡈⢱⠦⠄⣀⣀⠀⠀⠈⣁⡀⠠⠄⢲⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠉⠳⢤⣀⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⢰⠏⠉⠓⠒⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⢀⡇⠀⠀⠀⢸⠀⠀⠀⢀⡷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠒⠚⠻⡅
⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⣧⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠼⠦⠐⠒⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣼⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⣇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣸⠃⠀⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠉⠉⠛⠛⠒⠒⠒⠲⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠖⠒⠚⠛⠛⠛⠉⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⢖⢒⡒⠲⠶⣿⡇⠀⢀⡸⠿⠖⢚⣛⡻⢒⡶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠛⢋⠉⠀⡀⠄⣂⡽⠀⢯⣐⠀⠀⡀⠈⡙⠋⠁⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠑⠒⠂⠐⠒⠚⣉⣡⠴⠚⠉⠀⠀⠀⠈⠙⠲⢤⣉⡑⠒⠒⠒⠒⠉⣀⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡀⠀⢘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⡶
⠙⠛⠛⠓⠲⢤⣤⣒⣂⠤⠄⠀⠀⡀⢀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⢛⡟⠋⠛⠛⠛⠛⠅⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣃⣤⡄⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⢀⡈⠉⣉⣉⣵⣿⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣩⣴⣾⠗⠀⠀⠀⠘⠉⠀⢣⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠛⠛⠋⢉⣿⡿⠀⠀⠀⠘⠀⠈⠀⠀⠀⢀⠘⠃⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣔⣀⡒⠋⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⣶⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠿⠿⠿⠿⢿⣿⣿⣿⣧⡆⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣢⣶⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣥⣭⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣽⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠀⠐⣖⡦⢰⣀⠂⣆⡐⢰⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠘⠀⠂⠓⠐⠓⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠻⠿⣈⠱⡀⠀⠀⠀⠀⠀⠀⢥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠈⢣⡀⠀⠙⡰⠁⠀⠈⢣⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⢣⠀⠀⠀⣠⠋⠉⠉⢧⠀⠀⠀⡠⠋⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡶⡶⠶⢇⠀⠀⠀⢠⠗⠒⠒⢇⠀⠀⠀⢠⠗⠶⡚⢇⠀⠀⠀⢠⠓⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⢎⠛⠀⠠⢆⣷⠶⠶⢇⠀⠀⠀⢈⠖⠒⣶⡏⠃⠀⠁⢈⡶⢶⠶⡅⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡦⠤⠤⡎⣤⠀⠀⠈⡦⠤⠤⡎⠀⠀⠙⢋⣦⠤⢤⡇⠿⠈⠀⢘⣤⣤⣤⡃
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⡤⠤⠤⡞⠀⠀⠀⠘⣤⣄⢤⡎⣰⠀⠾⠘⡄⠀⢠⡎⠀⢈⡁⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⡜⠀⠀⠀⠙⣄⣀⣀⡜⠈⠧⠀⠱⣌⣀⣀⡞⠀⠀⠀⠱⣀⣈⣁⠎
⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠩⠵⡀⠀⠀⡰⢇⡍⢸⠳⡀⠀⢀⡜⠁⠀⠀⠣⡀⠀⢀⡜⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡠⠋⠉⠉⠣⡀⠁⠀⡰⠉⠉⠉⢣⠀⠀⠀⡰⣏⠉⠉⢣⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⢣⠀⠀⠀⢠⠋⠉⠉⢣⠀⠀⠀⡠⠋⠉⠉⢇⠈⠁⠀⡠⡛⠟⠛⣆
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡷⠶⠖⢇⠀⠀⠀⢀⡗⠒⠖⢇⠀⠀⠀⢠⠓⠒⠒⣅⠋⠀⠘⢪⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⢏⠡⠇⠁⢀⠗⠒⠒⣇⠋⠀⡧⢈⠖⢶⠶⡇⠀⠀⠀⢈⠖⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⡎⠀⠀⠀⠈⡦⠤⠤⡎⠀⠸⠀⢘⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⡎⠀⠀⠀⠘⣄⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠗⠀⠀⠀⠠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠀⣿⠿⡭⠋⣡⣤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠂⠀⠀⠉⢀⣠⣤⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣶⣲⣶⣤⡤⠀⢀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠢⠀⠀⠂
⠀⠘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠂⠁⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⠈⡐
⠀⠀⠐⠲⠯⠭⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠈⡏⣶⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣿⣦⣄⣀⡒⠶⠦⢤⡄⠀⠀⠀⠀⠀⢀⣠⣀⣀⣒⠲⠦⠼⣥⣤⣀⣃⢻⣿⣿⣷⣦⡄⠀⢀⣀⣈
⠀⠀⠈⠙⠛⠿⢿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠰⠦⣭⣭⣍⣛⠓⠶⠦⢬⣈⠘⣿⣿⣿⣿⡇⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢛⣿⣿⣶⣶⣶⣶⣤⣤⣭⣀⣀⡀⠀⠀⣠⣿⣿⣿⣿⣷⡄⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⡿⠟⣛⣛⠻⣿⣿⠛⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⢤⣀⡀⠀⠀⠐⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠠⢄⠉⠳⣄⣠⡄⠔⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡄⠀⠀⠠⠀⠀⠀⢀⠓⣄⠀⠑⠂⠛⠏⠘⠉⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠢⣵⣦⠀⠀⠀⠀⠀⠰⡈⠑⠄⠀⢀⢀⠀⢀⡒⠒⠀⣀⣲⣾⡛⠛⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣄⠉⠲⠦⠖⢇⠀⠀⠀⠀⠐⢄⣈⣤⠔⠀⠿⠃⠄⠠⣄⠀⠀⠀⠀⠈⠙⠳⢦⣤⡈⠁⠈⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣀⣀⣀⣀⣀⣀⣀⡠⠤⠐⠒⠀⠉⠀⠒⣤⢵⠶⡲⠤⡀⠀⠀⠀⡏⠿⢖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⠛⠦⠀⠀⠀⠀⠀⠎⠀⠀⣄⠈⠀⠈⠂⠀⠀⢀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠖⠒⠀⠀⠀⠐⠒⣄⠀⠀⠀⠀⡠⠚⠀⠓⠒⠄⢸⠀⠀⠀⠳⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⠶⠒⠒⠒⠒⠀⠒⠚⢆⠀⠈⠁⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠒⠒⠒⠒⠒⠒⠒⠒⠦⢼⡄⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢤⣤⠄⠀⠄⠤⠤⠤⣄⣀⣿⠀⠀⠀⠀⣁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠤⠙⢿⣋⣠⠤⠤⠤⠖⠒⠀⠙⡂⠀⠀⠸⠠⠄⠀⠀⣶⠒⣤⡆⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠠⣤⠞⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡇⢸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣉⣉⣉⣀⡠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠄⣀⡙⠟⠰⠿⠁⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠑⠓⠗⣷⢻⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠀⠠⠐⢀⡠
⠀⠀⠀⠀⠀⢁⣴⡶⠦⢤⢼⠿⡿⠿⢿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢯⣀⠀⠀⠀⢀⡠⠔⠊⣁⠴⠂⢀
⠀⠀⠀⠀⢴⣙⠛⠙⢲⠖⡶⠘⡇⠙⣎⣻⣟⣿⡿⠀⠀⠀⠀⠀⢶⣾⣟⠉⠤⠌⢹⣦⠐⠈⡁⠄⠂⠁⣀⣤⠊⠁
⠀⠀⠀⠀⠀⠈⢼⣥⣭⣀⣤⣬⣧⣤⣼⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡉⢀⣠⠴⠛⠉⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⠁⠀⠀⠀⠀⡹⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠁⠀⢀⡠⢿
⠀⠀⠀⠀⠀⠀⢸⠁⠘⠴⠀⠀⠀⠀⠀⠸⡯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⢀⣀⠀⣿⠤⠊⠉⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⢀⠄⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⢝⠀⠒⠠⠦⢤⣀⠀⠀⠀⣇⣀⡤⠞⠉⢹⠑⠄
⠀⠀⠀⠀⠀⠀⠈⢶⣈⠉⠉⠁⠀⠀⢀⠠⢼⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠀⠰⣟⠁⠀⣠⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠠⢿⣽⠇⣿⡏⢹⠟⡴⣼⠃⠀⠀⠀⠀⠀⠐⡽⣠⢠⣐⠲⠦⣤⡀⠀⠀⣿⢇⣰⣾⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣙⠙⣻⡴⡞⠭⠁⠀⠀⠀⠀⠀⠀⢸⢼⣟⣃⡟⢷⣦⣤⣌⠘⢻⡿⡻⢿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠙⠿⢳⡿⢖⣿⢿⡷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠉⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠇⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠱⠦⣀⣯⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠘⠉⠒⠤⣄⣀⠁⠀⠠⠘⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⢀⣻⡌⢯⡑⠂⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣈⢧⠀⠊⠁⠙⢆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⠘⡀⠀⠠⠀⠘⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⢸⡀⠐⠄⢀⣀⠜⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣄⠀⠀⠀⠀⠸⡄⢀⠄⠃⣤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡤⠋⠀⠀⠈⢡
⠀⠀⠀⠈⠒⠴⠤⢄⡀⠟⠀⠀⠀⠉⢀⣀⣤⠤⠲⠄⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠤⣼⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠃⣴⠂⠀⠄⠂⢀⠀⠀⠃⠀⠀⠀⠈⠒⠒⠆⠀⡠⠃⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⢃
⠀⠀⠀⠇⠀⠀⠁⠀⠀⠈⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠙⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣨⠖⠐⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣥⣤⣉⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣤⣿⣶⣆⢠⡀⠻⣿⣶⣶⠆⢀⡄⣴⣿⣽⣿⣿⣟⠀⢀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢿⣿⣿⣿⡩⣅⠸⡿⢊⡴⣤⣦⡁⢾⠇⣡⠌⣿⣿⣿⣞⣿⣿⢯⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠚⠛⠿⠿⠷⠎⠳⠀⣸⣏⠻⣿⣇⠀⡞⠱⠞⠻⠻⠛⠛⠛⠉⠈⠀⢆⡀
⠀⠀⠀⡀⠀⣠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⢀⣼⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠲⡦⠅⠂⢄
⠀⠀⠐⠀⠀⡘⣧⣕⡠⠀⠀⠀⢀⠀⠠⠄⠀⠀⠸⣿⣾⣿⣿⣿⡇⠀⠂⠠⠄⠀⣀⠀⠀⠀⠄⣊⣶⣄⣠⣰⡌
⠀⠀⡄⠀⢸⣿⣯⣿⣿⣶⣦⡄⠀⠠⡴⣓⢤⣦⠤⢿⠏⠿⣿⡿⠤⣰⡦⠘⢦⡄⡀⢀⣠⣶⣾⣿⣿⣿⣿⠟⠃⠆
⠀⠀⢄⠀⠼⣿⣛⣿⣿⡿⢟⣁⣀⠪⣵⢿⠇⡼⢶⣥⣴⣶⣾⣯⡴⢧⠘⣿⡦⠑⣀⣬⣙⠉⢿⣻⣿⣿⡤⠀⡀
⠀⠀⠀⠙⠂⠈⠛⢋⣥⣶⠿⠛⠉⠑⠢⠉⣐⠃⣼⣁⣠⣶⣶⣿⣅⠀⣃⠉⠀⠀⠉⠛⠿⣿⣦⡈⠉⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⡟⣴⢹⣥⣤⣴⣾⣿⡍⣤⢻⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡠⠏⡄⣿⡀⢧⣀⣬⣿⡦⠰⣷⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡃⢟⣮⡌⠻⢿⢟⣡⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠛⠷⠞⠛⠋⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⡠⠚⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠦⣤⣤⣀⢀⣀⡀⡄⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⡭⢽⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⢱⣆⠀⠀⢿⣷⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣶⣿⡏⠁⠀⠀⡀⠂⠀⣤⠞⠉⢠⠏⠀⠀⠀⣸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣬⣿⡵⠋⠠⠀⠀⣼⢶⢦⣀⢷⣿⣿⣿⣯⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⢉⠆⠀⠀⠀⣼⣷⢸⣿⣾⠏⢻⡌⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⡃⠀⠀⡀⠀⣼⡿⠉⠀⣿⡆⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣶⣿⣿⣦⡶⠋⠀⠀⠀⠁⠀⠂⢀⣾⠉⠀⠀⠀⢸⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⢀⠀⠀⠀⢀⣤⢻⣿⠀⠀⠀⠀⠈⢿⡆⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠀⠀⠀⠀⠀⢀⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⡷⢀⡄⡀⠀⠀⠀⢾⠀⠀⠀⢀⣀⣴⣿⠇⠀⢀⣿⡆⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢏⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢉⣼⣿⡏⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⣆⣿⣰⣶⣶⣵⣿⣿⣿⠿⠁⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠛⠛⠻⡿⣿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣠⣤⣠⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉


⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠤⠴⣄⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠁⠀⠀⠀⠺⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⣀⣴⠟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣴⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠔⠀⠀⢀⣴⠟⡀⠊⠀⠀⠀⠀⠀⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⣴⠿⠅⠈⠁⠀⠀⢀⡠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⣴⠿⠥⠄⠀⢀⠠⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠋⠉⢿⣦⠀⠀⢀⣤⣤⣤⡀⠀⢠⣿⠁⣠⣿⡏⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⠴⣶⣄⡀⢻⡗⣺⢟⣻⠻⣿⣿⡄⢸⠃⢰⣿⣿⣟⠄
⠀⠀⠀⠀⠀⠈⠋⢀⣴⠟⠁⠀⠀⠙⠻⣶⣷⡏⣿⣿⡀⢹⣿⠧⠀⠀⠘⠁⠏⠔⠀⣀⣀⣠⣤⣤⡀⠲⣶⣦⣄⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢿⣿⣇⣿⣿⣥⣼⣯⣄⠰⣀⠐⣂⣠⣤⣿⣿⣦⣾⣦⡼⠦⠄⠈⢻⣿⣧⠀⠈⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣡⣻⣿⢫⣟⣢⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠀⣀⣼⣿⣿⠀⠀⢬⣿⣿⣷⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⠃⠀⢠⣾⣿⣿⡿⠀⡸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⢻⣿⣿⣿⣿⣯⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣀⣴⣿⣿⣿⡿⠁⣴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⠸⠿⣿⣿⣿⠿⣿⣿⡏⣻⣿⣿⡟⣻⣿⣿⣀⣺⣾⣿⣿⣻⠟⢭⠀⣾⣿⣿⣿⠏⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠀⠀⠀⠀⠻⣾⣯⣝⠣⣿⣿⣇⠏⢛⡏⣹⣿⣿⡿⡿⣿⡿⠿⠟⣫⣶⡟⢰⣿⣿⣿⢏⣳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡟⠭⠃⠀⢸⡿⣿⣿⣿⣿⡔⠋⠑⣀⣼⣿⣿⣶⣷⣿⠋⣱⣾⣿⡿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⡿⠞⡿⢋⣴⣾⣿⣿⣏⣩⣧⣸⣾⣿⣿⠿⢛⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣻⢗⣴⣶⣿⣿⣟⡉⡈⠛⠿⣿⣿⣯⣭⣿⣿⣿⠿⣛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣇⢱⠀⠀⠀⠈⠐⠻⢿⣷⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠆⠻⣿⠸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠙⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠗⠃⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⢤⣤⣤⣤⣀
⠀⠀⠀⣴⣾⠟⠋⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣥⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢦⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣴⣾⠟
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⢺⣷⡶⠾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣿⡷⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣤⣶⠿⠛⠛⠛⠛⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⠛⠓⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡈⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠁⠨⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠠⠔⠒⠉⠉⠉⠉⠁⠐⠠⢌⡀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠐⠤⣄⢀⠀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⠤⣤⣄⣀⣀⡀⠒⠦⠁⠀⠈⠂⢀⠹⣧⣾⢷⣾⣷⣤⣤⣄⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣷⣤⡶⢶⣄⣀⣘⠢⣴⣀⣀⣿⣿⣿⣿⣿⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣇⣤⣿⣿⣿⣿⣿⡛⡿⠿⠿⣰⣿⣿⣷⣸⣿⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡘⢶⣶⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠈⢿⣿⣷⣴⣿⣿⣿⠿⣷⣾⠛⠿⢻⡟⡟⢡⡈⢿⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣷⣦⣤⠀⠙⢿⣟⣵⣿⠏⠀⣾⣿⠀⠀⠈⠃⠁⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠈⠻⣿⣿⡿⣷⣿⡿⠁⢀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠹⣦⠔⠆⠀⠀⢀⠔⠀⠀⣀⣴⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣴⣩⣿⣿⡏⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠉⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⣿⠏⣿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⡿⠊⣡⢂⠀⡀⠀⡠⠔⠊⠈⠁⠀⠀⠉⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠿⠇⠸⢧⣾⣪⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢠⠔⠀⠀⠀⠀⠀⢻⣾⡇⠔⠊⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣻⣿⡍⠃⠀⠀⢀⠈⠀⣰⣿⣿⠿⠿⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠃⡠⠀⠀⣈⣴⣾⣿⣏⠙⠓⠂⠀⠠⠀⠀⠀⠉⠐⠒⠄⠀⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣝⣿⣿⣿⠟⠿⢿⣮⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡀⠈⠁⡾⢫⢯⠏⠸⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⠯⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢄⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⣎⣷⠀⠀⠀⠀⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠊⠀⠀⠀⠀⠀⠻⡅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡴⣢⠀⠀⠀⢀⡀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⡜⠋⠑⣦⣀⣞⠀⠀⠀⠀⠰⣿⣟⣟⣭⣳⣦⣌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣯⣽⠿⠀⢀⣼⣿⣻⣿⡳⣄⡀⠀⠛⠛⠁⠀⢻⡜⣿⣯⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣯⠀⠀⠀⢀⡼⣿⣿⣯⣿⢿⣿⣯⣷⢻⢿⣷⡶⣶⣿⣮⣟⡶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣲⢾⣿⣧⣷⣷⣂⣿⣸⣿⣿⡿⢿⣷⣿⣾⡿⣿⣛⣿⢝⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣁⢀⠀⠀⠊⠁⠀⠁⠀⠀⠀⠀⠈⣿⣾⣿⣷⣿⠿⣿⣷⣿⣿⣟⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⡫⠿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣯⡿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⣀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣎⡉⣊⣿⣽⣿⣿⣾⣽⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡉⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⣼⣿⣯⣽⣿⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠁
⠀⠀⠤⣴⣆⣠⣾⣿⣤⠀⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣽⢟⣿⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⡤⠀⠀⠀⣠⣾⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣧⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⡽⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⠀⢀⣠⣄⣀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠁⠀⠀⢰⠏⠀⠀⠈⢱⡟⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣸⡀⠀⠀⢀⣸⡀⠀⠀⢀⠘⠃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⢱⡞⠉⠀⠈⠁⡞⠁⠀⠀⣴⣾⣷⣤⢰⢾⢸⠟⠉⠉
⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⢸⡆⠀⠀⠀⢀⡇⠀⠀⠀⠉⡏⠋⠀⠀⠀⠉
⠀⠀⠀⠀⣶⠞⠉⠉⠐⢤⠞⠉⠉⠒⣠⡾⠋⠉⠒⢠⣴⠞⠙⠒⢠⣶⠟⠉⠒⠀⣴⠞⠛⠒⠄
⠀⠀⠀⠀⡇⠰⡇⣧⣄⣀⣤⣄⡀⠀⢿⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠃⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠿⠿⣿⡴⠛⠢⠄⣠⡴⠚⠢⠄⣀⣴⠞⠲⠤⣀⣴⠞⠳⠄⢀⣴⠞⠲⠤
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡏⠀⠀⠀⠀⡏⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠼⠧⣄⢀⣠⡴⠧⣄⠀⣀⣤⠧⣄⡀⣀⡤⠧⢄⡀⢀⣠⠾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⣸⠉⠀⠀⠀⢸⠏⠁⠀⣠⣼⡏⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣿⣀⠀⠀⣀⠈⠀⠀⢠⠿⢿⣅⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢁⡞⠁⠀⣄⢻⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠈⠆⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⢻⢽⡀⡯⠌⢸⠥⠁⠾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠑⠈⠈⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⠘⢦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠓⢤⡀⠀⠀⢣⡀⢻⡆⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⡀⠉⠓⢄⠈⢷⠈⣷⠀⠀⠀⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢢⠈⢧⢹⣇⠀⢠⣿⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣆⡑⢬⡳⣿⣦⠘⢇⣤⣤⣶⣦⣄⡟⢀⡤⠤⡄⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⣶⣭⣿⣿⣿⣧⡈⠉⠻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⢠⣶⣶⣶⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠛⠛⠛⠛⠁⠙⠛⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣷⣶⣶⣶⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣴⠿⣿⡿⠋⠙⠉⢿⣿⣿⣿⣿⣿⣴⣻⣿⣿⣿⡠⣦⣌⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠟⠋⠁⠀⣰⣿⡃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡻⣧⢾⣝⠻⢷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣼⢟⠟⠁⠀⠀⠀⣰⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣟⠛⠋⠈⠳⣮⠛⠦⣬⡉⠛⠒⠠⣄⡙⠛⠏⠩⠭⠙⢲⡀
⠀⠀⡀⣀⡴⠞⠉⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢻⣿⢿⣄⠀⡀⠀⠠⠀⠀⢀⡉⠉⠀⠂⠀⠉⠉⡁⠉⠐⠀⣸⠟
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⢀⣸⣿⠈⢿⣷⣷⠀⠀⠀⠐⠠⠙⢶⣤⣄⣀⠀⠀⢀⢑⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠤⣀⠙⢿⣿⣿⣿⠿⠋⠀⣾⡏⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠛⠛⠉⠀⠀⣠⣾⡿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣾⣿⡟⠁⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⢦⡀⠀⠀⠀⠀⢹⠀⠀⡀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠢⡀⠀⠀⠸⠀⢠⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠂⠀⠀⢠⡾⠀⢼⣿⣷⡆⠀⠀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⢰⣿⣿⣷⣝⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⠷⠀⢤⣄⢸⣿⣿⣿⣿⣆⣠⡤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⣵⣿⣆⠈⠻⣮⣝⠛⠛⠋⠉⠁⠤⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⣤⠀⠹⣿⣿⣷⣄⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠈⠻⢿⣿⣿⠂⢧⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⢿⣿⣶⣄⡀⢉⡾⠁⢸⢱⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠉⠛⠋⢁⡼⠁⠀⠘⠀⠑⠦⣄⣀⣀⣀⣹⠶⢤⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠶⡶⠆⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠸⣏⣇⣀⣷⣀⣼⠋⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⣀⢶⠀⠀⠀⠉⠁⠀⣀⣼⣿⣿⣼⣿⣧⣀⠀⢔⣠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣽⠓⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡠⠖⠉⣵⣲⠋⠙⢻⣿⡿⣿⣿⣦⡀⠀⠰⠶⠦⠀⠀⠀⠀⠀⠀⡀⠙⢲⡿⠂⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠂⠀⢀⣴⠞⠁⠁⠘⠱⠇⢠⠃⠈⡏⡇⢋⢳⡍⢿⣷⣄⠀⢠⣤⠀⠀⠀⡀⠀⡻⠀⠀⠀⢁⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⡇⢹⠸⡀⢻⠻⣯⢻⣷⣄⠁⠁⠀⠀⠷⢛⠡⣎⠐⢀⣼⡀⠴⡴⠶
⠀⠀⠰⡿⣆⠀⠀⠀⠀⡠⢶⡄⢀⣾⠇⠈⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⢸⡄⡇⠃⢧⠹⢳⣻⣿⣦⡀⠀⠀⠆⣼⠦⠅⢠⠚⠃⡰
⠀⠀⢀⠀⠈⢰⠀⠄⠀⠈⠉⠀⣿⡿⠀⡀⡀⠀⠀⠀⠀⠀⠀⡇⣸⠀⣇⡸⢃⣯⣴⣬⣆⣾⣷⣿⡿⡧⠀⠀⢀⠌⣑⢿⡏⠀⠚⠛⠒⠂
⠀⠀⠈⠰⣀⣏⢾⡆⠀⠀⠀⢀⣿⣁⣉⣁⣈⣁⣘⣓⡄⢛⣉⣬⣭⣤⣽⣷⣿⣶⣿⣿⣿⣿⣿⠿⠷⢶⠀⡀⢻⣦⣸⣷⡜⠿⡿⠆⠸⠷⠠⡀
⠀⠀⠀⠀⠙⣶⣦⢧⢤⡀⣰⣾⣏⣉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⢉⣉⣉⣉⣩⣭⣥⣤⣴⣴⣶⣶⣿⣴⡇⠀⠀⠀⠠⣼⡿⣟⠀⠀⠤⠀⠀⠃
⠀⠀⢠⡄⠁⠸⢆⣀⠼⠛⠁⣽⠛⠛⠛⠛⠛⠒⠒⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣉⣭⣭⣵⣴⣶⣦⣸⠀⠀⠀⡀⣴⣿⡿⢶⡚⠛⢀⡀
⠀⠀⠀⠛⢧⡘⣧⡄⣜⡅⢀⡿⠿⠷⠶⠶⠶⠶⠴⠴⠶⠶⠶⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡛⣛⣛⠙⠀⠀⠛⠦⠈⡏⢀⠀⠀⠉⠿⣷⡀
⠀⠀⠀⠰⡉⢹⣏⢼⣛⣲⢸⡿⢶⣶⣤⣤⣠⣤⣄⣄⣄⣀⣀⣀⣀⣤⣤⣴⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⢶⡆⠹⣶⣷⠄⣣⣀⣘⣧⣶⣤⣈⠁
⠀⠀⢠⣾⣧⣜⢀⣦⡼⠗⢸⣷⣠⡄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⣉⣉⣉⣉⣩⣭⣭⣥⣴⣴⣯⣶⡅⢶⣶⣂⠜⣋⡼⣿⡓⡈⠙⠺⠆
⠀⠀⠘⣿⣿⠻⠷⠿⢟⡓⣼⣿⣏⡙⠛⠛⠛⠛⠿⠲⠶⠷⠶⠶⠷⠷⠾⠟⠛⠛⠛⠛⢛⣛⣛⣍⣩⣧⣌⣥⠈⢀⣰⢟⣩⠿⢏⡑⣶⠶⣐⣄⡄
⠀⠀⠀⠿⣻⠀⠳⠗⢀⡇⢸⣿⠉⠛⠶⠶⣤⡤⢄⣀⣀⡄⣀⣀⣠⣤⣄⣴⣶⣾⣿⣾⣿⡿⠿⠿⣛⣋⡭⢹⡟⢿⣧⡎⠉⣦⠄⢡⡿⠏⢁
⠀⠀⠀⣀⠏⠳⠶⠶⣿⣷⠻⣿⣷⣦⣄⣀⣀⡀⠀⣀⠈⠀⠉⠉⣿⣿⣿⣀⣉⣁⣠⣤⡶⣶⣾⣿⣿⣿⣷⣿⡗⠀⠙⣧⠀⣯⣴⣿⣛⡶⡁
⠀⠀⠀⢹⣟⠲⣭⣹⣝⠃⠀⠀⠉⠙⠛⠛⠿⠿⠿⠷⠿⠾⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⣿⣷⡾⠋⢻⣨⣉⣻
⠀⠀⠀⠀⣿⣟⣿⢯⡇⠀⠀⠀⢀⠀⠀⠀⠀⡀⠴⠄⠀⣀⠀⠀⠀⠀⠠⠰⠰⣄⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣧⣾⣨⣿⣯⢉⡖
⠀⠀⠀⠈⠳⣙⣿⣶⣿⠀⠀⠀⠠⠀⠀⠠⣉⠉⠀⠀⠄⠁⠀⠀⠀⠀⠤⠀⠊⠀⠀⠲⠀⠂⠂⠀⣀⣀⣀⣃⣀⣀⣀⣿⣷⢫⣿⢻⣿⠋⠴⢣⠞⡀
⠀⠀⠀⠀⠐⠾⣷⣿⣿⣤⣤⣤⣴⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣛⣟⡟⡿⠚⢁⣘⠋⡀⢀⠀⡸⠇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠀⠀⠁⣿⣿⣿⣿⢛⣟⣽⣻⠟⣱⣯⣟⣻⣿⢱⣿⣏⣤⣽⠀⠀⠀⣿⠿⢶⠿⢴⠗⣋⣽⣷⠡⠖⠋⣸⡃
⠀⠀⠀⠀⠀⢨⡍⠳⢾⣟⣶⣾⡟⣹⡄⠀⠀⣿⣣⣞⠛⠛⠫⢟⡛⢟⣫⡿⠋⢾⣷⠾⢿⣟⣤⡾⢷⣤⣤⣿⠶⣿⣥⣯⢜⣣⣿⣱⡶⡶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠟⠛⠒⠁⠉⠛⠑⠒⠈⠋⠈⠙⠋⠉⠛⠁⠐⠁⠐⠛⠹⠛⠻⠛⠛⠷⠍⠘⠓⠉⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⣦⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣤⠾⠛⠉⠉⠈⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠈⢿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠙⢿⡄⠀⢸⡇⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠿⠷⣤⣀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠉⢳⣤⣴⡶⠶⠺⣿⣷⣤⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⡏⠉⢻⣿⣿⡟⠛⢿⣿⣛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠋⠀⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⢸⣿⣿⣿⠇⠀⣾⣿⣿⡇⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢠⣿⣿⣿⡟⠀⢀⣿⣿⣿⠇⠀⣾⣿⣿⠃⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠻⣿⠃⠀⣠⣿⣿⣿⡟⠀⠀⣼⣿⣿⡿⠀⢰⣿⣿⡟⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿⠟⠀⠀⣼⣿⣿⡿⠁⢀⣿⣿⣿⠃⢀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡃⠀⣠⣾⣿⣿⡿⠁⢀⣾⣿⣿⠃⢠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣟⣀⣠⣿⣿⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠙⣆⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠉⠉⠛⠶⣤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡼⠁⠀⣈⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣸⠴⢒⣾⣷⢴⡏⠁⠀⠘⠛
⠀⠀⠀⠀⠀⠀⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣠⠋⠀⡜⠁⢀⠈⢳⣈⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢄⡈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⠀⠀⢄⠻⠿⠃⡜⣀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠲⠄⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠑⠒⠉⠐⠭⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠾⣿⣷⣍⠉⠉⠻⣿⣯⠱⣄⠀⠐⢦⣀⣀⣀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⠀⠀⠈⢿⣿⣦⠀⠀⠙⣿⣧⠈⢳⡦⠤⠭⠥⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⢻⣿⣇⠀⠀⢹⣿⠀⡼⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠈⣿⣿⠀⠀⢸⣿⢟⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⢿⣿⣿⣷⠀⠀⣿⣿⣀⣤⠞⢁⣼⠇⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠛⠛⢩⡿⠁⣾⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠟⢠⣾⠃

⡄⠽⣰⡶⣶⡀⠀⠀⠀⣰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⠧⠰⢡⣶⠿⣦⠀⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡘
⠀⠀⢻⣧⣼⠏⠀⠀⠀⢻⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡘⣿⣤⡟⠀⠀⠀⠘⠷⣿⠿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇
⠀⠀⢠⣥⠦⠀⠀⠀⠀⢠⡶⠲⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣶⡖⢀⠀⠀⠀⢀⠾⠂⢢⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁
⠀⠀⠋⠁⢀⢁⣴⣶⣄⢻⣆⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠈⡴⣶⣶⡙⣧⣤⡿⢡⣤⣦⡄
⠀⠀⠀⠁⠀⠸⣇⣡⡿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣾⠃⠀⠀⠀⢻⣧⡉⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣆⠁⡀⢸⢱⣤⣄⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⣰⣯⣤⣡
⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡀⣤⡀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠡⠷⠟⠛⢊⢉⣤⠤⠄⠰⠄⠤⠤⠤⡧
⠀⠀⠀⠀⠀⠻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢞⡽⣿⣧⣃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠄⡀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⢻⡿⣿⣿⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠡⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⣀⣀⣀⣀⣀⣀⣀⡀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⢰⣯⣅⡁⠀⠀⢷⠀⠀⠀⠀⠀⠉⠉⠛⠒⠦⣄⡀⠤⠀⠐⠊⠉⠐⢲⡆⠀⠀⠀⠀⠀⠀⠀⢄⣽⢏⣯⠉⠉⠉⠁⠀⠀⠁⠈⢻⡇
⠀⠀⠀⠀⠀⠀⣸⠏⠙⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠄⠀⠀⠀⡐⠞⠃⠀⠀⠀⠠⠄⠴⡸⣟⠁⠀⠀⠀⠀⠀⠀⠀⣀⢾⠃
⠀⠀⠀⠀⠀⡌⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡴⠀⠄⠀⠀⠀⢄⠀⠈⠁⢀⡀⠀⠀⠀⠂⠀⠀⠀⠙⠫⠅⠈⠠⣬⣈⡁⠁⠉⠁
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠈⣁⠀⠀⠀⠬⣯⠖⡀⠀⠀⠀⠀⠄⠀⢰⣾⠖⠻⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⣔⡂⣹⠶⠀⠰⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢠⣾⣷⣇⣠⠄
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠉⢯⣴⠊⣿⠀⠀⠀⠂⠚⢻⣄⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠋⠁⠀⠀⠀⠠⠀⡀⢸⢀⠄⠀⠀⠀⠐⠚⣿⣿⡿⢿⡶⠶⠖
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠁⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠂⠀⠀⠀⠠⠀⢹⣏⣿⠉⠀⠀⠀⠀⠒⢁⡟⡷⣚⡵⡆
⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⣄⠇⠀⠀⠀⠀⠚⠀⠀⠀⠁⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠜⠘⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠹⠪⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣄⣠⠞⠁⠀⠀⠉⢷⣀⣀⣴⡋⠉⠉⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡼⠁⠀⠀⠀⢀⡴⠞⠉⠁⠈⠙⢦⡀⠀⠀⠙⢦
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣠⡴⠚⠛⠳⣦⣼⠷⠒⠶⠦⣤⡞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣠⡤⠼⢧⡀
⠀⠀⣴⠋⣩⣯⣍⣻⢦⣴⠋⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠙⣆⠀⢀⣀⣀⡀
⠀⠈⣏⠓⣧⠀⢀⣉⣻⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠴⠚⠛⠛⠛⠛⢦⡀⠀⠀⢹⡶⣯⡽⢥⣽⡆
⠀⠀⠈⠳⣍⣻⡟⠛⢻⣦⣀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⣿⣷⣤⢾⣴⠃
⠀⠀⠀⠀⠈⠹⡗⠾⣭⣀⣉⠽⠟⠒⠶⢾⣧⣤⣤⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⡤⢴⡶⠶⠚⡿⠛⢻⠇⢀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢻⡚⠶⠤⢉⡛⠶⠶⢾⣥⣄⣠⣔⣋⣁⣀⣴⣊⣁⣈⡴⠊⠁⣀⣔⣁⣀⣠⣮⣤⡤⠾⠚⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠐⠶⢬⠍⠛⠛⠀⠲⠤⢭⡍⢉⣭⣍⣉⠉⢩⣉⣉⣙⠉⠉⣭⣭⣭⠤⠀⠰⠶⠚⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⣤⣀⣈⠙⠛⠂⠀⠲⠶⠤⠄⠀⠴⠦⠤⠄⠀⠠⠤⠤⠄⠀⠠⠶⠶⠚⢋⣁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⢦⠈⢉⣀⡐⠒⠶⠶⠀⠐⠲⠶⠶⠀⠶⠶⠶⠶⠀⠀⠶⠶⠶⠆⠀⠋⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠲⠤⣬⠉⣛⠁⠘⠓⠒⠒⠀⠐⠒⠒⠒⠀⠐⠒⠒⠒⠀⢐⡒⠚⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣉⣛⣓⠀⠀⠛⠒⠒⠂⠘⠓⠒⠒⠂⠀⣉⣉⣭⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣿⣿⢻⢿⢛⠿⡿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡴⠶⠶⢦⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠈⠉⠙⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⣴⠟⠙⠀⠀⠀⠀⠋⠻⣦⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠋⠉⠁⠀⠀⠀⠈⠉⠳⣦
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇⡀⡀⣀⣀⣀⣀⣀⣀⡀⢀⣸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡟⠉⠉⠉⠉⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣤⣤⣤⣶⠶⠟⠛⠉⠁⣰⣿⣤⣤⣤⣤⣤⣤⣿⣆⠈⠉⠛⠻⢶⣶⣤⣤⣤⣀⣀⣀⣀⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⠀⠀⠀⠀⠀⣰⣿⡿⡿⠿⠿⠿⠿⠿⢿⣿⣆⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣠⡴⠋⠸⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡏⠙⢦⣄⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢶⡶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠛⠛⠛⠛⠛⠛⠲⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣷⣴⣚⢿⣿⣿⣷⣶⣤⣴⢶⣖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣷⠝⣿⣿⣿⣿⣿⡎⣿⣷⣶⣶⣦⠤⣤⣀⣀⠀⠀⠀⣀⡼⠁
⠀⢀⣀⣀⡀⠀⠀⣀⣤⣶⣾⣷⣶⣍⢻⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣦⠈⠉⠙⠛⠛⠉
⠛⢋⣭⠭⠟⢳⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢸⣿⣿⣿⣯⣿⡸⣿⣿⣿⣿⣿⣿⣷⡄
⠐⠋⠀⠀⣰⣿⣿⣿⠿⠋⠑⣿⣿⣿⣿⣿⣿⣿⣿⣟⣈⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢷⣮⣟⢿⣿⣿⣿⣿⣿⢘⣛⣛⠿⠿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣧⠀⠀⠀⣀⣼⣿⣿⡿⣫⣿⣿⣿⣿⢼⠿⠟⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⣷⣮⡙⢿⣿
⠀⠀⠀⠀⠸⣿⣧⣴⣾⡿⠿⠛⠉⠀⠻⣿⠿⣫⡴⣾⣿⢹⣿⣿⣿⡟⣡⣮⣭⣝⡻⢿⣿⣿⣿⣦⡙
⠀⠀⠀⠀⠀⠙⢿⡏⠁⠀⠀⠀⠀⠀⠀⣡⣾⣿⣯⣻⢿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣮⣭⣛⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣮⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣌⡻⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠐⠒⠶⠶⠿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⣶⡶⡶⡶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣞⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠈⠙⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⡋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⠚⣿⣿⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠆⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠈⠚⠻⠟⠊⠀⠀⠀⣀⣤⣶⠿⠿⣶⣤⣀⠀⠀⠀⠙⠦⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠻⢛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⠃⢸⣇⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣤⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡄⣸⠇⢸⠏⢹⡏⠴⣷⣿⣿⣿⣷⣄⣄
⠀⠀⠀⠠⣼⡇⢻⡄⢹⡆⢸⡄⢲⣿⣿⣟⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠈⠻⠘⣿⢨⠷⠬⠷⠀⡟⠛⢿⡿⢿⣟⠈
⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠙⡆⠀⢁⠀⢋⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⢀⡀
⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠉⠀⠀⠀⠀⠀⡀⣸⣿⣿⣟⣿⣥⣤⠂⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣿⣿⣿⣿⣿⣿⣿⡏⢀⣼⡟⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠋⠻⡟⠋⢹⠙⠛⣿⣿⠿⠛⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣦⣄⠀⠀⠀⠀⠀⠈⠀⡝⠀⠀⠈⠀⠋⠀⢀⡴⢿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠏⠀⠰⣶⡶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡿⠟⢻⣻⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣖⣿⣿⡶⣾⣿⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣭⡛⠒⢛⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡴⢶⣌⠉⠛⢋⣡⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠳⣬⣙⣛⣩⠏⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⢬⡽⠆⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢀⣠⣀⣤⣤⣤⣄⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉⠠⠀⠀⠀⠀⢰⣆⡚⠩⠶⠀⠈⣁⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠚⠉⢀⠠⠀⢈⡠⠔⠊⣠⠀⠀⠀⠛⠁⢰⣶⡬⠽⠽⠃
⠀⠀⠀⠀⠀⠻⣿⣏⡿⠍⢻⣿⢛⡟⢛⠀⠀⠀⢀⣠⣴⡿⠛⠉⠿⣖⣁⡠⠴⠊⡁⠄⠂⠉⡀⠔⠀⢀⢤⡰⣤⠁⠀⣤⡌⢠⣐
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⣿⣟⡸⠛⠉⠀⠀⠀⠉⠉⠉⠀⠀⠡⠈⠙⣧⡤⠒⠁⢀⣤⠴⢻⠃⠀⠀⠉⢰⡳⠉⠡⣀⠉⠀⣶⠛
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠞⠋⠀⠀⣸⠀⠀⠀⠁⣭⡄⠰⠿⠃⢘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠈⠀⠀⠐⠟⠃⠀⠀⠐⠀⠀⠤⢤⣄⡀⠀⠀⢸⣆⡠⠶⠋⢹⡀⠀⠀⠀⠃⠀⡤⢠⡄⠁⠙⠻⠄
⠀⠀⠀⣠⡿⠶⠀⠀⠀⠙⠢⣀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠐⢾⡋⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣧⡄⠀⠘⡶⠤⢄⣀⣀⡀⠀⠀⠀⢺⠀⢀⣠⠶⢻⣖⣀⠀⠀⠀⠿⠀⡠⣶⣰⡆⢀⣠⡄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠃⠀⠈⣧⠀⠀⠀⠈⠉⠓⠂⠀⣾⡟⠋⠀⡀⢀⣇⠁⠀⠀⠀⠀⢰⡃⣭⣟⣽⣍⠀⠄
⠀⠀⠀⠀⠙⠷⣤⣤⡄⢀⡁⠀⠀⠈⢫⠁⠀⠀⠐⣛⣠⣀⢤⣤⣀⡀⠀⠀⢸⣷⢈⣼⣷⣼⡿⠀⠀⠀⠠⠀⢀⡶⠟⢻⣿⣿⣵⣄⡀
⠀⠀⠀⣼⠶⠶⠿⡟⠉⠉⣧⠀⠀⠀⠸⠀⠀⠀⠈⣿⣿⢿⢿⣾⣭⣍⣒⠶⠾⣿⡿⣿⣿⣿⡅⠀⣠⣾⠷⠁⣿⣷⣶⣿⣿⣿⣷⡇⠉
⠀⠀⠀⣧⣉⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⣀⡄⠀⠀⠉⠹⠿⠋⠠⢿⡿⣿⣷⢶⣿⣿⣷⡿⠋⠀⠀⠙⠛⠖⢠⡟⠻⣿⣿⣿⣟⡉
⠀⠀⠀⠈⠻⠷⢦⣤⠤⠚⠁⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠊⠉⡁⠀⣀⡀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⡉⠀⠀⠀⢙⣷⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠖⠃
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣀⡽⠖⠊⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠢⣄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠘⢦⣀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣠⣤⣴⣶⣾⡿⠟⠁⠀⠀⠀⠀⠸⡏⠠⠀⠀⠀⠀⠤⢤⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣀⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣤⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀⢀⣰⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠴⠯⡽⠚⠳⠋⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢧⢀⣼⡇⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠛⡟⠘⢿⠛⠓⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠁⠀⠀⣥⣾⡿⠁⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣠⣬⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⣀⣀⣤⣤⣴⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠦⠤⢤⣠⣶⡿⠷⢤⡷⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡋⣁⡀⠀⢀⠀⠀⢻⣦⣾⣧⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⣒⣒⠛⢛⣋⡉⠭⢨⣟⢲⣿⡟⣿⡞⠋⠙⣷⠼⣿⣿⠟⣿⣦⠟⠉⠛⠛⠒⠶⠶⠶⠴⠖⢤⣄
⠀⠀⠀⠀⢀⡤⠒⡡⠊⠉⢑⠀⠠⡔⠀⠈⠁⠀⠛⠉⢀⣤⡾⠉⠾⣿⡿⣿⣶⣾⣿⣿⣷⠈⠿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⣠⣴⠞⢉⡞⣰⣇⠈⣿⣧⣙⢿⡿⣿⣿⡋⠀⠀⠘⡇
⠀⠀⠀⠀⠁⠀⠄⠀⠀⣀⣀⣀⣀⣠⠴⠺⢿⡿⠃⢠⣾⠅⢿⣿⣶⡍⠛⠿⣿⡞⠲⡏⠀⠀⣾⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⢿⣿⣄⠈⠣⠴⠛⢿⣦⠘⣿⣿⣏⣀⣀⣼⣷⠚⠉⣀⠞⠙⠛⢭⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣡⡀⠘⢿⣿⡀⠀⠀⢀⣼⡿⠷⢟⣿⢟⣟⠟⡼⣿⡷⠊⠁⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⢀⣠⠿⡭⠭⣯⡈⢿⣿⣷⡀⠙⢿⣦⠀⠘⣿⣀⡰⠋⢡⣾⣧⣾⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠋⠁⠀⠀⣬⣿⣿⡌⠻⣿⣷⡀⠘⣿⣿⡶⠋⢘⢷⣴⠟⠁⠽⠁⣿⠻⣟⡒⢢⣄⡀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡿⣿⣄⠙⣿⣿⣦⣘⡿⠅⠀⠉⠛⢳⣄⡔⠰⣺⠇⠀⠈⠻⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣌⢿⣷⣌⣿⣿⣿⠀⠀⠀⢀⡔⢣⠋⠀⢠⡏⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠉⠉⠉⣠⡏⠀⠠⠖⠉⢀⠄⠁⠶⡞⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⠀⠤⠐⠁⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠈⣀⠖⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠦⣠⠾⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠑⠀⠉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠃⠀⠀⠈⠐⠐⣠⠈⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠀⠒⠰⠤⠒⠉⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠡⠆⠠⠌⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡺⣿⠕⠁⠀⠀⠀⠀⣀⣔⣤⣂⣠⢄⡤⢒⣈⡩⠤⣔⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⣿⠿⣶⣄⠀⣀⣔⣮⣷⠿⢶⣀⡤⠝⠫⠤⠤⠜⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣴⣿⢿⡿⣿⣿⣿⣿⣿⡿⣟⡿⠿⣿⣭⣶⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠨⣼⣿⣿⣿⣿⡵⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⢻⣷⣶⢀
⠀⠀⠀⠀⠀⠀⢸⡟⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠃⣼⣿⠟⢰⣷⡀
⠠⠄⠒⡨⠑⠓⢾⡇⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠐⡂⠀⠛⠃⢠⣿⣿⡿⣦
⠀⢠⠎⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣻⣿⣿⣿⣿⣿⣿⣾⣿⡶⢀⡀⠈⠙⠟⣹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠋⣁⣩⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣿⠟⠛⠋⠙⠛⢻⣿⣿⣌⠛⠛⢻⣿⣿⣿⣿⣿⣿⣶⣿⡿⢛⣩⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⠀⠀⠀⠀⠀⣾⣿⠛⢿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢻⣆⠀⠀⠀⣠⣿⠏⠀⠘⠛⠷⠄⣽⣿⡈⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠈⢿⡄⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠈⠙⠿⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠼⠋
⣿⣿⠛⢿⢻⠿⡿⢻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣉⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⣀⡠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⠈⠓⢄⠀⠀⠀⠀⢀⡀⠀⠀⢠⢀⡠⠀⠀⠀⠀⡠⠊⠀⠀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣀⡀⠀⠙⠲⣄⠀⠀⠱⡄⠀⢀⣀⡽⠿⠽⠺⠿⠤⣤⣀⡀⡜⠁⠀⣠⠞⠁⢀⣤⠶⠚⠛⠛⠲⣤⡀
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠛⢶⣄⠀⠈⠳⣄⣠⣽⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡞⠁⣠⡶⠋⠁⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣠⡾⠋⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠈⢿⣄⠀⠀⡐⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⢦⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡜⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢄⠀⠀⠳⣼⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⣿⠀⢠⠎⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠑⢄⡀⣸⡇⠀⠀⣴⣿⡿⠛⠙⢲⡀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠛⢦⠀⠀⢹⡖⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠙⢿⡇⠀⢸⣿⣿⣧⡀⢀⣸⣷⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⢀⣼⡇⠀⣸⠇⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢄⡀⠸⣧⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⢀⣿⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⡳⠿⣦⠀⠈⠚⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠚⠿⠟⠋⠁⢀⣾⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢽⣷⣄⠀⠀⠀⠀⠀⠀⠠⢤⣠⠤⠖⠀⠀⠀⠀⠀⢀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣄⣀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣨⣿⢻⠟⠒⠒⠒⠒⠺⡟⣿⣥⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⣾⡟⣷⢃⡟⠀⠀⠀⠀⠀⠀⢷⡸⡿⣟⠳⣽⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡡⠞⠁⣿⢳⡏⣸⠋⠒⠤⠤⠤⠔⠚⢹⡇⢿⣿⠀⠈⠑⢦⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠹⣿⢁⣟⡑⠢⠤⠤⠤⠤⠔⠚⣇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢾⡷⢍⣓⠲⠦⠤⢶⣶⠟⣿⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡼⠀⠀⠉⠙⠛⠛⠉⠀⠀⢹⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⠡⢐⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢂⠡⣐⠈⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⡡⢔⡪⢶⡿⠃⡠⠂
⠀⠀⠀⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⡡⢔⡪⠕⠈⠁⡰⠋⡠⠊
⠀⠀⢀⠔⠁⠀⠀⠀⢰⠀⠀⠀⠀⡀⠄⠂⡁⢄⡢⠕⠊⠁⡀⠄⡒⠋⠁⠉⠑⢄
⠀⢠⠁⠀⠀⠀⠀⠀⡆⢁⡠⠒⡁⠄⡂⠅⠂⠁⣀⠤⠒⢁⠠⠎⠀⠀⠀⠀⠀⠀⠱⣄⡀⠀⣀⡀
⠀⠸⠀⠀⠀⠀⠀⠀⡰⠋⡠⠊⠂⠁⣀⠤⡒⠋⠀⠀⠚⢅⡀⠀⠁⠀⠀⠀⠀⠀⠀⡱⠊⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠠⠐⠉⢀⠄⠀⠀⠀⠀⠀⠀⠡⡀⠂⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠄⠀⢀⠈⡠⠊⢀⠀⠒⠀⠐⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠔⠊⠁⠐⠢⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠂⢄
⠀⠀⣇⠔⡡⠊⠀⡠⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢄⠀⠂⠀⠀⠀⠀⠀⡠⠃⠀⡠⡾
⠀⡔⡡⢊⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣤⠵⠒⠐⠢⢴⠂⠐⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠐⠂⢉⢤⡢⠵⠈
⠀⢸⡋⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠠⡐⠌⠂⠁
⠀⠈⠢⢕⡢⢀⠀⠢⠤⣎⣀⣀⡀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢛⠒⠲⠤⠀⠒⠈⡀⢄⠢⠕⠋⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢹⠲⠭⠠⠥⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠠⡒⠕⠊⠁⠰⠀⢀⠤⠤⠤⠾⣀
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠑⠠⣄⠀⠀⠢⢄⣀⡀⢀⣀⠠⠔⡩⢔⠪⠆⠁⠀⠀⠀⢀⠜⠈⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠯⢔⠤⣀⠀⠀⢀⠤⡢⠕⠈⠀⢸⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⡀⠈⠐⠭⠍⠂⠁⠀⠀⠀⠀⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⣀⣀⣀⠠⠳⠄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣀⣀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠄⠀⠀⢀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⣀⡀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠁⠂⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⢣⡁
⠀⠀⠀⠀⠀⢀⠀⠘⢧⡀
⠀⠀⠀⢃⣼⠋⣴⠗⢠⣌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠸⢃⣾⠋⣰⣿⣿⣿⠀⣀⣰⠚⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣷⡆
⠀⡀⣀⣤⣈⠁⢼⣿⣿⣿⣿⣿⣿⣿⢴⠀⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⠀⠛⠉⠁⢿⣿⣿⣿⣶⣆⠀⠀⠀⢀⣘⠿⣿⣿⣿⣿⡿⢟⣻⢿⣿⣿⣿⣿⠿⣃⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠩⠇⠒⠛⠁⠀⣤⣶⣿⣿⣿⣾⣝⢛⣽⣾⣿⣿⣷⣮⣟⣫⣵⣿⣿⣿⣷⣤⡀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⣄⠀⢀⣠⣴⣿⣶⣽⡻⠿⢟⣭⣶⣿⣮⣝⡿⠿⣛⣵⣾⣷⣯⣛⠿⢟⣫⣷⣿⣶⣝⡻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⣻⣵⣯⣻⢿⣿⣿⢿⣫⣷⣝⡻⣿⣿⡿⣟⣭⣮⣟⠿⣿⣿⠿⣻⣵⣭⣻⢿⣿⡿⢟⣫⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⡎⣾⣿⣿⣿⣿⣿⣷⢵⣾⣿⣿⣿⣿⣿⣮⣴⣿⣿⣿⣿⣿⣷⡎⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢿⣃⡻⢿⣿⣿⣿⣿⢟⣙⡿⣿⣿⣿⣿⡿⣟⣛⢿⣿⣿⣿⣿⠿⠃⠻⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣯⣶⣿⣿⣿⣷⣯⢛⣽⣾⣿⣿⣿⣶⣝⢫⣵⣿⣿⣿⣿⣮⡝⠋⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠈⠙⠻⠟⠋⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢤⡀⢰⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⣂⠴⠚⠁
⠀⠀⢧⠀⠈⢦⣧⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣹⣶⣿⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣯⠠⠈
⠀⠀⠀⠙⠲⢄⣳⡍⢇⣀⠀⠀⠀⠀⡤⣊⡵⢆⠜⣷⠶⣿⠦⡱⢮⣑⢤⠀⠀⠀⠀⢾⣿⢀⡍⡔⣇⣦⡀
⠀⠀⠀⢠⣾⣇⡮⠇⠘⠟⠀⠀⠀⠈⠉⠛⠚⠁⠀⢘⡿⠍⠀⠈⠓⠛⠉⠁⠀⠀⠀⠠⠂⠈⡀⠸⡙⢟⠇
⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠨⠁⠂⠄⠀⣰⣆⠀⠠⠐⠈⡅⠀⠀⠤⣄⣀⡀⣠⠶⣤⢀⣀⣀⠤⠤⡀⢀⠤⠤⠄⣀⢠⣶⣄⢀⠀⠤⠤⣄
⠀⠀⠹⠛⠓⢿⠷⠾⡿⠚⠛⠏⠀⠀⠀⠀⠀⠀⠀⣽⠒⣿⠀⠀⡀⠄⠀⠀⠈⠒⠶⡒⣨⢿⠿⢿⢭⡐⡲⠖⠊
⠀⠀⠀⠀⠀⠈⢽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠉⠳⣄⢰⣄⡠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⢠⢢⢀⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡱⡎⠀⣀⣀⣀
⠀⠀⠈⠓⠒⠂⣡⣈⠒⠒⠚⠁⠀⠀⠀⠀⣏⠀⢀⣨⠞⠉⠀⠀⡷⠀⠀⠀⠀⠘⠤⣄⢈⣁⡷⢞⣉⠀⣤⠔⠁
⠀⠀⠀⠀⠀⠘⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⡝⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣯⣵⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠐⠲⣕⣦⡔⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡔⠉
⠀⠀⠀⠓⢒⣾⣿⣿⣶⡒⠚⠀⠀⠀⠀⠀⠀⣀⠴⣞⣙⣳⠤⡀⠀⠀⠀⠀⠀⠀⠂⠉⣩⣤⡼⣦⣬⣉⠁⠂
⠀⠀⠀⠚⠁⠐⣟⡿⠀⠉⠂⠀⠀⠀⠀⢀⠜⠁⡠⢧⠀⡼⣄⠈⢢⡀⠀⠀⠀⠀⠲⠟⠋⠐⣛⡛⠈⠛⠷⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠉⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢤⣀⣠⣄⣀⣄⡀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣶⠙⠛⠿⠿⠿⠛⣯⡄⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⣀⣀⣄⣀⣄⣀⡹⠇⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠖⠒⢲⣤⡎⢩⡬⠿⠰⢼⣼⣭⣽⡆⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠙⡧⠟⠀⠃⠨⣤⠉⡤⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣼⡇⠀⡶⠂⠀⠠⡎⠿⣁⡆⠄⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⢨⡷⣞⣷⢧⠘⢃⡋⠀⠀⠠⢀⠜⠁⣸⣿⡟⠓⣤⡾⠉⠒⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠈⣿⡜⡿⢆⠈⢹⣿⣿⣿⣟⠀⢠⠟⠉⠀⣜⡧⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⠀⠀⠰⣷⡾⣤⠁⠈⠋⠃⠀⡠⣛⣶⣿⠿⠋⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠃⠀⢀⠃⠘⠓⣛⣂⣤⣴⣴⡞⠛⠉⠀⢸⠀⡀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠤⠀⠘⠀⠀⠀⠀⡌⢀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣦⡄⠀⡇⠸⠀⠈⠃⠀⠐⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⡘⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣾⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠀⠁⠐⢸⣿⢿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⢿⣿⣄⠀⠀⠈⠣⡀⠀⠈⠃⠀⠹⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠟⠁⢸⡋⠙⠛⠙⠛⠟⠛⠿⠻⠿⠿⢿⢻⣟⠀⠙⢿⡄⠀⠀⠀⠑⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠤⠀⠀⣰⣿⠀⠀⢈⠉⠁⠈⠉⠉⠁⠀⠚⠒⠒⠊⠉⠉⡏⠀⢠⣿⠓⢄⠘⠆⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠠⠊⠀⢻⣧⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠃⠀⢸⡟⠀⠀⠉⠒⠤⢀⣁⣀⣀⠀⢀⣨
⠀⠀⠀⠀⠀⠹⠇⠤⠤⠄⠒⠉⠀⠀⠀⠀⠈⣿⠂⠘⣿⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿⣿⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⠓⠓⠿⠿⠿⠿⠿⠿⠛⠋⢹⠃⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣤⣴⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⢀⣠⣤⣶⣶⡾⠿⠛⠓
⢰⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⢀⣴⣾⠿⠛⠋⠉
⣼⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻⣀⣀⡀⠀⠀⠀⢠⡟⠁⠀⢠⡾⠟⠉
⣿⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡴⠋⠉⠉⠉⠓⠒⠒⠿⠶⠶⣴⣏⡀⠀⣀⡀
⣿⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠁⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠈⠙⠚⠉⠉⣇
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣠⠟⠀⠀⣼⡟⠁⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢰⣿⡗
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠘⡇⢰⠇⠀⠀⠀⠸⣇⠀⠀⠀⠠⣿⣿⣷⣄⠀⠀⠀⠀⠈⣿⣇⠈⠄
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠙⠦⣄⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠙⢿⣶⣷⣶⣿⣿⣿⣿⣧⠀⢠⠀⠀⢻⣿⣷⣬
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠉⠳⣤⣠⠴⠟⠓⠛⠒⠾⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⠈⡇⠀⠀⠻⣿⡿
⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠃⠀⠇⠀⠀⠀⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⡔⠀⠀⣠⣤⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀
⠀⣶⠶⠦⠤⢤⣄⣀⣀⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢰⡏⠀⠈⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠘⣧⠀⠀⠀⠀⠀⠀⣈⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⣧⠴⠶⠚⠛⢋⣉⡉⠉⠳⣦⣤⣤⡶⡇
⠀⠀⠈⠳⣄⠀⣠⡾⠛⠉⠁⠀⠀⠀⢠⣤⡶⠾⣇⡀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠶⠶⠚⠛⠉⠉⠙⠳⢤⠆⠀⠀⢸⡇
⠀⠀⠀⠀⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠋⠙⠓⠶⣤⣠⣾⣿⡷⠖⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡟⠀⠀⣀⡤⣤⣀
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⣀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⣼⣤⠞⢡⡶⠋⠉⢀⣠⠼⠷⣄
⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠳⣦⠀⣹⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⡼⠋⠘⢧⣿⠀⠀⣴⠋⢰⠎⠀⠈⢷
⠀⠀⠀⠀⠈⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠒⠒⠒⠚⠳⠤⢤⡤⠶⠚⠛⠢⠀⠀⠘⣯⢀⡴⠛⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠈⠳⢤⡀⢀⡾⠉⠀⠀⠙⢲⣶⠶⣞⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⠀⠎⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢻⣿⣦⣄⣀⣀⠀⠀⣠⡟⢉⠀⠀⠀⣠⣶⠛⠁⠀⠘⢶⣄⣀⣀⣀⣀⣀⣠⠏⠉⠉⠀⠠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠘⢿⣿⣿⣿⣭⣉⣉⣉⣉⣉⣩⣴⣿⣿⢿⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠞⠳⠦⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋⠁⢀⣾⣿⡏⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟⠁⢠⣿⣿⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣾⣿⡿⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠉⠛⠻⠿⠿⣿⡿⠿⠟⠛⠁⠀⠀⣠⣿⣿⣿⠃⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠃⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣤⣤⣶⣿⣿⣿⡿⠟⠁⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣠⣴⡿⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣄⣀⣀⣀⣤⣤⣶⣿⣿⣯⣄⣀⣈⣻⣷⣄
⣶⣴⣶⣦⣶⣶⣴⣦⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣤⣴⣶⣤⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⠋⣉⣻⡋⣹⢛⢻⡝⢋⣿⠟⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣤⣤⣤⣠⣤⣤⣤⣄⣀⣤⢤⣄
⠀⡀⠀⠀⣥⣘⠁⡘⠚⠹⠇⢀⢨⣿⣿⣿⡟⠉⠛⢿⣿⣿⡋⠉⠋⢝⣦⡉⠉⠑⣆⣀⡀
⠀⣄⢚⣹⣼⣿⣌⠜⠂⢠⡆⣌⢫⣽⠧⢬⣁⡀⠀⠈⠓⠻⣷⣀⠀⠉⢛⢿⡍⠀⠈⠉⠁⠠⡀
⠩⡋⢿⣿⣇⣹⣷⣄⣁⡬⣿⢬⣿⡟⠟⡃⢁⡠⠀⢢⡀⠀⠘⣿⣷⣤⡀⡀⠘⣆⠀⠀⠀⠄⢌⠠⠠⠀⡀
⢰⣿⣢⣌⣉⢃⠁⢠⡄⢖⡝⢈⣷⣿⣶⣴⣮⣿⣷⣾⣿⣾⣷⣾⣿⣿⣿⣿⠿⠿⣶⣷⡶⠲⠛⠃⣠⡂⠀⢀⡀
⠀⢿⡟⢋⠿⣟⣠⣤⣬⣿⡿⠈⠿⣿⣿⢇⠁⠁⠀⠀⠀⠨⣿⣿⡿⠃⠀⠀⠀⠀⠸⣿⡇⢸⣇⢰⣧⣀⡖⠁
⠠⠟⠃⠀⠞⡯⣴⠿⣿⢿⡗⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡋⠀⠀⠀⠀⠀⠀⢹⡇⢸⣿⠛⣠⣭⠁⠀⢀
⢸⡆⢂⡀⢼⣽⠓⠠⣿⣻⡟⠀⢸⣿⣿⣇⣀⠀⣀⣬⣀⣀⣰⣯⣀⣀⣀⢀⣄⣀⣀⠾⠇⢾⣧⡻⠇⣾⠂⣠⢛
⣸⣯⢼⣟⣿⣿⣇⣿⢿⡟⡗⠀⣬⣤⣬⣽⣿⣶⣿⣶⣿⣿⣶⣿⣿⣾⣶⣶⣶⣶⡾⢿⠧⢸⣯⣽⣤⣧⣯⣭⡮⡂⠠
⣶⣶⣧⣿⣿⣌⡏⠝⠀⢻⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷⠤⡤⠀⢿⣩⣋⣽⣯⢹⣯⣛⢡⣤⣂⠔
⡸⢴⣾⣿⡿⠷⡶⣦⣹⣦⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠨⠊⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣠⣠⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⣠⡀⠀⢀⣴⠿⡍⠈⠁⣽⢻⣦⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠸⣿⣿⣿⡀⢀⣿⣿⡿⢀⣠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⠿⠛⠛⠿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡞⠀⠀⠀⠀⠲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣾⣿⡁⠀⠀⠀⠀⣠⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣩⠟⠛⡛⣻⣿⣴⢤⣄⣶⢿⣟⠛⠛⢿⡛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⣠⠾⠃⠀⣶⢿⣟⣁⠀⠀⣈⣀⣼⣿⣿⣦⠈⠳⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠠⣿⣸⠿⢿⣿⣿⣿⣿⡿⠟⡏⢹⡆⠀⠙⢦⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⠀⠀⠀⣸⡟⢹⣶⣦⣤⣤⣤⣤⣶⣿⣷⠘⣿⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡾⠛⠁⠸⣬⣉⣉⣉⣉⣩⣭⣭⡏⢀⠘⠿⣆⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⢫⣽⣛⣛⣛⣫⣭⣽⠁⠀⠓⠀⠈⠳⣦⡀⠀⠁
⠀⠀⠀⠀⢰⣇⣀⣀⠦⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⠛⣛⣛⣻⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⠀⠀⠀⢀⡊⠀⠀⠀⠀⠆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠁⢣⢭⣥⡤⠤⠶⠧⠅⡐⠔⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡔⠋⠀⠀⠓⣠⠀⠀⡀⢂⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⡄⢠⡶⠒⡦⠄
⢀⡄⠀⠀⠀⠐⠲⣤⠀⠀⠀⠀⢀⣯⡉⠁⠀⣀⣈⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢏⠓⠠⠀⠀⠀⢤⡾
⠈⡉⠖⠒⠒⠰⠶⠀⠀⠀⠀⠀⢸⢄⡀⠀⢸⣿⢻⣇⠠⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⠠⠀⠀⡀⢠⠄⢤⣶⡄
⠀⠢⠤⠦⠦⠴⠤⠂⠀⠀⠀⠀⠘⣦⠀⠀⠀⠉⠁⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠛⠀⠀⠀⠂⠈⠀⠘⠛⢣
⡀⢀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠳⢦⡀⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢏⠁⠀⠀⠀⠀⠠⠈⢩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⡧⠤⡏⠀⠡⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⡀⠀⠀⠀⠀⠀⠀⠓⠘⣄⣀⡘⠒⢃⠀⠀⢀⡔⠉⢁⠀⣤⣀⡀⠀⢀⣀⠀⣀⢀⣄⡬
⠀⠀⠀⠀⡀⠁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠸⠀⠐⠁⠀⠈⠀⡈⠀⠀⢸⠀⠀⣸⠀⢙⡛⠃⠀⠀⠊⠀⠃⠈⣋⠃
⠀⠀⠀⠉⠡⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠛⠃⠀⠀⠀⠀⠈⠀⠶⠃⠀⠀⠛⠻⠤⠦⠤⠼⠇⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣹⣿⣿⣱⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡟⢿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⣿⣿⣿⣿⣤⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣏⣹⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣉⣿⣿⣻⠟⠁⠀⠀⠀⠀⠀⠙⣯⣯⣽⣭⣯⡝⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣟⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⣤⣼⣿⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣯⣟⣿⢿⣾⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣟⡿⣿⢷⣷⡇⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣶⣿⣿⣾⣿⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠻⣿⢉⣿⣿⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⣰⠁⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⠓⢴⠁⠀⠀⠋⠈⡇⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⢱⠀⠀⠀⠈⡃⣠⠶⣀⡜⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠸⠇⠀⠀⠀⠒⠧⣄⢸⠀⠀⠀⠀⠀⠀⠐⠁⢀⡴⠁⠀⡰⠁⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠴⢆⣀⣔⢦⠀⠀⠈⢦⡀⠀⠀⠀⠀⠌⢀⡴⠋⠀⠀⠀⠠⠄⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡅⡀⠈⡀⠨⠈⠀⠀⠀⠈⡇⠀⠀⢀⢊⡼⠁⠐⠒⠀⣈⡡⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠑⠣⠥⠜⠀⠀⢰⠆⢠⠙⡄⠠⠂⡾⠐⠈⠉⠉⡩⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠒⠂⠀⠀⢀⠔⡩⣠⡃⠀⠈⠀⠊⠀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣤⣴⣶⣿⣿⠟⣿⣿⣯⠙⢿⣿⣿⣷⣆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⠟⠁⠄⢸⣿⣿⡆⠀⠹⣿⣿⣿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠉⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⢀⣠⣿⠀⣿⣿⣿⣄⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠊⣀⡱⠀⠀⡠⠘⢿⡤⣟⠛⡓⢌⠑⠠⣖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⡄⠙⡄⠀⠀⠑⠲⠀⠀⣘⡠⠼⣦⠿⠭⡊⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠰⣉⣀⡠⠗⢹⡇⠀⢃⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⠒⠒⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣄⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠔⠂
⠀⢀⡀⠤⠀⠠⠤⠄⢀⡀⠀⠀⠀⠀⠈⢳⣦⠰⣾⣿⣿⣿⣿⡿⢠⣶⠋⠀⠀⠀⠀⠀⣀⠀⠤⠤⠀⢤⠄⣀
⠀⠯⣀⠀⣈⢡⡉⠭⠤⢪⠭⢔⠂⠤⢀⣀⠙⢷⡾⠁⠀⠹⣿⣶⠟⢁⣀⠠⠄⢒⠌⢭⠢⠤⠍⢱⢉⡀⢀⡨⠇
⠀⠀⠀⠢⢄⡀⠵⠒⠒⣐⠍⣉⣈⣁⠛⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⡟⢃⣉⣈⡉⠕⡐⠒⠲⠅⣀⠠⠂
⠀⠀⠀⠀⠀⠑⠲⠂⡥⠀⢚⡔⠒⡲⠟⢭⡿⠿⣿⣶⣄⣿⣿⡿⠿⣯⠝⠷⡒⠒⣜⠂⠠⡅⠲⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⢋⣲⣬⠷⢶⣿⣿⡿⠿⣿⣿⣿⣿⠶⢮⣴⣊⠓⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠲⠟⠋⠁⣰⣻⣾⠿⣷⣶⣿⣿⡿⣾⣳⡀⠉⠛⠳⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣏⡀⠀⠀⢻⣿⣷⡇⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣟⠛⠿⠿⢿⣿⡟⡇⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⠛⠷⠶⢿⣿⣟⠇⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠘⣟⣒⣒⣿⣿⡟⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠽⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠣⡀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠂⡑⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠈⠻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡛⠲⣄⣤⠀⠀⠀⠀⠘⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡑⠦⣠⠙⠆⠀⠀⠀⠀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡓⠚⠷⣆⡀⠀⠀⠀⠀⠀⢸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡤⠤⠉⠀⠀⢀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠰⣄⠃⠀⠄⠀⢻⡆
⠀⢀⣠⣴⠶⠿⠿⠏⠭⠭⠙⠻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠁⠈⠂⠀⠀⢠⠈⣿
⣴⢟⡛⢗⡛⠿⣁⠂⠂⠀⠀⣀⣀⠀⠀⠉⠙⠲⢦⣄⣀⣀⠀⠀⠈⢷⣄⠀⢀⣲⣤⣮⣧⣼⣧⣤⣀
⠙⠶⢭⣽⣃⢷⡏⣭⣉⣐⠢⣄⣀⠐⠂⠀⠀⠀⠐⠬⡙⠿⣿⣷⣦⠀⣽⡷⠛⢣⠋⡀⠉⠩⡖⠩⢻⣿⡄⢀⣀⣤⣤⣀
⠀⠀⠀⠈⠉⠛⠿⠿⣿⣭⣽⣒⣮⣛⣶⣤⠀⠀⡀⠀⠀⠀⠀⠩⡿⢷⣿⣠⣶⣾⣿⣿⣿⣷⣷⡂⠀⢼⣿⡿⠛⠉⠉⠙⠻⣦⡀⠀⠀⣀⣠⣴⡶
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣤⣤⣤⣘⣶⢍⠛⠻⣿⣿⠿⠿⣿⣿⣿⣷⣿⣿⠇⢠⡶⠶⣄⠀⠙⣷⡠⢺⠗⠋⠉
⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⡇⠉⠁⣿⣿⣿⣿⢹⠋⠟⣹⣿⡏⠙⢿⣿⣿⣿⣿⣇⠀⢀⡀⠈⣉⣻⣯⢍⣿⡇⣿⡇⠀⠈⣧⢀⢸⣯⣴⢶⣄⣀
⠀⠀⢀⣴⣿⡿⠈⣿⣿⣿⣇⠀⠀⠸⣿⣿⣿⡇⠀⠀⢈⣿⣧⠀⠀⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠋⢱⣿⡄⣿⡅⠀⠀⣿⢨⣹⡟⠉⠀⠙⠢⢕⣂⣄
⠀⠀⣾⣿⣿⡕⠀⠘⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣆⢠⣤⣽⣿⣆⠀⡹⣿⡏⠠⠏⠘⢿⠉⠸⣍⠀⠀⢴⣿⡇⢸⣷⣆⣴⠇⢀⣿⠀⠀⠀⠀⠀⠀⠈⠈
⠀⣸⣟⢻⣽⣷⠀⠀⠘⢿⣿⣿⣦⡠⣔⣜⣿⣿⣿⣶⡛⠷⠿⣿⡷⠿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠀⢀⣾⣿⣿⣀⢉⠛⠁⠀⣸⡟
⠀⣿⣿⡎⢿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣾⣿⡿⢋⡵⢿⣿⣷⣦⣤⡴⣾⡏⠙⢻⣷⣼⣧⣶⡿⣿⣶⠿⠿⣿⢿⡛⠿⠿⠿⣤⣿⠇
⠀⣿⣿⣿⣄⠻⣿⣟⢦⡀⢠⣈⣻⣿⣿⠉⢠⡿⠀⣀⡀⠈⠁⠀⠀⢸⣧⠀⠈⣏⠛⠿⠿⢿⡿⡶⢶⣿⡇⠈⢷⠀⣀⠀⠙⠋
⠀⣿⢿⣿⣿⣦⡙⠿⣷⣿⣿⣿⡿⢿⣇⣠⠟⠁⠫⢝⣻⢷⣶⣄⡀⠀⣿⡆⣀⣿⠘⠷⣪⢴⡶⣶⡆⠸⣷⡀⠘⡇⠑⣪⠔⡊
⠀⢹⣄⣹⣿⣿⡿⠿⠿⢟⡿⢫⡴⠋⣽⠁⠀⠀⠭⢓⡪⢿⡿⠿⣛⡄⢸⣿⣾⠃⠀⠈⡀⠕⡋⢵⣺⣧⠹⣇⣀⣿⠀⢞⡭⣒⡡⢀⡀
⠀⠀⠉⠉⠉⠀⠀⣀⢀⣠⣴⠟⢀⡼⠁⠀⠀⠀⠀⢂⠩⠐⣂⠽⣿⠃⡾⠉⣿⠀⠀⠀⠂⠀⡪⠝⡫⠵⣦⡈⡇⢸⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡤⠾⣯⣈⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡼⢱⢀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠅⢧⣸⡇
⠀⠀⠀⠀⣴⣒⡿⠗⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣄
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⡀⠀⠀⣼⠃
⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⠉⠉⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠶⠶⠶⢦⣤⡀
⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⣠⠟⠁⠉⠀⠀⠀⠀⠉⠈⠻⣄⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣿⡟⠉⠉⠉⠉⢻⣿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⠾⠟⠛⠉⠁⣴⣯⣤⣤⣤⣤⣤⣤⣽⣦⠈⠉⠛⠻⠷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⡿⠛⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠙⠛⢿⣍⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣷⡀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣀⣴⠛⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠛⢦⣀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠛⠋⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠙⠛⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣿⣿⣿⣷⣷⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠉





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

⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⡠⢊⣭⣓⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⣶⡄⡠
⠀⠀⠀⠀⠀⡰⢫⣶⢷⣶⠰⣿⣿⣿⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠺⠹⣿⡿⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠹⣾⣿⣜⣟⠀⢙⡛⢛⡵⠃⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠤⣵⣯⡥⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠄⠀⠀⢘⣃⣾⣿⣇⡿⣿⡎⡇⠀⠀⠘⣷⣷⡎⣵⣿⡮⡃⠀⠀⠀⠉⢠⠞⣿⣒⣺⢲⠈⠁⠀⠀⠀⠀⢀⣤⠾⠟⠋
⠀⠀⠠⠔⢣⡿⣟⢯⠋⠷⣿⡿⢟⡱⠋⢀⢔⣥⣝⢁⣤⣍⡁⣨⣼⡢⠀⠀⠀⠋⠀⢻⣤⠇⠀⠑⠀⠀⢀⣤⠾⠋⠁
⠀⠀⠀⠀⢿⡬⠞⡁⠀⠀⠈⠉⠉⠀⠀⠰⡸⠟⠫⡘⠟⠋⢃⠿⡛⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⡿⠇⣾⣿⠷⠘⠀⠀⠀⠀⠀⣠⣄⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠤⠓⠒⠤⠑⠁⠀⠀⢠⣴⣿⣿⣿⣯⠀⠀⠀⠀⡉⠙⠛⠛⠛⠛⠛⠙⠆
⠀⠀⠀⠀⠀⠀⣀⣤⣶⠦⠴⠴⠶⠶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡿⠟⠋⠁⠀⠀⠀⣮⣀⣠⠉⠉⠉⢃⠀⠀⠱⡄
⠀⠀⢀⣠⣴⠾⣛⣽⣮⣗⢤⡀⢼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⠁
⠀⠀⠉⠙⡁⠈⠀⠀⠟⠉⠛⠋⠻⣿⣿⡿⠿⠿⠿⠛⠛⢛⠛⠁⠀⠀⢀⠀⣼⣤⣀⡀⠀⠀⠀⠀⠸⣧⠈⠙⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⠈⠉⠉⠉⠉⠒⠒⠂⠦⠐⠒⠊⠉⠉⠉⠉⠁⠀⠀⠀⠐⠻⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⢻⡆⠀⠈⠛⢿⣿⡿
⠀⠀⠀⠀⢸⠢⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⡛⠉⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⢤⣒⡢⠤⣖⣲⢄⢀⣴⡿⠂⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⢸⠉⠁⠒⠂⠀⠠⢄⣀⣀⣠⠤⠄⠐⠈⠁⠀⠂⠀⠀⠀⡠⢿⠿⠛⠸⡿⢟⡵⡛⠁⠀⠀⠀⠀⠀⣸⠿⠃⠿⠟⡇
⠀⠀⠀⠀⢸⠤⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⠤⠒⠃⠀⠀⣮⣾⣷⡌⡶⣳⠞⣿⣿⣮⠃⠀⠀⠀⠀⠀⠀⢰⡿⠷⠈
⠀⠀⠀⠀⢸⠀⠰⠾⣿⣿⡗⠒⠤⡤⠔⠊⠉⠁⠀⢀⣠⡅⠀⠀⢫⡋⢑⣵⣞⢑⣢⣝⡉⡪⠂⠀⠀⠀⠀⠀⠀⠈⠐⠉
⠀⠀⠀⠀⠘⠿⠶⠂⠤⠀⡀⠀⠀⠁⠀⣀⣤⣴⡞⠋⠉⠁⢀⣴⣿⣿⡿⠟⠫⡸⠟⠋⣹⠀⠀⠀⢠⡀⣤⣦⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣶⡟⠋⠉⠁⠀⠀⠀⠀⠹⢿⠿⠋⠈⠒⠉⠈⠑⠊⠁⠀⠀⠤⣄⣉⢹⣿⣟⣁⡠⠄
⠀⠀⠀⢀⢀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⣵⣿⡅⠉⠂
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⢠⠸⣷⣒⡞⢠
⠀⠀⠈⢿⢿⠿⡿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠞⠀⢿⣶⠇⠘⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣰⡶⣆⣎⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡘⠺⢧⣀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⣤⣞⠻⠟⢡⡴⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠲⣾⣁⡀⢶⣌⣙⠷⠆⣣
⠀⠀⠀⠀⠀⠀⠀⠈⠓⡎⣿⡄⢠⣿⢱⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠈⠹⢶⣄⣙⠣⢤⡄⠙⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣹⢳⣾⣯⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢶⡍⠉⢣⣬⡍⠛⠂
⠀⠀⠀⠀⠀⠀⣀⢨⣯⡆⣿⠛⢻⣿⣰⣅⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢧⣤⠽⠋⢀⣤⡛⢻⡆⣅
⠀⠀⠀⠀⠀⠀⠙⠀⢸⢯⣛⠻⢟⣣⣼⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠖⠀⢀⣈⠓⢶⡄⠉
⠀⠀⠀⠀⠀⠀⠠⢀⡾⠉⢍⣻⣟⡻⠋⢷⡔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡹⢧⡿⢇⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠲⠒⠀⢚⣥⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠤⡽⣿⡄⢠⣾⠿⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⢈⣁⣈⣉⣏⣭⣶⣾⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⣹⠧⣼⣏⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡈⡀⠂⠀⢤⣮⣟⣉⣩⣿⣭⣶⠟⢿⣮⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⠿⠿⠟⣓⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠒⠛⠻⣷⢤⡤⠽⠶⣿⣿⡟⣋⣽⣿⡄
⠀⠀⠀⠀⠂⠐⠀⠀⣴⢯⡛⠛⠛⣛⡿⣦⠀⠀⠂⠀⠀⠀⠀⠀⠄⡤⢄⣿⣙⣛⣛⡿⣦⡴⠞⠛⣻⣿⣿⣿⡟⣡
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⢉⣛⣛⡻⠁⢸⡆⠀⠀⠀⠀⠀⠀⠈⠀⣿⡶⠦⣾⣿⣿⣛⣉⣿⡿⣷⣿⣿⣿⣿⣿⢏⣱
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⠉⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⠒⠦⠭⠀⠈⠻⠿⢿⣁⣝⣵⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⢰⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢳
⠀⢰⠒⢺⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⢳
⠠⢺⠀⢸⠀⠀⠃⠀⠀⠀⠀⢀⠤⠶⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠴⠲⠤⡀⠀⠀⠀⢀⡇⠀⢸⠀⢸⠂
⣴⢸⠀⢸⠀⠀⢸⠉⠉⠉⠩⢽⠠⠄⠀⠫⠥⠤⠭⠭⠭⠀⠈⠉⠀⢄⠃⠀⠲⢰⠇⠤⠤⠠⠬⡇⠀⢸⠀⢸⢰
⢩⣸⠀⢸⡆⠀⢸⠀⠀⠀⠀⠀⣷⡤⠤⠊⠀⣀⡄⠀⠀⠀⢀⡀⠀⠀⠑⠒⣶⠃⢀⠀⠀⠀⠀⡇⠀⢸⠀⢸⡠
⠀⠉⡀⢘⡇⠀⢸⠀⠀⠀⠈⠉⢸⡀⠑⠠⣀⠉⠁⠐⢀⠀⠘⠉⢀⠔⠈⠀⡏⠉⠁⠀⠀⠀⠀⡇⠀⢸⡀⣸
⠀⠀⠉⠉⡅⠀⢸⠀⢠⠋⠀⠀⠘⡇⠀⣀⡄⠀⠠⠆⠀⠠⠀⠀⠠⣄⠀⢠⠇⠀⠀⠈⠢⠀⠀⡀⠀⣸
⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⢹⠔⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠆⢈⠢⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⣆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢹⠀⠀⠀⠀⠠⠘⠀⠁⠠⠁⠤⠀⠀⠀⠀⠀⠀⢐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠤⢀⣀⡀⣀⡐⠀⠈⠀⠂⠀⣀⣀⣀⣀⣀⡀⡜⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠉⠈⠉⠀⠈⠉⠉⠉⠉⠉⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠐⠒⠒⠒⠒⠒⠀⣒⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢲⠀⢸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢤⠤⢾⠀⡸⠧⢤⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠈⣀⠠⠒⠁⠑⠠⢀⡀⠀⠀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⢄⣀⡀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢀⣠⣀⣀⣠⠤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢀⡄⠡⣀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⠚⠉⠉⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⢤⣤⡤⠠⣤⠤⠄⠠⠤⡶⠀⠚⠉⠉⠀⠀⠠⠂⠉⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠚⡩⠉⠀⠀⢀⠸⠁⠀⠀⠀⢀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⢁⠎
⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⡐⠁⠀⠀⡨⠁⠀⠀⠀⠀⣠⣿⡏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠄⠚⠀⠀⠀⠀⢠⣾⣻⣟⠻⠋⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣴⣆⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣾⡿⢍⣭⢭⣽⠷⠘⠘⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⡎⢰⣿⣿⣿⣶⠒⢒⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢿⠜⣿⡟⢙⠁⢀⣩⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣵⣿⣽⣯⣿⣯⠤⠑⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⢿⢿⡿⡿⣷⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⢀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣄⠠⣠⣤⣤⡤⠠⠖⠒
⠀⠀⠀⢡⠐⠈⠚⠀⠄⠠⠙⠀⠀⠀⠀⠀⢠⡄⡉⣶⣆⠲⠀⠒⠀⠀⠀⠀⡄⠄⢆⡀⠀⢠⢠⡼⠡⠁⠀⠀⣾⣟⢻⡏⠹⡮⠠⡈⣷⡶⠴⠄
⠀⠀⠀⠠⣦⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⡗⠿⣾⣿⡥⢦⠆⠀⠀⠠⠹⠋⠈⠀⠁⢈⢽⠏⠀⠀⠀⠀⠀⠙⡟⠀⠀⢻⡆⠁⠐⢢⠁
⠀⠀⠀⡄⠀⠀⢒⣿⣂⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⢋⣉⡌⣄⠀⠀⠀⢰⣄⣈⣤⣤⣤⣾⡘⠀⠀⠀⠀⠀⠀⡃⠀⠀⢼⣿⠀⠤
⠀⠀⠀⠐⠄⠀⣼⡟⠿⣹⣿⠟⠀⠀⠀⠀⠀⠡⡴⢲⣿⡇⢉⣄⡗⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠡⢘⠀⠼⠟
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠨⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢀⠀⠀⠀⠀⠀⠀⡴⠂⣸⣃⣟⣧⠑⠀⠀⠀⠀⠀⠀⠀⢀⠠⢖⣴⣤⡀⠠⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣤⣾
⠀⠀⠀⠀⠀⡆⠀⡲⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠩⢿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⡒⠃⠀⠀⠀⢀⡀⠀⠠⣍⣿⠿⣿⣁⡤
⠀⠀⠀⠐⢂⠡⠘⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⢋⣿⠏⢸⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠜⠀⠃⡰⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⢠⠇⠀⣽
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⡟⠒⠛⠻⠿⣿⡃⠀⠂⠀⠀⠀⠂⠠⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠄⠰⠧⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡐⣤⠀⠘⢻⠠⠈⠀⠀⠀⠀⠗⠟⠭⠻⠻⠻⠄⠙⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠠
⠀⠀⠀⠀⠐⠀⠀⣈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠐⢉⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠼⢇⡨
⠀⠀⠀⢠⣂⠁⢀⣤⠞⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠳⣽⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⣘⣋⠡⢀⠁
⠀⠀⠀⠸⠟⢿⡏⠀⠶⠘⠈⠀⠀⠀⠀⠀⠀⡽⢿⣿⣿⣧⣌⡹⣀⠀⠀⠀⠀⠀⠀⢠⠋⡁⢹⢣⠀⠀⠀⠀⠀⠀⠀⢺⣫⡿⠁⠊⠀⠐
⠀⠀⠀⠀⠢⢼⡅⠁⠛⠀⠀⠀⠀⠀⠀⠀⠠⠖⠏⠘⢽⡍⠉⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠐⢁⡀⢷⡰⠆
⠀⠀⠀⠰⠃⣼⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⣀⣄⣄⣠⡌⣅⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠡⠇⢀⣌⣯⣯⠚
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠋⠉⠋⠃⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠈⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡇⣰⠀⠀⠀⠀⠀⠀⡔⡀⠀⠀⠀⠀⡀⠞⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡶⢃⠉⠀⠀⠀⠀⢄⡠⠊⠁⠀⠈⠀⣠⠈⠀⠀⠀⠀⠀⠀⠈⣞⡡⠄⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⠰⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣀⡤⠒⠁⠀⠀⠑⢄⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡟⢰⢃⠀⠀⢀⠄⠐⠚⠠⢄⡀⠀⠀⠀⠀⠀⠈⣷⠞⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⡄⣿⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠐⢤⡀⢀⣀⡴⣧⡀⠀⢀⡠⠔⠂⠉⠑⠢⣁⠀⠀⡔⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡦⠁⢿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠹⡤⠾⠒⣚⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣬⣷⣦⡀⠘⡇⣸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠹⠿⣭⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢛⣛⣿⣧⣭⣁⠹⣼⠀⠅⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣉⢥⣾⣩⡤⢀⣀⡸⡎⠇⠀⠀⠀⠀⠀⢀⠁⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⠤⢼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠩⣐⡭⣥⣀⠹⣄⢀⠀⠀⠀⠀⢠⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⢀⢠⠃⡀⠠⠤⠌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣩⣵⢟⡉⠁⠀⢼⣦⣘⠥⢄⢀⠸⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠎⠀⠀⠒⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⣁⣠⠄⠒⠒⠋⠛⠳⠮⣽⣷⣿⡌⢯⣀⠄⠀⠀⠀⢀⣴⣿⠇⠠⣈⡴⠧⠄⠀⠛⠶⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠠⠈⣉⠁⠰⢖⡶⣋⡀⠀⠀⠀⠀⠀⠹⢦⡙⠋⠛⠟⠋⣠⠾⠿⠶⠚⠉⢀⡀⠀⢦⣴⣶⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠗⠊⠀⠀⣰⡿⠋⡕⠀⣀⣶⠿⢰⣀⠀⠀⠉⠓⠒⠒⠋⢁⡀⠀⢀⠠⡙⠞⠿⣷⡦⣝⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠉⠀⠀⠐⠃⡏⠈⠀⢺⡥⢀⡆⢻⠈⢷⡈⢷⡈⢳⡕⢦⣙⢮⣿⡄⠈⠉⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠈⢀⠂⠈⠆⣳⡏⢷⣾⣿⠈⠉⠁⠻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠐⢸⡇⠀⠈⠋





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⢟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣦⣶⡇⡔
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣦⣤⣥⣥⡼⠶⠷⠶⠶⣶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⡟⠱⣿⡗⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⢹⡟⢻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⠂⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠟⠁⠘
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠠⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⡇⠀⠀⢈⣼⠤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢈⢻⣿⠿⠶⠒⠲⠶⠒⣿⠟⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠲⠟⠅⠀⢸⡟⢠⣀⣠⣴⡠⢠⢿⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠋⠁⠀⠁⡀⠀⠀⢀⠀⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⢟⡛⢻⡻⣻⡿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⢀⡴⠛⠉⠉⠙⢦⡀⠀⢀⣤⠖⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⣠⠿⠚⠛⠓⢦⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣀⠀⣼⣃⣀⣀⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⣧
⠀⠀⠀⣠⡤⢶⡶⢤⣄⠀⢀⡴⠋⠁⠀⠀⢙⡷⠋⠉⠉⠉⠙⠳⢿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣤⡶⠛⠉⠙⠳⣆
⠀⠀⣾⣇⣰⠟⠛⠶⣿⣳⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⣀⣸⣏⣀⡀⠀⠀⠀⠸⣇⢀⣤⢶⡶⢦⡀
⠀⠀⢻⣌⣹⣆⣀⣠⣬⣿⠃⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠞⠋⠉⠁⠀⠀⠈⠙⢦⡀⠀⠀⣿⣻⡷⠟⢳⡖⣿
⠀⠀⠀⠙⠷⣌⣿⠉⢉⣻⣦⣄⣀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣿⣿⢿⣶⣻⡴⠋
⠀⠀⠀⠀⠀⠈⢻⡛⠿⢤⣤⣨⡽⠛⠛⠛⢲⣿⠶⢤⣤⢤⣤⡤⠴⠯⣤⣤⣤⣤⣤⣤⠤⠶⢶⠾⠻⠛⣻⠋⠉⢹⠀⣠⡟⠉
⠀⠀⠀⠀⠀⠀⠈⣧⠛⠶⠤⢉⡛⠳⠶⠾⣥⣤⣀⣤⣖⣉⣀⣀⣤⣚⣁⣀⣠⠖⠉⠀⣠⣔⣁⣀⣠⣴⣥⣦⠴⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⠶⣬⡉⠛⠛⠂⠰⠦⣬⣭⡍⢉⣉⣉⣉⡉⢉⣉⣉⣛⣛⠋⠉⣉⣉⣭⣥⠄⠀⠶⠶⠚⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⣄⡀⠀⠛⠒⠖⠀⠀⠤⣤⣤⡄⠀⢠⣤⣤⣍⠉⠉⣭⣤⣤⡄⠀⠀⣤⡤⠶⠞⠛⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣌⡉⠛⠁⠀⠶⢤⣤⣤⠀⠠⢤⣤⣤⡄⢠⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⠀⠰⠚⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣁⣈⡛⠓⠶⠶⠀⠴⢤⣤⣤⠀⠠⢤⣤⣤⠄⠀⢤⣤⣤⣤⠀⠠⣤⡤⠶⢂⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣉⡁⠐⠶⢤⡄⠀⠠⢤⣤⣤⡄⠀⣤⣤⣤⣤⠀⠀⠶⠶⠶⢂⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣼⣾⣿⣿⡧⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⣽⣿⣿⣷⣄⣴⢂⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠈⠉⢉⠉⠙⣛⠿⠿⠿⣷⣿⣿⣾⡷⠟⠛⠿⠉⠀⠐⠂⠀⠀⠀⠢⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣠⢤⡒⢻⣿⣿⣿⡖⣂⣤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠒⠉⢀⠞⠉⣤⣉⡉⠁⠀⠈⢻⠩⢷⡀⠈⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠖⠃⢀⡾⠁⣽⣉⣉⢻⣿⣿⣷⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣛⠛⠿⣿⣿⣿⣿⡃⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⢰⠏⠙⡅⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢻⠿⠷⠿⢿⣿⣿⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⢿⠿⠿⣿⣿⡟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢤⡆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠿⢿⣿⡟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠓⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠼⠿⠿⠤⠤⠤⢤⣄⣀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⢉⣳⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⣅⣀⠙⠶⣤⣀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣴⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠁
⠀⠀⠀⢠⣴⣮⣭⣉⡉⠉⠉⠉⠀⠈⢣⡀⠀⣠⠶⠛⢋⠁⠀⠀⠉⠳⠍⠡⠔⠉⠀⠀⠉⠹⠷⣦⣄⣀⠀⢰⣦⢄
⠀⠀⠀⠀⠀⠀⢀⡤⠈⠓⠀⠀⠀⠀⠀⠑⢬⣥⡴⠞⢉⡗⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠐⠛⠉⠙⠂
⠀⠀⠀⠀⠀⣴⡥⠴⠖⠒⠒⠲⠶⠤⠤⠭⠍⠀⠀⠚⣯⡄⠚⠶⠀⠀⠀⠀⢠⣼⠁⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠀⠉⠘⠃


⣿⢿⢿⠿⣿⢟⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⠁⢻⡀⠀⠀⠀⠀⠀⠀⣸⠇⠙⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣰⣾⣷⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡄⢸⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠉⠁⠉⠙⣛⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢶⣛⣮⠙⠳⢮⡶⠛⢫⣼⣛⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣿⣿⡯⠴⠻⣷⣀⣼⣤⣠⣾⠟⠦⣿⣿⣿⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠽⠟⠀⠀⣠⣿⣾⣿⣿⣧⣧⡀⠀⠘⠿⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢿⣿⣿⣿⣿⠿⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⣠⣶⣿⣿⣿⣿⣦⣄⠠⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣱⣾⣿⣿⡻⠿⠿⣿⣿⣿⣶⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡏⡜⠙⢿⣿⣿⣿⣿⠟⠙⣇⣿⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⠟⠀⠀⠀⠉⢻⡟⠁⠀⠀⠈⢳⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠛⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡟⣟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡖⠲⠲⢶⡶⣦⣄⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡔⣺⠛⠓⠀⠈⠙⠛⢩⡿⡷⢶⡥⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⢉⣴⡛⠋⠛⠛⠛⠉⠉⠛⠛⢛⠓⠛⣛⣛⣦⡀⠈⠉⠙⡲⢤⣀
⠀⠀⠀⠀⠀⣠⠖⠙⢤⡈⠀⢀⡼⠛⠛⣛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⣿⣛⣧⡄⠶⠀⠁⠀⠨⡛⢶⣄
⠀⠀⢀⡴⢯⡀⠑⠂⠀⠤⠄⢺⣷⣯⣽⡿⠿⠷⠶⠦⠴⠶⠶⠶⠾⠿⠿⠿⢿⣿⣟⠀⠀⠀⠀⠨⠒⠉⠈⠽⢦
⠀⢠⠞⠙⠉⠰⢄⠐⠀⠀⢰⣿⣤⣡⡀⢄⣀⣀⠀⠀⢠⡀⢀⢴⣄⣨⣥⣶⣾⣷⣿⡇⠀⠀⠀⠀⠀⠀⠐⢊⡭⣳⡄
⢠⡏⡀⠀⠀⠠⠼⡀⣀⠤⠒⣿⣿⣿⡟⠋⠉⠉⠉⠉⢩⣿⡏⠉⠉⣉⡉⣍⣭⣿⣿⡧⠒⠐⠦⠤⢀⠀⣰⠥⠀⠀⢹
⡾⠁⠈⠁⠀⢀⣀⣡⠼⠻⠼⣿⣿⠿⠾⡷⡶⠶⠶⠦⠴⠿⠷⠤⠴⡶⠷⠿⣿⣾⣿⣃⣤⠒⣶⠒⢦⣋⠁
⡇⠀⠀⠀⣀⡾⣆⣨⡉⠸⣄⣿⣿⣽⣔⣯⣥⣤⣤⣂⣤⣀⣠⣤⣤⣾⣶⣿⣿⣿⡿⣠⣎⠻⠺⢶⡰⣍⣳⣄
⢻⠶⠶⢴⣿⡣⣽⣶⣏⣸⣿⣼⣿⣷⣶⣤⣀⣀⣂⣤⣀⣀⣀⣀⣀⣠⣶⣶⣾⣾⡷⣿⣿⣿⣷⠜⢦⠤⣧⣿
⠈⢧⣤⣾⣿⣿⣿⣯⣽⣧⣄⣀⣿⡟⠋⡛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⢛⢛⣛⣟⣒⣒⣛⣿⣯⣮⣿⡶⢷⣿⠶⢶⡾
⠀⠈⠻⣿⡿⢿⣿⣿⣿⣿⡇⢻⣿⡟⢹⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢻⡟⢹⣻⡉⣙⣿⣿⣿⣿⣿⣿⣁⣤⠟
⠀⠀⠀⠈⠳⣖⠒⠛⡉⢹⡇⣘⣿⡇⢸⣿⣿⣿⣿⣟⣿⢿⣿⡷⠶⢤⣬⣿⣇⠈⣿⡇⢸⠇⢐⣊⡭⢥⣲⠞⠁
⠀⠀⠀⠀⠀⠈⠙⠮⣍⡻⠧⠟⢻⡇⢸⠿⠟⠻⠶⠤⠀⠀⠈⠁⠛⠉⠓⠺⢿⣴⢿⡇⢨⡖⢋⣹⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠼⣷⣼⣀⡀⢀⡢⠀⡢⡀⠤⡀⡀⡅⠀⣁⣈⣬⣿⠷⠞⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣾⣶⣾⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡠⠤⡀⢸⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠄⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡀⠐⠚⠁
⠀⠀⢧⡀⠘⢾⢆⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡼⠯⣿⠤⡤⣀⠀⠀⠀⠀⠀⠀⣠⡠⢧⣮
⠀⠀⠀⠉⢒⡨⣷⠜⢤⡄⠀⠀⠀⣴⣪⠴⡣⠞⢽⣛⣿⠳⢜⠦⣕⣦⠀⠀⠀⠘⢿⠇⡴⢴⣩⡴⡄
⠀⠀⠀⡰⣷⠮⠊⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠨⡟⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠆⠀⢇⠉⠁
⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⢀⣀⡀⣤⡟⣆⣄⣈⣀⠄⠀⠀⠀⠒⠀⠀⢸⣋⡷⠠⠀⠀⠀⠀⠀⢐⠀⢒⠀⢠⣾⣷⡤⠀⡐⠀⡢
⠀⠀⠀⠀⠀⠉⣭⡝⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣒⣿⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠊⡯⢽⢋⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠐⠲⣄⠀⣀⠀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠂
⠀⠀⠢⠤⠬⠑⣉⠛⠥⠤⠔⠀⠀⠀⠀⣴⠋⠉⠘⡨⠖⠋⠑⣆⠀⠀⠀⠀⢎⡉⠑⠂⢼⣸⠄⠂⠉⣩⠂
⠀⠀⠀⠀⠀⢸⣡⡁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢛⣲⠖⠐⠒⠁⠀⠀⠀⠀⠀⠈⠒⠈⢵⣶⠍⠒⠋
⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠒⢬⡒⣄⠔⡠⠒⠂⠀⠀⠀⠀⠀⠀⠈⢑⠤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⣠⠒⠁
⠀⠀⠐⠒⢢⢽⣿⣯⣔⠒⠂⠀⠀⠀⠀⠀⢀⠤⣞⣛⣳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢉⣥⣬⣥⡤⣉⠑
⠀⠀⠀⠈⠁⠐⣛⠆⠈⠁⠀⠀⠀⠀⠀⡔⠁⡠⢧⠀⡼⢄⠈⢢⠀⠀⠀⠀⠀⠺⠛⠁⢛⡛⠊⠙⠻⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠉⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⣴⢶⡦⠀⠀⠀⠀⡀⡀⣄⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢰⣌⠉⠉⢹⡥⠄
⠀⠀⠀⢀⢴⡿⠻⣆⡄⠀⠀⠀⠐⣿⣾⠗⠀⠀⢠⣿⣷⣼⣲⣶⣴⣶⣆⠀⠀⠀⠀⠰⠀⠀⠠⠞⠛⠒⠂⠚⠓
⠀⠀⠀⠀⠆⢸⣼⠙⠆⠀⠀⠠⠀⡧⣼⠹⡀⠀⠐⠛⠛⠉⡟⠀⠈⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠛⠒⠞⠋
⠀⢀⠄⠉⣠⣀⠔⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢀⣈⣼⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠘⠀⠀⠀⠈⠀⠀⢸⠀⠤⠤⠄⠀⠀⠀⠠⢤⡿⡿⣿⡿⣧⣀
⠀⠀⠛⠿⢾⣿⣿⠮⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠊
⠀⠀⠀⠀⣤⡀⠀⠀⣾⣿⣿⡇⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣀⠘⢿⣧⡀⠙⠛⠛⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⣀⡵⠃⠀⠀⠀⠈⠁
⠀⡚⠛⢛⣷⡘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⢀⣁⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡄⠀⢰⡄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣀⣠⣏⣉⡉⣙⣀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠈⠁⠀⠀⠀⠈⢸⠧⠆⡄⠇⠀⠀⠀⠀⢸⣅⡀⠀⠀⠀⣂⣿
⠀⠀⢈⡉⠙⠉⠉⢛⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⢀⣃⢀⡀⠀⠀⣸⣿⣶⡀⢐⣲⣯⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠁⠀⠀⠸⠃⠃⠻⠛⠼⠇⠀⠀⠿⠿⢿⣿⣿⣿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⢃⠀⠀⠀⢠⠣⠐⠒⠀⡀
⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⠃⠀⠀⠈⢣⢒⣒⣒⡃⡁⠀⠀⠀⢐⢀⣀⣀⣀
⠀⠀⠀⠀⡄⠀⠑⠄⡣⠀⢀⠀⠀⡼⠉⠉⠉⢯⢧⣀⣀⣰⣿⠋⠀⠈⠱⡔⠄⠤⠠⢢⠎⠀⠀⠈⢦
⠀⠀⠀⠀⠈⡁⢀⢰⣷⣾⣿⠄⠘⢇⠀⠀⠀⣼⡷⠛⠛⠳⡷⡀⠀⠀⣠⣿⠒⠒⠒⣜⣆⠀⠀⢀⣞⠞⠛⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠈⢰⣟⠷⣼⣶⠄⢈⣷⣶⣾⣻⡁⠀⠀⠀⡹⣹⠿⠿⣽⣇⠀⠀⠀⢸⣮⠿⠿⢯⣯⠀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢠⡞⠀⠀⠀⢳⡱⣤⣤⡼⡽⠁⠀⠀⠘⣞⢦⣤⣴⢿⠃⠀⠀⠀⢳⢳⣶⣶⡎⠀⠀⠀⠀⠀⢀⠂⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀⣀⣾⠟⠉⠉⠙⣿⣆⣀⣀⣴⡿⠉⠉⠉⢯⢳⣀⣀⣠⣫⠋⠈⠉⠹⡄⠀⢀⣀⠰⠇⢂⠉⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠙⣄⠀⠀⢀⣞⡜⠛⠛⢮⢧⠀⠀⠀⣼⡷⠛⠛⠳⣷⡄⠀⠀⢠⠏⠀⣘⣽⣷⣿⢄⠐⣈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣶⣦⢤⣶⡆⠀⢈⣿⣻⣏⢞⠀⠀⠀⢈⣿⣿⣾⣾⡹⡁⠀⠀⠀⡹⣹⠿⠿⣅⠀⢶⡿⠵⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⠢⣿⣿⣾⣃⠁⣠⠏⠀⠀⠈⢮⢧⣤⣤⢞⡞⠀⠀⠀⠱⡝⠦⠤⠞⣽⠁⠀⠀⠘⣦⢀⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠂⢹⠜⠛⠁⠀⠘⢆⠀⠀⢠⣯⠏⠉⠉⠻⣳⣀⣀⣀⣾⡟⠉⠉⠙⣜⣆⣀⣀⣴⡿⠉⠉⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠠⠋⠀⠀⡀⠀⠀⣨⠿⠿⢧⣳⡀⠀⠀⢠⢿⠞⠛⠻⡼⣄⠀⠀⠀⣼⡞⠛⠛⢾⣧⠀⠀⠀⣰⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⣳⣹⣶⣶⣻⡏⠀⠀⠀⢘⣟⣶⣶⣞⢿⠀⠀⠀⠀⣿⣹⠿⢿⡁⠠⢿⡷⣆⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⡴⡿⠃⠀⠀⠙⣿⢤⣤⡤⢿⠏⠀⠀⠈⢯⠳⣤⣤⢞⡟⠀⠀⠀⠹⡄⠀⣷⣾⣿⡔⢒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⣀⣰⠣⠂⠀⠀⢌⢦⡀⠀⣠⣾⠏⠉⠉⠹⣷⣄⣀⣀⡜⠁⠀⠉⠁⡆⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠅⠀⠀⠀⢀⠊⠍⠩⠥⡻⡀⠀⠀⢠⠏⠈⠉⠉⠀⠀⠀⠀⠀⠑⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢡⠂⠀⠀⠀⢱⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⣠⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣶⣶⣦⣤⣀⡀⠀⠀⠀⡴⠋⠉⢢⡀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⢤⣸⡀⠀⡀⠀⣇⠀⡠⠚⠉⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠒⡶⣶⣤⡴⣪⣥⠙⡾⠧⢄⣿⠜⠁⠀⠀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣾⠞⢋⢟⣾⣯⣽⡿⣢⠤⣈⡟⠀⠀⢀⡖⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣴⣥⣾⣿⣿⠿⢡⣃⡰⡹⠁⠀⣰⠏⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⠻⠟⠋⣁⡴⠟⣩⠾⢷⣤⣴⠗⠂⣡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣀⣠⣴⠾⠿⠶⠛⠁⠀⠀⠉⠓⢶⣚⣓⡛⠛⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢼⢽⣷⣌⡨⠦⣬⣦⡀⢈⢷⡈⣤⠀⠼⠽⣭⠭⢁⣠⠴⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣾⡿⠁⣠⣏⣽⠀⠀⡬⠿⣿⡇⠀⣠⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣯⣁⡉⠙⠻⢟⠁⠀⠘⣷⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣌⠢⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠭⢿⡻⢿⣿⣿⣿⣷⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⣀⡀⠈⠂⠹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⢀⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠻⢝⣚⣭⣭⣤⣽⣿⣿⠟⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠑⡄⠀⠀⣠⠖⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡇⠀⡼⠁⣠⠎⠀⠀⢀⡀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⣞⣀⣠⣷⣮⣤⣤⣤⣤⣃⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣴⠾⡿⠏⠛⠉⡝⠛⢍⠁⢸⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣩⠔⠋⠀⠀⣇⠈⡆⠀⢧⡀⡝⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⢋⡠⠔⠋⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠉
⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠖⠚⠁⢠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠙⠋⠉⠋⠉⠉⠉⠁⠀⣀⡤⠴⠒⠒⠢⠤⣈⣙⡒⠦⠤⣄⣀⣀⡀⠀⠀⢀⠴⢒⣡⠜⠁⢀⠤⠊⡽
⣤⣂⣠⣀⣀⣄⣀⣄⣀⣄⣠⣄⣤⣤⠦⣒⠒⠛⠛⠓⠒⠢⢤⣀⠀⠀⠀⠀⠉⠉⠑⠒⠲⠞⠛⠛⠻⣟⠓⠥⢤⣄⣀⣮⣤⣚⡥⠤⢤⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠑⢦⠀⢀⡷⢤⡈⠓⠲⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠶⠬⢄⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⠀⠸⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⣰⠉⢉⣉⠒⠒⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠄⠒⠊⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⢦
⠀⠀⠀⠀⠀⠀⠀⡼⠛⠒⠒⠤⠤⠀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠐⠒⠈⠁⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠘⡆⠀⣑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⡼⠷⠦⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠐⠈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣒⠒⠀⠀⠀⠈⠉⠉⠉⠉⣡⣴⡖⠄⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡃⠌⢀⣀⠤⠚⡇⠀⠀⠀⠀⠀⠀⣠⣦⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠁⠒⠀⠤⠤⠄⠤⠀⠀⠒⠂⠉⠉⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢸⣋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⠉⠈⠉⠁⠈⠉⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢰⡛⡆⠀⠀⠀⠀⡴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣏⣉⣉⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡿⠃⠀⠀⠠⣷⣺⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠔⠃⠀⠀⠀⠀⠏⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠠
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⡖⠒⠒⣢
⢰⠁⠀⠸⡀⠙⡑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⢿⣤⣶⣶⣶⣶⣾⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡠⠄⢂⡉⠀⠄⢴⠃⢀⠔⢸
⠈⢆⠀⠀⠳⡄⠈⠓⠀⠀⠉⠶⠀⢄⡀⠀⠀⠸⣿⣦⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣾⣿⠃⠀⣀⠴⠒⣹⠆⠁⡀⠀⢠⠔⡡⠖⠁⣰⠃
⠀⠈⡇⠀⠀⠈⠓⢤⠄⣐⢀⡘⠦⣄⡈⠑⠢⢄⡙⢿⣧⣄⣿⠟⡋⠉⠉⠉⠉⠛⠛⠿⣄⣠⣿⣃⠔⠊⠔⢈⡤⣚⣩⡤⠖⠉⣽⠏⠀⠀⢸⠃
⠀⠀⠈⠲⣤⣄⣀⣀⠐⢤⣈⠉⠁⠘⡙⠢⢄⣀⠈⠛⠿⣿⣱⣈⣷⣾⣦⣾⣾⣷⣤⣀⣈⡿⠋⣁⡨⠴⢊⡡⣃⣕⡥⢶⠖⢩⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠢⢌⣑⡒⠬⠐⡦⠤⠭⣥⣖⣦⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣖⡭⢴⡾⠋⣑⡨⢿⡷⠖⢃⡴⠟⠂⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠣⣅⣀⡈⠁⠂⣬⣍⣉⣀⣉⣀⠽⠾⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡾⠯⠭⠤⠭⣤⠦⠥⣤⣴⣭⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠉⢩⠥⠀⠤⠤⣂⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠥⡒⠲⠒⠛⠢⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠧⠤⠔⢒⡩⠔⢊⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⣌⡐⠚⠚⠃⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠖⠊⠁⣠⣾⡟⠀⠀⠈⠀⠋⢹⠟⠩⠙⠉⠈⠹⢽⣿⣷⣄⠉⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⣿⣃⡀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢰⣿⣿⣿⣷⣷⣶⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⠀⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢻⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣻⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠘⡟⠉⢻⣦⡹⣇⠀⠀⠁⠀⠑⠀⢀⡼⠋⠀⢻⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠻⠯⣤⣠⣃⣠⡴⠞⠋⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⠀⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡽⠛⣿⣿⣷⡾⠿⠦⠤⢤⠤⣤⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⢟⣋⣭⣥⡶⣶⣿⣿⣿⣷⣶⣟⡽⢁⠀⠀⠈
⠀⠀⠀⠀⠀⡠⣠⣬⣶⣾⣿⠟⠫⠉⠃⢛⠉⢿⣿⣿⣿⢏⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣤⣠⣄
⠀⠀⠀⢠⣾⣿⣿⡻⣱⣿⢷⢄⠀⠀⠀⠀⡙⢿⣿⣿⡿⡿⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣴⡟⠹⢽⠯⡷
⠀⠀⠀⢸⣻⠿⣾⣿⠾⣭⣿⣿⣤⣀⣤⣃⣰⠿⠿⠾⢷⣭⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣽⣷⣗⣶⢂⡄⠀⣠⠬⣻⢶⠦⢄
⠀⠀⠀⠀⠠⠀⣌⡷⠿⢛⣹⢿⣭⡡⢊⣁⡉⠸⢿⠟⣶⣶⣿⠄⢀⣀⠀⠀⢠⡴⣶⢰⡿⢡⣧⣿⣿⣿⣿⣿⣶⣏⣷⣧⣋⢷⡾
⠀⠀⠀⠀⠀⢹⡿⢰⡟⣛⠁⠛⢙⣿⣿⣿⣷⢼⣟⣼⢟⣿⡋⢻⣄⠰⣲⠿⠃⣴⢻⣿⠁⣸⣯⣽⣷⣿⣧⣿⣯⣿⣿⣿⡋⡼⡇
⠀⠀⠀⠀⠀⠈⢻⢯⡛⠘⣿⡄⠄⡁⣈⣹⢁⣒⣙⣥⡿⠁⢀⡾⠀⢀⣿⢠⠆⢁⣼⣧⢰⣿⣿⢿⣿⣻⣿⣽⣿⣯⣿⡿⠀⣿⠁
⠀⠀⠀⠀⠀⢠⡏⠉⠃⢱⣫⣥⣈⠀⠛⠋⠟⢩⡥⠂⠐⡆⢨⣳⡆⢸⢽⠈⢻⣺⣿⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⡰
⠀⠀⠀⠀⢠⠋⠀⠀⠀⣌⢻⣇⣿⠂⠀⠠⠀⠀⡇⠀⠀⠀⠸⡿⠋⠙⠛⠏⠚⣿⡏⢘⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⠃
⠀⠀⠀⠀⢸⡗⠀⠀⠀⠘⣅⢻⣿⡆⠀⠀⠀⠀⠇⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡮⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠏
⠀⠀⠀⠀⠘⣽⡄⠀⢀⡀⠈⣹⣿⣷⡀⡆⠀⠀⢸⣿⡀⠀⣸⠁⠀⠀⠀⠀⠸⠠⢢⡿⠿⣽⣿⣿⣿⣿⣿⣿⣿⢁⡞
⠀⠀⠀⠀⠀⠙⣷⠀⠿⠃⣠⣯⣿⣿⣿⣶⣰⣧⣾⣿⡇⠀⣸⠀⠀⠀⠀⠠⡟⡈⠘⣿⣿⣿⣿⣿⣿⣽⣿⣿⠇⣼⠁
⠀⠀⠀⠀⠀⢰⣿⣿⠀⠉⠘⠍⠉⢠⠄⠋⠽⣿⣿⢿⣡⣾⡟⠀⠀⠀⠠⡱⠐⠀⡠⢺⣿⣿⣟⣿⣿⢿⣿⠏⢰⠇
⠀⠀⠀⠀⢀⢺⣟⣿⣷⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠒⢪⠉⠶⠓⠆⠈⠈⠕⠿⠿⣿⣻⠯⣿⢟⠋⣭⣿⣿⢀⡆
⠀⠀⠀⠀⠈⠻⣅⠀⣿⣳⣀⠀⠀⠠⣤⣶⣤⡶⢤⣀⡏⠠⣶⡴⢶⣤⣈⣛⠲⡤⠶⣭⠙⠒⡮⢶⣿⣿⢃⡬⠁⠀⠉
⠀⠀⠀⠀⠀⠀⣨⣱⣾⣿⠿⠟⢻⠶⠶⠶⠦⢤⣭⣭⡧⣮⡍⣽⡆⠛⠉⠓⠁⠀⠀⠀⠀⠈⠐⠛⠶⢥⡾⠁
⠀⠀⠀⠀⠀⠀⣹⣯⡾⠁⡀⠚⠙⠁⠂⠘⠁⡟⣼⠟⣹⣏⡱⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠐⠊⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⠋⠞⠁⠊⠀⠸⠳



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡀⢠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿
⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃
⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⣶⠆⣠⡀⠛⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⠟⢀⣾⣷⣷⠀⠀⠃⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⠋⣰⣿⣿⣿⣿⣁⣄⣴⠏⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣤⢄⡈⠰⢿⣿⣿⣿⣿⣿⣿⣿⡷⢋⠀⠙⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠀⣿⣿⣿⣿⣿⣾⡆⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⡟⠉⡟⠓⠚⢻⠅⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⡀⠀⠊⠁⠀⠄⡀⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⠐⠈⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⢿⣿⣿⡟⠀⠹⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⠀⠈⢻⣦⣄⠜⠀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡛⠟⠀⠒⠂⠘⠣⢴⡂⡀⠀⠠⣐⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠴⣿⣿⣿⠏⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⡿⠓⠲⠂⠀⠀⠀⠀⠤⠬⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⣀⡎⠙⠋⠁⠒⢁⠤⠻⠛⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣤⣶⣿⣿⣇⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠗⠀⣰⣾⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠟⠁⠀⠀⠀⠈⢹⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣶⣿⠀⠀⠀⣦⣄⣀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣄⠀⠀⢸⣿⣿⠀⠁⢠⣾⣉⣷⣼⣶⣯⣀⣠⣤⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⣼⣿⡟⠀⠀⠾⠿⡯⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠰⠂⡜⠛⠿⡛⡿⢿⡿⠛⣁⣴⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⠃⡇⠸⢱⠛⢉⣥⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢰⡘⡄⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠙⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⣿⣿⣷⣶⡦⡀⢀⣴⣿⣿⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⣠⡃⠈⠁⡀⠘⣿⡿⠋⠀⢀⣍⣸⣿⣿⣿⠏⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⡋⠀⠀⠀⠀⠀⡄⠀⠶⠀⠀⠀⠀⠀⣶⣿⣿⣦⣄⣙⢦⣟⣤⡦⠀⠀⠄⢋⣿⣿⣿⣿⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⢸⣿⣿⣨⠄⠀⢀⠀⠀⡀⠘⠒⠤⠄⠀⠀⠀⠀⠈⢙⣉⠁⠈⠉⠉⣨⢿⡍⠀⠀⠘⢡⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⣿⣄⢻⣿⡟⠉⢰⠇⡀⠀⠳⣄⣀⡤⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⢀⣸⡏⠀⠀⠠⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡽⣿⣿⡷⠋⠀⠀⠸⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⣶⣿⣿⠋⠀⡀⠀⡆⣹⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠻⢦⡤⢷⣼⣷⠆⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡄⢀⣀⠀⠀⠀⠀⠀⠀⠺⠓⣄⠀⢃
⠀⠀⠀⠀⢻⣿⣶⣶⣤⣀⠀⡀⠙⠀⠘⠀⠛⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⡼⠀⢄⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⢣⠀⠀⠀⡀⠀⢀⣼⣧⠶⠖⣦⡀⠀⠀⠀⠀⠀⠴⠆⢨⠀⠀⠀⠀⠀⠀⠀⢈⠀⣶⣦⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣆⠘⢧⣰⣷⣿⣤⠟⠃⠀⠀⠈⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠠⡂⣰⣿⣿⠃⣄
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡁⠸⣿⣿⡿⢳⡶⣤⣤⣶⣿⣟⡁⠀⠀⠀⠀⠀⠀⢀⡌⠈⢠⠄⢸⡄⢷⢠⣷⣿⡿⠃⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣷⣿⣿⣀⣄⠻⠢⠉⠛⢿⠿⠟⠀⠀⠀⠀⠀⠀⠒⠁⠐⠃⢀⠜⠁⢸⠈⠻⣿⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣴⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⠃⠀⠈⠙⠛⢿⣷⡿
⠀⠀⠀⠀⠐⠻⠿⠿⠟⠛⠉⢸⣿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠿⠋⠉⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⢻⣿⢻⣦⡀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣄⠉⠛⠟⣷⣶⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⣿⣽⣷⣄⠀⠙⣛⠘⣵⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠈⢿⡻⣿⡿⠃⢻⣇⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠧⠄⠑⠁⠀⠀⠀⠻⣆⢘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣦⣆⠰⠀⠀⠀⠀⠁⢦⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣈⡧⠀⠀⠀⠀⠀⠀⢿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⣿⣿⡥⠀⠀⠀⢀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠳⣿⣻⣧⠉⠀⠀⣸⣷⣦⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⡇⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢰⣿⡏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣿⠷
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣶⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡆⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠙⠃⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⢰⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⡄⢠⣄⣤⣀⣠⡤⣦⣤⣀⣀⣠⣤⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣯⡿⠳⡋⢀⣉⡀⣡⠶⠠⠤⠶⠚⠁⠉⠉⠉⠛⢶⣀⠔⠢⣉⠉⣑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢈⣥⣬⣷⣆⠀⣠⠞⣡⣤⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠡⣶⢶⡾⠛⢛⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠓⡿⠋⠙⢋⣹⡟⠻⢯⡘⠛⠃⠐⠚⠋⠀⠀⠀⠀⢀⠀⣠⣤⣴⠶⣿⣿⣿⣿⠛⠛⢋⣙⣷⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⣨⡟⢉⣧⠾⠒⠫⢶⣦⣤⣤⣤⣶⣿⣶⣶⠴⠿⠟⠛⠛⠉⠀⢬⠞⠻⢶⣤⣀⡽⢋⣇⣹⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠛⠛⠉⠁⢀⣤⠶⠚⠉⠉⠀⠀⠩⢻⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣳⣦⡼⠟⠘⠂⣼⠛⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠿⠀⠀⠀⠀⠀⠀⣠⠜⠀⣳⣤⣤⡀⠀⠀⠀⠀⠊⠉⠉⠀⠘⠐⠀⠀⠹⣞⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠋⣼⡉⠀⠀⢀⣳⡶⠶⣤⡦⠭⠔⠖⠉⠉⠉⠉⠀⠻⣷⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠟⣳⠏⣿⣟⡆⠀⢸⣅⠀⡠⠤⠴⠂⠀⠀⠀⠀⠁⣀⣉⣿⣭⣿⣟⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⡟⣉⡿⠉⡿⢡⠄⠙⠉⠀⠠⢤⣴⠶⠖⠛⠁⠀⠀⠀⠀⠈⠉⠉⢉⣴⣾⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠂⢀⣴⠗⠊⠁⠒⠉⠉⠀⠀⠀⢀⢀⣀⣀⣀⣠⣄⣤⣀⠀⠰⠼⢿⣿⣿⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣀⢤⠀⠒⠀⠉⠀⠉⠉⠀⠈⢈⣀⣀⡀⣀⣤⣠⣬⣿⣵⡐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⠠⠖⠊⠉⠁⠀⠀⠀⡀⢀⠰⠲⠒⠀⠈⠀⠁⠤⡤⢶⡶⢾⣶⣿⣿⣧⣤⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠈⠠⠄⠀⣠⢠⣶⣾⣷⣦⣰⡎⠁⢀⣀⠀⠀⡀⢀⢀⣀⡀⠀⢶⣏⣿⣍⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⡠⠔⠚⣡⣿⣿⣿⣿⣿⣿⡇⠀⠉⠁⠈⠉⠛⠋⠉⠉⠹⠿⠿⣿⣟⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⡠⠋⠠⠊⠁⠈⣿⣿⣿⣿⣿⣿⣋⡀⠤⠄⠒⠒⠒⠂⠀⠶⣶⡶⣶⢷⣾⣾⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠇⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⣀⠠⠴⠖⠒⠖⠒⠳⠶⢦⣦⣩⣷⣤⣙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠁⣠⠀⠁⠀⡀⠀⠀⡀⠀⠴⠒⠀⠀⠀⠠⢤⠤⣤⣤⣄⠠⠭⣟⡻⠟⣿⡳⣄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⡇⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⣿⣶⣽⣿⣷⣦⣭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣠⡞⠁⢀⣠⠶⠠⠀⠀⠀⣀⢀⣤⣤⣤⣤⣤⣤⣤⣽⣮⣟⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣀⣴⠟⠉⠀⣠⠴⠀⠈⠉⠈⠉⣤⣬⣤⣬⣹⢿⣿⣿⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⣤⠞⠉⢠⣤⣶⡶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡰⣿⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⡿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠛⠙⠛⠛⠛⠛⠓⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠑⠰⣀⢀⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠂⠠⠁⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣶⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⠾⠿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠉⠀⠉⠙⢿⣦⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⢤⠀⠀⠀⠀⠀⠘⠛⡋⠀⠀⣶⣶⣶⠀⠀⢙⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠛⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠐⠀⠀⢠⣾⣷⡆⠄⠁⡂⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠸⡾⠁⠀⢀⠀⠀⠀⠀⠀⠲⠒⠶⢀⠀⠀⠀⡀⠶⠒⠖⡀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡁⡆⠀⠾⠏⠀⠀⠀⢉⠀⠀⠀⠽⠀⠀⠀⠏⠀⠀⠀⡃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠟⠃⣸⡇⣠⠆⠀⠀⠀⠀⠀⠀⠚⠐⠀⠳⣄⠀⡠⠚⠀⠂⠓⠀⠀⠀⠀⢀⣀⣘⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣀⣀⣈⡳⣄⠀⠀⠀⠀⠀⠌⠙⠛⠉⠛⡉⠻⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠰⠎⠀⠈⠉⠉⠁⠁⠈⠳⠆⠀⠀⠀⠀⠀⠀⠤⠄⠁⠀⠁
⠀⠀⠀⠀⠀⠜⠈⢣⢠⠊⠉⡄⢠⠉⠙⠀⠀⠀⠀⠀⠈⠛⠋⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⢦⣉⣉⣉⣡⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠿⠷⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠆