Computer graphics Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠸⠄⢠⣿⣿⠄⠀⠀⢠⣶⣦⠀⠉⡏⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣿⣿⡟⠀⠀⢀⣾⣿⡟⠀⠀⢀⡈⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠿⢿⠁⠀⣰⣿⣿⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣿⡿⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⢻⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠈⠓⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠹⣿⣿⣶⣴⣶⣿⣿⡿⠟⠁⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠈⠛⠿⠿⠟⠋⠁⠀⠀⢀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠛⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⣿⣿⣿⣿⢿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠉⡁⣈⠁⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠠⢌⡣⠥⢠⡌⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡃⡞⠀⠊⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠇⠈⠧⣀⢀⢀⡓⠀⠰⠀⡆⠢⡀⠀⣠⠆⠀⠀⠀⣰⢦⠀⢠⢶
⠀⠀⠀⠀⠀⢁⠀⠁⢖⡛⠛⡓⠊⠁⣠⠟⢡⠀⠃⠙⠀⡨⠬⠥⣼⣆⠀⠀⠙⢾⡤⡾⠋⠀⠀⣰⠉⣇⡐⣲⠀⡀
⠀⠀⠀⠀⠀⠂⡖⣀⠀⢙⡆⠀⡀⠈⣈⠕⠂⡎⡤⠒⠢⡀⠠⠤⣄⢉⡄⠀⠀⢈⠀⠇⠀⠀⢠⠤⠀⡄⠀⠙⢠⡞⢀
⠀⠀⠀⠀⠀⠸⡇⣧⠄⠚⢉⣈⠁⢰⠃⠀⠀⠿⠁⠀⠀⠑⣠⠴⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠻⣦⠀⢡⠚⠁
⠀⠀⠀⠀⠀⠡⠙⢀⡴⠋⠉⠁⠀⠚⠂⠀⢀⡴⠋⠉⡥⠋⠁⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠰⠄⠸⡏⠀⠀⣩⠁⢈⡅⠶
⠀⠀⠀⠀⠀⠠⠀⠈⣠⠀⠘⣇⣠⠴⠒⠒⡿⠁⡔⠉⢧⠀⠀⠀⢈⠐⠲⡅⠩⠥⠀⠬⠅⠌⠀⣄⠀⣀⠴⠏⢀⣘⢢⡄
⠀⠀⠀⠀⠀⠥⠶⠄⣏⠀⡀⠈⠃⠀⠀⠀⡇⠀⠃⣠⠄⠂⠀⠀⠀⢱⡀⠘⡇⠻⣿⠟⠀⠀⢠⠏⠈⠁⠀⣤⢌⣧
⠀⠀⠀⠀⠀⠀⢀⠴⠛⢲⡧⠖⠒⠂⠀⠀⠁⢀⡞⠀⡔⠂⠀⠀⢀⠼⠁⠀⡇⠀⠘⡆⠀⢠⠞⠀⣸⠇⠀⠙
⠀⠀⠀⠀⠀⠀⠏⠀⢠⠏⠀⡔⠀⣠⣤⣄⠀⢸⠀⠀⣇⠀⢄⡀⠀⠀⠀⠀⠀⠀⢀⡇⠐⢁⠤⢰
⠀⠀⠀⠀⠐⣴⠒⠂⢾⠀⠸⡅⠈⢀⡠⠤⣄⣘⣆⠀⠘⣆⠀⠉⠛⠂⠀⠀⢀⡠⠊⠀⣰⠁
⠀⠀⠀⠀⠀⢳⠀⣀⠘⢆⠀⠈⠁⡏⠀⠀⠀⠈⠉⠀⠀⠘⡆⠀⢸⠀⣀⡤⠤⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⢀⣥⠀⠀⠒⠂⣶⠐⠀⠀⠁⢀⣘⣛⣁⣀⣀⣀⣀⣘⠀⠀⠀⢢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠉⠀⢠⡀⠀⣿⠠⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⢠⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⢄⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠚⠆
⠀⠀⠀⠀⠁⢈⡆⠀⠀⠂⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠠⠀⠄⠀⠂⠤⠀⠀⠀⠀⠀⠀⢀⠀⡀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠆⢉⡀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⢀⡴⠀⡀⡲⠅⠀⠁⠀⠈⡁⠀⠀⠀⠀⠀⠌⠜⠀⠀⠀⠀⠀⠀⣦⠀⠁⣈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢠⣀⣠⣤⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠌
⠀⠀⠀⢔⠒⢂⢀⠀⠀⠤⠤⠌⠀⠀⠀⠀⠄⠀⠀⠠⠄⢀⠈⡀⠁⠀⡇⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠀⠸⠂⠄⢘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠸⣀
⠀⠀⠀⢀⡐⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠚⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠈⠣⡼⢆⠂⠀⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠚⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠁⠂⠈⠄⠶⠀⡀⠘⢄⠃⣀⠂⠀⡀⠄⠀⠀⠀⠀⡀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡠⠀⢺⠀⠉⠀⠈⠀⠀⠀⠠⠤⢀⠁⣛⡇⠂⠀⠀⢀
⠀⠀⠘⢀⠀⠀⠀⢧⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠒⢈⠤⡀⠀⠡⠐⠀⠀⢂⠀⠘⠋⢸⠆⠀⠀⠆
⠀⠀⠀⠀⠉⠣⠀⠈⠀⠀⠀⡠⡆⠀⠀⠀⠄⠀⠀⠀⠀⠄⠉⠁⠀⠨⠀⠀⢀⠀⡆⠀⠀⣸⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⠛⠂⣀⠀⠀⠦⠀⠀⢀⠀⡀⣀⢀⢄⡁⢀⠔⠒⠁⠁⠀⠈⢣⣬⠂⠰⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈

⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⢀⣀⣀⠀⣸⣿⣿⣿⡄⠀⠀⢠⣶⣶⣾⡂⠀⠀⢀⣤⡀⠀⠀⠀⠰⢾⣿⣿⣿⠆
⠀⢀⣤⡴⠶⣶⣮⡅⠀⠀⠀⣈⡉⣻⡇⠸⠿⠿⠛⠐⢦⡀⠸⣿⣿⣿⡃⠀⠀⠘⠿⠛⠓⠲⠶⠶⢬⠟⣻⣯
⠀⠸⡇⠀⣸⣿⠏⠻⠶⠞⠊⠉⠁⢻⡇⠀⠀⢸⣿⣠⡾⠃⠀⠈⠉⢿⣿⣄⠀⠀⠀⠀⠀⠻⠷⣤⣄⣸⣿⣿⡆
⠀⢰⣧⢀⣿⣟⣀⣀⣀⡀⠀⡴⠀⢸⡇⠀⢀⣼⣿⠋⠀⠀⠀⠀⣀⠀⠻⣿⣿⡛⠛⣿⠂⠀⠀⠀⠈⠉⢸⣿⣷
⠀⠀⠀⢸⣿⠉⠉⠉⢹⡇⠈⠀⠀⢸⣇⣴⠟⣻⣿⠀⠀⢀⣴⣿⣿⣿⡄⠙⣿⡟⠛⠛⠛⠶⣤⣼⠃⠀⣴⡿⢻⡆
⠀⠀⠀⢸⣿⠀⠀⠀⠘⠳⠀⢀⣴⣿⠟⠁⠀⠙⣿⠀⠀⠀⠙⠿⣿⠿⡃⠀⠘⣷⡀⠀⠀⡀⠀⠀⣠⡾⠋⠀⠘⣿
⠀⠀⠀⠸⡿⠀⠀⣤⣶⣶⣴⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⣤⣦⡄⠀⣿⣿⡀⠀⠘⣷⠀⠀⠇⠀⠀⣿⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠘⠿⠦⠀⣿⣿⣿⡟⠙⢷⣀⣀⡀⠀⣴⡷⠀⠈⠿⠿⠛⠲⢾⣿⣇⠀⠀⠐⣷⡴⠆⠀⢀⣿⠀⠀⠀⠀⠈⣿
⠀⣠⣴⣦⡀⠀⠀⠈⠙⣯⡁⠀⠀⠉⠉⢉⡧⠀⠀⢲⣀⣀⣤⣤⣤⣌⣿⣿⡀⢀⣤⣤⣄⠀⠈⠉⠉⠀⣀⣀⠈⠉⠉
⠐⣿⣿⣿⡿⠂⠀⠀⠀⣌⡗⢀⣠⣾⣿⣦⡀⠀⠀⠈⠉⠉⣁⣀⠀⠉⠉⣿⡇⢾⣿⣿⣿⠷⠀⢀⣀⣼⣿⣿⠆
⠀⠈⣛⣯⡀⠀⢀⣀⡀⠈⠀⠈⠹⣿⣿⡿⠃⢐⣧⡀⠀⣾⣿⣿⣷⡄⠀⣿⡇⠈⢻⣟⣡⠶⠟⠋⠁⠀⢉⣡⣤⣄
⠀⠀⣿⣿⣿⡄⣿⣿⡿⠶⠶⠶⠶⠶⣶⣶⠀⠀⠀⠁⠀⠙⠿⠿⠋⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡇
⠀⠀⣿⠈⢿⣿⡆⣉⣤⣶⣄⠀⠀⠀⢹⣿⣧⠀⠀⢸⡟⠛⣿⣿⠀⠀⠀⣽⡅⠀⣿⣿⣠⣴⡶⣷⡀⠀⠀⠙⣿⡏
⠀⠀⣿⠀⠈⢻⣿⠋⠁⠀⠙⠷⣄⣰⠎⢿⣿⡆⠀⢸⡇⠀⣿⣿⠀⠐⠛⠛⠃⠀⢿⡟⠉⠀⠀⠈⢻⣄⣀⡀⣿⡇
⠀⠀⠋⠀⠀⠈⢿⡄⢸⡀⠀⠀⠈⢃⣴⠿⠻⣿⠀⠈⠁⠀⣹⣿⣤⣤⣄⠀⠀⠀⢸⡇⠀⠈⢦⠀⠀⠛⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣠⡾⠛⠁⠀⠀⢻⡇⠀⠀⠀⣿⡏⠉⢩⣿⠀⠀⡶⢟⠁⡀⠀⠀⢀⣀⣤⣤⠶⢹⡇
⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣾⡇⢸⣿⣿⣿⡌⢻⣄⠀⠀⣿⡇⠀⠨⣿⣤⠘⠟⠋⣄⠹⠿⠘⠋⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⣠⣿⠀⠘⠿⣿⡿⠃⢀⣹⣷⡀⢿⡇⠀⠀⠀⠀⠀⢀⣾⠋⠀⣀⣤⠀⠀⠀⡇⠀⢸⡇
⠀⠀⡈⢧⣀⣼⡿⣦⣄⡀⠀⠀⢀⣶⣶⠶⣶⠀⠀⠀⠀⠀⠘⢛⣦⣀⠀⠀⢠⡾⢁⣴⠾⠋⠀⠀⠀⠀⠁⢀⣼⡇
⠀⠀⣇⣈⣉⣉⣀⣈⣙⣿⣶⣶⣿⡿⠃⠀⣿⠀⠀⢸⠀⠀⢀⣿⣿⣿⣷⢰⣿⣷⣿⣷⣶⣶⣶⣶⣶⣾⢦⣿⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠀⠀⠀⠀⠀⠈⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣀⣀⣠⣀⠀⠀⢀⣀⣀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢼⡁⠀⡇⠀⡇⠀⠙⠂⢸⠀⢸⠀⢠⡾⠋⠀⠀⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⣀⠔⡆
⠀⠀⠀⡞⠁⠀⠧⠀⡇⠀⡆⠀⣿⠠⠘⠀⠉⡀⠐⠀⠀⠀⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠄⠀⠐⠒⠉⠁⠀⠀⠋⡖⠒⢲⡏⠂⡁
⠀⠀⠈⠁⠀⠀⠀⠊⠁⠀⠁⠐⠋⠐⠋⠀⠀⠐⠈⠉⠀⠀⠁⠀⠈⠓⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠄⠀⡠⠂⠐⠐⠒⠠⡀⠀⠀⣄⣧⣤⢼⡇⡄
⠀⠀⣀⠂⠀⢐⠂⠋⠘⡒⠀⠀⢰⠈⠉⡆⢀⡄⠀⠐⠖⠀⠠⠲⡂⠀⣀⠀⠀⣠⠄⢠⡤⢠⣄⢠⣶⠠⣴⠌⢰⡀⢠⠄⡀⢰⡀⠀⡄⠉⠀⠀⡀⠈⢁⡄
⠀⢸⡌⠀⣀⢠⠤⠀⠠⡄⣀⠀⠀⠓⠂⠀⠈⠁⠀⠀⠀⢐⡀⠐⠀⠀⠋⠁⠀⠙⠂⠈⠓⠉⠉⠋⠃⠀⢋⠀⠀⠌⠀⠀⠀⠐⠀⢀⡀⠀⠄⢀
⠀⠀⠇⠀⠰⢀⣁⠑⡈⡀⠇⠐⠀⠅⠈⠀⠀⠄⠀⠁⠤⠄⠀⠠⠂⠰⠄⠀⠀⡁⠀⠀⠀⠘⠈⠀⠈⠐⠉⣤⠀⠈⠳⠲⢞⠀⣠⡄⠁⠀⠸⡏⠀⢄⠀⢰
⠀⠀⠄⠀⠀⠅⣙⢒⡋⠰⠀⠀⠀⠁⠠⠀⠠⠀⢀⠀⢰⡆⠀⠿⠀⠀⢠⡠⠆⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠉⠠⠅⠈⠀⢈⡠⡲⠀⠀⠇⠀⠈⠉⠙
⠀⠀⠀⠠⢀⠀⠹⠈⠅⠤⠀⠂⠠⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠉⠀⠉⠀⠀⣀⣀⣈⣀⣂⣀⣁⡀⠀⠀⢄⠀⠠⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⢴⠀⠠⠄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣿⡁⢀⣀⡀⠀⠀⠐⠉⠉⣉⣉⣉⣉⢉⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠡⠈⠀⠀⠀⣀
⠀⠀⠀⡀⠓⠌⠀⠀⠀⠓⠒⠁⠰⠀⠈⠈⠀⠀⢰⡏⠀⠉⠁⣿⠈⠉⠻⠋⠉⢳⡄⠿⡄⢠⣭⣀⢀⣥⡿⠀⢀⣀⠀⢀⠀⠀⠈⠀⠠⠁⠈⠀⠀⢀⡄⣿
⠀⠀⠠⠄⠀⢸⠀⠈⠀⠙⠀⠀⢀⡀⠈⠀⠀⣀⠘⢳⡀⠀⠀⣿⢸⣷⠀⢠⣿⠀⡇⠀⡇⢸⣿⣿⠸⡇⠀⠐⠛⠛⠒⠛⠛⠀⠀⠀⠀⠀⠂⠀⠁⠀⣤⠄
⠀⢀⡀⠀⠆⠈⢀⠀⢀⠈⠀⠀⠐⢰⠢⠤⠄⡞⠀⠈⢪⣀⠀⣿⢸⡿⠀⠸⠟⢰⡇⣀⡇⢸⣿⣿⠠⡇⠠⢠⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⢀
⠀⢨⣧⠀⡀⠃⢚⠀⢐⠒⢂⡀⢀⣼⠀⣼⢀⡇⠀⠀⠀⣽⡀⢿⡤⠴⠻⣤⡴⠎⠘⡯⠤⠤⠿⣷⣴⡇⠀⠁⢈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⢀⣈⡁⣤⡁⠀⢀⡀⡀⠁⠀⠉⠉⠉⠀⠀⠀⣀⣀⣬⣥⣄⣀⣀⣀⣋⣀⣀⣀⡀⢀⣀⢀⣀⣛⣀⣀⡀⢀⣀⣈⣀⡈⠈⠈⢀⠀⠀⠀⡀⠀⠀⠅⣀⠬
⠀⠐⠈⠡⡤⣤⡄⢹⡅⠠⡤⠀⠀⡀⠠⠂⢻⡙⣿⠏⣩⠀⣤⡀⠉⢿⣿⠈⠀⣶⡌⠹⢋⣉⠻⢡⣤⣾⡇⣿⢸⡁⠶⢾⡇⠠⠀⠀⠀⠠⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣶⡀⠁⠄⠀⠈⢷⡘⢀⡏⢸⣿⡇⠀⢸⣿⠀⠀⠛⣡⣴⡸⢿⣶⠘⢛⣿⡇⣿⢸⡇⡶⠺⡇⠀⠄⠀⠀⠄⢸⡄⠲⢖⢾⡄
⠀⠠⠰⠻⢻⠁⠄⠈⠈⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⢸⣿⠘⠿⠃⡄⢸⣿⠀⠀⣷⡌⣿⢻⡆⠙⢠⣿⣿⠀⣏⣸⡇⣷⠀⡠⢆⡤⡄⠀⠀⠀⢆⢹⣘⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⠀⠀⢠⣤⣤⡄⠀⠀⣧⣸⡟⠶⠴⠞⠳⣤⣥⣾⣤⣿⣧⣽⣦⣤⡾⠦⠤⠼⣧⠭⠽⣧⣿⠈⢋⠉⠉⠁⢠⡎⠀⠘⢛⠉⠉
⠀⠀⠈⢶⠃⠀⠀⠀⠄⠠⠀⠀⠸⠿⠿⠇⠀⠀⠀⡉⣁⣀⡤⣠⠀⠉⠀⠈⠉⠙⠀⠀⢸⠇⠀⢴⠒⠠⣀⠀⠀⠁⠀⠀⠘⣆⡇⠀⠉⠀⠀⠀⠀⠀⢢⠶⠂
⠀⠀⢀⡀⠀⠀⠀⠈⠉⠉⠁⢀⣀⢀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠠⡀⠀⠀⠂⠀⢀⠀⢀⠀⡢⣀⡠⠋⢀⣠⣄⣀⣀⠀⠙⠁⠐⣿⢿⣿⡏⠃⠀⢸⡆
⠀⠀⠈⡀⣤⠀⠀⠄⠠⠤⠄⠠⣬⠐⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠰⠂⠁⠆⠀⢠⡈⡾⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠏⡁⠀⠀⠘⠇
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⡀⠁⠇⣆⠀⠀⠈⠀⢀⣾⠀⠀⡀⠄⠀⠀⠈⠢⠤⠁⠀⠀⣀⠀⡀⠀⢀⡀⠀⠥⠁⠀⠀⢀⠄⠀⠐⠑⠃⢈⠃⠁⠀⠀⢤⡀
⠀⠀⠀⠀⠁⠀⡶⠂⠀⠐⠻⠇⠀⡇⡴⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢶⡄⣒⡆⠀⠀⠠⠀⠰⡆⠀⠊⠂⠍⠀⠀⡀⣀⡩⠂⠘⠈
⠀⠀⠀⠀⡀⠀⠀⠅⠀⠨⠄⠀⠀⡆⡆⠀⠈⠀⠀⠀⠀⠀⣀⠈⠀⡁⢀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠈⠀⠂⠀⡀⠀⠨⠅⠀⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠸⠀⠇⠀⠀⠀⠨⠐⡀⠀⡄⠃⡧⠀⠀⡡⠁⠀⠀⠂⠈⠐⠀⠄⠂⠀⠀⠀⠂⠀⡀⠂⢄⣐⠄⠀⠀⠀⠀⠀⠈⡅⠀⠉⠁⣠⣤⠀⠀⢠⣤⡀⠀⢹
⠀⠀⢰⠀⢀⡀⡀⠘⠓⠛⢀⣀⡅⠀⠃⠀⠀⡮⠀⠀⠀⠂⠀⠀⠂⠀⠀⠈⢀⢀⠀⠀⢀⠀⠀⡇⠀⣀⢀⡁⠀⣀⠀⡉⢀⣀⡈⡉⠉⠀⠀⠈⣉⣉⣀
⠀⠀⢀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠩⠐⠂⠀⠀⠃⠀⢠⢀⠈⠀⠘⠁⣀⠀⢀⡘⠀⠀⠠⠀⠀⠀⡇⢸⣏⡸⠇⠀⡷⠀⠿⠌⠉⠁⡇⠹⣶⠁⡏⢉⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⢠⡶⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢸⡇
⠀⠀⠀⠀⢰⣿⡇⠀⢰⡖⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇
⠀⠀⠀⠀⢸⡜⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⢸⡇⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠈⡇⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⣿⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷
⠀⠀⠀⠀⠀⣿⠸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⢹⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⠤⠾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡈⣷⠀⠘⢧⠤⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣀⣀⣀⣠⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠡⠀⠀⠆⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣷⠿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⢤⡤⠤⢤⠤⠒⢶⠒⠒⣖⠒⠛⡞⠙⣏⠉⢏⠉⢳⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻⡄⠀⠀⣶⠒⠛⠻⡋⠉⢹⡍⠈⣧⣀⣸⣄⣀⣵⡤⠼⣦⠤⠼⡶⠶⠾⡖⠒⢻⠒⠛⡗⠙⣟⠉⢳⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢷⡀⠀⠘⣷⠔⠒⢻⡚⠉⢻⠉⠙⡇⠀⢻⣀⣀⣧⣠⣼⣦⠤⠼⡴⠦⠻⡖⠚⢗⠛⠻⡉⠹⡍⠉⢧⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢿⡀⠀⠘⣧⡤⠤⢷⠔⠒⢷⠊⠙⡏⠉⢯⠁⠈⢇⠀⠹⡄⠀⢹⣀⣀⣹⣄⣸⣦⠤⢵⡤⢷⠤⠚⢇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡄⠀⠸⣆⠀⠈⣧⣀⣈⣧⡤⢽⡤⠼⣶⠒⠚⡗⠛⢻⡉⠉⢹⠁⠀⢳⡀⢹⣄⣀⣧⣀⣧⣤⣼⠆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡄⠀⠹⡏⠉⠙⣇⢀⣈⣧⣀⣱⣄⣼⣤⣤⣼⣤⣤⠷⠶⠶⠷⠚⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢷⡀⠀⠙⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⢀⣤⣤⣤⣤⡤⠴⠶⠶⠒⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠶⠶⠶⠒⠒⣖⣒⣚⣉⣉⣹⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣉⣉⣈⣡⣤⣤⡤⠴⠶⢶⣒⣚⣻⣿⣿⠿⠶⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣷⣤⣤⣤⣤⠤⠶⠶⠶⠚⣛⣛⣛⣛⣉⣭⣭⣭⠭⠵⠶⠶⠚⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠖⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⢏⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠖⣀⡤⠴⠚⠃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠋⡁⠀⠀⢀⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠻⣷⣤⠴⠚⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠐⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠒⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠐⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⡄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢠⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠟⠉⠉⠙⢛⢿⣿⣿⣿⣿⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡟⠛⠛⣿⣿⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⣿⣿⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣠⣿⣿⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠍⠉⠉⠉⠡⣿⣿⣿⣿⣿⣿⣿⣿⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⣷⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣎⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢻⣿⣿⣿⣿⡁⠀⢀⣿⣿⣿⣿⣉⣿⣿⣶⣄⢠⣤⣹⣿⣿⣿⣿⡿⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠙⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⣿⡿⠛⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠛⠿⢿⣿⣿⣷⣶⣾⡿⠿⠛⠉⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⣀⠉⠉⣀⣀⡠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣤⣤⣤⣄⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠁⠀⡠⠤⠤⠤⠤⠄⠀⢨⠞⠃⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠉⠩⠭⠭⠭⠽⠶⣤⡀
⠀⠀⠀⡇⠀⠣⠤⠤⠤⠤⠜⠀⢸⠀⠖⠒⠒⠀⠐⠒⠀⠀⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⣀⠀⢣
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠁
⠀⠀⠀⠀⡇⠀⠀⠀⡠⡀⠀⠀⠀⢸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡸
⠀⠀⠀⠀⢰⠀⠀⠀⠉⠀⠀⠀⠀⠀⢇⠀⠂⠄⠀⠀⠀⠠⠤⠤⠀⣀⣀⣀⣀⣀⣠⠤⠁⢀⠇
⠀⠀⠀⠀⢸⠀⠀⢰⠁⢱⠀⠀⠀⢰⠀⠉⢒⡤⠤⠤⠤⠤⡤⠤⠤⡤⠤⣤⣤⡤⠤⠤⠤⠊
⠀⠀⠀⠀⠀⡆⠀⠀⠉⠁⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⢀⡇⠀⠀⢇⠀⠈⠯⠷⠾⠯⣷⠖⣒⠶⠦⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠚⠁⠀⠀⢀⡠⠋⠉⠉⠀⠀⠀⠈⠉⠙⢶⢶⠦⡀⠈⠛⢄⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈⢉⣉⣉⣉⣉⣽⢛⣻⣿⣿⣿⣾⣵⣃⣀⣀⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⠘⠃⠐⠂⠒⠂⠐⠖⠠⠶⠀⠤⠄⠤⠄⠠⠤⠠⠄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠥⠀⠉⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠠⠤⠘⠃⠺⢓⡐⠒⠂⠧⠇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠛⠛⠛⠓⠒⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠅⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢠⠀⢌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠒⠠⠀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⢉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠂⠀⠀⠤⠀⠀⡄
⠀⣀⡠⣀⡀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃
⡔⠀⠀⠀⠑⡤⠤⠤⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⠁⠉⠣
⢁⠀⠀⠀⠀⠁⠀⠀⠘⢢⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⡀⠀⠀⠴⠁⠁⠀⠃
⡜⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⡀⠀⠀⠀⣀⠀⢓⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠘⠠⠤⠆⠀⠀⠀⠀⠀⢠
⠀⠈⠑⠀⠉⡋⢀⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠊⠀⠘⠗⠆⠠⠐⠂
⠀⠀⠀⠀⠀⠁⠈⠉⠂⢄⡑⢄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡠⠖⣁⠔⠒⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣅⠢⣇⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⢊⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⢀⠚⠀⡐⠀⠀⡈⠀⠀⡂⠀⠀⠀⠀⡀⠀⢃⠀⠘⣂⠀⠳⡀⠈⢢⡀⠱⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠴⠁⠀⠬⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⡂⠀⠐⠂⠀⠐⡀⠀⠐⡀⠀⢐⣄⠈⢠⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⣿⣧⠄⠀⠈⠿⠧
⠀⠀⠀⠀⠀⢀⠀⡆⢀⢸⠀⡇⠀⠀⠀⣿⣿⡍⠠⠤⢤⠍⠉
⠀⢐⠂⡀⢰⢸⠀⡇⢀⢸⠀⡇⠀⠀⠀⣿⣿⠷⣀⣲⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠄⠤⠤
⠀⠀⠀⠀⢀⠀⠀⣶⢸⡇⠀⣶⠀⠀⠀⢀⣤⣤⣤⣶⡄⠀⣀⣀⣀⣀⠀⠀⢸⡏⠁⠀⠀⠀⠩⠭⠥⠤
⠀⠀⠀⣀⢸⡇⡀⣿⢸⡇⡇⣿⠀⠀⠀⠿⣿⡿⠟⠁⠻⡾⠋⠙⢿⣿⠀⠀⢸⣿⣿⣆⠀⠀⠈⠤⢤⠄
⠀⢀⡀⣿⢸⡇⡇⣿⢸⡇⡇⣿⠀⠀⠀⣶⣄⣴⣶⣿⣶⣴⣶⣶⣶⣤⠀⠀⢸⣿⡿⠉⠀⠀⠀⠲⠚⣆⡀
⠀⠀⠁⠉⠈⠀⠁⠉⠈⠀⠁⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠭⠭⠭⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⡿⢸⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣭⣭⣤⣤⣤⡤⡄⡀⠀⠀⠀⢸⡇⡇⢻⢠⠘⡇⠁⠘⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣉⣉⡉⠁⠀⠀⠸⠁⠃⣀⢨⡀⡀⣦⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁⠉⠈⠉⠁⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⡇⡀⢸⠀⠀⠀⢠⣄⡀⠀⢀⣴⣶⣦⣄⢀⣄
⠀⠀⡀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⡄⣶⢸⠀⡇⡇⢸⠀⠀⠀⠘⠻⣿⣶⡿⢿⣿⣿⣿⣿⡿
⠀⠐⠒⠒⠒⡐⠒⠒⠐⠒⠂⠀⠀⠀⠀⢸⢸⡂⡇⣿⢸⠀⡇⡇⢸⠀⠀⠀⢠⣄⡀⢉⣤⣤⣉⣤⣄⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠉⠈⠀⠁⠁⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⢰⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢸
⠀⠀⠀⠀⢰⠀⠀⠀⢰⣱⠀⢀⠤⠒⠈⠹⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⢸⣼⢠⠃⠀⠀⠀⢸⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⢸⢺⣧⠀⠀⠀⢀⣤⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⢡⠀⣀⠔⢩⠃⠀⠀⠀⠀⡌⠀⠬⠱⣄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⣄⠀⠆⠀⠀⠀⣀⠜⠀⠀⣀⣀⡇⣱⣔⢨⠀⠢⠑⢄⡀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠉⠀⠀⠀⠀⠤⠤⣯⠤⠤⣿⠒⠒⢠⠤⠡⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣟⣂⣐⣻⡀⢨⢸⠭⢹⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠟⠤⠤⠻⠤⠤⠘⠤⠼⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡶⣂⣤⢠⣄⡲⣶⡶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢫⣾⢟⣭⣬⣝⢛⣤⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣋⢘⡃⣿⡇⢉⣿⡇⡛⢈⣋⣥⣤⣤⣄⣀⠀⡄⣤⢠⡄⣤⢠⡄⣤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⢿⣌⡛⠟⣋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡄⠉⠈⠁⠉⠀⠁⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠦⠝⠛⠘⠋⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣷⠦⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠈⢷⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⡄⠀⡇⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⠘⠃⠛⠸⣯⣿⣮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⡇⠀⠾⡿⠂⠀⣷⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⣀⣀⣀⣈⠛⢯⡷⢤⣤⣤⠖⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⡿⠃⠀⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⠈⢸⠀⠈⣷⡄⠙⠻⣄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠃⠀⠀⢀⠈⠳⣤⣤⣤⡼⠃⢀⠀⠀⠰⢶⣶⣶⠶⠀⢠⠟⠻⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⢶⣾⣿⣄⠀⠀⠀⠀⠀⢀⣼⣿⣶⣤⣀⠻⠇⠀⠀⢿⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⣿⣧⠀⠙⢦⡹⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣸⢁⣤⣤⠈⣛⠁⣤⣤⡌⣧⠙⣥⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡘⠿⠟⠀⣉⡀⠻⠿⢃⣠⣾⣿⠗⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢾⣿⡿⠀⣤⣾⣿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠆⢠⠈⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⢤⡖⢦⣶⠀⡖⣦⠀⡖⢠⠲⣤⠐⡆⡖⣦⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠀⠉⠁⠀⠁⠈⠉⠈⠀⠁⠉⠁⠁⠁

⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣒⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⣼⠋⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡶⠒⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡏⣿
⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⡿
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢸⡇⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣊⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⢀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⢻⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⣙⣛⣛⣛⣃⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠶⣖⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣲⣒⣶⣒⣶⣒⣶⣒⣶⣒⣲⣒⣲⣒⣲⡀⢰⠛⣿⠛⣿⠿⡍⢷⠀⠀⠀⢸⣣⠖⠋⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⡼⠲⡿⠲⠗⠒⡷⠒⢿⠒⢾⠖⢺⠖⠺⡧⠸⡇⠈⣯⠽⣭⠽⣭⠽⡌⢷⡀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢠⣏⣀⣉⣉⣉⣉⣉⣉⣙⣛⣉⣛⣛⣛⣛⣛⣛⣙⣛⣋⣀⣸⣶⣿⣶⣟⣶⣟⣈⣷⠀⠀⠀⠹⣦⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⠧⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠈⠛⠶⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⠀⡾⠛⣶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⣷⣴⠟⠶⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⠀⠀⢀⣴⠟⢙⡷⠛⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠃⠐⠛⠁⠀⠀⠻⠶⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣤⣤⣤⣤⣤⣤⣄⣤⣧⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢛⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⠛⣛⣛⣛⡋⠀⡦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠋⠉⠉⠀⠉⠉⠉⠁⠈⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁

⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⡀
⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣄
⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣀
⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⣄⡀
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣄
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣀⠀⣰⣆
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⣿⠆
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣼⡇⠈⠁⠈⠁⠈⢹⡇
⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢼⣇⣀⣀⣀⣀⣀⣸⣟⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣿⣃⣀⣀⣼⣇⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⣿⠉⠉⠉⠉⠉⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠸⣿⡿⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⢉⡉⠀⠙⠻⠃⠀⠀⠀⠀⢸⣿⡇
⠀⢰⣿⣷⠀⠀⠀⠀⠀⣿⣿⠀⡿⠋⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⢀⣼⣿⡿⠋⠉⠀⣤⣤⠀⠉⠙⢿⣿⣦⡀⠀⢸⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⡏⢠⣿⣿⠋⠀⠀⠀⠀⣿⣿⠀⣿⣷⡄⠙⣿⣿⡄⢸⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⠀⣾⣿⠇⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡇⠀⢸⣿⣧⠀⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡇⠀⢨⣿⣿⠀⣿⡇
⠀⢸⣿⣿⢀⣀⣀⣀⣀⣿⡀⢻⣿⣇⠀⠀⢀⣀⣀⣿⣿⠀⣿⣿⡇⠀⣸⣿⡏⢀⣿⡇
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢿⣿⣦⡈⠻⢿⣿⣿⣿⠀⠿⠟⢁⣼⣿⣿⣀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣀⣀⣀⣀⣤⣶⣿⡿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠟⠛⠉⠀⠈⠛⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⡖⣂⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡆
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠸⢀⠰⠆⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⡠⠒⠀⠂⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠆⠀⠀⠀⠀⠀⠀⢴⠀⠉⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⣇⣑⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⣁⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣓⣒⣒⣒⣒⣒⣒⣒⣒⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠒⠒⠒⠲⠖⠖⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⠇⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⠀⠐⠋⠻⠵⢢⣀⢕⣀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢑⣀⣠⢻⠀⠀⠀⠀⠘⠈⠈⠠⠤⠠⡐⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣢⠓⡽⣶⠂⡀⠀⠀⠠⡞⢉⣀⠠⠂⠀⢀⠀⣷⠀⡏⣠⡇
⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣷⢄⣄⣢⠇⠀⢀⠁⠀⠀⠀⠀⠉⡀⠀⠀⢹⡄⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠢⠽⡿⠀⠀⠀⠈⠀⡄⣶⡶⠈⠁⠀⢸⡀⠻⢃⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⠀⠀⢸⡦⣄⣀⢸⢘⠀⣿⠃⡅⢠⣄⠸⣇⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡎⠀⠀⠀⠀⣧⡀⠉⠚⠚⢲⠃⠠⡄⠀⢻⣆⣫⣴⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⡀⠀⠐⢀⣿⣿⣦⣤⣠⣏⣀⣴⣷⠀⠈⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣴⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⣀⣠⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠗⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠙⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⠆⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡤⡔⠁⠀⠀⠭⣿⡍⣥⣆⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⡾⡀⢢⠀⠖⠂⢸⡆⠀⠉⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣾⡇⢻⡌⠀⠀⠀⡈⣰⡃⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠊⣧⣷⠈⠁⠀⠀⠀⠐⠊⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡚⣋⢱⢼⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡶⠔⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣤⠈⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡿⣦⠿⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠛⣿⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⣴⡟⢻⡆⠀⠀⠀⣠⣾⠛⠛⠁⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠈⠛⠛⠛⢷⡟⢻⡟⢀⣤⣤⣤⠀⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣠⣤⣤⡀⠈⠛⠛⠁⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⣿⣿⣿⡇⢀⣀⣀⡀⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⢿⣿⣭⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠙⢿⣶⣿⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣰⡄
⠀⠀⠀⠀⠀⢠⡞⣲⡀⠀⠀⠀⢀⠀⠄⠀⠊⠈⠃⠁⠎⢱⠀⠀⢱⠁⠀⠁⠀⠁⠀⠀⠐⠀⠂⠀⠀⠰⠒⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠁⠀⠋⣠
⠀⠀⠀⠀⠀⠁⠀⠀⣣⠀⡆⠐⠐⠆⠠⡆⡀⠠⠀⠄⠀⠈⠀⠠⠈⠀⠀⠠⡀⠀⠀⠀⠀⠃⠸⠄⡰⠶⠀⠘⠅⠴⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠇⢃⠈⠁⠀⠀⡄⠀⡀⢃⠀⠠⠁⠁⠌⠙⠕⠀⠠⠀⢈⠉⠀⠄⠀⠀⠀⠀⠀⠁⠰⠈⡄⠒⠂⡀⠀⠀⠀⠀⢀⠂⠀⡀⠀⠀⢌⠀⠁⠘⢁⡀
⠀⠀⠀⠀⠀⠀⣀⡂⢀⡀⠐⡄⠠⠁⡠⢄⠀⠀⢠⠴⠉⠃⠀⠀⠀⠀⠤⠀⠼⢠⠈⠀⠀⠀⠀⠀⠀⠀⡋⡶⠁⢤⠰⠆⠀⠀⠰⠀⠀⠀⠀⠀⠂⡀⠀⠠⡠
⠀⠀⠀⠀⠈⠀⢨⣞⠡⠠⠀⠭⠗⠜⠀⠀⠂⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠳⠤⠊⠀⠐⠀⠀⠀⠒⠀⠀⣤⡇⠀⠀⡠⡠⠁⠀⠠⠀⠄⠈⠂⡀⠀⠈⢔⠆
⠀⠀⠀⠀⠀⢀⠈⠁⠀⠰⠈⠤⠀⠤⠀⢠⠤⢠⢠⡤⣄⠀⠀⡠⢀⠀⠀⠀⡔⠀⠀⢄⠀⠀⠀⠀⠠⠀⢁⡀⠀⠐⠠⠁⠀⢠⠀⠀⠀⠀⠀⡀⠐⠀⠈
⠀⠀⠀⠀⡠⠀⣍⠏⠀⠀⠀⠀⡀⠀⠀⢸⠋⠉⠉⠉⠹⠀⠐⠁⠁⠀⢀⢀⠁⠀⠀⡄⠀⠆⠀⢰⠈⡀⠈⠀⠄⢈⠄⠐⠀⠸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣀⡆⠀⠐⢆⡦⠀⠀⠙⠉⠉⢉⠀⠀⢠⠄⠈⠁⡁⢠⡀⠂⠸⠁⠀⠐⡀⢢⠀⢀⠀⡘⠀⠀⠀⠀⢀⠂⠄⠀⠀⠈⠀⠐⠀⠠⠆⣤⠖⠁
⠀⠀⠀⢀⠕⢫⠐⡄⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠐⠀⠛⠓⠂⠈⠚⠀⠉⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠒⠀⠀⠁⠤⠀⣻⣀⡄⠠⠄
⠀⠀⠀⠀⠀⠈⠆⠼⠂⠠⠀⠠⠀⠂⢼⠂⡄⠀⠘⠀⢀⠀⠄⠀⠠⠄⢜⠠⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢉⠄⡜⠀⡌⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢐⣛⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠠⢏⠄⡀⠀⠰⠅⠻⣘⠕⢮⢀⡐⠀⢐⡅⠀⠀⠀⠀⠀⠀⠀⡟⢀⠁⠀⠀⢃⡀⢐⠀⢀⢶⣷⠊⠀⠆
⠀⠀⠀⠀⠐⠚⠃⠐⠀⠂⠐⠀⠀⠀⡀⠁⣀⣀⡀⠀⠀⣴⠀⠀⠅⠀⠈⢶⡁⢣⡈⡈⠀⠦⠀⠀⠀⠀⠀⡀⠀⣋⡊⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠠⠀⢀⠄
⠀⠀⠀⠂⡀⠠⠀⠡⠁⠞⡆⠀⠀⢈⠀⠀⠁⠁⠀⠊⠀⠘⠶⠰⡆⠀⣀⠄⠱⣂⠱⡀⠐⠀⠀⢀⡠⠂⠀⠀⠀⠄⠀⠀⡀⠀⠙⠂⡁⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑⠂⠀⠈⠃⠐⠀⠀⠀⠀⠀⠒⣀⠄⢴⠀⠈⣹⡄⠂⡃⠀⠀⠀⠀⣀⢀⠀⠐⠃⣾⢿⡀⠅⠀⠄⠀⠠⠀⠀⠈
⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠀⢠⠀⡃⠐⠀⠠⠀⠀⠀⠈⠛⡀⣀⡼⠁⠀⠀⠀⢤⠑⡀⠀⠈⠀⡈⠉⠀⣦⡶⢹⡎⠀⠘⡀⢀⠂⠒⡆
⠀⠀⠀⠀⢀⣄⡀⢀⢀⠨⡶⠀⢀⠀⠀⠀⢲⠀⠃⡀⠀⢐⠂⡀⠀⠀⠀⠈⠀⠠⡖⢲⠀⠄⠐⡂⠁⠀⠀⡈⢠⠀⠀⠁⠀⣸⡗⠀⠀⠀⠉⠅⢀⠁⠀⢄
⠀⠀⠀⠀⠀⠀⡸⠣⡀⠀⠉⠀⠀⠠⠐⢀⢴⠀⠀⠄⠀⠠⡀⠁⠀⡄⠀⠀⢀⡀⠑⠉⠀⠀⠀⡥⢘⠀⠀⣂⣀⡇⠀⠀⠃⡞⡏⠀⠒⠂⠀⠁⠸
⠀⠀⠀⠓⠀⠀⠀⠲⡇⠀⠀⠀⠀⠐⠀⠹⠿⡦⠤⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⡀⠚⠈⠀⢀⣠⡄⠧⠄⠒⠒⠻⢇⢤⡐⣦⣀⣀⠄⡠⠆
⠀⠀⠀⠀⠈⠀⠀⠅⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠁⠀⠁⠀⢌⠀⠆⠐⠒⠐⠂⠒⠈⠒⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠽⠤⢄⠈⠉⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣴⣿⣿⣗⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠐⢲⠆
⠀⠀⠀⣸⣿⣿⣿⣷⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⢸⢸⣆⢀⡀⢀⡏⢷⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠏
⠀⠀⠀⢺⣽⣿⣟⣽⣛⣄⠀⠀⡤⠀⠀⠀⠀⠀⢸⢸⠙⠎⠙⠾⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠈⢀⡌
⠀⠀⠀⠈⠹⣾⣿⣿⣿⣭⣢⠔⠁⠀⠀⠀⠀⠀⢸⢸⣤⣤⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠐⠓⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡄⠀⠀⡾⣄⠀⡞⠀⠹⠄
⠀⠀⠀⠀⡤⠖⠋⠉⠁⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢻⠀⢸⠛⠙⠾⠃
⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⡇⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡏
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠁


⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⡧⡆⠀⠀⢠⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⣒⠈
⠀⠀⠀⣗⡇⢰⡆⢸⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⡃
⠀⠀⠀⡧⡗⢸⡇⢸⡀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢠⠊⠉⠒⠂⠀⠀⠀⠀⠀⠀⣿⣭⣭⣭⣭⣭⡭⠭⠭⠅
⠀⠀⠀⠧⠧⠼⠧⠼⠧⠼⠧⠼⠦⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣬⣥⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣋⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣉⣉⡉⠉⠉⠛⣲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠞⠁⠀⢀⣀⣠⡀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠋⠀⠀⠊⠉⠀⠈⠁⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡴⠁⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⠃⠀⢀⣀⠔⣾⣯⠁⠀⢈⠛⣢⣄⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡸⠁⠀⠀⢀⠯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠃⠀⠀⠓⠒⠒⠤⡅⠀⠀⢰⠀⠙⠛⢣⠀⠀⠀⠀⠀⡜⠀⠀⡸⠁⠀⠀⢀⡎⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠇⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡸⠁⠀⡰⠁⠀⠀⠀⡼⢀⠆⡇⡇⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡼⢰⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⠀⠀⢰⠃⡜⡸⠰⢡⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠇⠀⠑⢤⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡠⠂⠀⡏⠀⢀⠇⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠉⠀⠀⣸⠀⠀⡸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⠓⠦⣄⡀⠀⠈⠑⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⢀⡇⠀⢠⠇⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⠀⠉⠙⠒⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠀⠀⠀⢸⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⣀⣀⢀⣀⣉⠵⠶⠤⣄⡀⠀⠀⠈⠉⠉⠉⠙⠓⠒⠋⠀⢀⡇⠀⠀⠀⣀⢞⠉⠁
⠀⡤⠊⠉⠀⠀⠀⠀⠄⢙⡿⣋⠔⠠⠭⢍⣒⠚⠯⠽⢤⣋⣟⠑⠒⠲⣤⣤⣤⣀⣀⣀⣀⣸⡥⡔⠊⡹⠁⠀⣳⢄
⢸⠀⠀⠀⠀⠀⠀⣠⢖⡡⠎⣀⡀⠁⠐⠁⠰⠪⢨⠝⣀⡰⠒⢨⠉⣑⣚⣒⠚⠭⠭⢭⣛⠑⠒⠚⢋⣁⠤⠚⡝⢢⢳
⠀⠑⠢⠤⠤⢴⡊⠀⠃⠤⢄⣀⠀⠉⠀⠒⠀⠤⢀⣀⠊⢀⠜⢡⠞⠁⠔⠁⣨⠟⠀⠀⠈⢏⣉⣉⣀⣀⠤⠚⡠⢊⠞
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠉⠐⠒⠤⢄⣀⠀⢀⡜⢁⠴⢁⡤⡀⣀⠞⠁⢀⠠⠤⠤⠮⠤⠤⠄⢒⣒⡭⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢄⣀⠀⠩⠁⣐⠣⠤⣀⣀⠜⡡⠊⠀⢈⡩⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢌⣁⠒⠠⠈⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠋⠉⠀⠉⠙⠛⠻⢿⣿⣿⣿⣷⡄⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⢉⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠛⠿⠏⠀⠀⠀⠀⠀⡀⠿⠇⡀⠀⠀⠀⠀⢀⣴⠟⠁⠸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂⠀⠀⢀⡀⠾⠋⠀⠀⠻⣦⠀⠀⣴⠟⠁⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠶⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣦⣌⠻⣦⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠛⠛⠛⢛⣛⣛⣛⣛⡛⢿⠀⠀⠀⠀⠙⣿⣿⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠈⠻⠟⣡⣾⣿⣶⣤⣤⣀⣀⣀⡄⢠⣶⣿⣿⣷⣌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣍⣉⣩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣶⣌⡙⠿⢋⣴⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇
⠀⠀⠀⠀⢀⣠⣶⣿⣿⣦⠹⡿⢃⣤⠙⡿⢃⣾⣿⣷⣦⣄⠀⠀⠀⠀⢹⣿⣿⣷⣄⡀
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⡆⢸⣯⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿
⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣈⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢸⣿⣟⣿⡟⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⣤⠶⢆⡴⠶⣄⢴⣄⢰⢀⡴⠆⢰⠀⢰⠀⣶⡀⣴⡄⣶⠶⢠⡶⣦⠀⠀⣴⣆⠀⣦⡀⡆⢀⣶⡄⢰⡄⠰⣄⣴⢠⡶⠆⣴⢠⡶⠆
⠀⢯⣀⡸⣇⣠⡟⣼⠙⣿⢀⣙⡷⢸⣅⣼⢀⡟⣷⢻⡇⣿⣋⢸⡟⣿⠀⢰⡷⢿⡀⡏⢻⡇⣸⠷⣧⢸⣇⡀⢹⠃⢈⣹⡆⣿⢈⣙⡦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢀⡼⠉⣷⢦⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢀⡞⢁⡼⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣠⠶⠛⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢠⡞⢀⡾⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⡼⠁⢠⡶⢦⣄⡀⠈⢳⡄⠀⠀⠀⠀⢠⠟⢠⡞⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠰⡇⠀⢸⡇⠀⢈⣹⠀⢸⡇⠀⠀⠀⢀⡿⣤⡟⢠⡞⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⢻⡄⠘⠷⠞⠋⠀⢀⡼⠁⠀⠀⠀⢸⡇⣠⡽⠛⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠙⠳⢤⣤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡟⠉⠉⠉⠉⠉⢻⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠧⠤⠤⠤⠤⠤⠾⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠇⡄⡔⠆⣠⠢⠰⠰⠀⢸⠅⢠⠒⡇⠄⠆⡔⢢⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁⠁⠈⠀⠈⠈⠀⠈⠁⠈⠈⠁⠀⠁⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡗⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⡞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄⠀⡇⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠉⠍⠉⠀⠀⢸⠇⠀⠀⠀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡩⢭⡭⢭⡭⠭⣭⠭⢭⣉⣉⣛⣛⣛⣛⣓⣒⡒⠒⠒⠒⠒⣲⠟⠛⠛⠉⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡼⢁⣞⣹⣟⣉⣟⣉⣹⣛⣒⣞⣓⣶⠓⢲⡞⠥⣤⠿⢭⣽⠇⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢠⡞⣠⠧⣤⠯⣤⠏⢀⡼⢁⣠⣏⣀⣜⣁⣨⣋⣉⣝⣉⡽⡷⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢠⠏⠰⣷⣶⣷⣶⣷⣶⣾⣤⣾⢣⣤⣯⣤⣾⣥⣴⡯⢴⣻⠊⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢀⡿⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣈⣉⣈⣉⣉⣁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠁
⠀⠀⠀⠈⠓⠒⠒⠲⠶⠶⠶⠦⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣇⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⢠⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣄⡀⠀⣀⣴⠌⠿⠿⠟
⠀⠀⠀⠀⠀⠀⣭⣭⠉⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⠿⣃⣬⠿⠻⢯⣄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣛⣛⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⠴⢚⡋⠁⠀⠀⠀⠈⢱⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⡇⢰⣍⡻⢿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⣶⣶⠀⣿⣿⣿⡇⢸⣿⣿⣶⠍⣻⡿⢟⡭⢖⣚⡉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⣭⣭⣴⣿⣿⣿⡇⢸⠟⣫⣵⣾⡟⡱⢫⣾⣿⣿⡇⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⣛⣛⠻⣿⣿⣿⣷⣴⣿⣿⣿⣿⢱⢣⣿⡟⣛⣛⡃⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠿⠿⠀⣿⡿⠿⠿⠿⢿⣿⣿⣿⠸⢸⣿⡇⠿⠿⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⢛⣉⢰⢸⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⣰⣄⣀
⠀⠀⠀⠀⠀⠀⣭⣭⠉⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⢸⣿⡏⣭⣭⡅⠀⠀⠀⠀⠀⢻⡛⣿⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠛⠛⠛⠛⠛⠛⠓⠙⠛⢸⠘⠛⠃⠛⠛⠃⠀⠀⠀⠀⠀⢸⡅⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⢀⡄⡆⠆⠀⠠⡄⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣀⣮⠄⠀⠀⠀⠀⠀⣀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⢸⡇⠇⢰⣷⠀⡇⠀⠀⠀⠀⠀⣿⣿⣶⣭⣾⣿⣿⠀⠀⠀⠀⠀⠀⣿⠐⣾⡇⣢⡄⠀⠀⠀⠀⠀⠀⡝⠛⠛⠓⠒⡄
⢸⡇⣄⢸⣿⢀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢈⣿⢀⣿⡇⣻⡇⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡦



⢀⣴⡿⠻⢿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣴⣺⡭⣭⣶⣄⠀⠀⠀⠀⠀⠀⣠⠖⣶⢐⡦⣄
⣿⡏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢸⣿⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⢸⢹⠋⠀⠀⠁⠸⠀⠀⠀⠀⠀⢰⠧⣉⠿⢠⣇⢸
⠻⣷⣄⣀⣠⣬⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⣷⠗⡄⠀⠀⠰⠀⠀⠀⠀⠀⠈⢋⢵⡫⠝⣾⡝
⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉


⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣾⣾⡆⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠄⢸⡇⡜⡆⠀⠀⠀⠀⢲⢂⠒⡰⡾⢛⢟⣌⠀⠀⠀⠀⢠⢄⣀⣤⣎⢀⣱
⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠀⡀⠘⠃⠣⠂⠀⠀⠀⠀⠐⠘⠻⠓⡐⠠⠂⠙⠃⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿
⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉


⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢶⣶⣶⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣦
⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⢠⡜⠛⣿⠀⠀⠀⠀⠀⠠⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⡇⣿⠘⣿
⢻⡿⡫⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⠏⠹⣿⣷⣶⣿⠀⠀⠀⠀⠀⠐⠒⠐⠒⠐⠒⠒⠒⠂⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿
⠀⠎⣀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣟⣯⡙⠛⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠻⠿⣿⣿⣧⢹⠏⢫⡹⡇⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢰⣿⣿⣿⣿⣿⣿⣎⣧⢀⡘⢙⣯⠀⠀⢸⡃⡄⠀⢀⠀⠘⠺⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⣿⣟⣿⣿⣿⠿⡿⣿⣿⣿⣿⣴⣿⣤⣦⣾⣱⣤⣀⣮⣴⠂⠀⣻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⣡⡦⢘⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⡻⣿⣫⣩⡷⠎⠀⠀⠀⢹⣿⣟⠻⠭⠉⠙⠛⠛⠿⢿⣿⣿⣌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠈⠙⠻⠻⣿⣽⣷⢦⣄⠁⠀⠻⣟⠻⢶⣦⣀⠀⠀⠀⠀⠈⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠘⠻⠷⢶⣦⣌⠐⠈⢢⡌⢠⣿⣷⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⡂⠀⠀⣼⣿⠻⣦⣤⡝⣦⡀⠐⣻⣾⡟⠉⠦⣀⠀⠀⠀⠀⠐⠲⣤⣀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡛⠉⡘⣧⠀⠀⠙⢷⣄⣸⣿⣟⣿⡻⠊⣝⡟⠃⠀⠀⠈⠂⠠⣁⠀⠀⠀⠀⠈⠉⠠⡘⣿
⠀⠀⠀⠀⠀⠀⠀⣤⠃⢁⠀⢀⡘⢳⢠⡄⠀⠈⠉⠉⠉⠘⠁⠀⣹⣆⠀⠐⢄⠐⠀⠀⢙⢷⣄⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠸⡻⢷⡈⠶⣤⢤⡛⢶⠀⠀⣾⣿⣿⣦⣀⣾⠿⠻⣿⠀⠀⠈⢳⡀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⢀⡼⡿⠊⠙⠀⠈⠂⢳⣟⢠⣠⢸⣿⣿⣿⠗⢾⣧⡀⠘⣆⠁⠀⠀⠘⠦⠀⠀⢿⡿⣿⡿⠆⠀⠀⠞
⠀⠀⠀⠀⠀⢻⣋⡟⠀⠀⠀⣢⣤⣤⣜⠀⡁⠈⠀⢉⢀⡄⡉⠛⠿⠆⢈⡳⣀⠀⠀⠀⠀⠀⢸⣷⢹⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣸⣿⣿⣿⣿⣷⠀⠀⢀⣠⣾⣿⣿⣶⣶⣿⣿⣿⣏⢷⡀⢀⢀⡌⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⢯⡻⣿⣿⣿⢿⢿⣧⣾⣶⣾⣿⣿⣿⣿⣿⣛⡛⣿⢿⡿⣧⣹⣦⢣⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠸⠶⠊⠁⠀⢻⡆⠀⠀⠨⡍⠙⣻⣿⣯⣿⣿⣯⣿⣿⢸⡇⠸⠇⢻⢾⣿⠃⡸⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⡄⣿⣷⣘⠄⣐⣠⣲⡿⠟⠉⢁⠿⣹⣿⡧⢸⠇⠀⠀⠀⣸⠏⠀⠃⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣵⣿⣿⣿⣷⢫⢟⡟⡷⠂⡀⠃⠀⠻⠛⢀⡿⣠⠀⠀⢸⡏⠀⠀⠀⣠⡾⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠈⡟⠛⠑⣿⢻⡿⣷⣯⢟⡞⣽⠃⠆⠀⠀⣰⣶⡿⠁⢣⣀⣴⣿⠁⠀⢀⣾⠋
⠀⠀⠀⠘⠇⠀⠀⠀⡰⣧⠀⠀⣿⣄⠁⠹⣷⣏⣼⣱⣿⣤⠀⢠⣿⡟⡱⢃⣾⠉⣸⠇⠀⠀⣼⠃
⠀⠀⠀⠀⠐⣤⣴⣿⣿⡿⡄⠀⣿⡈⡄⠀⠙⠛⣻⣟⣿⣿⡄⠷⢟⠔⣵⣿⡏⢀⡟⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠁⣴⣿⣸⡇⠀⠀⢸⠿⣯⣿⣿⣷⠀⡊⠀⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡣⠁⠀⠀⢸⣿⣿⡙⣿⣿⡄⠁⠸⠏⠿⢷⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⠁⢄⡤⠠⠌⠶⣦⡹⣾⣿⣿⡀⠀⠀⠀⠸⣿⠃⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠠⣶⠠⠌⠀⠰⠀⠐⡦⢷⢿⣿⣿⡦⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⡡⠈⠴⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠄⢒⢒⠎⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⡿⠓⢫⡾⠀⠀⣄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⣺⣾⡇⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⣿⣿⣿⡏⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠁⠈⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⣶⠀⠀⠀⠀⠀⢰⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡤⢤⡤⢤⡤⠤⡤⢤⡤⢤⡤⢤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢛⡛⢛⡛⢛⣛⢛⡛⢛⡛⢛⡛⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡗⠚⠓⠚⠓⢰⡄⠚⠓⠚⠓⠺⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠄⣨⣥⣬⣥⣼⣏⢻⣥⣬⣥⣬⣭⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡇⠀⠠⣤⣀⠀⢻⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃⣿⣿⣟⠻⠿⣿⡄⠻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠻⢾⣿⢦⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣶⣤⡙⠀⡹⡿⣿⣿⣀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠋⠙⠿⣶⣶⠋⠉⢢⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⠀⣴⣾⣄⡉⠉⣶⣶⡝⣿
⠀⠀⠀⠀⣿⡧⢤⡤⢤⡤⢤⡤⢤⢸⣦⠠⢴⣶⠉⠓⠤⡾⠁⠀⣿⣿⣿⣿⡅⢙⡛⢛⡛⢛⡛⢛⡛⡏⠹⣟⡛⠉⣶⣭⣛⣁⣿
⠀⠀⠀⠀⠘⠓⠚⠓⠚⠓⠚⠓⠚⢸⡿⣧⠚⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣬⣥⣬⣥⣬⣥⣬⣥⡗⢀⡙⣧⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⠜⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⣀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡶⢀⠀⠀⢀⡄⠀⠀⠀⠐⠀⠀⡆⠀⠀⠀⡄⠀⣀⣀⠀⠀⠂
⠀⠀⠀⠀⢠⠄⡄⠀⠁⠀⠀⠄⠀⡂⠈⠰⠃⠂⠠⠀⡌⠁⠀⠀⠀⢺⡠⠀⠁⠀⡀⠐⠂⠈⠀⠡⠄⠁
⢠⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⢃⠀⢀⡀⣠⡀⠀⠀⢲⣖⣾⠀⠈⣻⠖⠀⠐⠀⠀⢁⠈⢀⠁⠁⠐
⠈⠀⠀⠀⠀⠀⣤⠀⠀⣀⠀⠀⢸⠘⠐⠀⠀⠉⠀⠀⣠⠟⠛⠛⠀⣄⠉⠀⠘⠃⠀⠀⣤⢀⡄⣤
⠀⠰⠆⠀⠘⠀⠀⠀⠀⠀⠀⢀⠸⠐⠀⢦⠐⠄⠀⡀⠀⠰⠐⡀⠀⢄⠀⡄⠂⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⡐⠀⢴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⣌⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠰⠂⠀⠀⡦⡆⠀⠀⠀⡰⠀⠀⠅⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠆⣀⢈⠳⡷
⠀⠒⠀⣀⠉⠁⠀⠀⠀⠁⠀⠶⠀⠀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠃⠠⠐⠀⠀⠀⡀⠀⠀⠀⠀⠐⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘
⠀⠀⠀⠀⠀⠀⢆⠀⠀⢈⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂
⠀⠀⡀⠀⠀⠀⢀⠀⠐⠀⠠⠄⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠀⡀⠄⠀⠃⢘⠀⠀⠀⠀⠐⠒⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠐⠟⠐⠀⢘⠃⠘⠁⠬⠁⠀⢠⠀⠀⢠⠄⠀⠀⠀⠀⠀⠐⠀⠃⠘⠐⠀⡀⠀⠀⠀⠀⠀⠘
⠀⠘⠀⠸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠒⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⠐⢮⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠢⡨⠂
⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠈⠀⠉⠀⠀⠀⢀⢀⢠⡴⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⡀⠀⡀⢀⢀⣀⠂⠕⠔⠁⠀⠀⠀⡴⠒⣉⣔⡄⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢀⢀⡴⠞⠋⠁⣀⡀⢀⡀⠀⠀⠀⡷⠤⣷⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⣠⣠⠴⠀⠑⠒⠁⠀⠀⠀⣘⡒⢠⣾⣼⠀⠀⠀⢣⣈⣟⣿⡇
⠀⠀⠀⠀⠀⠀⢀⢠⠨⠤⠞⠉⠀⢀⣤⠤⠀⢀⣈⠀⠀⠣⠤⢿⣿⣿⡄⠀⠀⠰⠆⠷⠶⣧
⠀⠀⣀⠠⡰⠜⠋⠁⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠆⠀⢘⣆⣘⣟⣿⡇⠀⠀⣸⣩⣭⣿⡟
⠀⠀⠀⠊⠀⠀⠐⠋⠉⢡⡬⣴⠀⠀⣏⣈⣛⣛⣿⠀⠀⠐⡦⢤⣶⣾⡇⠀⠀⡲⠤⡿⠾⡇
⠀⣠⠤⠀⡤⡀⠀⡏⢘⣛⣿⣽⠀⠀⢱⠁⠽⠷⣿⠁⠀⢸⣉⣚⣛⣻⡆⠀⠀⠯⠁⣟⣿⡷
⠈⠤⢰⡾⡯⣧⣀⡦⠴⠶⠶⣆⣠⣄⡨⢉⣹⣭⣽⠀⢀⣸⡊⢽⣭⣿⠃⠀⢀⣟⢒⣲⣶⣆⣀⡀⢀⡤⠀⠄⣀⢤⡀⠀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢻⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⣾⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣭⣷⣶⣦⡝⠛⠘⠛⠛⠛⠃⠛⠛⢉⡤⠖⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢀⣠⣄⣀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢿⣿⠟⣁⠀⠀⠘⠲⣄⡀⠀⠀⠀⣀⡤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡗





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⡿⢟⣡⣾⣧
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⡏⣸⣿⣿⣿⡿⢟⣩⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⠟⢰⣿⣿⠟⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⣭⣤⣤⣈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⡙⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡙⠛⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠤⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠙⠛⠛⠒⠚⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡇⠀⢸⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⡇⠀⣿⡟
⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠁⠀⣨⡇⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣧⡇
⠀⠀⠀⠀⢸⠛⠓⠒⠒⠒⢶⠛⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠏⡇⢸⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⢿⠃
⠀⠀⠀⠀⢸⡆⠀⢰⠀⡇⢸⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣼
⠀⠀⠀⠀⠸⡇⠀⢸⠀⡇⣿⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠦⠃⣿⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡏⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣈⠀⣿⠀⠀⣷⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠚⠀⢸⣷⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠙⠁⣿⢀⣠⠟⢲⠖⠒⠶⠶⠶⠶⠶⣶⠦⠤⠤⠤⠤⣤⣤⢤⡤⢭⢬⡥⠤⠼⠏
⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠛⠋⠀⠀⠻⢄⣀⠀⠀⢠⡴⢞⣉⣉⠉⠉⠉⢭⣫⠇⠀⠳⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⣶⣶⡶⠦⠷⠤⠼⠿⠯⢭⣭⣽⣛⣛⣛⣁⣀⣀⡀⠀⠀⠀⠈⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⢾⣾⣓⣞⣳⡟⢢⠿⢭⠿⢭⠯⣴⣖⣒⢆⣔⣾⣩⣭⡍⢩⢿⡀⢠⠴⢾⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠥⠬⠉⢘⣒⣚⣒⡫⠬⠯⠭⠯⠽⣋⣲⣛⣲⢮⢞⡼⣥⢯⠝⡰⣣⠏⠀⣿⠊⠙⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠲⠶⠦⠭⢭⣭⣍⣐⣒⣒⡒⠂⠬⠭⠭⠯⢭⢎⡴⠃⠀⠀⣿⣄⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠈⠛⠿⠟⠛⠁

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡦⡤⢄
⠀⠀⠀⠀⢠⣶⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣸⠆⠀⠀⠀⠀⠀⠀⣿⢠⡝⠛⠉⠈⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠃⠀⠱⡀
⠀⠀⠀⠀⠙⠿⠟⠀⠅⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠦⠾⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠙⠗⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢟⣭⣲⡤⢄⡇
⠀⠀⢀⣼⣿⣿⣟⣛⣿⣿⣿⣅⠀⠀⠀⠀⠈⠛⠛⢛⣿⣿⡛⠙⠛⠦⠀⠀⠀⠀⠀⠀⣿⢀⣤⣠⣴⠆⡇⠀⠀⠀⠀⠀⠀⠈⢿⣵⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁


⠀⠀⠀⣀⣀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡴⢶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⢤
⠀⠀⢸⡏⠉⠩⠉⠉⠍⡉⠉⡇⠀⠀⠀⠀⠀⣸⣇⣠⡿⣤⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢻⡇
⠀⠀⢸⡇⢐⢸⣦⣥⣿⣶⠀⡇⠀⠀⠀⠀⠀⠸⣏⡀⣹⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⣤⣾⡇
⠀⠀⢸⣇⣘⣛⣛⣛⣛⣛⣀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠉⠋⠛⠙⠃
⠀⠀⠀⠈⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠚⠛⠛


⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢰⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⢀⡞⠉⢠⣭⣷⣴⣦⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠈⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⡆⡀⢈⠁⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠶⢤⡀⠄
⠀⠀⠐⠻⠟⢿⡻⠃⢀⡾⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⣀⡀⣤⣾⢈⣿⠀⠀⠀⠀⠀⠀⠀⠇⡅⢨⡁⢨⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣴⣿⢹⠂
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⢦⡀⠀⠀⠀⠀⠀⠈⢿⣜⠙⠙⠙⢛⣾⠏⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠛⠃


⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣤⡀
⠀⠀⢸⠿⠿⠿⠿⠿⠿⠻⠿⣇⠀⠀⠀⠀⠀⣼⠋⠀⣠⣾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠎⠾⠀⡧⠀⠦⠢⡀
⠀⠀⢸⢀⣄⢀⣄⡔⢉⣉⢦⣿⠀⠀⠀⠀⠀⢻⣜⠿⠿⠟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⡦⢰⡆⠀⡧⠀⢰⠀⠆
⠀⠀⢸⠈⠉⠉⠉⠙⠯⠽⢇⡟⠀⠀⠀⠀⠀⠀⠙⠛⠒⠛⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠰⡔⠦⠀⣗⠉⢁⡴
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠷⠟⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠀⠀⠈⠉⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⠇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⠻⢿⣿⣿⣿⠀⠀⠀⠈⣁⣴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣀⣁⣤⣤⣴⠾⠛⠁⠙⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣠⣀⣉⣉⣉⡉⠁⠀⢰⣶⣄⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⣄⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢄⠀⡀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⠿⣉
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠄⠀⠀⠀⠀⠀⢀⣴⣶⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⡠⢟⠟⠡⣄⠜
⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⡀⠀⠀⢀⣀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣀⣀⠈⠿⠿⠿⠟⠁⠀⠀⠀⠀⣀⣤⡔⠁⠀⠂⢀⡷⠁
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠰⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⣁⣠⣄⡀⠀⠀⠀⡿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⢀⣴⠟⣡⡄
⠀⠀⠀⠀⠙⠿⠿⡿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠖⠛⢻⠛⠉⠁⠀⠀⠀⠃⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡦⢴⣯⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠰⠀⠀⠀⠀⠀⠻⢾⠶⣆⣐⡦⠀⢘⠛⠳⠆⠀⠀⠠⠀⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⢄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠈⠉⠀⠉⠀⠀⡀⠀⠀⠄⠐⠆⠈⢡⡀⠠⠆⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀
⠀⠀⡀⠘⠒⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠂⠀⢀⣈⠉⠀⠀⠀⡒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠣⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢠⢦⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠁⠀⢸⠠⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠈⠉⠀⠀⠐⠁⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠉
⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠷⠟⠀⠀⠀⠀⣠⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡁⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠙⠃⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠠⠊⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀
⠀⠀⠐⠀⠄⠀⠐⡄⠢⠀⢀⢈⠓⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠌⠀⡁⠁⠀⠈⠀⡀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠒⢃⣀⠁⢀⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠤⡐⠒⠀⢐⠠⠊⠢⠑⠄⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢀⠀⠀⠂⠀⠀⠀⠀⡆⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠤⠤⠤⠴⠤
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠄⡤⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠠⡄⠁
⠀⢘⠀⠈⠁⠁⢀⠄⠛⠒⠲⡌⠂⡄⠱⡤⠀⠦⣀⡈⠁⠀⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠸⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⡄⠁⠀⠈⠲⣶⠛⠀⡀⠁⠀⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⣀⠀⡘⠀⢄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠔⠀⠑⠶⠄⠐
⠀⠀⠀⠀⠉⠀⠈⠑⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠋⠁⠀⠀⠀⢀⣀⠀⠀⣾⣿⡆⠀⠙⢿⣆⠀⠀⠀⠀⢀⣾⠟⠁⠀⣴⣶⡄⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠻⣷⡄⠀⣴⡿⠃⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣤⣤⡄⠈⢿⣾⠏⠀⣀⣀⡀⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣶⣶⡆⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢀⣀⡀⣄⢚⣁⡀⠀⠀⠀⠀⢠⣶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠆⠉⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⡟⣩⣭⣭⣭⣽⣭⠰⠀⠀⠀⣥⣍⢸⣬⣥⣥⣜⢨⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⢻⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⡿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠿⠿⠸⠿⠿⠿⠿⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣴⡄⠀⠀⠀⠀⠀⠂⠚⠘⠘⠃⠃⠘⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣮⣛⣛⣵⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢟⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣆⠀⠀⢸⣿⣿⣿⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⢿⡆⠀⢸⣿⣿⣿⢀⡼
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣃⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣈⣁⣀⣘⣛⣛⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⣀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢸⠀⠀⠀⢀⣠⡴⠞⠉⣤⣤⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⣠⣀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡜⢢⠀⣀⠀⡰⣦⠃⠀⡀⠀⠀⢸⠀⠰⠛⢉⣥⠀⣿⡇⣿⣿⢸⣿
⠀⣿⠀⡠⣄⣀⣤⠞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣁⠞⢄⡠⠫⣀⠟⠜⠀⠱⠜⠁⠀⠀⢸⠀⣶⣶⢸⣿⠀⣿⡇⣿⣿⢸⣿
⠀⢿⣎⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣟⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⠀⠀⢸⣄⣸⣟⣸⣿⣀⣿⣇⣹⣟⣸⣿⣀⣠


⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡧⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢺⣅⠀⣀⢰⣶⠀⠀⠀⢸⡀⠀⠀⡀⠀⠀⢈⠀⠤⣀⣄
⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡁⣴⡆⣿⢸⣿⠀⠀⠀⢸⠆⠐⠀⡀⡄⠁⢀⠠⠒⠀⠝⠈
⠀⠀⡟⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⢸⡇⣿⡇⣿⢸⣿⠀⠀⠀⢸⠀⠫⠒⠄⠉⠅⠀⠀⠁⠀⠀⢀
⠀⠀⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⣿⠆⣿⢸⡇⢿⠇⣿⠸⡿⠀⠀⠀⢸
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆
⠀⣿⠀⠀⢀⡄⠀⠀⠀⢀⠔⣁⡀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣤⡄⣿⡇⣿⡇
⠀⣿⠠⠚⢡⡌⢆⡠⠖⢡⡄⢻⡇⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀⣚⡂⣛⡀⣛⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⣾⡆⣿⡇⣿⡇⣿⡇
⠀⣿⢰⣶⢸⡇⣠⡀⣶⢸⡇⢸⡇⣿⠀⠀⠀⢸⡇⠀⠀⢠⠄⢬⠅⢬⠄⢭⠄⢭⠀⠀⠀⠀⢸⠀⣶⡆⣿⡇⣿⡇⣿⡇⣿⡇⣿⡇
⠀⣿⣘⣿⣸⣇⣻⣃⣿⣸⣇⣸⣇⣿⣀⣀⠀⠸⣇⣸⣂⣸⣂⣺⣂⣺⣂⣺⣂⣺⣀⣀⡀⠀⢸⣀⣿⣇⣿⣃⣿⣃⣿⣃⣿⣃⣿⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠯⠿⠯⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⣾⡟⢛⠛⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠐⠀⡿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⠻⣄⣠⠄⠀⢠⠗⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣈⡟⠀⣄⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣆⠀⠟⢦⣳⠖⠏⢹⠆⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣷⣀⠀⠀⠀⠀⡿⠄⠐⢘⣈⠐⠀⡃⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⠿⠷⠟⠛⠛⠛⠻⠿⠿⠽⠯⠿⠿⠿⠭⠿⣽⠿⠽⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠩⠒⠻⠟⠿⠛⠿⠳⠦⠅⢘⣊⣐⣦⣭⣼⠿⠿⠿⠿⠿⠿⠿⠞⠳⠌⠢⣄
⠀⠀⠀⠀⠀⢠⣴⠩⠤⢤⣤⡤⡤⠤⣤⡤⣤⣤⣤⢤⣯⡽⡽⣿⠿⡾⢤⢤⡤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣵⣦
⠀⠀⠀⠀⠀⠈⠛⠚⠛⠛⠛⠓⠚⠚⠛⠛⠓⠛⠛⠛⠛⠚⠒⠛⠛⠓⠚⠛⠚⠓⠛⠚⠛⠛⠛⠓⠚⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢰⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠰⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⡀⣀⣴⣄⠀⠀⠀⠀⡀⠀⢀⣀⣀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⣠⣤⡄⠀⠐⠀⠀⠀⣡⡾⣫⡟⠉⢉⠀⠈⠁⢁⠒⠀⡉⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠴⠆⠈⠀⠀⡇⠀⠀⠠⣤⡼⠛⠛⠓⠂⠀⠀⡴⠪⠁⠨⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⣴⠁
⠀⠀⠀⠀⠀⢈⠀⠶⠀⢠⣶⣤⠀⠤⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⣥⡄⠀⡛⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⡠⠃⠀⠀⠦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠉⣦⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠘⠀⠐⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠁⠁⠉⠀⠀⠀⠀⡄⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠸⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣾⡿⢷⣦⣀
⢠⣾⠏⠀⢀⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢠
⣿⣯⡀⢠⣿⠏⠀⠀⠈⠛⠿⣶⣄⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣬⣿⠀⢸⣿⠿⢿⡇⢸
⠈⠙⠿⣿⣯⡀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠀⢸⣿⣤⣽⡇⢸
⠀⢠⣤⠈⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠁⢸
⠀⢸⣿⠀⠀⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠿⢿⡇⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡉⠻⢿⣦⣄⡀⠀⠀⠀⠀⣰⡿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣀⣽⡇⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⢿⣶⣄⣀⣼⡟⠁⠘⢿⣆⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠁⢸
⠀⢸⣿⠀⣴⣶⣶⣶⡄⢸⣿⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣶⣶⣾⣿⣦⡀⠀⠀⠀⢸⣿⠀⢰⣿⠿⣿⡇⢸
⠀⢸⣿⠀⣿⡇⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⠀⢸⣿⣀⣿⡇⢸
⠀⢸⣿⠀⠙⠿⠿⠟⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠛⠛⠁⢸
⠀⢸⣿⠀⣴⣶⣶⣶⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⠿⣿⡆⢸
⠀⢸⣿⠀⣿⡇⠀⣿⡇⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⢸⣿⣀⣿⡇⢸
⣀⣸⣿⣀⣻⣿⣿⣿⣃⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣀⣈⣛⣛⣛⣃⣸
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⣴⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢿⣿⢏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⣛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⠦⠉⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⡇⠀⠀⠀⣯⡹⡿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣴⣶⣶⣶⣶⣭⣙⠿⡇⠀⠀⠀⠛⠛⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⡞⣵⣿⣶⣶⣶⣶⣶⣶⣶⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⢿⡟⣼⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡄⠀⠀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡟⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⣇⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠇⠀⠀⣿⣌⠛⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡻⠿⣿⣿⣿⡿⠿⣛⣱⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣷⡎⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠈⠻⠿⠇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠠





⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⣶⠶⢶⠶⠶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠀⢰⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠿⠇⠀⢀⠀⠘⠿⠃⠀⠿⠇⠀⠸⠿⠀⠸⠿⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⡇⠘⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠀⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠸⠇⠈⠀⠇⢠⢶⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⡃⠸⣌⢧⡀⠸⠀⡰⢃⡞⠀⣘⡛⠛⢛⣛⠛⢋⣀⠛⠛⣛⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣁⡀⠘⣆⠱⣄⡞⢡⠎⢀⣀⣛⣃⣀⣘⣛⣀⣘⣛⣀⣀⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠏⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣰⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢚⣉⡀⣰⠋⢣⠀⣉⣙⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣇⣀⡿⢸⠀⢿⢸⣁⣨⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠭⠔⠃⠀⠈⠳⠬⠥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠐⠂⠃⠈⠒⠀⠘⠀⠒⠀⠀⠀⠀⠉⠋⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡶⢶⢶⢶⠶⡶⡶⢶⢶⡶⠶⡶⡶⡶⢶⠶⡶⡶⢶⢶⠶⣇
⠀⠀⠀⠀⠀⠀⣠⢞⢑⠛⠗⡛⡻⣻⢚⠟⡱⠫⠞⠸⠇⠳⢻⡙⡊⢳⠓⡙⡚⡎⢛⢊⢧
⠀⠀⠀⠀⠀⢾⠓⠒⣶⡖⠒⠲⠶⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠖⠒⠚⠇

⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⣄⢸⡇⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⣠⡾⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠰⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀
⠀⠀⠀⠀⣶⢸⣿⢸⡇⣿⢸⣿⠀⠀⠀⠀⢀⣴⡾⠋⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠑⠖
⠀⠀⠀⠀⠛⠈⠋⠘⠃⠛⠈⢋⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀


⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣾⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠁⠀⠀⠀⠀⠀⢀⡄⡆⣶⢠⢸⣰⡇
⠀⠀⠀⠀⣴⣾⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠈⠁⠁⠁⠉⠈⠁⡀


⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠉⠀⠀⠀⣀⡀⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡏
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠅⠤⡇⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⣁⡀⡀⡃⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠂⠀⠃⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢠


⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⡀⠀⠛⠛⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡷⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠛⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⠁⢸⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣤⠿⠉⠲⠶⠂⠀⠀⠀⡇⠘⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠘⠀⠉⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⡿⠛⡿⢿⡿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣈⣿⠀⠀⠀⣴⠟⠛⠛⠛⠛⠛⣷⡀⠀⠀⢸⣇⣹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣉⣉⡁⠀⢀⣾⠃⣼⠛⠶⣤⣀⠀⠈⢷⡄⠀⢈⣉⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⣿⠀⢾⡃⠀⣿⠀⠀⠈⢙⣷⠀⠈⣿⠀⢸⡏⣻⡇⣼⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠛⠋⠀⠘⢷⡀⣿⣀⣤⠾⠛⠁⠀⣼⠏⠀⠘⠛⠛⣽⣇⡀⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠛⣷⠀⠀⠈⢷⣌⣉⣁⣀⣀⣀⣾⠃⠀⠀⢸⡟⣿⠏⠈⠙⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⠶⠟⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⣿⠏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠉⠛⢷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡀⢠⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⡀⢰⠀⠀⡆⠀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠘⠀⠃⠀⠐⠀⠀⠀⠘⠀⠀⠂⠘⠀⠃⠣⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⢷
⠀⠀⣰⣿⣿⡿⠟⠛⠛⠋⠐⠀⣀
⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⣀⣀⡀
⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⣤⠒⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⠐⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⠏⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣦⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⠿⠛⣫⣄⠰⢿⣶⡿⠟⣡⣾⣷⣤⣉⣩⣥⣶⣌⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡋⠱⣀⣦⣡⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⢮⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡁⣂⣴⣾⣿⣿⣛⣩⣤⣌⣙⠛⠉⢁⣈⣉⡙⠉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡈⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⠛⠋⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⠖⠚⠛⠋⠉⠉⠙⠓⠒⠲⠶⢤⣀⡀
⢀⣤⣤⠤⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠒⠊⠉⠉⠀⢹
⡇⠀⠀⠉⠐⠒⠤⢄⣀⣀⠠⠤⠖⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⡖⠒⠂⠤⠤⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀
⣷⠙⠢⠤⠤⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣴⠛⠛⠛⠓⠒⠛⠉⠩⠭⠭⠍⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠩⠭⢭⢍⡙⢦
⢸⠀⠐⠒⠂⠤⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠠⠒⠒⠀⠠⠤⠤⠄⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠈⢁⣀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢
⢸⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⠇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡆⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⡇⠀⠀⠀⠀⡅⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡇⠀⠀⠀⠀⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⢣⠀⠀⠠⠒⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⠀⠀⠘⠒⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⣿⡙⡇⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠸⣄⠀⠐⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠉⣀⠠⣴⡿⢁⢧⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠒⠠⠦⠤⠴⠃
⠀⠀⠈⠓⠶⢤⣀⠀⠀⠀⡇⠀⣀⣀⣠⡤⠤⠶⠒⠋⠉⣀⣀⣀⡤⢂⣭⡴⠞⣻⠞⠓⠋⣉⣉⡻⢿⣶⣶⠖⠒⠶⡶⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⡰⣋⠥⠶⣏⡀⠙⠓⣚⣛⣛⣭⠭⠽⠖⠒⠋⠉⢁⡤⠤⠤⠤⣟⡀⠀⣫⣀⣀⠈⠦⢬⣷⣒⡺⠭⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⠤⠴⣶⡶⠿⠛⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣔⣁⣀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⡷⠀⠀⠉⠓⡌⠱⡄
⠀⠀⠀⠀⠀⠀⣀⡤⠶⢯⡉⠉⡎⢳⠋⠉⠀⠀⠀⣠⢖⡒⡒⠂⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠒⠊⠀⠀⠀⢀⣠⠇⠀⡇
⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠉⣉⡤⠞⠀⠀⠀⢀⠜⠁⣜⡖⢁⢙⠘⢀⣂⠒⠐⠒⠆⠀⠦⠄⠠⢤⠄⣭⣉⢉⣉⠉⠙⣶⣒⠒⠲⠶⠶⠶⠒⠒⠋⠉⠀⣀⡴⠁
⠀⠀⠀⠀⠻⣄⣀⣀⣀⠴⠊⠁⠀⠀⠀⢀⠔⢁⣀⡛⠃⢀⣦⠆⠠⠯⠈⢠⣬⠙⢁⣐⠒⠂⠠⠶⠄⢀⠤⣄⠀⡠⢊⡼⠉⠉⠉⠉⠛⠛⠒⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⡧⢀⣈⡁⠁⠈⠋⠩⠭⠭⠍⠁⠲⠖⠒⠂⠀⠰⠐⣓⣐⡁⠉⠴⣡⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⠤⠬⠭⠭⣭⣉⣀⣒⣒⣒⠒⠒⠒⠒⠂⠠⠭⠭⠥⣀⣔⡵⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠚⠛⢻⡧⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠀⠀⠰⣛⡧⢨⡇⠀⠉⠓⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣀⣤⣤⡤⠴⠶⢦⡄⠀⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⠦⠤⠤⠴⠶⠶⠞⠃⢀⣷⣀⣀⣤⣤⠴⠶⠖⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠙⣯⠉⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣤⣤⠤⠶⠒⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠶⠶⢶⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣠⣤⠶⠶⠚⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠉⠉⢈⢵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⠀⠐⡃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠶⠶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⡷⠀⠀⠀⠀⢀⣠⠶⠞⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⣀⠀⠀⠀⠀⠉⠙⡿⠒⠶⠶⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⣤⠞⢻⡥⢤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠉⠙⠓⠲⠶⢤⣤⣳⣤⣤⣤⣤⣤⣄⣀⣈⡉⠙⠛⠳⠶⠶⣤⣤⠶⠚⠓⠋⠉⠀⣠⠞⠁⠀⠀⠀⠉⠳⣤
⠀⠀⣀⠴⠊⠉⠀⠀⢀⡤⢶⣙⣶⠶⣀⡀⠀⠀⠀⣠⠔⠀⠀⠉⠉⠙⠛⠒⠶⠤⢭⣭⣙⣛⠒⠒⠒⠲⠶⠶⠶⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⣼⠁⠀⠀⠀⠀⠚⠛⠶⠾⣉⠽⠛⠉⠀⢠⡴⣯⣷⢛⣧⠶⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠛⠓⠲⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠓⠲⠤⣤⣀⡀⠀⠀⠈⠁⠀⠀⠀⠙⠙⠺⣥⠼⠋⠁⠀⠀⠀⠀⣠⠶⣛⡷⣶⣤⣂⡀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠇⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣄⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠜⠛⠧⢮⣥⣛⣩⠞⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁⡾⠀⠀⠀⠀⠰⠿⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠶⠤⣤⣄⣀⣀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢀⣠⠴⢋⣀⡤⠾⠃⠀⠀⢀⣀⣤⡤⢤⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⣤⣄⡀⠀⡴⣚⣭⠶⠚⠉⠁⠀⠀⢀⡤⠞⠛⠳⢤⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣆⠠⠖⠀⠀⢹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠉

⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣷⣦⣴⣦⣶⣾⣿⣷⣿⣷⣦⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣺⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⢀⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡿⠛⠻⣲⣶⣶⣶⣾⡏⢀⣼⣽⣿⠻⠈⣹⣿⣿⠟⠉⢻⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣶⣾⣿⣿⣃⣠⢸⣿⣿⣿⣷⣶⣦⣾⣟⢿⡿⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣤⣀⣀⠀⣀
⣿⣿⣿⠏⢡⢹⣿⣶⣾⣧⣿⢡⡀⣽⣿⣿⣿⣿⠛⢷⣦⡀⢩⡟⠻⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠛⢿⣿⣿⠛⠛⠃
⣿⣿⣿⣧⣿⣿⣮⡍⠏⠷⣻⣿⣿⣦⣴⣿⣧⣭⣶⣿⡿⣿⣿⣷⢦⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢻⡏⠀⠀⠐
⣿⣿⣿⣷⣥⢰⣿⣿⣦⣼⣿⣟⠟⠙⣿⠿⣿⣿⢿⣿⣧⡀⣀⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣷
⣿⣿⣿⣿⣷⣾⡛⢯⠉⠛⣛⣽⣷⣦⣤⣤⣿⡏⢀⣀⢹⣿⠿⠿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣀⣀⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢰⡆
⣿⣿⡗⠟⢛⣻⣷⣶⣦⣼⣿⠀⢰⣙⣋⠈⠙⣿⣿⣷⣾⣧⣀⢼⣶⣾⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣯⡅⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣷⣄⢈⣤⣾⢟⡝⠛⣿⣦⣼⣿⣿⣦⣴⣿⡉⠻⣣⣄⣙⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣤⣤⣿⡇
⣿⣿⣿⠿⣿⣿⣧⣤⣥⣼⣿⠀⠸⣿⣿⣿⣿⡿⠿⠿⣿⡿⣛⢛⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣠⡀
⣿⣿⢇⣀⠙⠘⣻⣿⠉⣽⣿⣿⡾⠿⢿⣿⡿⠙⢃⣴⣽⣥⣉⢀⣼⣿⣿⣿⣯⠀⠀⢀⠀⢸⣿⣿⠉⣿⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣸⡿⠟⢿⣿⣯⣄⣸⣿⣦⣨⣶⣿⣿⡿⢻⠿⣿⡟⠿⢟⠋⠻⣿⣿⣿⣯⠀⠀⠈⠈⢹⣿⡿⠀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⢿⣛⠿⠿⢿⣿⠚⠒⠒⠒
⣿⣿⣿⣿⣦⣘⣿⣿⣿⣟⠛⠙⣟⣿⡿⠏⠁⣤⣖⣿⣧⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣷⢐⣿⣿⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠚⢚⠓
⣿⣿⣿⠿⠛⠛⠁⠀⠉⠙⠃⠊⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠸⢻⣿⣿⣿⣿⣿⠠⠀⠀⠀⠿⠛⢋⡘⠛⠛⢣⣸⣿⡟⠛⠟⠛⠟⠙⠛⠉⠛⠋⠙⠃⠀⠈⠙
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠃
⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣿⣿⣿

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢸⠄⡧⠀⠀⠀⢼⠰⠀⠀⠀⠀⠀⠀⡠⢤⠀⡐⢆⠀⠀⠀⠀⠀⠈⠁⠈⠀⢨⡅⠀⠀⠀⠀⠀⡴⠊⠀⠀⠈⠐⡄⠀⠀⠀⠀⠀⠄⢒⣉⡂⠰⠄
⠀⠀⠀⢸⡅⡇⠐⢂⡄⢸⢨⠀⠀⠀⠀⠊⠋⠀⢸⢲⠘⠀⡇⠀⠀⠀⠈⠙⢍⢫⠝⡡⠊⠁⠀⠀⠀⢸⠀⢠⠪⡭⠒⠁⠘⠀⠀⠀⠀⡜⢰⠁⡇⠈⡂⢣
⠀⠀⠀⢸⣒⣇⣈⣁⣀⣸⣒⡀⠀⠀⠀⠑⠓⠄⣸⠁⠜⡠⠃⠀⠀⠀⠠⠒⢤⡣⢞⡤⠒⠄⠀⠀⠀⠘⢄⠂⠀⠀⠀⢂⠜⠀⠀⠀⠀⠘⡈⠫⠧⠔⢁⡁
⠀⠀⠀⠘⠂⠃⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⠊⠀⠀⠑⠐⠃⠀⠀⠀⠀⠈⠑⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⢀⠄⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⠀⠀⠀⠀⠀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠤⠠⠄⠤⢠⠄⡤
⠀⠀⠀⠀⢠⣸⡁⠀⢈⣇⡄⠀⠀⠀⠀⠂⠳⣭⣬⢗⣊⣉⡀⠀⠀⠀⠀⠉⢉⠉⠉⡉⠉⠀⠀⠀⠀⢸⡀⠀⣠⡆⡀⠀⡨⠀⠀⠀⠀⢛⠉⠁⢉⡈⠁⡟
⠀⠀⠀⠀⠸⠸⡂⠀⢐⠆⡇⠀⠀⠀⠀⠗⠚⠐⠃⠚⠐⠓⡇⠀⠀⠀⠀⢠⢸⠀⠀⡇⡄⠀⠀⠀⠀⢘⠗⠒⢯⡇⠗⠒⢟⠀⠀⠀⠀⢸⡠⠒⢪⠤⢄⡇
⠀⠀⠀⠀⠀⠑⠊⢭⠁⠊⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢘⠘⠀⠀⠃⡃⠀⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⢺⠒⡆⡶⢰⠂⡗
⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠈⠁⠉

⠀⠀⠀⢀⠄⢠⠤⠤⠤⣄⡤⠀⠀⠀⠀⡠⠀⢄⠄⠠⡀⠀⠀⠀⠀⠀⢈⡇⣉⢨⡅⣍⢸⡁⠀⠀⠀⠀⢀⡄⣄⣀⣀⠒⡄⠀⠀⠀⠀⢀⠔⢈⠤⡁⠢⡀
⠀⠀⠀⢸⣰⣁⠊⣍⡑⣉⣆⠀⠀⠀⠀⣦⠀⠼⠄⢠⡇⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠇⡗⠒⠆⡇⠉⠀⠀⠀⠀⠣⣒⠆⣉⠱⣒⠈⡄
⠀⠀⠀⢸⠈⡌⠢⣉⠔⢡⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⣏⠉⡃⠀⠀⠀⠈⠀⣀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠃⢓⣒⠃⠓⡆⠀⠀⠀⠘⣇⢼⣲⣭⣖⡆⣰⠃
⠀⠀⠀⠈⠒⠚⠓⠚⠚⠓⠚⠀⠀⠀⠀⠓⠒⠒⠒⠒⠃⠈⠁⠀⠀⠀⠨⠅⠭⠨⠅⠭⠨⠅⠀⠀⠀⠀⠓⠂⠀⠀⠓⠃⠀⠀⠀⠀⠀⠈⠻⠭⣤⣭⢿⣥

⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⡀⡀⣀⣀⢀
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠧⠜⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⢠⡄⢠⡄⠀⠁⠀⠀⠀⠸⠨⠤⠇⠇⠧⢼⠸⠀⠀⠀⠀⢡⣌⠉⠉⠉⡩⡌⡆
⠀⠀⠀⠀⠔⠛⢅⣶⡨⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⡷⠀⠀⠀⠀⢀⠀⠘⠓⠚⠃⠀⣀⠀⠀⠀⠀⠀⠀⢙⢩⡄⢸⠀⠀⠀⠀⠀⢸⠀⡱⠀⢎⠀⡆⡇
⠀⠀⠀⠘⡄⠀⠸⣀⠇⠀⢠⠀⠀⠀⠀⢀⠀⢀⡖⣆⠀⢀⠀⠀⠀⠀⠙⠀⢠⠀⠀⡄⠀⠋⠀⠀⠀⢰⠲⠒⡖⡖⡖⢺⢲⠀⠀⠀⠀⣘⣊⣀⣀⣀⣑⣃⠇
⠀⠀⠀⠀⠈⠑⠂⠉⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣔⣁⣀⣀⣀⣀⣀⣀⣉⣢⡀⠀⠀⢶⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠟⠛⠛⠛⠛⠛⠛⣿⣿⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⣠⣤⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠔⠊⠀⢠⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠈⢉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠢⣀⠎⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠻⡟⠿⠻⠿⠻⠛⠿⠿⠿⢿⠋⠀⠂⡈⣩⣦⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⣀⣀⡀⠤⠊⠁⠀⢆⣴⣾⡟⠋⠛⠁⠀⠀⢸⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⡿⣿⠉⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⠁⠂⠀⠀⢤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠙⠛⠁⠀⠈⠀⠀⠀⢀⡠⠐⠉⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⣠⣤⡀⠀⠂⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢠⣿⣦⣠⣶⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⡇⠀⠀⠆⠀⠿⠿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⠙⢿⡇⠀⠀⠀⠂⠀⠀⠀⠀⣷⣿⣷⣿⡿
⠀⠀⠀⠀⡐⠀⠰⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⣿
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⡆⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠰⡿⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣂⢸⣿⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⠏⣬⣭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠋⠀⢤⣿⣿⣹⣿⡇⢠⣤⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⡿
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢰⣀⣨⣉⣉⣉⣉⡇⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⡇⢸⣿⠿⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠿⠿⢿⡇⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣧⣀⢼⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣿⣀⣀⣀⣀⣀⣻⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣿⣿⣿⠶⢾⣿⣿⣿⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⢿⠇⢸⡿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣀⠀⠀⣿⣿⣿⣧⣀⡀

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⠀⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⠀⡿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢻⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⣤⠤⢤⣸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⡏⠉⢹⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡇⠀⣿⠀⠀⠀⠀⣶⠒⢲⣾⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢸⠉⠉⡇⡇⠀⢸⣿⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⣿⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⢰⠒⠒⣾⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢸⠀⠀⡇⡇⠀⢸⣿⡇⠀⣿⢸⠉⠉⡇⣿⠀⢸⣿⡇⠀⢸⢠⠤⠤⡄⡇⠀⢸⢸⠀⠀⣿⡇⠀⢸⣤⠤⢤⡄⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢸⠀⠀⡇⡇⠀⢸⣿⡇⠀⣿⢸⠀⠀⡇⣿⠀⢸⣿⡇⠀⣿⢸⠀⠀⡇⡇⠀⢸⢸⠀⠀⣿⡇⠀⢸⣿⠀⠀⡇⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢸⠀⠀⡇⡇⠀⢸⣿⡇⠀⣿⢸⠀⠀⡇⣿⠀⢸⣿⡇⠀⣿⢸⠀⠀⡇⡇⠀⢸⢸⠀⠀⣿⡇⠀⢸⣿⠀⠀⡇⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢸⠀⠀⡇⣇⠀⢸⣿⡇⠀⣿⢸⡀⠀⡇⣿⠀⢸⣿⡇⠀⣻⢸⠀⠀⡇⡇⠀⢸⢸⠀⠀⣿⡇⠀⢸⣿⠀⢀⡇⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⢾⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⡿⣿⣿⣾⣿⣿⣷⣿⣿⢿⣿⣿⣿⡷⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⣿⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⣿
⠀⠀⠀⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿
⠀⠀⠀⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢄⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⢀⡄⠀⢀⡜⠀⢈⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣀⢀⠈⠄⠀⣿⠉⠠⡀⠉⠀⠀⠈⠛⣿⣶⣷⣺⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠁⠀⢠⠃⠀⠀⠉⢀⣀⠤⣶⣿⣿⣿⡿⢿⠿⢧⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⠀⠐⠚⣩⣆⣶⣮⠟⠛⡏⠀⢀⠞⠒⢍⡛⢿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⣿⣾⣖⣃⢀⣀⡤⢿⡿⠇⠀⠀⠀⣠⢿⠒⠀⣠⣿⠆⢼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⠋⣩⣼⣾⣿⡏⠉⢿⠟⠉⠉⠀⢀⠀⠘⠁⠆⢠⢀⣾⢋⣦⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠌⢠⣾⣿⡿⠿⢿⣭⠟⠋⠀⠀⠀⠀⠀⠃⠀⠀⠀⡘⠿⢃⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣷⣀⣋⢥⣖⣷⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢸⣿⡠⢾⠉⣻⠀⠀⠀⠀⠀⠠⣼⠀⣀⡀⡀⠀⠀⠀⣰⠇⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡯⠀⠤⣥⡏⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⢄⡈⠉⠋⠁⢀⣴⠇⠰⡶⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠅⠀⡝⢿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⢀⣠⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⣷⣽⡆⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣄⣴⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡀⠀⠀⠈⠛⠋⠁⠠
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠹⠟⠷⣦⣄⣀⡀⠀⠀⠀⠀⢠⠏⠘⠓⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠻⠷⠦⣄⡀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣹⣿⣿⣤⢰⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⢖⡶⡖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣿⣿⢇⠞⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⡫⢊⡔⡇⠀⣤⠤⠄⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⠞⠁⠀⠀⠄⠀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡡⢊⠔⡇⠀⡷⡐⡵⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠊⠀⠠⠊⠀⡀⠸
⢸⣟⠟⡽⡇⠀⠀⠀⠀⠀⠀⡗⡱⢡⢊⡇⠀⣿⢊⢞⠹⠀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡻⠁⠀⢀⠄⠀⢀⠔⠊⢀
⢸⣏⢎⡴⠁⠀⠀⠀⣀⡀⠀⣏⠔⡡⠡⡇⠀⢗⡕⡡⠄⠀⡧⡪⣂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠲⡦⢅⡀⠔⠁⢀⠔⠁⡀
⢸⡧⣪⢞⠁⠘⠝⠝⡡⠆⠀⣏⢊⠔⡠⡇⠀⣋⢔⠄⡏⠀⣗⠔⡡⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠱⣌⢳⡘⢦⡘⢷⠢⢄⡀⠈⢠
⢸⡗⡱⣫⡇⢸⡫⢊⡤⡇⠀⡇⡡⢊⢈⡇⠀⡥⡪⢂⡇⠀⡇⢪⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣉⢷⡘⢦⡙⣆⠳⣄⠳⣄⠉⢢⠌
⠀⠏⠞⠞⠇⠸⠗⠡⠂⠇⠀⠋⠐⠁⠁⠃⠈⠁⢁⣉⢁⣀⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧⡹⣆⠹⣄⠻⣌⠳⡈⢧⡙⢦⠊
⠀⠐⠒⠀⠐⠒⠒⠒⠚⠒⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡻⡌⢳⡘⢦⠈⢷⡘⢦⡘⢆⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆⢳⠈⢳⡀⠻⠨⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⡄⠀⠄⠀⠀⡄⠀⡄⠀⠀⢲⠀⠰⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡜⠡⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⢠⠎⠀⢀⠀⠀⠑⠄⡀⠀⠀⢀⠀⠔⠊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠘⠗⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣏⠌⠹⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⢀⡴⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⢊⠔⡃⠀⡀⠀⠀⡀⠀⡄⠀⠀⢸⠀⠠
⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠢⠊⡅⠀⠝⠉⠁⡃⠀⡇⢀⡀⣸
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⢈⡇⠀⡧⠀⠀⡁⠀⣿⠉⠕⢹⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠡⠇⠀⠏⠀⠀⠁⠀⠋⠈⠀⠈⠀⠐⠋⠉⢉⣀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠒⠦⠤⢤⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⠶⠯⣭⣤⣤⣄⣀⣀⣠⠴⣲⣿⣛⣋⣉⣀⣀⣀⣀⠉⠉⠉⠉⠉⠛⠒⠒⠲⣤⡄
⠀⠀⠀⠀⡇⡐⠒⠒⠒⠒⠒⠠⡀⡿⢸⡇⠀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⡉⠉⠛⠓⢲⡏⠀⡇
⠀⠀⠀⠀⡇⡨⠭⠭⠭⠭⠉⢉⠀⡇⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡷⠀⢸⠁⢸⠟⡆
⠀⠀⠀⠀⡇⠑⠒⠒⠒⠒⠒⠊⢠⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡾⠀⢸⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⡟⢰⠇
⠀⠀⠀⠀⣧⠀⠘⠋⠒⠒⠂⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⢀⡇⣸
⠀⠀⠀⠀⢻⠀⠀⠀⣀⠀⠀⠀⡿⠀⢸⡀⠘⠒⠒⠶⠶⠦⠤⠤⠤⠤⠤⣤⡼⠀⣸⠀⣸⠖⠃
⠀⠀⠀⠀⢸⡀⠀⠀⠒⠁⠀⠀⣇⡴⠋⠛⠓⢲⢖⡶⠒⣶⡶⠶⠤⢤⡤⢤⡤⣤⡿⠞⠁
⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⡛⠉⠀⠀⠀⡊⠁⠸⣧⣤⣀⣉⣉⣉⣉⣤⡾⠀⠈⠒⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡩⢭⢭⠭⡭⢭⢉⡉⣛⣓⡒⠛⠻⠿⠯⠭⣭⣁⣀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⡼⡰⢥⠯⡯⣹⣩⣏⣞⣱⡓⡞⢺⢡⢮⠏⣴⣰⠂⡰⣹⠀⠀⣠⠖⣻⠟⠙⣆
⠀⠀⠀⠀⠀⠀⢸⣥⣍⣉⣚⡒⣓⣒⡒⠀⠧⠼⠥⠃⠎⢞⣲⣲⢃⢜⡴⠁⠀⡼⠉⠉⠉⠒⢤⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠒⠾⠿⠭⠭⢤⣄⣒⣲⡾⠋⠀⠀⠀⢷⣄⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠀⠀⢰⡆⢸⡇⠀⢀⣴⣿⣿⣶⣦⡀⠀⠀⣿⣿⣿⣿⣿⣧⡾⢋⠆⢀⣾⣿⣿⣿⣦
⠀⠀⢠⠀⣿⠀⡇⢸⡇⢸⡇⠀⢸⣿⣿⢿⣿⣻⣷⡀⠀⣿⣿⣿⣿⣙⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⣸⣀⣿⣀⣇⣸⣇⣸⡃⠀⠈⠿⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⠿⠟⢻⣦⡀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀
⠀⢸
⠀⢸⠀⠀⡏⠉⠉⠉⡇
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⡀⠀⠀⢀
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⠀⠀⣀
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⡤⠤⠤⠤⡄
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠐⠀⠠⡄
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠘
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⢐⢿⠒⠒⠒⢺⣿
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠣⣻⠀⠀⠀⢸⣟⠕
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠁
⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸
⠀⠘⠒⠒⠓⠒⠒⠒⠓⠒⠚⠒⠒⠒⠚⠒⠒⠚⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⠓⠒⠚⠒⠒⠒⠚⠒⠒⠒

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠛⢛⣛⣋⡛⠛⠛⠻⣆
⠀⣠⠖⠛⣛⣉⣉⣉⡉⠥⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠋⠙⠛⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠳⡄⠀⢹⡄
⣰⠿⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⣇
⣯⢸⡄⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢿
⢿⠈⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡆
⢸⡀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣇
⠸⡇⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿
⠀⣧⠸⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡆
⠀⢻⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣇
⠀⠸⡇⢻⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢻
⠀⠀⣷⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡆
⠀⠀⢹⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇
⠀⠀⢸⡇⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿
⠀⠀⠈⡇⢿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿
⠀⠀⠀⣿⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠃⢀⡟
⠀⠀⠀⢹⡘⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⠖⢚⣛⣉⣉⣀⣠⣤⠤⠶⣿⡁
⠀⠀⠀⠘⣇⡇⠀⠹⣄⣀⣀⣀⣀⣠⣤⡤⠶⠒⠛⠋⣉⣉⣉⣉⡤⠤⠤⠤⠴⠒⠒⠛⠋⠉⠉⠉⠉⠁⢀⣀⣀⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠙⢿⣦⣤⣀⣉⣤⡤⠤⠴⠶⠖⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⢴⡖⠛⠛⠻⡁⠈⢙⣦⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢸⠻⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⡤⠤⠶⠶⡖⠚⠋⠙⣏⠉⠀⣙⣦⡠⠤⠷⣄⠒⠚⠙⢯⡀⣀⣙⣦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢻⠀⠱⡄⠀⠐⣏⠉⠉⠉⢯⡁⠀⠀⢈⣦⣀⠤⠤⠼⢶⠒⠒⠙⢏⠉⠁⠀⣳⣄⣠⠼⢶⡒⠚⠉⠻⣌⢀⣀⣙⣦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠘⣧⠀⠹⡄⠀⠈⢦⡤⠴⠖⠻⡛⠉⠉⠁⢳⡀⠀⣀⣨⣧⠴⠶⠚⢷⠉⠉⠉⠙⣄⣀⡤⢷⡖⠒⠚⠙⢯⣁⣀⡠⠽⢦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠹⣄⠀⠀⢳⣀⣀⣠⣽⠶⠒⠊⠉⠻⡅⠀⣀⣸⣦⡤⠤⠘⠳⡒⠈⣉⣉⣧⣤⡤⠿⠶⣖⠋⠉⢁⣀⣀⣠⣤⡽⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⣆⠀⠀⠹⣅⣀⣨⣧⠤⠖⠒⠈⢻⡉⠁⣀⣈⣧⣤⠴⠶⠛⠛⠉⣉⣠⡤⠴⠖⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⢆⠀⠀⠘⢇⣀⣸⠧⠤⠶⠒⣚⣟⣋⣩⣥⣤⠤⠤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠘⢆⠀⠀⠈⠷⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠒⠚⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡤⠤⠶⠚⠛⠉⠉⠀⠀⢀⣀⣀⣤⠤⠴⠶⠖⠚⢛⣉⣉⣥⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⢒⣒⣂⣉⣩⣥⣤⡴⠶⠶⠒⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⢦⣀⣀⣀⣀⣀⣤⠤⠴⠶⠒⠒⠚⠉⣉⣉⣡⣤⠴⠖⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣬⣭⣥⣤⣤⣤⡤⠴⠶⠒⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠑⠠⠑⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠠⠀⢐⠀⠂⠀⡠⠀⠁⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠰⢁⠠⠀⠀⠂⠀⢀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠂⠈⠁⠀⡇⠨⠭⠍⠀⠀⠂⠀⠀⠀⠂⠈⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠊⢁⠁⡀⠀⢀⡈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠤⠤⠄⢘⠃⠀⠘⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠈⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠤⠠⠤⠀⠠⠄⠤⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠊⠀⠒⠀⠘⠀⠒⠂⠀⠀⠀⡆⠙⠑⢄⠀⠀⠀⠀⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⢀⡀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⡀⡠⠠⡀⠀⢈⡁⡀⣉⡄⡄⡄⠀⠀⠀⠄⠃⠣⠜⡠⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⡀⠁⡀⠀⠀⠀⠁⠀⠁⠄⠀⢠⡀⠄⠀⠀⠑⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠅⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠒⠒⠁⣇⠈⠀⠀⠀⠀⠀⡀⠀⠑⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⣿⣿⣿⣿⣧⣤⣤⣠⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡄⠙⠁⠈⣿⣿⣿⣿⣿⣿⡿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦⣤⣀⣀⣈⠛⠉⠉⠉⠁⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⣿⣹⣯⣿⢿⣿⣿⣳⣦⣄⠀⠀⠀⣼⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣏⣿⣼⣿⡞⠛⡙⣯⠉⠻⡝⣷⡔⠉⠀⠀⠠⠆⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⣟⠉⢹⡇⣸⣿⣿⣤⡤⠘⣷⠢⢹⡜⣿⡖⠻⣶⡀⠀⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⣧⠀⣖⣇⣩⣿⣿⣧⡄⠱⣾⣶⣧⡷⠿⢷⣴⣿⡶⠞⣦⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⣷⡀⣎⣹⣽⡿⠿⣿⡟⣿⣹⣧⣤⣾⣾⣿⡿⢃⢡⠸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢾⣿⣹⣿⣬⣿⣷⣾⣿⣿⢿⣿⣿⣿⡿⣟⢻⣧⠸⡈⡆⡍⡗⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣟⢻⣿⢄⡙⢻⣉⣿⣿⣿⣾⣿⣿⣿⠃⠸⡜⣿⡄⣇⢰⢰⢹⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡌⠹⣿⣿⣾⣿⠿⣿⣿⡏⠉⡁⣸⣀⣄⣧⣽⣿⣿⡷⠦⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣧⠀⢷⠀⣀⣸⣤⣼⣿⣽⣿⣿⠛⢻⣟⣿⡵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡼⣶⡾⢿⣟⢋⣿⣉⣿⢧⣾⡿⠿⠿⠟⠁⠀⣿⣅⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠻⠿⠿⠿⠛⠹⣭⣤⣤⣶⠇⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣹⣆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⡄⠀⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⡀⠀⢰⣿⣿⡿⢿⣟⣻⠃⠈⠁⠀⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠉⠛⠟⠃⠀⠀⠀⢀⣾⣷⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⣶⣴⣶⣶⣶⣿⣿⣿⣿⡇⠀⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠦⠄⠀⠠⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡶⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣤⡶⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧⣼⠃⠀⠀⣼⠋⣉⡉⠉⠉⠉⢷⡄⠀⠀⢿⣤⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⡀⢀⣾⠃⣺⠏⠛⠶⣤⡀⠈⢻⡄⠀⣠⣤⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⣼⠅⠸⣇⠀⣿⡃⠀⢀⣨⡿⠀⢠⡿⠀⣿⣄⣿⣰⡟⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣭⣅⠀⠀⠹⣆⠹⣧⠾⠋⠁⠀⢠⡟⠁⠀⣨⣭⣤⡿⢦⣄⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⣹⡅⠀⠀⠙⢷⣤⣤⣤⣤⣴⠟⠀⠀⠀⣿⣡⡟⠀⠀⢈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣈⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⢧⣤⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣇⠀⢈⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠾⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢈⢀⠃⠆⠐⠀⡈⠀⠀⠰⠀⠀⡁⡹⠐⠀⠁⠐⠘⠁⠁⢀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⡿⠉⢙⡟⡟⠻⠿⠛⠿⡛⠿⠻⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⣿⣿⣿⣿⡛⣿