Adhesive bandage Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⡍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠰⠂⠀⠉⠳⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠠⡀⠀⣀⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⠴⠋⠄⠀⠀⠆⠀⠘⠀⠈⢳
⠀⠀⠀⠀⣸⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠙⠦⣀⠀⢀⠔⢋⠀⢀⡄⠀⢠⠄⠀⢠⠀⢀⠈⡇
⠀⠀⠀⠀⣿⠈⡀⠰⠀⠀⠉⠀⠀⠉⠀⠀⡠⠤⣈⠙⠧⣀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⠁
⠀⠀⠀⠀⠙⢦⣀⠀⠤⠀⠠⠄⠀⠂⠀⠔⠁⠀⠀⠑⠠⡈⠙⢦⡈⠁⠀⠀⠁⠀⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⣀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄⠉⠢⣀⠰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠧⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠉⢂⠈⠳⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡶⢄⡑⠤⡀⠀⡀⠀⠀⠀⠀⡠⠂⠀⠲⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠚⠀⠈⠂⢍⠲⣌⠲⢄⠀⢀⠀⡐⠁⢀⡀⠀⠤⠀⠰⠌⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⢡⡄⠀⠰⠀⠀⡤⠀⠑⢌⢙⠦⡑⠢⠜⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢤⠹⡆
⠀⠀⠀⠀⠀⣾⢡⠀⢀⠀⠀⣀⠀⠀⣀⠀⢀⠀⢁⡴⠛⠳⣄⠒⠀⠐⠂⠀⠈⠁⠀⠈⠀⠀⢰⠇
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠁⠀⠀⠁⠀⢀⡴⠋⠀⠀⠀⠈⠓⢦⡀⠠⠄⠀⠰⠀⠀⠓⢀⡞
⠀⠀⠀⠀⠀⠀⠳⣔⠘⠁⠀⠚⠀⠈⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠰⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠒⠚⠛⠒⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⡆⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠎⠉⠙⠞⠉⠙⡆⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠳⢄⡀⠀⣠⠞⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣈⣋⣀⣀⣀⣀⣀⣀⡼⠀⠀⠰⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⢤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠾⠋







⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠑⠢⣄⠀⠀⠀⠀⠀⢠⠞⠁⠀⠉⠀⢀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠃⠀⠀⠙⠢⣄⠀⡴⠁⠀⠚⠀⠀⠀⠀⠀⠤⠀⢀⠎
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠒⠀⠀⠀⠈⠀⠀⠀⠙⠦⡰⠀⠀⠀⠈⠀⢀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠹⡀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠉⠀⣀⠈⠓⢌⡀⢀⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⠀⠀⠀⠋⠀⡠⠋⠈⠑⠦⡀⠉⠲⢅⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠃⠀⡜⠁⠀⠀⠀⠀⠈⠓⢄⡀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠑⢦⡀⠙⠦⡀⠀⠀⠀⠀⠀⢀⠇⠀⠆⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠐⠀⠈⠓⢄⡈⠓⢄⡀⠀⡠⠃⠠⠀⠀⠀⠒⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠠⠄⠀⠀⠀⠃⠀⡙⠢⣄⠈⠉⠀⠄⠀⠀⠐⠂⠀⠀⠐⠂⠀⢱
⠀⠀⠀⠀⠀⠀⢀⡞⠀⡀⠀⠀⠀⠆⠀⠀⠀⠀⡰⠋⠙⠢⢄⠀⠀⠶⠀⠀⠀⠂⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡄⠀⠀⠀⠁⢀⠞⠁⠀⠀⠀⠀⠙⠢⣀⠀⠐⠂⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠒⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣛⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⣻⣷⠄
⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠰⠛⠋⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠶⠶⠆⠀⠀⠀⠀⣶⠶⢶⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⢶⡆⠀⠀⠀⠀⢹⣦⣼⢧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣴⠟⠀⠀⠀⠀⠰⢶⣤⣤⣀⡀
⠀⠀⠀⡶⢦⠀⣴⡄⢰⡄⢠⢠⠶⣄⢀⣦⠀⡤⠲⠄⣴⠶⢀⡴⠦⠀⠀⠀⠀⠀⠀⠀⢶⣭⣍⣁⡀⠀⠀⠀⠀⢀⣸⣧⡶⠟⠃
⠀⠀⠀⣏⡽⢴⠷⢷⢸⠙⢾⢸⣤⠾⠼⠾⠇⢧⣬⡗⢿⣭⠤⢭⡽⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡽⠟⠀⠀⠀⠀⢈⣭⣤⣤⣤⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⢴⡄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⣠⠀⣹⡇⠀⠀⠀⠀⠛⠛⢛⣛⣋
⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⢹⠞⠚⠁⠀⠀⠀⠀⠸⣥⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠋⠀⠀⠀⠀⠀⣿⠛⠋⠉⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠴⠴⠆⠠⠆⠀⠀⠀⢈⣿⡽⠆⠀⠀⠀⠀⠈⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡟⢻⡇⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠈
⠀⠀⠐⠖⠒⠂⠂⠠⠰⠀⠀⠀⠨⠶⣶⠆⠀⠀⠀⠀⢬⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠛⠘⠇⠀⠀⠀⠀⠙⢿⡶⠶⣤⡄
⠀⠀⠀⠢⠀⠶⠰⠐⠤⠀⠀⠀⠐⠿⢓⣒⠀⠀⠀⠀⠴⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠐⠂⠀⠀⠀⠀⢠⣼⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⡽⠀⠀⠀⠀⡖⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⠀⠀⠀⢀⡴⠛⠛⢳⡄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢲⡯⣤⡀⠀⠀⠠⣽⣚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣅⠀⠀⠀⠠⢷⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣥⣤⣤
⠀⠀⠀⣠⣶⠟⣷⣦⡄⠀⠀⠀⠀⢺⣠⢨⠇⠀⠀⣞⣉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠀⣿
⠀⠀⢰⣿⣛⣙⣿⣹⣿⡄⠀⠀⠀⢰⠶⡖⡦⠀⠀⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢈⣀⣉
⠀⠀⠈⢯⣭⣭⣽⣭⡿⠀⠀⠀⠀⠘⠀⠁⠁⠀⠀⠃⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠰⠀⠀⠠⠀⠀⡏⣭⣭⣭⠭⠭⠉⠉⠉⠉⠉⢹⠀⠀⠄⠀⠀⠆⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠁⢠⠀⠁⢠⠀⠀⡇⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠈⠀⡄⠈⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠂⢀⠀⠂⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠐⠀⡀⠐⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠁⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⡿⣿⣿⡟⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⢻⣿⣿⢿⣿⣿⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⡇⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣷⣿⣻⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣟⣿⣾⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣿⣿⣷⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⡄⠈⠀⠀⡁⠁⡀⠄⠐⠉⠉⠉⠁⠀⠀⢸⠀⠀⠁⢠⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⡀⠐⠂⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠂⢀⠀⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠁⠠⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠄⠈⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠀⠀⠀⡀⠀⢠⢖⣒⣒⣒⣒⣶⡶⠶⠶⠖⠶⠲⡄⠀⢀⠀⠀⠀⡀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠆⠀⠀⠴⠀⠀⠀⢸⣸⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠦⠀⠀⠰⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡄⠈⠀⣠⠀⠁⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⣄⠀⠁⢠⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠰⠀⠀⠀⠆⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠰⠀⠀⠀⠆⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⣿⣿⣿⢻⣿⣿⢉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⣿⣿⡟⣿⣿⣿⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⡿⣿⣯⣿⢿⣿⣿⢸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣽⣿⢿⣯⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣷⣿⣟⣿⣾⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣻⣿⣾⣟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠠⠠⠀⠀⢀⠠⠤⠤⠤⠶⠆⠂⠀⡄⠀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠃⢀⡀⠙⠀⡀⠀⠘⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠋⢀⡀⠘⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠀⠴⠀⠁⠀⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠀⠦⠀⠁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠘⠁⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠈⠃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⠀⠐⠗⠀⢀⠀⠀⠾⠀⢀⡴⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠓⢦⡀⠀⠷⠀⠀⡀⠀⠺⠂⠀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠛⠀⢀⣄⠀⠘⠃⠀⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠘⠃⠀⣠⡀⠀⠛⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣴⠀⠀⠁⠀⢰⡆⠀⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⢠⡆⠀⠈⠀⠀⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⠀⠐⠗⠀⢀⡀⠀⠿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠟⠀⢀⡀⠀⠺⠂⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⠀⢀⣄⠀⠘⠁⠀⣤⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠃⠀⣤⠀⠈⠃⠀⣠⡀⠀⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣥⣤⣤⣤⣤⣬⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠻⣿⣿⣿⣿⠛⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⠛⣿⣿⣿⣿⠟⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣤⣿⡿⢿⣿⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⡿⢿⣿⣥⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣟⢛⣿⣷⣾⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣷⣾⣿⠛⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣉⣿⣿⣿⣿⣏⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣹⣿⣿⣿⣿⣉⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣴⣿⣿⣿⣿⣤⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣤⣿⣿⣿⣿⣦⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠉⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⡛⠛⠛⠛⠛⢛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⡛⠛⠛⠛⠛⢛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠀⠈⠋⠀⢠⡀⠀⠛⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠛⠀⢀⡄⠀⠙⠁⠀⣄⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠉⠀⠠⡦⠀⠈⠁⠀⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠀⠈⠁⠀⢴⠄⠀⠉⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠀⠀⡀⠀⠸⠇⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠘⠇⠀⢀⠀⠀⠟⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣤⠀⠈⠋⠀⢠⡄⠀⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠀⢠⡄⠀⠙⠁⢀⣤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠀⠠⡶⠀⠈⠀⠀⠶⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠟⠀⠀⠶⠀⠀⠁⠀⢶⠄⠀⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠚⠓⠲⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠉⠉⠉⠛⠲⣤⡀
⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠳⣴⠋⠀⠀⠀⢀⡴⠏⠁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠟⠁⠀⠀⣠⠞⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢹⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠻⣄⠀⠀⣠⠞⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠘⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⢀⣴⢶⣄⠀⠀⠀⠈⠳⣾⠁⠀⠀⢀⡴⠋⠀⠀⠀⣠⠞⠀⠀⠀⣼⠁
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠙⠷⣄⠀⠀⠀⠈⠳⣤⡴⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⢀⣰⠞⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠳⣄⠀⣠⠞⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠠⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣅⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢠⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠳⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢦⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢙⣦⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠂⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠏⠀⠙⢦⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢠⠟⠀⠀⠀⢀⡴⠋⠁⠀⠀⣠⠞⠛⢦⡀⠀⠀⠀⠙⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢀⡟⠀⠀⠀⠴⠋⠀⠀⠀⣠⠞⠁⠀⠀⢀⡿⢦⡀⠀⠀⠀⠙⠷⠟⠁⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⠋⠀⠀⠙⣦⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠈⣇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠋⠀⠀⠀⣠⠞⠁⠙⢦⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠟⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠁⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⢤⡤⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣳⣤⣶⣿⣾⠛⢻⡿⢶⣄⠀⠀⠀⠀⠀⣠⣶⠞⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⣿⠖⠰⠂⢀⣙⢷⣄⢀⣴⢞⠉⠀⠈⠛⢛⠛⡻⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠞⣿⠟⠈⠛⠀⠀⢀⢔⡩⢉⢳⡽⢟⠕⡙⠻⢦⣀⠀⠀⠈⠀⠈⠻⣿⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⢀⠔⢁⠂⣤⡵⢋⠔⠡⠈⠀⠀⡀⠝⠳⢤⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡻⣤⡐⣽⠏⠔⠁⠈⠁⠀⠀⠀⠀⠄⠛⢀⡽⢠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⡿⢣⠊⡀⠀⠀⠁⠐⠀⠠⠈⣠⠔⢋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡴⠣⠉⡀⠀⠠⠁⠠⠀⣠⠞⢁⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠸⢯⡠⠌⠠⠔⢀⠈⢠⠞⢁⣴⣿⠉⠃⢈⢿⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠙⠦⣅⡠⠂⡴⠋⣴⣟⠛⠈⠔⢀⣢⠃⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⣀⡀⠀⠀⠀⠈⠙⠋⢠⣾⣍⠻⣔⢈⣤⠞⠃⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠘⣿⣧⣘⣫⣽⣿⣍⣀⠀⢄⣴⠟⠁⠙⣷⡌⠉⠉⠀⠒⣤⣶⣶⣶⣿⣥⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠻⣿⣿⣿⣟⣯⣩⣴⠿⠃⠀⠀⠀⠈⠻⢷⣄⡛⠠⢿⣿⣿⣿⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠸⠿⠃⠀⣠⣤⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⣄⠀⠘⠿⠇⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢿⡷⠀⠀⣠⡀⠈⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⠉⢀⣄⠀⠀⢾⡿⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣶⡆⠀⠀⡀⠈⠻⠋⠀⢰⣶⡄⠀⠀⠀⠙⢦⡀⢀⡴⠋⠀⠀⠀⢠⣶⡆⠀⠙⠟⠁⢀⠀⠀⢰⣶⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠉⠀⠀⠺⡿⠂⠀⣤⣄⠈⠉⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠉⠁⣠⣤⠀⠐⢿⠗⠀⠀⠉⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣾⡧⠀⢀⣀⡀⠙⠋⠀⠀⠀⠀⠀⢀⡴⢋⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣀⡀⠀⢴⣷⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢀⡴⣋⣼⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣼⢿⣿⣿⡏⢹⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡴⢋⣼⣿⣧⣤⣿⣿⣿⣿⣿⠛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⣴⣿⣿⡿⠿⣿⣿⣁⣹⣿⣿⣿⣿⠿⢿⣿⣿⣧⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢻⣿⣿⣷⣶⣿⣿⣿⣿⡏⢙⣿⣿⣶⣾⣿⣿⠟⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣿⣿⣿⣿⣿⠛⢿⣿⡟⣩⠞⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⣸⣿⣿⣶⡟⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⣩⠞⠁⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢿⠷⠀⠈⠉⠁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣡⠞⠁⠀⠀⠀⠀⠀⣠⣄⠈⠉⠁⠀⠺⡿⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣀⠀⠀⢴⣷⠄⠀⠛⠋⢀⣀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⣀⡀⠙⠛⠀⠠⣾⡦⠀⠀⣀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠿⠇⠀⠀⠁⢀⣴⣄⠀⠸⠿⠃⠀⠀⠀⣠⠞⠁⠈⠳⣄⠀⠀⠀⠘⠿⠇⠀⣠⣦⡀⠈⠀⠀⠸⠿⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣾⡷⠀⠀⠙⠁⢀⣄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣠⡀⠈⠋⠀⠀⢾⣷⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢰⣶⡄⠀⠙⠛⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠛⠋⠀⢠⣶⡆⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠛⠛⠛⠓⠒⠶⠶⠶⠶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠠⠴⢛⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣉⠉⠓⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠋⣉⣉⠙⠲⡄⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⢦⠹⡄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣰⠃⢀⣤⠶⠛⠛⢶⣄⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠰⠃⣠⡟⠁⠀⢀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣰⠏⠀⣠⡾⠛⢻⡄⠀⢸⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣰⠏⠀⣴⠋⠀⠀⠀⣿⠀⠈⣷⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠁⢀⡟⠀⠀⠀⠀⠀⣾⠀⠀⡟⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡟⠀⣸⠇⠀⠀⠠⢤⣀⣿⠀⢸⡇⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⠲⠤⣍⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠐⠒⠶⠤⣼⡏⠀⣼⠁⣼⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⠓⠲⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⢀⣘⠒⣾⠁⢠⡏⢀⡏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡀⢸⡇⠀⣇⠀⠀⠀⠉⣹⠏⢀⡾⠀⣸⠁⠀⢠⡿
⠀⠀⠀⢀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢹⠸⡇⠀⣿⠀⠀⠀⣰⠟⠀⣼⠃⢠⠇⣰⠀⣼⠇
⣴⣶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⡇⠀⠀⠀⠸⡆⢿⡀⠘⣧⣤⡾⠋⢀⡾⠃⢀⡏⢠⠏⢰⡟
⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠘⡇⠀⠀⢠⠀⢳⡈⢷⣄⠀⠀⣀⣴⠟⠁⢠⠞⣠⠏⢀⣿⠁
⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⣷⠀⠀⠘⣆⠀⠳⣄⠈⠛⠛⠋⠁⠀⠀⠀⠀⠁⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⣆⠘⢦⣀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⣠⠆⡤⠀⠀⠘⣇⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠁⠸⢡⠏⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣄⣀⣀⠙⢷⣤⣀⠀⠀⢀⣀⣴⠞⠉

⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠀⠀⠀⠀⠐⠢⢄⡀
⢀⠄⡂⠁⠂⠀⠠⠀⡀⠀⠊⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⡀⠀⠄⠀⠠⠀⠀⠄⠀⠤⠈⠆
⢇⠀⠄⠀⡁⠀⢂⠀⠀⠀⠠⠀⠈⠀⠘⢀⠠⣄⠠⠐⠳⢦⣁⠠⠄⠀⠂⠀⠐⠀⠀⠒⠀⠐⢠⠃
⠈⠓⠤⡀⠐⠀⠠⠀⠈⡠⠔⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠄⠈⠑⠦⠀⠐⠀⠈⠀⠀⢈⣠⠖⠁
⠀⠀⠀⠀⠑⠦⡀⠘⠯⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠑⢦⡞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢃⣠⠶⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠔⣈⠀⠢⡠⡈⠀⠀⠀⠐⠔⢂⠤⠊⢁⣠⠞⠋⠀⠀⠀⠂⠨⠐⠠⣀
⠀⠀⠀⢀⠄⠨⠀⠀⠄⠀⠠⠀⠘⢓⠄⠀⠀⢖⢃⣤⠖⢉⠀⠀⠀⣀⠤⠚⠁⡀⠀⠉⠀⠁⠢⢀
⢀⠄⠺⠀⠀⠀⠀⠐⠀⠀⠁⠀⡐⠀⣀⠉⠰⣢⠯⣈⠑⡢⠀⠀⠈⠁⢠⠀⠀⢀⠀⠈⡁⠀⠈⡀⠈⠐⠠⣀
⡁⠀⠂⠀⠐⠀⡀⠃⠀⡈⠀⢠⠀⠀⢀⡴⠊⠁⠀⠈⠑⠪⢄⠀⠐⠀⠠⠄⠀⠠⠀⠀⠀⡀⠀⢈⡀⠀⢁⠀⢑
⠐⢔⠂⢀⠘⠑⣈⡩⠤⡄⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠄⠀⠀⠄⠀⠀⡀⠀⢀⣠⠄⠀⡰
⠀⠀⠉⠒⠤⢄⣘⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠤⠔⢐⣓⣒⠚⠛⣂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡤⣠⣤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠛⣿⣿⡟⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣾⡿⠛⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠻⣿⣾⡟⠛⣿⣾⣿⠟⢷⣄⠀⠀⠀⠀⠀⢀⣴⠿⢿⣶⣾⡿⠿⣿⣶⣿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡟⠛⣿⣾⣿⠟⢿⣶⣾⣿⣷⣄⠀⢀⣴⣿⣿⣦⣾⡿⢿⣧⣴⡿⠿⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⠿⣿⣦⣾⣿⡿⠋⠉⢛⣵⣿⠟⠉⠙⢿⣿⣦⣼⡿⢿⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣾⣿⡿⠋⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢺⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣾⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣤⣾⡿⣿⣿⣦⣀⢀⣠⣾⠟⣁⠀⣠⣾⣿⡿⢿⣷⣴⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⣠⣿⣿⣿⣤⣼⡿⣿⣿⣿⠟⠁⠘⠻⣿⣿⡿⢿⣦⣼⡿⢿⣧⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⣨⣿⣿⣏⣀⣿⣿⣿⣤⣼⠟⠁⠀⠀⠀⠀⠈⠻⣦⣼⡿⢿⣧⣴⣿⣿⣿⣀⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣏⣈⣿⣿⣯⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⣿⣿⣧⣀⣽⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⣀⣤⣤⣾⣿⣷⣤⣴⣶⣶⣿⣯⣀⡀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⡿⠋
⠀⠀⠈⠙⠷⣦⣤⣀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠰⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣀⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠈⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣶⣦⣤⣤⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⡿⠛⠉⠉⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠈⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⡏⢹⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡷⢹⡀⠀⢰⠁⠈⡆⠀⢀⡠⡎⡟⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢓⢤⡀⠀⠀⡇⡄⢧⡀⡸⠀⠀⢇⡰⢉⠊⡜⠁⠀⢀⡤⡚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⢌⠓⢤⣧⣘⠤⢽⣇⣠⣄⣸⡧⠼⣀⣇⡤⠚⡡⢊⠞
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠙⣄⠑⢄⣈⠗⠊⠉⠀⠀⠀⠀⠉⠑⠺⣁⡠⠊⣠⠋⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⢍⠒⠒⢺⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡴⡟⣉⠭⠉⣙⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⣉⣇⡎⠀⠐⣋⣭⡛⢦⡀⢀⡴⢛⣭⣙⠂⠀⢱⣸⣠⠞⠉⠁
⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠒⠊⠉⣹⠀⠀⠸⢯⣿⠟⠀⡇⢸⠀⠿⣿⡿⠇⠀⠀⣏⠉⠑⠒⠒⠢⠤⢤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⢄⣀⣹⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆⠀⠀⠀⠀⠀⠀⣏⣀⡠⠤⠤⠔⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⡏⢇⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⡸⢹⣉⡑⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣫⣍⣀⣒⣉⣼⠞⢣⡀⠀⠀⠈⠩⠭⠭⠍⠁⠀⠀⢀⡔⠳⡧⠤⠤⣑⠵⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠊⡠⠊⢉⡶⢄⣀⠀⠀⠀⠀⣀⡠⢴⡉⠑⢄⠙⣄⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⢊⡤⠚⢹⠉⡖⢺⡏⠙⠋⢹⣗⠒⡍⢻⠓⢤⡑⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡬⠚⠁⠀⢀⡜⡠⣁⠎⢱⠀⠀⡎⠈⢳⠘⢸⠀⠀⠈⠓⢥⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣼⡸⠊⠁⠀⠸⡀⢀⠇⠀⠈⣇⢾⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣇⡸⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡀⠀⠀⠀⠀⠀⢝⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠲⠄⠀⠀⠀⠀⠀⣀⣀⡇⠀⢸⣀⡀⠀⠀⠀⢀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠬⠍⠀⠀⠀⠀⠀⣿⠈⠁⠀⠈⠀⡿⠀⠀⠀⢀⠥⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠰⡦⠀⠀⠀⠀⠀⠙⠒⡆⢠⡖⠒⠀⠀⠀⠀⠠⢅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠷⠼⠇⠀⠀⠀⠀⠀⢲⣍⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢁⣀⣀⣀⡤⣤⠤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠰⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⠟⢉⡤⢊⡡⠔⣡⠞⡠⠊⠀⠈⠢⣕⡠⣉⠛⢍⡓⠲⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣫⣖⡯⠒⣩⠔⣊⠔⠈⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣍⠲⣜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣡⠔⣋⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢊⡤⠊⠀⠠⠤⠤⠄⣀⡀⣀⠀⢀⣀⢀⣀⣀⣀⣀⠀⠘⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡏⠉⠡⠈⠀⠀⠀⠀⠢⢀⠶⠓⢶⡄⠄⠀⠀⠄⠐⣌⣭⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⡀⡘⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⣧⡂⠀⠀⠀⢀⢿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣻⡅⠈⠛⠤⠤⠭⠭⠖⠃⠀⠀⠀⠈⠓⠤⠤⠬⠄⠊⣿⣧⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠉⠓⠦⠤⠤⠤⠖⠋⢩⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⡶⠲⡖⡺⡻⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡝⠲⠶⡶⠶⠶⡶⡤⣤⣄⣀
⠀⠀⠀⠀⢀⣤⡖⢿⠋⠁⠂⠈⠀⠀⠀⢀⡞⠁⠀⢸⢣⣄⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠘⢦⠀⠀⠀⠀⠀⠀⠳⠹⠹⣻⠳⣤⡀
⠀⠀⠀⡴⢏⣼⠁⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⢸⠀⠋⠹⠓⠒⠶⠒⠊⡉⠉⢰⠃⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⡻⣦⡀
⠀⠀⡞⢉⠢⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡇⠀⡑⢎⡡⠀⣀⡶⠡⠀⡼⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣩⣷⡀
⠀⡸⢍⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣶⣤⣄⡀⠀⣇⠀⢌⠣⠁⣐⣾⠃⠀⢠⠇⠀⠀⢀⣤⡖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡫⢝⣿
⢠⡓⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡾⠃⠀⢸⠀⠀⠀⠰⣼⢃⠂⡰⡞⠀⣠⡶⠋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⣻⣇
⣸⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⡆⠀⠀⣹⢃⠢⡰⣹⠃⠀⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡥⣿
⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⢱⠀⠠⠃⠂⣰⢣⡏⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣒⣿
⡇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣦⡀⠀⠀⠈⡆⠀⠀⢰⣿⣾⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡊⢽
⣇⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢳⣄⠀⠀⢱⡎⢀⣷⣹⠇⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡊⣹
⡧⠤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢷⣄⠀⣇⢸⢣⡟⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻
⣏⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠸⣧⡿⠀⠀⢀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⣃⣀⣀⣀⣀⣀⣀⣀⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣟⣓⣒⣒⣚⣒⣒⣖⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤
⣿⣿⡿⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢁⣀⡤⠤⠴⠤⠤⠴⠤⢆⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣠⣒⣲⣶⠶⠄⠀⠰⠀⠹⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠿⠤⠤⠼⠭⠽⠿⠟⠆⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⣀⢄⠤⡠⢂⠄⠴⡠⠂⡠⠀⠴⣀⢄⠔⡢⢂⠴⢂⠔⡠⢂⠔⡠⡢⢂⠔⡠⡢⢊⠔⡠⢂⢔⡠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠁⡡⢊⢔⠁⡡⠊⡠⢊⠔⡡⢊⠔⣡⡊⠴⠡⠎⣤⣪⢒⡁⡪⢊⢔⠕⡩⣊⢔⡡⢊⢔⠕⡉⢒⠕⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢊⢔⠕⡡⠊⡠⢊⠔⡡⢊⡴⠗⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢕⡅⡨⢊⠔⡩⢂⠔⡡⡪⠀⠁⡪⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⡡⢊⠔⡩⠔⡡⡪⢂⠍⠀⠀⠀⠀⢀⠄⡠⣤⢠⠀⠀⠀⠀⠀⠙⢔⡡⠊⢐⠕⡩⢊⢔⡡⡪⠔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢊⠔⡡⢊⠄⡪⢊⠔⠏⠀⠀⠀⠀⠀⠀⡠⠊⢔⢹⠀⠀⠀⠀⠀⠀⠈⢺⢊⠔⡩⢊⠕⡡⢊⠔⡡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡡⢊⠔⠡⢊⠔⡡⣺⠀⠀⠀⠠⢶⢶⡺⡢⠐⢕⠝⡲⢒⠖⡆⠀⠀⠀⠈⡅⡪⢒⠥⡊⢔⠡⡪⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡃⢈⠔⡁⢂⠔⡥⢊⠔⡅⠀⠀⠀⢸⢔⢄⡪⡪⢐⠕⡪⢊⠕⡪⡇⠀⠀⠀⠀⣫⠔⡡⠊⢔⠅⡪⢒⠕⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠂⢔⡵⡫⢚⡑⡫⢾⠀⠀⠀⠸⠴⠧⠮⣔⠅⡪⢒⣵⠡⠮⠗⠀⠀⠀⠀⠖⡡⡒⢕⠅⡪⠒⡡⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠕⡡⢊⠔⡡⢊⠔⡩⣆⠀⠀⠀⠀⠀⠀⡇⡪⢂⢕⡇⠀⠀⠀⠀⠀⠀⣰⡫⡊⢔⠡⣊⠔⡩⢊⢔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⢊⠔⡡⢊⠔⡡⢊⠔⡡⡣⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⠔⡡⡪⢔⡡⢊⠔⡩⢊⠕⡡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡡⣊⢔⠕⡫⢔⠕⡫⡪⢂⠜⡱⡢⢤⢀⡀⡀⠀⠀⠀⢀⣀⡤⢐⢟⡥⢊⠔⡩⢊⠕⡪⢒⠕⡩⢐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠨⢊⠕⡡⢊⠔⡡⡪⡪⢚⠕⡨⡪⢐⠕⡫⡪⢋⠝⡡⣋⠔⡡⣀⠕⡡⢊⠕⡨⢊⠕⡪⢐⠕⡪⢊⢔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣊⣔⣁⣪⣪⢋⢔⡅⡪⣊⢔⡁⣪⣊⢚⠕⡩⢊⠕⡨⢊⠔⡡⢊⡄⡊⢚⠕⡪⢂⠕⡨⠠⠑⢅⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠽⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⠘⠑⠈⠒⠈⠂⠁⠀⠁⠂⠑⠈⠐⠈⠑⠨⠔⠪⠐⠈⠂⠑⠊⠁⠂⠄⠂⠕⠈⠐⠨⠂⠀⠂⠁⠈⠐⠈⠊⠑⠈⠂⠐

⠀⠀⠀⠀⢷⡀⢣⠘⢷⡄⠀⠐⣄⠀⠀⠸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣤⢀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⢀⣤
⠀⠀⠀⠀⢀⠙⣆⠳⡌⢿⣦⡀⠈⡆⠀⠀⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣰⣿⣷⠈⠂⠀⠀⢰⠏⠀⠀⠀⠀⠀⢠⠤⠀⡀⢀⣴⠏⢠⡿⠁⠀⠀⢀
⠀⡄⠀⠀⠈⢣⠘⠀⣿⠸⣿⣅⠆⠀⠀⠀⠹⣄⠀⠀⠀⢸⡟⠀⠀⠀⢹⢈⡟⢢⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣀⡰⠁⣾⠁⣠⠎⡄⠀⢀⣴⣿
⠀⠀⡀⠠⠀⠀⠑⣸⠋⢤⣟⠉⠺⣦⠀⠀⠀⠈⠃⠀⠀⠈⣷⠄⠀⠀⢨⢘⣿⡆⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠋⠀⢰⡏⠰⠈⠆⠀⣴⡿⠛⢡
⠀⠀⢀⣤⠀⠀⠀⠀⢇⠈⢹⣆⠐⠟⢷⣀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢸⠸⣇⠴⢀⡾⢃⠀⠀⠀⠀⠀⠴⠁⡄⢠⡟⠀⣧⡘⠀⣸⠏⣀⣴⣿
⠀⠠⡀⠀⠈⠳⣌⣠⣿⡀⠀⠻⡄⣇⠈⢳⡄⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡾⣰⠏⢸⣼⡧⠀⢠⠜⠀⡀⠐⠀⠀⣰⣿⠇⢀⣿⠁⢠⡏⣰⢋⣼⠇
⠀⠀⠈⠂⠐⠢⠤⢁⡍⢻⡄⠠⡘⡀⡆⠀⠗⠀⠀⠀⠀⠀⢹⣧⠠⠀⠀⡆⢹⠀⣧⣿⠁⣄⠄⠀⢰⣰⠃⠀⢠⣿⠏⠀⣼⠋⠠⢋⡴⣧⠟⠁
⠀⠀⠀⠠⡄⠀⡀⠀⠘⡄⣿⣄⡐⢰⡷⢄⠐⠀⠀⠀⠀⠀⣿⡁⠀⡄⢠⠃⣼⠀⢻⡅⠀⣇⠀⢀⡟⠀⣠⠀⢫⠇⣰⣟⣡⠎⢠⠋⠘⠁⠀⠔
⠢⣄⠀⠀⠘⣂⠈⢦⠀⠘⢬⡛⢿⡄⠳⣈⡇⠀⠀⢀⠀⠀⢈⣿⣶⠑⠈⢾⢃⣴⠿⢃⣼⠟⢀⡾⠃⢾⠁⡠⠋⣠⡷⠋⡸⢀⡄⠀⠀⠐⠂⣄⡴
⠀⠘⡃⠈⠀⠹⢆⡀⠂⣀⠀⠉⣿⠃⠀⠠⡉⢦⡀⠀⠀⠠⣿⣿⣇⡀⠐⢹⣿⡇⠀⣼⠁⢠⡿⢀⡶⠃⠈⢠⡾⠋⠀⠀⢠⡟⠁⡰⣂⣤⠞⡝⢣
⠀⠀⠈⠲⣐⠀⠀⠙⠂⠙⢦⡄⣿⣇⠀⠀⠈⠜⠽⣢⠐⠀⠈⠙⣿⣿⣦⠈⠹⣿⡀⣿⣴⡿⠁⡀⠁⢲⣶⠟⠃⠀⠀⣠⢞⣠⠀⣴⢋⡤⣞⡶⠆
⠀⠈⢢⣁⢨⣇⡀⠀⠐⢦⠘⣯⠈⠻⣷⣦⣄⣀⠠⣽⣀⠁⠀⠀⣼⣿⣿⡇⠀⣿⡇⢹⣿⠁⠰⣁⣠⣾⠃⠀⠀⢀⠞⣁⣾⡥⢾⣿⣩⡶⠋⡠⠖
⠀⠀⠈⣏⠉⠙⢿⣅⠀⠈⢣⠙⠲⣤⣀⠈⠻⢿⣷⡌⢻⣷⢇⣴⣿⣿⡿⢠⣾⣯⣎⣾⡿⠀⠀⣿⠉⡠⠀⠀⡀⢀⣴⣾⣏⣴⠾⠛⢁⡀⢈⣤⣾
⠀⠶⢤⣈⡛⠛⢆⠨⠳⣄⠘⠳⣄⠀⢸⡇⠀⠘⣿⡿⢸⡟⢻⣿⡟⣿⢡⣿⣿⣿⣿⣯⣤⣾⣤⡿⠀⠃⡠⢂⣤⡾⣻⡿⠏⠁⣤⠔⢃⣼⣾⠷⠉
⣄⡀⠀⠀⠙⠶⠾⣟⢿⣉⢓⣦⠸⣄⣀⣙⣶⣴⣿⠁⣾⣷⠙⣿⣇⢿⣿⣿⣿⣿⣿⣿⡟⣛⣉⣡⡾⠋⣰⣿⠍⣰⡟⠀⠴⣉⣤⣿⡿⢋⡁
⠀⡉⠑⠄⠀⠀⠀⠘⢦⣙⣿⣿⣷⣤⣄⠀⢹⣿⣿⣧⡘⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⢋⣭⣭⣥⣾⣯⣥⠾⠫⢤⣾⠿⠿⢛⡿⠛⠋⠁⠀⡠
⢦⣄⡀⣈⠁⢀⡀⣄⠀⠀⠀⠙⠛⠛⣿⣇⢿⣿⣿⣿⣿⣿⠟⠋⠩⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣟⣁⢠⣶⣶⣟⣡⡶⠾⠋⣀⣠⡔⣂⣻⣷
⣀⡀⡀⠀⠈⠁⠉⠛⠷⠶⠶⠾⢶⣄⡹⢿⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣤⣼⡿⢿⣛⣿⣭⣭⠿
⣋⡉⠁⠂⠉⠛⠶⠶⠶⣦⣤⣤⠶⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣭⡿⣧⠿⠶⠟⣉⣉⡄⠐⠂
⠙⠾⠶⣿⣁⠴⠶⣤⣤⠴⢦⣄⣀⣬⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⢛⣉⣹⣧⣤⣴⡚⢛⣷⣾⣧⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣏⠉⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⠟⣿⠟⣛⣛⠋⣻⣿⣟⢉⣉⠙⠿⠿⢛⣁
⠠⠀⠄⠤⣀⣀⣀⡀⣀⣽⠷⣦⣌⣛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠛⢿⣛⠛⡿⠿⢿⠿⠿⣟⣛⣛⣋⣩⣍
⢀⡤⠌⠀⠉⠛⠑⣉⠉⢡⣶⣄⠉⢉⣼⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⢻⣬⡟⠲⢦⣉⠛⠛⠳⠾⠓⠚⠛⠛⠓⠢⠀⠄
⣀⣀⣤⢶⠾⠟⠾⠛⠳⠿⡥⠈⠟⠿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣶⣤⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣮⡛⠿⣦⣉⡉⠛⡢⣤⢀⣀⡀
⠋⠉⠀⠀⠀⠀⠀⠀⠐⠀⣁⢀⣶⠶⢿⢠⣼⡿⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣌⠉⠻⣿⣿⣷⣌⡙⢻⣶⣤⣠⡀⠀⠈⠛⠿⠛⢣⣶
⠀⠀⠀⠐⠉⠁⠀⢀⡄⣴⠏⠉⣁⠔⣤⢶⣿⣴⣟⣸⡏⣿⣏⣿⠏⢘⣯⢿⣿⡟⢧⡻⣿⣿⣧⣀⠈⠙⠳⠦⡷⢶⡍⢻⣯⡉⠤⡀⠠⢀⡈⠀⠈
⠀⠀⠀⠀⣠⡤⠴⠏⠀⠀⠔⠉⠰⠞⣁⣼⡏⢁⣼⠏⢀⣾⣏⣿⠀⢻⣇⢨⣿⢃⠸⡋⣿⣯⡛⢻⣷⣄⡀⠀⠀⠁⠙⠦⠹⣿⣤⡈⠉⠠⠀⣀
⠀⣄⡲⠿⠋⠀⠀⠀⠀⣠⢴⠿⣋⣾⣿⠛⠐⡏⠁⠀⣿⢹⣿⠃⠀⠸⣯⠹⣷⡘⢆⠙⣋⢿⠿⣿⣿⣿⣿⣌⡲⣦⡀⠑⠢⣝⠻⡿⢶⣶⣄⡀
⠚⠁⠀⠀⠀⠀⠀⠀⢈⣡⣁⣼⣿⠏⠉⠂⡔⢁⠀⢀⣾⣦⣿⠀⠀⢰⣿⡇⠈⢻⡎⡆⠹⡈⠀⠈⣿⣿⡏⢿⣷⣜⢷⡄⠀⠻⣄⠘⠊⢻⣏⠻⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠋⢉⡟⢻⡉⠠⠀⡠⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⣿⠇⣀⣾⡃⢨⡀⠁⠀⠀⢻⣎⡳⣤⣙⠿⢷⡍⠻⣦⠀⠙⣦⡈⠉⢷⡌
⠀⠀⠀⠀⡀⢨⣿⢀⣸⡏⢀⣭⠋⠀⣼⠀⠀⠀⠠⢾⣿⡅⠀⠀⠀⠈⢻⣤⡙⡯⣿⠘⣧⡀⠀⠘⠙⢈⠙⢦⠈⢇⠀⠰⡆⣹⢷⣄⡘⠷⣄⡀⠈
⠀⠀⢠⣤⣤⣿⠁⢾⣩⣾⠟⠁⢀⢾⡏⠀⢀⣦⣴⢾⣿⠟⠀⠀⠀⠀⠀⣿⠟⠁⣼⠃⠈⣿⣦⡀⠀⠈⠀⠈⠂⡀⠐⠄⠀⠘⠷⣄⡙⠳⡀⠹⣧
⠀⢀⣿⠁⠀⠀⢈⣾⠛⠋⠀⢀⡟⢸⡇⢠⢻⠉⠀⢀⣿⠀⠀⠀⠀⠀⠀⣹⣷⡄⡈⠃⠄⠈⠚⣿⡆⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢌⠻⣆⡡⠀⠻
⡰⠟⠋⠀⠀⢠⣞⠅⠀⡀⢠⠊⢠⡇⠀⠸⠀⣧⠀⢸⠇⠀⠀⢀⡠⠖⠈⢿⡟⢧⣁⠀⣴⡀⠐⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠌⣻⢷⣄
⠁⠀⠀⠁⠀⠼⠃⠀⢠⡸⢀⡤⢿⠀⣠⣴⠾⠛⠀⡞⠀⠀⢀⡏⠀⠀⠀⣟⢧⡘⠏⠐⠨⣿⣄⠀⢦⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙
⠀⠈⠀⠀⠃⠀⠀⢤⠋⢠⢸⡴⠃⢸⡏⠀⠀⠀⠸⠇⠀⠠⠊⠁⣄⠀⠀⢹⠆⠣⠈⢠⡄⠀⢻⡆⡘⠌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠈⠛
⢠⠄⠈⠀⡀⠀⠰⠃⠀⢸⣼⠃⠀⢼⡇⠀⠀⠠⠀⠀⠠⠀⠀⢠⡁⠀⠀⠹⢦⡀⢣⠈⠉⢦⢼⡇⣶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠁⠀⠀⠀⠀⠀⠀⣠⠞⣱⠏⢀⠔⡘⠀⠀⢠⠀⠀⠀⣰⠀⠀⣸⡇⠀⠀⠀⠀⡅⠈⢄⠀⠸⡈⢿⠻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⡞⠁⡼⠃⠐⠁⠖⠁⠀⠀⠃⠀⠀⡀⢙⠂⢀⢳⠈⠇⠀⠀⠸⡃⠀⠀⢠⡀⢸⡇⢣⠀⡄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣜⠷⠈⢰⠀⢿⠀⠀⠀⠑⠀⠀⠀⠇⠸⢷⡠⡋⠡⡀⠁⠀⠀⠀⠀⠈⠋⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠙⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⣾⡄⠻⡀⠀⠀⠀⠀⠀⡃⠰⠒⠂⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⣠⡔⠐⠆⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⢉⠠⠴⡇⠁⠘⠯⣢⣴⠾⠒⢌⡠⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠤⠒⠈⠀⠀⠀⠀⡇⠀⠀⠀⣈⠽⢷⣋⡩⢇⣀⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠖⠊⠁⠐⠀⠁⢀⣠⣼⣷⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣯⠁⠈⢁⣄⠀⠀⠀⠸⠤⠒⠀⠄⠂⠉⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠁⠀⠀⠙⠢⣿⡛⠁⣙⡦⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⣦⣀⡀⠠⠐⠙⣯⠁⣚⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣧⣼⡟⠛⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⣿⣿⠟⠀⣹⣿⡇⢀⠀⣿⡇⢸⡇⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⣿⣿⣿⣿⣿⠀⢰⣶⣋⣿⡿⠿⠛⠃⣀⠈⣶⠐⣿⣿⡇⢸⠀⢻⡇⢸⡇⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡇⣿⣿⣿⣿⣿⠀⢸⣿⠉⣿⡆⢰⣾⠀⢻⣾⣿⠀⣿⣿⠃⠸⠃⢸⡇⢸⡇⠘⠁⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣿⠀⠘⣻⠀⣿⡇⢸⣿⣷⡀⠹⣿⠀⣿⣿⠀⢠⡄⢘⣇⣼⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣿⢹⣿⣿⣿⠀⢸⣿⠀⣿⡇⢸⣿⠋⣿⠀⣿⠐⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⢿⣿⣿⠀⢸⣿⠀⣿⡇⢸⣿⣄⣠⣼⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢈⢀⣿⣿⠄⢸⣿⣀⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠸⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣿⢀⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⢻⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠚⠉⠛⠛⠛⠓⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡄⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⣸⠇⠀⢸⣆⣀⡀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠁⢸⡇⠀⢸⠋⠉⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⣀⣤⣬⠿⠷⣯⣄⡀⢀⣀⣀⡀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠋⣉⡥⠀⠀⠀⠀⠀⠀⢹⡏⠁⠈⠉⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⢀⡤⠚⢁⣀⠀⣠⠄⠀⠀⡼⢸⡇⠰⡄⢠⣄⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⢣⠾⠚⢋⣡⡽⠞⢁⣤⢠⠞⣱⠏⢷⡀⠻⣦⠘⣆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠞⢋⣡⡴⠞⣹⣃⡤⠞⠁⠀⠈⢷⡄⠙⠀⠘⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⠋⣡⠤⠴⠿⠉⠀⠀⠀⢀⣠⢤⣝⢦⡘⣧⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣴⡏⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⢰⣶⠈⠀⠙⣿⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢹⡇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣿⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠀⢸⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣆⠀⠀⠀⢀⡀⠀⠀⠉⠀⢀⠀⠀⠀⠀⡿⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠳⣦⣤⣤⠶⠋⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣤⣤⣤⣤⣴⣾⠋⡾⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡇⠀⠀⠀⠀⣸⡟⣦⡇⠀⣶⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⢸⡇⠀⠀⠀⠀⢻⠇⠈⠻⣦⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣿⠁⠀⠀⢘⣇⠀⠀⠀⠀⣿⡀⠀⠀⠘⣟⠻⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣙⠛⢶⡶⠋⢻⡶⣄⣀⢴⡏⠙⢷⣤⠶⠛⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀⠀⠀⠀⣾⠁⠀⠈⣷⢾⡵⣾⠇⠀⢀⡽⠃⠀⠀⢀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠈⠻⢦⡀⠘⣷⢠⡏⢀⡴⠋⣀⣀⣀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠹⣦⡸⣏⡴⢯⡤⠾⠧⢶⣿⢦⡼⣧⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠀⢸⣷⣿⠂⠿⣟⢸⡇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣿⠀⢸⣧⣭⣤⣬⣭⠼⠇⣸⢤⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⣧⡀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⢠⡄⢿⠀⠀⠀⠀⠀⠀⠠⣾⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠃⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠼⠧⠤⠤⠤⠤⠤⠤⠤⠿⠤⠤⠤⠶⠶⠶⠶⠿⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠉⠉⠈⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠳⠀⠄⠠⠤⢤⠀⠀⠀⢠⠤⠤⠤⠄⠴⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢀⣀⣀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠉⠂⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠊⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣻⣩⣛⣻⣛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣯⣭⣭⣿⣿⣍⣿⣽⣭⣭⣭⣯⣭⣿⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⡍⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⣸⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡗⠒⠒⠒⠒⠒⠒⠒⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠞⢑⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠉⠓⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⡯⠭⠭⠭⠭⠭⠭⠭⡅⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⢨⠀⡱⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠑⠚⠒⠓⠒⠒⠒⠒⠒⠒⠒⠓⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠉⢙⠛⠛⡏⠉⢢⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠘⠛⠛⠁⠐⠁⠀⠀⠀⢸⣇⣀⣀⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣙⢺⣉⡆⣋⠀⠀⠀⠀⠀⡠⠚⢣⡠⠌⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣁⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠂⠐⠂⠂⠐⢦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡝⠒⠄⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠙⠂⠀⠀⠐⠀⠋⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠁⠒⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠚⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢢⠀⠀⠸⣀⢨⡀⠈⠆⠀⠀⠀⠀⠀⠡⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠉⠈⠉⠁⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣀⡤⠀⠒⠒⠒⠒⠒⠂⠀⢰⠿⠆⡍⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⠠⠤⠒⠐⠈⡭⡄⢰⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠁⡔⢢⠀⢧⠔⠀⠑⠃⠀⡆⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠦⠤⢇⠈⢁⡀⢀⠄⠄⠰⣉⠆⢸⠤⠤⠤⠤⠤⠤⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠉⠈⠉⠉⠈⠁⠉⠀⠀⠈⠈⠁⠀⠀⠀⠀⠁⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠇⠧⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢜⢛⡆⠀⠀⠀⠰⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⡆⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠔⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢐⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣠⠾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣠⣾⣿⣷⣮⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣷⣶⣶⣶⣾⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡧⢻⡏⠀⠀⠐⠛⠲⠄⠀⠀⠀⠀⠀⠀⣽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠘⡄⠀⠀⠙⠳⣦⣦⠀⠀⣀⠛⠁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⠻⣇⠀⠀⠀⠀⠀⠐⠀⠴⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣴⠏⠀⣿⣆⠀⠀⠈⠛⠓⠶⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⢻⡄⠀⠸⣿⣷⣄⡀⠉⢉⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠒⠚⠛⠋⠁⣿⠀⠀⠀⢻⡄⠀⠙⢿⣿⣿⠇⢠⡀
⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡀⠀⠀⢈⡏⠀⠘⣿⠶⣤⣄⡀
⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣷⡀⢀⡞⠀⠀⠀⡟⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢂⡟⢰⡏⠉⠙⠛⠙⠛⠛⠛⠛⠛⠓⠓⠓⠓⠚⠛⠛⢻⣿
⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⣰⠃⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀
⠀⠀⢠⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⡖⠒⠂⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢘⣷
⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⣡⣿⡃
⠀⠀⣼⣋⣠⠤⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⣼⠃⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⢀⡞⡿⢀⣴⡆⣼⠟⠁⢀⣿⣄
⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⠁⠀⣼⠃⠀⠀⠀⠀⡴⠃⢰⠇⠀⠀⣠⡟⢰⡧⠊⡼⢿⣏⡴⠚⣁⣀⡙⢷⡄
⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣷⣴⠏⠀⠀⠀⠀⣼⠁⠀⠘⠷⠒⠛⠉⠠⢏⡤⠊⣠⠟⢿⣿⣛⣉⣉⠀⣀⠙⣦⡀
⣠⠇⠀⠀⠀⠀⣀⠴⣚⡩⠉⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠴⠿⢋⣠⣾⡏⠀⠀⣿⠉⠉⠙⢧⣌⡀⠘⢷⡀
⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⢛⠙⠛⠓⠒⣤⣤⠾⠃⠀⠀⠀⠀⠀⢀⣀⣤⠶⣶⠋⠁⠀⢰⠇⠀⠀⠀⠀⠈⠛⠀⠈⢷
⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣰⠃⠀⠀⠀⢀⣠⡤⠖⠊⠉⠀⠀⣸⣏⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢰⣯⡴⠶⠒⠛⠛⠳⠶⣶⠶⠶⠶⠶⠛⠉⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠉⠛⠛⠛⠿⠶⣦⣄⣀⣾⠀⠀⠀⠀⣾⢣⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠹⣆⡀⠀⣀⣀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠷⠶⣤⣄⣤⠟⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⠞⣿⠀⠀⠈⠛⠋⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣤⣤⣬⣁⡀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣠⠞⠁⣀⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠠⣶⣬⣍⡛⠓⠀⠀⠀⠀⠀⠀⣱⠀⠀⠁⠀⠈⠁⠀⠘⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠠⠀⠀⠀⡄⢠⢿⣷⡀⠁⠀⠁⠀⠐⡀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣤⡀⠀⠂⠀⠀⠀⠿⠸⢿⣇⠀⠀⠀⠀⢀⡴⡫⣷⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠹⡌⢎⢳⣤⠐⠀⢀⢸⠁⠀⣆⢹⡀⠀⠀⣰⠞⢱⢣⡟⠀⠀⠀⠈⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠐⠀⠀⠀⠸⡇⠈⢄⠟⣷⡆⠀⠇⠀⠀⡇⣼⣷⠀⡴⠃⢀⣏⢎⡟⠀⠀⠀⠈⠀⣀⠈⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⢿⡳⣴⣄⣀⠀⠐⣇⠀⠘⣞⣰⣽⣿⠤⠤⠶⠻⠿⠿⡿⣅⢀⡞⡿⣜⡟⠀⢁⣠⠤⠚⣡⢾⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢮⠪⣝⣗⢶⣾⣀⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⠔⠋⠁⣠⢞⣵⡏⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠄⠐⠠⡀⠀⠘⢧⠀⠙⠪⣪⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣠⣞⢕⣿⡏⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠘⢧⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣀⡄⣠⡤⠤⠶⢦⣴⡶⠂
⠀⠀⠙⠻⣿⠯⣟⣻⢏⣓⠿⣖⣻⠿⠀⠀⢀⡤⢴⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣀⣀⠀⠀⠀⠹⡅⠀⠀⣀⠤⢒⣭⠾⠛
⠀⠀⠀⠠⠉⠓⢦⡉⠙⠛⠿⢶⡿⡀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣟⢷⡀⠀⠀⢀⡴⠟⣥⣀⣀⣴⣉⣀⠀⠀⠀⠀⠸⣦⠛⣠⣴⠞⠋⠀⠄
⠀⠀⠤⠄⠀⡀⠀⠉⠳⢤⡀⣼⠁⠀⠀⠀⠀⠁⠀⣻⣿⣿⣇⣽⣿⣷⠀⠀⣼⠻⠓⠛⠹⣿⣿⡟⣨⡗⠠⠀⠀⠀⢻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⣿⡄⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠠⠀⠸⡅⠉⠙⠓⠶⠆⣠⣀⠀⠁
⠀⣀⣠⣶⠶⠞⠋⠭⣭⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣧⣤⣤⣶⣶⣶⣶⣴⠿⠖
⠀⠉⠿⠏⠩⢉⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣶⠖⠚⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠑⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⢐⣰⢿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⢀⠈⠲⢦⡀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⡴⣏⡬⠗⠋⠉⠙⡄⠈⠀⠀⠀⠀⠀⠀⠀⠲⠔⠓⠒⠦⠤⠚⠛⠛⠒⠒⠀⠂⠀⠀⠀⠀⠀⢠⣿⣷⣿⣟⣾⣥⣂⣽⣷⣄⠂
⠀⠀⠀⣠⣾⣗⣋⡥⢤⠤⠴⠖⠶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣄⣀⠋⣤⢊⠂⢀⠀⠀⠀⠀⢀⡴⠉⢻⡀⠁⠀⠉⡁⠉⠙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⠫⡫⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠠⠐⠀⠀⠀⢀⣴⢿⡢⡀⠀⠩⡄⠈⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⢀⠄⠊⠀⢀⣼⡋⣠⠞⠁⢀⣹⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣀⡤⠞⢿⠷⣴⣝⢮⡲⢄⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⢁⣠⢖⠋⠘⣯⢋⣻⠋⠛⢳⣶⣦⣤⣤⠤⠴⢶⣶⣿⠋⠄⠀⢸⡄⠌⠉⠻⠿⢦⣕⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠵⠞⡁⠀⠀⠀⢸⢇⢈⠇⠀⣰⠋⢸⡏⢿⠀⠀⠀⡜⠘⠿⣆⣌⠄⠈⣏⠂⠀⠀⠀⠀⠁⡉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⢀⠀⠀⢸⡏⡌⠀⡞⠀⠀⠈⣿⢸⠈⠀⢰⠁⠀⢠⠘⢿⡌⠄⢧⠀⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣾⡝⡰⠃⠀⠀⠀⠀⠘⣷⢠⢀⡇⠀⠀⠀⠀⠀⠹⣤⣬⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡀⠀⠐⠀⠀⠀⠀⢻⣼⡘⠃⠀⠂⠀⠠⠈⡄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠂⠈⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⣀⣭⣭⣭⣭⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⣤⣶⠾⠟⠛⠉⠉⠁⠀⠀⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣑⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣰⡿⠁⠀⠀⠀⠀⠀⢀⡠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⣼⡟⠀⠀⠀⠀⠀⢀⣴⣿⣧⣀⡇⠉⢿⢿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡄⢰⡟⠀⠀⠀⠀⠀⡠⠃⠈⠙⣿⣿⣿⣶⣜⣯⣿⣿⣿⣿⣿⣾⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠰⢀⣿⠃⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⠿⠛⠟⠁
⠀⠀⠀⠀⠀⠀⡀⢸⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠃⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡇⠀⠀⣀⡤⢤⣤⣀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠉⠛⠄⠄⢀⡀⠀⢸⣿⣿⣿⣯⡞⠀⠀⠀⠁⢀⣤⣀⠈⠁⠀⠀⣰⡫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠁⠊⠉⠀⠀⠀⠀⠀⠋⠛⠃⠀⠀⠀⠀⡛⠃⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⢿⠿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣇⣤⣴⣾⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⡤⠴⠶⠶⢶⡖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠙⢶⣤⠤⣾⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠢⠄⠀⠀⠀⠀⠉⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⡊⣁⢀⣠⣤⣤⣿⡇⠀⡀⠀⠀⠀⠀⠐⡆⠄⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣿⣿⣿⣿⢿⠋
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠙⠛⠛⠛⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠐⠢⡄⡀
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⡀⠀⠉⠐⠠⡀
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠢
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠐⠈⠀⠀⠀⠑⡀⠀⠀⠀⡀⠌⠀⠉⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⠀⢰⣿⠛⠛⠛⠛⠛⠛⢻⡆⠀⢸⡇⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣯⣭⣽⣦⣤⣿⣤⣼⣿⣤⣤⣤⣤⣤⣤⣼⣧⣀⣼⣇⣠⣏⣉⣩⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⠀⠀⠀⠸⢦⣤⣤⡄⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠷⠤⠤⣤⠀⠀⠀⣤⠤⠤⣤⠄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣉⣤⠤⠤⠤⠤⢤⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠃⠘⠋⠃⠀⠈⡈⠁⠀⢀⢀⠀⠀⡀⡉⢉⡁⡀⡁⡈⠉⡉⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⢀⢔⠄⡠⡪⡠⢀⠄⠔⡅⣀⡠⡊⠠⡊⡨⡪⡪⡢⠊⠄⢈⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠁⡪⣪⠞⠈⠀⠀⠀⠀⠀⠀⠉⠚⢎⠄⠈⠪⡢⡢⡠⠁⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢂⢔⠕⠡⠎⣠⠂⠀⠀⠀⠐⠰⠒⣴⠀⠀⠀⠀⠑⣄⠜⠈⠪⡪⡈⠪⠀⠇
⠀⠀⠀⠀⠀⠀⠃⢀⢔⢅⠔⠡⡨⡂⠀⠀⠤⣤⠼⡀⠃⠻⠴⠴⡄⠀⠀⠸⠔⠄⠠⠪⡂⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢕⠑⠁⡠⡪⡪⡇⠀⠀⡇⣠⡀⢁⠕⢀⢁⠀⡇⠀⠀⠀⣗⠅⣀⢘⠠⠊
⠀⠀⠀⠀⠀⠀⠃⠁⠀⠊⡪⡪⠊⢇⠀⠀⠉⠉⠹⡆⠀⣹⠏⠉⠁⠀⠀⢠⠵⠁⢁⢕⢁⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠇⠀⡠⡪⠪⡠⠊⢈⢦⡀⠀⠀⠀⠛⠚⠛⠁⠀⠀⠔⢒⠛⡚⡚⢒⣵⣷⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠇⠨⡪⡪⡪⡀⡰⣣⡪⡪⡲⡢⡤⣀⣀⡀⡀⡤⢄⢾⢍⠥⡮⡩⡥⠭⢥⢥⠼⡇
⠀⠀⠀⠀⠀⠀⠢⡀⠪⡪⠊⢪⠞⠉⠎⠘⠉⠨⢜⠅⠀⠊⠊⠠⡂⠀⢕⠅⠈⠈⠢⡢⢀⣠⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠋⠚⠛⠘⠘⠑⠓⠃⠃⠃⠺⠾⠾⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠋⠉⣉⠭⡭⢍⡉⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢀⠎⡡⠼⠹⢤⡙⡆⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡀⠓⢲⢰⠒⠃⡸⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠳⣄⡸⢼⣀⠴⠁⠀⠀⢠⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠛⠶⠶⣦⣤⣤⣬⣭⣤⣤⠴⠶⠶⠛⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣴⠞⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡟⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢸⣿⣦⣄⡀⢀⣠⡴⣿⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣴⡇⠀⠈⠙⠋⠁⠀⣿⣤⣤⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠞⢛⣿⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⢹⡟⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⣠⡾⠋⠉⠙⢷⡜⢷⡄⠀⠀⠀⠀⣠⡞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⣆⠙⣦⡀⢀⡼⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠻⠟⠁⠀⠀⠀⠀⠀⠘⣇⣠⡴⢦⣄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡸⠇⣽⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣈⣛⢲⣆⣀⣰⡖⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣋⣁⣀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⣄⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⠀⢹⣷⣄⠀⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡈⢻⣿⣿⣿⡆⣾⣿⣿⣴⣿⣿⡏⠀⢀⣾⡇⠀⠀⣠⣾⣿⠋⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡿⠀⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣶⣶⣾⣿⣶⣤⣀⠀⠹⣿⣿⣿⢿⣫⣽⣶⣶⣶⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⣿⣷⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⡿⠟⠉⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣿⣿⣏⣾⣿⣭⣥⣭⣝⣿⣿⡿⠿⠻⠿⣿⣧⢻⣿⣿⣷⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⣿⣿⢹⣿⣿⣿⣟⣧⣿⣿⣿⣾⣿⣿⣻⣾⣿⡟⣿⣿⣛⣉⣀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣯⡉⠉⠙⠛⠛⠋
⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠉⢁⣴⣾⣿⣿⣯⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣾⡿⠟⠛⢋⣿⣿⣶⣽⣛⣿⠿⠿⣿⣛⣭⣾⣿⣿⣿⣿⡛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⢸⣿⣿⠏⣿⣿⣿⠏⢿⣿⡆⠀⠀⠻⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠸⣿⠃⠀⣿⣿⣿⡄⠀⠉⠛⠶⠄⠀⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠹⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⠀⠀⣸⣿⠀⠀⡀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢿⣤⡄⣿⣿⠀⢰⣇⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢳⣔⣦⣿⣿⣦⣼⣿⣿⣿⣿⣦⣿⣿⣧⣿⡿⠁⢀⡄⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣻⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣇⣴⢟⡆⢀⣤⣶⡿⠟⠁
⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠐⢦⣔⡶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣤⣀⡈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⣤⡶⠚⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣀⣤⣤⣤⣶⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⡶⠦
⠀⠠⠴⠶⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣽⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⢿⣿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⢶⣤⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⣨⡿⠛⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣯⡉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠮⠻⢦⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢻⡟⠀⣿⣿⢿⣿⡟⠻⣿⣿⢿⣻⣆⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠚⠀⢠⣿⡟⠈⢻⡇⠀⢻⣿⠀⠁⠹⠄⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⣤⣤⡀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠩⠄⠿⠿⠿⠿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣷
⠀⠀⠀⠀⠀⠀⢠⠞⡡⠒⠊⠉⠁⡆⠀⠀⠀⡔⣡⡶⠛⠉⠉⠙⠛⢶⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠃
⠀⠀⠀⠀⠀⡰⢣⠊⠀⠀⠀⠀⠀⡇⠀⠀⣈⣰⠏⠀⠀⠀⠀⠀⠀⠀⠙⣆⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⡰⢡⠃⠀⢀⡀⠀⠤⠄⡤⠀⣼⣿⣿⣧⢀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣷⣄⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢡⠃⠀⠀⢸⠀⢒⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢔⢄⠄⠴⠈⣷⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢢⠏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⢎⠣⠀⠀⠀⣿⠀⠀⠀⠄⠀⡀
⠀⠀⡸⢸⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠀⠒⡄⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠆⣿⠀⠀⠀⠀⢠⡇
⠀⡴⠃⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⡏⠀⠀⠀⠀⠸⡀
⠀⡇⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠃⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⢒
⣠⡅⡀⠀⠀⠀⢀⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠠⡄⣅⠀⠀⠀⠈⠡⣆
⢿⡗⠿⠐⠀⠰⢡⣾⣿⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢾⡠⣀⣀⠀⠀⠄
⠀⠁⠀⠀⠀⠅⣾⣿⣿⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠬⠀⠀⠀⢀⢔⠅⠛⢻⣷⣤⠀⢸⣧⠁⠒⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠂⠀⠀⠈⠛⠁⣾⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣊⠊⠀⠀⠀⠀⠀⠀⠀⢉⡟⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⣾⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⢀⣀⡀⢀⢾⠟⠋⠉⠑⠫⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⢠⠒⢉⠥⠐⠂⡭⡽⣦⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⠀⠀⠀⣠⣾⣼⠁
⠀⠀⡆⢀⠃⠀⠀⠀⠱⡐⠬⠿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⣿⣿⣿⠫⠑⠁
⠀⠀⢳⡘⣆⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⢰⡇⠀⠀⠀⢀⣤⠘⠛⠋
⠀⠀⠀⠙⠦⢕⣂⠀⢀⡀⠀⠀⠀⠀⣠⣿⢀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠛⠛⢛⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠴⠋
⠀⠀⢠⠚⠛⠳⠶⠐⠠⠔⠛⠁
⠀⢠⣀⢉⣋⣾⠟
⣤⣤⣽⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣭⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿

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



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣄⡀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠞⠉⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⠀⠀⠀⠀⠀⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⣷
⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⢿⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢿⠲⢤⣀⣀⣀⣀⣀⣤⡶⠀⠀⢀⡇⠀⠀⠀⠀⠐⠛⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⠤⣀⣉⣉⣩⠵⠋⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠈⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣒⣒⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠋⠉⠉⠉⠉⣭⡄⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣴⣶⣿⣷⣦⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠉⣿⡏⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠀⠳⣄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣰⠃⠀⠀⠹⣦⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡼⠃⣀⠤⠤⠀⢹⣧⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡠⠚⠁⠀⢀⣴⠟⠀⠀⡤⠄⢀⣀⡆⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢀⣘⡆⠀⠀⠀⢠⠀⢸⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡎⠀⢸⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢆⠀⠓⢿⠚⠟⠚⠟⠀⡼⠀⢀⢏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⣠⠜⠀⠀⢀⠎⠀⠀⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⢠⠏⢀⡤⠄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢀⡶⠒⠒⠘⣆⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡆⠀⠘⠀⠈⠀⣀⡴⠀⢀⠞
⠀⠀⠀⠀⠀⠀⢺⠀⢰⠓⠀⣹⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢻⡀⠀⠀⠒⠚⢉⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠣⣈⠀⠒⠋⠀⢀⣠⠞⠁⠀⢀⠀⠀⠀⠀⠙⠒⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠉⠉⠀⠀⠀⠀⠈⠳⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⠀⢰⣿⠛⠛⠛⠛⠛⠛⢻⡆⠀⢸⡇⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣯⣭⣽⣦⣤⣿⣤⣼⣿⣤⣤⣤⣤⣤⣤⣼⣧⣀⣼⣇⣠⣏⣉⣩⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⠀⠀⠀⠸⢦⣤⣤⡄⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠿⠤⠤⣤⠀⠀⠀⣤⠤⠤⠼⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⢶⣶⣿⡿⣿⣿⣿⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡟⣭⣿⡶⢮⡻⣏⡛⣿⣷⣿⣿⣿⣿⠿⠿⣛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⠛⠿⠗⣝⣻⣿⣿⣷⣾⠿⠿⣛⣫⣭⣵⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢾⣿⣿⡿⣿⣿⣿⣹⣿⣿⣷⡿⠿⣛⣛⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣎⣙⠿⣿⣿⠿⣟⣫⣭⣶⣾⣿⣿⣿⣿⡿⠿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡸⣟⣫⣭⡆⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢛⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⡿⢟⣛⣭⡌⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⣿⣿⣿⣿⠿⣸⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⣛⣭⣵⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣼⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⢸⣷⣶⣶⣶⡀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⠀⠀⠀⢠⣴⡶⠷⠿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⡇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⣿⡎⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⣿⢀⣀⣤⣤⣶⣦⣶⣾⣿⣿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣷⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠘⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠰⢶⣤⣤⣄⣠⣤⣤⣶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣀⣀⣀⣀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⣠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣯⠉⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣀⠀⠀⠀⠀⠀⠁⣀⠈⠹⣷
⠀⠀⠀⠀⠀⢸⣿⠀⠐⠲⡤⠁⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠻⠛⠃⠀⠀⠀⠀⠎⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⣴⠞⠛⢿⣆⢀⣤⠀⠀⠀⠀⠀⠀⣸⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣴⣏⣀⣀⣀⣀⣠⣤⡿⠟⠁⠀⠀⠀⠀⠀⣼⡟⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣏⣉⣩⡿⠋⠀⠀⠀⠀⠀⠀⢠⣾⠋⢱⣆⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⡀⠀⢠⠉⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠹⣦⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⠀⠀⡐⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⢿⡀⠀⠘⢷⡄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠘⠀⢸⠇⠀⡸⠀⠘⢻⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⡇⠰⠀⢱⡄⠀⢻⡄⠀⠀⢻⡀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⠀⠀⡇⠀⡆⠀⠀⡇⠀⡇⢸⡇⠉⠛⠛⠿⠿⠾⠿⠛⠛⠁⠀⠘⣷⡀⠀⠈⠃⠀⠘⠃⠀⠀⠀⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠁⠀⠇⠀⠀⠇⠀⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⡀⠆⠀⠀⠀⠀⠀⠀⡅⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⢠⠀⠰⠀⠘⣦⣤⣾⣿⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠙⢿⣦⡀⠠⠆⠀⠀⠰⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣈⣠⣤⣾⡿⠟⣹⡿⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠙⢿⣦⣄⣀⠐⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠁⠀⠀⣿⠃⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢻⣟⠿⣷⣶⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⢿⡆⠀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠿⣷⣄
⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⣠⣼⣏⡀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣤⣴⠟⠛⠿⠿⠟⠋⠈⠙⠻⠷⢶⣶⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠶⣶⠀⢶⡶⠐⠂⠐⠂
⠀⠀⠀⠀⠀⡀⠀⠶⠶⠶⠆⠀⠸⠿⠇⠀⠀⠀⠀⠼⢿⡄⠀⠴⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡖⣶⣦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣅⠀⠀⠀⠀⠀⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣
⠀⠀⠀⠘⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⢀⢐⣀⡂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣦⣤⣴⣶⡾⠛⠀⠀⠀⢀⠸⣄⠟⡐
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⣒⠈
⠀⠀⠀⠀⠀⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄⠤⠴⠅⠤⠀⠤⠠⠄⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⢀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠨⡀⢀⣴⡶⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣀⣤⣾⠟⠁
⠀⠀⣰⠋⠀⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡣⠈⠳⡄⠀⠀⠀⠀⠀⢻⡋⢀⣼⠗⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣉⠙⠛⠋⢉⣀⣀⣀⡀
⠀⢀⡏⠀⠀⣽⣹⣍⣉⣉⣉⣉⣉⣉⣩⣉⣏⣉⣍⡇⠀⠀⢹⡄⠀⠀⠀⡀⠀⢁⠘⠉⠀⠈⠀⠀⠀⢰⠁⣰⡦⠄⢄⣶⠄⠀⠀⠀⢀⣶⠀⣴⠄
⠀⢸⡇⠀⠀⢾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡇⠀⠀⠘⡇⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⢸⠀⢶⣦⠀⢤⣶⠄⠀⠀⠀⢀⣤⠀⣬⡄
⠀⠈⠧⡤⠖⠻⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠿⢦⡀⢰⠇⠀⠀⠠⠄⢠⣤⣤⣤⠠⠠⠄⠀⠀⢸⠀⢤⣤⠀⠤⣤⡄⠀⠀⠀⠈⣉⠀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠀⢻⣀⣀⣸⠃⠈⠀⠀⠀⢘⠀⣠⣤⠀⣄⣤⡄⠀⠀⠀⠈⣋⠀⢙⡁
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡐⠛⠀⠻⠁
⠀⠀⠀⠀⢰⠢⡈⡄⠐⠐⡀⠐⠀⠀⣀⠀⠀⠀⠀⠠⢀⣀⣀⣀⣀⡐⠄⠀⠶⢶⡶⠶⠶⣶⠶⢶⣶⠆⠀⠀⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢀⠘⠀⠄⠘⣁⠀⠁⠈⠀⡆⠀⠀⠀⠀⢨⠀⠀⠀⠀⡇⠀⠀⣶⠀⠀⠀⠀⢸⠀⠻⠟⠀⠀⢸⠋⠛⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠶⢶⡀
⠀⠀⠀⠀⣋⠸⢆⠈⠒⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⢺⡇⠅⠀⠀⣼⡆⠀⠀⠀⡄⠀⠈⠛⢻
⠀⠀⠀⠄⠘⢀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡀⢀⡃⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠺⠇⡄⠀⠘⠃⢻⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠄⠈⠢⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣑⠖⢳⣚⠳⢂⡄⠀⣹⣀⣆⢀⣀⣼⠀⠀⠀⡀⠀⢸⠀⠀⡇⠀⢠⡤⢼⠀⢠⣄⢰⠀⢠⣤⣼
⠀⠀⠈⠄⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⢹⡏⠉⠉⠉⠁⠀⠘⠂⢐⠃⠀⠘⠒⡚⠀⢸⣿⠨⠀⢸⣿⣿
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠡⠀⠀⠀⣀⡤⠞⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠘⠉⠸⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⠛⠛⡛⠛⠀⠀⠀⠀⠸⢿⠿
⠀⠀⠀⠀⠀⢤⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠰⠶⠷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣠⡶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣶⡄⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣴⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢛⣛⣉⣉⣉⣉⣛⡛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⣴⠾⠛⠋⠉⠉⠉⠉⠙⠛⠷⣦⣝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⡾⠋⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠙⢷⣌⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⠏⠀⠀⠀⠀⠀⠀⣿⠉⠉⣿⠀⠀⠀⠀⠀⠀⠻⣧⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⠀⠀⢰⣶⠶⠶⠶⠾⠿⠀⠀⠿⠷⠶⠶⠷⣶⡆⠀⠀⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⣿⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣿⡇⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⡄⠀⠈⠉⠉⠉⠉⠙⣿⠀⠀⣿⠋⠉⠉⠉⠉⠁⠀⢠⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⣷⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣾⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡜⢿⣄⠀⠀⠀⠀⠀⢿⣶⣶⡿⠀⠀⠀⠀⠀⣠⡿⢣⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣬⣙⡛⠷⠶⠶⠶⠶⠾⢛⣋⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠶⠶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣧⢸⡇
⠀⢀⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⡀
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠲⡆
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⠾⠀⠀⠀⠀⠀⠀⠷⠶⠶⠶⣤
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⢀⣀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⣀⣀⣘⣲⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣖⣃⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠘⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠰⡄⠀⠀⠀⡟⠀⠀⣾⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⣄⠀⠙⣄⠀⠀⠹⡄⢀⠀⡇⡀⢰⠇⡀⠀⡴⠁⠀⢀⡤⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⠳⢄⠈⢢⠐⢄⠱⠸⠄⡇⡇⡞⡜⢠⠎⡠⢀⡴⠋⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠠⡑⠄⠑⠌⠀⠁⠀⣇⠀⠐⡰⠃⢊⠔⠉⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣄⡀⠨⣑⠈⡀⠀⠠⢀⠠⠤⠤⠄⡈⠢⠀⡀⠔⣋⠤⠂⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣄⣀⣀⡨⠁⠂⠁⢀⠋⡐⠁⠀⠀⠀⠀⠈⢢⠁⠀⠠⠀⠂⠉⣀⣀⣤⢄⣠⣤⣤⠖⠒⠶⠤⠶⠒⠲⠦
⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⣀⡀⠀⠈⠉⠈⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⡖⠉⠉
⠐⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠓⠤⢄⡀⠀⠀⠀⢣⣀⣀⣀⣀⣀⠤⠚⠂⠉⠉⠉⣡⠏⢁⣠⠀⠀⠠⠤⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⡀⠄⠂⢀⡀⠀⠀⠀⠀⢀⠀⠉⠑⠒⣍⣁⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠚⢁⣐⠊⢀⡀⠀⣠⠤⠒⠉⠉
⠀⠀⣀⡀⣀⡀⢀⠀⠀⡁⢈⣁⣐⢒⣤⣍⣀⣀⣈⣨⣽⣦⠄⠀⠀⠀⣀⡼⠁⠄⠐⣀⠀⠀⠀⠀⡩⠄⣲⠉⠲⡒⡢⣀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⡼⣃⡤⠷⣬⠶⠷⠬⣁⣀⣀⣐⣠⣅⣀⣄⣈⣉⣀⣠⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢖⡒⠒⢦⠶⠚⢛⡛⠉⠠⠤⠤⠤⠤⠤⠴⠀⠨⠉⠁⠀⠀⠈⠉⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠴⠚⠉⠉⠉⠉⠉⠉⠙⠯⢤⠀⠀⠀⠀⠤⠶⠮⠍⠤⠤⠥⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡟⠉⠉⠉⠉⢻⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⣀⣸⣇⣀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠘⠛⢻⡟⠛⠃⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⠈⠁⣀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣀⣸⣿⣉⣉⣉⣉⣿⣇⣀⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠚⣉⣉⠓⢦⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡞⢠⠤⠇⠸⠤⡄⢳⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡘⠛⣆⣰⠛⢃⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠦⢭⡭⠴⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⣠⡀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠈⠀⠀⢀⣬⣿⣿⣶⣦⣌⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⣿⣯⠉⠀⠣
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣾⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⠙⢛⠻⢻⣿⣿⣿⣿⣿⣿⡹⣦⠈⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠚⠻⣿⣿⣶⣤⡘⣯⣿⣿⣿⣿⣿⣵⡃⢀⠄
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⣥⣦⣤⣼⣿⣻⡿⠿⠿⠿⠿⢿⣿⣿⠿⢿⠋
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢻⠃⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠐⠉⠉⡉⠙⠛⠀⠀⠀⢜⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⠀⠀⠀⠀⠈⠁⣰⣶⣶⣿⠟⢻⢿⡟⠀⠀⠀⠀⠰⠛⣿⠁⠀⠀⠀⠸⠗⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠳⣄⠀⠀⠀⠀⣀⡀⠠⠀⠠⠀⠐⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠦⡀
⠀⠀⠀⠀⠀⠀⢸⠉⡃⢉⣉⣿⣦⣀⠀⠙⠳⢴⠁⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⢀⠜⠐⠄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠆⠊⠱⠁⠀⡠⢨⠄⠠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡉⠁⠢⡀⠀⠀⠀⠰⠁⠀⣜⠗⠁⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⢄⠀⠐⢄⡘⠀⠐⠄⠚⢅⣠⠐⠉
⠀⠀⠀⠀⠀⠀⡞⢀⠘⠏⠉⢉⣉⣉⣿⡇⠀⠀⠈⠁⠒⠀⠠⠄⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣷⣾⣷⣿⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢈⡛⠿⠿⠿⡟⠉⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠁⠐⠠⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣗⠠⠀⢀⠀⠠⢔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠒⠀⠁⠀⠁⡀⠀⠀⠀⠄⠈⠉⠁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⢿⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠀⡅⡃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣀⣤⠤⢄⡀⠀⠀⣾⠑⠄⠀⠀⠀⡠⠞⡠⠚⡠⠃⠀⠼⠋⠅⠀⠀⠀⠀⠀⣸⡏⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣨⣭⣈⠉⢢⡈⢆⠀⠉⠀⣄⠀⠀⠎⠁⠀⢀⣴⣁⠔⠂⣠⠔⠁⠀⠀⠀⠀⠀⣼⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠳⠀⡇⢨⡀⠘⠀⠸⡖⠀⢀⠀⣀⣆⣻⠁⠀⢰⡟⡀⠠⢀⠀⠀⠀⠚⠁⣠⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠘⢷⣇⠀⣠⠴⣛⣋⡭⠭⠭⠭⣍⣛⠲⢦⣠⠈⠀⠀⠀⠀⠀⡉⡡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡾⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⢌⡳⣤⢨⠾⠭⣀⡀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠉⠱⣀⣀⠠⠁⣴⢋⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢳⡀⠀⣀⣠⠀⣁⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈⠙⠓⢸⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⡈⢉⠁
⠀⠀⠀⠀⠀⣠⣺⣍⣉⡉⠢⣄⣳⡀⢀⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⡗⠒⠠⠐⢄⠀⠀⠀⠀⢀⣤⠶⣤⡀
⠀⠀⠀⢀⡼⠛⣁⣤⣄⡈⠢⠈⠙⠭⢽⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠈⠂⠑⠤⠴⠶⠛⣡⡶⠋⠉
⠀⠘⢿⣯⣰⡾⠋⠀⠀⠈⠢⡀⢀⠀⢘⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⠚⢿⠳⠄⡑⠦⠤⠤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⢧⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⠈⢣⠀⠉⠓⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠤⠾⠂⠈⢧⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⡟⢀⠽⠓⢄⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠆⠀⠠⠤⣀⣼⣳⣌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠃⠈⠄⠄⠀⠈⠐⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠒⠛⠓⠀⠈⢱⢮⣙⠲⠤⢤⣄⣠⣤⠤⠖⣚⡩⠖⠛⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣡⠒⠉⣁⣀⠀⠀⡂⠀⢀⢈⠉⠙⢲⡶⠖⠒⢚⠋⠉⢄⠀⢀⠏⢧⠀⠆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⠟⠁⠀⠀⠀⠀⠀⡸⠃⢀⡠⢺⡇⠀⠀⠈⠀⠈⠙⠆⠈⠀⠘⡀⢆⠈⠛⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⠀⠀⡉⢀⠀⠀⢠⠉⡠⠀⡡⠊⠀⠀⠰⡀⢸⡆⠀⠙⠢⢟⣶⠶⠴⠦⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⠟⠀⠀⠀⠀⠀⠀⠓⠋⠀⠰⡃⡞⠀⣾⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣣⡀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⣻⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⡿⢿⣿⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⢉⣉⣠⣤⣤⣶⣿⣿⠿⠟⠛⠛⢻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⠿⠿⠛⠛⠋⢉⣉⣀⣿⣿⠶⠶⠚⠛⠋⢉⣙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠟⠛⠛⠉⣉⣁⣽⣿⠶⠶⠖⠛⠛⠉⣉⣀⣠⣥⣴⣶⣶⠾⠿⠟⠛⠛⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣠⡴⠚⠛⠋⢉⣁⣈⣥⣤⣶⣶⡾⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⠏⠀⣠⣶⠿⠟⠛⠋⠉⠉⠁⠀⠀⣀⣤⠴⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡤⢶⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢸⠀⠠⣇⣀⣀⡀⠘⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⢠⡤⠶⠾⠀⠀⠉⠉⠉⡇⠀⡟⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣾⠀⢸⣀⣠⣤⠀⢠⡶⠛⠛⠁⣸⠇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡆⠈⠉⠀⢸⠀⢠⡇⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠘⠛⠋⢁⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠛⠋⠁⠀⠀⢀⣀⣀⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⠿⠿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣤⣤⣤⣶⣶⡾⠿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠇⠀⠀⠀⠀⠀⢀⡤⢀⠀⠀⣀⠀⡀⠀⠀⠘⠤⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠧⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠄⠀⡁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢀
⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⠈
⠈⢄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠈⠁⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢂⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢀⡀⠤⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⢸⠀⣳⠘⣇⠈⠀⢹⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇⠀⣿⢸⡟⣅⢀⡈⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⢀⢠⡀⡂⡄⢤⠀⣴⡈⠀⡂⢠⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡆⡇⡇⣸⠀⣾⢣⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⢀⡈⢃⢃⢛⡁⡀⡙⠘⡂⢃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠀⠀⢸⣸⠿⢀⠿⢀⡿⣇⠿⡇⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠰⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠤⠤⠖⢖⢒⠖⣲⠄⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠆⠀⠀⠀⣀⢀⡀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⢠⠚⠂⠘⠳⠒⠢⡀⠀⠀⣐⠘⠘⠒⠒⠙⠗⠀⠀⢰⠆⠐⠒⠚⠛⢢⠀⠀⠀⠁⠄⣀⠀⠀⢀⡀⠔⠁⡀⠀⠀⡀⠀⠀⣀⣀⠠⢼⠈⢻⠖⠓
⠀⠘⢸⠀⠀⠀⠀⠀⢰⡃⠀⢈⣯⠀⡀⠀⠀⠐⠹⠀⠀⠬⠀⠀⠀⠀⠀⡄⡂⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠄⡴⣰⣞⠖⠉
⠀⠈⠘⣀⠧⣠⣠⢀⡔⠃⠀⠀⢫⠀⢀⡘⢀⣤⠍⠀⠀⠈⡀⡌⢄⢠⢠⡽⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠛⢤⠞⡻⢻⡀
⠀⠀⠀⠀⠉⠚⠉⠉⡀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣀⣀⡀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⡭⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡗⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣟⠛⣛⣿⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⣁⣹⣄⠀⠀⠉⠻⢿⣾⣿⣿⣿⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⡞⣷⣾⣿⣿⡿⠀⠀⠀⠀⠀⠁⠈⠉⠁⠉⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠸⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣤⣿⡄⠀⠀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠑⠒⠛⢉⣭⠉⠙⠻⠇⠀⠀⢀⣴⡾⢛⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⡋⠁⠀⠀⠀⠤⠷⠶⣿⡿⠆⠢⠀⠀⣾⠿⢶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠴⢞⣁⣤⣤⣤⣄⣀⠀⠀⠀⠀⢠⣿⣄⣈⣿⡁⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⣿⡇⠙⠛⢻⣿⣏⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢻⣿⣶⣄⢠⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣿⣿⠻⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢀⣿⡆⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⡟⢁⡾⠉
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⢿⣿⣾⡷⠂⣼⠃
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉⣹⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠁⣼⠇
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣶⣤⣄⣀⣤⡴⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣶⣄
⠀⠀⠀⠀⠰⠾⡿⠿⠟⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣿⣿⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢳⡀⢻⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠈⠁⠈⠉⣿⠀⠀⠀⠀⠉⣿⣿⣿⡏⠀⠀⠈⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⢠⡏⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣠⣶⣿⠆⠐⢦⣤⡀⠀⠈⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⣴⣾⣿⡿⠟⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⠟⠁⠀⢠⣄⣤⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣇
⠀⠀⡠⠖⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠦⡀
⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠀⠉⠉⠒⠒⠢⢄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠳⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⣀⣀⣀⣸⠀⠀⠀⢸⣄⣀⣀⣀⠀⠀⠀⠀⢱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣸⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⡰⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⠶⠒⠒⠋⠁
⡇
⡇
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠈⠓⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠋






⠀⠀⠀⠀⣿⡀⠀⠀⣾⠀⢸⡋⠉⠉⠀⢸⠉⠉⠙⢦⠀⡿⠀⡴⠋⠉⠉⠀⠀⡜⢣⠀⠀⣿⠀⠀⠀⠀⠀⡟⠉⠉⢳⠀⠀⣴⢳⡀⠀⡴⠋⠉⠙⠂
⠀⠀⠀⠀⡇⠹⣄⠞⢸⠀⢸⠏⠉⠁⠀⢸⠀⠀⠀⣸⠀⣟⠀⣇⠀⠀⠀⠀⣸⠤⠬⣦⠀⣿⠀⠀⠀⠀⠀⡟⠉⠉⢳⡄⣠⠧⠤⣧⠀⣇⠀⠀⠠⡆
⣤⣤⣤⣤⣥⣤⣬⣤⣼⣤⣼⣶⣶⣶⣤⣼⣶⣶⣾⣥⣤⣯⣤⣬⣷⣶⣾⣴⣥⣤⣤⣼⣧⣽⣶⣶⣤⣤⣤⣷⣶⣶⣾⣥⣯⣤⣤⣬⣧⣬⣥⣦⣤⣥⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿