Mould Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⡃
⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⢸⣿
⠀⢀⢀⣐⣐⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠇⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠂⠀⠁⡄
⠰⠀⠔⠀⠸⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⢨⣇⠀⠀⠀⢀⡢⠃
⠀⠈⠒⠄⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠈⢤⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡏⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⢰⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢁⠒⣄⠏⠀⡌⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠆⠐⢲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⡈⠙⠀⠶⢁⠀⠀⠁⢱⠄⠀⠀⠀⠦⠤⠄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⣁⣀⣀⠀⠀⠀⠀⠀⠠⠀⠄⣨⠐⠡⠎⠀⠀⠀⠂⠀⣄⢀⡀⠀⠀⠉⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠉⠛⠋⠓⠻⠤⡤⠤⠴⠺⢴⣞⠉⠉⠑⠒⢁⠀⠐⠈⠉⠦⣀⠀⠀⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠲⢉⠁⠀⠀⠈⠀⠀⠐⣢⠁⠀⠀⠀⢆⠏⠉⠙⠀⠀⠀⠈⠐⠒⠐⠒
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠋⠀⢁⠖⠒⠓⠲⠂⠀⠀⢀⠀⠀⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠉⠃⠀⡀⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠔⠀⡠⠄⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀
⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣬⠐⠀⠀⠀⠠⠤⠂⠀⠀⠀⢠⠖⡆⢹⡟
⠀⠀⠀⠀⢀⠀⠁⡘⠈⠀⠂⣀⠐⠁⠀⠀⠀⠀⠣⠋⠀⠀⠉⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠙⣾⣷⣀⡀⠈
⠀⠈⠀⠖⠂⠙⠒⠓⣷⣶⡏⠁⠀⠀⠀⠀⠶⠂⠀⡀⠀⠀⣠⡅⠀⠀⠀⠂⠀⢀⣀⠄⠀⠀⢁⣾⡏⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢘⣿⢿⠂⢸⣾⢋⣄⠹⠇
⠀⠀⣤⠀⠁⠀⠀⠚⣿⣿⠳⡾⠃⠀⠀⠀⡀⠀⠸⣦⡗⠀⠀⢀⣀⣠⣤⣖⣿⡽⣼⣆⣣⣀⡾⣛⠀⠀⠀⠀⣤⠀⠀⠳⠀⠀⠀⠸⣿⡔⠀⠈⠻⣿⣁⡄
⠀⠀⢀⠀⠘⠀⠀⢰⡟⣃⠀⠂⠰⠆⠀⢰⣿⠆⠀⡖⣌⢟⡯⢋⣉⣹⣾⣿⣿⢿⣿⣾⣿⣿⣷⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⠈⠠⢄⠀⠀⠉⠉⠁
⠀⠀⠀⡀⠀⢀⡤⠚⢉⠝⠀⢀⣴⣄⠀⠀⠉⣠⣼⡶⣿⣆⢻⣾⣿⢿⣿⣿⣿⣽⣿⣿⡞⡅⢿⡭⠀⠀⠀⢠⣿⡦⠀⠀⠀⠀⠠⡀⠀⠀⠀⠃⠀⠀⠀⠴⣢
⠀⠀⠡⡿⡧⠉⠀⠀⠊⠀⠠⠼⠿⠏⠑⠀⠀⢃⢸⠑⠈⠝⣦⣭⣿⣾⣿⣿⣿⡿⣿⣿⣷⣷⣿⣿⡄⠀⠀⠀⠘⠀⠀⠀⢀⡀⠐⣁⡴⠀⣜⠀⠀⠀⠀⠙⡇
⠀⠀⠀⣴⣱⣦⣤⠄⠤⠀⢀⣀⠀⠀⠀⠠⠤⠉⠳⠤⠄⢿⣟⡻⣿⣷⣿⣿⣿⡀⣨⣿⣿⣿⣿⡿⠷⠄⠀⠀⢀⣴⣤⠀⠀⢹⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠈⠁⠁⠀⠀⠀⠀⠚⠹⠀⠀⠀⠀⠠⠚⠓⠓⣿⣿⣿⣽⡟⠨⢾⣽⣻⣿⣿⣿⣿⣿⡟⢃⠀⢀⠀⠀⠀⠉⠁⠀⠀⠀⠙⢷⣶⣤⠔⣑⣖⠲⠀⠀⠿⡅
⠀⠀⠀⠀⠈⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢲⣄⣠⣾⣟⣳⣿⣿⣿⠇⠛⣿⣥⠀⢸⠿⡿⣷⣉⣞⣤⠂⠀⠊⠀⠀⠀⠀⣀⠀⢀⡀⠉⠁⠀⠀⠀⠄⢀⠀⠄⣤
⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⣽⣹⡟⢻⣏⠀⠸⣾⠀⣽⣥⣿⣿⡇⢹⣟⣻⠙⠏⠑⢤⣀⣠⡶⠀⠀⢈⣰⣿⢷⡄⡇⠀⢢⢠⠆⠀⢐⢰⠈
⠀⣰⣿⣿⣿⣿⣿⡆⠀⠠⡾⠛⠈⡆⠀⠀⠀⠀⠩⢛⣿⣾⠿⢠⣠⣟⣡⣵⣶⣿⣿⣷⣾⣿⡟⠀⠀⠀⠀⠉⠹⠇⠀⠀⢰⣻⣿⣾⡃⠇⠀⠘⠘⠅⢠⢸
⠀⠈⠛⠛⡟⠛⠋⠁⠀⢹⢷⡔⠒⠍⠀⠀⠀⠀⠀⠀⢻⣲⣾⣿⡿⣿⣯⣼⢾⣿⣿⣿⡿⡟⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⢨⡿⣬⣟⣁⠀⠀⢀⠠
⠀⠀⠀⢀⣅⣀⠀⠀⠀⡿⢬⣄⠀⠁⠀⠀⠈⠀⠀⠀⠀⢸⡿⢿⣿⠻⢡⠃⡾⣿⣿⣿⡾⠓⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⡇⠐⠀⠠⠀⠂
⠀⢀⠞⣙⡁⠉⠁⡀⠈⠁⠨⡷⢣⠀⠀⣴⣆⠀⠀⠀⠀⠀⣳⣘⣿⣤⣿⡾⠠⣟⡇⣿⣀⢹⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠃⠠⣤⡄⠠⠀⢠⠄
⠀⢸⣷⡶⢮⡀⡈⠃⠀⠀⠀⠁⠀⠀⠀⠩⠉⠀⠀⠀⠀⠠⠿⠙⠻⠏⠙⠳⡦⢿⣿⣟⠛⠉⠉⠉⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠙⠓⠚⠛⠃⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣶⠷⣿⡏⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣴⣶⣶⠿⠿⠿⠋⠀⠀⣿⡆⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣠⣴⣦⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⣀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠀⢀⣿⠇⢸⡟⢻⠀⠀⠀⣉⣴⣿⣿⡿⠀⠀⠀⠀⠀⠁⠀⠀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠻⡟⠀⠘⣡⡶⠶⠾⠟⠛⢿⣿⣿⣄⣀⠀⠀⢀⣀⣠⡄⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢇⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣾⣿⡿⠉⢢
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣨⣿⡿⠁⠀⢈⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⢹⣟
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⣿⠃⠀⡀⣾⣧
⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀⢳⢘⣿⡀
⠀⠀⠀⠿⣿⡟⠁⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⠏⠀⠀⠀⠻⠿⡇
⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠀⢤⡠⣄⣀⣀⢀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⢰⣇⡂⠀⠁
⠀⠀⠀⠀⠀⠀⢃⢻⣏
⠀⠀⠀⠀⠀⠰⡟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡈⣹⠁⣦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠒⢀
⠀⠀⠀⠀⠀⠀⠓⠃⡸⢿⣆⢠⠀⣂⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠉⢈⠻⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡶⠁
⠀⠀⠀⠀⠀⠀⠀⣜⠀⠂⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢩⣇⡈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡻⡣⢀⣬⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣯⡗⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⢄⣀⡠⡠⢀⣀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠻⣟⣥⢔⠶⠂⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢾⠀⣮⢄⣭⣠⡅⢀⠀⠑⢀⡀⠀⠀⠀⠀⢉⢻⣿⣧⣴⣧⣤⣤⣴⣦⣴⣒⡛⣪⣵⣶⡿⣿⠋⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠐⢨⣯⡀⡋⢉⢿⡧⣁⠅⣈⣹⣤⢴⠈⢠⠙⡳⣾⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠹⢿⣴⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢧⣽⣞⣡⣆⢰⣧⣈⣦⣿⣿⣿⣹⣎⣾⣦⣭⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠟⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠚⠉⡶⠉⠉⠛⡻⡞⢟⡿⢅⠿⣿⢿⡿⠿⠯⠿⠛⠛⠙⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠸⠀⠐⠁⠐

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠋⢀⣙⡹⣿⣿⣿⣿⣿⣿⣿⣿⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢽⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⣬⠏⢫⣿⣿⣿⣿⡿⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣾⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣇⣳⣻⣿⣿⣻⣿⣿⣿⡿⠿⠛⡛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣯⣽⠟⢋⣯⣿⣿⣧⣿⣿⣾⣷⣭⣭⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣨⣾⣿⣿⣯⣷⣾⣿⣿⣿⣿⣼⣿⣿⣿⣧⣫⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣿⣿⣿⣿⣿⣿⣿⡟⠃⢹⠘⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣯⡿⣯⣿⢿⢿⣿⣿⣿⣿⣇⣦⡞⠗⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠛⡛⠿⣻⡿⠋⣽⡏⣿⡎⠉⠑⠛⢳⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣧⢹⣿⡟⠀⣰⣿⡇⣿⣿⣦⣄⠀⢰⣿⣿⡿⣹⣿⣿⣿⣿⣿⣷⠐⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡟⢠⣿⡀⢀⣿⣿⣟⣘⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣷⣷⣿⣿⣿⡧⢻⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣧⢻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣾⢿⣿⣿⢁⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠇⣿⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣁⣿⢓⣿⣽⣿⣿⣯⣿⡏⠸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣽⢾⣟⣹⣿⣿⣾⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⢻⡇⣾⡟⣻⣟⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠈⣿⡟⢩⣿⣿⣿⡇⣸⡿⢛⣿⣿⣿⠵⢻⡟⣷⢀⣿⣿⣿⣿⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣧⣿⣧⣾⣿⣿⣬⣿⠟⢧⣽⣿⣿⣿⣷⣾⠇⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣦⣯⣭⣬⣾⣿⣯⣤⣴⣾⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣭⣬⣩⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠒⠒⠒⠲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⠒⠀⡲⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠁⠀⠀⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠢⡀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⣀⣼
⠀⡟⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠊⡁⠈⠃⠐⠁⠀⠀⠀⠀⢀⡠⠔⠚⢉⣠⢷⣈⣉⣛⡭⠟⠁
⠀⢧⡀⠀⠀⠉⠓⠤⣀⡀⠀⠀⠐⡅⠈⠀⠀⠘⡆⠀⠀⠀⢀⣠⠴⠚⣁⡤⠴⠚⠉⠀⠀⠈⠁
⠀⠀⠈⠓⠦⣤⣀⠀⠀⠉⠓⠦⣄⡙⠒⠊⠉⢉⣠⠤⠒⠊⣉⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⡀⠉⠓⢶⠊⢉⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠾⠚⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⣠⣄⣈⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⣿⣿⣋⡉⠋⠉⠀⠀⠀⠀⠀⢀⣴⣦⣀⣀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠈⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣭⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠉⠀⠈⠻⣿⣿⣿⣿⡟⠁⠀⠀⠀⢠⣤⣤⣤⠙⢿⣿⣿⡿⢟⣡⣤⣤⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠈⠉⠹⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⢀⣸⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠃⢸⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠦⣄⠀⠀⢀⣀⡀⠀⠀⠀⣴⠿⠷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⣿⢑⠂⣿⠀⣰⠏⣉⢻⡆⠀⠀⢷⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⡟⢉⠉⡇⠉⠻⡟⠁⠀⠻⣄⢈⣼⠇⠀⠀⠀⣿⠁
⠀⠀⠀⣠⣤⣄⠀⠻⣾⡤⠃⠀⢸⠇⣠⣶⣤⡀⣿⠀⠀⠀⠀⢈⡇
⠀⠀⢼⡇⠃⠸⡆⢀⡏⠀⠀⠀⢸⢸⣿⠀⢀⡇⢸⠀⢀⣠⢤⣈⣷
⠀⠀⠘⢿⡦⠛⠀⢸⡇⠀⣠⡶⢻⣤⣹⡷⠞⠁⢾⠀⣾⠀⣧⣹⣧⠀⠀⠀⣠⡾⠗⣲
⠀⠀⠀⢸⠇⠀⠀⢸⡇⢠⠏⠀⣾⠀⠿⣦⠀⠀⣸⠀⠙⠿⣶⠛⢹⠀⠀⠀⢿⡄⢀⣽⠃
⠀⠀⠀⣿⠂⠀⠀⠸⣧⠏⠀⠀⡃⠀⡇⠸⣆⠀⢿⠀⠀⠀⡿⠀⢸⡄⠀⠀⠈⠙⡟
⠀⠀⠀⣿⠀⠀⢀⠾⡇⠀⣠⣤⠇⠀⡇⠀⢻⡄⣿⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⢠⠞⠀⣧⡞⠁⢸⠷⣶⡃⠀⠀⢻⡟⠀⠀⢀⡇⠀⢸⡇⠀⠀⠀⢸⠇
⠀⠀⠀⣿⢠⡟⠀⣰⡞⠀⠀⢸⠀⣹⡇⠀⠀⢠⣇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⣼⠆
⠀⠀⠀⢸⣿⠁⣼⠛⡇⠀⠀⢸⠀⣹⠿⡀⠀⣾⢻⡆⠀⢸⠃⠀⢸⠇⠀⠀⠀⣿
⠀⠀⠀⢸⣿⡴⠇⠀⣿⠀⠀⢸⡇⢸⠀⣷⢀⡟⠀⢷⡀⣾⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣏⣷⠀⠀⣿⠀⠀⠸⡇⢸⡇⠈⣿⠁⠀⣼⠋⠉⠳⠀⣾⠀⠀⠀⢀⣿
⠀⠀⠀⠈⢉⠙⡆⠀⣿⠀⠀⠀⣇⠸⡅⠀⡾⢆⠀⢇⣀⢀⡽⠀⣿⠀⠀⠀⢠⡇
⠀⠀⠀⢀⣿⣰⡇⠀⢹⡄⠀⠀⢹⠀⣦⢀⡇⠈⠣⡀⢹⠃⠀⠀⣿⠀⠀⠀⣸⠃
⠀⠀⠀⢸⣣⣏⠀⠀⢸⡇⠀⠀⢸⠀⢿⣘⠁⠀⠀⠀⣆⠀⠀⠀⡟⠀⠀⠀⣿
⠀⠀⠀⠘⡏⢸⡀⠀⠀⠄⠀⠀⢸⠀⠘⣿⠀⠀⠀⠀⣟⣲⡐⠚⣧⠀⠀⢀⡏
⠀⠀⠀⢠⠃⢘⡇⠀⠀⠇⠀⠀⢸⡀⠀⡇⠀⠀⠀⠐⠸⣇⠂⠀⣹⠂⠀⢸⠇
⠀⠀⠀⢸⠀⠈⡷⡄⠀⡟⠀⠀⢸⡇⢸⡇⠀⠀⠀⢀⡄⠈⠁⣤⠉⠀⢀⡟
⠀⠀⠀⢸⡆⢸⡇⠹⣆⡛⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡅⠀⠀⡟⠀⠀⢸⠃
⠀⠀⠀⠈⣧⢸⠇⠀⠙⣷⠀⠀⢠⡄⢸⣧⠀⠀⠀⠸⡇⠀⢠⡇⠀⠀⡿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠻⣧⠀⢸⡇⢸⣿⠀⠀⠀⣦⠀⠀⣸⠁⠀⢸⡇
⠀⠀⠀⠀⢠⣿⡆⠀⢀⡃⠸⣆⢸⠇⢀⣿⠀⠀⠀⣿⠀⢀⡿⠀⠀⣸⠃
⠀⠀⠀⠀⢸⠁⢿⠀⢸⡇⠀⠻⣾⠀⢸⣿⠀⠀⠀⢿⠀⣼⠇⠀⢀⡿
⠀⠀⠀⠀⢸⡆⢻⠀⢸⡇⠀⢠⣿⢠⡆⢹⠆⠀⢸⡄⢀⡿⠀⠀⣼⠃
⠀⠀⠀⠀⢘⡇⣼⠀⢸⡇⠀⢸⣙⡷⣀⣼⡆⠀⣼⠁⢸⠁⠀⣸⠃
⠀⠀⠀⡀⠀⡗⢏⠀⡸⣇⣤⣉⣏⣀⠘⠹⣧⢤⣻⣠⣈⠛⠛⠋⣷⣄⡀⡀
⠀⡴⣦⣄⡵⢊⠙⣩⣧⡙⢷⢈⠃⠀⣠⠊⣿⣦⣾⡿⡿⣦⢀⠀⠀⢸⣿⣖⠒⠂
⠀⠀⢈⠛⠧⣀⡀⣿⡀⠙⢧⡀⢉⠬⠇⢸⣡⠏⣽⡀⠘⢳⣦⣀⡠⢃⠙⣝⠳⠤⠤⣴⣃⣀⡀
⣈⡿⠃⠘⣤⢁⣸⠌⢿⡀⠈⠃⠙⢀⠰⠋⠀⣴⢇⠀⢰⠎⠸⢧⣀⠎⢢⡐⢄⠀⠀⠈⠈⠛⠢⣄⣠
⠀⢁⢠⡔⡻⢒⠟⢀⠀⣙⠢⠈⢳⠞⡧⢬⣤⠻⠀⡗⠂⢰⢇⠐⠙⡧⣈⠀⠘⠣⣀⠀⠀⠘⠃⠈⠑⠖⠒⠻⢤
⠀⠁⠲⡠⣧⠈⡛⠆⡰⢹⠃⠀⠠⡎⠠⡞⢡⡀⣴⠃⠔⠋⠘⠦⣤⢇⠸⠗⠠⢠⢉⡍⠙⠓⠶⣄⠀⢀⣁
⠀⢤⣶⢇⢾⡀⢱⣄⠘⢡⡗⠀⢀⠰⡾⠋⣦⠁⠈⣀⡤⠲⡏⠒⠋⢈⢀⡷⡀⠀⢀⠉⢦⠀⠀⠈⠃⠈⠁
⠀⣀⢾⠀⡛⠀⠈⠻⡄⢣⠇⠀⠈⣸⡄⠢⠙⡆⠀⢱⠀⠸⡧⡀⠀⠈⠛⠁⣼⠢⠛⠀⠤⣀
⣴⠇⣦⠸⡳⢦⡀⠀⠀⠸⠐⣀⠞⢨⠀⠇⠘⠀⠛⢸⠀⡰⢃⠋⠀⠀⡤⠚⡧⣀⠀⣿⠀⠉⢒⠲⠄⢤
⡷⢍⠉⡀⠁⠘⠂⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⣷⠀⠉⠁⡵⠈⠀⠀⠀⣠⢼⠧⢀⠚⠀⢆⠂⣼⢰⢤⣤⠴⠒
⢡⡾⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠳⠂⠀⠀⠀⢠⣌⠿⢺⠀⠀⠈⠀⠰⠸⠂⠔⠚⢷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣖⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⢾⣿⣿⣟⣻⣿⣿⣿⣿⣿⡳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣭⣧⠿⡼⣿⣾⣯⣿⣽⣟⣻⣟⡧⡭⢀⡂⠲⣄
⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⢿⣿⣾⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣧⣭⣀⢥⡀⠀⠀⠀⠀⠀⢀⠄
⠐⠒⠀⠈⢠⣤⣤⢐⠀⠀⠀⠀⠉⠓⢷⣾⣯⣿⠿⢻⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡄⠀⠀⢀⡜
⠀⠀⠀⠨⢩⠿⡉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣯⠀⠸⠟⠿⠿⢿⣯⣛⣿⢽⠿⠿⠋⠀⠀⢀⠊
⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠲⠿⣳⠤⢄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⢦⣎⣩⢉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⢸⣿⠿⡞⠙⣠⡤⣴⢶⠶⡶⢶⡤⣀⣀⡀
⠠⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⠁⠈⡐⠃⢹⣤⣼⣾⡞⢻⣶⣿⣵⣯⣫⠳⣄⢀⣀⣀⣀⡀
⠀⠀⢀⡠⠤⠤⠤⡀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠁⠀⣷⣶⣿⣟⠿⣄⠄⢀⣀⣈⣽⣟⣛⣿⣿⣿⣷⣿⣿⣟⢷⡀
⠀⠀⢘⠀⢤⣀⡠⠭⣭⣥⠏⢳⠀⠀⠀⠐⠀⠀⣿⢿⡀⢀⣿⣿⣿⠿⠿⠛⢿⣾⣯⣼⣷⣿⣽⣏⣿⣷⣶⣾⣿⣿⣖⣿
⠀⠀⠈⢳⣤⣤⣄⠀⣁⣤⢤⡾⠀⠀⠁⠈⢲⢳⣍⢎⡇⢸⣿⣯⣳⣾⣵⣜⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣯⣾⠟
⠀⠀⠀⠀⠁⢿⡏⣷⣿⣠⠂⠀⠀⣄⡀⣰⢌⣿⣿⢹⠁⠀⠈⠙⠛⠿⢿⣿⣻⣿⣿⣿⣿⣿⣽⡿⠟⠋⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣤⣙⣌⠓⠿⣀⣿⣇⢸⡙⣄⣿⣿⣿⢸⠂⠀⣟⢲⡀⠀⠀⠈⠻⣿⣧⠁⢿⡿⠋
⠀⠀⣠⠖⠋⣉⣁⣉⠙⡆⠨⣿⣿⣺⡇⣿⠧⣼⣿⣿⠄⠀⣷⣾⣧⣠⠒⣀⣀⣿⡿⠀⠘⣶⣖⣘⣂⣠⣄⣀⡀
⠀⢰⠃⣴⣿⡟⠋⡍⢡⣷⡀⠱⣿⣿⠁⣿⡆⣿⠿⡿⠀⠀⣿⣿⢾⣟⣃⣿⣿⣿⡧⠀⣴⣯⣭⣩⣭⣽⣿⣍⣿⣷⣦⡀
⠀⠈⠣⠻⠛⢷⠀⢷⢿⢻⢳⡀⠈⠻⡿⡉⠙⣻⣷⢲⠁⢀⣻⣾⣼⣘⣻⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⣷
⠀⠀⠀⠀⢰⢮⡇⠸⣮⠁⠀⢟⡢⢤⣸⣅⢠⣿⣤⠿⣰⣿⣿⣻⠃⠙⣿⣿⣟⡟⠀⠀⢸⣿⣿⣿⡿⠏⠫⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠈⠈⡇⠀⢻⡀⢀⣾⡟⠓⣬⢡⣾⡟⠙⠠⡝⢿⣿⡿⢿⣿⣿⣽⣿⣷⣀⢀⣾⣥⣷⣿⣿⠂⠀⣟⠛⣋⢉⠉⠐
⠀⠀⠀⠀⣀⣶⢿⡀⢀⢃⢈⣿⣧⡀⠰⣿⠟⠗⣚⣃⣓⣞⡏⠀⠘⢿⣿⣿⣿⣾⣏⣽⣿⣿⣟⠿⣇⡠⣼⠟⠿⠠⠮
⠀⠀⠀⠀⣈⠁⠐⠉⠉⣤⣤⣼⣿⡿⠋⠙⠻⠛⠁⣮⣙⣿⣇⡀⢀⣸⡿⣿⣧⣉⣭⣍⠉⠀⠀⠀⠐⠀⠀⣀⢀⡈⠒⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠾⣾⣿⡇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣯⣿⣿⡿⠟⠶⠬⠄⠤⠤⠄⠀⠀⠀⠈⣀⢀
⠀⠀⠀⠀⠐⠀⠀⠚⠁⠀⢱⣿⣧⡣⣄⣠⢶⣟⣿⣿⣿⠟⠛⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⡻⠯⠿⠛⠑⠏⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠛⠛⠛⢈⣉⣉⠙⠻⢻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⣋⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣌⣛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⢿⡏⢭⡘⠇⡵⢘⡟⢿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⢿⣿⣢⣿⣧⣦⢠⣶⣽⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣿⣿⣿⢱⢈⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⣠⣪⣥⣬⣿⣷⣶⣦⣄⡀⠀⠀⠈⠙⠛⢻⠀⠸⡏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀
⠀⠀⣀⣤⣾⡿⠛⢛⣉⣙⣛⣉⣉⣛⡻⠶⡄⠀⠀⠀⠸⡃⠀⡇⠀⠀⠀⠀⡀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣶⣌⣦⡀
⠀⣬⡾⣻⣭⣴⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⠆⠀⠀⠀⢠⠁⢰⣿⠀⠀⠠⣿⣥⣶⣶⣶⣶⣽⣦⣒⣶⣲⣶⠮⢥⣙⣄
⠀⢋⣴⣿⣿⣿⣿⣶⣷⣿⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇
⠀⠈⠛⠛⠋⠉⠀⠀⠈⢛⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡄⠀⠀⠸⠿⠿⠿⠛⠛⠿⣝⡿⢙⣭⣉⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⡟⡁⠸⠛⠛⠻⠿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⣿⣝⣛⣿⣿⣶⣄⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠸⡄⠀⠀⠀⠀⣸⠄⢀⣿⣿⣯⣽⣯⡩⣿⣿⣶⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⡾⠅
⠀⠀⡆⠄⡀⠀⠀⠀⠅⠂⠀⢷⣦⢸⡆⠀⠀⠀⢺⣋⢸⡟⣿⣿⡇⢸⡇⠉⠉⠉⠉⠀⢀⣿⠐⡆⠀⠀⠘⡷⠇
⠀⠀⠴⠂⠁⣤⠀⠀⠉⠀⣀⠈⠻⣦⠣⡀⠀⠈⣉⣇⣼⡇⠉⠉⡇⢸⢁⠀⢼⡀⠀⠀⣾⡇⢰⠀⠀⠸⡷⠷
⠀⠀⠀⠶⡶⠇⠀⡀⠑⢒⠀⡄⠀⠹⡇⠑⣥⠀⠤⡇⢸⡇⠀⠀⡇⣿⡘⢈⣻⠂⠀⣾⠏⢀⡆⠀⠲⣦⣧⠀⡀⠐
⠀⠀⠀⠀⠠⠤⠉⠃⡀⢈⡀⣴⠀⠀⣹⣤⣌⠳⣄⣏⣹⡇⣸⣠⣧⡟⡇⠐⠷⢦⣾⠏⠈⠈⠀⡄⣠⡅⠀⠶⠀⠵
⠀⠀⠀⠆⠀⢾⡅⢀⣞⡀⠓⢀⣤⣈⢿⡶⢾⡦⡿⣿⣿⡥⢸⣿⣻⢃⡍⢃⣤⡾⢡⠆⣴⢠⠰⢿⡏⠑⡇⡠⡀⡀
⠀⠀⠛⢀⡖⣀⢩⣽⡞⠗⠈⢴⡌⠀⣾⠁⣸⡧⠿⣿⣿⣿⣼⡿⢇⡾⣻⣿⡿⣱⡇⢱⣏⢨⣀⡈⠯⢧⠨⡤⠈⠉
⠀⠀⠀⠀⠈⢉⠆⢊⠸⠘⣤⠘⣋⣷⣿⠀⣿⡀⠀⣻⠟⢻⣿⣴⣾⣿⣿⣿⠁⠉⢀⣿⣿⣿⣾⣵⣄⣼⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠉⣀⣾⣦⣥⣾⣿⣿⣿⣛⣿⡋⠻⣿⣠⡾⠁⠈⣹⣿⣿⡇⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⠌⠐
⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢧⣿⣧⠶⠷⡿⣿⣿⠷⣾⣿⠻⢿⣿⣿⠟⠛⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠋⠛⠛⠋⠑⠒⠿⠃⠙⠲⠦⠂⠈⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⡤⣘⣁⡀⠀⢄⡤⡞⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⡈⢀⠋⠐⠋⢣⡭⣤⡾⠁⢀⣀⠨⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠲⠀⢶⡰⣤⠅⠃⣦⡗⢀⢂⡤⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⢉⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠄⠃⠸⣧⠘⠢⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⢻⡶⠓⠆⠀⠋⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠺⠃⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⡄⠀⡀⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠈⠂⠀⠀⠀⠀⣼⣅⠂⠀⠼⣄⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠁⠰⠀⠀⠀⠀⣀⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⠚⡤⠀⠄⠀⠀⡀⣠⠄⢸⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡇⢀⠳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠⠞⠠⢶⣦⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⣈⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠒⠀⢠⠀⠀⠀⡀⠊⠀⠀⠐⠂⠈⠀⠀⠀⠀⠑⠀⠆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢒⡩⠝⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⣀⣠⣤⣄⣠⣴⣴⣟⣿⣿⣿⣿⡟⣿⢿⣿⣆⠀⠀⠀⠀⠀⣀⠤⠄⠂⣀⡄⡒⠙⡡⠒⠁⠀⠀⠄⠤⠤⡀⠈⠃
⠀⠀⢠⣶⣿⣿⣾⣯⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣹⡟⠀⠀⠀⢠⠎⠁⠀⠈⠁⠛⠁⡠⠊⠀⠶⠀⠀⠀⠀⠀⡀⠘⠂
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡶⠀⣀⡀⡀⠀⠀⠂
⠀⠀⠸⣿⣿⢿⣿⣿⣿⣿⣻⣿⣷⣬⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠈⢅⠀⢤⠀⠀⠀⠀⠔⢆⠀⠙⠏⠀⠄⠀⠀⠂
⠀⠀⠀⠈⠻⠿⣿⣿⢿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⠉⠙⢳⣦⣤⠀⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣽⣟⣻⢿⣿⣾⣿⣿⣷⣶⠖⢫⣵⣤⡀⠀⠀⠀⠀⠀⠀⠼⡚⠑⠃⡖⢤⡀⠉⠀⠀⠀⠝⣭⠿⠟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⠠⠀⡀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣿⣽⣭⡿⠟⠋⠀⠀⠀⠀⠀⠀⣦⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠁⢉⡙⠉⠉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⡄⠅⠈⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠆⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⡀⠀⠠⢀⠀⠀⠰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⢿⣿⣿⣿⣿⣷⡧⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣸⡇⢰⡀⢠⠀⠀⠁⣝⣄⣠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠃⠿⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠨⣛⣾⣷⣿⣶⡀⣰⠟⠉⠀⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣠⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⡿⠿⡿⠛⢿⠛⢿⢻⠻⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢛⡁⠀⠤⠠⣬⣔⣵⣄⣦⣄⣨⢞⠁⠂⡀⠉⠙⠛⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣤⣀⣈⣅⢀⣙⣿⢉⢬⠠⢉⣿⣿⣶⣟⣻⣶⣶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣛⠂⢀⠀⢹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⣶⡴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⡀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡞⠀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⡼⠁⠠⢀⣾⠀⠀⢸⡄⣠⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣷⠃⣼⠀⡞⡏⠀⢰⠿⡷⢁⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⢿⣿⣄⡿⣾⢡⣵⣧⣷⣾⠗⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠈⠟⠃⠛⠸⠏⠟⠁⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⠐⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⢐⣘⡆⠐⢀⠀⠀⡀⢠⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⢊⠒⠆⡩⣉⠇⠀⠁⠔⠒⠙⠁
⠀⠀⠀⠀⠀⠠⠀⡠⠀⠀⡒⠀⠥⠜⠛⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠢⢠⠀⣤⡄⠰⠚⠂⠀⠀⢀⣤⠤⠔⠊
⠀⠀⠀⠀⠁⢀⡄⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⢀⣤⣈⡦⠄⢀⠁⠄⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢦⡀⠁⠀⢤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠒⠠⠤⡷⠂⠠⠌⣠⠂⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣋⣝⢡⠒⣡⠬⠦⣀⡀⡽⠦⢀⠨⡁⠠⠴⠂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠈⠀⠀⠀⠿⠒⠓⠒⠾⠄⠽⠒⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠊⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣎⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠛⠿⠁⢙⠆⢠⣴⣥⠶⢀⣠⣤⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠀⠁⠀⠀⠀⠘⠋⡫⣁⡄⠘⠃⠀⠀⠀⠀⠘⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡀⢉⣅⣈⣉⢀⡴⠈⡿⢿⡆⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡀⠿⣥⠬⣉⣀⣠⡟⠛⢏⡫⠋⠀⠀⡀⠀⢀⡀⠀⠀⠠⠈⠆⠲⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠲⢢⠀⡉⢈⠡⠌⠀⠀⡰⠈⢀⣄⡀⠀⠀⠀⣀⣀⡤⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠀⣄⡀⠀⠀⠀⠀⠋⠀⠀⢀⠐⠛⣦⡒⢚⡛⠈⠛⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠀⣼⡿⠲⣤⣄⣠⣴⢛⡀⠹⠂⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢇⡻⠩⠀⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⡀⠈⠙⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣿⡿⠿⣿⣷⣦⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⢿⣿⣧⣄⣀⣿⣿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠈⠛⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⢀⣀⣀⣀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⣠⣾⣿⠿⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⣠⣿⡟⠀⠉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣶⣿⣿⣿⣷⣦⣄⡀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠉⠉⠉⠁⠀⠈⠉⠛⢿⣿⣶⣄⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⣀⠙⠻⢿⣿⣦⣄⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⢿⣷⣦⣄⠉⠛⢿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠉⠛⢿⣿⣶⣿⡿⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣶⣶⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⢀⣿⡿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⣼⣿⠇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⣰⣿⡟
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣧⣤⣤⣼⣿⣿⣤⡄
⠀⠀⠀⠀⠀⢠⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣆
⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⢰⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠈⢷⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⣦⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⡁⢤⠀⡄⢠⠀⠀⠒⢠⣄⢠⠀⠂⠀⠀⠀⠀⣿⠀⢹⡆⠘⢧⡀⠀⠠⠛⠶⠀⠀⠀⠂⠀⠀⠀⣠⠶⣥⣛⠶⣮⠃⠀⠀⠀⠀⠀⠀⢀⣰⢶⣄
⠀⠀⠉⠙⠉⠁⠘⣄⠏⠸⠀⠀⠰⠶⠶⠶⠶⠛⠀⠀⠀⠀⠻⠇⠈⠁⠀⣰⠇⠀⠀⠤⠰⠶⠔⢠⠀⠀⠀⠰⢫⣾⢱⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⡗⣬⠟
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⢄⠶⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠢⡀
⠀⠀⠀⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠾⠂⢠⠀⠀⠀⠷⣿⣷⣿⠿⠃⠀⠀⠀⠴⠀⠉⠒⢄⢀⡀⠀⠀⠀⢰⣶⣶⣶⣾⣧
⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⣮⠙⠃⠀⠀⠀⠀⢷⡆⠉⠀⡠⠋⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣾⠃⣀⡀⠙⠷⠀⠀⠀⠈⠉⣙⠿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰⠈⠁⠈⢁⡀⠐⠀⠀⠀⢀⡀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⠀⠰⠏⠁⣀⣉⣁⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠉⠛⠉⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠁⠂⠀⠀⠀⢠⡀⠀⢛⠿⠀⣀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⢴⠁⠐⠀⠀⠀⠀⢸⡇⠀⠀⠙⠂⠀⠐⠀⠈⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠁
⠀⠀⠀⠀⠀⢨⣯⡹⡭⠀⠀⠀⠁⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠟⡷
⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢐⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣦⠀⠀⠀⠀⠀⢀⡀⠲⡀⠚⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠛⠃⠀⡘⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⢁⡇⠀⠀⠀⠄⠘⠃⢀⡵⠚⠃⠀⠤⠀⠀⠈⠂⠀⠃⠀⠀⠀⡟⠻⠿⠿⠛⢋⢳⡆
⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡄⠀⠀⣤⠀⠀⠀⠀⠀⢤⡄⠀⠠⢦⣤⠇⠀⠐⠲⠖⠲⠟⠁⠀⠀⠀⠀⠲⠐⠆⠀⢠⡤⠄⠀⠀⠀⠈⠢⠄⠀⠴⠋⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣮⠀⠀⠀⠀⠀⠈⢀⠀⠐⠀⠀⠀⠀⠀⢀⠄⠴⣿⡟⠀⠀⢀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠒⢠⡆⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠀⢀⡤⠈⠀⠀⠀⠈⠀⣄⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⣄
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⠀⠠⢾⣥⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠊⠀⠀⠀⠀⠀⠀⠉⠉⡆⠀⠀⠉⠀⠀⠀⠈⠀⠂⠰⣆⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠊
⠀⠀⠀⠀⠸⠷⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢟⡻⢿⣧⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠰⠾⠦⠀⠀⠀⢰⠆⢀⡛⡄⠀⡀⠀⠀⠀⣠⣶⣶⣴⡆⠐⠓
⠀⠘⢶⣶⣄⣤⣴⣶⡞⠀⠀⠈⠛⢧⣼⣿⡶⠟⠀⠀⠀⡀⠈⠁⠈⠀⡀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠂⠀⠰⠃⣠⢻⡿⠓⢾⠉⢓⡄⠘⠿⠶⣤⡞
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠞⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⢾⣤⠴⠛⠓⠋

⠀⠀⠀⢀⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠤⣴⡄⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖⢠⡀⠀⠀⠀⠀⠀⠂⠀⡈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠄⢀⡤⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢲⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓⠇⠀⠀⠄⠀⠀⠀⠙⠷⣶⣶⠶⠟⠁
⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠆⠈⠄⠀⠑⠄⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠀⠀⠀⣤⣙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣧⡄⠀⢀
⠀⠀⠀⠴⠆⠀⣤⣾⠃⠀⠀⠤⠤⠤⠌⠉⢫⠀⠀⠀⠀⣤⣹⣿⣧⣄⠉⠀⠀⠀⠀⠀⢠⡄⠐⢳⡄⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢠⡤⠲⡦⠴⠶⠀⠀⠂
⠀⠀⠀⠤⠄⠻⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠋⣻⡑⢫⣧⠀⠀⠀⠀⠤⠸⠃⠶⠊⠀⠀⠀⠀⠿⠟⠀⣀⢠⣦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠐⠛⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠉⠀⠀⠀⠈⠤⢀⣀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠉
⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡦⠄⠀⠀⠀⣀⠐⠂⠀⢠⡤⠀⠀⠀⠀⠠⠶⠶⠦⠀⢀⠀⠀⠀⠀⠛⠏⠀⠀⣤⢶⠒⣄
⠀⠀⠀⣤⣴⣶⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠀⠀⠀⠀⣴⠿⠛⠉⠀⠀⠀⠘⠀⠀⠁⠀⣄⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡌⠄⠀⠀⠀⠁⠂⠂⠀⠐⠫⠜⠋
⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠟⠃⠀⠀⠀⢈⣿⡷⠲⠶⠿⠓⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡿⢿⣿⡿⠛⢿⡿⣿⡿⣿⠿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣥⣤⣼⣷⣠⣾⣠⣴⣷⣬⣴⣿⣥⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠋⠛⠛⠛⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠐⣿⠛⢿⠛⠛⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⣷⠀⣺⡁⠀⠀⠘⡷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣠⠞⠛⠳⣆⠈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⣧⠀⠀⠀⣿⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡿⠀⣽⠂⠀⠈⢻⡖⣿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⢸⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠛⠲⢤⣀⣿⠀⠀⠀⠀⠀⠿⣤⠿⠦⠴⠦⠾⠁⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⣄⡀⠀⠈⠙⠶⣤⣀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢻⣿⣷⣦⣄⡀⠀⠉⠙⠲⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣰⠟⠻⢿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⣤⣀⠀⡴⠃⠀⠀⠀⣼⡏⠉⠉⠉⢹⡏⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⡹⢿⡛⠳⣄⢀⡞⢸⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠾⠋⠀⢸⣧⠤⠤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⢻⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⠀⠀⠳⢶⢶⡶⠶⠾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣇⣀⣀⣀⣀⣼⣸⣇⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠓⠒⠒⢾⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢲⡶⠟⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡤⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⡴⠛⠉⡉⠉⠛⢦⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡾⢠⡞⠉⠉⢳⡄⠈⣧⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣄⠀⢠⠟⠀⠀⠀⠀⠀⠀⣧⠘⣧⡀⠀⣸⠇⠀⡿⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠒⠒⠒⠒⠒⠃⠀⠈⢳⠏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠉⠉⢁⣠⡾⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣰⣏⣀
⠀⢠⡶⠖⠒⠚⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠒⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠙⠛⠓⢦
⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣛⣿⣿⡿⣿⣿⣿⣿

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢿⣷⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⠖⣏⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣵⣆⢳⠟⣹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠡⢅⠞⠁⢸⡿⢳⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⢦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠏⠀⠀⠘⢷⡠⡎⣿⠀⠀⠀⠀⠀⣠⣶⢴⣄⠀⠀⠘⠛⠏⠁
⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢹⣳⠆⢿⡗⠀⠀⠘⡟⠊⣁⢩⣿⠆⠀⠀⠀⠀⠀⠀⣠⣀⣰⣆⣀⡀
⠀⠀⠀⠀⣰⢋⠛⡚⣛⢳⣄⠀⠀⠀⠀⠘⠛⢼⠞⠃⠀⠀⠐⣿⣦⢹⡊⣿⡀⠀⠀⣠⣴⡖⠿⢩⣥⢉⡹⢻⡀
⠀⠀⠀⠈⠻⢜⡞⠀⠸⠈⠉⠳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⡹⣯⠀⠀⢴⠿⢢⠰⠎⣃⣨⣍⣵⣾⡇
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠴⠖⠒⢰⡎⢹⡶⣤⣀⠀⠀⠀⠀⠀⡼⣁⠟⣶⣿⡀⠀⠘⢻⠞⠛⠋⠙⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣶⠀⡘⠁⠸⡇⠙⣻⡄⠀⠀⠀⣾⠇⠹⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⠆⢰⠀⣈⡽⠁⠀⠀⣰⡦⠞⠠⣖⣸⡟⠀⣀⣶⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠒⠺⠃⠀⠀⠀⠸⣧⣄⣴⡾⠉⠀⣴⢿⣷⣬⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡴⣶⢾⡗⢲⢖⣶⢤⣤⡀⠀⠀⠀⠀⠈⢀⣀⡶⠝⠓⣬⣽⠉⠀⠀⢀⣴⠷⢶
⠀⠀⠀⠀⠀⠀⠀⠰⣟⢣⠖⣠⡄⠃⣤⠰⢚⠊⠰⣷⠶⠀⠀⣠⡴⣿⠟⠐⢟⣉⣿⠍⠀⠀⢀⡼⣫⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢻⣯⣬⣩⣤⢿⡬⠵⠾⠽⣧⠟⠀⠀⠐⢿⣰⢋⠀⣿⣨⠟⠃⠀⠀⠀⣸⡧⠡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⣴⣦⣦⣀⣀⢀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢨⣥⡹⠟⢿⠧⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣥⡐⠯⡄⠇⠞⠢⠏⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠗⢾⡧⡾⢤⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠏⠀⠀⠑⠈⠉⠻⢛⡛⠛⠛⠛⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣄⣀⡀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⠾⠋⠋⠁⠌⠛⢷⣤⡄⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡿⠁⠀⠀⠀⠀⠀⣀⡠⠄⠋⢉⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡼⠀⢀⣀⣰⡄⠀⠢⡈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⢀⡤⢖⣋⣵⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠿⣆⡀⠀⣰⣿⣾⡿⢋⢉⡉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠠⠴⠲⠶⠿⠿⢿⣶⣿⠀⠀⠘⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⢀⣠⠬⠿⠿⣿⠏⡇⠀⠀⣿⣿⣩⠥⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠒⠠⠃⡇⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠁⠀⠹⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠆⠑⢧⠘⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡇⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠃⠀⠛⠿⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠁⣀⠀⠀⠘⠢⢀⠀⠀⠁⠀⠀⠀⠀⡄⠀⣰⡟⠁⠀⠀⠀⠀⠈⠂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⠓⣿⠙⢣⣀⣱⣶⣄⣲⣀⠀⠀⢠⢸⡿⢀⠰⠄⠂⠀⠀⠄⣤⣷⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠈⡟⠛⠁⠈⠉⠁⠀⠀⠸⡿⢟⠁⡀⣀⣤⡦⢄⡀⡀⡽⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠝⣿⣿⠅⠀⢸⣿⣫⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡇⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣧⠀⠀⠀⠀⢰⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢸⡄⠀⠀⠀⢸⡷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠐⠒⠚

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⣰⠋⢳⡄
⠀⠀⠀⠀⢀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣩⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⣤⠐⠿⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⠛⣡⢼⡛⠷⢯⣷⡀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠒⠚⠉⠀⠀⢸⡆
⢀⡞⣹⠷⠒⠿⣄⠀⠀⠈⠓⠦⢤⣄⣀⡄⠀⠀⠀⣸⣴⣣⢾⠷⠶⢿⢻⡞⠁⢧⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠛⠛⠳⣄⠀⠳⣄
⠉⠉⢻⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⠿⣽⠀⠀⠀⢻⠙⠛⠻⠶⠶⢾⠏⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡼⠀⢸⠀⠀⠀⠀⣹⠀⠀⠈⢳⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠉⠛⠛⢦⣴⡆⠀⠀⠀⠈⢦⠀⠈⠁⣰⠋⠈⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠈⠳⢤⣤⠴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⠤⢿⣸⠇⠀⠀⠀⠀⠈⢧⡀⣰⠃⠀⠀⠘⠀⠠⠈⣇⠀⠀⠀⢿⡀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⠀⠀⠀⢸⡆⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⠀⠈⠀⠀⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠙⢦⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⣠⠤⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⡟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠙⣦⠟⠳⣦⡟⣏⠹⣞⣦
⠀⢠⠶⠶⠶⠶⠚⠓⠓⠒⠒⠒⢲⡄⠀⠀⠀⠀⠀⣞⣛⣛⣛⣛⡇⠀⠈⢇⢹⢀⣤⣄⣠⡿⠋⠀⠀⠀⣏⣛⠛⢦⣞⢹⢠⡿⣆⠘⢧
⠀⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏⠁⠀⠀⠀⠀⡴⠛⠉⠉⠉⠉⠑⢦⠀⠞⢀⢸⣄⠈⢹⡇⠀⠀⠀⠀⢀⣈⡟⣆⠈⢻⣸⠃⣼⣄⣨⣷
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣞⠉⠙⢿⡳⠞⠁⠀⠀⠀⠀⠀⢻⠉⠉⠙⠛⠛⠉⠉⠁⢠⡇
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠶⢿⡶⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣀⣷⣠⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⡏⠐⠈⠙⣏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠒⠒⠒⠶⠟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⡿⢦⣧⡴⠋
⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠲⠶⢤⣄⡀
⠀⠀⠀⣰⠿⢞⠳⠮⣍⡹⣯⣽⣇⣤⣀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠶⠒⠒⣖⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⣠⠀⠈⠉⠳⢤⡀
⠀⢀⡞⠁⠀⠈⠀⡄⠀⠙⢦⡸⢭⣳⣈⠱⡄⠀⠀⠀⠀⣴⢋⡀⠳⠀⠶⠀⠡⠆⢈⠳⡄⠀⠀⠀⠀⠀⢸⡷⣤⡈⠉⠓⠦⣤⡄⠀⠀⠙⢦
⠀⠸⡆⠠⠀⠀⠀⠀⠀⠂⠀⠹⡄⢿⣽⣇⢹⠀⠀⠀⠀⢷⣌⣁⣀⣀⣀⣖⣀⣈⣋⣁⣹⠀⠀⠀⠀⠀⢸⡷⢈⡇⢀⣩⡤⣤⣙⠶⣞⠀⣈
⠀⠀⠘⠦⣀⠈⠁⠀⢀⠀⠈⠃⠹⡄⣹⢾⣼⠀⠀⠀⠀⣸⣭⣭⠭⣍⣉⣩⠽⢯⣍⣩⠿⡄⠀⠀⠀⠀⢸⠟⠋⢠⣯⡴⡖⣟⣮⠷⠞⠋⠉
⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠠⠄⠀⢷⡷⢺⠃⠀⠀⠀⠀⠹⣦⠤⠶⠶⠿⢶⣶⠶⠶⠖⢺⠁⠀⠀⠀⠀⢸⠶⣄⢘⣦⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄⣸⡴⠃⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣈⣹⣦⡴⠋⠀⠀⠀⠀⠀⢾⠴⠛⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⢀⠄⠀⠀⡀
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⠀⠈
⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗
⠀⠀⠞⢀⡖⠁⠈⠉⢀⠀⠀⣀⠠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀
⠀⠀⠂⠈⠁⠀⠀⢀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠
⠀⠀⠀⠀⠄⢁⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣠⠆⠲⠒⢿⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠦⠠⢤⣀⠀⠀⠀⠈⠀⠀⣤⡀⠀⠀⠀⠀⠠⠆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣹⠁⠀⠀⠀⠀⠠⠊⠁⠐⠀⠀⠀⠀⠀⠐⠠⠓⣄⠀⠀⠀⠠⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⡀⠀⠈⡄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠀⢈⠀⠠⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢻⣄⣀⡀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠄⠃⠀⢀⠂⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⢀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠀⠀⠀⠀⠀⠃⠀⠄⠀⡱⠊⠀⠀⠀⠀⠐⠀⠀⢀⠀⡀⠀⡀⠤⠄
⠀⠀⠀⠀⠑⠀⠠⠙⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠠⠂⠈⢂⠤⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⣄⡀⠀⠀⠀⠐⠀⣀⢀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠐⠊⠈⡁⡠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⡂
⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠉⠀⠀⠓⠉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠙⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠐⢒⠒⠶⠶⠂⠀⠈⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠐⠦⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⡀⢀⣀⡀⣠⡤⢀⡤⣀⣀⡀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣀⠁⠠⠖⣋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉
⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣷⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠒⠋⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⢀⠁⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠛⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠚⠁⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠰⡀⢄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠦⣄⠀⠀⢀⣠⡴⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⠀⠀⠐⡈⠢⠁⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⠘⢀⣀⠈⣠⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠄⢘⡴⠤⢄⠀⢈⢳⡌⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠈⣠⠉⠄⠐⡀⢦⡀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱⣆⠀⠀⠀⢀⣤⢀⡽⠀⠈⠠⠐⠀⢄⡀⢄⠀⣄⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⡀⠀⠈⠀⠉⣉⡡⠄⠀⠀⢃⠈⣬⠓⠤⡛⠂⠀⠀⠀⠂⠀⠀⠀⠀⢀⡴⠞⠛⠙⠁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⡛⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⢁⠤⢈⠄⣠⠃⠀⣦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡿⣿⡀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠒⠲⠦⣄⡀⠀⢙⠳⠶⣤⡀⠀⠀⠀⢀⠈⠈⠛⠶⣌⢰⠞⠁⠀⠀⠆⡉⠠⣄⢂⡀⠀⠀⠀⠀⠀⢁⠘⣷⣄⣀⣤⡾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠀⣀⠀⠀⠙⠓⠶⣄⡁⠀⢙⠳⢦⣤⣆⣄⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠱⢾⠶⠈⠰⠄⣀⣀⣀⡀⠊⡠⠛⠛⢣⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠁⠀⢀⡀⠀⠉⠱⠦⣌⠀⠈⡙⠷⣿⣦⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠁⣀⡀⠉⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠒⣀⣠⣉⡐⢀⠀⠀⠙⠲⢤⡁⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠢⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣈⠙⠓⠾⣴⢦⡀⠀⠈⠓⢦⡌⠀⢉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣝⠂⢉⣛⡲⠤⣷⣤⡈⠑⠂⡀⠀⠈⠹⢦⣈⠀⢈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠿⣷⣿⣿⣶⣤⠛⠻⣷⣤⡀⠁⢊⡀⠊⠉⠃⠢⡈⠂⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣙⠻⢿⣿⣿⡒⠈⠛⣿⣶⣀⠙⠂⠐⢂⠀⠀⠑⢄⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣌⡛⢿⡶⣬⡿⠋⣿⠂⠀⠀⠀⠈⢒⣄⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢂⣤⣤⣤⣤⡈⠀⢰⠀⠀⢠⠈⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠈⠻⣤⠘⠄⡀⠂⠀⠀⠈⢳⣄⡀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣩⠀⡐⠁⠠⠔⠀⠀⠀⠉⠙⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣠⠟⠠⠁⠀⠁⠀⠊⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⢀⠛⡛⢙⣉⣉⢹⣿⠛⢻⣟⣛⠛⠓⠒⠲⡄⠀⠀⠀⠙⠒⠒⢶⠛⠁⡔⠀⠀⠀⠀⠈⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⠛⠭⠭⠭⠭⠤⠌⠩⠿⣍⡉⠉⠉⠛⠷⠆⠀⠀⠀⠀⠀⡰⠂⠀⡐⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⣰⠆⠀⠀⠰⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠸⠃⠀⠀⡄⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⢀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠄⠀⠶⠄⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡶⠙⢻⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠒⠻⠟⠀⠀⠀⠀⠀⣠⣤⣤⣴⡆⠀⠀⠀⠀⠐⠊⠁⠉⠁⣀⠐⠂⢀⠀⠀⠁⠋⠙⠀⠀⠀⠁⠀⣀⣀⣀⣀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢠⡎⢴⡉⢹⡿⠓⠐⠢⡀⠐⠖⠾⠿⠟⢻⠿⠯⠛⠛⠃⠀⠀⠀⠀⠊⠃⠀⠐⠉⠉⠉⠛⢹⠋⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠀⠙⠋⠂⠀⠀⠀⠀⠀⠂⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣄⢀
⠀⠀⠀⠀⣤⡀⣠⡄⡀⠀⠀⠀⠀⠀⢷⣴⠖⣀⣈⠀⠂⠀⠀⠀⠀⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⣤⢠⡆⠀⠀⠀⣄⡀⠀⣰⠨⠜⡇
⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋⠉⠉⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠈⡝⡿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⢠⣤⣄⡀
⠀⠀⠀⠀⣠⠴⢒⣶⣦⣄⠀⠀⣤⣤⣤⡤⣶⠶⠶⠶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠋⠉⠉⠀⢀⠀⠀⠐⠶⠄⠂⠀⠀⢀⡆
⠀⠀⠀⠀⣉⠒⢚⡿⠝⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠲⢶⣤⣶⣤⣤⠜⠉
⠀⣤⡚⠽⠝⠋⢉⡃⣠⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠟⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠈⢉⣻⠃
⠀⠈⠁⠀⢣⠀⢰⡆⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⠇⢀⣀
⠀⠀⠀⠀⠈⣦⣾⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠁⠸⠁⠻⠿
⠀⠀⠀⠀⠈⠛⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣤⣤⣿⠄⠀⠀⠀⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠑⢶⠁⢐⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⣤⣾⡟⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠺⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣎⡇⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢘⣿⣿⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠉⠉⠀⠈⠉⠉⠛⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⣾⣿⣷⠀⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠘⣿⣧⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠸⣿⡟⠋⢁⣀
⠀⠀⠀⠀⣠⣶⣾⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠉⠈⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⢿⣿⠇⠀⠀⠀⠻⣿⣅
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⣄⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠘⠛⠋⠉⢿⣧⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠙⠻⢿⣶⣾⣿⠋⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⣶⣾⣶⣄⠀⠀⠈⠻⣿⣦⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠉⢻⣿⣶⣄⠀⠉⠛⠿⠿⠿⠟⠛⠁⠀⠰⣿⣿⡇⠀⠀⣸⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⣿⣿⠿⠿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣠⣿⡿⠻⢿⣿⣷⣦⣄⣀⣀⡀⢀⣀⣠⣴⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⢀⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡈⠻⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣿⠈⠻⣦⣈⣻⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⣷⣄⠙⢷⠌⠉⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠻⣯⡙⠃⣿⡏⠻⠿⠛⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣄⠰⣶⣾⡄⢻⣤⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠻⣦⡈⠻⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢶⣄⠙⢷⣌⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡈⠻⣦⣨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⡙⢷⣄⠙⠷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣶⣤⣸⣿⢠⣌⣻⣦⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⠛⣧⠘⡿⠿⠆⠙⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⣯⡉⠻⣦⡀⣿⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣀⡐⢷⣄⠙⢿⠀⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠹⡗⠤⣀⣀⢀⢶⡤⣀⡀⠠⠤⠤⠤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡅⠀⠀⠀⠨⣁⣅⠔⠀⠀⠉⢲⣄⡀⠀⠀⠀⡴⠁⠀⠁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠄⡀⠀⢀⡽⠳⣤⡀⠀⢀⡼⢀⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⠙⠳⠶⠊⠀⠈⠙⠫⠴⠊⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠲⡶⠶⠤⠴⠶⠶⢶⣶⡾⠤⠤⣴⣒⡶⠴⠶⢻⠉⠉⠉⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢳⠒⠒⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠦⠄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠦⠤⠤⠤⠤⠐⠒⣁⠤⢺⠦⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⠒⠒⠒⠒⡟⠣⣀⠴⠊⡠⣷⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠲⠄⠒⡇⠀⠈⠛⠛⠒⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⡒⠒⡺⠧⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡟⠂⠄⢉⡉⠀⠀⠀⠤⠀⣿⠒⠢⡀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣀⠈⠒⠦⠤⠤⠤⠤⠤⠐⠒⠁⣀⠔⡇⠀⠀⠀⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠉⠉⠒⠒⠒⠒⠒⠒⠚⠉⠁⣀⠔⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠓⢲⠒⠒⡆⠐⡆⡏⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣄⣸⡀⠀⣇⢀⣧⠿⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⣹⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠐⢒⣎⠁⠀⠀⠀⠀⠀⠁⣢⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⡠⠟⠈⣉⠁⣁⠸⣌⠙⠒⠦⠤⠤⠒⣂⣹⠤⠤⠐⠒⠒⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢁⡴⣊⠴⠚⠉⠉⠁⠢⢄⣀⠽⣖⠒⢉⣉⣁⠠⠤⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢍⡑⠻⢉⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠜⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡉⠂⢄⡀⠀⢠⠊⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡈⠒⠧⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣇⡀⠀⠀⠤⠤⠐⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢋⣉⣉⣤⣤⣤⣤⣉⣉⡙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⣁⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠉⠻⢷⣦⡈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⢁⣴⡿⠋⠀⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⠀⠀⠀⠀⠙⢿⣦⡈⢻⣧⡀
⠀⠀⠀⠀⢀⣾⠏⢠⣾⠏⠀⠀⢀⣿⣿⣷⠶⠓⣠⣤⣤⣄⠀⠀⠹⣦⣼⠋⠀⢀⣤⣤⣤⡀⠙⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣾⡏⢠⣿⠃⠀⠀⢀⡿⣹⡏⠀⠀⠀⢻⣆⣀⣹⢷⣴⠾⠋⠙⠷⣦⡾⣃⣀⣼⠇⠀⠘⣿⡄⢹⣷
⠀⠀⠀⣸⡿⢀⣿⠇⠀⠀⠀⣼⢷⡟⠀⠀⠀⠀⠀⠉⠋⠙⣷⠀⢈⣀⠲⠂⠀⣾⠋⠉⠁⠀⠀⠀⠸⣿⡀⢿⣇
⠀⠀⠀⣿⡇⢸⡿⠀⠀⠀⢰⣏⣾⠃⠀⠀⠀⠀⠀⣀⣤⣤⡿⠀⣏⣍⣳⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⢿⡇⢸⣿
⠀⠀⢀⣿⠀⣿⡇⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⣼⠏⠀⣱⡟⠻⢾⡍⣥⡶⠛⢷⣍⠈⢹⡆⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⣸⠇⢻⣄⠀⠀⠙⠛⠛⠁⠀⠀⠀⢸⡿⠀⣿
⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⢸⡟⢿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣾⡏
⠀⠀⠀⠀⢿⣇⠘⣿⡄⠀⠀⣿⣼⡇⠀⠀⠀⠐⣶⣼⡷⢦⣤⣤⠶⠾⠛⠛⠛⢷⣴⡟⠀⠀⠀⢠⣿⠃⣸⡿
⠀⠀⠀⠀⠈⢿⣆⠘⢿⣆⠀⢸⡇⣿⠀⠀⢘⣻⡏⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠃⠀⣰⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣧⡈⠻⣷⣌⠛⠛⠀⠀⠉⣹⣷⣬⣀⡐⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⣠⣾⠟⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⢷⣦⣀⠀⠀⠉⠰⠟⢹⠟⠛⠛⠉⠉⠁⠀⠀⣀⣴⡾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⢉⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣌⣉⣉⠛⠛⠛⠛⣉⣉⣡⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉

⠀⠀⠀⡠⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢀⠠⢐⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⣀⣢⢠⣈⣀⣥⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡿⠂⠀⠀⡐⢁⢲⡀⠀⠸⠀⠀⠀⠀⣠⠤⠶⠶⠿⠿⢶⡄
⠀⠘⠈⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠾⠀⠀⠀⠀⠀⠛⢾⡡⠀⢁⡆⠀⠀⠀⢹⠀⠀⠀⠄
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠠⠀⠀⠀⠀⣶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠀⠐⠀⠀⠀⠐⠒⠘


⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⠀⢀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢘⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠰⣆⠀⡀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⡄⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠠⠂⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠲⢎⠣⣄⠀⠀⠈⠀⡃⠈⠠⠈⠀⠠⠀⠑⠠⠀⠀⠀⢀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢙⡧⠄⠀⠀⠀⠀⠐⠨⠤⠒⠀⠡⠀⠀⠀⠀⡁⢈⠀⠠⠋
⠀⠀⠈⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠊⠀⣀⣤⣤⣀⡈⠀⠀⠀⠀⣿⢿⡄⢸⣟⠖⠁⠀⠀⠀⠀⢀⡨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠐⠀⠂⠀⡰⢛⡅⠈⠀⠁⠀⠀⠰⠀⠀⢨⠉⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢋⣀⣠⡠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠨⡀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠠⡬⠀⠀⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠀⠀⠀⠀⠀⢀⣠⠄⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢀⠂⠈⠂⠀⠀⠀⢠⡏⠃⠀⠀⠀⠙⡆⠀⠀⠀⡀⠔⠒⠂⠀⡀⢀⠠⠀⠀⢀⠔⠀⠀⠀⠑⠄
⠀⣀⠀⠀⠐⠚⠛⠛⢲⠇⠀⠀⢀⠈⠀⠂⠂⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⢈⠀⠀⠒⡄⠶⠀⠒⢄⡜⢂
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆⠤⠁⠔⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠘

⠀⣀⠀⠀⠀⠀⡀
⢀⠀⠀⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣰⣤⣤
⠀⠀⡀⠙⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠃
⠀⠀⡇⠀⢣⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⡜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠦⡀
⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠶⠒⠃
⠀⠀⢀⠀⠸⠀⠀⠠⠀⠘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠄⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡇⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠺⠟
⠀⠀⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⡉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⡅⠀⠀⠙⣴⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⢿⠃⠀⠁⠴⢀⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠐⠀⠀⠀⠔⠄⠀⠀⠀⠒⠀⢻⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠁
⠀⠀⠀⣜⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢂⠤⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠠⠠⠀⠀⠀⠀⠀⠀⠰⡭⠂⠀⠾⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⣐⠲⣮⣈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⡀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢴⠀⠀⠁⣷
⠀⠀⠀⠐⢋⠾⠿⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢲⣀⡆⡲⠟
⠀⠀⠀⡞⠉⣿⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿
⠀⠀⠀⠙⡿⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢘⡓⣿
⠀⠀⠀⠘⣦⣠⣄⡅⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⣏⣏⡹
⠀⠀⠀⠀⠈⠀⠈⣇⢀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠻⣿⠇
⠀⠀⠀⠀⠐⠶⠿⢻⣿⠋⡄⠱⠀⠀⠀⠀⢁⣠⡴⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎
⠀⠀⠀⠀⠀⠤⣀⣤⠏⠄⠈⠀⠀⠀⠀⠀⠀⢃⣀⡼⠗⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢁⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠋⠰⠚⠉⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⣁⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠉⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠰⡄⠒⠒⠠⢤⠀⠀⠀⠀⠀⠀⠀⠐⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀⠀⢀
⠀⠀⠀⢀⠃⠀⠀⠰⠀⠰⠄⢰⠀⠀⠀⠀⠐⢀⠆⠈⠀⠀⠈⢡⠄⠀⠀⠀⠀⢠⢟⡶⡟⢷⡐⠽⡷⡀⠀⠀⠀⠀⠀⠐⠀⠄⠁⠈⠣⡘
⠀⠀⠀⢘⠀⡉⠀⠀⣀⠠⠄⠀⠇⠀⠀⠀⠀⠋⡐⠀⠄⠤⠀⡠⠀⠀⠀⠀⠀⢾⣳⣂⡝⠀⢠⡲⣠⣧⠀⠀⠀⠀⠀⠀⢰⣄⡬⠄⠒⢳
⠀⠀⠀⠘⣄⣁⠐⢀⡐⠀⠄⡛⠀⠀⠀⠀⠀⠁⠙⣀⣀⡄⠴⢄⠀⠀⠀⠀⠀⠈⢉⣾⣿⣯⢤⣇⣰⠏⠀⠀⠀⠀⠀⠀⢸⡧⣄⠈⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠰⠀⠅⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠄⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⢀⣀⠀⠀⠀⠠⠌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⠏⠁⠀⠘⠛⠀⠀⠀⠀⠀⣠⡌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠀⠀⠀⠙⠒⠦⠤⣄⡀⣀
⠀⠀⠀⠀⠀⢀⣤⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡾⠇⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠚⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠐⠦⣄
⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⡦⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⢀⣸⡧
⠀⠀⠀⠀⠙⠻⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠞⣉⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣛⣿⠶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⢤⡴⠶⠒⠒⡨⠛⣉⡠⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣼⣿⣮⣬⣉⣙⣭⡉⠉⠉⠉⣹⡙⠄⣀⣴⣤⣶⡮⠶⠶⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢻⣿⠟⠛⠃⠐⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠀⢸⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣼⠻⠳⠦⠆⢶⡊⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⣿⣷⣾⣤⠶⠚⠛⢧⠀⠀⠀⢠⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⡀⡇⠀⣿⡿⠃⠀⠀⠀⠀⠘⡆⠀⠀⡟⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⢄⢳⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠹⠀⢸⡇⣠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡎⣾⡙⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢠⡇⢰⠁⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣧⡿⣷⣸⣿⣦⠀⠀⠀⠀⡇⠀⠀⠀⣿⢸⣀⡾⠊⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠑⣯⣿⡏⣿⠀⣀⠀⢠⠀⠀⠐⠀⢻⡞⢠⠇⢰⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⢧⣿⡇⣿⠂⡇⠀⡆⠀⠀⠃⠀⣿⡇⡾⢠⡟⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣾⣿⡗⣿⣰⠀⢸⠀⡄⠀⢸⠀⣿⣿⣵⡾⢋⣉⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣿⣿⡄⢸⡀⣷⢰⣸⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠷⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢦⠀⠀⠀⠑⢦⣁⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⠀⠘⡐⠓⡀⠀⠀⠀⢻⠻⣄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠂⠀⠂⠀⠋⠀⠀⠀⠀⠀⢿⠏⠳⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡔⠈⠂⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠠⠀⠀⠀⠁⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣄⠀⠀⠁⠂⠀⡀
⠀⠀⠀⠀⠀⣱⡀⠜⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠓⢀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⢉⠀⢄⠀⠀⠀⠀⠀⠀⠉⢀⡀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡀⢈⡆⠀⠀⠀⠀⠠⡄⠀⢛⣆⠀⠸⣅⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠇⠈⠁⠀⠀⠀⠀⠈⢠⠄⠘⢀⠱⡀⠀⢰⠄⠀⠀⠀⠀⢐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠙⣷⠀⠀⠐⠁⠀⠁⠈⠀⠀⠄⠀⠀⠲⣄⠀⠀⢐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠳⣮⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠙⣆⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⠏⠳⣄⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣂⣀⣀⣀⣈⣁⣀⣀⣀⣀⣠⣚⣁⣀⣀⣌⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠛⠛⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⢔⣁⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⢀⣴⣶⣿⣧⣶⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠯⠛⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⣠⠗⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠿⠒⣲⣀⣒⣂⣲⣲⣶⣓⡲⢋⣴⠿⡫⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣷⣶⣶⣶⣦⡿⣿⣿⡍⢿⡑⢀⠠⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡿⠿⠿⠿⠿⡗⠉⠉⠀⠀⠈⠣⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⣠⡾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡼⠓⠀⢰⠄⠘⠻⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠸⣀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠐⠖⠒⠒⠒⠐⠲⡖⠶⠒⠒⠒⣗⠐⠐⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠂⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⢀⡀⠀⠀⠈⠃⠈⡽⠛⠛⠛⠛⠛⠛⡏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠒⠒⢲⠆⠀⠛⠒⠛⠒⠒⠒⠚⡇⠀⠘⠓⢛⡆
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠾⠷⣁⡟⠉⢽⣿⣷⣶⣿⣿⠈⠈⠁⠉⠉⠇⠀⠸⠉⡌
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⣾⣷⣿⣿⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡷⠀⠈⠙⠃⠙⠃⠉⠒⠒⠒⠚⣿⣷⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⡟⠈
⠀⠀⠀⠀⠀⠀⠀⡘⢆⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠘⠀⠀⠀⠀⢀⣀⡀⡇⠀⠀⠀⠀⠀⠂⠂⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠛⠋⠄⡇⠀⠀⠀⠀⠀⠀⠀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠁⠀⠉⠀⠀⡶⠀⠀⠀⠀⠛⠂⠘⠦⡀
⠀⠀⢀⡀⠠⠒⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⠔⠂⠀⠀⠛⠀⠐⠒⠒⠐⠒⠒⢧⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣇⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀⣀⣀⣀⡀⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠈⡁⠀⠘⠀⠾⠂⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣦⡠
⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⡀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠷⠾⢓⣆⠀⠂
⠀⠀⠀⢠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣦⠖⣾⣯⡉⠀⠀⡀⠀⣴⣷⣿⣼⣿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠟⣷⢿⡏⠉⠂
⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠐⣴⣷⣏⣩⡅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣄⠀⠀⠀⠀⠀⢤⠿⠙⠍⠋⠈⠀⠀⠀⠀⣠⣤⢰⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⡀⢰⡤⠀⡀⠀⠀⠀⠀⢺⡃⢰⡆⠀⠈⡀⠀⠀⠀⠻⠀⠀⡅⢻⠋
⠀⠀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠁⠰⠆⠀⠀⠈⠁⠀⠙⣦⡀⣿⠀⠀⠀⠘⢶⡰⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢠
⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢶⣴⣇⣀⠀⠀⠀⡀
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⣾⣭⣻⢻⡷⡔⠚⠁
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠈⠀⠀⠐⣟⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⣼⣩⡄⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⣼
⠀⣀⠀⠀⠀⠰⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢀⣠⣞⠁⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠿⠀⠀⠀⠀⠄⠉⠙⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢈⠀⠀⠀⠀⠰⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠈⢘⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡄⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣲⣾⣿⣞⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡚⢲⡄⠀⠀⠘⠟⢻⣿⠛⠃⠀⠀⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠎⣰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠉⠳⡖⠀⠀⢠⠆⠀⠈⠀⠂⠀⠀⠀⡀⠠⢥⣮⣿⣿⣷⡀⠀⠠⠄⠀⣇⠀⠉⢸⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⠻⠟⠑⠦⠀⠀⠀⠉⠀⠀⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣴⠆⠁⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠒⠀⠀⠠⣤⠉⠀⠀⠄⠀⢨⠀⠀⡀⠀⢼⡴⠁⠀⣀⣀
⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⣀⡴⠒⣫⡟⠁⠀⠀⠀⠀⢰⡀⣠⡔⠀⠀⠀⠛⠀⠀⠀⠀⠀⠗⠀⠞⠀⠀⠈⠁⠐⣴⠛⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠐⠘⢿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢄⣸⣿⣯⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣸⣧⠖⠚⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢴⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⡉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⠰⠀⠒⠄⠀⠀⠀⠀⠀⠠⠰⠀⠀⠄⠆⢀
⠀⠀⠀⠀⠀⠀⠸⠤⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⢃⢀⠞⡍⠌⣂⠄⡀⠀⠀⠀⠀⠐⢯⢨⠭⠅⠭⠝⠹⡆
⠀⠀⠀⠀⠀⠓⠖⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⡤⢁⡀⣤⠀⠀⡖⠒⠀⠀⠀⠀⠀⢀⠉⠲⡠⠔⣇⡄⠴⠀⠀⠀⠀⠀⠇⡀⠀⢆⠂⠀⠠⠇
⠀⠀⠀⠀⠀⠰⠉⠈⠉⠡⠀⠀⠀⠀⠀⠀⠀⠨⠀⠨⠤⠄⠅⠀⠑⠀⠀⠀⠀⠀⠀⠈⠚⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠀⠀⠈⠀⠠⢀⠄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠄⠀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠊⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠰⣤⠚⡖⣰⠒⠀⠀⠀⠀⠀⠀⢠⣾⠒⢠⡘⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠠⡢⠀⣠⠀⡔⠄⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠈⢬⡱⡀⠰⠹⠀⠀⠀⠀⡔⠁⠀⠈⣤⡀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣈⠉⠀⡀⠡⠂⠀⠀⠀⠀⡄⠀⣠⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡠⢀⠁⠐⢄⠀⡠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⢦⠀⢤⠂⠀⠀⠀⠀⠀⠀⢀⡔⠓⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠜⠁⠀⣠⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⡿⠉⣤⠉⠙⢺⣣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⢀⣺⣿⣴⣤⡸⠂⢙⣋⠀⠀⢰⢁⡞⠀⠀⠀⢀⣰⣦⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠲⠀⠈⠉⡿⢿⣿⣵⡺⠾⠙⠁⠀⣆⣾⠀⠀⢀⠴⢛⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠘⠃⠉⠁⠀⠀⠀⠀⠻⠋⠀⠀⠑⠒⠁⠀⠀⢶⡴⡦⣴⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢰⡷⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢶⢧⢠⡉⣽⣿⣏⡀
⠀⠀⠀⠀⠄⠒⡫⠟⠀⠀⠀⠉⠀⠀⠀⠀⠈⠹⢿⠄⠀⢸⣥⠄⠃⠀⠀⠀⠀⠀⠀⠘⠻⡆⢨⣤⠑⣻⣿⣥⠀⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⠈⠙⠉⣀⠀⠀⠀⠀⢰⢻⣧⠘⠛⢶⡤⣶⠛⠃⠀⠀⡜⣺⡏
⠀⠀⠀⠀⠀⢀⡿⠏⡈⣛⣿⡴⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣦⣿⣤⣶⢀⡀⠈⠫⠸⠇⠀⠀⠀⣀⡀⢀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣽⠠⡥⢻⣿⡗⠀⠀⠀⠀⣿⢻⠀⠀⣤⣟⠓⠋⠿⣿⢟⣿⠅⠀⠀⠀⠀⠀⠐⠿⠷⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠶⠎⠋⠉⠀⣄⣶⠄⡽⠠⠀⠀⠀⣷⡦⠙⠡⡶⠈⣾⡄⠀⡰⣶⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣤⣄⢀⣄⠀⠈⠚⠃⠀⠣⠜⠀⠀⠀⠉⠿⠓⣶⡖⠿⠀⠀⣰⣱⠃⠀⠀⠀⠀⠀⢉⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⠉⠀⠀⢠⡄⣤⣠⡄⠈⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⡤⢤⡄⠀⠀⠀⠀⠀⠛⢻⡇⠀⠀⠀⣤⣽⣍⣋⣿⣄⠀⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⣴⣿⣔⢃⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⠁⠆⠹⢠⡯⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣻⢿⡦⡴⠇⠀⠀⡰⠀⠀⠀⠺⡷⠄⠈⠀⠿⢶⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠙⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⣶⡄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⠄⡀
⠀⠀⠀⠀⠀⣴⡄⠉⠁⢀⡃⠂⠈⡋⢁⣶⡄⠀⠀⠀⠐⢀⢶⣦⣶⣶⡄⢂⠀⠀⠀⠀⠄⡢⠆⠔⠔⡠⡀⡀
⠀⠀⠀⠀⣀⠉⡁⠰⠷⣴⠇⣻⠃⣤⡤⡉⣡⡄⠀⠀⠠⠸⠿⣿⣽⣿⠇⡘⠀⠀⣐⠜⠁⠀⠘⠀⢃⠀⠑⢒⢀⠀⠀⠀⠀⠀⠀⣰⠎
⠀⠀⠀⠘⠟⠱⠸⠋⣴⣦⠘⠻⠃⣽⡄⢜⢙⡃⠀⠀⠀⠡⡈⠛⢛⠅⠒⠀⠀⢀⠾⠀⡃⠀⠃⡀⠈⠀⠂⠠⠦⠀⠀⠀⠀⢀⠰⠏
⠀⠀⠀⢰⣷⠁⠘⣛⢠⣦⠐⠿⢃⣬⢁⠀⠿⠇⠀⠀⠀⠀⠀⠁⠁⠀⡀⠀⠀⠀⡢⠀⠄⠼⠀⠀⢀⠀⡄⠠⢑⠀⠀⠀⠠⣮⠃
⠀⠀⠀⠀⢡⣴⠀⢅⠰⠷⠐⢿⠆⠅⠘⣿⠆⠀⠀⠀⠀⠀⠠⠐⠋⠉⠁⢢⠀⠀⠁⢣⢀⠂⠀⢁⠀⠰⠠⠁⠄⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠈⠉⠀⣴⣴⠁⣥⡁⠈⣷⡆⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠈⡁⢂⠠⡠⡘⠃⠉⠀⠀⠀⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠃⠀⠀⠀⢀⡠⠒⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠋⠠⠖⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⣠⣖⡭⣛⡤⠀⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠑⠅⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⡴⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡡⠟⣙⠋⣵⠃⠀⢀⡞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠴⠃⣀⡀⠠⢼⠜⠊⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡀⣀⣈⠫⠾⣋⢾⡛⠃⠁⠀⠀⡨⠇⣁⡘
⠀⠀⠀⠀⠀⠈⠀⠀⡠⠃⠀⢤⡑⠺⡑⡯⠀⠀⠀⠀⠀⡾⢗⣩⢉⣶⠾⠟⠉⠀⠀⠀⠀⡂⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠
⠀⠀⠀⠀⠀⠀⠔⠊⠀⠠⣹⡄⢾⠧⡈⠂⠀⠀⠀⠀⠐⢋⡘⢡⣤⠟⠀⠀⠀⠀⠀⠖⢀⠉⠈⡓⣁⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⠛⡦⣍⠂⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠦⠈⠳⠈⢈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠈⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡑⠲⣄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡀⠀⠀⠀⠀⠀⣤⠀⣀⢠⢘⠁⠀⠀⡀⠀⠀⢀⠤⠦⣄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣰⢱⡞⡧⣹⠀⠀⠀⠀⠀⢀⢔⠱⢇⡂⠓⢆⠈⠁⠀⠀⡌⢘⠐⠂⢱⠀⠀⠀⢰⣾⣦⣀⠀⠀⠀⠀⠀⠐⠲⡒⢦⡁
⠀⠀⠀⠀⠀⠀⠿⣈⢡⡦⣹⠀⠀⠀⠘⠃⢸⡀⠀⠋⢂⠕⡞⡀⠀⠀⠀⢷⠈⡀⠂⠀⡅⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⢠⢃⠞
⠀⠀⠀⠀⠀⠀⡷⠿⣤⢹⠏⠀⠀⠀⠀⠀⠀⠙⠢⠬⠥⠈⠀⠁⠀⠀⠀⠘⣆⠁⠐⠠⢇⠀⠀⠀⠁⠙⣿⣷⠀⠀⠀⠀⠀⢸⣻⣄⣀
⠀⠀⠀⠀⢀⡼⢰⡗⢫⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⡄⠂⢸⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⡆
⠀⠀⠀⠀⢸⣵⠆⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡁⠖⢉⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡾
⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠉⠻⣟⠓⢛⡟⠉⠀⠀⠀⠀⠀⢸⠿⣶⢒⡛⢻⡛⢙⣧⢰⡘⣇⠀⠀⠀⠄⠤⠀⢠⠶⢚⡋⡉⠀⠀⣠⠀⠛⠀⢃⢈⠆⢠⡈⠻⣆
⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⣻⢸⣷⡞⡇⡎⠘⠜⣧⠸⣆⠀⠐⣦⣴⠀⠈⠒⢬⡙⢡⣄⡆⢨⡄⠱⡀⠘⠋⠀⡈⢁⡄⠈⠛⢲⡄
⠀⠀⠀⠀⠀⢰⠟⢻⠀⠀⠀⠀⠀⠀⢀⡟⢀⠸⡎⠟⣷⢀⡇⢶⢠⡙⣧⠹⣆⠀⠈⠁⠀⠀⠀⠀⠛⠶⢦⣄⡀⠹⠶⠟⠀⠆⠈⠃⢀⠙⠦⠴⠀⠻⢄
⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⣼⡷⣼⠀⢿⡀⣿⠘⣿⠸⣧⢷⣘⢧⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣶⣾⠋⠛⠓⠒⠒⠉⠉⠑⠋⠁
⠀⠀⠀⠀⠀⢸⠀⠸⡆⠀⠀⠀⠀⠠⣿⣧⡏⢸⢸⣇⡟⣠⢟⣼⣧⣠⣽⡷⠟⠁⡠⠶⠒⠶⠒⠦⣄⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⢸⡀⠀⢷⠀⠀⠀⠀⠀⠈⠿⠷⠷⢾⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⣿⡇⠀⠀⠐⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠘⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⢻⠀⠀⠀⠀⢸⡇⠂⠠⣤⡄⠀⠀⠀⣷⠀⠀⠀⠀⣼⣿⡇⢠⣀⠀⡀⠀⣱⠀⣇⡀⡄
⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡸⣿⡇⠀⠀⠀⠈⠳⠶⢤⣿⣀⠀⢠⡞⠁⠀⠀⠀⢠⣿⣿⠁⠘⠛⠛⠛⠛⢉⠋⠉⠉
⠀⠀⠄⠠⠀⠀⠀⠈⠲⠾⠃⠀⣰⣿⣷⣆⠀⠀⠀⠀⠀⣿⡧⠿⢿⡀⠀⠀⠀⠀⣰⡿⠁⠈⠉⠉⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠉⣁
⠀⢔⠀⠀⠀⠐⠀⠀⠀⠀⠀⢰⢧⡉⢉⡼⣣⠀⠀⠀⠀⡏⢠⣦⣤⣷⡀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠠⡀⢠⠤⠔⠀⠀⠀⠀⠀⣿⠀⠋⠍⠀⠸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣰⡟⢴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠈⠁⢔⡀⠀⠀⠀⠀⢠⣇⣩⠖⠦⠦⠴⢹⡀⠀⠀⣿⣿⠿⢉⣿⠙⡇⠀⣿⡇⠀⠀⠀⢀⣠⣶⣿⠏⢀⣾⠃⠀⠀⠀⠀⡀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠦⣤⠀⠀⢀⠎⠀⠁⠀⠀⠀⠀⠀⢱⡀⠀⢹⡇⡄⣿⣿⣦⣷⠀⠙⠃⠀⢀⣴⣿⣿⠟⠁⢀⡾⠃⠀⠀⠀⣤⣴⣷⣾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠦⢴⣦⣤⠖⠛⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⡿⣁⢂⣴⠟⠁⠀⠀⡠⢿⣿⠟⠿⠿⢛⣷⡆
⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢸⠉⠈⡀⠀⠀⠀⠀⠀⠘⣿⣇⣉⣉⡿⠀⠀⠀⠸⣿⣿⣷⡴⠟⠁⠀⠀⠀⠈⠢⠤⡤⣤⢤⢄⡈⠐⠛⡄
⠀⠀⠀⠀⠘⣾⠱⢧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢀⣰⠉⠁⠁⠁
⠀⠀⠀⠀⡄⢊⠈⠀⢄⠀⠀⠀⠀⠀⡇⠀⠰⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠶⣶⠲⣤⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿
⠀⠀⠀⣘⠊⠉⠉⢈⣠⠇⠀⠀⠀⠀⢡⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⠷⢏⣦⠸⠟⢡⡍⠛⠓⢄⠀⠀⠀⠀⠀⠀⣸⡧⡟⠀⠀⠀⢀⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡾⠿⠿⠿⠿⠿⠿⢷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠙⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠋⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⢶⣖⣰⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⡿⡿⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠷⠶⠶⠶⠶⠶⠶⣶⣶⣶⣀⠀⣼⠋⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠻⣄⣢⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠏⠁⠀⠀⢼⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠛⠛⠛⠛⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢶⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢇⠈⢧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣧⠈⢇⠈⢆⠈⢇⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠠⣦⠘⢇⠘⣇⠘⣇⠙⢧⠈⢆⠈⢆⠈⢆⠈⣦⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣈⣿⣿⣿⣿⣿⣿⡙⡇⠘⣄⠈⣆⠘⣆⠈⣆⠸⡧⠸⠇⠸⠇⠸⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠛⠋⠈⠛⠛⠿⣿⣿⣿⣿⣧⠘⡄⠈⡄⠘⡄⠈⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⢋⣬⠐⡄⠘⣄⠸⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⡷⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡠⠞⠋⠁⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⣀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠂⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢁⣀⣤⣤⡴⢴⣶⠶⢤⣤⣄⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣞⣋⣯⢦⢺⡇⠀⣿⡴⣌⢿⣿⣿⠄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⠻⢿⣷⣯⣼⡇⠀⢸⣿⠽⠿⣛⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢦⡀⠀⠀⠀⠈⠙⠒⠲⠶⢾⠃⠀⢸⠗⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠏⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣾⠀⠀⠀⠀⣠⣴⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠉⠉⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢰⠇⠀⢀⡏⠀⣤⡶⢛⠉⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢾⣿⣯⣿⠉⣿⣻⣳⣦⠀⣷⠀⠀⠀⢀⡟⠀⠀⣼⠁⢸⡇⠁⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠬⡏⠀⣯⣭⡭⠥⠞⠁⠀⠀⢀⡞⠀⠀⢠⠇⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡟⠀⠀⠀⠀⠀⢨⡟⢳⡶⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡄⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⠁⠀⠀⠀⠀⣠⠏⠀⡼⠀⠀⢀⣀⡴⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⡀⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠀⠀⠀⣴⠃⠀⣼⠁⣴⠚⠋⠉⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⡀⠀⢳⡀⠀⢳⡄⠀⠀⢰⡇⠀⠀⢸⠁⠀⠀⠀⡼⠁⠀⣼⠃⠀⠻⣜⢯⣹⡗⢢⣄⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠛⠶⣄⢳⡀⠀⠙⣆⠀⢸⡇⠀⠀⣼⠀⠀⠀⣸⠃⠀⣸⠃⠀⠀⠀⠈⢱⠟⢀⣟⣺⢟⣠⠟
⠀⠀⠀⠀⠀⠀⣼⠟⠅⠀⠀⠀⠀⠀⣺⠇⢻⡄⠀⠈⢧⣾⢀⠀⡄⣿⠀⠀⢠⡟⠀⢠⡏⠀⠀⠀⣀⡴⠋⢠⠞⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⡤⢴⡖⠋⠁⠀⠀⢻⡄⠀⠘⣿⡸⢠⢲⣻⡆⠀⣸⢷⢰⢸⡇⢀⣤⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⣄⠀⠀⠀⠀⢷⢁⠄⢻⣏⡿⡘⣿⣷⠀⣿⣾⣾⢸⣷⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠻⣶⣶⣶⡜⣟⢄⡠⢿⡹⡱⡣⠹⡇⣿⠿⢡⣾⣿⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣶⣶⣶⠏⢻⣃⡆⠊⣿⣴⣥⡼⠃⢹⡇⡴⠰⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢧⣥⡼⠏⠀⠀⠀⠀⠀⠙⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠂⠠⢄⣀⣀⠠⠤⠶⢀⠀⠤⡄⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠒⠻⢤⣀⠀⣀⣐⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠰⢠⠏⢿⠁⠀⠉⠙⣶⣦⡀⠀⠀⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠊⢅⠀⢘⢦⣀⣁⡼⠁⢇⣠⠔⣉⢽⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡰⠀⠀⠀⠈⠑⠬⣙⡁⠀⠀⠀⢀⣀⢠⠤⠎⠡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡾⣝⠢⣀⠀⠀⢀⡼⠀⡝⠭⠭⡟⣁⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢈⢀⠃⠈⠐⠁⢰⠀⠃⠀⠰⢀⠇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢱⡀⠀⠀⠀⡘⡠⠀⠀⢠⡆⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡜⠀⠈⠁⢉⠁⠁⠀⠀⠀⠃⡠⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⠄⠀⠀⢀⣠⡊⠀⠀⠀⢀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⢄⡀⡯⠀⠀⠑⣄⠠⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⠈⢳⠤⠖⡊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠣⠄⠀⠀⠀⢠⠄⠒⠁⠤⠀⠤⠀⠀⠀⠳⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠤⢀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⢸⢄⡀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⡀⠀⠀⡈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠠⠀⠀⠉⠒⠒⠠⠐⢦⠀⠈⠉⠒⠒⠂⠤⢤⡄⠐⠁⠀⠀⠀⠈⠀⢀⠄⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠒⠉⠀⠨⡀⠀⠀⠀⢀⠂⠂⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⢠⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣟⣟⣿⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠁⠠⠬⠐⢂⠀⠀⠀⠀⡦⠀⡐⠉⢂⢀⡀⠀⠀⠀⣀⣧⡵⠖
⠀⠀⠀⠀⠀⣥⠜⠁⢢⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠸⡀⠁⠐⠀⠂⢉⡜⠀⠀⠀⠈⢢⡠⣯⡟⣍⣈⠏⠀⠀⢼⠁⢈⡇
⠀⠀⢀⠀⡀⠀⠀⠰⢀⠀⠀⠘⡁⣤⠁⠠⡀⢀⠀⠀⠑⠤⡄⠀⡠⠎⠀⠀⠀⠀⠐⣁⣸⠨⢵⡋⠑⡀⢀⡴⠚⢯⠉
⠀⠀⠈⡉⠅⠀⠠⢂⠌⠀⠀⠀⠐⢄⠀⠀⠐⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠈⠉⠀⠀⠈⠉⠚
⠀⠀⠀⢰⣶⣿⣷⣷⣀⠀⠀⠀⠀⠈⠰⢤⡾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⠑⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⡈⢀⠀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠀⠀⠀⠠⠘⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⡠⢊⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠉⡇⠠⠀⠀⠀⠀⠀⢻⣷⠄⠀⠠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡦⢄⠤⠖⠁⠀⠀⠀⠀⠀⠠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠄⠊
⠀⠀⠀⠀⠀⠠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡡⠀⠀⠀⠀⠈⢤⡐⢀⠆
⠀⠀⠀⠀⢠⠁⠏⠀⠀⠀⠄⢀⠴⠀⠀⠀⢠⠿⢿⠿⣿⣿⡿⠷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠂⠐⠔⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠒⢀⠸⠈⠂⠀⠀⠀⠀⠀⠀⢂⡀⠀⡰⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣈⠁⢈⣤⣤⡗⠀⠀⠀⠀⠀⢠⠊⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡍⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂
⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⡆⠀⠄⣀⠀⠀⠀⠀⠀⠀⡠⢐⣤⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠠⠐⠁⠀⠑⢩⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⣀⣀⠀⡄⠀⠀⠀⢰⡸⠏⠟⢀⢰⠀⠀⠀⠈⡀⣬⢢⠀⠀⡠⡂⠥⠀⠠⠁
⠀⠀⠀⡁⡄⠀⠐⠒⠄⠅⠀⠀⠀⠀⠀⣠⣴⡾⠛⠻⢿⠃⠀⠀⠀⠀⠀⠃⠈⠄⢉⡀⠂⠀⠀⠀⠐⠠⢙⢠⣌⠜⢁⠠
⠀⠀⠀⠑⠈⠀⠒⠨⠈⠀⠀⠀⠀⠀⠠⡈⠛⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⣀⣰⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠓⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⢦⣶⠛⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠀⠀⠀⠙⠘⡀⠀⠀⠀⠁⠉⣦⠂⠆⣔⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⢎⣱⣿⠷⣶⠉⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⢻⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠄⠈⢋⣿⠢⠁⢄⠈⢸⣏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⣧⠘⠺⠅⠀⠀⠔⡀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡛⠃⠀⠐⠚⠻⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⡟⠀⠀⠠⠀⡗
⠀⠀⠀⣀⠀⠐⠈⠀⠀⢀⣔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢄⡂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡀
⠀⠀⢸⣿⠀⠀⠀⠀⣤⡼⠟⠒⠒⠀⠰⠂⠀⠀⠀⠀⢰⡀⠚⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢤⡏⠁⡀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⡆⠀⠀⢂⣀⠃⢉⡽⡀
⠀⠀⢸⣿⡇⠀⠀⠈⠛⠚⣁⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣆⠀⠀⣤⣦⣞⡜⠁
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠿⠟⠻⢿⡿⠇⠀⠀⣽⠝⣸⣃⠄⠀⡀
⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⠄⠒⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⢬⠀⣴⠞⠶⣿⡿⣿⣶⠋⠀⣿⣿⠆⣸⠃
⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠀⠀⢰⡟⡰⠁⣄⡠⠄⠀⠀⠀⠀⠀⠀⢁⡂⠀⠈⠙⠻⠆⠠⣈⠋⣈⢫⣤⣤⣿⣿⣿⣇⣆
⠀⠀⠈⢿⣿⣿⣿⣄⣆⠀⢀⣤⣶⠀⠀⣿⣷⡇⠀⡀⣰⡷⠀⠀⠀⠀⣤⣦⣄⢀⠀⢀⡄⠀⠀⠀⢻⡿⠿⠿⣿⡿⠿⠿⢛⡠⠝⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣧⣡⠍⠀⢸⣿⡇⣠⡘⢛⣻⣿⡀⡀⡄⠍⠁⠉⠻⠀⣣⡜⡂⠀⠀⠀⣾⡇⠀⠠⣶⡄⠒⠒⠁⠐⠀⣀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⢙⣇⣼⢻⡟⣀⣸⣿⠛⠉⠀⠀⠙⣯⠀⠀⠀⡀⠸⢿⣿⣷⣶⠄⡀⣿⣧⣾⣦⡛⠂⠀⠀⢠⡶⠋⢁
⠀⠀⠀⠀⠀⠉⣶⣿⣿⡏⠋⠻⢿⣷⣾⠃⠀⠈⣷⠀⠀⠀⠀⢰⣧⣤⣀⣤⡇⠀⣤⣷⠚⡛⠊⢳⣿⡿⠟⢻⣿⡆⠀⠀⡎⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢀⢸⣿⣿⠈⣷⣤⠏⠀⠀⠀⠀⠈⢻⠿⢫⠥⠁⠀⠛⠉⠀⢛⣛⣤⣶⣷⠆⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠈⠘⠛⢿⡈⠿⠿⠦⣀⣤⣤⣤⡤⠜⠀⠀⠀⠀⠤⠴⠶⠿⠿⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠘⠋⣡⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢈⣤⡀⠈⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⠟⠿⣿⡀⠈⠑
⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⢠⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣈⣥⡦
⠀⠀⠀⠀⢀⡀⡁⠀⠀⠠⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣄⠋⠁⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⡂⠀⠀⠀⠀⠀⠀⠃⠻⠀⠀⠀⠀⠀⢰⣶



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣋⣍⣹⣟⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢢⡀⠀⠀⠀⡐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠠⠀⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠱⠀⠃⠀⠀⠀⡇⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠔⠃
⠀⠀⠀⠁⢰⠓⢢⠀⠓⠀⠀⠀⠀⠀⠀⠰⠀⡂⠀⠀⠈⠳⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣠⠀⢸
⠀⠀⠘⡶⠋⠀⠀⠑⢄⡀⠀⠀⠀⠀⠔⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⠠⠀⠊⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣌⠀⠸⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠊⠀⠀⠀⠔⠀⠂⠀⠄⠀⠀⠄⢀⠀⠀⠀⠀⡃⢸⠀⠀⠀⠀⡁⠇⠀⠀⠀⠀⠀⢢⡼⢖⠣⠀⠀⠀⠠⠂⠂⠀⠄⠂
⠀⠰⠁⠀⠀⠀⠜⢀⠀⠀⠀⠀⠁⢸⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠇⢸⠃⠀⠀⠀⠀⠀⠀⠈
⠠⠤⠄⠀⠀⠀⢀⠈⠂⠴⠀⠀⠀⠘⠀⡀⠀⠀⠀⠤⠇⢰⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠤
⠈⠁⠐⠀⠀⠤⠠⠂⠀⠀⠁⠊⠀⠸⠀⠁⠀⠀⠀⢲⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠘⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣠⣽⣯⠀⣧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⣘⣛⣚⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠅⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⣿⣿⣿⣅⢰⡟⣅⠉⢳⡤⣭⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣍⠈⢳⣶⡾⣟⣂⣀⠀⠐⠬⣙⡳⣦⣀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⢺⣿⣦⣴⣶⣾⣧⣶⣤⣤⡙⠦⠹⣦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠄⠋⣿⣿⣿⣿⣿⣿⠿⣿⣿⡍⠈⢢⠈⢟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡆⠇⢽⣿⡏⠁⣀⣹⠀⠀⠈⠻⣦⢂⠁⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣓⠾⣷⣿⠟⠶⠒⠋⠀⠀⠀⡀⢹⣟⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠸⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⣾⡟⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠰⣿⡿⠿⠀⠀⠀⠀⠀⠀⡠⠔⠀⣠⣞⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣠⣤⣾⣿⣿⣿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣏⠻⣙⠻⢿⣿⣿⠿⣏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣿⣿⣥⣯⡶⣏⢧⠀⠉⢻⣷⣾⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⣦⣶⣶⠶⠖⢺⣿⣿⣿⣿⣿⣿⣿⡆⠂⢀⠈⣻⣿⣿⣿⡟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⠛⠛⠉⠁⠀⣿⣿⣿⣿⣿⣿⣷⣿⣾⣴⣶⣶⣯⣼⡿⠛⢁⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣁⣀⣀⣠⣀⣈⣋⣉⣍⣉⣉⡉⣉⣉⣉⣉⣈⣀⣀⣀⣀⣀⣀⣑⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠏⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠉⠁⠀⠀⠉⠁⠂⠓⢤⡁⡘⠆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢅⠀⠄⣀⠒⠾⠰⠀⣠⡀⠀⡀⡀⠀⢠⢆⠠⢠⠀⠀⣀⣤⡜⢯⣳⣷
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠈⠐⡶⡤⣤⣄⣀⣠⣁⡤⠀⠤⠤⠀⠠⠄⠁⠉⠠⠤⠀⠋
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⡐⠶⠐⠆⠂⠀⠀⡐⠀⠂⠀⠀⠀⠀⠀⢱⠀⠀⢠⣅⠀⠈⠉⠻⢇⣿
⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠠⠿⣦⠗⠛⠉⠛⢾⣿⣤⡄⠈⠓⠀⠀⠀⠀⢃⠀⢸⠇⠉⠐⣄⢀⣠⣽⡇
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⣸⡃⠀⠀⠀⠀⠘⣿⣆⠐⠂⠀⢯⠀⠀⠀⢸⡄⢈⠀⠀⠀⠀⠈⠀⣿
⠀⠀⡞⠀⠀⠀⠀⠀⠀⣾⡥⣿⡇⠀⠀⠀⠀⠀⠈⢻⣄⡈⠁⠭⠄⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠛⣷⢹⡇⠀⠐⠤⠠⢄⠀⣸⣷⡥⢌⠍⠁⠀⠀⢸⠁⢠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢊⡚⢻⡆⠀⠀⠀⠀⠛⢻⡇⠝⠃⠀⠀⠀⡀⠃⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠘⡅⠀⣀⡀⠠⠊⠀⠀⠀⢸⠄⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠢⣤⠀⠸⣼⠀⠀⠀⠀⠀⣼⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠲⢷⣦⣿⠇⣰⠀⠀⡀⢹⢧⣮⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡜⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⡤⣀⣡⣾⡜⢷⢣⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠰⣀⠏⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠁⠯⡟⡁⢣⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠠⡀⠀⠀⠀⠀⠀⠀⡘⠱⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢦⡆⠟⡧⠹
⠀⠀⠀⠀⠀⠀⡀⠸⢸⢋⠀⢘⡆⠘⡂⣨⠀⣶⢟⣸⡀⢀⠀⠘⠀⠀⡀⠀⡀⣠⢏⡛⣆⠇⢀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠾⠖⠿⣧⡇⠿⡈⡇⡟⠈⡏⠃⠎⠐⡀⢠⣰⡾⢶⡟⠉⠀⢳⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠰⠈⠃⠘⠠⠇⢾⠚⠷⠔⠋⠀⠖

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣿⣟⣧⠀⠀⠀⠀⠀⠀⠎⠹⠄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡠⠦⡄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢴⣿⣶⣶⣶⡄⠘⣿⣯⣿⣟⣆⠀⠀⠀⠀⠀⢠⢉⠀⠀⠀⢀⡠⢞⡉⠉⢻⡇⠀⠀⠀⣤⢠⡄⢝⠫⠂⢀⣧⡴⠃⡔⠒⣮⣠⠕
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡀⠀⠸⣾⣏⣿⣻⡄⠀⠀⠀⠨⣁⡼⠀⢀⡴⢋⡄⢀⡀⠀⣼⠇⠀⠀⠀⢠⠤⡈⠁⠀⡠⢿⣤⠇⣀⡉⠉
⠀⠀⢠⣞⣿⣷⣤⡀⠀⠘⢿⣦⠀⠹⣾⢿⣟⣿⠀⠀⠀⠀⠉⢀⡴⡋⣰⡆⡄⠈⢃⡾⠁⠀⠀⠀⠀⢸⠶⣇⡖⠙⡷⠔⠁⢸⣿⣨⡦⢄
⠀⠀⠀⠛⢿⣿⣿⣿⣷⣄⠀⠀⣤⡄⠙⠛⠛⠁⠀⠀⠀⠀⢠⡞⢈⡑⠂⠶⣀⡴⠋⠀⠀⠀⠀⠀⠀⠘⢯⣻⡕⠊⠀⣀⡀⢎⡉⠈⠳⠴⠃
⠀⠀⠀⠀⠀⠉⠻⢷⣿⠟⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣈⣡⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣈⡇⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠘⠂⠀⠁⣤⣤⣦⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⢠⡮⠛⠁⠀⠀⣴⢫⡶⠶⠶⣭⡇⠀⠀⠀⠤⢀⣼⣉⣹⢷⣟⣿⡀⡀⠸⠿⠀⠀⠀⠀⢀⣤⣤⠀⡶⣿⣼⣏⣽⣟⠁⢠⣾⣷⡀
⠀⠀⠀⠀⠀⢀⡣⠃⠀⠀⠀⢀⡽⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣹⣿⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠉⠈⠉⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⢀⡤⠶⣚⣚⣛⣋⣭⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⠛⠻⠉⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣴⣮⣵⡄⠀⢠⡿⢻⣽⢶⣦
⠀⠀⠀⠀⡏⣾⠋⠉⣉⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⡘⠁⠀⠘⠇⠀⠀⣶⣾⣷⣆⠠⠀⠀⠀⢠⣼⣿⣤⡿⢷⡀⠀⢻⣿⣿⡾⠉
⠀⠀⠀⠀⠻⣼⠆⠘⠯⣟⣒⣛⠭⠝⠛⠭⠟⠀⠀⠀⠀⠘⢷⣿⠗⠀⠀⠀⠀⠀⠈⢧⣿⣻⠿⢀⠀⠀⠀⠨⣽⣶⣏⢙⣿⡅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠀⠈⠘⠛⠻⠯⠁

⠀⠀⠀⠀⢠⠴⠒⠒⢦⠀⠀⣠⡶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⣠⣤⠀⠴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣄⡀
⠀⠀⠀⢠⡇⠀⠀⢀⡼⠀⢸⡏⠀⢠⠀⠀⠙⣷⡀⠀⠀⠀⢀⣿⡏⠀⠀⠈⠙⡛⠛⠃⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢿⡆
⠀⠀⠀⠘⡇⠀⠀⠸⡀⠀⠈⢻⡄⣤⠀⠀⠆⠘⣧⠀⠀⠀⠈⠛⣡⣶⣾⠿⠽⠟⢀⣴⡿⠋⠀⠀⠀⢀⣠⢴⡶⣶⣦⣤⣀⠈⠙⠋⠋
⠀⠀⠀⠀⠙⠦⠬⠴⠃⠀⣰⠟⢀⠀⠠⠀⠀⠀⣿⠀⠀⠀⠰⣿⠞⣩⣤⣤⣶⡾⠟⡋⠀⠀⠀⠀⠀⣾⣧⣝⣟⣿⣿⢿⣽⡿⣦⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⡀⠀⣀⣠⠀⢸⡇⠀⠀⠀⢀⣄⣀⠉⠉⠉⠀⠀⠘⠛⠻⠟⠀⠀⠀⠹⣯⣿⣿⣳⣾⣾⣿⣻⣿⣧⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠈⠐⠆⠀⠀⣠⡟⠀⠀⠀⠀⠻⠾⣼⣟⡖⣶⢶⢶⢲⣶⣲⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⡿⡿⠿⠊⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣝⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣿⣿⣿⣿⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠍⠛⠛⢱⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡷⣀⣤⣄⡀⢀⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣱⣿⣿⣿⣿⣴⣿⣶⣶⣶⣶⣶⣶⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣾⣿⣿⣿⣿⡿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣸⡿⢿⡟⡿⠿⣋⣛⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡴⠖⠚⠛⢋⠙⢻⡟⣉⣑⡒⢂⣶⠀⣠⡀⠀⠂⠀⡸⠏⠃⠉⠟⢛⡒⠻⠿⠧⠃
⠀⠀⢀⣠⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣾⠗⠛⠛⠛⠙⠟⠻⢿⡿⣿⡿⠃⢯⡖⠭⣀⣂⣉⣥⣤⣷⣬⣶⣿⠯⠋
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⣭⣿⣿⣿⣟⢾⣢⠼⠫⠛⠉⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⢿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠶⠾⠧⢤⣀⡀⠈⣙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢷⣾⣿⣿⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠢⠠⠄⠘⠂⠤⠄⠘⠿⠿⠿⠿⠷⢶⠖⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣧⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠀⣿⡇⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠠⠦⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣶⡿⢧⣤⣴⣿⠟⠉⠩⢿⣉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣷⣾⣿⣿⡏⠀⠀⠀⠛⠳⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⢠⣶⣄⠀⠀⢀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣟⣀⣠⣾⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢋⡤⠂⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡙⠛⠿⢷⣶⣤⣤⠙⠃⠀⣸⣿⠋⠻⠿⠋⠁⠀⠀⠻⣶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠛⣻⣶⣶⣬⣍⣻⣷⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠻⡆⠙⠛⠿⢿⣿⣿⣍⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢰⣿⣸⣀⡶⣦⣻⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢰⢏⡿⠉⠿⠷⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣬⡀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣘⣛⣿⣉⣛⣛⣛⣏⣉⣹⣏⠉⣻⣋⢹⣿⣛⣃⣠⡿⠀⠀⠀⡰⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠁⠚⠿⠿⣿⣿⡇⠀⠀⠀⠀⠊⢁⡰⠻⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠓⠢⠤⠲⣾⣟⣱⣾⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢹⡿⠟⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⣀⠀⠀⠀⠀⢣⣿⡇⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣤⣤⣤⣴⣶⣾⣿⣷⣶⣦⣾⣿⡇⠀⠀⠀⠀⠘⠀⠻⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣽⣿⣧⡀⠀⣤⣀⣠⣤⣤⣤⣤⣤⡼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣙⠛⠛⣻⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣻⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠤⠬⠭⠼⠛⢒⣶⡟⠛⠛⠛⠛⣁⣹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡍⠁⠀⠀⣀⣀⣀⡀⠴⠶⠶⠾⠿⠿⠿⢿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠂⠀⠀⣤⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠋⠉⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⣠⡀⣀⠀⣀⡀⣠⢀⠀⡀⢀⣀⢠⠠⣀⢀⠀⣀⠀⢄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠁⠈⠀⠀⠁⠈⠈⠀⠀⠀⠁⠀⠈⠁⠁⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡆⢀⠀⡀⠀⡄⠘⣆⣘⣄⣸⣤⣧⣴⣥⣎⠎⡠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⢰⠸⡀⢠⠀⣇⢈⣆⣡⣤⣧⡼⠶⠷⣚⠛⠻⠉⡉⢩⠄⠀⠀⠀⠈⢝⢿⣴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢱⠀⢇⣀⣱⣬⣦⡴⠶⢷⡛⠛⠋⠉⠉⠑⡀⢀⠦⢠⠄⠀⠀⠶⠀⠁⡄⠀⠀⠀⠀⣘⠃⠁⢹⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⣼⠞⠛⠩⠉⣅⠀⠀⣈⣙⡤⣄⡀⢀⢀⠁⠀⠁⠀⠀⠄⠀⠙⠀⢠⠄⠀⠤⠀⠀⢠⡀⠀⠠⠆⠀⣷⣒⠂⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣹⡞⡑⠙⠆⠀⠀⠀⠀⠀⠐⠢⣌⠁⠮⠋⡣⠑⠀⠘⡃⠀⠀⠁⠀⠀⠀⠀⠋⢀⡀⠀⣀⡀⠀⠖⠐⣼⡓⠤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠤⡤⣿⠀⠸⠃⠛⠀⠀⠀⠀⠀⢸⣀⣼⣧⠶⠠⠃⡜⠀⢀⠀⠠⠠⠀⠀⠀⠀⠖⠀⠆⠀⠲⠈⠠⣐⣥⢾⡓⠬⠁⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⡀⡠⡄⠉⢀⡄⠶⠀⠀⠀⠓⠀⠉⠤⠍⠙⠁⠤⠈⢐⡀⠫⠄⣀⣀⣀⣤⡤⣶⠶⡖⢛⠻⡙⠄⠣⠉⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡨⢷⣜⠀⢃⠀⠀⠶⡀⠀⠀⠘⠀⣀⣒⣠⣤⣤⡴⠶⡖⠺⡟⢻⠉⠋⠃⠘⠀⠉⠀⠁⠈⣠⣴⡶⠶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢊⡝⢻⠶⡶⡷⢶⠶⡞⢻⠛⢏⠹⡉⢣⠸⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠘⠀⠃⠘⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⡶⠾⠋⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠨⠃⠀⠀⠐⠉⠅⣀⠀⠀⠀⠀⠀⢀⠁⠐⠆⠀⠂⢄⠀⠀⠀⠐⢄⠈⠒⠘⢂⠔⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢀⠀⠑⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠊⠄⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠊⠁⠈⠉⠶⡀
⠀⠀⠀⠀⠀⠀⠂⢀⣀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠉⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠘⠃⠚⣊⠁⢺⠀⠑⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡆⠈⠑⢄⠀⠀⠀⠀⠠⠀⠚⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⢄⡐⠩⡠⠀⠀⠱⡀⠀⠀⠀⠋⠘
⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠞⠁⠀⣄⠀⠑⡄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⡀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⢠⠀⠉
⢦⡀⠀⠈⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠨⢀⠀⠀⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠐⠁
⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡅⠆⠀⠐⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠐⡥⠆⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠂⠈⠐
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠁⠀⠀⠰⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢠
⠀⠀⠀⠀⠀⠈⠒⠳⠀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠈⠀⢀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡄⠀⠐⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⡠⠒⠀⡈⢤⡀⠀⠀⡠⠂⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⠔⠊⠀⠀⠀⡴⠉⡠⢦⠄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢧⠀⡇⢌⠀⠀⠀⠀⠈⠈⠐⢉⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠
⠀⠸⠅⢌⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠑⠄
⠀⠒⠈⠉⠀⠁⢀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡈⠀⡀⠂⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠆⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠀⡀⠀⠈⠁⠐⠀⣀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢠⡄⢤⣤⢤⣤⡄⣤⣤⢠⣄⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣇⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⠀⠀⠤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣿⡿⠀⠀⠀⠀⠀⠀⢰⡆⠈⣿⠀⢻⠇⠘⡟⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣠⣾⣿⣷⣄⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡡
⠀⠀⠀⠀⠀⠀⢠⡿⣟⠽⠋⢹⣿⣿⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⡂
⠀⠀⠀⠀⠀⢀⡿⢊⠁⠀⢀⣿⣿⣿⠃⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢀⡤⠒⠒⣀⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠐⠻⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⢰⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠸⣇⡁⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⡷
⠀⠀⠀⠀⠻⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣤⢠⣀⡄⣀⣠⢀⡀⡄⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠰⠇⠎⠼⠰⠡⠆⠮⠠⠠⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⣶⣿⣶⣦
⠀⠀⠀⣰⣋⡘⣘⣁⢋⡋⣘⢁⢀⢀⠈⠀⠐⠁⠀⠀⢀⡔⠄⠠⠁⠀⠀⠀⠉⠀⠠⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢰⠆⡴⠰⠤⠆⡶⠴⠠⠀⠄⠤⠠⣀⠁⠀⠀⠀⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣀⣀⣀⣀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⢶⣶⡶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣤⣤⣬⣥⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣩⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣉⣩⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⠋⠛⠛⠋⣛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣼⣿⣿⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣻⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⣿⣿⡅
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠉⠉⠉⠉⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂
⡒⠶⢶⠤⢄⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⠔⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠠
⠠⢀⠀⡇⠀⠀⠀⡠⢤⣶⣆⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢀⠆⠀⠀⠀⠀⠀⠉⢄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠙⠋⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠄⠉⠉⠉⢠⠁⠀⠀⠀⠈⠳⣤⣀⣀⢴⢣⠀⠀⠀⠀⠀⠠⠎⠉⠑⡄⠀⠀⠀⠀⠸
⢀⠇⠀⠀⠐⠄⣀⡀⠀⠀⢀⡀⠈⡀⠤⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡼⠶⣄⠀⠰⠋⠙⠳⡄⠀⠀⠈⠧⣀⡴⠁⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢺⡀⢀⡸⠀⠘⢤⣀⠴⠃⠀⠀⠀⠀⠀⡶⠖⠢⡀
⠀⡠⠶⢤⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡞
⠀⣇⠀⣠⡦⣀⣀⢄⡀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠚⠁
⢀⣈⠉⠁⡸⠋⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠈⢳⠄⣇⠀⠀⠀⢠⠆⠀⠀⠀⢀⠄⢤⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠈⠀⠀⠀⠘⠀⠙⢄⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣀⠠
⢤⠴⠋⠀⠈⠲⠤⠖⠃⠀⠀⠀⠀⠹⢄⣀⠇⠀⠀⠀⠀⢀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⠀⠀⠆⠻⠟⠀⠚⠂⣤⠄⠀⠀⠀⠀⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠁
⢀⣤⠆⢱⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠠⠉⠐
⠉⠀⠀⠀⢢⠀⠀⠘⢅⣀⡼⠓⠢⢼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠾⢁⡤⠦⠠⣄⠀⠀⠀⡠⠄⢄⠀⠀⠀⡠⠲⠶⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⢄⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⡧⠀⠘⢅⣀⡼⠀⠀⠀⠈⡂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠁
⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⠋⠀⠀⠀⠉⢣⠀⠀⠀⠀⢠⠀⠲⡎⠉
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠘⢄⡀⠀⠀⣠⡎⠀⠀⠀⠀⠸⡀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠃⠀⠀⠀⣸⣙⠉⠉⢱⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⢴⠘⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢱⠀⢣⡀⠀⣨⠃
⠀⠀⠀⠀⠀⢠⠒⠒⠄⠀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠡⠀⢀⠌⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄

⠲⡎⠱⢠⡔⢤⡔
⣧⠍⠈⠀⠔⢲⣆⡀
⠛⠳⢄⡂⣰⠟
⠀⠀⠞⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⢀⣀⣤⠀⡀⠀⢀⡀⠀⣀⢀⣄⣄⢀⡀⠀⢀⢀⣄⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⣄⣿⢸⣧⠤⢸⡇⠀⢸⡇⠀⣿⢸⡧⠄⢸⡿⣆⣸⠀⣠⡟⠁⢠⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠈⠟⠘⠇⠀⠘⠷⠦⠈⠳⠾⠃⠸⠷⠦⠸⠃⠈⠛⠐⠿⠶⠀⠟⠁⠙⠇
⠀⠀⠀⡀
⣰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡀
⠎⢳⣿⢲⡆⣠⠎⠀⠀⠀⠀⠀⠀⠙⠋
⠠⠈⢀⡁⢠⣿⡄⢀⡤
⠠⠄⠈⣀⠉⠉⣘⣡⠄

⡆⠠⡄⠀⠀⠴⣯⡅
⠀⠠⡄⠀⠑⢆⢀⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢲⠀⣄⠀⣴⣠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⣤⣄⣹⡰⢿⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡄⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠙⠃⠸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⣠⣜⠓⠂⠀⠀⠀⠀⠐⠶⢤⣴⢧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠿⢹⡈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣷⣶⠾⣶⣶⠜⠀⠀⠀⠀⠀⠀⠠⣄⠈⢛⠀⢸⠃⢰⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠋⠁⠈⣦⡄
⠐⠾⠇⠀⠀⠀⠀⠀⠙⣹⣧⣤⣿⡛⠳⠆⠀⠀⠀⠀⣤⠀⣘⡶⠾⠛⠛⣟⠿⠃⢴⡎⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⡿⠟⢋⠀⠀⠀⠀⠠⣄⣩⠾⠇⠘⢗⠀⠀⠉⠀⠀⠰⠞⠛⣶⡞⠉⠀⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠀⣀⡀⠀⢨⡟⠘⠳⡄⠈⢀⠀⡿⠁⢀⠴⠃⠶⠟⢷⠖⠛⠁
⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢙⣋⠀⢈⡁⠈⠳⠈⠀⠰⠂⢀⣄⠰⠶⠿⢶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⣨⣄⣠⣃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⠀⡈⣁⢀⡀⠀⠷⠀⡀⠀⠀⡀⠀⠠⣴⡇⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⡭⢱⡄⠀⠀⠀⠈⠷⠘
⢻⣌⠁⠈⠀⠿⠄⡶⢀⢀⡤⠚⠁⠀⠀⠀⢠⣤⠄⢿⡴⠟⠉⠀⠀⣠⠀⠀⢁⠐⠶⡉⠳⣶⡾⠷⠄⣠⠄⠀⠀⠀⠀⠀⠈⠳⠴⠛
⡀⠙⠀⢀⡔⢀⠘⣧⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⣰⡆⠀⠉⠀⣤⠀⣧⠄⠀⣦⡸⠷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠲⠀⠈⠀⠀⠀⠀⢤⠿⡞⠁⠀⠀⠀⠀⠀⠀⠚⠋⠀⣘⡿⢅⣠⣜⣇⠀⢀⣼⣀⠴⢾⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠛
⢀⠤⠀⠀⠀⠉⠛⠰⠖⢀⡷⠄⠀⢤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠉⢻⠛⡛⠙⠇⠀⠀⠻⠖⠀⠀⠀⠀⣿⢀⠤⢤⡄⢻⡁⠀⠀⠀⠀⠀⠘⢋⡰⠖
⠋⠠⠄⠸⡏⠐⣤⠔⠶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠀⠷⠀⠀⠐⢷⣆⡀⠀⠀⠀⠈⡷⢠
⡄⠦⠀⣤⠤⠦⡁⢠⠤⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢀⠁⠀⠀⠀⠀⠀⣠⠀⠠⢈⣡⡞⠃⠀⠈⠁
⠱⠶⢆⡻⠀⠄⠉⠲⠀⠈⠣⡤⠀⠀⢠⣄⠀⣱⣄⡄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠳
⠇⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣁⢈⡁⠶⠈⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠓⠻⡧⠌⣠⠀⠴⠒⢴⣧⣀⠀⠀⠠⠼⠃⠀⠀⠀⠀⠘⣭⠀⠀⠴⠀⠀⠀⠰⠆⠀⠀⠈⠀⠄⡴⠀⠀⠀⠋⠓
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣶⡀⠰⠂⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠁⡴⢤⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⢧⠄⠐⡦⠀⣀⠀⢠⠿⠾
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡬⠁⠐⠈⠁⢡⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠
⣰⢦⡗⢀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣧⠸
⠉⠉⠁⠁⠩⠶⠒⢄⣰⠃⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠐⢢⡄⠀⣀⢨⡄⠈⠀⠉⠀⠙⣿⠶⣆⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠘⠆
⠀⠀⢌⠁⠀⠀⠈⠙⣃⣢⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠋⢠⡀⠁⠀⠐⡂⠀⠀⠁⠀⠉⣱⣖⠁⠀⠀⠀⠀⠀⠀⣀⡱⠀⠀⠈⠉⣻⡉⢁⡄
⠀⠀⠀⢀⠈⠋⠀⠀⡡⠙⡶⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡯⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣦⣤⣶⣤⣴⣶⣶⣶⣶⣾⣶⣤⣶⣶⣶⣶⣶⣶⣶⣴⣾⣷⣶⣷⣶⣿⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣦⣶⣿⣦⣶
⣿⣿⣿⠻⠍⠛⠟⠉⠙⠛⢻⡟⠏⣹⡿⢻⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⠀⢀⣤⠤⠴⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⡘⠛⠫⣉⠀⠀⠈⠉⠙⠛⠷⢶⣤⣄⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⠁⠀⠉⠙⠻⢦⣄⡑⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⢁⠤⡀⠀⠀⠀⠨⢿⠃⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠠⠴⠒⢠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠛⠛⠛⠛⠛⠶⢦⣜⡆⠀⠀⠀⠐⠋⠁⠠⠤⠀⠞⠐⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠶⢦⡀⠀⠀⠀⠀⢀⡠⠭⣿⠀⠀⣴⠿⠛⠛⠻⠿⠿⠷⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠽⡄⠀⠀⢰⣏⣤⡴⠶⠶⠶⠶⢧⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢷⣦⡀⠐⢤⠀⠀⢸⣿⣅⡀⠀⠀⠀⠀⠐⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡛⢷⣾⣷⠤⠬⠷⠭⠿⢄⡀⢀⡏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣫⠭⠖⠒⠊⠉⠉⢙⡿⣿⣿⣧⣤⡤⣤⣤⣀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⡊⠁⠀⠀⠀⠀⠀⠀⢀⣜⣾⠟⠉⠀⠀⠀⠀⠀⠉⠛⢿⣵⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⠧⠠⡀⠀⠀⠀⠀⠀⠀⣠⠤⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⢸⡆⠀⠀⠀⢠⡿⢧⣀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⢀⣀⣀⠎⠀⠀⠀⠀⡜⠀⢀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⣀⠀⠔⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠂⠀⢀⠀⠀⠀⠀⠀⠘⢣⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠉⠉⠀⠂⠀⠀⠠⢄⣀⠤⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢤⣀⠡⠄⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠒⠛⠂⠐⢢⣀⢈⢁⡒⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠭⠀⠀⠀⠀⠄⠐⠀⠒⠐⠶⢶⢎⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠉⠙⣫⣍⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⡦⠄⠠⠠⢠⣄⡀⠀⠀⠀⠀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣔⣤⣀⣩⠥⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠦⠉⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠚⠋⠁⠐⠶⣀⠂⢀⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠥⠌⠀⠀⠀⠸⠀⠀⠈⠠⡥⡍⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡠⠟⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢹⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣃⣥⡠⠤⠤⠀⠀⢀⡤⠔⠋⢠⠤⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣔⣓⡶⠒⠒⠀⠀⡄⠄⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠰⣯⡽⠇⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠓⠒⠐⢊⠔⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢉⢣⡀⠀⠀⠀⠀⢀⠈⠒⠄⠠⠀⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠒⢆⠀⠀⠀⠀⠀⠀⠁⠀⠲⢜⡀⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣚⡂⣀⣀⢀⣀⡀⠀⠀⠀⢙⡓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠕⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄