Road construction Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠀⠃
⠀⠀⠀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠃⠀⣴⠂⡆⡤⡄⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠀⣰⠀⠀⢹⢸⢱⠇⡇⣧⣸⠁⠀⠘
⠀⠀⠀⢠⠔⠀⢸⡇⠀⠠⣁⡀⠁⠀⠀⠀⣈⠡⠀⠉⠀⠀⠀⠀⠀⣇⠀⠈⠉⠘⠘⠾⠠⠿⠇⠀⠀⡁
⠀⠀⠀⠰⠀⠀⣈⠁⠸⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⢢⠀⠁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⡶⢤⠤⣄⡠⠔⠋
⠀⠀⠀⠈⢂⣽⠟⢩⣶⠆⣠⣶⠃⣰⡶⠀⣰⣶⢂⣾⠇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈
⠀⠀⠀⠀⣿⣏⣠⣿⣏⣰⣿⣃⣼⣿⣁⣼⣿⣡⣾⣇⡆⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢸⣷⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢴⡕⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣸⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⢠⣧⢸⡇⠀⠀⡧⠤⠀⠀⣀⣀⣀⠼⠥⣼⡄⠀⠀⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠖⢃
⠀⠀⢸⡏⢸⡇⠀⠀⠙⠀⠀⠐⠂⠀⠀⠀⠁⢹⡇⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⡐⠀⠀⠀⠀⢸
⠀⠀⣾⠁⠸⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⡤⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡄⠜⡆
⠀⠀⡿⠀⠀⢿⠀⠀⠐⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢷⠤⡀
⠀⢸⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣿⠀⠀⠸⠀⠀⠀⠀⠻⣄⡀⠣⠄⠀⠀⠀⠀⠀⠈⣠⡼
⠀⠈⠃⠀⠐⢻⡇⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠘⢹⡄⠀⠀⡄⠀⠀⠀⠀⠈⠛⢦⣄⣀⣀⣀⣤⡴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣿⣟⣛⣟⣛⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡥⠊⠀⣀⠀⠈⠺⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠊⠀⠀⢀⠄⢄⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣔⠠⡐⢄⠀⠀⠀⠑⣄⠔⡡⠛⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠁⠀⠀⠀⠊⠀⠀⠀⠀⢀⡀⣀⠘⣶⣅⡚⡼⠀⠀⠀⠀⠈⢯⠔⡡⢚⢎⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠀⡠⠁⢠⢎⡠⠀⠄⡠⢀⠠⠑⠌⠉⠈⠀⠀⠀⠀⠀⠀⠀⠻⣀⠥⡈⢇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠂⠀⠀⠀⠀⠀⢠⢃⢄⡾⠋⢙⡄⠄⠀⢐⡂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠔⡠⢒⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠁⠀⠀⢀⠌⠀⠀⢸⠰⣽⡤⣠⡦⠐⠊⠀⠐⠄⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠔⡡⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⡈⡰⠁⠀⠀⢀⠊⠀⠀⠀⠀⠉⠀⡥⠄⡊⠕⡢⣝⡗⣥⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠔⡉⠻⣆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⠜⢀⡠⢌⠡⡖⠻⣄⢔⣓⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠱⣎⠔⡡⢻⡄
⠀⠀⠀⠀⠀⠌⠄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⣂⠶⣣⠆⢷⡢⠽⣄⠙⠷⠟⢷⣦⣀⠀⣀⠴⣛⣭⡴⣄⠀⠀⠀⠀⠘⢏⠔⡡⠸⡷
⠀⠀⠀⢀⠄⠈⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣰⠬⠀⡼⠁⠀⠀⠻⡅⣸⡀⠀⠀⠀⢈⡿⢟⡳⠝⢋⠁⠡⠈⢧⡀⠀⠀⠀⠈⢫⠔⡠⡘⢷⡀
⠀⠀⢀⢂⠂⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡴⠁⣲⠟⠀⠀⠀⠀⢰⠃⣸⠀⠀⠀⣴⠋⡊⠅⢒⠡⠀⠂⢑⠦⠛⣳⡀⠀⠀⠀⠀⢫⠐⡠⢊⡗⡀
⠀⠀⠀⠆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣜⡈⡴⠃⠀⠀⠀⠀⠀⢸⠅⡚⠀⣠⠞⠂⠕⣂⠉⠐⠈⠑⠊⠁⠂⠑⡂⠝⣦⠀⠀⠀⠐⢃⠔⡡⢸
⠀⠀⡀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⠓⠐⠒⠀⠒⠛⠓⠛⠉⠚⠋⠘⠋⠋⠛⠋⠀⠀⢀⠜⣡⢊⠔⡙
⠀⠀⠰⡱⡄⠀⠀⠀⠑⠒⠀⠀⠠⠀⡰⢆⠒⡲⢒⠖⡒⢒⠒⡲⢒⠖⠲⢂⠔⡠⢂⠆⡰⢀⠖⡸⢉⢏⠟⡹⢋⢄⠖⠜⡩⢁⢄⠁⡡⡞⠡⠁
⠀⠀⠀⠱⣌⢦⣀⠀⠀⠀⠀⠀⢠⢞⠔⠡⢊⡔⡡⢊⠔⡡⢊⠔⡡⠘⡔⢡⢊⡔⡡⢊⠔⡡⠊⢊⡔⡡⢊⠔⠁⡠⢊⢊⣐⣑⣣⠾⢊⠔⠁
⠀⠀⠀⠀⠀⠑⠀⠍⠀⣒⣒⣚⡓⣒⣒⣓⣛⣒⣂⢉⠈⠁⢉⣩⢭⠭⡥⡥⠭⠀⠁⠀⠊⠛⠙⠉⠉⠉⠉⠉⠩⠥⠤⠤⠐⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠠⠪⠀⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡈⢔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢐⠅⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢒⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠡⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠒⠀⠀⠀⠀⢀⠀⠀⠀⠐⢈⣤⠦⠒
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡲⠁⡄⠀⠃⠀⠀⢠⣰⢀⢀⣀⠀⣆⡄⢸⡆⠑
⠀⠀⠀⠴⠀⠘⠞⠲⡀⠀⡣⠀⠀⢀⣰⡷⠇⢰⠠⠀⠆⠀⢀⣘⠋⠘⢈⠉⠈⠮⠵⢂⣷⣡⠄
⠀⠀⢸⡏⠀⠐⡀⠰⢺⠁⠀⠀⠀⠈⣙⠒⠼⡈⠄⠀⢖⠀⢀⠈⠀⠀⠐⠀⠀⠄⠈⡘⢨⡍⠁
⠀⠀⠐⡀⢀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠁⢀⠀⡏⠁⠀⠸⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠁⠀⠹
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠇⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⢀⠀⠠⠠⠀⠀⠃⠂⠀⠠⠀⠀⣄⠤⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⠒⠒⠀⠤⠼⠭
⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⡀

⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠶
⠀⠀⠀⠠⠄⠠⠀⠠⠄⠠⠄⠠⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠠⠄⠀⠄⠠⠄⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⣷⣤⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠰⠀⠀⠀⠀⣿⡷⠶⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠴⠃⠀⠀⠠⠀⠘⢷⠀⠀⠀⢰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠈⠀⠀⠀⠀⠀⠠⠐⠦⠀⠀⠀⠁⠀⠀⠀⣀⣀⣠⣾⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⣤⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡄⠀⠠⣤⣤⣤⣤⣤⡤⠵⠄⠀⠴⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠒⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⣌⠀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠙⠒⠲⠶⠒⠀⠀⠂
⠀⠀⠀⠉⠉⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠶⠶⠦⠤⠤

⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡄⠀⢠⣄⠀⢀⣠⡀⠀⣀⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠻⣷⡄⠙⣷⣄⠙⢿⣦⡘⢿⣦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣄⠀⢠⣤⡀⠀⣤⣄⠀⢠⣤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠻⣷⣄⠙⢿⣦⠈⢻⣦⡀⠻⣷⡄⠋⠀⠀⠀⠀⠀⠀⠀⠠⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡄⠀⠀⠀⠀⠀⠀⠘⢇⣤⡀
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠰⠄⠀⠠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠂⠠⠤⠀⠀⢀⢀⠀⢀⠰⢀⠀⠀⢀⠀⠤⠄⠸⢷⠠⠀⠀⠀⠀⠀⠀⢠⠉
⠀⠂⠀⠀⠀⠈⠣⡠⢌⠈⠈⠠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⠀⢠⡄⠀⠐⠐⠒⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠁⢀⣀⣀⣀⠀⠀⠈⠆⠛⠰⠀⠀⠴⠁⠁⠀⠀⠀⠀⠀⢠⠇
⠀⢀⠀⠀⠀⠀⠈⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡋⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⠀⠉⠒⠒⠂⠀⠀⠀⠀⠠⠄⠀⠳⠄⠀⠄⠀⠀⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⣤⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠀⠀⠠⣀
⠀⠀⠀⠀⢀⠀⠠⠡⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠣⠃⠀⠠⠄⠉⠁⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣈⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣤⡤⠤⠤⣷⠶⠲⠠⠰⠆⠤⠤⠀⡄⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠤⠄⠀⠀⠀⠀⠈⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡆⠀⠒⠀⠖⠀⠰⠀⠠⠄⢨⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⡀⢀⡀⠀⠀⢀⣤⡀⠀⠀⠀⢸⣿⡇⠀⠒⠀⠆⠀⠤⠀⠠⠀⢠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢽⠀⠀⠀⠀⣾⠋⠀⠁⠀⠀⠀⢘⣱⡇⠰⠦⠄⠦⠀⠴⠀⠠⠀⠰⢰⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣼⠀⠀⣀⠀⣿⠀⠀⠀⢿⠛⠁⢸⡩⠇⠀⠆⠀⠒⠀⠒⠀⠀⠀⠠⢸⠆
⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⢥⠐⠂⢘⣀⡇⠈⠁⠀⠁⠀⠂⠀⠐⠀⠆⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⢨⠀⠀⢘⡁⡇⠀⡇⠀⠇⠀⠅⠀⢈⠀⣃⣘⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠃⠀⠐⣿⠃⠆⠀⠒⠀⠀⢠⡴⡧⠸⠗⠒⠖⠲⠶⠶⠶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⣿⠀⡀⠀⡛⡀⠰⠊⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡏⢴⠀⠀⠀⠁⠘⡃⣜⡇⠒⠒⠒⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⡇⠀⠰⢃⢸⢠⡄⠀⠀⠈⡋⠁⡅⠀⠀⠀⡅⢨⠀⠀⣤⢨⠄⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⠀⡇⠀⠠⢸⢸⢸⡇⠀⠀⠀⠀⣠⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⢸⠘⠐⠀⠀⠀⣴⠖⠀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⠂⠀⡴⠈⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠠⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠹⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⡄⠀⢀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠗⠰⢠⠃
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠠⠀⠱⠀⠀⠤⠶⠒⠂⠀⠤
⠀⠀⠀⠀⠐⠋⡀⡁⠀⠀⠀⠀⠀⠀⠂⣀⢠⡀⠀⢀⣦⡌⠀⠀⠒⠠⠒⠀⠀⠀⣧⠀⣄⠰⠦⣤⣀⡀
⠀⠀⠀⠀⠠⡀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠋⠀⣡⡀⠀⠉⠂⠑⠒⠒⠒⠂⠀⠀⠒⠃⠈⠁⠀⠀⠀⠈⠙⠓
⠀⠀⠀⠀⠈⠉⠐⣒⠀⠀⠀⠈⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣐⣢⣶⣴⣒⣲⣶⣒⢆⣸⠄
⠀⠀⠀⠀⠉⠀⢄⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠰⠂⡄⠀⠀⠈⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣿⣿⡿⠻⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠋⢸⣿⢹⠛
⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⢸⣿⠘
⠀⣿⣿⡷⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⠘
⠀⣾⢽⢿⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠐⡇⠀⠀⠀⢸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄
⠀⠛⠿⠿⠾⡿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⢸⡇⠠⠀⠀⢰⣽⢸⠀⠀⠂⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⢀⠀⢠⡄
⠀⠉⡳⣿⡯⠷⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⡇⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠰⢬⣅⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠀⢻⠀⢸⡁⠀⠀⢠
⠀⠀⢀⣋⣀⡀⠨⢻⡀⡦⣀⠀⠀⠄⢠⡀⠤⡀⡿⣿⣤⠼⣗⠀⡀⣤⣼⡿⢾⣠⣬⣤⡀⣼⡽⡇⣀⣼⣷⣦⡀⢀⣰⣤⣼⠿⣤⠼⠀⠉⠑⠂⠈⢛
⠀⢢⠼⣴⡁⣠⣴⣟⣤⡀⠉⠂⣽⠚⣴⡯⢤⡀⠨⢽⣿⡦⣿⣾⣷⣶⣿⢷⣿⣼⣿⣿⣿⢟⣻⣇⣿⣿⠿⢻⣷⢖⡻⣋⠳⠆⣅⠡⠀⡀⠀⠐⢉⡠⠄
⠀⢀⣺⠛⢭⡿⠿⢿⣿⢯⡀⢻⣭⠰⣄⡗⣚⠻⢒⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⠏⠁⢜⠀⠀⠘⠍⠓⠳⠤⢵⣦⡼⠳⠦⣽⡿⢥⠀⢀⠂
⠀⠀⠰⢶⣿⣤⣟⣓⠗⠞⢿⣷⠿⡄⢻⣦⠉⠿⠟⢿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⢣⡟⢹⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠐⠀⠄⠖
⠀⢈⠛⠅⣠⢀⣁⣎⣩⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣨⣟⣹⣩⣿⣿⡿⣿⣿⣿⣰⠏⣾⠁⠸⠀⠀⠀⠀⠈⠂
⠀⠈⢹⣶⠆⠁⠘⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣔⠭⠇⠍⠁⠙⡴⠏⢻⢯⠏⣰⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠉⠂⠅⢑⡒⠒⠽⠷⠄⠩⠗⢠⣿⠀⠀⠈⠁
⠀⠀⠉⠀⠂⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡬⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⡌⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⠋⠑⠺⠄⠐⠀⠵⠤⠁⠐⠀⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⢣⠁⠈⡌⠁⠀⠀⢠⣤⣾⣦⣤⣄⠀⢰⡉⣛⣛⣉⡛⠛⣉⡛⢛⣉⡛⠛⠉⣟
⠀⠀⣼⣿⠻⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠰⣾⣿⣿⣿⣿⠉⠀⠘⠛⠐⠛⠓⠐⠛⠓⠐⠚⠛⠐⠚⠛
⠀⠀⣿⠙⣧⠀⠠⡦⠀⠀⠀⢠⣬⣄⢠⣥⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣂⣶⠖⣠⡶⢂⣴⠶⢂⣶⡆
⠀⠾⠁⠀⠿⠀⠶⠾⠷⠄⠀⠘⠿⠟⠘⠿⠃⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠛⢥⠞⠋⠰⠛⠁⠾⣿⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣰⣆⣀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⣿⠄
⠀⣴⠛⠉⠋⠉⢻⣆⠀⠀⣴⣿⣿⡏⣿⣧⠀⠀⠀⡟⠛⠉⢳⡞⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠰⡗⠂⠀⡇⠀⠀⣿⠀⢀⠟⢻⡟⢻⡟⠻⡆⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢤⣾⣿⣿⣿⣦⡄⣤⣤⣤⡄
⠀⠻⣦⣀⣀⣠⡼⠋⠀⠀⢣⡀⠀⠀⢀⡜⠀⠀⠀⣇⣀⣀⣀⣀⡇⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⡴⠃
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣉⡷⠺⠯⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣀⢀⣾⣿⣷⡄⣀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣴⣿⡿⠤⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣦⡀⡔⡆⢄
⠀⣿⣿⡈⢭⣭⡭⢅⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⣷⣶⣾⣦⠀⠀⠀⠀⡎⠻⢿⣿⣿⣿⣿⡟⣷⣷⣾⣷
⠀⢉⣿⣿⣷⣶⣶⢿⠿⡄⠀⠀⠀⢰⣿⣿⡟⠛⠛⠚⣿⣿⣿⠛⠀⠀⠀⠠⢿⡥⣴⡤⣼⠿⠷⠶⠿⡿⣿⠿
⠀⠀⠃⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠙⠁⠙⠁⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⢀⣠⣿⡇⣿⣿⣀⡀⠀⠀⠀⠠⣤⠀⢀⣴⣄⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣤⣤⣤⣬⣶
⠀⢘⣛⣛⡃⣛⣛⣛⡁⠀⠀⠘⠷⠿⣇⣴⠟⢿⠇⠀⠀⢈⣛⣛⡀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣛⡇
⠀⠘⠛⣿⡇⣿⣿⠛⠃⠀⠀⠀⢀⣴⠟⠳⣄⠀⠀⠀⠀⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠘⠛⠙⢻⣭⣭⣽⡟
⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠙⠉⠉⠉⠙⠃⠀⠀⠀⠀⠒⠒⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠙⠉⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠄⠴⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠠⡀
⠀⠀⠀⠀⠤⠂⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠁⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢸⠀⠀⢀⡤⠄⡴⢀⣀⡀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠴⠃⠀⠀⡆⠀⠀⠘⡇⢠⡇⣸⢉⡇⣼⠀⢰⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠔⠪⣀⠀⠀⠀⠀⠀⢠⠀⠀⢀⢀⡠⠂⠁⠀⠀⠀⢰⡇⠀⠀⣀⡿⣸⠀⡟⢸⠁⣿⣦⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡴⠒⠠⡀⣧⠀⠀⠀⣇⡀⠀⠀⠉⠀⠀⠀⠀⡉⡡⠅⠂⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠙⠀⠳⠞⠠⠟⠿⠁⠀⠀⢠
⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠀⢸⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡃⡅⠀⠖⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠀⠀⢀⡠⢧⡀⢀⣀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠛⠛⡗⠖⠦⠤⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⣡⣿⠟⠉⣽⣿⠏⢉⣿⡿⠉⢉⣿⣿⠋⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠸
⠀⠀⠀⠀⠀⢸⣿⠟⠀⣴⣿⠟⠀⣼⣿⠋⢀⣾⣿⠁⣠⣿⣿⠃⣰⣿⢃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡄
⠀⠀⠀⠀⢀⡾⢛⠓⠛⢻⡟⠒⠚⠿⠻⠖⠿⠻⠷⠶⠿⠿⠿⢞⠛⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠐
⠀⠀⠀⠀⢈⣻⡂⠀⠀⠀⠃⠁⠀⠀⠈⠈⠀⠀⠀⠈⠉⢹⣷⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗
⠀⠀⠀⠀⢸⠿⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⣸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⣎⠆⡟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⢠⣽⠀⡷⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠀⠧⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⡄⠀⠀⢀⠁⠀⠀⠀⢘⡀
⠀⠀⠀⢸⣼⠤⣿⡃⠀⠀⠀⡇⠔⠖⢀⣒⣀⣀⣀⣠⠺⠿⠴⢾⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣟⠀⢀⠀⠀⠀⠐⠀⠀⠀⠚⠉⢃
⠀⠀⠀⣾⣿⠀⣾⡇⠀⠀⠀⡷⠀⠀⠀⠀⠂⠀⠀⠐⠉⠈⠃⢹⣦⠀⠀⠀⣁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠿⠠⣿⡥⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠅⢀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⢐⣿⠀⠀⠙⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠈⠈⣿⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠒⠊⠁⢧
⠀⠀⢸⡗⠀⠀⠀⢿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡂⠀⠀⠘⠁⠀⠀⠀⠀⠀⣠⠄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⡀
⠀⠀⣼⡇⠀⠀⠀⡿⡇⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⢷⣄⠀⠐⢅⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⣸⠆
⠀⠀⢿⣇⣀⣀⣀⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣃⣀⣀⣀⢻⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠉⠀⠀⠀⠀⠀⣁⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣤⣤⣴⡶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⡿⢿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠁⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠟⡹⢋⡿⣀⠀⠀⠀⠀⣰⠏⠁⠀⡄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠐⢩⡔⠁⠀⠀⠀⢠⣟⣀⠀⠀⠣⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠋⢀⣰⠄⠀⠀⠈⣿⠙⠛⠶⠶⣶⣶⣶⣶⣼⠷⠀⠀⢀⡴⠤⠤⣤⣤⣤⣤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠶⣦⡤⠶⠞⠛⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⡴⠋⠀⣀⡶⠋⠀⠈⢦⡀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡸⢋⡴⠋⠀⢠⡾⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⣠⡀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣴⣷⡉⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡾⠟⠉⠃⠀⠀⣠⣽⣿⣧⠞⢁⣴⠖⠀⡶⠀⢀⣴⣦⠀⠀⠀⣀⢸⡷⣄⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢸⣧⣤⡤⠶⠛⢻⡏⡏⢀⠀⠀⢈⣿⠸⣄⠀⠲⢊⣽⡏⣿⡃⠀⠀⠻⣦⠀⡗⠀⢸⡇⣽⠂⢸⣸⣿⣿⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡇⡇⢈⠀⠀⣾⣿⠀⠙⢷⡼⠋⣿⢡⣿⠉⢦⣀⠴⠿⠃⢷⡄⠘⠷⠟⠀⠘⠿⠘⠟⣠⡴⢻⣿
⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⡅⢸⠀⠰⡏⣿⠀⠀⠀⠀⢰⠏⠘⢿⣄⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡷⠾⣷⠀⠀⠀⠀⢸⡇⡇⠘⢰⠀⡇⢿⡀⠀⠀⠀⡿⠀⠀⠠⠉⢷⣄⠀⠈⠷⣄⠀⠀⠀⠀⠀⢀⣴⠋⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠛⠛⠛⠶⣆⢸⡇⣧⠀⢨⣄⠇⢸⡇⠀⠀⣼⠃⠀⠀⢸⠀⠀⠹⣦⡀⠀⠙⢷⣄⠚⠃⣠⠞⠁⢀⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⡛⢻⠀⠈⢿⣀⣼⠃⠀⠀⣆⢸⠀⠀⠰⡎⢹⡶⠶⢦⣹⡷⠾⢷⡤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⡇⣿⠀⠀⠈⣿⠁⠀⠀⠀⡏⢸⠀⢸⠀⡇⢸⡇⠀⠸⣿⣙⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢠⡄⠇⣿⠀⠀⠀⣿⠀⠀⠀⠀⠇⠸⠀⠀⣴⢁⣾⣇⠀⠀⣿⣭⣀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣇⣸⣀⢨⣯⠀⠀⠀⣿⠀⠀⠀⢰⠀⡆⠀⢠⣿⣯⣭⣽⣶⣄⡽⠲⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢈⣻⠍⢀⢀⡀⠀⠀⣿⠀⠀⠀⢸⠀⡇⠀⢸⣇⢀⣀⠀⣧⠈⡃⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢢⡿⠒⠉⢀⡇⠀⠀⣿⠀⠀⠀⠈⣶⠁⠀⡘⣿⣬⡭⠼⡟⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⣼⠀⣚⢠⡄⠀⠹⣧⣀⠀⠇⣿⠀⠀⣧⠂⣾⠀⠀⣇⠀⢰⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢻⡆⠀⣨⣤⣤⠴⠏⠉⠛⠛⠿⠶⠶⠿⠞⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⢤⠶⠿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠛⠷⢶⣦⣤⣤⣤⡶⠶⠿⠛⠋⠉⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠢⣦⢤⣤⣤⣤⣐⡒⢲⡿⠁⠀⠀⠀⢸⣯⠀⠑⠒⠒⠒⠦⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠒⠒⠂⠀⠈⠉⠁⢸⡇⠀⠀⠀⠀⢸⣿⡈⠉⠉⠉⠓⠒⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠀⠒⠒⣒⣂⣀⢸⡇⠀⠀⠀⠀⠀⣿⣧⢠⣉⠛⠒⠒⠒⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠋⠉⠉⠉⠹⠇⠀⠀⠀⠀⠀⣸⣿⠀⠉⠛⠛⠛⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠉⠀⠀⡠⠋⠀⠠⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⢀⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡅⠀⠀⠀⠀⠱⠆⠁⢹⡀⠀⠀⠢⠀⠀⠀⠀⠀⠁⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠁⠀⠀⠀⠀⠀⠀⠀⢨⠳⡄⠈⠂⠀⢄⠀⠀⠀⠘⠀⡔⢰⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡦⠀⠀⡐⠀⠀⠀⠄⠀⠈⠣⡈⢢⡀⠈⠀⠈⠤⠤⠒⠈⡠⠂⠠⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⠁⢸⠀⠀⠀⠣⡀⠀⡄⠀⠑⠂⠀⠉⠐⡦⠠⢤⡔⡈⠠⠄⠒⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⣸⠓⠒⠒⠒⣻⠤⢄⠀⠀⠰⡀⠀⢠⠁⠀⢰⠈⣀⢀⠀⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡼⠋⡦⠄⠠⠾⣱⡓⢄⠀⠀⠀⠙⠔⠁⢀⠀⠈⠁⠿⡀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠸⡃⢀⠏⠉⢡⡀⢈⣑⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⢱⠃⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⣦⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠄⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠈⢳⠲⠂⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⢂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣟⠂⠈⣇⣠⡀⠀⠀⢀⠀⠀⠀⠀⢰⠖⠀⠀⢨⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⣤⠄⠀⡰⠁⣀⣴⠗⢲⡧⢀⠄⠊⠉⠢⢄⠀⡶⢂⡄⠀⠘⠃⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣟⡛⠁⠀⠀⡇⡰⠁⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⣰⡷⠋⠀⠠⠁⠠⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠀⠀⠀⣀⠞⠉⠑⢄⠠⠀⠀⢀⣇⡀⠈⠑⠦⣲⣍⢡⡀⠐⡤⠔⢀⣁⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢴⠖⣠⣴⣾⡟⠀⠀⠀⠀⠑⠤⣠⣾⢝⡹⡧⢆⡠⢀⢙⢆⠈⢠⡁⢠⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣉⠓⣪⠷⣫⠞⠀⢰⠊⡠⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠈⠛⠛⠋⢩⠃⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠘⠁⠲⢆⡐⠀⢀⠊⣩⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⡴⠒⢰⠃⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠚⣀⠸⡍⠚⠣⢄⢀⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡀⠀⢀⡜⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠶⠂⠀⠠⡇⠀⠀⢀⢈⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢤⣤⠴⠶⠷⠀⠀⠀⠀⢣⡀⠀⠀⣀⠐⠂⢠⡄⠠⡀⣠⣄⡍⠈⠀⠀⠀⠘⠲⠤⢿⣿⣿⢋⣶⠕⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠒⠀⠐⢺⠁⢀⣄⣀⢠⣄⣹⡷⣏⡀⢀⡀⡾⣿⢙⡻⠷⡼⡄⠠⢄⣀⢠⣤⠤⢐⡶⣿⠟⢁⡺⢷⠲⢀⠄⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⣿⡙⠗⣜⡻⢋⡉⣍⣧⣉⢫⡾⡿⠿⣛⡦⣀⣠⡍⠰⣉⣡⣱⡖⠨⡉⣠⠖⠶⠋⢃⢨⣯⡶⠠⣭⣥⣋⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣠⣤⡀⠀⠿⣧⣤⠌⠋⠙⠋⠀⣹⣩⠿⠧⣤⠠⣆⣁⣴⣷⠶⡿⢋⣘⣆⣀⠐⢉⠁⡔⠀⡠⠗⠶⠥⣬⠂⡤⡼⠅⠻⡿⠥⠈⠙⠓
⠀⠠⠤⠒⠒⠉⠉⠁⠀⠀⠀⠈⠛⠋⢰⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠂⠉⠰⠎⠲⠘⠉⠁⠀⠈⠉⠐⠤⠒⠉⠁⠀⠀⠀⠀⠈⠉⠁⠞⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠆⠂⠄⠄
⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣸⣶⣀⢤⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣴⣴⡆⠒⢲⣤⣀⡀
⠀⠀⢀⠆⠀⢀⡀⠀⠀⠀⠸⣅⣼⠀⠀⠀⠀⠀⠻⣿⣿⣼⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⣸⣿⡿⢿⣿⡷⣷⢟⣿⣿⡧
⠀⠀⣸⢷⠘⣿⡿⠀⠀⠀⠀⡾⣧⠀⠀⠀⢀⣄⣠⡿⣿⣽⡿⢿⣿⣿⣿⣿⡟⠀⠀⠸⡸⠽⣸⠸⠿⠷⠧⢯⠯⢟⡇
⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠉⠉⠉⠀⠈⠉⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀
⠀⠀⠀⢰⠀⠀⠀⣤⠀⢸⣿⠈⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡿⠛⠛⢛⡇
⠀⠀⣾⣿⣷⣶⣾⣿⣶⣾⣿⠚⡗⢺⢀⣶⢶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢲⡀⠀⠀⢀⣴⢾⣷⣶⣷⣶⣶⣾⣷⣶
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢇⣠⣤⣤⣤⣼⣿⣿⣷⡆⠀⠀⠀⢸⣿⣦⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⢿⣄⣼⠛⠛⠻⣅⣼⠟⠛⠋⠉⠀⠛⡏⠀⠀⠀⠸⣧⣸⠟⠃⠀⠀⠀⢸⡏⠁⠸⣿⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⠂

⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⢸⡄⣯⠉⠉⢹⡇⢀⣦⡾⠋⠙⠛⠶⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⡾⢿⢹⣷⠤⢾⡿⠿⢿⡿⠿⢷⣤
⠀⢀⣾⣷⣿⣶⣶⣶⣿⡿⠋⠀⠀⠀⠀⠀⢸⠟⠁⢀⠿⣀⡀⠀⠀⠀⠀⠀⣤⣦⣤⣧⣼⣶⣿⣀⣸⣷⣀⣸⣧⣀⣸⡏
⠀⠘⢛⣻⠿⠿⠿⠿⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⠈⠁⠀⠀⣒⡀⠀⡟⣻⣿⣿⣿⣿⡾⣶⢶⣦⣤⣴⣶⣴⣤⠁
⠀⠀⢿⣿⣒⣒⣒⣚⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣶⠀⣠⣭⣤⠀⠁⠘⢷⣴⠏⠈⠉⠉⠁⠿⣤⠿⠻⣤⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣽⣿⣯⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣐⠝⡄⠀⠀⠀⠴⠃⠈⢣⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠀⠀⠀⠻⣂⣀⠀⠀⢱⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠍⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⠀⠈⢦⡀⣉⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠊⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣩⣎⣀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔⢥⠄
⠀⠀⠀⠀⠀⢠⣦⠆⣀⠀⢀⠀⠁⠄⠓⣒⠋⠀⢀⠤⡀⣀⠿⠀⡭⡾⡀⣰⠅⠀⠀⠀⠀⠀⢉⠖⠁⡠⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⢈⠁⣚⡓⠀⢀⠄⠀⡠⢦⣰⡇⠂⠀⠀⠀⠉⢁⢐⠕⠀⠈⠁⠈⠀⢀⠀⠀⠔⠀⣠⠚⣇⠀⠀⠀⠀⠥
⠀⠀⠚⡂⠃⢠⢀⣀⣀⠀⠁⡠⠂⡁⠚⠛⠁⠀⠀⠀⣀⠀⠀⠁⠲⠆⢈⡁⣠⡄⠈⠀⠀⠀⠊⢀⠞⠀⠀⠀⠀⠀⠀⣓
⠀⢠⡄⢁⣠⣈⠛⠟⠋⠡⠊⠤⠀⣀⠄⠈⠀⠀⡀⠀⠀⠠⠀⠁⠀⠑⠺⠣⠄⡄⠰⠤⠀⢀⠐⠁⠀⠎⠀⠀⠀⠀⡂⠘
⠀⠀⠀⢀⠀⡀⠀⠀⠀⢠⠄⣤⢀⡍⣠⣆⡄⢠⠀⠀⠀⢀⡀⣀⡀⠀⠐⠐⠪⡱⠤⠤⢒⡀⣀⠀⡁⣀⠃⠀⠀⠀⠡⠄
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠁⠉⠉⠉⠉⠁⠉⠉⠑⠀⠉⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⠶⡶⠒⠶⠶⣶⣶⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣔⣦⣀⣀⣤⣤⣼⢸⠀⣇⣼⣇⠀⡇⡇⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣬⣿⣿⣿⣿⣾⣿⣿⣿⣿⣳⡇⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣷⣶⡶
⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⢻⣿⣿⣿⣿⣷⠚⠛⣛⣛⣛⣛⣛⣒⣒⣒⣒⣀⣀⣀⣀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢷⣾⣿⡏⠀⣽⠃⠀⠀⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣛⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⢃⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣛⣛⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢾
⠀⠀⠀⠀⠀⠀⠀⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠁⠀⠒⠄⠀⠀⠀⠀⠀⡇⠉⢙⠁
⠀⠀⠀⠀⠀⠀⢸⡏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣄⠐⡆⡔⠆⡖⢾⠀⠀⠀⡠⠲⡛⢽⣦⣱⡦⣀
⠀⠀⠀⠀⠀⠀⡆⢹⢿⡿⢿⠤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠮⠃⠁⠑⠀⠁⡠⠀⠀⠀⠀⢀⣗⠀⢻⣿⡃⡎⠀⠢⡀
⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⢸⡄⠈⠉⠉⠉⢡⠹⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣤⡤⠐⠁⠀⡠⠃⢠⣎⡇⢀⣾⣿⡿⠉⣒⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠈⡿⣧⣸⡇⠀⡀⢠⢲⢾⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡌⠀⠀⠈⠆⠐⢹⣛⣋⣉⣩⠭⣷⡀⠀⠉
⠀⠀⡔⠀⠀⠀⣯⢹⡇⣿⢿⡄⣴⡅⠈⢉⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⢸⢇⠀⠀⠀⢹
⠀⢸⡇⠀⠀⠀⡧⣜⢯⡟⢹⡧⠛⠷⠳⢸⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢘⣎⣀⣁⡀⠀⠘
⠀⢸⡇⠀⠀⠀⡇⣿⣇⡇⣿⡇⢡⡍⢹⡼⣹⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⠀⢀
⠀⠘⣇⣀⣀⣀⣀⣇⠈⠃⢺⣷⣛⣛⣿⣿⣿⡾⠤⢤⡄⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠙⡆⠀⠀⢀⡟⠀⠀⠀⣠⡏⠀⢸
⠀⢠⡖⢚⢷⡟⢯⠙⠄⠀⠠⠤⠿⢸⣞⠳⠾⡟⢳⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣇⣀⣀⡁⢈⡇⠀⠀⣼⠀⠀⠀⡴⣯⠀⠀⣟
⠀⢸⡇⠈⠠⣧⢸⠆⠋⠉⠛⠚⠋⠉⣿⡊⡉⢿⢸⡇⠗⠀⠀⠀⠀⠀⠉⣀⠤⠀⠀⠀⠘⢢⡆⠠⠰⡇⠀⣧⠀⠀⡸⠀⠀⡐⠁⡇⠀⠀⡀
⠀⠀⠻⠮⠶⠿⠚⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠰⡇⠀⢹⠀⠀⡃⠀⠀⠁⠀⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠷⠶⠶⠷⠀⢸⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡆⠀⢈⠂⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣀⣩⣷⡶⠦⠬⠭⣭⡭

⠀⠀⠀⠀⢀⡴⠉⠀⠣⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠸⡇⣶⡀⠀⠀⠀⠀⠀⠾⠯⣟⣀
⠀⠀⠀⠀⠀⠓⣿⣅⠀⠀⢠⡶⠒⢲⠶⠦⠌⠹⠿⣶⡶⠆
⠀⠀⠀⠀⠀⠀⢹⣿⣆⢀⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠈⢸⣿⣿⠁⠀⢸⠛⠛⠷⠶⢦⣤⣄⣀⠀⠚⠃⠈⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠸⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣄⢹⣄⣠⣤⣄⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⡆⠹⣿⣿⡈⠛⠉⠉⣿⣻⣿⡷⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣿⣷⠀⠀⠀⠻⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⢀⢀⠂⠙⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⣀⢹⣿⣤⣤⣤⠘⣷⣿⣿⣿⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠸⣷⣇⢻⣷⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣛⣛⣄⠛⣛⣛⣿⠧⣤⡤⣤⣬⡤
⠀⠀⠀⠀⠀⠀⠄⠠⡟⠛⣊⡷⠈⠉⠈⠀⠀⠀⠀⠃⠀⠠⠜⢻⣯⣍⣉⣿⣿⣿⣶⣿⡷⠶⠶⢿⣀⡁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠇⠀⠀⠳⠀⠰⣿⣿⣿⣿⡿⣿⣷⣿⣿⣻⠿⠏⠉⠉⠿⢴⣿⠺⣷⡙⢻⡆
⠀⠀⠀⠀⠀⠜⠀⠀⠁⠀⠈⠁⠀⠁⠀⠐⡄⠩⣿⣾⡿⢿⢛⣿⣍⣿⣿⣤⣄⣠⣤⣁⣼⣯⣤⣿⣱⣾⣷⣀⣶⣄
⢀⣤⣴⣄⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠐⠀⠀⠚⣻⣿⣭⣿⣵⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⠿⠿⠿⠷⠤⠤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣤⣷
⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠀⢸⡿⠀⠀⠀⠀⢠⡤⠤⡤⠄⠀⠀⠀⠀⠀⠀⢰⡷⣄⡀
⣤⣶⣶⣴⣶⣤⡀⡁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣷⢶⡇⣰⣄⠀⠀⠀⠀⠀⣿⡦⣿⢃⣀⣤⡀⣤⣤⣀
⠉⢩⣉⣙⣛⣛⣏⣡⡀⠀⠀⠀⢀⢷⡀⠀⠀⠀⢹⣿⣛⣟⣛⣻⣴⣶⠀⠀⠀⠀⠀⠻⠿⣿⣻⡷⠿⢿⣿⠦⣴
⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁
⠀⢠⣶⣶⣾⣷⣦⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄⡀⣄⠀⡇⠀⠀⠀⠀⠀⣠⣴⢶⣶⣦⣿⣿⣿⡶⣤⣄
⠀⠚⢿⣟⣿⢿⣿⣿⣿⣿⡷⣤⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣶⣷⠀⠀⠀⠀⠀⣿⡿⡆⢹⣿⢻⣿⣿⣾⢿⡇
⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉

⣠⣤⣤⡤⣤⡤⣤⣤⣤⡾⡫⢭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠉⠙⣻⣿⣿⣿⣿⣟⣴⣿⣿⣷⣦⠀⠀⠀⠀⢰⠒⠂⠀⣀⡤⠖⠛⠁⠀⠀⣤⣶⣾⣶⣗⣶⣦⡄
⠀⠀⣾⣿⣿⣿⢹⣿⠛⣿⣟⣿⣿⠉⠀⠀⠀⠀⣾⣷⣌⡾⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣋⣻⣿⣷⣆⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⣤⣤⠄⣙⡋⠞⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠰⠀⠛⠿⠁⠈⠁⠀⠈⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⠀⠀⠠⠀⣆⠘⣃⠀⠀⠒⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣿⣾⠇⠀⣀⡀⢐⠀⠀⠀⠀⠁⠀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⢃⡀⢴⣖⣤⣬⣤⣤⣤⣬⣤⣶⡂⠛
⠀⠀⠀⠀⣶⣶⣦⣆⣀⠀⠀⠀⠀⠀⠁⠀⢀⣿⣇⡀⠀⡀⣠⡼⢽⣿⣿⣿⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣛⣛⣛⣿⣿⠀⠀⠀⣶⠀⣀⣴⣿⣿⣧⡟⡈⢁⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⣿⣿⣿⠿⢿⡀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡤
⠀⠀⠀⠈⠋⠙⠉⠃⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣐⣶⣼⣿⠛⠻⣾⣿⣏⣉⣉⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢹⣯⣭⣿⣿⣾⣿⣿⣿⣯⣭⡭⠭⠭⠭⢿⣉⣉⡙⣿⣯⣭⣿⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢤⡉⢉⣀⣀⢀⠀⠁⠛⢻⡇⠐⠒⠒⠒⢚⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣤⣤⣤⡤⠈⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⣀⣀⣤⣤⢤⣖⣷⣲⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢀⣴⣿⣿⡏⠋⠉⣍⣋
⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⡿⠷⠶⠟⠿⣿⠾
⠀⠀⢈⡀⢀⢸⠀⠀⠀⠀⢸⠀⢀⡄⣤⣴⣶⣤⣒⣶⡄⠀⠀⠀⠀⢰⣤⣤⣴⣦⣤⣄⣀⣀⡀⢠⡤
⠀⠀⣾⣿⣤⣾⠀⠀⠀⠀⠼⠀⠈⠋⠹⣽⠿⣽⠿⡽⠥⠾⠇⠀⠀⠸⢹⣟⠿⣿⣿⣯⣿⣯⣿⣿⣶⣶
⠀⠀⠉⠉⠉⢉⡀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⠟⠛⠻⠿⠛⠿⠟⠛
⠀⠀⠀⣴⣶⠋⢻⠃⠀⢀⣭⠀⢀⣀⣄⣦⣀⣸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡆
⠀⢠⣿⣿⣿⡄⠸⠀⠀⢘⢘⡃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⣤⣄⠀⢠⣏⣿⣿⣷⣶⣿⣶⡆⡀⡀
⠀⠀⠉⠉⣩⠥⢀⣄⠀⢐⢐⡂⠀⠈⠈⠻⠟⠉⠉⠛⠛⠿⠛⠒⠻⠿⠀⠀⠉⠙⠞⠉⠉⠉⠻⠛⠛⠻
⠀⠀⣠⣞⠁⠀⠀⠛⣀⣀⣀⣂⣀⠀⠀⣰⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣏⢑
⠀⣸⣶⣃⣷⡀⠀⠀⠀⠀⠀⣀⡄⠀⠀⣿⣽⣠⣄⣄⣠⣤⣄⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣤⣤⣤⣀⡀
⠀⠛⠻⡿⠻⡷⠀⢀⣠⡾⠟⠉⠉⠀⠀⠉⠈⠛⠻⠿⠛⠛⠿⠻⠗⠀⠀⠈⠙⠛⢿⡿⠋⠛⠛⢿⣿⠟⠃
⠀⠀⠀⠀⣀⣤⢞⠛⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣄
⠀⠤⣶⣟⡋⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠟⠋⠉⠀⠀⣿⡇⠐⠛⠛⢿⣿⣿⣿⡿⢡⣾⣿⣿⣦⡀
⠀⣤⣤⣽⣿⣿⣤⣾⣷⡆⠀⠀⠰⠿⢿⣿⣦⡄⠀⠀⠀⠀⠀⢯⠀⠀⠀⢰⡟⢻⣿⢿⣿⣿⡟⢻⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡤⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣆⢄⣀⡠⠈⠉⠉⠉⣛⣛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣩⣷⡶⠈⢻⣭⠤⣤⠒⠒⠒⠊⠉⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⡁⠉⠁⠚⣡⣾⠛⠉⡠⠖⠊⠉⠋⠈⠁⠀⠄⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⢻⡔⠚⠉⢈⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡿⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣠⣀⣀⡀⠤⡰⠁⠀⣾⠗⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣿⠀⣿⣴⣿⠉⣠⠃⠀⣸⡏⣠⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣆⣼⣿⣿⢀⠇⠀⢠⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡲⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠈⠓⠚⠛⠿⣿⣿⣿⠏⠀⠠⡞⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡁⠀⢨
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡙⠗⠀⠀⠸⠁⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠷⠶⠾
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢻⣄⢄⣀⣰⡦⠜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⢀⠀⢘
⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠈⠀⠈⠻⠏⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠀⠳⠄
⠀⠀⠀⠀⢀⣤⣊⡍⠀⣀⣀⠀⠀⢀⠀⠀⢀⣠⠤⠀⠁⢀⠭⠄⠀⠈⢾⣶⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⢠
⢀⡀⢀⡀⠉⢀⠈⠙⡆⢀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠒⠂⠡⠠⠀⠀⣀⣤⠁
⠈⢳⣾⠇⢾⣿⣿⡆⠘⣄⣃⠀⠀⠀⠀⠸⠀⠀⣠⣤⣀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰
⠀⠈⠁⠈⢀⠉⠛⢃⢀⣿⡟⠁⠀⠀⠀⠀⠉⠈⡻⣿⣿⣧⠀⠠⢄⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠐⠂
⠀⠀⠀⠀⠀⠛⠻⣿⣿⣶⡶⡆⠤⣀⡦⢀⣀⡀⣀⠈⠁⠀⣰⢬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠂⠀⠸⠙⠚⠹⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⢒⣂⣀⣀⣐⠒⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡦⢖⣉⠤⠒⠊⠉⠁⠀⠀⠀⠀⠈⠉⠑⠂⠬⣉⡲⣔⢤⣄
⠀⢰⡖⢀⠀⠀⠀⠀⡨⣋⣠⡍⡐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣄⡙⢄⠀⠀⠀⠀⠄⣶⡄
⢠⣾⠻⡀⠑⢄⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⣶⠻⢉⠉⡛⣶⡀⠀⠀⠀⠀⠀⠀⢈⠑⢄⠑⢄⡠⠊⢠⠟⣷
⢠⡽⠄⠈⢆⠈⠣⡎⠀⠀⡇⠀⠰⡀⠀⠀⠀⡿⠛⠛⠾⠿⠛⠓⣿⠀⠀⠀⢀⠃⠀⢸⠀⠀⢣⠌⠀⡔⠁⡠⢯
⠘⢇⠈⠢⡀⠑⢄⠈⢂⠀⡀⠆⠀⢱⠀⠀⢰⡇⠐⠶⠀⠀⠶⠀⢸⠆⠀⢀⡇⠀⠀⢨⠀⠔⠁⡠⠊⢀⠔⠀⡼
⠀⢠⡳⣀⠈⢦⡈⠣⣄⣑⡵⠀⠀⠀⠑⢴⣾⣷⡦⠠⠀⠠⠄⣶⣾⣷⠤⠁⠀⠀⠀⣦⣊⣤⠞⢀⠔⠁⣠⢾⠄
⠀⠀⠙⠉⠳⠶⠛⠟⠋⠊⠉⡖⢤⡄⠀⠀⠀⠻⠧⡘⣟⣻⢃⠼⠏⠀⠀⠀⢠⠤⠐⠉⠃⠛⠻⠛⠶⠞⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠙⢦⡄⠀⠀⠀⠘⠋⠙⠡⠂⠀⠀⢠⡴⠃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡸⢁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⠄⠀⠀⠀⣸⣇⠀⠀⠀⠐⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠐⠀⠁⠀⢉⠉⠀⠉⠀⠂⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⠃⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠁⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⢿⣶⡤⢤⡤⢤⣶⡿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⠢⢄⡘⢃⡠⠐⠙⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠆⠳⡀⠀⠀⠄⠀⠈

⠀⠀⠀⠀⢀⡀⠀⡀⠀⣴⠖⠀⢠⡄⠀⠀⢠⡆⠀⠀⣲⡆⠀⠀⠀⢰⣯⡀⣰⣿⠂⢀⣤⡀⠀⡏
⠀⠀⠐⠒⠉⠄⠱⢅⢀⠞⠁⠈⢻⠇⠀⠀⢺⡧⠾⢻⡯⠽⢶⣶⡦⠹⢿⣧⢼⡉⠐⠺⡇⢀⠀⣅
⠀⠀⠀⠸⠇⠀⡀⠀⠀⠀⣀⡤⠛⠒⠒⠒⡛⣡⠀⠘⢡⣄⡤⢤⡤⢤⠰⢃⣠⠄⠋⠘⣀⠚⢿⣿⠖
⠀⠀⠀⡀⠀⠸⠃⣠⠴⠚⠀⠀⢠⣠⣠⡘⠣⠉⣔⠉⠨⠿⢴⠃⠼⢭⢧⡌⣑⡒⢦⠀⠽⢠⢌⣴⣤⠗
⠀⠀⠀⠃⠀⣠⠜⠁⢠⡀⣳⡴⠟⡫⠀⠊⠈⠈⠇⠣⠀⠀⢊⣉⣀⣬⣤⡀⣀⣠⠀⢂⡀⣈⣿⠁
⠀⠀⠀⢀⡠⠀⠀⢲⣔⠷⠧⠀⠈⠂⡠⡼⠚⣳⣤⠋⡉⠹⡟⠒⡂⣦⢀⡌⠁⠬⠡⠜⠃⠀⠸⠆
⠀⠀⠀⠸⠁⠀⠒⡦⢣⡆⢨⢀⠔⠋⠇⠉⠀⠈⠓⠓⠀⠀⠏⡇⢡⣏⠸⣁⣶⣠⠆⠀⢡⣀⢰⠄
⠀⠀⠀⡄⠀⠈⠿⢄⠁⠐⡶⢦⡝⡦⠚⠡⠷⣀⠈⣀⠖⣾⢺⡅⣟⡫⢖⡵⡜⠹⢠⡘⣄⠡⢨⡀
⠀⠀⠀⠆⢘⣿⠷⡦⣡⣷⠖⠀⡖⢱⠀⠀⠀⢑⠖⣶⣈⣻⡖⠶⣹⣿⢏⢬⠄⠁⠈⡃⠉⢠⡘⡀
⠀⠀⠀⣧⡌⠁⢈⣄⠋⡆⠈⡓⣀⣠⠰⣦⢤⣞⢲⡆⢿⣿⣿⢺⡃⣿⢁⡤⣌⠐⠁⠐⠧⢀⣿⠅
⠀⠀⠀⠘⠀⠀⠿⣛⣷⡾⠶⣬⣥⣵⡿⢼⠗⠚⢷⡑⢶⠯⠽⠙⣼⢏⡿⢼⡛⣇⢀⠀⢾⣿⣿⡀
⠀⠀⠀⠀⠀⠶⠀⠛⠙⡁⠉⣉⠁⠀⠀⠀⠘⠶⠂⢉⠗⡳⢞⠋⠹⡌⠳⠞⢣⡿⠨⠀⢨⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠜⠀⠓⠁⠱⢤⣗⣠⠀⠂⢅⠀⡙⠀⠑⢢⡈⠉⡟⠡⠄⡂⢀⠟⢰⢸⡂
⠀⠀⠀⠀⣧⠀⠀⠀⠐⠲⡀⠂⣤⣶⣶⡌⢿⣿⣿⠈⠀⢄⡒⠠⢈⡘⡃⠽⣶⠶⠟⠈⠠⠃⢸⠃
⠀⠀⠀⠠⢿⠄⠀⠀⠀⠀⠈⣲⣽⣿⣿⠇⠈⣿⣧⠖⠦⠆⠒⣉⣠⡖⣒⢶⣂⣠⡶⠄⣉⡺⢬⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣶⠖⠈⣰⡟⡋⢁⡺⣀⣌⠀⢁⣴⣿⣿⢿⡿⠭⣈⣩⣽⡷⠒⠚⠉⠉⢻
⠀⠀⠀⣀⢬⣷⠷⠋⣡⣴⠞⢁⠉⢸⡆⠙⠢⣤⠴⢉⣼⡟⢡⣌⡴⠞⠡⠐⠛⢿⡦⢴⠄⠀⢸
⠀⠀⠀⠀⠀⠉⠀⡺⠹⠏⠀⠈⠀⢏⠀⠂⡄⡪⢶⣻⢟⣡⠶⣯⡀⠀⠁⠀⠀⠾⣿⡎⢀⡅⢸
⠀⠀⠀⠀⠀⠀⠈⠀⢀⢶⠀⠀⠀⠸⠤⣾⡍⣀⡾⣡⢏⡅⠀⠈⠹⣦⠀⠀⠀⠴⢿⣧⣟⢁⣼
⠀⠀⠀⠀⠀⣄⠀⠈⡈⠉⠀⠀⠀⠀⠠⠘⡻⠀⢳⡏⠀⠀⠐⠀⠀⠈⠻⣤⣮⠶⠛⣿⣭⡄⢸
⠀⠀⠀⠀⣀⠚⠀⠰⠁⠈⠰⠀⠀⠀⠀⠂⢉⣾⠋⠙⠳⢦⣶⢶⣄⣂⣼⢟⣧⣀⢈⡙⣿⠄⢸⠄
⠀⠀⠀⠀⡇⠠⣌⠠⠀⠇⠀⠀⣜⠀⠀⣇⢩⣇⡐⠈⠀⠘⠻⢻⣿⣿⣇⡸⠛⢙⣇⠀⢻⣶⣾⡀
⠀⠀⠀⠀⠁⠐⡀⠀⠁⠀⠠⡄⠔⠀⠀⠰⢾⣿⣻⣧⡠⡀⢰⣾⡿⣡⠈⠙⠶⣏⡉⢻⡾⣿⢸
⠀⠀⠀⠀⠇⠀⠐⠁⠠⠀⡇⣿⠀⠀⠛⠂⣟⠉⠿⢿⠙⢿⡿⡟⣷⣶⠷⢦⣴⣷⣏⡓⢯⣿⣿⢀⡀
⠀⠀⠀⠤⣂⠀⠈⢁⠀⠀⡀⢉⠸⠼⠥⡬⢥⡠⠤⣤⠠⡬⢤⡩⠭⠭⣄⣞⠩⡤⠭⠭⠭⠭⣿⢿⠷⠖
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⣀⣤⡄⠀⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢐⣀⣀⣀⠀⠀⠀⠀⢀⠔⠒⣤⣄⣴⣾⣿⣿⣿⡧
⠀⠀⣤⡾⣿⣿⣿⣿⣿⣿⡻⣿⡇⠀⠀⣄⠀⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠷⠽⠟⠀⠀⠘⠿⡵⠏⠀⢀⣼⣿⡷⠋⢿⣿⡿⠉⠉⢿⣿⡟⠉⠁⠀⠀⣿⡿⢻⣿⣿⣿⠻⣿⡟⢿
⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣉⣀⣀⡤⠤⠤⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠉⠁⠀⢀
⠀⠀⢠⡟⠀⢻⣦⢀⣀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⢰⠋⠉⢣⠀⢀⣤⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣰⠛⠢⡀
⠀⣤⠏⠀⠀⢠⡁⢠⣤⣄⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⡇
⠀⠛⠿⠶⠂⢸⣶⣿⣿⣿⠀⠀⠀⢸⡏⢡⠉⣿⡿⠿⠿⣿⡏⣉⠙⣿⠉⠀⠛⣟⡿⣿⡟⠛⠛⠻⣿⠿⣻⠛⠛⢻⣻⠛⠁
⠀⠀⠀⠠⠞⠻⠟⠇⠿⠸⡃⠀⠀⠘⢷⣤⣴⠟⠀⠀⠀⠹⢧⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀
⠀⠀⠀⢰⠛⠛⡆⣴⠀⠀⠃⠄⢀⠀⡤⠠⡀⠀⢀⠤⢤⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢀⣾⠋⡇
⠀⠀⣠⣼⠀⠀⢰⣿⠀⠀⠀⣼⣾⣷⣷⣤⡆⠀⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣴⣶⣶⣦⣴⣾⣄⠘⡿⠀⣿
⠀⠀⠿⣿⣷⣶⢾⠿⠧⠀⠀⢹⢿⠿⡿⣿⢧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⠀⠀⣿⣿⡿⠿⢿⣿⣿⡿⠿⠇⢸⣿⠇
⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⣀⣈⡉⠉⠉⠉⠉⠀⠀⠈⣹⡆⠀⠈⠋⠈⠉⠁⠉⠋⠀⠀⠈⠋⠁⠀⠀⠙⠛⣁⣤⣤⣤⡀
⠀⠠⠀⣤⣤⣴⠶⠾⣻⠯⡉⠀⠀⠀⠀⠀⢀⠤⣪⡾⠁⡇⠀⠀⣀⣆⣀⡏⠉⡏⠁⠀⠀⠀⠄⢠⡀⣴⣾⣿⣿⣿⣿⡧
⠀⢸⣤⣿⣿⠆⣤⡄⣷⣤⣴⠀⠂⣬⠀⣿⣷⣾⠟⠀⠀⠁⣀⢸⣿⣿⣿⣁⣀⣿⡇⠀⣶⣿⣶⣾⣷⣿⣿⣿⣿⣭⣾⡇
⠀⠿⣿⡿⢿⡿⠿⠿⢿⣿⠿⠀⠀⡩⠿⠿⠿⢇⠀⠀⠀⢀⣿⣬⣿⣿⣿⣿⣿⣿⣧⠀⠛⢿⣿⠋⠉⠻⠟⢻⣿⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⢠⠆⠀⡆⢣⠀⠐⣄⠀⠀⠈⣷⠀⠀⠈⣦⠀⢠⠇⠀⠀⠀⠀⠀⡌⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠘⠄⡈⠀⠀⣧⠀⢀⢀⠈⡄⢠⠀⢱⠀⢠⡄⠈⢁⣼⠀⠀⠀⠄⡀⣸⠏⡄
⠀⠀⠀⠀⠐⠒⢾⣇⠀⠀⠹⣇⢿⣏⠀⠸⠛⠀⢸⡆⠘⠇⠀⢸⡇⠀⣆⣰⠏⣴⠋⠀⠇⢠⠴⠂
⠀⠀⠀⠀⠀⠀⠻⠉⠉⠲⣄⡛⢘⠃⢠⣤⣰⣦⣼⣧⣶⣤⢠⡟⣤⣀⣍⣩⣼⢇⠀⢒⠀⢀⡴⠁
⠀⠀⠀⠈⠲⠦⡄⣄⣿⠀⠈⣷⣿⠟⠊⠙⠈⢡⠈⠁⢠⠁⠀⠁⠉⢻⡿⣿⡃⢸⣟⠃⢠⡞⠀⠄
⠀⠀⠀⢀⡀⠀⠀⣿⣿⣷⣤⡉⠉⢁⠀⠀⢈⣤⣼⣲⣬⣄⣀⠀⠒⠈⡃⠈⢷⣬⢨⣴⡿⠉
⠀⠀⠀⠈⠻⡖⢤⣤⢻⠏⠸⡇⠷⢦⡆⠀⠈⠙⠛⠉⠋⠁⠀⢻⡓⢺⣷⣶⠛⡿⢳⡟⢀⡄
⠀⠀⠀⠀⠀⠈⣀⠉⣿⡔⠄⠺⠗⠋⠁⠐⢂⣴⣦⣰⣦⠀⠀⠈⠓⠺⠆⠻⠒⢻⡈⠇⠞⠀⣠⠆
⠀⠀⠀⠶⡖⠀⢼⣷⣜⡀⠈⣦⠉⠀⠀⠒⠀⠈⠉⠩⠄⠀⡤⠀⠀⠀⢸⠗⠀⢨⣇⣼⢶⡾⠛⠉
⠀⠀⠀⠠⠼⣄⣤⣿⡿⢃⠀⣀⣠⡤⢤⣤⡉⠰⢿⠾⠗⢀⣤⠔⢶⠶⢼⣀⠀⠈⢿⣷⠨⢄⡀
⠀⠀⠀⠀⠊⠁⠰⡌⡅⢠⡞⢋⡤⠶⠲⠦⣙⣾⠀⠀⣴⢊⠴⠶⠶⠶⠦⡍⣳⠀⢲⡟⢀⣦⢤⠂
⠀⠀⠀⠀⠉⠑⣄⠙⣦⣸⣡⡷⠶⠶⠖⢶⠟⡸⠃⠈⢫⡈⢟⡛⠓⠓⣳⣞⣦⣱⣿⡴⠋⠄
⠀⠀⠀⠀⠀⡀⠸⢿⡿⠓⠸⣿⣍⣛⣭⣱⠞⣁⣼⣷⣀⠙⢳⠶⢿⣯⠿⠟⠃⠀⠻⠟⢠⡀
⠀⠀⠀⠀⠀⠃⠀⠐⢄⠐⠀⠀⠉⠉⢈⠹⠉⣫⣿⣿⣯⡁⠀⠈⠀⠉⠀⠀⠀⠠⠊⠀⠀⡁
⠀⠀⠀⠀⠀⠰⡄⠀⠀⠱⣤⡴⢶⣄⢈⡰⢤⣿⣿⣿⣿⣿⢷⣦⡀⣾⡟⢳⡈⠀⠀⢀⡈⠁
⠀⠀⠀⠀⢤⣤⡰⣦⣤⡶⠄⣴⣎⣉⡽⠷⠁⣹⠏⠾⡛⣷⠀⠘⢫⣍⣷⠗⠙⠓⣶⡞⠛⣿⠟
⠀⠀⠀⠀⠀⠹⣖⡀⠋⠀⡀⣠⠿⢻⣿⠲⣤⣧⣤⣤⣤⢼⣤⣴⣿⣿⠙⢦⡁⡈⠀⠐⠶⡃
⠀⠀⠀⠀⠀⠀⡼⢂⣄⠀⡼⠃⢤⢸⣿⣦⣻⣅⣅⢹⡁⣸⣿⢿⣹⡧⢰⠈⢳⡄⣠⠌⠀⠁⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠙⣻⡁⠀⡴⠀⠟⢻⡿⣿⣠⣄⣇⠿⢴⢦⢱⠇⡜⠆⣀⡹⣇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡄⠀⠀⡰⠇⠿⣆⠀⠐⣢⠛⠀⢈⡁⠻⡇⠈⠘⠘⣏⠛⠀⣠⠟⠉⠻⣦⠄⠀⠃
⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠈⠳⣄⢹⠇⠬⠅⢢⡶⢾⠐⠂⠀⣿⢋⡴⠁⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡿⣀⠀⠀⠘⢦⠞⠀⠂⠀⣸⣧⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠁⠀⠀⠘⣆⠀⠀⠀⣠⠞⠀⠙⢦⡀⠀⢀⡀⠀⢀⡼⠃⠈⠳⣄⣀⣀⣰⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢙⣛⠉⠁⠒⣀⠒⣚⠳⣦⣶⣷⣤⠞⣛⠈⣦⡙⢈⡉⠩⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠚⠀⠕⠒⠞⠓⠈⢩⡾⠁⠘⠓⠒⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢦⡀⠀⠘⣶⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠤⢾⠋⠀⠀⣴⠃⠂⠠
⠀⠀⠀⠂⢀⣀⣀⣀⣀⣀⣘⠃⣀⣀⣈⠀⣠⠄⣀⣄⣠⣤⣍⡀⠀⠀⢠⣀⣀⡄⢩⣤⣤⣤⣠⣤⠀⠉
⠀⠀⠀⠀⠈⢯⡉⢉⣩⣭⣥⣀⢁⣍⠬⠀⣍⡇⡭⠁⠉⠉⢳⣀⠜⠃⡁⠀⠀⢠⣷⣤⡤⠀⣼⠇⠀⠄
⠀⠀⠀⠄⠀⠈⢷⡈⣿⣟⣽⠃⢊⣨⠊⡂⠘⠲⣇⠇⡯⡄⢸⡿⠿⢿⣧⠘⢆⠘⣿⣿⣇⣼⠃⠀⠀⠐
⠀⠀⠀⠀⠴⢶⠌⢁⡜⢋⠵⠴⡆⣩⢸⡗⠆⢹⡏⠒⣤⠇⢜⢧⠀⢱⢻⣶⡎⡰⡄⢈⣄⠩⠶⠶⠓
⠀⠀⠀⠀⠆⠀⠀⠀⢳⡌⠠⣦⡅⠆⢸⠃⠃⣼⠁⠠⣜⢀⣘⡘⠆⢸⡿⠜⢈⣷⢊⡾⠃⠀⠀⠀⠠
⠀⠀⠀⠐⢶⣦⠄⠀⠀⠛⡎⠃⢳⢆⠦⣔⠋⡅⢰⡇⢠⣂⢉⢹⣟⣉⠷⢀⠄⢉⣾⠁⠀⠀⠠⢴⠖
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⢟⣱⢎⣭⡼⢫⠖⢣⠮⠸⡄⡈⡻⠇⢈⡈⢳⣌⢃⠿⠁⠀⠠
⠀⠀⠀⠀⡄⠀⠀⠀⠂⠀⡄⢡⡾⢨⠇⠋⠀⡸⠀⠒⡃⠃⠀⠀⠈⠧⠀⢼⣿⣀
⠀⠀⠀⠀⠄⢰⠀⠀⡃⠀⡴⠋⠀⢚⣠⡴⠶⠷⡉⡭⠉⢉⣻⡟⠷⣶⣤⡨⢡⢿⡄⣀⠈⠀⠷⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⠥⢚⢛⣩⡄⢒⡶⠶⣶⣶⣿⣿⡦⢭⣝⠻⣰⣎⠱⣾⣆⠠⢘
⠀⠀⠀⠀⠀⢰⠀⡀⢁⣟⣋⣩⠉⠙⣛⡽⣛⣡⣶⣿⣿⣿⣾⡦⢄⣙⠒⢶⣤⠬⢽⡃⠘⠀⠙⠀⣀
⠀⠀⢀⣄⡀⠈⠀⠈⠸⣭⢔⣂⣈⣭⠴⠞⣯⢹⣿⣿⣿⣿⣿⡍⡳⠲⠤⠂⢙⣳⣦⡇⠀⠤⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣸⠋⠑⠀⠀⠖⣠⡅⠺⡿⣿⣿⢻⡿⠃⠘⢰⡀⠆⠀⠉⠹⡓⠀⡀
⠀⠀⠀⠀⠐⠐⢀⠤⡒⡿⢠⡔⣶⣦⠀⣁⢾⠛⡏⣧⠿⠬⢴⣇⣶⢦⡈⣴⡏⣱⡆⡧⢰⡟⡀⢀
⠀⠀⠀⠀⠀⠐⠁⡈⠋⣧⢸⣧⢸⣽⠟⣱⣺⣭⡤⠄⠴⠴⠶⠸⣌⠳⣿⣿⡇⣿⢧⣧⡯⠺⡅⠈
⠀⠀⠀⠀⠀⠂⡶⣞⣷⣾⣧⣛⠀⣿⣿⠉⠉⠀⠁⠀⠸⠀⠄⠀⠈⠉⠙⣿⠃⣶⣿⣿⠻⠚⢳⢄⡀
⠀⠀⠀⠀⡠⠞⠐⢧⡞⠹⢍⠇⠀⠨⡀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⣹⡴⡲⠉⢔⡎⠂
⠀⠀⠀⠸⣇⡈⡓⣀⣹⣧⣿⣶⠀⢀⠀⡄⠒⠠⠴⠊⠐⠀⠐⠒⠀⠠⠐⣁⠎⡼⡿⣿⣷⣿⣷⠒⣩⡛
⠀⠀⠀⠛⣍⠷⣀⣨⡛⣉⣁⣴⣆⢀⣀⡄⣀⣐⣸⡛⠋⡟⢙⡛⣳⢶⣤⣁⣴⣷⣦⠈⣿⠛⢙⠃⡙⢁⣀
⠀⠀⠀⠀⢸⣸⣭⣹⣭⠤⢝⡛⠿⡿⢟⠛⠛⠻⢿⠇⠰⠁⠸⡿⠟⠛⢛⡛⠏⠉⠣⠄⠂⠶⢛⠁⣽⠆⠹
⠀⠀⠀⠀⠸⠁⢿⣉⣥⣤⣴⣶⣶⣶⣷⣾⠳⢦⣾⡇⠀⠀⣺⣧⠆⠲⡶⢰⣿⣵⣾⣿⣿⣶⣦⠹⡌⣆
⠀⠀⠀⠀⠰⢦⣀⡙⠛⠿⠟⠙⠻⣿⣿⣯⠳⠄⣈⡉⠉⠉⢉⣀⡤⠞⠁⣿⣿⣋⡹⠟⡋⢩⣯⡲⣶⡣⠁
⠀⠀⠀⢀⠀⢸⣿⣧⣿⣥⣾⣿⣿⣿⡿⠿⡆⠀⠀⣿⠉⠉⣿⠀⠀⠸⡶⢿⣿⣿⣿⣿⣱⣿⣿⣿⣿⡷⡅
⠀⠀⠀⠀⢣⠐⠈⠻⠿⣿⣿⣥⡆⠈⠠⡀⠀⠀⣰⣿⠅⠀⣿⣀⠀⠀⠉⢀⠈⠉⠩⣿⣿⠟⠿⡋⢃⡀⠁
⠀⠀⠀⠀⠀⠀⠂⠰⢤⠀⢀⢈⡤⠖⠀⠀⠻⣶⠏⢿⢀⣠⣟⠳⠴⠆⠀⠀⠀⠋⠥⠄⠶⠎⠐⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠚⠪⠕⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢸⣄⣀⣰⡀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⡈⢃⣴⣾⠷⠿⠟⠓⠚⠻⢿⡿⣷⣍⣰⡀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣢⡿⠛⠩⠀⠐⠀⢴⠀⡁⠠⠀⠀⠀⠈⠙⠳⣮⣐⠀⡖
⠀⠀⠀⠀⠀⠀⠙⠒⣾⠿⣡⡐⢋⡍⡠⠏⢠⡇⠀⣭⠀⢙⣫⣤⡀⠹⡄⠈⠹⣾⣤⡆
⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠱⠅⣽⢸⠷⠖⣷⠁⢠⣿⣤⡼⡉⠀⢿⣞⡃⠀⠀⠈⢻⡿⣠⠂
⠀⠀⠀⠀⢀⣲⣿⠃⠲⠀⣿⡄⣆⣈⢳⡤⠗⣛⢾⣿⠶⠿⢧⣤⣿⣟⣣⣤⡤⠟⠀⢻⣧
⠀⠀⠀⠀⢩⠟⠩⠻⡿⣷⣮⣦⡼⢛⠻⡗⠀⠉⣸⡿⠀⠂⡈⢸⢿⣿⡿⢿⣀⣾⡧⠈⣷⡛
⠀⠀⠀⢠⣟⢀⠀⠂⣹⣽⣷⣿⠿⢟⣟⣻⣦⣶⣻⣯⣵⣤⣤⣾⣿⣿⣷⠞⠻⣇⣴⣿⢿⡟⠂
⠀⠀⠀⢸⣿⣾⣿⣾⣯⣫⠿⡟⠄⠐⠀⠀⢹⡉⣿⢹⠏⠏⠀⠀⢠⣿⣿⠦⣆⣿⣿⣉⣶⡏
⠀⠀⠀⠈⢉⡧⠐⢻⡧⠁⠀⣹⡆⠀⠈⠂⠀⢠⣴⣛⣿⡀⠀⠀⢸⡈⠻⣠⣶⣟⢩⣿⣿⡇
⠀⠀⠀⢰⣾⣿⡻⠛⠀⠀⠀⢻⡄⢀⣤⣴⣦⣬⡙⢿⢏⣥⣦⣤⣼⡃⠀⠀⠀⠹⣟⣿⠿⠳⠄
⠀⠀⠀⠀⢿⣿⡁⠔⠉⢡⣥⣬⠻⣿⣿⣿⣿⣿⢇⣀⠸⣿⣿⣿⣿⢇⣀⡁⠉⢲⣯⣧⣼⣤⣆
⠀⠀⠀⢠⣯⣨⢷⡠⠿⠻⠟⠊⣴⣈⠙⠛⣉⠰⢹⣿⡶⢨⣩⣽⠇⠉⠿⠿⠿⣦⣿⣟⣯⡿⣦⠞⠁
⠀⠀⠀⠀⢹⣿⣾⣷⡀⠀⠀⠀⠉⣇⠈⣥⢨⠆⢾⣿⣿⡤⢻⣇⠀⠀⠀⠀⠀⢸⡟⣻⣷⣿⠧⣄
⠀⠀⠀⠈⠹⠻⠻⣿⣿⣶⡄⠀⠀⠈⠻⢧⡀⡄⢾⠏⢳⠐⣸⠟⠀⠀⠀⠀⠀⢸⡇⣦⣽⡛⠀⢸⡆
⠀⠀⠀⢀⣿⣻⣶⢸⠜⠻⢾⠀⠀⢠⣶⣾⣷⣶⡼⢼⠎⣴⣾⣶⣦⡀⠀⠀⢠⡟⢿⣿⣏⣻⣄⡀⢀
⠀⠀⠀⠘⢛⣿⣿⣷⣿⣶⣮⡀⠀⠀⠉⠹⡟⢿⣗⣖⣺⣿⣿⠉⠋⠁⠀⣠⣾⣽⣥⡿⣏⠻⠋⠈
⠀⠀⠀⠀⢁⣷⡿⢛⣿⣿⣉⣽⢶⣤⡀⠀⣿⠓⣈⡉⡀⣠⡏⠀⢀⣴⣾⠟⢡⡿⣟⣢⣿⣾⣷⣤
⠀⠀⠀⠐⢋⢘⣿⣿⣿⡾⠟⣋⣿⣉⣹⠷⠾⣿⣿⠻⢿⣿⣷⣶⠟⢹⣤⡶⣿⢷⣿⢿⣿⣿⠇⠴⠎
⠀⠀⠀⠼⣿⡄⣩⢤⠸⣿⣽⡛⠻⢿⣋⢲⢤⣄⣙⣉⢛⣀⣠⠼⣿⣿⣿⣧⣴⣦⣴⣶⡿⣶⠀⠀⣄
⠀⠀⠀⣻⠛⠿⡟⢸⣶⣯⡿⠿⣧⣄⡙⠳⢷⣥⣹⣙⣏⣋⣭⡶⠿⢭⣯⣿⣯⣟⢿⣿⠓⣼⣶⣞⠁
⠀⠀⢰⣿⣶⣿⣉⣩⠟⡿⣿⣦⡌⠛⠿⣾⣦⣤⣬⣥⣠⣄⣠⣤⡶⠟⡛⣹⣏⣝⣿⠿⢤⣿⣭⣵⣦
⠀⠀⢸⣟⠁⣏⣀⣿⣀⢀⡁⠛⢛⣿⣶⣢⣠⠈⡍⠉⣉⡁⡈⣄⡀⣤⣬⣿⠿⠛⠀⠀⢠⡿⠿⠀⢹⡇
⠀⠀⢸⡿⠀⠁⠀⠈⣿⣉⣷⣀⣠⡈⠛⠋⠛⠙⣶⠟⠿⠟⠿⠙⠯⠋⠁⢁⣀⣀⣼⣍⣏⠀⠀⠊⠉⠇
⠀⠀⠀⢡⡀⢈⡆⠀⠉⠁⠈⢹⣧⠿⠶⣴⡟⣦⣀⣤⡴⣦⣀⣤⣟⢦⡤⠿⣯⡟⠁⠉⠉⠀⠦⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠟⠁⠀⠈⠻⠋⠉⠈⠻⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⡾⠛⠧⠞⠻⣦⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⣿⠀⠀⠀⠀⠀⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣜⠷⢤⡤⡤⠞⣃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣶⣶⣖⣛⣀⣀⡀⡀⠸⠛⠒⢒⣒⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢻⡍⠁⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⡽⠃
⠀⠀⠀⠀⠀⠰⣯⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠒⠲⠶⠤⠤⢤⣤⣄⣀⣀⣀⣀⣼⠗⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⢀⡀⣀⣠⣴⢶⡝⠉⢫⠝⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢶⣦⣔⢾⣿⣶⣷⣾⣷⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⣿⣽⡧⢠⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣙⠖⢴⠉⠻⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠓⡇⠀⠸
⠀⢀⣀⣀⣀⣀⣀⣴⣄⣠⣼⣦⣾⣦⣤⣿⠿⣻⡿⣿⣿⣿⣿⣿⣿⡏⢸⢿⢿⣿⡿⣿⣟⣳⣒⣒⣷⣠⣰
⠀⠈⠁⠈⡉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣀⣀⣀⣀⣀⣀⣤⣤⣼⣾⣿⣽⣯⣿⡏⢽⣿⡿⣿⣻⣿⣻⣷⠂
⠀⠀⠀⠀⠐⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⠾⠿⢿⡿⠶⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡜⠻⣿⢿⡿⣿⠙⡿⠛⠛⠀⠁
⠀⠀⠀⠀⠀⠈⢾⡏⣨⣿⣿⣿⣿⣿⣿⣿⡇⢉⣉⣉⣉⡉⣩⣭⣭⣌⣹⣶⠖⣰⣾⣿⣿⣿⣶⣷⣿⣀⣿⠏
⠀⠀⠀⠀⠀⠀⢿⣿⠋⡟⢷⡀⢸⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣦⣶⡛⢷⣾⣶⣿⣿⣿⣿⣿⢿⡟⠛⠉⣿
⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿
⠀⠀⠐⢲⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠿⠿⠿⠛⠛⠛⢋⣩⡉⡭⠥⠧⣗⣛⣛⣛⠩⠭⠿⠿⠛⠛⠃
⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣀⣀⣤⣤⣤⢶⠖⠚⠋⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⣤⣤⣤⣤⣀
⠀⠀⠀⢰⠂⠈⠀⠀⠀⠀⠀⠉⠋⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠛⠛⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠲⠌⡃⠀⢀⠠⠤⠲⡄⠀⠀⠀⠄⠂⠒
⠀⠀⠀⡠⠠⠀⠀⠀⠀⣠⣀⡄⠀⠀⠅⠠⠧⠂⠀⠓⠿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⡀⢀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣿⡍⠀⠀⠀⢶⣶⣶⣶⣾⣷⣾⡇⠀⠀⠀⠀⠀⢀⣒⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠄⠤⢽⠀⠀⠀⠁⠻⢿⣷⠾⢾⠿⠟⠻⠦⠤⠚⠛⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢐⣀⠀⠸⠀⠐⠠⠀⠀⠀⠤⣄⣹⣶⣛⣳⡈⢛⣃⣛⣛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⢀⣀⣴⣶⣀⠀⠀⠀⢐⣿⣿⣽⣿⣿⣿⣯⡄⢘⠡⠀⠭⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠃⠸⠿⠿⠻⠍⠉

⠀⠀⣰⣄
⠀⢀⣿⡿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⡗⡆⠀⢀
⠀⠀⣿⡇⠀⠙⢿⣦⠒⢲⢲⠀⡀⠀⠀⠀⠀⣀⠀⣠⣄⣀⣇⣌⣀⣿⣰⣦⣄⠀⠀⣀⣠⣤⣶⡶⠂⠠⣤⣾⠒⠲⣷⣷⣶⣿⡆
⠀⠀⣿⠁⠀⠀⠈⡿⠤⢾⣼⣿⣿⣿⠄⠀⠀⣿⢯⣿⣿⣿⣿⣧⣤⣿⣿⣿⣟⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡧
⠀⠀⣿⣿⡟⣠⣤⣴⣶⣾⣿⣿⣿⣽⠀⠀⠸⠿⠾⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⠟⠉⠙⠋⠻⣿⡿⠋⠁
⠀⠀⣈⣉⣀⣙⣛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢀⡀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⡄
⠀⠀⢀⣌⣉⣋⣿⣦⢤⠤⡤⡤⡤⢤⢤⠀⠀⠀⢸⠀⣸⢀⣿⣇⠀⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣸⣧⣧⣀⣰
⠀⠀⣾⣿⣿⣿⣿⣿⣀⣆⣥⣴⣼⡞⠛⠁⠀⠀⠘⠉⢻⣿⣿⣉⣏⣿⣹⣹⣏⡟⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠿⠿⠽⢿⠿⠿⠯⠿⣿⣿⣿⡿⠿
⠀⠀⠉⠁⠻⣿⣿⠟⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⣠⢤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢺⠛⠙⠙⢹⡇⠀⠀⠀⠀⠀⠀⢰⣹⠆⡷⢪⡗⢸⠖⡂
⠀⠀⢰⣶⣿⣸⣧⣀⣼⣹⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⣾⣏⣿⡴⠄⢀⣾⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡁
⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⡟⠉⢹⡧⠀⠀⠀⠀⠀⣿⣿⣿⣅⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢸⡿⣿⣿⡿⠇⠹⠿⣿⣿⡿⣿⠟⠀⠀⠀⠀⠀⣀⣀⣠⢿⣉⡿⠿⠿⠿⠿⢿⣻⠇⠀⠀⢠⡄⠀⠀⣆⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⠉⠀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣠⣬⣥⡤⠀⠀⣾⣧⠀⢐⡳⠀⢸⣯⣉⣉⣹⡇
⠀⠠⡆⠐⠒⢲⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠴⠶⢶⣆⠀⣠⣾⣿⣿⣿⣿⣿⡅⠀⠈⠉⠉⠀⠉⠉⠁⠈⠉⠉⠉⠉⠁
⠀⠀⢱⡾⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢳⡦⢤⣼⣧⣤⣿⣿⣿⣿⠿⢋⣿⡅⠀⠀⠀⠀⣄⠀⣀⢀⡀⢀⡀⢀⡄
⠀⠀⢸⣿⣿⣿⣿⣭⣼⣭⣿⣿⣿⣿⣿⠇⠀⠀⣸⣷⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠈⠛⠁⠀⠁⠀⠈⠉⠁⠙⠋⠀⠀⠀⠉⠉⠙⠛⠁⠉⠉⠁⠙⠛⠈⠛⠃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠚⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⡏⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢹⣆⠹⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡁⢘⢦⠹⡀⣣⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣳⠟⠉⠈⠉⠉⠙⠓⠒⠦⣤⣄⣀⣤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀⠀⠀⠀⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠳⡄⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠛⠿⡀
⠀⠀⠀⠀⢰⠲⣠⠎⣀⣀⣀⡀⠀⠀⠀⠘⠲⣇⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠲⡤⢄⡀
⠀⠀⠀⠀⠈⠳⠔⠋⠁⠀⠀⠈⠑⠦⣄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⢦⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⡹⠶⠒⠶⠶⠦⠤⠤⣄⡰⠀⠀⠀⠀⠀⠀⠉⢷⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠼⠖⠒⠒⠛⠓⣒⣯⡀⢀⣀⡤⢤⣔⠒⠒⣇⠀⠉⠓⢄⠀⠀⠀⠀⣀⡼⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⢀⡠⢄⡀⢀⣇⠀⠀⠀⠀⠀⠐⠯⣵⠟⠋⠁⠀⠙⠟⠀⠀⢸⡀⠀⣠⠼⠣⠀⢰⠺⣁⣀⠬⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⢺⡀⠀⠙⠇⠈⠓⠲⠤⠤⠤⠔⢺⣇⠀⠀⠀⠀⢀⣀⣤⣶⠉⠁⡼⠃⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⠓⠦⣀⠀⣀⡀⠀⠀⠀⠀⡼
⣏⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡙⠛⠛⠛⠉⠉⠁⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⣬⣿⢁⡨⠇⠀⠀⡸⠁
⠀⠉⠉⠉⠉⠒⠒⠲⡒⠀⢤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣉⡉⠲⡄⠀⠀⠀⠀⠈⢧⠀⠀⣰⢷⣯⢽⠟⠉⠂⠠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣙⠢⢎⣩⠖⢤⡀⠠⡀⠀⣠⠤⣄⣉⠈⢉⡡⠃⠀⢀⢷⠘⣄⣸⠶⣋⠴⠊⠈⢁⣀⠔⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣍⡐⠃⠬⠆⢻⡏⣇⡞⠁⠈⠉⢣⢄⣀⢀⡼⠺⢀⣯⣴⣊⣡⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣉⣒⣲⠚⢷⣬⡇⠀⠀⠀⣇⣀⣠⡭⠔⠚⠉⢠⣞⡥⡴⢶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠲⠉⢹⠀⠀⠀⠙⢯⠛⢿⢉⣡⠴⡉⣠⠀⠀⢠⠃⠀⠀⢸⡌⢇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠯⠵⠮⠤⠃⠀⣦⢍⡋⠀⢸⡧⣀⡰⠋⠁⠀⠀⢸⣄⡀⠀⢸⢇⣼⡜⡀⡁⢈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠹⠵⠉⠉⢀⣠⠁⠀⠀⠀⠀⠸⡄⠉⠛⢻⠻⢤⢻⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣩⠟⣽⢒⣒⣶⣶⣖⡿⠀⠀⠈⠒⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠛⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⡆⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣶⣶⣶⣶⣿⣇⠀⠀⢶⣶⡶⠶⠶⠶⠶⠶⠲⢶⣥
⠀⠀⠀⠀⠀⢠⠾⠿⢿⣿⣿⣿⣟⣟⣿⣻⣿⣿⣿⠛⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣟⠛⣻⣟⠛⣛⠿⣷⣦⣝⣿⣦⡀⣀⣀⣠⣤⣬⣿⣆
⠀⠀⠀⠀⢠⠃⣀⣴⣿⡿⠿⠿⢷⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⡿⢋⣤⣼⣿⣿⣿⣿⣿⣿⣧⣬⡝⢿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣾⣿⢟⣩⣾⣶⣿⣷⣾⣦⣙⠻⣿⣿⣿⠀⠀⠀⠀⣾⣿⡿⣡⣼⣿⣿⠟⠉⠭⠬⠍⠛⢿⣿⣷⣄⢻⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢸⡿⣡⣿⣿⠟⡋⠉⠭⡛⢿⣿⣧⡜⣿⣿⣤⣤⣤⣼⣿⣿⠃⣹⣿⣿⢡⠋⠀⠀⠀⠀⠘⡎⢿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⣿⣾⡇⣽⣿⡇⠈⠀⢀⡀⠀⠆⢿⣿⣧⢸⣿⣶⣶⣶⣾⣿⣿⠘⣿⣿⣇⢠⠀⠀⠘⠃⠀⠀⡀⣸⣿⣿⠇⠀⠀⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠿⠿⠏⢻⣿⣇⠃⠀⠈⠀⢀⠀⣾⣿⡏⠸⠿⠶⠶⠶⠾⠿⠿⠀⢿⣿⣿⣎⠣⠀⣀⣀⠀⠜⣡⣿⣿⣿⠀⠀⠀⠀⠀⠰⣦⣄⣤⡿⠛⢻⡟
⠀⠀⠀⠀⠀⠙⢿⣿⣦⣝⣂⣀⣭⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣬⣥⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⢿⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⠿⢿⣿⠿⠿⠏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣶⣶⣶⣿⡟⠛⠛⠛⣿⣸⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠤⠴⠟⠛⠛⠛⠛⠒⠋⠉⢹⣻⡟⢻⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢹⡇⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⡇⠀⠉⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣿⠀⠀⠀⠀⠀⣿⣷⣀⣀⠀⠀⢸⣿⣧⡼⠛⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⣀⣀⣠⣿⣿⣿⣿⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠾⠇⠻⠿⠟⠛⠛⠛⢻⠀⣾⢿⣸⣿⡇⠀⢀⣀⣀⣀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣾⣦⣿⢸⣺⣿⣇⣀⣸⣏⣭⣭⣤⣿⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣿⡏⢉⣩⣸⢿⣿⣿⣛⡿⠋⣼⣿⣿⣿⠏⣻⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢹⡇⣿⣿⣿⢺⣿⣿⡿⠁⣼⣿⣿⣿⠏⣴⣿⣿⣷⣤⣨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢸⣇⣿⣿⣻⣾⣿⡟⠀⣼⣿⣿⣿⠏⣼⣿⣯⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣽⣿⣿⣿⣿⣟⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣿⣼⣿⠁⣸⣿⣿⣿⡟⢰⣿⣯⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣠⣾⣞⣯⣽⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣴⣿⣿⣿⣿⣁⣾⣿⣿⣿⣿⣿⣷⡄⠹⣿⣷
⠀⣀⣾⣿⠿⣻⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣷⠼⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣠⣟⢿⣯⣾⣿⣿⣿⣿⣥⡈⣿⠀⢻⣿
⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣭⣭⣍⣿⣿⣿⣿⡍⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣷⢲⣾⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⡇⣿⡇⢸⣿
⣸⣿⣿⣫⣽⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣛⣭⣿⣿⣿⣿⣿⡿⠛⢻⡆⠈⣿⣿⣿⣿⣟⣼⣿⣿⣿⣟⢿⣶⣿⣿⣿⣿⣿⣿⡇⣿⠇⣸⣿
⢿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⠀⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⡿⢛⣽⣿⣿⣿⠋⣰⡿⢀⣿⡏
⢘⣿⣿⣥⣾⣿⣿⡄⠹⣿⣿⣿⣿⡟⠀⢠⣿⡿⠿⠿⣿⣿⣾⠟⣋⣽⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⡿⢿⣿⣿⣿⡟⣁⣾⡿⠃
⠀⢿⣿⣿⣟⣽⣿⣿⣦⡈⠉⠉⠁⣀⣴⣿⡿⠀⠀⠀⢠⡙⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⡏⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⠿⣿⣿⣿⣿⡿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠸⣿⣾⡿⢛⣿⣿⣿⣿⣿⣿⣀⣴⡿⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣧⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣥⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣥⣾⣿⠿⠿⠟⠁
⣿⣿⡟⠻⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⢤⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣾⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠉⠙⠿⠋⠓⠒⠒⠐⣀⠀⣀⡀⢸⢦⠀⢀⡀⣀⡀⣀⡀⣠⡄⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣿⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠒⠘⠚⢻⣾⣿⠐⠒⠐⠒⠒⠓⢒⣓⠘⠂⠓⠀⠈⠛⠋⠀⠀⠀⠈⠛⠋⠈⠛⠛
⠀⠀⠀⣸⣿⣄⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣇⠀⢠⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠻⣿⣿⣿⠟⢿⣿⣿⡟⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠈⠉⢉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠉⠉⠙⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠀⣠⣴⡾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣉⡀⠀⢀⣀⣀⡀⠀⢸⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⡇⠀⢸⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣤⣾⣿⣿⣿⠀⠀⢀⣀⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠉⠉⠀⠀⣿⣿⣿⣇⠀⣸⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠻⠿⠛
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠽⠿⠿⠯⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⣶⣶⣶⣶⣦⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣶⣾⣷⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⢶⡦⢰⣶⣶⣶⣶⠀⠉⠲⢼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣀⣀⣀⣈⣛⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⡉⠉
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠛⠛⠛⣿⣿⡿⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠈⠉⠉⠉⠈⠻⠿⠿⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣽⣭⣿⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣶⣷⣿⣷⣷⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠟⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡾⠋⠀⠀⠈⠹⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠃⠀⠀⠀⠀⠀⢹⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢻⡄⠀⠀⠀⠀⠀⣸⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣼⣷⣤⣤⣤⣤⣤⣏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣴⡿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⢷⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠮⢭⣭⡴⠶⠛⠋⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠈⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣴⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡇⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠛⠛⠁⠀⠘⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠆⠀⠀⠀⠀⢿⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠃⠀⠀⠀⠈⣷
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣸
⣾⠁⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⠖⠒⠒⠚⠛⠛⡇⢠⠖⠛⠛⠛⠳⣄⠀⢸⠛⠛⠲⣆⢰⠶⢦⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣰⡟
⢻⡄⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⠀⠀⠀⣀⣀⣀⡇⡏⠀⠀⣀⡀⠀⠘⡆⣸⠀⠀⠀⠸⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣰⡟
⠈⢿⡀⠀⠀⠀⠀⠀⠀⠉⠋⢹⡄⠀⠀⡏⠉⠉⠀⡇⠀⠘⠷⠗⠀⠀⡟⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⣰⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠀⠀⠀⠹⣄⣀⠀⢀⣠⡾⠁⣇⠀⢸⢷⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣾⠏
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠙⠋⠀⠛⠛⠒⠞⠃⠀⠀⠀⠀⠀⢀⡼⠃⣠⣴⠿⠋⠁
⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠟⠋⠁
⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠛⠛⠛⠓⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢀⡀⠀⠀⣀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⣴⠿⠛⣧⣀⣼⠛⢿⣦⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣿⠃⠀⠀⠀⠁⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠹⢷⣄⣀⠀⠀⢀⣠⡾⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠈⠉⠉⠉⠉⠁⢀⣴⡞⠋
⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣖⣒⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⠙⠛⠛⣛⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⣶⡞⠋⠉⠉⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⢸⣿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⣿⡟⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⢸⣿⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⢠⣿⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⣸⡿⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⢿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠶⠶⠦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢠⡈⠂⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠡⠘⠀⠀⠰⡶⠙⠀⠢⠠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠁⠚⡁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠂⡀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⡁⡀⠅⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣂⣄⡀⠤⡤⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡘⠑⠀⠀⢰⠂⠈⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠂⠨⠀⠀⢸⠀⠀⠀⠀⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣀⢊⠗⠁⠀⠔⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠖⠖⠖⠲⠆⠀⡅⠸⡀⢐⠀⠀⠘⡆⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣌⠁⠁⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⢌⣀⡀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠇⡅⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠄⠆⠀⠀⠄⠀⠀⠀⠀⠀⠠⠠⠀⠄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⣀⣀⣀⠀⣠⣀⣄⣀⡀⢀⣀⣀⡀⣠⣀⣀⣀⣀⣆⣄⣀⢀⣠⣠⢀⣀⣀⡀
⠀⠀⣀⠐⠀⡉⠀⠠⣀⣁⡀⠀⢀⢐⣈⡂⠀⠀⢠⣈⣐⠀⠀⡀⣂⣐⠀⠀⠀⣄⣁⠀⠀⠈⠐⢕⡤⠀⠀⣀
⠀⠠⠦⠠⣇⣹⠆⠰⡏⠄⣹⠠⠄⣏⠠⢹⡊⠄⣸⡡⢈⡇⠎⢸⡁⠌⣗⠉⢸⡁⢌⣳⠰⢜⣉⡎⠐⠠⢀⡍⠰⠀⠀⢀
⠀⠀⠘⢠⡨⢁⠀⠐⠉⡙⠁⠀⠀⠨⢙⠉⠈⠀⠊⢙⠉⠁⠀⠂⠝⡋⠅⠁⠀⠽⡛⠁⠀⢀⠉⡪⠚⢠⡏⠁⡈⡁⠠⠝⢀
⠀⠀⠀⠀⠈⠀⠃⠁⠉⠉⠁⠉⠉⠁⠉⠈⠉⠉⠋⠘⠀⠉⠙⠉⠉⠈⠈⠋⠉⠙⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡼⢿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣼⣇⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠋⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⣿⣿⠗⠈⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠎⠀⠀⢀⡴⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⢿⡄⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⡼⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢸⣧⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣿⡄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣁⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠘⠛⠉⠙⣿⣿⡧⠆⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠀⢠⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣖⣿⣷⣄⢸⣾⠏⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡇⢠⣿⣿⡽⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⡟⠁⡼⠏⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⠏⣿⠁⠀⠛⠋
⠀⠀⠀⠀⠀⣤⣤⣷⣤⣿⣯⡾⠁⠀⠀⠀⠀⠀⠀⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢰⡆
⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠹⣿⣯⡟⢧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢹⣤⡤⠤
⠀⠀⠀⠀⠀⣀⣨⣀⣤⣿⣿⣧⣀⣳⡆⡄⠀⠀⠀⠀⢴⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣼⣿⡇
⠀⠀⠀⠀⢠⡟⢿⠉⡟⢿⣿⣟⠉⢙⣿⡅⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡓⢿⣿⢿⣛⡓⠒
⠀⠀⠀⢀⣾⣷⣬⣾⣤⣼⣿⣿⣧⣼⣏⣧⠀⠀⠀⠀⠀⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣟⣾⣿⡀
⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⡼⣼⡿⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣕⣯⣥⢿⣿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡘⠫⢻⢏⠉⢣⡹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⣇⣀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣴⣶⣾⡿⢣⣿⣷⣿⣷⣲⣷⣤⣧⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⣿⣿⡇⠀⠀⠀⣰⡏⠀⠀⠀⠀⠉⠉⠉⠉⠗⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⣭⠉⢳⡀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣾⣷⣾⣟⣃⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣄⡀⣀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⢀⡏⢹⣦⣤⣤⣀⡀⠀⠨⠈⠙⠿⣷⣶⣤⣤⣀⡀⠀⠀⠐⣷⣶⣶⣿⣾⣿⣷⡶⠀⠀⡀⠀⢠⡿⠛⢻⡇⠀⢀⣶⣦⣼⣷⣆⣀⠀⠀⠀⣤⣴⣆⣠⣼⣶⣤⡀
⠀⠈⠀⠛⠋⠉⠻⠛⠛⠀⠀⠀⠀⠀⢨⣅⣹⣽⡿⣿⣧⠀⠀⠙⠋⠋⠉⠉⠉⠋⠁⢠⣶⣦⢀⣾⠀⠀⢸⡁⠀⠈⠙⠛⠛⠛⠁⠈⠀⣴⠶⠿⡿⠛⠛⢿⡿⠛⠁
⠀⠀⣀⣀⣘⠐⠀⠀⠀⠀⠀⢸⠶⣾⣿⡿⠿⢿⣿⡿⠿⡇⠀⢀⡟⣦⣥⣤⣄⣀⠀⠈⠿⠿⠿⠗⠂⠀⠈⠃⢀⣠⣤⣀⡁⠀⡀⠀⠀⣀⡄⠀⠀⠀⠀⠀⣀
⠀⠠⠿⢿⣿⠿⢾⣿⢧⣶⡀⠀⠀⠈⠉⠀⢀⣀⡉⠁⠀⠀⠀⠈⠀⠙⠋⠉⠛⠙⠂⠀⠀⣀⣤⣤⣤⣤⢦⠀⠺⢿⣿⠿⠷⣿⡿⠀⠀⢿⣿⣾⣦⡀⠀⣾⠛⢆
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣤⣠⣒⠚⠛⠉⢹⡇⠀⢀⣤⠶⠞⠛⠂⠀⣰⣶⣤⣶⢲⠘⠟⠉⠉⠀⢸⡿⠀⠀⠀⠀⣤⠀⠀⠀⠄⠀⠀⠀⠀⢀⣤⡘⠃⠀⢸
⠀⠀⣿⣤⣔⠋⣸⠀⠀⠀⣤⣿⣿⣷⣶⣤⠀⢘⡇⠀⠘⠟⠓⠚⠟⠃⠀⠙⣛⣼⣿⣿⣷⡇⡀⠀⠀⠈⣿⠀⠀⣠⣘⣿⢿⣾⣿⡟⡤⠀⠀⠴⠾⠿⠿⢿⠖⠛⠂
⠀⢀⣈⣉⣀⠀⠁⠀⠀⠀⠀⢉⡀⠀⠉⠀⠀⠈⠁⠀⠀⢀⣤⠶⠶⣶⠀⠀⠑⠛⠛⠛⠛⠓⠁⠀⠀⠈⠉⠀⠀⠉⠉⠛⠛⠛⠛⠉⠙⠀⠀⠀⠠⠄⠄
⠀⢘⣿⣿⣿⣿⣾⣧⡇⠀⣴⣶⣦⣦⣤⡄⢀⠀⠀⢶⣶⣄⡄⠀⠀⣟⠀⢰⣶⣦⣥⣄⠀⠰⣷⣶⣾⣧⣦⡄⠀⢰⣿⣶⣶⣾⣹⣧⡄⠀⠀⣴⣷⣦⣀⣶⣶⠄
⠀⠈⠛⠙⠋⠉⠉⠋⠁⠀⠈⠁⠛⠛⠃⠉⠛⠂⠀⠘⠛⠛⠛⠒⠀⠋⠀⠈⠛⠛⠛⠛⠂⠀⠘⠋⠉⠉⠛⠁⠀⠈⠛⠛⠉⠙⠉⠛⠁⠀⠀⠈⠙⠋⠉⠙⠋⠙⠃
⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣶⣀⣀⣀⠀⠀⠀⠀⣠⣔⣴⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡇
⠀⠀⠀⠉⣿⠉⠉⣉⠁⠀⠀⠈⠋⢡⠛⠛⠁⣾⢣⡀⠀⠀⣰⣿⣧⣼⣶⡲⣄⡀⠀⠀⠀⣨⣀⡀⢡⣧⣤⡄⠀⠀⠀⠀⠶⠛⢉⡤⢄⠁
⠀⠀⠀⣀⣿⣀⠀⠃⠀⠀⠀⠀⠀⠀⣟⡿⠛⢿⡻⠃⠀⠀⠈⠧⠞⠉⠣⠜⠛⠗⠀⠀⠀⢛⠟⠛⢟⠯⠟⠃⠀⠀⠀⠀⢟⠿⠿⠿⡻⠂


⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠰⣾⣶⣤⣧⡀⠀⠀⠀⠀⣤⢶⣏⡷⢱⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣕⣢⡀⠀⠀⠀⠀⢸⣤⣴⣤⣤⡀
⠀⠀⠘⢯⡿⢿⡿⣿⡄⠀⠀⠀⠛⠉⠁⡴⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣎⡿⠚⢏⡹⠃⠀⠀⠀⠐⢒⡪⠿⠯⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣴⡾⠿⣷⡀⠀⠀⠀⠀⠀⣠⣴⣾⡇⡤⢄⠀⠀⠀⢠⣤⣧⣈⣧⠾⣷⡀⠀⠀⠀⣤⣯⠈⣧⣤⣤⡄⠀⠀⠀⠀⣷⣬⡹
⠀⠀⠈⠉⠀⣴⣿⣇⠀⠀⠀⠀⣠⡝⡏⣷⠷⡟⣻⠇⠀⠀⢸⣟⣛⣛⡅⠀⣼⡇⠀⠀⠀⢟⣹⡋⣷⡆⢎⣱⠀⠀⠀⠀⢻⡿⢯⡷⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁


⠀⠀⢠⣼⣉⣙⠀⠀⠀⠀⠀⠀⡒⠘⠉⠓⢢⡤⡀⠀⠀⠀⠀⣎⣉⣤⡀⠀⠀⠀⠀⠀⠀⣀⣸⠉⣦⣴⣦⠀⠀⠀⠀⢀⡀⠀⢀⡴⣿⣀⡀
⠀⠀⠸⡟⢛⢿⣻⣦⠀⠀⠀⠀⠸⡷⣶⢶⠿⡷⣿⠀⠀⠀⡘⣿⢻⣿⣯⣿⣷⣄⠀⠀⢀⣿⣿⡿⣏⠀⢼⡧⠀⠀⠀⡿⢷⢶⠾⡸⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠀⠁⠀⠁

⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⢠⢖⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⢰⣤⡲⣾⣕⡆⠀⠀⠀⠀⠀⠛⠾⣶⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⢀⣴⡖
⠀⠀⠀⠈⢯⡮⠇⠀⠀⠀⠀⠀⠀⠀⢀⠮⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁⠀⠀⠀⠀⠀⢠⠼⣿⠷⣄⠀⠀⠀⠀⣿⠿⣶⣶⢯⡀⠰⠇
⠀⠀⠀⠀⢾⣥⠆⠀⠀⠀⠀⠀⠰⠾⠶⠶⠶⠿⠶⠀⠀⠀⠀⠀⠀⠴⣾⡷⠄⠀⠀⠀⠀⠀⠈⠸⣿⠇⠁⠀⠀⠀⠀⠈⠒⠁⠈⠚⠁