Cute symbols Emojis & Symbols

⠀⠀⠀⠰⠀⠒⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢚⣛⣓⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⢏⡉⠉⠉⠉⠉⡧⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠤⠤⠀⢸⠀⠀⠀⠀⠀⠀⠐⡚⠐⢧⠀⡸⠉⡀
⠀⠀⠀⢸⣸⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠓⡴⡏⠀⣇⣀⡇
⠀⠀⠀⠈⣇⢀⠀⠀⣠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠢⠤⣄⡸⠀⠀⠀⠀⠀⠀⠀⢐⠁⡇⠀⢹⡅⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠦⠇⠀⠘⠷⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⠰⠀⠀⠤⣤⠤⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⣛⣛⣛⡛⠋
⠀⠀⢠⠦⡤⠀⢸⠀⠀⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⡏⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢰⠶⡏⡄⠀⠀⠀⢹⠶⡄
⠀⠀⠞⠀⠣⠐⠋⠂⠠⠏⠈⠃⠀⠀⠀⠀⠀⠀⠀⠞⠚⢳⠐⠂⢸⠀⠀⠀⠀⠀⠀⠀⠈⠚⡇⠁⠀⠀⠀⢸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣉⣸⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣜⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠾⠤⠴⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡇⠀⡆⡆⣢
⠀⠀⠀⠀⢸⣄⡠⠤⢺⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⠷⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⢸⣥⠤⠔⢺⠀⠀⠀⠀⠀⠀⠀⠈⡦⠤⠤⠤⠤⠒⡺⢅⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠸⣄⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠒⠒⠒⠋⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⣀
⠀⠀⠀⠘⡯⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⢸⣅⣀⣀⣑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣛⣛⡚⠛⡂⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠈⢇⣸
⠀⠀⠀⢸⡀⠀⠀⢠⣤⡽⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣓⣒⡋⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⠉⠑⠢⡀⠙⠈⠙⢦
⠀⠀⠀⠀⢧⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡩⠭⠅⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⢀⣴⡎
⠀⠀⠀⠀⠘⠤⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⣀⣀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠤⠤⠊

⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⠄⠀⡀⠈⢣⠀⠀⠀⠀⠁⡰⠀⠀⠀⢀⠀⠀⠀⠀⣩⣯⠁⠀⠀⡀⠄⠀⠀⠄⣐⠘⢄
⠀⠀⠀⠀⠀⠂⢀⣍⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠊⠁⠈⢃⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⡀⠚⠂⢦⠀⠰⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠹⡉⣅⡁⠀⠀⠀⢛⠂⠀⠈⡄⠘⠀⠀⢦⠴⠒⠚⡆⠀⢄⡆⠀⠀⠀⠀⠀⠀⠁⠘⠚⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠄⠀⠀⠉⠀⠀⠘
⠀⢠⠀⡇⠀⢸⠑⠉⡅⠀⠀⠐⠀⠀⠀⠡⣘⣄⠀⠀⠀⠀⠀⠀⡇⣬⠊⠀⠀⠀⠐⠂⠀⠀⢸⠙⠀⢢⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠐⠀⢀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣄⡀⠈⠸⠆⣖⣰⠶⠵⠞⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠡⣁⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢤⠀⠀⠀⠀⢀⠀⠀⠀⣠⠃⠈⠘⢀⠀⠀⠀⠀⠀⠀⠸⠩⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠰⠔⡖⠀⠀⠑⠀⠀⠀⣄⠌⠀⠀⠀⠤⡆⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠂⠘⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⢠
⠀⠀⠀⢺⡇⠀⠂⠁⢈⠅⠀⡠⠤⠀⠀⠀⠀⠀⠰⠉⣤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠈⠐⢢⠀⠰⣐⡦⣂⠀⠀⠀⠀⠠⠃⠌⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⡆⠀⠀⠠⠄⢉⠙⣁⠆⠀⠀⠀⠀⠀⡰⠀⠠⠂⠀⠀⠁⠋⠃⠀⠀⠀⣆⠃⠀⠰⢀⡀⡀⠀⡠
⠀⢀⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠐⠁⠀⠀⡆⡄⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠈⢂⠀⡰⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⡠⠀⠗⡠⢆⢀⠒⠢⠀⠀⠀⠀⠀⡀⠀⠀⠙⢫⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠰⠖⠚⠺⠀⠀⠀⠀⠀⠤⠯⠤⠄⠀⢰⢡⠆⠀⠁⣨⣷⠦⢴⠂⠀⠀⠀⠌⡄⠀⠀⠀⠸⠀⠀⠀⡠⠊⡤⣠⠄⡀⠀⠀⡀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠺⠞⠃⡖⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⡀⠸⠋⠁⣫⣆⠀⠢⣀⠠⢂⠞⠀⠀⠀⠀⠊⠀⠀⢠⠀⠐⠀⠀⠀⠸⠀⠀⠀⠀⢙⠁
⠀⠀⠀⠀⢀⡀⡀⢻⠃⡄⠯⠈⠁⠀⠀⠀⡄⠀⠀⠴⠶⢦⠀⠑⢄⠂⠀⠈⡆⠀⠀⠀⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠂⠀⠀⠀⠀⢣⠠⠀⠀⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⢿⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠀⠀⠢⠤⠀⠀⢸⡄⠀⠠⠁⠀⠀⡀⢀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⣴⠟⠀⠈⠀⠀⠠⠀⠀⠀⠘⡷⢾⠀⠀⠀⠀⠀⡠⠄⠀⠀⢀⢤⡄⠀⠂⠐⠀⠀⠐⠀⠀⠀⢀⣀⠠⡀⠀⠀⠀⠀⠀⠀⣡⡇⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠉⠀⠀⠀⠤⠀⠀⠳⠄⠀⠋⠀⠀⠀⠀⠀⠀⠘⠃⠂
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣄⠀⠁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠎⠈⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠻⢄⠉⠑⣦⠀⣄⠜⣀⡀⠀⠀⠦⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠒⠃⠀⠀⠀⠈⢁⠔⠒⠠⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠂⠠⡀⠀⠀⠀⠀⠀⠈⢢⠀⡔⠀⢢⠈⠉⢢⠀⠀⠀⠀⡴⡀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡄⡦⢀⣄⠷⠀⣄⠀⠀⠀⢰⠁⠀⢑⠒⠊⠀⡖⠁⠀⠀⠀⢰⠀⠰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢇⠀⠀⣣⡤⢃⡀⡜⠀⠀⠀⠀⠑⠐⠈⠓⠄⠔⠃⠀⠀⠀⢀⠘⠤⠃⠀⢠⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠈⣁⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠀⠡⠆⣀⣀⠀⠈⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠊⠁⢀⡀⠁⠀⠀⣴⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⡎⠀⠀⠱⠤⠤⢄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠤⠊⠀⠈⠙⡄⠀⠀⠉⠁⠀⠀⠸⡀⠀⢠⠀⠀⠀⠉⠁⠀⠀⢀⠵⠀⡔⠐⠄⠀⢈⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⣑⠒⠁⠺⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠁⠉⠉⠦⠀⠔⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠎⠀⠑⠤⠒⠉⢢⠀⢀⠔⢲⠀⠀⠀⠀⠀⠀⡋⠢⡀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠆⢀⠔⠂⠄⠀⡰⠀⠋⡠⠆⠀⠀⠀⠀⠀⠀⠈⠢⠇⠘⢤⠇⠀⠀⠀⠀⠀⠀⡔⠁⡍⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠀⠠⡀⠀⠨⠀⠉⠆⠉⢤⠂⠠⣀⠀⠀⠀⠀⠤⠀⠤⡀⠀⠐⠁⠉⠢⠀⠄⠈⡠⠚⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠑⠒⠀⠀⠀⠤⣀⡠⠆⠀⠀⠑⠠⠄⠇⠀⠈⠐⠂⠐⠀⠠⠒⠛⡠⠀⢄⠀⡀⢀⡔⠒⠒⢢⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣀⡀⠢⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠣⠀⠜⠀⠈⡀⠀⠁⠈⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠊⢠⠄⢰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠀⠀⠀⠀⠇⠀⢀⠖⠒⠊⠁⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠔⠁⠀⠨⡀⠁⠀⠀⠀⢰⠓⠄⠀⠀⠀⠀⠀⢘⡠⠂⠀⠀⠀⠀⠈⠉⠁⡘⢣⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠖⠀⠀⠀⠈⢄⠈⠀⢠⠖⠒⠢⣨⠄⠀⢄⠀⠀⠀⠀⠀⠀⠠⣠⠀⠀⡄⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡙⡁⠡⡀⢠⠄⠥⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠴⠃⡔⠁⠐⠄⠰⠀⠫⡀⢏⠑⠢⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠱⢄⡀⠖⢄⢀⡴⠁⠀⠑⠦⠵⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠢⢤⣀⠀⠀⡄⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣤⠀⢠⠄⠰⠊⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣇⡀⠀⠀⢀⠔⠁⠀⠑⢄⠀⢀⠷⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠈⠑⠲⠋⠀⠀⠀⠀⠀⠑⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢄⣀⣀⣀⣀⣀⣀⣀⠠⠔⠊

⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠙⠛⠙⠙⠋⠛⠛⠛⠉⠙⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠿⣿⠿⢿⣿⡛⠛⠻⠿⠟⠋⠉⠙⠛⠿⠿⠿⠿⠟⠛⠛⢿⡿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⢻
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾
⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⢠⣾
⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠠⠌⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠⠀⠀⠀⠠⠐⠀⠀⢻⣿
⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠤⠄⠀⠀⠀⠙⠉
⡏
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡧⠀⠀⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⣦⠁⠠⠉⣠⢫⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣘
⣿⠄⠀⠀⠀⠀⢄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠇⠀⠚
⣿⣷⠀⠀⠀⠀⠀⠈
⣿⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠫⢂⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘
⣿⡁⠀⠀⠀⠀⠀⢀⡀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⣿⣧⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣶⣶⣿⣿⣧⣠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠃⠀⠈⢿⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠉⠁⠠⡤⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⠟⣵⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⠇⣿⣿⣿⡛⠟⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⣈⠛⠿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⡿⠟⠋⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⢦⠀⣠⠊⠁⠀⢹⠀⢀⡤⠒⠋⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣽⡴⡆⠀⠀⠀⠀⠀⢠⠋⠀⠀⣸⡜⠁⠀⠀⠀⣼⠖⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣉⡘⢓⡿⠂⠀⠀⢀⠏⠀⠀⠀⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠁⠀⠀⠉⠙⠲⢄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠰⡦⢄⣀⡞⠁⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠱⣴⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠙⣦⡼⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⢈⡧⠖⠚⠉⠉⠉⠙⡆
⠀⠀⠀⣾⠵⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠋⠉⠉⢢
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠒⠶⠖⠒⠋⠁⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⣩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣁⣀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⠀⠀⠀⣀⣀⠤⠒⢫⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣧⡰⠀⠀⠀⣀⡀⠀⠻⠟⠀⠀⢠⣤⣴⠄⠀⠀⠀⠀⣀⡴⢦⡀⠀⠀⣰⠛⢦⣀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⡆⡀
⠀⠀⠀⢠⡞⠉⠙⢦⡴⠛⢉⠷⡏⠀⠀⠀⠀⠀⠈⣁⡤⣤⣶⡒⠶⣴⠋⠟⠀⠀⠀⠀⠘⢇⡀⠌⢳⡀⡰⠉⠢⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠘⣧⠀⠀⠈⠁⠐⠋⣸⠃⠀⠀⠀⠀⠀⢰⡏⠰⡇⠈⣷⠀⣹⠄⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣗⣧⡤⠞⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠠⣄⣨⢷⣄⣹⣶⠿⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠟⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⡤⠠⠐⠈⡇
⠀⠀⠀⠀⢰⣤⠋⠳⠞⠁⠀⠀⠀⠀⠀⠀⠐⠟⠧⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢄⡀
⠀⠀⠀⠀⠀⠀⠘⢛⡙⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⢀⣠⢞⣥⣴⡆⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⡴⠟⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⢯⡉⠙⠛⢻⣍⣹⠿⡃⠀⠀⠀⠀⢀⣴⠞⠛⠳⠛⠛⢦⡀⢀
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢿⡾⠂⣿⠀⠀⠠⠄⣿⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⠖⢦⡊⠁⢸⡇⠀⠀⠀⠈⢻⡟⠒⠶⠶⠶⠶⢾⡿⠋⠁
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢰⣾⣿⠀⠀⠀⠀⠀⠀⣿⣴⣛⣁⣀⣀⣙⢲⣼⡇⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⠶⠟⠁
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣀
⠀⠀⠀⠀⠀⣤⠶⠾⠁⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⣀⢬⠑⡀
⠀⠀⠀⠀⠀⢷⣄⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⢰⡟⠛⢛⣻⣛⣟⡛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠉⠙⠿⠋⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠛⢛⣉⡳⡄⠀⠀⠀⠀⠀⠀⢠⡼⠓⠶⠶⠛⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠿⠃⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠘⠿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡷⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⢖⣛⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⢾⣏⢶⣙⣎⡇⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⠤⡤⡤⠤⢤⣤⠀⠀⠀⠀⠀⠀⣠⣴⣇⠀⢀⣿⣤⡀⠀⠀⠀⠀⠀⣟⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠈⠙⢻⠚⠋⠀⠀⠀⠀⠀⠀⡏⠳⣄⠀⢴⣤⡆⠀⣠⠞⢹⠀⠀⠀⠀⠀⣾⠁⠀⠘⢷⠟⠀⠀⢹⡆⠀⠀⠀⠀⣟⠉⡩⢿⢯⣵⠻⡍⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣤⠀⠀⠀⠀⡇⠀⠈⠳⣄⠉⣠⠞⠁⠀⢸⠀⠀⠀⠀⠀⢻⡄⠀⠀⢴⠄⠀⠀⡼⠃⠀⠀⠀⠀⣇⠀⢣⡘⠇⠺⣇⠜⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢊⡥⠋⠀⠀⠀⠀⠓⠒⠒⠒⠚⠛⠳⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠙⢦⣄⠈⢀⣤⠞⠁⠀⠀⠀⠀⠀⣧⣀⣀⣉⣲⣞⣁⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋


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

⣀⣀⣶⠂⠀⢠⡆⠀⠀⠀⣠⡾⠀⠀⠀⢀⣾⡀⣄⣀⣀⠀⠀⠀⣰⠃⠀⢀⣾⣷⡶⠀⣴⣴⢷⡆⢠⣴⠿⣤⠀⠁⠄⠆⠄⢤⡄⢻⣄⢀⣸⡶⣶
⠙⠋⠉⠃⠀⠙⠛⠲⠄⢸⣿⠁⠀⠀⠀⠿⠿⠀⠹⠛⠿⠀⠀⢛⣟⠁⠀⠈⢿⡿⠿⠁⠿⠷⠾⠃⠘⠖⢴⠆⠀⠈⠑⠀⠀⠸⠧⢶⠏⠀⠻⡿⠛
⣤⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣠⠀⠀⢀⣠⠀⠀⢀⣠⣄⠀⠀⣀⣄⡀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⢠⣀⡀
⠻⣷⠿⠇⠀⣹⢷⣦⠀⣠⣶⣼⡄⢸⣷⣿⣟⠀⠀⢴⢏⠀⠀⠀⡿⠁⠀⠰⣿⠁⡿⠀⣿⣯⣿⠇⠸⣿⣿⡇⠀⢯⢋⢽⠂⢶⣾⣻⡷⠀⢶⣯⢽
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁⠀⠉⠉⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠉⠀⠀⠉⠀⠀⠀⠈⠉⠋⠀⠈⠋⠙⠁⠀⠈⠉⠋
⠾⣿⣿⡆⠐⣿⣴⣿⠀⣷⣤⣴⡇⢰⣦⣠⣶⠀⣶⣄⣴⡆⢰⣦⣴⡾⠀⢀⢄⠭⡐⠄⣶⠞⢻⡄⠰⣶⠾⣷⠀⠘⢿⣾⠃⠀⢹⣼⠁⠀⠈⣷⡯
⠀⠀⠿⠇⠈⠉⠈⠉⠀⠻⠟⠻⠃⠀⠛⠙⠋⠀⠘⠟⠛⠁⠘⠋⠙⠃⠀⠀⠉⠻⠅⠀⠻⠶⠾⠁⠘⠟⠾⠏⠀⠈⠼⠿⠀⠀⠼⢿⠄⠀⠳⠿⠷
⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠀⢀⡄⠀⠀⠀⢠⣄⡤⠀⠠⣤⣤⠄⠀⣄⣀⡄⠀⢠⣤⣤⠄⢠⣤⣤⡤
⠸⣿⣿⠷⠀⠰⠿⠀⠀⡀⠿⡃⠀⠐⢻⣿⠓⠀⠚⣻⡘⠂⠐⢙⣏⠃⠀⢠⢶⣿⡇⠀⣄⣿⣿⠀⢀⣸⣿⠀⠠⣠⣿⣿⠀⢤⣿⣿⡀⠘⠛⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠀⠀⠉⠉⠀⠀⠈⠉⠉⠀⠈⠉⠉⠁⠀⠀⠈
⠀⣠⣦⡀⠀⣄⣴⣠⡄⢠⣴⣶⣤⠀⡴⠒⢦⡀⢠⡴⢦⣄⢀⡴⠶⣦⡀⣸⣴⡶⣶⢀⣀⣾⣿⠀⢸⣷⣲⢦⠰⣏⣁⡴⠀⠲⣦⣄⠀⠠⢶⣿⡶
⠀⠉⡏⠁⠀⠾⢿⠻⠄⠸⢿⣿⠿⠈⢧⣙⡼⠃⠸⢯⡽⠷⠘⢧⣯⡼⠂⠈⠛⠿⠏⠀⠙⠻⠛⠁⠈⠳⠽⠟⠀⠈⠙⠟⠀⠀⠘⠙⠓⠀⠘⠛⠓
⠀⡀⡀⡀⠀⣀⡀⣀⡀⢀⣀⢀⡀⠀⣀⠀⣀⠀⠀⡀⢀⡀⠀⣀⠀⣀⠀⢠⡀⠀⠀⠀⣤⣀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⡀⣀⠀⢀⣀
⢰⣟⢝⣗⠈⢿⣿⣿⠇⠸⣿⣿⠟⠘⣏⠉⣹⠇⠃⠀⢀⡿⠸⠉⠉⢸⠇⢸⣿⣦⣄⠀⢾⣿⡏⠁⠾⢿⣶⠏⠐⢾⡷⠶⠆⠰⣿⣿⡏⢸⢿⣿⠛
⠀⠉⠋⠁⠀⠀⠙⠁⠀⠀⠈⠋⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⢰⣶⣴⣶⡀⣀⣴⣀⡀⢀⠠⠆⢀⠀⣠⣤⣄⠀⢀⡤⢤⡀⢀⣠⣤⣤⡀⢰⣶⡶⢆⠀⠀⢤⣤⡀⠘⢴⣿⣷⠀⣤⣤⣾⠁⢠⣶⣿⠃⠘⣷⣤⣤
⠈⠻⠿⠋⠀⢹⠿⢯⠀⠈⡄⢤⠁⠀⠸⠿⠟⠀⠘⠧⠼⠃⠘⠿⠿⠿⠃⠈⠈⠀⠀⠀⠀⠘⠉⠃⠀⠀⠁⠘⠀⠘⠀⠉⠀⠈⠈⠋⠀⠀⠈⠀⠉
⠀⠀⢀⠀⠀⠀⠀⢀
⢰⠉⠀⢑⠀⡙⠋⣈⠃
⣤⣬⣬⣤⣤⣭⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣽⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠉⠉⠉⠁⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣀⣀⠀⠀⠄⠀⠐⠐⠒⠂⠀⠀⠤⢍⡒⢤⡀
⠀⠀⠀⠀⠀⢀⣠⣦⣒⣊⣉⡀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠬⠷⢿⡄
⠀⠀⠀⣀⣴⠟⠛⠉⠁⠈⠍⠉⠉⠉⠉⠉⠉⡉⠩⠑⠢⢄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⣠⠆
⠀⠀⢀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠐⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢀⡼⠁⢀⣀⠀⡀⡀⢀⢤⢀⡄
⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠰⠃⠈⠁⠀⠈⠙⠈⠡⠇⠈⢻⠙⠉
⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⠀⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢤⡄⠈⠑⠖⠒⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢸⡦⡀⠀⢀⡠⠚⡇⠀⢀⡇⠀⠀⢸⠀⣀⠄⢄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢈⡃⠈⠉⠁⠀⣀⠷⠚⠉⠈⠢⣄⠜⠂⠀⢢⠀⠱⡀
⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠡⢀⠄⠢⣈⠣⡀⠀⠀⠀⢀⡬⠧⠀⠀⠀⣇⣀⣵
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡁⠫⡀⢀⠄⠁⠀⠀⠈⠢⡈⠢⣠⠞⠁⠀⠇⣠⣔⣊⡭⢔⡁
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡐⠁⠢⢄⠀⠉⠓⢬⡈⠲⣄⠀⠀⣀⠔⢻⠀⡇⣀⡤⠞⠛⠉⠉⠀⠀⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠉⠲⣤⣰⢄⡀⢀⠞⠙⠢⠀⠀⠈⠳⢄⠑⠞⠁⠀⣸⡴⠛⠁⠀⠀⠀⠀⠀⣨⠶⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠛⢀⠔⠁⠀⠀⠢⣀⠀⠙⠦⣤⠚⠁⠀⠑⠠⢀⣀⡠⠔⠉⠀⠀⢇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠲⢄⡀⠀⢠⠞⢢⢀⠔⠁⢆⠀⠀⠀⢀⡠⠛⢧⠀⠀⠀⠀⢘⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠲⠅⣀⡠⠋⠀⠀⠈⣧⡠⠔⠉⠀⠀⠘⣆⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠋⠑⠢⣠⠞⡅⠀⠀⠄⠊⠁⠙⢄⠀⠀⠀⠀⣈⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⡔⠁⠀⠈⠢⣄⠀⠀⠀⠀⣈⣡⠤⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠂⠠⡀⠀⠀⢀⠊⠡⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⡀⠀⠐⠀⠀⠂⠀⠐⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢀⠀⠐⠀⠐⢀⡸
⠀⠀⠀⠀⠀⠀⡄⠀⠸⢀⠜⠀⠀⠃⠐⠀⠀⠀⠄⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠃⠑⠈⠦⢀⣀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⢀⠠⠊⠀⠄⣆⠀⢀⠁⠌⠀⠀⠀⠀⠀⠀⢀⠔⠉⠂⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⡠⠄⠒⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠐⠀⠙⢦⡚⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠱⣏⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠄⠪⠊⠀⠀⠀⠀⠀⠀⠠⠊⠀⠄⠒⡖⠂⠄⡀⠢⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠀⠀⡇⠀⠀⠘⠄⠘⢄⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡆⠀⠀⠀⠗⠀⠀⠀⠂⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠠⡀⠀⠀⡇⠀⠀⡠⠃⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠐⠂⠧⠐⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⡤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠐⠒⠂⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠔⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⠀⠀⠸⠀⠀⢠⠀⠀⡀⠄⠀⠀⠀⠀⠐⠂⠀⢄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⡀⠀⠀⠀⠂⠀⠘⠂⠀⠐⠂⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠒⠀⠀⠐⠀⠀⠈⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠨⠀⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠰⡂
⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠠⠒⠈⠁⢂⢸⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⡠⠀⡠⠂⠘⠢⣀⠄⠠⡀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢐⢘⠈⠀⡠⠀⠠⢀⠃⠀⠀⠀⠘⠁⠀⠈⠑⠔⠈⠑⡆⠈⠁
⠀⠀⠀⠀⠈⠢⠀⠀⢒⠎⠒⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢩⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⢀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠀⡇⠀⢘⠀⠀⢀⠀⠀⢸⢸⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠤⠀⢠⣔⡀⠀⠀⠀⠠⡷⠀⠀⠀⠳⣄⡀⢠⣄⠈⠇⣠⡄⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠑⢦⡀⠀⠀⢾⠀⠀⠀⠀⠀⠀⣖⠆⣠⠖⣾⣿⣷⣮⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⠢⣅⣇⣸⣨⠔⡹⡃
⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⢸⠀⠀⠀⢱⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡾⢁⡀⣿⣿⢟⣿⣇⠷⠉⠀⠀⠀⠀⠀⣀⣀⣛⣨⡷⡉⠎⠹⣷⣾⣀⣛⣀⡀
⠀⠀⠀⠀⠀⠹⣇⣀⠀⠉⡹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣔⡆⣧⠈⠀⠿⣿⣿⣿⡟⡀⠀⠀⠀⠀⠈⠙⠛⠓⣒⠲⣦⡀⢘⣰⣿⡷⠐⣒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠛⣢⠴⣁⡀⠀⠀⢰⠋⠓⠤⡀⠀⠀⠀⠀⠀⠀⣘⢦⣄⣀⣻⣿⠟⠱⠏⠂⠀⠀⠀⠀⠀⠀⠀⢉⠞⣡⠛⡟⢻⠃⢌⢦⡉
⠀⠀⠀⠀⠐⢖⡒⠉⠁⠀⠈⠉⢓⡶⢧⣶⠤⠴⠇⠀⠀⠀⠀⠀⠀⠏⠃⠈⠉⢭⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠊⠘⠛⡇⡌⠺⠃⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠈⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⢶⢆⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠊⠀⠀⠀⠀⢩⢢⠀⡀⠀⡔⡏⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣤
⠀⠀⢰⣿⡆⠀⠀⠀⠛⢍⠉⠑⠢⢄⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⢄⠈⣺⣁⣁⣘⠴⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⠔⠊⢉⡴⠋⠀⠀⠀⠉
⠀⠀⠀⠉⠀⠀⠀⢢⡆⠂⢳⠀⠀⢀⠙⣄⠀⠀⠀⠀⠀⠑⠪⠵⢤⠊⡡⢤⣤⣌⠑⢄⣠⢒⣲⠖⠊⠀⠀⠀⠀⡜⢡⡟⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢘⠆⠀⢈⣇⠘⡄⠀⠀⠀⠀⠀⠤⠀⡇⢸⠁⠸⣯⣿⡆⢸⠈⣁⠀⠀⠀⠀⠀⠀⢸⠉⣻⠀⠓⠊⠀⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡤⣉⡿⠀⡇⠀⠀⠀⣀⡄⣒⠴⠸⣌⠢⣤⡿⠟⢁⠮⡄⢄⡀⠀⠀⠀⠀⠀⢸⣀⠼⡀⠀⠀⠸⡁⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠤⢸⡿⠁⡼⠀⠀⠀⠉⠉⠀⠀⠤⠂⣨⡗⠒⠒⣚⡁⠠⡈⠑⠚⠲⠄⠀⠀⠀⠀⢣⡐⠓⣤⣀⠐⠛⢓⣒⡾⡻⠋
⠀⠀⠀⠀⠀⠛⢯⣉⠀⠐⠛⠋⣁⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡡⠃⠰⠀⢳⡱⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠙⠮⣄⣉⢉⣏⣛⡬⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋


⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠼⠁⠀⢀⡴⠚⠉⠃⠀⠀⠀⠀⠀⠹⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠁⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠈⡇
⠀⠀⠀⡰⠚⠉⠉⠀⠀⠀⠀⠀⠀⠷⢤⡀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠿⠀⠀⢠⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣠⠇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣀⡀⠀⠉⣀⠤⠤⠤⣀⠉⠀⢀⣠⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠉⠛⢀⠊⠀⠀⠀⠀⠀⠑⡄⠙⠁
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠤⠤⠀⠀⠀⠋⠃⠀⠘⠙⠀⠁⠀⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠀⠐⠤⠃⠀⢠⠇
⠀⠀⠀⠀⠀⢀⣠⣤⠎⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠚⠋⠀⠈⠒⠠⠤⠄⠒⠁⠀⠘⠳⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⢤⡀
⠀⠀⠀⠀⡜⠁⠀⠀⠀⡀⠀⠀⠀⡀⠉⠓⢦⠀⠀⠀⠀⢠⡟⠀⠀⣦⠀⠀⢻⠆⠀⠀⠀⠀⠀⣀⡤⠤⠏⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⡇⠀⠀⠀⠈⠈⢠⢤⠀⠈⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢
⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠀⡠⢢⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠋⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠳⠤⢤⢤⠤⠤⠤⠤⠤⠤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠒⡡⢢⠑⠊⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⡀⠀⣀⠀⠓⠲⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⣸⠄⠈⠒⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣈⣁⣀⣈⡱⠟⠉⠉⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠋⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡳⣞⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⢿⣤⣉⣉⣤⣿⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⣀⣤⣀⠀⠀⣸⢧⡈⠓⠤⣏⠀⠀⣀⣤⣀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⡇⠀⠈⠉⠉⠹⣆⠉⠲⢤⡏⠉⠉⠁⠀⢸⡂⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡖⠒⠋⠀⠀⠀⠀⠀⠀⢯⣑⣂⡼⠀⠀⠀⠀⠀⠀⠙⠒⢲⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠙⢦⣄⠀⠀⠈⠧⠤⠴⠒⠒⢦⠀⠀⠀⠀⡴⠒⠒⠦⠤⠼⠁⠀⠀⣠⡴⠋⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣇⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠈⠑⠶⠖⠋⠁⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⣸⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡟⠓⠚⠙⣆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣰⠛⠓⠚⢻⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢿⡀⠀⠀⠘⣆⢀⡴⠛⢦⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⡴⠛⢦⡀⣰⠃⠀⠀⢀⡿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠁⠀⠘⢧⣀⣠⡞⠁⠀⢳⣄⣀⡼⠃⠀⠈⠉⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢦⣀⣀⣤⣄⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣠⣤⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⣰⠞⠛⣦⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣴⠛⠳⣆⠀⠀⡼⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠸⣆⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠀⠙⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄⠀⠀⢀⣾⠻⣧⡀⠀⠀⣠⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢈⣿⠀⠀⢸⣇⣀⣽⠇⠀⠠⣿⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⢀⣉⣛⣉⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⢸⣿⠉⣿⠀⠀⠀⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣀⣠⣼⣿⠀⣿⣤⣄⣀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢿⣇⣸⣿⠉⠉⠹⣿⣤⣿⠉⠉⠉⣿⣄⣸⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣌⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣡⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣯⠉⠛⠛⢻⣿⠛⠻⠿⠟⢻⣿⡟⠛⠛⢉⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⠷⣦⣴⠟⠻⣷⣤⣀⣤⡾⠛⠷⣦⣴⠾⠃⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⡈⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠉⣁⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡟⠛⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠟⠛⢻⣯⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⠛⣷⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⢠⣾⠻⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⠷⠶⠾⠋⠈⠻⣶⣤⣤⣤⡾⠟⠈⠛⠷⠶⠾⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⢸⣧⣼⠀⣼⣷⠀⣿⢹⡆⣿⢹⡎⢷⣴⠏⠀⠀⣿⣽⡇⣿⢸⡏⣷⠉⣿⠋⢸⣧⣼⡇⡟⢻⡆⣸⣷⡙⣧⡾⠁
⠀⠀⠸⠇⠹⠰⠟⠛⠇⠿⠋⠁⠿⠋⠁⠀⠿⠀⠀⠀⠿⠾⠇⠿⠸⠟⠿⠀⠿⠀⠸⠇⠹⠃⠷⠾⠳⠟⠛⠧⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠦⡄⠀⠀⠀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⢀⡟⠀⠀⠀⠀⠘⠄⣀⣴⠇⠀⠀⠀⠀⠠⡊⠉⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢠⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣧⠀⠀⢃⢾⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡟⠀⠀⢣⣾⠟⠿⠶⣶⡀
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠠⣒⣦⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠢⠀⠐⠂⠉⠀⠀⠀⠀⠀⢁⠤⠖⠛⠁⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠍⠻⠿⡁⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠄⠀⠐⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⢸⡧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠀⡅
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣼
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠰⡄⡐⠘⡄⠀⠸⣿
⠀⠀⠀⣇⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢸
⠀⠀⠀⢹⣶⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⠋
⠀⠀⠀⠈⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⣼
⠀⠀⠀⠀⡟⠔⠀⠀⠂⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣰⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⠐⠀⢀⣀⡀⠄⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⡟
⠀⠀⠀⠀⠸⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⠔⠂⠁⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡏⠛⠐
⠁⠀⠀⠀⠀⠀⠺⠗⣣⠘⢸⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠞⠉
⠀⠀⠀⠀⠰⠀⠀⠀⠈⠛⠢⢄⡁⠙⠛⠳⠶⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠈⠉⠒⠲⠤⣄⠀⠈⠈⠉⠉⠑⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠤⠤⠤⡀⢠⠔⠒⠒⢤⡀⡠⠤⠠⢤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⣀⡤⢄⡀⣰⣋⣀⡤⠽⠖⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠓⠾⠥⢄⣈⣱⡄⣀⠤⢄⡀
⠀⠀⠀⡞⠁⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠘⡆
⠀⠀⠀⣧⠒⠋⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠓⢦⡇
⠀⠀⠀⡇⠀⠀⠀⠀⣷⠊⠉⠉⠑⣄⣠⠔⠒⠦⡀⠀⣠⠤⢤⡀⢀⡤⠖⠒⢤⣀⡔⠉⠉⠉⢲⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⣀⣀⠴⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡏⠀⠀⠀⠈⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡷⢄⣀⣀⠔⠁
⠀⠀⠀⠀⠐⡅⠀⠀⠈⠢⠤⠤⠖⠙⢆⡀⠀⣀⡼⢧⠀⠀⠀⣠⠿⣄⠀⠀⣠⠞⠑⠤⠤⠴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠳⡄⠀⠀⠀⠉⠉⠁⠀⠀⠉⢒⠊⠁⠀⠀⠉⠉⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡗⠒⠊⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠙⠒⠒⡇
⠀⠀⠀⠀⠀⡟⠢⢄⣀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠖⠉⠀⠀⠀⠈⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⢀⣀⠤⠚⡇
⠀⠀⠀⠀⣠⡏⠒⠤⣈⡉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠋⣉⡠⠔⠊⣧⡀
⠀⠀⠀⢰⠁⡇⠀⠀⠀⠉⠉⠒⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠀⡇⢹
⠀⠀⠀⠈⠢⣈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢊⡡⠊
⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠚⢉⣉⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⣖⣒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣖⣒⡶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠭⢿⠉⠉⠉⢹⠯⠭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⢸⢚⡲⠄⡄⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠙⡟⠂⢠⣀⢂⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣤⣀⣀⣀⣀⣈⣀⣀⣭⡶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠉⢉⡉⠉⠉⠉⠁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠁⠠⠤⠀⠀⠀⠤⠄⠐⣀⠀⠀⠂⠐⠀⠀⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⠀⣀⠀⠀⠄⠀⠐⢄⢖⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣧⣴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣁⣀⣀⣤⣤⠶⠞⠛⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣤⣤⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⡀⠄⢂⠀⠡⠂⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠍⠀⠀⠈⢵⡄⠈⠐⠢⢦⣶⣄⣀⣀⢀⡀⠀⠀⣀⢀⣀⠀⣤⠴⣖⡞⢀⠀⠀⠀⠀⠘⣡⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠱⠀⣀⣋⠀⢠⢙⠃⢠⠀⢼⠉⠷⢶⠀⡀⠠⢐⠃⠀⠊⠙⠂⢠⠀⠐⠤⠌⠀⢀⠀⣀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡷⠧⠉⠒⠄⠁⣄⡀⠂⠈⠀⠠⠀⠀⠂⠀⠙⠀⠁⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠂⡙⠃⠢⠐⢉⡂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣇⡀⠀⠀⢀⠐⠒⠄⠈⠁⢀⠐⡀⢠⠀⠀⠀⠐⠀⠐⠀⠀⠀⢤⠦⠀⡄⠀⠀⠀⢐⣤⣶⣶⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⠛⠻⣶⣦⣤⣤⣄⡂⠀⠀⠀⠀⡉⠀⠑⠂⠀⠀⠀⢈⠀⠀⠀⣀⣠⣤⣦⣴⣶⣿⡿⠛⠋⠁⡐
⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⠀⢬⡀⠀⠍⠉⠛⠻⠿⢿⠿⠿⢶⣶⣶⣶⣶⣶⣿⣿⡿⠿⡿⠟⠛⠛⠉⠉⢁⠀⢈⠀⠄⠊⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠈⢻⡀⣀⠀⠀⠀⠀⠉⠒⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⡤⣆⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠒⠃⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⡖⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢧⡤⢤⣀⣠⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⢀⡦⣄⡞⠲⠾⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠒⠈⠉⠉⢛⠋⠉⠷⢞⢹⡶⠎⠳⢶⠉⢲⠋⡙⠛⢋⠛⠁⠉⠠⠤⠤⠤⠤⠀⣀
⡇⠀⣀⠠⠀⠀⠒⠈⠉⠉⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠄⠂⠘⢀⠀⢀⡘⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢠⢀
⡇⠁⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⠤⡦⠀⠀⠀⠀⢠⠄⠰⡀⠀⠀⠩⠄⡆⠠⠣⠈⡃⠀⠐⠀⡠⠀⠀⣀⠐⡄⠀⠶⣀⠀⣀⢀⠀⢀⡀⢀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠀⠤⠬⢀⠤⠄⠀⠀⠐⠁⠀⠀⢀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠐⣨⠂⠀⠘⣈⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠀⠘⠠⠒⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑
⠏⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠁⠀⠀⢀⠈⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⡠⠀⠀⣀⠤⠂⠒⠀⠉⠉⠁⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢢
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠓⠒⠒⠒⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃
⠀⠀⠀⢻⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⢸⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⡰⠃
⠀⠀⠀⠀⢇⠄⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠔⠈⢿⣿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠐⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠢⣀⡀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠢⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠐⠒⠂⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⡏⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢀⡠⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡡⠐⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡠⠒⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠂⢁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⡧⢂⠡⢺⠁⠀⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠳⠥⠄⠐⠀⠀⠀⠀⠀⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠈⠏⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠔⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⠀⡏⠁⠒⠆⠀⠀⢤⠀⠄⣤⠠⠀⠖⠒⠈⢹⠀⠀⢠⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠰⠀⠀⢰⠀⠀⢰⠀⠀⢸⠀⠀⡇⠀⠀⡆⠀⠀⡆⠀⠀⠆⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠀⡄⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⢠⠀⠀⠸⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡀⠀⢠⠀⠀⡆⠀⢠⠀⠀⠀⠀⠰⠀⠀⡄⠀⢀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⡀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠂⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠧⠄⢠⡀⢰⠀⢠⠀⠀⠆⠀⡆⢀⣄⠀⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⠙⠓⠒⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⣀⡤⠴⠒⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⣤⣀⡀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣴⠒⢦⡔⠛⣷⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⡴⠋⠀⠀⠀⠀⣀⢴⡄⠀⠀⠀⠀⠀⠙⠶⣤⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠳⣄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠟⠁⠀⠀⠀⢠⣞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠈⢳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⣴⠏⠀⣰⠏⠀⢀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⢾⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣷
⠀⠀⠀⠀⢰⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⠀⠸⣧
⠀⠀⠀⠀⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡇⠀⢹⡆
⠀⠀⠀⢰⡟⠀⢰⡇⠀⠀⠀⠀⠀⢠⡴⢤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⣾⠙⠶⠚⢳⠀⠀⠀⠈⣷⠀⠈⣧
⠀⠀⠀⢸⡇⠀⢸⠃⠀⢀⡀⠀⠀⢸⡄⠘⠋⣻⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣄⢀⣴⠏⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣾⠇⠀⠻⠟⠀⠀⠀⠻⠶⠞⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣶⠀⣿⠀⠀⢹
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⢾⣿⠀⣿⠀⠀⣾
⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠟⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀⢀⣴⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠔⢀⡿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣿⡄⠀⢾⡽⠋⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⡴⠛⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡇
⠀⠀⠀⠀⢷⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣼
⠀⠀⠀⠀⠘⢧⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⣆⡀⠀⠘⠟⠀⠀⠀⣠⣤⡴⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣤⠖⢄⣀⡀⠀⠀⠙⠚⠀⢠⠏⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠻⣦⡀⠀⠀⠀⠸⣧⣀⡁⣼⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⡽⠀⠀⠀⠀⢠⠏⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⠯⣽⣓⣶⣤⣄⠀⠀⠀⠀⠈⠳⠶⠚⠁⠀⠀⢀⡴⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⢶⣄⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠶⠀⠀⠀⠀⢀⣠⡴⠋⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠈⠻⢦⣄⡀⠀⠀⠻⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠉⠛⠳⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⢄⣠⠴⠚⢉⡀⠙⠒⢦⣀⡠⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⢁⣤⣶⣄⠀⠙⣦⣾⣿⣿⣷⣆⡜⠁⣠⣤⡀⠈⠳⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡰⠃⠈⣵⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠞⠉⢀⡴⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢋⡱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠉⢀⠔⠋⢠⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⢋⡔⣈⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠏⡀⢠⠎⢸⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠤⠖⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⠲⢤⣁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠈⡞⠁⠤⠚⢡⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⡇⢲⠀⠈⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⡿⡀⣇⠀⣀⡤⠊⠀⢀⠜⠋⡰⠉⠻⢿⡿⠿⣿⡿⠛⢿⣿⢿⡿⣿⠟⠋⠰⢈⠙⢧⠀⠊⢀⡜⠀⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⢾⡦⣄⣀⢀⣰⠃⢀⡴⠃⡟⠀⠀⢻⠞⠁⢠⠏⠀⠙⢦⡾⠁⢀⡰⠃⢸⠀⠀⣇⣀⠀⣀⡠⠞⣡⠋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⢬⣁⠹⣄⠀⢀⠔⠁⠀⢀⣾⠐⠚⠁⠠⠃⠀⠀⣧⡀⠈⠀⠰⠃⠀⣠⠏⠉⠉⢁⡠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⡀⠀⠀⠈⠑⠺⠷⣶⣶⠖⠒⠋⠘⠦⣀⣀⣀⣀⡤⠞⠀⠉⠒⠲⠶⠖⠚⢁⣠⠤⠒⠉⠀⢀⡠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠚⠋⠉⠁⢀⡴⠒⠒⢀⣞⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠙⠒⠒⠒⣞⠉⠉⠓⠦⡀⢀⣀⣠⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠒⠂⠀⣮⣀⣀⡠⠞⠀⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠙⠲⠤⠤⠖⠻⣄⡀⠀⠉⢓⣠⠖⠉⠉⠉⠃⣀⠜⠡⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⢹⠁⠀⠀⠀⡏⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⢄⠀⠀⡠⠤⠀⢀⡀⢀⡀⠀⠀⢀⠀⣠⠲⡄⡠⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⠇⢸⠀⢰⠃⠀⠒⠋⡇⡏⠘⠀⠀⡏⠉⠁⠀⠧⠇⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⢤⠼⠀⠀⠀⢠⠃⢹⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠀⠳⠴⠃⠀⠀⠀⠀⠀⠀⡏⠉⠓⠦⣀
⠀⠀⠀⠀⠀⢀⣞⠁⢰⠉⡳⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢞⠉⡦⠈⡳⡀
⠀⠀⠀⠀⠀⠸⡌⠂⠀⠀⠀⠀⠀⠀⠀⠉⠩⡙⠓⠒⠒⠒⠒⠒⠒⠒⢋⠍⠉⠀⠀⠀⠀⠀⠈⡠⠚⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⢢⠀⠀⠀⡀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠇⡜⠁⢸⠀⠀⠀⠈⠋⠀⢱⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⢀⠀⠀⠀⣼⠵⠤⣄⠀⣴⡸⡀
⠀⠀⠀⠀⠀⠈⢲⠃⠀⠸⡄⢀⠆⠀⠀⠀⣼⠀⠀⢀⡀⢸⠀⠀⡇⠀⠰⠛⣆⠀⢀⡇⠀⠀⠘⠚⢹⠃⢣
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠊⠀⠀⠀⠀⢹⠀⠀⣼⠐⠁⠀⠀⢧⣠⠇⠀⣿⠀⠈⡇⠀⠀⠀⠀⠸⣆⡼
⠀⠀⠀⡠⠤⡴⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠀⢈⡗⢦⠤⣄
⢀⣠⠞⠧⠴⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠘⠦⠼⠳⣄
⡏⢯⠀⠀⠀⠀⠀⠀⣙⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣒⣋⠀⠀⠀⠀⠀⠀⡽
⠘⢆⡓⢤⣀⠀⠀⠐⢅⡨⠂⠀⠈⠉⠉⠓⠒⢒⣶⠶⠶⠶⠶⠶⠶⣶⡒⠒⠚⠋⠉⠁⠀⠐⢅⡨⠂⠀⠀⣀⡤⢚⡱
⠀⠀⠙⠲⢬⣙⠓⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣉⣉⡉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⢉⣉⣉⡤⠤⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣀⢛⡦⢄⠀⣀⣀⣀⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠚⠛⢇⣀⣭⠙⠤⡶⠆⠸⢉⣵⡐⠲⠗⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠖⣂⠄⠀⢁⡀⠀⡀⢀⠀⡀⣤⠄⡤⠤⣢⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠤⢬⡕⣴⣆⡿⠁⢈⢰⠴⡇⣉⣣⣇⣰⠀⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠶⡒⣄⡀⣫⠈⢉⢁⢸⣆⣀⣏⣉⣉⣀⣤⣭⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣁⠒⠤⠤⣌⣉⣈⣂⠉⡙⠉⠉⠈⠉⣉⣉⣠⣥⠴⠞⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣉⡸⣂⠤⣠⡄⢤⣈⡩⣉⣉⣉⢉⣉⣠⢁⠄⢰⡆⠚⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡌⢒⠛⠛⠲⠨⢤⣼⣤⣙⣁⣼⣀⣹⣌⣧⣭⣭⣲⠟⢟⢛⣹
⠀⠀⠀⠀⠀⠀⣀⣠⣸⠧⣄⠉⠃⠙⠓⠖⠶⢲⡤⡬⣀⣩⣭⣥⣤⣤⣽⡴⠶⠶⢛⢋⣩⣀
⠀⠠⡀⠒⠐⢅⠀⠀⠙⠲⢄⣁⠘⠙⠼⠶⠤⢤⣤⣨⣄⣄⡤⣤⣤⣤⣔⣦⢴⠶⠟⣋⣹⠏⠉⢓⠅⣀⠂⠄
⠀⠀⠀⠁⠐⠀⠠⠄⠀⠀⠀⠀⠉⠀⠂⠠⠄⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠶⠒⠒⠉⠁⠀⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⣩⠝⠉⠀⠀⠀⠀⠉⠛⢭⡙⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣉⣤⠤⠔⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢭⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢠⠖⠚⢉⣁⡽⠀⠀⢰⠋⢳⠀⠀⠀⠀⢀⡠⠖⡄⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠀⠀⠀⠀⢸⠀⣾⠀⠀⢀⠔⠋⣠⠖⠁⠀⠀⠀⠀⢸⢧⡀
⠀⠀⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣀⠇⠀⠀⠘⠒⠋⠀⠀⠀⢸⡉⢣⠀⠸⡆⠱⡀
⠀⠀⠀⣰⠁⢰⠁⠀⠀⠀⣏⣉⣉⣉⣁⡵⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢣⠀⢣⡀⢱⡀
⠀⠀⢀⠇⡰⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠑⠒⠉⠉⠛⢆⡀⠀⠀⠀⠀⠀⠀⠑⠜⠁⠀⠈⠢⣇
⠀⠀⢸⠞⠁⠀⣇⠙⣄⠀⠀⠀⠀⢀⡴⡶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡑⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⡄
⠀⠀⡏⠀⠀⠀⠈⢦⠘⢆⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢀⡠⠚⢁⠼⠀⠀⠀⡇
⠀⠀⣇⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢏⡠⠞⠁⠀⠀⠀⣼⡇
⠀⠀⢹⢆⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃
⠀⠀⢸⠈⢧⠀⠀⢀⡜⢁⡜⠀⠀⢸⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠞⠀⠀⠀⠀⢠⠋⣳⢸⠀⢸
⠀⠀⠈⡆⠈⡇⠀⡞⢀⠞⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠀⠀⠀⢀⠏⢠⠃⠘⡄⡎
⠀⠀⠀⢹⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢄⣀⡤⠤⣀⡠⠔⡿⠀⠐⣏⠙⠦⡀⠀⠸⠤⠏⠀⠀⢹⠁
⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠉⠉⣀⣀⠀⠀⠑⢦⡈⣣⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⢣⠀⣞⢉⣉⣉⣉⡱⠀⠀⠀⡠⠊⢁⠇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠉⠁⠀⡠⠖⣫⠋
⠀⠀⠀⠀⠀⠈⢣⡈⠉⠁⠀⠀⠀⠀⢠⡋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⡜⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡒⠢⠤⢤⣀⠉⠁⠀⠀⢰⡉⠲⢤⣀⠀⠈⠣⠞⠀⠀⠀⠀⠀⢰⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠙⠢⣄⠀⠀⠉⠓⠤⣈⡵⠀⣠⠴⠒⠦⢤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠽⠦⢤⣀⣀⣀⣠⡾⠥⠤⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠄⠀⠀⠀⠀⠈⠣⠍⠌⠄⠋⠉⢠⠀⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡺⠁⠈⠂⠀⠨⡹⠀⠀⠀⢀⠄⢄⠀⠀⠈⠒⠂⠀⠈⢫⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣊⠉⠁⠀⢀⠤⡀⠀⢀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠤⠒⠀⠀⠀⠀⠁⢄⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠈⠤⠃⣀⠀⠀⠑⠁⠀⠡⠼⠀⠀⠀⠀⠀⡔⠒⡀⠑⠚⠀⠀⠀⠀⠀⢀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡄⡄⠀⢸⠀⠑⡰⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⡁⠊⠀⠀⠀⠔⢠⠀⠀⠀⠣⠔⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠑⠁⠀⠀⠁⠉⠀⠀⠀⡠⠤⠤⢠⡊⠠⠠⠄⢘⠠⢀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⡈⠢⠀⠀⠀⢀⠔⠊⡂⠀⢠⡒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⢂⠀⠀⢘⣙⠀⠀⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠑⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠁⠀⠀⠀⢀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⠀⠀⢠⠒⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⢀⠤⡀⠀⠀⠀⢇⠰⠀⠒⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠀⠀⠈⠒⠁⠀⠀⠱⡠⠃⢐
⠀⠀⠀⠀⠀⠀⠀⠰⢠⠀⠈⠒⠁⠀⠀⣀⠀⠀⠀⠀⢃⣈⠐⠤⢀⣀⣀⣀⠠⢊⠸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠣⡀⠀⠀⠀⠘⠴⠁⠀⠀⠀⡄⢄⠈⠆⣀⠄⠂⢐⠀⠊⠀⠀⠀⢆⡁⢸⠀⠀⠀⣎⢱⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡆⠀⠀⡎⢢⠀⠀⠀⡔⠱⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢔⢰⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣀⠀⠀⠀⠈⠈⠁⠀⠰⣁⡑⠀⠐⡅⠠⠕⠀⠀⠀⢠⠂⠉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣈⣚⠠⠀⢤⠀⠀⠀⡀⠀⠀⠀⡀⠀⢈⡉⠀⠀⠀⡰⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡇⠀⠈⠚⠀⡠⠊⠀⠀⠀⠈⠁⢀⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠛⠒⠀⠀⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡎⠀⠇⠀⢀⠔⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡌⠙⠒⢼⠠⠐⠛⠠⡟⢀⣔⡿⠒⠒⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠡⡀⠀⣠⠏⠸⠁⢈⡒⢢⡀⠘⣄⠀⠁⠀⠀⠀⠀⠘⢏⠉⠁⢈⡸⠁⠑⣏⠈⣧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⣱⡯⠣⢴⡆⠙⡤⠸⠊⢙⣶⣿⣷⣶⣄⠀⠈⠀⠀⠸⠶⣈⣁⠴⡄⢴⠁⠈⢦⢠⡯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢤⣾⠑⢦⢸⠀⠋⢁⡔⠛⣾⡿⣺⣘⠽⢼⡽⣦⣄⢤⡧⢊⡥⢖⠛⠃⠀⠱⠀⠣⡀⣁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⡇⠀⠀⠀⠀⠀⡰⢻⡿⠒⣤⢞⣿⢿⢷⣷⣲⣏⢏⢱⣳⡿⠼⠒⠛⠲⠧⢄⣠⠁⠉⡤⠐⢇⠈⡦⢜⠉⠓⢤
⠀⠀⠀⠀⣠⠊⠁⠐⠀⠱⡀⠀⠀⠀⢠⡀⠀⠀⣼⣯⠮⣗⣏⠿⣻⣟⣿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠓⡄⠸⠣⣀⡸⠈⠃⠀⠱⡀
⠀⠀⠀⡸⠁⠀⠀⠀⣀⡀⠈⠑⠒⠒⠟⠳⢄⣀⣿⣟⣿⣿⢎⣸⣛⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠛⠶⠚⠁⠀⠀⠀⣀⠀⠇
⠀⠀⠀⡇⠀⠀⠃⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⢿⣻⣮⣾⣿⠿⠃⠸⣏⡒⠄⢒⣒⣒⠦⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠪⠤⠷⠀⠀⠀⡄
⠀⠀⠀⡼⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡈⠉⠉⠀⠈⠀⠉⠢⣕⠢⣄⠀⠀⢠⡇⠀⠀⠤⠄⠀⠀⢀⠔⡇
⠀⠀⠀⡇⠈⠳⡌⠀⠄⠀⠠⠤⠀⠀⢀⣀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠙⠲⠭⠿⠟⠁⠀⠀⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⡇⠀⠀⠈⢦⡀⣀⢀⡀⠀⠠⠌⢉⡀⡀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⡰⠆⠠⠀⠀⠈⠁⣀⠤⠒⠒⠊⠁⣰⢻
⠀⠀⠀⠘⣄⣀⡀⠀⠀⠀⠀⠈⠒⠒⠒⠦⡀⣁⣉⣀⣁⢀⣀⠈⠀⠉⠀⠁⠒⠂⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡿⢦⡀⣰⠿⠛⠛⠉⠨⡇
⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠀⠀⠄⠊⠁⠈⠁⠀⠉⠀⠀⢀⡾⠁⠠⠀⡇⢻⡀⠄⢀⠔⠁⣧⣀
⠀⠀⣠⢴⠈⠣⣉⡇⠀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⢒⢶⣄⣀⣀⣀⠀⠀⣾⠀⠀⠀⠀⡇⢸⣢⠐⠀⠀⠀⡧⠈⠓⣄
⢀⡔⠁⣸⠀⠀⠈⡇⠠⡟⢘⠥⡂⢙⢿⣷⣄⠀⠀⠀⠀⠀⣠⠖⠏⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⡧⠀⢿⠀⠀⣀⠠⡷⡏⠀⠀⠀⢀⣠⠃⠀⠀⠈⢦
⡜⠀⠀⠈⣦⣄⠀⠑⠚⠀⠉⠀⠛⠐⠀⠨⢿⡆⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠃⣿⢠⠞⠛⠉⣻⠀⠀⠀⠀⠈
⡇⠀⠀⠀⡯⠘⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡎⠀⠀⠀⢀⣇⣸⠎⠀⠀⠀⣹
⢳⠀⠀⠀⠓⢦⡀⠙⢿⣦⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⡇⢀⣠⠞⠉⠉⠁⠀⠀⢀⡴⠉⠀⠀⠀⠀⡸
⠀⠳⡀⠀⠀⠑⠉⠢⣀⠉⠛⠿⠷⣦⡤⠒⠶⣾⠀⠀⢷⣤⣤⣤⣤⡀⠀⠀⣀⣤⣤⡤⠞⠋⠉⠓⣏⠀⡸⠁⠁⠀⠀⠀⠀⢀⠴⡪⠊⠀⠀⠀⢀⡔⠁
⠀⠀⠈⠢⣄⠀⠀⠀⠀⠉⡒⠤⣀⠀⠀⠀⠀⢸⡀⢀⡎⠀⠉⠉⠙⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡀⠄⡪⠁⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠁⠀⠉⠔⠒⠠⢬⡅⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠆⠁⠀⠁⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢄⣀⡀⠀⠀⢸⠁⠀⡧⠋⠁⠈⠩⠟⠭⠬⠬⠛⠋⠀⠈⠙⠀⠀⠁⠀⠀⠀⢀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⡏⠀⠀⢸⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠜⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⢂⠀⢀⠔⠀⠀⠀⠀⠀⠀⠠

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢄⠠⠊⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠁⠠⠐⣂⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡀⢀⢈⠉⣀⡠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⠃⠉⠀⠀⢀⢠⢄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⡐⢀⠁⢀⠥⠼⡁⢄⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡗⡌⢄⡤⢾⢉⠉⠉⠑⡓⠀⠀⠘⡦⢀⣲⠃⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⠈⣉⣁⣈⣂⣀⣀⣒⡀⠀⠀⠀⠉⠠⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠤⡀⠀⠀⠀⠠⡀⢀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠒⠤⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠐⠈⠁⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠐⠒⠂⠀⠤⠤⠀⠀⠀⠤⠤⠀⠒⠒⠒⠂⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢠⣓⡄⠀⠀⢀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠇⠀⠀⣿⣩⡇⠀⠀⢿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣭⡇⠀⠀⣟⢩⡇⠀⠀⣟⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⡇⠀⠀⣟⢥⡇⠀⠀⣟⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇⠀⠀⣿⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣴⡇⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠆⠒⠛⠛⠓⠀⠉⠉⠉⠉⠉⠁⠉⠛⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡖⠉⢢⢀⡴⡄⡎⢸⠀⢸⠁⢸⠀⡇⢡⠀⡎⠀⢱⢠⠒⠀⢴⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⢸⠈⡇⠓⠂⢸⠀⠸⠀⢼⠀⢃⠼⠀⡇⠀⣆⢈⠀⠓⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠁⠀⠀⢨⠀⣸⠃⠈⠒⠂⡇⠀⢸⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠤⠤⠆⠒⠒⠒⠚⠛⠉⠀⠉⠉⠈⠁⠒⠚⠒⠂⠤⠤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠒⢤⠀⢀⣀⢀⡊⢦⠀⡰⠋⢱⡀⡎⠱⠀⢠⠊⠑⡄⢀⢤⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠇⠀⢰⠀⢂⠸⣠⠆⠘⠀⢃⠀⢘⠃⢣⢀⠀⢣⠀⠀⡇⢸⠐⠤⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣄⡸⠀⠀⠀⡇⠀⠸⠀⠹⣀⡸⢸⠀⠈⡄⠀⠣⠞⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠀⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⠀⢠⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡜⠒⡄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠈⠲⠤⠍⣐⣒⠒⠐⠲⠆⠀⠀⠤⠤⠤⠄⠀⠀⠐⠶⠒⠒⣒⣒⡩⠤⠖⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠬⠭⠍⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⠉⠭⠥⠤⠤⠐⠒⠂⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢕⣠⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣊⡤⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⠭⠉⠀⠀⠐⡷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣀⡠⠄⠀⠀⠀⢀⡗⢆
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠐⠒⠒⣊⠩⠀⠼⠓⡄⠀⠀⠀⠀⠀⠤⠐⠒⠂⠐⠒⠂⠀⣉⠥⠄⠤⠋⡆
⠀⠀⠀⠀⠀⠀⠤⠒⠒⠀⠀⠤⠔⠊⢁⠤⠄⠀⢠⣁⠀⠀⠀⠀⠀⠔⠒⠒⠂⠤⠤⠒⠉⢀⠤⠄⠀⢀⠇
⠀⠀⠀⠀⠀⠾⢦⡄⣀⣀⣤⣴⣂⣀⣀⡤⠤⡤⡸⠻⠀⠀⠀⠀⠀⠚⠒⠒⠀⠔⠒⠒⠊⠓⠉⢊⠉⡇
⠀⠀⠀⠀⠀⢘⢤⢨⠀⠙⠉⠉⢉⠁⢀⠉⡈⢀⠀⡆⠀⠀⠀⠀⠀⠈⠄⢆⢰⠀⡄⣄⢰⠀⡇⡘⡘
⠀⠀⠀⠀⠀⠈⡘⠘⠀⠰⠀⠀⢸⠀⠈⢀⠃⠘⢰⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘⠀⠇⠻⠈⠠⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠈⠢⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢓⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⣈⠂⠀⠀⠊⣢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠲⠀⠀⠁⠉⠉⠀⠥⡀
⠀⠀⠀⠀⠀⠀⡇⠸⡉⠒⡒⠤⢤⣉⠒⠒⢉⣀⣰⠀⠀⠀⠀⠀⠀⡄⢘⠦⣀⡀⠀⠐⠤⢀⠠⠔⠁⢄
⠀⠀⠀⠀⠀⢠⡯⣁⣈⣓⢌⣓⣦⣠⢕⡢⢤⡠⠠⡅⠀⠀⠀⠀⢀⠣⣈⠢⡀⠤⡉⠑⠢⢄⠀⠐⠐⠂⣀
⠀⠀⠀⠀⠀⠈⡄⢠⠀⡄⢁⠀⠀⠀⡄⢀⠀⡰⢀⠃⠀⠀⠀⠀⠟⠶⣤⣤⣬⣀⣈⢭⣤⣤⡬⣤⠶⠞⡙
⠀⠀⠀⠀⠀⠀⠘⡌⠇⢳⠈⡇⢸⠀⡇⣸⠀⠇⠎⠀⠀⠀⠀⠀⢨⢀⢨⠀⡉⢈⠀⢩⠀⠀⠀⡄⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠈⠘⠀⠇⠘⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡘⠘⠀⠡⠈⠀⠘⠀⠇⢰⠁⠎⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠠⠤⠤⠤⠤⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣔⠿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠷⠬⠝⠖⠃⠀⢀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠉⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⢀⣀⡀⡀⠀⠀⠀⠀⢰⡆⢰⡆⢲⡆⢺⡇⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⢹⡿⣷⣶⡿⢻⣿⡟⣿⠁⠀⠀⠀⠀⠀⠸⣷⢸⡇⢸⡇⣾⠁⣿⠀⠀⠀⠀⠘⠛⠿⠛⠻⡿⠟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⢸⡇⣿⢠⡿⠀⠀⠀⠀⢰⣦⣀⣠⣤⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣄⣇⣸⡇⣿⣸⠇⠀⠀⠀⠀⠀⠛⠻⠛⠻⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠁⣠⣬⣍⠀⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣹⡿⠿⣿⣯⣀⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⣿⣷⡿⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⣿⠉⣿⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠥⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⡧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠙⢆⠀⠀⠀⠀⠀⡄⠀⠀⠰⠀⠈⢀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈⠀⠀⠀⡐⠀⠀⠠⠄⠀⠀⠀⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⣀⠁⠀⠀⠀⠀⢀⡀⠄⢀⣀⠤⢀⣀⠤⣀⠀⠀⠀⠐⢄⠄⠐⠄⠠⡀⠲⠄⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡏⣹⣿⢻⣿⠀⠀⠀⠀⠀⠛⠃⠀⠘⠋⠀⠙⠛⠀⠛⡃⠀⠀⠀⠀⠐⣿⠀⢸⣿⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣷⣿⣧⣬⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⠀⠸⠿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⡄⠀⠀⠀⠀⢠⠃⢆⢣⠀⠀⠀⢀⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡆⢱⠀⠀⠀⠀⢯⢸⢸⢸⠀⠀⠀⢸⢠⠱⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⣄⡜⠀⠀⠀⠀⠈⣻⣿⢿⡄⠀⠀⠘⣼⣾⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⢲⡀⠀⠀⠀⡞⠛⢩⣼⠃⠀⠀⡴⠻⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⢸⡇⠀⠀⢸⣴⣿⡗⣿⠀⠀⠀⣷⣰⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢚⣿⡇⣀⡀⢈⣿⠦⣌⣏⠀⣀⠀⢸⣿⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠶⣤⣶⣾⣿⣻⡏⠭⠛⣿⣿⣭⣿⡯⣑⠢⣿⣿⣭⣿⣿⠿⣋⣿⣷⣶⣶⡴⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⢾⣿⣷⣿⣛⣛⠋⠉⠉⠉⣸⡧⢐⣫⣧⠀⠀⢰⡗⠠⢍⣿⠀⠀⠀⣿⣈⠤⣿⠉⠙⠛⠛⠛⣷⣶⣽⣟⣛⣳⣆
⠀⠀⠀⠀⠀⢾⣷⢻⣽⣶⣿⣭⣭⣿⣶⡞⠲⣮⣩⣭⣭⣥⣤⡶⢮⣭⣛⣋⣭⣴⡶⢦⣭⡿⡿⢭⣴⡞⣛⣛⠺⣿⣷⣴⡟⣿⢻⡿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⣚⣿⡸⣿⣿⣿⣿⣾⣽⣶⢶⣾⣿⣿⣶⣮⣻⢯⣯⣭⣿⣶⣿⣯⣿⣷⣭⣿⡿⣿⠿⢿⣿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡯⣽⣽⠿⣿⣿⣿⣮⣿⣯⣿⣾⣿⣯⣽⣿⣽⣿⣿⣟⣟⣫⣾⣯⣿⣷⣿⣷⣷⣿⡿⣿⣻⣿⣟⡾⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡷⡏⣵⠟⣿⣿⣿⣞⣭⡭⢿⣟⣯⣿⣿⣟⣯⣭⢯⣟⣿⣯⣷⣿⣿⣷⡿⠞⢾⣿⢿⣿⢫⡷⣿⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⣸⠇⠀⢹⡟⣿⠉⣿⡝⣹⠟⠉⣿⣯⡿⠁⠹⣟⣿⣿⠿⣿⡿⢡⡟⠀⠀⠀⢻⣏⢃⡾⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠀⠀⠘⣷⣻⡿⠃⣴⠏⠀⠀⠉⠉⠁⠀⠀⢿⣭⣿⣠⣿⠇⣼⠃⠀⠀⠀⠀⠙⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣘⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠟⢁⣴⡟⠀⣀⣀⣀⣠⣤⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣫⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠩⠻⣯⡛⠿⠗⢒⣺⣾⠶⢾⣖⠾⣿⣿⠿⢟⣫⡶⠞⠛⠻⢮⣟⣟⣩⡴⠞⠉⠉⣇⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠶⣻⣄⣀⡀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠉⠓⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣠⡶⠿⣟⣷⣄⣀⡀
⢀⣠⠴⠞⠋⠉⠉⢿⡟⣽⢿⣯⣟⢛⣶⡶⢦⣤⣤⣄⣤⣤⣀⣤⣤⣤⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣻⣭⣽⣿⣿⣿⡿⠋⠉⠉⠛⠶⢤⣀
⣾⣧⣄⡀⠀⠀⠀⠈⠻⠾⢿⣽⣿⡿⡷⣿⣿⣷⣷⣿⢿⣿⣫⣴⣶⣮⣿⣿⣛⣿⣭⣴⣦⣽⣷⡾⠿⣶⣾⢿⣻⣿⣵⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽
⠈⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⠈⠛⠿⠿⠻⠷⡿⠿⣿⣯⣿⢾⣿⣿⠿⣯⣭⣽⡽⠿⣿⡿⠟⠛⠛⠛⠛⠛⠉⠀⢀⣀⣀⣀⣤⣤⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢛⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡢⢔⡪⠋⡇⠀⡎⠆⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⡡⠊⠁⡠⠌⠀⡠⠃⡆⢀⡿⢟⠶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣊⠡⠭⠴⠶⢮⣤⡤⣮⠥⠼⠐⢡⠃⡠⠀⡇⢡⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣾⢂⠥⠒⠀⠉⣉⣀⣀⡀⠀⠀⠤⠄⢊⠥⠊⢀⠜⡠⢣⠈⠦
⠀⠀⠀⠀⠀⠀⠀⡆⠬⠺⢿⣓⠴⠦⠍⣐⠶⠤⠀⢀⡤⠤⠖⣊⠴⠖⠚⣓⠾⠛⡡⠊⢀⢷
⠀⠀⠀⠀⠀⠀⠀⡥⠍⠑⠐⢒⣈⡉⠥⢐⣒⡈⠭⠐⠒⠉⣁⠠⠔⠒⣉⠤⠒⢉⡠⠒⡡⣪
⠀⠀⠀⠀⠀⠀⠠⠕⠆⢡⠍⠀⠒⠈⣉⡀⠤⠤⠐⢂⣉⠡⠤⠒⣊⠩⠄⣒⣩⠤⠶⠛⠈⠀⠉⠢
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠉⠉⠙⠀⠐⠒⠒⠛⠃⠠⠒⠒⠙⠓⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡴
⠀⠀⠀⠀⠀⠀⢿⠈⠏⠀⢲⠂⠲⡖⠀⣤⠀⢤⠄⢤⠄⠠⡤⠠⡤⠰⡔⠐⠖⠀⠺⠁⠈⠁⢰⠇
⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⢸⠀⠀⡄⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⡇⠀⠃⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡇⠀⡇⠀⠇⠀⡇⠀⡆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⢁⠀⢠⠀⠀⠀⢀⠀⠸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⠀⢨⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠬⣀⣸⡀⣀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⣇⣀⡅⠼⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠉⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠘⠦⣤⣉⣉⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣀⢴⡏⠀⠀⠀⠀⠀⠈⠢⣈⠑⣆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⣠⠞⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⡤⠞⠋⠉⠉⠓⠦⣤⣀⣀⡤⠎⠀⠀⠉⠉⠉⠀⠀⠀⠹⡆⠀⠘⣏⠛⢦⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣼⠋⠀⡏⠀⠀⣠⠖⢋⡆⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⠀⠀⠈⠣⣄⠈⣧⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠇⠀⠀⢹⠀⡞⣁⡴⡋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀⠀⠨⣙⠲⣄⠈⠳⣄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢹⡆
⢸⡏⠀⠀⢀⡞⠀⠉⠁⠚⠁⠀⠀⠀⠀⠀⡇⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣌⠳⣌⢳⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠏⠸
⣿⠀⢀⠀⠈⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠃⡽⢠⠏
⢻⡄⠸⡆⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⢠⡖⢉⠇⠀⠀⠀⢰⣃⡼⠁⠘⡆⡰⢀
⠘⣷⠀⢷⡀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠒⠂⡄⠀⠀⠈⠙⠓⠶⠦⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠉⠀⠀⠀⢠⡏⣠⠊⠀⠀⠀⠀⠀⠀⣀⡤⠞⢱⠃⣸
⠀⠸⣧⠘⢷⡀⡞⠀⠀⠀⡞⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠃⢠⡟
⠀⠀⠘⢧⡈⢳⡹⣄⠀⣰⠇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡤⠖⢋⡽⠃⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠋⢠⡟⠁
⠀⠀⠀⠈⠻⣆⠙⢮⡉⠁⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠻⠴⠚⠁⠀⠀⠀⠀⠀⠘⠳⠦⠤⠌⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠇⢀⡾⠃⣴⠏
⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠉⠉⠒⠶⠞⢋⡴⢛⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠦⣤⣤⠞⠉⠹⡄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⢚⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡼⠁⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠶⠶⠶⠤⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠙⠂⠀⠀⢦⡄⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠉⠁⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠛⠉⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⢤⣤⣄⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣅⡀⠀⠀⠈⠙⣦⣀⡴⠋⠀⢀⡀⠀⠀⠀⠈⠳⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣷⠀⠘⢷⣄⣠⡴⠛⠻⡆⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⣇⢀⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⣠⠤⠦⠤⠴⠞⠁⣾
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⠀⢀⡞⠁⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⠶⠚⠋⠉⠉⠛⠲⢶⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⡁⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⡈⠙⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠋⠉⠉⠉⠁⠀⣀⣠⣤⠴⠖⠒⢦⠀⠀⠀⠀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⣀⣀⡤⠴⠋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢳⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⣠⠞⠋⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⡴⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠸⣇⣠⡴⠋⠁⠀⠀⠀⣰⠞⢲⡄⠀⠀⢸⡄⠹⡄
⠀⠀⠀⡼⠁⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⡄⠀⠸⡇⠀⠹⡆
⠀⠀⣼⠁⠀⣸⠁⠀⠀⠀⠀⢸⡋⠀⠀⢀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⡄⠀⢻⡄⠀⢹⡄
⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣴⡿⠿⠛⠓⠦⠤⠴⠚⠛⠯⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡿⠀⠀⠙⠲⣄⢷
⠀⡟⢀⡞⠁⢀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢻⡆
⢸⣷⠋⠀⠀⠘⢇⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻
⣼⠁⠀⠀⠀⠀⠘⢧⠀⠘⣆⠀⠀⠀⠀⠀⢰⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀⠀⢀⡴⠚⠁⢨⡇⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⢘⡇⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⠖⠋⠀⣠⠞⠉⠀⠀⠀⠀⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠻⣄⡴⠋⠁⠀⠀⠀⠀⠀⣰⢿
⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢸
⢸⡇⢳⡀⠀⠀⠀⠀⠀⢀⡞⠉⢹⠄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣼⠁⠀⣿
⠀⡇⠀⠹⡄⠀⠀⠀⢠⠟⠀⣰⠏⠀⠀⠀⠀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠂⣿⠀⢀⡇
⠀⢻⠀⠀⢻⠀⠀⣠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠉⠳⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⠏⠀⢹⡀⢸⠃
⠀⠸⡇⠀⢸⠀⠀⠘⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⣴⠖⢦⡀⠀⠀⠀⠀⣼⠁⢠⡟⠀⠀⠈⣧⡟
⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣓⢶⣤⡴⠖⠓⠶⢤⣶⠚⢉⡼⠁⠀⠀⠻⢄⠀⠉⠢⣄⠀⠀⠙⠶⠛⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢻⡀⠀⢀⡤⠤⠶⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⢀⣤⠞⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣷⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⢀⣠⠴⣾⠋
⠀⠀⠀⠀⠀⢧⠀⠸⢄⣤⣤⣤⣤⡤⠤⠞⠀⠀⠀⢀⡴⠋⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⣠⠶⢦⣄⡀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠉⠉⠛⠲⠦⣄⠀⠀⠀⠀⠀⠹⢤⣀⠈⠙⠓⠦⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠈⠙⠲⣤⣀⣸⠇⠀⢀⡴⠖⠒⠒⠶⢤⣤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣌⣙⣦⣄⡀⠀⠀⠀⠀⠉⠁⣠⠞⠉⣀⣀⣤⠴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣓⣶⣶⣶⣶⣞⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠹⡄⠈⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠠⠷⠂⠀⠘⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣄⠀⠀⠀⠀⠀⠀⣠⠏⢱⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠈⢓⣦⣤⡤⠶⠋⢁⡴⠋⠀⢈⡷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠚⠉⣉⣀⣤⠤⠴⠒⠋⠀⠀⠀⡼⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠖⠁⣀⡤⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢰⠏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⢠⠎⠀⠀⣿⣤
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⡞⠁⢀⡤⠀⠀⠀⠀⢀⡀⠀⠐⠚⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠟⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⣠⠏⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⠞⣠⣿⣽⠁
⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣆⣇⡇⠀⢀⠞⠁⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢀⣴⣧⣾⠏⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⡿⠛⣷⢚⡥⡄⠀⣠⡀⠀⢀⣼⣁⣀⣀⣤⣤⡖⠲⣿⣿⠁⠀⡟⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⢸⡁⠀⢹⠋⠁⢹⡖⠋⠈⢻⠋⠁⠈⢻⠁⠀⠀⡇⠀⢰⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⠈⡇⠀⢸⡇⠀⠈⡇⠀⠀⢸⠀⠀⠀⣾⠀⠀⢸⡇⠀⡾⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢳⠀⢳⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡿⠀⠀⢸⠀⢰⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠇⢸⡄⠀⣇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣼⠀⡼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠃⠀⠻⠀⠀⣧⠀⠀⢸⠀⠀⠀⠇⠀⠀⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠉⠀⠀⠈⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢞⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠘⠁⠀⠀⡜⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⡠⠋⠀⠀⠀⡠⠀⠀⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠎⠀⠀⠀⠀⠔⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠁⠀⠀⢀⠔⠃⠀⠀⡠⠁⢠⠓⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢀⡦⠀⠒⠒⢂⢤⡎⠀⠀⢄⣤⠊⠀⠤⠋⡈⠐⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡐⠋⠢⣌⡠⠔⠊⠁⠀⣀⠤⠒⠂⠁⠀⠀⠀⠀⠀⠄⠀⠀⡄⠹⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣣⡈⠛⠤⢋⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠠⠁⢐⢦⠀⠱⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠈⠁⠒⠀⠤⢏⡀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⢀⣴⠡⡴⠊⠀⠆⠀⠃⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡒⠓⠤⠄⠤⠀⠀⠀⠀⠀⠈⠁⠲⠾⠤⠤⠀⠒⠂⢈⠉⠤⠐⠊⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⣑⡠⠤⠀⠀⠀⠂⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠀⠀⠀⢀⡀⠤⡴⠊⠀⠀⡰⠀⣰⠃
⠀⠀⠀⠀⠀⡀⠄⠖⠋⠙⡁⠀⠉⠐⠠⠄⠀⠀⠀⠀⠀⠠⠤⠄⠀⠒⠒⢀⡉⠁⠄⠂⠁⠀⠀⡠⢚⡠⢊⠆⢀⡀
⠀⠀⠀⠀⡊⡀⡌⠀⠀⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠐⠂⠉⠁⠀⠀⠀⠀⡀⠄⠒⡉⢔⡡⠐⠉⠢⠀⠈⠑⢂
⠀⠀⠀⠀⠑⡙⢳⣄⡀⡀⠀⠀⠀⠀⠀⠈⠁⠉⠄⠀⠀⠀⠀⠀⠠⡤⠀⠒⠂⢉⡁⠠⠐⠋⠁⠀⠀⠀⠀⢀⣂⢀⡔⠟
⠀⠀⠀⠀⠀⠘⢄⠡⡡⡘⡎⢶⠒⢤⠀⢄⠤⢄⡀⡀⢀⣀⠀⢀⠀⢈⣉⠉⢉⡀⠀⢄⡠⠢⡤⠂⡔⢰⢁⢃⢏⠨⠂
⠀⠀⠀⠀⠀⠀⠈⢂⠐⠜⠈⠄⢂⠀⠄⠘⡀⠈⠀⠈⠃⠀⢹⠀⠈⠁⠀⠸⠀⢨⠁⠰⠁⠀⠀⡜⠠⢡⢃⢂⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠌⠌⠄⢣⠘⠀⠁⠀⢃⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⡀⠀⠁⠠⠁⡘⢀⢃⢂⠆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⡌⠜⡀⠆⢁⠘⠀⠘⠀⠸⠀⠀⠀⢠⠀⠀⠀⢠⠁⡌⠀⠆⢰⠀⠀⠄⡌⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⡐⠐⠘⠈⡀⠃⠀⡁⠀⡄⠀⠀⢸⠀⢰⠀⠈⠰⠀⠰⠀⠆⠰⡘⠘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠠⠀⠃⠸⢀⠃⢁⡣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠬⣰⢠⠀⡀⢰⠀⢀⢀⠀⡂⠀⡇⢰⠀⡀⢀⠀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡈⠀⠉⠈⠈⠁⠀⠁⠈⠀⠉⠉
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣚⣯⣍⣉⠉⠉⠛⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣚⣉⣀⣠⠞⠁⠀⠀⠈⠙⠒⠋⠉⠉⠻⡟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⠉⠈⠉⠀⢰⡆⠀⠑⠦⠀⠹⡄⠀⠀⠀⠻⢤⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣠⠞⠀⢤⡀⠀⠀⠘⠃⠀⠀⢀⣀⠀⠀⣠⠖⠀⠀⡄⠈⠳⡌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠉⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠰⠇⠀⠀⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣇⠀⢀⠤⠖⠂⢀⡇⠀⢀⣽⠶⠒⠒⠒⠶⣄⠀⠘⠓⠂⠀⡀⠀⢧⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠃⠀⠀⠀⠀⠀⠘⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⡀⠀⠙⠆⠀⠙⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠲⠦⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠋⠀⡀⠀⠀⣹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⢲⡀⠀⠀⠀⢦⡀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡾⠀⠰⠋⠀⠀⣇⠀⢠⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡆⠀⠁⠀⣶⠀⠀⠁⠀⠘⠳⣄⣀⣀⣀⣤⠞⠁⡀⠀⢠⠞⠀⠈⠀⢸⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢧⣀⠀⢠⡇⠀⠀⠀⢲⠀⠀⣠⠍⠉⣉⣀⠀⠀⡇⠀⠀⠀⠲⡄⠀⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢳⡀⠀⢠⣀⠀⠈⠃⠐⠃⠀⠀⠈⠉⠀⠀⠀⡤⠀⠀⠀⠀⣠⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢧⡀⠀⠈⠀⠀⠀⠰⣄⠀⠀⠲⡄⠀⠀⠸⠁⠀⠐⠲⢾⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⡛⠓⠦⣄⠀⠀⠘⢃⣀⡀⠙⠀⠀⠀⣠⠴⣲⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣬⣝⣓⣚⣉⣉⣉⣳⣶⣤⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢻⠇⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣀⡃⠀⠸⡀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⢀⡴⣊⠀⠈⣿⢆⣿⡇⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⢶⡀⠀⠀⡄
⠀⠀⠀⢀⡴⢀⠄⠁⠀⠀⠀⢀⣠⣠⣏⣾⣿⣿⣿⣵⣿⣿⣧⢀⠞⠛⠀⠀⠀⠀⠀⠰⢆⠘⣿⣄⣀⣀⠀⠀⠁
⠀⠀⢀⣿⣵⠏⠀⡄⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠠⠕⡌⠻⣿⣿⡆⠀⠒
⠀⠀⢸⣿⣄⡁⠀⠣⢀⡀⠤⠊⠁⠀⢀⠈⠀⠈⠀⡠⠚⠋⠀⢀⠜⠝⢿⣶⣄⠲⡀⠀⣳⣼⣧⠀⠈⠉⠁⠀⡄⠀⡀
⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣦⠀⣤⣔⣿⡿⠀⢀⡀
⠀⠀⠀⠀⠮⣻⢿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⣿⣿⡛⢾⣿⢷⡄
⠀⠀⠀⠱⣆⠀⠀⠫⠛⠻⠿⠿⠿⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉⠉⠀⠀⠀⣠⡾⣫⣿⣿⡟⠀⠙⡄
⠀⠀⠀⠀⠈⠙⠒⠄⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠉⠀⠙⠟⠉⠁⠀⠀⠈⠒⠂⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠶⠶⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣫⣍⡀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣥⡀⠀⠀⠀⠀⠀⠀⣀⣩⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠑⠚⢿⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⣻⠳⠾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠶⢾⠀⠀⠀⠀⠀⠀⡏⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⣿⠲⠦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣀⣸⠀⠀⠀⠀⠀⠀⡿⠢⣄⣀⣯⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⣿⠀⠉⠒⢿
⠀⠀⠀⠀⠀⢀⡴⠢⣤⣀⠀⠀⠀⣀⣀⣀⣿⣦⣄⣀⣸⣄⣤⣤⣤⣄⠀⡿⢢⣤⣤⠷⠤⣤⣀⠀⠀⣀⣿⣄⡀⠀⣸⠀⣀⣀⣤⣀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⢳⣴⠛⠉⠉⠉⠉⠑⣦⡝⠋⠁⠀⠀⠀⠈⢻⣧⡞⠉⠀⠀⠀⠀⠉⢧⡞⠉⠀⠈⠙⢿⣿⡞⠉⠁⠀⠈⠙⣦⠞⠉⠉⠉⣷
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠷⣄⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠀⠉⠛⠲⠤⠴⠚⠋⠉⠓⠤⠤⢄⣤⠤⠞⠋⠙⢦⣀⣀⣀⣀⡤⠞⠻⢤⣀⣀⣠⠞⠉⠓⠦⠤⠴⠋⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⣄⡀⠀⡇⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡼⠋⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⠀⠈⠻⣄⣠⠶⠛⠋⠉⠉⠉⠛⢶⡄⢀⡴⠚⠋⠁⠀⠈⠉⠻⣆⣠⠶⠊⠙⠋⠑⠶⣄⣠⠶⠚⠛⠛⠛⠛⢶⣜⡶⠞⠋⠙⠶
⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠟
⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼
⠀⠀⣟⠉⠉⠓⠚⠋⠙⠶⢤⣤⣤⣤⣤⡤⠖⠲⢦⣤⡀⠀⠀⠀⣀⣤⡴⠖⢶⣀⠀⠀⠀⠀⠀⣀⡤⠾⣄⡀⠀⠀⠀⣠⠞⠳⣤⣄⣀⣠⣴⠏⠀⠙⠒⠒⠚⠉⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠑⠒⠶⠖⠊⠉⠀⠀⠈⠉⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡞⠛⠛⠳⢦⡀⠀⢀⣀⠤⠤⠦⠤⣤⡀⠀⢀⣀⠴⠶⠶⠖⠶⠦⣄⠀⠀⣀⡴⠆⠛⠛⠓⠶⢦⡀⠀⣠⡤⠤⠤⢄⡀⠀⠀⢀⡤⠶⠶⠶⠦⣄⠀⢀⡤⠦⠤⣮
⣯⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠙⣦⡼⠋⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠈
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠲⠶⠤⠤⠶⢦⣄⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⢀⡜⠛⠶⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠉⠛⠓⠶⠶⠶⠞⠛⠁⠀⠈⠳⠆⣀⣠⣠⡴⠞⠋⠈⠛⠶⠦⠤⠶⠛⠁⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⠴⠶⠦⠤⠤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⡠⢄⠀⠀⠀⠀⠘⠧⢭⣉⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⠀⠀⠀⠀⠀⠑⢦⣙⡆⠀⣀⣤⣀⡀⠀⠀⠀⠀⢀⠤⣤⣀⣤⠴⠶⢤⡀⠀⠀⣀⡀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⡼⠁⠀⢀⣀⠀⠀⠀⠀⠈⡰⠚⠁⠀⠀⠉⠓⠶⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢣⡙⠳⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⡾⠁⠘⡇⢀⠔⢋⡴⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠤⣀⠈⢧⠀⠀⠙⠢⠼⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠃⠀⢀⠟⠘⠚⠽⠂⠀⠀⠀⠀⡇⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠶⣌⡑⢌⠳⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⢠⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠃⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡞⢸⡇
⠀⠀⠀⢸⡇⢀⡀⠈⠂⠤⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠔⠁⣀⠀⠀⠀⠀⡜⢁⠇⡞⠀⠀⣷
⠀⠀⠀⠀⣷⠀⣇⠀⠀⠀⣸⠃⠀⠀⠀⢀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠁⣠⠎⠉⠀⠀⠀⠸⠱⠋⠀⡵⡐⢠⡇
⠀⠀⠀⠀⠸⣇⠸⡄⠀⡔⠁⠀⡠⠀⠊⠁⠀⡀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠧⠔⠀⠀⠀⠀⠀⣠⠖⠉⣰⠃⣾⠁
⠀⠀⠀⠀⠀⠙⣦⠹⣆⢇⠀⢀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡤⠖⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣰⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣌⠫⡙⠋⠀⠀⠀⠀⠀⠘⠲⣄⠀⠸⠥⠖⠉⠀⠀⠀⠀⠐⠭⠭⠝⠂⠀⠀⢀⡀⢀⠀⠀⠀⢀⡇⢀⡼⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠒⠒⣋⡴⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⠴⠊⠁⠹⡄⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⣉⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⣀⣀⣠⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠚⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠒⠂⣤⡉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⠶⣈⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⡠⣪⡿⠀⠀⠀⠉⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠐⢷⣄⣲⠄⠀⠈⢲⢢⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⠗⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠞⠀⠢⡀
⠀⠀⠀⠀⡠⢂⠄⣠⢀⣽⠇⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⠇⠀⠀⠀⠀⠀⠀⠀⢰⠢⡀⡀⠀⠀⠀⠀⣤⡘⠄
⠀⠀⠀⡰⠁⠎⠀⠛⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⠀⠀⠀⢼⡾⠀⠘⠆
⠀⠀⣀⠡⣄⠀⠀⠀⢰⢸⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⢰
⠀⠠⡥⠞⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣶⠀⠆
⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠲⡅⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⠀⠀⠀⠀⠀⡀⠸
⠀⠰⡀⠀⠀⠀⢰⣽⢳⣶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠄⠤⠄⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⡿⠀⢀⠀⠀⢠⣾⢁⠇
⠀⠀⢆⠰⢶⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢗⣿
⠀⠘⢌⣄⡈⠻⣷⣤⣀⠀⢠⠄⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⢐⣀⣠⠀⠀⠀⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢛⣵⣿⡟
⠀⠀⠸⠛⢿⣷⡙⣿⣿⠳⢬⣟⠖⠃⠀⠀⣰⣹⠃⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢴⣿⣾⣽⡟⠁⢰⣿⣿⣿⠃
⠀⠀⠀⢆⠀⠙⢻⣮⣭⣀⠀⠨⣤⣦⡄⢠⢌⣥⣾⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣤⣜⣻⠯⠍⠁⢀⣠⣿⣿⡿⠃
⠀⠀⠀⠈⠢⡀⠀⠈⠻⢿⣦⣀⣀⣉⣉⠁⠈⠉⠛⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⣊⣭⡉⠉⠉⠙⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠈⠛⠛⠿⠿⢿⣿⣷⣄⡀⠉⠉⠛⠉⣡⣤⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠛⠟⢿⣦⣠⣤⡾⠿⠿⠿⢻⠿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⣄⣀⠀⠈⠁⠉⡠⢤⣶⣖⣻⣿⣿⢿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⣰⡎⣹⣏⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⣀⣻⠛⠙⠛⢸⠾⠇⢰⣿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⣀⠀⠒⠃⢀⣠⣾⡿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⡛⢋⢀⡴⠚⠉⣅⣳⣶⣿⣿⢧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢶⣿⣿⡿⠋⠀⠀⢀⣻⡿⣫⡿⣿⡾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⡺⣿⣧⡶⠚⢉⡔⣡⣾⣿⠶⠛⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣼⣿⣿⠟⠁⢀⡴⢫⡾⢻⣿⣶⣶⣾⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠍⠛⠿⣶⢶⡿⠓⣛⢛⠛⣿⢿⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣴⣦⣑⣈⠂⡀⢼⡿⣏⡑⣷⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣦⣿⣿⣦⠀⣴⣦⣿⣿⡿⣿⣿⣿⡑⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⣿⡙⣿⡇⠾⢻⣿⠻⣿⡧⠙⣿⡏⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣧⢸⡇⡄⢸⡗⠀⣿⡇⢰⣿⠇⣾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⣸⡿⡇⣿⡇⢀⣿⠄⣿⣿⣼⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⢹⡅⣿⣷⢸⣿⢸⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠷⢾⣿⣿⣿⣿⣿⣿⠟⠋⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣼⣿⡿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⣿⡇⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣤⣤⣼⣷⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⡿⠛⠛⢿⣦⣴⡟⠉⠙⢻⣦⣄⣀⣀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠉⠉⢹⣇⡀⢀⣼⡏⢿⣆⠀⠀⣸⡿⠉⠉⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣤⣽⣿⣿⣋⣀⣈⣻⣿⣿⣿⣥⣤⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡿⠿⠟⠋⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠁⠙⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠛⣿⣿⣶⣶⣶⣿⣿⠏⠈⠻⣿⣿⣶⣶⣶⣶⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⢸⣿⣿
⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀
⠀⠀⣠⣾⣿⡿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⢿⣿⣷⡄
⠀⠀⣿⣿⡃⠀⠀⠙⠿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⠿⠋⠀⠀⢹⣿⣿
⠀⠀⠻⣿⣷⣤⣀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⣀⣤⣾⣿⠏
⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢚⡉⠉⠐⠃⠀⠐⠂⠀⠚⠀⠀⣀⠉⠳⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠠⠀⢀⡤⠖⢚⣉⣉⣉⣹⡆⢤⠀⠀⣀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠆⡀⠀⠀⠸⢴⣞⣩⣥⠤⠖⠋⡀⠀⠀⠀⠁⣰⠒⠋⢻
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⣏⡀⠀⠀⠀⠠⡄⠀⠀⠀⣠⠄⠀⠀⠀⢁⣀⣀⠀⣠⠏⠀⠀⢸⡇⠀⠀⠐⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠴⠦⡄⠀⢀⠀⠀⣀⣀⣀⡀⠀⠀⣰⠋⠛⠛⠉⠓⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⢦⣌⣠⡞⠁⠐⠒⠽⠿⠫⠅⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠓⠦⢤⣄⣄⣀⣀⣀⣠⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡆⢀⣀⡀⠀⣀⣤⡀⢀⡀⠀⣄⢀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣀⣠⡼⢳⡏⠁⢹⡆⡏⠀⢹⡸⡇⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠛⠒⠛⠀⠃⠀⠘⠀⠙⠞⠙⠂⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣝⣟⣽⣿⣦⣼⢿⠶⠛⠛⠉⠉⠛⠛⠛⢯⡉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣟⡛⠛⡓⠀⠀⣀⠀⠀⠀⠀⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠈⠁⠀⠈⡆⠀⠈⢻⣦⠀⠀⠰⠀⠉⠙⠳⣄
⠀⠀⠀⠀⢠⣄⡴⠋⠙⣝⠢⢈⠙⠛⠛⠛⠛⠉⠀⠀⡼⠀⢠⠆⠀⢸⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠌⠣⡀
⠀⠀⠀⠀⠀⡍⠀⢀⠀⠈⠑⠀⠀⠠⠄⠀⠀⣀⡴⠚⣀⡴⠋⠀⠀⡞⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡼⠂⠠⢄⣠⣤⣤⣤⣤⠶⠖⠛⠉⠀⠚⠉⠀⠀⢠⠎⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡄⢸⠀⠀⡀⠀⠠
⠀⠀⠀⠀⢨⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⡴⢋⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠘⢮⣁⠒⠒⢒⣒⣒⣋⣩⣤⣤⣶⣶⠿⠟⠉⠀⠀⣀⠴⠚⠉⠀⠉⣀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠇⠀⢰⡇
⠀⠀⠀⠀⠀⣠⠊⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⢀⡿⠀⠀⣤⡾⠀⢀⣾⠑⢄
⠀⠀⠀⢠⠞⠁⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠴⠒⠋⡁⠀⠀⠀⠀⢀⣴⡟⠁⠀⣰⡟⠁⠀⣼⣿⠃⠈⢣
⠀⠀⢠⠇⠀⠙⢿⣿⠋⢩⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⣠⡾⠋⠀⠀⣰⡿⠃⠀⠘⢀⡆
⠀⠀⢸⡀⢀⡆⠀⠙⣆⡀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠖⠛⠉⠉⢀⣠⠴⠞⠉⠀⢀⣠⡾⠟⠁⠐⠀⣠⣾⠁
⠀⠀⠈⣧⡘⣧⡀⠀⠈⠙⠛⠛⠛⠛⠋⠉⢦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⣤⣄⣀⣀⣀⣠⣤⠶⠏⠁⣀⣤⣴⣶⡿⠟⠁
⠀⠀⠀⠘⢿⣮⣁⠀⠘⠃⠀⠀⠂⠀⠀⠀⠀⠙⠛⠷⠶⠾⠿⠟⠛⠍⠀⡀⠆⠈⠉⡉⠉⠁⠀⢀⣠⠚⣿⡏⢰⡟
⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣶⣦⣤⣴⣷⣦⣄⡀⠀⢀⠀⠈⠀⠀⠀⣀⣤⣴⣶⣃⣀⣤⣤⣶⡾⣿⡟⢸⣿⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡄⢿⣿⡀⢸⣿⡟⠿⣿⣿⡿⠿⣿⣿⠿⢻⣿⠉⢹⣿⣿⠛⣿⡿⠀⣿⡇⣸⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣈⣿⡸⣇⢸⣿⡇⠘⣿⣇⠀⢸⣿⡇⠀⣿⣏⠀⢸⣿⠀⢈⣿⡏⠀⣿⡇⠀⣿⠀⣿⢇⣟
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣧⢻⡄⣿⣷⠀⢿⣿⠀⠘⣿⡇⠀⣽⣯⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇⢸⡿⢰⣿⣸⣿⣿⣶⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣧⢸⣿⡀⢸⣿⡀⠀⣿⡇⠀⢹⣯⠀⢸⣿⠀⢸⣿⡇⢀⣿⠁⣼⡇⣸⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⣿⡇⠀⣿⣧⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⢸⣿⠀⣿⡇⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣿⣿⣷⣴⣿⣇⣀⣽⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⣸⣿⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⠿⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠛⠛⠉⠉⠉⠉⠛⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠆⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣧⣀⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⣿⣿⣿⣧⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⠁⠀⠀⢻⣿⣿⣿⣿⡿⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣴⡄⠀⠙⠛⠛⠋⠁⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠻⠿⠶⠶⠶⠤⠤⠶⠖⠀⢠⣄⠈⠉⠉⠀⠀⢀⡈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠛⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠶⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠛⠿⠿⠶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠈⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⣶⣿⣧⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⢹⡟⠛⠛⢻⣿⡏⠁⠀⢸⣿⣿⠀⠈⠉⣿⣿⣿⠿⠿⢿⣿⡿⠿⠿⢿⣿⠋⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⠀⠀⠈⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⣾⡿⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⡄⠀⠀⣿⣿⡿⠀⠀⣼⣿⠀⠀⢰⣿⠇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⣿⠀⠀⢿⣿⡀⠀⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⣿⣿⠀⠀⣼⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⡆⠀⢸⣿⡇⠀⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⢰⣿⡟⠀⢀⣿⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢻⣧⠀⢸⣿⣇⠀⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⢸⣿⡇⠀⣸⣿⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣿⡄⠈⣿⣿⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇⠀⣼⣿⠇⠀⣿⡿⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣧⠀⣿⣿⡄⢸⣿⣿⣿⠀⣸⣿⣿⡇⠀⣿⣿⠀⢸⣿⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠿⠿⠷⠼⠿⠿⠿⠤⠾⠿⠿⠧⠼⠿⠿⠖⠛⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣤⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠉⠀⢏⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡞⠱⠁⠀⠀⠀⢸⠀⠈⡄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡔⠁⠀⡆⠀⠀⠀⠀⢸⠀⠀⠘⢆⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠋⠀⠀⡜⠀⠀⢰⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠑⠦⡀⠀⠀⠉⠒⠲⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠑⠂⠤⢀⡀⠀⠀⠀⠀⠣⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠐⠇⠀⠀⠀⠱⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⢃⠀⠀⢣
⠀⠀⠀⠀⢠⣀⡴⢉⡎⠀⠀⠀⡰⠢⡀⠀⢣⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡸⠀⣀⢠⢧
⠀⠀⠀⢠⠃⡃⠀⠈⠃⠀⠠⡄⠇⠀⠈⢆⡀⠹⡒⢄⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢑⡼⠁⠀⡞⢄
⠀⠀⠀⠇⠀⡇⠀⠰⠇⠀⠀⢲⡄⠀⠀⠀⠈⠢⣱⠀⠈⠑⠙⠲⠦⠤⣀⣀⠀⢀⡠⠂⠲⠀⠤⠬⠥⠖⠒⠀⠀⠈⠉⠀⠀⣰⠤⠀⠦⡀
⠀⠀⢸⠀⠀⡇⠀⠀⢃⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠶⣆⣀⡒⠒⠒⠒⠀⠐⠒⠒⠈⠁⠀⠀⠀⢀⡜⠁
⠀⠀⣸⠀⠀⠱⡀⠀⠈⢢⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠤⢀⣀⠀⠀⠀⠀⠀⠠⢻⣀⡀
⠰⣿⣿⡀⠀⠀⠱⡄⠀⠀⠙⠢⡀⠀⠈⠳⡄⠤⢀⡀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠰⠶⣾⣷⣆
⣴⣿⣿⣷⡄⠀⠀⠈⢦⡀⠀⠀⠈⠢⡀⠀⠈⠢⡀⠈⠉⠒⠠⠤⣀⠀⠀⠀⠉⠒⠠⠤⠤⠄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣿
⠨⡾⣿⣿⣿⣦⡀⠀⠀⠙⢄⠀⠀⠀⠈⠒⢄⡀⠈⠢⡀⠀⠀⠀⠀⠈⠙⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀⠀⢸⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣦⣀⣀⣀⣉⣦⣀⠀⠀⠀⠉⠐⠢⠌⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠒⡆⠀⠀⠀⠈⠑⠾⣿⣿⣿⣿⣯
⠀⠘⡀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣾⣿⣏⠉⣹
⠀⠀⢣⠀⢠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠛⢠⠃
⠀⠀⠈⢆⠀⡀⠀⠀⣿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣷⠈⠙⠋⠀⢀⠎
⠀⠀⠀⠈⡄⠸⡀⠀⢀⠀⠀⠘⠛⠋⠀⢻⣿⡿⠏⠉⢻⣿⣿⡿⠿⣿⣿⣿⠛⢿⣿⣿⡟⠙⢿⣿⡏⠀⠙⠛⠀⠀⠀⠁⠀⠰⠀⠀⡌
⠀⠀⠀⠀⢳⠀⢃⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠋⠀⠀⠈⠛⠁⠀⠀⠙⠋⠀⠀⢀⠉⠀⠀⡀⠀⠀⠀⡘⠀⢠⠃⠀⡘
⠀⠀⠀⠀⠘⡆⠈⡄⠀⠸⠀⠀⠸⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠀⠀⢰⡂⠀⠀⡎⠀⠀⢀⠃⠀⠀⢠⠁⠀⡎⠀⡜⠁
⠀⠀⠀⠀⠀⢃⠀⢣⠀⠀⡆⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⢠⠇⠀⠀⣸⠀⠀⠀⡌⠀⣸⠁⡜
⠀⠀⠀⠀⠀⠘⡄⠈⣇⠀⠰⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⠀⢸⠀⠀⢀⡇⠀⠀⢰⠀⢠⠃⡰
⠀⠀⠀⠀⠀⠀⠃⠀⢉⠀⠀⡆⠀⠀⢸⠀⠀⠸⠂⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⡈⠀⠀⡌⠀⠀⢸⠁⠀⢀⠂⠀⡎⢠⠇
⠀⠀⠀⠀⠀⠀⠰⡀⠸⠀⠀⢡⠀⠀⠀⠇⠀⠀⠇⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⡇⠀⢀⠃⠀⠀⠆⠀⠀⡌⠀⠰⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢆⠀⠈⡄⠀⠀⢰⠀⠀⠘⡀⠀⠀⢃⠀⠀⠀⠸⠀⠀⢰⠀⠀⢸⠀⠀⠸⠀⠀⢰⠁⢀⡧⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢧⡀⠀⠘⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⡄⠀⠀⡄⠀⠀⡘⠀⠀⠇⠀⢀⡧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⢄⣀⣸⠀⠀⠘⡀⠀⠀⡇⠀⠀⡇⢀⣀⠧⠤⠖⠓⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⡀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⡠⠂⠁⠀⡄⠀⡀⠀⠈⠐⠄⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠊⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠠⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠁⠈⠈⠀⠀⠀⠀⠀⣔⠝⠀⠀⢠⢂⠀⠀⠀⡀⠀⠈⠄⠡
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠠⠂⠀⠀⠀⡠⢐⠄⠀⡀⠀⠀⢀⠀⠀⠂⠀⠀⠘⠂⠀⠀⢠⠀⠡
⠀⠀⠀⠀⠀⠐⠀⠀⡐⠁⠀⠂⠀⠀⠈⠀⠔⠈⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠔⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠂⠔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠰⠕⠁⢀⠀⠄
⠀⠀⠀⠀⠀⠀⢂⠸⠀⠨⣠⠀⠀⠀⠠⠄⠀⠁⠂⠀⠀⠐⠈⠀⠀⠀⠀⠄⠄⠀⠀⡠⠂⡐
⠀⠀⠀⠀⠀⠀⠀⢂⠡⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀⠀⠈⠁⡠⠊⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠐⠠⢀⠀⠀⠀⠀⣔⠝⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠐⠠⡀⠀⠀⠀⠀⡄⣀⠀⠀⡀⠔⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠈⠐⠠⠄⠠⠅⠀⠂⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡆⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⠀⠀⠀⠀⣰⡀⠀⠈⢳⠁⠀⠀⢀⢣⠀⠀⠀⢯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⢸⣁⡇⠀⢰⠀⡇⠀⠀⣏⣸⠀⠀⠀⣈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⠀⠀⢀⢿⠀⠀⢸⠀⣷⠀⠀⡼⢇⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣀⣀⣼⢸⡧⠤⢼⠀⣿⠤⠤⡇⢸⠤⢤⣀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⡇⡟⠉⠀⠀⢿⢸⡇⠀⠈⠳⠃⠀⢀⡇⢸⠀⠀⠀⣇⣸⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠑⠃⠀⠀⠀⠸⣸⠁⠀⠀⠀⠀⠀⠘⣇⡜⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⢸⠀⠘⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠁⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠶⠖⠒⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣾⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡆⡇
⠀⠀⠀⠀⠀⢹⡼⢸⢠⠞⠉⠙⠦⣄⣀⣀⣠⠤⠶⣄⠀⢀⠞⠉⠱⡄⢀⠖⠒⢄⡀⢠⠟⠚⠁⠀⢷⠇
⠀⠀⠀⠀⠀⠀⡇⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⡇⠈⡇⠀⠀⠉⠁⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⡴⠶⠞⠉⣰⣶⣦⣄⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⠗⠀⠈⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣈⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣈⣁⣤⣤⡶⠶⠞⠛⠛⠋⠉⠉⠉⠀⠘⠛⢶⣄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠷⠾⠛⠛⠉⠉⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⣾⣾⣷⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⡾⡿⣃⣤⠶⠞⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠷⠶⠶⢦⣤⣤⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⠗⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣉⠈⣛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠶⠆⠀⠶⠶⠞⠛⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠛⡛⢋⣈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡾⢻⣦⡾⣷⣀⣾⣧⢠⣾⡆⣰⣷⠀⣾⡆⢠⣷⡀⢰⣷⡀⣼⣧⣠⣿⣆⣾⢷⣼⠿⣾⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠘⣯⠀⢸⡟⠀⢻⡟⠈⣿⠏⠸⣿⠏⢻⡿⠈⢷⡿⠘⣿⠏⠘⣿⠁⢹⡏⢈⡿⢀⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⠀⣿⠀⠸⣇⠀⢸⡇⠀⣿⡄⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⡆⢹⡆⠀⣿⠀⢘⡃⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⢸⡇⣸⡇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⡇⠀⢿⡀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⣿⠀⣾⠃⢼⠃⣿⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⠀⣿⠀⢸⡇⠈⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢰⡏⠀⣿⠀⣤⠀⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡄⢿⡀⢸⡇⠀⣿⠀⢸⡇⠀⢹⡆⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⣿⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢨⡄⠈⣿⠀⣿⠀⠸⣇⠀⢸⡇⠘⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⢸⡇⢸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠘⣧⠀⣿⠀⢿⡀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢰⡏⢸⡇⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄⣿⠀⢹⡆⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⠛⠀⢸⡇⢸⡇⣸⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡇⢻⡄⢸⡇⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⡇⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣸⡇⠘⣧⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⢸⠇⣿⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⡒⠒⠒⠒⠒⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡊⠁⠀⠀⠀⠘⣍⡆⠀⢀⡤⡄⠀⠀⡈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣸⣹⠀⢠⡶⢤⡀⠈⠀⠀⠻⠞⠁⠀⢾⢹⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡀⠈⠁⠀⠀⠉⠉⣀⠤⠤⠤⠤⣀⠀⠀⠈⠁⠀⡰⢻⠂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠳⢍⠆⠀⢠⢶⡄⢰⡁⠀⠀⡄⡀⢘⡆⠯⣑⡆⠀⠉⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⠀⠙⠊⠀⠀⠛⠯⢭⣭⠽⠛⣠⣄⠀⠀⢠⢦⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠯⠭⠇⠀⣾⢳⠀⠰⣟⢦⠀⠀⠰⠧⠏⠀⠀⠈⠧⠃⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠳⠤⣄⠀⠀⠘⠋⠀⣀⣈⠉⢠⡤⣄⠀⠀⣖⣒⡆⣠⠤⠞⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠲⠤⠤⣄⡸⠵⠚⠀⠀⠙⠚⢁⣠⠤⠤⠖⢁⢠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣠⠀⠀⠀⠉⠙⠋⠉⠉⠙⠋⠉⠀⢀⠠⣈⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣂⣀⣐⣀⣄⡥⠴⠖⠋⠁

⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣤⠀⠀⠀⠀⠀⠀⠀⢀⢶
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠈⢅
⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠨⠀⠀⠀⠀⠀⠀⣠⠂⠿⠀⢦⡀⠀⠀⠀⠀⢀⡀⣼⣖⠀⠀⠀⠀⠀⠀⣠⠒⣭⠐⠂⢄
⣰⡎⠑⠿⠿⠓⣰⣄⠀⠀⢠⣶⠿⠯⠭⢷⣦⠀⠀⠀⢀⠃⠀⠀⠀⠀⠁⡄⠀⠀⠜⠤⡁⠀⠒⠉⠉⢆⠀⠀⢰⠁⠀⠙⠋⠈⠱⡀⠀⠀⣸⡉⠑⠒⠂⠀⣙
⢻⢻⡾⣷⣾⣿⠿⡛⠀⠀⣇⢀⣀⠀⣀⡀⢀⡗⠀⠀⢣⣀⣀⣀⣀⢤⡖⡎⠀⠘⢦⣰⡤⣤⣤⢴⡖⡞⠀⠀⢣⣀⣠⣄⣠⢤⡖⡆⠀⠸⣥⡉⠉⠉⠛⢉⣉
⠸⣼⡇⣧⣿⢸⢸⠃⠀⠀⢸⣽⡏⡏⣿⣹⢹⠀⠀⠀⠘⡟⡇⣿⢸⢸⢷⡇⠀⠀⠘⡏⡇⣿⢸⢸⢷⠇⠀⠀⠘⡟⡇⣿⣿⢸⢻⠇⠀⠀⢸⣽⡟⡏⣿⣹⢹
⠀⠯⣇⣿⣿⣾⠞⠀⠀⠀⠀⠯⣇⣇⣿⣿⠟⠀⠀⠀⠀⠣⢧⣿⣿⣸⠼⠀⠀⠀⠀⠣⣧⣿⣿⣸⠽⠀⠀⠀⠀⠣⣇⣿⣿⣸⠼⠀⠀⠀⠈⠻⣧⣇⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⡄⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠸⣿⣾⡿⡀⠀⠀⠀⠀⠀⠀⢲⣶⣦⡀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣿⠂
⢀⡤⢠⣾⣷⡄⢀⠀⠀⠀⠀⣠⣼⠿⢿⢤⡀⠀⠀⠀⠀⡌⠛⢁⡈⢴⡆⠀⠀⠀⢐⠊⠄⢀⣠⠝⠢⡀⠀⠀⢠⠔⠛⠿⠛⠳⢄⠀⠀⠀⢠⠷⠌⢁⠈⠅⠵
⣿⣷⣤⣬⣥⣤⣾⡷⠀⠀⡜⠛⠉⠉⠉⠁⠛⣄⠀⠀⡔⠠⠀⠀⠀⢀⣀⡠⠀⠰⡄⢌⠀⠀⠀⣀⣀⣱⠀⠀⣜⠀⠀⠀⠀⢀⣀⡃⠀⢠⠞⠒⠢⠤⠤⠤⠚
⢸⣸⡍⡟⣻⢹⢵⡇⠀⠀⢳⢶⡶⡶⣶⢢⢴⠃⠀⠀⠸⡶⡆⣶⢺⢹⣇⡇⠀⠀⢹⡾⡏⣿⢻⢹⣇⡇⠀⠀⢸⣶⡎⣿⣿⢹⣧⡇⠀⠈⢹⢣⣤⡤⣶⢶⢶
⠈⡿⡇⡿⣿⣼⣸⠀⠀⠀⠘⣿⡇⡇⣿⣼⣼⠀⠀⠀⠀⡇⡇⣿⣼⢸⢹⠃⠀⠀⠀⣇⡇⣿⣼⢸⢸⠁⠀⠀⠀⣇⡇⣿⣿⢸⢸⠁⠀⠀⠘⣿⡇⡇⣿⣾⣼
⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠊⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣾⡿⠀⠀⠀⠀⠀⠀⠄⠐⠣⠀⠀⠀⠀⠀⠀⣰⢿⡿⠷⢦⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠎⠈⠰⠒⢄
⣴⣎⠐⠿⠾⠋⣰⣄⠀⠀⢠⣾⠿⠿⠯⢽⣦⠀⠀⠀⢀⠓⠀⠂⣃⠉⢳⡄⠀⢀⠜⠤⠀⠐⠒⠁⠈⢆⠀⠀⢸⠀⠀⠀⠀⠈⠑⡄⠀⠀⣸⣋⠉⢉⠈⢉⣛
⢛⢻⠿⣿⣿⢿⠟⡋⠀⠀⣇⣀⣀⣀⣀⡀⣀⡗⠀⠀⢣⣘⣁⣉⣠⢵⡖⡏⠀⠘⢧⣱⡤⣤⣤⢴⡖⡞⠀⠀⢣⣀⣠⣄⣤⢴⡖⡆⠀⠸⢿⡀⠉⠉⣍⣉⣀
⠸⣾⡇⡇⣾⢸⢸⠃⠀⠀⢸⣽⡏⡏⣿⣸⢹⠀⠀⠀⠈⡏⡇⣿⢺⢸⢷⡇⠀⠀⠘⡏⡇⣿⣸⢸⢳⠇⠀⠀⠘⡟⡇⣿⣿⢸⢻⠇⠀⠀⢸⣽⡟⡏⣿⣹⢹
⠀⠳⣧⣿⣿⡾⠞⠀⠀⠀⠀⠻⣧⣇⣿⡿⠞⠀⠀⠀⠀⠣⢧⣿⣾⣼⠜⠀⠀⠀⠀⠣⢧⣿⣿⣼⠜⠀⠀⠀⠀⠳⣧⣿⣿⣼⠞⠀⠀⠀⠀⠻⣧⣇⣿⡿⠟
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿