Dress up Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⢤⣉⣰⠤⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢣⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡁⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠐⠢⠌⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⠌⠀⠡⣤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⡿⡄⠀⠈⠙⢣⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣌⠀⠨⡀⠀⠀⡀⠀⢀⠄⠀⠀⠈⡇⢷⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠛⠃⠐⠶⠂⠶⠦⠆⠞⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⢐⡒⠂⢰⠀⠀⠀⠀⡇⠘⡇⠀⠀⢠⠆⠠⠀⠲⠰⡄
⠀⠀⠀⠀⠀⠀⢀⠂⡈⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠇⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠂⢸⠀⠇⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⡐⠀⡀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⣇⠠⡌⠀⢰⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣶⡠⢤⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠙⡇⠀⠀⢰⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠄⠀⠀⢀⠏⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠂⠁⠀⠀⠀⡄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡌⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡐⠡⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠊⡰⠀⠀⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢃⠂⠀⠐⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡠⠁⠀⢳⠈⡃
⠀⠀⠀⠀⠀⠀⢀⠇⡰⠀⠀⠀⠸⡀⠣⢀⠀⠀⠀⠀⠀⠀⡔⠀⠌⠀⠀⠀⢫⡈⢢⡀⠀⠀⠀⠀⠀⢀⠆⡠⠁⠀⠀⠘⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠑⠤⡨⠆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠡⢄⡵⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠐⠤⢈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡁⢀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⠁⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⡇⣼⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡿⠻⣿⠇⣿⣿⡯⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⠻⠁⣾⠃⣰⣿⠀⣿⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡄⣼⢃⣾⣿⡿⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠉⠙⠋⠉⣿⣿⣿⣿⣿⣇⢀⣿⣯⣾⣿⣿⣧⣾⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⢿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠛⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡤⠃⢸⣦⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠙⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠐⠊⠁⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠀⣀⢠⣀⠤⡀⠀⠀⠀⠀⠀⢀⠐⠒⠄⢠⡀
⠀⠀⠀⠀⠀⡀⠂⠀⠀⠘⠢⠀⠀⠀⡎⠀⠠⠀⠄⠀⣀⠀⢐⠄⠀⢀⠊⠉⠀⠀⠠⠄⠀⢀⠂⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠰⠀⠀⠀⠁⠠⡀⠃
⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⢀⡄⠀⠀⢆⠰⠀⠀⠀⢀⠘⠇⢨⠀⠀⢀⠀⠀⠀⠀⠄⡴⠀⡀⠁⠀⢀⠀⠠⠀⠀⠀⣤⠀⠀⠁⢀⠀⠠⠀⠀⡁
⠀⠀⠀⠀⠀⡆⠀⢀⠐⠀⠀⡇⠀⠀⠈⢆⡀⠀⠂⠀⠀⠔⠁⠀⢀⠼⠀⠀⠀⢀⡰⠃⠀⠀⡁⠀⠀⠀⠀⠀⠘⣒⠀⠀⠀⠡⣄⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠹⠋⠁⠀⠉⠫⠀⠀⠀⠀⡠⠚⠁⠘⠢⠄⠀⢀⠰⡆⡖⠊⠁⠈⠑⢀⠀⠁⠀⢡⡤⠔⠂⠈⠉⠉⠄⠀⠀⠀⠀⠀⠜⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⢖⠀⠀⠀⠌⢀⠀⠀⠀⡀⢀⠀⠴⠆⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⡀⢸⠆⠀⠀⠘⠀⠀⡜⠠⡃⠀⠀⠀⡇⠘⠀⠀⠀⠘⢀⠁⠀⠀⠘⢸⠀⠀⠀⢠⠀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢀⠃⠸⠀⠀⠀⠘⡆⠀⠈⢰⠀⠀⠀⠀⡇⢀⠀⠀⠀⠂⠆⠀⠀⠀⠜⢸⠀⠀⠀⠸⠀⠇⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠂⠨⢸⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠘⠀⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠹⠋⠃⠘⡄⠀⠀⡘⠀⠀⠀⠸⠀⠀⠀⠀⠡⣆⡀⠀⠀⢾⠀⠀⠇⠀⠰⡷⠂⠀⣾⡤⠆⠀⡐⠁⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠐⣴⠆
⢸⣟⠀⠀⠀⠀⠀⣠⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⢐⠀⠀⠀⠀⠀⠀⢂⠀⠈⠄⠀⡀⠀⠀⠀⠐⠀⢠⠁⠀⢢⠀⠐⡀⠀⠀⠀⠀⢃
⢸⣿⠀⠀⠀⠀⡐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⣆⠈⠀⠀⠀⠀⠀⠀⠃⠀⢠⠃⠰⠁⠀⠀⠀⢨⠀⡇⠀⠀⠀⢑⠀⢃⠀⠀⠀⠀⢈
⢸⣿⠀⠀⠀⠀⠀⠘⠄⢸⠀⠀⠀⠀⠀⠁⠀⠇⠠⠈⠄⠀⠀⠀⠀⠰⠀⡇⢠⠁⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⢂⠀⠆⠀⠀⠀⠀⠀⠀⠇
⠘⣿⠀⠀⠀⡐⢡⠁⠀⠤⡄⠀⠀⠀⠀⠸⠀⠄⠀⠔⠸⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⢀⠇⠈⠀⠀⠀⠀⠀⠀⠢⡈⢄⠀⠀⢀⠆
⢘⣿⠀⠀⠐⠀⠂⠀⠀⠡⣀⣰⠠⠀⠀⢀⣀⠀⠨⡀⠘⠀⠀⠀⠀⠀⠐⣀⡑⠒⠂⠀⢴⣁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢀⡀⡀⠁
⢸⣿

⡿⢯⣹⠿⣏⡽⢿⢉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⡍⠉⠉⠉⣉⠉⣩⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⡉⠉⠉⠉⣉⠉⠉⣉⠉⣯⡽⠿⣭⡿⢿
⣷⡞⢙⣶⡏⢳⣾⠸⠟⠋⡟⠻⡿⠾⠿⠿⠾⡿⠿⡯⠷⠿⢧⣿⣇⠨⢿⠷⢿⡷⢿⠵⢿⠵⢿⠗⣿⠶⣿⠆⠻⡬⠼⠿⢿⣿⠇⢰⠿⠦⠟⢻⠀⡟⢳⣶⠋⣷⣞
⡇⠹⠿⠀⠿⠏⠘⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠶⠶⠿⠯⠈⠿⠇⠸
⡇⠀⠀⠀⠠⠀⠀⠀⠀⠠⠉⠈⠠⠀⠠⠈⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢤⠀⠀⠀⠀⣴⠂⠀⠀⠐⠖⠀⠀⠀⢀⠶⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠓⠀⠐⠂⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠀⠀⢂⠠⠀⠀⢂
⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠐⠈⢯⠀⠘⠛⣧⡀⢀⠀⠀⠀⠀⠄⠄⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠙⡿⠎⠁⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⢸⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⡁⠀⠐⠀⠀⠐⠀⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠁⠀⠐⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⡁⠀⠀⠀⠁⣀⠠⠀⠡⣀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠄⠀⠃⠀⠀⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⠀⠀⠁⢀⡀⠀⠀⠀⠰⠂⠀⠀⠀⡀⠉⠒⠐⠆
⡇⠀⠀⠀⠀⠀⡐⠀⠀⠀⡀⢱⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⠀⠀⠈
⡗⠂⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠦⠤⠤⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡀⠀⠀⡄⠀⠀⠀⠠⢣⠈⠂⠀⠐⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠹⡄
⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢄⡔⠈⠄⠀⡄⠀⠀⠀⠄⠀⠄⠐⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠄⠀⡀⠀⠀⠠
⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⡇⠀⠀⠀⢴⣩⡵⠦⣄⠤⠸⠄⣁⠼⠤⠤⠤⠒⣩⣔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⣀⣀⡀⠐⠀⠀⠁⠂
⡇⠀⠀⠀⢈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⣀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠩⠁⠁⠉⠉⠉⠉⠁
⡇⢰⠈⠀⠀⢸⣄⣀⣠⣤⣀⣀⣠⣤⣀⣀⣀⣤⣄⣴⠀⠀⠀⠉⢧⠱⢄⠀⠀⠊⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⡆⠀⡇⠈⡄⠀⡠⢄⠀⠀⠀⠀⡠⠤⡀
⡇⢸⠀⠀⠀⢸⠀⢀⡈⠃⠐⢀⡈⠃⠐⠰⠀⠾⣄⠹⠀⠀⠀⠀⠨⡆⡄⠐⢰⠀⡇⠀⡠⠠⠀⠀⠀⠀⠀⠀⢹⠀⠀⠣⠄⠃⠀⡗⠁⠀⠀⠑⠂⠂⠈⠀⠀⡀⠃
⡇⢸⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⡇⠈⠂⠀⠀⢧⠈⡡⠒⠠⠀⠀⠀⡐⠂⠹⡆⠀⠀⠀⠀⢀⠉⢢⡀⠀⠀⠀⠀⠀⠀⡔
⡇⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠱⠂⠀⠀⠆⠈⠱⡄⠀⠐⡀⠀⠀⢇⠀⣰⠋⠀⠀⠀⠀⠸⡄⠀⢡⡀⠀⠀⠀⠀⠀⡆
⡇⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⡁⠀⠸⠂⠀⠀⠀⠀⠄⢱⠁⠀⠀⠁⠃⠀⠀⠱⡀⡘⠃⠘⠃⠌⠀⠀⠃
⡇⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⠀⠀⠀⠀⠀⠐⠀⢈⡀⠀⢀⢀⡆⠀⠀⠀⠂⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸
⡇⢸⠀⠀⠀⢸⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡇⠘⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠨⣦⡀⠀⡏⠄⢘⡀⣀⣀⠈⣀⡀⠃⣰⠆⠀⠀⠀⠀⠠⢬⡀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣄⢀⡀⠀⢀⠀⣀⠰⡀
⣇⣀⣀⣸⣝⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣫⣔⣙⣀⣉⣙⣉⣉⣋⣁⣉⣋⣀⣂⣀⣐⣂⣀⣀⣀⣈⣉⣀⣀⣀⣀⣙⣘⣋⣘⣃⣀⣘⣓⣂⣛⣀⣛⣀⣃

⡏⠉⠉⢉⣭⣭⣤⣤⣀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠉⠉⠉⠀⠡⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⡇⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠅⠂⡀⠆⠄⡄⠀⡀⠄⢸⠧⠀⢀⢠⠤⠀⠀⠖⠀⡀⡠⠄⠤⠀⠀⠤⡄⡄
⠁⠀⠹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠂⠞⠀⢀⠡⡇⠁⠁⠋⠈⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⣁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣤⣤⡤⡴⠦⡈
⠀⠀⠀⠈⠛⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠠⣀⠀⣀⢀⠀⠄⠀⠀⠀⡈⠄⡀⠀⠄⢰⠐⠀⠀⠠⡎⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠇⢀⠀⠀⠘⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠜⠀⠁⠀⠀⠈⠀⠂⠀⠁⠀⠀⠀⠀⠀⠄⠄⠀⠀⠈⠀⠀⠀⠀⡔⠠⢠⡄⢶⠩⠊⡼⠀⠀⠀⠀⠀⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠦⣺⣥⣤⡅⣠⣀⡀⡎⣂⡀
⠀⠀⠀⠀⠀⠀⠀⣦⡄⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⢾⠄⠀⡀⠈⠂⠀⠈⢁⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠈⠉⠀⠉⠉⠉⠉⠑⠟
⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⠠⡄⡂⠀⠁⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠬⠐⠠⠀⢆⠀⠂
⠀⠈⢦⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⡄⠀⠀⠀⠤⠅⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠂⠀⠀⠀⠀⢀⠁⠀⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠐⠀⠀⡁
⠀⠈⠑⠒⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡴⠛⠀⠻⡄⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡄⢠⣄⡴⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⡄⠀⠀⢘⠀⠀⠀⠀⠸⠀⠀⠰⠇⡸⠓⠁⣾⠙⣇⡀
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢳⡐⠝⡒⠒⢀⠀⠀⠈⢀⡀⠀⠀⠀⠘⡇⠀⠀⠸⡆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠚⠀⠃⠀⠀⠀⠀⠀⠀⡀⠘⠒⠛⠀⠈⡀⠄⠀⠀⡀⠀⠀⠀⠀⢠⠝⡀⠀⡃⠀⠀⠀⠀⠐⠠⠀⣀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡶⠀⠀⠀⠀⠀⠈⡡⠀⢀⣧⠠⠰⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠁⠐⣀⠀⠀⠀⠀⠁⠀⠈⠈⠘⠂⢀⣠⡄⠘⣇⣀⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⡷⠀⠀⠋⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠋⠉⠁⠠⠁⠀⠀⠀⠀⠠⠀⣀⡀⣀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⡀⠈⠁⠀⠀⠠⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⠀⠚⣯
⡄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠄⠸⡀⠑⠂⠐⠀⠂⠂⠀⠀⠠⠒⣄⡀⠀⠀⠂⠀⠀⠀⠀⡀⠂⠀⠀⠀⠐⠈⠠⡁⠀⠀⠀⠐⠀⠀⢀⠀⠘⠣⠞⠁
⡇⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠂⡤⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⡇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠐⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡐
⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣃⣐⣂

⠀⠀⠀⠀⠀⢀⠄⠂⡔⢍⠉⠠⠐⠠⡀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠁⠀⠀⣆⠍⠊⢠⠀⠀⠀⠢⣀⠤⠉⠀⠠⠄⠀⠀⠀⡀⠀⠐⠈⠆⢀⡤⠈⠈⣆⠀⠀⠉⠑⠂⣀⠴
⠀⠀⠀⡁⣀⡤⠄⠀⠀⠀⠀⠒⠒⠤⢄⡀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠊⠀⠁⠁⠉⠐⠈⠐⠀⠈⠁⠀⢐⢀⡀
⠀⠀⠀⠌⠉⠀⠀⠀⠐⡛⡀⠀⠈⠂⠀⠈⡗⢈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠉⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠄⠐⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠊⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢀⠀⠨⢆⡀⠂⠐⠀⣐⠁⣀⠀⠀⠈⠀⢤⠀⠀⠀⠂⠀⠀⢀⠩⠈⠁⠀⠀⣩⠹⠶⠦⣔⢒⠤⠶⠯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡄⠈⠀⠀⠀⠈⠂⣠⠄⢐⠀⠀⠈⠉⠈⠀⡆⢤⡀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠀⠀⢠⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡰⠥⣁⣘⠀⠀⠈⠀⠀⠀⢃⣉⠱⡀⠀⠀⠠⡇⠀⠀⡀⡨⠀⠀⢸
⠀⡈⠀⠀⠀⡐⠀⠀⠀⠀⠁⠀⠀⠀⢀⡰⣇⠒⠂⡎⠀⠂⠀⠀⠈⠭⢥⠐⢂⡽⠀⠀⠐⠀⠄⠀⡿⠇⠠⠀⠰
⠮⢄⠀⠀⣺⠅⠀⠀⠠⠀⠁⠀⠀⠠⠜⠁⠐⠀⣰⣃⣈⡉⠁⠀⠀⢂⣰⡂⠀⠂⠀⠀⢰⠤⠤⠤⠤⠤⠤⠤⠰⠀⠀⠀⠁
⠀⠈⠊⠉⠀⠁⠀⠀⠀⠈⠁⠀⠀⠑⡤⡀⣀⠸⡛⠀⠀⠀⠀⠀⣀⣂⣐⡃⢊⡁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⢨⠈⠀⠀⡿⠭⠉⠉⠹⠉⠁⠠⠴⡆⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⠁⠁⠀⠀⠋⠀⠀⠀⡧⣴⡒⠂⢾⠤⠐⢂⡠⡅⠀⠁⠐⠒⠄⠀⠀⠀⢸⠄⠀⠀⠀⢤⠲⠤⠂
⠀⠀⠀⠀⢀⠐⠀⠀⠐⢆⡰⠂⠀⠀⠂⠀⠀⠀⡅⠀⠠⠤⢶⠠⠤⠄⠀⡃⠀⠀⠀⢠⣀⣀⣀⠈⡈⠀⠀⠀⣀⣉
⠀⠀⠀⠀⢠⡘⠛⠛⠛⢸⡌⠛⠛⠛⢃⠆⠀⠀⣿⡿⠿⠿⣯⡿⠿⠿⣿⡵⠀⠀⠀⢠⡘⠛⠛⠛⣸⡙⠛⠛⠻⢡

⠀⠀⠀⠀⢠⠀⠀⡄
⠀⠀⠈⠆⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⣤
⠀⠓⢄⣸⣶⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢻⣿⡿⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣿⠿⠟⢻⣿⡿⠋
⠀⠀⠀⣤⡘⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣧⡄⢸⣯
⠀⠀⢀⣿⣿⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣧⡄⢻⠟⠁
⠀⠀⣾⢻⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣠⡄⢀⣀⠖⠀⢹⣿⣿⠿⠟⠋⠀⠦⡀
⠀⠀⡿⠘⣿⡄⠁⠀⢀⡀⠀⠀⡶⠛⢛⡍⢁⣾⣿⡅⢸⣿⣄⣴⣿⣿⠀⠀⠀⠐⠻⠶⣤⡄
⠀⢠⠁⠀⢿⣷⠘⣐⢛⣩⣤⣤⣴⣾⣿⢁⣾⠋⣿⡇⢸⣿⣻⣿⣿⡏⠀⠀⢀⣴⡿⠒⣶⡆⠀⣤⡄
⠀⠀⠀⣄⠈⣿⡿⠿⠛⠛⠋⠉⡉⣡⡟⢸⠇⣰⣿⡇⠘⣿⣿⣿⡿⠀⢠⣾⡿⠋⢀⣴⣿⠃⢠⣿⡇
⠀⠀⠀⣿⣄⣨⣵⣶⣶⣶⡿⠿⠛⠛⠁⡞⢠⣿⢿⣷⠀⣿⣿⣿⠃⣴⡿⠋⢀⡼⠋⣿⡟⢀⣿⣿⣇
⠀⠀⠈⠛⠿⠿⠭⠁⠀⠀⠀⠀⠉⠉⠀⡇⢸⡇⢸⣿⠀⣿⣿⣧⡾⠋⢀⣴⡟⠀⣼⡿⢀⣼⡏⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣾⠃⣾⣿⣆⣿⠟⠋⠀⠀⣿⣿⠃⣰⡿⣁⡾⢻⡇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⡿⢀⣿⠋⠿⢁⣤⠆⠀⣾⡟⠁⣼⠇⣾⣿⣷⣿⣷⠀⢿⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣸⡟⠀⢠⣿⡏⠀⣾⡟⠁⣾⠁⣾⠃⣿⡟⢻⣿⣇⠘⣿⣇⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢰⡏⢀⣿⠁⠀⣼⣿⠀⢸⣿⠁⢰⡏⣰⡟⣶⡯⠁⠀⠘⢿⣄⣻⠛⣿⣏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣿⠀⣾⡟⠀⠀⣿⡇⠀⣿⡟⠀⣿⠀⣿⣇⣿⡇⠀⠀⠙⡾⠻⣿⣆⠈⠻⢦⡄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢸⡏⢠⣿⠁⠀⣼⣿⠁⢸⣿⠇⢸⡏⢸⡿⣸⡟⠁⠀⠀⠀⠸⣧⡘⢿⣷⣦⣄⢈⣲⣶⣓⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡿⠁⣼⡟⠀⢀⣿⡏⠀⣾⡿⠀⣸⠇⣼⡇⠻⠀⠀⠀⠀⠀⠀⠈⠙⠢⠌⠉⠻⠦⠉⢛⣿⣿⢯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⡇⣸⣿⠁⠀⠈⣿⡇⢰⣿⡇⢀⣿⡇⢸⣿⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠄⠈⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣰⡿⢠⣿⠇⢀⡄⠀⣿⡇⢸⣿⠀⣼⣿⠃⣼⡟⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣰⡿⠃⣼⡿⠀⣿⡇⢀⣿⡇⠈⣿⡆⢸⣿⡀⢻⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡥⠴⣿⡃⢰⣿⠃⢰⣿⡇⢸⣿⡇⠀⣿⡇⠘⣿⡇⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠃⢸⣿⡆⢸⣿⡇⢸⣿⡇⣠⣿⣇⢀⣿⡇⠸⣿⡇⢹⡆
⠀⠀⠀⠀⠀⠀⢠⠟⢠⣿⠏⢀⣿⡿⠀⣼⣿⠁⢸⣿⠀⢸⣿⡇⠘⣿⡇⠐⣿⡇⠸⡇
⠀⠀⠀⠀⠀⢰⡟⢠⣾⡟⢀⣼⡿⠁⣰⣿⠇⢠⣾⣿⡆⠘⣿⡇⠀⣿⣷⠀⢻⣿⠀⢿
⠀⠀⠀⠀⢀⡟⢀⣾⠟⠀⣼⡿⠁⣰⣿⠏⢠⣾⠏⠹⣷⠀⢿⣿⠀⢹⣿⡄⠸⣿⡆⠘⣧
⠀⠀⠀⠀⠸⢀⣾⡟⠀⣾⣿⠁⣰⣿⠏⢠⣿⣿⠃⠀⢹⡇⠸⣿⡆⠘⣿⣇⠀⣿⣷⠀⣿
⠀⠀⠀⢠⠀⣼⡿⠀⣸⣿⠃⢠⣿⡏⣠⠟⣽⠋⠀⠀⠀⢿⡀⢿⣧⠀⢿⣿⠀⢹⣿⡄⢹⡇
⠀⠀⠀⠀⢰⣿⠃⢰⣿⡏⢀⣾⠏⣰⠏⣼⠏⠀⠀⠀⠀⠸⢿⣼⣿⡀⢸⣿⡆⠘⣿⡇⢸⡇
⠀⠀⠀⢀⣾⠏⢀⣿⡟⢀⣾⠏⣼⣏⣼⠏⠀⠀⠀⠀⠀⠀⠾⣧⡹⣧⠈⣿⡇⠀⣿⣷⠀⠃
⠀⠀⠀⣼⡟⠀⣾⡿⠀⣾⠏⣸⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⣆⢹⣿⠀⢸⣿⠀⡆
⠀⠀⢰⣿⠇⢸⣿⠇⢸⣿⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣿⡌⣿⡇⠘⣿⣇⠁
⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢻⣇⢸⣿⠀⢿⣿⢠⡗
⠀⠀⠸⣿⠀⢸⣿⠀⣿⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠸⣿⢠⣿⠀⢸⣿⢸
⠀⠀⠀⣿⡇⣼⣟⠀⣿⡇⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⣿⢸⣿⡇⢸⣿⠀⡀
⠀⠀⠀⢸⡇⢸⣿⢰⣿⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢿⣆⣿⡇⠈⣿⠀⠇
⠀⠀⠀⢸⡇⢸⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⠿⣿⣧⠀⣿⢠⡇
⠀⠀⠀⢸⣇⠘⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢿⣿⠀⠏⢸⡇
⠀⠀⠀⠈⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⣿⡇⠀⢼
⠀⠀⠀⠀⢿⠀⢻⣿⢹⡇⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣤
⠀⠀⠀⠀⢸⡀⢸⣿⡀⢿⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⢹⣿⠀⢸⡄
⠀⠀⠀⠀⢻⣷⣼⣿⡇⢸⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⣿⡷⢸⣿
⠀⠀⠀⠐⠃⢸⣿⡏⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡹⣿⣷⣾⣇
⠀⠀⠀⢰⣿⣿⣿⣤⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⣿⣿⣿⣀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠄
⣠⣴⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡦
⠈⠛⠛⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⡀⠀⠠⣄⠀⢀⡄⠀⠀⢠⡶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣇⡀⠈⣷⡄⢰⠇⠀⣼⠇⠀⢀⡿⠁⢠⡿⢠⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⢸⡇⢠⡟⠀⢻⡆⣴⠋⢀⣴⠟⢁⣴⠟⠀⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡎⠛⣦⠻⣦⡸⣇⠹⣇⢸⡇⠀⣾⠁⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠹⠇⠈⠃⠉⢰⡇⠘⠁⠀⠋⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠈⠁⣀⠀⠀⠀⠀⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠃⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣤⡀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠦⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠛⠛⠉⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣧⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠟⠛⠛⣋⠉⠉⠉⠉⠉⢉⢉⣉⠉⠉⢉⡍⠙⠛⠛⠻⣃
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠙⣷⠀⠀⠀⠀⢀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠴⢛⣀⠀⢘⠁⠀⣴⠞⣿⠀⢼⣏⣶⠄⣿⠠⡾⠋⠀⠾⠀⢰⡏⣽⠋⣠⣤⡀
⠀⠀⠀⠀⠀⠘⣧⠛⠉⠀⢸⡇⠀⠛⠖⠛⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠘⠳⠾⠃
⠀⠀⠀⠀⠀⠀⠙⠃

⣤⡀⠀⠀⢀⣀⠀⠀⢀⢤⡀⠀⠠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⢰⣶⣶⣖⣂⣀⣒⣒⣀⣠⣂⣰⠶⣶⣶⣶⠂⠀⢺⠛⠛⠟⢿⣿⣿⡇⣿⣶⣶
⣿⣇⠀⣔⡄⠈⠀⠉⠋⠈⠙⠆⠈⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢈⠀⠀⠀⠀⠀⠀⢸⠿⢹⡇⣿⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣾⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⣀⣀⣀⣠⣩⣤⣼⣇⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⣿⡟⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⠿⣿⡏⠁⢰⣶⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣸⡇⣿⣿⣿
⣿⡇⠀⢠⣿⣿⣿⣿⣽⣿⣿⡀⣿⣿⣿⣿⠿⠟⠋⠉⠀⢀⡀⢠⡟⠋⢹⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⣿⠁⣿⣿⣧⣿⣿⣀⣿⣿⣿⢿⣷⣿⣿⣿
⣿⣷⠀⠀⡿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠃⠀⠀⣀⣤⣶⠄⠻⣧⣾⡇⢀⣾⣿⠀⢀⣿⡇⠀⢸⡿⣀⣴⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⣿⣿⣿⣿
⣿⣧⢀⣤⣧⣾⣿⣿⣿⣿⣿⠀⣿⣿⣴⣾⣿⣿⣿⡿⠀⣀⣬⣿⡇⠨⣿⣿⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣅⣆⢀⢘⣿⣿⣿⣿
⣿⡇⣈⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⡇⠀⢹⣿⠀⠀⣿⡇⢀⣀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⡇⠀⠘⠛⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣿⣿⣿
⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣷⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡏⠀⠀⢀⣶⣭⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠇⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡿⠿⢿⣿⣿⢿⡿⢿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⣿⣿⣿
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢠⣧⠀⠀⠀⠀⠂⠀⠀⠀⢳⣼⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⢶⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣤⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣿⣿
⣿⠀⠀⠀⣀⣄⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡆⠀⠀⣿⣂⠀⣀⣸⣏⡀⣀⣄⡄⠀⢘⣿⢀⣀⣴⣼⣿⣦⣿⣦⣀⣀⣀⠂⣀⣀⣤⣼⡿⣿⣿⣿
⡿⠀⠀⢺⣄⣾⠀⠀⠀⢀⡀⣠⡄⣴⣦⣾⢁⣞⣿⡄⢸⡟⢿⡇⣿⡏⣿⣿⣿⠻⣿⠀⢸⣿⢸⣿⣿⡟⣿⣿⡇⢿⣿⣿⢻⣇⣿⡟⠛⢿⠛⣿⣿⣿
⡇⠀⢾⣸⣿⡇⢠⣾⣿⣾⡿⣿⡿⢻⣿⡿⠁⠛⠋⠀⠸⣿⣎⠀⣿⡇⣿⡟⣿⣶⣟⠀⠸⣿⣾⣿⣿⡇⣿⣿⡇⢸⡏⢻⣷⡅⢻⣷⣶⡇⠀⣿⣿⣿
⡇⠀⣤⢉⣿⡇⠻⣯⠟⣿⠇⠘⠃⣴⣿⠇⠀⠀⠀⠀⢰⡎⢻⣇⣿⡇⣾⡇⣿⠀⣿⡟⢀⣿⠈⣿⣿⣿⣿⣿⣷⢸⡇⣶⠙⣿⣾⡏⠉⣆⢠⣿⣿⣿
⠁⠀⠻⠾⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⠟⠀⠀⠀⠀⠀⠸⣿⡾⠃⠙⢷⠿⡷⠿⠿⠟⢹⣿⣿⠰⣿⣿⣿⡿⠛⠿⡿⠇⠻⣿⣿⡿⣿⣿⣿⠛⣿⣿⣿
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠘⡅⢀⣰⡇⠀⠀⣠⣦⣤⡄⡀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣯
⠿⠿⠿⡿⠿⠿⠿⠿⠿⡿⠿⢿⣿⠿⣿⡿⠿⠿⠿⠿⣿⢿⣿⠿⠿⢿⠿⣿⣿⠿⠿⡿⢿⠿⡿⢿⣿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠙⠁⠐⠛⠒⠒⠒⠒⠒⠛⠒⠚⠓⠚⠛⠓⠒⠒⠒⠒⠛⠚⠛⠛⠓⠛⠒⠒⠒⠒⠒⠒⠒⠚⠓⠛⠛⠛⠒⠺⠿⢼⠗⠐⠛⠓⠂⠀⠐⠀⠘⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢄⠀⠀⣀⡤⠔⠚⠉⣍⡉⠑⣄⣀⣀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⢸⡇⣀⣠⣖⠉⠀⠈⢦⡀⠀⠘⠇⣠⣿⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⣠⡘⠉⠀⠹⣿⣧⠀⠀⠀⠳⡄⠀⠀⠙⢿⣿⣿⣿⢿⡿⠿⠿⠿⠟⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⢀⣤⠄⣠⣾⣿⣿⡀⠀⠀⠹⣿⣷⠀⠀⠀⠙⢦⣀⣤⣾⠟⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⣾⣿⣿⢰⣿⣿⣿⣿⣷⡀⠀⠀⠘⠛⢀⣀⣠⣴⣾⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠋⠓⠒⠢
⠀⠀⠀⠀⠀⠀⣠⣴⣇⣾⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣾⡿⠟⠋⠁
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣹⠀⠀⠀⠈⢹⣿⣿⣿⡿⠟⠉⣀⣤⣤⣶⣤⣶⡶
⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⣁⣴⣾⣿⠀⠀⠀⠀⠘⡇⠀⣠⣴⡷⠾⠿⠿⠖
⠀⠀⠘⣿⣿⣿⣿⣟⢁⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣏⠉
⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠿⠻⡋⠹⡀⠀⠀⠀⢀⣠⣾⠇⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣇⢀⣠⣶⠟⠋⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣿⢉⣿⠿⠂⣿⣿⣿⣿⣿⠿⣿⠇⡼⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⣤⣶⣾⠟⢉⡍⢻⡏⣴⡿⣋⢀⣦⡘⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣈⢻⣿⣿⣆⡻⣣⣾⣷⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣷⡙⢿⣽⣷⢳⣶⠶⢎⣿⣠⣵⡘⣻⡟⡡⣼⡿⡡⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⢡⣶⣶⣿⣿⠿⠛⢿⣿⠏⢈⣾⠏⢘⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣶⣝⠿⣿⣇⠼⢟⣼⣿⠰⣛⣵⡰⣟⣽⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣰⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀⠙⠻⣿⣿⣿⣿⠟⠋⢀⣴⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⠋⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠁⢀⣤⣾⣷⣄⡀⠈⠙⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⢶⡶⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⣥⣏⣰⢉⡤⠞⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠝⠉⢁⣠⡴⠟⠉⠀⢀⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⢸⠉⠉⠁⠀⠀⠀⠀⠸⣥⣾⢰⡏⣠⠖⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠐⢧⣸⢾⠑⡟⣸⠇⣠⠾⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⠀⠀⠀⠀⢀⠈⠰⠛⠚⡱⢯⡴⣇⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⣠⡜⢀⡀⡀⠀⠀⢀⣍⣬⠷⠞⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣀⣤⣀⠀⠀⠀⠻⡇⠈⠁⠁⠀⠰⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⣇⣠⡉⢳⡀⠀⠀⢹⠀⣀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡈⠛⢿⠀⠛⢦⣀⣸⡄⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⣶⠲⠞⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢹⣶⣾⠀⠀⠀⠀⢨⣷⣀⡾⢠⡀⠀⠀⠀⠀⢰⡖⠲⣇⢸⣄⢳⣠⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠺⠿⠃⠀⠀⠀⠀⠀⠉⠙⠛⠁⠈⠳⢦⣄⣀⠈⠉⠙⢿⣋⣉⠋⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⢲⡆⠀⠠⣄⣰⢀⡤⠀⠀⠀⠀⠈⠉⠛⠲⣤⠀⠉⠹⡄⢻⡀
⠀⠀⠀⣤⣤⣶⣶⣾⣿⡿⣄⣀⣠⣤⣤⣶⣶⣿⣿⡆⠀⠀⠀⠀⠘⡇⠀⣠⠈⠉⠛⢀⠀⠀⠀⠀⠀⣠⠾⣿⣻⠃⠀⠀⡇⠸⡇
⠀⠀⠐⠟⠛⠉⣹⣿⣿⢶⣿⡏⣿⣿⢻⣿⣯⣿⣿⠇⠀⠀⠀⠀⢰⡇⠀⠉⢀⢀⠀⠋⠀⠀⣦⠀⣾⣷⣦⣄⡙⠓⠶⠶⠟⠀⡇
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⣸⠇⠀⠀⠚⠷⢦⠀⠀⠀⡿⢸⣉⣩⡴⠋⠉⠛⠶⠶⠶⠾⠃
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣛⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⣰⣿⣿⡿⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⡛⠲⠾⠛⠋⠁⠈⠻⣄⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⣋⡙⢻⡀⠀⠀⠀⠀⠀⠀⠈⠳⠦⡤⠖⠲⡟⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣾⡏⠉⢿⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣿⢳⡄⠘⣿⣧⠀⠀⢀⡴⠚⢣⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⡄⢻⡀⢹⡿⠀⣠⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣷⣄⠙⠶⠶⠞⠁⠀⠀⠀⡟⠀⠀⠀⠀⢀⣀⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠒⠶⣄⠀⠘⣏⣀⠀⠉⠓⢦⠀⠀⠀⠀⠀⠰⡇⢠⣤⣶⡟⠉⣿⠛⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣺⠷⠷⠿⣖⣮⣟⢦⣾⡍⠗⠲⣴⠋⠀⠀⠀⠀⠀⠀⠳⣿⣉⣉⣿⠀⢸⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⢞⣳⠮⡹⣿⣦⡀⠀⣴⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⠋⠵⠈⠳⣭⡷⣬⡋⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣭⡐⠢⡍⠳⣽⣦⠈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣁⠈⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣸⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡾⠙⠷⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢧⣤⠶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⣟⣳⠈⣀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣟⡀⠉⠁⠀⢙⡿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣶⡀⠀⣠⡴⠋⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣵⣰⠋⠀⠀⠀⠀⠀⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⣳⣦⣤⠤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⠂⠀⠀⠀⠀⣀⣠⡄⢶⣾⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡏⣠⣤⣶⡆⢻⣿⣿⡇⢸⣿⣿⡇⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠁⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⣧⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠉⠁⠀⣸⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠉⠉⠙⠻⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣿⡿⠁⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⡀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠹⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠈⣏⡀⠀⠀⠀⠀⣾⣿⣶⢸⠀⡀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣧⡆⣾⣇⣀⣀⣀⣿⢿⣿⣺⣿
⠀⠀⠀⠀⠀⠀⣿⡟⡽⣇⠀⠀⠀⠀⠛⣉⣿⣾⣿⣵⣦⡄⠇⠀⠀⠀⠀⠀⠀⠿⠧⢹⡿⣿⣿⣿⣿⣼⡇⢸⣿⣠⠄
⠀⠀⠀⠀⠀⠀⢸⢃⣗⡟⠀⠈⣉⢠⣤⣿⣿⣧⣼⡟⢻⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣷⣿⣾⡿⣿⣇⣿⣿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⠷⠾⠿⠿⠇⣤⣄⠀⠀⢀⣀⣀⢸⣿⣿⣿⣿⠃⠛⠛⠛⢻⣿⣿⣿⠅
⢠⣖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠸⣭⠀⠀⢺⣽⠿⠘⠛⠛⠛⠛⠀⠀⠀⠀⠘⠿⠟⢇⢤
⠀⣿⡿⣧⣠⠀⠀⠀⠀⠀⠀⠂⠢⢸⣿⡿⠿⣻⣿⠀⠀⠈⠀⢀⣤⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢳⡀⠘
⠠⣿⣿⣿⣻⣀⣀⣀⣀⣰⠿⣄⡀⡘⠛⠛⣻⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⡆⠀⠀⠀⠀⢀⣂⣩⣭⣍⠂⠈⣟⡱
⠠⡿⣿⢿⣿⣿⣿⣿⣿⣿⣔⠹⠾⣿⠀⠀⢽⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⠉⠀⣷
⠀⠖⠸⢿⢸⣿⣿⣿⣿⡿⠿⠿⠶⠶⠀⠀⢾⣿⣿⣀⣀⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠉
⠀⣿⣿⣾⣼⣿⣿⣿⣿⡏⠐⠎⠂⠀⠀⠀⠸⠿⠿⢼⣿⣿⣁⠙⢿⡿⠋⣀⠛⢛⣻⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢤⠀⠀⠰⣿⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡛⣛⠃
⠈⡿⠛⠛⢿⡇⢰⠀⠈⠐⢄⠉⠀⠘⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢠⣷⣦⣀⠀⠀⢲⣷⢠⣶⣿⣷⣾⣿⣿⣿⣟⣤⣤⣤⣤
⠀⣧⣤⡀⠀⡇⠠⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⣿⣿⣷⣾⡇⠾⠿⠿⠟⠀⢀⣾⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣇⣀⠀⠀⣀⣿⣿⣿⣿⣦⣤⣤⣠⣤⣿⣿⣿⣿⡇⠀⠈⠀⣶⣶⣾⣿⣿⢿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠿⠿⠿⢠⣴⣿⣿⣿⣿⣿⣿⡿⠛⠛⠷⠜⠛⠛⠛⠛⠃⠀⠀⡀⣿⣿⣦⣽⣿⣈⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣾⡿⠉⣿⡛⠋⠋⢋⡋⠠⣾⠿⢿⣷⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠘⣧⡀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣶⣾⣿⢀⣀⠀⢘⠛⢀⡀⠀⣼⣿⠀⠐⠂⠀⠘⠳⣤⠂⡿⠛⠛⠛⠛⡄⢠⡍⠉⠃⠠
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢿⠀⣙⠁⢀⠀⢀⣄⠀⠀⠀⠀⠀⢰⣶⣿⣶⡞⠋⠀⠀⢀⣴⡆⢻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣯⣤⣾⣯⣿⣻⠄⠀⠀⠀⠀⣿⣿⣿⣿⣇⣥⠆⠀⠀⠉⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⣾⣿⣧⠀⠀⠀⠀⠉⠙⠛⠛⢳⡖⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠸⣇⠸⣇⢸⡟⢰⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⣼⡋⡿⣡⡟⣠⡟⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⠬⠿⠔⢋⡼⢋⣴⠟⣩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢀⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡆⢶⠀⠀⠀⠀⢀⣤⣤⡀⣟⣹⡇⠸⠇⣾⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣹⣤⠞⣧⠀⠀⣿⠻⣄⢹⡿⣿⣻⠇⠀⠁⠀⠀⣀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⢠⡿⢶⡄⠘⢧⠈⣾⠃⠈⣿⡄⠀⠴⠀⡼⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠋⣠⠾⠛⢢⣼⠀⠉⠀⣰⢟⡀⠀⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣤⡄⣠⠟⠁⢀⣴⡾⣷⢿⣷⣤⣼⠟⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰⠟⢶⡀⠙⢟⠀⠈⠈⠁⠈⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣰⠿⠾⠛⠙⣦⠈⢻⣆⡴⣄⢠⡞⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣿⣰⣶⣤⠀⠈⣷⡀⠻⣥⠘⡾⠁⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣿⠟⢉⣤⣿⣷⣼⠋⣰⣄⠙⢿⡃⠀⢀⣀⣠⣤⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⣡⡴⠿⢧⣌⣽⠏⠀⠀⠙⢦⡈⠻⣾⡟⢻⡿⠛⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠛⠋⠀⠀⣤⠟⠁⠀⠀⠀⠀⠈⠻⣄⠙⠃⢸⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⣴⣶⣶⣶⠶⣤⣤⣀⠀⠀⠀⠀⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠸⠋⢻⡟⠛⠶⠶⠾⠛⠻⢶⣤⡀⠐⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣶⣶⣶⣶⣤⣤⣄⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠙⠻⣿⠈⣿⠿⢿⣇⢠⣤⣤⣶⢶⣶⣶⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⠀⣿⠟⠛⠛⠿⣭⣙⣿⡄⣿⣁⣀⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⠀⠀⠀⠀⠉⢹⡇⢻⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠘⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢿⣄⣤⡀⠀⠀⠀⠀⣠⣿⡆⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣧⣨⣿⢌⡿⠀⠀⠀⢾⡉⠿⢷⣼⣦⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣍⡉⣁⣾⢿⣦⠀⠀⠈⣿⡷⣄⣀⣀⡽⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⢃⣬⣿⠋⢡⣤⣿⣄⠀⠀⠹⣧⢀⣉⠉⣡⣴⣧⣀⣀⠀⣠⡤⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠛⠋⠛⠷⣦⣶⣾⠻⣦⠀⢸⣅⡍⠙⣦⠀⣠⠿⢏⠙⡇⠀⠞⣩⡟⢋⡿⠋⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⢿⡈⠃⢀⣀⣀⣠⣤⠶⠿⣦⡿⣦⣌⣁⣠⣄⣀⣀⣠⣿⠁⠀⠀⠀⠀⠀⣀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣦⣄⣀⣀⣤⣤⡴⠾⠟⢛⣋⣉⣥⣭⡶⠟⠛⠛⠛⠷⣶⣶⣬⣭⣭⣭⣩⣉⣛⣛⣛⣛⣛⣋⣩⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣬⣭⣭⣥⣤⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠐⠒⢄⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⣀⡀⢃⡀⣈⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠂⠁⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠀⠴⠀⡿⠀⠀⢀⡉⣁⠰⠂⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠠⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠒⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠈⠆⡈⠒⠰⡀
⠀⠀⠀⠀⠀⠀⣀⠔⢈⣀⡠⠤⠁⢲⢒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠙⠋⠈⠀⠀⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢰⠶⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡘⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠂⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠁⠀⠀⠀⠀⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠃⠄⠉⠒⠒⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠅⡆⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠓⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠓⡜⠁⠄⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠆⠀⢀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⡇⠀⠀⠠⢰⡀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠹⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠛⠃⠀⠀⠓⠀⠀⠀⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⠶⠶⠶⣶⣶⣶⣦⠀⢠⣶⡄⠀⢤⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡇⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢖⠒⠒⡖⠚⠛⠛⠛⠂⠘⠛⠛⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⢠⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⡉⠉⠙⠋⠋⠋⠉⡇⠈⠋⢩⠋⢀⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⡅⠀⠀⠀⠀⠀⠃⠀⡇⡆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠂⠀⠀⠀⠀⠀⠀⡇⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡄⠀⣀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢱⠹⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠱⡄⠉⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣡⡀⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢳⣀⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠃⠁

⠆⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠋⠀⠀⠀⠀⠉⠛⠓⠶⣄⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠋⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀⠐⢇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠀⠐⠋⢠
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠳⣀⣀⣀⣴⠀⠼⣄
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠌⠋⢁⠀⣶⡀⠈⣦
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⢳⡀⠘⣧
⠀⠀⠀⢀⡿⠀⠀⠀⠀⣀⣀⢀⣠⣀⣀⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣄
⠀⠀⠀⣼⠷⠶⠺⠏⢻⠉⠉⠉⠋⠉⣻⣿⡿⠛⣿⠉⠉⠉⡙⠋⢱⣶⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⣿⠀⠀⢿
⠀⠀⢠⡿⠀⠀⠀⣤⡌⠀⠀⠀⠱⡀⠻⣿⣿⣿⡟⠀⠀⠀⡇⠀⣿⣿⣿⣄⣼⡿⠀⠀⢹⠋⢻⠶⠶⣿⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠁⠈⠛⠁⢀⣀⠀⠀⠈⠢⢈⣿⣿⡿⠟⠀⠀⠀⢸⡤⠎⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⡠⢶⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡰⠀⣀⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠂⠐⠛⢉⣠⡾⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠀⠠⠀⢀⠌⢠⡊⠄⠀⣀⡝
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠿⠛⣹⠇⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠰⠀⢷⡀⠀⠈⠁⠔⠛⣉⡀⠦
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢊⣡⣴⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠙⢆⠀⠀⠒⠠⠍⡁
⠀⠀⢻⡆⠀⠀⠀⢀⣀⣠⣤⣤⠴⠖⠛⠛⠒⠲⢤⣤⣤⣤⡤⣤⡴⠒⠉⠉⠉⠉⠉⠉⠉⠁⠓⠒⠒⢦⣤⣄⡀⠠⡇⠀⠀⢘⡀⠀⠀⠀⠀⢀⠖⠒⠀⠉
⠀⠀⠸⡷⠶⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠆⠀⠀⠌⠁⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠔⠲⠒⠂⠉⠀⠀⠉⠲⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢨⠉⠉⠉⠉⠉⠀⢰⠄⢀⣠⣀⣀⣠⠋⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⢄⠀⠀⠀⡄⠀⠀⠀⠁⠀⠃⠀⡀⠀⠒⠀⠈⠀⠀⠀⠳⢄⠀⠀⠸⠓⠶⠶⠤⣤⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡷⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⠆
⠀⠀⠀⠀⠀⠔⠁⠀⢀⡔⠋⠀⠀⠉
⠀⠀⠀⠀⠐⠦⣄⡀⠈⠐⠢⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⠀⠑⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢀⣀⣀⣀⣀⣤⢠⣄⣀⣀⡤⠦⣄⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⣠⠋⠀⠈⠏⠀⠀⠀⠀⠙⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡝⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡧⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣇⠀⠀⠔⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⡀⠠⠀⠀⠉⠀⠀⠀⣀⠤⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠦⢀⣀⣀⠀⠤⠄⠒⣃⡡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⣄⠀⠀⢀⣀⠞⢱⡄
⠀⠀⣦⠀⣀⣈⣉⣡⣤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠐⠓⠈⠉⢀⣰⠇
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠒⠲⠚⠉

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣏⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⢿⣿⣿⣿⣿⣄⠀⠸⠿⠆⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⠛⠁⠀⠀⠀⣹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⣰⣿⣿⠃⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⣀⣈⣿⣿⣤⣤⣤⣤⣀⣸⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠿⢿⣤⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣴⡆⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣄⠀⠀⢸⣿⣆⠀⠀⠀⣿⣧⠀⠀⣼⣿⡿⠁⠀⣠⣾⡏⠀⢀⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠙⣿⡧⠀⠀⣿⡏⠀⠀⠸⣿⡀⠀⣼⡿⠉⠀⠀⣾⠋⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⣿⣇⠀⠀⣿⣇⠀⢀⣼⡿⠁⠀⣸⡇⢀⣀⣤⡿⠀⣀⣠⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠻⣿⣦⡀⢹⣿⠀⢸⣟⠀⠀⣾⠟⢡⣿⠟⠋⠀⣼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠹⠟⠁⣼⡿⠀⠸⠟⠀⠈⠛⠀⠼⠃⣰⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢿⣿⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⢸⣿⠀⠀⠀⣿⡇⠀⢸⣿⡄⠀⠀⠀⠈⠉⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣼⣿⡇⠀⠀⠹⠇⠀⠘⠿⠁⠀⠀⠀⢀⣀⣠⣾⠟⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢿⣧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⢉⡉⠀⣠⣤⣠⣴⣾⣿⡟⠻⣷⣶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⠞⢿⡿⠙⢷⣤⣾⣿⣦⡀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⢁⣾⠋⢹⣿⢃⡀⢸⣷⠀⢹⣯⠈⣿⡟⢿⣦⣤⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣿⠇⢸⡇⠀⢸⡇⢀⣼⣿⣧⣤⣿⣷⣶⣶⣶⣶⣶⡶⠶⠶⠶⠿⠿⠿⠿⠿⠟⢻⣿⠃⢸⣿⠀⢸⣟⠀⣿⠁⢸⣿⠁
⠶⢶⡿⠿⠟⠛⠻⠿⠛⢻⣿⠘⣿⠀⢸⣇⠀⢸⡇⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣸⡇⣰⣿⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣿⡀⠘⣿⡀⠸⣿⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⣴⣿⡷⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣷⣦⣿⢷⣤⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠒⠒⠒⠒⠂⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⡿⠀⠸⠿⠟⠛⠛⢶⠾⠟⢿⣭⣤⣴⣦⣴⣦⣴⣦⣤⣤⣤⣤⣤⣤⣴⣤⣽⣿⣦⣤⣤⣴⣶⡤⠶⣶⠖⠂⠀⢸⡆
⠀⠀⠀⣼⠁⠀⠀⣇⠀⠀⠀⠀⣤⣈⣁⣀⣈⣉⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⡁⣠⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇
⠀⠀⠀⣿⠀⠀⠀⣽⡄⠀⠀⠈⢉⢿⣬⣿⣿⡿⠀⡳⠀⠀⠀⠀⠀⢸⣗⠘⣿⣿⣿⠃⠀⢹⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⠀⠀⠘⣦⠀⠀⠀⠈⠠⠉⠉⠉⠀⠜⠁⢀⡤⢤⡀⠀⠈⠉⠛⠻⠛⠋⠀⣠⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠙⠀⠀⠀⠁⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠙⣦⣄⠀⠀⠀⠘⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠶⢶⣶⣶⡿⢷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠠⠄⠀⠀⠀⠀⢀⣴⣿⣀⣀⣀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠋⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠋⠁⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠰⢋⡄⠙⠛⠛⠳⣶⡶⠴⣶⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⣇⠀⠀⠀⢀⣼⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇⠀⠀⢈⣤⡋⢱⣆⠉⣷⡦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠞⣷⠿⠆⠶⣦⡉⠀⠉⠀⠉⠉⠀⢀⡙⠋⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠈⠛⠃⠠⠤⠀⠒⠃⠈⠀⠀⠀⡀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣿⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡿⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠁⠀⠀⠒⠒⠂⠀⢀⣀⣀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠛⠛⠛⠳⠶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠛⠓⠶⢶⣆⣀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠻⠿⣶⠶⠶⠷⠶⠾⣿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡞⠃⠀⢸⡇⣤⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠊⠉⠀⠀⠀⠀⢸⡇⠀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⢀⣀⣤⠴⠶⢿⡇⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⠔⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣤⣴⡶⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣶⣦⣄⣉⣈⣈⣹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠙⠋⠉⠁⠀⠀⠀⠉⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣤⠶⠶⠶⠆⠀⠀⣤⣶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣂⡐⠀⠀⠀⠈⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠾⣿⡿⠈⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠫⢥⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠾⠛⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⡘⠀⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠒⠲⠤⠤⢤⣶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⡿⣻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠓⢀⠀⠭⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡹⠇⠀⣄⣈⣩⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣴⣾⣛⣻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀
⠀⠙⢢⠅⢠⣀⠀⠀⠀⠀⠀⠀⠀⡙⣄⢇⢇⡇⡞⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⢲
⠀⢰⡉⣰⢸⠘⢆⠀⠀⠀⠀⠀⠀⠘⠈⠚⠈⠗⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡌⠦⠊⠐⢃⣀⡤
⠀⠀⠘⠋⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⣭⠱
⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⣀⠀⠀⠁⠀⠀⡈⠀⢀⠔⡒⢄⠀⣀⠤⠐⣀⠤⠒⠈⠐⠒⠊⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠉⠢⢼⣰⡌⠒⠤⣠⠀⠧⠚⠁⠀⢿⣊⣡⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢠⡇⠀⠀⠀⠒⠊⠀⢀⣀⣀⣩⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣈⠤⢶⠂⠀⠀⠀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⡠⠐⣺⣟⣁⠔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⡿⠻⠋⠉⠀⠀⠁⠒⢉⣽⡗⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⡆⠀⠀⠀⠈⠉⣥⠦⠿⠽⠦⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡗⠒⣖⡒⢹⢢⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⢄⡈⢃⡼⢅⠃⠈⣡⡇⢸⣄⡠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠄⢀⠤⠄⠀⠀⠘⢉⢌⡁⠀⢸⣽⠚⠉⠁⠀⠀⠉⠉⠉⠉⠓⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠀⠠⠊⠀⣠⣄⣉⡅⣷⠼⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣚⠓⠆⠀⠤⢣⢤⠀⡔⠋⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠒⠒⡋⡴⠒⡄⠀⠀⢇⡠⡺⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣑⡢⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠣⣬⡤⢀⣀⣠⢥⠾⠤⠤⠀⠀⠀⣀⣀⢤⣶⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠢⠭⠭⠥⣒⣒⣒⣀⣙⣛⣓⣒⣒⣒⣒⠲⠦⠭⠟⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠢⣤⠀⠀⠀⠀⠀⠀⢀⠄⠠⢄⢀⡀
⠀⠀⠀⠀⢀⠂⠉⠀⠑⠂⡀⠂⠀⢀⠆⠀⡠⠀⠀⠀⣄⠀⠑⡄⠀⢀⠀⠀⠀⠀⠈⠠⠀⠄⠂⡙⡥⠀⠀⠀⠀⠀⠘⢲⠀⠀⠀⠠⠁⠀⠀⠀⠠⡀⠁
⠀⠀⠀⢠⠁⠀⠁⠀⠀⠀⡁⠀⠀⠀⡄⠰⠀⡀⠀⢀⠘⡄⠈⠆⠀⠀⠀⠀⣀⠀⢀⢀⠀⠀⠀⠠⠒⠀⢀⠀⠀⡀⠀⠠⢆⡀⠀⢀⠀⠀⢀⠀⠀⠑
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠱⡀⠀⠀⠄⠀⠀⡠⠊⢀⡄⠀⠀⠀⠀⠀⠀⡈⠠⠂⠀⠑⠁⠀⠀⠀⠀⠀⠐⠢⡌⠁⠀⢠⡈⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠣⠶⠚⣭⡱⢲⠁⠀⠀⠀⠀⡈⠵⠂⠰⠔⡈⠀⠀⠂⣖⠡⢤⠒⠀⠲⠍⠀⠀⠀⠀⠀⢇⣀⣠⠜⠒⠒⠒⠊⠁⠀⠀⠀⠉⡰⠀⠀⠒
⠀⠀⠀⠀⢸⠀⠀⣿⡇⢠⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠸⠀⢀⣤⠌⠐⠰⠐⠀⠀⠀⢢⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⢸⠀⠀⠈⠂⠀⢃⠀⠀⠜⢀⠃⠀⠀⠀⡂⠠⠀⠀⠀⠀⠂⠀⠀⠁⠀⡄⠸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠨⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⣲⣭⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢠⠁⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⣜
⠀⠀⠀⡠⢦⣜⡠⠤⠠⠀⡜⠀⡈⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠸⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⣴⡤⢼⠀⠑⠀⠀⠀⠇⠀⠑⠤⢀⠀⠀⠀⢀⢇⡘⡀⠀⠀⢀⡇⠀⢰⠀⠀⢁⣀⠀⠀⠀⣠⠀⡈⠀⠀⠀⠀⠀⢂⡑⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⢠⣤⠈⠀⠀⠁⠂⠀⢀⠔⠀⠀⠀⠀⢠⠀⠀⠀⠰⠈⠻⠀⠀⠀⠈⠁⠀⢈⠀⠀⢘⠁⠀⠀⠀⠛⠃⠁⠀⠀⠀⠀⠀⠘⠟⠃⠀⠉⠒⠀⠀⠀⠐⠚⠃
⠸⣿⠀⠀⠀⠀⡜⠀⠘⠀⠀⠀⠀⠀⠀⡆⢠⡀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠸⢨⠀⠸⠀⠀⠀⠀⠀⠘⠁⢐⠒⠦⠤⢤⠀⢊
⢸⣿⠀⠀⠀⠸⠀⡆⢨⠀⠀⠀⠀⠀⠀⡇⠀⠃⡀⢠⠀⠀⠀⠀⠀⠠⠀⢰⠀⢠⠃⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⠈⠄⠈⣄⠀⠀⠀⠀⠀⠀⢀
⠸⣿⠀⠀⠀⡔⠸⠡⡈⠄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠠⣼⠠⡆⠀⠀⠀⠀⠀⠀⠇⠈⠁⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣿⠀⢀⠌⠰⠀⠀⠃⠐⢄⠀⠀⠀⠀⠸⠀⡀⠠⠁⠸⠀⠀⠀⠀⠀⠈⡄⢠⡘⢢⠀⠀⠀⠀⡰⠃⡜⠀⠀⠀⠀⠀⠀⠀⢂⠀⠤⡀⠀⠊⠀⠐
⢠⣿⠀⠈⠂⠀⠀⠀⠈⠢⠤⠃⠀⠀⠀⠡⠤⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠉⠉⠀⠀⠀⠘⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠜⠂⠤⠄
⠨⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠾⠀⠀⠉⠀⠀⠉⠉⠉⠑⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢢⡀⠀⠀⠀⢰⢄⡀⣠⠚⠢⣍⣁⡀⠀⠞⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠙⠢⣄⡀⠘⡀⠀⠀⠀⠀⠀⠈⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡄⠀⣤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⡇⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⡇⠀⠀⢠⡆⠀⠀⠀⢀⠔⢛⠀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠀⢀⡰⠋⢀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠋⢀⠴⣿⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢲⡁⢀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠤⠤⣤⣤⡤⣤⣼⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠓⣄⠀⠀⠀⠀⠀⠀⠀⠅⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡀⠀⠀⠀⠀⢀⠰⠧⣤⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡾⠉⠢⣄⡀⠀⠀⠀⠀⡜⠀⢘⡦⠴⠒⠒⠒⠒⠤
⠀⠀⣀⠄⠐⠂⠀⠀⠈⠃⠀⠀⢳⡄⠤⠐⠊⠁⠀⠀⠀⢉⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢯⡀⠀⠀⠀⠉⠉⠒⠒⠚⠀⠀⠈⠀⣀⠀⠀⠀⠉⠀⢉
⠀⣮⡡⠤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣨
⢦⡠⣤⡴⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣀⡤⠴⠒⠉⠀⠀⢠⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠙⠲⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡠⠞
⠀⡔⢁⣠⡤⠀⠀⠀⢀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠙⠉⢤⣠⠞⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠤⠴⠧⠤⠼⠤⠤⠤⠐⠒⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠤⠤⠤⠔⠋⠳⠐⢲⠚⠛⠛⠛⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠀⠀⠆⠀⠀⠀⠀⠸⠂⠀⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢳⡤⠄⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⢄⠠⠤⡆⠀⠀⠀⠀⠀⠀⠀⣷⠤⠤⡴⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢤⠃⠀⠀⠀⠀⠀⠀⠀⢻⡔⠀⠁⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠐⠧⣤⣀⣀⣀⡤⢻⠁⠀⠀⠀⠀⠀⠀⠀⢸⡳⢤⣀⣀⣠⣤⠴⠂⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠈⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⠁⠀⠀⠀⣠⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣦⣤⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣦⣤⣴⣖⣚⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠉⠉⠉⠁⠉⠉
⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠠⠈⠁⠀⣀⠀⠈⢀⣀⢀⣀⢀⡤⠆
⠀⠀⠀⠀⠞⠂⠔⠈⠖⠐⠰⠖⠀⠀⠀⠂⠀⠀⠁⠦⠁⠎⠨⠰⠀⠀⠂⠜⠡⠁⠀⠠⠀⠀⠏⠠⠒⠀⠇⠄⠹⠀⢤⡼⠂⠀⠊⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠐⢄⣀⡀⡀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠂⠀⠈⢣⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡄⠐⠆⡀⠁⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⡂⠂⠰⠀⠐⠐⢂⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠈⠐⠈
⠀⠀⠀⠐⠒⠆⠀⠐⠂⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠈⢰⠀⠀⠀⠠⠀⠀⠐⠀⠄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠂⠀⠀⠜⠀⠁⠈⠀⠰⡀⠀⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⢀⣀⠀⠐⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠐⠀⠀⠠⠀⠀⢀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠂⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠊⠄⠀⠀⠀⠀⠄⠀⠀⡴⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠀⠀⠠⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠄⠀⠀⠠⠁
⠀⠀⠈⠀⠄⠂⠀⠄⠐⠂⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠀⠀⠀⢄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡄⠄⠀⠀⠀⠀⢰⠀⠀⠀⠠⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⠀⠀⠀⠈⠀⠀⠀⠄
⡅⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢀⢀⠀⢐⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠇⠀⠤⠀⠀⠀⠀⠰⠀⠀⠀⠁⡀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⢻⡶⠒⠃
⡇⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡏⠀⠀⠀⠀⠀⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠂⢠⠄
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠲⠖⠈
⠀⠀⠈⠀⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠰⣿⣆⠀⠀⠀⢰⣿⠀⠀⠀⣤⣾⡿⠁⠀⢀⣾⠟⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣆⠀⠀⠻⣿⣦⠀⠀⢸⣿⠆⠀⠘⣿⡟⠀⠀⣴⡿⠟⠀⠀⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⠀⣽⣿⠀⠀⢸⣿⠀⠀⢀⣽⡷⠀⠀⣿⡇⠀⠀⣸⡿⠀⠀⢀⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⢻⣿⣦⠀⠸⣿⡄⠀⣾⡟⠁⢀⣴⡿⢡⣶⣿⡟⠁⣴⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠹⣿⡷⠀⣿⡇⠀⣿⡆⠀⢸⡏⠀⣿⠋⣀⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠉⠀⣸⣿⠁⠈⠉⠀⠀⠀⠀⠀⠁⣴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠙⣿⡇⠀⠀⢠⣦⠀⠀⣴⡄⠀⠀⠀⠀⠺⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠶⠶⠟⠋⠀⠀⠀⣀⣤⣴⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣦⡀⢈⣿⣆⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⢠⣶⢀⣴⣿⣿⣾⠟⠛⣿⡄⠙⣿⡟⢿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⣿⢻⡿⠋⢹⣿⠀⢸⣿⣿⠛⢻⣧⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣧⣼⣷⣤⣾⣧⣶⠆⢹⡇⠀⢹⡇⠈⣿⠁⢿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⠁⣿⡇⢸⣧⠀⢸⣿⠐⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠋⠉⠉⠉⠉⠉⠁⣿⡏⠀⢸⣿⠀⣸⡇⢸⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⡇⠘⣿⡀⢸⣿⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣿⣏⣠⣿⣡⣿⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣧⣽⣧⡀⣿⣧⡀⢻⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡟⠈⡙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣻⡯⠀⠈⠂⠀⢙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⣷⣄⠰⠇⠀⢸⣿⣿⣿⣿⣷⣦⣠⠴⠖⠛⠛⠉⠉⠉⠉⠙⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡅⠀⠰⣄⠀⣸⠃⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⡆⠀⠈⠉⠁⠀⢀⣨⣟⠛⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣿⣷⣶⣴⣿⣿⡿⠀⠀⡀⠀⠀⢠⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠉⠀⠠⠃⠀⢐⢀⠀⠀⠀⠀⡀⣠⠢⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠐⠓⠀⠂⠐⠙⠀⢀⠰⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠂⠀⠂⠀⠀⠀⠀⠘⡇
⠀⠀⡀⠸⡍⢠⡈⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⡩⠀⠈⠛⠁⠀⢹⣿⣿⣿⣿⣿⣡⣿⣿⣿⠀⠀⠀⡀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⣤⣤⢤⠀⠀⡇⠀⢠⡄⢄⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⠈⠀⠘⡇⠀⢸⡇⠊⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⡻⣦⡀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣿⣟⢹⣟⠻⣿⠛⠟⣻⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠒⠲⢢⡄
⠠⡶⣄⢸⣍⠲⣿⡜⢆
⠀⠙⠪⢝⡠⠽⢿⠀⡆
⠀⠀⠀⠀⠈⠢⠤⢄⠢⡀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⢆⠀⠀⠀⠀⠤⣳⣜⢮⡧⣳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣮⠯⠞⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡑⢄⠀⣨⣚⡯⠫⠃⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠹⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡣⣀⠥⢭⢣⠀⠀⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡨⠧⢩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠮⡻⡇⠿⠔⠄⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣭⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡿⠁⠀⠑⢌⡆⢀⣄⣀⠀⠀⠀⠀⠀⣠⠜⣫⠎⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠢⢄⡀⠀⠛⢉⣉⡀⠙⠒⢠⡴⣊⠵⠋⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⡿⠁⣱⣀⠔⣫⡖⠻⠤⢄⣀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣧⢴⣿⣅⢳⠛⡩⢞⣫⠜⠉⠉⠐⠒⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⡭⠓⣉⡭⡩⡾⣟⢯⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⢘⡤⡈⠯⠋⠁⣠⠼⢒⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⡀⠘⢢⠝⣤⡴⢋⠔⠊⣉⣈⡩⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⣄⣈⢛⣋⣴⡥⢚⣉⡿⢛⡤⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣩⡿⣿⠁⠀⠀⠀⠀⠀⠁⠙⠛⠒⠛⠛⠉⣩⣭⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣉⡛⠚⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣀⡀⠀⠀⢸⣿⡟⢡⠋⣹⢂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⢢⡀⠉⠙⠲⢬⡭⠟⠁⡰⢣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⡦⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⣀⢀⡜⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⣉⡙⢮⣆⡠⣌⢧⡀⠀⠀⠀⣀⣤⠊⠀⠀⢀⣸⡼⣏⡾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⠙⠧⠍⢸⣈⣵⣭⣒⣻⠩⠍⣉⣙⡌⢧⡤⠶⡺⡉⢢⠴⢶⡁⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠤⢯⣻⠦⣊⠀⠀⠉⠒⠲⠦⠥⠼⡧⣌⠲⠂⠀⢞⣿⡖⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡆⠀⠨⢿⡟⠚⠽⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢭⣢⢤⡀⢨⠛⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⠒⠋⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⡳⠤⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣳⢤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⡴⠃⡴⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠚⢡⢊⡥⡼⠉⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢰⠃⠀⢠⠀⠀⠀⢔⢓⡚⠉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠈⠀⠀⢀⡀⠀⠀⠀⠠⢍⡭⢟⣁⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠈⠰⠃⡠⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⢠⠞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⠀⣰⠋⠙⠋
⠀⠀⠀⠀⠀⢀⠖⠛⠒⠦⣄⠀⢸⡆⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⡀⢀⠠⠄⠤⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠧⡘⡇⣸⠁⡠⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠑⠠⠚⡉⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢦⣬⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢳⣚⡅
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⠆⠴⠋⠘⢷⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⡴⢃⠔⠑⠒⠚⠁
⠀⠀⠀⠀⠀⠜⠀⣀⣀⠀⠀⠘⢦⡀⠠⣀⠀⡄⢀⠀⠀⠈⠳⡄⠀⢀⡜⡱⠃
⠀⠀⠀⠀⠀⠒⠈⢹⡏⢹⡉⠿⢖⣙⡦⠘⢦⣹⡎⡆⠀⠐⠺⣅⠀⡞⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠃⠀⠈⠉⠀⠀⠀⠃⠀⠀⠐⠐⠀⠈⠛⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠦⢤⡄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠶⠾⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡤⣤⡄
⠀⠀⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⢷⡀
⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢷⣄⠀⢺⣷⣀⣴⠋⠉⠻⢦⣄⡀⠀⣶⣄⣿⠈⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠙⠿⡿⠀⠙⠋⠀⠀⠀⠀⠉⠛⠻⣿⠛⠿⡄⠀⠀⠉⠛⠷⣤⣤⠀⡀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣦⡀⠀⠀⠀⢸⣿⠀⠀⣾⠃
⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⠀⢰⡏
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣠⠶⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⢠⡀⠀⠀⠀⢸⡟⠀⣼⠃
⠀⠸⣧⣤⠿⠿⠿⢧⣤⣿⠀⠀⠀⠀⢾⠁⣠⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⣄⠀⢱⠀⠀⠀⣼⠁⣸⡇
⠀⢠⡿⠁⢠⡤⠄⠀⠛⠁⠀⠀⠀⠀⢾⣀⠈⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠁⢀⡘⠃⠀⠀⣿⢿⡏
⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠸⣇⢸⡇
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟
⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⡖⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠙⠻⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⣤⠽⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡘⢀⡴⠋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠗⠒⣦⣤⣤⣤⣤⣤⣤⣤⡀⠶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠢⣀⣴⠁⢠⡿⠋⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⠿⣇⡀⠀⠀⠀⢈⡟⠛⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡆⠀⠻⠁⠀⠀⠀⢠⡾⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠠⠛⠛⢁⡀⠉⠁⠀⠀⠀⠀⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⠀⠀⠀⢀⡴⠆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡄⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⢀⡴⠛⠁⢀⣹⡶⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠼⢷⡄⠀⣠⠞⠋⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⠉⠢⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠈⢁⣠⣾⡿⠟⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠑⢶⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣴⠶⠋⠉⠉⠁⠀⠀⢀⡠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠉⣦⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠳⣄⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠘⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠛⠻⣏⢈⣷⣀⣤⡤⣶⡶⢶⣶⣶⣶⡦⣤⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠁⢀⡀⠈⢿⣟⠉⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠈⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⡇⠻⣄⠘⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⢷⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⣻⣤⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠶⠶⠾⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⢻⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⢀⣾⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢠⢺⣿⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⣤⣤⣤⣤⣿⠈⣿⣤⣤⣤⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠛⠛⡟⠉⠀⠀⢈⡉⣹⢰⣿⠉⡉⠀⠀⠈⠙⣟⠛⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⣉⣉⣉⣀⣠⣤⣈⣉⣹⠿⢿⣈⣉⣤⣤⣀⣈⣉⣉⣀⣸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡿⠛⠋⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⣻⠄⢀⣾⢋⣤⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢶⢸⣇⡹⢠⡞⣡⠞⣡⠞⢋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠁⠾⠘⠁⢖⠥⠞⣋⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⡀⠀⠀⠀⢠⡞⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣼⡀⢁⠘⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣀⠀⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⣷⠀⠀⢠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣤⣍⠻⣆⢠⣟⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⢸⡇⠸⣿⠛⣆⢹⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠛⠁⠀⠀⢸⡇⠀⣿⠀⢿⡀⣷⣌⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣤⣤⡀⢀⣠⣴⢶⠿⣧⡄⣿⠀⢸⡇⢸⡿⣦⡀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡿⠋⣹⣿⠁⣿⣸⠞⣷⠃⢻⣄⢸⡇⠘⠇⣙⣿⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⣛⣿⢸⠇⠙⣞⠁⠀⣿⢿⣾⣇⣀⣿⠟⣧⡙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⠞⠃⠀⠉⢻⡀⣀⠀⣧⣤⠶⢿⡞⠛⠛⢿⡛⡿⣯⣻⣆⠹⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⠙⠻⠶⠶⠤⣦⣼⡇⢸⡇⣠⡤⠶⠟⠁⠀⠀⣼⠓⣿⡶⠿⣿⣷⣌⣻⣶⠶⢤⣤⣀⣀⠀⠀⠀⣀⠴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⠶⠶⣶⠶⣾⠟⠉⠀⠀⠀⠀⢀⣼⠋⢀⡿⠙⢷⣄⠈⠙⠻⢿⣷⡶⠤⢤⣤⣍⣉⡉⠋⠀⠈⠁⠐⣀⠉⠋⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣼⠋⠀⠀⠀⠀⠀⠰⠟⠁⣿⡿⣤⣤⡀⠙⢷⣄⠀⠀⠈⠙⢶⡄⠀⠀⠈⢯⡀⠀⡼⠀⢈⡛⠛⠛⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣸⡇⠀⠀⠀⣀⣴⢟⡀⢀⡴⠋⠹⣦⡈⠙⠶⣦⣈⡳⣄⠀⠀⠀⠙⢦⡀⠀⠈⠙⠶⡄⢠⡈⠻⣵⠒⢤⣤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣿⣤⣤⣴⡞⠋⣀⣿⣿⣯⣄⡀⠀⠈⠳⣄⠀⠀⠉⠙⠻⢷⣦⡄⠀⠀⠹⣦⠀⠀⠀⢻⡌⠟⠰⣀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣼⢷⣶⣾⣿⣾⡉⠀⠈⢷⡈⠙⠳⢦⣄⡘⢷⡀⠀⠀⠀⠈⠙⠻⣤⡀⠀⠘⢷⡀⠀⠈⠳⠞⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡾⠁⢈⡝⢷⣌⢿⡙⢦⣄⡀⢻⣆⠀⠀⠈⠙⠻⢿⣦⣀⡀⠀⠀⠀⠈⠻⣤⡀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⣾⠁⠀⠈⣷⠀⠙⢷⣿⣆⠈⠻⢦⣙⣧⡀⠀⠀⠀⠀⠹⠿⢧⡀⠀⠀⠀⠀⠈⠻⣄⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⣀⣀⢀⡿⠀⠀⠀⢻⡄⠀⠀⠹⢿⣦⠀⠀⠙⠻⢿⣄⡀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠈⢻⡿⣿
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⣰⠏⠙⠛⠁⠀⠀⠀⠸⣧⡆⠀⠀⠀⠙⢷⣶⡄⠀⠈⠻⠷⣤⡀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⣾⣱⠏
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⣀⣠⣬⣭⣝⠷⣦⣤⡀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠉⢳⣾⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢻⡆⠀⠀⠀⠀⢀⡟⢠⣾⣿⣿⣿⣏⠈⢿⣋⣰⠟⣿⣙⣷⣶⣤⣄⣉⠳⣦⣄⠀⣠⡶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⡿⠀⠀⠀⠀⠈⢷⣌⡛⢖⣀⣀⣽⠆⢸⡏⣻⠀⡿⠉⠁⠀⠈⠉⠉⠛⠾⠿⣿⠿⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢩⡟⢀⡾⠁⣿⢰⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣾⠁⢰⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡼⠃⠀⢸⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⠁⣼⠃⠀⠀⢸⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣼⣿⣆⢀⣠⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠟⢷⣾⣿⡦⠛⣿⣿⣾⡏⠹⣏⣰⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢀⣴⣿⢻⡟⣧⡾⠉⣀⣸⠾⣧⡘⠻⣻⡿⠷⣦⠀⣤⠤⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣯⣳⠞⠁⢸⣿⢾⣟⠀⣾⢉⡙⠿⢫⣤⣴⣯⠟⠀⠀⣤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢧⠀⠀⠀⢴⠞⣿⣼⠱⣏⣹⡇⠰⢟⡿⢶⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢷⡀⠀⠀⢿⣯⡿⢦⣬⣍⠀⠀⠈⠁⢉⡼⠋⠀⠀⠀⠈⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢷⣀⣴⠋⠁⠀⠀⠀⠉⢳⡤⠤⢤⢾⡥⣤⠤⢤⡤⠶⣟⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠹⣧⣀⣀⢀⣀⣀⣠⣾⠟⠓⠒⠒⠒⠒⠒⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣭⣉⣋⣻⠭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⡀⢸⣿⠁⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢶⣤⠈⣧⠘⣿⠀⣿⠉⣴⡿⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⡁⠀⣿⡆⣿⠀⣿⡀⣿⢸⡏⣴⠟⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⢻⣄⢹⠓⠿⢰⠟⢁⣿⡟⢿⣧⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠛⠋⠙⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢉⠀⢀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠸⠃⢻⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣤⣤⠀⠀⠘⠀⠀⣎⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⢠⡄⠀⢰⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢻⣿⠀⢠⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⢷⣼⡟⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⢷⡄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠉⠀⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⣿⣠⡞⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠁⣀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣶⡽⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⢿⣦⠿⡇⢸⡇⠀⠀⠀⠀⠀⠀⣺⠁⣰⡿⠁⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢡⡄⢷⣤⣷⡀⠀⠀⠀⠀⣠⣿⣦⡟⠁⣴⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢀⣠⣴⣶⡎⣵⡚⠁⠘⣷⠀⠀⠀⠰⡏⠁⡘⣧⣤⠿⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠐⠿⣾⠻⣿⣁⣬⡿⠟⠃⢰⣶⠟⠁⠀⠀⠐⢿⣀⣇⢈⣿⣤⠶⣋⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣷⠀⣿⠋⠉⠀⠀⠀⠈⢻⡀⠀⠀⢀⣠⡾⢋⣼⣏⣉⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⢿⡀⠀⠀⠀⠀⠀⠘⢷⣤⠶⠟⣡⡴⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⠸⣇⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣧⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⠀⣻⡆⢹⣧⣤⣴⣛⣛⣿⣿⠟⢹⣟⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⣷⠈⢿⡋⠙⠛⣻⠉⣻⣦⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢻⣆⠘⣷⡟⠀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣹⡶⠋⠀⠀⠀⢀⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠿⠋⠀⠀⠀⠀⠀⢸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢻⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣠⣄⣀⣤⣤⣤⣶⣶⣿⡿⢻⣷⠈⢻⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⠟⠛⣿⠀⣽⡏⠉⠀⣀⣉⣡⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠶⠾⣿⠀⣸⡿⢿⣿⠛⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢸⡇⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⢸⡏⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡇⣸⠇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢰⣟⠀⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢸⡇⢰⣿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣶⣿⠃⣼⣇⣸⡏⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⠿⠿⣶⡿⠛⣿⣧⣼⣿⡿⢷⡄⠀⣠⣴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⡀⠀⢠⣤⣾⣏⡈⢉⣽⣶⣿⠁⠀⣿⠁⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠿⢿⣟⠉⠉⣿⠟⢉⣩⣿⠀⣾⠏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⠟⣶⠀⠉⣠⣾⣅⠐⠿⣿⣿⣛⣁⣄⣀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⣀⣼⠂⠈⠉⣴⠿⢿⣶⣿⣯⣿⣿⣿⣿⡉⠉⠉⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⢛⣿⠟⠁⠀⠀⠀⠈⠻⣧⡀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⢦⣤⣤⣤⣤⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⣀⣸⣧⣠⣤⡾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣤⣤⣄⣈⣉⣉⣉⣙⠛⠛⠛⠛⠛⠛⠿⠛⠛⠉⢉⣿⣤⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠠
⠀⠀⠀⠀⠤⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡌⠢⡀⠀⠀⠸⢠⡥⠄⠀⠓⠐⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁⠡
⠀⠣⠱⠂⠢⠀⠐⠆⠒⠀⠀⠀⠁⠀⢀⣂⢤⠀⠠⠄⠀⠤⠀⢀⢄⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡟⡄⠀⠀⠠⠠⠀⠐⠀⠀⠐
⠐⠀⢴⠀⠂⠀⠐⠀⠈⠀⠆⢀⠂⠀⠀⠈⠛⢄⠀⠀⠀⠀⢀⠜⠊⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⢠⡀⣿⡀⠀⠀⠀⠀⢀
⠐⠇⠀⠀⠀⡀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠒⠂⠐⠃⠀⡀⠀⠀⠀⠀⠀⠘⠳⠤⢀⠀⢀⠀⠚⠁⠌⠀⠀⠀⠀⠀⠠⠐⠀⠀⠒⠂⠀⡀
⠀⠀⠀⠀⠰⠀⢀⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣄
⠀⠣⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⡆⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢸⡄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡈⡃⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢀⡈⡃
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢠⡀⡀⠀⠀⠀⡈⠉⠀⠀⡠⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⢀⠀⠀⠈⡤⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠀⠀⠀⠈⠁
⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠁⠀⠀⠀⠇⠀⠀⠀⠀⢫⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠐⠢⠁⠀⠀⠀⠃⠀⠀⠀⠀⠣⠐⠂
⠀⠀⠀⢀⠀⠤⠀⡄⢠⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠁⠀⠀⠀⠀⠀⠇⠀⠀⢰⠀⠀⡀⠀⠀⠸
⠀⠀⠀⠈⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠆
⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠙⠉⠁
⠀⠀⠀⢸⢀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠰⠀⠘⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣠⣠⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠐⠀⠐⡀
⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⡀⠀⠠⠐⠊⠉⠈⠇⠀⠀⠀⠀⠈⠁⠩⠑⠂⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠊⠉⠈⡇⠀⠀⠀⠀⠘⠉⠉⠑⠂
⣀⣠⣤⣤⣤⣂⣀⣐⣂⣤⣤⣘⣀⣶⣤⣤⣶⣂⣁⣀⣀⣀⣀⣈⣁⣶⣤⣤⣴⣂⣀⣐⣤⣤⣁⣘⣤⣤⣜⣀⣐⣶⣤⣤⣶⣂⣁⣀⣀⣀⣀⣈⣐⣶⣤⣤⣴
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⡀⡀⠀⠀⡀⣀⡀⠆⠀⠀⠀⠈⢀⠀⣀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠂⠃⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠤⠚⠐
⠀⠀⠀⠙⠻⠿⠿⠿⠟⡋⠔⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣅⡀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠈⠀⠒⢂⠬⠤⠤⢀⠀⠀⡀⠄⠀⡰⢠⠀⠀⠀⠐⠈⢦⢾⠁⢂⠀⠀⠀⢐⠁⠀⠀⠀⢁⠀⠀⠀⡀⢄⠀⠀⢀⣄⠀⠀⣤⠀⡆⠈⠍⡂⠀⠀⠈
⠀⠀⠀⠀⣀⠀⠰⠁⠀⠀⠀⠀⠱⠀⠑⠀⠈⠀⠈⠀⠐⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠉⠈⠆⠀⣿⠀⢿⠈⠰⣤⠀⡀⠰
⠀⠀⢸⠀⢸⠀⠀⡄⣄⠀⠠⠄⡠⠁⠠⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠠⠀⠄⠀⠀⠤⡀⠀⡀⠀⠀⠀⠁⠂⠈⠓⠉⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠱⣺⠀⠀⠐⠀⠀⠀⠄⠀⠀⢨⠀⠀⠀⠀⠆⠈⠅⡰⠫⠁⠈⠃⢄⡰⠀⠀⠈⠀⠀⠀⠀⠦⠀⠀⠠⠀⢰⠁⠀⠀⠀⠐⡀⠀⠀⠀⠠⠐⠀⠈⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠂⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⡐⢵⡴⠿⣠⣄⣀⣤⣤⣸⠂⢀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⣀⠀⠀⠀⠈⠐⠈⠁⠈⠀⠖⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⢁⠠⠀⠀⠀⠄⡄⠀⡀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠈⠁
⠀⢰⡀⢠⠇⠀⠀⡀⠰⠀⠀⠀⠸⠀⠐⠀⠀⠀⢀⠃⠂⠀⠀⠀⠀⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠁⠈⡄⠀⠀⠠⠀⡀⠀⠙⠷⠀⢄⠂⢀⠆
⠀⠀⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⢢⡠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠢⡀⠀⠀⠰⠀⠁⠀⠀⠀⠀⢀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠐⠈⠀⠰⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠐⠅⠲⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⡧⠀⠀⠀⠄⠀⢘⠀⠀⠘⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠩⠀⠰⢶⣦⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢠⠄⠠⡀⠁⠈⠀⠀⡏⠀⠀⡒⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠠⠚⠊⠀⠙⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠠⡄⠀⠘⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡀⣿⡄⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠒⠂⠀⠈⠀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡀⠸⠷⠟⠁⠢⠀⠀⠀⠐⠄⠀⠀⠘⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠈⠄⠀⠀⠂⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠄⠶⢤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢰⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠂⢀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⠈⠙⢀⠀⡀⣀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⡄⠉⠘⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠀⠀⠀⠀⠀⠰⠤⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠤⠆⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⣄⣄⢀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⡁⣀⣀⠡⡀⠀⠀⠀⠀⢀⣀⣀⢀⠐⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢰⡤⣤⠤⠄⠀⠀⠋⠍⠿⠷⠂⠀⠉⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠂
⣿⣿⣿⣧⣤⣼⣿⣶⣾⣿⣿⣿⣿⡛⣋⣸⣇⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⣯⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠾⢷⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠉⡏⠙⡏⢹⡏⣿⡟⣩⢻⠙⠏⡏⢩⣽⠉⣽⠉⠏⢹⣿⠙⢩⣏⢹⢉⡙⣏⠩⣿⣿⣿⣿⡿⠉⠀⠀⡀⠹⣿⣿
⣿⣿⡿⣿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣧⣼⣤⣧⣦⣥⣌⣧⣍⣧⣍⣼⣧⣤⣧⣈⣹⣄⣩⣤⣄⣼⣧⣴⣬⣏⣸⣄⣥⣯⣅⣼⣿⣿⠋⠀⠀⠀⠸⣿⣤⠙⢿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡇⠈⠙⠋⠉⣽⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠋⠀⠀⠀⠀⠀⠻⣿⣷⣾
⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⣿
⠉⢉⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡉⠉⠉⠀⠉⠉⢍⠉⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠠⠄⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣀⠀⠄⠀⠀⠀⠀⠠⠤⠀⠠⠤⠄⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠁⠀⢨⡤⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠰⠲⠆⠂⠂⠀⢄⠀⠀⠀⠀⢀
⠀⠀⠠⠠⠀⠀⠀⠀⠠⠀⠀⠀⠠⠋⠈⠙⢆⠀⠀⠀⠀⠀⠄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠂⠐⠐⠒⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠀⠈⠀⠀⠀⠀⠠⠂⠀⠀⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠁⢹

⠁⣠⣴⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢀⡀⡀
⢰⣿⣿⣿⣿⣿⣿⣧⠀⡀⠔⠤⡀⢘⠀⢀⠀⡄⠀⠐⢂⠄⡀⠀⠠⢰⠁⢀⡄⠀⡏⠠⠀⠀⠠⠀⠁⢐⠀⠠⠄⠠⠀⠀⠀⠀⠈⢉⠀⢹
⠈⠿⣿⣿⣿⣿⡿⠋⡀⠀⣄⠀⠁⠀⠀⠉⠀⠀⠀⠂⠐⠀⠀⠀⠀⠈⠀⠘⠀⠀⠑⠂⠀⠀⠚⠀⠀⠈⠀⠐⠡⢗⠁⠀⠀⠈⠀⠀⠀⠀⠆
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠘⠀⢀⠁
⠀⠀⠀⠀⠀⠶⣆⠃⠀⠋⡴⠶⠂⠀⠄⠀⠀⠀⠜⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠠⠤⠔⠊⠀⠀⢀⠀⣀
⡀⠀⠀⠀⠀⠀⠘⠆⠀⠸⠃⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠄⠂⠀⠀⠀⠾⠭⠵⠂⠀⡐⠢⠀⠐⠀⠀⠀⠀⠠⠤⠴⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠠⠄⠀⠀⠉⠀⠀⠀⡖⠘⠖⠀⠀⠀⢌⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⡂⠀⠄⠀⠀⡄⢆⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⠁⠀⠀⠠⠄⠀⣂⠀⠀⠀⠀⠈⡆⠃⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠒⠀⡠⠀⠀⠀⡈⠈⠀⡁⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⢃
⠀⠀⠀⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠈⠀⠀⠀⠈⠴⠲⠦⣉⡓⠀⠀⡛⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁
⠀⠀⠴⠖⣢⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⢀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠅⠀⢠⠀⠀⡐
⠀⠀⠴⠂⠈⠀⠀⠀⠈⠀⠀⠄⠊⢂⠀⠸⠃⠀⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠉⠁⢈⡐⡆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⣥⡀⠸⡇⠀⠳⠤⣀⠔⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠢⠀⠀⠀⠅⠀⠐⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠠

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠀⠈⠉⠀⣀
⠀⠀⢀⠀⠄⠒⠂⡄⠀⠀⠀⠄⠀⡀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⢀⠀⠀⠀⠀⠋⢁⠀⠀⢀⠀⠒⠀⠉⠐⠆
⠀⠀⠋⠃⠀⠀⠀⠀⡀⠀⠈⡀⠜⢁⠀⠀⢳⠀⠇⠀⠀⠀⢀⠀⡀⡀⠀⠈⠘⠂⠀⠀⢀⠀⠨⣀⠀⠂⠀⠀⠀⠀⠃
⠀⠀⠀⡄⢀⣀⡀⠀⡁⠀⠀⠑⢄⠀⠀⢀⡀⠂⠠⢂⡀⠀⠀⣀⡠⠁⠀⠈⠉⠀⠀⢀⡀⠈⢒⠍⠀⠰⡄⠀⢀
⠀⠀⠀⠘⠉⢹⣾⢉⠀⠀⠀⠀⠂⠁⠈⠑⠀⠀⠀⠓⠘⡋⠀⠙⠀⠀⠀⠀⠀⠴⠒⠉⠉⠉⠀⠀⠀⢸⠖⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠿⠈⠀⠀⠠⢀⠀⠀⠀⠀⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠀⠀⠀⡇⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⡀⢳⠶⡒⠲⠒⡆⢰⠀⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠲⠀⠀⠀⠈⠴⠀⢀⠀⠀⠀⠀⠀⠀⢄
⠀⠈⠗⠙⠀⠀⠀⢰⡄⠀⠉⠂⠀⠀⠀⠳⣦⠀⠀⠲⠀⠀⠀⠀⠶⠀⠀⠐⠇⠄⠀⠀⠀⠀⢰⣤⠐⠠⢀⠀⠀⠀⢤⠌
⠀⠀⠀⠀⢀⠆⠐⠉⠀⠀⠀⠘⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⢡⠀⡄⠀⠀⠀⠀⠆⠠⠠⡀⢀⠀⠂⠀⠀⠀⠄⠀⠘
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⢠⠃⠰⠁⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠠⢊⠃⠆⢂⠀⠀⠀⠀⡀⠀⠀⡀⠂⠀⠀⠀⠀⡾⠂⢄⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠈⢀⠐⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠁⠀⠀⠐⢄⣠⠀⠀⠀⢃⡐⠀⠀⠃⠀⠀⠀⠀⠱⣘⠆⠃⠀⠀⢔⣡⠎⠀⠀⠀⠀⠀⠀⠠⢈⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣿⣿⡿⣿⠿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠻⢿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠇⣿⣿⡿⣟⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢶⡆⢸⣿⣿⡆⢿⣿⣿⣿⣿⡿⣸⣿⣿⠗⣹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣨⡃⠈⣿⣿⣿⢸⣿⣿⣿⣿⢃⣿⣿⡟⢿⡿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣺⡟⢻⣿⡏⠀⠀⢿⣿⣿⡄⣿⣿⣿⡏⣼⣿⣿⠀⠀⢹⣞⣿⣘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣦⣤⣄
⠀⠀⠀⠀⠀⣰⣾⣧⣾⣿⣿⠀⠀⠀⢸⣿⣿⣇⣿⠿⣿⣤⣿⣿⡏⠀⠀⠀⠸⣿⠗⣲⢦⡗⠀⠀⠀⠀⠀⠀⠀⣴⡏⢸⣿⢾⡟⣽⢟⠀⣤
⠀⠀⠀⣰⠙⣻⢋⡅⣹⣿⠃⠀⠀⠀⢸⣿⣿⣿⢷⣠⡾⣿⣿⣿⣷⠀⠀⠀⠀⢻⣯⡛⣭⢷⡘⠆⢀⡀⠀⠀⣼⣿⠇⣾⣿⣿⡇⣶⣿⡇⢿⣧
⠀⢀⣴⣥⣿⠇⣬⡿⢉⡜⠀⠀⠀⣰⣿⣿⣿⡇⢨⣟⢃⢸⣿⣿⣿⣆⠀⠀⠀⠉⣯⢙⣶⡌⣿⡓⣨⡇⠀⣼⣿⣿⢠⣯⣴⢿⣷⣿⣽⡏⠸⣿⣧
⠀⠸⢟⡙⢷⣾⠻⣿⣿⠁⠀⠀⢰⣿⣿⣿⣿⠇⣌⣹⣿⠈⣿⣿⣿⣿⡆⠀⠀⠀⢿⣿⣿⢛⣻⣿⡷⠁⢠⣿⣿⡏⠈⣻⣯⣿⣷⢿⣏⣿⠀⣿⣿
⠀⠀⠈⣭⣾⣯⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⠘⣧⡴⠟⠃⢻⣿⣿⣿⣿⡄⠀⠀⠀⠺⣿⠋⣿⢿⠇⠀⣸⣿⣿⡇⢰⢟⣽⣿⣽⢿⣿⣿⠀⣿⣿
⠀⠀⠀⢡⣿⡟⠶⡎⠀⠀⢀⣿⣿⣿⣿⣿⡇⢸⠿⣤⣰⢦⠘⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣯⣤⠈⠀⠀⣿⣿⣿⠀⣿⣼⡟⣴⡜⣿⣿⣿⠇⢸⣿
⠀⠀⠀⠘⣟⣥⣾⠁⠀⠀⣸⣿⣿⣿⣿⣿⡇⣾⡆⡟⠰⢊⡀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⣿⡿⠂⠀⠀⣿⣿⡿⢀⣿⣿⣗⢿⣟⠻⣿⣿⣆⢸⣿
⠀⠀⠀⠀⢛⣿⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⢑⡿⢻⡇⢰⢿⡇⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢷⣇⠀⠀⢿⣿⡇⠸⣿⣿⢿⣿⣽⡀⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠈⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏⢸⡔⢋⠐⢻⡦⢀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⠇⢰⣿⣷⣾⣿⣻⣧⣼⣿⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢠⡜⣆⡙⣹⣧⣿⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡿⠿⢿⣿⣿⣿⣿⣿⠁⡹
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⡌⣴⠋⠑⢌⣿⣋⡄⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡼⣿⡿⡷⣾⣿⡟⢛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⠸⡷⠸⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣅⢻⣿⡻⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣽⡿⢶⣝⠀⢸⣿⣷⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣽⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⢠⣷⣤⣿⡋⣧⣈⣿⣿⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⠿⠻⣏⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢠⠘⣧⠛⠰⣟⡉⢉⣻⣷⠀⣻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣗⢸⣼⣷⣀⢸⡍⢫⣉⣸⣿⣤⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠧⠼⠿⠿⠻⠿⠻⠶⢅⠙⣿⡿⠸⡿⠿⠿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⣠⣴⣯⠀⠀⡀⠭⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠛⢻⠛⠉⢫⠀⣿⣷⠂⠰⠁⠰⣿⣋⣶⣀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢻⢻⡄⠀⠀⠀⠉⢰⠀⠀⠓⠤⠿⠛⠁⠀⠙⠳⠦⠤⠔⢋⡀
⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢸⠈⣧⠀⠀⠀⠀⠀⠉⠁⢀⡀⢠⡄⠀⠀⠀⠀⠞⠁⠀⠉⠉⠰⢄
⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⠇⠀⠈⢦⡀⠀⠀⠘⢷⣤⡤⠀⡜⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢀⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠀⠁⠀⠀⣀⣤⠖⢛⡀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⡜⠁⢀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠶⠒⠖⠉⠉⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠛⠓⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠳⢄⡀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠛⠠⠤⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⠄⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠐⠀⠀⣯⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠐⠒⢲⠇⢀⠀⠈⠉⠉⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⢉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠤⠄⠈⠃⡄⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠲⠀⠄⠀⠄⡚⠄⠀⠀⠀⠃⠬⠀⠀⠄⠀⠀⠠⣉⡀⠠⠀⠀⠠
⠀⠀⠹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠂⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠐⠃⠀⠀⠒⠂⠀⠒⠀⠀⠂
⠀⠀⠀⠈⠉⠛⠋⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠉⠁⢀⡀⠤⢀⡀⠀⠔⠀⡀
⠀⠀⠀⠀⠀⠠⠊⠉⠉⠛⢷⠀⠐⠐⠀⠀⠀⡄⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⢤⠀⠀⠀⢀⠘⢲⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⡨⠀⠀⠀⠀⠂⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠈⠀⠀⡡⠃⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠠⠀⠺⠖⠋⠀⣀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⠀⠀⠀⠠⠠⠀⠄⠀⠐⠀⠀⠖⡆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠰⡀⢀⠆⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⡕
⠀⠀⠀⠀⠀⢀⢀⠆⠀⠀⠸⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢣⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⡤⠈
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⡍⠀⠀⠀⠀⠘
⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢠⠀⢂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡈⠀⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢅⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠐⠀⠒⠒⠁
⠀⠀⠀⠄⠀⠈⠀⠁⠀⠢⡀⠀⠀⢀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂⠀⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣳⣦⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⢸⠋⣼⠋⣹⠃⢀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⣷⠿⠞⠋⠘⢛⣡⡶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠉⣤⣤⣤⠾⠛⠁⠀⠀⠀⢰⡆⢠⡇⢠⡶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡇⣿⡁⣶⠋⣤⡴⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡸⠖⣯⢸⡏⢠⡿⢠⡴⠛⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠞⠁⠚⠰⠟⡴⠞⢁⡾⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⣄⢀⡀⠁⠀⠀⣠⣋⣤⠶⠶⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢀⡀⠀⠀⠀⠀⠘⢧⣿⠀⠁⠘⠁⠀⠠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠹⣟⠁⣈⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⠻⢿⣧⠈⠳⣄⠀⠀⢻⡄⠘⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣠⢄⣴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣄⣀⣽⠀⠀⠈⠛⠃⠺⣧⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡎⢹⡇⢨⡇⠀⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣿⣿⡏⠀⠀⠀⠀⠀⠘⠿⣦⣾⣅⠟⢦⣄⡀⠀⠀⠀⠘⢯⣤⣍⣳⣤⡿⣤⡿⠾⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣛⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠛⢦⣤⣀⡀⠀⠈⠙⢦⣤⡄⠣⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡇⠀⠀⠰⣤⣴⡆⣴⠆⠀⠀⠀⠀⠀⠀⠀⠉⣉⡓⣦⠀⠀⠀⣿⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣄⠁⠈⠈⢁⣄⠀⠀⠀⠀⠀⢀⣴⠾⢿⣟⣿⠀⠀⠀⠸⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠉⠀⠀⡀⠈⠁⠀⠀⢰⡄⢠⣿⣷⣦⣤⣈⡙⠳⠶⠦⡴⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠲⠾⠿⣤⡄⠀⠀⠀⢠⠛⣬⠋⣉⣤⠾⠋⠙⠳⠶⠶⢤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣄⣀⣹⣤⡽⠟⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣄⠈⠉⠉⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⣀⡀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⣤⣤⣩⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠉⣿⣤⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⢿⡄⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⡎⢷⡀⠀⢿⣿⡆⠀⠀⢀⡴⠚⠉⢻⡀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⡈⢿⡄⠈⣿⡿⠀⣠⡞⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣸⣧⡈⠻⢦⣭⡴⠞⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⢀⣤⠴⠶⢦⣄⡀⠀⠰⣟⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣀⣤⣴⠶⠛⢻⡿⠿⢆⡿
⠀⠀⠀⠀⢰⣿⣷⡶⠶⠦⣌⣻⣦⣀⣸⡗⢶⣄⣄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠈⣧⣼⠟⠛⠻⣧⠀⢸⣧⡴⠟⠁
⠀⠀⠀⠀⢸⡏⢀⣠⠞⣉⡷⣟⢧⣌⠋⠛⠀⢠⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠚⢻⡄⠈⣿
⠀⠀⠀⠀⠀⠻⣦⡔⠛⣻⠶⠈⠳⣝⠶⣄⠘⢷⡄⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡘⠋⠤⠜⢻⡬⣛⡷⢦⡀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⡁⠠⢉⠛⢮⡟⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣬⣀⣀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡟⠻⣧⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢸⡄⣀⣤⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢟⢤⡀⠛⠃⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣯⠀⠿⠾⠃⠀⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡝⢦⡀⠀⠀⠀⠠⠛⣙⣷⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡝⣦⠀⢀⣴⠟⠉⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣧⣾⠁⠀⠀⠀⠀⠀⠀⠀⣨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣛⣲⣶⣤⣤⣔⣒⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠛⠉⠉⠉

⡏⠉⣩⣽⣶⣦⣄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡠⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠃⠰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠄⠁⡰⠀⠠⠀⠋⠀⠀⠂⠀⠈⠀⠀⠀⠊⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⡀⢀⠀⢈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡔⢱⠀⠀⠀⠀⠀⠀⢀⢸⠁⠁⠁⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠁⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠆⢃⠇⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠹⠖⠺⠴⠶⠦⣴
⠀⡀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⡌⠀⠐
⠀⠑⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠰⠆
⠀⠄⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⠉⡄
⡀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⠀⠀⠠⠰⠆⢢⡒⣇
⠇⠀⢀⢀⠀⠀⠀⠀⠀⠢⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠙⠀⠀⠀⠀⠀⠂⠀⠉⠰⠀⣀⡀⢲⡀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡱⠀⠘⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⢀⠀⠁⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣨⠇
⡇⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅

⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢦⡄
⠀⠀⠀⠀⠘⡿⠿⠿⠟⠀⠀⠀⠸⠟⠿⠿⣷⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⢠⢒⣦⣤⣤⡀⠆⠀⠀⣤⣦⣴⣄⣄⡀⣼⡦⠐⠃⠀⠠⢶⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣰⣷⢸⣧⡀
⠀⠀⠀⠀⠀⣽⠛⢿⠀⠀⠀⠀⠸⣿⣿⣿⡏⠙⠛⡇⠀⠀⠀⠀⠘⢉⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⢴⠀⠀⠀⠀⠈⢋⣿⢾⣏⠁
⠀⠀⠀⠐⠛⠋⠀⠙⠛⠃⠀⠀⠶⠿⠀⠸⠷⠦⠈⠀⠀⠀⠀⠀⠺⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠛⠻⣷⠀⠀⠀⠀⠀⢀⡴⠂⠀⠒⠣⠀⠀⠀⠀⠀⠰⣾⣿⣿⣏⠀⠀⠀⠀⢠⣴⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡖⣴⣶
⠀⠀⠀⠄⣶⣄⢀⣾⣀⡀⠀⠀⠀⢸⠀⠀⣩⡌⢃⠁⠀⠀⠀⠀⠀⠁⠉⠙⣋⠁⠀⠀⠀⣘⠀⠈⢀⣀⠀⠀⠀⠀⠘⠀⢀⢀⣸⠀⢀⡇⠙⠋
⠀⠀⠀⢸⣿⡟⠛⣿⣿⡄⠀⠀⠀⠸⣂⣸⣤⣴⣿⣤⠀⡄⠀⠀⢶⣴⣦⣶⣉⠀⠀⠘⢯⣿⣿⣚⣿⣯⠟⠀⠀⠒⠀⠈⠙⠉⠁⠀⠀⡇
⠀⠀⠀⠈⣹⣿⠻⣿⡋⠀⠀⠀⠀⢀⡏⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⢸⣿⡿⠛⣿⣤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠛⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉

⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠈⠈⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠤⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⠶⠶⠖⠊⠉⠉⠉⠉⠉⠉⠉⠻⠿⢶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣸⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢹⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣶⣷⣦⣴⡶⢶⣶⣿⣶⣴⣶⣶⣶⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⡏⠀⢩⡇⠀⠈⣿⣿⣿⣿⠋⠉⢹⣿⠉⠉⠉⠉⠉⣻⡏⠉⠉⠉⣿⣿⣿⣿⣿⣿⡿⢷⣶⣶⣾⣿⣤⣤⣤⣤⣼⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⠳⣀⠀⢻⣿⣿⣿⣾⣷⡿⠃⠀⡀⠀⠀⠀⠻⣇⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⣿⡿⠉⠉⠉⣿⡟⠉⢻⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠉⠁⠾⠿⠿⠿⠛⠉⢠⡶⠶⠃⠀⠀⠀⠀⠹⣷⣄⣸⣿⣿⣿⣿⣷⣿⣷⣿⠟⠁⠀⠀⣰⡿⠇⢀⣽⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀⣸⣿⣧⣴⡟⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⢀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠟⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⢶⣶⣤⣤⣤⣶⣶⠿⠿⠟⢻⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠛⠁⠀⢹⡇⣀⡀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠠⣿⣀⣀⣼⡇⠙⠃⢠⡇⠀⠀⢠⣀⣀⣀⣴⣦⣴⣿⣷⣀⣀⣀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠾⠇⠀⠀⠈⠉⠙⠉⠀⠀⠰⣿⣧⣤⣶⡿⠛⠛⠋⠉⠀⠉⠉⠀⠉⠛⠛⠛⢷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠉⢹⠟⠋⠀⠀⠀⠀⠠⣤⣤⣤⣴⠀⠀⠘⠟⠛⠛⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠚⠋⠀⠀⠀⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠏⠀⠀⠀⠀⣀⣠⣴⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⠀⠀⢀⣠⡶⠞⠉⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠈⠹⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣶⡟⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣀⠀⠀⠀⠉⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢠⡄⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⢷⣤⠀⠀⠀⠀⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⢡⡄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⠛⢢⣤⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢨⣷⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⡴⠟⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡾⠇⠀⡀⣀⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠏⠀⠀⠹⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣀⣀⠈⠁⠀⠤⠄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠉⠙⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⠛⠇⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠚⠛⠛⠉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⣄⡀
⠀⠀⠀⠀⠙⠻⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠢⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣶⣶⣶⠞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣤⣶⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⣶⣶⠶⠶⢤⣤⣤⣤⣶⠿⠟⠋⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⣿⠉⠈⠻⠿⠿⠿⢿⡏⠉⣋⠀⠀⠀⠀⠀⠉⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠸⣶⡦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠸⣇⣠⣿⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⣀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡀⠀⠀⠀⡉⠉⠻⠿⣦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠘⠃⠀⠀⠀⠃⠀⠀⠀⠈⠉⠿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠘⠛⣶⣤⡄⠀⠀⠀⠀⠀⠀⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡏⠈⠿⠷⣤⣄⠀⠀⠀⠀⠈⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠈⠉⠳⠶⣄⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⠿⠗⠀⠻⠃⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠏⠁⠀⠀⠀⣀⠘⡿⠀⠀⠀⠀⠀⠀⢠⣮⡁⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡈⠀⠀⢀⣀⣀⣴⠎⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠀⠙⠛⠚⠛⠛⠛⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠀⠀⠀⠀⠀⢀⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠺⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠈⠀⠈⠀⠈⠑⠂⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⡀⠀⠄⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡜⠀⠄⠂⠄⠀⢤⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠰⡆⠀⡖⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠁⠁⠀⠐⠁⠀⠈⠁⠀⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠎⠑
⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠈⠉⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⡎⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠝⠀⠸⢒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠜⢀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠋⠀⠀⡀⠀⣀⡇
⠀⠀⠀⠀⢀⠜⢀⠎⠁⠀⠀⠀⠀⢚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠈⢀⡈⠊⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⣀⣀⡀⠀⠀⢀⠀⠀⠀⠀⡰⠖⠠⠀⠀⠂⢄⠃⠐⠀⠀⠀⠀⡠⠠⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠻⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠠⠀⠀⠀⢁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠞⠀⠺⠀⢈⡀⠀⣀⣀⡀⠀⣀⠠⠂⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠀⢼⣆⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢷⣶⣶⣶⣶⣶⣶⣦⠀⢠⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣿⣿⡄⢰⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢰⣙⠿⣇⠀⠀⠀⠀⠀⠀⠅⠀⢆⠀⠠⣤⣤⣤⣦⣤⣤⣤⣤⡤⠀⣆⠀⢤⣤⣤⣤⣬⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠢⠀⠀⠀⠀⠀⠠⠛⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠘⡀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢆⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠈⠄⠀⠀⠀⠈⠚⠃⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠀⠑⣀⠓⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⢀⠌⠀⠘⠀⠀⠀⠀⢸⠀⠃⠀⠀⢀⠂⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡸⠀⠨⠀⠀⠂⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠆⠀⠈⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠤⠜⠀⠀⠁⠒

⠯⠀⠄⠠⢀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠉⠀⠉⠈⢁⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠂⢀⣤⣾⠇⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠹⣾⠟⠋⠉⠃⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠚⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠆⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠙⡄⠀⠀⢀⠈⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠙⠦⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣀⣠⠌⠀⣀⠆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⡄⠠⠁⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠙⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠰⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⢤⠖⠁
⠀⠀⠀⠀⠀⡘⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⢀⠃⠀⠆
⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⣤
⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠳⡆⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠈⡇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸
⠃⣰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣤⣤⣤⣤⠔⠀⢧⣀⣀⣀⣤⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢹⠀⠀⠀⠀⢀⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢸⠀⠀⠀⠀⢸⠀⠘⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢸⠇⠀⠀⠀⠀⢸⠆⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡞⠀⠀⠀⠀⠀⠸⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⠁⠀⠀⠀⠀⠀⠀⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠛⠲⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⣀⡶⠷⠤⢀⣀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠉⢧⡌⢦⠀⠀⠀⠀⠀⠀⠀⠟⠠⠀⣀⠤⠤⠤⠿⢦⣀
⠀⠀⠀⠀⠀⠘⢣⣤⣀⣀⠀⠀⢈⣱⠎⠀⠀⠀⠀⠀⠀⠀⠐⢆⠚⠁⠀⠀⠀⠀⠀⢹
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣵⣶⣶⣶⣶⣶⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠛⠛⠿⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣠⣤⣤⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿