Weather sky summer Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢠⣾⣦⡀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣛⢷⡍⢵⡯⠿⣠⠾⣛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠦⢛⣨⣽⣶⣾⣿⣿⣷⣶⣮⣝⡺⠇⣞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣙⡚⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢺⠇
⠀⠀⠀⠀⠀⠰⣿⢻⡭⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢛⡻⢶⡶
⠀⠀⠀⠀⠀⠀⠙⢧⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣣⡿⠁
⠀⠀⠀⠀⢀⣴⢞⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣩⡺⣶⣄
⠀⠀⠀⠀⠙⠿⡮⣋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣙⣯⣵⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣾⢫⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠾⠷⣮⣥⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣭⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡽⢰⡎⣝⡻⠿⢿⠿⣟⣛⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣭⠶⢋⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠄⡀⠀⠀⠀⠀⠀⠔⠁⠀⠠⠂⠐⠀⠀⢀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠂⠀⢰⠀⠀⠀⠄⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢆⣰⣠⠂⠀⠔⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⢀⠀⡀⠀⠀⠐⠀⠀⠀⠂⢈⠋⡀⠀⠀⠠⣀
⠀⠀⠐⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠰⠂⢀⡀
⠀⠀⠀⠀⠠⠐⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠀⠀⠀⠥⠂
⠀⠀⠀⠂⠀⡠⠤⠤⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠌⢠⡒⠠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⢠⣓⣒⢩⠉
⠀⠀⠠⠤⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⢄⠀⡀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣗⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠘⣤⠦⡔⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠐⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢩⡎⠀⠀⠈⢦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⠀⠀⠀⣠⠔⠳⣄⣀⡠⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⢀⠠⠀⠜⠀⠉⠘⢆⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠
⠀⠀⠀⠀⠀⠈⠒⠒⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠍⢙⣓⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠀⠀⠀⠐⡀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠂⣐⠋⣠⠔⠉⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠈⠂
⠀⠀⠰⠃⠀⠀⠄⠀⠁⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⡐⠁⡰⠋⠀⠀⢀⠄⠀⠀⠿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠐⠃⢀⠀⠀⠀⠀⣆⢰⠖⠀⠳⠀⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡈⠃⠈⠀⠀⠀⡀⠀⠀⠀⠀⠠⡀
⠀⠁⠀⠀⠁⠀⠤⠒⠉⠀⠁⠀⢰⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠓⢈⠀⠄⠀⠄⠀⠘⠒⠠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠑
⠀⠀⠸⠁⠀⢰⠀⠠⠂⠀⠰⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢠⠇⠀⢀⠂⠀⠃⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠰⡆⠀⡀⠀⠀⢠⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⢀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⡀⠂⠀⠀⠀⠀⠀⡀⠅⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⢀⠔⢀⠏⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⡀⠀⡈⠀⡀⠀⠀⡠⠀⡆⡘⠂⠀⠁⠀⠀⠰⠉⠀⠢⡑⢄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠄
⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠇⠰⠃⠈⠂⠀⠀⡀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠑⠄⢀⠀⠀⠁⢊⠂⠀⠀⣀
⠀⠀⠀⠀⢘⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⠇⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠁⠀⠀⠀⡀⠀⢀⡀⠠
⠀⠀⠀⠀⠈⣄⠀⠀⠀⠂⠀⢀⡄⢠⠀⢀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⢀⠇
⠀⠀⠰⠁⠀⠀⠀⠄⢀⠀⣀⠀⠐⠁⠀⠁⠀⢠⠀⠀⠀⠀⠀⢀⡔⠀⠀⠄⠀⠀⠆⠀⠀⠀⠠⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣂⠘
⠈⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠁⠀⠀⡤⠀⠀⠰⠀⠀⠀⠀⠀⢠⡤⡀⠀⣀⢀⡤⠄⣴⡄⡀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠰⠂⠀⠄⠈⠃⢀⡢⠀⡱⡆⡀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠪⠄⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠀⠈⢀⡨⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠆⠀⠀⠀⠀⠀⠁⠼⠃⠀⠚⡀⢠⡐⡈⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⡠⡶⠃⠀⠈
⠀⠀⠀⣀⠀⠐⠀⠤⠄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠘⠘⠛⠀⠁⠀⠀⠀⠀⠀⠀⡀⠞⣀⠊⠀⠀⠀⡀
⡄⢀⠔⢙⠛⠫⢤⣀⣀⣀⣀⣈⠣⠀⠁⠀⠠⡧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡂⠁⢀⢂⠔
⠁⠀⢠⠎⠉⠁⣂⡀⠤⠥⠀⢤⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠇⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠸⡢⠦⣀⠀⠀⠞⠀⠀⠊⢀⡴⠋⠁
⠀⠀⠈⡷⢖⣠⡤⣀⡈⠉⠩⠍⠉⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡴⠀⢂⠀⠀⠌⠀⠀⠀⠀⠀⠀⡶⠇⠀⢋⡱⠢⠀⢂⠀⠀⠊
⠀⠀⠀⠀⠠⢤⣎⡁⠤⠄⠀⣂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠑⠊⠁⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢘⠃⠠⠴⠎⢁⣀⠀⣈
⠀⠀⠀⠀⠀⠰⢉⣁⠤⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡙⠀⠀⢂⡿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⢀⠔⠁⠀⠨⡝⠠⠄⡠
⠀⠀⠀⠀⠀⠀⠘⠁⣖⡥⠜⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠁⠀⠀⠀⡆⠀⠢⠴⠟⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡷⠠⡀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⠆
⠀⠀⠙⠲⢀⡤⠒⠂⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣴⣶⣶⣦⡁
⠀⠀⢀⡀⡏⠀⢀⣠⠤⠖⠒⡒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⢿⣛⣧⣤⣤⣤⣄⣀
⠀⠈⠉⠁⢉⠔⢋⠴⢚⣉⣭⣭⣍⣙⠲⣌⠓⣄⠀⠀⠀⠈⠉⠁⠘⣫⡶⣛⣭⠶⢶⣶⡶⢾⣽⡻⣦⡀
⠀⠀⠀⢰⠋⡴⢁⡔⢋⠤⠖⠒⠦⣍⠳⣄⠳⡌⢧⠀⠀⠀⠀⠀⣼⢏⣾⣫⡶⠛⠋⠉⠙⠻⣮⡻⣮⢻⡄
⠀⠀⢀⡿⠛⠓⠛⢳⣇⣠⠤⢤⣀⣨⠓⠞⠉⠹⠾⣇⠀⠀⠀⣠⣷⣮⣶⣮⣀⠀⣠⣄⢀⢀⣬⣥⣾⣶⣭⡀
⠀⠀⣏⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⡄⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢀⣿⣇⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⢿⡆⢸⣿⣿⠠⣿⠁⣀⣤⣼⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣶⣾⣿⣿⣶⣦⣾⣟⣿⣿⣿⣿⣷⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⡆⢨⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣟⣛⡛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡐⠻⠶⠄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⠱⣿⣷⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡆⠈⠙⠿⣆
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠟⠁⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⢠⠞⠢⡀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤⣉⢣⡜⢳⣈⠖⣉⢄⠸⡀⣀⣀
⠀⠀⠀⢸⡉⣉⣉⣻⡼⠒⠊⠉⠉⠉⠉⠉⠓⠼⣄⡯⣥⠀⡇
⠀⢀⣠⠤⠇⢷⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣰⣅⣀
⠀⠱⡀⢖⢩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⢲⠄⣹⠁
⠀⢀⡼⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡴⢅
⣴⠋⢴⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡑⣀⡱⠤⠤⣀⣀
⠀⠙⡶⢫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⡜⠀⠧⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠉⠉⠑⡖⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢦⡀
⠀⠀⠀⠀⡇⠘⢒⡏⡶⠤⣀⡀⢀⣀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠤⣄
⠀⠀⠀⠀⠉⠉⠉⢇⠘⢚⡡⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠓⠒⠒⠲⣶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣷⡐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠎⡀⠀⠀⠄⡀⠚⠀⠀⠀⠀⠐⠀⠀⠉⠂⠠⣄
⠀⠀⠀⠀⠀⠀⠈⡹⠷⣦⡑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢇⠀⠀⢹⢽⡝⠶⠶⠴⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠓⢤⣽⣦⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠰⠘⢂⢀⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⡤⣀
⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠘⠋⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣜⠁⢻⣨⠗⡄
⠀⠀⠀⠀⢸⣅⣠⣏⢣⣤⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⡗⠠⢠⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠶⠋⠁⢠⠔
⠀⠀⠀⠀⠈⠛⠀⠛⠿⣄⠈⠫⡙⠒⠲⣄⣈⣓⣀⡀⠀⠀⡶⠒⠛⡉⣀⣼⣿⣶⣇⠉⠉⠉⠙⠙⠛⠛⠓⢲⡚⠋⠉⠉⢃⢈⡀⠔⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣑⠂⠀⢀⣀⡇⡀⠈⠀⠀⠀⡃⠀⢲⡍⠁⠀⠉⠈⠢⠈⠁⠀⠀⠋⠀⠀⠵⠀⠹⠒⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠩⠤⢴⡮⣄⣀⣀⡼⢡⣤⠊⠉⠀⠰⠠⠖⠚

⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠂
⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠴⠓⠁⠀⠀⠀⠀⣀⡤⢴⠒⡖⣲⢦⣀
⠀⠀⠀⠀⠀⠀⢠⣞⡍⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣀⡀⠤⠊⠀⠀⠀⠀⠀⢠⠺⡅⠃⢰⠀⠀⠁⠈⡘⢹⢦
⠀⠀⠀⠀⠐⠀⠈⠙⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠂⠱⠀⠀⠀⠀⠀⠐⢀⠊⡼⡇
⠀⠀⠀⠀⠀⠘⠒⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⠠⢤⠄⠁⠀⠀⠀⠀⠀⠙⠦⣬⠁⢀⡠⣤⢄⡀⣤⠔⠛
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⡍⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣤⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⢡⠀⠀⠀⠀⠠⠂⠄⠈⠀⠀⠜⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⣰⢁⠀⡈⠡⠔⠩⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠁⠒⢠⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠳⣄⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣓⡔⠀⠀⠀⠀⠀⠀⠒⠤⠀⠒⠁
⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⡅⠀⠀⠈⠠⠆⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠇⡀
⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⠒⠀⠑⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠈⠀⠀⢀⢷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠪⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠂⠀⠀⠄⠀⠀⠰⡙
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠈⠡⠤⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡀⡇⠰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠎⡄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠙⠒⠂⠂⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⢤⣤⣀⢀⡀⠀⠀⠠⠌⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠁⠁⠀⠀⠈⠓⠇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⢀⠀⡰⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢁⠜⠁⠀⠀⠁
⠀⠀⠐⡵⢋⠞⠡⠄⣀⢀⠀⣀⠀⡄⢢⡘⢮⡳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠠⠇⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢡⠏⢀⠉⠐⠃⢈⠀⠸⠀⢠⠀⢱⣌⡇⠀⠀⠀⠀⠀⠀⠀⠈⠘⢸⠸⠀⠀⢀⠄⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠳⢾⡀⢼⠀⢸⠀⠠⡄⠀⣧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⡇⠀⣀⠔⠁⠀⠀⠀⠀⠈⠀⢔⠢
⠀⠀⠀⠀⠀⠀⠑⠚⠐⠚⠀⠐⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠆

⠀⠀⠀⢀⢀
⠀⠀⠊⠉⠳⢄⠈⠙⠋⠉⠉⠀⠁⠀⣁⠨⠜⠋⠁⠀⠀⠀⠀⣠⠀⠤⠈⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠋⠁⠀⢀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢃⣀⣀⣀⡴⠏
⠀⠀⠀⠈⠐⠠⠖⠋⠀⠉⠀⢀⡀⣀⠀⠀⠀⠈⠁⠀⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠚⠁
⠀⠠⢀⣀⠠⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠂⠛⠂⠃
⠀⠀⠀⠀⡠⠴⡄⠤⠠⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠸⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⢅⠀⠀⡄⠀⠀⠀⡤⢀⡄⡄⡄⡀⠀⠀⠀⠀⠀⠘⠦⠀⠠⣔⣰
⠀⠀⠰⡀⠠⠆⠠⠤⠴⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠋⠁⠉⠀⠁⠉⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠐⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⡞
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢆⠀⠀⢠⠅
⠀⠀⠀⠀⢀⠐⠒⠂⠄⠀⠀⠀⠈⡄⠀⠄⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠐⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⢀⡴⠞⠁⢠⣀⣀⣠⠤⠖⠒⠲⠶⠶⠶⠄⠀⠉⡑
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣀⣀⣀⣤⡙⢛⣷⣶⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠂⠋⠉⠑⢒⡒⠒⠓⣶⠀⢂⡒⠘⢽⣿⣿⣿⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠻⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠞⠛⢓⣛⣫⣽⣿⣿⣿⣿⣽⣭⡿⠷⣦⢤⡀
⠀⠀⠀⠀⠀⢠⠖⠀⠄⠠⢄⠽⠠⠦⠤⠼⠬⣥⠬⣿⣿⣽⣿⠭⠿⠿⢿⣿⣟⣽⣿⣿⣷⣮⣄⣙⠋⠙⢷⣄⡀
⠀⠀⠀⠀⣰⠋⠁⠠⢤⣤⣀⣆⣀⣐⣀⣄⢤⣤⠠⠤⠤⢤⣴⣶⣶⣶⣿⠿⣾⣿⡷⣿⣿⣿⣿⣿⣷⣦⣄⠙⠻⣤⡀
⠀⠀⠀⢀⠎⠀⠂⠉⢁⣈⣈⣁⣀⣉⣁⣈⣉⣙⣏⣉⣉⣉⣉⣭⡤⠤⢶⣶⣿⡿⠗⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣷⣄
⠀⠀⠀⢠⠀⠀⢌⠐⠒⠂⠐⠳⠒⠒⠒⠒⠒⠲⠗⠒⠒⠒⠖⠛⢛⣋⣉⣯⣿⢷⣫⣿⣿⠛⠛⢿⣿⣻⠓⠂⠀⠐⠉⢻⡆
⠀⠀⠀⠘⢀⡠⢼⣒⣒⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⢭⣭⡭⢽⠿⠿⢿⣟⣯⡥⣶⣿⣷⣦⣛⣿⣿⣖⠲⠤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⠀⠂⠹⢯⣀⡠⠤⠌⣃⠀⠀⠀⠠⠠⠟⠂⠀⠀⠒⢒⣚⣻⣿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣉⠄⣒⠀⠄⣀⠀⠘⡙
⠀⠀⠀⢨⠀⡄⠈⠻⡄⠀⣀⡠⠄⠀⠀⠀⠀⠀⣚⣉⣀⣉⣭⣥⣼⣗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⣀⠀⠀⠀⢈⡓⢱
⠀⠀⠀⠀⣅⠋⠘⠑⢨⡥⠤⠐⠂⣐⣀⣀⠈⠭⠭⣥⣀⣖⣾⣿⣯⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡛⠛⠷⢮⣍⡒⠀⡀⠉⠹
⠀⠀⠀⠀⢨⡀⠼⠂⣀⠴⠒⠈⣉⣠⡤⠤⠶⣒⣺⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣈⡁⠂⠤⡙⠳⢬⣑⠀⠂
⠀⠀⠀⠀⠀⠉⡼⠋⣠⡴⠚⣁⣭⠴⢒⡻⠭⣵⣶⣿⣿⣿⢿⣿⣿⣿⣿⣽⣭⣿⣿⣟⣿⣿⣿⡍⠉⠉⠛⠛⠶⣤⡑⠢⣙⠻⠃
⠀⠀⠀⠀⠀⠀⠐⢾⠁⡠⠚⣁⠴⣚⡽⣶⣿⣿⠿⠛⠉⣱⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠤⢈⡒⠤⣀⠉⠛⢷⣄⡑⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢅⡼⣡⠞⣡⣮⢞⠁⢀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠈⠹⢷⣮⡛⠦⣄⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣼⢵⠁⠈⠔⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠋⠙⣶⣤⣀⠠⢉⠛⣷⣬⡙⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⢐⢿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣟⠋⠉⢷⠦⣄⠀⠙⠛⢿⣦⣁⠀⠈⠻⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣾⡄⠹⣿⢸⣿⣿⣿⣿⣻⣿⣶⠬⠉⠁⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⡀⢿⣿⡆⠟⣾⣿⣿⣿⣿⣿⡿⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡅⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⡗⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠊⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⢸⣿⣿⣼⣿⣿⣿⣿⣯⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠛⡷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠻⣿⣿⣿⣿⡿⣿⡧⡉⠢⡀⠀⢢⡀⠀⢠⡀⠀⠳⣄⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⣿⣿⣷⡙⣮⠳⡙⠄⠈⢆⠀⠹⣆⠀⢹⣄⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠏⠉⠛⢿⡜⣧⢹⡈⢆⠈⢧⠀⠸⣧⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠱⢸⣎⡇⠘⣇⢸⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣤⡤⣀⡀
⠀⠀⠀⠀⡈⠘⢄⠠⢔⡲⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠓⢺⣅⠀⠏⣷⣰⠉⢲
⠘⠯⠭⣉⠁⡷⡆⣰⠋⠀⠀⠀⣰⢹⣭⡭⠷⠦⢙⣶⣶⣶⠆⠀⠀⠀⣀⣀⠠⢤⣀⠀⠘⢯⡿⣿⠇⢰⢻⡁⠠⣁⣿⣿⣆⠘⡇
⠀⠀⠀⡜⣠⠖⠢⡘⣆⠀⠀⠈⠻⣇⣛⣛⣋⠉⣈⠿⠋⠀⠀⢀⠴⠿⠤⣍⢢⡀⣿⠈⢢⡀⠉⢿⡇⠘⣗⠀⢘⢠⡅⠙⢿⣶⣿⣄
⠀⠀⠈⠚⠁⠀⠀⠙⠚⠃⠀⠀⠀⠘⠛⠒⠂⠉⠀⠀⠀⠀⠀⢮⣿⣿⣷⣮⣿⣧⣇⡠⠏⠁⠀⠈⠋⠙⣯⠀⣰⣰⣀⡴⠶⠻⠿⣿⡧
⠀⠀⠀⣀⢤⠴⠶⡶⡤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠤⢤⠠⠀⠀⠉⠙⢫⠞⠻⣟⠒⠒⡏⠀⠀⠀⠀⠈⠋⠉⠉⠁⢠⡴⠶⢤⡀
⠀⣴⠻⠹⠀⠀⡄⠀⢀⠃⠞⣳⣄⠀⠀⡠⠊⠣⡀⢣⡀⣹⠀⠇⠀⠀⠀⠘⠣⣧⠈⠹⠞⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⣿⢏⠢⠡⢹⡄
⠈⡎⢂⠁⠃⠀⢀⠀⠈⠈⡰⠡⢋⠆⡐⠙⠢⣤⠟⠉⡏⢻⢆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣸⣷⠀⠀⠀⡇⡈⠘⡄⡂⠆⣧
⠀⠘⢆⢢⢠⣠⢘⠀⠀⠐⠐⡡⠋⠀⡗⠲⠴⡟⢒⣶⡷⣯⠤⡇⠀⠀⣰⠇⡢⠀⠄⡁⠨⢳⡄⠀⠀⡯⠰⡄⠀⠀⢻⢁⠀⠀⠀⠀⢻
⠀⠀⠀⠳⣕⢷⣿⣾⠌⣠⠊⠀⠀⠀⠘⢦⠒⢛⠥⣮⢶⠛⣤⠇⠀⠀⣥⠊⣠⠎⡔⢠⠁⡅⡇⠀⣘⣋⠉⢵⠀⠀⠸⡼⡠⡀⠀⠀⡿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠙⠻⠤⠧⠜⠛⠁⠀⠀⠀⠋⣴⠃⣼⠁⣾⠀⣇⡿⠀⠫⣤⣺⣿⡷⠀⠀⢿⡵⣣⢇⢢⡇
⠀⠀⠀⠀⣠⡤⣀⢤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠒⠛⠴⠟⠒⠉⠁⠀⠀⠸⠿⠋⠁⠀⠀⠈⠻⣵⣯⠞
⠀⠀⡄⠊⠀⢳⡀⠈⢁⡆⠙⢦⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠻⣟⠛⠒⠚⠳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣼⣀⣀⣠⡜⢋⠓⠺⢀⠠⠈⢳⣄⠀⠀⡼⣛⣫⡈⠛⣷⣄⠀⠀⠉⢢⡀⢀⠀⠃⠈⠙⠦⣄⠀⠀⠀⠀⠀⢴⣾⣿⣿⢧⣄
⠀⢱⠀⠏⣇⡼⣟⡖⠈⢹⠶⠛⠉⣿⠀⠀⡏⣴⣾⣿⣮⡟⣿⣆⠀⠀⠀⠙⠒⠒⠓⠒⠒⠒⠚⠓⠀⠀⠀⣠⡾⣿⣛⣫⣤⠛⠙⡦⡀
⠀⠘⣦⠚⠙⠑⡎⠉⠺⡇⢠⠀⣆⢺⠀⠀⢣⡻⣿⣿⣿⣿⡿⠛⠀⣀⠤⢤⠞⠛⠙⣟⠓⠦⣄⣀⠀⢠⢞⡙⠀⠈⠀⠀⠀⠐⡜⡄⢽
⠀⠀⠈⠙⠲⠶⠧⠖⠲⠶⠚⠒⠛⠛⠁⠀⠀⠙⠚⠛⠋⠉⠀⠀⢰⡡⠊⠀⢂⠀⠀⠘⣄⠳⣈⡟⠀⠸⡕⢡⢀⠁⠃⡛⡈⡁⡐⡜⣼
⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣔⣚⠉⠓⢔⠄⡄⠈⣳⠋⠀⠀⠀⠘⠧⣼⢐⡃⡃⡇⢡⣱⡴⠋
⠀⠀⠀⣴⣿⣿⣛⡷⡄⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⠈⠳⣝⣛⢛⣿⣚⣷⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠉⠁
⠀⢠⢚⢝⡉⠀⢉⣶⡿⡆⠀⡟⡩⠋⡥⠼⣧⡈⠉⢀⣴⣦⡌⢷⡀⠈⠈⠉⠀⠉⠀⠀⠀⠰⡒⡖⡲⠉⡟⠉⢹⠖⠘⠳⢦⣄
⠀⣇⢏⢮⠸⣼⣿⡿⣿⠁⢠⡋⢰⠺⢷⡄⠈⠻⣦⠈⢿⣿⣿⡎⣧⠀⠀⠀⢀⡖⠒⠦⣄⠀⠘⢶⠃⢀⠀⠀⠀⠀⢐⠈⠀⢘⢆
⠀⠈⠲⢽⣽⣿⣫⡞⠁⠀⢈⣶⡛⠳⣆⠙⠷⣄⠙⣦⢸⣿⣿⣧⣽⠀⠀⣀⡼⠅⠀⠀⠠⠛⣄⠈⠛⣇⠀⢠⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠘⢏⠙⠶⢌⣙⡓⢮⣿⣌⢣⣻⣿⣯⠏⠀⢸⠙⠌⠀⠀⠀⠀⠄⢹⠀⠀⠈⠛⣇⠀⠐⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣭⣭⣴⣍⣰⣇⠉⣿⡟⠀⠀⠈⠣⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⢶⣄⡀⠀⠀⠠⠀⢛⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠟⠉⠉⠀⠀⠀⢁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠁⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⢀⠠⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠐⠀⠀⠑⠈⢀⠀⠠⠀⠀⡤⢘⠢⠀⠀⠰
⠀⡘⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢟⠃⠃⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠙⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠄
⠀⠴⠦⣖⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠿⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠈⠣⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠀⠈⠀⠈⠀⠂⠁
⠀⡆⢐⠀⠈⠀⠤⠀⠐⠀⠋⠀⡄⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⡀⠀⢠⡀⠀⡄⠐⢀⠀⠀⠀⡐⠌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠈⠏⢂⡈⠀⠀⡠⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⡀⠀⠀⡀
⠀⢀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⢀⠄⠁⠐⠄⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠊⠁
⠀⠀⡈⠉⠀⠀⠀⠀⠑⣄⠀⠀⠰⠀⡋⠀⠀⠀⡀⠐⠐⠁⠀⣐⠾⠛⠁⠀⢀⡀⠄⠀⢦⠢⣄⠀⣠⢀⠈⠈⠀⡄⠈⠓
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠑⠚⠓⠒⠂⠛⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⢠⡆⠀⠀⢷⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠳⢄⣀⣀⣀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢧⠀⠀⠀⠓⠒⢠⡄⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⢠⣦⣤⣭⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⢶⣾⡿⣼⣿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣤⣽⣿⣿⠋⠀⠠⡇⠀⠘⠲⣄⡀⠉⠓⣆⠀⡀⣠⣿⡇⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⡌⣿⣿⣿⣿⠀⢤⠀⠑⣄⠀⠀⢸⡇⠀⢠⣿⣿⢡⣿⣿⡧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⣮⣿⣿⣿⠀⢠⡆⠀⢸⡇⠀⢿⣷⡆⣿⣿⣿⣤⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⠇⠀⣾⣇⠀⠈⢷⡄⠘⣿⣇⠻⣿⣿⣽⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢼⣿⣿⡿⠋⢠⡀⣼⣿⠂⠀⢠⡇⠀⢸⡿⢠⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⣼⡿⠿⠟⠋⡴⢀⡜⠠⣿⣏⠀⢀⣾⠁⢠⡿⠁⣠⣾⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡟⠋⠀⢠⠄⡗⠰⡃⠀⢸⠀⣿⠹⠀⢸⣧⡀⢸⣇⢠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠋⠀⠀⣇⢸⣆⣻⣢⠟⡤⠿⠶⠿⠧⣤⣾⡿⢃⣤⣿⠸⣧⣤⣤
⠀⠀⠀⠀⠀⢀⠊⠀⠀⢠⢸⣧⠿⠊⠉⠉⠀⠀⠀⠀⠀⠒⠒⠒⠈⠽⢿⣿⣿⠶⠿⠛⠛⠁
⠀⠀⠀⠀⠀⣧⣤⣴⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠉⠉⠓⠢⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣀⢄⣰⠁⠀⠀⠀⠀⠀⠀⠈⣗⠒⠤⠔⠒⠉⢧
⠀⠀⠀⡔⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠙⠒⢤⡑⢤⣀⣀⡀
⡰⠋⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⠀⠀⠀⠀⠘⢆⠀⡼⠁
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⡆⢇⡠⠤⠒⠒⠒⠢⠤⣀
⠀⠉⠙⠛⠛⠛⠛⠛⠛⢋⡖⠓⡞⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⢣⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⣄⠀⠀⢀⠔⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣈⡱⠶⡞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡠⠎
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣧⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠈⠀⠐⠀⣀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠝
⣤⣤⣤⣴⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠐⠂⠀⠌⠳⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣀⣄
⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢤⣄⡀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠚⠀⠠⣌⠹⣷⣧⡞⠁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡘⢋⣴⣬⣦⢹⡆⣹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢻⣿⣦⠄⠂⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⣿⢏⡾⠃⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⢢⡀⣹⣦⣀⣠⣿⣿⣾⣛⣁⣠⡴⠏
⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠉⠛⠿⠛⠛⠉
⠀⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄
⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣾⡧⢀⡀
⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠈⠀⠀⠀⠀⠸⠏⠀⢸⡿⢦⣄
⠀⠘⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣧⠀⠀⠀⢰⡀⠀⠈⡄⢈⣄⡽⠶
⠀⠀⠘⢟⣀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢀⣀⣿⡗⠠⠖⠛⠋
⠀⠈⠉⠉⢿⣧⣤⣴⠞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠿⠃
⠀⠀⠀⠀⠈⠙⠛⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠁⢀⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣦⠤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠦⠴⠾⢿⣷⣦⡤⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡎⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⡉⠝⠉⠁
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠌⠑⠄⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⣄⠀⠀⠀⢀⡾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣈⣷⣤⣤⣾⣥⣀⣹
⠀⠀⢀⣀⡀⠀⠀⢀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⣶⠖⠛⠋⡿
⠀⠀⠈⢿⣍⠛⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⣼⣥⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⣀⣤⡴⠖⣿⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠺⠯⣤⣤⣤⣸⣦⣤⣤⣤⣤⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠓⢦
⠀⢻⡄
⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⢦⡴⠶⣤⡴⠲⠲⠶⠶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠹⣿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⠍⠁⠈⠁⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⣿⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣿⠁⠀⠀⠀⠀⢸⡆⢀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣧⣄⡀
⠀⠀⠀⠀⠀⣠⠴⣾⡇⠀⠀⠘⡌⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠇⠂⠀⠀⠀⣸⠿⠿⠉⢷⡀
⠀⠀⠀⠀⢰⡇⠀⠹⣧⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠈⡧⠀⠀⠀⣸⡀⠈⠀⠀⡼⠃⠀⠀⠀⠀⡟
⠀⠀⠀⢀⣯⠀⠀⠀⢱⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⣧⠄⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠁⠀⠐⣾⠓⠀⠀⠀⠀⣼⡿⢦
⠀⠀⢠⣟⠉⢦⠀⠀⠀⢣⠀⠀⠀⠘⡂⠀⠀⠀⠀⢸⡄⠀⠀⠀⡅⠀⠀⠀⢸⠀⠀⠀⣰⠀⠀⠀⢰⠉⠀⠀⠀⠀⠼⠋⠀⢈⡇
⠀⠀⢸⡇⠀⠈⢲⣄⠀⠠⢦⠀⠀⠀⠱⡀⠀⠀⠀⠈⣡⠀⠀⠀⣧⠀⠀⠀⣾⠀⠀⢀⠏⠀⠀⢠⠇⠀⠀⠀⢀⡜⠀⠀⢀⣼⣷⡄
⠀⠀⢨⢧⡀⠄⠲⡿⣆⠀⠉⢧⠀⠀⠀⢷⣖⠀⠀⠀⡏⡆⠀⠀⡿⠀⠀⢀⢿⠀⠀⡜⠂⠀⢀⣞⠀⠀⠀⢀⡜⠀⠀⢠⠎⠀⢀⡇
⠀⠀⠸⡆⠘⢄⠄⠈⠻⡆⠀⠀⢳⡆⠀⠘⣿⠀⠀⠀⢇⠃⠀⠀⠁⠀⠀⢸⠂⠀⣠⡇⠀⠀⡟⠄⠀⠂⢀⡞⠀⠀⡴⠃⠀⡠⠎⡇
⠀⠀⠀⣿⠳⣾⢷⡀⠀⠙⢶⣄⠀⢿⠀⠀⢹⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⣿⠀⠀⡿⠁⠀⣼⠇⠀⠀⡠⡣⠄⢀⠞⠀⣰⣯⠕⣾⠁
⠀⠀⠀⠘⣷⣈⣷⡙⢦⠀⠀⢿⣆⠀⢣⡀⠀⢧⠀⠀⠀⡇⠀⠀⠁⠀⠀⡏⠀⣸⠁⠀⣰⠏⠀⢠⡞⠁⢀⡴⢅⡠⣪⣞⣵⢴⠋
⠀⠀⠀⠀⠙⢮⡻⣝⢮⡳⣤⠀⠹⣆⠀⠹⡄⠈⡆⠀⠀⢣⣠⢀⢠⡤⢴⣁⢀⡧⠀⢰⠹⠀⢀⡏⠀⣠⢞⡱⣫⣺⠖⣫⡷⠋
⠀⠀⠀⠀⠀⠀⢹⣚⢷⣝⣮⡣⣄⠘⢷⡄⢹⣤⢿⠁⠁⠸⡅⠸⣂⠀⡾⠀⡼⠛⢲⣿⣀⣠⠋⢠⢞⡕⣫⢞⣩⢶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡿⠿⣮⣢⣌⠿⣦⠙⡄⢣⠀⠀⡇⠰⠁⢠⠇⢠⡇⢀⡾⠉⡵⢷⣶⣗⣡⣎⣪⠭⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⣭⣻⢷⣬⠳⡘⣌⢇⠀⢿⢸⡇⢸⢀⣾⢀⣾⢀⣼⣵⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠷⢽⠿⢿⣦⡹⣞⢞⣆⢹⠸⣇⡏⢈⡟⣾⣫⣾⣿⣿⣿⠇⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢲⣮⡟⣁⡀⠀⡿⣿⣯⣿⡌⡄⣹⡟⣾⡼⣱⣿⡟⠉⢡⣴⡏⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠤⠽⠋⠉⠙⠳⠦⢌⣿⣿⣇⣿⣴⣿⣾⡟⢡⣷⠖⢚⣿⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠖⠶⠾⠗⠒⠒⠋⠉⠻⠿⠿⠟⠓⠛⠛⠛⠒⠿⠿⠶⠚

⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⡟⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣴⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⠳⣄⡀⠀⠀⠀⣸⠁⠀⠀⢸⡆⠀⠀⠀⢀⣠⠞⠋⠀⢀⡞⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠙⠦⣄⣀⣿⣤⣤⣤⣼⣧⣀⣠⠴⠋⠁⠀⠀⣰⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢦⡀⠀⢀⡾⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣴⠾⠛⠛⠛⠛⠷⣦⡀
⣿⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠶⠶⠒⠛⠛⠉⠉⠉⠁⠀⣿⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠙⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⠤⣤⣤⣀⣀⣀⡀
⣿⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠶⠶⠤⣤⣤⣄⣀⣀⣀⢀⣷⣠⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠛⠛⠛⠿⣿⡛⠉⠉⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠾⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣴⡖⠛⠛⠛⠛⢶⣶⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣶⡞⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢻⣶⠶⢦⣄
⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⡇⠀⠀⠉⠳⣦
⠀⠀⠀⣰⠋⠀⠹⣆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡷⢦⣄
⠀⠀⣰⠛⣆⠀⠀⢹⣆⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠏⠀⠀⠈⠻⣄
⠀⠀⣿⠀⠸⣆⠀⠀⢿⡄⠀⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⣿⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢿⠀⠀⢻⡄⠀⠘⣷⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⢰⡏⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣴⣿⢷⡀
⠀⠀⠸⡆⠀⠀⢿⡀⠀⢻⡆⠀⠀⠀⢸⣇⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⣿⠁⠀⢀⣼⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠙⣆
⠀⠀⠀⢳⡀⠀⠈⣧⠀⠸⣇⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣸⠃⠀⠀⣼⠃⠀⢀⣾⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⢧⠀⠀⠸⡆⠀⣿⠀⠀⠀⢀⡇⠀⠀⣼⠁⠀⢰⠏⠀⠀⣼⠃⠀⢀⡾⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣇
⠀⠀⠀⠀⠘⣧⠀⠀⢻⡀⢿⠀⠀⠀⢸⠇⠀⢠⡇⠀⢠⠏⠀⠀⣼⠃⠀⢠⡿⠁⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠘⣦
⠀⠀⠀⠀⠀⠸⣆⠀⠈⡇⢸⠀⠀⠀⣾⠀⠀⡾⠀⢠⠏⠀⢀⡼⠃⠀⢠⡿⠁⠀⢠⡾⠁⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⡆⠀⢿⢸⠀⠀⢀⡏⠀⢰⠇⢀⡞⠀⢀⡼⠁⠀⣰⡟⠁⠀⣰⠏⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣾⠀⠀⢸⠃⠀⡟⢀⡞⠀⢠⡞⠁⠀⣰⡟⠀⢀⡼⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣤⡴⠾⠛⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠘⣿⠀⠀⡿⠀⣸⢁⡞⠀⣠⠏⠀⠀⣼⠏⠀⢠⠟⠀⠀⢀⣴⠟⠁⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⣀⣠⡏
⠀⠀⠀⠀⠀⣠⠞⠋⠈⣇⣿⠀⢰⡇⢠⠇⡼⠀⡴⠃⠀⢀⣼⠃⢀⣴⠋⠀⢀⣴⠟⠁⠀⣠⠶⠋⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⣽⠀⢸⠇⡞⡼⢁⡾⠁⠀⣠⡾⠁⣠⡞⠁⠀⣠⠟⠁⢀⡴⠋⠁⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⣿⡇⢸⣼⣱⢣⡞⠀⢀⣴⠋⢀⣼⠋⠀⣠⠞⠁⣠⠖⠉⣀⡴⠞⠋⠁⠀⣀⣀⣤⣤⣶⡶⠶⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣷⢸⣿⣧⡟⠀⣠⠞⢁⣴⠟⠁⣠⠞⢁⡤⠚⣡⠴⢛⣁⡤⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡿⢀⡜⣁⡴⠛⢁⡤⠞⣡⣴⣫⢔⡫⠔⣚⣉⣀⣀⣤⣤⣤⣤⡤⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⠿⠚⣉⡤⠖⣫⣴⣞⣻⡽⠾⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⢿⣵⠶⠟⠛⠋⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠤⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠞⠁⠀⠀⠀⠀⠀⠀⠨⠖⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠉⠙⢄⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢄
⠀⠀⠀⠀⢀⠤⠤⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⡁⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠓⠐⠠⠤⠤⢄
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠀⠒⠒⠄⠀⠀⠀⠀⠀⡀⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢀⡾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠨⠷⠤⠄⠀⠀⠀⠀⠀⠐⠀⠀⠉⠐⠢⢄
⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢄⣀⠀⠔
⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠉⠂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⠀⠀⠀⠸⡠⠀⠀⠀⡰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠢⡀⠀⢀⡠⠄⠒⠀⠉⠁⠀⠒⠠⢀⡈⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⣔⡩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠤⡀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠊⠀⠈⠐⠤⡰⠊⠁⠀⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠈⠁⠒⠤⡐⢭⡥⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞
⢠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠁⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣑⣄⣀⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅
⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠋⠀⠀⠀⠑⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⢑⠤⠄⠤⢔⢲⡀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠤⠤⠐⠋
⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠲⡩⠢⡀⠀⠀⠀⠁⠑⠦⢀⡀⢀⣀⠤⠊
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠡⡱
⠀⠀⠈⠢⢀⡀⠀⣀⠤⠒⡄⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠤⠠⠤⠢⡀⠀⠀⠀⠀⠀⡔⠢⠤⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣢⣤⣤⣔⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢛⣠⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣴⣶⣶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣍⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣠⣴⣾⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣝⡛⠿⢿⣿⡿⠿⠿⠛⠉⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡶⠖⠀⠀⠠⡄⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠼⣿⣿⣿⠟⠁⠀⢠⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃





⡟⠉⢻⡟⠿⠿⠿⠻⢿⠛⠟⠻⠿⠿⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⣀⣁⡀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠉⠁⠒⠋⠀⠀⠀⠀⢀⡤⠒⠒⠒⠤⡀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠑⢄⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠏⠀⠀⠀⠀⠀⠉⠀⠑⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢄⡠⢰⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠒⣄⣀⡀
⠀⠀⠀⢀⡴⠋⠋⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⡄⠀⣀⠀⠀⠀⠀⠈⠄⠘⠛⠢⢄⠀⠀⠀⠀⠃⠒
⢠⡊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⠤⡀
⠀⠑⠒⠑⠢⠤⠤⠤⠒⠢⠄⠤⠒⠚⠢⠤⠤⠀⠄⠀⠀⠀⠀⠠⠀⠆⠠⠀⠄⠒⠄⠤⠒⣁⡀⠤⢀⣀⣀⠠⣤⣀⡀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠠⠤⠄⠂⢒⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢀⡈⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠒⠋⠑⠒⠒⠒⡺⠷⠆⠀⠈⠀⠀⠀⠀⠉⠀⠀⠐⠖⢶⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠰⣉⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⣀⠜
⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠀⠉⠉⠉⠁⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠢⠤⠤⠤⠢⠄⣤⠤⠔⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠠⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⣁⠉⠀⡈⠁⠈⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠈⠉⠙⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣒⣠⣤⣒⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⠿⠙⠯⠹⠯⠻⢟⡻⢶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠏⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠋⡝⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⢳⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡀
⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢀⣠⣴⣶⡶⡾⣶⢶⣶⣤⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⢀⣿⠉⠁⠀⠀⣠⣾⡟⠿⠙⠀⠀⠀⠈⠉⠘⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⡏⠁⠀⢀⣼⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⣾⠒⠀⠀⣾⡯⠁⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⢿⡄⠀⢰⣿⠄⢠⣾⠟⠋⠉⠉⠘⠙⢻⣧⡄⠀⠀⠀⠀⠀⢈⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇
⠀⠀⠀⠀⢸⣟⠀⢸⣿⢠⣿⣡⡶⣶⠶⣶⡄⠄⠀⠙⣿⡄⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⢿⡆⠀⣿⣼⣿⣿⣿⣿⣦⣽⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠈⢷⣄⠘⣿⣿⣿⣿⣿⣟⣰⡿⠀⠀⢠⣿⠁⠀⠀⠀⠀⣘⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⡻⢿⣿⣿⡛⢉⣀⣤⣼⡿⠁⠀⠀⠀⠠⢠⣼⠟⠛⠻⠶⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣍⠙⠛⠛⠛⠋⠁⠀⠀⢠⡀⣠⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣷⣦⣤⣦⣶⣦⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠒⠤⣤⡠⠤⡤⠒⠤⠤⠐⠂⠠⠤⡀
⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠊⠉⠚⠀⠀⠀⠀⡀⠘⣇⣀⣧⢠⠀⢀⡴⠂⠀⠀⠙⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠠⠤⠤⠤⢤⠴⠶⣾⠗⠉⠀⠀⠩⡻⣯⣄⣤⣴⣷⡶⠒⠚⠛⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡏⠀⠀⠀⠀⠀⢹⣾⢍⣉⡉
⠀⠀⠀⠀⠀⠀⢀⡰⠒⠦⠤⣀⣀⠀⠀⠈⢙⣧⡀⠀⠀⠀⢀⣼⣿⡉⠉⣉⣉⡔⠲⠤⡔⠒⠤⠤⡀
⠀⠀⠀⠀⠘⠓⠛⠒⠒⠒⠒⠒⠚⠋⠀⠚⠉⢠⠟⡦⢤⣶⡿⣟⠃⠙⠛⠓⠲⣤⡤⢤⣤⣤⠤⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠈



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣤⡀⠀⠀⠀⠀⠰⠋⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣤⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠚⠛⢛⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣛⣛⣿⣿⣿⣷⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣋⣭⣍⡛⢿⣿⣿⣿⣿⡿⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⠃⠀⠀⣠⡤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⣷⠀⠈⠳⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠤⠜⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣴⠂⣶⠆⣤⠤⢀
⠀⠀⢀⠀⠀⢠⣶⡶⢐⣀⡀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⡜⣿⡄⣿⢰⣿⢠⡾⢉⡶⡄
⠀⠀⠀⡅⠀⣿⠋⡾⣽⣿⣿⡦⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡽⣿⣽⣷⣿⡇⣿⣼⠇⣾⢡⡟⣱⠿⡆
⠀⠀⠉⠇⠈⣿⣾⣗⢿⣿⡿⢣⠃⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢸⢣⢟⡾⣡⢞⣩
⠀⠀⠐⠶⠛⠛⠳⢉⠀⠀⠀⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⢇⣏⢏⣮⣞⣵⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣹⠏⣜⣻⠿⠛⠋⠁
⠀⠀⠠⣠⣤⣶⣦⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣠⣿⣯
⠀⠀⠀⠙⢿⣟⠛⠛⠛⠛⠙⡋⢩⣙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠽⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠈⠙⠿⣩⠩⠉⡭⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣢⣄
⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣈⠁⣽⡄⠀⠀⠲⢦⣤⣤⣀⣀⣸⣿⣄⣀⣤⣤⣀⠔⠂⠀⢠⣿⣯⣿⣶⡄
⠀⠀⠀⠀⠀⣾⣏⣻⡀⠀⠀⠀⠀⠀⢠⡿⠘⠙⣷⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣸⣿⣿⢿⡻⣿⡆
⠀⠀⠀⠀⣸⣿⣿⣧⣧⡀⠀⠀⠀⠀⣠⠀⣼⢢⣿⡆⠀⠀⠀⠀⠀⢀⣾⡿⠻⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣏⡅⢎⡿⣿
⠀⠀⠀⢀⣿⣿⣿⠛⠼⣳⠀⠀⠀⢠⡿⠑⠈⢂⣿⡇⠀⠀⠀⠀⢠⡿⠛⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⣿⣿⡷⠜⡡⢞⡿
⠀⠀⠀⣼⣿⣿⣷⠛⡲⣿⡆⠀⠀⠨⠀⡀⠆⡿⢁⣷⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⢹⣿⣿⣣⢑⢹⡇
⠀⠀⣰⣿⣿⣿⣁⣼⠳⣄⣿⠀⠀⢈⣀⠦⠻⣹⡯⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣬⠹
⠀⢠⣿⣿⣿⣿⣧⡄⠻⣀⢽⠆⠀⠈⠄⣘⢴⣿⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⡷
⠀⢸⣿⣿⣿⡗⠒⢉⠗⠜⠺⡄⠀⠀⠠⠟⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠙⠋⠿⣿⡷⠺⡷⠚⠓⠁⠀⠀⠀⢰⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠸⢀⣠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢢⠀⠀⠀⠀⠀⠀⠈⠄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⣠⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣾⡿⣿⣶⣄⠀⠀⠀⠀⠀⢠
⠀⢻⣿⠀⢀⣾⣿⣿⣿⣦⠀⠀⣴⣿⣿⣷⣦⠀⠀⣿⣦⡀⠀⢀⣿⡟⠻⣇⡿⠛⣿⡆⠀⢤⣀⣀⡜⣇⡀⣀⡀
⠀⢸⡇⠀⠘⣿⣿⣿⢿⣿⠂⠀⠛⠛⠉⠛⠛⠀⠀⠻⣿⣿⠀⠘⣿⣿⠟⣹⡙⢿⣿⡇⠀⠀⠈⢳⣺⣓⡋⠁
⠀⠀⠃⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⣿⣧⣿⡿⠟⠁⠀⠀⢠⠓⠁⠙⠣⡀

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⣾⣿⠂⠀⣠⣤⣤⣤⡀⠀⠀⢀⣤⣤⣄⡀⠀⠀⣷⡀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣸⡆
⠀⢿⣿⠀⢸⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡀⢀⣿⣿⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠓⠶⣶⣿⣷⣶⠶⠒
⠀⠸⡏⠀⠈⠿⣿⡿⠛⠿⠇⠀⠉⠻⣿⠟⠉⠀⠀⠙⠻⡿⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⠿⢿⣇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠉⠀⠀⠀⠚⠁⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠀⠀⠼⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢀⣀⠤⠤⣀⡀⠁⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠀⢀⡔⠉⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠒⠒⠒⠦⣄⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡠⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠙⠒⠪⣄⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣘⣤⣿⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠢⠂⠀⠀⠑⠁⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠤⠓⡤⠊⠄⠀⠀⠀⠀⠀⡀⠐⠐⠂⠀⠓⡞⠀⠀⠀⠀⢀⠀⠆⠠⠀⢰⠠
⠀⠀⠀⠀⠀⠀⠀⠊⡄⠐⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠀⠀⣃⡀⠠⠤⠤⠾⠄⠑⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣄⠀⠀⠀⣸⣷⠨⡥⠤⡄⣀⣀⠀⠀⠀⠀⠈⠐⠠⡀⠑⢄⠤⠠⢄
⠀⠀⠀⡀⡄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠗⢠⠀⠸⠀⠃⡀⢃⠔⠀⢢⠝⠖⢄⡀⠀⠀⠀⠈⠢⡧⠰⠀⠀⠃
⠀⠀⠐⣿⡫⠒⠀⠀⡀⠀⠀⠐⢦⣄⢀⠀⡑⢰⡀⢀⠰⠆⠄⠾⢀⠀⣁⠐⡁⢀⢙⣄⠀⠀⠀⠀⠈⢄⠀⠀⠣
⠀⠀⠀⠀⠁⠀⠀⠀⠙⠋⠀⠀⠀⠱⢄⠁⣌⠠⠉⠀⠀⠀⠀⠀⠀⠈⠡⢈⡤⠥⠤⠁⢣⠀⠀⠀⠀⠀⠄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⢄⠀⠠⠌⠀⠒⠲⠤⠀⠀⠠⠴⠒⠂⠈⠄⠀⠤⠤⢬⡆⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⠂⠉⢛⠀⠀⠋⠉⠀⠀⠀⠀⠈⠉⠃⠀⢘⠋⠀⠒⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢀⣀⠐⠂⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢄⠒⢀⡘
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠉⠉⠈⠉⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢀⠀⠁⣨⠁⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⡤⠒⠀⣤⠖⠀⠀⢀⣀⢁⠍⡀⢈⡤⢀⠀⠀⠀⠀⢀⡠⡄⠠⠀⢄⢙⡴⠃⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠔⢀⠄⠈⢸⠃⠃⠛⠀⠀⢘⠐⣌⡠⠊⠀⠀⠀⠀⠀⡐⠩
⠀⠀⠀⢰⠀⠀⢠⠉⡉⠑⡀⠀⣠⠀⠀⣠⠇⠉⠒⢖⠡⠦⠄⠦⠼⠴⠘⠋⠁⠀⠀⠀⠀⠀⣠⢊⠀⢡
⠀⠀⠀⠀⠢⡀⠀⠉⠀⡠⠁⠈⠁⠀⠀⠁⠀⠀⠀⢰⠏⠢⠤⢀⣀⠀⠀⠀⠀⣀⠀⠄⠐⠁⠀⢀⠔⠂
⠀⠀⠀⠀⢠⠚⠁⠀⠉⠀⡠⠀⠠⢄⠀⠀⢸⡆⣀⠈⠀⠀⣆⠄⡈⡩⠈⠻⡄⠑⠀⠂⠀⠠⠔⠁
⠀⠀⠀⠀⠀⢃⠀⠀⠈⠉⠆⡔⠀⢈⠀⠀⠀⠀⢸⠀⠀⠈⠃⠀⢸⠀⠀⠀⠀⣀⢄
⠀⠀⠀⢀⠀⠀⠁⠒⠒⠎⠀⠈⠀⠁⠀⠀⠀⢀⠜⠀⠀⢠⠀⠒⠁⠀⠀⠀⠈⠟⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠐⠐⠒⠂⠉⠑⠄⠤⠊⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⡀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠦⣤⣀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠶⣤⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢀⣠⣤⡤⠄⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⣀⡤⠖⠒⠋⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢠⠏⠀⠀⢠⠤⠶⠚⠋
⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠶⣏⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠛⠁




⡴⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴
⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢀⡤⢤⡀⡄⠤⡤⠀⣤⠀⣤⢤⠀⡄⠀⡤⠄⠀⢠⠤⠀⢤⠄⢠⠤⡀⡠⠤⡄⢠⢀⠄⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⢸⡇⢠⠇⡇⠀⡇⡸⠸⡆⣿⢺⠄⡇⠀⣟⠂⠀⠈⠓⡄⢸⠀⢸⠺⡅⣇⠀⡼⢸⠣⡀⠗⠂
⣶⣶⡶⠶⠶⠶⣶⣶⣾⣿⣾⣿⣿⣶⣷⣾⣷⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣶⣾⣿⣶⣾⣶⣿⣶⣷⣾⣿⣶⣿⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣴⣾⠟⠛⠉⠉⠙⠛⢿⡿⠟⠛⠉⠙⠻⢿⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠛⠛⢿⠟⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡟⠋⠉⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠹⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠟⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡗⠀⠀⠀⠀⡄⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⠀⠐⠀⠀⠀⠀⠸⢷⣄
⠀⠀⠀⢀⣴⠿⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⣰⡿⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠀⠀⠀⡞⠀⠀⠀⡐⠀⠀⠀⣼
⠀⠀⣿⡇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢻⠀⠀⠀⢿⠀⠀⣸
⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣾⡟⠙⢧⡀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢻⠀⠀⢸⡆⠀⠃⠀⠀⠀⠀⠀⠀⢠⡞⠁
⢸⣿⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠘⡀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠘⣿⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠹⣷⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⢄⠀⠀⠑⠀⠀⡀⠀⠰⠀⠀⡜
⠀⠀⣿⠿⢦⡀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢦⡀⠀⢳⠀⢡⠀⠀⠀⡌
⠀⠀⣿⠀⠀⠙⠦⣀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠳⣄⠀⠀⠑⡄⠀⠃⠀⠃⠀⠠
⠀⠀⢻⡇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠓⠦⡀⠀⠀⠈⠑⢄⠀⠀⠠⡀⠰⡀
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠙⠳⢄⣀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⠈⠓⠂⢀⡀⠀⠀⠠⡀⠑⢄
⠀⠀⠀⠀⠈⢳⡦⣄⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⠉⠛⠂⠤⣄⣀⠀⠀⠀⠉⠒⠄⠀⠀⠑⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠈⣧⠀⠉⠒⠦⣄⡀⠀⠀⠀⠈⠉⠓⠶⣤⣀⠀⠀⠀⠀⠉⠑⠲⠦⢤⣄⣀⡀⠀⠈⠉⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣄⣀⡀⠀⠀⠀⠉⠉⠉⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⠦⠤⢤⣤⣀⣉⣉⣓⠲⢦⣤⣄⣀⣀⡀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⢂⣉⣉⡠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠍⠉⠛⠛⠛⠛⠛⠓⠒⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠐⠂⠀⠀⠀⠂⠀⠂⠂⠀⠂⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠔⠊⠉⠁⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠉⠉⠢⠔⠉⠈⠉⠉⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠣⢄⣀⡤⠂
⠀⠀⠀⠀⠉⠓⠒⠤⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇
⠀⠀⠀⠀⡰⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⣔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡹⠄
⠀⠀⠀⠀⠉⠓⠒⠤⡄⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⠴⠒⠒⠓⠚⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⢀⠰⠀⠀⡄⢀⠀⢠⠘⡌⠀⠀⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⠱⡅⠀⠄⢷⠀⠀⢸⠀⠈⢺⠁⠰⠘⡌⢀⠆⡌⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠠⡑⡄⠀⠡⠹⡄⠀⠈⣤⠀⠘⡦⠀⠘⡄⠀⡜⠀⠌⠞⠀⠠⢂⢞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢌⢾⣆⠈⠈⠂⠠⡀⠀⢥⠀⠀⠇⠀⡇⠀⢠⠀⠀⡜⠀⠈⡀⠀⠡⠟⢁⡔⡡⢂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠪⣢⢄⠑⠘⠆⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢈⠔⠀⣡⠪⠊⢀⠄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠄⡁⠂⠑⠢⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⢈⠗⠀⣊⢕⠪⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠭⢋⠲⠖⢤⡀⠀⠁⠀⠀⠀⣠⡴⠚⠉⠉⠀⠀⠈⠉⠙⠲⢤⡀⠀⠀⠀⠀⠁⢀⡮⠂⠀⢐⣨⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠨⠔⠤⣄⡠⢀⡀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠁⠀⣀⠜⠊⠁⡀⠠
⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠁⠀⢀⡀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠁⠀⢀⣀⠲⠴⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠘⠛⠉⢁⣒⣬⣥⣆⣠⣤⡿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣚⣁⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⣶⠟⠉⠀⠀⡿⠋⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣯⣀⣴⣾⠿⠻⠛⠛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⢀⣀⣠⣤⣀⣁⡀⠀⠀⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠉⢙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠸⣇⣀⣴⣾⠿⠛⠛⠉⠛⠛⢿⣦⣤⣤⣤⣤⣔⠃⠈⢻⣆⣠⡶⠶⣶⠏⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⡍⠉⠉⠙⠻⣦⣻⣿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⢿⣆
⠀⠀⠀⠀⣀⣤⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⠛⠷⣶⣄⠀⠀⠀⠀⢀⡄⠀⢠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⣾⣿⢷⣄
⠀⠀⠀⣰⡿⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⣀⣼⡇⢀⣻⣿⣿⣦⣀⣀⣀⣠⣤⡾⢃⣠⣿⣀⣾⡀⢋⣼⡿
⠀⣰⡿⣿⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⠿⠿⠿⠿⠿⠿⢿⣟⢿⠛⠿⠿⠟⠿⢿⠿⠟⠛⠛⠋⠛⠛⠋
⠀⢻⣧⣙⣢⣿⣄⣻⣦⣈⣳⣦⣤⣤⣠⣤⣴⣿⣿⣿⣀⣘⣷⣄⣀⣀⣼⣧⣴⡆⠀⣠⡿⢢⢀⠈⠀⠡⡐⡀⠨⡳⠅⠀⠈
⠀⠀⠉⠛⠋⠉⠛⠛⠛⠿⠿⠟⠋⠛⠻⠛⠛⠟⠙⢻⢻⠟⠛⠿⡿⠿⡟⠋⠏⡛⠛⢛⡄⠀⢩⢆⢀⠀⠙⡌⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠎⢠⠹⢠⠁⡆⠃⡇⠀⡇⠃⠸⢱⢀⠀⠞⠊⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠃⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⣤⡔⠒⠓⢦⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠀⢀⡔⠉⠀⠀⠉⠓⢄
⠀⠀⠀⠀⡠⢰⠃⠀⢸⡇⠀⠀⢸⠃⠀⠹⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⢲⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⠀⡸⠀⠀⠀⠀⣀⠤⠼
⠀⠀⠀⢠⠁⠘⡄⠀⠀⡇⠀⠀⢸⠀⠀⢠⠁⠈⡄⠀⠀⠀⠀⠀⢀⣀⣠⠞⠛⠛⠓⠚⠋⠉⠀⢀⡇⠈⠟⠲⡄⠀⠀⡾⠀⠘⡄⠀⠀⣧⡤⢲⠒⠛⢢⣄⡀
⠀⠀⠠⠻⡄⠀⢱⡀⠀⢡⠀⠀⡎⠀⢀⠎⠀⢠⠛⠄⠀⠀⣠⣾⡉⠀⠉⠛⠒⠶⠶⠶⠶⠶⠒⠋⠀⢀⡆⠀⣷⠀⠀⡇⠀⠀⠈⠒⢠⡟⢤⢾⣄⢺⡀⣀⣙⡄
⠀⠀⢠⠀⠘⢄⠀⢷⠀⠸⠀⠀⠃⠀⠞⠀⡰⠁⠀⡄⠀⢐⣇⡀⠉⠓⠲⠦⢤⣤⣤⣤⣤⠤⠴⠶⠚⠉⢀⡼⢁⡇⠀⢳⣄⠀⣀⣀⠠⣧⣈⠆⢾⢀⡏⠀⠈⢣
⠀⠀⢸⡳⢄⡈⠳⡀⢣⠀⠇⠸⠀⡜⣀⠎⢀⡠⢚⡇⠀⠈⠣⣍⠛⠒⠦⠤⢤⣤⣄⣀⣀⣀⣤⡤⠴⠚⠉⢀⡾⠀⠀⠈⢧⠀⠀⠀⠀⢈⠿⠂⠾⠋⠘⢦⢀⠇
⠀⠀⠀⠙⢢⡍⠒⢌⣂⣣⡀⢀⣈⠐⡁⠀⢡⠔⠋⠀⠀⠀⠀⠀⠙⠓⠢⢤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠑⢢⠒⠀⠁⠀⠀⡐⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠳⣌⡹⠿⣍⡛⠋⡩⠿⣏⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠔⠚⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⠀⠰⠂⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠃⠈⠢⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠃⡀⢘⣤⡄⠷⢀⣰⠀⠱⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⣆⡀⢠⡤⣤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡋⠀⣹⣄⠀⠀⢨⡇⢸⠒⢄⡀⢀⣀⠀⠀⠆⠁⢄⣠⠾⡁⠀⠑⡀⠀⠉⠑⠆⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠀⢸⢿⠀⢸⡀⠉⣹
⠀⠀⠀⠀⠀⠀⢰⡇⠀⣵⠋⢸⠀⠉⠒⠾⠁⢸⠃⢻⠙⢁⡜⢀⠞⠢⠄⣴⡁⠀⣠⠟⠛⡉⠙⠣⡀⠼⠃⠀⠙⠀⠀⠀⠀⠀⢰⠏⡔⠙⣧⠘⣏⢧⡀⠉⠀⡇
⠀⠀⠀⠀⠀⢠⡏⢰⡼⢋⠀⢸⠀⠀⠀⢸⣀⠸⡆⢨⠟⠁⠀⠼⢄⣀⠀⡇⠀⡀⡜⠀⣞⠁⠃⢠⠇⣠⠇⠀⢱⠀⠀⠀⠀⠀⣼⢸⠀⠀⠈⢣⡈⠓⠍⠀⠈⠷⡀
⢠⣶⣖⣶⣾⣩⣶⡋⡇⠸⡄⠈⣇⣠⠖⠙⡇⠀⡼⠉⠀⠀⢠⣆⠀⠀⠀⢸⡊⠀⡴⢆⠈⠗⠚⠁⣀⠞⠂⢠⠏⠀⠀⠀⠀⣰⠣⠃⠀⠀⠀⠀⢹⠦⢄⣀⠀⣀⡟
⠀⠙⠿⠿⠿⠟⠻⢯⣍⠓⠻⠶⠚⣇⠀⠀⣹⠤⠇⠀⠀⠀⣿⠀⠁⠀⠉⠀⠑⢶⠃⠈⠁⠛⢆⠀⠉⢀⡤⠎⠀⣤⣀⣀⣤⣶⠶⢟⣻⢶⣀⠈⢁⡠⠊⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠢⣤⡇⠀⠀⠀⠀⠀⠹⠤⠤⠶⠒⠒⠒⠀⠵⠚⠧⠤⠄⠗⠒⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠲⠤⠥⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠈⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣞⣦⣷⡼⠳⠛⠶⢦⣝⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⠶⠖⠣⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⢲⡒⠲⣤⠤⣄
⠀⠀⠀⠀⠀⠀⢀⣞⠡⠁⠈⡖⠀⠀⠀⢸⣏⣀⣀⡀⠀⠀⠀⠀⠀⣹⠋⡀⠀⠀⠀⠑⢢⡉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢇⠀⠘⣆⠀⣇⠀⡇⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣷⠂⠀⠸⣄⣁⡄⠚⠁⠘⣷⠊⠁⠀⠀⠀⠀⣸⠷⣾⡶⠲⢦⡄⠀⡀⢹⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⡎⣀⠀⠱⡄⢹⡄⢸⠀⡇⠀⢠⡇⢹⡀
⠀⠀⠀⣠⠤⠒⠃⠹⣦⡀⠀⠘⡹⢷⡂⠀⢀⣿⠘⠁⠀⢦⣲⠿⢇⠀⠀⢳⠀⠀⠹⣏⠉⠙⢷⣀⢙⣷⣦⠶⣝⠀⠀⣾⠀⠈⢳⡀⢹⡌⡇⢸⢀⡇⠀⡼⠀⡜⢳
⠀⠀⠀⣇⠁⠂⠀⢀⠜⠉⠉⢫⠄⠀⠘⢤⣼⣋⠳⡀⠀⠀⣿⠀⠪⣧⠀⢈⣧⠀⠠⠸⢧⠈⠀⠹⣇⠀⠈⢻⡇⠀⠀⡜⠙⢦⡀⢳⡀⣧⣧⡸⣸⠁⡼⠁⡴⠁⡞
⠀⠀⠀⠉⠉⠙⢶⣏⠀⠀⠀⣎⠁⢀⣠⡞⣁⡈⠉⠉⠀⠀⠹⡀⠈⠺⡇⠀⢌⣆⠀⠀⠈⣧⡀⠀⢸⠗⠀⠈⠀⠀⠀⠙⠤⠄⢹⡄⢧⣿⣿⣇⣏⠞⡠⠊⣠⠞
⠀⠀⠀⠀⠀⠀⣴⠝⡛⢳⠶⡿⢿⢹⡓⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⣿⡀⠠⣹⣷⣄⣠⠞⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣈⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠜⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣶⡀⠀⣴⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣿⠳⠶⠋⠙⠚⠉⠳⠞⠻⣄⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡏⠉⠁⣀⣤⣤⣶⣶⣶⣦⣤⣀⠈⠁⢷⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣯⡭⠤⠴⢾⣏⡉⠁⠀⠀⠉⠉⠛⢿⣷⣦⡀⠀⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⢤⣀⢀⡼⢛⣭⣶⡶⣶⣶⣶⣤⣝⠳⣄⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⣶⠾⠿⠿⢿⣶⡮⢉⠞⠋⠁⠀⠀⠀⠀⠈⠙⠻⣷⣌⢷⣀⣀⠀⠀⠀⠀⢻⣿⡀⠈⣻⠖⠂
⠀⠀⠀⠀⠀⠀⠀⡼⡡⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⣶⠶⢶⣶⣤⣄⡘⢿⣶⣦⣭⣙⠳⢤⡀⠘⣿⡇⠀⠳⣄⡀
⠀⠀⠀⠀⠀⣀⣸⠁⢀⣠⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠉⠙⠿⣷⣤⣽⣛⣛⠷⣤⣞⠉
⠀⠀⣠⡴⣫⡽⣷⡾⠛⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⠉⠙⠛⠿⣿⣦⣝⢷⡄
⠀⡴⠣⠊⠁⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠹
⣼⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⡴⠞⠁
⠀⠀⠀⠈⠙⠓⠶⠦⠤⠶⠖⠋⠁⠀⠉⠉⠉⠀⠙⠲⢤⣤⣀⣠⣤⠴⠞⠋⠈⠙⠓⠲⠶⠶⠚⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣿⣿⡋⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣾⣢⣹⣧⠤⢬⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢸⠻⣥⠛⠓⠈⢯⣿⣤⣤⣄⡈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣝⠧⣾⣤⠀⠀⠀⡀⣀⠘⣿⠀⠉⠉⠓⠺⠻⢻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣷⣾⡿⠩⠈⢻⣇⣤⠤⣀⣀⣀⠀⠀⠀⢁⣟⣷⠟
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣿⣛⣷⣶⣤⠤⡉⡛⠛⣷⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠋⠩⣿⣿⣿⣿⠿⠿⣿⣿⣿⡏⠉⠉⠉⢩⡓⣾⡙⢿⣤⢘⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠫⠟⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠤⢼⠼⠷⠿⠷⠾⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⢀⠤⣖⡒⠒⠒⠒⠢⢶⠁⠀⠈⠁⠀⠁⠀⠀⠀⣀⠴⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠒⢶⣄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠁⠀⠀⠉⠓⢄⠀⠀⠀⠑⠀⠀⠀⠀⢄⡀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⣄⡀⠀⠰⠛
⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢀⠄⠚⠋⠀⠀⠀⠀⢀⣠⠄⠂
⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⢀⣀⣸⠗⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⠉⠐⠀⠀⠀⠉⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠉⠐⠒⠊⠉
⠀⠀⠀⠀⠀⢄⣀⣀⡀⣀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢀⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢠⠀⠈⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢀⡘⠁⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠢⢄⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢀⠀⠀⢀⣀⣵⡖⠊⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠙⠒⠒⠒⠒⠉⠉⠀⢀⠀⠀⠉⠉⠙⠻⠟⠂⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠂⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⢶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢞⠀⣀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣘⠃
⠀⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠚⠉⠀⠀⠁⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣔⡞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢂⠀⠀⠀⢠⠃⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠠⠤⢤⠴⠞⠋⠀⠀⠀⢸⡀⠀⢀⣰⠀⢀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠡⢴⡀⡀⠁⡠⢀⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠁⢤⠀⢄⠀⡖⡠⢄⡠⠄⢀⢀⠄⡀⡄⠀⢄⢸⢢⢀⠀⡇⡹⢠⠀⠀⠠⡠⠀⢠⢠⢠⣸⠤⣀⠀⠀⠠⡀⡠⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠁⠀⠁⠀⠀⠉⠀⠁⠁⠀⠈⠈⠈⠈⠀⠁⠁⠀⠁⡈⠃⠁⠈⠈⡙⠀⠉⠈⠉⠁⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠷⡀⢀⠾⡀⠀⣠
⠀⠀⠀⠀⠀⠀⡶⢄⠀⡇⠑⡼⠀⠱⠎⠀⢧⠎⢸⠀⡠⢶
⠀⠀⠀⠰⡤⢄⣸⠀⠉⠃⣀⠤⠤⠒⠒⠤⠤⣀⡈⠉⠀⣇⡠⢤⠆
⠀⢀⣀⣀⣱⡀⠈⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠁⢀⣎⣀⣀⡀
⠀⠀⠑⢄⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⢀⡠⢎⣀
⠐⢶⡊⠉⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⠁⠀⠀⠈⢣
⢀⡠⠬⠂⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⡄
⠉⠑⢢⡄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⢢⠀⠀⢀⣀⠤⠤⢄⡀
⠠⠖⣁⣀⡀⢣⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠈⠑⣄
⠀⠀⣠⠎⠀⠈⢣⡀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠉⠉⣩⠃⠀⠑⣦⠤⠴⠃
⠀⠀⠀⠰⠗⠚⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⣀⣀⣀⣀⣀⣀⣀⣑⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡔⣃⢀
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⡟⣶⣿⡿⢻⣶⣾⡟⢷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⠀⠉⣿⡇⠈⢸⡿⠁⠈⣽⡿⠉⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⠛⢻⣿⡀⠛⣿⡄⠀⣿⢦⠀⣿⣇⠀⢸⡟⠀⢀⣿⠋⠀⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠻⣿⣧⠀⣿⡯⡀⣿⡇⡀⣿⢀⢀⣿⠀⢀⡿⠃⢀⣾⠃⠀⣰⡛⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⡧⠘⣿⣀⢸⣷⢶⣿⡁⡧⣿⢸⢸⡟⢣⣸⣧⡀⠾⠉⢀⣼⠟⠀⠀⠩⡶⢤
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣷⡾⣿⣽⣿⡏⠙⣿⠀⢸⡇⣇⣿⢸⣸⠃⢀⣿⠨⣡⡀⢀⣿⠉⠀⢀⡄⠋⠀⢸
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣼⢿⣿⣿⣿⠙⣿⡆⣿⡂⢹⡇⢸⡿⠈⣿⠀⣾⠇⣶⡏⣐⡾⢻⠀⡴⠃⠀⢀⡀⠺⢧
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣽⣿⣿⣿⣯⠹⣧⢿⣇⢸⡇⠸⡇⢸⡇⠠⡇⢀⡿⢀⡟⢠⡿⠁⢠⠟⠃⢀⠴⠂⠀⠀⣌
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⡎⢿⠀⣧⠀⣧⢸⡇⢰⡇⢸⠇⣸⠁⡾⠀⡵⠋⢀⠴⠏⠀⠀⠀⠴⠾
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡌⣷⣸⣇⢿⠀⣿⢸⡇⢸⠃⣾⢠⡏⡼⢁⠀⠀⡤⠁⠀⠤⠀⠃⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⢿⣸⡇⢹⠀⡇⣸⢀⡏⡼⢰⢃⠏⠀⠀⠐⠀⠈⢧⠠⠐⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠯⣿⣿⣿⣿⡸⡇⣷⢸⠀⡇⣿⢸⢣⢃⠏⠌⠀⢀⠀⠀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣌⣻⣿⣿⣷⣿⣽⢸⣿⣧⡏⣾⣼⡸⡈⠀⡀⠀⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣇⡿⣿⣇⣷⣿⢻⣷⢏⡴⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⢿⣿⣿⣿⣿⣷⣛⡿⣏⠛⣀⡤⢿⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠛⠛⠙⠿⢹⣯⠰⠏⠑⠛⠲⠾⠿⠿⠁