Unasked Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢹⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠛⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡾⢰⡟⡁⠀⢘⡇⠀⠀⠈⠀⠀⠀⠀⣀⣠⣄⣴⣶⡎⣄⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⣤⣿⣴⣿⡿⠀⠀⣴⢐⣶⣴⣿⣿⣿⣍⣿⣿⣿⣿⣤⡼⢿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣯⠼⠟⢡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⢘⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠻⠀⣿⣿⣯⢿⣿⣿⣿⣽⣿⣿⣟⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣀⡄⠀⠀⠀⣠⠀⠀⠻⠛⠀⣼⢉⡀⢻⡅⢹⣟⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠘⠁⠈⣱⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣤⣤⣴⡂⠀⢀⣤⡀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠿⠏⠀⠀⡀⠀⠀⠀⠀⢰⣿⢿⣿⣉⣽⣿⡿⠟⠛⠁⠀⣠⢦⡞⢾
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⣸⣿⣿⣧⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠰
⠀⠀⢀⠀⣤⣤⠀⣘⡆⠀⠀⡀⠀⠀⠀⠀⠙⣿⡁⢀⣠⣤⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣨⡟⢀⡇⠀⠀⠀⢘⣆⠀⠀⡄⠀⠰⢻⣿⡟⢛⡿⣿⠿⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠳⠚⣿⣿⣶⡗⠀⠀⠙⠋⣠⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣠⣞⡙⠋⠁⠀⠀⠀⠀⠐⠃⠈⠀⠀⠀⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠏⠉⠀⠀⠈⠀⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⡀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠚⠒⡀⠀⠀⢀
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣹⣧⣿⠀⠈⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⣤⡦⠀⠀⠠⣼⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⣦⣼⣿⣶⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡸⡏⠀⢹⠟⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠉⢀⣶⠏⡀⠈⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢾⠁⠈⠁
⠂
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠢⣾⣿⣏⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⡆⠉⠛⢿⣧⠀⠀⣠⡀⣠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣶⣶⣿⣥⣶⡶⣄⠀⠀⠀⠻⠧⠀⠙⠿⣯⠱⣴⠿⣿⣄⡀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⢠⣤⣤⡴⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠙⠆⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠙⢶⠦⣾⡿⠿⠛⢟⠷⣤⣄⣤⠞⠋⠉⠻⠦⢀
⠀⠀⠀⠈⠛⠙⠇⠈⠻⠿⢁⣴⣿⣿⣿⠆⠀⠀⠀⠀⢀⣠⣤⣶⣶⢠⣀⠀⠀⠐⠀⢠⣄⣀⣀⠀⠀⢀⣴⠾⣿⣯⠙⠆⠀⠀⠀⠈⠙⠳⠤⠶⠒⠒⣦⣄
⠀⠀⠀⠀⠁⠠⣶⣾⢿⡄⠈⠻⣿⣿⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡇⠙⠻⠔⠄⠀⠀⠉⠉⠉⠃⠒⠉⠀⠀⢀⣿⠀⠀⠈⠂⠀⣰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠂⠄⠀⠙⢶⣶⣶⣾⣿⣿⣿⣿⠟⣻⢿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠘⠃⡜⠀⢠⠟⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠣⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⠔⠀⠐
⠀⠀⠀⢠⣀⣀⠒⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠉⠓⠀⣠⠀⠀⢀⡶⠛⢉⠀⠈⢀⠀⠀⠀⠀⠀⠈⠻⢿⢿⣆⢀⠀⠀⠀⠸⣿⣿⣿⣤⡴⠂⠐⠃
⠀⠀⠀⢸⣿⣿⣷⡖⣤⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠐⠆⠉⢀⡠⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠻⠿⢿⠛⠀⢀⣻⣿⣿⣿⣿⣅
⠀⠀⠀⠘⠻⠉⠉⢙⣿⣿⣿⣶⣿⡆⣀⣄⢸⣿⣧⠀⣠⡀⠀⠀⠀⠉⠺⠿⣿⣿⡛⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⢀⢢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣿⢿⠀⠀⠀⢀⣴⡄⠀⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⣤⡀⠀⣀
⠀⠀⠀⠘⠷⢾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⡄⣸⣿⣷⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠛⠿⠿⠿⣿⡟⢿⣿⣿⣷⣿⣿⣿⣿⣷⣾⣧⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠁⠀⠈⠉⠉⠙⠛⠛⠻⠿⠧⠀⠀⠀⠾⠷⠾⠿⠟⠉⠉⠋⠙⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠄⠖⠀⡼⣄⡀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡀⠀⢰⠂⠁⣏⠁⠀⠀⢠⣜⣶⠆⠶⠴⠃⢸⡤⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠀⢄⠀⠀⠀⠀⠀⠀⢐⡀⠹⠤⡿⢠⣷⠟⢻⣤⡄⠀⡼⣤⡹⣁⡀⠀⠀⡀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⠀⠀⠠⠞⣷⡄⣀⠀⠀⠀⠈⠉⠁⣖⣰⣾⣅⣦⣄⠤⢤⣲⢬⣋⠐⠛⣁⣶⣾⣿⡐⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠚⠛⠀⠀⠀⡀⢀⡴⠾⠛⠃⠀⣐⡈⠙⡋⢀⣴⣿⣿⣋⣜⣻⣗⣾⣿⣿⠷⡖⠻⠿⣿⣡⡀⢀
⠀⠀⠀⠀⠀⢀⠀⢖⡻⢦⣶⣟⣠⣖⡀⢤⣯⣧⣉⣠⡶⠟⢿⡿⠟⢿⣿⣿⠿⠟⠋⠉⠀⢥⣴⡆⠉⠋⢋⣴⡾⢂⣤⠀⣯⣹⣾
⠀⠀⠀⢀⢠⣤⣈⣯⣍⡷⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠄⢚⣿⠀⣴⣀⣤⣠⣤⠞⠁⠀⣤⣴⡛⣀⣴⣴⣿⣿⡿⢟⣿⡾⠻⠋⣹
⠀⠀⠀⠉⠙⠻⠟⠟⢿⣁⣭⣶⡺⣯⣿⣿⣿⣟⣧⣀⣶⣾⣯⣴⣴⣯⣬⣿⣧⢀⣈⠻⢻⣿⣷⣏⣉⡯⠽⠂⠔⠊⠛⠋⠳⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡍⠉⠋⠉⠙⠛⠛⠹⠛⢋⡿⣿⠟⣿⣿⣿⣟⣿⡿⣧⣾⡿⣫⡽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠟⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠛⠋⠹⣯⣰⣿⠿⣝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣨⡄⢄⣠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠒⠋⡐⢂⣀⣿⣿⣤⣞⣠⠂⠀⠀⡄⠀⠀⠀⠰⣶⣀⠂⢐⣸⣟⣯⣻⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⡥⠽⠷⠶⢶⠿⠿⢻⠿⠽⠧⠤⠷⠟⠓⠚⠛⡓⠀⢠⣤⢤⣼⠿⡿⡍⠛⣿⣿⣿⡿⠿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢤⢤⡀⣐⣶⣆⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⢕⣲⣾⡿⠟⠛⠛⠛⠛⠋⠉
⣶⣿⣿⠷⠟⠛⠀⡀⡀⡀⣰⣷⢿⣚⣴⣾⢿⢿⣿⣶⣿⣟⣥⣤⣷⣤⣀⣀⣤⣀⣠⡀⠀⠀⠀⢀⣹⣃⠒⣂⣀⣠⣤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠋⠉⠉⠛⠉⠁⠈⠙⠉⠋⠉⠉⠁⠀⣀⠀⠀⠉⢉⢁⣀⠉⠡⣀⣏⣉⣉⠉⡬⠡⢠⣬⣉⣐⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠛⠉⠙⠛⠋⠉⠉⠉⠁⠊⠛⠋⠉⠉⠁⠐⠋⠉⠉⠉⠁

⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣫⡍⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⣽⣿⣿⣿⣿⡗⠊⢀⣾⣿⡟⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠘⠿⠿⠟⠛⠻⣇⣠⢿⠛⠛⠠⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⢀⣶⣶⣶⣶⣶⣾⠸⢑⡀⢳⣆⠀⠴⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠈⠘⢁⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠀⠈⠁⠈⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠾⣿⣿⡿⣾⣿⣿⣿⢟⠋⠡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⢿⣿⣿⣿⠁⠀⣱⣤⣠⣀⡀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣤⣾⣿⣿⣿⡄⠐⢸⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⣾⣯⣟⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⣷⣦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣺⣿⣿⣷⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢠⢮⡾⠛⠉⢟⡻⠉⠛⢷⡷⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣦⣤⡶⠶⠚⠻⠿⣧⣠⢔⡾⢷⡢⣄⣼⠿⠟⠒⠶⢦⣤⣴⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⣶⣄⠁⠀⠀⡸⡳⠁⣨⣅⠈⢞⣇⠀⠀⠈⣠⡲⡟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠄⠙⡻⢎⣤⡶⢽⡷⢋⣉⣉⡙⢾⡯⠶⢤⣱⢟⠋⠠⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣿⡆⠀⠀⣠⡯⡮⣿⡟⡔⣵⢚⡓⣮⢧⢻⣿⣽⢿⡄⠀⠀⢰⣿⣲⢄
⠀⠀⠀⠀⠀⠀⢀⣞⣾⠋⠉⣻⢶⡪⢷⡷⢛⡭⡁⠀⣑⡃⢘⣊⠁⢈⠭⡛⢾⡾⢗⡶⣟⠉⠙⣷⣳⡀
⠀⠀⠀⣀⣀⣀⣾⣾⣧⢄⣐⡵⡁⣠⡏⢰⡱⢛⠵⠼⢿⣷⣾⡿⠇⠮⡛⣎⡆⢹⣄⢈⢮⣂⡠⣼⣷⣷⣀⣀⣀
⠀⠀⠀⠉⠉⠉⢿⢿⡟⠊⠹⡳⡁⠙⣇⠸⡹⣬⡲⢰⣾⡿⢿⣷⡆⢖⣥⢏⠇⣸⠋⢈⢾⠍⠑⢻⣿⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢯⢿⣄⣀⣽⠾⢵⡾⡷⣭⣲⡁⢀⡩⡅⢨⣍⡀⢈⣖⣭⣾⠷⡮⠷⣯⣀⣠⡿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⣿⠇⠀⠀⠘⣇⣗⣿⣧⠧⡻⢬⡥⢟⡜⣼⣾⣻⣺⠃⠀⠀⠸⣿⠽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠂⣠⣵⢎⠛⠷⣺⡷⣌⣉⣉⣡⢾⡟⠶⠚⡳⣮⣄⠐⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⠾⠋⡀⠀⠀⢱⡵⡀⢙⡋⢀⢮⡎⠀⠀⢀⠙⠷⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠟⠛⠷⠶⢤⣴⣶⡟⠙⠪⢳⡾⠗⠋⢻⣶⣦⠤⠶⠾⠛⠻⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠘⢞⢷⣤⣀⣮⣵⣀⣤⡾⡳⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢽⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⡞⠀⠀⢰⣞⡟⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⢀⣠⢞⣵⣤⣾⠃⠀⠀⠐⠹⣷⣜⣷⠀⠀⠈⣶⠂
⠀⠀⠀⠀⠀⠀⢀⠾⣧⡀⠀⠠⠀⠉⠛⠿⣿⣧⡀⠀⠀⠀⠀⠈⣙⣿⠀⠀⠀⠸⣆
⠀⠀⠀⣠⢴⡏⠁⠀⠉⠓⢠⣄⢀⠀⠀⠀⠈⠓⢷⡀⠀⠀⠀⠀⠉⣿⡶⡀⠀⠀⠈⠂⠀⠀⠀⠠⣤⠜⠀⣠⡎
⠀⠀⠈⠛⠻⢧⡀⠀⠀⠀⠀⠈⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠃⠧⣿⢦⣀⠀⠀⠀⠘⢧⣤⣄⠀⠴⠋⠁
⠀⠀⠀⠀⠀⠈⠙⣆⠄⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⡼⠃⠀⠀⠘⠁⢣⡟⡠⡀⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠚⠀⠀⠀⠀⡆⠀⠋⣠⣼⠇⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⣤⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⣤⠀⠀⠀⣰⡀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠠⢺⠏⢀⣬⡾⠃⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⢠⣿⡇⠀⠀⣿⡇⠀⠀⡀⠈⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠾⢿⣧⢀⢠⣿⣇⠀⢸⡗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠾⣿⡧⠀⣽⣿⣸⣿⡆
⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⠏⢼⣿⡷

⠀⠀⠀⠁⢀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠐⢀⡀⠀⠐⠀⢀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⣀⠖⣦⣀⠀⠀⠀⠀⠀⠀⢀⠞⠛⠛⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢽⠖⣶⠋⢀⡀⠀⠀⠁⡀⢰⡖⠀⠀⠰⣾⠀⠀⢠⣿⠌⡷⠹⣦⡔⠐⠀⠀⠀⠀⠠⣞⣿⢏⣻⣽⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣼⠿⠳⣄
⠀⠀⠈⠄⣬⣧⠁⠀⠀⠀⠀⠀⢀⠁⠄⠀⠘⠋⠀⠀⢸⡩⢻⣿⠟⠉⠇⠀⠀⠀⠀⠀⢄⠈⠻⣶⣝⣸⠃⠀⠀⢤⣶⠚⣥⡔⢢⠀⠀⠀⠀⡟⠀⠀⠀⣛
⠀⠀⢰⣰⠆⠨⣹⣿⣿⣿⡗⠀⡇⠰⠀⠀⠀⠀⠀⣶⣶⠻⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⠙⣯⠀⠀⠀⣥⢾⠲⠙⢁⠘⠀⠀⠀⠀⢱⢦⡀⢤⠟
⠀⠀⣿⡇⠀⠀⠈⠻⣿⣗⢻⡀⠀⠀⢠⠀⠀⢀⠀⣿⣧⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⢀⠀⠋⣤⣤⣤⠞⠻⣀⣅⣠⣄⣀⣀⣤⣀⡐
⠀⠀⣿⡍⠀⠀⢆⣤⢾⡿⠞⣷⣴⣧⣴⡌⠠⡈⢰⣿⣟⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⢀⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣈⠿⣿⠀⡄⠀⢀⢃
⠀⠀⣿⣷⠀⠀⢨⣅⢀⣤⣐⡛⣯⣽⣿⠏⠀⠀⢹⣿⡧⠤⠤⠺⠉⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⢻⡄⠸⡿⠿⠟⠽⣍⣷⡇⠰⣿⡖⣾⢾⡁
⠀⠀⣿⣿⠀⢀⣘⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⡀⠀⠙⠇⠀⠀⠀⠈⢧⠘⣿⣿⣿⣿⣿⡟⢀⠀⠀⠀⠀⣿⣿⠃⠈⣧⢀⣀⣁⠀⣈⣸⣿⣿⣷⣬⣁⠈⣼⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠈⣧⢿⣿⣿⣿⡿⠁⠈⠀⠀⠀⢀⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⢻⣿⣿⡟⠋⠉⠂⠸
⠀⠀⠀⠁⠈⠁⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸⡿⢁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⡈⠻⢿⣶⣴⣾⣿⣿⣿⣄⣰⣿⣷⣤⣄⡀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣹⣿⠁⠐⢛⣿⢿⣿⣿⣿⣿⡙⠻⢛⡛⠿⠿⣿⣴⣿⣿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⡿⠷⢶⡄⠘⠋⠘⢿⣿⣿⣿⣇⢀⡻⣓⠾⡷⠛⢹⡟⢿⣒⣐
⠀⠀⠀⠀⠀⣴⣶⠿⢿⣷⣧⣤⠰⠶⢿⣾⣿⡟⠀⠀⠀⠉⠉⠈⠿⣿⡷⣾⡿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⢻⣥⣶⡿⠟⠠⣴⣿⣶⠊⠉⠉⠁⢀⡀⢀⡀⠀⣤⣀⣀⣀⡛⠡⠀⢍⣷⡿⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠫⣿⢗⣼⣶⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⡿⡇⠀⠀⣾⠿⢀⠀⣀⠏
⠀⠀⠀⠀⢀⣠⣴⣿⣾⣛⠉⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡀⣿⣧⣶⣶⣦⣿⠇
⠀⠀⠀⠀⠘⠟⠉⠻⣿⡟⠀⢀⣠⣿⣧⠀⢠⣶⣿⣶⣀⡀⠁⠀⠀⠉⣏⡈⢉⠉⠷⣄⣀⣠
⠀⠀⠀⠀⠀⠠⠈⠁⠙⠇⢸⣿⣿⡏⠉⣲⢾⠁⠀⠀⢹⣷⠾⣿⣿⣷⣧⣴⣦⡴⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠻⣿⣿⠁⠀⠬⠭⣤⣦⣤⣴⣿⠀⠸⣿⣿⠿⠙⠛⡇⠀⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠀⢘⣛⣛⡛⠛⠛⣾⣿⣷⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⢹⡃⢀⣴⣿⣿⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠃⣇⣀⣤⣀⣀⠀⠀⣀
⠠⣄⠀⢠⣶⠛⠛⠓⠿⠌⠁⠀⠀⢈⡷⢞⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣀⣀⣀⡀⢠⡄⢀⠀⢀⣀⣀⢀⡀⠀⣀⣀⣀⣀⡀⠀⣀⢀⣀⣀⡄
⠀⣭⠛⠶⠾⠶⠀⠀⠀⡀⠠⠀⢶⣏⣀⠘⢧⣽⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠈⠈⠉⠉⠁⠈⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠀⠉⠈⠉⠉⠁
⠀⣈⠷⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⣟⢉⡿⠀⠀⠀⠀⠀⠇⠰⠆⠄⠠⠦⠴⠆⠶⠀⠐⠲⠶⠀⠘⠃⠤⠂⡼⠀⠰⠶⠶⠀⠈⠇⠲⠤⠜⠃
⠋⠀⠀⢀⡀⠀⠃⠀⠀⢀⡤⠀⠀⠐⠦⠘⡄⢰⣾⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⢀⣀⡀⢀⡀⠀⣀⠀⠀⣀⣀⣀⡀⣀⢠⡄⢀⣄⢀⠀⡀⠀⢀
⣺⠟⠀⢸⢍⠲⠄⡀⠀⠀⣤⠄⢸⡇⣤⠀⢃⠈⡾⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠁⠉⠀⠀⠉⠀⠀⠉⠈⠉⠈⠉⠀⠀⠁⠀⠉⠀⠁⠀⠈
⠥⣴⠂⣰⣮⣀⣀⠀⠀⠀⠀⠀⠘⠷⠀⠐⣡⡞⢡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠀⠶⠀⠆⠶⠶⠖⠒⠆⠀⠶⠶⠶⠴⠶⠒⠶⠀⠒⠰⠆
⠘⣣⡶⣏⠠⣭⣽⣧⣀⣹⣖⣐⢠⡄⣒⣾⣿⣿⠄⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⢀⡀⢠
⡞⠃⠀⢿⣀⣉⡉⠉⠉⠉⠋⣍⠙⠉⡿⠁⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠈⠉⠉
⡇⠀⠀⣠⣉⣈⠉⡷⠀⠀⠀⣭⡿⠈⡇⠀⠀⠾⠋⠀⠘⡇
⠁⠀⠀⠶⠂⠈⠉⡗⠀⠀⠐⠀⠀⠀⢦⠀⠀⠀⠃⠀⢀⠃
⠀⠀⠀⠀⢀⣤⢶⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢶⣀⠸
⠈⣀⣠⡴⠋⠁⡘⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⢠⠹⡇
⠀⠈⠙⣦⠀⠀⠃⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢠⡇⠀⠀⢰⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠐⠴⠀⠰⠐⠀⠀⠴⠄⠀⠖⠀⠶⠆⠀⠆⠀⠀⠀⠠⠤⠤⠀⠠⠤⠀⠄
⠛⠓⠶⠶⠦⠼⠦⠀⠀⠀⣸⠷⠶⠀⠘⣧⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⡆⠈⡁⠀⠀⠀⣤⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠁⠀⢦⠔⠿⠒⢦⠀⠂⠀⠸⣄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠆⢠⠤⣀⣆⠐⠖⠐⠦⠀⠀⠀⠀⢠⡄⣁⠀⠀⡁⠀⠀⠀⠄⠠⡆⠀⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠙⠂⠀⠈⠓⠲⣶⠀⢐⢀⣀⠀⢸⣧⣤⡀⠾⠶⠾⠂⣀⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⣿⣟⢱⣆⠀⠀⠓⠐⠃⣤⣀⣉⡍⣣⣼⣿⠉⠀⠆⣠⣆⣀⠀⠁⣼⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠛⣳⡎⢁⣤⡄⠘⢣⣤⣀⣀⠀⠀⠈⡹⠟⠉⢟⠁⡤⠀⠀⠹⣿⠄⠈⠟⠶⣯⣿⣿⡀⠛⠃⠙⠉⠉⠀⢰⣿⡏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⡀⢟⠁⠀⠀⣄⠀⠀⢿⡉⠉⢀⣀⣀⠃⠀⠀⠈⠳⣷⠀⡖⠉⠀⣴⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⣀⠀⠀⢻⠔⠋⣴⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⠞⠒⠀⠀⢋⡀⠆⠀⠙⡄⢠⡿⣟⠀⠀⠐⢆⠀⠈⠁⢢⠀⠀⠸⡆⠆⠀⢨⡝⢿⢶⣶⣆⠲⣿⠛⠀⠀⢠⡴⣦⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢤⣌⢂⡐⠲⣷⠀⠉⠹⠟⢿⡷⣦⠁⣾⠁⣿⣀⣠⣤⣤⡄⠀⠀⠈⣦⠀⠀⠙⠖⢠⡏⢫⡝⡄⠉⠙⢄⠀⠀⢀⠀⢻⡛⡯⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠉⠁⠀⢀⣀⣤⣤⢤⠀⠀⣻⠂⠀⠸⡆⠻⠉⠤⠒⠸⣇⠀⠀⠀⠘⢧⠀⠀⠀⣰⠀⠀⠓⣧⣴⡒⠶⠟⠀⠈⠀⣸⠉
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠙⠛⢦⡀⠘⢧⠁⡰⠂⢀⡰⠃⠀⠐⠚⠛⠷⢀⠀⠀⠀⠈⢷⠚⠛⠓⠋⠳⣄⠀⠿⠀⠀⠀⡘⠛⠉⢤⣤⡴⠞⠻⣏
⠀⠀⠘⣄⠈⣳⠄⠀⠉⠐⠂⠀⢮⣝⡀⠀⠸⣤⡶⠶⠴⣦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⡀⠘⠃⠀⠀⢰⡂⢀⡴⠋⠀⠀⠀⢠⡟⣧⠀⠀⠈⠳⣄
⠀⠀⣸⡈⢳⢥⡄⣁⠀⣀⡐⢄⣸⠟⠉⠉⠉⠋⠓⠦⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠦⠀⠀⠀⠸⡇⠁⠀⠀⠀⠀⡰⠈⡇⠘⢇
⠀⠀⢀⠀⠈⡼⢋⣽⣉⣧⠞⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⢷⠀⠀⠀⢀⡼⠁⠘⡇⠀⠘⣦⠀⠀⠀⢠⠜
⠀⠀⠈⠒⠀⠀⠈⠻⠷⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⡿⠀⠀⠀⠈⢳⡄⣠⠞⠀⠀⢀⠁⠀⠀⠈⠳⠤⠖⠁
⠀⠀⡐⠢⠤⣦⡀⣠⡄⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠁⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⢧⡀⠀⠀⣀⠀⢹⠀⠀⠀⠀⠰⠶⣤⣤⣤⣀⣀⡠⡔⠀⠁
⠀⠀⠀⠙⠛⢚⣿⣖⣿⣶⣤⣴⣶⣞⠛⠀⠀⠀⠉⢉⡝
⠀⠀⠀⡀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢀⡟
⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣀⡀⠀⡄⠀⣄⣠⢄⣀⡀⣠⡀⢀⣀⣀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠉
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢸⠀⡿⠞⠃⠼⠲⠇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢛⣛⣩⣭⣤⣶⣶⣶⣶⣭⣭⣭⣟⡛⠷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣡⣾⣿⠿⠋⠁⢀⣀⣋⣉⣉⣛⣛⣻⣿⣿⣅⡀⢉⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣴⣿⣿⣿⣦⣶⣾⣿⠿⠿⠟⠛⣛⣋⣛⣿⣿⣿⣿⣿⣷⣦⣍⣙⡛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣼⣿⣿⣿⡿⠟⠢⢄⣀⣠⣤⣴⣶⣶⣶⠶⠾⠿⣿⣿⣿⣿⣿⣿⣍⠠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣴⢟⣡⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣩⣥⣤⡶⣂⡉⠀⠀⠀⠹⣿⣿⣿⣦⡹⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⠟⠁⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⠿⠷⠞⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⣹⣿⣯⢠⣤⡿⠃
⠀⠀⠀⠀⠀⢰⡟⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣼⠇⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣼⡇
⠀⠀⠀⠀⣰⡏⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣿⣇⢸⡇
⠀⠀⠀⠀⣽⠗⢸⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠆⠹⣿⣿⢣⣼⡟
⠀⠀⠀⠀⢻⣆⢸⣿⣿⣿⠇⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣀⣠⣤⣤⣸⡿⠤⢍⠻⣆
⠀⠀⠀⠀⣾⡋⢸⣿⣿⣏⣈⣉⣉⣛⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⣿⣿⣿⣿⡿⣿⠣⠀⢀⢠⡿
⠀⠀⠀⠀⢸⡇⡄⠀⡿⣿⣿⣿⣿⣿⣿⠟⣛⣿⠷⢲⣤⣄⠀⣴⣾⣿⣿⡿⠁⣼⣿⣿⣿⣿⢣⣿⢀⣠⢣⡾⠃
⠀⠀⠀⠀⠸⣧⡳⣄⢤⣿⣿⣿⣿⣿⣵⣿⠟⢁⣴⣿⣿⣿⠟⠿⢿⣿⣿⠃⣼⣿⣿⣿⡿⣣⣿⣿⠚⢡⡿⠁
⠀⠀⠀⠀⠀⠈⢳⣎⢷⠹⣿⠟⣽⣿⠟⢁⣴⣿⣿⣿⣿⠇⠀⠀⠈⠻⢷⣴⣿⣿⣿⣿⠿⠛⠉⠘⣠⢻⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣜⠦⠙⡿⠿⠤⣶⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠃⠀⠀⠀⠀⢀⡴⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⢄⠀⠀⠀⠀⠀⠀⠌⠀⡆⠀⢀⡤⢂⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⢗⣩⣶⠦⣄⠀⠀⠀⠀⣁⠴⣩⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣵⣾⣿⣿⣿⠀⠈⠋⢽⡇⠀⢹⣶⣭⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⣿⣿⣿⠀⢴⣿⡟⠀⠀⣼⣿⣿⣿⣷⣌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣱⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠃⠀⠀⢈⠙⣿⣿⣿⣿⡎⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⢐⠢⢀⣠⣿⣿⣿⣿⣿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⣿⣿⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠰⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢮⣭⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣜⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣣⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣭⣭⣛⣛⣛⡟⠻⠿⠿⢿⣛⣛⣛⣭⣭⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⡠⡪⠐⣀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⣠⣾⢂⢎⡾⢋⠔⢊⡤⢐⡀⠄⠀⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢮⠐⢄⡢⢄⢄⡀
⠀⠀⠀⣀⣰⣿⢡⢎⣿⠕⣡⡾⠟⠋⠁⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠠⠀⠐⡄⠀⠱⡀⠳⡀⠱⡄⠙⢄⠑⣌⢢⡀
⠀⠀⣾⠛⣿⢏⠎⡾⢃⡴⠉⠀⠀⠀⠀⠀⠀⠀⣀⡸⠁⠀⠀⠀⢰⣥⡀⠀⠙⣆⠀⢱⠀⠱⡀⠘⢄⠈⢧⠈⣆⢣
⠀⢰⡗⣀⣿⢀⠜⢁⡾⠀⠀⣀⣸⣿⠀⠀⠀⠾⡷⠦⠀⠀⠀⠀⢁⣀⡀⠀⠀⠈⢷⡀⡇⠀⠱⡀⠈⠣⡈⠆⠸⢸
⠀⢨⡯⡿⠿⠈⠈⠡⠁⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⡿⡗⠄⠀⠘⠦⡀⠘⢠⠀⡆
⠀⠈⢧⡇⠘⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢸⠰⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡀⢰⠀⠈⠐⣤⡤⢴⠦⡄
⠀⠀⠀⠙⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⣈⣁⣠⡀⢠⠀⡇⠘⠀⣷⠀⠀⠀⠀⠀⠀⢹⣄⠈⠡⠃⠈⠒⠦⠐⠀⠀⡛⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣒⣴⠆⠈⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⡀⠀⠀⠄⣧⡆⢎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⡤⠒⠀⠀⠀⠀⡇⠀⣼⠃⠀⡜⢀⣿⡇⢸⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢡⢰⡿⢀⡜⢀⢎⣾⠁⡸⠀⠇
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢾⡵⠋⡠⢫⠎⠈⠀⠃⡘
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠜⠐⠁⠤⣀⠒⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠄⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠤⢤⠀⢠⠄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⡆⢠⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⢣⠐⠀⠂⡀⢠⠁⠀⠀⠀⠀⠃⢠⡆⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠉⢱⠁⠀⠀⠀⠀⠀⠂⠀⠃⠘⡇⠀⠀⠀⠠⠐
⠲⠰⠀⠀⠀⠀⠠⢬⣀⡀⢦⡀⠈⠀⠀⣆⣠⠀⠀⢀⠀⠀⠚⠀⠀⠠⠀⠄⠀⢱⣾⠴⢤⡏⠀⢠⠎
⠀⠀⡅⠀⠠⡁⠀⠀⢠⠀⠀⠙⢮⠀⠂⡩⢉⣀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠀⡀⠠⠀⣠⣄⣤⠔⠁⠀⠀⠀⠀⠄⠐⠦
⠀⠀⠀⠀⠀⠀⠂⢀⠐⠀⠀⢀⡂⠁⠀⠀⢀⡀⠩⠠⠀⠀⡛⠀⠀⢀⠤⠞⠑⠲⠶⢋⣉⠤⠐⠒⠒⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠀⠀⠀⡐⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⣄⡀⠀⠀⠀⢠⡧⠊⡁⢠⣤⡤⣤⣄⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣻⢯⡻⡾⢶⠀⣸⡁⠘⠁⢺⢿⣧⣧⣽⡂
⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⠀⢥⠁⢸⠀⠀⠀⠙⢾⣼⠁⡇⠀⠀⢸⣼⡇⣟⣉⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠈⠀⢸⡆⠀⠀⠀⢸⠿⣤⠇⠀⠀⢸⢸⣇⣧⣦⡅⠀⠀⠀⠠⣤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠸⠀⠀⠂⠀⢸⠀⢹⠆⠀⠀⠸⠜⠃⢧⠟⠇⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢀⡄⣶⢐⢙⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠐⠀⡀⠀⣀⠁⠂⢠⠐⠾⢿⠿⠾⡿⠦⣵⣏⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢠⠂⢀⡔⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡴⠁⢀⠎⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠁⢀⠎⠀⠀⠀⠐⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠎⠀⢀⠎⠀⠀⣠⠊⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡠⠃⠀⢀⡔⠁⠀⣠⠏⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⠞⠀⠀⢠⠊⠀⠀⢠⠋⠀⠀⠈⠉⠁⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠠⡶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠁⠀⢀⡴⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⢤⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠞⠀⠀⠒⠉⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠘⠡⠧⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠬⠶⣤⠤
⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⡀⠀⠛⢀⡔⣀⡀⠀⣀⣠⠾⠃
⠀⠀⠀⠀⢀⠹⡄⠀⠻⣦⠙⢦⠀⢸⡏⠁⢹⡆
⠀⠀⠠⡀⠀⠳⣄⠄⠀⠘⣧⠈⠳⣼⡧⠀⠀⠃
⠀⠀⢀⠑⠄⠀⠙⠶⣄⡀⠙⢦⡀⠘⣷⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢤
⠀⠀⠈⠀⠐⣄⠀⠀⠈⠻⣄⠀⠹⠀⠘⣧⠀⠀⠀⠉⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠳⡀⠈⢧⣄⡀⠀⠙⠆⠀⠁⠀⢸⠳⣄⠀⠀⠀⣷
⠀⠀⠀⠀⠙⢆⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠰⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠓⠆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⡌⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠙⠓⠤⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠙⠲⢤⣄⣀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⢰⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡴⠖⠛⣋⣽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠯⢭⡉⠙⠳⠤⠞⠁⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⢀⡞⣁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠧⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠞⢀⠀⠀⠐⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⢷⠀⠀⣷⠈⠛⠦⣽⣟⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢀⣀⠌⠉⠛⠲⠦⣤⣀⡀⠹⣏⠙⠛⠲⣶⠤⣤⣈⣛⣦⣄⠉⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣩⠖⠚⠓⠶⣤⡀⠀⠀⠈⠉⠉⠁⣀⠀⠹⡄⠀⠀⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠙⣦⠀⢀⣤⠖⠒⠛⢧⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⡾⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⠀⠀⠀⠘⡇⠀⣹⠦⠤⡄
⠀⠀⠀⠀⢠⡟⢁⣀⣀⣀⠙⠻⣵⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢉⠟⠒⠳⡄
⠀⠀⠀⠀⠈⣇⠀⠀⠙⠮⠿⡄⠙⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡀⢠⡇⢠⣤⣄⠀⠀⢸⡇⠀⠈⢷⣉⠛⣧
⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣯⣿⡿⠣⣷⣾⡿⢀⣠⠟⢀⣠⠤⣄⠸⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⢙⣓⣶⠞⠁⠀⠀⠉⠉⠉⠀⠠⠋⠀⠀⣸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⢀⡄⢀⡴⠒⠛⣚⣧⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⠀⣼⠀⠀⠀⠀⢠⡏⠉⠙⢲⣒⣒⣾⣤⣬⠵⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣇⣠⡇⠀⠀⠀⠀⢸⡗⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠚⢧⡞⠀⢸⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡑⠀⠁⠀⡞⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⠤⠤⠞⠁⠀⠀⠀⠀⢀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣦⠤⠶⠶⠶⠒⣾⢻⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⣸⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠀⠉⣹⣉⣁⣼⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠢⠤⠤⢴⢶⢖⠟⣻⢀⣈⣷⡤⣾⠇⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢝⣒⣒⣒⣛⣛⣚⣉⡩⠥⠖⠋⠉⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⠒⠒⠀⠠⠤⠬⠭⠉⠉⠻⠿⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠯⠭⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣆⠀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠛⠉⠁⢀⣤⣤⣤⣉⡻⢿⣿⣿⣷⣌⠻⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⡄⠀⠁⠀⠀⠉⣙⣿⣾⣿⣿⣿⡏⠁⠘⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⣸⠀⠀⠀⢠⣾⡟⠛⣿⣿⣿⣇⣾⡇⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡀⠀⠸⣄⠛⠁⢸⣿⣿⡿⢙⣿⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢦⣤⡙⠿⡲⣿⣿⣿⣷⠞⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⡄⣤⢒⢀⠀⠠⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣉⡟⣷⣧⡞⣫⠤⣰⣼⡟⣾⣛⣿⣷⡢
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣾⣿⣿⠻⣴⡶⠀⡸⠟⣯⢽⢩⣟⢿⣿⣏⠈⣀⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⡋⠀⢀⣸⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠠⣐⢾⣿⣿⣿⣿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡎⠉⠉⠁⠈⠛⠛⠋⠉⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⠀⠀⠀⠀⠴⠶⢶⣶⣤⡄⠀⣤⣴⡶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠻⡆⠛⠀⠀⠀⠀⠁⠚⠋⠉⠉⠀⠀⠋⠉⠉⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⣀⡠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠘⣋⠐⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣄⠀⣸⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠈⠻⡿⡿⠀⢀⡽⠋⢉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠉⣠⠖⠉⣀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠚⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠘⢄⠀⠀⠀⠙⠲⢤⣠⡏⠀⠀⠀⠀⢠⣴⡇⣠⠏⠑⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠞⡿⠀⠀⠀⠀⠀⠼⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢆⠀⢰⠃⠀⠀⠀⠀⠈⣴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⢀⠞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠹⣄⠀⠀⠀⡤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢶⠒⠤⠤⣀⠀⠀⠈⣇⠀⠀⢰⠋⠀⠀⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠽⢳⡄
⢸⠀⠀⠀⠸⣀⠀⠀⢸⠀⠀⠈⡇⣠⠖⠉⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣶⡚⠛⠛⠒⠒⠃
⠸⣆⢤⣀⠀⠀⠑⠢⣼⠀⠀⠀⠙⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠉⠒⠤⡀
⠀⠁⠀⠈⠑⠦⣄⠀⠀⡖⢦⡄⣖⢴⡆⣰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠆⠀⢠⠎⠀⠈⠲⡀⠀⢑⠦
⠀⡠⠛⠦⠤⠤⠬⠿⠦⢦⣤⢰⣇⢲⠂⠑⠒⠒⠦⠤⠞⠳⣄⠀⢠⠖⠒⠲⠤⣄⡀⠀⠀⠀⠀⣠⠖⠒⠒⠲⣤⡠⠴⠒⠛⠓⣆⡴⠋⠀⢀⣀⠤⠼⠀⣌⢳⠆
⠾⣅⡀⢀⣀⣀⣄⠤⠤⢤⡄⠀⠀⡨⠤⠤⣄⣀⣀⡀⠀⠀⠈⢢⡘⢦⣂⡀⠀⠀⠈⠉⠓⠲⠤⣽⣄⡀⠈⡷⣯⠄⠀⠀⢀⡼⠃⠀⠀⣠⣿⡶⠚⠓⠦⠉⠃
⠀⠀⠉⠚⠀⠀⠀⣀⣀⡞⠀⠀⡰⠁⠀⠀⠀⠀⠀⢹⣀⠴⠚⠁⠀⠀⠈⠙⠓⠲⡦⠤⠤⠤⠤⠷⠂⠉⠉⢳⣄⣀⣠⠶⠋⠀⠀⣠⠾⠿⣏
⠀⠀⠀⠀⠀⠀⠀⢳⠉⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄⠀⠀⢀⡞⡵⠶⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠚⣻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣰⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡰⠥⠾⣇⠀⠲⢄⡀⠀⠀⠀⣠⠴⠋⢀⡴⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢒⣼⣆⠀⠀⠀⢀⡤⠚⠁⢀⡴⠋⠀⠀⢀⠀⠀⠙⠖⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⢯⣮⣬⣧⣠⢖⡉⠀⠀⡰⠋⠀⠀⣄⠀⠀⠣⡀⠀⠀⠀⠈⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⡏⠉⠁⣎⣿⣧⠀⠙⠢⠞⠁⠀⠀⠀⠈⣆⠀⣠⠟⠀⢀⡤⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢚⣿⣿⢀⣴⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⡿⣧⠴⠋⢀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠿⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡜⢆⢠⢫⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠤⢤⣤⣤⣤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠘⢦⡛⠉⣈⣉⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⣌⣢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⠙⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠋⠽⣛⣙⣿⣿⣛⣷⠶⠶⠖⠒⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠽⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠔⠉⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢳⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⣇⠀⠀⠀⢠⠇⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢀⡄⢀⠈⢦⠀⠀⢸⡀⠀⠀⠉⠀⢀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠉⠓⢌⣇⠀⢀⠷⠒⣒⣒⢲⣯⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠻⣈⣋⣀⣤⠞⠑⠚⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢵⠀⠀⠀⠚⠁⠠⡄⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⡸⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠱⠚⠒⡀⠀⠀⠀⠀⠀⢙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠢⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠑⠦⢄⣂⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡜⠉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⣰⠁⠀⣾⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⢀⢇⡴⠚⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⡦⢧⣀⠀⠀⠈⠀⠀⠀⢻⣀⡄⠀⡌⡞⠠⣾⠟⢶⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠬⣉⡒⠢⠾⡓⠲⡞⢇⢸⠈⠛⢹⡄⠀⠀⣎⣉⡉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡙⢷⣤⣸⡀⠟⠙⢾⣆⠀⡼⠙⠦⣀⣯⣀⡈⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠉⠳⣌⠓⢯⣑⢄⢩⢻⡷⠣⡀⠥⣼⣴⡒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠑⢦⡈⠙⠛⠁⢀⡔⢉⡶⢥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠙⠦⣤⣴⣉⠹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡛⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠒⠶⠤⢤⣀⣀⡀⠀⠀⠀⢠⣧⣀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡴⢋⠜⠉⡩⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣀⣤⣴⣫⡔⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣜⠁⠀⠀⠀⢀⠔⢁⣁⣰⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠥⠤⠼⠿⠂⠙⠛⠉⠉⠉⠉⠛⠒⠻⠥⠬⠉⡑⠆

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⣦⣄⣀⣀⡀⢸⡇⣇⠀⠀⣇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢻⣄⠰⠒⠒⢦
⢳⡀⠉⠁⠀⣿⠷⢹⡄⠀⢻⡄⠀⠀⠱⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢰⠉⠓⠦⡀
⠸⡇⠀⠀⠀⣿⢀⠀⢳⡄⠀⣿⠀⠀⠀⠋⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠏⠀⠀⣿⠀⠀⣠⠆
⠀⢙⠄⠀⢠⡟⠈⢧⠘⣧⠀⢹⡆⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣸⠀⠀⢹⠀⠀⣇⠀⣀⣀
⠀⠈⣆⠀⢸⡇⠀⠸⣇⠘⢧⡀⢻⣄⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⠀⠀⢸⠀⠀⠈⡆⢁⣍⡽⠋⠉⠁
⠀⠀⠹⣤⡼⠃⠀⠀⣿⠀⣼⠁⢸⡏⠀⢿⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡆⠀⠀⢇⣽⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠸⣇⠀⢸⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡇⡀⠘⠦⠀⠘⠄⠘⠆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠤⠿⠄⠀⢠⣇⠀⠀⠣⡀
⠀⠀⠀⠀⣀⣠⠴⣻⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠲⢸⠄
⠀⠀⠀⡖⠀⢀⣠⠏⠠⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠉⠑⠒⠦⣄⣀⣀⣤⡀⠄⢺
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠙⠛⠮⣟⠋⠛⠉⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⢤⠔⠉⠁⠀⠀⠀⠈⢧⡀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣤⣀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠁⠀⠉⠛⠿⣿⣿⣿⡿⠟⠉⠁⠀⠉⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣦⣄⡀
⣠⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦
⣿⣿⡉⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⣻⣿
⠘⢿⣿⣶⣄⠀⠀⠀⠻⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠈⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠃⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⢻⣿⣧⣤⣴⣶⣶⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣾⣿⡿⠋⠉⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⢻⣿⣧⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣶⣶⣿⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠀⠐⠟⠛⠛⠛⠛⠛⠛⣁⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣤⣤⣤⣤⣤⣤⣤⡾⠟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣽⣷⠶⠞⣿⣻⡇⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⡄⠠⠐⠘⢋⣉⡄⢤⠸⡆⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣻⣭⣴⣶⡿⣿⡉⢟⣫⣿⣴⡶⠾⢿⣛⣼⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠄⠒⠛⢉⢁⠀⠰⡤⠆⠣⠘⠁⣉⣠⠠⠗⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣟⣷⣿⣭⠶⠿⣟⣛⣩⣭⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠐⠈⠁⠐⣋⣁⠠⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣯⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⠀⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣄⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣠⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣷⣶⣄⣀⣠⣴⣶⣾⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⡇⠀⠀⢸⣿⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠰⠿⠿⠿⠿⠛⠛⠛⢻⣿⡇⠀⠀⢸⣿⠋⠛⠛⠛⠛⠻⠿⠿⠿⠷⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣄⣀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣾⣿⡇⠀⠀⢸⣿⣶⣶⣶⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣿⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⠛⠉⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣶⣶⣶⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⢸⠿⠻⠛⠿⠄⠀⢀⡀⢀⡼⠈⣥⣠⢄⣦⣴⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⡞⡿⢪⡅⢻⡻⡋⡉⣿⢭⢻⣄⣾⣶⠂⢂⠀⠀⠀⠀⠀⠀⠚⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⡀⣠⢖⣿⢉⡄⠉⣀⣤⣴⣶⣶⣾⣷⣬⣾⡗⢿⡿⡽⢦⣞⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣩⢱⠞⢋⣷⣿⣻⡿⣛⢿⠉⣿⢻⡙⠿⢿⣿⣤⡲⡯⠝⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⡿⠟⢇⣾⣿⠋⢭⡔⢡⣤⡟⡷⢲⠏⢲⡆⠻⣿⣿⡄⢠⢧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣭⣥⣶⣃⣼⣷⠿⡴⠬⣱⠆⠿⠓⠗⢛⠞⠑⠞⠓⢿⣿⣧⢤⡴⠷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣯⡯⠃⣿⣿⣤⣦⣼⣥⣴⣤⣴⣤⣦⣤⣦⣤⣧⣼⣿⣷⠀⠒⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡌⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⡟⣿⣿⣽⡇⣿⢻⣿⠏⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿⣿⣿⠹⣿⣻⡇⣿⠏⣿⣸⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⡅⣿⢸⡇⣿⡐⣿⠻⣿⢿⣿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢺⡿⣿⣿⣿⣿⣧⣿⢸⡄⣻⢂⣿⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠦⠀⠀⢸⣿⣿⣷⣿⣿⣏⣿⡜⣷⣸⣿⣿⡯⢿⣿⣿⣿⣿⠂⠀⠀⠀⠂⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠛⠋⠉⠉⠉⠙⠋⠉⠉⠉⠛⠛⠋⠋⠉⠛⠉⠛⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡶⠀⢠⠀⣶⡆⠀⡖⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡏⠀⣿⠀⣿⠁⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⢠⢸⡇⣇⡀⢻⡀⢹⢠⡀⣇⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⢉⠀⡈⠁⠈⡀⠀⢉⠀⢈⠀⡀⠀⠀⠸⢷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢹⠈⡿⠃⢸⠇⡇⢽⠄⢸⠀⡇⠀⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣄⠀⢽⠀⡿⠀⢸⠀⡇⢰⠀⢻⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠂⠸⠀⠓⠐⠘⠂⠁⠺⠒⠸⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠶⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣀⣀⡠⠤⠄⠀⢀⣀⡀⠀⠀⠀⠉⠁⠶⠆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢾⠏⠉⠉⠉⠳⣄⠀⠀⠈⠉⠉⠶⢦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠶⠶⠀⣀⣴
⢀⣠⣤⣀⣀⠀⡀⠐⠒⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⣦⠀⠀⠀⠀⠘⠻⣶⠶⠶⠄⣀⡀⠀⠀⠀⠀⣀⠴⠋⠉⠰⠆⣀
⠈⠻⠃⠈⠁⣀⡀⠐⠲⠶⠖⠀⣼⣆⡀⠀⠀⠀⠈⠀⠀⠈⠶⡀⠀⠀⠀⠀⠘⠧⠀⠀⠈⢩⣶⣄⠰⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠿⢧⣀⠀⠀⠀⠀⠀⢹⣤⣀⣠⣀⠀⠸⡿⠒⠂⠀⠈⢹⡆
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠈⠀⠀⠉⢳⣤⡀⠚⠓⠀⠉⠻⣄⠀⠀⠀⢰⡆⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⣦⡀⠀⢀⡄⠀⢻⡇⠀⡄⣼⠗⠚⠀⠺⠋⠙⣿⠟⠢⣤⡀⠀⠈⢳⣄⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠂⢀⡌⠀⠀⢸⠀⠀⠀⠈⣶⡄⠘⠿⠃⠛⠋⠙⠻⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣷⠀⠀⠀⠀⢸⡄⠀⠀⠘⠋⠀⠀⠀⠆⠀⠀⠀⠁⠀⠘⠛⣦⣤⠤⠄⠀⠀⡀⠀⠤⠤⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠻⡆⠀⠀⠀⠀⠙⣷⣄⣀⠀⣴⡄⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⢤⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢋⡄⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠉⠙⢿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⢶
⠀⣴⣇⡀⠉⠀⠀⠀⠈⢣⡀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠁⠁⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠈⠁⠀⠀⠀⠶⠶⢾⣉⠉⢉⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⣀⣀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⢀⠀⠀⠂⠈⠉⠁⠈⠉⠉⠁⠲⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⢾⡷⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢀⣀⡀⠀⠀⠀⣀⡀⠀⠶⠦⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡆⠀⠉⠉⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠒⢀⣀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢂⣀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠘⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣤⣤⣦⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠰⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⣦⣤⣤⡘⠿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⡿⠿⠛⠉⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⣠⡴⠛⠛⠻⢶⣶⠀⠀⠀⣠⣴⣶⡿⠛⠛⠒⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡗⠡⣤⡶⢶⡶⢶⣌⣷⠀⠀⢼⣷⡶⢶⡿⢧⣄⡀⠸⢣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢘⣇⠀⠀⠀⠈⠙⠀⠉⣿⠀⠀⠀⠨⠀⠈⠁⠀⠈⠁⣀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⡄⠀⠀⠀⢠⠞⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡝⢀⠀⠀⠀⠀⠈⠓⠲⢦⡴⠞⠚⠛⠀⠀⠀⠋⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⣠⡀⢄⣠⣄⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⠋⣽⠀⠈⠉⠀⠉⠑⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣶⠀⢰⠆⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢰⠃⠀⠰⠀⠀⠀⢀⣴⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⡇⠀⢰⠀⢀⣠⣿⡟⠁⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢩⣿⠁⠿⣿⣿⡇⠀⠀⣶⡿⠿⠋⠀⢀⡷⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⢻⡇⠀⠀⢹⠇⡀⠄⠉⢠⣀⢀⣀⣀⡁⢒⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠹⣷⠛⠀⢠⡋⢀⠀⣀⠴⠋⡉⠉⠉⠙⠃⢉⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⢦⠀⠀⠀⠈⠑⠢⣼⡗⠀⠉⠁⢀⣴⠟⠛⠛⠲⠦⠀⠀⠀⡼⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢸⣷⣄⠀⠒⠋⠀⢰⣶⣶⣴⠂⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⢀⣠⡤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠈⣿⣿⣦⠀⠀⢻⡿⠿⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⡀
⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⣹⢿⡆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⠂⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢷⠀⠠⣀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠈⣿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠘⣴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣾⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡀⠀⠀⠸⣿⣤⣿⠇⢸⣿⠿⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠛⠿⠀⠀⠀⠈⠉⠁⠀⢸⣿⣦⡄⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⣿⡇⠀⢀⠀⣴⡿⣷⡄⠙⠋⠀⠀⣀⣴⣶⣤⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⣿⡇⠀⣿⣇⣿⡇⠿⠃⣀⠀⢠⣾⠟⢉⣤⣿⠃⠀⠀⠀⠀⢸⣿⠛⠛⠻⠷⠀⣼⡇
⠀⠀⠀⠀⣿⡇⠀⠘⠛⠋⣠⣴⡿⠿⣷⡈⠻⠿⠟⢋⣤⣾⣷⡄⠀⠀⢸⣿⠿⢷⣶⠄⢠⣿⠁
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣿⠙⠟⠀⠙⠁⠀⠠⣾⠟⢻⣧⣾⠏⠀⠀⢸⣿⣶⣤⣄⠀⣼⡏
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⠃⢀⣴⣾⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠁⢠⣿⠃
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣏⣄⠐⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣄⣼⡟
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢉⣠⣶⣿⢻⣷⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠛⠿⣷
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣽⡿⠿⠋⣠⣄⠀⠀⠀⠀⢸⣿⠀⣾⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣴⣿⡟⢻⣦⠀⠀⠀⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠙⠃⠀⠉⣤⡀⠀⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⣽⣿⣄⠀⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠈⠋⠀⠀⠀⢿⡇⠀⣿
⠀⠀⠀⠀⣻⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡠⠏⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡤⢄⣀⣀⣀⣀⣤⠤⠖⠒⠳⠬⠙⠃⠉⠀⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠓⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠿⢝⡂
⠀⠀⠀⠀⠀⠀⠻⣖⣒⣒⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡴⠃⣀⣤⠴⠶⠶⠦⣄⡀⠙⢆⡀
⠀⠀⠀⣀⡴⠚⠉⢉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠤⣄⣹⣞⡴⠚⠉⠀⠀⠀⠀⠀⠈⠹⣄⠀⠙⢦⡀
⠀⠀⠀⠈⠉⢉⠟⠁⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠹⠏⠀⠠⠶⢤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⣳
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢬⣙⠳⡄⠀⠀⠘⡇⠀⠀⣧
⠀⠀⠀⣼⠖⢹⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠁⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⠶⠒⢸
⠀⠀⠀⠀⠀⢸⠠⠤⢼⡄⠀⣀⣀⣀⣀⣤⣤⣴⠾⠛⠋⣴⡄⠀⢠⣆⠀⠀⠀⠀⠀⢀⣿⠀⢠⡏⠑⠂⢸
⠀⠀⠀⠀⠀⢸⠀⠈⠉⡇⠀⠈⢻⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣼⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⢳⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⣤⡿⠁⠀⢠⡇⠀⠀⣰⣧⣄⡀
⠀⠀⠀⣠⠶⠒⠚⠢⠤⠼⠂⠀⠀⠀⠈⠉⠛⠛⣟⡿⠋⠀⠀⠠⠖⣦⠀⠀⠉⠉⠉⠀⠀⠀⠳⠶⠊⣡⡴⠒⠙⣆
⠀⠀⠀⡏⢀⡴⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⣿⠀⠀⢹
⠀⠀⠀⢷⡀⠀⠼⠈⡧⢸⡀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⠂⠁⠐⠒⠒⠤⣄⡀⠀⠀⠀⠀⢠⣆⠙⠀⠋⠀⢀⡿
⠀⠀⠀⠀⠛⢦⣄⣀⣠⠼⢧⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣠⣤⣾⣿⣿⡆⠀⠀⠀⣼⠉⠛⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⡀⠀⠘⢿⢿⣿⢿⣟⣋⣛⣛⣛⣿⣿⠿⠿⣿⣿⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠲⠤⢄⣀⣀⣉⣁⣀⣀⣠⠴⠞⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠚⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣶⣿⣿⣻⣿⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢴⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣚⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠐⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤
⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠂
⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠄⠀⠙⢷⡄⠀⠀⡴⠾⠛⠛⠛⠓⠄⣿⣿⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠰⠶⠀⠀⠀⠀⠀⠀⠐⠶⠂⠈⠄⢀⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠰⠒⣟⣻⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⠶⠁
⠀⠀⠀⠀⠀⠀⠐⢎⠻⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣸⣿⣟⠽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠩⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡎⠩⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⡿⣦⣄⠀⠀⠀⠀⠀⢀⣴⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢛⢒⠀⢐⢛⣋⠁⢸⡀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣠⣀⣀⡀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣤⣄⣠⣄⣤⡀⣠⣄⣀⣀⣀⣀⣀⡀⣀⣀⣄⣀⣀⣄
⠀⣽⠏⠁⠼⠂⢹⣿⣿⠀⠘⠀⠀⢠⡐⢠⡤⠄⠀⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⢠⣷⠀⠀⣿⣿⡀⠀⠀⠘⣿⠀⠀⣽⠟⠛⣿⣿⣿⡤⣈⣹⣿⣿⣿⣿
⠀⢸⠔⠂⠀⠀⠘⠛⠋⡈⠀⠀⠀⠀⠋⠈⠀⠀⠃⠀⠂⠀⠀⠀⠀⢰⡏⠀⣀⠀⣀⣨⣄⠀⠀⠂⠀⢿⣿⡟⠐⠚⠀⣿⠀⠀⠉⠀⠀⣿⣿⣿⡿⢿⡏⠉⠉⠙⣿
⠀⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⠓⠻⢿⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢸⣿⣿⣃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣯⡄⠉⠙⣦
⠀⢸⠀⠀⠀⠀⠀⠀⢸⠋⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣄⣿⡚⣿⣇⢸⣷⡰⠇
⠀⢸⠀⠀⠀⠀⠀⠀⠊⠁⣽⣤⣉⠐⠀⠠⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⠀⠀⢂⣻⠁⣿⣿⣿⣿⣷⣦⣶⣤⣴⣶
⠀⢸⣠⠄⠀⠀⠀⠀⢠⠀⠰⠿⠾⠃⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠑⠀⠀⢸⣧⡀⠀⠀⠀⠈⠁⢀⣿⣏⣿⡠⢿⣿⣿⣿⣿⣿
⠀⢸⠁⠀⠘⠂⠀⠀⠈⣠⣞⠂⠀⠀⠀⠀⠀⠀⢘⠄⠀⣤⡜⠃⠉⠀⣄⢠⣤⡾⠟⠛⠳⠻⣆⠀⠠⡇⢀⠀⣰⡍⠳⣶⠀⢀⠐⠀⠉⣻⣿⡃⣀⢸⡟⣿⡖⠻⣿
⠀⢸⡄⠀⠀⠁⠠⡄⠀⠀⠙⠁⠐⢦⠀⠀⠀⠀⠈⠀⣸⣿⠗⠀⠤⠐⣤⣎⠉⠓⠲⢦⢀⣠⣬⣦⠀⡇⠈⠀⣿⡇⠀⢿⠀⠈⡀⠀⠀⣿⣿⠁⣿⣷⣏⠛⡉⠙⣦
⠀⣾⣿⡂⢀⠀⠘⠃⠀⣿⣰⠞⣀⡠⠀⠀⠀⠀⠀⣰⣿⡟⠶⠐⠶⠄⣿⢋⡂⠀⡆⠀⠈⠀⢺⣯⡀⡇⠀⠀⢹⡿⣤⣼⣴⣿⠑⠂⠀⣿⠉⠀⣹⣧⣹⣼⣿⣷⣦
⠀⣹⠋⠉⠉⠀⢰⡇⠀⣮⡥⠀⢟⠳⠀⠀⠀⠀⣸⣿⢸⣷⡾⠆⠀⢸⣿⣆⠁⡤⠱⣦⣶⠀⠌⢉⡥⣿⠟⠃⠙⠛⠟⢻⠛⠿⣴⠆⠀⢿⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⠀⠀⢸⡇⠀⣤⠀⢲⣌⡴⢀⣠⣴⣾⣟⣿⣾⡟⠓⠂⠀⢿⣿⣏⣠⣦⠼⣟⣿⣀⣼⡿⢹⡷⠀⠀⠀⠀⠀⠛⠳⣀⣿⣄⡀⠘⢇⠛⠻⣉⣰⣿⣿⣿⣿
⠀⢻⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⢋⣿⣫⠟⠛⢋⣠⡼⠷⠶⣶⢎⣽⣿⣿⣿⣿⣿⣿⡟⠛⢋⠤⠼⠃⠀⡀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣦⠌⠀⠰⣿⣿⣿⣿⣭⣿
⠀⢸⠀⠀⠀⠀⢸⡁⢀⡹⠿⠛⠋⣼⣿⣯⡴⠊⢁⣀⠀⠶⢞⣛⣻⣿⣿⣿⣿⣿⣿⢿⣯⣤⣤⣴⠗⠀⠀⠈⠲⣀⠀⠀⣠⠶⡄⠀⠑⢤⠀⠒⠚⢶⣿⣿⣿⣽⣿
⠀⢸⣦⡀⠔⠀⢸⣿⠟⠓⠖⢨⣾⣿⣯⣥⣶⠾⠿⣿⡿⠉⠉⠻⠿⠻⣿⣿⣿⠿⢿⣮⢹⣿⣿⣯⣆⠈⠲⡄⠀⠈⠠⠐⠟⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⢻⣟⠛⣿
⠀⢸⡧⠀⣀⣶⠸⠁⠀⠈⣰⢿⣿⣛⡿⢿⣿⠀⢰⡿⢁⣶⣤⡀⠀⠒⠛⢿⠿⠶⢆⠙⢾⣧⡀⠀⠛⠣⢀⠈⠁⠀⡀⠐⠐⠀⠂⠀⡀⠀⠙⠉⠉⠉⣿⡿⠛⢳⣏
⠀⢸⣿⡛⢋⣑⠚⠂⠀⢠⡿⢸⣿⡏⠑⠃⠻⣿⣿⡷⠛⣹⣿⣿⣿⣦⣤⣀⠀⠀⠈⠁⠈⣿⣧⡶⣠⡀⠈⢳⣄⠀⡀⠀⠠⣤⡿⠟⠀⠀⠐⣤⣤⣶⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣦⡆⢀⣿⠇⢸⣿⣷⡄⠀⠀⠀⠉⣱⠆⠙⠿⠛⠿⣿⣿⠿⣿⡶⣶⣤⣼⣿⣿⡐⠟⣷⣴⣾⠿⢷⣦⣰⣤⣠⡴⠛⠀⠀⠐⠛⠩⠌⠙⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡏⠀⠇⣼⡿⠀⢸⢿⣯⣼⣿⣿⣦⣤⣀⣤⣀⣶⣦⣤⠸⣿⠃⠹⣷⣿⣿⣿⣿⣹⠇⠀⣿⠛⣧⡀⠀⠻⣿⣁⣤⣤⠿⠠⠀⠀⠀⠰⣤⣼⣿⣯⣏⣿
⠀⢸⣿⣿⣿⣇⡀⢾⣿⣷⠀⠈⣸⣿⣿⠿⡿⢆⣉⡙⠻⠿⡿⠋⠉⡀⣛⢀⠀⠉⢿⣿⣿⣷⡿⠀⠀⠉⢠⣿⣿⣶⣤⣌⠁⢠⡉⠢⣀⠀⠀⢉⢲⣶⡾⣿⣿⣿⣿
⠀⢸⣾⣿⣿⡿⢿⣿⣿⡇⠀⠀⣧⡌⠀⠐⠀⠀⣿⠋⢸⠾⠋⢈⣉⡑⣿⣿⠀⢠⣾⣿⣿⣿⠃⠀⠀⠀⢸⡟⠁⠀⣠⡏⠹⠆⠹⠆⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣷⣶⣦⡇⠸⣿⣿⡇⠀⠀⣿⣷⣦⡀⠀⢠⣿⠀⠀⠀⠀⠈⠁⠁⢿⣯⠀⢺⣿⣿⣭⣤⣤⡤⣤⡀⢸⣿⠛⠙⢨⡗⠀⠀⠀⠐⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡇⢸⣿⣿⡟⠀⢰⣿⣿⣿⣿⡗⣿⣷⣶⠿⠃⠉⠀⠀⠘⣾⡟⠀⢹⣿⣿⣿⣿⡿⢣⣼⡈⠻⢿⣷⡄⢸⡟⠀⠀⠀⠀⠙⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡁⣿⣿⣿⣿⠀⢸⣿⣿⣿⠹⡇⣿⡏⢹⠂⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣻⡇⢸⡇⠀⠀⠀⠀⠀⠁⢠⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢨⣿⣿⠿⡇⠘⢻⣿⣿⡆⠸⣿⣿⣿⡇⠀⣿⠇⡾⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣿⡇⢸⡇⠀⠀⡜⠃⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⡟⣀⡇⠀⠀⢻⢿⣇⢀⣿⣿⣿⣿⣿⣿⣶⣶⣶⠛⠛⠛⠛⣲⣾⣿⠀⡿⣿⣿⣿⣿⣷⡈⠳⠁⠘⠏⠛⠀⠘⠋⠀⠀⠁⠀⠀⠀⡆⠀⢸⣿⠿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠇⠀⠀⣾⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣾⠇⢿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠿⠿⠾⠟⠋⣿
⠀⠀⣿⣿⣿⣧⣠⢷⡀⠉⠛⠟⠁⠀⠻⣿⣿⣿⣿⣿⣧⠀⠀⢠⡟⢻⣿⠉⢻⡀⠘⣿⣿⣿⣟⣿⣿⣦⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣡⡄⣷⣿
⠀⠀⣿⣿⣿⣿⢿⣿⡷⠀⠀⠠⣢⡄⠤⣀⠠⠹⣿⣿⣿⣦⡀⠘⡇⢸⡏⠀⡼⠃⠀⠻⣿⣿⣿⣿⣽⣿⣷⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿
⠀⠀⣿⣿⣿⣿⣾⣿⣤⣿⠶⠿⠛⠛⠒⠋⠀⠀⢹⣿⡿⣿⣧⠀⠈⣾⣿⢤⣀⠀⠀⠀⢻⣿⣿⣇⣨⠛⢿⣿⢦⡐⠀⠀⠈⡀⠀⠀⠼⠂⠀⠀⢱⠀⠠⡏⠽⠟⣿
⠀⠀⣿⣿⣿⣿⣿⡿⣿⣷⣶⠖⠀⠀⠀⠀⠀⠀⠚⣿⣷⣿⣿⠀⠀⢸⣧⠈⣉⣽⣟⠳⠌⢻⣿⢻⣯⢰⣿⠁⠀⠉⠀⣤⣄⠙⠂⠀⠀⠀⠀⠀⠘⣧⠀⢹⡄⠤⠻
⠀⠀⣿⣿⣿⣿⣛⠻⠿⠛⠁⢠⠄⢘⣀⠀⠰⠦⠀⣿⡏⢹⣿⡆⠀⠈⣿⣿⣿⣧⠿⠶⠀⢸⣿⣿⣿⢾⣿⠀⢰⠀⠀⢸⣿⣿⣦⣄⠃⠄⠀⠀⠀⡿⠀⠘⣀
⠀⠀⣿⠙⠛⡛⠡⠤⡤⢀⣠⣶⡤⠀⣁⣤⠄⠄⠀⢾⣷⠈⣿⡇⠀⢸⣿⠻⠛⣋⣰⣦⣾⣿⣿⣸⣿⣿⡏⠀⠸⡆⠀⠀⠋⠹⣿⣿⣷⠀⣀⠀⠀⠟⢸⣆⠈⣆
⠀⠀⣷⣼⡛⠿⠀⠀⠀⠈⠉⠃⣤⣾⠛⢻⠱⠶⠀⠀⣿⡀⢹⡇⠀⢸⣿⣿⣿⣯⣥⣽⣿⣷⣶⣿⣿⣿⣷⣾⣿⡷⠶⠶⡟⠚⣻⣿⣿⡀⠹⠃⠀⢀⡈⢿⣧⡈⠳
⠀⠀⣿⠽⢿⣿⣦⣴⣶⠖⠛⠻⠿⢏⣵⣿⣷⣶⣆⣴⣿⣧⣾⣇⠀⠚⣿⢿⠟⢛⣿⣿⢿⣿⣯⡿⣿⣿⣿⡟⢿⣧⣾⡾⠻⢿⣿⣿⣿⣇⠀⠛⠀⠀⢷⡀⠻⣷⣤
⠀⠀⣷⠀⠀⠿⠟⠁⠀⢠⣶⡶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣟⠐⣛⣿⡿⣿⣿⣷⣶⣾⣿⣶⣿⣿⡿⠟⣀⣈⣥⣾⣶⣿⣶⠟⢻⣿⣿⣧⡀⠀⣦⡌⠻⣆⢉⣻
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣛⠉⣉⣬⣿⣿⡯⠤⢯⠀⠀⠀⠀⠀⣉⣽⣿⣛⣉⣁⣀⣠⣭⣩⠆⠈⠙⠛⠐⠒⠋⠀⠈⠉⠙⠛⠓⠤⠤⠤⠭⠿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠦⠤⠚⠀⣀⡤⠖⠀⠉⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣿⠂⠀⠀⠀⠀⠠⠤⠤⢤⣤⣶⡶⣀⡀⠀⠀⠠⠤⢶⠦⢤⣤⡴⠾⠥⠠⠤⠤⠤⠄⠤⠀⣠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣄⠀⣀⣰⡄⠀⠀⣠⣤⣴
⠀⠀⣿⠠⣄⡀⠀⣀⣤⣤⣼⡿⢉⠉⠁⠈⠀⠀⠀⠀⢀⡴⠶⠎⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠉⠁⣀⣀⣀⣀⡀⠀⠀⠰⠌⠙
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠻⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣄⡸⣰⡿⠭⢗⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣇⣿⣵⠿⠁⠀⢀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣼⣡⠾⠿⠒⠛⠁⠀⠀⠀⢸⡞⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣁⡈⢻⠏⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣶⡶⠶⠾⢯⣾⣿⣿⣿⠿⣟⡳⠦⣍⡁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠀⢀⣤⠖⠛⠉⠁⠀⠀⠘⠁⣈⣻⡇⠀⠀⠴⠖⢺⣭⠙⠛⠿⣷⣦⣈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⣠⡾⠋⠀⠀⠀⠀⠀⢾⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠉⠻⢿⣦⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠈⠛⠛⢿⣿⡿⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠛⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⠁

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

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⢻⡀⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⣦⣄⣀⣀⡀⢸⡇⣇⠀⠀⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣧⡀⠶⠒⠲⡄
⢻⡀⠉⠁⠀⣿⣷⢹⡄⠀⢻⡄⠀⠀⠳⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡎⠙⠒⢦
⠘⡇⠀⠀⠀⣿⢀⠀⢻⡆⠈⣿⠀⠀⠀⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⡇⠀⠀⡇⠀⢀⡼
⠀⠙⠄⠀⢠⡏⠈⣧⠘⣧⠀⢹⡆⠀⠀⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⡷⠀⢸⡄⢀⣀⡀
⠀⠀⣇⠀⢸⡇⠀⠸⣇⠘⣧⡀⢻⡄⠀⣿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡇⠀⠀⠇⠀⠀⢙⠊⣨⣭⠏⠉⠉
⠀⠀⠹⣦⡼⠃⠀⠀⣿⠀⣾⠁⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀⠀⢸⠀⠀⠸⣨⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠀⠸⣇⠀⣿⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⢸⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠘⠢⠀⠸⠀⠘⠄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠜⠧⠀⠠⢼⣀⠀⠘⡄⡀
⠀⠀⠀⠀⢀⣠⠾⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠇⡷
⠀⠀⠀⡾⠀⠀⡠⠃⠢⡄⠀⣅⠀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠉⠙⠲⠦⣤⣀⣤⣤⠤⠀⡇
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠛⠾⣝⠉⠉⠉⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡤⡤⠊⠁⠀⠀⠀⠀⠹⣆⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠦⣤⣤⣤⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠐⠾⠛⠠⣴⣶⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⢀⡀⠀⠀⠀⠀⠲⠶⠄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠸⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠻⠀⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⠀⠀⠀⢾⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡃⠀⠀⢀⡈⠀⠀⠻⣄⠀⠀⠂⠤⠀⣀⣀⣀⣀⠀⠠⠤⠘⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⣤⡜⠃⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⡠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⣤⣤⣄⣀⣠⣄⠰⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⠤⠤⠤⠶⠄⠛⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠑⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠆⠀⠀⠀⠀⡆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠉⠉⠲⠶⠆⣀⣠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠁⠀⠀⠀⠀⠀⠁⢸⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⠔⠃⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡧⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⡀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠸⡇⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢛⡀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠘⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⡆⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⢻⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⢣
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠼
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⢠⣧⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣌⠉⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⠙
⣉⣤⣤⣤⣤⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣀⡀⠀⣠⠤⠤⣄⠀⠀⠀⣀⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠞⠁⠀⠀⠀⠈⠟⠁⠀⠀⠀⠹⠉⠹⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⣀⡀⠀⠀⠠⠃⠀⠀⠀⠀⠟⠒⠀⠀⢄⡀⠠⢀⡀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⠙⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠙⠀⠀⠀⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⡆⠀⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⡄⠂⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠣⡄
⠀⠀⠀⠀⠀⠀⢨⠦⠄⠘⣄⠀⠀⡀⠀⠀⡵⠦⠖⠃⠀⠈⠓⠒⠳⣄⠀⠀⢀⡼⠤⠔⢣⠔⠁⠀⠀⠢⡀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠸⣄⡄⠀⠁⠀⠀⢉⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⢀⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠉⢻⠀⠀⢠⠔⢊⣰⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠒⣄⠘⣄⣀⡔⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢆⡀⡀⠀⠀⢀⡞⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢹⡀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⠉⣗⠀⠀⠐⠢⠉⠔⢄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠄⠀⢸⠓⠒⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡔⢒⣿⠀⠀⠂⠸⠶⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠀⠐⠀⢸⡤⢤⡀⢄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⡆⠁⢹⠀⠀⠀⠂⠀⠂⠁⠀⠀⢀⣄⠀⠀⠀⠑⠂⠀⠐⠁⠀⣼⠒⠀⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣸⡀⠀⠀⠀⠀⠀⠀⢀⠔⡞⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠘⢎⡇⢸⣉⠏⠀⠀⠀⠀⠀⠀⣠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡴⠶⠤⠤⡇⢸⡅⠀⠀⢀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢒⡀⠀⠀⠀⡏⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁⢤⠀⠀⠀⡧⠤⣼⠦⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠙⢲⠃⠀⠀⢠⡏⠉⠁⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⣆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⡀⠀⠀⢸⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢳⡇⠀⠀⠈⡇⠀⣀⠴⠋⢳⡃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢿⠉⠀⠀⠀⠀⢿⣅⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠸⠀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣻⡿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠁⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣘⠋
⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⣦
⠀⠀⠀⠀⣼⡏⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠹⠷⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡗⠦⣀⠀⠀⠀⠙⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢋⣤⡄⠀⠀⠀⣀⡀⠀⢀⣹⠀⠀⠙⠲⠤⣤⠼⠀⠈⠳⣄⠀⡷⢦⡀⠀⠀⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠈⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃⠀⠀⠀⠀⠀⠀⣈⡃⠀⠀⠀⠀⠄⠠⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡴⠋⠉⠉⠓⣆⠀⠀⣠⣤⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠘⡆⢸⠱⠀⠈⣧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠦⣀⡞⠀⠀⠀⠸⡄⠀⠀⠀⠀⢿⡇⠘⣆⠀⢀⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠛⠓⣌⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡼⠀⠀⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⢆⠀⠀⠀⠀⠀⠈⠦⠒⠚⠁⠀⠀⣈⠀⣸⠂⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⠦⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡔⠀⠀⠀⠉⡷⠒⠶⠴⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢲⠞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣍⡛⠃⠀⡞⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣂⣀⡴⠧⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠉⠁⠀⠠⢤⠬⢍⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⠉⢻⣙⣒⣶⣶⢟⡒⣻⠋⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠟⠚⠉⠈⠑⠛⠽⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⢀⠤⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⣀⣁⣀⣤⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⣶⣿⡿⠛⠁⠀⠉⠙⠛⠛⠛⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡴⠶⠶⢶⣤⡄⠀⠀⠀⠀⠀⣠⣴⠶⠾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠫⠘⠿⠃⠴⠀⠆⠀⠀⠰⠆⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠖⢄⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠞⠀⠀⠀⠀⢠⠀⠀⠠⠀⠄⠀⠘⢆⠀⠈⢂⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠀⠀⠀⠠⡤⠀⠁⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⡾⠀⠤⠀⣾⣿⣿⣿⣿⣿⡦⠄⠘⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠈⠻⠶⠶⠾⠋⠁⠀⠀⠘⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠃⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢌⠀⠀⢠⣼⠂⠀⠤⢐⠺⣵⠤⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢀⣀⡴⠀⢸⣧⣶⡿⢩⠷⠆⠐⠒⢙⠛⣟⠩⣿⣿⣦⡀⠐⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠶⡯⠐⣚⠛⢻⡷⣔⠉⠐⠋⠛⠳⠄⢲⣍⠁⠾⡖⢋⡕⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠢⢼⡇⠁⠈⡌⠉⠁⠀⠀⢈⣀⣀⡀⠀⠈⠀⠉⠲⣷⣀⣓⣧⡴⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢾⠣⠐⠦⠘⠄⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠂⠾⠫⡥⠀⠀⠘⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⢀⣰⣇⢠⠎⠀⠀⠀⣾⣿⣿⣿⠋⠉⢻⣿⣿⡇⠀⢠⠀⠈⠠⣄⠐⠻⠖⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣉⡾⣝⡋⠛⠂⠀⠀⠀⠉⠉⠉⢁⠀⠀⣸⣿⣿⡏⠀⢈⡿⣅⡀⡽⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠻⢬⠩⠤⠀⠀⢹⢀⡄⢔⣢⡤⠂⢀⣴⣿⣿⣿⠃⠀⠈⠁⠡⡆⣱⡶⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠐⣧⠄⡸⠃⣀⣚⠁⠂⢠⣿⣿⣿⡿⠁⠀⠀⡀⢀⡞⠀⠀⣄⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠉⣀⣡⠠⣶⣹⡀⢿⡁⠀⠀⣿⣿⣿⡏⠀⠀⠄⠒⠋⢻⡟⠢⢁⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣽⣇⠂⠀⠻⣤⡏⣁⡀⠈⠛⠛⠉⡡⢀⣴⠒⠐⢂⡉⠸⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢯⠠⠔⢃⣿⣿⡟⠃⠀⣿⣿⣿⡄⠀⢛⢡⣀⣼⠀⠀⠉⠋⠓⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⣇⢠⣿⢿⣹⣿⡄⠀⠿⠿⠿⠃⢀⣞⠚⡉⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢋⣼⣇⣹⣿⡥⠃⠀⠤⠠⠖⠞⠉⠛⠉⡙⠉⠙⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢈⣁⣀⣁⣤⣤⣄⣠⣄⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠉⠉⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠤⡄⠀⣠⠤⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⣷⠀⠀⠀⣾⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠻⠏⠙⠃⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠄⠂⠀⠈⠉⠉⠀⠒⠢⢄⠀⢀⡼⠇⠀⠀⠀⠀⠀⠤⢱⣄⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠦⣄⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⡄⠀⠀⠀⢳⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠒⠚⢛⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠚⠉⢀⣀⡉⠓⣄⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⣽⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣧⣤⢸⡄⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⣣⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠈⢧⣀⠈⠿⡿⠿⠋⣸⠃⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡼⠀⠀⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡆⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠀⠒⠁⠀⠀⠀⠀⠈⠂⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣴⠲⢦⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠴⠲⡄
⠀⠀⠀⠀⠀⠙⢦⣄⠉⠳⢤⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣫⠴⠛⢁⣤⠞⠁
⢀⣴⢒⡛⡏⠉⠉⠉⣤⣤⡀⠹⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠞⣽⠁⢀⢤⡌⠉⠉⠉⣿⣿⡲⣤
⣿⠥⠤⠒⠒⠀⠀⠀⠀⠀⢹⢸⡅⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠂⠀⠀⣽⢠⡁⠀⠀⠀⠀⠀⠒⠲⠦⢬
⢳⣀⣤⠤⠤⠤⠤⠴⢶⡖⠋⠀⢧⠀⠀⠀⠀⣠⠏⠉⣟⠲⠶⠦⣤⣤⡤⠶⠶⣾⠛⢯⡀⠀⠀⠀⢠⡏⠀⠓⣶⠶⠦⠤⠤⠤⠤⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢧⣄⣤⠞⠁⠀⢠⡏⠢⠤⠚⢿⣿⠟⠢⠄⢹⡀⠀⠙⠦⣤⣠⠞⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⢰⣼⡄⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠖⠒⠒⠚⠉⠀⠀⡇⠀⠀⠀⠈⢙⣧⠀⠀⠀⢣⠈⠉⠒⠒⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢿⣿⡯⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣶⠒⠲⡆⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢰⠀⢸⠇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣠⠞⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣟⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣬⣧⡀⠀⠀⣴⣏⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡶⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢪⠊⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⡄⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⣒⡒⢴⡉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠭⢤⡴⠊⠀⠁⠀⢀⡀⠀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⣙⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠑⠢⢄⣸⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠔⡆⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣀⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠒⠾⡐⢞⣃⢀⠀⠁⡀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⣙⠶⣷⣌⠈⣿⣄⣌⠀⠂⡔⣂⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠑⢌⠑⠦⠶⠋⣈⠂⣽⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⠤⣠⣄⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠉⠒⢲⠄⡤⠤⡤⠞⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣀⣀⣔⡡⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣎⡀⠀⢀⣠⡋⣁⣔⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠛⠈⠉⠉⠀⠀⠉⠀⠙⠒⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣁⣈⣉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡋⠉⠉⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⣠⠆⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⠈⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⡇⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠀⠀⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⠶⠄⠀⠀⠀⠀⠀⡞⠉⠙⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⡉⠒⠊⡇⠀⠀⠀⢀⠀⠀⣠⢒⡩⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠋⠀⠙⣦⠀⠀⠀⠀⢸⣄⣀⣀⡏⠀⣸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣟⠓⠈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⠀⡜⠉⠑⠂⠓⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⣻⠟⠀⠀⠀⠀⠀⠀⠈⣪⣉⢼⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡘⠒⠀⠀⠀⠀⠀⠀⠈⢁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠣⡀⠀⠀⠀⣀⠴⠊⠙⣿⠃⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠀⠀⠀⠀⠀⣀⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⣈⡩⠤⠖⡋⢸⣻⡄⠀⠀⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣀⣤⣄⠐⢯⣀⣨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡯⣒⡇⠀⠀⡏⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠽⢷⢶⡏⣀⡸⠀⠀⠀⣾⡕⠉⢱⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠖⠁⠀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⡼⠀⠀⠈⠙⠒⠶⢤⡟⠳⢤⡻⠔⠊⠈⢆⠀⠀⡔⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣀⣀⣀⢀⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠼⠀⠒⠒⠀⠀⢻⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠓⢨⡥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠓⠚⡄⡳⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⣧⣷⠇
⠀⠀⠀⠀⢀⣀⡀⢡⠀⠀⠀⠀⠀⢸⠁⢀⣤⠀⠀⢣⡞⠉⢙⡂⢠⡴⢦⠀⠀⣈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⡏
⠀⠀⠀⢰⠁⠀⢉⣈⡀⠀⠀⣠⣤⢤⣍⠀⠈⡆⠀⠀⠰⡖⠋⠀⠹⣀⠠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⡀⠀⡇
⠀⠀⠀⠈⢦⣤⠼⠁⢩⠀⠀⢯⡀⠀⣹⣀⣤⡥⠀⠀⠀⢣⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠷⣾⡤⣇⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⠇
⠀⠀⠀⠀⠀⠀⠑⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠠⢤⡏⠀⢸⡤⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢄⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀⠀⠀⢸⠀⠀⠸⣆⣀⣀⡴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠙⠶⢤⣼⢀⡤⠞⠉⠀⠈⢧⣀⡀⠸⣄
⠀⠀⠀⠀⠀⢀⣠⠴⠒⢹⡏⠀⠀⠀⠀⠀⢀⣴⣚⠭⠔⠒⠉⠉⠙⢻⠁⢘⣦⠙⡏⠓⠦⣄⡀
⠀⣀⡤⠖⠋⠉⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠉⠙⢺⣄⠀⠀⢹⠃⠀⠀⠀⠈⠙⠲⢤⣀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢾⠀⠀⠀⠀⠀⠀⢧⣠⠼⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠶⠦⠤⣄⣲⣦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠽⠿⠒⠒⠀⠉⠃⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⠛⢻⡖⠒⠦⢀⠀⠀⠙⣛⠓⢢⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡎⠀⢠⡄⠉⣏⠙⠃⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠀⣀⣐⠀⠀⢸⠀⠀⡸⢡⠖⠠⠏⠑⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⠿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⢩⡯⠀⠈⢳⡀⡌⠀⢰⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠤⢺⠀⠀⠀⠀⢿⠁⠀⣾⣻⠁⠀⠀⠀⢀⡴⠒⠒⠢⢄⠀⠀⣀⣀⢈⡀⡰⠛⢦⡀⠀⠘⢒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢸⠀⢠⣟⡧⠔⡒⢢⡀⠈⠦⣀⣀⣠⡼⠓⠉⠀⢀⡴⠋⠀⢀⠞⠉⠁⠀⠙⠻⣍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⢁⠣⣀⡀⣠⠎⠀⠘⠋⠔⠋⢁⠼⠓⠒⠠⠤⠴⡏⠀⢀⣠⠔⠋⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠘⡄
⠀⣀⠠⠤⠐⠒⠒⠉⠉⠁⠀⠀⢀⠼⡇⠀⠈⠉⠀⠀⠀⢀⡖⠒⠛⠓⠦⠤⠤⠤⠤⡄⠉⠉⠉⠀⠀⠀⠀⠷⢖⣒⠶⢄⠀⠀⠀⠀⢀⠇
⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⢸⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠬⡭⣭⠵⠋⠀⠀⠀⠀⡜
⠑⠤⣀⣀⣀⣀⠤⠔⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢠⣄⣨⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡷⢌⠳⡸⡄⠀⠀⠀⠀⢸⡀⠀⠀⢠⡞⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⢄⠱⠁⠱⣦⣤⡀⠀⠨⡍⠓⠊⠽⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⢡⣏⣶⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⢄⠀⠀⠀⢸⠤⢒⡒⢲⡄⠀⠀⠀⠀⠀⠀⢸⠀⡤⠘⠳⡉⠀⠘⡖⢹⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠲⣾⠀⠀⠀⢸⡠⠞⣡⠋⠀⠀⠀⠀⠀⠀⠀⡜⢸⠃⠀⢀⡼⢆⢀⡵⠋⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡇⠀⠀⠀⢀⣠⠔⠋⠀⣀⠝⠀⠀⠀⠀⠀⠀⠀⢠⠃⡏⠀⠀⢺⡴⣴⠻⣄⣠⠏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⢶⣧⡤⣖⠊⠉⠀⠀⡠⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⡎⣸⡡⠔⠊⢁⠂⢀⠀⠈⠁⠀⠈⢲⣌⠳⣄⠀⠀⠀⢠⠶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣠⡋⠀⠸⡆⢀⠔⠉⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢸⠋⣋⠤⠀⠀⠉⣆⠘⠆⠀⠀⠀⠀⠈⢏⠳⣌⠳⣄⠀⢸⠀⠇⡎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠚⠙⠁⠀⠀⠙⠁⠀⡟⠀⠀⠇⠛⡒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⡄⠈⠳⣌⡧⣼⢰⠞⣰⣃⠔
⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⣤⠼⠈⠈⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢘⡇⣁⠀⢀⣨⠴⠊
⠀⠀⠀⠀⠀⠀⠙⡶⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⣯⠤⠖⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠲⠶⠶⢶⣶⣶⡾⢡⣖⣩⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢯⠙⡟⠓⠒⠒⠛⢋⡉⣹⢠⡇⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈⠉⠁⡀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⣧⣸⡀⠀⠀⠀⠀⣀⠤⠊⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠑⣶⣖⠒⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣸⣀⣀⠈⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⣀⣈⣎⢆⠘⣌⢆
⠀⠀⠀⠀⠮⣅⣀⠤⠽⠓⠋⠉⠉⠙⠒⠢⠶⠶⠶⣦⣒⣶⠞⠓⠒⠲⢄⠀⠀⠀⠀⠈⠂⣤⠒⠒⠒⠛⠛⠛⠺⣗⣚⡈⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⠉⠉⠉⠙⠒⠒⠰⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣀⠤⠤⠤⠤⠤⠀⣀⣀⡀⢀⢀⣀⡴⠊⠀⠰⡄⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢤⣤⣤⡄⠀⠀⠀⡤⣴⣦⣦⢀⠀⠀⢸⠓⠠⠀⣿⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠈⠉⠉⠁⠘⠄⠀⠉⠉⠉⠉⠉⠀⠀⠸⡡⠀⣠⣧⡀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠂⠺⠶⠀⠀⠀⠀⠂⠲⡶⠤⠀⠀⠀⠙⣄⢋⠀⠇⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢀⡇⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡼⠁⠀⠻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣰⠯⠤⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠙⠂⢈⡉⠈⠀⠌⠈⠀⠀⠀⣠⠞
⠀⠀⢀⣀⣀⣸⣌⠢⡀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⢠⠞⡱
⠀⢰⠟⠒⠃⠀⠐⠦⢈⡄⠀⠀⠀⠀⠀⠈⠉⠙⣳⠞⡛⠛⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⠌⠁⠙⠟⠟⣆
⠀⠈⠓⠒⠒⠒⠠⡔⠋⢳⡀⠀⠀⠀⠀⣤⠒⠚⣧⣾⣆⣀⠜⠓⠦⣄⠀⠀⠀⠀⠀⡠⠓⠧⡀⠤⠤⠤⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠁⠙⢦⡀⢠⠞⢸⠀⠀⣴⣿⠠⠀⠀⠀⠸⠋⠳⡀⠀⠀⠴⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⡁⠀⣰⠆⠀⣿⡟⠀⠀⠀⣰⠢⡀⠀⠙⡖⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⡤⠞⠁⡇⠀⠛⠀⠀⠀⢠⡇⠀⠈⠢⣄⠃⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠛⣄⣀⡠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⢹⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⢉⠓⡾⠉⠙⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠒⠈⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠒⢄⠀⠀⠀⠀⠀⢠⠊⠀⠀⢀⠀⠀⢠⡀⠀⣠⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣦⣵⡀⠀⠀⢀⠂⠀⠀⠀⠈⠳⠰⠀⠉⠲⠃⠃⠀⠀⠀⢠⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠦⢂⡔⠁⠀⠻⣇⠀⠀⢸⠀⠀⠀⠀⠐⠛⢂⣀⠀⠀⣀⡘⠆⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⢻⡇⠀⠏⢀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢀⠘⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡆⠀⠀⠅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠘⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠇⡤⠂⠁⠀⢸⠀⠀⠷⢤⡀⠀⢠⡙⠀⠀⠀⠀⢀⠠⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⢀⡀⠔⠁⡌⠀⠀⠀⠀⠀⡄⠀⠀⠀⢉⠁⠀⠰⠤⠤⠀⠂⠁⠀⡇
⠀⠀⠀⠀⠀⠄⠀⡄⢀⡠⢄⠀⣀⠹⡍⠉⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠦⠊⠀⣠⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⠰⢿⡉⡓⠾⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⢀⠁⠀⢀⠻⡆⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢣⠀⠀⠉⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⢠⢀⡠⠂⠀⠀⠘⠀⢀⠘⠄⢹⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⡤⢤⢷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢠⠀⡘⠀⠀⠀⠀⡈⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢰⠀⣦
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⢀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠂⠀⠉⠉⡇
⠀⠉⠲⠀⠠⠤⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⡼⠦⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠌⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤
⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣈⣀⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠋⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⢿⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢹⡓⢄⠀⠀⠀⠘⠈⠂⠀⠐⠒⠃⠀⠀⠀⠀⠔⣻⠇⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⠄⠀⣀⣴⠀⣀⡀⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠀⢒⠃⠀⡗⠂⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠀⢈⠋⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠑⢤⡀⠰⠀⠀⣸⠀⠀⠀⢀⡠⠞⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠈⢷⣄⢙⠇⠀⠀⣴⣤⠴⣞⠋⠀⢠⠞⠩⡙⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢸⡇⠀⢀⡹⠿⠒⠚⠉⠁⠀⠀⠘⢦⡴⠃⠀⠀⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⡇⠀⠀⠀⣀⠴⢚⡿⠁⠀⠀⠘⡇⢰⠋⠀⠀⠠⠤⠤⠤⠤⠀⠀⠈⣷⠠⡀⠀⡇⢀⠀⠀⠙⢦⠀⡀⠀⠀⢸
⠀⠀⠀⠀⣧⠴⠒⠋⠁⢀⡞⠀⠀⢠⠇⠀⢹⡏⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⠸⣤⠃⠀⡇⠀⢦⡀⠀⠈⠳⡈⠓⢄⣸
⠀⠀⠀⠀⣧⠀⠀⠀⢀⠏⠀⠀⢀⡞⠀⠀⢸⠁⠀⠀⠀⠈⠉⠉⠉⠓⢆⠀⢸⡄⣧⡀⠀⣧⠀⠀⠙⢦⡀⢀⠝⠀⠀⣼
⠀⠀⠀⠀⢸⡀⠀⠀⠈⠒⠦⢄⠞⠁⠀⢀⡏⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠂⠀⡃⠁⠈⣦⡿⠀⠀⠀⠀⠙⢧⡀⠀⢀⡇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⡿⢿⠋⣀⠀⣠⢸⠅⠀⠔⡧⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼
⠀⠀⠀⠀⠀⠈⢧⠀⢰⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡏⠀⢀⡴⠋⠀⡇⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢳⡀⢳⡀⠄⢠⠞⠁⠀⠀⠀⠀⠀⠀⣇⡴⠋⠀⠀⠀⢻⠸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡴⠃⡇⠀⠀⠀⠀⠈⠀⢷⠀⠀⡇⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠱⡄⢀⣀⡤⣞⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣈⢢⠊⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⢸⡆⢸⣁⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣷⣠⣇⣀⣀⣀⣀⣠⠤⠼⠓⠋⠁