Multiple dolls Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢀⡘⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠐⠒⠊⡓⡀⢄⡀⠀⠀⠀⠀⠊⠐⣌⠉⠁⠉⠉⠁⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠋⠀⠈⢂⡉⠢⣀⣀⡄⠸⠊⠀⠈⠐⠢⢄⡀⠀⠀⠀⢹⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠤⠊⠀⠀⣀⣴⠆⠉⠠⡘⡜⠀⣇⣀⣀⣤⡶⠔⠃⠈⢆⠀⠀⠘⡀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠋⠐⠐⠒⠋⠉⠁⠀⡀⠀⢠⠃⢸⠀⠈⠀⠁⠀⠀⠀⠀⠘⡀⠀⡦⡗⠀⠀⠀⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣧⠀⡈⡀⠀⠈⠀⠀⠀⠀⢀⣀⡀⡎⢀⢿⠀⣀⣀⠀⠀⠀⣠⣤⠀⢷⠈⠁⢽⡄⠀⣰⠁⠀⠘⡀
⠀⠀⠀⠀⠀⣠⢞⣁⠔⠩⠙⠀⡅⠀⠚⠻⠇⠀⠀⠈⠋⠁⡇⠘⢎⡆⠙⠛⠀⠀⠀⠘⠉⠀⣸⠆⠀⢁⣆⢀⡍⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡇⠀⠳⠌⠀⠀⣠⡇⠀⠀⠀⠀⡠⢤⠀⠀⠀⡔⣸⡀⡁⠀⠀⠠⠤⡄⠀⠀⠀⡹⡄⠉⠀⠱⣤⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢱⡀⠀⠀⠑⠓⠴⣙⡀⣀⣀⡀⣀⠀⣤⡤⠌⠴⠛⠋⣿⠢⡄⠀⣀⢠⡤⣄⠔⣵⡀⠁⢀⡼⠋⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠙⠣⣤⠳⢺⠦⡄⠀⣰⡑⠀⠂⢼⢂⠦⠠⠓⠚⢄⠄⠀⣁⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠀⢰⠙⠁⠀⠀⠀⡼⠀⠀⠀⠀⣠⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣐⠀⠀⠀⠀⠂⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢀⠀⠀⠀⢀⠤⠄⠀⠀⠀⡈⠑⢄⠀⢀⣤⡒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠄⠘⠐⠆⡄⠀⢀⡆⠀⠀⠀⠀⠌⡙⠉⢙⣉⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠉⠲⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠱⠄⠋⠀⠀⠈⣇⠐⢂⡀⣥⡽⢳⡤⢿⡶⠤⠄⠠⠀⢀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠋⠐⠂⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠌⠋⠀⠀⠘⠁⢨⠓⢀⠀⠀⠀⠒⠶⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠢⡤⠀⠀⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠸⣇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠐⠀⠴⠀⠄⠰⡤⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢦⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⡀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠡⠋⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠤⠤⢤⣀⣀⣱⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠐⠒⠒⠲⠖⠠⠤⠤⠤⠤⠤⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⢬⡁⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⢌⢣⡉⢀⡉⠒⠀⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠑⠀⠡⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠤⠤⠄⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠂⠀⠈⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠄⠀⣉⠀⠀⠀⠀⠀⠀⢀⡃⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⡂
⠀⠀⠀⠀⢐⠁⠀⢠⠢⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠈⣊⠘⠃⠀⠀⠀⠀⠀⠓⢀⠎⠀⠀⠀⠀⠀⢀⠂⠀⢀⠀⠀⠀⠀⠀⡀⠠⣲⡀
⠀⠀⠀⠀⠙⢤⠞⠑⢄⡊⠀⠀⠀⡀⠃⠀⢠⡀⠘⠆⠀⢨⠐⢀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠘⡀⠇⠀⠸⠀⠀⠀⡀⠀⠀⠀⠀⢖⡈⠔⠑⠄⠸⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⡠⠈⠤⠄⠁⠤⠀⠠⠀⠀⠚⠁⠈⢰⠀⡃⢀⠀⡀⠀⠀⠠⠀⡇⡏⢀⣈⠙⠀⠑⠦⠈⠂⠰⠒⠚⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠃⢀⣤⣤⡀⠀⠀⠀⠀⠀⠞⣯⡳⣦⡔⠀⠀⡄⠀⠀⢠⠁⠀⠰⣼⢋⣹⣷⠀⠀⠀⠀⠀⢤⡶⣄⡈⠁⠀⠈
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠐⠈⠂⠛⢠⣿⣷⠀⠀⠀⠀⠀⢿⠿⠃⠁⠁⠀⡀⠀⢘⡇⠀⢠⠀⠈⠀⠈⠙⠛⠀⠀⠀⠀⢰⣾⣿⠈⠙⠁⠀⠀⠂⠀⢠⠔
⠀⠀⠀⠀⢤⠀⠁⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡈⡔⠀⠒⠁⠀⠄⠀⢠⠙⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡀⠈⡁⠖
⠀⠀⠀⠀⠀⠈⠁⠋⢠⠁⢣⣜⡄⠀⠀⠀⠀⠀⠓⠃⠀⠀⢀⠠⠂⣀⠁⢠⠀⠀⠀⢠⡀⠀⣁⠈⠢⡄⠀⠀⠙⠋⠀⠀⠀⠀⡀⠼⠰⠂⠈⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⣸⢄⠀⢄⡀⠀⡡⠴⠶⡖⠒⠂⣾⠛⠚⠣⡀⠈⠁⠀⠀⠀⠀⠈⠀⠈⠁⠀⠚⠓⠛⢿⠉⠀⣰⢲⠳⠤⡀⠠⣄⡠⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⡠⠀⠍⠂⠀⠁⠀⣆⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⡔⠀⠁⠄⠠⠀⡀⢠⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⢀⠃⠀⠀⠀⠀⣾⣙⠙⠂⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣐⠁⠀⠀⠀⠀⣎⣹⡟⣀⢀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠀⢸⡀⠈⢀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠏⠀⠀⠀⠀⠀⠀⠁⠀⢹⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠔⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢃⠀⠀⠀⠀⡌⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠄⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠄⠊⠀⠔⠈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢆⠀⢆⠀⠀⠐⠀⠐⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠈⠑⡀⠈⢀⠄
⠀⠀⠀⠀⠀⠶⢿⠄⠊⠀⢀⡔⠁⠀⠉⠐⠀⠒⠒⠒⠀⠄⠂⠈⠀⠈⣲⡀⠀⢱⡆⠀⢀⣏⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⣱⡄⠀⠈⠠⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⠍⠑⠓⠋⠙⠛⠁⠙⢑⠦⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⡻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠉⠙⠒⠒⣒⡒⠒⠚⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠈⠩⠉⢩⡍⠉⠍⠁⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⡸⠀⠰⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠆⠀⡄⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠠⢠⠇⠀⠸⡦⠄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠀⢼⠀⠀⢱⡠⠄⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡛⠦⣼⠀⠀⠀⠭⢝⣛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣓⠦⠽⠀⠀⢸⠥⣟⣛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠠⢈⠑⠺⠀⠀⢘⡒⠋⡀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠧⠀⡈⠓⢺⠀⠀⠘⠒⢁⠠⠈⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⣳⡋⠀⠀⠨⢁⡲⢁⡄⠀⠀⠵⠀⠀⠀⠀⠀⢠⠣⠀⠀⠤⠷⢊⠡⠀⠀⠀⢳⣆⡤⠀⠀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⠈⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢰⣆⢀⣶⠀⠀⠰⣦⣀⡿⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣾⠃⠀⠀⠀⠘⣿⡇⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⡞⢻⣇⠀⠀⢀⡼⠛⣷⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡉⠀⠈⠁⠀⠀⠈⠁⠀⠈⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣦⣤⣤⣤⣤⣶⣶⣿⣿⢯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⠟⠋⣻⠟⠛⠉⠉⡿⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣾⠏⠛⣻⡷⣦⠀⠀⠈⣷⡀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣼⡟⠀⠀⣿⡇⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⢀⣠⠶⠖⠛⠒⠶⢦⣄⠀⠀⢀⡎⠀⠀⢀⣿⡇⠘⠛⣿⠻⠂⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠘⣿⡄⠀⠀⣠⡴⠶⠒⠒⠲⠶⣤⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢰⡶⠈⢻⡄⢸⠃⠀⠀⢸⣿⡇⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⣿⡇⢀⡾⠃⢴⡆⠀⠀⠀⠀⠀⠙⢷⣄
⠀⢀⣿⠁⠀⠀⠿⠿⢷⣶⣿⣁⠀⢀⣷⣼⣇⠀⠀⣸⣿⣧⡐⠟⢿⠉⠋⠀⠀⣀⣀⣀⣿⣿⡿⢿⣦⣤⣾⣿⣧⣼⡇⠀⢀⣹⣶⡶⠿⠿⠃⠀⠀⣿⡄
⠀⠸⣿⡄⠀⠀⠀⣀⡾⠉⠉⠙⠛⣼⡿⠁⣹⠿⠿⠿⡿⠸⣷⡀⠈⠀⠀⣰⡟⠉⠀⠈⢻⣿⡁⠀⠉⠙⠛⣧⡀⢻⣧⡚⠛⠉⠈⢿⣄⠀⠀⠀⢀⣿⡇
⠀⠀⠻⣿⣦⣄⣀⣙⣃⣠⣤⣶⣿⣿⣥⡞⠁⠀⠀⢸⡇⠀⠙⢿⣷⣶⣶⣿⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠈⠳⣤⣿⣿⣦⣤⣄⣈⣛⣀⣀⣴⣿⠟
⠀⠀⠀⠀⠉⢉⡿⠿⣿⡋⠀⢨⣿⡽⣇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠉⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢨⣯⣽⣅⠀⠉⣿⠿⢿⡉⠉
⠀⠀⠀⠀⢠⡟⠀⢀⣿⡇⠀⠠⣽⠤⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⣿⢿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡤⣿⡄⠀⠀⣿⡄⠀⢹⡆
⠀⠀⠀⠀⠸⣧⣤⣿⠿⣧⡀⠀⠟⣰⡏⠀⠀⠀⠀⢿⡆⠀⠀⠀⢀⣿⡟⢸⡇⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢸⣇⠹⠆⢀⣴⠿⣿⣦⣤⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡿⣶⡾⠋⣿⠀⠀⠀⠀⠘⢿⣤⣤⣤⣿⡿⠁⠈⢿⣤⣀⣀⣀⣼⣿⠇⠀⠀⠀⠀⠀⣸⠉⢻⣶⢾⡏⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠸⣧⣠⡞⠀⠸⣧⣤⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠹⣦⣴⡟⠀⠻⣤⣴⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⡻⡿⢛⠿⢿⢿⢻⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⢀⣴⣾⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣤⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣜⠿⣿⣿⣿⡇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣵⣿⣟⣩⣥⣤⣤⣤⣉⡙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⣿⣿⣷⠀⣸⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣦⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⠉⠀⠀⢀⣠⡄⢹⣿⣿⡄⣿⣿⡿⠀⠀⠉⠉⠛⠛⠛⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠰⠛⠂⠀⢀⠀⠀⠀⢸⣿⣿⠀⢿⣿⡇⠈⠉⠃⠀⠀⠀⠶⡆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢄⡀⠀⠀⠀⠀⢀⠤⢺⣿⠏⠀⣾⣿⣷⣄⡀⠀⠈⠁⠀⠀⣀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠄⣩⡛⢆⠈⡩⢳⡄⠾⠋⠀⢀⣿⣿⣿⡿⣩⠳⡀⠀⡘⢊⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠣⡀⠉⣗⠔⢁⠜⠆⠀⠀⣼⣿⣿⠏⡜⢄⠉⢛⢎⠔⠠⠾⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⡅⠀⠀⠀⢠⢁⣜⠿⠟⠁⢠⠀⠀⠁⢫⡔⠈⠀⠀⡂⠻⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⠈⠁⠀⠁⠀⢸⠀⠀⠀⢰⡇⠀⠀⠀⡇⠀⠀⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠌⠉⠣⡀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⡠⠋⠙⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣭⡈⠁⠀⠀⠀⠈⢀⣫⣿⣷⣶⣶⣿⣿⡃⡈⠀⠀⠀⠀⠁⢘⣽⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣷⣶⣿⣶⣿⡿⠿⠿⠛⠛⠿⠿⣿⣿⣷⣾⣶⣷⣾⡿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠔⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡦⠛⠘⠣⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡃⠀⠀⠀⣻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣧⣤⣤⣤⣤⣤⣤⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠗⠀⠄⠐⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠉⠉⠉⠉⠉⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣸⠿⡟⠀⠀⡀⠀⠀⠀⡀⠀⠈⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠏⠀⠀⣄⠀⠀⢀⡄⠀⠈⠟⢻⣿⣿
⠀⠀⠀⠀⠀⢹⣄⠀⠄⠄⠉⠀⠀⠀⠉⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠒⠂⠀⠀⠀⠀⠀⠐⢂⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡳⠶⠦⣤⣤⡤⠶⠲⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠲⠤⠤⠴⡒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣑⡨⡄⠠⠠⠄⠠⠈⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣌⠀⠀⠀⠀⢈⡄⠀⠀⡀
⠀⠀⠀⠀⡀⠚⠁⠀⠀⠰⠂⠀⠀⠀⠐⠈⠀⠀⠙⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⣀⠰⣿
⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠄⠀⢻⠀⠀⠀⠀⠀⠈
⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⣧
⠀⠂⠀⠀⠀⢀⣀⠀⠂⠇⠀⠀⠀⠀⠀⠇⠀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠢⠀⠀⠀⠀⣀⡴⠿⠀⠀⠀⠀⠀⠀⠸⠷⣄⣀
⣶⣶⣶⣶⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠢⣄⣀⡠⠤⠤⢀⡀⠀⣀⠔⠒⠀⠉⠉⠉⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠦⠤⠸⢅⣨⠁⠉⠑⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠀⠢⠤⠂⠀⠀⠀⠠⡄⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠎⠡⡀⠀⠀⠠⣄⠀⠀⠀⠙⢆⠀⠀⠀⠈⠑⢤⢄⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡌⠀⠀⠈⠢⢄⣀⢈⡲⠄⣀⠠⠞⠑⠂⠤⠤⠔⠁⠀⠁⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡀⠀⠀⠀⠔⠂⠒⠄⠀⠀⠀⠀⠀⠐⠁⠀⠉⠃⠀⠀⠀⢠⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢄⠀⠠⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡜⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠢⡄⠀⠀⠀⠀⠉⠒⠂⠐⠂⠁⠀⠀⠀⢀⡠⠊⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠑⢦⣄⣀⠀⠀⠀⠀⠀⢀⣀⢠⡔⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⣠⣏⠀⠉⠈⠉⠁⡞⠋⠁⠁⠀⡱⠤⡄⡀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡉⠁⠀⠀⡴⠈⠁⠀⠀⠑⠒⠀⠰⠊⠉⠒⠲⠒⠋⠀⠀⠀⠀⠉⣶⠀⠀⠉⠉⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣶⠷⠀⠀⠀⠀⠀⠀⠴⠀⠴⠃⢸⠆⠀⠀⠀⣀⠀⠀⢀⠋⠓⠀⢤⡖⡀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢱⣀⢠⡀⠀⠀⠈⠢⣀⣠⠊⠀⠀⠀⠀⠩⠐⠶⠛⠒⠠⠄⠀⠀⠀⠀⠀⠁⠀⠙⡆
⠀⠀⠀⠀⡀⠤⠀⠶⠚⠁⠀⢀⡠⠔⠋⠉⠸⠀⠀⠀⠀⢀⡈⢁⡄⢀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠀⠠⠞
⠀⠀⠀⡎⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠂⠀⠀⠀⠐⢍⠀⠋⠀⡠⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠱⢤⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠦⠔⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢀⠠⠚⠢⡀⠀⠀⠀⢀⠠⠊⠈⠐⠒⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠈⠁⠈⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⢠⣄⠀⢀⢀⡠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢀⣀⡠⠒⠉⠢⣄⠀⠀⠀⠀⣀⠴⡁⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⡆⠉⠁⠀⠀⡀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠘⢆⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠣⣀⠴⠛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⣤⠾⠙⢄⠀⠀⠘⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠱⢦⡠⠇⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠞⠀⠱⠄⣀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠜

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⢦⣤⡀⠀⢀⣀⣶⢿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⢷⢦⣸⣿⣷⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⡉⢉⣻⢦⡀⢻⣽⣿⣿⡿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠘⡗⡿⣄⣿⣿⣿⡇⠰⠃⢰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠀⠀⠘⢛⣿⣹⣿⣿⡄⠀⠠⢄⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡛⡦⠀⢸⣿⣿⣿⠿⠁⢰⣴⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣶⣿⠿⠙⢿⡈⢩⣏⢻⡭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⠅⠫⠉⢸⠆⠀⣼⡇⠘⠏⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣠⣾⡏⠀⠀⠀⠀⠀⢠⣀⢡⢸⣷⠶⠿⠛⢷⡢⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⢀⠸⠛⠁⠀⠀⠀⠀⠀⠀⣸⡦⠠⠜⣇⠀⠀⠀⠀⠹⣶⡀⠀⠀⠀⣠⠜⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⢈⡥⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⡇⠂⢆⣼⠀⠀⠀⠀⠀⠀⠉⠳⣤⣤⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⢰⠀⠈⢿⣿⣷⡀⠀⢀⣤⡤⢄⠻⣟⣶⣽⠷⡇⠀⠉⠀⠀⠀⠀⠀⠀⢰⣟⣋⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠷⠂⠀⠀⠻⣿⣯⣭⣷⠏⠈⢻⡇⢙⣿⡀⠀⠑⠄⠆⠀⠀⠀⠀⢀⣠⣿⠝⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠙⠻⢾⣇⠀⠀⠀⠀⣠⠊⠻⣾⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣾⡿⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⡤⠒⠲⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠈⠉⠉⠐⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣉⠤⠄⠶⠶⠷⠤⢼⣄⣸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⠞⢁⠴⠊⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡚⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀⠎⢠⠋⢠⠊⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⡆⢸⢠⠃⢠⠃⠀⠀⢣⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠘⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡐⢀⡠⠄⠘⠢⠤⢤⣀⠀⠀⠀⠘⡄⠀⠀⠁⢸⡘⠀⠆⠀⠤⠀⠀⠑⠳⠤⠤⠀⠤⢈⣆⠀⠀⠀⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡸⠴⠀⢠⠁⣀⢔⣀⠀⠀⠀⠀⠀⠀⢀⣀⢦⣘⠀⠁⡴⢼⡃⢐⠀⣠⢖⣀⠀⠀⠀⠀⠀⠀⢀⣐⢮⣢⣀⠀⢸⠤⡃
⠀⠀⠀⠀⠀⢠⠊⡠⠜⢀⡆⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣧⠇⠐⡼⠳⠦⠙⠆⠀⢣⣿⣿⠆⠀⠀⠀⠀⠀⢾⣿⣧⠃⠘⣆⢼⠤⡈⢂
⠀⠀⠀⠀⠀⣷⠸⣇⢘⡙⢳⡀⠀⠉⠉⠀⠀⠀⠂⠀⠀⠀⠉⠁⠀⣰⠁⡅⢀⡇⣸⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⢧⡎⣠⠓⢸⠂
⠀⠀⠀⠀⠀⠘⠢⢍⣋⣡⠴⢕⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠽⢆⠠⡭⠖⠓⠼⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡳⢄⡈⢉⡠⠋
⠀⠀⠀⠀⠀⠀⠀⡜⢐⡁⠀⠀⠀⡨⣗⠒⠲⢔⡢⠶⠒⢺⢥⡀⠀⠀⢈⠄⢁⠀⠀⠀⠀⣠⡟⠒⠲⠦⣠⠴⠒⠒⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⡡⠶⢤⠎⠀⠘⠦⡠⠞⠑⢤⡤⡎⠀⠑⣤⠶⣋⡠⠆⠀⠀⢀⠞⠁⢘⠦⣠⢼⠹⢦⡠⠞⠁⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡘⠀⠀⠀⠀⠀⠀⠰⡀⠀⠘⡄⠀⠀⠀⠀⢀⠎⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⢣⡤⠲⡁⠀⠀⠀⠀⠀⡷⠤⣴⠂⠠⠀⢀⠀⠀⠠⠀⢧⡤⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠇⣀⠀⠀⠀⠀⠀⠀⢀⡨⡆⠀⢡⠀⠀⠀⠀⢸⠀⢀⠋⠀⢀⠀⠀⠀⠀⢠⠀⠈⣆⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⡎⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠘⡎⠉⠃⠀⠀⢠⠋⠁⡎⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⢘⡎⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠃⠀⠀⠀⠓⡞⠀⠁⠒⠒⠐⠚⠘⠒⠒⠒⠈⠁⠙⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠒⠲⠦⡤⢤⠴⠆⠒⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡗⠂⠶⢤⠠⡴⠆⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠃⠘⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢋⣚⣙⡀⠀⡋⢋⡉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⡉⡇⠀⣏⣹⡉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡀⢨⡆⠐⡅⢀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⣀⠀⡇⠀⡄⢀⡀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠀⠀⠙⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠈⠒⠒⠊

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⡆⠠⡀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⡿⠋⠉⢑⣦⠀⠀⠀⠠⠀⠀⠀⠉⠁⢹⣿⣿⣿
⣿⣿⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣠⣥⢰⣏⠀⠀⢸⣿⡄⠀⠀⠀⠒⠒⠠⠠⣀⡀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⣁⡀⠀⢀⠐⠈⠀⠀⡀⠀⠀⠸⣿⣿
⣿⣿⣿⠀⣶⣿⣼⢯⠇⠀⠈⠹⢁⣧⢹⣾⣿⣷⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⢸⣿⡇⠀⠀⢀⡄⡀⠀⠐⠀⠀⠀⠠⣄⡁⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⣶⠄⣀⠴⠟⠁⠈⣿⣿⣿⣿⣿⣿⡆⠀⠀⠶⠀⠰⣶⠀⠀⣾⠆⠄⠀⠀⠀⢸⣿⡇⠀⠀⠀⣇⣤⡁⠘⠀⠀⠀⢐⣿⡋⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠉⠀⠀⠁⠰⠿⠿⣿⣿⣿⣿⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⣿⡿⠅⠀⠠⠄⠀⣸⣿⣏⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠰⠛⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⣿⣿
⣿⣿⣿⠿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⣀⠀⠀⠘⠇⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠛⣿⡧⢀⡀⠀⠀⠀⣠⣤⣾⠿⣿⣟⠁⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠇⠀⠀⠀⠀⠻⠀⠀⠐⣁⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⢸⡇⢼⣗⠀⣿⠀⣿⣿⣿⠐⠧⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠈⠉⠻⠀⠿⠰⠇⠙⠋⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠰⢄⡰⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⣿
⣿⣿⣿⢶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⡶⢾⣿⠶⠶⠶⣶⣶⣶⣿⣾⣷⣶⣶⣶⣶⠶⠶⠶⣿⣷⣶⣶⠶⠶⠶⢶⣶⠷⢿⣶⡶⠶⠶⢶⣶⣶⣿⣿
⣿⣿⣿⣾⡛⣷⣿⣄⠈⠁⠀⣄⠈⠉⢀⣿⣾⡛⣿⣾⣿⠀⠀⠀⠸⠟⡉⠉⠉⠉⠉⠙⠻⡏⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠈⠳⠞⠛⠀⠀⠀⠀⠈⢻⣿⣿
⣿⣿⣿⡟⠛⡏⢉⣤⠀⠀⠀⠈⠰⣦⣄⡍⠹⡟⢻⣾⣿⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡟⠀⡴⡛⠀⣀⠤⠐⠦⢄⡀⡀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠶⢛⡅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⢿⠈⠘⠃⡾⠀⠀⠀⢤⠢⢀⡄⠀⣾⢻⣿⣟⠀⠀⠀⢈⠁⢰⣒⠀⠀⢒⣆⠀⠀⠀⠀⠀⢸⡿⣷⣶⣿⠁⢧⡄⠀⠀⡄⠀⠀⢸⣦⣀⠀⢀⣻⣿
⣿⣿⣿⠻⠁⠀⢀⡀⠰⠀⠀⢀⠀⠇⠈⠦⠈⠀⢟⢹⣿⠀⠀⠀⢠⡅⠘⣍⡰⢆⣉⡏⠀⣄⠀⠀⠀⢻⣷⠿⠿⣿⠀⠚⢢⢤⣤⢶⡇⠀⠀⣿⡛⣿⢟⣿⣿
⣿⣿⣿⠇⡀⠀⠀⣿⣶⡀⠀⠀⠀⣤⣤⠀⠀⢀⡠⣿⣧⠐⠆⠀⠐⠁⠀⠀⠈⠉⠀⡀⠐⠁⠀⣾⠇⢸⣿⣷⣾⡇⢀⠀⠁⠀⠀⠀⠀⠀⠀⠹⠿⣿⠟⣿⣿
⣿⣿⣿⠞⠋⠀⠀⢠⡇⢃⠀⠀⠴⣻⣾⠀⠀⠘⠓⣿⣿⠀⠀⠀⠀⠀⢀⠘⠂⠀⠈⠁⠀⠀⠠⡏⠀⢸⣯⣽⣿⣿⣿⡦⠀⠀⠀⠀⠠⣾⣿⣧⡞⠁⠀⣿⣿
⣿⣿⣿⡷⠆⠀⠀⢈⠀⠈⠀⠀⠀⢀⡏⠀⠀⠰⠾⣿⣟⠀⠸⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⢸⡇⠉⠻⣿⣟⠁⣄⠀⠀⠀⠀⠈⣻⣿⣿⣛⣿⣿⣿
⣿⣿⣿⠛⠂⣤⡀⠀⣼⠷⠀⣶⠐⣿⡁⠀⣠⡀⠛⣿⣿⠀⠀⠀⠀⢲⣄⣀⢀⣀⣀⣠⡄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠻⠀⠛⡀⢲⣤⣤⠘⡿⢋⣽⡿⢿⣿⣿
⣿⣿⣿⣷⣾⢛⡇⠀⣿⣶⠆⣿⠆⣿⠁⢠⡟⣿⣶⣿⣟⠀⠀⢀⠀⣼⠟⠻⠸⠃⢿⠹⡇⢠⡄⠀⠀⢸⣧⠀⠀⢀⣴⢨⣤⠷⠘⠋⠁⠀⠀⣼⣻⡇⢸⣿⣿
⣿⣿⣿⣯⣽⣿⣥⣤⣤⣤⣄⣤⣤⣤⣤⣬⣿⣯⣽⣿⣿⣤⣤⣼⣥⣥⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣼⣿⣧⣴⣿⣯⣠⣤⣤⣤⣤⣤⣤⣼⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣭⣭⣥⣿⣿⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣟⣿⣻⣟⣿⣛⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣯⣽⣯⣽⣯⣽⣿⣭⣿⣽⣿⣯⣿⣯⣿⣭⣿⣽⣭⣿⣿⣯⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣯⣯⣽⣯⣿⣯⣿⣯⣿⣭⣿⣿⣯⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣽⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣿⣷⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣷⣿⣿⣷⣾⣾⣿⣶⣿⣷⣾⣿⣷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠟⠻⠻⠟⠟⠛⠛⠛⠛⠛⠛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⢰⡆⡶⠠⡆⣶⠀⢀⡀⣄⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢸⡇⣿⢸⡇⣯⠀⢸⡅⣿⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⢸⠇⡿⠈⠇⣿⠀⢼⠇⣿⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⣤⠀⠹⣷⡄⠀⠀⠀⢀⣤⡾⠋⠉⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠺⣄⡏⠀⠀⢹⣿⡄⠀⣠⡾⢫⡀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⡀⠀⣀⠀⠀⡀⠀⠹⡆⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⠀⢈⡗⢦⣠⠀⣿⣿⣾⡟⠀⠀⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢳⣸⠟⠀⠈⢻⣰⠆⣧⠀⠀⠀⠀⠀⣧⠲⢤⣥⠀⠀⠀⠸⠇⠈⠁⠀⣿⣿⣿⠀⣠⡞⢹⡄⠀⠀⠀⠀⡶⢀⡀⠀⣿⠇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼⢷⡀⠀⠰⠋⣧⠀⡿⠀⠀⠀⠀⠀⢹⣆⠀⢸⣍⠚⠃⠀⠀⠀⠀⢰⣿⣿⡏⠀⠈⠁⠘⠃⠀⣀⣀⣴⠗⠋⠁⣰⡟
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠛⠃⠘⠋⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢻⣧⠈⠁⠀⠀⠀⠀⢀⣴⡿⠿⠻⣷⡀⠀⠀⠀⠀⠀⠙⢡⡞⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⡴⣶⠟⠁⡀⠀⠀⠈⢻⣦⣀⠀⠀⠀⠀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⣠⠤⢿⣿⠿⠿⠛⠛⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣼⠃⠴⣶⠧⡆⠀⠀⠀⢻⣿⣿⠶⠾⣿⣿⡉
⠀⠀⠀⠀⣠⡟⠁⠀⠀⢻⠀⠀⠀⣤⡼⡦⣬⢣⠈⠳⢦⡀⠀⠀⠀⠀⠀⣰⠏⠀⢠⡏⡀⠀⡟⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠈⢿⡄
⠀⠀⠀⣰⡟⠀⠀⠀⠀⢸⠀⠀⠀⢠⣄⣱⣀⠈⣇⠀⠈⣷⠀⠀⠀⠀⢰⡏⠀⠀⢸⡇⠛⢺⡗⢶⡆⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⢿⡄
⠀⠀⢰⣿⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣸⠈⠁⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠃⢀⠘⡇⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠸⣧
⠀⠀⢺⣿⠀⠀⠀⣠⣾⠀⠀⠀⠀⠸⠋⡏⠙⠀⣿⣷⡴⠏⠀⠀⠀⠀⢿⣄⠀⢀⣿⡄⠙⠛⣗⠾⠂⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⢀⡟
⠀⠀⠈⠻⠷⠶⠾⣿⡿⠶⣤⡀⠀⠀⠀⠃⢀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣧⠀⠀⠙⠀⠀⠀⠀⢀⠀⠐⠚⢿⡟⠶⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢳⣤⣤⣤⡶⠋⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠹⣷⡀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⡏⢸⣿⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠻⢷⣶⣶⠿⢿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣿⡏⠀⢸⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⣀⣀⣀⣀⣿⠃⠀⢿⣷⣤⣤⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣠⣿⡇⠀⠸⣇⣀⠀⠀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⡆⢤⡀⣀⢤⢤
⢀⣤⡴⠋⠁⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⡀⠀⠈⢿⠟⠀⢰⢆⡀
⠛⣿⡅⠀⠄⠈⣠⡧⡄⠄⡀⣀⠀⠀⠀⠀⠀⢨⡀⠁⣈⠀⠀⠂⠀⠉⠻⠃
⠀⠸⠛⠒⣶⠒⠋⠀⠀⢠⣀⠀⠧⡀⠀⠐⠁⠀⡄⠀⢿⣧⠀⢐⡀⠤⠀⣠⡄⠂⠨⣆⡆
⠀⠀⢀⠀⡉⢢⠀⢄⢠⡼⠳⣎⠁⠒⠀⠘⠃⠀⠀⢀⠂⣀⠕⠤⠴⠒⠀⠀⠁⠀⠠⢬
⠀⣴⠡⠀⢀⠎⠙⠓⠲⠤⣤⣀⣁⠀⠀⠐⢠⣰⠒⠘⠃⢁⠄⠀⢀⠀⠀⣸⡁⠐⠀⠈
⠀⢸⣡⢗⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⢙⡉⡀⠀⢀⣄⣠⡖⠀⠀⠀⠰⠭⡙⣓⠲⠦⠤⠄⠒⠚⠒⡂⢤⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠖⠂⠀⠀⠀⠉⠉⠁⠐⠢⠄⠬⠁⠀⠀⠀⠈⠁⠀⠀⠠⠀⣀⣀⣀⠀⢸⣿⡇
⠀⠀⠀⠀⠰⠔⣦⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⢀⢀⣠⣧⡴⠁⠀⠀⠂⢻⣿⡇
⠀⠀⠀⠀⢸⠒⢸⠛⠛⢲⡉⢹⣄⡀⢃⣀⣀⡠⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⡁⠀⣠⣴⣶⣿⠿⠧⢤⡀
⠀⠀⠀⠀⠈⠒⠛⠀⠀⠸⣄⣼⠀⠈⠁⠀⠀⠀⠳⡌⡈⣇⡀⠀⠀⠒⢢⠀⢸⠀⠀⠀⠀⠀⢆⣿⣿⣿⣿⣿⡻⢽⣿⡟⡱⠈⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⠇⠈⠉⢡⠲⣸⠤⢼⣴⣀⠀⠠⡄⠘⢿⣿⣿⣿⣿⣿⣷⡾⠰⠀⣰⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠈⠉⠒⢤⠀⠀⢫⠉⠋⠻⣿⣿⡇⡃⠀⠘⣐⣁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠃⣼⠂⡀⠀⡷⠈⠍⠑⠚⢉⣉⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠴⠃⡇⠁⢠⡏⠒⠒⠈⠉⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣦⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⢤⡀⠀⠀⠀⠀⠄
⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⢺⠅⠑⠀⠈⠁⣼⠀⠀⠀⠀⠰⠦⠀⠀⠐⠂⠀⠃⡇⡂⠰⠀⢈⠀⡌⢀⠂⢐⢤⢂⠐⠈⠐
⠀⠀⠹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠄⠀⠀⠠⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⠠⠀⠀⢄⠀⠁⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⢠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⠃⠀⠀⠀⠈⢀⡹⠀⠉⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠠⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⠐
⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠈⠀⠠⡄⠠⠀⠀⡐⠀⢀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠐⠄⠀⠀⠀⣤⣀⠀⣀⠐⠠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⠀⠀⡀⠀⠀⡀⠁⠡⠀⠀⠣⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⡀⠀⠠⠁⠘⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠄⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠇⠅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢒⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠙⢿⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠻⣷⣄⡀⠀⠀⠈⠉⠙⠛⠶⣤⡀⠀⠀⠀⢀⣤⡶⠞⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠉⠛⠛⠟⢿⣶⣶⣤⡀⠀⠀⠹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣤⡴⠏⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⣿⡇⠀⠀⠀⣀⣤⣄⠀⠙⣷⠉⠷⠀⠀⢰⣿⣥⣤⣤⣤⣤⣀⣀⡀⢰⡟⠁⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠈⣿⣷⠀⠀⣾⣿⣿⣿⠇⢠⠟⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠘⢿⣷⣄⣙⢿⣿⣧⣤⣄⣀⣤⠴⣿⣥⣤⣄⠀⠀⠀⠀⠀⢀⣴⣶⠤⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠿⢿⡿⢁⣋⠉⢉⣿⣿⣿⡄⠀⠀⣰⣿⣏⣤⣠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢼⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣨⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣿⣿⣿⣿⣿⡿⡿⠿⣇⢰⡿⢿⡿⣿⣿⣿⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⠿⣿⣿⣿⣶⣤⢴⣷⠀⠳⣤⣾⣿⣿⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠳⣄
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠈⠉⠉⠀⡜⣽⣄⡄⢈⠉⠉⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠘⢷⡀
⢠⡟⠉⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣠⣾⡛⠘⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠾⠃⠀⠀⠀⣰⣿⣽⣦⡀⠀⠀⣀⣠⣴⣿⣿⡄⠀⠀⠀⠀⢻
⡿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠙⣿⠿⣿⣷⣦⡀⠀⠀⣴⣾⣷⣶⣾⣷⣆⠀⠀⡴⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣧⠀⠈⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⢿⣿⣷⣄⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣇⠀⠀⠀⠀⢠⣿⣿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢦⣀⠀⠀⠸⣏⠙⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣦⠀⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⣿⠀⠀⠉⢻⣿⣿⣷⣶⣤⣤⣤⣤⣾⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣠
⠀⠈⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢿⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⠾⠋
⠀⠀⠀⠀⠀⠙⠶⣤⣤⣄⣀⣤⡴⠞⠛⣧⠀⠀⢀⣴⠇⠀⠀⠙⢦⣄⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠆⢀⡿⠁⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣙⡛⠿⠿⠿⠃⠟⢿⠀⠀⠀⠙⢿⣿⡿⣿⣿⠿⠛⠛⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠦⡤⠾⠀⠀⠀⠀⠀⠉⢧⠈⠙⠛⠳⠶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢀⠀⠀⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢲⡀⢀⡀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⡑⠠⡀⠀⠀⠀⠀⠀⢳⣐⠂⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⡀⠑⢄⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠁⠀⠀⠃⠀⠀⠑⠄⠆
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢣⡀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠴⢅⠈⠉⢵⠀⠀⠀⠀⠀⢀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠄⡀⠀⠀⠀⣀⡠⠐⠁⠀⠀⠡⡀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐
⠀⠀⠀⠀⠄⠀⠄⢀⠔⠀⠀⠀⡄⠁⠐⠄⠀⠀⠀⠀⠀⡉⠢⠀⠄⠄⠁⠊⠙⠠⡀⠀⠀⠂⠠⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠁⠀⠠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⡄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢃⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠈⠡⠀⠀⠈⢠⠤⠄⠀⠂⠉⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠈⠑⠀⠠⠂⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠒⠄⡀⠀⠀⠀⣀⠊⠀⠀⠀⠰⠋⠀⠀⢀⣌⣠⠁⠔⠂⠉⠐⢧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠄⠀⠄⣀⠓⠀⢀⡀⠀⠈⢀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⢀⠊⠀⡀⠀⠀⠁⠲⣀⣂⡀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢀⠠⠄⢒⠀⠀⠀⠀⠀⠈⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠔⠉⣆⠀⠀⠒⠶⠂⠒⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢁⠊⢀⠔⠐⠂⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠀⡄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⢠⣄⠀⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣦⣄⣿⣷⣾⣿⣷⣿⣿⣾⣿⣷⣾⣿⣀⣴⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀
⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣛⣹⡏⢹⣿⣿⣿⡟⠁
⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⠋⣩⣥⣼⡆⢰⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡿⠂
⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣋⣩⡅⢰⣶⣾⣿⣿⡇⢸⣿⣿⣷⠈⣛⣉⣭⣤⣿⡇⢹⣿⣿⣿⣷⡦
⠀⣀⣽⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⢀⡌⢻⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⢹⣿⣿⡿⠿⢿⣈⣛⣩⣥⣤⣄
⠀⠙⠁⠈⢿⣿⣿⣿⠁⡆⢸⣿⡟⢸⣿⣆⠹⣿⣿⣿⡆⢹⣿⣿⣿⣿⡇⢸⣿⣿⣷⣬⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⡉
⠀⠺⢧⠸⣆⠹⣿⣿⢰⣿⠈⣿⡇⢈⣭⣥⣦⡘⢿⣿⣷⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠠⣾⡄⢿⣷⡘⠏⢸⣿⡇⢹⣇⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⢀⣤⣸⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⠉⠀⠀⠀⢀⠔⡒⡢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠟⠋⢻⣿⢿⣿⡿⣿⣿⡿⣿⣿⢿⣿⠋⠻⠇⠀⠀⠀⠀⠀⠀⠀⢺⠀⠒⠆⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠘⠋⠀⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢲⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠤⢤⠞⠁⠀⠀⣸⡀⠀⠀⠙⢦⠤⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⡦⠴⠖⠋⠁⠉⠓⠶⠤⣾⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⣀⢸⡄⠀⠀⠂⠀⠀⠂⠀⠀⣼⠀⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⠦⣄⣀⣀⡤⠆⣰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⡿⠲⠤⣤⡤⠴⠺⡷⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⡼⠁⠀⠀⣖⡆⠀⠀⠹⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⠁⠀⠀⠀⣈⡀⠀⠀⠀⠹⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠤⢤⡤⣤⠤⠤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠇⢿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠆⠉⠉⠉⠉⠉⠉⠉⠁⠰⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⡈⢣⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠙⢦⣳⡄⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣹⣷⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠳⠦⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢻⣇⠀⠈⠹⢦
⠀⠀⠀⠀⢀⡼⠀⠀⠀⢀⢿⡇⠀⠀⢠⡎⠀⠀⠀⠀⠀⢀⡴⠛⣀⠀⠀⠀⠀⠀⠀⢀⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢸⡿⡀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⡸⠃⠀⠀⠀⢸⢸⡇⠀⠀⡞⠉⠁⠀⠀⠀⠉⠉⠀⠀⠉⠑⠶⠶⠶⠶⠂⠉⠀⠀⠈⠉⠁⠀⠀⠒⠀⠉⠉⢳⠀⠀⢸⠇⡇⠀⠀⠀⠘⢇
⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⢃⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡈⠀⡇⠀⠀⠀⠀⢻
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣶⠟⠉⣻⠀⠀⠀⠀⣀⠴⣿⡛⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⣷⠦⣀⠀⠀⠀⠀⣟⠙⠛⣤⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⠁⢀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⣿⡄⠸⠀⠀⠀⠀⡆⠀⠀⢹⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣷⡀⠀⠸⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⢀⠇⠀⣠⣾⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢀⡟⠀⠀⠀⠂⠀⠀⣸⠁⠈⠑⠲⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠋⠁⠀⣇⠀⠀⠀⠀⠀⠀⢻
⠀⡾⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⠀⠀⢷
⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⢧⡀⠀⠀⠀⠀⢳⣈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠛⠳⣶⠖⠒⠒⠒⠲⠲⡶⠟⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡖⠀⠀⠀⠀⢀⣼
⠀⠀⠉⠓⠶⠶⠶⠞⠉⠉⠁⠀⠀⠀⠀⠀⣀⣤⠶⠊⠙⠋⠀⢀⠀⠀⠉⠁⠶⠶⠈⠉⠀⠀⡠⠀⠙⠋⠐⠶⢤⣀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠁⠀⠀⠉⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡼⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠳⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⢀⣠⠞⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣏⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀
⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢶
⣇⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠉⠓⢦⡀
⠈⠳⠶⠲⠶⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⢦⡀⢴⠶⠒⠞
⠀⠀⠀⠈⠷⠋⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠈⠉⠁⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⠀⣀⣀⡀⣤⡤⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠓⠒⢤⣤⣤⣤⣤⠄⠒⢶⠂⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠢⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠨⠀⠀⠀⠀⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡀⠤⢀⠀⠀⡵⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⠒⠁⠀⠀⠀⠀⠀⠀⠀⠳⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢡⠀⠀⠀⠀⠀⠀⠰⠻⣧⡄⠀⠀⠀⠀⠀⢀⣤⣶⣆⡘⣿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⠀⠂⡐⠀⢈⡞⠈⠁⠀⠀⠀⠂⢁⣤⣿⣏⠁⠸⣷⠀⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠁⠀⠀⠠⢶⠃⠀⣽⡷⠿⢶⣶⡀⠀⠀⣾⣏⣤⣿⣇⠀⣹⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠚⠒⡤⠖⢯⡀⣼⣿⣶⣶⣶⣟⣧⠀⠀⢞⣿⢿⣿⣫⣿⠛⠦⠀⠀⢠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣤⣀⠀⣼⠃⠀⠀⠇⣻⠛⢻⣿⣟⠉⠻⠆⠀⠘⢣⠾⠋⣏⡋⠐⠀⠀⠀⠀⢈⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠴⠯⡗⠚⠉⢀⡚⠁⠀⢀⣎⣰⣇⠀⠀⠈⠉⠉⠀⠀⣰⡛⡀⠀⠀⡿⠿⢦⣴⣶⣄⢀⣼⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠠⣼⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣩⣙⣥⠀⣰⣇⢀⠀⣿⠷⢿⣿⣏⣁
⠀⠀⠀⠀⠀⠀⠠⠶⣦⡈⠀⠀⠀⠀⢰⣧⠸⡆⠙⠻⠿⡧⠀⠀⠀⠀⠺⣿⣿⡿⢡⣿⡟⠘⢿⣿⣳⣿⣧⣀⣨⠏⠲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡗⣠⠀⠀⣢⠋⠓⠛⠒⠂⠀⠀⠀⠙⢷⣄⣀⠀⢁⣠⣿⣷⣀⡀⢤⣠⣿⠛⠄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣄⣀⠀⠀⢀⣀⣀⣦⡄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⠿⢀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⣿⡿⠋⠁⠀⠀⢈⠇⠀⠀⢀⣴⣿⠋⢹⣿⣿⢻⣯⡟⡫⠿⠷⣴⣒⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⢠⠋⠀⠀⠀⠀⣠⠞⣠⣴⢿⡋⢳⡌⠱⡜⠉⢻⣦⣾⣷⣀⣴⡾⠻⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠇⠰⢿⠃⠈⣉⠅⢀⣠⠷⠴⠿⣋⣍⠻⣿⣿⠷⠾⠶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡠⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⡏⠀⠼⣧⣶⡿⣶⣮⣽⣾⣿⣿⡶⣦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⣸⠷⢻⠞⢠⡀⣴⣿⣾⣾⣿⣿⡶⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣤⣶⣶⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠁⠀⠀⠈⠉⠁⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠰⡪⢶⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣠⡾⢝⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣸⠇
⠀⠀⠀⢀⠔⠊⢉⠄⡿⠁⠀⠔⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢋⠀⠈⠁⠢
⠀⠀⠔⠁⠀⠔⠁⠠⠀⠀⠊⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⣄⠌⣆⠀⠐⠀⠀⠠⡀
⢀⠎⠀⠀⠀⠀⠀⡇⡀⡟⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢸⠀⠀⠀⠀⠀⠱
⠈⠀⠀⠀⠀⠀⢠⡇⠁⡇⠀⠀⠀⠀⠦⠀⠀⠈⣀⠀⠀⠀⠄⠀⠰⠁⠠⠈⡀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠀⢡
⡇⠀⠀⠀⠀⠀⢸⠇⠀⢧⠀⡠⠂⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠄⠀⠸⠀⡜⡇
⢇⠀⠀⠀⠀⠀⢸⠘⣤⠚⡊⠀⣰⢿⢿⣿⠛⣧⠀⠀⠀⠀⠀⣸⢿⣿⠙⡿⣆⠈⢆⠓⢤⠁⡇⠀⠀⠀⠀⠀⡸
⠈⢆⠀⠀⠀⠀⠈⢇⢠⢀⠐⠀⢻⠸⡘⠿⢃⡞⠀⠀⠀⠀⠀⠳⡘⠿⢃⠆⠟⠀⠋⠀⡀⡰⠁⠀⠀⠀⢀⡴⠁
⠀⠀⠙⠂⠤⡀⠀⠀⢊⠢⣀⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠔⢁⠃⠀⢀⡠⠐⠉
⠀⢀⠊⠀⠀⠈⠐⠄⠈⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⢸⠀⠀⢁⠀⠀⠀⠠⡀
⢠⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠒⠂⠤⢄⣀⡀⠀⡀⣀⢠⠤⠀⠒⠉⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠑
⢸⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠔⣥⡖⠒⣂⡖⠓⣢⣸⠢⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠂⠀⠀⠀⢠
⠀⡧⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⢀⠔⠁⡐⠀⠉⠁⠇⢸⠈⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢼
⢰⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⡠⠈⠀⢀⠀⠀⠄⠄⠠⠀⠀⠄⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡆⠉⠢⡀⠀⠈
⠘⠦⠀⠁⠀⠀⢠⠀⠀⠀⡠⢆⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⢀⠵⢀⠀⠀⢀⡇⠀⠀⠈⠀⡴
⠀⠀⠂⢄⠀⠀⢸⠀⠀⠸⠀⠄⢉⠖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠲⡁⡤⠀⠃⠀⢸⡀⠀⠀⡤⠈
⠀⠀⠀⡸⠀⢀⡜⠀⠀⠀⠀⢈⡵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠁⠀⠀⠀⠈⢧⡀⠀⠇
⠐⠂⠚⠓⠊⠁⠀⠀⠀⠀⠠⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡇⠀⠀⠀⠀⠀⠉⠁⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠲⢤⡀⠠⠔⠒⢢⠤⣀⡀⠀⢀⣀⣠⠶⠅⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢸⠀⠈⡅⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⢒⣒⠒⣹⠀⢰⡇⢰⢒⠒⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⠀⠀⢸⠀⢰⡍⠀⠀⠈⢀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣒⣶⠦⣤⣦⡞⡦⡇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠀⢀⣾⣵⠛⣉⣻⣿⣷⣬⣿⣤⣅⣧⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠜⠋⠘⠛⣋⣀⠀⠴⠜⠿⣿⣿⣿⣿⣧⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⡄⠀⠀⠀⢹⣏⠀⡄⠀⠘⢿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢦⣤⣤⣶⠙⠃⠐⠟⣿⣿⣶⣶⣾⣴⡿⡟⢻⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⡇⠀⣿⣿⣧⣘⣠⣴⣿⣿⣿⣿⡿⣿⣷⣤⣾⡕⡉⠽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣿⠈⣻⠛⠉⢙⣍⣟⣛⣻⣿⣿⣿⣿⠿⣿⣍⡸⠻⣿⣿⣷⣾⣿⣤⣄
⠀⠀⠀⠀⣄⣀⣀⣰⣾⣿⣿⠈⣤⣄⠀⢹⡞⠿⠼⡟⢛⢍⣿⣯⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⠿⢏⡭⠴⠄
⠀⠀⠀⠀⠀⠈⣿⡉⠹⣿⡍⠈⠹⢍⠻⠿⣿⡶⢶⣧⣤⣼⣿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢶⣾⠿⠚⠋
⠀⠀⠀⠀⠀⠀⣹⡇⢰⣿⠶⢶⣤⣮⣄⡀⣈⣧⠈⠙⠑⡿⣿⣶⣿⣿⣿⢿⡟⣛⣺⣟⣿⣟⣧⠀⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣿⠇⠘⠁⠀⠐⠛⠇⠙⠁⠙⢿⣄⠀⠀⠀⠋⣻⣿⠽⠿⠧⠖⣡⣤⣍⠛⠛⣿⠀⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠁⠀⢑⠂⠺⡄⠠⠔⢳⡄⢀⠈⠛⠓⢷⡄⢨⣷⣾⠻⢿⣶⣶⣿⠛⠻⣶⣤⣸⠀⣹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⣀⣤⣷⣸⡇⠀⠀⠀⠳⣄⣿⣿⣷⣿⡶⢶⣿⡂⣬⣾⣿⣿⣷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢄⣽⠿⡿⠉⣹⡿⠿⡗⠀⣀⢀⣽⠟⠟⠛⠛⠛⠛⠛⢃⣼⣿⡟⡋⢻⣿⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠋⠀⢨⠁⢿⠃⠀⠻⢀⡙⠀⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣤⣶⠀⣾⣤⣤⣦⣤⣷⣾⣷⣷⣶⣶⣶⣶⣶⡮⠿⣿⣿⡾⢾⣄⣼⡇⢀⣀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠙⢻⡏⠁⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⣐⠢⠤⣝⠋⣁⣸⠀⣿⣯⣾⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣶⣟⣡⣠⣠⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣴⣶⣶⣶⠾⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⢀⣴⣿⣠⣴⣶⣶⣶⣶⠶⠖⣦⣼⠥⠞⠲⢶⡶⠖⠂⠀⢸⣤⣧⣿⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⡻⠶⠷⠚⠛⠃⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣾⣿⣿⡿⠿⠛⠛⠛⠛⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⢸⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠃⡠⡄⠙⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠲⠰⠂⠚⠂⠛⠰⠆⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣽⡻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣋⣵⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣷⣯⣻⢷⣽⢿⣷⣴⣤⣀⣤⣴⣤⣴⡿⢋⣵⢞⣯⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⣶⣿⣿⣷⡶⢶⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣟⣡⣛⣿⡿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣶⣶⣿⣿⢿⣤⣜⣉⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢻⣟⣫⣵⢞⣭⣾⣿⡿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣫⣵⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢻⣿⣿⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⡿⣿⣟⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣿⢁⣿⣯⣿⡇⣦⡀⠀⠀⠀⠀⠀⣴⣇⣿⣿⣿⣿⣿⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡏⣷⣽⣸⣿⣿⣿⢹⣿⢱⡦⣀⡀⣤⡀⣿⣿⣿⡽⠟⢻⣿⢿⡾⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⢻⢹⣿⠏⠀⠈⠛⣿⣧⣿⢧⣿⡁⣿⣇⣿⣿⡏⠀⠀⠀⢿⣎⣧⡿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⢿⡿⣼⡟⠀⠀⠀⣿⣿⣿⡿⣿⣧⢿⡟⣿⣿⣿⣄⠀⠀⠀⠈⣿⣿⣧⢧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣸⣧⡟⠀⠀⠀⣤⡿⣿⣿⣷⣿⢻⢸⡏⣿⣿⣿⣿⡆⠀⠀⠀⠈⢿⣿⡸⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⣇⣿⣼⠁⠀⢀⣼⣿⣿⣿⣿⡇⣿⣸⢸⡇⣿⢻⣿⣽⣇⠀⠀⠀⠀⠘⣿⣇⣿⡸⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⢸⣿⠇⠀⠀⣮⣵⣿⣿⡿⣼⢣⣿⣿⣼⣇⣿⣼⢏⣿⣿⡄⠀⠀⠀⠀⠀⢿⣼⢧⢿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⢹⡿⣷⠋⠀⢀⣾⣿⣿⣿⣸⡇⣿⢸⣹⣿⣿⣼⡏⣿⢸⡟⣿⣷⡄⠀⠀⠀⠀⠈⣿⡞⣾⢣⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⡞⣷⠋⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⢸⣧⣿⣿⣿⡇⣿⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⢿⣿⡿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⣷⢳⡏⠀⠀⠀⣿⣿⣿⣿⡏⣿⢱⡟⣼⣿⠀⣿⣿⣷⢹⡏⣿⢻⣿⢻⣷⠀⠀⠀⠀⠀⠈⣿⣧⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⢳⣿⡾⠁⠀⠀⠀⣿⣿⣿⣿⡇⣿⣸⡟⣿⡏⠀⣿⣿⣿⢸⡇⢻⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠈⣿⣼⢧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⡜⣷⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣌⡏⣷⣿⡇⠀⣿⣿⣿⢸⡗⢸⣿⣿⡅⡿⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣧⡇⣿⣿⡇⠀⣿⣿⣿⢸⡇⢸⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡸⣿⣧⣹⣿⠁⠀⣿⣿⣿⢸⡇⢸⣿⣸⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣿⢸⣏⣿⠀⠀⢿⣿⣿⢸⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⢸⣿⣿⠀⠀⢸⣿⣿⢸⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣿⢸⣿⡇⠀⠀⠸⣿⣿⠿⡇⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⢸⣿⡇⠀⠀⠀⢿⣿⢰⡇⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣿⣾⡿⠀⠀⠀⠀⣾⣿⡟⡟⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣿⠀⠀⠀⠀⠀⣹⣿⡇⣷⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣿⠀⠀⠀⠀⠀⣿⢹⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣿⠀⠀⠀⠀⠀⣿⣾⡇⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡿⣿⠀⠀⠀⠀⠀⣿⡟⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣿⠀⠀⠀⠀⠀⢿⡇⣿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣧⣿⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⠁⠀⠀⠀⠸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⢡⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡠⣞⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣧⡴⣶⡤⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣾⣽⣿⣻⣿⣿⣷⣾⣿⣇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⣽⣿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣿⡟⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡿⣿⣿⣷⣿⣿⣿⣛⣿⢿⣿⣿⣿⣯⣿⣿⣿⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣟⣿⣫⣿⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⣿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣽⢛⣟⣋⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡍⠙⢿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢀⣸⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠋⠁⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣿⣼⡿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠻⢆⠀⠀⠐⣿⣿⣿⣿⡿⠋⠙⠟⠋⠸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⠿⠖⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⢻⣿⢹⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣴⣿⣶⣿⠿⠿⠇

⠀⠀⣿⣿⠿⠿⣿⣿⣿⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⠿⠿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣇⠺⠇⡹⢿⣿⣟⣙⣷⣿⣝⣚⣻⣿⡿⡏⠿⠆⣹⣿⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣏⣻⢟⣿⣩⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⣿⣻⣷⣗⣿⠺⣻⠽⢻⠿⣽⢿⡙⠽⡛⢖⣷⣸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡿⢯⣿⣿⡎⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣷⣟⡷⢲⣶⣾⣹⡧⠁⣽⣟⣶⣷⡖⣿⣿⣾⣿⣿⠀⠀⣿⣷⣿⣏⣹⡏⢰⣿⣏⢍⣟⣏⣙⣿⣷⠸⣿⣹⣿⣷⣿
⠀⠀⣿⡘⢲⡿⣶⠿⣏⣿⣗⠲⡶⠖⣺⣟⣹⢷⡶⣿⡞⢹⣿⠀⠀⣿⣿⡿⢯⣭⣾⣿⣿⣟⣿⣿⣽⣿⣾⣿⣿⣬⣭⣿⣿⣿
⠀⠀⣿⣡⣶⣿⣍⣷⠿⠇⣛⡇⣀⢸⣛⠼⠿⣞⣹⣿⣦⣸⣿⠀⠀⣿⣿⣕⣗⣿⣷⢿⣿⡟⢋⣉⡉⠛⣿⣿⣾⣿⣟⣃⣿⣿
⠀⠀⣿⣽⣟⣿⠥⣿⡫⢼⣿⣿⠩⣿⣿⡤⣛⡯⢭⣿⣻⣿⣿⠀⠀⣿⣿⠩⣿⠝⢽⣿⣟⠠⡏⢵⢙⡦⢘⣿⣿⠯⣿⡯⢹⣿
⠀⠀⣿⠻⣿⣿⠷⣿⣥⡌⣛⡏⠛⢻⣛⢠⣭⡟⢾⣿⣿⢻⣿⠀⠀⣿⣿⣟⡟⣿⣿⣿⣿⣆⡙⠓⠋⢀⣾⣯⣿⣿⢟⡻⣿⣿
⠀⠀⣿⠇⣽⣿⣿⣡⡟⣷⣟⣡⣤⣈⣻⣞⢻⣽⣿⣿⣎⢸⣿⠀⠀⣿⣿⣧⡵⠿⣷⣿⣿⣿⣿⢾⢾⣻⣿⣿⣾⠿⠯⣥⣿⣿
⠀⠀⣿⣾⣷⣟⣦⣹⣿⣿⢳⡤⠀⢤⢞⣿⣿⣃⣴⣿⣾⣿⣿⠀⠀⣿⣿⣿⡟⢻⡎⢹⣿⡟⠛⣟⡟⢛⣾⣿⢩⣾⢻⣿⣿⣿
⠀⠀⣿⣿⣷⡟⣷⣠⣫⢬⣻⣧⢷⣽⢋⣥⣇⣔⣾⢫⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣦⡽⣿⣿⡋⣻⣿⣟⣵⣾⣿⣿⣿⣧⣿
⠀⠀⣿⡟⣩⡅⢭⣼⣿⣿⢛⣯⣿⣽⠛⣻⣿⣮⡅⣬⡝⢻⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣜⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣳⣬⣡⣿⣿⣿⣿⣻⣷⣿⣾⣟⣿⣿⣿⣷⣩⣥⣿⣿⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣹⣿⣯⣻⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⢠⣾⠿⠶⠾⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠤⠠⠬⠽⠿⣿⣴⠀⢹⣧⡀⠀⠀⠀⢠⡴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⠀⣰⣞⠏⠀⣯⢿⣽⣶⣶⣶⣿⣾⣿⣎⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠈⠁⠀⠀⢻⡾⠿⣿⣿⣿⣿⣿⣿⡿⢷⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⡅⠸⣷⠀⠀⣴⣾⡿⠀⠀⠸⣿⣛⣿⣿⣿⣿⣿⣿⠃⠀⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠼⢋⠴⠋⠀⢀⡀⠀⠀⠉⠉⡁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣛⢅⡀⠀⠀⠀⠙⢿⠛
⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⢀⣴⣿⣿⢲⡔⣲⣿⣄⠀⠀⠀⠈⢸⣯⠿⣿⠏⠀⠀⠈
⠀⠀⠰⠿⠇⠈⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⡆⠀⣾⠀⠀⠀⠀⠁⠸⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡁⠀⡿⠀⠀⠠⠀⠀⠀⠿⠁⠠⠈⠳⢂⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠾⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢸⡇⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢿⣿⡏⠍⢹⣿⣿⣿⣿⣿⣶⡌⣿⠀⠘⠋⠙⠀⢸⠇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⢸⣿⡿⢻⠀⠙⣿⠇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣸⣿⡇⠀⠀⠼⠛⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠉⠀⠐⢶⣶⣤⣴⣾⣿⣿⠿⠻⣿⣿⣷⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⣦⠶⠛⠙⠒⠒⠛⠋⢙⣛⠲⢴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠷⠦⣴⣴⣇⣈⠀⠀⠀⠀⠀⠀⠀⠀⡤⠺⢿⠤⢿⣀
⠀⠀⠀⠀⠀⡠⠚⠡⠀⠀⠊⣼⣀⡠⢬⠃⡉⠠⣂⢄⡀⠀⠈⠒⣤⣼⠅⢄⠈⡙⢦⡀
⠀⠀⠀⢠⠞⢁⠈⠀⠠⠀⠀⢸⠉⠑⠒⠒⠒⠉⠁⠀⠈⠉⠉⠉⠀⠸⡆⠀⠡⠀⠀⢳⡀
⠀⠀⠀⠻⡤⠀⡀⠠⠁⠐⠀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡇⠀⣆⠱⣄⠂⣧
⠀⠀⠀⢸⣇⣰⣤⠁⢀⠀⢀⢸⠀⠀⠀⠀⠟⠗⠀⠀⠘⠰⠃⠀⠀⢠⡇⡀⢸⠤⢾⡛⠋
⠀⠀⠀⠀⠈⠁⠘⠦⠞⠲⡴⣞⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣤⣱⠞⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⣀⡀⠀⠀⠀⠈⣀⣀⣤⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠉⠉⡉⠉⡁⡀⠀⠈⠙⠲⡶⠦⠴⠖⠛⠙⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣀⠀⢀⠆⠀⠸⡀⠉⢀⠎⠸⡶⠤⣤⣇⣀⣀⠀⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⡷⠋⣇⠀⠀⠈⠐⠁⠀⡠⠳⠦⠤⣤⣭⣉⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡞⠁⣴⠋⠓⠒⠐⠒⠀⠀⠀⠀⠒⠀⠀⡤⠤⣫⠷
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠸⡇⠀⡏⠀⠀⠀⠀⠀⠈⠐⠀⠀⣠⠒⠒⠧⠼⣧⣀⣀⣠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⢦⣹⠀⡇⠀⠐⠀⠀⣀⣦⣠⠤⠞⢥⣀⠀⠀⢸⠁⠀⡹⠁⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠁⠀⣇⡠⣀⣏⠉⠁⠈⣲⣞⡋⣉⣬⣙⠲⠾⣄⣀⣇⠀⠇⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠛⢦⣀⠎⠁⡨⠋⡡⠂⠉⢷⠀⠀⠉⠙⠒⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢰⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣤⡤⠶⠋

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣄⢀⠄⢸⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠻⢧⡄⠀⠀⣀⡳⣋⠸⣿⣿⣿⣿⣿⠿⠟⢣⢀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⣰⣿
⠿⣹⣻⣿⡛⠿⠿⠿⢿⢿⡿⡿⠿⠿⣿⡻⠟⠛⠉⠁⠀⠀⠛⠁⠉⠀⠀⠀⢠⣴⠿⣻⡿⠉⠈⠀⣞⡉⡾⠛⠿⠿⢿⠻⡻⡿⣿⠻⣿⢿⣿⠟⠟⠻⠿⠿⢯
⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠈⣿⢻⢻⡏⣿⢻⢻⣿⡂⡸⠟⠁⠔⠉⠉⣿⠿⣟⣿⣿⣻⡏⠁⠀⠀⠀⠀⢸⡟⣿⢻⣿⡟⣿⢻⡟⠁⠀⠀⠀⠀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣾⣾⣿⣿⣸⣾⡟⠋⠀⠀⠀⠀⠀⠀⢉⣡⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⡇⣿⣸⣿⣇⣿⣸⡇⠀⠀⠀⠀⠀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⣠⣤⣤⣔⣤⣀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠩⢞⣬⣻⣧⣼⣷⡀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠾⠶⠖⠀⠂⠹⠿⠿⠿⠿⠿⠿⠇⠀⢟⡡⠭⠿⣿⡿⠇⠀⠿⠿⠿⠿⠯⠷⠲⠿⠿⠏⠫⠿⠿⠿⠿⠿⠿⠿⠇⠓⠛⠛⠺⠛⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣩⢟⣯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠏⣠⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣄⣰⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠴⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡇
⣴⣶⡄⣶⣴⣦⣤⣤⣦⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣦⡷⣶⣦⡷⣶⣶⣶⣶⣶⣶⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣦⡤⠶⠶⢤⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⣦⡘⢦⠀⡁⠀⣀⡽⠛⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢠⠞⠉⠉⣈⣣⣥⢞⣥⣴⡒⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠠⣏⢸⡀⢓⡜⡍⢣⠖⣀⠈⢹⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠙⠦⢭⡭⠚⠁⠙⢤⣉⠴⣸⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⠶⠀⠙⠁⠙⠲⡄⠒⠋⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠘⡗⢕⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⣰⠏⢀⣠⣤⣤⣀⠀⢀⡠⠴⢚⣩⢵⣚⣧⠹⣫⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⣀⣀⣀⣀⠀⠀⣀⡴⠞⢁⡴⠋⠀⠀⢀⠟⢋⣡⣴⡾⠗⠛⠉⠀⠀⠑⠝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣨⡭⠭⠯⣉⠉⠻⣄⠀⣼⠃⠀⠀⠀⢬⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡾⡅⠀⠀⠀⠈⠙⢦⠈⣯⡟⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡇⠀⠆⠀⠀⠀⠀⠀⠑⠿⠤⠀⠀⡄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠳⣄⠀⠒⠀⡀⠀⠀⠀⠀⠀⡠⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣉⢿⣆⠀⠀⠈⠳⠦⣤⣁⣀⠒⠀⠒⢀⣴⠋
⠀⠀⠀⠀⢀⣠⢤⡲⠭⠒⠊⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠎⠉⠉⠙⠋⠉⠙⣦
⠀⣠⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⣇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⢀⠀⠀⡄⠀⠤⠀⠠⠀⠀⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠚⠉⠋⠛⠳⣄⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⠏⠀⠀⠀⠃⠀⠀⠘⣆⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⠀⠀⠀⠀⠁⠀⠀⠀⢹⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠂⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠀⠀⠈⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⠀⠀⢘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⢈⠀⠀⠀⠀⠀⣠⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣳⣶⣶⣾⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⢰⡇⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣾⣿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⣡⣾⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣴⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣄⢠⢣⣿⣿⣿⣿⠟⠋
⠀⣸⣦⡄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⡤⢊⣡⣴⣶⣿⣿⣿⣿⣶⣝⣿⣿⣿⠟⠁
⠀⢿⣿⣿⣿⣿⣷⣦⣭⣑⣒⣲⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣤⣥⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠉⠛⠙⠛⠉⠉⠀⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣿⣿⠏⠀⣿⣿⣿⣝⣿⣿⡟⣿⣿⣬⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣇⠀⠐⣿⣿⡿⢿⣿⣿⣿⣝⠏⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡞⣿⣿⣿⣿⣿⣷⢠⡀
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣯⠝⠋⡀⠀⠹⣎⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢸⠁⣽⣿⣿⣿⠹⡟⢰⡇
⠀⠀⠀⠀⠀⠀⠸⠛⣿⡿⠇⠀⠐⠀⠀⠀⠹⠿⠟⠻⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⡟⠀⢱⣿⠻⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⡌⢠⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡸⠁⠀⠀⢳⡀⠙⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠻⠿⠿⠃⢀⠜⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⠁⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠲⡟⠲⡞⢇⢀⣼⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡄⠀⡘⣦⡙⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⣉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⡼⣿⣿⣿⣿⣿⣧⢻⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢤⣴⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣎⠭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠘⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⠿⢿⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⣄⣀⡰⠤⠜
⠀⠀⢪⡀⠀⠀⠀⣀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⢩⢤⡍⠘⠩⠞⠁
⠀⠀⠀⠈⠉⠓⠚⠁⠰⡀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠼⠤⠂
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠺⣟⡛⠛⢲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠙⢾⡓⠿⠉⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣤⢤⣤⢬⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡿⠦⠉⠃⠉⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⣛⣶⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡏⠉⠛⠿⣍⡉⠉⠛⠛⢩⣭⡭⠿⣿⣿⠳⢶⡶⠶⠶⠒⣶⣤⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⡀⠀⠀⢸⡇⠀⠀⣤⣈⡙⢄⠀⠀⠀⠬⣽⣿⡗⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠜⠉⠀⠀⠀⠀⢷⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⣿⡋⠉⠀⠀⠀⠘⠁⢀⣠⡤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡟
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⣻⣿⡹⠀⠀⠀⠀⠀⢸⣿⣿⣳⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠉⠁⠀⡀⠀⢀⠀⠠⠉⠉⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠘⠀⣀⣉⣶⣏⣀⠐⠀⠂⢀⣠⠴⣿⠋
⠀⠀⠀⢀⣾⠇⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠉⠓⢦⣄⣀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠘⢧⡀
⠀⢀⡤⠞⠁⢀⡀⠀⢰⡟⠀⠈⠻⣦⡀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⣴⢋⡤⠖⢠⡏⠀⢀⡿⠀⠀⠀⠀⢸⣿⡋⣀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠈⠙⠷⠤⠴⠛⠛⠛⠁⠀⠀⣀⡴⠋⠁⠘⢛⣷⡄⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⢀⣰⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⣢⡀⠀⣨⣿⠿⠒⠛⠋⠛⠓⠶⠶⠶⠶⠚⠛⠋⠉⠛⠻⣦⡀⠀⢀⡐⢿⣿⠑⠀⠈⠛⢦⣄⡀
⠀⢀⡤⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣾⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⡟⠃⠀⠀⠀⣶⣄⣈⠙⠳⠶⣤⣀⡀
⠀⠿⠧⣤⠖⠀⠀⣠⡆⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣼⡋⠀⠁⢀⠀⢠⣄⡀⠉⠙⢶
⠀⠀⠀⠻⠤⠴⠚⠁⠹⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡅⠈⣳⣄⢈⡿⠶⠖⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣥⣬⣽⣧⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣶⠿⣾⢻⡾⢷⡞⣷⠟⣶⠻⣾⢳⡾⢷⡞⣷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣋⣿⣹⣿⣹⣟⣻⣏⣿⣛⣿⣹⣟⣹⣏⣻⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢠⠀⠀⠀⠀⠀⠀⠀⠿⣧⡿⣬⢿⣼⠏⣹⣿⢿⠟⠛⣿⠛⠼⣯⡽⣧⡿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⣶⡟⣶⠛⠂⠀⢠⣿⡇⠁⠀⢂⣿⡄⠀⠈⠱⡟⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⣉⣿⡉⠁⠀⠀⣿⡿⠃⠀⣠⣾⣿⣇⠀⠀⠀⠘⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⢻⣿⣦⣀⣠⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⣀⡀⣛
⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⡄⠀⢰⢆⢀⠀⡄⢰⡀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠹⣿⣿⣿⡿⣿
⠀⠀⠋⠐⣋⢠⠇⠠⠀⠘⠑⡃⣡⡐⣦⠼⠳⠞⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠽⠿⠛⠁⣦
⠈⠒⠀⣨⠅⠞⠠⢁⡴⢸⣏⡍⢁⠀⢯⡀⠁⠀⠀⣾⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛
⠀⠀⣀⣠⠀⠀⠃⢘⡠⢸⠐⣿⣀⡤⠞⠀⠀⠀⠀⣨⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⣿
⠀⠀⠀⠀⠀⠒⠢⢬⠆⡼⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻⣶⠿⣶⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⢷⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣛⣿⣻⣗⣢⣄⣤⣄⣤⣀⣶⣻⣟⣻⣟⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣭⣿⣽⣯⣽⣯⣽⣯⣿⣭⣿⣽⣯⣽⣯⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⠰⠶⠖⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠲⠶⠆⣤⣄⠀⢀⣤⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠙⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⡴⠋⠀⣸⠦⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠴⠶⢾⣁⣠⠞⠁⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢀⡰⠋
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠙⣆
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠹⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢧⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠉⠳⢦⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠁⠀⠀⠀⠈⠳⣄
⢠⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢠
⠈⣧⠀⠀⠀⣤⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡆⠀⠀⠀⡾
⠀⠙⢆⡀⣀⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣁⣀⢀⡜⠁
⠀⢀⡞⠁⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠙⢧
⠀⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈
⠀⠹⡄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸
⠀⠀⠘⠳⠤⠤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠂⣤⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⢤⣤⠐⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠈⠻⢍⡁⠀⠈⠁⣀⡿⢦⡀⠀⠀⠀⢀⡭⠏⠁⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⢀⡾⢧⡀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⡜⢷⡀
⠀⠀⠀⠀⠀⢸⡅⠀⠳⣄⡀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⡴⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠒⠓⠋⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠉⠑⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠚⠓⠢⠤⠤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠔⠚⠛⢙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⡄⠶⠶⠄⣤⡀⠀⡜⠀⠀⠀⠠⡇⠀⣀⣤⠰⠶⠂⢤⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣁⠀⠀⠀⠀⢀⣩⠟⠁⠀⠀⠀⠀⠘⢿⣁⠀⠀⠀⠀⠀⣨⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠑⠤⠀⣀⠀⠀⠀⠀⠒⣶⠀⠀⠀⠀⠀⡀⠀⠀⡠⠘⠛⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠒⠈⠉⠀⠉⠉⠀⠠⠀⠀⠤⠁⡀⠀⣠⡿⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⢠⡄⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣀⠖⠙⢧⡀⠀⠀⢾⠟⠉⠀⠀⠀⠈⠁⠀⣀⠰⠄⠀⣀⠂⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⢁⠐⠦⣀⣀⣤⣦⣠⣴⣾⣿⣿⣿⣇⣠⣾⡧⢸⣄⠀⠁⠀⢀⠠⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠛⠀⢀⣰⣿⣿⣿⠿⣿⡿⠏⠉⠙⣿⡿⣭⣷⡾⠋⡀⠀⢀⡴⠄⠙⣃⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢙⣦⣴⣿⠉⣰⣯⣤⣄⡀⠀⠀⠀⠘⠉⠁⠈⣷⣾⣶⣤⣶⠋⠀⠀⠙⠁⣠⡀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣏⣹⣿⣿⣶⣿⣿⣏⠉⠛⠛⠒⡆⣤⣄⣠⡞⠻⣿⣿⣿⡿⠀⠀⠀⠀⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣾⣿⣿⠟⢫⣿⢋⣩⠆⠀⢈⣭⡀⠸⣿⣿⠗⠲⣿⣿⣿⣤⣤⡐⠊⢱⣦⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣸⣿⣤⣸⣿⠛⠟⠀⠀⠙⠿⠛⠀⠙⣿⠆⠀⢻⣯⢃⠀⢹⠿⢻⣆⡉⢻⡗⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢿⣿⣿⢿⡏⠀⢀⣀⠀⠀⠀⠀⢠⡄⣸⣷⠀⠁⢴⣿⣷⣿⣤⣿⣿⣿⡇⠀⢿⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣾⣿⡀⠈⠛⠃⠀⠀⠀⠀⠛⣿⣿⣿⣦⡄⠙⣿⣿⣿⠛⠿⠛⢷⣤⣤⡅⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⣀⣤⣾⠋⣨⠙⣷⣄⡀⠛⢿⣿⡷⠺⣧⡈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠟⢩⣿⣏⣿⣿⡿⠛⠛⠛⣿⣿⣾⣯⣤⣿⣿⢿⡶⣾⡏⠆⢀⣿⣷⡀⠙⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠁⣼⡏⢿⣿⠀⠀⠀⠀⠙⢿⣟⣡⣿⢿⣿⠾⠿⢿⣷⣆⣼⠿⣩⡗⢠⣿⣥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠿⠋⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⠋⠀⠀⢸⣯⡼⠏⣀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢟⣁⣀⡀⣀⠀⠀⠀⠀⠈⠁⣠⠁⠀⠀⠀⠀⢿⣧⣬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠂⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣤⠿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⠀⢸⠀⡆⢀⠀⢰⠀⢠⣤⣤⣶⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⠿⢿⣥⣭⣿⣿⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠿⣿⣿⣿⣿⠿⢟⣋⣤⣶⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠈⠁⠙⠛⠛⠉⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⡐⠂⠀⠀⠀⣇⣀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⡀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠐⢿⣧⣴⣷⠄⢀⣤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠠⢀⣀⣯⣿⢇⡀⠀⡹⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⣀⡘⣿⣿⡿⠛⠛⢙⣾⣥⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠉⠉⠀⠀⠙⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸⣀⠀⠀⠀⠀⠀⡰⣻⡳⣀⠳⣦⣄⠀⢀⣠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠊⠁⠈⠉⠓⠒⠒⠚⠣⢿⢫⣴⣵⠘⠀⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⡗⠪⠒⠛⠋⠀⢀⠀⠀⢠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢄⣀⣀⡀⢤⣾⠇⠀⠀⠀⠀⠀⠈⡗⠒⠁⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠒⠒⣒⠮⢡⠎⠀⠀⢀⡰⠃⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠀⠛⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⡐⠑⣂⡥⠚⠒⢚⡿⠀⠀⠀⠀⣿
⠀⠀⠀⡄⠰⢆⠀⢸⣀⡀⠀⢠⠃⡤⠤⢀⡀⠀⠈⠒⠒⢊⠠⠒⠉⠉⡧⠖⣋⠀⠀⠀⠀⠀⡿
⠀⠀⡜⠻⠁⠘⠋⠉⠈⠉⠑⡇⢘⠄⠀⠀⢳⠀⢀⠔⠊⠁⣠⠔⢊⠼⠚⠉⡀⢱⠀⠀⠀⠀⡇
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠑⣭⢞⣀⡠⠁⣸⠐⣕⡀⢰⡟⡡⠚⠁⠀⣠⠜⣱⠃⠀⠀⠀⢰⠃
⣤⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠞⠁⠀⠀⠉⢹⣞⢁⠄⢠⠚⠁⠔⠁⠀⠀⠀⠀⡞
⡍⠇⠀⠀⠀⠀⠀⡴⢋⠀⢀⣴⠋⢳⣀⡀⠀⠀⢀⡤⠋⠈⠘⢲⠋⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠇⠀⠀⠀⠀⠀⠀⠈⠛⡤⠄⠈⠆⢸⠀⠙⣶⠊⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠸⡀⠀⠀⠀⢀⠀⡸⠳⠇⠀⠀⢸⠂⠀⠀⡽⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠱⣄⠀⠀⠘⡗⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⡠⠔⠊⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⢔⣒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⡀⢀⠀⢄⠈⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠐⢀⠎⠁⠒⠤⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡔⠁⣄⠀⠲⠀⠀⡟⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠳⡀⠀⢀⡠⠄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢹⡦⡄⠤⢐⠯⠷⡲⢄⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⣸⠁⠢⠯⠓⠋⣀⡵⣄⠑⠄⢸⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠀⢻⣠⠤⠄⠀⢉⣡⠦⠜⣷⠀⠸⣄⣀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⣄⠀⢠⠦⠒⠘⠉⠁⠀⢀⠀⠈⣄⠀⣨⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡠⠸⠦⠋⢦⠤⠤⠐⢀⣀⠕⠔⠉⠑⡙⠃⠨⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠊⠀⠐⣄⣠⠇⠃⠊⠉⠁⠀⠀⢀⡠⠄⣙⡖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⢧⠀⠄⠀⢀⣂⡭⡠⠒⠊⢁⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠰⠓⠚⠊⠁⠁⠀⣀⠠⠔⢊⡥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⣒⡢⢈⠽⢤⠾⠊⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢰⠀⡄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⡆⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣀⣄⠰⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠙⠛

⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠛⢿⣿⣟⣁⣾⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢀⣀⣀⠀⢾⣿⣿⣿⣿⣷⣶⣶⣤⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⢷⣾⣿⣿⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿⢿⣿⢃⡄⢀⣾⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⢸⣿⡿⣁⢸⣿⣿⢀⣾⣿⣿⣿⣿⣿⠁⠙⣄⣷⠈⠻⢿⣿⡿⠟⠛⠛⣿⣷⣄⠀⣦⢹⣿⣿⣿
⠀⠀⢸⣿⣿⡟⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⡆⠀⠨⢷⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⣄⠹⣿⣿⣿⣿
⠀⠀⢸⣿⠟⠀⢀⣾⣿⣿⣿⣿⡿⢻⣿⡟⠀⠀⠀⠏⠁⠀⢰⡿⠀⠀⠀⠀⢰⡏⢿⣿⣦⣝⣻⣿⣿⡆
⠀⠀⢸⡟⢀⣴⡿⣿⣿⣿⣿⡟⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠃⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢸⣧⣾⠟⢀⣿⣿⣿⣿⠇⠀⠀⡇⠀⣠⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣼⠉⠀⠀⣿⣿⣿⢿⣿⣿⡀
⠀⠀⢸⣿⠁⠀⣼⡿⢿⣿⣿⣦⠀⠀⣧⣰⠟⢇⠀⠀⠴⣻⠇⠀⠀⠀⣾⠅⠀⠀⠀⣿⣏⣿⡆⠘⣿⡀
⠀⠀⢸⣿⡇⣼⣿⣠⡖⣿⡟⠛⠳⣦⣿⣿⣦⣈⣆⢀⣴⠏⠀⠀⠀⠀⢻⣶⣾⣿⣇⣿⣿⣿⡇⠘⣿⠁
⠀⠀⢸⣿⢣⣿⣿⣧⣷⣾⣿⠀⠀⣸⣿⡟⠁⠉⠿⣿⣧⣆⣀⣀⣰⡶⠋⠉⣻⣿⣿⣿⢡⣿⠀⣸⣿⡆
⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⠿⣆⣾⠛⠛⠿⠷⠶⣶⠿⢛⣿⡿⢯⣝⢿⣿⡿⠟⠋⠉⢿⣿⠇⣼⣿⣿⠃
⠀⠀⢸⣿⣿⣿⡇⢿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠋⠳⣿⠴⣤⡴⠞⠀⠀⠀⠀⠀⠀⣾⣿⡄⢿⣿⣿⡄
⠀⠀⢸⣿⣿⣿⣇⢠⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⠓⢦⣼⠶⠿⠷⣤⡞⠂⠀⠀⢀⣾⢿⣿⣿⣎⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢻⡿⠛⠋⠀⠀⢀⣴⣿⡅⢸⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣿⠁⠀⢀⣠⣶⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠉⠉⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⡤⠤⠤⠤⢤⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠞⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸
⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠘⠀⡜⠀⢻⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠒⠲⢤⡞⠀⣠⠏
⠀⡀⢀⡠⠴⠒⠚⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠈⢧⡀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⢊⣀⠀⢀⠤⡈⠀⠈⢀⠀⠀⠀⠛⢦⣤⡴⠃⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡰⠁⠀⡇⡇⠀⠘⣆⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⢧⠁⡷⡷⠀⢸⠀⠀⠘⢄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠦⠤⠋⠀⠹⣄⣀⡜⠀⠀⠑⡌⠢⣄⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠊⠉⠉⠉⠈⠉⠉⠙⢢⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇⠀⠲⠀⠀⢀⡾⠆⠀⡼⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠘⠦⣜⣀⣆⣨⠧⡤⠞⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇⠹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⡤⠤⡞⠉⠳⣶⢶⡖⠛⡉⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⠁⠀⠹⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠛⠛⠉⠀⢹⠀⠈⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣸⠃⠀⠀⡼⠂⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⡴⠯⠚⢀⡴⠁⠀⠀⣰⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡄⠀⠀⠀⠠⡜⠲⠖⠁⠀⠀⡀⠀⣀⡴⢚⠁⢀⠄⠀⣼⠁⠀⠀⢰⠃⠀⢠⠏
⠀⢀⡠⢤⣀⣀⡀⠀⠀⣀⣀⣠⠴⠞⠁⠀⠀⡟⠙⠓⠒⠒⠘⠲⣄⠀⠀⠀⠹⣎⠀⠈⠛⠖⠾⠴⠖⡵⠋⠉⠉⠉⠀⢠⠏
⣰⠋⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣤⠼⠗⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⠧⡜⠀⠀⡆⠀⢹
⣇⣠⡇⢠⠀⠀⢀⠀⢀⣀⣀⣤⠴⠞⢋⡥⠖⠒⠊⠉⠉⠉⠀⠀⠀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚
⠀⠉⠛⠾⢦⣤⡼⠏⠉⠉⠀⠀⠀⠀⡟⢠⠂⠀⡖⠀⠀⣴⠶⠚⠋⠉⠉
⡀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠓⣻⣤⣴⣧⣤⡾⡁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⣀⢀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡠⠀⠄
⠀⠀⠀⢀⠀⠙⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠈⠂⢐⠑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣁⢀⠠⠀⠁
⠀⠀⠀⠀⠠⠈⠐⠒⠹⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣄⠴⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠐⠆⠐⢐⠂
⠀⠀⠀⠀⠀⢀⠊⠀⠠⠄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡠⠂⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣡⡤⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⢠⡀⠀⠀⢌⠀⠘⢠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⠂⠀⣀⠀⠀⣄⠀⠀⠐⠘⠂⠀⠀⠀⠀⠰⠎⠁⠉⢰⠆
⠀⠀⠀⠀⠀⠐⠁⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠄⢀⠀⠀⠀⠈⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⢛⣀⡔⠉⠀⢄⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠘
⠀⠀⠀⠀⠀⠐⠖⠀⠲⠆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠘⠂⠤⠀⠤⢀⡀⡀⠠⠄⠀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠘
⠀⠀⠀⠀⡐⠀⠀⠀⢁⠐⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢡⠈⠠
⠀⠀⠀⠀⠀⠎⠀⠠⢇⠀⠠⠔
⠀⠀⠢⠄⠂⠀⠀⠀⠘⣠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣤⣄⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣯⣍⠓⠰⢋⡴⠿⠿⣿⠶⠃⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣍⣁⣉⡉⠃⠀⣩⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠈⠙⠛⠛⠛⠁⠀⠈⠉⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⢀⣤⣤⣤⣶⣄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣯⣿⣿⣯⣿⡿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠹⠿⠛⠟⠛⠻⣿⣽⡀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠨⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⢴⣶⠀⠀⠀⣶⡤⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣆⠀⠀⠀⠶⠂⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡿⠿⠛⢷⣄⡀⠀⠀⢀⡾⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠈⠉⠋⠛⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⠀⠀⠀⢴⡀⠀⠀⢠⣤⣀⣠⣤⠀⠀⢠⠄⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⢦⣄⡀⠚⠁⠀⠀⠉⠉⣿⣏⠉⠀⠀⠀⠀⠀⣴⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢰⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞
⠀⠀⠀⠀⠈⢟⡀⣀⣀⣀⣤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢳⡀⠀⠀⣀⢠⠶⠋⠁⠻⣧⣄⡠⠤⠐⠃⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡉⠓⠀⠠⢄⡄⣠⠤⠌⠓⠐⠂⠠⢠⡀⠀⠁⡀⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⢹
⠀⠀⠀⠀⠀⠐⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠄⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⢀⠠⠄⠀⠀⣤⢤⡿⢘⡇⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣤⣤⣾⣧⠀⣿⣿⢶⣶⠶⢿⠀⠀⠐⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠈⢉⣽⣿⡟⠀⢻⣿⣦⣀⣀⣸⡆⠀⠄
⠀⡀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠙⠿⠿⠟⠋