Yours Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡔⠈⠑⢆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢱⣄⡀⣘⠀⠀⠀⡇⡠⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠄⠤⠀⢊⠉⢻⠉⠀⠀⢰⠉⢩⠋⠛⡏⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⡎⢀⢀⠀⢈⡆⠊⠉⠒⠀⠒⠁⠙⠢⠐⠃⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡋⠊⠴⣾⠿⣀⣀⣀⠀⠀⠀⠀⡠⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢞⠆⠒⠉⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣢⠤⠤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⢀⡠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠤⠔⠊⠁⢀⡰⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⣀⠠⠐⠊⠁⣀⠴⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠠⠤⢲⠋⢀⣀⡤⠖⣛⠢⠬⣁⠒⢤⣀⠤⠊⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⠢⢔⠛⠥⡜⣀⠀⠉⠈⠉⠁⠀⡀⡡⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⠪⢕⠢⠬⠭⢿⡤⡁⠒⠀⢐⠬⠡⠔⠁⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠉⠀⠀⠁⡠⠭⠙⠁⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠀⢎⠀⠀⣀⡀⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡶⣦⡔⠂⠒⠲⠶⠶⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡉⠉⠉⠓⢤⣤⣤⣀⣀⠀⠀⠉⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⣀⠤⣶⠞⡋⠉⠉⠉⠍⣙⠻⢟⠿⠟⣶⠆⠀⠀⠈⠉⢙⡷⠦⠤⢤⣀⡙⠲⣄
⠀⠀⠀⠀⠀⣠⠾⠟⠀⠈⠁⢀⣤⠶⠋⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠉⢠⡔⠊⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠙⠛⠶⠷⣦⣤⣀
⠀⠀⠀⠀⣞⣁⣤⣖⣚⣋⣉⣉⣉⣀⣀⣀⣀⡘⠀⢠⡀⠠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣄⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢡⠟⠁⢀⡼⠋⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡱⠶⠾⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢠⠊⠀⠀⢸⡇⠀⡇⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣤⣄⡠⣀⣠⣤⣄⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢤⠃⠀⠀⠀⡘⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠃⡀⠀⠀⠀⢀⣠⡴⠿⡉⠁⢈⡀⠊⠀⠈⠀⠈⢁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡹⠆⠀⠀⠀⠀⡇⠀⠀⡇⠀⡼⠁⠀⠀⡄⠀⠀⣸⠟⠃⣀⣤⡶⠞⠿⠉⠀⢀⣀⠀⠈⣿⠀⠠⢈⠀⢀⠰⠞⡋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⣄⠃⠀⠀⠀⠀⢀⠃⠀⠀⢧⡾⠁⠀⠀⠀⠇⠀⠀⢃⠀⠫⠀⠈⠉⣀⣂⣀⠀⠀⠹⡇⠀⢿⠤⠑⢂⣠⠄⠀⢾⣁⠀⣧
⠀⠀⠀⠀⠀⠀⣀⣧⡴⣿⡀⠀⠀⡄⠀⢸⠀⠀⣰⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠒⠂⠤⠤⠬⠭⠭⠤⠀⠙⠃⠀⣭⠤⠚⠋⠀⠀⠀⠀⠻⣦⠼⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡅⠀⢸⠀⠀⠸⡀⢰⠟⠀⠀⠀⠀⠀⠀⠈⣧⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡆
⠀⠀⠀⣠⠤⠼⠷⡏⠉⠉⣿⠀⠸⡆⠀⠀⡧⠀⣆⢠⠂⠲⠀⠐⢢⢀⡟⠀⠻⣦⣾⠟⠀⢀⣤⣶⣤⡔⠒⠖⠈⢲⣤⡀⠀⠐⠂⢤⡀⠀⠀⠀⣈⣻⡦⠤⣄
⠀⠀⡘⠀⠀⠀⢀⡇⠀⠀⢸⣧⣸⠇⠀⠀⢱⡄⠈⠙⠂⠀⠀⢠⣴⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣏⣻⠎⠀⠀⣌⣀⠀⡳⠋⠀⣠⠌⠛⠠⠤⡌⠀⠇
⠀⠲⡇⠀⠀⠀⠀⡇⠀⠀⢸⡿⠋⠀⣠⠞⠉⣧⠀⠀⢀⡄⠀⢸⣿⣿⣿⣿⡶⠀⠐⢶⣿⣿⣿⣿⠟⠃⢀⠀⣼⣯⡉⠛⠁⢀⠀⠙⢷⡖⠒⠀⢶⠉⠀⠀⠀⢸⠆
⡇⠐⡇⠀⠀⠀⠀⡇⠀⠀⢸⡁⠀⢸⣧⠀⣶⣿⡇⠀⠘⢿⠀⠈⣿⣿⣿⣿⠇⠀⠀⠸⣿⠟⠉⠀⠀⣀⡶⠼⠛⠉⠀⢀⠔⣿⡇⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢸
⡇⠀⡇⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⢸⣿⣱⣿⣿⣿⠀⠀⠈⡄⠀⠈⣿⡿⠃⠀⠀⠀⠀⠙⢷⣤⡰⠛⠁⠀⠀⠀⢀⣴⣿⣞⣿⡇⠀⢸⠇⠀⠀⡼⠀⠀⠀⠀⢸
⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⢣⣠⡼⠁⠀⠀⢀⣄⣤⡀⠀⠀⠈⢧⣄⡀⢌⡦⢠⣿⣿⣿⣿⡿⠀⠀⡄⠀⠀⢀⡅⠀⠀⠀⠀⠈
⢡⡀⢰⠀⠀⠀⠀⠘⡇⠀⠀⠘⡀⠀⠈⠻⢿⣿⣿⣿⠖⠚⠋⢉⣀⠀⢀⠆⣾⣿⣿⣷⠀⠀⠀⣀⡉⠛⠛⠳⣿⣿⣿⡿⠛⠁⠀⢀⠃⠀⠀⣸⠁⠀⠀⠀⠀⠇⢀
⠘⣷⣦⡜⣶⣀⠀⣀⣿⠀⠀⠀⠳⠄⠀⠀⠀⠈⠛⠉⠀⠀⠀⠿⡟⠀⡀⣸⣿⣿⣿⣿⡆⢀⠀⢻⠿⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⡾⠀⠀⢀⣿⡀⠀⣀⣶⢡⣼⣾
⠀⠉⠚⢷⡹⣿⣿⣿⣿⣇⢦⣴⣿⡶⠤⠄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⢡⣿⣿⡃⢙⣿⣿⡌⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠠⠤⢾⣷⣦⡴⣸⣿⣿⣿⣿⢇⡾⠓⠃
⠀⠀⠀⠀⠻⢮⣙⣛⣛⡻⠶⢻⠷⠿⣶⣄⡀⣘⣻⣿⣿⣿⡷⣄⠀⠀⣾⣿⡿⠃⠘⢿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣟⣂⢀⣠⡞⠟⠿⠏⠶⢟⣛⣛⣋⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⡇⠉⠉⠻⣌⠁⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠁⠘⠈⢰⡏⠙⡇⢸⠋⠉⢰⠛⡷⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣯⡟⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢰⡇⢠⠀⠀⢾⠀⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢸⡁⣿⠀⠆⠘⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⠋⡗⣾⠻⡆⠀⠀⡀⣾⠙⠀⣤⠀⢸⠁⠀⠀⣿⢀⡼⠛⠀⡌⠉⠀⠀⠀⠉⠁⢠⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣿⠀⡇⢀⣴⡇⣿⡄⠉⠀⠀⡄⠀⢹⠀⡇⠈⠀⠀⠀⢰⠀⢸⡇⢰⡛⠤⢿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡏⠀⡇⢸⡃⡇⠾⠹⡆⠘⢣⠆⢀⣼⠀⣷⠐⡄⠀⡀⢸⢠⣸⡇⢸⡇⠀⢸⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠇⠘⠃⡇⠸⡄⡇⢰⣶⠀⡏⢹⠀⣽⠀⡇⢠⣌⠁⠘⢸⡇⢸⡇⠀⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⣄⣰⠀⢧⣰⠇⡇⢸⡇⠶⠇⣼⠀⢿⠀⠳⠖⢀⡆⢰⡈⠻⠛⠀⠀⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠁⠀⡇⢸⡇⠀⠀⣿⠀⢸⡆⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⢿⠀⢨⡇⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢸⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠈⠳⠋⠀⠀⠀⢠⡇⢸⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠒⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⣀⠁⠂⢄⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠀⡐⠁⣴⣤⣀⣈⣻⠀⣖⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢰⣅⠈⢀⡤⠂⠈⠙⢷⡄⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢇⠀⠀⠀⠀⠀⣉⠄⠙⡞⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠄⠁⠀⠀⣳⠂⠰⢄⠐⠁⠀⠴⠁⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡵⠀⠀⢐⠁⠀⠃⠀⠀⠈⢣⣀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⠀⢹⠇⠀⠀⠀⠈⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠠⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠐⢀⠎⠀⠀⠀⠀⢰⠀⠀⠀⡈⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⠀⡁⠀⢠⠃⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⡆⡀⠁⠀⠀⠀⠀⠀⠀⢠⡑⠄⠀⠂⠀⠀⣌⠎⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠱⠁⠄⠀⠀⠈⠀⠀⢀⡨⠉⠉⠓⠰⣶⡀⢟⢀⠔⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠃⠒⠒⠀⠈⢀⡀⠀⠁⢀⡠⠜⠓⠒⢚⣿⢾⡈⠀⠁⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠤⠄⠀⠀⠤⠀⠀⠤⠤⠀⠁⠀⠀⠒⠁⠀⢠⠾⣽⣧⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠁⠀⡏⠀⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⢢⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣒⣲⠻⣟⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⢾⠉⠁⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠒⠦⣤⡤⠴⢾⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠖⠒⡏⠐⢣⣀⡠⡍⠀⣷⠀⠀⠈⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⢔⣲⣤⢷⡀⠌⡓⠚⠁⢤⡿⢦⣤⣖⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⣇⠀⡇⣾⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⢿⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⡱⣉⡉⠩⠭⢇⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣈⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠎⡔⢁⢂⡄⡆⢪⠳⠃⠀⣀⠀⠀⠀⢰⣿⡥⢹⢏⣭⡙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⠇⡀⠀⡈⠘⠃⠈⠀⢀⠀⠀⠑⠁⢀⠀⢸⣏⣛⣨⣦⣩⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠿⠀⣀⠀⠰⠃⣠⠗⠒⢲⣈⣧⣈⢳⠖⣲⠀⠥⠃⣼⣏⡺⡇⣺⡕⠾⣿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣩⢇⡴⠛⢻⠖⢦⡏⢻⣠⠾⣏⣙⠁⠀⠀⠀⠘⢧⣵⣷⡾⠟⠋⢱⣿⡖⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣲⣼⡇⣾⠙⣧⠈⢳⡀⠹⡄⠙⣍⠹⡄⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⣀⢿⡄
⠀⠀⠀⠀⠀⠀⢀⡞⡞⠉⢹⣽⠛⣆⠘⣆⠀⢳⡀⠙⠀⠘⣦⡗⠀⣿⡇⢰⣆⢸⡇⣠⣤⡀⣾⣏⠘⣷⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠀⠙⢒⡿⠛⣠⢼⣆⠘⠆⠀⠁⠀⠀⠀⠈⢧⠀⢸⣇⣾⢿⣾⣿⣏⣿⣧⣠⣽⠇⠻⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡏⠀⠀⢻⡀⠙⠆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠻⠟⣤⠉⣤⢙⣫⣌⣡⡄⣶⣿⣴⣶⡄
⠀⠀⠀⠀⠀⠀⢸⡆⠈⢧⡀⠀⠀⣹⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠹⣶⣿⣿⣏⣿⠻⣦⡿⢹⣏⣈⢠⣶⠷⠄
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠉⠛⢻⠛⢾⠙⠲⢤⣀⠀⠀⠀⠀⠀⢳⡀⢠⣄⠠⣤⡿⢡⣍⠁⣶⣄⣿⣸⡏⢹⡇⠙⢷⣆
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣠⠟⠓⠋⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢳⡈⣿⠀⣹⡇⣿⣻⣧⢻⡟⣿⡇⣿⣼⢷⣄⣠⡿
⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡜⠁⢹⡟⠛⣷⣿⠋⠙⠿⠷⠈⠃⠘⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠲⠦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠊⠁⠀⠀⠘⠗⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣃⣤⣶⡆⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣸⢹⣿⣿⣯⣅⠀⠻⣿⣿⣿⣷⠀⢸⣷⣤⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢰⡽⠸⠿⣿⣿⣿⡆⠘⢿⣿⣿⣿⠄⣼⣭⡈⠋⠀⠀⡇⣔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢺⣄⣄⠀⠘⠛⠿⠃⠀⠀⠀⠉⠁⠀⠙⠻⣯⠀⡀⠀⣇⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢦⡆⣆⢹⣃⡄⠀⠀⠀⠀⠀⢠⢶⣶⣦⣤⡤⠷⣾⠀⢁⠀⢛⣨⢾
⠀⠀⠀⠀⠀⠀⠰⡰⡄⣿⣴⠘⣷⣶⣶⣧⣤⣄⡢⠄⢸⡟⢋⣈⣙⠶⠉⣭⠘⢷⠋⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠰⠞⠿⢻⠉⠁⠉⠛⠃⠹⠿⣿⣿⣷⣀⠛⠃⣌⣬⣶⢁⢸⢟⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠣⣵⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣥⡛⢢⠌⡍⣱⡷⠟⠠⠻⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠚⠶⠶⠤⠤⠤⣀⣀⡨⡥⣤⡤⠸⣦⠐⢊⡉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⠀⢒⡩⠲⡤⠄⠒⠋

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣄⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠘⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣴⠃⠀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣼⡄⠀⠀⠀⠀⠀⠀⡀⠂⡨⠙⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣷⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⢸⣗⠀⠀⠐⠚⡏⠉⠀⢸⣿⡆⠀⠀⠀⢸⢠⣏⠀⠀⠘⠃⢹⣿⡿⠇⠀⠀⠰⣿⣿⠀⠉⢙⡓⠂⠀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⢌⡀⢉⡿⢂⣶⣶⡾⠹⠄⠀⠛⠻⣅⠀⠀⠀⠘⢿⣿⣿⡏⣾⣿⢟⡝⠁⠀⠀⠀⢀⠟⠛⠁⠀⠞⢳⣶⣶⡀⢻⡋⢀⡱
⠀⠀⠀⠀⠀⢸⣿⣟⡄⣼⣿⠟⢀⣤⣶⣼⠓⣴⠿⢆⣀⣂⡠⢤⡀⢹⡇⢸⣿⠁⣀⣠⣤⣄⣐⡻⢧⣌⢷⣶⣤⡀⠙⢿⣷⣀⣻⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⣴⡿⣿⢟⣿⣊⡴⠞⠉⠉⠉⠉⠻⣾⣿⡇⣼⣿⣾⡿⠋⠁⠀⠀⠉⢳⣾⠻⣟⢿⣿⣦⡀⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣧⠉⢿⣿⠇⣼⡟⠁⣡⡿⢡⡟⠣⢄⠀⠀⠀⠀⣀⠈⢻⣟⣵⣮⣝⣂⠤⠀⠀⠀⠀⠀⠘⣷⠹⣧⡁⢹⣷⡈⣿⣿⠃⣠⡇
⠀⠀⠀⠀⠀⣿⣷⣌⢿⣸⡿⠀⠰⣿⠁⣿⠇⠀⠀⠀⢀⠞⣡⣚⣉⡝⢫⣻⣅⣤⢹⡼⣰⠀⠀⠀⠀⠈⣿⡇⢹⣇⡀⢿⣇⣻⢃⣾⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣷⢶⣧⡟⠒⣿⡗⠀⠀⠀⢸⣆⠸⣍⣹⠷⢿⣿⣯⣭⡻⣾⠃⠀⠀⠀⠀⢉⣿⡗⢸⣿⡇⣼⣿⢟⣿⣿⠃
⠀⠀⠀⠀⠠⣄⡈⠳⣌⠈⠻⣾⡏⣿⢀⣿⣿⠀⠀⠀⠀⠻⣦⡀⠻⢿⣷⣿⣳⣿⣿⣯⡑⢆⠀⠀⠀⣸⣿⠁⣸⡝⣿⠟⠁⣠⠞⢁⣠⠄
⠀⠀⠀⠀⠀⠙⢿⣿⣾⣷⣄⠈⠻⠜⣧⠘⣿⣧⡀⠀⠀⠀⠈⣻⣶⣄⡙⠻⣽⡋⣿⣦⣿⠈⡇⠀⢰⣿⠏⢡⠯⠟⠋⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣙⠺⢭⣿⣷⣄⠀⠘⢷⡈⢿⣷⡶⠶⠶⠶⠿⠞⠉⠛⢶⣤⣉⣐⡿⢃⡼⠁⣴⣿⠋⣢⠏⠀⢀⣴⣿⡭⠗⢋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⢇⣘⣮⣷⣼⣟⢿⣦⣤⡒⠤⠄⠠⠤⠄⠈⠛⢋⡴⠟⢤⣾⠟⣗⣼⣧⢖⣠⠟⠛⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⢾⣿⣿⣿⣿⣞⠏⢻⢮⡉⢻⣧⣤⡀⠂⡀⢀⣨⣴⣾⠋⢀⣳⡾⠋⢠⣾⠡⢏⣾⣿⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠈⠉⢉⣵⡿⠻⣿⡈⠳⣄⠙⢿⣯⣬⠻⣯⠅⣀⠀⢷⣼⠟⢀⡴⠃⣸⠿⠿⣷⣍⠉⠁⠀⠠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⢸⣿⣷⠄⣸⣻⣗⠈⠢⣄⠻⢿⣷⠌⠐⣽⣾⠟⠁⡰⠊⢐⣿⣿⡀⢴⣿⣿⠀⢀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠟⠀⠈⠳⠵⠾⠋⠁⠙⣟⢷⣾⡷⣠⠻⣿⣿⡿⢋⣠⣾⡿⣺⠟⠀⠉⠻⠦⠷⠋⠀⠺⠁⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠢⢄⡀⢨⣻⣿⣿⠍⢳⣌⣋⡴⠛⣿⣿⣟⡥⠀⣠⠤⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣿⡋⠉⠁⠙⠟⠁⡉⢉⣹⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠓⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⡠⣤⣠⣾⣷⣶⣿⣿⡀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄
⡿⢡⡇⠀⠀⠠⣤⣶⣴⣾⡛⢿⣿⡟⠁⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠁⢸⣿⠀⠀⠀⠀⠀⠉⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⠿⠟⠉⠉⣿⣶⣤⣤⡤
⠀⣾⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠁⠀⠀⠈⢻⣿⣿⣾⣿⣷⣿⣿⣿⣿⡉
⣿⣿⣄⠀⠀⠀⠀⠀⢸⠿⣿⡿⢻⣿⠿⢿⣿⣿⣇⠀⣠⣦⡀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠
⡏⠈⠉⠀⠀⠀⠀⠀⢸⠿⣿⣧⣄⣹⣆⣤⢿⡟⣻⣿⣤⣿⡽⢏⣿⣿⣿⣯⡀⣬⣝⡮⣿⠃⠀⠀⠀⠰⣷⡀
⣈⠀⣪⠀⠀⠀⠀⠀⠈⣠⣤⣽⣿⣿⠽⠟⠻⢾⣿⣦⣈⣽⣿⣿⡿⠛⣩⣽⡿⠛⣿⠷⢿⠀⠀⠀⠀⠀⠙⣿⣄
⠇⢀⣹⠀⠀⠀⠀⠀⠀⢹⣿⡻⠚⡯⠙⢶⣦⣬⣿⣿⣿⣿⣻⣿⣶⣿⣟⣃⣷⣞⣿⣫⣹⣄⠀⠀⠀⠀⠀⠘⣿
⠀⣾⣿⠀⠀⠀⠀⠀⣤⣨⣧⣴⡶⣿⡿⢛⣋⡍⢹⣿⣿⣷⣶⠋⠉⠛⠿⢿⣿⣶⣿⣶⣸⣏⡀⠀⠀⠀⠀⠀⠙
⢸⣿⡏⣴⣿⠀⠀⠀⠸⢿⣧⣤⣼⣿⣀⣈⠟⣤⣤⣴⣿⣿⣿⣿⣷⠐⠦⡼⠿⠟⣟⣿⣿⠿⠁
⣾⣿⣷⣿⡟⠀⠀⠀⠀⠀⠈⠓⢿⣿⣝⣿⣴⣿⣿⣿⣿⠟⠉⠉⣀⣀⣉⣰⣶⣶⠻⣋⡀⠀⠀⠀⠀⠀⠀⢰⡀
⣿⣿⣿⣿⠃⠀⠀⠀⠰⡿⢀⠀⠀⣿⢿⣹⣿⣿⣿⠿⣷⣶⣶⣾⢋⢻⡏⣷⣿⠋⢀⡙⠋⠀⠀⠀⠀⠀⠀⣼⣧
⣿⣿⣿⡏⠀⠀⠀⠀⠀⣄⠈⠁⠀⣿⠀⢹⣯⣼⣯⣰⢹⠛⢸⣷⣿⣷⣼⠿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠁⠻⣼⣿⣿⣿⣿⣿⣾⠀⣾⣿⣿⣿⠅⠨⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠈⠀⢼⣿⠄⢸⣿⣿⡟⢿⣿⡀⣿⡿⠋⠉⠀⢠⣿⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠨⣿
⣿⣿⣿⣠⣾⣿⡆⠀⠀⠀⠀⠀⠈⢁⡄⠀⣿⣿⡇⢸⣿⣿⢿⣤⣤⠔⠀⢸⠏⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⢿⣿⡇⠸⡇⠁⠘⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡐⡀
⠀⠀⡠⠄⠒⠒⠒⠠⢀⠀⠀⢀⣀⡀⠀⠀⣹⣄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⢎⠁⠀⠳⣖⠉⠀⢙⣦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⡀⠀⠙⢦⠐⠁⠈⠑⠅⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⡇⠀⠀⠀⠈⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠊⠀⠀⢀⠀⠘⠢⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠊⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡤⠖⠒⠒⠶⠶⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠄⠒⠀⠀⠀⠒⠐⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⣡⣬⠥⠤⠤⠤⠖⠒⠒⠒⠦⢄⡀⠀⠀⠀⠐⠀⠀⣀⣀⣀⣤⠤⠤⠔⠒⠒⠋⠉⠉
⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⢠⠔⠚⠓⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠉⠉⠉⠁
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣨⡍⠉⢉⣉⠽⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣠⠤⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⢀⣠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠴⠊⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠔⠒⠒⠒⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠃⢀⡠⠔⠋⠉⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⡽⠉⠀⠀⣀⠤⠚⠉⠁⠀⣀⡠⠤⠒⠛⠉⠉⠈⠀⠀⠀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠤⢶⠋⠁⠀⣀⡤⠖⠋⠁⠀⠀⢀⣀⣀⠤⠖⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠹⣅⣀⣠⠴⠒⠋⠁⠀⠀⠀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠤⠤⠤⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠤⠤⠴

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡇⢀⡠⠀⠦⢬⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠈⠈⠈⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠐⠄
⠀⠠⠂⢠⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⠄⠀⠀⠀⠂⠀⠈⠀⠀⠀⠠⠉⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠓⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠁⠐

⠀⠀⠀⠒⠲⠄⠀⠀⠀⢠⡄⡄⢠⡄⠀⢀⣦⠀⣠⠠⢠⡄⡄⠀⠀⠀⣰⡄⢠⡀⠀⢠⠤⡀⠀⠀⣄⠀⢀⢠⡄⣠⠀⡄⢰⡆⢰
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡏⢱⢸⡇⠀⠞⢻⠀⣿⠀⢸⡿⡄⠀⠀⡰⠛⡇⠘⢿⡇⢸⠇⡇⠀⠀⢿⣴⡆⢸⡇⣿⢸⡇⢸⡇⢸⠁⠀⠀⠀⠈⣀⠄⠄⠃
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠁⠈⠀⠈⠁⠉⠀⠈⠁⠀⠀⠀⠁⠀⠉⠀⠈⠁⠈⠉⠀⠀⠀⠈⠈⠁⠈⠁⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⢿⡀⣏⡐⠈⡏⢀⡿⠁⢰⡏⠀⣷⣀⠂⣯⠀⠀⠀⠀⣴
⠀⠁⠀⠀⠀⠀⠈⢛⡃⠙⠀⠀⠀⠀⠀⠀⠸⠇⠀⠏⠸⠇⡟⠂⠘⠇⠸⣧⠄⢸⡇⠀⡏⠿⠀⢘⠇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⡀⣀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠠⡀⠀⠀⠁⠀⠍⠁⠀⡂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⡀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠧⣧⡆⢠⠀⠀⠀⠀⠀⠀⠠⣠⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⠀⣀⣴⣿⣿⣿⣿⣿⡿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⠁⠀⣠⣴⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣾⠿⠋⠻⢿⣦⣄⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠉⠀⣠⣴⡿⠟⠁⠀⠀⠀⢀⣤⣦⣄⣤⣤⣄⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢸⣿⣿⣿⣿⠟⠉⠀⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠉⠻⣿⣿
⠀⠀⠀⠘⠉⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣶⣶⣶⣶⡄⢠⣶⣶⣶⣶⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣤⣠⣄⣀⠀⣀⡀⠀⣀⣀⣄⢀⣠⡀⣤⣠⣤⢠⣤⣤⢤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠛⣿⡇⣿⢛⡟⢿⣴⡿⢱⣿⣿⡸⣿⠸⣿⡃⣿⣉⠿⢸⡏⢿⡄⢻⣿⡙⢷⠟⣿⡧⣾⣿⡏⢸⡟⠛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⡇⢸⣧⡙⢸⣿⠃⢸⣿⠉⠁⢿⣷⣿⡅⣿⣿⠄⠘⣷⠈⣷⠀⣿⠃⢠⢤⡿⠁⠀⣿⠃⣿⠁⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡠⠀⠹⡇⠀⣿⠀⢸⣿⠀⡤⢸⣿⢻⡇⣿⡧⢠⠁⡿⢀⠏⠀⠋⣠⠃⣼⠋⣠⠆⡏⢸⣟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠲⠦⠀⠀⡀⠉⠐⠘⠏⣨⠇⢸⡏⠈⡇⠸⡏⠆⠀⠁⣉⢬⣰⢄⠀⣸⠀⢠⠟⠸⠁⡾⠁⠀⣸⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⡀⠀⢠⠀⠀⠀⠠⢧⣇⠈⣀⡷⠀⠔⠃⠀⠑⡲⠽⢎⠕⠁⠀⠑⡣⠙⠀⡉⠐⠀⠀⡇⣦⣼⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠱⠀⠧⠘⣡⡥⢬⢆⣨⣉⠀⣤⣶⣶⡿⢚⠶⠖⠚⠁⠀⠀⠀⠀⣰⠻⡆⠈⠲⡄⢐⡇⠸⠁⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⡇⡰⣾⠋⠀⠀⠣⣉⣥⠞⠁⣀⡿⠚⣁⣀⡤⡴⠂⠒⠤⡀⠀⠙⢷⣌⠛⢀⠘⠠⡄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡜⠡⡕⠁⣠⠔⣤⣄⣙⢆⠀⠀⠀⠑⢜⡙⠌⠑⠈⡰⠁⢀⠹⣦⡀⠀⠎⠳⣌⠻⡆⠹⣄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣖⠟⣠⠞⠃⠀⠡⠈⠘⢷⠀⣀⣀⠀⢀⣉⣦⣰⣾⠃⢀⡾⠁⠐⢛⣢⣰⡔⠈⠳⡙⣆⠹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠢⢅⣀⠊⠀⣦⣴⣾⣵⡞⠟⠁⣿⡿⣿⡿⠛⠁⠀⢸⣧⡤⠤⢬⣽⣭⠃⠀⠀⠹⡌⣄⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡆⣤⠁⠀⠙⠿⣿⣟⣥⣶⣄⣈⢷⡖⡲⠀⡠⣰⣿⣿⡆⠀⢸⣇⠀⡀⠀⠀⠀⢻⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⣿⣿⢀⡀⢠⣿⢻⣿⣿⣆⠛⠘⢯⣴⣿⣎⣻⣿⣿⡿⢀⣿⣿⣿⣥⠀⠀⢀⠈⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⢉⡿⠼⠿⠿⠋⣿⡿⣿⣿⣧⠆⢰⡈⢀⡀⠈⠉⠁⠀⠈⣿⢿⣿⣿⠀⣰⡋⠀⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⢨⡇⠐⠂⠔⠘⠿⢇⡸⡿⠳⠇⠌⠙⠈⢉⡀⠀⢀⡤⠊⠀⠀⠘⣿⠾⠟⠁⠀⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡠⣷⣰⠶⢶⡀⢶⠘⠳⠀⡆⠰⡀⡈⢋⣿⣿⠷⠊⠀⠀⠀⠀⠀⢷⠀⠀⠀⣸⠃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠋⣠⠐⣬⣳⣆⣤⢤⡴⠆⢠⡠⣆⠀⡀⠘⠋⠙⣴⣠⣀⡔⠈⠳⡀⠈⡧⠀⡴⠋⣜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⣟⠉⣣⠈⢨⣭⢀⠄⡄⠤⡄⢄⡡⢈⠉⣶⡄⠉⠛⠛⠉⣠⣾⡀⢙⣠⢃⡞⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⡇⡇⣼⡟⠂⢀⠀⠀⡠⡄⠐⠁⠀⠀⠰⡿⢧⡤⠒⠋⠀⠀⡟⠛⠒⠊⢸⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣟⢿⣰⠀⠀⠱⠀⠠⠀⠀⢀⠀⠀⣼⠶⠋⠀⠀⢀⠠⢠⠷⣇⢇⢠⠼⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢤⡍⠀⠀⠈⡴⠟⡀⠂⠀⠀⢠⠆⠀⠀⡤⠾⢛⡡⠎⢸⡏⢸⠀⠀⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠲⠠⠑⠆⠿⣸⣓⣳⡍⣇⠼⠓⡷⢒⢒⠒⠊⠉⢁⣶⠀⢸⠁⠈⠘⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⡄⠠⣾⢸⠗⢉⢸⡏⣁⠾⣄⢀⡌⢷⠋⢙⠀⡆⠀⠀⠁⠸⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢺⠀⠈⠛⢧⢪⠎⠙⠘⠀⠀⠀⠀⠘⠀⡀⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢸⠂⠘⡰⠀⠐⠔⠁⠈⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣴⡿⠋⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣴⠟⠁⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣠⡾⢯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⣠⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠁⠐⠂⠤⠀⠤⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠐⠒⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠠⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠄⠀⠐⠃⠀⠀⠀⠀⠀⠀⣠⠞⢁⠴⠁⠀⠀⠈⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡀⡄⠀⠠⠁⠀⠀⠀⠀⠀⢀⠜⡁⠀⠁⡄⠀⠁⠀⢁⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⢅⠀⠠⠠⠀⠥⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⠀⠠⡀⠀⢀⠈⢀⠢⠤⡀
⠀⠀⠀⠀⠀⠀⡀⠆⢈⣠⠀⠀⡹⠀⠀⠀⠀⢠⠎⢀⠔⠁⠀⠀⠀⠀⠰⠄⠀⠄⠈⣀⠲⠦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡰⠀⠀⠀⢀⡔⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠲⠆
⠀⠀⠀⠐⠚⠀⠀⠒⠠⢐⡀⠀⠀⡠⠔⠉⠀⡼⠁⠀⣄⠁⠢⡀⠀⠀⠀⠚⠂⠰⣢⡶⠾⠶⠾⣟⢦⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠵⠒⠉⠀⠀⢀⠜⠀⠀⠀⠈⠉⠐⠈⢢⡀⠀⠀⠓⢨⡥⠴⠶⠶⠶⠶⠿⠷⢦⠄
⠀⠈⠒⠄⠠⠄⠒⠊⠉⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠒⠠⠴⠁⠀⠀⠠⠤⠤⠀⠒⠈⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠂⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⡄⠀⠠
⠀⠀⠀⠀⠀⢀⠀⣴⣛⣶⣄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡀⠀⣀⠀⠀⠁⢄⣤⠒⠀⠁
⠀⠀⠀⠀⠀⢸⡆⢽⣟⣻⡝⢣⠈⠀⠀⠌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠃⠀⠉⠀⠀⠲⣌⠡⠆
⠀⠀⠀⠀⠀⠈⠁⠈⠻⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠲⢾⣷⠀⠰⡖⠀⠠
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢀⠀⡀⢰⢒⠄⠀⢴⠄⠈⠰⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠦⣤⡈⠀⠀⠈⡀⠁⠀⠉⡔⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡧⠀⠐⢁⠁⣁⠀⢀⣡⡦⠠⠐⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣅⠉⠙⠀⣷⢄⠀⡘⠛⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠐⠈⠄⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⣤⠀⢀⡀⣀⠠⣄⠀⠀⠼⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠑
⠀⠀⠀⠀⠀⢠⡝⠀⠈⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠐⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠠⠀⠐⠀⠀⠀⠀⡞⠠⡀⠁⠂⠀⠀⠀⠀⠀⢁⠤⠠⠐⠄⠠⢄⣀⡐⠶
⠀⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠀⣀⡏⣡⣴⠴⣠⣴⢶⡴⡀⠁⡴
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⡀⠀⢴⠄⢱⡈⡘⠷⠇⢾⣃⣙⡗⠲
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠈⢉⡉⠉⠀⠈⠁⠀⠀⠀⡉⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⣈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠔⠁⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠒⠤⢄⡀⠑⢤⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠋⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠒⠤⢀⡀⠀⠈⠐⢄⠑⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠐⠁⢀⠄⢀⠎⠀⡠⠊⠑⢄⡀⠉⠂⠄⣀⠈⠉⠀⠒⠂⠀⠄⠸
⠀⠀⠀⡀⢊⠢⡏⢂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⣡⠔⠁⡠⠊⠀⠀⠀⠀⠈⠐⠠⢄⡀⠉⠁⠒⠠⠤⠄⠀⠀⠆
⠀⠀⠈⠪⡙⠆⠉⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠁⠤⠒⢋⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⠤⠤⡜⡀
⠀⠀⠀⠣⡉⠀⠀⠀⠀⡠⠓⢄⠀⠀⠀⠀⠀⠘⠦⠀⠖⠂⠉⠁⠀⠀⠘⠟⠀⠀⠀⡀⡀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠇⡣⠁⡇
⠀⠀⠀⠀⠈⠑⢠⠐⠉⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⠪⣰⡀⠀⠀⢀⢀⠀⠀⠀⠀⡀⠈⢀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠰⠉⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠑⢄⠀⣐⠒⢀⠀⠱⡀⠀⠣⠠⠇⠀⠀⠀⠈⠓⠉⠀⠀⠀⠘⠤⠜⠀⠀⣠⡃⠐⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠙⠢⣀⢀⠎⠊⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠈⢃⡠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢀⠏⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⠠⠔⢺⣄⠀⠀⠀⠀⢱⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠁⠈⠁⠉⠁⠀⠀⠀⠜⠈⠳⡀⠀⠀⠈⢆⠀⢂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠐⠒⠖⠂⠄⠠⠀⠒⠉⠀⠀⠀⠈⢢⠀⠀⠀⢯⣤⡶⢗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡜⢨⠹⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠎⡇⠹⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⢀⣀⣀⡀⠆⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⠀⢀⡠⠔⠈⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠽⠤⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃

⠀⠀⠀⠀⢀⠀⣠⡶⠶⠶⠶⠶⠶⠒⠒⠒⠚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⠒⠒⠶⠶⠶⣤⡀⢀⡀
⠀⠀⠀⠀⠎⣼⠃⠀⣴⠶⠒⠛⠛⠛⣛⣛⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⢉⣩⣍⠉⣉⣉⡙⠛⣷⠀⠀⢹⡆⠓
⠀⠀⠀⠀⠀⣿⠀⠀⣿⢰⣟⣻⡇⢼⣏⣻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠒⠚⠀⠻⠶⠇⠀⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠹⠟⠁⠈⠙⠿⠁⠘⠷⠶⢤⣤⣤⣤⣤⣤⠾⠃⠸⠭⠝⠀⠯⠭⠇⢰⡏⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣓⣚⣒⡒⠲⠶⠶⠶⠶⠶⠶⠶⠛⠛⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣤⠶⠞⣛⣩⠭⠭⠭⠭⠭⠭⢭⣛⠳⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠾⢋⠴⠒⠋⢁⣀⣠⣤⣤⣤⣤⣤⣄⡈⠙⠲⢬⡙⣿⡉⠉⠛⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃⡴⠁⢠⡴⢛⣩⠭⠒⠚⠛⠛⠛⠒⠮⣝⢷⣄⠀⠙⣎⢻⡝⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⡼⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡹⣆⠀⠸⡀⢿⡀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠘⡇⢀⡶⢾⡇⡇⠀⢸⡅⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⡀⠀⣇⢸⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣷⠘⣇⠸⡇⣇⠀⠸⣇⢧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⢸⠸⡇⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⢻⡸⡄⠀⢻⡌⢮⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠁⠀⢸⢰⡇⠀⢠⡏
⠀⠀⠀⠀⠀⢠⢸⡇⠘⠳⠾⢿⡜⣆⠀⠙⣦⡙⠦⢌⣀⣀⣀⣀⣀⣀⡤⢞⣱⠟⠀⢠⢏⡾⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠘⠈⣇⠀⠀⠀⠀⢻⣌⠳⣄⡈⠙⠳⠶⣤⣭⣭⣭⣭⣤⠶⠛⠁⣀⠔⢁⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠳⣦⣙⠲⠤⣀⣀⣀⠀⠀⢀⣀⡤⠖⢊⣡⡴⠋⠀⠀⠀⢀⡟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠐⠦⠉⠛⠶⠶⠤⣬⣭⣭⣥⠴⠶⠞⠋⠉⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠒⠶⠶⠶⠶⠧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟
⠀⡀
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⣀⣭⢤⣄⣀⠀⠈⢇⠐
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⠄⠠⡀⠀⠀⣴⠻⣿⣿⢿⢾⣽⣳⣲⢄⣖⡀
⠀⠀⠀⠀⠀⢷⣿⠙⢸⠁⠀⠀⠀⠀⡜⠾⢩⢿⠷⠦⢴⡯⣛⠿⣿⡿⠛⢷⣿⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⣷⡴⢩⣵⠛⡷⢾⢦⡏⣹⣏⢫⣶⣾⣿⣿⣷⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠲⠧⠀⠀⠀⠀⠘⡟⠞⠋⢠⠒⡇⢺⠉⢠⣶⡼⢹⣟⣿⣿⣷⡿⣿⢿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠁⡞⠐⡇⣯⠀⢶⢀⣜⢻⡦⣽⣟⣿⣿⡿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠬⢀⡿⡗⠀⣤⠈⠁⡻⠿⢷⣬⠛⣿⣿⣿⣿⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡂⢸⡇⢰⠄⢍⠁⢨⣉⣟⢠⡜⠓⢻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣂⣸⣁⣼⣿⣮⣤⣹⡗⢿⠈⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣋⢪⡿⣿⣏⠉⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⢢⠀⠀⠀⠀⠀⠺⣿⠋⠙⢻⣿⣿⣾⣾⣷⣤⣼⣧⣼⢿⡿⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃⠈⢢⣀⣘⣀⡀⣤⡀⠀⠀⣿⡀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣆⢷⡹⣧⡘⣿⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠡⠄⠀⠀⠛⢉⣿⡗⠈⠁⠈⠉⠉⠁⠀⠀⠀⡟⠈⠻⣿⣿⣿⣿⣿⣾⣎⢳⣜⢿⣿⣇
⠀⠀⠀⠀⡔⠉⠀⠀⠀⡀⠂⣀⡴⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠠⣸⠃⠀⣼⣿⠻⣝⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣄⣀⠀⣀⠘⢦⣴⠁⠀⠀⣘⣇⠀⠀⠈⣿⠋⠻⣿⢿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⣶⣶⣾⣾⣿⣿⣿⣤⣾⣿⣿⡇⡀⡤⢿⣤⣶⣤⣿⡀⠀⠘⢷⡈⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⡛⠉⠙⠛⡛⢛⠿⢿⣿⣿⣷⣷⣧⢸⣿⣿⣿⣿⡇⠀⠀⠈⢹⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠏⠳⠦⠤⠀⠀⠴⣿⣿⣿⣿⣿⠘⢿⣿⢁⣿⠁⠀⠀⠀⠀⠗⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠀⢘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠌⠈⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠤⡤⣤⢒⣖⣒⣒⣮⠇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠘⢹
⠀⠀⠀⠀⣧⠃⣠⠊⠊⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠳⣀⡀⠤⠤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠃⠁⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⢠⠁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠊⠀⠀⢀⣀⠠⠤⠄⠀⠀⠠⠤⢄⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡌⠀⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠤⠤⡇
⠀⠀⠀⠀⠀⡇⠀⠆⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⢒⠁
⠀⠀⠀⠀⠀⠃⢀⡀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢌⠀⢨⠧⠀⠠⣈⠄
⠀⠀⠀⠀⢰⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠷⠬⠉⠹⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠐
⠀⠀⠀⠀⢸⠀⢤⠄⠠⠀⠣⠀⡄⠀⠀⠀⠀⡜⠂⠒⠂⠀⠀⠀⠐⠚⡆⠀⠀⠀⠀⠀⢀⠀⠅⠒⠀⠁⠀⠀⠈⠁⠈
⠀⠀⠀⠀⢸⠀⠀⡀⢀⠀⢰⠀⡂⠀⠀⠀⠀⠡⠀⢠⠀⢀⣀⠠⡀⢀⠁⠀⠀⠀⠀⠀⠂⠄⠀⠬⠇⢈⠀⠆⠀⠑⠒⠀⡀⠀⠉⠁
⠀⠀⠀⠀⢠⠀⠈⠁⠈⠀⢸⠀⡇⠀⠀⠀⠀⢨⠀⢸⠀⠠⠤⠀⠄⠘⠀⠐⠒⠂⠀⠀⠀⡈⠀⠰⠀⠐⠀⠉⠀⡶⠀⠂⠠
⠀⠀⠀⠀⠘⣄⣀⠉⠀⢁⣸⡊⠁⠀⠀⠀⡴⢁⣃⣀⣉⣀⣀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠭⠄⠀⢀⡀⠀⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠈⠱⠉⠁⠀⠀⠀⠀⢀⡼⢴⠁⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠘⢦⠒⠀⠮⠀⠏⠁⠏⠁⠋⠐⠶⠁⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠌⠴⠆⣀⠀⠠⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠒⠒⠈⠉⠀⠀⠀⣀⠤⠔⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠀⠒⠒⠊⠉⠁⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⣤⣤⣠⡟⠁⡴⠃⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡾⠋⠁
⠀⠀⢀⣀⠀⠀⠓⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢶⣤⣀
⠀⠀⣏⠀⠴⢤⠦⣾⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⠿⠆⠀⢰⣿⢐⡇⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣸⠀⠀⢀⣤⣤⠞⠋
⠀⠀⣀⣌⣤⠆⣼⠃⢸⣷⠀⢸⡇⠀⢰⡀⠀⠀⠀⠀⣠⠄⠀⢠⣿⠀⠀⣀⡈⠁⢀⣴⠟⠉
⠀⢰⡏⠀⠁⠀⢹⡄⢹⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⣼⡿⠀⠀⢸⡏⢀⡀⣨⠟⠀⣼⡟
⠀⠀⣿⠂⣀⣀⡀⢻⡌⢻⡀⢸⡇⠀⢸⡟⠀⠀⣰⡏⣴⠀⠀⣸⡟⠈⣹⠁⠀⣼⣿⡁
⠀⠀⠈⢻⡋⠀⠁⢀⣽⠶⢿⠈⣧⠀⣿⡁⠀⠀⣿⠃⢿⠀⠀⣿⣁⡿⠋⢀⣾⠟⢉⣷
⠀⠀⠀⣾⣧⡾⠀⣾⠃⠀⡘⣧⣹⡄⢸⣇⠀⠀⢿⡀⠘⢧⣀⡟⠈⣠⡴⠛⠁⠀⠈⢿⡀
⠀⠀⠀⢿⠀⠀⠀⣿⢀⡾⢁⠀⠉⢳⣜⣿⡀⠀⢸⡇⠀⠀⢉⣴⠾⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡷⠂⠀⢻⡾⣱⠏⠀⣴⡿⠉⠛⢻⡄⠈⣿⢀⣴⡾⠋⠀⠀⠀⠀⠀⢀⣷⠏
⠀⠀⠀⣼⠋⠀⠀⠸⢷⡟⢀⣸⡟⠁⢀⡖⠀⢻⣦⠟⠋⠁⠀⠀⡄⠀⠀⢀⣷⠾⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠘⠛⠛⠋⠀⠀⠻⠶⠶⠛⡉⠀⠀⠐⢦⡖⠃⠀⣀⡾⠁
⠀⠀⠀⠸⣧⡀⠀⡀⠀⠀⠀⢧⣠⠀⠀⢀⣀⣠⠷⣄⣀⣠⡾⠃⠀⠉⣿
⠀⠀⠀⠀⠸⣧⣴⠏⠀⠀⠀⠀⢙⣻⣷⡚⠉⠁⠀⠸⣏⠉⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠛⠋⣩⢙⠻⢷⣤⣀⠀⠈⠛⠒⠚⠋
⠀⠀⠀⢰⣞⣷⢸⣿⣄⡀⠀⠘⠶⠟⣠⠤⢤⡈⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠁⢸⡇⠈⠛⢶⣄⡀⠀⠙⠚⣯⣤⣶⣶⠀⠙⠻⢶⣦⣄⠀⠀⠀⠀⣏⣹⠆
⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠋⡵⢶⣻⠆⠀⠈⠙⢻⣶⡄⠀⠈⠉
⠀⠀⠀⠀⣴⣋⠙⢷⣄⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⣀⣤⣤⡶⠞⠋⠉⡇⢀⡠⢤⡀⠀⠀⠀⡶⠛⡆
⠀⠀⣀⣸⣇⠙⢷⣾⣉⠳⣤⡀⠀⠀⠀⠀⠀⠈⠙⣿⠟⠋⠉⠀⠀⠀⠀⠀⣇⠈⣀⣨⡿⠀⠀⠀⠀⠉⠁
⠀⠈⢯⡽⠙⠛⣿⠀⢈⣷⠈⠙⢶⣄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁⣰⠛⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⢺⠀⠀⠀⢀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠻⠤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣟⣛⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⡀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡛⢿⡻⣿⠛⣻⢿⠷⠀⢼⣠⠋⢀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⢸⣿⠴⠀⠉⠉⠉⠹⢽⣭⣉⣉⣣⣽⣦⣹⣿⣤⡏⠈⣧⠀⠘⣧⠖⣫⣡⣞⣉⣩⣽⡯⠟⠉⠉⠉
⠀⠀⠀⠤⣚⣥⣤⣤⣤⣀⣀⣀⠀⠀⠈⠉⠉⠉⠻⣿⡇⢹⡇⠀⠘⣧⠀⣿⡾⠋⠉⠉⠉
⠀⠀⠀⠀⠻⣉⠯⢭⣻⡟⣻⡻⠇⠀⠀⠀⠀⠀⠀⠈⠻⣾⡇⠀⠀⣿⣼⠟⠀⠀⢀⣤⣴⣾⣷⣿⣿⣦⣄⡀
⠀⠀⠀⣀⣤⣬⣅⣀⣇⡝⠉⢾⣿⢷⣶⣶⡄⠀⠀⠀⠀⠙⢿⣆⢠⣿⠋⠀⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣶⣆
⢠⣴⣴⣯⠻⡿⣿⡿⣽⡅⢰⣯⣤⣬⠔⠰⠿⢶⡦⠀⠀⠀⠈⢻⣿⣿⠀⠀⠈⠻⠿⡿⣿⢿⠳⡟⣹⢿⢿⡿⠟⠃
⠀⣬⣶⣶⣦⣍⢶⣳⠇⠹⣯⡞⠓⣾⣿⠿⣿⠆⠀⠀⠀⠀⠀⠈⣿⣿⠀⢀⡀⢲⣰⠇⡈⠻⣧⢹⡷⠚⠉
⠀⠀⠑⠏⠓⠙⢦⣹⠀⠀⢹⡤⠚⠉⠀⠋⠀⠀⢀⣀⡀⠀⠀⠀⢸⣿⡆⠀⣽⣾⣿⣿⣁⠀⣿⡾⢁⣠⣤⣶⣦⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⣰⠏⠀⠀⢠⣴⣶⣶⣾⣿⣿⣿⣿⣦⠀⠸⣿⡇⠀⣾⣿⣿⣿⡦⠀⣿⠃⣿⣿⡯⢏⡻⠏⣿⣿⡄
⠀⠀⠐⣿⠃⠀⠀⠈⣿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢻⣿⣿⠀⠀⣿⣧⠀⠈⢉⡏⠉⠁⠀⣿⠁⠛⢢⣇⡌⣡⠔⠳⠿⠃
⠀⠀⣰⡏⠀⠀⠀⠀⣿⠁⠀⠀⢰⢸⣿⡿⠿⠿⠿⣿⡏⢹⣿⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢤⠿⡖⠁⢀⣴⡄
⠀⠀⣿⣿⣶⣦⡀⢰⣿⣿⢸⡀⢁⣿⢻⡆⠀⠀⠀⢸⡇⠀⠛⠋⢀⣿⣿⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣸⡼⢁⣠⣤⣽⣿⡀
⠀⢰⢿⠉⠙⠿⡇⠈⣿⣿⣾⣇⣼⣿⣹⣷⣶⣷⣶⣻⣧⣠⣤⣴⣺⣿⣿⠀⡀⢸⡇⠀⠀⣼⣿⢳⣷⡟⢀⣿⠿⠿⣿⠛⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢾⣽⣿⣿⣿⣿⣯⡗⠀⠀⠀⠀⢀⣤⠴⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠇⣀⠁⣀⣀
⠀⠀⢿⣿⡿⠁⠎⢻⣿⡿⠀⠀⠀⠀⣾⣿⣷⠰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠘⠃⠨⠄⠉⠁
⠀⠀⢫⢿⣿⠀⠀⢸⣿⣍⠁⠀⠀⢸⣏⠉⠀⠁⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⣿⣤⣤⣼⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡖⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣀⣈⣉⣩⡅⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⠀⡀⢀⡀⢀⡀⣀⢀⢀⠀⢀⢀⢀⠀⣀⢀⠀⢀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀
⠀⠀⠀⠀⠀⣔⣆⠆⠀⠀⢶⣌⠉⠀⠀⠀⣱⢸⠀⠺⡇⣿⢾⢸⠇⢿⢸⢹⠀⢿⠈⡇⢸⠀⢻⡇⡟⡇⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢹⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣿⡎
⠀⠀⠀⠙⠁⠙⠛⠈⠋⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢶⣦⠿⠚⠿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⠶⣿⡇
⠀⠀⠀⢠⣤⡀⢀⣀⡄⠀⠀⠈⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⣷⣶⠇⠀⠐⠀⠘⣷⣶⠀⠀⠀⠀⠀⢿⣿⡤⡀⠀⠁⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⢐⣂⣀⣉⣭⡅⠀⠀⠀⠘⠇⠀⠀⠀⠿⠁⠀⠀⠀⣶⣾⡀⠀⠀⠀⢀⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢰⣿⢲⣶⣾⢿⡧⠉⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣶⡇
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣉⡛⠈⠀⠀⠀⠀⣴⣶⡖⠀⣨⣭⣅⠀⠐⣶⣶⠆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠇

⡏⢀⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣴⠄⠀⠀⠤⠀⠀⠈
⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠉⠀⠀⠀⠀⠀⠀⠘⠚⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠐⠢⣴⣟⢙⣶⣶⣿⣾⣧⣀
⣤⣠⠀⠠⠀⠀⠀⠀⠀⠀⣠⣤⣶⢾⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠿⢉⣻⣿⣿⣿⣿⡯⡿
⠚⠅⠀⠀⠀⠀⠀⠁⠀⠈⠙⠛⠃⠈⠫⠏⢻⣲⠞⠹⠻⠏⠀⢀⡦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣤⣿⣤⠀⠀⠘⠋⠀⠈⣝⠛⠿⠿⡿⠓⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡄⠘⢹⡟⠛⠋⠀⠀⣤⣤⡄⠀⠀⠀⠉⠁⡅⠀⠐⠂⢀⣀⣤⣶⣶⣾⣶⣤⣇⡀
⠀⣀⣀⡀⠀⢶⠐⣦⠂⢉⠀⠀⠀⠀⠀⠘⠁⠠⢀⣀⣀⡀⠀⢀⢨⠆⠀⠒⡶⠀⠙⠋⢰⡶⠀⠀⠀⠀⢃⡐⠐⣿⠿⠻⣯⢽⠿⢟⠗⠈⣿⠿⠓
⠈⠉⠙⠃⠀⠀⠀⠀⠀⢸⣤⣴⡶⢦⠀⠀⢐⢺⢫⣯⣿⣿⣷⡀⢰⠂⣶⠀⠀⠀⠀⢁⠈⠁⢀⣠⣤⣶⢿⣿⣿⣿⣷⣤⣌⣱⣶⣧⣤⣦⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠛⠿⣯⣿⡽⠛⠋⠲⢶⣟⣑⣶⣿⣻⣶⣅⣀⠈⠛⠛⠁⠙⠽⠛⢓⡶⣟⣛⠁⡴⣶⣻⣿⣻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⠀⠀⠐⣌⠯⢩⢿⣭⡿⣿⣟⣨⣷⣀⣤⣥⣢⡀⠀⢸⠁⠐⠹⠛⣿⣟⣹⣿⣽⠿⠛⠁
⠀⠀⠀⣠⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡈⠁⠀⠀⣟⡈⠀⠈⠓⢈⣋⢉⢻⣾⣷⣟⣿⣿⡟⣷⠀⠏⠀⠀⠀⢀⡘⠾⣿⡏⠉⠶
⠀⠀⠛⠛⠻⡟⠋⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢲⣾⣏⣹⣾⣿⣵⣾⠯⣾⠋⠉⠉⠉⢁⢻⣛⠛⠓⠛⣴⣶⡿⠟⠁⠀⠽
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⢁⣀⠀⠘⠀⠀⢠⣵⠋⣴⠿⣼⠛⣿⣏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠝⠋⠀⠀⠀⠐⠄⡀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢛⠟⠛⠇⠀⠀⠉⠁⠀⠀⠀⠀⣈⠉⠁⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠙⠊⠱⠏⠀⣖⣶⠿⠛⠧⠀⠀⢐⡺⠋⣽⣽⣿⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢻⢏⣿⣯⠟⠋
⠿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡘⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡘⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠓⠲⠦⢤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⠁⠀⠚⠋⠁⠙⠑⠶⢤⣤⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠉⠃⠀⠀⠀⠈⠳⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡎⠀⠀⠀⠠⠊⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡀⢀⠑⠀⠀⠀⠀⠀⠀⠘⡆⢰⠁
⠀⠀⠀⠀⠀⠀⣠⠎⠉⠙⠾⠀⠀⠀⠀⢠⡌⣼⣇⡾⠀⠀⠀⠀⠀⡴⠶⠀⠀⠀⠀⠀⠀⣧⢸⣿⣰⠀⠀⠀⠀⠀⠀⠀⠿⠉⠉⠑⢆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠲⠖⠒⠒⠒⠲⡆⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⠀⠀⠀⠀⢀⡹⠷⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠈⠉⠙⠉⡀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀⠀⠀⠀⢀⠞⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⡼⢁⠴⠲⢌⢳⡄⠀⢀⡜⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠈⠉⠁⠀⣸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣀⢀⣼⣇⠀⠀⠀⠀⢀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⡠⠤⠶⠒⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⣤⢤⣤⣤⣭⣿⠀⠀⠀⠀⠘⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠿⠤⡖⠒⠉⠉⠳⡀⠀⠀⠀⣀⣀⡀⠀⢋⠁⡀⠀⢠⡄⠀⠀⢀⣿⠉⠀⠀⠀⠀⠀⣠⣿⣶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⠳⣄⣈⠋⠉⣥⣎⣉⠙⢉⣤⠋⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⡝⠉⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢶⡀⠀⠀⠀⠀⠈⡷⢦⣄⡀⠀⠀⠉⠉⠉⢀⣛⠀⠉⠉⠀⢆⣠⡴⡎⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡅⢸⠀⠀⠸⣤⠇⠀⠀⠀⠀⠀⡇⠀⠈⠉⠘⠛⠒⠒⠂⢼⢯⡀⠤⠄⠚⠋⠁⢠⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡟⠉⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣤⣄⣤⣀⢀⣀⠄⣠⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡉⣉⣉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⣉⡉⢙⠇
⠀⠀⠀⠀⠀⠈⠫⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠄⣀⣀⣀⣀⣀⡀⠤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⢿⣄⠄⠀⢤⡤⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠸⣽⣷⣦⣀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢂⣶⣿⣷⣾⣿⣷⣦⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠁⢀⢤⣽⣿⣿⣷⡄⠀⠀⠀⡇⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡟⠻⣷⣒⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡿⣏⠋⢹⡇⠀⠀⠀⡇⠀⢸⠀⠀⢸⠋⣿⣪⡟⢸⡇⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⣃⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠉⠁⠉⠉⠐⠟⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⢘⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣴⣆⣴⣤⣄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠄⢀⡀⠴⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⢿⡏⢛⡻⣿⣗⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣠⣯⣥⣬⠆⠀⠀⠀⠀⡇
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣍⣃⡈⢠⣿⣿⣦⠄⠀⡇⠀⢸⠀⠀⢀⣀⢂⣩⣟⣻⣝⡁⠁⠀⠀⠀⡇
⠀⢀⣻⠁⠀⠛⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⣶⣾⣿⣿⡟⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠁⢿⢹⡯⡟⠐⠓⠁⠀⠀⡇
⣾⡿⠋⠤⠠⠀⢤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⢺⡿⠿⠋⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣷⣶⠄⠀⠀⠀⠀⠀⡇
⠉⠃⠈⣶⣿⣤⡷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡇
⣧⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣶⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣔⡒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⣌⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡻⣷⣦⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⡿⣦⡀⠙⢕⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢎⠇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⢤⣤⣄⡀⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠳⠀⠀⢀⢠⣤⣤⣤⣶⣾⣾⣼⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢠⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣴⡏⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣶⣶⠟⠋⠁⣀⣤⠶⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣤⡴⠖⠋⠉⢀⣀⣠⠄⠐⠒⠒⠀⣀⠀⠀⢀⡀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⡾⠋⠁⠀⣠⡴⠾⠋⠁⢀⣀⣠⠤⠀⢈⡁⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⣀⡠⠴⠾⠟⠋⠁⣀⡤⠞⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠉⠀⢀⣠⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠿⡏⠉⠩⡈⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠀⠀⢀⠀⠁⠀⠀⠀⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣶⢠⡀⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢠⡱⡆⠑⢤⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠙⡅⠀⠈⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢣⠀⠀⠀⡇⠄⠀⠀⡸⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⢀⢷⠀⡠⢿⠂⠀⠂⠀⠀⡀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠍⠉⠁⠈⠻⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⡀⠑⠀⠀⢀⠀⠄⣀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⠀⠸⡄⠙⠒⠁⠀⠀⠈⠙⠐⠄⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⠀⠀⠘⠆⠈⠄⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠂⠠⢄⡀
⠀⠀⠀⠀⠀⣸⣿⠀⡀⢀⠠⠀⠀⠀⠁⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⡆
⠀⠀⠀⠀⠀⠿⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠤⠀⠀⠠⠁⠀⠀⡇
⠀⠀⠀⠀⠀⣷⠀⠁⠀⢃⠀⠀⠈⠀⠁⠀⠀⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠧⠲⣄⠶⢏⣤⠐⠛⠁
⠀⠀⠀⠀⠀⡿⠀⠀⠀⢘⡷⠦⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠶⠒⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢃⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠛
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠋⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣾⣷⣦⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠈⠛⠓⠀⠀⠀⠈⢸⣿⡏⠉⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠰⠋⣁⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠉⠁⠀⠀⠈⣹⠂⠀⠀⠀⠀⠀⠀⠀⢿⣥⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡻⠛⢷⣄
⠀⠀⠀⠀⠀⢈⢳⣤⣤⡤⠤⢶⡖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣼⣜⣀⣠⡴⠶⣦⣀⣴⢟⠜⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⡾⣹⠿⠦⠤⠤⠤⠼⠧⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⠫⠂⠁⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⡇⣧⠀⢀⣀⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠳⣬⠟⠉⠉⠉⠉⢳⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠶⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢀⡴⠒⣄⠀⠀⠀⠀⠀⣀⣠⡾⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢠⣏⣠⠴⠃⠀⠀⠀⣠⡼⠋⠉⢻⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⣷
⡔⠓⠦⡀⠀⠀⢀⣄⡀⠀⠀⢠⡇⠀⢸⣀⣀⡉⠁⠀⠀⠀⠀⣀⣠⣿⡀⣠⠞⠛⠷⣄⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠙⠲⠤⣝⣦⠀⢯⡀⠙⡄⠀⢸⠇⠀⢸⣏⡉⠉⠛⠛⠛⠛⠋⠉⠉⠈⣿⠉⠀⠀⠀⠈⠻⣦⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣤⣾⠀⠰⣿⡙⠛⠳⠶⣤⣤⣤⣤⡴⠶⠶⠛⢷⣄⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⣤⣬⡿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠤⠤⠤⣄⡀⢹⣿⣭⣤⣤⠦⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠶⠶⠶⠛⠛⠷⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠲⠒⠊⠉⠀⠠⣿⣯⣥⠶⢖⣀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣀⠤⢖⡖⠀⠀⠀⠀⢀⣄⠸⠿⠶⢾⣟⣩⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣞⠁⣠⠞⠀⠀⠀⢀⠞⢉⡇⠀⠀⠀⠈⠉⠁⠀⠀⢰⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢶⣶⠶⠟
⠈⠉⠁⠀⠀⠀⠀⠻⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⣶⣶⣶⣶⣲⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠻⢿⣿⣟⣿⣿⡟⠀⠀⣤⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢦⣶⣿⢾⣧⡘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣨⣿⣿⣆⢿⣯⣛⢜⣀⣦⠀⡀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣌⣙⢻⣿⣿⣿⣿⣿⣌⠿⢿⡾⠿⠁⠀⠁⠀⠀⠀⠀⣠⡾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⣈⣁⣀⣀⣤⣤⣤⡶⠾⠟⠉⠉⠉⠳⣽⣿⣿⣿⣧⣿⣿⣦⣦⣀⠀⠀⠀⢀⣈⣤⣾⣿⣧⣿⡆
⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡛⠃⢏⣹⣅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣦⡄⢀⢰⣴⣶⡀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣻⣿⣌⣿⠋⣿⣷⡿⣗⡓⣏⣛⢻
⠀⠀⠀⠀⠀⠀⠉⠠⢀⣤⣿⣿⣧⣤⣿⣿⣿⣤⣤⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣨⠃⠀⢻⣿⣻⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢿⣹⣿⣿⠟⠿⢿⣿⣿⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⠂⠀⠈⢱⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⡀⠙⡿⠋⣀⣀⡈⣻⣿⣟⢿⣇⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣷⠈⠀⠀⠸⡿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⢫⡛⢿⡟⠙⢛⢿⡟⢿⣾⣿⣿⣻⣧⢿⡟⠀⠀⠈⣭⢽⣿⡄⠀⣀⡖⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠙⢾⣧⣿⣻⣿⡏⢀⣸⣋⠀⢙⣶⣿⣷⣶⡀⠀⠹⡯⣥⣶⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢄⠉⠉⠉⠻⣼⢡⣙⣿⣿⣿⠿⠟⠀⠀⠀⣀⣀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢻⡏⠻⠍⠽⢁⠀⠀⣈⡤⠤⠛⠁

⣀⣀⣀⡤⠞⢧⣤⠤⢤⣀⡀
⢻⠁⢠⢒⢗⢦⠙⣦⠀⡇⢸⠉⠉⠉⠉⠉⠉⠉⠉⠛⣆
⢸⠇⠘⢮⣛⡼⣰⠁⣠⠧⠼⠒⠒⠒⠒⠒⠒⠲⣄⠀⢹
⠘⠲⡖⠲⢤⣄⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣤⠼⠲⡄
⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⣉⣉⣉⡇
⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠉⡇⠀⠀⢾⢣⠀⠀⣠⡲⠂⠀⢀⠞
⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣇⠀⠀⠈⠉⠀⠀⠈⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠄⠀⢸⠀⡏⠀⠀⡔⢩⢷⣄⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⢀⣡⠦⠶⣧⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡲⠶⠀⢀⠔⠉⠀⠀⠀⠈⠳⣄⡀⠈⠳⠤⠤⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡇⠀⡧⠀⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠜⠀⢠⠁⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡜⠀⠀⡞⠀⠀⢻⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢦⣴⠇⣀⡀⣸⠠⡄⡽⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢮⣩⠵⠯⣽⣎⣡⡤⠴⠚⠉

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⣀⣀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣀⡀
⠀⠀⠀⠀⠙⣸⣿⠻⢥⣀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⣠⣾⣿⣿⣿⣷⣬⡻⢦⡀⠀⠀⠀⠀⠀⠉⠙⠛⢉⣉⣉⠁⠙⢷⡄⠀⠙⣿⡟⠁⣼⡿⠞⠋⠉⣉⣉⡙⠛⠋⠁
⠀⢀⣾⣿⣫⣿⣿⣿⣿⣿⣿⣦⠻⣆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡙⢶⡀⡟⠀⢸⡏⠀⣰⣾⣿⣿⣿⣿⣿⣷⡦
⣴⣿⣿⣿⣿⠿⠿⠿⢻⣿⣿⣿⣷⣌⢷⡀⠀⠀⠀⠀⠉⠙⠻⢭⣛⢯⡉⠛⢿⣧⣿⠀⢸⣧⡾⣛⡭⠿⠿⠛⣉⣉⡀
⠻⠿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⡹⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⣹⣿⣠⡾⠛⠉⠀⢀⣀⣴⣿⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⣭⣓⡲⢦⣀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡟⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡳⢤⣀⣀⣀⣀⡀⠀⢹⡇⠀⠀⠈⠉⠉⠉⠉⠛⢻⠀⠈⣯⠟⢉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣬⡙⢦⡀⠀⢀⣴⣶⣶⣦⣼⡇⣀⡿⠚⠉⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⠀⠀⢉⠉⢉⠉⢧⣸⠁⠀⣸⠽⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣧⠀⠉⠿⠮⢢⣸⡏⡠⠞⠓⠋
⠀⠀⢠⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣧⠀⠛⠓⠀⢹⡿⠁
⠀⣰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⡘⠻⠿⢿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⡇⠈⣿⣦⢠⣦⠀⢸⡇
⠀⠀⠀⠈⣿⣦⣀⣀⣀⡀⠀⠀⠀⠀⢀⣿⣿⣿⢏⣾⣿⠀⠀⠀⠀⠀⠀⠀⠰⣌⠻⣿⣿⣿⡇⠀⠈⠻⢿⡿⠀⢸⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⠃⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡌⠻⣿⣧⠀⠀⠀⠀⢳⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⣯⢣⠀⠀⣿⣿⠃⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠙⣿⡆⠀⠀⠀⢸⡆⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⢻⡇⠀⢀⣿⠃⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⢻⣷⠀⠀⠀⠈⣷⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⠀⣇⠀⣸⡟⠀⠀⠀⠀⠀⢸⣿⡀⠀⣀⡀⠀⣰⣿⡇⠀⠀⠀⠀⣸⣿⠁⢀⡀⠀⣿⣸⣷
⠀⠀⠀⠀⣀⣼⣿⣤⣰⣧⣤⣿⣶⣿⣿⣶⣦⣤⣶⣦⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣴⢺⡶⠖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣦⣽⠛⠛⠁⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⠼⢤⣄⡀⠀⣀⣀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡞⢩⠄⠀⠀⠤⠌⢻⠉⠉⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣀⡀⢸⡇⠀⠸⣕⣫⠇⠀⢸⡄⠀⢀⣸⡄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⢋⡴⠚⠛⠳⢬⣔⣂⣀⣲⡬⠟⠙⠛⠓⢺⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣢⡀⣿⣀⣸⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢥⠜⡧⠀⠀⠒⡚⣤⢄⠀⠀⠀⠀⠀⠀⠀⢠⣴⢶⣶⣶⣤⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠓⠋⠜⠀⡏⢦⠱⡈⠎⠛⠁⢀⠤⡀⠀⠀⢠⣿⣴⠂⡟⣴⣶⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠃⡀⠀⡀⠀⠉⠀⡀⠀⡀⠀⠀⠉⠀⣀⡀⠘⣷⣘⣃⣿⣬⡥⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡀⠀⠰⠁⣠⡷⠚⠳⣆⣸⣤⡈⣶⠛⣶⠀⠠⠃⢸⡯⡒⢿⢐⣿⠸⢿⣿⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣩⢇⡴⠚⢻⡗⢦⣞⠛⣄⡴⢿⡌⠛⠁⠀⠀⠀⠘⢷⣭⣾⣶⡾⠟⠋⢴⣿⡖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⢸⡅⣼⠛⣧⠀⠻⡄⠘⢧⠀⢻⡉⠳⡄⠀⢀⡀⠀⠈⠉⣥⠀⠀⠀⠈⠉⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⠙⢻⣹⠾⡄⠘⣧⠀⠹⡄⠈⠇⠀⠳⣄⡇⠀⢸⡇⢀⣤⠀⣿⠀⣀⣀⠀⣾⡟⠸⣷⣶⢿⡆
⠀⠀⠀⠀⠀⠀⢀⡟⠈⠷⠤⣮⡷⢀⣹⣆⠘⣧⠀⠙⠀⠀⠀⠀⠹⡅⠀⢸⡇⢸⣿⣆⣿⣾⠟⣿⡇⢉⣻⡇⢿⠇⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞⠁⠀⢿⠈⠻⣆⠈⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⢿⣾⢃⠙⠋⠹⠿⠟⠻⢋⠉⣄⣤⣀⣩⡀
⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣇⣸⣷⣾⠟⣷⣿⡁⣿⢿⣿⠛⠃⣀⣤⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠙⠦⣤⣤⣾⣹⠦⣄⡀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠙⢻⣿⠻⠿⠋⣈⠛⣯⢨⣷⢶⣄⢿⣯⣉
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣸⣄⣸⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠘⣆⠀⣿⠀⢻⣿⢁⣿⣦⠈⣿⣷⣿⡏⣿⢀⣿⠀⠈⢻⡆
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢘⡆⢻⣇⣤⣿⣸⣿⣽⣷⣹⡏⢻⣧⢻⡿⠛⠷⣶⠿⠃
⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢀⡠⠞⠀⠘⣿⠁⢹⡿⠟⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⣤⠀⠃⠀⠻⢅⡶⠀⠀⠀⠀⠀⢀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠙⢧⠀⣠⠤⡀⣐⣄⡄⠀⠀⢴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠁
⠀⠀⠀⠐⢿⣯⢉⠒⢠⠄⢤⡧⠀⠀⢘⠄⠀⢠⢄⢬⠀⠀⠀⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⠀⠀⣀⢢⠀⣾⠁
⠀⠀⠀⠀⠀⠙⢎⠀⠃⠂⣯⠕⣋⠄⠨⣆⠀⠀⡺⣄⢢⠄⣀⠋⠁⠠⠀⣤⡒⠀⠀⢰⡇⠈⠁⠉⢰⣄⣉
⠀⠀⠀⠁⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⡈⡅⣿⠘⡐⣻⣂⠀⠀⠀⠘⢿⣂⣀⢼⡆⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠈⠁
⠀⠀⠀⣀⢤⣇⣾⡶⠄⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣉⠁⠃⠁⠔⠀⣴⣶⡀⠀⠀⠀⠠⠀⠀⢦⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀
⠀⢠⣬⡇⠀⣰⣧⡔⣲⣨⣶⡄⠀⠀⠀⠀⠀⢨⡿⢿⣷⡠⣄⠀⠀⠀⠀⡌⡠⢀⢄⠀⢦⠀⠀⠀⡄⠀⢱
⠀⠈⢹⡅⠀⠉⢸⡸⢿⣻⣏⣡⡖⠀⠀⠠⢤⡗⠚⣲⣤⠱⠿⠷⠀⠀⠀⡇⣠⠐⠀⠁⠈⣷⢁⡀⠑⡀⢸⠃
⠀⠐⠞⢃⠀⠀⠙⢧⣸⢁⢛⣃⣠⠀⠀⠀⠈⠛⠄⠈⢋⣾⡟⢰⡿⠀⠀⠑⡘⠄⢀⡀⢢⣼⣄⠷⡖⢘⠑⠄
⠀⠀⠀⠀⠁⠀⠀⠠⠀⠉⠉⠅⠀⠀⠀⠀⠀⠠⠀⠈⠉⠒⠒⠂⠃⠀⠀⠀⠲⠧⠠⣁⢈⢈⢀⡤⠖⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⢤⣴⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠰⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣠⣤⣧⣤⣾⡀⢀⣧⣤⣤⣤⣄⡀⠀⠈⠙⢷⣌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠚⢯⣁⢀⣀⣀⡀⠉⠉⠀⢀⣀⣠⠬⣝⠳⣦⡀⠀⠛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡖⠁⠀⢀⡸⠋⠉⠉⠉⠉⢉⣻⠟⠉⠉⠁⠀⠈⣇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⣰⡶⠚⠛⠛⠛⢣⣀⣠⢿⣤⣀⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⢹⠄⠈⢷⣄⣀⣀⣀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣻⣿⡶⠶⠤⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠆⠘⢧⣀⣀⣤⠀⠀⠀⣠⣼⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠴⢧⣀⡀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠲⠤⠖⠁⠈⠷⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⡇⠀⠀⠹⡛⢻⡁⢀⡿⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠆⢨⠿⡟⢿⠄⠀⢀⣧⣄⣉⣉⣀⣀⣀⣀⡤⠤⠔⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠃⢪⡀⠀⢸⠋⢻⠛⡏⠉⡿⠛⠃⠀⠀⠀⠀⠠⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡍⠛⢿⡶⠾⠿⣶⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⣀⣤⡶⠛⠛⠛⠓⠒⠶⠶⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣁⠀⠈⢳⡒⣦⣀⣀⣀⠳⠤⠴⢶⡀⠀⢀⣖⣋⣀⣤⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠉⠁⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠉⠀⠀⠠⠖⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡞⣠⠖⠉⠀⢠⡞⠁⢀⡾⠁⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣠⠗⠁⠀⢀⡠⣾⠁⠀⣾⠀⠀⡼⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣩⣤⡤⠴⠒⠉⠀⣿⠀⣸⠇⢀⡾⠁⢠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⣰⣯⡶⣋⠤⠚⠛⠳⠆⠹⣄⠀⡆⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠾⠋⠀⠀⠉⠉⠉⠀⠀⡠⠀⠐⢤⠀⠘⣶⡇⢪⡖⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠂⣤⠠⠙⠒⠀⢠⢩⡆⠀⣠⣬⣌⠑⡄⠀⠀⠀⢰⣿⣿⣶⡀⠁⠀⠛⠁⠈⡛⠠⠞
⣀⡀⠤⠄⣠⠂⠀⠀⠀⠁⠀⠀⠙⢄⡀⠄⠐⠈⠀⠀⠑⠻⠀⠹⢿⣿⡇⠄⡠⠖⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⡜⢀⠀⠄
⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠚⢄⠀⠀⠀⠀⠙⠒⣀⢰⡄⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠉⠀⠀⠀⠀⣀⡤⢲⠙⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡀⠸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢲⠶⡲⠖⠒⡉⠍⠀⠃⠀⠀⠀⢡⡀
⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⡀
⠀⡇⠀⡇⠀⠀⠧⠆⠀⠀⡇⠀⣿⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⣀⣠⡤
⠀⣷⠀⣧⠀⠀⠀⠐⠀⠐⠓⠂⠉⠀⠀⠀⠀⡀⠀⠠⠤⢤⣀⣀⡠⠔⠁⠀⢑⣄⡄⠀⠀⠀⠀⣀⠜⠐⠂⠠⡤⠀⠀⠀⠈⢄⣤⠴⠒⠋⠙⠢⢄
⠀⢹⠀⢸⡀⠤⠄⠀⠀⣀⠠⠄⠂⢀⡀⢀⣀⠀⠤⠀⠠⠗⣴⠂⠀⢀⠠⠖⠋⠡⢑⠦⠂⠐⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⣦⡀
⠠⠘⠉⠀⠀⠀⡠⠂⠁⡀⠀⠀⠐⠃⠀⠀⠀⢙⠁⠀⠹⢤⡙⡢⠈⠉⠒⠀⢴⡒⠈⡀⠀⢀⡀⠄⠐⠉⠀⠀⠀⠀⢀⠠⢖⠉⠄⣈⡱⠶⢖⡊⠉
⠀⠀⠀⠀⠀⠀⣄⠀⠣⡀⠀⠀⡈⠀⢠⠉⠑⠥⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠆⣠⠊⠑⠠⣀⢀⡀⠄⠒⠈⠀⠀⠀⠂⠌⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡈⠑⣤⠀⠀⠆⠀⠀⣠⠼⠆⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠏⠲⣄⣀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢌⣂⢐⠦⡀⠁⠀⢀⡰⠶⢃⡀⠁⠒⠠⣀⠀⠀⠀⠀⢀⠠⠀⠊⢀⡤⢺⠐⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠈⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡈⠑⠤⣀⠻⣀⡉⡼⠀⠀⠀⢀⣀⠦⠐⠈⣀⡠⠔⠊⠁⠀⠸⣠⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠉⠂⠤⠤⠄⠒⠈⢁⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢠⠌⠙⠤⠄⠀⠐⢒⣉⡠⠤⠛⠻⢅⡀
⣀⣤⠴⠖⠋⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡄⠀⠀⢨⣅⠀⠀⠀⠀⠀⠈⠙
⠧⣄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡐⠳⡀⠀⠈⡄⠉⣒⣤⣤⠖⠊⠉
⠀⠀⢉⣲⠤⣔⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠗⠂⠔⠒⠈⣱⠀⣈⠢⠀⠙⠲⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⣬⣷⠶⠛⢾⠿⢶⣤⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣡⣾⣿⣾⣿⡷⡀⣸⣧⡀⠎⣽⢷⡝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢫⣼⢇⠋⠙⢉⣠⠷⠿⠬⢳⣮⡻⠧⢿⠸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡲⣛⡵⡞⠉⢭⢀⣴⣟⣽⣶⣶⣆⠐⠂⠌⣙⠿⡉⣧⣿⡿⢿⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⣾⣾⡍⡆⢱⠀⣿⡿⠛⠁⣾⠿⢿⣿⠿⣷⣦⠘⡷⢘⢿⢿⡿⠏⢹⡎⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣾⠛⠿⠟⠁⣸⣼⣋⣡⣀⠡⡘⢇⣼⣷⣤⣿⡿⡟⢃⣜⣙⣯⠻⢖⠀⢳⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠈⢐⡶⢛⣉⣤⣬⣭⣙⣛⡻⣦⣍⣙⣫⣭⣥⣶⠿⢋⣉⣁⣤⠬⢿⣦⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣁⣼⡾⠻⢫⣶⠟⢿⣿⠏⡉⡍⢙⠿⠚⢿⣿⣶⢶⡿⠿⠛⠋⢏⠻⣻⣷⣾⣼⠙⠛⠓⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⢟⣽⢿⣷⠇⣸⣴⣯⣵⣬⣶⣶⣾⠞⣫⢿⠭⢭⣻⡟⣿⢺⠟⠶⠶⣷⣶⣷⣾⣿⠿⢿⢻⣿⣿⣿⡦⣬⣧
⠀⠀⠀⠀⠀⠀⢠⠎⢩⢣⡟⢁⣀⡴⠿⣟⡽⠟⠋⠩⣉⡛⢌⠩⠡⠀⠀⠀⠀⠀⠆⡠⡀⢂⡤⢒⠉⠁⠉⡛⠲⢦⣦⣽⣿⣿⣴⣩⣝⡷⡀
⠀⠀⠀⠀⠀⠀⠸⡀⠸⢻⣊⡩⠗⣂⠉⠅⢀⣠⡤⢶⣦⠽⢦⠀⠀⡆⠀⠀⠀⣀⢠⡑⣴⣿⠖⠦⠀⡒⠂⢀⡹⠶⠬⠉⠉⣙⢛⡡⣍⢷⠆
⠀⠀⠀⠀⠀⠀⠀⢳⣄⡪⠙⠿⠷⣦⣄⡀⢘⡫⠊⡿⠛⠛⠛⡆⠆⠀⠀⡀⠀⠸⡾⠁⣿⢿⢿⣷⣒⡀⠀⠀⠀⠀⣠⡌⢉⢅⡶⠼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠭⡑⠢⢕⣛⣛⢛⠛⠷⣧⣆⣐⡇⠀⠀⠀⡇⢠⢀⡇⢰⣿⠀⢀⠱⠌⠀⠤⠚⠋⢉⣠⡴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠚⠛⠳⠤⣘⣋⡃⠀⠆⣰⠇⢸⠸⠀⢂⣿⣉⠉⠁⠠⠀⡲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⠀⡐⠜⠀⢸⠀⠀⢊⠎⢧⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡈⠀⢠⠆⠀⠀⢸⡄⠀⠀⠡⠨⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡼⠀⠀⠀⢠⠳⠀⠀⠄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠘⠀⠃⠐⠈⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢶⠀⣹⡇⠀⠀⠀⠀⠀⠀⠇⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢆⠀⢻⡄⠀⠀⠀⡀⠀⡄⢸⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣂⠹⣷⠱⡀⠀⡃⢀⣣⢇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣵⣽⣾⣷⠾⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠀⠀⢤⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⠤⠴⠶⠖⠃⠏⠉⠓⠲⠶⣤⣤⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⠁⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣤⣤⠶⠶⢤⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠶⠚⠀⣀⣠⠴⠂⠀⠀⠀⠀⣀⣠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠽⠛⠒⠛⠛⠉⠀⠀⠰⣧⣀⠀⣠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌⠙⠳⣶⣶⣯⠵⠂⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⣠⠔⠊⡕⠒⠒⠶⢤⣀⡀⢠⡀⠀⠀⠙⢿⣭⣥⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠴⣮⣥⣀⣀⣀⣀⣀⣀⣀⡤⠄
⠀⢀⡴⠊⠀⠀⡴⢿⣾⣄⠀⠀⠈⠉⠛⠿⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢉⣳⣄
⣐⠉⠀⠀⣹⠞⢷⣄⡆⠉⠻⢾⣦⡀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠚⠋⠉⠉⠈⠀⠙⠂
⠙⡻⠟⠋⠀⠠⣀⡹⠷⣤⡀⠀⠈⠙⠒⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠷⣤⣤⡴⡞⠁⠀⠀⠈⢙⣷⣤⣀⡀⠀⠀⠉⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠶⠶⠖⠚⡍⠉⠈⢙⣻⣷⣶⣤⣀⠀⠈⠙⠳⢦⣀⡀⠀⠀⣀⣀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣌⠀⠆⠀⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠀⠉⠳⢯⣝⣓⠶⠤⣄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠿⠯⣭⣥⣼⣇⢿⡀⣶⠑⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣷⣿⡣⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⢿⣇⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⢿⣿⠿⢿⣷⣼⣿⣦⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣿⣇⠀⢀⣿⠀⠀⢹⣏⠀⣸⣿⢀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣼⡿⠛⠻⠛⠁⠀⠀⠈⠛⠻⠛⠻⢿⣯⣠⣿⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⣠⣶⡀⠀⠀⢀⣤⣤⣤⡀⠉⠻⢷⣶⣿⠋⠙⢿⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣀⣴⡿⠋⢹⣷⣠⣶⠟⠋⠀⢙⣿⣤⣤⣄⠉⠻⢷⣤⣾⠟⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⠟⠁⠀⢀⣾⡿⠛⠁⠀⢀⣴⡾⠛⠁⠈⣻⡇⠀⠀⠉⠻⣷⣄⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣶⣟⠁⠀⠀⠀⠀⢸⣿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠉⠹⣷⠀⠀⠀⠀⣼⡟⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠉⠀⠀⠀⣶⠟⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣾⣟⠀⠀⢀⣾⣯⣾⠟⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣤⡾⠛⠉⢻⣷⣰⣿⡿⠋⠁⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⣠⣴⠟⠋⠀⠀⣠⣾⣿⠟⠉⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠛⠁⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣴⠟⠋⢀⡀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⢀⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣏⣀⣤⣤⣴⣾⠇⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣶⣶⣶⠾⠟⠋⠁⠉⠉⠉⠉⠉⠀⢿⣦⣴⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢟⣭⣭⡉⢙⣛⣉⠉⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣟⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠛⣿⣿⣷⣿⣾⡄⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⢼⣿⣿⣭⣴⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄⢈⣿⣿⣿⣿⣷⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠍⠡⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⢸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣶⣾⣶⣾⡀⠙⣿⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⢪⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠦⢹⣏⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠏⠀⠉⠠⠈
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⢀⣴⠾⡻⠛⢍⢻⢹⣟⣶⣶⢶⡄
⠀⠀⠀⠀⣾⠔⣉⣲⣶⣾⣿⢾⣿⣿⠷⠚⠋⠈⠁⠐⠒⠶⣿⡶⡄
⠀⠀⠀⠀⢻⣿⣽⣿⣿⣿⣷⢀⣿⡿⣛⣒⣠⣤⡤⣤⣶⣶⣾⣿⣿⠎⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⣀⠙⠋⠉⠉⠙⢿⣿⡿⠞⣋⣠⣴⣾⢾⣷⣥⡶⠭⠞⣽⣧⣤⣶⣶⣷⣯⠉⠻⣦
⠀⠀⣰⣟⠛⣯⣏⣋⣳⣶⣼⣿⣿⡀⢔⣾⣿⡇⢠⣿⣿⣿⣖⢋⣻⣿⡏⠀⣿⣿⣿⣶⢀⠽
⠀⠀⠘⠿⢿⣮⣿⡟⠛⣿⣿⡿⣿⣷⣿⣯⣼⣄⣼⣿⣽⣷⣽⣿⣟⣻⡷⢠⣿⡭⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⣡⠾⢿⣿⣿⡟⢻⣿⣿⡟⢈⣿⣿⡏⢹⣿⣿⣿⣿⡈⣻⣶⡶⠶⠒⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠺⣿⡀⣾⣿⣿⣇⢸⣿⣿⠇⣾⣿⣿⠵⠿⣿⣿⣿⡿⡗⠉⠈⠻⡖⠒⠂⠀⠀⠀⠀⠈⠳⢄⣀⡤
⠀⠀⠀⠀⠠⠁⠠⡿⠿⠿⣿⣿⣿⣽⣿⢏⣼⣿⣿⢖⣲⡖⣿⠿⠒⡞⠉⠳⠀⠀⠀⠀⠀⠀⠀⣠⣴⣖⠒⠾⣿⣿⡿⢻⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠾⠿⣿⡿⢿⠏⠆⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠈⣿⣷⠿⠟⠛⠋
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄⡀⠀⠁⠀⠀⠀⠘⣿⡏⠀⠀⠀⠠⢄⠈⡆⠀⠀⢳⡄⠀⠤⢚⣉⣛⠟⣿⣟⡹⣧⣿⣾⢸⣳⢆⠀⣀
⠀⠀⠀⠀⢹⣶⣄⡀⠀⠀⠀⠑⣾⡀⠀⢀⠀⠀⠹⣧⠀⠀⣠⠤⠦⠿⠿⠤⣀⣾⢃⣤⣾⣿⡟⢋⣴⡭⠛⣿⣿⣿⣵⡾⡷⠾⠷⠃
⠀⠀⠀⠀⠸⠛⠉⣉⡀⠀⠀⢀⡿⢁⡴⣡⣶⣶⣶⣭⠀⠠⠁⠀⢀⠠⠴⢶⡟⢁⢻⣿⣿⣿⣿⣮⣴⠇⠀⣨⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣄⠞⠹⢡⣠⣿⣿⣿⣿⣿⣄⠃⠀⠀⠁⠀⠀⠀⡷⠘⠌⢿⣿⣿⣿⢟⣉⠄⣸⣿⣿⣿⠟⣋⣥⣄
⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣀⠀⠀⢿⡛⢸⣿⣿⣿⣿⡀⠀⠀⣴⣶⠤⠚⠁⠀⠀⠀⢀⣀⣤⣿⠀⠀⣿⣿⣦⣴⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠘⡇⢸⣿⡿⣻⣿⣷⣆⢬⠑⠻⠿⣿⣿⣿⡇⠀⠀⢠⢶⠀⢤⣤⣤⣤⣤⣄⡀⠐⢿⠀⠀⠈⠓⠉⢉⠀⢀⠉
⠀⠀⠀⠀⠀⡄⠐⠛⠙⠊⠻⣿⣿⣿⣄⢳⠀⢠⣦⡈⢸⡇⣄⠀⠀⠸⢢⣦⣿⠏⣦⢻⣿⣏⠀⠀⠁⢠⣤⣄⡘⣦⣅⣸⡆
⠀⠀⠀⠀⠀⠸⣄⠀⠙⢷⡄⡿⠻⣿⣿⡆⠀⠀⠹⠇⠘⢰⡿⠢⣦⣶⣾⠋⠁⠀⡿⠨⠉⢹⠛⣛⢻⣻⡋⠙⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠒⠋⠉⠁⠀⠀⠀⠀⠀⠛⠇⠀⠀⠈⠁⠀⠀⠰⡇⣷⠑⢤⠭⠿⠯⠶⢦⡀⣼⠿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⢀⠀⠀⢀⠀⠀⡀⢀⣀⡦⠂⠀⠀⠀⠀⠀⢂⠀⠛⠉⠃⠀⠀⠀⠀⠀⠀⢋⠁⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡚⠦⠶⣿⠋⡿⠩⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⡘⠿⠟⠛⢿⢻⠋⢻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⢻⡀⠈⣷⠞⣡⡼⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣦⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡷⣄⣿⠀⢻⠀⣼⠋⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣀⡠⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣄⣼⠃⢻⣠⡞⠁
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣷⡂⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣧⡀⢀⣿⠇⠀⢀⢀
⠀⠀⠀⠀⠀⠩⠿⡟⣿⢿⠟⠂⠀⣼⣿⣿⣿⣿⣿⣿⠆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢿⣷⣿⠁⣀⡴⠟⠁
⢠⣴⣷⣶⡄⠀⠀⢀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢹⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⣿⣿⠛⠉⠀⡀
⠐⠻⢻⡟⢻⠀⠀⠀⣿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⣿⡇⠀⢹⣿⣿⡿⣿⣿⡏⣰⣿⣿⣷⣤⣿⣿⠀⣴⡾⠋
⠀⠀⠈⢧⣼⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⢻⣿⠀⠀⣻⡇⢷⢹⣿⡇⠻⣿⢹⣿⡉⣿⣿⣼⡏⣠⡴
⠀⢀⡄⠀⢻⣹⣿⣦⣿⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⡟⠁⡄⠀⠀⠀⠸⣿⣄⢠⣿⡇⣼⠀⣿⠇⠀⡟⣾⣿⠁⣿⣿⡿⠛⠉⣠⠋
⠀⣼⠁⠀⢸⡟⣿⠁⣿⠇⢦⣤⣴⣦⢸⣿⠇⣿⣿⠀⠸⡇⠀⠈⢲⣴⣿⣼⣦⣿⣷⡏⣸⣿⡄⠀⣷⣿⣯⣾⣿⠏⣳⣴⣿⡇
⠀⡟⠰⣄⢸⡇⢿⠀⣿⠀⣠⣫⣥⣅⣿⣿⠀⣿⣿⠀⢀⣄⡀⣐⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⢃⣾⡟⣿⣿⠃
⠸⣇⢰⠋⢸⣧⣾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⡇⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣿⣿⣶
⠀⠈⣿⠘⢶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣤⣤⣤⣤⣤⣭⣤⣥⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⡀
⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣡⣦⣌⣉⣡⣴⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣤⣉⣙⣉⣡⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⡿⠟⢿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠏⣰⣿⣦⠹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠀⣿⣿⣿⡆⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⠀⣿⣿⣿⡇⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⢈⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⡟⢸⡇
⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢸⣷⣬⣭⣭⣭⣩⣭⣭⣥⣾⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠔

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




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠿⠒⣴⠞⣴⠛⣱⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⣿⡏⣀⠁⡐⢃⡴⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠔⠚⠘⣿⠿⢆⣿⣴⢳⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣴⣿⣦⠀⣘⠙⠿⣟⠻⠈⣾⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣤⢾⣴⣫⣍⡻⡎⣶⡕⢸⡿⢼⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠋⣾⣏⠙⢓⣣⣿⣷⢈⣽⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢿⣦⣭⣭⣿⣧⣤⡰⣾⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣽⣿⡟⠁⠘⣷⠘⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⣋⡾⣮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠉⠙⣿⣿⣿⣿⠟⠳⣬⢳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠸⣿⣿⡇⠀⡄⠘⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣇⠀⣠⣿⣿⣿⣶⣿⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⡟⠛⠉⣿⠏⠉⠙⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢻⣦⡀⣿⡆⠀⠀⡿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢿⣾⣷⡀⠐⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⡧⠐⢿⠂⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⡉⠑⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢡⠃⠆⠠⣷⡄⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡹⠁⠀⣸⠷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⠘⠿⣲⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⣐⣂⣁⣤⢤⠛⢷⡀⠀⠀⠀⠀⣀⣤⣶⣦⡴⢁⣎⠉⠁⠀⠀⠀⢀⣴⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⢸⠃⠈⠁⠀⠘⠊⠉⠪⡑⠦⢐⡨⠿⣿⡯⣿⣷⣼⣯⣷⡄⠀⠀⣠⠏⠈⢯⣦⣿⠋⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⣿⣿⣞⣯⣿⡼⢏⠳⢔⣫⡟⣴⠀⣸⢹⡀⢸⡾⡇
⠀⠀⠀⣛⡭⠭⠝⠒⠒⠉⠉⠉⠛⠓⠒⠲⠤⠤⠤⠀⣀⣀⣀⠀⠯⠽⣿⣛⣿⣿⡥⠄⠀⠉⢩⢎⡾⢹⠀⢸⡄⢳⢈⣧⡙⢦⡀
⠀⠀⢰⠋⡿⠿⢿⣶⣶⣶⣦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡾⠯⠝⢻⣷⠁⠀⠀⠀⣇⣾⢁⡾⠀⢈⡇⢸⠸⢸⡎⣇⣷
⠀⠀⢸⠀⡇⠀⠀⠀⣀⣈⠉⠉⠉⠙⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡟⣿⣶⣿⣇⠀⠀⠀⠈⠉⠻⢧⣀⣼⣤⡷⠤⠼⠃⠈⠁
⠀⠀⢸⠐⡇⢀⡔⣫⠭⠭⡙⢷⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣽⣻⠿⢿⣿⡆
⠀⠀⢸⠐⡿⣿⢸⠃⠀⠀⠘⡌⣿⣤⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣥⣹⣷⣶⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣀⣀
⠀⠀⢸⢸⡏⠹⡜⢧⣀⣀⡴⢠⡿⢭⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⣿⠉⠀⠀⠀⠀⠀⠀⢀⣜⣹⡭⢷⣿⠋⠁
⠀⠀⢸⢸⡇⠀⠈⠒⠭⠭⠔⠋⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡤⣤⠤⠿⠀⠀⣀⣀⣀⣀⣀⢎⣾⡿⢣⡿⠁
⠀⠀⢸⢸⡇⠤⠤⢀⣀⣀⣀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣠⠔⠒⢉⣩⠭⠤⠒⠲⠏⢾⡷⢳⡿⠳⢤⡀
⠀⠀⢸⢸⡧⢤⣀⣀⣀⠀⠀⠉⠉⢹⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⡀⠔⠋⠁⢀⡀⠈⢀⡀⠤⠀⡉⠙⢂⣠⡏
⠀⠀⢸⢸⡗⠂⠤⠤⠄⣉⣉⠉⠓⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢛⣏⠙⢛⣟⡲⠲⠶⠾⠗⠶⠚⠻⠿⣿⣏⠗
⠀⠀⢸⣸⡋⠙⠒⠂⠄⠤⠤⢈⣉⣹⡇⢸⠀⠀⠀⠀⢀⣤⣶⠋⠀⠀⠀⠟⠘⡆⠈⠻⢀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠛⠻⠿⢷⣶⣶⣤⣤⣄⣀⣸⡇⢸⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠢⣀⣀⠀⠀⠀⠀⠀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠸⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⣤⣀⣸⠏⠉⠛⠋⠁⠈⢙⣛⣶⡤⣤⡀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠻⣦⠄⠀⢀⣠⠰⠦⠦⠝⢋⢽⠟⠋⠁⢀⠀⢩⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡶⠛⠛⠉⠉⠀⣀⣠⣴⡶⣶⣷⡄⢡⣷⣞⣟⣁⣀⠂⠐⠚⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠈⠙⣷⠀⠀⢢⣾⣿⣿⠋⠀⠳⢴⢿⢈⣽⣿⠟⠛⠋⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⢠⣞⣹⣬⣶⢟⣿⡿⢋⣦⠾⣇⠀⠏⣘⡾⢧⣀⠀⠀⠀⣀⠠⠤⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠈⠉⠉⠁⠀⣼⡟⠀⠈⣿⣷⣭⡇⢲⣿⣿⣶⠸⡆⠀⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⢠⡀⠀⠀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠀⠀⠹⠙⣿⣿⣤⣍⡀⠀⠀⢻⠀⠀⠀⠀⢠⠂
⠀⠀⢸⡷⣄⠀⠠⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠐⠀⠀⠀⢡⠙⢷⣍⢳⣌⣠⡾⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠹⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡏⠘⡀⠀⠀⠀⠐⠄⠀⠀⠫⡑⢯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⡠⢒⡤⠾⠷⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⡀⠀⡤⡊⢱⠄⠴⠄⡍⠢⡀
⠀⠐⣁⣠⣐⣒⠢⠍⠛⢆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠁⠀⠀⢄⠻⣿⣧⡈⠀⡜⣠⡁⣠⣠⡀⢀⡈⠥⣈⠄
⠀⣨⠖⠋⢁⣉⢿⣷⣦⡂⠳⡀⠀⠐⠀⢀⠀⠀⠀⠀⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣷⣽⣿⡇⠀⡍⡅⠈⠁⠈⠉⠉⠁⠀⠄
⠀⠀⠈⢀⣅⠤⡄⣙⢿⡷⣤⠱⡆⠀⠀⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢦⣼⣿⣿⣿⣷⠀⢱⡘⢄⠀⠄⠀⠀⣀⠜⡠⠁
⠀⠀⠊⠁⠀⠀⣀⠤⠱⣿⣞⢧⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣆⣾⣿⣿⣿⣿⣿⠀⠀⠑⠢⢀⡂⡀⣈⠥⠚⠁
⠀⠀⠀⠀⣴⠏⠀⠀⣀⠒⢯⣇⠙⡇⠀⠀⠀⠂⠁⠀⠃⠀⠘⠀⠀⠀⠀⢀⠀⠀⢠⡾⠋⠋⡿⠇⠙⠟⢨⡇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣠⠴⠂⠈⠢⠀⠟⢶⡌⡄⠉⠂⠀⠀⠀⠀⠀⢀⡀⣠⠀⠠⡳⠂⠀⠀⠀⠀⠀⠃⢠⣼⣼⣿⠇⡤⠀⠀⠀⠂⠀⡈⠂
⠀⠀⠀⠀⡼⠁⠀⡠⢒⣉⡈⠂⠀⢁⡀⣴⣀⠀⠀⠀⢀⣤⣾⢀⡟⠀⠐⠁⠀⠀⠐⠀⠀⠈⣖⣼⣿⣿⡿⠀⠀⠀⠈⠀⢀⡄⠁
⠀⠀⠀⠀⠁⢀⡴⣪⡽⠟⠛⠂⢐⣿⡗⠀⠀⣀⣡⡾⠟⣩⡣⠊⠀⠀⢠⠀⠀⡀⡠⠀⠁⣸⣿⣿⣿⣿⠁⠀⠰⠀⠀⢠⠚
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠨⢷⠭⠉⠀⠀⠀⠀⣸⠞⠉⠀⠀⠀⠀⢠⡀⢰⢣⢡⢠⢣⠟⡟⣸⣿⠃⠀⠐⠀⠀⠷⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢀⠈⢰⠗⠀⠀⠀⠀⢠⠇⢻⡧⡷⠓⠱⠁⠈⣠⣿⡿⠁⠂⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⣴⣿⣧⣴⣿⣴⠟⣡⣶⣯⣤⣾⣿⡿⠋⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈⠉⠛⠛⠋⠿⠿⠿⠿⠿⠛⢛⠉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠒⢛⢻⠒⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⢻⣹⣥⣀⣠⢄⠀⠈⢩⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠏⠁⠢⠋⠙⠶⢀
⠀⠀⠀⠀⠀⢠⣶⡴⠿⠛⠛⠻⢿⣿⣾⣾⣤⣀⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠑⠓⠂⠒⢗⡆⡄⡀⠠⢠⡀
⠀⠀⠀⣰⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠋⠺⣶⣠⣿⣦⡀
⠀⠀⠀⡻⢏⠛⠀⠀⠀⠐⣿⣿⣷⣶⣿⣿⠓⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣺⣄⠀⠀⠀⢀⣠⡀⣀⣀⣀⣀⣀⢀⡀⠉⠁
⠀⠀⠀⠀⠉⠀⣴⢲⠀⢲⠮⣿⣿⣿⣿⣿⡇⠀⢀⣀⠾⣽⡇⠀⠀⠀⠀⠀⢛⠶⠀⡀⠀⠀⡘⢿⡇⣾⠋⣩⣭⠁⠀⠀⠀⠄
⠀⠀⢰⠿⢰⡇⢴⡟⣠⠈⢻⡙⡛⢿⢿⣿⣛⠀⢯⠘⣣⣼⡗⠀⡀⠀⠀⠀⡠⢀⠄⢁⠅⠀⠆⠙⣱⣥⡀⠁⣿⠀⢀⠒⠄⠁⢂
⠀⣈⢻⡃⣾⡴⠺⢦⣻⣿⣬⣽⢧⣠⣦⣤⣿⣶⣻⣷⣧⣿⣇⡞⠁⠀⠠⠌⡀⠐⢀⡥⠐⡪⠄⠂⠀⠈⠋⠛⠃⠀⢀⣤⣴⠳⠈⠠⠂
⠀⠾⠋⠉⠻⠋⠄⠈⢻⡿⣞⢷⡏⢙⣷⣯⣻⣿⣟⠁⠙⠛⠿⠛⠃⠀⣒⠤⠄⣰⠄⠈⠈⡻⡦⢘⣫⠖⠙⠳⢀⢒⢁⠀⠈⣵⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠼⠿⠟⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠋⠈⠀⠈⠁⠀⠉⠓⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⠀⣤⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡠⢒⡦⠐⠒⠈⠉⠉⠉⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡟⡀
⠀⠀⠀⠀⠀⠀⠠⣂⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠰⠦⣤⣀⡀⠊⠑⠶⣤⣄⣀⡀⠁⠄⠀⠁⠀⠀⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⢬⡍⠁⠈⠀⠀⠀⣉⠉⠃⣌⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠌⢠⠶⠶⢤⠀⠀⠀⠀⣠⣍⠛⢠⠅⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠆⢛⠂⠤⠈⠀⢀⠀⢰⣶⡆⠀⠀⣼⣄⠘⠳⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⣟⠀⠀⡴⠄⢀⢀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠒⠘⠛⠀⠀⠀⠻⠧⠞⠀⠄⠀⠀⠀⠀⣏⣇⠀⠀⠀⠀⡰⢊⢿⡀⠰⠍⠉⡐⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⡀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠣⣯⠒⣤⣄⠜⡜⣮⣡⠇⠀⠀⢰⢉⢺⠀⠀⡀⡠⢄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠈⠉⠀⠉⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⢱⣝⢠⡧⠊⡐⠈⠁⠀⠀⢀⣍⡶⡁⠀⢀⡧⢊⡤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢏⠀⠁⠀⢶⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠷⠈⠀⠀⠀⠀⠀⠘⢁⠐⠀⡷⠘⡷⠋⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠊⠤⠤⠌⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠐⢄⠀⠀⠁⠀⠀⠡⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⢣⠄⠁⠈⠢⠀⠀⢠⡚⢅⣀⡀⠉⠢⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠈⠠⡀⠀⠠⠁⠀⠁⢺⣄⡀⠀⠀⠑⢠⡄⣩⡏⢠⣌⠶⡀⠈⠎⠁⢀⡀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠲⢦⡀⠀⠀⠀⠈⠁⠒⠂⠐⠁⠐⠻⠄⣴⣴⡦⠴⠀⠘⠃⠉⠁⠲⣄⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣢⡤⠠⠄⠤⠀⣠⠀⢀⣰⡶⠞⠋⠀⠀⡇⠀⣿⣭⠅⠣⠀⡑⢤⠄⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⠄⢀⡀⠀⣠⠤⠒⠋⠉⢀⡀⠤⠐⠒⠀⠀⠀⠈⠏⠀⣄⣖⣒⣰⡀⡀⢀⠀⢀⡜⠁⠀⠀⠀⠀⢀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⢈⡉⠳⣄⠈⠛⢤⡀⠀⠀⠀⢀⠀⣠⠀⠦⢄⣁⠀⠀⢸⠧⠤⠚⠈⠉⢀⣀⣤⠔⠒⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀⠉⠢⣄⠀⠀⠉⣀⠀⠔⢸⠉⠛⠋⠁⠀⣀⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠷⡀⠀⠀⠀⠉⠢⣄⡁⢭⣉⠀⠤⢀⣂⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⠈⠦⣀⠀⠀⠀⠀⠙⠲⠶⠚⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠠⠀⠀⠓⠈⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠉⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⢴⠖⠂⠚⠂⢠⠾⢩⡗⠀⣠⣄⡄⠀⢶⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣤⠐⠒⠈⢩⠗⠂⠚⡄⠀⠀⠂⠥⠤⠐⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣮⠈⠢⠀⠀⠀⠉⠁⠀⠀⠠⠀⠀⠒⠈⡃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠱⡄⠒⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠨⠖⠉⠁⢢⠀⢠⠀⠀⢀⠤⠐⠒⠒⠠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠔⠁⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⢀⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⢿⢿⡿⡿⣿⣿⣿⢿⡿⢿⡿⠿⣿⣿⣇
⠀⠀⠙⣬⠋⣝⡻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢿⣿⡝⢿⡆⡇⠳⣹⡏⢸⡇⣸⣗⣟⣠⠾⣻⣿⣿⣇
⣀⣄⠀⢸⡼⠋⠙⢃⣤⣤⣤⣴⣖⡒⠤⣄⣀⣀⠀⠀⠀⠀⠀⠙⠦⣙⢷⡀⢹⡷⣿⣟⣹⣫⣾⣷⣯⣉⠉⠉⠛
⠸⠿⠳⣸⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠙⠳⣼⣇⠟⢁⣸⡛⢻⡿⢿⣿⣶⣄
⠀⠀⠀⢹⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⡟⠀⠾⣿⣷⡀⢷⢣⠃⣜⡉
⠀⠀⠈⢻⢛⣿⠿⠛⠛⠛⠙⢿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⢸⡇⠀⠀⢸⡏⢧⣸⣇⠞⠉⠉
⠀⠀⠀⢸⠸⣿⠀⠀⠀⠀⠀⣾⣿⢿⣿⡟⠛⠿⠿⠿⠿⣿⣿⣿⡄⢣⠀⠀⢸⡇⠀⡀⢸⡇⠀⢸⡇
⠀⠀⠀⠸⡆⠻⣤⡄⠀⠀⢠⣿⠃⠀⢻⣷⠀⠀⠀⠀⢸⣿⠀⠙⣷⡀⣀⡀⣼⡇⢰⣿⢸⡇⣄⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣶⣶⣶⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⡟⢛⡿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠻⣿⣾⣿⣿⣏⣹⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣥⣤⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠛⢿⣿⣴⣿⣿⠿⢻⣿⣧⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⠟⠁⠴⣾⡿⣿⣿⣿⣽⣿⣿⣝⠃⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢀⣾⡤⠾⣿⣿⣿⣿⠉⠙⠛⠛⠉⠁⠈⣿⣿⣶⣀
⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠁⠀⠀⠀⠈⠉⠀⠀⢸⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⢦⣀
⠀⠀⢀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡄⠀⠀⠀⠀⢠⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⠀⠘⣿⣧⠀⠉
⠀⢀⠈⣽⡏⢀⣿⡿⠋⢻⣿⠛⠻⣿⣿⣿⡀⢻⡀⠀⠀⠀⣰⢀⣿⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣿⣇⣀⣄⣠⣤⣀⣀⣬⣃⢀⠀⣿⣿⠀⠀⢸⣿⠀⢀
⣀⠬⣷⡟⠀⣸⡿⠁⡀⠀⣿⡆⡀⢸⣿⠙⣿⣆⠃⠀⣸⡞⠁⢸⣿⠀⠀⡟⡇⠀⠀⠀⢀⠄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣼⣿⣤⣤⣧⣿⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⠀⠝⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡤⠀⠴⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⣠⠀⠀⠈⠃⣴⠃⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⣿⠏⠀⠀⠀⣄
⠀⠀⠀⠀⠈⣷⠀⠀⣤⠃⣰⡇⠀⠀⢠⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⣿⣄⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣀⠀⣠⠆⠃
⠀⠀⠀⠀⠀⠸⣆⠀⢁⣠⢿⠁⠀⠀⠀⠀⠀⠀⠙⠙⠗⠀⠀⠠⠆⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻
⠀⠀⠀⠀⡄⣰⠹⣶⡈⣧⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠂
⠀⠀⠀⠀⢱⡏⠐⠋⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠁⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣆⣠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠄⠀⠀⠀⢀⠤⢴⠲⠶⠶⠛⠉⠃⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡿⢦⠄⠤⠼⠛⢻⠀⠇⣠⠀⠀⠀⡈⣠⢆⠀⠈⠇⠀⠤⠆⢠⡖⠀⠀⠀⢸⡇⣠⠛⠢⠀⠐⠁⢀
⠀⠀⢠⠃⣰⡇⠀⠀⠀⠀⠀⠀⣇⣼⠇⠀⢀⣴⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⠃⠀⠀⠀⠀⠀⣸
⠀⠀⢸⣾⡁⠧⠶⠄⠀⠀⠀⠀⠸⠿⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣙⠛⢗⣤⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡶⠿⣷⣿⠉⠷⢿⡞⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⡻⠃⣤⣈⣉⣠⣶⣄⣴⣮⣰⣯⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣶⡤⠿⢞⣛⣋⣭⣭⣭⣭⣉⣉⠛⠿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⣉⣴⣶⠟⠛⣋⣩⣍⣀⣠⠀⠉⣻⣷⠄⠈⣿⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢰⡟⠁⣈⣻⣿⣿⣿⣿⡿⠿⣛⣩⠞⣋⣠⣾⢟⡻⠿⣟⠿⣶⡖⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣿⣾⣄⠀⠀⠉⠃⠉⠋⠉⠙⢻⣿⣿⠉⠉⠈⠀⣿⢡⢾⢳⣿⡟⣤⡑⢮⣹⢯⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣽⣿⣧⣾⣷⡤⠀⠀⠁⠀⠀⠀⠈⣿⣿⠄⠀⠀⠀⠀⡾⡷⣏⢣⣴⣞⡷⡄⢿⣻⡷⣾⡃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢚⠓⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠰⠿⠓⠚⠋⣻⣥⣀⣠⡄⣻⣳⠿
⠀⠀⠀⠀⠀⢎⡵⢶⣾⡿⣷⣼⠾⢷⣷⣶⣶⣦⣄⠀⡇⠀⢠⣿⣿⣿⠀⠀⠔⠀⠤⠀⣴⠾⣹⣿⣿⣿⠷⠧⢿⡛⡆
⠀⠀⠀⠀⠀⢾⣳⢼⣿⡳⣾⣧⠀⢰⣿⣿⣿⣿⢿⣼⢇⣴⣿⣿⡿⠁⠠⠂⠀⠀⣠⡞⢙⣶⢿⣿⠫⠻⠙⣾⡎⣟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠥⠼⠟⠉⠀⠀⡟⢾⣟⣷⣿⠟⠛⠿⠟⣿⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠨⠙⢄⣠⡸⠿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⡄⠀⠉⠀⠈⣧⡀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠙⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⠿⠿⠳⠀⠀⢠⣮⣹⣷⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣴⣤⠀⠀⠿⢻⡟⡉⡹⢏⣀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⣀⡆⣀⡿⣷⣼⣿⡄⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠿⢋⠟⠁⠀⠘⣿⣿⡟⣿⣷⢿⣹⡄⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⢆⠀⠀⠀⢻⣼⣾⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡂⠈⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣲⡶⠶⠶⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣤⡇⠀⠀⠀⠀⠀⢠⡒⠒⠒⢲⠀⠀⠀⠀⠀⢀⡔⠒⠒⣎⠀⠙⠢⢄⣀⣠⠤⠚⠁⠘⡖⠒⠲⡄
⠀⠀⠀⠀⠀⡴⠒⠒⡟⠒⠒⠒⢳⡀⠀⠀⠀⠀⢸⠉⠉⠉⠉⡆⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⠲⢤⢴⠋⡦⠤⠤⠒⠋⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⡇⡎⡜⠀⠀⠀⠀⠀⢳⠀⠀⠀⣠⠞⠒⠒⠀⠚⢧⣀⣀⣠⣋⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣧⠟⠀⠀⠀⠀⠀⠀⠀⢣⢠⠎⠁⠀⣀⣀⣀⠀⢀⡈⢳⠖⠤⠤⠬⠭⠭⣉⣉⠭⠶⣆⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⠋⠁⠀⠈⡆⣿⢱⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣤⡿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⡇
⠀⠀⠀⠀⠀⠳⠦⠤⠤⠤⠤⠤⠤⠴⢲⡏⠀⡇⠀⠀⠀⠀⡇⣿⢸⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠯⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡇
⠀⠀⠀⠀⠀⢰⠤⠔⠊⠉⠉⠉⠒⠒⣾⡇⠀⡇⠀⠀⠀⠀⡇⢿⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣶⡟⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⠉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠀⠀⠀⠙⠒⢄⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠷⡿⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠛⡆
⠀⠀⠀⠀⠀⣘⡒⠤⠤⠤⠤⠤⠤⠐⣻⡇⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠤⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡅
⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠉⠁⠀⣇⠀⠈⠉⠐⠒⠒⠂⠉⠁⠀⡟⠒⠒⠲⠦⠤⠤⣧⠤⠲⣟⡿⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠇
⠀⠀⠀⠀⠀⠳⠤⠤⢀⣀⣀⣀⠤⠤⠔⠻⠤⣀⣀⣀⣀⣀⣀⣀⣀⠴⠋⠙⠛⠓⠒⠲⠶⠾⠖⠚⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠃⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⡌⢠⠇⢀⠀⠀⠀⠀⠀⠀⣠⣴⠿⡉⠀⠀⠙⠃⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢡⠎⢠⠏⢀⡜⠀⠀⠀⠀⢀⡴⠋⠘⠒⢦⡀⠀⠀⠀⣶⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡇⡇⡴⠃⢀⡞⠀⠀⠀⠀⣰⠟⢁⡈⠻⢷⡒⠃⠀⡰⠁⣼⠛⠷⠶⠶⠛⠀⠀⠀⠀⠀⢀⣠⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢸⣼⠀⡇⠀⢸⠇⠀⠀⠀⣰⠇⠀⠪⣉⡙⢲⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡏⢰⡇⠀⣸⠀⠀⠀⢠⡿⠀⢨⣁⠤⢭⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⣟⣧⠸⡇⠀⡟⠀⠀⠀⠘⠁⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⢀⣠⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠈⠛⢧⢻⠀⣇⠀⠀⠀⠀⠀⠈⠀⣀⣀⣘⣷⣤⣤⡴⠚⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠚⣿⡇⣿⠀⠀⠀⠀⠀⠄⠈⠉⠉⠉⠀⡠⠋⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠹⢤⣀⣘⣇⡿⠀⠀⢀⡀⠘⠒⠒⠒⠒⠒⠉⠀⠀⠀⠀⢀⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⡀⣀⣾⣀⣀⣀⣀⢀⢀⣀⣀⣀⣠⡄⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡈⠙⠲⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣶⣶⣶⣒⣴⣧⡀⠀⠙⣿⣷⡄⢹⡎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣮⣿⣿⣿⢷⣄⠀⠈⣿⣧⡀⠁⠂⠹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣾⠁⣿⣷⣶⣦⣾⣿⠍⠀⠠⠄⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡛⠿⣿⣿⡟⠛⠀⠀⠀⢀⣴⠀⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⢻⣿⠛⠻⣤⠉⠛⢠⠈⠁⠈⠉⠁⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿⣿⣿⣷⣾⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⡿⠋⢉⣿⡿⣷⣀⣀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⣾⡿⠃⠸⠛⠛⠋⢻⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠁⠉⠛⠛⠛⠉⠉⠀⡀⠀⠀⠀⠘⢿⠀⠀⠘⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡤⠄⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡔⠃⠀⠀⠈⠉⣉⣱⡦⠶⠆⠀⢀⣴⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⡀⢁⡠⢔⣰⣿⣿⣏⣴⣶⣶⡾⠟⠛⠁⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⣬⣶⣼⣿⣿⣿⣿⠟⠛⠁⠀⠰⣤⣄⠂⠀⠀⠀⠄⠀⠀⠀⠀⢀⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⢠⣰⠂⠀⠀⠀⢂⣤⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣾⣯⣧⣿⣿⢻⠛⣿⠁⡉

⠀⠀⠙⠐⣀⡦⠒⠁⠀⠃⠈⠀⠀⡞⣶⠀⠀⠀⠀⣴⠳⠀⠀⢠⡤⠀⠀⠳⠀⠀⠀⠐⠗⠀⡈⠀⠀⠋⢲⡦⠀⠀⠀⠀⠛⠠⣀⠀⣠⡄⢀
⠤⠶⠚⠋⠁⠀⠛⠇⡀⠀⠀⠀⣰⠦⣩⠞⠁⠀⠀⣿⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⡀⠈⠀⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠽⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢄⠀⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠄⠀⢰⠒⣦⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠐⠀⠈⠛⠁⠀⠀⠀⠀⣰⠧⠴⠋⠀⠀⡇⠀⢀⣀⠀⠀⣀⢀⠀⡷⠀⠀⠀⠀⠀⠀⡔⣀⡆⡏⠀⠀⠀⠐⡴⡄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠐⢀⡀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠔⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠋⠁⠀⠀⢸⡇⣠⢀⡀⣤⣤⠀⡠⢀⡀⣿⢀⡄⠀⠀⠀⠀⠻⠆⢀⡤⠀⠀⠀⠀⠀⠀⢰⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢿⢼⠅⡯⢸⠐⢇⢸⡇⡧⠸⣁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠵⡃⢀⡀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠀⠀⢀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠠⠂⠘⠀⠀⠈⠁⠉
⠀⠀⣠⣤⣄⠀⠀⠙⠋⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢈⡈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠤⠄⠀⠀⢀⠀⠰⣦⣄⣀
⠀⢘⡿⠉⠙⠃⠀⠀⠀⠀⠀⠀⠼⢀⠁⠀⠀⠠⣀⢀⠀⠀⠀⠀⣾⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⠀⠁⠁⠀⠀⠀⠉⠉⠂
⠀⢸⡇⢠⣶⡄⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⡀⠡⠃⠄⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠐
⠀⠀⠙⢶⡍⠁⠀⠀⠀⠘⠁⠖⠀⡀⠚⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳
⢀⠀⠀⠈⠁⠀⠀⢀⢁⠘⠃⠀⠴⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠹⣿⣧⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣈⠁⢀⢁⡃⢠⣭⣿⣗⡿⣂⠀⣒⡤⠀⠀⠤⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄⠀⠀⠉⠉⠉⠉⠀⠀⣄⡀
⠀⠲⠆⠀⠰⠆⠀⠀⢸⠇⠋⠀⢸⠚⠃⠰⠾⣿⣿⣿⡍⠀⢻⣞⠀⠀⠀⠒⠀⠀⠀⠛⠻⠿⠟⠛⠁⠀⠐⠋⠀⠘⠓⠀⠀⠈⠈⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣫⡵⣛⣭⣷⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⡾⣩⣾⣿⡿⠟⠛⠛⠛⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⣿⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠿⡿⠿⠇
⠀⠈⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡌⢀⢼⠃⠀⡴
⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡤⢲⡆⠀⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⢒⠖⠋⠉⢉⣩⠟⠋⠉⠀⢠⡇⢰⡃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠶⠚⠉⠀⠀⢀⠤⠖⠁⢈⣿⠁⠃⡗⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡼⠁⠀⠀⠀⠀⠉⠉⠒⠒⠒⠚⠒⠒⠰⠷⠶⠧⠤⠤⠤⡀
⠀⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⢤⣤⣤⣀⣀⣀⠀⣼⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠶⠒⠒⠒⠓⣦
⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⡰⢚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠛⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠀⠈⠀⠀⠀⠀⠀⠂⠈⠉⠀⠀⢀⣠⡤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡄⠀⠀⠀⠁⠀⠀⠀⠀⠤⠐⠂⠉⠁⣠⠟⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠲⣍⠀⠑⢦⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⢋⠉⢳⠦⣄⠈⠻⡲⢄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠚⠛⠓⠶⠦⠤⣤⣤⣤⣤⣤⢤⠶⢻⠁⡄⠀⢨⠓⠒⠁⡆⠙⠚⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣎⡄⠀⠀⠘⡃⢦⡄⡇⢴⠠⡃⢸⠀⠇
⠀⢠⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢁⠀⠀⠀⢧⣜⡇⡇⢸⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠛⣇⢣⡆⡸⠃⠨⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⡿⢸⠇⠇⠄⣆⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⣷⡄⡀⠀⡇⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠏⠀⠇⠀⠿⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⣶⣄⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣯⣍⣉⣙⠛⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠻⠛⣋⣩⣄⣭⣭⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣻⣤⣾⣷⣿⣿⠿⢿⠟⠿⣿⣿⣿⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣈⣧⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠻⠫⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣴⣾⣷⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠻⠿⡁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣧⠤⣤⣴⣿⣿⣿⣿⣦⠐⠄⠀⢀⣀⣤⣶⣾⡿⢿⠟⠉⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢁⣴⡿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⡿⠟⠛⠛⠁⣌⣶
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⡿⠋⠁⠀⣴⣿⣯⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣥⣤⡶⠂⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣶⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠛⠉⠉⠘⣿⣿⣷⣀⣤⣶⣿⣿⣿⣿⣿⡿⠟⠉⣠⣿⣿⣿⣽⣿⣿⣿⠇⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢀⠀⠰⣾⣿⣾⣿⠙⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣷⣺⡿⠿⣿⡟⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢠⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣔⣷⡈⢶⡕⠻⠗⠀⠀⠀⠀⠀⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠈⢀⠀⢠⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣄⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡸⠁⠬⠀⢂⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢳⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡖⠀⠄⣿⢿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠉⠙⠛⠻⠿⠿⣿⠿⠛⠋⠉⠀⢸⠀⢣⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠿⠀⠸⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⣠⠤⠠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⣼⡀⣷⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⡏⠈⣿⢶⣆⠀⠀⠀⠀⣠⣴⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⠀⣿⠀⣿⠀⠀⠀⠠⣿⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣄⠀⠀⢰⡟⢠⡾⠟⠷⣿⡀⣿⣶⣄⠀⠀⠙⠷⠶⠛⠁⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⠟⠀⢀⣾⠟⠛⠁⠀⠀⢸⣧⣿⣇⣿⡄⠀⠀⠀⠀⣠⡾⠋⣹⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢀⣀⡀⠀⠀⠙⠛⠛⢷⣆⠀⣠⡾⠋⢀⣾⠋⢀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡶⠟⠃⠀⠀⣿⠉⠻⣦⠀⠀⠀⠀⠀⣿⡿⠋⠀⣴⠟⠁⣠⡿⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠰⣿⡉⠙⠻⣦⣸⡇⠀⠀⠀⠀⣹⡇⠀⢻⡆⠀⠀⣠⡾⠋⠀⣠⡾⠋⢀⣴⠏⢀⣼⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠀⠈⣿⡁⠀⠀⠀⢀⣿⠀⠀⢸⡇⣠⡾⠋⠀⢀⣴⠟⠀⢠⡾⠃⢠⡾⢃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣿⠁⠀⠀⠀⢸⡇⠀⣠⣿⠟⠋⠀⠀⠀⠙⠁⠀⣴⠟⠁⣰⡟⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⣷⠄⠀⠀⣿⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣼⠏⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⣿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢻⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⢻⡆⠀⠙⢷⡶⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⠀⠀⠈⢻⣆⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢰⣾⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠂⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠈⠀⠀⠀⠀⠀⣺⣿⠄⠀⠀⠀⠀⠀⠀⠹⠿
⠀⠀⠀⢰⣶⠀⠀⠀⠐⠆⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⢀⠀⠀⠀⠤⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⣶⣆
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠒⠒⠲⠢⠤⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠙⠁
⠀⠀⠛⠀⠀⠀⠃⢀⠀⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⢈⠁⠂⠤⢤⣤⠤⠥⠤⠒⠒⠂⡒⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⡀⠑⠤⣀⡀⣂⣤⠤⣼⣄⣌⣤⢂⡠⠄⠀⠀⠄⢊⠕⠀⡀⠀⠈
⠀⠀⠀⠠⣤⣆⠀⠀⠀⠀⠑⢄⣀⠈⣡⣶⠶⢶⣾⠃⠀⠀⢀⢹⣿⣄⡀⠠⠤⠐⠊⢁⡠⠎⣠⡴⠁
⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠠⠬⣙⠋⢭⣭⣽⠃⠀⠀⠀⠘⡽⡍⠳⣤⣉⢈⡩⠁⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⢀⠀⠀⠀⠀⡟⠛⠓⠊⠒⠂⠀⠉⠀⠀⠒⠀⠄⢀⠀⠀⠀⠀⠀⢀⡀⠤⠂⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠁⠠⠆⠀⢀⠀⠀⠀⡀⠠⠆⠀⠘⠃⠀⠀⠈⠋⠀⠇⠀⠀⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠒⡵⠖⠀⠐⠥⠆⠀⠀⠀⠀⠀⠀⢀⠧⡀⠀⠁⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢶⡆⠀⢈⠄⠀⠑⠀⠀⠀⠀⠀⠀⣱⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠰⠀⠀⠀⠀⠈⠈⠁⠀⠠⠄⢡⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣠⣦⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠒⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆
⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠁
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠓⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⢸⣠⡀⢀⠤⢄⠤⡄⢰⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⡇⠸⠀⠳⠜⠀⠈⠒⠁⠘⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠈⠉⠉⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠢⠤⣀⡀⡠⠖⠉⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⢀⡤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠔⠒⠒⠒⠢⡄⠀⠬⠉⠀⠀⠀⠀⢒⡖⠀⡩⠭⠝⠛⠢⢄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⢥⣀⣈⡆⠈⠁⠀⡇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠤⠤⠄⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡾⡓⠤⣄⣀⣀⣠⢤⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢱⠀⠀⢣⠈⠲⠤⠤⠤⠖⢊⡜⠀⠉⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢨⠀⠀⠀⠱⡄⠀⠀⠀⣠⠋⠀⠀⢠⠃⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⢸⣦⣄⣾⠄⠀⠀⠀⡎⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡠⡜⠀⠀⠀⠈⢹⣧⠤⣿⡂⠀⠀⠀⢣⡀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠀⣧⣀⣀⠤⠚⠛⠀⠀⠑⠲⠤⢄⣀⣀⡟⢆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣇⠀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡮⢀⠤⣼⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢶⠀⣼⣩⣉⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⣴⠮⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠹⠟⠾⠓⠃

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣶⣶⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢋⡉⠉⠙⢿⣿⣿⠿⠿⡷⠄⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⡿⠻⣿⠋⠉⠙⢃⣤⣤⣀⣀⣀⡀
⠀⣴⣾⣿⣦⠀⠀⠀⠀⠀⣀⣤⡞⢀⡞⠀⠀⠀⠘⡎⠀⠀⠀⠀⠀⣀⠀⢠⣾⣶⣶⣆⣀⣀⠀⠀⠀⠈⠀⠀⠀⠸⠟⢿⠟⠋⠛⠃
⠀⠀⠈⡉⠉⣡⣶⣶⡄⢠⠟⠟⢱⠿⡇⢀⡀⠀⠀⣷⠀⣤⡀⢰⣿⣿⢿⣾⣿⣿⢻⣿⣿⡿⣇⠀⠀⡆⠀⠀⠀⢠⣤⣴⣤⣤⡄
⠀⣠⣤⣤⣤⣽⣽⣿⣥⣤⣤⣤⣯⣤⣥⣬⣥⣽⣤⣿⣤⣽⣿⣼⣿⣾⣤⣿⣿⣿⣤⣿⣧⣧⣯⣤⣤⣧⣤⣤⣤⣿⣽⣿⣿⣤⣧⣤⣤⣤⣤
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣀⢀⠀⡀⢀⢀⢀⣀⢀⠀⣀⣀⡀⢀⠀⠀⣀⢀⡀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠹⠃⠟⠆⠽⠘⠛⠇⠀⠏⠸⠼⠘⠤⠛⠛⠅⠘⠛⠖⠛⠾⠙⠆⠤⠇⠭⠆⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠃⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠁⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠
⠀⠀⠀⢠⡖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢠⣶⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⡄
⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠈⠓⠚⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐⠂⠂⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠒⠀⠒⠀⠒⠂

⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢲⡄
⠀⠀⠀⠈⠓⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⢀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠰⠤⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠒⠒⠀⠂⠂⠒⠀⠂⠂⠐⠀⠐⠆⠀⠀⠰⠶⠶⠀⠶⠂⠐⠖⠤⠤⠶⠀⠀⠀⠀⠀⠐⠒⠒⠶⠒⠲⠖⠲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⢠⣶⣢⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⡄⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠓⠋⠠⠊⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⢀⠐⠀⠀⠀⠈⡓⠀⢠
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠐⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣠⡄⠂⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣰⣿⢀⡆⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣼⠋⠀⠘⠄⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠀⠀⠀⡼⠛⠿⠟⠋⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⣀⣠⣤⣾⣿⣯⣷⣞⡿⣿⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⣴⣏⠀⣴⣾⣷⣾⡿⣿⠛⠻⣿⡿⣁⣿⣆⠀⣎⠀⠀⠀⠀⠘⠀⠀⣼⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣿⢿⣼⣿⣿⣿⣿⠋⠋⠒⠶⠿⠟⠛⠋⢹⠀⠹⡄⠐⣄⢳⢁⣼⠏⠙⢿⣜⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠟⣾⣿⣿⣿⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠸⡆⢸⡎⢈⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣴⠟⠻⣿⣉⣿⣿⣿⣿⣷⣿⡿⢻⡟⢻⣿⣭⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠉⠀⡀⢀⡀⣿
⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⡿⠿⠟⡛⣋⣀⠟⢁⣸⣿⣿⠀⠘⣦⢻⡿⠓⠿⢳⡶⠆⠀⠀⡆⠀⠘⢆⡀⢠⠁⠀⠀⣿
⠀⠀⠀⠸⣿⣦⣶⣿⣿⣿⣷⣤⣤⡿⠯⡉⣀⣾⠈⠻⣿⣔⣛⡁⠈⠐⢦⣆⣈⣧⠀⠀⢤⣷⠐⠂⢨⣿⣿⠂⠆⢰⣿
⠀⠀⠀⠀⣸⣹⣹⣿⠿⠥⠾⠷⠦⠶⣾⣿⣌⡙⠛⠚⠚⠛⠛⠓⠒⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⡾⢿⡿⢿⣿⢛⠛⠋⠃
⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⡛⡿⠿⡿⠿⠿⠛⠛⠛⠉⠙⠛⠛⠻⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣯⡍⠉⠀⢈⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠲⠽⣛⠛⣻⠿⠛⠻⣿⠛⡿⣿⣿⣿⣿⣶⣤⡀
⠠⣤⣴⣶⣾⣿⢿⣿⠿⢿⠿⠿⠿⢿⡃⡾⠉⠉⣀⡀⣠⣴⣦⣴⣦⠀⣄⠀⢀⡾⣡⣄⣀⠀⠈⢦⣘⡦⠴⠒⠋⠉⠀⠻⠷⠿⠿⠻⠿⢿⡶⠶
⠀⠀⠀⠀⡀⠘⢂⠱⡊⣀⣤⣦⢀⣀⢹⡅⣾⣿⣿⣿⣿⠻⣿⣿⠻⠷⠞⣶⣿⡇⠉⠀⣿⣷⡄⡾⠁⣠⣴⣾⣿⣷⡤⣠⣦⣤⣄⠐
⠀⠀⠀⠀⣁⠀⣴⡋⣿⣟⣿⠁⣈⣿⢠⡗⠻⣿⣟⣻⠿⡄⣿⣟⠀⠀⠐⠏⠈⡁⠀⣀⣘⣉⣹⣧⣀⣟⣻⣛⣿⣀⣠⣿⣿⣻⣟⣀⣹⣄⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣀⣠⣤⠤⠶⢶⠶⠦⢤⣤⣀⡀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⢴⠟⠍⡁⡀⢹⠀⠀⠘⡇⡀⡀⢄⢪⠻⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⢦⡄⢳⡀⢳⣃⠎⡜⠰⠀⢸⡇⠀⠀⡇⢂⠰⡈⣦⡵⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⢦⡓⢦⣈⣙⠓⠛⠾⢾⡇⠀⠀⣗⣚⣋⣩⠥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡈⠉⠉⠙⠛⣻⠀⠀⠀⡏⠉⢀⣠⠴⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣠⡤⠶⠶⡶⠒⢲⡶⠦⣤⣄⡀⠙⣆⠀⠀⠀⡟⠀⠀⢰⣇⡴⠋⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⡕⡐⡀⡀⡇⠀⢸⡇⢀⢀⢈⢻⡆⣸⠀⠀⣸⠃⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣝⣓⠳⠷⡇⠀⠘⡶⠾⠶⢛⣩⠴⠃⠀⢠⡏⠀⠀⢠⡇⣀⣀⣤⣤⡤⢀⣀⣀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠤⣄⡀⠉⠉⠉⣧⠀⠀⣿⠛⠉⠉⠀⠀⠀⢀⡞⠀⠀⠀⡾⠻⣭⣀⣀⢲⠀⠀⡯⠈⡉⣙⣦⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠦⣀⠀⢹⡀⠀⢹⡄⠀⠀⠀⠀⠀⡾⠀⠀⠀⣰⠛⠲⠤⣌⣉⡿⠀⠀⣟⣋⣉⣉⡥⠖⠃
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣇⠀⠈⢧⠀⠀⠀⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⠀⢠⠇⠀⢰⡏⠉⠁
⠀⠀⠀⠀⠀⠀⢿⠀⣴⢖⠛⢻⠉⢹⢋⣉⣻⠆⢨⠃⢹⡄⠀⠘⣇⠀⠀⢠⡇⠀⠀⠀⡾⠀⠀⠀⠀⢀⡞⠀⠀⣸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠳⠬⣭⣙⣻⠀⢸⣭⠭⠴⠖⠃⠀⠀⢷⠀⠀⠘⣆⠀⡾⠀⠀⠀⢰⠇⠀⠀⠀⢀⡞⢀⡴⠚⠉⠀⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢧⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣦⡇⠀⠀⠀⣾⠀⠀⠀⢠⠞⢰⠋⣀⣀⣀⣀⣀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢧⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⡇⠀⢀⡴⠋⠀⠘⢦⣛⠦⣾⠃⢈⣛⣓⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠳⡄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⡄⠀⠀⡇⣠⠟⠀⠀⠀⣠⠏⠉⢙⠏⠀⡼⠷⠽⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⢦⡀⠀⠀⠀⠀⢷⠀⠀⠀⢹⡀⠀⡟⠁⠀⠀⢀⡼⠁⠀⣰⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⣦⠀⠀⠀⠸⡇⠀⠀⠀⢧⠀⢧⠀⠀⣠⠏⠀⣠⠞⠁⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⢳⡀⠀⠀⣷⠀⠀⠀⢸⡄⠸⡄⣴⠃⢀⡼⠃⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠻⡄⠀⢹⠀⠀⠀⠈⡇⠀⢻⡁⢠⠟⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢹⡄⣾⠀⠀⠀⢰⠇⠀⢸⣇⡟⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⣸⠇⢻⣄⠀⢀⣾⣄⣤⠞⠘⣧⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣐⡻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢿⡟⠛⠋⠉⠉⠙⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⣀⠀⣀⣀⣤⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⡿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣍⣛⠻⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠰⣤⣤⣙⣿⣿⣿⣶⣦⣭⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⣿⣶⠆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣭⡛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣼⣡⣿⣿⠟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣾⣿⣿⣶⡦⡔⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⡉⢿⣿⣿⡜⡞⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣾⣿⣿⣿⣿⣿⣿⣿⣇⢠⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⡏⡈⣘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢾⢿⣿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⠿⠿⡇⠓⠦⠀⠀⠀⢐⣀⣀⣶⣤⠤⠔⣠⣴⠟⠂
⠀⣀⣀⣀⣀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠃⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠈⠉⠉⠄
⠀⠈⠙⠛⠛⠛⠿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠷⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣸⠙⠻⣿⢠⣶⣬⡻⣇
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣾⣿⣿⣷⣯⢸⠟⠋⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⡙⡋⣿⢿⡿⠿⡇⡏⡜⠛⣿⣡⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡛⣅⣀⠁⢀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⢼⡉⠁⠀⠏⢿⡁⣰⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠈⠛⢻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧⡁⠠⡀⢸⢾⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣽⣼⣠⣼⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⣄⣹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁