Fruits basket Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠘⠻⣶⣄⠀⠀⠀⠀⢠⡎⣿⣤⣀⣿⣀⣹⣯⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⣷⢿⠛⠦⠄⡀⠼⢿⣿⣯⣽⣿⣿⣿⣿⣿⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⢻⡽⠿⣷⣿⣁⠀⠈⡃⣀⠠⣌⢻⣿⣿⣿⣿⣿⣏⣰⣦⣵⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⣶⠻⠦⢠⣼⣿⣿⣶⣿⣿⣿⣦⣼⣾⣿⣿⣿⣿⣿⡿⠉⠉⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣷⡀⡀⢠⠀⣿⣿⣿⣿⣿⡟⣿⣿⡿⠻⣛⣿⢿⣿⣟⢛⠶⣤⣤⣄⣤⡇
⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣿⣿⣷⣶⣿⣷⣨⣿⠯⣶⣷⣭⠛⢿⠛⢧
⠀⠀⠀⠀⠀⠀⠹⣧⣀⣸⡟⣿⡏⠀⢈⡇⣹⠍⠁⠀⢸⠈⣿⡋⠉⠉⠀⡇⢸⠁⠀⠀⠈⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢻⣯⢁⣿⡾⣿⣿⠋⢹⡿⠝⠀⠀⢨⣴⠏⡅⠀⠀⡤⡶⢌⡖⢀⠒⠟⡙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣇⣀⡸⢿⡷⠾⡇⠀⢺⣶⣶⡀⠀⠀⣦⣾⢭⠀⠀⢹⡾⠧⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣢⣊⣿⢿⡁⣀⠀⢻⣦⠾⠀⠀⢿⣦⣸⠀⠀⠩⠿⠷⡧⢀⠰⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣷⡀⢵⣿⠷⣉⡀⠘⠿⠷⢬⡀⢀⣼⡾⠧⢄⡀⡷⠟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣿⣿⣠⠿⣿⢾⣝⠀⢸⣷⠆⠃⢀⠰⡾⠛⠃⡘⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣤⣿⣿⣿⢇⣀⣸⣾⠷⠠⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠟⠿⠛⠙⠓⠒⠚⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠀⠀⠀⠀⠀⣀⢇⡜⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠐⠲⢾⠋⠈⠁⠒⣄⠀⢀⢎⠴⠋⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠤⠲⡁⠭⡁⠀⢹⠍⣦⡴⠧⢤⠀⢄⡀⣀⣀⣀⣀⠀⢸⢀⢎⢀⠇⠀⠀⠀⢱
⠀⠀⠀⠀⢠⠊⠉⠊⢉⠄⠀⣈⣀⣈⣶⢫⡭⠤⢽⡜⠉⠠⣄⢠⡂⠈⠉⠻⡅⢂⠎⠀⠀⢀⠀⢸
⠀⠀⢀⡄⢼⠋⠉⣝⡚⢢⠋⠀⠀⠀⠒⠺⠁⠀⠀⠈⢦⠀⠁⠀⠀⠀⠀⢀⠟⡁⠀⠀⢀⠆⠀⡌
⠀⠀⠘⢦⠈⠀⡂⠀⠈⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⢔⠪⠑⠈⠀⠀⣠⣃⣀⡰⡷⠤⡀
⠀⠀⠀⠘⠄⣀⣼⣒⣊⣩⠙⠋⠉⢛⠖⠒⠒⢒⠶⠖⠚⠒⡾⠓⢒⡳⠒⠋⢉⣟⣉⣉⣌⣀⡤⣥⠔⠃
⠀⠀⠀⠀⠀⠀⢧⡀⠻⡉⡩⠛⡉⣩⠻⡉⡒⠣⡀⢀⠟⠋⠉⠉⠉⠟⢍⠉⢉⠍⠁⡀⠀⡐⠱⡇
⠀⠀⠀⠀⠀⠀⠈⢧⣀⢞⠀⠠⡎⠀⡠⡋⠀⠀⡈⠋⠀⠀⠀⡤⠀⠀⠀⢁⠎⠀⠀⢈⠎⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡠⠋⠀⣨⠟⠀⠀⡦⠊⠑⠄⠀⠀⠐⠢⡀⠀⠀⠃⠀⢀⡠⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠈⢂⠤⠪⡀⠀⠀⠠⡃⠀⠀⠀⡠⠋⢀⠀⡠⠊⠁⡰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠌⣀⣄⡄⠛⢅⠀⢈⣠⠒⠋⠀⣀⣤⣋⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢌⣉⣉⡉⠉⠉⠉⠉⠉⣉⣉⣉⠥⠚
⢀⣤⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠂⠀⠒⠒⠂⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠁⣀⠠⠤⠄⠒⠒⠒⠒⠂⠤⠤⢀⡀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡔⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠱⡀
⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠱⡀
⠀⠀⠀⠀⠀⠰⠀⡜⠀⠀⠀⠀⡏⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢃
⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠣⣀⣀⡇⠀⠀⠀⣁⠀⠀⢠⠦⡀⠀⠀⠀⢀⠀⠀⡠⠔⡆⠀⠀⠀⠇⢸
⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠶⣈⢹⠦⢀⠔⠁⠉⠙⢆⠸⡀⠘⡄⡠⢄⡋⢆⢸⣄⠜⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⢀⠔⢳⠀⠀⠀⡿⠀⠀⠂⠀⠙⡄⢑⣦⣼⡔⠁⠑⠺⠾⣉⣐⠆⡠⡀⠀⢘⠀⡇
⠀⠀⠀⠀⠈⠀⢀⠐⠯⡑⣌⠀⢸⡠⠊⠉⠀⠀⠀⠀⢠⠞⠉⠀⠀⠉⠉⡲⣤⠐⠒⠂⢤⣎⣮⠤⢤⢼⠀⡇
⠀⠀⠀⠀⠀⠇⢸⠀⠀⢈⣺⡶⢻⠁⠀⠀⠀⢀⣀⣠⣃⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠒⠲⡁⡌⢰
⠀⠀⠀⠀⠀⠰⡀⢆⠖⠁⠀⠀⠈⡄⠀⡠⠚⠉⠀⠀⡄⠈⠑⢄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠀⠀⠹⠃⡆
⠀⠀⠀⠀⢀⡠⠵⢼⡤⠤⠤⠤⢤⠼⠶⠤⠤⡤⠤⠤⠼⠤⡤⠤⠧⠤⠤⢤⠼⠤⠤⢤⡬⠤⠤⣤⠤⠾⡀
⠀⠀⠀⠀⠘⢦⠤⠤⠬⠷⠤⠤⠤⠭⠦⠤⠤⠬⠷⠤⠤⠤⠬⠵⠤⠤⠤⠤⠵⠤⠤⠤⠽⠦⠤⠬⠦⠤⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠠⡀⢀⠄⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠈⠒⠊⠀⠀⠀⠐⠦⠔⠀⠀⠀⢠⣀⡤⠀⠀⠀⠐⠄⠔⠀⠀⠀⠀⠢⠤⠂⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠑⠊⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠐⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠃⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣖⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡯⠟⠋⠁⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⠡⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡃⢰⢣⣾⣤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⣱⢣⡄⣾⡟⣻⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢇⠛⢺⣿⣾⠾⣛⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢤⣱⠈⣿⣫⡟⢙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⠶⢿⣿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⡶⠛⢧⡀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣠⠖⢦⠀⠀⠀⠀⠀⠀⠀⠈⡀⣶⡎⣧⣄⡾⡾⢻⡄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⡰⠁⠀⢸⡀⠀⠀⠀⣀⠀⡀⡚⢛⣏⡙⣯⣿⡽⠿⣊⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠖⠁⢐⡖⠀⠀⠀⠔⠁⠀⠀⠉⠀⠀⢰⡿⣶⣿⠿⠛⠋⠐⢾⣙⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⢀⠀⠈⠀⠐⠢⡀⠐⢴⠞⠀⠀⠀⣠⠞⠿⠛⠏⠀⠀⠈⠀⡠⠿⠿⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣇⣀⠀⡀⠀⠀⢹⡀⠀⠀⠀⢈⣧⠇⠀⠀⡠⠆⡤⠀⠢⡎⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡴⣳⠘⣄⡆⡄⢢⡘⢯⡷⠒⠒⠻⣄⢀⡴⠋⠀⡰⠁⠀⣠⡿⠄⠀⠀⢈⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠒⡯⠎⣹⡄⣿⢹⡀⣿⠀⢠⡖⠀⢸⡞⠀⠀⣰⠁⣠⣾⠋⠀⠀⢀⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢢⠋⣉⡧⢉⡆⡀⣹⠀⠀⠁⠀⠸⠶⠖⠏⠹⢶⣿⠁⢀⢈⣴⠋⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡆⢡⠄⣾⠉⠁⢹⠀⠀⠈⡏⠀⠀⠰⣦⠜⠋⢸⡖⠛⠁⢸⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡇⠈⠀⢸⠀⠀⠸⠀⠀⢠⡇⠀⠀⢰⠀⠀⠀⢸⠁⠀⠀⡎⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢷⠀⠀⢸⠀⠀⠠⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡾⠀⠀⠐⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠤⣀⣘⡆⠀⢸⠀⠀⢸⡇⠀⠀⢸⠀⠀⢀⣇⣀⠤⠾⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠠⠄⡠⠋⠉⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡔⠁⢀⠊⢀⣀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡠⢣⠖⠉⠀⠀⠀⠈⠛⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠲⠦⢄⡀⠀⠀⢀⠎⠀⠀⢀⠔⢁⢔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢁⡷⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⡠⠊⠁⠀⠰⠶⠂⠀⠀⠙⢦⡀⢸⣀⡀⠤⠮⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡤⠴⠧⢼⡇⢠⠖⠠⡀⡏⠈⠑⣄⠤⠖⢤⠀⡅
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⠀⣼⠁⠉⠒⢄⠀⠀⠀⠀⢀⠔⡕⠁⠀⠀⠀⠀⡄⢇⠀⠀⢠⡵⢀⠀⠋⠀⠀⣰⣠⣃
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠱⡄⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢃⡼⠓⠲⡁⠀⢀⣹⣦⡤⠚⠉⠀⠀⢙⠆
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⢀⠜⠉⠉⢁⡜⠁⠘⠂⠰⣴⡒⠁
⠀⢠⠚⠼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢩⣀⣠⠔⠋⢧⡀⣠⣆⢀⡼⠘⡃
⠀⠀⠑⠶⠤⢤⣀⣉⡉⠉⠀⠐⠒⠒⠘⠦⠤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣠⣛⣀⣀⣀⣀⣀⡀⠀⠀⠠⠤⠀⡴⠋⠁⠸⠁⠀⠀⡜⠀⠱⡄⠙⢶⠋
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠉⠉⠁⠒⠐⠀⠤⠤⠀⠠⡤⣤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡤⡤⠤⢴⠁⠀⣠⠚⠤⣤⣚⠀⠀⢀⡇⠀⣨
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠗⢺⠁⠀⠀⡌⠈⠑⡖⠛⢌⡙⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠃⠀⢸⠄⡠⣼⠀⠀⢠⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠘⠤⢴⠃⠀⠀⣸⠃⡶⠋⠈⢶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢄⣠⢴⡃⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢧⠴⠋⣦⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⣠⠇⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠆⡈⠉⠁⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠾⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣷⡶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣲⠄⠀⠀⠈⠉⠛⠀⠄⠀⠀⣄⡀⠀⠀⠀⠀⠀⢼⢣⣴⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢠⣾⡏⠀⠀⠀⠀⠀⠀⣌⠉⠓⢤⣀⢉⠐⠀⠀⠀⠀⠀⠙⢿⣼⣿⣃⣾⣆⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⢠⡄⠀⢸⠁⣻⣿⠇⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⢸⠋⠠⣤⣤⠄⠀⠀⠀⠀⠙⡿⠿⢿⣿⣿⣿⣾⡆⣦⡀⣀
⠀⠀⠀⠀⠀⢀⣠⡄⣿⣜⢿⣿⡨⢿⣦⠙⢫⣜⢿⣀⣀⠀⠀⠀⣀⣼⣧⣀⢀⣀⣸⠀⠚⠉⠁⠀⠀⠀⡀⣀⠀⣀⣴⣾⣿⣿⣯⣹⡛⢂⣮⠹
⠀⠀⠀⢴⣦⣛⣿⣦⣍⢻⣶⣼⣷⣎⢻⢿⣆⢷⠌⡿⠿⢿⠿⠛⠋⠉⠉⠙⢟⠻⣿⣥⡆⠀⠄⠀⠀⠘⠳⣿⣾⣿⣿⣿⣿⢙⣿⢻⣿⢿⠆⡾
⠀⢰⣶⣿⣸⡏⣾⢈⣿⠎⣿⣿⣮⡟⢿⣆⣟⢸⣧⢛⡰⠁⠀⣠⣤⡔⠀⠀⠈⠿⠟⢿⣷⣴⣂⣀⠀⠠⠀⠈⣙⣿⣿⣾⣏⢻⡝⣾⡿⣿⣣⣿⣼⠇⠀⠀⠀⢀⣶
⠠⣾⠻⣆⣿⠪⣿⣮⣿⣶⣼⣿⣿⣷⣏⣽⠛⣿⢇⣮⡅⢰⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⢀⣾⣿⣿⣿⣉⣿⡿⠿⠛⠃⠉⠁⣁⣀⠤⠄⠀⠀⣿⠏
⢠⡿⢇⣾⣿⣿⡙⣾⣟⣿⣏⣿⣯⢻⣿⠙⣧⡛⢰⡆⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢾⠿⠿⠛⠋⠉⠀⠀⣀⣀⣤⠖⠚⠉⣀⡀⠄⠀⣠⡴⠋
⣨⣝⣿⣝⣿⢹⣿⣮⢱⡟⣿⣿⣿⢧⣿⣅⢹⠓⣿⣨⣿⣾⣿⣿⣿⣁⣤⣄⣀⣾⣿⠿⠿⠛⠋⠉⠀⠀⠀⢀⡀⢀⣀⡀⢀⣀⣀⠔⠊⢉⣁⣠⣴⣶⣿⣯⣤
⠨⣿⣷⣎⣛⢲⣎⣷⣿⣀⠛⠿⣿⠾⡿⠛⢁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣤⣀⣡⣠⣤⣴⣶⣶⣶⣦⣭⣈⣉⣡⣤⣶⣿⣿⣿⣿⢿⣿⣿⣩⣿⠃
⠀⢛⣯⣽⣿⢋⠀⠻⣿⣿⣷⣄⣀⠀⠀⣿⣿⣿⣿⣯⣽⣭⣵⣾⣶⣯⣿⣿⣭⣽⣫⣝⢻⣻⣿⣿⣿⣛⣟⣛⣿⣿⣿⡿⢿⣿⣿⡿⢿⣟⣛⣿⣻⣿⣿⡍⠋
⠀⠀⠉⠈⠙⠀⠀⠀⠉⠻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣷⣶⣾⠷⣍⣩⠭⣭⠭⠍⡙⢻⣿⣿⣟⣿⣻⣏⣉⣉⣭⣛⣻⢷⣿⣷⣾⣿⣿⣽⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢶⠢⣭⣿⡮⢭⣦⣀⣭⡉⣚⣛⣿⣿⣿⣿⣿⣬⠛⠲⣒⣶⣿⣿⣿⣿⣿⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣶⣶⣷⣶⣭⣾⣿⣿⣿⣿⣿⣷⣫⣿⣿⣶⣿⣷⡾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠙⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡖⠚⡉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠳⡌⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢞⣆
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⢦⠈⠳⡄⠀⠀⠀⣠⠴⠒⠒⠒⣒⣻⣦⡤⠴⠒⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢃⠣⠹⡄⠀⢰⠃⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⠤⢄⡠⠖⠒⢤⡠⠤⣄
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⠘⡆⢠⠹⡄⢸⠀⠀⣀⣤⠤⠤⢤⣀⣀⣠⠒⠉⣱⠖⠚⢣⣔⣓⠒⠾⠀⠀⢀⡤⠓⠀⡜⠋⠒⢦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢂⠹⡄⠣⠈⣿⠖⠋⠉⠀⠲⣄⠀⠀⠀⠉⠛⢅⣹⣃⣀⡈⢛⠹⣠⠂⠉⠐⠊⠀⠤⢄⡘⠉⠓⠎⠉⠲⡄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠆⠀⠀⠀⠠⠙⢄⣸⠁⠀⠀⠀⠀⠒⠛⠘⢯⡁⠀⢠⠞⠉⠉⠉⠉⣹⡄⠋⠉⠉⠉⠙⠲⣄⠀⣳⣀⣠⠦⠤⢤⡟
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⣆⠀⠀⠀⠐⢌⠻⢤⣀⡄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠘⡆⠁⣈⣽⡀⠀⠀⢹⠉⢲⡀
⠀⠀⠀⠀⢀⣠⣼⣧⠀⠀⠈⢦⡀⠀⠀⠀⠉⠢⢍⡒⠤⣀⡀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡎⠀⠀⠀⢲⠀⠋⢀⣠⠇
⠀⠀⠀⢰⡋⠀⢰⠉⠉⠛⢖⠒⠷⠤⣤⠤⣤⣄⣀⣈⣓⣀⣉⡓⣦⡀⠅⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⢤⣤⠾⠟⢧⣀⣀⣠⠎⠀⠀⢀⡇
⠀⠀⠀⠀⠉⠛⢿⠶⣦⠤⣬⣦⣄⣀⣀⣱⣀⣀⡀⠉⠙⢍⠉⠉⠙⠯⡉⠉⠉⠉⠛⢏⠉⠉⠉⠉⠁⢦⡀⠀⠀⠈⣙⣦⣀⣀⣤⣽⣦⠤⠴⠊
⠀⠀⠀⠀⠀⠀⢸⡤⠉⢆⠀⠀⠀⠀⠙⢏⠉⠉⠉⢉⠛⡏⠉⠙⠛⠛⢛⠟⠇⠀⠀⠀⡵⢖⠚⠛⡿⣛⠛⠉⠹⢯⠉⠉⢨⠇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⢦⡠⠐⠁⠀⠀⢢⣀⠔⠁⠀⠀⢀⠀⠀⡀⠀⠀⠈⢆⡤⠊⠀⠈⠳⡞⠀⠈⠢⣔⠀⠀⠑⣴⠁⠀⠘⡞
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠣⡀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠱⡊⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣨⠢⡀⠀⡸⠓⠀⢀⡼⠣⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣠⠓⠄⠀⠀⠀⠀⡔⠉⠢⣤⠄⠀⠀⠙⢎⠀⠀⠀⠙⢄⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡈⠷⡈⠁⠀⠀⠀⢢⡐⠊⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠈⠳⣄⠀⠀⣀⠟⠄⠀⠀⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠢⣀⡠⠔⠊⠉⠢⡀⠀⠀⠀⠀⡘⠂⠀⠀⢀⣀⠔⠉⠳⢎⡁⠀⢀⣸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⠘⠳⣄⠀⠀⠀⠼⠓⠤⣐⠋⠀⠀⢀⡹⠷⢄⡀⣀⠔⢃⣠⣵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠙⠛⠶⠿⠷⠤⣤⣤⣶⡭⠵⠶⠶⠭⠤⠶⠶⠟⠛⠛⢉⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⣿⣬⡵⠶⠦⠴⠬⣖⣕⣝⢒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣣⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢔⡜⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣳⠝⠉⠀⠀⠀⢀⣖⡦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣌⡑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⡟⠁⣤⡤⣢⣤⠤⠼⣴⡷⠒⠛⠶⠲⠶⠶⣤⣀⡀⠀⠀⠀⠈⢣⢨⢣⡀
⠀⠀⠀⠀⠀⠀⢀⠎⢾⠏⠀⠀⠘⣷⣦⡉⢙⠎⠀⠀⢀⠀⠀⠀⠀⠀⠈⠪⠭⡛⢦⡀⠀⠀⠹⣄⠱⡀
⠀⠀⠀⠀⠀⢀⢏⣴⠃⠀⠀⠀⣀⣀⣨⣷⠃⠀⠀⠀⢻⠅⣉⠝⠂⠄⠀⣤⣀⣸⠒⠛⠐⠢⡀⠸⣄⢰⡀
⠀⠀⠀⠀⠀⡼⢝⡏⠀⢀⠔⣭⠀⠀⠀⠀⠑⢦⡀⢀⣾⠟⠀⡄⢠⡼⠶⠧⠛⠰⡏⢽⡟⠖⠸⠄⢹⡄⢧
⠀⠀⠀⠀⢰⢣⡾⠀⢀⠊⠀⠀⠀⠀⡀⠀⢀⣠⣷⣾⣥⣤⣀⣰⠋⠀⠀⠀⠀⢀⡽⢖⠻⡿⣤⣖⡀⣧⡌⡄
⠀⠀⠀⠀⢸⢚⡇⠀⢀⣀⣠⣴⠚⠉⢙⣷⣿⡉⣯⠟⠁⠀⠀⣻⣀⣠⣤⠀⠰⠁⠀⠘⠁⠀⠉⠁⠙⣾⡐⡃
⠀⠀⠀⠀⣞⣚⣇⣴⡯⠋⠉⠁⠘⣰⢋⣾⣭⣽⠃⠀⣤⣶⣮⠋⠉⢣⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⢿⣛⣻
⠀⠀⠀⣅⠈⠉⠉⠉⠑⠒⠒⠒⠓⠓⠞⠿⠷⠧⠤⠼⠿⠿⠧⠤⠤⠼⠄⠀⠀⠲⠀⠀⠒⠒⠒⠂⠉⠉⠉⠁⣩
⠀⠀⠀⠀⡏⠛⠒⠒⡶⠶⠶⠦⠤⢤⡤⢤⢤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⡤⢤⠤⠤⠶⠶⠶⢶⠒⠚⠛⢹
⠀⠀⠀⠀⢹⠒⠶⣀⡧⠤⢤⣤⣤⣤⡅⢠⣀⣀⣀⣀⣀⡇⢠⣀⣀⣀⣀⣀⣄⣸⣤⣤⣤⠤⠤⢾⢰⠖⠒⡏
⠀⠀⠀⠀⢈⠀⠉⠁⠁⠒⠒⠒⠒⠐⠃⠿⠤⠤⠤⠤⠤⠯⠭⠤⠤⠤⠄⠄⠓⠘⠒⠂⠐⠒⠂⠉⠉⠁⢁⡅
⠀⠀⠀⠀⢸⢉⣚⡏⣷⠆⠀⠤⠒⢒⡆⣠⣀⣤⣤⠀⠠⣤⣤⢀⣤⣤⣄⡀⡴⢶⠶⠤⠶⠖⠒⡚⢻⣋⠉⡇
⠀⠀⠀⠀⢠⣄⣀⡅⢈⡈⠉⠀⠉⠁⡇⠙⠒⠒⠒⠒⠒⡇⠘⠒⠒⠒⠒⠂⡇⢸⠉⠉⠈⠉⠉⡇⢸⣀⣠⡄
⠀⠀⠀⠀⠀⡧⠬⠇⣽⢙⣋⣛⠛⠛⡇⢸⠖⠶⠶⠶⠶⡗⠺⠶⠶⠖⠒⠒⡧⢼⠛⣛⣛⣉⢉⠷⠾⠤⢴
⠀⠀⠀⠀⠀⠘⠤⠤⠤⣄⣀⣀⣀⣈⡉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⢉⣁⣀⣀⣀⣀⣤⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠹⠔⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠗⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡤⡀⠀⠀⠀⡾⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢋⡑⠊⢢⡀⠈⠀⠠⠀⠈⢢
⠀⠀⢀⡀⢠⠒⠉⠤⠰⠀⠹⠣⣙⢄⠀⣰⠃⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠉⠉⠀⠈⠐⠢⢄⣀⠀⠀⣧⠀⠀⢰⠢⣤⠄⡀
⠀⢰⢇⡄⠈⠓⠤⠤⠤⠒⠇⠀⠈⠆⠷⠁⠀⠀⠀⠀⠀⠀⠀⠉⠖⠙⣆⠼⠇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⢀⣸⠛⠀⠀⠋⡃
⠀⡏⠀⠘⣄⠀⠀⠀⢀⡠⣇⠤⣠⠼⠜⠒⠦⡀⠀⠀⣀⣀⣀⢠⡄⡘⢁⣠⣔⡁⠀⠀⠀⠀⠀⠀⣠⠤⠤⣀⣠⠧⠤⢤⡠⡔⠀⠀⡄⠀⡩
⢀⡇⠀⠀⠈⠳⣄⣰⠁⠀⠀⠀⢘⠀⠀⠀⠀⡇⡰⠋⠁⠀⠈⠉⠣⠿⠋⠁⠈⠉⠳⡄⠀⠀⣀⣞⠀⡠⠔⢨⠃⠀⠀⠀⣱⠈⣢⠤⠤⠴⢥
⠈⡇⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⡼⣄⣀⣀⡴⣷⠇⠤⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⠋⠁⠀⠙⠀⠀⠀⠣⠎⠀⠀⠈⢻⠅⠂⠀⠙⡈
⠀⢹⡀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠼⠄⡠⠊⠙⠦⣠⠖⠺⡄⠀⣠⠤⢼⠀⠀⠀⠫⠏
⠀⠀⠹⣄⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡇⠀⠀⠀⡇⠀⠀⠈⢛⠀⠀⠀⠃
⠀⢠⠖⠚⠓⠚⠒⠒⠒⠛⠓⠒⠒⠒⠒⠛⠓⠀⠋⠉⠉⠉⠉⠉⠒⠒⠒⠒⠒⠚⠛⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠓⢦
⠀⠸⣦⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⡤⠋
⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠘⣶⠲⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠃
⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡏





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⣒⣭⣿⣵⣽⣵⣤⣥⣖⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣉⣴⣷⡾⠿⠛⠛⠛⠉⠉⠙⠙⠛⠻⣟⣴⣱⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢑⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣬⡜⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡇⠀⠀⠀⠀⠀⢈⡏⣡⣄⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⢹⡇⠀⠀⣠⣾⣗⣟⠿⠾⠛⢻⣤⡄⠀⣡⣤⠐⢿⣿⣶⣶⣶⣤⡄⡰⠂⠀⠐⣿⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣤⣤⣭⣉⣉⠀⠄⣀⡀⣾⡇⠀⠀⠉⠁⠀⠀⠻⢹⣯⣉⣛⣿⣿⡔⣤⢸⡏⣋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢉⣿⣿⣿⣿⠋⠁⣀⡀⠈⠻⢞⣥⣴⣶⣦⣤⣄⣼⣆⣾⡟⡿⣋⣉⠝⠳⣄⣶⡌⠻⠧⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣿⣿⣿⣿⠀⠀⣿⠀⠈⠛⠁⠰⣴⣿⠃⠀⠈⠁⣻⡟⠛⠛⠋⠙⠛⠛⠻⣄⠀⠀⠀⠀⠀⣹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⠿⢇⣤⣿⣦⣄⢀⡀⢀⣿⣌⠣⣀⣀⣸⣿⡟⣡⣤⣈⡓⠸⣿⣇⣿⣷⠶⣶⣾⠾⠟⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣁⡙⠓⠲⠾⠥⠴⢭⣾⣋⣽⣉⣼⣋⣵⣋⣽⣛⣉⣻⣿⣿⣛⣛⣶⣈⢫⣿⣥⣶⡾⡷⠖⠊⠉⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠁⠂⠂⠠⢤⠤⠀⠄⠀⣨⣍⢉⣉⡙⣋⣛⣛⣛⣿⣽⣻⡿⣿⣿⣟⠙⠷⣾⣉⠉⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠴⠒⠚⠿⣿⣿⡈⠀⢰⣾⣋⡑⡂⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣙⡛⠒⠂⠦⠤⠀⢤⣤⡀⠀⣈⡁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣐⠩⠟⢻⣿⣿⢿⣭⣭⣷⣦⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠛⠘⣿⣅⣀⣠⣶⣦⣤⣤⣤⣤⣄⣀⣉⣁⣀⣉⣁⣀⣀⣤⣤⣴⣖⣘⣉⣽⡌⢿⣝⣿⢿⣤⠦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⠿⢨⣿⣯⡛⢘⣛⣿⣦⣤⣤⣤⣾⠿⠿⠸⠿⢿⣭⣍⣉⣤⣼⡛⠿⠸⢛⣿⣧⢘⣿⡶⢖⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣶⡆⣾⣿⠿⠨⠿⢿⣦⣁⣨⣽⣿⣿⣷⣹⣾⣿⣿⣍⣉⣉⣽⠿⠏⠹⢿⣷⡼⣤⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⡤⢾⣿⡿⠇⠿⠿⣏⣉⣉⣉⣹⣷⣶⣶⣶⣿⡛⠛⠛⢛⡿⠷⠆⠶⢾⣿⢥⣤⣿⣏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣭⣩⣽⣷⠶⣶⡾⣟⡛⠙⢛⣻⣧⣬⣤⣤⣿⡻⠿⠿⢟⣷⣶⣴⣶⣿⣛⣊⣽⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠶⢲⣶⣿⣟⣋⣛⣻⣿⣭⣭⣭⣽⡿⠟⢻⣿⡷⢶⠴⠶⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⢧⣀⣀⣀⡤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠇⠀⠀⠳⣭⠤⠤⠤⠤⣀⡉⠳⣄⢀⠀⣖⠢⢄⡀⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡥⠞⢤⡖⠊⠙⠳⢄⡀⠀⡗⠦⣁⠀⠈⢿⠑⣼⡤⠦⣍⡇⠂⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠊⠀⠀⢸⢈⢀⢠⣄⣀⡽⠖⠓⠲⠬⣝⠲⣼⣼⢫⢀⡐⢀⡉⠢⣄⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡠⠤⡃⠀⠀⠀⢸⠈⠊⠈⢇⠈⠙⠲⣤⡁⢀⡜⢉⡺⡏⠀⢣⡐⠂⠀⢠⡈⠑⣌⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⡄⠚⠒⠢⣄⣸⣀⠀⠀⠈⣆⠀⠀⠠⡙⢧⣀⠰⠁⣿⠐⠀⠱⣄⠘⢄⠈⠶⡀⠱⣄⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢀⡀⠀⣖⠚⠫⢤⣀⠀⠸⡀⠀⠀⡈⢀⠻⣄⡌⠻⡌⢄⠢⠙⠷⣄⠑⣀⠜⠂⠈⠿⣌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣮⠬⡓⠺⠦⠈⠂⠀⣩⠓⠓⠤⣄⣌⢂⠑⠘⣌⠮⢱⡀⣀⠑⢈⠪⡳⢌⠀⠀⠃⠀⠹⣦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠉⣹⠤⢤⡼⡒⢢⣀⣀⠀⠀⠀⡎⢱⠈⣏⡭⡉⠚⠺⢦⡛⢵⡏⢳⢚⡢⡈⠂⠱⣄⡄⠈⢄⠘⢆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣉⣷⠒⡇⠃⢀⠷⠒⢎⠰⣌⣆⠤⠒⢲⠘⢀⠏⣸⠖⡆⠻⣍⠳⡌⡇⣸⣼⠋⠩⠑⢦⠈⠳⣤⠈⢢⠘⢆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠣⣀⡞⠉⢻⠀⠰⢌⣏⡉⢳⠀⠊⠉⠉⠺⠴⣥⠚⢄⡔⢽⠗⠚⠉⠁⠰⢈⠁⠀⠀⢣⡑⢝⢧⠁⠴⠙⣾
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢰⠉⠒⠚⠶⠤⠬⢷⣖⣛⣶⣵⠚⠀⠦⠊⠀⠀⠀⠈⠇⢸⠀⠈⠀⠀⠀⠀⠀⠈⢰⣀⣀⣸⡬⠦⠾⠷⠖⠛⠋
⠀⠀⠀⠀⢀⠎⠈⢉⡜⠀⠀⠀⢨⠀⠀⠘⠀⠀⠀⢰⠀⠀⠀⢨⠉⠉⠉⠉⢙⠋⠑⠒⠒⠞⠓⠒⠙⡟⠉⠉⠉⠉⠏⠀⠀⠀⠁
⠀⠀⠀⠀⡜⠀⢊⠎⠀⠀⠀⠀⠘⢤⣀⣀⠀⠀⠀⢸⠀⠀⣠⠼⢖⠋⡹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⡰⠋⠈⠁⡟⢟⢦⠀⠀⠀⠀⢸⠀⠩⣉⠝⠉⣚⠶⠋⠀⢀⠈⢹⠥⠤⣬⠤⣤⣤⣤⣤⣤⣤⡤⠧⠤⠤⠤⠤⡦⠤⠒⠒⠛⠚⡹⠛⠁⠀⡜
⠀⠞⠀⠀⠀⠀⡇⠘⣆⠳⢄⣀⠀⢘⣇⣤⠽⠖⠊⠁⠀⢀⠴⠃⢀⠇⢀⣔⣁⢢⠀⠀⠀⢀⠔⠁⠐⠄⠀⠀⠀⠔⠀⠈⠢⡀⠀⡔⠁⠀⠈⢢⡇
⣼⠀⢀⠀⠀⠰⡇⠀⠈⠳⢄⣈⠉⠉⠀⠀⠀⠀⣀⡤⢚⣁⡤⠔⠚⠉⢯⣀⠎⠀⠱⡀⡠⠃⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⢈⢎⠀⠀⠀⢀⢺
⡇⠀⠸⠀⠀⠀⢏⠢⡀⠀⠀⠈⠉⠒⠒⠒⠛⠛⠛⠉⠉⠀⠀⢀⡀⠀⢀⡞⠀⠀⢠⠚⢄⠀⠀⠀⠀⠀⡰⠙⢄⠀⠀⠀⢠⠊⠀⠑⡀⢠⠃⡎
⣇⠀⠀⢇⠀⠀⠈⠳⢌⠉⠒⠠⠤⠀⣀⣀⣀⣠⡀⠤⠤⠒⠈⠁⢀⡤⢎⠀⢀⠔⠁⠀⠈⢢⠀⠀⢀⠜⠀⠀⠀⠢⡀⢠⠃⠀⠀⠀⢈⠧⣸⠁
⠘⣆⠀⠈⠢⡀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠶⠶⠤⠤⠤⢄⣠⡴⠚⠉⠀⠀⢱⡎⠀⠀⠀⠀⠀⠱⣠⠊⠀⠀⠀⠀⠀⡸⠅⠀⠀⢀⣠⡥⠔⠃
⠀⠈⠣⣀⠀⠀⠑⠢⠄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢎⣉⡽⠒⠲⠤⠴⠥⠬⠦⠤⠤⠤⠤⠴⠭⠦⠤⠤⠤⠤⠔⠓⠚⠋⠉⠁
⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣀⡤⠚
⣠⣤⣤⣤⣤⣠⣠⣭⣉⣳⣶⣶⣶⣶⣶⣶⣶⣋⣉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣄⣤⣠⣄⣤⣤⣤
⣿⣿⣏⣉⣩⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣀⠀⠘⠣⡀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣠⠀⠹⡄⠀⠇⡀⠀⢠⢚⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⡀⠓⠐⠀⠐⠃⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠠⠜⠃⣤⠄⠘⠁⠀⠈⣐⣦⣀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡘⠣⠀⢀⣁⠀⠄⠀⠀⠘⠁⠠⣜⣆⠀⠀⢀⠀⢀⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣈⠒⠄⡙⠛⠀⠆⠀⠀⠀⡀⠀⡼⠛⠐⢦⠊⢠⡼⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡎⡅⠀⠈⠉⠒⠲⠤⠤⠤⢁⣈⣁⣀⣈⠩⠥⢴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣽⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠒⡀⠀⠀⣀⠺⣾⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠿⡀
⠀⠀⠀⠀⠀⠁⠭⢶⣦⣈⡷⠀⠘⠵⠶⠿⠛⠉⠙⢦⡀⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠈⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⢀⣸⣿⠷⠖⠒⠒⠒⠛⠋⠑⠦⠤⠴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠘⠊⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡴⠒⠋⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣠⠞⠁⣤⡀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⠞⢁⠜⠁⠀⡇⠀⠀⠀⠀⣠⠤⣀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢹⣸⣀⣀⠤⢄⣀⣰⠃⠀⡜⡰⠁⠀⠀⠀⠀⠀⠀⠀⢹⡴⠋⣠⠋⠀⠀⢀⠇⡰⠋⠁⢺⡀⠀⢸⣶⡟⠒⢤⡀
⠀⠀⠀⠀⣠⠴⢚⠿⡟⠒⠦⡀⠀⠙⢦⣰⢳⠃⣀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡜⠁⠀⠀⠀⡾⠒⠓⣤⠤⢯⡏⠉⢹⡄⠳⣄⠀⢱
⠀⠀⢀⡞⠁⢠⠏⠀⡇⠀⠀⣹⠒⠉⢉⣹⣼⡭⠉⠀⠑⢦⠀⠀⣠⠎⢠⠎⠀⠀⠀⠀⡜⢣⡤⠼⡅⠀⢈⡧⠤⢾⡁⠀⠀⠈⠉
⠀⠀⡾⠀⠀⡼⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢧⡴⠁⡰⠃⠀⠀⠀⠀⣼⣥⣾⡅⠀⣸⠖⠻⣇⠀⢀⠇
⠀⠀⡇⠀⠀⡇⠀⠀⠀⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡜⠁⠀⠀⠀⠀⣼⠋⠀⠈⣿⠋⢻⡀⢀⣏⠉⠁
⠀⡔⠧⣤⣀⣳⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⢀⡞⠀⢣⣤⣜⠹⠶⠒⠋⢉⣸⠃
⠀⠙⣦⣀⣀⠀⠉⠉⠉⠓⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠚⠋⠉⠉⠉⠀⣀⣀⡠⠤⠒⠊⢹⡇
⠀⠀⢸⡄⠈⠉⠉⠒⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠠⠶⠶⠶⠒⠒⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢳⠀⠀⠀⢦⠀⠀⠀⢀⠀⣠⠖⠀⡀⠀⠀⣀⢤⡀⠀⠀⡠⢦⡀⠀⠀⡰⢧⡀⠀⣠⠞⠀⠀⣰⠃
⠀⠀⠀⠈⢧⠀⠀⠈⢧⢀⡤⠞⢫⠀⠀⠀⢘⣤⠞⠁⠀⢱⣤⠞⠁⠀⠳⣠⠞⠁⠀⢳⣴⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠈⢧⠀⠀⠘⢧⠀⠀⠀⢣⣠⠔⠋⠹⡄⢀⡴⠊⠙⣄⠀⣠⠞⠙⣄⢀⡴⠋⠈⠃⠀⣠⠋
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⣣⡤⠖⠋⠳⡄⠀⣠⠜⢯⠀⠀⠀⡨⢿⡁⠀⢀⡼⠻⣄⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠑⠀⠀⠀⠼⢯⡁⠀⠀⢳⣴⠋⠀⠀⠙⠶⠋⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⣹⡿⢟⠛⣶⣄⠀⠀⠀⠀⣠⡶⢦⣄⠀⠀⠀⠀⢀⣠⣴⢶⡄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⣿⠒⢳⡇⡟⢷⡀⢀⡾⠁⡏⠁⠙⣧⠀⣠⠶⠋⢡⠊⠘⣧⠀⣀⡴⠞⠛⢫⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣇⣤⣄⣀⡀⢀⡿⠀⠀⠀⠀⠀⠀⢻⣷⠿⡝⠳⣬⣿⡟⠀⠀⡇⠀⠀⠈⣿⠃⠀⠀⠎⠀⠀⢸⡿⠋⠀⠀⠀⡆⠘⣇
⠀⠀⠀⠀⢠⡴⠞⣿⡟⠠⣼⡍⢟⠿⣧⡀⠀⢠⡶⣦⣄⣠⡏⠀⢁⠀⠀⠹⣇⠀⠀⠇⠀⣀⣼⡷⠞⠃⢸⠀⠀⢠⡟⠁⠀⠀⠀⡰⠀⠀⡿⠀⣀⡀
⠀⠀⠀⣰⠏⠀⠀⢹⣿⣍⣁⣉⢾⡀⢸⠻⣆⣾⠉⡀⠈⠙⠷⣤⡘⠀⠀⠀⠹⣇⠀⠂⠈⢉⣿⣧⠀⢀⠃⠀⣰⠏⠀⠀⠀⠀⡰⠁⣠⡾⠟⠛⡯⣷⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠁⠙⢷⣤⡤⠼⣦⣴⠿⠛⠛⠛⣓⠲⠦⣌⡙⢧⡀⠀⠀⠹⣾⠀⠀⢸⣿⣿⣄⠏⢀⡾⠁⠀⠀⠀⢀⢜⣵⠞⠉⠀⠀⢀⠃⠘⣧
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⢻⡾⠋⠀⠰⠶⠋⠀⠀⠀⠁⠪⠙⢦⡻⡄⠀⣀⣽⣦⣄⣸⣿⢿⣿⣄⣾⡁⠀⠀⠀⡰⢫⡾⠁⠀⠀⠀⠀⠰⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢷⣽⡾⠉⠀⠀⢨⣿⡟⢸⡟⠉⠉⠙⢷⡄⠈⣰⠟⠀⠀⠀⠀⠀⢀⠃⠀⠀⣿
⠀⠀⣠⣿⣧⠀⠀⢀⣠⠶⠛⠋⠉⡉⠉⠙⡛⠶⣄⠀⠀⠀⢠⡟⠁⠀⠀⠈⢣⠀⠀⣰⠟⣽⠋⣿⣆⠀⠀⡠⠞⠓⢾⡅⠀⠀⠀⠀⠀⢀⠎⠀⠀⣸⣧⡀
⢠⡾⠋⢳⡿⢧⣠⠟⠁⠀⠘⠲⠚⠋⠀⠀⠈⠢⠘⣧⣠⣤⠾⢷⡀⠀⣀⠠⢠⣷⡾⠓⠶⣏⠀⣿⠀⠉⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠁⠀⢀⣴⣿⣌⠻⣦
⣿⠁⠀⣸⣷⣬⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠋⠀⢀⠠⠽⡞⠁⠀⠀⢹⠀⠀⠀⠈⢶⡟⢄⣀⣿⢦⡤⠤⠒⢻⣄⢀⠔⠋⠀⢀⡴⢟⣴⠏⠙⡵⣹
⢿⡀⠰⡟⠀⠙⢻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡔⠁⠀⠀⠡⣀⠀⢀⣼⣄⠀⣀⠤⣾⢥⠊⠁⠟⢹⠀⠀⠀⠀⢻⠅⠀⣀⣴⣿⠟⢻⢣⠀⠀⢘⣿
⠈⠻⣧⡇⠀⠀⡆⡆⠀⠉⠙⠛⡷⡶⢦⣤⣤⣄⣀⣈⣿⣓⡂⠁⠐⢢⡏⠉⠁⠈⠀⣻⠁⠀⠁⣸⣀⣀⣀⣈⣦⣤⡤⣶⡿⠛⠛⣿⡁⠀⠀⢸⡎⠀⣠⡾⠋
⠀⠀⠈⠛⢶⣤⣇⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⢹⠉⠉⠉⠉⠉⢻⠻⠛⠛⢻⢻⠛⠛⠛⠛⠛⣻⠉⠉⢛⢫⠁⠀⠀⠀⢸⢸⠀⠀⢹⡇⠀⢀⣰⣾⠟⠋
⠀⠀⠀⠀⠈⣿⡙⢿⠶⢦⣤⣀⣻⡀⠀⠀⢸⢸⡀⠀⠀⠀⠀⢸⢀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡏⡀⠀⢸⢸⠀⠀⠀⠀⢸⣸⣀⣠⣾⠷⣾⠏⣽⠇
⠀⠀⠀⠀⠀⠸⣿⠖⣬⡍⢩⡭⠛⣟⠻⢷⣶⣷⣷⣤⣤⣤⣤⣸⣼⣄⣀⣀⣿⣄⣀⣀⣀⣀⣧⣥⣤⣼⡼⠶⣶⣶⡿⠟⣻⠛⢡⡭⠭⣴⣪⡟
⠀⠀⠀⠀⠀⠀⠹⣞⢁⣱⠤⣙⣒⣚⣑⡶⢦⠀⠰⣖⠋⠙⢤⣙⠋⠩⠝⢋⣩⠛⠯⣉⡙⠓⣒⡫⠴⣁⣉⡲⠆⢀⡶⢊⣉⣉⣡⡔⠚⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⢤⡋⠙⣄⠑⠦⢤⡱⠦⠤⢉⣉⣉⣁⣩⠟⠛⢅⣀⠉⠀⠉⢁⡠⠋⠒⢤⠤⣤⡤⠒⠛⠒⠒⣉⠴⠧⠚⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠉⠉⢉⡶⢖⠠⠀⠶⣞⣉⡳⠤⣈⣉⣂⣋⣡⡜⠛⣯⣀⣉⣉⣉⡠⠔⠧⠬⠛⠉⢉⣝⣉⠷⠂⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣝⢯⡉⠙⠲⠖⠛⢒⡤⢤⡄⠰⠶⣉⣙⠶⠤⣤⠬⠭⠤⣴⠚⠯⠭⠶⠶⠶⢆⡶⠮⣅⡀⢤⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣬⣭⠟⢛⣯⢭⣉⣉⣩⣵⣶⡶⠶⠶⠾⠿⠷⠶⢾⣭⣭⣷⣒⣒⣖⠈⠓⠒⠒⠁⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⣥⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢶⣖⣹⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠐⠖⠲⢄⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠐⠀⠈⣀⠈⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠘⠒⠂⠉⠀⠀⠀⠀⠉⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⡚⠀⠀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠩⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⢠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⣰⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡄⠠⠀⠠⠤⠤⠀⠄⠐⠂⠀⠂
⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡄⠀⡆⢀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⠈⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠁⠈
⠀⠀⠀⠀⠀⠨⠁⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⢠⢀⠄⠀⠤⠤⠀⢰⢀⡆⠀⠒⢲⠀⠀⠅
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠐⠀⠘⠀⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠨⠀⢱⠄⠀⠀⠀⢀⠈⠐⠀⡂⠐⠂⠐⠀⠐⠐⠂⠀⡆⢘⠀⡹⠀⡄⠠⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣀⡀⠉⠀⢈⠀⠁⠀⠁⠈⠀⢈⠀⡁⠀⠀⣀⣀⣀⠀⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠈

⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣯⣭⣭⣭⣭⣭⣭⣤⣒⣒⣒⣒⣒⣒⡒⠲⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⣶⣶⣬⣭⣭⣍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⠂⠒⠂⠙⢻⡖⠚⠒⢛⡇⠠⠼⢧⠄⠀⠰⣶⣖⠒⠒⢶⣤⣤⣀⣤⣤⣀⣀⣀⣀⣀⢀⡀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⢾⠿⡿⠶⠦⣤⣿⣦⣤⣄⣷⣀⣀⠀⣿⡄⠀⠀⢩⡍⠉⠁⠉⣧⠀⠐⠊⠹⡛⠛⠃⠘⣃⢻⡇⣸⠰⣇
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⣇⣿⡟⠈⠀⠀⡀⠀⠀⠀⠀⡎⣿⠉⠉⠉⠉⠉⠉⡛⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠒⠒⠿⢿⡇⣿⢴⣽
⣿⡅⠀⠀⠘⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣀⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠇⠀⠀⠰⠸⠃⣀⣠⣴⣏⡛⢳⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢃⣀⠀⠀⠀⠉⣢⠀⠀⠀⠻⣂⠀⠀⠙⠟⠉⠁⠻⡿⠓⠛⠒⢶⣖⠒⠒⠒⢾⢷⣴⣿⣿⣿⣿⣿⣟⣥⡌⣿⣿
⠀⣇⢠⡆⠀⠰⠉⠉⠉⠙⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣄⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢀⣦⠀⠀⢀⣸⣿⣿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢐⣄⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠠⠀⠀⠠⡁⠀⠀⠈⠉⠙⢙⠙⠩⡭⠍⠉⠋⠛⣉⠛⠹⠋⠀⢾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠬⠉⠉⠉⢹⡟⠛⠿⠛⠛⠛⠒⠒⠛⠿⣷⣦⣤⣴⠾⠧⠀⢀⣤⣄⡁⢀⣀⣠⡆⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⡃⡁⠀⢰⠀⠑⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠷⡶⡶⠲⢟⡚⠂⠓⠚⠛⡿⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠸⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣴⣶⡶⠧⠀⠀⢼⣦⣄⣀⣀⣠⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠀⠀⠀⢠⠳⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡏⣀⠀⢁⡁⠈⠀⠀⠀⠀⢸⠨⢹⠹⠀⠒⠀⠀⠀⢘⠿⠛⠛⢹⠇⠌⠁⠚⠛⣿⣷⡶⡾⢷⠧⠤⠤⠷⣤⣴⣤⣤⠶⡿⠃⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠶⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⡀⢸⣄⣁⡀⠀⣠⠇⠈⠀⠃⣠⠈⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡾⠛⠛⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠎⠉⡏⢿⠀⠉⠀⠀⠀⣿⠉⠉⠉⢨⠀⠌⠉⠁⠉⡉⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢿⡟⣿⠃⠀⣸⢻⣠⡿
⠀⠀⠹⢶⣶⣤⣼⠦⠀⢤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢘⠛⠂⠀⠀⡏⠉⠉⠁⡅⠀⠀⠀⠀⣿⣗⣿⢶⣾⠏⠉⢩⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠉⡟⠛⠛⠉⡇⠀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣇⣁⡒⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢇⣸⡁
⠀⠀⢀⣿⢀⣀⣼⣄⣀⣀⣀⣼⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠉⠉⡛⠉⠙⠁⢸⡇⠁⢀⣼⠟⢻⢿⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠶⣶⡶⢾⠖⠓⠒⠂⢾⣤⣤⣠⣤⣥⠤⢤⡀⣤⡀⠀⠀⠀⠀⠁⠠⠀⠀⣾⣥⣶⢿⡗⠀⢸⠸⣿⠃
⠀⠀⠈⢿⣀⣀⢀⣠⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⠤⠄⠀⠀⠀⠉⠙⠉⠉⠀⢤⠀⠀⠈⠙⠛⢿⠿⠛⠃⠀⠀⢂⠙⢃⠀⣹⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⢀⣠⣐⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⠀⠁⠁⠀⠀⠀⠉⠢⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢄⠀⠀⠀⠀⠈⠃⠂⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠠⠈⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⠀⠀⠀⠀⢀⣀⣠⠴⢀⠒⠂⠀⢒⣷⠞⠀⠯⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢴⠠⠂⠚⠁⠈⠀⣁⣀⣀⣀⡸⠟⠉⠁⠀⠀⠇⠀⡐⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠒⠀⠀⠌⠀⢷⠀⢠⠤⣴⡶⠚⠛⠛⠛⠉⠀⠀⢀⠀⠀⠀⠀⡃⠂⠀⠀⠀⠀⠀⢀⢠⠰
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⠴⡀⠂⡀⡜⠀⢐⣟⠈⠉⠀⢸⡟⢨⣁⡀⠀⠀⠀⠈⠀⠐⠁⠀⠤⡆⠀⠀⠀⠀⠀⠀⠀⣰⠎⠆
⠀⠀⠀⠀⠀⢠⠀⣿⠈⠠⡇⠀⠰⠀⠘⠇⠀⠈⢿⠏⠉⠈⠙⠉⠻⡋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⢧⡠⠂⠀⠀⠀⣀⠀⢁⠇
⠀⠀⠀⠀⢄⠞⡇⢂⡄⠀⠣⠀⠀⠀⠀⠈⠢⠀⠈⢄⣀⠀⠀⠀⠀⠈⠑⠢⠤⠀⠀⠀⠀⠀⠀⣼⡀⠀⢀⣁⠀⠀⡠⢀⡎
⠀⠀⠀⠸⣾⣁⡇⠀⢑⠁⢀⠑⠊⠀⡀⠀⠀⠈⠀⠈⠧⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢰⠉⢠⣟⠹⠆⠠⣄⠀⣤⠕⠀⠃
⠀⠀⠀⠀⡇⠐⠋⠢⣨⣀⠀⠣⣀⢀⠘⠢⣀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢈⠀⠀⠤⢠⣏⢔⠶⠢⣻⠀⠐⠓⠀⡊
⠀⠀⠀⠀⠘⠢⡄⠁⠋⠠⠓⠒⣬⢄⠄⣀⡠⠤⢀⠀⠂⣉⠍⠐⢋⡉⣋⠀⢰⣾⠙⢁⢠⡄⠀⠛⠘⠁⠀⠀⡅⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢹⣇⠀⣶⣂⣩⠀⠈⢁⢏⡠⠀⠀⣀⣀⠹⠂⢀⡴⠆⣀⠤⢘⡉⠁⠀⢸⡇⠀⠀⠀⠃⠀⠸⠅⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠓⡄⠀⠈⠲⣷⠀⠀⠀⠉⢱⠀⠀⠁⢹⣧⠀⠀⠀⠸⠆⠀⠀⠸⡇⠀⠀⠀⠆⠀⢨⠂⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢩⠀⠀⠀⢹⡆⠀⠀⠀⢘⠆⠀⠀⠀⢻⡀⠀⠀⠈⡗⠀⠀⢐⡇⠀⠀⠀⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠱⡄⢀⡀⣟⢀⠀⠀⠀⣦⠀⠀⠀⢸⡧⠀⠀⠐⢧⡀⠀⠐⡇⠀⠀⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣵⣀⠀⠘⣦⡀⠀⠀⠲⡀⠀⠀⠀⣿⠀⠂⠀⢰⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠄⠙⢟⠀⠀⠀⠱⠄⠀⠀⠽⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⠄⠀⢀⣀⣲⣿⣦⣀
⠀⠀⠀⠀⠀⣠⠤⠤⢀⣀⡄⡀⣠⡏⠀⠤⠀⠀⡤⠀⠙⣁⠀⢩⠁⠙⣷⣄⣀⣀⣤⠤⠶⠒⡒⠒⠒⠲⣦⣄
⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⣉⣻⣾⣽⣳⣶⣴⡞⠋⠠⢀⡴⠖⠲⢦⣤⡿⠛⢋⣡⡴⠖⣛⣭⠶⠂⣀⣼⣿⣿⡆
⠀⠀⠀⠀⢻⡀⠠⠴⠾⠛⠛⠛⠛⣛⣿⣿⣿⣧⠀⠀⡟⠀⣀⡴⠚⣁⣴⠞⠋⢁⡴⠞⢋⣠⠶⣛⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠠⠭⠟⠒⠒⣻⣿⣧⣄⠀⣿⡿⠋⣠⠾⠋⠁⡠⠞⠉⠀⢐⣩⣴⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢰⣟⠛⡗⠲⠤⣀⣀⣀⡀⠉⠛⢻⣿⡷⠾⠋⠀⠚⠁⠀⠀⠀⠀⠀⠤⠾⣛⣛⣿⣿⡿⠿⣿⢹⠄
⠀⠀⠀⠀⠈⠛⢿⡾⣦⣄⣀⣀⠀⠙⠋⠉⠙⠳⠛⠉⠛⠲⣞⠛⠛⠓⢾⣯⣉⠉⠙⠿⣦⣭⣙⣛⠛⡖⠁
⠀⠀⠀⠀⠀⠀⠘⣷⠋⢉⣉⠙⠿⡛⢛⣿⡶⠶⢿⡷⠶⠶⢾⣿⡶⠶⢶⣾⣿⣛⣻⠿⢿⣿⣟⡟⡼
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⠻⣀⠀⠸⡏⠉⢙⣶⠋⠉⢳⣶⣏⣉⣙⣿⣿⣥⣴⣿⠿⣿⣿⣻⡿⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠦⠛⢃⡀⢠⢿⣋⠉⣹⣾⣉⣀⣉⣿⣿⣉⣩⣿⣿⣷⣶⡿⢻⣿⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠈⠓⣀⠀⣸⣿⣅⣀⣩⣿⣍⣀⣩⣿⣿⣷⣶⡿⠟⣿⣿⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢦⡴⢶⣉⣙⣤⣤⡼⠻⣅⣠⣼⡿⠿⣧⣴⣿⣛⣿⣿⣿⠷⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⣦⣌⣦⣈⣻⣍⡉⠙⢿⣉⠛⢿⣯⣙⣻⣿⣤⣭⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⢈⣁⣈⠀⡀⢁⡈⠁⠐⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⣠⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠄⣀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠃
⠀⠀⠀⠀⠀⠠⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠂⡐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢰⡁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⡅
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠘⠓⠒⠲⠀⠤⠤⠤⠤⠤⠤⡀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⢠⡤⠤⠤⠤⠤⠴⠀⠖⠒⠚⠃
⠀⠀⠀⠀⠀⠆⠤⢤⠀⣄⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣀⣠⡀⡤⠤⠰
⠀⠀⠀⠀⠀⠃⠀⠘⠙⠂⠀⠤⠈⠁⠀⠡⢰⣃⠈⠉⠉⠉⠉⡃⢘⠉⠉⠉⠁⠀⢈⡁⠉⠈⠉⠠⠀⠀⠐⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠆⠐⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⢤⢀⡔⠂⠲
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⠔⠐⠖⠀⠀⠀⠀⢀⡃⢐⠀⠀⠀⠀⠀⠨⠀⡭⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉
⠀⠀⠀⠀⠀⢓⠂⠰⠀⡤⠀⠤⠄⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣀⣀⠀⣄⠀⠤⠤⠤⠤⢦⢀⠒⠚⡛
⠀⠀⠀⠀⠀⠈⠈⠈⠀⠂⠀⠀⠀⠀⠀⠰⠠⠇⠀⠀⠀⠈⠈⠅⠨⠁⠀⠀⠀⠀⠨⠁⠃⠀⠀⠀⠀⠀⠀⠈⠉⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢁⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠐⠀⢉⡀⠀⠄⢀⠀⠄⠀⠌⠁⠐⠀⠠⢄
⠀⠀⠑⠢⢀⠉⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠧⠄⠀⠈⠉⠉⠁⠉⠀⠈⠀⠀⠢⢄⡀⠀⠈⠐⠄⡀
⠀⢂⠀⠀⠀⠀⠀⣀⢰⠂⠈⠉⢖⠉⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢁⠀⠀⠒⢄
⠀⠀⠑⠀⠀⠀⠀⢀⠌⢂⢀⡀⠄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠂⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠳⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢢
⠀⠀⠀⠄⠀⠀⡀⠔⠩⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠉⠀⠰⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈
⠀⠀⠀⢀⠊⠔⠰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⡀
⠀⠀⠀⡀⠀⢀⠀⢀⡀⠐⢀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⢀⠀⡀⡆⠀⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡀
⠀⠀⠈⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢸
⠀⢰⡉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⡆
⡌⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⠋⠉⠉
⠑⢠⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡄
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠒⠒⠒⠒⠒⠊⠈⠓⠒⠈⠉⠉⠉⠁⢈⠀⢀⠀⠀⠀⡇
⠀⠀⡀⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⣀⠀⢀⠀⠀⣀⠀⡠⠀⠠⡀⢠⠄⠀⢰⠀⢸⠀⠉⢉
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠰⠄⠀⠘⠐⢪⠀⠀⠄⠀⠄⠀⠰⠀⠈⠂⠀⠚⠀⠈⠉
⠀⠀⠆⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⠀⠀⢤⢀⡤⠀⠀⢰
⠀⠀⠃⠐⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⠉⠇⠸⠁⠉⠱⠀⢌⠉⢈⡉⠉⣁⡀⠨⠀⠸⠄⠀⠄⠀⠐⠀⠒⠘
⠀⠀⢦⠠⠀⡀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⡁⠀⠅⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠄⡴
⠀⠀⠀⠄⠄⠸⣀⣊⠀⠉⢆⠀⠀⠀⠀⠀⢀⠐⠃⠂⠀⠆⠀⠰⠄⠠⠂⠀⠰⠀⠐⠀⠐⡇⠀⡃⠀⠰⠍⢬⠁⢀⣇⠀⠧⠄⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠐⠚⠂⠀⠒⠀⠃⠀⠐⠂⠐⠂⠀⠂⠀⠐⠀⠀⠃⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠉⠀⠐⠒⠐⠂⠀⠒⠂⠀⠀⠠⠠⠤⠤⠀⠤⠄⠀⢄⡠⠠⠤⢄⣀⡠⠤⠤⠤⠤⠄⠒⠒⠀⠐⠒⠛⠋⠈⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⣐⡒⣒⣂⠒⠂⡐⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣂⣀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠄⡐⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣄⠐⠦⢚⠂⠍⠃⠉⠀⠀⠀⠱⠄⣧⡀⠂⠀⣲⢐⡀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠉⠅⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠸⠈⠒⠘⠯⢃⡠⠰⡄⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡔⠋⣄⠓⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠆⠀⠂⠀⠀⠀⠂⠐⠀⠐⠀⠘⠀⠃⢙⠿⣷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣆⣫⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠃⠐⠀⠘⠀⠈⠀⢉⠞⡿⢞⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠱⢿⡀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⢙⣿⠷⢥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠂⠠⣄⠀⠀⠀⠁⠐⠀⠀⠀⠠⠀⠄⢀⠀⢠⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⠄⡈⡅⠃⠠⡆⠀⡄⢀⣀⣀⢠⠀⣠⠀⡀⢀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠔⢀⠆⠀⠒⠀⠉⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠃⠸⠀⡶⠀⡦⢩⠌⣿⡈⢣⣈⡁⣻⣄⠙⢅⣒⡀⢀⡄⠰⣠⣀⠠⠀⡠⠄⢸⠔⡦⠚⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⢰⠀⡄⠀⡀⠈⠀⠈⠀⠋⠀⠟⠀⠿⠀⡆⠀⠚⠁⠁⡅⠀⠁⠌⠀⠭⠀⠚⢀⡁⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⠆⠠⡄⢉⡀⢁⠀⠂⠚⠀⠰⠄⠶⠀⠶⠀⠤⠀⢠⠄⠠⠄⠀⠐⠀⠰⠆⠈⠃⠘⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡀⢁⠈⣁⠘⠂⠸⠈⠧⠀⠆⢰⠆⢰⡀⢰⡀⠠⡄⠀⡄⠀⣐⠀⠲⠀⠞⠀⠓⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠘⠇⠐⡀⢤⠠⠀⣄⢀⡄⢠⡄⢀⡀⠀⠀⠀⠄⢠⠄⠰⠄⠸⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠘⠁⠈⠂⠈⠦⠀⡆⠀⡄⢠⠀⣨⠀⣉⠀⡁⢈⡁⢀⠀⢀⠁⡄⠀⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⢃⠀⠂⠀⢦⠠⡄⠠⡈⢁⠉⡀⢉⠀⢉⢈⡁⢈⠀⡉⢀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠐⠂⠰⠆⠠⠄⠄⡇⢈⣃⣉⢈⡁⣉⢀⠁⠤

⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢴⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴
⠀⠀⠀⠀⠀⡴⢋⣀⠄⢀⡞⣷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡼⠁
⠀⠀⠀⠀⠈⠀⠉⣀⡴⠟⠁⣿⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠤⠒⠋⠉⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢳⣶⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠙⠋⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣸⠃⠀⠀⠀⡔⠘⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠉⠉⠙⢻⡄⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⠇⠘⠢⢤⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠷⢂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⠀⢀⣴⠶⠾⠲⠶⣤⡀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⠻⠿⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠖⣦⡰⠀⢤⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠘⢆⠸⣷⢁⣾⣥⣾⣤⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⢴⡚⢲⡤⣄
⠀⠀⠀⠀⣠⠖⠒⠚⢂⣽⠾⠋⠁⠀⠉⠻⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⢘⡥⢤⡿⠛⠦⣤⠷⢤
⠀⠀⠀⠀⠈⠓⣶⡾⠋⠁⡀⠀⠀⠆⠀⠀⢹⣇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⣸⠀⢀⣧⡀⠀⠘⠣⠚⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⡄⠀⠠⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣰⢸⡏⠙⣇⠀⠈⡷⠒⢺⠙⢻⡅
⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠹⣮⡳⠶⢾⡓⠛⢷⣤⡴⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠠⠀⠰⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣤⣬⣿⠶⠚⣹⠶⠋
⠀⠀⣀⡀⠀⠀⠀⠀⠉⠲⢤⡁⠀⠠⡀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⠶⠟⠶⠶⠋
⣴⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠘⢆⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠐⠶⣤⣄⡀
⠀⠈⠂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠈⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⠀⠉⠻⣦⡀
⠀⠀⠀⢀⠘⠛⠙⠛⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⡟⠁⠀⢀⠀⠀⠀⠀⢀⡟⠲⣄⠈⢻⣆
⠀⠀⠀⣿⡇⠀⢄⡀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣿⠀⢀⠀⠀⠑⢄⠀⠀⠌⠀⠀⠘⣆⠀⢿
⠀⠀⠀⠸⣷⡀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿⠀⣼⠀⢀⣀⡤⢽⡿⠂⠐⠒⠒⢻⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠙⠛⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠘⣿⡀⠸⡏⠉⠀⣠⠏⢠⠈⠢⣄⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠹⣄⡰⠃⠀⠀⣇⠀⠈⣻⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡈⠛⠶⠦⠤⠾⠶⠛⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣤⣤⣶⠾⠟⠁

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠈⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠉⠄⠛⠉⢉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡀⠀⠘⠀⠙⠿⢷⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠂

⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠀⢰⠂⣈⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠈⢳⡞⢤⡴⠎⠀⠀⠹⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣫⡷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠠⠆⠀⠐⣮⠛⢉⣁⡛⠞⠓⠧⠾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⢘⡀⡄⢀⣄⢐⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣤⣼⠁⠀⡈⠛⢿⢠⡎⠀⠀⠀⠀⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣠⡿⢳⡀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠒⠒⢀⡌⠁⠀⠉⠓⡄⡌⠋⠀⠁⠀⠲⠐⠒⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢀⣀⡥⠞⠋⠉⠓⠋⠀⠀⣀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠼⠃⢄⣀⠀⠐⠻⢀⡇⠀⡀⠀⠀⠀⣀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡋⠀⠀⡀⠀⠀⡀⠤⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠤⣀⡉⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠌⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠦⢞⠖⣲⣆⠁⡈⠴⠂⢒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⣃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠋⠙⠁⠀⠀⠀⠈⢿⣯⠦⣨⣿⡋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⢿⡂⠀⢠⠶⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⣈⠀⢘⣹⣷⢯⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⣀⣐⡦⢄⠞⠉⠀⡛⢢⣠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣤⠀⠀⡙⠉⣲⣉⠹⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠶⡏⠀⠀⠙⡋⠙⣤⡄⠏⠉⠉⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡡⠃⢤⡄⠀⡴⠿⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠲⠀⠀⢠⢤⠄⠞⠁⠀⠈⠉⠈⠀⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣆⠂⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠁⠘⠛⠃⢄⣀⠀⠀⠀⣁⠜⠂⠀⠀⠁⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠛⠛⠉⠉⠉⠉⠐⠠⣀⠈⠉⠉⠙⡙⠛⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⢀⣀⣬⡵⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠳⠾⢦⣄⡀⠀⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⢈⣭⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⠄⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡌⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠇⡠⣿⠀⠀⣀⣀⣤⣤⣤⡤⠶⠶⠶⡶⠖⠒⠛⡻⠟⠛⠛⠛⢛⠿⠛⠲⠶⠶⡶⠶⢦⣤⣤⣤⣄⣀⣀⡀⠀⠀⣿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠿⢛⠟⠉⠉⣀⣊⣀⣤⣤⣤⣮⣤⣤⣤⣾⣤⣤⣤⡤⠴⣧⣤⣤⣤⣴⣥⣤⣤⣤⣴⣈⣀⣀⢉⡩⠛⠛⠳⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠉⢀⣠⣦⡶⠾⡟⠛⠋⣩⠭⠅⠀⠀⡰⠖⠒⠒⠀⣀⡀⠒⠒⠒⠂⠀⠀⠐⠒⠒⠶⠄⠉⠩⢭⣝⠛⠛⠳⠶⣦⣿⠊⢸⣷⡀
⠀⠀⠀⠀⠀⠀⢿⡉⠁⠻⣭⣁⣐⣉⡁⠠⠶⠂⠀⣀⡋⠉⠁⣠⠤⠤⠉⠉⠁⡤⠤⠀⠉⠉⠉⠠⠤⠄⠀⠚⢛⣂⣐⣲⣦⠬⠭⡷⢺⡿⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⢶⣦⣅⣀⣀⣈⠍⠋⠉⠉⠉⡹⠛⠛⠛⠛⡛⠗⠛⠛⠓⢒⠲⠒⠛⠛⠛⡻⠛⠋⠉⠉⡩⠋⠁⠀⣀⣠⣬⣤⣼⣧⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠠⢤⣈⡉⠉⠙⠛⠛⠛⠛⠛⠛⠒⠲⠶⠞⠷⠶⠶⠶⠶⠿⠶⠶⠶⠶⠾⠖⠒⠒⠚⠛⠛⠛⠛⠛⣉⣉⡁⠀⠤⠴⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡔⠒⠀⢠⣀⣀⣈⠉⠉⠁⠀⠀⠀⠒⠒⠒⠂⠀⠀⠒⠒⠒⠀⠀⠀⠒⠒⠒⠂⠀⠒⠚⠛⢃⣀⣈⠉⠀⠤⠴⠂⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣤⠀⠀⠀⢀⣀⣀⣈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠛⠓⠓⠀⠀⠈⠉⠉⠉⠀⠀⠉⠁⠀⠀⣀⡀⠀⠤⠤⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠠⠤⠤⠤⠀⠀⠀⢤⣄⣀⠉⠉⠉⣀⣀⡀⠉⠉⢉⣀⣀⡀⠙⠛⠉⠤⠤⠌⠛⠉⠁⠤⠤⠉⠁⠲⠶⠂⠠⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⠤⠤⠄⠀⠤⣤⣤⠀⠀⠀⢠⣀⣀⡈⠉⠁⣠⣤⣤⠀⠀⠀⠤⠤⠤⠄⠀⠤⠤⠤⠄⠀⠀⠤⠤⠄⠐⠒⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠒⠒⠒⣀⣀⣀⠒⠒⠒⠀⠀⠐⠒⠒⠒⠀⠀⠒⠒⠒⠀⠀⠀⠒⠒⠀⠀⠀⠙⠙⠉⠀⠀⠋⢉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⡠⠤⠀⠀⠤⠤⠄⠉⠉⢡⣤⣤⠍⠉⠉⠠⣤⡤⠍⠉⠉⣤⣤⠛⠛⠡⠤⠄⠉⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣤⣤⣤⣉⣛⣃⣀⣀⣼⣛⣣⣤⣤⣤⣴⣶⣦⣤⣤⣿⣭⣴⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⢻⢿⢛⠻⠿⡿⠟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢸⣿⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠸⣿⣿⣶⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⢿⣿⡟⠁⠀⣸⣿⣿⠀⠀⠙⠻⠟⠁⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⣿⣿⣧⣤⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⢶⣾⣿⣿⣷⣦⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣭⣟⡻⠿⣧⢻⣿⣷⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣷⣶⣿⣆⠀⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⣼⣿⠿⣛⣛⣯⣭⣭⣿⣶⣶⣶⣶⡆⣭⣭⣟⡻⠄⠻⠿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⡁⣙⡻⣿⣿⡇⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣾⣿⣿⢧⣿⣿⡞⣿⠇⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⡿⣸⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⣵⣾⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢟⣵⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⢀⣴⡞⠓⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠲⠶⣦⡀
⠀⠀⢠⠏⠀⠳⣄⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⣠⡴⠋⢧
⠀⠀⠘⢆⠀⠀⠈⠙⠖⢄⡀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⢀⣤⡶⠟⠁⠀⠀⣸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⡂⢄⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⣀⢔⡪⠟⠉⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣁⠢⡀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⡠⠔⠉⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠈⠑⢄⠑⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⡀⠐⠉⠀⠀⢀⡠⠖⠉
⠀⣠⡤⠶⠒⠒⠒⠒⠒⠒⠛⠓⢄⠀⠀⠀⠙⠻⡉⠀⠁⠀⠀⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠀⠀⠀⡠⠔⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⣦⣄
⣸⠋⠒⠒⠶⠶⠶⠶⠄⠀⠄⠀⠀⠑⠂⠀⠀⠀⢀⡠⣤⠤⠤⠤⠤⠠⠤⠠⠤⠠⠤⠤⠴⠶⠶⠶⢶⡶⠈⠀⠀⠀⠀⠴⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠾⠽
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣄⡸⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢹⣀⣀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⢩⠧⠀⠐⡛⠀⠀⠀⡀⠀⠀⠦⠀⠀⠀⠶⠖⠓⣤⡀⠀⣴⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⢄⠀⢀⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⣒⡒⠒⠂⢚⡿
⠀⢰⡤⡤⠄⠐⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢐⠀⠒⠓⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠁⢘⠁⠀⠀⠈⠉⠉⣉⠀⠀⠀⠁⠀⠀⠬⠇⡗
⠀⠀⢉⣉⡉⢉⡂⠀⠀⢐⡒⠀⠀⠀⠀⠀⢈⣉⠀⣭⠀⡁⢈⣏⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠭⠠⠀⠠⠥⠄⠀⠤⠀⠄⠠⢠⠀⠀⠐⠀⠀⠀⠂⠀⢐⡖⣺
⠀⠀⢰⠴⠦⠀⡀⠀⠀⠀⡀⠀⠨⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⢤⠀⠀⠀⠠⠐⠂⠐⠀⠀⠀⠈⠀⠀⠒⠀⠀⠐⡂⠉⠉⢉⡼
⠀⠀⠘⡒⣒⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠛⠀⠀⠀⡀⠀⠀⠀⢐⠐⠒⠂⠛⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⢐⠀⠀⠁⠀⠉⢉⣁⡀⠯⠴⡇
⠀⠀⠀⢣⣈⡁⠸⠀⠀⠀⢠⠀⢈⠁⠀⠀⠀⡁⠀⠈⡇⠀⠀⠸⠤⠀⠀⣁⠀⠀⠀⢉⠀⠀⠤⠽⠀⠀⠀⠠⠀⠀⡈⠁⠀⠀⢀⠁⠭⠥⠤⠠⠀⠂⠀⣶⣺⠁
⠀⠀⠀⠸⠂⠂⠀⠄⠀⠀⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠠⠤⠀⠀⠒⠀⠀⠀⠐⠀⠒⠂⠀⠐⢲⠂⠈⣉⡜
⠀⠀⠀⠀⢳⣀⡀⠃⠀⠀⠒⠒⠒⠒⠒⠒⠂⢀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠈⡈⠀⠀⠄⠀⠀⠀⣀⠀⢈⠁⠈⠉⣁⠠⠴⠛⡇
⠀⠀⠀⠀⢀⣀⠀⠭⠀⠀⠀⢨⠁⣀⠀⠀⠀⢀⠀⠀⠬⡅⠀⠀⠽⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⢹⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠀⠘⠒⢒⣾⠁
⠀⠀⠀⠀⠀⢳⡆⠠⠄⠀⠀⠀⡄⠐⠂⠀⠒⠚⠂⠀⢀⣇⠀⠀⠘⣢⣀⣈⣤⣤⣤⣤⣀⣀⣈⣩⣀⣀⣠⣭⣭⣭⣥⣤⡀⠉⠉⢥⣿⣄⣀⣀⣨⣨⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣐⠤⣀⠀⠀⠀⠘⠁⡤⠞⠓⠄⢀⠠⠂⠀⠀⢀⣘⣷⣻⢆
⠀⠈⠒⠦⠘⠄⠀⢀⡰⠀⠀⠘⡆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠘⠛⠮⠻⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⠐⠃⠀⠡⠖⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢠⠀⢄⡀⠀⠀⠙⠄⠀⠀⠀⠀⠒⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⠈⡀⢁⠀⠑⠀⠀⠸⣄⠴⠋⠱⡀⠀⠀⠂⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢁⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠤⠙⠂
⠀⠉⠃⠀⠈⠉⠒⠠⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠒⠂⠀⠀⠀⠠⠀⡠⠃⠂

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣀⡀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠉⠁⢉⠀⠈⢸⢳⠂⠀⢀⠴⠋⢠⠄⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣛⣻⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣽⡷⣿⣿⣿⣧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⠿⠿⠿⡄⢠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡎⠙⠶⠾⠿⠟⢣⣤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣰⣾⡯⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⡄⣤⣶⣾⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡉⣠⡆⠀⠛⢻⣾⣾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡝⠇⠃⠁⠀⠀⠀⠀⠈⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢴⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣮⣠⢀⣠⣀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣛⣛⣛⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠙⠛⠙⠛⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠴⡒⣉⠝
⠀⠀⠻⢍⣉⣉⡉⠻⢷⡿⠿⣟⣿⣝⣗⣦⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣶⣫⣿⣿⣛⡿⠭⠥⠿⠗⠒⣲
⠀⠀⡤⠤⠬⠟⠶⢚⣋⣽⡭⣳⣯⣯⣞⡄⣧⠴⠚⠋⠉⠉⠉⠉⠻⢗⠦⣄⣸⠹⣻⢯⣿⢭⡯⣟⣁⠒⠾⠯⢥
⠀⠀⠙⣒⡲⠶⠚⣅⠵⢚⠟⣼⣏⣇⣇⢒⠸⡖⠦⢤⣀⠀⠀⠀⠀⠀⠱⡀⠙⢴⣰⣽⣼⠳⡈⢢⣴⣙⠛⢿⠉
⠀⠀⠈⠳⢶⡾⠞⣱⡶⡏⣠⠋⡿⢸⢹⢻⣰⣮⡆⠀⠈⠙⠢⢄⠀⠀⠀⠐⡀⠈⣿⡏⣏⢳⣈⡢⣷⣽⣫⠉
⠀⠀⠀⠀⠈⠒⢻⣋⣴⡷⣣⡜⢃⡜⡾⡟⡏⢿⠃⠀⠀⠀⠀⠀⠑⠢⢀⡀⣃⣠⠂⣿⢋⢿⣌⣟⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠗⢫⣇⣿⡇⣧⣳⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠞⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡖⠠⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣀⡰⠀⣀⣠⠔⠊⠀⠀⡴⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡒⠚⠛⠫⠩⠂⠀⠀⢀⢜⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠴⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⢄⣀⣠⢀⣀⣀⣀⡠⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⣵⠟⠁⠉⠈⠙⠩⠿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⡴⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣫⣿⣦⡀⠀⠀⠀⠘⣿⠀⠀⠀⣸⡏⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢨⣿⣿⠙⢿⡄⠀⠀⠀⣿⢀⣀⣤⣿⠶⠶⠞⠛⠛⠋⢫⡽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣼⣿⣯⣤⡞⢻⣆⣤⠾⣿⠋⠉⠀⣿⡄⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣿⠀⠀⢹⡆⠀⠀⠘⣷⡀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠸⣿⡀⠀⠀⠈⢻⣦⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⢠⣴⡴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠪⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠄⠂⠁⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠐⢠⡀⠈⠑⡤⠀⠂⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢢⣲⡀⠀⢳⠀⠰⠁⡈⡀⠀⢾⡨⠄⠀⠂⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣷⣄⠜⠃⠂⠀⠀⠛⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⢀⡝⠯⢀⣀⠃⠘⠃⠀⠀⠉⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢳⡆⠀⠀⠨⠁⠀⡃⠀⠀⠀⠼⠉⢉⠙⣦⠀⠀⠀⠀⡀⠀⠐⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢢⡈⠂⠤⣿⡼⠀⡁⠀⠀⠀⠀⠀⠀⢱⣼⡇⣀⠀⡰⠀⠀⣸⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠓⢤⠈⠒⠦⣀⡉⠐⠂⠀⠀⠀⢀⡆⢀⡜⠁⠀⣀⣳⣀⠈⠟⢉⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⠀⠀⠠⢿⠨⡆⠀⠀⠀⠈⠉⠒⠒⠂⠤⠤⢤⢤⡤⠤⢤⡤⠤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠬⣶⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⡛⠿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠌⣽⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⢉⣿⣿⡟
⠀⠀⠀⠀⠀⠡⠔⠚⢆⢀⡀⠓⣤⣀⠘⢗⢌⣋⢿⣿⡷⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠁⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢾⣁⠀⠈⠁⠉⠉⠀⠀⠀⠀⠈⣷⣂⠀⠀⢀⠀⣀⣀⣼⣽⣇⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢀⣀⣼⠿⠛⠋⠉⠉⠁⠉⠁⠀⠀⠀⠙⠒⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠙⠀⠀⡀⠀⢉⣵⣆⠀⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠄⠀⠀⠀⠠⠀⠘⠋⠀⠐⢁⡴⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣤⡔⠁⠀⠀⠀⢀⣴⠞⠉⢀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠶⣄⠀⠈⠛⠷⣦⣴⡶⠓⠈⠁⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠂⠰⠦⢤⡙⣿⡄⠀⠀⠞⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣷⡄⠀⠀⠀⠙⠧⠀⠔⠂⢋⡤⠦⠈⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠛⠻⡦⠐⠿⠿⠶⠁⠀⠀⠞⠁⠚⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣶⣤⠾⠶⣶⠮⠐⢶⡾⠂⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢰⠆⣀⣁⣤⡶⠦⢶⣦⣾⡷⡄⠀⣄⡈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣨⢉⢹⣿⣯⣀⣾⠋⠸⣿⡿⢶⣼⣿⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢻⣿⠃⣿⡟⢠⠀⠈⣿⡡⠄⠸⢧⠀⠙⡎⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠸⣷⢴⣿⡇⠉⠀⠀⣹⠀⠀⣄⠀⢃⡿⠀⠉⢠⡔⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⣤⡘⢷⠃⠙⣇⣠⠴⠚⠹⣆⠀⠉⠀⢈⢷⡶⢄⣤⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣷⠋⠀⠀⠈⠁⠐⠶⡄⠈⣷⣀⠔⠁⠀⠛⣄⢀⡄⠁⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠁⣄⡈⠻⡴⠚⡉⠙⢇⠀⠋⠀⢀⣼⠿⡠⠴⠶⠄⠘⡟⠀⠸⡇⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢠⠀⣀⣾⡅⢻⣓⡀⢘⣧⣠⠔⠉⠀⠀⠻⣆⢀⠤⠂⢻⡂⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢾⡟⣉⠉⢏⠉⠀⢉⣠⠴⢏⡒⠶⠿⠦⠄⡟⠧⢤⣄⡀⣷⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡇⠧⡄⠈⢣⡴⠋⢀⡀⠀⠹⣀⣀⠤⠐⢿⣄⠘⠩⠉⠈⠉⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣤⣧⡀⣤⠖⠘⢧⠲⠟⠧⢄⠠⣿⠀⢠⣆⠀⢘⣇⠀⠀⣠⡸⡇⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⢻⡇⣴⠃⠀⢀⡘⢀⣤⠄⢾⣀⠤⠟⠉⣉⠸⢷⡴⠋⠁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠻⣦⠁⠀⠈⣿⠉⠀⣀⠀⠙⣆⢠⠞⠁⠀⠀⠻⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⢡⣼⣿⣶⠶⠾⠟⣢⡴⠿⡄⠀⠙⣟⠀⠠⠞⠣⠀⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣇⣶⣄⠀⢱⡄⢠⡶⠒⠉⠉⠳⣀⡄⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣆⠛⠽⢡⡼⢉⡛⠀⠠⣄⡀⠠⠥⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠄⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⡠⠄⠢⢄⡈⠉⠢⡄⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⣷⣮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⠊⠀⠀⠀⠀⠈⢢⡀⠈⢦⠀⡠⠴⢿⡀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢀⠇⠀⠀⢀⠄⠀⠀⠀⠰⡄⠀⢫⠀⠀⠀⢑⠀⣀⠤⠴⣿⠃⠀⠀⠀⡠⠂⠀⣠⠔⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠀⠙⠛⠋⠐⠂⠄⣀⣹⠘⣧⠀⠀⠀⢡⡀⠘⠆⠀⠀⢈⡾⠁⠀⠀⠀⡇⢀⠔⠁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡽⠂⠀⢀⠘⢃⠀⢺⠀⢠⠞⠀⠀⠀⠀⢠⡕⢡⡶⠞⡡⠔⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢒⣿⡆⢙⠀⠰⡆⠚⠒⣶⡄⠀⡠⢋⢔⢟⠅⠊⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡊⡄⠁⠸⠃⠀⣃⠀⠀⠀⢠⢜⠕⢕⡵⠁⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠁⠀⠀⣀⠄⠂⠀⢀⠀⠀⠀⠀⠰⡆⠀⠉⢀⡄⡀⣸⡣⠚⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣠⠞⡇⣸⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠔⠈⠉⠀⠀⠛⠀⡀⠀⠀⠀⠀⣇⠀⠸⢆⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⣤⠖⠁
⠀⠀⠀⠀⢠⠇⢀⣷⠃⢀⠄⠀⠀⠀⠀⡇⢠⠀⣰⠃⢀⡠⠖⠀⠀⠀⡄⠄⠑⠀⠀⠀⣇⠀⢸⠀⢣⠀⠀⠀⢈⣦⣠⡴⠋⢁⡜
⠀⠀⠀⠀⢸⡄⠐⢿⢀⠁⠀⠀⠀⠀⣰⣤⢼⡒⠛⠒⠺⡀⠀⠀⢠⠂⠀⠀⠀⠈⠀⠀⣞⡀⢛⡀⢸⠀⠀⢂⣠⠞⡛⢀⣠⠎⡁
⠀⠀⠀⠀⠀⢳⣀⠘⠛⢄⡀⠀⢀⡾⠁⠀⠀⠋⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠩⡇⠀⠀⣷⡸⠷⠓⠉⠁⣀⣴⠊⠱⢨
⠀⠀⠀⠀⠀⠘⣏⡷⢤⣀⡉⠁⠺⠧⠄⣀⣀⠀⢀⠀⠀⢀⠀⠀⣇⢀⢀⣀⡀⠤⠤⠔⠓⠐⠘⠁⠀⣀⡤⠔⡊⠁⠄⠀⡈⠸
⠀⠀⠀⠀⠀⠀⣷⢸⡀⢹⠛⠛⠶⠤⢤⣤⣀⣀⣉⠀⣉⠁⠈⡁⠀⣀⠀⣀⣀⣀⣠⣤⣇⠠⠟⠚⠉⠁⠀⠀⠅⠀⡁⠀⢂⡇
⠀⠀⠀⠀⠀⠀⢹⣝⡆⠸⡅⠂⢹⠀⠀⠀⡁⠈⠉⠩⠉⠉⠉⠛⠉⠉⠉⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢈⠱
⠀⠀⠀⠀⠀⠀⠘⣧⢭⠀⡃⠀⠐⠄⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡜⡄⢸⡀⠀⡁⠀⠀⠁⠀⠀⢀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡈⡃⠀⠠⠀⠀⢀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢸⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠸⡄⠨⣂⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠂⣔⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣑⡄⢳⡀⠀⢡⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⣠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠤⣬⣆⣀⣨⠀⠀⠤⠀⠀⠀⠀⣀⣂⣠⡴⠷⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⢠⠏⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧
⠀⠀⠀⠀⡞⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠈⣆
⠀⠀⠀⡸⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠘⡄
⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢳
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⢿⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⢸⠈⢻⣦⡀⠀⠀⠀⠈⣿⡄⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠘⡆⠀⠙⢿⣦⣄⣀⣀⣸⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⢱⠀⠀⠀⠉⠛⠿⠿⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣴⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏
⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⣤⣴⣶⡿⠿⠛⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠻⡛⠋⠉⠁⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⠶⠿⠟⠋⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣰⣾⠟⠉⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⣼⠟⠁⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣀⡀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣤⣄⣀⣀⣀⣈⣙⣳⣦⣤⡤⠤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⠶⣶⣶⡶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠳⣾⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢤⣤⣤⣴⣶⡶⠾⠶⣶⣤⣀⠸⠃⠈⣷⡀⣀⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢷⡄⢠⣿⠟⠋⠀⠀⠀⠀⠈⢉⣷⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⠀⠉⠙⢦⣼⠿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠨⠽⠧⠤⣴⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢠⣤⡤⠖⣂⣤⠴⠖⣲⡿⣿⠇⣺⣿⠟⠉⠉⠉⠉⠉⠛⠳⠶⠤⠤⠴⠶⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣛⣭⣶⣶⠟⢁⣴⠏⣼⣿⣿⢠⣤⣂⣤⡀⠀⠀⣤⣤⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡽⠋⢁⣴⠿⡟⢸⡏⠘⠻⣷⣭⣭⣭⣤⣤⣶⠶⠶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⢠⡟⢁⣴⠟⠁⢸⡇⢸⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣠⣶⠿⠛⡉⢉⡿⠿⠿⠷⣶⠏⢠⡞⠁⠀⠀⠸⡇⢸
⠀⢠⣾⠏⠀⠀⠀⠳⢮⡶⠂⠀⢀⡏⢠⣿⡄⠀⠀⢀⣠⣧⢸⣤⣤⣤⣤⣀
⠀⣾⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⢠⡏⢸⣿⣀⣶⡿⠟⠻⡄⢫⣉⠉⠛⠛⠿⣦⡀
⠀⣿⡇⠸⣇⠀⠀⠀⣀⣠⣤⣤⡇⣼⣀⣼⣿⣿⠏⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠈⠻⣦
⠀⠘⣿⣆⠉⢀⣴⡿⠟⠉⢁⠘⡇⡏⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠈⠻⣷⡿⠁⠀⠀⠀⠈⠻⣷⡷⠏⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡴⠾⠋⣠⣾⠟
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢰⣿⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣀⣀⣀⣤⡾⠏⢀⣴⣿⠋⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣭⣭⣭⣭⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠛⢁⣠⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⣿⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⢀⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⣴⣶⣤⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠋⡉⠁⠸⢿⣿⣿⣿⣿⣷⣦⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣠⣾⣿⡏⢠⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣼⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⢠⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠀⡀⠀⠌⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠡⡰⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢀⣀⠀⠀⠠⠀⣒⠂⠒⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠁⣵⠂⠻⡐⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠊⠉⠀⠆⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⢸⠃⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⣠⣾⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠭⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⠢⣤⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠂⠀⠀⠠⠞⠉⠀⠤⡀⠀⠀⢀⠤⠤⠤⠦⠸⢿⣿⣿⣿⡿⢀⠀⠀⠀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠯⠉⢉⠔⠉⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠊⠀⠐⠆⠀⠀⠀⠀⠀⠈⠉⠀⠁⠑⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⡀⠤⢦⡤⠶⠖⠢⠀⠲⢺⣶⣖⡲⠿⠗⣒⣶⢺⡦⣴⣤⣶⣶⣶⣤⣠⣠⣤⡀⣨⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠀⢙⣾⣁⡲⠖⢛⠓⡂⠀⠈⠩⠈⠁⠀⠩⠉⡛⢣⡧⠨⠤⢼⢽⣛⡶⠷⣮⣭⡟⣬⣟⠿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⣮⠞⣦⣴⣝⠋⠩⠭⠤⠤⠿⠯⠤⠭⣥⣀⣀⣬⠍⠚⢽⠒⢀⢠⣬⡈⣽⣻⣿⣿⣽⣿⣶⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠸⣉⣘⠐⠶⠦⢛⠓⠶⠶⣶⢞⣒⢒⠒⠒⠲⠖⣲⢆⡒⠒⠚⠋⠹⠶⠖⣍⣉⠁⣤⡈⠉⣽⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢾⣿⣋⠐⠨⠓⢂⡷⠄⣈⠠⣭⠽⠓⢲⠌⠁⠚⠦⠿⢛⡋⠡⠤⠥⠶⣛⣋⠁⠀⡤⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⣭⣃⠽⠀⠈⠙⡒⠒⠂⢈⡍⠒⡒⠒⠒⠒⠋⠨⠉⠉⠉⣉⠂⣀⣀⠐⠆⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠬⠥⡀⠁⠡⠂⠐⠂⣒⠒⠀⠐⡂⠒⢀⡬⠁⣀⠀⠉⠀⠠⠀⠠⠰⡞⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⠕⠩⠭⠥⢔⣒⣒⡐⠤⠤⣠⣤⠤⠀⠁⠄⠨⠍⢀⡐⠂⢄⣽⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠨⠅⠡⠭⠤⢀⡐⣒⡊⠐⠒⣒⠂⠀⠂⠀⠨⠁⡀⡂⣈⣜⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⣀⡦⠄⠀⠤⡀⠒⠀⢀⣀⡀⠈⢂⠠⠜⡀⠀⠚⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠰⠄⠒⠛⣷⠉⠉⠉⠉⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣤⣤⣤⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠄⠀⣠⡶⠛⣏⣠⠊⠁⠀⢀⣩⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣠⠴
⠀⠀⠀⠀⣴⣋⣠⣤⡼⢽⣖⣒⠚⠉⠀⠀⠈⢷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠐⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠆⢰⡏⠁⠀⡼⠀⠀⢀⠈⠉⡒⠦⣀⠀⠸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⠔⠀⠀⢀⠴⠚⠉
⠀⠀⠀⢸⣇⡴⠚⡏⠉⠓⢤⡀⠀⠀⠀⠈⢣⢀⡇⠀⠉⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠁⢻⡄⠀⣇⠀⠀⠀⠹⡄⠀⠀⠀⢀⣿⠃⠀⠲⡀⠀⠀⠀⠀⠀⢁⡀⢀⡴⠀⠚⣡⠞⠁
⠀⠀⠀⠀⣆⠻⢦⣘⡄⠀⠀⠀⢳⠀⢀⣠⡞⠁⠀⢀⠀⠙⣆⠀⠀⠀⣠⠏⠀⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠉⠛⠲⠾⠶⠶⠛⠋⠁⠲⣄⠀⠀⠳⡄⠘⠆⠀⣰⠃⠀⠀⡤⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠒⠒⠀⠀⢦⡀⠀⢠⡀⠘⠆⠀⠰⠃⠀⠀⡼⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠓⠀⠀⠙⠆⢀⡞⠰⣠⠎⠀⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠓⡠⠀⡀⣆⠀⠉⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⠈⠠⠈⣘⠡⢚⣡⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡶⠛⠛⠛⠛⠛⠳⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠉⠙⠻⢶⣄⡀⠀⠀⢠⡿⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⡾⠁⠀⠀⠈⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣀⣀⣀⣀⣀⣠⣤⡴⠞⠻⣦⡀⣠⡴⠟⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠾⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⡼⢿⡍⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠀⠀⣻⣤⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⣠⡞⠉⢿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⣰⠏⠀⠀⠸⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣿⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢿⣥⣤⠶⠶⠟⠋⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠠⠀⠀⠀⠀⠠⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⣀⡀⠠⠤⠤⠤⠄⣀⡀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡄
⠀⠀⠀⠀⠀⠀⡘⠀⡜⠀⠀⠀⠀⢸⠉⠒⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢡
⠀⠀⠀⠀⠀⢠⠃⢰⠁⠀⠀⠀⠀⠈⢆⠀⢄⡇⠀⠀⠀⠀⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠀⠀⠀⠀⢃⠈⡄
⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠠⡆⠘⠻⣇⠀⣠⠖⠉⠋⠢⡀⢸⠀⠘⢄⠀⣀⢀⠛⡄⠠⡃⢀⠆⠀⠀⠀⠀⢸⠀⢃
⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢀⡤⡌⠁⠊⠁⢢⠃⠀⠀⡀⠀⢘⡀⠳⣀⢈⡞⡥⠊⠦⣸⣤⠽⠡⢄⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⢀⠀⡇⢀⡄⢤⠀⡎⠀⢸⢀⡠⠔⠊⠀⠀⠀⠀⠀⣨⠆⠒⠒⠻⠞⢤⡀⠀⢀⣈⣐⠒⢉⠜⡝⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠇⠀⠉⠢⣹⡇⢀⣦⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⠈⢫⠁⠀⠀⠉⠪⣞⣒⣉⠽⢁⠀⡌
⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⡠⠜⠟⠃⢸⠀⠀⠀⠀⣀⠤⠄⠾⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠈⠑⡄⡌⢠⠃
⠀⠀⠀⠀⠀⠀⠘⡀⢣⠊⠀⠀⠀⠀⠈⡄⠀⡴⠋⠀⠀⠀⠀⠄⠀⠈⠳⡀⠀⠀⠀⠀⢠⠆⠀⠐⠀⡀⠂⠀⠀⠘⠁⡎
⠀⠀⠀⠀⠀⢠⠄⠳⠾⡐⠀⠂⠀⠢⢤⠘⠾⠂⠰⢤⠒⠢⠐⠚⠢⣔⠀⠳⠒⠂⠲⢤⠞⠰⠰⠦⣄⠀⠀⠤⡄⠐⠾⢄
⠀⠀⠀⠀⠀⠑⢤⠤⠄⠈⠑⢤⠀⠀⠀⠙⢤⠀⠀⠀⠙⢦⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠱⡤⠀⠀⠈⠣⠄⠀⠈⠦⢤⠜
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⢄⡠⠀⠀⠀⠀⠠⡀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⣄⣀⡄⠀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠑⠤⠖⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠈⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠂⠀⠀⠀⠀⠖⠒⠒⠈⠁

⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⣿⠏⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⢿⣿⣿⣿⣿⣯⢰⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣟⡛⠛⣷⣝⣿⡟⠅⠀⢿⢹⢰⡟⠁⢀⣼⢳⡾⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠻⠟⠻⣿⣜⣷⣎⠀⠈⠈⡿⠁⠀⣾⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣌⠻⣟⢿⡀⢄⠀⠁⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡻⡛⣦⠘⢾⣃⠀⡴⠉⠀⠀⠀⢀⣿⣿⣿⡿⢛⡿⢻⣿⣿⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢉⣹⡿⢷⣾⣩⠻⠶⣍⣧⡀⠹⡄⠀⠐⠀⠀⠀⠀⠈⠛⣣⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣍⡙⢿⣾⣆⠘⢷⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣬⡿⢷⣮⣙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣠⣿⡿⠿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣋⣉⠺⡉⠃⠹⣆⠀⠀⢀⠀⣀⠀⠉⠀⣉⣤⣆⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⡛⠻⣿⢐⣦⣙⡇⠀⠀⠀⢈⣤⠂⡼⠉⠛⢛⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠐⠿⠿⣖⣊⣻⠷⠌⢭⡛⢷⣶⠷⠞⠁⠀⠠⣠⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠒⢾⡷⢏⣙⠲⣇⠀⢙⡾⠧⠤⢀⣾⡷⠃⢴⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡉⠀⣈⣿⡷⠠⣭⡿⠶⠶⢀⡼⠟⢠⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢏⣉⠩⣝⣦⣤⡯⠓⣣⠾⠦⢴⡟⣲⢏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠇⠐⢠⠶⡦⣾⣋⣉⣁⣄⣈⣃⣹⣦⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⠿⠋⠁⠐⠃⠀⠰⣿⠓⣼⣿⣿⣿⣏⡘⢿⣧⠀⠙⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⢀⠄⠐⠆⣀⠠⠛⡿⠁⠈⠹⣦⠉⠉⠛⣇⠀⠀⢃⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠀⠀⠀⠀⠁⠀⡃⠐⠢⣧⣤⡔⠂⠀⠠⣤⣰⠁⠀⠰⡾⠁⣰⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣲⣄⡜⠓⢶⡃⠀⠀⣏⣀⢀⡸⠃⠈⢣⣤⣤⡤⠀⡈⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠢⣴⠇⢬⣽⡋⠈⠉⣿⣂⣀⣼⠋⠀⢱⠖⠁⠀⠛⢼⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣭⠓⠐⣧⠀⣀⣹⣋⢀⣚⡟⠉⠉⢻⣄⣀⣼⠖⡇⠀⢖⠤⡀⠀⠀⠀⠀⠀⠈⠉⠚⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⢲⣿⣤⣵⣎⣁⠉⢹⣗⠚⣀⣿⢁⡍⣿⠊⢳⠶⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣏⡉⠙⣿⣉⣤⣿⣂⣿⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣨⣿⡧⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣉⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⢟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣰⣾⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠋⢙⣿⣿⣿⣿⡿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠈⠙⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢁⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣉⣁⣀⡀⢺⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠷⢄⠀⠀⠀⠀⠀⢀⣶⣾⣿⣉⣙⠲⣇⣀⠉⠉⠛⣿⣳⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⢀⣾⣟⣉⡡⣤⢬⣹⠟⠛⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⣿⣟⣻⠏⠀⠀⠠⠀⣱⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣿⣧⣼⢿⣶⠖⢛⣾⣾⢁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⡿⣿⣋⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⣀⣤⣤⣶⡆⢰⣶⣤⣤⣀⠀⠀⠀⣿⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠁⢀⣤⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⣤⡀⠉⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⢀⣴⣿⣿⣆⢿⣿⣿⣿⡇⢸⣿⣿⣿⡿⣰⣿⣿⣦⡀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣎⠻⣿⣿⡇⢸⣿⣿⠟⣰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣬⣛⠃⢘⣛⣥⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢘⣛⣛⣛⣛⣛⣿⣟⣛⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡐⣶⢆⣴⣶⣶⣶⣆⢲⣶⢂⣶⣶⣶⣶⣆⢲⡖⣰⣶⣶⣶⣶⣄⢶⢂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⢾⣿⣿⣿⣿⣿⡧⠡⣿⣿⣿⣿⣿⣿⢆⠸⣿⣿⣿⣿⣿⡿⢂⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣎⢿⣿⣿⣿⡟⣱⣷⡙⣿⣿⣿⣿⢃⣾⣷⡙⣿⣿⣿⡟⣱⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠻⣿⠏⣼⣿⣿⣿⣌⢿⡿⣡⣿⣿⣿⣷⡜⢿⠟⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠉⣾⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⢆⢺⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⣶⡜⢿⣿⣿⣿⢏⣼⣧⡹⣿⣿⣿⡿⢣⣾⣦⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣎⢿⣿⢃⣾⣿⣿⣷⡙⣿⡟⣱⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠡⣿⣿⣿⣿⣿⣿⠌⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁⠀⠹⣿⣿⣿⣿⠏⠀⠈⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠹⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⣒⡺⢿⣟⡛⠿⢿⣷⣖⣒⠢⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣛⣋⣩⡽⠿⠛⠛⠻⠿⠿⠶⠦⢭⣽⣿⣶⣍⡻⣟⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣭⣷⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣧⡉⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣫⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣙⣷⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡩⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣡⡾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢹⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣿⢷
⠀⠀⠀⠀⠀⠀⣼⠏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⡇
⠀⠀⠀⠀⠀⢰⣟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⢸⡟⢹⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⢠⣿⡀
⠀⠀⠀⠀⠀⣼⠶⢶⡿⠛⠛⢛⣉⣉⣩⣭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠭⠭⣭⣍⣉⣛⡛⠛⠲⢶⣟⠛⣹⡇
⠀⠀⠀⠀⠀⢻⢨⣿⢀⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⡄⢹⡯⣾⠇
⠀⠀⠀⠀⠀⢸⣭⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡿⡯⡿
⠀⠀⠀⠀⠀⠀⠹⣧⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⢸⡷⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠉⠛⠻⠿⣶⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⠶⠾⠛⠋⠁⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡙⠲⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠘⢻⣍⠉⠙⢟⠲⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠾⠛⠛⣹⠇⢀⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢈⣫⣍⠀⠛⢯⣉⠀⠒⠚⣛⠦⡄⠀⣤⡠⢤⣟⡒⠂⠀⠐⣚⡻⠶⠆⠐⠒⣻⠦⠀⢛⣹⠂⢈⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⢩⡦⠀⢈⢛⣭⠀⢈⣉⣙⠶⠦⠀⠤⠔⠖⣯⣍⣁⠀⣉⣩⡙⠛⠀⠈⣉⡟⠂⢀⣩⡝⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠠⡷⠆⠀⣉⡶⠄⢠⣬⣭⡗⠒⠀⠒⠒⣛⠷⠤⠤⠀⢤⣴⣞⣉⠀⣈⣤⣙⠀⣠⣴⡅⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠾⠖⠀⠠⣿⠒⠀⠤⠴⣟⣋⠀⢉⣉⣹⠟⠒⠶⠀⠶⠶⣭⠅⠀⠤⢾⡉⠀⠤⣦⠀⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⢛⣓⠀⠴⣛⡂⠐⣛⡧⠄⡀⠀⣀⠤⣟⡓⠂⠀⣒⣛⠷⠆⠐⠖⣧⠀⠰⠾⠄⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣌⣩⣄⠈⢫⣥⡀⢩⡽⠒⠒⠀⠖⠲⣋⣉⡁⢀⣩⣽⣉⠀⣀⡙⠂⢀⣙⢃⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣌⣷⡆⠀⠴⣯⡁⠀⠀⣩⡷⠤⠄⠠⣴⠧⠄⠠⣼⣋⣁⣤⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠷⠶⠶⠾⠻⠶⠶⠞⠛⠷⠶⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⣴⣶⣦⣶⣶⢶⣶⣨⣭⣝⡒⠤⣄⡀
⠀⠀⠀⠀⠀⣴⠃⣴⣷⢿⣿⣯⣿⣿⣾⣻⣿⣿⣿⣟⣷⣞⢦⣭⡒⢤⡀
⠀⠀⠀⠀⢰⣿⡀⢿⣿⣿⣿⣿⣯⣿⣾⣿⡃⠉⢘⣻⡟⣻⣿⣿⣷⡶⡌⢢⡀
⠀⠀⠀⠀⣿⣿⣷⡄⠰⣾⣿⣷⣿⢿⣿⣿⣿⣶⣻⣿⣿⠾⢷⢾⣽⣟⣳⠆⢱
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣌⠻⠿⠿⣫⣿⣿⣿⣟⡛⢃⢶⣷⡄⠂⠀⠝⠻⣗⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣆⣰⣾⣿⣿⠁⠀⠀⠀⠈⢻⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠀⠀⠀⠁⣠⣶⣾⣿⣿⣛⣉⡍⠛⢷⣦⣤
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣣⡄⠰⠀⢀⣾⣿⣿⣿⣿⣿⣿⣮⠀⢸⣶⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢟⣔⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣝⠿⣿⣿⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠦⠀⢴⣶⠆⠆⠹⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⠀⠀⠀⠀⠆⡀⠸⠅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣶⣄⣤⡤⣾⢆⡄⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⡟⠙⠂⠈⠙⠻⣿⣿⣿⠇⡠⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⢻⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠁⢁⠐⠠⠀⠀⡉⠉⠻⣿⣿⣤⣠⣄⣤⡈⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠄⠄⠀⢀⣴⣦⠙⢿⣿⣿⣟⣤⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣿⣿⣧⣸⣗⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⣀⠄⠂⠀⠛⢏⠐⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣔⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⢄⣀
⠀⢠⠾⠓⠂⠉⠁⠀⠀⠂⠀⠀⢙⣄⠀⠀⠀⠀⠀⢴⣻⣿⣿⣿⣟⣓⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⣤⢚⡁⠀⣀⣀⢱⠀⢸⠑⢦⡀
⡰⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠀⠆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢯⣿⡇⣭⢑⢿⡄⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⡸⠉⢺⢤⡞⠱⡄
⡇⠀⠀⠀⣀⠴⠚⠁⠀⠀⡆⠀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣫⣶⣿⣿⢻⣿⢻⣧⡻⠀⠀⣼⠀⠀⠀⠀⢀⡠⠚⠁⠀⡇⠀⠉⢢⣳
⡇⠀⡴⠛⠁⠀⠀⠀⠀⣰⠁⠀⢓⠀⢀⠀⠀⢹⣿⡿⣫⣶⣿⣿⣿⣿⡏⣿⣿⣼⣿⣷⠀⠀⣿⠀⠀⡠⠚⠁⠀⠀⠀⢸⠁⠀⡆⠀⢻
⠘⡞⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⣸⢠⠂⠀⠀⠘⢟⣾⣿⣿⣿⣿⣿⡿⣸⣿⣿⡇⣿⠇⠀⠀⠸⣄⠎⠀⠀⠀⠀⠀⢠⠇⠀⠀⡇⢀⡏
⠀⠈⢆⡀⠀⠀⠀⡴⠋⠀⠀⣰⡷⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣵⣿⣿⣿⠻⠋⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢠⠏⠀⠀⢠⣣⠎
⠀⠀⠀⠈⠒⠒⠾⠥⠤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠫⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣔⣁⣀⡠⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠄
⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠹⡄⠀⠀⢸⡇⠀⠄
⠀⠀⠀⣠⣊⣤⠤⠴⠶⠶⠦⣴⣧⣀⣀⣼⠁⠀⢀⣤⢤
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢹⡟⠒⠦⣼⡁⠀⢱
⠀⠰⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣾⠀⠀⠀⡏⠑⠢⡀⢁
⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠈⢾⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢻⠀⠀⠀⠸⠃
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⡇⠀⢀⠁
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡇⡰⠏⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠁⠀⠀⠲⢄
⠀⠀⠀⠀⠈⠂⢠⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠤⠤⠤⠄⠒⠒⠉⠁⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣀⣠⣤⡤⠴⠶⠶⠶⠶⠶⠶⠴⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣀⠀⠀⠀⠑⠀⠉⠓⠶⠤⣤⣤⣤⣄⣤⣤⣤⠴⠖⠛⠉⡠⠋
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠤⠤⠴⢾⡶⠖⠒⠊⠉⠀⠰⠄⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⣀⣤⣤⣀⣀⠀⠈⠀⠀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠀⠐⠀⠉
⠀⠀⠀⠂⠀⣀⣤⠴⠒⠒⠉⠉⠁⠈⢻⠉⠀⠀⠀⠈⠉⠓⠲⡄
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⣀⡤⣼⣶⠤⣄⣀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠸⡇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⢄⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⠇⠃
⠀⠀⠀⠈⢣⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠿⠿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠦⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢠⢠⠏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⢷⢄⢁⡿⢿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣎⠛⣾⣮⣧⠿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⡂⠘⣿⡵⢋⡖⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢿⢲⣿⠟⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠊⡙⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠎⠉⡆⠀⠀⠀⠀⠀⢀⣤⣾⣧⡿⡾⣻⣕⣇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⠔⠁⡠⠃⠀⠀⠓⠀⠀⠐⠀⠀⣰⣄⣷⣦⠿⠿⢭⡵⢾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠐⠁⠠⡀⠀⢄⡔⠀⠀⠀⣀⢿⡾⠿⠁⠀⠀⠀⣱⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⣀⡀⠀⠀⠈⣆⠀⠀⠀⢐⣤⠁⠀⢀⠤⢄⠀⢠⠊⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⢚⠈⣧⠄⡄⣆⠩⡵⠒⠐⠳⣌⣤⠆⠁⠠⠁⢀⣼⠇⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠹⢊⣸⡆⣏⠡⢸⡇⠀⡖⠀⢹⠃⢀⣠⠇⣰⡿⠁⠀⢀⠄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣎⠤⠆⢸⡡⠠⡇⠀⢀⡤⠚⠛⠙⠈⣛⢿⢀⣀⠔⡏⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣟⠰⠛⣇⠀⠀⡇⠀⠀⡇⠀⠀⠙⠋⠀⢸⠋⠀⢀⠇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⠀⠀⢫⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⣸⠀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⣆⡀⢰⠀⠀⡄⠀⢸⡇⠀⠀⡇⠀⠀⡇⣀⣀⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠚⠓⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣀⣈⢁⡀⢁⡈⠁⢐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⣠⠤⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⠐⠄⡀⠄⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠌⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡆
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠐⠒⠲⠦⠠⡤⠤⢤⣄⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⡀⢀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣠⡤⠤⠤⠀⠴⠖⠒⠂
⠀⠀⠀⠀⠀⠄⢀⡀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⠀⣄⠀⠤
⠀⠀⠀⠀⠀⠂⠀⠘⠈⠅⠀⠀⠉⠈⣉⣡⢰⡗⠀⠒⠒⠒⠒⠇⠸⠂⠐⠒⠂⠀⢘⡁⣉⠉⠁⠀⠀⠀⠸⠀⠃⠀⠐
⠀⠀⠀⠀⠀⡆⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⢠⡤⠄⠲
⠀⠀⠀⠀⠀⠁⠀⠺⠀⠡⠀⠀⠀⠀⠀⠰⠐⡆⠀⠀⠀⠀⠀⡇⢚⠀⠀⠀⠀⠀⢐⠉⣉⠀⠀⠀⠠⠄⠀⠀⠂⠀⠘
⠀⠀⠀⠀⠀⠲⠠⠰⡀⡤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠠⠤⣄⢀⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠤⠀⠀⠡⢀⣇⠀⠀⠀⠀⠀⡃⢙⠀⠀⠀⢀⡀⠈⠀⠅⠀⠤⠀⠀⠀⠘⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠤⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠠⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⣠⣶⡿⠟⠛⠻⣝⢻⣦⡀⠀⠀⠀⣤⡾⠛⠉⠙⢯⡛⣷⣤⠀⠀⠀⠀⣤⡾⠟⠋⠛⢯⡛⣷⣄⠀⠀⠀⠀⠀⠒⠲⢤⣸⡆⣀
⠀⠀⣰⣿⠉⠉⠙⠒⠒⢚⣯⡬⢿⡆⢀⣾⡋⠉⠉⠒⠒⠒⣛⣧⠽⣷⡀⢀⣾⡏⠉⠙⠒⠒⠶⢻⣧⡽⣷⠀⠀⣀⡤⠴⠶⠚⣩⠿⣧⠤⣄
⠀⠀⣿⡇⠀⢀⡤⠔⠚⠉⡽⣷⢺⣿⢸⣿⠀⠀⣀⡤⠖⠋⢩⢿⡖⣿⡇⢸⣿⠀⠀⣀⡤⠖⠋⢩⢿⡶⣾⡇⠈⠀⠀⠀⣠⠞⠁⣸⠋⢧
⠀⠀⢿⣷⡚⠉⠀⠀⠀⡞⠀⣿⣼⡟⠘⣿⣶⠋⠁⠀⠀⢠⠏⠀⣿⣿⠃⠸⣿⡶⠋⠁⠀⠀⢠⠏⠈⣇⣿⠃⠀⠀⢀⡴⠁⠀⠀⣿⠀⠈⠇
⠀⠀⠈⠻⣿⣦⣀⣀⡞⣁⣤⣿⠟⠀⠀⠙⢿⣷⣦⣤⣠⢏⣴⣿⡿⠋⠀⠀⠙⣿⣶⣄⡀⣠⢏⣠⣴⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⢛⣛⡛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠈⠿⣿⡶⠶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠛⠋⠁⠐⢒⣤⣤⣾⠿⠛⠛⠛⠲⠿⣶⣄⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠠⣀⢀⣈⣭⠿⢺⠏⠁⣰⠋⠀⢀⣠⡴⠚⠛⠚⠿⢷⣆⣰⠟⠂⠀⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣌⡉⠙⠛⠛⢋⠝⠋⠀⠰⠋⠀⠐⢁⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣤⣤⣴⣾⣛⣥⣤⣤⣶⣶⣶⣶⣶⣤⣤⡿⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣭⣶⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⣿⠃⢠⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⠶⣿⣄⠉⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣶⢶⣭⣭⣭⣭⣉⣐⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡫⠕⠊⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⠒⠤⣀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣫⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⡴⢃⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠳⡄
⠀⠀⠀⠀⠀⢀⡞⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⢦
⠀⠀⠀⠀⠀⡞⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⢣
⠀⠀⠀⠀⠸⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢇
⠀⠀⠀⢀⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⡄
⠀⠀⠀⠸⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢱
⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡄
⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣷
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠈⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠇
⠀⠀⠀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⡇⠀⢻⠀⠀⣀⣀⣀⠠⠤⠤⠤⠀⠐⠒⠒⠒⣲⠖⠊⠉⠀⠉⠳⡆⠀⠤⠤⠤⠄⣀⣀⣀⠀⠀⡾⠀⡎
⠀⢀⡠⠷⠒⢛⣉⡩⠔⠒⠒⠶⢖⠒⠛⣓⣊⣉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠘⣗⠓⠒⠒⠒⣦⡤⠤⠯⢽⡇⢠⠧⢄⡀
⣰⢁⡤⠒⠉⣁⡞⠁⠀⠀⠀⠀⠀⠙⢧⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣩⠟⠉⠀⠀⠀⠀⠼⠀⣼⡒⢤⡈
⣏⠻⠤⣴⣋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⢀⠀⢰⣃⣧⠤⠛
⣏⠑⠒⠤⢄⣉⢉⡒⠒⠢⠤⠤⠤⠤⢀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⠤⠤⠤⠤⠐⢲⠎⠀⠘⣅⠤⠔⠚
⢸⡙⠓⠶⠤⣄⣈⡉⠙⠛⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⢤⡤⠤⠤⠤⠤⠶⠖⠒⠚⠛⠲⣒⣚⠤⠤⠖⠚
⠀⣇⡉⠒⠢⠤⣀⣈⣉⠉⠒⠒⠒⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠤⠐⠒⠒⠊⠉⣉⣀⣠⠤⠔⠒⣸
⠀⢺⣉⠙⠒⠶⠤⢤⣉⣉⠙⠛⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠛⢋⣉⣉⠤⠤⠶⠚⢋⡿
⠀⠈⣧⣉⠒⠤⠤⣀⠀⣀⠉⠉⠁⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠒⠂⠉⠉⠁⢀⣀⣀⠤⠔⠊⣹⠃
⠀⠀⠘⣌⡙⠲⠤⢄⣀⡉⠉⠉⠛⠓⠒⠒⠒⠶⠶⠒⠒⠒⠒⠒⠒⠲⠶⠖⠒⠒⠒⠛⠋⠉⠉⢀⣀⡠⠤⠒⣩⠃
⠀⠀⠀⠘⢯⣐⠢⠤⣄⣈⣉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢂⣉⣉⣁⠤⠄⣒⠽⠃
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠬⠭⠍⣉⣙⣛⣉⣑⣒⣂⣒⣒⣒⣒⣒⣒⣋⣙⣛⣋⠩⠭⠭⠅⠒⠒⠚⠉⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⣠⡴⠋⠁⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣄⠀⠀⠀⠀⢠⡾⠁⠀⠀⣀⣀⣀⣤⣤⠤⠤⠦⠤⠠⠄⣀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠉⠛⠷⠶⢶⣿⠗⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⣦
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⡼⢀⣠⣴⠶⠾⠟⠛⣻⡟⠛⠛⠛⠛⠿⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⠟⠋⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣶⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠋⠁⠀⠀⣿⠀⠀⠀⠉⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣄⣾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢈⡇
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⣠⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣀⣀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣴⣶⣤⣾⣷⣿⣶⣿⣿⣿⣿⣿⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠉⠉⠉⠋⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠄⠠⠀⣀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠠⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠊⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠂⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣘⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠙⠒⠂⠖⠂⠦⠤⠤⠤⠄⠤⠤⠄⠀⠀⠀⡀⢀⠀⠀⠠⠤⠤⡤⠠⠤⠤⠤⠖⠒⠲⠐⠒⠋⠉
⠀⠀⠀⠀⠘⠀⠰⡀⡦⠤⠄⠀⠀⢀⠀⢀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⡀⠀⣄⢠⠀⠀⠀⠤⠤⠴⠠⠆⠂⡃
⠀⠀⠀⠀⢈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠅⠨⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠨⠀⢐⠇⠦⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⡤⢴⠀⠀⠀⠀⠀⡒⢘⠉⠈⡅
⠀⠀⠀⠀⠠⣀⣀⡀⢀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⡁⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠅⠩⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠆⠰⠀⠀⠀⠀⠀⠆⢘⠀⠉⠉⠉⠉⠇⠪⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⣽⡶⠴⠷⠶⠧⠮⠶⢵⣝⣔⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣭⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢵⡙⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣱⠝⠉⠀⠀⠀⢠⡾⣷⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣬⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣣⡿⠁⠰⣶⠯⢶⢖⣚⡷⠟⠉⠉⠛⠙⠛⠓⠶⢤⣀⡀⠀⠀⠈⢆⡊⢆
⠀⠀⠀⠀⠀⠀⡼⢙⠝⠀⠀⠀⠹⠻⣦⣨⠏⠀⠀⣠⠄⢄⣀⠀⠀⠈⠐⠐⡝⢢⡀⡀⠀⠣⡆⢧
⠀⠀⠀⠀⠀⣸⣴⡟⠀⠀⢀⠤⠄⠐⠾⢧⡀⠀⠀⣘⣣⠔⠈⠉⢓⢒⠶⡤⢫⠬⣀⣈⠒⡀⢳⡆⢇
⠀⠀⠀⠀⢀⠗⡽⠀⢀⠔⠹⠃⠀⠀⠀⠀⠙⢆⣠⠿⠃⠀⢆⡼⠋⠉⠉⠉⠹⣔⣻⣜⡉⢉⡀⢇⡺⡀
⠀⠀⠀⠀⣈⡼⡇⠀⠘⠀⠀⣀⡠⠤⣤⣠⡶⣿⢿⠿⠛⠢⣾⠀⠀⠀⠀⠠⠚⠛⡧⠛⠿⠿⠢⣸⡇⡇
⠀⠀⠀⠀⣷⣽⠀⣀⢴⠶⠿⠣⡄⣠⢫⡿⠷⡿⠁⠀⣀⡠⡾⠶⡚⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼
⠀⠀⢀⠔⠓⠾⠶⠿⢇⡀⢀⣰⣴⣁⣿⣿⣿⠀⢠⣿⣿⡟⠀⠀⣳⠀⠀⣡⣀⣀⣀⣀⢀⡀⠠⠿⠷⠚⠢⡀
⠀⠀⠀⠓⡤⠤⣤⢄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⣤⠤⢤⠚
⠀⠀⠀⠀⣧⣤⣤⢸⣀⣀⡀⠉⠉⡉⢸⠉⠉⠉⠉⠉⡏⠙⠉⠉⠉⠉⠉⡇⢉⠉⢁⣀⣀⣀⡀⣧⣤⢼
⠀⠀⠀⠀⡗⠂⠚⠛⠥⠭⠍⠉⡉⣳⢼⡟⣛⣛⣛⣛⣇⣚⣛⣛⣛⣛⣙⡏⡏⣉⠉⠭⠥⠼⠃⠓⠒⢺
⠀⠀⠀⠀⣻⠰⢶⣢⡤⡀⣄⡠⠤⣤⢀⠀⣀⣀⠀⢀⣀⣀⣀⣀⢀⡀⢀⣠⣤⣄⣠⣤⠤⢤⠶⠖⠒⣛
⠀⠀⠀⠀⢇⠈⢙⠀⠃⠐⠀⠒⠒⢻⢸⠏⠉⠭⠤⠤⡏⠹⠬⠭⠍⠭⠸⡇⡗⠒⠒⠒⠀⢸⠀⡋⣁⡸
⠀⠀⠀⠀⠘⡍⢹⣒⡟⠓⠒⠒⠶⢾⢸⡦⠶⠶⠶⠦⡧⢴⠶⠶⠶⠦⠴⡇⡷⠒⠒⠒⢛⣻⢲⡍⢩⠃
⠀⠀⠀⠀⠀⠱⠄⢀⣀⣀⣉⣉⠁⠉⠈⠁⠀⠀⠒⠀⠃⠘⠒⠂⠀⠀⠈⠁⠉⢉⣉⣀⣀⣀⡀⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢂⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⡁⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⡂⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠙⡄⠀⠑⢶⠉⠐⠢⡒⠒⠤⡠⠤⢄⣀⠤⠤⢠⠔⠒⠠⣴⠂⠒⠰⡉⠀⠑⢄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠁⡏⡖⠒⠂⠳⠤⠀⠱⠤⠀⠰⠤⠀⢉⣠⡄⠀⠱⠤⠤⠤⠓⠒⠒⠚⠁⡇⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠒⠓⠗⠀⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⢤⠤⠀⠄⠐⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠤⡤⠀⠀⡀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣼⠀⠠⠤⠐⠂⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠤⢄⣄⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⢹⠀⡏⠀⠀⠀⠀⠀⢀⣀⡀⠤⠐⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⣀⠀⠀⠀⠀⠈⠉⡏⠉⠉⠀⠀⠀⠉⠀⠉⠉⠀⠉⠀⢹⢈⠀⢀⠀⢠⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣍⡉⠉⠁⠀⠒⠒⠃⠀⠒⠒⠒⠒⢲⠲⡖⠂⠀⠀⠀⠈⠉⠁⠀⢀⣰⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠂⠠⠤⠤⠤⠤⠤⠼⠤⠧⠠⠤⠤⠀⠀⠐⠂⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠄⠀⠀⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡛⠝⠒⠈⠉⠉⠉⠉⠙⠛⠒⠠⢀⠈⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡫⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠐⠛⣐⡀⠩⠅⠀⠀⠐⠀⠀⠀⠒⢀⣀⣀⣀⡀⠒⠀⠀⠀⠀⠀⠀⠤⠍⢁⣐⣲⠁⣬⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢉⠤⠒⠉⣁⠠⠤⠐⠒⠀⠉⣉⣉⡁⠀⠠⠤⠤⠤⠤⠤⠄⠀⣈⣉⣉⡁⠐⠒⠂⠤⢄⡍⠀⠗⠤⡈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠠⠆⣁⣠⠐⠐⢁⡉⠥⠤⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠠⠠⠌⢉⡀⠂⢲⠀⣘⠡⠄⠚⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣈⠑⠒⠤⠄⣉⣉⠉⠒⠒⠒⠚⠩⠭⠭⠤⠤⠤⠤⠤⠤⠭⠭⠭⠉⠒⠒⠒⠒⠊⣹⠃⠀⡨⠔⠒⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢍⣙⠒⠒⠠⠤⠄⣉⣁⠀⠉⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠒⠀⠘⠉⢈⣉⡁⠠⠥⠈⠖⠐⢉⣡⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⢄⣉⠁⠒⠂⠤⠤⢀⣀⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⣁⣀⡀⠠⠤⠐⠒⠈⣉⡠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠢⠄⣈⠉⠙⠀⠒⠒⠠⠤⠤⠄⠈⣉⣉⣉⣉⣉⣉⣉⡉⠁⠤⠤⠤⠀⠒⠒⠀⠋⢈⣁⠤⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡑⠢⢄⣈⠉⠐⠒⠒⠀⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠒⠒⠈⠉⣁⡠⢔⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢔⠂⠤⢈⣈⡉⠀⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⣉⡀⠥⠄⡂⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠤⠭⠉⠉⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠭⠥⠤⠐⠒⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠋⠉⠉⡉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠙⢛⠛⠒⠒⠶⠤⢤⣀⣀⡀
⠀⠀⠀⢀⡴⠚⠉⠀⠐⢶⡀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡏⠀⠁⠀⠀⠀⢈⡉⠉⠒⠶⣄⠒⠒⠚⠻⢏
⠀⠀⢰⠃⡴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠰⢄⠙⣆⠖⠂⠀⠞⠳⡖⠚
⠀⠀⠸⡀⠑⢶⣀⠀⠀⠈⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢰⣣⠞⢀⡟⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠈⠲⣤⣀⡉⠒⠶⠧⣀⣀⣑⣀⡀⠀⠀⠀⣠⡀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣤⠊⢀⣀⣠⡤⠖⠋⢀⣤⣾⡗⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⣦⣤⣀⣀⠉⠉⠓⠒⠒⠛⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⠋⠉⠉⢉⣀⣠⡴⠞⣿⣾⢛⡇⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠈⠉⢻⠳⠒⠒⠲⠶⠶⠶⠶⠶⠶⠖⡶⠒⠒⠋⠉⠟⡍⠉⠀⣀⣉⠭⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢄⢱⡇⠀⠸⠦⡀⠈⠀⠑⢄⠀⠀⠀⠂⠀⠀⠀⡼⠀⠀⠀⠀⢀⠀⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠑⠀⠿⡀⠀⠘⠷⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⢠⠀⠀⡇⠈⢢⠄⠀⠈⢷⡀⠀⠘⠇⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⢡⡴⠀⠀⢀⣠⠀⠁⠀⠈⠀⠀⠀⠀⢿⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⡘⠑⣄⠀⠀⠛⢢⠀⢸⣇⠀⠀⣷⡄⡄⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢢⣄⠀⠀⢱⣇⠈⠓⢠⠈⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢄⡼⠉⠳⣤⠆⠀⠢⡀⠈⠀⠸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠁⠀⣀⠀⠀⠠⠚⢭⣀⡴⢣⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠦⠃⠠⠛⠀⢀⡄⠹⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈

⠀⠀⠀⠀⢀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠤⠒⠀⠄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠡⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠀⠊⠀⠀⠁⢀⠀⠀⠈⠆⠀⠂⠀⠀⠀⠁⢀⠂⠀⠀⠀⡔⠁⠀⠑⠄
⢀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢁⠀⠹⠐⠀⠀⠀⠀⠀⠀⠒⠈⢀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠢⣀⡠⠃⠀⠀⠁⠄⠈⠄⠈⢀⠀⠀⠸⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠀⠑⢄⡀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢀⠂⠐⡀⠀⠀⠈⠀⠈⠁⠀⢀⠀⠀⠀⠀⠃⠄⠀⣄⠡⡄⠀⠑⠤⠤⠐
⠀⡀⡀⠀⠀⠀⢌⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠅⠀⠀⠀⠀⠈⠀⠠⠀⠐⠀⠁⠀⣀⠀⠠⡀
⠀⢸⡀⠈⠀⠀⠀⠈⠐⠠⡀⠀⠀⠒⠋⠑⠀⠀⢀⣤⣀⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡄⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⡌⢃⠀⠀⡀
⠀⠀⠣⡀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠂⠀⠐⠀⠀⢹⣿⣿⣿⣷⣿⡄⠈⠢⠄⠀⠀⠀⠇⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⣀⡩⠞⠁
⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀⠀⠀⠈⠐⠀⠐
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢢⡢⠀⢀⡀⠀⠀⡠⠀⠀⣀⣀⠠⠐⠁⠀⠀⠠⠀⠠⠄⠂⡀⠀⠀⡀⠤⠀⠀⠀⡠⠂⠁⠈⠉⠙⢂⠐⠒
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠀⠐⠁⠀⢊⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠠⠀⠀⠐⠀⠀⠉⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡂⡄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠑⠄⡀⠀⠀⢀⠄⠁
⠀⠀⠀⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⢉⡃⠀⠀⢠⠀⢂⠀⠀⠀⢨⠀⠀⠑⠠⠆⡀⠀⠀⠀⠀⠀⡠⠒⠂⠐⠠⡀⠀⠈⠁⠉
⠐⠂⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢘⠁⠀⠀⡅⠃⠀⠸⡄⠀⡄⠀⠀⠀⠁⠐⠃⣀⠠⠀⠀⠀⠄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠁⠀⠉⠀⠀⠀⢁⠀⠀⠰⡀⠀⠆⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡀⠀⠐⠌⠐⠡⠄
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠀⢈⣉⢐⠀⠀⠐
⠀⠀⠀⠐⡁⠉⠒⠄⠐⠀⠐⢄⠀⠀⢀⡀⡠⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⣴⣆⣀⡀⡀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠉⠉⠁⠢
⠀⠀⠀⡀⠀⠁⢂⡀⠊⢀⠀⢀⡁⠈⠁⠀⠀⢠⠊⠁⠀⠹⠓⠤⡀⠀⣠⣾⣿⣿⡟⣿⣿⣿⣿⡿⣿⢿⣟⠀⠀⠀⢇⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢘⡤⠤⢠⣀⠀⠀⠘⠄⡀⢈⡀⣀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡇⢸⣿⣿⣿⣿⡇⠉⠋⠁⠈⠁⠉⢉⠉⠀⠀⠀⠀⠁⠂⠀⠀⠀⡆
⠀⢀⣭⣦⣴⣿⣿⣿⣦⠀⠐⠀⠀⠀⠀⠀⠀⠱⡠⢄⣀⡀⠔⢋⠀⠀⠙⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠄⠐⠁
⠀⠙⣿⣿⣿⣿⣿⣯⡟⠀⠀⠀⡀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠠⠊⠀⠑⠆
⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⢀⠊⠀⠀⠳⢄⠀⠀⠉⠀⠀⡀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⢀⠠⠀⠁⠀⠈⠀⠉⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠑⡀⠀⠀⠀⡠⠀⠐⠒⠂⠀⡀
⠀⢀⣴⠃⠀⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠚⠈⠉⠁⠢⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠰
⠀⢸⣿⣆⠀⠀⠀⢠⠆⠸⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠻⣿⣦⣄⣀⡥⠀⠀⠢⡀⠀⡀⠔⡡⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠀⢀⠠⠊
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐