Cinemaman skibidi toilet Emojis & Symbols

⠀⠀⠀⠀⡍⠀⢙⠁⠈⠁⠁⢸⡂⠸⢎⠁⠀⠀⠈⠈⠁⡘⠁⡷⢸⠁⣘⡂⠸⠆⡁⠀⠀⠀⠀⠀⠀⠀⣄⣤⡄
⠀⠀⠀⠀⠛⠀⠘⠂⠀⠃⠀⠉⠁⠐⠘⠃⠀⠀⠚⠀⠘⠃⠀⠛⠀⠀⠋⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢛⣶⡟⠁⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠙⣷⣼⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣽⢿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⣻⣿⢿⣽⣿⣿⣾⠃
⠀⠀⢠⣤⣤⣶⠶⣶⣾⣿⣿⣿⣷⣾⣿⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⣶⣿⣿⣿⣿⣤⠤⣤⣤⣤⣄
⠀⠀⠀⠉⣀⣴⢞⡿⠉⣿⣿⣿⣿⣿⣿⣿⡄⣿⣧⣠⣄⣠⣤⣤⣤⣤⣤⣄⣼⣧⣾⣿⣿⣿⣿⣿⣿⠏⢿⡷⣦⣄⠉⠁
⠀⢀⣤⡾⠋⢁⣾⠁⠀⢸⣿⣿⣿⣿⣿⣿⣧⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⡟⠀⠸⣷⡈⠛⢿⣦⣄
⠀⠘⠋⠀⠀⠈⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⠃⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⣿⣿⣿⠀⢿⣿⣿⣿⡟⠛⢿⠛⣿⣿⣿⡇⠃⣿⣿⣿⣿⠇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⢻⣿⣿⣿⠀⣸⣿⣿⡿⠀⢠⣿⠀⢹⣿⣿⣷⠀⣿⣿⣿⣿⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡉⡍⣠⣿⣿⣿⠃⠀⠀⡇⠀⠀⣿⣿⣿⣇⡌⣉⢉⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠥⠘⠛⢉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⡉⠻⠻⠯⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀⠀⠀⠀⣄⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⢺⠃⠈⠀⠀⣀⣀⠀⡍⠀⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢹⡁⢀⠀⠋⠉⠁⢡⢅⠀⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣸⡖⠆⠸⠛⡛⠛⢻⠰⠒⣇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⣇⣴⠈⡘⠓⢛⡈⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢻⠉⣹⣤⣌⣁⣀⡄⣟⠉⡗⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠋⠁⠈⠁⠀⠀⠀⠀⢹⡏⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣶⣿⣆⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢁⠆⠐⡇⢣⠀⠀⠀⠀⠀⡎⢰⠃⠈⠹⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠥⠞⢅⣤⠹⠇⢸⠀⠀⠀⠀⠀⡇⠈⡼⣇⠀⣧⣘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡀⠀⢭⠀⡇⠸⣀⣀⣀⣀⣠⠇⠸⡅⢘⠎⠁⡀⠈⢆⠀⠀⠀⠸⠿⣶⡤⠰⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⣤⠿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡾⣀⠀⠁⣠⡾⠀⠀⠀⠀⠀⡈⢁⡤⢄⣉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⢈⣙⣒⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠋⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢶⣤⢼⣿⠿⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠉⢘⣽⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢻⣯⡒⠒⠄⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠨⡛⠁⢸⠁⠉⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣻⠦⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢁⣠⡴⠊⢸⠢⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡇⠀⢸⡀⠀⡀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠛⠛⣃⣶⡾⠯⠘⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡆⠀⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠃⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢾⣷⣦⣄⣠⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⢸⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡼⠆⠀⠀⠀⠀⠀⠈⣹⣇⣀⡉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠒⠋⠀⠀⠀⠈⠙⠒⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠍⠀⠀⠀⢩⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣴⣄⣀⣀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⠀⡠⠂⣀⣀⣀⣀⣀⣀⡐⢄⠀⠀⠀⠀⣀⠀⠀⡴⠶⢶⣗⠓⢲⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢉⢢⣤⠪⡄⠒⡆⠀⠀⠀⠀⠀⠖⢠⠜⣢⡔⣈⢀⡀⠀⠰⠒⢚⡟⠀⢻⠛⠲⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠉⡐⠋⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠥⠔⣳⣀⠬⠂⣒⠛⠛⠛⣂⠐⢥⣀⡚⢢⠍⠂⠀⠠⠈⠀⠀⢠
⠀⠊⠀⠀⠂⠀⡀⢙⡟⠒⠓⠒⠂⡛⠟⢀⠀⢐⠀⠀⠙⠉⠁⠀⡀⠂⣖⠉⣾⠘⢀⠀⠈⠉⠉⠀⠀⠈⠡⠀⠠⠀⠐⠀⠀⠀⠠⠁
⠀⠀⠀⠀⡁⠀⠁⢀⡀⠁⠀⡐⠈⡁⡀⠈⠁⠀⡆⠀⠀⠀⠀⠊⠀⠀⠇⠉⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠞⠀⡀⠀⡄⠀⠀⠀⢈⠀⠀⠠⠀⠃⡀⠀⠀⠈⠀⠀⢀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠈⠀⠈⢰
⠀⠀⠀⠘⡀⠀⠀⠀⠂⠐⠤⡀⡀⠒⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠋⠁⠁⣍⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠖⡲⠀⢠⠀⠀⢀⠂⠁⠀⠀⠀⠖⡐⠘⡀⠒⠀⠀⠀⠀⡐⠀⠓⣀⣠⣤⣶⠀⠀⠂⡈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⠀⡀
⠀⠀⠀⠀⠈⠉⠀⠌⠀⠂⠸⠘⠐⠀⡤⠀⠘⠁⣰⣎⠀⠀⠀⠈⣫⣤⣾⡿⣿⠋⠟⠋⠀⠀⠀⣲⣆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣁⣤⣶⡾⠟⡿⠁⠛⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⢻⣦⠀⠀⠀⠀⣠⣤⡄⠄⠀⠀⠀⠀⣠⣭⣷⡾⠿⠛⠉⠀⠁
⠀⠻⣧⡀⠴⠚⣿⣿⡅⣀⠀⠀⢰⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⢀⠼⣷⡙⣆⠀⢉⠿⢳⣿⢿⣶⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠁⠀⠰⡀⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⡀
⠀⠀⠀⠀⠀⢀⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⡻⠳
⠀⠀⢀⣀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠆⡄⠀⠜⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⠐⠊⠀⠘⠁⠀⠀⠀⠀⢲⣶⣄⠀⢸⣿⠿
⠀⠀⠀⣸⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣆⠀⣿
⠀⠀⠀⣿⢿⣿⣿⣿⡗⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠜⠈⠂⠀⠀⠀⠐⠀⠀⠀⠀⠹⣿⣿⣿⣶
⠀⠀⠀⠀⠸⠇⠁⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢴⣤⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⣠⣴⠆⠀⠀⢶⣤⣀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⣠⣴⠄
⠀⢀⣀⣠⠉⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠈⢡⣄⣀⠀⢀⣀⣤⢩⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡬⢡⣄⣀
⠀⠈⠉⣁⡤⠀⠀⠀⠀⠤⠠⠀⠠⠀⠄⠀⠀⠀⠠⣤⡈⠉⠁⠉⠉⣠⡤⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠣⣤⡈⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⡈⢻⣿⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠠⣿⣿⣿⣿⣿⣿⣿⡧⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⣿⣿⣿⠟⢿⣿⣿⡆⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠛⠛⠁

⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠈⠉⢽⠢⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⣻
⠀⠀⠀⠉⠀⠀⠀⠀⠀⢙⣗⣐⣦⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠉
⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⢿⣿⣿⣿⡦⠤⡀⠀⠀⡺⠿⣿⡿⢟⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠒⡂⠀⠀⠤⢴⣿⣿⣿⡟
⠈⠉⠉⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⡀⠂⠀⠁⠘⠀⠀⠀⠁⠀⠀⠙⠉⠉⠁
⠀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⡖⠀⠀⠈⠀⠀⢀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⡀⢀⡀⢀⠀⠁⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠘⠉⠉⠉⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠁⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠲
⣀⣀⣀⠀⠀⠀⢐⢀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣷⣦⡿⣼⡼⡃⠀⠀⠀⠀⠀⢈⠧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿
⠿⠿⠿⠛⠁⠀⢰⢷⠂⠀⠈⠀⠁⠀⠐⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣷⣄⡀⠀⠀⠀⠇⢠⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠂⠀⠀⠀⠀⠐⠀⠀⠀⣀⣠⣾⣿⣿⣿
⠛⠛⠻⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠂⠠⠤⠤⢤⣀⣠⣼⣿⣋⣉⣉⣛⣻⣇⠀⠀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠴⠀⠀⠤⠤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠉⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡁⢨⣭⣭⠉⠉⡏⠀⠀⠀⠀⢀⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⡘⠿⠟⢀⠜⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡧⣿⠟⠲⠶⠻⠠⣷⣦⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⠶⠋⢩⡿⠿⣿⣿⣄⣀⢀⣸⡷⠘⠇⠀⠉⠙⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡠⠀⠂⠉⢹⡶⠖⠒⠒⠒⠒⠒⠒⠞⠀⣀⡠⠽⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣴⠟⢿⣦⡀⠀⠀⠀⡾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣼⡁⠀⠀⠀⠀⣆⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉⠉⢹⠏⠉⠉⠁⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡏⢠⠔⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⣄⠰⠀⠀⠀⠀⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⡐⠄⠀⠘⠠⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⣥⠐⠂⠭⡬⠭⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠶⢲⠐⢢⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⢸⠃
⠀⠐⠀⠀⠀⠀⠀⡄⢰⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡦⠆⢫⢁⣽
⠀⠀⠈⠄⠀⠀⠀⠸⡄⠆⠀⢂⠀⠰⠀⢿⣤⣤⣠⣤⣤⣤⣤⣤⣠⣄⣠⣀⣀⣼⠀⠰⠸⠀⡀⠘⢠⠃⠀⠈⠁
⠀⣀⣀⣈⡄⠀⠀⠀⠹⠈⡈⠀⣀⠠⠴⠖⠔⠀⠰⠀⠀⠠⠤⠆⠀⠀⡄⠀⢤⠀⠠⢌⠀⡼⢁⡣⠫⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡙⣤⠁⠀⠀⠚⠒⠶⠇⠀⠂⠀⠀⠀⠠⠀⠹⠶⠒⠀⠀⠀⠘⢥⠊⡔⠁⠀⠈⣷
⠀⠀⠂⠀⠀⠀⠀⠀⣀⠀⠐⠂⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠛
⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⡈⠀⢀⠉⠐⢈⠄⣅⡥⡁⠀⠁⠈⠨⡇⠀⠀⠀⠀⠈⠄⠀⠀⡸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢧⡀⠀⢱⣤⢤⠉⠀⠘⣤⠀⠂⠀⢠⠄⢀⠆⠀⠀⠀⢸⠀⡀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⡇⢀⢰⠀⠀⠀⠸⠁⠀⠘⢠⡄⠊⢽⣄⢀⣔⡻⠸⡁⠊⠁⠀⡾⢰⡄⠀⠀⠀⡏⡡⢻
⠀⠀⠒⠀⠀⠀⠀⡙⠈⠉⠀⠀⠀⡅⡄⠀⠀⠄⠘⠀⠀⠁⠀⠠⠂⠈⠑⠀⠀⢀⡤⠈⠆⠀⠀⠀⠧⠁⡌
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠰⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠌⠀⡴⠀⠀⠀⢈⠀⢈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⢸⠁⠘⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠋⠈⠀⠸⠀⠀⠀⢰
⠀⠀⠀⠀⡸⠁⠊⢰⠀⠀⠀⠀⠸⠒⠒⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡂⢠⠒⠒⠀⣧⠀⠀⡀⣼
⠀⠀⠀⡰⢁⠂⠀⢺⠆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣀⣀⡿⢉⣁⡿⠁⠀⠀⠀⠦⠴⡰⠊⠀⠀⠸⠇
⠀⠀⢰⡇⠆⠀⠀⢰⠀⢠⠶⠀⠆⠀⡼⠀⠠⡀⠀⠀⠀⠈⠈⠀⠀⠀⢠⠀⠀⠘⡤⠳⠊⡇⠀⠀⡆⠀⠀⠄
⠀⠀⠀⣇⠀⠀⠀⠈⣆⠈⢆⠊⠀⠀⠀⠀⠑⠁⡀⠀⠀⡀⠀⡀⠀⠀⠀⠁⠀⠀⢃⣠⠀⠀⣐⡔
⠀⠉⠁⠉⠉⠉⠉⠉⠉⠢⠌⠏⢉⠃⠀⠀⠀⢀⠀⠀⠀⡦⢠⠀⠀⠠⠀⠀⠀⠀⠀⠋⠛⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⡘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⠁⢀⠀⠀⠀⠁⠀⢠⠉⠉⠉⢡⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠉⠉⠉⠉⠉⠉
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠾⠀⠈⠀⠀⠀⠀⠀⡘⠒⠒⠒⠒⢃⠀⠘⠀⠀⠀⢀⠀⢰⠀⠒⠒⠒⠒⠒⠒
⠀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠰⡇⠀⠀⠀⠀⠠⠆⠤⠤⠠⠤⠰⠆⠀⠀⠀⠀⠀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⢀⡾⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣾⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠋⢹⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⡆⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⡿⠇
⠀⠀⢰⣿⣿⣿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⡿⠻⠿⠟⠛⠉
⠀⠀⢾⣿⡿⣏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢸⣿⣇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⢷⣄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⣠⣤⡀⣰⣿⡟⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠞⠲⣄⠀⠀⠀⢴⠀⢀⣴⣿⣿⡿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠻⠿⠃⣿⣿⠀⢠⠀⠐⢄⣀⡤⠏⠀⣿⣇⠀⠀⠋⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠐⠂⠈⣻⣿⣿⣿⣷⣶⣶⣾⣿⣿⣦⣤⣄⡀⢀⣴⡄⠀⠀⢹⣿⣦⣤⣴⣶⣶⣶⣶⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠸⠷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣋⣭⣭⣿⣿⣿⡏⢸⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣶⣿⠿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⣬⣿⣿⣿⣿⣿⡿⢛⠛⠻⣿⡿⠀⠈⣿⣿⣿⠟⢛⣻⣿⣿⣿⣿⣿⣭⣤⣬⣽⣿⡿⠋⠀⠀⠀⠀⠀⢹⣧
⠀⣰⡟⠉⢳⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠃⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟
⠀⢿⣧⡀⠀⣾⣿⣿⣿⣿⣿⣟⡿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⡿⠿⢿⡿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠲⠖⠋
⠀⠀⠛⠿⢿⢿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠸⣿⣿⣿⣿⣿⣿⣿⡷⠾⠿⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠉⠙⠛⠛⠛⠉⢩⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣀⠉⢉⡛⠿⣿⣿⣿⣿⡏⠀⠀⢀⣀⣀⣀⠀⢻⡿⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⣤⣤⣴⣿⣿⡟⠉⠛⢿⣷⡈⠁⣠⡤⠿⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⠁⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠰⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢹⣷⠀⣿⡀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠻⢿⣿⣿⣿⠟⠁⠀⡅⠀⠀⠀⢸⡟⠀⠻⣿⣶⣾⣿⣿⡿⢿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣀⠀⠀⠀⠀⠙⠦⠤⠶⠛⠀⠀⠀⠀⢹⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠈⠻⢄⡀
⠀⠀⣄⣀⣠⢴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿
⠀⠈⠉⠉⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⡀⠀⠀⠀⠀⠀⢼⡟⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠐⣿⣤⠴⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀⠀⣀⣠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣡⣶⣿⣿⣿⣇⠀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣋⣭⣽⣿⣿⣿⣿⣋⣤⣿⣿⣿⣧⡻⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⢤⣀⢀⣀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣬⣿⣿⣿⣿⣷⣌⣻⣿⣿⡏⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣍⣉⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣶⣤⡈⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠉⠉⠉⠉⠻⢶⣄⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠉⠁⠀⠀⣠⡶⠶⢦⡀⠀⠀⠻⣦⠀⠀⢀⠏⠠⠀⠉⠓⠶⠤⣀⣠⠞⣉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠙⣆⠀⠀⠹⣇⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⢠⡶⠾⢶⣄⠀⠀⠀⠈⢧⠀⠘⣧⣤⠼⠄⠀⠀⢹⣾⠁⠛⠀⠀⠀⢀⡴⠋⠈⠃⠀⠀⠀⠀⠀⣀⣹⠶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⡆⠀⢻⡄⠀⠀⠀⠈⠳⠟⠋⣀⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣀⡤⠴⠚⠋⣥⠀⠀⠁⠀⢣
⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠀⣿⣀⣬⡅⠀⠀⠀⠀⠀⠠⢋⣤⣶⡦⠀⠀⠀⠈⠻⣄⣠⠎⢀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠡⠞⠋⢉⣁⣀⣀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣳
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢋⣵⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⡌⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡜⢀⣿⡏⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠂⣠⠏⠀⣸⣿⠃⠀⠀⠀⠀⠠⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠲⠤⠃⠀⣀⣾⡿⠁⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡆⠀⢰⠋⣀⣀⣀⣉⣀⣀⣀⣤⣴⣾⣿⡿⠁⠀⣴⡟⡸⠀⠀⢀⣤⡴⠶⠟⠻⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠙⢦⡘⢦⣄⡉⠉⠉⠛⠿⠿⠿⠿⠛⠋⣀⣴⡿⠋⢠⠃⢀⡼⠋⠁⠀⠀⠀⣠⠄⠀⠀⠉⠛⠷⣶⣤⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⠪⢝⡛⠶⠶⣦⣤⣴⡶⠶⠟⠋⠁⠀⠀⡞⢠⡟⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⡰⢳⡾⠁⠀⠀⢤⣄⣛⣁⣤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣮⡑⠢⢄⣀⣀⡤⠚⠁⣼⠁⠀⠀⢀⣀⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣬⡳⠀⠀⠀⠀⠀⠀⢺⣆⠸⠏⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⢀⡤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠀⠀⠀⠀⣼⠃
⠀⠀⠀⡞⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⣶⠏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣍⠢⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠹⣄⠀⠀⡇⢀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⡇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⢆⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠼⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠀⣠⠚⠉⠉⠓⠒⠦⣵⣒⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⡆⢇⠀⠾⠿⢿⣿⣿⣶⣌⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢀⡼⠈⠑⠲⠦⣤⣀⠉⠛⢿⣷⡄⠈⢷⡄⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡀⠀⣉⣵⠚⠁⠀⠀⠀⠀⢤⡄⣠⠋⠀⣇⠀⠀⠀⠀⠉⠛⠶⣄⡈⠃⢀⣼⠇⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⠁⠈⠳⢄⡀⠀⠀⠀⢀⡼⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠉⣛⡿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡤⠋⠀⠀⠀⠀⠀⠙⢦⣀⡀⣀⣠⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⣄⠀⣠⠄⠒⠂⠀⠀⠐⠒⠒⠈⠉⠀⠀⠀⢡⠀⢀⠖⢉⠤⠄⣉⡑⡄
⠀⠀⠀⠀⠀⢀⠤⠊⠀⢀⣤⠶⠒⠂⠘⡖⢂⠀⠀⠀⣀⣠⣀⠀⢀⡤⠶⠤⣄⠀⢸⠀⢸⠀⠇⠀⡠⠚⣉⢝⠠⢄
⠀⠀⡠⠔⠊⠁⠀⣀⠀⠸⠀⢀⣤⠤⠄⠘⡌⡄⠀⠚⠁⠀⠈⠁⠈⠀⣀⣀⡀⠀⢨⠔⠁⡸⠀⠀⢧⡞⣊⠥⠒⠉
⠀⢎⠀⠀⠀⣰⠟⠉⠁⠀⠀⠸⠁⠀⢀⡀⠘⣷⠀⢠⠶⠛⠓⠄⠀⠘⠉⠉⠉⠀⡖⠒⠊
⠀⠈⠢⡀⠀⠃⠀⣴⠞⠃⠀⠀⡀⣠⠎⢱⠀⢹⢃⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠈⡶⢄⠀⠁⠀⠀⣀⡭⠞⠁⠀⠸⠀⢸⠈⢆⠀⣠⢶⣒⠛⠿⠟⠻⠄⠸
⠀⠀⠀⢠⠀⠎⠑⠤⡀⠙⠤⣀⣀⣀⠔⠁⠀⡌⠀⠈⢦⡉⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠈⣼⡀⠀⠀⠈⠒⠤⠤⢀⣀⣀⡠⠔⠁⠀⠀⠀⠉⠢⣀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠈⠫⣁⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣈⠆
⠀⠀⠀⠀⢐⣉⡁⠬⠄⠒⠊
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠴⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⠶⠀⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠉⠁⢀⠀⠀⢠⣿⣿⣿⣿⣻⣿⣿⣿⠿⠄⠁⠀⠀⠀⠠⣤⡀
⠀⠀⣀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣈⠙⠁⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣦⡀⠀⠀⠀⠀⠙⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⡛⢃⣰⡿⠋⠁⢻⣄⠀⠀⠀⠀⠀⣿⣿⡆⢀⣀⠄⠀⡌⢻⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣏⣿⡿⠋⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢻⣿⢧⣾⣿⡄⠀⠂⠀⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣧⠸⡆⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⣽⣧⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠘⠺⠇⠀⠀⠀⠈⠿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⡿⠁⠀⣨⡉⠛⠛⠛⠙⠿⢿⠿⠿⣷⣤⡀⠀⢀⣤⣤⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⡇⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢶⣾⣾⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠿⠾⠛⠛⠙⣿⣿⡻⠿⣿⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣽⣿⡿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⠀⣠⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠤⠤⠤⠴⠒⠊⠉⠀⢀⠀⠀⠻⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡆
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠛⠛⠁⠀⠂⠀⠀⠀⠀⣴⠓⣦⠀⠀⠀⠠⠀⡊⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠆⡀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⢀⠀⠠⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⢸⡏⣛⢛⡛⡧⠀⠀⢰⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠉⠈⢰⡇⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⡀⠀⢰⡄⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡾⠃⠀⢠⠆⡆⣀⣀⣀⠀⢤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⣠⣶⣇⡀⠀⠀⠀⠀⠀⢀⣠⣴⢺⣿⡏⣿⣿⢻⣦⡀
⠀⠀⠀⣿⣿⣿⣿⣦⣀⣥⢴⣿⣿⣿⣿⣸⠿⠷⠿⠿⢼⣿⡏
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢰⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⡿⠟⣛⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢟⣛⣛⣛⠿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⡇⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠋⠁⣀⣉⢻⣇⠘⣿⣿⣿⣶⣤⣀⣀⡀⢀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠙⢿⣷⢻⣧⣶⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⠿⠟⣻⣿⣿⣿⢣⣶⣬⣛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⡇⣿⣿⣵⣶⠾⠿⠿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣠⣿⣿⢿⣿⣿⢡⣿⣿⡿⢁⣀⣀⣀⣈⣿⣿⢻⡏⣀⣀⡈⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣸⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡈⠛⠻⠿⣿⣿⠿⠟⠋⠀⢀⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢈⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠈⠻⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣤⣤⣾⣿⠏⠀⠀⠀⠀⠀⠙⣿⣿⡏⢀⣠⣤⣤⣤⣀⠀⠘⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣿⣿⣿⣿⣿⣧⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⠋

⣿⠿⢿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣟⣿⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⠶⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠟⠛⠛⢉⣁⢤⡀⢰⣟⣉⡉⠁⠀⠉⢉⣿⡆⠀⣤⣀⠈⠉⠛⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠶⢤⣤⡈⠉⠒⠉⠀⠉⠛⣿⣿⣿⣿⣟⠋⠀⠀⠶⣉⡀⠖⠉⠀⠀⠀⠉⠻⢷⣦
⠀⠀⠀⠀⢰⡿⠁⠀⣀⣀⣤⣤⣤⣤⣀⡈⠛⣃⣴⣶⠛⣿⣿⣟⢉⣿⣿⣿⣷⣦⡙⠁⠀⣴⣶⡛⠿⣿⡟⠶⣦⡙⣿⡄
⠀⠀⠀⠀⢻⡇⠀⢾⣯⡉⣻⠿⠛⠋⣙⣿⠆⣿⣿⣿⣇⣼⣿⣿⠀⣿⠸⣿⣿⣿⡗⠀⠸⣿⣀⣁⣚⣉⣁⣠⣼⠇⣸⡇
⠀⠀⠀⠀⠈⣿⣦⣌⠉⠛⠻⠷⠾⠿⠟⠉⠀⠀⡙⠻⢿⣿⣿⣿⣴⣿⣿⡿⠟⣩⡐⠶⢦⣬⡉⠉⠙⠛⠉⠉⢁⣴⣿⠁
⠀⠀⠀⠀⢸⡏⠉⣻⣿⣦⣄⡀⠛⠁⠴⠛⢠⠟⢀⣴⣟⠻⣿⣿⠟⠛⣶⣄⠰⡄⠉⠲⣄⠀⠙⠁⢀⣀⣴⡾⢿⡏⢻⡆
⠀⠀⠀⠀⢸⣇⠀⢻⣦⣈⡙⠻⣿⣶⣦⣤⣤⣀⣈⣿⣿⣿⣯⣵⣾⣿⣿⣏⣀⣤⣤⣤⣬⣴⣾⣿⣿⣿⣭⣴⠟⠃⣼⡇
⠀⠀⠀⠀⠀⠻⣷⣄⠀⢉⣿⣿⠿⢿⣿⠉⣹⣿⣿⡿⠿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣿⡟⠁⢀⣼⣿⠿⠛⠋⢁⣼⠛⠋⠉⠁⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⡿⠿⣿⣶⣤⣤⣄⣙⣻⣶⣤⣤⣤⣴⣾⣯⣤⣤⣤⣶⣶⣾⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣤⣄⣉⣉⡉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⣿⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠉⠉⠛⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣾⣇⠀⠀⠀⣀⣴⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⣿⣿⣷⣶⣿⣿⣿⠟⠉⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠁⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠛⠛⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡀⠀⣠⣶⣿⣿⠿⠋⠁
⠀⠀⠀⣠⣾⣿⡿⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣿⣿⡿⠛⠁
⠀⢀⣴⣿⠟⠁⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉
⢀⣾⣿⠋⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠉
⣾⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋
⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⢀⣤⣾⣿⠿⠋
⣿⣿⣆⠀⠀⠀⠀⠀⢀⣿⣇⣴⣿⡿⠟⠁
⣿⣿⣿⣧⡀⠀⠀⠀⣾⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣦⣀⣴⣿⠟⠉
⣿⠃⠈⠻⣿⣿⣿⣿⣧⣀
⣿⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠁⠀⢹⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⢁⡀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠇⡀⠀⢰⠗⠒⠭⣁⣶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠭⠉⠀⠀⠀⠀⠀⠀⠀⢰⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠈⡀⠁⠉⣷⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⣾⣗⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⣠⠌⠀⣿⡄⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⣀⠀⢐⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡝⠒⠒⠒⠒⠓⠚⠀⢸⡐⣾⣿⠇⢴⣿⣢⠀⠀⡙⠚⠟⠛⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⣷⡟⠁⢛⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⢠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢲⡀⠀⠀⠀⠀⠐⠋⠙⠀⠆⠤⢿⣏⡀⣶⣧⡌⠂⠀⠀⠃⠀⠒⣴⠶⠚
⠀⠀⠀⠀⠀⠀⠘⢦⡶⡲⠚⠝⠁⠀⠀⣄⢂⠀⠀⠰⣤⣤⣂⣸⡿⠀⠈⠙⠁⠀⠀⢁⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠅⠂⠀⠐⠀⣹⣏⡟⡿⠁⠐⠀⠀⡄⠀⠀⡞⠉⣑⠒⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣤⣶⡀⠀⠀⠀⠀⠀⢀⠏⠹⠿⡆⠀⠀⠐⠢⡲⠦⠤⠁⣾⢏⠁⡲⠀⠰
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠳⢽⡿⠛⡇⠀⠁⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠱⡥⠀⡀⠐⡟⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠰⡇⢰⠃⠀⠀⠐⠁⠐⠈⠺⠐⠀⠒⠂⠲⠀⠫⣻⡉⠸⠆⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡿⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠙⢯⣢⠄⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⢋⠀⠀⠀⠀⠀⢤⣤⠰⡔⠂⣒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠋⠉⠉⠉⠙⠀⠀⠀⢠⡄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⢆⣀⣠⡀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⣤⡀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⢀⣼⠗
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣶⡶⠟⠁
⠀⠀⠀⠀⢠⣀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠐⠛⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢹⡿⠋⠁⠀⣠⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡏⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣄⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⡉⠉⢹⠻⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠉⠁⠀⣱⠀⠀⠀⢰⠁⠀⠱
⠀⠀⠀⠀⠀⢀⡠⠔⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡠⠔⠚⠋⠉⠉⠳⠖⠄⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠦⣄⡀⠀⠀⣰⠏⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⡾⠀⠀⠈⢂⣀
⠀⠀⠀⠀⠀⠠⢤⣤⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣼⣥⣤⣤⡶⠉⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⣷⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣼⣿⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⡟⠋⠉⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣦⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⠛⢿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⣿⣧⣤⣼⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣷⣶⣤⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠈⠉⠛⠻⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣶⣦⣤⣀⡀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠉⠙⠛⠿⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣤⣀⣀⠀⠀⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⠛⠻⠿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣥⣤⣀⡀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠙⠛⠿⢿⣿⣿⣿⣿⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠖⠒⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣯⣁⡀⠀⠀⠀⠀⠀⣠⣽⠿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⡞⠋⠉⠉⠉⠻⣿⣿⣷⣤⡀⢿
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡛⠿⠿⣿⣿⣿⣿⣶⣦⣴⠟⠋⣀⣀⣤⡤⠴⣶⣶⣾⣯⡉⠁⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⢿⢰⣶⡄⠉⠙⠲⠤⣍⣹⠿⠿⠛⢶⣿⣿⣿⣅⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⣀⣀⣈⡿⠿⡿⠃
⠀⠀⠀⠀⠀⠀⢸⡎⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⡙⢿⣿⣿⣷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⣀⣠⠤⠽⠟⠛⠋⠉⠉⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡏⢦⠙⢿⣿⣿⣷⣤⣤⠤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣠⣶⣆⠀⠀⠀⢀⣀⣀⣤⣤⠽⠶⠟⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠟⠛⠋⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣷⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠶⢶⡞⠛⠛⠉⠉⠈⣿⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣤⣴⠶⠶⠛⠛⣿⠉⠁⠀⠀⠀⠘⣧⠀⣀⣀⣤⣤⣾⠷⠶⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢀⣸⣧⣤⣤⠶⠶⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠶⠟⠛⠋⠉⠉⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⠶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡴⠶⠾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠶⠶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠖⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠖⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⣠⡤⠴⠶⠒⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡶⠾⠶⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⡅⢀⡞⣾⡖⣶⣦⣽⠃⠈⢸⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⡗⠛⠏⠹⡰⣴⠆⠈⡹⠿⢺⠀⠀⠀⢀⠀⢓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡇⢶⡟⠈⡗⠒⠚⠀⢷⡦⢸⠀⠀⠀⠈⡠⠎⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢄⡀⢃⣀⣒⣀⡇⠀⢀⠀⣆⢀⡘⢀⣠⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣺⡏⠉⠁⠀⠈⠉⢹⣿⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢁⠹⣧⠀⠀⠀⢠⠋⣻⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⠀⡾⠀⠀⠀⡇⠀⣸⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⠀⠓⠒⠒⠐⠗⠀⠌⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠛⠉⠉⠉⠉⠉⠙⠒⠲⠤⣀
⠀⠀⠀⠀⠀⢀⣠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢹⡾⠀⠀⠀⠀⡀⢤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣾⣶⡄⠀⠀⢰⡇⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣷⡄⠀⠀⠀⣀⠀⣧
⠀⠀⠈⠀⠀⣠⣤⣤⡀⠀⠙⣿⣿⠗⠋⠉⠻⢁⠀⠀⣾⡁⠀⠀⠀⠹⠍⠀⠀⠀⠉⢿⡏⠀⢀⣴⣿⣿⣻⡟
⠀⠀⠀⢄⣸⡿⣛⠿⢿⡆⠀⠀⢧⡀⠀⠀⠀⠈⣷⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⣼⣁⠈⢹⡋
⠀⠀⠀⠈⢻⣿⠁⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠏⠉⠁⠉⡇
⠀⠀⠀⠀⠈⠉⠁⠀⢰⠁⢄⠀⠉⢱⠶⣤⡀⠀⠀⠈⣿⣇⠀⠀⠀⣴⠚⠛⠛⠿⣠⣤⣄⠀⣠⣀⠀⣸⠃
⠀⠀⠀⠀⠀⣄⠀⠀⣼⣤⣴⡿⠟⣃⣀⣈⠙⣆⠀⠀⠸⣿⡄⠀⠀⠁⢸⠀⠂⠀⠀⡀⠉⠉⢉⣽⡞⠁
⠀⠀⠀⠀⠀⠘⢦⡀⢸⠋⢡⡶⠋⠁⠀⣈⡉⠚⢧⠀⠈⡿⠹⡄⠀⠀⠀⠳⣀⠀⠀⠀⢀⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡃⠈⠀⣠⠖⣋⣩⣤⢤⠎⢀⣼⠃⠀⠹⣄⠀⠀⠀⢈⣛⢛⣛⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣈⣡⠞⠋⠉⠀⠀⣠⡾⠁⠀⠀⠀⠈⠢⣀⠀⠀⠈⠉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠶⣄⠀⠀⢀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⠀⢀⠎⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣧⠋⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⡇⢀⣀⠀⠵⠀⢤⡤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠉⢻⣷⠀⡁⣈⣟⢩⡖⠺⣿⣼⡟⢢⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣤⣾⡿⠛⠛⠛⠙⠛⠓⠒⠓⠛⠒⠒⠋⠑
⠀⠀⠀⠀⠀⠀⢀⣠⠀⠂⠉⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠤⣄⡀
⠀⠀⠀⠀⣠⣺⣽⡆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⢰⣯⣗⣄
⠀⠀⠀⠸⢾⣿⣿⡇⢿⣷⣄⠀⠀⠀⡘⠀⠀⢀⣠⢶⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡟⢸⣿⣿⣷⡅
⠀⠀⠀⠨⣿⣾⣻⠷⢶⣒⣓⣛⣂⣤⣤⢶⠛⣽⡶⠟⠋⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠑⠲⢮⣟⣿⣿⡇
⠀⠀⠀⢐⣿⣿⣿⡇⣴⣶⣶⣶⢰⣶⣿⣿⡗⠁⠀⠐⠛⠛⠀⠐⠀⠂⠀⠐⠄⠂⠀⠂⠐⠂⠀⠈⠓⢯⡅
⠀⠀⠀⠈⠺⣹⠿⡇⣿⣿⣿⣿⢸⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠈⠙⠲⠬⠍⣟⣏⡬⠭⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠉⠉⠛⠻⠶⢦⣤⣄⣀⠀⠀⢰⣇⠀⠀⠈⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠻⣷⡶⢶⣾⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠈⠁⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⢷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣶⣶⣦⣤⣤⡆⠀⠀⢰⣼⣂⣰⣄⣉⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢴⡿⠋⢁⡠⠶⠬⠿⣝⢿⣿⣧⣹⢰⣿⣿⣿⠟⠻⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠒⢁⣊⣥⣶⣾⣿⣿⣷⣿⣿⡍⠓⠘⣿⣿⣶⣿⣷⣾⡿
⠀⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠀⡿⢿⣿⠿⠟⠁⠂⠀⠀⠀⠙⣿⣿⠟⢛⣿⠁
⠀⠀⠀⠀⣼⠛⠋⠃⠈⡀⠀⢠⠀⠀⠀⠂⠁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠻⣿⡄
⠀⠀⠀⠀⢹⣇⠀⠀⡀⠀⠀⠜⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣟⣢⣽⡇
⠀⠀⠀⢀⠼⢿⡀⠀⣷⠎⡠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⣦⣴⣶⣦⣤⣰⣿⡾⣿⡇
⠀⠀⢠⣿⡷⠦⠀⢄⡏⣸⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡿⣿⡿⣿⣿⠃
⠀⠀⠸⣧⣇⠀⠀⠲⡷⣻⡿⠿⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⣖⣈⡳⢖⣿⣅⡍⢷⡿⠃
⠀⠀⠀⢿⣿⠀⠀⠀⡟⢾⣷⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⢻⣟⠛⣿⣏⡟⠁
⠀⠀⠀⠸⣿⢧⠀⠀⡆⠘⠹⣿⠂⠑⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠲⣦⣤⣴⣿⣾⣿⡿⠁
⠀⠀⠀⠀⢿⣮⣂⣴⢄⡴⠀⣿⣄⡢⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⣿⡏
⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠘⢧⣿⠛⠂⠀⠙⠳⣦⣄⣀⡀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡒⠖⣠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⢤⣤⡤⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠁⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠶⠂⠒⠶⠂⠒⠳⠓⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⢑
⠀⠀⠎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⡓⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⡎
⠀⠀⠳⡄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡇
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢤⠠⠄⠄⢤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣵⣦⣤⣤⣤⣤⣤⣶⣵⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠤⠤⠤⠤⠤⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⣀⣰⣄⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴

⡇⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣄⣦⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⡜⠀⠀⠀⠔⢲⡀⢙⣛⠿⣾⠧⣄⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠳⡀⠀⡞⠁⠀⠀⠀⠀⠈⣿⣨⠭⠉⡀⠁⠈⠢⡙⠢⠀⠀⠀⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠸⣿⠀⠀⠀⠀⣀⣨⠶⠀⠀⡀⢀⣀⣠⣴⣿⣿⢿⣾⣷⠆⠈⢷⡀⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿
⡃⠀⠀⠀⢀⣿⠀⠴⠖⠋⡠⠃⠀⠀⢰⣿⣿⡟⠃⢹⠙⠀⢸⡙⠛⢦⡀⣸⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠂⢸⡇⠀⠀⠀⡰⠁⠀⠈⠒⢺⡿⠇⠑⠘⢉⠀⠀⠈⢳⣤⠀⢻⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⡇⠀⠀⠀⠁⠀⠀⠀⢀⠊⢹⣒⣀⣼⣷⡷⠶⠈⣾⣿⢹⠎⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠁⠻⡿⡏⣇⠀⠀⢳⠀⣸⣀⡿⠁⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡜⠀⣿⣿⣤⣤⣸⡶⣷⣾⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⡇⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡎⠙⠏⠀⣼⣿⣿⣿⠉⢻⠁⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠆⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣪⠊⢹⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⢄⠀⠀⠀⠀⠀⣿⠇⢀⠠⠄⠀⠀⠒⠒⠒⠒⠀⠤⢅⡂⠁⠀⠀⠀⠀⢀⢧⡎
⠀⠀⢀⠂⠄⣀⠀⠀⢀⣀⣀⡤⣤⡶⠞⠋⠁⡘⡂⢣⠀⠀⠀⣾⡽⡰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢰⣯⠛
⠀⠀⠀⠀⠘⠩⡙⠛⠈⠉⠉⠈⠀⠀⠀⢀⠀⠈⡢⠈⡄⠀⣸⡽⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢕⡕⡄⠈⢻⣦
⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠖⠀⡙⣩⣅⣀⣨⡀⡇⠀⠹⣧⡇⠂⣠⣴⣦⡀⠀⠀⠀⢀⣤⣤⣤⡀⠀⢂⢕⠁⡱⠀⠀⡗⡆
⠀⠀⠀⠀⡅⡨⠀⠀⠀⠀⣀⣠⣴⣟⠅⠀⠈⠉⢩⡅⢣⠀⠀⢹⠀⠈⣁⣄⡈⠛⠀⠀⠐⠋⣁⠀⠉⠿⠀⢐⠩⠀⡇⠀⣰⣧⠃
⠀⢀⢤⣴⠀⡪⠀⠀⠀⠠⣍⣀⣉⣡⡆⢰⣹⠼⠿⢅⡈⣆⠀⢸⠀⠼⡛⠂⢬⡄⡆⠀⣴⠿⢉⡉⢢⠀⠀⠀⠊⠀⣤⡾⠛⠁
⠀⣿⡏⠙⠨⡂⠀⠀⠀⠀⠑⠤⠴⠟⠇⠀⢳⡁⠀⠉⠀⠘⡄⡆⠂⠀⠀⠉⠀⢠⠁⠈⠁⠤⠤⠌⠲⠀⠀⠀⠀⠀⡇
⠀⢻⣷⢠⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⢙⡄⠀⠀⠀⡿⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠅⠀⡇
⠀⣸⡏⠸⠈⣂⠀⠀⠀⠀⠀⢠⠀⠀⣈⣽⣷⣛⡈⢢⡺⡣⣏⠈⣕⠒⠄⠸⣄⣀⣤⠴⠀⢀⣀⡀⠀⠀⠀⠀⣀⠀⡇
⣰⡿⠀⠀⢇⢑⠀⠀⠀⠀⠀⠇⢠⠊⢀⣀⣀⣈⡙⣷⠁⢰⡇⠀⣿⠦⡀⠀⠈⠚⠁⠀⠀⠀⣠⠆⠀⠀⠀⡅⡂⢠⠁
⣿⡁⠀⠀⠈⢦⠣⠀⠀⠀⠀⠀⣧⡾⠋⠀⠐⠒⠈⡉⢀⡟⡂⠀⠹⣧⡈⠁⠒⠒⠒⠒⠒⣩⠎⠀⠀⠀⠐⠑⢀⠎
⢹⣧⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⡌⠀⡘⢻⠄⠀⠀⠙⠿⣦⣤⣀⣀⠤⠖⠁⠀⠀⠀⠐⡐⡠⠊⡔⡠
⠀⣿⡇⠀⠀⠀⠀⠈⠳⢄⠠⢄⡀⠀⠀⠀⠀⠀⠅⡰⠁⠈⢆⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠰⢂⠜⠁⠊⠈
⠀⣿⢣⣶⠀⠘⠻⢷⡄⠀⠉⠒⠬⣄⡒⠢⠄⢊⡴⠁⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣩⠔⠁
⠘⠛⠚⠋⠀⠀⠀⠈⠿⣦⣤⣴⠾⠋⠁⠉⠉⠁⠢⠔⠀⠀⠀⠀⠈⠓⢌⡒⠤⠂⠒⣙⡨⠔⠉
⠀⠀⡀⠀⡄⢄⠀⡠⢀⠀⡀⠀⠀⡀⢀⠀⡀⡀⢀⠄⡀⠀⠄⠠⡀⢀⠄⡨⡩⢉⠍⡠⠠⢀⠔⠠⡂⢀⠔⡠⡠⠂⢄⢄⢄⠄⡠⢄⢀
⠀⠀⠁⠊⠂⠑⠩⢒⠅⢊⢔⡡⡪⢀⠅⡪⡨⢐⠁⡨⢊⠔⡡⢊⠔⡡⢊⢀⠔⡡⢊⢀⢔⠕⡡⢊⠔⡡⡤⢊⢔⠔⠕⠕⠡⠺⠓⠑⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⢠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠷⠿⠶⠶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⠟⠛⠀⠉⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡴⠟
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠉⡘⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠠⠁
⠀⠀⠀⢀⢦⡄⢊⣥⣤⣬⠒⠀⠀⠀⠀⠀⠀⠀⠀⢁⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠙⡜⢛⡳⡉⣦⠀⠀⠀⠀⠀⠀⠀⠀⢊⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠳
⠀⠀⠀⠀⢀⢠⣥⠂⠘⣱⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠓⢦⣤⡀⢀⣀⠀⣀⡤⢒⡍⠚
⠀⠀⠀⠐⠂⠀⠙⠻⠿⠚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡤⠋⠀⠀⠀⠀⠘⠓⠲⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⣴⡾⠿⠟⠛⠛⠛⠻⠿⣦⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⣾⢟⣠⣴⠶⠚⠊⠉⠙⠛⠒⢦⣽⡆⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⢠⡿⠃⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣷⡶⠞⠋⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠁⠀⠀⠀⠀⠀⠀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣿⣿⣷⠤⠄⠀⠀⠀⠀⠀⠀⠀⣾⠀⡀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣶⠆⠀⠈⢳⡈⠀⠀⠀⠀⠀⠀⠀⠃⢠⡇⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣸⡟⡀⠀⠀⠀⠀⠀⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⡿⣯⣤⣤⣤⡤⠴⠊⠀⠀⠀⠀⢢⡄⠻⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠤⠤⠶⠶⠖⠓

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⡻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⡛⢻⣿⡟⠿⢿⡿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢣⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣿⣿⣿⣆⣠⣾⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣷⣦⣠⡿
⠀⠀⠀⠈⠹⠿⠛⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣸⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣄⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢹⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣠⠀⠀⠀⠀⢀⡾⠂⠀⠀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣿⣧⢶⣀⣠⣴⠟⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠻⣆⡘⢿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠈⠛⠛⠛⠉⣻⣿⣿⣿⣿⣿⡷⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⣶⠄⣴⣶⣆⢈⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢹⣿⠁
⠀⠀⠀⠀⢠⣿⠀⣻⣿⣯⣾⡟⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠟⠀⠀⢤⣄⣀⠀⣀⣻⣿⣟⣀⢾⣿⣿⠟⢐⡟
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⢻⣿⣿⡿⣿⣿⣿⣶⣾⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠟⠉⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠻⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡿⠀⠙⣿⣟
⠀⠀⠀⠀⢠⡼⠇⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⠀⠀⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⡀⠀⢀⠀⣇⠀⠀⢀⣤⣤⡆⠀⠀⠀⡇⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠠⡇⠀⠑⠛⠏⠉⠀⠈⠻⠟⠇⠀⠀⠀⡇⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢰⡇⠀⠀⠀⠐⢷⣤⣤⡴⡗⠀⠀⠀⠀⣇⢀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣈⣁⡤⠄⠀⠀⣄⠉⠉⣰⠁⠀⠐⢤⣄⣉⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠦⠤⠐⠶⠶⠧⠬⠤⣾⡟⠛⠳⠶⠚⢯⣉⣀⣀⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣒⠀⣿⡉⢉⣻⡟⡇⡿⡍⠿⠸⠿⠉⡽⢽⡉⢹⢿⠻⠛⢻⣿⢻⢓⡧⢄⡛⠪⣥⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠈⢀⣠⡄⠂⣈⢶⡇⡇⣿⣿⣀⣿⣪⣦⡘⢋⡩⢾⣼⡿⣿⣿⣿⣸⢯⠲⢀⣇⠀⠘⠀⠈⠉⢿
⠀⠀⠀⠀⠀⠀⠀⡰⢨⢂⠠⠤⣶⠞⠙⠁⣿⣤⣥⣿⠿⠃⣧⣾⢳⡆⠉⡻⡇⢘⡧⢸⣺⠀⡛⢰⡟⠙⠃⠉⠉⠉⠹⠉⠉⣾⠀⡼⠆
⠀⠀⠀⠀⠀⠀⡔⢠⠃⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣬⠽⢠⣾⣿⣧⠌⣷⣼⡿⠾⢿⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢛⢢
⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠃⣬⣥⡟⡋⢀⣭⣼⣙⢁⣤⣼⣷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠸⡜⡆⢀⣀⣠⣤⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣷⣀⣙⣛⣛⣓⣒⣻⣞⣾⣶⣿⣘⣻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⠟⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣤⣄⡉⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠲⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣷⣦⡈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠋⠉⠉⠀⠀⠈⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡔⠋⠀⠀⢀⣈⣵⣦⠀⠀⠀⣴⣯⣁⡀⠀⠀⠙⢦⡀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡞⠀⣀⣴⣾⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣷⣦⣀⠀⢳⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⡗⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⣀⣤⣤⣄⡀⠙⠛⠻⠟⠛⣩⠴⠶⠒⠶⠤⣍⠛⠻⠟⠛⠉⣀⣠⣤⣤⣀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡴⠋⢰⣿⣿⣿⣿⣷⡄⠀⢠⠞⠡⡉⣱⠀⠎⢉⠌⠳⡀⠀⣠⣾⣿⣿⣿⣿⡀⠙⢦⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠁⠀⢸⣿⣿⣿⣿⣿⣿⠀⡏⡠⠢⡀⢀⣀⢀⠁⠄⢄⠃⢠⣿⣿⣿⣿⣿⣿⡇⠀⠈⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣇⠑⠒⢁⡈⠿⢜⡈⠂⠊⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠳⣄⠸⣿⣿⣿⣿⡿⠃⠀⠘⢦⠘⢁⡰⠀⢅⡨⠂⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⣠⠞⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⠙⠛⠛⠋⠁⣠⣤⣤⣤⣤⣉⠂⠄⠀⠀⠀⣀⣤⣤⣤⣤⣀⠉⠙⠛⠛⠉⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢇⠀⠉⠻⢿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⡿⠛⠉⠀⡼⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⢀⡠⣤⠰⠄⠖⠲⠲⡆⠲⠰⠄⡤⢌⣳⣄⠀⠈⠣⣀⠀⠀⠈⣹⣿⠛⣿⠃⠛⠹⠿⣿⣠⡄⣀⣠⠞⠁⣀⣰⡞⠷⠘⠋⢻⠲⢦
⠀⠀⠀⢀⣼⠏⢻⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⠀⠈⢸⡏⠛⠰⠆⡬⣉⡉⠉⡿⠣⣄⣿⢀⣀⣀⡀⣸⠀⠉⠋⠿⣲⡾⣌⢁⡀⠀⠀⠀⣸⣀⣼
⠀⠀⠀⢸⡉⠀⢸⣆⣤⢤⣴⢻⡟⠃⠋⠈⠁⢻⡞⠺⡆⣄⠀⠀⠀⡟⠘⠛⠗⢴⢿⣌⣈⠁⠉⣾⠋⢷⣦⡄⡀⣾⠀⠈⠈⠁⣻⠙⠛⠛⢻⡍⡄
⠀⠀⠀⠀⢓⡄⠲⠛⠉⠀⡗⢸⡇⣀⢀⣀⡾⢸⠇⠀⠀⣹⠷⢠⡤⣇⠀⠀⠀⠀⢸⠇⠉⠙⠁⠋⢹⡞⡏⠉⠛⠽⠦⣦⣠⡄⣿⣀⣀⡀⣸⣷⠅
⠀⠀⠀⠀⠈⡗⢳⡴⣠⡄⣇⢀⣀⣯⣀⣀⡷⣼⣠⡤⢿⠃⠀⠀⠀⠉⠘⠣⢦⣠⢼⡀⠀⠀⠀⠀⢈⡇⡟⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢹⠌⣧⠀⠈⠉⠉⡗⠉⠙⠉⠉⢹⠇⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠘⠋⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠶⣶⣤⡤⣧⢠⡄⣤⣠⡞⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠁⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⡄⠀⠹⠤⠤⢠⠖⠚⠆⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠀⠀⠄⠀⠴⠖⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⢰⠂⠀⠉⣦⠀⠐⢰⡀⠠⠀⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠈⠛⠓⠒⠋⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⣄⠤⢃⠢⠤⢤⠄⡹⡇⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⢸⡏⡏⡟⢠⣷⣸⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⠆⠀⠀⠀⠀⠁⠀⠀⠀⢀⣾⡿⠁⢀⣀⡀⢀⠀⡀⢀⠀⡀⢩⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠐⠇⠱⠇⠰⠿⠿⠼⠻⠼⠻⠇

⠀⠀⢀⣤⡤⣤⡀⠀⠀⠀⠀⠀⡔⣻⣽⢦⣠⢺⣭⠷⡀⠀⠀⠀⠀⡤⡤⠤⠤⠤⡤⣄⠀⠀⠀⠀⢀⡀⡀⡄⠄⠄⠂
⠀⣴⠛⢿⣤⣼⠿⣦⠀⠀⠀⠀⠻⣽⣏⠟⠘⢭⣏⡽⠁⠀⠀⠀⠀⡗⡇⢠⣀⠀⡗⣿⠀⠀⠀⠀⣤⣴⣦⣦⣦⣄⣄
⠀⣿⡶⠿⣤⠿⣤⣾⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⣏⡇⠸⠛⠁⣏⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠧⣴⣿⣤⠼⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠧⠧⠤⠤⠤⠯⠿⠀⠀⠀⠐⠿⠿⢿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣤⡄
⠀⠀⢠⠆⠀⠀⢦⠀⠀⠀⠀⢸⠙⠙⠙⠙⠽⠛⠛⠋⠫⡇⠀⠀⢀⣿⠿⠿⠿⢿⣇⠀⠀⠀⠀⣀⣴⣞⣙⣾⣙⣶⣄
⠀⣰⡿⠀⠀⠀⢩⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⠻⣉⡽⠋⠉⠀⠀⠀⠈⣷⣶⣶⣶
⠰⠷⢧⣤⣤⣤⣤⠯⠷⠀⠀⠸⠽⠽⠽⠽⠽⠿⠿⠿⠯⠇⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⢠⣙⣛⣛⣻⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠶⠀⡠⠠⢄⠀⠀⠀⠀⠀⠀⠀⢰⡆
⣤⣤⠀⠀⠀⠀⠀⠄⠤⣤⡄⠀⠀⣀⣀⡠⠤⢒⣊⣽⣿⠀⠀⠀⠐⡟⢻⡟⢻⡟⢻⡇⠀⠀⢀⡀⠀⢀⣾⣧⠀⠀⢀
⠻⣿⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠸⡇⢸⡇⢸⠃⠀⠀⠈⠙⠿⣿⣱⣎⣿⠿⠋
⣾⣿⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠉⢹⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⣧⢸⡇⣾⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠒⠠⡀⠀⣀⠄⠒⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠒⠒⠢⢄
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⡀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠠⠤⠤⡀⠀⠀⢀⣀⡀⢀⡀⠤⠤⢼⣠⢚⠉⠙⠒⠲
⠀⠀⠀⢱⡀⠀⠀⠀⠢⢄⠞⠁⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠘⠁⠀⠀⠀⠀⠈⢂⠀⠀⠀⡸
⡠⠚⠣⠚⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⣠⡄⠀⠀⠀⠀⠃⠀⢠⠃
⢣⠀⠀⠀⠀⢰⣉⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢀⠃
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⢠⠄⠀⠀⡜
⠀⠈⢧⠀⠀⠀⢠⣤⠴⠒⠳⡀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘⠐⠒⠒⣟⣀⣠⠼
⠀⠀⠈⢇⠀⠀⠈⡀⠀⠀⠘⣌⠂⠄⠤⠀⠀⡰⠻⡑⠀⠀⠀⠠⠀⢨⡇⠀⠀⠀⠀⠀⠀⠠⠞⠉⢱
⠀⠀⠀⠈⢆⠀⠀⣱⠀⡄⠀⠈⠑⠒⠀⠒⠊⠀⠀⠑⠢⠤⠤⠤⠒⠱⣇⠀⠀⠀⠀⠀⠀⢰⠼⠚⠁
⠀⠀⠀⠀⠈⠶⣉⡤⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠜⠁⢠⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠠⠔⢦⡀⠀⠀⠀⣀⠔⠳⣄⠀⠀⠀⣠⡀⠀⣀⠜
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢠⣦⣄⣿⡟⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠛⣿⣿⠇⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⢉⣽⣿⣿⣷⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⣰⣾⣿⡉⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠙⠿⣿⣿⣷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠘⣿⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣾⣋⠀⠀⠀⠀⠀⠀⣀⣨⣍⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⠿⠿⠿⠿⣷⣆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⣀⡀⢀⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⣬⣷⣵⣿⠏⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣙⣿⠛⠛⠛⠷⠷⠟⠛⠛⠂⠀⠀⢠⣶⠾⠶⠷⠿⠿⠿⣿⣷⣄⠀⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⡀⡀⡄⢀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠶⠛⠛⠛⠛⠻⠿⡾⠾⠷⠶⠷⠴⠶⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣬⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣶⣶⣶⣴⣤⣀⡀⢀⠀⣀⣠⣠⣀⡀⢀⢀⢀⣀⣤⣤⣀⡀⣀⣠⣠⣤⣤⣶⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⣀⣤⣴⣶⠿⠿⠿⠛⠛⠻⠿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣛⣽⢿⣿⣟⠳⠶⣯⣭⣻⣧⠀⢀⣾⣿⣷⣶⣤⣄⣀⣀⢀⣀⡤⠞⠋
⠀⠀⣀⡤⠤⠶⠶⠶⣼⣿⡵⠞⠋⠁⣸⣿⣿⣦⣄⣠⣤⣭⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⡋⠀⠀⠀⠀⠀⣼⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠻⣷⣤⣄⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣀⢻⣿⣿⠏⠉⠉⠛⣿⣿⠁⠀⣀⣀⣀⣀⣀
⠀⠀⠈⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡾⠛⠉⠉⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⢀⣠⣤⣿⣶⣦⣼⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⣿⣿⣷⠈⠛⠿⢿⣿⣿⠿⠿⢻⣿⣿⣿⢏⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠟⠁⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢫⣿⠋
⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣠⣤⣴⠾⠿⠷⣶⡄⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⣀⣀⣠⣶⣿⡿⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⣿⣄⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠈⠉⠉⠁

⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡠⠄⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣖⡶⠆⠁⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣼⡧⣠⡦⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠚⠚⠰⠐⠒⠓⠖⠒⠒⠃⠘⠂⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠋⠄⠲⠘⠒⠒⠖⠒⠂⠐⠐⠒⠒⠒⠂⠀⠒⠐⠖⠖⠐⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣶⣶⣶⢀⠀⠀⢘⣶⣶⣶⢶⣶⣆⢸⡆⢠⡎⣰⣶⡶⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⠿⠀⣴⣾⣿⡉⠁⠀⠀⢿⡄⠀⠀⠀⣸⠇⠀⠀⠀⠙⣿⣿⠟⠻⠿⣿⣿⠛⠁⠈⠙⠟⠁⠀⠉⢻⣿
⢻⣿⠛⠁⠀⠀⠀⠛⠻⡄⠀⠀⢠⠛⠃⠀⠀⠀⠛⢀⡀⢀⣀⣀⡟⠋⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿
⠘⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢷⡄⠘⢼⢢⢘⣁⢀⢀⢀⠗⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⣆⢠⠿⡼⣿⠼⠆⣸⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣻⡮⠟⠛⠋⠉⠀⠳⢼⡇⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤⣄⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣾⣿⣧⠀⣀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢻⡁⠈⠈⠁⠈⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣾⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⣇⣀⡀⣀⣀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣼⣬⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠀⠀⢸⡀⢰⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⡀⠀⢸⠇⢸⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣼⢹⡟⠀⣿⣿⡇⠀⢸⠇⢸⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⠯⠛⠋⠛⠧⣴⣀⠀⠀⠀⠈⢿⠗⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⡿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡭⠚⠉⠛⠲⠤⣀⡀⠀⠀⠀⢀⣠⡴⣮⡧⠟⠛⣹⣿⠛⠃⠀⠀⠀⠈⠹⢿⢟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣮⠝⠉⠀⠀⠀⠀⠀⠀⠀⠉⢓⣶⢾⣽⡶⠛⠁⠀⣠⣼⠟⠓⠦⣤⣀⡀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⣿⡾⠛⠁⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠈⠉⢓⣶⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡽⠋⠉⠙⠓⠲⠤⣤⣀⢀⡴⣏⣷⠟⠁⠀⢀⣠⡾⠛⠉⠓⠦⢄⣀⠀⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢯⠟⠀⠀⠀⠀⠀⠀⠀⠀⡽⣯⡿⠋⠀⠀⢀⢴⡿⠋⠀⠀⠀⠀⠀⠀⢈⡹⣾⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣡⠃⠀⠀⠀⠀⠀⠀⠀⢠⢮⡿⠋⠀⠀⢀⣴⡽⠋⠓⠢⠤⣀⡀⠀⣠⣖⡧⠟⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⢳⠷⠦⣤⣀⣀⠀⠀⠀⣴⣻⠟⠁⠀⢀⣴⡷⠋⠀⠀⠀⠀⠀⢀⡨⣯⡷⠋⣀⣴⡾⠛⠉⠉⠉⠐⢦⠄⣤⣄⡀
⠀⠀⠀⠀⠀⢠⢯⡏⠀⠀⠀⠀⠉⠉⢓⣞⣾⣯⠀⢀⣠⣞⡞⠲⠤⣤⣀⠀⠀⡰⣯⡿⠋⣠⣾⡟⠋⠀⠀⠀⠀⠀⢀⣼⡿⠟⠁
⠀⠀⠀⠀⠀⣾⣽⠀⠀⠀⠀⠀⠀⠀⡾⣽⠃⠀⠀⠀⠿⡷⣽⠟⠀⠀⠈⢉⢿⡿⠋⠀⣴⡳⠋⠉⠑⠢⢤⣀⢀⣴⡿⠋
⠀⠀⠀⠀⢠⣗⡏⠀⠀⠀⠀⠀⠀⣸⣽⡟⠀⠀⠀⠀⣰⣳⡏⠀⠀⠀⣰⣯⡟⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⡼⣿⠋
⠀⠀⠀⠀⢸⢿⡟⠛⠓⠒⠲⠶⢴⣟⣿⠓⠶⠤⣄⣀⢯⣿⠳⠦⣤⣠⣟⡿⠀⣰⡿⠛⠢⢤⣀⠀⠀⣠⣺⠞⠁
⠀⠀⠀⠀⢸⣽⡇⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⣜⣾⣧⣀⠀⡀⢸⣾⣇⣼⠟⠁⠀⠀⠀⠈⢙⣞⡷⠋
⠀⠀⠀⠀⠐⣿⡇⠄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⣷⡟⠙⠵⣿⣿⣿⣿⣿⡷⣤⡀⠀⠀⠀⣠⣻⠞
⠀⠀⠀⠀⠀⠙⠿⢼⣦⣄⠀⢀⣻⣽⣿⣦⣄⣀⣿⣾⠃⠀⠀⠀⠈⠐⠻⣿⣧⠀⢉⣳⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠬⣿⣿⣤⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡃⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠤⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠹⠆⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠆⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣿⣿⣷⣶⣤⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⠇⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⡼⢩⠟⣹⣿⣿⠛⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⢀⠏⢀⣿⣿⣿⡆⢠⣿⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠀⠈⠁⡟⢸⡇⣼⡟⠃⠇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢨⡇⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢿⠁⣿⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣽⣿⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢹⣿⡟⠉⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠰⠶⠿⠿⠗⠘⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣈⡁⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⣿⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢠⣾⠟⠿⠄⠀⠀⠀⠀⠀⠟⢣⣾⡿⢛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣿⣿⣶⣤⣄⠀⠀⠰⠶⣶⣾⢁⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⠛⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣮⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢸⡖⠒⣶⡖⣂⡏⠀⠀⠆⠰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃⠈⣄⣉⠄⡀⠀⠨⢀⣤⠇
⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⢉⣖⡀⠀⠀⢰⣿⣿⣀⣀⠀⡈⣷⡄⠀⠀⠀⠀⠀⠸⠀⣻⣺⣻⢉⠀⣄⢸⠀⢂⠿
⠀⠀⠀⠀⠀⠻⠷⠗⠒⠞⠛⠋⠹⠙⠻⠿⡿⠧⠮⡍⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⣎⡼⢿⢾⠿⣽⡿⠿⠦⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠚⠋⠁⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⡐⠀⠀⡰⠂⠀⡀⡄⠐⣦⠀⠸⢦⠀⠀⠀⠀⢈⡰⠋⠀⠀⠀⠀⠀⣠⣤⡤⢤⣶⡆⢰⠟⠗⠂⠤⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⡇⠙⠊⡅⠀⠀⠈⢣⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢠⠟⡷⠃⠊⠉⠁⠴⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠀⢸⠀⡘⠀⢀⠏⠁⠉⠃⠀⡆⠀⠀⠀⢀⡄⠂⣺⢀⣀⣀⠤⡔⠊⠀⠰⡀⢀⡀⠀⢤⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⡘⠀⠀⠀⠘⢄⠘⡄⠀⠀⠀⠙⠉⠀⠀⠽⢠⠀⠉⣈⡆⠀⠁⠀⠀⠀⠈⡀⠀⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⡐⠁⢀⡴⢦⠀⠈⢢⣀⠠⠀⠀⠀⢣⣀⡤⠴⠾⠛⠉⠉⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⣀⡌⠀⢀⡮⠤⠬⢧⠀⠀⠸⠇⡤⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢡⠀⠘⡀⠀⠀⠀⠈⠛⢿⣷⡴⠿
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠊⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢃⠀⠁⠀⠀⠀⠀⠀⠀⢙⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢠⡀⢁⣠⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠀⠄⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣀⡠⠄⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡼⠒⠒⠂⠀⠁⠉⠀⣀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢰⢃⠀⢀⡤⠒⠲⠄⠚⠁⠉⠉⠀⠥⡱⠂⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡇⠀⣆⠈⢀⡤⠤⠄⠀⠞⠉⠉⠀⠀⠆⠀⣀⣀⡀⠉⠐⠂⠀⠠⠄⢀⠀⠀⡇
⠀⠀⠀⠀⠀⣇⢊⠤⠆⠈⠀⠀⠀⣀⣀⡠⢴⠀⢾⠀⠈⠉⠉⠙⠆⠠⠤⣄⠀⠀⢀⠀⠀⣇
⠀⠀⠀⠀⠀⣷⡆⠀⠈⢆⠘⡉⠉⠉⠁⢀⠌⢀⢻⠀⠈⠉⠓⠀⠀⣀⣀⠈⠑⢀⠎⢀⠎⡡⠬⣁⠢⡀
⠀⠀⠀⠀⠀⢸⢌⠢⡀⠀⠢⢈⠑⠂⠒⠁⢠⠂⢸⠀⢀⡀⠠⠀⠀⠀⠈⠓⢀⡚⠂⣁⢼⠁⡠⠄⠓⡄
⠀⠀⠀⢀⡄⠠⢧⠑⠌⢢⠀⠀⠑⠂⠀⠒⠁⠀⠘⡐⠛⠋⠻⠷⡦⡄⠀⡠⠃⠈⠉⢀⠇⠀⢖⠋⠛⠂⡂
⠀⠀⠀⠈⠙⠢⡒⣪⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣁⠔⠁⠀⠀⣠⠋⡠⠐⠉
⠀⠲⡂⠈⠀⠀⠌⠀⠉⠂⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠈⠀⣀⠠⠀⠂⠁⠩⡀⠀⠈⠀⡒⠆
⠀⠀⠈⠂⠄⠪⣀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠂⠀⠀⠀⠀⠀⠒⠀⠉⠁⠀⠀⠀⠀⠀⢀⡰⣀⠄⠊
⠀⠀⠀⠀⠀⠈⠙⠳⠖⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠶⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠀⠀⠀⠀⠀⠒⠂⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡇⢸⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣰⣶⡟⣷⢷⢄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢑⠂⠀⠀⠀⠀⠀⠰⢡⣿⡤⣀⢅⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢾⠐⠀⠀⠀⠀⠀⠀⣑⣟⣌⡈⠜⠇⣸⠀⠀⠙⣦⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠉⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠠⡀⣲⢤⠠⢖⢿⢻⠻⠈⠈⠘⠀⠀⠑⠄⠀⢘⠆⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠉⠘⠀⠁⠠⣰⣸⡆⠳⡀⢺⢦⡀⠀⠀⢠⣻⣇⠀⠀⠀⠀⠻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠸⠁⠈⠐⠀⠀⣠⢠⣧⠀⠆⢸⠘⡇⠂⡀⠀⠿⢻⡄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣃⡴⠯⠖⠛⣤⡇⠀⡇⢳⠀⠁⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠋⠠⠒⠐⠂⢣⠀⠀⠀⢸⠁⠀⡇⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃⢀⠓⠐⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠈⢢⠘⠒⠀⠐⢺⠿⣧⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠂⠀⠀⠀⠀⠀⢈⠠⡄⠁⠀⠀⠀⡀⣀⣀⣠⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠜⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣄⡠⠄⠊⢀⣠⣾⣿⣦⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⠉⠈⠁⠀⠀⢀⣴⣾⣿⣿⠿⠛⠉⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠘⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣸⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣾⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠉⠉⠛⠓⠒⠶⠦⠤⠤⠤⠤⠤⠴⠖⠒⠊⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠈⣿⡟⠀⠀⢠⣶⣿⣿⡿⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⢧⣀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠶⠶⣄⠀⠀⣧
⠀⠀⢸⡏⠀⠀⠀⣠⣴⣶⣶⣶⣄⣀⣾⠟⠁⠀⢀⠀⠀⠀⠱⠀⢹⢀⡤⠶⠶⠶⠶⠦⠤⢤⣄⣀
⠀⠀⠀⢷⠀⢠⡟⠋⠀⠀⠀⠈⠙⢿⡏⠀⠀⠀⣼⣧⣀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⢸⡆⠟⠀⠀⢸⣦⢠⣷⣶⡄⠁⢠⣠⠞⣩⣤⣶⣦⡄⠆⠀⣿⣷⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⢧⣠⣦⡠⠈⣁⣭⣭⣛⡇⠀⠈⠩⣼⣛⣉⡀⠀⠁⠗⠦⢻⣵⠊⠉⠁⠀⢉⡇⠀⠀⠀⠀⡴⢶⣤⡀⠀⠀⠈⢱
⠀⠀⠀⠀⢸⡟⠻⡡⡿⠛⠉⠉⠙⠁⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⣿⣤⣤⣄⣙⣿⡇⠀⠀⠀⣜⡀⠀⠈⠙⢦⠀⠀⡎
⠀⠀⠀⠀⠀⢧⣠⠉⠉⠁⠀⠀⠀⢀⠀⠀⡀⠲⣄⠀⠀⠀⠀⠀⠀⠀⢿⡎⠙⠛⠛⠯⡄⠀⠀⣾⣭⣄⣀⠠⡀⠀⠳⢸⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢯⣵⠍⡔⠚⠋⠀⠀⢀⡉⠀⠀⠀⢸⣿⡇⠀⠐⠀⠀⠀⠀⢿⣉⠛⠻⠟⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢷⠀⠀⣠⠆⠀⠀⠀⠀⣀⠛⣀⣤⡴⢞⣿⠃⠀⠀⠀⣸⡿⠅⣠⢢⠄⠀⠀⢀⠀⠁⢠⡇⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠘⡇⠀⢷⡘⠳⣿⣟⣛⣛⣙⣉⣥⣶⣿⠇⠀⠀⠀⢠⣿⡧⠀⠈⠚⠷⠤⣤⠸⡆⠀⠈⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠙⢦⡈⠻⣿⡿⠟⣋⡁⠠⠋⠀⠀⠀⢀⣾⡷⠁⠀⣀⣀⡚⠀⠀⠀⠁⠀⢰⡆⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠁⠀⠀⠀⢥⡤⠄⠀⠀⠀⠀⢠⣾⢿⣷⠿⠛⠉⠉⠙⠛⢶⣦⡀⠀⠻⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⡈⠀⠀⠐⠛⠛⠓⠀⠀⠙⠟⠆⡀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⣀⣀⣴⠾⠃⠸⣆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣒⣂⠀⠤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠈⣽⠋⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⠤⠤⢄⡀⠀⣀⣀⣀⣀⡐⢳⣄⣀⣀⣀⣀⣀⣤⣄⣤⣤⡍⢱
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠈⠙⠉⠉⠀⠀⠀⠈⠛⠛⠛⡃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⣾⡤⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⠅⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⡄⢸⠂⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⣀
⠀⠀⠀⠀⢠⡇⢸⡄⠀⠈⠀⠀⠀⠘⠤⠴⠼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠋⢸⠀⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿
⠀⠀⠀⠀⠘⠇⢸⡁⠀⠠⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⠠⠄⢸⠀⠀⠀⠀⠀⠀⠀⠸⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⣼⠏⠙⠄⠀⢼⡺⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢠⢸⠅⠀⢸⠀⠀⠀⡴⠁⠀⠀⣸⠀⠘⢋⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾
⠀⠀⠀⠀⠀⢸⢸⡂⠀⢸⡄⠀⠀⢳⣦⣤⣴⣟⠀⠀⠉⠠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻
⠀⠀⠀⠀⠀⠈⢸⡇⠀⣼⣇⡤⣤⡧⡻⠿⢟⣠⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠏⠀⣿⠈⠹⢿⠰⣀⣉⣀⡼⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⢿⣀⣼⠒⠫⣉⣿⡖⠒⠛⠛⠃⢹⣦⣤⣤⣤⣤⣤⣤⣤⢤⡆⢸⣧⡤⠤⠤⠤⠤⣤⣤⣤⣾⡇⢸
⠀⠀⠀⠀⠀⢘⣸⠟⢻⢻⠀⠉⠁⠐⢤⣤⡽⠇⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣁⢸⡇⠁⠀⠀⠀⠀⠀⠀⠉⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠻


⣀⣠⣠⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀
⣿⣷⣺⣯⣝⣽⣩⣙⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣼⠛⠛⠶⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠞⠛⢻⡆
⠙⠷⠶⣤⣤⣀⣀⠈⠉⠉⠛⠛⠓⠶⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠛⠛⠋⠉⠉⢀⣀⣠⣤⡴⠶⠞⠁
⠀⠀⠀⠀⠈⠻⣯⠙⠛⠳⠶⠶⠶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠶⠛⠛⠋⠉⣽⠏
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠾⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⠟⠉⠉⠙⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠋⠉⠉⠻⣆⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣋⣿⣛⣛⣛⣭⠭⠭⠽⠖⠒⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣀⣤⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⢹⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠻⣝⠒⠤⠤⣀⣀⣀⣀⣠⣤⣦⣀⣀⣀⣀⡠⠤⠖⢚⡽⠋⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣷⠘⡇⠀⠀⠀⠀⠀⠀⣀⣼⡤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡶⠶⠶⠶⠶⣶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⣤⠤⢶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣟⣺⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠛⠶⣭⣛⠿⠿⠿⠷⣶⠾⠿⠿⠿⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠻⡍⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠢⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠠⠀⠀⠀⠀⡨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠈⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠈⠲⣶⣿⣿⡿⠁⠀⣠⡴⠀⠀⠒⠀⠉⠉⠉⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠂⠄⡀⠀⠀⠙⠢⣀⠀⠀⠄⠀⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⠙⠢⢤⣹⡀⠠⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠤⠠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠁⢐⠃⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠔⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢄⣈⣠⠞⠀⠀⢀⡀⡎⢧⣠⣴⣶⣶⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣄⠙⢛⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⣏⣶⣄⣤⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠖⠒⠲⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣠⠄⠛⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⡇⠀⠀⠀⠀⣠⡇⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣹⠆⠀⠀⠰⣏⠀⠰⡏
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡁⠀⠀⠀⠀⠙⣦⠀⠉⠢
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠋⠀⠀⠀⠀⠀⣠⢸⡆⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣦⠄
⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠀⠀⠀⢀⣠⠞⠁⠀⠳⢤⣄⡀⠀⠀⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣀⣹⠦⢤⣄⡀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠙⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡅⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠻⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⢀⣴⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣠⢿⣀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠤⠤⠤⠶⠶⠚⠛⠉⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⢸⡆
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠄⠘⢀⣾⢁
⠀⠀⠀⠀⠀⠠⡂⢻⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⡱⢃⠞⣠⠂
⠀⠀⠀⠀⢀⡩⠒⣁⠜⠛⢳⠶⣦⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⠴⢶⠞⣻⠟⡱⢣⠎⡔⠁⠴⠁⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠐⠁⠘⠁⠈⠀⠋⠀⠉⠀⠋⠐⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢄⣀⠀⠀⢠⡇⠀⣀⡤⠖⠂
⠀⠀⠀⠀⠀⢀⡠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⠄⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⡞⡤⠀⠀⠒⠒⠌⠉⠀⡌⠢⢈⣽⣻⠚⢛⣍⣁
⠀⠀⠀⠀⠀⠘⣦⡀⠀⣄⡀⣀⠀⠀⠀⠒⠂⡴⠩⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⣳⣴⠇⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠉⠉⠁⠀⠉⠒⠂
⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⠉⢉⡀⡀⠌⠃⢀⡃⠀⠀⠀⠀⠀⠀⠀⠂⠒⠊⠉⢱⠶⠚⢃⡇⠀⠀⠈⠁⠀⠀⠰⢰⣀⠇⠠⢄⡶
⠀⠀⠀⠀⠀⠀⠈⣷⠶⠘⣎⣙⡟⠚⠑⠀⠚⠫⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢈⡙⣟⣢⣤⡤⠤⠶⠒⠚⠉⠙⠲⠦⠭⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣶⣼⣷⣠⣃⣀⣿⣩⡷⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡔⠨⠀⣠⠄⡀⠀⠔⠂⠀⡀⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠉⠀⠉⠉⠀⠈⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣀⡁⢁⡃⠄⠰⠄⠂⠀⢹⠓⢦⡀⠀⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣶⡖⠒⡖⠀⣴⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⢡⠀⠄⠂⠐⢈⢰⠀⠘⠀⠀⢳⠀⠸⣾
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢹⡄⠋⠁⠈⠉⠁⡟⢛⠙⢦⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡂⢰⣄⣂⣸⣧⣬⠼⠋⠀⠄⠀⢸⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠏⢘⠘⡇⠀⠀⠀⠀⢠⡇⢈⠀⠀⡇⢀⠐⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠉⠹⣯⣀⣤⣤⢺⠀⠀⠀⠘⡀⠀⣇⣀⡆⠁
⠀⠀⠀⠀⢠⡤⡬⠀⢸⠀⡷⠦⠶⠦⠶⠾⣃⡀⠀⠀⢳⠨⣧⠀⠀⠀⠀⠀⠒⡴⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⢣⣀⠀⠀⠀⡘⢁⡄⡐
⠀⠀⠀⠀⢸⣀⠆⠀⠀⠉⠁⠀⢀⡀⠀⠈⡄⠀⠀⠀⠐⡖⠈⠳⠖⠀⠀⠠⣸⠀⠀⠀⠀⠀⡡⠀⠀⢠⣶⡄⠀⠙⢄⠀⣀⢈⣾⣯⣁⠀⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣠⠋⠙⢦⡀⠈⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠀⠀⡟⠋⠹⡄⠀⠀⠉⠁⠀⠉⠙⠻⠇⠀⠙⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡼⠁⠀⠀⠀⠳⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠰⢦⣄⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢴⣶⣦⣉⠻⣿⡷⠄⠀⠀⠠⢀⡆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⡙⠻⣿⣦⠌⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⢿⣷⣤⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢁⠆⣩⣤⠄⢠⣤⡄⢠⣤⡤⢀⣤⣤⠄⢠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠨⠼⠿⠏⠠⠿⠏⠠⠾⠏⠀⠼⠿⠇⠠⠿⠿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣠⣤⠴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠛⠋⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏⡻⠿⢛⣛⣿⡿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣧⡀
⠀⢀⣴⣾⠿⠛⠋⠉⠉⠻⣿⣿⠟⣛⣡⣾⣿⣿⣿⠟⠛⠿⣿⣇⠀⠀⠀⣀⣀⡤⢾⣿⣿⣿⣿⣿⣦⡀
⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠈⢹⣿⣿⣧⣤⣤⣤⣈⣿⣄⢠⡟⠉⠀⠀⣠⣽⡿⢿⣿⣿⣿⣿⣶⣤⣀⣀
⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢷⣄⣀⢠⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠙⠛⠛⠛⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣨⣭⣿⣯⣄⠈⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⠶⠶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⠟⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠉⠙⣿⣿⣿⠁⠀⠀⠀⠀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⣿⠋⠉⠀⠀⢀⠀⠀⢹⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⠛⣡⣴⣶⣾⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠀⠀⠙⣿⣆⣠⣾⢟⣛⣻⣿⣾⡏⣿⣿⠈⢿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣇⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⡶⠟⠛⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⠃⠙⠿⣿⣿⣿⠿⠋⢸⣿⣿⠀⠀⠀⠀⠈⠉⠉⣡⣴⣿⠟⠉⠀⠀⠈⠻⠶⠶⠛⠋⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⢀⣀⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⡛⠛⠛⠳⠶⠶⠶⢤⣤⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢳⡄⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⢴⣿⣿⣛⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠁⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁
⠀⠀⠀⢠⡟⣷⠀⠀⠀⠀⠘⠦⣤⡀⠀⠀⠀⣀⣀⣤⠇⠀⠀⠀⠀⢀⣴⡦⠶⣦⣤⣤⣤⡀
⠀⠀⠀⠈⠛⠋⠀⣠⣤⣤⣤⣴⠾⠁⠀⠀⠀⠙⢯⠁⠀⠀⠀⠀⠀⠈⢳⣤⣄⠀⠀⠀⣩⡗⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠻⠦⣤⣤⡄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⢸⠋⠛⠛⠁⠀⠀⠙⠛⠓⠶⠶⠶⠶⣦⠀⠛⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⡷⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢧⣀⣀⣀⣤⠶⠶⣄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠾⠋⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠘⣇⠀⠀⠀⠈⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠘⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠙⣧⣄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣧⠀⠀⠀⠀⠀⢸⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⣯⡿
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣴⠞⠛⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠒⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⡀
⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠿⠿⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆
⠀⠀⢸⠁⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠶⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⣤⡀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣇
⠀⠀⣹⡀⠀⠀⢀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⠶⠶⠾⠿⠶⣦⣤⣀⠀⠀⣽
⠀⡼⠋⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣟⠛⢷⣄
⢸⠃⠀⠀⠀⢀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢹⡄
⢼⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡇
⠸⣆⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⢈⣻⣶⡶⠶⠾⠿⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣠⡿⠛⠻⠶⢶⣶⣤⣤⣤⣶⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠈⠙⠻⠷⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠿⢷⣤⣀⣀⣠⣤⡶⠟⠙⠻⠶⠶⠶⠾⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣘⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢀⣶⣿⢿⢿⡿⠛⣣⣄⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡼⣫⣶⣿⣷⡜⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⡷⠙⢵⡾⠟⠡⣾⣿⣿⣿⣯⢻⣿⣿⣯⣭⣭⣭⣟⣛⠻⠿⣷⢄
⠀⢀⣠⣾⣿⣿⣿⣿⠋⠀⠀⠐⣳⣾⣿⣿⣿⣿⡿⠏⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣴⣿⣿⣿⣿⣿⢟⠉⠀⢀⡀⠈⠽⣿⣿⣿⢿⡗⠰⣧⠿⢠⡈⠛⢫⡿⠿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀
⢿⣿⣿⡿⠿⠕⣣⠊⠀⢻⣿⡄⣘⣉⡉⠉⠃⠀⢠⣾⣷⡦⠀⠀⠁⠀⢻⣿⣿⡿⠛⠂⠱⠀⡀⠀⠀⠀⠀⢀⣰⣵⣶⠂⠀⠀⠹⡄
⠈⠻⠻⡓⠀⡜⠁⠀⢠⣞⣥⣤⣭⣿⣯⠍⢀⣴⣿⣿⡻⠄⠀⠀⠀⠀⢤⣤⣈⡇⠀⣀⣼⡿⠃⠀⠀⠀⣠⣾⣿⣿⢋⡤⠀⠀⡠⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢿⡿⣿⣿⠟⣋⠡⠶⠚⢻⡿⠟⠳⢤⣗⠦⣀⣙⣿⣾⣉⣁⣤⡙⣿⣷⡄⠀⠀⣰⣿⣿⣿⣿⣿⡇⢠⣾⣿⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠛⢁⣼⣿⣦⣤⣴⡾⣷⣦⣤⣄⣝⣴⣄⠉⠻⣿⣿⣿⣿⣿⣿⠏⡇⠀⣰⣿⣿⣿⣿⡿⣫⣶⣿⣿⣿⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠀⠸⡿⣟⣿⡾⠿⠷⠿⠿⣽⡻⣿⣿⣿⣿⣧⠉⠙⠿⠻⠟⠋⠀⠁⣰⣿⣿⣿⣿⡽⣿⣷⣿⣷⣿⠋⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢰⡌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣓⣀⡀⠀⢠⣠⡴⠀⠘⢛⣯⣵⡿⣻⣾⣿⣿⣿⣿⣽⡇⢣⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣽⡿⠁⠠⣿⠟⣁⣀⣒⣛⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⡎⣶⡤⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣽⠏⠀⠀⢠⠏⣾⣿⣿⣿⣿⠻⢿⣿⣿⢻⣿⣿⣿⣿⣿⣯⣿⢻⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠀⢿⣷⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⡿⢋⣴⣯⣾⡟⣰⣿⣿⣿⣿⢿⣿⣦⣹⣿⣼⣟⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⣾⣿⡿⢿⣿⣿⣷⣶⣶⣶⢟⣵⣿⣴⣿⣗⢹⡟⣰⣻⣿⣿⣿⣿⣿⣿⠋⣿⢻⣏⠿⠟⡫⢴⣿⣿⠉⣻⡞⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡂⠉⣿⣝⣿⣷⣶⣾⣿⣿⣭⣩⡿⣋⣴⣿⣿⢿⢫⡞⣼⣿⣿⣿⣿⣿⣿⠿⠗⠀⢣⡿⢿⠃⠀⣠⣤⣤⡤⣆⣿⣿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⢩⡾⠿⠛⠛⠛⠛⢿⣿⣿⢿⡿⣻⢋⡴⣫⡀⢙⣛⣋⣭⣷⣶⢆⡤⠀⣠⣄⢸⣿⣷⡈⠻⣿⣿⣿⣿⣿⡿⢸⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⣦⣶⣶⣾⣷⣦⣤⣄⣀⠀⠉⠀⢒⡁⠀⣿⣿⣿⣿⣽⠿⣫⠞⠉⣠⢞⠙⢿⡓⠻⣿⣷⡀⠐⢿⣿⣟⣡⠄⣼⣿⢇⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣭⡅⣧⢾⣿⣯⣿⣤⣈⣐⣒⡛⢑⣿⣾⣾⣧⡀⢸⣿⣷⣈⣿⠻⣿⡇⠴⢿⣿⣿⣇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢹⣯⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⣃⡀⣿⣿⣿⡍⡄⢸⣷⣿⣿⣿⣿⣏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠟⠉⢠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⣿⣿⠗⠙⢿⣿⣿⡟⠋⠁⡀⢀⡜⢿⣿⡷⣼⣿⠿⣳⡧⠀⣿⢿⣿⣿⣿⣿⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠔⢂⠄⠙⣿⣶⣤⠀⢸⣿⣶⣶⣾⣷⡶⢿⡿⠭⠀⣿⠈⣿⣿⣿⣿⣷⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠾⠿⠟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣨⣿⣿⣿⡇⠸⢿⣿⣿⡽⠟⠛⠋⣠⣶⣤⣿⠀⢸⣿⣿⣿⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢈⣽⣿⣿⣿⡇⠀⠘⡿⣡⣴⣶⣾⡿⠟⢁⣿⠏⠀⠀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⡇⣾⣼⣾⣯⣶⣦⣤⣶⣶⣶⡗⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠙⠻⣯⡙⠋⠿⠿⠛⠛⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠻⣿⣿⣿⠁⠀⠈⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⣸⣿⣿⣦⣤⣴⣿⡟⠋⠛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣾⣿⣿⠟⠛⠛⢿⣿⣇⠀⢀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠙⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣼⣿⣿⣧⣀⣀⣀⣴⣿⣿⠀⠀⠀⣿⣿⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⠿⠿⣿⣿⣷⣶⣾⠛⠙⣿⣇⢀⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠰⣾⣷⡀⠈⢻⣿⣿⣿⣄⠀⢀⣿⣿⡇⠀⠀⢸⣿⣿⣿⡿⢷⣾⡿⠛⠻⣿⣀⣨⣿⡄
⠀⠀⠀⠀⠀⢤⠀⠘⢿⣿⣿⣄⠀⠹⣿⣷⡄⠀⠻⠟⠻⢿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡿⣿⣄⣠⣿⣇⡀⣀⣿⡏⠉⣿⡇
⠀⠀⠀⠀⠀⠘⣷⡀⣾⣽⣿⣿⡆⢀⣘⡉⠁⠀⣀⡀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠻⣿⡟⠉⣻⡿⠛⢻⣿⣾⡿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⠀⠀⠙⠻⢾⣿⣿⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⢈⡿⡾⢹⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⣷⣶⣾⣿⣷⣶⣾⣿⣷⣶⣾⣿⣷⣶⣾⣿⣷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⣿⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠙⢿⣿⣿⣷
⢀⣿⡟⣹⣿⣿⣿⣿⣿⠿⠿⠛⠻⠿⠿⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇
⣸⣿⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⣿⣷
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⣄
⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠉⠙⠂⠈⠋⢹⡇
⠘⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⣠⣄⡀
⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⠉⠈⣻⡄
⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠟⠀⠀⠀⢠⡄⠀⠀⢸⡇⢀⡏⠀⢀⣿⣀
⠀⠀⠀⣼⢋⣩⣉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢸⣿⠋⠉⠱⡟⠀⢹⠷⣦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣤⣤⣤⣤⠴⠶⢾⠋⠀⠀⠀⠀⠀⣸⣿⠀⠶⢾⣇⣀⡟⠀⣼⠁
⠀⠀⠀⠘⠷⢦⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⣈⡆⠀⠀⠀⠀⢠⡟⠹⣦⡀⠀⠉⠉⠙⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠉⠀⠀⠀⢀⣴⠟⠀⠀⣸⠇⠀⠀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠛⣶⣦⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⠴⢞⣻⡟⠁⠀⢄⡀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠀⢿⠉⠉⠉⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠈⠻⣷⣤⣄⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⣤⣼⠷⣶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠀⠀⢠⡾⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠻⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢹⡆⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧
⠀⠀⠀⠀⠀⠀⠙⠶⣆⠀⢀⠀⠀⣦⡾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠛⠛⠉⠙⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠶⠶⠋⠀⠀⠀⠀⠸⣧⣠⣤⡴⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠒⣶⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣴⠶⠶⠛⠛⠉⠀⠀⠀⢀⡟⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⡀⠀⠹⣧⡜⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠷⢦⣍⣑⠂⠤⢨⡟⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣏⣹⣌⡟⠛⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣍⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡯⠤⠤⠧⠤⠤⠤⠤⠤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⠂⠉⠉⠐⠪⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡟⡟⠈⣻⣻⠃⠙⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣴⡕⠁⠀⠀⠀⠀⠀⠀⠈⢫⣦⠤⠤⡄
⠀⠀⢀⣀⣀⣀⣀⣠⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣹⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁
⠀⠀⠈⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡞⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢀⣀⡀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡢⣀⣀⡀⠀⠀⢀⣀⣠⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠠⠤⠄⠤⠤⠤⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠓⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢠⡤⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠶⠈⢀⠁⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⢐⠀⠀⠀⠠⠀⢤⠄⠀⠀⠀⠠⠀⠄⣤⠀⠀⠀⠤⠀⠖⠊⠂⠀⠂⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠁⠀⠀⠠⠐⡀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠙⢿⣦
⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠲⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠈⢻⣷
⠀⠀⠀⣾⠀⠀⠀⠀⢀⡄⣀⠤⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢐⡗⠀⠀⠀⠀⡨⠋⡉⢚⢁⢠⢀⣀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣸⠇⠀⠀⠀⠀⡑⣒⢉⠊⡋⠛⠈⠑⠊⠃
⠀⢀⣿⠁⠀⠀⠀⠀⠛⠙⠊⠓⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢐⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣽⣿⣯⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⢿⣷⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⡀⠀⠈⠙⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⠛⠿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠛⠻⠿⢿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠠⠀⠤⠤⠤⠤⠤⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠐⠲⠤⣄⣀⡀⠐⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⢤⣤⣤⣉⣀⣀⡀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠄⠀⠀⠀⠈⢉⣉⠉⠁⠂
⠀⣀⠀⠀⠀⠀⠀⠀⡜⠀⡏⠀⠀⠀⠀⠀⡰⠒⠒⠒⠒⠒⠒⠶⠤⣤⠤⠤⠤⠀⢀⣀⠀⠈⠒⠒⠒⢲⠒⠒⠢⠤⠤⠭⣝⣡⣲
⠀⠀⠈⠉⠐⠒⠂⠀⠃⢰⠃⠀⠀⠀⠀⠀⣧⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢰⡄⠀⠇⠀⠀⠀⠀⡇⠀⠀⢠⠂
⠀⢤⠤⠤⠤⠀⢬⣼⡃⠋⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⣠⠊⠀⣾
⠀⠀⠓⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡾⡵⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣿⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡜⠀⠀⠀⢀⣽⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⢿⠀⠠⠤⠤⢄⣀⣀⣀⠀⠀⠀⠀⡅⠀⣷⠀⠀⠀⣼⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡆⠀⠀⠀⠀⠀⠘⠀⠠⢤⠤⠤⠤⢤⠤⢤⣌⣀⣀⣁⠰⠃⠀⠀⠀⢻⠇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠔⢋⡑⠠⡐⡓⠀⢀⠶⣤⣀⡀⠀⠀⠀⠀⡸⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠒⠤⢤⡠⠄⠊⠉⠀⠓⠀⠈⠐⠯⠗⡚⠁⡠⠀⠈⠉⠓⠚⣯⢅⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠠⣊⠔⠀⠀⠀⡠⠊⡠⠂⠀⢽⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠂⠀⠚⢤⡊⠀⠀⠀⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣍⡀⠐⠢⠤⣥⡀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣄⣬⣿⡟⠉⠘⠁⡄⠐⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⣽⠏⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠋⠈⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⣸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⡀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⢻⣿⡿⠛⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠉⢀⡀⢿⠟⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⣀⣴⣾⡇⣿⠃⠀⣼⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠅⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣈⣉⣙⠛⢷⣌⢿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣷⣦⡉⠀⢻⣿⣿⣿⣿⡿⢸⡇⠀⠀⣿⣉⠛⣿⣿⣿⣷⣶⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⡿⢟⣽⠇⠀⢸⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⡇⢸⣏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⠛⠛⠛⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠋⢠⣾⣿⣷⣾⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡟⠛⢻⣏⣨⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡗⠶⠀⠐⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⠾⠛⣉⣀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⠘⣷⡙⠿⣿⣿⠿⠟⣋⣙⣛⡛⢿⣿⣿⣿⡿⢋⣴⠟⢋⣤⣶⣿⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡌⠻⠷⡶⠶⠞⠛⣉⣉⡙⠛⠷⣦⣭⣥⡶⠟⢁⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⢀⣤⣶⣴⣾⣿⠟⠋⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠔⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟
⠀⢻⣿⠃⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⡏⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⡿⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻
⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⡈⢰⠁⠀⠂⡄⠐⡄⠈⠀⠐⠀⡦⠀⡆⡆⠀⢰⠀⠢⠐⠂⠀⡁⠀⡆⠀⡆⡄⢠⠀⡆⠐⠀⠆⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠁⢸⠀⠀⠀⡁⡘⠀⠀⠀⠀⠀⡇⢃⡇⡇⠀⢈⠀⠇⠀⡀⠀⡅⢠⠐⡜⠃⡇⢸⠀⡇⠀⠀⠐⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠈⠒⠀⠒⠁⠃⠀⠀⠂⠐⠂⠁⠘⠁⠃⠘⠀⠂⠀⠀⠁⠀⠃⠘⠀⠁⠀⠐⠊⠀⠇⠐⠂⠐⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⢠⣤⣤⣀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠘⠿⠟⠀⠻⠿⠃⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠐⠃⢀⠀⠚⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠃⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠛⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⢀⢀⡀⢀⠀⡀⡀⠀⠀⠀⠀⢁⠀⠀⠀⢠⠀⠀⠀⠀⣶⠉⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠈⠈⠁⠀⠀⢁⡁⠀⠀⢀⡀⠛⠀⠀⠀⠘⠁⠂⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠀⠙⠁⠀⠀⠀⣿
⣿⣿⠀⠀⠀⡍⠙⠦⠞⠉⡅⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⣶⠀⠀⠡⡆⠀⠀⢈⢹⡻⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⢣⠟⢝⣁⣤⡤⠴⣿⢾⣟⢀⡷⢤⡶⣔⠂⣨⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⣠⣤⣞⣂⡌⣀⡿⠀⠀⠙⣋⡙⢾⣢⠎⠀⠈⠻⣃⣠⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣸⡝⠛⣣⡳⠚⢋⣿⣉⣴⣆⣔⣶⣯⡅⣸⡍⢠⣤⣠⢒⡙⠚⠋⡀⢸⡟⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠠⠄⢻⡇⠀⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⡧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠀⠀⠀⠀⠀⠀⠈⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⣀⡀⠃⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢡⠀⠂⠀⠠⠅⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡄⠤⢀⠀⠀⢀⣠⣤⣴⣄⠀⠀⢀⠀⡄⠄⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⣀⣠⢴⣶⣿⡏⣿⣿⣿⡗⢲⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⣾⡟⠉⠙⣿⡗⠈⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⢶⣺⣿⡆⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⡀⢂⡀⠀⠀⠻⣿⣦⣶⣿⠃⠀⠄⢀⣈⡉⠀⠉⠁⠉⣈⣉⣭⣽⣿⣿⡏⣿⣿⣿⡇⢿⣿⣟⣧⣽⢿⣿⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⣸⣒⡚⣿⣽⣿⡆⣿⣿⣿⡇⣿⣿⠿⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠁⠀⠀⠠⠀⠀⠀⠀⢀⣼⣿⣿⡇⣿⣿⣿⡇⢿⣿⡿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠋⠈⠀⠈⠁⠁⠀⡀⠴⢧⣿⣿⣿⣧⣿⣿⠽⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣿⣿⣿⣿⠀⠘⢲⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡇⣿⣿⣿⣿⣿⠀⠀⠈⡇⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢈⠇⣿⣿⣿⣿⣿⠀⠀⠀⣇⢿⡿
⣿⣏⠛⠿⣿⣿⣟⣩⢍⣙⣛⣛⠛⠃⠈⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣷⣶⣤⠤⠶⣶⡲⢄⠀⢀⣀⣤⠆
⣿⣿⣿⣷⣶⣤⣌⡙⠀⠀⠉⠛⠷⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣥⣴⣾⣿⣿⡴⠾⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣤⣀⠀⢹⣿⣿⣿⠀⠰⡿⠿⠛⠁⢻⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⣶⣤⣤⣤⣤⣴⣶⣿⣿⣿⢣⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠛⠛⠛⠛⠛⠉⠁⠀⠀⢸⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⡿⢿⣿⣟⣛⣛⡟⣸⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⠄⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⠤⡤⠄⡟⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣷⣴⣾⣿⣿⣿⣿⡇⣿⣿⣦⣌⣿⣿⠿⠿⢿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠛⠁⠀⠀⠀⠀⢀⡇⠀⠉⠳⠆⠀⢀⣀⡀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠛⠻⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣠⣤⣀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣾⣿⣿⠇⢹⣿⣝⠻⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠊⠉⠀⠈⣠⣧⠀⠰⣤⣀⣀⡀⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⢻⣿⣷⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣦⣤⣤⣤⣤⣾⣿⣿⣧⡀⠈⠉⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣾⣶⣷⣿⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⢁⣈⣉⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⣠⠞⠋⠉⠉⠛⢦⡈⢿⣦
⠀⠀⠀⠀⠀⣰⣿⡿⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠹⡄⢻⣆
⠀⠀⠀⠀⢠⣿⡿⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⣿
⠀⠀⠀⠀⣾⣿⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⡇
⠀⠀⠀⢠⣿⡟⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣿⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣼⣿⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⣿⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⣇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏
⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⢛⣫⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⢿⣿⣄⣠⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢛⣉⣥⣾⡿⠿⠛⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠈⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⠋⠁⠀⠀⠀⢠⣾⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢷⣦⣄⠀⠀⠀⡙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠘⡄⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣄⠀⠀⠀⠙⠛⠶⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠟⠋⠀⠀⠀⣰⠇⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠙⢮⣟⠿⣿⣶⣦⣄⣀⡄⠀⣀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣀⠤⠔⣋⣥⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠈⠛⠶⣭⣛⡻⠿⣿⣿⣷⣶⣶⣭⣭⣤⣤⣤⣭⣭⣽⣿⣶⣶⣾⠿⠟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠈⠉⠛⠒⠶⠭⢭⣭⣽⣛⣛⣛⣛⣛⣋⣉⡉⠉⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠻⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠉⠛⠛⠿⠿⠷⢶⣶⣶⣶⡿⠿⠿⠟⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣉⠓⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣷⣶⣦⣬⣍⣉⣉⣙⣛⣛⣉⣀⣠⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⢢⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠀⢀⠇⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡠⠚⠉⠀⠀⢠⡇⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠸⡀⠀⠀⠀⠀⡇⢀⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⡤⣄⢰⢻⠄⠀⠈⠓⠒⠃⠀⠀⡤⣄⠈⠉⠀⠀⠀⡤⣦⣠⢤⢠⢶
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣟⡏⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⣇⡀⠀⠀⠀⠉⠀⠈⠙⣸⣾⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠉⠉⣦⡀⠀⠀⠀⠀⠀⠙⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠒⠀⠀⠀⣹⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⣀⡴⠋⠉⠐⠒⠒⠒⠒⠒⠂⠉⠁⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣜⣁⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠑⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠄⠐⠐⠚⠛⠉⠓⢦
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⡤⠶⢄⣀⣀⡤⣄⣀⣀⡴⠦⠤⠤⠤⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⡄⢠⣀⣰⠒⢦⣀⣽⡟⢀⡆⣦⡆⠀⢀⣄⠀⠀⠀⢠⣶⢿⣿⣶⡂⠀⠀⡇
⠀⠠⠀⠀⢽⣿⣿⡟⠻⣦⢀⢾⠖⠉⢼⡛⠐⠙⠛⣇⢰⢸⣷⣿⡁⠀⠀⣈⠰⠂⢀⠗⠀⣿⡍⣿⣇⠀⠀⠁
⠀⠀⠀⠀⠀⢹⣧⢽⡦⠐⣧⡝⣉⠋⣻⣧⣀⢤⣾⣟⣼⣿⠘⢻⣭⣼⣷⡏⣾⣷⠏⣶⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠐⠚⠛⠙⣿⡀⠻⢡⣴⣶⣶⣿⢧⢠⣿⠟⣻⣿⣷⣌⣉⣽⡄⠇⡏⠰⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠈⢳⣉⡉⡴⠏⠛⡟⠁⠀⠘⣿⣿⣿⡟⢛⣶⣦⠸⠃⠀⣰⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣄⢶⢇⠌⠀⠀⠀⠀⠈⢿⣿⣑⡈⠗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡏⠀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢈⡇⠀⢀⡀⡀⠀⠀⡀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠘⠛⢻⠛⠛⢻⠟⠛⠓⣟⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⢲⣄⠤⣌⠔⠰⣆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡼⠀⢸⠯⡶⢿⡀⢸⠈⡆⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠁⠂⠀⡀⡁⢸⠀⢸⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡄⣸⢠⠀⠀⠉⠉⠹⠀⠀⠀⢲⠰⠀⠀⠀⠀⠀⣄⡀⠀⢀⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣐⠃⠀⠀⠊⢠⠞⡄⡇⠀⠁⢩⡶⠀⠀⠀⠀⠀⠙⠻⡟⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠀⠀⡆⡜⠀⢣⢁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡂⢴⣶⣶⣤⣉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠈⡌⡀⠀⠡⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣽⣀⣀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠉⢹⠒⠒⠠⠤⠤⣤⡤⠤⠤⠤⠤⠤⠒⠒⠊⠉⠉⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⣀⣠⣤⡀⠀⠀⠀⠠⠞⠒⠈⠁⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡠⠖⠒⠄⠀⠀⠆⠀⠀⠀⠀⠘⢟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢂⠈⢹⠉⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⢀⠇⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢻⣶⣦⣤⣄⣀⣤⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⡼⠀⠀⡜⠀⠀⠀⡠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⠗⠢⠀⡘⠀⣰⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠓⠤⠥⠼⠒⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢸⢦⠀⠛⠁⢾⠉⣀⡠
⠀⠀⠀⠀⠀⢠⠒⡄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠊⠁⠀⠀⠀⠀⠀⢈⡼⠀⠀⠀⠀⠙⠋⢲
⠀⢠⠔⠒⠠⣼⡄⠧⢄⠀⠀⣸⣀⣀⣀⣀⣀⣀⠀⠀⠀⡔⣤⠤⠬⢭⣟⠻⠤⠤⠞⢥⣄⣀⠀⠀⠀⠀⠀⠀⣠⠔⢋⣤⠊⠑⡂⠉⠉⠈⠉
⠀⠀⠑⢂⣦⠀⠀⠀⠀⣉⡀⣠⠤⠤⠤⠤⠤⠤⠬⢉⣿⡟⠁⠀⠀⡸⠙⢅⡰⢆⡰⢻⠀⠀⢹⢧⠤⠔⢒⡉⠄⠊⠁⠀⠉⡹⠃
⠀⠀⡞⢁⡠⠔⢲⠀⠖⢱⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⢇⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠀⣸⣹⠃⠉⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠈⠁⠀⠀⠘⠤⠜⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠖⡞⠀⠀⠀⠀⠀⠀⢠⡤⠔⠁⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠄⣀⠠⠤⠤⠒⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⠉⢐⣶⠀⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠭⠁⣒⡒⠠⢄⣀⣾⣋⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡴⠒⢢⣀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⢤⠊⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣠⠎
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⠤⣄
⡏⠹⡷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢈⡇
⡇⠀⢇⢣⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠡⣞
⡇⠀⢸⠘⡀⠀⠀⢀⣠⠤⠒⠚⣉⡩⢇⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⣀⣀⣀⣀⣀⠤⠔⠊⠁⠀⠀⢸
⠃⠀⠀⡆⢧⢴⢎⣍⣀⠴⠒⠉⠀⠀⠈⠓⠤⠤⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⢸⠀⠀⡇⢸⡾⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠴⣄⡀⢀⣠⣄⣀⣀⡠⠔⠁
⠈⣆⠀⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸
⠀⠘⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠓⠂⠉⠉⠁⠒⢒⣶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣉⣉⣒⣒⣒⣒⣒⣊⣉⣉⠠⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠒⠒⠒⠒⠈⢉⠟⠁⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⢸⠒⠒⠒⠀⠤⠤⠤⠄⠒⡎⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠈⡏⠉⠁⠒⠒⡖⢲⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡇⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢣⢈⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⡀⠀⢇⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢸⡇⠀⠈⢣⣤⣤⣴⣾⡿⠧⠤⠤⠤⠤⠤⠤⠤⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⡤⠬⣶⣥⠔⠒⠘⣿⡿⣏⠀⠠⣶⠶⠟⠛⠛⠛⠋⠩⠿⠶⠶⢤⣍⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣄⣉⡉⠒⠢⠵⢮⣍⣒⡪⠭⢉⣁⣒⣒⣒⡒⠒⠒⣒⣚⣁⣠⠤⣚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠉⠒⠲⡄⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠚⠓⠒⠒⠒⠉⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠑⠒⠒⠒⠚⡏⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠬⣉⡑⠒⠢⠤⣄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠬⣑⡒⠤⣀⣇⣀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠬⢍⣙⣛⠲⠶⠶⠖⠚⣉⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁