Hearts with stars Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡠⠄⠀⠀⠀⠀⡠⠐⠉
⠀⠀⠀⠀⠠⢀⢀⠐⠀⠀⠀⠀⠀⠀⠈⣤⡝⡅⠻⡀⠤⠂⠀⠀⠀⠀⠀⠀⠀⢰⠁⠠⠋⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠐⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⡘⠀⣠⣷⠀⡦⢀⣀⠀⠀⠀⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠒⠒⠀⣀⣀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⢄⠩⠉⠘⠎⣙⣛⠠⠀⠒⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢠⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠈⠉⣭⠼⠣⠤⠀⠒⠒⠒⠺⠃
⠀⠀⠀⠀⠀⠰⠂⠀⠉⠉⠁⣀⣤⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢨⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠤⠤⠜⠪⠄⠚⠣⠄⠚⠃⠚⠡⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⠀⠀⡆⡄⠀⠀⠀⣰⠃⢀⠞
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⢀⠀⠀⠀⠪⠶⠀⢀⠃⠀⠀⣔⣁⠀⠉⢒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠰⠊⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡈⠁⡇⠀⠀⠀⡏⠀⡌⣠⠀⠀⣠⠎⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⠀⢜⡲⠀⢀⠀⠀⠀⢀⣀⣀⢀⡴⢦⡀⠀⠀⠀⠊⢸⠀⠠⢶⠀⢠⢡⡄⢡⠃⢀⠔⠁⠰⠃⣠⠄⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⢀⠔⢣
⠀⠀⠁⠀⠜⣸⠃⠀⢾⡄⠈⠛⠀⠀⡿⠀⠀⠀⠀⠀⡄⠄⢸⠀⠀⡰⢠⠃⠀⢉⠝⢁⡠⠊⠁⠀⠀⠀⠀⠀⠀⢀⠴⠁⠐⠈⠀⠀⠀⠀⠀⠄⠐⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⣦⡀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡥⠁⢀⡔⡡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⠁⠰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⢀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠓
⠀⠀⠠⡀⠛⢀⠇⠀⠀⠀⠀⠀⠀⠔⡂⠀⢢⠀⠀⡆⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⠄⠀⠀⠀⡰⠂⠀⠀⢆
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⡸⢀⠜⡜⠀⢰⠁⠀⠀⠛⠛⠀⠀⠀⠂⠀⠀⢰⠀⣼⠀⣼⠀⡰⠂⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢈⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠋⠉⠀⠉⠀⠉⠇
⠀⠀⠀⠀⠀⢀⠀⠀⢠⠆⠀⠀⠀⠀⠈⡠⡄⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⠴⠶⠶⠦⠤
⠀⠀⠀⠀⠄⠘⠇⠀⠀⠀⢯⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⢋⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⡿⡂⠀⠀⠀⠀⠀⠀⡜⠀⡆⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠃
⠀⠀⠀⠐⠋⢰⠀⢰⡀⠰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡻⣿⣿⣿⣄⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠃⠀⠀⠀⠀⠀⠀⠀⠰⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣤⣄⠀⠀⣀⣤⣶⣿⡟⠉⠉⠉⠙⠛⠷⢦⣄⠀⠀⠀⠀⣀⣴⠶⠛⠛⠉⠉⠉⠙⠛⠷⣦⣄
⠀⠀⠀⠀⢿⡉⠛⠾⡿⠟⠋⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠛⠛⣶⠶⣦⠀⠀⣰⠶⠶⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠘⣧⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣄
⠀⠀⠀⠀⢻⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⢿⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⠟⠹⣧
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠀⢰⡏
⠀⠀⠀⠀⣠⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣤⠾⢻⡟⠀⢀⣴⠟
⠀⠀⠀⠀⣿⣰⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠳⢿⣭⣴⠾⢻⣯⡴⠛⠁
⠀⠀⠀⠀⠙⣿⣄⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉⣿⠀⠀⠈⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⢯⣉⠛⢿⡟⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣿⣦⣄⣀⣀⣀⣀⣤⣤⣤⣤⣤⠴⠶⠶⠶⠞⠛⠛⠉⠻⠿⠶⣤⣤⡀⠀⠀⣤⣤⡴⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⢷⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡴⠾⠛⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⠀⠂⠠⠐⠃⠈⠈⠛⠃⠀⣀⠀⠂⠰⠐⠃⠀⡈⠛⠃⠀⣀⠀⠂⠰⠐⠃⠈⡈⠛⠃⠀⣀⠀⠂⠰⠐⠃⠈⡈⠛
⠀⠀⠀⠋⠀⠀⠀⣠⡄⠒⠀⠀⠀⠀⠋⠀⠀⠀⣠⡄⠒⠀⠀⠀⠀⠋⠀⠀⠀⣤⡄⠒⠀⠀⠀⠀⠛⠀⠀⠀⣠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠾⠇⠀⠾⠆⠀⠐⠂⠷⠀⠀⠾⠇⠀⠾⠆⠀⠐⠂⠗⠀⠀⠾⠇⠀⠾⠆⠀⠐⠂⠗⠀⠀⠾⠇⠀⠾⠆⠀⠐⠂⠗
⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀⡀
⠀⠚⠀⡀⢈⢀⡄⠀⠰⣿⡆⠀⠚⠀⡀⢈⢀⡄⠀⠰⣿⡦⠀⠒⠀⡀⠈⢀⡄⠠⠰⣿⡆⠀⠒⠀⡀⢈⢀⡄⠠⠰⣿
⠀⠒⠀⡤⠈⠀⠀⠀⠂⣀⠠⠀⠒⠀⣤⠈⠀⠀⠀⠂⣀⠀⠀⠒⠀⣤⠈⠀⠀⠀⠂⣀⠠⠀⠒⠀⣤⠈⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠾⠇
⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄
⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠁
⠁⣀⠀⠀⠰⠂⠀⠀⢀⣤⡀⠁⣀⠀⠀⠰⠂⠀⠀⢀⣤⡀⠀⣈⠀⠀⠰⠀⠀⠀⢀⣤⡀⠀⣀⠀⠀⠰⠂⠀⠀⢀⣤
⠀⣀⠀⠂⠰⠐⠃⠀⠈⠛⠃⠀⣀⠀⠀⠰⠐⠃⠀⠈⠛⠋⠀⣀⠀⠀⠰⠐⠃⠀⡈⠛⠃⠀⣀⠀⠂⠰⠐⠃⠀⠈⠛
⠀⠀⠀⠋⠀⠀⠀⣤⡄⠒⠈⠀⠀⠀⠛⠀⠀⠀⣤⡄⠒⠀⠀⠀⠀⠛⠀⠀⠀⣤⡄⠒⠀⠀⠀⠀⠛⠀⠀⠀⣤⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠺⠇⠀⠾⠆⠀⠐⠂⠗⠀⠀⠺⠇⠀⠾⠆⠀⠐⠂⠗⠀⠀⠾⠇⠀⠾⠆⠀⠐⠂⠗⠀⠀⠺⠇⠀⠾⠆⠀⠐⠂⠗
⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠚⠀⡀⢈⢀⡄⠀⢰⣿⡦⠀⠒⠀⠀⢈⢀⡄⠀⠰⣿⡆⠀⠚⠀⠀⢈⢀⡄⠀⠰⣿⡆⠀⠒⠀⠀⢈⢀⡄⠠⠰⣿
⠀⠖⠀⡤⠈⠀⠀⠀⠂⣀⠀⠀⠒⠀⡤⠈⠀⠀⠀⠂⣀⠀⠀⠲⠀⡤⠈⠀⠀⠀⠂⣀⠀⠀⠒⠀⣤⠈⠀⠀⠀⠂⣀
⠀⡁⠀⠀⠀⠀⠀⠿⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄⠀⠀⣠⡄⠀⣠⡀⠀⢀⡀⣄
⠘⡁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠘⠁⠀⠉⠁
⠁⣁⠀⠀⠰⠂⠀⠀⢀⣤⡀⠁⣀⠀⠀⠰⠂⠀⠀⢀⣤⡀⠀⣀⠀⠀⠰⠂⠀⠀⢀⣤⠀⠁⣀⠀⠀⠰⠂⠀⠀⢀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⣤⠉⠦⠀⠿⠂⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⠀⣤⡁⠛⠋⢃⡄⠠⢠
⠀⠀⠀⠀⠀⠀⢰⣷⠠⠐⢾⣿⡷⠊⢡⣴⣷⣤⡙⡇⢠⣄⠀⠀⠀⢀⠠⡸⠿⠰⠈⢻⣿⣿⠁⠲⣾⣿⡶⠀⣡⣄⡀
⠀⠀⠀⢀⠼⢃⣠⣆⣈⠤⠛⠉⠻⠔⣀⣿⠿⡏⠀⢀⣦⠀⠀⢂⠠⢚⣀⣶⣄⡙⣠⣉⠉⢹⡔⠄⢛⠙⠧⢄⠽⢿⠀⢣⡄
⠀⠀⢀⣀⠃⠈⣿⣿⡏⠠⠸⢟⠀⠛⢨⠁⠔⣂⠙⣿⣿⡟⠑⣨⡘⠀⣹⣿⣿⢁⣌⠁⠴⢀⣠⣦⣀⠠⣤⣾⣦⡌⢾⡆⣐
⠀⠀⣨⡟⣤⣦⡅⠀⣁⣼⣆⣈⠐⢶⣿⣷⠖⠸⠆⠉⢈⣡⡈⠿⡟⠀⣬⡀⢊⣤⡉⠀⠶⠈⣿⣿⡏⠀⢸⠿⢿⠀⢡⡄⠉⢀
⠀⠀⢘⣄⠘⠛⣠⡁⢹⣿⣿⢁⠠⡸⢛⠻⠤⣂⢲⣿⠆⠉⣀⣼⣆⣀⠩⠶⠹⠿⠇⣘⠃⠨⣡⡀⢡⠄⠲⢆⣀⠻⣿⣿⡟⢉⡀
⠀⠀⠈⢉⣤⠀⠛⣥⡄⠶⠰⠎⠁⣴⡈⠰⢷⠀⢋⠈⠸⡄⢸⡿⣿⡁⠴⠰⣶⠐⣶⣿⣷⠆⠉⠃⣁⣼⣦⣈⠰⠖⠋⢉⣗⢢
⠀⠀⠘⣿⣿⡿⠃⠉⢡⣆⠘⠉⢻⣿⣿⠃⡀⢶⣾⣷⡦⢰⣦⠀⣠⣧⡠⢆⠣⠄⠚⠛⠻⠐⠿⠂⢸⡿⢿⣁⠐⣾⣷⢊⡹⠂
⠀⠀⠀⢫⠉⣉⠐⠙⣿⣿⡟⠀⠚⢁⠉⠀⡁⠸⠟⠻⡄⢶⠌⢃⠘⠛⣣⡉⢠⣴⣷⣤⠘⠃⣠⠘⢋⡐⠄⢀⣤⠉⢉⡼⠁
⠀⠀⠀⠀⢹⡿⡏⠀⣉⠈⠁⢾⣷⠆⠰⣾⣿⡶⠘⠃⡘⠠⣴⣿⣦⠄⠉⠃⠀⡿⠿⡇⠀⢿⣿⣿⠃⢶⠘⣿⣿⡟⠁⠌
⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⠂⠩⠍⠆⣠⠟⠛⠇⢀⡸⠋⠄⠼⠛⠿⠤⡄⠾⠆⠠⠄⡶⢀⣞⠉⠙⢀⣤⡀⠋⢩⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠚⢋⡛⢤⣴⣷⣤⠉⠉⠈⡿⢉⣠⣾⣦⣈⠷⠺⠇⡀⣤⣾⣧⡤⡀⢹⠿⠁⠘⣿⣿⡿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡿⠿⡇⠰⣾⡶⢠⡄⢹⡿⣿⠁⠰⣾⡖⢠⢸⠟⠿⣠⠀⠩⣦⢈⣤⣉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⣈⠉⢁⣦⠀⠛⠤⡈⣁⣄⡡⢱⡆⠐⢆⠀⣠⣼⣦⣀⡸⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠙⣿⣿⡟⠁⠒⠁⣽⠻⣁⣠⣷⣀⡈⠁⢸⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡍⢣⣤⣿⣤⡌⠶⡈⣿⣿⡏⠐⣶⡈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣏⣀⢲⣶⢀⠀⣶⠴⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢉⣠⣦⣀⠛⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠤⣤⡀⠘⠃⠀⠀⠀⠀⡟⠀⠀⢀⠔⠁⠠⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢰⡇⠀⣴⠃⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣵⠆⠀⢸⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢸⣿⣇⣠⡿⠉⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⣸⣷⣿⠉⠀⠀⣠⡤⠶⣿⡷⣹⣿⡧⠤⠴⠞⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⣼⣿⡟⠁⠀⢀⣼⣿⠗⠒⠊⠁⠉⠀⠀⠀⢀⣀⣠⣴⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣯⢿⣷⠂⠀⠀⢼⣿⣿⡇⠀⠀⠀⢀⡴⠶⠟⠻⢿⣟⣛⣛⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣋⡔⣿⣶⡀⠀⣺⣿⣿⠁⠀⠀⢀⡎⠀⠀⠀⠀⠀⡾⠛⠿⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⣿⣎⣿⣿⣴⣶⡾⠋⡀⡀⠀⠀⣼⠁⢀⣰⠦⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣧⡾⠋⠉⠻⣿⣢⡾⠃⠀⠀⢸⣷⣾⠏⠁⠀⠈⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⢹⠧⣰⠀⠀⢹⣿⡟⢠⡄⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣷⣤⣧⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠙⠻⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⢣⡀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠤⠊⠁⢸⡇⠀⠀⢳⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠘⠄⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⡀⠀⠀⠀⢠⡟⠀⢧⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠤⢀⣠⡟⠀⠀⠀⠀⠀⣈⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣗⢠⣄⣤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⠏⠁⠉⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⡟⠉⠈⠙⡿⠋⠀⠉⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⠾⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡏⠁⠀⠈⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠙⠛⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⣿⣿⣧⣤⣤⣀⡀⠀⠀⠀⠀⣀⣠⣤⡤⠞⠀⣿⣷⣤⣤⣄⣀⠀⠀⠀⠀⢀⣠⣤⣤⠾⠋⠀⠙⠷⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⠞⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣤⠶⠛⠦⣄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠤⠀⠀⠀⠀⠀⠀⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠤⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣄⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⢰⣶⠄
⠘⠿⠂⠀⣀⡀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠛⠁
⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁
⠀⠀⠀⠀⠐
⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁
⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠁⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠄
⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣟⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⠀⠀⠐⢄⠌⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⢄⠌⠀⠀⠀⠀⠀⠠⢤
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠈⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠁⠈⢀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠁⠒⠀⠀⠀⠀⢰⢔⠀⠀⠀⣀⠀⣀⠀⠀⠀⠔⠀⠀⠁⠲⠀⠀⠀⠀⢰⢔⠀⠀⠀⣀⠀⣀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⢸⠉⠛⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⢸⠉⠛⢀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠌⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠌
⠐⢄⡀⢀⠤⢄⢀⠤⡀⠀⠀⠀⠀⠌⠀⠠⢀⣀⠀⠀⠐⢄⡀⢀⠤⢄⢀⠤⡀⠀⠀⠀⠀⠄⠀⠠⢀⣀
⠀⠀⠀⠈⠀⠈⠇⠀⠇⠀⠀⠀⠀⠀⠀⠴⡿⠓⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠰⡿⠓
⠀⠀⠀⠈⡄⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠌
⡄⠀⠀⠀⠐⢄⠌⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⢄⠌⠀⠀⠀⠀⠀⠀⢤
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠈⢀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠁⠈⢀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠒⠀⠀⠀⠀⢰⢔⠀⠀⠀⣀⠀⣀⠀⠀⠀⠔⠀⠀⠀⠲⠀⠀⠀⠀⢲⢴⠀⠀⠀⣀⠀⣀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⢸⠉⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⢸⠉⠛⢀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠌⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠌
⠐⢄⡀⢀⠤⢄⢀⠤⡀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠐⢄⡀⢀⠤⢄⢀⠤⡀⠀⠀⠀⠀⠄⠀⠠⢀⡀
⠀⠀⠀⠈⠀⠈⠇⠀⠇⠀⠀⠀⠀⠀⠀⠰⡿⠓⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠆⠀⠀⠀⠀⠀⠀⠰⡿⠓
⠀⠀⠀⠈⡄⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠌

⠀⣀⠀⠐⠠⠄⠒⠀⠀⠛⠛⠀⢀⡀⠀⠂⠤⠐⡃⠀⠘⠛⠃⠀⣀⠀⠐⠠⠄⠒⠀⠀⠛⠛⠀⢀⡀⠀⠂⠤⠐⠂⠀⠘⠛
⠀⠈⠀⠚⠀⠀⠀⢀⣄⠐⠀⠁⠀⠁⠐⠃⠀⠀⠀⣠⡁⠂⠈⠀⠈⠀⠚⠀⠀⠀⢀⣌⠐⠀⠁⠀⠁⠐⠃⠀⠀⠀⣠⡀⠂
⠀⠀⠈⠀⠀⠀⠀⠈⠉⠀⠰⠄⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠆⠀⠀⠈⠀⠀⠀⠀⠈⠉⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⢴⡦⠀⢴⡦⠀⠀⠆⠲⠆⠀⠠⣶⠄⠠⣶⠄⠀⠰⠐⠶⠀⠀⢴⡦⠀⢴⡦⠀⠀⠆⠲⠆⠀⠠⣶⠄⠠⣶⠄⠀⠰⠐⠶
⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠴⠄⠀⠘⠃⠀⠀⠀⣴⣦⠀⠠⠦⠀⠀⠛⠀⠀⠀⢠⣶⡀⠀⠴⠀⠀⠘⠃⠀⠀⠀⣴⣦⠀⠠⠦⠀⠀⠛⠀⠀⠀⢠⣶
⠀⢤⠀⢈⠐⠂⠉⠀⠀⠉⠉⡀⠠⡄⠀⡁⠒⠈⠁⠀⠈⠉⢁⠀⢤⠀⢈⠐⠂⠉⠀⠀⠉⠉⡀⠠⡄⠀⡁⠒⠈⠁⠀⠈⠉
⠀⠀⠀⠉⠀⠀⠀⢠⣦⠈⠀⠀⠀⠀⡈⠁⠀⠀⠀⣴⡄⠁⠀⠀⠀⢀⠉⠀⠀⠀⢠⣦⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠺⠗⠀⠸⠗⠀⠀⠃⠙⠃⠀⠐⠿⠂⠐⠿⠂⠀⠘⠈⠛⠀⠀⠺⠗⠀⠺⠗⠀⠀⠃⠙⠃⠀⠐⠿⠂⠐⠿⠂⠀⠘⠈⠛
⠄⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⣀
⠀⠚⠂⢀⠈⠁⣀⠀⠀⣾⣷⠀⠐⠓⠀⡀⠉⢀⡀⠀⢰⣿⡆⠀⠚⠀⠀⠈⠁⣀⠀⠀⣾⣷⠀⠐⠓⠀⡀⠉⢀⡀⠀⢰⣿
⠀⠲⠀⣠⠈⠁⠀⠀⠀⢀⠀⠄⠐⠆⢀⡄⠉⠀⠀⠀⠀⡀⠠⠀⠲⠀⣠⠈⠁⠀⠀⠠⢀⠀⠄⠐⠆⢀⡄⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠾⠆⠀⣀⠀⠀⠠⠀⠀⠀⠀⠰⠷⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠾⠆
⢀⡀⠀⢀⡀⠀⠀⡀⣀⡀⠈⠀⣀⠀⠀⣀⠀⠀⢀⢀⣀⠀⠉⢀⡀⠀⢀⡀⠀⠀⡀⣀⡀⠈⠀⣀⠀⠀⣀⠀⠀⢀⠀⣀
⠙⠋⠀⠘⠋⠀⠀⠁⠈⠁⠀⠈⠛⠁⠈⠛⠀⠀⠈⠀⠉⠀⠀⠙⠋⠀⠙⠋⠀⠀⠁⠈⠁⠀⠈⠛⠁⠈⠛⠁⠀⠈⠀⠉
⠂⢈⠀⠀⢠⡄⠀⠀⠀⢀⡀⠐⠀⡁⠀⠀⣤⠀⠀⠀⠀⣀⠀⠂⢈⠀⠀⢠⡄⠀⠀⠀⢀⡀⠐⠀⡁⠀⠀⣤⠀⠀⠀⠀⣀
⠀⠉⠀⠠⢀⡀⠤⠀⠀⠿⠿⠀⠈⠁⠀⠀⣀⠠⠄⠀⠸⠿⠆⠀⠉⠀⠀⢀⡀⠤⠀⠀⠿⠷⠀⠈⠉⠀⠀⣀⠠⠄⠀⠸⠿
⠀⠙⠀⠴⠀⠀⠀⠀⡐⠠⠀⠂⠈⠃⠠⠆⠀⠀⠁⢀⠂⠄⠐⠀⠙⠀⠴⠀⠀⠀⠀⡐⠠⠀⠂⠈⠃⠠⠆⠀⠀⠀⢀⠂⠄
⠀⠀⠐⠀⠀⠀⠀⠘⠛⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠛⠃⠀⣄⠀⠀⠐⠀⠀⠀⠀⠘⠛⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠛⠃
⣠⣄⠀⣠⣄⠀⠀⡄⢤⡄⠀⢀⣤⡀⢀⣤⡀⠀⢠⠠⣤⠀⠀⣠⣄⠀⣠⣄⠀⠀⡄⢤⡄⠀⢀⣤⡀⢀⣤⡀⠀⢠⠠⣤
⠈⢁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠉
⠁⣠⠀⠀⠰⠆⠀⠀⠀⣠⡄⠈⢀⡄⠀⠀⠶⠀⠀⠀⢀⣤⠀⠁⣠⡀⠀⠰⠆⠀⠀⠀⣠⣄⠈⢀⣄⠀⠀⠲⠀⠀⠀⢀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⡟⠁⠀⠀⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠛⠛⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠛⠻⠿⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠙⠁⠀⠉⠀⠈⠛⠁
⠀⠀⢀⡀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆
⠀⠀⠈⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⡿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠄
⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⢀⡴⣦⡀⠀⣠⣤⡀⠀⠀⠤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⣦⡱⢞⣷⣹⠇⠀⠀⠀⠐⠦
⢀⠀⠠⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣮⡻⢟⡵⠋⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤
⢘⡀⡇⣈⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣉⠈⠙⠄⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠
⠀⠻⠀⠙⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣮⣻⣷⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⠀⠢
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⠟⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⢤
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⣠⣤⣄
⣠⠞⣛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡏⣭⡻
⣫⣾⢋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡹⣿
⢟⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠠⠀⢠⠀⡴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢈⠀⡇⡜⢠⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠆⠑⠞⠀⠘⠃⠈⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠉⢀⣄⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⡞⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠰⣿⣷⣴⡾⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤
⠁⠰⠃⠀⠀⠀⢠⣶⡄⠀⠀⠀⠃⠀⠀⠀⠙⣟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡾⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣤⡀⠀⠀⠀⠠⣾⠄⠀⠀⠀⠀⠉
⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⢾⢭⡳⣴⣯⣷⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡻⣿⡿⠃⠀⠀⢀⣀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠸⠿
⡿⠛⠀⠀⠀⠀⠀⠀⣮⣦⣠⣒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⢡⢰⠀⠴⢠⠋⡆⠀⠀⠐⠻
⣃⣀⣀⣀⣀⣀⣀⣀⣛⣻⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣀⣠⣄⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣸⣈⣀⣃⣐⣚⣁⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⣀⣴⣶⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⢥⣾⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⡘⣿⣶⡘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣼⣿⣿⣌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠰⢾⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⣌⢻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠟⣡⣷⣘⠿⠃⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣤⣙⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⠤⠤⣠⠤⠤⢄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠀⠀⣀⣀⠤⠤⠤⠤⡃⠀⠀⠀⠋⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⣀⠤⠒⠉⠉⠀⢀⣀⡠⠤⠤⢧⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⢰⠋⠢⣀⡤⠊⠀⠀⢀⡠⠖⠉⠀⠀⣀⠤⠒⠋⠁⠀⢀⣀⠤⠤⠷⣄⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⣀⣀⠴⠟⠒⡄⢀⠴⠊⠁⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁⠀⠀⢀⡤⠊⠁
⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⡴⠋
⠀⠀⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⣠⠊
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣀⠀⠀⠈⢖⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⠞⠁⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢤⣄⡀⠀⢀⣠⡴⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠈⠻⣤⠟⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⣀⣠⣤⣤⠤⠟⠀⠀⠀⠈⠳⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣠⣄⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⡴⠞⠋⠁⠈⠙⠳⢦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣿⣿⣻⣦⣟⣿⣿⣾⣿⣷⡀⠀⠀⠀⠉⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢿⢟⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⡟⠿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣠⠶⠒⣲⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⡴⠻⡀⠀⣼⣁⣀⠀⢀⣙⢦⡀⠀⠀⠀⠀⢀⡤⠶⣏⠉⠉⠙⢍⡛⠲⣄⠀⠀⣠⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣸⡿⠀⠈⢳⠇⠀⠈⠉⢉⣀⠤⢵⡄⠀⠀⣰⠋⠀⠉⠊⠳⡀⠀⠀⠈⢉⣉⣻⠾⣿⣶⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⣏⠀⠀⢀⣎⣀⡠⠤⣴⡋⠀⠀⠠⣿⡀⡼⢁⣠⠤⢤⡤⡤⠽⠦⠤⠤⢤⡞⠹⡀⠀⠀⠁⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡴⠻⠷⠤⣀⣠⣿⡍⠉⠉⠁⠀⠀⠀⠀⠙⠢⣀⡀⠉⡿⠓⠉⠀⡰⠛⠂⠘⣆⠀⠀⣰⠏⠀⠳⠝⠦⣄⠴⠒⠉⠘⣇
⠀⠀⠀⠀⠀⣸⠁⠀⢀⣀⣠⣴⠃⠹⡾⠿⠷⠒⠒⠒⣲⣤⣀⡈⠉⢹⣧⡤⠴⠊⠁⠀⠀⣀⡬⠗⣾⡃⢀⡠⠖⠢⡄⠈⠳⣄⢀⠀⣿
⠀⠀⠀⠀⠀⣿⢀⣴⠁⠀⢰⡇⠀⠀⠙⣦⢄⡤⠔⠋⠁⠀⠉⠛⠒⣾⠀⣲⠵⠒⠋⠉⢹⠱⠂⡼⠁⡝⢍⡀⠀⠀⠹⡄⢸⠉⣎⢀⡇
⠀⠀⠀⠀⠀⢸⡡⣼⠀⠀⣾⡀⠀⠀⢀⡟⢦⠀⠀⠀⠀⢀⡴⠊⠉⣧⠞⡇⠀⠀⠀⠀⣸⢀⣼⠁⠀⠀⠀⠉⢢⡀⠀⠙⡏⠀⢸⡞
⠀⠀⠀⠀⠀⠈⣧⠋⠀⢀⠇⠱⡀⠀⡞⠀⠈⣷⡤⠿⠵⢯⣤⣀⠀⡏⡰⠃⣠⠤⡶⠚⠏⣹⠛⢦⣀⠤⠤⢄⣸⢳⠀⠀⢳⢀⡞
⠀⠀⠀⠀⠀⠀⠘⣆⠀⡞⠀⠀⡇⢸⠀⠀⢠⠇⢹⣄⠀⠀⠹⡌⠙⣟⡡⠊⠀⠀⡇⠀⢠⡏⠀⠀⠙⣦⡀⠀⡏⢸⠓⢄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⡇⢸⠀⢠⠇⠀⡜⠘⢦⡀⠀⠙⢤⣯⢀⡠⢂⡼⠁⢀⣼⢀⡀⠀⠀⡇⠹⡀⡇⠸⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣧⠞⠀⠸⣤⢾⠁⠀⠀⠻⣖⠲⣖⢿⡴⠚⠉⣠⢴⢏⡏⠳⣞⠉⠉⡇⠀⡇⣸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡏⠀⠀⢰⠃⢸⠀⠀⠀⠀⣿⣷⡌⠙⣇⡴⠋⡇⠀⢸⡇⠀⠈⣳⡀⢣⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⠋⠀⢈⡇⠀⠀⠀⢸⠃⠙⢦⣹⡄⣠⠃⢀⣼⡇⠀⣰⠁⣧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣈⣸⠀⠀⡰⢻⠀⠀⠀⢹⢿⣡⢴⣏⢸⡇⠀⠘⣄⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣇⠈⢧⠀⠀⢸⠢⢷⣼⠉⠈⣏⠲⣖⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠧⣤⣈⣣⠢⠹⣄⠀⣿⡌⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠻⣇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⢠⣶⡶⠀⣀⣰⠂⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠻⡁⠀⢲⣦⣄⠀⠀⠘⠦⠘⠆⠈⠓⠀⢠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⡀⠈⠛⠋⠀⠸⣿⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠇⠰⠂⡀
⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣁⡰⠋⣤
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⠁
⠀⠀⠀⢰⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠰⠦⣩⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡄
⠀⠘⠲⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃
⠀⠙⠓⠰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣶
⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠐⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⢠⡼⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠟⠁
⠀⠀⠀⠶⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⠶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤
⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⢿⣀⢞⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠓⠀⣦⠰⡄⢲⡀⠀⠀⠀⠘⠟⠡⠎⠶⠮⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢀⡝⣨⢁⡄⠀⠀⠈⠉⢾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⣾⣶⣶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⣒⣶⣤⣒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⢿⣿⣿⣿⣿⣿⣯⠐⠠⠐⢂⠐⢄⡀⠀⢀⢀⡤⠈⢛⢸⣿⣛⠋⠉⠳⠹⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣤⡿⣿⣿⣿⣿⣿⡟⣿⣿⢿⣷⢀⠁⠠⡦⠤⠹⣆⢀⣼⠄⠀⢴⡮⢙⣋⠘⡋⠠⠆⠕⢫⡿⠧
⠀⠀⠀⠀⠀⣀⡿⣧⣿⡟⠑⠽⡟⠀⠸⢿⣿⣽⢿⣧⠀⠘⠂⠰⠍⢹⠉⠰⠶⢈⣀⣜⠻⠛⢤⡤⢀⣴⠻⠉⢀⣶⡀
⠀⠀⠀⠀⠀⣿⣿⣼⡿⠁⠀⠰⡃⠀⠀⠀⠻⣿⡾⣹⣶⠀⠸⠷⢀⢾⠛⠰⠖⠈⠃⣀⣈⣶⡞⠴⠭⣀⡀⠙⠯⠌⣷⡀
⠀⠀⠀⠀⢰⣿⣎⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣏⣿⡾⢄⣰⠃⠸⠦⣀⣠⠽⠿⠉⠫⠙⢣⠙⠒⣤⡙⣅⠁⣀⣿⡇
⠀⠀⠀⠀⢀⣿⡙⣿⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⢹⣿⣾⡷⠋⠀⢠⣷⠔⣈⠤⠄⣢⢰⡄⠀⠀⡆⠄⢸⡟⢿⣁⣿⣿⡇
⠀⠀⠀⠀⠈⣿⡿⣾⣧⢀⠀⠀⢹⠀⠀⠀⡀⢀⡼⠋⢹⠁⠀⢀⣎⠔⢈⠁⣰⢖⣇⠀⠹⡷⠶⢟⠶⢼⡇⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣷⣬⣿⡆⠀⠀⠈⣧⠀⠀⡵⡟⠀⠰⢸⢠⢠⣟⡴⢶⠞⠉⢇⡌⠁⢢⣄⣈⣶⠴⢗⠛⣷⣼⢿⣿⡿
⠀⠀⠀⠀⠀⠀⣹⣮⣽⣿⡄⠀⠀⠘⣷⡾⠁⡁⠀⠨⠀⣾⣿⢉⢀⡏⢀⡴⠟⠛⠉⠉⠁⠀⣀⣤⣴⡾⠟⠑⣽⢿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣿⣄⠀⠄⣼⠁⠄⠐⡀⠀⣶⢃⠃⠸⢸⡟⠋⠀⠀⢀⣠⣴⣶⣿⠿⠛⠉⠀⣠⡞⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣿⣧⡀⢿⠇⠈⠀⠐⢼⣿⠘⣷⡸⢋⠔⢀⣠⣾⣿⠿⠟⠋⠀⢀⣠⣴⠾⢋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣿⣿⢧⠀⡀⠀⢸⡏⠀⡿⠡⠃⣴⣿⠟⠋⠀⣀⣤⣴⡾⠟⢋⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⡑⠦⡀⢌⡇⢸⢃⢁⣾⠟⢁⣴⣶⡿⠟⣋⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡠⡈⠑⢷⣼⢠⣿⡟⣴⡿⢛⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⠄⣧⢸⡟⣼⣫⠖⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⣿⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡷⠄

⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣟⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠈⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠗⣶⣹⠇⠀⢠⣤⡈⡆⠀⢠⡇⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⡁⣺⠗⠋⠀⠀⠀⠈⠙⣷⠀⠈⠀⠑⠀⠀⢀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢹⣿⢿⢇⠈⠀⠀⠀⠀⠀⠀⢄⠉⠀⠀⣀⣀⡀⠀⠈⠀⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠍⢻⣖⠂⣭⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠑⠀⢸⡯⢳⣻⣿⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠣⠀⠀⠀⠀⠀⢀⣬⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠔⠋⣀⠞⣡⢿⣇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠐⢚⡡⠞⣵⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡩⢒⣷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢶⣿⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠐⠋⠁⠃⠀⣏⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀
⣿⣟⣟⣿⣟⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣛⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⢠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⡿⠀⠀⣀⠘⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⠟⠡⣶⣾⣿⠇⡈⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣾⣿⣾⣿⡇⠐⢦⡈⠉⢛⡞⠘⢿⡧⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⠛⠿⠋⠀⢺⣷⠝⣦⣾⣠⡤⢄⡀⠛⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢀⡀⠀⠒⢤⣉⠉⠀⣾⢏⣴⡆⠿⠛⣤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡟⣤⣤⣄⠙⢷⣼⣿⠸⠿⣿⠆⠀⢻⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣬⠁⢬⣛⠡⣤⡤⣿⣿⢴⣤⡄⢀⡠⠌⢡⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠃⠹⡿⢈⠙⢾⣄⣿⣿⢀⣽⠞⠉⢺⡟⠈⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⢿⣿⡶⠙⣿⣿⡟⢡⣶⣶⣶⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⢸⣿⣇⠸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⠛⠛⠛⠛⠻⠶⠿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠋⠉⠉⠀⠀⠀⠀⣸⠀⢀
⠀⠀⠀⠀⠀⢀⣠⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠖⠉
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡠⠊
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡾⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠞⠀⠀⠀⠀⣀⠄⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠊⠁⢀⣀⣀⣴⠿⠁⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠈⠛⠯⣍⡓⠒⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠈⠙⠓⠶⢦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣶⣶⣶⣶⣖⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣀⠀⣀⡀⠀⢠⣀⡀⠀⠀⢀⣄⣿⡢⠤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠽⠉⢄⡉⠈⡉⠛⢉⡁⠚⣀⢍⠙⠉⠚⠁⡀⢈⠀⡀⠙⠹⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠒⣄⣤⠀⠐⡉⠦⢄⠖⠈⠀⠉⠤⣈⢡⠀⠠⣊⣀⢈⡆⠠⢌⠑⠠⢸⣇⣠⡀
⠀⠀⠀⠀⠀⢀⡀⠴⠚⠋⠀⢠⠱⠄⣀⠆⠘⠄⠀⠈⠧⡀⠀⠠⢠⠄⠀⢳⡈⠀⠀⠀⡗⠂⠀⡊⢓⡆⢉⠬⢧⣀
⠀⠀⠀⣀⡶⠚⠃⠄⣀⡘⠀⠠⠀⠀⠙⠠⠀⡀⠀⠀⠀⠘⢀⠀⠀⠒⠒⠂⠳⡀⠐⢠⠂⠀⠀⠑⣼⡔⠀⡀⠀⠜
⣤⠰⠒⢀⠵⢄⠐⠎⢀⡱⡌⠂⠀⠀⢉⠉⣙⣆⠀⠀⠀⠀⠈⢢⠀⠀⠐⠀⠀⢹⡄⡘⢀⣀⡖⢠⡏⠀⠤⢄⡸
⠈⡏⠙⠲⠤⣄⣛⢄⠈⠐⠘⢦⡈⠀⠀⠀⠁⠈⢧⠈⠉⠁⠤⠠⢱⡄⠠⠀⠊⠉⢷⡌⠠⠄⢀⡟⠀⣰⠒⢢⡃
⠀⠻⡰⠤⢤⠦⠭⠾⠗⠲⠤⢄⡱⢄⠀⠀⠠⠀⠐⢣⡀⠠⠤⢠⠄⠽⡄⠐⠒⠐⠘⣆⠀⠄⣸⠁⠠⠈⠂⡜⠁⠄
⠀⠈⣧⠠⠦⠤⠦⠴⡀⠦⠠⠶⠀⠙⠴⠠⣴⣄⠀⠈⠳⡀⠤⠐⠚⠂⠱⡀⠀⠊⣉⢹⠀⢰⡇⣀⣀⠀⡼⠄⠒
⠀⠀⠰⢇⠀⠂⠐⠀⢐⢀⠀⠰⠂⠢⣀⡄⠀⠈⣙⣻⣦⡷⠄⠀⠀⠂⢋⣻⡀⠄⢹⠌⢇⣼⠀⡀⢠⠎⠀⠠⠄⣀
⠀⠀⠀⢰⡃⠢⠡⢀⠆⠀⠡⠤⠄⠐⠚⠒⠛⠉⠉⠀⠀⠀⢁⠠⢤⡀⠉⠃⣧⠰⠚⠆⠚⡍⢂⣰⡃⠄⠼⠒⠋⣡
⠀⠀⠀⠀⠙⣦⣀⠀⠆⠀⠆⠀⠠⠀⠀⠀⣀⠘⠀⠰⠀⠃⠀⢠⠀⠈⠙⠲⣾⠷⠀⠘⠞⣿⣽⢋⠁⡀⣦⡠⣫⠟
⠀⠀⠀⠀⠀⢸⠇⢠⡀⠀⠀⠀⠀⠈⠺⠀⠈⠀⠈⢺⠀⠈⣢⣀⣥⠴⠒⠊⠉⠒⠲⣅⣲⢽⡿⣙⣩⡭⠴⠚⠉
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠉⡈⠁⠘⠓⠐⠓⠒⢲⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢄⠀⠣⣈⣙⣮⡃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠰⠞⢈⠀⠆⠀⠀⠈⣄⠀⢄⠀⠠⡆⠀⢱⠄⡀⢀⣀⠴⠊⢩⠁⠿⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠈⣄⠀⢦⡠⠄⢆⠘⠀⠡⡀⠢⣀⣈⣰⠴⠶⠚⢩⠂⠀⢠⠆⠀⢲⠀⠀⠘⢷⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⠉⣓⠓⢠⠥⠤⠄⢓⠶⡐⠋⡉⠉⡑⠑⢄⠐⢢⠃⠀⠲⡞⠀⡦⣸⡀⠀⠀⠀⠙⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠼⣉⠁⠠⣠⡴⠋⠀⠠⢀⠀⡜⠀⠑⠎⢐⠃⠀⢀⡼⠁⠀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣈⣁⠐⡄⠐⢀⡤⠋⡀⠀⢂⡔⢁⠀⠀⡼⢁⡆⢈⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢲⣖⣁⢀⣁⢌⣳⣅⡀⢁⣁⠀⣠⣅⠴⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣭⣭⣬⣭⣯⣥⣿⣯⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⣀⠀⠠⣤⠃⠀⠀⠀⣄⠀⢀⣴⡀⣠⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡝⠐⠁
⠀⠀⢠⡏⡠⠔⠦⣄⠀⠀⠀⠀⠈⠂⠀⠀⠀⢤⠀⠏⠀⠑⠘⠁⠀⠠⣀⢀⡀⠀⠒⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢄⠤⠚⠳⡒⠄⠀⠀⣏⢲
⠀⠀⠘⣧⣑⣐⣢⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡠⠃⠀⠀⠀⠙⠁⠀⠀⠈⠋
⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠄⡀⠀⢣⡀⣠⠧⡄⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⡀⠀⠀⠀⠀⠀⢀⠄⠰⠄⠀⠀⠀⠀⠀⠈⠓⢤⡔⠐⠘⠀⠀⢠⡵⠁⠀⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠄⢀⠤⠀⠀⣰⠇⠢⡄⠀⢤⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠡⡀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⢠⣄⠂⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⢆⠀⠀⠀⠀⢀⠤⠐⠀⠀⠀⠀⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠉⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠉⠛⠷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀⠀⢀⡤⠤⢄⡀⠀⠀⠀⠀⠉⠓⠤⠄⠀⠠⠤⠴⠚⠁
⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⣀⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠈⢶⠏⠀⠀⠀⠁
⠀⠀⠀⠞⠁⠀⢀⠤⠊⠁⠀⠖⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣿⡄⠀⠀⠀⠈⠀⠀⠀⢠⠁⠀⠀⢀⡀
⠀⠀⠈⠠⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⠤⠐⠒⠂⠉⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⣀⠀⢀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣄⠀⡀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡎⠀⢑⠀⡱
⠀⠀⠄⢀⠰⢷⡟⣈⡟⠀⠀⠀⠀⠀⡁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⢄⠁⠀⠁⠀⢰⠀⠀⡠⠊⠉⠃
⠀⠀⠀⠀⠑⡾⣈⡟⠁⠀⠀⠀⠀⣀⣅⡀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠣⡈⢶⡀⡌⢸⡄⠀⢀⠴⢃⡐
⠀⠠⡓⠀⠀⠀⠏⠀⠀⢸⢧⠑⣴⠻⢃⣽⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠊⠀⠀⠔⠁⠀⠀⠀⠀⠀⠐⠁⠂⠀⠠⠤⠤⠑⠀⠀⠀⠘⠤⢊⡥⠀⠀⠀⡀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠏⠶⣨⡰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠉⠒⡂⠀⠀⠀⠀⠀⠀⡛⡁⠀⠀⠀⢈⠆
⠀⠀⢰⣟⢢⣀⠔⣦⠀⠀⠀⢲⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠰⠟⣁⠄⠀⠀⠀⢀⢤⣤⡩⠉⠘⢛⢉
⠀⠀⠀⢏⠤⠿⢈⡟⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢀⠔⠋⠀⡾⠀⠆⢶⡈⢢⠀⠀⠠⡀⠉⠈
⠀⠀⠀⠀⠑⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⠉⢸⠀⠀⠉⠀⠱⣄⠀⢸
⠀⠀⠀⠠⠞⠁⠀⢀⠔⠒⠒⠒⠦⡀⠀⠀⣠⠔⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⢆⠀⠀⠀⠀⠀⠁⠈⠀⠰⠄⢸⠀⠀⡀⠀⠂⠄⠉⠁
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⠜⡄⢰⠃⠀⠀⠀⢀⠤⢱⡄⠀⠀⠀⠀⠀⠠⠎⣀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠊
⠀⠀⠀⠀⠀⠀⠸⡄⠠⡀⣀⠔⠁⢀⠇⢸⡀⢢⣠⠞⠁⠀⢰⠆⠀⠀⠀⠀⠀⢄⣀⣀⠀⠉⠐⠂⠠⠌⣐⡠⢄⣀⣀⡀⠀⢠⣀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠤⣉⠁⢀⡠⠊⠀⠈⠓⢄⣀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⣠⣿⢿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠹⠿⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠃⠀⠀⠀⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⡀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⣿⣦⣀⣀⡀⠈⠉⣿⣿⣿⠟⠃⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣶⣾⣿⣿⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠀⠀⠸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡆⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠤⣶⣾⣿⡿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠶⢤⡀⠀⣠⡴⠖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠹⡄
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠹⣾⠃⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣤⠴⠶⠖⠒⠛⠁⠀⠀⠀⠙⠓⠒⠶⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠶⠛⠙⠲⢤⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠃


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

⠀⠀⠀⡠⠒⠢⡄⢀⠤⠤⣄⠀⠀⠀⠀⢀⡤⠴⠤⣀⠀⠀⣀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷
⠀⠀⠰⡇⠀⠀⠸⠃⠀⠀⠀⢳⠀⠀⠀⡎⠀⠀⠀⠈⠳⡼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⢣⡀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⠿⣟⢹⠏⠉⠉⠹⣉⡽⠛⠁⠀⠀⠴⢞⡉⠀⠀⠀⠀⠈⣑⡦
⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⡟⠲⣤⡴⠊⢳⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⡔⠉⠁
⠀⠀⠀⠀⠘⢆⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣸⡵⠚⠁⠈⠓⠮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜
⠀⠀⠀⠀⠀⠈⠳⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⣄⢀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡀
⠀⠀⠀⠀⡜⠁⠈⠋⠀⠈⡆⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠋⠀⠀⠀⢹⠀⠀⠀⣀⣀⣤⠤⠎⠀⠈⠧⠤⣤⣀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠑⢤⣀
⠀⠀⠀⠀⠱⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠘⠛⠧⣀⠀⠀⠀⣠⠜⠛
⠀⠀⠀⠀⠀⠙⠦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢠⠏⢀⡤⢤⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⠎
⠀⠀⢀⣀⡤⠴⠚⠉⠉⠒⠲⠶⠴⠆⠀⠀⠀⠀⠈⠳⣄⡀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡾⠚⠁⠀⠀⠈⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡼⢱⣀⢤⠄⠀⠀⠀⠀⠀⠠⡊⡢⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⠀⠁⠀⠀⠮⣀⠀⠀⠀⠀⠀⠀⠙⠀⣠⠎⠘⢆
⠀⠀⢀⡀⠀⢀⣠⣄⠀⠀⠀⠹⡄⠀⠀⠀⣠⠃⠀⠀⠀⢠⠒⠲⡄⠀⡸⠀⠀⠀⠀⠉⠑⢲⠀⠀⠀⠀⡔⠚⠉⠀⠀⠀⠀⠀⠀⠺⢅⠀⠀⢀⠽⠂
⠀⠀⠀⠳⣀⣾⢀⡸⠁⠀⠀⠀⠈⠲⣄⡴⠃⠀⠀⠀⠀⠈⠳⣤⠧⠖⠁⠀⠀⠀⠀⠀⠠⠗⠊⢧⡘⠑⠺⠄⠀⠀⠀⠀⠀⠀⠐⠀⠈⢣⢠⠃⢀⠶⡀
⠀⠀⠀⠀⠈⠉⠣⣄⡀⠀⠀⣀⣠⠴⠋⠉⠒⠦⠤⠤⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠇⠀⠉⣦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠑⠮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠑⠦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠞⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠜⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡤⢦⠀⠀⠀⠀⠀⠀⡿⣻⣷⢙⡄⣴⣫⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡤⢦⡀⠀⠀⠀⠀⠀⡿⣿⣷⠽⣀⣴⣫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣠⠞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⢻⣿⣿⡿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⢻⣿⣿⡿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⢀⡀⣀⠀⠀⠘⣿⢿⠃⣾⢿⠟⠁⠀⠐⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⣀⠀⠀⠘⣿⢿⠃⣿⣿⠟⠁⠀⠐⠳⠟
⠀⠀⠀⢇⠉⢩⠇⠀⠀⠈⠳⡸⡷⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⢩⠇⠀⠀⠈⠳⡜⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢙⠈⢁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢻⠈⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣮⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡞⠒⢲⡆⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠈⡈⠝⠂⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⡞⠒⢲⡆⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⡉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⠸⡀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠑⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠑⠇

⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⣶⣓⢦⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣓⣦⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⣿⣿⣿⣏⣧⣾⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠚⢹⠆⠀⠀⠀⠀⠀⣿⣿⣿⣎⣧⣾⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠚⢹⠆
⠀⠀⢻⡿⣿⣞⢹⣿⣿⠟⠀⠀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢹⣿⣿⠟⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠋
⡄⠀⠀⠻⡟⢃⣿⡷⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢤⠤⡄⠀⠀⠻⡞⠂⣿⡿⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢤
⠃⠀⠀⠀⠙⢆⡟⠁⠀⠀⠀⠀⠀⠀⢠⠦⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡴⠃⠀⠀⠀⠙⢮⡟⠁⠀⠀⠀⠀⠀⠀⢠⠦⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠈
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋
⠀⠈⠂⠒⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣠⢤⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠘⠂⠲⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⢤⡀⠀⠀⠀⠀⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡒⠢⠐⠻⣋⠗⡐⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⡰⠄⢫⠿⠩⠭⡬⠛⠙⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠐⡈⢁⣤⠀⠀⠀⢀⢴⡁⠜⠈⣢⠌⢀⠐⠀⣁⡀⢤⠴⡜⠫⣷⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠚⠄⠀⠀⢀⠂⡀⠁⠀⠠⠀⡈⢒⣄⠀⡀⠊⡡⣄⣠⡶⠦⣠⣤⡟⢂⠡⢂⢜⠢⠄⢹⡥⢆⠠⠈⢴⣚⣵⡄
⠀⠀⠀⠀⠀⠀⣐⡉⢆⡠⠠⠐⠀⠁⢔⡀⡢⠐⠁⠄⠣⠘⢑⢄⡀⠐⢸⡷⣖⠚⠉⠸⠶⠱⠂⠍⠠⢐⡤⠛⠄⠹⢆⡉⠊⠩⠧⢛⡄
⠀⠀⠀⠀⠀⠸⠃⠀⠫⠠⠐⣈⠀⠁⠀⢂⠈⠤⠁⠀⠀⠈⠈⠀⠉⠒⠌⣿⡺⠏⠀⠄⡀⠀⣀⡱⠖⣋⡂⡡⡨⠀⢣⡾⠂⢁⡏⠚⣷
⠀⠀⠀⠀⠀⡆⠐⠈⢀⠐⠀⢠⣶⣌⠐⢁⠎⠀⠀⠀⠐⠒⠂⡀⠀⠁⠀⣿⠄⡀⠁⢒⡡⠞⢅⠒⣁⡍⠌⠂⠝⠆⠀⢢⣬⣑⢘⡡⣻⠁
⠀⠀⠀⠀⠘⡗⠔⢀⠀⢈⢀⡀⠀⠂⠚⢲⠀⠂⠀⠡⠔⠀⠂⠀⡠⠀⠂⢽⠀⣀⠖⠏⠲⠜⠅⠄⡂⢀⠃⠙⢶⠄⠤⡾⢀⠘⡎⣧⣅⡁
⠀⠀⠀⠀⠀⢶⠀⡘⠀⣀⡨⠋⢐⠀⠀⡂⠳⡀⠀⡀⠀⢠⠀⠀⣘⠶⠀⣸⠖⠃⠚⠠⠆⠀⠆⢁⢉⠫⢈⠀⠙⡠⠚⠍⣉⡢⠱⠤⡱
⠀⠀⠀⠀⠀⠘⡆⢁⠀⠀⠰⢫⡬⠁⠆⠁⠀⠘⢄⠀⠀⠀⠈⠒⡠⠂⠌⣿⠂⠀⠄⠀⠠⠂⡀⠈⠁⣡⠔⠓⠉⠲⠀⣇⡳⠝⡀⢠⠏
⠀⠀⠀⠀⠀⠀⠸⡟⠱⠌⠀⠁⢑⠂⠠⢀⠠⣀⠈⠳⣄⠁⠈⡈⠀⠈⠐⣿⠠⠄⠀⠀⠄⢀⣡⠖⠚⠁⣔⡁⠈⡜⣒⠁⠔⢂⢨⠎
⠀⠀⠀⠀⠀⠀⠀⠘⣆⡙⠰⢁⡈⠀⡂⠀⠲⠀⠠⠅⠈⠳⣼⠐⣄⣩⠀⣿⠠⠐⢈⡥⡖⠋⠀⠄⠄⠀⠂⡉⣏⠒⠀⡓⢀⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠱⣀⠍⠓⢬⢀⡀⠂⠀⠀⢠⠀⠈⠓⢄⠠⠀⣿⣠⠶⠋⢀⠂⠤⠂⢀⠀⠀⠠⢀⡄⡤⠙⣈⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⣀⢀⠂⠈⠊⠋⣑⠀⠄⡤⠀⠂⠊⠑⣤⣿⠀⡤⠀⠚⣈⠁⠆⠀⠑⠀⡀⡢⢆⣢⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠀⠁⠀⢀⠉⢠⠀⠠⠁⠁⠂⠤⣸⡇⠐⠀⠀⢀⠀⡀⠂⡀⠀⡀⠜⣈⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠂⠄⢈⠃⠀⡀⠀⠀⢸⡇⢀⠀⠀⠄⠑⠑⠆⠁⣢⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠢⠰⠀⠀⠁⠈⠁⢺⡇⠀⠀⠰⠀⠀⣡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⢼⡇⠄⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣉⠀⣹⡇⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠹⠴⠶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢕⡮⣅⣀⡠⠔⠊⠁⠀⢀⣉⣑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢠⠎⠀⠀⠀⠀⠰⠷⠬⠝⠉⠙⡄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠿⠀⠀⠀⡊⠛⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣔⠝⡻
⠀⠀⠀⠀⠀⠀⠀⠞⡦⠀⠸⣤⡥⠊⠀⠀⠈⠚⠀⢸⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠊
⠀⠀⠀⠀⠀⠀⠈⠰⣗⠤⠚⠉⠉⠉⢙⡖⠦⡀⠀⠀⠢⢗⣼⠀⠀⠀⠀⠀⠀⣀⡀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠀⠀⠠⣯⢁⠄⡜⠦⡀⠀⠀⠙⠀⠀⠀⠀⠀⠘⠨⣙⣆⠇
⠀⠀⠀⠀⠀⠀⡎⢔⡛⣫⠋⠀⠀⠀⠈⠋⠀⢂⠰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠡⢪⠕⡓
⠀⠀⠀⠀⢀⣀⢣⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠿⡀⠀⢠⠗⠛⠑⠊
⠀⠀⠀⠘⢆⣈⡿⠣⡀⢰⡕⣣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣯⡤⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡳⣄⠀⠀⢀⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠯⣓⡙⠿⠳⢄⠃⣠⠄⠀⠀⠀⣰⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣕⣧⡀⠀⠀⢰⣓⢃⠀⢀⣞⡀⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⡪⠿⠓⠤⡘⢶⡌⡠⠃⠈⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠳⠊⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠃⠘⠷⠃⠀⠀⠀⣀⣀⠀⠀⠈⠣⠋⠀⠀⠘⠦⠃⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢒⠒⠤⣤⡀⠀⠀⠣⡴⢃⡄⡄⠀⢰⠒⢲⠀⣀⣀⠀⠙⢁⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠯⠃⠀⢯⣈⠗⠀⠀⠑⢧⡀⠀⠀⠀⠉⠁⠀⠀⠑⠋⠀⠳⠴⢁⠄⠈⠒⠁⠀⠙⠁
⠀⠀⠀⠀⢠⡤⡄⠀⣄⡄⠀⠁⠀⠀⠀⠠⢀⣳⣄⡴⠃⠀⢠⡒⣲⠀⠀⠀⠀⢀⣼⡤⠄⠀⠸⣉⡽
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠉⠁⠀⠀⢀⣴⠋⠀⢀⢄⣤⡀⠈⠀⠘⠛
⠀⠀⠀⠀⠀⠸⣄⠟⠀⠀⠼⣆⠀⠀⠀⣔⡆⠀⠀⠹⣧⠀⠀⠀⠀⠀⣴⠟⡡⠠⡀⠘⢄⡴⠃⢰⢡⠆⢦
⠀⠀⠀⠀⢯⠕⠀⣀⡀⠒⠋⠉⠛⠶⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⣠⡾⠁⠀⠳⠴⠃⠀⠀⠀⣠⠏⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠋⠀⣠⠂⢦⠀⠈⠻⢶⣄⠀⠀⠀⢻⣆⣰⣟⣠⣤⠴⠶⠶⠦⠤⠤⠞⠋⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠋⠀⠀⠀⠈⠻⣷⣄⠀⢸⣿⣿⠟⠉⠀⠀⢰⠒⡲⠀⠀⠀⠀⠙⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣇⣇⣿⣿⣇⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⣾⠿⢦⡟⢹⡿⠠⣦⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠻⣿⡟⠀⠻⣶⣄⣠⡾⠁⠀⠛⠃⠘⠻⠷⢄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⣿⡇⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠧⣀⡄
⠀⠀⠀⠀⠀⢀⣀⢀⡴⠁⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⡀⣀
⠀⠀⠀⠀⠀⠛⢛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡱⡟
⠀⠀⠀⠀⠀⣀⡎⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠳⡀⣤
⠀⠀⠀⠀⠈⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⡟
⠀⠀⠀⢀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠻⠟⠁
⠀⠀⠀⠀⠸⣿⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠷⢶⡆
⠀⠀⠀⠀⢠⡶⠼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠶⠋
⠀⠀⠀⠀⠈⠛⠦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡯⢍⣁⣤⣶⠀⠀⣀⣤⠀⢀⣤⠀⣠⣦⠔⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⢻⣏⠓⠒⠛⣿⠒⠒⠛⠻⡍⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢆⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢵⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣩⢅⣉⠱⢄⠀⠀⠀⠀⣀⠤⠖⠚⠛⠛⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢭⣑⣶⡷⣤⠴⠋⠁⠀⠀⠀⠀⣠⠶⣔⣦⣬⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠰⠷⠯⢭⠤⠝⠀⠉⢆⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⡃⠀⠀⠀⢠⡖⣶⣦⡠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⠖⢹⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡞⢩⡜⢁⠇⠀⠀⠀⣬⢖⡕⡪⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢯⡘⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⢦⠀⠀⢣⣴⣨⠤⠋⠀⠀⠀⠀⠉⠉⠈⠀⡙⣬⠁⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣸⡠⠀⣠⠴⠗⠒⠒⠒⠒⢦⠤⣀⠀⠀⠀⠀⠐⢦⠱⢆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠋⠀⠀⠀⠀⠀⠀⣠⣾⠶⡄⠙⣆⡀⠀⠀⠀⠉⠲⢷⡇⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⡦⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⣀⣀⠀⠀⠀⠀⢯⠱⢈⡆⠀⠏⢿⢦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠣⣣⣘⡇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠴⢪⡟⣻⠋⠀⠀⠀⠀⠀⠙⠏⠀⠀⡆⢠⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⢧⣚⣒⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎⢰⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣠⠴⡺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡞⡰⡏⡤⠌⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡼⣿⡄⠀⠀⠀⣼⡱⠾⠫⠴⠒⠁
⠀⠀⠀⠀⠀⣤⢒⡛⢯⣺⢧⠀⠀⠀⣴⢛⡝⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⡥⠻⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠈⠳⢤⠴⠟⠉⢣⡀⢰⣷⣉⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠾⢂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡤⢤⣌⠢⣀⠀⠀⢠⠖⠏⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢥⣚⣂⢗⡹⠚⠷⣄⠸⣸⣸⡴⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠑⢬⡇⠀⠀⠀⠀⠀⠰⣧⢳⡀⠀⠀⢀⣼⠥⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣭⢒⠨⣶⢄⡀⠀⠀⢘⠸⠂⡇⠀⢀⠾⢷⣮⣕⣋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣭⣥⣿⠗⠛⠲⣄⡈⢷⣧⠃⣠⠏⠀⠀⠉⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅
⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⣤⣄⣤⣤⡄⠀⠀⠀⠀⠀⠦⠜⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢣⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⢲⠀⠀⠀⠀⠀⠀⠤⡰
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢂⠀⠎⢀⡜⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⠎⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠰⠈⠋⡠⠁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠣
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⢠⠐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣴⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠋
⠀⠀⠈⠁
⣀⣴⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡄⠀⠀⠀⠀⣶
⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⣿
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠐⠄⠀⠃⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣄⣀⣘⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠖⠒⠒⠒⠛⠛⠒⠒⠒⠶⡴⠊⠉⠙⠲⡄⢀⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣼⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠉⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠈⢢⣀⡴⠋⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⣠⠤⠴⠒⠚⠢⡀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⢄⠀⠀⠀⣀⣴⡯⠤⢤⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⢀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⢀⡞⣠⠞⠁⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⣀⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢀⡴⠋
⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡰⠋
⠀⠀⠈⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡞⠁
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋⠀⠀⠈⠉⠉⠙⠓⠋
⠀⠀⠀⠀⠀⠀⠈⡇⠀⣠⠏
⣤⣤⣤⣤⣤⣤⣤⣽⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣆⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣵⣋⡵
⠀⠀⠀⠀⠀⢀⡀⠀⠀⣦⡀⢘⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣼⢻⣾⣹⠆⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠋⠀⠰⡇⢸⣾⠊⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠸⣥⣽⠃⠀⠐⢷⣿⠎⢻⠀⠐⠿⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠻⡟⠉⢉⡀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢠⡟⠀⢀⣤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⢦⣀⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⡴⠾⠿⠳⠷⣶⠶⠖⠚⠉⠀⣰⢋⡤⠶⠦⡌⢳
⠀⠀⠀⠀⠿⠆⠀⠐⣏⠛⠀⣠⠶⠋⠉⣤⠀⠀⠀⠉⠙⠲⢤⣀⠀⠘⠿⠀⠀⢀⡴⠋⠁⠀⡀⠀⣞⠻⢨⡇⠀⠀⠀⣤⣿⢸⡇⢾⣤⠟⣸⠁⢀⣄
⠀⠀⢀⡤⣄⠀⠀⠀⢈⠑⢺⠃⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢠⠏⠀⠀⠀⠈⠛⠀⠈⠉⠉⠶⠆⠀⠀⠙⣿⡎⠻⠶⠶⠞⠁⠀⠀⠉
⠀⠀⠘⢷⡞⡤⢄⠀⠙⠃⣼⢰⠫⢭⢳⡄⣀⢤⡄⠀⠀⢠⡄⠀⠀⠘⢧⣀⡏⠀⣄⠀⠀⠀⠀⠀⢴⠤⢄⠀⣠⠶⣄⠀⢹⡇
⠀⠀⠰⣏⡹⢍⣹⣉⠆⠀⠘⣎⣓⣋⣼⢿⡁⣀⠗⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⢷⡷⢀⡼⠀⢸⡇⠀⢀⣀
⠀⠀⠀⠀⠰⣋⣿⠉⡛⠲⢤⡀⠉⠉⣡⢴⠟⣷⣞⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠖⠛⠿⡀⠀⣼⠃⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⣈⠯⠤⣄⣙⣦⣴⠃⠸⣄⣼⠙⠒⠖⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠻⠤⠾⠃⡇⣰⠃
⠀⠀⠀⠀⠀⠀⡞⣁⡀⠀⠀⠉⢻⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⡿⠷⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠳⠾⠏⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⣠⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⣠⡄⠀⢀⣴⡞⠁⢀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⢦⠈⢦⡀⠀⠀⣠⠎⢸⡁⠀⠟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣨⠇⠀⡇⠀⢰⠃⠀⠀⠳⣤⣤⡴⠟
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣌⣁⣠⡴⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⣧⡔⠛⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢀⡖⠻⡿⡙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠁⡇⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣟⠀⠀⢺⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠏⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣟⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⠛⢿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⠷⢦⡤
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢿⣿⣷⡄
⣼⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⡄
⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣾⣿⣿⠇
⠘⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠛⠋⠉
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠾⠿⠿⠿⠿⠟⠿⠿⢿⡿⠿⠿⠟⠛⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉

⠀⢠⡄⠀⠀⠠⠶⣀⠀⠀⠠⠄⠀⠀⠀⠀⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠶⠴⠀⡀⠀⠀⡀⠘⠁⠀⡄⠀⣀⠀⡄⠀⢠⡄⢠
⢀⣀⠀⡀⢠⡄⠀⠀⡀⠀⠠⠀⠰⠀⠀⠀⡀⠀⠀⢸⡿⣀⣰⠖⠀⠛⠀⠀⠲⢀⠀⠒⡀⢀⠈⠋⢠⠄⣁⠀⠴⠀⠀⠀⣠⠀⠀⠠⠆⡀
⠀⢡⡄⠁⠀⠀⠀⠀⠰⠜⠗⠀⡀⠀⡀⠷⠀⠀⠀⣠⣴⠄⠀⠀⣀⠀⠖⠀⠀⠈⠀⠀⠀⠈⠀⠠⠐⠀⠉⠀⠀⢠⡄⠀⠙⠃⠀⠀⠀⠀⠘
⠀⠀⠀⢤⡄⢠⠀⣤⠀⡴⠦⠈⠛⠶⠉⠀⠀⠀⢀⠃⠴⠀⠀⠋⣉⠢⠀⢀⠀⡀⠘⠃⣁⠀⠀⠀⠀⠛⢂⠀⠀⢀⠰⠀⠀⠘⠁⠀⠀⠀⠄
⠀⡀⠀⢰⠀⠁⠲⠂⠀⠀⠀⢀⠀⠀⠘⠛⠃⠀⠈⣥⠀⠠⠄⢠⣄⠁⠀⢀⠀⠸⠠⠀⠙⠙⠒⠈⣁⠆⠀⡤⠀⠀⠀⠀⠸⠇⠰⠖⠈⠛
⠀⠁⠀⠘⢀⡀⠚⠇⠀⢠⣴⠎⣤⠀⢀⡄⠘⠂⠀⠀⡀⢄⠏⠄⠀⠄⠀⠀⠤⠀⠠⡦⠀⠘⠃⢀⡙⠅⢠⡄⠰⠆⠺⠀⠀⠈⠁⠀⢤
⠀⠐⠷⠀⠀⠀⣀⡀⠠⡄⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠁⠀⠀⠰⠀⣀⠀⠐⠀⢀⡇⠀⠀⠘⠓⠈⠑⠂⠀⠀⠁⠀⠁⠘⢣⣀⡀⠀⠀⢀⡀
⠀⡀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠃⠉⠤⠋⡤⠈⠁⢀⠠⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠃⣬
⠀⡛⠀⠆⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠛⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠁⠶⠀⠐
⢈⠁⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⣀
⠈⣉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠉⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣄
⠶⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣤⠀⡄
⢠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠐⡇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠘⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠐⠆⣀⢀⣤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠾⠀⠐
⠸⠓⢀⠀⢤⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣉
⢙⡄⠰⠶⠀⣀⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠔⠊⢀⡀⠙⠁
⠀⣁⠀⠀⡀⠉⠀⢶⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠙⠀⠀⠳⢀⠰
⠀⠉⠀⠀⠐⠦⠀⠐⡃⠀⣀⡐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⣀⣀⡀⠀⠄⠒
⠀⠛⠂⢴⡄⠀⠀⠶⠾⠀⢈⡀⢀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠘⠋⠈⠀⠀⢠
⠀⣷⠶⠀⠀⠒⠆⠀⣤⡀⠈⠁⢈⠁⣤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⠄⠘⠃⢀⡀⠠⡦⠀⣾⠆⡤
⠀⡟⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠿⠇⠀⠘⠂⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠈⢩⠀⠀⣃⡀⠀⡤
⢠⣷⡄⠀⠀⠰⠇⠀⠰⣭⢂⡠⠜⠂⠀⠽⠿⠀⢀⡀⠀⣤⡀⠈⠢⠀⠠⠄⠘⠁⠀⠀⠀⠦⠰⡶⠀⠀⢰⣶⠀⠈⠁⠀⠀⠀⠘⠿⠂⠀⢠
⠀⣻⢀⡀⠐⠒⠀⠀⠀⠀⠘⢡⣄⠤⢀⠀⠀⠀⣈⠃⢤⡄⠀⠀⣠⡠⠄⠀⠀⠀⢀⣀⠀⠚⠃⠀⢠⡄⠀⠁⠖⠘⠃⠀⠀⠀⠀⢠⠄⢰⡆
⠀⣇⠀⠉⠀⠄⠀⠀⠀⠀⠀⢠⡀⢠⡄⠀⠀⢠⡯⠀⠀⠀⠀⠂⠉⠀⠀⣾⡀⠟⢿⣯⡀⢠⣄⢠⡄⠀⠀⠶⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀
⠀⠽⠆⠀⠀⠰⠗⠀⢠⡆⢄⠘⠁⠀⣠⣤⠀⠦⠀⠀⢀⣀⠀⠀⠀⠐⠓⠙⠁⠀⠀⠈⠁⠀⠀⣴⡆⢠⡀⢠⡀⠠⣤⠄⠀⠀⠸⠿⠀⠀⣤
⠀⠸⠶⠇⠀⠠⣦⠀⣼⠟⠁⠀⠀⠀⠙⠛⠰⠞⠃⠠⣾⣼⠃⠀⠰⠗⠰⣶⠀⠀⠒⠀⠾⣤⡄⠈⠁⢠⡄⠈⠱⠆⠀⠰⠆⠲⠀⢀⡀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣁⢸⢉⡀⠏⠉⣱⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠈⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⡹⣠⠸⡇⠇⠈⠛⠀⠛⠲⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠙⢆⡀⠀⠀⢰⡼⠊⣡⢀⠀⠀⠀⢀⢆⣠⠄⡈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣤⠘⠖⠓⠛⠛⠛⠻⠦⣄⣧⠀⠀⠀⠀⠨⠵⠞⠛⠛⠛⠛⠛⠻⠾⣄⡀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠂⢀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣶⡙⣇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣀⠔⠁⠁⠀⠀⠀⠂⠘⠃⣬⠂⠀⠀⠉⠉⢲⣤⠠⠀⠀⠀⠀⠘⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⣈⠣⣔⠀⠀⠀⠀⠀⠻⢷⡀⢀⠀⠀⠠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠐⣠⡄⠀⠹⣏⡄⠀⠀⠀⠀⠾⢿⣯⢀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢈⣽⡗⠀⠀⢹⣄⠀⠀⠀⠀⠀⠘⠿⣷⠀⠀⢼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡿⠂⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⢉⡤⣧⠀⠀⠀⢹⣟⠀⠀⠀⠀⠀⠼⢿⡇⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠠⣶⠇⠀⠀⠀⠀⡠⠄⣿⠦⠀⠀⠠⣿⠲⠂⠀⠀⠀⠀⢺⣷⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⠴⠃⣿⠂⠀⠀⠀⢾⡉⠃⠀⠀⠀⠀⣹⣿⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠐⢋⣿⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⣸⡯⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⣹⡄⠀⠀⠀⠀⠀⠉⡿⠧⠀⠀⠀⢘⡃⠀⠀⠀⠀⠐⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⠞⢻⡄⠀⠀⠐⢾⠇⠀⠀⠀⠀⣽⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣯⠀⠀⠀⠀⠀⡴⢾⡆⠀⠀⢰⣿⢆⠀⠀⢀⡶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⢠⣼⡇⠀⠀⣾⣿⠆⠀⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠉⣸⡀⠀⣾⣿⣧⣄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢰⣿⣅⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢄⢰⣾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣶⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⡿⠿⠿⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠘⠿⠋⠀⠀⠀⠀⣠⣴⣾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⠟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣦⣄⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠐⢿⣿⣧⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⡆⠀⠀⠘⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣷⣦
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠛⠟⠿⠿⠿⠿⡷⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠙⠛⠛⠛⠿⢿⣿⣶⣤⣄⡀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣦⣄⡀⠀⠉⠉⠛⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⡷⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠆




⣿⣿⠿⠻⡿⢛⠿⢿⠟⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⡀⠀⢨⠠⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡌⡀⠠⠐⠢⡀⠀⠰⡆⠀⠀⡄⠃⠉⠈⣧⠘⡀⢤⣀⠀⠀⠀⠀⠈⠀⢄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡇⠀⠁⢀⠀⣁⡠⢤⠦⠀⠀⠰⢄⣀⣌⣀⡱⢐⣌⢰⠁⠀⠶⠄⠈⠒⠊⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠐⠈⠀⡃⠃⠋⡔⠃⡇⠀⠀⠤⠠⠥⠃⡀⡀⠀⢽⢦⢤⣾⠂⠄⠁⢀⠰⠂⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⡈⠀⠄⡀⠠⣰⡄⢠⠁⢠⣁⢲⢀⡀⠾⣂⠈⢂⠀⡒⠒⡌⢲⡈⢄⡣⠚⠈⠃⠰⡡⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠈⠠⠚⠡⡠⢒⠄⠛⠉⠉⠙⠒⠮⡄⠰⠎⢰⠂⢠⠔⠉⠈⠉⠈⠓⠤⡰⢢⣅⣀⡌⢸⡫⠐⠀⠜⡁⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠑⠃⣄⢠⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⡀⠘⣵⠟⡀⡡⠂⣁⠁
⠀⠀⠀⢀⡀⠈⢶⢤⣀⠀⡼⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣢⠴⠛⢶⠚⠉⣀⡠⠄
⠀⠀⢄⣀⡀⢨⠢⢀⠉⠛⢇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡏⠐⠀⣘⣆⢢⡀
⠀⠀⢀⡀⠀⠀⣀⠉⢦⣀⠐⠃⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠈⠊⢲⠴⡁⠀⠡⢡
⠀⠀⢁⠈⡪⠃⠉⠉⠙⠤⠦⣠⣀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠵⠤⣄⡴⠈⠐⠅⠙⡆⠿
⠀⠀⢂⠉⠀⠱⣜⠢⣞⠀⠤⠨⣏⠀⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⠂⣰⠏⠰⣄⢀⠘⡀⠽⠆
⠀⠀⠀⠈⠁⡀⠈⠥⢨⣄⣠⠜⠽⠓⢯⠁⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡠⠊⠰⠃⢲⠞⠁⠠⠀⠋⠈⢰⠌⠀⠀⠠
⠀⠀⠀⠀⢎⡀⠄⠚⠙⣦⡾⣄⠀⠀⢈⠗⠆⠛⢆⠱⣄⡀⠀⠀⠀⠀⠄⡀⠊⢈⣁⠀⡀⢠⠄⠞⠠⠊⠀⠀⡀
⠀⠀⠀⠀⢀⢤⠔⡁⠀⠈⠏⡀⠟⠉⢙⡒⠢⡀⠐⣆⠀⡟⠆⡀⠀⣠⠏⠤⠉⣄⠈⠁⢀⠐⠛⠀⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠐⠀⠈⡠⠀⢇⠁⣠⠺⠌⣢⣌⣳⣨⣬⡛⠍⡛⠔⠳⠶⢖⠂⠊⠁⠀⠠⠂⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠈⠛⠙⠀⢃⠨⠁⠑⣌⢂⣀⣑⢨⡆⠄⢢⠐⢅⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠑⠓⠀⠂⠬⢴⡄⠀⠀⣁⠈⠆⠢⠄⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣁⠆


⠀⡁⣈

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⣰⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢛⡛⠁⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡿⠋⡽⠉⠉⠈⠇⠀⠰⢋⣾⡥⢹⠀⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡇⠀⡇⠀⠀⣠⠀⠀⠀⣿⢟⡥⢸⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⡇⠀⢣⣀⣴⣿⣷⣤⣶⠟⠋⠀⡞⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢠⡇⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⣿⣿⠿⣿⣿⣦⣄⣀⠀⢀⣀⣼⣀⣤⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣐⠅⡁⢀⢀⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⠺⠓⠻⠘⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠂⠤
⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠖⠛⠋⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢸
⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⠀⠀⠀⠀⠀⠀⠸⣇⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠞⠛⠓⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⠁⠀⠀⠀⠀⠀⢸⠃
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡆⠀⠀⠀⠀⠀⠀⢀⣤⠾⠤⠤⠤⠴⠶⠶⠒⠛⢯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⣀⡀⠀⠀⠀⢸⡇
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣾
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⣠⠾⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⣤⣾⠃⠀⠀⠈⠉⠙⠛⠛⠒⠲⢶⡖⠒⠒⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⡤⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⣰⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⣿⣿⢿⣿⣿⣍⣛⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⡏⠈⣗⠌⠉⠹⡿⠿⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠭⠛⠓⣢⣄⠀⠀⡀⠀⠀⠀⠓⠄⡘⠀⠈⠦⠀⠀⢉⠀⠀⢄⣡⡎⠭⠟⢳⣄
⠀⠀⠀⠀⠀⠀⢀⡿⢫⣅⡀⣀⣁⣘⣆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣾⣞⣫⣍⡀⠀⠀⠉⠻⣿⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣿⡟⢤⣤⠖⠀⠀⠢⢤⣿⣿⣿⣿⣿⣿⣳⣦⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠻⠃⣀⣄⡀⣀⣼⣿⣿⣿⣧⡇⠙⠙⣞⡇⠀⠀⢠⣶⣿⠛⣻⣿⣶⣶⡟⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠸⣯⡀⠐⠁⠀⠀⠘⣿⢿⡟⠀⣿⠌⠀⠀⣯⡇⠀⠀⣿⣿⣵⣿⡇⠀⡼⠿⣿⡖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠐⠂⠛⣿⡿⠀⣿⡄⢉⢂⢰⣶⠏⠀⠀⠀⠹⣿⣿⣿⣃⡸⡇⠀⠸⢿⡄⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠒⢠⣾⣿⡇⠎⣸⢀⣶⠷⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡤⢠⡄⠈⢿⡑⢢⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢖⡴⠋⠀⣼⠁⢀⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣟⣷⡄⡘⣷⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠖⠚⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣮⣾⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿


⣶⣶⣶⣶⣦⣤⣤⣦⣴⣴⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣴⣦⣶⣶⣦⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠔⠒⠒⠤⠤⣄⣀
⠀⠀⠀⠀⠀⣤⢀⠴⠚⠉⠀⢀⠠⠔⠒⠋⠉⠉⠉⠉⠀⠈⠙⢦⡄⢀⠀⢀
⠀⠀⣔⠻⠋⠸⠁⢀⠠⠐⠈⠀⠀⢀⡠⠤⠖⠒⠋⠉⠀⣠⡤⠖⣋⠵⡶⠃
⠀⠀⢈⠗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉⠁⠀⢉⣵⠞⣇⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣲⠶⠖⠒⠒⠲⠤⣄⠀⠀⢀⣠⣤⣀⡀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉⠀⠀⢀⣀⣠⡴⠞⠋⠀⠰⣸⡀⠀⠀⣠⠴⡶⢊⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠒⠻⢦⣏⣤⠂⠈⠙⣆
⠀⡞⢠⠁⢠⠃⠀⠀⠀⢠⠀⠀⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿⠇⢠⡞⡕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⡝⣆⢉⡀⢸
⠀⡇⢸⠀⠈⢀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⢀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⢀⡽⣼⡄⠀⣸
⠀⡇⠘⠆⡰⢁⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠁⠀⣸⢸⠸⢀⠧⣄⣀⣤⣀⡀⠈⠉⠒⠤⣀⠀⠉⠲⠦⣤⡴⢞⠅⣧⡤⠔⠁
⠀⢿⠀⢰⢣⡏⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⢀⡇⠈⢇⣸⠠⠀⢈⡄⠀⠉⠙⢦⡀⠀⠈⠳⡀⠀⠀⠀⠐⠋⡰⡇
⠀⠸⣇⠀⠈⠣⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢇⡞⠀⠀⠀⢻⢀⠄⠀⠁⠀⠀⠀⠀⠳⢸⡍⢣⠁⠀⠀⢀⠀⡰⢣⡇
⠀⠀⠹⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣀⠴⣫⠏⠀⠀⠀⠀⢸⡈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠶⠞⠀⠀⠀⡡⠜⢁⣾⠁
⠀⠀⠀⠈⠳⢬⣓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣡⠞⠁⡀⠀⠀⠀⠀⠀⢳⡤⠤⠞⠁⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⢀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠦⢄⡀⠀⣀⣤⠤⠶⠒⠉⠀⠀⠙⠃⠀⠀⠀⢀⣄⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠘⡆⠀⢒⣋⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡀⠾⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠉⠀⠀⠀⠀⠉⠓⡆⠀⡠⠖⠲⠿⠯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠁⠀⠉⠢⡀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⠀⠀⠀⠀⡠⠂⠙⠒⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢄⠀⠀⠀⠀⢀⠘⡄⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠈⡄⢇⡀⠀⠀⠀⠈⠛⠿⠃⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠒⠂⠀⠀⠀⠀⠀⢡⠀⠈⠑⠒⠤⢤⠖⢦⣤⠤⠖⠋⠹⠀⠀⠀⠀⠀⠸⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢣⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡞⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢏⣢⠀⢀⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⡩⡅⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡤⣆⠀⠀⢠⣴⢺⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⠊⠀⠰⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣈⠉⠒⠛⠃⠛⠋⠁⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡴⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠙⠛⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣊⣑⠄⠑⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠭⠃⡔⢚⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠖⠒⠒⠚⠛⠛⠛⠒⠒⡶⠚⠉⠙⠢⣀⡠⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠶⠶⡇⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⣀⡤⠖⠊⠉⠁⠀⠀⢀⣀⣀⡤⠤⢷⡀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠖⠢⡀⠀⣠⠔⠉⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⢀⣀⣳⡄⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠘⢞⠁⠀⠀⠀⣠⣔⣉⡀⠀⠀⢀⡤⠚⠉⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠈⠑⠤⠔⠊⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠖⠒⠚⠉⠉⢀⠇⡠⠞⠁⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⢀⡴⠋
⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡴⠋
⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡰⠋
⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠞⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠖⠒⠲⠤⠤⢤⣸⠄
⠀⠀⠀⠀⠀⠈⡇⠀⢀⠞⠁
⣀⣀⣀⣀⣀⣀⣹⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀⠀⠚⠿⠋⠁⠠⣔⠋⣄⠞⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠆⠈⣡⡀⠀⠻⣿⣦⠀⠀⠀⠙⠀⠙⠀⠀⠉⠀⠐⢤⡀⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠉⠉⠀⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠝⢀⠏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣥⡄⠟⢡⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠊⠁
⠀⠀⠀⠀⠀⠀⣆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠰⣤⠙⣒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⢦⡀⢉⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇
⠀⠀⠀⢴⣤⡈⣉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⢀⣀
⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⠄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠠⠶⠇⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠘⠁
⠀⠀⠀⠀⠀⠐⠶⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠖⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣷⠀⡴⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠢⣄⢀⡀⢀⡀⢠⠀⠀⠀⠀⠀⢾⡿⢀⡜⣫⣘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠈⠷⠘⠇⠀⠀⠀⠀⠒⢤⣬⣄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠼⠁⣾⠀⣷⠀⠀⠀⠀⠀⠙⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠆
⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣼⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠸⠴⠀⣆⡿⡄⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⢿⣰⠀⠦⠇
⠀⠀⠀⣴⠋⣹⡆⠀⢸⡇⡃⣿⣿⡶⣲⡄⢰⣥⣾⠆⢠⣴⣢⣦⣀⠓⠈⣆⣠⣖⢶⣿⣿⠸⢸⡇⠀⢰⣏⠙⣦
⠀⠀⠀⣇⠀⠈⠀⢰⢼⣷⣶⣿⣽⢯⠛⡻⢧⣿⠼⠀⣿⣿⡗⢿⡆⢰⡿⣱⣶⣿⡽⣟⣿⣦⣾⡧⡆⠀⠀⠀⣸
⠀⠀⠀⠘⢦⡸⣆⢸⡎⡟⣿⣍⣿⣿⣆⣫⣛⣟⣿⢾⡹⣿⡁⢼⣻⣾⣟⣿⡟⠳⣷⣻⣿⣿⠾⢱⡇⣰⢇⡴⠃
⠀⠐⢏⠂⠀⠙⠻⣿⡟⣤⣳⣽⣯⢿⣟⣿⣿⣏⣻⣿⣿⣳⠈⣸⣿⢛⡿⠹⣶⣻⣻⣿⣿⡟⣤⢻⣿⠟⠋⠀⠐⡹⠂
⠀⠀⠀⠉⠁⣤⠚⡛⢉⣽⣿⢿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣽⣿⣽⣿⣿⣿⣿⡉⢻⠓⣤⠀⠉
⠀⠀⠀⠀⠀⡳⣾⡟⢾⣿⣿⣝⢿⣿⣿⠟⠉⠀⠈⠉⠻⣿⣿⠟⠉⠁⠀⠉⠻⣿⣿⡿⣫⣿⣟⡗⢻⣷⢞
⠀⠀⠀⠀⠐⡅⠋⠘⢦⣱⣽⣿⣷⣿⣏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣯⣏⡴⠃⠙⢨⠂
⠀⠀⠀⠀⠀⠈⠒⠬⣿⢿⣿⣏⣛⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣛⣹⣿⡿⣿⠥⠖⠁
⠀⠀⠀⠀⠀⠀⠧⡤⡜⣯⣢⣻⢍⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⡩⣟⣄⣿⢃⢤⠼
⠀⠀⠀⠀⠀⠀⠀⢆⠁⢌⣉⣁⡲⠤⠠⠽⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠄⠤⢄⣈⣉⡡⠈⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⡟⡙⠟⠂⣶⣿⢾⣿⣷⣦⣀⣀⣴⣾⣻⣷⣿⣷⡐⠻⢋⢻⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠓⠀⢸⡏⠛⠘⣿⣯⣻⡿⢿⣿⣿⠿⠏⠛⣿⡗⠀⠚⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢱⠶⠚⢻⡏⢻⣆⣸⡟⣿⠚⠳⠦⣯⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢸⡇⠘⢾⠿⠇⢿⠀⠀⠀⠀⠈⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⡉⠀⢀⠤⢄⠀⠀⢠⡔⠀⠀⣀⠼⠛⠓⢷⠀⢃⢀⣀⠀⠀⠀⠀⠀⠔⠁⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢘⠏⠡⠁⠀⠀⡇⢀⣀⣀⠀⠄⠙⣄⠀⢀⠏⠑⡌⢆⠙⡜⠢⠀⣤⡀⠑⠄⠜⠀⢡⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢈⠀⠈⠇⢰⢠⠉⣀⠖⢡⠞⠆⠀⠀⢨⡈⠙⡹⠉⠉⠀⢙⣧⣁⣀⡰⢀⡈⠂⠀⢀⡤⣘⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢔⡸⠀⠢⢀⠈⠊⣄⢄⢹⢠⠃⠀⠇⢤⡀⠀⢠⡢⠀⢈⠉⢦⡄⣅⠳⡝⢋⠂⣇⡤⠘⠆⠁⠇⡠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⢀⡴⡀⢀⡍⢀⠼⠿⠷⠾⢀⡜⡓⠊⣡⢣⡆⠘⣂⡤⠮⠘⠆⠼⢐⠘⢢⡕⠋⠀⠰⢲⡜⠂⡀⢀⠆
⠀⠀⠀⠀⠀⠇⠈⡄⢡⣰⠁⠀⠈⢣⠞⠁⠀⠀⠀⠀⠀⠈⠣⣤⠁⠀⢧⡔⠋⠀⠀⠀⠀⠀⠀⠁⢢⡜⠀⠒⢣⢔⣽⡄⠄⠈⠔⠙
⠀⠀⠀⠀⠄⠐⣀⡀⠈⠀⠘⣦⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣃⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀⡀⢀⣽⣋⣦⡤⠀⠒
⠀⠀⡀⡀⠖⠀⡌⡛⠳⢬⣸⠃⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⣶⠉⠀⢹⣑⡀⠒⠒⠉
⠀⠀⠑⠘⠦⠀⡆⠡⡄⠀⠈⣦⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠾⡣⡀⠀⡴⠓⢌⢧
⠀⠀⡀⠠⡀⣁⢰⣄⣈⡆⢴⠁⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢹⢙⠤⣀⣀⣰
⠀⠘⡀⢄⠄⢋⢠⠀⠀⡘⠉⠓⣤⡴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠛⢰⣦⢛⠀⠈⢃⡀⢳⡘⡀
⠀⠀⠑⢄⡀⠈⣳⣍⡻⡅⠀⠂⣸⣅⣀⣸⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⢚⠀⠈⣁⡼⠃⢸⣶⢤⠈⠆⡟⠇⠂
⠀⠀⠀⠀⠀⠠⠀⠒⣂⣶⠤⡶⠉⢊⠙⢣⡀⠈⣑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡡⢊⠀⡏⡁⠽⠃⠀⠐⢠⠃⠠⡸⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠢⠠⠔⢊⠃⡻⣾⢣⢄⢀⡀⣼⢛⠊⠉⢃⠚⢦⣄⠀⠀⠀⠀⢀⣀⣊⡀⠠⣄⠠⠄⠴⣐⠋⠀⠋⠈⡀⡠
⠀⠀⠀⠀⠀⣔⡔⠡⠊⣊⠜⢣⢸⠃⠀⢨⡛⠢⣄⠘⢦⣀⣉⡓⣄⠀⢠⠞⠐⠀⠴⣄⠉⠀⣠⠉⡉⠀⠒⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠆⠘⣈⢀⡤⢳⠬⣠⣬⡱⣨⠦⢍⠭⢉⠲⠛⠖⠲⣒⠈⠉⠀⠀⠐⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠀⠘⠃⡁⡈⢇⢲⢃⠀⣌⢢⣀⣈⣢⣗⠠⠳⠔⠣⣌⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⠘⠓⠈⠂⠤⢲⡄⠀⠀⣈⡀⢡⠑⠤⠤⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠂⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠷⢦⣄⠀⢀⣤⡶⠾⠛⠳⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠈⠉⠙⠳⣦⡀
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠙⣶⠟⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠾⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠈⢷⣀⣀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⠀⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠼⠇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠰⣶⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠒⠒⣿⠒⠒⠂⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡶⣤⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡴⠋⠀⠀⠙⠷⣤⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣰⠏⠀⠀⠀⠀⠀⠀⠈⠙⠶⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⠶⠖⠒⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⣀⠔
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⠁⠀⣀⣀⡀⣀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠚⢀⡔⠉⠈⠁⠀⠁⠀⠀⠀⠀⠉⠳⠒⠀⠒⢤⣀
⠀⠀⠀⠀⠀⢄⠉⢀⠃⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⡇⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣶⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢰⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢆⢸⢹⡁⠀⠀⣠⠄⠀⣀⠀⣀⠼⠤⠤⢆⣀⣜⡐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⠈⣿⠉⠁⢒⣩⠭⢍⡉⠉⠉⠁⠀⣠⠤⠤⣄⠀⠉⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⣰⠚⢉⣩⣳⣤⠴⠲⣾⣷⣶⡄⠈⢻⢿⣤⣤⠎⠀⣴⣶⣿⡦⠖⢦⣾⣶⣶⡄⠈⢷⣶⣶⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⡇⠀⠸⣿⣿⣿⠀⠀⢻⡻⠿⠃⢀⡞⠀⡟⠛⢆⠀⠙⠿⢫⠇⠠⠀⢯⡛⠟⠁⢀⠟⠉⠉⡧⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠂⠀⠀⠀⠙⠦⣄⣠⠴⠃⠢⡴⠀⠉⠓⠚⠉⠀⢀⠇⠀⠀⠙⠒⠊⠁⠀⠓⠁⠀⠉⠒⠚⠁⠀⠀⢀⣇⡼⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡞⠁⠰⠈⣳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡎⠈⠉⠉⠉⢛⠛⢉⣉⡉⠁⠀⢳⢱⡀⠀⢰⠃⡜⢸⠉⠉⠙⠛⠒⠛⠋⠉⢿⠸⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⣸⠀⠀⠀⠀⣎⠁⠙⠊⠀⢸⠀⠀⠈⣥⠇⠀⠧⣤⡧⠁⠂⠠⠀⠄⠀⠀⠀⠀⠀⢣⣯⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠢⣀⢀⡰⠃⠀⠀⠀⡇⠀⣀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣶⠤⢤⣤⣤⡤⣭⣤⠤⠤⡶⠊⠀⠀⠈⠀⠀⠑⡖⠦⠤⢤⡤⠤⡤⠤⠤⢴⡞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⠥⠃⠀⠘⠧⣤⠴⠓⠒⠉⠁⠉⠉⠑⠒⠻⠄⣠⠜⠀⠀⠳⢄⣀⡼⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠑⠐⠂⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢢⠀⢠⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠀⠀⠀⢁⠀⠤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⡀⢠⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠆⠠⡜⠑⠂⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⢀⡐⠀⢀⢀⠀⢸⠆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⡜⠂⠀⠀⣄⣠⠤⢄⣉⠀⠀⢰⠀⠶⢀⡀⠀⠀⠀⢈⡇⠀⠬
⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀⠀⠀⣿⠀⠀⠀⢀⡞⠀⠀⠈⢀⠀⠦⠠⡄⠀⠁⠈⣏⠀⠀⠈⢣⡔⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠄⠀⢀⡀⠀⠀⣿⡀⠀⠀⢸⡀⢠⠀⠀⠂⢉⠈⠁⢈⠀⠀⠈⢻⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⣈⠀⠀⠠⢸⡄⠀⠉⠘⣧⠈⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⡟⠐⠀⠀⠀⣏⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢈⡈⠸⣇⠀⠀⠘⠙⣇⢀⠀⢀⠀⠀⠀⠀⢀⠀⣽⠁⠀⠀⠀⢇⡟⠁⠐⡄⢈
⠀⠀⠀⠀⠀⠀⡀⠘⡖⠀⠀⠀⠤⣿⠀⠀⠀⣤⠈⠳⣄⡼⠀⠀⠀⢀⣡⠞⠁⠀⠀⠀⠀⢤⡷⠆⣀⡟⠀⠠⡤
⠀⠀⠀⠀⢀⠀⢀⡀⠉⠲⠲⢤⡀⣿⠀⢀⠀⠀⠀⠰⠈⠙⠶⣤⣵⠋⡅⠀⠀⢠⠡⠘⠀⣸⢇⡴⠟⢰⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢻⡏⠀⠀⠄⠀⢀⡀⣰⡶⠞⠋⠉⠛⠳⣦⣤⡉⠀⡀⠐⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⠀⠁⠖⢀⣤⠿⢯⡄⠌⢡⠠⠂⠀⢈⠈⣙⢿⣦⣤⣿⡇⠀⠀⠐
⠀⠀⠀⠀⠁⢀⠀⠄⠀⠠⠀⡂⠀⢹⣆⠠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠰⠉⠘⠀⠈⢻⣿⣷⠀⢊⠇⡄
⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⡀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠠⠀⢸⣿⣿⠀⠀⠀⣵⠒
⠀⠀⠀⠀⠀⠁⠑⣮⠀⠀⢠⡍⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⡏⠁⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠈⠙⢦⣸⣇⣠⣀⠀⣹⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠟⠿⠄⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠉⠉⠙⣷⣾⣿⡇⠀⠀⠀⠀⣴⣦⣴⣶⡄⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⢠⣿⡟⠻⣿⣆⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⣿⠀⣿⣿⠆⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣿⣿⢰⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⣿⣿⠿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢹⣿⡟⠁⢻⣿⠀⠀⠀⠀⠀⢸⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⢸⣿⡇⠀⠈⣿⣆⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⣿⣿⣿⣄⣀⣀⣾⣼⣇⠀⢀⣿⣿⠀⠀⠀⢀⣿⣿⣿⣷⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣷⣶⣶⣶⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠒⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢀⣠⠆⠀⠋⠀⢸⡏⠀⢰⣤⠆⠀⠀⠀⡇⠀⠀⠀⠰⣷⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠃⠀⠀⣄⡠⠀⢀⣀⡀⠀⠀⠀⠀⠀⡇⠀⢠⡀⠈⠈⠀⢴⡖⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⡖⠀⠸⠇⠀⠀⠟⠀⠀⠀⠀⠀⠀⡇⠀⠛⠃⠠⠐⡀⠈⠀⠀⠀⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⠁⣀⢀⡀⠀⢠⠀⠀⢷⠇⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠉⠀⠘⠏⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣆⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠉⠃⠠⣾⠄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⠃⠀⠈⠃⠀⠀⠀⠀⠀⡇⠀⠻⠃⠀⠀⠀⠀⠀⠸⠷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣤⠀⠀⢀⠈⠃⠀⢺⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠉⠀⠀⠿⠂⠀⠃⠀⠀⠀⣴⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢾⣿⡆⠀⠀⠘⠇⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠀⠀⢰⢀⣤⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡄⠀⠃⡀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠸⠇⠀⠀⠀⠀⠈⠀⡠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⣄⠀⡗⠀⢴⡄⠀⣴⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠛⠇⢀⣀⠻⠀⠀⠛⠰⠂⣠⠀⠰⠗⢴⡄⠀⠸⣿⣿⣿⣿⠀⠀⣴⠜⠷⠀⢠⡀⠲⠘⠃⠀⠸⢃⣀⠀⠟⠃
⠀⠀⠀⢤⠀⠶⠄⠈⠁⠀⠐⠀⠀⠃⠀⠙⡁⠀⣤⠈⠀⠀⠀⠙⠿⠟⢁⡀⠀⠈⢠⡄⠀⡙⠁⠀⠃⠀⠐⠀⠀⠉⠀⠴⠆⢠⠄
⠀⠀⠀⣴⠆⠀⠈⠀⢀⣁⠀⡀⣅⡀⠀⠀⠀⠀⠈⠀⢀⣾⣿⣿⣦⣼⣿⣿⣦⠀⠈⠀⠀⠀⠀⠀⣀⡅⡀⢀⣁⠀⠈⠀⠀⢶⡄
⠀⠀⠀⠀⠛⢠⠎⣄⠀⢡⡆⠀⣨⢄⣤⠀⠀⠀⠈⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠀⠀⢠⣄⣬⡀⠀⣦⠁⢀⡌⢦⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠺⠆⠈⠀⠘⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠛⠀⠈⠀⠾⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋





⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠹⡆⠀⠉⠙⠒⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢦⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠒⠛⠙⠓⢦⣹⣄⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢳⡀⠀⠀⠙⣆
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠈⣧⠀⠀⢳⠀⠀⠀⠸⡆
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⢹⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡼⠀⠀⠀⠀⠀⠹⠀⠀⠈⠁⠀⠀⠀⢹⡀
⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇⠀⠀⠀⠀⠀⢠⡇⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢰⡇⠀⠀⠀⠀⠠⣄⣀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡾⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⣧⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢧⣄⣀⣀⡀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠘⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⢹⡄⠀⠀⢻⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋
⠀⠀⠀⠀⠳⣄⠀⠀⠙⢦⡀⠙⠳⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⣇⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠉⠓⠦⣤⣀⣀⣀⣀⣠⡴⠆⠀⠀⢀⡤⠞⠉⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠈⠉⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸