Colon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠤⠀⡀
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠠⢄⡘⠒⠢⡤⠤⢀⡀⠀⡀⣀⣀⠀⢀⣀⡀⢀⡀⠔⠋⢈⣠⠄⠀⠰⠈⡄
⠀⠀⠀⠀⢀⠆⠐⠢⠴⡄⠀⡈⠁⠋⠐⠠⠤⠈⣀⠀⣙⣁⣀⣈⡁⡀⠀⠡⠅⠒⠌⠂⢁⡐⠕⠉⠰⠁
⠀⠀⠀⠀⠈⡆⠀⢠⠀⡏⢈⢟⠀⠔⠦⣀⣀⢦⡀⡀⣄⠀⠀⣄⠀⠀⠀⣈⠠⠤⢲⠒⠁⡃⢰⠀⢢⠃
⠀⠀⠀⠀⠀⢄⠀⣾⠀⢾⡀⠑⠩⠘⢄⠀⠈⡄⠫⡦⡀⠉⠋⠄⣁⡐⠊⡠⠀⠢⠓⢀⢼⠀⡾⠀⡠⠆
⠀⠀⠀⠀⠀⠪⠀⡟⠀⣱⠌⡢⢀⠠⢤⢔⠕⣁⠠⠌⢀⣊⣤⢄⡀⠀⢙⢄⠀⡐⠨⠂⠘⠀⠇⠀⡙⡄
⠀⠀⠀⠀⠀⣱⠀⠃⠀⠽⠁⠒⠥⢐⠀⢀⠮⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠋⠐⠄⠀⠨⠃⢠⠈⠳
⠀⠀⠀⠀⠰⡈⠀⢰⠀⢘⠇⠠⢬⡐⠀⡘⠀⠀⠔⢀⠒⠉⠡⢀⠀⠀⡀⡠⠀⠀⡈⠢⣰⠕⢸⠀⢴
⠀⠀⠀⠀⠀⠎⠀⠀⡇⠀⡃⠀⢠⢏⣂⠃⠀⢸⡀⠘⣜⢄⠣⠑⠩⠍⡒⢷⠀⢸⠪⠂⢠⡁⢸⠀⢄⠇
⠀⠀⠀⠀⠀⠡⡴⠂⠡⠀⠈⣡⠘⡘⢀⡇⠀⠠⢏⠢⢄⡙⠫⠖⠠⢊⠐⠉⢀⢌⠆⠈⢣⡀⢸⠀⡸⡄
⠀⠀⠀⠀⠀⠀⢄⣀⠀⠑⡄⠉⡏⢀⡀⢰⢄⠀⢙⠀⠉⠘⠑⠂⠀⢠⡓⠀⠹⡀⠀⠁⣮⠀⠈⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠃⠤⠠⠄⢄⢐⠂⠈⠀⠀⠁⠁⠁⠖⢀⠉⣑⠒⠮⠀⢤⡄⠾⠁⠉⠀⡠⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠸⠦⠸⠂⠠⣙⠲⠦⠬⠀⠠⠄⡒⠉⢤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠀⠢⠉⠁⠑⠂⠐⠓⠐⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢷⣄⡙⠋⠉⠻⣷⣤⣤⣀⣀⣀⡀⢀⣀⣀⣠⣤⣤⣶⠟⠋⢀⣠⣴⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣤⠉⠛⠷⣦⣄⣀⠀⠉⠛⠛⠉⠛⠛⠋⠙⠋⢁⣀⣤⣶⠾⠛⠉⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⢸⡿⢶⣶⣦⣀⣉⠙⠛⠿⠶⠶⣶⣶⠶⠶⠾⠛⠛⠉⢁⣤⣤⣴⡿⣷⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣼⡇⢰⣿⠉⠛⠛⢷⣶⣶⣦⣠⣤⣤⣠⣤⣄⣤⣶⣦⡾⠏⠉⣿⡆⣿⡆⠰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠁⢀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⣿⡄⢸⡇⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠘⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣸⡟⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠘⣷⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣴⠟⠃⣰⡟⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⢹⣧⠀⠀⣿⡆⠀⠀⣠⡾⠛⠿⣿⡏⠙⠛⠋⠉⠛⢉⣉⣴⠾⢋⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⠀⠀⠹⣷⣾⠋⠀⠀⠀⣿⡇⠀⠀⠘⠿⠶⠶⠶⠶⠿⠛⠋⠁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⠾⠋⣿⡄⠀⠀⣼⡟⠀⠀⢶⣄⠀⣀⣀⣠⣤⣤⣴⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧⠀⠀⣿⡀⠀⠀⠈⠙⣿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⡶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣀⣀⣀⠉⠛⠉⠉⠙⠛⠿⣦⣤⣤⣤⣶⣦⣤⣄⡀⣀⣤⣤⣶⣶⣦⣴⡾⠛⠉⠉⠉⠉⠉⠀⣀⣀⡀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠉⠛⠿⣶⣤⣀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠙⠻⠛⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣤⡀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⣴⡆⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠙⠻⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢰⣷⠀⠀⠈⠙⣿⣦⣄⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣾⢿⣿⠟⠋⠁⣄⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣹⡏⠙⠛⠛⠛⠛⠛⠿⣶⣦⣤⣴⣶⡾⠟⠻⠷⢶⡶⠾⠟⠛⠁⣼⡏⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣾⡇⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⢸⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠗⠀⠀⢠⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⣼⡟⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⣰⡿⠁⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠘⠛⠀⢀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠛⠀⢀⣴⡿⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⡄⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠋⠀⠀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣌⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢀⣠⣤⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣰⡿⠋⠉⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⠁⠀⢰⣶⣤⣤⣴⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠸⠿

⠀⠀⠀⠀⢀⡠⠤⢤⡤⠒⠒⠒⠒⠦⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠐⠖⠊⠉⠉⠉⡄⠤⠤⢄
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⣀
⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⣀⡠⠤⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆
⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠒⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠒⠊⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣄
⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⢄⣀⡀⠤⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⡰⠃
⠀⡝⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠐⠘⠒⠶⠶⠆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⠢⣄⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠸⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⠀⠙⡅
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠱⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠂⠀⠀⠀⢡
⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢩⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡤⠂⠁⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⢄⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠑⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡔⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⣀⡤⣶⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⢀⡠⠞⠁⠀⠀⠙⠂⠈⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣽⣤⣵⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠋⢉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣬⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡌⠀⠀⠀⠈⠐⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢠⣤⡤⣀⡀
⠀⠀⠀⠀⢀⣾⣿⡟⠿⠄⢻⣿⢻⣿⣦⡄⠠⡌⢁⣀⣤⣀⣀⣀⣀⢀⡀⣤⣴⣶⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣆⣦⡄
⠀⠀⠀⠠⣾⣿⣿⠁⠀⠀⠀⠀⠈⠀⠉⠁⠀⠄⠛⠀⠛⢩⠟⢻⡿⣿⡷⣿⣿⠿⣯⡘⠮⣹⣿⣿⡚⠟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⡟⠁⣀⠀⣾⣿⣿⣿⣿⣶⣶⣦⣀⣈⠀⢀⣘⠀⠀⠘⣇⢉⣈⣀⣀⣴⣾⣿⣿⣿⣿⡆⢼⣻⣿⣿⣷⠷
⠀⠀⠀⢸⢸⡟⠁⣶⠄⢰⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⢳⣿⠐⣹⢿⡿⠓⡇
⠀⠀⠀⠸⠉⠀⢰⡳⠄⠈⣿⣧⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⡷⢰⡏⠀⡹⠿⠛⠁
⠀⠀⠀⠠⠃⠀⢘⡓⠢⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⣠⠀⠀⠀⠐⣦⢀⣴⡦⠀⢳⠀⠠⠀⣼⡇⢸⣟⡲⣷
⠀⠀⠀⢠⠀⡄⠈⣗⠀⡀⢸⡷⢰⣀⣈⣻⣦⡀⠐⠛⠀⠀⠀⠀⠀⢀⣤⡟⡿⠁⠀⠠⠟⠀⠘⠀⣿⠃⣼⠋⣙⠇
⠀⠀⠀⠈⠀⢹⡆⠻⡞⠁⠈⢷⣮⠉⡋⠈⠁⠛⠁⠀⠈⡷⢲⡴⠿⠿⡏⠀⠈⠀⠀⣸⠀⠀⠆⠀⣿⠁⣿⠃⢀⡀
⠀⠀⠀⢰⡀⠸⣯⠀⠀⠀⠀⠊⣿⣧⡐⢶⠞⠑⠲⠶⠒⠁⡄⠀⠠⠄⡀⡀⣸⠒⣻⡁⠀⠀⡀⠀⢹⣴⣹⡏⠈⠙⣆
⠀⠀⠀⠀⢹⠀⢻⡄⠀⠀⠀⠀⢸⣿⠉⠐⠂⠀⠐⠰⡄⠈⠱⣄⡀⢘⡍⠉⣥⣀⣄⣀⡀⠀⡀⠆⠀⢿⣛⣏⠵⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠷⠀⠃⠀⠀⠀⠀⢸⣿⠈⠀⠄⠀⣤⣀⠈⠀⠀⠟⠐⠋⢀⡀⠈⠉⠁⢀⣠⣴⠇⠘⠆⠘⢇⣻⣏⣓⣁⢹⣇
⠀⠀⠀⠀⠀⢴⡀⠀⢀⣀⠀⠀⢸⣿⡄⠀⠀⠀⠁⠉⠙⠒⠏⠀⢀⣤⣼⢷⣤⣀⣤⣾⡛⠶⠂⢨⠁⢄⡘⣿⣿⡛⢉⠘⣿⡀
⠀⠀⠀⠀⠀⢸⠉⠀⡿⠋⠀⠀⣿⣇⡁⠀⠀⠀⣀⣤⡀⠈⠁⡦⠘⢻⠛⠀⢹⡏⠀⠞⠃⠀⢸⠟⠄⠠⠀⢹⣿⠆⠶⢠⣿⡇
⠀⠀⠀⠀⠀⡰⠂⢨⡟⠛⠀⠀⣿⠋⢳⡀⠀⢉⡈⠙⣿⠖⢻⠂⠀⣼⡄⣠⡌⢱⣤⣠⣤⣴⠟⠀⡄⠀⡇⠰⣿⡇⡙⢸⣿⡏
⠀⠀⠀⠀⠠⣄⠀⠠⠗⠀⠀⣸⣿⠀⠀⠙⢻⡟⠀⠀⣿⠟⠛⠧⣄⡀⠸⡏⠀⣸⠃⣀⣀⣈⣤⠾⠁⡔⢀⣼⡞⠃⢲⣿⣿
⠀⠀⠀⠀⡇⠀⠀⢸⣷⠄⠀⣿⣿⡀⠂⠀⠀⠿⠃⠉⠙⣤⣴⡆⠈⣧⡄⢠⣴⣿⠿⢋⣩⣿⣧⣤⣚⣤⠞⠯⡀⢀⣿⡟⠁
⠀⠀⠀⠀⡗⠀⠀⢾⡥⠀⠀⢿⣿⡝⠳⢄⡀⢀⣠⠄⢀⡐⠘⢧⢄⣀⠀⢨⣿⢀⣴⣿⡟⠋⠉⠉⠉⠘⠋⠂⠀⢸⣿⡇
⠀⠀⠀⢰⡅⠀⠀⠘⣧⡄⠰⠸⢿⡷⣦⣀⠉⠉⠩⡀⢈⠁⠰⠀⠀⠸⠿⢋⠁⢾⣿⣷⣟⠘⠀⠀⠀⢤⠀⣀⣰⣿⡿⠃
⠀⠀⠀⠈⢻⠀⠀⣆⠙⢷⣄⣿⣶⣶⣜⠛⠷⣤⡀⠉⠫⣤⣴⣾⣦⡄⠀⠀⢡⠘⢿⣯⠋⠁⠛⣷⣶⣶⣾⣿⣿⣿⡗
⠀⠀⠀⠀⠸⣄⠀⢹⣇⠈⠛⠿⣿⣿⣿⣿⣷⡿⢷⣄⠀⠀⠁⠀⣀⠀⣀⣠⡾⠀⠈⢿⣦⣤⡄⠈⢍⠛⠛⠛⠋⠁
⠀⠀⠀⠀⡀⢙⣇⣈⣀⣿⣤⣀⢶⣿⣽⣿⣿⣷⣾⣿⢆⡄⠀⢸⠉⠛⠛⢋⣡⣤⣤⣄⡈⣿⣿⣀⠘⣇
⠀⠀⠀⠀⠀⠀⠻⣯⣦⠙⡛⠻⣿⣿⣿⣿⣿⣿⣿⠋⠀⡇⠀⣸⠀⢠⣾⣿⣿⠿⣿⣿⣿⣿⣿⠤⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣾⣿⣿⣿⣿⣯⣾⣿⠀⢠⠇⢀⣯⢠⣿⡿⣟⠛⠂⠀⠈⠉⣓⡁⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⡿⠿⠿⠛⢻⡇⠀⠈⠀⣸⣅⣿⣿⠃⠈⠀⠀⠀⠀⠁⠿⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠾⠋⢹⣿⡏⢰⠇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⢉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠶⠒⠙⠓⠒⢢⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠋⠛⠳⢦⡀
⠀⠀⠀⢀⣼⣁⣴⣿⣾⠋⡴⠛⠭⠿⠽⠛⠷⣄⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣴⣶⣒⠒⣾⠇⠈⠀⠀⠉⢡⣤⠿⢄
⠀⠀⢰⡟⠀⢉⠍⠻⠝⡛⣥⣀⠀⠀⠀⠀⠠⡟⠉⠉⠉⠉⠻⣤⡶⡾⠞⠳⢶⣤⡴⠶⠶⣶⣦⡴⠺⠛⠛⠉⣿⣥⠞⠁⠀⠀⠣⢤⣠⡴⠊⠉⠉⠁⢠⡦
⠀⠀⢸⡍⣶⠋⠀⣠⠾⠋⠀⠛⣇⣤⣤⡄⠴⣁⡀⠀⠀⠀⠴⠟⠇⠀⠀⠀⠘⠋⠀⠀⠀⠙⢿⡀⠀⠀⠀⣀⡿⠃⠀⠀⣀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣾⣿
⠀⢠⣾⡿⣿⠀⢰⡏⠀⠀⠀⣴⡇⠀⠀⠉⠓⠦⠭⠷⣒⡒⠓⣛⣤⣤⣀⣀⣠⠤⠤⣀⣠⡤⠚⡙⠛⣻⠿⠟⠒⠛⠓⢛⠁⣀⠀⡈⢦⡀⠂⢀⣠⡾⢿⣿
⠀⡾⣻⠤⠙⢧⣼⣇⣄⣄⣼⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢛⠉⠉⠙⠉⠑⠂⣴⠚⠋⠉⠉⠉⠭⣿⡁⠀⠀⠀⠀⠀⠈⢶⣦⣬⣧⣼⣿⡏⣿⣿⡄⠹⣛
⠀⢧⠋⠀⠀⢸⣿⡿⢿⣿⣭⣷⣱⡀⠀⠀⣿⡀⠀⠀⠀⠀⣸⢄⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⠘⢷⡀⠐⢀⡀⢀⣠⡿⠃⢸⠙⠿⢻⣿⣟⠉⢀⣀⣰
⠀⢈⣧⡄⠀⣸⣿⠀⠛⠉⡉⠽⡟⠻⠿⠛⠋⠻⣿⣷⣶⣤⠾⣧⡑⠤⢤⣔⣀⣿⣄⣀⠄⠠⡴⣀⡤⠏⠉⠛⠛⠛⠋⠉⠀⢀⣼⠷⠶⡆⢸⡿⠿⢷⣿⣵
⠀⣼⡟⠁⠀⢣⡈⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠈⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠅⠀⠀⣷⠚⠀⠀⠀⠀⢹
⠀⢿⡇⠀⠀⠘⣷⠀⠒⠀⡴⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡠⠤⢾⣿⡆⣀⡀⠀⠰⣹
⠀⠘⢿⣤⡤⣠⢿⠀⢰⣿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠦⡎⢸⠉⠻⠯⢴⣾⡟
⠀⣰⠟⠛⠳⠇⢸⡆⠂⠀⠰⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡝⠀⠀⡇⡈⠀⠀⠀⠠⣿⣧
⠀⣿⠇⠀⠀⣆⢈⠁⠀⠀⢠⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠠⣇⣦⡄⠀⠀⣰⣿⡿
⠀⢻⡇⠀⠀⠁⢈⠀⠀⠀⢂⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⡀⢰⢘⡟⠀⠤⠠⡤⠽⠁
⠀⣼⠟⠶⣎⠀⣿⠀⢡⣴⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⣽⡄⠸⢈⠁⠀⠀⠀⠀⢰⣧
⣸⡁⠀⠀⢰⠀⢻⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⣼⠀⠀⠀⠈⢠⣾⡿
⣿⡀⠀⠀⢸⠇⡿⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡞⢰⠙⣄⢤⣠⣤⣼⣿⣄
⠹⣏⠢⣄⣼⠀⣿⡀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣿⠁⢸⢀⠏⠀⠀⠀⠞⠻⣿
⢀⣼⣟⠛⢣⣄⢻⡿⠛⠛⢛⡋⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠨⠇⠀⢸⢹⠀⠀⠀⠀⠾⢂⡿
⢸⡿⠉⠀⠘⢹⣦⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⢿⣥⣀⠙⠙⢦⣄⣤⣀⣀⠀⠀⠀⠀⠀⢠⣾⣷⡤⠀⡌⣸⠂⠸⣿⣶⣴⡿⠃
⢸⠇⠀⠀⠀⠀⣿⣤⠀⠀⠀⠀⢐⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠴⠀⠀⠀⠙⠯⣑⠻⢄⠉⠉⠉⣷⢶⡿⠓⢶⡿⠹⠋⠉⢰⡰⠃⠀⠀⠈⠉⠽⣷
⠘⣦⡣⣄⣀⢀⣾⡟⠃⣀⣄⣴⠿⢿⠿⣧⠀⠀⠀⠀⠀⠀⢰⡗⠈⣀⣦⣤⣠⡀⡂⠈⠉⠛⢶⡔⠶⣟⠈⠀⠀⠸⡇⠃⢀⡴⢣⠁⠀⠀⠀⠀⠀⣻⣿
⠀⠈⠳⣶⣾⢾⡟⠙⠳⡷⣭⠀⠀⠈⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣶⣿⣝⣿⡿⠏⠀⠀⠀⢈⡷⢤⣿⣷⣔⠛⣛⡲⠿⠞⠋⠀⢀⣁⠀⡀⣺⣼⠇
⠀⠀⠀⣾⣡⠈⠀⠀⠀⠀⠬⡛⠎⣀⣰⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠛⠉⠉⠹⣿⣦⣶⠀⡄⣼⠃⡏⢰⡁⠁⠈⠁⠀⠀⠀⠀⠈⢦⣦⣵⣿⠿⠋
⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠐⢨⣶⣦⣕⠢⣄⠀⠀⠀⠀⠀⠈⠘⡇⠈⠀⠀⢸⡆⣿⣿⡿⠿⠷⠿⣄⠛⠀⡤⠀⠀⣷⡀⣦⢤⠄⣴⣿⡿⠁
⠀⠀⠀⢻⣏⢱⠦⣄⡀⠀⣸⣾⡿⢄⣹⠓⣬⡄⠀⠀⠀⠀⢠⡇⠃⠀⠀⡀⠈⡿⢿⣿⣧⠀⠀⠀⠈⠛⠲⠶⠾⠛⠋⠙⠛⠛⠶⠛⠋
⠀⠀⠀⠀⠙⠻⠶⣬⣧⣤⣾⣉⣀⣈⡽⠁⠙⠟⠀⠀⠀⠀⡾⠀⠀⠀⠀⣧⠀⢰⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⠀⠘⡀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠆⠀⣠⠀⣿⢰⠀⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢼⠀⠉⠀⣿⠘⢠⡇⠘⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⡆⣦⠀⢸⠀⣾⠁⡀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣽⡇⠻⠀⣟⣧⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⠆⢀⡽⢁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣤⣟⣵⠟⠁
⣷⣾⣶⡿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣶⣶⣾⣿⣿⣷⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣿⣿⣾⣷⣿⣷
⣿⣿⣿⣀⣀⣀⣤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠛⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⡀⠲⡿⠒⠀⣀⠀⣷⠀⠒⣿⠒⠲⠂⠀⠀⣀⠀⠀⣀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠇⣿⠎⣿⠀⡇⠀⣾⣩⠇⡿⣦⠀⣿⠀⣿⠀⣿⡎⣽⠀⣾⣩⠗⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠀⠿⠀⠿⠜⠷⠔⠻⠄⠴⣥⡿⠖⠻⠔⠻⠤⠻⠀⠻⠴⠻⠤⠔⣥⡼⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠉⠀⠀⠀⠀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⢀⣀⠀⣀⠤⠄⠈⠀⠀⠐⠀⠀⠀⣠⠟⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠙⠓⢤⣀⡀⠀⠀⠀⠀⠐⠀⠠⠄⠀⠄⠠⠤⠀⠀⠀⠁⠀⠀⡀⣠⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⢀⠀⢀⠘⠦⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣠⣞⡉⠉⠉⢣⡀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢡⠈⣦⠈⠻⡄⠀⢈⡇⢹⡛⠛⣶⠶⠖⣷⣶⡞⠉⠻⡄⠀⡀⠁⠀⠀⣰⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⢡⠀⠸⠀⠀⣿⠀⠈⠁⣸⣅⣀⡉⠓⠆⠀⠈⢃⠀⠀⡇⣀⡉⢉⡉⠙⢇⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠢⠐⡀⠀⠒⠻⣤⠤⠺⡋⠀⠈⠉⠲⣅⣀⡴⠃⠤⠞⠉⣈⣁⡉⠀⢀⡜⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⠃⠈⣆⠀⠀⣀⡀⠀⣀⠤⠖⠒⠦⡈⠻⢄⣀⡠⠔⠋⠁⠀⠁⠙⢯⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠋⠉⡀⠉⠉⠀⢀⠀⠀⠀⣹⠀⠀⠠⣀⠐⠒⠛⠁⠀⠀⣤⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⠀⠀⠱⢲⠖⠒⠚⡱⠊⠉⠀⠉⠁⠢⠧⠀⠀⠀⣦⠖⠚⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⡷⢄⣀⡀⣀⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⢦⣀⡀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢀⡴⢞⠙⠦⠤⠔⠻⡄⠀⠀⠈⢲⠖⠚⠳⢄⣠⠴⣄⡀⢀⣶⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠉⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡅⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⡤⡄⠆⢀⢤⡀⡠⣄⠀⢀⠤⠀⢤⠀⡤⡄⢠⠄⢀⢄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠘⠤⠜⠀⠸⠤⠃⠇⠸⠀⠸⠤⠰⠽⠀⠇⠘⠣⠄⠫⠬⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠴⠚⠉⠙⠒⠦⣤⠖⠛⠉⠛⣶⡶⠟⠛⠛⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢀⣤⣦⣤⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⠴⠶⠒⠒⠀⠀⠒⠀⠤⠤⠤⢼⣿⠤⠴⣿⣿⣿⣿⣷⠀⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣿⣄⠀⠙⠿⠿⢿⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⢀⡴⠋⠙⠒⠒⢋⣉⡉⠓⠲⢾⡻⣿⣷⣀⣀⣸⣧⡾⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⣄⠹⡆⠀⡏⠙⣆⠉⢿⣍⡉⢹⡄⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠀⠀⠀⣸⠀⣴⠒⠒⠶⠤⢞⣠⣹⣞⣁⣠⠟⠀⠀⡿⠁⠀⢳⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠀⠀⢰⡃⠀⠈⠉⠓⢦⡀⠘⢦⣠⡤⠴⠶⠶⣄⠀⡇⠀⠀⢸⠂⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⣷⢰⠒⠒⠒⠉⢀⡴⠒⠒⠒⠶⠶⢚⣁⣤⠷⠀⠀⡼⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⢀⡏⢈⣉⣉⣹⠆⢸⣀⡤⠤⠤⠴⠞⠉⠀⠀⢀⣠⠞⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢸⠀⠀⢺⣄⠀⠀⠁⠀⠀⢸⠏⠀⢀⣀⡠⠤⠤⠶⠞⠋⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠀⢸⠏⠙⠒⠶⠦⢴⡏⠀⣰⠋⠀⠀⠀⠀⠀⠀⣸⠒⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⡤⠋⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⢰⡶⠦⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢡⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡟⢁⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠿⢿⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⠟⢋⣴⣿⠿⣟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣬⡙⠷⣾⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣤⣿⠿⢋⣡⣾⣿⣿⡿⣻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢟⠙⣿⣿⡿⣿⣷⣬⣙⡛⠿⠿⢿⣿⣿⣿⣶⣿⣷⡾⠿⠿⠟⣛⣩⣴⣾⣿⣿⠉⣯⣽⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢠⣾⣽⣶⡝⢿⣿⡿⢻⣿⣶⣶⢶⣶⣤⣤⣴⣶⣶⣶⣾⣿⡿⠿⠟⠻⡿⠃⠸⣿⣿⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣍⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠋⠁⠙⠛⠋⠀⠉⠉⠁⠀⠀⠀⠀⠀⣴⣿⣿⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡏⢸⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢸⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡆⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡙⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠛⠢⠃⠀⠀⠀⠀⠀⠀⢠⢊⣥⣬⣍⡛⠻⢷⣦⣠⣄⡀⠀⠀⠀⠀⠠⣾⣿⡿⢸⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣌⣙⠻⠷⣤⣶⣄⣾⣿⡿⠟⣠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣭⣤⣶⣾⡯⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠉⠈⠻⠿⠟⠹⢿⣿⠟⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠹⣿⣦
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣿⠇⠀⠀⢻⣿⣇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⠀⢿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠛⠁⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠈⠙⠻⢿⣷⣄⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⠀⠀⠿⠿⣿⣷⣦⣄⠀⠙⣿⣷⡀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠘⣿⣷⠀⠘⣿⣷
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢹⣿⡆⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⠛⠃⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣤⡄⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⠂
⠀⠀⠀⠀⠸⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠸⠿⠇⠀⠸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡝⠿⣿⣿⣿⣿⣿⣿⠟⣫⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢟⣱⣿⣶⣭⣭⣍⡱⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⣫⣭⣭⣿⠿⠿⣿⣭⣭⣝⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⡶⣼⢧⡝⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⡿⣸⢧⡟⣼⢣⡝⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢇⣿⣼⣣⡟⣼⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡼⣿⣿⣿⣿⣿⣿⢸⢟⣵⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⣹⣿⣿⣿⡿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠇⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡻⢁⡴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣷⠋⣼⣡⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣾⠁⡼⢫⠟
⠀⠀⠀⢀⠀⠀⠀⠀⣸⠃⠀⠁⢈⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⠋⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢋⡤⠖⠒⠦⣄⠀⠀⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠘⠤⢄⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠙⣶⠻⠅⠀⠈⢦
⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠐⠳⠤⣀⠀⠀⠀⠙⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣄⣀⣀⡠⠋
⠀⠀⠀⠀⠀⢸⡇⠀⣠⢾⠁⣴⠀⠀⣠⣤⣟⣦⡀⠀⠀⠉⠳⢾⡇⠀⠀⠀⠀⠀⢰⡏⠉
⠀⠀⠀⠀⠀⠈⢷⣼⠃⣾⠀⡟⣆⡼⠁⠀⠉⠻⣿⣦⠀⠀⠀⠀⠻⣄⠀⠀⠶⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠈⠀⠀⡴⠒⠛⠛⠿⢧⠀⠀⠀⠀⠈⠙⢛⡿⠋⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠴⠖⢲⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⣄⠀⠉⠙⠓⠶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠉⠓⠦⣌⣀⡉⠂⠀⢂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⣦⣄⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠄⠐⣯⠙⣧⠈⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡰⠀⠀⠀⠀⠀⠀⠈⣇⠈⠙⠾⣦⡀⠹⣮⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⠀⠀⣹⣦⣙⠀⠀⠀⠈⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠛⠦⣄⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢺⣁⣀⡽⠟⠢⠤⣄⣀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣲⠶⢤⣀⣈⡏⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠳⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⠀⠀⠈⠉⠉⠒⠒⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⣷⢤⡿⠆⠀⢀⣀⣘⣦⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣄⡀⠈⠀⠂⠀⠀⠀⠀⠈⠉⢛⠶⣄⢠⠇⠀⠙⠚⠛⠉⠉⣿⣿⠱⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠁⠀⢉⡙⠢⣤⣀⠀⠀⠀⠀⣰⠏⠀⠘⠻⢦⡀⠀⠈⢦⡀⠀⣿⣿⣿⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡉⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠛⠲⢦⣴⠏⠀⠀⠠⢴⣾⣷⠀⠀⠀⠙⢶⣿⡛⠛⠒⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣦⣿⡄⠀⢠⠞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠷⠛⡄⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣳⠞⠉⢳⡄⠀⣠⣿⣿⢿⣠⠏⠰⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣸⠁⢀⡖⠈⡇⣰⢻⡟⠉⠻⠏⠀⣠⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠖⠒⡙⠶⠞⠀⠀⣿⠃⡾⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⢶⠚⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠻⣄⣐⣦⠀⠀⠐⢇⡀⠀⠀⠀⠉⢻⠖⠲⠲⠶⠶⠶⠒⠒⠒⠛⠛⠉⠉⠁⠀⢸⠁⡼⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠈⠉⢈⡷⠒⠲⡬⠻⡄⠀⠀⢀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣀⡴⠇⠀⠀⠀⢙⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣼⣀⣤⡤⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠄⠀⠀⠀⠀⠀⠀⠐⠚⠛⣛⠾⢻⠿⠍⡁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣑⣀⢤⡐⠄⠀⠀⠀⠐⠂⠉⠀⠀⢀⡏⠀⠀⠀⠀⠀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⣻⣿⠿⠛⠛⠲⠤⠴⠦⠤⠶⠶⠒⠚⠛⠓⠒⠒⠶⠞⣽⣩⠏⠉⠙⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠲⣿⣿⣿⡗⢲⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠛⢛⣛⣛⠛⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣼⣿⣏⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⣿⣿⣿⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣿⣿⣿⣭⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣻⡿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠟⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠀⠀⠈⠻⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟





⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠄⠀⠒⠦⢄⣂⣀⡀⠂⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠀⠤⠤⢠⠶⠖⠢⠤
⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠂⠀⠐⠒⢶⠒⠈⠀⠀⠐⠶⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢄⠀⠀⠸⠓⢶⠷⠦⢤⣤⡈⢦⣀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣆⣠⠴⡾⠈⠀⠀⠈
⠀⠀⠀⠀⢸⠦⠀⠐⠀⡌⠀⢀⠀⠙⢃⠀⠀⠉⠋⠉⠉⢻⠛⠉⠉⠉⠙⠿⣿⠛⠈⠉⠉⠉⠂⠀⣧⡀⠀⠀⢼
⠀⠀⠀⠀⢁⠀⠀⠀⠀⡁⠀⠉⢂⠀⠀⡆⠀⠀⠀⠀⠀⡜⠀⠀⢰⡂⠀⠀⠘⢦⠀⠐⢣⣀⣀⣠⠋⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠦⠀⠀⠠⡇⠀⠀⢸⠀⠀⡇⠀⡸⠒⠀⠸⡅⠀⠀⠀⠑⢦⡀⠀⠀⣧⠀⠀⠀⠀⠈⣧⠀⠀⠀⠼⡅
⠀⠀⠀⠀⢾⠀⠀⠀⠀⢸⠀⠀⢿⡀⠀⠀⣰⠁⠀⠀⠴⠛⠒⠂⠀⣠⠤⠃⢀⣠⠟⠛⠉⠛⠃⠀⡇⢀⠀⠀⠀⢹
⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⣇⠀⠀⠉⠳⢾⣁⣀⣠⡤⠤⠤⠤⢤⣾⠁⠀⠐⠛⠁⢀⡴⠋⠉⠑⣾⠷⠘⠀⢀⣠⠏
⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⢪⡷⠦⢤⡀⠀⠀⠀⣀⣠⠤⠤⠄⠀⠈⠑⠒⠶⠒⠊⠀⢀⡴⠀⢠⠃⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⡜⠀⠀⣤⠀⠀⠉⠀⠀⠀⠀⠀⢀⡰⠊⠁⠰⣤⠖⠒⠀⠀⢀⠄⠚⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⡆⠀⠈⠂⠐⠒⠒⠐⠒⠀⢤⠀⠁⠀⡀⠀⠉⠀⣀⣀⣴⠋⠀⠀⠀⠀⠀⣠⠴⠃
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠷⠤⢄⡀⣀⣀⣀⣆⡀⠀⠀⢳⣀⣠⣷⣤⠖⠋⠁⠀⠀⠐⠁⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⢸⠃⠀⠐⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⡹⠒⠶⠤⠤⠤⠤⠤⠖⣻⠀⠀⠀⠀⠀⠀⠀⣦⣀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣤⠞⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡐⡄⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⠂⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢻⡷⣄⠀⠀⠀⠀⠀⢀⠘⠀⢋⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠘⣅⢀⠋⠲⠀⣰⡿⠖⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡴⠛⠛⣻⠟⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⣩⠃⡀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⣆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣾⠟⠀⢸⠃⠄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠹⣿⣆
⠀⠀⠀⠀⠀⣼⡏⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣬⣻⡄
⠀⠀⠀⠀⠀⣉⠇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⢺⡉⣷
⠀⠀⠀⠀⠀⠙⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡏⢀⠘⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣱⠀⠁⢻
⠀⠀⠀⠀⠠⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡟⠀⠀⠸⡇
⠀⠀⠀⠀⢲⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⡙⡆⠀⠀⡇⠀⠀⠀⢠
⢦⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠢⠄⠀⢠⡇⠙⠀⠄⡇⠀⠀⢀⡎
⢸⡇⠀⠀⡆⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⢸⠀⠀⡇⢀⡴⠉⡇
⢸⣿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⢸⡄⢠⠃⠉⠀⠘⠃
⣼⣏⢷⣄⡰⢀⡇⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢸⡇⠘⠠⠃
⠛⠀⢆⠀⢛⠾⡇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢿⢹⡞
⠀⠀⠈⢁⡞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢺⡀
⠀⠀⠀⠀⠱⢸⡿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢨⠞
⠀⠀⠀⠀⠀⠛⠇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⢂⡄⠙⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢀⣤⢻
⠀⢾⡀⠀⠀⠀⣼⠀⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢨⡇⡟⠀⠀⠀⢠⡀
⠀⢨⡷⢄⡀⠀⠀⡆⢠⠈⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⣧⠤⣷⡆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠐
⠀⠀⢳⠀⠉⠣⠚⠧⠀⣀⢼⢄⠀⠀⠀⠀⠀⢀⡴⢀⡟⠀⢐⡇⠈⠂⢤⣼⠅⠀⠠⠈
⠀⠀⢸⠑⢄⠀⠐⢄⠈⠉⣸⣀⠂⣀⣀⠠⠔⠁⠈⣤⠁⠀⡼⠃⠀⣰⠁⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢧⡉⠙⢁⣠⠲⠒⠶⠂⣤⡀⢾⠖⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⢻⠶⢎⡩⠓⠭⡴⠾⠤⣆⠁⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠶⠆⠰⠚⠓⠀⠷⠶⠤⠾⠅⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣤⣿⣤⣷⣒⣒⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⡀⠀⡀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢠⣶⣤⣀⣠⣤⣶⡿⠟⠈⠙⠻⠿⠿⣿⡆⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢸⣿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⣿⡆⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⢰⣿⠇⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢻⣷⣾⠿⠿⠿⢿⣿⠿⠿⠿⣷⣾⡟⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⡟⠁⠀⠀⠀⢸⣿⠃⠀⠀⠈⢻⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣠⣼⣿⡁⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⢈⣿⣧⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⣿⠋⢿⣿⣷⣦⣴⣿⠟⠻⣿⣦⣴⣾⣿⡿⠙⣿⣦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠉⣻⣿⢿⣷⣄⣠⣾⡿⣿⣟⠉⠀⠀⠈⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣾⡿⠋⠀⠈⠛⠛⠁⠀⠘⢿⣷⡀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣄⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣠⣼⡿⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⢿⣧⣄⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠚⠑⠒⠛⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠉⠙⠛⠛⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠳⡄⠀⠂⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠀⠈⠉⠲⠞⠉⠉⠒⠇⠤⠒⠀⠒⢤⠔⠋⠉⠉⠒⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣤⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⢈⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⡀⢠⠀⡰⢄⡀⣀⣀⣀⠠⠤⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢠⢋⠤⠒⠐⠊⠉⠉⠀⠒⠀⠐⠒⠂⠐⠒⠒⢠⡀⠀⡉⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠡⡁⠀⠀⠀⠐⠂⠊⣉⠒⢤⠠⠄⠀⠀⠄⠀⠀⢸⠀⠔⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⡎⡆⠀⠀⠀⠑⠒⠂⠒⠀⠒⠤⠤⠤⠂⢸⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠐⡄⢇⠀⠀⠁⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠈⠀⠁⠒⠀⠀⠒⠀⠀⠀⠂⠀⠀⢡⠈⡀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠢⠐⠑⠒⠁⠀⠀⣄⡀⢀⡀⠀⢀⠀⠀⠀⠀⢠⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠳⡀⠠⢄⡀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠁⠈⠀⢱⢠⠇⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣐⣠⠤⣀⣀⠄⠠⠄⠒⠂⠀⠀⠀⡨⣐⠀⠀⠀⠀⠀⠀⠐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠉⠁⣡⠴⠊⠁⡀⠀⠤⠀⠠⠔⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⠀⠀⠀⠀⠀⠀⢸⠀⢀⠅⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣠⠋⠀⠸⡀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠉⠀⠀⠀⠈⠑⠚⡞⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣱⠒⠓⠒⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢭⠩⠭⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠙⠀⠀⠀⣠⣴⠶⣊⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠃⠐⠐⢾⠟⠛⠊⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠈⡹⣿⣆⠀⠀⠀⣠⣶⣿⣿⣿⡍⠉⠙⠀⠁⠁⠻⣻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠚⠟⣿⣿⣶⣿⣿⣿⣿⣍⠻⡙⠃⠄⠄⠀⠐⠒⠀⠀⠛⠓⢚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⣀⠀⠂⠌⢿⣿⣿⢿⣿⣮⡿⣦⠁⠀⠀⠀⠁⠀⠀⠀⠈⠉⠿⣿⣿⡿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⡀⠀⢸⣿⣿⡎⣷⡝⣧⠸⢷⣄⠂⠀⠀⠀⠀⠀⠀⠐⠲⠲⣿⣷⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢺⣿⢻⣿⣿⡟⡌⣧⠹⣮⢻⣆⡀⠀⠀⠀⠀⠀⠀⠂⠸⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⡏⣼⣿⣿⢻⢻⠻⡇⠹⣧⡙⢦⡀⠀⢀⠀⠀⠈⠀⣀⣀⣒⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢡⣿⢸⢻⠘⡉⡆⢿⡀⠹⡝⢄⠈⠀⠀⣈⠁⠀⠀⠀⢀⢉⣉⡁⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⡟⣹⢨⠀⢣⢹⡘⢷⡐⡜⣆⣁⠀⠀⠀⡀⠀⠀⠁⠉⢉⣉⣉⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢸⡇⣿⢸⢰⠸⠈⡇⠈⢷⡝⣞⢿⡆⠀⠀⠀⠀⠀⠈⠹⣟⣍⣋⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⡟⠀⣿⢸⢸⡀⡇⢿⠀⠰⠹⡘⠆⠙⠄⠀⠀⠀⠀⢀⡀⣀⣰⣐⣁
⠀⣠⣴⡊⢱⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⡟⠀⠀⠉⢈⠸⡇⢡⠸⠆⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠩⠭⠭⡵⢶
⣾⡿⠟⠋⣽⢿⣿⣦⣄⠀⣷⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢡⡞⠈⢸⠀⠀⠘⡄⢠⠸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⠶⢻⢿
⢰⢠⠀⠀⢨⠘⡻⣿⣿⣦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⣠⠏⡀⠀⣾⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡿⡏
⠈⢿⡏⢈⠀⠀⢸⣻⣿⡿⣻⠿⣶⠶⢒⣶⢶⡶⡶⢶⣶⣶⢶⣶⡟⠉⢁⠰⢡⡞⡏⢰⠛⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣈⣁⣶⣾⡿
⠀⠈⠳⣈⣆⠴⣻⣿⠟⠠⠃⡄⠡⢀⠎⠀⠎⠀⠀⠁⡇⠀⠀⠀⢀⠜⠡⢀⣞⠁⠂⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣨⣽⣿⡿⠁
⠀⠀⠀⠈⠉⠉⠻⣯⡆⢀⡼⡄⡰⠊⠀⠐⠀⠀⠀⡀⢣⠀⠀⠀⠃⠀⠀⠜⡄⠙⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⣽⣿⡿⠁
⠀⠀⠀⡤⢄⠀⠀⠙⢦⣿⣿⣳⣃⡄⠀⠀⠀⠀⠀⠁⠐⣀⠔⠁⠀⠀⠈⠀⠀⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣐⣢⣰⣶⣿⡟⠁
⠀⠀⢰⠇⠞⠀⠀⠀⠀⠈⠹⣿⣯⡗⠀⠀⠀⠀⠀⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠂⢤⣀⠀⠀⠀⠈⠉⣛⣿⣿⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡷⣧⠀⣂⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⡀⠀⠀⠀⠈⠛⠦⣄⣐⣈⣻⣯⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⢈⠰⡀⠀⣀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠐⠀⠀⠀⠢⢤⣬⣶⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣤⣄⣈⢀⠀⢀⠀⠀⠀⠀⠈⠂⡀⠘⠺⡶⣀⢬⣞⣶⣼⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣷⣤⣶⣬⡾⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠐⠀⠆⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⢀⣴⣾⣿⣿⣶⣄⣠⣤⡤⠄
⠀⠀⢀⣤⣤⣤⣀⡉⠙⠻⣿⣿⣿⣦⣴⣾⣿⣿⣿⣦⣤⣴⣶⣶⣦⣤⣴⣶⣶⣶⣤⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⠿⠋⢁⣤⣶⣶⣶
⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠿⠿⢿⣿⠟⠋⠉⠉⢠⣶⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣄⠉⣉⣁⣀⣈⡉⠉⢉⣠⣤⣤⣤⣄⠉⣠⣴⣶⣶⣦⣤⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣰⣿⣿⣿⣿⣿⣿⢿⡛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠁⢿⣦⡙⠿⣿⣿⣿⣿⡿
⢿⣿⣿⣿⣿⣿⡿⢸⡷⠀⢠⣌⠉⠉⠻⢷⣝⠿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⠟⢋⣀⣀⣀⡀⠀⠀⠀⠀⣽⣿⠆⣸⣿⣿⣿⣧
⠘⣿⣿⣿⣿⠟⢁⣿⣅⠀⠀⠙⢷⡀⠀⠀⠹⣇⠀⠈⠀⠀⠀⠀⠀⢹⡿⠻⠟⠛⠉⠀⠀⠀⠀⠈⠻⣾⠋⠉⠉⠉⠙⠛⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⡟
⣰⣿⣿⣿⣧⠀⢻⣿⣿⣷⡀⠀⠈⣿⠀⠀⢀⡿⠀⠀⠀⣦⠀⠀⠀⠘⣧⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠸⣇⠀⠰⣦⡀⠀⠀⠀⠀⢻⣿⣧⢨⣿⣿⣟
⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⢸⡆⠀⠘⠃⠀⠀⢀⡿⠀⠀⠀⠀⠘⠷⠀⢀⠀⠀⠹⣧⠀⠀⠀⢀⡿⠀⠀⠈⠙⠳⠶⠶⠞⢻⣿⡇⢸⣿⣿⣿⡆
⠈⠻⣿⣿⡟⠀⣾⣿⣿⠛⠀⢀⣀⣼⠃⠀⠀⠀⠀⢀⣾⡷⠞⠛⠷⢶⣄⠀⢀⡿⠀⠀⣰⡟⠀⠀⠀⣸⣧⣄⣀⣀⣠⣄⠀⠀⠀⠸⣿⣇⠸⣿⣿⣿⠃
⠀⣰⣿⣿⣷⣆⠈⠻⣿⣷⣄⠛⠉⠙⠷⣤⣤⣤⡶⠛⠁⠀⠀⠀⠀⠀⠉⠻⣟⠁⠀⣰⠟⠀⠀⠀⢰⠏⠀⢈⣩⣭⣭⣀⡀⠀⠀⢀⣼⡿⠀⣹⣿⡁
⢰⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠙⢷⣤⡟⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠉⠻⠆⣴⣿⡿⠁⣰⣿⣿⣷⡀
⠸⣿⣿⣿⣿⣿⡿⠀⣿⣿⣏⠀⠀⠀⣀⣤⣄⡀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠙⢷⡀⠉⠛⠶⠶⠞⠛⠉⠀⠀⠀⣸⠇⠀⠀⠀⠀⣿⣿⡇⢰⣿⣿⣿⣿⠃
⠀⠘⢿⣿⣿⣿⡁⠸⣿⣿⣿⣷⡄⠛⠉⠀⠉⠛⠻⠛⠋⠁⢀⣠⡄⠀⠀⠀⢸⣧⣤⣴⣤⣤⡀⢀⣤⡴⠶⢶⡏⠀⠀⠀⢀⣤⣿⣿⡄⢸⣿⣿⣿⠃
⠀⢀⣾⣿⣿⣿⣿⡆⢸⣿⣿⣿⠇⠀⠐⢦⣀⠀⠀⠀⠀⣰⣟⣁⣀⡀⠀⠀⠾⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⣁⣠⣼⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⠇⢸⣿⣿⣏⠀⠀⠀⠀⠙⠛⠶⠶⠶⠛⠋⠉⠉⠙⢷⡄⠀⠀⢸⡇⠀⠀⠀⠋⠀⠀⢀⣴⣾⣿⣷⡟⠁⣰⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠻⣿⣿⣿⡏⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⠀⢀⣤⣶⣶⣿⡿⠛⠋⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⢸⣿⣿⣷⣦⡈⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⣿⣤⣤⣤⣿⣦⣴⡿⠛⠛⠛⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⢹⣿⣿⣿⠀⠉⠛⠛⠶⠶⠞⠛⠁⠀⠀⢀⣰⣿⠿⠛⠋⠉⠉⠉⢠⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⣿⠏⠈⠓⠦⣤⣀⣀⣠⣤⠶⠚⠉⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠉⠳⠎⠁⠀⠉⠳⡴⠛⠉⠙⠳⣴⠋⠉⠉⠙⠳⠖⠋⠙⠲⡎⠉⠙⠻⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣼⣦⣀⠀⢀⣠⣧⡀⠀⠀⠀⣠⠶⣤⣀⣀⣀⣤⠞⠙⢦⣤⣤⠂⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠉⠛⠛⢉⣀⣙⠓⠚⠛⠁⠄⠀⠉⣉⠉⠀⠐⠒⢄⠀⣺⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣸⠀⠀⢢⠉⠀⠐⠒⢄⠀⠈⠠⠀⠀⠠⠊⠀⠠⠀⢀⠀⣀⢈⠀⢈⡷⠄⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠀⠀⠙⣆⠀⠔⢠⠊⠁⠀⠀⠂⡠⠄⠊⠀⡁⠀⠀⠐⠄⠁⠀⢨⠀⢀⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀⡠⠀⣂⠉⣁⠀⠪⡀⠀⠈⠀⢀⠠⠀⠀⠀⢆⡐⢁⠄⢺⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣼⠀⠀⠈⠀⠀⢀⠉⢢⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⡃⢰⠙⣧⠀⠠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⠙⡆⠠⡀⠀⠀⢀⠀⢸⠀⢢⡈⢤⠂⠀⠀⣀⠤⡀⠠⠓⠄⠀⡞⠑⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡇⠀⠀⡠⠔⠁⢀⡘⢆⡀⢂⠘⠀⠀⡌⠀⡀⠄⠀⠀⠂⠘⣇⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⡄⠀⠀⠈⠳⣤⠟⠊⠉⠉⠢⠙⡄⠘⡄⡰⠀⠀⡇⠀⢀⠀⠐⢀⠈⢠⠿⢦⠀⠈⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⢀⠄⢀⠀⠐⠈⠀⠀⠀⠀⠀⡰⢡⠊⡡⠄⣀⠁⠀⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠰⣏⠓⠀⠀⣣⡀⠁⠀⣀⣐⠀⠊⠀⠁⠈⠀⣠⠴⠗⠚⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢹⠉⠉⠂⠈⣩⠽⠛⠲⠴⠒⠛⠛⠳⢦⡼⠁⠀⠀⠀⠀⠀⠀⠠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⢀⡜⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠊⠀⠀⠀⠀⢻⡀⠀⠀⠀⠠⣤⠼⢦⣀⣀⣠⡴⠳⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⣿⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⡀⠀⠑⠶⠒⠋⠛⠉⠀⠀⠀⢉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢇⣀⢀⠒⠉⠉⠓⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠋⠈⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠜⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠈⠁



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

⠀⠀⠀⢀⠤⠴⠠⠔⠂⠀⠐⠲⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⠒⠉⠉⠉⠢⠀⠀⢄
⠀⠀⠰⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠢⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠒⠒⠦⠄⠀⠢⢄⡠⠄⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠋⠀⠀⠀⠀⠈⠀⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡁⠂⠀⠀⠀⠤
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈
⢣⡀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠓⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⢄⡀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠀⠀⠀⠀⠠⠀⡈⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠤⠐⠃⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠴⠚⠻⣦⠀⠇⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣤⣤⣴⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠘⣿⡹⣧⠹⣿⡻⣿⣷⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣾⣷⠹⣧⠘⢷⡙⢷⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢹⡆⠈⣷⡈⢿⡄⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡀⠸⣧⠈⢿⡄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⣿⠀⠸⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠀⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠠⠄⣀⢀⠔⠒⠒⠒⠁⡠⠔⠚⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠈⠓⠊⠁⠀⠀⠈⠋⠀⠀⠀⠀⠁⢀⣀⠤⠒⠋⠀⠀⣠⠃⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⡀⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠋⢉⡁⠀⠀⣀⠼⡁⠉⠸⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠉⠀⠀⣀⠀⢀⣴⢲⡤⠤⠔⠋⢗⠒⠒⠊⠁⠙⠛⠛⠒⠒⠞⠀⢸⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠄⡤⣔⠉⠉⠁⡜⠀⢣⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠰⡀⢸⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡜⠁⢩⣀⣠⠴⡅⠀⠀⠑⠦⣀⠀⠀⠀⠈⠉⠉⠙⢯⠀⠀⢰⠁⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢰⠁⢠⠇⠀⠘⠀⠈⠢⢄⡀⢀⣀⣈⠉⡉⠁⢖⠢⠀⠈⡆⠀⠘⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢣⠀⠀⠀⡀⠀⠐⡄⠀⢹⠉⠉⢣⠀⠀⢸⠀⠀⠀⢰⠀⢰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠇⠀⣸⡀⠀⠀⢡⠀⠀⢰⠀⠈⠄⠀⠀⠣⡀⠀⠆⠀⠀⠸⠃⢈⠆⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢇⢹⠀⠀⠀⡇⠀⢨⠀⠀⢰⠰⡀⠀⣑⡦⠼⢦⣀⠀⠀⢸⠀⠸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡄⠀⣜⠈⠀⠀⡰⡁⠀⠘⠆⠀⠀⠀⠈⡟⠁⠀⢄⠀⠈⠉⢉⠋⠀⠇⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠙⣉⡂⠉⡀⠙⢦⣀⣀⣠⡞⢩⣉⡉⠲⠤⠤⢑⠤⡤⠼⠂⡜⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢇⠀⠘⠤⡉⢺⡁⠀⠘⡄⠜⠁⡀⠀⠀⠈⠒⠤⣀⠀⠉⠀⣠⠞⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠈⠢⣀⠀⢸⠀⠑⠀⢀⢼⠀⠀⠑⢤⣀⣀⣀⡀⠀⠈⠉⠉⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣈⡳⡦⠤⣤⠤⠊⢠⠂⠀⠀⠰⡀⠀⠀⠈⠑⠂⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠁⠒⠺⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁



⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠋⠁⠀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⠉⠙⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠻⢦⣤⡴⠶⠶⠶⢦⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣿⠋⠁⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢹⡿⠶⠤⣤⣤⠶⠶⣤⣄⣀⣠⣤⠶⠶⢶⣶⠞⠋⠁⢸⠇⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣾⠋⠉⠁⠀⢀⣴⠟⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠀⢻⣤⡴⠶⠶⠶⠾⢷⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⠄⢸⡷⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠙⠿⣟⠛⢻⡿⠉⠁⠀⠀⣾⠁⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢿⣄⣠⡴⠶⠶⢦⣄⡀⠀⠀⠙⣷⡟⠀⠘⢦⣄⠀⢿⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠈⠙⢷⡄⠀⠈⢻⡄⠀⠀⠉⠳⢾⡧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣷⣄⣀⡀⠀⣸⡇⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣶⡟⠁⠀⠀⠛⠲⠶⢦⣤⣤⣤⣤⡴⠟⠀⠈⠉⠉⠉⣹⡇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣠⡤⠶⢦⣴⠟⠉⠷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣠⣴⠟⠉⠛⠶⠶⣤⣤⣤⣴⡟⠁⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣇⠀⠀⠀⣀⣤⣤⣄⣠⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⡀⢀⡐⣲⡀⠀⠀⠀⠠⠤⢀⣤⣤⣤⡐⢧⣥⢞⠃⠀⣸⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠲⡀⠈⣴⣁⢉⡍⣬⢭⠀⠀⠄⢄⠀⠀⢰⠄⠀⠀⢈⠤⢩⠁⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣱⠀⠀⠒⠻⠗⢼⡁⠀⠘⠀⠈⠁⣠⠢⠤⠔⠒⠀⠂⠉⢰⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠾⢿⡼⡀⠀⠀⠉⠁⠉⠈⠀⡈⢉⠉⠀⠁⠀⠀⠐⠁⣀⠀⠙⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡔⠆⠀⠇⠠⠬⠀⢰⣀⠀⠂⠢⡀⠀⡠⠀⠠⢀⣀⡁⢘⣄⣥⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡼⠁⣅⠀⠠⠤⠄⠀⠁⠀⠅⠊⠀⡀⠀⠀⠀⠉⠀⠀⠁⡸⠸⠟⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠲⡠⠤⠤⠄⠀⠀⠀⠀⠀⢄⡈⠉⠛⠀⢁⣠⣤⠀⡃⠐⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢲⠀⠀⠠⠄⠀⠄⠀⠀⠂⠄⢀⠜⠉⠓⠎⢀⣄⣴⡡⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢈⡌⠳⡀⠀⠀⠀⣀⠀⠀⣀⣄⢀⣤⠒⢂⣎⡰⠎⠂⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠦⡈⠑⠀⠀⠁⠠⠎⠀⢼⠉⠈⠉⠩⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠂⠀⠀⠀⠀⠀⠀⠔⣀⠰⠆⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢰⣧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣏⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢨⠠⢠⠨⡀⠀⠅⠀⠁⠅⠁⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣠⠖⠒⠛⠯⣝⣒⣒⣒⠢⢄⣠⠤⠤⠤⣀⡤⠤⠤⠤⠤⡤⠔⠒⠒⠲⠶⣋⡉⢉⣹⠗⠒⠲⢄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠁⠀⠀⠈⠉⠖⠒⠊⠉⠛⠲⡶⠚⠉⠉⠉⠓⠞⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⡞⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⢧
⠀⠀⠀⡇⠀⠀⠛⠓⣾⠷⠤⢄⣀⡰⣄⡀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣀⡠⢴⡟⠋⠀⠀⢸
⠀⠀⠀⡸⠂⠀⠀⠀⡇⠀⠀⠀⠙⠄⠀⠀⠙⠏⠉⠉⣿⠛⠉⠉⠉⠛⢿⡟⠊⠉⠉⠈⠙⠀⠀⡆⠀⠀⠠⣞
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠙⣆⠀⠸⡆⠀⠀⠀⠀⢀⡏⠀⠀⢲⠀⠀⠀⠙⣄⠀⠘⢆⣀⣀⣼⠁⠀⠀⠀⢸
⠀⠀⠀⢰⠄⠀⠀⢠⡇⠀⠀⡼⠀⣰⡇⠀⡶⠂⠀⢸⡀⠀⠀⠀⠓⣄⠀⠀⠈⡆⠀⠀⠀⠀⢹⡦⠀⠀⠀⢼
⠀⠀⠀⡆⠀⠀⠀⠀⢱⠀⠀⣇⠀⠀⠀⡼⠀⠀⠀⠶⠓⠂⠀⠀⣠⠼⠃⢀⡴⠟⠛⠙⠛⠀⢸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⢰⠄⠀⠀⠀⣸⣄⠀⠀⠙⠲⣿⣀⣀⣠⠤⠤⠤⠤⢤⡎⠀⠀⠘⠋⠀⣠⠔⠉⠉⢳⣾⠧⢀⠀⢀⣴⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠈⣎⡷⠤⢄⣀⡀⠀⢀⣀⡠⠤⠤⢀⠀⠈⠓⠲⠶⠒⠋⢁⣠⠦⠀⡸⠁⠀⠁⠀⠀⢸
⠀⠀⠀⠰⡄⠀⠀⠀⢀⡏⠀⠠⡄⠀⠉⠉⠉⠀⠀⠀⠀⢀⡗⠊⠉⢢⡤⠖⠊⠉⠀⣠⠴⠓⡀⠁⠀⠀⠀⡘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⡀⠀⠙⠒⠒⠒⠒⠒⠒⠢⢄⠈⠃⠀⠀⠀⠁⠀⢀⣀⣼⠁⠀⠈⠀⠀⠐⣄⠔⠁
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⠧⠤⢀⡀⠀⢀⡠⠄⠀⠀⠈⣧⣀⣠⣦⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⢹⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⡷⠒⠦⠤⠤⠤⠤⠴⠒⣟⠀⠀⠀⠀⠀⠀⠀⣆⡀⣀⡠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣯⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣀⣀⣤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡣⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿

⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢊⠁⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⢀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠄⠀⠀⠀⢂⠀⠡⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⢀⠠⠀⠅
⠀⠀⠀⠠⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠈⡀⠄⠈⠐⠀⠄⠀⠀⠀⠺⢦⡄⠀⠀⠠⠀⠀⠀⠈⠀⢠⠀⠂⠈⡀⠀⠈⠐
⠀⠀⠀⠠⠀⠀⠀⠓⠀⠂⠐⠀⠀⠀⡀⠀⢤⠘⠚⠀⠈⠀⠠⠀⠀⠀⠀⠀⡰⠐⢘⠿⠀⠂⠀⠀⠀⠀⣀⣀⣤⣐⣰⣥⣶⢦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⡀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣀⢼⡤⠀⠄⠀⠀⠀⡀⠀⢷⠻⣇⡼⣽⣫⡽⠀⠀⡀
⠀⠀⠀⠘⠀⠀⠀⠄⠁⠀⠂⠀⠉⠄⠀⠁⠁⠅⠠⡀⠀⡂⠆⢀⠀⠀⠀⠀⣋⢈⣸⡇⠁⠀⠂⠀⠈⠇⠀⠈⠉⠏⠈⡿⠋⡂⠠
⠀⠀⠀⢈⠀⠀⠀⠠⠠⢄⠀⠂⠀⣈⠁⠈⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠐⣋⠀⠜⣇⢀⠌⠀⠆⠀⢀⠁⠈⠀⠈⡀⠀⠀⠀⠄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠐⢀⡀⠈⠀⠀⠠⠀⠁⠀⠀⠀⠀⠓⢄⣉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠂⠀⠉⠐⠰⠀⠢⠐⠈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠐⠂⠀⠉⠑⠐⠄⠢⠐⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣨⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀⠀⠀⠀⠀⢀⡀⠀⢠⡀⣀⢀⢀⠀⢀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠐⠋⠉⠏⠃⠀⠀⠀⠀⠋⠉⠚⠙⠁⠋⠉⠙⠘⠀⠙⠉⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠷⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣴⡶⠿⠿⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⢠⣤⣤⣄⡉⠉⠉⠉⠉⠻⢷⣶⣶⠶⠶⠶⣶⣤⣀⣤⣶⠶⠶⠶⢶⡾⠛⠁⠀⠀⠀⠁⣀⣠⣤⡄⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠉⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉⠁⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢰⣦⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⣾⠇⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠷⠶⠶⠾⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢀⡈⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠿⠋⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣿⡇⠀⠀⠀⢹⣿⢶⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣀⣠⣴⡿⢋⣿⠋⠀⠀⣶⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⣿⠂⠀⠀⠀⢸⡿⠀⠀⠉⠉⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠉⠙⠛⠋⠉⠁⠀⢸⡟⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⢸⡇⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡄⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣾⡇⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿⡇⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⣿⠇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢿⡇⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢰⡿⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣿⠃⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠈⠿⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠇⠀⢠⣾⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣤⣄⢠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⠶⡿⠋⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⣀⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⢀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡿⠋⠉⠀⠀⠀⠀⠀⣠⣶⠶⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢸⡟⠀⠀⣶⣤⣤⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢸⡧⠀⠀⢹⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠸⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠴⠝⠒⠤⡀
⠀⠀⠀⠀⠀⠄⠀⠉⠓⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⢀⣀⠐⠀⠀⠀⡁⡀
⠀⠀⠀⠀⠀⢄⡀⠀⠠⠀⠈⠐⠢⡀⠀⠀⠀⢀⠀⠀⠀⣀⠠⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⣀⣠⡐⠃⢠
⠀⠀⠀⠀⠀⠀⠃⠛⢆⠀⠀⢀⠄⠉⠉⠑⠰⠖⠐⠒⠂⠲⠄⠐⠈⠉⠈⠁⠀⠀⠀⠀⠔⢁⢈
⠀⠀⠀⠀⠖⠀⠀⠀⠨⠁⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠅
⠀⠀⠀⢘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠀⠀⠎
⠀⠀⠀⢀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠨⠃⠐⠤
⠀⠀⠀⠰⠀⣀⣠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠰
⠀⠀⠀⢠⠀⠐⠁⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠄⠒⠛⠉⠉⠂
⠀⠀⠀⠠⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⡖⢃⠦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡉⢀⠒⠀⠈⠀⠀⠀⠀⢀⠔⠒⠂⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⠒⠀⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠑⠀⠀⢶⠀⠀⠀⠱⢄⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡔

⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡁
⠀⠀⠀⠀⢀⠀⠢⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠠⠀⢀⠰⠀⠄⠀⠀⠀⢁⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠀⠈⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⡀⢐⠀⠈⠀⠂⠀⠀⠀⠘⠢⣄⡀⠁⠂⠀⠀⠠⠀⠠⠄⠐⠀⣀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢈⠃⠘⠀⠀⠀⠀⠠⠀⠐⠄⠉⠀⢀⠈⠐⠀⠄⠀⠀⠀⠑⠀⢸⠉⠀⠀⠀⠀⠀⠠⢤⢴⣀⠥⣵⣺⣷⡄⠂
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡠⠀⢃⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⡀⢸⠂⡀⠀⠀⠀⣠⠀⠘⣍⣻⡴⣸⣷⡾⠁
⠀⠀⠀⢀⠀⠀⠐⠀⠀⡈⠀⠀⠐⠀⠀⠀⢀⠀⠅⠀⠄⠀⠠⠀⠀⠀⠀⡍⠰⢺⠀⠀⠈⠀⠀⠀⢀⠀⠀⠘⡀⠸⠛⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠈⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠂⠄⠀⠀⠀⠈⡄⠀⢍⢇⠐⠂⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠂⠐⠄⠁⠤⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠉⠂⠒⠊⠀⠀⠀⡀⠐⠀⠠⠀⠰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢈⠁⡁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⡁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇

⠀⠀⠀⠀⠀⠦⠖⢰⠴⠀⠀⠀⠀⠢⠶⠤⠾⠇⠤⠖⠢⠲⠔⠴⠦⠖⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣆⠀⢠⡀⠀⢀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⢠⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣸⣿⣿⣷⣼⣿⣸⣺⣾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢀⣼⣧⠀⣸⠀⠀⣾⣿⣿⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡺⣿⡇⠀⡏⠀⢰⣿⣿⣿⡟⣇⣇⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢆⣿⠅⢀⠀⠀⣸⣿⣷⣿⡇⣿⣿⠇
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⢠⡿⠲⡄⣀⣀⠀⢀⣤⣀⣀⡀⠀⣀⠤⠓⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⣽⣧⣤⡇⣧⣀⣾⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⡀⣀⠀⠁⠀⠠⠄⣀⠀⠀⢘⣿⣿⣿⡇⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⢀⣀⣤⡶⢿⣿⣿⣷⣿⣿⣿⡿⠛⠿⠿⣿⣧⣷⣤⡀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠉⠒⢸⣿⣿⣿⠇⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠈⢱⡤⢤⣥⣭⣭⣽⡿⠉⢻⣷⣟⣦⣴⣹⣿⣿⣮⣳⣶⣶⡀⢁⠈⠙⢿⡧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠛⠋⠉⠁⠈⠈⢀⠈⠛⠛⢿⣿⡇
⠀⣼⡇⠀⡖⠒⢺⣿⣧⣯⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⡋⠛⣛⣛⣙⣷⣾⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⣠⣦⠼⠂⠙⢶⡷⢶⣒⣞⣉⣇
⢀⣿⡇⠀⣇⣀⣀⣉⣛⣉⣀⣀⣀⡀⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠀⢠⣿⣿⣿⡿⡿⠿⣿
⢘⣿⡇⠀⠆⠀⠀⠐⠆⠀⠰⠀⠀⠰⣷⠖⠲⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⡄⣾⣿⣿⣳⣿⣿⣿⣦
⠀⣿⡇⠀⠀⠀⠰⣆⠂⠀⠀⠀⠀⠀⣯⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⢿⠂⠀⡇⠀⣿⣿⣷⣿⣿⣿⣿⡿
⣠⣿⡇⠀⡀⣀⢀⣀⣀⠀⠀⠀⠀⣘⣟⡀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡄⠀⠀⢸⣿⣿⣿⣟⣸⡷⣾⡅⠃⣿⡟⣿⣿⣿⣿⣿⡇
⠟⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡇⠀⠀⢀⣿⣿⣿⣿⣹⡷⣏⣷⣴⣿⣽⣿⣿⣿⣿⣿⡇
⠈⣿⠃⠀⠃⠀⢀⡤⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⡷⠀⠀⠘⣿⣿⢻⣿⣿⣃⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅
⠰⣿⡆⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣦⣭⣽⢛⣛⣉⣽⣿⣷⡇
⠘⣿⡇⠀⠓⠐⠒⠒⠒⠒⠒⠂⠐⢲⣿⠒⠒⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢉⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡁
⢠⣿⡇⠀⣴⣶⣶⣦⣴⣤⣶⣶⣷⣿⣽⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣼⣿⣿⡄
⠈⢿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣇⣿⣾⣿⡿⣿⣿
⠀⠀⠈⠛⠉⠫⠿⢟⠻⠿⠿⡿⠿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣟⣋⣱⣦⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⢿⠿⢿⣶⣷⡀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣈⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣉⣉⣛⣛⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠤⠒⠤⠒⠀⠀⠐⠢⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠒⠊⠉⠉⠱⠄⠀⠠⡀
⠀⠀⡔⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡄
⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠢⠤⠒⠒⢄⠠⠐⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸
⠱⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠶⠆⠒⠁⠍⠀⠀⠀⠀⠀⠀⠘
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠁⠒⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢂⠀⠀⠀⠠⠄
⠑⣄⠀⠀⠀⠀⢀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠑⠂⠐⠂⠒⢄⠀⠀⠀⠀⣀⠀⠀⠀⣀⠔⠒⠂⠊⠁⠀⠀⠀⠀⠀⠎
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⠔⠁⠀⠀⠀⠂⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢀
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠘⢤⡀⠀⠀⠘⠀⠀⠀⠐⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⡤⠖
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠀⠀⢰
⠀⢄⠀⠀⠀⠀⠂⠀⠀⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠠⠀⠀⠐⡃
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠣⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⠤⠰⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠁⢣⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⣀⠔⠤⠤⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣠⠔⠻⣦⡀⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠐⠊⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠶⣤⣄⣀⣀⣀⣠⣤⠴⠞⠉⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠉⠉⠳⣤⣀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠉⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⠙⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣸⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⠄⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣄⣼⠖⠋⠉⠉⢉⣀⢀⡤⣄⠀⠈⠉⠉⠉⠓⢾⣄⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⡟⠉⡿⠀⣼⠶⣄⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠃⢸⠇⢠⡏⠀⣟⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⣦⠀⢀⡟⠀⡿⠀⣼⠁⢸⠏⣹⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡆⣸⠁⢸⠇⢠⡇⠀⡞⠀⣿⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣧⡏⠀⠀⠀⠈⠁⠸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⠟⠉⠉⠛⠓⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⠀⠀⠀⠀⠀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧



⣇⢸⠆⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠐⠒⠒⠒⠒⠒⠒⠐⠂⢾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⡇⠈⡆⡇⠈⠁⢠⢻⡀⡧⢼⢸⠀⠀⡇⠀⠀⠪⣄⠀⡇⠀⣅⡕⣸⠀⢱⢈⣖⠁⠬
⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣷⣶⣥⣧⣤⣤⣦⣤⣥⣷⣮⣼⣶⣤⣷⣦⣤⣴⣮⣤⣥⣤⣤⣼⣬⣶⣮⣤⣤⣥⣴⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⣋⣤⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢁⣶⣶⣦⣡⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡙⠻⢿⣿⣿⣿⣿⣿⣿⡿⢡⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢋⣩⣤⣤⣤⣍⣁⠀⠀⠀⠀⠀⠀⠈⢿⣟⠻⣿⣿⣦⡈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢿⣧⣙⣿⡿⢿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⣿⣿⣿⡿⢋⣥⣤⣌⠻⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣾⣿⣿⣿⠆⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⡟⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⡟⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢰⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⠃⠀⠀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⣿⣿⣿⣿⣿⣿⣶⣤⣉⡛⢿⠀⠀⠘⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⡛⠻⢿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣉⡛⠿⠿⠋⡀⠀⢀⡉⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣄⠀⠈⠑⠒⠠⠠⠀⠀⠂⠀⠀⢠⠏⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠠⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡎⠀⠀⢦⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢸⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢀
⠀⠀⠀⠀⠀⡠⠂⠉⠉⠠⠤⣉⡉⠲⠠⣄⣀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠈⢁⡠⠀⠀⡄⢱
⠀⠀⠀⠀⠀⡣⠀⠤⣀⣄⠀⠀⠘⠳⠒⠤⢀⡀⠘⠀⠀⠻⠋⠈⠑⠊⠉⠉⢈⡃⠤⢔⠢⠁⠁⢜⠔⠃⡸
⠀⠀⠀⠀⠀⢇⠀⠐⠀⢸⠒⢺⠆⢀⣴⡀⠀⢀⣄⠉⠀⠉⠉⠉⠉⡁⠀⠀⠀⠀⣀⡰⡤⠔⠹⠀⡤⠀⢸
⠀⠀⠀⠀⠀⡮⠀⢠⡇⢉⡄⠑⢕⡂⢆⠉⠉⢹⠈⡷⡉⠙⠂⢖⡉⠚⠠⠤⠊⣉⠩⣐⠅⠀⡎⢀⡇⠀⣹
⠀⠀⠀⠀⠀⡸⡂⢸⠃⠰⡕⢄⠀⠀⠀⠑⡠⡪⠃⠈⠂⠅⠄⣀⠀⠉⠐⠲⡎⠀⠀⡠⣒⠈⡅⠐⡇⠠⢌
⠀⠀⠀⠀⠀⢂⡀⢸⠀⢐⡯⠠⡈⠐⣊⠛⠊⣔⠊⠉⠉⠈⠤⠭⠉⠢⡀⠀⠊⡦⠮⡀⠁⠀⡢⠀⡇⠴⡸
⠀⠀⠀⠀⠀⡾⠂⠀⡀⠀⣷⡀⠀⠩⠒⠂⠞⠀⠀⡀⠀⣠⠤⢄⠀⠀⠇⠀⠀⡄⠀⠘⢄⠀⡡⡀⡇⠀⡸
⠀⠀⠀⠀⠀⠣⠄⠀⢧⠀⣪⠀⠈⢻⢄⢠⠁⠀⠰⠀⢰⢠⠀⡌⢖⠠⠤⢔⢴⡀⠠⣔⢄⠑⠪⠀⢹⠀⣱
⠀⠀⠀⠀⠀⢧⠀⣀⠸⠀⠰⠤⠀⡇⠳⢺⡀⠀⠻⠆⡀⠳⢕⡬⣂⠉⡡⢐⡡⠇⠀⠏⠢⢁⠓⠀⠹⠈⢜
⠀⠀⠀⠀⠀⠀⡟⠁⠀⢣⠀⠰⢇⠕⠁⠜⡇⠀⠠⢇⠈⠔⣤⢈⠁⠉⠑⢄⣀⢠⠊⠎⠠⣀⠷⠀⠆⠀⡺
⠀⠀⠀⠀⠀⠀⠑⢤⠂⠀⠑⠀⠐⡀⠤⡢⠜⠢⠀⠼⣀⠀⣀⠀⢁⠀⢘⠎⠀⠀⠣⡀⢀⡼⠇⠀⠃⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁⢂⡏⠀⠀⠀⠀⠀⠀⢀⠋⢠⠀⠢⣅⡙⠈⠑⠖⠉⠁⠀⢀⠀⠁⠀⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢈⠓⠐⠉⠐⢦⡉⣓⠒⠒⢒⠐⢨⡁⢐⠔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⠀⡁⡅⠀⠀⠉⠂⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⣯⣩⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⣠⠞⣭⣶⠋⢻⡆
⠀⠀⠀⠀⠀⢠⡴⠛⠯⢅⣠⠞⠋⢛⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠈⣻⢣⡞⠁⠈⣧⡼⢷
⠀⠀⠀⠀⣰⢋⡟⠙⠳⣦⠉⠳⣤⠞⠀⠀⠙⣷⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣤⠶⢾⡏⠈⠳⣤⡴⣻⠋⠙⢄⣴⠛⡃⢸⠇
⠀⠀⠀⠀⣿⠀⣧⠀⢰⠉⠳⣄⠈⠳⣄⣠⠞⠁⠀⠀⣿⠁⠉⣷⠞⠉⢳⡞⠉⠀⠙⡇⠀⠘⣧⠀⢀⣹⣦⠴⢋⣴⣇⠀⠀⣸⠏⢰⡗⢻⡄
⠀⠀⠀⢠⡟⠦⣜⣧⣯⠀⢠⠋⠛⢦⣈⠙⠓⠦⠤⣄⣁⡀⠀⣿⠀⠀⢸⣇⢀⣀⣀⣷⡤⠤⠞⠛⠉⣉⣤⣶⠋⠀⠈⠳⣾⠛⣿⢸⣇⣰⡇
⠀⠀⠀⠸⣇⠀⠀⢹⠉⣷⣎⠀⠀⢠⠟⠓⠦⣄⣀⣀⡈⠉⠛⠛⠛⠛⠛⠉⠉⢉⣉⣀⣠⣤⠶⠲⣏⠀⠀⠈⢳⡀⠀⠀⣼⡀⣃⢸⡇⠉⣇
⠀⠀⠀⢠⡿⠳⠶⣾⠀⡟⠛⣆⣀⡞⠀⠀⠀⠀⡟⠉⠉⠉⢻⠟⠛⠛⠻⣟⠉⠁⠀⠘⡇⠀⠀⠀⠸⡀⠀⠀⠀⢻⣶⠏⠉⠉⢿⠈⣧⣴⡇
⠀⠀⠀⢸⡁⠀⢀⡟⢰⡇⣠⡞⠉⢳⣄⠀⣀⣼⠃⠀⠀⠀⣼⠀⠀⠀⠀⢿⠀⠀⠀⠀⢿⡀⠀⠀⢀⣿⠖⠖⠖⠋⠘⣷⣄⡀⠸⡆⡇⠀⢹⡄
⠀⠀⠀⣾⡷⠶⢾⠃⡾⠋⢙⡇⠀⠀⠉⠉⠉⠉⠛⠲⠖⠚⠛⠛⠶⠶⠶⠛⠛⠶⠶⠶⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⠉⠙⠻⢇⢱⣤⣾⠁
⠀⠀⣼⠋⠀⠀⣿⢰⣁⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⡀⠁⠈⣷
⠀⠀⢹⡦⠴⢶⢯⡟⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠒⠲⡇⢸⠖⢿⡄
⠀⠀⣞⠀⣀⣼⢸⡷⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣧⢸⡀⣀⡟
⠀⢠⡟⠋⢹⡇⣼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⢻⠘⡟⠙⢧
⠀⢸⣅⣀⣼⠀⣿⣤⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣸⡇⢃⠀⣈⡇
⠀⣼⠋⠉⣿⠀⡏⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⣷⢸⠛⠉⢳
⠀⣿⣀⣠⡟⠀⣷⠶⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢘⡌⣄⠀⠀⣶
⢰⡏⠀⠀⣧⠀⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠙⡇⢿⠋⠙⢻
⢸⣆⣠⣤⣿⠀⡿⠲⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠒⠚⠷⢸⠗⠒⠺
⣸⠋⠁⠀⣿⠀⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣠⡆⢸⣇⣀⣀
⡯⠀⢀⣤⣿⠀⣿⠖⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠈⠁⠈⠁⠀⠈
⣿⠞⠁⠀⢿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠓⢶⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣤⡄⢰⣄⣀⢠
⣿⠀⠀⠀⢸⠀⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⣸⣦⡀⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀⣾⠁⠀⢠⠇⣼⠉⠉⣿
⢻⡀⠀⠀⢸⡀⡿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠴⠞⠻⢦⡙⢦⣀⠀⠈⠙⢶⣄⠀⣀⡴⠿⢦⣀⡿⢠⠏⠀⠀⣿
⠸⣧⠀⠀⢸⡿⣁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠙⠲⢤⣀⣹⡏⠙⢧⣀⣠⠟⢀⣮⠀⠀⣰⠇
⠀⠘⠓⠒⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠲⣦⣀⣠⣴⣦⡀⠀⠀⠀⠀⠉⠓⠦⣤⣈⠉⠛⠒⠚⠉⢁⡠⠟⠉⢳⡶⠋
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⢦⡀⠀⠀⠀⠀⠀⠀⠉⡿⠛⠛⠛⠛⢿⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠙⢦⣄⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠓⠒⠾⢧⣤⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠐⠛⠛⠻⢶⣄⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣅⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣥⡜⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⢀⡎⠱⣤⣼⡏
⠀⠀⠀⠀⠀⢠⣞⣙⣻⣩⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢹⡄⠀⠀⠀⠀⣰⡿⠋⣱⡿⠰⣤⣼⣿⡇
⠀⠀⠀⠀⢀⣾⣟⣰⣿⠿⣿⣿⣛⣷⣶⣶⣖⣦⣄⢀⡀⠀⢸⣇⠀⣨⣧⣀⣠⣤⡾⣛⣠⣾⠋⢤⣄⣼⠟⣽⡇
⠀⠀⠀⠀⢰⡟⠙⣿⣷⣰⣾⠃⣹⠓⠻⣿⢯⣟⣛⣛⣛⡿⣟⣛⣿⢿⣉⣭⣥⡼⠷⣟⠁⠈⣷⣤⡿⠿⣟⣿⡇
⠀⠀⠀⠀⢸⡷⠞⣻⡿⣿⡿⣾⣿⣀⣾⡇⠀⣼⡍⠉⠉⣿⠉⠙⢻⡏⠉⠉⣷⡀⢀⣸⣧⣴⠿⣋⠀⠀⢹⣿
⠀⠀⠀⠀⢺⣇⣬⣿⣀⣽⡇⣾⡏⠉⣹⠿⠿⡿⠿⣶⠾⣿⢤⣤⣼⠿⢤⣶⣿⣙⣛⣉⣠⣤⠞⠃⠀⢀⣾⣿
⠀⠀⠀⠀⡟⠈⠀⣿⠉⢿⡆⠹⡇⠀⠙⠶⠞⠀⢠⡇⠀⡇⠀⢻⡇⢀⡞⠁⢀⣀⣀⠈⠀⣀⣀⣀⣠⣞⣹⣿
⠀⠀⠀⠀⣿⠶⢾⣿⢠⣾⣧⡀⠙⢤⣀⠀⢀⡴⢋⡇⠀⣇⠀⢸⡇⢸⡇⠀⠀⠉⠉⠙⠋⠉⠉⠉⣉⡈⠉⢳⡀
⠀⠀⠀⢸⡇⣀⣰⣏⢀⣿⡌⠛⠷⠀⠈⢹⣥⠤⡼⠀⣸⠇⠀⢸⢧⡈⢧⣴⣶⡟⠛⠛⠲⠤⠶⠛⠉⢀⣀⣴⡇
⠀⠀⠀⣸⠟⠻⢿⡿⣿⡟⠻⣄⣀⣀⣠⡾⠁⡀⢧⡀⠁⢀⣠⠟⠛⢻⡏⠀⠀⠘⣦⠤⠤⣤⣤⣶⡚⠉⢁⣿⡟
⠀⠀⠀⣿⣤⣤⣿⣠⣸⣿⣤⣈⠉⠉⣉⣠⠾⠃⢈⡿⠋⢉⡴⠀⢀⣼⣣⢿⠁⠸⢧⡤⠖⠋⠀⠀⠉⣮⠽⢿⣷
⠀⠀⢠⣟⠉⢙⣿⠙⢻⣧⠞⠙⠻⢿⡏⠀⣤⡴⠟⠁⣰⡏⠀⠰⠋⣰⠧⣬⣳⣤⣀⣀⣠⣤⠞⠀⢀⣾⣄⣨⣿
⠀⠀⠀⣿⠖⢛⣿⡗⢿⣿⣇⠀⢶⡈⠷⣄⣤⣤⢤⡞⠹⣦⣠⣤⣴⣃⣀⠀⠈⡏⠉⠉⣡⣤⣤⠴⠛⠁⠈⡟⢿⡆
⠀⠀⠘⣿⣤⣬⣿⣷⠾⣿⣮⡇⠈⢿⡀⢹⡄⡇⠀⣧⠀⠚⠁⡼⠛⠛⠿⣿⣆⡙⢦⣀⣀⣀⣠⡴⠏⢁⡼⣿⡟
⠀⠀⠀⠸⣏⣅⣾⣿⣏⣙⣿⣷⣤⠟⡇⠐⣇⣿⠀⢸⢲⠖⠊⡁⠀⠀⠀⠀⠈⠙⠓⠪⠭⣍⣡⡤⠔⣋⣠⣿⠇
⠀⠀⠀⠀⠈⣿⣤⣼⡿⣧⣤⣾⠃⠀⠻⣄⠈⠉⢀⡞⢸⣆⠘⢧⣧⣦⣤⠀⣀⠀⠀⠀⠀⣰⡀⣀⣤⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠷⠤⠼⠋⠉⢷⡀⠀⠉⠛⠛⠉⣰⠃⠉⠓⠂⠈⢛⣿⠿⢾⣾⣮⣦⣿⠿⠛⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⣿⠀⠰⢦⣤⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢧⠀⠀⠈⠉⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⣦⠤⠦⠤⠀⠀⠈⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠠⠤⣇⡀⠀⠘⠦⣀⣀⣤⣋⠉⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠈⠱⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⢹⡠⠾⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣠⠋⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣢⠤⠤⣤⠒⠉⢳⠒⠋⠁⠀⠀⡠⠂⠀⠀⠘⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠁⠀⣰⡇⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠤⣖⠊⠁⠈⠲⠤⠤⠘⢦⣀⡀⠀⠀⣰⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠙⠆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠻⡍⠀⠀⠀⡗⢤⣀⣀⣀⡠⠖⠋⠉⠓⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⡠⢄⣀⠀⠀⣀⠜⠁⠀⡼⠁⠀⠰⢤⡀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⠈⠙⢯⠴⠒⠲⢼⡁⠀⡀⠀⠀⠃⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢤⠀⠀⠀⠈⣆⣀⣀⡀⠙⢆⠙⠦⣀⣀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢺⠀⠀⠀⢠⠇⠀⠀⡽⣆⠈⠳⣄⣀⠴⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠁⢀⣠⠔⠁⠸⣄⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠓⠲⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡖⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⢳⡈⠳⢤⣤⠴⠚⠡⢄⡀⠀⠀⠀⠀⡇⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢧⠀⠈⢧⠀⠀⠀⠀⢳⡀⢦⠙⣄⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⡆⠀⠘⣆⠀⠀⠀⠀⠃⠘⠂⠘⡆⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⠋⠹⡄⠀⠉⠉⠉⠉⠉⠉⠉⢳⡄⠛⠀⠀⡇⠀⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠐⢦⡰⠊⠀⠀⠀⠙⠶⠤⠤⢤⡤⠤⠤⠤⠾⠤⠤⠤⠤⠇⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠓⠲⠶⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣘⣆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠒⠒⠒⠒⠀⠀⠀⠒⠒⢺
⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠆⠈⠁⠧⠘⠀⠀⠈⠀⠐⠀⠉⠸⠀⠀⠀⠦⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣀⠀⠈⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡉⠉⣉⣍⠛⠛⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢼⠇⢲⡏⣸⠇⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾⢠⡟⠀⠀⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣠⡀⢸⠇⣼⠁⠀⠀⣿⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠻⠑⡿⢠⡟⠀⠀⢠⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⣼⠁⠀⠀⣼⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⢠⡏⠀⠀⢠⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⡟⢴⡇⣸⡅⠀⠀⣼⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣼⢃⡏⠀⠀⠀⡿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡿⣸⠃⠀⠀⢸⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⡿⠀⠀⠀⣾⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡗⢠⣾⢸⡇⠀⠀⢀⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇⣼⠁⠀⠀⣸⢃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⣧⡟⠀⠀⠀⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⣿⠇⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢴⠆⢰⣿⣿⠀⠀⠀⡿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠁⣹⣿⡏⠁⠀⢸⡇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⣿⡇⠀⠀⣾⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⠀⠀⢰⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣤⣀⣸⣿⣟⠀⠀⣼⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠃⠈⣿⣿⡏⠀⢠⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⣿⠀⠀⣼⢃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣄⣸⣿⣟⣠⡾⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⣿⠛⠉⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡏⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⣿⡃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣴⠟⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠿⠻⢿⠟⠛⠿⠿⡿⠟⢻⣿⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣾⣷⣾⣷⣾⣿⣶⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣶⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⢹⠟⣡⡆⢻⣿⣿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢿⠿⠟⣛⣭⣶⣧⣶⣾⣿⣷⣶⣶⣶⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠀⠀⢾⣿⣿⢫⣝⣿⡿⢿⣿⣋⡍⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⢻⣿⣦⣿⣿⣿⡌⢿⣿⣵⣾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣛⠻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢦⠀⠀⠀⠈⢿⣿⢋⢸⢿⠘⡘⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡜⣎⢧⣅⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡐⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣦⠻⣿⣌⡻⣿⡿⢟⣠⣴⣆⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⠟⣤⣶⣿⣿⣿⣿⣌⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡁⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⣾⣇⣿⢸⠗⢯⣸⡯⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠈⠈⠉⠈⠉⠈⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢹⣁⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠛⢳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢠⣤⣤⣠⣀
⠀⠀⠀⠀⢀⣶⣿⣶⡿⣿⣷⣿⣦⣴⣾⣿⣿⣦⣤⣄⣀⣀⣀⣀⣤⣴⣶⣶⣿⠿⢻⡿⢻⠿⠛⢙⣻⣿⣿⡴⡀
⠀⠀⠀⠀⣾⣿⠃⠉⠀⠉⠉⠉⠙⠻⠟⠹⡟⢿⣻⡿⢻⢿⣿⠿⣿⠿⢿⠿⠛⠀⠀⣠⣤⣄⣀⠉⠉⣀⣽⣷⣿⠂
⠀⠀⠀⣸⣿⡿⠄⢀⠠⣴⣾⣶⣶⣶⣶⣦⣤⣌⣉⡀⢈⡀⠀⠀⠡⢀⣀⣤⣤⣤⣾⣿⣯⣦⡌⣄⠀⠀⣤⣶⣿⢛
⠀⠀⠀⢸⡿⠃⣴⣄⣨⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠇⣿⠀⢀⣙⣿⣋⠝
⠀⠀⠠⠀⠀⢸⣇⠀⢹⣿⣇⠀⠈⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢄⠀⠀⠘⠀⣿⠀⣠⣏⣉⡁
⠀⠀⠀⠂⠀⢨⠷⢄⡀⢻⡟⠀⠀⠀⠐⠂⠀⠀⢀⠉⠻⣦⡀⠀⠀⢻⣃⣴⠶⠆⠐⡇⠀⠀⢰⡟⢐⣿⣌⣻⠃
⠀⠀⠀⠀⠀⠸⣆⠀⠀⢸⣇⢠⣀⣘⣻⣄⡀⠺⠿⣦⣀⠀⠀⢀⣰⣿⠿⡇⠀⠐⠿⠃⠀⠋⢸⡏⢸⣿⠡⠟
⠀⠀⠀⠤⠀⠄⢹⣟⠁⠘⢿⣮⠙⡋⠹⣏⠛⠁⠀⢈⣿⢿⠿⠛⠻⠇⠀⡁⠁⣰⡇⠀⢈⠂⢹⡧⢼⣿⣀⡤⡀
⠀⠀⠀⡀⠀⠾⡿⠝⠀⠒⠈⣿⣧⡹⢶⡟⠛⠷⠶⠟⢁⡇⠀⠶⣦⣄⣠⡿⠉⡿⠠⠤⠸⡆⠈⢿⡾⣿⠈⠀⠘⣄
⠀⠀⠀⠰⠂⠈⣇⠻⠇⠚⠉⢸⣿⠉⡙⡶⠂⠛⠺⣆⠈⢻⣦⠀⣼⠇⠹⢦⣤⣴⠤⠄⢘⡌⡉⠈⣿⣽⣧⣉⡁⢿⣷
⠀⠀⠀⠀⠰⠄⠹⢐⡒⠒⠀⢸⣿⢀⡄⡆⠀⣦⣤⣉⣁⣼⡟⠛⠏⢰⡀⠀⠳⠀⣴⣤⠞⠁⢨⡃⠘⣿⢿⣶⣴⣾⣿⡆
⠀⠀⠀⠀⠸⡀⠈⣀⣥⣤⠄⢸⣿⣎⢠⠴⠏⠁⠉⠙⢿⣍⠀⢰⣶⢿⠿⣶⣶⣾⢿⡍⠋⢀⣿⠀⠲⠪⣿⣷⣀⡤⣿⣷
⠀⠀⠀⠀⠀⡉⠀⣺⠛⠀⠀⣼⣯⣸⠁⠠⣀⣠⣴⡄⠈⢙⡿⠋⢹⠋⠀⢽⡇⠀⠋⠁⢀⣿⠁⡄⠐⡀⣿⣿⠉⢽⣿⣿⡆
⠀⠀⠀⠀⠠⠐⠀⣾⣟⠋⠀⣽⡇⢹⣤⣀⣈⣠⠈⣿⣋⣹⡇⠀⠾⢦⣴⠖⣸⡷⠶⠶⠾⠋⢰⠅⢸⠇⢼⠫⣑⣚⣿⣿⠁
⠀⠀⠀⠀⠰⡀⠀⣿⠃⠀⢸⣿⡇⢈⡜⠛⣿⡁⣀⣾⠋⠉⠓⢦⡤⠚⠣⣀⣿⡀⣶⢤⣴⡾⠋⣐⡏⣱⡿⠛⡮⣽⣿⠏
⠀⠀⠀⢸⠀⠀⢠⣿⡧⠀⢿⣿⣧⣺⠀⠀⠺⠋⠁⠉⢻⢶⡗⠀⠻⠦⠼⣿⡟⢛⣥⣾⣿⣿⢿⣿⣿⡯⡈⠢⣹⣿⠇
⠀⠀⠀⢨⠁⠀⠘⣿⡟⢀⢾⣿⣧⠙⠓⢤⣀⣴⡖⢀⡠⢀⡻⠶⢤⣤⣴⠿⢣⣿⣿⣿⣿⢾⣿⣿⡛⠟⢳⣠⣼⣿⠇
⠀⠀⠀⢸⡀⠀⠀⠹⣶⡇⢏⡹⠻⣿⣶⣄⠀⠀⠧⣬⡄⠈⢡⡀⠐⠛⠁⢄⠸⣿⣿⣿⡄⣤⣄⣀⣙⣢⣶⣿⣿⡏
⠀⠀⠀⠈⡏⠀⢘⡄⠙⢷⣽⣿⣿⣿⣭⣹⣿⣦⠀⠀⠻⠾⠟⠛⠷⠄⠀⢸⠀⠙⣿⣷⠛⠈⠿⡿⢿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠘⣄⠀⠙⣆⡀⠙⡔⣻⣿⢿⣿⣿⠻⣿⣆⢀⠅⢀⣴⢦⣤⣼⠿⠀⠀⠈⠻⣿⣧⠄⡹⣆
⠀⠀⠀⠀⠀⠈⣇⢄⠠⣽⣶⣌⣻⣿⣿⣿⣿⣿⣿⠟⢺⠀⠈⡇⠀⢀⣤⣾⣿⣿⣿⣶⣼⣿⣿⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠘⢶⣶⡈⢊⣸⣿⣿⣿⣿⣿⣿⡏⠀⢸⠀⢸⡇⢠⣿⣿⡿⣯⠙⢿⣿⣿⡿⠚⠉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⠿⣿⣿⣿⣿⣿⡃⠀⠼⠀⣾⣧⣿⣿⠋⠆⠀⠀⠀⠻⢿⣷⣬⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠀⠟⢣⣀⣀⣴⡿⣿⣿⡷⣴⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠉⠁⠐⠛⠉⠃⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠤⠖⠚⠉⠉⠓⠢⡀
⠀⠀⠀⠀⠀⡤⠚⠉⠉⠉⢉⡹⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⣠⠔⠚⠉⠛⠒⠦⣄⠀⠀⠀⠈⠳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠳⣀⣀⣀⣀⣀⣀⣀⣀⠴⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠜⠁⠀⠠⣏
⠀⡇⠀⠀⠈⠓⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠉⠁⠀⠀⠀⠀⠀⢸
⢀⠇⠀⠀⠀⠀⣿⡈⠙⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠋⠀⡸⠀⠀⠀⠀⠀⠀⠀⢨
⠸⢄⠀⠀⠀⠀⡟⡇⢠⠇⠌⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠖⠉⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡼⠀⠀⠀⢸⡡⠃⡏⢸⠀⠀⠀⠙⠉⠉⠓⠦⣄⣀⣀⣠⠤⢤⠀⠀⣀⡤⠴⠚⠉⠛⠋⢄⠁⠂⠀⠀⠀⠀⠀⠠⢹⡆⠀⠀⠀⠀⠀⠀⠠
⠀⢧⠀⠀⠀⣾⡁⠀⠘⣎⢄⠀⠀⠀⠀⠀⡀⠠⠀⠂⠉⠀⠀⠈⠉⠉⢀⡀⠀⢀⡀⠀⠀⠀⢡⠀⣀⣀⣀⡠⠔⠁⢸
⢠⡏⠀⠀⠀⣷⡇⠀⠀⣸⢀⠃⠐⠀⠈⠁⠀⠀⠀⠀⠀⡀⠤⠐⠂⠈⠀⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠈⠢⡀⢸
⠈⡇⠀⠀⠀⢸⡇⠀⠀⣇⠈⠀⠀⠀⢀⡀⠠⠀⠂⠁⠉⠒⢠⠄⠀⠀⢀⣀⡀⢀⣀⣀⠀⠐⠁⠀⠀⠉⠢⡀⠀⠈⢾
⢀⡞⠀⠀⠀⡼⡇⠀⠀⠈⢳⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠁⠂⢄⠀⠀⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣔
⠘⣇⠀⠀⢀⠇⡇⠀⠀⠀⢣⡁⠠⠄⠀⣀⣀⣀⠀⠀⠤⠀⠀⠐⡲⠉⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠈⠐⠐⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈
⣰⠋⠀⠀⠘⡄⣇⠀⠀⠀⢸⡀⠀⢀⡀⠤⠀⠀⠀⠠⠤⢀⡀⠐⠀⠀⠀⠀⠠⠊⠉⠁⠀⠀⠨⠐⣤⣀⠀⠀⠀⡠⢾⡀⠀⠀⠀⠀⠀⠀⢠
⡇⠀⠀⠀⠀⠱⡘⡄⠀⠀⠀⠑⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢌⠀⠀⣧⠀⠀⠀⠀⠀⠀⠸
⢧⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢀⡏⠀⡀⠤⠀⠒⠒⠀⠤⢀⠀⠀⠀⠀⠈⠁⠒⢅⡀⠀⠀⠈⠁⠒⠠⢀⡀⠀⠀⠡⡴⠁⠀⠀⠀⠀⠀⠀⣴
⠈⡇⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠁⠑⠀⢀⠳⡀⠀⠀⠀⠀⠀⠀⢘
⠀⢧⠀⠀⠀⠀⠀⢰⠙⡆⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠴⠒⠒⠒⠲⠤⣄⠀⠀⠀⠀⠀⢀⠠⢢⠞⠁⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠙⠢⢤⣀⣠⠼⡆⢿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡤⠤⣄⣈⡡⠴⢇⡀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⡄⠀⠀⠀⠀⠀⠀⡞⢠⠏⠀⠀⠀⠐⠋⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡇⠘⣄⠀⠀⠀⣀⣀⡀⠀⠀⣀⣄⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠳⣄⠀⠀⠀⠀⢀⡜⢁⡞⠀⠀⠈⠉⠛⠋⠉⠉⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠳⣦⢄⡴⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢈⡏⠀⠀⡸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠖⠛⠒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠟⠉⠀⠉⠀⠀⢀⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠙⠓⠛⠛⠲⣤⡤⠤⣤⡀⣀⣀⡀⣀⣤⣤⣤⡴⠚⠓⠲⡏⠀⠀⠀⠀⠀⣀⡠⠔⠚⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⡀⠀⠒⠦⣄⣀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠉⠉⠙⠋⠀⠀⠈⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠤⠤⣀⣀⣀⣀⣀⠤⠤⠤⠤⠖⠒⠊⠉⠉⡀⠀⠀⢀⣼⣀⣤⠀⠀⠀⡄⠀⠈⣷
⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⢄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⣀⣀⡴⠓⠶⠒⠋⠀⠀⠹⣄⠀⠀⡇⠀⣰⠇
⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⢻⡗⠒⠚⠳⢤⣤⣤⠴⠷⣤⣤⠴⠛⠳⠶⠶⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇⠀⢀⡿
⠀⠀⠀⠀⠈⣧⡠⠄⠀⡇⠐⠂⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠂⠀⡇⠐⠻⣆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⡇⠀⠀⣹
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⡀⢠⡇⢀⣴⠏
⠀⠀⠀⠀⠀⠸⣆⡠⠀⠘⡆⠀⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢸⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢱⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⡼⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢧⠐⠂⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠁⢠⠃⠀⠊⢿
⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⠀⠈⢧⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠀⢀⡎⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠳⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣠⠴⠶⠦⣤⣠⣤⣤⣠⠶⠒⠾⠃⠀⠀⢀⠞⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠃⠀⢀⡾⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠴⠃⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⡤⣴⠛⢧⠀⠀⠀⠀⢸⠁⠀⠀⠀⠒⠤⢄⣀⣀⣀⡠⠤⠖⠊⠁⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡾⠀⠀⠀⠀⢠⡏⠉⠂⠀⠀⠀⠀⢠⠤⠶⠛⠛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠀⠀⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠃

⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣟⣿⣿⡿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⠟⠃⡀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡟⢉⡝⠀⠀⠀⢩⡟⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠉⠀⢰⠀⠀⠀⠀⠀⢠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⢀⣽⣒⡠⢖⣢⣀⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡏⠀⠈⠑⠋⢹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠓⠦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⢀⣼⣿⣶⣄⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠬⠭⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠉⠉⠉⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣶⣶⣒⣒⣒⣒⣒⡲⠤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠛⠒⠒⠒⠒⠒⠒⠒⠲⠯⣵⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠂⢀⡤⠆⠀⠀⠰⢤⡀⠐⣇⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠇⠀⢈⣀⡀⠀⠀⢀⣀⡁⠀⢸⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣿⠀⢰⡋⠄⢹⡆⢠⡏⠠⠙⡆⠀⣿⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡟⠀⠀⠓⠶⠊⠀⠀⠑⠲⠚⠀⠀⢻⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇⠀⠀⠀⠀⢤⠀⠀⡤⠀⠀⠀⠀⢸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢈⡷⢾⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠜⠁⠀⠳⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣀⣠⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠲⢄⣑⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣬⡑⠦⣉⠃⠢⡀⠀⠀⠀⠀⠀⠀⠈⠰⢀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⠁⠂⠄⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠖⠂⣉⣉⡙⠻⠿⣶⣤⣈⠑⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢀⡀⠀⢠⡏⣰⣾⣿⣿⣿⣿⣿⣷⣦⢉⡛⠀⠀⠈⠐⠄⠀⠀⠀⠀⠂⠀⠈⠄⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣌⣧⠹⣿⣿⣿⣿⠙⠿⠿⠃⢼⣿⣷⣤⡀⠀⠀⠑⢦⡠⠒⠁⠘⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣌⠛⢿⣯⣴⣦⣀⣦⣿⣿⣿⡿⣿⣦⠀⠀⠀⠁⠀⠠⡀⢁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⣿⣿⣿⣿⣶⡀⠀⠈⠿⣿⣿⣷⡀⠄⠀⠀⠀⠡⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⣿⣿⣿⣿⡏⡐⠀⠀⠘⠿⢿⣿⣷⠀⠀⠀⠲⣀⣀⠅⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⣀⣄⢀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠐⣛⣿⣿⡆⠀⠀⢰⠀⠀⢸⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢄⠀⠈⡇⢸⣿⣿⣿⣷⣿⡶⠖⠀⠀⠦⠀⠙⣮⣿⡇⠀⠀⠈⠀⠀⡜⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣦⡄⠀⢨⠳⣄⢹⠀⢻⣿⣿⣿⣯⣍⣀⠠⠄⢠⣘⣷⣿⡟⠀⠁⠀⠄⠀⠀⠃⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠆⠀⠉⠀⠀⢙⣿⣭⣭⣙⡟⡓⠠⣴⢻⣿⡿⠁⠀⠀⣤⠃⠄⠘⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⢐⠀⠀⠀⣰⣿⣿⡧⠂⠈⢹⣿⣷⣿⠿⠃⠄⠀⠀⡞⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⠃⠠⣡⡟⠀⠀⣰⣿⣿⡿⠃⠀⠀⣾⡿⠟⠁⠀⠀⠀⣠⠊⡴⠋⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠁⠛⠁⠀⢠⣿⣿⠟⠃⠀⢺⡾⠋⠀⠀⠀⠀⡀⢢⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡇⠀⠀⠀⠀⣾⣿⡿⠀⢀⣿⠂⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣇⣀⣼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠃⡠⠀⠀⠀⡈⠻⡏⠉⠉⢹⠀⠀⠙⠀⠊⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠵⢿⣤⠂⠀⠀⠙⠁⢸⣶⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⡸
⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠂⠀⠀⠀⢹⡇⠃⠀⠀⠀⠈⣿⡇⠀⠾⡧⠠⠀⡧⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⢘⣭⢴⡬⢠⣤⢤⠤⠀⢀⠘⡭⠀⡀⠀⡀⡄⢻⣧⡀⠸⣿⡀⠃⠁⠀⠀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠙⢤⣄⣄⣀⣐⣲⠒⠈⠀⠀⠀⠂⠀⠀⢧⡂⠘⡿⠿⠓⠛⠓⠂⠐⠚⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⠀⠐⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠐⠒⠒⠒⠒⠒⠀⠘⠉⠁

⠀⠀⠀⣠⡤⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠑⣦⣄⡀
⠀⢠⣾⣡⣤⣀⣀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⠀⠀⢀⣴⠟⠀⠙⣄
⢀⡟⠋⠉⠉⠉⠻⢷⣦⡀⠀⠈⠓⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠁⠀⠀⢀⣠⣴⠿⠉⠀⠀⣰⠛⡆
⢸⠁⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⠉⠉⠉⠙⢦⣠⠤⠤⣄⣀⡤⢤⣀⡴⠒⠲⠤⠊⠁⠀⢀⣠⣴⡾⠿⠋⠁⠀⠀⣠⣿⡇⠀⢧⡀
⠈⢧⣀⣠⠴⣦⡀⠀⠀⠀⠀⠙⠻⠷⢶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⠾⠿⠛⠋⠁⠀⠀⢀⠖⣾⠋⠁⣿⠁⠀⡼⠁
⠀⠘⡇⠀⠀⣿⡟⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉⡇⠀⠀⣿⠀⠀⡷
⠀⣰⠃⠀⠀⣿⠁⠀⠀⡸⠉⢓⡶⠚⠋⠉⠳⢄⣀⢀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣤⠤⢤⠴⡞⠉⠙⢻⣹⡁⠀⢀⣰⡇⠀⠀⣿⠀⠀⣧
⠸⡅⠀⠀⠀⣿⠀⠀⠈⣷⠋⠉⠀⠒⣄⡠⠖⠚⠙⠛⠳⢤⡀⠉⡩⠖⠦⣍⠉⡟⠉⠉⢢⡀⠙⣆⠀⠀⠉⢀⡴⠋⢸⠁⠀⠀⣿⠀⠀⡇
⢀⡿⠀⠀⢸⣿⠀⠀⣠⠏⠀⣀⣠⣤⣼⡅⠀⠀⠀⠲⣄⠀⠙⠶⠃⠀⢠⡈⠳⠃⠀⢀⡀⠙⢦⣹⡄⠀⣠⠞⠀⠀⣸⠀⠀⠀⣿⠀⠀⣇
⢸⠀⠀⠀⢸⣿⠀⠀⢹⣆⡞⠁⠀⠀⠀⠈⠂⠀⡀⢀⡽⠳⣄⣀⡤⠴⠒⠛⠒⠲⠦⣼⣙⣆⠀⠀⠉⠉⠁⠀⠀⢀⣿⠀⠀⠀⣿⡇⠀⢸⡄
⠘⡆⠀⠀⠘⣿⠀⠀⢼⡙⣄⠘⠳⠶⠟⠛⠉⠉⠉⢻⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣄⡀⠀⢀⣠⡴⠋⢸⡄⠀⠀⣿⡇⠀⢸
⣸⠁⠀⠀⠀⣿⠀⠀⠀⠑⣌⠓⠶⠶⠶⡶⠋⠉⠁⡼⠋⠀⠀⠀⠀⣀⡤⠶⠒⠲⡄⠀⠀⢸⣃⡴⠛⠉⢹⡞⠁⠀⠘⡇⠀⠀⣿⡇⠀⠈⣧
⣸⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡆⠀⣄⢸⡀⠀⠐⠚⠁⠀⠀⣀⠴⠊⢁⡞⠁⠀⡴⠁⠀⣠⠎⠁⣠⡀⢀⡞⠀⠀⢠⡄⢳⠀⠀⢹⣧⠀⠀⡏
⣇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⢧⠀⠘⣆⠙⠒⢶⣦⡶⣶⠋⠳⡄⢠⠾⢦⡀⠀⡇⠀⠀⠁⠀⡴⡿⠀⠘⠁⢀⣴⡿⠁⠈⡆⠀⠘⣿⠀⠀⠙
⢸⡀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠘⣧⠏⠉⠑⢤⡏⠀⢻⡇⠀⡄⢹⡿⠀⠀⢹⠀⣸⠶⢤⡴⠚⠰⡇⠀⠀⣠⡾⠋⠀⠀⠀⣇⠀⠀⢿⡇
⢸⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢠⡟⢀⣄⠀⢸⠃⡀⢸⡇⢠⠇⠈⠁⢠⣦⠸⠾⠁⠀⠀⢹⣀⡴⠛⠒⠛⠉⠀⠀⠀⢀⡴⢹⠀⠀⢸⣷
⢸⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡼⣧⡜⣿⠀⠸⠀⡇⠘⠁⢸⣆⠀⢀⣼⣳⣄⣀⡴⣇⠀⠘⠿⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⢸⠀⠀⢸⣿
⠸⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⠀⠀⣿⠀⠀⠀⣇⠀⠀⢸⣬⣿⣿⣤⣄⠀⠉⠉⠉⠓⢦⣀⣀⣠⠏⠙⠛⣻⠉⠀⠀⣀⡼⠀⠀⣸⣽⠀⢠
⠀⠙⢦⣀⡀⠀⢀⣠⠴⠋⠀⢿⡄⠀⠸⡄⠀⢠⠏⠳⠴⡿⠁⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠙⠉⠓⢦⡠⠞⣁⠀⣀⡰⠃⠀⠀⣠⣻⠃⠀⢻
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢘⣷⠀⠀⠙⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣄⣀⠉⠉⠉⠉⠁⢀⣀⣤⣾⠟⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣆⡀⠀⣀⣀⡀⠀⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠉⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠉⢻⠉⠀⠳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡄⠀⠀⠄⠀⡀⢠⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⢀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠒⠺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉