Twins한테 우승할 거냐고 물었더니 ok했어요 But qulaity start하는 선발과 home run치는 빠따 같이 있으면 I am 신뢰에요~
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
엘레발 안합니다 우주의기운이여...🙏젭알 엘지에게
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀https://m.cafe.daum.net/Duckgu/D5zP/13696?svc=cafeapp❤️🖤 무적엘지 🖤❤️
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
엘레발 안합니다 우주의기운이여...🙏젭알 엘지에게
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⠶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢰⣿⣿⣿⠁⢸⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣯⠅⢠⣾⣿⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⣼⣿⣿⡿⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠶⠖⣶⣶⣶⠆⢰⣶⣶⠆⣰⣶⣶⠶⠶⠶⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⢀⣿⣿⣟⣀⣿⣿⡟⢀⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠛⣿⣿⣿⠃⣼⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⢰⣿⣿⡏⢰⣿⣿⡏⢰⣿⣿⠿⠶⠶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣿⣿⠿⠟⣿⣿⣿⠇⢠⣿⣿⣿⣇⠀⢰⣿⣿⡏⠀⣿⣿⣿⠟⠛⠛⠛⠀
⠀⢠⣿⣿⣿⠃⣸⣿⣿⡟⠀⣼⣿⣿⣿⣿⣄⣿⣿⣿⠀⣸⣿⣿⣟⣀⣀⡀⠀⠀
⠀⣼⣿⣿⡏⢠⣿⣿⣿⠃⢰⣿⣿⡏⢻⣿⣿⣿⣿⠇⢠⣿⣿⣿⠉⠉⠉⠀⠀⠀
⢰⣿⣿⣿⣤⣼⣿⣿⠏⢀⣿⣿⣿⠁⠈⣿⣿⣿⡟⠀⣾⣿⣿⣧⣤⣤⡤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
https://m.cafe.daum.net/Duckgu/D5zP/13696?svc=cafeapp
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