Eggs Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⢤⣤⣤⣤⣀
⠀⠀⠀⣴⣾⠟⠋⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣥⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢦⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣴⣾⠟
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⢺⣷⡶⠾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣶⣿⡷⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣤⣶⠿⠛⠛⠛⠛⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⠛⠓⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣄⣠⠞⠁⠀⠀⠉⢷⣀⣀⣴⡋⠉⠉⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡼⠁⠀⠀⠀⢀⡴⠞⠉⠁⠈⠙⢦⡀⠀⠀⠙⢦
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣠⡴⠚⠛⠳⣦⣼⠷⠒⠶⠦⣤⡞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣠⡤⠼⢧⡀
⠀⠀⣴⠋⣩⣯⣍⣻⢦⣴⠋⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠙⣆⠀⢀⣀⣀⡀
⠀⠈⣏⠓⣧⠀⢀⣉⣻⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠴⠚⠛⠛⠛⠛⢦⡀⠀⠀⢹⡶⣯⡽⢥⣽⡆
⠀⠀⠈⠳⣍⣻⡟⠛⢻⣦⣀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⣿⣷⣤⢾⣴⠃
⠀⠀⠀⠀⠈⠹⡗⠾⣭⣀⣉⠽⠟⠒⠶⢾⣧⣤⣤⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⡤⢴⡶⠶⠚⡿⠛⢻⠇⢀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢻⡚⠶⠤⢉⡛⠶⠶⢾⣥⣄⣠⣔⣋⣁⣀⣴⣊⣁⣈⡴⠊⠁⣀⣔⣁⣀⣠⣮⣤⡤⠾⠚⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠐⠶⢬⠍⠛⠛⠀⠲⠤⢭⡍⢉⣭⣍⣉⠉⢩⣉⣉⣙⠉⠉⣭⣭⣭⠤⠀⠰⠶⠚⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⣤⣀⣈⠙⠛⠂⠀⠲⠶⠤⠄⠀⠴⠦⠤⠄⠀⠠⠤⠤⠄⠀⠠⠶⠶⠚⢋⣁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⢦⠈⢉⣀⡐⠒⠶⠶⠀⠐⠲⠶⠶⠀⠶⠶⠶⠶⠀⠀⠶⠶⠶⠆⠀⠋⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠲⠤⣬⠉⣛⠁⠘⠓⠒⠒⠀⠐⠒⠒⠒⠀⠐⠒⠒⠒⠀⢐⡒⠚⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣉⣛⣓⠀⠀⠛⠒⠒⠂⠘⠓⠒⠒⠂⠀⣉⣉⣭⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣿⣿⢻⢿⢛⠿⡿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠊⠉⡁⠀⣀⡀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⡉⠀⠀⠀⢙⣷⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠖⠃
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣀⡽⠖⠊⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠢⣄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠘⢦⣀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣠⣤⣴⣶⣾⡿⠟⠁⠀⠀⠀⠀⠸⡏⠠⠀⠀⠀⠀⠤⢤⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣀⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣤⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀⢀⣰⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠴⠯⡽⠚⠳⠋⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢧⢀⣼⡇⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠛⡟⠘⢿⠛⠓⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠁⠀⠀⣥⣾⡿⠁⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣠⣬⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⣀⣀⣤⣤⣴⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⠡⢐⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢂⠡⣐⠈⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⡡⢔⡪⢶⡿⠃⡠⠂
⠀⠀⠀⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⡡⢔⡪⠕⠈⠁⡰⠋⡠⠊
⠀⠀⢀⠔⠁⠀⠀⠀⢰⠀⠀⠀⠀⡀⠄⠂⡁⢄⡢⠕⠊⠁⡀⠄⡒⠋⠁⠉⠑⢄
⠀⢠⠁⠀⠀⠀⠀⠀⡆⢁⡠⠒⡁⠄⡂⠅⠂⠁⣀⠤⠒⢁⠠⠎⠀⠀⠀⠀⠀⠀⠱⣄⡀⠀⣀⡀
⠀⠸⠀⠀⠀⠀⠀⠀⡰⠋⡠⠊⠂⠁⣀⠤⡒⠋⠀⠀⠚⢅⡀⠀⠁⠀⠀⠀⠀⠀⠀⡱⠊⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠠⠐⠉⢀⠄⠀⠀⠀⠀⠀⠀⠡⡀⠂⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠄⠀⢀⠈⡠⠊⢀⠀⠒⠀⠐⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠔⠊⠁⠐⠢⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠂⢄
⠀⠀⣇⠔⡡⠊⠀⡠⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢄⠀⠂⠀⠀⠀⠀⠀⡠⠃⠀⡠⡾
⠀⡔⡡⢊⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣤⠵⠒⠐⠢⢴⠂⠐⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠐⠂⢉⢤⡢⠵⠈
⠀⢸⡋⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠠⡐⠌⠂⠁
⠀⠈⠢⢕⡢⢀⠀⠢⠤⣎⣀⣀⡀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢛⠒⠲⠤⠀⠒⠈⡀⢄⠢⠕⠋⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢹⠲⠭⠠⠥⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠠⡒⠕⠊⠁⠰⠀⢀⠤⠤⠤⠾⣀
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠑⠠⣄⠀⠀⠢⢄⣀⡀⢀⣀⠠⠔⡩⢔⠪⠆⠁⠀⠀⠀⢀⠜⠈⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠯⢔⠤⣀⠀⠀⢀⠤⡢⠕⠈⠀⢸⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⡀⠈⠐⠭⠍⠂⠁⠀⠀⠀⠀⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⣀⣀⣀⠠⠳⠄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣀⣀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠄⠀⠀⢀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⣀⡀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠁⠂⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣹⣿⣿⣱⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡟⢿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢻⣿⣿⣿⣿⣤⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣏⣹⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣉⣿⣿⣻⠟⠁⠀⠀⠀⠀⠀⠙⣯⣯⣽⣭⣯⡝⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣟⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⣤⣼⣿⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣯⣟⣿⢿⣾⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣟⡿⣿⢷⣷⡇⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣶⣿⣿⣾⣿⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠻⣿⢉⣿⣿⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡇⣰⠀⠀⠀⠀⠀⠀⡔⡀⠀⠀⠀⠀⡀⠞⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡶⢃⠉⠀⠀⠀⠀⢄⡠⠊⠁⠀⠈⠀⣠⠈⠀⠀⠀⠀⠀⠀⠈⣞⡡⠄⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⠰⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣀⡤⠒⠁⠀⠀⠑⢄⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡟⢰⢃⠀⠀⢀⠄⠐⠚⠠⢄⡀⠀⠀⠀⠀⠀⠈⣷⠞⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⡄⣿⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠐⢤⡀⢀⣀⡴⣧⡀⠀⢀⡠⠔⠂⠉⠑⠢⣁⠀⠀⡔⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡦⠁⢿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠹⡤⠾⠒⣚⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣬⣷⣦⡀⠘⡇⣸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠹⠿⣭⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢛⣛⣿⣧⣭⣁⠹⣼⠀⠅⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣉⢥⣾⣩⡤⢀⣀⡸⡎⠇⠀⠀⠀⠀⠀⢀⠁⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⠤⢼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠩⣐⡭⣥⣀⠹⣄⢀⠀⠀⠀⠀⢠⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⢀⢠⠃⡀⠠⠤⠌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣩⣵⢟⡉⠁⠀⢼⣦⣘⠥⢄⢀⠸⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠎⠀⠀⠒⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⣁⣠⠄⠒⠒⠋⠛⠳⠮⣽⣷⣿⡌⢯⣀⠄⠀⠀⠀⢀⣴⣿⠇⠠⣈⡴⠧⠄⠀⠛⠶⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠠⠈⣉⠁⠰⢖⡶⣋⡀⠀⠀⠀⠀⠀⠹⢦⡙⠋⠛⠟⠋⣠⠾⠿⠶⠚⠉⢀⡀⠀⢦⣴⣶⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠗⠊⠀⠀⣰⡿⠋⡕⠀⣀⣶⠿⢰⣀⠀⠀⠉⠓⠒⠒⠋⢁⡀⠀⢀⠠⡙⠞⠿⣷⡦⣝⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠉⠀⠀⠐⠃⡏⠈⠀⢺⡥⢀⡆⢻⠈⢷⡈⢷⡈⢳⡕⢦⣙⢮⣿⡄⠈⠉⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠈⢀⠂⠈⠆⣳⡏⢷⣾⣿⠈⠉⠁⠻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠐⢸⡇⠀⠈⠋





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⢀⡴⠛⠉⠉⠙⢦⡀⠀⢀⣤⠖⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⣠⠿⠚⠛⠓⢦⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣀⠀⣼⣃⣀⣀⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⣧
⠀⠀⠀⣠⡤⢶⡶⢤⣄⠀⢀⡴⠋⠁⠀⠀⢙⡷⠋⠉⠉⠉⠙⠳⢿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣤⡶⠛⠉⠙⠳⣆
⠀⠀⣾⣇⣰⠟⠛⠶⣿⣳⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⣀⣸⣏⣀⡀⠀⠀⠀⠸⣇⢀⣤⢶⡶⢦⡀
⠀⠀⢻⣌⣹⣆⣀⣠⣬⣿⠃⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠞⠋⠉⠁⠀⠀⠈⠙⢦⡀⠀⠀⣿⣻⡷⠟⢳⡖⣿
⠀⠀⠀⠙⠷⣌⣿⠉⢉⣻⣦⣄⣀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣿⣿⢿⣶⣻⡴⠋
⠀⠀⠀⠀⠀⠈⢻⡛⠿⢤⣤⣨⡽⠛⠛⠛⢲⣿⠶⢤⣤⢤⣤⡤⠴⠯⣤⣤⣤⣤⣤⣤⠤⠶⢶⠾⠻⠛⣻⠋⠉⢹⠀⣠⡟⠉
⠀⠀⠀⠀⠀⠀⠈⣧⠛⠶⠤⢉⡛⠳⠶⠾⣥⣤⣀⣤⣖⣉⣀⣀⣤⣚⣁⣀⣠⠖⠉⠀⣠⣔⣁⣀⣠⣴⣥⣦⠴⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠰⠶⣬⡉⠛⠛⠂⠰⠦⣬⣭⡍⢉⣉⣉⣉⡉⢉⣉⣉⣛⣛⠋⠉⣉⣉⣭⣥⠄⠀⠶⠶⠚⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⣄⡀⠀⠛⠒⠖⠀⠀⠤⣤⣤⡄⠀⢠⣤⣤⣍⠉⠉⣭⣤⣤⡄⠀⠀⣤⡤⠶⠞⠛⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣌⡉⠛⠁⠀⠶⢤⣤⣤⠀⠠⢤⣤⣤⡄⢠⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⠀⠰⠚⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣁⣈⡛⠓⠶⠶⠀⠴⢤⣤⣤⠀⠠⢤⣤⣤⠄⠀⢤⣤⣤⣤⠀⠠⣤⡤⠶⢂⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣉⡁⠐⠶⢤⡄⠀⠠⢤⣤⣤⡄⠀⣤⣤⣤⣤⠀⠀⠶⠶⠶⢂⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿
⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃
⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⣠⠶⠒⠲⢤⡀⡼⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠚⠉⢀⣠⣤⣄⡀⢀⡼⠚⠋⠉⠳⣄
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠙⢧⡀⠀⠀⣀⡴⠚⠋⠉⠉⠉⠳⡞⠁⠀⠀⠀⠙⢯⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸
⠀⢀⡎⢠⣏⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡝⣆
⠀⠸⡇⡀⠉⠓⠶⠤⣤⣀⣀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣠⠿⠃⡿
⠀⠀⠳⣄⠁⠠⠀⠀⡀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠖⠒⠚⠛⡋⠉⡉⠀⠀⢠⠇
⠀⠀⠀⢹⡓⠦⣤⣀⡀⠈⠀⠐⠀⠀⠂⠀⠀⠀⡄⠀⠄⠀⢄⠀⠰⢀⠐⢀⡀⠂⠀⠁⠄⠀⠂⢀⣠⡴⠋
⠀⠀⠀⠀⢳⡀⠀⠄⠉⠉⠛⠒⠒⠶⠶⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⠤⡤⠤⠤⠴⠶⠖⠚⠋⠉⢰⠃
⠀⠀⠀⠀⠀⠱⣄⠘⠀⢖⠈⡄⠀⣀⠄⢀⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢀⠆⡠⠂⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠈⠂⠉⠶⠉⠱⠊⠱⠊⠈⠎⠀⠛⠀⠛⠠⠈⠁⠂⠀⢉⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠶⠶⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠖⠒⠚⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠚⠉⠉⠓⠒⠋⠁⠀⠀⠀⣀⠤⠤⢀⡠⠐⠂⠄⠀⠀⠑⠤⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠼⠁⠀⠀⠀⠑⡤⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠢⠀⢠⠊⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⢀⠀⠀⠀⢠⣾⡄⠀⠀⠀⡔⠁⢧⡀⠀⠀⠀⣀⣖
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢱⠀⠀⠈⡏⠉⠛⠒⠚⠒⠒⠒⠛⠛⠛⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⡇⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠑⠲⠤⠤⣤⠤⠤⠤⠖⠊⠀⠀⢠⠎⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣋⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢜⠉⠀⠀⠀⠈⠀⠀⢉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣄⡤⠊
⠀⠀⠀⠀⠀⠀⠑⠒⠶⠦⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⠤⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠁⠈⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⡴⠊⢹⣀⣄⡈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠙⢦⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢸⣀⡈⠓⠶⣄⠀⠀⠀⠀⠀⡰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠀⡇⠀⠀⢀⡤⠊
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠻⠖⠚⠁
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢲⡇⠀⠀⠀⠀⠀⣀⣀⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠊⠉⠀⠀⡟⡇⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠘⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣀
⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢄⡀
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠊
⠀⠀⠈⠓⠢⢤⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠴⠖⠒⠒⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⣤⠴⠶⠒⠚⠒⠒⠶⠶⢤⣀⡀
⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠛⠶⣄
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠁⠀⠀⠈⠉⠉⠛⠲⠦⣤⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻
⠀⢳⡀⠀⠀⠀⣀⢀⡀⢀⣀⣄⣀⢴⣂⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡄⠈⠀⠀⢸⡇
⠀⠀⠙⢦⡀⠉⠊⠳⢶⣿⣧⠶⢎⡩⠛⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣗⣤⣄⠀⠙⢦⠀⠀⠀⠀⢀⡠⣄⡌⢶⢍⡐⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠲⢤⣀⣀⡀⠀⠁⠀⠈⢁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣞⣿⣿⣽⣽⣿⡶⠀⠈⣧⣤⣼⣦⡒⢽⡲⢟⡛⠀⠈⠀⢀⡞⢀⣀⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⢷⡀⠀⠀⠀⢀⠠⡄⣀⡀⣀⢈⣀⣻⣿⣿⣿⢿⣿⣿⣿⠟⠀⢀⡏⢙⠾⠏⠻⠇⠋⠉⠈⠀⢀⣰⢮⣼⣯⣽⣿⠷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠁⠀⠙⠾⡃⠿⠿⢙⣛⣿⡯⢿⣿⠿⠛⠀⠀⣠⠾⠧⢤⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠈⠉⠉⠙⠑⠋⠀⠀⠉⣀⣀⣤⣴⡾⣥⠤⣄⣤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠲⠶⠶⠶⠿⠿⠿⠷⠿⠿⠭⠭⠭⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠋⠀⠀⠀⠀⠀⠉⠙⠢⢤⣤⣄⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣲⡶⠽⠿⠿⠯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⠿⠶⠖⠲⢄⡀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠸⢃⣡⠞⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⠀⠀⠀⠀⡠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣭⣵⣄
⠀⠀⠀⠀⠀⡔⡱⠖⡊⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣦
⠀⠀⠀⠀⢠⡄⡎⠘⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⣿⣇
⠀⠀⠀⠀⠀⡆⠇⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣋⠰⣾⡎
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⡛⠿⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⣀⠀⠀⠀⠀⠀⠀⠠⠐⠀⣁⣴⠟⣻⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠻⡉⠀⠀⠀⠀⠀⠀⠀⣛⢿⣤⣈⣑⣒⣒⠢⢤⠤⠶⠿⢿⣛⣛⣽⣿⡷⠦⠗⢚⡧⠖⣻⣽⡷⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢀⠲⠶⠒⠈⢟⣛⡛⢿⡿⠿⠟⡐⠬⠓⡉⢤⣶⢿⣯⢕⣲⣯⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢙⣯⣶⣤⡀⢐⡒⠤⠀⠒⣬⠩⢽⣯⠭⠠⠶⠟⠚⠂⢾⠭⢒⣪⡍⠁⠀⠬⢶⣻⣅⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⢷⣶⣶⣦⣼⣿⣈⣝⣭⣀⣤⣤⣧⣴⣬⣬⣤⣤⣥⡿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠋⠉⠛⠛⠶⣤⡀
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⢤⣤⣀
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⢀⣼⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣿⠀⠀⠀⠈⣯⡉⠛⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⣿⣩⡇⠀⠀⠀⢠⡞⠀⠀⠀⢷⠀⠀⢀⡀⣇⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡾⠛⠛⠋⠙⠁⠀⠀⠀⠻⣦⡀⠀⢠⡘⠷⠶⠛⠉⠙⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣼⣁⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠺⡇⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠻⣆⠀⣠⠞⣡⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠠⡆⠀⠘⠳⣆⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⢷⣤⠤⢤⣿⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣭⣭⣉⡉⠀⠈⠙⠷⠤⡤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⣾⠁⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠈⠚⣁⡴⠟⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢼⠋⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠃⠀⠀⠀⠀⢀⡤⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣄⣤⣤⣤⣄⣀⣀⣀⣀⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢴⡚⢛⣻⡍⠉⣉⡉⠳⠾⠿⠿⠞⠛⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢸⣥⠿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠘⠓⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠌⣀⠀⠀⠀⡀⣀⡼⣯⣄⠀⠴⠀⠀⠀⠀⣤⡄⢤⣤⡵⠶⢻⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠀⠉⠠⠀⠈⠀⠸⣧⠀⠀⠀⠀⠀⠀⡌⠀⠙⠀⠘⠿⢷⡴⠞⣡⣠⠀⠤⡄⠀⠀⠰⢞⡿⢦⠙⠿⣿⣿⠆
⠀⠀⠀⠀⠀⢀⡀⠺⠀⠂⠂⠀⣀⣀⣀⣾⡆⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠦⠔⠳⢶⣦⣀⡏⠁⠴⡆⠀⠀⠀⠀⢦⠶⠶⢼⣋⣟⠻⣙⠃⠀⣰
⠀⠀⠀⠀⠂⠈⠙⠧⣦⠀⠐⢢⣀⡎⢍⠀⠈⠃⡰⠀⠀⠀⠀⠀⠨⡀⠀⢠⣤⠓⠂⠉⠀⠀⣠⠶⣴⠇⠀⠀⢠⠘⣴⡆⢯⠘⢣⡋⠼⣧⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠑⠫⠶⠜⣀⠤⠖⠁⠀⠀⠀⠀⠀⡀⢰⣐⣤⠀⣀⣀⣠⣠⡞⠉⠀⠀⠀⠀⠀⠀⠁⠈⠳⠞⠖⠈⠅⠓⠈⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠔⣊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠁⠘⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣀⡔⠚⣄⠀⠆⠀⠀⠀⣀⡈⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢀⣿⠃⠀⢯⣀⠀⠁⠀⠀⠈⢁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣽⡇⠀⡏⠘⢠⡀⢠⡄⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⣿⡉⡀⢳⠈⠁⠀⠀⠀⢀⠀⢠⡿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠈⢻⠁⠘⠀⠈⠧⠀⠀⠙⠁⠞⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠷⢄⠀⢀⡀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣼⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⢁⠋
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣐⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡄⠢⠀⠂⠐⠀⠃⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⣰⡰⡄⠀⠀⡸⠠⠄⠀⠐⠀⠀⠀⠀⠖⠄⠀⡄⠀⢠⠀⠀⠀⠴⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⢀⠇
⠀⠀⢀⠀⠀⠀⠁⠆⠀⠀⠀⢠⠈⠁⠙⡀⠠⡇⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⢀⡀⠈⠁⠠⠄⡀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠈⢀⠀⠀⠘⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠈⠁⠀⠁⠀⠀⠧⠀⠀⠢⡀⠀⠀⠂
⠀⠀⢀⣀⡤⠀⠈⠀⡠⠄⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠉⠉⠙⠒⠶⣄⠀⠠
⠀⠀⠈⠉⠀⠠⠀⠒⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⡄⠀⠀⠀⠀⠀⢠⡇⠀⠐⠀⡀⠁⠀⠀⢰⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠁⢀⡀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠉⠀⢢⡔⠢⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠀⡀⠐⠀⠢⠄⠀⠖⠚⠃⠁⠀⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠀⢀⠠⠀⠀⠤⢀⣀⠠⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⢀⣀⡙⣁⣤⠤⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⢀⠀⠀⡆⠀⠀⠃⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠁⣀⠀⡢⠴⠇⠀⠀⠃⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⠀⠦⠀⠀⠀⠀⠀⠂⠉⠀⠀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⠤⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡀⠂⠀⠓⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠐⠋⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠛⠀⢀⣦⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠦⠀⠀⠀⣸⣿⣿⢻⣿⣟⣿⣿⣿⡟⣿⣿⣿⣿⡇⠀⢀⢨⠾⠡⠁⠀⠀⣠⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠸⡉⠁⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠖
⠀⠀⠀⠀⣀⠀⠻⠃⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠈⠃⠀⠀⠀⠼⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠸⠆⠀⢠⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⠈⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠰⡆⠀⠀⡀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠰⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⣀⡀⠀⠰⠀⠀⠀⠀⡀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡿⠻⣿⠛⠿⢿⡿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠧⣷⣤⢜⣫⣧
⠒⢬⠂⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢨⠃⠠⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⣠⠀⠉⠻⠶⠻⠆⠀⠀⠀⠀⡀⠀⡀⢠⡄
⠒⠉⠱⣣⠆⡀⠀⠀⠀⠀⠀⠀⢠⣤⠠⢘⠃⠠⠴⢣⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣿⡟⣴⣤⡀⠀⠀⠀⠀⠀⠶⢀⡉⠉⣱⡂
⢁⠀⠈⠡⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢌⠁⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡇⠏⢻⡿⢿⡦
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣷⣤⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠒⢩⣤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀
⠀⢰⠁⠈⡙⢿⣷⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⢹⣏⣉⣀⣢
⠀⠈⠀⢇⠀⠹⣿⣧⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢤⢀⡄⠀⠀⠈⠛⢯⡙
⠀⠀⠀⠀⠀⡀⠙⠛⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣴⠖⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠙⢥⠖⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⢺⣽⠀⠀⠀⠀⠀⠹⠁⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⢲⠟⠛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⡶⠠⡄⠀⠀⠀⠀⠀⠀⠀⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⢸⠁⢀⠆⠀⡐⠂⠲⠀⠀⠀⣿⠁⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⣀⠚⢢⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢷⠀⠀⠉⠁⠀⠀⢣⣠⣀⠀⠀⠀⠋⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⡀⠶⣀⠺⢂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠳⠄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠀⠀⠀⠀⠘⠋⡤⠉⠴⢏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣠⡀⠛⠴⠎⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡅⠀⠀⠀⠀⢀⡌⣹⣦⡀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠇⠀⠀⠀⠀⠀⠤⠉⠁⠛⣷⣟
⠀⠀⠀⠀⠀⠀⣠⠾⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⢄⡀⠀⠀⠀⣀⣀⡉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠁⠀⠊⠉⠲⡀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠡⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⣈⠉⡆⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢠⡤⠄⢇⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠆⠠⠂⡐⢦⣍⣠⢟⡀⠀⠀⠀⠐⠐⠠⠀⢀⡔⠁⠀⠐⠀⢑⢠⠔⠀⠀⠀⠀⠑⠄⠀⠀⢁
⠀⠀⠀⠀⠀⠘⠀⠀⢈⡈⠦⡄⠀⣄⠈⠂⡤⠀⠀⠀⠀⠀⣹⡌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠐⢢⢨⣰⠂⠠⠴⠁⢤⠀⠀⡀⢀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⡙⡘⢣⡗⠀⠰⠀⠀⠠⠁⠀⠀⠁⠀⢄⠤⠟⠃⠐⠐⠀⢀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠦⠀⡀⠈⠁⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⣠⠄⠃⠀⠀⠀⠀⠀⠉⠠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂⠐⠒⠒⠃⡀⠂⠀⠐⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠐⡀⢠⠖⠀⠀⠀⠈⠀⠈⠑⠖⠀⠠⠛⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠱⡈⠢⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄⠀⠁⠈⠑⠒⠣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠄⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠠⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠔⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠁⠒⠒⠈⠀⠂⠀⠀⣀⡠⠤⠚⠋⠀⠁⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁


⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⠚⣿⣷⡆⠈⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿
⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢠⣀⣿⣿⣿⣆⠀⠀⣠⣾⣀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣿⠟⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⣿⣿⣿⣛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠛⠻⣿⣆⠀⢤⠄⠀⠀⢠⠆⣤⣤⣤⣤⣶⣶⣄⠀⠀⠀⠀⣠⣤⣀⣄⡷⠀⢀⣤⣶⣦⣚⡟⠃⣼⣿⣿⣿⢿⣿⠿
⣿⣯⠀⠀⠐⣸⣿⣧⡆⢀⣂⡀⣀⣰⣀⣼⣿⣿⣿⡿⢻⣷⡀⣀⢼⣿⣷⡛⢻⣧⣤⣾⣿⠛⠛⣿⣿⣷⣿⣯⣀⠀⡀⣿⣿
⣟⣿⣧⢀⣠⣿⣧⣿⣿⣿⣧⣠⡀⣼⣿⣿⣿⣷⢉⠈⢹⠟⠁⠱⠈⢛⣋⢘⠛⡻⣿⣿⣟⣛⣘⣻⣿⡟⠻⣿⡄⠄⢠⠟⢹
⡉⢿⣿⡄⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⢷⡶⠋⡤⠀⠠⡤⢼⣯⠍⢠⡇⠈⠟⢿⣬⣿⣿⡿⠀⠀⠘⠛⢃⠀⠀⢸
⡍⠽⠏⠛⣿⣩⣁⣀⡙⠛⠛⠛⠉⡉⠉⠉⢁⣀⠀⠧⡜⢀⣄⣀⣾⣿⡿⠷⠖⢒⡹⢖⡸⣿⣿⣿⠂⠀⠀⠐⣰⠇⣀⠀⣿
⣿⣦⣴⡾⣿⣿⣿⡿⠛⠒⠒⠒⠚⠛⠓⠚⠛⠛⠡⠄⠀⠈⠀⢀⠀⠤⠤⠂⣰⣤⣃⡈⣠⡌⠁⠶⣤⡀⠐⠂⠈⠋⣉⣠⣿
⢿⣿⣿⡇⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡁⠒⠉⣁⠀⠒⠚⠉⠉⠁⣿
⠀⠙⡟⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⠀⠐⠂⢉⡠⠔⠁⠄⠀⠀⣴⣿
⠀⠀⢻⡦⠈⠻⢿⠀⠀⠀⢤⠀⠂⢹⢰⡇⡀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⣶⠀⣀⡖⠀⡀⠀⠀⠐⣰⣿⣿
⢠⣧⠀⠀⠀⢠⣶⢀⡄⠀⠸⠀⠀⢸⡈⣷⡇⠀⠀⢀⠀⣼⢸⠇⠀⣰⠀⠀⣿⡁⠀⣼⠀⠋⢀⡇⡅⢠⡇⢠⢰⣸⣿⢻⣿
⣾⣿⣷⣴⣥⣸⣿⣮⡃⠀⢸⡆⠀⢸⡇⣹⡇⡆⠀⢸⡆⡿⣿⢸⢰⢸⡄⢠⣾⣅⢠⡏⠀⠄⣼⠐⡷⣼⣶⣿⣿⣿⣦⣾⣿
⣿⣿⣿⣿⣤⣿⣿⣯⣦⣴⣾⣧⣤⣼⣥⣿⣷⣷⣶⣾⣿⣷⣿⣾⣾⣾⣷⣾⣯⣿⣾⣧⣤⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣀⠀⢈⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⡟⠛⠛⠛⢛⣿⣶⡆⠀⣴⣿⡿⠁⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⠟⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠃⣰⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠏⢀⣴⣾⣿⣿⣶⡄⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣀⣤⣶⠀⠻⣿⣿⣿⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⢉⣀⣀⡈⠙⢉⣉⠙⠿⠏⢁⣴⣾⣿⣿⣿⣷⣤⣀⠉⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠃⢰⣿⣿⣿⣿⣶⣿⣿⡗⠀⣴⣿⡿⠁⣼⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣤⠈⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⣠⣼⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⡟⠀⣼⣿⣿⡿⠁⣹⣿⡇⢸⣿⣿⣿⣿⡄⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⡟⢀⣀⠙⠻⠟⢀⣼⣿⣿⠇⢸⣿⣿⣿⣿⡟⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣄⣀⣠⣼⣿⣿⡟⠀⣾⣿⡟⢀⣾⣿⣿⠆⢠⣾⣿⣿⡿⠀⣾⡿⣿⠇⢀⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⡅⠸⣿⣿⣷⡀⢻⣿⣿⣿⠁⣰⣿⣧⣤⣴⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⣿⣿⣿⣷⡀⠹⣿⣿⣧⠀⢿⣿⠃⣰⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢀⣿⣿⣿⣿⣿⡄⠹⣿⣿⣆⠈⠏⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡁⠰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠷⠆⠀⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⣠⡂⣤
⠀⢀⠤⣀⣀⢐⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢈⣻⠔⡻
⠀⣧⣿⠿⠿⢷⣅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠖⠋⢀⠠
⠀⠻⣏⣀⢀⡸⣫⠁⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⢰⠠⠆⠀⠠⠄⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⠍⠀⠀⠀⣀⣀
⠀⠀⠈⠉⠗⠋⠁⠀⠀⠀⠀⠀⠀⣀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀
⠀⠀⠀⠀⠀⢐⠀⣠⡤⠴⠖⠒⠂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡡⠌
⠀⠀⠀⠀⢀⡿⠊⠁⠀⣄⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠗⠒⠀⠀⠀⠀⣤⣳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠠⠀⠀⠀⠀⣀
⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⢄⠑⠠⡀⢤⣀⣸⣿⡎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⣿⣦⡱⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣄⣌⣙⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣧⠀⠀⢸⣿⡇⡁⡀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠈⠄⠋⠀⠀⠀⠀⠀⠀⢀⠎⠙⢻⡀⢸⣿⡟⣰⠀⠠⠀⠀⠀⠀⢀⡴⠀⠀⠀⠘⢮⡳⢴⣶⠿⠊⠀⡈⠀⠀⠀⠀⠶⠄⠀⠄⠀⢰⣍⣳
⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣈⠂⡂⢻⣷⣿⠏⡔⠉⠀⠀⠀⠀⠠⠂⠙⠁⠀⠀⠀⠀⠀⠉⠉⠉⠒⠉⠁⠀⠀⠀⠀⠄⣀⠀⠄⠀⢀⣮⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠿⠶⠿⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠒⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⢬⡍
⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⠃⠀⡠⢀⣠
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠂⠄⠈⠀⠀⣈⠅⠀⢠⣾⣦
⠀⣀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠖⠀⢀⠌⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠙⡬⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠄⠑⢄⡦⢄⠀⠈⡄⠀⠈⠄⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠠⠀⠀⠐⡂⠈⠙⢣⡔⢢⡅⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠀⠃⠀⢀⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠄⠀⡤⠠⡀⠈⠀⠳⢤⡄⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⠈⠑⠆⡬⢠⠤⡄⠀⢠⠏⠀⠀⠑⠦⡱⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⠀⢼⠀⡈⠀⣖⣴⠎⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡔⠜⢑⣆⠐⠀⠀⠀⠆⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣃⠀⠠⡀⠀⡄⠀⠀⡆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠸⠀⠀⠉⠱⠃⠀⠇⠀⠀⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⢃⠈⠰⡀⠀⠀⡃⠐⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡞⠁⢈⠉⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠑⡶⠜⠁⠘⠀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣀⣈⣆⠀⠀⢡⣀⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠤⣀⣭⣉⣉⣁⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⣀⣀⣀⣤⣤⠤⠏

⠰⢀⠉⠀⠀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣉⠒⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠥⢄⣉⠈⠁⠀⢠⡘⠀⠇
⠀⠀⠂⠀⠐⡀⠁⠠⠁⠀⠀⠁⠀⠀⠀⠀⢉⠈⣉⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠲⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡆
⣠⡐⠃⢀⢁⡄⠀⠀⠀⠀⠀⠁⠤⣀⠀⠠⠀⣠⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠋⠁⡉⠡⠀⢠⣄⣐⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠦⠊⠀⢀⠀⠀⠀⢆
⠀⠤⠁⠐⠃⠀⠀⠁⡠⡙⠄⠀⠀⠀⠀⠀⠀⡀⠐⠀⠒⠀⡤⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⣄⠀⢠⡆⡆⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⠀⡿⣤⡈⠻⢅⡀⢸⡄⢸⠀⣿⢸⡇⣰⠛⢸⡇⢠⡄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢳⡒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⣧⠀⠈⣿⡄⢸⡇⢸⣇⠾⠼⡟⣼⠁⣿⠀⢸⡧⢸⡇⠀⠐⣄⠙⠦⠤⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠸⡆⢄⡿⠃⠈⠁⠀⠁⠀⠀⠀⠻⠀⠉⠀⠘⠇⢸⡇⠀⠀⠀⠁⠢⠀⠊
⠀⠀⠀⠀⠀⠁⠂⠠⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠄
⣄⠀⠀⠠⠤⠀⠀⠀⢠⠀⠀⠲⢘⠉⠀⠀⠈⠉⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠄⠈⠀⠀⠀⠀⠀⢠⠈
⡍⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⢀⣀
⠈⠂⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠾⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⡀⠁⠀⠀⢢⠋⣹⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠱⠀⢁⡂
⠔⣂⠸⢟⢠⠄⢀⢹⢰⠄⠉⠴⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠂⢀⠈⣣⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠙⢍⣘⠁⠀⠀⢘⣸⡀⠠⠀⢈⣫⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢶⠈⣁⠌⠀⠀⠀⠌⠀⠀⠠⠀⠀⠀⠀⠀⠐
⠢⣀⠉⠀⠀⠜⢻⣤⡵⢶⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠁⢈⠈⠁⠀⠀⠀⠊⠘⠄⠀⠐⠀⠀⠀⠀⠀⠁⡀
⠀⠈⠪⡰⠄⡀⡊⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠡⠚⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠁⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢮⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠸⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠤⠄⠠⠊⠁⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣆⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡠⠀⣤⠀⠠⡀
⠀⠀⠀⠀⠀⠖⠉⢰⡁⠀⠡⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡅⠀⠽⠀⠀⠁
⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⡐⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠐⠄⡀⠀⡠⠃
⣀⣄⣤⣤⣤⣬⣦⣤⣤⣬⣤⣤⣄⣠⣤⣔⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⠐⡤
⠀⠀⠀⠀⠀⠀⠀⡰⠒⣆⠀⠀⠀⠀⠀⠀⣉⠀⢀⣠⢄⡀⠋⡙⠀⡀⢀⣀
⠀⠀⠀⠀⢀⣄⠀⠁⠀⣿⡀⣴⡟⣿⡇⢠⢿⣇⣾⢃⣾⠃⣰⡏⢰⡟⢁⣾⠀⣠⡴⢄
⠀⠀⠀⠀⠀⣿⡆⠀⢰⣿⠠⣿⡀⢿⡄⠂⣼⡇⠉⠁⠿⠈⠙⠀⠉⠀⣾⣡⣾⠋⣤⡞⠁
⠀⠀⠀⠀⠀⢹⣿⡈⣼⠇⠀⠈⠀⠀⠀⠀⣼⠇⣀⣀⠀⣀⣀⡀⣄⠀⠈⠀⠈⢰⡿⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠸⣿⠈⠁⠀⠀⢀⠒⡄⠀⢀⡿⢰⡇⢸⢀⡀⢀⣽⠗⠤⣤⣴⠆⠈⠓⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⢡⠃⠀⣿⠀⣈⣀⡀⠀⢡⡟⢡⣾⠏⠀⣤⠄⢀⡀⠠⡀⣠⡆
⠀⠀⠀⠀⠀⠀⠛⠀⢸⣿⡌⢀⣼⡟⢸⡇⣾⠡⠁⣿⠐⢹⡏⢀⣼⠏⣰⣿⠃⢀⡼⢤⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⢃⣿⠃⠀⠀⢀⣠⠤⣀⡀⠘⠃⠁⠈⠉⣼⠏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠛⠃⡄⠀⠀⡏⠀⠀⠀⠉⠓⢤⣀⢀⣼⠏⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠤⣉⢏⡀⠑⢄⠀⠀⠀⠀⢀⣼⠟⠳⠦⣤⣤⡶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠤⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡠⠒⠛⢢⣀⣀⣀⠀⠀⠀⠀⡨⠎⠀⠁⠓⠲⢤⡀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠃⢖⠛⣆⠀⠀⠀⡴⡚⢇⠀⠀⢠⣅⣀⣀⣉⢢⠀⡌⠀⢰⣿⠇⠀⠀⠀⠉⠔⢲⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⡀⠀⢸⠀⢠⡞⠀⡇⠈⠫⣉⣁⣀⡠⠤⢌⡙⢧⡄⠀⠀⠰⣯⠇⣾⠟⠀⢨⠇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠐⠆⠀⡘⢀⠀⡇⠀⠈⠢⣄⡀⠀⢀⣀⣀⢀⣈⣾⠉⢦⡐⢶⡀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠙⢦⡈⠉⠑⠒⢊⠑⡄⢣⡘⠢⣀⣀⠀⢀⣀⣀⡤⠴⠖⡞⢹⠃⠀⠈⠐⠀⠤⠄⠴⡊
⠀⠀⠀⠀⠀⠀⠀⢖⣈⠈⠳⣄⠙⢦⡀⠀⠀⠑⠌⢂⢩⡙⣭⣭⢓⣭⣥⡲⡆⠼⣒⠇⡲⢄⠀⠀⢰⠒⠒⡆⠀⠑⠂⠀⠰⡎⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⠱⣆⣀⠈⠳⢄⠉⠒⢄⡀⠈⢢⠱⡇⣿⣿⣿⣿⡿⢃⣴⣧⡉⣿⣿⢣⠀⠀⠈⠓⠋⣀⠤⣠⣖⡐⣦⡥⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢀⡀⠹⠢⢄⡈⠒⠤⣑⠆⣿⡇⠹⢷⡶⠎⣹⡟⢁⣽⢻⣷⢱⣄⠤⠒⡩⠔⠊⠀⠈⠳⡅⠒⢌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠻⠶⠧⢄⠤⢍⡲⠤⡌⣃⣿⣿⣿⡿⢂⣀⡹⢿⠟⠙⢛⡫⢞⡠⣴⠉⢄⠀⠀⢞⠑⠒⠼⣆⠀⢂⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⢁⡠⠔⠒⠚⠃⡀⠈⢈⢸⣟⣻⣧⣄⡀⣿⣟⣿⣀⣀⣀⣸⣷⣼⣇⠉⢆⡀⢤⡀⠀⢉⢑⠒⠼⣖⡪⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢖⠉⠹⡍⠀⠀⠀⠀⢄⢀⡂⣸⢸⡟⡋⣿⢿⣇⣿⣿⣯⡉⢻⡏⡭⣼⡟⠆⢰⠋⠀⣠⠇⠰⡁⢸⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣇⠀⡐⠀⠄⠈⠀⣠⡿⠜⠥⢹⡿⡛⣿⡟⡕⠩⢛⢸⡇⡦⠿⠊⠀⠀⡉⠉⠣⡀⠀⢈⡨⠔⠨⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠓⠺⣅⠀⠀⠂⢀⡠⢾⡝⠁⠀⠔⠱⡀⠉⠊⠈⠀⠀⠀⠁⠈⠑⠢⣀⠐⡆⡀⠀⠀⠙⣊⠥⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠢⠔⠀⠀⠀⠁⠀⠈⠁⠀⡚⢡⣀⠜⡄⠀⠙⠲⢤⣤⡤⡀⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡐⠁⠀⠀⠘⠦⣀⣀⣀⣠⠤⢄⡀⠀⢆⠀⠀⠀⠀⠈⢇⢀⡀⠀⠀⢀⠀⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⠳⢤⣀⢀⠀⢸⠒⠛⠦⠴⠋⠀⠙⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠉⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡞⣢⡎⣦⡶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠁⠁⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣦⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠘⠇⠀⢸⠅⠀⠀⠀⠰⡆⠰⡇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠲⠦⣄⡀⣤⠶⠶⠶⠶⠶⠶⠶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⣄⠀⠀⠀⠀⠀⠈⠻⣿⢰⡆⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⢧⡿⠀⠀⠀⢀⣶⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡶⠶⠶⠶⠶⠖⠛⠙⠳⣶⠀⡇⢠⡆⢠⡆⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⡇⠀⣶⡆⠀⠀⣶⣶⠀⣿⠛⣧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣇⠀⠀⠀⢀⠀⠀⠀⠀⣿⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣄⠀⠾⠋⠙⠆⠀⣰⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⢿⠳⢶⣶⣶⡶⢻⡇⠀⠀⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡶⢿⣅⣨⡿⢾⡇⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢹⡇⠀⣠⣤⣤⣤⣤⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣧⠀⠻⠶⠶⠶⠾⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⣤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢠⡤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠚⠃⠀⠘⠛⠛⠛⠓⠛⠀⠀⠛⠚⠛⠛⠚⠃⠀⠈⠓⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠲⠦⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡗⠀⣠⠴⠖⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⣇⠀⢳⡀⠀⠀⠀⠀⢀⡴⠃⢰⠃⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡏⠀⠀⠉⠓⠶⠶⠒⠋⠀⠀⢹⡀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠓⠦⡤⠶⠋⣀⣀⡴⠖⠋⠉⠉⠙⠒⠦⣄⢀⣙⠲⢤⠴⠞⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢦⠀⠀⣠⠴⠛⠉⠉⡿⠋⠉⠉⠳⡄⠀⠀⠀⠀⠀⢠⠞⠉⠉⠙⢯⡉⠛⠦⣄⠀⠀⡴⠋⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⡴⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡇⠀⠀⠈⢧⠸⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣠⠴⠋⢸⣅⣄⣤⣤⣤⣤⣹⣦⣄⣤⣾⣡⣄⣤⣄⣄⣤⣌⣷⣤⣠⣤⣎⣤⣤⣠⣠⣨⡇⠙⠦⣤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠙⠓⠦⡀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠲⢤⡀⠀⠀⠀⢀⡤⠖⠛⠙⠓⠲⣄⠀⠀⠀⠀⢀⠴⠚⠋⠛⠒⢦⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠤⠤⠼⠆⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠾⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇⠰⠧⠤⠤⠤⠤⠤⠤⠤⠤⠿

⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠤⠀⡀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠈⠀⠠⠀⠀⢈
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠉⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠁⠀⠀⢠⠁⠀⠀⢀⠀⠉⠂⠀⠀⠀⠀⡀⢀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠒⠂⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠱
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣤⣄⠨⡧⠀⠀⢀⡀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡷⡹⠄⣾⣿⣿⣿⣿⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣟⢛⣴⣿⣿⣿⣿⡍⣿⣿⣿⣿⣿⡃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣾⣿⣷⣤⣀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠈⠉
⠀⠀⠀⠀⠀⣀⣶⣾⠿⠋⠙⣻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠀⣼⣿⣿⣿⣿⣿⢿⡿
⠀⠀⠀⢀⣶⣿⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⠴⢿⣿⠁⡟⠉⠀⠈⠁
⠀⠀⠀⢨⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢡⠿⣿⣿⣿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣉⡀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣴⡿⣿⣿⣤⣬⣿⣿⣧⠹⠿⠿⠛⠋⠁
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠘⠉⠟⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢺⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⣾⣿⣥⣤⡀
⠀⠀⠀⠀⠀⠙⠻⣿⣤⣴⡀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀

⣀⣄⣀⠀⣀⣄⡀⢀⣀⣀⡀⢀⣠⣀⠀⣀⣠⣀⠀⣀⣄⡀⢀⣀⣄⡀⢀⣀⣀⡀⣀⣠⣀⠀⣀⣄⣀⢀⣀⣄⡀⢀⣀⣄⡀⢀⣠⣀⠀⣀⣠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢽⡻⢛⣟⢙⣻⣿⣭⡛⣿⡟⣿⣏⣙⣟⡟⣿⣿⣟⣿⣛⣟⡛⢻⡟⠛⠛⢛⡛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⠷⠤⣭⢤⢼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣥⣿⣭⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣠⠔⠋⠙⠢⣄⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠞⠁⠀⠀⠀⠀⠈⢳⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠋⣿⠀⡟⠒⠒⠦⢤⣀⡀⠀⠀⢀⣀⡤⠴⠒⠒⠛⠉⠉⠙⠛⠒⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⣠⠴⠒⠚⠉⠉⠉⢻⠀⣟⠉⠓⠲⠦⣄⡉⠓⢾⣉⣠⠴⠖⠚⠋⣹⠉⡟⠉⠉⠉⠓⠒⠦⣤⣉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⡀⠀⠀⣠⠞⢉⡷⢦⡈⠳⣄⠀⠀⢀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣈⠑⢤⡀
⠀⠀⠀⠀⠀⣰⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢷⣠⠞⢡⠔⠉⠀⠀⠉⠲⡌⠳⣄⡾⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⣄
⠀⠀⠀⢀⡞⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡼⢁⡴⠃⠀⠀⠀⠀⠀⠀⠘⢦⡼⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢳⡀
⠀⠀⠀⠈⢳⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⢠⡞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡞⠁
⠀⠀⠀⠀⠀⠙⢦⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡞⠙⢦⡈⠳⣄⠀⠀⣠⠞⢁⡴⠋⢳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⠁⠀⠀⠙⢦⣈⠓⠾⣅⡴⠋⠀⠀⠈⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣈⡙⠒⠦⠤⣤⣀⣀⣼⣀⣧⡤⠤⠖⠚⢉⣉⠷⠦⣈⡉⠓⠲⠤⣄⣼⠀⣧⣀⣀⣠⠤⠴⠒⢋⣁⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠤⢤⣤⣤⣤⣤⠤⠶⠒⠛⠉⠀⠀⠀⠀⠉⠙⠒⠶⠤⢼⠀⢿⣤⡤⠤⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⣀⠀⠀⠀⠀⢀⠞⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⣠⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⣀⠀⠀⣀⡀⠀⠀⢀⣀⢀⣀⡀
⠀⢠⣿⣿⣿⠆⢸⣿⡆⠈⠋⣀⡀⢀⣸⡇⠀⠛⠛⠛⢛⣻⣿⣧⡀⢀⠀⢶⣴⣿⣿⡿⠿⠃⠀⠛⠁⠸⠿⠟⠀⣼⣝⣿⣿⡟⣷⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠐⠄
⠀⠘⠿⠿⠋⠀⠈⠉⠁⠀⠈⠁⠽⠏⠋⡡⠀⠀⠀⠀⢈⢿⣿⠍⠀⡸⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⡀⠀⣤⠘⠿⣿⣼⡽⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠴⠒⠖⣋⣻⣾⣗⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠓⠉⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣧⣀⣿⣄⠀⠀⠀⠀⠀⠀⣤⣶⣤⣶⣶⣶⣾⣶⣄⡀
⠀⢀⡆⠀⢠⣟⢙⠿⣤⣿⡆⠻⢀⠀⠰⢶⣦⣿⣄⢀⣾⣿⣿⣿⣿⣶⡄⢀⠀⢠⡔⠊⠒⠄⠀⠀⡀⠰⢽⡼⣿⣹⣦⠀⠀⠀⠀⣦⣋⣻⣿⠏⠛⠚⣉⣉⣩⣧
⠀⢸⣿⡀⠀⣋⠀⠀⠀⠈⠃⢉⣹⠀⠀⠛⢶⣯⠭⣭⣭⣭⣭⣽⡷⠋⠀⠸⡄⠸⣇⣀⣀⡞⠀⢀⠃⠀⠞⠛⠛⠋⢡⣤⡟⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢧⣙⣦⣌⣀⣀⣀⣠⣴⣿⡟⠀⠻⠇⠀⠉⠉⠙⠛⠛⠉⣩⢤⡤⠄⢠⠁⡀⠈⠉⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⢈⣿⠇⢠⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠙⠻⠭⠉⢀⣩⠥⠴⠋⠠⣶⠤⠄⠀⠀⠀⠀⠒⠒⠚⠷⣶⡶⠗⠘⠦⠤⣄⣤⡴⠴⠶⠖⠀⠀⠀⠦⠤⠤⠼⠿⠀⠀⠐⠿⠻⠿⣿⠟⠛⠛⠋⠉⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣤⢠⡄⢀⡄⢠⡀⢀⡄⢀⡄⢠⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠁⠈⠉⠈⠉⠈⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠨⠬⠬⠼⠼⠭⠧⠥⠥⠥⠽⠇

⠀⠀⣠⣤⣶⣶⣶⣶⣤⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣦⡀⠀⢀⣀⣀⠀⠀⡠⠢⣀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⣤⢀⣤⣄
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⡇⣠⠒⠒⠤⣀⠀⣀⠀⠰⠀⠙⠻⠟⠠⣿⣿⡿⠀⢀⠈⠠⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣍⣐⣶⣶⣷⣶⣶⡇⠀⢤⣙⣺⣻⢿⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⣠⠤⢄⠀⠀⢡⠄⠀⠻⣃⣤⣤⣤⡤⣄⡀⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠈⠈⠉⠒⢻
⠀⠀⠸⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢧⣀⡀⠁⠀⢀⠀⣠⣾⣁⣿⣿⣿⣟⠉⠹⣔⡀⠸⢿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠐⠚⠛⠟⠟⠛⠀⢠⣤⠀⠀⠀⠁
⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠛⡠⠄⣸⢿⣃⠀⠑⢝⠿⢿⣽⣿⡿⠋⠀⠀⠀⠉⠗⠀⣠⡶⠶⠂⠀⢀⣀⠀⠸⠟
⠀⠀⠀⢑⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⢀⡀⠀⠀⠄⠀⠈⣿⣿⣿⣷⣶⣶⡴⠟⣱⣾⡟⠀⠀⢀⣀⠀⢀⣠⠴⠒⠀⠀⠀⢀⣔⣛⡋⠉⣳⣦⡑⣬⣷⣄⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣟⣷⠀⢿⣿⠗⠀⠰⣶⡀⠘⣯⣿⡯⢭⣤⡶⣾⡽⠟⠁⣴⣾⠿⠿⡟⢉⠀⠀⢴⡶⠀⠐⢉⢳⣄⣿⣦⡸⣿⣿⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠈⠛⠒⠀⠀⠈⠀⠀⠙⠛⠁⠐⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠁⠓⠘⠛⠉⠁⠀⠀⠛⠓⠒⠉⠀⠀⠀⠀⠀⠈⠀⠈⠘⠛⠛⠻⠟⠛⠛⠛⠛⠋⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣤⣝⣥⣮⣭⣿⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢠⠏⠉⣇⣤⠤⠤⠤⠤⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠙⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⢰⡄⠀⠈⡄⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠰⣄⣘⡦⠄⠴⢉⡲⠤⠤⠾⡵⠦⠤⠾⠽⢶⣞⠑⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⡦⢤⡀⠀⠀⢣⠉⠀⠖⠊⠀⠠⠆⠀⠀⠀⠀⠀⠶⠀⠀⠈⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠣⠬⠷⣄⢀⡸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠂⠁⠐⠒⠈⠀⠀⠀⠉⠉⠀⠐⠊⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⣰⠚⢻⣍⡇⠀⠀⠀⠀⠀⢀⡞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠁⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣀⡤⠖⣉⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣠⠞⢯⠀⠀⠀⣰⣀⣀⡤⠚⠉⠉⠙⣓⣒⣒⣒⡒⢎⢉⡉⢀⣀⣠⠟⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠈⠙⠛⠋⠁⢨⡏⣴⢋⠭⠛⠉⠁⢀⣈⠷⠝⠂⢻⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣈⣀⣀⡤⠔⠚⠉⠓⢦⣤⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠇⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣉⣹⠟⠛⠙⣏⣉⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⠀⠀⠈⢧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣸⠃⠀⠀⠀⠀⠸⣆⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⡸⠛⠁⠁⠈⠛⠈⠋⠘⠉⠶⠒⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠇⠈⠀⠉⠀⢀⣀⣠⠤⠤⣄⣀⡀⠀⠀⠀⢨⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡉⠀⠀⢀⡠⠖⢋⣁⡤⠴⠶⠶⠦⢤⣌⡙⠲⢄⡀⠀⠉⠉⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠄⠁⢀⡴⠋⡠⠞⢉⣠⠴⠖⠒⠒⠒⠦⢤⣉⠳⢄⠙⢦⡀⠀⠀⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠓⠀⢀⠞⢠⠎⢀⡴⠋⡤⠖⠒⢤⡀⠀⢀⠀⠈⠳⣄⠱⡄⠳⡀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⢀⡎⢠⠇⢠⠏⠀⢸⠀⠀⠀⠀⢳⠀⠀⠀⠐⠂⠈⢦⠘⡄⢱⡀⠀⠀⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠁⠀⢸⠀⡟⠀⡏⠀⣀⠘⢦⣀⣀⡠⠋⠀⠀⠂⠀⠀⠀⠈⡆⢻⠀⡇⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⢸⠀⡇⠀⡇⠀⠀⡀⠀⠀⢀⡀⠀⠘⠀⢀⠀⠈⠁⠀⡇⢸⠀⡇⠀⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⢸⡀⢷⠀⢳⠀⠘⠀⢀⡀⠀⠀⡀⠀⠀⠀⠁⠀⢀⡰⠃⡾⢀⡇⠀⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡖⠀⠀⢧⠘⣆⠈⢧⡀⠀⢀⠀⠀⠀⢁⡤⠖⣚⡍⠉⡉⠀⣰⠃⡼⠀⠀⠠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⢧⡈⢦⡀⠑⢤⡈⠀⡀⢐⡭⠚⠉⣀⡤⠊⢀⡴⢁⡼⠁⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠑⢄⡙⠢⣄⡉⠉⠁⠘⠒⠒⠉⢁⣠⠔⢋⡠⠊⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⠆⠀⠀⠙⠲⢤⣉⡙⠒⠒⠒⠒⢋⣉⡤⠖⠋⠀⠀⢤⣐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣰⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣄⣠⣀⣦⣀⣄⢀⣤⣠⠦⠞⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡙⢦⠯⠟⡠⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢸⡼⠧⠤⠄⠂⣆⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢰⣄⠀⠘⠒⠣⠴⣧⡴⠷⣦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡀⢈⣀⣀⣀⠀⠀⠀⠛⠁
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠘⡉⠩⠗⡆⠀⠀⡸⠛⠚⠣⡴⠀⠀⠀⠀⠰⢯⣬⡷⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠸⣤⣈⡁⠀⠀⠋⡿⢃⡤⠁⠀⠀⠀⠀⠆⢹⣻⡆⠦⠀⠀⠀⠀⠀⠀⢱⣤⡄⠀⠀⠀⢀⠀⠰
⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠉⠓⠒⠄⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⣤⣛⠀⠀⠀⠀⠀⠀⠛⠂
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⣠⣔⣲⡇⠀⠀⢀⡂⠀⠀⠀⠀⠖⠁⠁
⡷⠉⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⢶⣰⣤⡀⠀⠀⠸⢿⡽⠻⠄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢦⡙⠾⢷⡷⡽⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠭⣄⣾⠯⠐⠀⡀⢷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠠
⡄⡨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠶⣄⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠰⠗⠄⢀⣤⡺⡄⠀⠀⠈⣧⠀⠀⠀⢠⠀⡀
⢦⣤⣠⠆⠀⠀⠀⠀⠀⠀⠀⣟⠳⣶⢶⣆⠀⠀⠀⢰⣶⣾⢿⠿⠂⠀⠀⠀⠀⠀⠰⠂⠀⠱⡤⠀⠀⣴⡇⠀⠀⠀⠀⣆⠙⢏
⠀⣀⣤⠤⠒⠋⠀⠀⠀⠀⠀⠙⠳⠿⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⡀⣤⡴⠟⠁⠀⠀⠀⠀⠘⠀⠴⠖
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡡⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠐⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⡡⠎⡱⢎⡱⢆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠌⠡⢞⣹⡃⣱⠎⣡⡶⡀⠀⠀⢠⠀⠀⠀⠀⣠⢖⣶⡶⢶⣄
⠤⢤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠱⢎⡹⠟⣹⣾⣷⣿⡇⠀⢠⣾⠀⠀⠀⠠⠿⣾⣻⣿⣿⣽⠇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣽⣦⣌⣩⣾⡿⣯⣿⡤⠄⠀⠈⢸⠀⠀⠀⢠⣲⣈⠉⠙⠻⣬⠀⠰
⠀⠀⠾⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⠎⣹⠿⠋⠀⠀⠀⢀⣦⣀⠀⠀⠀⠈⠙⠿⠛⠙⠇⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠴⠼⣣⠿⠗⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣿⣭⣯⡥⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣤⠐⢌
⠁⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀⢫⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣿⣄⠀⠀⠀⡄⠐⠒⢣⡌⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⢁⣀⠀⠀⠐⢄⠀⠀⠀⠀⠐⢿⣿⣿⡻⠃⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠾⠿⣯⠋⣉⡙⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠈⢢⠱⠀⠄⠀⠀⠰⠶

⣟⣿⣿⢻⡏⡟⢛⣻⠛⣿⣿⣿⣿⣿⣏⣿⣿⢿⣻⣿⡿⣏⣿⢻⠛⢻⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠾⠽⠾⠯⠷⠿⠽⠶⠶⠾⠷⠽⠦⠷⠿⠿⠿⠷⠿⠧⠿⠷⠾⠶⠾⠾⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠿⠶⠶⠶⠿⠷⠷⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠋⠉⡤⠉⠉⠂⡄⠉⠉⠻⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠃⠀⠈⠂⠙⠀⠀⠀⠀⠀⠀⢹⣿
⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⠀⠀⡀⠀⠒⠂⠀⠐⠀⡀⠀⢸⣿
⡛⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⡟⠙⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⢹
⢈⠀⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣼⠃⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⢱
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠂⠂⠂⠂⠀⠂⠀⠀⠀⠀⠈⡇⢸⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈



⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡛⠋⠀⠙⡇⢀⣀⣀⣀⡀⡤⡤⠤⢤⠤⠤⠤⠤⢤⡤⠁⠉
⣾⣓⡠⢀⡚⣧⣆⣀⣀⣇⣀⣠⣤⣤⣼⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⢟⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠒⠶⣶⠟⠁⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣠⣤⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⠿⠿⠋
⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠀⠀⢡⡸⠠⠄⠁
⠀⠀⠀⠀⠀⡠⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠂⡀⡂⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠓⠋⠀⠀⠸⠗⠆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⣀⢀⠁⣠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⢀⢠⡤⠒⠉⠀⠀⠀⠀⠐⠄⠤⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡆⢀⠄
⠀⠀⠀⠀⠸⠀⠠⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⡄⢀⠀⡆⠀⠀⠀⠀⠀⢨⠈⡟⣀⣤⠛⣀⠸
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠈⠂⠀⠁⠉
⠀⠀⣠⢄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢒⠧⠏⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠄⣀⠀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣙⠛⣁⡴⠞⡁
⠀⠀⠀⠀⠀⣀⠤⠛⠁⠀⠀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⢁⣠⠔⠂⠀⠀⢄⠀⠀⠢⠀⠀⣥⢈⣥⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠢⢠⢈⠀⠀⠀⠀⠀⡰⠉⠂⠀⠉⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⢀⣼⡏⢛⠛⣻⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⢰⣿⣿⣿⡄⠀⣿⣿⠷⠿⢶⣿⡆⢠⣾⣿⠟⠛⠻⣿⣧⠀⠀⠀⠀⣠⣶⠶⣄⠐⠀⢰⣿⣿⣿⣿⣿⣇⡙⠿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⢁⡀⠀⣘⣿⣿⣿⠗⠀⢻⢃⡀⢀⣀⢿⠇⢸⢻⡅⣀⠀⣀⠈⠏⠇⠀⠀⠀⢠⡄⢠⠌⠀⠀⢸⣿⣿⢟⡿⠻⡿⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠻⠈⠁⠀⠉⠸⠛⠛⠁⠀⠈⠀⠁⠀⠁⠈⠀⠀⠠⣦⡉⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠈⠁⠈⠁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠠⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠰⡆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠀⢤⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⢃⢀⠀⢀⡀⡈⠀⢠⡀⡀⠀⠀⠀⠇⠤⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠤⠀⠠
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡀⠰⠂⢀⡀⠀⠈⠈⠡⡀⠀⠀⠀⠈⠁⣤⡤⢤⡔⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠀⠤⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠊⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠠⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⠁⠀⠀⠁⠀⠀⠒⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣴⣾⣾⣿⣿⣿⣷⣠⣶⣿⠿⠿⠿⣦⠀⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⠀⣴⣷⡆⠀⣶⣆⢠⣶⣾⣿⣶⣦⡀⠀⣠⣴⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣤⣤⠀⠁⠙⣿⣿⢀⣠⣾⡿⠀⢈⣿⡏⠀⢈⣿⣿⣤⡀⠀⢰⣿⣿⣧⠀⣿⣿⠀⢻⣿⠇⠀⠉⣿⢸⣿⡟⠉⠸⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⡟⠛⠛⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⢸⣿⡇⠀⠘⣿⡟⠛⠃⠀⢸⣿⢻⣿⠀⣿⡟⠀⢸⣿⠀⢀⣴⡿⠈⠻⠿⠿⣿⣮⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣿⡿⢿⣿⣶⣶⢦⣾⣿⣷⡄⢠⣿⣷⣶⣦⡄⣿⣿⠘⣿⣿⣿⠇⢴⣾⣿⣶⣿⠟⠁⠘⣷⣤⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠀⠘⠋⠉⠉⠉⠁⠈⠉⠀⠈⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⡽⠩⣻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣗⡦⢠⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠙⠟⠙⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣾⣿⡆⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢇⣴⣦⡸⠦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣀⣨⣿⣀⣠⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠐⠀⠀⢰⡷⢸⣿⣿⣿⡁⣠⡾
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢄⣢⣠⣴⣿⣿⣿⣿⣿⣿⣿⣦⣌⣁⠂
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣯⣉⣉⣿⣿⣿⣿⠿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠛⠛⠛⠛⠻⡟⠛⠉⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠈⠻⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢀⡀⠀⠉⠀⠀⠀⠀⠔⠋⠀⠈⠁⠁⠈⠒⠄⠀⠀⠀⠐⢂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠄⠉⠥⠠⠐⠀⠰⠄⢀⡢⠀⠀⠗⢠⠀⠀⠈⠤⡈⡀⠒⡀⠑⠙⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⡃⠰⣢⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠤⡀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡾⡇⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠃⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠂⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⡜⠿⠃⠀⠀⠀⠀⠀⠸⠿⠁⡈⠃⠀⢀⠄
⠀⠀⠀⣾⣰⠘⠀⠀⠀⠣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⡤⢾⠇⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢹⣼⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠘⣂⠈⠀⠠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠔⣿⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠄⠀⠀⠀⢀⠠⠦⡉⠀⠀⠈⢉⠤⠀⠀⠀⠀⠀⠀⡈⠐⠁
⠀⠀⠀⠀⠀⠀⡂⠇⢀⢄⡀⠃⠇⠀⠀⠀⠀⠀⠊⠆⠒⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠄⠠⣁⡜⡶⢀⣁⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠃⠀⠅⠀⠈⠙⠀⠀⠀⡆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠴⢯⠵⢮⠦⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡑⠀⠀⠨⠂⠂⠀⠠⠀⡀⠀⠀⣠⠀⠀⡀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⡄⢠⣤⣤⣠⣤⣄⣤⣤⣀⢀⣤⣄⠀⣤⡀⣄⣤⣤⣄⣤⣤⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⣿⡇⢸⣿⡯⢸⣿⡍⣿⣟⡿⢾⡟⢻⡇⢻⣿⠃⣿⣿⠹⣿⣿⡿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠛⠊⠛⠓⠘⠛⠃⠙⠋⠀⠈⠛⠛⠀⠈⠋⠀⠛⠛⠂⠛⠙⠃⠘⠃

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡘⠋⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢶⠀⠤⢑⢀⠀⠀⠀⠄⡀⠀⠀⠀⢀⣤⡤⠄⠀⢀⣀⡀⠻⠀⠰⠾⠄⡄⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠂⠐⠀⠀⡀⣈⠲⠃⠀⠀⣀⠄⠉⠀⠈⠁⣀⠉⠃⢦⠀⢀⣤⡟⠀⣤⠂⠙⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⢀⠀⢖⠀⠉⠉⠀⢄⠉⡰⡥⢬⠂⠄⣀⢲⣄⣀⣄⠀⠠⣴⠊⠀⠀⡠⠔⣤⣀⢰⡔⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⢀⣨⠁⠠⠐⠀⠀⢀⠝⠄⠻⣿⠗⠎⠀⢩⡟⠿⠛⠓⠀⠀⠀⠀⠈⠁⠀⠀⣿⣇⠙⠂⡦
⠀⠀⠀⠀⠀⠀⠀⢰⡵⣥⡟⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⢨⣿⠴⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠹⣏⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠹⠈⠰⠴⢂⠰⢤⠀⠀⠠⢂⡴⠞⠦⠄⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠹⣶⠉⢧
⠀⠀⠀⠀⠀⠀⡘⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠈⡄
⠀⠀⠀⠀⠀⢰⠇⠀⠄⠀⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣧⠤⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⢀⡆⢈⠁⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⢨⠉⠐⠄⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢰⢀⠃⠀⠀⠄⠒⢛⡞⢉⣥⣆⣈⡉⠑⠒⠤⠶⣀⣄⣤⡤⠖⠚⠋⠉⡀⢤⣬⣍⠳⣎⠀⠂⠀⠠⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢻⢹⢀⠀⠀⠀⠀⢺⡼⠁⠀⠁⠀⠉⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠊⠀⠁⠘⢤⠗⠠⠀⠀⠀⠀⠀⠀⠀⢀⢋
⠀⠀⠀⠰⠆⠞⠑⠄⠀⠀⠈⠩⢄⣀⠐⡄⠀⠠⢊⣹⣢⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠂⢰⠐⠅⠀⠀⠀⠀⠀⠈⠣⢼
⠀⠀⠀⢠⡄⡃⠀⠀⢰⡂⠂⢻⡶⡦⢁⡀⠀⡐⠊⠈⣿⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⡀⠀⠀⢀⢎
⠀⠀⠀⠸⣗⢅⡤⠀⠀⠀⠀⠡⢁⡇⠀⠙⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌
⠀⠀⠀⠈⠁⠆⠀⠡⠀⠈⠓⠁⠀⠲⠀⠀⡤⢲⣞⡓⠻⣧⠀⠀⠀⠀⢀⣿⠛⠤⠀⡀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠻⡀⠀⠳⣀⠀⣱⠄⠠⠂⠀⠀⣀⣻⡇⢀⠈⠻⢷⣄⢀⣴⣿⠏⠀⠠⣤⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⣀⡖
⠀⠀⠀⠀⢰⣅⠀⠀⠀⠀⠀⠘⠁⠉⠒⠉⠀⠛⠆⡀⠀⠀⡀⠈⢻⠈⡀⠁⠀⠤⠃⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⡆⠀⠀⠀⠐⠒⠢⣄⡀⠈⣀⣠⣿⡷⠀⣀⠀⡀⠀⠀⠁⠁⠰⣶⠒⠠⠤⢤⠤⠤⣤⣀⣸⡿⠇
⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠈⣤⠀⢀⠀⠐⠀⠐⠟⠠⢀⠀⠈⡀⠀⠌⠒⠁⠀⠀⠤⠀⠄⠀⠀⠀⡻⣀⠀⠀⠀⠈⠛⣶⠄
⠀⠀⠀⠀⠀⠘⣧⠆⠀⠀⢠⠀⠀⣨⢷⡄⠀⠈⠠⠄⠈⠁⡤⢈⣾⡿⢀⣀⡀⠀⠁⠀⢶⡈⠀⠐⢀⠀⢈⠁⠀⠄⡠⠅⣠
⠀⠀⠀⠀⠀⠀⠓⠀⠈⠁⠀⠀⠈⠂⠀⠐⡴⢄⠂⠀⠀⠰⠠⡌⠀⠀⠀⠴⢇⠀⠀⠀⠈⢃⠀⠀⠂⡀⡀⠄⠐⠀⠏⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠀⡴⠀⢣⡀⠀⠀⠀⠤⠄⡠⠄⠊⠀⠀⡤⠤⠂⠀⠁⠁⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⡴⠋⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⣀⣀
⠀⠀⡇⠀⠀⠀⠀⡷⠚⠉⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣄
⠀⠀⠘⠢⠤⠤⢾⠁⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠉⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠢⣄⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠈⢑⡆⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⡰⠋⠀⠀⡠⠋⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣴⣿⣿⡿⣫⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡀⢀⡿⡞⠁⠀⢠⢞⡁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⣿⣿⣿⠟⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡇⠀⠀⡇⠀⣇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠘⢆⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠈⢧⡀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢳⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠃⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⣀⣼⠉⠉⠉⠉⠉⠉⠉⢡⠻⡉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠇⠀⠀⠀⠀⠀⠀⠀⠀⡎⢳⢸⠀⠀⠀⠀⠀⠀⠧⣄⠀⠀⠀⠀⠀⠀⠀⢸⣀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⣸⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠀⠀⠀⣴⠃
⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠁⢀
⠛⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢂⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢐⡄⠀⠘⠿⠿⢾⡵⠿⠿⠃⠀⠠⡂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢀⣀⡀⢀⡀⢀⢀⡀⣀⣀⢀⡀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⢸⣧⠟⢸⠤⠀⣼⣇⢸⣿⠀⣿⠄⢸⣷⠘⢧⡅⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠙⠋⠃⠘⠒⠂⠋⠛⠘⠙⠂⠛⠀⠛⠙⠈⠒⠃⠀⠃
⣄⣀⣀⣤⣄
⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠋⠁⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠛⠀⠀⢈⣀⣤⣴⣶⣤⣀⣤⣦⣄⣀⣠⣔⣂⠀⠀⠟⠏⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣦⣄⡀
⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠘⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠹⣿⣿⣷
⡟⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⣤⠶⠃⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢀⠀⠄⠁⠃⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢈⡟⠘⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⢿⣷⡄
⠀⠀⠀⠀⢠⡿⠻⠿⠿⠿⠿⠛⠙⢧⠀⠀⠀⠀⠀⢠⣽⣿⡿⣿⣷⣄⢸⡇⠀⠀⠀⢀⣀⣤⡬⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⣿⣿⣽⣿⡇
⠀⠀⠀⠀⣾⠀⠀⠀⡀⠀⣀⠀⠀⠸⡇⠀⠀⢸⣿⠛⠛⠛⣣⣬⣿⣿⢾⡇⠀⠀⠀⣿⣼⣛⣛⣛⣛⣧⣽⣄⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠸⡀⠈⠉⢀⣤⠈⠉⠀⣸⠁⠀⠀⢸⡏⠀⠀⣰⡟⠰⠾⣿⠾⠇⠀⠀⠀⢷⢻⣿⣿⣿⣿⣿⣿⣀⡗⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠙⢦⣀⣈⢉⣀⣠⠞⠁⠀⠀⠀⢸⡇⠀⠀⡿⠁⢀⡖⠉⢢⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢢⣶⣦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠋⠙⠓⣦⠀⠀⠀⠀⠀⠀⠀⢩⣼⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⢰⡏⠠⢤⡄⠀⠀⢀⠈⠙⣦⠀⠀⠀⠀⢀⣿⢻⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⣖⡆
⠀⠀⠀⢸⡀⠀⢀⡴⣿⣿⡷⣄⠀⠀⠀⠀⠀⣼⠁⢀⣞⡀⣲⢆⣽⡁⠀⣷⠀⠀⠀⠀⠸⠃⢸⡿⣿⡀⠻⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣛⡇
⠀⠀⠀⢸⣤⣤⣼⣥⣿⢿⣧⣽⣤⣤⣰⠀⠀⠹⢦⣄⡀⠀⠛⠂⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⣿⡇⢻⡇⠀⠀⠀⠀⠀⢠⡄⣠⠠⡤⢀⣠⠄⣠⢠⢠⠄
⠀⠀⠀⢸⠛⠛⠛⠹⣟⢛⡿⠛⠛⠛⢻⠀⠀⣀⠾⠆⠙⠶⠞⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⡇⠀⠀⠀⠀⠀⠘⠀⠋⠃⠃⠈⠙⠋⠙⠊⠘⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠈⢻⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠭⠉⣿⣿⡆
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠶⣶⣦⡀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠉⠀⠀⠀⠀⠀⡀⠀⠀⢛⡟⣀⡀⢤⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣯⢉⣗⣺⣼⣿⡏⣹⠆⠀⠀⠀⠀⠀⠈⢸⡟⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠒⣼⡃⠺⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣧⣬⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⠀⠹⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣤⣬⣭⣭⣭⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢿⠀⠀⠀⠀⠀⠀⡯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⢦⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡁⠄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣄⠀⣸⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠂⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠻⣿⣷⣄⠀⠀⠀⠀⠀⢸⢿⣿⣿⡿⣇
⠀⠀⠀⠀⢠⣤⠼⠿⠿⣉⣻⣿⣧⣼⡇⠀⠀⠀⠀⠀⠈⢿⣩⣽⠟⠀⠀⠀⠀⠀⣾⡿⠿⠟⠛⢉⠀⠀⠀⠙⣿⡆⠀⠀⠀⢠⡿⢸⣿⣿⡇⢻⡄
⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⢛⣿⣯⣽⡇⠀⠀⠀⠀⣠⣶⣶⣾⣿⣷⣦⡀⠀⠀⢰⣿⡇⠀⠤⠖⢀⠐⠦⠄⠀⣿⣿⠀⠀⠀⠀⠀⢸⡏⢹⣇
⠀⠀⠀⠀⣼⠃⠀⢀⣿⠁⠀⡨⠧⡀⠀⠀⠀⠀⣰⡿⢹⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣄⠀⠀⠻⠃⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⢸⡇⢸⡿
⠀⠀⠀⠀⠛⠖⠀⠈⠁⠀⠘⠀⠀⠘⠀⠀⠀⠀⠛⠃⠘⠛⠛⠛⠓⠙⠋⠀⠀⠀⠉⠉⠉⠙⠒⠲⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠃⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠁⠀⢸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⠛⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⣠⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠐⠂⠡⣴⠂⠀⢀⠀⠠⠀⠀⡁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠊⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⣀⠤⠀⠄
⠀⠀⠀⠀⢓⠄⠉⠄⠈⠳⠄⠀⠀⠀⠀⠈⠓⡦⠀⠂⠀⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠐⠂⡤⣄⣠⡇⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠑⠐⠉⣩⣇⠀⠠⠄⠐⣀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠬⠍⠀⠒⢺⣇⣈⡡⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⠤⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣄⣐⣚⣉⣁⠀⠖⠂⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠐⠒⠒⠛⠛⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠔⠄⠀⠀⠀⠀⠀⡆⠀⠀⠠⡀⠀⠀⠀⣇⡷⢀⢀⠀⠀⠀⡀⡀⣿⠀⢰⡏⠀⢀⠀⠀⡀⣯
⠀⠀⠀⠀⠀⡠⠥⡀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢀⡄⠀⠀⠀⡏⢱⢸⠈⢹⠖⠃⡅⡇⣿⣆⢸⡇⢨⢸⡇⠳⡄⣇⠀⠀⠀⠀⠀⣦⠀⠀⠉⠀⡀⠈
⠀⠀⠀⠀⠀⠀⢄⠀⢂⠀⢀⡆⠀⠤⠘⠀⠀⠁⠀⠀⠀⠈⠉⠁⠈⠀⠀⠁⠀⠀⠁⠉⠈⠀⠁⠀⠈⠁⠀⠀⠈⠀⠁⠀⠀⠀⣽⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠈⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣬⢄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠉
⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠂⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⣦⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠉⠳⠄⠀⠀⠀⠄⠸⡄⠀⠈⠛⠈⠀⢀⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⢤⣀⣀⣤⡴⠿⠓⠀⠖⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠔⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⠀⣀⣀⣀⣀⡀⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠖⠂⠀⠉⡉⢀⡇⣄⠀⠈⠉⠀⠀⠀⠀⠀⡠⠀⢢⣼⠖⠒⡂⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⢰⠏⢀⠜⠁⢠⣶⣽⡟⢱⡖⣿⢻⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠥⠟⠚⠚⣰⠋⣙⢤⣀⡀⢄
⠀⠀⠻⣿⡦⠄⠚⠆⠛⠃⠴⠿⡧⠔⠋⡙⢫⠴⠧⠄⣆⣀⣰⠇⠀⠀⠀⠀⢱⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠚⠛⠋⠸⠔⠒⠓⢒⠊
⠀⠀⠀⠈⠂⠀⠀⠂⠀⢈⡛⠷⣶⡿⠶⠶⠶⠾⠷⠟⠛⠉⢁⡀⠄⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢠⡂⠀⠀⠀⠀⠀⠀⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢍⡛⢛⠒⠢⢤⣤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠈⢠⣀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠶⠖⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣩⣴⣶⣶⣿⣷⣶⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠿⠿⠿⠟⠋⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⢠⡞⠙⣇⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⢠⡆⠀⠀⡄⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠰⣄⠐⣦⣀⡰⠋⢢⣤⣤⣞⣱⠤⠤⠼⠱⣦⣴⠓⢲⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣂⣀⠀⠀⠀⢣⠉⠁⡦⠂⠁⢠⡄⠀⠀⠀⠀⠀⠤⠀⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⠧⣐⣳⡄⠀⣸⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠜⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠉⠂⠐⠂⠐⠂⠁⠀⠈⠀⠀⠀⠤⠚⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠻⣙⡦⠀⠀⠀⠀⠀⢀⡼⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⠖⠁⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣀⡤⠖⣋⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⡴⣯⠀⠀⠀⣠⣠⠎⠑⠲⢤⣀⣒⣒⣒⡖⠒⠒⠒⢋⠉⠁⢀⣠⠞⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠈⠓⠒⠚⢡⠇⠀⠀⠀⠀⢀⣀⠈⠉⣟⠒⠒⠒⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠂⡖⠋⠉⠉⡇⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠹⡀⠀⠀⢱⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢱⡀⠀⠘⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠳⡀⠀⢱⣀⠓⠲⣄⠀⣠⣄⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⠄⠒⠚⠙⠦⠤⠬⠯⠭⣭⣩⠃⡿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠮⠤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉