Stationery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠚⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠄⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⣉⡠⠒⠕⠂⠱⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⠀⠀⠀⠘⠀⠀⠤⠤⠤⢀
⠀⠀⠀⠆⢀⡤⠄⠁⠁⠠⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠻⠿⠛⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠈⠇⠤⠀⠀⠀⢰⠄⠀⠀⢱⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⢸⠀⠀⠉⠀⠀⡡⠅⠈⢸
⡂⢀⡜⠀⠈⡰⠦⠜⠀⠈⡃⠤⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⢰⡀⢐⢸⠉⣃⣀⠈⠉⡑⡀⢀⠀⡀
⣇⣎⠃⠀⡰⠀⠀⠀⠀⡴⣁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠘⠀⠉⠁⠀⠭⠤⠤⠬⠭⠠⠈⠀⠀⠃
⠨⡹⠀⠊⠈⠁⠀⠀⠀⢤⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣀⠠⠇
⠀⠘⢦⡘⠀⢠⣀⡰⠌⣀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠉
⠀⢀⠐⠀⠉⠙⠃⠙⠉⠁⠂⠁
⠀⠀⠀⠀⠒⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⣂⠠⠤⢀⣄⣂⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⢌⠐⠒⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⠀⢌⢆⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠹⡄⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠦⠀⠈⠇⠀⠐⡀⠀⠀⠀⡃⠀⠀⠀⠀⡠⢈⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠐⠈⠲⡄⠀⠀⠑⠀⠂⠈⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⡀⡜⠀⠂⠐⠀⠀⠀⠀⡇⢀⢀⠀⡀⠀⢀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⠀⠀⢀⠌⠀⠀⠀⡄⠈⠀⠄⠀⠀⠀⠀⠨⡭⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠀⠂⠠⠐⠒⠀⠂⠂
⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠃⠐⢄⠀⠀⢀⠄⠀⠀⠀⠠⠤⠠⢄⠀⠀⢃⠄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠁⠁⠠⠀⠀⠁⠅
⠀⠀⠀⠀⢀⡴⠃⠀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠄⠈⠄⠀⠀⠀⠒⠐⠂⠀⠁⠀⠀⠀⠀⠑⠃⠂
⠀⠀⠀⣠⠊⠑⠄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠌⠁⠁
⠀⢀⠾⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⠤⠤⠄⠐⠊⠁
⠀⠈⠢⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡅⢢⡔⠀⠀⠀⠀⠀⠀⠀⠆⠈⠢⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⢀⠔⣡⠞⢉⠔⠉⡀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠄⢀⠊⠀⠀⡐
⠀⠀⠀⢀⠔⢁⠔⢁⡼⠋⡠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⡠⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣠⢁⠀⢀⠐
⠀⢀⡐⢡⣔⣁⣴⠋⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠘⢑⠞⠓⠅⠀⠀⡀
⢀⠘⠁⠀⠀⠀⠁⠜⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡐⠁⠀⠠⢈⠀⠀⠢⠐
⠉⠀⠀⠀⠀⠀⠃⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⠉⠀⠀⠀⠀⠀⢕⠄⠀⢁
⠐⠒⠒⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⣇⡶⣼⣠⣴⢴⠢⣶⡖⢲⠂⠀⢴⢲⡦⠶⢰


⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡤⠀⠀⢤⡄⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠮⡀⣠⠇⠀⠀⠈⣰⣆⠀⠀⠀⠀⠀⡐⢂⡀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠂⡠⠁⠈⠢⡄⠀⠀⢀⠞⢻⠏
⠀⠀⠀⢠⡄⠀⠠⠋⠀⠀⠀⣌⠆⠡⣱⠀⠀⡠⠎⣰⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠰⠀⠀⠚⡩⠀⠀⢏⡠⠂
⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠑⠒⠒⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠈

⠀⠀⠀⢰⠀⠀⠐⠒⡆⠀⠀⠀⢀⠦⡄⠀⢠⠦⠖⠴⠤⠆⠀⠀⡔⠒⠒⠒⠂⠀⠀⠀⣴⣦⠀⠀⢀⠀⠤⢀⡒⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡒⠇⢴⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢱⢈⠈⠠⡁⠀⠀⠰⠩⠭⠆⠀⠀⠑⠠⠤⠄⠒⠉⡄
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣮⠃⠈⠀⠀⢘⠀⠀⠉⣠⠇⠀⠀⡇⠈⠁⡀⠁⠀⠀⡱⠀⠀⢊⡀⠀⠸⡀⠀⠀⢐⠒⠗
⠀⠀⠀⠈⠓⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢠⡶⠒⢦⡀⠀⢠⠢⠴⢦⡒⡄⠀⠀⠀⢀⠄⠂⠀⠀⠰⠀⡆⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠀⡀⠰⣒⢤
⠀⠀⠀⠀⢸⣄⠀⣠⠇⠀⢸⠨⠉⠩⠁⡇⠀⠀⢠⠃⡠⠃⠀⡠⠊⠀⠉⢢⠀⠀⢰⠋⠉⢉⠒⠀⠀⢸⠰⡸⢀⢎⠆
⠀⠀⠀⢀⢎⡟⠉⠁⠀⠀⢸⢀⠀⠈⢀⠃⠀⠊⠉⠒⠁⠀⠀⢏⠀⠑⡈⢩⠃⠀⢸⠐⠈⠐⢸⠀⠀⣨⠳⠤⠢⣟⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠈⠑⠒⠒⠁⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣦⠀⣀⣠⣤⡤⠄⠀⠉⠀⠀⠀⠀⠀⠠⠐⡧⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡁⠀⢀⠀⠀⠀⠀⠀⠠⠖⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⣀⢀⣀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⢑⡤⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀⠤⠤⠐⠂⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠑⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡈⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠠⠄⠀⠄
⠀⠀⠀⠐⠀⠀⠀⢀⠀⠁⠈⠀⣄⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡁
⠀⠐⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⠟⢀⣀⣠
⠀⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠹⣄⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢌⠉⠀⣶⠁⠀⠄⠄
⠀⠈⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⡀⠀⡂⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡌⡄⠀⢹⣧⣔⡢⠂⠑⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣃⣉⣀⣵⣘⡦⠀⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢻⣷⣿⠀⠈⣿⣷⡀⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣻⠁⠀⠩⠃⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⡆⠌⠙⢠⠦⠤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⠀⠀⠙⠀⠀⠰⢤⡴⠋⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⣄⠀⠀⡰⡀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢠⡆⠀⠀⠀⠀⠀⠀⠇⠈⢀⠀⠙⠷⠄⠂⡅
⠀⠀⠀⠀⠂⠀⠘⠋⠘⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣼⠴⠛⠉
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠒⠋⠀⠐⠦
⠀⠀⠄⡴⠁⠀⢀⣘⠀⠀⠀⡰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⣠⣴⡾⠛⠉⢁⣀⣀⣤⡤⣐⡴⡀
⠀⠀⠀⠓⠂⠀⠰⠰⠀⢴⡾⠥⠤⠴⠇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⡀⠀⠁⠀⠁⠀⠀⠀⠚⠒⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠄⠒⠒⢒⠒⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⢀⡠⢁⠀⠀⠰⠂⠁⢸⣿⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⣗⠀⠀⠀⠀⠀⢀⢘⠚⡉⠉⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⡘⠠⡤⠫⠚⠛⠘⣃⣠⡇⠀⣿⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡯⣿⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡂⢠⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⡀⠸⠀⠀⠀⠈⣿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠇
⠀⠀⠀⠀⢠⡥⣤⣤⣤⣿⣿⠀⠀⠀⠀⠈⠶⠶⠻⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢐⢘⠂⠀⠀⢀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⢵⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⣍⢹⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠘⠘⠀⠀⠃⡞⠀⠀⠀⠀⠀⢀⠀⠛⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⢸⡍⢹⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⠠⠜
⠀⠀⠀⠀⢸⡓⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⣴⠀⠀⣀⣀⣘⣉⣀⣘⣻
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡆⠀⠀⠀⡇⡇⠀⠀⠀⠈⠀⠂⠈⡄⢀⡀⠀⠀⠀⠀⠻⠉⠓⠒⠺⠿⠒⠛⠻⠃
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⡀⠔⡜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢰⡆⠀⠀⠀⡤⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡇⠇⠈⢆⠀⠣⠀⠀⠀⠀⠀⠞⣰⠃⡨⢄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⡇⢾
⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠑⠀⠐⠀⠀⠀⠀⠤⠎⠀⠀⠀⡈
⠀⠀⠀⠀⢸⠾⢻⠀⠀⠀⠀⢸⠤⠄⠀⠀⠀⠘⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠲⣯⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠈⢦⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⡶⣾⠉⠀⢀⡠⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢿⣯⣿⣠⢳⠁⠀⠀⠀⠀⡤⠀⠐⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⣾⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣿⣥⠀⠉⢹⣛⣁⡠⠀⢠⣷⣲⣚⣛⣩⡐⠂⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣶⠀⠀⣾⡈⠁⠀⠐⠋⠉⠉⠉⢉⠉⢁⡀⢀⡀⡠⠟⠀⠀⠀⠈⢰⡆⠀⠀⠀⠀⠀⠈⠋⠙⡛⠉⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⡿⠷⠠⠤⠤⠤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢧⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⣰⠋⠑⠢⣄
⠀⠀⠀⠀⡔⢋⣉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⠀⠀⠀⡏⠀⠸⠀⠀⡴⠃⠀⠀⠀⡜
⠀⠀⠀⠀⡄⠸⡀⠱⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⢄⡀⠀⡆⠀⠸⡀⠀⣸⠀⠀⡇⠀⡼⠁⠀⠀⢀⠞⠀⣠⠔⢾
⠀⠀⠀⠀⠘⢄⠑⢄⢱⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢶⢫⡱⡀⠹⣤⠶⡇⠀⣷⠦⣤⢁⡞⠀⠀⠀⢀⠎⢀⡜⡝⡳⡼
⠀⠀⠀⠀⠀⠈⠳⣄⠙⢧⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⡱⡘⣄⢹⡀⢻⢀⡏⢠⣇⠞⠀⠀⠀⢠⠋⢀⢎⠜⡜⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢴⠉⠙⡦⣤⠤⢤⡀⢀⣀⣀⣀⣀⣳⣱⣜⣌⣆⣷⣀⣿⣁⣼⣏⣀⣀⣀⣠⠇⠠⠯⠮⠾⠼⢤⣐⣒⠢⠭⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠊⠁⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠧⠝⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠚⠀⠀⠀⠀⠀⢴⣰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⣔⢲⠀⠀⠀⠀⠓⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣄⠀⠑⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠚⠀⠀⠀⠀⠀⠀⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠂⠀⠀⠀⢯⡹⠀⠀⠀⠀⠰⠽⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣤⡴⠟⠋⠀⠰⠁⠀⠀⠀⣀⡴⠚⠉⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠀⠀⠀⠠⠄⣀⣘⣦⡶⠟⠛⢡⡶⠂⠀⡆⢀⠀⣠⡴⠛⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣴⠾⠛⢰⣿⡀⢠⠇⡎⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⢀⡀⠀⠤⠒⠂⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠒⠒⠀⢠⠿⠞⠋⢁⣴⣾⣞⡇⢿⢸⢠⣱⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⡷⠛⠃⠉⠀⠀⠀⠀⠀⢀⣀⣀⠟
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣇⢀⣴⣾⢿⠋⢘⠈⠁⠛⠛⠘⢻⡶⠛⠛⠉⠁⠀⢠⠀⠀⢀⣇⣤⣤⡤⠤⠶⠶⠟⠛⠋⠁⠒⠒⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠚⡿⠋⢁⣼⣿⣿⠀⠀⠀⠀⠀⣾⣧⣄⣠⣤⣤⠶⠃⠀⠀⣼⣿⣿⢂⣀⣀⣀⣀⣀⣘⣂⣀⣀⣐⣐⣺⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠄⠠⠄⠀⠀⣀⠀⠀⢧⣴⠿⠋⣠⠴⠀⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⠀⣠⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣬⡆⠀⠀⠀⢀⣿⠤⠤⠀⠠⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⢀⣼⠿⠋⠁⠀⠀⠀⠾⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠚⠇⠄⠛⢒⣶⣌⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠂⠀⠀⠀⠀⠀⠉⠉⠛⢆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢎⢔⡞⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢿⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⢛⡍⣼⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣴⣿⣿⠏⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⡀⠀⠀⢀⣐⣶⣿⡿⠟⣁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⣠⡾⠒⠀⠀⠀⠀⠀⠈⠀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⠻⠻⠻⠟⠛⢙⣋⡴⠊
⠀⠀⠰⣤⣤⣤⣤⣦⣤⣰⣼⢀⡾⣋⠤⠤⠄⠀⠀⠀⠀⠀⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠤⠓⠂
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣿⣿⣿⣷⠆⢀⣐⣠⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠘⣷⣤⣄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠛⠛⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠁⠿⠛⠉⠀⠀⠀⠀⠀⣨⡀⠈⠀⠀⠀⡀⠀⠰⣔⠒⠼⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠩⣝⠢⣄⡀⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠠⠚⡃⠀⠀⠀⠀⠦⠀⠰⣘⢫⡟⢨⡓⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣑⣱⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣖⣤⠆⠀⢠
⣀⣤⣆⣼⣴⣄⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡁⠀⠀⢸⡀⠀⣀
⠉⠙⠊⠉⠀⠈⠉⠀⠈⠀⠀⠀⣠⠔⠛⠁⠀⠐⠃⠀⠀⠀⠀⠀⠘⠉⣉⠉⠉⠉⢉⡛⠀⠠⠈⠀⠄⠀⠀⠀⠏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠤⠀⠀⠤⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⡈⠨⣮⡏⣹⠋⠀⠀⠀⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠄⢜⠲⢏⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀
⣷⢮⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡇⠀⠀⡎⠉⡖⠉⠉⣧⠀⠀⠈⠈⠉⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣦⣥⣽⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⡷⣟⣾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠁⠀⠀⠠⡦⠀⠀⡀
⠔⠀⠀⠀⠀⠀⢼⡤⢀⡀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⠓⡀⢠⠂⢀⠀⢠⢺⠿⠟⠛
⡾⠇⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣇⣀⡾⢠⠏⠀⠸⢶⣶⠶⠶
⠐⠛⠄⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⣤⡄⠀⠀⠐⠋⠀⠀⠀⢰⣿⠛⣧⠀⢢⠀⠀⠈⣧⠘⣆⣷⠃⠀⠀⢸⠷⠁⠚⠛
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠁⠀⠀⠈⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤
⠘⠀⠀⠀⠀⡀⢀⣀⡀⠀⢠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢚⠥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⡆⠀⠀⠀⠀⢀⡴⠖⠒⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢒⡒⠶⣇⠀⠀⠀⢠⢿⣀⣀⣄⣀⣸⠀⠀⠀⠀⠀⢘⠀⢸⠋⠉⠉⠉⠉⡏⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢒⣒⣋⣿⠀⠀⠀⢸⡌⣿⠀⠀⠈⡏⠀⠀⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠈⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⢸⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡗⠀⢸⠀⠀⠀⠀⠀⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠸⡞⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠱⠅⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠈⠹⡆⠀⢻⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⠀⠀⠀⠀⠀⡧⠀⢸⡀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣴⠃⠈⠲⢄⡀⢀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢉⡞⠁⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠋⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢸⡆⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⣾⠀⠀⠙⠢⢄⡴⠋⠀⠀⠀⠀⢸⣇⡤⠤⢼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠹⣦⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡗⠀⠀⡇⢀⣀⣀⣀⣇⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡇⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⢖⣒⡢⠤⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣥⣶⠯⢃⣁⣄⠳⡄⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠒⠈⠀⠀⠉⠀⠐⠒⠒⠂⢄
⠀⠀⠀⣀⠞⠙⠲⠖⠢⡀⠀⠒⠨⡳⡀⠄⠠⠀⠀⠀⠀⠀⠀⠱⠽⠿⠟⠒⠉⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⣠⢀⡀⣠⠠⠀⡀⠠⢀⣀⡄⣀⠉⠘
⠀⠀⠄⠘⣁⠦⡀⠀⠀⢹⠂⢀⡠⠘⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⡄⠃⠀⠃⣇⢀⡀⠁⢀⢠⡿⠀⠘⠀⠀⡄
⠀⢨⠂⣠⠃⠀⢀⠛⠶⢎⠀⠘⡁⠦⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⡇⢧⣀⡇⣇⣠⠧⠄⢀⣀⠿⣄⣸⠰⠀⡇
⠀⠸⣄⣍⠐⢀⣆⠀⠀⠀⢀⠞⡤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢀⠃
⠀⠀⠣⡻⠉⠁⠈⠀⠀⠀⣀⠦⡀⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢀⣀⠀⠤⠘⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⡹⢤⡉⠂⢴⣈⠒⢡⣀⠴⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⣠⠁⠀⠡⠍⠉⠩⠍⠐⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠀⣢⠤⠤⠄⣦⣸⠀⡐⠁⠉⢢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠤⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣌⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠉⠲⡔⠢⢱⡀⠀⠀⠀⠀⠀⠁⡖⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢼⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡧⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠈⠂⠀⠋⠀⠀⢠⠄⠀⠀⠀⠀⠀⠔⠄⠀⠛⠀⠐⡁⠀⠀⠀⠀⠀⠉⠡⠈⠀⠁⠉⠩⢸⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠐⠊⠂⡀⠀⠀⠊⠀⠀⠀⠀⠀⡀⠀⠀⡀⣀⠄⠀⠀⢀⢤⠀⠀⠀⢡⠀⠀⠀⠀⠀⡀⢰⢐⠀⠀⠂⢐⢰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⢄⠀⠀⢀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠒⠂⠐⠉⠀⠐⠰⢠⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢄⠂⠀⢀⡠⠄⠀⠀⠀⠀⠀⠤⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠄⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠜⠤⢰⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡅⠤⢀⠂⠀⠀⠀⠆⠓⠊⠈⠒⠀⠑⠚⠈⠒⠂⠆
⠀⠀⠀⠀⠀⡰⠋⠢⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡠⠋⠈
⠀⠀⠀⡠⢎⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠄⠀⠀⠀⠀⠤⠕⠊⠁
⠀⠀⠀⠳⢄⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣏⠲⣈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⠼⢻⡽⠋⡉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠂⠀⢠⠊⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠔⢁⡴⢙⡵⠋⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢂⢔⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⣱⡁⠈⠀⠔
⠀⠀⠀⠀⠔⢁⡴⡙⡴⠊⢀⠀⠁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠐⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡑⠞⢳⠷⢖⣁⣀⡀
⠀⠀⢀⠞⠉⠉⠉⠉⠁⠶⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠀⠐⡆⡰⠀⠐⠀⠔⠀⠀⠍⠢⡀
⠀⠰⠃⠀⠀⠀⠀⠐⡆⢀⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣀⢼⠍⠀⠀⠀⠈⠺⡄⡀⢀⠀⠅
⠀⠀⠤⠤⠤⠤⠤⠤⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠤⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠒⠁⠀⠀⠀⠀⠀⠀⠉⠂⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠚⣿⠃⢀⡴⠾⢉⣋⣉⡻⠲⣄⠀⣀⣄⠰⣿⠆⠀⣼⠁⠀⠲⡌⢳⡄⣴⣶⣾⡓⣶⣤⡼⢧⡼⠃⠀⣠⡴⠒⠚⠳⢬⣍⠳⣦
⠀⠀⠀⠀⠀⣰⠏⣣⠞⠉⠡⠈⠙⢳⡌⠛⢉⢹⡄⢀⣤⠀⢿⠀⠀⠀⢡⢨⡇⠈⠉⠛⠛⢋⡉⢻⡛⣷⢠⡞⠁⠛⠋⢻⠀⠀⣸⢷⡈⢷
⠀⠀⠀⠐⠀⣿⠃⣏⠀⠉⣠⡴⠚⢉⣀⣦⠞⠋⢷⡛⠈⣳⠌⢧⡀⠀⠀⡼⠁⣀⠀⢰⣆⢸⡿⣮⡉⠁⣾⡴⠶⠶⠦⠾⠃⢸⡅⠈⡇⢸⡇
⠀⠀⠀⢾⣷⠘⣏⠹⠶⠋⣁⣰⡶⠚⠉⠰⣶⠆⠸⠟⠳⠧⢀⣀⠙⠳⣿⡇⠀⣿⢷⣿⣩⣿⡷⣟⢧⠀⢹⡷⠛⣩⠷⣴⡄⠘⢓⣻⠇⣸⠁
⠀⠀⠀⠠⠀⣶⢋⡀⣰⠶⢋⣡⣦⢀⣤⠶⠶⣤⡴⠖⠚⢋⠉⠙⣶⢶⡀⢻⠀⣿⢻⡹⡜⣎⢧⢹⡌⢧⠀⠳⣄⣹⡄⠙⠁⣰⡿⢋⡴⠃
⠀⠀⠀⢶⣶⠹⠶⠋⠁⣴⡋⣹⢃⣞⣠⣤⣿⡎⡷⣖⢛⣙⡇⠀⢹⡈⣧⠸⣆⠸⡎⢧⢻⡸⡜⣇⢳⡘⣧⠠⠀⠉⣻⣿⣯⡭⠖⠋⠀⣀
⠀⠀⠀⠀⠀⠠⠀⢀⡞⣡⣟⡽⠃⣯⡛⠉⣀⡼⠃⠉⣉⣡⡤⠀⠈⣧⢹⡄⠘⡇⢹⡜⣇⢷⣳⡘⣆⣷⠾⣆⢺⣉⠟⠓⣆⠸⡯⣽⠆⣭
⠀⠀⠀⠠⣶⡄⠀⡼⠛⠁⣠⠞⢙⡯⠉⢻⡉⠤⠀⠛⠉⣀⣠⠀⠀⠸⡆⢳⡀⢧⡀⢳⣸⡾⣿⠋⢹⣄⡤⣿⠀⠉⠙⣉⡁⠀⡇⣿⠰⠦
⠀⠀⠀⢀⣨⠴⠶⡆⢰⡞⢁⡴⠟⠀⠀⠈⣇⠀⠀⠒⠋⢉⣀⣤⠀⠀⢻⠈⢧⠈⣷⠈⢧⣠⢾⡿⠽⠋⠉⢡⣦⠀⣾⠽⢣⠞⠁⠘⢧⡀
⠀⠀⠀⠘⢶⡖⢾⠁⠀⠙⠋⠀⠀⡿⣆⠀⢹⡀⠒⠀⠘⠉⠁⣀⡄⠀⠈⣧⠘⡆⠘⠂⠈⠙⠉⢀⡴⢚⡦⢈⡵⣤⠀⣰⢿⣋⡽⠟⠉⠳⡄
⠀⠀⠀⠀⢈⡇⠘⣧⣀⠀⠈⠀⢸⣇⠹⡄⠈⣧⠀⢁⠀⠚⠋⣉⣀⣤⠤⢾⣠⡽⢀⣤⡶⢺⠃⠙⠋⠉⠀⡼⠧⣇⠸⠧⠤⠤⠤⠶⠶⠶⠟
⠀⠀⠀⢠⡟⢁⡀⣠⠼⣷⠀⠀⣾⡀⠀⢻⡄⠸⣆⣤⠴⠖⣋⣩⡤⠖⢛⡉⠀⢀⡟⠈⣹⠏⠀⡟⠛⣛⣿⣓⠒⠛⠲⠶⡄⠀⡶⢻⡛⠓⣆
⠀⠀⠀⠘⣷⠋⠉⠛⠚⣻⠀⢠⣏⠀⣤⠀⢻⡄⠀⠙⠖⠛⣉⡀⠦⡿⠿⢃⡴⠋⣹⠋⣡⡴⢠⣇⣰⡿⠒⢾⣇⣤⡀⠀⡇⠀⡇⢸⣥⣄⣿
⠀⠀⠀⠀⠈⠳⠶⠶⠚⠁⠀⣼⡍⢰⡟⣇⠀⢷⡀⢠⡴⣿⣿⣷⠀⢀⡴⢯⣠⠞⠁⢀⣷⠀⢸⣏⣁⣀⣀⠀⠙⠀⠙⢺⡇⠀⡇⢺⡉⠋⣿
⠀⠀⠀⠈⢀⣾⣆⣴⡟⠀⢠⣯⠀⣼⠀⠸⡆⠈⢷⠀⠙⢯⡿⠁⣰⠋⢀⡴⠃⣠⡞⣿⠀⠀⣼⠉⠉⣉⡽⠏⢿⠙⠛⣻⠀⠀⡇⢼⠃⠀⣿
⠀⠀⠀⠀⢸⡇⠋⣾⠀⠀⣾⠅⠀⠧⣤⣤⣿⠀⠘⣧⠀⠄⢀⡞⣡⠖⢋⡴⠛⢯⣿⠁⣀⢀⣿⠖⠋⠁⠀⣠⠞⠀⠀⡿⠀⠀⡇⣸⠇⠀⡏
⠀⠀⠀⠀⠘⢧⠀⢿⠀⠸⣧⣤⣤⣄⣀⣀⣀⡀⠀⢹⡆⠀⠚⠋⠁⣠⠞⣵⠛⢶⡟⢸⣋⠉⠉⠛⠛⠓⠒⠻⠶⠦⠤⣧⣄⠀⣷⡛⠒⢺⡇
⠀⠀⠀⠀⣴⠚⠓⠚⠳⠦⣤⡀⠠⠀⢈⣉⣉⣉⡉⠛⠋⠀⣤⠀⡴⢯⣄⡉⣳⠏⢀⣤⡉⢩⠟⢛⡟⠓⠒⣶⠶⣤⢤⣤⡟⠀⠌⠉⠉⠉
⠀⠀⠀⠀⡟⠐⠒⠛⠓⠶⣤⠙⡶⣋⣭⣭⣭⣍⣉⠓⣦⠀⡟⢦⡙⠲⣬⣙⣏⡷⠈⠋⢠⡟⢠⠟⠀⠒⡀⢿⠀⡇⠀⣤⢶⣶⣶⣒⣲⡶⣦
⠀⠀⠀⠀⡇⠐⠋⠉⠛⠲⠆⢸⢳⣇⣀⣀⣀⣠⠟⢰⠇⠀⠳⣄⡷⢀⡤⡍⣭⣤⣄⢠⡟⢠⠏⠀⣴⣀⡀⢸⠀⡇⠀⣿⣿⡿⢏⣉⣉⡇⣿
⠀⠀⠀⠀⡇⠐⠋⠉⠙⠳⠀⡟⢨⠭⠤⠤⣭⡉⢀⡟⢀⢠⡶⠶⠦⡄⠙⠁⣿⠒⠛⠘⠓⢋⣀⣠⡟⠛⠁⢸⣀⡇⠀⣿⢨⢉⡉⡍⢥⠀⡏
⠀⠀⠀⠘⢧⡵⠶⠶⢤⣄⢸⣇⣀⣠⣄⣀⠀⠀⡾⠀⢈⣸⡏⠉⢛⡇⢠⠶⡏⢀⣴⡆⣴⠋⠉⠙⠛⢳⠀⣬⣭⡁⠀⢻⠰⠀⠂⢲⡟⡇⡇
⠀⠀⠀⠠⠀⠛⠛⠛⠛⠛⠻⠛⠓⠶⢤⣨⠟⠾⠃⠀⢯⡽⠀⢾⣹⠇⠈⠛⠁⣾⢹⠇⠻⣄⠤⢀⣠⠞⣴⣌⢧⣙⡇⢸⡈⠁⠁⠁⠙⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠉⠉⠁⠀⠉⠁⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠀⠀⠀⢀
⠀⢈⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠤⠤⠤⠴⠦⠤⠦
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⣬⣼⠀⠀⠠⠤⠶⠶⠶⠶⠶⠶⠄
⠀⢀⠀⠀⠀⠀⠀⣀⣀⣆⣀⠀⠀⢠⠀⠀⢀⣏⡛⠨⡿⠿⠫⢦⠀⠀⠀⠀⣀⣴⡶⠀⠀⠀⠀⠀⠑
⠀⠘⡀⠜⠛⠛⠛⠋⠛⠋⠉⠒⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁
⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀
⠀⠀⢀⠰⠄⠂⡆⡰⠂⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠈⠀⠀⠀⠀⠐⠩⠂⠁
⠀⠀⠀⢢⠸⣽⣷⠁⠀⠀⠀⡄⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⡀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣴⠇⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠇⢀⡇⠠⢸⠂
⠀⠀⠀⠀⡨⠐⠀⠀⠀⠀⠀⠀⢨⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠠⠰⠇⠀⠀⠂⠀⣸⣻⣿
⠀⠀⠀⣠⢦⡀⠀⠀⢀⡤⠀⠐⠀⠀⠐⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣤⠄⠀⠀⠂⠀⠺⠹⠚⡇
⠀⠀⣰⢇⡲⣌⠓⢤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢰⠀⠀⠁
⠀⠓⠭⡺⢴⢃⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠀⠀⢠⣀⠀⠤⠀⠠⠄⠐⡄⠀⠀⢸
⠀⠀⠀⠈⠐⠶⠃⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠋⠀⠀⠀⠀⢻⠇⡩⠠⡪⢋⡻⠁⠀⠇⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠂⢘⠶⡣⠀⠀⠀⠓⠃
⠀⠀⣈⠗⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢢⣾⠅
⠀⠀⠀⠀⠊⠄⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣠⣴⣄⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⢿⣿⣿⠆⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢨⠾⠛⠉⠀⠀⠀⠀⠿⣤⡿⠁⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⣀⣀⣀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣴⠟⠉⠉⠉⠛⣦⡀⠹⡆⠀⠀⠀⠀⢠⡞⠛⠛⡶⠶⠦⣤⣄⡀⠀⢀⡴⢋⡠⠊⢠
⠀⠀⢀⣤⠶⠛⠋⠉⠙⠳⢦⡀⠀⠀⢸⠁⠀⣼⠃⠀⠀⠀⠀⠀⠈⣧⠀⢿⠀⠀⠀⠀⣸⠁⠀⠀⠇⠀⠀⠀⠏⠙⣷⢋⡴⠋⢠⢀⡟
⠀⣴⠋⠀⣀⡤⠶⠶⢦⣄⠀⠙⣦⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡇⠀⠀⢠⠇⠀⠀⢸⠀⠀⠀⢸⠀⠀⡿⠊⡠⠔⣡⠟
⣼⠁⠀⡼⠋⠀⠀⠀⠀⠈⢷⡀⠘⣧⠸⡇⠀⣇⣀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⡞⠀⠀⠀⡏⠀⠀⠀⡏⠀⣰⠷⡄⠀⠊⠁
⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣧⣷⠸⡋⠙⡇⠀⠀⠀⢀⣀⣸⣇⣠⡇⠀⢰⠃⠀⠀⣸⠁⠀⠀⢸⢃⡼⠁⢀⠃
⣿⠀⢸⡄⠀⠀⠀⠀⣶⣤⡀⠀⢻⡄⠈⢿⡆⢃⠀⢱⠀⠀⠀⡏⠁⠀⠀⠀⢹⠀⡯⠀⠀⢀⡟⠀⠀⠀⣼⡾⠁⠀⡜
⢹⡄⠀⢷⡀⠀⠀⠀⣷⣈⢷⣄⠀⢻⡀⠘⣷⠾⠒⠛⢋⣻⡄⣃⣀⣀⣀⣀⣀⣼⠃⠀⠀⣸⠁⠀⠀⢀⡟⠀⠀⣰⠁
⠀⠹⣆⠈⠳⣄⠀⠀⢹⡀⠀⠙⢦⡈⡇⠀⣻⡶⠞⠋⠉⠉⢿⡧⣤⣤⡤⠤⠤⢿⠀⠀⢀⡟⠀⠀⢀⡾⠀⠀⢰⠇
⠀⠀⠙⢷⣄⠈⠳⢄⡈⣧⠀⠀⠀⣻⣇⢺⠉⣷⡀⠀⠀⠀⠘⣷⠒⠲⠖⠶⠒⡎⠀⠀⣸⠃⠀⢀⣾⠁⠀⢀⡿
⠀⠀⠀⠀⠙⠷⣄⡀⠉⠹⣖⠒⠋⠀⠹⣎⠋⢽⡇⠀⠀⠀⠀⢿⠀⢀⠀⠀⢸⡇⠀⠀⡟⠀⠀⡼⠁⠉⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠻⣆⠀⠀⠀⠹⣶⡸⣿⡀⠀⠀⠀⣿⠀⣸⠀⢸⢸⡇⠀⢸⠇⠀⣼⠃⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⣷⣿⣧⠀⠀⠀⣿⠀⣿⠀⣿⠀⡇⠀⡿⠀⣼⠃⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠹⣿⣿⡄⠀⠀⡿⠀⣿⠀⣿⠀⡇⢰⠇⣰⠇⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠹⣏⢳⠀⠀⡇⠀⣿⠀⡿⠀⡇⡞⢰⠏⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⡎⡇⠀⡇⠀⠹⠀⡇⠀⣇⢡⠏⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠼⠦⠤⠤⠤⠿⠾⠤⠷⠤⠶⠶⠷⠶⠷⠾⠶⠶⠶⠶⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠐⠂⠠⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠞⡄⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢀⠖⠉⠒⠠⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠒⠁⠀⠀⠀⠀⠑⠲⠦⠶⠚
⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⠀⠈⠀⠂⠀⠀⠄⠡⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢀⠔⠊
⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⡎⠣⡀
⠀⠀⠂⠀⠁⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⠀⡈⢡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⣿⢙⠛⠛⠛⡛⠛⡎⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⡄⠎⠀⠀⠀⠀⠁⠻⢶⣦⣤⣤⣴⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠈⠉⠉⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲
⠀⠀⢀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⡑⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡄⠀⠀⠀⠀⢠⠀⠀⠠⠈⠂
⠀⠀⠄⠀⠀⠐⠁⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣀⠀⠤⠀⠢⠠⣥⣤⡀⠀⠀⡰⠀⣀⡌⡄⢰
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⣄⣀⠤⠤⢅⣩⠛⡻⠁⠀⠀⡟⢀⣶⣧⠁⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠉⠉⠙⠛⠓⠚⢛⡔⠁⠀⠀⠰⠇⢸⠙⠙⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⢄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆
⠀⠀⢀⣀⠀⠀⠀⠐⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢀⠐⡄⠀⠈⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠆⢠
⠀⢰⣏⠀⠀⠘⠠⠊⢠⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⠀⠀⠀⠲⠂⠀⠬⢷⠀⠀⠀⠀⠂⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⢀
⠀⠀⠉⠁⠀⠀⠀⠀⠚⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠀⠀⠀⠀⠀⠂⢲⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢰⡌⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠲⠖⠾⠱⠌⠭⠳⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠢⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠁⢶⡾⠿⣤⠀⠀⣤⠀⠀⣽⣿⡅⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇
⠀⢶⡶⠀⠉⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠐⠂⠠⠀⢸⣿⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿
⠀⠀⠀⠀⠈⠀⠈⠁⠄⠀⠀⢠⣦⣴⡂⠀⠨⣉⡡⠀⠀⠀⠀⠂⠀⠈⠀⠀⠉⢄⠤⠬⠠⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠿⠾⠗⠘⠀⠁⠀⠀⠀⢡⣀⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠠⡀
⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⠀⠀⠀⠀⠀⠙⠓⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠅
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣁⣨⣅⠀⠐⠒⠄⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢀⡀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠿⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠕⠀⢡⠀⠀⠀⠀⣼⠩⠏⡧⠔⠲⠶
⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⡎⠀⠀⠀⠀⠙⠦⠿⠃⠀⠀⠀⠐
⠀⠀⠀⠜⠀⣀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⠄⠀⢠⠁⠀⠀⠀⣷⡆⠀⠀⠀⣄⡄⠀⣀
⠀⠀⠀⢠⠄⠇⣘⢛⠀⠈⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠇⢿⠀⠀⠀⠈⣆⠀⢿
⠀⠀⠀⢸⡄⠁⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⢢⡀⠄⠀⠀⠀⠀⡋⠒⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠘⠉⠁⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠒
⠀⠀⠀⠀⠀⣤⢈⠟⢀⠀⠀⢰⠌⠀⢰⠀⠀⠀⡀⠐⠳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⡾⠰⠈⠀⠀⠘⠈⠉⠈⠀⠄⠘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⣷⠀⢀⡈⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠇⠘⠀⠀⠁⠀⠀⠀⠀⣿⢒⡄⠀⠀⠂⠀⢀⡀⠀⠀⣤⠀⡀⣠⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⡿⠀⠀⠀⢨⣴⣶⡆⠀⠤⣭⣿⠀⠀⠀⠀⠀⠰⠆⠀⠀⠤⠈⠀⢹⡟⢠⣿⡀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠀⠀⠀⠀⠘⠉⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⡂⠀⠄⠀⠀⠁⠀⠀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠂⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⡠⠀⢀⠐⠂⠀⠘⠛⠛⡀⠀⠀⠀⢠⠖⠄⠀⡴⠛⠛⣷
⠀⠀⠀⠀⠀⠈⠀⠋⠁⠀⠐⠉⠀⠠⠉⠂⠀⠀⠈⠳⢤⣀⠈⠢⠄⠥⠀⠤⡀⠀⣾⣯⠙⢯⠀⠀⠀⠀⠛⠛⠛⠛⠛⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠇⠀⠀⡔⠛⠲⠆⡔⠒⠚⠓⠲⠦⠴⠂⢣⡿⠀⢈⡇⠀⠀⠀⠐⠒⠒⢂⣀⡐⠲⢬⣳
⠀⠀⠀⠀⠀⠀⠀⠡⠀⡆⠀⠀⠁⣀⠜⠀⠀⠀⠑⠄⡀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠢⢄⡀⠀⠀⠀⠐⠃⠀⠈⣳⡄⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⢀⠀⢒⠤⢿⡇⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠴⣀⠀⠀⣠⣰⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠈⠓⠶⠞⣋⠴⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢉⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢢⠀⠉⠉⢹⠁
⠀⠀⠀⠀⠀⣀⣀⠔⠀⣰⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢀⡏⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠇⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⢀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣣⠔⠓⣹⠆
⠀⠀⢄⠰⠶⣶⣶⠤⠤⠤⠤⠤⠤⢤⡤⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⢸⣆⣀⣀⣙⣀⠐⠀⠂⠀⠀⣀⣰⠀⠚⠛⠓⢸⠁⠁⠉⠀⠠⢄⣀⠀⠀⠀⠀⠤⠰⡄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢙⠈⠐⠒⠤⠤⠄⣀⠃⢀⠤⠄⠈⡄⡇⠀⠉⠐⠂⢤⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡘⠀⢀⣀⠐⠂⠐⠂⠀⠒⠀⠀⠀⠉⠉⠉⡇⠀⠀⡀
⠀⠀⢸⠀⠀⠀⡠⠚⠉⠁⢀⣀⣀⠈⢀⠱⡀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢀⠤⠀⠒⠒⠀⠀⠀⠉⡆⠀⠀⠀⠀⠡⡀
⠀⠀⢸⠀⠀⡎⡀⠀⠀⠀⡁⠀⠄⠑⡀⡆⡇⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⡀⠀⣇⠃⠀⠀⠘⠁⠀⠘⠀⡅⠃⡇⠀⠀⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⢨
⠀⠀⠀⡇⠀⠘⢮⡢⡑⠦⢄⣀⣤⠾⢊⡜⠀⠀⢠⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠉⠓⠲⠤⠤⠤⠒⠋⠀⠀⠀⠸⠀⠀⠀⠀⢀⡇⠀⠀⠀⣀⠀⠓⠀⠤⠄⣀⣀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⠃
⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠁⠀⠀⠀⡀⠀⢉⠐⠂⠤⠀⠀⠉⣉⠉⠁⠀⣀⡀⠤⡂⠉
⠀⠀⠀⠸⠤⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠴⠋⠀⠀⠀⢀⣤⣤⠄⢀⣁⣈⠛⠒⠒⠢⠬⠙⠛⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⠋⠁⠠⢐⣴⡦⠀⠀⠀⠸⠆⠀⣠⢤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠤⢄⣀⡠⠔⠐⠈⡀⠴⠂⢲⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣀⣚⣁⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠘⠿⠛⠛⠛⠛⠛⠛⠓⠲⢶⡶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣶⣾⣿⣧⠤
⠀⠀⠀⠰⠷⡶⠶⢶⣶⣶⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢀⣠⣯⠭⠭⠭⠽⠿⠿⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠛⢛⢼⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣧
⠀⠀⢰⣿⣋⣁⣀⣀⣀⣠⣤⣀⣀⠀⢹⡼⠀⠀⠀⠀⠀⠀⠀⡘⢀⣼⣁⠘⠇⢿⣿⣿⣿⡏⠀⡠⡀⠈⣿⣿⣿
⠀⠀⢸⣿⠻⢿⣿⣿⣷⣿⣿⣿⣿⣇⡠⣿⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠈⠻⡿⣿⠏⠉⠀⠀⢀⣾⣿⡟
⠀⠀⢸⣿⣶⣾⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠚⠦⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⣿⣷⣤⣄
⠀⠀⢸⣿⣿⣿⠟⠢⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣿⠀⠀⠀⠀⣟⠦⣀⣀⣀⡤⠞⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷
⠀⠀⢸⢸⣿⣿⣷⣴⣿⣿⣿⣿⣿⡟⠉⠙⠃⠄⡀⣰⣿⣿⣷⣤⣤⣾⣿⠀⠀⠙⢤⡀⠀⣀⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⢸⢸⠁⣹⣯⣀⣸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠉⠉⠙⠻⢿⣿⣿⠇⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢳⣿⡇⢇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⢸⣿⣿⣿⣿⣿⣏⠉⣿⣿⣦⣾⣿⣿⢌⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠘⣌⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠣⣀⡀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠉⠁⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⢀⣾⣇
⠀⠀⠀⠠⠄⠀⡰⠁⠉⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠈⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⠀⠋⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠋⠁⠒⠢⠀⢀⠋⠛⢶⡇⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡊⠄⠤⣾⡷⠀⠈⠉⠁
⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠟⠡⡄⡆⠛
⠀⢱⣿⠯⠆⢀⣶⣶⣾⣿⣋⢿⣷⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠛⠀⢠⡄
⠀⠀⠀⠀⠀⣼⢿⡿⠛⣻⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠴⢾⠁
⠀⠀⠀⠀⢘⠟⢋⠱⠊⠁⣼⣷⢟⣽⡿⢢⠾⠄⠀⠀⠀⠀⢰⡄⠳⣆⡀⠀⠀⠉⡀⣰⡧⠀⠊⠀⠀⠈⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠸⣿⣽⣿⣿⠃⠀⠀⠓⠀⠀⠀⠀⣾⡐⠐⢾⡇⠀⢠⡄⢁⠏⠋⣤⠀⠀⠀⠀⠀⠀⠀⡟⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇⡿⣿⣿⠿⠀⠈⠀⢣⠀⠀⠀⠀⡙⠁⠀⠈⠠⠀⠸⠇⠈⢀⣷⡉⠀⠀⠀⠠⣦⡀
⠀⢀⡀⠀⢀⠄⠈⣍⣹⣇⡿⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⡀⠀⠂⠸⢛⡆
⠀⢸⣿⣧⡀⠀⢠⣿⣿⣟⠀⠀⠀⠀⣦⣼⡇⠀⢀⠀⠀⢀⠀⢠⣠⡆⠀⠀⠄⠀⡄⡠⠛⠩⢁⣠⠐⠞⠉
⠀⠐⠚⠙⢿⠀⣊⡸⣩⣿⣁⠀⠀⠀⣿⢿⡇⢾⣯⠂⣽⢛⠀⣼⡿⣇⠀⠀⢂⣸⠟⠀⠸⣦⠍⠁⠆⢰⡀
⠀⠀⠀⠀⠨⣿⠹⣇⢿⣾⠓⢻⣦⣠⠟⠻⠤⣅⠁⠀⠂⠈⡖⢻⣟⢋⣁⣤⣼⡁⣾⣷⠖⡑⡢⣼⠃⢠⠞⠈⠙⡶⣄
⠀⠀⠀⢸⠧⣿⡷⣏⣺⣿⣦⣈⢹⣟⢀⡀⠀⣾⣀⡐⣀⡀⣿⠀⠁⠸⡧⢿⣿⣼⣿⣿⣿⡟⣧⣄⣀⠸⣶⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡭⣿⣿⣿⠟⣶⣯⣼⣇⣼⣤⣄⣾⠧⣼⣿⡟⠛⠉⠛⣿⣿⣿⠁⠸⣿⠶⠀⣦
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣻⣿⣿⣾⠿⠧⢄⣠⠄⣀⣀⡀⣛⠛⠓⠀⠀⠤⢽⣄⣀⠠⢟⣻⡿⠁⠑⠁⠀⢠⣄
⠀⠀⠠⠐⡋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣟⣓⠋⠀⠀⠘⠛⠛⣛⣻⡿⠿⠶⠦⢄⣀⣿⣴⡎⠁⠐⢀⡀⠀⠀⠘⣻
⠀⠀⠀⠶⠆⠠⠤⠤⣤⣤⣾⣞⣁⡀⠀⠤⢈⣁⠀⠰⣿⣿⣿⣭⣥⣤⣤⣤⣠⣾⣿⡿⠏⢨⠀⠘⢫⡤⢤⣁⠀⣏
⠀⠀⠀⠀⠉⠛⠛⠂⠈⠙⠛⠉⠉⣹⣠⢤⡾⠃⠀⢉⠙⠙⠻⠛⠛⠻⠿⣿⣿⣿⣿⣤⠀⢤⡆⠰⠈⠀⠀⠈⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠛⠛⣹⣻⣁⠀⠀⢠⡤⠀⠀⢀⣴⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠾⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⠅⢀⣶⠀⢁⣠⣼⠟⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡪⠃⠈⠉⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣿⡆⡀⢀⡀⣸⣿⣯⠅⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⢨⠇⠘⠛⠻⠟⠛⠻⠿⢿⠆⠀⠀⠀⠛⠿⠾⡛⢋⣿⡛⠠⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃⠘⣿⣶⣦⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⢷⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠁⢢⠀⠀⠀⠀⠀⠠⠒⠀⢸⠀⢀⠀⠀⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠄⢀⠀⠀⠀⠀⠰⡖⠈⠶⠐⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠠⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠐⢄⣀⠐⠃⠀⠀⠀⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⠤⠤⠥⠀⠸⠀⠀⠉⠉⠉⢸⠀⠠⠀⠐⢤⡨⢨⡔⢐⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢅⣨⠄⠼⣩⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡂⠀⠀⠢⠀⠀⠀⠀⡀⠈⠉⠀⠠⠐⠐⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡙⡌⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠑⠐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠁⠨⠀⢀⢠⠄⡀⠀⠀⡔⢐⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠕⠊⠀⠐⠔⠔⠀⠈⠀⠀⠀⠀⢂⠈⠁⠀⠂⠀⠂⠀⡄⠀⢰⠉⡣⠊⠔⣃⠀⠈⠀⠀⠀⠃⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⡆⠀⢀⠠⠨⢖⡡⢂⢦⠍⠀⠐⠂⠀⠁⠀⢠⡕⠀⢸
⠀⠀⠀⠀⠀⠀⠈⣈⠀⠀⡠⠷⠈⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⣁⡉⠁⠀⠀⡄⠄⠀⠀⠀⡤⠾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠊⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⢀⠄⠀⠀⡀⠄⠀⠄⠀⠀⠀⠤⠄⢤⠰⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠾⡆⢊⠁⠀⠀⠀⠈⢤⠃⣼⠀⠢⠂⠀⢀⠠⠀⠀⠀⠄⠀⠀⠑⠀⠀⠀⠈⠂⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡐⠠⠀⠄⠀⠀⠀⠀⠿⠯⠧⠯⠿⠇⠀⠠⠀⠀⠐⠂⠂⠀⠀⠐⠃⠂⠢⠀⢀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠁⠐⠀⢂⠄⠀⠀⠀⠰⠤⠤⠤⠤⠆⠀⠀⠀⠰⠀⢨⡄⣀⣀⠀⡌⠀⠘⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠁⠀⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠂⣀⣁⣀⣁⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡒⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠘⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⣠⠀⣀⠀⢤⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢉⣆
⠀⠀⠀⠀⠀⢀⡀⠂⠀⠈⠠⠀⠀⡴⠱⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡾⢄⠈⢏⡡⠦⠔
⠀⠀⠀⠀⠀⠈⠀⢰⣷⣃⣠⢠⡇⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⢱⠀⠈⢳⠖⠉⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤
⠀⠀⠀⠀⠀⠳⡄⠠⠍⠐⠀⠠⢿⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡐⡤⢤⡷⠖⠀⠀⠀⠀⠀⢀⣠⠤⠴⢅⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠎⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠂⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠖⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠐⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⡠⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠘⠢⠄⢀⠀⠠⠞⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠰⠄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠁⠚⡆⠊⢱⠻⢆⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡤⠀⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠌⠂⠞⣩⠟
⠀⠀⠀⠀⠀⠈⡀⠤⡈⢧⣎⠠⠞⠠⠖⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡘
⠀⡀⠀⠀⣰⠋⠀⡀⡤⠐⠉⠰⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠂⠀⠀⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠃⠀⢀⠄⠀⠀⡰
⠀⢇⠀⠀⢨⠬⣁⠴⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢀⠀⠀⢠⢀⠀⢰⠀⠄⠂⠀⠀⠀⡀⠀⢠⠎⠀⠀⡼⠁
⠀⠈⠀⠀⠀⠚⠃⠰⠋⠀⠀⠁⠀⠀⠄⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡎⠀⠀⠸
⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠊⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠘⡛⠂⠀⠀⠀⠉⠁⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆⠀⠀⠀⣶⡀⢀
⠀⠀⠈⠁⠀⢐⠊⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣁⠒⠂⠄⣀⡰⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⢸⢀⡇⠀⠀⠁⣾
⠀⠀⠀⢰⠀⠈⠁⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢀⠇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⡌⠳⠀⠂⢸⠐⠑⠀⠀⠀⠋⠗⢢⡄⠄⢀
⠀⠀⠀⠘⠀⡸⠵⠦⢔⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠿⢧⠀⠀⠘⠀⡄⠀⠀⠀⢠⡄⠀⠉⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⢀⠠⠲
⠀⠀⠀⠀⠀⠀⠂⠢⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⠈⢰⢀⠇⠀⠀⠀⠁⠀⠈⠧⠈⠀⠀⠾⠈⠁⠀⣼⠄⠀⠀⠀⠐⠃⠀⠀⠀⠛⠂
⠀⠘⠦⢔⣢⠄⡲⠒⢁⠀⠀⠀⠀⠀⠀⠀⠐⢿⣥⣐⡀⣤⠠⠌⠂⠀⢙⣛⣯⡀⠀⣰⡠⠚⠀⠀⠀⠀⠢⠐⠐⠐⠀⠀⡀⠤⠁⠀⢄⠀⠤⠄⠀⠄⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠈⠀⠄⠀⠀⠀⠀⠀⠓⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢼⠁⠈⠈⠁⠀⠀⠀⠒⠒⠒⠒⠓⠒⠒⠶⠦⠤⠤⠤⠤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠙⠂⠤⠀⠀⠀⠄⠴⠐⠒⠀⠀⠀⠀⠀⢒⣀⣀⣀⣀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⣀⡶⠶⠶⠖⠢⡀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⣀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⡤⡶⠮⢑⣂⣩⠥⠤⠐⠒⠈⠉⡇⢧⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠢⡀⠀⠀⠀⠸⠑⢪⠒⢌⡆
⠀⠀⠀⠀⠀⠀⡇⠇⡎⠁⢀⣀⠠⠤⠤⡀⡎⠇⢠⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠸⡘⠬⠤⢊⡞⠢⣄
⠀⠀⠀⠀⠀⠀⢸⠇⢠⠀⡇⠀⠀⠀⠀⢃⠇⢸⢘⠈⡂⠀⠀⠀⠀⠀⢰⡠⠒⡶⠂⠠⠤⠤⠤⠄⠰⠒⠋⠀⠀⡇⠀⠀⠀⠀⠈⠁⠈⠁⠈⠓⠦⣽⡢
⠀⠀⠀⠀⠀⠀⠘⡗⠸⡀⣇⣀⣀⣀⡤⠼⠞⣊⣩⢔⠣⣄⠀⠀⠀⠀⠈⠁⠀⠑⢄⣀⠀⠀⠀⠀⠀⢀⣀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠁⠤⠤⢄⡲⠾⣟⡻⡝⢯⡱⣬⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠙⠃⠀⠠⠤⠤⠤⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢝⢦⠰⣆⠽⢶⣚⣮⢙⡦⠝⢒⡩⠗⠋⠀⠉⠢⡀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠠⠤⢄⠀⠀⠀⠸⠒⠊⠤⠤⢀⣀⣀⠉⠉⠑⠒⢦
⠀⠀⠀⠀⠀⠀⣀⡀⠈⠣⡑⣌⠲⡭⢳⣮⠥⠒⡨⠕⠂⠑⣄⠀⠀⢀⣨⡆⠀⠀⡠⢊⠥⣴⡶⠯⠯⣅⠋⠀⠀⠀⡇⠀⣀⢀⠀⠀⠀⠀⠈⠉⠉⠐⡎
⠀⠀⠀⠀⠀⢘⢠⣌⡆⠀⠈⢮⠢⡀⠀⠀⠀⠀⠙⠦⠒⢊⣡⣴⢊⡡⠔⠁⠀⠀⠉⠱⡿⠉⡊⢢⠉⠁⠀⠀⠀⢰⠀⠀⠉⠉⠀⠋⠛⠁⠱⠲⠆⢀⠃
⠀⠀⠀⠀⠀⠘⡌⠁⡇⠀⠀⠀⠑⣜⠢⠤⠤⠄⠒⣒⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠃⠒⠒⠂⠠⠤⠤⢀⣀⡀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⠴⠁⠀⠀⠀⠀⠈⠑⠂⠒⠊⠁⠀⠀⠀⣀⠤⠐⠠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡤⢐⣒⣒⡒⡂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠢⢄⠀⠀⠀⠀⠀⠀⢠⠁⠀⡠⣀⠸⠤⢤⡀⠀⠀⠀⠀⡇⠇⢁⡠⣀⠿⣩⠈⡄⠀⠀⠀⢠⠄⠒⣀⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡓⠒⠐⠐⠒⠂⣻⡄⠀⠀⠀⠐⠉⠀⠘⡆⢸⠃⠀⢀⡔⠀⠀⠀⠀⢩⢸⠘⡁⣈⣉⠨⠄⢡⠀⠀⠀⢹⡄⠒⢐⣂⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡱⠢⠄⠤⠺⡀⠇⠀⠀⠀⠈⠓⠒⠒⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢮⡄⠀⠀⠀⢀⣀⣸⠀⠀⠀⢈⣟⣭⢐⡢⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠁⠀⣀⣀⡀⠬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢠⡤⢄⡀⠀⠘⣍⡉⠭⠕⠋⠉⠀⠀⠀⠀⠘⡼⡀⠰⠎⠭⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣷⣻⣕⣀⡽⠂⠀⠀⠀⠀⠀⢀⠤⠀⠤⣄⠀⠀⢣⢳⣒⣐⣩⠭⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠤⢀⣐⡒⢒⣀⠀⠠⠬⠕⠲⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡤⣀⢤⠈⢣⠀⠈⣮⣤⣄⣻⡦⡴
⠀⠀⠀⠀⠀⣶⡽⠛⠋⠉⠉⠀⠀⠀⠄⠀⠐⠀⠀⢀⣀⣀⠠⠤⢾⠀⠀⠀⢀⡤⡔⠒⢖⢢⠀⠀⠀⠀⠀⠸⡀⠑⠤⠊⠀⡸⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠇⣧⠤⠤⠤⠤⠐⠒⠒⠒⠚⠋⠈⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⢨⠱⣘⣀⠬⠆⣇⠀⠀⠀⠀⠀⢱⡴⠒⠒⠊⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢰⢠⠀⢀⡤⠤⠄⢦⠀⠀⣃⠴⠤⠛⠚⠓⠉⠀⠀⠀⡇⠀⠀⠀⠇⢠⢄⠔⢲⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇
⠀⠀⠀⠀⠀⠸⠘⡀⠘⡀⠀⠀⠈⡄⣠⠥⠄⠒⠒⠈⠉⠉⠙⡄⠀⣄⠀⠀⠀⠘⣌⣒⣂⠭⠞⠀⠀⠀⠀⠀⢠⡖⢤⠀⠆⡠⠄⠀⡎⢉⣬⠙⡆
⠀⠀⠀⠀⠀⠀⡆⠇⠀⠇⠀⠀⠀⢣⢡⠀⠀⠀⠀⣀⣀⠠⠤⠗⠒⠟⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣧⠔⢳⠀⠤⠀⠀⠓⠬⠭⠤⠂
⠀⠀⠀⠀⠀⠀⢡⢒⠀⣸⣀⡤⠤⠴⠚⠒⢂⡭⡉⠀⠀⠀⠀⢀⣀⠞⠀⢀⠔⠉⠀⠀⠱⡀⠀⠀⢀⡴⠊⠀⠀⠹⣶⠉⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⣜⡁⠀⠀⠀⠀⠀⠀⣀⣀⡉⠤⠤⡖⠊⠉⠀⠀⠀⠀⡎⠀⡞⣱⡀⡠⠁⠀⠀⠸⣜⣄⣠⣤⠒⠛⠓⠁⠀⠀⠀⠀⠏⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠈⠉⠉⢹⠘⡀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠰⡀⠉⠀⢉⠀⠀⠀⠀⠀⠀⠈⠑⠿⠇⠀⠀⠀⠀⠀⠀⢰⣀⣀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠝⢃⣀⣠⠤⠤⠚⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠘⠊⠉⢭⡄⠈⠩⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⡂⠈⠙⣟
⣀⣈⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠐⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠸⠸⣿⣿⣿⣿⣾⣷
⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣿⣧⠁⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⡧⣀⠀⠤⠀⣘⣿⣿⠁⠈
⢀⣴⠏⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣯⣿⡿⢂⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠉⠛⡆
⠉⠉⠀⠀⢠⣨⣀⠀⡁⠀⠀⠀⠄⡀⠘⢫⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠡⣿⡀
⢀⣤⣶⣾⣿⣿⣿⡇⠈⠀⠀⡀⢈⣱⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠙⠛⢟⡻⠟⡿⢻⠁⠀⠀⠀⠀⣈⢧
⣾⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠋⣩⡭⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠐⣤⣿⡿⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠍⠍⠒⢶⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣤⣴⣤⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢀⣀⣆⣀⠀⠤⠤⠤⡀⠀⠀⠀⠀⠀⢀⡀⠋⠈⠙⠛⠀⠌⣿⢀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⢤⣶⡌⢯⢿⢍⠀⠀⠀⠀⠀⣰⠄⠀⡃⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⢻⣯⠠⠀⢠⠟
⣿⣿⣿⣿⠿⠛⠉⠄⠀⠈⢿⣿⣿⡿⢭⣈⣳⡈⣆⠈⠒⠀⠊⠐⣾⣿⣷⡄⢓⢒⣲⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⣶⠂⠁
⣿⣿⣿⣟⢢⠀⠐⠈⠀⠀⠉⠈⢱⠏⠉⠀⠀⠀⢀⡀⠀⡀⢠⠀⠛⠉⠉⠉⡆⠋⠜⠉⠐⠀⠀⠠⠀⠀⠀⢀⣬⣽⣻⣷⣦
⣿⣿⣿⣃⠁⠑⠉⠀⠀⢠⠀⡀⠀⠠⠤⠀⠀⠐⠁⠁⡀⠀⢰⡄⠀⣀⠠⡲⣦⣤⣄⢰⣄⣀⣀⣠⡀⠄⠀⠀⣨⣾⣿⣿⣿
⠈⢹⣿⣿⣷⡆⠀⠀⠀⠀⠑⣌⠀⠀⠀⠀⠀⠀⠈⠐⠂⢄⡰⡀⠀⠘⣞⠹⣷⢝⡾⠿⣼⣿⣿⠏⠐⢄⠀⠹⣿⣿⣿⡏⠉
⣠⣾⣿⣿⡟⠙⠂⣀⠀⠀⠀⣼⡶⠙⢠⠄⡀⣴⣆⣤⣤⣌⡰⣧⡀⠀⠈⣀⣺⣭⣄⠰⣿⣿⣏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾
⣿⣿⡿⢛⡅⠂⠁⠀⠀⢸⣿⣿⡿⠓⠤⠴⠉⠻⢿⡿⠟⢛⣿⠁⠈⠀⣿⣿⠿⠿⠿⠗⠾⢿⣏⣦⠄⠀⣠⣾⣾⣿⣿⣿⣿
⣿⣿⠧⣀⠧⡀⠀⠀⣂⣄⢸⣟⠁⠀⢤⣤⣴⣖⣶⣶⣿⣷⣸⣠⣶⣾⠉⢱⢠⣀⢀⣀⣤⣼⣿⠾⢡⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣖⣻⡀⢆⡸⢯⡿⣽⣿⣷⡀⠀⠀⣈⣿⣿⣿⣿⣯⣾⠁⠢⠄⠛⠋⡤⣻⣾⣿⣿⣿⣿⣷⣿⣿⣿⣻⢿⡿⢽⣿⣿
⣿⣿⣿⣿⣠⣶⢿⣛⢥⡻⠛⢿⡟⠙⠀⢳⣿⣿⣿⣿⣿⣿⡈⠓⠶⣤⣤⣤⣴⣟⠻⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⢣⡀⠀⠄
⣿⣿⡿⣏⣹⠢⣷⣤⠶⢦⣀⣀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡦⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠲⢤⣄⣄⠈⣧⡾⢀
⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣐⣠⣮⡽⢂⣭⠐⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⣏⠉⠁⣀⣴⡶⢬⣭⢰⣯

⠀⠀⠀⣠⡀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⣀⠀⠀⣠⠴⠲⠦⣄⠀⠀⣀⣀⡀⠀⢠⠶⣄⠀⠄⠀⢀⣰⠤⢤⣀
⠀⠀⠀⠙⠁⣴⢋⡧⠼⠶⠬⣙⠷⡤⠶⡄⠛⠃⠀⡇⠀⠈⠃⢸⡜⠿⣿⣯⡿⠷⣯⣷⡃⣠⠶⣯⣭⡉⠙⢲⡌⢳⡀
⠀⠀⠀⠄⢸⠅⡎⠀⠀⢁⡤⠞⢁⣀⡦⣗⡴⠻⣄⢳⡀⠀⠈⣸⠁⠀⠀⣀⢰⣦⡻⠾⢱⣃⣀⣀⣀⡧⠠⡞⠹⡄⣷
⠀⠀⢠⣶⡜⣖⢳⡴⠚⢉⣤⠼⠋⢡⣤⢨⡷⢶⡏⠀⠙⠶⣶⡇⢠⣷⣼⣟⣾⢷⡿⡄⠸⣧⠖⣲⣄⣄⠐⠧⣾⠇⡟
⠀⠀⠀⠄⣴⢋⣀⡦⠞⣋⣤⢀⡤⠴⢤⡤⠶⠒⡛⠉⢳⠶⡌⣷⠸⡷⡟⣏⣏⣇⢷⠹⡀⠱⣄⣳⠘⠋⢠⡾⢏⡼⠁
⠀⠀⠰⣷⠌⠶⠋⣠⣞⣩⡇⣏⣴⡼⠷⣽⣾⣉⡽⠆⠈⣇⢷⠸⣄⢳⡹⡼⡼⡜⣎⢇⢳⡀⢀⣉⣿⠯⠽⣒⣉⢀⡄
⠀⠀⠀⠀⠐⠀⢰⣣⠞⢟⣁⡿⢭⣠⠴⠃⣈⡤⠶⠂⠀⢹⡘⡆⢸⠀⢧⢳⣹⣿⣽⡾⠛⢳⠸⢬⣉⡽⠈⡗⣿⠐⠂
⠀⠀⠀⠻⢃⣀⡋⢀⡴⠋⣠⠃⠀⢳⠈⡀⢀⡤⠶⠒⠀⠀⢧⠹⡌⢳⠈⣿⠋⣿⣤⣿⠾⠽⡀⢀⣴⡶⢠⠇⢻⡈⠁
⠀⠀⠀⣞⣩⣼⠇⠙⠶⠚⠁⣤⡀⠘⡇⠠⠀⠠⠖⠛⢁⠀⠸⡆⢳⠈⠇⠘⠿⠟⢉⡥⢤⠘⣛⡈⠋⣱⡷⣶⡶⠿⣄
⠀⠀⠀⠀⡇⠸⣄⡀⠀⠂⢰⣇⢳⡀⢹⡀⠀⠀⠴⠚⢉⣀⣤⣿⣈⡇⣀⡤⢶⠆⠛⠓⠋⣰⣧⡇⢼⣭⣭⣥⡤⠤⠼⠂
⠀⠀⠀⡼⢁⣀⣠⢿⡆⠀⣼⡁⠈⢧⠈⢧⣤⠴⢒⣋⡭⠖⢚⡉⠁⣰⡋⣹⠏⢀⡟⢛⣾⣗⠒⠛⠲⢦⠀⡴⢲⡒⢲⡀
⠀⠀⠀⢻⡋⠈⠙⣫⠇⢀⣯⠀⣤⠈⢧⠀⠈⠛⣉⣄⠐⠾⠛⣡⠞⣩⠏⣡⠖⢸⣧⠾⠛⠻⣧⠦⣄⣸⠀⡇⢸⣴⣼⡇
⠀⠀⠀⠄⢉⡛⢋⡁⠀⣸⠃⢸⠋⣇⠘⣧⠐⣿⡿⣿⠃⣠⠞⢳⡞⢁⣤⠜⠀⣸⠤⠤⠤⣤⣬⣀⣈⡟⠀⡇⢹⠄⢸⡇
⠀⠀⠀⠀⡟⠷⣿⠁⢀⡟⠀⣞⠀⢸⡄⠘⣆⠈⠛⢁⡼⣁⡴⣫⣤⢾⡼⠀⠀⣏⣠⠴⠚⠁⣹⠀⢠⡇⠀⡇⢹⡄⢸⠃
⠀⠀⠀⠀⣇⠀⣇⠀⣼⣉⣀⡉⠉⠉⠁⠀⢹⡄⠀⠾⠞⠁⡴⣣⠦⣽⠃⡖⠒⠿⠤⠤⠤⢼⣥⣀⣸⣁⠀⣧⠿⠤⣼
⠀⠀⠀⢠⠼⠷⠾⠦⢤⡉⠉⠉⠉⣉⣛⠓⠒⠃⠀⡄⢠⢾⣀⠙⣶⠃⣠⡙⢛⡖⢲⠖⠶⢤⠤⣤⣄⣹⠃⠌⠛⠒⠋
⠀⠀⠀⢸⠐⢒⣛⠒⠦⠍⡶⣫⡭⠭⣭⣍⠑⡦⢰⡷⣌⠓⢬⣙⣿⠆⠙⢡⡞⣰⠋⠐⢀⢸⠀⡇⢠⣶⣶⣶⣒⣲⢲⡄
⠀⠀⠀⣸⠀⣉⣉⣉⠓⢰⠧⡧⠤⠤⣤⡞⢰⠃⠀⠳⠼⠀⣶⡆⡶⢶⣄⣞⣰⠃⢠⣦⣤⢸⠀⡇⢸⡿⣕⣧⣤⡼⢻⡇
⠀⠀⠀⣿⠀⣁⠀⠈⠁⣼⠐⠚⠛⠓⠆⢠⠏⠠⢸⣭⣭⣷⠀⣀⡏⠉⡀⢉⡥⠤⣼⣍⠁⠸⠦⠇⠸⡇⠂⡂⣂⣶⣸
⠀⠀⠀⠉⢯⠭⠭⠽⣦⣷⣶⣛⡓⢲⣤⡞⠀⡴⣾⢀⡤⡿⠸⠽⠃⡞⡇⢺⠀⡀⠀⢨⢇⡙⣗⢦⡀⡇⠅⠄⠾⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠈⠷⠃⠈⠙⠓⠚⠁⠘⠛⠈⠋⠀⠙⠒⠒⠒⠒⠚

⠀⠈⠉⢻⣶⢞⡛⠹⠷⢶⣦⠤⠄⣀
⣤⣄⣀⣸⡇⠑⠀⠴⠒⠒⣤⠠⣍⢑⡺⠗⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⣶⣂⣤⣀⡀⣀⣀⡀
⣿⣿⣿⣿⣕⠠⠁⣀⠶⠔⢸⣴⡡⡳⣧⠛⠀⢹⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣎⣓⣸⣿⣯⣷⣋⣽⣿⣿⣽⣿⣿⣿⣿⣿⣦⡦⣀
⣿⣿⣿⣿⣿⣿⣶⣦⣬⣅⣒⡦⢭⣭⣉⣒⣀⣼⣧⣀⣀⣀⠉⠉⠓⠒⠶⠤⡄⠀⠀⠀⠐⠐⣿⡀⣞⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢮⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡟⠀⠀⠀⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣿
⢹⣿⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣠⣿⡻⠷⣆⣤⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⢸⣿⠀⠀⠀⣤⠂⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⢿⣿⣿⣽⣿⣿⡏
⣿⣟⠀⢠⠦⠁⠀⠀⣿⣿⣿⣿⣿⠟⠶⢶⣿⣷⣿⣟⣇⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠤⠼⢿⣿⣿⣿⡿⠿⠿⠿⠻⠿⠟⠛⠛⠛⠛⠛⠉⠉
⣿⣿⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⢀⡀⣈⣧⡽⠇⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡎⢡⣿⡇⠀⠀⢠⡏⠉⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠁⢀⠀⢀⣤⣤
⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠨⠯⠹⠁⠀⠀⡇⡇⠀⠀⢀⡀⢀⠀⠀⢸⠱⣿⣿⣿⠆⠀⢸⡇⠀⢐⣦⡀⠸⠿⣿⣿⣿⠇⠀⠀⠀⠁⢠⢻⣿⣯
⣿⣿⡀⡄⢲⡆⠀⣾⣿⣿⣿⣿⣇⣃⣓⣢⣟⣻⣂⠀⢀⣃⣷⠀⠀⠍⠙⠀⣠⣆⢾⡗⣿⡟⠁⠀⠀⢸⡧⣧⣾⣿⡇⠀⠡⣹⣿⣽⣦⣤⡀⠀⠀⠘⢬⣷⣷
⣿⣿⠀⠁⢼⡇⠀⢿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣛⣟⣻⣝⣻⣿⢀⠀⠀⠀⠘⢵⣿⣞⢻⣿⠛⢹⡀⠀⢸⡥⠶⣿⣿⢤⡀⠀⣴⢍⣤⠞⢻⢻⣄⠀⠀⢀⣾⡼
⣿⣿⠀⠀⢸⣇⠀⠀⣿⣿⣿⣿⣿⢿⠏⠉⣽⣭⣿⣭⣧⣿⣿⣷⡀⠃⠀⢽⣟⢿⣿⣿⣿⣿⣿⣧⠀⠘⢡⡄⢈⢀⣾⣷⡄⢣⠠⠿⣿⣏⣾⣿⡆⢀⢾⡛⣷
⣿⣿⡃⠀⢸⣟⡃⠀⣿⣿⣿⣿⣿⠘⠀⣸⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠈⣿⣧⣽⣟⠿⠿⢿⣧⠀⢸⢾⡗⠛⠙⣿⢿⡷⠈⢶⣦⣹⣿⣿⣿⠁⠈⠺⣇⢹
⣸⣿⠁⠀⢺⣷⡁⠀⣿⣿⣿⣿⣿⠀⢀⢟⠙⣋⠛⢐⣿⣿⣿⣿⣿⡃⠀⢠⣿⠿⢿⣿⣿⡾⣷⡿⡇⣸⣬⣷⣶⣿⣿⡾⠁⠀⢨⣻⣿⡛⣿⠏⠀⠀⠘⣿⣷
⣿⣧⠛⠀⡼⠛⠟⠂⢸⣿⣿⣿⠹⢰⣾⣾⣶⣴⡄⢸⣿⣿⣿⠋⣻⠉⠁⣿⠏⡦⢨⣾⣿⡟⢿⣼⣿⣿⣿⣿⣿⣿⣿⠇⢀⣰⡀⢻⣬⣿⣿⡖⡀⠀⢠⣿⠿
⣿⢻⡄⣀⣀⣠⣤⣤⣼⣿⣿⣿⠀⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣝⡄⣿⠀⠱⣾⣿⡟⠙⠛⠛⠃⢸⡏⢿⡿⢻⣿⠹⠶⠿⠧⡈⢻⣿⣇⣾⣷⣄⢀⡟⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⣮⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⡼⣿⣿⡇⠀⠀⠀⢖⣩⣽⣿⢶⣼⡿⣶⣶⣿⣆⠐⡹⣿⢀⣴⣦⣶⣦⢰⢹
⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣧⣿⣯⡇⠀⠀⠀⢿⣿⡏⢿⣹⣿⣷⡟⢉⣿⣿⠀⣺⠟⠸⡿⣯⣿⣿⣶⣈
⣿⡇⣷⣶⣿⣻⣿⣿⣿⣭⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣯⣷⣾⢺⣟⣃⣾⣿⣿⣿⣿⣲⣿⣿⣤⣇⣈⣻⡇⣿⣿⣿⠃⢹

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⡶⢖⣶⡶
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠙
⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞
⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⣤⣀⡀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡀⠀⠠⣤⡀
⠀⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠘⠃⠠⠠⠄⢰⠄⠀⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⢯⢈⠐⠢⢙
⠀⢤⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠒⠶⠋⠀⠀⢤⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⢈⠓⡞⠻
⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄
⠘⠋⠀⡆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁
⠀⡀⢸⡶⠿⣿⣿⠏⡠⠤⡶⠦⢤⠀⣀⢸⠇⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⣀⢸⠃⢀⠤⠴⣤⠀⠲⠶⡤
⠀⠃⢈⡳⠀⡀⠙⠀⠓⠒⠂⠂⠀⠀⠉⠀⡀⢔⡁⠈⠛⠊⠩⠍⢢⠀⠀⠋⠀⡀⠀⠐⠒⠙⠂⣀⠒⢂⡃
⠀⠺⣾⠕⠚⠀⠀⠀⠀⠐⠈⠙⠙⠁⠘⣶⠁⠀⠀⠠⠀⠐⠤⠔⠊⠂⠀⠚⣶⠀⠀⠀⠂⠀⠀⠈⠏⠛
⠀⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣐⣲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠈⠟⠲⢌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡔⢶⡖⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣧⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢽⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣯⣵⣿⡟⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⣀⣴⣾⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡴⠛⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠭⢭⠭⠭⣤⡤⠤
⠀⠀⠉⠛⠛⠛⠛⢿⣷⣿⣶⡬⢀⠀⡀⢀⣠⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠛⠛⠓⠂

⠀⠀⠀⡠⠤⠤⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠈⢀⠄⡩⠋⢰⢠⡀⡥⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⢀⠑⠊⠀⠖⠐⢱⠄⠀⠀⠀⠀⡠⠇⠒⠒⠀⠈⣉⣀⠀⠒⠂⠼⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠁⠀⠀⢸⠢⠀⠠⠠⠤⠤⠤⠤⠀⠠⠄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠰⠂⠀⠒⠒⠒⠒⠒⠂⠒⠒⠒⠁⠀⠀⠀⢀⠤⠄⠀⠀⢀⠀⠠⢂⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠓⠈⠘⠘⠀⠚⠉
⠀⠀⡇⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠆⠈⡄⠀⠀⠀⡞⢉⡽⢋⡝⠉⡇
⠀⠀⡁⠀⠀⣀⢀⠀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⡷⠊⡠⠋⡠⠊⡇⠀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠁⠐⠀⠀⠀⠐⠀⠀⠀⠀⢀⠁⠀⠀⢀⢀⡀⠘⠀⠀⠀⠀⠓⠚⠲⡞⠒⠒⠃⠀⠀⠀⠀⠀⠀⠁⢈⢠
⠀⠀⠀⠃⣀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠁⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠒⠀⠈⠙⠀⠀⠀⠀⠀⠀⢀⠀⠺⠑⠈
⠀⠀⠈⢀⠤⠤⠤⢄⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡇⠀⠀⡀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⣎⠤⠔⠒⠒⠒⠒⠒⠤⣈⣄⡀
⠀⠀⢠⠇⠀⠀⢤⠄⠋⠤⡄⠀⠘⣄⠀⠀⠀⠀⢀⠘⠀⠀⠘⠀⠘⠊⠉⠉⠉⠉⠉⠉⠉⠋⠀⠱
⠀⠀⠀⠀⠀⠀⠈⡦⠒⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡔⠒⠒⠂⠀⠀⠀⠒⠒⠢⡤
⠀⠀⠘⠤⠤⠤⠐⠓⠀⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠒⠢⡄
⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⣠⠿⢤⡀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⡎⣩⠖⠒⡄⠀⠀⣃⣀⣀⣀⣀⣠⡇
⠀⠀⠸⠡⠀⡲⠒⢲⢦⠨⡆⠀⠀⢸⠀⠐⢸⠐⠀⢸⡇⠀⠀⠀⢸⠱⣇⡠⢴⠁⠀⢸⠀⠀⠀⠀⠀⢸⠃
⠀⠀⡇⠃⡰⠁⡰⠁⢸⡒⠇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢀⠄⠘⠀⢄⠓⠊⠀⠀⢸⠀⠀⠀⠀⠀⡘⡆
⠀⠀⠣⠉⠁⠈⠁⠀⠁⠜⠀⠀⠀⠸⣀⣀⣸⣀⣀⣸⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄⠀⠀⢀⡜⠁⠀⠑⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢠⠇⠀⢀⡞⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⡄⢹⡀⢹⡀⠀⣀⣠⣤⠤⠤⠤⠤⣄⠀⠀⠀⢀⡟⢀⡞⠀⢀⡞⠀⠈⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠹⡌⡇⠈⣇⡞⠉⠁⠢⣄⡀⠀⠀⠈⠳⣟⠛⡾⠁⣜⠀⢠⡞⠀⠁⡠⠚⠓⢧⡀
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢷⢹⠀⢸⡇⠀⠀⠀⠀⠉⡞⠉⠁⠀⡸⢰⠃⠰⠉⠙⢯⠀⢀⠞⠀⠀⡇⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠘⣿⡆⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢀⣣⠃⢠⠁⠀⠀⠈⣤⠋⠀⠀⠀⠹⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡸⠷⠤⣧⡔⠉⠉⠙⠲⡇⠀⠀⣰⠇⢀⠇⣀⡠⠤⢤⡉⠑⢆⠀⠀⠀⠈⠓⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠎⠀⠀⠀⠈⠁⠀⠀⠀⢀⡼⠒⠚⠛⠢⡜⡿⠥⢄⣀⠜⢱⡀⢸⠀⢀⣀⡠⠤⠶⠛⠲⣄
⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠶⠤⠼⣄⣀⣀⡀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠘⣧⠀⢀⣁⡤⠤⠓⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠚⠶⠶⠦⠤⠤⠶⣶⠿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡽
⠾⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢸⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠉
⠀⠀⠀⠉⠙⠲⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⣀⠤⠒⠋⠁⡇
⠀⠀⠀⠀⠀⠀⠹⡄⠈⠉⠓⠦⢤⣀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢣⣠⠴⠊⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⠉⠓⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⢰⠞⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀⠀⠀⠀⢀⠀⣀⣠⡤⠖⠚⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣳⣶⣾⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠒⠆⠄⠒⠲⣴⣎⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠁⠠⠀⠀⠀⠀⠙⠉⠛⢦⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢖⣶⠖⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢷⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠉⠉⠀⠈⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⣺⢸⡿⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣉⣴⣿⡾⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⠟⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠀⠀⠀⠀⠺⠧⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⣖⣶⢶⡾⠷⠿⡿⢋⡠⠊
⠀⠀⢠⣀⠀⣀⣀⣀⣀⠠⣸⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⢶⠀⢀⣿⣟
⠀⠀⠉⠘⠛⠛⠛⠛⠚⠿⣿⣷⣯⣶⠭⠥⢀⠀⡀⠀⠀⢀⣴⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠐⠊⠓⠚⠛⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡿⠿⠾⠧⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆⡆⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠁
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⢻⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠠⠆⠀⣲⡄
⠀⠸⠟⠀⢀⠓⠄⠀⠀⠀⠇⠀⡇⠈⡆⣀⠐⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⢠⡀⠀⡄⡄
⠀⠿⠿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⢷⠈⡃⠀⢠⣙⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢀⠀⢠⠀⢠⣤⡆
⠀⣤⣤⠀⢸⠿⡇⠀⠀⠀⠰⠀⠁⠀⢸⠀⠃⠀⠀⠻⠿⠿⢷⡄⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣯⠥⠤⢤⠤⠀⠤⠄⠀⠠⠀⠒⢻⡿⠁⠀⠀⠀⡤⠀⠀⡅⢀⡥⡅
⠀⣛⣿⠀⠀⢆⠀⠀⠀⢠⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠠⠤⠌⠻⠀⠀⠀⢠⣾⡿⠟⠋⠁⠋⠀⠀⠀⠀⠑⠠⠤⠀⠀⠀⠀⠰⠻⠃⠀⠀⠀⠀⠀⠀⣠⢀
⠀⢛⠛⠀⠀⡆⠀⠀⠀⢘⢂⡀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌
⠀⠈⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⠞⢚⡀⠀⢿⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⢀⡀⠀⠁⡜⠉⠀⠀⠜⠀⡀⠀⢴⣆⣩⠄
⠀⠀⠀⠀⠀⠀⡀⠃⢶⡆⢿⠀⠈⠚⠀⠀⠐⠤⠂⠀⣤⠤⢄⠰⠠⣀⠀⠁⠀⠀⡬⡤⠆⠀⠈⢡⡶⠐⢄⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠁⠀⠀⠀⠀⠀⠒⠊⠀⠀⠐⠀⠀⢊⣾⣷⠈⠂⠀⣀⠀⠃⠠⠀⢋⣈⠄⠈⠀⡬⢉⣄⠀⢀⠀⠀⠀⠀⠀⠁⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠆⠉⢈⠰⠄⠀⠀⠀⠀⠀⠀⠀⠤⠌⠉⣣⢾⣢⠙⠈⠏⠀⠈⢁⢀⠴⢤⣆⡀⠀⠀⠀⠐⠼⡿⢆
⠀⠀⠀⠀⠀⠀⣼⢭⠀⡄⠥⠀⠀⠂⠀⠀⢤⣬⣄⠀⢈⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠰⠄⠀⢈⣄⣩⢪⡆
⠀⠀⠀⠀⠀⠀⡿⣺⣦⠐⢄⣠⣀⡠⢀⠠⣔⠀⠋⠓⢤⠴⠇⠙⠉⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠀⠜⠿⢍⠁⢊⡥⢷⡄⠀⠀⠐⠳⣬⠢⠀⢹⡇⠂⠈⠐⡄⢄⣀⣰⠁⠀⠀⠀⠀⠀⢐⠃⡔⠄⠀⠠⠀⠒⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⠀⠠⠸⡷⠞⠥⡆⠀⢲⠑⠁⣘⢇⣣⠀⠀⠊⠁⠀⠠⣄⡜⠁⠀⠀⠀⠀⠀⡈⠃⣀⠀⠆⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⡁⠀⠀⠁⠀⠀⠘⠃⠀⠬⠀⠀⠀⠀⠀⠲⢶⠤⠀⠖⠚⠙⠀⢀⠸⠒⠈⠈⠛⡉⡠⣌⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⣤⡀⠀⠀⣉⠀⠙⠂⠠⠴⣀⢠⠄⠀⠒⠆⠀⠀⠀⠀⢀⠂⠀⠄⠩⠀⠀⠀⢸⣤⣃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣓⣶⣶⣾⣯⠿⣷⣦⣔⡠⢀⠀⠀⠀⠀⠀⢉⣉⣉⡁⠤⠤⠤⠤⠀⠀⡤⠤⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡬⠟⣋⣉⣛⣙⡛⠛⠛⣓⣻⡆⣉⣐⣒⠛⠻⣿⣯⣤⣬⣤⡤⣤⣀⣀⠀⠍⠄⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠒⠛⠁⠒⠲⠢⠶⠦⠤⡤⡭⣉⣉⡉⠛⢃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⢀⠤⠤⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠡⢂⠔⡱⠂⢢⢨⠈⣢⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠀⠀⠈⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⢀
⠀⠀⢸⠘⠥⠋⢠⠔⠥⢫⠈⣩⠀⠀⠀⠀⣸⠥⠤⠄⠒⠒⠒⠒⠂⠤⠤⢨⡇⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠢⡈⠄
⠀⠀⠀⠑⠂⠀⠀⠠⠤⠷⠤⠂⠀⠀⠀⣎⣀⠀⠀⠀⠈⠉⠉⠉⢀⣀⣀⣀⢨⠂⠀⠀⠈⠰⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡄⠀⢀⣀⣀⣀⣀⡀⠀⠠⠤⣤⠴⠃⠀⠀⠁⠠⡀⠀⠈⠂⠈⠈⠀⣀⠀⡅
⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠲⢭⣍⢀⣦⣰⣆⣀⣵⠞
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⠉⠀⠀⡇⠀⠀⠀⢸⢀⡔⢉⡴⠃⣠⡇
⠀⠀⣀⢀⠀⠠⠆⠤⠤⠤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⢸⠋⡠⠋⣠⠞⠁⡇⠀⠀⠀⠀⠀⠒⢐⠠⡒⢲
⠀⠀⡆⠈⠉⠉⠀⠀⢸⠀⡄⠀⠀⢀⠃⣀⠀⠀⣀⣠⠀⠘⠀⠀⠀⠀⠈⠛⠓⣻⣓⡒⠚⠁⠀⠀⠀⠀⢠⠀⠠⣑⡤⢎
⠀⠀⡇⡀⠀⠀⠀⠬⠥⡄⡇⠀⠀⢸⠀⠀⠀⠀⠉⠈⡅⢠⠀⠀⠀⠀⠀⠈⠁⠒⠂⠊⠀⠀⠀⠀⠀⠀⢸⡀⠐⠟⠂⡀
⠀⠀⠉⢁⡠⠤⠤⠤⡀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠴⠒⠒⠒⠒⠒⠒⠒⢤
⠀⠀⠀⢸⠀⠀⢀⠀⠸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣸⣁⠤⠴⠒⠒⠒⠒⠧⢤⣀⣇
⠀⠀⠀⡸⠤⠤⢌⡠⠤⠧⢔⡄⠀⠈⡄⠀⠀⠀⠀⠀⠀⡸⠀⠀⢰⠁⠈⠗⠒⠒⠒⠒⠒⠒⠒⠒⠾⠁⠹
⠀⠀⢸⠀⠀⠀⠀⢳⣀⠤⠔⠇⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠰⢀⣠⠥⡤⠤⣀⣀⣀⣀⣠⣤⣆⣀⡠
⠀⠀⠸⡀⠀⠀⠀⡸⠤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⢀⣀⣀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢻⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢣⡸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢀⡤⢄⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⡤⠤⠶⠮⠭⠵⠤⢄⠀⠀⠀⠀⡇⠀⡀⡇⢀⠀⢸⠀⠀⠀⠀⠀⡞⢠⠊⠁⢉⠆⠀⢀⡗⠖⠒⠒⠒⠒⢾⡇
⠀⠀⢸⡠⠊⢩⠋⢉⠟⢱⠚⡇⠀⠀⠀⡇⠀⠁⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠳⢴⠒⡧⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠃
⠀⠀⡶⡇⣰⠃⣠⠋⠀⣸⣙⠃⠀⠀⢸⡇⠀⠀⡇⠀⠀⢸⠀⠀⣠⠐⠈⠁⠒⣌⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⢻
⠀⠀⠑⠬⠭⠭⠭⠭⠭⠤⠞⠀⠀⠀⠘⠦⠀⣠⢧⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠙⢿⣿⣶
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣀⣀⣀⣀⣘⣛⣫⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠴⠂⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⢠⣤⢘⠿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠈⠉⠛⠁⠿⢰⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠈⠙⠻⢦⠀⠀⠀⠀⠀⢀⡀⣀⡀⢀⣾⣛⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠂⣀⣠⣤⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠸⡄⠐⠶⠶⢠⣤⣼⡄⠀⣠⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠛⣫⣽⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣀⠀⠀⠀⠀⠀⠙⢆⠀⢀⣾⣿⣿⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠠⣤⣤⣴⣿⡇⢀⣠⢈⣙⣓⣀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣤⣖⣒⣶⣶⣶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠈⠹⡿⠿⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣖⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣀⣤⣤⣤⣤⣤⡀⠀⠉⠙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠰⠁⢀⣼⣿⡄⠀⠀⠀⠀⢹⡄⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⣿⣿⠿⠿⢿⠀⠀⠀⠀⠘⢤⣾⣿⡿⠁⠀⠀⠀⠀⠈⢧⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢄⠀⠀⠀⠀⠀⠀⢀⠴⢤⣀⠀⠀⠠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠀⢀⠠⠋⠀⠀⠀⠠⣄⣀⣁⣀⡔
⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠁⠐⠀⠤⠠⠁⠄⡀⠁⠀⠀⢌⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠡⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠊⠠⠀⡀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⢀⡀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠐⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣧⣤⣤⣤⣬⣵⣌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢀⠂⠀⠀⠀⠘⢺⣖⣀⡐⠀⣒⣀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠗⠀⠀⠀⠀⠀⠀⠠⡍⠛⠛⠛⠛⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠁⠠⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠮⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⠿⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑
⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡑⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠄⠃⡀⢄
⠀⢀⠂⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣦⡃⢸⠀⠀⠀⠀⠀⡃⠀⠀⠇⠐⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠀⠀⠀⠠⠁⢀⢸⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⢤⠠⠀⡀⣰⠀⠁⠀⠀⠀⠀⠀⠼⡿⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⡉⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠓⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⡌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⢁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡠⢘⠀⡁
⠀⠀⢀⣤⠖⠂⠠⠀⡠⠑⠦⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠆⠀⠀⠘⢀⡑⠀⠠⣴⡆⠀⠀⠈⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠈⠀⠂
⠀⢀⠘⠷⡄⠀⠀⠈⠀⢰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢁⣁⡀⣝⠃⠀⠀⠀⠈⠐⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⣒⢐⣀⣀⡀⠤⠠⠤⢄⣤⣀⣢⣤⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠈⠉⠉⠁⠊⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⢠⣀⣀⠀⣀⡀⡀⠀⢀⣀⡀⢀⡀⢀⡄⠀⠀⡀⢀⡀
⠀⠀⠀⡀⠀⡄⡁⢀⡀⠀⣈⢀⠀⠀⡀⢀⠀⠀⢀⠀⢀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠁⠀⠀⠀⡀⢀⢀⠀⢀⠀⠈⡀⣀⣀⠀⠀⡀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⡇
⠀⠀⠀⢀⡀⠀⠀⡀⢀⡀⡀⡈⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠶⢶⣶⡄
⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡀⠀⠀⠈⢀⡈⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠤⠤⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢂⠜⠀⠀⠀⡰⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠷⠏⣡⡄⠀⠀⠶⢖⠶⠉⠐⠀⠀⠊⢠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡣⡷⠈⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡙⢻⢾⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⠟⠉⠈⠑⠀⠀⠀⠀⠀⠲⠀⠠⠞⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣷⣄⠀⠀⠀⠁⠀⠀⠀⢠⠀⢸⠀⢰⣤⣄⣂⡖⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⣀⣾⣿⣿⡡⠭⡴⢦⣀⣆⠀⠀⠀⠀⠮⠽⡄⡔⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣖⣀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣭⢂⠀⠀⡀⠀⠀⢀⣠⡤⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡑⠎⠀⠶⠚⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⠀⠀⠀⠀⠀⠀⢰⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡂⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠛⠛⠿⠛⠋⠁⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⠀⠀⡴⠃⠀⠑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠈⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡸⢁⡎⠀⡼⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠁⠈⡆⡇⢸⣰⠛⠫⢍⡉⠀⠉⠲⡖⢶⠃⡜⠀⡜⠀⢀⠔⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠸⣼⠀⢿⠀⠀⠀⠉⠋⠁⠀⡃⠎⠐⠉⠙⠄⡠⠁⠀⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢻⣆⣘⠀⠤⠤⢀⡇⠀⢠⡏⢠⠁⠀⢀⠺⢄⠀⠀⠘⢤⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⠁⠀⠈⠃⠀⠀⢀⠵⠒⠚⢄⣶⢎⣀⡨⠣⠀⡇⢀⣀⡀⠤⠷⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠛⠐⠒⠧⠤⠄⣀⣀⡀⠀⠎⠀⠀⠀⠀⢻⣀⡀⠥⠐⠓⠉⠁⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⠽⠏⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠠⣾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⢶⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⠀⠒⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠉⠒⠤⣄⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⣀⣠⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣠⣶⣶⡆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣦⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⠟⠻⠿⣿⣿⣿⣿⡿⠟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⠛⠛⠛⠻⠿⠿⠛⠛⢿⣿⣿⡃⠀⠈⣿⣿⡏⢀⣠⡄⠀⠀⠀⠀⢤⣄⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠕⠒⠀⠀⠀⠀⠐⠢⠄⢸⣿⣿⠏⠀⠀⢰⣿⠃⣤⡄⢄⠀⠀⠀⣠⠄⠠⠀⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⢟⣿⠃⠀⢀⣦⠀⠀⠀⠀⣰⣶⠈⡯⠇⠀⠀⢸⠈⠻⠀⢿⣿⠀⠀⠀⠀⢿⣷⠀⠀⠼⠋⠃
⠀⠀⠀⠀⠀⠀⠀⢆⣹⠀⠀⠛⠛⠀⠀⠀⠀⠛⠋⢸⠁⠆⠀⠀⠈⠈⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⢀⡀⠀⠀⣬⠀⠀⠀⠠⠀⠇⠀⠀⠀⠀⠘⠅⠀⠨⠁⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠉⠛⠋⠀⡀⢴⠉⠡⠀⢀⠁⠰⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢴⠂⠀⢲⠍⠀⢄⠰⠒⠲⡁⠠⠃⠀⠀⢀⡄⠤⠔⠇⣀⡠⠳⡄⢅⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠃⠀⠑⠒⠀⠀⢿⣧⠀⢀⢠⡜⠀⣀⠄⠂⠉⢀⠂⠀⠀⠐⠈⠀⠄⡀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠊⣼⢿⠀⠀⠀⠀⠀⠀⠈⢻⡇⠉⢄⠀⠀⢉⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⢀⠛⠢
⠀⠀⠀⠀⠀⠀⢀⠖⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⠀⠀⠀⢰⠉⠱⠌⠚⠛⠃⢀⠇
⠀⠀⠀⠀⠀⠀⠆⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢠⡙⠀⠀⠀⠀⠀⠀⠈⠰⠚⣛⡏⠉⠉
⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠈⠀⠑⠌⡃
⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠸⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⢀⣾⠦⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⢀⠀⠐⣀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠹⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠀⠀⠀⠀⢨⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢰⠁⠀⠀⠀⠀⠀⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⡋⠀⠀⠀⠀⠀⠀⡃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⢸⠀⠀⠀⠀⠀⠀⢠⣀⡁⠀⠀⠀⠀⠀⠀⠀⢠⢀⡃⠀⠀⠀⠀⠀⠀⣁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆⠀⠀⠀⠀⠀⡂⠀⠀⠄⠀⠀⠀⠀⠀⠐⠁⠀⢰⠀⠀⠀⠀⠀⢐⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢘⢀⡤⠞⠁⠀⠀⠀⠀⠀⠙⠦⣄⢘⠀⠀⠀⠀⢰⡁⣤⠴⠋⠀⠀⠀⠀⠀⠈⠳⢤⡔⣙

⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣟⢦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⠁⠀⢸⣻⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠈⠳⣄
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡜⠋⢉⡠⠍⣢⡀⠀⠀⠀⠀⠀⢠⠟⢓⠛⣆⠀⢸⢸⠀⠀⠀⠀⠀⢠⣿⣤⡀⠀⠀⠀⢠
⠀⠀⠀⣠⠾⠷⣄⠀⠀⠀⠀⠀⠀⠘⢕⡎⠱⠶⠰⢆⡹⠂⠀⠀⠀⠀⡟⠘⠆⠁⢸⠀⢸⢸⠀⠀⠀⠀⠀⠼⣿⣿⣿⣷⣿⣽⠿
⠀⠀⠶⣥⡀⣀⣈⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⠴⠚⠁⠀⠀⠀⠀⠀⠀⣧⣄⣫⣀⣼⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢤⣀⣠⠼⣿⣿⣿⣿
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡴⠋⡠⠄⣠⠉⠲⠤⠒⡆⠀⠀⠀⠀⠀⢀⣠⠔⢒⣓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⠻⡟⢿⡟⣻
⡟⠂⠀⠁⠀⠒⠃⠀⠀⡇⠀⠀⠀⢠⠖⠉⣴⣪⢞⠧⠃⣨⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠⠄⠠⠀⠤⢸
⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸⡑⠠⡐⢋⠡⠐⣨⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠁⠆⠀⠀⣼
⢣⡀⠀⠀⠀⣠⠶⠤⠚⠀⠀⠀⠀⠘⠽⣦⣸⣥⠖⠟⠁⠀⠀⠀⠀⠀⢠⡴⠊⠩⠻⠷⠀⢈⣿⠀⠀⠀⠀⠀⠸⡇⠀⠇⠀⢀⡇
⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣢⣖⡶⠖⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⢀
⢠⠾⣏⢻⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠙⠢⢤⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣺⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠛⢹⠆
⠀⢳⡙⠆⠁⠁⣻⣇⠀⠀⠀⠀⣠⠶⠊⠀⠀⠀⠀⠀⠀⣋⢳⠀⠀⠀⠀⣾⢣⣾⠽⠒⠉⠙⢢⡀⠀⠀⠀⠀⠀⣠⠜⠛⠻⢄
⠸⣍⠃⠀⠀⠀⠘⡟⠀⠀⠀⠀⣻⠁⠂⠄⡀⠀⡀⠤⠊⢀⣼⠀⠀⢀⡔⠻⣸⠀⠀⣀⣴⣾⣯⠗⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠳
⠀⠀⡏⠢⡀⠀⠀⠘⢆⠀⠀⠀⠻⣦⣄⡀⠀⠸⠀⣀⣺⠟⠁⠀⠀⣸⣱⣷⣤⡴⣟⣫⠜⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⢸⣇⣀⢡⣀⣤⠶⠋⠀⠀⠀⠀⠀⠙⠺⢶⣶⡬⠚⠁⠀⠀⠀⠀⠈⠉⠳⠿⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⡀⠀⠀⣀⣀
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁
⠀⠀⠀⣀⢠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⢣⣀⣠⢾⠁⠀⠀⠀⠀⡖⠒⣆⣀⡀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⣠⠴⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⢘⡟⢻⣵⣟⣲⡄
⠀⠀⠀⢸⠟⢻⠀⠁⠀⠀⠀⠀⠹⣄⡟⠀⠉⠉⠉⠉⠉⣧⢰⡇⠀⠀⠘⣿⠒⠶⠶⠶⠶⣺⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠉⢳
⠀⠀⣴⣁⡀⠈⢢⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢹⠦⢄⣀⡤⠖⡿⠀⠀⠀⠀⠀⠀⡧⠉⠉⠉⠉⠉⢹
⠀⢀⣿⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⠷⣤⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⡗⠤⠤⠄⠀⠤⠌

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢻⢯⣿⡟⠛⢻⣯⣯⣏⣭⠭⠭⠝⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⠭⠟⠏⠉⠉⠉⠩⠭⠯⠽⠝⠛⢙⣋⠉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠶⠿⠇⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣆⠈⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⡟⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⢿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡅⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢻⣿⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣤⣾⣦⣠⣦⣠⣶⣤⣶⣿⣷⣦⣼⣿⣤⣤⣾⣮⣶⣴⣤⣦⣠⣄⣀⣤⣤⣤⣦⣤⣠⣼⣆⣷⣧⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢠⡄⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⢄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄⠀⢀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⣾⡀⢸⣆⡀⠀⠀⠀⡀⠀⡤
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠠⠤⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⡙⣦⣤⣤⢞
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠉⠁
⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠁⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠒⠀⠛⠒⠛⠃⠛⠛⠓⠚⠓⠁⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠠⠀⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠔⠁⠠⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠤⠀⠀⠀⠀⢄⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠒⠒⠂
⠠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠧⠀⠀⠀⠀⠀⢀⠰⠄⠀⠀⠂⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⡆⠀⡌⠀⢠⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⣀⣠⠃⢠⠏⢀⠎⢀⣀⡀⣠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠆⠀⠉⠀⠏⢀⡞⢀⡎⠀⢹⠃⢀⣤⣀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡠⢂⡁⠀⢀⡒⡄⢀⠈⠳⠴⠏⢰⡟⠤⣼⠀⣰⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⣁⡨⢂⡒⠬⢣⢃⢔⡆⣀⡀⢈⠓⠒⠀⣰⠃⠀⢀⡄⠀⠀⠀⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠀⠀⢤⣸⢈⣀⠀⠈⠘⠐⠡⢇⢾⠂⠀⠀⠀⠀⠀⢠⣿⠴⠀⠀⡞⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⣏⠢⠇⠀⠀⠀⣀⣤⡈⠀⠐⠞⠛⠛⣦⠀⠸⡇⠀⠀⢿⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⣦⠀⠀⠈⣁⠀⢰⣶⠞⠻⣾⠋⠉⢿⡆⠀⣴⠛⠛⢻⡄⠀⢿⣄⡄⠈⠑⠒⠂
⠀⠀⢀⠀⠤⠀⠀⠀⣀⣠⡀⠰⢿⡟⠃⠀⢿⡄⠀⣿⡀⠀⢹⡇⠀⠘⣷⠀⠻⣦⡤⠞⠓⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⡀⠀⠈⣷⠀⠀⠘⣧⠀⠸⣧⢀⠈⠿⠀⠀⠉⠀⢀⠀⠀⠠⠴⠒⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣷⠀⠹⣦⠆⠀⠛⠀⠀⠁⠠⡂⡀⠀⠀⢀⠰⢅⢑⠄⠀⢀⣀⠴⠒⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⠚⠁⠀⢲⠂⠤⡄⠀⠀⠀⠠⢀⡌⠀⠀⠠⣄⠑⠄⠑⠀⠀⠀⢀⠔⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⢠⠀⠉⠂⠀⠀⣎⠕⡀⠉⠀⠀⠙⠉⢡⠘⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠈⠆⠀⠀⠀⠀⠀⠀⠌⠠⢠⠉⠀⠀⠀⠠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⢠⣾⠀⠀⢀⠀⡀⠀⠀⠀⢐⣅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⢠⣴⠄⢀⣤⠀⠀⠀⠀⠀⠀⠉⠭⠁
⠀⡃⠉⠄⠢⠈⠢⠐⠀⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢀⣹⡀⠀⠀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣟
⠀⠷⡄⠈⢃⠀⡀⠀⠈⡄⠀⡀⢘⠀⠀⠀⠀⠀⠰⣳⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠐⠋⠙⠁
⠀⠂⠀⠀⠀⠃⠈⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠀⠙
⠠⣄⣤⡀⠀⠀⠹⣿⣆⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⢀⣶⡄
⠀⠛⠀⠈⠋⠀⠀⠈⠛⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢠⠀⢠⠁⠢⡀
⠀⠀⠈⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⡤⠞⢱⠀⠐⠘⠀⢘⠀⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠐⠀⠲⣾⣄⠈⠀⠀⠸⠀⠰⢸⡇⠀⠀⠠
⠀⠀⠀⡆⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⣶⣿⣷⠀⡆⠈⡂⢀⡾⠁
⠀⠀⠀⠕⢂⠀⠐⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⡤⠤⠀⠀⠀⠙⢄⠀⣶⣾⣿⣿⠟⠀⢉⣢⡷⠋
⠀⠀⠀⠀⠁⠀⠠⠂⢹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠩⠭⠤⠒⠒⠉
⠀⠀⠀⠄⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⢟⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡀⠂⠀⠀⠀⠠⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⢹⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⢈⣱⠄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣀⠴⠔⠒⠋⠉⠀⠀⠀⠀⠀⠓⠠⠀⠀⠀⠀⢁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣸⣶⣶⣶⣶⣶⣶⡆⠀⢸⡇⠀⡆⠠⣶⠻⣿⣶⡤⠀⢀⠄⠀⣾⣆⠀⠘⠃⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠟⠛⠛⠛⠛⠛⠛⠂⢀⣤⠀⠀⢠
⣞⣿⣿⣿⣿⣿⣿⡇⠀⢸⠇⠀⡇⠀⠈⢱⠆⠁⠀⠀⣾⠀⠀⣿⣿⠀⠀⠀⠀⠁⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢈
⣿⡟⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⣿⣿⠀⠀⠃⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢷⣾⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⠇⠀⢸
⢿⡀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠇⠀⠀⠘⠀⠀⠀⠀⡟⠀⠀⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠠⠄⠶⠆⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠙⢦⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠄⠀⢸
⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣤⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠠⠀⠀⢠⡇⠀⠀⠀⠀⢻⡗⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⢸⠀⡀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠠⠆⠀⠀⠀⢻⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⠈⢇⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈
⠀⢀⡤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣻⣏⣶⣤⡄
⠀⢸⣷⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠒⠶⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⡇⢐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢸⣿⡟⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣷⣾⣿⣷⠞⠀⣠⣤⡶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⢀⣿⣼⣿⣯⠙⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠃⢸⣿⡥⢟⣫⣿⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠋⠁⠀⠈⠛⠛⠛⠋
⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⣠⣤⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⣠⣾⡯⠁⠀⠫⣿⣿⣆⡀⠀⠀⠀⠄⠠⠠⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣼⣿⡇⠀⠀⠀⣠⣿⣿⠟⢿⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡁⠀⠠⣶⣿⣿⡷⢀⣿⣿⣆⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣈⠛⣿⠉⠉⢩⡌⢻⣿⡇⢸⣿⣿⣏⣠⠄⢠⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠩⠁⠠⡀⠀⠀⡀⢂⡟⠰⣎⠙⠛⢩⣽⣆⠀⢀⡄
⠀⠀⠀⠖⠀⠉⡙⢺⡑⠶⠶⠟⢋⣻⡁⠀⠀⢻⣍⢌⠙⡟⢳⡟⣲⡿⠋⠙⠀⠀⣿⣦⡀⠀⣿⣿⣾⣿⣧⡤⠤⢤⡤⠤⢤⡄
⠀⠀⠀⣶⠠⢠⠀⠈⠧⠀⠀⣲⣜⠉⠀⠀⢾⣿⣏⣨⣚⣿⢿⣿⡹⠆⠀⠀⠀⣀⠇⠈⡧⠀⠘⡃⣿⣿⣿⡡⢂⡄⠀⠈⠁⡀
⠀⠀⢀⣇⣀⣠⣄⣀⣀⣠⠞⠁⠀⠀⠀⢀⡿⣴⣿⣭⣿⣿⠟⠉⠑⠀⠀⣠⡀⠀⠀⠀⣶⣆⠀⠰⣯⣿⣿⣉⡀
⠀⠀⠀⠉⡉⠁⠀⠈⠩⠍⠀⠀⠀⠀⡀⢼⠉⠛⠻⣙⠟⠋⠀⠀⠀⠀⠀⣘⣿⣀⡀⠀⠈⠁⠀⠀⣸⣯⣿⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠥⢸⡀⠂⢸⡄⠀⠀⠀⠀⣠⣴⣾⣿⡟⠿⢀⠀⠀⠀⠀⠀⠉⣷⣿⣬⣡⣀⡀
⠀⠀⠀⡤⣀⣀⣠⣄⣀⣄⣀⣀⣄⣸⣟⣷⣽⣿⣼⣿⣶⣔⣶⣾⣿⣿⣿⣿⣟⣳⣄⡀⠀⢄⣀⣀⣰⣿⣿⡿⢷⣄⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣾⣤⣄⡘⠙⢦⡆
⠀⠀⠀⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⢙⡏⠋⠉⢻⠁⠻⠿⣿⣿⣿⣹⣿⡶⠄⡃
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣹⣿⠟⢁⠟⠁⠈⠘⠉⠀⠀⠀⠀⠀⢸⠠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⠀⠠⣴⠞⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠀⣿⡜⢿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣷⠖⠛⣿⣿⣿⣿⡿⡿⣭⠿⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⠇⣼⣿⣿⣿⣿⡇
⠀⠀⠘⣿⣿⣧⣶⣾⣿⣿⡿⠋⠀⠈⠁⠀⢀⣼⡟⠀⠒⠀⢀⠀⠀⠢⠠⠄⣀⠀⢀⡀⠀⡄⠀⠀⠀⣀⡼⢙⣿⢻⣿⣿⣿⡇
⠀⠀⢀⣭⣽⣿⣿⣿⣿⣾⠃⣴⠒⠉⠀⠀⢰⣏⠇⠀⠀⠀⠉⠀⠀⠀⠀⠸⠉⣶⠾⠛⢂⠐⠂⢀⣾⣿⡇⣠⣯⣼⣿⣿⣿⡇
⠀⠀⢸⣿⣿⡾⣦⣬⠟⠿⣷⡙⠲⣤⣴⣦⣹⣿⠆⣀⠀⠀⡀⠀⠀⠀⠀⢠⡴⢿⢓⡂⠠⢤⣾⣿⠷⣿⣿⣿⠏⠻⣿⡏⠍⡁
⠀⠀⢸⣿⣿⡏⠀⠹⢦⡀⠈⢿⣿⣿⣿⣦⣿⣯⣿⣗⢲⡦⢿⣛⣋⣉⣐⣹⣤⣤⣶⣅⣰⣿⣿⡿⢿⣿⣷⣿⣿⣶⣿⡗⠀⠇
⠀⠀⢸⣧⣼⠃⠀⠀⣠⠄⠀⢈⢻⣏⣩⣟⠭⣿⠿⠿⠧⠼⠿⠿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⢸⣷⣀⡄
⠀⠀⢸⡟⠀⠠⢄⣴⣿⡷⠛⠉⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣯⣼⣿⣿⡇
⠀⠀⠀⣡⣶⣶⣿⣿⠿⠶⠶⠴⠦⠿⠇⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣠⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠦⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠾⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡀⢀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⢤⠴⠆⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠃⠈⠂⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢀⠁⠄⠀⠀⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⢀⠀⢀⣀⡠⠀⠀⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠐⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢩⠀⢀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢘⠀⠀⢨⠁⠀⢀⠀⣀⡠⠄⡄⠤⠈⠡
⠀⠀⠃⣀⡁⠀⠂⠈⠅⠀⠀⡰⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢂⠘⠈⠀⠐⢈⠀⠀⠸⠀⠀⠈⣉⠀⠈⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠈⠁⠀⢠⠘⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⢀⠀⠀⠀⠀⡄⢀⣡⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡍⠅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠊⠀⠁⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠇⠢⠠⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣄⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢰⡄⠀⡴⠂⠀⡄⡄⠀⢰⠀⠀⠀⠀⠀⠀⠾⠁⢈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠠⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⡄⠉⡁⠘⠒⢒⡓⢊⠉⠙⡆⠀⠀⠀⠀⠀⡀⢀⠀⠤⣁⡀⠀⠀⠂⠀⠀⠀⠀⠠⠒⠉⠀⠄⠠⠈⠉⠒⢄
⠀⠀⠀⠀⢀⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⠌⠥⠢⠳⠈⠁⠭⠄⢤⠄⠀⠀⠀⠀⠀⠁⠃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠤⠤⠀⠤⠠⠔⠆⢸
⠀⢠⠀⠀⢈⠑⠀⠀⠀⠄⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠈⣀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁

⠤⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⡀⠌⠁⠀⠀⠁⠈⠀⠀⠀⠀⢠⠂⠀⢀⠰⢤⠂⢤⡀⡀⠠⠌⠒⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠁⠐⠂⡠⠀⠀⠈⠁⢸⣁⡤⢈⡁⠀⠀⠀⠀⠀⠉
⠂⠀⠀⠶⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠍⠈
⠀⠀⠐⢿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⠀⠀⠀⠄⢀⠄⠐⠀⠀⠀⡀
⠀⠀⠄⢸⡇⠈⠄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠂⠠⠤⠠⠂⠈⠃⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠃⠀⠀⠀⠁⠂⠂⠀⠁⠀⠡⠠⠄
⠀⠀⠠⠀⣷⠀⡇⠀⠀⡀⢀⠛⠂⢤⡀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⣀⠀⠀⠀⢀⠐⢃⠚⠡⠁⠀⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠁⠘⠀⠂⠀⠈⠀⠆⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡠⠄⠀⠀⠉⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄
⠔⠶⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⣓⠀⠀⠄⡀⠀⠄⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠦
⠚⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠁⠀⠄⠀⠐⠀⠀⡐⠀⠀⠐
⠀⠀⠀⠀⠀⠩⠄⠐⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠤⠂⠒⠀⠰⠀⡀⠀⠀⠁⠀⠐⠈⠀⠈⠀⠀⡀⠀⠄⠀⢠
⠀⠠⠁⠀⠀⠀⡠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⢀⠐⠀⠄⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡀⠛⠀⠀⠀⢀⡉⠤⠈⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠅⠀⢀⣀⠀⠄⠀⠀⠀⠀⢐
⠔⠂⠀⠀⠀⠀⠄⠀⠀⠀⢂⡰⠦⠦⡀⢠⣈⠀⠀⠀⠀⠸⠉⠀⠀⠀⡀⠀⠁⠀⠠⠴⠀⠀⢰⠷⠡⣄⣰⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡
⠆⠒⠂⠰⠄⠀⠠⠀⠀⠀⢈⠁⠰⠀⠈⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠎⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡄⢀⣠⡰⠈⠀⠀⠀⠀⠀⠈⠁⠀⠰⠃⠖⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠈⠰⠄⣃⠒⠀⠀⠀⣐⢌⡁⢠⢰⡁⠀⠀⠀⠂⠀⠀⠀⠘⠥⠔⠁⠀⠀⢤⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠁⠀⠂⠀⠄⠀⠀⠀⠀⠀⠁
⠁⠉⠀⠀⣆⠀⠀⠐⠀⠀⠀⠤⠀⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠤⠤⠄⠀⢀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠠⠀⠢⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠀⠈⠈⠀⠘⠀⠐⠀⠄
⠀⠂⠀⠀⠀⠐⠶⠀⠀⠐⠆⠒⠋⠩⠀⠀⠀⠀⠀⠈⠀⠒⠘⠀⠀⠀⠀⠐⠂⠐⠒⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠔⠀⠀⢠⠚⢁⡠
⠀⠀⠀⠀⠀⠀⣀⠐⠄⠀⠀⠰⠀⠀⠂⠀⠀⠀⠐⠈⠀⠄⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠨⠁⢸⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠒⠂⠈
⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠄⠤⠀⠀⠀⢀⡀⠀⠀⠀⠄⢒⠁⠀⠀⠘⠂⢾⠀⠀⠀⠀⠠⡂⡙⠀⠀⠀⠀⠀⠡⠀⠄⠡
⠀⠁⠄⠀⠀⠃⠀⠀⠀⠀⠂⢀⠀⠐⠠⠀⠀⢀⣀⣄⡐⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢰⠈⠁⠇⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠒⠋⠀⠀⣀⡐⠀⠀⠀⠠
⠐⠀⠀⠀⣴⡀⡀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢀⢀⠠⠤⢔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⠀⠀⠀⠀⠰
⠀⠀⠀⡂⠈⠁⢠⠀⠀⠀⠉⢠⠀⠠⠢⠀⠐⠀⠀⠀⠀⡀⢂⢤⠤⠀⠀⠀⠀⠀⣠⠀⠀⠶⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⡄⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠅⢿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠊
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢆
⠀⠀⢀⣀⠀⢂⣤⡠⡄⠀⠀⠀⢀⣠⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤
⠀⠐⠻⠻⠖⢲⠎⡓⢻⣒⢶⠞⠷⠙⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠉⠉
⠁⠀⢀⡀⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠐⠂⠂⠄⠀⠐⠒⠂⠒⠀⠂⠠⣖⣴⡖⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠐⡂⠀⠠⡀⠀⡤⡀⠀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣤⣀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⢸⢳⡎⡁⢀⠁⠀⠈⠁⠀⠀⠀⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠘⡄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠸⠓⢽⣁⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⠀⠀⡆
⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠤⡄⠠⠀⠐⠈⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠯⠎⠀⠀⠀⠀⠈⠀⡀⠀⠙⠃⠀⠀⡄
⠀⠈⠀⠀⠈⠀⠈⡂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡂⠐⠋⠁⠉⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠂⠐⠀⠠⠅⠄⠀⠀⣠⠤⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠜⠂⠀⠀⠀⠀⠀⠀⣀⠂⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠋⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⣤⣤⣾⣶⠀⠀⠀⣖⠐⠲⠶⠦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠂⠂⠚⠒⠚⠉⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠳⠤⠤⣄⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠈
⠀⠀⠀⢀⠠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠐⠀⠒⠢⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠑⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠠⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⠿⠿⠿⢷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣟⡯⠽⠒⠚⢉⣉⡉⠉⣉⠉⠓⠺⠭⣟⡿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⠕⠋⠁⠀⠰⣟⠂⠈⣿⠀⣸⢹⡇⣰⢳⡆⢀⠉⠓⢭⡻⣷⣄⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡫⠚⢁⠐⣏⣀⠀⠀⢨⣱⠀⠹⠀⠻⠤⢠⡏⡿⠀⣾⠴⠃⠀⢉⣪⣿⣷⣶⣶⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⠞⠁⠐⢧⡤⠈⢧⠴⠀⣀⡤⠴⠒⠒⠒⠲⢤⣄⣁⣴⣷⣶⣾⣿⡿⠿⠟⠛⠉⢉⣀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⠏⠀⠈⠳⢤⡙⠆⢀⠔⠋⢀⣀⣤⣤⣶⣶⣿⣿⠿⠿⠛⠋⣉⣁⠀⠠⣶⣶⢿⣶⡈⢻⣧⡀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠏⠀⠛⢦⣄⣴⣥⣴⣷⣾⣿⡿⠿⠟⠛⠋⢉⣀⣤⣴⣦⠀⣾⡟⢻⣷⡀⢿⣧⠀⢿⡇⠀⠻⣷⣿
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣼⣶⣶⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⣴⣾⢿⣦⡘⠋⢿⣯⠀⠀⣿⣇⠀⣿⣇⠸⣿⣶⣿⣧⡀⠀⠹⣿⡀
⠀⠀⢀⣶⣾⣿⡿⠿⠟⠛⠋⣉⣀⣤⠀⣶⣾⠿⠗⠀⠀⠀⢿⣧⡀⠉⠁⠀⠘⣿⡄⠀⢸⣿⡀⠸⣿⡀⢻⣷⠀⢻⣷⠀⠀⢿⣧
⠀⠀⠈⢉⡁⠀⠀⠠⣶⡄⢹⣿⠛⠉⠀⢻⣷⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⢻⣷⠀⠀⢿⣇⣀⣿⡇⠘⣿⠆⠘⠛⠂⠀⠀⣀⣀⣤
⠀⠀⠀⢹⣷⠀⠀⠀⢿⣧⠈⣿⣇⣀⡄⠈⣿⡿⠿⠃⠀⠀⠀⢠⣄⠈⣿⣇⠀⠘⣿⡆⠀⠈⠛⠛⠋⠀⣀⣀⣤⣤⣶⣶⣿⣿⠿⠿⠛⠃
⠀⠀⠀⠈⣿⡆⠀⠀⠸⣿⡄⢸⣿⡛⠉⠀⢹⣿⠀⠀⡀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠉⣀⣠⣤⣴⣶⣾⣿⠿⠿⠟⢻⢻⣿⠁
⠀⠀⠀⠀⢹⣿⠀⠀⠀⢻⣧⠀⣿⣇⠀⠀⠈⣿⠿⠟⠛⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⠿⢟⡿⠋⣙⠉⠙⠲⠄⢀⣏⣿⠇
⠀⠀⠀⠀⠀⣿⣧⣤⣤⠘⡿⠆⠘⠛⠀⠀⣀⣀⣤⣴⣶⣾⣿⡿⠿⠟⠛⠉⠉⠀⣠⠴⠋⠀⠲⣌⠳⢦⠀⢀⢞⣾⡟
⠀⠀⠀⠀⠀⠘⠛⠉⢁⣀⣠⣤⣶⣶⣿⣿⠿⠿⢛⡿⠉⡉⠙⠒⠒⠒⠒⠒⠚⣉⠀⠐⠛⣦⠘⢉⡷⠀⣠⣫⣾⠏
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠟⠻⣿⣟⡧⡀⠀⠴⣻⠃⣸⢧⡏⣸⢻⡆⢸⡆⠸⣍⡁⠀⠈⢩⠗⠀⣠⢞⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⢿⣮⣓⢤⣈⠀⠻⠾⠀⢿⣼⠁⣸⣇⠀⠦⠟⠀⢀⣠⢔⣪⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣾⣭⣗⣲⠤⠤⠤⣤⡤⠤⠤⢴⣒⣪⣽⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⡀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠎⠉⠀⠂⠒
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⡟⠢⡀⢀⠀⣀⡀⠀⠀⠘⠂⠀⠀⠀⠀⡀⠀⠤⢠⠋⠀⢀⡄⠠⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠉⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠓⠂⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠠⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠰⠄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠐⠄
⠀⠀⠀⠀⢀⢠⢴⡀⠀⠠⠁⠈⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⠈⠉⠀⢀⠀⣠⠴⠆
⠀⡠⠤⠚⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠⠴⠖⠒⠒⠒⠶⢦⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠁⠀⢀⠤⢤⠀⠀⠀⠙⠦⠀⠁⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠁⠚⠛⠏⠉⠉⠉⠐⠂⢄⠀⠀⢠⣀⠀⠀⠱⡀⠀⠀⠒⠚⠀⠀⢠⠀⠀⢀⠄⠀⠀⠀⠁
⠀⢀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢪⡆⡴⡖⢣⡀⠀⠀⠀⠀⢠⠃⠀⢰⡟⠀⠀⠀⡒⠀⠀⢀
⠀⢀⣤⣀⡠⣒⡩⠍⡒⠀⠀⢀⣠⠔⠒⣂⢄⢴⡮⠊⠀⠀⠀⣸⠇⠐⡾⣤⢇⣀⡄⢠⠐⠃⡄⡐⠀⠻⡄⠀⢀⠀⠀⢠⠟⠓
⠀⠀⠉⢸⡀⠀⠀⢠⣼⠖⠉⠙⣄⡤⠀⣠⡿⠊⠀⠀⠀⠀⠀⠃⠀⠀⢏⢯⢽⣬⢵⠀⡯⠄⠤⠁⠀⠀⢡⠀⠀⠀⢈⠅
⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣈⣀⡉⢶⡆⢡⠤⢼⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢒⠒⠒⠒⡒⠀⠀⠀⠀⠒⠒⠊⢉⡂⠀⠀⠀⠀⠇⠀⠀⠀⡇⠼⠾⡀⢸⠁⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠅⡛⢷⡇⢸⠀⠀⠘⠀⠀⠀⡾
⠀⠀⠀⠀⢠⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⢸⡍⠘⡧⠼⡀⠀⠀⡄⣀⠜⠁
⠀⠀⠀⠀⡌⢀⠄⠀⡄⠀⡇⠀⠀⠀⢰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠛⠀⠁⠀⠓⠤⠾⠊⠁
⠀⠀⠀⢰⠁⡜⠀⠀⡇⠀⢁⠀⢀⠁⡞⠀⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⣦
⠀⠀⢀⡇⠐⠀⠀⠀⠁⠀⠸⠀⠘⠀⠉⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡀⠀⠀⢀⢖⠶⠶⣲⡀⠀⠀⢀⣿⣸
⠀⠀⠘⠒⠒⠦⣄⡤⠶⠲⢦⡇⠖⠉⠙⠶⣤⠴⠛⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⢇⣀⣀⡈⠎⠀⠀⠸⣧⠀⣀⣠⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⠀⠙⠛⠓⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠲⢤⣀⡴⠋⠉⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠉⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡤⣤⢹⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⡦⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢠⠀⢄⡶⠃⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡔⣠⢤⠶⠖⠈⠀⠦⠀⠀⠀⠠⠄⠀⠀⠀⠀⣤⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⣀⡴⠀⠃⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⡄⠀⠀⠀⠐⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡞⠢⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⣠⣶⠻⣙⠿⠿⣾⣭⣿⠿⡛⣷⠀⠀⠀⠀⠐⡄⠙⠒⠉⠀⠱⣄⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡴⣺⡭⣶⠾⣿⣿⠛⢻⡏⡀⣤⣼⣦⠞⣶⣷⠏⢀⢤⠀⠣⠴⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡀⢻⢿⢥⡄⠁⠙⠀⣾⣠⡿⠶⣼⣝⣿⣿⣷⡶⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠠⡀
⠀⠀⠀⠀⠀⢀⣤⣽⣞⣾⠟⡱⠀⠀⠀⠈⠁⠀⠀⢨⣿⣭⢿⡶⣻⣿⡟⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⢱⠠
⠀⠀⠀⠀⠰⡫⢁⢿⣏⣡⡞⠳⢶⣄⢤⡀⠀⠀⣠⡾⣧⡶⢾⣿⣿⣽⣧⢤⡀⠀⠀⠀⠀⠀⢀⠔⢁⠠⠂⠀⢃⠰
⠀⠀⠀⢀⡠⣼⣷⠷⠛⣿⡇⢀⡀⠈⠀⣤⠄⠀⠁⣀⣀⣀⣸⠿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠘⡀⡃⠀⠀⠀⠈⢁
⠀⠀⠀⡏⠸⣉⣷⣾⡿⠛⠟⠛⠋⠂⢀⠃⠀⢄⠘⠙⠉⠙⣧⣄⣉⢩⣿⣣⡿⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠈⣹⣿⣽⡏⠱⣄⣀⣀⡀⠔⡁⠀⠀⠈⣷⠤⠤⠞⠁⡰⢿⢷⣟⡻⣷⣄⠀⠀⠀⠀⠀⠀⠍⠄
⠀⠀⠀⡜⣰⣿⠋⡷⢡⠆⠀⠀⠀⠀⠉⠛⠚⠉⠁⠀⠀⠀⠀⣨⣻⣿⣯⣾⠃⢸⡇
⠀⠀⠀⠈⠉⣻⣿⣧⡿⣌⣆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠰⢧⣏⠈⡩⢋⣹⣿⠁
⠀⠀⠀⠀⡞⠀⣸⣿⠙⢺⡏⢦⡀⠀⠀⠢⡀⠈⠃⠀⠀⠠⠁⣼⠟⢻⣛⣫⡽⠋
⠀⠀⠀⠀⠙⣾⡉⣹⢇⣾⡁⠈⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣿⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠘⠯⡉⠀⠉⡟⠀⠀⠀⠀⠂⠈⠁⠀⠐

⡄⠀⠠⡶⠀⠀⢀⠀⠀⠀⠀⣴⠀⠂⠀⠠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⣠
⣍⠀⠀⠀⡀⠀⠉⠀⠀⡀⠀⠁⢦⡀⣀⠀⠆⠁⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⣴⣄⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⢈⢽⣿
⢧⠀⠀⠀⠙⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⡽
⠀⢣⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠄
⠀⠈⣆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠛⠋⠀⠀⠀⠒⠠
⢡⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁
⠂⢀⠀⠀⠂⠀⠀⠠⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠂⠀⠈⠠⣺⣉⠃
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢸⣿⣿⠂⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣀⡬⠄⠀⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸⡿⠇⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠠⡀
⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠸⣿⣿⡷⠀⣤⣦⣄⠀⠀⠀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⠤⠰⠛⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠑⠿⠋⠀⠀⠀⠀⠀⠀⠠⠀⡄⢀⡀
⠀⠀⠀⠀⠰⠄⠶⠟⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⡂⡠⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠛⠀⠀⠀⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢘⡋⠈⠤⢀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠛⠻⠿⠻⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⠛⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠀⠀⠀⢠⣿⣿⡿⢛⡀⠀⠀⣀⣤⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⣮⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢛⣿⣿⡿⠿⠿⠛
⣇⢀⡀⢀⠀⠀⠀⠀⡟⠁⢈⣷⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠛⠋
⡟⠛⢿⣿⣿⠀⠀⠛⣟⣠⣽⣿⣿⣿⣿⣿⣿⠻⠟⠛⠉⠁⣤⣾⣿⣿⣭⣿⣷⣾⣿⣿⣿⣽⣿⣿⣿⣿⢿⠟⢫⣽⣾⣿⣿⣿⣿⣿⣷⣆⢀⣤⡀⠀⠀⢀⡀
⣷⠴⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⠟⠉⠉⠈⠀⠀⢀⣀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠟⣿⣿⣿⣻⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⠏⠙⣿⠟⠋⣿⡿⠀⠘⢣⣾⣷
⡏⠀⠀⠀⠉⠙⠛⠋⠉⠉⢀⣀⣤⣤⠖⣠⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣹⣿⠃⠞⠀⡎⢿⡿⠧⠀⠀⠀⠠⣿⣿⡶⠿⠿⣿⣿
⣧⡀⠀⢰⣶⣦⣴⣶⣶⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⣀⣿⣃⣤⣤⣤⣀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢲⠖⣋⠁
⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⣮⣝⣿⣾⣿⡷⠀⠀⢀⡀⠀⡀⠀⠂⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⣉⣿⡇⠈⠉⣿⣷⣬⠛⠿⠛⣋⣹⣿⣿⠀⣰⣿⣿⣦⡠⣿⣦⣆⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣷⣶⣾⠿⠿⠿⣉⠁⠀⠀⠰⣏⢻⣿⡶⠛⠟⠋⠉⡈⠰⢯⣿⣤⣴⣷⣶⣼⡷⠛⠃
⣿⠛⠿⡿⣿⣿⣿⠻⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣉⣁⠉⠀⠀⠐⠂⠀⠢⠂⠀⠀⠘⠫⠁⠀⠀⠒⠋⠁⠤⠒⡀⠉⠉⠉⠄⠤⣍⠀⣀
⣿⣶⣦⣤⡈⠛⠃⣀⣾⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠠⠃⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣷⣄⠈⢻⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠒⠀⠶⢶⡎
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢋⣾⣿⣿⣿⡿⠿⠛⣛⠃⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣴⣾⣿⣿⣿⠃⠀⡿⠀⣀⠀⠀⠀⠀⠈⠉⠁⠄⢀⠀⠀⠀⠀⡴⠂⠀⠘⠲⠶⠶⣦⣄⠀⠀⠀⠀⠀⠠⡾⠧
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⣤⣤⣶⡄
⣿⣿⣿⣿⣿⣿⣇⠸⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⡆⠀⠘⠟⠛⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⡀⣶⢠⣤⠀⠀⠀⠀⠀⠀⠻⠛⠛⠉⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠁⡼⢻⡀⠀⠀⠀⠀⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⣿⣿⣧⣠⣤
⣿⠿⠻⢿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⣰⡄
⣿⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢛⣩⣽⣿⣿⣿⠿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⠿⠉⠈⠀⣀⠀⠈⠉⠩⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠷⠀⠂⠀⠀⠀⠀⢤⣤⣤⣤
⣿⣿⣿⣿⢟⣷⣾⣿⣆⣴⡿⠟⠉⣁⣤⣤⣶⣶⣾⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠉⠉⢿⡀
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⡀⠹⣆⠀⠀⠘⠁
⣿⢿⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡏⣄⣀⢻⡶⣿⡄
⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣿⣿⣿⣿⣿⣷⡉⣿⡿⢲⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣽⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣫⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣯⠙⠋⠉⢻⣿⡇
⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣶⣾⣿⣿⣿⣿⣿⣴⣶⣄⣀⣀⡄⠀⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠤⠀⠠
⣿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠛⠉⠙⠛⠻⢿⣿⡿⠿⠛⠻⠿⠿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⣿⠀⢸⣿⣿⣿⠿⠿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠈⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠓⠋⠁⠙⡋⡉⠀⠉⠛⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠚⠀⠃⠃⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣦⠤⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣮⢷⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠙⠀⠉⠛⠃⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⣶⣿⣿⣿⣿⣿⣿⣶⣶⠦⠤⠤⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⢤⣤⣤⡄⠀⠀⠠⣤⣤⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⢀⡀⠈⠻⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⡀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠐⢿⡧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠲⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠂⠀⠰⠿⠿⠇⠀⠀⠀⠀⠾⠿⠻⠿⠄⠀⠀⠀⠀⠀⠺⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠃⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣱⠟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠀⢿⡇⢸⣇⢸⣿⢈⣿⠀⠀⠀⢿⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⡃⢠⡶⣶⡀⢀⣶⢶⡄⢸⡇⢰⡆⠀⠀⠀⠸⣧⣸⡇⠀⠀⠀⢸⡇⣼⣿⢸⡟⠈⣿⢶⣆⠀⣶⠀⢺⡿⠀⣴⠾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣴⡟⠀⣿⡇⠘⠃⣿⡇⢸⡇⢸⠇⢸⣇⣿⠀⠀⠀⠀⢀⣿⡏⣀⠀⠀⠀⢸⡇⡿⣿⣸⡇⠀⣿⢸⣿⠀⣿⠀⢸⡇⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⠀⣿⡇⢰⡟⣿⡇⢸⡏⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⢹⣿⡿⠀⠀⠀⢸⣿⡇⢻⣿⠀⠀⣿⢸⡏⠀⣿⠀⢸⡇⠀⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⡇⢸⡇⣿⡇⢸⡇⢰⡄⢸⡏⢿⡆⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠸⣿⡇⢸⣿⠀⠀⣿⢸⡇⠀⣿⠆⢸⡇⠀⣿⠲⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠀⢿⡇⢸⣷⣿⡇⠘⢧⣼⠃⠸⡗⠸⡧⠀⠀⠀⠹⣷⢿⡇⠀⠀⠀⠀⣿⠃⠸⡿⠀⠀⡿⢸⣷⠀⣿⠆⠹⣷⠄⠻⣤⡿

⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀⠠⡄⠀⠀⢀⠀⡀⣄⠀⠀⣄⡀⣀⡀⣀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⣴⣄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠇⢴⣼⣷⢰⣿⡇⠀⣸⣿⣿⣿⠀⢀⣀⡿⣼⡇⣿⣯⣟⣿⠛⣹⡇⢸⣿⡇⠀⢸⣯⣤⡀⠀⣤⣄⣄⢸⠘⡇⠀⢹⡾⢿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠹⠃⠀⠈⠉⠁⠁⠀⠀⠁⠁⠈⠁⠉⠉⠉⠉⠀⠹⠃⠀⠉⠁⠀⠈⠉⠉⠁⠀⠈⠁⠉⠉⠈⠁⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⢲⣲⡦⠀⠘⣶⠒⢾⣇⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠐⠊⠙⠻⣟⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣇⣴⣿⣿⣿⡿⣿⣿⣢⣬⣿⣠⡄⢠⢴⣦⢄⣐⣶⣶⣶⣦⣴⣦⣴⣾⣿⣿⡟⠹⠿⢦⣤⣴⣾⣿⣠⣤⣀⣀⡉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣟⡋⠹⠿⢿⠿⠷⡿⠿⠿⠿⠿⠿⠷⠶⠲⠿⠿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣾⣤⢿⣿⠿⠿⣿⡟⢩⣉⣉⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣯⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣤⣶⣍⣿⢿⣧⣀⡝⠒⢢⡼⠦⠈⠛⢨⣁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⢀⣴⢏⡸⢿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣉⣤⣶⡄⠺⠃⠀⠉⠁⠆⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠠⣷⠀⠀⢼⡆⠀⠀⢰⡆⠀⠀⣿⠆⠀⢰⣷⠀⠀⣿⢸⡧⠸⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⠛⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣈⡧⠀⠀⠃⠀⠀⠈⠃⠀⠀⠈⠁⣀⠀⠛⠁⠀⠘⠋⠀⠀⣿⠘⣗⣺⣻⣿⣿⣿⣿⡟⠛⢱⢿⣿⡿⠇⠈⣿⣿⠿⠖⠶⠖⠛⠒
⠀⠀⠀⠀⠀⠀⠀⣷⡇⠠⢠⣷⠀⠀⢰⡆⠀⠋⣶⣞⣿⣿⣶⡀⠀⢰⡶⠀⠀⣿⣧⣿⠿⠿⣿⣧⣤⣍⣻⣷⣤⢤⣿⠗⢰⣶⣾⡟⢠⣼⠶⣦⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠿⠣⣄⣈⡛⢀⠀⠹⠇⠀⠈⠙⠇⣼⠀⠿⠃⠀⠘⠟⠀⢀⡉⣠⡾⣲⣷⡶⠿⡛⠿⠿⢿⡿⢿⣷⣦⡀⣿⡿⠁⠀⣼⠀⣿⣏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠹⠄⠡⡈⠀⠀⠀⠂⠈⠛⠿⠾⣦⣤⣤⣤⣴⡶⢶⡾⠿⠿⡿⠿⢿⣿⣾⣻⣦⣠⣄⣠⣤⣠⡼⠛⡿⠁⠿⣦⣀⣠⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⡄⠐⠒⠀⠀⢀⡤⠄⠀⠀⣠⠀⣤⠀⠄⠀⣀⣤⣄⢠⣤⣀⣤⣠⣭⣍⣀⣉⣉⣉⣉⣿⣿⠀⠤⣶⡧⢘⣯⠛⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⠀⠀⠀⠒⣿⢰⣿⡆⠀⠀⠀⠀⠀⠠⣾⢟⡿⠙⠄⠙⡇⠄⢀⠾⣿⣿⣿⣿⣿⣿⢧⠟⠄⠚⣿⣅⣸⡿⠶⠶⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠉⢰⣄⠤⠂⣻⡟⢿⡁⠀⠀⠀⠀⠀⠀⢡⣮⠀⠀⠀⠀⠀⣀⡀⠀⡛⠛⠉⠋⣛⡛⠲⠀⠀⠀⢹⣿⡅⠺⠀⢰⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠠⠟⠀⠀⠀⢀⣻⣣⣌⣿⣄⡀⣀⠀⠀⠛⣤⠙⢷⣄⡀⠀⠸⣿⣿⠀⠁⠈⠃⠀⠀⠀⡛⠀⠀⠀⠀⣿⣿⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⣠⠘⠁⢰⡆⠀⠀⢠⡿⢟⢻⣷⠀⠉⠙⠉⠁⠀⠙⢷⣧⡀⠉⠿⠃⠀⢉⣴⣧⡀⠀⠈⠀⠀⠀⡅⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢢⣴⣿⣟⢻⡇⠀⠀⠀⠀⠀⠀⠈⢳⠿⡄⢠⡎⠀⠉⢤⣿⡇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⡞⠁⠈⠙⢻⡇⠀⠀⠀⠀⠀⣀⣀⣀⣤⣱⣄⣙⣷⣶⣤⣾⣧⣶⣉⣀⠀⡀⠛⠀⠀⢉⠉⣿⣿⠋⠀⠀⠐⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⣉⣹⣛⣻⡷⢸⣧⣀⣀⣀⡀⠀⠉⠉⠉⠙⠛⠙⠻⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⡿⠈⠛⠛⠛⢿⠿⢟⢿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢾⣉⠿⣽⡿⠿⣿⠿⠿⠿⢿⣿⢿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣾⣷⣄⣁⣀⠐⡈⢙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠉⠀⠉⠁⠈⠁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠈⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⡟⣿⡿⠻⣿⣿⠻⣿⣿⡟⢿⣿⡟⣿⢿⣿⠻⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⢛⢻⣿⡟⣿⣿⠻⣿⣿⡛⣿⣿⠻⣿⣿⣟⠿⣿⡟⢿⣿⢻⡟⣿⡟⠻⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣨⠎⠀⠀⠀⠀⡄⠀⠀⣘⡥⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⠀⠃⠃⢰⠛⠃⠀⢳⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠁⠀⡀⠀⠀⠼⡀
⠀⠀⢀⢴⠝⢁⠤⠲⣄⠀⠀⢿⠀⠈⠀⠀⠈⠀⠀⠀⠰⢄⠀⠀⠀⠠⣯⠆⠀⠈⠀⠀⡠⠀⠳⡤⠤⠛⠀⢀⡤⠒⠉⠀⠀⢀⠼⡗⠐⠀⠀⠀⠓⡆
⠀⠀⠀⠁⠐⠁⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡀⠀⠀⠀⠀⣾⠁⢧⠀⢰⠀⠀⠀⠛⠛⡂⠀⠈⠁⠀⣼⡇⠀⢀⠒⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠉⠀⣦⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⢀⡀⠀⠀⠀⠈⠀⠀⠢⠎⠁⠀⠀⠀⠐⠮⠂⠤⢴⠆⠀⠀⠰⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣄⠀⠘⠿⣶⣄⣠⣀⣾⠞⠁⠀⠀⣆⡠⠃⠒⢽⠀⠀⠀⠀⠐⠢⠺⢄⣠⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠠⢉⢃⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⡔⠀⡀⠀⢀⠀⠉⡀⢠⡀⠀⠀⠀⠀⠀⢰⢿⡆⠀⠀⠐⠛⠒⣦
⠀⠀⠀⠀⡀⠀⣀⡤⣦⣠⣦⣐⣽⠞⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠑⣄⠀⠀⠀⠀⠐⠁⠸⠻⣶⣶⣆⣀⣀⣿⠟⣷⠀⠄⠀⠀⠼⠟⠃
⠀⠀⠸⠖⠛⠛⠋⠉⠺⢭⠃⠀⠀⠀⠂⠀⠀⠀⢘⢀⢐⡠⠀⣷⠀⠈⠙⠟⠛⠀⠁⠀⡇⠀⠉⠋⠉⠁⠉⣿⢸⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⠀⠀⠤⠀⠰⢾⠀⠀⠀⠐⠠⠤⠤⠴⣾⣿⣋⣀⣀⣹⡇⠀⠀⠀⠈⢢⠘⠀⠙⠢⣄⡀⠀⠀⣸⣿⣸⣿⠀⠀⡀⠀⠋⠑⠀⢈⡀⠄
⠀⠀⠀⠀⠀⠂⠀⠀⡄⠛⡋⣤⠀⠀⣶⣾⣿⣿⠿⠴⣿⡹⢟⡽⢊⠄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠑⠺⠿⠛⠛⠛⠀⢨⣅⠀⠀⠀⢀⣾⡃⠀⣀
⠀⠀⠀⠈⠄⠀⠀⠀⢼⢹⡇⠸⡄⠀⠍⠉⣉⣛⠛⠓⠋⣾⣉⣴⠋⠀⠀⠈⠑⠆⡠⣹⡀⠀⠐⠓⠤⠄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠌⠉⠉⡀⠋⠙
⠀⠀⠀⠀⢸⠀⠀⠀⡆⠠⡧⠀⠣⠀⠀⡾⠷⠶⠛⠛⠛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⣿⣄⡀⠀⠀⢐⡁⠠⠀⠀⡀⠀⠀⠀⠀⠠⣀⢀⢀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⢤⠖⠀⡁⠀⠘⢷⠀⠉⠁⠀⠀⠐⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣉⡁⠠⠖⣉⠄⠁⢀⣀⡀⣀⡀⣐⠀⠀⠀⠍⠀⠀⠃
⠀⠀⠀⠺⠴⠀⠀⡼⠀⠀⠰⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠙⠢⠀⠀⠛⠼⠿⠿⠷⠼⠇⡀⠶⠶⣆⢸⡀
⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣨⠉⠑⠒⠦⠤⣌⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣀⠁⠀⠀⠂⠀⠆⠀⣉⢉⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⣛⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⢄⣀⡐⠳⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠒⠀⡴⠀⠀⠀⠈⠀⠂⠄
⠀⠀⠀⠀⠀⢰⡀⠀⠐⠀⡀⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⡜⠡⢀⠘⢍⠙⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠻⣌⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠛⠀⠰⠈⡀⠤⠇⠀⠀⣬⠀⠐⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⠀⠁⠀⠀⠂⣤⢤⡆⠀⠀⠀⠀⠈⠀⠀⠀⡩⠀⣄⡈⢀⡉⠉⠘⠩⠉⠀⡀⣀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠂⠤⠤⠀⢀⠀⠀⢀⠀⠀⠀⠄⠣⠀⣀⠄⠹⠛⠢⠄⠨⠉⠁⠐⠛⠛⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⣀⠈⠙⡠⠄⡀⠀⠀⠀⡤⠀⠓⠂⠀⠁⠀⠠⠐⠊⢠⠖⠀⠈⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠿⢗⠾⣀⠤⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡼⠉⠊⠛⠛⠛⠷⠶⠶⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⢠⣥⣴⣶⣦⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠷⠶⢶⣦⣤⣤⡤⠶⠞⠛⠋⠉⠉⠛⠛⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄⠀⣠⡤⢠⡤⠤⢤⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠠⠠⢀⠀⡀⣀⡀⠀⢠⣠⣀⠀⢀⡀⡀⢀⠀⣀⠀⡀⠀⠀⡄⢀⠀⣀⠀⣀⡀⣀⡀⢀⣀⢀⡀⠀⣀⡀⣀⣀⡀⠀⡀⠀⢀⣄⠀⡀⡀
⠀⠀⠀⠀⠈⠁⠑⠉⠁⠀⠀⠉⠘⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⡀⠀⠀⠉⠉⠀⠉⠁⠉⠉⠀⠀⠈⠁⠘⠉⠈⠉⠁⠘⠀⡁⠉⠉⠈⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠙⠊⠁⠐⠋⠛⠀⠈⠑⠀⠃⠈⠃⠊⠀⠈⠘⠀⠂⠋⠋⠂⠖⠐⠃⠒⠛⠊⠙⠘⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠑⣆⠀⡜⢉⠁⠀⡴⠛⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡄⠀⠀⠀⢦⠀⠀⠀⢠⠀⢀⡿⣸⠃⡆⢀⢔⠓⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣾⠀⠀⠀⠀⠈⠓⠒⠤⠞⠀⠘⣧⠇⢀⡱⠋⡱⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠻⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠎⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⡘⡰⢫⡵⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠸⣷⣄⡀⣸⠀⡀⠀⡀⠀⠀⠁⠀⡀⠈⠛⠐⢋⠀⠬⠚⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢉⠁⢰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠈⠓⠒⠦⠀⠀⠈⢁⣀⣤⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣶⣶⣿⢿⠟⠛⡏⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣧⠇




⡟⠉⣿⣛⣻⣛⣻⣛⣛⣛⣟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣿⣟⣿⣛

⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡀⠀⣠⡔⠛⣫⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠁⠀⠛⣷⣦⠛⠿⡁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠆⠀⠀⠀⠀⠀⠀⢠⡶⠙⢳⣦⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣦⠙⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⣸⣶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⢀⠀⠀⠀⠐⠀⢀⣰⣛⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢼⡟⠉⢻⣷⣦⣤⠀⠀⢤⣤⡤⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣸⡇⠈⡦⠂⠘⡟⠻⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠘⣁⣠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⠲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⡉⣀⡘⢿⣄⡀⢴⣶⠆⠁⣀⡄⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣇⢾⣿⠀⢀⣠⡀⣘⠟⠃
⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⣭⠶⠘⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠓⡀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤⣿⣿⣿⣿⣿⣿⣏⣤⣷⠂⣀⠀⠀⠀⠀⠀⠘⠂⡀⢶
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⠿⠿⢻⣻⣭⠀⢹⣿⣛⠏⣩⢿⣶⣿⣶⣶⣶⣶⠶⣄⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⠿⠿⠏⠀⢀⠀⠀⠀⠀⣸⡇⠘⣿⣿⣟⠙⣏⠙⣉⢀⠀⠀⣀⠀⠚⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢠⣀⡄⠰⠎⠙⠿⠗⠀⠀⣩⣍⣦⠀⣿⡿⠋⠘⣫⡀⢻⠈⠀⠀⢀
⠀⠀⠀⠠⠀⢀⣀⡀⠀⠀⠘⣿⠀⠀⢀⣤⡀⠀⡄⠀⠸⣿⠿⠂⠛⠛⢳⣦⣜⣿⡁⠈⠁⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⡤⠀⠘⣿⣧⡀⢸⡄⠘⡗⠀⠈⣀⣠⢀⡑⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⣇⡉⠀⠀⠘⠀⡄⠀⢈⡃
⠀⠀⠀⠓⠠⣾⡁⠹⣿⠋⠁⠀⢻⣦⠀⠉⠛⠛⠃⠠⢾⡇⠀⠆⠐⠆⢸⣏⣿⣿⣿⠀⠀⡀⠀⠀⢠⣤⣈⣀
⠀⠀⠀⢀⣴⣾⣿⡆⠀⢾⣤⣾⣿⠿⠆⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣀⡈⢫⡙⢿⣿⣦⠀⠱⠀⠰⢾⣽⣿⡇
⠀⠀⠀⠈⠛⠉⠁⠈⠁⠀⠈⠉⠀⠀⠀⠀⠠⠀⠀⠀⠰⣶⠄⠘⢿⡿⠃⢾⠀⠈⠋⠁⠀⠀⠸⠶⣈⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡦⠀⣀⣠⣢⡄⠀⠀⠀⢰⣾⡅⠀⠈⠁⠀⠂⢀⣤⠄⢤⣴⣿⣿⡿⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣀⢐⡤⠀⠀⠀⠉⠛⠀⠀⠈⢿⣿⡅⠀⠀⠀⠘⠛⢯⣠⣗⠸⠄⠁⠮⢵⣊⣡⣼⣿⣿⣗⠂⠉⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⢣⠀⠀⣰⠀⠀⠀⢸⡿⠓⠀⣄⣤⠍⣀⡀⠄⠉⠛⠓⠀⠀⠸⣟⣻⣷⣿⣿⣿⣦⣄⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠿⢷⠞⠀⠀⠾⠖⠸⣏⠤⣄⠢⢤⡷⠄⣈⣡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠏⠉⣿⣿⣿⣿⣿⣾⣟⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠦⠠⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠗⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣶⠾⠛⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣧⡀⠀⠀⢀⣠⠐⠂⠀⠀⠀⠀⠈⣁⣤⣴⠆⠑⠂⠀⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠈⣡⠴⠟⠛⠛⠻⠆⠀⠀⠀⠀⠺⠉⠿⠟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣶⠏⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠛⠙⠟⠛⠃⠀⠀⠀⠘⢷⣴⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠛⠛⠛⠂⠀⢀⠀⠀⠀⢀⣀⣀⣀⣴⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠿⠂⠀⠢⡀⠀⠀⠀⠀⠀⠀⠄⠈⠭⠭⠥⠄⠀⠀⠀⠀⢠⡈⠀⠶⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠄⠀⠀⠀⠈⠒⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣈⠀⠀⠀⡀⢦⠀⠀⠀⠂⠀⠀⠀⣀⢀⢀⡔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠳⡄⠀⠀⠀⠀⠀⠀⡰⠀⣶⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠈⠷⠙⠀⠀⠀⠀⠀⠈⠁⢓⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠦⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠠⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⢀⠎⠁⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠌⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠤⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠄⡀⠀⠀⡀⠂⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⢀⠈
⠀⠀⠀⠀⡎⠀⠀⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠘⠦⠄⢒⠂⠁⠀⠄⠀⠀⠑⡁⠄⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠄⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠤⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠀⠀⠀⠀⠀⢀⣤⡀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⢄⡀⠀⠀⠀⠀⠰⡀⢀⠤⠀⠀⠀⠀⠰⠄
⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠠⣀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠡⠂⡦⣠⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡀⢨⠛
⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⢀⡀⢀⡀⠀⠀⠀⠀⠀⠈⠦⠑
⠠⢀⠀⠄⣠⠳⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⣤⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠈⠉⠒⠂⢄⠀⠠⡀
⠤⠠⠄⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡈⠁⢐⠉⠁⠒⠀⠀⠀⠀⠀⣀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣤⠐⣶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠱⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀⠀⠀⡆⠀⠙⢆⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠈⠉⠉⠐⠒⠂⠀⠀⠤⠄⢀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃⠀⠀⠇⠀⠂⠈⠣⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡏⠀⠀⠀⠀⠁⠁
⠀⠀⢀⢤⠀⠀⠠⠔⠚⠉⠀⠀⠀⠀⠀⡇⠀⠂⠠⠀⠑⡄⠀⠀⠀⡜⠀⠀⠀⣸⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⡏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠤⠔⠒⠋⠀⠀⠀⠒⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢀⠂
⠀⠈⠇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⠀⠒⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠄⣄
⠀⠀⠀⠀⡠⠄⠄⠀⠀⠀⠀⠀⠀⠎⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂⣉⠀⠀⢘⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠘⠂
⠀⠀⢀⠊⠀⢀⠔⠈⡁⠀⢀⡀⠉⠑⠦⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠉⠁⠒⢠⠀⠀⠀⠀⠀⠀⠀⢀⡆⠊⠁⠰⣀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⢠⠇⠀⠀⢁⣠⣈⠁⠀⠀⠀⢱⠀⠸⠀⠀⠀⠀⠰⠂⠀⠀⠀⠐⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⢀⠖⠋⢉⠉⠙⠢⢄⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠈⠢⠼⠀⠀⠀⠀⡻⢁⢑⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⢀⠄⠡⠈⣦⡄
⠀⠀⠀⠀⠀⠢⡀⠀⠠⠀⠤⠊⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡁⠀⠉⠁⠀⡀⢀⠛⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⢓⣲⠂⠶⠔⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡊⠴⠃⠀⠀⠀⠀⠀⠀⠸⠤⠤⡆
⠀⠀⠀⠀⠀⢠⠇⣀⠔⠃⠓⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠍⢉⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⠔⠁⡰⠀⠀⠀⠀⠀⠈⠀⠱⢄⠀⠀⠀⠀⠀⠀⢀⡰⡄⣀⠀⢰⡄⠤⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠈⣉⢠
⠀⠀⠔⠁⢀⠐⠓⠠⡄⠀⠀⢠⠀⠚⢦⡀⠳⠀⠀⠀⠀⢀⠀⠰⠤⢀⠱⠾⠵⠶⡅⠀⠹⠋⡀⠀⠀⠀⠀⠀⠈⠑⠪⠜
⠀⠀⡁⢀⠀⠀⠀⠀⣸⠀⠀⣣⠀⠀⠀⢱⠠⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠘⠂⠒⠊⠀⠀⠉⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠅⠀⡖⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠈⡂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠤⠤⠔⡃⠎⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⢔⢦⠀⣑⣬⠂⣴⠋
⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠰⣮⠻⣟⣈⣇⣼⠋⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡽⣧⡿⠛⣏⣭⣸⣋⣱⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⢠⠉⠉⣁⠀⡉⢨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⡀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢌⢉⢓⠠⠀⣠⠂⠸⢇⡐⠣
⠠⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠣⢬⡖⠙⠥⢡⠶⠊⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠄⡀⠀⠀⢄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⢂⠔⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢲⠀⠈⠁⠄⠀⠄⡇⠀⠨⡐⢤⡀⠚⡬⠀⠀⠀⠀⠀⠀⠠⢤⠀⠂⠀⠂⢧⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⠀⠀⠄⠀⢠⢀⠃⠀⠀⠀⠐⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⣆⣈⣀⣟⡀⠘⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄⠦⡜⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⠀⠀⠀⠀⠰⠁⠀⠁⠉⠃⡄⠀⠀⠀⡀⢤⠆⠑⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠚⠁⠄
⠓⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀

⠀⠀⠀⠀⠀⠀⡖⠲⣄⠀⠀⠀⠀⠀⢠⠖⠂⠀⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠻⠳⡄⠀⠇⠼⠈⠇⠀⠀⠀⠀⠀⡷⠢⠤⠖⡎⠀⠀⠀⠀⠀⠀⠀⢀⠞⠿⣿⠆⠀⠀⠀⠀⠀⠀⠐⣗⡺⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⣾⠃
⠀⠀⠀⠸⣿⢿⣿⡿⣿⠇⠀⠀⠀⠀⠀⢧⠐⠿⠂⡇⠀⠀⠀⠀⠀⠀⢠⠊⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡞⠘⢿⠂⠃⠀⠀⠀⠀⠀⠀⢠⠞⢢⡴
⠀⠀⠀⠀⠳⠔⠙⠦⠋⠀⠀⠀⠀⠀⠀⠈⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢂⣕⠀⠀⠀⠀⠀⣴⠉⠉⠓⠚⠉⠙⡦⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠊⠹⣶⣄
⠀⠀⣤⣀⣀⣀⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⣬⣂⠽⠛⠀⠀⠀⠀⠀⠈⢹⠁⠳⠖⠸⡏⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣒⣆⠀⠀⠀⠀⠀⡏⠉⣴⣶⡄⣼⡇
⠀⠀⣿⢸⠈⠁⡇⡏⣽⠀⠀⠀⠀⠀⢀⣠⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣰⠇⠀⠀⠀⠀⢶⣶⣶⣶⡿⠿⢿⣻⡷⠀⠀⠀⠀⠻⣧⢈⣉⣀⡼⠁
⠀⠀⠿⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⣰⠷⣤⣄⣠⣾⣿⣦⠀⠀⠀⠀⠀⢘⡿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣶⠀⠀⠀⠀⠀⠐⠦⡀⠀⣀⠚⠁⠀⠀⠀⠀⠀⣛⣛⠂⠀⣻⣛⠂
⠀⠈⠋⢸⣿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠸⣿⡋⠒⢻⡿⠂⠀⠀⠀⠀⢠⣿⣤⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⢤⡬⣧⣥⣤⡄⠀⠀⠀⠀⢀⣷⣼⣀⣀⣿⣼⣃
⠀⠀⠰⣮⣃⡀⢀⣙⣵⠆⠀⠀⠀⠀⠰⣁⣹⠴⣏⣹⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠰⣥⠾⢷⠿⠀⠀⠀⠀⠀⢸⣿⣿⠿⠻⢿⣿⣿
⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠛⠚⠃⠀⠀⠀⠀⠘⠛⠋⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀
⠀⠀⢠⣶⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢶⢸⠇⠀⠀⠀⠀⠀⡠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣆⣰⣆
⠀⠀⠀⢽⣿⣿⡿⠛⡿⠀⠀⠀⠀⢠⣶⣦⣿⡿⣿⣿⣶⠀⠀⠀⠀⢠⣔⣚⢿⣺⠿⡤⡄⠀⠀⠀⠸⢿⣿⠿⠿⠿⠿⣿⡷⠀⠀⠀⣿⣿⣼⡽⢿⡿⣿⣧
⠀⠀⠀⠈⠙⠿⣿⠖⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠈⠛⠉⠀⠀⠀⠀⠘⣮⣟⠼⢿⡸⢄⡯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠁⠘⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠀⢡⣀⠀⠀⡄⠀⠀⠀⠀⢀⣠⠴⠳⣄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⢀⣠⣤⡶⢟⡋⢁⡀⠈⠀⠀⢀⣠⠔⠋⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠸⠟⣋⣭⠄⣿⡅⠀⡇⡰⣤⠖⠋⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠄⣐
⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⡀⠘⣆⣴⠿⠋⣡⡆⣿⢣⣰⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⡄⠤⠐⠂⠀⠉⠀⠀⠀⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣠⣴⡿⢻⠃⠿⠼⠿⠠⢿⣠⣴⠤⠄⠒⠒⠃⠀⠀⣻⠀⠀⢀⣀⣀⣤⣤⣤⡒⣒⣊⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⠀⠠⠀⠄⠷⣾⠟⠫⣶⣼⡆⠀⠀⠀⠀⣿⣃⠀⠀⢀⣀⡴⠃⠀⢀⣿⣿⠋⣉⠉⢠⠄⢀⡄⠀⡤⠀⠤⢀⡇
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠰⣇⣴⡿⠛⣉⡅⠀⠀⠀⠀⣿⠙⠛⠛⠋⠉⠀⠀⣠⠾⠟⠓⠚⠒⠚⠒⠒⠓⠛⠛⠛⠛⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⡴⠚⢁⣄⠀⠀⠀⢀⣿⣄⣀⠀⠀⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡁⣠⣼⠟⠉⠀⠀⠀⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠐⠛⠋

⣿⢿⠿⠿⡿⠟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢒⠀⢀⢀⡤⡶⣲⣶⣆⠤⠄⡀⢲⢀⠄
⠀⠀⠀⠀⠀⠀⠁⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡶⢞⠋⢁⠀⢸⣇⣀⣀⣿⣿⠀⠀⢀⡎⣸
⠀⠁⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⢀⣖⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠤⠀⢸⣷⣿⣿⡿⣿⠀⠈⠀⡇⡇⠀⢀⣀⢀
⠀⠀⠀⠀⠀⣀⠄⠈⠁⠒⠠⠤⠈⠙⠛⢃⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠀⠒⠀⠈⠉⠉⠉⠁⠛⠒⠒⠒⠁⠉⠉⠉⠉⠉
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠉⠖⡀⢁⠂⠀⠀⠁⠀⠤⠤⠄⠒⠒⢒⣚⡛⠓⠀⠀⢈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠑⡆⠈⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢉⡦⢤⡖⠀⠀⠋⠔⢈⠄⠀⠀⠀⠀⢠⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠜⠠⡀⢀⠀⠠⠀⠚⡡⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣀⣠⣤⣤⣄⣀⣤⣠⣠⠇⠠⡄⠀⠀⠀⠀⢀
⠀⠀⢠⠀⢠⣄⠀⠀⠀⠈⢀⠉⢀⠌⠔⠀⢀⡁⢀⡈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⡀⠀⠉⠀⠀⠀⢀⠄⠠⠒⡄⠀⡔⢀⢏⠐⠄
⠀⢀⠈⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠠⡤⢴⡇⠘⠄⠀⠠⢀⠈⠂⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢁⣴⠀⠈⢀⠄⠈⠁⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠜⢂⠓⠺⡅⠀⣄⠐⠀⠁⠚⠀⠀⠀⢀⠀⠱⠄⠀⠀⠀⢀⠈⠀⠀⠠⠊⠁⢀⠔⠁⠀⠀⠀⠀⠀⢤
⠀⠀⠀⢀⠀⠀⠀⠈⢁⣀⡀⠈⠀⠀⠉⠀⠈⠛⠂⠀⠀⠠⠀⠀⢀⣀⣀⡀⠀⠤⡌⠒⠀⢶⡋⠀⠀⢀⡦⢈⡐⠁⠀⠀⠀⠀⠀⠀⡐⠁⡄⠀⠐
⠀⠀⠈⠀⠀⠀⢀⡔⠁⠊⠀⠛⡖⠀⠀⠀⠠⠄⠀⠀⡌⠠⠦⢀⠀⠠⠤⠀⠀⠀⠔⠈⠐⠀⣀⣁⡀⡀⠀⠘⠋⠥⣂⠀⠀⡀⢠⠊⠀⠀⢭⡀⠐
⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢐⠀⠀⢀⣇⠀⠀⠀⠀⠐⠀⠀⣀⣀⡀⠀⠀⠊⠹⠾⠓⢁⡴⠃⠀⠀⠀⠈⠓⠒⠁⠀⠀⢀⡀⠀⢁
⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠚⠃⠀⡀⠘⠂⠀⠀⠀⠀⠐⠈⠉⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠤⠐⠀⠀⠀⠠⠦⠄⢀⠀⢠⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠂⠒⠀⠀⢠⢀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⢀⡀⢍⠙⠲⠤⠊⠀⡇
⠠⠄⠐⠒⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠶⢦⡄⠀⠀⠦⠄⠀⠀⠀⠀⠒⠒⠂⠲⠖⡖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⢀⡀⠤⠔⠒⠈⣉⣄⠀⠀⢀⡀⠀⣐⡠
⠈⣁⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⢳⠀⠤⠤⠀⣒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⠦⠤⠤⠀⠔⠀⠠⠔⠒⠟⠉⣁⣤⡌⠳⠓⠋⠡⠔⠂
⠠⠤⠀⣘⣀⡀⣀⣀⣀⣀⣀⣀⣈⣐⣒⣓⣀⣂⠠⠤⠀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣒⣒⣲⣗⣒⣂⡀⠀⠊⠃⠶⠒⠚⠋⠀⠠⠐⠀⣊⢀⡀

⠀⢺⠿⢿⣿⠿⠿⠿⠿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⠁⢻⣿⡟⢿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⠇⠈⠳⠶⠶⠶⠶⢶⣶⣾⣋⠀⢹⣿⣿⠛⣿⣿⡟⠛⢻⣿⣿⣿⣷⣼⣶⣿⣿⣿⠏⠀⠈⢿⣶⣾⣿⣿⣿⡄⠀⠈⢿⣉⣀⣉⣉⣹⣿⣿⣿⣿⡛⠉⢉⣹⡄
⠀⠀⠀⢤⣀⣀⣾⣿⣿⣿⣿⡟⠈⠀⢹⣿⠋⠀⠈⣿⡇⠀⣸⣿⣿⣿⠷⠿⡿⠿⢿⣧⠀⠠⠄⢸⣿⣿⣿⣿⢿⣷⠀⢤⡸⠏⠉⠙⢻⣿⠿⠟⠛⠛⠻⣾⠀⠈
⠀⠘⠃⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠸⡇⠀⠀⠀⢠⡄⠀⣉⠉⠉⣀⣀⣠⣦⣀⣼⣀⠀⠠⠀⠈⠉⠙⢿⡇⠀⢸⡇⠸⠛⣴⣖⣀⡼⠛⠶⢶⣶⣶⣶⣾⣄⣀
⠀⢰⡆⠀⠀⠀⠈⠛⠛⣿⢿⣇⠀⠀⠀⡟⠋⠻⠿⠁⠖⠀⢹⠀⢸⣿⣿⣿⠀⠈⠙⠿⠇⠀⠈⠉⠀⠀⠘⠁⠀⠘⠿⠀⢀⠉⣿⣿⡇⢀⡶⠿⠿⡿⢿⣿⣿⡿
⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠰⠒⠀⠀⠀⠀⠀⡀⠀⠸⠀⢸⣿⣟⢉⡃⠀⠻⡇⠀⠀⠀⠀⠀⠀⠘⠠⣤⣤⣴⣇⡀⠀⠸⣿⠷⠈⠀⠀⠀⢀⣼⣿⢿⡿
⠀⢸⡇⢀⡄⢀⣠⠀⠀⣿⣾⣿⢠⣾⣁⠰⣷⣤⡄⣀⠃⠀⢰⠀⠈⣿⡟⠉⠁⠉⠀⠀⠀⣀⠀⠀⠀⠰⠂⢰⡖⠻⣿⣿⠁⠀⢀⢻⣶⣄⣤⣤⡄⠘⠿⣡⡴⠷
⠀⢸⡇⠘⠿⠿⠇⠀⠀⠹⣿⡿⠀⡀⠼⣆⣀⣀⣀⣿⡇⠀⢸⡄⢘⣿⣧⣤⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⣤⡄⠀⠀⢿⣿⠗⢀⠿⢼⠿⠿⣿⣿⠇⠀⠀⣿⡧⠤
⠀⢸⡇⠀⣦⢴⡄⠀⠀⠘⣫⣴⠆⠁⠰⣿⣿⣿⣿⡟⡎⢠⣌⠀⠸⠟⢻⣏⠀⠀⢀⣄⠀⠛⠀⡀⣾⣶⢨⠁⠀⠀⢊⡀⠂⣀⠀⠀⠀⠀⠠⣤⣤⠀⠀⢿⣷⣆
⠀⠈⠁⢠⡇⣾⠇⡁⠀⢸⣿⣿⡄⠀⣰⣿⣿⡿⠟⠀⠿⠀⠙⠆⠀⢀⢰⡅⠀⠀⢸⣿⠇⠀⣀⣶⣿⣿⣀⡀⠂⠀⣿⠿⣿⣿⢀⠀⠀⠷⠖⠻⣿⡀⠀⢸⡿⣿
⠀⢰⣆⢠⣷⠠⣤⡀⠀⢸⠀⢸⡇⠀⢸⣿⣷⣶⣶⣾⡶⢀⡿⠄⠀⡌⢛⣀⠀⠀⠈⣿⡴⠞⠛⠿⣿⣿⠋⠀⠀⠀⢡⣾⣿⡿⠀⠀⠀⣶⣶⣾⣿⠀⠀⢸⡇⠁
⠀⠐⡇⢀⣷⠄⠀⠁⠀⠈⠀⢸⡏⠀⣟⣿⣦⣉⣹⣿⣧⠈⢁⠀⠰⠀⢹⡷⠀⠀⣾⣯⣠⣄⣀⣄⣀⣿⡴⢴⣶⣾⣿⣿⣿⡇⠀⠀⠀⢻⡉⢉⣟⠀⠀⢼⡇
⠀⢠⡏⠈⣿⠀⠙⠀⠀⢸⠀⠈⠳⣄⠹⣿⣿⣽⣯⣿⠤⣦⣴⠤⠾⠀⢸⡇⠀⠀⠀⠀⠹⠁⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠋⠀⣼⡇⠀⠀⣸⡇⢀⡀
⠀⢸⡇⠀⣿⠀⠀⡆⠀⣼⠀⢸⣧⡈⠰⣿⣿⣿⡏⠀⠀⣀⣐⠀⠀⢀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠟⠛⣿⣿⣿⡃⠀⠀⠀⠀⣸⡟⠀⠀⠀⣿⡇⣸⡃
⠀⠈⠁⠀⠋⠀⠈⠁⠀⠘⠀⠘⠋⠉⠀⠙⠛⠉⠛⣿⢻⡿⠛⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠛⠋⠙⠁⠀⠀⠀⠀⠋⠁⠀⠀⠀⠘⠋⠉⠁
⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠰⡤⠀⣠⣤⠤⠶⢤⣤⣤⡤⠀⡀⠀⢶⣶⣤⡄⠀⠀⠀⣴⣦⡶⠒⠶⢶⣄⣶⣶⣄⣲⣦⣶⣶⣶⠄⠀⠐⢶⣶⠤⠴⢶⣶⣶⡄
⠀⢸⣿⡇⠠⠶⢤⣿⣿⡟⠋⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⠷⣤⡉⠛⠿⢂⡄⠀⠀⠹⣿⣿⣷⣶⡿⠉⢻⣬⡛⡛⣯⣽⠻⠷⣶⠶⣾⡇⠀⠀⠀⣿⣿⡇
⠀⢸⣿⡇⠀⠃⠰⣿⡿⠃⢀⣴⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⢰⣿⣾⠛⣿⣶⣤⡛⠤⡄⠀⠀⠈⠿⠛⢉⣠⣾⡏⠹⠿⢻⡿⣿⢰⡆⠀⠀⠀⠀⠀⠀⠀⠩⡭⠁
⠀⢸⣿⡇⠀⠀⠐⢋⣤⣶⡇⠈⠠⠖⠀⠀⢠⣼⠇⠀⢰⣿⣶⣬⡿⠋⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⡶⠆⠀⢻⠛⣿⣇⠘
⠀⢸⣿⡟⠉⠉⠙⢿⣍⣽⡇⠰⠇⠀⠻⣿⡃⠀⠀⠀⠘⠛⠛⣧⠀⠀⣀⣼⣿⣿⣯⣤⣤⡿⠆⠀⠀⠀⢙⣿⣶⣾⣷⠇⠀⢸⣶⣿⣿⣶⡀
⠀⢘⣿⣇⡀⣀⠀⡌⠉⣿⡇⠀⣄⠒⣤⣼⠅⢠⣤⣤⠀⠀⠀⠃⠀⠀⠻⣿⣿⣿⡟⠉⠉⣷⠀⠀⠀⠀⠀⠙⠛⢿⡟⠀⣶⣾⣿⣿⣿⣿⣆⣸⠀⠀⠀⠀⠀⢸⠄
⠀⢸⣿⣿⣿⣿⠄⡇⠀⣹⣧⡀⠰⠀⢻⣿⠀⢠⠿⣿⠀⡀⢰⠃⠀⠀⠀⠘⠿⠓⠃⡀⢠⣿⣄⢀⠀⠀⠀⠀⠠⣼⣿⠀⣹⣯⣿⡿⢿⡿⠻⠿⠀⠀⠀⠘⠁⢸⡇
⢀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠁⣰⠀⢸⣿⡄⠈⠠⠄⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⣽⣿⣶⡆⠀⠀⠀⠀⠙⠃⠀⣿⡛⠁⠀⠀⠀⠀⠸⠀⠀⣠⣶⠆⢸⡇
⠀⢹⣿⣿⣿⣿⣿⣿⡇⠘⣿⠀⠹⡄⠀⣿⠇⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⢀⣴⡧⠀⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⡆⠘⠃
⠀⢸⣿⠟⡹⢿⣿⣿⣷⢸⣿⠀⠀⣤⠀⢿⡀⠀⠀⠀⢠⣾⣿⠃⢸⣿⠀⡄⠀⠻⠿⢷⡄⢷⣴⣶⣦⣶⣄⣲⣶⣤⣴⣶⣶⣶⣶⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⡀
⠀⢸⡟⣦⠀⠀⠉⠙⠛⠀⣿⡶⠀⣿⢀⣼⣧⠀⣤⣾⣟⣸⣿⣧⣰⣿⣴⡟⠀⠀⠀⠀⠸⠃⡠⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠃⠀⡇⠀⢀⡇⠀⠀⠀⠘⠋⢻⡇
⠀⠸⠷⠀⡀⠀⠀⢀⠀⣠⣿⣧⠀⣽⣿⢿⣿⡿⣿⣿⣯⣽⣿⣿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠂⠀⠾⣿⣿⣽⠛⠿⠿⠟⢿⣿⠉⠀⠀⠇⠄⠘⢧⡀⠀⠀⠀⠠⠾⠇
⣀⣀⣀⣀⡀⠀⠀⢀⠀⠀⠀⢀⠀⣀⣭⣀⣈⣴⡟⠋⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠾⠿⠛⠋⠀⠀⠀⢀⣀⣀⡀⢀⣤⣀⣀⣀⠀⢀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢷⡈⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡟⠀⠀⠶⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⠉⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⣤⣞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠊⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⢠⡾⠶⠾⡆⠀⡰⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠱⣸⡇⠀⠀⠅⠀⢃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠰⢻⠃⠀⢰⠁⠑⠘⠶⠶⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠊⡆⠀⣾⣾⣾⢰⣄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠰⠁⢠⠂⠀⢸⠁⠉⠈⠁⠸
⠀⠀⠀⢀⠆⠀⠀⠀⣀⡵⠀⠐⠒⣖⣖⠒⠀⠐⢧⡀⠀⠀⠈⢢⡠⠀⡜⠀⢸⠀⠀⡆⠀⡄
⠀⠀⠀⠈⠀⢀⣤⡺⡫⠔⠊⠁⠀⣀⡀⠀⠉⠒⠀⡹⢓⢄⠀⠀⣇⡆⣂⡀⣸⡀⣀⡇⢀⡆
⠀⠀⠀⠈⠶⠋⡡⠋⠀⣠⠖⠋⠉⢹⠉⠉⠓⢦⣀⠀⠣⡀⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⡐⠁⢠⠞⠋⠀⠀⠀⣸⡆⠀⠀⠀⠛⢦⠀⠐⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⢀⡏⠀⠀⠀⠀⠀⣿⡇⣀⣀⣤⠀⠈⣧⠀⢹⠀⢌⠉⡠⠀⠠⢍⠈⡠⠀⠨⡉⠈⠂
⠀⠀⠀⠀⠸⠀⢸⡗⠀⠀⠀⠀⠀⠫⠟⠛⠉⠀⠀⠐⣗⠀⢸⠀⢀⠰⠀⠀⠀⠈⠘⠀⠀⠀⢨
⠀⠀⠀⠀⠀⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡶⢐⠊⠀⠑⡂⢐⠂⠀⠑⡀⡐⠁
⠀⠀⠀⠀⠀⠐⡀⠈⢳⣤⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋⠀⡐⠀⠀⠑⢀⠊⠀⠀⠑⢠⠃⠀⠀⠱
⠀⠀⠀⠀⠀⠀⡏⠢⡀⠈⠓⠦⠤⣴⡤⠤⠖⠋⠀⡠⠊⡧⣀⣀⠔⠀⠆⣀⣀⠔⠈⠄⣀⣀⠜
⠀⠀⠀⠀⠀⢀⠇⠠⠉⠑⠢⠤⠀⣀⡀⠠⠤⠶⠊⠳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⠲⠾⣧⡄⠀⢐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⠊⠁⠀⠀⣿⣶⣶⣿⡇⠀⡚⡌⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠀⠀⠄⠈⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠓⠒⠂⠁⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠈⠄⠀⠀⠀⠀⠒⠂⠀⠀⠨⠍⠁⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠱⠀⠀⠀⠘
⠀⠀⠀⠀⠠⠀⠀⠀⠁⠹⠄⠤⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⡎⢀⣀⣀⣀⣀⣀⠃
⠀⢀⡀⢠⠀⠀⠀⠁⠀⡠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠄⠈⠉⠉⢈⠁⠀⠀⠁⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⣂⡷⠈⠀⡀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠔⠀⠠⠂
⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠐⠀⠹⠀⠂⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠀⠠
⠀⠀⠀⠀⠀⠔⠉⠁⠒⠂⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠂⠀⢀⣠⡄⡀⠀⠓⠲⢀⣀⠀⠄⠀⠈⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠐⠃⡄⠀⠸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠈⠉⠔⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⢀⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠉⠑⠒⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⡀⠁⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⢀
⢐⡀⠠⠀⠀⠀⠀⠀⠀⠀⢖⠀⠤⠀⡂⠠⠤⠠⠤⠤⠤⠄⠀⠤⠤⠤⠄⠄⠈⠤⠴⠖⣉⣁⠲⠐⠃⠍
⠀⣂⠈⠄⠀⠀⠀⠀⠀⠨⣭⠅⠬⠀⢀⠀⠅⠁⠀⠀⠀⠀⠀⠸⠿⠭⠀⠀⣁⠘⠈⠉⠀⠀⠀⠀⠤⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⣁⠉⠁⠈⠛⠛⠋⠉⠉⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⠿⠃⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠋⠉⠀⠀⠀⠀⠈⠛⠓⠀⢸⣿⡿⠋⠸⣿⡟⠻⠟⠛⠀⠀⠀⠀⠀⠖⠻⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣙⠿⠀⠀⣨⣷⡀⠀⠀⠈⢡⣿⡇⢈⡿⢳⠀⠶⣻⠱⣶⣆⠐⠀⠀⠀⢠⣶⠀⠐⠆⢹⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⡇⠀⠀⠛⠛⠁⠀⠀⠀⠘⠛⠁⢸⡀⠆⠀⢆⠸⡀⠻⠿⠇⠀⠀⠀⠘⠿⠇⠀⠀⡞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠆⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⠻⠲⠾⠋⠀⢀⠔⠀⠀⠐⢶⣿⣿⣿⡄⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⣠⠀⣀⠀⡄⢂⣁⠀⢀⠠⢤⠊⠉⡛⠛⠿⣷⣤⣀⠀⠀⢀⣠⣴⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠄⠒⠤⢀⠠⠓⠠⣤⡋⠀⠀⠀⢑⠊⠀⢀⣦⠔⡆⠫⢀⡀⠼⠣⠂⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣹⡿⠀⠀⠀⠀⠀⠀⠀⢻⣧⠠⠐⠈⢁⠄⠊⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⡠⠚⡀⠀⣀⠜⡃⠀⠀⠀⠀⠀⠀⠀⠃⣄⠀⠀⡙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢘⠀⠐⠳⠀⠿⡤⠃⠃⠀⠀⠀⠀⠘⠊⠣⠬⠟⠚⠓⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠁⠀⠰⡆⠳⢶⠆⠀⠀⠀⠀⠀⠦⢾⠀⡖⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢀⠖⢁⠆⠀⠀⠀⠀⠀⠀⠐⢄⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡅⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣤⣤⠀⣿⣿⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⡏⠀⠀⠀⠀⠀⡏⠐⠂⠠⠤⠤⠤⠤⠤⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⠿⠁⠀⠸⣿⣿⡿⠿⡟⠀⠀⠀⠀⠃⢭⠙⠛⠻⠿⠿⠿⠿⠿⢛⡛⢩⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⠀⠀⠀⢠⠀⠀⠏⠀⠈⠉⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⡀⠀⠀⠀⠀⠀⢘⠀⠠⡀⠀⠀⠀⠀⠀⢸⠄⢠⠀⠀⠀⠀⠀⠀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠁⠀⠀⠀⠀⠀⠈⡇⠘⠁⠀⠀⠀⠀⠀⢸⠁⠘⠀⠀⠀⠀⠀⠀⢘⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢃⣠⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠄⠀⠀⠀⠀⠀⢠⠃⠀⠡⡀⠀⠀⠀⠠⠂⠀⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢀⣠⡴⠃⠀⠀⠀⠀⠀⠘⢦⣀⡀⠴⡀⠀⢰⠣⣀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⣀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠁⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡭⢽⣟⠛⠛⠛⠛⠛⢛⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⠈⢈⠅⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠂⠀⠀⡔⠀⡁⢢⠀⠠⣶⣶⣆⠀⠀⣴⣢⣴⣶⡀⠀⠐⠒⠁⠁⢀⠔⠚⠉⠒⠂⠒⡄
⠀⠐⠚⠉⠀⠰⠀⠀⠓⠤⠥⠊⠀⠀⠿⠿⠿⠀⠀⠩⠿⡟⠛⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠄⠀⠀⢱
⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠠⠀⠈⠑⠒⠉⠁⠈⠁
⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠈⠁⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠓⠢⠀⠀⢀⠀⣀
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⢸⡀⠀⠀⠀⠀⠀⢅⠀⢠⣴⣶⣶⣰⣦⡄⠀⢇⠀⠀⠀⠁⠀⢠⠤⠤⠤⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠛⠛⠓⠋⠀⠈⠁⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠂⠈

⣀⣀⣀⣤⣤⠤⠤⡤⠶⠒⡆⣆⣀⡄⠀⠀⠀⠀⠀⠆⠀⡷⣶⣶⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⡿⣷⣿⣿⣿⣿
⡇⠀⠀⠀⣀⢀⣀⣇⣀⣠⡇⠋⡏⠀⠀⠂⠀⠀⡘⠇⠀⡷⣟⠛⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿
⠟⠛⣿⣯⠉⠉⣹⣏⠙⣿⡇⢀⣤⣄⠀⠀⠀⠸⣿⡆⠀⢹⡿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣉⡟⠁⠀⣻⡇⢀⣿⣷⣿⣥⣚⢀⠁⠁⠀⠁⡄⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣬⣤⣤⣷⣿⣿⣿⠻⡿⡙⣽⡁⠈⠒⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣘⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡟⠛⠏⢹⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠈⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⣿⣀⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⣭⠏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⢮⠀⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⡿⣻⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠿⠿⠿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⢠⣖⣶⢷⣼⠾⠿⠋⠟⠐⠋⠀⠈⠀⢀⠀⢀⣀⡤⡄⡄⡤⣐⡄⡼⡸⠘⠀⠐⠘⠈⠈⠀⠁⠀⠀⡀⢀⢰⠠⡠⠀⣄⠂⠦⠹
⠀⠀⠛⠋⢀⢀⢀⢀⢤⢸⢲⢰⡰⠠⠼⠹⠀⠙⠀⠁⠁⠉⠀⢀⠀⠀⠤⡄⠀⡄⢠⢲⢰⠐⠅⠏⠉⠂⠘⠈⠀⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠋⠃⠈⠈⠀⠀⠀⣀⠀⡀⢀⢠⢠⠀⡆⢖⠒⠅⠈⠀⠀⠚⠃⠀⠉⠀⠀⠀⡀⣀⡀⠄⡀⠄⡆⣗⢂⠡⠫⠱⠑
⠀⠀⠀⠀⠀⡗⡦⡖⠰⠼⠍⠎⠾⠀⠑⠈⠈⠀⠀⠀⡀⠀⣀⢠⠠⢠⠠⠰⡄⠦⠀⠱⠐⠘⠙⠘⠈⠈⠀⠀⠀⠀⠀⠀⣄⡀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⢠⢤⢄⠔⡢⢇⠀⠃⠃⠘⠀⠟⠂⠉⠁⠁⢀⠀⠀⠀⠀⡀⣀⠀⠠⡄⡄⠀⠂⠂⠂⠣⠇⠃⠑⠑
⠀⠀⠀⠀⠀⠠⠧⠣⠘⠘⠂⠈⠈⠀⡈⢠⠀⢀⣀⣀⢠⣤⢴⡦⣴⣶⠀⡜⢾⣏⠿⠉⠓⠘⠃⠀⠁⠀⠀⠀⢀⠀⡀⢀⢠⢠⠠
⠀⠀⠀⠀⠀⢀⡀⣀⣠⣤⣴⣆⢶⣞⣿⣸⡾⠏⠿⠻⠚⠛⠁⠉⠈⠉⠀⢡⠈⢀⢀⣠⢄⠀⣰⡄⢰⠹⠹⠸⠈⠃⠐⠈⠈⠈
⠀⠂⠀⢿⣽⡟⠷⠿⠛⠛⠘⠋⠉⠁⠀⡀⣀⢀⢀⠀⡆⡄⣰⡐⡤⠆⠐⠼⠀⠘⠈⠈⠈
⠀⠀⠀⠈⠉⠁⣀⡄⢄⢰⠐⡔⡟⠏⠄⠛⠘⠈⠂⠀⢁⠀⠀⢀⠀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠈⠀⠀⡄⠀⡀⠀⣄⠆⡄⠐⣐⡌⡆⠽⠘⠀⠋⠒⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⢠⠤⢠⡐⠄⠐
⠀⠀⠀⠀⠀⠀⢀⣶⢰⠹⠺⠵⠀⠓⠘⠉⠈⠈⠀⠀⠀⠀⢠⣄⡀⢀⣀⠀⠀⡆⢳⢢⢴⠂⠈⡏⠋⠀⠓⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢠⡄⢤⣴⣴⠶⣏⡷⠿⠙⠟⠆⠘⠘⠀⠀⠁
⠀⠀⠀⠀⢰⣖⣶⣧⣽⠺⠿⠉⠟⠒⠛⠈⠁⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠛⠋⠀⣀⣀⢀⢀⡄⢄⠰⣄⡆⠎⠧⡳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢠⠠⠠⡀⢰⠸⠐⠎⠘⠜
⣶⣶⡶⣶⣶⣶⣶⣾⣾⣾⣾⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠂⠠⣄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠘⠇⠈⠐⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠉⠀⠀⠐⢊⣉⣩⣄⡠⠄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢚⠉⣅⣐⡼⠭⠕⠒⠚⠋⠉⠉⠁⠀⠀⣀⣈⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⢉⡀⠤⠒⠚⠉⠁⢀⣀⣀⣠⣤⠤⠤⠶⠒⠒⠋⢹⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣉⣀⣠⣤⣤⣄⣶⣖⣒⣒⣙⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠒⠤⣀
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⢾⣻⣿⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠲⢤⣀
⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠙⠾⡇⠀⠀⠀⠁⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⢠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⠀⠀⠁⠀⠀⠤⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠜⠀⠀⠀⢀⠆⠀⡔⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠞⡡⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠎⠀⠀⠀⢀⠎⠀⡼⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢠⠂⠀⠀⠀⠠⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⢋⠔
⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⢀⠎⠀⠠⠁⠀⠀⠀⡐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⡟⣡⢞⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠠⠁⠀⠀⢀⠜⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⢰⠟⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡰⠁⠀⠀⢀⠎⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠁⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠦⡀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⢀⢀⠜⠁⠒⠢⢀⠀⠀⠀⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠲⠤⡀⠀⠀⠀⠂⠉⠢⡀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠒⠣⢄⠀⠀⠀⠀⠀⠀⠠⠎⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⠤⠖⠒⡒⠛⢻⠉⠋⢃
⠀⠀⠀⠉⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢠⠤⠤⠔⢒⠒⠋⠉⢅⠀⠀⠐⠀⠀⠀⠁⠀⠀⠁⠀⢸
⠀⠀⠀⠂⠤⣀⠠⠄⠀⠀⠀⠀⠀⠰⠒⠁⠀⠀⢀⡀⠀⡠⠤⠀⠄⠲⠀⠲⠘⠋⠉⠃⠉⠁⠰⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡇
⢠⠀⠀⠀⠀⠈⠑⠦⣀⢠⠄⠀⢀⠁⠀⠀⠀⠀⡌⡇⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹
⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠁⠀⠀⠀⠀⠀⠀⡓⣧⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠴⢶⢒⣒⣛⣙⣉⡍⠭⠉⠏
⠐⠦⡀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢀⢀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠰⠒⣒⣒⢒⡫⠭⠩⠄⠒⠒⠒⠈⠉⠉⠁
⠀⠀⠈⠑⠒⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣋⣈⠉⠡⠤⠤⠤⠤⠀⠀⠒⠒⠂⠈⠉⠉⠁⠁
⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡤⠶⠶⢦⡀⠙⢧⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⠀⠀⠀⠀⣠⠖⣁
⠀⠀⢀⣠⠴⠶⠒⠶⣤⡀⠀⠀⣾⠀⢠⠏⠀⠀⠀⠀⠹⣆⠸⡆⠀⠀⠀⣼⠀⠀⡞⠈⠉⢹⠓⢦⡞⡡⠞⠁⣰
⢀⡴⠋⢀⣠⠴⠦⣄⡀⠹⣆⠀⣯⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⣷⠀⠀⢰⠇⠀⢠⡇⠀⠀⡆⠀⣸⠊⠠⠖⡴⠃
⡾⠀⣰⠏⠀⠀⠀⠀⠹⣄⠘⣧⢻⠀⣳⣀⠀⠀⠀⠀⠀⢸⠄⢻⠀⠀⡟⠀⠀⣼⠀⠀⢰⠇⣠⠟⡆⠐⠈
⡇⠀⡏⠀⠀⠀⠀⠀⠀⠙⣆⠘⣿⡇⠃⠈⡇⠀⠀⢠⡤⠼⠦⢾⡀⢸⠁⠀⢠⡇⠀⠀⣾⣰⠃⢀⠃
⢷⠀⢻⡀⠀⠀⢸⡟⢦⡀⠘⣇⠈⣷⣰⣄⣼⠤⡄⠸⠀⠀⠀⠀⢃⡟⠀⠀⣼⠀⠀⠀⡿⠁⠀⡞
⠘⢧⠈⢷⡀⠀⠀⣟⠈⠻⣄⢸⠀⢸⣭⡤⠶⠒⢻⣞⣓⣀⣛⣛⣿⠁⠀⢠⡇⠀⠀⣼⠁⠀⣼⠁
⠀⠈⠳⣄⠙⠦⣄⢹⡀⠀⠈⣿⡀⡎⢻⡀⠀⠀⠀⣷⠶⠤⠤⠴⠾⠀⠀⣼⠀⠀⣼⠃⠀⢰⠇
⠀⠀⠀⠈⠳⣄⣀⠉⢷⠒⠋⠀⢳⡙⢩⣇⠀⠀⠀⢸⠀⠀⠀⡀⣷⠀⢠⡏⠀⣰⠃⠈⢀⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠈⢷⠀⠀⠀⢻⣎⣿⡄⠀⠀⢸⠀⣶⠀⡇⣿⠀⣸⠁⣰⠃⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⣿⣷⠀⠀⢸⠀⣿⠀⡇⣿⢀⡏⢰⠏⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⢻⡟⡆⠀⣼⠀⣿⢰⡇⣿⡸⢠⠏⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢳⡹⠀⠸⠀⠀⢘⠁⣿⢁⠏⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠷⠤⠶⠦⠷⠶⠾⠴⠶⠶⠶⠿⠾⠶⠶⠶⠿⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠶⠶⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠠⠄⡄⣀⣀
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⠀⠀⠀⠀⠂⠈⠨⠀⠋⢐⠲⠂⠆⠤⠤⡀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠠⠄⠀⠐⠦⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠂⠒⠀⠀⠀⠀⠀⣄⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⢀⠐⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠞⢉
⠀⠀⠠⠁⠀⠀⣘⠄⠀⠀⠀⠀⠀⠀⠄⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠊⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠄
⠀⠀⠀⠇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠁⢀⠂⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⢀⠒⠀⠀⠠⠭⠄
⠀⠀⢀⠀⠐⠀⢀⠀⠀⠔⠀⠀⡬⣀⠀⠉⠐⠢⢤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢰⢁⠂⠠⠅⣀⠀⠄⠀⠀⢀⠄⣈⠠⠤⢈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰
⠀⠀⠇⠀⠁⡠⠊⠀⠀⠀⢀⠃⠄⢀⡉⠀⠆⡌⠀⠀⠀⠀⠌⠀⠀⠀⠀⠈⠄⢀⣀⡀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠬⠁⡒⠀⡍⢀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⡀⠐⠀⠒⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠
⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣘⠀⠆⠀⠀⠀⠀⠀⠐⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠁⠀⣽⠿⠛⠚⠁⠁⠀⠀⠀⠀⠠⠘⠅⠀⠑⠁⠈⠢⢀⠀⠀⠀⣧⡠⠤⠄⣤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠳⣤⡐⠀⡀⢁⣄⠗⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⢄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣈⢶⣆⡙⢇⣦⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠒⢴⠋⡏⠀⠀⠁⠀⠉⠉⢳⠀⠀⠶⣘⠟⣤⡛⢡⡭⠚⠷⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠒⠂
⠀⠀⠰⠀⢩⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠮⣙⠓⠖⢮⡞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠰⡄⢸⠄⠀⠀⠀⠤⠀⣼⠀⠀⠀⠀⠀⠀⠈⠙⠶⠋⠀⠀⠀⠀⠀⠀⠉⠒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠
⠀⠀⠐⠃⢸⠀⠀⠀⠀⠀⠀⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣾⣶⣶⡟⠀⠀⠀⣶⠀⠂
⣀⣠⣤⣇⣼⣦⣶⣖⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣯⣸⠀⠀⠀⠀⡏⠀⠀⠀⢀
⠛⠛⠯⠜⠋⡏⠙⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠓⠛⠛⠓⠛⠿⠆⠀⢀⠈⠛⠀⠑⠰⠀⠀⠀⢟⣁⠠⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣴⣦⡤⠤⠤⣤⣤⠶⡤⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠤⠤⠤⠤⠤⠤⠴⢦⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠒⠉⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠐⠖⠲⢐⢶⡶⡲⡞⠁⠀⠀⠀⠘⠁⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭
⠂⢀⡨⡪⢃⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗
⣪⢐⢌⠺⠟⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠧⠀⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣆⢅⡴⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢿⡶⣛⣿⣺⠀⠀⠀⢠⠐⠒⣀⢒⣒⠢⣆⠀⠀⠀⠐⠏⠻⠷⠀⠀⠀⡠⠒⠡⠀⠆⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠀⠀⠀⠀⠀⠀⠐⡿
⠻⠿⠿⠿⠟⠀⠀⠀⢸⠀⠀⣽⡀⠤⢤⠼⠅⠀⠀⠀⠀⠀⠀⢀⠴⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⢠⡖⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡕⣶⢶⣲⡞⡀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣿⣾⣻⣇⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠄⡀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⠏⠨⠉⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠰⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠤
⢃⣥⠀⠀⠀⠀⠀⠀⠘⢻⡏⠁⡄⠀⠀⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠦⠠⡖⠀⢠⡄⠀⢰⡁⠂⠌⠈⠉⠉
⣿⢿⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⣅⣀⣰⡇⣰⠏⠀⠀⠈⠿⣿⡻⠿⠿⠿
⠱⠾⢧⠀⠀⠀⠀⠀⠀⢰⠅⠀⡯⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠂⡼⠋⠀⠀⠀⠀⢀⣶⡿⠿⣧⠀⠐⢆⠀⠀⠀⠈⢷⡀⢸⡃⢿⣴⠏⠀⠀⠀⢠⣯⣭⢭⠭⢭⠭
⠈⠀⠉⠀⠀⠀⠀⠀⠀⠘⡇⠀⡴⠀⠀⠀⠀⠿⠟⠇⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⢿⣧⣴⣿⠇⠀⠼⠀⠀⠀⠀⠸⠿⠄⠛⠿⠟⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄
⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡪
⠠⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢒⡆⠀⠀⠀⠀⠀⠀⠉
⣀⣈⣀⣀⣀⣀⣠⣄⣀⣠⣀⣄⣀⣀⣲⣀⣀⣀⣀⣊⣀⣂⣀⣀⢀⣀⣀⣀⣀⣏⣀⣈⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣰⣋⣡⡒⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿