Cute fish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢛⣛⣽⡿⠿⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠿⢿⣛⠛⠳⠦⣤⡴⠒⠒⢒⣚⣛⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣴⠟⣫⠷⠞⠿⢶⣄⠀⠈⠙⣦⡀⠀⠙⠶⣏⠉⢀⡤⠴⠚⠻⣦
⠀⠀⠀⠀⢀⣾⠟⢁⣞⣥⣤⡀⠀⠀⢻⡆⠀⠀⠘⣧⠀⠀⠀⠘⢷⡋⠀⢀⡴⠚⠛⠃⠀⠀⠀⣠⣴⠶⣷
⠀⠀⠀⣰⡟⠁⠀⣸⣿⣿⣏⡑⠀⠀⣸⠇⠀⠀⢀⣿⠀⠀⠀⠐⣄⠹⣴⠋⠀⠀⠀⠀⠀⣠⡾⠋⡠⠄⢸
⣠⣀⢰⡟⠀⠀⠀⢸⣿⣿⠟⠁⠀⣠⠏⠀⠀⢀⡾⠃⠀⠀⢱⣤⠋⢱⡘⢧⡀⠀⠀⠀⣰⢋⡔⠋⠀⣀⣸
⢿⡈⠙⠣⢄⡀⠀⠀⠙⠦⠤⠴⠊⠁⠀⣀⠴⠋⠀⠀⠀⠠⡞⠈⣧⡞⠉⣦⡻⣦⣤⡾⢗⣋⠴⠊⠁⢀⡟
⠈⣽⠶⠤⣤⣌⣉⣒⣤⣤⣸⣆⡀⠀⢸⡁⢠⡀⢠⡀⠀⠀⢸⢶⡁⢸⢖⠁⢹⢹⣿⠯⠭⠴⠒⣂⡴⠋
⠀⠻⢶⣤⣤⣤⣤⡤⠔⠚⠁⠀⠁⠀⢸⡇⢠⡗⢸⡷⣸⠐⢏⠀⡗⢏⢀⡗⢡⣾⣿⣿⡒⠢⠤⠽⣆
⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠁⠐⠋⠐⠁⠀⡸⠻⡄⡸⢋⣴⠟⠁⠹⣿⣏⠢⢄⡀⢸⡄
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⡴⠃⠀⢠⣤⣀⣀⡀⠈⠀⣠⢏⡴⠟⠁⠀⠀⠀⠹⣿⢆⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡤⠐⠉⠀⠀⠀⡾⢹⠙⡏⣿⢦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣧⡑⠂⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣰⡇⢸⠀⢧⠈⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢷⣌⠳⠤⣉⠓⠒⠚⠳⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣳⣦⣤⣭⣵⣶⣶⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠅⠨⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠴⡄⢠⠤⠧⠄⡀⠀⡀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⣀⠀⠀⣈⠥⠁⠐⠒⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⢰⠀⠅⠀⡅⠠⠀⢈⠀⠀⠀⡁⡉⢰⠂⣴⡁⡔
⠀⠀⠀⠚⠛⠁⠀⠀⠀⠂⠀⠈⠀⠁⠀⠀⠀⢀⠄⠀⢠⣤⠀⠠⢨⢷⠀⠀⠀⠀⠀⠐⠀⠀⠀⣐⡀⢰⠀⡇⢨⡀⣘⡀⢣⠀⠧⠒⠈⠁⠈⠀⠠⠴⡄
⠀⠀⢀⠀⠀⠀⠀⠸⠁⠒⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⠉⠀⡐⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠁⠀⠀⠀⠀⠀⠀⠐⢠⠁⡄⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠘⠃⠀⠀⠀⣠⠔⠈⠃⠒⠠⢤⡀⠀⠀⠁
⠀⠀⠀⢾⡰⠎⡁⠠⢈⠀⠨⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⢀⠀⠀⠀⠀⠉⠀⠠⢀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠠⠀⠀⠣⠄⠀⠀⠀⢈⠀⠀⠀⠤⠐⠀⠀⠈⠀⠤
⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⠠⠀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠛⠄⠀⠂⠀⡐⠂⠀⡀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀⢀⠀⠄⠀⠀⠀⠀⡠⠀⠐⠀⠀⠀⠀⠠⠄⣠⠆⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠠⠀⠈⠠⠀⠀⠀⠀⠈⠐⠐⠂⠐⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠄⠖⢠⣂⠖
⠀⠀⠀⠀⡔⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠇⠀⠃⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠂
⠀⠀⠀⠀⠁⠂⠀⢀⠐⠀⠀⠀⠀⠀⠀⡈⢐⠨⡉⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⠀⠂⠀⠀⠀⠀⠅⠀⠀⢠⡌⣠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⢀⠀⠀⢀⣀⢀⣀⣀⣀⠐⠈⠀⢁⠀⠁⠀⠀⢀⠀⠀⡠⠊⣀⢤⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠙⢋⣄⠀⠀⠀⣀⠂⠀⠀⠂⢐⠁⢊
⠀⠀⠈⠀⣘⠉⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠁⠀⡀⡀⢠⠀⠸⠓⠀⠀⠀⠤⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠈⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠈⣤⡄⠀⠀⠀⢠⠀⡄⡄⠀⠰⠐⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠴⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠶⠀⠀⠈⠀⡅⠁⠀⠨⠄⠂⠀⠀⠀⠈⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠈⠀⠀⢀⠀⡀⠀⠀⠁⠀⠒⠐⠂⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠂⠀⠀⠈⠂⢂⠠⠀⠀⠀⠀⡂⠑⢀⠀⠐⠃⠀⠀⠉⠒⠀⠒⠐⠀⠃⠉⠁⠀⠀⠀⠀⠤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠆⠀⢸⠀⠀⠌⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⡩⠀⢀⠠⠈⡀⠀⡇⠀⠘⠀⠀⠄⠀⠼⠗⠀⠀⠀⠀⠭⠂⠀⠠⠄⠀⠀⣠⡊⢠⠄⠀⠍⠉⠷⠲⠤⠠⠄⢤⢄⡤⢄⡀
⠀⡠⡀⠀⡎⠀⠂⣀⠀⠆⠀⡅⠀⢘⠀⠀⡁⠚⠂⠀⢁⠋⠀⠀⠀⠀⢀⠠⣀⠀⠃⠰⠀⠀⠀⠂⠀⠂⠀⠐⠀⠀⠀⠈⠀⡈⠁⢉⠀⠄⠀⡀⢀⠄
⠀⠈⠁⠀⠟⠀⠀⠀⠁⠤⠀⡀⠀⠐⠁⠀⠄⢀⡀⠐⠁⠀⠀⠀⠀⠠⢀⣀⠝⠁⠀⠀⠄⠈⠀⠀⠀⠂⠀⠂⡀⠂⢀⠁⠀⠀⠀⠀⢀⠠⠚⠃⠀⡇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠨⠈⠀⢀⠀⠀⠀⠱⠀⠀⠀⠈⠀⠀⠂⠠⡤⣀⣀⣄⢀⢀⠂⠀⡀⠀⠀⠤⠌⠀⠀⠈⠀⠀⡀⠀⠘
⠀⠀⠀⠣⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁⣤⣤⡴⠶⠶⠶⠶⣤⣤⣄⡀⠀⢀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡟⠋⠉⠉⠙⠳⣆⠀⠀⠀⠈⣿⣭⡿⠿⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠈⢻⡄⠀⠀⠀⠀⢹⡇⠀⣠⡾⠃⠉⠻⣦⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣾
⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⣷⡾⠋⠀⠀⠀⠀⠘⣧⠀⣀⡿⠉⠙⠳⣦⣤⣤⣤⡴⠞⠁⠀⢠⡿
⠀⠀⢀⡾⠋⠀⠀⢠⣼⣶⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⠉⠙⢷⡄⠀⠀⠀⠀⣿⢾⣯⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢴⣿⡁
⠀⢠⡟⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣿⣤⣴⠟⠁⠀⠀⠀⢿⡆⠀⢀⣴⠏⠀⠈⢻⣆⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠀⢸⣧⣶⡛⠁⠀⠀⠀⢸⡏⠙⠳⣦⡀⠀⢀⣠⣤⣤⣄⣀⠀⠸⡇
⠀⢹⣆⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⣸⠇⠀⠀⠀⢻⡄⠀⣠⡾⠁⠈⠙⢷⡀⠀⣠⡟⠀⠀⠀⢸⣧⡾⠋⠁⠀⠀⠈⠙⢷⣄⣿
⠀⠀⠙⢦⣀⠀⠀⠀⢀⠜⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⣷⣟⠋⠀⠀⠀⠀⠈⣷⣾⡋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠙⠳⣦⣀⠁⠀⠀⠀⢠⣟⠀⠀⠀⣀⣴⠟⠀⠙⣧⠀⠀⠀⠀⣰⠏⠈⢻⣆⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣴⡟⠙⠻⢿⣟⠉⠁⠀⠀⠀⣿⣤⣤⠶⠛⠁⠀⢀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢓⣶⣦⣿⣤⣀⣀⣠⣴⣋⣙⣷⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⣰⢿⡏⠉⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠁⠈⠷⣤⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠉⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣰⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢻⠲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧⠀⠸⡉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡖⠛⢿⡛⠛⠛⠓⠲⠶⣎⡀⠀⢳⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠹⡄⠀⠙⣆⠀⠀⠀⠀⠈⢿⡓⢾⣀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢻⠀⠀⠸⡀⠀⠀⠀⠀⠈⣇⠀⠙⢷⡄⠀⠀⣧
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣄⠀⠀⢸⡄⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⣄
⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⠀⢈⠃⠀⢸⡇⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⢹⣄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢈
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠁⣶⣆⣷⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⠈⣿⠁⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁⠀⣸
⡔⠐⠤⡼⠁⠀⣠⠀⠀⠳⠭⠽⠃⠀⢸⡇⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢿⡀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⢰⡼⠁
⢣⡀⠃⠀⢀⡴⢻⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠁⠀⠀⡿⠀⠈⠓⠶⠤⢤⡏⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠙⣏⣉⣡⠄⢩⠏⠀⠀⠀⠀⠀⠀⣾⢀⡟⠒⠧⢄⣀⣀⣀⣤⣼⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⢠⠀⠸⠕⠒⠁⣠⠖⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠤⣴⡟⣿⠀⠀⢸⠃⢀⡴⠟⠉⠉⢉⡟⠀⠀⠀⠀⢄⡀⠀⠀⢀
⠀⠳⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⣼⠁⡯⢤⣀⡀⠒⣒⡥⠞⢀⡇⠀⠀⡾⣰⠟⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠉⠳⢤⡞
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⠃⠉⠉⠁⠀⠀⣼⠁⠀⣰⡿⡇⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢠⠎⠷⣤⣀⣠⠜⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⡰⠃⢀⡴⠋⠀⡇⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⣆⢨
⠀⠀⠀⠀⠀⡞⠀⠀⠐⢹⠗⠶⣤⣴⣞⣁⣀⣀⣀⣀⣤⡾⠷⠚⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠘⡿
⠀⠀⠀⣠⠞⠁⠀⠀⢀⡾⠀⠀⠀⠀⠈⠉⠙⣇⡀⠀⠀⢱⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣰⠇
⠀⠀⠙⠓⠒⠒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⢸⠀⠀⠹⢤⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠸⣆⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣘⡦
⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠘⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣾⠤⠤⠥⣠⡈⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠙⠚⢤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⣀⡼⠁⣀⠀⠀⢀⠴⠖⠲⠦⣤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠠⣼⡟⠉⠀⠙⣶⠃⠀⠀⠀⠀⠀⢋⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢠⠶⢤⣸⠛⡇⠸⠿⠀⢿⠀⠀⢺⡿⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⠴⠚⠉⠉⠉⠒⠦⡀
⠀⠀⢯⠀⠀⠀⠀⠑⠠⠀⠤⠚⢄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⡴⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊⠁⠀⠀⠀⡠⠂⠀⠀⠂⠤⢀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⣇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠄⠀⠀⠀⠀⡀⠀⠈⠢⠀⠀⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠈⠓⠚⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠙⠠⡀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⡠⠔⠂⢰⡆⠙⡉⠑⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣀⣀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⣇⠀⠀⠆⣠⣤⣀⣀⣠⠤⠔⠊⠙⠚⠁⠈⠉⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣠⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣂⣤⣴⠶⠟⣿⣀⣠⠴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⣩⣾⠿⠋⠁⠀⠀⠠⠟⠉⠀⠀⠈⠳⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠈⠀⠀⠀⠀⠀⠐⠒⠶⢤⣤⣄⡀⠀⠀⠀⠐⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠋⣻⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣄⠂⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⣇⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠙⠛⠻⢶⣄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠾⠇⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⣧⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⡏⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣴⣤⣄⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣸⣿⡿⠛⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠉⠛⣦⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣸⣿⣿⣇⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⣿⣿⠇⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠀⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⣀⠀⢿⡀⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⢸⠟⠳⣬⣓⣤⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⣿⠀⠀⠀⠉⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠐⠀⠀⣀⣤⠶⠛⠁⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⠛⠛⠻⢿⣍⡀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢠⡾⠁
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤⣶⠟⠁
⠀⠹⣆⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠉⠛⠶⠦⣤⣤⣀⣀⣀⣀⣤⣤⠴⠶⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠳⢦⣤⣤⣤⠾⠋⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠉⠈⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠛⠶⢦⣤⣤⣀⣀⣀⣠⣤⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⡀⢸⡇
⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣦⣤⣤⣦⣤⣶⣤⣽⣿⣿⣿⣧⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣋⣙⣋⣈⣉⣹⣙⣩⣟⣻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⣩⠜⠉⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⣠⠁⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠶⢄
⠀⠀⡰⠑⢄⢰⠅⠂⠈⠁⠙⠂⢄⠀⠀⠀⠐⠖⠦⡤⢀⢈⠁⠀⢀⠀⠀⠀⣤⠀⠀⠀⠈⢂
⠀⠀⢇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠈⠓⢄⠀⠈⠀⠀⠠⠀⢂⠀⠀⠀⠀⠀⠀⣘
⠀⠀⢸⠀⠀⠐⡀⠁⠀⠀⠀⠀⢶⠀⠈⡄⠀⠀⠀⠀⠉⡆⠀⢀⡀⠀⠀⡣⣀⠀⠀⢀⠔⣈⡆
⠀⠀⠀⠤⢲⠀⠐⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢡⠀⢠⠉⠂⡜⠀⣠⠗⠋
⠀⠀⠀⠀⠏⣆⡠⠚⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⢄⠜⠁
⠀⠀⠀⠀⠀⠰⠁⠀⡔⢀⢀⣀⠔⢪
⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⡠⠒⠈⠁⠀⠉⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠒⠀⠖⡈⠉⠉⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠳⠀⢱⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠢⣀⠇
⠀⠀⠀⠀⠀⠀⠡⡌⠀⠀⠀⠀⠀⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠰⠂⠀⠀⠀⠀⠀⢡⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠈⡦⠀⡰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢄⢁⢸⠁⠀⢀⠇
⠀⠀⡠⠖⠒⠒⠒⠲⠀⠀⠀⠈⠀⠐⠘⠔⢁⡔⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⡠⠫⠈⢀⡌⠀⠆⠉
⠀⠀⠈⠂⠤⠤⠤⡀⠁⠂⠄⠤⢤⠄⠐⠊⡙⠀⠀⠀⠀⠀⠀⠀⠈⡖⠤⣄⣂⠉⣄⠀⡟⠁⢣⣠
⠀⠀⠀⠀⠀⠀⠀⠱⡀⡰⠀⠀⠀⠒⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠋⠉⠉⠉⡛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢙⠦⠄⣀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡠⢄⡀⡨⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠔⠊⠀⠀⢠⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣴⠖⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡄⢸⡇⢀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡇⠐⣿⡡⠧⢀⠠⠤⠤⠤⡀⠀⠀⠀⡐⢡⣖⠉⢿⡀⢸⡷⠋⠁⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⠋⠁⢀⡠⠤⠤⣀⠀⠀⣀⡀⠀⠈⠉⠒⠫⣤⡘⠁⢸⡅⠀⡴⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⡤⠐⢲⠣⠤⡀⠈⠓⢄⠀⠀⠀⠀⠁⠀⢸⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⣥⣶⣾⣧⣠⡆⠀⢈⠀⠀⣄⣀⣶⣄⠁⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣆
⠀⠀⠀⠀⢀⡴⠖⠺⡇⠀⢌⠻⠿⠛⠛⠛⠻⣿⠿⠛⠛⠻⠿⣿⣿⣦⡠⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⢸
⠀⠀⠀⡴⠋⠀⠀⠀⢻⡀⠀⠑⢌⠁⠀⠀⠀⠤⠄⠀⠠⠤⠴⠒⡋⠉⠈⢰⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡞⠁⠀⠀⠀⢠⠟
⠀⠀⢸⠁⠀⠀⠀⠀⣠⢷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⡀⠀⠀⠀⠐⡎⠙⠒⠤⡼⠀⠀⠀⢀⣴⣋⣤⣄⣀⡀
⠀⠀⢿⣄⣠⡤⠴⠋⠁⠀⠙⢦⡀⠀⠀⢤⣀⡀⢀⣀⡀⠄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢹⠴⠒⠒⠒⠒⠦⢤⣉⠁⠀⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣈⡁⠀⠀⢀⣀⣀⣀⣤⠤⠶⠚⢷⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠳⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⢀⣀⣠⠬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡖⠓⠢⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣌⣁⣰⣤⣭⣤⣦⣈⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⣋⠙⠢⢄⠀⠀⠀⠀⣀⣈⡉⢓⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠑⢤⡀⠑⠀⠒⣉⠤⠤⣨⠏⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠫⠔⠐⠐⠢⢄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⣀⣀⡀⠀⠀⠀⠑⠢⠤⠠⠤⠒⠈⣉⡉⣺⠁⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⢀⣠⣤⠤⢤⡤⠤⢤⣄⣀⣀⡀⠀⠀⠀⢠⡟⠈⠀⠀⠀⠀⠉⠐⠒⠠⠤⠤⠤⠐⠊⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠰⡯⠤⠨⢕⠢⠬⠄⠡⠤⠠⠤⠭⢉⡒⠶⡞⢀⡠⠄⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢰⡇⠀⠀⢠⠖⠲⣄⠀⠀⠀⣧⠖⢉⡟
⠀⠀⠀⠙⠶⣄⣂⠭⠐⠒⣂⣀⠐⠒⠄⠀⠈⢙⡗⡩⠔⠒⠒⠒⠢⠤⣈⠑⠒⠤⠀⠤⠒⡡⠐⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠒⢒⡶⠖⠈⠐⠒⠒⡨⠍⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠉⠀⣀⠠⠄⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠓⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡩⠀⠐⠂⢂⡠⠊⡠⠐⣹⡆⢀⠤⠒⠒⠒⠠⢄⡀⠀⠀⠀⢀⡠⠊⣁⠔⠂⢺⡀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⣴⠗⢋⠔⣊⠭⠭⠥⢄⣪⠴⠊⠁⠘⢧⡠⠂⠈⠐⠒⠤⢈⡉⠀⠉⢁⡠⠊⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⢳⡔⢁⠜⡔⣒⡤⠖⠋⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣠⠚⡱⣄⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⡤⠒⢒⣒⡒⠂⠀⠐⠚⡡⠞⠀⠈⣱⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠲⠮⣅⣀⡀⠉⠉⣉⣁⣠⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣏⠀⠈⣀⠉⠩⠋⠉⢚⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⢤⡤⠴⠚⠁

⢼⢦⠰⢂⠔⠁⠀⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⢢⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⠀⢰⠶⡆
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⡐⡣⠼⢆⠀⠀⠀⢇⠠⠂⠂⢀⠀⣤⣀⣀⠀⠀⠘⠥⠇⢠⣧⠿⢇⠀⢀
⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⠒⠄⢀⣀⡀⠀⠀⠑⡌⠏⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠙⢯
⠀⢀⢤⠒⠀⠉⠀⡖⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠗⣉⠴⠲⠤⢄⠁⠀⠀⠀⢀⡀⠀⠀⡀⢀⠈⠀⢀⡐⠀⠀⠀⠀⠀⢀
⠀⠀⠘⠠⢀⡀⠀⡇⠀⠈⠂⠐⢲⠖⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠢⠀⠈⠀⠀⠀⠀⢀⠀⠀⠐⠐⠂⠀⠀⠀⠂
⠀⠀⠁⠃⠀⠀⢱⡇⠔⠒⠀⠁⣀⠀⢲⢄⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠁⡀⠈⢀⠤⠀⣤⣀⣀⠀⠉⠀⠀⣣⣹⠆⠀⠀⠀⠀⢀⠀⠀⠀⠠⡆⠠⠄⠀⠘⠶⠖⠂⠀⠄⠠⡀⠀⡀⠀⠐⠂⠤
⠀⠀⠀⢀⠴⠃⠂⡴⣯⣀⢵⠋⠢⠀⠚⠛⠋⠐⠂⠀⠀⢀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠈⠀⠀⠀⠁⠄
⠰⠄⠠⠁⠀⠀⠊⠀⠑⠄⠈⠓⡊⠄⠀⠀⢠⠀⡤⠀⠤⣤⣤⣤⣤⡤⠤⡤⣴⡗⠀⠀⠀⠀⠁⠀⠔⠁⠀⠀⠀⠢⡀⠀⠠
⠀⠠⠁⠀⠐⠂⠀⠂⠀⢈⠢⡀⠀⠀⠀⠀⢸⣠⣇⡙⣀⣿⣿⣐⡘⣸⣸⣐⡿⡗⠒⠒⠀⠀⠀⠜⠀⣸⠀⠀⠒⠀⢐
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠋⠀⢰⣶⣶⣶⣶⣾⣇⣆⡢⢁⣁⣰⡆⡃⠀⠀⠐⠀⠀⠀⠀⠀⠉⠐⠄⠀⠂
⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠐
⠉⠢⡴⡂⢰⠀⢠⢉⢉⡁⢲⣄⢀⠂⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⡔⡃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠈⠣⢄⣣⠌⡀⢀⠀⢀⠜⠁⢀⣄⠀⠀⠠⠊⢁⠄⠒⣉⢉⠉⠉⠁⠐⢄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢃
⠈⠀⠀⠀⢀⠈⠑⡒⠒⠊⠁⠀⠀⠀⣯⡄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⣀⠐⠒⠒⠶⢢⣓⠈⠁⠀⠀⣀⣈
⠀⠀⠄⠀⠑⠄⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣏⠀⠀⠀⠀⠀⢀⠔⠀⠄
⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⣠⣤⠀⠀⠂⠠⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⠚⠃⠐⠀⠀⠀⠒⠀⠀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⢀⡀⠤⢖⡀⣬⠄⡀⣀
⠅⠀⠀⢀⠤⠆⠀⣠⠠⠤⡀⠀⠀⠀⣀⣤⠀⠀⢇⡠⠂⠉⡄⡸⠉⠑⠢⣄⣀⡎⢠⡀⢀⢀⣀⡀⣈⢒⣒⡒⠛⠭⠈⠑⠶
⠀⠀⠔⠃⠤⣴⠈⡃⡄⠀⠄⠑⠄⠀⠉⠠⠁⠠⠈⢄⠀⠀⠈⠀⠀⠀⠀⡩⠃⠠⠌⠉⠉⠈⠀⠐⠦⢠⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠿⠿⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢟⣋⣥⠴⠶⠖⠒⠒⠒⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠶⠾⠷⠶⠿⠷⣾⣯⣥⣶⣚⣛⣛⣛⡛⢀⣿⠃⠀⠀⠀⠀⠀⣀⣴⠟⢋⡠⠀⣼
⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢶⣤⣶⠛⠁⠀⠀⠀⠀⢠⡾⢋⡴⠞⠉⢀⣼⠏
⠀⠀⠀⣴⠟⢁⣀⣀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣠⡶⠋⢐⣩⠶⠛⢁⣾⠏
⠀⢀⣾⠋⢰⢡⣀⣶⢱⠀⠀⠘⣆⠀⠀⢀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⠖⠚⠋⢹⣿
⣠⠿⠁⠀⠈⠮⣛⣫⠞⠀⠀⠀⣿⢀⡴⣛⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠛⠛⢻⣧
⣹⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠬⢃⣼⠏⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣍⠛⢢⣾⠃
⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⢠⣾⠃⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣴⠞⠛⠙⠻⣦⡀⣝⢮⣙⠺⣿
⠀⠀⠀⠈⠙⠳⢶⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠈⠻⣎⠳⣌⠳⠽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣶⣶⣶⣶⣦⣤⣴⣶⣶⡶⢾⡿⣿⣭⣛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠙⢷⣮⡙⠦⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⣎⢻⡆⠀⠀⠀⠀⠻⣶⣝⠲⢭⣓⠒⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣥⣿⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣭⣉⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠶⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⣀⣰⠀⠀⣀⡄⠀⢠⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠁⠀⠀⠉⢠⡄⠰⣇⠀⢹⡆⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⠀⠀⠀⠀⠀⠢
⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠻⣄⠘⠦⣈⠇⣜⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⡀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠃⠀⠀⠚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠁⠐⠫⡈⠀⠀⠠⠀⠁⠀⠘⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⢀⡄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⣀⠐⠀⣘⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠧
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠛⠃⠀⠈⡋⠀⠀⠈
⠀⠀⠀⣀⠠⠄⠐⠀⠀⠀⣤⣤⡤⠀⠀⠀⡀⠤⢀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠈⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠈⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⢰⣏⡀
⠀⠀⠀⠃⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠲⣄⠁⠀⠀⠀⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠘⠀⠙⢀⠐⠂⠀⠀⠀⠀⠀⠚⢀⠘⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠁⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⢉⠛⠀⣈⣛⣉⣍⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡵⠚⠫⢍⠉⠉⠉⠉⠉⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠉⠢⡀⠑⠀⠒⣈⠁⣈⡱⠁⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠕⠀⠀⠢⢄⠀⠀⠀⠉⠉⠁⠀⠀⢸⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠀⠀⠀⣀⠀⠀⠑⠠⠠⠄⠂⡁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢀⡤⠶⡖⠒⠖⠒⠒⠤⠤⢤⣀⣀⠀⣸⠋⠀⠀⠀⠀⠀⠉⠀⠂⠐⠂⠂⠁⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢷⠀⣀⣄
⠀⠀⠸⣒⣈⡒⠬⣐⣂⡒⠂⣀⠐⠂⠬⢝⣇⠄⠂⣉⡉⠁⠂⠤⣀⠀⠀⠀⢀⡠⢂⠩⢼⠀⠀⠐⠋⠉⠂⠀⠀⢸⠎⢥⣎
⠀⠀⠀⠈⠙⠲⠥⢄⣐⣐⡂⠄⡉⢀⠠⢴⡧⠊⠀⠀⠀⠈⠁⠒⠠⠈⡁⠀⠥⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⡠⢞⣉⣀⠠⠀⡠⠊⡡⢧⠀⠀⡀⠠⠄⣀⠀⠀⠀⠀⠀⠀⡠⠒⡉⠙⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠁
⠀⠀⠀⠀⠀⢠⡞⠔⡡⢐⣒⣒⡉⢄⣪⠔⠋⢳⡉⠠⠀⠀⠤⢉⠐⠂⠀⠒⢁⠤⠊⠀⠀⠹⡄⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢸⡤⢊⠔⠅⣂⡤⠒⠉⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡠⢛⣄⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⢀⠔⠒⣒⡂⠀⠀⠀⢊⠤⠁⠀⣑⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⡲⠥⣤⣀⣈⣉⣉⣠⢤⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⣈⣠⠀⠐⠉⢀⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠶⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣶⠶⠿⠿⠿⠛⠿⠿⠷⢶⣦⣤⣀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣴⡟⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⣠⣶⠟⠛⠉⠉⠉⣩⡿⠃
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣾⠏⠀⠀⠀⠀⠀⢠⡿⠁
⠀⢀⣾⠃⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⠃
⠀⢸⡏⠀⠀⢸⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⠟⠛⠙⠛⠷⣦⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿
⠀⢸⡇⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣻⡷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠘⢷⣤⣀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠙⢷⣄⡀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠙⢷⣤⡀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠈⠙⢿⣿⣛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠉⠛⠿⠶⣶⣶⣶⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣤⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠛⠛⠛⠛⠛⠛⠋⠉⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⣶⣶⡶⠾⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠀⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠈⡠⠊⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⠀⠀⡰⠀⡀⠀⠀⠠⠔⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣣⣢⣠⣄⣠⣠⣼⠂⢀⡤⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠰⡞⠋⠉⡛⠿⡏⠉⠝⢿⣿⡿⠟⢶⣤⣂⣠⠀⠀⠀⠀⠐⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡻⣓⢾⠄⠀⠀⠀⢄⡠⠚⠍⠡⡑⣌⠃⡐⠒⢙⡯⢲⣤⣤⣔⠀⠀⠀⢀⡼⢃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠴⠦⠀⠀⢀⣾⡟⢾⠛⣳⠾⢁⣀⢄⠀⢆⠀⠁⠀⠀⢘⠪⠁⠀⠠⠡⣐⠢⠓⠠⣀⠀⣠⣾⣵⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⢀⡀⡀⠀⠀⣠⣞⣿⣿⢼⣿⣗⣎⠀⣸⠾⣦⡂⠈⠀⠀⠀⠄⡠⠰⣄⡰⣠⠔⠈⠀⠂⠀⢨⡿⢿⣿⣿⡵⠁⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⢸⠟⠁⡠⢚⣫⣛⠫⣽⡆⠀⢈⣉⠉⠁⡄⠜⠁⠀⢀⣧⢦⠪⠅⢄⡻⢨⡍⢀⠀⠃⠀⠀⠈⠑⢨⣿⣿⠷⠆⠀⠀⠀⢀⡴⠁
⣰⡃⠀⠈⡴⢡⡤⠀⢱⡘⢁⠠⠴⠟⠀⠀⠂⠀⠀⠘⠃⠀⣍⢄⠃⡐⠘⡉⠁⠒⠀⠌⡀⠀⠈⢒⣿⣿⣿⠀⠀⠀⠀⠀⠀⢇
⡇⠹⣆⠄⠻⣈⠛⣁⡼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠐⢜⠂⠂⢄⣜⠠⣤⣢⣼⠛⡉⠙⢿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠈⠧
⠘⢄⠙⠂⠀⢌⣉⡡⠔⠀⠀⠀⠀⠀⢀⠀⢁⢂⠀⠐⢀⡤⢼⢓⣤⣜⣧⣨⣶⡟⠈⠇⠁⠀⠸⣿⣿⢷⠍⠓⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠑⢦⠀⠀⣠⠀⠀⠀⠀⣀⠠⠘⠁⣰⡿⢠⠀⢠⠀⠰⠔⢠⣾⣿⣿⣿⡿⠀⠀⠀⠐⠒⠒⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠛⠴⡀⠁⠀⢀⣀⠖⡀⢴⣿⣷⡀⠑⠀⠈⠀⣴⣻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⢮⣿⣿⣿⣷⣾⣏⣿⣷⣾⣿⣿⣯⠀⠀⠀⠀⠄⠀⢀⡟⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠈⢣⣹⣿⣿⣿⣿⣾⣿⣿⣟⠁⠀⠀⠀⠀⠔⠀⠀⣸⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠙⠲⢤⣀⠀⠀⠉⠐⠊⠙⠀⠒⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠙⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⡀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⠄⠀⠈⠀⠅⠈⠑⠶⢄⡀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠠⠀⠀⠡⡀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠶⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⢉⣓⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣀⣀⡈⠙⢳⡅
⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠤⠤⣄⠈⠙⡆⠀⣿
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⣷⠸⠃⣰⠃⠀⠛⠀⠀⣾
⠀⠀⣸⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣿⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⢀⣀⠄⠀⠀⠀⢀⣠⡤⠖⢊⡉⠀⠀⣀⡠⠄
⠀⠀⣿⠀⠀⠀⠉⠳⢤⣄⣀⠀⠀⠀⠀⣠⠞⠁⢀⡤⢞⣩⠤⢂⣤⠶⣛⣩⠴⠖⢋⣁⡤⠖⣋⡥⠔⠂
⠀⠀⣿⠀⠀⠀⠑⠲⠤⠤⣭⣽⣿⣷⠚⠁⢀⡴⣫⠖⠋⢠⢞⣩⠴⠛⠉⠀⠀⠀⣩⡥⠖⠋⠁⠀⠀⢀⠀⠀⠠⣶⣶⣶⠄
⠀⠀⢿⡄⠀⠀⠀⠤⠶⠶⢶⣖⠒⠂⠀⠀⣨⠞⠁⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠘⠿⠟
⠀⠀⢸⣧⠀⠀⠀⠉⠉⢉⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⣷⢹⡀
⠀⠀⠀⢿⣦⠀⠀⠐⠛⠉⣉⣡⣤⠄⠀⠀⢦⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⣿⡲⠤⠄⠀⠀⠈⡇⢹⠘⡇⠀⠀⠀⠀⠀⠀⢠⣤⣴
⠀⠀⢀⡼⠁⢀⣠⠴⠖⠋⣉⣤⠤⠆⠀⠀⠸⣷⣄⡀⠙⠿⣝⡲⠦⣤⣀⣀⠈⠉⠛⠂⠀⠀⠀⢹⠀⢇⠘⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⢠⠞⠀⠀⠀⣀⡤⠖⠋⠉⡀⠤⠒⠛⢿⣦⣘⠳⢭⣓⠶⢤⣍⣛⡲⠦⠭⣭⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⢀⡏⠀⠀⠀⠈⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠙⠿⣷⣦⣌⡙⠓⠶⠤⠭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋
⣸⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⡖⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⠀⢤⣤⣤⣶⠶⠟⠛⠉
⢻⡀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠠⠴⠃⢀⣨⠇⠀⠉⠙⣦⠀⠈⠉⠁
⠘⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠚⠉⠁⣀⣤⠶⣚⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⢄⣒⣫⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣥⣴⣶⠶⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣩⡴⠶⠚⢛⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⡥⠚⠁⠀⢀⣠⠖⠟⠋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡴⠋⡀⠀⢀⡴⠋⠀⠀⠰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠋⠉⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠋⣀⣠⣤⣴⣯⣄⣀⠀⠀⣠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⡠⠖⠒⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠿⠋⠛⢇⠀⠁⢀⠐⠀⠉⠙⠶⢼⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⠋⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡿⡶⣶⢤⠀⢈⡑⠈⠀⠄⠀⠀⠀⠔⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡎⠀⢰⠃⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⢬⡙⢾⡽⣳⣿⡁⠰⡀⠀⣈⠳⠂⠺⡀⠀⠀⣰⠙⢦⡀⠀⠀⣠⡾⠀⡰⠃⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⢦⠘⢆⢹⣵⣻⣆⠀⠀⠉⠙⢀⠀⠑⡸⠂⠘⠳⡌⢀⡏⣿⢻⡅⣠⠞⠁⠀⠀⠀⣳⣄
⠀⠀⠀⠀⢀⣀⠀⡆⣿⣇⢈⡇⠘⡆⡯⠽⡷⠀⢒⢄⠀⡜⠋⠩⣧⠀⠀⠀⢸⠒⡇⣿⡼⣯⠀⠀⢀⣠⡴⠾⠛⠙⡇
⠀⠀⠀⠀⡎⠀⠁⢳⠙⠿⠿⡇⠀⡇⣿⠭⣿⡀⢂⠀⠀⡡⣀⣀⡼⠢⠀⢀⠌⠀⣕⣸⠉⣿⢶⡖⠋⠁⠀⠀⠀⣼⣀
⠀⠀⠀⠀⠣⡀⠀⠘⢦⡤⠞⠀⢠⠇⣿⣹⢿⠀⠀⠁⢻⠀⠀⡈⢀⡠⠀⠈⠉⢣⢡⣿⢽⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠈⡕⠻⠀⠀⠀⠀⡼⣰⣓⡾⠈⠡⢀⣀⡀⠀⠈⠀⠀⢄⠀⠀⠀⣌⢙⡼⠋⠁⠉⠻⡷⣤⡉⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠣⢀⠤⢄⡀⡴⣱⡓⢾⢗⢤⠀⠀⠀⠈⣄⠀⠀⢠⠒⠄⠀⠁⣠⠏⠀⠀⠀⠀⠀⠈⢮⡻⢦⣄⠀⠀⠀⠀⢈⣒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡳⣭⢟⣎⠜⠢⠠⡴⠚⠉⠀⠃⠀⠁⠀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠛⠶⢤⣤⣀⣼⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣅⡸⠀⠀⠀⠘⢦⣀⠠⣄⢀⣠⠾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⢀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⠤⣴⣥⡤⠶⠚⠯⣅⣀⣐⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠨⠭⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⣶⡟⣛⡛⣫⡿⡟⠭⣭⣭⣿⣭⣽⣓⡲⢴⣶⣿⡿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⢋⢷⡌⢿⣦⣍⣙⣷⣣⣴⣿⠶⣝⢿⣯⣽⣿⣷⣮⣝⠾⢛⡽⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⢾⣿⡌⢳⠑⡈⠻⠙⠏⠙⠁⠍⠀⡙⠛⠻⢹⣟⣿⣿⣮⡲⣛⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣿⣤⣿⣦⡘⢀⣆⣼⠀⠀⠀⠈⠀⢀⡷⡤⠊⣸⢿⣿⣿⣿⣿⣮⢾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡟⢩⠤⠤⣄⣈⠉⠙⠋⢀⣸⡿⠶⠶⠶⢊⣭⣠⠴⢋⣌⡈⢩⣼⣿⣿⣿⣿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣦⡘⠒⠒⠀⠋⢙⣻⣶⣦⣤⣤⣴⣮⣅⣐⡐⢁⣼⡿⣷⣶⣽⣽⡿⢿⣷⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣥⡶⠶⢽⣿⣿⡻⣿⡛⠷⠞⠉⠀⠈⠻⣿⣿⣿⡿⢟⣫⣥⣿⡞⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠈⠁⠈⠁⣤⣤⣀⣀⠀⠀⠈⠉⠉⠀⠻⠿⢟⣽⡇⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⡀⠀⠈⠻⣿⣿⡻⣟⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣷⠦⣄⡙⣾⣿⣾⡇⠀⠀⠀⠀⠀⢩⣷⣶⡇⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⠟⠁⠀⠀⠉⠛⣿⣿⣷⠀⠀⠀⠀⢀⣛⣛⣿⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⣻⠘⣿⣷⣆⢸⣿⣿⢋⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣶⣶⣶⡞⠋⠀⣿⢩⣿⣶⣶⣿⠟⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣛⣿⣿⡁⠀⢀⣽⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣽⣖⣻⣿⣿⣦⣘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣽⡿⣿⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢡⡾⣿⠏⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⡄⢠⣖⡂⠀⠀⠐⠄⢱⠀⠀⠀⠀⠀⠀⣀⡠⢤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡤⠚⠉⣠⠒⢦⠹⣤⡇⢸⣥⠶⠀⠀⠀⢂⡜⠀⠀⠀⡠⠔⠉⠀⠀⠀⠈⢢⡀⠀⠲⣭⠖⠀⠀⢀⣀⣀⡠⢠⣿⣿⣶⡄⠈
⠀⠀⠀⢀⡔⡁⢊⠀⠀⠳⠤⣋⣀⣬⠤⠤⠤⠶⠒⠒⠋⠁⠀⠀⡰⠎⠀⠀⠀⣀⠀⠀⠀⠈⠛⡄⠀⠈⠀⡀⠐⣁⣀⠈⠀⢐⠻⠟⠋⢣⡀
⠀⠀⢀⡏⡄⠀⠘⠧⢊⣶⡭⠤⢤⡀⠀⠀⠀⠀⢀⡴⢇⡀⠀⢀⠃⠀⠀⠀⢺⣿⣿⡿⡆⠀⠀⢘⡄⠀⢠⠀⠀⠻⠛⠂⠀⢻⣿⠗⠀⢀⠀⢱
⠀⠀⠸⡇⠀⠀⠀⠀⣀⠤⠖⠦⣄⡇⠀⠀⠀⠀⠀⠹⠋⠁⠀⡸⠀⠀⠀⠑⠌⠻⠿⢋⡥⠀⠀⠀⠇⠀⠐⠢⠀⢀⣀⢠⠀⠀⠁⠀⠀⣿⣷⠚⠄
⠀⠀⠀⠙⠦⠤⠤⠚⠁⠀⠀⠀⡻⠅⠒⠲⡒⣤⠒⠲⣄⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡸⠀⠀⠈⠀⠀⠀⠀⠀⠓⠠⣀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣾⣶⣿⠧⡴⠉⢏⠙⠎⡆⠘⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⢐⠋
⠀⠀⠀⠀⠀⠀⠠⠌⠀⠰⡘⠼⣟⡫⠕⠋⣀⡀⠈⢢⡜⡅⠀⠀⠀⠈⠉⢑⠚⠒⠲⠤⣀⣀⡼⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⡐⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠀⢠⣶⣾⣿⡑⠀⠀⠻⠀⠀⣀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⣤⣶⠉⠓⠲⠤⠤⣀⣀⠤⠔⠁
⠀⠀⠀⠀⠀⢠⡀⠀⣠⠀⠀⠘⢆⠀⠙⠻⠿⠃⠀⢀⠜⣰⣿⣿⣾⣍⣳⣄⣠⣤⣤⣤⣄⠀⠉⠁⠀⣼⣿⣿⡷⢄⣠⣄⡀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠈⢦⡀⠀⣀⡠⠔⠉⢰⣿⣿⣿⢫⣍⠻⣿⣿⠿⢿⣿⡟⣧⠀⠀⢠⣿⣿⣿⠀⢌⠀⠀⠉⠁⠙⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⠛⠳⢦⣀⠈⠉⠀⠀⠀⠀⠈⣿⣿⡏⠾⡃⠰⠆⠀⣽⢢⣿⡗⣿⠀⠀⣸⣿⣿⣿⠀⠈⢦⡀⠀⣠⠞⠁⠠⠮⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣴⣿⣿⣷⡀⠐⠃⠀⢀⠀⠘⢿⡆⢛⣵⣾⣦⡰⡎⠸⣿⡵⠃⠀⠚⢿⣿⣿⠃⠀⠂⠀⠙⠉⠀⠀⠀⢀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢿⣿⣿⣧⠀⠀⠲⣏⠷⠀⠈⠻⣿⣿⣿⣿⣷⣼⠿⠋⠀⠀⠀⠀⠸⠛⠁⢀⣤⣤⣤⣤⣀⣠⣶⣻⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⡀⠙⣠⠔⠢⡆⠘⠋⠉⠙⠀⠀⠀⠈⠀⡀⠀⠀⠙⠾⠿⠛⠋⠀⠀⢀⡤⠤⠔⠒⡄⠀⣰⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⡊⠴⠈⠁⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⠀⢀⠇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠶⠇⠀⠀⠀⡋⠀⠉⠉⠙⡄⠀⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠉⠒⠠⠊⠀⠀⠘⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⢀⣠⣄⠑⣄⠀⡠⠎⣤⣤⡄⠀⢰⡿⠋⠉⠛⠻⣿⣆⠀⡠⠒⠂⠄⠀⠄⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢹⠀⠙⠿⠏⠀⠀⠉⠀⠀⠘⠋⠁⣀⣿⠁⠀⠀⠀⠀⣼⡇⠀⡄⢸⣿⣷⣶⡆⠈⠀⠀⠙⢿⢿⣿⣿⣿⣿⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⡔⠉⠀⠉⠳⣄⣀⠀⣰⣿⠁⠀⠘⡌⢻⡿⠟⡁⠈⠀⠀⠀⠀⠢⠩⠙⠋⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⣿⣶⣶⣤⡤⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⠀⣄⡈⢳⠀⠀⠈⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣫⣭⣭⣵⡞⠀⠀⠘⡄⠀⠀⠀⣿⣿⠀⠀⠉⠀⢸⠀⠀⠀⠸⠀⠀⢠⠀⠀⠀⠀⠀⣠⣄⣠⣀⣈
⠀⠀⠀⠀⠀⣠⡾⠿⣫⣴⣶⣦⣼⣿⡿⣻⡟⠀⠀⠀⠀⠘⣄⠀⠀⠿⠁⠀⠀⢀⡴⠋⢀⣒⠆⠇⠀⠀⠀⢀⠀⠄⠀⠀⡯⠮⢵⣥⣸⠃
⠀⠀⠀⠀⠀⠀⠓⠾⣿⣿⣿⣿⠿⠓⠛⠋⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⣀⠤⠒⠉⠀⠰⣀⡘⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢇⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣾⣷⣄⣀⠀⠀⠀⠀⣠⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠻⠿⠿⢿⣶⣷⣶⣦⡠⡀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⠁
⠀⠀⠀⢠⡖⠋⢕⣶⣆⠀⠀⠀⠀⠀⠀⠴⠞⠿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠶⠦⢤⣠⣄⣜⠁⢀⡇
⠀⠀⠀⣀⠱⠤⠈⠉⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⠴⡖⠚⢹
⠀⠀⠀⠈⠑⠤⣄⡤⣄⣀⠜⠀⣸⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠋⠋⠀⠀⠀⠀⢳⣄⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⢻⣿⡿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠳⢽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠋⠉⠉⠉⠉⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡀
⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⢂⣀⡀
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣺⣿⠶
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⣿⣿⢿⣿⢟⡁
⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢦⣌⣹⣿⣿⡷⢆⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢠⣵⡞⠙⣿⣿⣿⣿⣩⡿⠋
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢉⡭⣷⣦⢿⡹⡇⣿⣼⣡⡀
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢄⣰⣿⢧⡀⢮⣿⡉⢳⣿⠿⣿⡿⠦
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⣏⣓⣿⣿⣿⡿⠻⣿⠧⢾⡟⢉⡽⣧
⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⢲⣯⡝⠛⢻⣽⣷⣬⣿⠋⢻⣴⣿⣶⠌
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣠⢴⣿⠋⣩⡷⣶⠚⢷⠲⣯⡉⠻⡟⣶⣋⡉⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⢁⡿⢧⣼⠹⡙⣆⣱⣼⡆⢸⠉⢦⣿⠡⠄⣡⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣏⠻⣿⡏⠳⣤⣹⣷⣛⣫⠵⢡⠇⡼⠀⡼⢳⡠⠾⢗⡠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢿⡟⣇⠨⣹⠋⢱⣄⡈⠲⡖⠾⠷⢒⡿⢺⡥⠞⢀⣼⡧⠤⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⣀⢮⣩⢆⡇⣴⣀⣸⠾⠶⢾⣦⡀⠳⣍⡉⠙⠓⠚⣁⣴⣋⡠⣴⡿⠙⢧⠤⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⢈⣛⣻⣾⣷⣿⣽⠶⢦⣭⣿⢁⣙⣷⡒⠾⣟⡋⠉⠁⢀⡤⠞⠻⠒⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠨⠽⠿⣿⣦⣤⣤⣼⢿⡏⠠⠏⠀⠋⢉⣡⠽⠿⣏⠳⡶⠶⠶⠖⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡚⢉⡟⠁⢚⣿⢸⣧⠤⢴⠖⣛⡭⠞⠳⢦⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣤⡾⠋⠸⠚⠁⠀⠘⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠙⠿⣷⣦⣀
⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⡀⠀⠀⠀⠙⠿⠿⠿⠿⠿⢿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⢿⣿⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠈⢿⣧⠀⠈⠙⠻⣷⣦⡀⢀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠙⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢠⣴⣤⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢀⣠⣾⡿⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⢠⣿⢏⣠⣤⣾⠿⠛⠁⠀⠀⠈⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢀⣤⣾⡿⠋⠁
⠀⠀⠀⠀⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⣽⣿⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣀⣤⣾⠿⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣷⣦⣾⣾⣿⣷⣶⣦⣀⣀⣤⣞⠋⡰⠊⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠏
⠀⠀⠀⠀⢀⣀⣤⣴⣶⢿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣷⣶⣾⣿⣷⣦⠀⡀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠞
⢀⣠⡴⠾⠻⣿⣿⡏⠙⠻⣝⣋⣉⣉⣭⣿⣽⣥⣿⣜⣃⣟⡹⠏⠘⠱⢋⡿⠉⠿⠛⣿⢻⣿⣿⣶⣦⣆⣤⣠⣿⣦⡾
⣈⡙⣄⢀⡻⠿⠋⠀⠀⡀⣹⡿⠛⠋⠉⠉⢉⣉⣀⡨⠭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡴⠾⠿⣿⣿⣿⡇
⠉⠛⠶⢮⣅⣀⠀⠀⣰⣆⣿⣭⣷⣶⣚⣩⣍⡁⠀⠴⠀⣀⣀⠀⠀⠀⢀⠀⣀⣤⣶⣿⠟⠋⠉⠀⠀⠀⠀⠈⢻⡉⠹⡀
⠀⠀⠀⠀⠈⠉⠛⠳⠿⠿⣯⣽⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡙⠻⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠙⠦⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣷⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡤⠤⣦⢴⣖⠦⡀⣀⣤⠤⠤⢤⠀⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡛⠓⠲⢭⣓⣌⣧⡼⠒⢋⠉⡀⠀⠀⠈⡆⠀⠀⣰⣶⣶⣦⡈⠉⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣯⣉⠉⠙⢓⠤⠊⢉⠔⠁⢊⡼⣧⠀⠀⠀⠀⠄⠀⠀⢿⠘⢤⣼⡇⠀⠀⠠⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠒⠲⠤⣉⡶⢁⣨⠖⠁⣊⡴⠫⡢⢹⡆⠀⠀⣰⣀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣋⣉⣉⣙⡶⠏⠀⣀⣤⣴⠛⠉⡢⢀⠔⢸⡇⠀⡴⠋⠙⢷⣄⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢶⣭⠥⠤⢤⡞⠀⠂⠨⠴⠛⠿⣦⡄⠂⠀⠊⣾⣿⣦⡀⠀⠸⠀⠈⣇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⢲⡯⠤⠤⣀⣄⠀⠐⠰⠈⢿⡄⢠⠞⡸⠃⠇⢱⡀⢀⣀⠀⢸⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠤⠀⠂⠘⠛⣷⣦⡀⠈⢹⡅⠀⡠⠀⠀⢘⣷⠋⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⡀⢀⠀⠘⢧⠈⠣⡀⡯⠀⢐⡥⠞⢉⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⡾⠻⠿⣟⠋⠉⠒⢌⡆⠄⢡⣇⡴⠉⠀⠀⠀⣇⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠘⣆⠀⠀⠀⢱⠘⣼⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣠⣤⣸⣄⡀⠀⢸⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠉⢠⣾⣯⡙⢦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⣿⣿⣽⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣏⢯⠻⡉⠻⣷⣶⢖⡒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⢸⡆⢃⠀⠙⣎⠳⡈⠳⢄⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠃⠘⠀⣀⣘⣆⠈⠢⣀⠑⠠⢙⢦⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠎⠀⠂⢰⠁⠀⠙⠢⢤⣀⣉⠉⠩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢣⠎⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣢⢃⡔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣉⡩⠭⢭⢖⣒⡠⠤⢀⡀⢀⡀⠤⢄⣒⡲⠭⠭⢍⣙⡒⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠠⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢼⢹⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡏⠷
⠀⠀⠀⠀⠀⠀⠀⡈⣆⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣻⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⣏⣀⣧⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡏⡄⣘⠝⣦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠫⣁⢠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣶⣮⣄⡙⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⢋⣠⣵⣾⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⡀⠉⡉⠿⢷⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⡾⠿⢍⠉⢀⣐⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡎⢠⠚⣉⠛⣿⢮⡳⣄⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⠛⣉⠓⡄⢱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠹⣄⠝⣶⠺⠂⠙⠮⡳⡄⠀⠀⣠⣞⠷⠋⠐⠷⠶⠫⣠⠏⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠍⣛⡻⢿⢿⡶⠾⣾⣦⣴⣿⠷⢶⣿⡿⣟⣛⠩⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠻⠟⠜⠣⠻⠞⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢰⢤⣤⢤⣠⡂⢴⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⢲⣲⣤⣀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠈⠉⠈⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⣉⠠⠄⢀⣀⣙⠓⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠈⠐⠄⠀⠀⠀⠀⠙⡿⠓⠦⣄⣤⡤⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⠐⠠⡀⠈⠄⠀⠀⠀⠀⠰⢡⠀⠈⠿⠮⣝⡒⠦⡙⣆⠀⠀⢀⡤⢞⣉⣉⠝⠳⣄
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡠⣤⠄⠀⠈⠀⠘⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠉⠙⠲⠼⠦⠖⢻⡦⠐⠉⢉⣦⠄⠚⣆
⠀⠀⠀⠀⠀⡼⠁⠀⠀⢰⠃⣔⣲⣧⠀⠀⠀⠀⠀⠀⠀⠀⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⠀⠀⢚⣋⣉⠀⣨⡄⠠⢼⡄
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠳⠬⠕⠃⠀⢠⠀⠀⠀⠀⠀⢐⣸⠤⠤⢤⡧⣅⠀⠀⠀⠀⢸⠀⠀⠀⢨⡅⠀⠀⣸⢀⣀⣸⡇
⠀⠀⠀⠙⣏⠉⠙⠲⠤⠤⠀⠀⠀⠀⢀⠂⠀⠘⠀⠀⢸⠅⠐⠒⠀⡰⠃⢸⠀⠀⠀⠀⡘⡀⠀⢀⠶⠆⠤⢠⣎⠀⠀⣸⠃
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠⠁⠀⣠⢞⡒⠀⠀⠌⢡⢚⠃⠀⠀⠀⣠⣡⣀⡠⠮⢏⠐⢢⠆⡀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠠⠐⠈⠀⢀⠔⠁⠀⠀⠀⠀⢨⠟⠘⠃⣙⣌⣠⣔⡲⢟⡽⠁⠉⠉⠓⠶⣞⣑⡤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠴⣆⣁⣀⡀⣠⣀⣀⣠⣮⠤⣶⠖⠩⣥⡖⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢣⠀⡐⠩⠍⣗⣲⠈⠙⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⢲⣳⣌⠢⢁⡞⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠳⢶⡵⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠍⠁⠀⢀⣀⣬⣿⣿⢦⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠃⢤⣀⣤⣾⣟⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⢟⠟⣴⣾⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠟⠉⠻⡻⣙⣸⡿⣿⢃⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⠀⠀⠀⠀⠈⠉⠉⡰⢁⣾⠿⠿⠿⣿⡦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠭⠒⣒⠢⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢸⣻⡄⠀⠀⠀⠀⠢⠄⠀⠀⠨⠔⠁⠀⠚⢁⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣷⡙⢦⣀⣄⠓⠦⡤⠄⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⡟⠁⠀⠀⣤⣶⡿⢟⡛⠋⢉⣿⡿⠛⠲⠤⣭⣍⣃⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠻⢿⣿⣷⣶⣿⠾⠁⠀⠀⣀⣤⣾⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣤⠶⠚⠙⣿⠿⠟⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⠀⠘⣿⡄⡀⣘⣧
⠀⠀⠀⡀⠀⠀⢠⣾⠖⠶⠦⡤⠘⣿⣷⣄⠀⠀⠀⠀⢠⡟⠁⢀⣠⣤⣤⣶⣶⣶⡎⠻⣿⣿⣿⠠⠶⢄⡀
⠀⠀⣾⠀⣀⢠⣮⠓⢶⣂⠀⢀⣉⣉⠛⢿⣶⣀⠀⠀⠘⢷⣶⣿⣿⣿⡭⣭⣽⣏⣀⣠⣶⣿⠶⠒⠉⢁⢣⢀⠇⢠⠷
⠀⠀⠘⢇⢽⡾⣟⡳⣶⣿⣟⠲⠾⢭⣉⡉⢙⣿⣿⣷⣤⣾⣿⣿⣿⣶⣾⣿⠟⣿⣥⡶⠾⠋⢅⠤⢒⣫⢏⡞⠜⠁
⠀⠀⠀⠀⠙⠟⣾⣿⣿⢿⣿⣷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣟⣭⣵⣶⣶⣶⣶⣾⠻⣵⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠛⠻⠟⠛⠻⠿⢿⣿⣟⣛⣛⣛⣻⣿⣿⡿⣿⣿⣟⣿⡿⠛⠿⠛⠙⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠡⠀⠀⢃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣶⣤⣶⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣘⣣⣱⣄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⠿⣿⠻⢿
⠀⠀⠀⠀⠀⢠⣰⣿⡷⠞⡿⣷⣶⡄⠀⠀⠀⠘⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⢀⣷⣿⠁⠃⠀⡆⠸⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄
⣷⠀⠀⠀⣸⣽⢅⠠⠀⠀⡇⠀⠚⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣾⠦
⣾⡆⠀⠀⢰⣾⣺⠀⠘⠿⠇⠀⢘⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣀⡄⠀⠀⠀⠀⠀⣼⣴⣦⡀⢠
⣿⡇⠀⠀⠈⢫⣿⣆⣀⣠⠄⡄⣮⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢿⣿⡿⠙⠘
⠈⠀⠀⠀⠀⠈⠈⠛⠻⠿⠾⠛⠋⠉⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⢀⣤⣄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⡀
⠀⠀⠴⠂⠀⠀⠀⠒⢚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣀⣄⡘⠃⠀⠀⠀⠀⠀⠀⠀⠸⣦⠼⠛⠵⣗⣀⡀
⠀⠀⠀⠀⡀⣀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠐⠙⢱⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⢐⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢴⡶
⠀⠀⠀⠀⢰⠈⠠⠀⠄⠘⠀⠀⠀⠀⢠⣦⡄⠉⠈⠥⠁⠑⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠋⠈⠁
⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⣦⠀⢀⣤⡀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠸⠿⠿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣾⣿⣷⣿⡇
⠀⠀⠀⠶⠢⣤⡤⠚⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡏⠛⠙⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠿⣿⠂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣲⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⠁⠘⠀⠸⣿⣿⣶⠄
⠀⠀⠀⡖⠢⣤⣴⠖⢻⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠁⠉⠖⠚⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠰⡶⠀⣿⣿⣷⡄

⠓⠚⠛⣿⣬⡟⠛⠀⠘⠋⣹⣿⣿⣛⣇⣠⡖⣇⠠⢉⣠⣀⠀⠀⣀⣠⡀⠐⣼⣿⡇⣀⡀⢰⣿⡀⠀⠀⣶⣷⠿⢳⣜⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⡌
⠀⣠⣴⣿⣉⠁⢤⠀⠶⠀⠀⠼⣿⡛⢺⡇⠑⠿⠃⠘⠻⠟⣠⣄⠛⠻⠁⣠⠋⠌⠉⠉⠁⠘⠻⣷⢐⣴⢿⣶⣶⡛⠋⣠⢠⠔⠳⠿⠿⠛⠻⣿⣿⣼⠟⠋⠁
⠀⢿⣿⣿⣍⡀⠀⠀⠀⠀⠀⢶⡿⠛⢿⣄⡐⠊⣧⠄⠀⠀⠁⠁⠀⠀⢨⠧⠀⠀⠀⠀⠀⠀⠀⢻⣟⣵⠋⠈⠀⠀⠐⡧⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡀
⣤⣼⣿⣿⣿⠷⣶⠀⣤⣀⣿⣿⣧⠀⠀⠛⠀⠀⡉⠐⣷⣶⡶⠶⠆⠈⡻⠀⣀⣀⢀⠀⠀⠀⠀⢠⡿⣁⠆⠴⠀⣀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣽⣷⡦
⠁⣀⠀⠉⢻⣡⣾⣿⣿⣛⠛⠉⠀⠀⠀⠀⠀⠈⠳⣦⡄⢹⠃⠂⠀⣾⠁⠀⠀⠉⠀⠀⢀⠀⠀⢸⠁⡉⠤⢐⠀⢸⣿⣄⠀⠀⠀⠀⠈⠀⢚⣦⠞⢫⣿⣏⠔
⠈⢛⠃⢠⡄⢹⣥⡈⣿⠇⠀⣤⣂⡄⠀⠀⢀⡀⠀⠈⢧⣼⠀⢁⠀⠹⠀⠀⠀⠀⠤⢤⠎⠀⠏⡸⠷⣄⣳⣶⣶⣿⡿⡟⢛⣶⣄⣀⣀⣠⣾⠀⠀⢿⡏⠴
⠀⠙⢣⣤⠀⢨⣿⣿⣿⠀⠀⠻⠿⠃⠀⠀⢿⣿⡿⠀⢸⣿⣧⣈⣠⠀⣣⡤⠂⠀⠀⠀⠀⠀⠀⠁⣴⣟⣛⣧⡜⣻⣤⡟⠋⢫⡼⠿⢏⣿⣿⣀⡶⠋⢀⡴⠦
⠀⠀⠈⢉⡴⣿⡟⣀⠻⣦⣄⣀⠀⠀⠀⠁⠀⠀⢀⣠⣞⢁⠀⠀⠄⢙⡟⠀⠀⡀⠀⠀⠀⣀⣀⠀⠈⣿⣅⣙⣡⣿⡿⢦⡶⢻⡷⠻⡟⢹⡿⠁⢀⡾⠋
⣠⠴⢻⣍⡄⠛⠋⢁⣃⢂⠈⣽⣿⣙⣀⣿⡟⣻⡏⠠⢮⠀⠀⠄⠀⠸⡇⠀⣾⣿⡷⠀⠘⠿⠿⠃⠀⢸⣿⡯⡿⢢⣤⠈⠗⠚⠣⠾⠻⠉⢳⣄⠀⠙⠀⢀⣴
⢤⡀⠠⡷⢤⠀⣸⠁⠬⣺⣤⣿⡱⣾⣣⣤⢮⣿⡇⣇⢀⡀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠯⠤⠾⠯⣭⡀⠀⢱⠀⠀⠀⠀⠀⠈⠁⢰⠁⠘⠧
⠀⠈⠛⢄⣠⣿⢿⣷⡴⠿⠿⠻⠏⠉⠉⠱⣿⡟⣧⠦⢠⡤⠴⠟⣷⡔⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠄⠄⠀⠙⠋⠀⠀⠀⠀⠠⣀⠀⠀⠛⣄⠀⣰
⠂⢠⣦⡄⠉⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⢋⡴⠒⣷⡆⢠⠾⠆⢂⠀⠀⢀⠀⠀⣠⡦⡤⠶⣾⢃⣀⠀⣤⣶⣶⣷⠲⣷⡄⠀⣀⠀⠀⠖⠶⣁⣤⠿
⣄⠀⠉⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⡐⠃⢈⣡⡁⢀⣥⠈⣶⡶⠋⠛⢈⠌⣉⣉⡀⠂⠀⣀⠁⢬⡋⠘⣿⡿⢿⣿⣧⣿⣿⣿⣯⣤⣄⣻⢦⠙⢦⣡
⣿⣵⣦⣄⣴⣿⣿⠋⠙⢤⠀⠀⠄⠀⡀⠺⣩⡿⠃⠈⠉⣀⡉⠛⡄⢸⣇⡄⠀⣿⠸⣏⢉⡿⠲⡟⠉⢳⡀⠁⠀⢈⠧⢠⠀⢀⠀⠀⢀⣀⠀⠉⠙⢳⣣⡈⠻
⠙⢿⡏⠉⠙⣿⣇⠀⢀⣴⣷⣤⣤⣤⣬⣔⢡⠸⣶⠂⠀⠙⢁⣰⣍⣀⣹⡯⢀⠙⠳⣭⣭⣤⣤⣽⣶⣿⠞⠁⠀⢱⠄⠀⠀⣀⠀⠀⠀⢀⡀⠀⠉⢙⡿⢷⣀
⣷⣾⣇⡀⠞⠀⠙⣿⣿⠃⣠⠤⠿⢏⣌⠁⣠⣦⢠⡴⠛⠓⠾⠿⠋⠁⠙⠙⣿⣦⣀⣠⣤⣴⣿⠛⠁⠱⠄⡴⢷⣾⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣽⣟⠻⠠
⣿⡽⣿⣧⡀⠀⠀⠈⢿⠏⠀⠀⠀⠀⢨⡗⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠛⠋⢀⢹⣏⣤⣤⣀⢻⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⡇
⣧⠞⠋⠀⠙⣤⠀⠀⢸⡀⠀⢠⣄⠀⢸⡀⠀⠀⠀⢠⣞⣳⡄⠀⠀⠀⠀⠀⠸⢇⠀⠀⡜⡦⢿⣍⢻⣿⣿⡟⠁⠘⠣⣀⣄⣀⣀⣀⣀⣀⣀⣀⡰⢋⣿⣿⠃
⠃⠀⣶⠀⠀⣸⣷⣭⣪⣇⠀⣰⠈⠙⠉⠳⣄⡀⠀⠈⠛⠋⠀⠀⠀⠀⣀⡀⠀⠀⢧⠀⢁⡷⠾⡿⠛⠛⠛⠁⣠⣤⠀⠀⠈⠛⢁⣼⠋⡛⠉⠉⣠⣿⡟⠁
⠀⠀⠛⠀⠂⢻⡥⠛⠁⠀⠀⠀⠙⢦⠀⠀⠀⣸⡶⢦⣀⠀⠜⠷⠀⢼⣿⣿⠀⠀⢮⣀⢞⣵⡟⠀⠀⠀⠀⠀⢹⠟⠁⠀⠠⠀⠀⠀⠀⠀⡴⢞⡼⠋⠀⠻⠃
⢀⣀⠀⢀⡴⠃⠀⠀⠀⢰⣼⣷⠀⠘⣄⠀⣾⠃⡀⠀⠈⠻⠢⢄⠀⠀⠉⠁⠀⠀⠀⠙⣮⠉⠹⡄⠀⠤⠀⢀⠞⠉⠁⠀⠐⡰⠀⠉⠳⢚⣛⠋⠀⠀⠀⠀⠘
⠀⠀⠈⠙⠀⢠⣤⡀⠀⠌⠙⠉⠀⠀⣹⠋⠉⠀⢀⡀⠀⠘⠃⠀⣼⠐⢤⣄⣀⣀⣀⢠⣿⠣⡉⢹⡴⠞⠛⢃⡈⠉⠁⠒⢦⣡⡀⠀⠀⠈⠧⣀⡀⠀⠀⠀⣠
⠀⠀⣶⣧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⣯⢀⡀⠀⢈⡁⠀⢠⡆⠀⣀⡀⠀⢸⣿⣏⢹⣾⣿⣇⠀⠀⣺⣿⣿⡿⠿⠶⢶⣤⡴⣍⢈⡁⠀⠀⠂⠼⠃⢀⡀⠰⠏
⣀⣀⣿⣿⣧⣀⠀⠀⠂⠀⠀⠀⠀⠀⠸⣟⣣⣤⣭⢤⣤⣀⣀⠀⠛⠋⢤⣿⣿⡿⠻⣿⡞⣿⣿⢂⢩⡿⠛⠿⠿⠁⣤⣬⣕⠁⠈⢁⡠⠄⠀⠠⠤⠬⡧⣌
⣿⣿⠟⠻⣍⣿⡷⠈⠁⠀⠒⠢⣠⠔⠋⠉⠀⠀⠀⠀⠀⠈⠻⣤⣆⣠⣾⡽⠃⣠⠐⢬⠻⣿⣼⡟⢀⣀⠀⠀⠀⢀⠈⠉⢩⡀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠉⠛
⡿⠁⣴⠁⢀⣠⣄⠰⣦⠛⠲⠞⠀⠀⠀⣠⣶⣄⠀⠀⢀⣄⡀⠈⣿⣿⠻⠇⠾⠁⣀⡤⠀⢨⡟⠀⢿⡿⠀⠀⠸⣿⡇⠀⣸⠁⠈⣀⠘⠀⠀⠀⠀⢀
⠉⠀⢿⣄⡈⣉⣙⡃⣾⣿⡁⠀⠀⠀⠀⠈⠙⠋⠀⠀⠻⣿⠟⢰⣿⡿⠓⢤⣀⠸⠋⢠⣄⠉⡿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠴⠻⢦⠀⠀⢀⣤⠀⠙⠳⢦
⠀⢀⣼⠿⠟⠉⢁⡀⠉⠉⣁⡶⠒⠀⠤⢀⣀⠀⠀⠀⠀⣀⣴⠟⠛⢀⠀⠀⡹⢿⠯⡥⠭⠾⠃⠈⠙⣇⣠⡄⢀⡀⢸⢿⣿⡇⠀⠀⢸⣷⣤⣀⠁⠀⠀⢀⣤
⣴⣿⣿⣴⠀⠀⢼⣿⠂⢸⡿⠃⣾⠛⡄⠀⣿⢤⠋⢻⣤⣿⡇⠀⠀⠀⠀⢸⠀⣿⠀⡏⠀⠠⠀⠀⢈⡟⣹⡿⠛⣻⣟⣾⣿⡇⢄⠀⢀⠴⠛⠛⠛⠶⢦⣤⣀
⣿⠿⠛⣿⠀⠀⣀⡀⠖⢸⡄⠠⣿⠀⣇⠀⣿⠀⡆⠀⣿⢿⣇⠀⠈⢀⡤⠜⠀⠛⠀⠳⠤⣦⡀⢰⡿⡉⠂⠄⣱⡿⠛⠉⠉⠙⢮⣽⠉⣿⣷⡆⠀⠓⣀⠈⢿
⠿⢷⣤⣿⣿⠀⢿⡿⠀⣿⠇⠀⣿⣤⠟⠋⢿⣤⠇⠀⢸⣾⣻⡀⡼⢁⣤⣴⡄⠀⢀⣶⣵⡆⠙⣿⣷⡟⠀⢰⣿⠁⠀⢴⠆⠀⠀⢡⠤⠈⠉⣤⠀⢸⣿⡶⢸
⣀⠀⠈⢻⣿⣶⣤⣀⣀⡇⠀⠀⠘⠋⠀⠀⠈⠉⠀⠀⣼⠿⣿⠧⣶⣄⠛⠛⠹⠟⠇⠙⠋⢁⣴⣶⣿⣷⠾⡿⢿⣆⠀⠀⠀⠀⠀⢸⣄⠀⠀⠁⠀⠀⠈⢠⣿
⣷⠘⠀⠀⠀⣺⠿⠟⠉⢻⣦⡤⢆⣀⡀⢤⣤⡦⢤⣴⠱⠛⢻⣿⣿⣿⣿⣶⣄⣤⣠⣴⠞⠉⠀⠨⡷⠀⠀⠀⠀⠳⣠⣶⣶⣿⣿⡞⣥⢋⣲⣤⣤⡤⠛⣿⣿
⠛⢷⡤⠚⠉⠁⠀⠀⠀⠀⢻⣆⢻⣿⡅⢸⡟⢧⡈⠅⢴⡷⢈⠁⠠⠉⠉⡙⠛⠧⠿⣿⣷⣤⡰⠄⢣⢌⠿⠄⠃⣸⡏⠉⠀⣹⣿⣷⡶⠟⠉⠀⣠⣤⠀⠈⠻
⣀⡘⣧⠀⠐⠄⠀⠀⢀⣰⣾⠏⢼⣿⣿⠀⣷⢨⡇⡐⣆⣔⢠⠾⠀⡄⠈⠁⠀⠾⠀⢠⣩⡿⢛⣦⣈⠀⠋⠀⠛⠉⢻⡀⠀⣿⡿⠋⣀⡀⠀⠈⠿⠟
⠀⣀⠘⣧⣀⣀⣤⣶⣿⡿⣿⣄⣾⣿⢏⣠⡟⠦⣧⠁⡙⣋⡀⠀⢂⡰⠆⠈⠐⠀⠀⣾⡿⠃⠈⠀⡝⠓⠺⠖⠁⠂⠈⠛⢾⠋⠀⠸⣿⡿⠀⠁⠀⠀⢀⠤⠚
⢸⣶⣷⣄⣿⣿⣿⣿⡾⠛⠛⢿⣟⣿⠀⣉⠑⠃⢤⣾⡅⠙⢡⡆⢻⣧⣭⣀⡤⣶⣾⠟⠀⠀⠀⠀⢾⠀⠀⠀⠂⠐⢀⣀⣠⣷⡀⠀⠀⠀⠀⣀⠤⠊⠁⢠⡀
⠀⠉⠉⠀⡏⠙⠹⠿⠀⠀⢀⣾⣿⣿⣷⣄⠺⡷⠈⣥⡀⠛⢣⣴⡏⠰⣾⣿⠁⣿⠃⠠⠀⠀⢀⢠⡀⠀⣠⣤⡀⢀⣶⣿⣿⠿⣿⣶⣦⠶⠊⠀⠰⠒⣰⣿⣄
⠀⠀⠀⠸⠀⡄⠀⠀⠀⠰⢟⣿⢿⣿⣿⢟⣿⣶⣦⡉⢁⣈⠈⢋⣤⣴⣿⡿⢸⣿⣤⣤⣴⣾⣿⣄⡙⠻⢷⣄⠹⠏⣽⣿⠈⠀⠑⣯⣿⣧⠠⠀⢀⣿⣿⣿⣿

⠠⢴⣶⡦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠤⠤⢐⡒⠤⢄⡀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠙⢦⠭⠍⣛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⢀⣨⡵⠖⡟⢉⣯⣉⣩⡠⢷⠏⢉⣽⣷⣶⣦⣄⡀
⠀⠀⠀⠀⣯⣐⣒⠽⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣴⠚⡏⢀⢇⡀⢱⠉⢠⠋⠸⡀⡠⢦⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⣰⢓⡀⣄⣺⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠻⣁⠴⣀⠬⡇⠀⢸⠉⢲⠔⠃⡖⢹⡀⢸⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⡼⡩⢔⠴⠛⠉⠀⠀⠹⣄⣏⣙⡖⢲⡒⣲⣛⠯⡩⠣⢌⣧⣀⡇⠀⣇⠀⡸⠒⠚⡤⠼⣄⣀⡧⣀⠟⢻⣧⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⢸⢫⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣯⣨⡇⢸⡀⡸⣀⠧⣀⡎⢠⠋⠉⡖⠉⡱⠣⣀⣸⡀⠸⡀⢨⡅⠈⡦⣀⣻⣷⣽⣛⣻⣿⣛⣵⠏
⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡞⢧⣸⡀⢨⡀⣈⠉⠲⠣⠴⠓⠤⣇⡀⣘⠀⠉⡚⠉⢇⣈⣽⢳⠀⢃⠈⠛⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠉⠓⠾⠥⡕⠓⣤⠸⢤⣬⠀⢸⠉⠒⣴⠿⠖⠊⠉⠙⢾⣏⣉⡯⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⡴⠛⠲⠧⢤⣎⣀⣉⣞⠂⠤⣍⣢⣄⣀⡀⠀⢸⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠀⢠⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⡀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡤⠀⣀⠝⠣⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⢰⡥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⠮⠀⠀⢀⠀⣀⣄⡀⠂⠀⠀⠤⢀⡄⠀⠀⠀⠀⠀⠐⡎⢀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢱⠇⠀⠀⠀⢨⠏⠁⠀⠋⠁⠁⡄⢀⠀⠀⠋⠑⡖⠀⠀⠈⢣⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢸⡁⠀⠂⠀⣾⠀⡀⠠⠠⠈⠂⠐⠀⠒⠀⠀⠐⠟⠀⠀⠀⠸⡇⠀⠀⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⢈⠃⠀⠀⠘⡇⠀⠐⠂⢿⠀⠁⠄⠀⠀⠁⠀⠀⢀⠄⠀⠀⣾⢠⠀⠀⠀⣿⠀⠀⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠠⣿⠀⠀⠀⠼⢿⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢶⠃⠀⠀⠀⡀⣿⠖⠀⡜⠀⠒
⠀⠀⠀⠀⠀⢀⠀⠙⣠⠀⠀⠁⢀⢸⡏⠀⠀⠀⠈⠳⣇⠀⡲⠀⠀⠀⠠⢂⡴⠓⠀⠀⠀⠀⠀⣟⡀⠀⢰⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠵⢤⣀⡀⠈⢹⡇⠀⠀⢀⠁⠀⣌⠿⣧⣀⠀⣄⡾⠋⠀⠀⠀⠂⠠⠀⢸⡏⢀⣴⢋⡄⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⢳⣾⠁⠀⠀⠀⠀⠀⠁⢀⣀⣽⠟⠿⣴⣅⣀⠀⠼⠀⠀⢀⣼⣷⠟⠁⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⡀⠠⢈⡀⠀⢳⣴⠞⠉⠠⢀⠀⠀⠈⠻⠻⢶⣤⡂⠀⣿⡏⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠐⠸⣇⠀⠀⣄⡴⠛⠉⠙⠀⠁⠉⠀⠀⢀⢐⠄⢲⠙⠻⣷⣿⣧⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠐⠀⠀⢿⣆⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⢸⣿⣿⠄⠀⠈⢒⣀
⠀⠀⠀⠀⠀⡠⢀⡠⠄⠀⠀⢠⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⢸⣿⣿⠄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⣠⠒⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣇⣀⣵⠾⠅⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠿⣤⣧⣄⢸⣿⣿⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠈⠃⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⣼⣿⡍⠙⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢹⣿⡏⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣸⣿⣷⣸⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣹⣿⡏⠀⢿⣯⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⣿⢿⠃⠀⠸⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣷⣄⣀⣠⣿⣼⣆⣀⣠⣿⣷⠀⢀⣀⣀⣿⣿⣿⣿⣄⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣶⣶⣶⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠒⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢁⣄⣠⠀⠈⣀⡀⠐⠀⠀⠀⠀⠁⡀⠡⠀⠀⠐⠀⠀⠒⠃⠀⣤⠀⠓⠒⠲⢄
⠀⠀⠀⣀⠀⠠⠈⠁⠀⣈⣁⣾⡀⠀⠿⠹⡿⢈⣀⢠⣿⡧⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⣀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠠⠿⠿⠿⠿⠄⠺⠆⠠⠈⠋⠈⠁⡀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠚⠃⠤⣀⡀⠐⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣦⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠄⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⠀⠀⠠⠀⠀⠐⠀⠀⠸⠂⠀⠀⠀⢀⠀⠀⢠⣶⠀⠀⢠⣄
⠀⠀⠀⠀⠈⠃⠀⠀⠐⠀⢠⣤⠀⠐⠀⠀⠸⠿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠲⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠂⠀⠀⠀⠻⠟⠀⠀⠀⢀⣀⡀⠀⠃
⠀⠀⠀⠈⡁⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⢰⣶⡆⠀⢴⣦⠐⠊
⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀⢀⠄⡈⠫⠙⠏⠀⠀⠄⠀⠀⠉⠁⠀⠀⠉
⠀⠀⡀⠀⠀⠚⠂⠀⠀⣤⢠⡄⠀⢠⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⡇⠈⡆⠀⠀⡆⠀⠀⢲⠀⠀⠁
⠀⠀⠁⠠⠔⠒⠓⠀⠘⠃⠀⠉⠀⠈⠐⠻⢿⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⢀⡀⠀⢤⡀⠀⠀⠀⠀⠀⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⣴⣦⠀⠀⠀⣾⣷⠈⡆⠀⠀⡀⠀⠀⠚
⠀⠀⠀⠁⠀⠉⠃⠀⣠⣴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠛⠻⠀⠀⠀⠛⠋⠀⠀⡀⠙⠉⢠⡿⠆⠸⠧⢀⡄
⠀⠀⠢⠀⢤⣴⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣄⠀⠀⠀⠀⠐⠶⠾⠂⠀⢠⠀⠐⠀⠀⠀⠀⠰
⠀⠀⢀⡀⣠⠐⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡷⢦⣤⡈⠀⠀⠛⠉⠢⣀⣀⡀⣀⡀⠀⠀⠀⠂⠀⠀⢀⡠⠀⠀⠀⢡
⠀⠀⠠⠀⠀⢶⠄⠈⠀⠀⠀⢠⠀⠠⠀⠳⣶⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⡏⢠⠀⠀⢠⣠⠄⠀⢀⡀⣀⠀⠀⢸
⠀⠀⠄⡀⠀⠀⣠⡄⠀⠀⠀⠉⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⢿⣤⠄⠛⠀⠓⠀⠐⠃⠀⣼⡿⠛⡻⠀⢀⠃
⠀⠀⠀⠉⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠀⠐⠒⢶⣌⠀⠀⠀⠀⠀⠀⢀⣦⣤⣄⠀⠀⠈⠁⠉⢀⠐⠣
⠀⠀⠤⠶⠦⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢑⣶⠎⠀⣤⠆⠀⠀⠀⠹⡟⠁⣠⣄⡀⠀⠀⢿⣿⣿⡇⠀⠀⣤⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠀⠀⣀⠀⠀⢀⡄⠀⡁⠀⣿⣿⣷⠀⠀⠀⠌⠁⠀⠀⢰⠇
⠀⠀⠀⠀⢁⡀⠀⢸⣿⡦⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠼⠧⠀⠀⠉⣁⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡁⠠⣴⠀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠴⠁⠂⠀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠂⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⡈⠉⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢰⠀⠀⠠⠆⠀⠀⠀⠀⠀⠐⠆⠀⠀⢤⣤⡄⠀⢄⠀⠀⢀⡀⢤⠀⢀⣴⠒⢦⡀⠀⠀⠦⣀⣀⡄
⠀⢰⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠐⠟⠘⠋⠃⠘⠛⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⣤
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠀⠀⠀⢠⣦⠀⠀⢠⣀⡄⠀⠀⠀⠀⠀⢀⣀
⠀⢀⠔⠐⠷⠀⠀⠀⠰⠖⠒⠒⢾⡷⠀⠀⠀⣤⠀⠘⢿⠟⠛⠛⠿⠟⠀⢀⡀⠛⢋⠀⠀⠈⠉⠁⠀⠀⣀⠀⠠⠎⠁⠀⠆
⠀⠠⡀⠀⠀⠸⠓⠀⠀⠀⠀⣀⠀⠠⠀⠴⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠘⠛⠁⠀⠈⣀⣀⣀⣠⠀⠀⠰⣧⣀⣀⣤⠋⠉⠂
⠀⠀⠀⠉⠩⡄⠀⠀⠀⠄⠀⠀⡀⢀⠀⢠⣿⠶⠂⠁⠠⣤⡤⠤⠤⠶⣾⠟⠂⠀⢶⠊⠁⠀⠉⠲⠀⠀⡍⠉⠉⢉⠐⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠂⠀⠀⠈⠐⠀⠤⠀⠘⠂⠀⢀⣀⡀⢀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠐⠒⠭⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠶⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠐⠒⠒⠒⠂⠤⠄⡀⠉⠉⠒⠒⠤⠤⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠒⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠙⠀⠀⠒⠒⢂⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠠⢒⣉⣥⢀⣀⣀⠉⠉⠑⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⣀⣀⣀⣠⣤⣴⣊⣉⠤⢤⠶⢫⡖⠀⠀⠀⠀⠀⠀⢠⠀⡠⠚⢁⠀⢀⠀⠀⠀⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠒⠀⠀⠤⠶⡁⠀⢧⡑⢤⡟⠀⠀⠀⠀⢸⡡⠀⠈⠀⠀⠀⠀⠀⡸⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣀⠀⠉⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡴⠁⣀⡀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠄⠊⠁⢀⣠⠤⠒⠉⠀⢀⣀⠠⠄⠀⠜⡑⠦⠤⣄⣀⣠⠴⢋⡀⠀⢀⣀⡀⠤⠖⠋⠀⠒⠀⠐⠂⢄⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣀⡤⠚⠉⠀⣠⠴⠒⠉⠁⢀⡠⠂⡡⠊⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠈⡅⠀⠀⠒⠈⠁⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣤⠞⠁⠀⢀⡴⢋⠁⠀⠀⢀⠔⠉⢀⡜⠁⠀⡔⠀⢀⠜⢀⠇⠀⣸⡀⠀⠀⢹⡀⠀⠸⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡴⢫⠃⠀⢀⡴⠋⢠⠃⠀⢀⡴⠁⠀⢠⢞⠁⠀⡸⠀⡠⠊⠀⣸⠀⢠⢡⡇⠀⠀⡼⣷⡀⠀⢧⠀⠀⠈⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠃⠀⣰⠋⠀⢠⠃⠀⢠⠞⠀⠀⡰⠋⢸⠀⢰⡅⠈⠀⠀⢰⠃⢀⡎⠈⣷⠀⠀⡇⡇⢳⠀⠈⢧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⢀⡜⠁⠀⡀⠁⢀⡴⠋⢀⡠⠚⢁⡀⢸⠀⡞⠀⠀⠀⢠⠏⠀⡼⠀⢸⢿⡄⠀⡄⢸⠈⣷⡀⠘⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⢀⠎⠀⠀⢁⡠⢶⠋⠀⠊⠁⢀⠔⡱⠀⢸⠀⡇⠀⠀⢠⢏⠄⣸⠁⠀⢸⠈⡇⠀⡇⢸⠀⢸⡄⢄⠸⡀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⠀⢀⠔⠋⢠⠏⠀⠀⢀⠔⠁⡴⠁⠀⣼⢸⠃⠀⡰⢣⠂⣸⠃⢀⠀⣸⠀⣷⠀⡇⢸⠀⠀⣧⠈⢆⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠔⠁⠀⣠⠏⠀⣠⠞⠉⢀⡞⠁⠀⢰⠇⣼⠀⠐⡔⢁⡼⠁⢀⠎⠀⡇⠀⣿⢀⡇⢸⠀⠀⢸⠀⠘⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠔⣁⠴⠚⠁⠀⡠⠋⠀⠀⡠⠋⢠⠏⡠⢊⡠⠞⠀⢀⠎⠀⣸⠃⠀⡟⢸⠁⢸⠀⠀⠘⡆⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠁⠀⢀⡠⠚⢁⣠⠴⠊⠁⣠⠏⠀⡴⠋⠀⠀⢀⡎⠀⣰⠁⡇⢰⠇⡏⠀⡏⠀⠀⠀⠇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠉⢀⣠⠴⠊⡍⠀⡾⠀⠀⠀⢀⠎⠀⢠⠃⠀⡇⠀⡸⠁⢰⠁⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⡇⠀⢧⠀⠀⠀⠎⠀⢠⠃⠀⠀⡇⣰⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⢂⠀⢸⠀⠰⠃⠀⠀⢰⠇⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡁⠀⠄⠀⠀⠀⠀⡌⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠘⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠁⠄⠈⠀⠐⠘⠠⠈⠀⠛⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⣾⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠻⢻⣿⡿⣷⡆⠀⠙⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠋⠀⢈⡁⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⢿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠈⠀⣠⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠑⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢀⠀⣤⠆⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣵⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⢿⣄⣀⡀⠠⠼⠟⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣀⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣦⡀
⠀⠀⠠⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣼⣿⡏⢹⣿⣿⣿⣿⣿⠀⠈⠛⠿⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢰⣿⣿⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠉⠛⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣼⣿⣿⠃⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢀⣿⣿⣿⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠹⣿⣿⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣶
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣁⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢾⣿⣿⣇⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷
⠀⠀⠀⠀⢸⠙⣿⣿⣀⠀⡏⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⢀⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣠⣴⣿⣿⣖⠈⢄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⠿⠟⠙⠉⢋⠛⠉⠋⠙⡉⢋⠛⠙⠓⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂
⠀⠀⢀⣠⡶⡶⢾⠉⢻⡄⠡⠀⢀⠐⠀⢀⠐⡀⢂⠐⡀⢀⠀⡈⠀⠠⠈⠍⠩⠒⠖⠂⠀⠀⠹⣿⣇
⠀⠰⢉⠛⠿⠃⠈⠀⢀⡇⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⡀⡀⢀⠀⡀⠀⠀⠈⢀⠡⡈⠀⠠⠄⢄⣿⣯
⠀⠀⠀⠓⠀⠀⠀⢀⠞⡐⠒⠲⠶⠒⠂⠀⢀⠐⢀⠂⠀⠐⢀⠀⠁⠀⠀⣀⡤⠴⠒⠀⠀⠀⠚⠿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⠀⠀⠄⠠⠀⠄⠀⠀⠀⠐⠚⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⢰
⠀⠀⠀⠀⢀⣴⣠⡬⠄⠀⠂⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣦⣶⣷⣄⣴⣿⠃⣀⣤⡶⡿⠶⠒⡒⠖⠂⠤
⠀⠀⠀⡔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣄⣿⣯⣭⣿⣿⣽⣦⣤⡄⠀⠀⠈
⠀⠀⠀⠈⠓⠶⡦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡋⠁⠉⢿⣿⣿⣿⢶⣮⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠒⣶⡶⠂⠀⠀⠀⠀⠹⣿⡿⠻⡿⠶⢷⣮⣝⢿⣷⣦⣤⣤⣀⡀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡀⠧⠉⠛⠻⠾⠯⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠁

⢡⡾⠟⠛⢶⣤⣿⣢⣤⣿⣿⣏⡻⢻⠿⣷⡴⡀⣿⣧⣽⣿⠀⢠⣿⠟⠐⠉⠓⠈⠻⠟⠉⠁⢨⣿⣿⣷⡀⢀⣄⠸⣏⡑⠀⠌⠁⠀⢼⣿⣿⣰⠆⣤⠀⠰⡟
⣿⡁⠀⠀⠀⢀⣾⣿⣿⣿⠿⡿⣿⣾⢃⣼⠿⠃⠈⠉⠉⠿⠀⠸⣯⡀⠀⠀⠀⢠⡆⣀⣤⣾⣿⣿⣿⣿⠿⠮⠩⣾⠟⠛⢦⣄⡀⠀⢀⠀⠈⢻⡀⠋⠦⣄⣀
⠀⠀⠀⠀⠀⠘⣷⣬⣶⣵⣶⣶⣿⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⢀⡴⠋⠁⠉⣽⠿⢛⠛⢻⣿⣅⠀⢠⡇⠀⠠⠁⢉⣿⢣⠀⠀⠀⢸⡇⢠⣶⣤⡾
⠀⠀⠁⠀⠀⠀⠀⠉⠛⠛⠛⢻⣧⢸⣷⡄⠀⠀⢀⣶⠿⠦⠀⠀⠀⢸⣯⠎⢀⠠⠔⠛⠒⠚⠟⡛⢿⣿⣏⠿⢿⣧⣴⡃⢠⣿⣣⠆⠀⠀⣠⣾⠁⢀⣿⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠇⢤⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠚⠿⢷⡶⠷⢦⡹⠖⢋⠁⠀⢠⠀⣿⠃⢠⡟⠀⠑⢄
⠉⠀⠀⠀⠂⠉⠀⠀⠀⢠⣤⣴⣾⣍⣀⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⡶⠎⠀⠿⠉⣠⢀⡼⢀⡿⠟⠟⠛⢶⣦
⣳⢤⣞⠀⠀⠤⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⠞⢡⣾⣀⡀⠀⠀⠈⣱⡄
⢇⠀⠙⠻⠟⣷⡶⠊⢿⣿⣿⣿⣿⣿⡟⠋⠀⢶⣤⣴⣶⣶⣾⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⢶⣄⠂⡍⠹⣄⠀⠀⢸⡿
⡄⠰⠖⢀⣼⠏⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⣉⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠉⠻⣧⡀⠙⢦⣀⡿
⣇⠀⢀⣼⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠿
⣿⣆⣸⡏⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⢀⣤⣤⣤⣤⣤⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣡⡾⠁⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢹⡿⢷⣄
⠉⠉⢹⣷⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡞⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢿⣿⣿⡏⣴⡷⠴⡒⠊⢹⡁⢈⠀⣄⠒⠦⠤⣀⣀⠀⡟⠦⣹
⠀⠰⣿⣿⠃⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⣀⣀⡉⢻⡇⠿⠓⠚⠋⠉⠉⠉⠉⠉⠉⠒⠒⠒⠡⢼⡄⣿⠀⠈
⢷⣤⡐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣄⠉⠉⢄⠈⠀⠀⠀⠀⠀⢠⣼⡏⠻⡶⠛⢻⣿⣧⣿⢣⣤⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡇⢻⡀⢑
⠀⠉⠁⠀⠀⠈⠃⢀⣀⢀⢀⠀⡀⢀⠀⢀⣸⣿⣶⠀⢈⣦⡀⠀⣠⣶⠶⣿⣠⠖⠚⠀⢴⣿⣿⣿⣿⢸⡿⠛⠛⢿⣿⠇⠀⠀⠀⠀⢰⣿⡿⠟⣿⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢛⡿⢿⣿⡟⠻⠟⣻⣿⣷⠛⠙⣿⣿⠋⠁⣼⠛⠉⣈⠂⠀⠀⠹⣿⣿⣟⢸⣿⣿⣷⣾⠟⠀⣶⣶⡦⠀⠸⣿⣶⣿⡿⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠠⠤⠄⡀⢀⣾⣿⣿⠐⣺⢿⣯⡟⣿⣿⣶⠟⠛⣷⠶⢶⡄⢻⣿⡬⢷⣯⡛⠿⡃⠀⠀⠀⣏⠀⠀⠀⢙⠿⣫⡞⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣤⣤⢶⣤⣴⣶⣿⡿⣿⣿⠀⣿⢸⣿⡇⢘⣿⣿⠀⢂⡇⠀⠘⣿⡌⢿⣤⠞⠿⣿⠇⠈⠙⠻⡄⠉⣀⠶⠛⠑⠀⢻⣇
⣤⠀⠀⠀⠀⠀⣿⢻⡟⠉⠀⠀⠀⠠⠀⠈⠛⢳⣿⠈⣆⣹⣾⣿⣿⣄⣸⣿⢄⡿⠀⠀⣀⠯⣷⡘⣏⢀⣼⢁⡄⠀⠀⠀⠐⠋⡝⠀⠀⠀⠀⠀⢻⡄
⠉⠤⠀⠀⡀⠀⢈⣿⠀⠀⠀⠀⠀⢀⠀⠀⣀⢘⣿⣦⣼⡷⠋⠁⠀⠀⠉⢣⣾⠃⠀⢠⠀⠀⢨⣷⡸⢟⣹⣿⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡛⢷⡀
⠁⠀⠀⠀⠀⡠⢚⣻⢀⣶⡆⠀⠀⠀⠀⢺⣟⣻⣭⡙⠏⠠⢤⡀⠀⠀⡀⠀⠛⠦⠴⠏⠀⢀⣎⠸⣷⡾⠿⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣦⣻⣦⡀
⣠⡶⣄⣰⠛⣠⣯⡉⣦⣽⠦⣤⣤⣤⣤⡄⠙⢛⡾⠳⡀⠀⠀⠄⠀⠀⠀⠁⣀⠐⠂⠀⠀⣿⣠⣴⣏⠿⣶⣄⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣠⣿⡽⣿⠈⠳
⣿⣵⡿⡇⠀⠀⢈⡁⢻⣄⡀⣉⠛⠛⠉⠤⣤⣾⠃⠀⠀⠀⠀⠐⠂⠀⠀⢀⠀⠄⠀⠁⠀⠀⢉⣈⣙⠿⣿⠿⢿⣿⣿⣶⣶⣾⣿⣖⣿⣛⣿⠽⣿⠿⢃⡀
⠟⠙⣿⣿⣷⣾⢾⣷⣾⠏⠀⢹⡆⢀⠀⠀⢹⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⣀⡏⠁⠉⠀⣿⡆⠔⠀⠈⠉⠙⠛⠉⠉⠉⠈⠁⢀⣿⣷⣿⠇
⠁⠄⠙⡿⢨⡿⠟⠋⠁⠉⠀⠀⠀⣇⠀⠀⠈⢧⠈⠀⠀⠀⠀⠀⠀⠀⡔⢠⣄⣵⢶⣾⣫⡟⠱⢶⡤⠊⠹⡇⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡏⠉⢿⣶⣾
⡔⠛⠂⠀⠀⠀⠀⠐⠆⠀⠀⠀⢻⡏⢷⡄⠀⠈⠳⠀⠀⠀⠀⣤⡀⠀⠁⠀⠀⠨⠉⢿⣿⣬⣡⠾⣶⠄⢠⣿⠀⠀⢹⠿⠟⠛⠛⠿⣟⠁⠀⢸⡧⠀⠒
⢹⠋⢤⠀⢀⠀⠀⠀⠀⢠⠀⡉⢸⠇⢨⡇⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⢀⠰⣶⣦⣭⣌⡴⢿⡙⠆⠈⣿⠀⠀⢸⣷⠀⣀⠀⣀⣽⠀⠀⢸⡇
⣣⡀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⡿⠦⢾⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡛⠃⢩⡿⠟⣛⡉⣙⠃⣄⠀⣙⠀⠀⣾⠁⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⠤⠤⠤
⠃⠀⠀⠤⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠠⠾⡟⠿⠞⣋⣄⣋⣉⣛⠻⣿⣌⠻⢿⡆⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⣿⠏⠁
⢶⡶⠶⠐⠆⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣛⠀⢻⠋⠈⠙⣿⠻⣦⣙⠛⠾⡇⠀⣿⢦⡤⠶⠖⠊⢻⡆⠀⣿
⢦⣀⡀⢠⣴⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠔⢱⣆⠹⣼⡿⠻⣿⢻⣿⣤⣿⠀⠀⠀⠀⠀⢸⣧⣶⡏
⣀⣝⢙⡛⣿⣶⣤⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠂⠰⠀⠆⢉⠆⠘⣿⣧⡌⠉⣿⠋⣾⣯⣴⣿⠁⠀⠀⠀⠀⣸⣶⣶⡇
⠁⠘⣷⣿⣯⠿⣄⣰⣿⢾⠗⣄⣀⣠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⣤⠃⣼⡄⢂⠺⣧⠉⠓⠬⣲⣼⡏⠤⣿⣇⠀⠀⠀⠀⣿⣶⡞⠷⣄
⠀⢠⣿⣿⡇⢤⡘⣻⣿⣷⣿⢿⣇⣹⣽⣷⠤⠆⠀⠀⢀⠀⠀⠀⠀⠐⠂⠀⣿⢠⣿⢿⣄⠳⠈⢷⠐⣠⡼⠏⣤⣾⠟⣿⠀⠀⠀⠀⣿⠻⣷⣶⠙⢳⣦⣀⡀
⠁⣜⣿⣼⡷⢤⡕⠛⢿⠀⣷⣚⣿⡯⢌⣷⣆⠘⣷⡶⢢⣠⣤⣄⢀⠓⠀⠀⣁⣦⣼⡁⠈⠳⡆⣨⠗⠛⠂⣴⣿⣿⣼⠟⠀⠀⠀⠀⢿⣄⡺⣿⣷⠆⠀⠀⢹
⠾⣿⠁⢙⠓⣀⠨⠀⠀⠀⠹⠟⠙⣿⡟⣟⣻⣿⢧⡀⠀⠹⣟⠸⣙⠑⠛⢀⠿⣼⢷⣹⣄⠞⣰⣿⡀⠀⠀⢘⡿⠾⠗⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⢀⣠⣤⡴
⠀⡇⠀⠙⠘⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠓⠀⠹⣧⣤⣴⣿⣶⢍⣴⡇⠸⡶⣇⢦⢣⡟⡛⠁⠀⠈⠉⠉⠁
⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⢠⡏⣎⢳⡜⢧⡹⣭⣎⣾⠛⡇
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣟⠓⠰⠎⣷⡘⣿⡟⠛
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢟⠠⠁⣆⡏⢸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣱⡸⡄⠀⠈⢀⡾⣾⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⠀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⣠⣴⣶⣶⣶⣦⣄⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡋⣤
⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣯⣴⣏
⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠑⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢰⠁⠀⠀⣀⠠⠤⢤⣴⣚⣋⡙⠂⠀⠀⠀⠀⠀⢀⢠⣶⣶⡿⣿⣟⣉⠛⢆⡀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡐⠃⠀⠰⡾⠶⠶⠶⠖⠿⣿⣋⠁⠀⢄⠀⠀⠠⠞⣠⠟⡙⠈⠀⢰⠈⢣⠙⢦⠙⣦⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⣁⠄⡴⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡸⠀⠀⠀⣼⠃⡎⠀⠀⠀⢸⠀⠀⡆⠀⢣⠘⣧⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠓⠶⠟⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠑⡀⠀⠘⠟⠀⡅⠀⠸⠀⠈⠀⠐⠁⠀⢸⠀⢻⡄⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⡄⢀⠞⠁⠛⣦⡀⠉⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠠⡄⠀⠀⠀⠠⠺⠿⠔⠋⠀⠀⠀⠈⢣⠀⢠⠘⣷⠀⠘⠛⠀⠀⠀⠐⠂⠀⠀⠀⡰⠋⡇⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠇⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⡀⠀⠸⠀⠸⠈⠳⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠷⠊⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠘⣶⣀⠑⠋⠛⠀⠀⠀⠈⠀⠀⣠⠃⣰⠃⠀⠀⠀⠉⠒⢤⣤⣄⣤⡤⠐⠋⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠙⠧⣀⠀⠀⠀⠀⠀⠀⢈⡽⠚⠁⠀⠀⠀⠀⠀⣀⠤⣤⣻⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⢤⡤⠀⠚⠉⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢢⣄⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡍⠉⠀⠈⠿⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠛⠀⠀⠀⢰⠀⢣⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⣴⠀⠀⠀⢘⠀⠀⠀⡹⢿⡆⠀⠀⠀⠀⠀⠀⣴⠛⠛⠳⡄⠙⢄⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡜⠀⣠⣤⠾⣄⠀⠀⠰⣤⡴⠚⠁⢸⡀⠀⠀⠀⠀⠀⠀⠻⣤⣠⡤⠇⠀⠈⡇⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⡰⠁⠘⢇⠀⠀⢈⠃⠀⠀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠑⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣀⣠⡤⠊⠀⠀⠀⡸⠁⠂⠉⠀⠀⠀⣴⠀⠀⠀⠈⠢⡖⠒⠒⡖⠲⠒⠒⢲⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⢀⡬⠁⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠀⠀⡇⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠦⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢈⠀⠀⡇⠀⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠷⠀⠀⡈⠀⠀⡇⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠉⠉⠉⢙⡏⠉⠉⠁⠀⠀⠀⠀⡇⠀⠀⡇⠀⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠃⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⠀⠀⢸⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠁⠀⠀⠀⠀⠀⣿⠉⢳⠀⠀⠀⠀⢠⡀⠀⠀⣸⠀⠀⢈⡀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠘⢆⠀⠀⠀⣈⠩⣏⡉⠉⠀⠀⠀⠉⣡⠟⠢⢄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣈⣀⣇⣀⢸⣄⣀⠀⠀⡸⠀⠦⠤⣤⠶⠶⠮⠥⠤⠤⠭⠶⠴⠶⠶⠬⠤⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠄

⠀⠀⠀⠀⠀⠘⠿⠿⢗⣶⡶⠶⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⢤⠀⠉⠙⠛⠶⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠠⢀⡁⠚⠢⣄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠙⠲⣄⠀⠑⢄
⠀⢀⣤⠒⠒⠉⠀⠀⠀⠤⠀⠀⠒⠀⠤⠀⡀⠂⠄⡐⠠⡢⠈⠣⠐⢀⠳⣄
⡔⠊⠀⠀⠀⢀⢀⡀⠀⠐⠠⡄⠀⠀⠄⢀⠀⠀⠀⠀⠐⣈⣄⣀⣀⣄⣠⣈⣿⣦⡀
⠸⠁⠀⡐⠈⠀⢀⠀⠈⠂⠀⠈⠂⠈⠀⠠⠀⠈⠀⠴⢾⣋⣉⣥⠷⣾⣷⣟⣮⣿⣿⣦
⠰⡀⡀⠀⣀⡴⠂⠒⠂⠤⠀⣉⠐⠂⠤⠲⠦⠦⠔⠊⠁⠛⢛⣶⣿⣿⣿⣿⣿⣿⣯⣿⣧⡀
⠀⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠶⠴⠶⠄⠚⠉⠉⠀⠉⠙⠻⣿⣿⡟⡉⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠱⢆⡹⣿⡇⠀⠂⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢿⣿⡙⠀⠁⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢨⣿⠁⠈⣶⣛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢠⣾⠏⠄⣸⡧⠽⡾⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⣀⣰⡿⠻⠀⢰⣧⢃⣟⣛⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠈⠛⠃⠈⠁⠀⣐⡮⠰⠤⣭⣭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣀⠗⣺⣚⠒⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠰⠀⢠⠀⣤⠰⣃⣩⡯⣼⣹⠟⣀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⡆⠀⠀⠀⠀⢬⢂⡩⠖⠶⣶⣿⠞⠍⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠳⢦⠆⠀⠀⠀⡉⠌⠡⠔⠘⣸⡿⠁⠈⡠⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⠿⠲⢤⢚⡀⢄⢚⠱⢊⠡⠔⠛⣸⡗⠀⠂⠀⣂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠿⠳⠴⢠⢊⠱⠈⠛⢢⡘⠣⠴⠚⢙⡧⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠗⠶⢲⢤⣁⠜⢰⠉⠸⠃⡄⠡⢁⡞⢝⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠦⢴⢠⣂⠘⠈⠅⡔⠁⠢⡉⢢⠙⢠⠞⢿
⠀⠀⣀⠀⢀⣀⡠⠠⢤⣀⠀⠀⣾⣧⣤⣤⢀⡌⡀⠁⠇⢄⠀⡠⠠⡸⠆⡠⡙⢤⠾⡇⠀⠀⡀⣀⡤⣄
⠀⣸⡀⠙⢋⠉⠑⠀⠀⠈⠳⠢⣿⣀⣤⠈⠃⢹⡑⢸⠤⠊⠨⠄⠀⠛⠀⠃⢈⡏⣈⣧⣠⠊⠉⠁⠀⠘⠓⠲⢤
⠈⣦⡀⠀⢀⠐⠠⠀⠢⡀⠁⠀⡝⡽⠁⠀⠰⠋⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠈⡇⢈⠀⡀
⠀⠈⠢⣁⠠⢈⠐⠀⠀⠐⠡⠮⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠈⠉⠉⠲⠀⠀⡸⡧⠚⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠙⠢⠬⣀⡀⠀⠀⠈⢀⡅⠀⠀⠀⡀⣤⠲⠀⢴⠀⠀⠀⠀⠀⠀⠀⢨⠐⣷⠷⣀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⡄⠀⠀⣸⣷⡄⢰⡈⠑⣦⢠⠄⠁⠈⠀⣾⣷⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⠛⠀⠚⠁⠀⠘⡋⠀⠀⠀⠀⠉⠀⣿⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢵⠏⠁⠪⠀⣠⠄⡀⠀⠀⣨⡀⠫⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠰⠁⠴⠠⠦⣬⣤⠼⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠱⡌⢿⣶⣶⣶⡖⣦⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠴⠊⠉⠙⠢⠬⢭⠥⠔⠋⠓⠠⠩⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣰⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⠷⠦⠬⠍⠙⢒⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢉⣩⠴⠖⣻⠉⠩⠥⠀⣀⠐⠒⡀⠀⡀⠈⠉⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⣉⠀⠒⠠⠤⠀⠐⠀⠀⠀⠀⠀⠀⡼⠀⠀⣎⢮⡇⠀⠀⣀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠘⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢉⣤⣶⠋⣉⡀
⠀⠀⠀⠀⠀⠀⣀⡼⠁⠂⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⠤⠄⠀⠀⠱⡀⠀⠀⠈⠉⠉⣁⡴⠃
⠀⠀⠀⠀⢠⡞⢹⠃⠁⣀⣀⠀⠀⠀⠀⣀⣀⣹⣏⠭⠀⠀⢀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠸⣇⣾⠀⢾⡁⢀⢀⡴⠚⠉⠁⠀⠀⠈⠛⠓⠚⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⢻⠀⠈⠉⠁⡞⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⡆⠀⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣤⠤⠴⠋⠀⢦⣸⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡀⢱⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢱⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢖⣶⡶⣶⢶⡶⣶⡶⣤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⢻⣯⣿⡿⡟⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢟⣿⢟⡿⢗⣾⣿⣟⡿⠿⣶⣶⣦⣤⣄⣀⠀⢀⡀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⣠⠶⣾⣿⣟⡭⣚⡽⡞⢩⡾⣫⣿⡟⢋⣴⡿⣫⡽⢿⠽⠿⠿⠛⠛⠛⠛⠲⣇
⠀⠀⠀⠀⠀⠐⠧⣀⣸⣿⣟⡾⡡⣪⡶⣫⡾⣫⡿⣡⡿⢋⠞⢩⡶⠡⣀⣀⡤⣀⡠⠀⠀⢀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣞⡽⠋⠴⠏⣤⡿⣵⠟⢡⡟⣴⠟⣯⡀⠻⠾⠃⢸⠇⠀⠀⠀⢤⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⡤⠖⠒⠒⠹⣿⣯⣾⢸⡇⣿⢸⣿⢙⡶⡴⢶⣿⠀⠰⣶⣄⠀⠙⣦⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠿⣿⢟⠕⠁⠀⠀⠠⢄⣀⢹⣿⣿⣿⣿⣿⡿⠉⣽⢎⡴⣸⠸⣧⠀⠈⢿⣷⣄⠈⢷⡘⢄⣀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠧⠐⠳⡿⢣⠟⢷⡹⣷⣤⡀⠙⠻⢷⡜⢿⣦⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠛⢸⣇⢷⢻⡹⣿⣷⣦⣄⡙⢦⣠⣽⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠮⠛⢳⡬⡙⠲⣿⡄⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠂⠈⠻⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣻⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡇⠼⠃⢀⡀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠐⠂⠀⠀⠀⢀⡩⠤⠤⡜⢸⡤⠒⢉⣉⡉⠉⠻⣿⣿⣏⠀⠀⢀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠤⠴⠅⠀⠀⢈⠰⠋⠱⠀⠹⠿⣿⢲⣄⣸⣿⣿⣿⠀⠈⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣿⠆⠈⢑⠊⠁⠐⠂⢀⡀⠔⠀⠃⠐⡤⢌⠉⠁⠘⡄⠀⠀⣠⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⡯⠒⢉⣈⡑⡄⠈⠈⢹⠤⣀⡠⠼⣀⠇⣸⣄⠀⡘⠀⠀⠰⠏⣩⠿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣰⢱⣶⠞⢿⣧⣸⡆⠀⢈⠖⠁⠀⠀⠀⠀⡀⠙⠑⡌⠀⠀⠚⠛⢿⣿⡎⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⢸⠀⢉⢻⢻⡿⠟⡓⠒⠚⠤⣀⠒⡶⠀⠘⢑⠀⠀⠈⠢⠤⠀⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠸⠦⠓⢾⡀⠀⢡⠊⠀⠘⢷⣇⣤⠖⠈⡣⠄⡲⣾⡟⣠⠊⠑⠆⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⢡⠳⢄⣠⡠⢠⠼⠋⠹⠀⠀⣀⠧⠤⢏⡁⣤⣨⠑⢢⠃⢗⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⢂⠩⡔⠸⣄⡀⠈⠀⠀⢀⠀⠓⣄⠎⠁⡀⢀⣀⣈⠫⡥⠒⣧⢡⢨⠋⢔⠀⡂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠤⢊⢓⣾⡅⠘⠃⠀⠘⠁⠀⢸⠀⠈⠃⠚⠛⠋⠀⣇⠜⠀⠀⡿⠐⠠⣄⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠨⠴⡈⢹⢁⠀⢶⠾⡿⠀⠀⠀⡄⡂⢐⢀⣾⠄⠀⠈⠀⢀⠀⣯⠀⠅⠈⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⣼⡦⠤⠤⠤⠤⠤⠤⠤⠧⠬⠥⠤⣥⣤⣤⣧⡤⠤⠤⠿⡐⠀⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠹⢿⡿⠟⠁⠀⠀⢀⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣤⣄⡀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡀⠀⠀⠀⠀⠀⣠⣴⣦⣄⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⣴⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⣀⠀⣒⣀⠁⡝⠻⣿⠦⣝⢛⡠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡢⠂⣂⡏⣼⡎⢶⢑⠂⣸⣃⠈⠅⠉⠻⣽⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡑⡐⢳⣬⣵⠋⠀⠅⣠⣈⡑⠄⡙⠳⠄⠈⠛⠲⠕⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣛⢃⠀⢆⠠⠈⡏⣥⢠⣯⢫⣯⡲⣅⠱⣦⡒⠶⣌⡀⠵⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⢠⢙⠋⡘⣧⡾⠶⢭⠟⠙⢮⣕⠂⠙⠪⠚⡟⢳⣤⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣧⡟⠙⢉⠂⢆⠀⠀⠈⠛⠢⠀⠀⠈⠲⡡⣭⡙⣥⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⣤⠈⢢⠀⠀⠀⠀⠀⢀⡀⠀⠈⠈⠛⢿⣧⡈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡡⠄⠠⢂⠀⠀⡀⡰⣄⡳⣳⡀⠀⢤⠈⢿⣧⠀⠠⢉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣄⣧⣳⣽⣿⣧⣻⢢⠈⣇⢈⢫⣟⠓⢶⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣰⠂⠀⢌⡹⢟⣷⡄⠀⠈⠈⡟⡍⠑⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⢉⠹⣿⣿⢰⠸⡇⠐⣏⠀⠑⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢠⠠⠈⣻⣹⠐⣿⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎⠠⠀⠉⠽⢯⣼⣷⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡀⢈⡟⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⡀⡰⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠄⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠂⠀⢀⠀⠀⠀⠁⠘⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠦
⠀⠀⠰⠂⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠒⠖⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⣠⠀⠐⢦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⠁⠉⠀⠈⡂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠔⢖⠛⠁⣴⣧⡀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⢠⣿⣿⡀⠀⠀⣿⠿⠿
⠀⠸⢫⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠈⠉⠁
⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠈⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠛⠀⠀⣀⡀
⠀⠀⠀⠀⠐⠀⠀⠂⡃⠀⠈⠀⠂⠀⠀⠀⠀⠂⠀⠀⠘⡀⠆⠀⠀⠀⠀⠀⠈⠀⠈⢂⠀⡍⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⡔⡂⡠⠀⠀⠠⠀⠀⠀⠄
⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠾⠧⠈⠘⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠉⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠦⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠐⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢄⡀⠀⠁⢢
⠀⠈⠉⠀⠔⠀⠀⠀⠀⠀⢠⠄⠖⠀⡁⠐⡀⠀⡁⢀⡄⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⠤⠰⣷⡀⠤⡁
⠀⠀⠈⠁⠀⠀⠀⢀⠀⠠⠃⠀⠐⡀⡱⢘⠁⠀⠀⠀⠀⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠁⠈⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠠⠐⠅⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠐⠠⠄⣀⠀⠀⡀⡴⢾⠀⠀⢢⠀⢀⠐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢩⣼⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠠⡠⠠⡀⠏⠐⠁⠀⢀⢀⠜⠉⡆⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡁⡸⠫⠴⠆⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⢠⡡⠒⠢⡄⣀⠈⠀⠀⠀⠱⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡁⠊⠁⣈⣴⠁⠦⠤⠀⠂⠆⢳⣀⡖⠐⢧⡈⠀⠀⠰⡇⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠵⠆⠚⠆⢤⠋⢐⡂⠋⢨⠛⠠⠇⠰⣰⢒⠘⠃⠈⠁⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⢂⡐⠄⠐⠄⠠⠒⠀⢀⢰⣚⠻⠀⠁⢀⠀⠠⡇⠀⠙⡀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠠⠄⠀⠀⢠⠑⠈⠀⠁⠀⠁⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣘⣂⣄⡤⢄⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢈⣄⠀⠉⠂⡀⠣⡀⠙⢜⠐⠫⡠⠄⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣲⢄⡀⠀⠀⣀⠑⢄⡑⠄⠑⠄⡀⠀⠀⠈⠉⠻⣄⠀⡤
⢀⣀⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣙⠂⠈⠑⠢⠄⡙⠢⡈⢀⢠⡤⠀⠆⠚⡛⠚⠓⢚⠒⠾⠦⣀⢀⡀
⠉⠑⠄⠀⢀⠀⢀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠊⠉⣀⡐⠀⠀⢀⡰⠶⠋⠁⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠈⠓⢤⢤⣀⠀⠀⢉⠳⢤⣀⡀⠀⠀⠀⠀⠈⠘⣀⡬⠖⡉⠀⠂⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠌⠀⠀⠈⠀⠈⠉⠹⠒⠀⠀⠰⠉⠡⠀⢀⠀⡀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣉⠁⠐⠒⠄⠀⠀⠀⠀⠁⠄⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠂⠀⠀⠇⠀⠚⡀⠀⠀⠀⠀⠀⠁⠰⠐⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢠⣤⢧⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣬⠀⠀⠀⠀⠀⠀⢘⠋⣸⠆⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠁⣠⠔⠁⠀⡠⠚⠉⠀⠠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⠥⠸⡇⠀⠀⠀⠀⠀⠐⠮⠴⢂⡴⠞⠋⡫⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠖⠋⠀⠀⢠⠎⠀⠀⠀⠀⠐⢦⡀⠀⠀⡀⠠⠄⠀⠙⠛⠐⣓⠀⠀⠒⠉⠀⠀⠀⠘⢄⠑⢄⠀⠀⢄⣀⣴⠫⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⡔⠡⣢⠞⡵⠊⡰⠃⠀⠀⠀⠀⠀⠀⢦⠤⠐⠈⠔⡀⠀⣀⠴⠒⢉⠄⡠⢂⡀⠀⣤⡀⠀⠀⠀⠙⠂⠥⢀⡀⡬⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢱⡞⢡⠞⢀⡴⠁⠀⠀⠀⠀⠀⠀⣠⣜⡂⠠⠆⠚⠓⠒⠁⠀⠀⠃⠘⠁⠈⠈⠁⢈⡉⠀⠒⠃⠘⢀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡠⠃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠔⠀⠄⡼⡀⠘⠀⠄⢀
⠀⠀⠀⠀⠀⢀⣤⣮⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢈⠜⠀⠳⡄⠀⠀⡬
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⡶⠊⠀⠀⠀⢀⡆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠋⠀⠀⠀⠀⠀⣸⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣾⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠖⠒⠒⠒⠲⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢉⡁⢀⡶⢀⡴⠀⢠⠞⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣱⠂⣰⠋⢠⠏⠀⡞⠀⢠⡏⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⢁⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⡤⠖⠛⣏⠁⠈⣇⠀⠀⠸⡍⠉⠹⡗⠦⣄⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠞⠉⠀⠀⠀⠸⡆⠀⢸⡄⠀⠀⢻⠀⠀⢻⠀⡌⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⣧⠀⠀⠘⡇⠀⠸⡇⠙⠸⡆⠈⢧⠀⠀⠀⠀⠀⣠⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡄⠀⠀⢿⠀⠀⣧⠀⠀⣷⠀⠈⣇⠀⢀⣠⠞⢁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣶⣿⠳⡄⠀⠀⠀⠀⠀⠀⣷⠀⠈⡇⠀⠀⢸⡀⠀⢹⠀⠀⢸⠀⠀⢹⠖⣫⡤⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠻⣿⡴⠃⠀⠀⠀⠀⠀⠀⢹⠀⠀⣷⠀⠀⠸⡇⠀⢸⡄⠀⢸⡆⠀⢸⡆⠐⣒⣛⣉⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣦⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⢸⡀⠀⢻⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠨⢭⣍⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡉⠁⠈⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠋⠓⠶⢤⣈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⠇⢠⡏⠀⠀⠀⠀⠈⠙⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣀⠀⡇⠀⢸⡇⠀⣸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠐⠦⠄⠀⢸⡇⠀⣾⠀⠛⢰⡇⠀⣸⣥⠖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣙⠓⠶⠤⠼⠤⢤⠿⠤⠴⠞⠛⢋⡁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣀⣆⠀⠳⠄⠙⠦⠀⠙⠂⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠈⠉⠛⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⣠⢀⢠⡆⠀⠈⠀⠘⣿⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⣷⣿⣾⠟⠉⢻⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⡉⠋⠈⠁⠀⢠⡈⡀⠀⠐⠀⠀⠢⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠶⢄⠀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠙⠈⢷⡑⠝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢸⠉⠾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡾⠟⠷⢿⣄⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠃⠀⠀⠀⠈⢳⣷⠀⠀⠀⠀⠀⠀⠀⣘⣷⠞⠁⠀⠀⡄⣟⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢧⡼⠃⠀⠀⠀⠀⠰⠙⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⢆⢿⡀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⢀⣾⡄⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠘⠿⣧⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⣠⠟⠻⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⣣⠀⡠⠀⠀⠀⠀⢀⡠⠔⣿⡏⢤⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠃⢀⣠⠔⠊⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠓⠲⠤⠤⠤⠶⠶⣾⣿⡟⠀⠀⢤⣁⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠻⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣤⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠏⠉⠋⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡟⠁⠀⠀⠀⠀⣾⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠄⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⡀⣹⣿⠈⣷⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⢿⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡣⠀⠀⠀⠀⠀⠾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⢹⡇⣿⠀⠀⠀⠀⠰⠀⠀⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣋⣉⣏⣨⣏⣩⣍⣉⣿⣋⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠈⠭⣕⣢⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡀⠀⠀⠀⠤⣤⣄⡀⠙⢦⡁
⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⢒⠶⣄⠀⢹⡆⠈⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠷⠘⠀⠾⠁⠀⠃⠀⢰⠇
⠀⠀⣿⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣠⠤⠂⠀⠀⣀⣠⠴⠒⣋⡥⠄⢀⣠⠤⠒
⠀⠀⣿⠀⠀⢀⠈⠙⠲⢤⣄⣀⣀⡀⣠⠊⠀⣠⠴⣫⠴⢒⣡⠶⣋⣭⠴⠚⢉⣤⠴⢞⣩⠴⠒⠁⠀⠀⠀⠀⢀⡀
⠀⠀⣿⠀⠀⠀⠉⠙⠛⠒⠒⣺⣿⠋⠁⢀⣞⡽⠛⠁⠰⣫⠴⠛⠁⠀⠀⠀⠠⠖⠚⠉⠀⠀⠀⠀⡄⠀⠀⢺⣿⣿⡇
⠀⠀⢿⡄⠀⠀⢀⣉⣭⣭⣭⣭⣭⠀⠀⠰⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣸⡇⠀⠀⠀⠉⠉
⠀⠀⠸⣧⠀⠀⠀⢀⣠⠤⠶⠶⠶⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⢿⠸⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢻⠗⠀⠀⢁⣀⡤⠶⠒⠛⠀⠀⢸⣆⠀⠀⢺⣷⣤⣀⠀⠀⠀⠀⠻⢭⣉⠀⠀⠀⠸⡄⢧⠸⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⡰⠋⠀⠐⠚⢉⣡⡤⠖⠛⢉⣀⣤⣄⠻⣟⡦⣄⣈⠳⠮⣝⣓⠲⠦⠤⠤⠀⠀⠀⠀⠀⠣⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁
⠀⡼⠁⠀⠀⠠⠒⠉⠀⡀⠔⠊⠁⠀⠘⠻⣷⣌⡙⠲⢭⣝⣒⠒⠬⠭⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⢰⠃⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠛⠉
⣿⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⣰⡆⠀⢲⡄⠘⠲⣄⠀⠈⠿⠟⠛⠉⠉
⢸⣦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⢁⠤⠖⠛⠁⢀⣠⡼⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⢀⡠⠔⣚⡩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣀⣠⣤⣤⡴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣦
⠀⠀⠀⢀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢉⠀⠀⢈⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠐⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢶⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠊⡄
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡃⠂
⠀⠀⠀⡠⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠿⢿⠟⠻⢦⠀⠀⠁
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠸⠋⠀⠀⠀⢀⠀⡃
⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠔⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⢀⡰⠶⡚⡛⠈⣠⣷⣄
⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠰⣿⣿⡗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⠠⣻⠇⠀⠀⠀⣰⣦⣤⠈⠀⠁⠸⣿⣿⣿⣆
⠀⠀⣠⣤⣶⡄⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⢰⠿⣿⠿⡆⠀⠀⠀⠛⠙⠋⠉
⠀⠀⠛⣳⡍⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠒⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⡀⠒⠀⠆⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⢰⡾⠀⠀⠀⠀⠀⠉⠀⠀⠁⠁⠛⠁⠀⠈
⠀⠀⠀⠁⠀⠀⠐⠀⠀⡀⢀⠀⠒⡀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⢀⠐⢀⠀⠀⣀⠂⠀⢰⢠⠂⠀⡀
⠀⠀⠀⠀⠈⠂⠃⠈⠀⠉⠈⡀⠄⠀⠀⠘⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⢩⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⡀⠐⠅⠀⠸⠛⡒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡔⡒⠒⠠⠐⠀⠀⢂⠀⠀⠂⠀⠄
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢠⣸⡄⠐⠠⡄⠀⠀⠀⠂⠀⠀⢀⠀⢀
⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠉⡶⠈⠘⢓⢄⠀⠀⠀⠀⠀⠀⢠⢞⠤⠀⢆⠀⠀⢀⠁⠈⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡁⢀⣤⠮⠦⣧⠀⠀⠀⠀⢠⠿⠃⠀⠈⠂⣧⡀⣀⠎⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⣈⠉⠐⠂⢄⡀
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠱⣷⣋⡁⠀⠀⢹⠀⠀⠀⠀⢸⠘⠢⠤⠤⠤⣈⠍⢓⠤⠈⠓⠂⢤⠘⡆⠀⠀⠀⠀⠀⠀⠀⠘⢁⠄⠀⠈⠀⠀⠉⠁⢀⡽⣶⡦
⠞⠉⠁⠀⠉⠉⠓⢦⣀⠀⠀⠈⢌⠑⠉⢯⢱⠀⠀⠀⠀⢸⡐⠀⠀⠀⠀⠨⡧⠑⠢⡄⠀⠀⠀⢀⠇⠀⠀⠀⠀⢠⠴⠅⢀⠀⠀⠀⠀⠀⠀⢀⡤⢋⠌⠸⣷⣄
⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢣⡀⠪⠃⠀⠀⠀⠀⠀⠱⣕⢄⠀⢰⠁⠇⠀⠈⢪⡑⠤⢆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠒⠀⢰⠋⠀⠀⡜⠀⠀⠈⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡁⠰⣀⣀⡀⠴⣃⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡰⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢀⡴⠁⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠹
⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⡠⠤⣖⠂⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⢀⡔⡩⡌⠁⠀⡇⠉⠑⣪⠆⠀⠀⢀⣠⠴⠒⠒⠛⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⡄⠂⠁⠈⢸
⠀⠀⠀⠙⠢⢄⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⠫⣆⠀⡏⡀⠊⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣤⠔⠈⠁⡰⠉⣧⠈⠙⠪⡞⡙
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠴⠶⠂⢚⡿⠋⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⢦⡢⢼⠁⠀⠱⣧⣀⢔⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⠔⠉⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠲⠶⠶⠮⠤⠚⠁
⠋⠭⢍⢉⣙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠈⠀⠀⠉⠲⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣀
⠓⣤⣈⠀⣀⠀⠀⢋⡈⣧⠀⠀⠀⠀⠀⠀⠀⢖⠚⠉⠛⣖⠲⢤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢰⠃⠎⠠
⢄⢺⡉⡖⠢⠁⠀⠁⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠙⣆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⠞⠉⠈⢀⠀⠀⠀⠀⠀⣿⢸⣀⣈
⠀⠂⡆⡈⠁⠀⢀⣠⢣⠇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠄⠀⠀⠘⠀⠘⢧⡀⠀⣀⠀⠀⢀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⣎⠐⠦⣄⡈⠄⠀⠀⠀⠀⢹⡀
⠀⡀⡇⢀⠀⢀⡴⣠⠏⠀⠀⠀⠀⠀⠀⣠⠎⠉⠀⠄⠀⠒⠄⠒⠸⠄⠁⠀⠀⠙⠒⠥⠤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⡼⢿⡄⠀⠀⠀⠀⠳⡌⠢
⣉⣀⣑⣂⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠢⢄⡀⠀⠀⠀⠀⣉⠡⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣱⠋⠀⢀⡟⠈⡀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢕⠤⠴⡃⠀⣱⡀
⠀⠀⠐⠒⠒⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢒⡰⠒⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹⡁⠀⠸⠂⠀⡔⠁⠀⠀⠀⢀⡠⠴⠚⠛⡛⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡆⠀⠙⠦⢀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣸⡎⠉⠛⠶⣄⣆⠎⠀⠀⠀⠀⣠⠏⡰⡀⠀⠀⢁⠈⠈⠐⠬⠳⣄⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠇⠁⠀⠀⠀⢄⠀⠀⠀⠀⢅⢦⣀⡠⠴⢾⠋⠀⠀⠀⠀⣸⢃⠆⠈⠙⠢⣀⢸⠀⠀⡀⠀⣃⠘⡆⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⠂⠀⠀⠃⠡⠀⠂⠀⢄⠀⠀⠀⠘⡴⡁⠀⡐⠁⠀⠀⠀⠀⠀⡇⢀⡀⠒⡀⠨⣝⢛⠖⠑⠈⠁⠈⡇⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⣢⣀⠀⠀⠈⠪⡶⠀⠀⠀⠀⠀⠀⠀⢧⠈⡉⠅⠀⠠⠸⢈⠁⠂⠀⠐⢈⣳⠇⠀⢸⠇
⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠈⣆⣠⠀⢄⠀⠀⠁⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡑⢄⡀⠀⠆⡆⠀⠄⠀⡎⣡⠏⠀⠀⣏⠀⡀
⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⣊⣀⡃⣐⣂⡭⠞⠁⠀⠀⠀⠈⠉⠛⢦⣀⡀
⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢀⡀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⡙⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⢄⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⣀⣠⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣠⠖⠙⠩⡍⠡⠀⠈⠙⣄⠀⠀⠀⠀⠀⠴⠂⠀⠀⠁⠉⠉⠙⢿⣤⠀⠀⠈⡈
⠀⠀⠀⠀⠔⠂⠀⢀⠇⠈⠇⠈⠉⠀⠀⠀⠰⠎⢧⠆⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠐⠀⠀⠈⡄⡆⠴⠀⠀⠀⠀⢀⠇⠀⡌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠠⠄⡌
⠀⠀⠀⠀⠀⠀⠀⢠⠎⡟⠦⠀⠀⠐⠂⢁⠠⡎⠀⠀⠀⠀⠀⠈⣤⣈⠒⠀⠒⣁⠤⠚⠂⠀⢀⠄⡠⠤⡀
⠀⠀⢀⠀⡔⢢⠀⠀⠉⠁⠀⠀⠋⠀⠀⠀⠀⢣⠀⢄⢀⠀⡠⠊⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠑⢄⠀⡠⠃
⠀⠀⠘⠠⢠⠂⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠈⡄⠐⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⡖⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠤⠤⠀⠠⠐⠃⠀⠀⠀⠀⠀⠁⠂⢰⡇⠐⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠘⢄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠖⠃⠀⠀⠙⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠊⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡠⠀⠀⡠⠁⠀⢋⠀⡀⠀⠀⠀⠀⠐⢀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢰⣶⣭⣤⣦⢜⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣄⣤⣶⢲⡗⣏⡽⣻⡟⢿⡻⣿⣾⠦⡍⢻⣯⡙⡟⢻⣷⣤⣀⡁⠀⠀⠄⡀
⠀⠀⣤⡀⣰⣷⡀⠀⣀⢠⣔⣶⣿⠛⣿⡻⢇⢃⡿⣾⠇⣿⢷⣬⡙⣶⢾⣫⡟⠘⠖⠸⠁⠃⠃⢠⠈⠛⣯⣿⣷⣾⣤⣀⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣻⡿⣿⣯⣏⣻⣠⣧⢟⡾⡇⢻⣧⡛⢷⣌⢷⡌⠳⣍⢻⣴⡀⠀⠀⢀⠁⡈⣸⠐⠻⣝⣭⣿⣿⣽⢻⣦⡀
⠀⠘⠻⠿⠛⢿⣿⣿⣯⣿⡿⣛⠍⠉⠡⠍⠘⠀⡇⣤⣝⠿⣠⣽⠀⣧⠀⣸⢧⣯⣽⠖⡠⡄⠐⡡⠋⠀⠀⠙⠳⢿⢿⠿⣕⡌⢻⡄⣆
⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⡧⢦⢧⡼⠧⢾⣿⢷⣿⢶⣤⣀⠀⠐⠀⠀⠄⢢⢂⢨⡻⡆⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣠⣴⡤⠈⠉⠉⠐⠂⠀⠐⠈⠯⠘⠛⠉⠀⠀⠈⠉⠒⠒⠠⡀⠚⡄⡟⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡎⠀⠑⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠤⠎⡁

⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠘⡃⢠⣊⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⡸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠱⡀⢰⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⡰⡥⢤⡀⠉⢣⣄⣀⠀⠀⠀⠀⠐⠒⡲⠒⠈⠉⠉⠉⠲⢞⠀⠀⠀⠀⠀⢉⠱⠦⠷⠯⠤⠤⣼⡡⠤⠤
⠀⠀⠀⠀⢸⠁⠦⠶⢣⡏⣻⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣟⡃⣰⢀⣀⡀⡊⢟⢿⠉⠂
⠀⠀⠀⠀⠈⢇⠀⠴⠌⡩⠃⠀⠀⠀⠀⠀⠀⠀⢸⠠⣇⢆⠇⠀⣫⡱⠀⡴⠀⠀⠀⠀⠨⡉⠒⡄⠀⢤⠈⢑⠉
⠀⠀⠀⠀⣠⢴⠃⠀⠀⠁⢻⡒⢤⠀⠀⠀⠀⠀⠀⠙⢲⡄⠠⠦⠀⠀⡎⠁⠀⠀⠀⠀⠀⠉⡾⠀⠀⠸⡞⠉
⠀⠀⠀⠐⠃⢸⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡄⢀⡴⠀⡃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⣘⣁⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡤⠤⡞
⠀⠀⠀⠀⠀⠀⣹⠒⠐⠂⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠐⢄⠀⡀⠷⠼⠶⡁⠀⠀⠀⠀⠀⣀⠀⢄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣤⣏⣀⣀⢀⡀
⠀⠀⠀⠀⠤⠤⣱⠞⣡⡠⠄⣞⡷⢘⠆⠀⠀⠀⠀⢀⣽⡞⠓⢓⣠⡀⠀⠀⠀⠀⢠⢎⢥⡨⣏⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢸⡀⠃⠑⠣⠴⢠⡎⠀⠀⠀⠀⢸⠸⡧⠞⠰⣟⡼⢳⠀⠀⠀⠀⢸⡙⠓⣡⢢⢰⠶⣄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⡶⠑⡄⠀⠀⠀⠈⠲⡄⠐⠂⢀⠀⠘⣆⠀⠀⠀⢰⠋⡷⢺⠛⠉⢀⡌⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡜⠀⠈⠦⣄⠠⠃⠀⡟⠀⠀⠀⠀⠀⣇⠙⠂⠘⠀⠀⡸⠀⠀⠀⠀⡄⢆⠈⡀⠀⡞⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⡠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢖⠒⠒⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠚⡡⠔⣀⡀⠀⠀⠀⠀⠀⡤⠤⢄⣈⣵⡦⢤⡧⠴⣎⣈⣁⠀⠀⠀⠀⡤⢰⡡⢤⡀⢀⢈⢊⡃
⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠢⡤⠄⠀⠀⠀⠀⣀⢤⠞⠱⠼⠇⠫⡸⠂⡈⢳⠈⠁⠀⠀⠀⠜⢩⠳⣂⠇⢦⣂⢶⡍⢀
⠀⠀⠀⠀⠀⡜⠀⣀⣀⡀⠀⢀⢹⠀⠀⠀⠀⠀⠁⢸⠀⠙⠋⠉⠉⢉⣉⡥⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡀⠀⠘⡧⠞
⠀⠀⠀⠀⡴⡇⠘⢥⠣⠇⠀⢷⠟⡧⡀⠀⠀⠀⢀⡟⡆⠀⠀⠀⢰⠧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠁⠑⢤⣀⣀⣒⣒⣢⠔⠁⠃⠀⠀⠀⠀⠀⠈⢦⢀⣀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣖⡲⢶⡴⣗⠢⣀⣀⠤⠤⠶⢶⠐⠒⠂⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⣉⡙⠲⢭⣦⡵⡞⠋⢁⡈⡀⠀⠀⠸⠀⠀⠀⣾⣿⠿⣦⠀⠉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠤⢄⡈⢉⠖⡊⣠⢜⠕⢀⡾⣷⠀⠀⠀⠀⠀⠀⠀⢧⡱⢤⡾⠀⠀⠀⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⣙⣛⡓⢦⡽⠣⠤⠚⢱⣡⠞⡡⠔⢸⡇⠀⢀⣶⣄⠀⠀⠀⠉⠉⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡯⠤⠦⠤⡽⠋⢀⡤⢶⣾⡉⠁⠄⠠⠊⢸⣇⡠⠎⠀⢈⠳⢆⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡷⠒⢒⣛⡿⠁⠀⠠⠚⠉⡙⠻⣆⠀⢂⢀⢿⡿⡷⡄⠀⠈⠀⠈⣇⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⡾⠓⠒⡒⠶⣥⣄⠀⠀⢙⢧⡰⠋⠎⠀⠣⢸⢄⡤⠆⠀⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠁⠀⠻⣟⠶⣘⠘⡧⢈⠄⠄⣀⡼⡟⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣠⣤⣤⣤⣄⣀⡹⡆⠌⢆⡟⢀⡶⠊⠁⠸⡁⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠳⣄⠁⠀⡑⢳⠨⢸⡷⠋⠀⠀⠀⠀⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠘⡆⠀⠀⢸⡇⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠿⠟⣋⡿⠳⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⣿⣿⣷⢬⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢹⢿⠻⡟⢿⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠘⡇⢱⠀⠻⣝⢯⡑⢄⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⡇⠀⠀⠀⠹⣆⠑⢄⠉⠢⣈⠢⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣸⠁⢸⢀⡞⠉⠻⢆⣀⠉⠒⢂⣳⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡰⠁⠀⣀⡜⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⡟⣡⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⣴⠆⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠑⢄⠀⠀⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠣⡀⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠃⠀⠀⠀⢀⢀⡀⢀⠀⢱⡆⢠⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⠤⠐⠁⠁⠀⠀⠀⠈⠉⠀⠰⢇⡀
⠀⠀⠀⠀⢀⡴⠊⠉⠀⠉⠉⠓⠢⠤⣀⣈⡱⠊⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⣰⢁⣠⣀⣄⡀⢤⠶⠂⠀⠀⢀⠴⠒⠒⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⡀⠀⠀⠱⡄
⠀⠀⠟⠋⠀⠀⠀⡴⠃⠀⠀⠀⡰⠃⠀⢀⠤⠚⡀⠀⠀⠀⡄⠀⠀⠀⢀⠂⠀⠀⠀⠀⠉⠀⠀⢀⠠⢻
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠁⠀⢠⠏⢠⠏⠑⢄⠀⢠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣈⡧⠴⠃
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡏⠀⠀⡼⢀⡏⠀⠀⠀⠙⠲⢤⡄⠀⢀⣀⣀⠀⠠⡤⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠜⠀⠀⠀⠗⠋⠀⠀⠀⠀⡶⠒⠁⢀⠂⡎⠀⠈⠲⣐⡇
⠀⠀⠀⠀⠀⣸⢂⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⢴⠋⡜⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠸⠞



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⣼⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⣴⠾⢟⣋⣵⠞⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⡿⣒⣛⣯⠭⠶⣛⣫⣥⢞⣿⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣵⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠒⠚⠛⠛⠚⠿⠵⣾⣫⣭⣭⠽⣶⣟⣩⠴⢞⣻⣆⠀⠀⠀⠀⠀⣸⢃⣾⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢯⣶⢞⣛⣻⣯⣵⠿⣷⡀⠀⠀⢰⡟⣼⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢶⣚⣻⣯⣷⡀⠀⣾⠇⣏⣴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠏⠠⣀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠒⠚⠃⢀⣿⢰⣿⠟⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⣸⡟⡼⠏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢚⣋⠜⠑⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠍⢐⡈⠜⣉⣭⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣓⡋⠈⠒⢚⣉⣥⡷
⠀⠀⠀⠀⠀⠀⡐⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠥⢒⠺⠯⣭⣉⣉⣉⣙⡆
⠀⠀⠀⠀⠀⠀⠅⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠴⠶⢮⣖⢭⡫⣍⣉⣷
⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠰⡙⣷⡙⣶⣍⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⢾⣤⣄⡀⠀⢸⡘⣮⠻⢯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡻⣟⡶⣾⡽⠃⡀⣸⠃⢹⣜⢶⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠾⣝⣿⡟⠉⠀⠀⠇⣿⠸⣆⠻⣷⣍⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⡟⢟⣍⢓⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⡚⠿⠀⠀⠀⢰⠀⣿⡆⡙⣷⣌⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⡁⠏⣼⢸⡆⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢭⡲⣭⣛⡻⠃⠀⠀⠀⢈⢸⣿⣧⠹⣌⠻⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⢀⢰⣷⢰⠿⢸⣀⢟⣦⣂⠀⠀⠀⠀⠀⠀⢀⠠⢖⢷⣝⢶⣽⣦⡼⠁⠀⠀⠀⠀⢸⢸⣿⣿⢂⠹⣿⣦⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⢿⠰⢸⡟⣌⠻⡝⢿⡣⡀⠈⠉⠁⠀⠀⠀⠰⢝⠳⣾⠋⠀⠀⠀⠀⠀⠀⠈⡄⣿⣿⠸⣷⣌⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣞⡇⣧⠻⡌⢷⣌⢺⣽⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠹⣿⣆⡻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣸⡿⣹⣏⢺⣿⣌⢺⣇⢳⡙⠷⢹⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⢣⡟⢸⠀⡎⢿⣧⢹⡸⣧⢷⡸⣿⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣼⡇⡿⢴⣷⠸⣿⠈⣇⢿⢿⣇⠈⣧⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠉⠁⠀⢻⣀⡿⢧⡝⣎⢿⡇⢦⢸⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠋⠉⠙⠚⠁

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠬⡤⠴⡠⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡘⠀⠀⠀⠀⠀⠑⠄⠀⠀⠃⠀⢄⠀⡀
⣀⠠⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⣪⡃⠀⠂⠀⠐⠀⢀⡠⠄⠆⠒⠒⠒⠃⠰⠄⣀⡀
⠀⠀⠀⠠⡀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠁⠤⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠘⡉⠀⠀⠀⠈⠓⠒⠤⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠈⠡⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠏⡆
⠀⠀⠀⠀⠀⠀⡐⠃⢀⠄⠂⢀⠔⠀⠀⣏⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⢤⠠⠹⠀⠀⠀⠀⠀⠬⢀⡴⠚⡹
⠀⠀⠀⠀⠀⠠⠔⢊⢄⠄⡐⠁⠀⠀⠀⡳⠀⠀⠀⠐⠀⢉⠁⠁⠒⠈⠀⠀⠀⠐⢄⡀⠀⠀⠰⣃⠴⠊
⠀⠀⠀⠀⠀⢠⠄⡱⢁⠌⠀⠀⠀⠀⢀⡸⠁⠠⠴⠤⠘⠀⠐⠐⠀⠒⠊⠓⠀⠤⠠⢀⠰⠀⠉
⠀⠀⠀⠀⠀⣸⢜⡴⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸
⠀⠀⠀⠀⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣀⠄⠀⠈⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠋⠀⠀⠀⡸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠹⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢰⣾⣦⠀⠀⠀⢀⢴⣧⡀⠀⢸⡇⣿⣿⠟⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⡠⠀⠉⠻⠦⠀⠔⠁⢾⣿⠁⢀⡼⠂⠉⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠂⠀⣿⠦⣄⢀⣀⣀⣀⣀⠞⢁⡔⠁⠀⣠⡾⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⢧⡀⠀⠁⢉⠉⠉⣀⡔⠛⠀⣀⣴⠿⡇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢸⡜⠙⠲⠤⠤⠶⣿⣿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠈⠛⢿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣾⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⢀⠠⢒⣴⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠼⠉⠰⠸⠤⠚⠣⢸⠓⠂⠀⡀⠈⠉⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈

⠀⠀⢏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏
⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢀⡾⢄⣀⣀⠤⠔⠊⠉⠒⢄⠀⠀⠀⡠⠚⠉⠉⠳⣄⠀⠀⣀⠔⠋⠀⠈⠑⢄⠀⠀⠀⡠⠊⠀⠀⠙⢦⡀⠀⠀⡠⠊⠉⠉⠱⡄
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠑⠂⠚⠁⠀⠀⠀⠀⠀⠉⠒⠉⠀⠀⠀⠀⠀⠙⡄
⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⢡⠋⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡆⠀⠔⠒⢆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢡⠀⠈⢙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢃⠀⠑⠐⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠠⠀⠀⢈⠀⠈⣄⠀⣀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⢀⣀⣀⠀⡰⠃⠀⠀⠀⠀⠀⢀⠀⡈⢄⠀⠀⠀⠒⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡠⠂⠀⠀⠀⢁⡠⠃
⡇⠀⠀⠀⠀⠀⢏⡀⠀⠉⠁⠀⠀⠀⠀⠀⡔⠁⣠⠎⠈⠢⣀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠑⡄⢈
⢹⠀⠀⠀⠀⠀⠀⠈⢙⠂⠀⢠⠖⠢⣀⠀⠑⠈⠀⠀⠀⠀⢀⡩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠈⣇⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⠀⠉⠒⠒⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠑⡀⠀⢀⠄⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡎⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢐⡢⠀⠉⠑⠄⠠⠔⢒⠀⠀⠀⠀⠀⠇⠀⠀⢰⠀⠀⠇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠄⠀⡌⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⡀⠀⠘⡀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠞⠒⠊⠁⠉⠢⠊⠀⠀⠀⠀⠀⠀⢡⠀⠀⡃⠀⡃⠀⡇⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣃⡴⠁⢀⠇⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠉⣀⣠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠞⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⢉⠝⠋⠁⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡌⠈⠑⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠨⣦
⠀⠀⠠⠒⢄⢠⡊⠄⠐⠒⠒⠢⢄⡀⠀⠀⠀⠠⡤⢤⣀⡀⠈⠇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠱⡀
⠀⠀⠧⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠘⢦⡉⠈⠘⠀⠠⠀⠃⢀⠀⠈⠁⠀⠀⠀⠀⡇
⠀⠀⠘⠀⠀⠀⠂⠔⠀⠀⠀⠀⢠⡄⠀⢡⠀⠀⠀⠀⠈⠂⡄⠀⠀⠠⠁⠀⢣⡀⠀⠀⠀⢀⡔⠳⡀
⠀⠀⠀⡄⣠⠀⠠⠄⡀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠀⢋⠀⠀⠓⠄⣀⠊⠈⣲⠠⠒⠁⠈⠉⠁
⠀⠀⠀⠈⠘⢆⠀⡠⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢄⡔⠀⠀⠈⢀⡼⠁
⠀⠀⠀⠀⠈⠙⡖⠀⠐⡀⠀⠀⠀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢄⡠⠞⠐⠂⠒⠫⢠⠇

⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⣐⠦⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⡐⠋⠀⠀⠀⠀⠀⢀⡈⠒⡄⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠈⠉⠲⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢘⠀⡌⠀⠀⠀⠀⠀⡠⠀⠀⠉⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠳⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠋⠀⠀⠀⠀⢀⠀⢁⡠⠄⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠔⠀⠀⢈⠆⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠄⠋⠀⠀⣠⠃
⠀⠀⢴⠒⠉⠉⠉⠘⠆⠀⠀⠈⠀⠀⠀⠐⢊⣠⠊⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⡠⠊⢣⢀⣰⠁⢸⠁
⠀⠀⠀⠑⠒⠂⠀⠆⠈⠁⠲⠂⠀⠰⠒⠈⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⢤⢀⡁⣱⡀⢈⠋⠀⢆⡸
⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⠆⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠂⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠀⠰⠇⢺⠂⠀⣾⡏⠏⠀⠀⠲⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣘⡆⠀⠀⠀⠀⠄
⠀⠈⠁⠀⠀⡄⠀⣤⡄⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠐⠂⠀⠛⠛⠃⠀⠀⠀⠀⡉⠉⠹⣶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠙⠁⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠄⠀⢻⣸⠀⠘⠛⠿⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠂⡀⢈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠘
⠀⠳⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⢴⡆⠀⠀⠀⠀⠀⠀⠰⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠷⠶⠶⠴⠶
⠀⠘⠿⠛⠀⠻⢿⠷⠀⠡⠄⠌⠀⡀⣄⡂⡄⠀⠾⡿⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠽⠖⠠⡤⠄⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣀⠖⠠⡤⠂⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠔⠊⠀⠀⠀⢂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠎
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢑⣮⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡒⢶⡜⠆⣿⣠⠶⠒⠒⣒⠶
⠀⠀⠀⠀⠀⠀⠀⡾⠉⢠⠾⠓⠉⠁⣀⠉⠉⠉⠐⠀⠀⠠⠧⣼⣗⠀⡿⠀⣿⠁⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠔⠊⠉⣀⢉⣂⣀⠉⠒⢄⠀⠀⠀⠈⠛⠀⠀⡿⢠⠞⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⢸⡇⡀⣂⣤⣶⡀⢈⠀⠀⠃⠀⠁⠀⣄⡀⠀⠀⠀⠀⠀⠀⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢦⡀
⠀⠀⠀⠀⣀⠤⢼⡇⠩⡻⣿⡿⠿⠿⠶⣶⣷⠶⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⣷
⠀⠀⢠⠞⠁⠀⠀⢷⠀⠈⠀⡁⠀⠄⠀⠈⠀⠀⢀⣀⡤⠼⠛⠋⠋⢀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⠏
⠀⢠⠇⠀⠀⠀⠀⣨⢧⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢢⠙⠲⠤⣼⠁⠀⠀⢀⣴⣃⣀⣀⣀
⠀⠸⣄⣠⠤⠴⠚⠁⠀⠱⣄⠀⠀⠠⢄⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡦⠖⠒⠒⠲⠦⢤⣉⠉⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣈⣉⣀⣀⣀⣀⣀⣤⡤⠴⠒⠛⢦⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⡤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣿⣿⣶⣾⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⡿⣟⣿⣿⣿⣿⢿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣻⠿⠻⠽⠛⠙⠛⠉⠉⠉⠁⠉⠉⠀⠉⠁⣈⣉⠀⠉⠉⢠⡿⠉⠉⠉⠛⠻⠿⣦
⢤⣤⣴⣶⣶⣶⣶⣶⡿⠋⠛⠛⢋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠛⠛⠂⢿⡇⠀⣀⣴⣶⣶⣿⠿
⠀⠉⠻⣿⣿⣿⣦⢻⣿⣶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠿⠿⠿⠟⠛⠛⠉
⠀⠀⠀⠈⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠉
⠀⠀⠀⠀⢸⣿⣿⠋
⠀⠀⠀⠀⠘⠟⠁




⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶