Startle Emojis & Symbols

⠀⠀⡠⠔⠂⠐⠒⠒⢄⡀
⠀⡜⠀⠀⢀⡤⠒⠉⠁⠈⣱
⠀⡇⠰⡠⠋⢀⠤⠒⢉⠁⠈⣷⡤
⠀⢁⠀⢣⣾⣇⠘⢡⣄⠀⣶⠈⢍⡄⠀⠀⡠⠂
⠀⠘⠀⡸⡟⠛⠁⠈⠛⣆⠀⣀⡆⢣⠀⠀⡇⠠⢀
⠀⠀⡆⡇⢳⣦⠀⠀⠀⠀⠘⠃⠀⡘⢀⠔⠉⠆⠁
⢠⠲⠴⡄⠀⠻⣅⠀⠀⠀⢈⣡⣔⠕⠁⢀⠌⠀⠀⠠⠂
⠘⠦⠔⠃⠀⠀⠀⠈⠁⢹⠣⠘⢐⡔⡔⣁⠤⠐⠂⠃⠈⡀⠈⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠂⠉⣀⠤⠐⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⠒⠒⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡄⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠈⠉⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡛⢄⠀⣠⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡠⠓⠳⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠜⠁⠀⠀⣇⣸⢆⡤⠒⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⢠⠚⢔⡫⣀⠤⠔⠒⠳⢤⠤⠤⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⣀⡸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⡀⠀⢰⣟⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣄⣀⡀⠙⠁⠀⠀⣺⡽⠀⠀⠀⠀⠈⠻⠿⠀⠘⠋⢴⣿
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣀⡴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄
⠀⠀⠀⠻⠶⡇⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠇
⠯⣵⡄⠀⢀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⣼⠀⢰⡇
⠀⠀⠀⠀⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⠀⣼⠻⡆
⠀⠀⠀⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣿⡀⠀⠀⣠⡿⠦⠿⢼⡛⣦
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣸⡇⠀⣸⠏⢀⣤⣶⡶⢛⡿
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢘⣷⣄⠀⣠⡟⠹⣇⠀⣼⠀⠀⠈⣩⡿⠛⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⢿⣄⠀⠀⠀⣸⠟⢤⡤⠴⠛⠀⠘⠉⢁⠀⠀⠹⣿⠙⠳⣄⣼⠃
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠴⠋⠻⣤⡴⠇⠈⠛⠛⠛⠉⢤⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⢷⡀⠀⢙⣷
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡾⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⣿⠁
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⡀⠠⣄⣀⣀⡀⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⢳⡀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠈⠛⢶⣤⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⡾⣭⠤⠒⠒⠦⢤⣤⣀⠀⠀⠀⠀⠀⢨⡇⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠻⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡾⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⢶⣄⣀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠴⢋⣠⠖⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣹⣶⠦⠀⠀⠀⠀⠐⠶⢚⣋⣥⠶⠞⠋⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣼⠃⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣠⡴⣤⣀⣼⠋⠀⢀⣼⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⣤⣀⠙⠷⣄⠀⣼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢨⡟⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠁⣄⠘⣆⠀⠀⠀⠀⠀⠀⠘⢷⣤⡤⠴⠖⠒⠚⢛⣛⣋⡉⠉⠉⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣧⠞⢹⣆⡿⢦⣹⡆⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡟⠉⠉⢻⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⠀⠀⠈⣷⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡿⠀⠀⠀⠀⢸⡇⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⣄⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣠⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣛⣉⣉⣩⣤⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣥⣤⣤⣴⡿⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠛⠛⠛⠛⠿⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣴⡾⢷⣆⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠉⢁⣸⡿⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗⠀⢀⣴⣾⡇⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⢸⣷⣦⡀⠀⠺⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⠏⢹⡇⠀⠀⠙⠉⣀⠙⠋⠀⢀⡀⠀⠙⠉⣀⠉⠋⠀⠀⢸⡏⠹⣿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⣿⡄⠸⣿⠀⠀⠀⠀⣿⡃⠀⠀⠘⢿⣆⠀⢨⣿⠀⠀⠀⢀⣿⠇⢠⣿⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠘⠿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠀⠀⠀⠀⠀⠀⢸⣿⣶⠿⠃⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠠⣿⡋⢙⣿⠆⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣬⣿⣦⣀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⣠⣼⣿⣥⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠉⠉⠉⠛⠿⣶⣦⣤⣤⣤⣤⣴⣶⠿⠛⠉⠉⠉⠉⠉⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣶⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠈⠉⠁⠈⠁⠀⢀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣿⠂⠀⠀⠻⢷⠿⠛⢷⠿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⣠⣶⣤⡀⠀⠀⣿⡇⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠙⠁⠀⠀⢹⣇⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠟⠉⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈



⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠁⠀⠄⠠⠂⠀⠀⠈⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠉⠀⠀⢈⠢⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣠⡾⠉⣹⡿⢢⠀⠀⠠⠄⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠁⠢⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⠰⠈⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠀⠈⠀⠠⠀⠀⠀⠈⢀⠀⠀⠁⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠠⡀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⢈⠂
⠀⠀⢀⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠄⡀⠂⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⠂⠀⠀⠂
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠰⠂⠁⠀⠀⠀⠀⠀⠈⠀⠀⢄⢴
⠀⠀⠈⡄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⠀⠄⣈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢿
⠀⠀⠀⠀⠀⠁⠀⠐⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⡤⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢔
⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠔⠈⠀⠀⠀⠀⠀⠂⢀⡄⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⣤⠢⠀⠀⣄⠀⠁⠄
⠀⠀⠀⠀⠙⡀⠀⠀⠐⠀⠀⡠⡀⠀⠀⠀⡀⠁⠂⠀⠀⠀⡇⢀⠀⠀⠀⡤⠀⠀⠁⠂⠔⠁⠂⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⠀⡄⡀⠀⠀⠰⢄⡀⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠠⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠉⢆⠀⠈⠀⠀⠀⠀⠁⠢⠀⡀⢤⠀⡙⠀⡀⠄⠀⠀⠀⠄⠈⠃⢀⠀⠐⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠐⠒⠀⠀⠠⠄⠀⠈⠉⠑⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠛⠛⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣾⠇⢸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⣠⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⡀⢸⣿⡿⠛⢉⡉⠛⣿⣿⣿⣿⠛⢉⡉⠛⣿⣿⡇⢀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⢸⡇⠸⣿⣿⣿⡟⢻⣿⣿⡟⠻⣿⣿⡟⢻⣿⣿⣿⠇⢸⡇⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⣿⣿⣿⣧⣼⣿⣿⣿⡆⢸⣿⣧⣼⣿⣿⣿⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠟⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⠻⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠋⣠⣄⠙⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣈⣁⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣄⡉⠛⠛⠛⠛⠛⠛⢉⣠⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢋⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡿⣿⣿⣿⠿⣿⠟⠻⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣼⣿⣿⣦⣤⣴⣦⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡈⠋⣠⡈⣻⣿⣿⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣯⣤⣈⠛⣁⣤⣉⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣠⣼⣷⡶⠶⠶⠶⢶⣦⣤⣀⣰⠏⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣴⠾⠛⠉⢀⠖⠒⠀⠐⠚⢦⠀⠈⠙⠻⢷⣦⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⣤⡀⠀⠀⣤⢌⠀⠀⠀⠀⠀⠈⠻⣷⡾
⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠙⢁⣀⣤⡽⠷⠶⣤⣄⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⣿⠁⠀⠀⠀⠀⣴⠞⠛⠛⠛⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠳⢦⣤⣀⣄⡀⢀⣀⣠⣷⠾⠋⠀⠀⠀⠀⠀⢺⣿⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠤⠔⠚⣿⠒⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣇⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠉⠒⠤⣀
⢠⡟⠁⠀⠈⣿⠀⠀⠀⠀⢠⠟⢷⡀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⣀⣴⢿⠉⢳⡀⠀⠀⠀⠁
⣿⠁⠀⠀⣼⠏⠀⠀⠀⠐⠁⠀⣼⠛⠳⣤⣀⠀⠀⠀⠲⠄⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⠱⡄⢳⡀
⢿⡄⠀⠀⢿⣄⣀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⠉⠀⠀⠀⠰⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠈⣷
⠘⢷⣄⠀⠀⠉⠙⠛⠷⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⣰⠀⠀⠀⢸⡆
⠀⠀⠉⠛⠶⢶⣄⠀⢀⡿⢸⡇⠀⠀⣆⠀⣠⠞⠉⠙⢳⡄⠀⠀⠀⢰⡃⠀⠀⠈⠙⢧⡀⠀⢀⠈⣧
⠀⠀⠀⠀⠀⢸⡏⠀⣼⠃⣾⠀⠀⠀⠘⣾⠁⠀⠀⠤⣼⠃⠀⠀⠀⠀⢙⡖⠋⠀⠀⠀⢳⡀⢸⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⢻⣄⡟⠀⢰⠀⢀⡇⠀⠀⡀⠀⣸⠀⠀⠀⠀⠀⠈⢧⡀⢀⡴⠀⠈⣷⠏⠀⣿
⠀⠀⠀⠀⠀⠈⠻⣦⣄⣙⡇⠀⠈⢷⣘⡇⠀⠀⢹⡞⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⣀⡼⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡇⠀⠀⠀⠈⠻⢦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⡶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠉⠉⠙⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠄
⠀⠀⠀⠈⠉⠓⠒⠢⠤⠀⠀⠀⠀⣼⠏⠀⣀⣠⣤⡶⠶⠶⠶⠶⣶⠄⠀⣀⣠⣤⣤⣤⡶⠶⠶⢶⣄⠀⠙⣷⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣴⠾⠋⠁⠀⠀⠀⠀⠀⢰⣿⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⢠⡶⠟⠛⠷⠀⠘⠃⠀⠀⠀⠀⠀⠰⠟⠛⠛⢦⡄⠀⠻⣶⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠁⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⣿⠀⠀⠀⢺⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢰⡇⠀⠀⣸⡏⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⢀⣸⣿⣤⣿⣧⣀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣿⠶⣶⣤⣿⠋⠀⣽⠋⠈⠙⣷⡾⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⣰⡟⠋⣤⣤⣶⣾⡟⠀⠀⣿⡀⠀⠀⣿⣧⣤⣤⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⡄
⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡇⢀⣴⠟⢷⣄⠀⣾⠋⠉⠉⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠙⣿⠏⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⠶⣶⠶⠶⠟⠃⠀⠀⠀⠀⠛⠿⠶⠶⠶⠾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⣶⣶⣶⣿⣶⣶⣶⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⣿⡟⠛⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⠿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠋⠁⠀⠀⣠⣴⣤⡀⠀⠀⠉⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠘⠛⠁⢹⣷⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢠⣤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⢰⣦⣄⡀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣠⣴⣶
⠀⠀⠈⠙⠁⠀⣴⡿⣿⡇⠀⠀⣴⣶⠿⠷⣶⡄⠀⠀⠀⠀⣴⡾⠿⢷⣦⠄⠀⠀⣿⡿⣷⡀⠀⠙⠉
⢠⣤⣤⡄⠀⢰⣿⠁⢻⣧⠀⠀⠈⠀⢠⡄⠀⠀⠀⣠⣄⠀⠀⢀⣤⠀⠀⠀⠀⢠⣿⠁⢹⣷⠀⠀⣤⣤⣤
⠈⠉⠉⠁⠀⠘⣿⣄⠘⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠘⢿⣦⠀⠸⣿⠀⠀⠀⠀⣼⡟⢀⣼⡟⠀⠀⠉⠉⠉
⠀⢀⣠⣴⡄⠀⠘⠻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠛⠀⠀⣴⣤⣀
⠀⠘⠛⠉⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣿⣷⣄⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⢀⣴⣿⣏⣀⣀⣀⣀
⠀⠀⠀⠀⣠⣾⠿⠛⠛⠛⠛⠉⠉⠻⢷⣶⣤⣤⣀⣀⣀⣠⣤⣴⣶⠿⠋⠉⠙⠛⠛⠛⠻⢿⣦⡀
⠀⠀⠀⣰⣿⣇⣀⣤⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣤⡀⣀⣤⣿⣷⡀
⠀⠀⢠⣿⠋⠛⠟⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠉⢻⣧
⠀⠀⣼⡟⠀⠀⢀⣤⠀⠀⠀⢴⣦⣴⣾⣶⣤⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠘⣿⡄
⠀⢰⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠈⠁⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣷
⢀⣿⠇⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣷⣾⠟⢿⡦⠀⠀⠸⣿⡀⠀⠀⠀⣿⡇
⢸⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣠⣤⣄⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⢀⣀⣾⣷⣿⠿⢿⡄⠀⢰⣿⣿⣿⣧⣶⣾⡟⢻⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⣭⡖⣹⡇⠀⠈⠿⣿⣿⣿⣿⣿⣷⣾⣰⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡟⠟⢿⡵⣉⣬⣿⣷⡄⠀⢠⣿⣿⡿⠟⠛⢿⡎⡥⢟⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠋⠙⠈⠃⠰⢲⣷⢌⠂⢺⣿⣷⠀⢨⡙⠇⠀⠀⠀⢈⠁⠀⠘⣽⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⡀⠀⡇⠀⡰⢸⠁⡭⣻⣿⣿⣿⠃⠀⢡⡀⠀⢇⡀⠀⠀⠀⢠⣴⢿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣛⠀⠀⠈⠀⢀⢄⠺⣷⣿⣿⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠐⠀⡼⢿⣿⣿⣿⢻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠀⢀⣀⣀⡉⣾⣙⢻⡯⣿⣿⣷⠀⢀⣼⡆⠀⠀⢀⣠⠀⣤⣾⣿⣿⣿⣿⢿⣿⣿⠇⠈⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣏⢥⣾⣟⡿⡙⠋⠀⡉⣯⣝⣇⠈⠻⠧⠤⠲⣿⠵⠋⠁⢹⣿⣿⡷⣯⣾⣿⣟⡀⢀⠂⢨⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠂⠀⠀⢼⣟⢿⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⢻⣿⡆⠶⠀⠐⣟⣿⢣⡀
⢠⣤⣄⠀⠀⣠⣿⢳⠞⣃⣠⣻⣷⣦⡀⣠⡶⠋⠀⠀⠠⠀⠀⠘⣴⣆⠙⠈⡡⠈⢻⢦⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⣿⡟⢉⠀⡾⠁⠄⠀⢶⣿⠀⠃⣨
⠉⢿⣞⢻⣴⡏⣿⡪⣺⣿⣿⣾⡼⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠛⠸⣿⣷⣮⣤⡄⢀⠸⣇⠀⠀⠀⠀⣾⣿⣿⣼⣿⣿⣷⣿⣿⠓⠀⢀⢴⣿⢏⠦⠀⣭
⠀⠀⠙⣿⣿⣩⣬⣿⣟⣿⣦⣜⡉⣿⣿⣿⣷⣇⣄⠀⠀⠀⢠⠆⠀⣿⣿⡿⡍⠀⢤⣄⣿⠀⠀⠀⣰⣿⣿⣿⠟⠀⢻⣿⣿⡇⡴⠀⣼⡿⠛⠎⠀⣠⣻
⠀⠀⠀⢿⣹⣿⡿⠟⠋⢹⣿⣿⣧⡿⢿⣿⣿⢿⣿⣷⣆⣤⣬⣿⣶⣿⣿⡇⢸⡁⠐⠀⣹⠀⠀⠀⢻⣿⡿⠁⠀⠀⢀⣽⣿⣿⣻⣠⡟⠀⠈⠀⢠⡟⠛
⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⣨⠟⠁⢄⣰⢶⣏⠍⠰⣙⠿⣿⣿⣿⣿⣿⣿⠀⠘⣧⡀⠀⠉⠒⠖⠢⡀⠈⠁⠀⠀⢰⣿⣿⣿⡽⢩⡉⠵⣀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣄⠀⠀⢙⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠛⠳⢤⣤⠴⠚⠁⠀⠀⠀⠀⣿⣿⣿⡿⠐⠃⣰⡻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢹⣿⠀⢴⣿⣿⡿⠿⠿⣿⣯⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⢺⡗⢣⣿⣦
⠀⠀⠀⠀⠀⠀⠘⣯⣻⡏⠨⢿⣦⣊⣿⣿⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⡨⣥⢀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⡀⢿⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣷⣿⠛⠿⣿⢿⣿⠠⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⢍⣤⡤⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠈⠋⠙⠻⠞⠚⠂⠛⠉⠉⠁⠁

⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠁⡀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐
⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⠀⠀⠀⡀⢀⠂⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠙⢄⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⠢⣄⠀⢐
⠀⠀⠀⠀⢀⡏⠀⠀⠠⠦⠀⠢⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⣠⠴⠊⠀⡄⠀⠃⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠠⣶⠃⢠⣤⢰
⠀⠀⠀⠀⠀⢠⠀⠀⠢⠕⠁⢌⣁⠞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠆
⠀⠀⠀⠀⢐⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠
⠀⠀⠀⢀⠂⠈⠓⠶⢤⣀⣀⣀⠀⣀⠆⠐⡆⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠸⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠘⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡼
⠀⠀⠀⠈⠂⠤⢤⠴⢊⠀⠙⠶⢤⣀⣀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⣄⢀⠜⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠨⠳⡄⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⢸⠦⠤⠤⣤⣤⡤⠤⠶⠖⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠈⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢠⠀⠀⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⣠⠖⠚⠁⠙⢦⡀⠀⠀⢀⠳⡄
⠀⠀⠀⠀⢀⠔⠒⠒⠒⠁⠀⠀⣼⠀⠀⢰⠀⠀⡆⠀⣈⡠⠀⠀⠉⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢹⠀⠀⢈⡼⠃
⠀⠀⠀⠀⠸⡎⢠⠆⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⢳⠀⠙⢤⡊⠀⠀⢀⣰⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠎
⠀⠀⠀⠀⠀⠉⠻⢤⣄⣠⠒⠚⠁⠈⠁⠀⠀⢀⡼⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠎⠉⠑⠒⠚⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⢀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣜⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⠀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⢀⡞⢁⡴⠒⠲⣌⠳⣴⢋⣤⠤⠤⣈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡤⠒⠲⢤⡽⠛⢋⣉⡑⢦⣄⡼⠋⣉⣉⣉⠳⣄⢹⣦⠟⢚⣉⡛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠭⣉⣾⠤⠤⢤⣾⢡⡞⠁⠀⠙⣦⢹⢁⡟⠀⠀⠈⣷⠈⣿⠟⢋⣩⣍⡙⢲⡈⢧
⠀⠀⠀⠀⠀⠀⠀⣇⢾⡀⢠⠏⣡⠖⠒⠲⣌⢻⡅⠀⠀⢠⠟⣼⣆⠳⠄⠀⢀⡿⢀⡟⢰⠋⠀⠀⠙⡆⢳⣸⠲⢤⡀
⠀⠀⠀⠀⠀⢀⡠⠬⣷⣥⡟⠠⡇⠀⠀⠀⣹⢸⡟⠲⠦⠴⠚⠁⠈⠓⠒⠒⠋⠠⠾⡇⢹⡄⠀⠀⣴⠟⣩⠭⢭⡳⣿⡄
⠀⠀⠀⠀⡴⢫⠖⡟⣩⠖⢻⡀⠳⣄⣀⣘⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠉⠓⠲⡇⢼⠁⠀⢀⡷⣸
⠀⠀⠀⠀⠳⣜⣎⣇⢧⠀⠀⢹⠆⣯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠓⣦⢴⣾⠭⣍⡲⡄
⠀⠀⠀⢀⡖⣩⠤⢭⡙⢶⠞⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢾⣁⣀⣨⣇⡽
⠀⠀⠀⢸⡸⣅⣀⣀⣹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⣩⠶⠲⢮⡳⡄
⠀⠀⠀⢠⢟⡵⠶⠮⡝⢾⡇⠀⠀⠀⠀⠀⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⠀⢸⡀⣧⣤⠤⣴⣣⠇
⠀⠀⠀⢹⡸⣄⣀⣀⣽⢸⣷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣡⠖⠛⠲⡝⣆
⠀⠀⠀⢠⢟⡵⠒⠶⣍⢻⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣷⡤⠤⣴⣣⠏
⠀⠀⠀⠸⣜⣦⣤⣄⣼⢀⡇⠀⣻⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⢀⣀⣀⣀⣀⠀⣠⡾⢫⡟⡵⠚⠛⠳⡝⡆
⠀⠀⠀⡴⢫⠖⠒⢦⣽⣿⣤⡾⠁⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠁⠈⠉⠻⣏⣀⣸⡄⣣⡤⠤⠶⣥⠃
⠀⠀⠀⢣⣹⡤⢤⡾⠁⠀⠈⢷⡀⠀⠀⠀⠀⢀⡿⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣼⡇⠀⠀⠀⠀⠀⢠⡏⠉⠉⢻⣥⠞⠋⠛⣎⢳
⠀⠀⠀⡞⣵⣛⣿⠁⠀⠀⠀⠀⠙⠛⠶⠶⠖⢿⡅⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣹⡶⣤⣤⠴⠾⠋⠀⠀⠀⠀⢻⣶⢲⡶⢧⡞
⠀⠀⢠⠟⡥⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣧⣹
⠀⠀⠸⣜⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢦⡙⡄
⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢼⣡⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠙⢦⣤⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠛⠶⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠟⠛⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⣿⠀⢀⡴⠋⠉⠀⠀⠀⠀⠈⠉⠛⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠻⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠶⠶⠶⠶⠶⠶⠶⠚⠃⠀⠀⠛⠶⠶⠤⠤⠶⠶⠶⠖⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⢀
⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣠⡶⠛⢶⡀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠉⠉⠉⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢀⡼⠃⠀⠀⠈⢿⠉⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠠⠆⣰⣧⣤⠴⠶⠖⠛⠛⠛⠛⠳⣦⣀⣤⡶⠋⠀⠀⠀⢀⣤⡼⠆⠀⠶⡆⠚⠃
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡀⣿⣦⣀⡀⠀⣠⠶⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠁⠀⠀⠀⣀⡼⢟⣀⠀⣶⣄⠀⢹⡄
⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡴⠀⠈⠉⠉⠻⣦⣁⣀⠀⠀⠀⣀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⣨⡿⣧⠞⠉⠳⣷⡌⢳⣼⠇
⠀⠀⠀⠙⠓⠺⠥⠴⣤⡤⠤⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⢍⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠭⠿⠧⣄⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢋⣤⠶⣶⣤⡀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣠⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠶⢶⡶⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠘⠻⣉⠛⠛⠻⠶⣶⡖⠲⡶⢶⡦⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡼⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣾⠉⠙⠛⠃⠀⠀⠀⠀⠉⠻⢦⣸⡇⠀⡗⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠡⢀⣩⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠇⠀⠀⠀⣀⡤⠔⠚⠉⠀⣀⡤⢶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠉⠀⠀⣀⣤⠶⠛⠉⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⣿⡄⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⠛⠋⠉⠁⠀⠀⢀⣠⠶⠛⠉⠀⠀⢠⡄⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢷⣤⣴⠶⠛⠉⠁⢤⡄⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⡀⠀⠀⠀⢻⡄⠀⠀⠹⢷⡖
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⡴⢞⣋⠥⠄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢤⣹⡇⠀⠀⠀⠈⢿⡀⠀⠀⠘⠙⠳⢦⣄
⠀⠀⠀⠀⣀⡤⠟⠁⢸⡏⠰⡯⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⣠⡼⠓⠀⠀⠀⠀⠀⢀⣼⠟
⠀⣀⡴⠛⠉⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⠶⡟⢻⡆⠀⠀⠀⣀⣤⠞⣻⠏
⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⣤⠶⠛⠉⠀⣰⠏
⠀⠹⣿⠳⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠚⠛⣇⢹⡇⠀⢀⣠⡴⢧⣄
⠀⠀⠈⠳⣄⡀⠀⠉⠙⠛⠓⢶⡶⢶⡤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠒⠛⠛⠋⠉⠉⢀⣴⠦⣤⣀⣀⡿⠈⠳⠶⢋⣁⣠⡴⠟
⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣉⣉⣀⠀⠀⠰⢯⣭⣥⡤⠴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⠀⠀⢹⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⣷⡀⠰⣶⠶⢤⣤⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠐⢶⣤⣷⣤⣷⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠳⣄⠈⠛⠳⡄
⠀⠀⠀⢀⣠⠴⠶⣶⣿⣥⣀⣉⣉⠀⠀⠹⡟⠛⠛⠫⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠙⠓⠚⠃
⠀⠀⠀⠈⠓⠶⠖⠾⠛⠖⠛⠛⠉⠙⠛⠛⠻⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠖⢻⢷⡶⢦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⢠⣴⣦⡀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠈⠁⣸⡇⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⢿⣿⠀⠀⣶⠾⠷⣶⠀⠀⠀⠠⡶⠿⠷⡶⠀⠀⣿⡿⣦⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠀⢸⣿⠀⣿⡀⠀⠀⢰⣦⠀⠀⠰⣦⡀⠀⣴⡆⠀⠀⢀⣿⠀⣿⡇⠀⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⣦⣽⡇⠀⠀⠈⠉⠀⠀⣠⣽⡇⠀⠉⠁⠀⠀⢸⣯⣴⠟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣈⣁⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢾⣏⣹⣷⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⡿⢷⣤⣀⠀⠈⠉⠉⠁⠀⣀⣤⡾⢿⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢁⣀⡀⠀⠀⠀⠉⠛⠛⠿⠶⠶⠿⠛⠛⠉⠀⠀⠀⣀⠀⢈⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⠿⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢠⣦⠀⠀⠺⣦⡾⢷⣴⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣤⣄⠀⠀⢸⡇⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠉⠀⠀⠘⣿⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠠⣶⣦⣀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠸⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠋⠉⠉⠛⠓⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⣠⠤⣤⡀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢀⣀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠉⠃⠀⠀⠀⣠⢶⡇⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⣼⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡟⠀⢹⡆
⠀⠛⠓⠀⠀⠀⣷⠀⠀⢷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢦⠀⠀⠀⢰⠀⠀⠀⠀⠀⢰⠇⠀⢠⡇⠀⠀⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠘⢦⣀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⠞
⠀⠠⠴⠂⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠁⠀⠀⠀⠀⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡿⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡽⣦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣠⡾⣥⣤⣀⣀⣀⣀
⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⢰⠯⣄⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡤⢤⣷⡀
⠀⠀⢀⡏⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⣇
⠀⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⢤⣀⣠⠶⣄⣀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡀
⠀⢠⡏⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣧
⠀⡾⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢦⣀⡴⠒⠆⠀⠀⠀⠀⣧⠀⠀⠀⠀⠸⡆
⢰⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢻
⣾⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸
⡏⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠳⠶⠋⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⠖⠋⠁⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡞⣡⠞⠁⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤
⠀⠀⠀⠀⢀⡟⣴⠃⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⣸⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡘
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣦⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢱⡞⡇⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠈⠉⠉⠓⠲⠾⠷
⠀⠀⠀⠀⢼⡇⢶⠀⠀⠀⠀⢸⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣿⡇
⠀⠀⠀⠀⣼⡗⠛⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢠⠖⠐⠂
⠀⠀⠀⠀⣿⠓⢶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢾⠁
⠀⠀⠀⠀⣿⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠠
⠀⠀⠀⠀⢿⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢸
⠀⠀⠀⠀⢰⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡿
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⢈⠓⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⡖⠒⠦⠤⠤⠄⠒⠒⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠊⢹⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀
⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠛⠲⠦
⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⡿
⠀⢰⡇
⠀⢸
⠀⡾
⢀⡇
⢸⠇
⠸
⡇
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⡉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀
⠀⠀⠀⠀⠀⡰⠀⠈⠀⠰⠖⠀⢊⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⣴⣉⣝⣳⣄⠀⠧⡶⢤⡦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣲⡁⢞⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡋⠉⠉⠉⡇⢀⠀⠀⠂⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢈⣄⠸⢦⡤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⣇⡘⠁⠀⠀⠀⡏⢂⡀
⠀⠀⠀⠀⠀⠐⠲⠂⠀⠒⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠄⠋⠁⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠀⠀⠆⠀⡀
⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢿⣿⣿⣦⠀⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⣿⠟⢱⣶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠇⢀⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠻⣿⣿⣿⣿⠗⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣶⠒⠒⠒⠒⠒⠚⠃⠀⢸⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣋⣀⣀⣀⣀⣿⠀⠀⡤⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠉⠉⠉⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠟⠀⢸⡟⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣿⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠶⠒⠒⣇⢳⠶⠲⣤⣤⣴⠐⢰⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣻⠈⠉⣉⣠⣶⣄⢨⣧⣤⣀⡤⠀⡙⠀⣤⡉⢉⣼⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣲⣿⣶⣾⣿⣿⣿⡿⢿⣿⣿⣿⡷⣼⣿⣿⣿⣿⣿⣦⣴⡾⢷⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⢙⣿⣿⡿⣿⣿⣿⣥⣼⣧⡀⣀⣿⣬⡁⣹⣿⣿⢿⣿⣿⣄⡀⣀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠉⠀⠉⣿⣿⣿⡇⣨⣿⣿⣿⡏⢀⠈⣿⠛⣿⣿⡍⣀⣹⣿⡁⠟⢿⣿⣷⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣤⣶⢠⣾⣿⣿⢏⣷⣿⣯⣩⡵⢻⣦⣼⠻⣦⡈⡾⢷⣿⣿⣿⡿⠗⢀⡀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⣶⣿⣿⣯⣦⣼⣿⣬⠷⠮⣄⣿⡅⠛⠾⡀⣄⡾⢷⣌⢻⣧⣶⡌⠿⣶⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠰⣿⠛⣿⣿⠃⠸⣟⢿⠀⠘⣿⢿⡏⠀⢸⡟⣿⠃⠀⢸⠇⣩⣿⡟⢠⢌⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⢀⣽⣷⡫⢙⣦⣤⠷⡿⣶⣾⣿⣸⣿⣶⣻⣧⣽⢧⡴⣿⣆⣠⢨⣿⢏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣻⣟⣾⣿⣿⡞⢻⣿⣿⡿⠛⠉⠉⠉⠛⠿⢷⣿⣿⠻⣾⣯⣧⣼⣿⣶⣨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⣾⣿⣿⣶⣶⠾⠟⠻⣟⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠛⡿⠀⣿⡇⠀⠀⠀⠀⢸⡇⠈⣏⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⢰⡇⠀⣿⡹⣄⡀⢀⡠⢃⡿⠀⣿⡀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⢀⣼⡷⠠⢿⡜⣎⠻⠋⠀⢀⡧⠰⢿⡷⢄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠀⠀⢠⡆⠀⠠⠀⠀⣬⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⢴⣾⠃⠂⡁⠀⡀⣸⣷⡶⣶⣿⣯⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠿⣣⡾⣄⣀⣀⣷⠀⣴⣷⣿⣦⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠻⠁⠈⣹⢻⢻⠟⢿⣏⠻⡜⢷⣾⡙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⢡⣿⢀⡆⢀⠀⡅⠀⢸⠇⡼⢸⠀⠀⢈⡾⣿⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣋⣠⠟⠁⠛⢦⣤⣤⣄⡀⠀⢀⣁⣀⢶⣻⣏⣤⣼⣿⣽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⢠⡟⠀⠀⠀⠀⠛⠛⠋⣥⣶⣷⡭⠉⠍⢰⣿⣿⣯⣿⣿⣷⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠐⢢⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⣾⣿⣿⡿⠛⠛⢷⡀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠎⠁⠀⠀⠀⠀⠀⣤⣠⣤⡼⠛⠛⠀⠀⠀⣨⣿⠁⠀⠀⠀⠈⢳⡏⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠈⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠻⠆





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠳⢦⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠲⢦⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠷⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣉⠙⠲⣤⠏⠀⢀⣀⣤⣼⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠼⣉⡛⠳⣴⣶⠀⣴⠿⠿⠟⢻⢹⠁⡏⢹⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣾⣀⡏⢙⣿⡏⢸⠀⢸⡆⠀⢰⢸⢸⠀⡇⢸⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⣤⣇⣀⠀⣼⣿⣽⣉⣛⣿⠏⠰⠀⡀⢸⣧⣦⡾⢾⠿⢿⣇⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⢙⣽⠟⡇⢸⣛⣿⠿⠂⠚⠈⢁⣈⣧⣤⢴⣞⠷⣦⣇⡉⠓⠳⢤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⣠⢤⣼⠛⠊⠉⣡⣿⣧⡤⠶⠞⠛⡛⠛⢿⣶⣶⣿⣿⡿⣿⣿⣷⣶⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⣀⣼⣧⣶⣾⣿⣿⣻⣷⣄⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡫⣻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣽⢿⣿⣿⣿⡏⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⠿⠿⠛⢛⠋⣩⠿⢦⣤⣄⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠉⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⢸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠷⣆⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣿⠆⠀⠿⠿⣦
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠐⠖⠘
⠀⠀⠀⠀⣰⡿⠋⣁⣀⠉⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⣤⣼
⠀⠀⠀⠀⣿⠁⠈⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢿⣆⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠿⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡟⠛⢻⡟⠻⣷⡀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠘⣧⠀⠘⣧⠀⢸⣷⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⢿⡀⠀⢿⡀⠀⣿⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠋⠀⠀⠀⠀⣿⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠙⠛⠻⠿⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⢀⣼⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣄⠀⠀⠀⠀⢾⡏⠀⣀⣴⡾⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠸⣷⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠈⠻⣿⠋⠁⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢹⣷⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠈⢳⡄⠀⠀⠀⢹⣧
⠀⣀⣀⣀⣀⣀⣀⣠⣴⡿⠃⠀⠀⠀⠀⣠⡾⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣼⡟⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⡾⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⢀⣿
⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⡀⢀⣠⣾⠋
⠀⢹⣿⠛⠿⠿⢿⣿⣷⡀⠀⠀⠘⣷⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡟⠉
⠀⠀⠛⢷⣶⡶⠟⠋⠹⣷⣀⣀⣠⡿⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠸⣿⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠠⣤⣤⣤⡶⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡉⣿⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⠿⠿⣿⠀⣿⡿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢰⣿⠀⢻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣇⣀⣀⣀⣀⣸⣿⠀⢸⣇⣀⣀⣀⣀⣰⣿⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣍⢻⣄⢹⠟⠛⠛⠛⢻⣿⠀⣸⡟⠛⠛⠛⠻⡟⢠⡟⢉⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢙⡉⠋⠉⠉⠀⠀⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⠀⠉⠋⠉⠛⡟⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣟⢉⢛⡙⠉⠉⠛⠋⠙⣋⠉⣛⡋⢉⣿⠆⣿⡋⠛⣋⠛⢉⡛⣉⣛⡋⠉⠙⢋⡙⢛⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡀⡤⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⢣⡀⢀⡀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠄⡀
⠀⠀⠀⠀⡏⠔⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠢⣀⠑⢄⡀⠀⠀⡀⠄⠐⢈⡁⠤⠀⠐⠐⠉⢔⠂⠀⠀⢀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠂⠠⢄⡀⠀⠀⠀⠀⠁⠢⣀⣰⡆⠀⠈⠈⠁⠀⡒⠋⠀⠀⠀⣀⠠⠀⠐⠈⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠁⠀⠀⠀⠀⠀⢀⣀⡠⠤⠀⠀⠈
⠀⠀⠀⠀⡀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⡄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠒⠀⠉⠀⢸⠀⠘
⠀⠀⠀⠀⠂⠸⠈⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠠⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣯⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢄⡀⠀⠀⣀⣀⢰⠀⠔⠐⠺⠟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠛⠿⠁⠀⠀⠀⠀⠀⢀⠈⠀⠘⠋⠿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⠃⠀⠀⠀⡀⠀⢠⣶⠙⠀⢰⠆⠀⠀⡟⠁
⠀⠀⠀⣨⡤⠶⢤⣤⡤⠤⠤⠶⠶⡶⠒⠒⠒⠒⠶⠶⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠾⠃⠀⠀⣧⡀⠀⠀⠀⡀
⠀⠀⣾⠁⣇⣠⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠁⢹⡄⠀⠀⡇
⠀⠀⠹⣄⠀⣀⡷⠋⠉⠉⠉⠙⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠰⡀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠦⠤⠞⠀⡴⠋⢹⠚⢳⡀
⠀⠀⠀⢸⠉⡏⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠀⣀⠀⠀⠀⠀⣀⣤⣞⣁⣠⣤⡤⠾⠃⢐⠊⠀⠀⡇
⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡠⠄⠂⠐⡖⠉⠀⠈⢋⠉⢉⠍⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⠐⠊⠀⠀⠀⠀⢠⠀⠀⠀⠘⡤⠶⠤⠤⠤⠴⠶⠖⠚⠋⠉
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⠑⠒⢲⠖⢣⡀⠀⠀⢀⠀⠀⠈⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠋⠀⠀⠙⢤⡴⣭⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠘⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠞⠁⣸⡄⠀⠀⢿⠀⠁⢸⡇⡀⠠⠀⠀⠂⢉⡀⠄⠀⠐⠈⠁⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠶⢾⣥⠴⠟⠁⣇⠀⠀⠿⠀⠓⠈⣁⣠⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⢸⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠃⠀⠀⠙⠅⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠀⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠇⡴⢀⡄⣠⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣾⣧⣾⣤⣇⣞⣰⠋⡼⢡⡶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⡋⠉⠉⠉⠙⠛⠻⢷⣿⣠⡏⢰⠇⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⣟⠦⠙⠦⣄⢀⡀⠀⠀⠀⠀⠉⠻⣧⣼⢋⠜⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠉⠓⠦⠀⠀⠀⠀⠈⠙⢯⣰⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⣬⣍⣻⣄⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢾⣿⣿⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣏⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣿⣿⣿⣿⣿⢿⣿⠉⢉⣼⣿⣿⠏⠀⠀⡼⣿⣿⣥⣌⡻⢦⡀⠀⢨⣼⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣿⣿⣿⡿⠃⠀⠈⠛⣩⣿⣿⠃⠀⠀⢴⠁⠸⡿⣿⣿⣿⣾⣿⠖⣤⡏
⠀⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⡶⠂⠀⠀⢠⣾⡿⠁⠀⢀⠀⡟⠀⠀⠻⣌⣴⡟⠉⠁⣠⣿⣠⣄
⢠⣴⠾⡿⠉⣿⠃⢠⡿⠋⣿⣿⣷⣿⣁⠀⢀⣾⠟⠀⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡏⣩⣿
⢸⡏⢠⠃⣸⠇⠀⡿⠁⣸⣿⣿⣿⣏⣰⣾⣿⠋⠀⠀⠀⣉⣙⣿⣂⢀⣤⣶⣦⣤⣤⣴⣿⣯⣾⡿⠃
⢸⣤⣾⣴⣿⢀⣼⣃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⠃⣰⠟⢁⡼⠉⢩⡿⠻⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣝⢿⣷⣍⠻⣝⢿⡻⣿⣟⣿⡿⠁⣰⠃⢀⣾⠁⣠⡟⢀⣼⣿⣯⡻⣮⡻⣿⣿⣝⠻⣝
⢸⣿⡿⣿⡻⣿⣝⢯⡻⣟⢿⣝⢝⢮⡳⣍⠳⣕⣮⡳⣝⢮⡻⣝⢿⣾⣿⣴⣿⣧⣴⣿⣶⣾⣝⠻⣟⢿⣮⡻⣮⠻⣿⢷⣌
⣸⣿⣝⢮⡛⢮⡻⢷⣝⢮⡳⣝⠳⣝⡮⡪⡻⣮⡻⣯⡪⡳⣝⠢⣕⢝⢿⣿⡷⣍⠻⣿⢯⡻⣯⡳⣮⡳⣌⠻⣮⡳⣌⠳⡝
⣿⣗⢍⠳⣝⢶⣝⢦⡙⢷⣌⠪⡑⢌⠻⣮⡢⡈⠻⣮⡙⢮⡪⡓⢬⡳⣝⢮⡻⣮⡳⣮⡳⣝⢮⡻⣮⡻⣮⡳⣌⠻⣌⢳⣌
⣿⣝⢷⡕⢌⠳⣝⢷⣝⢦⡙⣷⣌⠢⣑⢮⠻⣮⡢⡨⡻⣦⡱⣌⢦⡙⣮⡢⡙⢮⡻⣮⡻⣮⡳⣝⢮⡻⣮⡻⣮⡳⣌⠳⣝
⢿⢿⠳⡝⠢⠑⠌⠳⡙⢷⡝⢮⣿⣷⣜⢦⡑⣌⠻⣾⣮⣯⣿⣾⣷⣽⣮⣿⣮⢪⡻⣮⠻⣮⠻⡎⢣⠙⣿⣿⣮⡻⣜⢷⣌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠒⠒⠲⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⣄⣀⣠⣀⡀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠈⠛⢦⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠀⠈⠉⠙⠛⢶⣄⡀⠀⠀⠈⢻⡄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⠀⠀⠀⣰⣿⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣿⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⣿⠀⠀⣴⠋⣿⢀⡼⠋⠀⠀⠘⠛⠳⠀⠀⠀⠀⠈⢷⡀⢀⢸⡇⠀⠘⣧
⠀⠀⠀⠀⢀⣤⠶⢾⡇⠀⠀⠀⠀⠀⠀⣾⣿⣠⡞⠁⠀⠛⠋⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢷⣿⠛⣦⠀⠀⠘⣧
⠀⠀⠀⢀⡾⠁⠀⢸⡇⠀⠀⠀⠀⠀⣼⠋⠻⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠀⠀⠀⠈⠷⣄
⠀⠀⠀⢸⠇⠀⠀⠸⣇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠞⠙⠳⠶⠦⠤⠤⡼⠿⠶⠛
⠀⠀⠀⢿⠀⠀⠀⠀⠙⣦⡀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠉⢹⡆⠀⠀⠀⠀⠀⠀⢀⣸⡃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⢨⣷⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠈⣧⠀⠀⠀⠀⢹⣄⠙⠻⢦⣀⡀⣠⡀⣀⠀⠀⠀⠀⠘⢧⣄⣠⡾⠃⠀⠀⠀⣼⢿⡟⠿⠛⣿
⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⠉⠛⠶⠛⣿⢻⡏⣿⡟⣇⣤⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡿⠈⠁⠀⢀⡟
⠀⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⢻⡈⡧⢸⡇⢻⡏⣷⣤⣀⣀⣀⣤⣤⣴⣶⢿⡟⠁⠀⠀⠀⣼⠛⢦⡀
⠀⠀⠀⠀⢸⠇⠀⣰⠟⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠉⠻⣯⠙⠛⢷⣿⣅⣸⡇⠀⠀⣀⣼⠃⠀⠀⠻⣦⡀
⠀⠀⠀⣠⣟⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠶⣦⣀⠀⠀⠀⢘⣷⠴⠟⠀⠈⠉⠙⡟⠋⠉⠈⠻⣦⡀⠀⠈⠻⣆
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣹⠟⠛⠋⠙⣷⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠻⣄⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⡏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⢷⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠙⠦⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⡴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⢿⠿⣿⣿⣿⣿⣿⣿⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⢸⠉⠛⠙⠛⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣾⣾⣤⣼⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢻⢻⢿⣿⡂⡀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⠀⢹⣗⣷⣶⡇⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⠀⠀⢸⡊⣿⣿⡷⡷⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⢠⣸⣕⠟⠁⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡿⢾⠼⣽⡃⢠⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣦⣼⢠⡄⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⢸⡀⢻⣿⣧⣿⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⡇⠀⢸⡄⣻⣮⡟⣏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠃⠀⢸⠮⡿⠁⠂⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠁⠐⢻⠏⠀⠀⠀⠚⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⣿⣟⣛⣛⣛⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⢳⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣯⣿⣷⣈⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠟⣉⠉⣩⠍⣋⣷⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⢋⡉⢉⡭⣹⡇
⠀⠀⠀⠀⢀⠤⢤⣤⡤⣶⡾⢛⡀⢅⠓⢘⢰⣶⣿⣿⣩⡾⣿⠀⠀⠀⠀⠀⡠⠤⢤⡤⢤⣶⡟⣃⠨⡘⠆⡉⣾⣿⣿⡇
⠀⠀⠀⠀⠈⢦⡀⠙⣿⣿⢉⣈⣓⠠⣄⠘⢿⣿⣟⣵⡿⢀⣿⠀⠀⠀⠀⠀⠹⣄⠈⢻⣿⡟⣁⣙⣃⢤⡀⠹⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠉⠣⣿⠇⣹⣞⣿⣿⣿⣦⠘⡽⠉⠉⠀⢰⣿⠀⠀⠀⠀⠀⠀⠈⠙⢼⣿⢁⣷⣿⣿⣿⣷⡤⢋⠏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣋⣭⣭⣵⡿⠉⠉⡳⠔⠀⣠⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣩⣽⣭⣾⠏⠈⢉⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣤⣅⣀⠀⢈⣀⠀⢈⠿⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⣬⣀⡀⠀⣁⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣶⣿⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠷⣶⣶⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣶⠒⠒⠛⠋⠁⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⢩⣿⣿⣿⡿⠟⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⢀⣿⠿⠛⠁⠀⢀⣾⣿⣿⣿⠿⠟⠛⠉⣰⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠾⠛⠉⠉⠀⠀⠀⠀⣰⡿⠟⠋⠉⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠻⣆⠀⠀⠀⠀⠀⠀⠁⢀⣤⣄⡀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣀⣠⡆⠀⢀⣀⠀⠀⠀⠀⡟⠉⠉⡓⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⣤⡀⠀⠀⠈⠓⢲⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⡾⠃⠀⠀⠀⠀⠱⢶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠘⣷⡤⢀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠉⢀⣼⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⢀⣴⠞⠓⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⡟⠻⣿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣤⡶⠿⢿⡄⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠟⠃⠀⠀⠀⠳⡀⠁⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣈⣻⣿⡿⠛⠀⠀⣀⣠⣤⣶⡿⠛⠁⠀⠀⠀⠀⢀⣼⣄⡀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣹⠙⠛⠛⠿⠿⢿⣿⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀⢠⡾⠃⠈⠉⠑⠒⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢻⡀⠀⠀⣀⣤⣴⠚⠉⠀⠀⠉⠲⠤⠴⠶⠶⠛⠋⠁⠀⠉⢻⢆⡀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠃⠔⠚⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠹⣦⣠⡾⠋⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠁⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣀⣠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣴⡶⠿⠟⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠿⣶⣶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣶⣰⣶⣶⣄⣶⣶⣦⣶⣶⡄⣶⣶⣆⢀⣶⡆⠀⣶⣶⡄⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣶⣈⣿⣶⣏⣿⠀⡉⢸⣿⣿⠀⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⢿⣿⣿⣾⣿⣿⡋⠉⠉⠉⠛⢿⣿⣷⡛⠿⢻⡆⢿⠉⠁⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⢻⣿⣷⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢻⣿⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⣼⣿⣿⢹⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢻⣿⠸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⢈⣧⣆⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⠟⣸⠿⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢫⠁⣰⣇⣿⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⣿⣿⣿⣿⣯⣥⣀⣭⣴⠟⣹⢿⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⢿⣯⣿⠞⠛⣿⣿⣿⣦⣿⣾⠃⠀⠈⡿⢿⣿⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⣿⣿⠠⠤⣿⣿⣿⣿⣿⠏⠀⠈⣴⣧⡼⣫⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢐⣀⢻⣿⣿⣄⣀⣿⣿⣿⣿⠋⢀⠀⠰⢻⣿⣿⢵⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢻⣿⣿⣿⣿⣿⣿⣿⠌⠁⢀⣠⣦⠀⠸⣿⠝⡘⣟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣘⢿⣿⠿⠿⠯⣉⣁⣤⣶⣿⠟⢻⣀⣶⣿⢷⣌⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⢿⣿⣿⣿⣿⣿⣿⡿⡟⠋⢩⣴⣻⢿⣿⣧⢸⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣈⣉⣉⣉⣉⠀⠀⣿⣿⣿⣝⢻⡾⣿⣿⣼⠟⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢿⣿⣿⡏⠀⠀⢿⣿⣿⣿⡻⢇⡝⣿⠁⠚⠳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣸⣿⣿⣷⠀⣤⣾⣿⣟⡿⢟⣯⠞⠑⠄⠑⠒⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣾⣿⣿⣿⡿⠼⠟⠛⠋⠉⠁⠀⣿⣿⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠈⠁⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣿⡟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡋⠙⢫⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢜⣿⡁⣀⡤⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣾⡟⠀⠉⡀⣿⣿⠻⢧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢉⠉⢋⣵⠀⣤⣴⣿⠻⠿⠏⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⠛⠟⡅⠄⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡉⣻⣿⠀⠀⢠⠤⠤⠤⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⢘⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⠣⣬⡙⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢻⡗⠚⡇⠀⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠛⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠽⠟⠉⠵⠘⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡤⠖⠁⠀⠸⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣹⡝⠷⣶⠶⠇⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠨⡟⠛⠁⠨⠟⠗⠶⠒⠗⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣜⣠⣤⣤⡄⠀⠀⡀⢸⠒⣦⠧⠀⠤⠀⢀⣄⣀⡀⠀⢨⡟⢦⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢳⣤⣶⣾⡵⣿⣍⢠⠲⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡾⣋⡤⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⡿⢿⠋⠀⠀⠀⠀⠀⠒⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⢀⠤⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠀⠀⠄⠒⠤⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⢀⠑⡀⢸⠀⠀⠀⠀⠀⠒⠤⡤⠒⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠂⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⢆⠀⠀⠛⣠⠃⣸
⠀⠀⠀⠀⠀⠀⡠⢀⠀⢀⡠⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⡂⠄⢀⣀⠠⠂⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠀⢀⣀⠀⡄⠀⠀⢉⠀⠀⠀⠀⠀⠀⢄⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣤⠀⠀⡦⠀⠀⠀⠀⠁⠀⡠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢇⠀⠀⠀⠲⡁⠠⠀⠀⠀⠀⡠⠂⠒⠒⠊⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠊⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠘⠂⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠘⠃⠀⠛⠉⢁⡄⠀⡎⢣⢸⠉⠀⠔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠢⢠⠒⠂⠠⠒⢆⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠁⠈⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠁⠃⠀⠰⠀⠈⠈⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠘⠀⠈⠀⠐⠂⠸⠀⢠⡄⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣠⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⢩⣭⣭⠉⡭⢿⠍⢩⣭⣍⠈⢁⣵⡌⠉⣭⢭⡍⣩⣭⡍⣿⣿⣷⣿⣶⣂⡤⢄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⢸⣧⡄⠘⠷⣶⣤⣿⠀⠋⠀⣸⣏⣷⠀⢿⣤⠟⣿⣀⡀⣿⣿⣿⣿⣿⣿⣿⡽⢖⣀⡀
⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⢨⣷⣶⠄⣤⣴⠟⠙⠷⠶⠢⡿⠋⣽⡆⢼⡇⠀⣿⣤⡄⢿⣿⣿⣿⣿⢟⣿⣿⣻⡵⠖⣂⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣠⣍⡻⠿⣿⣿⣿⣿⣭⣿⣯⣥⠤
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡟⠻⣷⣮⣝⡻⢿⣿⣿⣷⣶⣋
⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠇⠈⡆⢹⣿⣿⣷⣬⡛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⢾⣽⣿⣿⣿⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢠⡇⣾⠁⠃⣿⠛⢿⣳⣬⢻⣿⣿⡍
⠀⠀⠀⠀⢽⠿⣯⣿⣿⣿⡇⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠀⠘⡇⣿⠘⠀⠉⠈⢸⣿⣿⣼⣿⣿⣿⡆
⠀⠀⠀⠀⢰⡿⡿⣿⣿⣿⣧⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡇⡇⠀⠀⠀⠀⡜⣿⣿⡏⣿⣿⣿⣷
⠀⠀⠀⠀⠐⣺⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡄⠀⡇⠁⠀⠀⠀⠀⡇⣿⣿⡇⣿⣿⣿⡟⠆
⠀⠀⠀⠀⢚⣫⣾⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠀⡇⢰⣦⠀⠀⠀⡇⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⡇⠀⡇⢸⠈⠀⠀⠀⡇⣿⣿⡇⣿⣿⣛⣿⠄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⢧⠇⢸⠀⠘⠀⠀⡇⣿⣿⡇⣿⣿⣟⣧⡄
⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⣷⣶⣦⡀⠀⠘⣿⣿⣿⡼⠀⢸⠀⠀⠀⣶⡧⣿⣿⡇⣿⣿⣿⣟⡀
⠀⠀⠀⠘⣩⢾⣾⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣧⠀⠀⣿⡇⡿⣧⡄⠀⡄⢀⣤⣿⡇⣿⣿⡇⣿⣿⣿⣷⠄
⠀⠀⠀⠈⠵⣫⣽⣿⣿⣿⣿⢸⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠤⣽⠃⠀⠀⣿⡇⣷⣿⡇⠀⡇⠙⢿⡟⠁⣿⣿⡏⣿⣿⣿⣭⡅
⠀⠀⠀⠠⢞⡿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡿⠀⣧⢳⡀⠀⣿⡇⣿⣿⡇⠀⡇⠀⣿⣷⠀⣿⡿⣧⣿⣿⣯⣿⣒
⠀⠀⠀⠐⣫⣾⣿⣿⣿⣿⣿⢸⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠋⡁⠀⣿⠿⡇⠀⣿⡇⣿⣿⡇⠀⠁⣤⣿⢸⢸⣿⣟⣿⣿⣿⣿⣭⣅
⠀⠀⠀⢈⡿⣿⣿⣿⣿⣿⣿⠘⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠋⠀⠀⢀⣿⡇⣿⣿⡇⡀⠀⣸⣿⢸⢸⣿⣯⣿⣿⣿⣿⡧⠄
⠀⠀⠀⢋⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠘⠉⠁⠀⠀⠀⠀⠐⠂⠀⠀⢠⠃⠀⠀⢀⠈⠉⢿⣿⣿⢇⣷⣆⣿⣿⣸⣾⣿⣅⣿⣿⣿⣷⠶⠶⠂
⠀⠀⠀⢰⢫⣿⣿⣿⣿⣿⡿⠁⠀⢠⠇⠀⠀⠀⠰⠀⠀⠀⠠⠀⣶⣼⢶⣦⠀⠀⠆⠀⠈⢿⣿⣿⣟⣿⣿⣿⢸⣿⣿⡅⣿⣿⣿⠿⣛⠥
⠀⠀⠀⠀⣻⣿⣿⣿⣿⡿⠁⠀⢠⡏⠀⠀⠀⠀⡀⣀⠀⠀⡀⠀⢸⣿⣸⣿⣆⠀⠸⡀⠀⠈⢻⣿⣯⣻⣿⣿⣾⣿⣿⣋⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠐⠿⣿⣿⣿⡟⠀⠀⠀⠼⠀⠀⠀⠀⢀⢁⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢣⠈⢆⠀⠹⣿⣿⣿⣿⣿⡿⣛⣭⣾⣿⣿⣿⡭⠖
⠀⠀⠀⠀⢘⣿⣿⠋⠀⠀⠀⠎⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠈⠇⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣵⣾⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⡉⠈⠀⠐⢣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠒⢄⠀⠀⠈⢑⠆⡠⠄⠀⢜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⡀⠘⠄⠈⢐⢀⠀⠡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⣀⡀⠀⠣⡀⠳⠎⠁⣈⠆⢀⡷⠁⠀⠀⠀⠀⠀⠀⠤⣐⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡈⠧⠤⠚⠀⠘⣓⢈⠑⡆⠀⠀⠉⠈⠐⠂⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⢠⠀⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⡖⠀⠉⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⢢⡄⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢄⠈⡌⠀⠁⠢⠜⡄⠐
⠀⠀⠀⠀⠀⠀⢀⠠⠆⠀⠄⣈⠢⡁⠺⡄⠀⠀⠀⢁⢧⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⠄⠐⠂⢈⢠⣈⠆⠈⠐⠂⠉⠁⡀⠀⠀⡞⡩⠃
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⢀⠃⠮⠄⠁⢅⢄⠒⡄
⠀⠀⣾⠉⠑⣄⠃⠈⠐⠄⣴⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠣⠕⠂
⠀⠀⠈⠛⢶⣿⡣⡀⠠⠑⠨⢃⣀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠙⠣⣒⠒⠤⠴⢏⡰⠳⠤⣦⣄⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡀⠙⢄⠀⣿⡥⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⠼⠀⠁⠒⠊
⠀⠀⢀⣀⡀⣀⠀⣀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢰⡉⠀⠀⠀⠀⠤⠤⣀⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠔⢉⠀⠂⠙⠛⠁⠀⠀⠈⣤⠦⣠⠤⣙⠲⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⡨⢄⣀⢤⠂⠀⣤⣀⠀⠀⠀⠀⠙⠲⢌⢳⡘⢆⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠚⠃⣰⢋⡖⠁⠈⢉⠔⣩⠞⠻⠂⠀⠀⠀⠀⠀⠀⡀⠹⠀⡇
⠀⠀⠀⠀⠀⣠⠎⠁⠇⠘⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡀⠒⠚⠦⡀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠅⠀⢠⠀⠀⢸⠀⢈⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⢿⡀⢳⠀⡆⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠃⠀⠀⠀⣜⠀⢀⡌⢀⡞⠀⣀⡀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠁⢠⠛⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⡾⠎⢠⠄⢀⣾⠃⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡘⢆⠧⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠈⣵⡖⠈⡀⢰⠇⢠⠎⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡵⠁⠀⠚⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡸⠋⢀⢈⣧⠀⡄⠀⠀⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣫⠴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⢉⢀⠈⣴⠙⠄⠹⠀⡄⠇⠈⠃⠀⠀⠶⢶⠂⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⣿⠇⠀⠀⠤⠀⠀⠀⠀⢸⡴⠖⠛⠋⠛⠶⣤⣀⡀⠔⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠈⡐
⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠂⠀⡄⠁⠀⠀⠀⠒⠶⢄⠀⠀⠀⠀⡌⠀⠀⡤⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢡⡀⠀⠀⠀⠁⠀⢠⠶⡘⠙⣄⠀⠀⠀⠀⢀⡤⠓⠢⢀⡔⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠆⠈⠁⠀⣆⠀⠄⢠⣈⠊⠀⠀⣟⢰⣂⠀⢰⠋⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢀⢠⡆⠀⡇⢀⠴⣿⠇⠀⠀⢰⡿⠀⠿⡀⣭⠒⠂⠤⠄⢀⣀⣀⠎⠀⢀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠸⣯⣷⡘⠋⣿⠀⢻⡄⠀⠀⢰⡅⠀⠀⢁⠀⠀⢃⠀⠀⠀⠀⠀⠀⡄⢸⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠙⢧⠙⣇⠈⠳⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠠⡏⠀⢸⠀⠀⡀⠀⣆⠀⠀⠃⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⠀⢼⠀⡖⠁⣸⠙⠀⣦⠀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣌⢁⡦⠀⣉⡳⣾⡆⠠⠤⠤⣄⡀⠀⠀⠀⣀⣀⣤⢼⡇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢸⡇⢀⣿⢰⡽⠃⠀⠀⠀⠈⡍⠁⠀⠈⢹⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠘⠁⢿⡁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠈⠶⠒⠒⢺⡏⠉⠙⡃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠘⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠐⣸⠤⡆⠿⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠾⠋⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣿⣶⣶⣶⣶⣿⣶⣶⣿

⠀⠀⠀⠀⠀⠀⢠⠀⡄⢠⠀⡄⢠⠀⡀⢀⡀⠀⠀⡄⢠⠀⡄⢠⠀⡄⢠⠀⡄⢠⠀⡀⢀
⠀⠀⠀⠀⠀⢀⣼⣤⣧⣼⣄⣧⢸⡄⣧⢸⡅⣤⢠⡇⣼⢠⡇⣼⣤⣧⣼⣄⣧⢸⡄⣧⢨⡄⡄
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢰
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡆⢰⠁⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⠃⡁⠀⠈⡇⢸⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⠸⡀⠀⠀⢣⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡞⠀⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸⠀⠘⡄⠀⠀⡴⠁⢸⠀⡇⢸⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠁⠀⠀⠁⠀⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠠⣀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠤⣀⠀⠀⠐⠦⡀⠈⠁⡀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢒⣂⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠀⠘⠀⢡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⣠⡴⠚⠉⠉⠀⠈⡁⢀⣀⠂⠠⠖⢀⠀⠀⠀⠀⠀⢤⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢺⠁⠴⠋⠀⢠⠂⠀⠀⠉⠉⠑⠀⠀⠀⠱⠀⠀⠀⢀⡈⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠴⠃⠀⠀⡆⠠⠐⠒⠀⠀⠀⠈⠉⠑⠄⠀⠀⣤⠣⠀⠀⡴⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡾⢠⠀⢰⣇⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠜⠉⡘⠘⠿⢠⠀⠒⠀⠘⠃⠤⠄⠴⠀⠀⠀⡐⢀⡄⠴⣼⠀⡠⠤⢄⢀⡔⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡘⠁⠀⠀⠀⠀⠂⠀⠀⡤⡀⠀⠀⠀⠠⠞⠟⠉⠀⠀⢀⠋⠀⣠⠋⠀⢀⣗⣈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠈⠁⣨⠀⢠⠇⢀⡔⠋⠀⢀⠗⠂⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⢈⠐⠀⠀⡀⠀⠀⠀⣠⢊⠁⠉⠉⢡⠀⠀⠀⠈⠀⠴⠚⠡⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠜⠉⠉⠉⠙⢷⠀⢿⡀⠁⡒⣉⣋⡁⣸⠓⠂⠀⠙⠀⠀⠀⠀⡠⠀⣤⡂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠒⢴⠒⠊⠉
⠀⠀⠀⠀⡀⠄⢈⠀⠀⠀⠀⠾⠰⡀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢤⠀⣤⠃
⠀⠀⡠⠊⠀⠐⠠⠀⠀⡀⡠⠂⠰⡇⠀⠀⠀⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠌⠀⠀⠀⠀⠀⠘⢠⠞⠁⠀⠀⠈⢢⡀⢰⠈⢀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠊
⡎⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠈⡱⠇⠀⡠⠦⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⣀
⠳⠤⣄⣀⡠⠔⠥⡎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠤⠄⡀⠀⠀⠀⡜⠀⠀⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠉⠐⠒⠶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠄⠒⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⠠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⣁⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⣀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡄⠀⠀⠀⠀⠀⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⣀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠄⠀⠀⠀⠠⠄⠦⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠙
⠀⣼⢦⠀⠀⠀⠀⢰⡄⠉⠀⢰⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠙⠋⠀⠀⠀⠀⢠
⠀⡆⢀⢧⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣜⡈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠙⡀⠀⠑⠖⠈⠉⠉⠀⠀⠀⠀⠉⠙⠉⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠘⢤⠀⠀⡄⠀⠀⢄⠀⠀⡀⠀⠀⠠⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡔⠁
⠀⡰⠁⠀⠈⠀⠠⠀⠀⡆⢀⠀⠠⠀⠀⠀⠀⠈⢒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⢀⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠈⡁⠝
⡜⠀⠀⠀⠀⠄⠀⠀⠄⠁⠈⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣶⠊⠁
⠓⠺⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣀⡀⣀⡠⠤⠤⠀⠂⠂⠈⠉
⠀⠀⠀⠀⠀⠑⠦⣀⠀⠉⠉⠁⢐⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⢈⠗⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠐⠒⡶⠳⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡠⠊⠀⢠⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⢠⠁⠀⣥⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡌⠀⡔⠁⠀⠀⠀⠈⡆⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⡇⢀⠜⠈⢆⠀⠀⢏
⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠱⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠃⠀⠀⠈⠣⡀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡯⣯⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⢿⣟⣿⣿⣷⣯⡻⠿⠿⠿⣟⣿⣿⣟⣷⣿⠿⠿⣿⣻⣿⣟⣽⣝⠿⠿⠿⢿⣻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢰⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣿⣿⣿⣿⣿⡿⡏⣾⣿⣿⣿⣿⣿⣿⣿⡾⣯⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠸⣿⡿⠿⠿⡿⢟⣾⠻⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣥⣥⣿⣽⣿⣿⣿⣿⣿⠹⣷⣿⣿⣿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⣵⣶⣿⣿⣷⣿⠀⠀⠀⣷⠀⠀⣰⡇⠀⠀⢺⡆⠀⠀⢀⣾⠃⢰⣷⠀⠀⠀⣿⣾⣿⣿⣶⣮⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣠⡾⠋⠀⠀⠀⠈⢷⣦⣴⠟⠁⠀⠸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢠⣤⣤⣽⣧⣤⣔⡿⡶⣿⣶⠶⢾⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⣤⣻⣟⣼⣯⣥⣤⣤⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⡿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠉⠉⢹⣏⣭⣚⣻⣄⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⣒⣿⣿⣭⡹⡯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣀⣰⣛⣛⣯⣭⠍⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⡩⣭⣽⣛⣷⣂⣀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣻⣟⣿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣿⢿⣞⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠛⠛⣛⡛⣛⡽⣯⣛⣿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣿⢩⣿⠟⠛⢿⡛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⠛⠛⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⣿⣿⡟⣿⠀⠀⠀⠸⣧⠉⠻⣦⠀⠀⠀⠀⢠⣴⠾⠛⠻⡟⠛⠷⣦⡀⣿⣻⣿⡿⢿⣫⡄
⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⢯⣖⣻⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⣞⣿⡝⣢⢻⣵⣿⣶⣶⣿⣿⡆
⠀⠀⠀⠀⢿⣿⡿⠿⢿⡿⣻⡿⢿⣿⣿⡿⠿⢿⣿⢿⣳⣿⢿⣿⡿⠿⣿⢿⣴⡻⣿⣿⣿⠿⠿⡯⣿⣟⣼⣿⣿⣿⠿⢿⠿⠇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣶⣮⢿⣻⣿⣿⣿⣷⣶⣾⣟⣽⣿⣿⣶⣾⣿⣷⣶⡝⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⢯⡾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠌⠘⠃⠉⣩⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡃⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠪⠅⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠑⣄⠀⠀⠀⠀⢸⠋⠁⠒⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣠⠜⠃⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠛⠓⠒⠒⠦⠀⠀⠘⢦⡀⣇⠀⠀⠀⠀⠀⢀⣂⣀⣀⣀⠀⠀⠀⢀⣤⡀⠀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⠀⠀⠀⢤⣒⠄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡀⡀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⡠⠠⠤⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⢤⡤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⣀⣠⠁⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢄⡀⠹⡈⠀⠈⠑⠣⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠉⠢⠱⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⡈⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢈⣁⣰⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠘⠤⠔⠀⠢⡀⢄⡘⢲⡄
⠀⣴⡋⠙⠲⡀⠘⠀⠉⠂⢄⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⢦⣱⠤⠃
⠀⠈⢷⠀⢀⣰⣧⡀⠀⠀⡦⠘⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠐⠝⢣⣕⣄⡰⠁⠀⠙⠂⢠⢤⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠂⢈⠑⠒⠀⠚⠇⠰⠛⠛⠀⢵⡆⢀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀⠀⠈⢦⠀⠀⣿⣓⡰⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡑⣄⠃⠙⠤⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⢀⣤⣤⡤⠤⢀⣰⣤⡀⠠⠄⢀⣤⡤⠄⣀⣤⣄⡀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣼⠁⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠹⣁⣄⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⡿⣠⣭⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⢳⡉⣩⣿⣿⣿⣿⡛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣾⣿⠿⣿⣿⣿⣿⣦⡻⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣴⣶⣶⣶⣾⣿⠟⠁⠀⠈⡻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⢱⠆⠀⠀⠀⢟⣼⣿⡿⠛⣿⣿⣦⡀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣼⠆⠀⢀⣴⣿⡿⠋⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⢹⢆⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⠒⠒⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣞⡋⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⣿⣿⣿⡿⠋⣼⡿⠿⠛⢁⣼⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠁⠀⠉⠀⠀⠀⠾⠛⠛⠉⠀⠀⣰⡿⠟⠛⠉⠁⠈⢻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⠀⠀⠛⠻⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠠⣀⠀⠀⠀⠀⠀⠀⢶⠖⠀⢠⡆⠀⠀⠈⢁⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⢣⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣀⣠⡖
⠀⠀⠀⠀⠀⢱⡄⠀⢀⣼⣇⠀⠀⠀⠘⢷⣄⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢘⠙⠏⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠈⢿⠛⠋⠁⢻⡆⠀⠀⠀⠀⠙⠳⣦⣄⡀⢻⣿⣿⠏⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⢀⡀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡀⠉⣿⠛⠛⠛⠿⣿⣿⣿⣉⠀⠀⠀⠀⠀⣰⠟⠉⠉⠠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠴⣾⠃⠀⠀⠉⠃⠒⠚⠛⠉⠁⠀⢹⡇⡀⠀⢠⡾⠋⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠈⠶⠟⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⠾⠟⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠛⠛⢻⡟⠃⠘⠛⡿⠛⠛⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⠋⣀⣠⣼⣷⠀⠀⢼⣿⣤⣀⠀⠘⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡠⡀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⢠⡆⠀⠀⠊⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡸⠊⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡀⠀⠀⠀⠀⠀⢀⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣰⠀⠀⠀⠀⣠⡊⠭⠊⠀⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡌⠀⡰⠉⢆⠈⢦⠊⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠪⡐⡡⠀⢆⠀⠀⠀⠈⠈⠀⠀⠈⠢⡀⠀⠀⠀⣀⢴⣉⣈⡈⠐⠂⢄⡀
⠀⠀⠀⠡⠱⢴⡖⣸⡑⠒⠀⠰⠄⠀⡀⢀⡰⠚⠉⠉⠁⠀⠀⢃⠀⠀⠈⠑⠠⣈⠢⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⠁⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠑⢤⠃⠀⠀⠀⢄⠙⠄⠀⠀⠀⢀⣀⠠⠄⠂⠒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢸⠐⢍⢧⡈⡢⠝⠀⠀⠀⠉⠉
⠦⡀⠀⠀⠀⢸⠁⢠⠀⠑⠤⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠨⣀⡄⠀⠹⡄
⠐⡌⠠⡀⠀⡜⠀⠘⠣⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢄⠀⠸⠤⠤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠈⠢⣈⠲⠀⢀⠃⠀⠈⠑⠄⣀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢣⠠⡇⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⢑⠑⡼⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠠⠀⢀⢀⣀⣀⣀⠔⠠⡀⠀⠀⠄⡈⢳⡈⠢⡀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠉
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠢⣤⢀⠀⠀⢣⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠊⠀⠀⠀⠱⣀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠖⢻⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠀⡀⠀⠀⠀⢘⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⡶⠶⣺⣿⡿⡿⠻⣻⡿⢛⣻⣿⠿⢟⡿⣿⠿⢟⣿⢿⣿⢿⣿⡿⣿⠿⣻⢿⡿⣿⡿⡿⠟⡿⢛⡿⣿⣿⠁⠀⠠⠀⠀⠀⠀⢠⣿⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢷⡽⠋⠨⠚⠁⠈⣠⢞⢕⡴⡫⠟⢁⠔⡩⠚⣡⠖⠋⠁⣠⠞⠉⠩⠚⠁⢀⠕⠋⠀⠁⠈⠀⣠⢞⠉⠜⣻⡇⡀⠀⠀⠀⠀⠀⠀⢾⣿⢸
⠀⠀⠀⠀⠀⢀⡾⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠊⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣨⠖⠁⢠⡾⣻⠁⠀⠀⠀⠀⠀⠀⠐⣸⡿⢸
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣼
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢡⣿⡀⠀⠀⠀⢀⣠⣾⠟⣹⡇⣿
⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣻⡷⢀⡴⠾⠿⢋⣩⣴⣿⡇⣿
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⡿⠻⠟⠟⠟⠉⠉⢿⡇⣿
⣿⣷⢄⣤⣀⣤⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⣿⡿⣻⡟⣹⣿⣿⣿⣿⣵⣿⣫⢞⣿⣿⣿⣿⣿⣿⠞⢡⣾⢏⢞⡾⣿⢯⠟⡠⡃⢁⡼⠃⠀⠂⠀⡰⣠⢦⠆⡴⢀⠄⡠⠂⡀⡠⠂⡴⣰⡶⢣⣾⡿⠁⣰⢿⡇⣿
⣿⣿⢋⣞⡽⢃⣿⣿⡿⡟⡵⣫⣻⡿⡿⣿⡿⠋⠁⡴⡻⡣⣣⢟⡼⡳⠃⡴⠁⣠⠞⠀⠀⠄⢀⣜⡵⠃⢀⠞⢡⠊⠐⢀⠎⠄⢁⡞⢝⠊⠀⣱⠋⠀⣼⣯⣿⡇⣿
⣿⣣⢯⡞⣠⢏⣼⣟⢌⣞⣝⡽⣓⢟⣾⠝⠁⢠⣞⣟⣕⡽⣣⢟⠜⢡⠎⠀⡴⠋⠠⠀⡀⣠⢮⠞⠀⣠⠋⡰⠁⠀⡴⢣⠂⣠⠋⡠⢁⠌⡼⢱⠀⣼⣶⡿⠍⡇⣿
⣿⣧⠋⢜⣵⡿⣿⣿⣫⣪⠎⣠⠎⡪⠋⠀⣰⡿⣫⠞⢪⡞⡱⡃⡴⠃⢀⠞⢁⠔⢁⢜⡴⣳⠋⢀⣔⠁⠈⠀⢀⠞⡱⢁⡜⢁⡼⣡⢣⣞⠾⢁⢮⡿⢃⢎⠜⡇⣿
⠿⠷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⣜⣙⣃⣚⣛⣑⣃⣐⣋⣚⣚⣚⣀⣀⣁⣀⣋⣀⣉⣚⣙⣁⣀⣈⣡⣤⣾⣥⣭⣈⣰⣋⣀⣋⣀⣁⣁⣀⣁⣃⣘⣡⣡⣬⣬⡇⣿
⠀⠀⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⣶⣻⠀⢴⣿⣿⣿⣿⡿⡿⠿⢟⡿⠿⠿⠿⠿⠿⠿⠿⣿⠿⡿⠿⡿⠿⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⡿⣿⣿⡿⠿⠿⠿⣧⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⡶⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣄⡴⠋⠉⠉⠛⢶⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠁⠀⣠⡟⠁⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⠖⠛⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢿⡄⣀⠔⠊⠁⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿
⠀⢀⣀⣀⣸⣿⣁⢀⣀⣀⣤⠴⠖⠛⠉⠁⣀⣤⠴⠖⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⣴⠏
⢰⠟⠁⠀⠈⠉⠉⠉⠉⠀⠀⢀⣠⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀
⢹⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠶⡟⠋⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠞⠛⠉⠙⠈⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⠂⡡
⠀⠀⠀⠉⠛⠛⠓⠚⠛⠛⠛⠉⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⠈⠉⠙⠻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⠟⠁⣼⠿⠟⣫⡿⠿⠛⠁⠀⠰⡏⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠈⠛⠄⠀⠀⢹⣿⠇⠀⠱⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⠀⢠⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠏⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣯⠈⢣⠀⠀⠀⠀⢀⣏⠈⠇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠼⠀⢀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⣤⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠋⠉⠀⠀⠤⠭⠋⠀⠀⠀⢻⣇⠀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡆⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢦⡈⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠀⢀⡼⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⢰⡟⠋⠉⠉⠀⢙⠁⠀⠀⢀⣴⠏⠀⢻⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠻⣦⣀⠀⠀⠀⠀⠦⠄⠒⠀⠀⠈⠀⢀⣴⠟⠁⠀⠀⢀⡙⠓⠰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠁⠀⠀⠉⠒⢤⡙⠻⠶⣤⣤⣀⣀⣀⣀⣠⣴⠾⢿⠁⠀⠀⠀⠀⣸⠋⠁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢯⡈⢢⡤⠚⠃⠄⠀⠀⠈⠲⣄⣀⣈⣉⣉⣉⠟⠛⣤⠠⣄⠁⠀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⢹⠃⠀⠀⠀⠀⠈⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠠⠴⠦⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠞⠚⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⡶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢦⠀⠀⠀⠐⣿⠙⠛⠿⠿⠷⣶⣶⡶⢿⡀⠀⢨⠛⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⢳⡄⠀⢠⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣠⡾⠃⠀⠈⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣄⢀⣤⠿⡶⠋⠀⠀⣠⠶⠷⠶⠶⠶⠶⠶⠟⠛⠉⠙⠛⣶⣖⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⢳⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣸⡇
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⣸⣿⣿⣿⢿⣿⠃⠙⣧⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣏⣠⣾⢿⣾⣿⣿⣿⣷⣟⡀⠻⣿⣇⣈⣤⣴⣞⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿
⡿⠉⢢⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠘⢷⠀⠙⠛⠟⠛⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠀⠀⠀⠀⠀⠈⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣌⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⠋⠉⠒⠀⠀⠀⠀⠀⢀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠎⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣇⡼⢻⣿⣿⣧⡀⢰⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⣤⡤⠄⠀⠠⠄⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠤⣦⣄⠀⠀⠈⠙⠛⠻⣿⡎⠿⣿⣿⣿⣿⣾⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠘⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⢤⣤⣙⣿⢿⠷⠀⠀⠀⠀⠀⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠙⠋⠀⢠⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣼⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡴⢦⣤⣀⠀⠀⠀⠀⠀⠀⣩⡿⠀⠀⠀⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢣⣤⣬⣿⠟⠋⠘⠺⢿⣿⣿⠃⠀⠀⠀⠁⠀⠚⠙⠻⠟⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠈⡍⠀⠀⠀⠀⠀⠀⢾⣧⣀⣴⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠠⣄⡂⠈⠀⠀⠀⠀⣀⣠⢴⣶⣶⣷⣶⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠚⠓⠿⠿⠛⡿⠟⠛⠛⠋⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠙⠛⠿⡟⠋⠉⠉⠉⠉⠻⣿⣿⣿⣿⠋⠀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠋⠛⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆⠀⠀⠀⠈⠏⢻⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣶⣿⣿⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⣤⣤⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠢⠀⠘⣿⡄⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠚⠃⠀⠀⢀⣈⣽⠇⠀⠀⣠⠀⠀⢠⡟⠀⠀⠀⡇⢹⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠦⣴⣿⡇⠀⠀⠀⢁⣳⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣾⣶⣿⣿⣿⡇⠀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠟⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡃⠂⠀⣀⣙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⡄⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢹⣗⡀⢰⠆⠀⠀⠀⠀⢰⣿⣿⣿⣿⠂⠀⠀⠀⢀⢾⣠⣿⣿⣿⣿⣿⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣷⣬⣶⣴⣾⣿⣾⣷⠞⠀⠀⠀⢠⢀⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣯⣝⣻⡿⣧⠀⠀⢀⣀⣀⣾⣿⣿⣿⣿⠀⠀⣠⠾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠋⠉⠉⠙⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠙⣟⠒⠶⣤⡀
⠀⠀⠀⠀⢠⡶⠋⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⣦
⠀⠀⠀⣴⠋⢀⡴⢊⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢧⠀⠀⠀⠀⠀⠀⠘⡗⢤⠀⠈⢷
⠀⠀⣾⠁⢠⡞⢀⡾⠀⠀⠀⢠⠖⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠋⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢻⠈⢷⡀⠘⣇
⠀⣸⠇⠀⡟⢠⢋⡇⠀⠀⢠⡏⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠳⣄⡀⠀⠀⢸⠀⠘⣇⠀⢻
⠀⣿⠀⠘⠀⡏⢸⡃⠀⠀⡾⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢈⣉⣁⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⢻⠀⢸⡆
⢸⣿⠀⠀⢸⠃⠘⡇⠀⢰⠇⠀⠀⢀⡴⠊⠁⠀⠈⠙⡄⠀⣠⠞⠉⠀⠀⠙⡄⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⢸⡇
⠸⣿⠀⠀⠈⠀⠀⢳⠀⢸⠀⠀⠀⠎⠀⢀⣠⣄⠀⠀⠱⠰⠃⢀⣤⣤⠄⠀⠐⠀⠀⠀⢸⡆⠀⡏⠀⠀⢸⠀⢸⡇
⠀⣿⡄⠀⠀⠀⠀⣈⣇⡘⠀⠀⠀⠀⠀⣿⠟⢣⣶⠀⠀⠀⠀⣾⡟⠓⣾⠀⠀⠀⠀⠀⠀⣇⣼⡁⠀⠀⠀⠀⢸⠃
⠀⠸⣷⠀⠀⠀⣸⢁⡀⡇⠀⠀⠀⠄⠀⠙⠲⠞⠃⣠⠠⣀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⡇⣀⢹⡄⠀⠀⠀⣼
⠀⠀⢻⣧⠀⠀⣿⠀⠘⡇⠀⠀⠀⠀⠐⡤⠤⠔⣿⠁⠀⠀⠁⠁⠒⡒⢀⠀⠀⠀⠀⠀⠀⣿⠉⡹⠁⠀⠀⢠⡇
⠀⠀⠀⢻⣆⠀⠈⠳⠴⡇⠀⠀⠀⠀⠌⠄⠂⠀⠘⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢿⡄⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢸⡇⠀⠀⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡄⠀⢸⡇
⢠⡖⠀⠀⣼⠃⠀⠀⣿⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢠⡇⠀⣧⡀⠈⣿⣄⠀⢀
⢾⣧⣤⠞⢁⡴⠀⣸⠇⠀⢸⢈⠳⣄⠀⠀⠀⠀⠀⠀⣇⢀⡇⠀⠀⠀⠀⠀⢀⡴⠋⢿⡄⢸⣇⠀⠘⢿⣦⣬⣿⡷⠋
⠈⢛⣛⣿⡿⠃⣰⠏⠀⣠⡿⠊⠀⠈⠳⢤⡀⠀⠀⠰⢌⡉⠀⠀⠀⠀⣠⠶⠋⠀⠀⠘⢿⣄⣻⣷⣤⣄⣀⣭⠟
⠙⠛⠛⠙⠒⠋⠑⠶⠛⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣠⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⢶⣶⠶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣷⣾⣶⣷⣾⣿⣾⣶⣾⣷⣷⣾⣶⣶
⣿⣿⣶⣷⣷⣾⣶⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠛⠛⠋⠙⠋⢙⡉⠛⠃⠠⠤⢄⡀⠀⣀⠠⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡰⠞⠁⠀⠀⠀⢀⡀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠉⠛⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠞⠉⣀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠻⢦⣤⣤⠴⠶⠋⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣘⠓⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠰⠀⠀⠀⠠⢀⣴⠃⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠘⠦⣀⠠⠎⠉⠂⡀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⠷⠶⢦⣤⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠑⢄⠀⠀⠀⠀⢰⡇⢰⡇⠀⠀⠀⠀⡄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⠀⠀⠀⠀⠱⠀⠀⠀⡌⠀⡜⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡤⠚⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡐⠀⠀⣀⡀⠀⠳⠀⢀⠃⢸⠃⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⣇⠀⣼⠃⠙⠆⠀⢣⡿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠸⣄⠀⠁⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣾⠁⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠰⠶⣄⣸⡄⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⢀⡤⠔⡶⠤⢤⣀⣀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⣄⡀⠀⠀⠠⢄⠉⠀⠙⠛⠛⠚⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⢸⠃⠀⢸⡇⠀⣀⣀⣤⡤⠤⢶⣤⣀⠀⠀⠀⠀⠸⠇
⣿⠀⠬⠉⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣧⠚⠉⠁⠀⠀⠀⠀⠀⠈⠑⠀⠀⢠⣼⠃⠤
⠈⠳⠖⠀⠁⠈⠉⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣰⠟⠉⠉⠙⠓⠲⠶⠞⠃⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⢷⣤⠈⠐⠠⡀
⠀⠀⠷⣤⡴⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⢀⡄⠀⢀⡀⠀⠀⠀⠀⠀⣠⣿⡀⢠⡀⠠⣇⠀⠈⣻⠀⠉⠉⠓⠶⠶⠤⠾⠋⢡⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣧⣀⣼⡇⠀⣀⡶⠒⠋⠉⠈⠉⠈⠻⠖⠛⠳⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣉⣀⢹⡿⣏⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠂⠉⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⣀⣀⣀⣀⣀⣀⣈⣷⣶⣶⣶⣶⣮⣉⣉⣁⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣭⣭⣬⣭⣯⣉⣉⣁⣀⣀⣄⣀⣠⣀⣀⣀
⣿⣿⣿⣿⠟⢻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣠⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢾⣿⡏⣤⠈⣿⣿⠿⠋⠀⠀⠀⠐⠂⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣗⣂⣽⣿⡶⠞⠋⠁⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣶⡆⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⠘⣿⣿⡀⡀⠤⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣶⣶⡶⠿⠟⠛⠙⣿⣷⠠⠙⠉⠁⠀⠀⠐⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀⣀⣤⣤⣤⣤⣴⣆⠀⠆⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠉⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡍⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠑⠠⠀⣀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠈⠡⠀⠀⠴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⢀⠀⠒⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⢡⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡠⠔⠊⠐⠒⠀⠠⠃
⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠂⠊⠐⠀⠂

⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠟⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⣿⣿⢿⣿⠿⣿⠿⣿

⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⣿⣿⣿⣿⣿⢉⠍⠁⢨⣭⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡖⣶⣿⠗⠒⢶
⠀⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⡧⠸⠿⢀⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡋⠀⣸⣀⣰⡿
⠀⣿⣿⣿⣿⣿⠀⠀⠀⢾⣏⣴⠃⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠸⢋⣿⣿⣇⣀
⠀⣿⣿⣿⣿⣿⠀⠀⠠⠞⣽⣿⢀⡈⠳⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣤⠀⢸⡿⣧⣍⠉
⠀⣿⣿⣿⣿⣿⠀⣠⣴⣾⣿⠃⣼⢁⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⣶⠞⠋⠀⢠⣾⢣⡿⠃
⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⣉⣛⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣷⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢋⣿⣿⣿⣿⣧⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣹⣿⣿⣿⣋⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠐⢿⠟⠁⢸⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⣰⣿⣿⣿⡟⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⡏⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣿⣿⠛⠛⣿⣿⡅
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠣⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢿⣿⣿⣿⣿⠟⠉⠁⠀⢄⠀⠀⠀⠠⢻⡿⠛⢉⠉⣿⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢒⣒⣢⣤⣀⠀⠀⢸⣿⡟⢀⡸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⠋⣽⣿⡿
⠀⠀⠀⠀⢀⠔⢉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣧⠈⠁⣿⣿⣿⣯⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣰⣿⣿⠇
⠀⠀⢀⡔⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⠀⠒⠀⠀⠀⠀⠀⣴⣀⣴⣿⣿⠏
⠀⢀⠎⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁
⠀⡼⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠉⢹⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣀⡤⢐⢠⣿⠿⠋⠙⣷⣶⣴⣶⣄⡀
⢠⠇⢀⣿⣿⣿⣿⣿⣿⢫⡉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢞⡾⠃⠀⠀⠀⠸⣿⣿⣿⣿⣷⡀
⡞⠀⢸⣿⣿⣿⣿⣿⡇⢸⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠊⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠁⠀⣿⣿⣿⣿⣿⣿⢀⠘⠱⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢰⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⣿⣿⡟⢸⣧⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⢐⠋⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣼⡶⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠶⠶⢶⣾⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣤⢀⡄⠘⠳⠄⠀⠀⠀⠀⠀⢸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇
⣿⣿⣿⠯⣿⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇
⣿⠟⠁⠀⣿⠀⠀⠀⣠⡜⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣦⣴⣤⣶⣾⣿⣿⣿⣿⣿⠇
⠁⠀⠀⠀⠘⠧⠀⡰⠉⠀⠠⠤⠀⠀⠀⠒⠘⢸⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⡆⣰⡏⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣧⠀⠀⣠
⠰⠀⢀⣿⣧⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⠟⣙⡿⣷⡦⠢⠬⢽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⠟⠁⠀⠀⠀⠀⠈⠛⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⣠⣤⡄⠀⠀⣀⣀⠀⠈⢻⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠰⠚⣉⠁⠀⠀⠀⠉⠙⠳⡆⠀⣿⣷⣼⣿⣿⣿⣿⣿⣿⠛⠁⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠭⢣⣀⢀⣼⠏⠙⠳⡌⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡄⢉⣿⣿⣿⢻⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠉⡟⠀⡄⠀⣠⣤⣄⣿⣿⣅⣠⣦⣄⠹⣆⡀⢿⣧⣽⣿⣿⣿⣿⣿⣨⣧⢸⣿⣿⣿⣾⢸⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠀⠀⠀⣈⠙⢿⠟⠋⠐⣎⠛⠯⣍⠃⠈⠀⠐⣿⠘⣿⣿⣿⣿⣿⢻⣿⣸⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⢹⢧⣿⣿⣿⣿⣿⣿⡟⢠⡆⠀⠀⠀⠀⠐⠁⠀⠉⠁⠈⢣⡀⠈⠁⠀⠀⠀⠘⣧⠹⣿⣿⣿⣿⡟⡿⣿⢻⣿⣿⣿⣿⣿
⣿⣿⣿⡟⡇⣾⣼⣿⣿⣿⣿⣿⡿⣇⣸⠃⠀⠀⠀⡀⠹⣿⣶⣤⣴⡦⠞⠁⡀⠀⠀⠀⠀⠀⠸⡆⣿⣿⣿⣿⣇⡇⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⢃⣇⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⢀⣶⢠⠀⢀⣉⣿⣃⣿⣄⣀⠀⢷⠸⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠟⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠋⡿⠘⠉⠙⢿⠿⠿⠟⠛⠛⠺⣇⡹⠊⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡏⢠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⡽⠀⠀⠀⠁⠀⠈⠻⢿⣿⣿⡆⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⣈⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡇⢺⣿⣿⣿⠋⢸⣿⣿⡿⠟⠋⢰⡀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡇⣼⣿⣿⣿⡴⠚⠉⠀⠇⠀⠀⠀⠹⠓⠲⠤⣿⡀⠀⠀⠘⠃⠀⠀⢹⣷⠤⠴⠶⠒⢻⠁⠀⠀⠀⢇⠉⠻⢦⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣇⢹⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣹⡟⠛⠻⣿⠻⣿⣿⠿⢶⣄⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿
⠀⢹⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠋⠀⠻⣦⠀⢙⠷⠊⠁⠀⠀⠈⠳⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⠁⠀⠀⠀⠀⠂⠀⠀⠀⠱⣵⠁⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⠛⠛⣿⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡿⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⣾⣿⣿⠻⣿⠆⠀⠀⠀⠀⠀⣿⡟⠋⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣴⣿⣿⣶⢲⣿⠄⠀⠀⠀⠀⠀⣿⡇⠀⢀⣀⣠⣤⠾⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠦⣄⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⣿⡷⠚⣋⡩⠅⠒⢀⣡⢬⣍⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣴⣿⣿⡟⣿⡏⠀⠀⠀⣀⣠⠴⣿⡏⠀⢨⠀⠀⠀⠉⠁⠀⠉⠑⢶⢈⡳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣟⣛⣿⣧⡶⠆⣿⡁⣼⣦⣿⡇⠀⢀⡀⠀⡀⢰⠀⢀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣏⣉⣿⣿⡦⠀⢉⠀⢸⣽⣿⣷⠀⣾⡇⠀⢿⣈⣁⣾⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣨⠜⢻⡟⣿⣿⠿⠁⠀⣿⠀⢸⣸⣿⣋⣷⣾⣿⣿⣶⣛⣧⣹⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⡇⢸⡃⣿⡇⢸⣤⣤⣾⡷⣿⣿⣿⣿⡾⣿⣿⣧⡈⠻⣦⡙⢧⣉⣤⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⣽⣶⣿⣽⣿⣿⣥⣌⠳⣮⣼⠇⢉⣿⣿⣍⣹⣿⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣷⣽⣯⡛⣯⣜⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣏⣰⣿⣿⠿⣿⣿⣿⣿⠟⠉⠙⡿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢈⣿⣿⣟⠛⢿⣿⣍⣹⣿⣿⣿⣶⣿⣿⡿⠃⠒⠈⠋⣰⣒⣠⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⣻⣿⣿⢋⣁⣼⣧⣼⣿⣿⣷⣭⣻⣿⡏⢀⣀⡤⢶⣚⣯⣽⡿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣄⡉⣿⣿⢿⣟⣻⢿⢙⣿⣿⣿⠛⡿⣯⡉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⣹⣿⣿⣿⣿⣿⡏⠚⠛⢙⣿⣿⣟⠀⡇⡌⠙⠓⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢛⣿⣿⡇⠀⠀⠀⣿⣿⣿⣀⡁⡆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⡍⣸⣿⡏⢩⣿⣿⡇⠰⣀⣤⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣈⣻⣿⣿⣏⣀⣠⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢎⡙⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣹⠛⣿⣿⣯⣿⣿⣿⣿⣉⣶⣾⣿⣿⣯⣽⣿⣿⣷⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠳⢛⣉⢝⣻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠟⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠛⣁⣾⣿⣧⣸⣿⣿⣿⡙⢿⣿⣿⣿⢿⣧⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⣿⣿⣿⣯⣿⣿⢿⣶⣾⣿⣿⠿⣟⢿⣷⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣟⣡⣿⣯⢫⣿⣇⡀⣸⣿⠟⠉⠀⠁⢸⣿⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⣻⣏⣸⠿⣿⣧⡿⠉⠻⣿⣿⠋⠀⠀⠀⠀⢸⣿⠀⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢩⡅⠉⡰⣾⢿⣧⡄⣼⣿⠃⠀⠀⠀⠀⠀⢸⣿⠂⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢙⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠃⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢶⠀⢀⣠⠤⠴⠒⠒⠒⠒⠦⠤⣄⡀⠠⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⣀⠀⠀⣀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠖⠂⠉⠱⠐⠙⠲⠶⡉⠒⠚⠉⠓⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡋⠄⠉⠀⠀⠀⢀⣠⢐⡂⠉⠀⠈⠒⠢⡀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢄⠀⢰⠉⠀⠀⠈⠉⠢⡀⠀⠀⡄⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠒⠶⣤⡤⢀⡀⠀⢸⣐⡪⢴⣾⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⠈⠙⠪⠭⠏⠳⢄⣠⠿⠬⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣊⠉⢲⠊⠉⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⢠⠇⠀⠀⠀⠀⠀⡾⠤⢤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⢤⠤⠤⠞⠑⠒⠤⠤⣄⣀⠟⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠴⠓⡏⠀⠀⠀⠀⢀⠴⠒⠒⠦⣄⠀⠀⢀⡿⠴⠊⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠱⡤⠋⠑⠦⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠞⠛⠛⠉⠉⠙⠲⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢴⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠉⠛⠶⠤⢀⣀⣠⠤⠖⠉⠁⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⣇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢸⡇⠀⠀⣿⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⢠⡟⠀⠀⠀⣾⡏⢨⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⠀⢸⡅⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣸⠀⠈⣧⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠳⣄⣀⣀⣀⣠⡤⠚⠋⠉⠀⠀⢀⣀⠀⠈⠉⠙⠛⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠛⠓⠶⠂⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠶⠛⠉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠⢀⡀
⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⢀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⣤⡀
⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⡟
⠀⠀⢸⡇
⠀⠀⣿
⠀⢠⡟
⠀⣼⠁
⠀⣿
⢸⡟
⠸⠃
⡇
⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣠⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⢩⣭⣭⠉⡭⢿⡉⢉⣥⣄⠁⠀⣴⡄⠉⣭⢭⣍⣩⣭⡍⣿⣿⣷⣏⣶⣂⡠
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢸⣧⡄⠘⠷⢶⣤⣿⠀⠋⠀⣸⣏⣷⠀⢿⣤⠟⣿⣄⡀⣿⣿⣿⣿⣿⣷⣿⡵⢖⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠸⣷⣴⠠⣤⣴⠟⠹⠷⠶⠢⡿⠋⣹⡆⢸⡇⠀⣿⣤⡄⢿⣿⣿⣿⣿⢟⣿⣿⣯⡵⢖⣂⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⣾⣿⣶⣶⣶⣶⣾⣿⠶⣿⢶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⢠⣍⡛⠿⣿⣿⣿⣿⣭⣞⣩⣭⠤
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⡏⡿⣷⣦⣝⡻⢿⣿⣿⣷⣶⣋⡀
⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠃⡇⣜⣿⣿⣶⣬⡛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠠⣾⣭⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢀⡇⣿⠁⠇⣍⠻⢿⣳⣬⢻⣿⣯⡍
⠀⠀⠀⠀⠽⠿⣯⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠘⡇⣿⠐⠀⠋⠀⡘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣷⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠁⠋⠀⢀⠀⠀⡷⣿⣿⡟⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣻⡿⣿⣿⣿⣿⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣠⠀⠀⢰⠀⢸⠀⠀⠁⣿⣿⡇⣿⣯⢹⠛⠆
⠀⠀⠀⠀⢚⣫⣶⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⠀⠀⢸⢰⠰⠀⠀⠀⣿⣿⡇⣿⣿⣷⣾
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠀⠀⠸⠈⢀⢰⠀⢠⣿⣿⡇⣿⣿⣛⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⡇⡇⠀⠀⠸⢈⠀⢸⣿⣿⡇⣿⣿⡿⢧⡄
⠀⠀⠀⠀⣫⣽⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣷⣶⣤⡀⠀⠈⣿⡟⣇⡇⡇⠀⡄⠀⢸⣼⡻⣿⣿⡇⣿⣿⣿⣟⡀
⠀⠀⠀⠚⣩⢞⣾⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⠀⠀⣿⡇⣿⣧⡇⠀⡇⣆⣶⣿⠗⣿⣿⣇⣿⣿⣿⡶⠄
⠀⠀⠀⠈⠵⣫⣿⣿⣿⣿⣿⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠤⣼⠁⠀⠀⣿⡇⣿⣿⡇⠀⡇⡟⢿⣟⠄⣿⣿⡗⣿⣿⣿⣭⡅
⠀⠀⠀⠠⢞⡿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡿⠀⣧⢳⡀⠀⣿⡇⣿⣿⡇⠀⡇⡇⣿⣿⠇⣿⡿⣇⣿⣿⣿⣿⣓
⠀⠀⠀⠐⣫⣾⣿⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⣇⠀⣿⠿⡇⠀⣿⡇⣿⣹⡇⡇⡇⡇⣿⢿⣴⣿⣟⣿⣿⣻⣿⣩⣄
⠀⠀⠀⢈⡿⣿⣿⣿⣿⣿⣿⠘⣋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⢋⠀⠀⠀⣿⡇⣿⣿⡇⡇⡀⡃⣸⣀⣸⣿⣫⣿⣿⣿⣿⡧⠄
⠀⠀⠀⢋⣾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠐⠀⠀⠀⠐⠂⠀⠐⡆⠀⠀⢠⠻⡀⠀⢠⠈⠉⢷⣿⣿⢃⡧⡇⡟⣿⣿⣿⣿⣁⣿⣿⣿⣷⠖⠲⠆
⠀⠀⠀⡰⢫⣾⣿⣿⣿⣿⡿⠁⠀⢠⠇⠀⠀⠀⢠⠀⠀⠀⡇⠠⣶⣴⢶⣾⠀⠀⠇⠀⠈⢿⣿⣷⣿⣗⣷⣿⣿⣿⣿⡅⣿⣿⣿⠿⣛⠥
⠀⠀⠀⠀⣻⣿⣿⣿⣿⡿⠁⠀⢠⡏⡀⠀⠀⠀⠀⣀⠀⠀⣧⠀⢸⣿⡸⣿⣧⠀⠘⡀⠀⠀⠻⣿⣯⣻⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠿⣽⣿⣿⠟⠀⠀⢀⠚⠐⠀⠀⠀⠀⢀⡇⠀⢀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢳⠘⢆⠀⠹⣿⣿⣿⣿⣿⡿⣛⣭⣾⣿⣿⣿⡥⠖
⠀⠀⠀⠀⢘⣿⣿⠋⠀⠀⢀⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠃⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⣿⡝⢿⢿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣵⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⡞⡹⠃⠀⠀⠀⣰⡩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⡔⢲⠄⠀⠀⠀⣠⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⡁⠀⠈⠉⠙⠢⡀⠀⠘⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⣽⢒⣦⣄⠀⠀⠀⢱⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡜⢀⣇⣘⡉⠠⢖⢲⠄⡼
⠀⠀⠀⠀⠀⢠⠎⢠⠊⢯⡙⠁⠀⠀⣫⠞⠁⠀⠀⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠓⠬⣓⣴⣮⣭⡔⢙⠀⠀⠀⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢜⠀⠈⡞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢖⠚⡅⠸⡄⠀⢀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡄⠈⣦⢱⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠧⠴⠠⠤⠯⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡸⠤⠬⠭⠥⠞⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⣂⠀⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⢀⣀⢴⠊⠈⢲⡆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⢤⠾⠛⠀⢀⣀⣤⣾⡁⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠈⠲⠤⣊⠁⠀⠀⠉⠒⠓⠬⣑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡯⢫⡏⠀⠐⠋⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣠⠏⡇⠀⠀⠀⠀⠀⠈⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠃⠀⠀⠀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⡶⢶⣾⣿⡿⠶⠶⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⢉⣉⠋⠀⠁⣋⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⡥⠒⠀⠀⣿⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠘⠁⠀⠀⠘⣩⣿⣿⠀⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣡⠀⠀⣤⣿⣤⣤⣻⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠞⣿⣿⠟⠂⠛⠛⠦⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⣼⠟⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⣿⡏⣠⣾⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠏⢀⠀⠀⣿⣿⣿⠹⠿⠶⠶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢠⠀⠀⠈⣡⣿⣿⣿⡇⠀⠀⣶⣀⣉⣉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣥⣶⠏⠀⠀⣿⡟⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠉⣱⣿⣿⡇⢠⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠁⠀⠀⣴⣿⢃⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢠⠀⣠⣴⣶⣷⣯⡏⠀⣸⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⣾⡿⡷⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣰⣾⣿⣿⣿⣿⡏⢀⣈⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⢰⠋⣆
⠀⠀⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⡖⠲⣌⢇⠘⣾⠀⣿⠀⠀⠀⠀⠀⡸⢣⡰⢱⢠⢦
⠀⠀⠀⠀⡜⠀⠀⠀⢀⠀⠀⠂⠈⠯⡀⠀⡀⠀⠀⣀⣹⣄⠈⢻⡆⢿⠀⡏⠀⠀⢀⡀⠀⣄⠘⡇⣸⢇⡎
⠀⠀⠀⢸⠃⠀⠀⠀⠃⠀⠒⢄⠀⠀⠚⡼⢹⠀⠀⢧⣈⠙⠿⣦⡙⠈⠠⠗⠒⠋⣁⠜⡀⢹⠀⡇⣟⡼⠒⡩⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠚⠁⠈⠑⠢⣄⠈⠑⠂⣬⠀⠀⠀⡴⠒⠉⠀⢫⡍⠉⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠈⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⡂⢄⠀⠀⠀⢈⠷⠒⠉⢀⡠⠒⠈⣀⡤⠖⠊⢁⣠⠤⠒⠒⠁
⠀⠀⠀⠀⠈⢲⠀⠁⠄⠀⠀⠀⡾⠀⠂⠈⠀⠐⠀⠀⣀⡤⠞⣉⡤⠖⠋⣁⡤⠔⠊⠉
⠀⠀⠀⠀⠀⠈⠒⠒⠉⠳⡄⠀⠀⠀⠀⠁⠀⣀⡴⣞⡭⠖⠋⣁⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠁⠀⢀⡤⠾⠟⠋⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠉⠐⠀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠹⡄
⡴⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠘⢆
⠇⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡰⢦⡀⠀⠈⠳⡀
⠘⢄⡀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⡰⠁⠀⠀⢀⡞⠁⠀⠙⢦⡀⠀⠙⢆
⠀⠀⠈⠉⠙⡆⠀⢠⠎⠀⠀⠀⡼⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠑⢄⠀⠀⠳⣄
⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⡼⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄
⠀⠀⠀⠀⢸⠁⠀⢸⠀⢠⠞⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤
⠀⠀⠀⠀⢸⡀⠀⠘⠖⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠢⣄⠀⠀⠀⡼⠁⠀⡠
⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠙⠒⠺⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠑⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⡁⢀⠎
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶
⣿⣿⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣄⠂⠒⠒⠲⠆
⠀⠀⠀⠀⠀⡟⠀⠂⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⢤⡀
⠀⠀⠀⠀⠀⣅⢀⠀⠈⢆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠘⢮⠖⠒⠚⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⠀⠀⠋⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⡷
⠀⠀⠀⣀⣀⢀⡤⠤⣤⡜⠀⠀⠘⣠⠚⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡶⠛⠉⠈⠳⠝⠶⣤⡀⠀⢸⡄
⠀⠀⠸⡤⠍⣉⣀⡴⠁⠀⠀⠘⣴⠁⠑⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢋⠴⡲⢊⣧⢆⠓⡒⢄⢹⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⢇⠀⠘⢆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣰⢳⠊⠜⣡⠃⣼⣄⠳⡘⠎⠓⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣀⠤⠤⠸⡆⠀⠘⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⠃⠃⠀⠀⠁⠞⢸⡏⠂⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡠⠁⣀⡄⠀⠙⠲⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢾⡀⠀⠀⠀⠀⠀⡟⠙⡄⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⢀⠾⣄⠀⠈⢇⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠸⣇⠀⠀⠀⠀⢀⠗⠒⠹⡄⠀⠀⠀⠸⣞⠙⣦
⠀⠀⠀⠀⠀⡇⠀⣼⠦⠖⠋⠱⣄⢀⡤⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡋⠀⠀⠀⠀⡼⢤⡤⠄⢳⡀⠀⠀⠀⢿⠀⠈⣇
⠀⠀⠀⠀⠀⡇⢀⠆⠀⠀⠀⠀⠈⠁⢤⣀⣀⠀⠉⠓⠀⡀⠀⢦⠀⠀⠈⠀⠀⠀⢠⠃⠀⠀⠀⡸⠢⢄⣀⣠⠴⠛⢦⠀⠀⠈⢣⡀⠸⡄
⠀⠀⠀⠀⢀⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠢⡼⠀⢸⡇⠀⢰⠀⠀⢀⠎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠱⡄⢻⡀
⣤⠤⠤⠴⢎⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢸⡇⠀⢸⠀⢀⡜⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠙⣎⢷
⠙⢶⣄⡀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⠾⣇
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢣⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠲⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇