Lily pad Emojis & Symbols

⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣿⠁
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣿⠟⠋⠁⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠁⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣁⣀⣀⣀⣀
⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠓⢆⠀⠀⡀⠀⠄⠀⠀⠃⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠟⠛⣿⣿⠿⠿⠿⢿⣿⣿⣟⠻⢿⣿⣿⣿
⠛⠛⠛⠛⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⠉⡧⠀⠈⠀⡀⠀⠀⠄⠠⡀⠀⠀⠰⠋⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⣿⣯⣽⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠣⠄⠢⠀⠀⠀⠢⡍⠀⢁⡀⣀⠠⠶⠁⠀⠀⡀⠀⠀⢠⠶⢛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣑⢀⠀⢦⡀⠀⠉⠂⡀⠀⠀⠈⠈⠔⠁⠀⠀⠀⠤⠀⠀⢠⣶⠷⠒⠁⠀⠀⠀⠀⢀⣤⣾⣿⣻⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⠀⠉⠙⠛⠢⢽⣦⣀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⢀⣤⣶⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣤⠀⠀⢀⡀⠀⠀⠉⠓⠒⠷⠄⠀⠀⠀⠀⡀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠒⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠛⠛⠓⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠉⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠻⣿⣿⣿⣿⣿⣿⣿⡍⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠈⠉⠛⠛⠛⠉⠁⠸⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣀

⠀⠀⠀⠠⣴⣄⠀⠀⠁⠀⠀⠀⠘⣷⠴⠉⠀⠀⠁⠀⠀⠀⠤⠾⠄⠴⠈⠀⠀⠐⠳⠤⠼⢇⣀⣄⠀⠀⠀⠀⠑⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⡄⣀⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠂⠸⠈⠋⠀⠅⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀⠀⣐⣊⣙⢀⠀⣄⠀⠀⢠⡍⠒⢀⠤⠉⠀⡇⠀⠀⠀⢠⡎⣵
⠀⠀⠢⠄⣀⠐⠀⡐⠁⠀⠐⠀⠩⢂⠂⠀⢰⠆⠀⠀⠀⢠⠩⠤⢀⠀⠀⠀⠀⠀⢠⡄⠀⣸⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⡀
⠀⠠⠆⠤⠻⠒⠚⠁⠀⠀⠀⠀⠘⠚⠂⠊⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠿⠚⠀⠀⠀⠀⠀⠀⠐⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⡐⢢⡄⠶⠤⢄⡄⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠄
⢤⡐⠂⠀⠀⠀⠀⠀⠰⡆⢹⠀⠀⠀⠀⠀⠏⢀⠐⠲⠈⠁⠶⠀⠀⠠⠄⠉⠙⠃⠘⠀⠀⠀⠔⠠⠠⡤⠍⠥⠀⠀⢀
⣐⠀⠈⠀⠀⠀⠀⠀⠀⢁⡁⠀⠀⠀⠀⠀⠀⠸⢄⢀⣦⠀⠀⠀⠀⢡⡄⠁⣤⠐⠁⠀⠀⠀⠀⠔⢒⢀⠆⠀⠀⠀⠘⠄⡀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠈⠉⠉⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀
⠀⢠⠀⣀⢨⢆⠠⠄⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⢀⡠⠄⠠⠄⠀⠀⠀⠀⠀⢀⠨⢆⠀⠀⠀⠀⠀⠠⢔⠒⠚⠲⠊⡤
⠀⠀⠀⠈⠀⢠⠘⢀⠀⠀⢀⠉⠴⠂⠀⠀⢠⠀⠀⠐⡂⠒⠲⠐⠀⠓⠀⠀⠀⠀⠸⡖⡿⠀⠀⠀⠀⠀⠇⠀⠐⠊⢡⠀⠐
⠀⢀⡈⢑⣶⢀⡸⠄⠀⠀⠀⠀⣀⣼⡀⡀⠉⠀⠀⠀⠀⠸⠘⠍⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠂⠀⠀⠀⠀⢷⣀⠜⠁
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⡔⣣⠀⠀⠀⠀⢀⡓⠬⠙⣁⠛⠈⠆⠀⠀⠀⣄⢊⠑⠀⠠⠀⠀⠀⠀⡂⠰⠗⢴⠀⠴⠀⠀⠀⠠⠖⠂⠐⢂
⠀⠀⠀⠈⠇⠙⠀⠀⠀⠀⠈⠁⠀⡈⠀⢰⡀⠁⠀⠀⠤⠀⡒⢠⠀⠀⢀⠆⠀⠪⢉⠢⠀⠀⡀⠄⠀⠀⠈⠅⡁⢃⣈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⣤⠊⡄⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠦⣄⡀⠀⠀⠀⠀⡼⡜⢰⠈⢳⡇⠀⡀⢀⠀⠘⡆⠀⠀⠀⠀⢀⡠⠐⠀⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠐⢍⠳⢄⡀⢰⢳⢇⢹⠀⣦⠙⣶⣿⢸⠀⣀⠷⠒⢂⡠⠚⡩⠀⠀⠀⢔⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢆⠢⡀⠀⠀⠙⣾⣾⠀⢘⠘⡄⠀⠘⣿⣼⠞⢁⢴⠀⢸⣴⣿⠎⠀⠀⠐⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠈⢢⠱⠀⢀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⣾⠇⣴⠇⠉⢀⠄⡿⡫⢊⣠⣤⠴⠶⠶⠧⠤⢤⡀
⠀⢠⠔⠒⠉⠉⠉⢉⢿⣜⢆⢀⠁⠀⠀⠀⠀⣿⣇⣸⣯⣀⢀⠀⢰⢣⡾⠇⠀⠀⠈⡄⢸⠃⠁⠀⠀⣈⠄⡁⠄⠀⢠⠃
⠀⢠⠀⠀⠀⠀⢄⡐⢭⣿⣎⢦⠡⡀⢀⠱⣕⣿⡜⠀⠀⠈⠛⢧⣧⢛⠀⢀⣀⡆⠀⠀⢸⠀⠀⠀⠈⠒⠉⡀⠈⢠⣟⠒⠒⠒⠦⢄⡀
⠀⠀⠱⡀⠀⠂⠤⣐⣿⣾⡟⠋⠉⢉⠉⠉⠙⢻⣷⡀⠀⠀⡀⢀⣻⣽⣠⣼⠞⠛⠛⢦⣯⣾⢂⢄⠀⠀⠀⢀⣴⣿⠢⠀⢀⠀⠀⠀⢘
⠀⠀⠀⣈⠦⠴⠓⠒⠿⠿⣧⣀⠠⣀⠀⠀⢠⣽⣧⠁⢽⣌⣼⠟⠚⠈⠛⢿⣶⡀⠀⣩⣿⣷⠕⠁⠀⢀⣴⠿⠿⠿⣯⢁⡀⠄⠀⡠⠊
⡠⠚⠉⠀⠌⠁⠀⠀⠀⠀⡙⢮⡦⠀⠙⠳⢶⣿⣯⢀⣼⣿⣟⡵⢸⡿⣷⣎⣿⡛⢦⢿⠏⠉⠛⠛⠲⣿⣯⣯⠁⠀⠀⠀⠈⠙⠺⣄
⢇⠀⠀⠀⠀⠈⠩⠿⢛⣛⡿⠟⠻⣧⡀⣀⣩⣿⡿⠛⢙⠹⠿⢟⣿⣧⣤⡡⣼⠁⢀⣿⡤⠀⠀⠀⢠⣿⡿⠛⠒⠀⠀⠀⡤⠄⠢⡄⠱
⠈⠢⡀⠀⠀⠀⠠⣤⡼⠋⠁⠀⣀⠬⢷⣤⣿⣿⣇⡀⢻⣷⣏⡉⠀⣻⠙⢫⡇⣴⣿⣯⣒⠀⢔⣫⡞⠭⠉⢁⡀⠀⠀⣰⡦⠍⠀⢀⠠
⠀⠀⠈⠢⣐⠒⣲⢏⠌⡀⠀⠀⠐⠊⢝⣻⣿⣿⠛⢶⡼⣿⣍⣿⣔⢨⣦⣿⣿⡟⣽⣿⣷⣞⡉⠉⢙⠛⢷⡖⠄⢀⣄⢠⡠⠒⢮⣁
⠀⠀⠀⠀⠀⣹⠇⠀⠀⠐⢂⡁⠐⠊⣙⡯⢵⠏⠀⢹⣿⣿⣧⣮⣝⣿⣯⣥⣤⣾⣿⣿⣿⣯⣆⡈⠁⠀⠀⠹⡏⠉⠍⠀⠀⠀⠀⠉⠳
⠀⠀⠀⣠⠾⠟⣲⢬⣁⣀⠀⠀⠂⠉⣤⣠⡿⠀⠀⠸⠛⠁⢹⣿⣯⣝⠿⣟⠀⠈⠉⠛⣯⠉⠙⠒⠤⣀⠀⠀⠹⣟⣂⠀⠀⣀⠠
⠀⢠⠞⠁⠐⠁⡊⠥⣒⣯⣿⠟⣵⡿⣻⣿⡗⠀⠀⠀⠀⠀⢀⣼⡎⡿⣗⣬⠙⠓⢀⣠⣟⠀⠠⠄⠀⠂⠁⠈⠀⣻⣅⠀⠙⣀⠠⠄⠒
⠐⠉⠀⠀⠀⠀⠀⠼⣿⢿⠏⠈⠀⡨⢛⣵⣿⣴⣤⣤⡖⠊⠁⠄⡇⠀⠋⠏⣿⣿⢿⡿⣿⣟⠛⠶⣶⠖⢶⣶⠞⠁⠈⠻⡀
⢠⠀⠀⠈⠒⠀⠀⠠⢒⡟⠀⠀⠀⢀⠔⠉⠑⠋⠿⠟⣧⠀⠀⠀⠇⠀⠀⠀⣯⡻⣯⢻⠈⠐⠀⠀⢻⣣⡪⡻⠧⠀⠀⠀⡙⢆
⠀⠉⠀⠀⠀⠁⠉⠁⠸⠀⠀⠘⠁⠁⡠⢀⡀⠀⠀⣨⣿⣕⢄⠀⠀⠀⣀⢹⢇⢣⠹⣇⢂⠀⠀⠀⠈⣗⠝⠢⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠡⠀⠀⠐⠋⣀⠔⢺⠀⢹⣿⡈⠂⠀⢠⣣⣮⣮⡂⢂⠀⠀⠀⠀⠈⠀⢩⣀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢚⣊⠤⠔⠋⠁⠀⢺⠀⠈⢹⢿⢮⠼⠏⠹⡏⡟⢯⡂⢄⡀⠀⢀⠄⠀⢸⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⡧⡀⢸⢸⠀⠀⠀⠀⢳⠁⠀⠉⠳⢬⡂⠀⠣⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⠈⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠙⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠂⠀⢀⠴⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣴⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢀⣤⣴⣶⠾⠿⠿⠿⠷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣦⣤⣤⣤⣤⣤⣴⣶⠿⠛⠉⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣤⣀⠀⠈⠻⣷⣤⣶⠿⠋⢹⣿⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠉⠀⠀⠀⠘⣿⣶⣶⡶⠿⠟⠋⠁
⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣠⣴⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢿⣷⣶⡾⠿⠛⠋⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⡐⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠈⢳⣄⠀⡐⠀⠀⠀⢸⡆⠀⢀⣤⠊⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⡀⠀⠀⢻⡏⠀⢣⡞⠀⢀⡼⠀⣴⣎⠀⠀⣀⡿⠀⢀⠔⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⢹⡇⠸⡆⠀⣇⢀⣸⣡⡀⣿⡇⢠⣿⠃⠀⡿⠉⠀⢰⣿⠂⢀⣤⣄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠀⣤⠸⣽⣆⣼⠘⣇⢠⣽⣿⣿⡟⢻⢿⣿⣾⣿⣯⣿⣶⣷⡇⠀⣄⣾⣿⡴⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄⠙⠿⣷⣎⠙⢷⣿⣿⡀⠙⣿⠻⣿⣿⠖⠲⣶⢾⣿⣯⣿⣻⣿⣾⡟⠁⠈⡿⠁⠀⠀⠀⡤⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣑⣤⡀⠐⢶⣦⣬⣿⡀⠀⠈⠛⢷⡄⣰⠀⠹⠏⠀⠀⠘⣿⣿⡿⠛⠻⣿⠏⠀⠀⣰⠀⠀⠀⢀⠎⣀⢀⣘⣁⣀
⠀⠀⠀⠀⠰⡀⠀⠀⠉⠙⠶⣤⣈⠻⣿⣿⣄⠀⠀⠀⠙⢽⡀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠀⢀⣰⣿⡴⠁⣠⠎⡰⡫⠊⠉⠉⠉⠛⠂
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⡀⠙⣻⣾⣽⣿⣷⣦⣀⣀⠈⠳⣄⠀⠀⠀⠀⠈⠃⢀⠆⠀⠀⠀⠀⣿⣏⣴⡿⢋⣼⣿⣷⣶⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠙⠷⣬⣐⡺⠶⣬⡤⠿⠿⠿⠿⣿⠋⠙⠛⠷⠿⢧⣀⠀⠀⣀⡠⠋⠀⠀⠀⠀⢀⣿⡿⢋⣴⣿⣿⣟⣫⣡⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠽⠋⠀⠀⠀⠀⠀⠀⣘⣆⠀⠀⠀⠀⠀⠈⠙⠶⣏⠀⠀⠀⠀⠀⢠⣾⣯⠞⠛⠂⠀⠈⠙⠫⣅
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⣤⣾⣷⣦⣤⣀⣀⣀⣀⣀⣤⣿⣶⣶⣶⣾⣿⣿⣷⣾⣭⣶⣦⣤⡀⢀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠰⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣾⠟⢹⣿⣿⣿⢿⣿⠻⢹⣿⣿⣿⡿⢿⣿⣛⣛⣛⣛⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒⠓⠛⠉⠉⠀⠀⢺⣟⠁⠃⠁⠁⠀⠈⠉⣿⣿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣠⣀⠀⢀⢀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠑⠋





⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢳⣄⢠⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠑⢺⡆⢰⣆⢻⠉⢳⣇⡀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠉⣄⡴⣧⣾⡿⠾⣧⣄⠋⢸⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⢶⡀⠰⣌⣷⠛⠿⣇⢀⢸⡏⠀⢸⣿⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣽⣿⣄⢰⡄⠙⣿⠟⠁⠸⡿⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠑⠚⢏⠉⠙⢳⣶⣏⡀⢠⠞⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠓⢒⡾⠿⠟⢳⣿⣾⡍⠙⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⣿⣦⣤⣶⡏⠛⢷⣤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠸⣿⣿⠏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠐⣿⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠤⡁⣸⡅⢸⡷⣧⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⢸⡆⡲⠀⠀⠠⡐⣼⡂⢻⡏⠹⠋⢻⡿⠉⡀⠆⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⣿⠓⣄⣸⡈⣡⠔⢁⣰⣟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⣂⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⣄⣾⠙⠻⣿⣿⣾⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠒⢾⡿⢤⣄⣼⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠊⠡⠑⠉⠍⠹⣏⣯⠿⠶⠟⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢒⡶⠞⠛⣙⠛⠗⠛⠛⣝⠻⢏⡛⠒⠂⠀⠀⠀⠀⠠⠀⠀⠀⠈⠐⠾⠛⠧⠤⢄⣴⣶⣬⣶⣴⣄⣆⡴⢃⣀⣤⣤⣁⡒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠁⠀⠀⠀⠀⠘⡄⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡶⠤⣿⡿⠿⠛⠙⣿⡿⣟⠻⡿⠿⣿⣥⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠙⣆⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠠⠄⠈⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣀⠀⢀⣴⡿⢿⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⣿⣷⡾⠃⠀⠈⢻⣆⣤⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠉⢹⡁⠀⣀⡀⢸⠟⠋⠁⢻⣇⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣠⡀⢰⠂⣽⣷⠀⠀⠀⠀⢼⡇⠀⠀⢀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢣⡁⠀⣼⣿⣇⠀⢸⠶⣿⠀⠀⠀⠀⠛⠁⠀⢀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⠀⠀⠀⠀⠀⠘⢿⣾⠟⠉⣿⣧⣼⠖⠻⠶⣦⣀⠀⠀⠀⠀⣀⣴⣶⣶⣶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣶⣤⣀⠀⠀⠉⠀⠀⠈⢻⣿⡀⠀⢀⡟⣥⣶⡄⠒⠋⠁⠀⠀⠉⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣁⠈⠑⠀⠀⣴⣶⣤⣮⣙⣻⣿⣿⡿⠿⡿⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂⠀⠀⠿⠙⠛⠉⠻⠿⣿⣧⣀⣀⡀⠤⣾⠟⠀⠈⡉⡉⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠈⠆⢀⣳⡴⠂⠉⠉⠛⢦⣤⡾⠧⠒⠛⠉⠽⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣷⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠋⠛⠶⠤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⣴⣿⣦⣠⣀⣀⣤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠠⠴⠦⠄⠀⣤⡤⢀⡀⠀⠀⢠⣿⠃⠘⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⣍⠻⠋⣿⠿
⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣿⠗⠛⠁
⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⢠⠤⠎⠀⠐⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠐⢲⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀⡀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⣴⣿⠋⣀⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠀⠃⠂⠀⠐⠁⠀⠀⠀⠀⢿⡟⠋⠘⠁⠀⠀⢰⣿⠋⠁⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣇⣀⠂⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣟⣛⣿⣿⣭⣏⣿⣋⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢴⠏⣹⣵⠂⡖⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⢶⠋⢹⡿⣥⣖⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⢿⠀⠺⡟⢡⣀⣾⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢦⣣⡰⣿⣏⣡⠈⠡⠤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠿⠻⣧⣠⣾⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢻⣿⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡆⢸⡐⠀⠀⠀⠀⠀⢀⠎⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠈⠿⠉⠋⣟⣰⠆⠀⠀⠀⠸⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⣧⣼⣷⠗⣆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣻⢧⣴⡿⡓⢀⠀⢀
⠀⠀⡀⠄⢀⡀⠀⣀⢀⣠⣉⣉⠉⣛⡧⡄⠀⠀⠀⠀⠀⠀⠀⠠⠤⣶⠦⠴⣤⢤⠤⢤⡤⠤
⠀⢈⠀⠽⠿⠿⢓⡿⡟⠛⠿⠿⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠠⡗⠐⡀⠀⣸⢀⡔⠁⢀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢿⠐⣆⣣⣠⣥⣸⣇⣼⣃⣸⠋⢰⣿⣀⣤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⠲⣿⣾⠘⣾⢿⣿⠭⣽⣿⣿⣿⣿⣿⠂⢾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⡀⢶⣾⣆⠀⠙⢷⣄⠈⠏⠀⠘⣿⠟⠉⠿⠁⢀⡆⠀⢀⢀⣄⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠙⠳⣽⣿⣷⣄⣀⠘⢆⠀⠀⠀⠘⢀⠀⠀⠀⣾⣋⡴⣫⣾⣤⠀⢀⡠
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣈⣳⣤⣶⠶⠾⠛⠛⢻⠉⠙⠛⠳⢤⣀⡤⠀⠀⠀⢀⣿⣯⠶⠿⣿⣥⣶⠋⠁
⠀⠀⠀⢀⣀⣀⡤⠽⢿⣿⣿⠟⠁⠀⠀⠀⠀⢘⣷⣤⣀⣀⣀⣈⣳⣤⣤⣴⣾⣯⣥⣄⣀⡀⠉⠻⢿⣿⣷⣦⠤
⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣥⣤⣀⣀⠀⠀⣀⣀⣀⣼⣿⣿⢿⠿⠟⢹⢿⡟⣯⣭⣽⣿⣯⣭⣴⠶⠟⠋⠉⠀⠀⠐⠒
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠙⣿⢿⠿⠿⠿⢿⣿⣿⣿⡛⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⠿⠿⠽⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠈⠉⠛⣻⣤⣤⡀⣀⣴⣿⠿⠿⠯⠤⠈⠀⠉⠉⠩⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠈⠉⠉⠭⢿⣿⡿⢿⣿⣿⡯⠭⠤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠈⠉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉⠉⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠄⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠂⠀⠀⠀⠀⠉⠉⠨⣤⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠐⠀⠀⠀⠂⢤⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠎⠁⢀⠀⢀⡓⠀⠄⣡⠀⣹⡀⢠⠀⠀⠀⠈⠀⢀⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣧⠀⡀⢠⠁⡽⢀⣞⣻⣿⣼⣿⠂⠄⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠒⠄⠀⠀⠀⠀⠸⣮⡃⠈⠃⠐⡾⣁⠉⠁⢻⠋⠀⣰⠀⠾⠀⡀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⣀⣼⠊⢀⣀⣄⢠⡠⠂⠀⠀⡀⠀⠀⠀⢋⠙⠛⡀⠡⠘⠀⠈⢆⠀⢐⠤⠒⠋⠀⠖⢊⠄
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⡇⠀⠀⢻⣿⢿⠁⠀⠀⠀⣧⣤⡤⠂⠁⠈⣅⡙⣦⡙⣆⠀⠈⡖⠁⠀⢠⢁⠴⠀⠀⠀⠠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠂⢤⡏⢿⡇⠀⠀⠀⠋⠀⠂⠀⠀⡠⠉⠋⠀⠀⠀⣸⠿⠛⠀⡿⠔⠷⠶⢦⣤⠴⠟⠥⡄⠀⠂⠁
⠀⠸⡆⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠁⡀⠀⠐⢠⠑⠄⠀⠀⠒⠂⠀⠀⡀⢀⠀⠀⠀⠀⠂⡼⠠⠀⢠⠶⡟⠙⢦⣤⡀⡀⠑
⠀⠀⠙⢦⣄⡀⠀⢀⡠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⣧⠆⠀⠀⠀⠀⢀⡀⡀⠈⠄⠈⠀⠀⠀⠀⠀⠀⣰⡉⠉⣰⠃⣰⠃⠐⢾⠈
⠀⠀⠀⠀⠈⠻⣷⡉⠐⢀⠀⠀⠐⠻⠆⠀⠀⠀⠀⠀⠁⡄⡰⣾⣮⣇⡜⢳⣿⣴⡵⠀⢀⣦⠄⠀⠀⠴⠛⠛⠈⠁⠀⡠⢌⣀⡸
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡊⢡⡀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠉⠀⢺⢻⡽⣻⣷⣷⣭⡼⠃⡀⠀⣆⡤⠊⠀⠀⠀⠀⠀⡴⠀⣠⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢷⣄⠀⠀⠀⠐⢆⠀⠄⠙⢀⠄⢄⠛⠋⠀⠻⡿⠉⠀⠐⠃⢰⠋⠠⠤⠀⠠⠄⢤⣾⣷⣩⡾⠋
⠀⠀⠀⠀⢙⢦⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠳⢬⣶⡇⠀⠀⠀⢀⠀⠀⠐⠐⠉⠂⠀⠀⠀⠈⠁⠐⠒⠒⠀⠀⠈⠁⠀⣀
⠀⠀⠄⠠⡈⠩⢳⡄⠀⠶⢦⣄⣀⠀⠀⠀⠀⠀⢀⡀⣈⡻⢤⠀⣀⣼⣟⡠⠄⢀⣰⠗⠁⠀⠀⡀⠠⠐⠉⢀⣀⣠⣤⡶⠦⠄
⠀⠀⠀⠀⠨⣳⢤⣕⣶⣶⣀⡈⠉⠙⠛⠻⠟⠁⠉⠁⠀⠀⠀⡀⠋⠈⠘⡆⠉⡯⠙⢿⠧⠀⠀⠉⠛⠍⡉⠉⠉
⠀⠀⠀⠀⠀⢀⡠⠟⢛⢷⡉⠐⠁⠉⡉⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠢
⠀⠀⢀⡴⢖⣻⡶⠶⠤⠁⠛⠳⣦⣤⠀⠀⠀⠀⣀⡄⠶⠟⠷⠄⢀⣀⣤⣶⡀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠡
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⡴⠾⠿⠿⠀⠀⠀⠀⢀⣾⡿⠛⠻⣷⣄⠀⠀⠀⠀⠈⠃⠉⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠰⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣩⠿⡷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢀⡴⠒⢤⡀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠜⣱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡍⢛⠇⢿⢤⣀⣼⢅⣀⢸⡷⣏⠉⡃⠀⠀⡀⠀⢀⣴⡁⠀⢴⣿⠃⠀⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⣤⣀⣰⣷⡈⢆⡞⠂⢹⠛⠚⢫⣌⡶⠛⡤⠓⠋⠤⢷⡶⢋⠈⠀⠔⣽⠃⠀⠀⠀⣀⡴⢞⡧⠟
⠀⠀⠀⠀⠀⠘⢄⠉⠃⡙⠈⢇⠀⢨⡦⢠⠀⣀⣀⣴⡀⢠⠞⢫⠎⠄⠀⠀⢀⡾⠁⠀⢀⡤⠞⢡⡴⠋
⠀⠀⠀⠀⠀⠀⠠⣷⣤⡀⠀⠀⢹⡅⠀⠀⣾⣿⣿⣿⣿⣀⢰⠏⢀⠀⠀⣠⡞⣡⢤⠞⠉⣶⣢⠟
⠀⠀⢀⣤⢄⠐⠒⠛⠒⠀⣀⡀⠚⠿⠦⠴⢿⣿⣼⣯⣽⠿⣟⢆⣀⣠⠾⢋⡉⠀⠠⣐⣾⠿⠋⢀⠀⢀⣠⡀
⠀⠀⠈⠑⠒⠒⠂⠐⠾⣿⣍⣠⡤⠖⠚⠙⡉⠁⠙⢻⣧⣶⣏⡍⣯⠀⠀⠠⠀⠀⣡⡾⠙⢦⡔⠉⠑⠇⠀⠘⡄
⠀⠀⠀⠀⣀⣠⠤⢤⡒⢒⡏⡵⠐⠂⠁⠀⠀⠀⢀⡼⠿⠾⣽⠞⣾⣄⠀⠀⣠⠾⠇⢰⠃⠺⣇⠀⠀⠀⣦⣄⣦⡴⠊⢹⡄⠀⣠⣤
⠀⣴⣾⣛⣁⠀⠀⠀⣒⡱⣀⠀⠐⠐⣀⣠⠤⡾⢏⠕⠀⢀⠜⣷⠽⣿⣷⡿⠉⠐⢆⡎⠀⠀⠸⠃⢦⠂⠁⠀⠏⠀⠀⢀⠗⠉⠀⡼
⠀⠙⠻⠯⠥⠮⠿⠵⠶⠖⠛⠚⠛⠋⢉⡴⠪⠀⠀⠀⠀⠀⢠⣼⣿⡽⣾⣧⣀⡧⠈⠻⡎⢳⢰⢰⠄⠓⡤⣀⡀⡄⠊⣾⠀⠀⣠⢥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠀⠀⠀⠂⣂⡴⣶⠟⠁⠘⢻⣏⢻⣿⡇⣔⣆⣵⢺⡻⣯⠃⠿⢅⢸⡇⠀⠀⣾⠖⠈⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢀⣺⠷⠒⠋⠀⠀⠈⠓⣄⢀⣄⢻⣾⡻⡽⣎⡯⣏⣿⣻⢭⡛⢺⠎⠁⢰⠂⡰⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢋⣠⠴⠚⠉⠀⠀⠀⠀⣶⠒⠀⠒⠚⢧⡀⠀⠹⣦⡻⣿⣧⣈⠋⠉⠻⢦⣾⠀⠀⣤⠴⠳⢢⣶⡮⡄
⠀⠀⠀⠀⠀⢠⢊⣠⡽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠤⣒⠿⣷⢟⡾⡎⠰⣤⠔⠃⠈⢁⠇⠀⢀⡡⢁⢀⠔
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠂⠉⠉⠓⠾⢛⠶⠷⠂⠚⢶⢶⡶⢿⡚⠙⢿⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣀⣠⠴⢿⣝⡆⠀⠀⢨⣞⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⢈⠘⠀⢀⡠⠔⠉⠦⣆⣀⡀⡀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⡰⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⡏⠈⢻⣀⠔⠛⣇⠀⣠⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠹⣆⠀⠀⠀⢳⠀⠀⠹⢀⡀⠀⡟⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⢆⠀⠀⢠⠀⡠⠚⠉⡿⡸⠃⠊⠉⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠒⠦⢄⢠⡟⠲⣄⠈⢠⠀⡗⠀⣠⠄⢀⣞⠤⠖⠛⣦⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⢷⡀⠈⠀⠸⠀⢳⠰⡿⣰⢺⣇⡄⠀⡰⠃⠀⠀⠉⢛⣶
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣵⢄⣠⠄⠑⢄⡀⠷⢰⢘⡘⢃⢟⡿⣾⠖⠋⠐⠦⣤⣔⠚⠛⠨⢽⡓⠶⢤⣄⣀
⠀⣠⡴⠖⠛⠉⠉⠉⠁⠀⠀⠀⠸⣦⡀⠀⢰⠁⠀⠈⠟⡠⢀⣴⢠⠟⠀⣀⠀⣀⣤⠟⠀⢀⣀⣴⠇⠀⣀⠀⠉⠙⠓⠦⣄⡀
⢸⡃⠀⠀⠀⠀⠠⠒⠋⠉⠉⠀⠀⣠⠍⢑⠈⠛⠒⠒⣊⠀⠀⠢⢤⣤⣤⠞⠀⠀⠀⠹⣍⠉⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠙⢦
⠈⢳⣄⠀⠀⠀⠀⠀⢀⡤⠀⠀⣰⠃⠀⠘⢦⣤⣤⡤⠈⠳⠦⠼⢀⡀⠀⠸⠂⢤⣀⣀⣘⡦⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀
⠀⠀⠈⠳⣤⡀⠀⠀⠸⣄⠀⠰⣧⣀⣀⣠⠤⠖⠂⡀⠈⢦⡀⠀⠀⠉⠛⠶⢇⡀⠈⠉⣏⠀⠈⠆⠀⠀⠀⠀⠀⡰⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠉⠓⠦⣄⣈⠂⠀⠀⠈⠀⠀⠀⠀⠐⢇⠀⠀⠙⠶⡤⠃⡷⡄⠀⠈⠙⠓⠋⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⢤⣄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠈⠢⣀⠀⠀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠢⠤⠤⠤⣤⣤⠇⠀⠀⠈⠉⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠉⠉⠀⠒⠒⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠔⠈⡀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠠⠤⢄⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠁⠒⠢⣄
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⡀⠄⠐⠒⠚⠢⢄⡀⠀⠀⠀⠀⠀⠱⡀⠀⢳⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣀⠀⠀⠱⠀⢸⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢀⠜⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⢃⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⢀⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢂⢳⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠘⡆
⠀⡎⠀⠀⠠⠤⠤⠄⠀⠐⠒⠒⠒⠒⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡀⡇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢄⣀⠀⠀⠀⠀⠑⣤⣾⢀⡇⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣾⠭⡉⠉⠀⠀⠀⠀⠀⢀⠠⠆⠐⠐⠂⠈⠉⠉⠉⠉⠒⠂⢳
⠀⡇⠀⠀⠀⠈⠉⠉⠑⠒⠠⠤⠄⠀⠀⠀⠤⠀⠤⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⢘⠁⠈⠑⢌⠑⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠉⠉⠉⠁⠀⠀⠀⠄⠘⠀⡀⢁⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡇⠀⢡⠈⢆⠀⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠃⠀⠀⠀⠤⠤⠤⠤⠤⠀⠐⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠈⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⢆⠀⠀⠀⠀⠑⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⢂⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠙⠫⡁⠒⠒⠤⢄⠀⠀⢠⠇
⠀⠀⠀⠀⢂⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠂⡜
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⡆⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠱⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠠⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠒⠒⠂⠤⠤⠤⠤⠤⠤⠖⠋

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠠⠐⡀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⠂⠄⠀⠂⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠄⡄⠠⠀⠀⠀⠂⡀⠀⠀⢀⠐⢀⠀⠀⠄⣀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠁⠀⠈⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠉⠰⠈⠀⠀⠂⠀⠐⠂⠠⠐⠀⠈⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣶⣤⣤⣤⣀⣰⣒⣿⣼⣃⣀⣤⣤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⣤⣄⣀⣘⣧⣿⣒⣆⣀⣤⣤⣤⣦⣥⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡁⠆⡈⣉⢩⠁⣽⢳⡵⣯⡱⣿⡦⠏⢎⡉⣉⣏⡉⠉⣩⡉⠩⠉⠉⢉⣉⠉⣁⣉⢉⡷⠹⢴⡻⢎⣽⢪⣟⣭⠉⡈⠉⠠⢀⡩⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢃⣀⣀⣘⣀⢠⡴⣿⡝⢩⣝⣯⣵⣳⣺⡆⣿⠉⠃⣼⠃⠘⣤⡞⢠⠗⠈⣿⣥⣿⢘⣷⣞⡮⣽⣫⡩⢸⢿⢧⣄⣃⣀⣀⣘⣀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡭⠛⠙⠫⡟⡭⠝⠻⢭⡿⢧⣼⠟⡽⣿⢻⣿⠈⠀⡊⠈⡈⠎⠀⢌⠇⠀⣾⣿⠾⠉⠉⣨⠛⢯⣼⢿⡭⠟⠛⠋⠭⢫⠭⠉⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠂⠴⢢⠔⠉⠁⢠⢒⠄⠊⠁⠠⠖⣇⠀⠈⠙⠂⡀⢱⢓⣤⣡⠀⢮⠀⢠⡿⠋⠀⡀⣰⡃⠴⢢⠄⠋⠐⠠⠖⠤⠈⠙⠠⠔⡦⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠤⠈⠉⠠⣖⠦⠀⠉⠀⢔⣲⠴⠋⠙⠃⢂⠀⠀⢧⣿⣤⠘⢧⠀⣼⢸⡟⢀⣴⡶⠋⠈⠁⠊⠉⠠⢖⠢⠄⠉⠀⢴⡲⠤⠉⠁⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⢖⣲⠐⠁⠁⠰⣒⡶⠋⢀⠔⠀⠀⠀⡈⣱⠴⠤⠌⢻⣄⠀⠀⢸⡤⠀⠘⢻⡄⠀⠀⠀⠀⠀⠀⠁⠁⠰⣒⠆⠊⠈⠀⢖⡲⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡒⣁⣀⣒⣊⡒⠊⠈⠁⠀⠁⢀⠂⠀⠀⠀⣠⢤⣔⠠⢤⣿⣆⠀⣾⣴⣟⣃⡉⠃⠀⠀⠀⠇⠀⠀⢈⡗⠊⠀⠑⢚⣑⡒⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠢⠀⠀⠈⠑⠒⠖⠚⠋⣿⠀⠀⣿⡍⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⠐⠣⠂⠐⠀⠉⠐⠄⠁⠀⠀⠀⠀⢀⡀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠁⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠂⠀⢠⡀⠀⠐⠀⠀⠈⠇⡀⠀⠐⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠠⡆⠀⢀⡘⡇⠀⠀⠂⠀⠀⡴⠀⠐⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠈⠉⠑⠂⠙⠛⠊⠀⠀⡰⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢃⠀⠀⠉⠚⠋⠑⠂⠉⠁⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣀⣀⣉⣁⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣄⣈⣉⣀⣀⣀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠶⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⠃⠀⡀⣀⡤⢦⡀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⢉⡟⠉⣧⢦⣤⠷⣦⣶⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣄⡟⠉⠳⣾⠁⠈⢧⢀⡿⢤⡙⣦
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡇⠀⢳⣀⣠⢿⡖⣶⠋⢉⣳⣄⡟⠘⣧⡀
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⠉⢨⡖⠋⢹⣟⢭⣼⡿⢷⡏⠹⣏⠀⠀⠘⣧
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠙⠲⡴⠋⠓⡟⠉⠙⣏⡀⠀⣱⠴⡎⠀⠀⠀⢹
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠖⠧⠴⣞⠉⣹⠋⠁⠀⡇⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡤⠟⠛⠉⠑⠒⠊⠁⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣲⣶⣦⣤⣤⣴⣖⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠘⠄⠀⠀⡐⠀⠀⠁⠀⠀⡀⠐⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠌⠀⠈⠄⡐⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠁⠒⠀⢄⠀⠀⠀⠃⠀⠀⠀⠠⠁⠀⠀⠘⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⢀⠐⠀⢹⠀⠀⠀⡀⠘⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠁⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠀⠀⠀⠈⠢⠡⡀⠀⠀⠈⠳⡀⠀⠀⠀⡠⠀⢀⠌⠀⠀⠀⠀⣘⠁⠐⠀⠉⠁⠆⠀⠀⠀⠊⠀⠀⠠⡀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠔⢆⠀⠌⠀⠀⠉⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠘⠂⠀⢸⠀⠀⠙⠀⠀⠀⠀⠀⢂⠀⢀⠂⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠉⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠑⠂⠀⠀⠉⠉⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠡⡀⠀⠒⠠⠤⡀⠈⢄⠀⠀⠀⠀⠠⠥⠄⠠⠄⠒⠠⠄⠀⠠⠴⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢙⠂⠲⠁⠂⠐⠈⠓⣐⠀⠀⠀⠀⠂⠀⠂⠁⠀⠀⠀⠢⡀
⠀⢀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠠⠤⠀⠀⠤⠄⠀⠀⢂⢡⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠠⠄⢀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠂⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊

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

⠀⠀⠀⠀⢀⣴⠋⠉⠳⣄
⠀⠀⠀⢰⣿⡿⠀⣦⣤⣭⣷⡾⡋⠉⢙⢦⡀
⠀⢀⣴⡿⠷⢾⡥⠖⠒⠂⣼⣿⣷⣾⣿⣿⣿⣷⢦⣄⣀⡀
⠀⣾⣿⣜⡀⠂⠀⠀⠀⠘⠿⣿⣟⣛⣫⣟⣟⣭⢳⡾⣭⣟⡿⣗⣶⣤⣄⡀
⠀⠳⣦⡭⢿⣻⠷⠶⣤⣄⣀⠈⠙⠛⠷⠟⣽⣿⣦⡀⠉⠉⠝⠓⠮⣍⠙⢛⠶⣄
⠀⠀⠀⠑⠀⡄⠈⠀⠂⠬⢉⡛⠳⢦⣄⣀⣛⣉⣻⡇⠈⠱⠆⡀⠁⠀⠉⣹⡻⢮⣷⣦⡀
⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠉⠀⠲⠏⠉⠉⠉⠀⠀⠆⠐⠇⣶⠁⣀⠙⠳⠆⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣅⡂⢄⠀⠲⠦⢀⡶⠄⠆⠁⣽⣿⣿⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡂⠀⠀⠀⠀⠀⠘⡿⣷⣤⣂⡍⠳⢮⣆⠀⠀⠀⠀⣠⣶⣿⠿⠛⠉⢉⡁⣬⣷
⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⠟⠲⣦⣤⡀⢀⠀⠈⠒⠽⣻⣿⣄⡲⢝⠳⢤⣠⣾⣟⡭⠊⢀⣨⣴⣻⡿⣿⣽
⠀⠀⠀⠀⠀⣠⠿⢿⣿⣯⣀⣀⣀⣙⣻⣦⣍⡀⠀⠀⠀⢹⣿⡟⣾⢁⣿⣿⣿⣿⣰⡌⣦⣽⡿⣫⣼⣿⡏
⢮⡥⠶⢶⣾⣣⡟⣼⠿⣿⠍⡛⠛⠿⠟⠈⠻⢿⣷⣶⣶⣿⣷⣻⣷⢿⣿⣿⣿⣷⣏⠹⠋⣩⣾⣿⣿⣻⠁
⠀⢰⣉⡵⠋⠉⡧⢏⠀⠈⠛⠁⠀⢿⣵⣤⣄⣠⣭⣿⣿⣿⣟⠏⣠⠋⣬⣿⣿⣟⣀⣀⣨⣵⣿⢿⢧⡏
⠀⠀⠉⠀⠀⠀⠓⠚⠀⠀⠀⢮⣤⣶⣬⣭⣿⣿⡧⠙⣿⠏⣠⠞⣵⣶⣾⡿⣿⣿⣿⡿⣿⠃⠀⣈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣽⠟⠛⠛⠓⠚⠁⠺⣬⠟⠛⢋⡝⢩⣴⠿⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡴⠶⠒⠒⠖⠒⠒⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠡⠀⠀⠠⠠⠀⠀⠀⠁⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣰⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠐⠀⡠⠊⠀⠀⠁⠀⠀⠀⠌⢳⡄
⠀⠀⠀⠀⣼⠋⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⢀⡇⢀⠊⠀⠀⢴⡋⠤⠠⠶⠚⠉⠀⢀⠀⠀⠀⢹⡄
⠀⠀⠀⣼⠁⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡗⠀⠀⡆⠀⠄⡠⠂⠁⠡⠤⠤⠤⠤⠄⠒⠊⠁⠀⠀⠠⡈⢻
⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⢀⠔⠊⠃⠀⠀⠀⠀⢀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢄⠀⠀⢀⠀⠐⢀⠠⠾⠁⠒⠀⠀⠁⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⢐⣧
⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠀⢀⡴⠀⡀⠐⠁⠀⠀⠀⠀⣉⢉⠐⠛⠓⠒⠲⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠘⢷⣤⣠⣄⣀⣤⣄⣀⡀⠀⠀⠀⣀⣤⠶⠛⠣⣤⠞⠁⠀⠈⠂⠀⠀⠲⣄⠀⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠤⠬⠙⠛⣩⣿⡟⠑⠀⠀⠋⠀⠈⠀⠀⡆⠠⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⡉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣄⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⠦⠤⠤⠶⠿⠶⠶⠖⠒⠛⠉⠁

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢠⠀⠄⠀⠀⠾⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⣭⣍⢢⣄⣁⣀⣾⡃⢀⣤⠗⡀⢙⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⢸⡿⠋⠻⣿⣿⣿⠿⠛⣩⣋⣴⠋⠀⠀⠀⠀⠀⣰⠖⢾⣽⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⣳⣾⣧⣀⣀⠙⣿⠃⠀⣴⣿⣟⡁⢠⡝⠀⠀⠀⠀⣌⣠⡞⠁⠸⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣤⣤⣤⡤⠽⡄⣙⠻⣿⣤⡾⠻⢷⡿⠟⠁⠀⠀⠀⠀⢠⠙⣟⠀⠐⡧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣉⣤⣤⣤⣾⡵⠟⢻⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣦⣿⡄⠆⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠈⠻⣷⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠠⠀⠐⠊⠁⣠⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠔⠛⠻⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠄⣸⡇⢀⡀⠠⠔⣺⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡾⠳⢦⣀⣻⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣤⣤⡴⠊⠀⠀⡀⠀⠀⣸⣿⢀⡤⠤⣼⠀⠀⠀⠀⠀⠀⢀⡀⣼⡇⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠠⣀⣀⡠⠔⠋⠀⠀⠈⢿⠁⠀⠜⠉⠉⠀⠀⠀⢀⠀⠈⠛⠋⠉⠁⠉⠉⠀⠑⠠⢀⠀⣼⠇
⠀⠀⢀⡄⠐⠈⠀⡈⠶⠈⠁⡀⢀⡀⠀⠙⣿⡀⠀⣾⡀⠀⣧⡤⡄⠀⠀⣀⢄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏
⠀⠀⠸⠤⠠⠶⢀⠀⠀⢷⣄⡀⠉⠻⣦⡀⠘⣧⠀⣿⠀⣰⠏⢰⣤⢀⡀⠀⠭⠚⣳⣤⣠⣄⠐⠀⠀⡠⢊⡤⢒⣿⡀⠀⠉⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡉⠛⠶⣤⣈⡙⣦⣜⣧⣿⣴⣿⣶⣟⣿⠈⠉⡀⠀⠀⢀⠙⠿⣿⣷⣴⣟⠀⡡⢄⣼⡏⠀⠀⠀⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠀⠠⠍⠽⣿⢿⠏⣴⠛⣽⠀⠀⣿⠀⠀⠀⠒⠤⠉⢁⣠⠄⠉⠛⠛⠟⠻⠿⣾⠛⠁⠀⠀⠀⠀⠀⢀⣵
⠀⠀⠀⠀⠀⢀⡀⠤⠄⠊⠀⠀⠀⢴⡀⠀⠘⣾⠀⢻⣦⣇⠞⢈⣿⠀⠀⠀⠀⠀⠀⠈⠙⢣⣀⢀⣀⡿⠆⣠⣿⣦⣤⣀⠀⠀⢀⣀⣀⡅
⠀⠀⠀⠀⡄⠀⠀⠀⠐⠲⣦⡀⠀⠈⢳⡀⠀⢻⠀⢸⣿⡜⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣿⠀⠀⢸⡏⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠁⠀⠀⢶⣤⣀⡀⠈⠙⠶⣄⡀⢻⡄⢸⢂⣾⣿⡅⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⡟⠀⠀⢸⡇
⠸⡃⠀⠀⣤⣤⣄⣀⣉⣙⠛⠳⠶⣦⣽⣶⣿⢾⡿⠋⢹⣇⠀⠘⠋⠉⠉⠁⠀⠀⠘⠷⣼⣧⡴⠾⠟⠀⠀⠘⠷⣀
⠀⠈⠀⠒⠶⠶⠤⠭⠭⠭⠭⠽⠿⠿⠿⠟⠛⢾⣄⡠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⡀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢢⡜⠋⠁⠀⠠⠀⠀⠀⠈⠢⠐⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣾⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠉⠁⠀⠀⢀⠀⡘⡇⠀⠀⠀⠀⠀⠀⣀⠀⢀⣰⣾⣦⠀⣆⣀⣀⣤⡶⠤⠒⠈⠉⠀⠀⠀⠀⡙⣠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠃⠐⢆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠠⣄⣠⠖⠈⢀⠿⠺⣿
⠀⠀⠀⠀⣀⠔⠁⡀⠀⢀⢠⡀⣶⡶⠀⢀⡜⠀⠀⠀⠛⢿⣯⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⠀⠀⢀⠠⠁⠀⠀⢸⡇⣸⠟
⠀⠀⠀⠊⠀⠀⠀⠈⢠⣈⣄⣿⡿⠃⠀⡾⠁⠀⠀⠀⠀⠘⣿⢦⣀⣀⣤⣿⠀⠀⠀⣰⣷⡀⠀⣠⡞⠉⠉⢻⡇⠀⠀⠀⢠⣏⡁⣿⡇
⡐⠀⠀⠀⠤⠤⢤⣤⣤⣿⡿⠏⠁⢀⡰⠂⠀⠀⠀⠀⠀⠀⢹⠀⣿⣿⡇⠈⢀⣿⢸⡏⠉⠉⠁⢸⡇⠀⠀⢸⡇⠀⠀⢠⡾⡿⠠⣾⡇
⡄⠀⠀⠀⠀⠀⣠⣼⠛⢃⠀⣠⠞⠻⣦⡀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⡇⠀⢸⠇⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⢀⡟⠀⢸⠺⣯
⡇⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠋⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⡇⢸⣿⡇⠀⣾⠀⢸⡇⠀⠀⠀⢸⡃⠀⠀⣸⠇⠀⣾⠃⠀⠈⠓⠃
⡇⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠉⢻⣆⠀⢀⣀⡀⠀⢱⢸⣿⣿⢀⡏⡀⢸⣇⠀⣀⣀⣼⣅⢀⡀⣿⡆⣸⣯⣀⣀
⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠈⢸⣿⡏⠸⣇⠀⣿⠋⠉⠀⠀⣿⡧⣶⣴⣿⣷⣾⣷⡀⠀⠀⠈⢙⣖⠐⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣼⣿⡇⢸⡇⠀⣿⠃⠚⠋⠀⣿⠦⣜⠩⣿⠁⣿⠋⠉⠁⠀⠀⠉⠉
⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⢸⣇⠀⠀⠀⠒⠃⠘⠃⠹⣤⣤⠿⣅⠁⠀⠠⠿⠄⢀⣼⣿⠠⠟⠒⠒⠒⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠤⠐⠀⠉⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠐⢀⠠⠀⢀⠀⠀⠀⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⣀⣠⣤⣶⣾⣦⣶⣶⣴⣿⣿⣷⣶⡦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠌⠘⠛⠿⠉⠛⠛⠉⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⠇⠀⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⢄⡀⠠⢶⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⠖⠁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣶⣶
⣿⣿⣿⠙⣉⠙⣏⢁⣽⢉⣹⡙⢉⣿⠟⣭⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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