DoRa LoL Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠛⠛⠛⠛⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠘⠋⠉⠙⠓⠲⢦⣀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⣷⣤⣤⡄⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠙⠳⢦⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣠⠖⠋⠁⢀⣀⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠉⠛⢭⡉⠉⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢋⡠⣴⠾⡉⠉⠉⣩⣍⠛⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣿⠗⠉⠀⢾⣠⠋⠀⠀⠓⠠⠧⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⣿⠳⢦⣀⡀⠀⢸⣏⠀⠀⠀⠀⠈⠁⠄⠀⣤⠐⢀⠀⣾⠁⠀⠀⠀⠀⠀⢀⠔⠙⣄⣀⣀⣀⣀⡸⠉⠰⣿⡈⠙⠛⠶⠶⠶⠶⠶⠟⠛⠉
⠀⠀⠀⠀⢻⡄⠀⠉⠙⠓⠶⠿⣧⠀⠀⠀⠀⠎⠀⣀⠸⠀⣀⡆⣿⣀⡀⠤⠤⠒⢲⠃⠀⠀⣸⠄⠀⠀⠘⠃⠤⢀⡈⣟⠛⠳⣶⡄
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢰⣾⣿⢸⣿⠃⡟⠁⠀⠀⠀⠀⡇⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠤⠒⢹⡇
⠀⠀⠀⢀⣴⠟⢻⣦⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⠤⠤⠒⢊⣉⡁⠀⠀⠀⠈⣷
⠀⠀⣠⡟⢁⠔⠁⠀⠙⣦⣄⠀⠀⢸⡇⠀⠀⠈⠓⢶⣒⢲⡒⠀⡿⠉⠉⠉⠀⠈⠁⠉⠉⢉⣴⣇⡒⢦⡀⢰⣿⣷⡆⠑⢄⠀⠀⢿⡄
⠀⣰⡏⢀⠎⠀⠀⢠⡾⠋⠉⠳⣦⡈⣿⡤⠖⠒⢤⡤⠤⢍⣉⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠙⠟⣿⣿⠏⠀⠈⡆⠀⠸⣧
⢠⡿⠀⠈⠀⠀⠀⣸⡁⠀⠀⠈⢻⡏⠉⢧⠀⠀⢸⡄⠀⠀⠀⠉⡇⠐⡀⠀⠀⠀⠀⠀⢰⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⡄
⠘⠻⠶⣦⠀⢠⡿⠛⠀⠀⠀⠀⠀⣿⡀⠘⡀⠀⢸⠁⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠀⠀⠈⣷
⠀⠀⠀⢿⡄⠀⠻⣤⣀⠀⠀⠀⠀⢸⡇⠀⠁⠀⡸⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡼⠑⢄⠀⢀⡠⠃⠀⠀⠀⢹⡇
⠀⠀⠀⠈⠻⣦⡀⠀⠉⠻⣄⠀⢀⡾⠁⠀⠀⢀⠇⠀⠀⠀⠀⡈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⠜⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢹⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢘⣷⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⠀⠀⠀⠀⢲⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠎⠀⠀⠀⠀⠀⢸⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⡽⠋⠉⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠈⢻⡶⣄⣀⡀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢘⣃⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠠⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠂⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠄⠀⠀⠈⠆⣁⠔⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⠲⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠈⢢⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢂⠀⡀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⣐⢀⡀⠀⠰⢂⠄⠀⠀⠀⠀⢀⠀⣗⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡬⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠠⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠈⠉⠒⠤⢄⡀⠀⠀⠀⢸⠐⠀⠉⠀⠀⠁⠀⠀⠀⠈⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠒⠚⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⣄⠀⠀⡃⠀⠀⠀⠀⠀⠈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⢀⠀⠀⠈⠳⡀⠐⠠⢀⡀⠀⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠀⠀⠸⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠇⠉⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⡀⠀⠀⣠⠞⠁⠙⢦⠤⠊
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡤⠀⠀⠀⠠⠌⠡⠁⠀⠀⠀⠀⠀⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠺⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢱⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠢⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣤⠀⠀⠀⠀⡀⣰⡀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣨⠁⠀⠁⠂⠐⠀⢐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡎⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⢀⡀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠓⠘⠞⠓⠚⠚⠛⠘⠙⠛⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠛⠐⠓⠻⠚⠃⠓

⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒
⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠛⠿⠋⠁⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⣄⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢀⣀⡔⣆⡀
⠀⠀⠀⠀⢠⠏⠀⢸⠂⠈⢉⠢⡀⠀⠀⠀⠀⣤⠑⠀⠈⠂⠀⠀⠠⡀⣸⡆⠀⠀⠀⠀⠠⠘⠎⢧⢬⣀⣀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡤⠞⠁⠀⠀⠀⠀⠀⡔⠉⠀⠐⠀⡈⠁⠀⢡⠀⢘⠶⠒⢋⣹
⠀⠀⠀⠀⠛⠦⢄⡂⠀⠀⠀⠀⠀⠀⠐⢂⠘⠀⢀⣠⠤⢶⡋⠁⠀⠀⠀⠀⡀⠀⢠⠘⣏⣠⡀⠰⠗⠀⠀⢲⠉⣀⣦⠤⠄⠚⠉⢀⡀⠤⠤⢀
⠀⠠⠀⠀⠀⠀⠀⠉⠙⠒⠒⣲⡄⣤⠤⢄⡔⠀⠀⠈⠁⠒⢣⣄⠀⠂⠀⠀⠀⠀⠐⢌⠈⠈⠀⢀⠀⢀⠀⡠⠔⡡⠊⠀⠀⢀⠔⣡⠔⠈⠑⢤⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠣⡀⠀⠀⠀⠀⠈⠢⢄⣀⢀⡐⠀⠀⡔⠊⠁⠀⠀⠠⢂⠼⠁⢄⠢⠤⠜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⠤⢤⠀⠈⠙⠶⠐⢦⠐⠒⣉⠤⠚⡀⠀⠀⠈⢆⣀⠄⠚⠓⡃⠀⢀⡀⠑⠒⠈⠁
⠀⠀⠀⠐⠒⠀⡠⠻⣀⣀⠼⢻⠀⠀⠀⠀⠀⢠⠄⡤⢙⢁⡇⢀⡀⠳⠶⢤⠾⠓⠁⠀⠀⠀⠀⠀⠣⣀⣠⣤⣈⣡⠀⣀⠀⠘⡤⠀⠐⠂
⠀⠀⠀⠀⡠⢺⣥⣔⣼⢧⠀⠘⢶⠆⠐⠂⠀⠀⠄⠀⠀⡏⠀⠁⡀⢀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠜⠓⢎⠁⠀⠀⠀⠀⠉⠂⠖⠁⢠⠤⠀⣀
⠀⠀⢀⣾⠑⢷⣲⣤⣌⡅⡀⠉⠈⢧⠀⣰⡀⠐⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘
⣀⠤⠈⣎⠲⣤⢟⡒⢻⢠⡇⠀⢀⡜⠓⠁⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣧⠞⡠⠒⠒⠂⠀⠤⠀⣠⣞⠁⠀⠊⢀⠤⠰⠄
⠀⠀⢀⡏⣉⢒⠣⠿⡵⠈⠁⠀⠈⠳⠶⠬⣭⡶⠞⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠢⡀
⠀⠀⢋⣙⡎⣄⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠱⠴⠣⠇⣶⠐⣤⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠶⠐⠉⠙⠤⣀⠀⠐⠀⠌⢀⡈⠙⠀⠀⠀⠀⠀⠃⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣩⡤⠶⠲⠖⠛⠛⠉⠉⠉⠉⠙⠋⠙⠛⠒⠶⣤⣀⠀⠀⠉⠒⢠⣄⡀⠀⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⢰⠁⠌⠁⠒⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢀⡀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠁⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠁⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⡀⡀⢀⡀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠁⠀⠈⠈⠁⠀⠈⠙⢦⣄⠠⠀⠠⢀⣄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠦⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠃⠉⠀⠀⠀⢠⠲⠀⠊⠂⠑⠠⢀⠠⠈⢀⠀⡈⠀⠰⠀⠀⠀⠀⠀⠄⡀⢢⠀⠊⠑⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠁⠀⠀⠀⠀⣙⡒⠤⡀⠀⠀⠀⢀⠀⢀⣁⣀⡀⠀⠀⠀⢀⣀⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠃⠀⣠⠔⠉⠁⠀⠈⠈⠙⠓⠤⠀⠀⠀⠀⠀⠉⠻⠀⡴⠞⠁⠀⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠃⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⢇⠀⠀⠀⠘⢄⡀⠀⢀⣀⠤⠔⢢⠶⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣄⡀
⠄⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠂⠀⠁⠂⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⠈⠉⠀⠀⠀⡰⠃⠀⠀⠂⠀⣀⣀⡀⠀⠚⠁⠀⠈⠻⡗⠤⣀⠀⠀⢀
⠤⡄⠀⢀⠀⠈⠀⠠⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢠⠋⢹⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠉⠉⠁
⢀⡸⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⣸⠦⣤⠜⠦⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠰⢤⠀⠀⠀⠀⠀⠀⠀⠸
⠋⠀⠀⣠⢦⠀⢠⡀⣠⣄⢀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⢠⠃⠀⠉⠁⠉⠁⠀⠈⠀⠀⠀⠀⠀⣠⠤⠒⠂⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠲⠀⠀⠀⢶⠒⠋
⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠈⠢⠤⠀⠤⠊⠀⠀⠀⢀⠀⠀⠀⢈⡆
⠀⢸⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⢣
⠀⢸⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⡰⢊⣤⠙⠦⠀⠀⠈⠳⡤⠚⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⡤⢂⡀⣤⠀⠀⢀
⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠑⠀⠈⠅⢈⠇⠀⠀⠀⠀⠀⢀⣀⠸⠁⠀⠀⠓⠉⢀⣂⠄⠊⡝
⠀⢸⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠂⠀⠾⠋⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠖⠀⠀⠀⢶⠒⠤⡅⠉⠀⠀⠀⣀⠀⠈⠀⢀⡜⣀
⠀⢸⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢠⠒⠁⠀⠀⠀⠀⠰⠲⠇⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠞⠉⢀
⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢰⠂⠧⠀⡀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢈⠠⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠤⠄⠐⠂⠂
⠀⠀⠇⠀⠈⠛⠒⠦⠤⠤⠄⢠⡤⢤⡂⠀⠠⡀⠐⠆⠘⠈⠂⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣍⠉⠀⡀⠀⠤⠀⠂⠈⠀⠀⢀⡀
⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠀⠀⠀⠀⠀⢀⡠⠖⠈⠃⠉⠑⠊⠹⢦
⠀⢀⠀⢇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⡠⠤⣤⡀⣀⣀⡤⠒⠙⠁
⠒⠀⠀⢀⡤⠤⠤⣾⡀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⢀⡔⠚⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⢰⠋⠀⠀⠛⠻⡴⠊⢳⠀⠀⢃⠀⠠⠄⠀⠀⠀⠀⠀⠉⢸⠁⠀⣔⠉⡁⠄⠂
⠀⠀⠀⢀⡞⣀⣠⣄⢰⠁⠀⠈⠓⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡴⠏⡀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⣃⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⠀⢠⡴⣶⠒⠂⢸⠁⠀⠘⠒⠒⠒⠺⣀⣀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠠⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⠀⠀⠀⢠⠇⠀⠀⠰⣅⠷⡀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠈⠀⠈⢑⠈⠀⠀⢀⢰⠒⠲⡄⠀⠀⠀⠀⠿⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢰⠋⣗⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠘⢤⡀⠸⠃⠀⠐⠗⡰⠁
⠀⠀⠀⣠⢀⣄⡀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠉⠀⢸⠀⡅⠀⠈⠀⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⣀⡀⠤⠚⠁⠑⠒⠠⠤⠤⠤⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠉⠀⠈⢉⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣠⣀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⣠⠠⡀⠀⢠⠖⠉⠢⡀⠀⠛⠉⠀⠈⠙⠃⠀⠀⣀⣤⡤⠴⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⠣
⠀⠀⠀⢀⡀⠼⠀⢀⠜⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠑⢄⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⢀⡠
⠀⠀⠀⡃⠀⠀⠀⠀⢦⣀⠀⠀⠀⡘⠀⠀⠀⠀⣠⠞⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠋⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠉⠒⠤⠤⠔⠊⠀⠉⠉⠉⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡐⠀⡠⠤⡀⠀⠐⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⡐⠈⠲⡀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⠴⡀⢊⣁⠀⠈⡄⠀⠀⠈⠁⠒⠠⠄⣀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⡊⠁⠀⢀⠄⠀⠀⠀⠀⠙⢦⣠⠶⣄⡞⠀⡴⠀⠈⠛⠠⠤⠁⠀⠀⠀⠀⢀⠔⠛⠈⠙⢅⠘⠀⢄⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠉⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠘⣄⠸⡇⣬⡤⠶⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢀⠀⠨⠀⠀⠈⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠢⢄⡔⠂⠈⠓⠀⠁⠮⢉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠀⠀⡶⠄⠀⢒⣦⠈⢧⠀⠀⠀⠀⠄⠀⢠⠀⠀⠀⡠⣜⡉⢢⡀⣰⠁⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡤⠄⠀⠘⠀⠀⠀⠈⠀⠀⠁⠠⠈⠉⢳⠀⠀⠂⠀⠀⠀⠀⠀⣗⠂⢄⠈⡿⡴⠤⠤⠤⠀⢀⣠⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠀⠀⠀⠐⠀⠂⠀⠀⠁⢄⡠⣾⠛⠄⢀⠴⠶⠖⠢⢘⡏⠝⠃⠀⡴⠧⠶⠖⠚⠛⠉
⠀⣠⠤⠒⠢⢤⡀⠀⠀⠀⢳⡀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡠⠷⢖⡦⠀⠀⠀⠀⠀⣁⠀⠀⣼⡅
⠀⠦⠒⠉⠓⡆⢹⠀⠀⠀⠀⠙⢤⡀⠈⠰⠀⢀⠀⠀⠀⠀⠀⢀⢊⣐⢦⠴⠃⠀⠀⠀⠀⠀⠼⠢⡴⡷⡏
⠀⠀⠀⢀⡴⢃⡜⠀⠀⠀⠀⠀⠀⡟⡲⠀⠀⢠⣤⡀⠀⢰⠶⠟⠊⠉⠡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⢀⡔⢉⠖⠋⠀⠀⠀⠀⠀⠀⠈⡥⠋⢈⡰⠶⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠂⠀⢄⠀⠇⠀⠀⠀⣷
⠀⡏⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡛⠀⠀⠀⣀⣤⣤⣄⠀⠐⠆⢀⠁⠀⠀⠀⠀⠢⠈⡈⠂⠀⢰⠃⠀⠀⣠⢦
⠀⣇⠸⡄⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠄⠉⣯⠴⡞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⠤⠶⠋⢠⡶⠶⠋⠈⠳⢶⣤
⠀⠈⠢⣌⣙⠒⠒⠒⣉⣉⢤⣶⠏⣠⠊⠓⠚⠀⣲⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠙⡧⠀⠀⠠⡟⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠀⢀⠎⠈⠀⠁⢹⡀⠀⡜⠉⠘⣧⠀⠀⠀⠹⠓⡀⠀⠀⢰⠖⣾⣉⡤⠞⠋⠙⠦⣄⠀⠰⠷⠚⠛⠶⠧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠀⠀⠀⠀⠸⠃⡸⠀⠀⠀⠓⣆⠀⠀⠀⠸⣇⠒⠀⠙⠉⠃⠁⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⠀⡇⠀⢀⡤⠾⠉⢠⠀⠀⠀⢸⡄⠀⠀⠀⢀⡀⢠⢤⣄⣀⠀⠄⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣠⠴⠃⠀⠛⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡟⠒⠒⠋⠉⠉⠉⠀⠀⠈⠙⠚⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠄⠒⠒⠛⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠁⢼⠇⠀⣴⠒⠀⢸⡀⢠⡶⠂⠀⣧⠒⠀⡶⠚⠀⠘⠲⠛
⠀⠀⠀⠁⣠⡇⠀⠀⠀⣠⡾⠁⠀⠁⢀⣰⠏⠀⠀⣿⠀⠀⠃⢀⡷⠀⠀⠀⠀⠀⢀⣈⠢⡀⠂⠐⠁
⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠈⠋⠉⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⢀⡀⠨⠽⠘⢂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⠁⣀⠀⠀⣀⠀⠈⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠀⢀⢀⠀⠀⠘⡀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠆⡠⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡜⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⡐⠒⠄⠀⠀⠀⠀⠀⠀⣀⠜⠀⢠⠠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢈⠑⠒⢐⠆⠀⠀⢢⢌⣉⣈⣩⠄⠣⠄⠀⠐⢜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠓⠒⠢⠤⣄⡀⠀⠀⠀⠀⢈⠀⠀⠀⠉⠢⣉⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠈⠪⠈⠁
⠀⠀⠀⠀⢀⡤⠖⠒⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠈⡄⠀⠀⢀⠔⠀⠑⠒⡄⢰⡀⠀⠒⠁
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠒⠚⠁⠀⠀⠀⡎⠀⠀⠈⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠘⡤⢀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢺⠆⠀⠀⠀⡘⠀⠀⠠⠈⠀⠀⠀⠑⠂⠤⠀⠒⠁⠀⠑⢦
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠥⣤⠀⣀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠔⠮⠀⠀⠀⠀⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⡹⠃⠀⢀⠀⠀⠀⠑⢀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡔⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠂⢸⡆⠀⡶⠓⠀⣷⠀⠘⠃⣸⡇⠀⠤⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠄⣀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠔⠋⠀⠀⠀⠈⢀⣼⠃⢀⠀⢀⣠⠿⠀⣤⠈⣋⡀⢀⡤⠄⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠉⠉⠁⠀⠉⠉⠈⠉⠁⠉⠁⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠋⠉⠉⠙⠲⢦⣄⡀⠀⢠⠀⠀⣀⡴⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣼⣠⠞⠉⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣸⡇⠀⢷⣤⣤⣤⣤⣤⣤⣠⣼⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠉⠉⠉⠉⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣀⣻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣷⡒⠦⣤⣀⠀⠀⠀⠀⠈⢷
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢦⣹⣿⣿⣿⣿⡟⢹⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣆⠀⠙⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠊⠁⠀⠀⠀⠀⢾⡸⣿⣿⣿⣿⠏⢸⡄⠀⡇⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠉⠙⠛⠛⠛⠀⠚⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣬⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⢦⡀⠀⠀⠀⠀⠀⠘⣏⠻⣟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⣠⣤⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠈⠑⠒⠊⠉⠑⣄⠈⠓⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⠗⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠶⠆⠒⢄⠀⠀⠈⠳⣤⠤⣤⣤⡤⠤⠖⠒⠛⠉⠛⣤⡻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠉⠀⠀⠀⠀⠈⠳⢤⣄⡀⠈⠲⣇⠀⢀⣤⠶⠶⠶⠶⢦⣽⠷⣿⠋⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡈⢷⡋⠀⠀⠀⠀⠀⠀⠣⡰⠋⠀⢿⣄
⠀⠀⠀⠀⠀⠀⣸⡿⠧⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⠀⠀⠀⢀⠀⠀⢠⢻⡂⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠈⢳⡄⠙⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡆⢀⢇⠞⠳⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣄⡸⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⡜⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⣧⡾⠂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠙⠒⠒⠀⠤⠤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢠⡿⠁⠰⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⠁⠀⣹⣷⠿⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠚⠁⠙⣶⠤⢌⣉⡑⠒⠂⠤⠤⠤⠄⠤⠤⠔⠒⣈⣩⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢰⡇⠀⠀⠀⠈⠉⢩⡒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⡘⣧⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡜⢸⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⠀⠀⢰⠣⡄⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⠀⠀⢠⠃⢸⡇⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⣇⢹⡄⠀⠀⣀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡞⠑⠺⠦⣄⣀⡀⠀⠀⣣⣀⣽⡀⠀⣀⣠⡤⠞⠋⠙⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⣀⠀⠀⢈⢉⣉⡟⠉⠁⠀⠙⢫⠉⠀⠀⢀⣀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠬⠭⠭⠭⢼⠀⠀⠀⠀⠀⢸⠓⠲⠦⠀⠒⠚⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣏⠑⠢⢤⡤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠠⠤⠄⢲⠋⢈⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣀⠈⣻⠶⠋⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠲⣏⠀⣠⠗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠉⠉⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⣱

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⡿⠿⠿⠿⢿⢿⠛⢉⠉⠀⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡰⠉⢈⡆⠡⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢰⠀⠀⠀⠁⠌⢖⡅⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠗⠃⠀⠃⠀⡜⡐
⠐⠂⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⠂⠀⠀⠐⠆⠁⡀⠎⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⢐⠂⠀⢂⠠⠀⠀⠀⠀⠠⠄⠀⠄⡀⠀⠀⣀⣘⡄⠧⣤⣀⠀⠀⡤⢈⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡞⠋⠀⠀⠀⠁⠀⠨⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡌⠀⠀⠀⢡⢊⡄⣠⣄
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⢫⠀⠀⢐⠀⠀⠀⠀⠈⢣⡠⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠀⠘⣄⠀⠈⠤⠠⡂⠀⠀⢮⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠔⠀⠀⢀⢀⣀⠀⠀⠀⠠⢀⣀⡀⢠⠀⠀⠀⠀⢂⢸⡇⣤⠀⠀⠛⠡⡆⠀⠀⠀⠀⠀⢠⢰⣯⡅
⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠲⠟⠃⠀⠀⠀⠀⢱⠀⠀⠀⠀⢠⠀⡸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠉⠀⡀⣀⠀⠀⠀⠀⠙⠀⠀⢀⠔⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠌⠈⠀⠘⠀⠁⠉⠀⠐⠐⠀⠀⠃⠈⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣦⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠘⠀⢐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⡀⠀⠙⢦⡀⠀⠢⡀⠀⠀⠈⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠐⠀⠘⠲⠄⠀⠀⠀⠙⢄⠀⠈⠁⠐⠂⢰⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠳⠤⡐⢉⣀⠀⠀⠀⠀⠸⠃⠘⡄⠠⠀⡜⠀⠀⠀⢠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⠄⠂⠀⠄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⢀⡜⠀⢤⣀⢀⠆⡐
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠁⠀⠐⡷⢀⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⢄⠈⠀⠀⢀⡴⠛⠈⠿⣄⠠⠚⠈
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡠⠔⠈⠀⠀⡀⠀⠀⢀⠀⠀⢀⡁⠀⠀⠈⢀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⠀⠉⠉⠀⡠⠦⡑⠀⠀⠀⠀⠀⠀⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠐⠉⠀⠑⠀⠀⠀⠀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⢀⠚⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⢷⠢⠤⢤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣆⠐⠈⠂⠀⠀⠀⣖⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣰⠛⠦⠢⠄⡀⠜⠉⡹⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡔⢠⠒⣴⢠⡖⣤⣶⢰⡤⣤⡔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠆⣬⣀⣍⢨⠅⣩⢠⡈⠈⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠘⠉⠙⠋⠙⠘⠃
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢰⢶⡀⠀⠀⠀⠀⢀⡴⠚⠓⠦⡴⠞⠋⠉⠉⠛⠳⣤⡀⠀⣠⡴⠞⠛⠛⢛⠟⠁⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢆⠳⣼⡆⢧⠀⠀⠀⠀⣿⠀⠀⠀⠀⢱⠶⠶⣄⠀⠀⠀⠀⠳⡞⠁⠀⠀⣠⠞⠛⣧⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢬⣆⢣⠘⣧⠘⣇⠀⠀⠀⠙⢦⣀⣀⣴⠏⠀⠀⠈⣷⠀⠀⠀⠀⠁⠀⠀⡼⠁⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠶⠋⠀⠀⠹⡆⣠⠴⢤⡀⠉⠉⠀⢀⣠⣤⣄⣼⠀⣤⠦⣄⠀⠀⠀⡧⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠆⠀⠛⣡⠴⠚⠁⠀⠀⠀⠸⣅⡀⠀⠉⠳⣿⡄⠈⢧⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡠⣴⠁⠀⣠⢤⣀⠀⣠⣴⣚⠛⠷⢦⣄⠈⣿⠀⢸⠇⠀⣀⣀⣀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⠀⢹⣆⡾⠁⢀⢙⢟⢡⣤⣤⣈⠳⡄⠈⠁⠉⣴⠋⠀⣰⠋⠀⠈⠙⢦⣨⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⡣⠀⠀⢸⡄⠀⠻⠁⢰⠉⡏⡌⠀⠛⠃⠈⡆⠹⠆⠶⠤⣌⠳⣤⡏⠀⠀⠀⢰⠏⠁⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠃⠀⠀⠘⣧⣤⠞⠛⠛⠚⠀⠱⡄⠀⢀⡰⢁⠔⣿⣿⠓⢄⠑⡈⣧⠀⠀⠀⢸⣄⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠈⣉⠁⠀⢀⠀⠈⠉⠀⢸⠀⡇⢸⠀⠀⠀⠀⠙⠓⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠈⠓⠤⠤⠔⢃⠞⠠⠿⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⣎⢁⠔⠒⠒⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢠⠁⠈⠒⠤⣄⡀⠀⠀⠀⠀⠘⣆⠣⡤⠞⠀⣴⠋⠀⠀⠀⢠⡞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢴⠃⢀⡀⣀⠀⢀⡠⠞⠃⠀⠀⠀⣿⣀⣀⡴⠞⠁⠀⣀⡤⠶⠋⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠙⠃⠠⠤⠛⠉⠀⠀⠀⠀⢀⡼⠧⠿⠿⠖⠛⠛⠉⣿⠀⠀⡘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠓⠦⣤⣠⣀⣄⣠⡤⠶⠚⠉⠀⠀⠀⢀⣀⣤⠶⠛⠙⣆⠀⠁⠀⢙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡴⠋⠀⠀⠀⠀⠀⢰⠀⣤⣠⣤⣤⣤⣤⠤⠶⠞⠛⠋⠁⠀⠀⠀⠀⠘⢦⡀⠀⣾⡑⢝⢦⡄
⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⣀⣀⡴⠛⠉⠙⡿⠁⠀⠀⠀⠀⠀⠀⡘⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡈⠻⣦⡑⣿
⠀⠀⠀⢀⡾⣓⠬⣑⢦⡈⠻⡁⠈⠑⣄⣠⢤⡱⡄⠀⠀⠀⠀⠀⠀⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⠟⠃
⠀⠀⠀⢸⡧⢄⡉⠛⢦⠑⡄⠀⠀⠀⢸⠁⠈⠳⣌⠲⠄⣀⠀⢀⠜⠀⡿
⠀⠀⠀⠸⡗⠠⣌⡁⠒⢧⠘⡀⠀⠀⢸⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⢻⡆⢤⣉⠑⠲⡆⠇⠀⣠⠏⠀⠀⠀⠀⢀⣠⡴⣾⠃⢀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⢉⣹⣇⣈⡉⠙⠲⣄
⠀⠀⠀⠀⠈⢳⡦⢌⣙⠲⠆⣁⡴⠃⠀⠀⠀⢀⡴⠛⠁⠐⢇⣀⡾⣄⠹⣄⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣀⡴⠞⠋⠉⠉⠉⠙⣦⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠻⣦⣈⣹⠿⠋⠀⠀⠀⠀⣰⢿⠁⠀⠀⠀⠀⠉⠀⣸⣄⠈⠳⠦⣤⡤⠶⠞⠋⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⢠⠇⠈⠓⠦⣤⣀⣀⣤⠴⠚⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⣴⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⢳⠀⠀⠀⠀⢿⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢃⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠉⠙⣧⠀⠀⠀⠀⠀⠈⠳⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠳⣄⠀⠀⢰⡇⠀⠀⠀⠙⠲⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠉⠙⠙⠂⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠒⠀⢀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠠⠋⠀⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢶⣴⣞⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⣶⣻⣿⣿⣶⡶⠀⡌⠀⢀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⢸⢻⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⠘⢌⠻⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠻⠿⡿⠿⢃⠎⠀⡂⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠘⠲⡙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠄⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠉⠋⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠣⣀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢀⠠⠙⠂⠀⠀⠰⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⣄⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠔⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠉⠥⠉⠈⠉⠉⠒⠲⠖⠉⠉⠉⠐⠂⠒⣒⠫⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⡇⠈⢢⠀⠀⠀⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠘⠋⢣⠀⡜⠙⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠤⠤⠚⠀⠑⠐⠀⠂⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠁⠐⠒⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠀⡀⠀⠀⢀⢈⡤⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⡿⠺⠋⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⠤⠀⠲⢾⠶⢷⣌⠐⠚⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠤⠖⠟⠉⠋⠋⠉⠙⠉⠐⢤⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠴⠋⠀⠀⠀⠀⠰⠀⠀⠀⢠⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠘⡀⠀⠀⠀⠀⢀⡀⠠⠄⠰⠐⠃⠀⠐⢄⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠀⠀⠀⠙⠺⠇⠀⠀⠀⠀⠀⠛⣁⣀⣄⣀⣀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⡶⢶⣶⣦⡀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠸⣿⢿⣿⣿⡿⣻⠀⠀⠀⠀⢯⠻⠿⠟⠃⡿⢰⣏⡶⢤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠟⠛⠛⠭⢿⣹⡆⠻⡀⢉⡉⠤⠁⠀⣨⣤⠀⠀⠁⠒⠂⠈⠀⣸⠛⠛⠁⠉⠀⠉⠉⠛⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠀⠀⠀⢀⠀⣤⠢⠐⠉⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣌⠉⡓⠂⠲⣤⡀⠄⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⣠⠞⢩⡄⠀⠶⠖⠶⠄⣀⡀⠔⠛⠀⢠⢤⠀⢠⠋⠑⠰⠶⡖⣶⢶⠦⣩⠹⠟⠛⠉⠀⠳⠀⢀⣀⠨⠛⠐⠠⢀⡈⠀⠀⠁⠀⣀⡥⡬⠷⣄
⠀⠀⢀⠞⠋⠉⠀⠂⣀⠀⠀⠀⠀⠀⢩⡄⠀⠀⠀⠈⠑⠣⢀⣀⣄⡤⠋⠀⡛⠋⠁⠂⠨⠧⠴⠄⠒⠛⠀⡄⠀⢀⡀⠀⠀⠐⠧⠞⠛⠀⠀⠀⠀⠀⢸⢳⡄
⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⢈⣠⠴⠒⢛⡓⠶⣇⣀⣀⣻⡖⢃⣄⣀⣠⠷⠒⠙⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠼⠐⠋⠊⠀⣿
⢸⣿⡇⠁⡠⠌⠉⠉⠁⠀⠄⠐⠈⢀⠡⣾⢀⡴⠋⠁⠀⠛⠐⠁⠀⠀⠈⢭⠄⠉⠍⠛⠣⠀⠀⠋⠐⠖⠀⢀⠈⠛⢧⡀⠀⠀⠀⠀⠇⠠⠀⡄⠀⠀⠀⠰⣿
⣿⢹⣿⠶⠠⠤⠤⠤⠤⠍⠀⠂⠈⠁⠀⣼⠏⠀⠐⠀⠐⠀⠃⠀⠉⠀⢀⣀⣀⡠⠠⡀⡀⠀⠀⠐⠢⠖⠈⠋⠉⠀⠀⠙⣤⠂⠲⠀⠀⠁⠀⠀⢀⠀⠀⣾⢻
⢿⡄⢿⡘⠀⣀⣀⣀⠀⣀⠀⣀⣤⡖⠉⠿⣧⡈⠀⢀⠄⣠⠄⢄⠄⠀⠃⠉⢑⠀⠛⣤⠁⠀⠀⠀⠀⠀⢀⠀⠲⠤⠀⠀⣸⡏⠀⠀⠀⠀⠄⠀⠁⣪⠟⢁⣾
⠸⣧⠀⠑⢄⠉⠀⢹⠀⠀⠀⡍⠀⠀⣦⠘⢣⡙⠲⢬⣁⡀⠀⠀⣝⡠⣄⣀⣄⠀⠀⠀⠀⠠⣀⠀⠉⠀⠀⠀⠀⣀⡴⢎⡌⠀⠀⠀⠀⠄⢀⡤⠞⢁⣰⠟⡟
⠀⣧⠑⢔⠀⠙⠲⢼⣀⠀⠀⢹⠀⠀⠀⡴⠛⠙⠓⠂⡬⢉⣐⠒⠀⠷⠤⠥⢤⣤⣄⣤⣥⠤⠭⠤⠶⠴⠒⠛⣉⠥⠒⠧⣀⣀⣀⣀⡤⠖⠉⠠⣀⠕⠁⣸⠃
⠀⠘⣇⠀⠑⠨⡀⠀⠈⠙⠓⠾⠦⣄⣀⣷⠀⠀⡆⠄⠐⠀⠀⠈⠉⠁⠲⠖⠒⢢⠀⠤⠄⠐⠒⠖⠒⠀⠉⢀⡏⣀⣠⠤⠔⠛⠉⡁⠀⡢⠔⠊⠀⠀⢠⠏
⠀⠀⠹⡄⠀⠀⠀⠁⠂⠬⠀⡀⠀⠀⠀⡉⠉⠓⠛⠒⠦⠤⠄⢤⣀⣀⣀⣀⣀⣘⡠⣤⠤⠤⠤⠾⠓⠒⠛⠉⢉⠁⠀⠀⣀⠠⠐⠂⠁⠀⠀⣠⠴⢲⡞
⠀⠀⠀⠹⣄⣠⣀⠀⠀⠀⠀⠋⠀⠀⠰⢤⡤⠄⢀⣐⠀⠀⠀⠀⠀⠠⠤⠠⠀⠄⠀⠠⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡞⠁⢠⡞
⠀⠀⠀⠀⠘⢧⡈⠳⣄⠀⠀⠀⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠉⠱⠒⠀⠀⠐⠶⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠤⠒⠚⠳⡄⠀⠀⠀⠀⡟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠙⢦⡈⢣⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠚⠀⢀⣀⣈⣣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠶⢶⢄⠈⠀⠀⠉⠀⠀⠀⠀⣠⠖⠛⠉⠍⠙⠛⠲⣤⠊⠀⢠⡿⠉⠉⢉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⢠⠶⠖⠦⡔⣻⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠀⠀⣆⡀⠀⠰⠈⠳⣤⠚⡷⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⣠⠞⠀⢸⠂⡀⢠⢸⠀⠀⠀⣀⣄⡴⡏⠄⠀⠈⣰⠋⢉⣉⣦⡐⠀⠀⢻⠀⣿⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠃⠀⠀⢸⠃⠀⠀⢘⣀⣠⡊⢁⡜⠁⣏⠄⡁⠆⣿⠛⠛⠉⢸⡅⢀⡀⢸⠆⣿⠂⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢸⡃⠄⠀⢈⡉⠉⣩⠋⢀⠀⢻⠀⠀⠂⠙⢦⣀⣠⠞⡀⠀⠀⣾⠁⣿⠀⠄⠁⠾⠦⠴⠶⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇⠄⠁⠈⠹⠈⠉⡉⠉⣿⠈⢷⣄⠂⡀⢀⠈⠀⠒⠀⢠⣼⠃⠀⢹⠁⠄⠁⠌⠰⠈⠀⠁⢀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⣄⣡⣄⣰⣤⣤⣠⣦⣏⡵⠀⠙⠳⢤⣤⣌⣤⡤⠴⠧⠞⠀⠀⠈⠛⠚⠓⠚⠓⠚⠒⢒⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⢄⠀⢠⠀⢠⠀⢠⠤⡄⠀⡴⢦⡀⢠⡖⣦⠀⣶⠀⢶⣒⠀⢰⣟⡃⠰⡇⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣙⣲⠄⠸⣄⡼⠀⢸⠛⠇⠀⠟⠊⠁⠸⠋⠳⠀⠛⠀⠲⠼⠃⠈⠓⠒⠀⠂⣀⣠⠞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠘⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⣀⣀⠊⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⡠⢄⡀⠆
⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⢔⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⡠⠓⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠒⠛⠛⠉⠉⠉⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠬⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⢢⠤⠄⣀⡀⠀⠀⡰⢊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡐⠁⡴⠞⢋⠙⠆⠉⠀⠈⠀⠄⢀⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⡀⢀⡴⠊⢹⠈⠰⣷⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡷⠶⣔⠊⢇⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏⠑⣮⠁⡰⠃⣀⣀⡀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢡⣄⠈⡀⠈⡆⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣄⠙⠀⠷⣋⣉⣉⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠐⠂⠀⠁⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠲⠞⠁⣀⠀⡉⢀⠈⠓⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠰⠀⠀⠀⡎⠀⠸⠟⠀⠌⠹⣷⢂⢙⣄⣀⠀⠀⠀⠂⠀⠠⠀⠀⠀⣤⣒⠗⠀⢱⡤⠞⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⠘⠂⠂⠁⠠⠠⠄⠁⠀⠀⠀⡘⠀⠠⠈⣷⡀⠀⠀⠈⠀⠀⠀⠀⣿⣍⣘⡲⠲⢓⠟⠀⠀⢀⣈⣡⡭⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠉⠲⣤⣞⣿⠛⠀⣩⠘⠛⠛⠛⠂⣭⠠⠉⠐⣄⠾⠛⠛⠛⠋⠉
⠀⠀⠀⢀⡤⠄⠂⠤⣄⠀⠀⠀⠀⢻⡄⠀⠈⢀⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠼⠛⣻⠗⠈⠁⠀⠐⢀⠨⠀⡂⢀⣿⡄
⠀⠀⠀⠧⠔⠒⠒⢶⠈⢣⠀⠀⠀⠀⠙⢦⡀⠈⠑⠂⠀⠈⠀⠀⠁⠀⠀⠀⡐⢁⣺⡥⠞⠁⠀⠀⠀⠀⠀⠰⡟⠶⣾⠻⡋
⠀⠀⠀⠀⠀⠀⢀⡾⢀⡞⠀⠀⠀⠀⠀⠀⣹⠓⡦⠄⠀⣀⣀⡀⠀⠠⣤⠾⠓⠋⠉⢄⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠁⠁⢻⡄
⠀⠀⠀⠀⢀⠔⢛⡴⠋⠀⠀⠀⠀⠀⠀⠀⢟⡼⠃⠒⣠⡼⠈⠁⠒⠉⠀⠀⠀⠀⠀⠀⠡⠀⢀⠠⠆⠁⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⣠⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠄⢸⠶⠀⠀⠀⠀⠀⢀⣀⠀⠀⡠⠄⠈⠃⠁⠀⠀⠐⠂⡈⠲⠓⠀⠀⣠⠏
⠀⠀⠀⣯⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⢆⠘⢧⣦⣀⣴⠾⠛⠛⠛⠣⠀⠀⠈⠁⠀⠠⠀⠀⣀⣀⣀⣼⣀⣀⣤⠞
⠀⠀⠀⠙⣆⡙⠦⣤⣤⣤⣤⡤⠔⠒⢉⣤⠆⣠⠤⣭⣤⠟⣽⢇⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯
⠀⠀⠀⠀⠈⠙⠳⠶⠦⠤⠶⠖⠒⢩⠛⠇⠰⠣⡄⠀⠀⣠⠿⣙⡆⠀⠀⠀⠀⡴⣄⠀⡀⣀⣀⣠⣤⡴⠛⣠⣴⡶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⣰⠇⠀⠀⣼⣂⠀⠐⠂⠩⢭⡆⡀⠀⢴⡧⣞⠳⠚⡁⠀⠀⠁⠫⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⢈⣽⡆⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠠⠀⠠⠀⢀⡀⠀⠀⠌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⡄⠀⣧⣀⡠⠖⠛⡁⠠⠀⠀⠀⠀⠸⣇⣀⣀⣀⣠⠴⣌⡶⠓⠦⠴⣤⣰⡀⢳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣭⣭⡵⠶⠋⠁⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠛⠒⠛⠓⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⢃⠜⠁⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⡠⠄⠐⠊⠀⠀⠐⠄⠀⠀⠀⠘⢆
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠈⠀⠤⡀⠀⠀⠀⢀⠰⠃⠘⡄⠀⡀⢸⠂
⠀⠀⢀⡇⠀⠀⠀⠀⠀⢰⠈⠀⠀⠆⠀⡀⣶⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢃⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⢙⡖⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⠀⠀⠀⠀⡀⠀⠠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠊⢝⠄⠀⢀⡨⠧⠚⠅⠀⠀⠀⠀⠀⢎⠁⠢⠰⠀⢡
⠀⠀⢸⡀⠀⠀⠁⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠉⠀⠀⠈⠡⠔⠋⠠⠈⠀⠀⠠⠊⠁⣤⡐⠒⠉⢆⠱⠀⢠⠤⡀
⠀⠀⠀⠁⠂⠤⠤⣀⡠⠀⠀⠈⠁⢀⠤⡄⠄⠈⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡄⠂⢀⠔⠀⠀⠈⠀⠁⣀⡄⠀⠀⣋⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠐⠰⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢆⠘⣾⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢰
⠀⠀⠀⠠⢀⡠⠐⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠐⠒⢞⠁⠀⠀⠀⠀⠀⠘⡄⠈⠀⠀⠠⠀⠀⠀⠀⠠⠄⠀⠊⢠⡀
⠀⢀⣐⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⢄⠈⠢⠀⠀⡀⣀⠐⠀⠈⠂⠀⢠⠇
⠀⠀⢇⣠⢀⠎⢽⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠄⡄⣀⢀⡀⠌⠁⠊⢁⠔⢋⠀⠉⠢
⠀⠀⠀⠀⠁⠀⢈⣳⠤⠄⢀⡀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⡂⠈⣄⢄⡀⠀⠀⠀⠀⡠⠆⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⠎⡐⠁⠀⢰
⠀⠀⠀⠀⢀⠔⠁⠈⠳⡄⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⢰⢉⠃⠀⠀⠆⠀⠉⡠⠄⠀⠀⠀⠙⣄⠀⢀⡀⢠⢌⡀⢠⠐⢄⠈
⠀⠀⠀⠀⠎⠀⠀⠠⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠐⡄⠀⠀⡀⠸⡞⡁⠀⠀⠀⠳⠈⠀⣀⠔⠁
⠀⠀⠀⢈⠁⠀⠀⡴⢃⢀⡀⠀⠀⣀⢠⢇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣏⠲⠀⠤⣀⢀
⠀⠀⠀⠈⠣⠤⡴⠁⠀⠁⠉⠒⠊⠁⢀⠆⠀⠀⡘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠁⠡⠀⠀⠀⠀⢂⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢠⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠫⠉⢢
⠀⠀⠀⠀⠀⠀⠀⢾⣤⡆⣀⠀⠀⢇⠀⢂⡡⠌⣇⡴⡆
⠀⠀⠀⠀⠀⠀⠈⠻⡿⡫⣿⡿⠻⣌⣶⢟⡫⢛⣯⠞
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡏⢋⣥⢀⣏⢽⣿⠿⠯⠤⣄⠀⠀⠀⠀⠀⣀⣴⠶⠋⠉⠉⠉⠳⣤⠂
⠀⠀⠀⠀⢀⢀⡀⠀⠉⠲⡜⢋⡰⣩⠋⠁⠀⠀⠀⠀⠙⡄⠀⢠⠞⢱⣷⡖⠏⡀⠀⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠻⠉⠻⣄⠀⢀⡏⡁⠀⣹⡄⠐⠿⠀⠘⠃⠀⣿⣀⠈⢷⠃⠙⠋⠀⣬⣽⣅⠀⡄⢀⡼⡆
⠀⠀⠀⠀⠀⠀⣀⢙⢋⠿⣣⢷⣎⣇⡷⡀⠀⠶⠶⣢⠐⠻⣄⠱⢮⢧⡀⣦⠄⠙⠛⠁⡓⠀⠛⡟⣇
⠀⠀⠀⠀⠀⠀⠬⠕⣿⣦⣼⣧⣼⣧⡄⠀⠀⠀⠀⠀⠀⠀⠐⣤⣠⡀⢯⠓⠠⠤⢀⡺⢷⣴⢞⡗⡙⢱
⠀⠀⠀⠀⠀⠀⠚⠉⠉⠛⠁⡼⠻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠓⠤⡉⠻⡒⢐⠞⠉⠀⠀⠈⢏⠢⣹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠙⠀⠀⠠⠄⠀⠀⠄⠀⠁⠀⠀⠙⡄⢋⢀⣀⣈⠈⢑⠲⡖⠉⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠊⠈⠉⢈⠊⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣢⠀⠀⠘⠀⠀⣠⠎
⠀⠀⢀⡤⠤⠤⠒⠒⠒⠒⠻⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡏⠁⢑⠂⠐⠺⣄⡀
⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣈⣁⣀⣁⣠⠤⠤⢤⡴⠚⠁⣾⣡⣤⠞⠀⢀⣀⡇⠙⠦⡀
⠀⠈⠉⠓⠒⠒⠲⠦⠴⠖⠒⠲⠤⣄⣀⣀⠐⠉⠀⣀⣀⣀⣀⣀⡠⠤⢄⣀⡀⣉⡩⠭⠥⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⣸⣿⣿⣿⣷⣀⣀⡀⠀⠀⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠋⠉⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡵⠟⣫⣭⣭⡛⠭⣉⠉⠙⠻⢿⣿⣿⡄⢀⡾⠁⢰⣶⣶⣤⣤⣤⣶⠶⠾⣛⠿⢟⣛⡻⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⣿⣿⣿⣾⣿⣮⡳⡑⡦⠄⣙⣿⣿⣿⡇⠀⣿⣿⡿⠿⠛⠛⠁⡠⠊⠁⣿⣩⣭⣝⣿⣿⣿⢿⣆
⠀⠀⠀⠀⠀⢀⡿⣴⣲⣶⣶⡟⢿⡿⣿⣿⣿⣇⢱⢱⣤⣤⣿⣿⣿⠏⠀⠻⣆⣠⠒⠒⡲⣰⠁⠀⣀⣻⠛⠛⠙⠽⣿⠿⣦⢿⡄
⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⣿⠗⣀⠸⣿⣿⣿⣾⢈⢶⣭⣽⣿⣿⣷⠀⠀⣸⡏⠛⣿⣿⡃⡇⣾⢩⣿⣍⢸⡉⡱⠸⣿⡿⣸⢸⣷
⠀⠀⠀⠀⢀⣿⣿⡸⣿⣷⣾⣿⣿⣷⣿⣿⢗⣋⣘⡺⢟⢿⣿⣿⣿⠆⠀⠘⣧⠀⠳⠞⠋⣣⠹⣌⣿⣧⣦⢨⣄⣸⣿⣿⡿⣼⣿⣇
⠀⠀⠀⠀⣸⣿⣿⣿⣜⡻⢿⣿⣿⣯⠟⣵⠟⠁⠀⢨⣷⡹⣹⣿⡏⠀⠀⠀⢸⣧⠀⡔⣫⡶⠒⠚⣭⡻⣿⡻⢿⣛⢿⢟⣽⣿⣿⣿⡄
⠀⠀⠀⢀⣿⣿⡇⠈⠛⠿⣷⣶⣶⣶⡄⣇⠀⣀⣴⡿⢋⡇⣿⣿⣿⠀⠀⠀⠻⣏⢸⢼⠋⠀⠀⣼⡿⣣⢨⣭⣭⣥⣶⠿⢿⣿⣿⣿⢿⡀
⠀⠀⠀⣼⢿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣧⡹⢿⣿⣷⣶⢟⣴⣿⣿⡟⠀⠀⠀⠀⢹⣷⡸⣦⣠⣾⣟⣵⡟⣼⣿⣯⠉⠀⠀⠈⢿⣿⣿⡞⣧
⠀⠀⢠⡟⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⢿⣟⠲⠦⣴⣶⣿⡿⠁⠈⠀⠀⠀⠀⠀⠸⢿⣷⣬⣛⣛⣛⣩⣾⣿⣿⣿⣇⠀⠀⠀⠈⢿⣿⣿⠹⡆
⠀⠀⢸⠧⣿⠁⠀⠀⠀⣾⣿⢟⡽⠃⠀⠙⠛⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣉⣹⣿⠿⠋⠘⣯⡻⣄⠀⠀⠀⠈⢿⣿⡇⣿
⠀⠀⠸⣧⡙⠀⠀⠀⠴⣟⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠚⠋⣠⠟
⠀⠀⠀⠈⠛⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉

⠀⢀⠔⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠢⢄
⠰⠁
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣷
⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣤⣀⣼⠿⢿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⣿⣿⣇⣀⣨⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣹⣿⣿⣿⣿⣿⣿⣿⡆
⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿
⡇⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛
⡇
⡇
⡇
⠰⡀
⠀⠈⠢⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⠀⠀⠈⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⠀⢀⠀⠀⣄⠀⠈⠈
⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⠰⠄⠀⠀⠂
⠀⠀⠘⠀⠀⢀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠂
⠀⠀⠠⡀⠀⠈⠿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢄
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡁
⠀⠀⠀⠀⠀⠁⠒⠂⠐⠀⠀⠀⠠⠤⠤⠄⠀⠀⡀⢀⣀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠓⠦⠀⠀⠀⠰⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠀⠀⢀⠁
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠁⠂⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠔⠐⠐⠇⠒⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⢘⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢅⣀⣴⣀⣀⣀⣐⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⢐⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⡐⢀⠁⠀⠀⠀⠀⣨⠑⠒⣂⠐⢀⡚⠒⢉⡀⠄⠀⠀⠀⠀⠛⠛⠀⠀⠀⠄⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⢄⠠⡀
⠀⠀⢀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠐⢁⣂⣉⠀⢈⣁⡢⠓⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢠⡔⠇⠐⠂⠂⠀⢄⠠⡄
⠀⠀⠘⠐⠁⠦⠤⠤⠤⠤⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⢈⠋⠁⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⢤⡤⠀⢀⢠⠁⠀⠀⠀⠀⠀⠀⠤⠁⠀⠈⠠
⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠤⠄⠀⢠⠀⠄⠅⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠴⠰⠤⠤⠤⠤⠤⡴⠴⠄⡀⠀⠀⠀⠈⠀⠈⠁⠁⠈⠀⠃⠀⠀⢠⠈⠁⡄⠀⢀⠀⠤⠐⢈⡁
⠀⠀⢘⠁⠀⠅⠀⠀⠀⠀⠀⠀⡇⡀⠘⠄⠀⠀⠈⠀⠔⠢⠈⠉⠁⠉⠉⣀⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠒⠈
⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⢀⠈⢘⠀⠀⠄⠑⠄⠐⠀⢁⠀⢀⠠⠀⢒⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠠⠂⠂⢀⢀⠀⢀⠀⠀⠁⠺⠗⢈⠀⠀⠈⠀⠀⠒⠀⠉⠁⠉⠁⠐⠂⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⢤
⠀⠀⠄⠀⠐⠀⠉⠈⠁⠈⠈⠁⠐⠀⠀⠄⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠘⠄⠀⠀⠀⠠⢀⠀⠀⠀⠠⢊⠠⠀⣤⠀⣤⠀⢴⢵⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠂⢄⠐⠀⡀⡀⠘⡁⠂⠂⡁⠀⠀⠀⢀⠤⡀⠀⠀⠄⠀⠆⠀⢀⠀⠒⠀⢀⣤⣤⣤⡀⠈⠊⠀⡀
⠀⠐⠃⠃⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠳⠀⠀⣂⠐⠀⠐⢡⠉⠁⠁⢄⠁⢄⠄⢁⠀⠀⠀⠐⠤⠈⠀⠉⠄⠁
⠀⠀⠖⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡷⠢⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⢙⠀⠀⠁⠀⠀⠀⣠⣄⠘⠀⠃⣀⣄⠀⠀⠐⠀⢀⠀⠀⠁⠀⠈⠀⠀⢀⠀⠁
⠀⠀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠄⣀⡀⡀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡁⢈⠂⠀⠀⠀⠀⠖⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡀⠀⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠈⠁⠀⠈⠁⠉⠀⠀⠉⠠⠂
⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠄⠉⠀⠀⣄⡀⣠⢠⠀⠜⠃⠈⠀⠀⠸⠿⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢠⠒⢢⠄⠀⠀⠀⠀⠀⠀⢀⡔⢢⡄⠀⠀⠀⠀⠈⠀⡼⢀⢀⠀⢨⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⠀⠉⠁⠀⠤⠀⠄
⠀⠀⠀⢑⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⡁⡡⠀⣉⢘⠁⠀⠀⠀⠀⠂⠔⠀⠒⠀⠒⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠃⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠂

⠀⠀⡀⠀⠀⠀⢀⠀⡀⢀⡀⠀⠀⢀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢠⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⡆⠀⠀⢀⠀⠀⠀⡾⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠰⠀⢠⠚⠻⣷⡄⠀⣇⠀⠀⢸⠀⠀⠀⠃⠀⠀⠸⠁⠀⠀⣰⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⢠⠀⠀⢀⠀⠀⠀⠰⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⣄⠀⠀⢸⡄⠀⠰⣿⠀⠀⣀⣀⡘⠀⠀⡿⠀⢀⡟⢠⠖⠳⣦⠀⢀⡴⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⡀⣼⠉⠈⠉⣷⡴⠶⢦⣄⠀⡏⠀⢀⣿⠀⠋⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣴⠾⠛⠛⠛⠋⠉⢉⣭⣭⣭⣭⣭⣭⡇⠀⠀⠀⣿⠀⠈⠁⣿⣭⣭⣭⣭⣍⠉⠉⠙⠛⠛⠻⢶⡄⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣠⠖⢂⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢀⡀⢸⣿⠀⡀⢰⣿⣿⣿⣿⣿⣿⠀⠀⣠⣶⡒⢦⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⡾⠰⢡⣄⡸⡟⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣏⣀⣿⣿⣿⣿⣿⣿⣿⢠⣤⡝⠛⣡⣤⡱⠸⡆⠴⠒
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡇⠀⠘⠛⣩⣥⠛⠛⣸⣿⣟⣩⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⣣⣦⡙⠛⠁⠀⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⡇⠀⠀⠀⠙⠛⣰⠟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣙⠛⠁⠀⠀⠀⡇⠐⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢹⡀⠀⠀⠀⠉⣿⠀⠀⠀⠛⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠁⠀⠀⠀⣸⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⢧⣀⡀⢀⠀⢹⡀⠀⠀⠀⢸⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠇⠀⣀⣀⡀
⠀⠀⠀⠐⠒⠛⠋⠉⠉⠀⠀⠀⠀⢉⡛⠛⠛⠛⣧⠀⠀⠀⠈⠉⠉⠙⠛⠿⠛⢿⠿⡿⠿⠿⠿⠿⣿⣿⠛⠛⠛⠛⠛⠛⢛⡋⠁⠀⠀⠀⠈⠉⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠖⠛⠉⠁⠀⣀⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢀⠈⠙⠦⣄⡀⠀⠉⠀⠀⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⣀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢀⠀⠑⠂⠀⠀⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠠⠚⠁⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠈⠁⠀⠀⠀⠢⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⣠⠆⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠶⣿⡟⠁⠘⠆⠀⠀⢦⡀⠀⠈⠳⠀⠀⠀⠀⠀⠙⠲⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣘⣁⣀⣀⢀⣞⣁⣀⣠⣆⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣧⣀⣀⣀⣦⣀⣀⣙⣆⣀⣀⣀⣙⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⠾⠉⣉⣉⣩⣉⣉⠉⠿⠿⠉⣉⣉⣩⣉⣍⠉⠿⠉⣉⣍⠙⠟⢉⣉⣍⠉⢉⣉⣉⣉⣍⣉⣩⡉⠉⢉⣉⣉⣉⣉⣍⡉⠹⣶⣀
⠀⢰⡶⠶⠶⠶⠾⠂⣶⣿⠉⠉⠉⠻⠿⠀⠀⣾⣿⠉⠈⠉⣿⣶⠀⠠⣿⣿⣧⣴⣾⣿⡿⠀⢸⣿⡏⠉⠉⠀⠉⠁⠀⢸⣿⡏⠉⠁⢹⣿⡆⠈⠻⠶⠶⠶⣶⣀
⠀⢸⡇⠸⠿⠿⠂⠀⣿⣿⠀⠀⠺⣿⣿⠀⠀⣿⣿⣤⣤⣤⣿⣿⠀⠈⣿⣿⠘⠟⢸⣿⡇⠀⢸⣿⡿⠾⠿⠿⠂⠀⠀⢸⣿⡿⠿⠷⢿⣯⡀⠀⠺⠿⠿⠀⠈⣿
⠀⠘⢻⣦⣤⣤⣤⡀⠛⣿⣤⣤⣤⠟⣿⠀⠀⣿⣿⠁⠀⠈⣿⣿⠀⢀⣿⣿⠀⠀⢸⣿⣇⠀⢸⣿⣧⣤⣤⣤⣤⡄⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⣠⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠘⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡜⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡈⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣠⡄⢠⣿⣿⣿⣿⣇⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡄⣴⣿⣷⣿⣿⡟⢿⣿⣿⣿⣿⣿⣇⢠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⡟⠈⢻⠇⠀⠘⠋⢻⣿⣿⣿⠞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣀⣠⡏⣙⠇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣤⣾⡸⣆⣀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢡⠱⢻⡀⣼⣿⣿⡇⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⡇⣿⣿⣧⣀⡟⠎⡌⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢫⡳⣄⠰⢦⠘⣀⣄⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⣿⣿⣿⢰⣀⠃⡴⠂⣠⢞⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠃⠀⠱⣭⣾⣿⣿⣇⣝⠷⢹⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠟⣻⣿⣿⣷⣭⠎⠀⠘⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⣳⣌⢻⣿⣿⢿⣹⣷⣌⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡿⣿⣿⣟⣡⣞⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠗⠛⣛⣛⠛⠛⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⣿⣿⡛⠺⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡿⠞⠁⣀⣀⣀⠀⢀⡀⠀⠹⠶⠶⠶⠶⠶⠶⠶⠶⠏⠀⢀⣀⡀⠀⣀⠀⠈⠳⣿⡻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⢀⡯⠟⢹⡀⠈⠉⠀⠀⠀⠀⢀⣀⣈⡀⠀⠀⠀⠠⠋⠉⠀⣞⠉⣹⠀⠀⠈⠻⣟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⡀⢸⣏⡉⠳⣤⠛⢉⣽⡇⠀⢀⣀⣀⠻⠭⠭⠟⣀⣀⡀⠀⢠⡞⠓⡎⠛⢡⠞⠳⡄⠀⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢰⠇⠘⠓⠳⡞⠈⢳⠞⠚⠃⣴⢫⠀⠈⢳⡄⢀⡞⡁⠀⠙⣦⠈⠓⠞⣡⠶⢬⠳⠞⠁⠀⠈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏⠸⠀⠀⠀⠀⠷⠷⠾⠀⠀⠀⠻⣜⠳⢂⣼⣿⣿⣧⡛⠦⣠⠟⠀⠀⠀⠻⢤⠞⠀⠀⠀⠀⣆⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⢱⠀⠀⠀⠀⠀⠀⠠⠄⣠⣴⠆⣈⣭⣭⣤⣭⣭⣤⣭⣭⣁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢾⡿⣼⠟⢡⢞⣁⣀⢀⣀⡀⣀⠀⣀⢀⣈⠳⡌⠻⣦⣄⠀⠀⠀⠀⠀⠀⠐⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣷⠀⠀⠀⠀⠀⠀⣠⡾⢃⡴⠋⢸⡇⣤⣸⣭⡗⣿⣾⣿⢸⡧⠀⠙⢦⡘⢿⣷⠀⠀⠀⠀⠀⠀⣠⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⣿⠀⠀⠀⠀⠀⠰⠏⣠⠞⠀⠀⠘⠳⠟⠘⠀⠛⠛⠋⠛⠘⠳⠂⠀⠀⠳⣄⠹⠀⠀⠀⡀⠀⠀⣿⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣷⣦⣀⣀⠀⢀⣾⠁⠀⠀⠀⠀⢉⡿⢸⡟⣿⣿⣶⡇⣿⣉⠀⠀⠀⠀⠈⣳⡀⠀⣘⣿⣩⣾⣿⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡙⠛⠟⠛⣉⣴⣻⣦⢳⡀⠀⠀⠀⢼⣧⢸⣧⡿⢿⠹⡇⣿⡤⠀⠀⠀⢀⡞⣵⣟⣦⣈⠛⠻⠛⢋⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⢿⣿⣿⣧⣙⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣋⣼⣿⣿⡿⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠀⠀⠀⠀⢄
⠀⠈⠒⠤⢤⠤⢄⣀⣁⡀⠀⠀⠀⠠⠤⠄⣀⢣⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⡀⣑⠀⠀⠀⠘⠆⢧⡄⠀⠀⡱⠊⢍⡉⠉⠐⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠀⠀⠀⠠⡀⡀⡀⠀⣄⢀⠀⠠⣀⠀⡀⠀⠃⠔⢱⢸⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⡄⠐⠒⠁⠇⠀⠠⡀⢠⠀⣀⠀⠠⠂⠉⠻⣄⠀⠀⡸⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⠚⠀⣬⡀⠀⢀⣱⢀⢀⣀⠞⣧⣤⣤⣴⠏⡷⠊⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⢾⠈⠙⠿⠍⠉⣼⠄⢠⡀⠀⠈⠉⢀⣼⡅⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣼⣦⣤⣠⣤⣶⠗⠛⠻⣌⣐⣓⣫⠽⠷⣄⠠⡀⠀⠀⠀⠀⠀⠈⣇⠄
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠉⠉⠀⠄⠀⠀⠀⠘⠛⠒⠒⠒⠾⢷⣾⣦⠀⠀⠀⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⢥⠀⠀⠀⠀⢻⠿
⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠠⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠘⢎⠓⠤⡄⠤⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣈⢉⣹⠧⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠴⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢧
⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢾⢾
⠀⠀⠀⠀⠀⠘⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞
⠀⠀⠀⠀⠀⠀⣟⣠⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣤⣵⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⢦⡀⠸⡅⠈⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣆⣬⢽⡀⠀⠀⣠⣤⡴⠦⡿⣅⠈⢸⡇⢠⡇⠀⡇⢀⣴⣶⣾⡿⠿⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢰⠃⠀⠰⣩⣯⡉⠰⣇⣼⣇⠀⢳⣸⣿⣦⡷⠋⢩⣴⣶⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⣤⣷⣤⣀⣿⣿⣷⠀⠻⢿⣿⣦⣤⠽⣯⣷⣶⣶⡿⣋⣵⢖⠛⣻⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣭⠾⠟⣛⣭⣴⣶⣮⣭⣿⣦⡶⠞⣿⣷⣤⠀⢿⣿⣿⣿⣵⣿⢿⣼⣾⣿⢟⣛⣻⣿⣦
⠀⠀⠀⠀⠀⠀⡞⣀⣰⣿⣻⣿⣟⣛⠿⣿⣿⣿⣷⣦⠈⠻⣿⣷⣦⣿⣿⣿⣿⣴⣼⣾⡿⠿⣿⣶⣿⡟⣿⣧
⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⣯⣭⢻⣿⣿⣮⢿⣿⣿⡿⠿⠾⠿⠋⢻⡉⠻⠿⢿⣾⣿⣿⣿⣿⣼⣿⡿⣱⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⠿⢛⣙⠿⣵⣦⡌⣿⣿⣿⣿⣿⣶⣤⣶⣤⡿⠤⢤⣤⣄⣀⡏⠀⠟⢻⣿⣿⣵⣿⣿⣿⡿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣗⢿⣿⣷⣿⣿⣷⣿⣿⣿⡿⢛⣛⢻⣿⣟⢴⣿⣷⣿⣿⠟⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡙⣆
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣇⣿⣻⣷⣿⣿⣾⣿⣿⠟⠁⢀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣭⣭⣭⣭⣾⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⡯⠀⢀⡎⠀⠀⠀⠙⠮⣽⣿⡿⠿⠿⣿⠟⡼
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠻⣿⣿⠛⠋⠀⣽⣿⢤⣤⣂⡼⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠊
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⡿⢣⢻⢦⣀⣹⣧⣀⠀⢜⣻⠁⣀⣽⠇
⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣶⡇⠀⢠⠃⠈⡷⠤⢤⣾⣟⣛⠛⠛⣋⡩⠏
⠀⠀⠀⠀⠀⠀⠙⢬⣛⠿⠿⣁⡴⠋⠀⠀⠉⠋⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣦⣰⣦⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣤⣤⣽⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡿⠉⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣷⠟⠑⠂⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣤⣎⣁⣠⣤⣤⠠⢬⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⣿⣩⢹⡿⣿⡟⢡⣾⣿⣫⣿⣥⣼⢿⣿⣿⣧⣀⢹⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠈⣿⣿⣿⣿⡟⢻⣇⣿⣦⡿⣼⣿⣿⣾⣿⣿⣿⡿⣿⣛⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢻⣿⠉⣿⠀⢸⣿⣎⢿⡇⣿⣿⣿⣷⣤⣼⣿⣿⠉⢵⣶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠘⣿⣧⣿⣄⢠⣿⣿⣷⡇⣿⣿⣏⡻⠉⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣯⣿⣿⠛⢻⣿⣿⣃⣴⣶⣶⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⢿⣿⣿⡉⢸⣿⣿⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣾⢿⣿⣤⣬⣏⣖⡿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⣿⠛⠛⠉⣿⣤⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣿⣷⣿⣶⣶⣿⣿⣽⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣾⣿⡿⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⢀⡀
⠀⠀⠀⢰⣦⡀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⣼⣷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄⠈⠢⠀⠀⠀⠀⠀⡀⡀⡠⠂⠀⠘⠁⠀⢀⡴⠤⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠱⡀⠀⠀⠀⠀⢀⠈⠀⠘⡀⠀⠀⢸⠋⠹⠇⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⢢⣼⣄⡀⠀⠰⠆⠀⢸⡀⠀⡆⠀⠀⠈⠁⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠗⢾⠁⠀⠈⢧⣠⣴⡦⠤⠾⠀⠀⣹⡄⢀⠔⢀⠀⠦⠸⣦⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⣀⣤⣴⣾⡟⠟⢿⠐⠀⠙⠢⣀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢰⠀⠀⢘⣦⣤⣴⣾⣿⣿⣿⣿⣿⣄⠴⣬⣧⡀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣄⡼⠀⠂⠀⣸⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣄⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠒⠊⠀⣿⣇⣸⣦⣿⣿⣿⣿⣽⠿⠛⠛⠉⠀⠀⠀⢀⣾⣿⣷⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡅⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠙⢿⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⢀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⠌⢂⠀⢸⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣙⣏⣍⣹⣏⣽⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⣀⠀⠀⣤⠤⣴⡟⠉⢙⣶⠾⠛⠲⣄⠀⣾⠟⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣁⣀⣀⡀⠈⠓⢾⣇⣀⣿⠁⠀⢸⡇⠀⠀⠀⠘⡄⣿⣀⣤⠴⠗⠒⠀⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠚⠉⣥⣶⡍⠙⢷⣄⠀⠉⠉⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⢻⠉⢀⠴⠞⢛⣛⡛⠶⣌⣆
⠀⠀⠀⠀⠀⠀⢀⡟⢀⣤⡀⠙⠿⠃⣀⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢿⣿⠇⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⣸⠁⠻⣿⠏⠀⠀⠐⣿⣿⠀⡇⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⣿⡇⠀⠀⢠⣿⣿⠘⣷
⠀⠀⠀⠀⠀⠀⣿⠀⢦⡀⠀⣾⣿⡆⠀⠀⠘⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⡈⠉⠁⣴⣶⡀⠙⠋⠰⢻
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠙⠲⠾⠭⠤⣠⠖⣂⣀⡀⠀⣷⠀⠀⠠⠈⠠⡀⠀⢀⠤⢒⡂⠙⠦⣄⣻⠟⢁⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠁⡾⠉⠉⢻⡄⣿⡆⠀⠀⠀⠀⠘⣆⠀⡼⠋⠙⢷⠀⡄⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣠⡾⢡⣏⣿⡄⠀⠀⠀⠔⠉⠳⣷⣀⣀⡾⢡⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⠲⠬⠤⠶⠋⠀⠈⠻⣤⡀⠀⠀⠀⠀⠙⢏⣩⣴⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠈⣧⡈⣿⣿⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢀⡜⠀⢿⣇⠀⠀⠀⠀⠀⠀⣰⣿⢿⡇⠀⠀⠀⠀⠚⠁⣿⠏⢿⣷⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡤⠴⠋⠀⠀⠸⣿⡀⠀⠀⠀⠀⢠⣿⠃⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣿⣄⡀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⢸⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣀⣠⣶⡾⠛⠛⢻⣿⣶⣦⣄⣀⣀⣀⣀⣀⣰⣿⣿⣁⣀⣀⣻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣠⡾⠿⣛⣛⣛⠻⢭⣍⡉⠉⠙⠛⠿⣿⣿⣿⣆⠀⣼⣿⣿⣷⣿⣿⡿⠛⠉⢉⣩⠭⢟⣛⣛⡻⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⣾⣭⣽⣭⣻⣿⣮⡙⢮⡲⣄⣀⣈⣛⣿⣿⣿⠋⠉⢁⣀⣀⣀⠀⢀⠔⠉⠀⢰⡏⣩⣭⡙⣾⣷⣽⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⢳⣽⣀⣀⣀⣿⣟⣿⠀⣾⣇⣀⣀⡼⢠⠏⠀⠀⠀⢸⡟⢿⣿⢟⣿⣿⣿⣷⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡇⡞⣻⣿⣿⣿⡙⠿⠛⣹⣿⣿⣿⢳⡌⣇⡿⠿⣿⣿⣿⣿⠀⠈⡹⠿⢿⡁⡏⣼⠛⣻⣿⡛⢃⡤⢤⡘⢛⣿⣟⠛⡆⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⡇⣿⣿⣿⣿⠇⣀⡘⣿⣿⣿⣿⢸⡇⡟⣳⣶⣾⣻⣿⣿⡀⠀⠳⠶⠾⠃⡇⣿⠸⣿⣿⠇⠘⢄⡠⠇⠺⣿⡿⠀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣧⢹⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⠿⣋⣀⣙⣛⠿⣿⣿⣿⣿⣷⡄⠀⡠⢖⣚⣁⣈⠻⢿⣿⣽⡇⣤⣤⣰⢿⣿⣿⣿⢡⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡻⣿⣿⣿⢿⣿⣿⢿⡿⣱⡾⠛⠁⠀⢨⣷⣌⢧⣹⣿⡿⢣⢞⣴⡿⠋⠀⠀⢩⣶⡹⣿⡟⢿⡿⢿⣿⣿⡿⣫⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣦⣍⣙⠓⠒⠒⣋⠀⡏⠀⠀⠀⣰⣿⡟⣻⢸⡿⣿⠀⣾⢸⡏⠀⠀⢀⣴⣿⠟⡇⢈⡛⠒⠒⢚⣉⣭⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠈⠙⠻⠿⣿⣿⣿⣿⡆⢿⣦⣠⣾⡟⣋⣴⡿⣸⣿⣿⣿⣿⡸⣷⣄⣴⣾⣟⣫⣼⠇⣾⣿⣿⣿⠿⠿⠛⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⢻⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⡙⠿⠿⠿⠿⢋⣴⣿⡟⠛⠛⣿⣷⣌⠻⠿⠿⠿⠟⣩⣾⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⢻⡄
⠀⠀⠀⠀⠀⡿⣾⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⡟⠛⠶⣶⣿⣿⣿⠏⠀⠀⠀⠈⢿⣿⠛⠳⢶⣾⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⢹⣿⣿⣿⠸⡇
⠀⠀⠀⠀⢸⡇⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣻⠏⠀⠈⠛⠳⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠲⠾⠿⠛⠉⠀⠈⢷⡹⣧⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿
⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⣸⣿⡟⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠃⠀⠀⠀⠀⠘⣿⣿⡇⣿
⠀⠀⠀⠀⠘⢧⡈⠓⠀⠀⠀⠚⣛⡵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠚⠛⠋⣠⠏
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⣾⣿⡀⠙⢿⣿⣿⣿⣿⡽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣯⣀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⡿⣆⠀⢿⣿⠀⣠⣾⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⣽⣿⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⣾⢹⣿⣿⣮⡻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⡏⣧
⠀⠀⠀⠀⢠⡏⣾⣿⣿⣿⣿⣶⣽⣿⣿⠟⣛⣟⡻⣿⣿⣿⣿⣿⣿⢟⣻⣛⠿⣿⣿⣫⣶⣿⣿⣿⣿⣷⢻⡄
⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⢹⣿⣿⣿⣿⡏⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⣾⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣮⣛⣛⣵⡿⠋⠉⠉⠙⢿⣮⣛⣛⣵⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷
⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⢸⣇⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⣸⡏
⠀⠀⠀⠀⠀⠻⣦⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠈⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠉⠀⠀⠉⣹⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣭⣭⣿⣿⣿⡏⠀⣹⣾⡁⠀⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡁⠀⣹⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢷⣄⣀⣴⠟⠛⠛⠛⠛⠻⣦⣀⣠⡾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⣀⣀⠀⣀⣀⡀⣀⡀⢀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⢀⡀⠀⡀⠀⢀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣿⢸⡏⢹⡇⣿⠽⣇⢹⡇⣿⠀⠀⣿⠭⠁⠀⣾⠉⣥⢀⣟⣷⠀⡿⣦⣿⡇⣿⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠙⠈⠓⠛⠃⠛⠛⠋⠛⠃⠛⠛⠃⠛⠛⠃⠀⠙⠓⠛⠘⠉⠙⠃⠃⠀⠘⠃⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠤⢀⢀⣀⣀⣀⣀⣀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣴⠚⣻⣿⣿⣭⢏⠍⡩⠋⢊⢞⢅⠝⠉⠉⡩⢒⢅⢷⡵⠟⡛⡿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⢻⠋⢻⡟⠉⣿⠛⠙⣶⠛⠛⠓⢄⢼⠉⢉⣹⣗⡯⠚⠛⠲⣖⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣾⡆⠈⠃⢠⣿⠀⠀⣿⠀⣺⣦⠘⣿⠀⠛⢻⡞⠀⣴⢲⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⢱⢳⠀⠀⣼⣩⠀⠀⣿⡀⠚⠋⣰⢿⠀⠿⢽⣷⡄⠉⠋⠀⡸⣻⣧
⠀⠀⠀⠀⠀⠀⣿⢸⢼⠖⡹⣋⠁⣓⠖⣡⠳⡶⠫⡵⠚⠖⢖⡟⠃⠹⠓⠲⢏⡀⢺⣿
⠀⠀⠀⠀⠀⡃⣿⡋⢡⠞⢋⣉⡈⢳⣊⣸⠋⠉⢷⢞⡏⠱⣬⡟⠉⢿⡏⣉⣹⡆⢹⣿
⠀⠀⠀⠀⠀⠀⣿⡑⡞⠀⣿⡞⠛⢾⣷⡏⠸⠆⠸⡵⡇⢤⠹⢠⠄⢸⡇⣉⣉⡆⢸⣟
⠀⠀⠀⠀⠀⢠⢸⠊⡼⢄⣈⠛⢁⣈⣿⣀⡶⢦⠀⢿⡇⡼⡆⣸⡀⣸⡇⠙⠛⣗⢘⣿
⠀⠀⠀⠀⠀⠈⠘⣌⣁⣀⣝⣴⢃⣀⡨⡡⢋⡉⣏⣩⣞⢅⡀⡄⣟⡕⣟⣑⠉⣱⣩⡟
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠐⠀⠀⠀⠘⠛⢻⣿⣿⡿⣻⣿⣟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠓⣦⣤⣤⣤⡤⣤⣀⡀⠀⢀⡤⢤⣴⣏⡀⣀⣀⡴⠃
⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠀⠓⠖⠶⠖⠲⠖⠖⠖⠴⠰⠲⠂⠖⠖⠖⠒⠒⠋⠑⠒⠐⠀⠀⠀⠙⣷⠿⠖⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠉⠉⠙⠒⢠⣄⣶⠛⠉⠛⣌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⡢⠄⡤⢿⡄⠒⢲⢆⠀⠀⠀⠀⢸⣏⡓⠒⠚⣃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⢎⠕⢀⣭⠨⡅⠒⢨⠒⡱⡀⠀⠀⠀⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⢶⠂⠀⠀⠀⢀⠁⠲⡄⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠢⠛⠟⠐⠈⠂⠊⠐⠑⠂⠙⠺⠻⠓⠐