Basket Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⣶⡚⠿⠭⣭⣭⣉⡀⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡫⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠤⠘⠒⣂⣀⠩⠭⠥⠤⠀⠀⠐⠒⠀⠒⠒⠂⠀⠐⠒⠀⠀⠤⠬⠭⢉⣀⣒⠲⡇⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠄⠒⢉⡉⠤⠤⠐⠒⣒⣀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣐⣒⠒⠀⠤⠄⣹⠀⡞⠠⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠣⠴⣊⣁⡤⠒⠂⢉⣁⠤⠤⠤⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠤⠤⠤⠄⣈⡉⠒⠲⠇⢠⡓⠤⠜⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣉⠒⠂⠤⠄⣉⣉⠁⠒⠒⠒⠓⠂⠠⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠒⠒⠒⠈⢉⡋⠀⣈⠖⠒⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠬⣉⡓⠒⠂⠤⠤⢈⣉⣉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⣉⣉⣉⠠⠬⠍⠒⠒⣋⡉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠦⠤⣉⡑⠒⠲⠦⠤⠤⠈⣉⣉⣉⣉⣉⠉⠉⠉⠉⣉⣉⣉⣉⣁⠠⠤⠤⠴⠒⠒⣊⡉⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠤⢄⣀⡉⠉⠒⠒⠂⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠀⠒⠒⠂⠉⣁⣠⠤⠔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡑⠢⠤⣀⣉⠉⠀⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠐⠒⠒⠂⠉⠉⣁⣀⠤⢒⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢑⠒⠤⠤⢉⣉⣙⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢈⣉⣉⡉⠥⠤⢒⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠒⠒⠂⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⠀⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠟⢉⣠⣴⣾⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠻⠿⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠂⣠⣤⣤⣀⣀⣀⣀⣁⣉⣉⣉⣉⣉⡉⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡈⠁⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⣼⣿⣿⣶⣤⣌⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢉⣠⣤⠀⣀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣰⣿⣿⡏⢠⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⣸⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠛⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠒⢒⣒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢉⠠⠔⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢮⡠⠠⢤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣀⢱⣄⠀⠈⢧⠀⠈⠱⡍⠁⠐⢴⠒⠒⢤⠖⠛⠢⢞⠉⠁⠑⢏⠀⠉⠙⢄⡀⡀⣡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⡏⠉⠀⠑⠒⠀⠘⠒⠀⠠⠒⠠⠤⡵⠶⠀⠤⠓⠒⠒⠒⠉⠉⠉⠉⠀⡇⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠉⠚⠃⠐⠀⠠⢤⠤⡤⠤⠀⠠⠤⠀⠠⠄⠤⠤⠤⠤⠤⠀⠤⠤⠐⠐⠒⠈⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠑⠲⠶⠤⠤⠤⠄⢠⣀⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡶⠤⠤⠄⠒⢐⠂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠴⢠⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⡁⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⣀⣀⠀⠀⠀⠀⠈⠀⠏⠉⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⣩⢨⠀⢀⠀⢤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣈⣹⠉⠉⠀⠐⠒⠒⠃⠐⠒⠒⠒⠒⠲⠖⠶⠂⠀⠀⠂⠀⠉⠉⠁⠀⠀⢸⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠐⠒⠒⠠⠤⠤⠤⠤⠤⠠⠰⠄⠥⠤⠤⠤⠄⠀⠀⠐⠒⠋⠉


⡶⠶⠶⠶⠖⠲⠶⠶⠶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠄⠐⠢⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠪⡖⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠑⠁⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠵⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⠠⠄⠐⠀⠋⠀⠀⣤⠤⠚⠁⢠⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢿⠀⣠⣠⣤⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⡀⠀⡄⠢⠐⢀⡂⠀⣟⣁⣁⣀⣯⣠⣄⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⣸⠲
⠀⠀⠀⠀⣰⠘⠃⠐⡇⠀⠀⠈⠃⠀⠘⠁⠀⠀⠁⠉⠠⡀⠀⠀⠀⠀⠀⠀⡾⠖⠁⠄⠀⠀⠀⣰⠁
⠀⠀⠀⣼⢠⠀⠢⠄⠈⠄⠂⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⢰⠉⠀⠀⠀⡀⢀⡷⢤⠐⡐⠀⠘⡀⠇
⠀⠀⠀⠏⠙⠃⣄⣁⠀⢄⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⡥⡪⡿⠀⠖⠉⡄⠁
⠀⠀⠀⠈⠲⣀⠈⠠⠃⡰⢄⡤⣀⠄⠄⠀⠈⡥⠀⢉⠍⠁⠰⣾⠉⠠⡆⠀⠓⢉⠀⢀⠁
⠀⠀⠀⠀⠀⢹⣄⢟⠀⠂⢀⡀⠁⠀⠀⣄⠄⠉⢠⡎⠀⠒⢀⡆⠀⠀⡇⠀⠀⠀⠀⢘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠹⣖⢆⠀⠀⢻⡀⠀⠀⠸⡀⠀⠀⢿⠀⠀⠀⠇⠀⠀⣥⠀⠀⠈⠀⢨⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢯⢄⠀⠈⣗⠀⠀⠈⡆⠀⠀⢸⡆⠀⠀⢇⠀⠀⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⠀⢸⣆⠀⠀⠳⠄⠀⠀⣷⠀⠀⠰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠃⠀⠀⠑⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠆⠐⠂⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⢀⡀⠀⠀⠐⠄⣀⣁⡀⠀⠂⠀⠁⠀⠁⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠮⠄⠀⢀⡤⠄⠉⠉⠀⠀⠀⠀⠀⠀⠉⠲⠠⠀⠀⠀⠀⠣⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⢠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠀⠈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠰⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠌⠀⣀
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠠⢀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠀⡘⠂
⠀⠀⠀⠀⠀⡁⠀⣀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠴⢀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠀⠄⠀⠐⠈⠁⠀⠀⠄⠀⢁
⠀⠀⠀⠀⠀⠐⠠⠄⣀⠈⡉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⣀⡠⠄⠒⠂⢉
⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠉⠀⠈⠀⠀⠂⠀⠀⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠠⠀⠀⠀⠐⠒⠀⠀⠁⠀⠈⠀⢀⡀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠀⠄⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠀⠀⣀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠀⠠⠄⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⣀⠀⣀⣀⣀⡀⣀⠀⠀⠤⠄⠐⠂⠀⠒⠈⠉⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠠⠄⠀⣀⠀⠀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠒⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠁⠀⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⠉⠀⠂⠒⠂⠀⠐⠀⠠⠀⠀⠄⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠉⠐⠀⠀⠀⠠⠀⠠⠄⠠⠄⠀⠠⠀⠤⠤⠠⠔⠂⠐⠀⠐⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⠀⠄⠠⠄⠤⠄⠀⠠⠄⠤⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣥⣄⣒⣒⣒⣒⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⢶⣶⣶⣬⣭⣭⣉⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⢂⠒⠀⠙⢫⡖⠚⠒⠛⡇⠀⠼⢦⠄⠀⠐⣶⣖⠒⠒⢶⣤⣀⣀⣤⣤⣀⣀⣀⢀⣀⠀⠀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⣾⠿⡿⠶⠦⣤⣿⣤⣤⣤⣷⣄⣀⠀⣷⡄⠀⠀⢨⡍⠉⠁⠉⣧⠀⠒⠊⠹⡛⠛⠁⠘⣃⢺⡇⣼⠰⣆
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⡇⣿⡟⠈⠈⠀⡀⠀⠀⠀⠀⡎⣿⠈⠉⠉⠉⠉⠉⡻⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠖⠒⠿⢿⡇⣿⢴⣿
⣿⡇⠀⠀⠈⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣁⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠃⠀⠀⠰⠼⠃⣀⣤⣴⣏⡛⢣⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢂⣀⠀⠀⠀⠉⣢⠀⠀⠀⠛⣂⠀⠀⠙⠟⠁⠁⠻⡿⠒⠛⠒⢷⣖⠒⠒⠒⢾⢧⣴⣿⣿⣿⣿⣿⣟⣡⡌⣿⣿
⠀⣧⢠⡆⠀⢰⠉⠉⠉⠉⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣀⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢢⣤⠀⠀⢀⣸⣿⢿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢘⣄⡀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠙⠙⠙⠩⡭⠉⠉⠛⠛⣋⠛⠹⠋⠀⣾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠩⠉⠉⠉⢹⡟⠛⠻⠛⠛⠛⠒⠒⠛⠿⣷⣶⣤⣴⠾⠦⠀⢀⣤⣄⡀⢀⣀⣠⡂⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠁⠀⢠⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠶⠶⡶⠲⢟⡚⠀⠓⠚⠛⡟⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠘⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣶⣴⡶⠧⠁⠀⢼⣤⣄⣀⣀⣀⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠀⠀⠀⢀⠣⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡇⣀⠀⢄⡀⠈⠀⠀⠀⠀⢸⠈⣹⠹⠀⠒⠀⠀⠀⢈⠿⠛⠛⢹⠁⠌⠀⠚⠛⣿⣷⡶⡾⣷⠧⠤⠤⠷⣦⣶⣤⣤⠶⡿⠋⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠾⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⠀⢸⣄⣁⡀⠀⢀⠇⠈⠀⠇⣠⠉⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡼⠛⠙⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠌⠉⡏⢿⠀⠋⠀⠀⠀⣿⠉⠉⠉⢈⠀⠌⠉⠀⠉⡍⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢻⡟⣿⠇⠀⣸⢻⣠⠿
⠀⠀⠹⢶⣶⣤⣼⠤⠀⠤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢐⠙⠂⠀⠀⠏⠉⠉⠁⡇⠀⠀⠀⠀⣿⣇⣿⢶⣾⠏⠉⢡⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠩⡟⠛⠛⠉⠇⢀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣧⣁⡂⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢁⣸⣁
⠀⠀⠀⣿⢀⣀⣼⣄⣀⣀⣀⣴⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠈⠉⡋⠙⠉⠁⢸⡆⠁⢀⣼⠟⢹⢻⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠷⣶⡶⢾⠗⠓⠒⠂⠾⣤⣤⣠⣤⣥⠤⣤⡀⣴⡀⠀⠀⠀⠀⠀⢠⠸⠀⣼⣥⣶⢿⡇⠀⢸⠸⣿⠃
⠀⠀⠈⢷⣀⡀⢀⣀⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⡤⠄⠀⠀⠀⠁⠙⠉⠉⠀⢄⠀⠀⠈⠙⠛⠿⠿⠛⠃⠀⠐⢒⠙⢡⠀⣸⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢲⠃⣀⠘⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢣⡠⠚⠁⠀⠉⠙⠢⡔⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠲⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠒⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠯⢉⡒⣿⣉⣩⣉⣉⣉⣉⣹⣋⠁⠒⢒⠶⠼⠒⢾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⣀⠄⠚⠛⠉⣉⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠙⠓⢴⡒⠤⡗⠦⣀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠴⠋⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⣀⠀⠐⠒⠀⠀⠤⠀⠀⡃⠒⢗⠲⢌⡱⢦⡀
⠀⠀⠀⠀⠀⡐⠀⠀⡄⠁⠀⠁⠀⠐⠂⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠈⠐⠀⣏⠑⢾⠀⠀⠑⣄⠁⡀
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠨⠀⠀⢀⠒⠂⠀⠀⠤⠀⠀⢀⠀⠀⠰⠤⠖⠀⠔⠂⠀⣏⠙⢺⠍⣂⢁⡿⠁⡇
⠀⠀⠀⠀⠀⡟⣄⠀⠙⢄⠀⠀⠀⢐⠒⠂⠀⠀⡈⡀⠀⢍⢁⠀⠈⢡⣤⠄⡢⠉⠀⡏⠑⢾⡒⣬⡵⢁⡰⡇
⠀⠀⠀⠀⠀⣷⡈⠢⢄⠀⠙⠢⠤⣐⡭⠅⠀⠀⣀⡀⠀⢀⣀⠄⠰⠐⢂⣀⠂⢉⡴⠭⠠⢾⣿⣁⠼⢋⡴⡇
⠀⠀⠀⠀⠀⢓⠦⠀⣄⠉⠒⠢⢤⣀⡈⠉⡖⠒⠒⠦⠤⠬⡭⡥⠤⠤⠤⠴⠖⠚⠛⢷⠖⣤⣈⡇⠐⢐⣠⡇
⠀⠀⠀⠀⠀⢹⠀⠠⡌⢑⠀⠀⠠⠠⢉⠉⠛⠓⠲⠤⠤⠤⠧⠤⠤⠤⠄⠐⠘⠀⠘⠛⠚⢁⡠⠀⠀⢰⢺⠇
⠀⠀⠀⠀⠀⢸⠦⠐⣢⡀⠀⠀⠨⢄⠂⠀⠀⠀⠁⠒⠂⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢺⢹
⠀⠀⠀⠀⠀⢸⠭⠀⢁⠊⠄⡀⢈⠠⢌⡁⠀⠀⠡⠒⠆⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⣿
⠀⠀⠀⠀⠀⢸⠓⠀⡾⠄⡀⠀⢘⣑⠠⠄⢀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⢺⣿
⠀⠀⠀⠀⠀⢸⡒⠂⡆⠑⠤⠤⠐⠢⠍⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡌⠁⠀⠀⠅⠐⠠⡿⡇
⠀⠀⠀⠀⠀⣨⣯⠤⡂⠑⠄⠀⠠⡝⠤⠀⠀⡐⠠⠄⠀⠐⠒⠈⠉⢀⠀⠀⠀⠐⡂⠀⠀⠨⡇⠀⡀⣿⣧⡀
⠀⠀⠀⠀⠀⠡⡘⣥⡬⢍⠢⠀⠈⠭⢉⡉⠀⠀⠈⠀⠀⢀⢀⣃⣀⡠⠄⠀⠀⢨⡥⠀⠀⠺⢶⡺⠓⣅⠔⠃
⠀⠀⠀⠀⠀⠀⠙⠣⣈⣹⠶⢤⣀⣩⣐⣒⡀⠄⡀⠀⠀⠀⠀⠀⠠⠐⠲⠤⠤⢚⣑⡤⠴⢚⡩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠮⠬⠉⣙⠒⠓⠒⡖⠒⠑⢺⠏⠓⠒⣒⣊⡉⠽⠆⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠾⠟⠛⠛⠛⠛⠻⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⣡⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣭⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⣧⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⢠⡿⠁⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⢰⡿⠁⠀⠀⣾⣤⣤⡴⣾⠷⠶⠒⠒⣿⠓⠒⠶⠶⠶⠶⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢠⣿⢁⣠⡶⠛⣿⠁⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣀⠀⠀⠀⢹⣇
⠀⠀⣸⣷⠟⠁⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣄⠀⣿⡀
⠀⠀⣿⠁⠀⠀⠀⣸⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⡇
⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⣿⡀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠈⢿⡄⢰⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠘⣷⣸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠾⠿⠶⠶⠶⠟⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⣠⡴⠋⠁⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣄⠀⠀⠀⠀⢠⡾⠁⠀⠀⣀⣀⣀⣤⣤⠤⠤⠦⠤⠠⠄⣀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠉⠛⠷⠶⢶⣿⠗⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⣦
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⡼⢀⣠⣴⠶⠾⠟⠛⣻⡟⠛⠛⠛⠛⠿⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⠟⠋⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣶⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠋⠁⠀⠀⣿⠀⠀⠀⠉⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣄⣾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢈⡇
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⣠⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣀⣀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣴⣶⣤⣾⣷⣿⣶⣿⣿⣿⣿⣿⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠉⠉⠉⠋⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠾⠟⠛⠛⠛⠛⠻⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⣡⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣭⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⣧⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⢠⡿⠁⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⢰⡿⠁⠀⠀⣾⣤⣤⡴⣾⠷⠶⠒⠒⣿⠓⠒⠶⠶⠶⠶⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢠⣿⢁⣠⡶⠛⣿⠁⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣀⠀⠀⠀⢹⣇
⠀⠀⣸⣷⠟⠁⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣄⠀⣿⡀
⠀⠀⣿⠁⠀⠀⠀⣸⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⡇
⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⣿⡀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠈⢿⡄⢰⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠘⣷⣸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠾⠿⠶⠶⠶⠟⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡴⠂⠀⡰⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣟⠀⢀⡧⠔⠚⠠⠤⣄⠉⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢃⠀⢈⠖⠁⠀⠀⠀⠀⠀⠀⠙⢧⡀⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡀⠈⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠢⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠒⠤⣘⡶⠒⠲⠒⠒⠒⠒⠒⠒⡶⠖⠠⠤⠄⣀⣀⡦⢄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⣩⣽⡷⠾⠿⠒⠛⠋⠉⠉⠀⠒⢛⣓⠶⠤⠤⢴⣆⡎⣅⡀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⢀⡴⠒⠉⠀⠀⠀⠠⡄⣀⡀⠀⠌⠀⠀⠀⠀⠒⠂⠀⠀⣒⠀⠙⢻⣈⠉⣇⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠤⠄⠀⢈⣉⣁⠀⠀⠒⠀⠀⢸⣀⠉⢫⣙⠲⣤⠚⠢⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠎⠀⠀⠊⠀⠀⠐⠂⠀⠀⠀⢦⠀⠀⠀⡀⠉⠀⠀⠐⣒⠂⠀⠀⢍⠀⠀⢸⡈⠑⢾⠄⠀⠀⢳⡀⠈⢆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠈⠑⠀⠀⠀⠒⠶⠂⠀⠤⣉⠠⠀⠂⠠⠤⠀⠒⣆⣤⠂⠀⡐⠂⠀⢸⠍⠓⢾⣍⠒⣈⠢⡿⠉⢽
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⢧⠀⠀⢀⠀⠀⢨⣀⡀⠀⠀⢂⠀⠀⠀⢠⠭⠄⠀⠐⠦⠄⠀⡀⢄⠾⠅⢘⠓⢦⣸⣧⣍⠓⣼⠁⠀⣾
⠀⠀⠀⠀⠀⠀⣧⠙⢆⠀⠀⠑⢤⡄⠀⠀⣐⣄⠄⠀⠀⢐⠒⠂⠀⠐⠂⠒⠀⢁⠘⣛⠋⢀⠒⠤⠄⣸⠆⢀⣸⣷⡽⠛⢥⡵⢊⣾
⠀⠀⠀⠀⠀⠀⢟⠮⠀⡙⠢⢄⡀⡘⠙⠒⠶⠿⣊⣀⠀⠠⠼⠆⠀⠐⣾⣖⠀⠘⢙⣒⠤⠢⠭⢡⣾⣛⡀⠘⠚⢿⣦⠔⠋⡠⠎⡟
⠀⠀⠀⠀⠀⠀⢨⠓⠠⠤⣦⠀⠈⠙⠒⠦⣀⣀⠀⣸⢉⠉⠙⠓⠒⠲⠶⠶⠖⠒⠒⠒⠒⠟⢟⠉⠉⢙⡯⢋⣲⣄⡽⠀⠁⢈⣅⡇
⠀⠀⠀⠀⠀⠀⢸⡂⠠⢤⡎⢍⠀⠀⠀⠤⠢⢈⠉⠙⠛⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠚⠀⢀⡙⠛⠋⠁⣀⠀⠀⠀⠰⢞⡇
⠀⠀⠀⠀⠀⠀⢸⣤⡄⠴⣀⠀⢁⠀⠀⣁⠂⠄⠈⠀⠀⠘⠂⠤⠤⠀⠀⠀⠐⠒⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⢂⡡⢿⢲⠇
⠀⠀⠀⠀⠀⠀⢸⡆⡂⡈⠭⢑⠤⠄⠀⡂⣁⠒⠒⠀⠀⠐⠢⠤⠤⠐⠁⠀⠠⠤⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⣹⢾
⠀⠀⠀⠀⠀⠀⢸⣧⡀⢀⣳⠄⡁⠒⠀⡢⢄⠁⠒⢀⠀⠀⠈⡉⣉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⢸⡒⠂⠈⢝⡓⠤⠀⠀⠭⠬⣉⠉⣀⡲⠀⠀⠤⠄⠀⡀⠀⠍⠠⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⣰⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠘⣏⡙⠨⢓⠈⢢⠤⠀⢙⡓⠦⠤⠀⠁⠀⠀⠀⠀⠀⠂⠀⢀⠠⠄⠃⠀⠀⠀⠀⠤⠀⠀⠀⠀⡖⠐⠁⢔⡟⡇
⠀⠀⠀⠀⠀⠀⢠⣏⣤⣈⡂⠑⠤⣀⠀⠠⠽⠭⠉⠀⣀⠒⠤⠤⠀⠀⠂⠲⠀⠨⠁⠀⠀⠀⠀⠀⠓⠀⠀⠀⠨⠗⠀⡠⡀⣯⣧⡀
⠀⠀⠀⠀⠀⠀⢣⠈⢳⣢⣙⡑⢄⡀⠀⣙⣛⠓⠒⠀⠀⠁⠀⠀⠀⢀⠀⠐⠒⠒⠀⣍⠀⠀⠀⠀⣫⠀⠀⢀⢬⢭⡵⣺⠶⡁⡡⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢾⡉⠲⢝⣤⡀⠀⠠⠤⠌⣉⠠⠐⢂⠀⠀⠀⠠⠁⠪⠍⠉⣃⢀⣀⣀⠀⣤⢓⡀⠁⣀⡵⠶⡋⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠾⢍⡙⠓⠾⠾⠶⣶⣖⣊⣑⢂⣀⣀⠠⠀⢨⡤⢌⣀⣀⣀⣠⠭⢤⡖⠛⣉⠥⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠼⠆⠀⠀⣨⣯⡉⠉⠉⣽⣍⣉⣉⠨⠤⠤⠔⠚⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠻⠟⠿⠶⠶⠤⣭⣁⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠩⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣆⠠⠤⠀⠒⠒⠂⢒⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⠐⠒⠒⠀⠤⠄⣠⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢚⡩⠤⠒⠒⢂⡉⠩⠥⠤⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠠⠤⠬⠉⣉⡐⠒⡞⢠⣏⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣁⡠⠒⢈⡁⠤⠔⠒⢒⣀⣀⡉⡉⠉⠭⠥⠤⠭⠭⠉⣉⣁⣀⣐⠒⠒⠠⠤⣹⠁⡸⣄⣈⠖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⠬⢉⣋⠐⠒⠒⠭⠥⠤⠤⠄⢐⣒⣒⣒⣒⣒⣒⣀⡠⠤⠤⠤⠬⠭⠲⠲⠎⠀⢫⠥⠄⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡑⠒⠤⠤⢉⣉⡁⠒⠒⠒⠒⠂⠀⠤⠤⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠒⠒⣉⣒⠢⠥⠔⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⣍⣑⠒⠶⠤⠤⢉⣉⣁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢈⣉⣉⠡⠤⠤⠖⠒⣈⡩⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠤⢄⣉⠁⠒⠂⠀⠤⠤⠬⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠭⠤⠤⠄⠐⠒⠂⢈⣉⠤⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⠢⠄⣉⡁⠒⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠐⠒⠂⢉⡁⠤⢐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠕⡂⠤⠌⣉⣁⡒⠒⠒⠒⠒⠒⠂⠀⠂⠀⠀⠒⠒⠒⠒⠒⣒⣂⡉⠩⠤⣔⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠠⠤⠭⠭⠍⠉⠉⠩⠭⠍⠉⠭⠭⠭⠥⠄⠀⠐⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⡉⠄⠀⠀⠒⠀⠀⠒⠀⠀⠤⢉⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠄⠀⠐⢂⣈⠉⠩⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠍⢉⣀⡐⠂⠀⠠⢀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡜⢁⠄⢒⠈⢁⣀⠀⠠⡄⢰⠀⠀⠀⠀⠀⠰⠆⠃⠀⠀⠀⠀⠀⢰⠀⡴⠀⠤⠄⣈⡹⠒⠆⡈⢣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣗⠈⡭⡅⠀⠀⠀⠀⢣⠘⠒⠀⠀⠀⠉⠉⠉⡏⠉⠉⠀⠀⠀⠙⢠⠉⠀⠒⠀⢠⣈⠛⢄⢈⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠐⠓⠲⠶⠤⠄⣀⣘⣚⡃⠀⠀⠀⠀⢸⡄⡗⠀⠀⠀⠀⢀⡁⣈⣀⣀⡀⠠⠶⠐⠛⠊⣁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣍⡐⠂⠠⡄⡄⠤⠤⠈⠉⠉⣁⣀⡀⣈⣉⣁⣀⣀⣀⣀⡉⠉⠁⠤⠤⠠⠤⡄⢀⣂⠩⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠈⠉⠁⢡⡟⡀⢀⣀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠇⠰⠀⠀⢀⣐⢂⡞⡸⠁⠀⠐⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⡀⠀⢆⢱⡄⠀⠀⣀⣉⣀⣏⠉⠀⠀⢀⣈⠋⣏⡁⡀⢀⠀⠴⠴⣀⠠⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠉⠆⠗⠐⠂⠀⠀⠄⢤⠄⠀⠀⠀⠸⢠⠃⠐⠂⠀⠉⢉⠃⣀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠩⠁⢙⣚⠂⠀⠀⠀⢄⠘⠄⠀⠀⠀⠲⣘⠀⠤⠀⠢⡏⠼⠀⠐⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⢥⠙⡄⢉⠉⢹⢀⣏⡈⠁⠀⡅⡥⠠⠄⠀⠐⣚⠃⠩⢥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⡈⣆⣋⣉⠀⢐⠂⠒⠒⠒⠒⠃⠋⠉⠉⢀⢁⣃⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⣁⠐⡒⡆⠀⠘⡃⢸⠉⠉⢹⠻⠋⠉⠉⡛⡘⢉⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠉⠁⠀⠐⠛⠚⠒⠒⠚⠛⠒⠀⠀⠉⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠕⠂⠁⠈⠉⠉⠙⠣⣅⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⡓⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠈⠫⡝⡙⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠆⠀⠀⠀⠀⠀⢠⠈⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠉⢀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡀⠀⠀⠀⢀⢀⡠⢤⠖⠒⡈⠓⠉⠔⢚⣷⠿⠁⢸⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡆⠔⠒⠃⠁⠈⠀⢁⡀⡀⣀⣀⠿⠟⠉⠀⠀⠀⠺⠨⢀⠊⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⡈⠀⢿⠀⠀⣠⣠⣤⡴⠞⠓⠛⠻⠛⠉⠀⠀⠀⠀⠄⠂⠀⢐⠐⠈⠀⠀⠀⠀⠀⠀⠀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣈⡄⠠⠀⢀⣾⠀⠠⡺⠇⠒⠃⠈⢹⠳⢐⠂⠀⠀⠀⠀⠀⠒⠀⠠⠂⠀⢀⡬⠨⠀⠀⠀⠀⠀⠀⠰⢁⣄⢨
⠀⠀⠀⠀⠀⠀⡀⠀⣷⠀⢀⣺⠀⠈⡇⠈⢾⡆⠀⠀⢮⡖⠶⠆⠒⠿⠷⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣌⠀⣠⠈⠀⠀⠀⠀⠀⠘⢣⠈
⠀⠀⠀⠀⠀⢀⣸⠐⡕⠠⠀⢿⠀⠀⠁⠀⠀⠣⡀⠀⠙⡁⠀⠀⠀⠀⠀⠀⠓⠤⡈⠁⠀⠈⠀⠂⠀⠀⠀⢸⡏⠓⠁⠠⠂⠀⠀⠘⡈⣠⡏
⠀⠀⠀⠀⣌⣶⢰⠁⠐⣇⡀⠈⢣⡀⠴⠀⠀⠀⠈⠀⠄⠐⠶⠂⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⢀⠤⠀⣺⣶⣀⡠⠂⠒⠀⠀⠬⠠⣽
⠀⠀⠀⠀⢯⡳⢜⣄⠀⠨⠀⠐⣄⠉⠀⠰⣄⠀⠀⠀⠀⠁⠈⠂⠄⣀⠀⠀⠀⢀⠜⠂⠀⠀⠀⡠⠛⠐⡠⣿⡄⠚⢀⡚⠧⢀⠒⠂⠁
⠀⠀⠀⠀⠸⡀⠍⠨⡱⣼⡤⡀⠈⠢⡄⠄⠈⠑⠤⡀⠀⠀⠀⠀⣀⡀⠈⣀⣀⣠⠀⠀⠐⢂⣱⡤⠪⠛⠞⣼⠇⣀⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠙⢢⣀⡁⠁⠰⠎⠀⣳⠴⣀⠤⣀⡤⠠⠤⠄⠈⠨⡡⢄⠍⠡⡠⣉⠀⠀⣿⣏⠙⠠⢵⡆⠐⠛⠋⢉⠀⠀⢀⠂⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⣶⢎⣈⡄⠀⠈⡉⢇⠠⠀⠠⢀⡀⡀⠳⠂⢀⡼⠦⣀⡤⠀⣃⠉⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⠻⡀⠀⠈⠑⢶⣦⠀⠀⠀⠊⢛⡆⠁⠀⠀⢻⣇⠀⠀⠀⠀⡯⠀⠀⠀⢸⡇⠀⠀⠀⠨⠀⠀⠸⠂⠀⢐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢳⡀⠀⠀⠘⣻⡀⠀⠀⠀⠀⢇⠀⠀⠀⠈⢿⠀⠀⠀⠀⢺⠤⠀⠀⠠⡧⠀⠀⠀⠠⡀⠀⢬⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡱⡈⠀⠀⠸⡷⠄⠀⠀⠀⢣⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⠁⠀⠀⠨⡇⠀⠀⠀⠀⠅⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡩⡀⠀⠈⢻⡄⡀⠀⠀⢘⡅⠁⠀⠀⠘⣿⠀⢁⠀⠈⡋⠀⠀⠀⡗⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡆⠀⠆⢿⣦⠀⠀⠀⠹⡀⠀⠀⠀⢽⡁⠀⠀⠀⠳⠀⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠙⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠈⠀⠀⠀⠈⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⣉⣀⠈⠀⠈⠀⠒⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢁⣀⠤⠄⠀⠉⠉⠁⠀⠀⠈⠁⠐⠂⠠⢀⡈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠋⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀
⠀⠀⠀⠀⠀⠀⠆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆
⠀⠀⠀⠀⠀⠠⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠆
⠀⠀⠀⠀⠐⠳⠬⠅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠭⠴⠓
⠀⠀⠀⠐⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠔
⠀⠀⠀⠀⠀⡀⠀⢨⠀⡋⠉⠉⠒⠒⠒⠲⠀⠶⠒⠲⠶⠒⠒⠲⠂⠲⠒⠲⠶⠒⠖⠒⠂⠐⠒⠒⠓⠋⠉⠉⠇⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡇⡀⠹⠀⡗⠒⠂⠠⠤⠤⢴⠀⢠⣀⣀⣀⣀⣀⣠⠀⢠⣀⣀⣀⣀⡀⢠⠄⡤⠤⠤⠄⠐⠒⠒⠆⠜⠀⡀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠃⠓⠂⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡉⠀⠐⠆⠦⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠠⠄⡤⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠠⠄⠰⠂⡏⠉⢉⡁
⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠀⠀⠀⠀⠐⠐⠁⠙⠁⠀⠀⠀⠀⠨⠁⠡⠀⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⠀⠸⠀⡃⠀⣀⡄
⠀⠀⠀⠀⠀⠈⡉⡐⡇⠸⠀⠐⠒⠀⠀⠠⡄⢠⠀⠀⠀⠀⣀⢠⡀⣤⠀⠀⠀⠠⠤⢤⡀⡧⠀⠒⠒⠒⠒⢺⠀⡋⡉⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠛⠛⠛⠒⠒⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣉⣀⡤⠴⠖⠒⠛⠛⠛⠛⠓⠒⠶⢤⣀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢁⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡼⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠙⣆
⠀⠀⠀⠀⠀⢀⡞⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠹⡄
⠀⠀⠀⠀⠀⢸⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢷
⠀⠀⠀⠀⠀⣿⠀⣿⣀⣤⠤⠶⠶⠒⠒⠚⠛⠛⡛⠛⠛⠛⠛⠛⠛⠒⠖⠒⠶⠶⠤⢤⣤⣀⣸⡇⢸
⠀⠀⠀⠀⢀⡿⠋⢉⣤⣤⠴⠶⣒⣛⠛⠛⡛⠽⠏⠉⠩⠭⠍⠉⠛⠿⠟⡓⠛⢒⣶⠶⠦⣤⣽⡇⢹⡄
⠀⠀⠀⠀⢸⡁⠘⠯⠅⣊⣀⣒⣀⣠⣌⣉⣠⡤⠈⠉⠠⠤⠈⠉⣁⣠⣄⣐⣒⣀⠴⠦⠬⠖⣻⢁⣿⠇
⠀⠀⠀⠀⠀⡟⡛⠲⠶⠶⠤⣤⣤⣤⣥⣤⣤⣬⣅⣀⣤⣍⣁⣀⣤⣍⣤⣤⣤⡤⠤⠴⠖⠒⣛⡋⢹
⠀⠀⠀⠀⠀⢷⠈⠉⢄⣀⡐⠒⢂⣀⡀⠒⠒⢀⣀⠒⠒⠀⠀⠐⠒⠂⠀⠒⠒⣀⣀⠉⠡⠤⠀⠐⢻
⠀⠀⠀⠀⠀⢸⡄⠂⠀⠀⠠⠤⠄⠀⠀⠤⠤⠀⠀⠤⠤⠉⠉⢀⣀⠀⠀⢀⡠⠄⠀⠠⢄⣀⠒⢂⡿
⠀⠀⠀⠀⠀⠀⢳⡠⠬⠉⠁⣀⣈⠉⠁⣀⣀⡒⠂⣀⣀⠉⠉⠠⠤⠌⠉⠀⠀⠈⠉⣀⡀⠠⠄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠹⢤⡐⠒⠠⠤⠐⠒⢀⣀⡐⠒⣂⣀⠐⠒⢀⣀⠐⠂⣀⡀⠉⢉⡀⠈⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣈⣉⣀⣤⠈⢉⣠⣤⣈⣉⣡⣤⣈⣉⣤⣀⣩⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠒⠒⠢⠠⣄⠀⠀⠀⠀⠀⢸⢧⠄⠀⠀⠀⠀⡀⠰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠄⠃⠘⠂⠦⠀⠙⢆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠆⠀⠀⠀⠀⠀⠘⠄⠀⠳⡴⠂⠉⠣⡀⠀⠀⢀⣴⡏⠀⠀⠀⢀⡀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⣼⠄⢌⠀⠀⢰⠇⣄⠀⠀⠈⠆⠀⢳⠀⠀⠀⢀⡔⠉⠉⠙⡄⠀⠀⠐⠋⣀⠴⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠺⡄⢹⡄⠀⠀⢸⠀⠀⡄⠀⢀⠏⠀⠀⠀⠀⡁⠔⣠⡴⢊⣁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠉⠑⠢⡄⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⣼⡄⡏⠀⢡⠠⠯⣤⣄⠀⠀⡔⣡⡾⡋⠔⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞⡉⠃⢰⠀⠘⠀⠀⠈⠀⡠⣫⠚⣩⠊⠀⠚⠀⠈
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠁⠀⢼⡄⠐⠇⢀⠀⢀⣏⠵⠋⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡴⢿⢀⡂⠀⠀⠀⠈⠣⠀⠀⠀⠀⣠⠔⠊⠁⠀⠘⠀⠀⠀⠀⠀⠀⡆⠀⠶⡀⠈⠁⠑⢄⠀⠀⠀⠀⣀⣤⠒⠁
⠀⠀⠀⠀⠸⠁⢻⡞⠀⡤⠀⠀⠀⠀⡇⢀⠀⡜⠁⠀⠄⠀⠀⠀⠄⠀⠁⠀⠀⠐⡇⠀⡀⠘⡄⠀⠀⢘⢷⣀⡴⠋⢁⡎
⠀⠀⠀⠀⢱⡀⠸⣇⠀⠀⠀⠀⠀⡰⠄⢾⡂⠁⠐⠠⠀⠀⢀⠆⠀⠀⠀⠀⠂⠀⠃⠀⢁⠀⡃⠀⢀⣠⠞⠋⢀⡤⢋
⠀⠀⠀⠀⠈⢦⡄⢙⠣⣄⡀⢀⡞⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡂⠀⣸⠤⠷⠊⠉⢀⣠⢴⠋⠐⠔
⠀⠀⠀⠀⠀⢸⢽⡓⢦⣄⣀⠙⠛⠀⠤⠄⠠⡤⠀⡠⠤⡀⠼⠠⠄⠠⠴⠀⠐⠊⡃⠀⡁⣀⣠⠶⠚⡉⠀⠄⠀⠅⡉
⠀⠀⠀⠀⠀⠘⡏⡆⠈⡅⠉⢹⡓⠒⠶⡦⠤⠤⣤⣤⣤⣤⣤⣤⠤⡤⠤⠤⠶⠖⠓⢊⠉⠀⠀⠀⠀⠂⠀⠄⢐⢡⠁
⠀⠀⠀⠀⠀⠀⢷⢫⠀⣓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠸⡟⡆⠸⠀⠀⠅⠀⠀⠅⠀⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⢻⣺⠈⢆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⠸⡄⠸⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡫⡀⢅⠀⠐⡂⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⡠⠀⠈⠀⣠⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠦⣀⣐⡀⠀⣂⠀⠈⠀⠀⢀⠀⠀⠀⢀⣠⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠛⠊⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣧⣶⣴⣶⣴⣾⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⣿⣅⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⡠⠒⠐⠆⢄⠀⠑⢤⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⣷⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡌⠀⠀⠀⠀⠀⠑⠆⠀⠱⣀⡤⠘⠻⣄⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡁⡐⠀⠀⢠⡆⣀⠀⠀⠀⢦⢀⢹⠀⠀⠀⠈⠀⡤⠒⠚⢿⠁⠀⠀⠀⠞⠁⣀⡴⠃⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠉⠉⠉⠉⠄⠉⠀⠠⣼⡄⢻⡄⠀⠀⠐⡄⠀⠃⠀⠀⢠⠏⠀⠀⠀⠀⠇⡠⠂⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠭⡀⠁⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠁⢞⠉⠀⢠⡄⢡⠀⠘⡀⢠⠋⠀⠀⠀⠀⣰⢂⣴⠟⡡⠔⠋⠠⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠟⠯⠘⡄⠀⠏⠉⠉⠛⠂⢀⢔⡵⠟⡡⢊⡠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠢⠀⠀⡇⠀⣰⠀⠀⠀⢰⡷⣫⠶⠞
⠀⠀⠀⠀⠀⠀⣠⡇⢀⠀⠀⠀⠀⢣⡀⠆⠀⠀⠀⠀⢀⡠⠆⠀⢠⠀⠀⠀⠀⠀⠈⠛⠀⢨⡀⠂⠠⠚⢎⠁⠀⠀⠀⠀⠀⠀⣀⠄⠃
⠀⠀⠀⠀⢀⡞⢹⣀⠗⠀⠀⠀⠀⠀⢱⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠑⡄⠀⠀⠈⣲⡀⠀⢀⡠⠖⠻⠁
⠀⠀⠀⠀⢸⠀⢸⣿⠀⠜⠁⠀⠀⠀⠘⠀⣆⡠⠇⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠄⠸⠀⠀⠀⠐⣳⡶⠋⠀⡴⠃
⠀⠀⠀⠀⠸⡆⠈⢻⣄⠀⠀⠀⠀⡠⠓⠈⢻⠄⠀⠀⠑⠄⠀⢠⠃⠀⠀⠀⠀⠈⢂⡀⠀⠀⣦⢠⠂⣀⠴⠞⠁⢀⡴⢚⢰
⠀⠀⠀⠀⠀⢸⡶⣀⠈⠓⠴⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣧⠀⢠⠟⠊⠉⠀⣀⡤⠖⠛⠀⡑⡪
⠀⠀⠀⠀⠀⠸⡇⡯⠙⣷⢤⣤⣈⡀⠘⠓⠀⠐⠒⠐⠒⠒⠖⠚⠒⠂⠀⠋⠁⠀⠁⣠⠀⣠⡠⠤⠞⠋⠁⠂⠀⠅⠀⠣⠄
⠀⠀⠀⠀⠀⠀⣷⢽⡀⢱⠀⠀⠯⠉⠙⠻⠖⠒⠒⠶⠶⠶⢶⠶⠶⠒⠖⠒⠒⠛⠋⠉⠉⠄⠀⠀⠀⠀⠀⠁⠀⠁⠨⢰
⠀⠀⠀⠀⠀⠀⢸⡘⡆⠸⡁⠀⢑⠀⠀⢐⡀⠀⠀⠁⠀⠀⢐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⢊
⠀⠀⠀⠀⠀⠀⠀⣷⢳⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣏⡆⠸⡀⠀⡂⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⡄⢷⠀⠢⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⡨⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⢧⠈⣅⠀⢐⡀⠀⠨⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠅⢀⣤⠄⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠽⢦⣀⣢⠀⠀⡂⠀⠈⠀⠀⢐⠀⠀⠀⢀⣀⡤⠤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠚⠒⠉⠉⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣍⣬⣯⣴⣭⣽⣭⣽⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠒⢒⣒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢉⠠⠔⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢮⡠⠠⢤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣀⢱⣄⠀⠈⢧⠀⠈⠱⡍⠁⠐⢴⠒⠒⢤⠖⠛⠢⢞⠉⠁⠑⢏⠀⠉⠙⢄⡀⡀⣡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⡏⠉⠀⠑⠒⠀⠘⠒⠀⠠⠒⠠⠤⡵⠶⠀⠤⠓⠒⠒⠒⠉⠉⠉⠉⠀⡇⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠉⠚⠃⠐⠀⠠⢤⠤⡤⠤⠀⠠⠤⠀⠠⠄⠤⠤⠤⠤⠤⠀⠤⠤⠐⠐⠒⠈⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠑⠲⠶⠤⠤⠤⠄⢠⣀⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡶⠤⠤⠄⠒⢐⠂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠴⢠⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⡁⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⣀⣀⠀⠀⠀⠀⠈⠀⠏⠉⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⣩⢨⠀⢀⠀⢤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣈⣹⠉⠉⠀⠐⠒⠒⠃⠐⠒⠒⠒⠒⠲⠖⠶⠂⠀⠀⠂⠀⠉⠉⠁⠀⠀⢸⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠐⠒⠒⠠⠤⠤⠤⠤⠤⠠⠰⠄⠥⠤⠤⠤⠄⠀⠀⠐⠒⠋⠉


⡶⠶⠶⠶⠖⠲⠶⠶⠶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣤⢤⣤⣤⡤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣻⡿⠟⠛⠛⠿⠶⠮⠽⠷⣮⣛⣗⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣝⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡝⢆
⠀⠀⠀⠀⠀⢠⢟⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢷⡀
⠀⠀⠀⠀⢀⣷⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣷⡀
⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣧
⠀⠀⠀⠀⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻
⠀⠀⠀⢸⡧⣼⠶⠒⣒⣛⣛⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⣒⣒⣒⡒⠶⢬⡗⢻⡆
⠀⠀⠀⠸⣷⣇⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣆⣿⣾⠁
⠀⠀⠀⠀⢻⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣹⠏
⠀⠀⠀⠀⠀⢷⡀⠉⠙⠛⠶⠶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠶⠚⠋⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠈⣷⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⣿⡅⢺⣉⠓⢲⠦⠤⠤⣤⣤⣤⣤⣄⣀⣠⣠⣤⣤⡤⠤⠤⠶⠖⣺⠏⣹⡧
⠀⠀⠀⠀⠀⠀⢹⡆⠽⡆⠈⣹⠅⠈⢩⣕⠂⠀⠀⣺⠥⠀⠀⠬⣝⡂⢀⣭⡃⠈⢽⠁⢼⡇
⠀⠀⠀⠀⠀⠀⠈⣧⠀⣯⠀⢒⣇⠀⣒⡺⠥⠈⠥⢼⣏⡂⢀⣻⡶⠂⢐⡺⠀⣐⡗⠠⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠐⣂⠨⢗⡀⠀⣾⠉⠀⠉⢽⣒⠒⠐⢲⡭⠀⠤⠯⠀⠴⠄⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⠀⠹⡆⠈⢿⣗⡀⢐⣸⠯⠅⠨⣿⠭⠀⢭⠂⢨⠏⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣄⣻⡄⠩⣶⡀⠀⢸⠯⠅⢬⡯⠁⢨⣓⣠⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠛⠛⠛⠋⠙⠛⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣭⣭⣿⣯⣭⣛⠻⠿⣯⣍⡒⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⣵⡶⠶⠞⠛⠉⠉⠉⠉⠙⠛⠛⠓⠛⠻⠷⣬⣮⡙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡹⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣿⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣣⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢻⣄
⠀⠀⠀⠀⠀⠀⢠⢫⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆
⠀⠀⠀⠀⠀⠀⣾⠟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⣿⣆
⠀⠀⠀⠀⠀⢸⡏⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⡄
⠀⠀⠀⠀⠀⣿⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢰⣟⠀⣿⣀⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⠸⣇⡼⣧
⠀⠀⠀⠀⢸⡏⣽⠋⣉⡤⠴⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠂⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠶⠦⢤⣉⠙⣧⠤⣿
⠀⠀⠀⠀⠘⡧⣿⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢹⡿⠁
⠀⠀⠀⠀⠀⠀⢹⡆⠈⠙⠛⠿⢶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠞⠋⠉⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠶⠶⠶⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣯⡑⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣻⡟
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⣉⣧⡄⠉⢙⣛⠒⠶⠶⡶⠶⠶⠤⠤⠤⣤⠤⠤⠤⠤⣶⡶⠶⠶⠖⡿⠛⢋⣩⠓⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠨⡷⠄⢉⣹⡦⠀⢉⣩⣝⠲⠀⠰⠀⢲⣯⡅⠀⠀⣬⣭⣛⡂⢀⣩⡝⠃⢈⢽⡇⠠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⢺⡃⠀⠤⠗⠀⠠⠤⢾⣛⡀⢘⣉⣩⡗⠲⠆⠀⠶⢪⣭⠀⠠⠴⡍⠀⠴⠾⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢙⣭⡀⠒⢾⣁⠐⠛⣻⠤⠄⠠⠤⢾⣭⣉⡁⢈⣛⡳⠶⠀⠒⣻⠆⠀⣚⠓⢀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠡⡦⠈⢙⡦⠀⠩⠽⣓⠂⠀⠒⢛⡦⠤⠄⠠⠭⣿⡁⢀⣭⡝⠂⣨⣍⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⠛⡂⠀⢟⣂⠐⣚⡯⠭⠀⠩⢬⠗⠒⠀⢐⣚⡷⠂⠀⠲⠍⠀⠶⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣄⣘⣧⠄⠠⢾⣂⠀⠀⣘⡯⡭⠁⢭⣽⡉⠀⣭⠓⣀⣸⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠛⠳⠶⠶⠾⠷⠶⠶⠞⠳⠶⠖⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⢉⣭⠟⠋⠉⠉⠉⠉⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣄⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠶⠶⠦⠤⠒⠤⠀⣀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠛⠻⠷⣶⣤⣤⣼⣿⠶⠶⠖⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣮⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣀⣀⣠⣤⣤⣿⣥⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⣤⡶⠿⠟⠛⠛⠉⠉⣿⡏⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⢶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣸⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⣶⣄⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⠾⠟⠛⠋⢹⣿⠉⠉⠙⠛⠻⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⠟⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠙⠷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣷⣠⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⣀⣤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣴⣄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣾⣿⣿⣦⣤⣌⣿⣧⠀⣦⣄⠄⢄⣲⣲⣴⣂⣶⣾⣿⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠹⠿⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠀⠈⠃⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠂⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡁⠄⠀⠀⠁⠀⠀⠀⠀⠈⠐⠂⠠⢈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⡀⠀⠀⠐⢂⡀⠀⠀⠀⠀⠥⠠⠀⠄⠀⠀⠤⠬⠀⠀⡀⠀⢀⡐⠂⠠⠀⢀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢋⠄⣐⡈⠁⠀⠠⠄⢰⠀⠀⠀⠐⠐⠒⣒⡀⠀⠀⠀⣰⠀⡆⠀⠤⠈⣙⠒⠠⡙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡌⡀⠆⠀⠀⠀⢈⣈⡉⠁⠀⠀⠀⡃⡁⠀⠀⠀⠀⡈⢰⠀⠈⠁⠀⠤⣉⢢⠵⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⢀⠉⠉⠉⠀⠲⠶⠦⠀⠀⠀⠀⠇⠇⠀⠀⠀⠠⠦⠖⠒⠒⠂⠉⠉⡀⠄⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠢⠄⡸⠨⠌⠉⢁⡀⠐⡂⢒⠀⠀⠒⠀⢰⣒⡂⣀⠀⠩⠠⠏⡏⡐⠂⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢩⠙⣀⠀⠀⠀⠃⢸⠂⠀⠀⠀⠰⢒⠒⠀⠀⠁⣈⡌⠀⡀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠁⠀⠣⠱⠒⠀⠀⠩⠬⠤⠤⠤⠀⠇⡘⠐⠂⠀⠸⡘⢀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠭⠈⣉⢂⠒⠀⢐⡀⣇⠀⠀⠀⣒⡓⠠⠀⠠⢃⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠀⠰⡈⣄⠠⠀⣀⠆⠄⠀⢰⢠⠂⠀⠀⡨⠭⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⢑⣲⡀⠀⡇⢨⠤⠠⣬⣤⣤⣤⣤⢰⠤⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠀⠶⠆⠄⠴⠼⠤⠤⠬⠤⠤⠀⠂⠂⢂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢶⡛⠋⠉⠉⠀⠈⠁⠂⣀⡀⠀⠉⠙⠍⠙⠛⠲⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⣀⣀⣤⠼⠶⠛⠛⠛⠛⠉⠉⠉⠙⠛⠛⠻⠶⣤⣀⠀⠈⠉⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣧⣄⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢰⣏⡠⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠜⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡠⠚⣇⣀⣤⣤⠶⠶⡶⠚⠛⠛⢛⠟⠋⠉⠉⡹⠋⠉⠉⠉⡩⠛⠉⠉⠛⡛⠟⠛⠛⠲⡶⠶⠶⢦⣤⣤⣀⡀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⣽⡷⠛⠋⠙⢁⣀⣤⣮⣴⡶⠶⠶⠿⠶⠿⠛⢛⡛⠛⠛⢛⣛⣛⡛⠛⠓⠛⠷⠶⠶⠶⠾⢦⣤⣤⣤⣄⣉⡉⢙⣿⡠⢻⡇
⠀⠀⠀⠀⠀⠀⣾⠡⢠⣤⡾⠟⣛⡯⠉⠀⠐⠒⠊⢀⣠⠤⠉⠉⠉⠤⠤⠤⠈⠉⠉⢤⣤⣄⠈⠉⠉⠉⣁⣀⡐⠒⡂⠀⠩⣍⡛⢳⡿⠀⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣄⠀⡙⠖⠶⠤⠤⢤⣭⣭⣤⣰⣶⣀⣀⣰⣒⣒⣂⣀⣀⣒⣒⣂⣀⣀⣀⣀⣒⣢⡤⠤⠤⣤⠴⠛⠓⠒⡻⠋⣹⠇⣰⣿⡏
⠀⠀⠀⠀⠀⠀⢸⡏⠛⠳⠶⠶⣤⣦⣥⣄⣀⣀⣔⣀⣀⣀⣀⣤⣈⣀⣀⣀⣠⣊⣁⣀⣀⣠⣀⣁⣀⣀⣠⣔⣥⣤⣤⡤⠾⠶⠛⠛⢛⡋⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣷⢉⣓⠒⠂⠀⠀⠠⢤⣬⠉⠉⠉⢉⣉⣉⣉⠉⠉⢉⣉⣉⡉⠉⠉⣉⣉⣉⡁⠉⣉⣉⣉⡀⠀⠠⠴⠖⠀⢀⡉⠉⡤⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠓⠒⠒⠂⠀⠀⠤⠤⠤⠄⠀⠀⠠⠤⠤⠄⠀⠀⣤⣀⣀⠀⠀⠠⠤⠤⠤⠀⠀⠤⠖⠒⠀⠀⠉⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠃⠀⠀⠀⠒⠒⠒⠂⠀⠀⠠⠤⠤⠄⠀⠀⠠⠤⠤⠄⠀⠀⢠⡤⠤⠀⠀⠠⣤⠤⠄⠀⠀⠤⠒⣂⣈⠉⠉⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣈⠉⠉⠁⠀⠀⠈⠛⠒⠂⠀⠀⠐⠒⠒⠀⠀⠀⠛⠒⠃⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⢈⣀⢉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⠉⢉⣀⣈⡉⠉⠉⢀⣀⣈⠙⠛⠛⣀⣀⣘⠉⠉⢡⣤⣤⠈⠉⠉⣥⣀⠉⠉⠉⠥⠤⠬⠉⠩⠥⠄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⣀⡒⠒⠂⣀⣀⠰⠶⠦⠀⠀⠠⠤⠶⠄⠀⠀⠠⠤⠤⠀⠀⠤⠤⠄⣀⡀⠶⠆⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢮⣥⣀⣈⠉⠉⠰⠤⠬⠉⠉⠡⠤⠤⠀⠉⠉⢡⣤⡄⠉⣉⣤⣖⣀⣉⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⢿⣿⠿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣬⣾⣶⣴⣧⣾⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠒⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⣀⡀⠐⠒⠒⠛⠀⠒⠂⠒⠠⠢⠄⣀⠀⠑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⡀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠁⡀⢁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠆
⠀⠀⠀⠀⠀⠀⠄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠁
⠀⠀⠀⠀⠀⢨⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡆
⠀⠀⠀⠀⡀⠬⠤⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⠬⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠉⠓⠒⠀⡶⠤⠤⠤⠤⢤⣀⡤⠄⣄⣀⠀⢀⠀⠀⢀⡀⢀⡀⢀⣀⢀⣀⣀⣠⠀⢤⣤⠤⠤⠤⠤⠶⢶⠀⠒⠚⠋⠉
⠀⠀⠀⠀⠀⢰⠀⣀⡄⠀⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⣅⡀⠠⠆
⠀⠀⠀⠀⠀⠰⠀⠀⠼⠀⠇⢀⠀⠈⠉⠉⠉⣡⠠⡗⠒⠒⠒⠒⠒⠒⠦⠼⠒⠒⠒⠒⠒⠀⢘⡁⣋⠉⠁⠀⠀⡀⠀⠨⠤⠇⠀⠂⠂
⠀⠀⠀⠀⠀⠰⡄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠆
⠀⠀⠀⠀⠀⠰⠀⠀⢹⠀⢓⢀⠀⠀⠀⠀⠀⢍⠀⣆⠀⠀⠀⠀⠀⠐⡆⢰⠀⠀⠀⠀⠀⠀⠰⠛⠻⠀⠀⠀⠀⣀⡀⡉⠈⠅⠀⠀⠆
⠀⠀⠀⠀⠀⠠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠃⠀⠀⠀⠀⠀⠒⠂⠐⠂⠀⠐⠀⠀⠀⠘⠀⠉⠈⠀⠀⠀⠀⠀⡀⠀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⢣⠁⣈⡂⢚⠀⠁⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⢐⡆⢴⠀⠀⠀⠀⠀⠀⢴⠀⠶⠒⠒⠒⠈⠉⠉⡗⢰⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠐⠓⠂⠂⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠒⠂⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠒⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢦⡄⠀⠀⠀⣠⣴⣾⠿⠋⠙⣷⡀⠀⠀⠀⣀⣴⣤⣭⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢿⣀⡴⠋⠉⠀⠀⠀⠀⠀⢸⣇⢀⣠⣾⣿⡏⠀⠁⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⣀⣀⠀⠀⠀⣨⣿⡿⠛⣿⣿⠐⠀⠀⣠⠊⠙⠿⣤⣀⡴⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⣠⣿⡿⠋⢀⠴⢾⠿⠛⢹⣦⣠⣾⠿⠋⠠⣾⣿⣿⣴⣧⠜⠁⠀⡆⠈⠀⡙⠓⢦⣄⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⣿⣀⠌⠀⣠⠃⠀⠀⠀⠨⣿⡅⠀⠀⠰⣿⣿⣿⣿⠏⠀⢐⠻⢀⠲⠀⠀⠀⢸⡏⠣⠀⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣄⣉⣿⣿⣿⣦⣶⣅⠀⠀⠀⠀⠀⢀⣷⡀⢠⣾⡏⣼⣿⠏⠀⣀⠈⢀⡈⡰⠈⠀⠀⣸⣦⠃⢠⡞⢩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣯⣄⠉⠐⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⢻⡿⣿⣷⣿⠏⠠⠀⠶⣮⠀⢉⠉⡘⠁⢠⡿⢃⣴⣏⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠻⣿⣿⣿⣷⣦⡀⠉⢻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⢀⠀⠀⡀⢀⡙⠦⠀⢠⣿⣵⣿⣿⡿⡋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣴⢉⣏⡟⣹⡻⠳⢢⠬⣿⣿⣧⣀⣀⣀⠀⠀⠀⠈⣹⣥⡀⠀⢨⣤⣹⣎⣋⣇⣀⣾⣿⠿⠻⣹⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⢷⣿⣿⣷⣾⣾⣾⣆⣇⣇⣯⡏⡏⡉⡉⠏⣻⠋⡏⡟⢹⡛⢻⣉⡏⣏⣌⣧⣾⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣻⣸⡇⢻⣿⠍⣹⣟⣟⢻⣿⣿⠛⣿⣿⣷⡷⠿⣾⡷⣷⣿⢷⣿⣿⢿⣿⠛⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⡿⡇⢸⣿⡖⠠⣯⣷⠨⣿⣿⠤⢤⣿⣿⡁⠀⣹⡇⣿⠆⠀⢛⣿⢿⡏⢀⣾⣿⢹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣏⠀⣿⡇⠀⣿⣿⡤⣾⣿⠄⠀⣿⣿⡄⠈⣿⡏⡟⠉⠉⠉⣿⣼⡏⢀⣿⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⣿⣧⠀⢸⣿⣇⣹⣿⡃⢈⣿⣿⠄⠈⣻⡇⣗⠀⠀⢺⣿⣿⣃⣰⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡸⣿⡄⠸⣿⣇⢈⣿⡇⠀⣿⣿⠉⠉⢻⡗⣿⠀⠀⢻⣟⡿⠉⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣷⣤⣿⣿⣄⣿⣧⠀⣿⣻⠃⠐⣿⣿⣿⠂⠐⣾⣷⣏⣸⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⢷⣿⣿⣷⣦⣾⣿⣿⣶⣾⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣄⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⢦⡀⠀⠀⣠⣴⠿⠿⠋⠀⢿⡆⠀⠀⠀⣠⣴⣶⣥⣏⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠈⣧⣴⠚⠁⠀⠀⠀⠀⠀⠀⣷⢀⣴⣿⣿⢿⠀⠀⠀⢉⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⣀⣠⣤⡀⠀⠀⣠⣿⠿⢋⣿⣿⠀⡄⢀⡴⠉⠉⢻⠦⣤⡞⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢠⣾⡿⠋⡀⠔⢛⠟⠋⠁⢿⣤⡾⠟⠁⠀⢾⣿⣿⣷⣷⠞⠀⣀⠇⠀⠀⠈⠙⢷⣤⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⣸⣿⣧⡔⠀⢠⠎⠀⠀⠀⠀⠻⣗⢀⠀⢀⣿⢿⣿⣿⠇⠀⢨⠘⢠⠙⢀⠀⠀⢺⠀⡇⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠤⢼⡿⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠸⣦⣰⣿⣏⢸⣿⠃⠀⠦⢠⠠⡄⣝⢠⡀⠀⣾⡞⢀⡴⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣮⣿⣷⣦⡀⠉⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣯⣻⣿⣿⠏⠀⠁⠛⠳⠀⣰⠀⠊⠀⣼⢏⣴⣿⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡹⢻⢿⣿⣿⣶⣄⡈⠻⢿⣿⣖⠀⠀⠀⠀⠀⠀⠹⢿⡏⠀⠰⠠⠀⣦⠰⣦⡃⠀⣰⣿⣿⣿⣿⠛⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣧⣼⣼⢠⣧⣏⣉⡟⣞⡟⢻⢳⢶⢤⢤⢤⣄⣀⣼⣿⣤⣄⣴⣶⣼⡷⡴⡧⠴⠟⢻⣋⣱⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣹⡟⣿⠻⣿⣿⠿⣿⣿⣾⣾⣾⣶⣼⣴⣦⣀⣼⣠⣇⣾⣸⣆⣼⣦⣇⣷⣾⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⣿⣿⠀⣿⣟⠐⢻⢾⠂⣿⣿⠅⠙⢿⣻⡟⠉⢻⣿⣿⡟⠛⣿⣿⣽⡿⠀⣿⣸⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⣿⡄⢹⣿⠀⢹⣿⡉⢹⣿⡋⠙⣿⢺⡆⠀⢾⡧⣿⠥⠤⠴⣿⢻⡧⠐⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⢘⣿⡀⠘⣿⡿⢹⣿⡧⠀⢿⣾⡇⠀⣾⡇⣿⠀⠀⢠⣿⣿⡇⢘⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡙⣿⡇⠀⣿⣿⠐⣟⡷⠀⢺⣿⡧⠠⢼⡇⣿⠀⠀⢼⡿⣿⠖⣺⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣽⣿⣀⢹⣿⡀⢻⣿⠀⢸⢿⡧⠀⣸⣇⣿⡀⠀⣰⣗⡯⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⣿⣾⣿⣦⣽⣿⣧⣀⣸⡗⣿⣃⣤⣿⣿⣷⣿⣿⠿⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⡿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣥⣄⣒⣒⣒⣒⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⢶⣶⣶⣬⣭⣭⣉⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⢂⠒⠀⠙⢫⡖⠚⠒⠛⡇⠀⠼⢦⠄⠀⠐⣶⣖⠒⠒⢶⣤⣀⣀⣤⣤⣀⣀⣀⢀⣀⠀⠀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⣾⠿⡿⠶⠦⣤⣿⣤⣤⣤⣷⣄⣀⠀⣷⡄⠀⠀⢨⡍⠉⠁⠉⣧⠀⠒⠊⠹⡛⠛⠁⠘⣃⢺⡇⣼⠰⣆
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⡇⣿⡟⠈⠈⠀⡀⠀⠀⠀⠀⡎⣿⠈⠉⠉⠉⠉⠉⡻⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠖⠒⠿⢿⡇⣿⢴⣿
⣿⡇⠀⠀⠈⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣁⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠃⠀⠀⠰⠼⠃⣀⣤⣴⣏⡛⢣⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢂⣀⠀⠀⠀⠉⣢⠀⠀⠀⠛⣂⠀⠀⠙⠟⠁⠁⠻⡿⠒⠛⠒⢷⣖⠒⠒⠒⢾⢧⣴⣿⣿⣿⣿⣿⣟⣡⡌⣿⣿
⠀⣧⢠⡆⠀⢰⠉⠉⠉⠉⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣀⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢢⣤⠀⠀⢀⣸⣿⢿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢘⣄⡀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠙⠙⠙⠩⡭⠉⠉⠛⠛⣋⠛⠹⠋⠀⣾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠩⠉⠉⠉⢹⡟⠛⠻⠛⠛⠛⠒⠒⠛⠿⣷⣶⣤⣴⠾⠦⠀⢀⣤⣄⡀⢀⣀⣠⡂⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠁⠀⢠⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠶⠶⡶⠲⢟⡚⠀⠓⠚⠛⡟⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠘⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣶⣴⡶⠧⠁⠀⢼⣤⣄⣀⣀⣀⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠀⠀⠀⢀⠣⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡇⣀⠀⢄⡀⠈⠀⠀⠀⠀⢸⠈⣹⠹⠀⠒⠀⠀⠀⢈⠿⠛⠛⢹⠁⠌⠀⠚⠛⣿⣷⡶⡾⣷⠧⠤⠤⠷⣦⣶⣤⣤⠶⡿⠋⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠾⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⠀⢸⣄⣁⡀⠀⢀⠇⠈⠀⠇⣠⠉⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡼⠛⠙⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠌⠉⡏⢿⠀⠋⠀⠀⠀⣿⠉⠉⠉⢈⠀⠌⠉⠀⠉⡍⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢻⡟⣿⠇⠀⣸⢻⣠⠿
⠀⠀⠹⢶⣶⣤⣼⠤⠀⠤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢐⠙⠂⠀⠀⠏⠉⠉⠁⡇⠀⠀⠀⠀⣿⣇⣿⢶⣾⠏⠉⢡⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠩⡟⠛⠛⠉⠇⢀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣧⣁⡂⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢁⣸⣁
⠀⠀⠀⣿⢀⣀⣼⣄⣀⣀⣀⣴⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠈⠉⡋⠙⠉⠁⢸⡆⠁⢀⣼⠟⢹⢻⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠷⣶⡶⢾⠗⠓⠒⠂⠾⣤⣤⣠⣤⣥⠤⣤⡀⣴⡀⠀⠀⠀⠀⠀⢠⠸⠀⣼⣥⣶⢿⡇⠀⢸⠸⣿⠃
⠀⠀⠈⢷⣀⡀⢀⣀⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⡤⠄⠀⠀⠀⠁⠙⠉⠉⠀⢄⠀⠀⠈⠙⠛⠿⠿⠛⠃⠀⠐⢒⠙⢡⠀⣸⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠒⠀⠒⠄⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⠉⠤⢀⡤⠤⠴⠖⠐⠂⠀⠤⠀⣀⡂⠁⢈⠲⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⢐⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠢⡐⠌⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠠⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠂⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠠⠁⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢡
⠀⠀⠀⠀⠀⠀⠜⠠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠁
⠀⠀⠀⠀⠀⢀⠄⠬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠦
⠀⠀⠀⠀⡀⠼⠥⢬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠤⠼⠄⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠘⠛⠓⠒⠆⢲⠦⠤⠤⠤⠤⢤⣤⡄⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣤⣤⡤⠤⠤⠤⠤⢶⠒⠖⠒⠛⠙
⠀⠀⠀⠀⠀⠀⡄⣀⣠⡄⢸⡀⠀⡀⠀⠀⠀⠀⠁⠀⠅⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡈⠀⣤⣀⡀⡤
⠀⠀⠀⠀⠀⠀⠦⠤⠈⠗⣺⠉⠉⠀⠒⠒⠒⠉⢇⢀⠧⠄⠤⠤⠶⠶⠶⠶⡀⡰⠖⠴⠦⠤⠄⠀⠨⠗⠒⠃⠒⠒⠂⠀⠈⠉⣩⠈⠅⠠⠤⠄
⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⡉⠀⠒⠯⠼⠅⠀⠀⠀⠐⠒⠀⡠⠀⡄⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠀⠀⠀⠀⠀⢠⠤⢴⡀⣒⠂⠀⠠⠄⠈⠟⠸⡃⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠻⠁⠀⠀⠀⠀⠠⢬⠁⠩⠀⠀⠀⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠉⠀⢧⢀⡆⠀⠤⠤⠄⠀⠀⣠⠀⢀⢀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⣀⣀⣀⠀⢸⠀⠠⠤⠤⠤⠤⠶⡇⢰⠓⠛⢉⠃
⠀⠀⠀⠀⠀⠀⠈⡁⠀⠐⠀⠂⠀⠀⠤⠀⠀⠀⢸⣀⣾⣀⣀⡀⠀⠀⠀⢘⡁⣙⠀⠀⣀⣀⣀⣀⢈⡁⠸⠀⠠⠤⠄⠀⠀⠐⠃⠈⠁⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠛⢁⣠⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⣿⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⢀⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⣴⣶⣤⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠋⡉⠁⠸⢿⣿⣿⣿⣿⣷⣦⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣠⣾⣿⡏⢠⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣼⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⢠⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠍⠂⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠤⠒⠒⠂⠒⠒⠢⢄
⠀⢠⠄⢀⡂⠬⠐⠀⠉⠀⠀⡀⠈⠠⠀⠀⠀⠀⠠⠁⡠⠰⠎⠉⣉⢦⣠⠌⡄⠀⠀⠀⡀⠀⢀⡀⠠⠄⠐⠀⠉⠑⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠂⠁⠀⠀⠀⠀⢉⣿⣾⣥⡄⠄⠆⠀⠀⠀⠀⠀⡀⢀⠜⠀⠱⠃⠋⡁⢰⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠉⠟⢻⡀⠀⠰⠘⡀⠀⠀⠆⡀⠰⣁⠀⠀⠀⡱⡄⠇⠄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⣀⠀⢤⠚⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠇⠃⠀⠀⢀⡀⠤⠽⠳⠀⠀⢃⢁⠀⠀⢸⣡⢆⠀⠉⠀⠈⠀⢠⠘⠀⠀⠀⠀⠃⢀⡀⠀⠤⠉⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠸⠈⡄⠊⠁⢀⡀⠠⠀⠐⠂⣉⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡇⠑⠒⠉⠀⠀⠠⠔⠂⠉⠁⠀⢀⠤⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠞
⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⡔⠒⠈⠉⠁⠀⠀⠀⠀⠀⡨⠂⠀⠀⢠⠖⢉⠇⠀⠀⠀⠀⣰⠖⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣠⡤⠤⠄⠒⠊⠁⠀⠀⢰⠃⠀⠈⠲⡄⠀⠀⠘⣉⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠀⠛⠘⠓⠈⠉⢡⠀⠀⠀⠀⠟⡄⠀⠀⠀⣇⠀⠀⠐⢓⣙⢒⡷⠀⢺⠀⠀⡔⠤⠄⠀⠀⠒⠒⢐
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠈⠑⢄⠀⠰⡁⠀⠀⠀⢀⣀⣠⠤⠰⠀⠀⠀⠀⠂⣹⢾⣭⣭⡁⠀⠀⠘⣇⠀⠀⠀⡠⢿⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⡀⠀⠀⠁⠈⠉⡋⠀⠄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠀⠑⣆⡀⢰⢡⠂⠀⠀⣇⣀⡀⠀⠀⠀⢀⣸⡀
⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠘⡀⠀⢀⣀⠀⠀⣠⠗⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⡠⠖⠛⢉⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⢡⢀⡤⠶⠂⡡⣀⡴⡊⠁⠀⠐⡀⠀⠀⠀⡠⠶⠀⠐⠃⠄⢀⣰⠀⠀⠀⠀⠀⠀⡠⣀⠤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⢸⠻⣓⠴⢾⣿⣿⣿⣦⠀⠀⠀⢣⠀⠐⠊⠂⠈⠀⠰⠦⢀⣄⠀⠉⠀⠒⠂⠀⠠⠖⠁⡠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢏⠀⠀⠐⣝⣛⡿⠟⢀⡠⠐⠁⠀⠐⠢⠤⣀⠀⠔⠒⠒⠠⡀⠛⠀⠓⠀⠀⠀⣰⡉⡄⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠈⢢⡔⠔⠊⡁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⠀⢀⠧⠀⠐⠐⠒⠒⠉⠁⠈⠁⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠤⠤⠤⠤⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠬⢤⠄⡁
⠀⠀⠀⠀⠀⠀⠀⣇⠤⠔⣀⠔⠐⠀⢲⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠤⢀⡀⠀⠀⠑⢄⠀⠀⢀⠔⠋⠊
⠀⠀⢠⠀⠀⡠⠁⠉⠢⣀⠋⠀⠀⠀⠈⠀⠀⠀⣠⡄⠼⠏⠁⠀⠚⠁⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠑⠐⠁
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠴⠦⠵⠶
⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠀⡀⠔⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠠⠤⠄⠐⠒⠀⠁⠁⠀⠀⠀⠀⠙⠛⠳⠶⣶⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠐⠖⠲⢄⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠐⠀⠈⣀⠈⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠘⠒⠂⠉⠀⠀⠀⠀⠉⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⡚⠀⠀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠩⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⢠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⣰⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡄⠠⠀⠠⠤⠤⠀⠄⠐⠂⠀⠂
⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡄⠀⡆⢀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⠈⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠁⠈
⠀⠀⠀⠀⠀⠨⠁⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⢠⢀⠄⠀⠤⠤⠀⢰⢀⡆⠀⠒⢲⠀⠀⠅
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠐⠀⠘⠀⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠨⠀⢱⠄⠀⠀⠀⢀⠈⠐⠀⡂⠐⠂⠐⠀⠐⠐⠂⠀⡆⢘⠀⡹⠀⡄⠠⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣀⡀⠉⠀⢈⠀⠁⠀⠁⠈⠀⢈⠀⡁⠀⠀⣀⣀⣀⠀⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠈

⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡿⠘⠀⠀⢻⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⣠⡠⠀⠠⢤⠴⠄⠀⠀⢀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄
⡀⠈⠛⠙⠚⣰⢊⡋⡛⠟⠧⠿⠎⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠤⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠁⠐⠒⠒⠚⠃⠀⠉⠈⠀⠰⠷⠿⢕⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⠀⠀⠀⠸⣉⡀⠂⠄⢠⣢⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠤⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠂⠀⠀⢸⡹⣆⡄⠄⢀⠀⠀⠀⠀⡀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠳⠈⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⡩⡺⢠⠀⠀⠀⠀⡀⠀⠐⢀⣁⠀⠀⠸
⠀⠄⠀⠠⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠒⠀⠂⠀⠁⣀⡀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠑⠁⠀⠀⠀⡀⠀⠠⠀⠀⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠤⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠁⠈⠀⡖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠇⠄⠀⠀⠀⠀⠀⢦⡰⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠂⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⡀⣀⣀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⣰⣀⣠⠤⠤⠠⠯⠿⠯⠿⠗⠀⠀⠀⡇⠀⠉⠉⠉⠛⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢁⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢤⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠒⠀⠄⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⡐⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣀⡀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⡟⠉⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⣀⠀⠀⣿⢿⡇⠀⠀⠠⠤⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⣯⣤⣿⡄⠀⠀⠀⠀⣾⣿⣿⣇⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢳⣶⣦⣀⠀⠀⣀⣤⡀⠀⣰⡿⠛⡙⠛⣷⡄⢀⣴⣾⣿⣿⣿⡋⣴⣿⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠘⣿⣿⣿⡶⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣅⣶⣿⣿⡇⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⣸⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⢀⡀⡄⣆⢳⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢺⡜⡎⣧⢳⢹⡜⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠧⠼⠘⠈⠁⠀⠀⣶⡄
⠀⠀⠀⠀⢀⣤⣤⣴⡖⠒⣶⣶⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣤⡀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠷⠤⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢽⣽⣧⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣾⣿⣿⠀⠀⢸⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡷⠿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠚⠋⠁⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⢱⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠴⠦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢳⣀⣀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠙⠯⣭⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠍⠅⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⠿⡀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⣴⣿⡿⡟⠻⠆⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣼⡿⠋⡀⠀⢠⣼⡿⠃⢸⣿⣿⣿⣿⡏⠉⢻⡟⠀⢹⣿⡄⠁⠉⠻⠿⡉⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠙⠀⣸⡿⠁⠀⢸⣿⣿⣼⣯⡇⠀⠘⡁⠀⢀⣽⣿⠖⠒⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⢸⣿⠏⢹⣿⠇⠀⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠈⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣯⣭⣭⣭⣭⣭⣭⣤⣒⣒⣒⣒⣒⣒⡒⠲⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⣶⣶⣬⣭⣭⣍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⠂⠒⠂⠙⢻⡖⠚⠒⢛⡇⠠⠼⢧⠄⠀⠰⣶⣖⠒⠒⢶⣤⣤⣀⣤⣤⣀⣀⣀⣀⣀⢀⡀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⢾⠿⡿⠶⠦⣤⣿⣦⣤⣄⣷⣀⣀⠀⣿⡄⠀⠀⢩⡍⠉⠁⠉⣧⠀⠐⠊⠹⡛⠛⠃⠘⣃⢻⡇⣸⠰⣇
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⣇⣿⡟⠈⠀⠀⡀⠀⠀⠀⠀⡎⣿⠉⠉⠉⠉⠉⠉⡛⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠒⠒⠿⢿⡇⣿⢴⣽
⣿⡅⠀⠀⠘⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣀⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠇⠀⠀⠰⠸⠃⣀⣠⣴⣏⡛⢳⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢃⣀⠀⠀⠀⠉⣢⠀⠀⠀⠻⣂⠀⠀⠙⠟⠉⠁⠻⡿⠓⠛⠒⢶⣖⠒⠒⠒⢾⢷⣴⣿⣿⣿⣿⣿⣟⣥⡌⣿⣿
⠀⣇⢠⡆⠀⠰⠉⠉⠉⠙⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣄⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢀⣦⠀⠀⢀⣸⣿⣿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢐⣄⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠠⠀⠀⠠⡁⠀⠀⠈⠉⠙⢙⠙⠩⡭⠍⠉⠋⠛⣉⠛⠹⠋⠀⢾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠬⠉⠉⠉⢹⡟⠛⠿⠛⠛⠛⠒⠒⠛⠿⣷⣦⣤⣴⠾⠧⠀⢀⣤⣄⡁⢀⣀⣠⡆⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⡃⡁⠀⢰⠀⠑⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠷⡶⡶⠲⢟⡚⠂⠓⠚⠛⡿⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠸⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣴⣶⡶⠧⠀⠀⢼⣦⣄⣀⣀⣠⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠀⠀⠀⢠⠳⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡏⣀⠀⢁⡁⠈⠀⠀⠀⠀⢸⠨⢹⠹⠀⠒⠀⠀⠀⢘⠿⠛⠛⢹⠇⠌⠁⠚⠛⣿⣷⡶⡾⢷⠧⠤⠤⠷⣤⣴⣤⣤⠶⡿⠃⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠶⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⡀⢸⣄⣁⡀⠀⣠⠇⠈⠀⠃⣠⠈⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡾⠛⠛⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠎⠉⡏⢿⠀⠉⠀⠀⠀⣿⠉⠉⠉⢨⠀⠌⠉⠁⠉⡉⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢿⡟⣿⠃⠀⣸⢻⣠⡿
⠀⠀⠹⢶⣶⣤⣼⠦⠀⢤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢘⠛⠂⠀⠀⡏⠉⠉⠁⡅⠀⠀⠀⠀⣿⣗⣿⢶⣾⠏⠉⢩⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠉⡟⠛⠛⠉⡇⠀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣇⣁⡒⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢇⣸⡁
⠀⠀⢀⣿⢀⣀⣼⣄⣀⣀⣀⣼⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠉⠉⡛⠉⠙⠁⢸⡇⠁⢀⣼⠟⢻⢿⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠶⣶⡶⢾⠖⠓⠒⠂⢾⣤⣤⣠⣤⣥⠤⢤⡀⣤⡀⠀⠀⠀⠀⠁⠠⠀⠀⣾⣥⣶⢿⡗⠀⢸⠸⣿⠃
⠀⠀⠈⢿⣀⣀⢀⣠⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⠤⠄⠀⠀⠀⠉⠙⠉⠉⠀⢤⠀⠀⠈⠙⠛⢿⠿⠛⠃⠀⠀⢂⠙⢃⠀⣹⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣛⠋⠉⠉⠉⠉⠙⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠈⠙⠻⢶⣤⡀⠀⠀⠀⢸⡟⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣠⡿⠁⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣴⠿⢿⣄⠀⢀⣠⡶⠟⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⡶⠶⠟⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⢀⣻⣶⠟⠉⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠙⣷⡀⣀⣀⣀⣀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⢀⣠⡾⣿⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⢠⡾⠋⠀⢹⣇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⣿⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣿⡆⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣴⣾⣏⣠⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⠄⠀⢀⣀⣲⣿⣦⣀
⠀⠀⠀⠀⠀⣠⠤⠤⢀⣀⡄⡀⣠⡏⠀⠤⠀⠀⡤⠀⠙⣁⠀⢩⠁⠙⣷⣄⣀⣀⣤⠤⠶⠒⡒⠒⠒⠲⣦⣄
⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⣉⣻⣾⣽⣳⣶⣴⡞⠋⠠⢀⡴⠖⠲⢦⣤⡿⠛⢋⣡⡴⠖⣛⣭⠶⠂⣀⣼⣿⣿⡆
⠀⠀⠀⠀⢻⡀⠠⠴⠾⠛⠛⠛⠛⣛⣿⣿⣿⣧⠀⠀⡟⠀⣀⡴⠚⣁⣴⠞⠋⢁⡴⠞⢋⣠⠶⣛⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠠⠭⠟⠒⠒⣻⣿⣧⣄⠀⣿⡿⠋⣠⠾⠋⠁⡠⠞⠉⠀⢐⣩⣴⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢰⣟⠛⡗⠲⠤⣀⣀⣀⡀⠉⠛⢻⣿⡷⠾⠋⠀⠚⠁⠀⠀⠀⠀⠀⠤⠾⣛⣛⣿⣿⡿⠿⣿⢹⠄
⠀⠀⠀⠀⠈⠛⢿⡾⣦⣄⣀⣀⠀⠙⠋⠉⠙⠳⠛⠉⠛⠲⣞⠛⠛⠓⢾⣯⣉⠉⠙⠿⣦⣭⣙⣛⠛⡖⠁
⠀⠀⠀⠀⠀⠀⠘⣷⠋⢉⣉⠙⠿⡛⢛⣿⡶⠶⢿⡷⠶⠶⢾⣿⡶⠶⢶⣾⣿⣛⣻⠿⢿⣿⣟⡟⡼
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⠻⣀⠀⠸⡏⠉⢙⣶⠋⠉⢳⣶⣏⣉⣙⣿⣿⣥⣴⣿⠿⣿⣿⣻⡿⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠦⠛⢃⡀⢠⢿⣋⠉⣹⣾⣉⣀⣉⣿⣿⣉⣩⣿⣿⣷⣶⡿⢻⣿⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠈⠓⣀⠀⣸⣿⣅⣀⣩⣿⣍⣀⣩⣿⣿⣷⣶⡿⠟⣿⣿⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢦⡴⢶⣉⣙⣤⣤⡼⠻⣅⣠⣼⡿⠿⣧⣴⣿⣛⣿⣿⣿⠷⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⣦⣌⣦⣈⣻⣍⡉⠙⢿⣉⠛⢿⣯⣙⣻⣿⣤⣭⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠉⠉⠁

⠀⠀⠀⡋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣧⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠄⠀⠀⠀⠀⠀⠠⠡⠊⠀⠄⠀⠑⠀⠀⠀⠀⠀⢀⠤⠐⡶⢐⡟⠉⠓⣄
⠀⠀⠀⠁⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠈⠢⣌⠥⣝⡭⢯⠓⢺
⠀⠀⠅⠌⣉⠫⠀⠀⠀⠀⠀⠀⠀⠀⠠⡩⢀⠘⣦⠈⡱⠀⠀⠀⠀⠀⠈⢌⠠⠀⠄⠠⢈⠔⠀⠀⠀⠀⠀⠀⠀⠓⢥⠂⠋⠁⠁
⠀⠀⠐⠒⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⣶⠠⠐⣀⠐⢀⠠⢢⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠢⡄⠀⠀⠀⠀⠀⢀⣤⣄⠁⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡃
⠀⡎⢀⡀⠈⡕⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢔⡛⣆⠀⠀⠀⠀⠀⠀⠀⠿⠝⠠⡚⠙⢲⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠅⣈⠀⠅
⠐⡆⠢⡙⠚⠟⠡⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣠⠺⣠⣀⠇⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶


⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠐⠤⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⠀⠁⠒⠫⡭⠂⠁⠀⠀⠀⠀⠀⠠⢀⠀⠄⠀⢁⣔⡤⠀⠀⠀⠀⠀⡁⠀⡀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣲⣄⠀⠶⠶⠖⠇
⢀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⠀⢐⣂⠀⡄⠀⠰⠍⡀⠀⠀⠀⠀⠀⠀⡈⠀⠓⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢀⡁⠀⢀⣀⠀⠂
⠀⠀⠐⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠻⠩⠈⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠙⠠⠀⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢀
⠀⣠⠄⣀⣐⠠⡌⠀⢢⠀⠀⠀⠀⠀⠀⡀⠠⠀⠐⠶⣶⠀⠀⠀⠀⠀⢀⠴⠶⠲⡊⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⣠⠔⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿⠈⠁⠃⡀⠉⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⠲⠒⢄⠀⠀⠀⠀⠀⠀⠈⠀⠛⠁⠈⠆⡄
⠁⠀⠀⠐⠁⠚⠁⡀⡀⠀⠀⠀⠀⠀⠸⣟⢲⡶⠦⢬⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠠⢲⣀⠀⢀⡐⠋
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠟⠲⠺⠟⠅⠀⠀⠀⠀⠀⠀⠀⣄⣣⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⠋⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠉⠻⠿⠿⢿⣿⣿
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠻⣿⣿⣶⣤⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠘⠛⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡻⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⣿⠟⢻⠿⢿⢿⠻⣿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣷⣿⣶⣿⣷⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⡿⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣉⣻⣿⣷⣬⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⠛⠛⢿⣿⡁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⣠⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡀⠈⠻⣿⣄⠀⣘⣿⣿⣦
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣤⣿⣿⣿⣿⣿⡿⣿⣷⡀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡿⠿⣿⣏⠁⠀⠹⣿⣷⡀
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠿⠿⣿⡇⠀⠀⢻⣿⣆⣀⣀⠹⣿⣷
⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⡿⠟⠛⠉⠀⢀⢈⣿⡇⣠⣴⣿⢿⣿⡟⠿⣿⣿⣿
⠀⢸⡏⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⡜⢸⣿⣿⡿⠋⠀⠀⣿⣿⡄⠀⠹⣿
⠀⣾⡇⣀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣾⣿⡟⠁⠀⠀⠀⢿⣿⣷⠀⠀⢻
⠀⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣸
⠀⢸⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿
⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣿⡿
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⢀⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣤⣀⣀⣀⣀⣀⣤⣤⣴⡾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⢛⣩⣴⣶⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢠⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⣰⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⢉⣉⡉⠛⠛⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠛⠃⠘⠛⠛⠻⠟⠁⢰⣿⣿⣿⣿⣿⣿⡿⠋⢁⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣝⡻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣵⣶⣾⠟⣠⣿⣿⣿⣿⠗⠀⣴⣤⣤⣈⡉⠙⠛⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⡿⠀⢠⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣷⣦⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣰⣿⣿⡿⠋⣠⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣿⣿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣸⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⠇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⣚⣛⢛⣛⡛⠻⠟⠿⠯⠿⠯⠭⠭⠭⠥⠤⠬⠭⠉⠍⢉⣉⣛⣛⣛⡛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿
⠀⠀⠀⠛⠛⠉⠉⠉⠀⠀⢐⣀⣤⡤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠈⠉⠀⠐⠒⠀⠀⠀⠈⠉⠉⠁⠘⠛⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣩⡀⠀⠀⣠⡿⠀⠀⠀⠀⠀⣠⣤⠀⠀⣼⣿⣃⡀⠀⢀⣀⡀⠦⣴⣿⣥⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣴⡟⠁⣠⢟⣿⣇⣤⡾⠋⠀⣴⡾⢛⡇⢀⣿⣧⠀⣰⣿⣿⡿⢣⣾⣟⡽⢃⣼⡿⠁⣠⣿⡿⢺⣷⠄⢀⣤⣤⣄⠀⠀⣠⣿⠇⣠⣾⠆
⠀⠀⠀⠀⠀⣾⡟⢀⡼⠋⣿⡿⠛⠉⢹⣷⢸⣿⠁⣾⣏⣞⢀⣿⢷⣿⠻⣏⣠⢾⣿⣋⣴⢾⣟⣠⠾⣿⠃⣠⣾⣿⣴⡿⠋⣰⡮⢀⣾⠟⢁⣾⡿⠃
⠀⠀⠀⠀⠀⠛⠗⠋⠀⠀⣿⡇⠀⣠⡿⠋⠈⠛⠋⠙⠋⠈⠉⠥⠤⠭⠦⠾⠷⠶⠾⠷⠶⠶⠿⠧⠤⠽⢿⣯⣉⣀⡹⠷⠺⣿⢴⣿⣫⣴⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠶⠶⠤⣭⣉⣑⠒⠢⠬⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⣰⡖⢥⣃⡂⠄⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⡁⢀⣴⠾⣧⣼⢟⠘⢍⠀⠉⢳⢌⠢⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠊⠀⠈⠀⠉⠑⣊⡟⡄⣡⢀⠀⢀⡼⠀⠑⠌⢂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠂⠡⠀⠀⠀⠀⠘⢄⡌⠙⢂⠀⠒⠁⠀⠀⠀⢈⡆⢃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⡀⠸⠙⠂⠀⠀⠀⠀⠘⡷⢛⡀⡀⢀
⠀⠀⠀⠀⠀⠠⠂⣀⣀⣐⠂⠄⠀⠐⣄⠀⢀⠤⢤⠘⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠚⠇⠁
⠀⠀⠀⢀⠤⠤⠤⠤⠤⠬⠧⠦⢤⡀⠈⠑⠴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠃⠆⢠
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠙⠉⠁⠁⠢⠄⡀⠀⠀⠀⠈⠀⡙⠠⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢁⢠⡄⠀⠀⠀⢠⠀⡄⠀⡀⠀⠀⠀⠈⠢⡀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠗⠛⠉⠉⢝⡭⢭⣍⢂⠀⠀⠀⠀⡰
⠀⠀⠸⠀⠀⠸⠇⠀⠀⠀⢹⠋⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⡠⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣤⠂⣿⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠄⡀⠀⠀⢃⡈⠀⢀⣘⠂⠄⠀⢀⡀⢸⠄⠄⠊⢂⠈⠉⠁⠰⠀⠀⠀⠀⠠⠂
⡔⠐⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠉⢳⠂⠀⠈⠉⠁⠀⠐⠊⠒⠀⠈⠁⠀⠒⡀⠀⠀⠀⠣⠀⠀⡄⠀⢀⡀⠤⠐⡞
⡯⢁⠀⢠⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠍⠁⠀⠒⠀⠀⠒⠀⠉⡀⠀⠀⠀⠀⠀⠛⠀⠀⢀⢔⣑⡀⠃⠀⠀⠀⠀⠀⠐
⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⢈⢀⠀⣄⠀⠀⣠⢀⠈⢠⠀⠀⠀⠀⠀⠘⠈⡠⠢⠈⢹⡟⢻⠀⠀⠀⠀⠀⠰
⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠠⠀⠀⠀⠀⠀⠀⠃⡀⣄⣀⣀⣠⠀⠐⣋⢀⣀⣀⣤⠤⠼⠤⠤⠤⠤⠤⠴
⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⢠⡠⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡛⣿⣿⣿⠏⡣⣾⣿⣿⣿⣿⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣶⡿⣣⣷⣼⣿⣿⣿⣿⣿⣷⣿⣿⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠁⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⣽⣟⣛⣻⣿⣿⣿⣿⠟⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠋⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣾⠏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣏⠈⠉⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⢠⣬⣿⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⡾⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠴⠶⢦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠲⣦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⣤⣴⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠙⣷⡄⠀⢀⡿⠁⠀⠀⠀⠀⠀⠙⣷⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣯⠾⠛⠋⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠀⠀⢸⣷⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢿⡄
⠀⠀⠀⠀⠀⢀⡾⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠼⠿⣿⣟⠛⠋⢻⣏⠹⣿⠛⠶⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣾⢣⡾⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠘⣿⣆⠀⠘⣿⠀⠙⣷⡀⠀⠀⠈⠉⠛⠻⢶⣤⣀⠀⠀⣿⡀
⠀⠀⠀⠀⢸⡇⢾⠃⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠈⠛⢿⣦⣸⣇
⠀⠀⠀⠀⣾⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢹⣧⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢻⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠘⣇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢹⣎⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢻⣆⠻⠂⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠆⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⠀⢀⣼⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⣀⡀⠀⠀⢀⡼⠁⢠⣤⣴⣶⣛⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠷⠖⠚⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢁⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠐⠀⢉⡀⠀⠄⢀⠀⠄⠀⠌⠁⠐⠀⠠⢄
⠀⠀⠑⠢⢀⠉⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠧⠄⠀⠈⠉⠉⠁⠉⠀⠈⠀⠀⠢⢄⡀⠀⠈⠐⠄⡀
⠀⢂⠀⠀⠀⠀⠀⣀⢰⠂⠈⠉⢖⠉⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢁⠀⠀⠒⢄
⠀⠀⠑⠀⠀⠀⠀⢀⠌⢂⢀⡀⠄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠂⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠳⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢢
⠀⠀⠀⠄⠀⠀⡀⠔⠩⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠉⠀⠰⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈
⠀⠀⠀⢀⠊⠔⠰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⡀
⠀⠀⠀⡀⠀⢀⠀⢀⡀⠐⢀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⢀⠀⡀⡆⠀⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡀
⠀⠀⠈⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢸
⠀⢰⡉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⡆
⡌⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⠋⠉⠉
⠑⢠⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡄
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠒⠒⠒⠒⠒⠊⠈⠓⠒⠈⠉⠉⠉⠁⢈⠀⢀⠀⠀⠀⡇
⠀⠀⡀⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⣀⠀⢀⠀⠀⣀⠀⡠⠀⠠⡀⢠⠄⠀⢰⠀⢸⠀⠉⢉
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠰⠄⠀⠘⠐⢪⠀⠀⠄⠀⠄⠀⠰⠀⠈⠂⠀⠚⠀⠈⠉
⠀⠀⠆⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⠀⠀⢤⢀⡤⠀⠀⢰
⠀⠀⠃⠐⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⠉⠇⠸⠁⠉⠱⠀⢌⠉⢈⡉⠉⣁⡀⠨⠀⠸⠄⠀⠄⠀⠐⠀⠒⠘
⠀⠀⢦⠠⠀⡀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⡁⠀⠅⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠄⡴
⠀⠀⠀⠄⠄⠸⣀⣊⠀⠉⢆⠀⠀⠀⠀⠀⢀⠐⠃⠂⠀⠆⠀⠰⠄⠠⠂⠀⠰⠀⠐⠀⠐⡇⠀⡃⠀⠰⠍⢬⠁⢀⣇⠀⠧⠄⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠐⠚⠂⠀⠒⠀⠃⠀⠐⠂⠐⠂⠀⠂⠀⠐⠀⠀⠃⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠉⠀⠐⠒⠐⠂⠀⠒⠂⠀⠀⠠⠠⠤⠤⠀⠤⠄⠀⢄⡠⠠⠤⢄⣀⡠⠤⠤⠤⠤⠄⠒⠒⠀⠐⠒⠛⠋⠈⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢬⠉⠙⠒⠀⠀⠐⡆⠀⠐⠊⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣼⠀⢀⣀⣀⠀⠀⢇⣀⣀⣀⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠒⠊⠉⢀⠚⠛⠉⠀⠀⠀⡈⠋⠋⠉⠉⠈⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⢄⣀⠀⠀⢠⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠨⢆⠈⠀⠀⡸⠐⠒⠒⠒⠒⠒⠲⡀⠄⠀⠀⠄⠀⠉⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢰⡐⠄⠀⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠒⠒⠈⣀⠠⠘⠋⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠔⠈⠀⠉⡠⠂⠀⠀⠀⠀⠀⠠⠐⠀⡡⠔⠋⠙⠉⠻⠲⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⠀⠌⠀⠀⠀⠄⠈⢢⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠀⠀⢰⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣠⠀⣤⣤⣶⣆⣀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡲⠄⢀⣀⡀⠉⠁⡒⠒⠒⠂⠤⠀⣈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠧⡌⣯⠁⣹⠽⢿⣷⣧⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⠁⠀⠀⣕⠂⡤⢠⠄⠀⠤⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠴⠃⣿⣷⣸⡦⠀⣿⠁⠀⠀⠁⠐⠠⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⢀⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⡀⡀⠘⣆⣀⣀⣽⣿⣿⣷⣄⠀⢈⠂⠄⡀⠀⠀⠈⢄⢀⡴⠃⠀⠀⠀⠀⠀⢆⠠⠺⢉⡗⢒⠤⣠⢲
⠀⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠠⠀⠀⠒⠁⠀⠀⠐⡄⠰⢊⡴⢁⡞⠀⣠⢆⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠃⠈⠀⠀⠀⢠⣄⠀⢀⡜⠵⣋⣴⢏⣠⠞⠀⠏
⠀⠀⠀⠀⠀⠀⡘⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠄⠀⠀⠀⠀⠀⢈⣕⡶⢭⡋⢥⣠⠯⣣⡀
⠀⠀⠀⠀⠀⠀⠠⠰⠄⠤⠠⣤⠚⠓⢲⡴⠒⠒⢦⡀⣀⣀⣀⣀⣀⣇⠘⠁⠀⠀⠀⠀⠀⠀⠉⠐⠠⣈⡑⠪⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠙⠷⠔⠚⠛⠢⠴⠟⠉⠛⠃⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠀⠀⠀⠀⠑⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⣐⡒⣒⣂⠒⠂⡐⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣂⣀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠄⡐⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣄⠐⠦⢚⠂⠍⠃⠉⠀⠀⠀⠱⠄⣧⡀⠂⠀⣲⢐⡀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠉⠅⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠸⠈⠒⠘⠯⢃⡠⠰⡄⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡔⠋⣄⠓⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠆⠀⠂⠀⠀⠀⠂⠐⠀⠐⠀⠘⠀⠃⢙⠿⣷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣆⣫⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠃⠐⠀⠘⠀⠈⠀⢉⠞⡿⢞⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠱⢿⡀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⢙⣿⠷⢥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠂⠠⣄⠀⠀⠀⠁⠐⠀⠀⠀⠠⠀⠄⢀⠀⢠⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⠄⡈⡅⠃⠠⡆⠀⡄⢀⣀⣀⢠⠀⣠⠀⡀⢀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠔⢀⠆⠀⠒⠀⠉⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠃⠸⠀⡶⠀⡦⢩⠌⣿⡈⢣⣈⡁⣻⣄⠙⢅⣒⡀⢀⡄⠰⣠⣀⠠⠀⡠⠄⢸⠔⡦⠚⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⢰⠀⡄⠀⡀⠈⠀⠈⠀⠋⠀⠟⠀⠿⠀⡆⠀⠚⠁⠁⡅⠀⠁⠌⠀⠭⠀⠚⢀⡁⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⠆⠠⡄⢉⡀⢁⠀⠂⠚⠀⠰⠄⠶⠀⠶⠀⠤⠀⢠⠄⠠⠄⠀⠐⠀⠰⠆⠈⠃⠘⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡀⢁⠈⣁⠘⠂⠸⠈⠧⠀⠆⢰⠆⢰⡀⢰⡀⠠⡄⠀⡄⠀⣐⠀⠲⠀⠞⠀⠓⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠘⠇⠐⡀⢤⠠⠀⣄⢀⡄⢠⡄⢀⡀⠀⠀⠀⠄⢠⠄⠰⠄⠸⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠘⠁⠈⠂⠈⠦⠀⡆⠀⡄⢠⠀⣨⠀⣉⠀⡁⢈⡁⢀⠀⢀⠁⡄⠀⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⢃⠀⠂⠀⢦⠠⡄⠠⡈⢁⠉⡀⢉⠀⢉⢈⡁⢈⠀⡉⢀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠐⠂⠰⠆⠠⠄⠄⡇⢈⣃⣉⢈⡁⣉⢀⠁⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠂⢤⡀⠀⠀⠀⠀⢀⡠⠔⠂⢉⠀⠀⠉⠑⢢⡀⠀⠀⠀⠀⠀⢀⠔⠊⠉⡁⠀⠡⡐⢀⠀⠀⢀⡀⠀⠀⢀⠔⠈⠣⠄⠠⠜⠁⠢⡀
⠀⠀⠣⡀⠀⠈⠐⠂⢀⠍⢠⠀⢁⠚⠥⠈⠀⠁⠈⠁⠀⠕⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⠑⢆⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⠜⠂⣈⠕⠀⠈⠀⡡⠐⠒⠢⢄⠀⠀⠀⠀⡀⣀⠜⠁⠀⠀⢸⠠⠈⢈⡈⡀⠀⣠⠀⠔⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠘⠒⠫⠤⠄⠄⡤⠊⢀⠀⢀⡠⠚⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⠀⠀⡆⠁⢀⠀⡘⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠮⠤⠴⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣢⡈⢲⡰⠁⠀⢘⠖⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⣀⡀⡠⠔⠢⢄⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⣀⠀⠀⠀⣀⠀⠀⠈⠒⣄⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠇⢯⡱⢸⠒⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⡤⠴⠎⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠛⠁⠀⣠⠄⠒⠒⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁⣠⡀⡄⠀⢡⣧⠀⠀⠀⢨⠉⠉⡇
⠀⠀⠀⡀⠀⠐⠚⠀⠀⠐⠻⣄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⢰⠃⠀⣙⡷⠃⠀⣿⠇⠀⠀⠀⠈⠳⠞
⠀⠀⢰⠁⠀⠀⠀⠀⠠⡄⢠⠀⠃⠀⠑⠐⠊⠉⠉⠐⠢⠤⠀⠤⠔⠊⠀⠀⢀⠀⠀⠀⠇⠀⠐⠇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⠂⣠⣀⡀⠀⠀⣼⠇⠀⠀⠀⠈⠁⠀⣀
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠲⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠈⠁⢐⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡧⠀⠐⠒⠒⠀⢤⢄⠈⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠚⠉⠢⣄⠀⠀⠀⠀⠀⠙⠶⠶⢥⣤⣤⡾⠁⠀⠀⠀⠀⡚⠓
⠀⠀⣇⠀⠀⠈⠀⠂⠈⣾⠘⠃⡅⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣄⣴⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀⣠⣖⠠⠀⠐⠀⣷
⠀⠀⠉⡄⠀⠀⠀⠀⠀⠙⠐⡀⡇⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠙⠋⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠄⠀⢀⢸⣿⣿⡇⠀⠀⢸⡅
⠀⠀⠀⠲⠶⢤⠤⠤⡾⠡⡾⠐⠁⠀⠀⠀⠀⠀⠀⣀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠈⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⠛⠶⠶⠶⢴⣄⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣉⠀⢀⡂⠀⠀⠀⠁
⠀⠀⡀⠀⣀⠠⠖⠒⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠀⠠⠔⠒⠂⡄⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣤⣀⣀⣀⡀⢈⠀⠀⠀⠀⠀⠀⠀⢀⢄⠤⠄⠀⠀⠄⠀⠀⠰⠂
⠀⠀⢸⡀⠀⠀⠒⠡⡐⠀⠰⡀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⡄⠕⠁⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⡃⠀⠐⠂⠚⠁⠀⠀⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⡈⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⡀⠀⠀⠀⡧⡀
⠀⠀⠀⢣⠀⣤⠴⠖⠚⠀⠀⡁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣄⢣⣤⠇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠂⠀⠒⠊⠁⠈⠒⢄
⠀⠀⠀⠈⠆⡀⠀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠘⠻⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠉⠉⠐⠲⠀⡀⠤⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣡⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠛⢂⣶⡞⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⠻⢷⡀⠀⠀⠀⠀⠀⠀⡄⡤⢠⡄⡄⠤⡄⣄⢀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⣾⣾⡍⢮⣤⡀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠟⠁⠁⠈⢻⣄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠉⠉⠈
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⡄⠃⣠⣽⣿⣿⣷⣶⣶⣾⣿⠏⠁⡴⠊⠀⠀⡀⠈⠛⠛
⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⡈⣴⠶⢿⠉⠹⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄
⠀⠀⠀⠘⢀⣼⣿⢿⣿⡉⠛⣿⣿⠜⠁⠀⠀⠙⣉⡉
⠀⠀⠀⠰⠈⠈⢻⣴⢟⢷⡀⠋
⠀⠀⠀⠀⠃⠀⠀⠈⠂⢺⡅
⠀⠀⠀⠀⠁⠀⠰⣷⡦⣚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠹⡆⠀⠀⣿⠀⠐⠄
⠀⠀⢀⠬⠔⠒⠒⠒⠛⠒⢾⠧⠤⣤⣇⠀⢀⡴⠒⠄
⠀⢠⠈⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣼⠉⠙⣺⢇⠀⠘
⠀⠈⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⢰⠇⠀⠀⢼⠀⠈⠢⣰
⠀⠄⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⡀⠀⠀⢹
⠀⠃⣠⠊⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⡇⠀⠀⢨
⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣷⠀⠀⠈
⠀⠀⠀⢂⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⢠⠞⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠂⢤⡀
⠀⠀⠀⠀⠀⢀⡀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠐⠋⠠⠤⠤⠀⠒⠈⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡤⠤⠶⠶⠖⠒⠒⠒⠒⠒⠶⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⢌⠐⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⡡
⠀⠀⠀⠀⠀⠠⠤⠤⣄⣀⣀⣀⣧⣀⡠⠤⠖⠂⢀⡀⠀⠀⢄⠀⠈⠉⠉⠙⠛⠋⠉⠉⠉⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⣀⣀⡀⠀⠀⠑⠀⠀⠀⠑⠲⠤⢀⣀⣀⣀⠀⠀⠀⠊⠁
⠀⠀⠀⠂⠀⢀⣠⠤⠖⠒⠛⠉⠙⣿⠉⠉⠉⠉⠒⠂⢤⡀
⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⣀⣤⣿⡤⢤⣀⠀⠀⠀⠀⠑
⠀⠀⠋⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢻⠀⠀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢳⡄⡀
⠀⠀⠀⢄⠀⠀⣴⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡃⠁
⠀⠀⠀⠈⠇⣸⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠂⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠅⠀⠤⠒⣇⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠉⠾⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠋⢉⣉⣉⣈⠓⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠃⡔⠁⠀⠀⠉⠐⠂⡠⠄⠀⠤⠀⡰⠊⠉⣡⣾⣿⣿⣿⣿⣿⣿⣷⠖⣄⠑⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠐⠁⠀⠈⠀⠠⠀⠀⡬⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⢻⠟⠘⣿⣷⣦⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣸⠀⡀⠀⠀⠂⠀⠀⠀⠀⡞⠁⢰⣿⡿⠉⠩⠻⢿⣿⡇⠀⠀⠀⠀⠁⠘⡄⠉⠚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⣿⣿⣿⣆⣂⣀⡀⠈⢃⠀⠀⠀⠀⠰⠉⠳⠄⡓⢄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡇⠀⠀⠀⠀⠀⠀⣠⠎⢸⣿⡟⠉⠉⠀⠀⠈⡆⠘⣆⣀⡊⣝⣃⣵⡀⠠⡈⢪⢦⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢰⠀⠀⠀⠀⢿⠞⠁⠀⠀⠰⡈⠀⠁⡈⢻⠈⢦⡉⠁⢁⡙⠾⡙⠲⣿⡒⢷⣷⣆⣀⣤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⡀⠀⡄⢰⢉⠀⡀⢀⠀⢀⣷⠤⡼⡁⠄⠀⠀⠀⠀⠀⠁⢀⡠⠆⠉⠝⡏⠉⣻⡁⠀⠀⠀⣹⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣇⠀⢱⢨⠂⠰⣄⢈⣷⣌⢻⠀⠈⠐⢂⠴⢆⠀⠀⠀⡜⠁⡴⠊⠀⠀⠀⠀⠀⠉⠣⢤⠒⢻⠤⢬⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⡆⢦⣀⣄⡠⢷⣼⣮⢐⠀⠀⡆⠀⡈⢇⠀⢸⣄⠘⠁⠀⠀⠀⠀⠀⡄⠀⠀⢀⡗⠀⠀⠑⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⣆⠀⢣⠀⡌⢿⣿⡌⡆⠈⢧⠀⢿⣷⣦⣴⣯⣠⣀⠀⠀⠄⠀⠀⡼⠀⠐⡞⢀⠀⠀⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠡⣷⣤⡿⠟⠛⠲⡐⣢⠏⠀⠀⠀⠁⠀⠈⣗⡤⠌⠳⠴⠷⠴⠾⠓⠛⠉⠲⣽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠋⢩⡄⢀⠵⠊⠙⣾⡄⠀⠀⠀⢠⣇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⣢⠀⣼⠀⢘⠃⠁⣾⣆⡀⢀⡜⢻⣾⡅⠀⠀⠀⠀⠀⠀⣀⡠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢃⣀⡼⠀⢀⠇⠐⡥⠼⠋⠉⠀⠀⠈⠪⠳⡖⣶⠶⡿⢻⠟⣷⠓⢛⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠯⡀⣰⠉⢣⡀⠀⠀⠀⠀⠀⣰⠧⢿⣎⣳⣍⠷⠬⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠉⠂⠢⡤⠒⠉⠁

⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⡄⢶⣦⣄⡀
⠀⠀⠀⠀⢀⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣷⣦⡀
⠀⠀⢀⣴⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣦
⠀⢠⣾⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷
⢀⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⢰⡀
⣸⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡟⣸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⢡⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⣏⢿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⢻⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⡟⣡⣿⣿⣿⡟⠈⢳⡀⠀⠀⠀⠀⠀⡾⠁⢹⡆⠀⠈⢙⣿⣿⣿⣿⣷⣤⡀
⠘⣿⣿⣦⡙⠿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⢸⣿⣿⣿⠏⣴⣿⣿⣿⡿⠁⠀⠈⢷⡀⠀⠀⠀⣼⠁⠀⠀⣷⠀⠀⣾⠁⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠘⣿⣿⣿⣷⣦⣍⡛⠿⢿⣿⡇⣿⣿⣿⡇⣼⣿⣿⠏⣼⣿⡿⠟⣫⡄⠀⠀⠀⠈⣷⠀⠀⢰⠇⠀⠀⠀⢹⡄⢰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣶⢠⣬⣭⣍⢁⣍⣭⡉⣨⣭⣴⣶⡟⢹⠃⠀⠀⠀⠀⠸⡇⢀⡟⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁
⠀⠀⣸⣿⡻⣿⡿⠿⠿⠿⢟⣡⣿⣿⣿⠇⣾⣿⣿⡇⣿⣿⠟⢯⡀⢸⠀⠀⠀⠀⠀⠀⢻⣼⠃⠀⣀⣤⣶⣿⣿⡿⣿⠋
⠀⠀⠸⣿⣿⣌⠻⢿⡛⠿⣿⣿⣿⣿⠏⣼⣿⣿⠿⠟⠈⠁⠀⠈⢳⣼⠀⠀⠀⢀⣀⣤⣼⣿⣾⣿⢿⠟⣿⡇⣸⣷⠏
⠀⠀⠀⠈⠛⢿⣷⣶⣿⣦⣽⣆⣀⣀⣀⣀⣙⣿⣆⣀⣠⣤⣤⣤⣴⣿⣶⣾⠿⢿⡿⣿⡉⣽⠋⣸⢿⣤⡏⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢿⡟⣿⠿⣿⣻⠿⣟⢻⡿⣟⠛⠛⣻⠿⣍⠉⣩⠏⠙⢦⣠⠟⠀⢀⡿⢧⣴⠏⢠⡟⢧⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣈⡿⢦⣈⡿⣦⡈⠻⣶⡃⠀⠈⣿⢯⡀⠀⣰⠛⠷⣤⡞⠁⣰⠛⢳⣾⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣧⠈⣿⢧⡀⠙⣾⣇⠙⢳⣾⠃⠀⢙⣾⣇⠀⣠⠟⠳⣶⡃⠀⡾⠉⠳⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣻⣇⠀⠙⣾⡃⠙⢳⣞⠉⠛⢦⣞⠁⠈⣻⢯⣀⣼⠃⠙⣾⣅⠀⣸⠏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢧⡼⠃⠙⣶⡏⠈⠳⣦⡟⠙⢳⣼⡃⠀⡽⠷⣄⣸⠃⠈⢳⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠛⣆⣴⠋⠙⢦⣴⠋⠙⢦⣾⠉⢛⣾⡁⠀⣸⠿⢦⡀⣼⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡼⠳⣄⢀⡼⠛⢦⣠⡟⠉⢳⣾⠁⠙⢳⣏⡀⠀⢹⡿⣄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢙⣿⡁⠀⣰⠟⢦⣀⡞⠉⠳⢦⡟⠈⠙⢦⣾⠀⠈⠳⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⠏⠀⠻⣾⠃⠀⢀⡟⢧⡀⢀⡞⠙⢦⡀⢰⠏⠳⣄⢠⠏⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⢇⠀⢀⡜⠉⠣⣀⠞⠀⠀⠙⣾⡀⠀⠀⠈⡿⣄⠀⠀⢹⠦⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢳⡞⠀⠀⢠⠟⢦⡀⠀⡼⠁⠙⢦⡀⣸⠁⠈⠑⢤⡟⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠏⠹⣄⢠⠏⠀⠀⠳⣼⠃⠀⠀⠀⠙⣯⠀⠀⠀⢈⣷⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠙⣏⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⡟⢦⡀⠀⣸⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣠⡾⠻⣦⠀⠀⣰⠇⠻⣆⠀⠀⣸⠇⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣴⣤⣀⢰⣦⣷⣴⣿⢀⣤⣿⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⢻⣷⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡿⣻⣫⣿⣿⣿⣿⣟⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠻⣿⣿⣿⣿⣿⡷⡷⣟⣿⣼⡟⣫⣿⠟⣿⡝⣭⡽⣵⣿⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡾⠿⠷⠶⠛⠛⢯⣾⣿⣼⣿⣿⣿⣿⣿⣿⣧⣿⢇⢿⣎⠵⠺⠟⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢡⣵⣄⡦⠴⣶⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣶⣤⠘⠢⠶⢪⡉⠙⠠⠀⢘⣿⣿⣸⠟⠻⢿⣿⣿⣿⢿⠿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣏⠊⠉⠀⢙⠩⣶⠀⠀⠀⣽⣿⢠⣀⣀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠰⢑⠢⢀⡀⢡⠀⠀⢸⣿⣃⣀⣠⣴⣿⢧⣿⡄⠀⢠⠾⠟⡪⣿⣿⡿⢛⡵
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⠀⡇⠀⠀⠀⠉⢩⠉⠈⢹⡍⠈⣿⡆⢰⣿⠀⣼⣠⢼⣿⣿⠀⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡏⠀⠀⠀⠀⠀⠉⠀⠀⠈⣟⡩⢿⣻⣿⣿⣿⣻⡱⠞⠛⠛⠒⠿⢃⠐⣾⣶⣿⣶⣆⠀⠐⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡉⢑⠂⠀⠀⠀⢠⠀⠀⢠⣴⠞⠂⠀⢸⡃⠈⠈⠙⡷⠲⠆⠀⢰⠶⠗⠈⢻⣿⣿⣿⣷⡀⠦⠤⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⢈⠀⠀⠉⠀⠀⠀⠂⠀⠉⠁⠠⣄⠛⠻⣿⣆⠘⢿⣷⠂⠘⣿⡟⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⠀⠀⠀⠘⢀⡠⠀⠀⠀⡀⠀⠀⢘⣦⠀⠘⣷⡄⠘⣷⠀⢹⣿⡆⠀⢻⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⡤⠇⠀⠀⠀⠈⢿⠁⠀⠀⠀⡇⠀⠀⠀⣿⡆⠀⢸⣿⡀⢹⠆⠰⣿⡇⠀⢸⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⡦⢀⠀⠀⠀⠀⠀⣇⠀⠀⠐⡏⠀⠀⠀⢽⣷⠀⠈⣿⡇⢸⠁⠈⢻⡇⠀⢸⡿⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠈⠀⠀⠃⠸⡄⠀⠀⢟⡀⠀⠀⠨⣿⠀⠀⣿⡇⡼⠀⠐⢾⡇⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠘⡁⠀⠀⠐⣿⠀⠀⠿⠋⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢸⣿⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠸⣿⣿⣶⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⢿⣿⡟⠁⠀⣸⣿⣿⠀⠀⠙⠻⠟⠁⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⣿⣿⣧⣤⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⢶⣾⣿⣿⣷⣦⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣭⣟⡻⠿⣧⢻⣿⣷⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣷⣶⣿⣆⠀⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⣼⣿⠿⣛⣛⣯⣭⣭⣿⣶⣶⣶⣶⡆⣭⣭⣟⡻⠄⠻⠿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⡁⣙⡻⣿⣿⡇⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣾⣿⣿⢧⣿⣿⡞⣿⠇⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⡿⣸⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⣵⣾⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢟⣵⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠉⠉⠉⠉⠉⠉⠙⠋⠋⠛⠛⠛⠓⠒⠒⠶⠶⠤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣤⠖⠚⠉⠠⣤⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠁⢹⡆⠐⠒⠠⠀⠉⢉⠛⠒⠢⢤⣀⡀⣠⠠⠤⠤⣲⠦
⠀⠀⠀⡴⠋⣠⠂⠀⠀⠀⢸⠓⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠠⣈⠙⠦⣀⣀⣀⡈⣑⣲⣄⣀⡠⠄
⠀⠀⢰⠃⠸⡅⡀⠀⠀⠀⠈⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⠎⣱⠀⢹⠀⠀⠀⠈⠀⢘⠇
⠀⠀⠀⠳⣄⠈⠛⠦⣄⣀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢁⠀⡠⠊⠀⠀⠀⠀⢀⡬⠶⠋⣠⣿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠑⠶⢤⣄⡈⠉⠛⠲⠤⠤⢵⣤⣄⠀⠀⠀⢰⣦⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣸⣞⣀⣠⣤⡴⠖⠚⠉⢀⣠⢾⣿⣿⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⡦⢤⣄⣀⣀⠀⠉⠉⠉⠉⠙⠛⠛⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⣀⣀⣠⡤⠶⠞⣉⣿⣿⢋⡿⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢂⠀⠀⠉⢹⠻⡛⠓⠓⠲⠖⢶⠶⠶⠶⠲⠶⢲⠒⠒⡟⠉⠉⠝⢇⠀⠀⢀⣀⣩⠥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠰⡄⠀⠀⢷⢄⠀⠈⠀⠘⢄⠀⠀⠀⠰⠂⠀⠀⠀⢰⠇⠀⠀⠁⠀⢀⠀⠘⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⠄⠀⠐⠂⠱⣷⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡀⠀⢠⡇⠑⢄⠀⠀⠀⢻⡆⠀⠀⠸⣇⠀⠀⠀⠀⢰⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⠀⢸⢇⢀⠈⠁⠀⠀⡀⠙⠆⠀⢠⠀⠀⠀⠀⢠⣾⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡜⢨⢯⠀⠀⠀⢲⣧⠀⠀⢠⡄⠀⠀⢂⠀⠀⡛⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠂⠀⠳⡀⠀⠀⠀⠱⡀⡼⠳⡀⠀⠸⣿⢠⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⣾⣄⠀⠀⠸⠧⠀⠈⢱⠆⢈⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢢⣰⠁⠈⠳⡶⠆⠀⠑⣤⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠃⠀⢠⣠⠀⠀⡠⠚⠣⣄⡠⠞⡤⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠢⢔⠁⡰⠛⠀⢀⡠⠈⢇⠀⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⠀⠀⢠⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⣀⠊⣀⡴⣿⣯⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⣧⣄⠀⡀⠀⢤⡄⠻⡄⣿⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢉⠟⡨⠅⡛⢺⡇⡤⢉⡯⢡⠔⠀⠄⡠⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⢦⡲⢦⠏⠀⢻⣿⢠⡟⣋⠀⠀⠠⡶⠦⠄
⠀⠀⠀⠀⠀⢠⣀⠠⠖⠥⣤⣼⣧⣱⡠⡑⣿⣿⣾⣢⡕⠙⠋⠁⠀⣄⢀⣀
⠀⠀⠀⠠⣰⡎⢿⣯⣠⢀⢀⣽⡟⢙⢷⣿⣨⣍⠳⡟⣤⠖⢼⠗⠁
⠀⠀⣀⣶⣮⣿⣾⡿⡿⠦⠆⠀⢿⠀⠁⢿⣿⣿⡗⠻⢋⡡⠂
⠀⠐⠋⠩⣿⣺⣿⣽⠋⠀⠒⠗⠘⢆⣼⣦⢉⣿⡷⢏⡈⠾⢦⣠⠄
⠀⠀⠀⠐⢺⡛⢻⣿⠞⡁⠀⠀⠀⣨⢟⢻⣼⣶⠈⡉⣤⣞
⠀⠀⠀⣈⡟⣽⣷⣿⣷⡡⠀⠀⠀⣌⠸⣏⣿⠙⣧⣷⣹⣯⠴⡯⠂
⠀⠀⠀⣸⣷⣿⣻⣿⣼⡖⠀⠀⢀⡤⢧⣿⣿⣄⣿⣯⣿⠾⣦⠁
⠀⢀⣼⣿⣽⣼⣿⣿⣿⣿⡌⠐⠛⠤⣾⣌⣿⣧⢳⡟⢴⠞⡏⠀⣀
⠀⠉⠁⠈⠉⠉⢉⠛⠉⠀⢀⣀⣐⣲⢻⣿⣿⣿⡌⠇⡄⢸⣿⢛⡁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡡⣾⢹⣿⢻⣡⢹⢱⠀⢹⣞⣿⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣳⢺⢇⢸⢿⠄⣾⡂⡛⣿⣿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠹⣾⢷⣿⣾⢯⠀⣽⣿⢳⣻⢻⣿⡟⣏⢺⢻⡀
⠀⠀⠀⡔⡤⠤⠠⠒⢶⡤⣒⣿⣼⢿⢃⡏⣷⣼⢻⣿⣿⣾⡿⣸⣿⣾⣿⡣⡀⠀⠀⠀⣀
⠀⠀⠀⠈⣿⣀⠜⡡⠊⠉⣿⢯⠉⠹⣿⢼⣿⣿⢘⣹⠟⣿⣿⣿⣿⣿⡿⠋⠉⠉⡋⠿⣽⡷⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒
⠀⠀⠀⠀⠹⢿⢠⠁⠀⣠⣿⣸⣴⣣⠟⣀⠉⡛⣿⣿⣷⡽⣿⣦⣿⣿⠀⣘⢀⡌⠀⠀⡇⢰⢠⡈⣧⠀⡀⠀⣠⠀⢀⢣
⠀⠀⠀⠀⠐⣍⣾⣆⡾⣋⡥⠄⠠⢁⢀⣹⣿⣷⡶⣧⠛⣿⣿⡟⡾⠛⣧⣿⠘⣇⣤⠾⢧⣾⣼⣿⡿⠼⠻⡟⢫⡤⠉⠋
⠀⠀⠀⠀⠸⠫⡟⠁⢹⠁⡀⠈⢳⠈⣶⣆⡧⢌⢥⢀⠀⣈⡙⠡⣷⡍⠑⠐⠊⣿⢀⡳⢿⡿⠟⡻⠦⠼⠦⠀⠓⠃
⠀⠀⠀⠀⠀⠀⢆⢠⣸⣄⠳⣤⠼⢯⡙⣷⣦⡠⠔⠺⠒⠛⠛⠒⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠓⠀⠛⠷⠃⠘⠀⠀⠐

⠀⠀⠀⢀⣴⡞⠓⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠲⠶⣦⡀
⠀⠀⢠⠏⠀⠳⣄⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⣠⡴⠋⢧
⠀⠀⠘⢆⠀⠀⠈⠙⠖⢄⡀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⢀⣤⡶⠟⠁⠀⠀⣸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⡂⢄⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⣀⢔⡪⠟⠉⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣁⠢⡀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⡠⠔⠉⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠈⠑⢄⠑⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⡀⠐⠉⠀⠀⢀⡠⠖⠉
⠀⣠⡤⠶⠒⠒⠒⠒⠒⠒⠛⠓⢄⠀⠀⠀⠙⠻⡉⠀⠁⠀⠀⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠀⠀⠀⡠⠔⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⣦⣄
⣸⠋⠒⠒⠶⠶⠶⠶⠄⠀⠄⠀⠀⠑⠂⠀⠀⠀⢀⡠⣤⠤⠤⠤⠤⠠⠤⠠⠤⠠⠤⠤⠴⠶⠶⠶⢶⡶⠈⠀⠀⠀⠀⠴⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠾⠽
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣄⡸⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢹⣀⣀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⢩⠧⠀⠐⡛⠀⠀⠀⡀⠀⠀⠦⠀⠀⠀⠶⠖⠓⣤⡀⠀⣴⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⢄⠀⢀⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⣒⡒⠒⠂⢚⡿
⠀⢰⡤⡤⠄⠐⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢐⠀⠒⠓⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠁⢘⠁⠀⠀⠈⠉⠉⣉⠀⠀⠀⠁⠀⠀⠬⠇⡗
⠀⠀⢉⣉⡉⢉⡂⠀⠀⢐⡒⠀⠀⠀⠀⠀⢈⣉⠀⣭⠀⡁⢈⣏⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠭⠠⠀⠠⠥⠄⠀⠤⠀⠄⠠⢠⠀⠀⠐⠀⠀⠀⠂⠀⢐⡖⣺
⠀⠀⢰⠴⠦⠀⡀⠀⠀⠀⡀⠀⠨⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⢤⠀⠀⠀⠠⠐⠂⠐⠀⠀⠀⠈⠀⠀⠒⠀⠀⠐⡂⠉⠉⢉⡼
⠀⠀⠘⡒⣒⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠛⠀⠀⠀⡀⠀⠀⠀⢐⠐⠒⠂⠛⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⢐⠀⠀⠁⠀⠉⢉⣁⡀⠯⠴⡇
⠀⠀⠀⢣⣈⡁⠸⠀⠀⠀⢠⠀⢈⠁⠀⠀⠀⡁⠀⠈⡇⠀⠀⠸⠤⠀⠀⣁⠀⠀⠀⢉⠀⠀⠤⠽⠀⠀⠀⠠⠀⠀⡈⠁⠀⠀⢀⠁⠭⠥⠤⠠⠀⠂⠀⣶⣺⠁
⠀⠀⠀⠸⠂⠂⠀⠄⠀⠀⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠠⠤⠀⠀⠒⠀⠀⠀⠐⠀⠒⠂⠀⠐⢲⠂⠈⣉⡜
⠀⠀⠀⠀⢳⣀⡀⠃⠀⠀⠒⠒⠒⠒⠒⠒⠂⢀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠈⡈⠀⠀⠄⠀⠀⠀⣀⠀⢈⠁⠈⠉⣁⠠⠴⠛⡇
⠀⠀⠀⠀⢀⣀⠀⠭⠀⠀⠀⢨⠁⣀⠀⠀⠀⢀⠀⠀⠬⡅⠀⠀⠽⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⢹⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠀⠘⠒⢒⣾⠁
⠀⠀⠀⠀⠀⢳⡆⠠⠄⠀⠀⠀⡄⠐⠂⠀⠒⠚⠂⠀⢀⣇⠀⠀⠘⣢⣀⣈⣤⣤⣤⣤⣀⣀⣈⣩⣀⣀⣠⣭⣭⣭⣥⣤⡀⠉⠉⢥⣿⣄⣀⣀⣨⣨⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠛⠛⠋⠉⠉⠻⣿⣟⠛⠿⢷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣫⣥⣤⣤⣤⣤⣄⣀⣀⠀⢀⣾⡿⠀⠀⠀⠈⠙⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣥⡀⠀⠀⣠⣾⡿⠋⠙⢿⣷⣄
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⠟⠋⠉⠛⢿⣷⣾⡟⠉⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⢀⣾⡿⠛⢿⣦⣄⠀⢀⣴⣾⣿⣿⣷⡄
⠀⠀⢠⣿⠏⠀⠀⢀⣠⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠙⢿⣷⣾⡿⠁⠀⠀⠹⣿⡄
⠀⠀⣾⡏⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⢹⣿
⠀⢰⣿⢁⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⣷⡀⠀⠀⠀⣿⡇
⠀⣾⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣷⡀⠀⠀⢸⣿
⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣷⡀⠀⢸⣿
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢿⣧⠀⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡄⣿⡇
⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠈⣿⣷⡿
⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣁⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢷⣶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠴⡒⣉⠝
⠀⠀⠻⢍⣉⣉⡉⠻⢷⡿⠿⣟⣿⣝⣗⣦⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣶⣫⣿⣿⣛⡿⠭⠥⠿⠗⠒⣲
⠀⠀⡤⠤⠬⠟⠶⢚⣋⣽⡭⣳⣯⣯⣞⡄⣧⠴⠚⠋⠉⠉⠉⠉⠻⢗⠦⣄⣸⠹⣻⢯⣿⢭⡯⣟⣁⠒⠾⠯⢥
⠀⠀⠙⣒⡲⠶⠚⣅⠵⢚⠟⣼⣏⣇⣇⢒⠸⡖⠦⢤⣀⠀⠀⠀⠀⠀⠱⡀⠙⢴⣰⣽⣼⠳⡈⢢⣴⣙⠛⢿⠉
⠀⠀⠈⠳⢶⡾⠞⣱⡶⡏⣠⠋⡿⢸⢹⢻⣰⣮⡆⠀⠈⠙⠢⢄⠀⠀⠀⠐⡀⠈⣿⡏⣏⢳⣈⡢⣷⣽⣫⠉
⠀⠀⠀⠀⠈⠒⢻⣋⣴⡷⣣⡜⢃⡜⡾⡟⡏⢿⠃⠀⠀⠀⠀⠀⠑⠢⢀⡀⣃⣠⠂⣿⢋⢿⣌⣟⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠗⢫⣇⣿⡇⣧⣳⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠞⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡖⠠⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣀⡰⠀⣀⣠⠔⠊⠀⠀⡴⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡒⠚⠛⠫⠩⠂⠀⠀⢀⢜⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠴⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠈⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠔⠒⠒⠒⠒⠦⣄⠕
⠀⠀⠀⠀⠀⣀⣀⢠⠴⠶⣒⡶⠶⣬⣱⡿⠖⢂⣰⣿⣦⠀⢀⣀⣤⣤⣿⣤⣤⡴⠦⣀⣒⠶⠦⠤⠤⠴⠤⠄⢄
⠀⠀⠀⠀⠀⡁⠀⢀⡠⠎⠉⠀⠘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣼⠋⠀⢂⠀⠀⢀⠁⠆⡁⢸
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠐⠀⠐⠃⠀⠀⠈⢄⠉⠁⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⢛⠀⠀⠀⠑⢤⠚⠁⢰⡇⢸
⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠈⠉⠉⡇⠀⠀⠠⠀⠀⠠⠉⠀⠄⠀⠀⠀⠀⡈⠁⠀⣿⠀⠀⠀⠀⠀⡑⠄⠜⢣⠸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⡀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠑⠤⠊⠀⠀⠀⠀⠠⢰⡌⠁⢰⢸⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠆⢸⠘⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠙⠂⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠀⠵⡠⠀⡉⠏⠀⡇⢸
⠀⠀⠀⠀⠀⠧⠀⠀⠀⠠⡀⠀⠀⡇⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠁⠛⠀⠀⠁⢸
⠀⠀⠀⠀⠀⡄⢈⠢⠐⠈⠁⠀⠀⢡⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢂⢀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠢⡇⢸
⠀⠀⠀⠀⠀⠧⠬⠤⣰⠤⠤⠄⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⣧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠓⠒⠒⠤⠤⢭⡤⠎⠁

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⢈⣑⣿⣿⡇⠀⠀⢠⣤⣄⠀⠐⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠖⠀⠘⢀⣤⠟⠀⡀⠀⠀⢺⣶⣄
⠀⠀⠀⢀⣾⣿⡿⣿⣶⣂⡄⢘⣿⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⢠⣤⠄⠀⠀⠂⡠⣿⡿⠋⠐⠿⠀⠽⢿⡉⢉⡁
⠀⠀⠀⠘⠟⡁⠀⣮⠈⢃⣀⣤⣈⠀⠀⠀⠀⠀⠠⣶⣾⣧⠀⠈⠀⠀⠒⠀⠀⠉⠀⡀⠀⠀⠣⠀⠀⠉⠀⠀⠀⠈⠁⠈⠀⠀⠄⢴⣾⣶⣤⡑⠀⠊
⠀⠀⠀⠀⠀⠀⢸⣼⣿⣶⣿⣷⣿⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⡀⠀⡄⠀⡈⠀⠈⣿⣷⠀⠀⡆⠠
⠀⠀⠀⢀⠀⠀⡀⢈⣿⣧⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢻⣴⣿⣶⣷⣿⡟⠀⣀⠧⠖
⠀⠀⠈⠛⠿⠀⠁⠀⠻⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠙⠛⠋⠉⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢀⣀⡤⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣰⡄⠀⠀⠒⠈⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠰⡶⣴⠁⠀⠋⠉
⠀⠀⠀⢸⣿⣿⠄⢠⡄⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⡾⣤⡀
⠀⠀⠀⠈⠙⠋⠀⠈⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣧⡀⠁⠀⠀⠘⡅⣻⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠃⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠀⠀⠀⠀⠀⠀⠀⢾⣷⢸⡖⠀⠳⣤⡽⢀⡄
⠀⠀⠀⠀⠀⠀⡠⠀⠾⠁⠀⣤⣠⠀⢀⠀⠀⠀⠀⢸⡃⠀⠤⢀⠀⠀⠀⠀⠐⡄⠀⠀⢀⣄⠈⡧⣀⢋⡤⠅⠀⠀⠀⠀⢀⠀⢈⡀⢉⠠⣤⡀⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢠⡄⠀⠈⠀⠉⠛⠛⠃⢀⣈⡴⠚⠠⣿⣧⡬⠿⠁⠈⠋⠀⠀⠃⠀⠠⢔⡀⠀⠀⡒⣀⠀⠸⠃⠨⠇⠘⠛⡀⠀⣟⠉
⠀⠄⠀⠀⠀⠀⠀⠀⠋⠀⣴⡶⡴⠾⣷⣶⠀⠀⠀⢀⣾⣴⣿⡋⠀⠀⢰⠃⠀⠁⠀⠀⠠⠀⠳⠀⢠⢶⠀⠀⠀⠀⣦⣻⣁⣺⣿⣤⣶⣶⣶⣄⣁⡆⠈
⠀⠀⠀⠀⠁⠁⣀⣰⢿⣄⠙⣻⣆⠟⢿⣿⡇⠀⣼⣾⣿⢿⣿⡷⡖⠀⢰⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡉⠉⠻⣿⣿⠿⣿⡟⠀⢔
⠀⠂⠀⠀⠸⠏⢉⣤⠂⠁⠽⠀⠀⣮⠑⠡⠛⠂⠉⣿⣿⣿⢿⣷⣳⡤⢾⡄⠀⢠⡤⠀⠸⠆⠀⠀⠀⠀⢀⡄⣀⣰⡿⡿⣻⣤⣤⣼⠃⠀⠚⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠥⠚⠀⠛⢿⢸⣿⣠⠀⠘⡄⠸⠉⠉⠁⣶⣿⣟⠻⠿⢷⡮⢿⣷⣤⣠⡀⣠⣧⣴⣶⣾⣿⡏⡡⠇⠃⢽⠏⣭⣄⠾⠟⠇⠂⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠚⠂⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⠤⠂⠀⠙⢏⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢄⡀
⠀⠴⠋⠉⠈⠁⠀⠀⠀⠀⢀⡷⡀⠀⠀⠀⢀⣾⣽⣿⣿⣽⣇⣻⠿⣿⣆⠀⠀⠀⠀⣠⡞⠥⠀⠤⠤⢵⡀⡉⠑⣄
⡌⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⢟⣽⣿⣹⣦⣝⣧⠀⠀⡸⠁⠀⠀⠀⠀⣠⠎⢈⠓⠮⡈⢆
⡇⠀⣀⡴⠊⠁⠀⠀⢰⠀⢰⠀⠀⠀⠀⣿⣿⣿⢟⣯⣾⣿⣿⡏⣿⣟⣿⣯⠀⠀⡇⠀⠀⣀⠴⠊⠁⠀⡸⠀⠀⠈⢾
⢣⡴⠁⠀⠀⠀⠀⢠⠏⠀⠀⡆⡰⠀⠀⢹⣟⣵⣿⣿⣿⣿⡿⣹⣿⣿⣿⡟⠀⠀⢧⢀⠞⠁⠀⠀⠀⢠⠇⠀⢠⠀⡼
⠀⠣⡀⠀⠀⠀⣠⠏⠀⠀⣼⠔⠁⠀⠀⠀⠹⣿⣿⣿⣿⡿⣳⣿⣿⣿⠟⠁⠀⠀⠈⢧⡀⠀⠀⠀⢀⠎⠀⠀⣈⡴⠁
⠀⠀⠈⠑⠢⠶⠥⠤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣔⣁⣀⡠⠞⠋

⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠲⠶⢤⣤⣄⣀
⠀⢠⡴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠈⠉⠉⠉⠉⠉⠐⠂⡤⡀⠀⠀⠀⡏
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠑⠢⣸⡇
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⠢
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢘⠣⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠑⠂⠤⠤⠄⠠⠚⢎⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⢀⣀⡆
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⠁
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠙⠓⠶⢤⣤⣀⣸⡟⣄⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⢀⡠⠤⢤⡴⢶⡶⠖⠛⡿⢻⡛⠛⠛⢹⠇⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡴⠣⢤⣀⡀
⢏⡀⠐⢇⣀⠀⠙⣦⣎⠀⠀⠙⣦⡔⠁⠀⠀⢱⠄⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠵⣾⠋⢀⣹⠆⠀⢈⡧
⠸⣍⠑⠒⢶⢭⡍⠑⣾⣳⡦⠔⡧⣼⣦⡤⠶⠏⢠⡄⢌⠶⠶⠶⠶⠶⠶⣖⣚⣛⣓⣲⡏⡭⠥⠐⠒⢈⡟
⠀⠈⠳⡄⣠⠿⣄⠀⢀⡿⡁⠀⠀⠈⣿⠁⠀⠹⡅⡼⠁⠁⢹⡽⠁⠀⠀⢻⡴⠃⠀⠈⣷⠁⠀⠀⡠⠋
⠀⠀⠀⠘⢇⠀⠈⣷⡋⠀⠘⢦⣠⠞⠉⢣⡀⣠⠟⢧⠀⢠⠞⠳⡄⠀⣠⠊⠱⡄⢠⠞⠀⢳⣀⡞⠁
⠀⠀⠀⠀⠘⣆⡼⠁⢣⠀⢀⡞⢧⠀⠀⠀⣹⡇⠀⠈⣷⠁⠀⠀⠹⡴⠁⠀⠀⢸⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠹⣅⠀⠘⢦⡞⠀⠘⣆⠀⢰⠁⢸⠀⢰⠋⣆⠀⠀⣠⢧⠀⠀⢀⡞⢇⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠘⡆⢀⡼⢧⠀⠀⠘⣦⠋⠀⠀⢳⠏⠀⠘⢆⣰⠃⠘⣆⢀⡞⠀⠘⡆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⠈⢧⡀⢠⠛⣄⠀⢠⠏⢳⠀⠀⡸⢇⠀⠀⢸⡞⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⡽⢏⠀⠈⡷⡏⠀⠈⣳⡎⠀⠀⢳⣴⠋⠙⣆⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠀⠘⣦⠞⠀⢹⠀⢰⠃⠘⣆⠀⢠⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣿⣄⠀⠀⣧⠟⠀⠀⠸⣀⡞⠈⢦⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠃⠘⣆⡰⠋⢳⡀⠀⢠⠿⡀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⡼⢧⠀⠀⠳⣤⠏⠀⠙⣴⠃

⣿⡻⢿⣛⣿⡟⠛⠛⣛⠛⡛⠛⢻⣿⠛⠛⢟⠛⠛⠿⢛⠛⠿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠉⠀⠙⣛⠩⣉⡈⠘⠂⢶⣦⡀⠋⠀⠠⡜⠀⠐⠂⠁⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢄⠞⠓⠄⡀⠉⠹⢦⠀⠈⣿⢇⠞⠠⡀⠈⠑⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠉⠀⠀⠀⠀⢸
⣿⢸⣿⡼⠤⡀⠐⠖⠛⢧⡀⢛⣠⠒⠀⠂⠀⠄⠀⠘⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠈⠿⠏⠀⣷⡄⠀⣠⣿⡗⠁⠡⠀⠉⠂⢄⠨⠄⢤⠼⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠈⠀⠀⠀⣿⠁⢄⠈⠛⠆⠀⠀⠀⠐⠂⠈⢱⣶⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣠⣄⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⠐⠢⠖⣏⠙⠣⠀⢹⣿⣆⠄⠰⣀⡀⠀⠀⠀⢸
⣿⣠⠄⠀⠀⢦⣤⠁⠀⣸⣷⣴⣿⡄⢳⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣯⠀⠀⢠⣿⠉⠉⢀⣉⢱⠀⠀⢀⣿⡇⠀⠀⠀⢸
⣿⠀⡶⢽⡷⠚⠐⠐⠀⣿⡋⡉⣿⡤⣶⣦⣤⣀⠀⠀⠀⠀⠈⠑⡂⠠⠐⠂⠤⠾⡿⠤⠴⠿⠿⣘⠇⣀⠰⣟⠫⡁⠀⠀⢸
⣿⠀⠀⠘⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠤⢈⢹⣷⠔⠀⠀⠀⠀⠇⠀⠸⠇⣴⣿⣤⣿⣤⠿⠊⠡⠶⠿⢻
⣿⣏⡀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣐⠤⡂⢄⡠⢄⠠⣀⡛⢻⠂⡄⠀⠀⠀⡀⠀⢀⡠⢤⣽⢿⡿⢿⡖⡒⠀⠀⠀⢸
⣿⣒⡭⠭⢐⣒⡠⠥⠄⢀⡀⠀⠀⢀⣀⣨⠷⠼⠓⡛⠋⠉⠉⣀⢈⠀⠁⠀⠀⠀⠃⠀⢸⠀⢸⡇⢸⡇⢸⠁⠁⠀⠀⠀⢸
⣿⢖⣚⣩⠥⠖⣒⣩⡭⠴⠖⠚⡉⠉⠀⠐⢀⠀⠀⠀⠠⢊⠋⠈⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⡇⣾⢈⡀⠄⠀⠀⢸
⣿⣩⡥⠶⠚⠋⠉⠀⠀⠀⠀⠲⢴⣦⡀⠈⠁⠀⠀⠐⠀⠀⠀⠀⣘⣷⠀⠀⠀⠀⠐⠀⠘⠠⠾⣧⡾⠒⣿⠁⣾⣿⡀⠀⢸
⣿⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢠⠤⠀⠌⠛⠃⠀⠀⠀⠈⠿⠀⠀⠀⠀⢠⠀⢠⡄⢦⣾⠁⠀⢀⣶⡮⠀⠀⠐⢺
⣿⠀⠀⠐⠀⠀⢀⡀⠱⣿⠂⠀⠀⠐⠒⠀⠀⠀⠀⠀⢄⠈⠀⠀⡀⠀⠈⠀⠀⠀⠠⠀⠊⠀⣠⠛⠆⠀⣸⡿⠵⡧⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠰⠾⠿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠘⢸
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⠶⠶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣍⠙⠻⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠈⣹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣦⣤⣤⣄⣿⣧⣀⣤⣴⣾⠟⠉⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣿⡟⠉⠉⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣄⣀⣀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡾⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠸⣿⠉⠉⠉⠙⠛⠛⠿⢷⣶⣼⣿⡀
⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡇
⠀⠀⠀⠀⢸⣿⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣼⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠉⠉⠁⢸⣿⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢹⣷⡀⢰⣿⠁
⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⡏
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⢀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣴⣿⢃⣀⣠⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠶⠶⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⡀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⠖⠉⠉⢵⠀⠀⠀⠀⠉⠂⠙⠁⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡟⠀⢢⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠛⣿
⠀⠀⠀⠀⠻⣷⠆⠰⠸⠧⠤⠠⠤⠤⠐⢊⠲⢮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠴⣏⣋⣀⣈⣡⡿⣿⠗
⠀⠀⠀⠀⠀⠙⢶⣤⣀⡄⠀⠀⠐⢀⣤⣥⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠛⠀⠀⠀⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡹⣤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡿⠿⠿⣿⡿⠿⠿⢿⠿⠿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢉⡀⠲⠂⠀⠉⠀⠀⠠⠀⠈⠀⢡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣑⢰⠄⠀⠉⠀⠀⡀⠀⠈⠀⢡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⣄⣀⡀⣋⠀⣀⣀⡄⣂⡰⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣠⣾⡟⠛⠙⠻⣟⣷⣦⡀⠀⠀⣠⣶⠟⠋⠙⠻⣟⣳⣦⡀⠀⠀⢀⣴⠾⠛⠉⠛⢯⢻⣶⣄⠀⠀⠀⠀⠐⠒⠦⣬⡇⣀
⠀⠀⣼⣯⠉⠉⠙⠓⢒⣻⣧⠽⣷⠀⣰⡏⠉⠉⠙⠓⠒⣛⣧⠽⣷⡀⢠⣿⠍⠉⠉⠓⠒⢚⣻⡤⢿⣆⠀⣀⡤⠶⠖⠚⣩⠿⣧⡶⢄
⠀⠀⣿⡇⢀⣠⠴⠚⠉⣡⢾⡟⣿⡇⣿⡇⠀⣠⠤⠒⠋⢡⠾⣟⣾⡇⢸⣿⠀⢀⡠⠔⠚⠉⡴⢿⢳⣿⠀⠁⠀⠀⢠⡞⠁⢸⡏⢳⡀
⠀⠀⢿⣿⡋⠀⠀⠀⣰⠃⠀⣷⣿⠁⢻⣿⣏⠁⠀⠀⢠⠏⠀⣿⣿⠃⠸⣿⣞⠉⠀⠀⠀⡼⠁⢸⣼⡟⠀⠀⠀⡴⠋⠀⠀⢸⠀⠀⠇
⠀⠀⠈⠻⣿⣦⣄⣴⣋⣤⣾⠟⠁⠀⠀⠻⣿⣷⣦⣤⣯⣶⣿⡿⠃⠀⠀⠙⢿⣷⣤⣀⣼⣡⣤⣾⠟⠀⠀⠀⠈⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⢄⣀⣠⢀⣀⣀⣀⡠⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⣵⠟⠁⠉⠈⠙⠩⠿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⡴⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣫⣿⣦⡀⠀⠀⠀⠘⣿⠀⠀⠀⣸⡏⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢨⣿⣿⠙⢿⡄⠀⠀⠀⣿⢀⣀⣤⣿⠶⠶⠞⠛⠛⠋⢫⡽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣼⣿⣯⣤⡞⢻⣆⣤⠾⣿⠋⠉⠀⣿⡄⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣿⠀⠀⢹⡆⠀⠀⠘⣷⡀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠸⣿⡀⠀⠀⠈⢻⣦⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⢠⣴⡴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠪⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠄⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⡠⠄⠢⢄⡈⠉⠢⡄⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⣷⣮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⠊⠀⠀⠀⠀⠈⢢⡀⠈⢦⠀⡠⠴⢿⡀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢀⠇⠀⠀⢀⠄⠀⠀⠀⠰⡄⠀⢫⠀⠀⠀⢑⠀⣀⠤⠴⣿⠃⠀⠀⠀⡠⠂⠀⣠⠔⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠀⠙⠛⠋⠐⠂⠄⣀⣹⠘⣧⠀⠀⠀⢡⡀⠘⠆⠀⠀⢈⡾⠁⠀⠀⠀⡇⢀⠔⠁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡽⠂⠀⢀⠘⢃⠀⢺⠀⢠⠞⠀⠀⠀⠀⢠⡕⢡⡶⠞⡡⠔⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢒⣿⡆⢙⠀⠰⡆⠚⠒⣶⡄⠀⡠⢋⢔⢟⠅⠊⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡊⡄⠁⠸⠃⠀⣃⠀⠀⠀⢠⢜⠕⢕⡵⠁⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠁⠀⠀⣀⠄⠂⠀⢀⠀⠀⠀⠀⠰⡆⠀⠉⢀⡄⡀⣸⡣⠚⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣠⠞⡇⣸⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠔⠈⠉⠀⠀⠛⠀⡀⠀⠀⠀⠀⣇⠀⠸⢆⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⣤⠖⠁
⠀⠀⠀⠀⢠⠇⢀⣷⠃⢀⠄⠀⠀⠀⠀⡇⢠⠀⣰⠃⢀⡠⠖⠀⠀⠀⡄⠄⠑⠀⠀⠀⣇⠀⢸⠀⢣⠀⠀⠀⢈⣦⣠⡴⠋⢁⡜
⠀⠀⠀⠀⢸⡄⠐⢿⢀⠁⠀⠀⠀⠀⣰⣤⢼⡒⠛⠒⠺⡀⠀⠀⢠⠂⠀⠀⠀⠈⠀⠀⣞⡀⢛⡀⢸⠀⠀⢂⣠⠞⡛⢀⣠⠎⡁
⠀⠀⠀⠀⠀⢳⣀⠘⠛⢄⡀⠀⢀⡾⠁⠀⠀⠋⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠩⡇⠀⠀⣷⡸⠷⠓⠉⠁⣀⣴⠊⠱⢨
⠀⠀⠀⠀⠀⠘⣏⡷⢤⣀⡉⠁⠺⠧⠄⣀⣀⠀⢀⠀⠀⢀⠀⠀⣇⢀⢀⣀⡀⠤⠤⠔⠓⠐⠘⠁⠀⣀⡤⠔⡊⠁⠄⠀⡈⠸
⠀⠀⠀⠀⠀⠀⣷⢸⡀⢹⠛⠛⠶⠤⢤⣤⣀⣀⣉⠀⣉⠁⠈⡁⠀⣀⠀⣀⣀⣀⣠⣤⣇⠠⠟⠚⠉⠁⠀⠀⠅⠀⡁⠀⢂⡇
⠀⠀⠀⠀⠀⠀⢹⣝⡆⠸⡅⠂⢹⠀⠀⠀⡁⠈⠉⠩⠉⠉⠉⠛⠉⠉⠉⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢈⠱
⠀⠀⠀⠀⠀⠀⠘⣧⢭⠀⡃⠀⠐⠄⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡜⡄⢸⡀⠀⡁⠀⠀⠁⠀⠀⢀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡈⡃⠀⠠⠀⠀⢀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢸⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠸⡄⠨⣂⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠂⣔⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣑⡄⢳⡀⠀⢡⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⣠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠤⣬⣆⣀⣨⠀⠀⠤⠀⠀⠀⠀⣀⣂⣠⡴⠷⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢳⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⠉⡄⠉⠋⠉⠙⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣦⢤⣤⣾⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠘⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⣶⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⠿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠆⢸⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⢻⣿⠏⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢰⢆⠘⣯⠹⠀⡆⢐⣸⣿⣿⣿⣶⣄⣠⣀⡀⢴⣾⣵⣿⣿⠿⠒⠉
⠀⠀⠀⡷⢾⡿⠀⢺⠔⡠⡀⢺⡿⣷⣿⠿⢾⠬⡽⣿⣿⠿⡿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡄⠠⡄⡄⠠⣤⢠⡄
⠀⠀⠀⠀⣻⣷⡄⣼⠘⠉⠉⠙⠻⣿⠀⠀⠀⠀⠀⠁⠈⠀⠁⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠁⠀⠉⠉⠃⠚
⠀⠀⠀⠈⣼⣏⠳⠄⠀⠀⠀⢨⣿⣿⡄⢀⣠⡀⣀
⠀⠀⠀⠀⠀⠘⢶⣀⠀⠀⠀⠀⠈⠁⠛⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⢠⠏⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧
⠀⠀⠀⠀⡞⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠈⣆
⠀⠀⠀⡸⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠘⡄
⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢳
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⢿⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⢸⠈⢻⣦⡀⠀⠀⠀⠈⣿⡄⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠘⡆⠀⠙⢿⣦⣄⣀⣀⣸⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⢱⠀⠀⠀⠉⠛⠿⠿⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣴⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏
⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⣤⣴⣶⡿⠿⠛⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠻⡛⠋⠉⠁⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⠶⠿⠟⠋⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣰⣾⠟⠉⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⣼⠟⠁⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣀⡀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣤⣄⣀⣀⣀⣈⣙⣳⣦⣤⡤⠤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⠶⣶⣶⡶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⡇⠀⠀⠀⠘⡄⠀⠀⠀⢰⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⢠⠼⠤⠀⠀⢠⡇⠀⠀⠀⡭⠇⠀⠀⠄⣾⠀⠀⠀⢀⣧⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠂⠀⠀⠀⠐⡇⠀⠀⠀⡗⠂⠀⠀⠀⣿⠀⠀⠀⠘⠂
⠀⠤⠄⠄⠀⠀⣀⣀⣀⣀⠰⣾⠀⠀⠀⢰⣀⣀⣀⣀⣨⡇⠀⠀⠀⣧⣄⣤⣀⣀⣿⠀⠀⠀⢸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⣇⠀⠀⡄⡁⠉⠉⠀⠀⢸⡃⠀⠰⠀⠉⠀⠀⠀⠈⡇⠐⠀⠘⠃
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠠⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠒⠂
⠀⠀⠙⠂⠀⠀⠭⠩⠭⠉⠉⢽⠋⠙⠛⢻⠛⠀⠀⠀⠘⡏⠙⠙⠛⡟⠒⠒⠒⠐⣿⠉⠻⡏⠛⠃⠒⠒⠒⠛⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠀⠀⠀⡅⠀⠀⠀⠀⣻⠀⠀⠀⢀
⠀⠒⠒⠒⠒⠤⠤⠤⠤⠤⣤⣿⠀⠀⡀⢠⣤⠤⠤⠤⣤⡇⠀⢀⠀⣥⡤⢤⠤⠤⣽⣀⢀⠀⢼⡖⠶⠶⠶⣖⡒⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢹⠀⠀⠀⠀⢸⡆⠘⠀⠀⣦⠀⠀⠀⠀⡇⠀⠀⠀⣏
⠀⢀⣀⣀⣀⣀⠀⢀⣀⠀⠀⢀⣀⣀⣀⡀⣺⠀⠀⠀⢰⣁⣀⣀⣀⣸⡇⠀⠀⠀⣇⣀⣀⣀⣀⡇⢀⠀⢀⣠⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢿⠀⠋⠈⠙⠛⠀⠀⠁⠉⣏⠀⠁⠉⡋⠁⠉⠁⠈⣽⠉⠸⠁⢩⡉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢘⠀⠀⠀⠀⠀⡗⠀⠈⠀⠡⠀⠀⠀⠀⢽⠀⠀⠀⢠⠉⠁
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣾⠀⠀⠠⠴⣶⠖⠒⠒⢶⡧⠄⠀⠤⠗⡖⠒⠒⢒⡾⠄⠐⠄⠼⡟⠉⠉⠉⠫⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⢠⡇⠀⠀⠀⠠
⠀⠀⠠⠤⠄⠀⠤⠤⠤⠤⣤⣤⣤⣤⣤⣄⣼⠀⠀⠀⢰⣀⣤⣤⣤⣤⡇⠀⠀⠀⣧⣤⣤⣤⣬⡇⠀⠀⠀⠶⠶⠶⠶⠶⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠀⠀⠀⢸⡇⠈⠀⡁⠃⡇⠀⠀⠀⢘⢸⠛⠛⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠈⠇⠀⡇⠃⠃⡇⠀⠀⠐⢸⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠃⠀⠁⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠐⠒⠉⣁⣀⣀⠙⠹⠿⣿⡷⣾⣵⣤⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣀⣠⢤⡞⠉⠉⠙⡇⠀⠀⠈⠁⠛⠘⠛⠁⠀⠀⢀⣽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢡⠎⢀⣘⡁⠀⠀⠀⠀⠀⠀⢦⢆⣠⣶⣶⡄⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⡦⣴⣿⣿⣷⣿⣷⣿⣿⡆⠀⣴⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣷⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⢿⡟⠋⠁⠀⠀⠀⠀⢻⣿⣿⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠙⠛⢾⣿⣮⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⢀⣤⣼⣥⣄⠻⡿⠀⣴⣿⣿⣦
⠀⠀⠀⠀⠀⣴⣆⣾⣷⣄⡀⠘⠻⠿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⢀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣿⣿⣿⡏⠛⢛⠛⠉⠀⠀⠀⠀⣧⢸⠀⢴⡀⣾⣴⠸⣄⠀⡧⠀⠦⣄⢸⡇⠀⠀⣸⣷⠁⠀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠈⢻⣿⠁⣠⣼⣦⣄⠀⠀⠀⠀⠁⠈⠈⠀⠁⠉⠈⠀⠁⠀⠁⠀⠀⠁⠈⠁⠀⠐⠟⠃⣴⣾⣽⣿⣽⣿⡻⣆
⠀⠀⠀⠀⠀⠀⠛⠁⠸⣿⣿⣿⣿⢢⣿⡄⠀⠀⠀⠀⠀⣿⠀⡇⠘⡆⣿⢸⡇⠀⠀⠀⠀⠀⢀⠃⢠⣿⠿⠋⠈⢿⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣀⠙⠉⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⢀⠊⠀⣴⣷⣦⣾⣷⣠⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣴⣿⣿⣿⣷⣿⣷⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢇⣤⣼⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣬⡷⡿⠋⠘⣿⣿⣿⡟⣿⣼⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠿⢿⣇⠻⣿⣿⣿⣿⠇⣯⡿⠋⠀⣀⣤⣤⠀⠀⠀⠀⠀⠘⠛⠋⠋⠀⢰⠁⠈⠙⠻⣅⠘⠙⠨⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠏⠻⠿⠛⠛⢛⣡⣴⣿⣿⡿⠃⠀⠀⡀⠀⣄⠀⠀⠀⠀⢰⣿⣧⠀⣶⡀⠘⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠟⠀⠀⠆⠀⠉⠀⠘⢖⡀⠀⣠⣾⣿⣿⠀⢭⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⠟⠁⠠⢤⡀⠀⠐⠀⣀⠔⠋⢀⣾⣿⣿⣿⣿⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠆⢘⡤⠈⠛⠃⠀⠘⢿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣤⠄⣀⣀⣀⣀⡀⣀⠀⣠⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⠛⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⢸⠀⣿⢦⡾⣇⠀⣧⢀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡆⢹⠀⠀⢻⡆⣿⠉
⠀⠀⠀⠀⠀⠐⠛⠗⠀⠀⠉⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠘⠃⠀⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠕⠈⠉⠉⠓⢌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡤⠤⡤⠤⡮⠀⠀⠀⠠⠀⠬⣮⣇⣤⡤⢄⡠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⠔⠁⢀⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣆⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢮⠥⡽⠀⠀⠀⠀⠀⠀⠀⠀⠮⡅⡽⠂⠈⠢⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⣄⢾⣼⡷⠀⠀⠀⠀⠀⠀⠀⠰⣞⣐⡳⠀⠠⠔⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⡎⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⡰⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛⠛⠒⠒⠒⠂⠀⠀⠀⠐⠓⠓⠒⠓⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⣿⠙⢱⡎⢹⡆⠀⠀⠀⠀⠐⠒⡶⠒⠂⢶⢲⠀⠀⢀⣶⡀⢰⡀⢰⡇⢺⠉⠀⣴
⠀⠀⠀⠀⠀⠀⢿⠀⠸⣇⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⣄⠀⢼⠗⢷⠀⢳⣼⠁⢸⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠈⠀⠛⠀⠈⠀⠀⠋⠀⠘⠋⠁⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠖⣹⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣰⢏⣬⠁⣴⢿⢆⣄⣴⡆⢀⡦⢀⣴⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠾⠋⣾⢃⣼⠃⣠⣿⢣⡟⣠⡿⢁⣾⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠳⠋⠿⠜⠉⠁⠘⠛⠀⠛⠁⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠘⠃⠚⠃⠀⠛⠂⠘⠓⠀⠛⠃⠈⠋⠀⠘⠁⠈⠛
⠀⠀⠀⠀⢀⣀⠀⢈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠉⠠⢀⠀⠀⠀⣼⢿⣂⡤⠶⢚⠶⡄⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⣤⣼⢺⣅⣿⣴⣽⣤⢻⣒⣗⠁⢀⢳⡄⠀⠀⢠⠊⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠉⠉⢉⠛⠀⣄⣀⡠⢠⠏
⠀⠀⠈⠀⢶⡃⣹⣿⣿⣿⣽⣾⣈⣿⠽⣿⠿⣿⣶⡀⠀⠀⢤⡾⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢠⡄⢄⣰⣆⣐⠞⠀⣰⠟⠉⢠⡃
⠀⠀⠀⠈⠀⠝⠻⠿⠿⡿⠿⡁⠀⠁⠀⠀⠀⡄⠈⢡⣀⣤⡿⢲⡄⠀⠀⠀⠀⣆⣈⣉⡏⢠⡃⣠⡜⢯⣿⣿⣰⠎⠓⠀⢀⣰⡃
⠀⠀⠀⠀⠀⠀⠈⣶⣤⣈⣣⣐⣀⠀⣀⣈⡉⣉⣉⣉⣉⣤⣴⡞⠀⠀⠀⠀⠀⠹⣉⢺⣧⢿⡟⢷⣷⡈⣿⡟⣟⣅⣤⣾⡻⠋⡁
⠀⠀⠀⠀⠀⠀⠀⢱⢦⡸⢭⣉⠙⠉⡙⠛⢏⠩⡍⢛⠳⢅⣍⠃⠀⠀⠀⠀⠀⠈⣹⠽⢞⣮⢹⠨⡏⢛⡻⢿⣿⠾⠤⢿⣤⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣻⣓⠾⢿⢦⠾⠆⢿⠶⠶⣙⢛⡷⠁⠀⠀⠀⠀⠀⠀⠀⢾⣒⣿⢤⢺⣘⡇⡤⢆⢘⠏⢿⢶⡿⣻⢶⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠾⣛⣫⣥⣑⢯⣭⣙⡿⣮⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⢽⡮⣗⢊⣯⢸⠂⣯⣸⢲⠦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠘⠡⠮⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡄⠀⠀⠀⠰⡴⠤⠄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⣾⡻⠾⠿⢛⣿⡿⠿⢶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠆⣤⠁⠱⢀⣠⢄⢰⠇⠀⠐⡄
⠀⠀⠀⠀⠀⠀⢜⠛⠆⠶⡟⢦⣚⣚⣒⣳⣂⣘⣻⣥⣽⠿⠟⢻⡆⠀⠀⠀⠀⢶⣶⣾⡞⢠⡗⢋⣅⢱⡊⠱⠖⠳⠄
⠀⠀⠀⠀⠀⠀⠀⡿⠶⣤⣵⣤⣤⣤⣤⣠⣌⣤⣤⣤⣤⡶⣶⡟⠀⠀⠀⠀⠀⠘⣲⣉⢿⢻⣙⠿⣿⣦⣿⣤⣀⣸⡧⣴⣲⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣳⣔⡲⢄⡒⠁⣍⢉⡋⠰⠦⣭⢁⡲⡦⠁⠀⠀⠀⠀⠀⠈⢸⡞⣹⠹⢰⡃⡧⠁⠹⢹⣿⣋⠐⣻⣗⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢫⡽⢭⣛⣟⣒⣛⣃⣚⣛⣛⢍⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠛⣯⡵⢲⣽⠤⣗⠂⣣⠤⡃⣹⠫⠟⠯⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢭⠱⠶⣼⠳⣶⣬⠗⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠇⠫⡁⢼⠐⡅⠷⣈⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⡀⠤⢦⡤⠶⠖⠢⠀⠲⢺⣶⣖⡲⠿⠗⣒⣶⢺⡦⣴⣤⣶⣶⣶⣤⣠⣠⣤⡀⣨⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠀⢙⣾⣁⡲⠖⢛⠓⡂⠀⠈⠩⠈⠁⠀⠩⠉⡛⢣⡧⠨⠤⢼⢽⣛⡶⠷⣮⣭⡟⣬⣟⠿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⣮⠞⣦⣴⣝⠋⠩⠭⠤⠤⠿⠯⠤⠭⣥⣀⣀⣬⠍⠚⢽⠒⢀⢠⣬⡈⣽⣻⣿⣿⣽⣿⣶⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠸⣉⣘⠐⠶⠦⢛⠓⠶⠶⣶⢞⣒⢒⠒⠒⠲⠖⣲⢆⡒⠒⠚⠋⠹⠶⠖⣍⣉⠁⣤⡈⠉⣽⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢾⣿⣋⠐⠨⠓⢂⡷⠄⣈⠠⣭⠽⠓⢲⠌⠁⠚⠦⠿⢛⡋⠡⠤⠥⠶⣛⣋⠁⠀⡤⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⣭⣃⠽⠀⠈⠙⡒⠒⠂⢈⡍⠒⡒⠒⠒⠒⠋⠨⠉⠉⠉⣉⠂⣀⣀⠐⠆⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠬⠥⡀⠁⠡⠂⠐⠂⣒⠒⠀⠐⡂⠒⢀⡬⠁⣀⠀⠉⠀⠠⠀⠠⠰⡞⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⠕⠩⠭⠥⢔⣒⣒⡐⠤⠤⣠⣤⠤⠀⠁⠄⠨⠍⢀⡐⠂⢄⣽⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠨⠅⠡⠭⠤⢀⡐⣒⡊⠐⠒⣒⠂⠀⠂⠀⠨⠁⡀⡂⣈⣜⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⣀⡦⠄⠀⠤⡀⠒⠀⢀⣀⡀⠈⢂⠠⠜⡀⠀⠚⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠰⠄⠒⠛⣷⠉⠉⠉⠉⠈⠁


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

⠆⠙⠺⣿⡄⠤⠀⢤⠁⣀⠀⢻⠇⠀⢀⠀⠀⠉⠀⠈⠐⠀⠀⠀⠈⢰⣧⡀
⠀⣠⣄⡀⠀⠖⢦⡀⠀⢻⣧⢨⠀⠈⠃⠄⢀⠀⠀⠀⠐⢀⠐⢀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠰⣦⠀⣃⠀⠀⡤⠷⡄⠨⠇⡡⠠⠄⠀⠀⠉⢱⣤⡄⠀⠀⠈⠀⠈
⠘⢿⠟⠃⣷⡀⠀⣀⣾⠖⠑⠁⠐⠄⠀⢀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠐⠀⠀⢻⠃⢄⠙⠻⠀⠀⠀⠀⠐⠈⢳⣤⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⡀
⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠉⣶⣶⠂⢶⣦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⢩⡦⠄⠂⠰⢟⡓⠀⠈⣶⡀
⠀⢀⡤⠀⠀⠠⢄⢐⠀⢀⣾⣥⣿⡇⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣉⡀⠀⣾⡟⠀⣠⣾⢮⣇⠀⠠⠿⠁
⠀⠀⠟⠒⢹⠖⠛⠐⠀⢸⣿⢉⢹⡷⠶⠷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠠⠀⠀⣇⠀⣷⣀⣿⣠⡧⠐⣠⣤⣴⠶
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⠇⠀⠀⠀⠀⠀⠀⣀⢀⣈⢥⡿⢿⠗
⡲⠭⣂⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡒⢄⡢⢔⠠⣐⠤⣀⣄⡨⠶⠖⠚⠛⠉⢉⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢸⡇⢸
⡭⢵⣒⡪⠥⣒⡂⠥⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣽⠦⠟⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⢁⡂⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⣟⡀⣠⢀⠄
⣚⡭⢖⣚⡭⠔⣒⠭⠔⣂⠩⠄⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠠⢴⣦⡀⠀⠀⠀⣀⣀⠀⠀⠀⣽⡈⠀⠀⠀⠁⠀⠒⠚⠓⡾⠋⠹⠐⠿⠟⡀
⠶⣚⡭⠴⣚⡭⠴⣚⣩⠴⠒⢋⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⠃⠄⠀⠀⠈⠁⡀⠀⠀⠁⠀⠀⠀⠀⠂⠀⡢⠘⠋⡅⠀⠀⣿⡇⠀⠀⠂
⣋⡥⠖⣋⡥⠶⠛⣉⠤⠀⠉⠀⠀⠀⠀⠁⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⣀⣤⡀⠈⠀⢀⠀⠂⠀⠀⠘⠋⠘⠛⠀⢠
⣥⣶⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣐⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠄⠀⠀⢀⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⡄⠀⢀⣄⣀⡀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣷⣠⣤⡤⠾⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⡂⠇⠀⠀⣩⡟⠁⠉⠉⠛⠛⠻⠿⠿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⢀⣀⠤⠒⠛⡅
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⣼⣿⣿⣧⡀⠀⠀⢸⣇⠀⠀⠀⢀
⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠈⢹⡿⠿⢿⠷⠀⠈⣿⡀⠀⠀⠘
⡟⠉⠀⠀⢹⠘⢁⠘⠉⠀⠂⠀⠀⠀⢨⡇⠀⠀⢹⣿⣷⣼⠀⠀⠀⣷⠀⠠⠀⠀⠀⢿⡄⠀⠀⢀⣁⢀⡀
⣷⣶⣷⣶⣾⣿⣷⣦⡄⠀⡇⠀⠀⠀⢸⡇⠀⢀⣀⣙⣿⣿⡇⠀⠀⣿⣆⣀⡆⡀⠀⢸⣷⠒⠋⠉⢹⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠳⣆⢤⣠⠤⢔⢂⣰⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠠⠀⡀⢀⠠⣄⣠⣤⣿⡚⡟⢁⡰⡎⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡡⠒⠉⢈⠹⠎⠉⠀⠀⠙⢾⣥⣹⡀
⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢢⣴⠒⠒⠿⠋⠑⠄⠂⠙⣿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠤⠄⢢⡀⠇⠀⡰⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠉⡆
⠀⠀⠀⡀⢠⠔⠚⠒⠒⠒⠒⠻⠟⠀⠘⠷⠯⠤⢒⠷⢾⣶⣦⠢⣑⡀⠀⠴⠀⠐⠄⠀⠀⠈⣴⡠
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠄⠀⢈⠏⠀⠀⠀⠀⠀⠐⣄⠀⡔⠜⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢸⡄⠀⠀⠐⠒⠖⠙⠐⡥⠤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢸⠄⠀⠀⠀⠀⠀⠀⢆⠸⡐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠸⠀⡀⢀⢀⠀⢀⠠⢸⢐⠌
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣷⠶⠤⠤⠬⠠⠄⣊⡜⠋
⠀⠀⠀⠿⠦⢤⠤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢀⢒⠂⢄⣔⣵⣷⣭⠨⠤⠴⠚⠉⠀⣀⣠⡠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠃⠒⠒⠻⠚⠛⠋⠋⠁⠀⠠⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣤⣤⣤⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠄⠀⣠⡶⠛⣏⣠⠊⠁⠀⢀⣩⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣠⠴
⠀⠀⠀⠀⣴⣋⣠⣤⡼⢽⣖⣒⠚⠉⠀⠀⠈⢷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠐⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠆⢰⡏⠁⠀⡼⠀⠀⢀⠈⠉⡒⠦⣀⠀⠸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⠔⠀⠀⢀⠴⠚⠉
⠀⠀⠀⢸⣇⡴⠚⡏⠉⠓⢤⡀⠀⠀⠀⠈⢣⢀⡇⠀⠉⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠁⢻⡄⠀⣇⠀⠀⠀⠹⡄⠀⠀⠀⢀⣿⠃⠀⠲⡀⠀⠀⠀⠀⠀⢁⡀⢀⡴⠀⠚⣡⠞⠁
⠀⠀⠀⠀⣆⠻⢦⣘⡄⠀⠀⠀⢳⠀⢀⣠⡞⠁⠀⢀⠀⠙⣆⠀⠀⠀⣠⠏⠀⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠉⠛⠲⠾⠶⠶⠛⠋⠁⠲⣄⠀⠀⠳⡄⠘⠆⠀⣰⠃⠀⠀⡤⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠒⠒⠀⠀⢦⡀⠀⢠⡀⠘⠆⠀⠰⠃⠀⠀⡼⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠓⠀⠀⠙⠆⢀⡞⠰⣠⠎⠀⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠓⡠⠀⡀⣆⠀⠉⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⠈⠠⠈⣘⠡⢚⣡⢠⠄

⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢳⡰⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣅⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⠀⢀⢣⡱⡀⣔⡧⠀⠀⢀⢀⠤⠀⠀⢀⠊⠀⠈⡆⠀⠀⠀⡔⡄⢰⠁⡰
⠀⠀⠀⠀⠐⠄⠐⢆⡳⢼⠣⠊⠀⠒⢰⠟⠃⠐⠫⡄⠀⠀⢀⠇⠤⠤⠤⡣⢴⡞⠋⢤
⠀⠀⠀⠀⠀⠀⢈⠬⠭⠦⠤⢄⡨⢱⡆⠀⠀⠀⠀⠘⠀⢰⠁⠀⠀⠀⠀⢰⡂⢤⣈⠀⢶⣀
⠀⠀⠀⠀⢠⠊⢁⠄⠒⠀⠉⠜⠓⠟⠋⢅⠒⢄⡠⠊⠁⣘⠶⠒⠐⠢⡔⠊⠉⠙⠣⠛⣠⠝⢢⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⡇⠠⠁⠀⠀⡐⠁⠀⠀⠐⡀⠀⡕⠉⠁⠄⠘⠠⡀⠀⠀⠀⠉⡒⢄⢀⡤⠃⢳⡀⢀⢠⠯⠃⢀⡀⠤⠄⢒⡈⠬⠄⠒⠈
⠀⠀⠀⠀⢇⠃⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠡⡀⠀⠑⠀⠀⣀⠀⠐⠐⢊⠇⠘⡎⠀⠀⡼⠬⠃⣘⣨⣭⠤⠶⠌⠉⠐⣒⡂⠩⠥⠨⠘
⠀⠀⠀⠐⡭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣬⣥⠭⠉⠐⠐⠒⠀⠉⠁
⠀⠀⠀⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠀⠠⡌
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠐⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠐⠒⠀⠀⠠⠄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣐
⠀⠀⠀⠀⠀⠀⠀⢀⣵⣤⢤⣤⠀⠀⠀⠐⠒⠀⠀⠉⠀⠀⠀⢀⠀⣀⣀⠀⢤⠤⡜
⠀⠀⠀⠀⠀⠀⠀⣾⡁⣷⡔⣹⡦⠤⠄⠐⠂⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣸⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⠴⠖⠒⠦⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣁⣠⠤⠦⠤⣤⣀⣙⡆⠪⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⢔⢄⣠⣤⣴⡶⡟⣷⠾⣛⣽⡿⠶⢖⣿⣷⠲⠶⢶⣶⣾⣿⣬⡶⠮⣁⣾⣶⠶⠶⠴⠶⡶⢦⡀⢠
⠀⠀⠀⠀⠀⡁⣿⣀⠀⡠⠜⠉⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢰⠏⠁⢂⠀⠈⠉⢐⣐⠀⣷⢀
⠀⠀⠀⠀⠀⠀⣗⢠⠋⠀⠀⢐⣀⣘⡃⠀⠀⠡⣈⠁⠀⠀⠀⠀⠀⠀⠀⣂⣀⣘⡇⠀⠀⠑⢄⠊⠈⣿⠐⡏⢸
⠀⠀⠀⠀⠀⠃⣼⠁⠀⠀⠀⠈⠀⢸⡇⠀⠀⠂⠀⠀⢊⠀⠀⠀⠀⠀⠠⠁⠀⡸⠄⠀⠀⠀⠀⣑⠰⠹⠀⣿⢸
⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢱⠈⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡆⡇⠀⠈⠶⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⢑⡀⢀⠀⢤⠂⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡂⢻⠄⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠂⠀⠈⠑⠲⠆⠀⠀⢀⡇⢸
⠀⠀⠀⠀⠀⡃⣧⠀⠢⡀⠐⠃⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⢀⠀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠈⣷⢸
⠀⠀⠀⠀⠀⠃⢿⣐⣡⣈⣦⣤⣄⣀⣧⣀⡀⠀⠀⠀⠀⠀⠚⠃⠈⠁⠀⢸⠀⠀⠆⠀⠀⠀⠀⢀⠀⣹⣤⡟⢸
⠀⠀⠀⠀⠀⠠⠲⠠⠄⠘⠐⠀⠉⠘⠅⠐⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠺⠦⠴⠗⠒⠶⣤⣤⣥⡼⠋⠁⠖⢸
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠀⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⡇⠀⣤
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠐⢛⡇⠀⠀⠀⢘⠉⠉⠀⠀⠈⣿⠀⠀⠀⠀⡇⠀⠁⠀⠁⢿⠀⠀⠀⠀⡞⠛⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⢺⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠻⠇⠀⠀⠄⠜⡶⠒⠒⠒⢶⠿⠀⠀⠀⠠⢷⠖⠒⡖⠒⣾⠀⠀⠀⠀⢲⡖⠒⠖⢲⡆⠀⠀⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃
⠀⠀⠀⠀⢠⣄⣀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⠀⠀⠀⠀⠀⣀⣀⣀⡀⣸⠀⠀⠀⠀⣆⢀⣀⣀⣀⣈⡇⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢸⡏⠉⠩⠉⢹⠙⠀⠀⠀⠈⣿⠉⠉⠉⢹⠋⠁⠀⠀⠀⢻⠉⠉⢩⠉⠛⠁⠚⠁⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠠⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠄⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠤⠤⠤⠤⢤⣄⣀⣀⣠⣼⡇⠀⢀⠀⢸⣠⢤⠤⠤⣤⣼⠀⠀⡀⠀⣧⡤⣤⡤⠤⣼⡆⣀⣀⣠⣶⠶⠶⠶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⡃⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⡀⠀⠀⠀⢸⡆⠀⠀⠀⡟⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠒⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠁⠀⠀⠀⢸⠇⠀⠀⠀⢉⡈
⠀⠀⠀⠀⠩⠭⠭⠭⠭⠭⠶⠶⠶⠖⢶⡟⠛⡟⠛⢒⠿⠄⠀⠀⠀⢿⠉⠋⠛⠻⠿⠤⠀⠀⠀⢳⡖⠓⡛⠙⠛⠒⠀⠐⠒⠋⠉⠉⠀⠀⠈⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠁⠀⠠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⢉⠁
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⢘⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⣄⣀⣀⣀⣀⣸⡆⠀⠀⠀⣮⣤⣤⠤⢤⣤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠓⠒⠀⠀⠈⣿⠉⠁⠉⠙⠛⠀⠀⠀⠈⠈⡇⠀⠀⠀⠛⠁⠀⠀⠀⢸⡇⠂⡀⠀⠈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⡷⠂⠀⠀⠀⢸⠃⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⢶⠶⠶⠤⠤⢾⠀⠀⠀⠰⣦⠤⠴⢶⢶⠼⡇⠀⠀⠀⢧⡶⣴⣶⣶⢾⠂⠀⠀⠀⠋⠙⠛⠓⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢠⢨⠘⠀⡇⠀⠀⠀⠉⡃⠃⠉⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⢸⠈⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄