Aquatic Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⢟⣿⣶⣃⣠⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣼⢡⡞⣱⢟⣿⢷⣾⣁⡠⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⣼⢣⣟⣼⢣⡞⣱⢏⡽⣻⢷⣾⣿⣿⡿⣫⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⣿⣽⣷⣿⣾⣷⣿⣾⣵⣯⣾⣵⣯⣿⣿⣿⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢁⡯⠞⠛⠛⠛⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣭⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣻⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⢒⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⣫⣿⣿⣿⣿⣗⡩⠙⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⢟⣿⣿⣿⣿⣟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⡝⣧⠀⠀⠀⠀⠀⣀⠴⣺⣿⠃⠀⠀⢊⢿⣿⣿⣿⣯⣭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣰⣯⠖⠛⢿⣮⣷⣄⠀⢀⠀⠀⢀⡿⢸⣧⠰⣤⡶⣛⡵⣿⣿⡏⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣟⣿⡧
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠠⣿⣿⢿⣿⢇⣿⣿⣿⠀⠈⠀⠀⠈⣳⣤⣿⡆⢟⡾⣫⣾⣴⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡾⡷⠋⠀⠀⠀⠀⠀⠈⣿⣿⡟⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⢾⣭⣍⣉⠙⠒⠶⢤⣄⡀⠈⠉⢉⠉⠀⢀⠀⠀⠀⠀⠀⠀⢰⣽⣿⠃⣿⣿⣻⣿⣿⣿⣿⣶⣤⡀⠀⣸⣿⣿⣿⣿⣾⠏
⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣄⠈⡛⢦⡑⣤⣠⣀⠀⠀⠀⠈⠀⠀⢀⠞⣿⡟⣸⣿⣿⡿⣵⣿⣿⠿⠛⠉⢀⣰⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠸⢭⣛⣛⣉⣉⣛⣛⣛⣦⣈⣿⣎⣿⣿⣆⡀⠐⣈⣀⢁⣡⣾⡟⣡⣿⣿⣿⣾⡿⠿⠿⠒⠀⠀⣼⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠙⠻⠿⢯⣭⣍⣉⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⡿⠿⢻⠍⠄⠀⠀⢀⣠⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣾⣯⣭⣭⣵⣶⣿⠿⠋⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⠿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣿⡟⠻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⡄⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡦⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡠⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡁⠀⠀⠀⠀⣰⠥⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠂⣀⠔⠀⠀⠀⣠⠎⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡸⠁⠀⠀⠀⠀⠀⡰⢡⠎⠀⠀⠀⠀⡰⢻⠀⢀⠤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⢠⡰⠁⠀⠀⠀⠀⠰⠁⠀⡔⢁⡴⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢃⡰⢾⠒⢩⢔⠜⠉⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠜⠀⠆⢰⠁⠆⠀⠀⠀⠀⠀⡠⢊⠔
⠀⠀⠀⠀⠀⠹⡦⡄⠀⠀⢃⢰⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠸⢀⡌⠀⢠⠀⡜⠀⠀⠀⡠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠘⡌⡆⠀⠈⢻⣀⠀⠀⠀⠀⠀⢄⣣⡀⠀⠀⢀⡇⡏⠠⠀⢠⠋⠀⠀⠀⠊⡰⠃
⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠈⠦⡁⠄⠀⠀⠀⠀⠈⠑⡦⡄⠀⠃⢃⡰⢀⠆⡀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠈⠢⣱⠀⠀⠀⠀⢀⠖⣼⠎⠀⢨⠓⣼⠀⡇⠔⠉⠇⠀⣠⡴⠂⠀⠀⠀⢀⠜⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠠⡄⡿⡸⡌⢀⠜⢔⠟⠉⠀⠀⢀⣤⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⢠⡸⡌⢃⠀⣠⢃⡧⢰⡴⢃⡞⠁⠀⠀⠀⡴⡱⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢎⠲⢄⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⢹⠸⣀⠟⢡⣎⠔⡏⢠⠻⠀⠀⠀⠀⠀⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠠⣤⣀⣀⠈⠣⣄⡀⠀⠸⢀⡧⣦⡋⠤⠊⠀⢸⡘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⢦⢜⣌⢣⣦⢈⠜⠇⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⣠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡎⣇⠎⡘⢀⡠⢤⠶⠚⢛⠟⠲⠖⠾⠭⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠺⠋⡜⠰⡡⠊⢀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⡄⢷⡡⢊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⠛⠁⠀⠈⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣠⣀⣤⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠉⠉⠀⢀⣤⣴⡿⢿⣟⣿⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⠈⣨⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⡿⣬⢹⢿⣿⡿⠋⢋⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⠿⠛⡟⠉⠀⠀⠑⢭⣦⠴⠟⡼⢡⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⡿⠟⠛⠛⠛⠛⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⠖⠊⣩⠉⠂⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⡿⣆⠀⠀⠀⡀⠈⠢⠄⠀⠀⠐⠊⠀⠀⠊⢁⡠⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⣌⠲⣄⣠⡈⠲⠤⠤⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⠃⠀⠀⢠⣴⣾⠿⣛⠛⠊⢉⣿⣿⠛⠳⠦⢬⣍⣙⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣭⡾⠃⠀⠀⢀⣠⣴⣾⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣀⣤⠶⠚⢿⣿⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⢷⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣄⣈⢹⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣀⣠⣤⣤⣬⠻⣾⣶⣿⣷⢀⣀⡀⠀⡀
⠀⠀⢠⠊⠀⢀⢠⠻⣍⣀⠄⠈⠉⠒⠛⢿⣿⣦⡀⠀⠀⠀⢿⣀⣠⣼⣿⡿⠿⢛⣻⣿⠏⠀⢈⣹⣛⣧⡤⠥⠚⠇⠀⣢⠀⣢⡄
⠀⠀⠸⣇⢸⣬⣿⣷⣌⣻⣶⣤⣐⣲⠶⠦⠽⠿⣷⣦⣤⣀⢀⣿⣿⣿⣿⣋⣭⣽⣿⣿⡶⣛⣫⣭⡭⠁⢀⣀⡔⡼⢠⢇⡖⠉
⠀⠀⠀⠙⢌⢮⣝⣷⣽⣿⣿⣷⣌⡋⠙⠲⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⢧⣾⠿⢛⣉⣁⣈⣃⣩⣴⢟⣵⡋⠉
⠀⠀⠀⠀⠀⠉⠚⢿⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣶⣿⣵⣿⣿⣿⣿⣟⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠉⠋⠙⢿⣿⣷⣶⣦⣭⣽⣿⣿⣿⣭⡿⠿⠾⠟⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡤⣤⣤⣀⣀⣀⠀⣀⣤⣶⣾⣵⣰⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⢾⣯⡻⣿⢿⣤⡶⠈⠻⣿⣭⣙⠻⠿⣿⣿⣿⣿⣇⠈⠀⠁⠐⢢⠙⠒⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣍⠓⠄⠀⣠⡄⣼⣹⣿⣿⣶⣤⣙⠻⣿⣧⠀⠞⠓⠀⠘⠀⠒⢢⠳⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠀⠀⠀⠉⢜⣵⡿⡿⠿⢿⣿⣿⣿⣬⣛⢶⣄⣰⠋⠙⠢⢤⠤⠖⠛⠳⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣮⡿⣿⣷⣦⠈⢲⠰⢀⠍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⣦⣭⣁⡀⠀⠀⠉⠛⢿⣿⣷⣞⣿⣿⠀⣦⣤⣀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠙⠻⣿⣿⣿⡆⠲⡄⢹⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⠀⠀⠻⠿⠟⠛⠀⠘⢿⣿⣿⣿⣿⡢⠘⢿⣿⣷⠀⣁⣬⣔⣊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣴⠚⠲⣏⠙⡆⠀⠀⡇⠀⣈⠃⡀⠘⠊⢳⡀⠘⣿⡟⢈⡡⠴⠒⠆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⣝⠢⣄⢈⣧⡘⢄⠐⠒⠊⣉⢹⠔⣉⡀⢈⡇⣼⡿⠡⠋⠠⣒⣚⡛⠋
⠀⠀⠀⠀⠀⠀⢀⠤⡘⢁⢤⡤⣙⢮⡣⠀⠉⠲⣅⣒⣠⠞⢀⣈⣁⣨⣼⣿⠟⠁⣀⠴⠋⣉⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠥⣙⡲⠬⠁⠂⣀⣴⣾⣿⣿⣿⣿⣿⡁⠀⠤⠤⠤⣄⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡴⠛⠉⠹⢻⣿⣿⣿⣿⡇⠀⠁⢀⡠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⢠⡁⠔⠁⡔⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢻⠳⠾⠔⠅⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡌⠙⡣⠖⠌⠀⢑⣳
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠰⣧⢀⡤⠂⢠⠄
⠀⠀⠀⠀⠀⢀⠈⢦⣠⢀⠴⢛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠑⠀⢠⣴⡀⣀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⡄⢈⢳⠆⣐⣥⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠦⣀⣬⣩⡉⣠⢔⣨⠅
⠀⠀⠀⠀⠀⠀⠫⣀⡉⢅⡤⡰⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣀⣀⡈⣭⡌⢈⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠑⣭⡙⣆⢀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢈⢣⣠⡇⠈⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠘⢣⣷⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢩⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠁⣼⠄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢉⠋⠀⠗⠉⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⠋⠉⠘⠀⠀⠀⠀⠀⣀⠀⠑⢄⠉⡺⠠⢈⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠚⢠⡾⠀⠈⡠⠀⠀⠀⠀⠀⡄⠈⢊⠀⣺⠗⠆⡀
⠀⠀⠀⠀⠀⠀⠁⢤⡀⢰⠆⠠⠮⡄⠀⠀⠀⠀⠄⠈⠀⢠⠝⡀⠀⣊
⠀⠀⠀⠀⠀⠀⢈⡀⠀⣸⠂⠙⠛⠠⠂⠀⠀⢀⠁⠢⢴⡇⠤⠤⢂⠁
⠀⠀⠀⠀⠀⠄⡀⠁⠌⠸⡖⠊⠤⡱⠀⠀⠀⢬⢢⡀⣾⠆⠥⠴⢠
⠀⠀⠀⠀⠀⠀⠈⠐⠨⠘⠿⠆⠀⠀⠀⠈⠣⠀⠪⢎⡇⣀⡤⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⢰⣯⡁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⡠⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢘⢆⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⣀⡄⠀⠀⠀⠀⢘⡆⠀⠀⠀⢠⠙⠀⠀⠀⡀⠀⠀⠀⠐⡝⠀⠀⠈⠠⢠⠉⠀⣀⣴⠀⠀⠀⠀⠀⣒⡀⠀⠀⠀⢠⠋⠀⠀⠀⢄⠀⠀⠀⠐⡙⠀⠀⠀⠀⣬
⠀⠉⠉⠑⣀⠀⠀⠀⠈⣑⡏⠠⡀⠓⡀⠀⠀⢀⠙⣀⠀⠀⠐⢒⣸⡋⠤⡈⢓⠀⠀⠁⠈⠁⡙⢀⡀⠈⢉⣸⡋⢀⡈⢒⠀⠀⠀⠀⠀⡁⠆⠀⠐⢂⣺⠉⢄⠘⢂
⡶⣔⡭⠊⠉⣳⠀⠀⠀⠹⠀⠀⠇⠀⠙⡦⣞⡕⠈⠉⡲⠀⠀⠀⠛⠀⠐⠏⠈⠹⠦⣞⠕⠈⠉⡶⠀⠀⠀⠟⠀⠰⠇⠈⢱⠴⣊⠕⠉⠉⡶⠀⠀⠈⠗⠀⠸⡇⠈
⠀⣣⠄⠀⢤⡷⠶⠂⠙⢀⠀⠴⠤⠀⠀⠘⡡⠈⠀⢵⡷⠖⠂⠙⣀⠀⠴⠤⠐⠀⢘⡤⠈⠀⣼⠶⠖⠀⠛⣀⠀⠶⠤⠀⠀⢘⡤⠁⠀⣼⠴⠖⠈⠓⣀⠀⠦⠄
⠀⠀⢴⣀⣼⡆⠀⠦⠀⣼⠄⠀⢠⣀⣀⠀⠀⣖⣀⣾⡄⠐⠄⠀⡽⠄⠀⢠⣀⡀⠀⠀⣞⣀⣶⡄⠐⠄⢀⡽⠀⠀⢠⣀⡀⠀⠀⣆⣀⣾⡀⠐⠄⢀⡧⠀⠀⢤⣀
⠀⠀⠛⠍⠀⠠⡤⠀⣬⣁⡄⠀⢄⣫⠀⠀⠀⢫⠙⠀⠡⡤⢀⣬⣠⡄⠀⢀⣣⠀⠀⠀⢫⠉⠀⢡⠄⢀⣬⣠⠄⠠⣈⣣⠀⠀⠀⠫⠃⠀⢠⠄⢀⣌⣠⠄⠠⣘⣇
⠠⡀⠓⠀⠀⠀⠀⠑⢉⠸⠁⣀⠄⢹⡃⠀⡈⠓⠀⠀⠀⠀⠀⢉⠺⠁⣠⠀⣙⠃⢠⡈⠓⠀⠀⠀⠈⠐⣍⠮⢁⣠⠈⣹⠁⢠⡈⠃⠀⠀⠀⠈⠀⡁⠎⢀⣠⠈⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠃
⣤⣀⠐⠛⠽⠿⢦⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇
⠛⠒⠀⠀⠀⠀⠀⠙⠷⠦⣈⣹⡯⣤⣶⣞⠓⠄⠀⠀⠄⢤⣄⠀⠀⠒⠛⠶⣄⠀⠀⠀⣴⣾⣿⣿⡟
⠀⢉⠉⡁⠀⠉⠁⠀⣉⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⣀⠀⠀⣨⠉⠂⠀⠀⠀⠌⠙⠛⣝⡻⠿⢿⣿⠿⢿⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡠⠀⠒⠂⠀⠶⠶⠚⢷⣶⡭⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠘⠂⠀⠶⠀⠀⠀⠄⠀⠢⠀⢉⠒⠀⡦⢤⡶⢤⡐⠛⠛⠳⢦⡴⠤
⠀⠀⠀⠤⢤⣬⣁⣀⣠⣄⣈⠁⠈⠩⠷⠶⠶⣶⠤⠤⠐⠀⠀⠀⠀⢠⣴⣤⣀⡀⠀⠢⠤⠚⠋⢁⣀⣀⠀⠀⠀⠠⠶⠀⠀⠐⠄⠀⠀⠀⠐⠖⠀⠤
⡴⠦⢄⣀⡤⠌⠙⠛⠻⠦⠉⠓⠦⠄⠠⢦⣄⡁⠀⠶⢾⣿⣒⣒⡛⠋⠉⠁⠀⢀⣀⠀⠁⠒⠲⠟⠛⠛⠓⣶⣤⡤⠀⠀⠀⠀⠀⠀⠤⠶⠛⠓⠦⠠⣄
⣠⣀⣤⣴⣿⣷⣤⣤⣄⡛⠃⢀⣠⣤⣤⡀⠉⠛⠒⠀⠀⠈⠉⠉⠉⠉⠙⠿⠿⠿⠷⠶⠶⢦⣤⡄⠤⠄⠀⠀⠀⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⣟⠛⢛⣛⠳⠶⠄⠀⠀⠀⠀⠀⠀⣀⣠⣬⣁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⣀⣠⡤⠶⠈⠀⢀⡀
⠀⣀⣤⣤⣤⣄⣀⣉⣁⣀⣀⠀⠀⢀⣀⠀⠈⠉⠀⣀⣀⣀⠠⠠⠖⠒⠀⠈⢉⣴⠤⢶⣦⡄⠀⠀⠀⣀⣀⣀⣠⣴⣶⠿⣟⣉⣭⣡⣤⠀⠀⠀⠉⠀⣠
⠀⣉⣽⣿⣿⡿⠛⠛⠛⠛⠛⠷⣄⣀⣀⠀⠀⠀⠉⠁⠈⠛⠗⠂⠀⠒⠒⠆⠀⠀⠀⠈⠀⠀⢀⣉⣉⣀⣀⡀⠀⠀⣀⣠⣼⣿⠁⠀⢀⣤⢤⣤⠴⠞⠋
⠀⠛⠿⠿⠿⠿⠿⠶⠶⣤⣤⣤⣈⣙⠛⠶⠤⠄⠉⠙⠛⠀⠀⠤⠤⠤⠖⠂⠀⠹⣦⣶⠶⠿⠯⠭⠀⠀⠠⠤⠭⠭⠍⠉⠁⢀⠀⠈⠀⠀⢀⣀⣀
⠀⣐⣒⠀⠦⣤⣄⣀⣀⣠⣼⠿⠛⠛⠛⠒⠒⠒⠒⠚⠛⣛⣳⣶⣤⣤⣴⣶⣶⡶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⣤⣤⣶⣶⣶⢾
⣿⣿⣿⠿⠶⣄⡀⠉⠉⣉⣁⡀⢀⣠⣤⣄⣉⠉⠀⠀⠈⠉⠉⠉⢉⣥⡶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠄⠀⠀⢘⣛⠛⠋⢉⣉⣥⣌
⣤⣴⣶⣶⣶⣿⣿⡛⠛⠛⠛⠿⠛⠉⠉⠉⠉⢉⠛⠋⠉⠁⣀⣠⠀⠀⠴⢶⠶⠖⠛⠀⠀⢀⣀⡠⠼⠁⠀⠀⠀⠀⣠⠴⠶⠀⠀⠈⠙⠻⠿⠿⠿⠃⠈
⣿⣿⡿⠿⠿⠿⠟⠛⠻⠶⠶⠶⠒⠂⣠⠴⠚⠻⠿⠛⠒⠉⠉⠀⠈⠙⠂⠠⠖⠚⠋⠉⢋⣩⣥⢤⡤⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⢀⡄⠀⣠⣄⣠⣴⣾⣿⣿⣿⠗⢀⣀⣀⡀⠀⠀⣀⣀⡴⠋⠀⠠⠴⠂⠴⣾⣶⣦⠀⠀⠀⣹⣿⣿⣶⣦⣄
⠀⠀⢠⣤⣄⣀⣠⠔⠂⠀⣀⡀⠀⠉⠁⠀⠀⣈⡽⠟⠛⠛⠛⢉⣠⡾⠋⠀⢀⣠⠴⠛⠉⢙⣿⠟⠀⠀⠦⣄⠀⠈⠛⠋⠀⠀⠙⠛⠋⠉⠉⢉⣡⣄⣀
⠀⠰⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠁⠠⠖⠂⠀⠈⠋⠉⠀⠀⠈⠉⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠂⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠖⠶⠶⣒⣶⢞⣛⣿⣽⣿⣿⣒⠶⢤⣰⢶⣶⣾⣷⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠟⢲⡌⢻⣮⣉⡘⢿⡼⣀⣴⣿⣍⠻⣿⣟⡻⣷⣮⣝⡺⣴⠿⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡄⢸⣿⠆⠻⡟⠍⠻⡟⢿⠛⠟⢈⡃⢉⠻⡿⣯⢻⣿⣿⣦⣜⢥⠿⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢳⡆⣻⣏⠀⠇⢨⠀⡞⠀⠀⠀⠐⠀⢸⣆⡈⠜⣸⣿⣿⣿⣿⣷⣝⣭⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣴⠟⣛⣉⡉⠛⠓⠳⠶⠊⠙⡷⣦⣤⣄⣠⠠⠺⢈⣡⠂⡋⠹⠟⣻⣿⣿⣿⣮⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣌⣍⠩⡍⠉⡁⢒⠒⢦⣞⣉⡁⣀⠀⣠⡾⠛⡋⢡⠊⣱⣶⣾⣽⡻⣿⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣤⡤⢀⣢⣘⢿⣿⣿⣿⣿⣿⣏⡳⠞⠁⠺⣿⣯⣿⣿⣿⣿⠷⢝⣿⡞⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠉⠙⠛⠓⠉⠓⠂⠉⠀⠀⠀⠀⠈⠛⠿⠟⠋⢴⣿⣿⢿⣧⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⢴⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠈⣩⣴⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣦⣀⠀⠘⣿⢷⣜⢹⡅⠀⠀⠀⠀⠀⠿⢟⣛⣿⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⠟⠙⠲⢬⣯⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⡏⣼⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠁⠀⠀⠀⠀⠈⠻⣿⣧⢀⣤⣄⠀⢰⣶⡷⣾⢱⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠈⣿⣿⣷⣙⣛⣻⣥⠞⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⣿⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⢽⣻⣿⡀⠀⢠⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣯⣽⣿⣿⣷⣬⣿⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣵⡿⢛⣿⣿⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⣴⢿⡿⠃⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣀⣀⣠⣿⣿⣷⣇⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢤⣾⣿⣿⠆
⠀⠀⣠⢴⣯⣿⠛⡇⠘⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡌
⠀⠀⢃⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡀
⠀⠀⠀⠀⠉⠑⠒⠂⠀⢾⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⢤⣄⠀⠀⠀⠒⠋⠑⠄⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⡿⠇⠀⠀⠀⠀⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠛⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⡤⠀⡿⠀⠀⡆
⠀⠀⠐⣆⡤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡇⢀⠀⣷
⠀⠀⠀⠻⣴⠄⠀⠀⡛⠻⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣾⣷⣸⠀⠸⡆
⠀⠀⠀⠻⣇⣀⡐⢦⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠉⢹⠀⠀⠹⡄
⠀⠀⠀⠈⣻⡛⠿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠉⢠⠀⠀⠀⠀⠈⣇⠀⠀⠀⣼⢀⠀⢸⠀⠀⠀⠹
⠐⢾⣯⠖⢹⣷⣦⡏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠘⣧⢸
⠀⠀⣹⡾⣿⣿⣿⢷⡸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⣆⠀⢿⡆⠈⢻⡀⠀⠀⡄
⠙⣣⣿⣧⣼⣧⣿⣶⠛⠁⠒⢲⠆⠀⠀⠀⠀⠀⠀⢲⠅⠴⣶⠏⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠻⣧⡈⢿⡀⢸⣧⠀⢰⢁
⠀⢉⣳⣿⣽⣷⣯⣿⠒⠂⠀⣾⡒⠂⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠻⣎⣷⢸⣿⠀⡞⣼
⠀⠈⣙⣾⣿⣻⡞⠋⠥⠤⠀⠸⣿⠉⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠀⠀⣠⠆⠀⠀⠘⢿⣿⣿⣾⡿⠁
⠀⠀⣠⣽⣿⣿⠁⠈⠀⠀⠀⠀⢸⣆⢀⣾⠶⠂⠈⠓⢤⡸⣷⡀⣴⡇⣠⠀⠁⠀⢀⡏⠀⢹⡧⣤⡝⠀⠀⠀⠀⠈⢿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢿⣼⠃⠀⠀⠀⠀⠀⠙⢿⢿⡿⣿⠏⠀⠀⠈⣾⠁⠙⣷⢿⣿⣽⡃⠀⣠⣀⣀⠘⣿⠃⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣧⣤⣤⣀⠀⢰⣶⣶⣦⣆⢀⠏⠂⠀⠀⠀⡏⠀⠀⠈⢿⣿⣃⡛⠉⢋⣉⣡⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣼⣯⣿⣷⣤⣤⣤⣧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⢿⣿⡿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⢁⡴⠋⢁⡤⠖⠋⢙⣻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣛⠽⠋⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡞⣁⢀⡞⢀⡴⠋⢀⡴⠚⢉⣡⠽⠿⢷⣶⡄⠀⠀⣰⡿⠋⡴⠃⠀⣠⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣴⣧⣾⣠⣞⣀⡴⠋⣠⠖⠋⣀⡤⢶⣾⠟⠁⠀⣼⡟⢀⡾⠁⠀⣼⠁⠐⣻⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠿⠛⠛⠉⠉⠉⠭⠭⣍⣙⣛⠻⢷⣾⣥⣴⠋⣁⣠⣿⡇⠀⠀⣼⡟⢀⡾⠁⠀⣼⠃⠀⡴⠃⡴⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠁⠀⠀⠀⠓⠲⣤⣀⠀⠀⠀⠀⠉⠙⠲⢤⣉⠻⢿⣧⣴⡿⠁⠀⢰⡿⢀⡾⠁⢀⣾⠃⢀⡾⠁⠈⣴⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⢿⣧⡀⠀⣿⣧⡾⠁⣠⡿⠁⣠⡿⠁⢀⣾⠏
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠙⢷⣾⣿⣋⣤⡾⢋⣤⡾⠟⣀⢀⣾⠋
⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⣼⣿⡋⣿⠀⠀⢧⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⣛⣩⡴⠞⠁⣾⠏
⠀⠀⠀⠸⣿⠹⣷⣤⡄⠀⠀⠀⠘⠻⠿⠋⠀⠀⢸⡄⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠥⠤⠤⠄⢸⡿
⠀⠀⠀⠀⠻⣷⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠬⣉⡓⠒⠒⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣾⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢿⣷⣦⣄⠙⠲⣤⡀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⠀⠘⠁⠀⠀⣠⣾⣿⣟⢮⣙⠻⣦⡀⠀⠀⣠⣾⡟⢷⣦⡀⠀⢻⣿⣝⠻⣦⣄⠙⠦⡌⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣄⣤⣴⡾⠛⠁⠈⠻⣶⣬⣳⣾⣿⣴⣿⠛⢧⣉⠳⢬⡻⣷⡄⢻⣿⢷⣄⠙⢷⣄⠈⠂⠹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⢿⣿⡿⢿⡛⠻⣟⠻⣿⠳⣤⣈⣷⣴⣿⠿⠃⠀⢿⣧⠹⣧⡀⠙⣷⡀⠀⠠⣙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⡳⣄⠙⢦⡈⠳⡙⣷⣾⠟⠋⠁⠀⠀⠀⠀⠀⢿⣆⠈⢿⡄⠈⢿⡄⠰⣌⠙⣮⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢻⡿⣷⡈⠳⣄⠙⢦⡙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⢿⡄⠀⠻⣄⢈⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠳⡜⣿⣦⡈⠳⣄⠙⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢻⣄⠀⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣜⢮⣿⣿⡲⣌⠳⡌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠙⢦⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠙⢿⣎⠳⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠙⠻⣷⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠐⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⡿⠿⣷⣦⣄
⠀⠀⠹⣿⡌⠙⠻⢿⣶⣤⡀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠹⣿⣄⠀⠀⠈⠙⢿⣷⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡷⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⢀⣾⡟⠁⢀⣠⣴⣾⠟⠉⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢀⣤⣾⠟⠋
⠀⠀⣾⣿⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⣴⣾⠿⠋⠁
⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⠶⠦⠄⠉⢙⣳⣤⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡛⢛⣣⡤⠶⣚⡛⠉⢩⡄⠀⣀⠀⠶⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠋⠁⠤⢀⣈⠀⠠⠄⠀⠀⠉⠀⠀⠈⠀⡴⠁⠀⡴⣢⡒⡄⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⠀⠘⠃⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠾⠚⢁⣠⡴⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠾⣿⣿⠤⠄⣲
⠀⠀⠀⠀⠀⠀⢀⣤⣾⢃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣋⠙⠓⠒⠄⠀⠀⠙⠄⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢰⢏⢠⡇⠈⢀⣀⡤⠀⠀⠀⠀⢀⣀⣀⣼⣯⡡⠄⠀⠀⢀⣄⣀⣀⣀⣀⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⢸⣧⢸⠇⢠⡯⢒⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠙⠺⠶⠚⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠛⠗⠋⣰⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⢸⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⠏⠀⠐⣄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡶⠖⠊⠁⢀⠈⣦⠞⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠐⡄⠘⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡼⠋



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

⠀⠀⠀⠀⡔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣤⠀⠀⢀⣀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⢁⣀⣠⣤⣤⣤⣤⣀⣁⡄⠒⠈⠛⠂⠀⠄⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠉⠉⠉⠀⠀⠈⠉⠉⠛⠷⢦⣄⠀⠶⠀⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠸⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⢀⡴⠒⢤⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠓⠀⠀⠀⠀⠀⠀⣜⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡇⢩⠀⠀⠀⠗⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢥⡀⠀⠀⠀⡀⠀⠀⠈⠀⢀⠀⢠⠄⠒⠈⠁⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⡀⠠⠤⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⠀⠦⠀⠤⠀⠴⠆⠀⠀⠀⠁⠀⠀⢄⡀⠀⠀⠈⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠡⠋⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⢠⠎⠀⣠⡀⠀⠀⠀⢀⠠⠀⠀⠖⠀⠀⠀⠀⣀⡤⢒⡀⠀⠀⠀⠐⢣⡀
⠀⠀⠀⢣⠄⠀⠉⠁⠀⠀⠀⠘⠀⠀⠈⠀⢀⣠⠔⠛⠀⠀⢈⣉⡀⠀⠀⠀⠀⠈⠓⠤⣀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠐⠚⠉⠉⠰⠊⠀⠀⠀⠈⠉⠙⠛⠶⣦⣀⠀⠀⠀⠉⠙⠒⠂⠉⠀⠐⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⡼
⠀⠀⠀⠀⢢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⢀⣀⣄⣀⣀⣈⣀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠛⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉⠉⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⢊⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠒⠛⠉⠁⠉⠉⠈⠁⠐⠂⠒⠂⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠐⣤⢀⠀⠀⠈⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡀⢀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠘⠂⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⣀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⣶⣽⠀⠀⠉⠲⠄⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⢑⣆⣠⣬⣟⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠏⠑⠒⠦⢤⠉⢉⠤⢶⣶⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⠃
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠇
⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⡿⣛⣛⡿⠿⠿⠿⠿⠿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣽⣿⣶⣶⣾⣶⣶⣾⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣦⡀
⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠙⢧⣀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⢷⡀⠀⠠⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠈⠒⣦⣽⣄⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡴⠞⠿⣿⣷⣄⣇⠀⠀⠀⡀⢀⠠⠖⠉⣈⠝⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣴⠞⠛⠃⠀⠀⠀⠈⠙⣿⣿⣶⣶⡉⠁⠐⡄⣀⠌⠝⡀⢖⡴⠘⠀⠈⠉⢤⡀
⠀⠀⢠⡀⣤⣾⣥⡴⠚⠛⠿⠃⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⢳⠶⢄⠸⢂⠀⠅⠀⠝⠉⠀⠀⠀⠀⠀⠀⢇⠀⠶
⠀⠀⠀⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠀⠀⠨⣤⠀⠐⠀⢨⠁⠐⠀⣤⠀⡀⢀⠆⠀⠄⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⢱⠐⠁⢄⠘⣇⠀⠂⠙⠦⠥⠊⠀⠀⢸⡏
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡈⢊⡹⠤⠀⠀⠀⠀⢠⠶⠶⢈⠃
⠀⠀⠀⠉⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢘⡿⠛⢿⡩⠛⡛⢳⠀⠀⣀⣴⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⣀⠙⠋⢀⣿⠾⠛⠉⠻⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠁⠀⠀⠀⠀⠹⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣆⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣽⣿⣮⠁⠀⠀⠀⣠⣴⡦⠀⢒⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠿⠿⠋⠛⡛⠋⠛⠙⠏⠛⠛⡛⠛⠟⠛⠻⠿⠿⠿⠟⠟⠛⠻⠿⠿⠿⠿⠛⠒⠒⡚⠛⢻⢧⣻⣬⡉
⠀⠀⣤⡤⠖⠛⠋⠉⠁⠀⠀⠀⠀⡐⠁⠀⠆⠀⠀⠠⠈⠀⠀⠀⠤⠄⠉⠀⠀⢀⡀⠐⠀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠷⠄
⠀⠀⠐⠀⠀⠤⣤⣤⣤⠤⠴⠶⠞⣡⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢶⣦⠀⠀⠀⠒⠿⡿⣮⡓⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠅⠀⠀⠀⠀⠀⠀⢹⣾⡿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠖⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠁⠩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠒⢶⠶⠒⠢⠤⣄⡀⠀⣀⡤⠤⠒⠒⠛⠉⠉⠉⠉⠉⣩⠗⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠲⣶⡒⠋⠀⠀⠀⣀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢠⣤⣤⡀⠉⠓⠲⠤⠤⠤⣤⣄
⠀⠀⠠⣤⡔⠃⠀⠀⢀⡴⠊⠁⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⣿⢸⣿⣷⠀⠀⠀⠀⣠⠖⠉⡟
⠀⠀⠀⠈⡇⠀⢀⡴⠋⠀⠀⠀⠈⢀⡢⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⢠⠞⠁⠀⡜
⠀⠀⢰⡛⠀⣠⠎⠀⠀⠀⠀⠀⠁⠀⠁⠘⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣞⠀⠀⠀⠃
⠀⠀⠀⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣸⣀⠀⠀⠳⢦⣀
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀⠀⠤⠭⢽⣛⣒⣛
⠀⠀⢠⡇⠀⠀⠀⠀⣤⠞⠉⠉⠀⠀⠀⠀⠀⠀⠑⢄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡤⠔⠊⠁
⠀⠀⣸⠀⠀⠀⠀⢸⡗⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠻⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⠶⠒⠚⠉⠁
⠀⠀⣯⠀⠀⠠⠈⡄⢄⠀⠉⠛⠒⠒⠒⠊⠁⠀⠀⠀⠀⢀⣤⢾⢫⠃
⠀⢰⢿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠘⠀⠘⡆
⠀⡼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠸⡄⠀⠀⠀⢳
⢀⡇⠀⢳⠀⠀⠀⠀⠀⠀⠠⠡⠐⠀⠀⢀⡴⠋⠀⠀⠀⠙⠦⣀⡀⠈⣇
⣸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡏⠀⠀⠀⠸⣆⠀⠀⠀⠀⡀⠀⢠⠞
⠻⣄⠀⠀⠀⠸⣆⠀⠀⢰⠁⠀⣿⠀⠀⠀⢶⠤⢤⣀
⠀⠈⠙⠒⠶⠴⠋⢧⡀⣾⠀⠀⢹⠀⠀⠀⢸⡄⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣧⡀⠀⠣⣀⣀⣸⢃⠀⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠈⠉⠙⢮⢖⡡⢠⣼⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⢸⣿⠦⠤⠀⠀⠀⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢍⣑⠒⠀⠀⠀⠀⠀⠀⠈⢣⡀

⠀⠀⠀⢠⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣠⠀⣿⡏⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⣤⣀⣤⡤
⢀⠇⢸⣿⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣠⣴⣿⣯⣉⠰⠾⣿
⣸⠀⣾⡟⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠛⢿⡍⠛⠟
⣿⠀⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠸⣶⢼⣿⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢸⣿⡟⠀⠀⠀⠀⣀⣀⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠘⣿⡇⠀⠀⠀⠀⠸⠋⠉⠁⠀⠀⠀⣀⣿⣤⠆⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⢰
⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠘⠻⠉⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⣤⢶⣶⠆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣸
⠀⣿⡇⠀⠸⠿⣤⣄⠀⠈⣻⠄⢰⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠚⠻⠛⠁⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⣿⠀⠀⣴⣿⣿⠆⠀⣤
⠀⡿⡇⠀⠀⠀⠉⢿⣤⡀⢼⣷⣾⡅⠀⠀⠀⢸⣇⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢹⡆⠀⢸⣇⣤⣤⡶⢽⣶⣶⣶⠟
⠀⢳⠃⠀⠀⠀⠀⠀⢻⣟⣿⣿⣿⡃⠀⠀⠀⠀⢿⡀⠀⠀⢸⡆⠀⢀⣾⢁⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠉⠙⠛⠻⠏⠀⠀⠈⣷⢀⡟⠈⠉⢩⣶⣮⡙⠋⠉⢴
⣠⣾⣤⣤⣀⠀⠀⠀⣼⣿⣿⣿⣿⣆⡿⠆⠀⠀⢸⡇⠀⠀⠈⣿⢠⣿⣏⣾⠃⠀⠀⠀⢇⡀⠀⠀⠀⠒⣶⢤⣀⠀⠀⠀⢀⡀⢻⣼⠁⠀⠀⢈⡉⠻⡄⣤⣷⣦
⣿⣻⣻⣿⠿⣀⢀⣠⢬⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠲⣄⡀⢹⣿⣿⣿⢃⣠⠶⠃⠀⢸⡇⠈⠀⠀⠀⢻⣤⠹⣧⢀⣴⠟⠀⢸⡇⠀⠀⠀⢿⠿⠀⢹⣭⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⣿⠀⠀⠙⢦⣿⣿⡷⠋⠁⠀⠀⠀⢾⣶⡆⠀⠐⠶⣤⣻⡇⠻⡿⠋⠀⠀⣸⠇⠀⠀⠀⠀⠀⣀⣸⣿⣤⣤
⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣖⡀⠈⣿⣿⣶⣄⡀⠀⠀⠀⠸⡿⠇⠀⠀⠀⠈⣉⢳⣴⠛⠷⢶⣂⣿⣀⣀⣀⣠⣴⣾⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣦⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢠⡀⠀⠀⣀⣴⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢨⣥⠞⠀⠛⠙⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⡷⠀⠀⢠
⠀⠀⠀⠈⢻⣶⠆⠀⠀⠀⣀⠀⣤⣶⣶⣤⣤⣤⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠻⠟⢉⡅⠀⠀⢸⡇
⠀⠀⠀⠘⠻⠃⣀⡀⠳⣬⡿⠋⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡃⠀⡆⠀⣧
⠀⠀⠀⠀⠸⣿⡿⢿⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣏⣷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⣿⣯⣄⡘⣧
⠀⣠⣦⢄⡈⢾⣖⣀⢸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣾⣷⣿⡿⢸⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⡴⠀⠀⢸⡇⠈⠁⠈⢷
⠀⠉⢿⡏⣁⣤⣿⣿⣿⠃⢷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠈⡇⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢸⡇⢠⡀⢸⡇⠀⠀⠀⠈
⣀⡀⣠⣽⠿⣽⡿⣿⡿⢻⡜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⢸⣧⠈⢷⣼⡇
⠈⢛⣼⢿⣤⣼⣿⣼⣷⡾⠛⠁⠀⠒⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢻⣧⡀⠘⣿⡄⠀⢹⣇⠀⠀⠀⡆
⠀⠙⠻⣾⣿⣻⣯⣽⣽⡗⠒⠆⠀⠠⣭⠤⠄⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⣁⣶⠄⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠙⢿⣦⡘⣷⡀⢸⣿⡆⠀⢰
⠀⠘⠿⢿⣻⣿⣿⣟⣯⠝⠂⠀⠀⠀⣿⣦⠒⠂⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠚⠋⠿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⣜⣷⠘⣿⣧⢠⣏⣼
⠀⠀⠐⠚⢿⣿⢧⣿⠠⠌⠉⠉⠀⠀⠈⢿⡀⠀⠀⣿⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣤⡀⠀⠠⣟⠀⠀⠀⠀⠙⢿⣷⣿⣿⣞⡞⠁
⢀⣤⣡⣾⣿⣿⣿⣇⠀⡀⠀⠀⠀⠀⠀⠘⣿⠀⣼⡿⠛⠁⠀⠀⠉⠲⣄⢿⣧⢠⣿⣏⣴⡆⠀⠀⢀⡀⣾⢁⣀⡨⣟⣛⣶⣇⣀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⣿⣿⣿⣿⣿⠋⣻⣿⣾⣿⣿⣄⠀⠀⠀⠀⢻⣦⡟⠀⠀⠀⠀⠀⠀⠀⠈⠺⠿⢿⡟⣿⡟⠀⠀⠀⠀⣷⠃⠀⠉⣷⢻⣿⣷⣟⠃⠀⢠⣄⣀⣀⡈⣿⣿⠀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣿⣤⣤⣀⠀⠀⠀⢴⣶⣶⣤⣤⠸⠀⡿⠄⠀⠀⠀⠀⣿⠀⠀⠀⠈⢿⣿⡿⠃⠖⠊⠙⠛⠉⣁⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⠉⣷⠚⢶⣦⣄⡀⢀⣀⣿⣀⣀⣀⣀⣈⣿⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡿⠿⠿⠿⠿⠿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⢛⣉⣥⣤⣤⠶⠶⠦⠤⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⣟⣥⡶⢚⣋⣩⣥⣴⠶⠶⠦⠤⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠉⠁⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠛⠻⠿⣶⣶⣶⡒⠒⢒⣠⣾⠏⠀⠀⠀⠀⠀⠀⣠⡾⠛⣡⡴⠚⠁⣰⡿⠁
⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣭⡀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠟⣁⣤⠀⣼⡟⠁
⠀⠀⠀⣠⡿⠋⣠⠤⠤⣄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⠾⠋⠀⣩⠶⠛⣉⣀⣼⡟
⠀⠀⣼⠟⠀⣼⣥⣈⣷⡌⡆⠀⠀⠘⣆⠀⠀⠀⣀⣴⣶⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠁⣿⡇
⣠⣾⠏⠀⠀⠹⣌⣛⣛⡴⠃⠀⠀⠀⣿⠀⣠⠾⡋⠁⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠛⠛⠓⠻⣿⡄
⢻⣷⣤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⠘⢑⣪⠀⣾⠏⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡛⠶⢤⣰⡿⠃
⠹⢷⣬⡛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠰⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢶⣄⠀⠀⢮⣙⠦⣄⣿⡇
⠀⠀⠈⠙⠷⣦⣀⡀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⡾⠋⠁⠀⠀⠀⠙⢷⣌⠢⣍⠳⣄⠻⣧
⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⠳⣌⡙⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣿⠿⣿⠷⠶⠶⠶⠿⠿⣿⡻⢟⡻⢟⡦⠭⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡙⠢⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⣕⡘⣷⠀⠀⠀⠀⠀⠘⢿⣦⣙⠲⢭⣙⡒⠂⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣸⡧⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣬⣉⣛⣓⣨⣿

⠀⠀⠀⠀⠀⠄⠀⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣦⣄⡀⠀⠀⣠⡤⣤⣤⣤⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢶⣶⣤⣽⣿⣿⣿⡿⠏⣳⣾⣿⣿⡞⣿⣿⣿⡟⢈⡿⢛⡛⣿⣿⣿⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠤⢤⣭⣭⣿⣿⣿⠿⣉⣴⣿⣿⣿⣿⣿⡇⣯⣿⣿⡷⠘⣇⠻⢆⡟⠁⠀⣌⠿⠋
⠀⠀⠀⠀⠀⠀⣀⣉⣭⣭⣽⣿⠟⢡⣼⣿⣿⣿⣿⣿⣿⢟⣲⠽⠟⠀⠑⢄⠈⠉⠁⠀⠀⠘⠑⠶⢴⠄
⠀⠀⠀⠀⠀⠀⠊⣉⣩⣾⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠲⠄⠀⠀⠀⠉⠦⠀⠀⢠⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠚⠍⢿⣿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠄⠀⠀⢀⠰⢄⣀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⢴⢾⣿⠏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⣄⠀⠀⠐⠍⠉⠲⣦⠼⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠈⠖⠀⠠
⠀⠀⠀⠀⠐⠹⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠠⢾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣄⣤⠖⠒
⠀⠀⠀⠀⢀⣴⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⡆⢠⣖⣰⣶⣿⡿⠃
⠀⠀⠀⠀⠉⢙⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡽⡼⣾⣟⠯⢮⣰⣼⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠋⢣⢸⣿⣿⣿⣿⣿⣿⣿⣯⠘⠆⠘⠷⠻⠶⠽⠋
⠀⠀⠀⠀⠐⠀⢿⡀⣿⣿⣿⣿⣿⣿⣿⡷⢁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠘⠃⠀⠷⠹⣿⣿⣿⣿⣿⣿⣜⢠⠌⠀⠀⠀⠀⠀⠀⣰⠾⠛⠋⠉⠉⠛⠻⢮⡳⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠘⣏⡐⢇⣹⣿⣿⣿⣿⣿⣿⢫⣖⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠫⠻⣽⣆⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡘⢁⢻⣿⣿⣿⣿⣿⣿⣎⠄⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠏⣧⣇⠀⠀⠀⠀⠀⢠⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠉⣷⣸⣯⠙⢿⣿⣿⣿⣿⣿⣳⡂⠰⣾⣟⣟⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⠀⠀⢀⢀⣴⡏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡯⠸⣧⠹⢿⣿⣿⣿⣿⣟⣄⠀⠉⠀⠀⠙⠛⠚⠀⠀⠀⠀⠀⠀⠀⠂⠀⢋⣌⣿⣶⣶⣿⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡻⢳⢪⣭⠻⢿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣼⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⠪⣟⠃⡀⠉⠻⠿⢿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣤⣶⣥⣤⣠⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠶⠦⣭⣩⣭⣿⣻⣿⣟⣿⡿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⣠⡄⠀⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣾⣿⣶⣿⣿⣿⣿⣿⣆⣴⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠿⢟⣫⣶⣿⣿⣿⢭⣽⣛⡝⠂⠩⣭⣛⡛⠻⠿⠿⠿⢟⣛⣫⣵⣿⠟⣿⡿⢟⡪⣔⣮⠳⢍⡙⠛⢫⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣑⣃⣀⣠⠄⣐⣬⣽⢟⣋⡭⠷⠦⢶⣢⣤⡉⢔⣲⣭⣿⣿⣷⣮⣭⣿⣿⣿⣯⣙⣶⠾⠫⢾⣿⣿⣭⣖⣿⡶⠿⢛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠙⠋⣉⣉⣭⣭⣅⣛⠻⢭⣛⣫⡴⢮⣽⠷⠾⠿⠿⠶⡾⢿⣿⠿⣭⣷⣶⣮⠭⠽⠿⠛⠛⣒⣙⣫⡵⠾⠛⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⠻⠷⠶⢖⡫⠽⣛⣴⣬⠭⣿⣛⠤⣶⠾⢝⣟⣭⣝⣿⣿⣾⣷⣽⣍⣋⣙⣀⣈⣊⣛⠽⣵⣒⠴⢞⣋⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⣭⣭⣭⡭⢽⣓⠶⢿⣻⣶⣬⡵⢞⣛⣯⡥⢶⣿⣥⠯⠽⣟⣿⣶⠭⢭⣭⡉⣉⣩⣭⠭⢴⣞⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢭⣿⣶⣢⢌⣉⣑⡒⠒⠂⢘⣫⢭⠒⣉⣽⣖⣛⣩⣭⣽⣭⣭⣽⣛⠤⠮⣌⡕⠀⠚⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣭⣛⡻⠿⣙⣻⣤⣤⠈⠶⣯⣝⡻⣛⠭⣑⣻⣧⣶⣾⣿⡿⣛⡿⢾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⢿⣤⣞⠿⠯⠉⣭⣯⣿⡶⠾⠧⣬⣽⣿⢥⣼⣟⡻⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠟⠛⢭⡴⣬⠴⠾⠿⠟⠟⠋⠛⠈⠁




⣶⣶⣶⣶⣶⡾⢶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣾⢿⡾⠶⡶⠶⢾⣶⡾⠾⠾⠶⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠠⡀⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣦⣄⣠⣴⣛⣉⢀⡴⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡼⠃
⠀⠀⠀⣀⣤⣶⣿⣟⣛⡟⠙⢻⣾⡿⠽⠟⠒⠛⠺⠿⣿⠹⠟⠹⡟⢰⡟⢠⡟⢣⣾⠋⡾⢋⡿⢻⣿⠛⣿⡿⢿⣿⣾⣿⣶⣶⣠⣄⣀⠀⠀⠀⣰⣏⣀⣰⠇
⠠⢶⡿⠋⠉⢰⣴⣿⡧⠇⠀⠀⠈⣻⣶⣶⣶⣞⣿⣿⢻⠿⢿⡟⠛⠳⢶⡾⣶⣦⠀⠀⠀⠈⠀⠚⠃⠀⠉⠁⠘⠋⠘⠛⠟⠛⠛⠻⠟⢿⣿⣾⣿⣿⣻⡏
⣤⣠⠹⢦⠠⣌⠛⠛⠁⠁⠀⠰⠀⣸⡗⢹⠉⠀⠀⠀⣀⣀⣠⡤⠤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢾⠟⠛⠛⠛⢿⣿⣿⣼⣧
⠈⠙⠻⠶⣾⣭⣀⣀⠀⠀⠀⣾⣆⣾⣧⠭⣷⣶⣞⣁⣀⣀⣒⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠀⠁⠀⠀⠀⠀⠀⠀⠹⣮⠉⠹⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠾⢯⣭⣿⣿⣟⣛⣛⣭⡽⠿⢿⣷⣶⣶⣶⣶⣶⣶⣿⡿⣯⣭⣭⣵⣶⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢳⣾⣿⣯⣭⡭⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠙⠻⣿⡛⠛⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣽⣦⣄

⠀⠀⠀⠀⠐⠋⠙⠓⠶⣤⠀⣠⠆⠀⠀⠀⠀⢀⣺⣼⣶⣶⣶⣄⢰⠂⠀⠀⠀⠀⠀⣤⡤⢴⣦⣤⡀⣠⡄
⠀⠀⢀⠀⠂⠀⣀⡠⠒⣀⠀⣿⡀⠀⠀⠀⢴⣿⡿⣿⠟⠽⠋⠀⠛⠀⠀⠀⠀⡄⠄⠀⣤⠴⢒⣲⠄⠹⠇
⠀⠀⠈⠀⠀⢤⣌⠁⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠦⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⢈⣀⠀⠻⢠⣆⠀⠀⠀⠀⠀⡊⠁⠹⣿⣿⢿⣿⠉⠻⠇⠀⠀⠀⠀⠀⠄⠀⠿⣿⣿⣯⣤⣦
⠀⠀⠀⠀⠀⠈⠉⡠⠆⠘⠇⠀⠀⠀⠀⠀⠉⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣘⠓⠿⠇⠈⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⣠⣶⣤⡄⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢶⣴⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣄⢹⡄⡇⡇⡧⠠⣼⠀⠀⠀⠀⠀⠰⣟⢰⢷⣼⢱⠶⣇⠀⠀⠀⠀⠀⠀⢤⠀⣸⡷⢮⣵⣦⣀⣤
⠀⠀⠤⣾⡘⣧⠗⣧⣏⠈⠻⠀⠀⠀⠀⠀⠙⠿⢿⡟⠛⠻⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠥⠇⠰⠗⠂⠈⠋
⠀⠀⠀⠀⠈⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣄⡀
⠀⠀⠀⠀⢨⣿⣿⠿⠿⠓⢺⡇⠀⠀⠀⠀⢀⠠⠃⢀⠩⠙⠦⠀⡀⠀⠀⠀⠀⢀⣴⡟⢻⢻⣿⣿⣧⣶⣦
⠀⠀⠄⠈⠀⣙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠀⠀⠉⠀⠀⠀⠀⠸⠆⠀⡀⣸⠯⠿⠆⠈⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⣿⠀⡝⠣⣴⡆⠀⠀⠀⠀⠀⠀⠀⡩⡮⣿⣿⠂⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡉⠺⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉

⠀⠀⠀⠀⣠⣶⣿⢶⡦⣄⠀⠀⠀⠀⠀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠷⠾⠁
⠀⣀⠀⡀⢻⠸⣿⢸⠃⠘⠓⠒⠄⢀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠀⠈⠁⢸⠀⡇⠘⢸⡇⠀⠀⠀⠘⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⣶⠀⣆⢸⡧⠀⠊⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣠⡄⠰⠘⣿⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢩⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣉⣀⡤
⠀⠀⠀⠀⠀⠀⢠⣶⠤⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⣠⣤⠴⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠿⠛⠻⠿⢶⡆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠆⠀⠀⠠⣶⣛⠉⠠⠄⠐⠒⠒⠛⢛⣫⣇⠘⠀⠀⠀⠀⠀⢰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣛⡛⠿⠿⠿⢛⡛⠉⠁⠀⠀⠀⠀⣠⣦⠈⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢠⠘⣿⡷⠂⢤⡆⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠄⠁⠀⢹⣇
⠀⡤⠤⢤⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢰⠀⠞⠆⢰⠀⡆⢸⠋⢠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢃⢴⣿⣶⠀⠹
⠸⠁⢠⣶⣿⣯⠈⠉⠀⠀⡀⠈⠁⠀⠀⠀⠒⠤⢄⡀⠀⠀⢸⡀⢸⠀⢆⠀⢸⠀⡇⢸⠄⠘⣄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣾⣿⠑⣠⣦⡀
⠈⠰⣿⣷⣿⣿⠀⠀⠀⠀⠡⠈⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⢸⠀⢸⠀⠀⢣⢸⡤⡇⢸⠀⠀⠈⠆⠀⠀⠈⠁⣀⠄⠀⠀⠀⠀⠀⢀⣉⣼⣿⣿⠏
⠀⠀⠈⠛⠿⠃⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠀⢸⠀⠀⠈⢸⠀⡇⢸⠀⠀⠀⢸⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠸⠀⠦⠜⠸⠀⠇⠸⠄⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⡀⠘⢿⣿⡌⠙⢿⣿⡄⠐⣦⣤⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣤⠀⠀⣠⠄⢸⡿⠁⣼⠋⢈⡷⠂
⠀⠀⠀⠀⠈⠋⠀⢸⣿⡿⠀⢸⣿⡇⠀⣼⣿⡧⠙⠿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡷⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠐
⠀⠀⠀⠀⠀⠀⠰⠿⣿⣁⣴⣿⡟⠁⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢠⡾⠟⠀⠀⠻⠀⢸⣧⠀⢿⡄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠛⠁⠀⠀⠀⠀⠀⢀⡀⠆⠠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢀⣴⣇⠀⠀⢻⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⠀⠀⠸⡟⢂⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⠻⢉⣾⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡆⠀⠰⣷⢼⣷⡀
⠀⠀⠀⠀⠚⢿⣷⡄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⢿⡶⠖⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⣧⢼⡿⠁
⠀⠀⠀⠀⢤⠄⢹⡇⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢁⣴⣦⠉⠝⠃⣄⡀⠀⣠⣶⠇⠀⠀⠀⠀⠛⠃⠤⠐⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⢁⠆⠿⢟⣻⠡⣾⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⡿⠶⡗⠘⣿⠇⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣠⣤⣬⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⣄
⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠙⢿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⣠⣾⣿⣿⣿⣿⡿⠟⠛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⣿⣿⣿⣿⡿⠿⠛⠉
⢰⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠉⣹⣿⣻⣿⠞⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡈⠣
⠋⠁⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠁
⠈⢆⠀⠀⠀⠠⠩⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠩⠁⠒⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡠⠒⠠⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⡀
⠀⠔⠀⠐⠢⣙⡭⠀⠀⠀⠀⡄⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣿⣿⣿⣿⠄⠀⠈
⢠⣀⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠴⢶⠋⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠈⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠄⠀⠀⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠐⠀⢠⠁⣔⠀⠀⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢠⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢟⢾⣿⣟⠟⠳⣾⣷⣶⣿⡀⠠⠀⡀⠀⠈⠁⡀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡞⢏⣌⠀⠀⠀⠄⢃⠴⠒⠝⢍⠱⠈⠭⠻⣟⢤⣀⣀⡄⠀⠀⠀⣠⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢀⣤⠄⠀⠀⣼⡿⣝⢛⣭⠎⣀⣀⠈⢄⠀⠀⠈⠀⡳⡞⠀⠠⠃⡈⠯⠃⢀⠀⢀⣰⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⢀⢀⠀⠀⢀⣴⣿⣿⢽⣾⣶⡁⢀⡿⣧⡀⠈⠀⠀⠀⢀⠄⠆⡠⢀⠔⠈⠐⠀⠀⣽⠿⣿⣿⣧⠊⠀⠀⠀⠀⠀⣀⠔⠁
⠀⡾⠋⢀⢔⡫⢭⡛⢽⡆⠀⢈⡉⠉⠠⠘⠁⠀⠠⠧⠶⢫⠀⠘⢤⡏⠀⠀⠀⠀⡀⡉⢂⣿⣿⠷⠂⠀⠀⠀⢠⠋
⡴⣅⠀⠀⡏⣶⡂⢸⡌⠠⠀⠚⠁⠀⠀⡀⠀⠈⠁⠠⠅⠎⠠⠀⡩⠁⠀⢀⣀⣀⣁⣁⣾⣿⠿⠂⠀⠀⠀⠀⠘⡄
⢆⠘⣆⠀⠳⢭⡥⠞⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠈⢈⡀⠤⣴⢁⠶⣵⢾⡁⠀⠘⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠘⡀
⠀⠂⣈⠀⠐⠂⠒⠈⠀⠀⠀⠀⣠⠆⣠⡎⠀⠀⠐⠂⠘⢰⣷⣼⣶⣿⠇⠀⠣⠀⠀⣸⣿⡟⠂⠈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⠁⢤⣔⡃⠀⠀⠀⠂⡁⠀⣰⣿⠉⢠⠘⠀⠈⣀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠈⠑⠠⢤⣶⣷⣶⣮⡻⣿⣷⣤⣤⡤⣴⣏⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⠟⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠻⡻⣿⣿⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⡠⠁⠀⡞⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠙⠿⣭⣉⠉⠉⠑⠈⠛⠆⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠠⣀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠢⠀⠈⠀⡀⠈⠓⠲⠄⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠀⠀⠀⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⣄⡀⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠘⠀⢿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣤⣤⠐⣲⡿⠁⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⣀⠀⢸⣷⣮⣿⡯⣹⠋⠀⢀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣾⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠢⡤⡘⣿⣿⣷⣌⢻⣿⣿⢽⢿⣤⣌⠁⣈⡿⠆⠀⠀⠀⢨⠁⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣫⡿⣿⣿⣷⣿⣿⡅⠁⠉⠉⠉⠉⠉⠉⠁⠀⠈⢸⠳⢴⢃⡘⠈⠻⠋⠑⠉⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⣿⠟⠉⠓⠒⣲⠖⠒⠒⠒⠒⠲⡖⠒⠚⠢⡀⠙⠷⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⢀⡴⠞⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⢄⣀⢝⢶⣫⣤⣾⣿⣶⣤⣤⢀⠀⢀⠀⢀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⡇⠄⣩⣵⣶⢻⣻⣷⣾⢣⣿⣿⣿⣷⣷⣷⣷⣾⡏⣽⣿⣶⡆⣴⠀⡦⢤⡄⢠⡶⠀⠀⠀⡀⠀⠘⢿
⣿⣿⣿⣿⣿⣿⣿⣛⠿⠟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⠁⠺⠦⠻⣅⠠⠔⠈⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠉⠂⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣤⣄⣤⣤⣠⣠⣀⣀⡀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⢻⣟⢿⢛⢋⢋⢋⢋⢋⢻⣟⢻⢛⢛⢻⢿⢶⢦⣤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢙⠂
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠈⠌⠌⠌⠌⠄⠌⠌⠎⠄⠌⠆⠎⠌⠌⠌⠌⠌⠌⠄⠈⠍⠙⡦⢤⣀⣀⠀⣀⣠⣔⡥⡂
⠀⠀⠀⠀⡠⠞⠛⠋⠀⠀⠉⢳⡘⡘⡘⡘⡘⡘⡘⡘⡘⡘⡘⡘⣘⠘⠘⢐⢐⢂⢂⢂⢀⢂⢂⢂⢀⢂⢒⢂⢈⣿⣯⣄⠀⠀⢠⠃
⠀⢀⠔⠁⠰⣷⠀⠀⠀⠀⠀⡀⣧⠐⠀⠰⠐⠐⠄⠰⠄⠁⠆⠆⠆⠆⠆⠆⠆⠆⠆⠆⠎⠆⠆⠎⠎⠎⠆⠎⠎⣺⡇⠀⠀⠠
⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠌⠌⠌⠌⠌⠌⠌⠌⠈⠌⠌⠌⠌⡜⡜⡜⡘⡜⡘⡌⡜⡌⠌⠌⠌⠌⠌⢻⠇
⠀⠀⠛⠀⠄⣀⣀⡠⢊⣠⣔⣽⣇⠘⡌⠈⡌⡌⡜⠌⠌⠌⠌⠌⡌⠜⡜⡜⡜⡐⡘⡐⡐⠐⢘⡤⠀⠀⠀⠀⠲⢿⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠩⡔⠚⠓⠐⠂⠐⠈⠘⠀⠈⠈⠈⠌⠌⠌⠜⠔⠐⠐⠐⠠⢤⡖⠉⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⡀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠉⠉⠁⠀⠒⠲⡒⠒⠒⠀⠈⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠤⣟⡯⡙⣝⣦⠴⠒⠋⠉⠉⡅⠀⠀⣡⣤⣄⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⡙⠒⠆⠙⢋⢝⠀⣰⣧⠀⠀⠀⠁⠀⠸⡟⢏⣹⠂⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⣤⣛⣒⠒⣬⠶⠤⠔⢉⣡⠞⠁⠸⡆⠀⢠⣄⡀⠀⠈⠉⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⡺⠵⠒⢢⡽⠁⠠⣴⣿⡍⠀⠀⠀⢸⣇⡰⠁⢈⠛⢆⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⢨⡟⠩⢭⣟⣀⠀⠈⠁⠈⠙⣦⠀⣠⢛⠟⠛⡄⠀⠀⠈⣆⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠉⠙⢳⣤⣀⠈⣖⠁⠁⠀⠀⣫⠞⠁⢰⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣀⣀⣀⡀⠹⡌⢣⣸⠀⣠⠔⠋⡝⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⡋⠋⠙⢯⡁⠀⠑⢧⠀⣿⠞⠁⠀⠀⠸⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣀⢱⠀⠀⢸⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⢉⣽⣏⠢⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡿⣿⣿⣽⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡏⣇⢣⠙⢿⢿⠩⣑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠈⢧⠑⢄⠑⠌⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠃⠐⢠⠋⠙⠣⢄⣉⡐⠚⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣧⠃⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡶⠛⠁⢠⡾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢷⡄⠀⣿⡁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠻⣆⠘⢷⣤⣠⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡶⠟⠋⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣤⣤⣤⡶⠛⠉⠉⠉⠉⠻⢶⣤⣤⣤⡶⠟⠋⠉⠉⠉⠛⠷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣤⣤⠞⠋⠉⠉⠻⢦⣤⣤⠾⠋⠉⠉⠛⢦⣤






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢅⠀⠐⠀⠀⠀⡀⠀⠔⢀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠢⠀⠀⠀⠀⠀⢀⠘⢀⠀⠀⠀⠐⠁⠠⡀⠀⠄⠐⠠⢄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠄⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠑⣀⠌⠀⠀⠀⠈⢀⣤⣴⣶⣶⣿⡿⣷⣶⡶⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠴⠶⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⡿⠷⠿⠿⠿⠷⠤⠄⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⢀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⡏⠙⣷⢸⣷⠀⡖⣿⠁⢠⣿⡇⠀⡦⠉⣿⠁⣾⡇⠀⣸⣼⣿⠉⢷⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣷⠀⣿⠈⣿⣴⠇⣿⠀⢸⣿⣿⢸⠇⠀⣿⠀⣿⡇⢀⡇⣿⣿⣠⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣿⢸⣿⢀⡟⠀⢻⣿⠀⣿⠖⢸⡏⢻⣿⠀⠀⣿⠀⢻⣧⡾⠁⢿⣿⠻⡄⢸⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠋⠉⠀⠀⠈⠉⠀⠙⠃⠈⠁⠈⠁⠀⠀⠉⠀⠈⠉⠁⠀⠈⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⣀⣀⣀⠀⠔⢢⠀⠀⣀⠔⠂⠀⡃⠀⠠⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠈⠑⠑⠀⠁⠊⠁⠀⠊⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣤⣤⣠⣀⣀⠀⢣⠀⠀⣀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢿⠿⡿⠳⡿⣿⠛⠛⣿⣿⡳⣾⣷⣶⣶⣿⣿⠂⠀⠀⠀⢀⡠⠔⣲⡇
⠀⠀⠀⠰⢾⠟⠿⠛⠟⣽⡿⣆⣻⣤⣴⠿⣿⠀⢩⢿⡏⠀⢻⣿⡿⣿⡿⠝⢿⠟⠿⣿⣶⣦⡋
⠀⠀⠀⠙⠪⢍⠐⠚⢥⡍⠞⠠⠬⠛⠿⠒⠛⠀⠈⠿⠄⠀⠑⠋⠀⣈⡀⠀⠀⠀⠀⠛⢺⣄⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠄⢀⣀⣄⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠨⠄⠈⠄⠀⠀⠀⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠚⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣚⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡀
⡐⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠖⠀⠀⠀⠀⠂⢽⡛⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿
⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠋
⢐⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣻⣿⣧⡀
⠈⠻⠿⣿⣿⣿⣿⣿⣿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠖⠀⠀⠀⠈⠙⠻⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⡟⠿⠿⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⢤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣷⠀⠀⠀⠀⠀⢀⣾⡥⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠃⠀⠀⠀⢀⣤⠛⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡴⠚⠁⠀⠀⠀⢠⣾⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠃⠀⠀⠀⠀⠀⠀⢠⡞⣱⠏⠀⠀⠀⠀⠀⢠⠟⣿⠀⢠⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡟⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⢠⡏⢀⣇⡼⠉⣠⠞⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢸⣆⣼⣾⠖⠋⣡⢖⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⡟⢀⡞⢱⡋⠀⠀⠀⠀⠀⠀⢀⡴⢞⡿⠃
⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⡏⣧⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢠⡏⠀⡼⠁⢸⡇⠈⡇⠀⠀⠀⠀⠀⢠⣯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣟⢦⡀⠀⠀⢧⣸⠂⠀⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⣼⣠⣾⠁⠀⠸⣇⡾⠁⠀⠀⢀⡤⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣷⠀⠀⠈⢻⣄⡀⠀⠀⠀⠀⠀⠳⣌⣳⡀⠀⠀⠀⣀⡿⢿⠉⡇⠀⢠⣯⠀⠀⠀⢠⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⠀⠀⠀⠈⢯⡙⠢⡀⠀⠀⠀⠀⠀⠈⠛⣦⣄⡎⢠⡇⢸⡀⡇⠀⡏⣿⠀⠀⠀⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠉⠳⣌⢣⡀⠀⠀⠀⠀⠀⢸⣎⣧⡞⠀⠀⣿⣄⢸⠀⣿⢀⣰⢾⠇⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⣠⢯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⠀⠀⠀⠀⢠⡇⢸⡏⠀⠀⠀⣿⢘⣿⢠⣯⡞⠁⣼⠀⣠⣾⠟⠉⠀⠀⠀⠀⣀⣴⡵⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣇⠀⠀⠀⠀⢺⢠⣿⣇⠀⠀⠀⢻⢸⣏⡼⡿⢀⡼⣡⡿⠟⠁⠀⠀⠀⣠⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡀⠀⠀⠀⠸⣼⣿⡎⢳⡀⢠⠞⣸⠟⢹⡷⠋⣠⠋⠀⠀⠀⠀⢀⡾⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⡀⠀⠀⠀⠀⠀⠙⢮⣇⠀⠀⠀⠀⠘⡇⢿⢀⡷⠋⣴⣫⠴⡿⠀⣾⡿⠀⠀⠀⠀⠀⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠳⣄⣀⣀⠀⠀⠈⢿⣀⠀⠀⠀⢈⡇⢸⣟⣴⡿⢛⣡⠞⠁⢰⣷⡇⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠚⠛⠛⠛⢦⣄⠙⢿⡳⣄⢸⢃⡞⣫⡞⠋⠉⠁⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠢⣷⡘⣿⠋⡼⢡⠇⠀⠀⠀⢀⣀⣀⣿⣇⠀⢀⣀⣀⡤⠞⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⢹⡼⢣⡟⢀⡴⣶⠿⠛⠋⢉⡿⠉⠛⠛⠛⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢻⡿⢡⡏⣴⣻⠞⠁⣀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡇⣾⢰⣿⢃⡴⢛⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣻⣿⢸⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣯⣿⣿⣿⣦⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠿⠟⠋⠛⠋⠉⠉⠈⠉⠁⠉⣁⣈⣉⡈⠉⢡⡾⠉⠉⠙⠛⠿⣷
⠰⣶⣶⣶⣿⠿⣿⡟⠉⢉⣉⣁⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠉⠙⠛⠉⠁⢸⣇⣀⣠⣶⣿⡿⠟
⠀⠈⠻⣿⣿⣷⣹⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣩⣽⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⣿⠏



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

⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⡀
⠀⠀⠀⠙⣃⠀⣴⣿⣟⡆⢀⡀⢀⡀⠀⠀⠛⡂⡀⢸⣵⣟⡆⠀⠀⠀⡀⠀⠀⢶⠔⠲⣶⣤⣾⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠩⣤⡉⣭⠂⢽⡇⠀⠀⠀⠈⠁⠚⠷⣌⠉⣩⠃⢿⡇⠀⠀⠀⠒⠀⢿⠟⣿⠿⣛⠓⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣿⣤⣠⠀⣴⠆⠀⠀⠀⣠⣴⣾⡿⠿⠛⡛⢻⡟⠀⠀⠀⠀⠀⡀⠄⣲⡍⠋⡷⣺⠢⣿
⠀⠀⠀⢀⠔⠁⢹⠿⣛⠋⠥⠀⠻⠀⠀⢀⣼⡿⠟⡡⠴⠆⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣛⣤⠀⠈
⠀⠀⠀⠰⠆⠐⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⣰⣴⡶⣦⣤⣴⡄⠀⠀⠀⠀⠀⠀⠰⠌⠈⢹⣾⣿⣦⣀⡀⢀⡄⠀⠀⠀⠀⢀⡠⣔⠾⡳⢐⠂⣲⠏
⠀⠀⠀⠈⠂⠴⢨⠮⠛⠿⢚⡓⢺⡅⠀⠀⠀⠁⠂⠘⠯⣛⡉⣩⠛⢿⡇⠀⠀⢀⠔⠁⠐⣤⣒⠑⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠸⠮⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⡀⢤⣾⣷⣾⣗⣀⣠⡄⠀⠀⠀⣀⣤⣶⣶⣶⣾⢶⡶⠛⠀⠀⠀⠀⠀⣂⠀⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣂⠚⣿⣿⣿⣿⡛⠛⠿⡇⠀⠀⣾⣿⣿⠿⢻⡯⠞⠁⠀⠀⠀⠀⠀⠙⠦⡁⣸⣿⣿⣿⣿⡿⣾⠃
⠀⠀⠀⠀⠉⠁⠹⢿⠉⠉⠃⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠻⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠓

⣀⣀⣤⣴⣶⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣶⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣇⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣼⣿⣿⡷⣄⡘⣦⠻⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢻⢿⣿⣿⣿⣡⡱⣾⡝⢦⡈⠛⠛⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠈⠫⠳⣄⠻⢿⣿⣝⣾⣿⣷⠙⠲⣴⣷⣦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⣛⠛⠛⠉⣠⣴⣾⣰⣤⡴⠶⣤⣀⠀⠉⠛⠿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⣿⡿⡋⣠⣦⡈⡛⠿⣷⣾⣴⣴⣴⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⢀⠀⠀⠀⠀⣀⢠⢴⣄⢀⡀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠄⠀⢀⡀⣠⣀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠄⠈⠐⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠁⠀⠈⠛⠠⠀⠔⠉⠑⠀⠀⠸⠀⠀⠙⠟⠓
⠀⠀⠀⡀⠀⣠⡀⠤⠄⠀⠀⠠⡀⠀⠠⠄⠀⠀⠀⢀⡀⠀⢀⠤⠤⠀⣀⠀⠀⢀⠀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⢄⣀⡀
⠀⠀⠀⠛⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠊⠉⠃⠀⠐⠀⠛⠁⠀⠀⠁⠉⠘⠁⠉⠉⠀⠀⠉⠀⠓⠐⠀⠉⠁
⠀⠀⠀⠀⠀⣀⣀⡀⣠⡄⣠⠄⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠀⠀⠀⢀⠀⠰⠤⡀⠀⠀⠀⠀⣀⣤⣤⣆⡀
⠀⠀⠀⠀⠈⠁⠈⠛⠀⠊⠑⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠈⠁⠀⠈⠉⠑⠀⠀⠈⠉⠈⠆⠘⠉⠉⠂
⠀⠀⠀⢀⠀⡀⠤⠀⢀⡀⠀⡀⠀⢀⡀⡀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠠
⠀⠀⠀⠐⠀⠐⠂⠒⠃⠉⠀⠊⠉⠓⠀⠚⠃⠀⠀⠀⠉⠋⠙⠛⠙⠋⠀⠀⠀⠀⠀⠐⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠇⠀⠀⠉⠋⠀⠀⠚⠁⠀⠀⠉⠒⠀⠒⠊⠙⠀⠀⠈⠉⠛⠛⠛⠛⠛⠃⠀⠈⠉⠈⠁⠉⠈⠛⠅
⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⢤⣀⣀⡰⣤⣄⡀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠉⠙⠙⠉⠉⠉⠀⠀⠀⠈⠉⠉⠋⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠁⠀⠀⠚⠁⠋⠉⠀⠉⠀⠀⠈⠃⠋⠙⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠠⠒⠶⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠀⠀⠀⠀⠀⠀⢀⣵⡼⣶⣿⠀⠀⠀⣤⣤⣀⣀⣀⣄⣀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠒⠲⠶⣾⢟⢭⣴⣶⣿⣏⠁⠒⢶⡟⠀⡫⠅⠉⠛⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢉⠃⣾⣿⠟⠙⠓⠈⠐⢄⢻⡄⠋⠀⠀⠘⠞⣦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠂⢀⣒⣤⣄⡌⢠⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡷⡀⢰⠚⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣉⡠⠤⠐⠛⡭⡙⢀⢎⠎⠀⣦⡀⠀⠀⠀⣼⡟⠛⢻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⠴⣻⣿⠀⠀⠀⠀⢠⠁⣌⠃⠀⠀⠈⢿⣄⠀⠀⠙⠇⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⠁⡀⣿⡏⣀⠄⠀⠀⣼⡞⣤⡴⠈⡲⢟⣛⠿⠄⠐⢲⣾⢎
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠇⠀⢸⣿⠏⢁⣀⢠⣤⡿⣿⠩⠔⠁⠀⠉⠉⠀⢢⣄⠀⢧⠸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⣼⣿⠟⠉⠀⠀⠹⢷⡝⣥⠀⠀⠀⢠⣦⠚⠀⠹⣄⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡀⢠⢊⠄⢀⠀⠀⡅⡟⠂⠀⠀⢹⠏⠀⠀⠀⢻⣷⠀⠀⠀⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣿⣿⣧⣤⠁⣠⠎⠀⠀⠀⠀⣤⣼⠿⣦⣀⡀⠀⠈⠓⠤⣀⠀⠀⠉⠻⢶⣖⡈⠒⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢝⠻⣧⣾⣧⣄⣀⣀⢀⣀⠿⢏⡀⠈⠓⢮⣳⠶⢤⣀⠀⠈⠁⠒⠢⢤⣈⠻⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡉⠀⠀⠀⢘⣶⣦⣴⡞⠁⠀⠀⢀⡞⠀⠀⠀⣽⢧⠀⠀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠐⣹⢿⡇⣿⣷⡄⣀⣴⣿⣡⣤⣴⠤⠉⣸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠟⡘⠻⢿⣿⢀⠏⠈⠓⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠃⠇⠀⠀⠈⠁⠀⠀⢶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟⢿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⡾⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡿⢄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠠⣷⣤⣤⣤⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠩⠁⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⣀⣡⢴⠶⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠒⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡿⣷⢸⠀⠀⠈⠹⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⢠⠆⢀⣀⣀⣴⢨⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⠿⠷⢖⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣂⣈⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠒⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠋⠁⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉⢀⡖⣛⢶⡄⢀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⢸⣎⣿⢞⡴⢁⣾⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣀⡤⠖⠀⠀⠀⠀⠀⠁⠀⢠⡾⢁⣾⣿⣿⠏⡾⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⣠⠶⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣾⣿⣿⠏⡼⠁⣀⡴⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢁⠤⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⣿⣿⠿⠼⠛⠋⠉⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣿⡉⠙⠛⠲⢤⣀⢀⡴⠞⢁⣴⠞⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠀⠀⣀⡼⠋⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠙⠦⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⢀⡼⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣠⠴⢒⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⣰⠋⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⡴⠞⠋⡀⠉⠉⣉⣉⣀⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡼⠃⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠌⠉⠛⠛⠳⠚⠋⢉⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⡏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣒⠛⢛⣉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⢾⡻⣄
⠀⠀⠀⠀⠀⠀⠀⡟⢰⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠧⣤⡄⠀⢀⠀⠀⣀⠀⠀⠀⣠⡴⠛⠁⠠⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠖⠋⠁⣀⡴⠚⠁⠉⠛⠚⠓⠚⠒⠾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣴⠾⠛⠛⠲⠦⠀⢀⡤⠞⠋⠁⣿⠀⠀⠀⠀⠀⢀⣀⡴⠞⢁⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠒⠀⠀⠀⣀⡴⢿⡤⢀⠀⢠⡟⠛⠛⠛⠛⠋⠉⠁⠐⠊⣁⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣛⣉⣁⣤⣴⣞⠋⠀⠀⠙⢧⢎⡼⠁⠀⠀⠀⠀⠀⠀⠐⠈⣉⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢸⠉⠳⣄⡀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⢀⠙⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣤⠷⠋⠀⠉⠓⠦⣄⡀⠀⠀⢀⣈⠉⠒⠒⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣉⡙⠓⠒⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠺⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣞⣛⣛⣿⣿⣿⣓⣲⣤⣀⣤⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠁
⠀⠀⠀⠀⢀⣠⡴⣟⡛⠛⠛⠛⠋⠉⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠄⠀⠈⠉⠉⠙⠛⠛⠿⠷⠷⣯⣤⣄⣀⡀⠀⠀⠀⢀⡼⠁⢸⠃
⠀⠀⠀⠀⢫⡀⠘⣼⡿⠂⠀⠀⠀⠀⡀⠀⠈⠉⠉⢉⣽⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠲⠾⠤⡄⣾
⠀⠀⠀⠰⣖⠛⠂⠀⠀⠀⠀⢰⠀⢀⡇⠀⠀⠀⢀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠋⢿⠉⠀⣧
⠀⠀⠀⠀⠈⠑⠶⢴⡲⠤⠴⠃⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠎⠋⠀⠀⠀⠀⠀⠀⠈⢧⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⢯⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡻⣿⣿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠁⠙⠾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡄⠀⠀⠀⠀⠀⢀⣠⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⢿⡀⠀⠀⣠⡴⠋⠑⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠻⢶⣟⣩⠀⠀⠀⠀⠃⠀⠀⠀⢠⣿⠿⣿⣿⣩⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠉⠺⠧⢤⣄⣀⡞⡀⠀⠀⢸⣿⠀⠀⢨⡟⠉⠳⣄⡀⠀⠀⢀⣀⣤⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⢸⡟⠀⠀⢸⠁⠀⠀⠈⠛⢷⡾⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⣧⡀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣿⠛⢦⡀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⠇⠀⠀⠉⠳⣤⡀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣼⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⢠⡾⠋⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠀⠀⢀⣀⣀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣤⠶⢤⣤⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠠⠶⠚⠉⢈⣷⣌⡑⢆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢸⡇⠈⠻⣄⠁
⠀⠀⠀⠀⠀⡀⣴⣁⣀⣀⣀⡠⠤⠤⠤⠤⣔⣒⣒⣒⣶⣿⣿⠯⠭⠭⠽⠗⠒⠶⠾⢿⣭⣉⠲⢄⢹⡄
⠀⠀⠀⠀⠀⠈⠻⠷⢶⣶⠖⠚⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⡄⠀⠀⡇⠀⠀⡄⠹⢿⣿⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⣿⣴⠀⣿⣇⠀⢰⣧⠀⣦⣧⠀⢀⠀⠀⠀⢀⣷⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⢀⣿⣿⣿⡴⣋⣠⡕⠺⢿⢀⣿⣿⣤⣿⡄⠀⠀⢸⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⢀⠜⣉⣙⣿⣿⣿⣿⣵⣶⣆⡬⣿⣿⣿⣿⡇⠀⢄⠹⣿⡅⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⡙⡟⢁⣚⡟⢫⣾⣿⣿⣿⣿⣿⣿⡇⠙⣿⡟⢻⣿⡤⠀⠀⢹⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣿⢀⣿⡿⠿⠀⡾⣿⡷⢮⡽⠿⣿⡿⡷⢾⣭⠀⣤⡬⣏⣀⣀⠖⢿⣀⣙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠃⣚⠋⢘⠃⣾⠆⣼⠇⣿⢁⡚⢀⣡⡿⢀⡖⢸⡟⢰⡿⢠⡟⢠⡟⣰⠆⣿⠁⡣⡮⢶
⠀⠀⠀⠀⠀⠀⠀⢀⠏⢸⠁⠇⢾⣦⣵⣤⡵⣦⡴⠃⠑⠬⠭⠦⠞⠣⠬⠲⠬⣴⣬⢥⣬⣴⣿⠬⠕⠤⠭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠁⠀⠧⠚⠙⢿⣿⣷⣼⢻⣷⡀⠀⠰⡢⢔⠆⠀⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣬⣻⣦⡈⠠⠄⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⢻⣶⣾⡿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣏⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁

⠄⣉⣿⣾⣦⣤⣬⣉⡉⠙⠉⠉⠛⠛⠛⠀⠀⠙⠗⠈⠉⠉⣀⣠⣠⣾⣧⣘⣲⡤⠬⣍⡉⡉⠉⠀⣰⢖⣤⠤⣶⣞⢳⡿⠖⣭⣿⣥⣶⣤⣖⣀
⠶⢶⡬⡍⠉⠉⠉⠉⠀⠀⠛⠛⢀⣨⡶⠟⠋⠉⠉⣙⡒⠚⢿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣑⣒⣦⣾⣋⠟⠛⠿⡦⢶⡬⠉⣛⣛⣛⠻
⢶⣶⣶⣾⣶⡶⡿⠿⠿⠃⣠⣴⣾⣁⣀⣀⣠⣤⣤⡤⢤⣤⡞⣷⣄⣀⣀⣛⣻⣿⠟⣩⣽⡏⠙⠯⠙⠋⡉⠁⠀⠀⠀⠀⠀⠶⠶⣿⢉⣹⠏
⠖⢲⣶⣶⢶⠶⠂⣀⣀⣤⠤⣾⢿⡷⠿⢶⣤⡄⢒⢀⠚⢛⣻⣿⡉⠀⠉⠁⠈⠉⠀⠀⠈⠀⡤⠀⣀⣶⣀⣤⣶⣀⣤⣤⡶⠶⣶⣷⣄⠁⢚⣒
⠛⠋⠉⠐⢾⣿⣯⢭⣭⣽⣿⣿⣯⡥⣤⣶⣿⣿⠟⠁⠀⠈⠛⢿⣷⣤⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⢉⣉⡉⠋⠘⠛⢿⣶⣖⡲⠾⠿⣿⡟⠉⢩
⠿⣿⣿⡿⠟⠉⠉⠛⠓⠒⢶⣦⣀⣀⣀⡀⠈⠑⠂⠀⣀⣀⣬⣾⣿⢿⠿⠷⠄⠀⠀⣴⣶⣶⣶⡆⠀⠈⣁⣽⣿⡟⠉⠉⠉⣉⣻⣿⠆⠉⠳⠶
⠀⣽⣿⡷⠀⠀⠁⠀⠀⠀⠀⠉⠉⣉⣉⣉⣋⣉⣩⣉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⣬⡍⠉⠻⣿⣿⣿⠿⢋⣁⣬⣶⡾⠟⢛⣉⣴⣶⠟⣠⠶
⠀⠈⠻⣷⣤⠀⠀⠀⠐⢿⣿⣿⣿⣿⡿⠟⠛⠛⢛⣉⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢀⣙⣛⠛⢛⣛⡋⡍⠤⣶⠾⠛⠉⠁⠀⡴⠶⠿
⣀⣀⠀⠈⠛⢿⣦⣄⠀⠀⠀⣈⣥⣶⠶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⣤⡤⠤⠖⣛⣉⣴⣿⣥⣜⢿⡿⠿⣛⣢⣈⣵⣿⣦⣤⣤⠴⠶⢚⣻
⠐⠊⠭⣕⠒⠛⠛⠉⠀⠀⠀⠛⠛⠿⠶⠶⠦⢤⣤⣤⣤⣿⣽⣿⠿⠋⠁⣴⡖⡛⣍⣛⣉⠀⣀⣀⣤⣤⣴⠾⢟⣛⣿⣿⣿⣿⣟⣀⣀⣀⣈⣭
⠶⢶⣶⣿⡿⠀⠐⢿⣟⠋⠉⠙⢛⣛⠓⡒⠒⠒⠶⠶⠶⢶⣤⠤⠀⣠⡤⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⣀
⠀⠀⠀⠀⠀⣠⣤⣤⣌⣉⣑⡒⠀⠿⠧⠴⠴⠒⠐⠒⣂⣉⣡⣴⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠉⣉⡁⠀⠄⠘⠁
⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⠉⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⢉⣻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠚⠻⠿⠶⠂⠀⠱⠆⠀⠘⡟⠀⠀⠰⠶
⡀⠀⠀⠈⠛⠿⢿⣿⣷⣤⣄⣀⣀⣀⣤⣶⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⢙⣶⣤⣶⣦⣶⣶⣦⣤⣤⣤⣤⣤⣀⣤⣀⣀⣀⣄⣀⣀⣀⣠
⠿⠿⠶⠂⠀⠀⠀⢀⣈⣽⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣤⣤⣤⣬⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠚⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠀⠉⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⡀⣀⣉⡁⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣷⡀⢀⣀⣀⣤⣴⣶⠶⠟⠛⠛⠛⠛⠛⠛⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⡿⠿⠿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣳⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠠
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡯⠉⠉⠉⠉⠉⠛⠒⠂⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣡⣤⣶⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⣉⣭⣼⣿⣿
⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣷⣶⠶⠿⠂⠀⠀⢀⣀⣠⣤⣤⣴⣿⡿⠟⠋⠁⠉
⠿⠿⢿⣿⣶⣤⣀⣀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣁⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⣿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⢿⣿⣿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣹⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠶⢶⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠾⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣄
⢶⣶⣦⣤⣤⣤⣤⣤⣤⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠋⠷⠈⠾⠁⠚⠀⠉⠋⠓⠈⠹⠉⠋⡻⢿⣿⡀
⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⢟⠃⠃⠈⠰⠗⠀⠈⢀⣀⣤⠤⠶⠖⠒⠒⠚⠚⠒⠶⢶⣦⣄⣼⡿⢃
⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠟⢠⠀⠉⠀⠂⠘⠂⠀⠀⠀⠀⣠⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠟⠁⣼
⠀⠁⠈⠀⠉⠉⡏⠉⠀⡁⠠⠴⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠉⠉⠁⣀⣠⣴⡾⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡄⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠖⠒⠒⠒⠊⠉⠉⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠾⠖⠒⢚⡙⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠻⠶⣤⣀
⢀⠤⠤⠴⠶⠒⠒⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠐⡖⠒⠒⢤⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤
⡆⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⢠⠀⣴⠴⠶⠶⠆⢶⣄⠀⢸⡀⠀⠘⡇⠀⢸⡄⠀⠸⡄⢻⣠⠴⠚⠀⢸⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢹⢾⡀⠀⠀⢰⣆⠀⠀⠀⣏⠙⢦⠘⣆⠀⡌⠀⢻⣀⣀⣀⠀⢸⡍⢷⡈⣇⠀⠀⢧⠀⠈⢧⡀⢸⠃⢸⡟⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠘⣿⣇⠀⠀⢸⠘⣆⠀⠀⢹⡀⢘⡇⠹⡄⡇⠀⢸⡇⠀⠀⠀⠈⡇⠀⠙⢿⠀⠀⠸⠄⠀⠈⠙⠃⠀⠀⠃⠀⠙⠂⠀⠉⠉⠉⠁⠀⠀⠀⡠⠖⠁
⠀⢿⣿⠀⠀⡷⠖⠘⣆⠀⠈⣇⠜⠁⠀⢻⠁⠀⠀⠷⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊
⠀⢸⣿⡀⠀⠃⠀⠀⠙⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠀⠠⢤⣤⣤⣤⣶⣶⣦⣤⣤⣴⠶⠶⠶⠶⠟⠛⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⣤⣴⣖⣲⠶⣶⠶⠶⠖⠻⠟⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⢙⣳⣾⣤⣐⠶⠶⠮⠿⠛⠓⠛⠊⠉⠉⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠳⠀⠀⠀⠸⣤⡆⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⡄⢠⠀⠀⠀⢀⡿⠀⠋⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⢆⠘⢆⢇⠀⠀⣼⣷⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠣⠘⡞⠀⡈⣿⢿⣀⠞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡉⠪⠐⠄⢹⠷⣗⣨⠁⣁⠀⠀⠲⠊⠁⠀⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠈⠁⠠⠤⠭⠤⠄⠀⠐⠟⠛⠒⠚⠛⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠒⠀⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠦⠤⠤⠤⠔⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⡰⢀⡜⢁⡴⠁⠀⠂⡂⠀⠀⠀⠀⠀⢀⠀⠄⠀⠢⠂⠁⠀⠈⠀⠀⠀⡀⢀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡵⠿⢒⠋⡒⠍⡀⠠⠉⠀⡒⠲⠆⢦⣤⡆⣀⠔⠂⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⣀⠜⢁⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠕⠒⠢⠀⠀⠀⠀⠀⠀⠀⡠⠔⡰⠃
⠀⠀⠀⢀⠄⠀⠀⢠⣮⠎⡠⢊⣁⢀⡤⠜⣦⣴⠦⠦⠤⠤⣤⣄⣀⣀⡀⠀⠉⠘⠙⠋⠋⠂⣀⠴⠊⠁
⠀⠀⠠⠁⠀⠀⠀⢟⠳⢿⣊⣅⣸⡧⡞⢉⠀⠀⠀⠀⠀⠀⠀⠈⢋⡍⢉⡇⠀⠀⠀⠈⠀⠉
⠀⠠⠀⠀⠀⠁⠑⠢⡀⠸⡅⣾⣿⣗⣚⠲⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠃⣀⣀⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠐⢀⠆
⡐⠈⠣⠈⠁⠀⠀⠄⣸⠟⢁⡠
⡇⠀⠀⣠⣤⡬⡶⠚⠁⠠⠁
⠳⠴⠋⠀⣬⠝⠦⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢋⠉⠀⠀⠀⠀⠀⠹⣿
⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡿⠿⠿⠛⠋⠀⠀⠀⠀⣤⣤⣠⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⡁⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡎⣟
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠙⠋⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠀⠈⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣦⣤⣤⣤⣤⣀⣠⣴
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠙⠉⠉⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣦⠸⡦⠀⠀⠃⠚⠃⠀⠰⣉⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⡼⠈⢀⣀⣀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠓⠃⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠂⡀⠀⡏⡏⠀⢀⠀⠀⠀⢺⠆⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠃⠀⡀⠀⠀⠑⠬⠶⠋⠀⣀⡀⠀⠀⠀⠈⠀⣴⠄⠀⠀⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⠁⠀⠟⢀⣤⠀⠀⠀⠉⣰⢻⢳⡠⠖⡆⠀⠀⢈⡀⠈⠁⠀⢚⣁
⠀⠀⠀⠀⠀⠀⠀⢐⣊⠁⢀⠀⡠⠋⡏⢧⠐⠀⡰⠃⡜⠀⢁⡴⠁⠂⣠⠚⡟⣆⠀⡀⠙⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠚⠁⠘⣅⡸⠳⡞⠀⠸⠵⠂⡞⣞⠱⠘⠹⣤⠇⢈⠢⠀⠐⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠄⠀⢼⡧⠀⠈⠁⠀⠘⠄⠀⠀⠀⠘⣌⡆⠑⠀⠈⠀⢾⠦⠀⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣺⣟⠀⢠⣿⡄⠀⢰⠒⠦⠤⢦⡈⠇⣰⣷⡀⠐⣿⣗⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⢽⡿⡁⠰⣿⡢⢠⠋⠓⠤⢎⢿⣱⡄⢞⣿⠆⠨⢾⡮⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣻⣏⡂⣪⣿⢝⠀⠭⠍⠑⠚⠉⠥⠀⡻⡿⡅⢐⣽⣝⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠉⢔⣿⡳⠄⣱⣆⢩⠍⣴⡌⠠⢚⣟⡢⠉⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⠌⠂⢽⡷⡀⠨⣾⢮⠘⠵⡷⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠙⠁