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Welcome To Hell

Joseph Shabason hit rewind on his VHS copy of the skateboard classic “Welcome To Hell” from 1986 hundreds of times in his youth, each watch as thrilling as the last. That invigorating, improvisational, full-body experience of skateboarding is one that Shabason likens to jazz, where a shared language exists between the wheels and woodwinds. The way the skateboarder and musician command that language is what distinguishes them, adding definition to the mercurial concept of “style.” This connection becomes most apparent in collaboration; ensembles of skaters and musicians are a noisy, creative bunch. Reflecting on this relationship and the Toy Machine classic would ultimately lead Shabason to wonder: what does hell sound like?

Welcome To Hell (Full Length Rescore by Joseph Shabason)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⡀⠀⠀⠈⠀⠀⠐⠓⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠿⠀⠀⠀⣀⣤⣿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⢤⣄⠀⠀
⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⠿⣿⣉⣸⠃⠀⣾⣽⡆⠀
⢀⣠⠤⠒⠋⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣤⣖⡿⠟⠉⠀⠀⠀⠀⠸⣄⣀⣯⡿⠁⠀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠖⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠛⠻⠷⣶⣲⣶⢤⣤⣤⣤⣤⡤⣴⣾⣯⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡀⢹⠻⣍⡉⠉⠉⠉⢹⣿⠟⠓⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠓⠋⠉⠙⠒⠤⣼⠁⠀⣰⢿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣇⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀

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