Scooter Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠁⠀⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⠤⠀⠘⠛⠛⠀⠀⣙⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠻⣶⣶⣶⣶⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠈⢉⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠁⠀⠀⠑⠄⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⣀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠤⠶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⡀⡀⡀⠀⢠⡇⠀⠠⣤⣦⣤⣀⠀⠀⠀⠜⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⢫⡿⣿⣟⣙⡀⠀⠀⠠⣬⣴⡇⠠⣾⠀⢠⣶⣶⠒⠲⣶⣖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⡿⠋⠀⠀⠀⠀⠉⠉⠉⣦⠀⠀⠀⢸⣿⣿⠇⣸⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠘⠁⠀⠀⠘⣷⡡⣾⡿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣾⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣔⣶⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣺⣿⣿⣿⠿⠿⢿⣿⣿⣧⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣡⢖⣉⡀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣤⡶⠦⡄⠀⣾⣿⣿⣿⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠛⠧⠔⠃⠀⢙⣿⡿⢡⠒⠲⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣠⢷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠾⢼⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⣤⠔⢊⡴⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡿⠋⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢦⣠⠾⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡃⡇⠈⢳⣀⣠⠤⠤⠤⠤⠤⠞⠑⣦⣀⡽⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢻⢀⣼⣧⣼⡇⢀⡴⠒⠲⠶⠞⡇⠉⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠋⡼⠁⡇⠉⣩⢥⣤⣤⡤⠴⠷⠖⠒⠚⠛⠛⡇⠀⢰⠉⠉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡇⠀⢻⢻⡀⠀⣤⣤⣤⣤⣤⣴⣶⣶⣿⣶⠛⠻⠿⣟⣙⠛⢹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⡇⠀⠈⣆⠳⡄⠙⢦⠀⠈⠙⠻⣿⠟⠛⠋⢀⣀⣀⡀⠈⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢢⡀⣧⣄⣀⣼⡇⠀⠀⠸⡀⢹⣄⣈⣧⣄⠀⠀⠈⢣⠀⡼⠁⠀⠀⠈⠙⠲⢄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠈⠁⠙⠻⡻⣄⢳⡀⠀⢰⠗⢾⢉⣁⣀⣸⠄⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠙⢦⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣦⣴⠖⠶⣄⠀⠙⡜⢦⠻⡟⢿⣷⣤⣼⣿⣿⣧⡤⠤⠖⠃⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠚⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣦⣤⠟⠈⠓⠛⠚⠛⠛⠛⠚⠛⠛⠒⠒⠒⠒⠒⠒⢶⣶⣶⠚⠛⢛⣿⣿⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣾⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⣟⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⡿⠟⠛⢃⣼⣶⣄⣀⠀⢀⡈⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣰⣿⣄⣴⣿⣿⣿⣿⣿⣷⣎⠁⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⡿⠿⡏⠁⢨⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠟⠋⠉⠛⠠⠄⣀⣀⠀⠉⠑⣿⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⣼⡄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⣿⣿⣷⣶⣶⣶⣶⣶⡤⠀⡠⢀⢀⠁⠀⡀⠈⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⡡⠄⠒⠒⠂⠀⠒⠒⢄⡀⠀⠈⠓⠃⠋⠀⠀⡉⠁⠌⠀⠀⣿⠀⣀⡴⠶⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢠⡎⠀⠀⡀⠀⢀⣡⡿⠁⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠜⠠⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⢴⠙⢆⠒⠴⠌⠁⠀⢠⣄⣩⣷⣾⣿⠁⠀⢀⣴⡶⠶⣶⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣏⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣠⡞⢀⠃⠀⠀⠈⠒⠒⡒⢈⣹⡿⠻⠇⢀⣰⡿⠁⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠶⠖⠒⠒⠓⠉⠁⠀⠀⠀⠘⣿⣧⠀⠀⠄⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣈⣭⣿⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠋⠉⠓⢤⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢰⣿⡁⠠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣦⡿⠌⠓⡹⣍⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⡟⠙⢶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⠟⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡞⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⠤⠤⠔⠒⠒⠋⠉⠀⠀⠀⠀⠀⣀⡿⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣀⡠⠤⠄⠒⠒⠂⠉⠉⠉⠉⠙⠲⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆⢤
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠊⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠋
⠀⠀⠀⠀⡴⠎⢀⣀⠀⠀⠀⠣⠘⡄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠇
⠀⠀⠀⢠⠔⠂⠈⢉⡝⢲⢤⣀⠣⠈⢆⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⢣⡀⠡⣜⡄
⠀⢀⡔⠁⣠⠶⢲⠎⢠⡯⠀⠙⣟⠳⡀⠑⢄⡀⠈⠓⠲⠶⠶⠶⠖⠒⠛⢉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠚⣻⣝⠓⡒⢒⣄⠀⠙⣄⠈⠁
⠀⠈⠀⢰⠇⢠⡎⠀⣨⠀⢃⠀⠸⡀⠙⢦⡀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⣤⡜⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢦⡀⢸
⠀⢀⠀⠀⠀⡁⡇⢠⠛⠀⢸⠀⢠⠃⠀⠀⠈⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠓⠢⠤⠄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣠⠃⢸⠁
⠀⠈⢀⠀⠳⡌⠙⠓⠉⠐⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠘⠿⢈⣉⠛⠋⠀⣠⠃
⠀⠀⠀⠑⠠⢀⡀⠀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢀⣀⣀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣾⣿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣼⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣇
⠀⠀⠀⣠⣶⣿⣿⠿⠋⢙⣿⣿⠿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣶⣄⠀⠈
⠀⠀⣴⣿⠟⠁⠀⠀⠀⠈⠻⣿⣧⠀⠙⢿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⣀⡈⠻⣿⣧
⠀⠀⣿⣿⠀⠀⠀⠀⣸⠀⠀⢹⣿⡇⠀⠀⠙⠻⠿⢿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡄
⠀⠀⣿⣿⡀⠀⠐⠒⠁⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣿⣿⡟⠛⠻⠿⠿⠿⢿⣿⣿
⠀⠀⠈⢿⣿⣶⣤⣀⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣤⣤⣤⣴⣿⡿⠁
⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠤⡀⠀⠀⠀⣠⡤⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠑⡴⣋⣡⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠓⠶⠽⡚⠻⡖
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢴⡀⠈⢂
⠀⠀⠀⠀⠀⠄⣾⣉⠀⠀⠀⠈⠉⠑⠒⠠⠤⢤⣀⡀⠀⠀⠘⣧⠳⠀⠀⠡
⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣷⣶⣤⣤⣠⣠⣀⣀⣉⡽⡄⠀⠸⣧⣠⡀⠀⠐⠀⠴⢤
⠀⠀⠀⠀⢘⡿⠛⣛⣉⣛⣛⠒⠓⠯⢭⣭⣿⣛⣿⣯⡴⠃⠀⠀⢹⣿⣷⡀⢰⠶⡁⣸
⠀⠀⠀⠀⠀⢤⣄⠉⠛⢿⣿⣿⣷⣶⣄⠈⠻⣿⡏⠠⠀⠀⠀⠀⠀⢛⠹⣿⡤⠑⢷⣾⠁
⠀⠀⠀⢠⣿⣦⡙⠷⣦⡀⠉⠙⢿⣿⣿⣧⠀⢸⡄⠀⢂⠀⠀⠀⠀⠈⢰⣿⣿⣿⣛⣁⠀⠦⣄
⠀⠀⠀⠘⠋⣿⡟⠳⠬⡙⠂⠀⢀⣿⣿⠟⠀⣾⠁⠀⠰⠑⠠⠀⣀⢠⡿⣿⠏⢈⣉⣿⣿⣶⣌⠛
⠀⠀⠀⠀⠀⢿⣷⣄⣠⠴⣱⢶⣤⣤⣈⣠⣾⣋⡂⠀⠀⠤⠀⠐⠋⠚⠐⠃⣨⠉⠿⡿⢿⣿⡍⣀⣯
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡾⠟⡓⠠⠍⠉⣛⠛⠻⠷⠶⣦⣤⣤⣶⠟⢻⣿⡷⡇⠂⠀⢹⣇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠠⠀⠈⠍⢛⠂⠀⠠⢄⡀⠀⠀⠘⣿⣧⢹⡤⠇⣺⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠯⠝⡒⠦⣥⣽⣿⣶⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣉⣽⣦⣀⣀⡤⠖⠒⣶
⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⢿⣍⡀⠀⠀⣰⡿
⠀⠀⠀⣾⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠹⣄
⠀⠀⠀⣿⠀⠀⢸⡷⠶⠦⠤⠤⠤⠤⠤⣴⠲⠶⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⣆
⠀⠀⠀⣿⠀⠀⢸⣧⡤⠤⠤⠤⠤⠤⠤⣿⢳⣤⠤⠤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢧⡀
⠀⠀⠀⣿⠀⠀⢸⡇⣧⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢳⡀
⠀⠀⠀⠻⣄⣀⣼⡷⠋⠐⠛⠉⠉⠉⠉⠙⠲⢄⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢹⣄⣀⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡴⠞⠋⠉⠉⠉⠙⠓⢤⡀
⠀⠀⢀⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⠟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣙⣦
⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠁⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⣰⡟⠀⠀⠀⠀⣠⣾⡭⣥⡀⠈⠻⡍
⠀⠀⠈⠋⠉⣽⣻⢻⡉⠉⠉⠉⠉⣿⢻⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠞⢱⡇⣀⣤⠶⢺⠏⠀⠀⠀⠈⢦⠀⢹⡀
⠀⠀⠀⠀⠀⢿⢿⢸⡝⠲⠦⠴⠚⣹⢸⢿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢿⠀⢸⡀⠀⠀⠀⠀⣼⠀⢸⠃
⠀⠀⠀⠀⠀⠘⢮⢧⣙⠦⠤⠤⢞⣡⢏⠞⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠙⠦⠤⠤⠞⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠑⠮⢽⣷⣿⠭⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡤⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣄⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢄⠀⠀⠄⠂⠀⠠⢢⠶⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢤⡡⠄⠀⠀⠀⠠⢐⡃⠀⢠⠸⢦⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⡈⠁⢠⣞⡯⠤⣤⠤⡄⠀⠁⢽⣦⡵⠠⠚⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠚⠁⠈⠉⠀⠀⠀⠈⣤⣶⡶⠶⠞⠷⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠐⠒⠒⠒⠠⢄⡁⠀⠀⠀⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⡖⠓⢆⠑⡀
⠀⠀⠀⠀⠀⢠⢊⠅⠀⠀⠀⠀⠀⠀⠈⠑⠤⢀⡀⠀⣀⠀⠀⠀⠀⠶⠂⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢭⠒⠒⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠘⡄⠀⢣⠐
⠀⠀⠀⠀⢠⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⢧⢀
⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠁⠀⢄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠱⡀⠀⠀⠀⠀⡓⠶⠾⠄
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠣⠀⠀⠀⠈⢐⠦⠤⠎⠠⠇⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢡⠀⠀⠀⠀⢙⣛⣛⡇
⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠆⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⠉⠀⠀⠀⣀⣀⣉⢩⠡⠔
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⢀⠆⣸⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠈⠲⡂
⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠆⠀⠀⠀⠘⢄⢧⠀⠚⠐⠀⠁⣇⠀⠀⠀⠀⠀⠀⡎⣰⠇⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡱
⠰⡄⠉⣑⠢⢤⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠁⠷⠦⣢⠐⠒⠉⠁⠢⢄⣀⡀⠀⠶⠁⠀⠀⠄⠀⠀⠀⢀⠠⣐⣂⣀⠀⠀⡀⠀⠀⠀⠘
⠠⠆⠀⠀⠀⠀⠙⠏⠉⢓⠶⢶⡮⣅⢀⡀⣀⣠⣈⣀⡀⢀⣀⣀⡀⠀⠤⠀⢀⣈⡙⠒⠂⠠⠤⠤⠠⠤⠝⠁⠀⠀⠀⠀⠀⠀⠐⡡⣮⠎⣻⠛⠻⢦⡀⠀⠀⠀⡤
⠀⡀⠀⠀⢬⣝⡲⢤⣀⡀⠀⡛⢄⠈⡎⠁⠒⠨⡀⠉⠙⠃⠒⠤⢄⣠⣤⢄⣐⣢⡬⢿⣶⣶⡶⣦⡤⠂⠀⠀⠀⠀⡀⠀⢀⡄⢰⣉⠀⠀⢅⠂⢀⠙⠓⠀⠀⠀⠰
⠀⠈⡶⢬⡓⠦⣍⡓⠮⣙⠀⠈⠀⣀⠹⡀⢓⠂⢈⣲⠆⠀⠀⠀⠀⠀⠈⠉⠀⠉⠙⠛⠓⠊⠙⠋⠀⠀⠀⠀⠀⠀⠁⠢⢾⡇⢨⢁⠀⠒⢀⢎⠁⠈⣯⠀⠀⠀⠈
⠀⠀⢰⠀⢏⢷⢦⣍⡓⠀⠀⠀⢀⠇⠈⠙⡞⠀⡊⠴⠙⠢⠀⠀⠤⠤⠴⠶⠛⠛⠛⠒⠒⠲⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠘⡙⡈⢁⠀⠈⠂⢰⣿⠀⠀⠀⠆
⠀⠀⠀⠣⡈⠪⣓⠄⠍⠗⠲⠞⠓⠒⡺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠳⡀⠑⢕⡤⣤⢠⣜⡷⠁⠀⢀⡜
⠀⠀⠀⠀⠈⠂⠄⣈⡉⠀⢀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠉⠉⠁⠀⢀⡠⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣯⣥⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠮⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⡵⣦⠙⠂⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣟⣀⡐⠀⢠⣰⣄⠀⠉⣙⣻⣤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠈⣡⣶⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⠀⠀⣸⠀⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⠃⠀⠀⠀⠉⠀⠙⣿⣯⣭⡿⠛⠉⠉⠉⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠴⠖⠂⠀⠀⠈⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠿⠿⣇⠀⠀⠀⡄⠀⠀⢀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⢠⠂⠀⠀⣒⡭⢄⣾
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣆⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⠁⠀⠀⠀⡀⡽⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠘⠑⠲⢾⡧⠄⣀⣀⣤⣄⠀⠀⡇⠀⠀⣾⡀⠁⠀⠀⠠⢴⣿⢦⡝⠲⠿⠶⣦⡵⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣶⡴⢿⣿⣟⣰⠋⢹⢋⡻⢯⡟⠲⢤⣿⣅⠀⠀⠀⠀⠀⠀⢠⣤⡀⣴⣾⠋⠁⠚
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠇⣤⣁⡠⡿⠸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⠃⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣧⣀⣾⣿⡿⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠦⠔⠊


⣿⣿⣿⣻⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣟⣿⣟⣛⣛⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⡄⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿⣦⠶⠶⠛⠛⢋⠉⢁⣀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠉⠁⣀⣠⣤⣴⣶⠟⣿⣿⡻⣆⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢤⡶⠞⣛⣭⠿⠟⠉⠀⣠⠞⠻⣷⡙⣧⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣆⠀⠈⢿⡌⢻⣔⣄⣠⣴⡿⠷⠞⣛⣛⣥⡾⠗⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠈⢻⣄⠛⣋⣩⣤⠶⠞⠛⠉⠉⠀⠀⠀⠀⣀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⢻⣆⠀⠀⠛⠛⠉⠁⠀⠀⠀⣀⣠⣤⡴⠶⠟⠛⠻⣆⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣄⠀⢻⣆⠀⠀⠀⣠⣤⠶⠞⠛⢉⠁⠀⠀⠀⠀⠀⡀⠹⣧⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⣆⠀⠹⣆⠀⠀⠻⣆⠀⠰⣾⡿⠿⠀⠀⠀⠀⢸⣿⡄⠘⣷⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⢦⠀⠹⣧⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⢧⡀⠙⣧⡀⠀⠘⣷⡀⠀⢶⣿⡿⠆⠀⠀⢀⣀⣤⡴⠾⠃⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢳⡀⠘⣷⡀⠀⠈⢷⡀⠀⣀⣤⡴⠶⠟⠋⠉⢀⣀⣠⣤⢶⣄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠳⡄⠈⢷⡄⠀⠈⠛⠛⠉⣀⣠⣤⠶⠾⠛⠋⠉⠁⠀⠀⢻⣆⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠙⣄⠈⢻⡄⠀⠀⢸⡟⠋⢉⣠⣤⣦⡀⠀⠀⠀⢠⣶⡀⠹⣦⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⢦⠀⢻⣆⠀⠀⠻⣆⠀⠙⠋⠉⠀⠀⠀⠀⠈⠛⠛⠀⠙⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⢣⡀⠹⣦⠀⠀⠹⣧⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⢀⣸⣷⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠳⡀⠙⣧⠀⠀⠙⣧⠀⠘⠛⠋⢁⣀⣤⣴⠶⠛⠛⠉⠀⠀⠀⠀⣹⣧
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠹⡄⠈⢷⡀⠀⠘⣷⣴⠶⠟⠛⠉⠁⠀⣀⣀⣤⣤⡶⠶⠟⠛⠉⣿
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠙⣆⠈⢻⣆⠀⠀⣀⣀⣤⣴⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣆⠀⢹⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⢦⣸⡇⠀⠀⣀⣠⡤⠴⠚⠛⠉⠉⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢻⡖⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡇⠀⠀⢀⣀⣤⣤⠶⠞⠛⠉⠉
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⠶⠛⠋⠉
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢺⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢣⣀⣠⣼⠌⠘⠄⢀⠤⠤⢤⠀⠀⣠⠤⢖⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠉⢁⣀⠀⣸⠀⣸⣤⡼⠼⠒⠚⢋⣍⡦⣧⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠤⣝⢦⠀⠀⠀⣀⡩⢵⢶⡌⠢⢘⣥⣤⡀⢀⣀⣨⡴⣚⣿⠇⠿⢐⡇
⠀⠀⠀⠀⠀⣞⡉⠲⡀⠀⠀⠀⠀⣎⣠⠖⠻⢿⣒⠺⣩⣠⣠⣠⠸⢸⢮⡇⠉⠭⣼⡟⡉⣠⡏⢸⣿⣇⣸⣐⣷⣤
⠀⠀⠀⠀⠀⠈⢫⠖⢛⠯⡉⢻⡉⠀⡞⠄⠀⠀⠉⠊⠉⠒⢤⡈⠙⠫⡉⡇⠀⣓⣿⣃⢱⡿⣠⣦⣬⡍⣙⡛⢁⣿⠁
⢎⣙⢦⡀⠀⠀⢸⢸⠤⡷⠷⢌⣧⣡⠭⠿⢷⡀⠀⠰⡆⢤⣦⣈⠣⣄⣌⢇⠀⠀⢿⢻⣿⠃⠈⠛⠻⠿⠶⢋⣾⠛⢆
⠈⠣⣶⠙⠢⣄⢸⠀⠑⠁⡆⡑⡇⢸⠀⡭⡟⢧⣄⣈⠪⣶⡿⢉⣷⡘⣞⣷⣆⠥⣿⣅⠘⡄⣭⡵⠞⠛⠛⣿⠟⢆⠈⣆
⠀⠀⠉⠳⣦⣂⡽⠀⠀⠀⡆⡢⣇⠈⢶⣶⢋⡌⠠⢮⡟⣛⠟⢩⣿⣷⢹⡿⠿⣩⣿⡝⣺⣘⡤⠶⠄⠀⣼⣟⣦⠈⡦⣙⡆
⠀⠀⠀⠀⠈⣹⠃⠀⠀⠀⣇⠂⣿⣇⣹⠛⢶⠁⠨⣼⡿⣿⠰⣿⣿⡾⠋⣿⣶⣿⢿⣿⠃⣻⡽⠧⢶⣶⡿⠿⢲⢋⡇⢒⡇
⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠸⡀⠉⢿⠻⢿⡏⢀⡥⣿⣶⣿⢣⢄⣉⣡⣴⣿⡧⠿⣒⣋⢭⠗⡶⢫⢋⠎⡐⡱⡡⢣⡧⢽⠁
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠻⣼⠀⢐⣸⣾⣿⣷⡤⢾⣛⡿⡿⣳⢋⠝⡡⢣⢊⠞⡰⡡⢃⢞⠜⡔⡡⢡⠏⢽
⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢈⣦⢒⣛⡿⡿⡻⠫⢋⢎⢎⠔⡡⢋⠞⡔⡡⢃⢎⠜⡰⢡⢊⠞⡔⡱⣹⠤⢽⠢⣀⡀⠠⠠⠄⣀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠀⢽⢉⢔⢎⠔⠔⡱⡱⢡⢊⠜⡰⢁⢊⠜⡰⡣⢊⠎⡰⠡⢂⢎⠜⡔⣼⠭⣿⡑⢐⠀⠂⣙⡂⠈⠣⠥
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢀⠭⡧⢁⢪⢊⢎⠌⡔⡡⢊⠎⡔⡡⢋⢜⡔⡡⢃⠜⡔⡡⢣⢊⢞⣴⡾⢑⣟⡈⠠⢍⣀⡒⠂⣠⠤⠭
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⡷⡑⡡⡣⢣⠎⡔⡱⢁⢎⠔⡡⢋⢊⠜⠠⢊⠌⣔⣱⣥⣿⡻⣽⠷⠞⠩⠭⠉⠐⣒⡐⣃⡈⠉⠉
⠀⠀⠃⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠨⢽⠎⢜⠔⡵⢡⢊⠎⡰⡡⢊⡔⡱⢡⢊⣴⢥⣻⡹⠽⠶⠿⠉⢙⢛⣋⣈⣭⣭⣤⠀⠐
⠀⠓⠤⣘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⢨⢊⠎⡔⡡⢃⢎⡔⣡⣮⠼⣶⣻⠽⠾⠭⠭⠥⠭⠭⠭⠉⠁⠒⠒⠒⠂
⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⡀⠀⡀⠽⡡⢣⢎⣼⡵⡗⣞⣽⡽⡶⠏⠩⠭⠥⠦⠤⠭⠭⠭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠁⠓⡂⣽⣲⣯⣯⣷⣿⣛⣃⣤⣤⠶⢖⣀⣀⣀⠀⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⠿⠿⠟⢀⣐⣒⣒⣒⣛⠓⠓⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢧⡤⢴⢒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣈⣞⠃⠤⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠿⠛⢏⣿⡿⣿⡄⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠒⣿⡽⢿⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢿⡴⠚⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠅⠽⢿⠿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣡⢄⣿⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠿⢿⣻⡟⣿⣶⣿⣅⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠛⡫⢿⣿⡿⣗⣆⣠⣄⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣾⣧⣤⣥⣬⣭⣥⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣍⣩⣬⣩⣏⣽⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⡀⠀⡀⢀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠁⠁⠁⠈⠁
⠀⠀⠀⣾⣁⠹⠀⣿⣃⡜⠃⠘⣿⢉⠓⠚⢹⡏⠙⢠⡞⠈⠳⠈⣿⠀⢹⡏
⠀⠀⠀⣌⠉⣻⠀⣿⡙⢷⣄⢀⣿⠉⣠⠀⢸⣇⠀⠹⣇⣀⡠⢀⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠒⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⡁⣽⣠⣤⣄⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠤⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⢸⠰⠀⣦⢿⣿⣿⣩⣿⠀⡇⢸
⠀⠀⠀⠀⢻⠢⡀⠀⠀⠀⠀⣒⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢺⣟⡼⠃⢸⣿⣿⠟⣿⠀⡇⣼
⠀⠀⠀⠀⢸⠲⡝⢦⣀⠁⠀⠀⡀⣺⡇⠀⠀⠀⠀⠀⠀⠀⡄⢸⣼⢸⡟⠀⠀⢸⣿⣿⡎⣿⠀⡇⡇
⠀⠀⠀⠀⠐⠰⢈⡡⠉⠀⣴⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⡇⢸⣿⢸⡇⠀⠀⢸⣿⣿⠀⣿⣴⣿⣧
⠀⠀⠀⠀⠘⠘⠲⡄⠀⢠⣿⠀⠀⣰⣿⢃⠀⠀⠀⠀⠀⡆⠀⢸⣿⢸⡇⠀⠀⢸⣿⣿⡆⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣄⠙⠀⢸⣿⠀⠀⣿⣿⢰⢀⠀⠀⠀⠀⡇⠀⢸⣿⢸⡇⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣴⣦⡀⠋⠀⢸⣿⡀⠐⣿⣿⠘⢸⡀⠀⠀⠀⡇⠀⢸⣿⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⡄
⠀⠀⠀⣿⣿⣿⣿⣶⣦⣼⣿⣁⣀⣿⣿⠀⢸⡇⠀⣾⠀⡇⠀⢸⣿⢸⣇⣀⣀⣸⣿⣿⣼⣿⣿⣿⣿⡇
⠀⠀⠐⣻⣿⣿⣥⣿⣿⡟⣹⣿⣿⣿⣿⡷⣾⣇⣀⣿⣶⣿⣧⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⡈⣼⣿⡇
⠀⠀⠀⢿⣿⣟⠉⠉⠹⠘⠉⠋⠉⢉⣡⣴⣾⣿⣿⣿⣶⣌⡉⠛⠻⣿⠟⢿⣿⡿⣿⠙⣿⠷⣿⣿⡟⠇
⠀⠀⠀⠸⠁⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡈⠋⠉⡋⠁⠑⣾⠀⠙⣿
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⡀⠀⠉⠀⠀⢹
⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡂⠀⠀⠸
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁

⠀⠀⢠⡶⠞⠛⠻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⢸⡇⠀⠀⠀⠀⢿⡟⢧⡀⣀⣀⣀⠀⢀⡼⢿⡟⠉⠀⠈⢻⣆
⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣬⣿⠿⠉⠉⠛⢿⣷⡞⠁⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢻⡄⠀⠀⠀⢰⣿⣿⣿⡶⠄⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡄⠀⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢻⡄⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⣀⣀⣀⣀⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣿⣿⡿⣿
⠀⣿⣿⣧⣸⣿⣾⣿⣿⣿⣿⣟⣛⣛⣛⣛⠛⠛⣻⡿⢿⣿⣿⣿⡇⣿
⠀⣿⣿⣿⡛⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣟⣛⣿⣿⣛⣻⣿⣿⣿⠃⣿
⠀⣿⡇⣿⡇⣿⡏⠙⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⡆⣿⡆
⠀⣿⣇⣿⢧⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⢻⡇
⠀⢻⣿⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⢱⢸⡇
⠀⢸⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣟⣿⣿⣿⢸⡇
⠀⢸⣿⠇⡇⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠻⣿⣿⣿⢸⡇
⠀⢸⣿⡀⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢸⡇
⠀⢸⣿⡇⡏⣿⣷⣶⣶⣶⣶⣶⡶⠶⣶⣶⣿⣿⣿⣷⠶⣶⣿⣧⢻⣸⣇⠀⡀
⠀⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⢸⣿⣿⣷⣿⣿⡟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣸⣿⣿⡟⠿⡟⣿
⢰⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣦⣤⣀
⢸⣿⣿⠛⣴⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⡟⢿⣿⣿⣿⢿⣿⣿⢿⣿⣷⡀
⠘⢿⣄⠻⣿⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠙⡇⠀⠙⢿⣿⣿⣯⣿⡛⠿⣿⢷⡀
⠀⠀⢹⣦⡘⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣷⡝⠳⢿⣧⣇
⠀⠀⢸⣿⣿⣿⣿⣿⡿⡝⢟⣿⣿⡇⠈⢿⣿⣮⡳⣿⡗⠹⣿⣿⡽⣿⣿⣷⣄⠀⠀⠙⢿⣿⣽⣷⣾⡿⠿⠁
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡇⢪⡻⣿⣿⣾⣿⣦⡙⠻⣿⣮⠻⣿⡻⣷⣄⠀⠈⢻⣿⡅⣿⡇
⠀⠀⠀⣿⡿⠙⣿⣿⣿⣿⣿⣿⡿⠼⢿⣆⠑⡌⠈⢿⣿⣯⠿⣆⠈⠻⣷⡌⠙⢿⡿⣧⡀⢸⣿⡇⣿⡇
⠀⠀⠘⣿⢇⢸⣿⡎⢻⣿⣿⡿⣷⣀⣈⣻⣷⣌⣢⣀⣻⣿⣧⣌⣧⣄⡙⣿⣦⣠⡝⣎⣻⣦⣿⣇⣿⡇
⠀⠀⠀⣿⡞⡀⣿⣷⣼⣿⢿⡏⣿⣿⣿⣿⠿⠛⠛⡛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⣿⡇⣽⣿⠀⢻⣿⢺⣇⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡄
⣶⣶⣾⣿⡇⢸⣿⣤⣼⣿⢸⣿⣹⣿⣤⣤⣀⣀⣀⣀⣀⣸⣿⣿⢠⣿⣄⣀⣀⣀⠀⠀⠀⣹⡿⣿⣿⡇
⠸⣿⣿⣿⡇⢸⣿⣿⣿⣿⠈⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣿⣿⠿⡛⠛⢿⣿⣿⡇⢿⣿⣿⡶⣶⣦
⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣦⡀⠀⠀⢸⡇⢸⡿⣿⡇⠉⠹⣧
⠀⠸⣧⠈⠻⣿⣿⣿⣿⣿⣾⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⡇⢸⡟⣿⡇⠀⠀⠹⣇
⠀⠀⣿⡀⠀⠀⠙⢿⣿⣿⠗⣿⣏⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣸⢨⣿⣿⡀⠀⠀⠀⢻⣆
⠀⠀⠸⣧⠀⡀⠀⠀⠙⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠆⠈⠦⠀⠀⠰⢄⠈⠙⠻⢿⢿⢿⡿⠿⣿⠇⠀⠀⡀⠀⢻⡆
⠀⠀⠀⢿⣇⠙⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢈⣿
⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⠿⢿⡿⠛⡿⠿⣿⣿⠿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣶⣼⣷⣴⣧⣤⣿⣴⣼⣿⣴⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠠⠀⠄⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡈⢌⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⢀⣠⣤⡤⠤⠀⠤⠄⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀⢀⣠⣤⣶⣞⣿⣿⠿⠗⠛⠋⠁
⠀⠀⢠⡶⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢾⣟⣿⣿⡿⠟⠛⠉
⠀⢀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣳⡾⠟⠛⠉
⠀⢸⠁⠀⠀⠀⢠⣤⡄⠈⠀⠁⠀⠀⠀⠀⠀⠈⡘⠁
⠀⠈⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠆⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠢

⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⣇⣤⠀⠀⠀⠀⠀⠀⣾⣠⡄⠀⠀⠀⠀⠀⠀⣰⠗⠀⠀⠀⠀⠀⣀⣸⣃⡄⠀⠀⠀⠀⠀⢀⣴⡠⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⣤⠞⠀⠀⠀⠀⢀⡠⠞⠉⣸⠋⠀⠀⢀⡴⠚⠋⢩⡏⠀⠀⠀⢀⣤⠤⢲⠟⠁
⣠⣴⡟⠁⠀⠀⠀⠀⢀⠠⡾⠋⠀⠀⠀⠀⠀⢠⣶⡿⠉⠀⠀⠀⠀⠀⠉⠀⢀⠜⠁⠀⠀⠀⠈⠀⠀⢀⡞⠀⠀⠀⠀⠋⠀⢀⡾
⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⢀⡴⠋⠳⠄⠀⠀⠀⠀⠀⣠⣶⡖⠀⠀⠀⠀⠀⠲⢶⣄⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠐⣅⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⢀⣴⠏⠙⠗⠀⠀⠀⠀⢀⡼⠻⠿⠂⠀⠀⠀⢀⡾⠛⠿
⠀⢠⣦⠀⠀⢈⡗⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠠⣎⢻⣿⠏⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡶⠋
⠐⠀⠀⠑⠴⠛⠁⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠹⠞⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠐⠟
⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣇⣀⣰⡆⠀⠀⠀⢠⡠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⡍⠉⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⢀⣴⣾⣿
⠀⢸⡇⠀⢰⡆⠀⠀⢠⣿⠃⣾⣧⣄⣾⠇⠀⢀⡴⠋⣰⠎⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣾⣿⠟⠋
⠀⢸⡇⠀⠘⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⢠⠞⠁⠀⠀⠀⠀⠀⣔⡿⠁⠀⠀⠀⠀⠀⢠⣾⠿⠟⠛⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠐⠦⣄⡀⢰⡆⠀⠀⢀⣾⣛⣛⣿⣷⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⣾⣿⣿⣶⠶⠆⠀⠀⠀⠀⠀⢀⣤⣿⡷⠀⠀⠀⠻⠿⠿⠿⢳
⢀⣤⣤⣬⣿⣿⡇⠀⠀⣸⣟⠛⣿⣿⣿⠀⠀⣸⡟⠛⠛⢸⡆⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⢀⡄⠈
⢿⣶⣶⣶⣿⣿⡇⠀⠀⠉⠉⠉⠉⠉⡏⠀⠀⠻⠀⠀⠀⠸⠇⠀⠀⠀⠀⣿⣷⠆⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠖⠖⠒⠒⠒⠒⠀⠀⠀⣀⣀⠀⣰⠶⣦⠀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⣠⣶⠃⠀⠀⠀⣶⣶⣶⣶⡦
⠀⣰⣿⠿⣿⡆⠀⠀⠀⡦⠤⠤⠤⠤⠤⠀⠀⢸⣏⣹⡇⠙⠶⠛⠀⠀⣠⣶⣷⣾⡟⠟⠁⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠺⠿⣿⠿⠗
⢠⣼⣿⣿⣿⣧⡄⠀⠀⣤⣤⣠⣄⣤⣤⠀⠀⠀⠉⠉⢠⡟⢻⡄⠀⠀⣻⣿⣼⣿⡇⠀⠀⠀⠀⠸⣿⠥⠄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢀⡀
⣴⡾⠛⢷⡄⠀⠀⠀⢰⣿⠶⠶⠶⠶⠶⠆⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣤⣤⣯⣭⣧⣤⡄⠀⢀⣀⣤⣶⣾⡷⠁⠀⠀⠀⣴⣿⣾⣿⣷
⣿⣦⣡⣾⡃⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠚⠁⠀⣿⣭⣿⣿⣯⣽⡇⠀⠉⣙⣿⠿⢍⡁⠀⠀⢀⣴⣿⣿⣿⠿⠟

⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⢤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠹⢿⣿⣿⢿⣭⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⠉⠙⠛⠻⡿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⠛⠛⠉⡛⠛⠛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⣶⣤⣤⡀⠀⠀⠀⢼⣿⣿⣟⠛⠛⠻⣿⣿⣿⡁⠈⠻⣿⡷⢬⡛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡗⠁⠤⣨⣿⣿⣿⠄⠀⢩⣝⠿⣶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⠿⠛⣻⠿⠿⠿⠿⢿⢹⣿⣿⣿⣿⣯⠀⠀⣸⣿⣿⣿⡃⠀⠀⣉⣧⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣤⣴⣿⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⡅⠀⠀⠀⣩⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣶⣿⣿⣿⣿⡿⢻⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢽⣿⣿⣿⡇⠀⠀⠀⢀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⠛⠿⠿⠋⣠⣾⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠘⣿⣿⣿⡇⠀⠀⠀⢠⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣶⣾⠿⠛⠁⢀⣴⣿⣿⣿⣿⣿⡿⢊⣿⣿⣿⠶⠦⢻⣿⣿⡇⠀⠀⠀⢸⣿⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⡟⠉⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡛⠛⢤⣿⣿⡟⠀⠀⢿⣿⣿⠅⠀⠀⠀⢸⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣻⣹⣰⣿⡇⠀⣹⠆⠀⣸⣿⡟⠀⠀⠀⠀⠐⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠠⠀⠀⣿⣿⠃⠀⠀⠀⠀⠨⣿⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣐⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢲⣶⣾⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⢿⢿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⡑⠀⠀⠀⠀⠀⣀⣴⡾⠟⢻⣿⣿⣿⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡀⠀⠀⢰⡾⠋⠀⠀⠀⠘⢻⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣶⣄⠘⠇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣄⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠋⡀⠀⠀⠀⢀⢠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⢀⣤⣶⡿⡛⢛⣩⡄⠀⠀⣀⡀⠀⠀⣾⣿⡿⢟⠻
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣆⠀⠀⠻⠋⢩⣽⡟⣱⣿⣿⠇⠀⢠⣻⣿⣤⣾⣿⡿⠃
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⡽⢿⣿⣿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣿⣛⣫⠬⠉⠉⢛⠀⠙⠻⠛⠛⠋⠁⠙
⠀⠀⢸⣍⣁⣾⣿⣿⣿⣞⣣⣴⣾⡿⠋⠀⠐⢿⣿⣿⣿⣿⠟⠛⠁⠉⠀⠀⠒⠈⠝⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢸⣿⣿⡿⣫⣿⣿⣿⡿⠟⠋⠀⠀⠀⢰⣾⣿⠟⠉⠃⠀⠀⣀⡤⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉
⠀⠀⣸⣿⣿⣼⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⣠⣤⣶⠾⠋⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛
⠀⠀⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠟⠛⠋⠉⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡘⠻⡆⠀⠀⠀⢥⡀
⠀⠀⠻⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰⠶⠤⢀⣀⡀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠐
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⠀⡠⠶⠖⠀⠄⠀⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠻⡄⠘⠟⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠈⠇⠈⠉⢿⣿⣿⠃
⠀⠐⠚⠿⢛⠻⣤⣀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⠢⡀⠀⠀⠀⠀⠀⠈⠀⠀⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣾⡇⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⣿⡄⠘⣆⠀⠀⠀⢀⠄⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢛⣿⣏⠄⠘⡄⠀⠀⠈⢄⠀⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣤⣠⣴⣴⡶⠿⠟⠓⠤⠀⠀⡇⢠⣭⣿⡷⠂⠀⡇⠀⠀⠀⠀⠀⢈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠿⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠠⠬⣿⣟⣁⢀⠇⢀⠀⠀⢠⣆⣀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡯⢀⠎⠀⠈⠻⣶⡋⠀⠀⣽⣿⣿⠋⡨
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠈⠻⣶⣾⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠙⠢⣀⢀⢀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠐⠀⢉⣉⣀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⡀⣤⠄⢠⢈⠉⠀⡠⠀⠵⠀⠄⠀⠀⠀⠀⠰⠄⠀⠃⠀⠀⣆⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠚⣋⠉⠁⠀⠑⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠂
⠀⠀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⢰⣆⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠁⢀⡞⠁⠀⠈⠁⠀⠀⢀
⠀⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⣷⠊⠁⠀⠀⠈⠉⠀⠀⠀⠀⠰⡾⠃⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡇
⠺⠶⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠒⠠⠤⠀⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳
⡉⠁⠀⠀⠓⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣐⠦⠴⣆⣀⡀⡀⠀⠀⠈
⠁⠀⠈⠉⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣅⣐⣊⠉⠙⠐
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠉⠉⠁
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠑⠄
⠓⢷⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠠⠒⠈⠉⠉
⠀⠀⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠂
⠷⠖⠋⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢶⡶⠰⠰
⠀⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠠⣪⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡄⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠙⠁⠀⡘⠀⠀⢀⡀⠀⠰⠉⠀⠀⠀⠠⣄⡀⠀⢀⠀⠀⢀⠀⠀⢨⠀⠀⠀⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠧⠤⠀⠈⣧⠐⠖
⠀⠀⠰⢦⣀⢄⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠂⠂⠀⠀⢺⡷⢀⠀⠀⠪⣟⠆⠸⠆⠀⠀⠀⢰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣲⠶⢓⣠⡀
⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣸⣃⣴⣃⣀⣹⣾⣑⣀⣆⣀⣀⣀⣈⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣉⣉⣉⣁⣹⣀⣀⣀
⣿⢻⠿⡿⢿⢛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣻⣿⣟⣛⣿⣻⣛⣛⣛⣛⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣰⣶⣦⡀⠠⠄
⠰⠶⠲⠤⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡖⠐⠒⠂⠈⠉⠉
⠀⠤⠀⠀⠀⠀⠀⠠⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠢⠽⠿⠟⠁⠀⠀⠀⠀⠀⠠⠤⠮⠤⠄⠀⠀⠀⠀⠀⠀⠤⡤⢤
⣤⣤⣤⣤⣄⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⡀⢀⠀⠀⣤⣤⡄⠀⣤⣤⣤⣤
⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠄⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣤⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣷⣤⣾⢿⠯⠿⠛⣿⣯⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⡒⡺⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠴⣚⠶⠿⢦⣶⣮⣽⣿⣿⣿⣿⣿⣛⢛⣿⣶⣦⣌⣛⢷⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣯⣛⣻⠿⣿⣟⣛⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠒⠶⠒⠶⢶⣦⣴⡶⢦⣍⠉⢿⣿⣿⣿⡿⣛⢛⠉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣛⣫⣾⣻⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠥⢤⣄⣿⣷⣮⡥⢶⣶⣤⣬⣹⣿⣿⣿⠷⠖⠂⠙⢿⣿⣷⣶⣮⣝⡛⠿⢿⣿⣧⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣀⣀⣤⣤⣍⣙⣛⣛⡛⠛⠀⠀⠀⣊⣉⣙⡛⠛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⠀⠀⢻⣿⣿⣿⡇⠀⠀⠙⠷⣼⣢⣝⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⣿⣿⣿⣿⡟
⣀⠐⠾⣿⣿⠉⡇⠀⣖⣀⠘⡿⠿⢿⣿⣿⡧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⡽⣿⣿⣿⣿
⠙⠓⣾⣽⣿⣤⡇⠀⢿⢿⡉⣿⣦⣦⣸⣿⣧⠀⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⣿⣿⡗⣿⣿⣿⣿⢁
⠀⠸⣏⣉⢻⡿⡇⠀⠾⣼⠦⣿⣿⣿⣿⡟⣿⣿⣾⣿⣠⡀⠀⠀⣀⣠⣐⣾⣟⣿⡉⠙⠛⣿⣿⢣⣿⣿⣿⣿⣾
⠀⠀⣹⣿⡟⠀⡇⠀⠀⠀⣴⣿⣄⣙⠙⠳⡟⢛⠻⣿⣿⣧⠀⢸⡏⠉⠛⠛⣯⣻⠋⠩⠓⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⢹⣿⡗⠀⡇⠀⣤⣄⠈⣛⠿⠿⡿⠖⣇⣿⣿⣷⣾⡽⢿⠏⠁⠀⠀⠀⣿⣿⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣫
⣀⣀⣿⡟⢗⠀⡇⠀⣿⣿⠀⣿⣿⣷⣶⡆⠋⣷⣿⣿⣽⠅⠀⠀⠀⠀⠀⠀⠉⢛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠏
⠛⠛⡛⠻⠿⠿⡗⠀⠀⠀⠀⠉⠉⠁⠓⠃⣧⣿⣿⣿⣿⣀⠀⠀⠀⢀⡀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⣻⣶⣞⠀⣧⣤⣾⣶⣤⣤⣶⣦⣄⡀⣯⣽⠉⠉⠄⠀⠀⢀⣀⠀⠀⢀⡀⠈⠀⣀⢸⣿⣿⣿⣿⣿⣿⣯
⠀⠀⣹⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⣿⣿⡤⢼⠾⡇⣸⣿⣿⡷⣰⣎⢻⣦⠀⡿⢸⣿⣿⣿⣿⢗⡶⡷⡀
⠀⠀⠼⢿⣿⣟⣿⣟⣻⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠿⠃⢻⣿⣩⣎⡇⠁⢸⣿⣿⣿⣿⡟⠑⡅⠅
⣠⣤⣤⣾⣿⠷⣿⣏⣹⣧⠚⣛⠛⠉⠉⣉⣉⠉⠉⠟⠋⠀⠀⣰⡆⠀⠠⠈⠙⢿⣏⢠⣾⣿⣿⣿⣿⡂⢀⠐
⠀⠀⢀⢻⡟⠀⠸⣿⣿⣿⣻⣿⣿⣿⢛⣛⢻⣿⣿⣆⣒⣬⣵⣿⣅⣤⣤⣶⣧⣼⣿⣿⣿⣿⣿⣿⣿⣭⣤⣄⡠
⠀⠀⠀⠚⣻⣿⣾⣿⣿⣿⣿⣿⣿⣭⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣞⣛
⠀⠀⠀⠀⠐⢿⠟⠉⠉⠙⠻⠛⠛⠛⠛⠛⢛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣦⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣹⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠛⠙⠟⠋⠄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠳⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣻⣿⢀⠠⠆⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠚⠈⠳⣄⠀⠀⠀⠀⠀⠀⣛⠿⡷⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣖⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⢿⡟⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠂⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣛⠿⠶⠿⠿⠿⣿⣿⣿⣤⠀⣰⡶⠂⢠⠀⠀⠀⠀⠘⡓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠤⣤⣤⣦⣬⠙⠋⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣿
⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⢐⣢⣴⣶⣶⣶⣦⡤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⠆⢶⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⢃⡄⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠉⠀⢨⣯⣭⣥⣭⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠶⣶⣶⣶⣶⣶⠀⠸⣼⠟⢦⡿⢄⣢⡀⢀⣼⠟⠉⠀⠀⣰⡿⢓⣍⣉⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⡶⠶⠶⠆⢩⢽⣟⠛⠿⠿⠿⠟⠛⠛⠛⠛⢛⣛⣛⣛⡋⠁⠀⠀⠀⣾⣿⠡⡏⠐⢀⡀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⣌⣒⣒⣯⣾⣿⡟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢻⣿⣧⣙⣒⣋⣤⣿⣿⡟
⠀⡀⠀⠀⠀⠀⢀⣀⣀⠈⣙⡻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟⣻⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⡏⠀⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠛⠛⠛⠿⠦⢴⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠿⠷⢮⣍⠛⠻⠶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣾⡇⠀⠀⠀⠀⠈⣷⠀⠀⠀⠉⠙⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⣿⣂⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢳⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠛⠛⠺⠿⢯⣥⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢾⣇⢰⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠛⠺⠯⣵⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣴⠏⣸⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠿⠿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⢿⠶⢶⣿⣀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠟⣱⢃⡴⠋⠀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⡼⠁⠀⠉⠁⠀⠀⠀⠀⣀⡀⠘⣷⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣆⢻⡇⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠈⢹⣿⣶⣶⣶⡞⠁⠀⠈⣿⣧⣼⣧⡀⠀⠀⠀⠀⠀⠈⠻⢿⣍⣉⣁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠛⠛⠓⠶⠶⣤⣤⡤⠴⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⠀⠀⠈⠛⠶⣤⣄⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⣛⣉⣹⣿⣿⡇⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠈⣿⣿⣷⣀⠀⠀⢀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣄⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣘⣷⣤⣧⣾⡻⠋⠉⠙⠛⠲⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣣⠅⠼⠘⠞⠒⠝⠸⠞⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣬⣭⣻⣿⣿⠵⠾⠿⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⢾⡿⢛⡿⣯⣛⠟⠻⣶⣤⡈⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠞⣵⣿⡆⣇⠙⣦⡀⠈⠙⠆⠙⠅⠀⠀⠀⠀⣠⣼⣷⡛⣚⠷⠦⠀⢀⣳⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⡄⣤⢻⣿⡄⠹⢶⣽⣿⣄⠀⠀⠀⠐⡀⠀⠐⣣⢞⢿⣷⣬⠈⢳⢤⣴⠞⣻⣿⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠻⠘⣿⡇⠘⠀⢹⡷⠙⠐⠆⠀⠀⠀⠀⣸⠧⠈⠈⣿⣟⢷⡀⢸⡏⢺⡏⢌⠓⣆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⢠⡀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠸⣿⡁⠀⠀⠀⠁⠂⠰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠠⡀⠀⠈⠙⢦⣀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠤⠴⠖⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣆⣤⡀⠀⠀⠹⣿⡄⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣉⡀⣠⣤⠴⠚⠋⠀⠀⢠⢴⠖⠈⠀⠀⠤⠐⠂⠙⢿⣯⢦⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡤⠶⠶⠶⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⠐⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⣷⡀⠀⠈⠳
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⢤⠤⣤⡤⠂⢀⡤⠖⠲⠿⠟⠛⠋⢀⡾⠀⠀⠀⠀⠀⢀⣤⠖⠒⠈⠁⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⢞⣋⣩⣥⣤⡤⣶⢶⡶⠶⢶⣦⣤⣄⣀⣀⣀⣠⣤⡤⡶⠚⠋⠀⠀⣀⣀⠤⠚⢉⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠠⠤⠤⠤⠤⠴⠶⠖⠒⠒⠂⠉⠉⠉⠉⠀⣀⣀⡤⠨⠀⠀⠴⠒⠊⠁⢀⡀⠄⠚⠁⠈⠀⠀⢀⣜⠛⣋⣲⣆⣤⡤⠟⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢉⣉⠥⠀⠀⠀⠀⣀⠠⠄⠀⠲⠉⠀⠀⠀⠀⠀⣠⡖⣥⣦⡾⢸⡞⠈⢙⡓⠢⠄⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠚⠉⠀⣠⠴⠒⠋⠉⠀⠐⠂⠀⠠⠂⠀⢀⠤⠐⠛⠱⠋⠽⠇⠀⠙⠋⠙⠛⠑⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣋⠵⢊⠓⣧⠀⠰⠄⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣩⠔⢊⡤⠚⠉⡆⢿⠀⠀⠀⠀⢀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣀⡴⠚⡡⠔⠋⢠⠊⣁⠀⢺⡇⡇⢸⠀⣸⣿⣿⣿⢸⡏⡍⠭⢝⢦⣤⣀⠀⠀⠀⠀⣀⣠⠄
⠀⠀⢀⡴⢞⡡⠖⢉⡤⡆⠀⠘⡀⣿⠀⠈⠀⡇⢸⠀⠛⠿⠿⢿⢸⡇⠀⢀⡨⣸⣿⠿⢿⣟⣶⣯⠿⠚⠃
⠀⢸⢯⣖⢉⡤⠒⢁⣤⢰⠀⠀⡇⠀⣠⣄⠀⡇⢸⠀⠀⠛⠛⢻⣼⠷⠿⠿⠞⠃⠀⣠⢟⡽⠛⢮⢷⡀
⠀⢸⢸⠀⡇⢴⡆⠀⠿⢸⠀⠀⡇⠀⢛⡡⠖⣩⡾⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⣯⡏⠀⠀⠈⣿⡇
⠀⢸⢸⠀⢣⠘⠃⠀⠀⢸⠀⠀⠧⠚⢁⡴⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣇⠀⠀⣠⣿⡇
⠀⢸⡌⡄⢸⠀⢰⡶⢂⡸⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⣿⣿⠽⠛
⠀⢸⡇⡇⢸⢀⡠⠖⠉⣠⠴⠋
⠀⠈⡇⡇⡈⠁⣠⠴⠋⠁
⠀⠀⢷⣤⠷⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠔⠊⠉⠙⠓⢄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠻⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⡴⠋⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⢠⠗⢄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠈⠓⠶⠤⠶⠋⠀⢈⡇
⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⢀⡼⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠘⢧⡀⢀⡴⠋⠀⠀⠀⠀⠀⢱⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⡛⠀⠀⠀⠀⠀⢺⣄⡈⠻⠿⣟⠉⠈⢷⢦⣀⣀⡤⠚⢁⡴⡃⠢⣄⠀⠀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⢧⠀⠙⠻⢧⣛⡜⠦⣤⠏⢦⣭⢥⣖⡾⠿⠋⠀⠀⠈⠙⠒⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣬⠿⠶⣄⠀⠈⣙⢷⡀⡤⣶⣟⣉⣠⣴⣶⣦⣤⣀⣀⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⡷⡀⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡗⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢙⡌⠈⣢⡈⣛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠹⠤⠏⠉⢯⠟⠙⠪⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠃⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣻⣶⣶⣾⣿⠂
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡟⢂⣿⡏⢸⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⠟⠃
⠀⢠⣦⣠⣿⣿⣿⣿⡟⠈⠛⠻⢿⣾⣯⣤⣾⣿⣿⣿⣿⣛⡻⢿⣶⣦⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠉
⠀⠈⢿⣿⡏⠙⠻⣿⣿⡄⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆
⠀⠀⠈⠉⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣈⣽⣿⣷⣿⣿⣏⠀⢀⣀⣤⣤⣴⣶⠾⢿⣿⣿⣿⣏
⠀⠀⠀⠐⠛⠻⠿⠛⠻⢿⣿⣶⣶⣶⡶⢿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠛⠿⣿⣿⣿⡾⠿⠛⠉⣼⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣿⣿⣧⡀
⠀⠀⠀⠐⠲⠶⠶⢦⣴⡿⢿⣿⣿⡷⣦⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⠉⠉⠙⠛⠻⠿⢿⣷⣶⣤⣤⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⢀⣠⠶⠛⠙⠟⠉⠁
⠀⠀⢻⣏⣹⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁
⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⠶⠒⠒⠲⢤⡀⠀⠀⣀⣤⣄⡀⢘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠒⠋⠁⠀⠀⠉⠛⠋⠙⠻⣿⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⣀⡞⠙⢦⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⡴⠋⠉⠙⠳⣄⡼⠁⠀⠀⠀⠙⠓⠲⡄⠉⠙⠲⣤⠀⠀⠰⠿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠐⢦⠴⠃⠀⠀⡴⠋⠁⣀⣠⣤⣤⣤⠄⠀⠀⣿⠀⠀⠀⠈⢳⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⣠⠞⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⢧⣠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠿⣍⣛⣉⣁⡴⠊⠀⣀⣀⣀⣀⣀⣤⠖⠋⠁⠀⡴⠚⠲⣄⠀⢀⣽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⡿⠟
⠀⢀⣨⣭⣤⣤⠴⠚⠉⠀⠀⠀⠀⠈⠙⢦⡀⠈⢧⣀⡀⣈⣩⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⡴⠒⠒⠦⣀⠀⠈⠳⢤⣀⣀
⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠙⢄⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠈⠳⠦⣤⣤⠤⣴
⠀⢀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠟⠛⠛⠶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣷⣶⣤⣤⣶⣿⣿
⠀⢸⣷⣶⣶⣶⠾⠟⣋⣡⣴⣶⣶⣿⣷⣶⣶⣤⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⠿⠛⢉⣡⣤⣤⣤⣤⣤⣌⣉⠙
⠀⠀⠉⣉⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⢯⣭⣭⣤⣬⣥⣤⣤⣄⡉⠛⠻⠿⠿⠿⠟⠛⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠘⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⠿⠿⠿⠿⢿⣿⠷⠶⠛⣣⣴⣿⣿⣿⣿⣿⣿⣦⠤⠤⠶⠿⠿⠟
⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠙⠷⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠿⠿⣿⠿⠛⣉⣤⣤⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⣷⣦⣄⠀⠰⣶⣶⣶⣶⣶⣶⣶⠶⠟⣁⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢳⣴⠶⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣭⣭⣭⣭⣤⣶⣿⣿⣿⣿⣿⣿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣤⣤⣀⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠳⠦⠄⠉⠛⠻⠿⠿⢿⣿⣿⠿⠿⠟⢛⣉⣤⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣾⣿⣷⣦⣀⠛⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠈⠉⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣤⣤⣄⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⢿⣿⠋⣁⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⡿⠛⠋⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣠⣿
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠉⢠⡄⠹⣦⠀⠀⠀⣿⣿⣿⣇⢿⣦⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣯⣿⣿⣿⣿⠏⠀⠀⣠⡆
⠀⢠⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣆⠙⢷⡄⠀⠸⣿⣿⣿⡜⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⣿⣿⣿⣿⣿⣷⠀⢠⠞⠉
⠀⠀⠻⣿⡇⠈⢹⣿⣿⣿⣿⣿⠀⠀⠈⢿⣄⡰⣿⡀⠀⢻⣿⣿⣷⣾⣿⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⢿⣿⣿⣿⣿⣿⡴⠃
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣷⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⠃⣤⣿⣿⠋⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿⠛⣷⣀⠸⣿⣿⡟⠛⠻⣷⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢹⣧⡘⣿⣧⣹⡟⠻⢷⣦⣼⣿⣿⣿⣿⣿⣿⣵⣿⣿⡿⠁⢀⣶⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠈⢿⣧⠈⢻⣿⡿⢦⣤⡤⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⢠⣶⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠻⣷⡀
⠀⠀⠀⢠⣾⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠠⠻⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⠈⠀⠰⠄⢀⠀⡀⠀⣄⣀⡀⢠⠚⠆⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠋⠂⠱⠎⢿⡟⠉⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠸⡇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠹⡅⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢀⣼⠃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣼⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣉⣉⣉⣉⣉⣉⣉⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⢿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠉⠉⠛⠓⠦⠀⠀⠀⠀⢀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠑⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠒⠋⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠲⠶⠤⠄⠀⠀⣀⡀⠀⠀⠀⠄⠰⠖⠀⢀⣀⣤⠶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠙⠛⠓⠶⠶⠶⠶⠤⠤⠴⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣙⡓⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣤⡤⠴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠈⣉⡉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠶⢤⣬⣉⣉⣐⡒⠒⠒⠒⠒⠒⠒⢂⣀⣀⣀⣠⣤⡤⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠲⠶⠤⣬⣉⣉⣉⣉⣀⠀⠀⠈⢉⣈⣉⣉⣠⡴⠶⠞⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣤⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠈⠉⠉⠉⠉⠉⠉⠉⢉⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁⠀⢀⡀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠩⢉⡤⠠⠴⢀⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣻⣿⣿⣯⣤⠺⠯⠗⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡬⠉⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⣶⠖⠁⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢶⠖⠒⠛⢛⠋⣳⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⣐⠋⠐⠀⠀⣰⣵⡆⠀⠀⠀⠀⢀⣠⡦⠔⣚⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⠀⠀⠀⣸⣿⣧⣤⣶⡶⡟⠉⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠶⣶⣛⠻⣿⢿⡀⢂⠀⢨⣹⣦⠀⠀⠜⣡⠄⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⣠⠄⠀⠛⢻⣦⡀⠀⠀⠄⡄⠁⢉⠀⠀⠀⠁⠀⠀⠀⡀⠀⢺⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣞⣩⣥⣤⣤⣤⢼⡏⠑⠀⠀⢰⣿⣼⣧⣤⡤⠀⣀⠤⠀⠀⢀⣶⡖⣹⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⣩⡔⣾⠏⠛⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠤⠜⠅⡒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⢣⣜⣿⢀⡆⠀⠀⢀⠀⠀⠀⠀⠀⢀⣰⡾⠿⠋⢹⢻⡛⠶⠞⣡⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠘⣗⣼⡟⠀⠀⠘⠒⠒⣒⣂⣭⣤⣶⣶⣾⣿⣿⣷⣮⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠡⢤⣴⠏⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠒⠶⣒⣵⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠿⠿⠿⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠑⡄⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗⠠⠄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠈⠢⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠄⠀⠐⠁⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠑⡀⠀⠘
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⢠⠋⠀⢹⣷⣦⣤⣀⡀⡇⠀⠀⠀⠀⠀⢡
⠱⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢡⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆⠀⠀⡇⠀⠀⣿⣿⡇⠀⡔⢊⠃⠀⠚⠑⠘⢄⣰⠀⠀⠀⠀⢀⢄⣿⠾⠻⢷⣕
⠀⠀⢃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡇⠀⠀⡆⠀⠀⣿⣿⣧⢸⠀⢂⡀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⡌⣿⠁⠀⠀⠀⣿
⠀⠀⠀⢂⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⣿⣿⣿⢘⡀⠀⠉⠉⠁⠀⡰⠀⠀⠀⠀⠀⠀⡿⡙⢷⣤⣠⣴⢟
⠀⠀⠀⠈⢆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⣿⣿⠀⢙⠂⠄⠀⡤⠊⠀⠀⠀⠀⠀⠀⢀⠀⡀⠐⡬⠍⠒⠁
⠀⠀⠀⠀⠈⡄⠀⢰⡉⠑⠤⣀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠁⠀⠀⢸⣿⣿⠀⠈⠀⣤⡀⠆⠀⠀⠀⠀⠀⠀⢀⠎⣼⡟⡰⠁
⠀⠀⠀⠀⠀⠘⣀⠇⠈⠑⠢⠤⢈⡁⠒⠢⢄⡀⠙⡄⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⢰⠀⣿⠀⡄⠀⠀⠀⠀⠀⢀⢂⣾⠟⡐⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢲⣿⣿⣷⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘⢸⣿⠀⠀⠀⠀⠀⠀⢠⢃⣾⠏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⡇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠘⣿⣿⡇⠀⢸⡟⢸⠀⠀⠀⠀⡠⢁⣾⠏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠧⠧⠀⠀⠀⠀⠀⠼⠀⠀⠀⠠⠿⠿⠧⠤⠾⠧⠴⠀⠀⠀⠴⠥⠾⠏⠬⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣬⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣯⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣿⣿⡿⠷⢦⣕⠀⣀⣿⣿⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠇⠈⡿⠀⠀⠘⠆⢰⠟⢡⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠰⡀⠀⠀⠈⠀⢸⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣤⣿⡾⠦⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠟⠉⠓⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⢀⣀⣄⣀⣻⣤⣴⣶⣿⣿⡿⣿⣷⣯⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣲⣦⣶⣿⣷⣾⣿⣾⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⠉⠲⠿⠿⠦⠬⠭⡍⢉⣉⣉⠉⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠔⠒⠀⠀⢀⣠⣤⡴⠂⠄⠀⠀⢀⣀⡠⠭⠄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡀⠁⠠⠤⠀⣀⣐⣲⣦⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣶⠶⠿⠛⠁⣠⢄⠀⠀⠀⠪⠹⠭
⠀⠀⠀⠀⣀⣀⢀⣀⣀⡠⠭⠵⠶⠶⢚⢛⡛⠛⠽⠟⠛⠋⠉⠉⠉⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⣷⠶⢦⠀⠀⠐⠄
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣖⣲⡶⡺⠿⠿⠟⠛⠋⠀⢀⡞⠀⠀⠀⠀⠄⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠛⢛⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠞⢫⡀⠀⠀⠀⢀⡠⠔⠋⡀
⠀⠀⠐⠒⢀⣉⣉⣉⣙⣉⣉⣭⠤⠤⠶⠟⠛⠛⠋⠉⠉⠈⠃⠛⣉⣀⢀⣙⣩⠽⠛⠛⠛⠛⢛⣫⠭⠉⠓⠋⠉⠒⠻⠧⠒⣒⠉⠁⠀⢀⣀⣱⠄
⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠖⠒⡋⠉⠅⠐⠊⠉⠀⠀⢉⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢸⣶⣶⢷⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠀⠀⠀⢀⣠⡤⠤⠒⢈⠄⠙⠂⠀⠀⠀⠀⠀⠀⢀⡤⢮⣱⣎⡿⢟⣓⣿⠉⢀⣉⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠒⠒⠒⠛⠛⠉⠁⠀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠐⠀⠂⠉⠰⠏⣥⠼⠃⠀⠉⠉⠁⠘⢋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠒⠒⠂⡄⠀⠀⢀⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⣯⢽⠀⠀⠀⢸⣽
⠀⠀⠀⣀⡀⣀⢀⣇⣀⠀⠘⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⢺⠀⠀⠀⢸⢾⠀⠀⣠⠀⠀⣾⣿⡀
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠒⠀⡧⡟⠛⠛⠂⢰⡄⠸⢹⠀⠀⡇⠀⠀⣿⣿
⠀⠸⠇⠄⠀⠀⠀⡄⠀⣆⠀⠀⠈⠀⡆⣱⣄⣀⡆⢲⣶⡄⠰⣄⣿⡇⠀⠀⠀⢸⡇⣏⣉⡔⠚⣃⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⡷⠞⢛⠛⠉⣿⠤⡆⠀⢁⠀⢀⠀⠀⢰⠼⣧⡏⡀⠁⡴⠖⠛⠂⠛⢻
⠀⠀⠀⠂⠀⠀⠀⠃⠀⢸⡀⠀⠀⢀⣇⣀⣸⠀⣀⠛⠉⠁⠄⠀⠀⠀⡇⢰⢸⣴⣿⡇⡏⣧⠷⡄⠈⠀⠀⡼⢦
⠀⠀⠀⡀⠀⠀⠀⣀⣠⣮⡄⠀⠀⢐⠀⠀⢺⡁⣺⠀⠀⠀⠀⢀⡀⣀⣧⢼⠾⣷⠿⢇⠉⢯⣿⣓⣲⠀⠀⢳⣾
⢰⣶⡆⠰⠦⣶⣖⣿⡿⠿⠛⠚⠛⢻⣤⣤⣼⠤⠿⠤⠤⠤⢼⡤⠉⠀⣿⡾⠒⠺⡇⡏⠉⠉⢹⡟⠛⠁⠀⠈⢨
⠘⡃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠉⠀⠁⠉⠁⠈⡿⢹⢿⣿⠉⢽⠧⠼⠤⡄⠀⢸
⢸⣯⣓⣲⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⢷⢸⡞⢻⠀⣸⠀⡂⠀⡏⠀⠉
⠀⠉⠉⠀⠀⠀⠀⠀⠀⡇⡀⠐⠘⠁⠀⠀⠀⠀⠀⣀⠀⢠⡇⠀⠀⠘⠋⠉⠀⢸⢈⡃⢸⠰⡓⠚⠭⠉⠉⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠃⠀⠀⠐⠀⠀⡁⠀⢸⠉⣇⠘⡇⠀⠀⠀⠀⠀⠀⡏⢸⠃⠙⠈⡇⠀⠐⠀⠀⡅
⠀⠀⠀⢀⠀⠀⠀⢞⢸⡗⠀⠀⠀⠀⠇⢀⠂⠀⡞⠒⡇⢨⡄⠀⠀⢶⠀⠀⠀⠉⡟⡀⢸⠙⠁⠘⡦⡠⠤⠯⣴
⠀⠀⡀⠈⠀⠄⠀⢸⢸⡇⠀⠀⠀⠀⠘⣠⣦⣤⡧⠀⠋⢺⡇⠀⠀⡏⠀⠀⢀⠀⡇⡤⢰⢀⣀⡀⣧⠄⠀⠂⡇
⠀⠀⠁⠀⠀⠈⠁⡸⠼⢇⠀⠀⠀⠀⠀⠙⠒⠬⣙⣳⠾⠿⠇⠀⠀⠀⡀⠀⠚⣣⠅⡇⠀⠈⠃⠂⠀⠀⠀⣀⣧
⠀⠬⠀⠀⠀⠀⠀⢄⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠐⠐⠀⠀⠂⠀⠀⠀⢘⣇⡀⠠⠄⠀⠀⠀⢀⡇
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⢀⠀⠀⠐⠤⠄⠀⡇⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠸⠉⠉⣙⠂⡥⠔⠒⠊⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠹⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠿⣵⡆⠀⠈⢹⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡄⠄⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⢼⣸
⠀⠀⠀⠀⠀⠀⠠⠈⠈⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠂⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⡶⠶⠦
⠀⠀⠘⣠⣾⣿⣿⠏⠀⠈⠉⠛⠛⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣼⣿⣿⣿⣿⢶⡆⢐⣒⠀⣲⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣿⣿⣿⣷⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⡜⠁⠈⠉⠤⠉⠉⡽⠛⠋⠛⠛⠙⠙⠉⠋⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⠟⠛⠛⠋⠁
⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣀⣀⣀⡀⠙⢤⣀⡀
⠀⠀⠀⠘⠻⠿⣥⠤⠖⠊⠁⠀⠀⠈⠉⠛⠉

⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀
⠀⠀⠈⢀⠠⡄⠴⠠⠀⠀⠀⢀⠤⣀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⡄⠉⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠈⠈⠀⡀⠀⣀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠄
⠀⠀⠀⠀⠀⠀⡶⠛⢯⠛⣢⠀⠀⠠⠁⠀⠀⠀⣀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠈⠀⠀⠀⠀⡐⢀⠀⠀⠄⠀⠀⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣇⣀⠀⠀⠠⣾⠇⠀⠈⠈⠉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠛⠉⠑⠀⠀⠈
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠴⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠁⣄⠀⠀⠁⠀⡆⠀⠀⠀⠀⠸⠀⢀⠀⠀⠦⠄⠀⠀⠀⠢⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⡀⠀⠈⠋
⠀⠀⠀⠀⡰⠉⠉⠀⠀⠀⠁⢄⣀⣤⠰⠊⠀⠄⠀⠸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⠉⠀⠛⣉⠄
⠀⠀⠀⠀⠀⠐⠄⠀⢖⡀⠀⠀⠀⠀⠀⠤⠈⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢸⠃⠀⠒⠀⠀⠠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢠⠀⠆⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⡀⠁⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⣇⡼⠀⠀⠀⢀⢄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠃⠀⠀⠀⠀⠀⢠⡄⠀⢀⡠⠤⠐⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠀⠀⠀⠆⠘⠈⠴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⡂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠄⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⡴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠠⢀⡀
⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢚⣄⠀⢨⡆⠘⠊⠀⠠⠁⠀⢀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡄⠀⠀⠀⠁⠵⡋⠀⠀⠀⠳⢄⠀⠀⠀⢀⡠⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣾⡯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣀⡁⠀⠀⠀⠂⠐⠀⠀⠂⡀⠀⠀⠀⠁⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀
⠀⠀⠀⠀⠀⠌⢄⠀⠀⠀⠀⢩⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠠⠀⠃⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠂⢀⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠈⠀⠑⠴⠃⢛⠆⠤⠌⡀⡀⡀
⠀⠀⢀⢄⣀⠀⠀⡀⢀⠤⠀⢤⠄⡄⠀⠀⠠⣤⡊⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠐⡐⡉⣆⣀⠀⠀⠀⠋⠀⠄⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢜⢀⠁⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠁
⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠐⠀⠀⠀⢀⡀⠆⠀⠠⠘⠃⢀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⢠⠀⠀⠠⠀⠉⠀⠰⠀⡄
⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠂⠠⠄⠐⠀⠀⠀⠈⠀⢰⠀⠠⠈⢀⠀⠁⠀⠀⠂⠐⠄⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠣⠀⠀⢀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀⠀⠄⠀⠠
⠀⠀⠀⢸⡌⠁⠀⢀⣀⣀⠀⠐⢀⣷⣆⠀⠀⢀⠐⣿⣿⣧⠀⠀⠀⠀⠀⠁⣶⡀⠀⠀⣀⣀⣤⠤⠑⡀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢶⣶⣦⣤⡧
⠀⠀⠀⠈⣻⡄⠀⠈⠉⠉⠁⠀⠼⣿⣿⡇⠀⠈⢣⣿⣿⣿⣷⡀⠘⢿⣷⡀⠙⣷⡄⠀⠐⣶⣿⣷⣽⣼⢆⠀⠀⠀⠺⣿⣿⣦⣀⣀⣀⣀⣀⡀⠈
⠀⠀⠀⠀⣿⣿⣆⠀⠀⢠⢤⣦⠀⠀⠹⣿⣄⠀⠀⠙⠚⠛⠻⣷⡀⠈⠓⠃⠀⠘⢿⣄⠀⠈⠿⠿⠿⠿⢿⣆⠀⠀⣄⠀⠙⠿⣿⠛⠋⠉⠙⠁⠀⠀⢀
⠀⠀⠀⠀⣿⣿⣿⣦⣀⣤⣄⣀⣀⣀⣀⣸⣿⣦⣀⣀⣀⣀⣀⣈⣿⣄⣀⣀⣀⣀⣸⣿⣦⣤⠤⢤⣤⣤⣬⣿⣆⠀⢸⣷⣄⢀⢈⣷⣦⣤⣤⣶⣶⣶⣾
⠀⠀⠀⠀⢿⣿⣿⣿⢻⣿⣿⡿⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣗⠲⣺⣿⡯⣿⣽⣿⣿⣿⣿⣷⣶⣾⣿⣿⣤⣿⣿⣦⣾⣿⣧⣴⣾⣿⣟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⡍⡏⡟⣿⢿⣿⣿⡟⣿⡿⣿⣿⣿⣿⡿⡛⡿⣶⣿⡛⣿⡿⠷⠷⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⣿⣽⣜⣼⣿⣇⣿⡇⣿⣿⣿⣿⡇⡅⡅⣿⣏⠟⢿⣿⠷⢿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢰⣾⣿⣿⣿⣟⠛⠫⣟⣛⣋⢹⣿⣿⣿⣿⣶⠀⣾⡿⢴⣿⣿⡋⠉⠉⢉⣹⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇
⠀⠀⠀⠀⡯⣿⣿⣿⠺⣤⣤⣾⠴⠤⣸⣿⣿⣿⣿⢿⢳⢿⠋⣽⣽⣻⣿⣿⣿⣿⣿⣿⠿⠿⢿⣽⣿⣿⣿⣿⡟⢩⡉⣿⣿⣯⡽⣿⣿⣭⣭⣉⣹⣛⡃
⠀⠀⠀⠀⡇⢿⣿⣿⠀⣿⠿⢛⣉⣉⣉⣽⣿⣿⣿⢡⡍⣿⣧⣛⣿⣿⣏⣿⣾⣳⣯⣀⣤⡄⠀⠀⣷⣓⣛⣿⣏⢸⡁⣿⣿⠉⣴⣿⣿⣿⣷⡿⠿⢿⠆
⠀⠀⠀⠀⠻⣦⡉⢻⠀⣛⠛⠻⣷⣾⠤⣿⣭⣿⡿⠋⠛⣟⢧⣠⡶⣿⡿⠤⢾⣿⠿⠿⠚⢻⣷⣶⣿⣭⣭⠟⢿⣈⣀⡋⠻⠾⠛⠛⠙⠒⠚⠒⠂⠒
⠀⠀⠀⠀⠀⠈⠙⠛⠀⠉⠉⠋⠁⠀⠀⠀⠙⠛⠁⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠶⠊⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢄⠀⢊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣠⣶⣿⣿
⠀⠀⠀⠀⠄⠀⡀⠀⢠⠠⠈⢠⡷⠐⠱⠀⠀⡀⠀⠀⠀⠀⣠⣤⣤⣯⣾⣿⣿⣿⣿⣿⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠈⠢⣀⠑⢜⡡⠐⠊⡄⠂⠀⠒⠁⠐⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠁
⠀⠀⠀⠀⠡⡀⠈⢢⢎⢀⠀⠀⠘⠉⠀⣰⠄⠂⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣉⢂⡀⠀⠺⠁⢳⡷⠒⠲⠃⠠⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠡⡈⣡⡐⢄⣀⠈⠐⡘⢠⡔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠁⢰⣜⡁⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⣷⣯⣼⣝⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⡳⢻⠛⠟⡻⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⡀⣘⠀⣁⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⢠⠁⠀⠀⢀⣀
⠀⠀⠀⣤⢰⣦⣀⠀⣀⡭⡹⠶⡄
⠀⠀⢀⣭⣿⣿⣏⠠⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⡤⠾⠉⠿⣿⡇⣅⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⢆⢸⣇⣿⠬⠭⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣢⣴⡿⣿⡯⡶⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣧⡄⠰⠖⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠟⠉⠁⣧⣸⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣿⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⡀⢀⣬⣀
⠀⠀⠈⠁⣿⣯⣿⠛⡛⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠰⣸⣯⠧⠭⠓⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠽⣿⣭⣄
⣠⡤⢺⣿⣿⣇⣛⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⢻⡗⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡤⠶⡦⣴⣿⡡⠈⠉
⠉⠂⢠⠀⣿⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢸⣷⡶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠈⠀⠀⠀⠲⣿⢿⠶⣀
⠀⠀⠠⠁⣼⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢾⣿⣏⡃⠀⠀⠑⠀⠀⢀⠒⠯⠄⣴⡦⠀⠀⠀⠀⢀⠤⠶⣶⣿⠛⠀⠈
⠀⠀⣆⠀⢿⡗⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⡏⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⣹⡟⠳⠤⡀⠀⠀⠀⠀⣭⣿⠿⠒⠤
⠀⢠⠊⠠⣿⡇⢂⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡇⢣⠀⠀⠀⠀⠀⠀⠊⠈⠉⢽⣿⣤⡀⠀⠀⠀⠀⠀⡁⢿⡘
⠀⠐⡀⠀⣯⡇⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣼⡇⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⢞⡟⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⠂
⠀⠃⠀⠢⣯⡏⠂⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⢹⡇⠀⡃⠀⠀⠀⠀⠀⠈⠀⠀⢿⡟⠃⠒⠀⠀⠀⠀⠘⠁⣼⠁⢠
⢰⢣⡀⣉⣧⣷⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣛⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠁⠀⠀⠀⠀⠀⡐⠀⣿⠆⠈⡀
⢼⠛⠉⢶⣟⡿⠘⠓⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠣⣿⡯⠛⢺⠀⠀⠀⠀⠀⠀⠀⠐⢈⡇⠀⠀⠀⠀⠀⢀⡶⠾⣿⡷⠛⡆
⣿⣷⠶⠶⠿⢷⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣶⣶⣶⣶⣾⣷⣾⣿⣷⣾⣷
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡾⠋⠉⠉⠻⣷⠀⠀⠀⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠛⢻⡇⠀⠀⠀⠀⣸⠇⠀⠀⠈⠑⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣀⣴⣿⣶⠶⣄⣀⣀⣤⣼⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣯⣔⠋⠁⠀⠀⠀⠙⠿⣯⣍⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⠒⠒⠲⢮⡙⢻⣷⠀⠀⠀⠀⠀⠀⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣿⢨⡏⠀⠀⢀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣸⣯⡿⠀⢀⣾⣿⣿⠟⢉⣴⣶⣿⣿⣿⣿⣶⣷⣶⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⣶⣿⣶⣦⡀⢠⣿⣿⠃⠀⠸⣿⣿⣿⠀⠸⢿⠿⠿⠟⣛⣛⣛⣻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣰⣿⣿⣿⣿⣿⠁⣾⣿⡿⠀⠐⢦⣤⣤⠴⠶⠶⠾⠿⠿⠿⠛⢛⠛⠛⠛⠛⠃⣁⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣸⣿⣿⡇⢀⣤⡄⠀⠀⠀⠀⢠⣀⣥⣶⣿⣿⣿⣿⣿⣿⣷⣶⣮⣿⣿⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⠿⣿⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⢻⣿⣷⢸⣿⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱
⠀⠀⠀⢀⣴⠟⠛⠛⠉⠁⠀⠀⠈⠙⠻⣿⣆⠀⠘⡞⣿⣿⡘⣿⠄⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⢠⣾⣁⣀⣀⣠⣤⣶⣶⣶⣦⡀⠀⠹⣿⡆⠀⢰⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣵⡄⠀⠀⠀⠀⠸⡇
⠀⠀⢾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⠀⠀⢣⢻⣿⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢳⠶⠛⠻⣷⣶⡶
⠀⠀⠀⢨⡯⠉⣹⣟⠉⠹⠿⠙⢻⣿⣿⣿⣿⣿⡇⠀⠀⢇⢿⡀⢠⡂⠀⠀⢸⠆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠔⠐⡄⠀⣸⡇
⠀⠀⠀⣿⡓⠰⠙⠋⢣⡀⢀⠀⠹⠛⣿⡹⣿⣿⣷⣶⣶⣦⢊⢇⠀⢇⠀⣀⣾⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⠈⠀⠢⠀⠀⠀⢹⡇
⠀⠀⠐⣻⣏⣧⡤⠀⠤⠁⠹⡦⠀⢤⣾⡇⠛⠛⠿⣿⣿⣿⣧⣬⣆⠀⠙⠛⠻⠿⠿⠿⠿⡿⠿⠿⠿⠟⠛⡛⣿⣗⠀⣤⢀⣿⡿⠁
⠀⠀⠀⢼⡧⣏⠁⠀⠐⠀⠼⠳⡀⠈⣽⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢸⡧⢿⣶⣦⠀⠀⢀⠀⢼⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠓⠈⢿⣷⣦⣼⣿⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣾⡿⣿⡿⣻⠟⢿⣿⣽⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣶⡿⠿⢟⠛⢉⢥⣴⣻⡿⠻⢽⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⣿⡟⢡⣲⣾⣿⣮⣿⠟⠉⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣾⣟⡥⢙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⣀⢻⣿⣿⣿⣿⣀⣤⡶⡾⠒⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⡄
⠀⠀⠀⠀⠀⠀⡠⠂⣀⣤⣿⣿⠿⠀⢐⣾⣿⣿⡿⠟⠟⠉⢁⣀⣴⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠐⠉⠀⠀⠛⠉⢋⡀⣄⣶⣾⣿⣿⢯⠙⠐⠊⠉⠛⠿⢿⣿⣦⣀⣀⣠⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢺⣿⣧⣧⣾⣿⣿⣿⣿⣿⡻⠆⠀⠀⣠⣴⣄⣻⣿⣿⣿⣿⠟⠋⠀⠋⠙⢻⠟⡁
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣛⣛⣿⣯⣭⣿⠉⢂⠁⠀⣀⣸⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⢀⡤⣴⣾⠿
⠀⠀⠀⠀⠀⢻⡿⠿⢿⣿⣿⣿⡿⣯⡉⠉⠀⠀⢺⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⢠⣶⣦⣄⡀⠀⠅⠑⠀⠀⢀⣠⡀⣀⣦⣾⣿⣿⡟⠎⠙⠻⠷⠀⠀⠀⠀⢀⣤⣶⡿⠃
⠀⠀⠀⣿⣿⣿⣿⣷⣢⣦⣿⣼⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⣀⣚⣫⠭⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⣒⣚⡛⠓⠒⠤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⠭⠽⢿⣭⣭⣛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠴⢪⣥⣤⡀⡘⠿⠿⠋⢀⣠⣄⡈⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣫⡵⠚⠛⣿⣧⣀⣠⣼⡿⠿⠿⣷⢹⣿⣿⣿
⠀⠀⠀⠀⡔⣁⣀⠙⠛⠋⠀⣿⠀⠀⠀⠘⠿⠟⠁⣹⠀⠀⠀⢸⣿⣿⣿⣿⣫⡾⠿⣦⣤⣴⣿⠈⣿⣿⣿⣧⣀⣤⣾⠏⣿⣿⣿
⠀⠀⠀⡞⠸⠿⠿⠃⠸⣷⡀⣿⡀⠀⣠⣤⣄⠀⢠⡟⠀⠀⠀⢸⣿⣿⣿⢳⣇⣀⣀⣼⣇⠉⢿⠀⣿⣿⠿⠛⠻⣿⡿⢸⣿⣿⣿
⠀⠀⠀⢧⣤⣴⡶⠿⣷⠈⠀⢻⣧⡀⠛⠛⢋⣰⡟⠁⠀⠀⠀⢸⣿⣿⣿⡘⠛⠋⢉⣀⡙⣷⣿⡄⠸⢿⣤⣤⣴⠟⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⢸⠀⠘⠚⠛⢁⣠⣴⠿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⡇⣿⣧⣥⣤⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⠿⢟⣫⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⣽⣧⣈⣉⣉⣁⡤⠶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠻⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣄⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟⣯⣤⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⡝⠿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠞⠀⣿⣿⣟⡤⢤⣀⠀⠀⠀⠀⠀⠠⣖⣚⠡⠤⠤⠤⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣾⣿⡟⣿⣿⣜⢯⡲⡀⠀⠀⠀⠀⠀⠈⢹⡶⣶⢿⣗⣖⣲⣯⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠱⣝⢿⣿⣷⣤⡙⡄⠀⠀⠀⠀⠀⣼⠿⣻⣏⢿⣿⣿⣿⣟⣿⡿⣻⣶⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣿⡿⠃⠀⠈⠻⠶⣝⠶⣿⣿⡇⠀⠀⠀⠀⢰⣿⣼⣿⡿⣪⢟⡻⠋⣽⠏⠛⢮⠻⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣎⣭⠴⣚⣛⣛⣛⢿⣿⣷⣦⡀⠀⠀⠀⠈⢿⣶⣍⡛⠿⣶⣖⣤⣾⣏⣀⡟⣼⣿⡼⣇⣼⣋⠀⠀⠈⡇⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡥⠖⠋⠉⠀⠀⣼⡟⠫⠛⣿⣿⣆⠀⠀⢠⣶⡿⣿⣿⣶⣦⣍⠉⢋⣉⣩⣭⣭⣭⣽⠱⠯⢭⣷⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⠎⠀⠀⠀⠀⠀⣼⡟⠀⠀⣀⢸⣿⡿⡆⠀⠸⡞⣧⣻⣟⡛⠛⢻⣿⡿⣿⣿⠿⠿⢛⢓⠀⠾⠝⠃⠀⡼⢡⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠇⡟⠀⠀⠀⠀⣴⣶⣿⣶⣾⣿⡯⠞⣿⣿⡇⠀⠀⠷⣺⢟⣠⣶⣼⠧⠛⠛⠓⢲⣍⠣⣄⠀⠀⠀⢀⣤⢞⡵⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣷⠀⠀⠀⠀⠹⠿⠛⠁⠉⠀⠉⣹⢻⣿⡇⠀⠀⠀⠙⠺⠷⠿⠟⠀⠀⠀⠀⠀⠉⠳⠬⣍⣙⣉⠭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢡⠞⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡙⠳⠦⢤⣤⠤⠴⢚⣡⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠚⠋⠉

⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢂
⠀⠀⠉⠙⢻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠃
⠀⠀⠀⠀⠘⢿⠏⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣟⠉⠉⠉
⠀⠀⠏⠁⠀⢸⡂⣿⣹⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠁⠘⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡃⠉⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠊⠀⠇⠘⠀⠀⠀⣠⣴⠾⠛⠋
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣤⣾⠃⠀⠀⠲⠖⠊⠀⢈⡧⠶⡆⠁⠀⣶⣶⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⡔⣋⢰⡃⠀⠀⣿⣣⣴⠟⠋⢠⣴⠄⢀⣠⣦
⠀⣤⣴⡄⠀⢸⡇⠀⠀⠀⠠⠀⠀⣿⠃⠀⠰⡎⠀⠀⢀⡾⠻⠀⠀⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣯⢉⡟⠃⢸⣿⣛⡋⠟⠁⢀⢘⣿⡏⠀⠀⠀⢈⠿⣾⡿⠋
⠀⢻⣿⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡃⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢊⡧⠐⢠⡟⢻⣿⠄⡶⢰⠸⣿⡇⠄⠄⠀⢀⣾⠹⡃
⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⢀⡀⠀⣿⢠⠀⣤⣤⣤⠋⠀⠀⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠉⠀⠀⠘⢿⡆⠀⠀⠋⠸⣑⣯⡉⣠⡤⠐⣖⣿⠿⠀⣀
⠀⠀⠀⢠⣸⣄⣀⣀⣀⠀⢾⠃⠀⣿⠈⠀⢸⣷⣋⣅⡆⡇⡇⢸⢸⠀⠀⠠⣿⡿⠀⠀⠀⠀⡇⢀⠀⠀⠀⢤⢬⡹⠁⠀⠀⣠⡶⠟⢋⣭⡷⠛⠛⠉
⠿⠟⠛⠏⡙⠉⠁⠀⠀⠁⢢⣄⠀⡏⠐⣈⣬⢿⣿⣗⣓⡃⠉⠤⢼⠦⠤⠀⢻⡿⠀⠀⠀⠀⢳⢸⠀⠀⡿⢻⣿⡷⣦⡤⣿⣿⣶⡾⢿⣿⡉⠁⠀⠀⠀⣶
⣷⡆⠀⢰⠁⠀⠀⠀⠀⠀⠘⠛⠳⣶⡟⠋⢸⠿⣿⡁⢠⣤⠀⡀⡾⠒⠈⠀⠘⠗⠀⠀⠀⠀⢸⠘⠀⣦⣇⢸⣿⣷⢿⡇⣿⣟⣣⢜⢾⡇⣿⠀⡀⠀⢀⣀⣤
⠛⠁⠀⢸⠓⢶⠲⠶⠦⣤⣤⣤⣤⣬⡅⠀⠀⠁⢜⠏⠸⠋⠸⠃⡇⠀⢀⠀⠀⠂⠀⠀⠀⠀⢈⣶⢣⡆⠀⠉⠙⠻⢿⣿⣿⣿⡾⢸⢸⡇⡏⣿⣿⡇⢸⣿⡇
⠀⠀⠀⢈⡀⠀⠀⠀⣤⡄⠉⠀⣿⣿⡟⠀⠀⠀⠀⠂⠀⠀⠀⢀⡟⢸⣿⠀⠀⠀⠀⠀⠀⣤⣸⠃⠏⠷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⢻⣿⡇⡿⣿⡇⣼⣿⡇
⣶⡖⠀⢘⠇⠀⢀⡀⠋⣁⣴⣾⠿⠋⢁⣆⠀⠀⠀⠀⠀⠀⠂⣸⠀⣼⣿⢠⠀⠀⠀⠀⠀⣿⠁⠜⠀⠃⠀⠀⠀⠀⠀⠶⡲⠜⣻⣿⣾⣿⡃⠀⠈⠁⣿⣿⠁
⠛⠛⠀⢸⠇⠀⠘⠓⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⣿⡿⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⣿⣿⣿⣄⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠿⠿⣿⣷⣦⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣈⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣶⠥⡿⢽⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠬⠕⠾⢯⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢
⠀⠀⠀⠀⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠪⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⣄⠀⠀⠀⢀⡀
⠀⠘⠷⣄⠂⠈⢽⣇⡕⠏⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠲⠄
⠀⢠⣄⠙⢻⡀⠱⢃⣴⣤⣧⣦⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⣀⡀
⠀⠀⠨⢧⠈⢥⣠⢀⣌⡀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⣣⠜⣉⡁⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡜⢲⠟⠛⠷⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⡆⠃⢀⢠⠇⡄⢠⠃⡄⢀⠄⠀⠀⠀⠀⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡰⣌⢆⠣⢱⣠⣘⣘⡰⠡⢃⠎⡰⢋⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⢀
⠀⠀⠀⠠⠔⠀⢀⠀⠈⣇⠀⠀⠀⠐⠦⣄⡐⠦⣀⠦⡑⢌⠾⠋⠉⠀⠀⠀⠉⠓⢮⢊⠴⣋⠴⠊⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⢈⠳⠀⡿⠒⠒⠒⠠⠤⣀⣉⠓⠬⡑⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠵⢚⣁
⠀⠀⠀⠀⠁⠀⠈⠂⢧⢈⡉⠓⠶⠆⠀⠠⠬⢭⡑⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠭⠤⠒⠒⠉⠁
⠀⠀⠀⠛⠀⠀⠀⠨⠶⢦⡉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈
⠀⠀⠐⠂⠀⠈

⠀⠀⡀⡀
⣤⣤⣉⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣤⡀⠀⠀⣿⠉⢳⡀
⠀⠀⠀⠀⢺⡉⢹⡄⠀⢸⡇⠈⣧
⠀⠀⠀⠀⠸⡇⠀⢷⠀⠈⣷⠀⢹⣆⣀⡀
⠀⠀⠀⠀⠀⢿⡀⠸⣧⡤⠞⣧⣀⣿⣽⢷⣄
⠀⠀⠀⠀⠀⣨⢷⣠⣿⠀⠀⢈⣭⠟⠋⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠐⣅⣀⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠈⠫⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡟⠉⠉⠙⣦⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣇⠀⠀⠀⠈⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⣄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⣄⠀⠀⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣞⠃⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣾⠇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⣶⡴⠋⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⢀⣼⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠤⢤⣤⣤⣤⠴⠶⠋⠀⠙⣦⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠲⢽⡶⠶⢤⡤⠴⠞⠋⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣥⣀⣀⣀⣀⣠⡴⠞⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡞⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠲⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠉⠉⠓⢦⠉⠛⠳⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⡉⠉⠛⠓⠺⠿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣸⠇⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⣤⡽⠿⠿⣿⣏
⠀⠀⠀⠀⠀⢀⣠⡴⢟⠷⠶⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⣰⠋⢬⠔⠁⠀⠀⠈⢳⡄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⢰⡃⠀⠀⠀⠀⣠⣴⣶⡄⣷⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⡼⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠙⣷⣶⣶⡞⠉⠈⢻⣧⡿⣄⠀⠀⠀⠀⠘⠻⣯⣉⣁⣀⣀⣀⣀⣈⣳⣶⣿⠟⠒⠒⠶⢤⣤⠤⠾
⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢸⠇⠀⠈⠛⠲⠤⢤⣤⣀⣀⣈⣉⣉⣉⣉⣭⡭⠭⣿⣿⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡙⠀⠀⠀⢄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠔⣂⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡇⠀⢀⣀⡈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⢠⣁⣨⠟⢙⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠐⠐⠻⢉⣹⢠⣾⣭⣽⠟⠱⣦⡀
⠈⠛⠛⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⣢⣤⠀⠉⠉⠉⠉⣽⢲⡞⠀⢠⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠙⢦⣀⡄⣠⡤⠶⠿⣿⡇⠀⠀⠀⠀⢨⣿⣿⡃⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠤⣍
⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⠩⡅⠀⠠⠤⢤⣬⣙⣛⡂⠀⠨⣃⣀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠔⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠐⠀⢸⠅⠀⠀⠀⠀⠩⣿⡗⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠸⠄⠀⠻⠀⣠⠇⠀⠀⠀⠄⠀⠠⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠌⡆⠀⠀⠀⠀⠩⡽⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠂⠀⠀⠀⠀⢈⣯⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣂⣦⣀⢤⣄⡀⣲⣀⣐⣦⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢨⡎⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢁⣀⡙⠋⠁
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢀⠒⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇
⠀⠀⠀⠀⡚⠋⠀⠘⠁⠰⡄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢘⠀⠀⠀⠀⠂⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠇⠀⠀⠀⠘⠀⢓⠀⠀⠀⠀⠀⠹⢀⠀⢘⡆⠐⠀⠀⠀⠀⠐⠀⢠⠞⠊
⠀⠠⢡⣿⠁⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠁⠀⡈⠉⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡀⢰⡏⠀⠀⠀⠀⠀⠘⡰⣯⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠰⢀⣿⠁⠀⠀⠀⠀⠀⠀⠓⢻⡃⠀⠀⠀⠀⠀⡰⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰
⡆⢨⡅⠀⠀⠀⠀⠀⠀⠀⠸⡌⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⢀
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠘⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡇⡤⠤⠀⠀⠀⠒⠒⠂⠀⠠⠄⣀⡀
⠘⢄⡒⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠀⠤⠄⢀⣀⠀⠀⠀⠠⡀
⠀⠈⠙⢇⠤⣀⡠⠇⠈⠉⠁⠹⠁⠀⠀⠀⡙⠉⠁⠙⠒⠒⠂⢠⠭⠅⢒⣤⣄⠀⠀⠠⠄⠀⠀⠈⠻⢓⣈⡦⣶⠒⠀⠀⠣
⠀⠀⠀⠀⠈⠐⠩⠍⣒⡒⠠⠬⠄⠤⠤⠀⢣⣀⣀⣠⣄⠀⡀⣠⣀⣀⡤⢽⣽⠛⠋⠈⠀⠀⠀⡠⠒⢣⠀⡰⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠐⠒⠐⠒⠀⠀⠀⠐⠂⠂⠀⠉⠁⡠⠀⠀⠀⢀⡄⠉⠙⡆⡾⡪⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠳⠤⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⢢⠠⡴⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⣀⢀⣡⡲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⡀⠀⢀⡧⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠠⢔⠒⠉⠻⡀⠀⢀⣋⢝⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⡀⠀⠈⠄⠀⣀⡉⢔⡫⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠚⠓⠀⠁


⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠉⠉⠉⠀⠀⠀⠐⠒⠒⠂⠀⠢⠤⠄⠀⠀⠠⠤⠤⠤⢆⠀⠀⢀⡀⠀⠀⠀⡰⠄
⠀⠀⠠⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠺⡷⠛⠋⠉
⠀⠀⠀⠀⠉⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠄⠀⠀⠤⠤⠤⠤⠤⠀⠐⠒⠈⡿⠔⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢤⡀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠒⠂⠒⠂⠀⡛⠓⠀⠤⠀⣹⣅⠀⠀⠀⠀⠠⠁⠀⠀⠐⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀
⠀⠀⣄⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⢀⡄⠀⠀⠀⠀⠈⠉⠀⠐⢰⣥⠔⠄⠀⠀⠀⠀⠀⣠⡀⠀⠀⢄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠲⠀⠤⡀⠠⢀⣀⠀⠀⠀⠢⡀
⠀⠈⠀⠈⠁⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢀⠀⠢⠇⠀⠀⠀⠃⠀⠃⢀⠀⠀⠠⢂⢀⠛⠤⠱⠂⠈⠀⠂⠀⠌
⠀⠀⠀⠸⠀⠀⡴⠀⠀⠀⠤⠄⠀⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠈⠑⠂⠀⠀⡇⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⡤⢂⠀⠀⠀⠀⠆⠀⡠⢀⠀⠐⠀⠒⠀⠀⠀⠀⣀⣠⣆⠐⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁⠀⠉⠰⠀⠀⠀⠤⠄⠀⠀⠀⠀⡀⠒⢀⡀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠸
⠀⢀⠀⠀⢀⠀⠀⠀⠻⠀⠀⠸⠂⡐⠀⢠⠀⠆⠐⠤⠄⠐⠒⠀⠀⠰⡖⢀⣃⣀⣀⣀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠄
⠀⠀⢀⠀⠈⠀⢀⠤⠠⠀⠀⠂⠀⠅⠀⠄⠀⠀⠀⠄⠠⠄⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⢘
⠀⠐⠀⠈⡉⠀⢄⡀⠀⠀⠀⢤⠀⠀⠀⠀⡀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⡄⠀⠀⠀⡄⠈⢳⠄⠀⡠⠀⠀⣠⠀⢀⠀⠀⠀⠊⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⣛⠢⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⡇⠀⠰
⠀⠈⠀⠉⠁⠀⠣⢄⠀⠀⠀⠈⠀⠣⠀⠀⠀⠀⠉⠀⠀⠐⢰⠀⠀⠀⠀⠃⠀⠀⠃⠂⠠⠒⠂⠀⠀⠐

⠀⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠠⠀⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿
⠀⣿⣿⣿⡿⠻⠟⠛⠃⡚⣻⣿⣿⣧⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣽⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉
⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠋⠉⠉⠉⠉⠉
⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣿⢿⡿⠷⢦⡄⠀⣨⣿⡿⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠇⠀⡿⠀⠀⠘⠀⠸⠋⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣶⣿⡟⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠞⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⣆⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢦⣄⢠⣤⣤⣄⣿⢶⣴⠟⣽⣿⣿⣿⣿⣶⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣽⣦⠾⠿⠿⠿⡿⣿⠷⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠒⠒⠂⠀⠤⠄⠀⢉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⠃⠁⠀⣀⣤⡤⠒⠚⠐⠂⠀⣀⣤⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣤⣤⣤⣭⣽⣶⣶⠶⠶⠶⠤⠶⠶⠶⠶⠾⠖⠛⠋⠁⠀⠰⢀⣀⡀⠀⠑⠘⠂
⠀⠀⠀⠀⠀⠀⠤⠤⠴⠖⠒⠚⠛⠉⠭⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣤⡽⠟⠉⡧⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠶⠶⠒⠒⠚⠒⠒⠛⠛⠛⠉⠤⠰⠖⠉⠉⠉⠉⠁⠀⠀⣀⡤⠃⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠤⢤⣤⣀⣠⠤⠶⠶⠛⣛⣩⣤⣤⣶⠶⠶⡶⢶⠿⠶⠖⢾⡶⣦⣤⣤⣤⣠⣤⣠⡤⠴⢶⡾⣏⣁⣲⡄⠀⣀⠠⠄⠂⠁⠠
⠀⠠⠀⡤⠠⠤⠤⠤⠴⠖⠒⠒⠒⠂⠉⠉⠁⠁⠀⠀⠀⣀⣀⡬⠤⠄⣒⡤⠖⠒⠉⠀⠀⣀⠠⠒⠋⠁⠀⠀⠀⠈⠉⠉⠀⣶⡀⣀⡀⣤⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠒⠚⢋⡉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠠⡖⠋⠁⠀⠀⠀⠀⠀⠀⡠⢀⢠⣠⣀⠸⣿⠏⠿⠷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⣀⣀⣀⣀⣠⡤⠶⠛⠉⠀⢀⣠⡤⠖⠐⠉⠁⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠤⠊⡴⠾⢷⡛⠒⠾⡧⠀⣲⡾⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠁⠙⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⡤⠖⣋⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠂⠀⠀⠉⠀⠂⢄
⠀⠀⢀⡠⠴⠚⠋⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⣠⠖⠁⠀⠀⠀⢀⣀⣤⠤⢤⠶⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⡇⠀⠀⢠⣖⠨⠿⠗⠒⠒⠉⠉⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠙⡴⠚⠉⠀⠀⠀⠀⢀⣀⣀⡀⢠⡤⠤⣐⠊⠀⠀⠀⠀⠀⠀⢠⠃
⣾⠀⠀⠀⡤⢶⣾⡯⠭⠥⠲⠆⠒⠂⠀⠀⠙⡆⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⡀⠀⠀⡀⠠⢰⡀
⠹⣦⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⡼⠁⠀⠀⣀⡠⢤⣶⣒⣚⣉⡭⠥⠔⠈⠉⠲⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠒
⢻⡀⠐⢉⡥⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡼⣫⡟⠀⠀⢀⣤⣤⣲⡖⢒⠿⠛⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⠀⢻⠀⠀⢰⠟⠀⠀⠉⠙⡏⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⠀⣀⣐⣚⣉⣤⠤⠤⠤⠤⠧⠤⣤⣀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡔⠃⠀⠈⢢⠀⠀⠀⠀⠀⠀⠌
⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⡈
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⠂⠀⠀⠀⠱⠀⠀⠀⠀⠀⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠑⢄⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⠀⠀⠀⠀⠼⠤⠤⠤⢶⠃
⠀⠀⠈⡟⠋⠉⠙⠉⠉⠙⠋⠁⠛⠏⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣀⣠⣬⣽⡃⢆
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠐⢂⣐⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠒⠒⠒⠶⠶⠒⣒⡂⢊
⠀⠀⠀⣡⠀⠈⠙⠛⢉⣉⣽⣭⡭⠆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠒⠒⠒⣛⣿⣟⡃⢎
⠀⠀⠀⡳⠈⠉⢉⣉⣉⣉⣶⣲⣷⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠶⠖⠒⢛⣛⣛⠃⢂
⠀⠀⠀⠹⣂⠈⠉⢭⣤⣤⣴⡖⡦⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠛⠛⣻⠟⡴⠁
⠀⠀⠀⠀⠉⠳⡖⠶⠶⠶⣒⢺⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢶⠶⠶⣦⠴
⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣷⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣅⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⣥⣅
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠿⠄⢠⡄⡔⠒⡴⠈⡫⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣮⣅⠀⠀⠀⠀⠈⠅⢠⡀⠀⠄⠠
⠀⠀⠀⡀⠀⢼⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⢨⣬⡅⠀⠀⢀⢀
⠀⠀⠀⠈⠂⢠⡀⠤⠀⠀⠍⠈⠏⠛⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⢀⠀⣞⠙⣉⡺⠌⢉⣈
⠀⠀⠀⠂⡀⠂⢀⡀⠀⣀⡂⠉⠂⣶⡆⠀⠀⠈⠀⠀⠀⢐⠐⠀⠀⠀⠀⠀⠟⠛⡇⠀⠀⣀⡀⠀⠉⣀⡀⠉⠁
⠀⠀⠘⠉⠁⠂⠀⣠⠊⠛⠁⠀⢤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡶⣆⠀⢀⣷⡇⠀⢀⠀⢀
⠀⢀⣘⠀⠀⠀⣾⠀⣀⠀⠀⠙⠉⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣮⡁⠀⠀⠁⠈⠀⡉⠉⠩⢉⡀
⠀⠀⠁⠀⠀⢸⣿⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⢨⡆⠀⠀⠀⠈⠀⠀⠐⣠⡤⣄⡀
⠀⠀⠀⠀⠈⠈⣿⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠇
⠀⠀⠀⠀⠀⡀⣇⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆
⠀⠀⠀⣿⣿⠇⣿⠀⣿⠀⠀⢸⢩⢽⣷⠀⠀⡆⠀⠈⡇⣏⠀⠀⠀⠔⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶
⠀⠀⠀⠉⠉⢁⣏⠀⠉⠀⠀⠜⠸⠜⠽⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠈⠉⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢻⢩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⡙⡇
⠀⠀⠀⠀⠀⢸⣾⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⢸⡇⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⢀⣠⣤⠶⠶⢦⣤⡀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⡟
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡇⠀⣠⠟⡡⠖⠉⠉⠙⠢⡙⣦⠀⢸⡇⠀⢸⠀⠀⠀⣶⣦⠀⠀⠀⢰⣶⡆⠀⠀⣿⠀⢸⢠⡇
⠀⠀⠀⠀⠀⢸⣿⡀⠀⢸⡇⢠⡟⡞⠀⢀⣤⣤⡄⠀⢷⢹⡆⢸⡇⠀⣾⠀⠀⠀⣿⣿⠀⠀⠀⠈⣿⡇⠀⠀⣿⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⢸⣿⡇⠀⢻⡏⢹⡟⠀⣼⢸⠇⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⢸⡇⠀⢻⣝⢄⣸⡇⢸⣇⢴⣵⠟⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡗⡇⠀⢸⡇⠀⠀⠙⠳⢾⡇⢸⡿⠛⠁⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠘⠛⠛⠿⠃⠀⠀⠀⠀⣿⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠘⠷⣤⣤⣤⣤⣼⣧⠘⣧⣤⣤⣤⣤⡼⠇⠀⢹⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠤⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⢸⡇
⠀⠀⠀⠀⠀⠀⣧⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇⢸⣏⣛⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⣒⣒⣒⣒⣛⣛⣛⣒⣓⣋⣸⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣆⣴⡾⠷⠢⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣬⣝⣿⣿⡷⡶⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⢏⡽⡛⣝⠙⠷⣦⠠⡀⠀⠀⠀⠀⢠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠀⣿⡇⢱⣘⣷⡀⠀⠁⠀⠀⠀⠠⣸⣿⣏⠀⢍⠁⣠⢾⣶⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⢹⡗⠀⠈⣿⠙⠠⠀⠀⠀⠀⡾⠉⠘⣿⣧⡈⢸⠳⡟⢹⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠉⢿⡅⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠓⡂⣂⣀⣲⢄⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⠛⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠳⣄⡀⠀⠘⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀⡀⠀⠙⣶⠄⢴⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠲⣀⠹⣷⣄⢀⡈⠈⣲⣄⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠆⠀⠀⠀⠀⢀⣠⡴⠞⠊⠉⢉⡽⠥⣑⣌⠿⣹⡽⣟⣠⣶⠉⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣴⠾⠉⠀⡄⠀⣴⠖⡀⡄⢠⣆⠹⣿⣇⣤⡀⠘⢙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣭⢏⣴⣾⢐⡋⢡⢰⣷⡷⡿⠿⢿⠿⠿⠿⠿⢷⣄⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠿⠿⠷⠿⠷⠿⠋⠃⠀⠀⠀⠀⠀⠑⠀⠐⠀⠈⠁

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⣿⣿⣿⡿⢿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀
⠀⠀⣿⣿⣿⣷⣾⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡁⢀
⠀⠀⣿⣿⣿⡟⢻⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⣿⣿⣿⡃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⢀⢀⣿⣿⡇⢸⠀⠀⢀⡀⠀⠀⠀⣰⡇⠀⠀⠀⡆
⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⢸⣾⣿⣿⣇⣿⣾⣶⣿⡅⠀⢰⣾⣿⣧⠀⣀⢠⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿⠀⠀⣹⣿⣿⣿⠋⠁⢻⡇
⠀⠘⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡆⠀⠀⢀⡀⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⣿⣾⣿⣿⡄⠀⢨⡇
⠀⠈⣿⠉⠀⠀⠀⢹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣧⣶⢾⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠙⠻⣿⠙⠇⠀⢸⡇
⠀⢸⣿⠀⠀⠀⠀⠈⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⠛⠀⠀⡦⠈⡇
⠀⢸⣿⠀⠀⠀⠀⢠⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠇⠀⠀⢸⣿⣀⡄⠀⠀⠀⡇
⠀⢸⣿⠀⢀⡀⠀⣠⣤⣬⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⡇
⠀⢸⣿⠰⠿⠷⠾⠿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣷⣿⣾⣿⣿⠁⠀⠀⠀⠀⢱⡀⠀⠀⢸⣿⡅⠀⠀⠀⠀⣷
⠀⢸⣿⠀⠀⠀⠀⢶⡟⠃⢹⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿
⠀⢸⣿⠀⠀⠀⠀⢸⡁⡆⢸⡇⣶⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⢤⣿⣳⣾⣧⣿⣿⣿⣿⣿⡟⣿⢀⣼⣿⣿⣿⣷⡀⠀⢸⣿⡏⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⢸⣿⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣤⣾⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣶⣾⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⠏

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡼⣍⠒⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡻⠶⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢠⠁
⠀⠀⢣⡅⣝⣶⣍⣇⠀⠀⠀⠀⠀⠀⣠⠎⠉⠁⠀⠈⠑⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠈⠉⣶⠏
⠀⠀⠀⠉⠙⠛⠋⠛⠂⠀⠀⠀⠀⠠⢉⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠀⠀⠀⠀⠀⣼⣟⡐⢒⡒⣚⡼⡏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣉⣉⡭⠊⠁⡌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣉⣭⠟⠋⢰⢇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢀⠿⠀⣀⣀⣴⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣿⠏⣠⣃⣴⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡾⠿⠿⣿⠯⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⢿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠶⢶⣄⡀
⠀⠀⠀⠀⠀⡔⠣⡐⠒⠤⠤⠴⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣖⠶⠦⠤⢼⣿⣶⡄
⠀⠀⠀⠀⢈⠀⠀⢉⠢⠀⠀⠀⠀⡌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢹⡗⢦⡀⢀⣀⣤⠿⣦⡀
⠀⠀⠀⠀⠘⢣⡀⣿⠀⠈⠳⢤⡀⠀⠠⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⡇⠀⡻⢦⣤⡠⣵⣽⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠂⣰⢤⠀⢹⡷⣻⣷⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⢾⣿⣦⣼⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢩⣿⠷⢦⡄
⠀⠀⠀⠀⠀⣴⢚⣿⣦⠀⠸⡌⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⢻⡘⠋⢻⣳⡀⠹⡄⠹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⣷⡀⢙⣆⢻⡀⠀⠹⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠹⣷⡿⠋⠙⠳⡄⠀⣻⠙⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⠀⢘⣷⠀⠀⠀⠙⠛⣁⣤⣾⠟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢼⢛⠉⠉⠉⢁⣠⣤⡶⠾⠛⠋⠉⠀⢀⣴⢷
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠻⠿⠛⠛⠉⠁⢀⣀⣤⣤⠶⠞⠋⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣠⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⠀⠀⠀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣟⣋⣡⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢰⠏⠉⠀⠀⠀⠈⠉⠉⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⣾⡤⠖⠒⠒⠓⠒⠶⢤⣀⠀⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣼⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⠙⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡼⠁⠀⢻⡀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡜⠁⠀⠀⠀⠳⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⠏
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠞⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠙⠲⠦⠤⠤⠶⠋⠁⠀⢠⠟
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠘⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠰⠛⠁⠀⢀⡀⠀⢰⠉⠙⢿⡧⠀⠀⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⣄⠬⠀⠀⠂⠠⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠠⢀⠀⠀⠀⠀⠀⠠⠂⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡧⠁⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠐⠀⠀⠁⠈⠉⢂⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠈⠀⠀⠀⠀⠠⠀⠊⣀⠀⢠⣶⡄⠀⠀⠀⠀⢀⡠⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢄⠀⠀⠀⠻⠆⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠂
⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡄⠀⠀⢰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠄⠂⠀⢀⠀⠄⠠⠄⣀⠀⠀⠀⠈⠀⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠈⠁⢀⡀
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠐
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢠⠀⢀⡟⠁⠀⢠⡀⠀⠀⠀⠀⠀⡀⠘
⠀⢻⣀⣠⣄⠀⠤⠆⠀⠀⠀⠎⠀⠀⠀⣐⡤⠌⠀⠀⡇⠀⠈⠀⠀⠂⠀⠐⠄⠀⠀⠐⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢎⠀⠀⠀⠀⡠⠂⠀⠀⠐⠀⠁⠀⠀⠀⢰⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠴⣄⣄⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢤⡄
⠀⠀⠠⠀⠠⡀⠀⠉⠀⠀⠀⠀⣰⡟⠁⠀⣠⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⠴⢞⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠘⠄⣀⡨⠃⠀⠰⠊⠲⢤⠀⠀⠀⠐⠀⢠⡄⠀⢀⠀⠀⠈⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣤⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⡿⣿⠿⠷⢬⡀⠤⣽⡿⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⢃⠀⠈⠃⢰⠋⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⠀⠀⠀⢇⠀⠀⠈⠀⢸⠀⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⢿⡋⠒⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⢡⡀⠀⠀⠀⠀⠀⢳⠀⠀⣀⣿⣄⣦⣤⣀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣙⣶⣆⣶⣶⣶⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠀⠀⠀⢀⣀⡄⢀⡉⠉⠑⠒⢒⣒⣂⠠⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢒⣒⠒⠀⠠⣤⣄⠀⣀⣀⣀⢉⣉⣉⣉⣀⣀⣤⣤⡶⠞⠋⣉⠁⠀⠀⢐⢒⡟⠉
⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣐⣠⣬⡥⠶⠶⠶⣾⣻⠻⠿⠟⠛⠛⠋⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠈⠁⢲⣶⡤⣄⠀⠁⢠
⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣶⣶⣶⠿⠟⠛⠉⠀⡾⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⢛⣉⣉⣉⣥⣤⣤⣤⣤⣤⣤⡀⡀⠀⠈⠀⠀⠀⢀⣀⣠⣤⠶⢻⡅⠀⠀⠀⢀⡠⠔⢋
⠀⠀⣶⠀⠐⠒⢀⣉⣉⣙⣋⣉⣭⠭⠤⠶⠞⠛⠛⠋⠉⠁⠛⠙⣋⣁⣀⣉⣉⡽⠟⢛⠛⠛⢛⡭⠍⠑⠊⠉⠒⠺⠿⠖⣒⠉⠀⠀⣀⣈⡦
⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠋⠩⠍⠐⠊⠉⠀⠂⣉⡠⠖⠋⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⢺⣷⡞⣶⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠀⠀⣀⣠⡤⠖⠒⠉⠔⠈⢂⠀⡀⠀⠀⠀⢀⡤⢺⣼⣮⡿⠯⣵⣿⠁⣤⣴⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠋⠉⠉⠁⠀⠠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠈⠉⢀⡛⠴⠞⠃⠀⠀⠉⠀⠉⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⣀⣀⡀⢀⣀⣀⠀⢀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠸⣿⣿⣿⣿⣿⣿⣯⣿⠃⣿⣷⡀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣿⣿⣇⡇⠈⠙⠿⠿⠿⠟⠋⢰⣿⡷⡆⠀⢸⠀⠀⣼⣦⡀
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣏⣻⣿⢼⣧⠀⠀⠀⠀⠀⠀⠀⡀⣠⠷⣿⠀⢸⠀⢠⣿⣿⣿⣷⡄
⠐⡿⠶⢀⣀⠀⢀⣄⡆⠀⠀⠸⡏⢻⣿⠀⡿⠶⠶⠦⣤⡀⠀⠀⢐⠀⢴⣿⡀⢸⠠⣿⢿⣿⣿⡿⡀⠞
⠀⡇⠀⠈⠙⢿⡿⢻⠀⠀⠀⠰⡇⠀⠹⠀⡇⠀⠀⠀⠈⢿⡄⢘⣿⣦⣤⣿⡇⢸⠀⢀⢈⠥⠦⣰⠁⠀⢀⣤⣴
⠀⡇⠀⠀⠀⠈⠻⣮⠀⠀⠀⠐⠃⡀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣾⣿⣿⡷⣂⠀⢸⠀⠘⠇⠀⠀⠛⠁⠈⠁⠘⢿
⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠹⣇⠀⠀⡇⠀⠀⠀⠀⢀⣿⣿⣿⡿⠏⠛⠁⢸⣄⠀⠀⠀⠀⠀⢰⣤⣤⣦⢸
⠀⡇⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⣸
⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿
⠘⣷⣢⣤⣤⣾⣿⣿⣿⣷⣤⣶⣧⣀⡀⠀⠇⠀⠀⠠⠤⠤⠤⠀⠀⠀⠐⠒⠀⠈⠒⠀⠀⠀⠀⠀⠁⠁
⠀⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠁⠀⠀⠀⠀⠀⢀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡤⠲⠤⠀⡀⠀⠀⠘⢤⣤⠤⠊⠀⠐⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠥⠤⠤⠰⠊⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠀⠠⡀⠀⡈⠀⠢⡀⠀⣀⠀⡀⠀⣀⠅
⠀⠀⠠⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠚
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡔⠊⠁⠀⠈
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠈⠀⢀⠈
⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠡⡀⠀⠀⠀⠈⠂⠄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠂⠐⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡁⠀⠀⣀⠤⠐⠒⠀⠀⠐⠒⠰⠤⠄⠐⠂⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣀⣀⣠⡀⠤⠎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠁⠐⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠐⠒⠉
⠀⠀⠀⠋⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠘⡄⠀⠀⠉⠐⠒⠠⠤⢤⠄⠤⠤⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⣀⠀⠐⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠂


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

⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⡆
⠈⠠⠡⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⢠⠠⡅⠇
⠀⠀⠀⠂⠀⠀⠀⠀⠀⢘⢰⡆⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠲⣾⠗⡛
⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠈⠉⡽⠙⠆
⠀⠀⠀⢀⡄
⠀⠀⠂⠠⠇⠀⠀⡔⠀⠀⢀
⠀⠀⠈⠀⢈⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠤⠀⠀⠐⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣞⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠉⠉⠛⠻⢶⢶⣶⣶⣿⠆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣿⣿⣥⠀⠀⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠥⠐⠒⢉⣩⠭⢭⣉⡭⣷⡦⣄⡀⢢⣤⣥⣿⣟⠉⠀⠰⡄⣞⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⠔⣊⣹⠁⠀⠀⠉⠀⠀⠹⣶⣽⣿⠏⠙⠋⠋⠀⠀⠠⡂⢨⠆⡏⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⣴⠟⠋⢹⡄⠀⠀⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠀⣠⢃⡎⠰⣧⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⡶⠛⠁⡾⠉⠉⠀⠦⠴⠃⠀⠀⢀⡴⠴⠃⣀⣀⠜⠉⠉⠉⠁⢸⠆⢀⢤⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⣠⠾⠋⢠⠞⠉⠁⠀⠀⠀⠀⠀⣠⠤⣌⠉⠀⠤⠞⢁⣠⠜⠓⠒⠲⠖⢋⡠⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡵⠊⠀⠀⠴⠊⣡⢄⡤⠚⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠸⣄⣠⠤⠒⠋⠀⠀⢐⡏⠉⡇⠈⠳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠚⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⠦⣄⣀⡴⠚⢹⠀⠀⠀⠀⢸⣿⡤⣏⣷⠀⡴⠉⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠞⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⣿⣿⣌⠁⠀⢇⡀⣸⠁
⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣤⣉⣀⣀⡀
⠀⠀⠀⠀⣠⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢬⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣶⣿⣿⣿⣿⠿⠿⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠧⠀⣠⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠤⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡅⠀⠰⠿⠇
⠀⠀⠀⠠⠀⠒⠳⣤⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠠⡀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⠀⠀⠀⢠⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣿⣶⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡀⣠⠾⠿⠓⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠛⠉⠉⠁
⠀⡐⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠀⢈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⡁⡀
⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣀⢡⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠘⠇⠀⠀⠀⢀⡀⠀⣀⣲⣶⣷⣌⠳⠀⠀⠀⠞⠛⠛⠛⢿⠿⠷⢤
⠀⠀⠀⠁⠈⠈⢣⠀⠀⠀⢐⠉⢀⠀⠀⠀⠀⠰⠀⠀⠀⢸⢃⣘⣉⣽⣟⠻⠿⠃⠀⠀⠄⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠂⠀⠛⠀⠈⠀⠀⠛⠻⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣾⢿⣿⣯⠍⠀⠀⠀⡖⠀⠀⠐⡀⠀⠃⠀⠀⠀⠀⠐⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣡⠃⠀⠀⠀⠀⠀⠀⠱⠀⠹⠿⠀⢀⣠⠞⠀⠀⠀⠀⡃⠀⠀⠀⠤⠤⠤⢴⣤⣤⣤⣤⣄⣀
⠀⠠⠛⠀⠀⠀⡂⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣁⠀⠀⢠⣤⣶⣝⡛⠛⠛⠻⢦⠀⠙⠇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠀⠀⠀⠀⠘⠀⠠⡀⠈⠉⠉⠙⠃⠀⠀⢸
⠀⠀⠀⠁⢇⠀⠀⠀⠀⠀⠀⠐⢶⡄⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠀⠀⠐⠂⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠄⢀⡀⠀⠁⠀⠀⠌⠤⠤⠄⢁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡂⡐⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣴⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠠⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣠⣾⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⣬⣽⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⣥⣀⣨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠈⠁⠀⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠉⠢⢄⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣈⠾⠥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠤⠔⠊⢗⠐⠒⠛⡦⢜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡶⠖⡷⠤⠤⠤⢄⡘⢄⣀⣀⣱⠈⡣⢤⡄
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠤⠘⠻⢿⠿⠥⣍
⠀⠀⠀⠀⠀⠘⠤⣙⣿⣿⣿⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠳⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡴⠲⡻⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢣⢀⠀⠀⠀⠀⠈⢆⠀⠟⢄
⠀⠀⠀⠀⠀⠀⠘⣦⠕⠈⠳⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠑⠒⠤⣀⠀⠣⡸⢨⢣
⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠘⡄⠀⠈⢻⡿⠿⠿⠿⠿⢿⠇⠀⢑⠖⠀⠤⠤⢘⣀⣀⣀⣈⡎
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠱⡀⠀⠀⢱⣀⠀⠀⢀⡌⠀⢀⠎⠀⢀⣴⡾⠋⠁⠀⠀⢀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣄⢃⠀⠀⠀⡇⠉⠉⠁⠘⡀⡜⠀⣠⣿⠏⢀⣠⣶⣶⣶⣦⣥⣀⣀⠸
⠀⠀⠀⠀⠀⡹⠛⠿⣿⣴⣿⣿⣿⣿⣦⣄⡀⡇⠀⠀⠀⠀⣷⠁⢠⣿⣿⣶⣿⡀⢛⡵⡖⠒⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣁⢸⣷⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠀⢸⣿⡿⠿⣿⢣⠈⢡⣿⠘⡌⠋⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠸⣷⣝⡿⠇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠋⠀⠀⡟⡎⣆⠈⡝⠢⡁⠸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⢿⣦⣤⢴⣿⡿⠿⠟⠻⠿⠿⣿⣿⣿⣿⣧⣰⠀⠀⠀⣇⡇⡽⢆⡿⠀⡐⣀⣙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡰⡰⣿⡏⣉⡀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠀⠀⠠⠀⠀⠤⢀⠄⡀⠀⠀⠀⠈⢷⡱⣿⡃⣿⣿⣦⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣽⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⢻⢀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⡄⠒⢶⠀⠁⢨⡍⠙⢷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⣾⣦⠀⠀⡟⠆⠀⠀⠀⠀⠀⠀⢀⠀⣸⡲⣄⢞⡟
⠀⠀⠀⠀⠀⠠⠀⠀⠈⡸⢹⣿⠇⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠂⠤⡑⣯⡾⢶⠒⠆⠀⢀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡞⠡⠚⣟⠳⣹⡓⣆⣌⣧⡤⣔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡅⠀⠀⠸⡆⠉⢉⠜⡡⣿⡿⡌⡅⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⠋⣸⠉⠁⠉
⠀⠀⠀⠀⢉⣉⠀⢈⠠⠀⠉⠁⠀⠀⠐⠂⠀⠀⠀⠀⢀⠉⠉⠁⠒⠀⠀⠀⠘⡇⠰⠆⡗⠒⠈⠉⠀⢤⣘⠁
⠀⠀⠐⣢⢈⣉⡙⢃⠐⠛⠿⠀⠀⠀⠐⠛⠲⠆⢀⣁⢀⠀⠀⠀⠐⠠⠈⠱⠤⠷⠄⢸⠁⣈⣡⣀⡀⠉⠉
⠀⠀⠀⣽⣍⠉⠁⠸⠀⠀⠤⣴⣦⡶⡰⣤⠄⠀⠈⠙⠛⠋⠁⠠⠤⠶⣤⣄⣀⢐⠀⣘⣀⢀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠚⠐⠆⠄⠔⠠⠤⠤⠀⠈⠀⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⣇⡠
⠀⠀⠀⠀⠀⠀⠀⣠⣇⣀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠑⡀⢠⢀⣈⣷⢶⢾⠒⣾⣤⣼⡆⢤⠤⠄⡤⠂⠀⣁⠚⠢⢜⣿⡇⣭⣭⠐⠀⠀⠀⣀⠀⠀⠈⠙⠩⠈⠉⠉⠻⡇⠀⠀⣼⢐⡖⠁⠀⣀⠀⢱⣠
⠒⠈⠁⢀⡀⠈⠉⠙⠉⠉⠀⠘⢇⡂⡂⣿⡲⠊⠀⠀⠀⠳⡺⠷⠓⠒⠾⠀⠄⠄⠀⡃⠀⠀⠀⠀⠀⣧⣤⢤⡤⠼⠤⠤⠿⣱⠠⠠⠄⣶⠴⠴⡇
⣰⣲⣰⣪⡠⠤⠤⠄⢬⡧⡶⡴⠾⠒⠐⠻⡗⠒⠖⢺⡶⣶⣇⣀⡐⣄⣠⠀⢁⣀⣈⡄⠠⠀⠀⠀⠀⣾⠦⡖⠁⠀⢠⣀⣀⣽⠐⠐⠀⣿⢚⢚⣇
⠀⠀⠀⠀⠉⠋⠍⠉⠉⠙⠿⡥⠤⢼⣦⣴⡯⠨⡅⣽⣭⣭⡧⢾⣤⠿⠿⠠⢁⠁⣄⠈⢦⠀⠄⠀⠀⡻⠿⠯⠭⠬⠼⠯⠭⠿⢌⠈⠁⣿⣩⣩⡏
⢜⠀⠀⠀⠀⠀⠐⡀⠀⡀⣀⣙⣉⣉⣉⣉⢁⠀⠀⢨⣀⣀⣱⠂⠀⠀⡀⠀⠀⢹⢘⣛⣻⢠⠔⠒⠒⠀⠒⢄⠀⠀⠀⡀⣴⢀⢀⣶⠀⣿⠴⠴⡏
⢊⠀⠀⠐⠀⠈⢈⣓⠀⡓⠊⠁⠀⠀⠀⢩⢈⠀⠀⢸⣉⣉⣹⠄⠄⠄⢤⠤⠤⡾⠊⠉⠉⠁⠀⠀⠙⠂⡀⠀⠉⠲⡄⠄⢽⠤⠠⣿⠀⣟⣛⣛⡇
⣉⠀⠀⠀⠀⢀⢈⡇⠈⡇⠄⠄⠬⣧⡤⣬⢠⠀⠄⢬⣥⣭⣽⠂⠂⠆⠲⠶⠶⠦⠄⡄⠤⡇⡀⠀⢀⠀⢐⣀⣀⣀⣘⡇⣿⢚⣫⢉⢁⡉⣭⣉⣉
⠈⠂⠀⠀⠀⠀⠨⠇⠀⠓⠒⠂⠒⠓⠒⠺⢄⠠⠀⢸⣤⣤⣭⠀⠀⠉⠙⠛⣛⣛⠂⠂⠀⡇⠀⠀⢨⠀⢨⣯⣠⠏⠀⠀⡀⠀⢹⠠⠠⠀⣯⣬⣬
⣛⡃⠀⠴⠄⠐⠁⠀⢄⠀⠀⠀⠀⠀⣴⢀⠀⣶⠀⢸⡄⣦⣾⠁⠀⠀⠀⠀⠈⡓⠒⠁⠁⢆⠂⠀⠰⠀⠰⠷⢺⣓⣐⣀⣟⣛⣿⠐⠐⠂⡿⠶⠶
⣉⣗⡁⡤⠀⠐⠀⠢⣀⣑⣤⠀⠀⠀⣿⡬⠌⠿⠠⢸⠶⠒⠚⠒⠒⠒⠒⠂⣀⠥⣤⡌⣦⣤⡃⢀⣘⠈⠌⢁⡈⠉⠉⠈⠉⢉⠉⠙⣘⠀⣟⣛⣛
⠉⠡⡜⠀⠀⠄⠀⠀⠙⠥⢿⠀⠀⢠⠉⠀⠀⠀⡈⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠗⡒⡂⣷⣶⡕⢁⠀⠠⠀⢀⠁⢪⡀⠂⠀⢹⣘⠘⣯⡀⣯⡭⠭
⠀⠀⡾⠓⠛⡏⠀⠀⠀⢯⠛⠒⠒⠐⠢⡆⠔⠰⡆⠀⠰⠀⠀⠀⠮⠁⠈⠀⠅⡝⠋⠉⠉⠛⢭⠇⠀⠤⠀⠀⠹⠭⡇⡥⢠⡟⠁⠀⢀⡐
⠈⠈⣟⠓⢛⡓⠀⠂⠀⣃⣀⣀⡄⠀⠀⢘⠆⠸⠇⠀⠐⠀⠀⠀⠒⣁⣀⣀⠂⣆⣀⣰⣂⣀⣸⣛⡓⣿⠀⠂⠂⡿⠓⠒⠚⠲⡶⠶⢾⠆⠀⠂⠆
⠀⠀⣋⣉⣉⣇⡁⡁⣁⡭⠭⠭⠧⠬⠬⠬⠧⠸⡇⠀⠘⠀⠀⢠⠋⢀⡀⠈⢃⡧⠬⢽⡤⣤⢸⣭⣍⣿⠁⡁⡉⣧⣤⣴⡀⣀⢨⣟⣻⡃⠀⡁⡃
⠀⠐⣯⣅⣭⡥⠀⣔⠁⠀⣄⠀⠀⠀⠀⠀⢀⠀⠀⠆⠈⢄⡀⠰⠶⠆⠲⠶⠆⣟⠛⠉⠁⠀⣸⠶⠦⣿⠄⢄⠔⠚⠒⠛⠒⠒⠒⠓⠛⢅⠐⠄⡄
⠀⠐⣵⡤⣤⣗⠄⣟⠀⡀⣟⠀⠀⠀⣠⠎⠁⠀⣠⠀⠀⠀⠀⢺⣛⡃⢘⣛⡃⠄⠠⠀⠀⠄⢸⣛⣓⣿⠀⡷⠦⠶⡗⠄⠠⠂⡢⠒⠀⠈⠀⠉⠒
⠀⠀⠶⠦⠶⡖⠄⣯⠀⡀⣭⠀⠀⠀⣿⠭⠬⠭⡯⠨⠨⠨⠨⠭⣭⡅⣩⣭⡅⠄⠠⠀⠀⠆⢸⣭⣭⣿⠅⣟⡃⣚⡇⠂⢐⢸⣗⣒⣲⡟⡒⠒⠐
⠀⠀⠷⠖⠶⠧⠂⠷⠠⠀⣶⠀⠀⠄⣿⢀⢀⣀⣇⢀⢀⠀⠀⢘⠶⠆⠴⠦⠆⠀⠰⠀⠀⠆⠸⠶⠶⠾⠄⢿⠅⠤⡇⠄⠠⢸⣒⣒⣚⣓⡂⣒⣐