Sanrio Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠚⣡⣶⣶⣿⣶⠆⢠⠄⠀⠀⠀⣸⣾⣿⣷⣶⠀⠀⠀⠀⠀⣠⡸⠿⠂⠶⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⠀⠀⠀⡀
⠀⣴⡿⢛⣿⠿⣿⡞⠂⠀⠀⠀⠀⢿⣤⣯⣉⣿⠠⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⡁⠀⣤⠀⠀⠀⠺⠉⠙⠁⠂
⠀⠻⡇⠈⠉⠀⣻⠛⠀⠀⠀⠀⠀⣾⠟⢻⡿⠅⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⡀⠁⠀⠀⠀⢁⡶⣶⠀⠀⣤⣤⣤⠀⠀⠀⠀⠄⢀⣦⡤⠀⠀⠁
⠀⠘⠓⠀⠀⠲⠇⠀⠀⠀⠀⠀⠀⠓⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⠙⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⣤⣶⡶⢶⣶⣄⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⡷
⠀⠐⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⣾⣿⣥⡾⣿⣿⣿⣧⠀⠀⠀⣻⣿⣶⣾⣷⣦⣀⠀⠀⠀⠀⣰⣄⣡⣾⣄⣠⣄⠀⠀⠀⠀⠿⣿⣿⣿⡅
⠀⠀⠀⣃⠀⠀⢀⠄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠹⣿⣿⣤⣿⣿⡟⠀⠀⠀⠀⢿⠋⠁⠈⠙⡐⠄
⠀⠀⠀⠙⢿⠾⢿⠇⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⢿⠄⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠈⠐⠒⠒⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⣠⣀
⠀⣸⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⢿⣺⣿⣿⣶⣿⠀⠀⠀⠀⠀⢀⣠⣄⣤⡀⢀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣅⣠⠀⠀⠀⣀⣄⠉⢛⣿⣿⣿⣿
⠀⣽⣿⡯⠿⠻⢯⢿⠿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣽⡿⡿⡿⠁⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠃⠀⣿⡛⠉⢛⣿⡇
⠀⠙⢋⠀⠀⠚⠀⢀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⣿⡧⠀⠀⢾⡟⠋⣶⣿⣶⠉⢻⡷⠀⠀⠀⠀⢀⡈⢠⡀⣾⡏
⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠘⠛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠤⠤⣴⣶⣐⡀⠀⠀⠀⢠⡄⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣆⣀⡀
⠀⢠⠀⠀⠀⠉⠙⠻⢇⠀⠀⠀⢀⠊⠈⣙⣟⡁⠉⣆⠀⠀⠀⠀⢠⣽⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀
⠀⠸⠂⡐⠀⠄⠈⠀⠎⠀⠀⠀⢨⣦⣈⣤⣷⣌⣤⡇⠀⠀⠀⢠⡼⠯⡤⠠⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠙⢻⠗
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠹⠷⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢩⡭⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⢀⡀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⢿⣿⣶⣻⣿⣿⠇⠀⠀⢀⣀⣤⣴⣾⣶⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⣄⡀
⠀⠀⠀⣟⠉⠉⠡⢿⠇⠀⠀⠈⠛⠉⢿⣿⣿⣿⢿⣷⠄⠀⠈⠛⣿⣧⣼⣿⣦⣿⣧⠀⠀⠰⣿⣿⣿⣶⣶⣤⣴⡖⠀⠀⠐⣿⣿⣿⣿⣿⣺⣄
⠀⠀⠀⠀⠐⠞⠛⢈⡦⠀⠀⠀⠀⠊⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢿⡛⠀⠀⠐⢋⡟⠀⠀⠀⠈⠉⠉⠻⣿⣏⠛⠃⠀⠀⠀⠉⠘⠿⠏⠻⠋⠛⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⡾⠁⢦⣿⡃⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣼⣿⢴⣰⠍⠛
⠀⣤⢘⠷⣴⢦⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢻⣿⣯⡫⢠⡄⠀⠀⠀⠀⠉⣀⠴⢻⠿⣿⣿⡇⡀
⠀⣻⣷⣿⡗⠀⠘⠛⢿⣿⠟⠛⠋⢉⣻⣿⣷⡯⣿⠋⣻⠇⠹⣿⠛⢈⣄⣤⡄⠀⠀⠀⢧⣤⣤⡤⢿⡹⣳⣤⣘
⠰⣿⣿⣿⣇⠂⠤⠀⣶⠃⠀⠀⠠⣼⣿⣿⣿⣷⢿⣿⣿⡿⣿⣦⣴⣾⣿⣿⣿⠆⠀⣀⠤⠤⢼⡇⠈⠳⣿⠶⠟
⢈⣁⡽⣿⣿⣟⣶⠟⠁⠀⢠⣼⣿⣿⣿⣿⣿⣟⣿⠿⡿⠾⠻⠿⠿⠿⠛⠛⠀⠀⠘⢗⡶⠖⠒⣋⣀⠀⠘⠒⠖
⣩⣽⡀⠘⠻⣏⣁⣤⡴⠞⣿⣿⡿⠛⠉⠁⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠖⠋⠉⠁⠉⠛⠲⠶⠶
⡷⢖⣣⣤⣀⣀⣀⣠⣦⡤⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣀⠀⠀⠀⠀⠀⡀⠰⠂
⡵⠋⢀⣖⣿⣭⣿⣿⡏⠀⠀⠀⠀⠈⠄⠀⠀⠀⠙⡆⠀⠀⣤⣽⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠀⢀⣴⣶⣶⣶
⠀⣤⣸⣿⣟⣩⣽⡇⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠲⡄⠀⠀⠘⣿⣿⣿⣿⣿
⣀⡹⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⢸⡟⠉⠉⠙
⣾⠂⣾⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡇⠀⠀⠰
⣿⠟⠛⠙⢻⢜⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠘⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⡇⠀⠀⣤
⣙⠲⠶⠶⠋⢐⡇⠀⠀⠈⠀⠀⠀⠀⠙⠀⠀⠀⠈⠃⠀⠀⠀⠈⠃⠀⠀⠀⠙⠻⣿⣿⣿⡿⠟⠀⠀⡅⠀⠀⢹
⣿⣤⣶⣽⣼⣿⡇⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣁⠀⠀⠀⠀⢀⡴⠀⠀⠠
⣽⣿⣿⣿⣿⣿⣿⣶⣤⣾⠿⠿⠿⠿⠿⠛⠻⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠿⣿⣦⡀⣴⣿⣧⡶⢦⣭
⣿⣿⣿⡟⠋⠙⣿⣿⣿⠃⠀⠤⠀⠀⠀⠀⢶⣶⣶⣴⣶⣶⣤⣤⣴⣶⡄⠀⠀⠀⠠⡄⠈⣿⣷⣿⣿⣿⠃
⣿⣿⣿⣆⠁⣤⢹⣿⣿⢄⠀⠀⠀⠀⠆⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠤⠀⠀⠀⢰⣿⢹⣿⣿⣿⣧⣋⣀
⠙⣿⡿⠿⠿⠶⠾⣿⣿⡀⠀⠐⠄⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⣿⡏⢸⣿⣿⣿⣽⣿⣭
⣄⣈⡙⠒⣲⠴⠦⣿⣿⡧⠀⠀⠀⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠠⡄⠀⠈⢸⡟⠀⢸⣿⡿⠀⠉⠙⠳
⣿⣿⣿⣿⣿⣶⢦⣿⡿⣿⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⢀⠀⠐⠄⠛⠃⠀⢸⣿⠷⣿⣷⣶⣶
⣼⣿⣿⣿⣿⣿⣧⣿⣿⣼⡆⢀⣀⣀⣈⣀⣀⣀⣀⣂⣀⣀⠀⠀⠀⢀⠀⠀⠀⠢⠀⢻⣦⣄⣾⡿⣾⣽⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣷
⣿⣯⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣣⡄⠀⠀⠉⣿⣿
⠋⠁⠀⠀⢀⣀⣼⣿⣿⠿⠿⠿⠿⣿⠇⠀⠙⠿⣿⣿⣯⣽⠿⠟⠋⠁⠀⠀⠀⣀⠠⣄⣲⠞⠋⠀⣀⣠⡼⣿⣟
⣶⣾⣟⣿⣿⠏⠺⣷⣶⠶⠟⠓⠒⠚⢋⣀⠀⠀⠈⠛⠦⢤⣠⡦⢄⡶⠤⠾⣶⣿⣿⣿⣶⣦⡀⠈⢧⣀⠀⠀⠉
⠅⡼⠿⢹⣃⠀⣾⣩⣴⠶⠛⡛⢻⣛⣫⣛⠷⣶⣤⣄⣀⣀⣀⠀⢳⣄⡀⠀⠙⠦⢽⣯⡟⢿⣿⣷⣄⡈⠙⠳⠶
⣶⣾⣿⡞⡁⠀⠉⢥⢂⡀⣠⣻⣿⣿⣿⣿⣿⣧⣴⣽⠿⠍⠉⢙⠛⠿⠿⣿⡲⣶⢦⡙⣌⠳⢿⣿⣿⣿⣶⣤⣀
⡟⣿⠏⠁⢀⣌⠱⣾⣈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠈⠀⡀⠈⢷⡌⢳⣿⡌⢳⣄⠈⠙⠛⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⢷⠞⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠻⠿⣷⣶⣴⣿⠋⠁⠀⠈⠻⣷⣄⣀⣀⣀⡀⠀⠀⠀⣀⣤⣶⣶⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢹⣿⠃⣀⣀⠀⠀⠀⠙⣿⡿⠿⠿⠿⠿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣦⣤⣶⡿⠿⠿⣿⣏⠹⣷⠀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⢉⣿⠏⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣇⠀⠀⢰⣿⢻⣧⡀⠀⠀⢀⣿⣿⣶⣦⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠛⠛⠛⢿⣶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⢰⣿⠿⣷⣦⣄⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⣴⣶⣶⣶⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠙⣿⡟⠉⠉⠛⠃
⠀⠀⣠⣤⣴⣿⣿⠶⠀⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⢠⣤⣼⣿⣁
⠀⠀⠈⠁⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⠛
⠀⠀⠀⠀⣀⣤⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣾⣿⣇
⠀⠀⠀⠘⠛⠉⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣠⣴⣾⠟⠉⠈⠙⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠿⠛⠛⠿⣿⣟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⢉⣉⣭⣭⣍⣹⣿⠁⠀⠀⠀⠀⠘⠿⠋⠉⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢰⣿⠛⠉⠉⠙⣻⣿⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⣿⡇⠀⠀⠀⣰⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠸⣿⣄⠀⣰⣿⠃⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⢿⣿⡏⠀⠀⠀⠀⠈⠻⣷⣿⣇⠀⠀⠀⣀⣼⡟⠀⠀⣀⣴⡾⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠿⣶⣿⠛⠉⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⡀⠀⢹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁

⠁⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⢀⣀⡤⠞⠻⢿⣿⣭⣭⣭⣭⣷⣀⠐⠠⠐⠀⠀⠉⠀⢰⣏⣁⠀⠛⠁⠀⡠⢄⠀⠀⢀⣄⢠
⠀⠀⠀⠁⠀⠀⠀⠀⢈⡵⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⣞⠛⠲⣼⣇⣤⠴⠦⣄⠀⠈⠁⠀⠀⠈⠋⡏
⣠⣤⣤⣄⣀⠠⡤⠀⢸⠀⣠⠀⠀⠰⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⠀⢀⣹⣿⣟⣿⣿⣿⣿⣷⣶⣶⣿⣀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠙⢦⠀⠀⠀⢻⠃⠀⠀⠀⠀⠢⠜⢅⠄⠀⠁⠀⠀⣸⠞⣋⠁⠘⠻⠿⠛⠉⠹⢿⣿⣿⡇⠉⠙⠶⣄⠀⠀⠀⢸
⣴⣄⠀⠀⠀⢈⣧⡴⠚⠻⠛⠳⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣼⠋⠀⢀⣄⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⠈⢳⣄⣀⣤
⠉⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢉⡳⣄⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠘⠋⠀⠀⠄⠀⠀⣾⡆⠀⠸⣇⠀⣠⠼⠋⠁
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⠋⠙⠲⣤⣤⣤⣿⣤⡶⣦⣀⣀⣀⠐⠀⠀⠀⠈⠀⠀⠀⢙⡾⠁
⣤⣾⡏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣰⣯⣴⣮⣿⡉⠉⣷⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠿
⠸⣿⠃⠀⠈⠁⠀⢴⡦⠀⠀⠾⠆⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣽⣿⣿⡿⣆⣠⣤⠤⢤⣄⣸⠇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣴⠟⠁⠀⠀⠀⠈⠻⠤⠶⠒⠒⠲⢤⡖
⠛⠛⠶⠶⣴⠖⢶⣤⣤⣀⠀⠀⠀⢸⡥⠖⠀⢉⣀⣀⠯⣆⡀⠀⠸⠇⠀⠐⠛⠻⡟⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣾⣷⣿⣿⣿⡀⠈⣇⣀⣀⣸⣧⣀⣰⡋⠀⠈⠛⠉⠙⣦⠀⠀⠀⣈⢙⡞⠃⠀⠀⠀⠈⠋⠀⠀⠀⢾⡷⠀⠀⠀⣠
⠀⠀⠀⠙⠻⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠉⠉⠓⠞⢳⣄⠀⠻⣄⠀⠀⢨⡏⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣀⠀⠀⠀⣀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⢰⠻⠶⡆⣹⠀⠀⣸⡇⠀⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⢀⣾⠃
⠚⠁⠀⠀⠛⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠁⠯⡄⣠⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣤⣽⡶⠶⠶⠶⠶⣾⡇⠀⢰⡆
⠀⠀⠀⠀⠀⢸⡀⢠⣦⡴⠦⠤⠶⣄⣤⠀⠀⠀⠀⠀⢀⣾⡟⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⠁
⠶⣄⡀⠀⠀⠀⡟⠉⢠⡦⠀⠀⠀⠀⠈⠙⠻⣤⣤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠷⠲⢤⣀⣿⡀⠀⠀⢀
⠀⠈⠻⣄⣀⣀⣿⣀⣀⣀⣀⣄⢀⡀⠀⠸⠗⠀⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠉⠉⢙⣿⢛
⡀⢀⣤⠟⠋⠉⠉⠀⠀⠈⠉⠙⠳⣄⡀⠀⠀⠀⠀⢘⣿⠟⢉⡉⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢾⣿⣿
⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣴⣶⣶⣿⣿⣤⣜⠋⠀⠀⠀⠀⠀⢠⣄⠉⢿⣟⠂⢀⣄⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⡀⢀⣤⣶⣿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣿⠏⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠉⠛⠛⠿⢿⣿⣿⠿⠿⠟⠛⠛⢻⣿⠇⠀⢀⣴⣶⣶⣾⣿⣷⣤⣄⣀⣀⣤⣼⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⢀⣾⡟⠉⠀⠉⠻⣿⣿⣍⡀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠙⢻⣿⣇⠀⠀⠀⢠⣿⠇⢹⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠿⠿⠛⠻⢷⣶⣾⣿⣿⡶⠾⠏⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣠⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⢷⣶⣶⠶⠾⠶⠷⠷⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣾⣟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⢿⣿⡟⠙⠉⠙⣿⣿⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⣹⣿⣿⣀⣀⡀
⠀⠀⠀⠰⠾⠿⠟⣿⣿⣟⠁⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⡿⠀⢀⣀⠀⠘⣿⣆⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⢈⣿⣿⡟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀⣼⡿⠁⣾⠋⠉⢹⡆⠈⠻⣶⣄⣀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣀
⠀⠀⠀⠀⠀⢠⣶⠿⠿⢿⣿⣦⣀⡀⠀⠀⠀⣀⣠⣴⡿⠋⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⣩⣿⡿⠛⠛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡿⠿⢿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⢷⣶⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠋⠀⣿⠟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⣷⣿⡏⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠶⢶⣾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠹⣿⣿⣤⣤⣤⣤⠀⠀⠀⢠⣤⣤⣤⣼⣿⡿⠃⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣶⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠉⠙⠋⠉⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣦⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠻⣦⣀⣠⣴⣶⡿⠿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠙⠛⠿⣿⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⡿⠁⠀⠀⠀⠀⠈⢿⡟⠋⠁⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢠⣿⠁⠀⠀⣠⣶⣶⣤⣼⣷⣤⣄⠀⠀⠀⣀⣹⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⣿⣀⣼⠟⠁⠀⠀⠙⢿⡾⠛⠛⠛⠛⢻⣆
⠀⠀⠀⠀⠀⠘⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⢸⡿⢶⡄⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⠶⠾⠻⣷⣄⣀⣀⣤⣿⣧⣼⠟⠀⠀⣸⡏
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⢿⣄⠉⠁⠀⢀⣼⡟
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠟⢻⣷
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆
⣠⣤⣤⣤⣿⣧⣤⣤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠲⠾⠿⣿⡟⠛⠛⠛
⠉⠉⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⣀⣸⣿⣦⣤⠄⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠛⣿⡿⠿⠷⠶⠆
⠀⠀⠚⠛⠉⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠃
⠀⠀⠀⠀⠀⢀⣸⣿⣷⣟⠃⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠿⣶⣦⣀
⠀⠀⠀⢠⣶⠟⠋⠁⠈⠻⣿⠏⠁⠈⢻⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠀⠀⣀⠀⠀⠀⠀⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢾⣀⡷⠀⠠⣾⡏⣿⡏⠙⠛⠛⠛⠛⠋⠉⣿⠏⠉⠈⢿⣟⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡟⠀⠀⠀⡀⠀⠀⢸⡷⠸⣷⣄⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠈⢿⣧⣴⡿⠻⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠘⢷⣄⣠⣼⡿⢶⣶⡟⠁⠀⠈⠛⠿⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠉⠉⢹⣿⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⢸⣿⢻⣦⡘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡾⠟⠃⠀⠙⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠟⢿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢷⣶⣶⣶⡶⠿⠿⠿⠿⠷⣶⣶⣶⡶⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣤⣠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⣿⣤⠛⢿⣿⠿⠿⣰⡟⠿⣿⣿⡶⣠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⢇⠀⠀⠈⠙⠻⡈⠃⠀⠀⣸⣷⣾⣦⣼⠇⠀⠀⠀⣿⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠦⠶⠊⣿⣨⡄⣀⣀⢠⡀⢄⣓⣠⠄⣍⠉⢹⡿⠇⠾⢂⡀⣠⣿⡿⠀⢨⣦⡄
⠀⠀⠀⠀⢀⠘⠁⠐⣶⣶⣿⢿⡿⠞⠟⡊⣏⣿⣿⣿⣿⡏⣴⣶⣶⣦⣴⣶⣶⣦⡈⠡⠀⠈⢻⣷⠁
⠀⠀⠀⢠⡜⡶⣶⡚⢈⡿⠋⠛⠁⠀⠘⠛⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⠟⣭⣝⠇⠀⠀⠀⠘⠀⠀⣠⣤
⠀⠀⣠⡽⠸⣽⡿⢛⡋⠄⢠⣤⣶⣴⠀⢀⡀⠉⠉⠉⠙⠸⢿⠟⠉⠁⠬⢉⠘⣿⣶⣶⡀⠁⠀⠀⠀⢹⣯
⠀⠀⢿⣀⣼⣷⣭⣒⠊⢠⣼⣿⣿⣿⠆⣼⣷⣦⣀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣼⣿⣿⣧⡀⠀⠠⠠⠈⠁
⠀⠀⠀⠙⠿⠿⠋⠛⠃⠻⣿⣿⢿⣿⣮⡿⠿⠿⣿⣿⣿⣜⠿⣟⠋⢩⣿⣏⣹⣧⢠⣬⠟⠀⠀⣀⢀⣀⠂⢴⡄
⠀⠀⠀⢀⠀⠈⠠⣀⠇⣀⣠⢅⢁⣩⣴⣶⡜⣷⣶⣭⣭⣥⣿⡿⢺⡋⠉⠉⡿⣿⠇⠀⠀⠀⠀⠉⠈⠋⠀⣿⡿
⠀⠰⠆⡀⠀⠀⡀⣉⣐⡋⠁⢻⣿⣿⣿⣿⣷⡌⡿⠛⠶⠛⣻⡇⢂⣀⣈⠤⠐⠋⠀⡔⠀⠀⠘⠦
⠰⣷⡆⢃⠀⠀⣁⠙⠻⣿⣦⣟⠉⠹⣿⣿⠻⣷⡕⢠⣤⢤⠉⢁⢿⣿⣿⣷⣧⡀⠀⠀⠀⠀⠁⠠⠀⠀⢰⡷⣾
⠀⠁⣶⢈⡀⠙⠋⠀⣼⡿⠛⠻⢿⡇⡄⠀⠀⠺⠇⠀⠀⠀⠐⡫⢾⣿⣿⣿⡿⣿⣷⠄⠀⠀⣀⣴⣿⣷⣼⡓⠟
⠀⠀⣴⣿⣿⣶⣤⡄⠜⠁⠀⢨⡟⢡⡄⠠⠀⣀⠀⠄⢀⠠⠊⠀⠀⠀⠀⠀⠑⠄⠀⠀⠈⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠉⣿⣿⡟⣭⡱⡿⠤⠵⠊⠁⠈⠀⠕⡄⠀⠀⡀⠨⣶⡦⠄⢄⢿⢿⠋⠉⢿⣶⣶⣶⣭⡻⣿⣿⣿⡿⠁
⠀⠀⠀⠙⢛⡸⠋⠁⣼⢿⠟⣼⣿⠆⠀⢈⠀⠀⡎⠀⠴⢼⡔⠆⢀⡏⣓⣆⣐⠀⣸⣿⣿⣿⣷⠹⠻⡿⠃
⠀⠀⠀⠀⠈⠓⠀⠀⠈⠀⡿⡾⢫⣶⣄⣉⣼⠀⣼⣶⣶⣾⣿⣶⣿⡇⠙⠋⠙⣼⣿⣾⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠷⠔⠑⠳⡤⣸⣿⣿⢋⣿⡶⣜⡿⢿⣿⡿⠿⠟⠁⠀⠀⡘⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⡠⣤⣄⣾⣷⠄⠉⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⢼⡿⠛⣴⣷⣷⡞⠛⣿⠎⣋⡩⠵⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠛⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⢶⣦⣄⠀⠀⠀⢀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⣿⣶⣦⣤⣀⠀⠀⠀⢀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠈⠻⣷⣶⡿⠿⠛⠋⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠉⠙⠻⢿⡿⠿⠟⠛⠛⠛⢻⡿⠀⠀⠀⠀⣀⣀⡀⢹⣿⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡏⢩⣿⠿⠛⠻⢷⣦⣤⣴⣶⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠘⠷⣿⠃⠀⠀⠀⠀⢻⣏⠉⠀⠈⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⡾⣿⣆⠀⠀⠀⢀⣾⠟⣷⠀⠀⠀⣸⡗
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠻⢷⣶⣶⡿⠿⠶⠟⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣀⣀⣠⡾⢿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⢻⣧
⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣤⣤⣤⣤
⠀⢠⣴⣶⡶⢿⣿⡿⠷⠶⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠉⠉⢹⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣠⣤⣼⣿⣄⣀⣀
⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢹⣿⠋⠉⠛⠛⠁
⠀⠀⠀⠀⠉⠉⠀⠙⣿⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣿⣯⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⠻⠷⡆
⠀⠀⠀⠀⠀⠺⠛⠉⠀⠀⠈⠙⠿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠷⣶⣤⣀⣀⣀⣀⣤⣤⣼⡟⠁⠀⠉⢿⣶⠿⠛⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠈⠙⠛⠉⠉⠉⣹⡟⠀⠀⣴⢶⣦⣿⣤⣄⣀⣀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠳⣾⠁⠀⠀⢹⣏⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠞⠻⣦⣀⣠⣾⣿⡇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣄⣀⣀⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠘⣿
⠀⠀⠀⠀⣀⣤⣤⣿⣤⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠲⠞⣿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠠⢤⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠒⠛⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠛⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⢀⣀⣤⣤⣀⢀⣤⣤⣤⣀⢀⡄⠀⠀⣀⠀⠀⣤⣀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣀⡀⡀⣆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡇⠀⠀⠈⠙⠿⣰⣿⣿⠛⣭⣭⣿⣿⣿⡌⢲⣿⣷⡟⣠⣶⣿⣿⣿⣿⣿⣿⣌⠀⠀⠀⠀⠶⠆⡇⠢
⠀⢀⣿⣿⣿⣿⡿⢿⣏⣛⣿⣿⢇⠩⢉⣷⠠⠄⢤⠀⠀⣿⣿⣷⣿⡿⠻⠇⣮⢻⣿⢘⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣾⣦⣤⣾⢿⣶⣤⣶⣇
⠀⠸⠿⡿⠋⠀⠀⡴⠈⠉⢩⣴⣾⣿⣿⡋⡦⢀⣤⠠⡄⠟⣫⣭⣋⠔⠀⠀⠻⡸⡟⣼⣿⢇⣿⡼⠿⠿⠿⢿⡍⢛⣛⢿⣿⣇⢿⣿⣿⣿⣸⣿⣿⣿⠏
⠀⢀⡄⠢⠄⢀⡐⢀⠀⠠⠖⠉⠉⠹⣏⡁⠀⠈⠉⠸⠇⢀⣶⡆⢨⠀⠀⠀⠀⠁⢀⣭⣭⣌⡙⢓⣨⣥⡁⣀⣴⣿⡿⣨⣭⡍⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⣾⣷⣶⣶⣾⡄⣀⠙⠁⠀⠉⠁⠀⠀⠀⠈⠀⠈⠁⢸⢡⡀⠀⠀⠀⢐⡀⠛⠿⢿⣿⣿⣿⣿⡇⣿⣿⣯⡐⡿⠿⢿⠛⣫⣽⣶⣶⣮⣝⣛
⠀⢠⣿⡟⠉⣿⣟⠻⣿⣧⡈⢀⠆⠠⠀⡀⠀⠤⠀⠀⠀⢀⣡⣀⠙⢿⣿⣦⠸⢿⠇⠀⣤⡻⣿⢿⣿⣿⣷⡉⠉⠹⠿⣠⡿⢶⣾⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠈⢻⡅⠀⠀⠁⠀⠸⠛⠋⠈⠐⣿⠓⠀⠀⣿⣿⣦⣾⣿⡿⠟⠀⠀⠁⠀⠺⠆⠄⠀⢿⣷⣄⣤⡄⢿⣿⢣⣤⠀⠘⠻⣾⣽⣿⣟⡝⠙⠛⢿⣿⣿⡿
⠀⠀⡨⠥⠤⠤⣴⣶⣖⣚⣆⠠⢴⣿⣧⠤⠤⡉⣿⣿⣿⣿⣆⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⣿⣿⣿⡰⠀⠈⠁⢀⣠⠀⣭⠉⠳⣽⣤⢷⡆⣾⡻⠿⠁
⠀⠀⡇⠀⠀⠀⠙⠟⠻⢿⣿⠀⡤⣽⠡⣄⠀⢸⠈⠁⠀⠚⡿⢤⠇⠀⠀⠀⢓⠂⠀⠀⠀⠘⠿⠿⣿⣷⠄⠀⠄⢞⣛⢃⡘⣳⢄⡑⣀⡀⣀⡝⠁
⠀⠠⣅⠀⠠⠀⠀⠀⠀⠀⢸⠆⢠⣾⣧⣈⣠⣾⠰⡖⢐⡂⢀⠀⣀⣀⣀⡉⠀⠀⠀⠄⠀⠠⠐⠤⡽⠃⠀⠀⠸⣿⣿⣿⣷⣄⣮⢱⣬⣥⣬⣴⣿⣶⣆
⠀⢔⠃⠁⠐⠀⣉⣠⣶⣦⣘⠀⠘⠰⣬⣽⡛⠿⣂⣉⣡⣶⡿⣴⣿⣿⣿⣿⣬⣆⠀⣦⠒⠀⠀⠀⠀⢸⣿⣧⣤⡸⣿⣿⣿⣿⠡⣾⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠁⡶⠦⣾⣿⣿⣿⣿⣿⡷⠔⠃⠹⢿⣿⣿⡏⣿⣿⣿⡃⣿⣿⣿⡿⠿⠟⠑⠀⠘⠢⠀⠀⠀⠀⠈⠁⠙⠛⡀⠻⣍⡻⢋⠻⠎⢛⡛⠿⡟⣉⠛
⠀⠀⠀⣤⠀⠀⠀⠀⠈⠉⠻⢷⡄⠀⣀⢸⠏⠉⠛⠉⢬⢻⡇⠊⠛⠋⠘⠛⢫⠀⠀⠀⠀⢃⢀⠀⠀⠄⠀⠁⢠⠇⢰⣿⠇⠹⡟⣻⣿⣿⣿⣶⣿⠂
⠀⠀⢀⣿⣶⣄⡁⠀⠄⠀⢀⣤⣶⣾⣿⣷⠀⣠⣤⠤⡄⠉⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⣠⡜⠀⢷⣶⣴⣶⣦⢃⣤⣤⣍⣤⣦⣽⢻⣿⣾⣿⣿⣿⣿⠆
⠀⠐⢿⣿⠟⠛⠻⠃⡴⢾⣿⡁⢌⡿⠛⢻⡇⠀⣶⣶⡆⠀⠀⡀⠀⠀⠀⠀⠀⢰⣬⣛⠻⢿⠀⠼⠿⢿⡿⢣⣮⡀⠀⣸⡀⠀⢉⣇⢻⣿⣿⣿⣿
⠀⠀⠀⠉⠒⠀⠀⢰⣾⣦⠩⢙⣇⢶⣤⣜⣛⡀⠀⠉⠀⣀⠈⠁⠀⠀⠘⢀⡠⠈⠙⢛⣛⣠⣶⣿⣿⡷⣴⣧⣭⢹⣿⣿⣿⣿⣿⣿⠯⢟⣫⣭⣍⡀
⠀⠀⠰⠀⠀⢠⣄⣀⠉⠿⠿⠸⢟⣓⡙⣿⣿⣿⣿⡛⠿⠟⠋⠄⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡽⣷⠟⠟⠋⠀⢻⣿⣿⣿⡟⣫⣾⢟⣭⡻⣿⡇
⠀⠀⠀⠶⠖⢛⡉⠟⣣⣤⣶⣿⣿⣿⣿⡎⢿⡏⠸⠃⠀⠀⡐⠂⠄⠠⣴⣶⣒⣆⢹⣿⣯⡛⢻⠄⢀⡺⣶⣶⠖⣀⣛⠛⣛⠿⣱⡿⣀⣸⣿⣷⢸⣷⡄
⠀⠀⢰⣧⣤⣭⡉⠘⠿⣿⣿⣿⣿⠿⢿⣿⠌⠁⠀⠀⠀⠀⠇⠀⠀⠀⠛⠛⠿⠟⠀⠀⠛⠋⠰⠀⠆⠀⡀⢀⠘⠂⢺⣿⣞⣃⠹⠰⢿⣿⣿⣿⠰⣿⣿
⠀⠀⢸⣿⡿⣛⠇⣴⣦⣘⣛⣛⡃⠛⡼⠃⠀⠠⠀⠐⠀⠘⣇⠐⠀⢠⠄⠀⠀⣰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠛⠟⡁⠙⣃⡻⣿⣿⣷⣎⠋
⠀⠀⣿⢛⠆⠉⣼⣿⣿⣿⣿⣿⢋⡁⠀⠀⠀⠁⠂⠀⠀⣠⣬⢶⣏⣱⣤⣶⣖⠁⠐⣿⣿⣷⠀⠀⠀⠄⠀⠀⠀⠁⠐⠀⠈⠠⠃⢴⣮⣾⡋⠁⠘⠻
⠀⠀⢈⣬⣄⡘⠏⠀⠈⢹⢿⣧⡹⣷⣤⣤⡆⣾⣶⢖⣟⡟⣋⣊⠭⡖⣖⢮⣥⣄⠀⠸⠟⠀⣀⣀⢠⣤⣲⣼⣿⢿⣓⣾⣎⠓⣀⡴⢎⠣⠄⠠⠶
⠀⠀⠈⣥⣤⣥⣠⣥⣍⠀⠛⠿⡇⣤⣨⣿⣷⡮⣩⣾⣿⣯⣿⢓⣹⣟⠮⡧⣈⠋⣴⣶⣿⣿⣿⣿⣷⠹⣿⣿⠟⠛⢿⣽⡾⣷⡀⢳⣿⡀⣺⣷⣦
⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠸⣷⡄⠻⠍⠉⢛⢿⣮⠹⣿⢿⣿⡿⠏⠙⢛⣶⣱⠇⣹⣿⣿⣿⣿⣿⣿⣷⣌⢁⠀⠀⠀⣿⣿⣿⣯⢰⣶⣾⣿⣿⡿⠃
⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⣰⠟⠁⠀⠶⠤⠤⣾⠁⠀⡤⡀⠋⡏⠚⠛⢾⣷⡾⠸⣿⣿⣿⣿⣿⣿⣿⢙⠁⣦⣀⣀⠤⠻⠟⣛⠻⠈⢉⡿⠀⢤⣴⡄
⠀⠀⠈⣻⣿⠿⢿⣿⠟⠉⣛⠸⣷⠄⠀⠀⠀⠀⢀⣤⠘⠱⠇⢠⣀⣀⣈⡟⠀⠘⠻⣿⣿⣿⣿⣿⡿⠘⠻⠛⠉⠻⠖⣰⣿⣿⣟⣠⣿⣧⣤⣾⣿⣷
⠀⠀⠀⠛⠋⠀⠀⠋⠀⠀⠋⠑⠀⠁⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠙⠋⠉⠉⠛⠁⠀⠘⠚⠂⠒⠀⠉⠙⠿⠿⠻⠿⠿⠻⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣤⣀⢠⣀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣲⣦⡘⢿⣿⣿⣷⣿⢢⡾⠿⣿⣿⣷⡆⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡆⠂⠀⠘⠛⠿⡇⠛⠃⠀⠀⢸⣷⣴⣏⣈⣽⠈⠍⠀⠘⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⠙⠿⠈⣃⠂⠠⠀⠂⢘⠐⡤⢀⡀⠾⠛⠻⣿⣟⢡⣦⠀⠂⢀⣿⣿⠀⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠴⠀⣥⣤⣤⣿⣿⣿⡜⣿⣦⢿⢶⣶⣷⣾⣴⡿⢀⣀⣯⣄⠈⣠⣭⣄⡛⠻⠋⠀⠘⢿⣟⡢
⠀⠀⠀⠀⠠⡆⣀⢀⡴⠹⣿⡿⣿⠏⠁⠉⣶⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠿⢿⡀⠈⠀⠀⢈⡟⠃
⠀⠀⠀⢰⠟⡼⣹⣷⣤⡶⠋⠁⠀⣀⠀⠀⠀⠹⠿⠿⠿⠿⣿⢃⣿⣿⡯⠿⠛⢿⡅⣿⣮⢁⣀⠀⠀⠀⠀⠀⠰⣾⡧
⠀⠀⣰⡎⠀⣓⡺⣏⠽⣄⠂⢰⣷⣿⣿⡇⠀⣶⡀⠀⠀⠀⠀⠘⠛⠋⠁⠀⢘⣣⣤⣈⢿⣿⣿⡆⠈⠀⠀⠀⠀⢿⠷
⠀⠀⠙⣤⣴⣿⣿⣾⣭⠁⣰⣿⣿⣿⣿⡇⣰⣿⣿⣷⣤⣀⣈⢠⣶⣿⣿⣿⣿⣿⣿⣿⠸⠿⢿⣿⡄⠀⠀⠂⠂⠀⠂
⠀⠀⠀⠈⠛⠿⣋⠉⢉⠁⠻⣿⣿⠿⢿⣷⠮⠛⡻⠿⢿⣿⣿⣼⠛⣛⠍⣀⣿⣿⣄⢿⣦⠠⠴⠏⠀⠀⣠⡀⣤⡄⠐⣿⣆
⠀⠀⠀⠀⡐⠈⠀⢦⡨⢂⣀⡠⢆⠉⣬⣴⣾⣷⠹⣿⣶⣽⢿⣶⣿⣿⠘⡏⠉⠉⢩⡿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠁⢘⣿⠟
⠀⠰⠷⠐⠀⠀⢀⠀⣋⣘⡋⠁⠛⣿⣿⣿⣿⣿⣷⢹⡿⠛⠶⠛⡻⣷⢓⣀⣀⡥⠤⠚⠁⢀⡐⠀⠀⠀⠧⠄⠀⠀⠀⠀⡀
⢠⣶⡆⢡⠀⠀⢈⡈⠻⠿⣷⣦⡛⠋⠙⣿⣿⡿⢿⣦⡃⢀⣠⣄⡁⠇⢾⣿⣿⣿⣼⣆⠀⠀⠀⠀⠀⠐⠬⡀⠀⠀⣶⣶⣶
⠀⠉⣵⡄⠀⠘⠿⠃⠀⣾⡿⠿⠿⣷⣆⣌⠉⠁⠀⣶⡆⠠⠁⠀⠀⠚⣵⣿⣿⣿⣿⣿⣿⣶⢄⠠⠀⠀⣀⣴⣿⣆⣛⠷⡏
⠀⠀⢨⣶⣿⣦⣔⣀⡀⡻⠃⠠⢀⡾⠏⡆⠀⠀⠀⠀⠀⡀⠀⠀⠔⠈⠀⠉⠉⠉⠙⢀⠩⠁⠀⠘⢠⣾⣿⣿⣿⣿⣿⡇⠁
⠀⠀⠻⣿⣿⣿⡿⡛⣱⣦⡐⣆⡼⠛⠠⠋⠂⢅⠀⠃⠀⠀⢐⣀⣄⣀⡀⢠⣤⡤⠤⠤⣤⢠⣤⣄⡸⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⡏⣾⠿⠊⢭⣯⣥⢠⣴⡄⠁⠌⠜⠁⠀⡔⠀⢉⢻⢏⡀⠈⢊⢯⣁⡠⣀⠉⣺⣿⣿⣿⣶⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣶⡃⠀⠘⠿⠙⣥⣪⣿⣃⠀⢠⡆⡠⠀⣇⡀⢋⣹⣧⣉⣠⣮⠰⣶⣶⡶⢠⣿⣻⣿⣿⣿⣇⣁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡘⣟⠋⢱⣿⣷⣶⣾⣇⠁⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠈⠙⠗⣼⣿⣿⣏⣼⣿⢣⣮⣟⣛⣛⣛⣛⠏⠁⠠⠀⢀⠊⠿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢛⣼⣿⠿⡿⠿⢿⣿⣬⠲⣶⣼⣿⡟⠢⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡇⣿⡟⠉⣾⣿⣿⡎⠙⣿⡇⣈⡥⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠛⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠻⣦⣀⣤⣴⠶⠟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠶⣶⣤⣄⣀⣠⣤⣤⣴⣾⠋⠀⠀⠀⠈⢻⡋⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⢸⡏⠀⠀⢰⠋⣿⠟⠛⠳⣶⡶⠖⠺⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣻⡇⠀⠀⠀⢸⢦⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠉⠙⠦⣤⣴⠿⠞⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡴⠞⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠈⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⠛⠃⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠚⣿⡿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣤⣤⣀⠀⠀⠉⠁⠀⠀⠀⠀⣾⣋⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢉⣙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⣠⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡾⠛⠉⣰⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠈⠉⢿⡀⠀⠀⢀⠀⠀⠀⠀⠈⢻⣷⠶⢶⣶⠶⠛⠿⠿⣿⡿⢿⡏⢁⣠⠴⠊⠙⣿⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⠈⠛⢶⣶⠿⣧⣄⣀⣀⣠⡾⠃⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠿⣯⡤⠤⠤⠤⢽⣷⠤⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣿⡅⠀⠈⢹⡟⠋⠉⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣸⣿⠀⠘⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠻⠶⠶⠛⣤⣄⣀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣼⠃⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⢶⣦⡀⢻⣿⠟⠀⠀⣠⣄⣀⠀⠀⠀⠀⠈⠙⣏⠉⠈⣧⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡀⠻⣦⣀⠀⠀⠀⢹⣿⡿⠃⠀⢠⣤⣀⡀⢻⡀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣧⠀⠀⠉⠛⠛⠷⣤⡁⠀⠀⠀⠘⣿⠿⠃⠘⣇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡘⢧⡀⠀⠀⠀⠀⠈⠙⠛⠒⠲⣶⣦⣄⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣽⣦⣄⠀⠀⠀⠀⠀⠀⣠⡿⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⠦⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠷⢶⣤⣀⣴⣾⠿⠛⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠃⠀⠀⠀⠙⢿⡏⠁⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠿⢿⣷⣶⣦⣤⣶⣾⣿⠿⠿⠛⣿⠃⠀⠀⣴⡶⣶⣾⠿⠿⢶⣤⡶⠾⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⣠⡿⠁⠀⠀⠀⢹⣷⣦⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠈⣙⣿⣄⠀⠀⢀⣼⣯⣼⡏⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠉⠙⠻⠟⠻⣿⣉⠁⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠈⣿⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⢻⣿⠟⠛⠛⠃
⠀⠀⠀⠀⢀⣠⣤⣶⣿⣷⠶⠆⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣾⣟⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠸⣿⣄⣀⡀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣿⣅⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠻⠿⠦
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣻⣷⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠃⠀⠀⠉⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠛⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⢿⣿⡉⠁⠈⢿⣧⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣴⡿⠟⢛⣿⠟⠉⢻⣟⠉⠉⠉⠉⠉⠀⣸⡿⠀⠀⠹⣷⡄⠀⠈⢻⣷⡄⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠻⣷⣤⣿⣏⣤⣀⡈⠻⣦⣄⣀⣀⣠⣴⡿⠁⢀⣀⣤⣽⣿⣄⣀⣤⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣽⡿⠛⠛⠛⠛⠿⣷⣄⠉⠉⠉⠉⠁⣠⣾⠟⠛⠉⠙⠛⢿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⢀⣤⣿⣿⣶⣶⣶⣶⣶⣿⣷⣤⡀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠁⠀⠀⢉⣤⠀⠀⢠⡉⢀⡄⠀⠀⡀⢠⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠘⡀
⠀⠀⠚⠁⠀⠀⠈⠚⠋⠀⠀⠒⠒⠒⠒⠀⠀⠛⠁⠃⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠒⠓⠂⠁

⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⡀⠀⠀⠀⠐⠀⠀⠀⣂⡄⠠⡀⢀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⣠
⠀⠠⠄⠤⠀⠀⠀⠠⠄⠀⠀⠀⠠⡰⠀⠀⠀⠀⠀⠀⠀⢨⠿⠇⠆⠀⠀⠒⠂⠀⠀⣈⡀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠁⠀⠻⡀⡿⠃⠀⢀⣀⠀⠀⠀⠀⣀⢲⠆⠀⠀⠠⣤⠁⠀⠐⢀⡀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⡉⠀⠀⠀⠈⠙⠀⠀⡄⠈⠛⠤⠄⠀⠀⢹⠀⠀⢀⠀⠀⡤⢤⣤⢀⣻⢧⠀⠀⣤⡵⠀⠀⠀⠀⠉⠀⠀⠀⠠
⠀⠀⠛⠓⠀⠀⠀⠉⠁⠀⠀⠠⠛⠋⠘⠀⠀⠺⠘⠆⠀⠀⠨⠁⠓⠁⠈⠛⠛⠛⠀⠀⠸⠁⠀⠀⠀⠀⠘⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⢀⠀⠀⠤⣄⠠⠀⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠃⠁⠂⠀⠃

⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀
⠀⠀⣠⡄⠀⠀⠀⢀⠁⠀⠀⠀⣧⣈⠃⠀⠀⠀⠐⠀⠀⠀⢠⣤⠀⠀⠀⡀⠀⠀⠀⠀⢀⡈⠀⠀⠀⢀⡀⣬⠄⠀⠄⠀⠀⠈⠆
⠀⠀⠈⠁⠀⠀⠀⠙⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠠
⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠆⠀⢠⣜⣁⠀⠀⠐⠁⠀⠀⠀⠀⠐⠋⠀⠀⢀⡀⢀⣈⠁⣉
⠀⠀⠻⠀⠶⠀⠀⠰⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠆⠀⠈⠿⠻⠄⠀⠀⠐⠂⠀⠀⠀⠀⠚⠇⠀⠠⠬⠬⠭⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠓⢦⣀⠤⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣄⡀⣠⣾⠟⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠈⠙⣻⡿⠁⠀⠀⠀⠙⣿⣶⣶⣶⣶⣶⣴⡶⠿⠛⠉⠉⠙⢿⡄
⠀⠀⠀⠀⠀⣾⣧⣤⣤⣄⣤⡶⠿⢷⣿⠻⣧⠀⠀⢸⣷⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢰⡟⠉⠁⢉⣽⡏⠀⠀⠀⢹⣿⠋⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿
⠀⠀⠀⠀⢹⣧⠀⠀⣿⣻⣷⣀⣀⣀⣾⠟⠿⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇
⠀⠀⠀⠀⠀⣿⣷⣀⠈⠉⢉⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢸⡟⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⢀⣤⣤⣤⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⡀
⠀⠀⠀⠀⣿⡇⠉⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠈⠉⢹⣿⠋⠉⠛⠃
⠀⠠⠶⠶⢿⣿⠓⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⣤⠴⣤⡀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠠⢶⣾⣧⣀⡀
⠀⠀⠀⠀⠀⣻⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣾⠏⠉⠉⠁
⠀⠀⠀⠶⠟⠋⠛⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣴⠾⠿⢶⣶⡾⣛⣋⣀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⢉⣩⣽⣭⣹⣿⠁⠀⠀⠀⠙⠟⠋⠉⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢰⡟⠉⠁⠉⣹⡿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢻⣇⠀⠀⣸⡟⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠏⠀⠀⠈⠻⣦⣴⡿⠁⠀⠀⢀⣼⠇⠀⠀⣠⣴⠟⢻⣷
⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠹⣿⡀⠀⠀⠀⠀⠈⠙⠻⠶⢶⡶⠿⢿⣤⣶⠟⠋⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢻⣧⣄⣀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⣤⡀⣀⣤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠻⠋⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⠋⠁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣶⠿⠶⢶⣤⣿⠟⠉⠉⠻⣦⣠⣤⣤⣤⣤⣤⣿⡾⠟⠋⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣨⣏⣠⣤⡀⠀⠘⣯⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣤⠿⠶⠶⣶⠋⠉⠉⠻⣄⡿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿
⠀⠀⠀⠀⠘⡇⠀⢠⡞⢿⡀⠀⠀⣰⣯⣄⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠻⣄⠀⠛⠛⣹⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢰⡟⠳⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⢠⣤⣤⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠐⠖⢻⡟⠛⠒⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⢀⣀⣾⣇⡀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠐⠚⠛⣿⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⣏⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⠏⠉⠉⢠⡾⠋⠁⠀⠉⣷
⠀⠀⠀⠀⠀⣀⣼⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡿⠛⠶⣄⢠⡟⠀⠀⠀⣠⠆⣿
⠀⠀⠀⠀⠘⠉⠀⠈⠙⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠁⠀⠀⠀⠈⣸⠇⡀⠶⢞⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⢿⡟⠛⢻⡿⠛⠛⠛⠛⠛⢻⠛⠉⢻⡝⠳⣦⣀⣀⣀⣤⢞⣵⠞⠙⠛⠋⠁
⠀⠀⠀⠀⠀⢀⡴⠶⠟⠉⠻⢦⡟⠀⠀⠸⡧⠤⠤⠶⠶⠶⠾⠂⠀⠀⢻⣶⠏⠁⠉⢻⣵⠟⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣀⣀⣀⣠⣤⡀⠀⠀⠀⣼⠋⠀⠀⠀⢰⡇⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣸⠇⠀⠀⠀⠀⣾⠉⠈⠉⠁⠀⢻⠀⠀⠀⠻⣄⡀⢀⣠⠟⠀⠀⠀⣴⠿⢷⡀
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⠙⣿⠁⠀⢀⣴⠞⠛⠳⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠙⠓⠶⢾⡇⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣅⣤⠶⠳⢦⡾⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⢺⡟⠁⠀⠙⢿⡶⠶⠶⠶⠷⠳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠈⠉⠉⠉⠉⠉⣹⣏⡀⠀⠀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠭⠛⣛⣛⣛⡉⠉⠀⠀⣀⢀⣀⡀⠠⠻⠶⠒⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣤⣶⣾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠛⢷⣾⠟⠋⠁⠀⠈⣿⣆
⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⡀⣀⣠⣤⣴⣶⣶⣿⠇⠀⠀⣀⣄⣀⣿⣦⣤⣀⣀⣤⣼⣿⣤⣀
⠀⠀⠀⣸⡿⠋⠉⠉⠉⠛⠛⠿⠟⠛⠉⠉⠁⠀⣿⠀⠀⢸⡟⢹⡟⠉⠀⠈⠹⣿⣁⡀⠀⠈⣿⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠛⢿⣇⠀⠀⠀⢀⣿⣙⣿⠀⠀⣿⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣴⠶⠟⠛⠷⠶⠶⣿⡛⠛⠁⠀⣼⣏
⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠟⠙⣿⡆
⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠾⠿⠛
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠈⠉⠈⣿⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠐⢻⣿⠟⠛⠛
⢀⣤⣤⣾⣿⡶⠶⠂⠀⠀⠰⣿⣿⡆⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⣼⣿⡀
⠈⠉⠀⠀⢹⣧⣀⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢿⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠛⠛⠻⠆
⠀⠀⠀⣴⠾⠻⣿⣅⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⣿⡇⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠠⡾⠋⠁⠈⢙⣻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⢿⡟⠛⢿⣧⠀⠀⠙⣿⣄⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠋⢡⣿⠏⠀⠸⣿⡀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠻⣷⡀⠀⠘⢿⣦⣴⡿⠋
⠀⠀⠀⠀⠀⣿⡋⠉⠈⢻⣷⣿⣷⣶⣶⣤⣙⠻⢶⣶⣶⡶⠟⠁⣠⣴⣶⣶⣿⣷⣶⡶⠿⠛⠉
⠀⠀⠀⠀⢰⣿⠁⠀⢠⣾⠟⠉⠀⠀⠀⠉⢻⣧⡀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠻⣦⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣥⣤⣤⣤⣽⣿⣄⡀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣴⣶⠿⠛⠋⠉⠉⠉⠉⠉⠙⠛⠿⣶⣶⣶⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠶⣦⣀⣀⣤⣴⠶⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣄⡀⢀⣀⣀⣤⣤⣾⠏⠀⠀⠀⠈⢿⡟⠉⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉⢸⡏⠀⠀⢠⠖⢲⡾⠷⠶⣤⣤⡤⠴⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⢳⡏⠀⠀⠀⢸⣧⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠶⠞⠳⣄⣀⣀⣼⣧⠟⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣄⡀⣀⣠⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠾⠛⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣿⣦⡤⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⢠⣤⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⣠⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠛⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣾⠿⠛⠉⣀⡴⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡘⢷⣀⠀⣀⣤⡀⠀⠀⠀⠀⣸⡟⠙⣿⠟⠉⠉⠉⠙⠛⠟⠉⣿⡤⠖⠋⠁⠀⠹⣷⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣉⣿⠛⠙⠷⣦⣤⣴⠾⠋⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣞⠛⠛⠛⠚⣿⡟⠓⢸⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣿⣄⠀⣀⣿⠃⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣿⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⣛⠛⠋⠡⣶⣦⣦⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⡤⠾⡇⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⡿⢶⣄⠻⠟⠉⠀⠀⣴⣦⣤⡀⠀⠀⠀⠀⠀⢿⠀⠀⣼⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⠙⢶⣤⣀⣀⠀⠹⡿⠟⠁⠀⢰⣶⣤⣄⢸⡇⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣆⠀⠀⠈⠉⠉⠻⢦⣄⡀⠀⠀⠀⠿⠟⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⢧⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣻⡶⢤⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣿⣶⣄⡀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠁⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠈⢂⠀⠀⡀⠀⠘⠀⠀⠀⢊⣁⠀⠀⠀⢈⠛⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠐⠖⠀⠀⠀⠘⠴⠾⠂⠀⠠⠤⠤⠤⠤⠀⠀⠻⠟⠱⠀⠀⠀⠸⠟⠇⠀⠀⠈⠉⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠸⠷⠆⠀⠀⠂⢤⣦⠄⠂

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⣆⠀⠓⠀⠀⠀⠀⠁⠀⠀⡀⠀⣠⡀⠀⠀⠀⢀⣌⠀⠀⢀⠀⠀⠛⠰⠃
⠀⠐⠒⠐⠂⠀⠀⠀⠐⠊⠀⠀⠀⠀⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠖⠘⠀⠀⠀⠉⠁⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣄⡀
⠀⢀⠀⠀⠐⠀⠀⢿⠀⡸⠇⠀⠀⣀⡀⠀⠀⠀⠀⢀⠤⣶⠀⠀⠀⢠⣀⠉⠀⠀⠄⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠈⣠
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠙⠁⠀⠀⠈⠀⠘⠀⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠰⠄⠀⠀⠀⠀⢦⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠰⡄⠀⠀⠀⠀⠤⠀⠀⠀⠐
⠀⠀⢳⣶⡀⠀⠀⠀⠤⠄⠀⠀⠘⢠⣀⣄⢉⠇⠀⢠⡀⣇⠀⠀⠐⢠⡄⣘⢉⠚⣯⣴⣾⣽⠀⠀⢹⡿⠁⠀⠀⠀⠀⢄⣄⠀⠀⢀⡈⠀⡀⠀⢀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠈⠁⠉⠀⠀⠈⠀⠁⠈⠁⠀⠈⠁⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛⢷⠆
⠀⠀⠀⠀⠂⠀⠀⠠⣶⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⣁⣀⣀⣀⠀⠀⠤⣄⠁⠄⠀⠀⡠⢤⠆⠀⠀⠠⠤⠀⠀⠀⠀⠀⡤⣶⠖⠀⠈⠆⠁⠆⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠓⠀⠀⠀⠘⠛⠀⠀⠀⢀⡆⠰⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠙⠃⠀⢀⠀⠀⠀⠑
⠀⠀⠰⠿⠀⠀⠀⠀⣴⡄⠀⠀⠀⠈⠷⠶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠂⠀⠀⠀⠀⢠⣴⡀⠀⠀⠀⢠⡆⠘⠋⠀⠀⠃⠀⠀⠀⠂

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⢬⡀⢂
⠀⠀⠈⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠈⠛⠀⠀⣤⣍⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⣀⢂⣤⠀⢨
⠀⠠⠛⠇⠰⠶⠀⠀⠰⠄⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠸⠟⠻⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠚⠻⠀⠀⠤⠤⠬⠭⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠈⢿⠟⠉⠀⠀⠀⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣿⠋⠁⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⣶⣦⣄⣿⡷⠛⠉⠙⢿⣍⣀⣀⣀⣀⣀⣀⣀⣿⣶⡾⠟⠛⠉⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⢙⡿⠁⢀⠀⠀⠀⠹⣿⠛⠛⠛⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣇⣀⣀⣠⡶⠞⠻⢾⣏⠻⣆⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢰⡟⠉⠁⢀⣹⡏⠀⠀⠀⠀⣿⠾⠃⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⣿⣉⣷⣄⡀⢀⣠⠟⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⠉⢉⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⢰⡿⠛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⣀⣀⣀⣼⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠴⠶⣿⡷⠶⠶⠶
⠀⠀⠈⠉⠉⠉⢹⡏⠉⠁⠀⠀⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⣀⣤⣼⣷⡶⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⣤⠶⢦⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⣿⡿⠷⠶⠄⢀⣴⠾⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣾⣟⠀⠀⠀⣰⠟⠀⠀⠀⠀⡀⢹⡆
⠀⠀⠀⠀⠀⣀⣤⠾⠿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉⠙⠻⣦⢠⣿⠀⠀⠀⢀⣼⢃⣾⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⢀⣴⠟⣀⠺⠛⣋⣥⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣼⢿⣿⠛⠛⣿⡿⠿⠿⠛⠛⠛⠛⣿⡟⠉⠹⣯⠛⠷⣦⣀⣀⡀⢀⣴⢟⣡⠾⠋⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠟⠛⢿⣅⣾⠃⠀⠀⢿⣥⣤⣤⣤⣤⣤⣤⣿⠇⠀⠀⠹⣷⣴⠟⠉⠉⠻⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣠⠾⠛⠷⠾⠛⠻⣦⠀⠀⠀⠸⣏⠀⠀⠀⠀⣠⡟⠀⠀⠀⢀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠙⢶⣤⣤⠾⠋⠀⠀⠀⣀⣼⣏⣩⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠙⣧⣄⠀⠀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣠⡾⠋⠉⠉⠉⠀⣉⣙⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⢀⣿⣤⣴⠾⠛⠻⢶⠟⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⠶⠶⢿⣿⠋⠀⠈⠻⣶⡶⢶⠶⠶⠾⠾⠷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡋⠉⠉⠀⠀⠀⠀⣀⣤⡿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣤⣶⣶⠾⠿⠿⠶⠶⠶⠾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠒⠒⠒⠲⠆⠀⠐⠤⠒⠒⠒⠚⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠙⢷⣄⣤⣶⡶⠿⠿⢿⣆
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⠉⠙⠻⢷⣶⠶⠿⠿⠿⢿⣿⠁⠀⠀⢀⣀⡈⢻⡏⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠠⡟⢩⡿⠟⠛⠳⣦⣤⣶⣶⣾⣇
⠀⠀⠀⠀⠀⠈⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠙⣿⠁⠀⠀⠀⢸⣧⡀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠛⠻⣧⣀⣀⣠⣾⣉⡿⠀⠀⣸⡏
⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣯⡉⠉⠀⢀⣴⣿⡀
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⢹⣇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣤⣤⣤⡄
⠀⠰⠶⠾⠿⣿⠟⠛⠂⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⣿⣧⣤⡄⠀⠀⠸⢿⠏⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠐⠶⣾⡿⢶⣦⡄
⠀⠀⠀⠰⠟⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠁
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠛⠷⣦⡀
⠀⠀⠀⠀⠰⠟⠉⠀⠈⠙⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠶⢶⣶⣶⡶⠶⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣶⣦⣄⠀⠀⢀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⢿⣶⣦⣤⣀⠀⣀⣀⣀⣀⣀⣠⣾⠏⠀⠀⠀⠙⢿⣶⣿⠿⠛⠋⠉⠉⢿⣇
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠉⠙⠿⠿⠟⠛⠛⠛⢻⣿⠇⠀⠀⢀⣤⣤⣈⣿⣇⡀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⣋⣽⡿⠛⠛⠻⣷⣶⡶⠿⢿⣿⣇
⠀⠀⠀⠀⠀⢻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠈⣻⣟⠀⠀⠀⠀⢸⣿⣄⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠿⠛⢿⣄⣀⣀⣠⣾⣏⣿⠂⠀⠀⣿⠇
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠉⠉⠁⠀⣠⣾⣏
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣶⡿⠟⠉⣿⡄
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣀⡀
⢀⣠⣤⣤⣿⣧⣤⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠾⠟⢿⣿⠛⠛⠛
⠈⠉⠉⠉⢻⣯⠉⠉⠀⠀⠀⠀⣺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣀⣼⣟⡀
⠀⠀⠀⣀⣼⣿⣶⠶⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⢹⣿⠟⠛⠛⠂
⠀⠀⠈⠉⠉⠙⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣏
⠀⠀⠀⠀⢀⣠⣼⠿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠛⠿⣶⡄
⠀⠀⠀⠐⠟⠋⠀⠀⠈⠙⠿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⣿⣿⣿⢿⣿⡿⠿⡶⣶⣶⣶⡶⡶⣾⣿⡿⢿⣿⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡉⠀⢀⣼⡟⠁⠀⠀⠻⣧⡀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⢻⣷⡀⠀⢉⣿⣷⣄
⠀⠀⠀⠀⢀⣼⡟⠁⠙⠿⣷⣾⡟⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⢹⣷⣴⡿⠋⠈⠻⣷⡀
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⢹⣷⡀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠙⠻⢷⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣶⣤⣤⣤⣤⣤⣴⣶⠿⠻⣷⣦⣤⣤⣤⣤⣤⣶⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⢶⣦⣄⠀⠀⠀⣀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⠿⣶⣦⣤⣀⠀⢀⣀⣀⣀⣀⣠⣾⡿⠋⠀⠀⠈⠻⣷⣾⠿⠛⠋⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠈⠙⠛⠿⠟⠛⠛⠛⠛⣿⡿⠁⠀⠀⣠⣤⣄⣹⣧⣀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢸⣏⣹⡿⠛⠉⠛⢿⣶⡶⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢙⣿⠁⠀⠀⠀⢀⣿⣦⡀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠛⠻⣧⣄⣀⣠⣾⣏⣽⠇⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⡉⠉⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠿⠋⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⣴⣶⣿⣷⣶⡤⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠘⠛⢹⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣤⣼⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢰⡾⠛⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠈⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠙⠻⠿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠿⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⠿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠹⣷⣾⠿⠛⠋⠉⠹⣷
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠉⠛⠿⠟⠛⠛⠛⠛⠛⣿⠇⠀⠀⢀⣀⡀⢸⣇⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡟⢩⡿⠛⠉⠛⢷⣤⡶⠶⠾⢷⣄
⠀⠀⠀⠀⠀⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠻⣿⠁⠀⠀⠀⠀⣿⣤⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⡴⠿⣧⣀⠀⢀⣴⣟⣸⡗⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣏⠉⠉⠀⢀⣾⠃
⠀⠀⠀⠀⠀⢸⡿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣳⣶⡶⠛⣿⡆
⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⠟⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀
⠀⢠⣶⠶⠶⣿⣿⣿⣿⣿⣿⠟⠁⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡶⠀⠀⣀⣿⣿⣿⣿⣿⡿⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⢠⣴⠾⣿⣿⣿⣿⢋⣠⣶⣿⣿⣿⣿⣿⣿⡿⢳⡋⢙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠉⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⣠⡶⠟⠛⢿⣮⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣀⣴⡿⠋⠙⠛⠷
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠻⢿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⠷⣤⣶⠿⠋⠉⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⢀⣀⣤⣤⣶⣶⡿⠀⠀⢀⣀⣘⣧⣄⣀⢀⣀⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠉⠉⠉⠙⠛⠿⠟⠛⠉⠉⠁⢸⡇⠀⢰⣟⢹⠟⠉⠈⠙⢿⣍⡀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠙⣻⣄⠀⠀⢀⣼⣏⡿⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠛⠋⠙⠓⠖⠻⣯⡉⠀⣠⣾⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠈⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢻⡟⠉⠉
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⢠⣼⣿⣤⡤⠄
⠀⠀⠀⠀⢀⣀⣼⣿⣤⡤⠀⠀⠀⣶⣷⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠛⠉⠉⢻⣇⣀⡀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢾⣏⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠻⠷⠦
⠀⠀⠀⠀⠀⠀⣤⠾⢿⣯⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠿⣿⡇⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⣈⣽⣿⣿⣿⠷⣶⡶⠶⠾⠿⠿⠛⣿⡟⠙⢿⣄⠀⠘⢿⣆⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠾⣿⣇⣠⣿⠃⠀⠸⣧⣀⠀⠀⢀⣠⡿⠀⠀⠈⢻⣆⠀⢈⣿⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⢈⣿⡿⠟⠛⠻⢷⣬⠙⠛⠛⠛⠉⣠⡾⠟⠛⠛⠿⣿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢠⡿⠃⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⢀⣾⣏⣀⣀⣄⣹⣷⣀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣴⡶⠟⠛⠉⠉⠉⠉⠉⠛⠻⠷⣶⣶⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠻⣶⣴⣿⠟⠋⠁⠀⠹⣿⡄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣾⠃⠀⠀⠀⠀⠈⢻⣆⣀⡀⠀⠀⣀⣻⣷⣀
⠀⠀⠀⢀⣾⡿⠛⠛⠛⠿⠿⣿⣶⣿⠿⠿⠛⠛⠉⢹⡟⠀⠀⢰⡿⢛⣿⠟⠋⠙⠻⣶⡟⠋⠉⠉⠙⣿⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⣼⡇⠀⠀⠀⠀⢸⡿⢷⣆⠀⠀⣿⠇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⢀⣀⣼⣷⣄⡀⢀⣠⣾⣷⡾⠏⠀⢠⡿
⠀⠀⠀⠘⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠀⠉⠛⠛⠙⢷⣄⣀⣀⣠⣿⣷⡀
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⢿⣧⣀⣀⣀⣀
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⡟⠛⠉⠉
⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⢀⣿⣇⣀⣀
⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠘⢻⣿⠟⠛⠛⠁
⢀⣠⣤⣶⣿⣷⠶⠶⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣼⣿⡀
⠈⠉⠁⠀⠘⣿⣄⢀⡀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠸⣯⣀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠛⠿⠶
⠀⠀⠀⣠⣴⠿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣿⣥⣤⡀
⠀⠀⠀⠉⠀⠀⠈⢻⣷⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠃⠀⠈⠉⠙⣿⣆
⠀⠀⠀⠀⠀⢠⣶⠟⠉⠛⠿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⡿⣿⣿⠋⠉⠙⢿⣦⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠉⠁⠀⢀⣤⣶⡿⠟⣻⣿⠛⠛⣿⠛⠛⠛⠛⠋⠉⠉⣹⡏⠀⠈⢿⣧⡀⠀⠈⢿⣷⡀⢀⣰⣿⠃
⠀⠀⠀⠀⠀⢠⣾⠿⠿⢿⣷⣄⣼⣿⣁⣀⠀⠻⣷⣄⡀⠀⠀⣀⣴⡿⠁⠀⢀⣀⣻⣷⡀⢀⣀⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣹⣿⡿⠿⠛⠻⢿⣶⣌⠙⠛⠛⠛⠛⠉⣠⣶⡿⠟⠛⠻⠿⣿⣿⡛⠉
⠀⠀⠀⠀⠀⣿⡇⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠀⠀⠀⠀⠀⠘⢿⣦⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣏⣀⣀⣀⣀⣹⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣤⣤⣴⣾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣤⣤⣴⣾⠿⠋

⣾⠇⢠⡜⣻⡃⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡟⢿⡃⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⣸⣿⡤⣆⢸⠋⠳⢶
⠁⢀⠀⢻⣧⣉⣄⣀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡻⢂⢄⠀⠀⠀⠀⠀⠀⠚⠀⠀⣸⢧⣾⣿⣷⣿⡋⠀⠀⠘
⠀⢸⣧⣺⣵⣿⠉⠉⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣯⣿⢿⣤⡞⢿⣿⣷⡄⠼⠓⠀⠀⠀⠀⠀⠀⣴⠋⠀⠚⠈⣟⡿⣻⡆⠋⢀⡄
⠀⣼⣿⣏⣿⡇⠀⠀⠀⠈⠻⣿⠋⠁⠀⠀⠠⣶⣿⣿⣿⣟⢻⣇⣠⣿⣡⣙⡻⠃⠀⢰⣶⣾⣿⡀⠀⠀⠀⠙⠒⠚⢲⡞⠙⣷⢋⣿⠷⢤⣤
⠘⣾⢿⣿⣿⣇⠉⠰⠖⢘⡿⠁⠀⠀⠀⢐⣶⣿⣿⣿⣿⣿⢞⣿⣿⣿⠿⢿⣿⣶⣿⣿⣿⣿⣿⠟⠀⢀⣤⠴⠶⠶⢾⡇⠀⠘⢿⣿⠿⠛⠁
⠀⠁⣠⣿⣿⣿⡟⣳⣿⠟⠁⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣷⡿⠻⠿⠿⣿⠿⠛⠟⠃⠀⠀⠘⠷⣶⡿⠗⠚⢋⣀⠀⠀⠙⠶⠴⠶
⠛⢻⡇⠈⠻⢿⡿⠋⢁⣀⣤⣼⣿⣿⣿⣿⡿⠟⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣾⣡⠶⠛⠛⠋⠙⠳⠶⣤⣤⣤⣼
⢟⣛⣿⠆⠀⠀⠙⠛⠛⢩⣁⠀⠹⠿⢿⡉⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠉
⠟⣩⠴⠛⠻⣶⠶⢶⣶⣾⣿⠟⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢰⡄⠈⠁⠐
⡞⠁⠀⣈⣫⣽⣷⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠹⠀⠀⠀⢷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷
⠀⣠⣄⣹⣿⡟⣡⣭⣿⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠰⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⡆⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠉⣿⢿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⣀⡀⠀⠨⣿⠟⠋⠉⠛⣿
⣽⡎⢈⣿⣿⣿⣿⣿⣿⠂⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢯⡀⠀⠀⠀⡞
⣿⢇⣼⣿⣿⣿⣻⣿⡟⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠶⠈⠙⠛⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⠀⠀⠀⠀⣹
⣽⠛⠀⠀⠀⣹⡂⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢿⠀⠀⣀⣴⡾
⣉⠛⠶⠷⠾⠋⠈⣺⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠇⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠙⠻⣿⣿⣿⣿⠿⠋⠀⠀⢤⠀⠀⠀⠙⣿
⣿⣧⣤⣤⣵⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣈⠁⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠰
⢿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠿⠿⣿⠿⢿⣿⣷⣦⡀⠀⣠⣶⣿⣐⣤⣀⣺⣀
⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠈⠛⢿⣿⣤⣿⣿⣿⣿⠁⠉⠉⣿
⣾⣿⣿⣿⢃⡄⠀⢹⣿⣿⣿⠀⠀⠈⠑⠀⠀⠀⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠇⠀⣸⣿⢿⣿⣿⣿⣯⠀⣀
⣿⣾⣿⣿⣄⡀⢴⡼⣿⣿⣿⢲⠀⠀⠀⠀⠀⠓⠀⠀⠙⠛⠛⠻⠛⠛⠛⠟⠛⠿⠿⠟⢀⠀⠲⠄⠀⠀⠀⢠⣿⡟⢸⣿⣿⣿⣿⣦⣉⣀⣛
⠘⢿⣿⣿⣽⣿⣶⡶⢿⣿⣿⡀⠀⠀⠤⡄⠀⠀⠀⠀⠢⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⣾⣿⠃⢸⣿⣿⣿⣏⣾⣿⣭⣽
⡀⠈⠛⠶⠤⣦⣄⣤⣸⣿⣿⣇⡀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣿⠏⠀⢸⣿⣿⠃⠉⠛⠿⣯⣥
⣿⣷⣶⣦⣤⣷⣄⣀⠙⣿⣿⣿⠀⠀⠀⢄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⡀⣀⠀⢼⡿⠀⠀⢸⣿⣯⣤⣦⣤⣀⣄⣤
⢿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣏⢿⡆⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠰⠄⠀⠈⠁⣈⠁⠀⠀⣾⣿⢫⣽⡟⣽⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣿⢀⣤⣴⣄⣀⣠⣤⣤⣄⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣓⣀⣘⣷⣴⣴⣿⡟⣿⣶⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣾
⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢇⡀⠀⠀⠉⠻⣿⣿⣿
⠿⠟⠋⠉⠛⠉⠈⠙⣻⡿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢿⣿⣻⣿⣿⣛⣻⣿⣯⣭⠟⠋⠉⠉⠉⠉⠉⡉⠉⢭⣍⣻⡟⠁⠀⠀⠀⣰⣿⣿⢿
⣀⣀⣤⣄⣤⣴⡶⢾⣿⡿⣛⣋⣉⣉⡉⡉⣻⣇⡀⠀⠀⠉⠻⣿⡟⠛⠛⠉⠁⠀⠀⡀⠀⢀⣀⠰⣦⣬⣿⣖⠛⠀⠀⠀⣶⠶⠟⠛⠻⠿⠿
⣿⢿⣿⣽⣿⣿⠛⠈⣙⣿⠿⠟⠋⣉⣉⣉⣉⣉⣤⣤⠀⠀⠀⠈⠙⠓⠶⠦⠟⠶⠼⠟⠓⠚⢻⡿⢿⣿⣿⣿⣿⣦⣄⠀⠙⢦⣄⣀
⠅⡴⠿⠏⢸⣁⡀⣼⣯⣤⣶⠾⠛⢛⠉⣻⣉⣭⣍⡛⠿⣶⣦⣤⣄⣀⣀⡀⠀⠘⣦⣄⡀⠀⠈⠳⠦⢬⣳⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠶⠶
⢦⣴⣾⣥⠟⠉⠀⠘⢉⡡⠆⡀⢀⡘⣷⣿⣿⣿⣿⣿⣿⣥⣤⣬⣽⣿⡛⠛⠛⠻⠿⠿⢿⣿⡒⢶⣦⣄⠹⣎⠛⢮⣟⣿⣿⣿⣷⣤⣀
⣿⣿⣿⠻⠂⠋⠀⠒⣥⡞⠘⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⠀⠀⠀⠁⠒⠀⠀⠈⢻⡌⠻⣮⢷⡈⠳⣄⠈⠛⠻⠿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠉⠙⢿⣦⣀⣴⣾⣿⡿⠿⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁⠈⠉⠙⠛⠿⣿⣷⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⠟⠀⠀⠀⠀⠀⠀⠻⣿⠛⠉⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⣽⡏⠀⠀⠀⢀⣤⣤⣄⣀⣿⣇⣀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢠⣿⠋⢩⣿⠟⠋⠉⠛⢿⣦⣤⣶⣶⣶⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢿⣦⣿⠇⠀⠀⠀⠀⠀⢹⣯⣀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢉⣿⡄⠀⠀⠀⠀⠀⣸⡿⠻⣷⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⠿⠟⠛⢿⣦⣀⣀⣠⣴⣿⣧⣴⡿⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⡀⠉⠉⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣴⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡏⣠⣤⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣯⣥⣄⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣀
⠀⠀⣴⣶⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⠟⠁⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣡⣴⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠰⠾⠟⠛⢿⣿⣿⣿⡿⣃⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢿⣄⣠⣼⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠉⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⢿⣿⣭⡉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⢉⣠⣿⡟⠋⠛⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠾⠟⠋⠀⠀⠀⠈⠻⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁

⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢡⣶⣿⣿⣿⣃⠐⠀⠀⠀⣼⠿⡿⢿⠃⠀⠀⠀⠠⡆⠛⡁⠛⠀⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⢀⣄⢴⠾⠆
⠀⣿⠋⠿⠍⢿⡧⠀⠀⠀⠀⣻⣾⣷⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⣀⡀⠄⠀⠛⠀⠀⠈⠃⠀⠀⡀⠀⠀⠄
⠀⠸⡄⠀⢠⡜⠀⠀⠀⠀⠀⠏⠀⠹⠍⠀⠀⠀⠀⠂⠐⠖⠈⡤⠴⠀⠀⠀⠀⠸⠿⠇⠀⠙⠟⠃⠀⠀⠀⠀⠐⠿⠁

⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠⣶⡶⣶⣤⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⡆
⠀⠘⠓⠀⠀⠈⠀⠀⠀⠀⣼⣿⣵⣿⣿⣿⣷⠀⠀⢈⣿⣷⣾⣷⣦⣄⠀⠀⠀⣴⣤⡴⣧⣤⣆⠀⠀⠀⢘⣿⡿⣿⡀
⠀⠀⢨⣤⣀⣤⡂⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣟⠁⠀⠀⢹⣿⣷⣾⣿⡇⠀⠀⠀⠸⣇⣀⡀⠁⠃
⠀⠀⠀⢩⡋⣹⠁⠄⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠸⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣴⣶⣶⣶⣾⣷⣦⠀⠀⠀⢷⣶⣶⣦⣾⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣆⣀⠀⠀⠀⣀⠙⢻⣿⣿⣿⡇
⠀⣿⣿⠿⠛⠿⠿⠟⠀⠀⠺⣿⣿⣿⣿⣿⠟⠀⠀⢀⣼⣿⣿⡿⢑⡄⠀⠀⢀⣸⣿⢿⡿⣿⣇⠀⠀⠈⠋⠀⢾⠛⠛⣻⡷
⠀⠉⡁⠀⠈⠀⠠⠀⠀⠀⠀⢻⠿⣿⠿⡿⠀⠀⠀⠘⢿⣿⣿⣷⡶⠿⠂⠀⠸⡏⢱⣿⣿⠈⢹⠇⠀⠀⠀⢀⣄⢠⣰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⢴⠄⠀⠀⠀⠀⠀⠀⣠⡀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠻⠿⢿⠆⠀⠀⠈⠃⠐⢿⠗⠒⠄⠀⠀⠀⠀⣛⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠲⢀⠀⠄⠐⠀⠇⠀⠀⠀⣄⣈⣽⣍⣀⡜⠀⠀⠀⣨⠿⣁⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠉⠘⠗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠩⠭⠥

⠀⢲⣤⣀⣀⣠⣶⡇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡄⠀⠀⠀⣀
⠀⠀⢹⠟⠷⢛⣿⠀⠀⠀⠶⠿⣿⣿⣿⣷⣤⡀⠀⠻⢿⣿⣹⣿⣛⣧⡀⠀⢠⣿⣶⣤⣀⡀⢀⡄⠀⠀⣤⣴⣾⣷⣤⡄
⠀⠀⠈⠠⠴⠦⢉⡄⠀⠀⠀⠔⠉⠉⠉⠩⠉⠀⠀⠀⢸⡟⠍⠉⠩⢻⠇⠀⠀⠙⠛⠻⣿⣿⠻⠇⠀⠀⠚⠙⢿⠿⠷⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠁⠀⠀⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣤⠼⠻⢿⣿⣯⣉⣉⣉⣽⣷⡀⠈⠢⠴⠀⠀⠈⠉⠀⢸⣋⣁⠀⠙⠃⠀⢀⠤⡀⠀⠀⢠⡄⢠
⠀⠀⠀⠉⠀⠀⠀⠀⠀⢙⣤⠖⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠳⣤⡀⠀⢰⠖⠲⣦⣸⠉⣠⣤⣤⣄⠀⠈⠉⠀⠀⠀⠙⢋⡏
⢀⣀⣀⡀⠀⢀⣀⡀⠀⣾⠁⢀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣿⢿⣷⣾⣿⣿⣧⣴⣦⣾⡃⠀⠀⠀⠀⠀⠀⠀⣇
⠉⠉⠉⠉⠛⢧⡈⠁⠀⠙⣶⠏⠀⠀⠀⠀⢠⣈⣟⢀⡀⠀⠃⠀⠀⢸⣤⠾⠛⠉⢿⣿⣽⠿⠛⢿⣿⣿⣿⣿⠙⠳⢦⣄⠀⠀⠀⠀⢸
⣀⡀⠀⠀⠀⠀⢳⠀⣠⠤⣿⠶⣤⣤⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⢰⡆⠀⠉⠳⣄⠀⠀⢘
⠿⠟⠀⠀⢀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡿⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⣤⡀⠀⠸⣇⠀⠀⢀⣹⠿⠛⠋
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡝⣦⣤⣄⡀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⣁⠀⠀⠀⠻⠃⠀⠀⠻⣆⣴⠋⠁
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠙⠓⠛⠛⠛⣷⠟⣛⣷⡶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢀⡀
⢶⣿⡏⠀⠠⣶⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣧⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠋
⠘⣿⠃⠀⠀⠀⠀⠀⠻⠇⠀⠀⠙⠃⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⢻⣦⡴⠶⠛⠓⠶⣴⡇
⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣿⣿⣧⣾⠋⠀⠀⠀⠀⠀⠈⠷⠖⠛⠉⠙⠓⢶⣍
⠛⠛⠛⠒⣶⡾⢛⣶⣤⣤⣄⠀⠀⠀⢸⡧⠖⠂⢀⣠⣤⣐⢭⣇⡀⠀⠸⠟⠀⠀⠚⠛⢳⡇⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠈⣇⣀⣀⣠⣧⣄⣀⣟⠁⠀⠈⠋⠉⠙⣷⠀⠀⠀⢄⡉⣳⠟⠁⠀⠀⠀⠈⠋⠁⠀⠀⢸⣿⡇⠀⠀⠀⣠
⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠈⠉⠛⠲⠞⢶⡀⠀⠿⣄⠀⠀⠀⣽⠃⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⣀⠀⠀⠀⠀⠀⢈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠼⢿⠤⡄⢸⡆⠀⠀⣿⠀⠀⠉⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠲⠃⠀⠀⠺⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠡⣏⠀⢀⣳⣿⣶⣶⢿⣿⣶⣶⣦⣤⣄⣉⣳⣦⣤⣤⣤⣤⣴⣿⠃⠀⢠⡄
⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⣠⣄⣀⣤⡀⢀⡀⠀⠀⠀⠀⠀⢀⣷⣿⠟⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢺⡿⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⢻⡶⠏⢉⡁⠈⠉⠈⠙⠙⠷⠴⣆⠀⠀⢠⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⢸⡇
⠈⠛⢦⡀⠀⠀⠸⡇⠀⠙⠃⠀⠀⠀⠀⠀⢀⣤⡉⠹⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁⠀⠉⠻⠿⠷⠤⢤⣤⡶
⠀⠀⠀⢻⣶⡶⠾⠷⠒⠲⠶⠦⣷⣴⠂⠀⠀⠉⠀⠀⠉⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣴
⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⢀⣀⣼⣟⠉⢠⣦⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣾⣿⣿⡿⠿⣿⠷⣦⡀⠀⣄⠀⢀⠀⠀⢾⠆⠀⣿⠧⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⠀⠉⠙⢿⣷⣄⣤⣶⣾⣿⠿⠿⠟⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠉⠉⠙⠛⠿⣿⣿⣶⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠛⠉⠉⠉⠉⠉⣿⣿⠁⠀⠀⠀⣠⣴⣶⣦⣀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢰⣿⡋⢨⣿⡿⠛⠛⠛⢿⣷⣶⣶⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠈⠻⣷⣿⡏⠀⠀⠀⠀⠀⢹⣿⡉⠀⠀⠀⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣠⣼⣿⡆⠀⠀⠀⠀⠀⣸⣿⢿⣦⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠟⠛⠉⠹⣿⣦⣀⣀⣠⣴⣿⣯⣼⡿⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⡏⠉⠉⠉⠀⠀⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣶⣿⠟⢿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣄⣀⣀⣀⣀
⠀⣀⣠⣤⣤⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠟⣿⣿⠟⠛⠛⠛⠛
⠘⠛⠛⠉⠉⢻⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠶⣾⣿⣿⣶⣦⣤⣀
⠀⠀⠀⢠⣤⣶⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠉⠉⠁
⠀⠀⠀⠈⠉⠀⠀⠹⣿⣷⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣶⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⣻⣿⡿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⢿⣿⣟⠛⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠁⠀⢀⣼⣿⠋⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠻⣿⣆⠀⠀⠉⠛⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⢿⣷⣤⣀⣾⣿⠃⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠹⣿⣧⢀⣤⣾⡿⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠉⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣤⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣷⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣿⠟⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠻⢶⣤⣴⠿⠟⠛⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⢶⣶⣤⣴⣶⣶⣶⡶⢿⣿⡏⠀⢀⣠⣄⣻⣧⣀⠀⠀⠀⣸⣿⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢠⣿⠀⠀⣿⡉⣽⠟⠉⠙⢻⣿⣟⡉⠉⠹⣧
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠈⣻⣿⣄⠀⠀⣸⡿⠈⣿⠀⢰⡿
⠀⠀⠀⠀⠀⠀⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠛⠻⠿⢿⣟⠛⠋⢀⣾⡃
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣷⣶⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣷⣴⣤⡤⠶⠶⠶⠤⢤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠉⠉⠉⠉⠹⣿⣿⡟⠛⠛⠂
⠀⠀⠀⠀⢀⣸⣿⣿⡁⠀⠀⠀⢀⣀⠀⠀⠈⠙⣿⡿⠛⠉⠻⣿⡁⠀⠀⢴⣿⡆⠀⠀⠀⢀⣿⣿⣇⣀⣀
⠀⠀⠀⠛⠛⠛⣿⣿⠁⠀⠀⠀⢺⣿⡇⠀⠀⢠⣿⢃⣠⣤⡀⠹⣧⡀⠀⠈⠛⠁⠀⠀⠀⣠⣿⡿⠉⠉⠉
⠀⠀⠀⠀⢀⣠⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠸⢧⣤⠞⠀⠈⠛⠶⢦⣤⣤⣤⣴⠾⣿⣿⠷⣦⣄
⠀⠀⠀⠀⠈⠉⠁⢈⣿⣿⣷⣶⣶⣶⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠴⠟⠋⢩⡿⠋⠀⠀⠈⢻⣷⣶⣶⣦⣤⣤⣶⣶⣶⣶⣿⠁⠀⠀⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⡏⠉⠉⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡀⠀⣠⣿⣿⠟⠛⠛⠃⠀⠀⠙⠛⠛⢻⣿⣿⣧⣀⣀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠛⠛⢿⣿⣀⣀⣀⡀⠀⠀⢀⣀⣀⣸⣿⡿⠉⠉⠉⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢷⣶⣶⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣴⡿⠛⠉⠉⠁⠉⠉⠉⠛⢿⣤⣀⣀⣠⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠻⣦⣠⣴⣶⠿⠟⠻⣷⡀
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠈⠉⠛⠿⣶⡾⠿⠿⠿⠿⠿⣿⠋⠀⠀⢀⡀⠈⣿⠉⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠟⣻⡿⠛⠛⠷⣤⣤⡤⠾⢿⣤⡀
⠀⠀⠀⠀⠸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢷⣿⠀⠀⠀⠀⢹⣧⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⡴⠶⠿⣦⣀⣀⣠⣾⣥⡿⠀⠀⣼⠇
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣄⠉⠀⢀⣼⡏
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⢹⣷
⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡶⠶⣦
⠛⠛⠛⢻⣿⠛⠋⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢀⣀⣿⣤⡤⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠘⣿⡿⠶⠶⠆
⠀⠀⠋⠉⠙⢿⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠁
⠀⠀⠀⢀⣠⡾⠿⢿⣥⣴⠶⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠙⠻⠶⠄
⠀⠀⠀⠛⠉⠀⢀⣤⠿⠇⠀⠀⠛⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⣔⢑⡄⠀⣴⡿⣿⠛⠛⠻⠟⠛⠛⢿⡟⠛⠻⣿⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⣨⣿⣶⠀⠈⢉⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⣠⡿⠁⠀⠀⠹⣧⣠⡿⠿⠶⣦⡄
⠀⠀⠀⠀⠀⢠⣿⠁⠻⣦⣤⣾⡷⢶⡟⠁⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢹⣷⡌⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⡾⠃⠻⣦⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠛⠛⠛⠛⠿⠿⠿⢿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣀⣀⣀⣀⣀⣼⣧⣄⣀⣀⣀⣀⣠⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⠦⣤⣀⣠⠞⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣹⣇⣀⡀⠀⢹⡶⠶⠶⠶⠶⠞⠁⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠒⢺⠃⠀⠈⢷⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠰⠽⢦⣀⡤⠟⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠳⣄⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⢺⡗⠒⠂⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣷⠶⠦⣄⠀⠻⠇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠉⣿⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠓⢮⣳⡀⠀⠀⠀⠀⠀⠀⠣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⢧⡀
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢿⡀⠀⠀⠀⣿⣄⣀⣀⡴⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⢾⡁
⠀⠀⠀⡏⠈⠷⠤⠤⠾⠁⢹⠀⠀⠀⠀⠙⢦⣄⣀⡟⠈⠁⠘⡏⠉⠉⠳⣽⢶⡶⠒⢶⡞⠛⠛⠉⠉⠀⠀⠉
⠀⢀⡼⠃⢀⣠⣤⣤⣀⠀⠈⢧⡀⠀⠀⠀⠀⠈⡿⠉⠲⢄⣼⡁⢀⣠⠾⢁⡼⠋⠳⡜⣧
⢀⡾⠁⣰⠋⠶⠀⠶⠀⣽⣆⠈⢷⡀⠀⠀⠀⠀⠻⣤⡤⠞⠻⢯⡿⡷⢶⣙⡧⠤⠤⣷⠘⣧
⣼⠁⠀⡇⠶⠀⢞⣱⠀⣉⢸⠀⠈⢷⠀⠀⡤⢤⡀⡿⠀⢀⡴⢻⠁⠧⠤⣟⠀⠀⠀⡟⠀⠸⡇
⣿⠀⠀⢿⣳⣀⠀⠁⠀⣩⠞⠀⠀⢸⠆⠀⠓⣦⡿⣿⠚⠉⠀⣼⠀⠀⠀⠈⠙⠤⠴⠃⠀⣰⠟⠓⠲⣄
⠙⠦⣤⣤⣁⣉⣉⣉⣩⣤⣤⠤⠶⠛⠛⠛⠛⠉⠀⠙⠷⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⡤⠾⢯⣤⣤⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⠀⠀⣴⠋⠻⡆⢰⡏⢙⡆⠀⠀⠈⡃⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢠⣞⣀⣧⡀⠀⠀⣿⠀⠀⡿⣠⠟⠛⣧⠀⠀⢸⡇⢸⠇⠈⡗⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⠀⠀⠈⠏⠀⠰⠄⠙⠦⠾⠃⠙⠦⠴⠏⠀⠀⠸⠇⠸⠇⠀⠇⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠒⢤⣤⣴⣶⣆
⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⣴⣶⣶⣦⣤⣄⡀⠀⣀⣀⣠⣤⣤⣤⣤⡔⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠢⡀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣧⣸⣿⣧⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡴⠶⠶⠶⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣧⣤⣤⣤⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⡿⣫⣿⡷
⠀⠤⠀⠴⠦⠤⠦⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣴⣴⣂⠀⠁
⠀⢰⠀⣠⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣮⢿⣿⣿⣿⣇⡄
⠀⠸⠦⣿⡄⣠⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⣯⣾⣾⣭⣭⣭⣭⣭⣽⣿⣾⣿⠻⣷⣿⣿⣿⣿⣿⡸⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣼⣿⣿⣾⣿⢟⣿⣿⠛⣿⣯⣹⣿⣷⣿⣿⣼⣿⣿⣿⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⡹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣷⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡟⢻⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠁⠀⠉⠙⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⢷⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠋⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⢦⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠾⠋⠈⢻⣦⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢰⣿⠿⠟⠻⢷⣄⠀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⠻⢦⣄⣀⣀⣠⣿⣧⣤⣤⡿⠁⠀⠀⠀⠀⠹⣷⡾⠟⠋⠉⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠁⣿⠁⠀⠀⣠⡶⠶⣄⣿⣤⣀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⢿⣄⣼⠋⠀⠀⠈⢻⣶⠟⠛⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣀⣹⡇⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢦⣄⣠⣴⠿⡴⠟⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣄⠀⠀⢀⣤⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⠶⠾⣿⡗⠒⠂⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠉⠀⣼⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣧⣀⡀⠀⠀⠀⠻⡿⠏⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠻⡿⠏⠀⠀⠀⠀⠰⢶⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⢀⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠏⠀⠀⠉
⠀⠀⠀⠀⠀⣠⣤⣄⣀⣠⣤⣄⣻⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠿⠷⣤⣀
⠀⠀⠀⠀⣾⠋⠀⠈⠋⠁⠀⠙⣿⠈⠛⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠁⠀⠀⠈⠉
⠀⠀⠀⢀⣼⠇⠀⣠⠶⣄⠀⠰⣯⡀⠀⠀⠈⠉⠛⠛⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠿⠿⠿⣯⡀
⠀⠀⠀⣿⠁⠀⠀⢧⣀⡼⠃⠀⠈⣿⠀⠀⠀⠀⣠⡴⢾⡿⣫⣤⣄⠀⠀⠀⠀⢸⣿⣀⣾⣿⣷⠀⠀⣴⣿⣿⣦⡀
⠀⠀⠀⠙⠷⢤⡄⠀⠀⠀⣠⣤⣴⣏⣠⣤⣴⠞⠉⣰⡟⠸⣿⣿⣿⠀⣠⣴⣤⣸⡿⣯⠻⠿⠟⠀⠀⠻⠿⠟⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠏⠀⠈⠻⣯⠀⠀⠀⢀⣟⣀⡀⠈⠉⠁⠀⢿⣿⣿⣿⠃⠹⣧⠀⢀⣤⣄⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠉⢹⡟⠀⠀⠘⢷⣿⣿⣿⡇⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⣸⡟⠛⠋⠀⣠⣦⣤⠀⣰⡟⠀⠀⠀⠀⠀⠙⢿⣍⡀⠀⠙⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠙⣷⠀⠀⠐⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣧⡀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡟⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣤⣤⠶⠞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣃⣠⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠳⢦⣄⣠⣤⡄⣴⠋⠉⠙⣧⠚⠋⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠁⠀⢸⡇⠀⣾⣳⡾⠷⣤⣤⣤⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠀⠀⠀⠀⠀⠀⠘⢧⣤⣬⣿⡀⠀⣸⣧⡀⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⠛⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⣘⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⡁⠀⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⣉⣉⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣄⠀⠉⠉⠀⠀⠠⣾⣶⠄⠀⠀⠉⠉⠀⢀⣍⣉⡉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡛⠉⠁⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠎⠉⠙⣣⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠀⠹⣦⣀⠀⠈⠛⠶⣦⣤⣄⣀⣀⣀⣤⣤⠶⠟⠋⠀⢀⣠⡾⠋⠨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣄⣀⠙⠷⣤⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⣤⡶⠛⠉⣀⣀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣉⠛⠶⣤⣀⠀⠀⢀⣠⡴⠞⠋⣡⣴⠾⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡉⠛⠶⣭⣁⠤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⢊⣙⡳⢦⣄⡉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⡶⠟⢋⣡⣴⠾⠛⠉⠀⠀⠈⠙⠳⢦⣄⡉⠛⠶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠁⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠈⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⢻⠟⠛⠛⠳⢦⣀⡞⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⡿⢶⣶⣶⣶⣶⣦⣤⣤⣴⠾⠟⠛⠉⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣳⣄⠀⠀⠀⡴⠒⠢⡀⠀⠘⠓⠶⢦⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣼⠇⠀⢠⡾⠋⠀⠀⠀⠀⢧⣀⡴⠃⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⣀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⠁
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠳⠶⠤⠶⠞⢿⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠰⠶⠶⠶⢾⡷⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢾⡷⠶⠶⠶
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠠⠤⠶⠾⣷⠒⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠐⠲⣿⠷⠶⠤⠄
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⣀⣤⠶⠿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠿⠶⣤⣀
⠀⠀⠈⠉⠀⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⡟⠛⠉
⠀⠀⠀⠀⠀⠀⣠⣤⢤⡴⣾⠛⠉⢉⣿⠋⠉⠉⢿⡛⠛⠛⠛⠛⠛⠛⢛⡿⠉⠉⠙⣿⡉⠉⠛⣷⢦⡤⢤⣄
⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠘⣧⠀⣾⠃⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⣷⠀⣼⠃⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠈⠛⠶⠤⠴⠶⠛⠁⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠶⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠛⠻⠶⠶⠶⠶⣶⣶⣦⣤⣤⣴⣶⡶⠶⠶⠶⠶⠟⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣀⣀⣠⣾⣷⣄⣀⣀⣀⣀⣀⣤⡴⠾⠋

⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⢰
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢨
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠶⣤⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠻⣾⡟⠁⠀⠀⢠⠦⣄⠀⠸⡇⢀⣠⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠃⠈⢧⠀⢿⣁⣀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⠀⠀⠀⠉⢉⣤⠀⠀⠀⡽⠗⠚⠛⠛⠓⠶⣤⡀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠚⠋⠙⠦⣤⡀⠡⢈⣐⠄⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢦⡄⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢹⡀⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⢸
⠀⡇⣀⣀⡀⠀⠀⠀⡔⠁⠀⠶⠿⣿⠀⠀⠀⠱⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠇⠀⣰⠇⠀⣀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠈⠢⡀⠔⠁⠀⠀⠀⣠⡿⣷⡀⠀⠀⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠙⣳⡛⠻⠒⠂⠀⠀⠀⠀⠀⣀⣨
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡞⠉⠉⠉⠃⠉⢹⡀⠀⠀⠯⠽⠀⣀⡀⣀⠀⣻⣟⡀⠀⢀⣴⠟⠓⠶⠀⠈⠆⠀⠀⠠⠋⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠔⢒⣳⣄⣀⠀⠀⠀⢀⡿⣉⠢⠔⣀⣬⠶⠖⢶⡟⠉⠉⠙⢾⡛⠻⢦⠀⠀⠀⠀⠘⠖⠉⠁⠀⠀⢸
⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⡸⡴⠋⠀⠀⠉⠉⠙⠋⠉⠀⠈⠳⠞⠉⠀⠀⠀⠈⠙⠛⣆⣀⡼⢣⡘⢄⠀⠘⠀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⡎⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⣠⡴⠶⠇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡆⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⣸⠏⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢻⡄⠀⠀⠐⠤⠝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣸⣋⢉⣱⠄⡀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣸⣄⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣾⣡⠞⠁⠀⠀⠙⡆⠅⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠉⠱⢀⣙⠳⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣇⠂⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠹⡶⣄⣠⡴⡾⠟⠉⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⡫⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⠀⠀⠀⠈⡁⠀⠀⠀⠀⠈⠒⢛⠳⢦⡥⣤⣄⣠⠾⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠖⠚⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠧⠠⠀⠼⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⢤⠀⠤⠠⠀⠄⡤⠶⢤⠰⠠⠤⠤⣤⠄⠀⠀⠠⠤⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢱⣤⣀⣀⣀⡀
⠀⠀⠀⠀⢠⠊⠉⠉⠑⢾⡏⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⣤⣾⠋⠀⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠑⢦⡀⣀⣼⣿⣖⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣱⡦⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠫⠞⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⣠⠶⠛⠛⠋⠙⠛⠳⢦⣄⣠⠞⠋⠉⠀⠀⠉⠉⠛⢦⣄⢀⡴⠟⠉⠉⠀⠀⠉⠙⠳⣦⣀⣤⠶⠞⠛⠛⠶⢦⣄⡀
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢤⡀⠀⣀⡀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠘⢧⣤⣤⠀⠀⠀⠀⠀⠀⣀⡀⠹⣆⠀⡰⠒⠲⢤⣤⠤⡴⠁⡤⣼⣏⣁⣹⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣾
⠀⠀⠀⢻⣄⣀⣤⠀⠀⡞⣉⣹⠆⢹⠀⡇⠀⠀⠀⠀⠀⠣⣀⣻⡀⠀⣹⡄⢹⢰⡏⢰⠟⠳⡆⠀⢀⡀⠀⣸⡏⠉
⠀⠀⠀⠀⠉⠉⠹⢦⣤⣿⣬⣩⡴⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⠴⡇⠘⢧⣈⠛⣡⣧⣀⣼⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⡀⠉⣿⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡤⢷⡀⠀⠛⠀⠀⡠⠀⠀⠀⢰⠆⠀⣀⣼⣀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⠳⣄⣀⣀⡀⠀⠁⠀⠀⠀⡠⠊⠁⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠙⢧⣼⠉⠀⡟⢲⠒⠲⢖⡺⣁⣀⣤⣴⠟⠁
⠀⠀⠀⠀⢀⠠⠤⢤⡎⠀⢐⠀⠀⠀⠀⠈⠻⣶⣾⠁⠸⣄⡰⠊⠑⣄⣽⠟⠁⠀⠀⠀⠀⠀⠔⠢⢄⣀⡀⠤⢄
⠀⠀⠀⠀⠐⠤⡀⣀⡿⠦⠧⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠦⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣿⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⠁

⠀⠀⠀⠀⠀⣠⠀⠀⣠⠀⠀⠀⠀⣤⢶⡄⣠⠶⡄⠀⢀⠀⠀⠀⠀⢰⠀⠀⣤⠀⠀⢠⡄⠀⡄
⠀⠀⠀⠀⢀⣿⣀⣀⣿⣀⡞⣻⢾⡇⣸⠇⣏⢠⡏⡾⣏⣷⠆⠀⠠⣾⣤⣞⠁⢘⠑⢿⠓⢺⡟⠛⣰⠂⢰⠆
⠀⠀⠀⠀⠈⡟⠀⠀⡏⠘⠿⣥⡴⠿⢯⡤⠿⠯⣴⠷⡴⠏⠀⠀⠀⠿⠀⠘⠇⠿⠀⠻⠦⠞⠧⠶⠻⣶⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠙⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠻⣦⣴⠾⠛⠋⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠉⠳⠶⠛⠛⠛⠛⠛⣻⠃⠀⠀⠀⣀⡀⠘⣧⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡞⢉⡽⠛⠉⠙⠳⣦⡤⠶⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠳⣾⠁⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⠼⣧⡀⠀⠀⢀⣼⢁⣽⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣯⠉⠉⠁⠀⣠⡏
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⡤⠞⠉⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀
⠀⠤⠶⠶⢾⡷⠦⢤⠄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠛⠉⢹⡏⠉⠉⠛
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣠⣀⣿⣀
⠀⠀⠀⣤⠶⠻⣟⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⡞⠉⠙⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠙⣧⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣾⣏⣀
⠀⠀⠀⠀⠀⣠⠞⠉⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠉⠛⠆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠙⢻⣦⠀⠀⠀⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠹⣷⡾⠟⠋⠉⠁⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠙⠛⠻⢶⣦⣄⠀⣀⣀⣠⣤⣤⣾⡏⠀⠀⣠⠶⠲⢦⣤⣿⣧⣤⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⠉⠉⠉⠉⣿⠀⠀⠀⢿⣄⣰⡟⠁⠀⠀⠈⠻⣿⠛⠛⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠉⣿⡀⠀⠀⠀⠀⠀⣿⠶⣄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⠾⠿⢷⣄⡀⢀⣠⣾⣏⣀⡿⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣯⡀⠉⠉⠀⢀⣾⠋
⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣶⠾⠛⢿⣧
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣷⣶⣦⣤⣤
⠀⣀⣤⣤⣼⣿⡶⠶⠄⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠉⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠶⣾⣿⢶⣦⣤
⠀⠀⠀⢠⣴⠾⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣽⣷⣾⣷⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣶⠟⠛⠙⠛⢷⣮⣿⡿⠛⠷⠶⣦⣄
⠀⠀⠀⠀⢠⡶⠛⠁⣼⠏⠀⠀⠀⠀⠀⢻⡟⠛⠛⠛⠷⣦⣄⠀⠀⣀⣤⡶⠿⠛⢿⡇⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣤⡾⠃⠀⠀⠀⠀⠀⠙⢷⡾⠛⠁⠀⠀⠀⠘⠷⢦⣤⡀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢷⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠾⠛⣿⡄
⠀⠀⠀⣀⣤⣶⠶⠿⠷⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠾⠿⢶⣦⣤⣀
⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠘⠿⣦⣤⣴⡆⠀⠀⠀⠀⠀⣴⠟⠛⢶⡈⣿⠀⠰⠁⠀⡀⢰⠀⡆⠀⡄⠂⣼⡇⣰⠞⠻⣦⡀⠀⠀⠀⠀⠀⣤⣤⣤⡼⠏
⠀⠀⠀⠀⠀⠻⣧⣀⣠⣶⡄⠀⣿⡘⠷⠟⣠⡿⠀⠉⠁⠀⠈⠀⠀⠁⠀⠁⠀⢹⣇⠙⠶⠟⣼⠇⠀⣶⣄⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⠶⠛⠻⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢻⣶⡿⠛⠶⠾⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠘⠀⠀⠀⣀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣄⡀⠀⠀⠀⠀⢀⣀⣰⠟⠉⠉⠙⣷⣤⡶⠟⠛⠛⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠉⠛⠿⠿⠛⠛⠛⣻⡏⠀⠀⣠⣤⣌⣿⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣯⣼⠋⠉⠉⢻⡿⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⣤⣼⣿⡀⠀⠀⣰⡿⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠷⣾⡛⠛⠃⢀⣴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠟⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢾⡷⠶⠄⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⡀⠀⠀⠸⠿⠃⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠚⣿⠟⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣯⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣯⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣏⡉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢡⡾⠋⠁⠀⠀⠉⢻⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⡟⠉⠀⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡇⠀⠀⠀⠀⠀⣸⡏⠉⠛⢿⣿⣉⣹⣿⠟⠋⠁⢹⣇⠀⠀⠀⠀⠀⢨⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠈⠻⢶⣴⠾⠷⠾⠋⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠛⠷⠾⠻⠶⠶⠟⠁⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢼⠀⢠⠀⡄⠢⢠⠐⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠘⠐⠚⠁⡇⠀⢰⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡆⢸⢀⠐⢰⠆⡆⢸⠐⡆⠆⠂⢀⠐⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠈⠈⠁⠈⠁⠁⠈⠈⠁⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⢀⢸⡀⢦⠁⡃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⡀⠀⠀⢀⣤⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣤⡀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠉⠙⠻⣶⣄⠀⢀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠈⠻⣷⣀⣴⡾⠛⠉⠁⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠉⠉⠉⢉⣿⠁⠀⠀⠀⢀⣀⣀⣈⣿⣯⣤⣄⡀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⣟⠋⣽⡟⠋⠉⠈⠉⠻⣷⣶⠶⠶⠶⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⠻⣷⣿⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣠⣬⣿⣆⠀⠀⠀⠀⢀⣼⡟⠙⣿⡄⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠻⠶⠶⣶⡟⠛⠛⠛⠋⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣠⣴⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠸⣿
⠀⣀⣀⣀⣠⣤⣼⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣿⣤⣤⣀⣀⣀⡀
⠘⠛⠛⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣴⡶⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠰⣶⣤⣤⣿⠁
⠀⠀⠀⠠⣶⠾⠟⢿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣽⡟⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠶⠶⠶⠶⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢦⣤⣴⠾⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠛⠛⠿⢶⣶⣶⠶⠾⠿⢻⣿⠋⠀⣠⣄⣹⣧⣤⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠸⣏⡟⠁⠀⠀⢹⣏⠉⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣈⣷⣄⡀⢀⣰⣹⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠛⠛⣍⠉⢀⣰⣏
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠶⣿⡟⠛⠋
⠀⠀⠀⢀⣤⣶⢾⡷⠦⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⣤⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣖⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿
⠀⠀⠀⠀⠀⠰⠛⠙⢷⣄⣀⠀⠀⣀⣤⣄⡀⠀⠀⠈⠉⠀⣀⣤⣤⣀⠀⠀⠀⢀⣽⠟⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠷⣶⣿⣏⡉⠉⠙⢳⣄⢀⣴⠟⠉⠀⠀⣉⣿⢦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⠟⠉⠀⠙⡇⠀⠀⠙⠟⠁⠀⠀⠀⢸⡏⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣹⣷⣄⠀⢀⡴⣿⣇⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⣀⣠⠴⠋⠀⠈⠻⠋⠀⠈⠛⢦⣄⣀⣠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⠒⣒⠲⠒⠚⠗⠾⢤⡆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠛⠉⡗⠀⠀⢀⡀⠈⠹⣄⣏⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠰⠵⠈⢙⡆⠀⠈⠁⠀⠀⣿⠶⣻⠻⢛⣹⡏⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⢧⢀⡞⠉⠀⠀⠀⠠⠀⠀⡟⢻⣥⠆⠵⢽⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⠀⠀⠀⠀⠀⠈⠀⢠⣇⣰⡿⠞⠲⠿⣅⣤⠞⠀⡠⠤⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢴⡄⠀⢀⡾⢵⣾⡁⠀⠀⠀⢸⡆⠀⠀⠑⠁⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⠴⣄⠀⠀⠀⣀⣰⠋⠑⢦⡽⠓⠦⢤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⠻⠈⠳⠶⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣠⣄⣠⡀⣰⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⣧⣶⣹⡏⠋⠙⠙⢷⠏⠉⢙⣆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣾⠠⢹⠏⠀⠀⣤⠀⠈⠳⣾⣯⣼⠞⠉⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢺⢿⡿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣁⠸⡄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠺⠕⠃⠀⠀⠀⠀⠐⠀⠀⢸⣍⣷⠈⠓⠒⠚⢹⠁⠴⠻⢦⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠿⢋⡴⠒⠛⠒⢾⡄⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⣷⣦⣼⡀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣀⠀⠀⡀⠀⠀⣠⠞⢹⡏⠉⢑⡦⣤⡤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠛⠺⡗⢾⠛⠻⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣀⣸⣀⣠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⣠⣤⢙⡏⠋⠙⠹⢧⡀⢀⣴⠚⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⣿⠹⣿⠋⠀⠠⣤⠀⠀⢳⣞⣩⣷⣖⠟⢛⡟⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠿⠟⡇⠀⠀⠀⠀⠀⠀⠀⣿⣭⠎⢑⢅⢨⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠢⠔⠃⠀⠀⠀⠀⢐⠀⠀⣧⢸⡟⠦⠄⢤⣧⣤⣾⠀⠀⣤⠤⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢞⡣⣾⡥⢘⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠐⠶⠀⠀⢰⡟⢦⣈⣷⣭⣹⡇⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣄⡀⠀⡀⠀⢀⡤⠋⠘⢾⡁⠉⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⢻⠗⢻⠉⠳⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠐⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢤⣀
⠀⠀⠀⢀⣀⣀⣀⡜⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠙⢦⣀⡤⠖⠒⠒⠲⢯⣀⠀⠀⠀⠀⠈⠳⡄
⠀⢀⠞⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢻
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠋⠉⠉⠉⠓⢦⡀
⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣠⣍⣉⠉⠉⠉⢯⠇⣠⠞⠉⠳⣄⣠⡤⠴⢮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⡾⠁⠀⠉⠙⠓⠛⠛⢻⡇⠀⡴⢦⠼⠧⣄⣤⠼⣇⠉⠢⣄⠀⠀⠀⠀⠀⠀⣀⡤⠞⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣙⣇⠀⠀⣸⢦⠀⢸⠇⠀⠈⣳⢦⡶⠖⠚⠉⠁⠀⠀⠀⣸⣧⣄⣀⣀⣀⣀⣀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠛⣏⣉⣠⣾⠀⠀⠀⣱⠾⠁⠀⠀⠀⠀⠀⠀⠀⡽⠾⠃⠀⠉⠉⠉⠉⠉
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⡆⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠤⠴⢿⠦⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢙⡏⡹⠃⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⢀⡼⣶⠀⠀⠈⠋⠀⠀⠀⢠⠒⡄⠀⠀⠈⠋⠀⠀⠀⣹⠟⠓⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢀⡼⢶⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡽⠛⠦⠄⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠉⠀⠀⠈⠙⠓⢶⡦⠤⢤⣤⣤⣤⣤⠴⢶⡾⠋⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡴⠚⠛⣻⠶⢿⣴⣫⣤⡖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⢷⡀⢠⠇⠀⠈⡇⠀⠀⠹⣆
⠀⠀⠀⠀⢠⡞⠉⢹⡇⠀⠀⠀⠉⠛⠦⠤⠞⣷⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠳⠤⠤⠿⠦⢤⣤⣤⣤⣤⣤⣤⠿⠤⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⣤⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠰⠒⡭⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠘⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡁⠀⠀⠀⠀⣀⣤⠞⢻⣿⣿⡄
⠀⠀⠐⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⠀⠀⠀⠀⠀⡟⠛⢻⠿⠿⠏⠀⠀⠀⠀⠀⠀⣶⣶⣤⡄⠊⠀⠀⠀⠀⠘⢿⣿⣶⣾⣅⣨⣧
⠀⠀⠀⠈⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⠐⠀⠀⠀⠀⠀⠀⠾⠶⠾⣦⣄⠋⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣤⣶⣿⣶⣆⠀⠀⠀⠀⠀⠀⢸⠗⠁⠈⢢⠴⠦⠀⠀⠘⢳⣶⣶⣤⣤⣶⣿⣿⠀⠀⠀⣶⣶⣶⣦⠀⣄⣀⡀⠀⠀⠀⠆⣸⣿⣶⣶⣶⣤⡀⠄
⠀⢰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠶⠈⠡⠟⡆⠀⠸⣿⣿⣿⣿⣀⣿⣿⡿⠃⠀⠀⠸⠏⠉⢻⣿⣿⣿⡿
⠀⠾⠏⠽⡭⢹⣿⠿⠟⠛⠀⠀⠀⢻⢿⣧⣄⣤⣴⡀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⢠⣤⠀⠀⠀⠿⠋⠙⠃⠘⠿⠿⠇⠀⠀⠀⣀⠈⠈⠁⠻⣿⡿⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⢠⣶⣴⣶⣶⣷⣦
⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⢿⣿⡿⠿⠟
⠀⠀⠀⠀⠠⣀⣀⣴⠁⠀⠀⠀⠀⣤⣒⣤⣀⣠⣄⣌⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣰⣶⠄⠀⠀⠀⠀⢉⣀⣀⣻⠃⠀⠀⠀⠀⣿⣿⡿⠂⣴⣏⣠⣿⣇
⠀⠀⣶⡄⢳⡛⠉⠛⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣤⣤⣴⡾⠛⠁⠀⠀⠀⠀⣶⡀⠀⠉⠉⢀⡀⠀⠀⠀⠙⠻⠿⠿⣿⠿⠿⠛⠁
⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⡄⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠉⠀⠻⢿⣴⠀⣄⠀⠀⠀⠀⠘⠀⠀⠈⠛⠻⢿⠀⠀⠀⢀⣠⣤⣾⣿⣿⣳⣷⠶⠀⠀⠀⠀⠀⣰⠛⠋⡊⠛⢷
⠀⠸⡀⠀⠀⠀⢈⠂⠐⠂⠀⠀⠀⠹⣄⡀⠐⠀⢀⠼⠀⠀⠀⠘⣿⣿⠿⡏⠉⢧⣤⡄⠀⠀⠀⣀⢰⣿⣷⣿⣿⣿⣿⡇⠀⠀⠛⠁⠀⠀⠀⠀⠘⠳⠆
⠀⠀⣽⣲⣶⣾⡆⣠⢤⡀⠀⠀⠀⠀⢸⣷⣾⣿⣟⡀⠀⠀⠀⢠⣿⡟⠃⠀⠂⠀⠈⠁⠀⠀⠈⣅⢠⠍⢹⣿⣿⣿⠍
⠀⠀⠈⠉⠛⠙⠁⠿⠿⠕⠀⠀⠀⠀⠙⠛⠻⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣒⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣀
⠀⠀⠰⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⢙⣿⠛⠉⠻⣷⣿⣦⠀⠀⠰⣿⣿⣿⣵⣷⣵⣳⢿⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀
⠀⠀⢰⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⢠⡀⠀⠠⣿⡿⣿⠀⠀⠀⢈⡉⢿⡏⠤⣼⣿⢿⡀⠀⠀⠘⠟⢛⣛⣠⡌⣿⣿⠃⠀⠀⢀⣸⡿⠃
⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠺⠾⠟⠻⠴⠀⠀⠀⠀⠀⠀⠀⠛⠆⢀⡀⣸⠋⠉⠀⠀⠀⠀⠳⠄⠁⣀⢀⠋⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠈⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠠⠤⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠆⠀⠀⠀⠀⠓⠢⠀⡠⢄⠀⢀⣀⠀⢀⡄⠀⠀⠁⠀⠈⠂⢄⠀⠀⠀⢀⣠⠃⠀⠈⠊⠁⠀⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠎⠀⠈⠁⢫⠀⢆⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⢹⠙⠏⠒⢈⣤⡤⢣⣀⣂⣠⠆⠀⠀⠈⢣⣀⣴⠦⡠⠎⠀⠀⠀⠈⠢⢤⡀⠀⠀⠀⠀⠀⠀⡤⠔⠃
⠀⠀⠀⢸⣰⡴⠋⠁⠈⠛⠿⢁⣨⠕⡞⠉⠓⠢⡎⠀⠀⠃⠀⢠⠋⠉⠒⠒⡶⢋⣱⡖⠒⡎⠢⠤⠔⠁
⠀⠀⠀⢸⣬⡀⠀⠀⠀⢖⠒⠒⠒⠛⠲⡀⠀⠀⢳⠒⠒⢲⡀⡸⠃⠀⠀⠀⠑⠼⢇⣸⠏⡳
⠀⠀⠀⢸⠘⠑⢤⣀⠀⠀⢣⠠⡈⠀⠐⠐⡤⠒⠁⠑⢤⠤⠓⡇⠀⣀⠀⠀⠀⠀⠀⠑⢊⣇⡀
⠀⠀⠀⠘⠴⠀⠀⠀⠈⠉⠉⠱⡈⠂⠀⠀⡔⠀⠀⠀⠀⠀⠈⠽⣄⠀⠀⠐⠂⠀⠘⠀⣠⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠀⡏⢹⠀⢀⣀⣖⡤⠛⡖⢲⠢⢤⢔⡒⠉⠁⡠⠖⠤⡀
⠀⠀⢀⣀⠀⠀⡠⠄⠠⢄⠀⡖⠶⠀⠐⢤⡀⠀⢣⣨⠞⢩⠀⠀⠙⠦⠶⠮⠤⠚⠁⠈⠉⠲⡇⠀⠀⡇
⠀⠀⠀⠀⠉⠊⠀⠀⠀⡤⣵⠃⡱⢄⣠⠋⠀⠀⢯⣸⠀⠀⠀⠀⢶⠒⠒⠒⠒⠒⢦⠀⠀⠀⣻⠛⠉⠻⣤⡠
⠀⠀⡔⢢⣠⣮⠝⠂⠄⠈⠀⠉⠑⠀⠛⡄⠀⠀⡆⢹⠳⣄⡀⠀⠀⠣⡀⡔⠁⠀⠂⢣⡤⠊⠔⠓⠤⠤⠃
⠀⠀⠈⠻⡄⠢⣀⡀⡆⠀⠀⠀⠀⠀⣔⠀⠀⠀⢧⡸⠀⠀⠉⠉⠉⠉⠱⣄⠢⠒⠂⠀⡇⠀⢄⣀⡀
⠀⠀⠀⠀⠈⠲⠁⠈⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠀⠡⢀⡀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⣷⣦⣄⢀⣴⣾⣿⡿⠟⠋⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠙⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣾⣿⠃⠀⠀⠀⠀⣀⣀⠀⢹⣿⣄⣀⣀⠀⠀⠀⣀⣨⣿⣿⣤⣀
⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣾⣿⣿⣿⠿⠿⠛⠛⠋⣿⡟⠀⠀⠀⢠⣾⠿⢿⣿⡿⠟⠛⠛⠿⣷⣾⡿⠛⠛⠉⠉⠙⢿⣧
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣿⡀⣾⡟⠀⠀⠀⠀⠀⠈⣿⣷⣤⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡟⢙⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⣀⣀⣀⣤⣿⣿⣦⣀⣀⣀⣠⣾⡿⢿⡿⠟⠁⠀⢠⣿⠏
⠀⠀⠀⠀⠀⢿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠋⠁⠀⠉⠛⠛⠛⠛⢿⣦⣀⠀⠀⢀⣠⣾⣿⣦
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠿⠟⠉⢻⣿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⢿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⢀⣤⣴⣾⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣀⣀
⠈⠋⠉⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡿⠛⠿⠿⣿⣶
⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣟
⠀⠀⠀⠀⠾⠿⠛⠉⠻⣿⣧⣀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⠻⠿⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠛⠿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⠛⠉⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⣿⡏⠁⠀⠻⣿⣦⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⡟⠉⠁⣴⣿⠟⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠙⣿⣷⡀⠀⠀⠈⢻⣿⣧⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⠙⣿⣿⣄⣾⣿⣯⣤⣤⣀⡀⠙⢿⣷⣤⣀⣀⣀⣀⣤⣾⡿⠋⠀⢀⣀⣤⣤⣼⣿⣷⣄⣀⣤⣴⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠿⠿⠿⣿⣷⣤⠉⠛⠛⠿⠿⠛⠛⠉⠀⣠⣾⣿⠿⠿⠿⠿⠿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣤⣤⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣶⣦⣤⣴⣶⣿⡿⠋

⠀⠀⣀⣤⣤⣤⣀⣀
⢠⡾⠋⠁⠀⠈⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣄⡀
⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣍⣛⣶⣄⣴⠾⠛⠛⢉⡿⠋⠁⠉⠻⣷⣦⣀
⠸⣧⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠙⠻⢿⣿⣤⠀⢀⡾⠁⠀⢀⣀⡀⢹⡆⠙⢷⣄
⠀⠙⢷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠳⣾⠇⠀⢠⡿⢛⣿⠟⠛⢷⣄⣹⣧⣤⣄⡀
⠀⠀⠀⠙⢶⣄⡀⠀⠸⣧⡄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⠻⣾⠁⠀⠀⠀⢹⣇⡀⠀⠉⣿
⠀⠀⠀⠀⠀⠉⠛⠷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣴⠿⣆⡀⠀⣀⣾⣉⡷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠛⠛⣿⡙⠛⠁⢀⣼⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠈⠳⣶⡴⠟⠁⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠐⠛⠛⢿⡗⠒⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⣀⣸⣧⡤⠀⠀⠘⠿⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⡗⠀⠈⠙⣻⣶⣦⣤⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠉⠉⢻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣞⣿⠏⠙⠛⣻⣿⠿⠿⢿⣟⠛⢻⣿⣦⣄⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣭⣿⣭⣽⠏⢠⡾⠟⠻⣧⠀⠀⠀⣿⢷⡀⢿⡏⠉⠛⠶⣄⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠀⣰⡟⠀⢸⡇⠀⠀⠹⣷⡀⣠⡟⠀⢿⣀⣻⣦⣤⣠⡼⠛⠧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠀⠀⢸⣆⠀⠀⠀⣸⣿⡿⠶⢚⣛⣿⡭⣿⢹⡇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⡿⠀⠀⠀⠀⢻⣿⠿⣿⠿⠖⠛⠋⠉⠁⠙⠀⢹⡘⣇⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣈⣿⣦⣄⣠⣤⣼⣇⠀⠉⠀⠀⠀⠀⣀⣠⣞⡇⠘⣇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠉⠉⠁⠀⢻⡄⢠⣖⣰⣤⠖⠋⠉⠀⠀⠀⢻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⣷⠀⠚⠉⠀⢀⣀⣠⣤⠴⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠶⠶⠞⠛⠉⠉

⢀⣾⡿⠿⣿⣿⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⠿⢿⣷
⢸⣿⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠈⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⠿⠿⠿⠿⣿⣷⣶⣤⣄⡀⠀⠀⣠⣶⠿⠛⠛⠛⢿⣿⣿⣿⣟⡁⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣶⡟⠁⠀⠀⣠⡾⠋⠁⠀⠀⠉⢻⣶⢄⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⢸
⣿⣷⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⣎⣻⡇⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣸⡏⠙⠻⣷⣄⠀⠀⠀⣾
⢸⣿⡀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠉⠻⣶⣶⣶⣶⣿⣋⣀⣀⣠⣴⠟⠁⠀⠀⠘⢿⣷⡀⢀⣿
⠀⢿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣤⣤⡾⠟⠁⠀⠀⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢻⣷⣾⡿
⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁
⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠉⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠀⠈⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⣀⣠⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣀⣤⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⣴⠟⠉⠀⠈⠉⢻⡆⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⢻⣿⡄⢀⣠⣤⣶⠶⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣄⣠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠶⢶⣤⣄⡀⢠⣿⡟
⠀⠀⠀⠀⠻⣿⣌⠁⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠈⣡⣿⠟
⠀⠀⠀⠀⠀⠙⣿⣦⡀⣠⣴⠾⠟⠋⠁⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠈⠙⠻⠿⣦⣄⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⡀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⢀⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⡀⠀⠀⢀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⣷⣦⣄⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠙⢿⣷⣴⣶⣿⠿⠛⠛⠋⠙⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠈⠉⠛⠿⣿⣶⣶⣶⣾⣿⣿⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢀⣴⠾⢷⣦⣼⣿⣷⣤⣀⠀⠀⢀⣀⣀⢸⣿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣯⣀⣼⠟⠉⠀⠀⠉⠻⣿⡿⠿⠛⠛⠿⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣶⡶⠿⣿⡄⠀⠀⠀⠀⣠⣿⠋⣿⠄⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣾⠟⠿⠾⠛⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⢀⣠⣾⣿⣷
⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⡾⠿⠛⠁⠈⣿⣇
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⡿⠿⠷⠶⠶
⠶⠾⠿⠿⠿⣿⣿⠛⠿⠃⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⢠⣤⣼⣿⣄⣀⡀
⠀⠀⠀⢀⣀⣼⣿⣷⡶⠶⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠛⠛⠛⠃
⠀⠀⠀⠙⠉⠉⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠿⢿⣶⣤⣀
⠀⠀⠀⠀⠀⣠⣶⠿⠛⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣶⣶⣾⣿⣿⠟⠁⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⢰⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣟⠛⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣼⡟⠀⠀⠀⠈⢿⣧⡀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⣤⣴⠾⠋⠀⠀⢀⡀⠀⠀⢻⣷⡀⣠⣴⡿⠛⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣤⣤⣤⣬⣿⣷⣦⣤⣤⣴⣾⠟⠉⠁⠀⠀⠀⢀⣾⠛⠙⢿⡄⠀⢻⣿⡟⠋⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⢿⣟⣛⣿⠏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣼⠇⠀⠈⣿⣇⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣾⡿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣶⣶⣶⣶⣾⡿⠿⠛⠉⠙⠿⠿⣷⣶⣶⣶⣶⣿⡿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⢀⣠⣤⣶⣶⣴⣏⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⠈⢿⣧⣀⣠⣿⣿⣿⠋⠉⢉⣿⣿⣿⣿⣿⠀⢀⣀⣀⡀⠻⠚⠛⠛⠓⠦⣄
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠻⢿⣿⣿⣿⣿⣷⣶⣿⡿⢟⣽⣿⣿⠀⠙⠛⠛⢡⡶⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣶⢀⠀⠈⠙⠙⠛⠛⠙⠉⣰⣿⣿⣿⠇⠀⣀⡀⠀⠸⢿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣈⣉⡙⠛⠛⠛⢿⡇⢠⣶⣿⣶⣄⣀⣤⡤⣼⢿⣿⣿⣿⣄⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠃⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠈⠉⠛⠶⠖⠚⢻⣿⣿⣿⣿⣿⣥⣀⣀⣸⣇⠙⢿⣿⣿⣾⣼⣾⣿⣿⣿⡿⠟⠻⡄⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠉⣻⣿⠿⠿⠛⠋⠁⠀⠀⠀⣹⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⣿⣿⣿⣟⠀⠀⠀⣿⠿⠀⠀⠀⠀⠀⠀⠀⢈⡷⠼⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠠⠤⢾⡦⠀⠀⢤⣮⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠐⢺⡟⡽⠃⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⢀⣼⣧⠄⠀⠞⠛⠉⠀⠀⢠⠀⡄⠀⠀⠈⠋⠀⠀⠀⣻⠟⠓⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⣸⢷⣆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⡽⠛⠦⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠓⢶⣤⣤⣤⣤⣤⣤⣤⠤⢶⡾⠋⠀⠀⣀⣠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠶⢿⣴⣫⣤⡖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠇⠀⠈⡇⠀⠈⠹⡆
⠀⠀⠀⠀⠀⠀⢠⡞⠉⢹⣿⣿⣿⣿⣿⣿⣦⣤⣾⣇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠿⠿⠿⣿⣿⣿⡿⣿⡿⠿⠤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⣀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠛⠻⠿⣿⣶⣤⣀⢀⣀⣀⣀⣀⣠⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⠟⠛⠛⠉⠛⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠹⣿⡆
⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢿⣷
⣀⣤⣤⣤⣼⣿⣤⣤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣶⣶⣶⣤
⠉⠉⠉⠉⠹⣿⡏⠉⠉⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠉⠀⣹⣿
⠀⠀⠀⠀⠀⣿⣧⣀⣀⠀⠀⠀⠀⠘⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⢠⣤⣿⣧⣀⣀
⠀⠀⠰⠿⠿⠻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣽⣿⠋⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⡃
⠀⠀⠀⠀⣀⣴⡾⠟⠻⢿⣷⣄⣠⣴⣾⠿⠿⠿⢿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠶⣶⣦⣤⡀⢀⣤⣿⠟⠛⠿⣷⣦⡀
⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⣹⣿⠟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣶⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⠉⠉⠉⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣦⣤⣶⣿⣿⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠿⠿⣷⣦⣤⣴⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⠷⠶⠾⠋⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⣤⣼⣿⠶⠶⠶⠶⠶⢶⣶⠟⠋⠉⠻⢾⣿⣀⣠⣤⡴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢿⡟⠉⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢠⡞⠛⣷⠾⠷⢶⣄⣀⣀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠛⠛⠛⢻⡄⠀⠀⠈⠷⣾⠁⠀⠀⠀⢹⣏⠉⠉⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⡴⠶⢿⡄⠀⠀⠀⣸⠟⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⡟⠛⠛⠋⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣤⣤⡶⠟⠻⣇
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣤⣤⡶⢾⣷⢶⣤⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠰⠶⠛⣿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⣤⠶⠿⣿⠛⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢰⡟⠛⣷⡄⠀⠀⠀⢀⣬⠿⠛⠉⠉⠉⠉⠛⣿⡟⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣨⣽⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢻⡄
⢀⣴⠾⠿⢶⣄⠀⣀⣤⡶⠟⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⣿⣟⣋⣁⣀⣀⣀⣀⣨⣿⣶⣶⠶⠶⢶⡾⠋⠉⠉⠉⢛⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⠷⣤⣤⡴⠟⠉⠉⠙⠛⠉⠉⠉⠉⢀⡾⠁⠀⠀⠸⣇⠀⠀⠀⢠⡾⠁⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⠁⠀⠀⠀⠀⠻⣆⠀⣴⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠘⣯⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⡀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⣴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁

⠀⠀⠀⠀⠛⡆⠀⠀⠀⠘⠻⠆⠀⠀⠀⠀⠐⠻⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⠛⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣶
⠀⠀⢁⣤⠄⠁⠀⠀⢱⣠⣴⠄⠀⠀⠀⢀⠀⣀⡂⠀⠀⢹⣶⢢⡄⠀⠀⠀⢺⡿⡇⠀⠀⠈⠗⠒⠚⠀⠀⠀⠰⠀⡚⠀⠀⠀⠀⠀⢳⣶⡄⠀⠀⢧⢀⣠⣀⠀⡇
⠀⠀⠈⠁⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠠⠴⣤⠀⡀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐⢒⣠⢠⣀⠀⠀⠀⠐⢦⠀⠀⠀⠀⢀⠀⠲⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢰⣖⣠⡄
⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⡤⣄⠁⠀⠀⠐⠀⠠⠂⠀⠀⠼⡿⠷⢄⡙⠀⠘⣤⣀⠀⠀⠀⠐⠖⠀⠲⠖⠀⠀⠀⠀⠲⠶⠀⠀⠀⢄⠀⠀⠉⠋⡇
⠀⠈⠉⠈⠙⠂⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠋⠁⠀⠈⠀⠉⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠠⠠⠤⣠⣤
⠀⢀⠀⠀⠀⠂⠀⠐⣟⢀⣼⡿⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⢠⣴⡄⠀⠀⠀⣀⣀⠉⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠙⡆
⠀⠀⠀⠁⠀⠀⠀⠀⠘⠠⠃⠀⠀⠀⠼⠿⠅⠀⠀⠓⠀⠸⠃⠻⠃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠼⠿⠅⠀⠀⠀⠸⠿⠄⠃⠀⠀⠀⠀⠤⠉⠀⠀⠀⠉⠂⠀⠀⠐⠁

⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⣤⣀⡉⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⠀⠉⢃⠠⡄⠀⠀⠀⣉⠀⠀⠀⠀⠀⠈⢁⠠⠄⣤⠀⣉⠻⣇⠀⠀⢤⣈⡑⠀⠀⠀⠀⠀⠉
⠀⠀⠸⠷⠧⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢰⡶⠤⡴⠁⠀⠀⡦⠸⠄⠀⠠⠀⠐⠀⠄⡤⠀⠙⠿⡿⠿⠇⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⠲⠖⡀⠀⠀⠖⠀⠐⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠘⠛⠿⡆
⠀⠀⡀⠀⠘⠀⠀⠀⢰⣶⣆⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢤⣤⠁⣤⠀⠀⠠⢠⣴⠂⠀⠀⠠⠤⠀⡀⠀⠀⠀⠀⣴⣶⠞⠀⠀⠣⠀⣰⣀⠡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢶⡄⠀⠀⠀⠰⣶⠀⠀⠀⠀⢠⠀⣤⡀⠀⠀⠰⠤⠀⠄⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠘⠸⢿⡀
⠀⠀⢀⣤⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢻⣄⣈⠂⠀⠀⠄⠀⠈⠃⠀⠀⠈⣤⣤⡄⠀⠀⠈⣢⠠⠄⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⢀⡤⢤⡴⠀⠀⢧⠀⠀⠀⠀⠏
⠀⠀⠀⠉⠁⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣀
⠀⠀⠀⣤⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⡤⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠉⠀⠀⠶⡄⢡
⠀⠀⢀⠈⡅⠀⠀⠀⠂⠀⠀⠆⠀⠀⠀⠀⣉⠄⠀⠀⠀⢀⡀⢀⡇⠀⠀⠀⣀⡀⠉⠀⠀⠰⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⢤⠈⣤⣄⠁⡰
⠀⠠⠌⠻⠀⠾⠇⠀⠀⠴⠇⠀⠀⠀⠀⠈⠹⠂⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠐⠿⠋⠿⠀⠀⠀⠠⠹⠄⠀⠀⠀⠀⠀⠛⠿⠀⠀⠠⠶⠤⠥⠤⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠈⠈⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠁⠘⠂⠓⠁⠊⠀⠄⠀⠀⠄

⠀⠀⠀⣰⣶⣶⣦⣴⣶⣶⣦⢰⣄⡄⠀⠀⢶⣦⣠⣶⡿⣿⢿⣶⣄⢀⣤⣠⡄⣀⣤⣴⣶⣤⡼⠄⠀⠀⢀⡀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠚⠛⣧⢀⢀⠀⢱⣿⣿⣾⡿⡿⣝⢿⡾⢿⠟⣾⣿⣿⣿⣿⣿⣿⣦⣀⣦⣈⣵⣧⣄⣤⡄
⠀⠀⠐⠿⠟⠁⠀⠴⠉⠩⣷⣿⣿⡏⠆⣠⣤⡌⠻⣭⡯⠀⠀⠻⡸⣹⣿⣫⣿⠛⡿⠿⠏⣛⡻⣿⣟⢿⣿⣯⣼⣿⣿⠃
⠀⠀⠀⠆⣑⣀⣀⣀⡀⠂⢠⠀⠻⠄⠀⠀⠈⠁⠼⠗⠄⠀⠀⠀⠀⢴⣶⣦⣥⣼⣦⣠⣾⡿⢣⣶⣦⣹⡿⣿⣿⢿⣿
⠀⠀⠀⣼⡿⢻⡿⢿⣿⠚⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠶⣶⣤⢠⣶⠀⣈⢿⣿⣿⣿⡜⠛⠻⡎⣽⣭⣴⣿⣿⣿⣿⣶⡄
⠀⠀⠀⢻⠀⠈⠉⠀⠿⠛⠀⢰⡖⠀⢰⣶⣦⣾⡿⠟⠀⠈⠉⠲⠠⠀⢿⣧⣠⡌⢿⠏⣤⠀⠘⢿⣿⣿⣿⠛⠻⣿⣿⡇
⠀⠀⠀⠐⠀⠂⢰⣿⣮⣥⠀⠺⡿⠒⠢⡹⠿⠿⣷⠀⡀⠀⠀⣄⠀⠀⠀⢿⣿⣿⡔⠀⠀⣤⣆⢸⡄⠲⠷⠛⠲⡿⠛
⠀⠀⠀⡀⠀⠀⠀⠉⠉⠛⠄⢙⣇⠁⢀⡅⡄⢤⠉⠈⠀⠀⠀⠈⠀⠀⠀⠈⢉⣻⠏⠀⢠⣶⣿⣎⠘⡲⣔⣀⣐⣤⣤⡀
⠀⠀⠀⠋⠀⠂⢐⣠⣤⣐⠁⠊⢭⣟⡻⢇⣐⣨⣶⢣⣿⣿⣷⣤⡄⢤⠀⠀⠀⠁⢰⣦⣤⣹⣿⣿⣿⢡⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠖⠺⠿⠿⢿⣿⡗⠊⠘⢿⣿⣯⣿⢿⣏⢺⣿⡿⣿⡋⠀⠈⠃⠀⠀⠀⠀⠈⠉⡈⢩⡝⢭⣓⣙⣟⣛⣫⡝
⠀⠀⠀⠀⣦⣀⠀⠀⠀⠈⢙⣀⣴⣜⠁⢀⣀⡛⠏⠀⠈⠀⠁⠀⠀⠀⠀⠀⢠⣀⣀⣀⡀⣀⡛⢃⣘⢷⣿⣻⣿⣿⣧⡀
⠀⠀⠀⢾⣿⠟⠷⢆⣤⣶⠋⢹⠟⢿⡄⢩⣬⠅⠀⠀⠀⠀⠀⠀⢡⣓⠾⡇⠠⠿⣿⠟⣼⠉⢉⡍⠉⣳⡹⣿⣿⣿⠋
⠀⠀⠀⠀⠁⠀⠀⠰⣷⣈⢹⣕⢦⣬⣧⣀⣉⣀⣄⠁⠀⠀⠁⠀⠈⣛⣋⣴⣾⣿⣶⣾⣾⢹⣿⣿⣿⣿⡗⣛⣭⣭⡄
⠀⠀⠀⠀⣀⣠⠶⣤⠈⣋⣬⣽⣦⡻⣿⠟⡍⠙⠉⡀⠀⢀⣀⠀⠸⣿⣿⡿⡟⠛⣿⣉⣁⠀⣿⣿⣿⢱⠾⢻⣾⡻⣇
⠀⠀⠀⢠⣉⣐⡒⠰⣿⣿⣿⣿⢿⣧⠛⠀⠀⠀⠠⠀⠀⠘⠿⢷⠇⠉⠻⠆⠍⠄⠈⠋⠡⠄⣶⣶⢀⠿⢴⣿⣿⡇⣿⡇
⠀⠀⠀⢸⣿⢛⠃⣴⣌⣛⣟⣘⠣⠋⠀⠀⠀⠀⢰⡐⠀⠠⠀⠀⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡀⢣⣹⣿⣿⣮⠃
⠀⠀⠀⠻⠉⠀⣾⠿⢿⣿⡟⣴⡀⠀⠀⣀⡀⣤⣶⢸⠷⣶⡾⠏⠀⢹⡿⠃⠀⠀⠀⡀⣀⣀⣀⡀⡔⠀⡷⡿⠁⢀⠉
⠀⠀⠀⠐⣛⣓⣁⣂⠀⠹⣿⠎⣛⣿⣯⣛⣹⣷⣶⡖⣭⠷⢯⣿⢇⣤⣥⣴⣶⣮⢻⣿⡿⢿⣾⣿⣦⠺⣽⠊⣤⣌
⠀⠀⠀⢠⣿⣿⣿⣿⣇⠐⣦⠸⠏⠙⠻⣮⠹⡿⢿⣿⠏⠛⣷⣷⢈⣿⣿⣿⣿⣿⣦⠋⠀⠀⢹⣿⣿⡇⣶⣶⣿⡿⠇
⠀⠀⠀⠸⣿⣿⣿⣿⣇⣤⢋⡀⠚⠐⠒⠃⠀⢶⣌⠋⠉⠑⣿⠇⢘⣿⣿⣿⣿⣿⣩⣰⣦⣄⡊⣛⣭⡃⢨⡟⠀⣶⣆
⠀⠀⠀⠀⢿⠏⠙⠟⠀⠰⠌⠓⠠⠀⠀⠀⠓⠀⠉⠐⠂⠐⠂⠀⠀⠹⠿⠛⠿⠏⠈⠡⠄⠉⠑⠿⣿⣶⣿⣿⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣤⣀⠀⠀⠀⠀⣀⣀⣠⡾⠋⠀⠉⢻⣦⣶⠾⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠉⠙⠻⠿⠛⠛⠛⢻⡿⠁⠀⢀⣤⣄⣹⣧⣀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣤⡟⠉⠉⠙⢿⡟⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣿⣇⠀⠀⢀⣾⢷⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠷⢶⣟⠛⠛⠁⢀⣾⡃
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⠾⠛⠹⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣤⣤⡀
⠀⠀⠀⢠⣤⠶⢾⣷⠶⠄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠉⠉⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣷⣀⡀⠀⠀⠸⠿⠇⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⢻⣿⠷⠶⠄
⠀⠀⠀⠀⠀⠐⠛⠻⣯⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣃
⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⡉⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠚⢉⣾⠛⠉⠁⠈⠉⠻⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾⠟⠉⠀⠀⠉⠻⣧
⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⠀⠀⢀⣿⠙⠻⢿⣿⣛⢛⣿⡿⠟⠋⠉⣿⠀⠀⠀⠀⠀⠀⣸⣷⣦⡀
⠀⠀⠀⣠⣾⠟⠁⠈⠿⣦⣤⡶⠶⠶⠟⠁⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠙⠷⠶⠶⢶⣤⡶⠟⠀⠙⢿⣦
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⢀⣿⠇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⢸⣿⠀⠀⠀⠀⢂⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡄⠁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⣼⡏
⠀⠈⣿⡆⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠚⠲⣄⠓⡤⢲⠐⠀⡈⠀⠀⠀⢨⠀⡆⠀⠉⠱⡌⠙⡐⠱⠀⢠⣿⠃
⠀⠀⠘⣿⣄⠀⠀⢀⠀⠀⠃⠘⠉⠙⢶⠐⠂⡈⢆⠀⡘⢀⠈⠔⠂⠀⠀⢸⠀⡇⢠⠘⢠⠳⡀⠃⡀⢠⣾⠏
⠀⠀⠀⠘⢿⣦⡐⠞⠀⠀⠘⠦⠤⠔⠃⠲⠚⠁⠈⠖⠁⠈⠒⠚⠁⠀⠀⠀⠓⠁⠀⠑⠋⠀⠑⠚⣹⣿⠋
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⣷⣦⡀⠀⠀⣀⣠⣤⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠿⣶⣦⣤⣀⠀⠀⠀⢀⣀⣀⣀⣀⣼⡟⠁⠀⠀⠀⠙⣿⣶⡿⠟⠋⠉⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠛⠛⠛⣿⡟⠀⠀⠀⣠⣤⣤⣘⣿⣄⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢰⣟⢁⣿⠟⠛⠛⠻⣷⣶⣾⠿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠛⣿⡏⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⣶⡶⢿⣷⡀⠀⠀⢀⣼⠟⣻⡆⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⠛⠛⠋⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣴⡾⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⡷⠶⠶⠶⠄
⠀⠀⠀⠀⣤⣴⠶⢾⣿⡷⠶⠦⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠰⣾⣿⣷⣤⣤
⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⠟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡟⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣦⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⣧⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣁⡀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠟⢉⣴⡿⠋⠉⠁⠀⠉⠙⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠟⠋⠁⠀⠈⠉⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⡿⠶⠿⢷⣿⣿⣿⠿⠟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣀
⠀⠀⠀⠀⠀⣠⣾⡿⠟⢻⣇⠀⠀⠀⠀⡀⠀⢀⣰⡿⠀⠀⠈⠙⠿⣿⣦⣴⣿⠟⠋⠀⠀⠀⠘⣿⣄⠀⠀⢀⠀⠀⠀⢀⣾⠟⢿⣷⣆
⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠙⢷⣶⣶⠿⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠿⠷⠾⠟⠁⠀⠀⠘⢿⣷⡄
⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣄⡀⠀⠀⢀⣠⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠙⠳⣦⣠⠶⠛⠋⠉⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠉⠛⠛⠶⢦⣄⡀⣀⣠⣤⣤⣤⣤⣴⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢰⡏⠀⠀⠀⢀⡴⠲⡤⠚⠓⠢⣄⣠⡤⠶⠶⠿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢾⡀⡞⠀⠀⠀⠀⢹⡦⣄⠀⠀⠀⠀⠸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⣼⠀⣸⠀⠀⠀⠀⢸⠏⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⢻⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠛⠉⠓⠶⠶⣿⠁⠉⠀⠀⠀⠀⣠⡟⠃⢀⡿
⠀⠀⠀⠀⠀⠀⢀⡼⠂⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⣠⡴⠻⡆⠀⢿⡅
⠀⠀⠀⣀⣀⣀⢿⣄⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⢻⣄⣀⣽
⠀⠀⠀⠉⠉⠉⣟⡿⠻⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠾⡿⣿⣿⠛⠒⠶
⠀⠀⠀⠀⠀⢠⡟⠀⣸⣇⣀⣀⠀⠀⠀⢀⡀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠻⡆
⠀⠀⠀⠀⢀⡿⠛⠋⠉⣿⠉⣉⣀⡀⠀⠀⠹⠋⠉⠉⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⡇⠀⠀⠀⠀⠖⠛⢻⡟⠛⠛⢻⡶⢤
⠀⠀⠀⠀⣼⠁⠀⠀⣠⣼⡟⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣀⣀⡿⠀⠀⠀⠀⣇
⠀⠀⠀⢰⠇⠀⢠⣾⣥⣼⣧⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠳⢦⣄⠀⠀⣿
⠀⠀⠀⡿⠀⠀⣾⠁⠀⠀⠙⢆⠀⠀⠀⠀⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠈⠛⢀⡟
⠀⠀⢸⡇⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠛⠢⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⠁⠀⠀⠀⠀⠙⠓⠶⣴⠀⠀⠀⢿⡀⠀⠀⡀⠀⠀⢻⡛⠛⠛⠒⠶⠶⠶⠖⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠛⠒⠋⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⠀⣀⣀⣠⡴⠞⢋⣀⣠⣤⣤⣤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣤⡴⠞⠉
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣠⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣾⡥⠶⠶⠶⠚⠛⠛⠛⠛⠲⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠳⢤⣤⣤⣤⡤⠶⠖⠛⠉⠉⠉⠉⠉⠙⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡡⠀⡙⢾⣉⣬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠈⢄⠀⠈⠂⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠈⠓⠄⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⠞⠁

⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⡏⣩⣄⠈⣛⢀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⢸⡇⣼⣿⣿⣿⣿⣿⠛⡁⠈⣥⢹⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⡇⠙⠛⠀⠛⠘⣧⣄⡀⠀⢀⣸⡀
⠀⠀⠀⠀⠀⠀⡜⣸⣿⣿⣿⣿⣿⣿⣧⣍⣀⣱⠿⠋⢀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⠀⠀⠻⠇⠙⢿⣿⡏⣉⢰⣧
⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡉⢀⢉⡉⣉⠠⡶⢶⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⠀⠈⢿⣿⣄⠘⢫⣿⡛⠀⣁
⠀⠀⠀⠀⠀⠈⡄⢿⣿⣿⣿⣿⣷⠘⣿⣼⠏⡻⠓⠊⠃⠀⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋⠚⠛⠒⠒⠛⠻⢿⣾⣿⣉⠉⣀⠙
⠀⠀⠀⠀⠀⠀⠹⡜⣿⣿⣿⣿⣿⣷⡀⢠⣾⣿⣿⣿⣶⣶⣿⣿⡿⠛⣋⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡋⠉⠻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⢳⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣥⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⣶⣆⢿
⠀⠀⠀⠀⠀⡀⠔⢉⣤⣉⠛⠛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡈⢁⣸
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⡇
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠋⣩⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠈⠛⠿⠿⠿⢾⣿⡿⠿⢭⣤⣀⣀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣀⣀⣠⣼⣿⣧
⠀⠀⠀⠀⠈⣶⢧⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠉⠉⠀⣹⣿
⠀⠀⠀⠀⢀⣾⣷⣿⡷⠖⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⡷⠶
⠀⠀⠀⠀⢸⣻⣿⣿⣿⣄⣀⣀⡤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣤⣴⣿⠏
⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠻⠆
⠀⠀⠀⠀⠀⠰⣿⣿⣾⣻⡈⠻⣿⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣟⠡⠔
⠀⠀⠀⠀⠀⠀⠉⠹⣿⣼⢇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡖⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⣧⡀⠈⠻⣿⣿⣿⣿⡏⠉⠛⠦⣄⣀⡉⢉⣩⠟⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣽⡄
⠀⠀⠀⠀⠀⢠⢪⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⢉⣽⣏⡀⠀⢸⣿⣿⠟⠁⣴⣿⣿⣿⣿⠟⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⠹⣿⣿⣿⣷⣤⡀⠈⠛⢿⣿⣧⠀⠀⠠⢿⣿⠇⠀⣼⡿⠋⢀⣼⣿⣿⣿⣿⣿⣧⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⢿⣷⣤⣤⣤⣤⣤⣾⠏⣀⣴⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠻⣿⣿⣿⣿⡿⢁⣼⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⢿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠻⠷⣶⣤⣄⣠⣶⠟⠋⠉⠙⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⣹⠟⠁⠀⠀⠀⠀⠀⠹⣷⡶⢶⣶⣶⣶⣶⣤⣤⣾⠿⠛⠋⠉⠁⠀⠙⣿⡇
⠀⠀⠀⠀⠀⢀⣼⣧⣤⣀⡀⠀⣠⣴⠶⠿⣶⣶⠟⢷⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⢠⡿⠋⠉⠉⠉⠙⣿⠟⠁⠀⠀⠀⠹⣧⣼⠇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡞⢿⡀⠀⠀⠀⠀⢀⣿⣅⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠇
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠻⣦⣼⣷⣤⣀⣀⣤⡾⠋⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣻⣧⣀⠀⠀⢀⣠⣴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⢸⣿⠉⠛⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠿⠿⠿⠿⣿⡿⠶⣶⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣀⣀
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡆⠀⠀⠀⠀⠛⠛⣻⡿⠛⠛⠛⠛⠂
⠀⣤⣶⣶⣾⣿⠿⠆⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⢀⣀⣀⣿⠇
⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⠉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠷⠶⡦
⠀⠀⠀⢀⣀⣼⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣼⡟
⠀⠀⠰⠛⠋⠁⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠉⠛⠿⣶⣶⣶⣶⣶⣶⣶⣶⡾⠋⠀⠀⠀⠹⣶⣾⠿⠛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢠⣴⣦⣄⣽⣆⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣧⣾⠋⠉⠉⠙⣷⡶⠶⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣹⣧⠀⠀⠀⠀⣿⠷⣦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠳⠶⢶⡾⠿⠾⠟⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⢴⡶⠶⢾⣿⣤⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠶⠶⣿⡿⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⢿⣿⠛⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⣀⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢉⣽⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣧⡤⠼⣝⠻⣷⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⢺⣍⣭⣤⡤⢴⡶⠖⣫⣾⣯⣴⣿⠿⠛⠛⠿⣿⡟⠻⠿⠿⠿⠿⠿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⣼⡏⠀⠈⠘⣿⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠁⠀⠀⠀⠘⣿⡄⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⣠⣼⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢻⣦⣀⠀⠀⢀⣹⣿⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⡇⠀⠈⣿⡟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣴⢾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⣿⠀⠀⣠⣿⣧⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣧⣠⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⢰⡿⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠏⠉⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣀⣿⠛⠛⠛⠿⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣶⠶⠿⠿⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣭⣥⣤⣤⣀⣤⣀⣉⣉⣉⣙⣛⣛⣛⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢡⣶⡄⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣭⣍⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣭⣥⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣙⣋⣴⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠻⣷⣄⢀⣠⣤⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⠻⠷⣶⣤⣠⣤⣤⣴⣦⣴⣿⠃⠀⠀⠀⠈⢿⣟⠋⠁⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣿⠇⠀⠀⣴⠟⢻⣾⡿⢶⣦⣀⣤⣤⣼⣿⡀
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠙⢷⣿⠃⠀⠀⢹⣿⣉⠉⠉⠙⣿⡀
⠀⠀⠀⠀⠀⠘⣿⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⡶⠿⢿⣄⣀⣠⣾⣏⣿⠇⠀⢠⣿⠃
⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣏⠉⠀⢀⣴⣿⣇
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠾⠟⠋⠘⣿⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣷⣶⣦⣤
⠀⣠⣴⡶⢾⣿⠶⠶⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠈⠁⣽⡇
⠀⠀⠀⠀⠈⣿⣄⣀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⢛⣿⠿⠶⠶
⠀⠀⠀⠶⠞⠛⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣟
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⠻⠶
⠀⠀⠀⠀⢘⡋⠉⣀⡈⠙⠿⣶⣤⣤⣀⣀⠀⢀⣠⣿⠉⢻⣤⣄⠀⠀⣀⣀⣤⣴⡾⠟⣋⠀⠀⣀
⠀⠀⠀⠀⣿⣿⠴⣿⡿⣠⣤⡀⠈⠉⠙⠛⢿⣿⠋⠁⠀⠘⢉⣿⣿⣿⠟⠋⠉⣡⣤⡸⣿⡷⣾⣿⡇
⠀⠀⢿⣿⣆⣥⣶⣶⣤⡻⠿⠃⠀⠀⠀⠀⣼⣿⣄⢀⣀⣤⣾⣿⣿⣿⣆⠀⠀⠻⠿⣧⣤⣤⣬⣍⣾⣿⠇
⠀⠀⠀⠁⣾⣿⣿⣿⣿⣷⢀⣤⣶⣶⣦⣼⣿⣹⣿⡿⠛⠋⠀⠈⣿⣿⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⡎⠁
⠀⠠⣾⣷⡈⠻⠿⠿⠟⢡⣿⠟⠁⠀⠹⣿⣿⡟⠛⣿⣦⣀⣀⣼⣿⣿⣿⣿⣆⠀⠀⠛⠿⠿⠿⢛⣀⠀⣴⣿⡆
⣶⣶⡍⢩⣾⣿⣷⣆⠀⣾⡏⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⣴⣿⣿⣿⡎⢩⣶
⢉⣯⣅⢿⣿⣿⣿⣿⠀⢹⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣦⠀⣿⣿⣿⣿⡿⣈⣿
⠻⠿⢏⣬⡻⠿⠿⠋⠀⠀⠻⣧⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣼⣿⠀⠈⠛⠿⣻⣥⡙⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⣀⣀⣴⡟⠁⠀⠙⢷⡟⠋⠉⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠉⠙⠛⠛⠋⠉⠉⡟⠀⠀⡴⢲⡾⠷⢦⣤⡤⠴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⢙⣿⠀⠀⠀⣿⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠲⠤⡾⠓⠋⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠋⠁⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠶⢿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣾⡷⠦⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠠⣼⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣄⣀⠀⠈⠛⠁⠀⠀⠀⣴⠚⣲⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠈⠉⠻⢦⣄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡿⢉⣛⠓
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣤⣤⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⠾⠛⢉⣰⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠹⣄⡀⣀⣄⠀⠀⠀⠀⣿⠟⢻⠟⠋⠉⠙⠛⠟⠙⣧⠴⠚⠉⠀⢿⡄⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣨⣽⠋⠙⠷⣶⠶⠞⠃⠀⠸⣆⠀⠀⠀⠀⠀⠀⠙⣿⠉⠋⠉⢻⣿⠉⢼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣦⣤⡼⢃⡀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⢀⣼⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠶⣦⣀⢹⣿⠟⠀⢀⣀⠀⠀⠀⠈⠉⠙⣟⠉⢹⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣇⠙⢦⣄⣀⠀⠘⣿⠿⠃⠀⣴⣄⡀⢻⡀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢻⡄⠀⠈⠉⠙⠳⣤⣀⣀⠀⠹⠟⠃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢦⡀⠀⠀⠀⠀⠈⠉⢉⡿⠲⠦⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⢤⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠿⢿⣿⣿⣿⡿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⢻⣿⣿⠰⠿⠆⣽⣿⣿⢁⡉⣴⣿⢛⣿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡙⢿⣿⣆⣩⠿⠟⠛⠛⠉⠉⠙⠛⠳⠾⣧⣼⡿⢠⣼⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠑⢻⢿⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⠟⣈⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠙⠷⣴⠟⠁⣀⣀⡀⠀⠀⠀⠀⠀⣠⠶⠶⣄⣀⣠⣤⣤⠈⠻⣾⣿⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣉⠺⣿⠋⠀⣼⠋⠉⠙⠳⠶⠒⠛⣿⠃⢀⣤⣼⣏⡀⠀⣈⣇⠀⠘⣿⣤⣤⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢿⡀⠘⣷⠋⠀⢹⣏⠉⢻⡆⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⣿⣿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⢶⡞⠛⢀⣼⠃⠀⠀⢿⡿⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢹⡇⠀⠀⢸⣧⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⣿⠠⠶⢾⡶⠆⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠈⢙⡏⠉⠁⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠠⠼⢷⠂⠀⠈⠉⠀⠀⠀⣖⣲⠀⠀⠀⠉⠁⠀⣀⣽⠋⠓⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠿⢿⡄⢠⠼⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠳⢠⣾⣭⠙⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣾⣿⣿⣦⡀⠀⠀⠉⠙⠛⠲⠶⠶⠶⠶⠶⠖⠛⠋⠁⠀⠀⣰⠿⢧⣅⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⣡⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣧⣆⠄⣹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡿⠏⣼⣿⢻⡶⣤⣤⣄⣀⣀⣠⣤⣤⣶⢟⠻⣷⣷⣈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣃⣾⡿⢈⠃⣿⣿⣿⢡⣶⡌⣻⣿⣧⣽⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣾⣿⣿⣿⣶⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⣠⣤⡀⢀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⡀⠀⢀⣸⡏⠀⣙⣟⣁⡀⠹⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠸⣇⠀⣿⠉⣩⣏⠀⠀⣷⠃⠀⡿⠻⠶⠶⠟⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⡀⢸⣧⣈⣩⡷⠾⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⣀⠀⠸⣷⣶⣿⣧⡟⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠙⠻⠷⣿⣿⣿⣿⡋⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣼⣿⣿⣿⣏⡀⠀⠛⠀⠀⠀⣀⡀⠀⠀⢰⡦⠀⠀⢤⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠑⠊⠀⠀⠀⠀⢀⣀⣾⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠉⢹⠟⠛⢿⣶⣶⣿⣷⣶⣤⣤⣤⣤⣾⠟⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⣿⢻⣦⡏⠀⢠⡿⠋⠉⠉⠉⠉⠙⣿⠋⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⡴⠛⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡴⣿⠁⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠾⠿⢶⣤⣤⣤⠶⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⣀⡀⠀⠀⠀⣀⣀⠤⠤⠤⢄⣀⠔⠋⠀⠈⠑⣤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠉⠑⠚⠉⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⣀⠀⢱⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⢩⠟⠚⠓⢦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠙⡇⠀⠀⠀⠀⢹⠢⠤⠾⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠳⣄⠀⢀⡠⠛⠲⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠓⠶⠚⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠤⠖⠉⢧
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢾⠖⠶⠤⠤⣀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⢀⡠⠤⠄⠒⢾⠦⠤⢄⣀
⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠙⡄⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⡼⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⣍⣀⡤⠖⠒⠉⠓⠒⠢⣄⡀⠀⠈⠁⠈⠉⠀⣀⡤⠒⠒⠉⠑⠒⠦⣄⣈⡝⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⣀⡤⠤⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠦⠤⣀⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠂⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡤⠔⠒⠲⢤⣀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠤⣄⡴⠋
⠀⠀⠛⠒⠖⠒⠆⠀⠀⠀⠀⠀⣀⣰⠓⣆⡰⠉⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠋⠀⠉⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣰⣅⠀⢀⣵⡀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢰⠖⠒⢦⡀⢀⣀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⡠⠞⠁⠈⠙⠉⠀⠙⠦⣀⣀⣀⣠⣴⣋⡠⠴⠞⢳⡀⠀⠀⠀⢠⠦⣀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠟⠁⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⠁⠀⠀⠈⠹⠀⠀⢀⣎⠀⠀⠷⢤⡀
⠀⠀⠀⢀⡞⠉⠁⡎⠉⡆⢀⡠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡉⢰⠒⡆⠀⣹⠃
⠀⠀⠀⢸⡀⠀⢀⡌⠉⠀⢀⠇⠀⠀⠀⠀⠀⣠⠎⠙⠏⠀⠋⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⡌⠉⠁⢻⠁
⠀⠀⠀⠈⠉⠙⠉⠙⠒⠒⠚⠆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢉⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡈⠐⠨⠔⢒⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠑⠠⢈⠐⠀⠄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠠⠄⣼⠃⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢸⡁⠀⠨⣅⢀⣽⣥⣄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣂⣭⣄⡶⠞⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡂⠒⠂⠉⠏⠰⠑⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡠⠒⠒⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠚⠃⣀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡰⠁⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠈⠉
⠀⠀⠀⠀⢀⡴⠒⠁⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⠀⠀⠀⡘⠀⠀⣸⠁
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠛⠀⠀⠀⡰⠁⠀⣰⠃
⠀⠀⠀⢸⠁⠐⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡄⠀⠀⡔⠁⠀⣴⠃⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠸⡇⠀⠀⠀⠀⠀⢀⣸⠶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠄⢀⡾⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠤⠀⠀⠀⠀⠙⢍⡉⠉⠁⠒⠢⣀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠉⠓⠂⠔⠒⠉⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠑⠄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡎⠀⠀⠐⠁⡱⠂⠓⢦⡀⠀⠀⠀⠘⣍⠓⠆⢠⡀⠜⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠉⠉⠉⠉⢆⠀⠀⠉⢲⠀⠀⠀⠀⠻⢄⠀⠈⠑⠘⣦⣀⣀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠢⢀⣀⡴⠧⠔⠀⠀⡰⠀⢹⡀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⡔⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⢰⠛⠒⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣤⣠⡄⢈⣹⠆⠚⠤⡀⠀⠀⠸⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠤⢼⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⡌⢠⠁⠈⡌⢻⡀⠀⠀⣲⡤⠠⢄⠀⠀⠀⠀⠀⠀⡴⠒⢢⠀⠀⠀⠀⠘⠤⠆⠀⠀⠀⣀⣸⠀⢀⡟⠀⠀⠀⣀⡤⠀⢤⡀
⠀⠀⠀⠀⣀⣼⠁⠂⠉⠒⠀⠈⡃⢤⠟⠁⡀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⠏⣠⠞⠀⠀⢀⡜⠉⠀⠁⠀⠙⢆
⠀⠀⠀⠀⡀⢠⠈⠑⠒⠠⠦⡰⣿⣣⣀⡀⠀⠀⡂⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡯⠞⠁⠀⠀⢠⡟⠀⠤⠀⢀⣒⣒⢘
⠀⠀⠀⠀⠙⡒⠢⠄⢀⣀⠀⠠⠀⠈⠄⠀⠉⣡⠥⣙⣓⣲⣶⣤⣤⠤⠤⣤⣤⣀⣠⣤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠈⠉⠃⠀⠐⠂⡾⠁⠀⠈⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠘⢦⢀⣤⣤⣠⣤⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⡴⠟⠀⠀⠁⠀⠙⠦⡀⠀⠀⠈⠳⣉⣀⣄⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢤⣀⠀⠀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡤⣦⣠⠞
⠀⠀⠀⠀⠀⠀⡠⠔⠒⠲⢄⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⢕⡢⢌⡵⣊⠛⣄⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⠑⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⡴⠉⠀⠉⢣
⠀⠀⠀⠀⠀⠷⠊⠈⠋⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠳⣄⣀⠀⠀⠀⣨⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠙⢧⠘⠃⠀⠘⣄⣠⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⣇⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⢳⣄⢔⡢⢪⠭⠥⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢀⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠉⠳⠤⠡⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠿⠿⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠉⠻⣷⡀⢀⣤⣶⠾⠛⠋⠉⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⣀⣠⣤⣤⣤⣴⣶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣠⣤⣤⣀⣼⣷⣤⣤⣄⠀⠀⠀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢰⣿⠁⣽⠟⠉⠀⠀⠀⠙⢿⣾⠟⠛⠉⠙⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣴⡾⣿⠀⠀⠀⠀⠀⠀⣰⡟⢻⣆⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢷⣤⣀⣀⣠⣾⣿⣤⣼⡟⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢷⣄⠉⠁⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠟⠋⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣷⣦⣤⣤⣤
⠀⠀⣠⣤⣴⣶⣶⣿⡷⠶⠶⠶⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣠⣤⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠘⠛⣿⠟⠛⠿⠶⠆
⠀⠀⠀⠀⠀⣠⣴⠿⢻⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠈⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣆⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⠛⢶⣄⣀⣤⣤⣤⣤⣤⣤⣤⣶⠟⠛⠛⣷⣤⡶⠞⠛⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣴⠟⠁⢀⣀⣄⣹⣇⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣴⡟⢻⡿⠿⠿⢦⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠠⢻⣿⣿⢠⡄⢀⡀⠹⣷⣶⠶⠿⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣿⠟⣀⠁⠻⠟⣸⡟⢻⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣍⣱⣿⣿⡿⣷⡾⠏⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢿⣇⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⠻⣷⣶⣾⣿⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠛⣿⠉⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⣘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠔⠃⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⢨⡿⠉⠉⠓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠳⢤⣀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣞⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡶⠾⠟⠛⢁⣿⠃⠀⠈⢿⡿⠏⠉⠉⠉⠉⠉⢿⡿⠁⠀⠘⣷⡝⠻⠶⣤⣄⣀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⢿⣤⢀⠀⣿⠇⠀⠀⠀⠈⠳⣤⡄⠀⠀⣀⣤⠞⠁⠀⠀⠀⢹⣷⠁⢀⠐⣿⡛⠙⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢛⣷⣿⣿⠏⠀⢀⡴⠶⢤⠀⠈⠉⠛⠋⠉⠀⠀⢀⣠⣤⡀⠀⢿⣤⣿⣿⡏⠁⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢘⣋⣿⠏⠀⠀⠸⣄⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣹⠀⠘⣿⣿⠃⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⡐⠁⣸⠏⠀⣠⡴⠾⠿⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣎⠁⣼⠃⢠⡞⠁⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠟⠻⢻⣿⣷⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢿⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡠⠊⣿⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⠀⢠⣶⡀⠀⠀⣀⢀⣼⣿⢀⣤⣶⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣿⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣄⡾⠿⢻⣷⣾⠿⠿⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⣿⣇⡄⠀⢀⠁⠀⠀⠀⠀⢀⣿⡟⠃⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⢐⠎⢻⣿⣒⡞⢀⠀⢠⢀⣠⡾⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⠻⠷⣾⣶⠾⠿⠋⠀⠀⠈⠛⠳⠶⠶⠶⠶⠶⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣠⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣸⣿⣜⠻⣿⣿⡿⢿⣠⡿⡿⣿⣿⣶⢦⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⡐⠀⠀⠛⠻⢧⠛⠃⠀⠀⢸⣷⣶⣧⣨⡿⢈⠄⠀⢹⣿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⢬⣶⡤⢻⣃⣡⣈⡀⠂⢀⢈⡜⠶⢠⡄⡛⠛⢻⣿⠯⢷⠆⡈⠀⣼⣿⡇⠈⣢⣤
⠀⠀⠀⠀⠀⠰⠂⠰⢴⣶⣾⣿⣿⣧⢻⡿⢹⣟⣿⣿⣿⣾⡿⣠⣤⣷⣤⣠⣴⣷⣬⡉⠋⡀⠀⠙⣿⣽
⠀⠀⠀⢀⡸⣥⣄⡴⠏⣻⠟⠛⠟⠀⠈⠺⢿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⢟⣛⢷⠀⠀⠀⠀⠟⠁⠀⢀⡀
⠀⠀⠀⣸⢣⣟⣿⣿⡾⠁⡴⠛⠳⢦⣄⠀⠘⠙⠛⠛⣉⣍⡁⠿⠟⠓⠋⢝⠳⠘⣿⣆⣤⡄⠐⠀⠀⠀⠀⢻⡟
⠀⠀⣾⠃⢠⣯⣝⢮⡇⢸⡃⠀⠀⠀⠉⠉⠉⠛⢻⣿⣿⣿⣿⡶⠚⠛⢶⠈⣶⣶⡜⣿⣿⣿⡀⠀⠀⠀⢀⡹⠛
⠀⠀⠈⢶⣿⣿⡿⠿⠂⡼⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣼⡀⠿⢿⣏⠉⠙⢿⡗⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢈⠭⠒⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⡟⠠⢾⣿⣧⠙⠋⠀⠁⠰⠆⠼⠆⢨⣿⣷
⠀⢠⡄⠠⠀⠀⠒⠺⣷⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠁⠀⢘⣹⠏⠀⡀⠀⠀⢠⠀⠀⠀⠀⠛⠋
⠀⣌⡁⡇⠀⢀⡴⢾⡏⠈⣇⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣤⣿⣀⡉⢁⠀⠀⠐⠁⠀⠀⡌⠁⠀⠀⣀⣂⣢
⠘⠛⠃⠐⠀⠈⠀⠀⠀⠀⢙⡲⣤⠀⠀⠀⠿⠷⠀⠀⠀⠛⠁⠀⠀⣴⣇⡀⢠⣾⣷⣤⡁⠀⠀⠀⠈⢃⣤⡄⣿⣏⣿
⢀⠀⠀⠀⠀⠀⢀⢀⡀⢰⣋⣉⢘⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡶⣏⠀⠀⠘⢿⠛⠟⠋⠀⠄⣠⣶⣿⣿⣷⣶⡎⠁
⣼⣦⡀⢀⣴⣾⣿⣿⢧⣀⣈⣠⠞⠁⣉⠉⡛⠒⠒⠒⠒⠒⠋⡁⠀⠈⣁⣀⣀⣀⣙⡁⠀⠀⠠⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⡧⠂⣀⣀⡀⣀⣀⠰⡐⣨⠆⠀⣠⠈⠚⢿⡗⠉⠒⡽⡟⠃⡀⠘⠿⣿⣿⣿⣮⡻⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⠋⠀⢰⡿⢟⣑⣿⡟⡀⠀⣄⢀⠀⢇⠀⠞⢺⣎⠃⢀⡇⢬⣭⣬⡅⣰⣿⣿⣿⣿⣷⠛⠙⠏
⣿⣿⡿⠋⠀⠉⠀⠀⠀⢀⢺⠻⠋⣾⣷⣤⣥⣇⠂⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⣰⣿⣿⣿⣿⣿⣿⠟
⡿⠋⠀⠀⠀⠀⠀⠛⠖⠃⠙⠷⢆⣿⣿⣿⣩⣿⣗⣼⣻⣿⣿⣿⣟⠟⠁⠀⠀⠰⢹⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢟⣽⣿⡿⣿⡿⣿⣿⣔⢤⣤⣾⣿⠶⢄⠹⠟⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣟⣿⡟⠋⣶⣿⣷⡎⠙⣿⢇⣹⡡⠤⠖⠊
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠛⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⡄⠀⠀⠀⢀⠀⡇⢱⠀⡀⢤⣄⡀⠘⡈⡇⢀⡠⣤⡀⢰⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⣙⢳⣶⣆⢘⣀⣿⠻⣷⣭⠛⠚⣇⣀⠶⣉⣉⣽⠃⢛⣁⣱⣊⣀⣸⠀⣳⣶⠿⢛⡙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠙⠧⠬⢠⡟⠙⣧⡞⠟⠠⡟⠳⣞⣙⣦⢤⣀⣰⣋⣶⣞⠛⣿⢻⡄⣽⠉⢻⣡⠴⠃⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⣏⣹⣿⣽⣇⢈⣿⠿⠟⣻⠉⠙⡄⢛⠉⣉⠛⣛⠿⣿⠀⣿⣩⠿⢻⡝⢦⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠿⠬⠥⢀⡟⠉⣿⡼⢿⣋⣑⢺⠗⠺⡟⣩⠾⠿⢆⣿⠉⣻⡡⠜⠉⠉⠪⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⠟⡉⠷⡄⠀⢠⠟⢲⡞⠛⣄⠀⠀⡎⢩⡿⡍⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠈⢷⣀⣴⠀⠀⠀⠀⠀⠸⠧⠋⠀⠉⠑⠇⠀⣼⣰⠃⠈⠒⢬⡅⠠⠧⠞⠀⠈⠑⠶⠀⠀⠀⠀⠐⣄⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠈⠛⠛⠛⠳⣿⠶⠤⠄⠀⠀⠀⠀⢻⣟⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡇⠀⠀⠀⠀⠠⠤⠶⣿⠞⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣻⣀⣀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⢀⣀⣀⣏
⠀⠀⠀⠴⠛⠛⠙⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠋⠛⠳⠦
⠀⠀⠀⠀⠀⠀⢀⣘⣧⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣼⣃⡀
⠀⠀⠀⢠⡴⠞⠛⠉⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠈⠹⣿⣟⠛⠓⠶⠶⠶⠶⠦⠤⠤⠶⠶⠶⠶⠶⠛⠛⣻⣿⠋⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠹⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣼⣿⠃⢀⡴⣺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠙⠿⣷⡄⠙⠻⠟⠛⣛⣛⣻⣶⣄⣤⣾⣟⣛⡛⠛⠻⠞⠃⣠⣿⠟⠋⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠈⢿⡦⠶⠚⠋⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠙⠓⠦⢾⡟⠁⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢸⡧⠀⠁⠀⠁⠀⣀⣀⠀⠀⣉⡄⠀⠀⠀⠈⡀⣿⡇⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢀⣾⣷⣨⣤⡀⠄⢡⣏⣼⣷⣾⢧⣹⡄⠀⢀⣠⠅⣿⣧⡀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⣀⣀⣤⣾⡽⠿⠓⠺⣿⣾⣻⣿⣶⣤⣤⣶⣿⣟⣳⣿⠟⠚⠿⢾⣷⣄⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣽⠿⠋⠁⠀⠀⠁⠈⠄⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⡉⠛⢿⣯⣭⣀
⠀⠀⠀⠀⠀⠀⣠⣶⠯⠭⢤⡈⢳⣄⢀⣀⣠⣤⠴⠶⠶⠶⣤⣀⠀⠀⣠⡤⠶⠶⠶⠦⣤⣄⣀⠀⣰⠏⢡⠤⠭⠷⣶⡄
⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣷⣀⠉⠉⢉⣁⣤⣶⣲⣉⠓⣦⠙⠓⠞⢉⡴⢛⣛⣖⣦⣤⣈⠉⠉⠉⣠⣾⣿⣻⣿⣶⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⢿⣬⣭⡿⠿⠛⠋⠉⠉⠉⠻⣮⣓⡦⢶⣻⡵⠟⠉⠉⠉⠙⠻⠿⣿⣭⣥⡿⠛⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠦⠤⠤⠶⠶⠶⠒⠛⠋⠉⠙⠛⠲⠶⠶⠦⠤⠤⠶⠶⠶⠚⠋⠁