I love you this much Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣴⣿⡇⠸⡇⠀⢻⠋⠛⢢⡀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⣶⣦⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⢸⠀⠀⣰⣣⢶⡖⠀⡴⠋⣿⢠⠞⢹⡇⣷⠀⡇⠀⠀⠀⢹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠼⠖⠋⠁⠻⠞⠷⠆⠳⠖⠋⠘⠲⠺⠀⠙⢶⡇⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⡇⣂⡀⢈⢀⡀⠀⠀⣀⡀⠀⢀⢀⣄⢘⣧
⠀⠀⠀⠀⠀⠀⠘⡠⠪⡇⠞⠀⠈⠡⣌⡛⢉⠓⢟⠀⠀⢇⣸⣷⡙⠫⠾⠀⠀⠀⢦⠇⠠⠼⠾⠗⠀⠠⠻⠡⠧⠜⠤⠤⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠈⢳⡤⠴⠚⠋⠉⠉⠙⠓⠿⣄⣀⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣞⣩⠗⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠣⣼⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣏⠀⠀⢠⠟⠦⣄⣀⡀⡰⢉⡝⠀⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣸⡴⠋⠀⠀⠀⠀⢉⣉⣙⠒⠒⢻⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⡏⠐⠋⠉⠁⠤⠄⠉⢀⡈⠁⠀⠀⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢳⡀⠀⢺⡒⠦⣴⣚⣩⠇⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣙⣻⣥⣚⣁⣀⡤⠞⠁⠀⠀⠀⢀⣀⡤⠾⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡚⢳⣀⣀⣀⣀⣀⣀⣀⡤⠤⡞⠙⠭⠽⠁⢳⡒⠒⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⢤⣀⣀⣀⡀⠀⠀⢀⣀⡨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡏⠀⠀⠀⢸⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠀⠘⠳⠒⠋


⡿⢿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠒⠂⠀⠀⠀⠀⠐⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠖⠲⠄
⠀⠀⠀⠀⠀⠀⠞⠁⣠⣴⡶⠶⠶⠖⠒⠒⠂⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣤⡶⠒⣄⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⢰⣷⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⢰⣶⠀⠀⠀⣰⣿⠏⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣠⣴⠿⠋⠀⠀⣸⣿⡟⠀⠀⠀⠂⠀⠀⠀⠀⢀⣼⣿⠃⠀⣰⠏⠀⠀⠀⠀⠠⡣⠀⠀⠻⠀⡞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣄⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⡠⠚⠁⠀⢀⠀⠀⠀⠀⠁⣀⠀⠀⢸⠀⠃⠀⠀⠀⠀⡀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠛⠀⠎⠀⢈⣿⣿⠀⠀⢸⣿⡟⠀⠀⣀⠀⠀⠀⠢⠤⣼⣿⡟⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⢠⣿⣷⠀⢸⡄⠀⠀⣠⣾⡿⠋⣷⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠾⠟⠋⠀⢀⣾⣿⠃⠀⠀⠈⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⣰⣿⣿⠁⠀⡙⠀⢰⣿⣿⠇⠀⢠⠳⣄⣰⣿⠏⢀⡼⠋⠀⠃
⠀⠀⠀⠀⠀⠀⣇⠀⠄⠀⠀⠀⠀⢀⣾⣿⠃⠀⡀⠀⠠⢤⡀⠀⠀⢸⣿⡇⠀⠀⡰⣿⣿⠃⠀⠀⠀⢠⣿⣿⠏⠀⣰⠃⠀⣸⣿⠏⠐⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣤⡴⠿⠛⣡⠞⠁⠀⢸⣷⡀⣿⠀⠀⠈⢿⣇⡠⠊⠀⠹⣿⠀⠀⠀⠀⢸⣿⠇⢀⡼⠁⠀⠀⢿⣿⡀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⡀⠀⠀⣼⠁⠀⠀⣰⣿⣿⠁⠏⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⣸⡇⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⡿⠁⠀⣴⡁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⢠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣿⡿⠁⠀⣠⣿⣿⠏⢀⣴⣿⣿⡁⡀⠀⣀⣼⣿⠇⠀⢀⣾⣶⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢻⣿⠁⡀⢀⣿⣿⠏⠀⣼⣿⠏⠀⡙⠁⠈⣼⣿⠏⠀⢠⣾⣿⠏⠀⠀⠀⠀⢸⣷⡄⠀⠰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣼⣿⠏⠀⠀⣿⡟⢀⠜⠀⠀⢰⣿⡏⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠂⣀⡠⠤⠤⠤⠄⠄⣼⣿⠏⠀⠀⠀⠈⠛⠁⠀⠔⠀⠈⠛⠃⠀⠀⠿⠏⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣴⠋⠀⠀⠀⠀⠀⢀⣼⡿⠋⠉⠐⠲⢤⣄⣀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠃⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡇⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢰⣷⠀⠀⠈⠙⠻⢷⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⡿⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠖⠛⢉⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠛⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⡠⠂⢁⠤⠒⣦⠔⡀⠀⠈⠀⠀⠃⠀⢸⢀⠁⠀⠠⠊⠁⡠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⢟⣸⠁⠀⣸⠀⠀⢰⠀⢸⠘⠀⢀⠁⠀⠀⣁⣀⣀⠧⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡄⠀⠰⡀⠀⠈⡏⠴⠛⠙⠆⠀⠀⣴⢄⠳⠖⠞⠆⠀⠀⡅⠀⠀⢀⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣈⠬⠁⠀⠈⠢⠤⠈⠁⠭⠊⠀⠀⠀⠘⢄⣀⠰⠃⠀⠀⠀⠀⠢⠄⢈⠀⠬⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡇⠀⡇⠀⠌⠠⠉⣿⡆⠀⠁⡇⠘⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣗⠓⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣶⡇⠀⡶⠾⡀⠰⠀⣹⡷⠾⡀⣇⣾⠀⢸⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢦⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⡅⢠⠀⠀⠈⠐⠒⠉⠀⠀⠈⠉⠁⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢧⡀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠁
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠻⡄⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⢾⠉⠿⣕⢦⣄⠀⠀⠀⠀⠀⠀⠱⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠸⡄⠀⠈⠳⢌⡓⢦⡀⠀⠀⠀⠀⠙⣄⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⢦⣉⠳⣄⠀⠀⠀⠈⢣⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠉⠳⣌⠓⢦⡀⠀⠀⠙⢆⠀⠳⣄⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠱⣄⠈⠳⢄⡀⢀⣀⠤⠴⠛⠒⠢⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠙⢦⡀⠀⠈⢳⣄⠀⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢆⡰⠏⠈⠣⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⢠⠿⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣠⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠓⠂⠒⠒⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢘⠉⠉⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢤⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠚⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢀⡴⠃

⠀⠀⠀⠀⠀⠀⢠⣤⠤⠤⠤⢤⢤⢀⣀⣀⡀⠀⠀⠀⢀⣠⡤⠶⠢⠤⡀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣯⣀⣀⡀⠀⠀⣀⣀⣀⡥⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠳⡿⠋⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠚⠛⠛⣿⡁⠀⠀⡟⠛⠛⠁⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⢰⣿⣧⣀⣀⣀⣀⣀⣉⠁⢙⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠻⣷⡀⠱⡀⠀⢰⣿⠃⠠⠀⣠⣴⠶⠒⠦⡄⠀⢀⣤⡤⠤⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⢤⡿⠃⠠⢃⣾⡟⠁⠀⢴⣤⠀⠂⢻⣿⠀⠈⠀⠀⠀⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠈⠁⡠⠁⢸⣿⠃⠀⠀⠀⣿⠀⠀⣼⡿⠀⠸⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⢀⠁⠀⢸⡏⠀⠐⠀⢀⣿⠀⠰⣿⡇⠀⡄⠀⠀⢀⣿⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⠀⠀⣿⡇⠀⠀⣀⡼⠃⠀⡆⣿⠇⠀⡃⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⣼⠁⣿⠀⠀⣇⠀⣠⣿⠏⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠃⠀⠀⠈⠻⠿⢶⡶⠶⠚⠁⠀⣿⣄⠀⠀⠉⠉⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠖⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⡀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠈⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠳⠆⠀⢀⣀⣀⣀⡤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢼⣿⢥⣤⡜⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⠀⠀⠀⠉⠐⠂⠤⢶⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣣⣀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠘⢧⠴⣤⠀⠄⢻⢒⠁⣤⣄⣤⡔⢤⡀⠀⠀⠀⠀⢀⠴⠉⠀⡴⠋⠉⠓⠒⠂⢈⣅⢀⣀⣀
⠀⠀⠀⠀⠁⠙⠩⠂⠼⡍⣿⡗⠻⠟⢛⠃⠀⢁⠢⢀⠀⠄⠁⠀⣡⠊⠀⠀⠀⠀⠀⠀⠘⠋⠻⠋⠿
⠀⠀⠀⠀⢼⣿⣥⣵⣾⡇⢠⣶⣶⣾⣿⣿⠀⣸⣷⣴⣴⣶⣾⣿⣿⡀⠀⠀⠀⠀⡆⢰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣠⣤⣬⣽⡿⠷⣌⠻⢿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢻⡀⠻⣿⡿⠟⠁
⠀⠀⠀⠀⠉⠁⠉⢷⣤⣴⡉⠓⣦⣬⣷⣾⠿⠿⠿⠿⠿⣿⣿⠿⠿⢿⣿⣿⣿⠿⠶⠷⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢤⡄⢀⣠⠞⠀⠹⣧⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠈⠉⢉⣁⣴⠖⢤⣀⡴⣾⡇⢠⡿⢀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣼⣿⠓⠒⣻⠇⢸⣿⡇⣸⡇⣾⣿⣡⡿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⠏⢿⣇⣴⡟⠀⢹⣿⢁⣿⠀⣿⡇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⠏⣀⡀⠉⠁⣀⠀⠀⠛⠿⠃⠀⠈⠛⠖⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡴⠋⠀⣿⡇⠀⣼⣿⠇⢀⣤⣤⣀⣤⣶⡄⢀⣴⡄⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠚⢸⣿⡶⣿⠛⢺⠏⣼⡿⣠⢿⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⢿⣠⠎⠀⠻⠟⠁⣿⡏⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⣛⠻⣷⣄⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢠⣾⠁⠀⠸⣿⡆⠀⠢⣀⡐⠚⠄⢀⠀⠀⣠⡟⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣾⡇⠀⠀⢰⣿⡇⠀⠀⠀⠙⣀⠀⠜⠀⢰⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠛⠃⢸⣿⠀⠀⠀⣼⡿⠀⣠⠖⢦⣴⠀⢠⡶⢲⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠙⠆⠀⣾⡏⠀⠀⣼⡿⠁⢰⣿⠀⣼⡇⢀⣿⠁⢸⡏⠀⣠⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣀⣀⣾⠟⢀⣠⡾⠛⠀⠀⠘⠿⠞⠻⠶⠋⠻⠶⠻⠷⠞⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⠍⠄⠉⠉⠁⠀⢀⣠⣤⣴⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⡠⠁⠂⠀⠀⠀⠀⡿⠟⠋⣩⣭⠍⢭⣭⠍⠩⣉⠉⣉⣩⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠃⠀⣰⡾⢻⡆⣠⣠⣤⠘⣿⡄⣰⢿⡆⢠⠏⠀⢸⣇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢰⡿⢀⡾⠃⠻⢿⠟⠀⠸⣷⠏⠘⣿⡎⠀⠀⣸⣇⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠛⣿⠟⠋⢁⣤⣄⠀⠀⣤⠀⣩⠄⢀⣬⣤⠀⠀⠉⢉⡭⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⣿⠀⠀⣾⠁⣿⣇⣼⡏⢠⡟⢠⣿⡵⠏⣰⠢⡎⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣇⠀⠀⠿⡶⠟⠉⠻⠷⠿⠶⠋⠿⡶⠞⠁⠀⠈⢢⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡴⠟⠋⠙⠻⣶⣦⣤⡶⠀⢲⣶⠐⡶⠂⣴⠖⠲⣄⠐⢶⡖⠀⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⡄⠈⠉⠀⠀⠀⢹⣿⠁⢸⣿⠀⠀⣿⠆⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠄⠓⠚⠀⠒⠀⠀⠂⠀⠼⠿⠀⠀⠻⠦⠴⠋⠀⠘⠷⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡟⠀⢀⠀⠀⢻⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⢣⠀⠳⡀⡇⡆⠀⠀⠀⢸⠀⡾⠀⡜⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠸⠸⡀⡎⡆⠄⡆⡈⠂⢰⠠⢸⢣⢀⠇⠇⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡜⡎⡀⡇⠁⠙⠁⠣⠃⠸⠜⠈⠋⠘⢸⠀⢰⢣⠃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⢢⠀⡑⠥⠁⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠬⢀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠠⠈⠦⢃⣠⠤⠤⠤⠤⣄⡀⠀⠀⢀⣠⡤⠤⠤⢤⣀⠘⠔⠁⠇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢆⡔⠉⠀⠀⠀⠀⠀⠀⠉⠢⡴⠋⠀⠀⠀⠀⠀⠀⠙⢢⡰⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠈⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠁⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠗⢄⡌⠢⡀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢀⠔⢡⡠⠺
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠙⠀⠈⠢⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠔⠁⠀⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⣄⡈⢮⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣴⢁⣠⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⢋⣘⡭⠋⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢭⣃⡙⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣴⡿⠋⠘⣄⡀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⣀⡠⠖⠉⠀⠀⢀⡠⣦⣌⠻⣷⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⣴⠟⠀⣱⣦⡤⢀⣀⣈⠑⢢⡔⢊⣁⣀⡀⠤⣴⢲⡟⠻⣿⡙⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠿⡦⢼⡏⢠⡷⢿⡆⣼⠇⣶⡞⠃⠀⠘⢷⣼⡏⠈⠿⣦⠿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⢿⣁⣸⣿⠏⠀⣿⣯⡅⠀⠀⢀⣿⡧⠴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠒⠒⠤⣄⠀⠀⠀⢀⡤⠄⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠀⠠⡄⢠⠀⠀⠳⡀⡔⠋⠀⠀⠀⣄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⠀⠀⠉⠀⢀⣀⣀⣿⠀⠀⠀⠀⠂⠏⠀⠀⠀⡉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋⠀⠀⠀⠀⠀⠰⡏⠀⢹⠁⢇⣰⠋⠘⡆⠀⠀⠀⠀⠘⠲⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇⣠⠋⢀⣴⡿⢦⡀⠌⠁⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⢠⡾⢉⠁⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣔⠄⠀⠀⣀⠀⣀⢀⣠⣀⡴⣤⣀⣿⣿⣼⣦⣶⢈⢳⣤⣄⣀⣠⣼⢏⢻⣶⠼⠁
⠀⠀⠀⣀⣠⣤⠶⠾⠛⢿⣿⣿⣿⣿⣠⢹⡟⢿⣿⣷⡟⣉⣹⣧⣿⣽⡜⣆⣿⣿⣿⡌⡟⠿⣾⢯⣿⠉⠙⢿⣿⣿⡶⣶⣄
⠀⠺⣿⣟⡍⣰⣠⣼⣶⣾⣿⣥⣽⣿⣿⣎⣁⣿⣭⣯⣧⣼⣾⣿⣶⣿⣷⣿⣽⣿⣿⣷⣷⣷⣿⣿⣿⣾⣿⣻⣻⣿⣗⣾⡿
⠀⢀⣯⣭⣴⣿⣿⣿⡿⡿⠛⠛⠛⠛⠛⠛⠛⢛⡛⣛⡟⠙⠛⠛⢿⢯⠉⠉⠉⠉⠉⠿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠃
⠀⠞⠛⠉⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⣿⡾⠗⠋⠀⠀⠀⠀⠘⣾⡆⠀⡄⣀⢠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠀⠀⡀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢁⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠔⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠆⠀⢠⠠⢦
⠀⠰⠀⠀⡄⣀⠀⠀⢹⠀⠀⠀⣴⣩⠀⠦⠀⠀⠀⡰⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠂⠈⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠰⠠⣰⠁
⠀⠀⡀⠀⠐⠈⠀⠀⠆⠀⠀⠐⠁⠎⠀⢠⠚⠁⢠⠉⠂⠠⠤⠤⠄⠐⠀⢀⡌⠉⠑⡄⠀⠀⠀⠀⠀⠘⠀⢁⠌⠀⠀⢠⠄⢀⠴⡀⠀⡀⠀⢀
⠀⠀⠀⡀⠁⠒⠂⠊⠀⠀⠂⠀⠈⠀⠀⠠⠀⠀⠀⠳⢀⠐⠀⠐⢀⠀⠁⢀⡅⢀⠔⢀⠄⠋⠀⡀⠀⠀⠀⠈⠀⠐⠀⠀⢂⠀⠋⢀⠾⠅⠀⠘⠃
⠀⠈⠈⠅⠀⠀⠀⠀⠎⠀⠈⠀⠀⠄⠀⠀⠀⠈⠑⡀⠀⠀⠙⢄⠀⠀⠔⢈⡙⠈⠀⠀⠦⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⣀⡠
⠀⠀⠂⢄⠀⠀⠀⠘⠀⠊⡐⠂⠘⡐⡀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠉⡠⠂⠀⠉⠰⡀⠀⠀⣂⡹⠆⠀⡂⠂⠀⠀⡔⠁⠈⢠⣠⢮⢁⠂⠑⡄⠁
⠀⠠⠄⠈⢠⠈⡁⠄⠡⠁⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠢⠀⠀⢖⠈⢀⡀⠈⡀⠀⠑⡀⠀⡀⠄⣀⣠⡄⠤⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⡇⡠
⠀⠁⠀⠀⠀⠈⠤⣀⠀⠀⣐⠂⠀⢀⢀⠀⢹⠤⡠⡀⠂⠋⠁⠀⠘⠒⠁⠐⢾⣿⡀⠀⠇⠀⠽⠔⠉⠀⠑⢄⠀⢀⠔⠁⠀⠀⠀⢠⠂⠂⣼⠀⠔
⠀⠠⡀⠀⠠⠀⠀⠈⠈⠉⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⡀⠔⢈⢌⠐⠀⡁⠀⠀⢈⠀⠊⡠⠀⢠⣾⣿⣿⣷⣆⠁⠁⠀⠐⠈⠒⠀⠀⠈⠁⠀⢆
⠀⠠⠀⠜⠀⠀⠀⡩⠡⢠⠀⢑⠀⠀⠉⢁⠀⠀⠀⢈⡀⠈⠀⠐⠀⢀⡁⠀⠀⠀⠀⠥⠐⠀⢻⡿⣻⣿⣿⣿⠀⠀⠑⢀⠀⠄⡁⠀⠉⡀
⠀⢀⠀⣘⠉⡂⠀⠉⠁⠀⠀⠀⠀⠈⠫⠀⠃⠀⠀⠀⠈⠂⢄⡠⠐⠁⠀⠀⡀⠄⠀⠀⠀⡀⠈⠻⠿⢿⡟⠁⠀⠘⢙⠄⠐⠀⠠⣁⠌⠐⡁⠀⠄
⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠊⡐⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⠁⠀⠐⡂⠠⠀⠀⠀⠀⢠⣄⠃⠀⠁⠴
⠀⠑⠀⠐⠀⠀⠀⣀⠀⢀⠀⠀⣠⣤⣤⣴⣶⣶⣦⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠀⠢⠀⠀⠀⠠⠠⠐⠁⠘⠀⣥⠔⠉⡀⠴⠒⠃⠈⠆⠀⠂⡎
⠀⡓⠠⠀⠀⠀⢀⠆⢋⣠⠁⣸⡇⢀⠟⠟⠋⠀⢿⡇⠀⠀⠀⠠⠈⠑⠤⠀⠢⠀⠀⠀⠋⠐⠂⠘⠀⠀⢀⡰⡌⠤⠐⠒⠲⠐⠂⠈⠈⢲⡊⠁⡄
⠀⡀⠃⠀⠀⠀⠁⠀⠀⢚⡆⠹⣦⣈⣀⣤⣼⣷⡿⠃⠀⠀⠀⠈⠢⡀⠀⠀⠐⠀⠀⠀⠑⠀⠠⠂⠀⠀⠒⠃⢀⠀⠀⠀⠣⡀⡀⣀⠀⠔⠁⠘⠕
⠐⢭⠂⠀⠀⠀⠀⠀⢀⠠⠊⠀⠉⠙⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⢆⣠⠁⠁⠂⠀⠀⠂⠀⢀⢀⠈⠃⠠⡀⠑⢄
⠀⢄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡄⢀⠀⠐⣄⠊⠀⠀⠀⠎⠁⠰⠃⠀⠀⢤⠂⠠⠌⡀⠠⠀⠄⠡⠃⠀⠀⠓⢄⠇
⠀⢀⠈⠀⠂⣄⢀⠀⠀⠀⠀⠀⠀⡀⢤⠐⢀⠁⠇⠀⠘⡎⠌⠀⠈⠀⠄⠀⠀⡀⠀⠂⠄⡀⠁⠀⠀⠂⠀⠀⠀⠘⠁⠀⠀⠯⠕⢀⣴⣶⣶⣦⡀
⠀⠸⠈⠠⠈⠀⡀⠀⡄⠀⠙⠄⢀⡀⡀⠑⢌⠁⠄⠀⢀⠀⠀⠈⠂⠠⠤⠄⠊⢀⠄⢄⠀⢠⣴⣿⡇⠀⡀⠀⠀⠀⠀⠀⡀⡀⠀⣿⣏⠉⢉⣿⣷
⠀⠀⠆⠀⠀⠀⠀⠀⡀⢁⠲⠌⢀⠠⠀⠀⠀⠑⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⢹⣏⣴⡄⣥⢰⡖⠸⣟⠀⣧⠰⡄⠹⢿⣷⣾⡿⠏
⠀⢀⠊⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⢣⡎⠁⠀⠀⠡⠀⠀⠀⠀⢀⡀⠈⠀⡰⠃⠤⠀⠤⠠⡀⢸⡿⢿⣥⠛⣠⣿⢠⣿⠂⠨⠄⠓⡀⠀⠚⠁
⠀⠀⣙⣀⣀⣀⠀⠀⠠⢤⡀⠠⠀⠀⡇⠰⣶⣶⠀⠀⠀⡑⢢⡇⡇⡈⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⠀⠀⠀⠀⠀⠦⠀⠐⠀⠀⠰⠰
⠀⢨⠀⠀⠀⠨⠅⠀⡁⠀⠀⠀⠃⠀⣧⠀⠙⠋⠀⠀⠀⢣⠀⢀⠀⠀⠀⠀⠀⣶⣴⡄⠀⠀⠀⠀⠱⠀⠠⠃⠀⠰⠂⠀⠀⠀⠐⠀⠀⠀⠀⢀⠄
⠀⠁⠀⠐⠀⠀⠈⠀⠃⠐⠈⠐⠀⠀⠘⢆⠀⠀⣀⡅⠞⠼⠀⢼⠠⠦⢀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠁⠤⠉⠀⠅⠀⠀⠆⠀⠀⠀⠀⠐⡀
⠀⠠⡤⢠⡄⢠⡄⠀⠘⠀⠈⠀⠀⠀⠈⡁⠂⠀⠉⠀⠸⠀⠀⠀⠀⠰⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠒⠡⠠⠃⠀⠀⠈⠀⠈⠂⠁
⠀⠀⠠⡆⢰⠆⠀⠀⠀⠀⠀⡒⢀⠀⠐⡀⡁⠀⠀⠀⠀⠀⢺⡷⠀⠆⠀⠁⠀⠀⠀⡀⣀⡅⢀⠀⠀⠀⠀⠀⡒⡱⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐
⠀⠁⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⣾⣿⣦⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣦⡀⠈⠉⠁⣴⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣄⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⣠⣶⣿⣿⣿⣷⣄
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠻⣿⣿⠇⠀⠀⠸⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠻⣿⣿⣿⣿⠞⠛⣿⣿⣿⣿⣶⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠟⠀⢠⣄⠀⠀⠀⠀⣠⡄⠈⠻⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠙⠛⠀⠀⠙⠛⠀⠀⠀⠈⠉⣿⡧⠀⠺⠟⠀⠀⠀⠀⠻⠗⠀⢼⣿⠉⠁⠀⠀⠀⠛⠋⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⡐⠊⢸⠀⠀⠀⠀⠀⠀⣀⢸⠁⠯⢲⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⢠⠤⢼⡉⢣⠱⡀⠑⠞⡳⠀⠀⢀⡠⢔⡩⢃⠀⠀⠀⠀⡠⠠⢼⠁⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠰⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠑⢄⡉⠘⠆⠈⠢⠊⣠⠀⠀⠀⢛⠁⠀⢰⠆⠀⠀⢀⠀⠀⠀⠤⠒⠈⠙⠆⠀⠀⠀⠀⡠⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢨⠠⠦⡑⢄⠀⠉⠒⠆⢀⡰⠞⡁⡀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⢀⠄⠀⠀⠀⢀⢡⠇⠀⠸⠕
⠀⠀⠀⠠⡒⠢⡀⠀⠣⡐⠸⢈⠀⠀⠀⠠⠃⠀⠘⠤⠅⠀⠀⠀⠀⠀⠀⠤⠒⡆⠀⡄⠺⠇⠀⡠⠔⠁⠀⠀⠀⠀⠚⠛⠄⡀
⠀⠀⠀⠀⠱⡀⠙⣄⡠⡈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡖⢤⠀⠀⠀⠄⠔⠀⠀⠰⠤⠒⠁⠀⡔⠠⡄⠀⠀⠀⠀⠀⠰⠩⠂
⠀⠀⠀⠀⠀⠑⣄⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⡞⢠⢣⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡡⠐⠒⠂⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢣⣼⠁⣎⠎⢠⠃⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⣠⠆⠀⠀⢠⠄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡯⠔⠋⣨⣾⡎⢀⠃⠀⠀⠂⡁⢚⠔⢈⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠐⠈⠀⠀⠀⠀⠀⢠⠒⠁⠁⠀⠀⠀⠙⢤⣴⠿⠋⠁⡹⠊⠀⠀⠀⢄⢄⠒⢰⠎⠀⠐⠐⠊⠢⡀⠀⠐⠏⠇⠀⠸⠁⢀⠜
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠑⢄⠔⠊⠀⠀⠀⡀⠀⠀⠉⠳⣞⠀⠀⠀⠀⠀⠀⠈⠁⠈⠂⠤⠤⠒⠀⠁⠀⠀⡠
⠀⠀⠀⠀⠴⠈⢨⠗⢄⠀⠀⠀⠀⠀⠀⣠⠌⢢⠀⠀⠀⠀⠀⡠⣊⠜⢣⠀⠀⠀⠹⡄⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈
⠀⠀⠸⣄⡠⠒⠁⢠⠨⡆⠀⠀⠀⠀⠀⠈⢀⣈⡀⠀⠀⠀⠀⠻⡁⠀⠊⠇⠀⠀⠀⢽⡀⠀⠀⠑⠀⠃⠀⠀⠀⠀⠤⠌⠀⠀⠘⡀
⠀⠀⠀⠈⢂⠀⠀⠐⠔⠁⠀⠀⠀⡀⢀⢠⠃⠀⠈⠄⠀⠀⠀⢐⠳⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⢀⣀⡀⠐⠉⠑⡀⠀⢰
⠀⠀⠀⢰⠉⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡜⠁⠀⠈⠁⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠠⠠⠂⠀⠀⡠⠤⣀⠀⠀⡠⠤⠄⠀⠱⡀⠀⠀⠀⠀⠀⠇⠤⠜
⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠈⠁⠛⠒⠒⢒⢣⠀⠀⠀⠀⠘⠄⠌⠀⠀⡄⠆⠨⣂⡈⢀⢁⠜⠀⠀⠈⠑⠄⠀⢀⠜
⠀⠀⠀⠀⠀⢀⢉⠓⠦⣅⣰⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠁⠈⠠⢀⠀⠀⠀⠀⠈⠠⠷⢿⣷⠛⠃⡄
⠀⠀⠀⠀⢠⠂⠌⡐⠠⢁⠎⠑⠀⠀⠀⠀⢀⠔⠻⣌⢢⡀⠀⠀⠀⠈⠀⠀⠀⢐⠀⠁⢹⣿⠁⠀⡃⠀⠀⣀⡀⠤⢤⣆
⠀⠀⠀⡴⢁⢊⠈⡐⠡⠂⠀⠀⠀⠀⠀⣴⢁⠀⠀⠈⡳⠟⠀⠀⢀⠊⠀⠀⠀⠘⠀⠀⢸⣿⣀⢀⡤⠀⠀⠓⠚⠋⠉⠉⡀⠀⠀⠀⠀⠀⢄
⢀⠀⠠⠀⠉⠛⡶⢠⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠊⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⢨⠤⡀⠀⠀⠫⠂⠀⠀⠒⠐⠁
⠀⠀⢀⣀⣀⣀⡅⡄⠀⠀⠀⠠⠄⠁⠀⠀⠀⠈⠣⠃⠀⠀⠀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠁⠡⠀⠀⠀⠑⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣃⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣾⠟⠉⠻⣷⡀⠀⣿⡇⠀⠀⠀⣸⡇⠀⢠⣾⠟⠉⠻⣷⡀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⡏⠀⠀⠀⠹⣷⠀⣿⣷⠀⠀⠀⣿⠀⢠⣿⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⠀⢻⣿⠀⠀⠀⣿⠀⣼⣿⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⠀⢸⣿⡆⠀⢸⡇⠀⣿⣿⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢿⣧⠀⠀⠀⢰⡟⠀⠀⣿⣇⠀⣼⠇⠀⢸⣿⡖⠋⢡⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⣄⠀⣀⠘⢿⣦⣀⣴⡟⠀⠀⠀⠘⣿⣤⡿⠀⠀⠀⢻⣷⣄⣼⠇
⠀⠀⠀⠀⢀⣉⠀⠀⠀⢀⣀⠀⣀⠈⣉⣉⠉⣀⠀⣉⡉⠁⠀⠀⣀⣀⣀⡈⢉⣀⡀⠀⠀⠀⠈⠉⣁
⠀⠀⠀⠀⢯⠈⠣⣀⠀⠈⣿⣠⣿⣾⡟⣿⣦⣿⠀⣿⡇⠀⠀⠀⠉⣿⡟⢱⣿⠻⣷⠀⠀⠀⣠⠞⢉⡇
⠀⠀⢠⠤⠬⣗⡶⠬⠷⠦⢹⣿⡇⣿⡇⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⠀⠶⠯⠵⣖⡯⠤⢤
⠀⠀⠈⠓⠒⣫⠽⢒⡿⠛⠈⣿⠀⣿⡇⣿⡿⣿⠀⣿⡇⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⠀⠻⣗⠲⢭⡓⠒⠋
⠀⠀⠀⠀⠀⠧⠤⠊⠀⠀⠀⣿⠀⠻⣷⡿⠃⢿⣷⡿⠁⠀⠀⠀⠀⣿⡇⠈⢿⣾⠟⠀⠀⠈⠳⠤⠇
⠀⠀⠀⢠⣤⣤⣤⣤⣤⡀⢠⣤⡄⢠⣤⣤⣤⣤⡄⠀⢀⣤⣴⣦⣤⡀⢠⣤⣤⣤⣤⣤⠀⢀⣤⣶⣶⣤⣄
⠀⠀⠀⢸⣿⡏⠉⢹⣿⡷⢸⣿⡇⢸⣿⣏⣉⣉⡉⢀⣾⣿⠛⠙⠿⠟⢸⣿⣏⣉⣉⡋⠀⣾⣿⣏⣉⣛⠋
⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⢸⣿⡇⢸⣿⡟⠛⠛⠃⢸⣿⣧⠀⠀⣀⡀⢸⣿⡟⠛⠛⠃⠀⢈⡛⠿⠿⣿⣷
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⢸⣿⣷⣶⣾⣷⠀⠻⣿⣷⣾⣿⠟⢸⣿⣿⣶⣾⣿⠀⢿⣿⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⠈⠁
⠀⠀⠀⠾⠷⠲⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠘⣿⣿⠃⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⡀⠰⠉⡃⠀⠀⠀⠀⠀⠀⠀⢰⠋⠾⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡀
⠀⠀⠀⠀⠈⠂⠐⠁⠀⠀⠀⢠⣤⣸⠙⢆⠱⡀⠸⠤⢲⠄⠀⠀⠀⣀⡴⣪⠧⠀⠀⠀⠀⠀⡠⢤⡞⠁⠀⠈⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡈⠳⡨⡆⠘⢦⡠⠊⠀⠀⠀⠘⠗⠊⠁⢀⡄⠀⠀⠀⡎⠀⠀⠑⣀⠤⠐⠲⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⣓⢦⡀⠈⠳⢅⣸⠀⢀⣠⠞⠋⠀⠀⠠⣼⠀⠀⠈⠁⠀⠀⠀⡇⠀⣠⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⡜⣹⠁⠉⡷⡆
⠀⠀⠀⠀⣠⢤⠀⠀⠳⡘⢌⣣⢱⠀⠀⠀⢀⡴⠗⠁⡜⠑⡀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠇⢀⣿⠋⠀⠀⡠⠞⠀⠀⠀⠀⢸⣶⡃⠀⠀⠈
⠀⠀⠀⠀⢳⡀⠱⡄⠀⠈⠢⠤⠜⠀⡠⠠⠊⠀⠀⠀⠈⠉⠁⢀⣄⠀⠀⠀⠀⡉⢀⠆⠀⠘⡀⢉⡠⠖⠉⢀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢄
⠀⠀⠀⠀⠀⠳⡀⠘⠖⢱⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣠⣾⡿⢀⡗⣄⠀⠀⠈⠈⠀⠀⠀⠉⠁⠀⠀⠀⡁⣉⠇⢀⣀⣀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠑⠤⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⣏⠑⣸⠁⡜⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠊⠁⠀⠀⠑⠂⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣨⡷⡏⡸⡿⠁⡸⠀⠀⠀⣀⢀⠔⠒⡄⠀⠀⠐⠀⠠⣶⡓⠀⠀⠐⢎⠁⠀⠀⠸⡄
⠀⠀⠀⢀⡔⠄⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⢠⡿⠚⢁⣠⣼⠷⡁⡰⠁⠀⠀⠃⡔⠈⠎⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠸
⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⢪⡉⠀⡀⠀⠀⠀⠀⠲⣔⠯⠋⠁⣠⠜⠁⠀⠀⠀⠣⣡⣌⠹⡿⠀⠀⠓⠊⠉⠢⣀⣀⣈⠯⠛⠀⠐⠇⢋⠴⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠈⠓⠤⠊⠁⠀⠀⠀⣀⠀⠀⠈⠙⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠒⠉⠀⠀⠀⢀⡐⢱
⠀⠀⠀⢀⡴⠎⢀⡽⠳⡀⠀⠀⠀⠀⠀⠀⣀⠌⢱⠀⠀⠀⠀⠀⢀⣴⣯⠜⠃⡀⠀⠀⠈⢧⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠑⠀⠈
⠀⠀⠐⣇⢀⠞⠋⠀⡠⢰⠀⠀⠀⠀⠀⠀⠈⠁⣈⡀⠀⠀⠀⠀⠈⢛⠁⠀⢎⠇⠀⠀⠀⠸⣇⠀⠀⠀⠃⠀⠃⠀⠀⠀⢀⠀⠤⠁⠀⠀⢳
⠀⠀⠀⠈⠣⡀⠀⠀⠢⠔⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⢢⠀⠀⠀⠀⡔⡧⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠑⢆⠀⠀⡇
⠀⠀⠀⠀⠖⢳⠀⠀⠀⠀⠀⠀⠀⠔⠉⠈⠙⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⡔⠉⠉⠑⠂⠀⠀⠘⠀⠀⡇
⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢀⢀⢄⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣸⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠂⠶⠄⠀⠀⡼⠀⠀⠀⠀⠀⠠⠀⡠⠀⠀⡎⢠⢌⠢⢀⠊⠄⡄⡇⠀⠀⠑⠦⣀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢸⢾⢬⡐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠐⠢⡀⠀⠈⠁⠀⠀⠐⠬⣂⣱⣷⣥⣾⣋⠀⠀⠀⠀⠀⠀⠉⠐⠊
⠀⠀⠀⠀⠀⢠⠂⠆⡸⢩⠓⡷⢄⠀⠀⠀⠀⠀⢀⣠⣞⢦⡀⠀⠀⠈⠐⢢⠀⠀⠀⠀⡈⠭⠩⣿⡧⠀⠐⡃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡰⢁⠎⡔⢠⠃⠜⠀⠀⠀⠀⠀⠀⡴⠋⠀⠙⣤⢓⡄⠀⠀⠀⡰⠀⠀⠀⠀⡄⠀⠀⣿⡇⠀⠀⡇⠀⠀⣶⣚⡭⠭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠜⢱⢦⡊⡰⢁⠊⢄⠂⠀⠀⠀⠀⠸⠱⠀⠀⢀⡴⠋⠀⠀⠀⡔⠁⠀⠀⠀⠀⢇⡀⠀⠿⠧⠤⠴⠃⠀⠀⢩⠀⠀⠀⠀⣧⢄⠀⠀⠀⠀⢈⠅
⠠⠅⠂⠀⠆⡀⢸⠃⠗⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣴⢁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠆⠀⠀⠈⠊⠀⠀⠀⠉⠁
⠀⠀⢠⡤⡄⡦⢼⠼⠄⠀⠀⠀⡒⠃⢸⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⡁⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠺⠅⠠⠄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢲⡆⠀⢰⠖⠲⡖⠒⢲⡀⠀⠀⠀⢲⣆⠐⡖⠀⠒⣶⠒⢲⡆⠲⡖⠒⢲⡄⠀⡤⠀⢦⠀⠀⠀⠐⢶⣐⡶⠂⢠⡖⠲⡄⠲⡶⠒⣶⠂⢰⡆
⠀⠀⠸⣷⣷⣼⠀⠀⡷⢾⢈⡀⠀⠀⠀⢸⠻⡆⡇⠀⠀⣿⢾⣃⡁⠀⡷⢾⢈⡁⠀⣿⠀⢸⡇⠀⠀⠀⠈⣿⠁⠀⣿⠀⠀⣿⠈⡧⠀⣿⠀⢸⡇
⠀⠀⠀⠿⠻⠏⠀⠴⠷⠤⠾⠇⠀⠀⠠⣼⣦⠿⠷⠀⠤⠿⠤⠾⠇⠤⠷⠤⠾⠇⢤⣿⣤⠾⠁⠀⠀⠀⠶⠿⠦⠀⠘⢷⡴⠏⠀⠻⡶⠟⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⡙⠛⠓⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣼⡅⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⣿⣄⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⣩⠏⣸⡟⣠⠂⠀⠀⠀⡀⠀⠀⠀⠀⠛⢿⣿⣆⢀⠠⠀⠀⠙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠁⠀⣹⣿⠇⠀⢀⠔⢉⣤⠴⠶⡀⠀⠠⣀⠙⣿⣀⠀⡁⠀⠇⠈⠛⠑⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⢀⡞⢁⡠⠖⠚⠋⠀⠀⠈⢻⣾⡏⠀⢡⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣄⢠⣟⡔⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⢨⣄⠀⠀⠀⠀⠀⠀⠪⣧
⠀⠀⠀⠀⠀⠀⣇⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢰⠈⡇⠠⡆⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⢀⠿⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⢃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣁⠀⠀⠀⢰⠀⣷⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⡴⠃⠀⠁⠰⣦⡳⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣶⣄⠀⠀⠀⠀⠀⣀⣼⣿⣷⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣯⣴⣶⣿⣿⣿⣿⣷⣤⣄⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠈⣆⢻⡀
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⣿⣿⣿⣆⠈⠙⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣇
⠀⠀⠀⠈⡿⠷⣶⣄⠀⠀⠀⠀⠈⢻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣥⡀⠀⢻⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡹⡆
⠀⠀⠀⠀⣻⠀⡀⠈⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠉⠁⠀⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡄
⠀⠀⠀⠀⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣷⡀
⠀⠀⠀⠈⡇⠀⠀⠀⠰⢶⣤⡀⠀⠀⠀⠀⠘⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢻⣿⣀⠀⠀⠀⠀⠀⢻⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠠⠱⡀⠦⡐⢾⡇
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠁⠘⣿⣷⣦⣀⣀⠄⠀⠀⠀⠀⠂⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⢐⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠘⡹⢿⣷⣦⣥⣲⣥⣵⣤⣾⡿⣿⠏⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠪⣻⡿⠟⣿⡿⣿⣿⠉⣰⡏⠀⠀⠀⢀⣴⠟⠁⠀⢱⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠈⠻⢷⣤⡀⠀⠈⠁⠀⠈⠘⣡⣿⠇⠀⣿⣷⡔⠀⢠⠟⠁⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠈⠛⠿⣷⣶⣤⣒⣴⣿⡿⠋⠀⠀⠹⣿⣷⡀⢀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⠍⠉⣹⡿⠋⠀⠀⠀⠀⠀⠈⠻⢿⣾⣿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢛⣛⣶⣄⡴⠖⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⣿⣿⣿⣿⣴⣾⣿⣿⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣻⣿⣿⣿⣿⣿⣿⣿⢧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣿⣟⡻⣿⣽⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡴⠶⠶⠶⠶⠶⠶⣤⣤⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠄⠀⣠⣴⣶⣦⣤⣴⠶⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⢠⣿⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣷⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣷
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣿⠿⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠈⠛⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠉⠛⠿⢶⣤⣄⣀⣀⠀⣴⣿⣿⣿⣿⣿⡄⢀⣀⣀⣠⣤⠶⠞⠋⠁⠀⠀⠀⠉⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣀⣀⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠛⠛⠛⠲⠶⣤⡀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠶⢦⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡄
⠀⠀⠀⠀⢠⠎⠀⡤⣰⡄⠀⠀⠀⢀⣤⣄⠀⠀⠀⠠⣿⡇⠀⠀⢀⡴⢲⡄⠀⠀⠀⠴⣦⠀⠀⠹⣦
⠀⠀⠀⢠⡏⠀⠈⠳⢿⣾⠏⠛⢀⡿⢸⣿⠀⠀⠀⠀⢀⠀⣴⡆⢾⣇⡼⠁⣶⠄⠰⠈⡋⠙⠆⠀⠹⣇
⠀⠀⠀⣼⠀⠀⢠⠁⢸⣿⠀⠀⣸⡇⢸⡇⠀⢀⡀⠰⣿⠀⢹⡗⠘⠛⠓⠋⢀⡤⠀⢸⡇⢂⣀⠀⠀⣿⡀
⠀⠀⠀⣿⠀⠀⢧⠀⢸⣿⠀⠀⣿⡇⡾⠀⣼⠋⢻⡆⡹⢷⠾⠁⠀⣠⠴⣤⠸⣿⠀⢸⣧⣛⡸⠂⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠈⠳⣾⣿⠀⠀⢿⡿⠁⠀⢙⠷⣸⠟⠀⠀⢠⣶⠀⣿⡀⢻⡧⠛⠓⣊⡀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠸⡇⠀⠀⢀⡬⣻⡆⢀⡼⣿⡀⢀⡟⠛⠁⢰⡟⠀⢸⣿⠀⣮⣭⠟⠀⠀⢿⡠⡌⢷⠀⠀⢀⡿
⠀⠀⠀⠀⢻⣄⠀⠸⣼⠵⠁⡊⣀⠙⠛⠋⠀⠀⠀⡸⣧⣀⡼⣿⡰⠃⡀⣀⠀⡀⠀⠀⣠⠟⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠈⠳⢭⠈⠝⠀⢀⡤⠊⠀⣈⠭⠔⣿⡀⠘⠧⣌⣧⠽⠋⠉⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠛⠒⠛⠉⠀⣠⡞⡵⣊⠁⣿⠉⠑⠒⠂⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⢿⣇⠳⠽⣰⠏⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠙⠛⠚⠁⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⢀⡠⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢤⣀⢖⡗
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣠⣤⡀⣠⠴⠂⠀⠠⠒⠲⣄⠀⠀⠀⠀⠀⠀⠙⢮⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠀⡸⠀⣎⡴⠞⢻⠀⡄⠀⡴⢾⠶⠶⠃⣠⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⢸⠀⠀⡸⠀⣇⣰⠀⠘⠶⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡷⠃⠀⠀⠘⠶⠚⠁⠀⠈⢡⣶⣦⣤⡤⠖⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠊⢧⣀⣠⠞⠀⠀⢠⠀⢀⡆⠀⣩⡍⠙⡆⢧⠀⡴⣇⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣀⠌⢡⠀⡹⣥⡤⠃⠈⠋⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡴⠊⠀⠀⠀⠀⠀⠀⢠⣞⣶⣤⢶⣥⠄⠠⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡴⠒⠋⢁⣇⣼⡃⢀⣄⣠⠞⡇⠀⡏⠀⡙⡸⠃⢀⣣⠌⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⢋⡝⠁⠀⡗⠁⣼⠁⡐⠀⡠⠙⠋⠀⠛⠒⠋⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⠓⠒⠋⠀⠀⠼⠁⠀⠛⠀⠷⠊
⠀⠀⠀⠀⡄⠒⢦⣰⠏⢨⠇
⠀⠀⠀⠀⠛⢦⣄⠻⠀⡞⣠⣄⠤⡄
⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇⠻⣆⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⡠⠔⠒⠒⠛⠓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠘⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧⡀⢰⢻⠖⡄⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢠⠞⢹⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠁⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡰⠃⠀⠀⠀⠠⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠰⠹⢢⠀⠀⠀⡇⠀⠀⡤⠤⡴⠲⣄⣤⠀⡒⠆⢱⡔⠀⢹⠂⠀⢀⡖⢲⡐⠦⠂⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣧⠀⠘⣇⠀⠀⠀⡘⠹⡀⠀⠠⠸⡇⠒⠁⠀⠀⠀⠓⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⣓⠤⠖⠀⠀⠈⠂⠀⠀⠙⠢⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡴⢳⢤⣴⣦⠊⠹⠎⠳⣴⡆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⣿⠈⠦⡀⡀⠈⠸⣄⢀⠿⡀⠀⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⢀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⡈⠁⢸⢡⢆⣏⣴⠀⠈⠁⢠⠇⡴⣴⢀⢆⡶⠀⠈⠁⡞⢠⣷⣦⡆⡤
⠀⠀⠀⢀⣠⣄⡀⠀⢠⠖⠉⠀⠘⢿⣆⡙⠙⠋⠈⠐⢁⣀⡀⠚⠒⠓⢛⣋⣙⣐⠁⠀⠀⠓⡟⣑⠛⠛⠛⠁⠀⢀⣀
⠀⠠⡞⠛⠉⠈⠙⠶⡎⠀⠀⠀⠀⣼⣿⣿⡆⠀⢀⣴⣿⣿⠇⠀⢀⣴⣿⠟⣉⡀⠑⠀⠀⠀⠀⣿⣷⡀⠀⣠⣾⣿⣿
⠀⠀⠸⡄⠀⠀⠀⣀⣠⣤⡄⠀⠼⠧⣿⣿⣿⣠⣿⡿⣻⣿⠀⢠⣿⡿⠳⢌⠧⢼⣦⣤⡀⠀⢸⣿⢿⣧⣼⣿⢟⣿⡇
⠀⠀⠀⠳⣤⠤⠄⢺⣿⣼⣿⠂⠀⠀⠀⠻⣿⣿⡟⠀⣿⡇⡠⠛⠻⢀⡀⠼⠀⣸⣿⠀⠀⠀⣼⣿⢸⣿⣿⠋⢸⣿⠁
⠀⠀⠀⣞⠀⠀⠀⠈⡉⠉⠁⢦⡀⠀⢀⣤⠞⠉⠀⢰⣿⡇⠀⣄⠀⠻⠟⢀⣠⣾⠇⠀⠀⢀⣿⠟⠁⠙⣷⠀⣼⣿
⠀⠀⢠⡏⠀⠀⠀⢸⠁⠀⠀⠀⠙⣿⡟⠁⠠⠈⢳⠸⣿⡀⠀⢻⢀⣀⣄⠀⠸⠋⢀⣴⠟⠺⠿⠀⠀⠀⡾⠀⣻⣿
⠀⠀⠈⠉⠁⠑⠒⠐⣆⡀⠀⠀⡴⡽⠋⠑⢂⣄⠘⠀⠈⠉⠂⠉⠈⠉⠉⢭⡁⠀⠛⢄⠀⠀⠠⣼⣻⡦⠀⠀⠈⣩⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⠄⠀⢢⠄⠹⠟⠡⢤⠔⠁⠀⣠⠤⢀⠁⠀⡗⠀⠀⠈⢲⠖⠁⠛⠋⠁⠲⢤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⣀⡀⠀⠀⠈⢁⠀⠀⣾⡶⠀⠀⡠⠀⢸⡄⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠋⠀⠀⠘⠀⠀⠁⠈⠑⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢉⡴⠈⢻⣆⠀⠀⠀⠄⠀⠀⠀⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣼⠃⠀⢸⡿⠀⠀⠈⠄⠄⠀⣼⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡍⢠⡿⠀⢀⣿⠃⣾⠉⡿⢠⡞⢹⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⣠⡾⣁⣤⠟⠁⠀⠷⠾⠧⠚⠷⠾⠷⠋⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⠁⠀⠁⠀⢠⣴⡶⠶⠶⠶⠶⠦⣤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣬⠆⢀⡴⢦⢉⣁⡘⣿⠀⣿⡄⡹⠀⣿⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣾⣡⠟⠘⠿⠃⠘⠟⠈⠷⠁⠀⠿⠈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸⡏⠀⡴⣳⣄⣼⢀⡟⣰⣻⢆⢀⠤⠊⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣾⣁⠀⠷⠞⠉⠷⠾⠞⠻⠵⠊⠀⠑⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠉⠛⠷⠞⠈⢻⣤⠋⣴⠉⢳⡀⣿⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠿⠀⠻⠤⠼⠁⠻⠄⠄

⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢠⣶⡿⠻⢷⣦⡀⠀⢸⣿⡄⠀⠀⠀⢠⣶⠀⠀⢀⣴⣾⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⡏⠀⠀⠀⢻⣷⠀⢸⣿⡇⠀⠀⠀⢸⡏⠀⢠⣿⡟⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⣿⡇⠸⣿⣧⠀⠀⠀⣼⡇⠀⣾⣿⠁⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⠀⠀⠀⣿⠁⢀⣿⣿⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⡇⠀⢹⣿⡆⠀⢠⣿⠀⠘⣿⣿⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠸⣿⡆⠀⠀⠀⢠⣿⠀⠀⠘⣿⣇⠀⣸⡏⠀⠀⣿⣿⡛⠋⠁⣦
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠻⣿⣄⣀⣠⡿⠃⠀⠀⠀⠹⣿⣀⣿⠁⠀⠀⠘⢿⣷⡀⣰⡟
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠈⠙⠛⠋
⠀⠀⠀⠀⢠⡟⠳⣄⠀⠀⠀⢿⣇⢸⣿⣼⡿⣿⡆⣼⡗⠘⣿⡄⠀⠀⠀⠸⢿⣿⠿⢧⣾⠿⣷⡀⠀⠀⠀⢀⡴⠛⣷
⠀⠀⠀⠀⠈⠳⣄⣈⠳⣤⣀⠸⣿⣾⡇⣿⡇⢸⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⢀⣠⡴⢋⣀⡴⠏
⠀⠀⠀⣯⣉⣙⣶⠯⣉⣉⣉⡁⢿⣿⠀⣿⡇⢸⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⣈⣉⣉⡩⢷⣞⣋⣉⡷
⠀⠀⠀⠀⠈⢁⡴⠋⢩⡼⠋⠀⢸⣿⠀⣿⡇⢸⡿⢿⣇⢀⣿⠇⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⠈⠙⢮⡉⠓⣦⠈⠁
⠀⠀⠀⠀⠀⠈⠳⠖⠋⠀⠀⠀⠸⠿⠀⠻⢿⠿⠃⠘⠿⠿⠟⠀⠀⠀⠀⠀⠸⠿⠀⠈⠿⢿⠿⠀⠀⠀⠈⠛⠶⠋
⠀⠀⠀⠀⣶⣶⣶⣶⣶⣤⣄⠀⣴⣶⡄⢠⣶⣤⣤⣤⣴⡄⠀⢀⣤⣶⣶⣦⣄⠀⢠⣶⣤⣤⣤⣴⡄⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⣿⣿⡏⠉⢙⣿⣿⠀⣿⣿⡇⢸⣿⣟⢉⣙⣛⠁⢠⣿⣿⠟⠛⠻⡿⠇⢸⣿⣟⢉⣙⣛⠁⠀⣿⣿⣏⣉⡛⠟⠃
⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⠟⠀⣿⣿⡇⢸⣿⡿⠿⠿⠿⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠀⠀⠹⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⡏⠉⠉⠀⠀⠀⣿⣿⡇⢸⣿⣷⣤⣤⣤⣤⠈⢿⣿⣧⣤⣾⣿⠆⢸⣿⣷⣤⣤⣤⣤⢠⣾⣷⣦⣤⣾⣿⡏
⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠉⠀⠘⠛⠛⠛⠛⠛⠋⠀⠙⠛⠛⠛⠛⠉
⠀⠀⠀⢀⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠘⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⢿⡟⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠙⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠊⠈⠐⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢻⢀⡾⣆⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠁⠀⠈⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠸⢫⡜⣷⡆⡠⣴⢻⡇⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡄⠁
⠀⠀⠀⠀⠀⠀⠈⠂⣠⣤⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢻⡇⣵⡏⢟⣵⢸⡷⢋⣼⠂⠀⠀⠀⠘⢄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⣤⣄⣿⣿⡀⠀⠀⠀⠐⢡⠀⢁⡀⠤⠄⠀⠀⠀⠀⠨⢾⠰⢟⡥⣧⢞⢹⣀⣴⠟⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠁⠄⡀⠈⠀⠀⠀⢈⡀⠄⠂⠀⠀⠀⠀⠀⢹⣴⠏⡇⣡⣻⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠊⢡⡐⠋⠢⣀⠀⠀⣀⠔⠛⢀⡌⢱⠀⠀⠀⠀⡌⠀⠀⠉⠢⡄⠀⠀⢀⠔⠊⠁⠀⢱⠀⠀⠀⠀⣾⣿⣯⣕⠦⡀⠀⠀⢀⠔⠉⠀⠀⢡
⠀⠀⠀⠀⠀⢋⡝⠑⣬⠔⠙⢀⡐⠋⠢⣥⠊⢫⡙⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢂⣠⠋⠀⠀⠀⠀⡰⠀⠀⠀⠀⢿⢻⣿⣿⡯⣙⣄⡐⠁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠣⠁⠋⢑⣶⠚⠓⣶⡊⠙⠈⡜⠀⠀⠀⠀⠀⠀⢣⡀⡃⠀⠀⠚⠃⠀⠀⠀⠆⡰⠁⠀⠀⠀⠀⠈⢿⣫⢾⣿⡷⡺⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠹⡎⠁⣈⢹⡏⣅⠈⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠁⠀⢀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠳⡨⢿⣽⣿⣔⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡍⣤⣤⣹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡠⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡻⣿⣿⣇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡐⠉⠉⠑⠢⡀⠀⠀⢀⡤⠂⠈⠉⠑⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢣
⠀⠀⠀⣠⡖⠉⠀⠈⠉⠒⠴⣯⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⢆⢠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⢀⠄⠒⠉⠉⠉⢳
⠀⠀⠀⢓⡡⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⣠⣁⣶⡄⠀⠀⠀⠀⠡⠀⠁⠀⠄⠟⠁⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠙⢽⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡀⠣⡀⢀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠉⠚⠽⣢⠄⣀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⢻⣿⣿⠂⠙⢍⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣀⡄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠟⡶⣤⠆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠑⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⣸⠃⢀⣤⣄⡀⣠⢀⣄⠀⠀⠀⠀⠀⣰⣿⣿⣬⡍⣼⠛⡿⣦⣄⣀⣴⠀⠀⠀⠀⠀⣼⠀⠀⣀⠀⣀⠀⠀⡀⠀⠀⣿⠇
⠐⢹⣄⢾⢒⡟⢧⡿⣼⣞⣠⠄⠀⠀⠈⠁⣼⣯⡭⠵⠿⢾⣗⣋⠿⣻⣷⡾⠃⠀⠀⢠⡟⣵⣰⢝⡜⠉⡷⣸⣹⠂⣾⠛⠂
⠀⠀⠋⠈⠉⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠋⠉⠁⠛⠋⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⢒⡥⠀⠀⠀⠀⠀⠀⣀⣠⡄⢰⣶⡆
⠀⢠⠞⠉⠓⣴⠋⠉⠙⡶⠚⠥⠊⠁⠀⠀⠰⣾⡇⠙⠿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⣤⣤⣄⣠⣴⣄⠀⣠⠶
⠀⠘⢆⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢤⣄⠈⢿⣿⣿⣿⣿⡿⠀⣠⡤
⠀⢀⣨⠷⡃⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠧⣄⢸⡉⣹⢠⢋⡤⠀⠀⠀⣀⣠⠈⠻⣿⣿⠟⠁⣀⣀
⠛⠛⠀⠀⠙⣤⠞⠀⠀⠀⢠⡎⣩⠳⡴⣫⠙⢦⠀⠀⠨⠕⠀⠛⠋⠀⣉⠁⣀⡁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⢷⢾⡿⢃⠞⠀⠀⢠⠟⠀⡶⢰⠖⡟⠀⣿⣋⠀⠀⠀⠀⠀⡀
⠀⣰⢶⣦⣀⣶⣶⣄⠀⠀⠀⠀⠑⣄⢊⡴⠋⠀⠀⠀⠘⠓⠋⠙⠛⠀⠛⠉⠉⠁⠀⠀⠀⠀⠹⠳⠀⠀⠀⠀⢀⡴⠲⢄⡀
⠀⠹⣿⣿⣿⣿⣯⡟⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⣀⠴⠒⠲⡀⠀⠀⢦⡀⠀⣴⣋⣀⣀⣀⣈⡓⡄
⠀⠀⠈⢿⣾⡿⠋⠀⠀⠀⣀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣸⠦⢤⡀⠋⠀⠀⢠⠇⠀⠀⠁⠀⠀⡇⠀⣴⣤⣦⡀⠀⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣹⡤⢿⠀⢀⡀⢠⣄⠀⠀⠀⠀⠀⢧⡀⠉⠀⢸⠃⠀⢀⡴⠃⠀⠀⣴⡀⠀⠀⡇⠀⠈⠻⠋⠀⠀⡇
⠀⢲⠀⠀⣀⠀⡴⠦⡄⣶⢼⡆⣸⡻⣼⠧⠏⠘⠋⠀⠀⠀⠀⠀⠱⣄⡰⠛⣆⡠⠋⠀⠀⠀⠀⠋⠁⠀⠀⠓⠒⠒⠒⠒⠒⠒⠃
⠐⢻⠉⢰⣛⡟⠳⢤⡿⠛⠋⠙⠉⠀⠀⠀⠀⢀⣀⡄⣤⡄⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠾⠂⣠⡀
⠀⠘⠚⠉⠉⠀⡴⠊⡇⠐⣇⡀⣀⡄⣠⣄⣶⢈⡟⠧⠇⠛⠋⠀⠀⠀⠀⠀⠠⢦⣰⢰⠟⡦⠋⣧⡆⠀⠀⠀⠀⠰⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠲⠃⠘⣯⣞⡷⠧⠽⠟⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠈⠛⣡⣀⠉⠁⠀⣴⠋⠉⡓⢄⡴⠚⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⡴⢦⠀⠀⠀⠀⢯⣀⣸⢀⣀⡘⢁⣤⠀⠀⠹⡄⢀⠀⣈⠀⠙⡀⢠
⢀⡤⠤⠀⣀⡀⠀⠀⣀⡀⢀⠤⢤⠀⠀⠀⠀⠈⢣⣀⠇⠱⠤⠃⢾⠙⡇⠀⠀⠈⠉⠸⠹⠹⠸⠯⠆⠀⠀⠘⢦⠀⢠⠀⠃⡰⠋
⣠⠿⠂⢸⣿⣿⣷⣾⣿⣿⠄⠰⠯⡄⠀⠀⠀⠀⢀⣉⣀⣀⣀⣀⣈⡉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡤⠊
⠙⢂⡤⠄⠻⣿⣿⣿⣿⠏⠠⣤⠒⠁⠀⠀⠀⠀⢸⠑⢤⣄⣤⡴⠋⡇⠀⠀⠀⠀⠀⠀⣿⡇⢀⣀⠀⠀⢠⣤⣰⠀⠉
⠀⠈⠛⠒⠒⠈⠿⠟⠁⠒⠒⠋⠀⠀⠀⠀⠀⠀⢸⡠⠊⠻⠟⠣⣄⡇⠀⠀⠀⠀⠀⢀⣿⢁⡾⣭⡿⡆⢀⣿⣷⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣹⣞⣳⣞⣁⣳⣚⣈⣓⣊⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡿⠀⠘⠁⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⠀⠀⠀⠀⣾⠃⣰⣀⠀⡦⣶⡄⣅⡅⣴⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣸⡏⠀⢸⡟⢨⠃⢿⡇⡜⠀⣿⠃⡠⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢀⠂⣀⣰⡿⣀⡀⠘⠓⠁⠀⠈⠛⠀⠀⠛⠊⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠊⢁⡿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡾⢡⠞⣷⡄⠀⠙⠶⣄⣀⠀⢀⣀⠤⠚⠁⣰⡆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⡇⠀⣿⡇⠀⣶⠀⠀⡈⠉⠀⠀⣶⡆⠀⣿⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣿⡇⠀⣿⠀⠪⣠⡄⠹⡎⣿⡇⢠⠿⣇⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣸⣿⡀⠴⣿⠁⢀⡇⠈⠙⠉⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠻⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀⠀⣀⣀⠀⠀⢀⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⢹⣿⡀⠀⢹⣿⡀⠀⢨⠏⠀⢻⣿⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⣰⠏⠀⠀⠀⠘⠋⣀⣀⠀⠀⢿⣧⠀⡾⢿⣇⠀⡞⠀⠀⢸⣿⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠛⠷⢶⠏⠀⠀⠀⣤⣠⡀⠙⠋⠀⠀⠘⣿⣶⠃⠸⣿⣼⠁⠀⠀⣸⣿⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢠⡖⢰⡆⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠁⠀⠀⠀⠉⠉⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⣿⠒⠉⠀⣤⠴⣄⠀⣤⢠⣄⠀⣠⠤⡄⠀⠀⢠⡄⠀⣤⠀⣠⡴⣤⠀⣤⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⣠⡏⠀⠀⢸⡏⠓⣿⢺⡇⠈⡟⢺⡧⠞⢁⠄⠀⢸⡇⢸⣧⢾⡏⠓⣾⢛⡏⢀⣿⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠛⠛⠛⠳⠶⠋⠓⠚⠁⠀⠛⠊⠀⠀⠛⠒⠋⠀⠀⠘⢓⢽⡇⠈⠛⠒⠋⠈⠛⠋⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⣀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠈⢙⡋⠀⠲⠂⠒⠘⣿⠿⠀⠂⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⡞⣴⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡇⠀⠀⣠⢞⣿⡿⢀⣤⠖⠦⠀⣰⣦⢶⣆⡠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⡿⣿⣄⡜⠁⣸⣿⠁⣾⡏⢰⡧⣴⡿⢁⣾⠟⢠⡿⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢀⠞⠀⢹⣿⠀⠀⣿⡟⠀⠿⡤⠎⠀⠿⠁⠸⠟⠀⠺⠥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠤⠞⠁⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠉⠁⢀⠊⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡆⢀⡹⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⠀⠀⠀⠀⠀⡆⠀⢠⡀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠠⠒⠄⠀⠀⠄⣠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣠⡀⠀⠈⡝⢧⠀⠀⠈⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⣼⣁⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠁⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠂⠐⠀⠃⢤⡞⠁⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠛⢆⣠⠋⠁⠀⡀⠀⢦⡤⠖⠛⢣⠤⢄⡄⠀⠸⠁⠒⠃⣠⢄⡀⡀⠀⠀⠀⣸⡀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⡄⠀⠀⠀⢈⣏⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡀⠀⠦⠠⢦⠀⠀⠁⠀⠹⡄⠀⠀⠀⠈⢣⡔⠀⠀⢀⠀⠀⢄
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⢰⡇⠀⠀⠃⠀⢸⠁⠀⡠⠠⠀⠄⠉⠃⠘⠁⠀⠃⠀⠀⠀⠚⡇⠐⠁⡀⠀⠻⡄⠀⠀⠀⡀⠁⠈⠁⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⠛⠀⠀⠀⠈⣿⠁⠀⠠⠢⢸⡇⢀⠇⡄⠀⠀⠀⠁⠀⠈⠐⠂⡀⠀⠀⢀⡟⢂⠀⠡⠀⠀⣿⠀⠀⠀⡄⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡴⠲⠀⢀⠈⣃⢹⡆⠀⠀⠀⢈⣿⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⣀⣸⠁⠉⠀⠀⠀⠄⣿⣀⠀⢀⠴⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠃⠀⠀⠠⡄⠀⠻⣧⠄⠀⠀⠈⠈⢷⡀⣤⠀⢀⡄⠀⠀⠀⠀⠃⡀⠀⣸⡃⠀⠀⠀⠀⠐⢂⣿⠁⠀⠘⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣶⠆⠀⠀⠀⢠⣀⣿⠀⠀⠀⠀⢀⠀⠙⢧⣄⢠⠇⠀⠀⠀⠀⣘⣠⡾⠁⠀⠀⠀⠀⠀⠀⣨⣧⠶⠀⠀⣿⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠠⠜⠦⣤⣤⡂⠀⠀⣿⠀⠀⠀⠀⣈⠀⠀⢤⠙⠿⣦⣄⠀⢶⣤⠟⠉⠀⠀⠀⠈⠂⠠⠆⠀⢸⡇⠀⣠⡟⢁⡄⠄⢀
⠀⠀⠀⠀⠀⠀⠆⠀⠐⠂⠀⠀⠁⠈⠙⢳⣴⡿⠀⠀⠰⠀⠀⠁⠀⠉⠀⡀⢀⣹⡿⢿⣥⣼⣃⠀⠠⢄⠗⠀⠀⠀⡀⣿⣥⡾⠋⠀⠘⠁⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⢻⡇⢀⢀⠐⠀⠀⠀⣤⢀⣤⡿⠛⢉⠀⠀⠈⠉⠛⣿⣶⣶⣀⠀⡠⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⡀⠈⠐⠖⠀⣠⣼⠿⠭⡤⢠⠈⣠⠆⠐⠀⠀⠈⠀⠈⣻⣿⣷⣤⣸⣿⡇⠀⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⠀⢿⣇⠀⡀⣼⣶⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⢨⠕⠈⠇⠀⠙⢻⣿⣿⣷⠀⠀⠈⡃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⡀⠐⠀⠀⠘⣿⣆⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠐⠀⢫⣀⡀
⠀⠀⠀⠀⠀⠂⢃⣀⡀⢤⡄⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⢀⠀⣿⣿⣿⣄⠀⠀⠀⣾⠁⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠈⣶⡄⠀⠀⢠⡌⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⡟⠀⠰⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣧⣀⢰⡏⠀⡄⠀⠀⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡾⠿⣧⡈⠀⠀⢡⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠈⠉⠛⠻⠿⠿⣷⣄⣸⣿⣿⠀⠁⠀⠀⠀⠀⠀⣀⡀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⡉⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⡗⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢙⣿⣿⡏⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⣾⠏⣿⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣦⣤⣤⣿⣷⣿⣦⣀⣤⣾⣿⣿⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠋⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠙⠛⠓⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢃⣤⡄
⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣶⣾⣿⣿⣛⡄
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡿⠿⣿⣿⣯⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢤⠀⣀⣹⣶⣮⣿⡿⣿⡣⠂
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡶⣿⢀⢹⣿⣿⣿⢖⠟
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣠⠒⠛⣿⡩⣧⣧⣿⣾⣶⡆
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣟⣢⣿⣯⣦⣬⢿⡶⢨⣿⡯⠿⡟⠉
⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⠶⣾⣿⢿⣿⡁⣽⡯⣽⢏⣴⣊⠻
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠥⢤⣟⣛⣦⣀⣻⠿⢿⣿⣆⡸⠿⣿⣿⡅
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠋⣿⡇⡴⡻⢭⠳⡌⣇⠙⡗⢄⢹⡾⠒⠃⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⢿⣧⡞⣇⠙⣧⣼⠾⢖⡿⢻⠀⡇⢈⣿⠉⣡⣾⢙⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠓⢺⠟⢇⠈⠫⣍⣭⣟⣉⢴⣯⡞⣠⠎⢀⣿⢁⡉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⢰⢓⡀⡤⢨⠉⢳⣱⣬⣿⡀⠸⣝⠒⠺⠶⠤⠔⢋⡰⠋⣁⣤⡻⣯⣉⣁⡬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠘⠾⢿⣧⣧⣾⣻⣭⣀⣒⣾⠋⢲⣬⢍⣶⡶⠖⠒⠉⢉⡩⠿⡯⢤⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣌⠙⣻⣿⣿⣏⣉⣀⣼⣿⡏⢨⡟⠙⠖⠚⢉⣶⣶⠲⣭⣥⡤⡥⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠰⠛⡽⠫⢝⣿⢸⣂⣄⣤⠴⢖⣫⠿⢤⡈⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣾⣡⡴⠋⣹⠞⠁⠀⠛⠊⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⢠⣀⣀⣀⣀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⢀⣀⣀⣀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠻⠿⢿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠛⠿⢿⡿⠿⠿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢯⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⢦⣠⡾⠿⠿⣿⣦⠀⠀⠀⠀⠹⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠰⣘⠹⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⣹⡦⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠈⢻⠃⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⣀⢀⣴⠾⣿⣶⡄⠀⠀⠀⠙⢷⣄⠘⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠣⠀⠂⡙⡿⠁⠀⠀⣻⣿⠀⠀⠀⠀⠀⠙⠿⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠰⣷⠀⡀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣎⠀⠃⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢃⣀⡀⠀⡄⣠⣄⡀⣀⠃⣃⡄⢦⡄⠀⢴⣆⠤⣄⣀⡆⣶⣶⡄⢰⡄⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠁⠁⠉⠁⠉⠉⠉⠁⠀⠉⠀⠀⠀⠁⠈⠀⠀⡀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⠀⢤⠠⡄⠀⠀⠠⡅⠀⠀⢸⡇⠀⠀⢀⠀⢀⠀⠀⠐⡅⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠋⠉⠃⠁⠀⠀⠈⠃⠀⠀⠘⠓⠂⠃⠙⠊⠁⡀⠀⠀⠁⡼⠘⠋⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡆⣰⣰⡀⢠⢤⣤⡆⡶⠐⡀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⡈⡀⢀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠈⠀⠐⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⠄⠾⠒⠣⠓⠛⠀⠀⠸⣼⠾⠒⠛⠼⠄⠀⣠⣤⡾⣿⡿⠟⠉⠻⠟⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢀⡀⣀⠀⢠⠀⣀⣀⢀⠀⠋⢀⣀⣤⣤⣴⣿⣷⡿⠟⠻⠻⢿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠈⠁⠓⠀⠘⠈⠛⠙⠛⢀⡾⠛⠉⠉⣿⣾⣿⣿⣇⡀⠀⠀⢫⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⣤⢠⡄⢴⠀⠀⠀⣴⠃⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⠄⠀⢛⣜⣿⣿⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠙⠚⠃⠀⠀⠀⠘⡇⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⣸⣿⣿⣏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠄⠀⠀⠀⠹⡄⢸⡎⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸⡦⠀⠀⢀⢤⡙⣎⣚⠴⢿⣿⣿⡻⣽⢏⣿⣟⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⠃⠀⡞⢉⠉⠉⢾⣿⣿⣿⡿⣿⣿⡶⢿⣷⣿⣿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡀⠙⣧⣈⣀⠀⢸⣿⣯⡽⣿⡿⠋⠀⠀⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡻⣿⣶⣿⣯⣿⣴⠟⠩⣠⡾⠋⠀⠀⠀⠀⠀⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⣋⣉⣟⣨⡶⠞⠉⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠹⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢰⣾⣦⠀⠀⠀⢀⢴⣧⡀⠀⢸⡇⣿⣿⠟⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⡠⠀⠉⠻⠦⠀⠔⠁⢾⣿⠁⢀⡼⠂⠉⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠂⠀⣿⠦⣄⢀⣀⣀⣀⣀⠞⢁⡔⠁⠀⣠⡾⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⢧⡀⠀⠁⢉⠉⠉⣀⡔⠛⠀⣀⣴⠿⡇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢸⡜⠙⠲⠤⠤⠶⣿⣿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠈⠛⢿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣾⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⢀⠠⢒⣴⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠼⠉⠰⠸⠤⠚⠣⢸⠓⠂⠀⡀⠈⠉⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⡉⠀⠀⠀⠉⠓⢤⡤⠚⠉⠀⠀⠀⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡎⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⡠⠊⠀⠀⠀⠀⠀⠀⢹⣄⡤⠴⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣠⠼⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢀⡠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠚⠖⠚⠃⣰⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠆⠶⠀⠠⠟⠶⠖⢆⢠⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⣀⠈⣙⣛⣁⠜⠉⢹⡂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠖⠆⢐⡶⠓⢒⠐⠀⠟⠂⠚⠺⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣈⣉⢁⣠⡍⠉⠉⠈⠁⣛⡉⢉⡙⠀⠀⠀⠀⠀⠀⢺⡏⠉⠃⠚⠂⠘⠛⠛⠉⣰⠇⠛⠒⠀⠶⠀⠛⠒⠂
⠀⠀⠀⠀⠀⠀⢀⣁⣈⡉⠉⡁⠤⣟⡉⢛⠀⠛⡀⡉⠉⠉⢁⡹⣟⠙⠂⠐⠃⠘⠘⠓⠛⢀⠟⢙⣏⠀⢀⠋⠓⠛⠀⠒⠘⠘⡓⠐⠂
⠀⠀⠀⠀⠀⠀⣿⡁⢈⡁⠐⠃⠐⠋⠉⢉⡆⣸⠋⠉⠁⠐⠃⠐⠛⢉⡟⠁⣸⠏⠉⠃⠀⠛⠀⢘⡋⠉⣉⠀⡇⠛⠛⠀⠃⠀⡜⠙⠃
⠀⠀⠀⠀⠀⠘⢁⡍⠉⣀⠛⠋⠛⠀⠀⠘⢚⠛⠋⣘⠛⠒⠂⠘⠃⠘⣽⠙⠋⣀⠏⠉⠋⠘⠃⠈⠉⡟⠋⢀⡛⠛⠒⠀⠓⠐⣻⠛⠛
⠀⠀⠀⠀⠠⠀⠼⠗⠒⠃⠀⢖⡖⠂⠒⠀⠓⠚⠓⠋⠈⠗⠓⠂⡄⠐⠛⣋⠉⠁⣹⠘⠛⠃⠀⠃⣰⢛⠓⡚⠀⠒⠒⠒⠀⠒⠛⠒⠚⠁
⠀⠀⠀⠀⠐⣲⠖⠒⠐⠀⠠⠟⠚⠒⠚⠁⠐⢻⠋⠓⢁⡐⠂⠘⠂⠉⠉⡁⡘⣻⢟⠙⣂⡈⢃⣀⣃⡉⢉⠁⢰⣎⣟⠛⣘⠀⣘⠃
⠀⠀⠀⠀⠈⠋⠖⢚⡟⢀⣰⠛⠙⠓⠈⡀⠒⠛⠚⠉⣹⢀⠐⣛⠉⢉⣈⣃⡈⠋⢉⠉⠉⢀⣜⣩⣭⣥⠈⣁⣈⣙⡉⢉⠁⣼⣋⣉
⠀⠀⠀⠀⠀⠾⠀⠚⠙⠉⢉⠀⠘⣿⢏⡙⣀⡀⠃⣀⣉⣉⠉⢙⡀⠉⣽⢏⣍⣡⠉⢀⣬⣥⡀⢀⡄⢠⡗⣹⢤⠼⠂⣉⣈⣍⣉⠉
⠀⠀⠀⠀⠀⢘⡗⠛⢛⣖⣉⣀⡾⠉⣈⣉⣈⡁⢀⢁⡅⢉⣞⣍⣡⣬⠉⢁⣠⣤⡄⠀⣠⡀⢀⣞⡤⠤⠾⠀⣤⠤⡄⡉⠀⡴⠬⠆
⠀⠀⠀⠀⠀⠈⠛⢀⢊⣉⣩⠁⢀⣠⣾⣥⠈⠁⢀⣜⣡⣤⡤⠀⡠⣤⢤⣬⠁⠀⢀⣞⡤⡤⠤⠀⢠⡄⡦⣦⠃⠀⠼⠷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠉⡉⣉⣈⠀⣾⠋⣼⠱⠦⢴⠆⢠⠴⠶⠆⠀⡀⠡⠾⠷⠖⠆⠐⠶⠖⢶⠤⠆⠎⠸⠴⠶⠶⠀⢶⠾⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠨⢇⠉⣹⢣⢤⠴⠂⠰⡶⠦⠄⠎⠂⠠⠞⠶⠖⠖⠀⢶⠶⠶⠍⠀⠀⠚⠚⠒⠋⠀⠶⠶⠦⠶⠻⠓⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠦⠄⠐⠴⠗⠲⠒⡃⢰⠚⠒⠂⠐⠃⠤⠟⠐⠒⠏⠀⠻⠘⠛⠀⣚⡘⢛⡚⢛⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡖⠖⠶⡀⠰⠀⠐⠓⠛⠛⠁⠘⠛⠓⣦⡀⣐⡖⠛⠓⣁⣘⠀⠈⠉⣽⣉⣀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠰⠅⠒⠚⢃⡘⠛⡝⡋⢈⡉⠀⡉⡙⠋⠁⢀⢫⢏⣉⣀⠁⣀⣉⣉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢘⠙⢃⡿⢎⣈⠉⣉⣉⣁⣸⠃⠉⣹⣂⣁⡌⠉⣉⣉⣄⠍⡁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢎⣉⣉⠀⡩⣉⣉⣁⠀⣀⠉⣥⣤⣤⡄⢇⣠⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⢩⢆⣔⣯⡉⢉⣀⣌⡀⢀⡄⠀⣿⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣨⢤⡀⣴⣤⠀⣼⠤⠴⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠷⡶⠶⠂⠰⠶⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠓⡟⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⣉⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠌⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⢰⠀⠀⠀⠀⢠⠇⠀⢀⠀⠀⠀⠀⢀⡴⣺⠋⠀⠀⠀⢀⠀⠀⠀⢀⠀⢠⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠀⠀⠀⠀⣸⢀⡾⢋⡽⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⡏⢹⠀⢠⡏⠀⣟⡞⠀⢠⡾⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠎⢿⡀⠀⠀⡰⠃⣾⡗⠋⡠⠃⠀⠀⠀⣠⣇⠀⠀⣸⡏⢧⣼⣁⢼⡇⣠⠿⣄⡠⣿⠒⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠒⠈⠀⠀⠈⠛⠋⠁⠀⠀⠀⠚⠉⠉⠛⠊⠁⠙⠊⠉⠁⠀⠉⠁⠀⠀⠀⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⣴⣿⣷⡆⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⣰⣿⣷⡆⠀⠀⠀⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⡇⠀⢠⣿⣿⡿⠛⠻⣿⣧⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣰⣿⣿⣿⣿⡇⠀⣿⣿⣿⠁⠀⠀⢻⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⡿⢁⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠛⠛⠋⠀⢸⣿⣿⠇⢸⣿⣿⡇⠀⠀⠀⢸⣿⡿⠀⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣾⣿⡟⠀⠀⢿⣿⣿⡀⠀⢀⣾⣿⠃⠀⠸⣿⣿⣿⡄⠀⢀⣾⣿⡏⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠌⢿⣿⣷⣿⣿⠟⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠏⢠⣾⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⢈⣉⣩⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⣾⡏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡞⠛⢩⣿⠋⠙⠻⣷⣄⠀⣶⣶⠀⣶⣶⡆⢸⣷⣿⠆⢶⣶⡆⠰⣶⡦⠀⣸⣿⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣝⡀⠸⠇⠀⣿⡟⠀⠀⠀⠈⢿⣧⠈⠁⠀⠈⠉⠀⠀⠉⠁⠀⠀⠉⠀⠀⠈⠀⢀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣠⣤⣀⣠⡀⠀⠀⠀⠀⣠⣤⣤⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⣴⡿⠋⠁⣽⡿⠀⠀⠀⢠⣾⡟⠁⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⢠⣿⡏⠀⠀⠀⠀⢀⣾⣿⠃⣼⡿⠁⠀⢸⣿⠃⠀⠀⢀⣿⡟⠀⠀⢠⣿⡇⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡀⠀⣼⣿⠁⠀⠀⠀⣠⣾⡿⠃⢰⣿⠇⠀⢠⣿⡟⠀⠀⠀⣼⣿⠁⠀⠀⢸⣿⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⣹⣾⣿⣧⣤⣤⣴⣾⡿⠋⠀⠀⢸⣿⡀⣠⡟⢹⣇⠀⣠⡾⠹⣿⡀⠀⣠⣾⣿⡀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠈⠙⠛⠉⠀⠀⠈⠛⠛⠉⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣶⣿⣿⣇⠰⠄⠀⠀⠀⠀⠀⢀⡠⠄⠘⣛⣛⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⡭⢾⣿⣿⣧⠀⠈⢢⠀⠀⡐⠁⠀⠀⣼⣿⣿⣿⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⡄⠈⠀⠀⠀⢻⡏⠀⠀⠀⢠⡌⠀⠀⠀⢀⡿⠛⠉⠉⠀⠸⣿⣿⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠋⠉⠰⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠘⣷⣟⢿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠃⠀⠀⠀⢳⣌⡖⠈⠉⠂⠰⠀⠀⠀⠀⠀⢀⠟⠛⠛⠋⠀⠀⠀⠀⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣿⡇⠀⠀⢳⡀⢂⠀⠀⠀⡠⠊⢰⡆⠀⠀⠀⠀⠀⠀⢿⣿⠟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⡄⣄⣾⣿⠁⠀⠀⠉⠁⠀⠉⠰⠎⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠂⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠓⢊⠁⣁⠐⠒⠃⠙⢄⣀⣠⣤⡴⠞⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣭⣥⣿⣿⡿⢿⡇⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⢸⡿⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠈⠢⢄⣠⠆⠁⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣧⠈⠙⠛⠻⠿⠝⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠩⠿⠟⠛⠋⠁⡼⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠄⠀⠈⢳⠀⠀⢀⣤⠀⠀⠈⠉⠁⠈⠈⠁⠉⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⣸⠀⠀⣸⠇⠀⣠⠀⢠⡄⢀⣀⡤⠀⠀⠀⢇⣸⢠⠀⢀⣴⠀⡆⢿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠗⠆⠓⠀⠋⠣⠌⠙⠇⠀⠀⠀⢀⡝⠛⠀⠚⠛⠐⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⠤⠤⠤⠠⠤⠤⠠⠤⠤⠤⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⣩⣿⣿⣿⣷⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⡀⠈⠁⠈⠙⢻⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⠿⠛⠉⠂⢩⣿⣛⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠻⠃⢠⠠⠄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠰⣮⡻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠇⠀⠀⠀⢣⣘⡤⠒⠒⠆⢻⣿⣿⣿⣿⣿⣿⡷⠾⠟⠒⠀⠀⠀⠀⣺⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⣿⡇⠀⠀⢦⡈⢿⣿⣿⣿⣿⠟⢠⡄⠀⠀⠀⠀⠀⠀⣽⣿⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀⡄⣾⣿⠁⠀⠀⠛⠃⠈⠛⢿⡟⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣧⣿⡿⠃⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣅⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⠒⢒⣠⣤⣾⣿⣀⠀⢀⣀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠐
⠀⠐