Cocaine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⡀⣼⣿⠀⣀⡀⠀⠀⠀⠀⠘⠛⣧⣶⣶⣤⡛⠛⠀⠀⠀⠀⠀⠀⣠⣾⣿⣻⣷⠄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⣏⣹⣟⣉⡇⠀⠀⠀⠀⠀⠀⣾⡿⣧⣼⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣿⡿⠟⠀⠀⠀⠀⠀⠛⢛⡿⠿⡟⠛⠃⠀⠀⠀⠀⢠⣦⡟⣿⣿⡟⣦⣦⠀⠀⠀⢀⣀⠽⠷⠛⠻⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠙⠁⠀⠀⠀⠉⠈⠐⠒⠒⠒⠀⠊⠘

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠸⣶⣶⣶⡞
⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠛⣦⡀⠀⠀⠀⠀⠀⢀⣼⣿⣴⡾⠋⠀⠀⠀⠀⠀⢘⠘⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⠀⠈⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠡⠛⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠰⠛⢢⡔⠣⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡶⠻⣯⣿⠀⠀⠀⠀⠀⠀⠀⣏⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠣⣈⣶⣿⣦⡀⠀⠀⠀⠀⠀⠛⠉⣽⣿⡍⠙⠃⠀⠀⠀⠀⠀⢶⣟⣧⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣟⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⡋⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠚⣄⠀⠀⠀⠀⠀⠀⢀⣤⠤⢴⣶⣾⢥⡾⠃⠀⠀⠀⢸⡯⠿⠿⠿⠯⠤⡅⠀⠀⠀⠀⠀⣰⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠉⢻⣿⠀⠀⠀⠀⠀⠀⣾⢀⡞⠁⢹⡕⣿⠃⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⠀⠀⠀⠀⠀⠀⠹⢬⣃⣠⠞⢀⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠐⠓⠛⠛⠛⠛⠛⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣠⣀⣤⣤⣤⣀⣠⣀⠀⢀⣀⣤⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣾⠏⠙⠁⠙⣉⠛⠋⠙⠿⠛⠋⠉⣿⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠁⠀⠻⠂⠀⠋⠀⢠⡆⠀⠀⠸⠇⠈⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠶⠂⠀⠀⠛⠀⠀⠀⠰⠶⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠛⠃⠀⠶⠀⠀⠀⠠⠶⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢰⡆⠀⣠⡀⠀⠀⣠⠀⠀⢀⣄⠀⣿⠀⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣷⡾⢿⣿⠀⣿⣀⣀⣀⣀⣈⣁⣀⣀⣉⣀⣀⣀⣉⣀⣿⠀⣿⡏⠙⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⣀⠈⠁⢸⣿⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿⡇⢠⡄⠸⣷⣀
⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠉⠀⣤⡈⠉⠉⠉⢉⡉⠉⠉⢉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⢉⠉⢁⣤⠀⣀⠈⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠘⢿⣤⡀⠰⠆⠈⠀⢀⣀⣀⡘⠃⢀⣀⡙⣃⣀⣀⣀⣀⣈⠋⠀⣤⠀⠙⠁⠀⠁⠀⠛⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣤⣄⣀⣴⡿⠛⣿⠛⢻⡿⠛⠛⠛⠙⠋⠙⠛⠙⣿⣄⣀⣴⡶⢷⣦⣀⣀⣀⡈⠉
⠀⠀⠀⠀⠀⠀⢀⣶⡟⠃⠀⠉⠙⠛⠀⢠⣄⣀⣀⡀⠀⠀⠀⠾⠀⠾⠂⠀⠈⠙⠋⠹⠇⠀⠉⠹⠿⠉⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⢀⠸⠎⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠦⣄⡀⠀⠘⢶⡳⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠳⣢⣙⠓⠀⠈⢷⣿⠃⠀⠀⠀⠀⢀⡠⠴⠀⣠⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠳⣧⣄⠁⠈⠇⠀⠀⠀⠀⠀⠀⢐⠠⠔⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠂⠙⢾⢠⣆⠀⠀⠀⠀⠈⡨⠖⠂⠐⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⡉⠁⢂⠄⠀⠀⠀⠂⣿⡀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠠⠀⠂⣨⡥⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠢⠃⠀⠀⠀⠀⠀⠀⠀⢁⢄⢸⠏⠁⠁⠀⡠⢀⠀⡀⠰⢃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣉⠀⡔⣬⠀⠀⠀⠀⠘⣿⠯⠁⠀⠀⠀⠀⢠⡤⠃⠁⠉⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⣤⠄⠀⠀⠠⠄⠀⡀⠀⠀⠁⠀⡠⠻⢦⣄⣀⢀⠉⣤⠀⠀⠀⣰⣷⠋⠔⠁⠀⠀⠀⠐⠀⠁⠼⠋
⠀⠀⠀⠀⠀⢈⠉⠟⢀⠘⡂⢀⠉⠀⠀⠀⠀⠀⠀⠀⠯⣼⡆⠅⠀⠀⣤⠰⠈⠀⠀⠀⠀⠀⡀⢀⣀⡛⠠⠁
⠀⠀⠀⠀⠀⠀⠰⡐⠉⠠⢄⠒⠀⠐⠀⡀⠀⠀⠀⠀⠀⣙⠇⠚⣂⠟⠉⠀⠀⠀⠀⠀⠀⡪⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠄⠂⠙⠢⣈⠀⡀⠀⠀⠀⠀⢸⣾⠁⠀⠀⠀⠀⠀⠄⣠⠖⠀⠂⠐⢀
⠀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠂⠄⠀⠂⢀⠨⠓⢆⣚⡡⢄⣷⡌⣷⣄⠀⠀⠀⠰⣀⠾⠡⠌⠁⢀⠔⠁
⠛⠟⢴⣂⠤⢄⠀⡉⠉⠐⠠⠀⠈⠑⠂⠤⠀⢈⡙⡶⣫⢠⠀⣻⠉⠀⠀⢘⡴⡣⠔⠂⠀⠐⠁⢀⡀⠀⠤⠤⠤⠤⠀⢀⡀
⠀⠈⠆⠀⢤⠰⠌⡓⠀⢠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⢆⣠⡀⢀⣰⠯⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡴⢀⠄⠰⠂⢖
⠀⠀⠀⠠⡀⠰⠓⠆⠘⠤⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣶⣶⡹⠟⣣⣼⣿⠀⠀⠀⢀⠀⠂⠁⢀⠀⠰⢂⣨⠤⣀⠭⡁⢁⠎
⠀⠀⠀⠀⠑⢄⠂⠚⠉⢲⣌⠐⠢⣀⠀⡀⠀⠀⠀⠈⠈⠍⢣⣾⡝⠃⠀⠀⢀⠀⠈⠀⠠⠀⢈⡴⠞⣋⠁⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠉⠢⢑⠁⢤⠐⠒⢈⡑⠆⣀⠀⢀⡀⠀⠀⠹⣾⡀⠀⠀⠀⠀⠀⠐⢀⣴⠎⠁⠠⠈⠀⠀⢁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠅⠁⣀⡀⠐⠊⢷⣿⣿⣄⢻⠃⠿⠛⠀⠀⢀⠀⢡⠶⠉⢀⠈⠁⠖⢀⡩⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣿⡇⣠⡀⠀⠐⢀⠚⠀⠒⠀⠀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠁⡾⠧⡶⡰⠄⠀⠄⠐⠈⠁
⠀⠀⠀⠀⠀⠀⣶⢀⡸⠃⡶⢠⢰⡄⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⡞⠊
⠀⠀⠈⠛⠦⣀⠀⠈⠃⠀⠀⠉⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣷⡠⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣄
⠀⠀⠀⠀⠀⠛⢷⡀⢾⡲⣶⠠⠀⢲⡁⠀⠀⠀⠀⠀⠀⣤⢻⠃⠀⠀⠀⠙⣄⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠹⢂⣧⣧⣶⠊⠉⠁⢀⠆⠀⠀⠀⠀⡆⠺⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⡇⡇⠀⡄
⠀⠀⠀⠀⠀⠙⢀⡸⣿⣿⣿⣟⣁⡀⠴⠂⠀⠀⠀⠀⠀⠉⡿⠀⠀⢀⠀⠐⠈⢱⣆⣠⠀⠀⠠⠀⠈⠁⠀⠀⠀⡇⣇⠀⡇
⠀⢠⡖⠉⠉⠃⠸⠻⣏⢈⠁⠉⡎⠁⠉⠈⠉⠒⢄⠀⠀⠀⢸⡤⠀⠀⠹⠀⠀⠀⢿⢁⠀⠀⠀⠠⠀⡄⠀⠀⠀⡇⣇⠀⣇
⠀⠀⠙⠒⠒⠒⠒⠿⠁⠐⠀⠈⠍⠐⠶⠦⠤⠤⠞⠀⢸⡖⡋⠀⠀⠀⡀⠉⠀⠀⢀⡾⠀⠀⡄⢀⠆⣀⠀⠀⠀⢱⠑⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠐⢠⡤⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⡇⠀⠀⠀⠀⠢⠀⣠⠋⠀⠀⠀⠃⡈⠀⠏⠀⠀⠀⠀⠻⢫⠏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠃⠀⠀⠀⡂⠀⠙⠉⠀⠀⠀⣐⡆⠀⠀⠀⠀⠀⡴⠀⠐⠃
⣤⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠚⠶⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣴⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣿⡿⠟⢻⣿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢤⡶⠀⢀⣴⣟⠫⢱⣲⣿⣿⠎⣿⡿⠻⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣿⡿⠋⢀⣴⣟⣥⣿⣿⣞⢿⣩⣿⡼⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⡄⣠⣤⣰⣶⠶⣾⡿⠋⠀⣰⡟⣳⣾⣿⠟⠉⢠⣾⠷⠋⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢴⡶⠞⠉⠘⡷⠋⠀⣠⣾⣵⡶⠟⠉⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⡱⠛⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⢰⠊⠀⣠⠺⡿⢛⠉⢀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠎⢠⣼⠏⣰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠁⠀⠶⣷⣦⢞⣵⣪⣴⣿⣯⣿⣯⣅⣀⠀⠀⠈⠢⡀⠀⠀⢀⣶⠞⢁⡰⠁⣴⡿⠁⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⢾⣟⢯⣵⣿⡿⠻⡻⣿⠸⢿⣿⣿⣷⢎⣲⣿⣿⣦⣼⡿⠋⣰⠏⢀⣸⠟⢀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠈⢿⢿⣿⠋⠐⠒⣷⠹⠄⠀⠻⠿⢏⢨⢷⣵⣵⣾⡟⢡⡼⠁⢠⡾⠋⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⢈⠀⣠⡂⢀⣠⣧⣐⣼⣄⠰⠜⠻⡿⠷⠆⢺⠏⣠⠎⠀⣴⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⠢⢀⡠⠚⢿⣿⣿⢿⡏⢀⣿⣦⣿⣧⣤⣶⣷⣼⠃⣠⣾⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣤⣼⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣴⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠀⠀⠘⠛⠛⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣏⣀⣰⣿⡆⢀⡀⠙⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣘⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⠀⠀⠀⠀⢸⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣌⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⡀⠉⠀⣿⡿⠉⢙⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣧⣤⣤⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⠿⠿⢿⣶⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⣀⣀⣀⣀⠀⠉⠛⠻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⡾⢷⣾⠿⣿⠿⣶⣾⢷⣦⣤⣴⣾⠿⣦⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⡿⠃⢀⡀⠀⢠⣤⠈⠁⠀⠉⠉⠁⣀⠀⠻⣷⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠙⠃⠀⢈⡁⠀⠰⠷⠀⠀⠀⠛⠃⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⣟⠀⠾⠆⠀⠀⠘⠋⠀⠀⠀⠀⠾⠆⠀⠀⠀⣹⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠸⠗⠀⢠⣴⠀⠀⠀⠀⢰⡆⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣠⣤⣿⡇⢸⣿⠀⠈⠉⠀⠀⠛⠀⠀⠀⠻⠃⠀⠀⠘⠟⠀⣿⡇⢸⣿⡿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠉⢿⡏⠉⣿⡇⠸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇⢸⣿⠀⠈⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣤⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠶⠆⠀⢻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠁⠀⣤⡄⠉⠉⠉⠉⢉⡉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⢉⡉⠉⢠⣤⠀⣀⡀⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠾⠇⠀⠀⠀⢀⣀⠀⠘⠋⠀⢀⡀⠛⣀⣀⣀⣀⡀⣀⡘⠃⠀⣤⠀⠘⠋⠀⠀⠀⠀⠙⢃⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣠⣤⣀⠀⣀⣾⡟⢻⣿⠻⢿⣿⠟⠻⠿⠟⠛⠟⠙⠿⠛⢻⣷⡀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠉⠻⠻⣿⠉⠀⣀⠁⠀⠈⠉⠀⠀⠀⢠⣤⠀⣴⡄⠀⠈⠙⠿⠟⠻⣷⠀⠙⠛⢿⣾⠟⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣤⣤⣤⣤⣤⣤⣴⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣠⣶⠃⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢰⣿⡇⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⣿⠀⢠⣿⠀⠀⠈⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⡏⠀⠀⢸⣿⣇⢸⣿⡄⠀⠀⠘⣧⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢸⣿⡇⠀⠀⢸⣿⣿⡆⠻⣿⣦⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣤⣾⡿⣿⡇⠀⢹⣿⣧⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠸⣿⣷⡙⠛⠛⣵⡿⠁⠀⠀⣿⣿⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢿⣿⢀⣾⡟⠁⠀⠀⢀⣿⣿⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣾⣿⠀⠀⠀⠀⣼⡿⢹⣿⠏⠀⠀⢰⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣦⣴⣏⠀⠀⢀⣿⣿⣿⣤⣀⣤⠞⡉⢀⣿⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠾⣿⣿⣦⣤⣾⣿⢻⣿⣿⣿⣿⠀⡇⢸⣿⡿⣶⣾⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡛⢿⣿⠀⠻⣿⣿⣿⠀⡷⠄⢀⣴⡿⠉⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣧⣀⠁⠰⣆⠙⠛⠋⢰⠁⣴⣿⣿⡀⢀⣠⡿⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⣠⢀⣿⣿⣷⣦⡈⠻⣶⣶⣿⠀⠻⣿⠟⣿⡿⠋⠀⠀⠀⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢹⣿⣧⠀⢹⣿⣿⠷⠖⠀⣰⣿⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡙⠛⠋⠁⢸⣿⡏⣴⢿⡟⠁⢀⣴⣾⣿⣿⣀⠀⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣄⠀⠘⠋⢸⣿⠘⠀⠀⣿⣿⣿⠟⠛⠛⠋⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠘⡆⠀⣿⡀⠀⠀⠈⠉⣡⠖⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣰⣿⠇⢀⣵⠀⣽⠹⣦⣤⣤⣾⣿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡟⠀⣾⣿⢾⣿⡀⢻⣿⠏⣿⡿⢸⣿⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠄⠘⠿⠄⢉⣤⠆⠁⣰⠟⠡⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢋⡏⡄⠀⠔⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡰⠁⠀⠐⠀⢠⠇⠀⡡⢢⡄⢀⡴⢊⠭⢍⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡴⢡⠀⡇⡆⡆⡿⠀⠸⣇⠀⠀⠘⠀⣇⣶⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣇⠰⡀⢧⢸⠸⣿⡀⢆⠉⠳⣄⠐⡄⠻⣝⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠁⠈⠢⣳⡈⢆⢣⠻⣿⣌⢧⢀⠘⣷⠸⡄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⡅⠀⠀⠉⡡⡄⢱⣌⢿⣾⣷⣧⠹⣿⠘⣾⣦⣿⠇⡇⣈⠀⢸⡆⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣺⢩⣛⢦⣿⣿⣿⣶⣿⢀⣿⡿⣫⠞⠁⡡⢀⣼⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠠⡸⠖⠀⢸⠂⠹⣿⣿⣿⣇⣾⣯⡟⢁⣴⣿⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⠀⠀⢤⠀⢿⡄⢆⠹⣯⣿⣿⣿⣿⣷⣿⣴⣆⡀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⠍⢹⠒⡟⣰⠺⢿⣶⣷⣿⣿⠟⠛⠋⠉⠉⠁⠱⠉⠃⠙⠒⣶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠿⠃⣼⠀⠀⠁⠐⣠⠼⠛⠁⠁⠀⠠⠀⠀⠀⠰⢆⠀⡀⠀⣼⢡⢺⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠷⠶⠶⣧⠤⢤⣞⣭⣀⡀⠀⠀⠀⢀⡴⣋⠀⢤⠶⢦⠶⢾⣧⣷⡘⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡗⠀⣤⡤⡀⢀⢸⡀⢀⢮⣹⡆⠀⣨⣾⠛⢿⣃⡏⠠⠄⠀⣼⣿⡍⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡇⢀⡛⡇⠀⣀⣸⣧⣐⣊⣿⢷⣿⡁⠠⠀⠘⣿⡷⢦⠤⠼⠋⢙⡃⢁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠲⠶⢒⣻⠿⢛⠅⠈⢛⢽⠞⠻⢿⣴⣶⠟⠃⠐⠀⠁⠀⠃⠀⠀⠴⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠄⠒⠊⠉⣿⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⢀⣀⣠⡅⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣡⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⣿⣿⣿⣷⣾⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣹⣁⣼⢿⣿⡿⠛⢩⢿⠟⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠻⠿⣅⣛⣋⡹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠄⠀⠀⠘⢌⠢⠀⠀⠰⠀⠠⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠊⠀⠘⡠⠀⠀⠀⠠⠑⠀⠀⠀⠐⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⠀⡰⠁⠀⢹⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠁⠄⠘⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠐⢀⠁⠳⠉⢦⣠⠁⠀⠀⢸⠀⠲⢀⡶⢱⠀⢀⠀⠸⠎⠀⠀⡄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⡉⠀⠀⠹⡀⠀⠀⠸⠀⠀⠰⠁⠀⡇⠈⠴⠃⠐⡆⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢾⠣⣄⣠⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠀⡇⠂⠀⠀⢠⠃⠀⠀⣀⢀⡀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⢇⠀⠀⢠⢃⣄⣀⣤⡔⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⢈⠼⠊⢰⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠙⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⢀⠔⢠⠀⠀⠱⠁⠀⠰⠁⡾⠁⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣅⣀⠀⠀⠀⠀⠀⠀⠃⠄⠂⠖⠄⠀⡀⠈⠠⠄⠂⠀⠀⠠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⢐⡖⣻⣉⣉⠉⣩⣽⠶⣀⠀⠀⣀⣠⠤⢤⣀⡄⡦⠀⡠⢦⠐⠠⣤⢄⠂⠠⠾⠿⢷⣿⡂⡀⢰
⠀⠀⠀⠀⠀⠀⠹⠷⠼⠷⠶⠚⢧⡇⢠⣾⣶⣛⡻⣄⣵⢠⣼⠃⣓⢲⠀⢘⣧⡂⠚⢺⣇⣀⡀⡶⡞⣮⣭⠴⣾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠙⠛⠛⠁⠀⠙⠶⠖⠛⠉⠙⠳⠚⠋⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣃⣠⣤⣀⢀⠀⡀⣖⣿⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣷⣶⣮⡝⣧⢾⣱⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠛⣿⡮⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣽⣟⣴⣿⢷⡿⠿⠋⡏⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣏⠉⠉⢁⣤⣶⣤⡀⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⣿⣿⡄⠀⢿⣷⣷⣿⡟⡃⠀⣸⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣤⠁⢸⣍⣻⣦⣌⠙⠋⠁⢀⣧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣤⠾⣻⣇⠘⡿⢷⣴⠖⠿⡏⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣋⠠⡿⢺⣾⣁⠀⠀⠀⢠⡇⢀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⠟⣩⣧⣥⣬⣤⡔⠀⢀⡊⣃⡤⠋⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⡿⢿⣿⡷⠀⣸⣿⣿⣟⣦⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣟⣿⡟⠻⠿⢯⡿⠿⠶⠄⠿⠝⠿⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠻⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢰⣿⠁⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠟⠁⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠋⠀⠀⠀⠀⠀⠛⡛⠛⠃⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣈⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠿⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⢾⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣇⡏⠘⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⢸⠛⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠷⣿⡴⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠐⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣼⡆⡀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣠⡀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣷⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣶⡄⡀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⣼⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⠀⢶⣿⣿⣿⣿⣿⣷⠆⠀⠀⢠⣄⣾⣾⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⢠⣽⣿⣿⣿⣿⣅⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⢙⣻⣿⣿⡛⠁⢴⣼⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠈⠉⠛⣿⣷⣿⣿⣷⣿⣴⣦⣶⣩⣭⣿⣿⣿⣷⣟⣻⣿⣟⡛⣧⣼⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠛⠛⠋⢻⣿⣿⣿⡛⣿⣢⣄⣤⣀⣄⣀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⣿⣿⣿⣿⡿⣿⣿⡇⠀⣄⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢩⣤⣶⣾⠉⣶⣦⣋⠟⢻⡿⣿⢿⣿⣿⠿⡿⠿⠟⠿⠛⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠇⠀⢹⣿⣿⣷⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠀⠀⠇⠀⠘⠿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣷⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠻⣿⣧⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣼⠀⠀⠀⠀⢻⣿⡇⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡆⠀⠀⠀⢸⣿⠇⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣄⣀⣠⣿⡿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠈⣿⣿⣿⣿⠃⠀⢀⣾⣿⠏⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣿⣿⣷⣶⣿⣿⡟⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸⣿⣿⡻⣿⣿⣿⣿⡇⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⢀⣼⣿⣿⡇⠸⣿⣿⣿⣿⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠘⠛⠁⢰⣿⣿⣿⣿⣿⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⡄⠀⢰⣿⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⣿⣿⠃⠀⠈⠛⠀⢻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠤⠉⠐⠊
⠀⠀⠀⠀⠀⢇⠂⠔⠊⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⠀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠣⣀⠀⠀⣀⠏⠂⠐⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣐⣱⠄
⠀⠀⠀⠀⠀⠀⠱⡄⠌⠀⠉⠀⠀⠉⢢⡀⡼⠅⠀⠀⠀⠸⠎⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠄⠠⠄⡀⠀⠀⠀⢰⠲⢄⢀⣤⠆⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⠀⡞⠀⠀⠆⠀⠀⢀⡠⠖⠲⠤⡀⠀⢳⠰⠧⠠⠀⡠⠄⠒⠃⠈⠑⡆⢠⡈⣘
⢀⠼⠁⠓⡖⠀⠀⠀⠸⠴⠉⠓⠀⠀⠀⠀⢀⡞⠀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠖⠈⠀⠈
⠉⢰⠐⠒⠚⢀⠔⠒⠂⠐⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠉⠓⠒⠒⠀⠀⠄⠤⠀⠀⠀⡖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⠀⠀⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢶⣼⣟⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⣠⠴⠂⠀⠀⠀⠀⠶⠶⠄
⠀⠀⠀⠀⠘⠓⣯⠻⡟⠛⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀
⠀⠀⠀⠀⠀⣀⡀⠀⢠⣤⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⡎⣰⡿⠀⠀⠀⠀⠠⣶⡴⢷⣿⠾
⠀⠀⠀⠀⢸⡟⣰⡇⢨⣭⠀⠀⠀⠀⠠⠂⢀⣠⡴⡾⠛⠀⠀⠀⠀⠈⠻⠮⡰⡴⢏⡁⠀⠀⠀⠀⠈⢹⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣠⠆⠀⠀⠀⠀⠀⠀⠰⢍⡡⠒⠀⠀⠀⠀⠀⠀⠀⣘⣇
⠀⠀⠀⠀⠛⠛⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠒⠁⠈⠁⠀⠀⠀⠀⠀⠀⠐⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠴⠋⠐⠊
⠀⠀⠀⠀⠀⢇⠀⠔⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⢀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠧⣀⠀⠀⣀⠏⠂⠰⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣀⣱⠄
⠀⠀⠀⠀⠀⠀⠙⡄⠌⠀⠉⠀⠀⠉⢲⡀⡼⠅⠀⠀⠀⠸⠊⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠤⠠⠄⡀⠀⠀⠀⢰⠒⢄⢀⣤⠆⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠉⢦⠀⠀⢀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⢀⡎⠀⠀⠆⠀⠀⢀⡤⠖⠒⠤⡀⠀⢳⠰⠧⠠⠀⡤⠄⠒⠃⠈⠑⡆⢠⣌⣈
⠀⠘⠁⠓⣖⠀⠀⠀⠸⠴⠉⠛⠀⠀⠀⠀⢀⡞⢀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠒⠉⠀⠈
⠉⢰⠔⠒⠚⢀⠔⠒⠀⠒⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠁⠓⠒⠒⠂⠀⠠⠤⠀⠀⠀⠖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⠀⡀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⢹⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⡟⡆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣦⢸⢸⠿⡆⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢰⢿⠇⡇⣴⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣿⠀⡼⠹⠘⢸⠀⣷⠀⠀⠀⠀⣶⡰⣭⡆⠀⠀⠸⠈⡇⣇⠏⢣⠀⣿⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣡⣾⢸⣧⣙⣡⣧⠸⣤⣿⠀⠀⠀⣰⣿⣷⣜⠃⠀⠀⣷⡆⡇⣼⣌⣋⣼⠉⣧⣜⣷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣼⡟⣷⢧⡄⡇⢹⣥⣨⢣⣿⣾⠀⢀⢴⣿⡏⣿⢻⡦⡀⠀⣷⣿⡜⣅⣬⠋⢸⢰⡹⡿⢿⣧⢿⡇
⠀⠀⠀⠀⢠⡄⠀⢸⣦⣹⣷⠏⣿⠀⣿⣷⢻⡏⣿⠇⡿⢀⠎⣼⢹⡇⣿⢼⢃⣵⡀⢿⠸⣳⢹⡏⣾⣿⠘⣷⠻⣾⣿⢬⡇⠀⢠⡄
⠀⠀⠀⢠⡿⠀⠀⢸⣟⣹⡏⢆⡏⢸⡏⡏⡌⠑⡎⡀⡇⢸⡟⣿⠘⣇⢹⣧⣸⣿⡇⢸⢀⣿⠸⢡⣿⢻⡆⢣⢁⢹⣏⣾⣇⠀⠀⢿⡄
⠀⠀⢠⠏⣧⠀⣠⠇⡻⣿⣱⡟⣾⢸⡇⢣⢻⣄⠁⡇⢿⡜⣧⡇⣶⢻⡀⣿⣿⣼⣣⡟⣼⠈⣰⡟⡏⢸⡇⣧⢿⡆⣿⣿⠹⣄⠀⡸⢹⡄
⠀⠀⢸⢠⡘⣿⣡⣞⢠⡿⠿⢹⢿⢸⡇⣼⣆⠛⠆⢿⢸⣙⣿⢡⢿⣾⡇⢹⡇⣿⠉⡇⡿⠸⠋⣰⢧⢸⡇⣿⠘⠃⢿⡈⣣⣎⣿⢃⡌⡇
⠀⢠⣼⢼⡇⣹⡶⡽⣾⣷⣇⢸⡿⢸⡇⡟⡿⡜⡟⡌⣼⣿⢃⡿⢸⢸⣇⣼⡇⣏⠿⣏⢃⢿⢱⢿⢸⢸⡆⢿⠀⣼⣾⣇⢯⢶⣏⣼⢱⣧⡄
⢀⡾⢻⡏⣱⠏⣀⡰⣻⢿⡟⣧⢿⣸⠃⠀⠁⡇⡷⣱⢋⣿⣏⣷⡼⢸⡿⣿⢱⢟⣄⠹⣎⢾⢸⠈⢀⠘⡇⠿⣾⢹⡟⣿⣆⣀⠻⣟⢸⡟⣿
⣼⡷⣾⡿⣱⢇⣿⠾⣇⣾⠣⢻⣄⡿⢸⣧⢠⠃⣼⠃⢸⣿⡜⠘⢁⡾⢁⡏⡿⣾⠙⣦⡹⣦⢸⣠⣼⡆⣿⢰⡟⠸⣧⣼⠧⣿⡼⣞⢿⣗⢾
⡏⢻⣿⢣⢻⡘⣯⠘⡿⢣⡶⣸⣿⠇⣦⣿⢸⡾⡏⣶⠸⢀⡖⣸⢹⣧⣾⡗⣧⢣⡆⣼⢣⣿⢿⡇⣿⣰⠸⣿⣇⢶⡘⢯⠃⣽⢣⡟⡜⣿⡞
⢷⡟⢸⡸⠞⠄⣩⢞⣡⡞⣰⠿⡏⢸⣇⢻⠘⠀⡇⠙⠘⠏⡟⢉⠘⠛⡏⢣⠉⠘⠃⠛⠈⣿⠀⠁⡇⢸⡇⢻⠻⣦⠷⣌⠳⡍⢠⠳⢷⡇⣷
⠈⢿⡈⢧⠻⣷⣯⣞⣠⡾⢃⢸⠁⢸⡘⡏⣴⡄⣿⠀⡆⠀⢰⠞⠀⠀⠀⠈⠟⣧⠐⠑⠀⣿⠀⣆⢱⢙⡇⠘⡇⡘⣷⣌⢳⣽⣦⢟⡞⢀⡿
⠀⢬⣳⡌⢳⣿⢋⡞⣿⢣⣿⢸⣸⣇⠻⢠⡏⠀⡿⡄⠀⢸⡄⢶⠀⠀⠀⠳⠀⢹⡄⠎⣸⢿⠀⢹⡌⠟⣼⣇⡇⣿⡘⣟⢿⡙⣷⡞⢠⣞⡤
⠀⢸⣿⠇⢾⡻⣟⠠⣿⢸⣻⠸⣿⠘⡆⢸⢰⢰⡇⢰⣸⡿⡇⣾⢷⡆⢾⡆⢸⠂⣷⢰⡇⠸⠀⣌⡇⢸⠁⣿⢣⣟⡇⣿⢤⣿⢿⡁⣸⣿⡇
⠀⢸⡏⢧⡾⡁⣧⠃⣿⣸⢻⡇⢡⡄⣷⢸⢃⡟⢰⢸⡿⣦⢃⡟⠸⣳⢢⣿⠸⠁⡘⣿⢳⡄⢷⡘⡇⣿⢰⡅⢸⣿⡇⣿⠘⣾⢈⢧⡽⢹⡇
⠀⢸⣷⡜⢱⢃⣿⢷⡟⣿⡟⡴⢛⠃⣿⣴⡟⣠⢿⢸⡇⡿⣸⣇⢠⣏⡎⣿⣴⢸⡇⣿⡞⢳⣌⢻⣦⣿⠸⡛⢆⢻⡇⢿⡾⣿⡸⡎⣡⣾⡇
⠀⢸⡟⣸⠀⣼⣿⢀⡁⣿⢸⢱⡏⢸⢫⢏⣾⡟⡘⣼⠉⣵⡿⡏⣾⢏⡗⢹⡅⣼⠇⡿⢧⠎⣿⣦⡹⡝⡆⢹⡞⡇⣿⢈⡀⡿⣧⠀⣇⢻⡇
⠀⠀⢧⠻⢸⠇⣿⢘⢣⠈⣤⣾⠃⡾⠃⣎⢸⢱⢣⡇⣼⠹⡇⢳⡿⢠⢗⡟⡼⠁⣸⣧⠸⡜⡜⢂⢳⠘⣷⠘⣧⣥⢁⡞⡃⣿⢸⡆⢏⡾
⠀⠀⠈⢷⣼⡆⣿⠸⡾⣇⢿⡘⣸⢃⠸⡹⠘⣿⢸⡿⣏⣆⢳⡀⣷⠺⣬⢡⣽⣼⠋⣿⢿⡇⣿⠸⢾⠀⡘⣇⢇⡟⣸⣣⢇⣿⢸⣧⡾⠁
⠀⠀⠀⠀⠉⠃⠈⢧⡹⣿⣮⢡⡏⣷⡀⣧⡄⢻⠘⠁⣿⢙⣦⠳⣌⠷⠏⢣⡿⣱⡏⣿⠘⢠⡇⢠⡼⡄⣧⢻⡈⡿⣿⢋⡾⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠐⣦⡻⣍⣮⣾⡇⢿⣿⠘⠇⢸⠀⣷⠸⡎⣿⡆⠹⣷⣴⠏⢐⣯⣹⠇⣧⢸⡇⡞⠃⣿⡹⢸⣧⣽⣱⠟
⠀⠀⠀⠀⠀⠀⠀⢫⣳⡹⡏⢿⠀⡟⢸⣠⢰⣾⢰⡏⡄⣿⠘⣷⠀⢻⡏⢺⣘⠃⣿⢰⢹⠸⣇⠇⣄⠃⣷⢸⡇⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣥⢻⣾⡄⡇⣾⡿⡄⢿⡘⣧⡇⣿⠃⡁⣾⢸⣷⠸⡏⢸⣿⢾⣸⢰⡟⢸⣿⢰⣶⢸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣏⣣⢷⠉⡇⢷⢰⣄⠻⠇⣿⢠⣿⡏⣾⠛⣧⢻⢹⣿⠸⠏⣨⡄⣷⢸⢀⡏⣜⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠳⣏⢸⠸⣘⢧⠀⣿⠸⢹⣧⡟⢀⢹⣦⡟⣿⠀⠾⢹⠀⡇⣸⠟⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡻⠄⢿⡀⡆⣿⡼⣼⢹⡇⡿⢸⣿⡕⡿⢸⣠⡟⠰⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣍⣃⠘⣷⡉⢾⡕⣣⡟⣩⣼⢃⣉⣭⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣾⣷⡟⢞⣵⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠒⠂⡂⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⡀
⠀⠀⡒⠈⠂⢀⠃⠀⠀⠀⠀⠀⠨⠀⠂⠀⡀⠀⠀⠀⠀⠀⠁⡐⠆⠐⡠⠁⠀⠀⠀⠀⠀⢀⠊⠉⠐⠌⠀⠀⠀⠀⠀⡀⠀⠐⠠⡀⠐
⠀⠀⠀⠔⠀⠰⠀⠀⠀⠀⠀⠀⠨⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁⢀⢠⢀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠅⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡁⠁⠀⠀⠀⠀⠀⠂⠰⠀⢅⠠⡀⠀⠀⠀⠀⠀⠠⠐⠀⠠
⠀⡀⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠑⠊⢱⠀⠀⠀⠀⠀⠀⠀⣮⠠⠀⠀⠀⠀⠀⠀⠀⢐⠐⠂⠂⠀⠉⠃⠀⠀⠀⠀⠀⠁⣄⠀⠀⠃
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠂⠄⠘⠀⠀⠀⠀⠀⡀⠀⢠⠂⠀⡦⠀⠀⠀⠀⠀⠘⠐⠀⠁⡀⠄⠀⠀⠀⠀⠀⠀⡀⠠⡂⢀⠀⠀⠀⠀⠀⠘⢀⠀⠀⢤⡐
⠤⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠆⠀⠡⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠃⠄⠁⠁⡀⠀⠀⠀⠀⠀⢔


⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠔⠁⠀⠐⠄⠀⠀⠀⠀⠀⢰⡀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡁⢀⠐⠅⢐

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢠⣶⣿⠿⢟⣫⣽⠄⠀⠀⠀⠀⠰⣄⠀⣿⡆⢀⡴⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠹⣧⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⣀⠹⣧⣿⣧⡟⢁⡀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⢿⠟⠁
⠀⠀⠀⢀⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣿⠿⢿⣟⡉⠀⠀⠀⠀⠀⠀⢸⣧⣤⣿⢰⣉⣰⠀⠀⠀⠀⠀⢀⣨⠿⡕⠁
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠘⠛⠋⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣴⣦⣼⠃⠀⠀⠀⠀⠀⠀⢀⣔⠐⠷⠖⣲⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⢶⣶⠤⠤⠤⠤⠄
⠀⠀⠀⢀⡴⠻⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣹⣿⣹⠀⠀⠀⠀⠀⠀⠀⣿⡇⣤⣄
⠀⠀⠰⣿⣦⡀⠈⡻⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣑⠀⢠⣤⣴⠀⠀⠀⠀⠀⠀⠰⢧⣉⣉⣡⠿⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡆
⠀⠀⠀⠈⠻⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠿⠿⠿⠇⠀⠀⠀⠀⠀⠐⡶⠛⠉⠓⡶⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃


⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠖⠶⢲⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⣖⠉⣉⣆⠀⠀⠀⠀⠀⠀⠀⢀⡷⠓⠛⢾⡁⠀⠀⠀⠀⠀⠀⢫
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠨⢻⢯⡀⠉⣂⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠸⡇⠀⠀⠀⠀⠀⠠⣶⣾⡇⠀⢀⡀⣀⣤⡤
⠀⠀⠀⣛⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⢶⡇⠄⠋⠀⠀⠀⠀⠀⠀⢸⡇⣭⠀⠶⠂⠀⠀⠀⠀⠀⠀⣨⣿⣷⣾⠿⠟⠉
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠸⠒⠒⠒⠓⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢀⣀⡀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⡠⠊⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠾⡁⠀⠀⢀⣀⣤⡤⠆
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢇⡀⢀⡼⢫⠂⡰⡆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣴⣶⡿⠟⠋⠁
⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠛⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢶⣘⣿⣟⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠛⡆
⠀⠀⣹⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣽⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠄⠇
⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀
⠀⠘⣦⣸⣿⢠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢮⣿⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⢿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⣠⣪⣿⡇⠋⠀⠀⠀⠀⠀⠀⠈⠙⠃⢦⣄⡀⢿⡟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⢈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠐⢶⣤⣀⠀⠀⡊⢂⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠎⠀⠈⡇⠀⠀⠀⠀⠀⠀⣤⣽⣿⣥⡄⠀⠀⠀⠀⠀⠀⡼⠟⠛⡙⠛⢻
⠀⠀⠙⠿⣷⣦⡌⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠑⠤⠄⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠓⠤⢼⣿⡗⠊
⠀⠀⠀⠀⠈⠋⠾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⡠⣀⠒⣬⠢⡀⠀⠀⠀⠀⠀⠀⢀⣶⣳⢀⣀⡀
⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢃⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠑⢍⠦⠀⠳⡬⠂⠀⠀⠀⠀⠀⠘⠻⣋⡸⣯⣷
⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⠢⠈⠀⠀⠀⠀⠀⠀⠠⣿⣯⠗⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣶⢰⡆⢰⡆⣶⠀⣶⢰⣶⢰⡆⢰⡆⣶⡆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇⢸⡇⣿⠀⣿⢸⣿⢸⡇⢸⡇⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣴⣦⣴⣦⣶⣴⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣴⡘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣍⣍⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⢰⣿⣧⢹⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢲⣬⣙⠿⢸⣿⣿⠸⢟⣩⡶⢢⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡹⣿⣷⣼⣿⣿⣴⣿⡟⣡⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠩⣥⣤⣹⣿⣿⣿⣿⣡⣬⡍⢙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡦⠈⢛⡁⣙⠉⠠⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⢛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣶⣿⠿⠟⣛⣛⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⣛⣛⡛⢛⡛⠛⣛⠛⡁⢾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣦⡙⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⠿⠿⠿⠸⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣦⣝⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣶⣶⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⡿⡿⣿⣷⡘⣿⣿⣿⣿⣿⣷⣝⢻⠏⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠿⠿⠷⠮⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⢀⣀⣀⣿⣿⣸⣿⣇⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠸⠇⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢻⠀⠀⠀⠀⡇⣸⠃⢀⠀⢠⡈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠁⠀⠀⣰⠃⠀⠀⡞⠀⢈⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠸⠁⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠚⢸⡆⠀⢰⡆⠀⠀⣠⠀⢀⡀⠀⠈⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣞⠀⠀⠀⢻⠀⠀⢸⠆⠈⠁⠀⠀⣇⡔⢰⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠋⢠⠀⡄⠀⠀⠀⣀⠀⠀⠀⣼⠀⢉⠀⢸⣧⡇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣼⠃⠀⡠⠀⢀⡀⠆⠀⢀⢉⠀⠀⣧⠁⠀⠈⠀⠏⠏⠀⢰⠀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣇⠐⡇⠀⠀⠁⠀⢸⣷⠀⠃⣾⠀⠀⠂⠈⠀⠀⠁⠆⠀⠀⠀⢸⢃⡁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁⣸⡆⣦⢠⠀⠀⢠⠀⠁⠀⠀⠛⠀⢀⢰⠀⡄⠀⣆⠀⠁⠀⠀⠀⠸⠃⢸⠆⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⡀⣠⠠⠈⡃⠞⠀⠀⠁⡀⠀⠀⢀⠀⢀⠸⠆⣆⠁⡞⠑⠀⡀⣤⠀⠀⣠⠀⠊⠀⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⢳⣉⠀⠁⠑⠰⠓⣠⣷⠇⠀⠰⡌⠂⠰⠀⡄⠉⠀⠇⠐⠾⠁⣸⠀⣶⠀⣶⠄⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠋⡤⠛⠐⣷⡀⠜⠿⣿⡏⣻⣧⡐⠁⢀⠀⢸⡇⠀⠀⠀⠀⢠⣘⡧⣶⠛⣷⣤⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡀⠘⠄⢀⡀⠀⣄⣀⠈⡄⠙⠉⣿⡄⠉⠀⡠⢁⡯⠀⢠⠀⣸⡟⠁⠇⠞⠟⢁⣀⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡄⠙⣻⡆⢨⢉⣠⣿⣾⣏⢀⣔⢃⠈⣁⠀⡀⠇⠋⠛⠀⠀⠀⠋⠅⢡⣴⡀⢸⡇⢦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠓⠉⠙⠛⢾⡌⠙⣿⠇⠁⠈⠛⠙⢷⢈⣤⣅⠀⣄⢂⣼⣷⡀⢰⣾⠆⡿⠃⣾⣿⠆⠘⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⢠⣿⡿⠂⠉⠁⠒⢶⡄⠀⣤⣼⡿⠋⠁⠀⠈⠙⢿⣿⡆⠀⠀⠆⠉⠘⠳⣦⣤⡠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⡒⣶⠞⣻⣟⡀⢀⠀⣀⣼⣮⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⣸⣆⠀⠀⢀⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠯⢉⣛⣛⡽⣿⣦⢠⠞⣿⣿⠦⡀⢀⡀⣰⡿⠿⣿⣿⣯⣾⣽⣷⣀⣫⣾⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠦⠤⠔⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢄⠠⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⣠⣄⡒⠤⣖⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠋⠩⠇
⠀⠀⠀⠀⠀⢔⡚⠶⣍⠏⠒⠊⠁⠀⠈⠉⠓⠺⠭⣛⡲⠤⣄⡀⠀⡀⠀⠀⠀⠀⠔
⠀⠀⢠⠄⣂⡥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠳⠏⠓⠘⠁⠉⣡⢦⡤⣀⣠⢀⣴⡃
⠀⢻⠶⣤⠭⣒⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡲⢧⢰⠆⠀⠀⠀⠈⡃⠘⣿⣿⡿⣟⡝⠃⠠⡀
⠀⠈⠑⢄⡁⠪⣙⠷⣂⠍⠐⠠⠀⡀⠀⠀⢠⠴⡘⣆⣹⠶⡄⠀⡠⠀⠀⠔⠁⠀⠸⠛⠋⢩⠙⢄⢀⢈
⠀⠀⠀⠀⠈⠒⢄⠁⠨⡙⠦⣌⣑⣄⠱⡇⢄⣶⠟⠋⠁⠀⡴⠊⠀⠰⠧⢴⡄⠛⠟⢑⠀⢀⡧⢘⠿⠟⣻⣗⣂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠁⠪⣗⣿⣧⡿⠊⠁⠀⠀⠠⠊⢠⣾⣿⣶⠀⠀⢰⡆⠨⠄⠀⠈⢀⡠⠐⠈⠉⠁⢋⠔⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡈⠙⠫⢛⠦⣴⣖⣸⡗⠐⠞⠓⣻⡿⢇⠀⢸⣷⡴⠂⡀⠐⢁⠔⠀⢀⣴⠟⠃⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⣉⠎⠛⢠⣿⡶⠒⣏⣁⡸⠚⣶⡿⠏⠤⠊⣠⠖⠀⣠⣴⡿⠁⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣐⠒⠠⠊⠁⣲⠀⠀⣤⣾⣿⡴⠀⡤⠔⢠⠤⠴⠶⡽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡉⠈⠙⠪⣉⠻⢿⣟⣒⣲⠶⠓⣰⠶⠲⣲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡀⠀⠑⢠⡈⠛⢁⣴⣋⢡⡠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠈⢳⠉⡊⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣾⡴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠙⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠻⣿⣿⡿⠟⠉⠉⠀⢠⠄⠀⠀⠶⢿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⣀⣤⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠴⠶⠆⠀⠀⠀⢰⣿⣿⣿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⢀⣀⠀⠀⠀⣿⡿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢰⡟⣼⣿⣿⣿⣿⣿⣷⡄⠸⡿⠁⠈⠿⠇⠈⢿⡀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣸⣿⡏⠉⠉⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃



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

⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠⣿⣠⣾⣿⣿⣷⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒
⠀⠀⠀⠀⠀⠀⢘⣽⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠃⠀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠀⢹⣉⣹⣏⣩⠏⠀⠁⠀⠀⠀⢰⣮⣉⣿⡀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⢢⢬⠆⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠰⣶⠾⠻⣷⣿⠙⠷⣶⠆⠀⠀⠀⠈⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣾⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⢀⣤⣾⠟⠋⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⠛⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠈⠹⠁⠀⡀⢀⠄⠁⢰⣋⠀⠀⠀⠀⠀⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⡇
⠀⠀⠀⠀⡴⠟⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢤⡀
⠀⠀⠀⢀⠀⢸⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠘⢷⣼⣿⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠈⠀⣿⠀⠀⠀⠀⠀⠀⢠⣶⢦⣤⣄⣠⣤⣴⣶⡄⠀⠀⠀⠀⠀⠐⠀⣤⣼⣿⡿⣫⣦
⠀⠀⠐⠶⠶⢿⣿⣿⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⣿⠀⠀⠀⠀⠀⠀⠈⣿⣎⠛⠃⠙⠛⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠙⣫⣾⣿⡟
⠀⠀⠀⠠⠞⠋⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠠⠄⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣛⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⣶⣤
⠀⠀⠀⠀⠭⠂⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⡛
⠀⠀⠀⣤⣿⣧⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠘⠃⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⢀⡀
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⣱⣿⢻⣧⠀⠀⠀⠀⠀⠀⢀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿
⠀⠀⠀⠀⢸⣿⠘⣿⡀⠀⠀⠀⠀⠀⠐⢠⠘⣏⢻⢿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢁⣾⡏⠀⠀⠀⠀⠀⠰⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣦
⠀⠀⠀⢰⣼⠀⣤⠛⡇⠀⠀⠀⠀⠀⢰⢿⣿⢃⡀⢸⣶⠂⠀⠀⠀⠀⠀⢸⡇⠋⢀⢸⣯⣔⡇⠀⠀⠀⠀⣾⠉⡀⢸⡇⠀⠀⠀⠠⢠⣠⡾⣿⢠⡌⠹⣷⡀
⠀⠀⠀⢈⣏⠃⡝⣆⣷⠀⠀⠀⠀⠸⣿⠆⢁⡞⣇⠀⢛⡟⠀⠀⠀⠀⠀⠘⢿⣄⢼⣦⣿⡟⠀⠀⠀⠀⠀⣾⠄⣧⣈⡇⠀⠀⢀⣴⠛⢛⣄⣁⣼⣧⡆⡹⠁
⠀⠀⠀⠀⠉⠛⠓⠋⠁⠀⠀⠀⠀⠀⠈⠑⠂⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠚⠃⠀⠀⠀⠀⠀⠈⠑⠛⠉⠀⠀⠀⠘⠛⠀⠛⠈⠉⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⢃⣴⡎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠴⠀⠠⠀⠀⠀⠀⣶⣄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠄⢀
⠀⠀⠀⠀⢾⡟⢿⣷⡈⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠀⣠⣴⣶⡿⠀⠀⠀⠀⠀⠀⢿⣿⠿⣷⣆⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⠁⠀⢀
⠀⠀⠀⠀⣸⡇⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣆⡿⠋⣜⣥⣠⡌⠀⠀⠀⠀⠀⠻⣆⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢃⡴⣿⠠⣶⡿⢻⣿⢀⡴⣯
⠀⠀⠀⠀⠿⣟⢸⡄⡿⠀⠀⠀⠀⢀⣠⣰⣶⠏⣸⠟⢡⠜⠙⠻⢛⡵⠆⠀⠀⠀⠰⡶⣿⢠⡄⢸⣦⠀⠀⠀⣠⣴⣤⡴⠋⣸⡿⢚⡉⣠⢿⡿⠋⣴⠏⡀
⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠠⣿⢋⣛⣡⢦⣠⠶⠻⠴⣦⣤⣀⡶⣧⡀⠀⠀⠀⢹⡦⣾⡁⡸⠃⠀⠀⠞⡋⡉⣩⣞⣀⡀⢴⣋⣈⣥⣠⡄⠚⠟⣻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⣟⣻⣦⢀⠀⠀⠀⠀⠀⣀⠂⢀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠃⠘⣿⡏⢻⣆⠀⠀⠀⢸⣿⣷⣄⡠⢀⣁⣀⣒⣠⣤⣌⡁⠀⠀⠀⠀⠀⠀⣿⡿⣦⣤⣇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣧⠈⡀
⠀⠀⠀⣠⣦⡿⡁⠘⠉⡇⠀⠀⠀⠻⢿⣟⠛⠟⠛⠻⠿⣿⣿⠛⣿⣤⡀⠀⠀⠀⠀⠹⣧⠈⠙⠻⡿⣦⣷⣦⠀⣂⠀⠀⠀⠀⠀⠀⠀⣿⠻⣷⣿⣦⣤
⠀⠀⢼⡏⠋⣼⣧⠄⠸⣿⠀⠀⠀⠀⠐⠉⢻⣷⣶⡄⢲⣤⣈⡆⠙⢿⠇⠀⠀⠀⢀⢳⣾⢷⡄⠰⣤⣤⣍⣉⠻⡟⢷⠀⠀⠀⠀⢀⣗⠾⣆⢉⡛⠈⠻⠿⣆
⠀⠀⠈⠻⠦⠿⠸⠧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠧⠼⠷⠽⠷⠦⠟⠀⠀⠀⠰⠾⠿⠋⠁⠠⠶⠾⠧⠉⠉⠳⠤⠌⠦⠀⠀⠀⠸⠿⠆⠠⠾⠟⠓⠛⠲⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠁⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠂⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢌⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠐⠶⡶⣶⣦⣤⣭⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠂⠉⠒⣄⠀⠀⡔⠃⠀⠀⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⣀⣀⣠⣤⣀⣴⣾⠆⢘⣥⣤⣤⣤⣤⣈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠿⠿⢷⠹⡟⠋⠩⠃⠀⠈⠣⣍⡏⣿⣻⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠠⠀⠀⠀⠀⠘⠀⡇⡆⠸⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠏⠀⠀⠀⠀⢂⠀⠀⢀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠠⡿⠀⠀⡘⠠⠀⠁⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠁⠒⠚⠁⠀⢀⠀⡄⠠⠀⠸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣰⢰⠇⡄⠀⣠⠀⠀⠀⡼⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡾⠀⡇⠀⡅⠀⠀⠀⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠃⠀⠀⠀⠀⢀⠇⢠⠇⠀⠙⠀⠀⠀⠀⠀⢫⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⢠⡤⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⠋⠀⠁⠀⠀⣀⠀⠀⠀⠈⠁⠘⠂⢤⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠁⠀⣠⠄⠒⠀⠉⠀⠉⠈⠉⠘⠓⠰⠤⠀⠀⠀⣠⠞⢡⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⣠⠐⠃⠀⣀⣠⠤⠶⠒⠒⠒⠆⠀⠀⠀⢀⣀⣠⠞⠁⠀⣟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠠⠖⠁⢀⡴⠚⠉⠀⠀⠀⠀⢀⡴⡖⠲⢤⡞⠋⢀⡿⠀⠙⢤⡈⠉⢠
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠰⠃⠀⣰⠋⠀⠀⠀⠀⠀⢀⣴⠻⡄⠙⢦⡀⠓⢤⡞⠀⠀⠀⠈⢱⡀⠀⠲
⠀⠀⠀⠀⠀⢠⡆⠀⢐⠃⠀⡼⠁⠀⠀⠀⠀⢀⡴⢻⡈⢧⡙⠲⡄⠙⢦⣀⣷⠀⠘⣧⠀⠀⢲⠀⠀⠇
⠀⠀⠀⠀⠀⢰⠀⠀⡋⠀⢰⠃⠀⠀⠀⢀⡴⣏⠙⣄⠙⢦⡉⠃⠀⠀⢀⡼⠃⠀⠀⠸⡆⠀⠐⡆⠀⠸
⠀⠀⠀⠀⠀⣶⠀⢀⡃⠀⠈⠀⠀⢀⡴⠋⠳⡈⠳⣌⠙⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠀⡇⠀⠀⡶⠀⠘⠇
⠀⠀⠀⠀⠀⣶⠀⠈⡃⠀⠀⠘⢶⠃⠱⡄⢠⡉⠓⠀⠀⠀⢀⡴⢋⣠⠤⠴⠦⠤⣄⠀⠇⠀⠀⡖⠀⠘⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠃⠀⠀⠀⢈⣧⡀⠙⢦⡘⢦⡀⢀⡴⠋⡴⠋⣠⠶⠒⠒⠦⣌⠙⣄⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡴⠋⣠⠟⣦⣀⠈⢳⡿⠋⠀⢸⠃⣸⠁⠀⠀⠀⠀⠘⡆⠸⡆⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣏⠻⣏⠠⠞⣡⠞⠁⠈⠙⢯⠀⠀⠀⢸⠀⢸⣴⣚⡶⢶⣳⣶⠃⢠⡇⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⢾⡁⠀⠲⣤⣀⠀⠀⠀⠀⠈⢧⡈⠳⢧⣘⣃⡵⠞⢀⡞⠀⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠃⠀⡀⠀⠉⠉⠛⠒⠒⠒⠀⠙⠶⢤⣍⣩⡤⠖⠋⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠒⠂⠤⠄⣀⡀⣀⡄⠤⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠄⣀⡀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚
⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠠⡐⠠⠄⠀⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠊⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠠⠀⠈⠒
⠀⠀⠀⠀⢊⣀⣀⣙⣀⠂⡖⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⣀⣀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡠⠪⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢗⠄⠀⠀⠐
⠀⠀⠐⠴⣠⠤⠤⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠂⠤⠐⢳⠁⠙⠚⠂⠤⠊⠀⠀⠀⠀⠀⠀⢎⡀⠁⢀⠀⡀⠋⠀⠀⠀⠀⠀⠀⢀⡴⢅⠀⠀⡠⠁⣄⠄
⠀⠀⠀⠀⠀⠌⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⣈⠖⠁⠙⡀⢀⡀⠀⠀⠀⠀⠀⠈⠲⣄⠑⠊⣰⠞⠁
⠀⠀⠀⠀⠐⠆⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠬⠀⠠⠤⠌⠥⠴⠀⠀⠀⠀⠀⠀⠀⠀⠱⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠃⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⠁⠉⠁⠢⡀
⠀⠉⠀⠂⣴⠁⠀⢡⡄⠂⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⢄⠀⠀⠀⢄⠈
⠀⠀⠑⣂⡀⠁⠀⠘⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢈⡂⢤⠄⢠⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠃⡀⠀⠀⠃
⠒⠥⠀⠈⡄⢠⡄⢠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢴⠀⡀⠀⠠⢡⠘⠁⠀⠀⠀⠀⠀⠀⢋⠀⠀⢨⠀⡠⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠡⠀⠀⠐
⠀⠀⠀⠰⠔⠉⠈⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡁⢒⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⠀⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢄
⠀⠀⠀⢰⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠌⢳⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠳⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡆⠶⡀⠑⢄
⠀⠀⠀⢸⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⢏⢳⢄⠃⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣐⡑⢆⠁⢀⡘⠷⠀⠀⠀⠀⠀⠀⠀⠐⣁⢖⡰⠀⠄⡄⢰
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠈⣉⠦⡑⠤⠇⡠⠊⠀⠀⠀⠀⠀⠀⢠⠳⠁⠀⢀⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠀⠣⢀⠰⣀⠆⡠⠊
⠀⠀⠀⢠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⠜⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠊

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀
⠀⠀⠀⠀⠀⠀⠠⡈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠘⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⢀⠔⢂⡀⠜⠀⠀⠀⠀⠀⠀⠀⠠⡢⠁⠨⠍⢁⠢⡀
⠀⠀⠊⠀⠀⠐⠨⠛⠘⠨⠙⠂⠀⠀⠀⠀⠀⠀⠀⠄⡠⠒⢄⠀⡈⠶⠀⠀⠀⠈⠒⡂⠈⢒⣒⣀⡔⠁⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⠄⠀⡇
⠀⠀⢈⠠⣀⣀⠠⡊⠀⠀⢰⠁⠀⠀⠀⠀⠀⠠⡀⢚⣠⡹⠊⠂⠀⠀⠀⠀⠀⠀⠁⢀⡄⢁⡔⠋⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠆⡶⠂⠀⡇
⠀⠀⠀⠈⠐⢒⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠃⠃⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠇⠄
⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣈⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠼⣆⣄⣿⣿⣿⡏⣿⣽⣿⣿⣿⣷⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿
⢀⣿⣹⣿⣿⣿⣿⣿⣿⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣸⠃⢹⣿⣿⣿⣿⣿⣿⣏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿
⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⢋⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⣛⡛⠻⢿⣿⣿⣿⣿⣿⣯
⠏⣿⣿⣿⣿⣿⣿⣿⣾⣇⣠⣤⣶⣾⣷⣦⣤⡀⣀⣀⣀⣀⣀⠔⢋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿
⠀⣿⣿⣿⣿⣿⣿⣿⠿⣋⣩⣭⣤⣬⡉⠛⣿⣿⣏⢀⣀⡹⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⣹⣿⠉⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿
⣸⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⡀⡹⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿
⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠃⣿⣿⡿⠷⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿
⠼⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⠄⣼⣿⣿⣴⣤⣾⣿⣿⣷⣭⣝⣻⣿⢋⣩⡴⠿⣿⣿⣿⣿⣿
⠠⣶⣿⣄⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠟⣃⣼⣿⣿⣿⣿⣿⣿⠟⣿⣿⠏⠈⢈⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠁⡟⢱⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⣾⠿⠛⢷⡿⠇⠈⠉⢉⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠰⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣶⣦⣤⡀⠀⢸⡇⠀⠀⠀⣺⣿⣿⣿⣿⣿
⠀⠀⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⣰⣿⣿⠿⠿⠛⣛⣿⣿⣷⣸⡇⠀⠀⠀⡼⣿⣿⣿⣿⡿
⠀⠀⠀⠈⢿⣿⡹⢟⠛⣿⣿⣿⣿⣧⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⣰⣿⠿⣿⡟
⠀⠀⠀⠀⢠⠿⢀⡤⠈⠉⡿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠛⠁⢸⡇⢀⡀⣨⣾⡏⠉⠀⠸⡗
⠀⡀⠀⠱⣤⡀⣴⠀⠀⠀⣥⣟⠈⠻⣿⣶⣤⣄⠀⠀⠀⣴⠛⠛⠉⠀⠀⠀⢸⡇⣩⣾⣿⣽⠁⠀⠀⠀⠐
⠔⠀⠀⢆⣼⣿⣿⠀⠀⢰⣿⣿⣷⣶⡾⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⡀⣀⣼⣷⣿⠋⠟⠁
⠀⠀⠀⣼⣿⣿⠏⣀⡀⣼⡿⡿⢻⣿⡇⠀⠈⣿⣿⣿⣯⣄⣀⣀⣠⣴⣾⣿⢿⡏⠁⠀⠀⣾⡀
⠀⠀⠀⣿⠛⠈⣾⣿⣿⡏⠀⣧⣼⡿⣷⠀⠀⠘⠟⠉⠛⣿⣿⣯⣥⠠⠞⠁⢸⡇⠀⠀⢀⣿⣷⣀⡀
⠀⠀⠀⠀⠤⠺⣿⣿⠏⠀⠀⣿⢿⣤⢽⡀⣾⣾⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣿⣿⣿⡟⢂
⠀⠀⠀⠀⠠⠂⡜⣡⣶⡄⠉⣿⠪⢤⣼⡿⣿⡷⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⢰⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡿⡡⠋⣿⠀⠈⠛⢀⡙⠁⠀⠀⢰⣤⡄⠀⠀⠀⢀⣿⢻⡇⠠⠀⠸⣿⠿⣷⣞⠳⠄
⢉⡉⠛⠉⢙⡒⠟⢋⣀⣠⣴⣿⣴⣶⣾⣿⡿⢿⣷⣛⢋⡉⠀⠀⠀⠀⣈⡁⢸⣇⣴⣶⠞⠋⣀⠿⡛⣿⣤
⣦⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣿⣿⣿⣷⣄⠀⠀⠀⣹⣿⣿⢾⣿⣟⣿⣶⡀⢇⢸⣿⡏⢻
⢿⣿⣿⣾⣿⣿⡿⣿⡟⣉⢻⣿⢹⣿⡛⠹⣛⣯⣽⣿⣿⡿⠀⠀⢆⣹⣿⡿⢿⣿⣧⣧⣘⡿⣦⠺⣿⣿⣿
⡸⠙⢘⣿⣟⣿⡿⣟⣷⡿⢸⡿⣸⣿⡿⠰⣶⣿⣿⣏⡁⠀⠀⠀⣾⣿⡷⢶⣿⣿⣿⡋⠘⢿⡿⠛⠛⠛⠛
⠁⠀⣿⣧⡬⣿⣿⣾⠉⠛⠺⣏⢹⣧⢴⣿⣿⣿⣯⣅⣿⣾⣆⠰⠽⣿⣿⡔⠿⡿⢿⡿⣾⣷⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⢀⠀⡀⣀⡀⠀⣀⠀⢀
⠀⠀⢀⡗⠀⠀⠀⠀⢀⣴⣿⣾⡆⠀⣼⣿⣷⠀⠀⠀⢀⡀⡀⠀⠀⠐⣾⣿⣷⣿⣿⣿⣾⣿⣿⡿⢀⣉⡇⣨⡽⢃⡀
⠀⢠⣾⣿⣴⡄⠀⠀⣸⣿⣿⣿⣿⡀⠁⠹⠏⠀⡐⡜⣨⡵⣿⣷⣤⡠⠙⠛⠛⡛⠛⣛⣛⣛⣋⠀⡸⣿⣜⡿⢳⡞⣖
⢀⣿⡟⠉⢿⣷⠀⠀⠻⣿⠿⢿⣿⠇⠀⠀⣠⣾⣷⣿⣿⣿⣿⣯⣿⣿⣦⣄⢼⣿⣙⢺⣟⡋⠛⠁⠘⠿⠻⣷⣾⠟⠋
⠀⠛⠄⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣼⣿⣿⠋⠀⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢰⣠⢼⡰⢠⢠⣀⠀⠀⠁⠊⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠀⠢⠀⠀⠰⡄⣠
⠀⠀⠐⡄⠀⢰⣺⣽⣿⣿⣾⣽⣼⣿⣿⠀⠀⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⠐⠀⠈⠼⠷⠁⣨⢷⣿⢕⠗⠀⢀⣘⡆
⠀⡄⣾⢁⠀⠈⠙⠛⡉⠉⠉⠙⠛⠛⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⠀⣠⢞⢢⡇⠀⠀⢀⣈⣿⣿⣏⣀⠰⣞⣮⣷
⠈⢷⣙⣾⣦⠀⠀⣴⣻⣶⡄⠀⢀⡺⣿⣎⠠⣄⠈⠻⣿⣿⣿⣿⡿⢠⣶⣿⡏⣿⣷⡇⠀⠉⠉⠉⠉⠉⠉⠀⣤⣿⠇
⢀⣾⣼⣿⡏⠀⣼⡏⠹⢿⣿⠀⢢⣹⣯⣟⣵⡝⡄⠠⣿⡿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣗⠀⠀⢀⣠⡄⠀⠀⠈⠻⣧⣄
⠀⠛⠿⠟⠃⠀⠈⠓⠀⠘⠃⠀⠘⠛⠛⠛⠛⠛⠋⠀⠘⠇⠸⠋⠀⠰⠿⠿⠿⠿⠿⠟⠀⠶⠿⠿⠿⠷⠶⠀⠶⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡼⠋⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⢳
⠀⠀⢠⣾⡿⢟⣩⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⠀⠀⣠⠎
⠀⠀⠘⣿⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢿⣿⢣⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢟⣷⣾⣤⡄
⠀⠀⠀⠀⠁⠀⠤⠴⠶⠾⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⢧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡷⠋⠀⢿⣷⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠐⣆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⡟⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⠤⠤⠤⠤⠤⠽
⠀⠀⠀⢸⡇⢠⠞⠁⠀⠀⠲⣿⠇⠀⠀⠀⠀⠀⠀⣾⠉⠉⣿⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣴⣶⣾⣶⣶⠄
⠀⠀⠀⠀⠙⢈⡄⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⣶⣶⠀⠀⠀⠀⠀⠀⠀⠰⡆⠒⠂⠐⠀⠀⠀⡲
⠀⠀⠀⠀⠀⠙⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣶⣿⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈

⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢿⡷⢿⣗⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚
⠀⠀⠀⠀⢠⣽⣙⣯⠾⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⡖⠨⠉⠀⠍⢹⣶⠀⠀⠀⠀⠀⢠⣾⣿⣦⣼⣥⣾⢿⣧⡀
⠀⠀⠀⠀⠈⢶⣮⣣⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠒⠒⢳⣧⡰⠟⠓⠄⣼⣿⡀⠀⠀⠀⢰⣿⣉⢈⣿⣿⣿⣽⢿⣽⣷
⠀⠀⠀⠀⠀⠘⣿⣁⣤⠴⢟⡂⠀⠀⠀⠀⠀⡄⠸⠗⢸⣿⠐⠶⡾⠃⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠩⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠁⠉⠉⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠙⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣭⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣽⡷⣶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡹⣿⣿⣿⣷⡎⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠀⠀⠀⠁⠿⠿⠟⣿⣿⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡃⣷⣤⡄⢠⠀⢀⢀⣴⣾⣿⡿⠟⢀⣴⣿⣿⣿⣶⣤⣄⣠⣶⣶⡝
⠀⠀⠀⠀⠀⠀⠀⢇⣌⠹⣟⣷⢧⣾⣿⣿⣿⡟⠀⢠⢸⣿⣿⣿⣿⠃⠀⡆⡻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢟⢧⡈⢍⢻⣿⣿⣿⡿⠃⠀⠈⠧⠙⠋⠋⠁⠁⠀⣱⣿⠙⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡟⣮⠈⢟⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⡏⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣷⣿⣅⠙⣿⣿⡟⣙⣶⣦⣄⠀⠀⠈⠈⠋⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣿⣇⠉⠰⣿⡏⣿⡿⠻⠃⢀⠀⠀⣀⢀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣿⢗⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⠀⠀⠙⡃⢹⣧⠤⣈⠉⡃⠀⣉⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢫⡞⣡⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⢛⣻⡇⠠⠀⢿⡆⠩⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣯⠿⣞⢡⡶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣼⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣝⣻⣿⣾⡟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣷⡀⠻⢿⣿⣿⣿⣿⡛⣶⣄⣀⡀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠫⣿⡈⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣇⣼⡏⠶⣽⣿⣿⣿⡟⠀⠈⢷⣌⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⡇⡴⠁
⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⡇⣿⣿⡄⠀⠉⠉⣹⣿⣷⡀⢸⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠹⢿⣸⠁
⠀⠀⠰⢚⣹⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⡀⠀⢀⠿⣿⣿⡓⠉⢻⣿⣿⣿⣯⣭⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⡀⠉⠻⢆
⠀⠀⠀⠀⠋⠛⢿⣿⣿⣿⣿⣇⣿⣿⣿⣷⡀⠀⠘⢸⣿⣿⣄⠸⣿⣿⣿⣿⣿⣷⣜⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣤⣀⠁⡂
⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣷⡀⠀⠸⣿⣿⣿⣆⣿⣿⡿⢿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⠟⣷⣿⣿⣿⣿⣿⡝⣇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣾⣭⣿⣿⣿⣄⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⠸⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠇⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠁⠙⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣯⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠃⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡙⢿⡛⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⣼⡟⠁⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⢀⣼⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⣼⣿⠁⣸⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⣠⣾⠇⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⢀⠃⢰⣿⣿⢀⡇⢸⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⢀⣼⣿⡏⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⣿⠀⢸⣿⡟⠸⡇⠋
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⣰⣿⣿⡏⠀⣠⣾⣿⣿⣿⣿⠋⢠⠂⠀⢰⡿⠀⢸⡿⢁⡆⠁
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⡇⣸⢿⣿⡟⢀⣾⣿⣿⣿⣿⠟⠁⡰⢃⠆⢠⣿⠇⠀⡞⢁⡾⢱⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⠟⠁⢸⢻⡿⢰⡏⣸⣿⣰⣿⡿⢋⣾⡿⠋⠄⡼⣡⠟⣴⡿⠃⠀⠀⣰⣟⣷⠏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⠏⠀⠀⣼⠈⡇⣿⠀⣿⣿⣿⡟⢀⣾⣿⢃⡏⣼⣷⣯⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⣀
⠀⠀⠀⣶⠀⣼⢿⡀⠀⠀⢸⣿⠀⢠⠀⡟⠀⠃⠟⢸⣿⣿⠛⠀⣾⣿⠇⣾⢡⣿⣿⣿⡟⠀⣰⣿⣿⠟⠁⠀⣠⣴⣿⠇
⠀⠀⠀⣿⠀⠸⣟⣧⠀⠀⢸⡇⠀⣾⣴⡇⠀⠀⠀⢸⣿⠇⠀⢸⣿⡿⢸⣿⢸⣿⣿⣿⡇⣼⣿⣿⠃⢀⣴⣾⣿⡿⠃⢀⠆⢀⠄
⠀⠀⠀⣿⡄⠠⢹⣿⡆⠀⢸⠃⢠⣿⣿⠃⠀⠀⠀⢸⡏⠀⠀⣿⡿⡇⣿⣿⢸⣿⣿⣿⣷⣿⡿⠁⢀⠼⡫⠓⢉⣠⡶⣋⠔⠋
⠀⠀⠀⣿⣧⠀⣧⣻⣷⠀⢸⠀⣼⣿⡿⠀⠀⠀⠀⢸⠃⠀⢠⡿⢰⢱⣿⣿⠸⣿⣿⢹⣿⣿⡇⢀⡾⠋⣠⣶⣿⡿⠛⠁
⠀⠀⠀⢻⣿⣧⢸⣿⣿⠀⡀⢠⣿⣿⠃⠠⠀⠀⠀⣎⠀⠀⢸⢇⡟⣼⣿⣿⢸⣿⣿⠸⣿⣿⡇⢸⠇⣰⣿⣿⡩
⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⢃⣾⣿⠃⠀⢰⠂⠀⠀⠋⠀⢸⣿⡼⢡⣿⣿⢇⣾⣿⡟⣸⣿⣿⡇⠀⢰⣿⣿⠋
⠀⠀⠀⠀⠀⢻⣻⣿⡟⠀⣾⡿⠃⡀⠀⣸⠃⠀⠀⠀⢠⣿⣿⢃⠟⣸⢏⣾⣿⣟⣵⣿⣿⡟⠀⣴⣿⠟⠁⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠈⢿⣿⠃⣼⡿⠁⣼⠃⣰⣿⠀⠀⠀⠀⣾⣿⢃⢂⢠⣫⡾⣻⣿⣿⡿⠟⠋⡠⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡟⣸⡟⠀⣼⠃⣰⣿⡏⠀⠀⢀⣼⡿⠁⢂⣾⣰⣟⣽⣿⠿⠋⠀⢀⣠⠄⠀⢀⣠⣴⠾⠟⢉⣴⠋
⠀⠀⠀⠀⠀⠀⢀⢱⡟⠀⣸⢃⣼⣿⡿⠁⠀⢀⣾⠟⠁⠀⣼⡇⣏⣿⡟⠁⠀⣠⡾⠋⠀⣠⡶⠟⠉⠀⣴⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⣿⣿⣿⡟⠁⠀⢀⣾⠋⠀⠀⣼⣿⣇⢻⡟⠀⢠⣾⡿⠀⢀⠾⠋⠀⢀⣴⣾⢿⣿⡏⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⣿⣿⠋⠀⠀⠀⡾⠁⠀⠀⣼⣿⡟⢻⢸⡇⣰⣿⣿⠃⠀⠁⠀⠀⣰⣿⣿⣳⣿⡟⠀⡜⣯
⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⠃⠀⠀⠀⠀⠁⠀⢀⡾⢋⣿⡧⣀⣼⣠⣿⣿⠏⠀⠀⠀⢀⣼⣿⡿⣷⣿⠟⠀⡰⠁⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣰⠏⣴⣿⣿⡇⣿⣿⣿⣿⠋⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⡰⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡰⢡⣾⣿⣿⣿⣼⣿⠿⠋⠁⠀⠀⠀⣰⣿⣻⣿⡿⠋⠀⢀⡔⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡄⠀⠀⢀⣴⢟⣽⣿⡿⠛⠉⠀⠀⠀⠀⠀⣠⣾⣿⡷⠛⠁⠀⣠⣴⣿⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⣼⠁⠀⢀⠞⣱⡿⠋⠁⠀⠀⣀⣤⣔⣀⡴⠞⠛⠉⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⣳⠏⠀⠀⢊⡞⠁⠀⢀⣤⡾⠿⠋⠁⠉⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⠏⠀⠀⠀⢋⠀⢀⡴⠟⢁⡀⠀⠀⠔⢊⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢀⡴⢃⠤⢊⣠⠞⠁⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⣼⡿⠋⠀⣠⣴⣾⠟⠀⢀⣴⡿⠁⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⣼⠋⢀⣴⣿⡿⠟⠁⣠⡴⠿⠋⠀⠀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠚⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣠⣀⣤⣤⣤⣀⣠⣀⠀⢀⣀⣤⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⠏⠙⠁⠙⣉⠛⠋⠙⠿⠛⠋⠉⣿⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠁⠀⠾⠂⠀⠛⠀⢠⡆⠀⠀⠺⠆⠈⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿⠀⠶⠀⠀⠀⠛⠀⠀⠀⠰⠖⠀⠀⠀⣿⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠛⠂⠀⠶⠀⠀⠀⠀⠶⠀⠀⣿⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢠⡆⠀⣀⡀⠀⠀⣀⠀⠀⠀⣀⠀⣿⠀⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣶⡾⢿⣿⠀⣿⣀⣀⣀⣀⣈⣁⣀⣀⣉⣀⣀⣀⣉⣀⣿⠀⣿⡟⠹⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⣀⠘⠁⢸⣿⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿⡇⢠⡄⠸⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠋⠀⣠⡈⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⢁⣄⠀⠀⠈⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠰⠆⠉⠀⢀⣀⡀⠘⠃⠀⣀⡙⢃⣀⣀⣀⢀⣈⠛⠀⣤⠀⠛⠀⠀⠉⠀⠛⢀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣤⣄⣀⣤⡿⠛⣿⠛⢻⡿⠛⠻⠛⠙⠋⠙⠛⠙⣿⣄⣀⣠⡶⢶⣆⣀⢀⣀⡈⠉
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠉⠙⠏⠀⢠⡄⢀⣀⠀⠀⠀⠀⠶⠀⠾⠀⠀⠈⠙⠋⠹⠇⠀⠉⠹⠿⠉⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠾⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡠⠔⠢⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠱⡀⠀⠀⠉⠀⠀⢀⡜⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⣀⠀⠀⠱⡦⠦⣀⠀⣠⠎⠠⣇⡀⢀⠠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⢀⡀⡖⢼⠄⠁⠀⠀⢣⠀⠈⠻⣄⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢐⠈⠀⢀⡀⠀⠀⢐⠐⠬⠈⠁⠀⠀⠀⣀⠤⠃⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢃⠀⠘⠑⡢⠀⠈⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢆⠀⠈⠁⢀⡠⠔⠈⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⢦⠄⠺⠁⠀⠀⠀⠀⠀⢀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠤⢄⣀⣀⠆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠤⠒⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠒⠐⠒⠂⠈⠀⠀⠉⠁⠐⠒⠒⠂⠁

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠶⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣦⠈⠳⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠏⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠲⣯⠞⠙⠃⠀⠹⣆⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⡏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⣠⡴⢋⠀⣠⠞⠀⠀⠀⠀⠀⢹⡄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢾⡁⢤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣮⡷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣠⡾⠗⠋⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⣸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠹⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⣠⠏⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⢦⡀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠙⠶⠃⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⢀⡇⢠⡎⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠤⠶⠄⠀⠀⠀⠺⠃⠊⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⢠⣦⢀⠀⡤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣉⣉⣀⢀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⢭⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⢀⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠐⣯⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⢢⣬⠗⠀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣤⣄⣁⡀⣸⣿⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣿⣿⣿⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠠⠈⣠⣤⣀⣀⠀⢀⠀⢀⣀⣦⣄⠑⠄⠀⠀⠀⠀⠐⢁⣤⣄⣀⠀⠀⠀⠀⢀⣰⣄⡀⠓⢄
⠀⠀⠀⠈⠐⣾⡟⠁⠀⠈⠉⠉⠉⠉⠀⠀⠈⣿⡷⠰⠀⠀⠃⢴⣿⠋⠉⠉⠉⠛⠛⠋⠉⠁⠀⠹⣷⡦⡁
⠀⠀⠀⠀⢃⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⠃⠀⠀⢰⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢠⠁
⠀⠀⠀⠀⠈⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⡀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠁⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⡀⠤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠠⠤⠀⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠠⠤⠐⠒⠠⣀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢤⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⣄
⠀⠀⠀⡀⢂⣠⣾⠿⠶⠦⣤⣤⣤⠴⠶⠛⠶⣤⣑⠆⠀⠀⠀⢀⣴⡿⠷⠶⢤⣤⣤⣤⠴⠞⠳⢦⣄⡑
⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠸⠀⠀⢂⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠄
⠀⠀⠀⠀⢃⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠃⠀⠀⠈⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡜
⠀⠀⠀⠀⠈⢆⡃⠀⠀⠀⢀⣠⠤⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠘⠛⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠂⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢀⣴⣶⣾⠀⠀⠀⠀⠀⣀⠀⣶⡀⣉⡀⠀⠀⠀⠀⠀⣠⣴⡾⣿⣳⡄⠀⠀⢸⣿⣿⡆⢠⡤⣤⠀⠀⠀⠀⢸⡶⠶⡶⣿⡆⠀⠀⠀⠀⠂⠉⢣⠜⠁⠂⠄
⠀⢀⣴⠋⠻⣿⡿⠃⠀⠀⠀⠀⢻⠄⢻⡇⠠⣅⠀⠀⠀⠀⠀⢿⣵⠿⠟⠛⠀⠀⠀⠀⠉⢉⣀⡹⠿⠿⠁⠀⠀⠀⣸⣦⣤⣤⣿⠁⠀⠀⠀⠘⣠⢶⡀⠶⠇⠠⠁
⠀⠈⠻⣷⡤⠋⠀⠀⠀⠀⠀⠀⢠⡀⢻⡝⠀⡄⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣶⣾⣟⠁⠀⠀⠀⠀⠧⡤⠇⠃⠬⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⠀⣠⡐⠾⠖⠀⠒⠒⠀⠀⠀⠀⢀⠀⣼⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⠉⢉⣉⠉⠙⡄
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⠃⠀⠀⠀⠀⠿⣧⣶⡆⠀⠀⠀⠀⠀⠀⢀⣈⢷⣽⣴⢏⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⠛⠀⢀⠏
⠀⠀⣛⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠁⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠨⠽⠛⠻⠭⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁⠴⠁
⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⡴⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠖⢀⡀⢶⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢠⡌⠙⠛⢡⡄
⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠸⣁⠰⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠷⠆⠀⠀⠀⠀⠼⠿⠿⠛⠿⠿⠿⠄⠀⠀⠀⢤⡈⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⢰⡎⠁⠀⠀⠀⠀⠰⣶⣶⠆⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣴⣶⣷⣶⣄⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⣤⠤⠴⠶⣤⣤⡀
⠀⢘⣿⣿⣿⠻⣟⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⣏⠀⠀⠠⢹⡇⠀⠀⠀⠀⡿⣿⠀⢨⡿⡇⠀⠀⠀⠀⢀⡘⠿⠷⢁⡀⠀⠀⠀⢸⡇⡄⣦⢠⢸⣿⡇
⠀⠰⣿⣿⣿⡿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣶⣾⣿⠁⠀⠀⠀⠀⠁⠄⠈⠀⡀⠀⠀⠀⠀⠀⢈⣭⠶⢶⣭⠀⠀⠀⠀⠈⢧⣤⣤⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⢸⠛⠛⠛⢻⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⡇⠀⠀⠀⠀⡴⣏⠙⠋⣽⢆⠀⠀⠀⠀⠀⢿⣭⣭⡟⠀⠀⠀⠀⠀⡀
⠀⢠⠊⠙⢿⡿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⡇⠀⠀⠀⢸⡶⠀⡅⢊⠀⢾⠀⠀⠀⠀⠀⡏⠀⠀⢹⠀⠀⠀⠀⠈⠇⢀⣀⣤⡤⠖⠂
⠀⠈⠢⠔⠋⠢⡈⠁⠀⠀⠀⠀⢸⡶⣶⡶⣾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠲⣗⣠⡄⡿⠎⠀⠀⠀⠀⠀⣗⣭⠀⣾⠀⠀⠀⠀⠀⠺⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⡄⢢⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⣛⣛⠛⢓⠀⠀⠀⠈⢳⣤⣠⣤⣤⣄⠀⠀⠀⠀⠀⡏⠉⠉⢉⠀⠀⠀⠀⠀⡆
⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠀⠀⣿⢾⡿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⣤⡦⠀⠀⠀⣀
⠀⠘⢿⣧⣾⠟⠂⠁⠀⠀⠀⠀⢸⣿⠀⠲⠀⠀⠀⠀⠀⣼⣿⣿⡛⢿⣿⣿⡄⠀⠀⠀⠰⣤⠤⠠⡤⠀⠀⠀⠀⠀⠀⣇⠀⢀⣈⠀⠀⠀⠀⠀⣬⣷⠶⠛⠋⠁
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡀
⠀⠀⠀⣠⠈⣳⢖⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢫⣿⡂
⠀⠀⢠⢿⡇⠘⢦⡈⠝⣦⠄⠀⠀⠀⠀⠀⠘⢿⣦⣿⣧⣾⠟⠀⠀⠀⠀⠀⠠⣾⡿⠣⣼⠿⠋
⠀⠀⠈⠛⠁⠀⠀⠙⠞⢿⡶⠀⠀⠀⠀⠀⠒⢾⣿⣿⣿⣿⠶⠂⠀⠀⠀⠀⠈⣋⠔⠉⠩⢉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠓⠒⠒⠒⠒⠒⠚⠓

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⡔⣻⢭⡟⣗⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⡙⣿⡀⠀⠀⠀⠀⠀⡞⠀⠈⠉⠍⠙⠒⡆
⠀⠀⠀⠻⠭⠍⣭⣭⠩⠭⠟⠀⠀⠀⠀⠀⢠⡦⠙⠻⠦⠴⠟⠁⠀⠀⠀⠀⢰⣧⡄⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠛⣀⠛⢸⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡹⢿⡿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠘⠿⠿⠶⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀⡴⠞⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠶⣄
⠀⠀⢰⠏⠻⣦⣀⣾⣗⠀⢹⡄⠀⠀⠀⣰⠋⢳⣄⣰⡀⢀⠈⢳⠀⠀⠀⠀⡼⠉⢳⣤⠐⢆⠐⡌⢷
⠀⠀⢸⠀⠀⢰⣿⣿⡁⠀⠀⡇⠀⠀⠀⣿⠀⣘⣿⣿⣷⣏⡀⢸⡇⠀⠀⠀⡇⢰⣄⢸⠷⣾⠟⠁⢸
⠀⠀⠘⢧⡀⠜⠉⠀⠹⣦⡼⠃⠀⠀⠀⠸⣆⠈⠙⠛⠛⠻⣤⡾⠀⠀⠀⠀⠻⣄⠙⠻⠖⠉⢳⣤⠟
⠀⠀⠀⠀⠙⠲⠦⠴⠖⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠶⠞⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠶⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⡠⠳⣜⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠒⢺⡃⠀⠀⠀⠀⠀⠀⠀⢧⡽⣭⠅
⠀⠀⡠⣊⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⣠⣊⠀⢀⠇⠀⠀⠀⠀⠀⠀⢸⣠⣦⠻⣄⢹⠀⠀⠀⠀⠀⢠⠷⣸⣿⣷⡰⢧
⠀⢸⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣿⠟⣡⡶⣄⠀⠀⠀⠀⠀⠸⢷⢴⣶⢗⢹⠀⠀⠀⠀⠀⢀⣀⡨⠗⠯⣀⣀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠚⠋⠀⠀⠀⠀⠀⠘⠂⠅⠹⠒⠊⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤
⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⣀⠀⣀⣀⣀⡙⠇⠀⠀⠀⠀⠀⠀⢠⣶⠾⠿⣟⣻⡆⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢸⠀⡇
⠻⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠟⠛⠋⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⡦⠎⠀⠉⢆
⣠⠤⠐⢦⠔⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠀⠠⡄⠀⠀⠀⠀⠀⢀⠏⠢⡀⠀⠈
⢿⣿⣿⣦⣾⣿⣿⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⢾⣿⣾⣾⣶
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠃
⣖⣒⣒⣒⣒⣒⣲⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠆⠀⣀
⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢷⣦⡸⣿⣇⣤⡾⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⣌⣏⡴⠊
⣷⣿⣿⣿⣿⣷⣸⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣿⣋⣀⣀⠀⠀⠀⠀⠀⠉⣭⢉⣭⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⡰
⡿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠈⠉⣩⡿⠉⢿⣍⠉⠁⠀⠀⠀⠀⠀⠐⣿⡄⣽⠛⠀⠀⠀⠀⢰⠁⠙⠿⠿⠟⠃
⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣦⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⡇⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⢘⣛⣤⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣶⣶⣶⠂
⠘⠮⠃⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⣿⣿⡇⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣼⡇
⣶⣶⣶⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣾⣿⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⣟⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⣀⣴⢾⣷⠀⠀⠀⠀⠀⠘⠉⢆⠀⠀⠀⠀⠀⠀⣐⠉⠇⠀⠀⠀⠀⢠⠒⡶⡄⠀⠀⠀⠀⢤⣰⣆⡠
⠀⠙⠟⢋⣁⣀⡀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠘⠾⠤⠃⠀⠀⠀⠀⠚⠿⢿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢤⣀⠀⠢⠀⠀⠀⠀⢸⠿⠿⡇⠀⠀⠀⠀⠀⡅⢨⠀⠀⠀⠀⠀⣠⡴⣮⠕⡀⠀⠀⠀⣼⣧
⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⢸⣄⣠⡇⠀⠀⠀⠀⠀⡃⢘⠀⠀⠀⠀⠈⢔⡻⠞⠋⠀⠀⠀⠀⣇⢘⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⣀⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⢴⣿⣿⣏⠀⠀⠀⠀⢀⣤⣄⠠⠀⠀⠀⠀⠾⠿⣟⣷⠀⠀⠀⢀⣤⣀⣂⣥⠀⠀⠀⠀⠀⠙⣏⡀
⠀⠀⣾⣛⣻⠃⠀⠀⠀⠀⣼⣯⣽⠟⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⣾⣥⠿⠿⣿⣷⠀⠀⠀⣄⣀⣀⣠
⠀⠀⠉⠉⠋⠀⠀⠀⠀⠈⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⣠⡀⠀⡀⠀⠀⠀⢸⠛⠛⠛⡇⡄⠀⠀⠠⠐⠂⠐⢲⡄⠀⠀⠠⠐⠂⠐⢲⡄⠀⠀⠀⠀⡹⢻⠃
⠀⠀⠈⠀⠈⠁⠀⠀⠀⢸⣿⠿⣿⣧⡇⠀⠀⠀⠀⠄⠄⣾⡇⠀⠀⠀⠠⠄⠀⣾⡇⠀⠀⠀⠼⣷⡾⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠑⠀⠒⠀⠛⠃⠀⠀⠐⠀⠒⠀⠛⠃⠀⠀⠀⠀⠈⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⣴⢴⡡⠀⠒⠊
⠀⠀⠀⠀⠀⠀⡰⠃⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠻⡒⠀⠀⣀⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠙⣄⠀⠀⠈⠉⠁
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠹⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠟
⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡄⠀⠀⡎⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢣⠀⢰⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⡀⡎⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⠟⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢶⣤⣀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣰⡿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⣰⡟⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⣰⠿⣦⣄⡈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠻⣆
⠀⠀⣰⠏⠀⠀⠀⠀⣴⠟⠙⢷⣄⠀⠀⠀⠀⠙⢷⣴⠏⠀⠀⠉⠛⠷⣦⣄⡈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠹⣆
⠀⢰⡟⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢻⡆
⢀⣿⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠈⠛⠷⣦⣄⡀⠀⠀⠹⣇⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣹⠟⠀⠀⠀⢻⡀⠀⠀⠀⢸
⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘
⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⢸⣷
⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⠀⠀⠀⠀⠙⢷⣶⠶⠶⠶⣦⣤⣴⠏⠀⠀⠀⠀⠀⠀⢸⡟
⢿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣠⣤⡴⠶⠛⠛⠉⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠄⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠
⢸⡇⠀⠀⠀⠈⣿⠀⠀⠀⢀⣾⣣⣤⠶⠟⠋⢉⡀⠀⠀⠀⠈⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢶⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸
⠈⣿⡀⠀⠀⠀⢹⣇⠀⠀⠀⠈⠙⠷⣦⣅⡀⠀⠀⠀⠀⠁⠀⠀⡀⠈⠁⠀⠹⣷⣄⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢀⣿
⠀⠸⣧⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣅⡀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣼⠇
⠀⠀⠸⣆⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⠀⠰⠀⠀⠃⠀⠀⢀⣿⢷⣄⠀⠀⠀⠀⠙⣦⣀⣴⠏⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠹⣧⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⠀⠂⢀⣾⠃⠀⠙⢷⣄⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣾⠃⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⣶⣦⣤⣤⣤⣤⣴⡶⠶⠾⠛⠛⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⡏⢸⣿⣿⣷⣦⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⠂⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠀⢸⣿⣿⣿⠁⢸⣿⣧⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣹⣾⣷⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⡄⠘⣿⣿⣿⠀⢸⣿⣿⢨⣿⣿⡄⣐⠠⠀⡀⠀⠀⠀⢀⣿⣿⣿⣿⠟
⠀⠀⠀⢠⣿⣿⣾⣿⣦⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⠀⣼⣿⣿⠀⣿⣿⣟⣟⢿⣷⣌⠁⣀⣠⣿⡿⠋⠡⠐
⠀⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⠀⣿⣿⡟⢀⣿⣿⣿⠀⢸⣿⠿⣷⣎⢿⡟
⠀⠀⠀⠀⠉⢙⠻⣿⣷⡀⠀⠐⢠⡸⣿⣿⣿⡏⣿⣿⣿⣿⣿⣷⠀⣿⣿⣧⢸⢹⣿⣿⡇⠀⢿⡇⠈⢿⣌⠃
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⢠⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⡟⠀⣿⣿⣿⠀⠀⣿⣿⣇⠀⠘⣿⡄⣾⣿⣷⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⢷⡏⣿⣿⣿⡄⠀⠙⣿⣿⣿⡇⠀⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠘⢿⡞⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣾⠃⢸⣿⣿⡇⠀⠀⢿⣿⣿⡇⠠⣿⣿⣿⣿⡿⠿⠟⠃⠘⠀⠀⠂⢻⡎⢷⣻⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣸⣿⣤⠀⠘⢿⣿⡇⠀⣴⣌⣛⢛⣣⣤⣭⡉⣬⣭⣶⣶⣷⠀⠀⣾⣿⣿⣦⣥⡌⠟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢼⢯⣜⢿⡄⠀⠀⣿⡇⠈⠿⢿⣿⣿⣿⠿⠛⠉⢸⣿⡿⢿⣿⠀⠀⣿⣿⠋⢉⣭⣤⣤⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠸⣿⣯⠁⠀⣀⣈⣁⠀⠀⠂⢸⣿⣿⠀⠀⠀⢹⣿⠃⣼⣿⡆⠀⣿⣿⣤⣿⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⣿⣆⣰⣿⣿⣿⡀⠀⠀⢸⣿⣿⡇⠀⠀⣾⣿⠀⣿⣿⡇⠀⢹⡿⠿⠋⣸⣿⡟⡐⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⡿⠻⣿⣇⠀⠀⢸⣿⣿⠃⠀⠀⣿⣿⠀⣿⣿⠀⢰⣆⠀⢀⣠⣿⡿⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⠋⠀⠀⢼⣿⡆⢀⠸⢿⣿⠆⠀⠀⣿⣿⣾⣿⣿⢀⣿⣿⡆⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⢠⣾⣿⡇⢸⣧⢸⡿⠀⠀⣀⠻⠿⡛⢛⣵⡾⢟⣙⣥⡆⠙⢡⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⣿⣿⣾⣿⠋⣰⣿⣿⣦⣁⡀⣼⣿⢀⣿⣿⠘⣿⣆⣙⣿⣿⠟⣰⣿⣿⣶⣮⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣴⣿⣿⡌⢛⣛⣵⣾⣿⣿⣥⣽⡿⠋⣾⣿⣿⣿⡿⠘⠿⠿⠛⠁⠀⠈⠡⠈⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠋⠁⠛⠿⠿⠿⢋⠙⢿⣿⡄⠐⠿⠟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠉⠁⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⠀⠀⠀⠀⣆⠀⢃⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⡏⠳⢄⠐⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡈⠀⠀⠀⠀⠹⣀⠄⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠌⡇⢀⡄⠀⠀⠀⠐⢤⠀⠀⠙⢆⠀⠀⠀⠀⣠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡏⢸⠱⡀⣀⠀⠀⠀⠑⣄⠀⠈⣇⠀⠀⠌⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠤⠐⡇⠀⠑⠹⡌⣏⢢⡀⠀⢹⢀⠈⢸⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠲⡀⠻⡄⠀⠀⢀⡇⠐⡧⢠⠏⠸⠀⢸⠀⢠⡾⡀
⠀⠀⠀⠀⠸⡗⢄⡀⠀⠀⢳⠀⠡⠈⠢⡈⢢⣀⠞⢠⠀⠿⠁⡐⢀⠀⡜⠀⢸⠁⢇
⠀⠀⠀⠀⠀⠑⢄⠈⢦⠀⠀⠱⣄⠡⠀⠈⢄⠛⡐⠁⠃⡠⠊⠀⠌⡸⠁⣠⠏⠀⢹⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠐⠲⡤⣍⠀⠀⠀⠘⡆⠑⠀⠈⣤⠁⠀⠞⠀⠀⠌⣰⠵⠚⢁⡄⠀⣼⠀⠀⡠⢊⡾
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠉⠢⡀⠀⢸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡁⠔⠂⡑⠀⣰⠃⠀⠨⠐⣉⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⢆⠹⡄⡞⠠⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⡎⢀⡔⠁⣠⢀⡴⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠂⠛⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡞⣰⢾⢃⡎⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠘⡀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⡿⢨⢸⣼⠰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢁⠈⡄⠁⠁⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠀⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠀⠀⣀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠨⠀⠄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠠⠊⠁⠀⠈⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣳⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠉⢻⣿⡿⠿⠛⠻⠿⣿⣿⠉⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣤⣨⠋⠀⠀⠀⠀⠀⠈⢇⣠⣤⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⣠⣶⣶⠀⢰⣶⣦⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⡈⠛⠋⣤⡈⠛⠋⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠟⠛⢫⡀⠀⠉⠁⢀⡼⠛⠟⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⢀⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠻⡏⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠑⢌⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⣀⣽⣴⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠑⢌⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣸⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣧⣀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡒⠒⠒⠒⠒⠒⠠⠤⠄⣀⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠉⠀⢹⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣩⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣀⣠⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⢀⣀⣤⡤⠴⠶⠶⠶⠶⠶⠶⠦⢤⣤⣀⡀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢀⣠⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣠⠞⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⣰⠏⠀⠀⠈⠳⣄⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢻⡄
⠀⠀⠀⠀⢀⡟⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠈⣧
⠀⠀⠀⢰⡇⠀⠀⡿⠀⠀⣤⣤⣤⣀⠀⠀⠀⢠⣤⣬⣷⣄⠀⠀⠙⢷⣄⠀⠀⢀⡄⠀⠀⢀⡴⠶⠦⣄⠀⠀⠀⣠⠴⠶⣤⡀⠀⠀⢿⠀⠀⢸⡆
⠀⠀⠀⣸⠁⠀⢰⡇⠀⠀⡇⠀⠀⠙⢧⠀⠀⢸⡇⠀⠀⠈⢳⣄⠀⠀⠙⢷⣄⢸⡇⠀⢀⡟⠀⠀⠀⢹⡆⠀⣼⠁⠀⠀⠀⠻⠀⠀⢸⡆⠀⠈⣇
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⢀⣼⠋⢷⣄⠀⠀⠙⢾⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢀⡇⠀⢸⡏⠉⢻⡏⠁⠀⠀⣿⢳⣄⠀⠀⠙⢦⣸⡇⠀⠀⣀⣀⡀⠀⠀⠀⠉⠛⢶⣄⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⢹⡄⠀⠸⡇⠀⠀⡇⠀⠀⠀⣸⠃⠀⢸⡇⠀⠀⢻⡄⠀⠀⣿⠀⠙⢷⣄⠀⠀⠙⢧⡀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠀⢹⡆⠀⢸⡇⠀⢀⡏
⠀⠀⠀⠸⡇⠀⠀⣷⠀⠀⣧⣤⣤⠾⠃⠀⠀⢸⡇⠀⠀⠀⢷⠀⠀⠙⢦⣤⣤⠿⢷⣄⠀⠀⠙⢦⣤⠞⠀⠀⠘⢧⣄⣀⣠⠞⠁⠀⣾⠀⠀⢸⠇
⠀⠀⠀⠀⢻⡀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⠀⠀⠀⣰⠇⠀⢀⡟
⠀⠀⠀⠀⠈⣧⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠙⢦⡀⠀⠀⣠⠏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⡴⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠈⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⢀⣰⣷⡄⠀⠀⢀⢰⣧⠀⠀⠀⠀⣾⣧⠀⠀⠀⢀⣼⣧⡄⠀⠀⠀⣾⣄
⠀⠀⢾⠿⡹⣿⠀⠀⢰⣿⣿⣿⠀⠀⢾⠟⠙⣿⠀⠀⢸⣾⣯⡤⠀⠀⢰⣿⣿⡆⠀⠀⣽⡟⠻⣷⠀⠀⣿⠏⢻⣶
⠀⠀⠈⠘⠃⠉⠀⠀⠈⠛⠛⠁⠀⠀⠈⠃⠐⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠐⠃⠉⠀⠀⠈⠀⠀⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣄
⠀⠀⣰⣾⣿⣧⠀⠀⠀⣼⣿⠀⠀⠀⢀⣿⣷⡀⠀⠀⢀⣿⢷⣄⠀⠀⢠⣾⢿⡆⠀⠀⣠⣿⣿⡀⠀⠀⢠⣶⢿⡄
⠀⠀⠻⢿⡽⠟⠀⠀⠰⣿⣿⠟⠀⠀⠸⡏⠘⠟⠀⠀⠸⣧⣆⠟⠀⠀⢸⡇⠸⡇⠀⠀⢻⣿⣿⡟⠀⠀⢸⣣⡌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣰⣷⡄⠀⠀⠀⢰⣦⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⢰⣶⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⣾⣆
⠀⠀⢴⠟⡈⣷⠀⠀⢨⡟⢹⣶⠀⠀⢰⡿⠹⣧⠀⠀⢀⣿⢿⣀⠀⠀⣰⣿⣿⡇⠀⠀⣤⣿⢿⣧⠀⠀⣤⡟⢹⣧
⠀⠀⠘⠚⠃⠋⠀⠀⠘⠃⠀⠋⠀⠀⠘⠃⠀⠃⠀⠀⠈⠃⠈⠃⠀⠀⠘⠻⠿⠋⠀⠀⠙⠋⠈⠋⠀⠀⠙⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡩⠐⠒⠒⠠⣅⣂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢊⡠⡈⠀⠁⠈⠑⠺⢦⣠⡿⠮⣑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢐⡱⠊⠀⡀⣀⡀⠀⠀⠀⠉⠛⠶⣬⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡴⡡⠊⣠⠖⠉⣴⡠⢀⠈⠑⢦⠀⠀⠀⢀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢊⠎⠀⡜⠁⠀⢀⡄⡁⠛⠀⠀⠰⠀⣀⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡔⡁⠁⠀⠘⠀⢠⣄⠈⠛⠰⠂⢀⠔⣡⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⢎⠞⠀⣀⠠⠜⠀⣀⠉⣘⢃⡤⠐⣡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠠⠃⠀⠀⠀⠉⠁⠉⠀⠁⠀⠈⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢉⠭⠤⡔⠒⡖⢤⢴⡟⠁⠀⠀⢀⠎⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣀⣘⣂⣐⣁⣐⣌⣠⠋⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠤⠅⠠⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠩⠍⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⣰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⣀⠠⠄⠊⠀⡐⠂⣰⠧⡐⠀⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⡀⠀⠀⢀⣠⠞⣑⣂⠂⢀⣾⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠘⠀⠉⠁⠈⠀⠀⠀⠁⢠⣟⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⢊⣉⣀⣫⠀⢈⣉⣉⡆⢠⠏⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⡠⣔⠎⠓⢙⣙⣩⡇⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⡉⠄⡴⠋⠉⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⡜⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠔⣠⢎⡔⠀⠀⠀⠀⠘⡀⠀⡀⢄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⣲⣲⣰⣼⣦⣮⣭⣭⣭⣥⣄⠀⠀⣀⣒⣐⠒⠀⢀⠀⣠⠄⠀⠀⠐⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠳⢟⣋⠩⠉⠈⠉⠀⠀⠀⠐⡰⡀⠀⡠⢠⡀⠀⠀⢉⠱⠎⠉⠉⠛⠋⠛⠋⠃⠠⠓⠨⠐⠀⠚⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠚⠒⠒⠓⠓⠒⠓⠓⠃⠉⠉

⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠙⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠣⠤⠤⠤⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠠⠄⠀⠐⠀⠉⠍⠀⠀⠀⠐⠀⣆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠉⠀⠀⠀⠈⠀⠣⠀⠀⠀⠀⠀⠀⠀⣀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠐⠘
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⢀⠔⠈⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠠
⠤⠄⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⢀⠄⠀⠠⣄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤⠂⠀⠀⠀⡀⠈
⠠⡀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠐⠈⠁⠀⠐
⠁⠐⠀⠀⠑⢀⣠⠄⠊⠀⠀⠀⢀⠀⠀⡐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠐⡀⠀⠀⠀⢠⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠀⠒⠋⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⣀⡀⠀⠀⠀⠀⠐
⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠠⠎⠁⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠐⠤⠀⢀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⠀⠀⠀⠀⠁⠀⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣄⣂⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⠶⠖⠛⠛⠋⠉⠉⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⢷⡀⠀⢸⡇⠀⠀⠀⢀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⢻⡄⠈⣇⠀⢼⣁⡟⢹⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⢻⠀⣿⠀⠀⠉⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠶⠿⠶⠶⠶⠶⠶⠶⠾⢧⣄⡀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞⠋⠙⠛⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⠤⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢀⣠⡤⠖⠚⠛⠉⠉⠉⠉⠉⠉⠛⠓⠲⢤⣄⡀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡶⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠙⢦
⠀⠀⠀⠀⠀⡼⠁⠀⣰⠋⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢧
⠀⠀⠀⠀⣼⠁⠀⣰⠃⠀⠀⠀⠀⠈⠹⣆⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⣧
⠀⠀⠀⢰⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠸⡆
⠀⠀⠀⣼⠀⠀⣾⠀⠀⡶⠶⠦⣄⠀⠀⢠⡶⠾⠷⣄⠀⠀⠙⢦⡀⠀⢰⡄⠀⢀⡶⠛⠓⢦⠀⠀⣠⠖⠛⠲⣄⠀⠀⣷⠀⠀⣷
⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠘⣆⠀⢸⡇⠀⠀⠈⣷⣄⠀⠀⠙⢦⣸⡇⠀⣾⠀⠀⠀⠸⠇⠀⣇⠀⠀⠀⠈⠀⠀⢸⠀⠀⢹
⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⣿⠀⢸⡧⠤⣤⠶⠃⠈⢳⣄⠀⠀⠙⢧⡀⣿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⢸⡃⠀⢸
⠀⠀⠀⣇⠀⠀⡇⠀⠀⡇⠀⠀⠀⡿⠀⢸⡇⠀⠹⣆⠀⠀⢾⠈⠳⣄⠀⠀⠙⢿⡀⠀⠘⢻⡆⠀⠀⠀⠀⠈⢳⡄⠀⢸⠀⠀⣸
⠀⠀⠀⢻⠀⠀⢿⠀⠀⣇⣀⣠⡾⠁⠀⢸⡇⠀⠀⠹⡄⠀⠘⣆⣀⣈⡷⣄⠀⠀⠙⢦⣀⡼⠁⠀⢲⣄⠀⢀⣼⠃⠀⡿⠀⠀⡟
⠀⠀⠀⠘⡇⠀⠘⣆⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠈⠳⣄⠀⠀⠙⣦⡀⠀⠀⠈⠉⠉⠀⠀⢰⠃⠀⢰⠃
⠀⠀⠀⠀⢻⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⢠⠏⠀⢠⡟
⠀⠀⠀⠀⠀⢳⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄⠀⠀⣠⠏⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⠶⠃⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠙⠓⠦⢤⣤⣀⣀⣀⣀⣀⣀⣤⡤⠴⠒⠋⠁⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠚⠛⠋⠉⠁

⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⠒⡄
⠀⠻⣶⣌⣿⣠⣶⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠞⠀⠘⠷⠶⠀⠀⠀⠀⢀⠙⣿⡗⢁⡀
⠠⣤⣤⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠉⠑⣤⡔⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠏⠀⠈⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⢀⡠⣤⡄⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒
⠀⠀⢰⣦⣤⣤⣤⡄⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣽⠿⣯⣷⣿



⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⣦⡄⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⡄
⠀⠀⢳⣤⣿⣦⣀⠀⠀⠀⠀⠀⠀⠈⢹⡟⢁⣤⡀⠀⠀⠀⠀⠚⠙⣿⠙⠃⠀⠀⠀⠀⢠⣧⡄⢸⠀⣤⣧
⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣸⣧⡈⠉⠁⠀⠀⠀⠀⢠⠞⠉⠣⠔⠃⠀⠀⠀⠈⣿⡇⢸⠀⣻⡟
⣶⣶⠶⠾⣿⣿⣦⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣾⣶⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢀⣀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⣦⣄⣈⠒⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠆
⠀⠀⠀⠀⢈⣰⣦⣀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⠆
⠀⠀⠀⡠⠚⠋⡙⠛⠓⠤⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧
⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⢠
⠀⣷⠀⣶⣤⣤⡀⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⡇⠀⠀⠀⠀⠸
⠀⠸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⣿⣿⣄⠀⠀⠀⡄
⠀⠀⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡾⠋⠀⠈⠉⠁⠀⠀⡇
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣱⡿⠁
⠘⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣱⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⢀⣁⢠⣽⣿⣦⣀⠀⠀⠀⠀⣠⢟⡴⠋⠀⠀⠉⠁⠀⠀⠀⣠⣐⢾⡏
⠀⠀⠀⢀⡔⢛⡵⠋⠱⡙⣿⣿⣷⣦⣀⠀⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⡊⣠⠏⠀⠀⠀⠘⢮⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⣀⣤⠴⠶⠒⠒⠀⠸⣧
⠀⡾⠛⣇⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣤⣴⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠹⣧⡀
⢰⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡞⠓⠒
⠘⣶⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠂⣔
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡷⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⣸⠟
⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠸⡿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠙⣿⣿⣿⡗⠁⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡄
⠀⠙⣄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⣹⣿⠙⠇⠡⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠈⢿⣦
⠀⠀⢈⡿⠋⠀⠂⠤⣤⡀⠒⠀⠀⠀⠀⠀⠀⣿⠿⡇⠀⠀⠱⠀⠀⠘⠷⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠙⠒⠤⠄⣠⣭⣵⣆⣀⣀⣀⣀⡀⠀⠛⠄⠹⠄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣾⣾⣿⡿⢦⣄⣀⢀⠀⣀⣀⣢⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⣷⣿⣷⡿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣶⣾⣷⣾
⣿⣿⣿⣀⣀⣠⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⡰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢄⠀⠀⡆⠀⠀⠀⠀⠀⢀⡄⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⣠⡤⢠⠀⠃⠀⣘⠀⢀⡏⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⠦⠂⢠⠊⡜⠁⠈⠀⢡⡀⠘⠦⠚⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⢧⣀⠄⠀⠀⡇⠀⢀⢻⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸⣆⠀⠀⠇⠀⠀⠀⠀⢰⡥⠔⠁⡸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⡌⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⢃⠀⠈⠓⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⠟⣠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢀⡈⠑⠊⠿⣶⣲⠤⠶⠦⠖⠶⠭⠐⠋⠁⠀⠒⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠂⠀⠀⠩⣒⡦⢤⣀⡈⢉⠥⠔⠒⠈⠁⠀⡀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⣄⣀⠀⢀⠀⠀⠐⠊⠉⠀⠀⠀⠠⠂⢀⡀⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠚⣁⠄⠀⢀⡀⠠⠀⠀⡀⠀⠒⠊⠉⣁⠒⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⡰⢚⡑⢂⠀⠀⠀⠀⣀⡠⠤⠒⠊⠁⠤⢀⣐⡦⠤⢀⠀⠀⠀⢀⠞⠩⣁⢀
⠀⠀⠀⠀⠀⠀⠳⣎⣁⣾⠠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡀⢸⠀⠄⣰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣿⠀⠀⣠⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⡿⢿⡆
⠀⠀⠀⠀⠈⠛⠛⠉⠉⡆⣼⣿⣿⡄⠀⠀⠀⠀⠀⠹⣷⣄⢸⣿⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠠⣶⣶⣶⠆⠀⠀⠀⠀⠀⣀⠻⢶⣟⣦⠾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⣿⠿⠃⠀⠀⠀⠀⠐⠲⣾⣿⣮⢣⣿⣷⠶⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠛⠲⣮⣩⣭⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠸⠃⠀⠀⠀⠀⠀⠀⠐⠶⠛⠉⠀⠈⠙⠳⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⣠⡀⢿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢙⡿⠋
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠟⠻⠃⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⡎⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠁⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠣⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠂⣀⢀⡀⡀⢀⠀⡀⠅⠀⠀⠀⠀⠀⣶⠿⠋⢉⣥⣼⠇
⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠁⠁⠀⢹⠀⠀⠀⠀⠀⠀⡀⠉⠈⠁⠉⠈⠁⠉⡀⠀⠀⠀⠀⠀⠹⡶⠟⠛⠉⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠉⢉⣀⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⢀⠛⠘⠃⠛⠘⠃⠛⠄⠀⠀⠀⠀⠀⠀⠀⣴⣦⡾⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠈⣿⢉⣠⠴⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣄⣀⣠⠄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢠⡀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣷⠈⣡⣤⡄⠀⠀⠀⠀⠀⢸⠀⠀⡿⢿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⠇⠀⡿⠉⠈⢳⠀⠀⠀⠀⢸⠀⠀⣇⠀⢸⠃⠀⢸
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠤⠴⠎⠀⠀⠀⠀⢸⢀⣤⣿⣤⣼⣦⣄⢸
⠀⠀⠀⠀⠀⠀⠈⠩⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠋⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⡇⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠃⠀⢀⣾⠟⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣌⠀⠀⣠⣿⡏⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣠⡾⢻⡿⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⣾⡿⣡⣿⣧⠆⠘⠁⢸⣿⠀⡀⠀⠷⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣟⣵⣿⣿⣇⠀⠀⣠⡾⣿⣿⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣦⡾⣽⣿⣹⣟⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣾⡟⣱⣿⣿⣿⣿⡟⣱⣿⣿⣧⠻⣯⠜⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⢣⣿⡟⣼⢿⣯⣿⣿⣽⢣⠟⣿⣿⠹⣦⠙⢧⣀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡀⡆⢸⣿⠃⣿⡿⢰⡟⣿⡿⣿⣿⣏⠸⡆⢸⣿⣿⣿⡄⡈⢻⣧⡈⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣼⣿⡇⣿⢱⣿⣿⣿⣿⡿⠇⠁⣾⡈⣿⣿⣧⢰⡀⢻⣿⣆⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⠀⢿⣰⡇⡿⠁⣘⡇⢀⣼⣿⠇⢸⢻⣿⢸⡇⠀⣿⣿⠆⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⢻⣿⣿⣀⢸⣿⡇⠀⠀⣧⣷⠘⢿⡏⠀⣿⢹⡏⣸⣇⡀⢸⣿⡇⠀⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⣿⣿⣿⣌⣿⣧⣀⠀⠻⣿⠆⠈⣿⣰⢃⡾⢡⣿⣿⡁⢸⣿⡇⠀⣿⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠻⣿⡿⠿⣧⣼⡻⣷⡄⠉⠀⣰⣯⣿⡾⢡⡞⢹⣿⠁⣸⣿⡇⠀⣿⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣙⠓⠪⡿⠶⣿⣷⣿⣮⡻⣦⣬⣿⡿⠋⠐⠋⠀⣼⠟⣰⣿⡿⠁⢠⡏⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢽⣿⣿⣿⣷⣬⣉⠉⠁⠀⠀⠴⠊⣅⣼⣿⠋⠀⢠⠟⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡏⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⠟⢀⡴⢋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣿⣿⣿⣿⣿⣿⠿⢛⣋⣤⠶⠋⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣷⠶⣿⠶⠶⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡟⠿⡿⠛⡿⠿⣿⠿⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣾⣶⣷⣶⣿⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠶⠰⠆⠠⠄⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⢀⡀⣠⠀⠤⠠⣄⢀⡀⠀⠉⠐⠆⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢠⠔⠚⠈⠀⢀⣀⣀⣀⡀⠀⠀⠙⠂⠀⢀⠔⠁⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡀⠚⠀⣀⠴⠚⠉⠉⠁⠀⣈⣁⣀⢀⡤⠖⢲⠁⠠⠀⠣⠼
⠀⠀⠀⠀⠀⠀⡘⠁⢀⡌⠁⢠⠞⠁⠀⠀⠀⠀⣠⢾⠉⢣⡈⠻⣄⣠⠏⠀⠀⠘⣂⠀⠉⡄
⠀⠀⠀⠀⠀⣈⠁⠀⠖⠀⣰⠃⠀⠀⠀⠀⣠⢾⡙⣆⠳⣄⠙⢦⡀⢳⠀⠀⣆⠀⠈⣄⠀⢡
⠀⠀⠀⠀⠀⡅⠀⠸⠀⢰⠇⠀⠀⠀⣠⢾⠙⣆⠳⣌⠑⠀⠀⠀⢈⠟⠀⠀⠸⡄⠀⢨⡀⠀⠆
⠀⠀⠀⠀⢠⡄⠀⡋⠀⠈⠀⠀⢠⠔⠙⣄⠳⢌⠓⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡇⠀⠀⡆⠀⠲
⠀⠀⠀⠀⠰⠆⠀⣃⠀⠀⠘⣞⠉⢦⡀⢌⠓⠀⠀⠀⢀⠔⣁⡤⠤⠶⠤⢄⡀⠃⠀⠀⠆⠀⠛
⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⣸⢦⡀⠑⢦⡱⣄⢠⠔⢁⡜⢁⡴⠚⠛⠒⢤⠙⢦⠀⠐⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⠞⣡⠞⢙⠦⣀⣉⠟⠁⠀⣸⠀⡞⠀⡀⠀⡀⠈⡇⠘⡆⠀⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡈⢧⡘⢁⠔⠁⠀⠀⠙⠂⠀⠀⢸⡀⢹⠿⠽⣛⠭⢿⡇⢰⠇⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⢳⠀⠈⠙⠢⢤⣄⣀⣀⣀⠳⣌⠉⠧⠤⠞⢉⡤⠋⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠛⠉⢀⡤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠄⣀⠀⠈⠁⠘⠃⠛⠁⠉⠀⢀⡀⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠒⠂⠒⠐⠒⠐⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢤⣀⡞⠀⠈⢳⡀⡴⠚⠒⢦
⠀⠀⠀⢠⠎⠉⢢⡞⠁⠙⡦⠒⠲⣄⠀⠀⠀⠀⠀⢠⡟⠉⠉⢻⡆⠀⠀⠀⢰⡇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠁⠀⠀⠀⢣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⡄⠀⠀⠘⢷⣤⣤⠟⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢉⡤⠦⠄⠀⡄⠀⢠⠀⣠⣤⣤⠀⢰⣦⠀⠀⣴⠲⢤⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⣇⣀⣸⠀⣿⠀⠀⠀⣸⠘⣇⠀⣿⠀⣸⠇⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⡏⠉⢹⠀⣿⠓⠀⠀⣿⣤⣿⠀⢸⠛⠁⠀⠀⠀⠀⢀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠦⣤⡄⠀⠇⠀⠸⠀⣿⣠⣤⠀⡇⠀⠸⠇⠸⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣤⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⢰⠶⠄⢠⡀⠀⡤⠀⡶⢤⡀⢰⠶⠦⠀⣄⠀⢠⡄⢠⠶⠀⢰⡆⢠⠀⠀⡤⢠⡶⠆⠀⠀⣿
⠀⠀⠀⠠⣾⡋⠀⠀⠀⠀⢸⣀⡀⠀⢳⡾⠁⠀⣇⣀⡷⢸⣤⠄⠀⣿⡄⢸⡇⠸⣄⠀⢸⡇⢸⡀⢰⠇⢸⣇⡀⠀⠀⣿
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢾⠉⠁⠀⡼⢳⡄⠀⣏⠉⠀⢹⠀⠀⠀⣧⠹⣼⡇⠀⠘⡇⢸⡇⠈⣇⣾⠀⢸⡏⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠿⠤⠦⠸⠃⠀⠛⠀⠋⠀⠀⠘⠒⠒⠀⠛⠀⠘⠃⠐⠚⠁⠘⠇⠀⠘⠇⠀⠸⠧⠤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠦⣄⠈⢷⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠻⣎⠻⣦⣀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠸⣆⠀⠀⠀⠀⢹⡆⠈⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⣦⠀⠹⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠁⠀⠘⣇⠀⠘⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡀⢀⡾⠃⠀⠀⠀⠘⢧⣀⣸⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⣇⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡼⠃⣾⡁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢦⡀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⠀⠀⠈⠻⢦⣄⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠹⣦⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠀⠀⠈⠉⢿⠓⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡟⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠃⠀⠀⠀⠀⣠⠞⣿⠇⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⡆⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⠞⠁⠀⢀⣤⠶⠛⠁⣠⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⡇⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠐⣇⠀⣤⠞⠋⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡇⢸⡇⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡀⠀⡼⠃⠀⢀⡼⠁⢸⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⡄⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⡇⠊⠀⠀⠀⣾⠤⠒⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⡄⠀⠰⠾⣡⣶⣟⣯⣤⣦⠀⠀⠈⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣦⡀⠀⠀⠀⠀⢀⡀⠛⢿⣷⣦⣤⣠⣴⣿⣷⣿⣿⠟⠃⠀⠄⠀⠂⠈⢁⣤⣶⡆⠀⠀⠀⠀⠀⣠⡟⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠶⠾⠿⣶⣤⡀⠰⠄⠠⣤⠄⢈⣩⣥⣾⠿⠿⠛⢉⣤⣄⡀⠰⣶⡿⠿⣿⣛⡉⣁⡀⠀⠀⢀⣤⡾⠛⠛⠛⠛⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠛⠛⠋⠉⠉⢛⣿⣶⣦⣤⣤⣿⡿⠛⠿⣶⣶⣦⣬⣽⣿⣿⣿⣶⣄⠈⠙⠛⣛⣩⣷⡶⢾⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⠶⠶⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⣿⡿⠿⢿⣿⣿⣛⣛⣻⣛⡻⠿⢿⣶⡶⠶⠦⠬⣭⡉⠛⠛⠓⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠋⢁⣚⡯⠟⠛⠉⣀⣤⣄⠀⠀⠀⠉⠁⠉⠉⠙⠒⠲⠤⣀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣻⣅⣤⡤⠶⠚⠋⠉⠁⠀⠰⠞⠛⣁⣀⣘⠛⠉⠙⠛⠒⠒⢦⣤⣤⣤⡶⠒⠾⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠋⠉
⣀⡀⣀⣀⡀⣀⣀⣀⢀⣀⢀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠖⢀⠀⠀⠀⠀⠀⠈⠁⠀⠻⣾⣿⣦⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣷⣿⠀⠀⠀⠀⠈⠁⣤⡀⠰⢷⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⠀⠀⠀⠀⠀⠀⠀⠉⣲⣤⡤⠶⠾⠇⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠆⠘⠟⠋⠁⠀⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠷⡄⠀⠠⠄⢀⣤⡀⠀⠀⠀⠘⠃⠈⠀⠀⡄⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣾⠶⣃⠀⠀⠀⣈⠋⠀⠰⠆⠀⠀⠀⢀⣄⠀⢀⡀⠀⠀⠀⢀⠴⣶⣄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠋⠘⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⢿⡟⠀⠀⠀⠻⣶⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⢨⡕⠶⢌⡁⢀⠀⣴⡄⢠⣾⡟⠓⡀⠀⠀⠀⠀⠐⠰⠆⠘⠦⠌⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠀⢶⠀⠀⢀⠀⡅⠙⠁⠦⢀⠀⠡⠼⢶⣥⠀⠀⠀⠀⠐⠆⠘⠲⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠿⠛⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣤⡈⠅⣤⡐⠊⠀⣤⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠣⡀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⠀⠀⠉⠀⠤⠀⢠⡄⠀⠀⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠦⣤⣤⡶⠚⠛⢦⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣷⣬⣿⡶⠆⠁⢀⡀⢀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠘⢿⣷⡄⠀⠀⠙⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏⣀⠿⡆⠛⠁⠀⠆⠀⠴
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠈⠳⣄⠙⢄⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣟⣀⡁⠀⠘
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠳⣄⠑⢄⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣍⠋⠄⠀⠁
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠈⢷⣄⠳⣄⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡛⠃⡀
⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠙⢷⣌⠳⣄⣤⠶⠛⢉⣿⣿⣿⡇⣶⠄⢀⠈
⠀⠀⣧⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠹⣷⡇⠀⠀⠀⢸⣿⣿⣿⡆⠻⠀⠉⠁
⠀⠀⠹⣄⠀⠈⠓⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⡆⠀⢀⣠⠬⠟⠀⠀⢀⣼⣿⡿⢡⠀⠀⠀⠁
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠁⠀⠸⠟⠋⠉⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣾⣿⣶⣿⣿⣷⣾⣿⣦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠿⣛⣩⣭⣴⠶⠶⢶⣤⣭⣙⡻⢿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⢋⣵⠾⣋⣭⣶⣶⣾⣿⣶⣶⣦⣍⡛⢷⣌⡻⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣴⢟⣵⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣷⣝⢷⣌⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⡾⢣⣿⡏⣿⡏⣿⡏⣯⢋⡏⣿⡏⡏⠤⢹⡙⣹⣧⡹⣇⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣼⣣⣿⣿⣧⣭⣷⣬⣵⣧⣦⣷⣬⣴⣧⣿⣼⣧⣿⣿⣧⢹⡆⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣥⣴⣶⣶⣶⣬⣭⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⠙⣃⣙⢉⣿⡌⣧⢹⣿⡆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⢛⣛⢻⣿⡿⢟⠿⣿⣿⣷⣦⣭⣙⡻⠿⣧⣭⣥⣾⣿⠇⡿⢸⣯⠸⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⢇⣿⢈⣋⢰⡏⣼⣿⣷⢸⡏⣶⣬⢻⣿⣿⣿⣶⣦⣭⣭⣉⣚⣃⣛⣛⣁⣂⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⣿⣿⣿⣸⣿⣿⣼⣿⣾⣿⣮⣝⣥⣾⡇⠿⠟⣸⡇⣿⣿⠀⣿⢟⣛⡻⣿⠿⠿⣿⣿⣿⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⡿⠿⠟⣛⣛⠛⣛⣛⡻⠿⠿⣿⣿⣿⣿⣿⣧⡙⠟⣡⣇⢿⣿⣿⣿⣿⢰⣿⣿⣿⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣉⡲⠾⣿⡄⠿⠿⣷⣝⠿⣬⡛⠿⣶⣮⣍⣛⠶⢭⣙⡛⠿⣿⣶⣭⣴⣿⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠀⠀⢻⡿⠿⣦⣍⣛⠲⠶⠮⠽⠿⠷⢆⣉⣙⡛⠶⠮⠭⣭⣭⣭⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⢻⣿⡿⠻⣿⡿⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⡙⢿⣷⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⠀⢹⣿⣿⣷⡌⣿⡆⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⣦⠀⠀⠀⠀⠀⣿⣿⣿⡇⠸⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠙⢶⣦⡀⠀⠀⠀⠀⠸⠀⣾⣿⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠋⢻⡀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀⣤⣴⣿⣿⣿⠁⠀⠘⣷⣦⡀⠀⠀⠹⣿⣷⡄⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣆⠀⠀⢿⡇⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⢠⣿⣿⠃⢀⡀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀⠈⠇⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⡏⠀⠈⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡄⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⢀⠄⠀⠠⠂⢀⡀
⠀⠀⠀⠀⠀⠘⠀⢀⠆⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠯⡪⠊⠁
⠀⠀⠀⠀⡀⠀⡀⠚⢄
⠀⠀⠠⠉⠀⠀⠀⠀⠰⠀⢀⡰⠂⠒⠒
⠀⠀⠀⠆⠄⠀⠀⠀⠘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠏⠀⠉⢁⡆⠄
⠀⠀⠀⠋⠒⢲⡇⠐⢄⠀⣰⠧⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⢸⡀⠂
⠀⠀⢠⠂⢀⠚⠃⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⠒⠀⠁⠈⡀⠐⠒⠈⠨⠁⠒⠂
⠀⠀⠀⡈⢀⠄⠁⠀⠀⠐⠦⢄⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢁⣀⠀⠀⠀⠀⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠀⣀⡀⠀⡀⠀⢸⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠠⠄⠀⠶⣁⣠⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄
⠀⠀⠈⠁⠀⣠⠊⠀⠀⠀⠄⠀⡀⡀⡠⠃⡠⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠉⠁⠀⠀⠈
⠀⠀⢀⠁⠹⠁⠀⠀⠀⡀⢠⠄⠀⢅⠀⠀⠀⣉⣠⡂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠒⠁
⠀⠀⡈⠔⠁⠈⠁⠙⡿⡁⠀⢐⣢⠀⠂⡆⠈⡡⠄⢽⠀⡠⠀⢠⠤⠺⣀⣀⠀⠀⢠⣁⣠⠄⠀⠀⠘⠃
⠀⠀⠀⠐⠀⠐⠠⢤⠰⠀⠈⠤⠢⡅⣤⠋⠉⠪⣀⢀⣥⠔⠂⣀⠀⠀⠀⠀⠉⠀⠞⢩⠂⡶⠤⣖⠤⡀⢐⡆
⠀⠀⢀⠗⠀⣀⡀⠀⠀⠀⠀⠀⠴⠆⠈⠢⣔⠮⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠴⠁
⠀⠀⠈⠂⠀⠀⠀⢀⡁⠀⠀⠠⢠⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠻⠁⠀⠀⠘⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠔⡄⠀⠀⢀⡤⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠌⠀⠐⠦⠂⠀⠘⠄⠊⢁⡠⠦⠐⡊⠉⠀⠀⠀⠀⠁⣢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⠠⣀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⢊⡉⠀⠀⠀⠀⢁⣀⠂⢀⠀⠆⠸⠄⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⠔⠀⠀⠘⠀⠉⠐⠆⠑⠤⡀⣄⠈⡆⠀⢡
⠀⠀⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠈⠀⠰⡄⠉⠁⠸⠂⠀⠀⠄⠀⢁⡀⠃⠀⠀⠆
⠀⠀⠀⢀⠀⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠐⠒⠂⠹⠀⠸⠀⡁⣄⣰⠀⠀⠑⠒⠊⢀⣀⣄⠤⠞
⠀⠀⠀⠀⠠⡀⠐⢒⣢⣤⡀⠀⠀⠀⠀⠀⣔⢸⣄⠚⠀⠀⠀⠀⣀⣀⡀⡔⠁⠀⠀⢀⣀⡤⠔⠒⠋⠏⣁⡀
⠀⠀⢀⡀⠤⠃⠀⠘⠋⢀⣿⣤⠤⣤⣤⣄⡁⠀⠈⠳⣄⠀⠀⠀⠀⡀⠈⠤⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠝
⠀⠈⠁⢄⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠈⠳⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣁
⠀⠀⠀⢀⠑⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡖⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠶
⠀⠠⣔⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠳⣜⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁
⠀⢠⠖⠛⠛⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠻⠓⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⢿⡘⠶⠀⠀⠀⠀⠬⠿⠇⠀⠀⢀⣸⠆⠀⢀⣠⣴⣤⣄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠊
⠀⠈⣿⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣴⣿⣿⣿⣿⣿⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⢸⡇⠀⠀⠀⠀⠀⣤⣶⣶⣶⣞⠛⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠉
⠀⠸⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠻⣆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⠁
⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⣸
⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⢤⣤⠤⢶⠶⢞⡻⠫⠀⠀⢀⠤⡀⠀⠀⡜⠢⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⠱⠤⠃⠀⠈⠢⡐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⣐⠒⠊⠉⠉⠍⠭⠅⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠸⠝⠿⠶⠿⣷⡆⠀⣾⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢤⣤⣤⣞⣉⣤⣦⠤⢤⣄⡀⠀⠀⠁⣀⣼⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠥⠂⠀⠀⠀⠀⠢⠶⣦⣄⣀⣈⣉⣁⣀⣈⠅⢀⣨⣞⠕⠋
⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⣤⢖⣀⡀⣀⡀⠀⠀⠀⣈⠩⠟⣉⠥⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⡞⠘⠁⠀⠀⠙⠿⠖⠋⠭⣻⡆⠠⠊⣡⠖⡩⠄
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠪⠭⢑⣒⠤⢄⡈⠁⠠⠁⡼⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠤⢄⡼⢰⠃

⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠐⠀⠤⠀⢀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠠⠄⠒⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠂⠀⠠⠤⠄⢹⣿⣿⣿⣿⢉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠤⠤⠀⠀⠂⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠤⠠⠤⢼⣿⣿⣿⣿⠘⢃⡄⠀⢀⡀⠀⠀⢠⡀⠀⠀⣿⡦⠤⠠⠄⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⣀⣸⣿⣿⣿⣿⠀⠈⠛⠠⡼⣇⠀⠀⢸⣷⠀⠀⣿⣅⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠀⠼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠂⠛⠛⣿⣆⢠⣿⠤⢀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠒⠉⠀⠀⡀⠄⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣼⣿⠄⡀⠀⠈⠐⠂⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣴⣶⣶⣶⣶⣶⣿⡿⠿⠛⢿⣏⡁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠉⠉⠀⠈⠛⢿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣶⣦⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⢤⢻⣿⣿⠧⠔⠀⣸⣿⣿⡿⢻⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⠀⠀⠀⣿⡇⠀⠀⢠⡿⣿⣷⣾⣿⣿⣿⣿⣇⠀⢸⡇
⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣇⠀⢰⣿⣿⠀⠀⣾⣿⣯⣻⣿⣿⣿⣿⣿⣿⡄⢸⡇
⠀⠀⠀⢸⡇⠘⠛⠛⠛⠛⠛⠛⠛⠛⠓⠙⠛⠛⠀⠚⠛⠛⠃⠘⠛⠛⠑⠛⠛⠛⠛⠛⠛⠛⠓⣸⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐⠂⡀
⠀⠀⠀⠀⠀⢀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢸⣿⣷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠌⠷⡄
⠀⠀⠀⣄⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢾⣿⣿⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣛⣛⡛⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⢳
⠀⠀⣀⣼⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡿⣿⣿⣿⡾⣦⣌⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢼⢃⠊
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣾⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣀
⠀⠀⢳⣤⢸⣿⡇⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠺⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⡇
⠀⠀⠲⣿⣿⣿⣿⣿⣥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣿⣆⠻⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢆⣤⡀⠀⠈⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠬⠿⠿⠿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⢀⡀⠀⠀⠀⠀⠀⠀⡁⢀⠇⡰⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠶⢠⠃⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷
⠈⠙⢿⣶⣤⣀⠀⠸⣈⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⣀⣄⡀⠉
⠀⠀⠀⠙⠿⣿⣿⣦⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⠑⠦⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣶⣶⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⣿⣿⡗⠋
⠀⠀⠀⠀⠀⠈⠛⠫⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡁⠫⠢⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣶⢀⣀⡀
⠀⠀⠀⣾⣿⣿⣿⣧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⢉⡉⢉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠢⣢⠈⠩⢢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠸⣯⡾⠃⢾⡏⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠣⡤⡈⠪⠎⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⡎⠻⠞
⠀⠀⠀⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠟⠁

⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠿⢿⣿⠋⣽⠍⢻⣿⣿⣭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⡿⠀⣿⣧⠸⡟⠙⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠿⣿⡙⠄⠸⣿⡀⡇⣠⡿⠋⢘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣟⡿⡀⠛⠑⢨⡿⣄⣴⠟⠉⢋⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⡧⣜⣦⣤⣼⡇⣽⣷⣀⣴⠞⢉⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣼⢸⣿⢾⢷⣿⢻⣿⣏⣴⡿⠋⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⢹⣿⡿⣨⠟⣿⡾⣿⡇⣾⡟⣿⣿⣠⣾⠛⣰⡿⣿⣦⡀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢯⣼⣿⣿⣿⣿⢺⡇⣷⣿⠀⣿⢇⣿⣿⣿⢅⣼⠟⢡⣿⡿⣿⡄⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢞⣵⢋⣬⣭⣵⡿⣿⢸⡇⣿⢹⠀⣿⢸⣿⢹⣿⣾⣿⣤⣿⠏⣰⣿⣿⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⣫⡾⠛⣉⣩⣥⣦⢸⡏⣧⢹⣸⡄⣿⣿⣇⣿⡿⢻⣿⢸⣯⣰⣿⣿⣿⣇⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⡾⠋⠚⠛⠛⠉⠉⢻⡟⡇⣿⡸⣿⣿⣿⣿⣹⣿⢡⣿⣿⢸⣿⣹⣾⣿⡏⣼⠃⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡹⢻⣿⣿⣿⣿⣿⡿⢿⠇⣼⢠⡇⢸⣇⣽⣿⣿⢇⣿⡿⣼⣿⡏⣿⣿⡏⣿⣿⣿⣿⣶⣾⣼⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢋⣁⣠⣤⣤⠶⣶⢸⡇⣸⣇⣼⡿⢿⣿⢏⣼⣿⢣⣿⣿⢳⣿⣿⡇⣿⣷⣷⠹⣯⢷⣻⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⠟⠛⣫⣁⡶⣿⡼⠧⠛⠉⡷⣾⡿⢫⣾⡿⢃⣾⣿⣿⢸⣿⣿⡇⣿⣿⢿⣧⣿⡞⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣀⣠⣭⡿⠟⠋⠁⠀⠀⠀⠀⢳⣌⣴⣿⠟⣡⣾⣿⣿⠇⣸⣿⣿⡇⣿⣿⡜⠃⣿⣷⢹⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡉⣁⣴⣿⣿⡿⢃⣼⣿⣿⣿⡇⢸⣿⣷⠈⣿⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠟⠉⢠⣾⣿⡿⢃⣿⣷⢸⣿⣿⡆⣿⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⢠⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⣴⣿⣿⠏⣠⣾⣿⣿⠈⣿⣿⡇⢸⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⣴⣶⣶⣼⣥⣤⣧⣄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⣶⣿⠟⠋⣡⣾⣿⣿⡿⠃⣸⣿⣿⡇⣼⣿⢻⣿
⠀⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠘⢿⡋⢠⣾⣿⠟⠋⢁⣠⣴⣿⣿⡿⠀⣿⣿⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢻⣧⡀⠹⡿⠟⢁⣴⣿⣿⣿⣿⣿⠟⠁⣼⣿⡏⢸⣿
⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠙⢿⣦⣀⣰⣾⣿⡿⠟⠋⠉⠁⢀⣼⣿⠏⣠⣿⣿
⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠉⣿⡿⠋⠁⠀⠀⣠⣴⣾⣿⠟⢁⣴⣿⢿⣿
⠀⣿⣇⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣙⣷⣄⣀⣀⣀⣀⣠⣾⣿⣛⣋⣁⣠⣿⣛⣁⣸⣿
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠥⣏⣳⢾⣹⢶⣏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⡀⣈⠀⣀⣁⣀⣉⡀⢀⣀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠸⠼⠻⠧⠇⠼⠸⠤⠄⠏⠠⠇⠧⠼⠸⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡏⣷⣴⣿⡮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢄⠀⢹⣏⠁⢀⠿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡐⠊⠁⣱⡄⠁⣼⢸⡄⠁⣔⠁⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣥⣠⡾⠛⠋⠉⠋⠙⠋⠉⠋⠀⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢏⠈⢀⣤⣶⢶⡦⡀⠀⠀⠀⠦⣀⣴⣲⣀⠔⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⣿⣫⣿⢞⣿⠀⠀⢀⣔⣓⣒⡒⠒⠓⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠽⣫⣽⣶⣷⠝⠀⠀⢸⡧⠄⠦⠤⠢⢽⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⣀⣀⣀⣀⣈⣉⣉⡳⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠿⠷⢤⡾⢦⠿⢿⡇⡀⠀⡠⢺⣟⠒⠒⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣉⣉⣉⣉⣉⣉⣉⡹⠙⠞⠁⠸⣜⣭⣭⣭⣭⣟⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣿⠿⣿⣿⣿⣿⢿⣿⣿⣷⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣨⣿⣿⣽⣙⣱⣽⣿⣿⣿⣍⣉⣱⣿⣿⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁