Resort Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⡠⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠐⠃⠸⠀⡀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⠀⢀⢀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠹⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⢀⠸⠀⠈⠀⣀⣤⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣷⣖⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠲⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⠌⣿⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣀⣠⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡀⠒⠀⠀⠀⠈⠡⢤⠀⠐⠀⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⣿⣿⣙⣍⣫⣬⣉⣽⣫⣿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⣶⣶⣾⣿⣿⣿⣅⡁⠀⠀⠀⠀⢀⣴⣶⣿⣿⣦⣾⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠼⣿⡿⢿⣿⣿⣿⢿⣳⡭⢳⣤⡀⠀⠸⡿⣩⣿⣿⣿⡏⣿⣿⣿⣻⣿⣧
⠀⠀⠀⠀⣶⣿⠻⠊⣧⣿⠃⣿⣿⡀⢙⣛⠿⢷⣦⣀⣿⡿⠘⢿⣧⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣾⣿⠀⠀⠙⢻⠃⠈⠃⠀⠀⠙⢆⠀⠀⢸⠟⠷⠀⢿⡇⢹⡙⣿⠛⢷⣀⢰⠶⡇
⠀⠀⠀⠀⠉⠃⠀⠀⠀⠠⠀⠀⠀⣰⣶⣦⠈⠆⠸⠃⡀⠀⠀⢼⡇⢘⣛⣘⡇⠸⣟⣍⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠰⢚⠀⠀⠀⠀⡿⢾⣿⡷⡌⣰⠋⠀⠀⠀⠹⡇⢈⢋⡜⣻⡟⠟⠋⢿⢷⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢘⢩⠀⠀⠀⠀⣿⠶⠤⢿⣿⣟⣠⠤⠀⡀⢀⡇⠘⠟⡷⠛⡴⠆⠀⠤⠀⢺⡷⠤⠁
⠀⠀⠀⠀⠀⠀⢀⠛⡴⠀⠀⠀⠀⠿⣿⢿⡃⣉⣥⣄⠀⢠⢗⢈⡇⠀⠈⠀⠀⠁⠀⠀⠀⠁⠉⡆
⠀⠀⠀⠀⠀⠀⠚⠀⠁⠉⠀⠀⠀⢰⡟⣸⣿⣭⣙⢿⣀⡐⠊⢽⡇⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠁⠠⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣸⠀⣯⠊⢥⣤⣬⣿⣿⣒⣻⠅
⠀⠀⠀⠀⠂⠀⢠⡆⠀⠀⠴⠛⠀⠏⢸⣿⣾⠭⠉⡷⠚⠫⣙⡾⡆⠀⣣⡄⠀⣠⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠀⠀⢀⠙⢻⣦⠠⣰⡃⠈⠐⠀⢌⣬⣷⠿⠿⠼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⠸⢏⣿⣷⣶⡶⢫⠄⣨⢩⣴⣾⡽⡋⢩⡹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠋⠐⠒⠚⠙⠻⠛⣿⠛⠑⠁⠀⠀⠀⠀⠠⠚

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡄

⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠖
⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠸⣧⣉⠁⠀⠀⠸⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⢰⠀⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠟⠛⠛⠛⠛⠻⠻⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢛⣯⣔⣛⠿⡏⠀⠛⢻⣿⣿⣿⠿⠿⣿⡿⢿⣿⣿⣿⡟⠛⠀⡿⠟⣀⣝⠻⠿⠟⠛⠁
⠀⠒⠶⠶⠶⢶⣶⣆⠐⣶⡆⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠘⠛⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠶⠒⣢⠤⠤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠠⡀⢄⣰⠞⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡦⠀⡄⠔
⠀⠀⠀⠀⣠⡤⠈⠾⡧⣺⣧⣄⠀⠀⢠⢰⠆⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣺⡿⢨⢭⣡⠠⠅
⠀⠀⠀⠀⠙⠀⡸⠀⠴⠹⢦⣄⣔⣦⣶⣸⡌⠠⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠈⠀⠇⠀⠀⢀⠈⣧⠈⢻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⣚⣿⠿⠛⠛⢿⣷⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠐⡓⣿⣸⣸⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠰⣿⣁⣂⣒⣺⣛⣑⣒⣺⢧⣠⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠐⠈⠉⣹⣿⣯⣻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡿⠀⠛⠙⠻⢽⣿⣋⡠⡤⠈⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣁⡁⢙⡟⠁
⠀⠀⠀⠀⡠⠔⠁⡀⠀⠅⠀⣀⠀⠈⠀⠸⡈⠘⠉⡁⠠⠄⠐⠀⠙⠒⠲⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⡁
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⢣⣀⠀⣀⣄⡀⢒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠉⠉⡍⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠆⠤⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⣀⡐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⣴⣿⡿⠲⠂⠀⠀⠀⠀⢈⣿⠟⠀⠀⠀⠀⠉⡂⠒⠒⠊⠁⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣤⢠⡄⡀⠀⠀⢈⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⣼⠿⠁⠀⢠⣤⣶⣿⢰⣤⣤⣠⠀⠂⠒⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⠿⠸⠃⠿⢀⡀⠿⠃⢰⡀⢸⡆⡀⠀⠀⠀⠀⠀⡀⠀⣀⠼⠟⠛⠉⠉⢡⡈⡉⠺⣄⠀⠞⠤⢤⡶⠏
⠀⠀⠀⠀⢉⣀⠀⢰⡆⣤⢀⠉⠑⠲⠾⣇⣸⣿⣧⠀⠀⠒⠒⠐⡇⣴⠀⠀⠀⠀⢠⡇⣸⣧⣿⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠁⠘⠇⣿⢸⡄⠀⠀⠀⠀⢀⡀⢉⠀⠐⠒⠒⠚⠓⠛⠒⠒⡂⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⢤⡀⣿⢸⡇⣾⠀⣷⠀⢀⣠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠛⠃⠉⠉⠁

⠀⠀⣿⣿⣶⣶⣦⣀
⠀⠀⣿⣿⣿⣿⣿⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣿⣿⣿⣯⣙⡯⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠁⠐⢦⢄⣀
⠀⠀⣿⣻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⣀⠀⡀⣠⣌⣁⠇⠀⠀⠄⠒⠉⠱⣀
⠀⠀⠁⠟⢹⡟⣿⢿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⣠⠄⠃
⠀⠀⠀⠀⠸⠀⢹⠈⠻⡇⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⠄⠀⠀⠀⠐⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣠⡒⠉⠀⠈⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠿⠗⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠒⢬⡑⠢⢄⠀⠈⡄⠱⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣴⠏⠈⠑⠢⢍⠂⢰⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠉⠐⠒⠠⠄⣀⠈⠘⠉
⠀⠀⠀⠠⠄⠒⠋⠉⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠢⠤⠀⠀⠀⣀⠀⠀⠠⠯⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢅⡀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠈⠁⠀⢂⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⣀⡀⠀⠀⠀⢀⣰⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⢀⣠⣤⣤
⠀⠀⠀⠠⣀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣀⢹⣿⣴⣿⡟⠛⠃
⠀⠀⠀⠀⠘⢷⣄⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⢿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠈⢻⣦⣿⣋⣀⣤⣄⠀⠀⠀⠀⠀⠶⢶⣦⡄⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣰⣇
⠀⢀⣴⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠷⢄⠀⣠⠀⠀⢸⣿⣷⣶⣄⠀⠀⢠⡿⠋⠀⣾⢻⣿⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢰⣿⡟⠀⢀⣠⡀
⠀⠉⠀⠀⠀⢠⣿⣿⣿⠛⠿⣿⣿⠀⠀⢸⣿⠀⠀⢸⣿⣿⠈⢻⣷⣄⠈⠀⠀⢠⣿⠸⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⠿⠛
⠀⠀⠀⠀⠀⣿⡟⢸⣿⠀⠀⠈⠻⠀⢀⣈⣿⡇⠀⢸⣿⣿⠀⠘⣿⣿⣀⣠⣤⣼⣧⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠟⠀⣾⣿⡟⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⣿⣿⠀⠀⣿⡟⠉⠉⠉⢹⡇⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⣿⡿⣿⡍⠛⠿⣧
⠀⠀⠀⠀⠀⠀⢀⣿⢿⣧⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⢀⣿⣇⣀⣀⣀⣸⣇⣀⣀⣘⡻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⢹⣧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⣟⣥⣬⣿⣦⣤⣤⣤⣤⣤⣿⣧⠀⠀⣿⣿⠴⠛⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⡆⠈⠛⠛⠛⢻⣿⠀⠀⣿⣿⠀⠀⠻⠿⠿⠇⠀⠀⣿⠛⠛⠛⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣿⡄⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣀⣠⣤⣷⣴⣶⣾⣿⣶⣶⣶⣾⣿⠀⠀⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣝⣀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠻⠿⡍⣿⣿⣿⠁⢹⣿⡿⠿⢿⣿⡇⠀⣿⣿⡇⠀⢿⣿⣿⡿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣼⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣀⣀⣀⣸⣷⣤⣤⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣄⣀⣉⣉⣙⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠰⣾⡿⢻⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⠀⢸⣿⡏⠉⢿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠈⠳⢼⡏⠉⠁⠀⢸⣿⣁⠀⠹⢿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⣿⣿⣿⣧⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⢿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠸⣶⣄⠀⠀⠀⠀⠀⠀⠘⣷⡄⢹⠈⣿⣿⣿⡆⠀⣿⣿⣷⣶⣶⣶⣤⣤⣾⣯⣤⣄
⠀⠀⠀⠀⠀⠀⣰⡄⠘⣷⠀⠉⢉⣿⡟⠛⢻⡟⠛⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⠻⣷⣄⢻⣷⣾⠀⠸⣿⣿⡇⠀⣿⣦⠉⠻⠋⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⢸⣿⠁⠀⢸⡇⠀⠙⠏⢹⣿⡿⣿⣿⣿⠏⠀⢀⡘⣿⣾⣿⣯⣠⠄⢻⣿⡇⠀⣿⣍⠁⠀⢀⢠⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣾⠥⢤⣿⠤⠤⠿⠿⠤⠶⢾⡷⠶⠶⠶⠾⢿⣷⣾⣿⡿⠶⠶⠾⡿⢿⣿⣿⣿⠷⠶⠾⠿⠷⠶⠿⠿⢶⣿⡿⠶⠾⠿⠶⠶⠶⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⣴⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣧⣀⣀⣀⣀⣀⡀⠀⠀⠸⠿⠷⠶⠶⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢰⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣦⡀⣼⣿⣿⣿⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠃⠉⠉⠀⠀⠈⠙⢿⣿⣿⣛⣫⣥⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡿⢷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⢀⣾⣿⠟⠟⠋⠁⣴⢟⣿⣿⡟⢿⣷⣤⡁⠸⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠀⠀⠀⠀⣾⠟⠃⠀⠀⠀⣼⠏⣼⣿⣿⣿⠈⢿⣿⣿⣦⠀⠛⣿⡇
⠀⠀⠀⠀⠰⠺⠿⢿⣶⣦⣼⣿⢁⣤⣴⣶⣶⣧⣀⠀⠀⠀⣸⡏⠀⣻⣿⣿⣟⠁⠀⠸⣿⣿⣇⠀⠘⠃
⠀⠀⠀⠀⠀⣠⣤⣶⣬⣽⣿⣿⣿⣟⣛⠙⠛⠻⠿⢷⡄⢠⣿⠀⢘⣿⣿⣿⣿⡄⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣾⡿⠟⠋⠙⢛⣽⣿⣿⣿⣿⣿⣦⣄⠀⠀⠉⣼⡇⠀⠘⣿⣿⣿⡟⠁⠀⠀⠀⢹⡟⠀⠀⠀⠀⣠⣾⣧⣀
⠀⠀⠀⠈⠁⠀⠀⢀⣴⣿⣿⣿⣿⠻⣯⡙⢿⣿⣆⠀⠀⣿⠃⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠃⠀⢀⣤⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⣿⡏⢻⣇⠙⣷⡌⠁⠙⠀⢸⣿⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⡿⠀⠀⠉⠀⠘⣿⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⡀⢀⣀⣘⣿⣄⣀⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⣿⡄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⣤⣿⣿⣧⠤⠤⠤⠴⠒⠒⠒⠲⠤⠤⢤⣤⠤⠤⠖⠒⠒⠒⣿⡗⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠦⠤⣤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠓⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣂
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡏⠢⡀⠀⠀⠀⠀⠀⠀⣨⣴⣿⠿⠓⠄⠐⠦⣀⠀⢀⠴⣆⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢧⠀⠊⠙⠦⢄⣠⣄⠀⡛⠉⣁⡀⠀⢀⡔⢀⠈⢀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠂⠀⠀⠀⠓
⠀⠀⠁⠊⠿⣿⣿⠿⢟⠁⣰⣷⣤⣄⣠⣿⡿⠈⢓⣴⡞⠫⣀⠉⡻⡇⢈⣉⣤⡤⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠔⢉⠔⣽⣿⣶⣿⡿⠁⠀⠉⠙⠶⠤⣍⡛⠃⣤⠀⢉⣩⡾⢙⠛⠉⠁⠐⣦⣄⣀⣀⠄⠀⠀⠆
⠀⠀⠔⠡⠒⠁⢸⠿⢛⠍⠁⠀⣀⠀⠀⠀⠀⠀⠀⠉⠙⢫⠄⢋⣚⣡⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠀⠀⠄⠒⠊⠁⢀⣀⠀⠀⠀⠀⠀⠀⠶⡶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠈⠁⠉⠉⠀⠀⠄⠀⠤⠄⠤⠤⠤⠀⠀⠤⠠⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⠀⢽⠀⢀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⢸⡁⠀⢀⡀⠀⠀⠀⠀⠐⢀⢄⠀⠘⠀⠀⠀⠉⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠔⣤⡴⠀⠈⠙⡄⠘⣠⠖⠀⠀⠀⠀⠀⢀⡁⠀⠑⠇⢠⡠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠝⠃⢘⢥⣀⣀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⠅⠀⠀⡄⠀⠀⣠⣦⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠔⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⢀⣼⣿⣿⡄⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠉⠀⠀⠉⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣄⣀⣀⡇⠫
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⠈⠉⠀⠉⠉⠉⠋⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡠⠒⠒⠒⠒⠒⠲⡶⠶⢀⠄⠀⠉⠉⠉⠉⠻⣶⣶⣶⣶⠂
⠀⠠⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠶⠶⠶⠾⠷⠒⠆⠀⠀⠀⠀⠀⠀⠀⠘⣞⠛⠒⠲⠦⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⡄⠀⠈⢷⡀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠘⠉⠁⠀⠋⠛⠛⠛⠛⠛⠛⠛⢳⡒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠹⣦⣤⡾⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡧⠀⠀⠘⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⣦⣤⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⡀⠀⠀⠙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⢿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⠿⠆⠀⠀⠀⠀⠳⡅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢦
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⡏⢓⣓⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣀⢔⣼⡾⠿⢛⠛⠟⠲⢦⣤⡄
⠀⠀⠀⠀⣴⠋⠁⠀⠈⠉⢧⠠⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢄⡀⠐⠋⠀⠀⠀⠀⠀⣱⣿⢾⣿⣝⣻⣿⡬⣤⡾⡿⣱⠁
⠀⠀⢀⠀⢻⣶⣤⣤⣴⣲⣿⡥⣾⣿⣷⣦⣄⡀⠀⠀⠀⢀⣠⣤⠶⣺⡋⠉⠻⣦⡙⢦⡀⠀⠀⠀⠀⠀⣏⠙⠺⠽⠿⢠⡿⠷⠟⠷⠓⡛
⠀⠀⣮⠀⣟⠏⠉⠻⠿⢗⠻⠿⠟⠋⢉⡿⢈⡇⠀⠀⢰⠙⣛⣫⣰⡷⠃⠘⣁⣨⣽⣾⣛⠆⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠈⠑⠤⣭⣶⣄⣣⣤⣬⣄⢀⠈⠁⠐⠁⠀⠀⠀⠀⠠⡇⠀⠉⠉⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⢀⣲
⠀⠀⠀⠀⢀⣠⡴⡖⠞⠉⡳⢶⣤⣤⣀⡐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⣀⡘⠛⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠒⠒⢒⢉⣤⣿⣶⡤⣅
⠀⠀⡐⢂⣼⣭⣳⡶⣬⣅⡲⠠⣺⣿⣷⡌⢢⡀⠀⠀⠀⢀⠀⠀⣐⣋⣡⣬⣗⣳⡿⡝⠳⡀⠀⠀⠀⢠⢾⣿⣡⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⡆⢹
⠀⠰⠀⢞⠿⠿⠷⠿⠝⣿⠯⠡⠷⠿⢛⠟⣸⠇⠀⠀⡐⡣⣶⠿⠛⠛⠉⢁⠔⢉⣀⠵⠐⠁⠀⠀⠀⠘⢌⠢⠛⢃⠙⠶⠿⠛⠛⢛⣋⡤⠔⣁⠜
⠀⠀⠓⠤⣀⠑⠀⠀⠀⠀⠀⢀⣀⣈⣡⠞⠁⠀⠀⠀⠘⠷⣧⡀⠄⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠂⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⢀⣠⠀⠄⠄⢐⡒⢒⠖⠐⠒⣖⢦
⠀⠀⢀⠤⠄⣶⡶⢦⣶⢶⢿⢶⣿⣿⡏⢷⡀⠀⠀⠀⠀⢀⠤⠒⡒⠲⣶⢺⡞⢩⠻⡀⠈⢱⠀⠀⠀⠀⠀⡰⢻⣿⣷⠛⠻⠭⠝⣠⡼⠦⣤⣘⣎⣦⡀
⠀⠰⢣⣯⣽⣭⣙⣩⠏⠹⣬⡗⠺⣿⣷⣾⡿⣆⠀⠀⢀⠁⠦⣰⡄⢳⠈⣃⣸⣁⣿⣿⡿⣿⣷⠀⠀⠀⠀⠇⢸⣿⣿⣿⣖⠶⠛⠬⣛⣓⡖⠁⢸⢸⡇
⠀⠰⣌⠻⢤⣙⢯⣉⡙⠿⠶⠾⠿⠁⠀⡰⢣⡟⠀⠀⢸⣧⠆⣀⢉⡧⠀⢾⠛⠙⢋⡧⠊⠀⣼⠀⠀⠀⠀⠘⢄⠋⠀⠒⠸⡀⠀⠀⠨⠇⣀⡴⢋⡜
⠀⠀⠈⠑⠦⢍⡙⠋⠉⠀⠀⠂⢀⣀⣡⠴⠋⠀⠀⠀⠀⠙⠢⢝⡻⠖⠀⠀⠈⠉⠀⢀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠀⠤⠤⠭⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡆⣜
⠀⠀⠀⡔⠒⠻⣍⢻⡍⣹⠦⣠⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣠⣤⣄⣀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⢿⣽⣿⣿⣷⡤⣄
⠀⣴⣾⡷⣤⡤⠛⠉⠛⡝⠳⢮⣛⡿⢻⣦⡀⠀⠀⠀⢀⣤⣴⡎⢉⣉⠙⣿⣿⣦⣾⠛⢱⠿⣝⢢⡀⠀⠀⠀⢠⡞⢫⠶⣶⡿⠀⠀⠀⠀⣸⣜⣾⡱⡄
⠘⣇⠣⡀⠀⣷⡙⠀⢠⠳⠐⢍⡹⠳⡄⣱⣹⠆⠀⠀⣾⢿⠁⠑⣏⠂⠑⠀⣀⣿⣷⠚⣁⣳⣨⢋⡇⠀⠀⠀⡌⠀⡟⡦⠖⠊⠓⣤⣤⣤⣿⠉⢈⠇⡏
⠀⠈⠳⢤⣄⡘⠻⠶⠶⠶⣶⡐⠒⠒⣛⡽⠋⠀⠀⠀⠘⢎⠀⠠⠌⠉⠁⠈⠀⠉⠥⠤⠒⢚⡵⠟⠁⠀⠀⠀⠘⢄⠐⢌⠂⠄⠾⠁⠧⠒⠉⡠⢊⡼⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠲⠒⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠬⠀⣠⣤⠀⠤⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠉⠁⠀⠀⠀⠀⠀⣈⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠦⣈⠛⢦⠀⠀⢀⠴⣶⠶⢤⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠁⡎⣸⣿⣿⣆⠙⣿⣞⡾⣥⣿⣍⣉⣙⣒⠲⢤⣤⣄⢂⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡆⢫⠙⣿⣟⠛⢋⢿⣝⢿⣿⣶⣌⠙⢷⣶⣖⠚⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⣹⢿⣿⣷⠘⢧⡀⠛⠃⣸⡼⣯⡼⡟⢻⣿⣿⣦⣮⡻⣿⣃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣱⣾⣃⣏⣻⣿⣇⢀⣹⣧⠀⢡⠄⡏⠃⣿⠇⠟⢉⣿⣿⣿⣮⡻⣤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠴⠶⠶⠦⢬⡻⠿⢿⣶⡶⠚⡈⠀⣼⣿⡿⠄⠀⠉⢹⣿⣷⣽⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣤⣒⠢⡀⢀⡀⢄⠒⠤⠄⡴⢺⣿⠟⠋⠀⢀⣴⢻⡿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣌⡑⠛⠦⠕⠒⠊⠀⠀⠈⠓⠂⠒⢫⡍⣨⢁⣾⢻⣿⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⡏⣼⢿⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡞⢆⠰⣤⣄⣀⠀⠀⠀⠀⠀⣉⣾⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢧⡀⠳⣜⠿⣮⠙⢶⣄⠀⠀⢈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⣻⣷⣦⡈⣆⣼⣿⣷⣬⡛⠿⣄⢼⣿⣷⡄⠈⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠿⢿⣿⣿⢿⣿⣿⣿⣾⡿⡟⠿⣹⣷⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⡀⢀⡀⠀⠀⠛⣦⣹⣿⣷⠻⣿⣿⡈⠁⠉⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⣷⠀⠀⣿⣿⣿⣿⣯⠈⢉⣟⣿⡶⠒⢹⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⢀⣮⣿⠀⣷⣿⣿⣿⢿⡟⢰⠿⣫⣟⣡⣤⣼⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠏⣼⣿⢇⣿⡟⣼⡠⠴⣺⢿⣻⣿⣿⣿⠻⣿⣟⠀⠙⠆
⠀⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠀⠀⠀⣠⣴⣶⣿⣿⡿⠋⣰⡿⢋⣾⠟⡼⠉⠀⢘⣵⢿⣿⣿⠿⠏⠙⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⢂⣼⡿⣛⣽⣾⣿⠁⡈⠉⣴⡿⠃⠈⠀⠀⣰⠟⣵⠿⠟⠉⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠫⣾⣿⠿⠋⠛⠛⠁⠸⠋⠀⠀⠀⠀⠈⠁⠘⠁

⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣴
⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠘⠛⠂⣠⣾⣷⡦⠀⠀⠀⠀⣛⠅⠀⠀⠀⠘⣛⠃
⡏⣾⣿⡇⠀⢠⢤⣤⣤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⢿⣷⡄⠀⢸⣿⣿⡟⠀⠀⠀⢠⢖⣿⣷⡄⠀⢠⢞⣿⣷⡄
⡇⣿⣿⡇⠀⢸⢸⣿⣿⠀⠸⡅⣿⣿⣿⠀⠀⠀⠀⠈⠛⢿⣆⠾⠋⠉⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠈⢆
⡇⣿⣿⡇⠀⠈⢳⡟⠁⠀⠀⠙⢾⡟⠋⠀⠀⠀⠀⠀⠀⣠⡹⣷⡀⠀⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠀⢸⣿⡶⠦
⣇⣿⣿⡇⠀⠀⣨⣇⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⠟⠀⠘⢿⡆⠀⠀⠀⠀⢸⣼⣿⣿⡇⠀⠸⣼⣿⣿⡇⠀⢸⠹⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⣖⣒⣒⣒⣒⣒⠀⠀⠀⣶⣒⣒⣒⣒⣒⠀⠀⠀⠀⠘⢶⠀⠀⠀⠰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣘⣃⡀
⣿⣿⠿⠿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⠶⠶⠶⢾⡅⠀⠀⠀⠀⠀⠀⠀⢰⠀⣆⠀⠀⠀⢰⣿⣿⡄⢸⢸⣿⡇
⣿⣿⡇⠀⣸⣿⠀⠀⠀⣿⣟⢀⡏⢸⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠼⠀⠟⠀⠀⠀⠘⢿⡟⠁⢸⢸⣿⡇
⣿⣿⣮⢰⣿⣿⠀⠀⠀⣿⣿⢸⣿⢸⣿⠀⠀⢀⣠⠤⠜⢮⣉⣩⠞⠡⢤⣄⠀⢸⡛⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⢸⢸⣿⡇
⣿⣿⣯⣬⣿⣿⠀⠀⠀⣿⣿⣼⣿⣼⣿⠀⠀⡞⠀⠀⠀⠀⣴⠀⠀⠀⠀⠈⡇⠀⠳⡘⢿⣿⣿⣿⣿⡿⠃⠀⢸⡇⠀⠈⢩⡍⠁
⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠓⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠃⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠘⠃⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡤⠦⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⣻⠈⡇⠀⠀⠀⢀⣤⣞⠉⠳⣯⡀
⢠⣟⣭⣤⣭⣛⣷⣶⣤⡀⠀⠐⢿⣾⢛⣂⣉⣂⣀⣋⣀⣚⢻⣾⠃⠀⠀⠀⣠⢴⣾⣿⣷⣤⡁⠈⠀⠀⠀⠀⣋⣀⣀⣀⣀⣀⣘
⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡆⠀⠈⠁⠈⢧⣻⣿⣿⣿⡿⠃⠈⠁⠀⠀⢀⡞⢱⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⣜⣿⣿⣿⣿⠟
⣏⠙⠛⠛⢋⣡⠴⠶⠦⠤⠇⠀⠀⠀⠀⠀⠈⠙⡏⠁⠀⠀⠀⠀⠀⠀⠸⠁⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠉⣿⠉
⠈⠙⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠒⠛⠒
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄
⡤⢤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣴⣦⡆⣼⣿⡇⢀⡴⠋⢉⣀⣀⠉⠳⣆⠀⢠⣿⠀⣼⡆⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⡿⢈⡇
⣷⣶⠒⢺⠃⠀⠀⠀⠀⢠⣿⡇⢿⣿⡇⠙⣿⠃⡞⠀⣴⠋⠁⠉⠳⡄⠈⣇⠸⣿⠀⣿⠇⣾⡇⠀⠀⣾⣿⠄⠀⡶⣶⣶⣶⣶⣆
⢺⣀⠴⢾⠀⠀⠀⠀⠀⠀⣿⠀⠈⣯⠀⠀⣿⠀⣇⠀⢷⠀⠀⠀⢀⡇⠀⡿⠀⣿⠀⢻⡄⢻⡇⠀⠀⢸⡏⠀⠀⢧⢻⣿⣿⣿⣃
⢸⡟⠐⣾⠐⣶⣄⣀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠙⣆⡈⠙⠒⠒⠋⢀⡼⠁⠀⣿⠀⢸⡇⢸⡇⠀⠀⢸⡇⠀⠀⠘⠞⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣟⣛⣻⣻⣛⣛⣛⣟⣟⣛⣛⣛⣟⣛⣛⣻⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⡏⢿⢛⡿⣻⣝⢿⡝⣭⡟⠭⣽⢻⣿⣿⣿⢽⣿⣿⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣶⣜⣧⣛⣋⣼⣇⣿⣏⣗⣻⣸⣛⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣿⣿⣿⣿⣷⣾⣯⣿⣭⣿⣭⣭⣯⣽⣭⣿⣭⣽⣭⣿⣭⣿⣷⣿⣿⣿⣿⣿⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⡤⣬⢹⣿⣿⣿⣿⣿⣿⢫⡤⣮⢹⣿⣿⣿⣿⣿⣿⢫⡤⣮⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⣦⣶⣼⣿⣿⣿⣿⣿⣿⢰⣦⣶⡄⣿⣿⣿⣿⣿⣿⢰⣦⣴⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢨⣏⣿⣽⣿⣿⣿⣿⣿⣿⢨⣇⣿⡅⣿⣿⣿⣿⣿⣿⢨⣏⣽⡍⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡘⠟⠻⢻⣿⣿⣿⣿⣿⣿⡘⢓⠻⢃⣿⣿⣿⣿⣿⣿⡘⢛⠻⢓⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠐⠛⠛⢸⣿⣿⣿⣿⣿⣿⠐⠛⠛⢸⣿⣿⣿⣿⣿⣿⠐⠛⠛⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡿⣿⢿⣿⣿⣿⣿⣿⣿⢸⡧⣿⡇⣿⣿⣿⣿⣿⣿⢸⡿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣷⣿⣾⣿⣿⣿⣿⣿⣿⢸⡗⣿⡆⣿⣿⣿⣿⣿⣿⢰⣷⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣬⣥⣭⣽⣿⣿⣿⣿⣿⣿⣬⣥⣭⣵⣿⣿⣿⣿⣿⣿⣬⣥⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⣍⣝⢻⣿⣿⣿⣽⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢟⣍⣍⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢨⣅⣭⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢨⣅⣭⣐⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⢘⡟⣻⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠀⢶⣿⣿⣿⣿⣿⣿⣿⠸⡿⢿⠟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠃⠛⠛⠛⠛⠓⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠖


⣶⣶⣶⣾⣶⡿⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⡾⠷⠾⠿⠿⢿⣶⡶⠶⢶⡿⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣻⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣾⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣾⣿⣿⡿⠿⠿⢃⣀⣀⣀⣀⣤⠴⠶⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⢟⣩⣴⣶⣶⣾⣿⡿⣻⣿⡟⠡⡜⢿⣼⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣀⠸⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⢷⢹⢸⡿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣮⡉⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⠀⡟⠀⡟⡾⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⢹⣿⡇⣿⣿⣧⣈⣉⡙⢿⣷⣶⣤⣀⡀⠀⢙⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣻⣽⡔⢮⣅⣈⣛⣛⣫⣥⣾⣷⣮⣝⠻⢿⣿⡿⠿⠛⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⡿⣦⣝⡛⠿⠟⠛⢋⣛⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⠉⠉⢉⣴⠟⠉⠉⠀⠙⠃⠀⠀⠀⠐⠳⣶⣶⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣼⡿⠿⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⣤⣤⢀⣤⣤⣤⣤⢠⣤⡄⣤⣤⡤⣤⣤⢠⣤⣄⢠⣤⡄⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡌⠁⢸⣿⠘⢿⣷⣬⣉⠀⣿⣦⣼⣿⠀⣿⡇⢸⣿⣿⣦⣿⠀⣿⡏⢈⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⣾⣿⠼⡿⢶⣿⠿⢰⣿⡆⢼⣿⠤⣿⣧⢼⣿⠌⠿⣿⠀⠻⣿⡶⢿⡏

⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⢀⠀⠀⠀⡠⠀⠀⠀⡀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⣀⡢⠀⢂⠀⢀⠀⢂⠀⠀⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠄⢠⣂⡉⠦⠂
⠀⠀⢠⡀⠀⠀⠀⠑⠀⠀⠢⢀⠀⠀⠁⠀⢐⣓⡅⠀⠀⡐⡀⠀⠂⠀⠀⠀⠀⡀⠁⠀⠉⠂
⠀⢆⠀⢀⠀⠀⡠⠐⢂⠂⠂⠠⡀⠀⢰⠍⠘⣵⠂⠀⢠⠊⠀⠐⠀⠰⠐⡠⠊⠀⠈⠁⠒⠂⠀⠀⠈⠡
⠀⢀⢄⠈⠀⢈⠀⢀⠤⢀⡦⠦⠏⢀⠤⢄⡀⠻⠀⠀⠈⠂⠠⠛⠑⠀⠀⠀⠀⢀⡀⠁⠁⠀⠂⠁⠂
⠀⢸⠀⠣⠀⠉⠀⠡⠬⠅⠒⠊⠀⡘⠀⠀⡌⠀⢀⠀⠀⠦⠄⠀⣠⣤⢶⣞⣤⠀⢀⠀⠀⠀⠀⡄⠒⠆
⠀⠸⡐⢀⡇⠀⠀⠖⠂⠀⠀⢠⠆⠑⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⡈⠹⠉⠉⠉⡁⠀⢀⠘⠀⠈⠁⠈
⠀⠀⠈⠁⠐⠢⠀⠄⠀⠀⠀⡀⢀⡠⣶⠴⠀⠀⡀⠀⠀⠰⠳⠀⠀⠀⠀⠉⠀⠀⠠⠀⠄⢀⠄⠙⣈⣠
⠀⠓⠀⠀⠀⠀⠀⠀⡄⠀⠄⠐⠂⠉⠠⢊⠐⠃⢃⡲⠖⠀⠀⠀⠀⠤⠀⢀⡀⢈⡀⢀⠀⡀⠀⡀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠴⠔⠒⠂⢉⠴⠀⠀⠀⡀⠀⠀⠂⠅⠀⠀⠐⠈⠠⠈⠀⠃
⠀⢂⠀⠀⠐⡀⠀⠀⢴⡄⠀⠀⣠⠤⠤⠸⢇⣀⠐⠋⡀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⡠⢐⠂⠚⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠁⡀⠁⠀⠀⠀⠂⠠⠈⠁⠀⠀⠀⠂⠐⠉⢀⠀⠀⠀⠈
⠀⠀⠠⢀⠀⠀⡔⡄⠀⢀⠀⠄⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢄⠀⠲⠆⠈⠁
⠀⠀⢀⣀⠀⠀⢡⠁⡀⠠⠁⡆⠀⠂⠀⠀⢀⠀⢰⠂⡀⠀⠀⠀⠀⢀⠰⠂⠀⠐⢣⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠖⠀⠀⠀⡀⠐⠀⠾⠀⠀⠀⠈⠀⠠⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⢀⠜⡄⠀⠈⠿⠂⠁
⠀⠀⠂⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠄⠀⠀⠄⠒⠒⠪⠐⠂⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡐⡀⠈⠁⠠⠒⡀⠃⠀⡙⠀⠀⠀⠀⠀⢀⠀⠀⠠⡰⠠⢀⠆⠄⠂⠀⣀⠀⠀⢀
⠀⠐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠃⠀⠂⠠⠀⠀⠉⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⡉⠀⠀⠀⢩⠃
⠀⢰⢙⠡⠃⠀⠚⠀⠂⠀⠀⡐⠀⠀⡡⠐⠘⠂⠀⢀⡀⠍⠀⠀⠀⠀⠀⡙⠙⠁⠀⠀⠀⠐⠀⠀⠐⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡎⠀⠐⠁⠀⡠⢀
⠀⠀⠄⠀⠀⠐⠀⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠠⠄⢀⡀⠀⢀⡇⢸
⠀⠀⠀⠐⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠂⠀⢂⠠⠄⣁⢀⣈⣉⣀⠉
⠀⠘⠀⠠⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠐⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠞⠀⡉⠒⠢⠻⠤⠤⠀⠔⠉
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠌⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⢄⢴⡆⠀⠀⠀⠀⠠⠀⣀⠈⠙⡀
⡀⠀⠀⠈⠂⠄⣀⡈⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⡉⠻⠀⢀⡤⠂⠀⣎⠂
⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠴⠰⠈⠤⣀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠠⠘⡦⠴⡤⠤⠖⠁⡀⠔
⠀⠀⠈⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠢⡀⠀⠁⠀⠀⠈⠲⠄⠀⠀⠈
⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⣀⠀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢄⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⢀⡠⠲⠀⣶⠤⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡈⠀⠀⠀⠐
⠀⠀⠎⣠⠊⠙⡟⢲⢳⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠲⠤⢀
⠀⠀⣥⠨⡓⡿⣞⠄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠎⠀⠠⣄⢡⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠈⠳⠍⡵⠙⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣⡀⠀⠀⢨⠀⠀⠀⣹⠷⠈⠉⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠘⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⢦⠀⠀⠀⠀⠀⠀⠑⠂⠤⠄⠒⠁⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⡴⠃⠀⠀⠀⠀⠀⠤⠒⠀⠉⠉⠀⠀⠀⠀⢀⠀⠈⠀⠐⠀⢠⠘⠂⠀⣀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⢈⠉⠁⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠂⢰⡀⠲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠐⡀⠀⠀⠀⠀⠘⠈⠀⠈⢰⠃⠈⠁⣈⣀⠀⠀⡀⠒
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠠⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⣶⣿⣿⠆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⠠⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢈⠁⠒⠔⠃⠀⠈⠿⠛⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠐⠒⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠘⠑⠂⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢒⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⢤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣆⣀⠀⣀⣤⣶⣿⣟⣛⣿⣿⣿⣿⣿⡟⢿⣷⣶⡅⠀⠀⠀⠀⢀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣼⣷⡘⢷⣽⡿⠿⠿⣛⡋⡉⠛⠛⠻⣾⣿⠏⣴⣿⣶⣄⠀⠀⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣞⠉⠀⣴⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠈⣉⣉⣉⣡⣄⣜⣷⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡁⢈⣧⣾⣷⣾⣿⡯⣄⡀⠀⠀⣠⠴⡒⡋⠉⠉⠀⠈⠠⠀⠀⣉⣻⣿⠿⢿⡿⢿⡿⣿⡿⢟⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢍⣉⣿⣿⡿⠋⠀⠀⠉⣽⠟⠉⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠞⠐⣛⠛⠈⢀⡼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢠⠀⣱⠟⠇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠠⣄⡈⣿⣦⣾⣥⣇⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⠀⣒⠿⡈⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣛⠶⣄⠈⠁⠉⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢦⣄⡠⠀⠀⠀⣤⠀⠀⣰⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢖⣛⣿⡦⠖⢻⣿⣿⣿⠦⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡿⠉⣹⠃⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⢰⢖⡓⢲⠶⠚⠁⠀⢰⠇⣰⠏⢇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣷⣀⠀⡀⡠⠚⠙⡟⡇⡿⠀⠀⠀⠀⢸⢞⣅⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢻⣿⣿⣿⣷⣾⣄⡜⡇⢀⣿⠇⠠⣀⠀⣀⡄⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡱⢄⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣆⠀⢹⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⠀⡄⡌⠙⢻⣶⣯⣿⠿⢿⣿⡿⠿⠿⣿⣿⣿⠿⠛⡿⠲⠁⠀⡠⡀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢳⠮⠥⡘⠃⠀⠀⠀⠙⢿⣷⣆⠈⠚⢿⣿⣿⣿⡿⠁⠀⡰⠃⠀⠀⠀⠈⠛⣀⠭⢶⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⣤⠀⠀⠀⠀⠙⢻⡄⠀⠈⠹⣿⣿⠀⠐⡏⠀⠀⠀⠀⢀⡔⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣥⠀⠀⠀⠀⠀⠀⠿⠒⠦⣤⣿⢟⠁⠀⣧⠀⠀⠀⠀⢤⡁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⠀⠀⢸⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠀⠉⠉⡏⠀⠀⢸⠀⠀⢸⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⢀⣤⣠⣦⣾⡀⠀⢸⢸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸⠉⠉⠉⠀⠑⠁⠙⣋⠙⠿⠿⣳⣜⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣭⣐⣂⠩⢝⣛⣿⣿⠿⠀⡀⠀⢀⣇⣀⣸⣀⣀⣀⠀⡛⠆⢼⣿⢬⣥⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡟⢫⣽⡾⡎⠉⠉⠉⡏⠉⢸⠀⠀⢸⠀⣻⠆⢀⡄⣪⣿⣿⣿⢹⢀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⢸⣿⡇⢸⡇⣼⢹⢱⠁⡆⠀⠀⡇⠀⠸⠆⠐⢾⠂⠈⡷⠈⣸⢧⣿⠟⢉⡼⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠿⢇⡘⠗⡏⢸⢘⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠙⠞⠛⡢⢋⠔⠁⣨⠦⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠘⠈⠀⡇⠀⠀⣧⠤⠤⠤⠤⢼⠀⠀⠀⠈⠻⡿⢂⡤⠚⠁⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⡆⠀⠀⠃⠀⡀⢚⢦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢩⣿⡍⣙⣤⣿⣄⠀⠀⠀⢰⢁⡉⠀⠼⢧⣠⡤⠤⠤⠤⠤⠤⠤⠄⢰⠳⠃⡠⠌⢢⠀⢠⣆⠀⠀⢹⣿⡇⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠮⢙⡰⣿⣿⢿⠇⢸⠀⢸⣿⠐⠂⢰⠍⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⡄⣸⠴⢤⡀⠡⢸⡿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⣦⠀⠀⡗⠘⢿⣤⡐⠳⠛⣼⠟⠤⠤⠤⠤⠤⠤⠤⠤⠘⣷⡗⠤⠔⡃⡀⣬⠁⠀⠀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⡀⠰⡄⠀⡇⠀⠀⡀⢹⣤⣴⣇⡀⠄⢠⡄⠀⠠⠄⠀⣤⡀⠈⠃⠀⡰⠁⠀⣾⡇⠀⢀⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣶⣶⣴⣟⠊⢸⡇⣤⣶⡾⣿⣋⡀⣰⠄⡶⠀⠀⠀⠀⠀⠘⣧⣀⣀⡜⠁⠀⠀⢿⡇⣾⣼⡇⢸⠇
⠀⠀⠀⠀⣀⠤⣤⣶⣿⣿⣿⣷⣬⣍⠙⠳⠤⠵⣿⣋⡐⣿⡇⠀⠨⣤⣇⣀⣀⣀⡀⣠⡀⠹⠻⡻⣧⣤⣀⠀⢸⣿⣿⡟⠀⠸
⠀⢠⣶⠉⠀⠀⠻⣿⣿⡿⠿⠿⠛⠋⠀⠄⠀⠀⠀⢹⣷⠈⡃⠀⠀⢀⣠⡅⠀⣉⠄⢸⡏⠳⢤⣻⣮⣶⡆⠃⢸⡟⠁⣀⣤⣶⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⣼⣿⠀⠥⠛⠟⢫⣾⣷⠀⢸⣷⣶⣶⣴⣯⡍⠉⢹⣿⣿⡿⣳⣾⣿⡿⣿⣧
⠠⡟⠁⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡄⢰⢦⣩⣿⣆⢠⡄⠲⠀⢯⣍⣣⣼⠯⠉⠉⠉⠉⠡⠚⢸⠟⢁⣴⣿⣿⡿⣿⣿⣿⡀
⠀⠀⣀⣈⣉⡟⠙⠋⡿⠛⠛⢻⠛⠉⡿⠑⣦⡄⠀⢹⣿⣷⡠⢷⠂⠓⠂⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢠⢔⣿⣿⣿⣿⣽⣿⣿⣟⡧
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣷⠘⡆⠻⣿⣧⠈⠇⢈⠁⠀⡀⠀⠀⡤⠀⠀⠀⠀⠠⢸⣿⢟⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣇⠠⣑⠌⠁⡡⡀⠈⡄⠐⢽⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠻⣿⣿⣿⣿⠀⠀⢿⣿⠆⠻⠿⠾⢰⣧⠀⢰⠀⠈⠻⣦⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠀⠀⢸⣿⣦⣤⣄⣰⣿⠃⠀⠈⡄⠀⠀⠑⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢏⡾⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠉⠙⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⠿⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢡⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠎⡐⢁⠞⡠⣊⢔⡁⢒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣘⣃⣃⣊⣐⣡⣊⣊⠕⡰⠲⠕⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣲⠟⢹⣿⡿⡪⠋⠛⣽⣽⡝⡟⠹⣷⣷⣯⣀⣠⡾⠪⣂⢐⢌⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⢀⣤⠔⠛⠿⠱⠑⡀⡢⠙⣿⡇⡄⠜⣾⣿⣟⣄⣜⣿⣿⣻⡟⠊⠻⣿⣷⡶⢵⣯⡇⠀⠀⠀⠀⠀⠀⣠⣶⣫⡂
⢀⣠⠖⣁⠣⠖⠇⠀⠀⠀⠀⠍⠉⠎⢅⢄⠌⢜⣿⣞⢀⠈⠜⣿⣽⡟⠔⠴⣽⣽⣟⣔⢜⣿⣿⢁⣦⣿⣷⣘⡮⣿⣥⠂⢀
⠫⣁⠑⢬⡁⣧⢠⠆⠀⠂⡙⠂⠃⣀⢂⡎⠊⠊⠻⠏⠔⠐⡠⣻⣿⠏⡊⡀⣾⡿⣫⠎⠨⠛⠋⠉⣉⢉⢩⣉⡡⣿⣆⠡
⢀⠈⣢⢤⠳⡈⠜⣠⠤⠈⠀⡠⢠⡾⠛⠇⠀⠀⡐⠄⡸⡈⢀⡿⠋⠈⢁⠁⠙⠈⢄⢠⣢⣥⢾⣉⠀⠀⠀⠀⠙⠯⣍⠒⡠
⠀⠀⠈⠁⠉⠐⠲⠤⢤⡄⠀⠐⠰⡋⠅⠲⡀⠄⡠⢑⠀⠀⠎⡈⣖⣱⣕⡤⠴⠚⠻⠛⠈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢺⣷⠖⣚⣒⠛⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣲⡽⡟⢌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⢀⣀⡀⢀⣀⡀⠀⣀⣀⠀⢐⣀⡀⢀⣀⡀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⡇⢸⠀⡀⠀⡇⢘⠀⢀⠀⡇⢸⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠉⠉⠉⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⡆⢰⠒⠂⠀⡒⠲⠀⠐⠒⡆⢰⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠃⠘⠀⠂⠀⠃⠘⠀⠐⠀⠃⠘⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢉⢉⡉⢉⡉⡉⠉⡉⢉⠉⢉⢉⡉⢉⡉⡉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⡇⢸⣀⡀⠀⣇⣨⠀⢀⣀⡇⢸⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢃⠀⠸⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢬⠇⠀⡼⢱
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⡄⠀⡇⠒⠂⢰⠒⠀⡖⠒⠐⠂⠒⢲⠀⠒⡆⠐⢒⢸⠀⢠⠅⠘⡂
⠀⠀⠀⠀⠀⠀⠀⠘⡲⣞⠁⢀⠇⠢⠆⠸⠴⠠⡇⠀⠀⠀⠀⢸⡀⠦⠇⠰⠔⠸⡀⠈⡲⢆⠃
⠀⠀⠀⠀⠀⠀⠐⠚⠒⠚⠒⠛⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠛⠒⠓⠒⠓⠂

⣀
⣿⣀⣀
⣿⣿⣿⣷⣀
⢻⣿⣿⣿⣿⣀⠀⠀⠀⣠⣄
⣶⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣦⣄⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣄⡀⣀
⡿⣿⡄⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢴⣤⣄⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠋⠀⠀⠈⢸⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⣿⡿⣿⡟⠏⡟⣿⣿⣿⠛⣿⣿⣯⢽⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⢾⡟
⠀⠐⠀⠀⠀⢸⠟⠹⣿⡇⠱⠆⠸⠻⠏⢩⡝⠛⠏⢁⠃⠀⠈⠓⠠⠿⠶⠤⢬⣽⢓⠞⡌⣻⢻⠥⣽⣿⣿⣟⡋⠀⠩⢷⡻⠽⠟
⠀⠀⠀⠀⠀⠀⠃⠐⢪⡇⠠⣤⡃⣷⠅⠀⠁⢢⠀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠐⠃⡁⠂⣀⠋⣀⢒⡐⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠁⠀⠈⠀⢠⠂⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠞⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⡀⠀⢀⣀⣠⣤⣶⣶⣿⣟⣉⣉⣀⣤⣀⣀
⣿⣿⢛⠿⡛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣀⣀⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠠⡀⠀⠑⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠉⣶⣄⣻⣯⣿⠿⢟⣻⡦⠀⠀⠰⡆⠀⠄⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⠀⢿⣿⣿⣏⠀⢸⣽⣽⠇⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡰⣿⣿⣦⣀⣬⣙⣛⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⣻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⠟⠛⠋⣀⣤⠞⠋⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⣤⠤⠴⢶⣯⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣿⣿⣿⣷⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⣿⣿⣿⣿⣿⡟⣻⠷⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣿⣿⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠙⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⡌⠀⠹⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠐⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣆⣶⣶⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣧⠺⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⣀⡤⣀⢀⡠⣄⠀⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⠚⣀⣘⢒⢃⣀⡓⣚⣀⣘⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣭⣭⢩⢫⡉⢿⠉⡯⢩⡍⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠤⠤⠤⠬⠭⠤⠬⠤⠥⠤⠥⠤⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀⠀⡧⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣿⢸⠀⠀⡇⢸⠀⢸⡇⠀⣇⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢼⠀⠀⠙⠛⠋⠈⠛⠛⠁⠈⠛⠋⠁⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⢸⠀⠀⡏⠉⣷⢸⠉⠉⡇⢸⠉⢹⡇⠀⡏⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠓⠒⠋⠘⠒⠒⠃⠘⠒⠚⠃⠀⡗⠒⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⣀⢸⠀⠀⠀⠀⣠⠤⠤⠤⠤⣤⠀⠀⠀⠀⡧⠤⠤⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⢸⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⣿⣀⡀⣸⣸⣀⣀⣀⣀⣿⣀⣀⣀⣀⣸⣀⣀⣀⣀⣇⣀⣀⣀⢸⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠺⣭⣭⣭⡭⣉⣡⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣩⣤⣭⣭⡽






⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡏⢸⡂⢻⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⢀⡞⣵⣛⠶⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠚⠓⠀⢇⡗⡆⠀⠠⣭⡭⣥⠆⠀⠀⠀⢷⠘⠃⠀⡽⠀⠀⣀⡤⠀⡀⠀⠀⠴⣣⠯⣾⠟⠁⠀⠀⠀⠀⢠⡯⣹⠇
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠚⠁⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣄⣠⣀⠀⠀⠀⡀⠄⡀⠉⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠄⢠⡲⠄⠀⠀⠠⣄⠻⠈⣠⠇⠀⠀⠈⠙⠛⠁⠀⠀⠀⣡⡆⠈⠐⢦⠀⠀⠘⠛⢿⡟⠉
⠀⠀⠀⠀⠶⠀⠀⠀⠠⡌⠂⣋⡀⠀⠀⠀⢀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⠶⠀⠸⠋⣀⣉⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⠒⠆⡀⠀⠀⠈⠛⠠⣤⠀⠀⠀⠀⠰⠦⠆⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠍⠙⠳⣦
⠀⠀⠀⠀⣠⣀⡀⠀⢠⡎⠀⠀⠀⠀⣴⠀⠈⠣⠀⠠⠈⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⣒⠆⠀⠀⠀⠀⠀⠀⠈⠀⣠⠔⠚⠁
⠀⠀⠀⠀⠼⣝⠇⠀⠀⠁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠴⠆⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠠⠀⠘⢡⠀⠀⢀⠀⠆⢐⡤⠂⠀⠄⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠖⢤
⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠤⠀⠠⠦⠜⠀⠐⠒⠐⠊⠀⠀⠀⠐⠂⠂⠀⠤⠄⠀⠀⠈⠂⠄⠀⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠆⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⢠⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢻⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠛⣼⣧⡹
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⣴⡶⣲⢶⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠴⠆⠀⠠⠶⠀⠀⠀⡆⢈⢛⠀⡀⠀⠀⢠⣤⣤⡄⠰⠆
⠀⠑⢶⣦⣶⣶⠎⠀⠀⠙⠳⠿⠷⠛⠀⠀⣄⡈⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠠⢺⠏⢻⡍⣱⠀⠛⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠉
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢰⡆
⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢴⠆⠀⠀⠀⠘⢻⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣡⣴⡀⠀⠀⠀⠀⠀⣄⣀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠄⠈⠀⠐⠄⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⣌⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤
⠀⠀⠐⠃⡠⠾⡁⠀⠐⠒⠒⠀⠙⠀⠀⠀⣦⣽⡷⣦⡁⠀⠀⠀⢀⡆⢈⡷⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠖⠒⠒⠛
⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⣤⡄⠀⠀⠀⠒⠊⠐⠃⠘⠃⠀⠀⠠⠁⠁⠭⠀⠀⠀⠈⠉⢴⠆⠻⠂⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⠓⠁
⠀⠀⠦⠀⢀⠀⠀⠀⠀⠀⠉⢡⡀⠀⠀⠀⣀⣤⡶⠖⠀⡀⠀⡀⠂⣀⠰⠆⠀⠀⠀⠒⠲⠂⠀⡄⠀⠀⠘⠋⠀⠠⡖⢳⡄
⠀⠀⠰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠐⢺⡗⠀⠀⠠⣤⣄⣀⣧⡔⠀⠀⠀⠀⡠⠀⠀⠁⠈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⠏⠛⣿⠉⡟⠛⣟⠟⣛⡿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣁⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣁⣤⡶⢾⣛⣿⡿⡿⢛⢿⣟⣳⣦⡀⠀⠀⠀⠀⠀⢀⡶⠴⠒⠒⢏⢡⢠⡙⢦⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢸⣿⣫⣼⠟⠛⠉⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⢘⡏⠑⢦⠀⢻⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀⣠⣦⠀⠀⢸⣿⣿⠀⠀⣀⣤⠾⠛⠻⡤⠚⠃⢉⠛⠒⠶⠞⠛⣧⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⡤⠀⠀⢈⠁⢠⣦⠀⠀⣿⠋⡍⠿⠋⠀⠀⢀⠞⠁⠀⢠⡎⠀⠀⢸⠀⠀⠸⣆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⣠⡄⠀⢸⡀⠀⠉⠀⠀⠀⠀⠙⣧⠀⢀⡔⠃⠀⠀⢠⡟⠀⠀⠀⢸⡆⠀⠀⢻⡄⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⠸⠇⠀⠠⣤⡀⠀⠐⡟⣁⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣷⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡸⠛⠁⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⢷⣀⠀⠀⠤⠔⠋⣀⡤⠖⠉⠀⠀⠀⠀⢀⣤⠿⠃⠒⠒⠒⠒⠒⠛⠛⠉⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠙⠶⣤⣤⠴⠛⠉⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⠁⠀⢠⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⣼⡏⣷⣄⠈⣇⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⡴⢟⡿⠋⠀⠀⠸⣇⣿⠛⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠁⠔⢋⡴⠀⠀⠀⠀⢻⣿⠀⣿⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡾
⣼⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⡴⠋⠀⠀⠀⠀⠀⠈⢿⣠⣿⡏⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⡼⠁
⢸⡆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⢻⡀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡾⠁
⠀⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⣠⠔⢲⡾⢿⠟⣹⣆⠀⣠⠞⠁⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣹⣟⣿⣟⣼⡫⢿⣎⣿⣿⡁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⣿⢎⡵⣯⣚⣽⡦⣿⠏⣻⣷⡀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢯⣿⣧⣛⣼⡷⢋⣾⡿⣿⣛⢌⣻⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠽⣳⢞⡶⣩⣿⣵⡿⣻⢎⡳⢉⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢏⠶⣭⢻⣵⡿⣻⢏⡱⢯⠛⣽⢻⣝⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢪⡟⣴⡳⢾⡷⣭⢳⡜⡳⣛⠾⣱⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡳⢎⡲⣉⣾⣟⠶⣙⢮⡵⢯⡚⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡷⢫⣝⠤⣿⢎⡳⣭⠛⣜⣣⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠚⠉⢹⡟⣬⡳⢎⠷⣿⢻⣝⡦⣛⢾⣽⢯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠸⣟⡶⡝⢫⣾⡾⣳⢎⡱⢯⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢼⡳⣟⠶⣉⢲⣝⡿⣋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣮⣽⢯⣝⡦⣋⣾⡱⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢹⡳⢌⣱⣿⠳⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣴⣿⡓⢮⣛⢤⣹⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣝⡳⣏⣳⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢺⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣟⣉⠛⠛⢋⣩⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⢩⠉⣭⢩⠭⣍⠩⡭⢭⡭⠍⣭⠉⠉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠿⠿⢿⡇⠸⠉⠟⠹⠤⠞⠀⠇⠸⠯⠅⠺⠤⠀⣿⠿⠿⠿⠿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣶⠶⢶⡆⢸⡇⢀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⣀⠀⣿⠀⣶⠶⢶⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣀⣸⡇⢸⡇⣿⠉⠉⣿⠀⡏⠉⠉⡇⢸⡏⠉⢹⡇⣿⠀⣿⣀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣭⣭⣿⠀⣽⠿⢿⡄⢸⡇⠻⠶⠶⠿⠀⠷⠶⠶⠇⠸⠷⠶⠾⠃⣿⠀⣼⠿⢿⡅⢸⣯⣭⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠒⣦⣿⠀⣿⠀⢸⡇⢸⡇⣿⠉⠉⣿⠀⡏⠉⠉⡇⢸⡏⠉⢹⡇⣿⠀⣿⠀⢸⡇⢸⣧⡖⢲⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣶⣏⣿⠀⣭⠭⢭⡅⢸⡇⠿⠤⠤⠿⠀⠷⠤⠴⠇⠸⠧⠤⠼⠃⣿⠀⣭⠭⢭⡅⢸⣏⣷⣾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣤⡿⣿⠀⣿⠀⢸⡇⢸⡇⠀⠀⠀⠀⢀⡴⠶⠶⣄⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸⡇⢸⡿⣧⣼⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠛⣷⣿⠀⣭⣭⣭⡁⢸⡇⠀⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⣩⣭⣭⡅⢸⣷⡟⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠿⣏⣿⠀⣿⠀⢸⡇⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⣿⠀⢸⡇⢸⣇⡿⢿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠶⠟⣿⠶⠿⠿⠿⠷⠾⠷⠶⠶⠶⠶⠿⠶⠶⠶⠾⠷⠶⠶⠶⠶⠿⠶⠿⠿⠿⠷⢾⡟⠷⠾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣆⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⠿⣿⡿⠿⠿⢯⣭⣿⣿⣾⣿⣮⣜⡿⣆⠀⢉⣦⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⠚⠓⠈⢀⣀⣀⡼⢥⣿⣿⠼⠋⠛⠻⢿⣼⡄⠀⢀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⣾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠒⠒⠢⣤⣤⠰⢿⣿⡦⠌⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣤⣤⣤⡾⠙⠏⢀⣼⠅⠀⠀⠒⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⡔⢿⣿⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠘⢧⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠲⣄⣤⡴⢞⡛⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⢹⣦⢀⣀⣤⡍⠀⠠⢏⣴⣥⣤⣴⣞⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠇⠀⡀⢀⡍⠉⠹⠖⠃⣠⣾⡟⠁⠰⢚⣭⠽⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢈⣿⠏⡱⠔⢾⡏⠋⠀⠀⠀⡴⣤⣿⡻⠧⠀⠘⠩⠖⢻⣽⠿⣿⣧
⠀⠀⠀⠀⠀⢠⣾⠃⢸⣅⠤⢼⡇⠀⠀⠀⢰⢰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠐⠛⠉⣿⡠
⠀⠀⠀⠀⠀⢸⡏⠀⢸⡁⠀⠈⣧⣀⠀⠀⠸⣾⠃⠀⠉⠹⡆⠀⠀⣠⣴⠄⠰⠟⣿⣤
⠀⠀⠀⠀⠀⠘⣧⡀⢸⡇⠀⠀⠻⡌⠙⠲⢤⣸⠆⠀⢰⡦⠁⠀⠀⣡⡀⠀⠀⢠⢟⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠦⢿⡀⠀⠀⠙⠢⣄⡀⠘⡇⠀⠀⠀⡀⡀⠀⠙⠁⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠉⠑⠻⠦⠤⣴⢁⣇⣀⡀⠀⠔⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠙⠛⠛⠉⠉⠩⣤⣀⣀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⢸⡏⠙⣿⠼⢿⡟⢷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⡿⠛⢿⠓⢺⡟⠚⣿⠓⢿⡟⠻⡿⠛⠶⠦⢤⣀
⠀⠀⠀⠀⠀⣀⡤⠾⣿⠷⢾⡿⠨⣿⠇⢿⡿⠬⣿⠥⢿⠧⢼⡿⠴⡿⡧⢾⡿⠿⣷⠦⣤⣀
⠀⠀⢀⣤⡾⢿⣷⠲⣿⡖⢾⡷⠒⣿⢖⣾⣷⣶⡿⠶⠿⣶⣾⣶⣐⣷⡆⣼⣷⣤⣿⣤⣼⣭⢽⣦⣄⡀
⠀⣴⡿⣿⡦⣼⣧⣤⣿⡦⣼⣧⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⣼⣧⢠⣿⣀⣼⣤⣀⣭⣈⣹⣦
⢸⣏⣀⣼⣇⣸⣇⣀⣿⣅⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣏⠈⣯⡁⣹⣉⠈⣻⡉⢹⡏⣷
⠈⠿⣄⣹⡇⢹⣟⠈⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⠋⢻⡛⠙⢻⠋⠻⣿⣿
⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣿⣟⠚⣿⣗⣾⠟⠁
⠀⠀⠀⠀⠀⠳⡶⠶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣝⡛⠿⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠈⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡽⠋⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡆⢸⠃⠀⠀⠀⠀⠀⠰⣇⣨⠇⠀⠀⠀⠀⠀⣀⣴⠃⣠⠞⠁
⠀⢀⣤⣤⣴⡚⠉⠓⣾⣶⡀⠀⠀⠀⠀⠀⣼⢇⠀⠀⠀⠀⠀⢸⣿⣏⡉⠉⢲⣤⣤⣄
⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠧⠴⠤⠤⠤⠴⠧⠼⠦⠤⠤⠤⠤⠬⠥⠥⠬⠿⢿⢿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡈⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⡂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡃⠀⠀⢀⠇
⠀⠀⠠⠀⠂⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢸⠅⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⠀⣸⡆⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠨⡇⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⣼⠔⠀⠀⠀⠀⠀⢀⠀⠀⡼⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠠⠀⡀⠐⠂⡥⢘⡩⠀⠀⠀⠀⠀⠀⠊⠀⢰⢧⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⠄⣀⠐⢢⠇⡾⠘⠔⢌⣀⠀⠀⠀⠀⠶⠲⠂⠀⠶⠖⠐⠱⠁⠂⢀⣀⣀⡠⠤⣀⣒⠠⠬
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠓⠂⠚⠁⠀⠀⠀⠀⠁⠀⠀⠀⠂⠐⠒⠒⠒⠐⠒⠀⠐⠒⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠡⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠂⠀⠀⠀⠐⠊⠀⠀⡀⠀⢠⠇⠀⠒⠒⠀⠐⠀⠐⠂⠀⠂⠀⠘⠀⠂⠂⠀⠒⠀⠀⠀⠀⠂⠀⠐⠒⠒
⠠⣀⢄⡁⠀⢄⣄⠤⠀⢀⠀⣀⠀⢀⠒⢈⠂⣀⣠⢸⣔⢀⠀⠀⠠⡀⢡⢠⠄⠄⠀⡄⢆⠄⢀⢐⠀⠀⠀⠀⢐⠆⢀⠀⠀⠀⠄⠀⡌⢀
⠀⠈⠛⢃⠔⠂⠀⠀⠡⠀⠆⠦⠂⠠⠐⠶⠁⠁⠉⠉⠈⠳⣪⠄⢢⡜⠊⠈⠕⡤⡰⠀⠀⠈⠀⠱⠐⡀⠀⠐⠰⠟⠐⠈⠜⠦⠁⠆⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢦⠰⡞⠛⠶⠴⠛⠛⣶⠛⠛⠶⠶⠛⠛⣶⠛⠛⡦⠶⠛⠛⡶⠛⠛⠦⡞⠛⠳⡶⠛⠳⠦⡞⠛⢳⡞⠛⠳⠦⠞⠛⢳⡞⠛⠳⠴⠞⠛⠲
⠈⠳⣭⣤⣽⣿⣥⣽⣭⣯⣤⣿⣯⣤⣽⣭⣯⣤⣿⣯⣤⣭⣭⣧⣬⣿⣯⣤⣭⣭⣥⣬⣿⣯⣬⣯⣽⣥⣬⣿⣥⣬⣭⣽⣤⣽⣿⣥⣬⣅⡴
⠀⢸⡏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⢸⡇⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣎⣀⣀⣀⣣⠀⠀⠀⣜⣀⣀⣀⣙⡀⠀⠀⠀⣎⣀⣀⣀⣳⠀⠀⠀⠀⢰⣁⣀⣀⣈⡆⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡇⠀⠹⠀⢸⠀⠀⠀⡏⠀⢸⠀⠈⠁⠀⠀⠀⡇⠀⠏⠀⢹⠀⠀⠀⠀⢸⠁⢨⡇⠀⡇⠀⠀⠀⡇⠀⡏⠀⢹⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡗⠒⢿⠒⢺⠀⠀⠀⡿⠒⢺⠒⠺⠂⠀⠀⠀⡗⠒⡟⠒⢺⠀⠀⠀⠀⢸⠓⢺⡗⠒⡇⠀⠀⠀⡗⠒⡿⠒⢺⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣧⣀⣬⣀⣸⠀⠀⠀⢧⣀⣼⣄⣠⠄⠀⠀⠀⣇⣀⣧⣀⣼⠀⠀⠀⠀⢸⣄⣸⣇⣠⡇⠀⠀⠀⣇⣀⣧⣀⣼⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣜⠁⠀⠀⢳⠀⠀⠀⢰⠁⠀⠀⠙⡄⠀⠀⠀⡜⠁⠀⠀⢳⠀⠀⠀⠀⢀⡋⠀⠀⠈⡆⠀⠀⠀⡤⠤⣤⠤⣤⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡏⠉⢹⠉⢹⠀⠀⠀⢸⠉⢹⠉⠉⡇⠀⠀⠀⡏⠉⢹⠉⢹⠀⠀⠀⠀⢸⠉⠉⡏⠉⠉⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡷⠀⢾⠒⢺⠀⠀⠀⢸⠒⢺⠆⠰⡇⠀⠀⠀⡷⠒⢾⠂⢺⠀⠀⠀⠀⢸⠖⠲⡗⠒⠆⠀⠀⠀⡏⠉⡟⠉⢹⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣇⣀⣸⣀⣸⠀⠀⠀⢸⣀⣸⣀⣀⡇⠀⠀⠀⣃⣀⣸⣀⣸⠀⠀⠀⠀⢸⣀⣀⣇⣀⡅⠀⠀⠀⠧⠤⠷⠤⠾⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⢠⠖⠋⠙⢦⠀⠀⠀⠀⠔⠋⠙⠢⡀⠀⠀⠀⢠⠞⠉⠙⢦⠀⠀⠀⠀⠀⡴⠋⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡺⠀⢴⠄⠸⡄⠀⠀⢸⠆⠰⠆⠰⡇⠀⠀⠀⣾⠀⢰⠄⢸⡇⠀⠀⠀⠀⡗⠐⡦⠒⢾⠀⠀⠀⡖⠒⡶⠒⢲⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣀⣀⣘⣀⣀⡀⠀⠀⢸⣀⣈⣁⣀⡇⠀⠀⠀⣾⣀⣸⣀⣸⡇⠀⠀⠀⠀⣇⣀⣇⣀⣸⠀⠀⠀⣇⡀⣯⣀⣼⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠭⠀⢈⠀⠈⠁⠀⠀⢸⠀⠈⠁⠀⡇⠀⠀⠀⢻⠀⢸⠀⢸⡇⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⡇⠀⡏⠀⢸⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠙⠒⠚⠒⠚⠁⠀⠀⠘⠒⠚⠓⠒⠃⠀⠀⠀⠙⠒⠚⠒⠚⠁⠀⠀⠀⠀⠃⠐⠛⠀⠋⠀⠀⠀⠉⠁⠉⠉⠉⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⢀⡴⠒⠲⣄⠀⠀⢀⠞⠉⢹⣉⣏⡽⣯⢻⡟⣽⡞⣸⠉⠉⠑⣄⠀⠀⢀⡔⠊⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⢸⠤⣤⡤⢬⠆⣴⣋⣀⣀⣘⣀⣋⣓⣛⣘⣃⣙⣒⣛⣒⣀⣀⣈⣣⠀⢸⠦⠤⡤⠴⡇⠀⠀⠀⡖⠒⡶⠒⢦⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⣇⠀⢐⠀⢀⠇⣼⠀⢸⡍⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⢽⠀⢠⡀⢸⠀⢀⡇⠀⡇⠀⠀⠀⣇⣀⣧⣀⣸⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⡛⠉⢹⠉⠉⢡⣿⡆⢸⡇⠀⠀⠀⠀⢰⣾⣶⠀⠀⠀⠀⠀⢸⠀⣿⣇⢸⠉⠈⡍⠉⡇⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠰⠤⠼⠤⠴⣿⣿⣷⢸⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⢸⣿⣿⡘⠒⠒⠓⠒⠃⠀⠀⠀⠓⠒⠛⠒⠛⠀⠀⠀⢸
⠀⠘⠧⠤⠤⠤⠤⠤⠤⠤⠤⢿⠿⡿⢾⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡹⠋⠐⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠉⠉⠁⠀⠀⠀⠐⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⣀⣀⡠⠶⠾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣤⣤⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠁⠍⠻⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⡀⠀⠉⠹⢦⡀⠀⠀⠈⠂⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠐⠉⠛⠛⠳⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠶⠛⠁⠀⠀⠹⢦⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⠄⠀⠠⠴⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠸⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠋⢀⡀⠀⠀⠀⢩⡿
⠀⠀⢠⣀⠀⠀⠀⠀⠉⠛⠲⢿⣆⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠤⠀⠀⠈⠁⠀⣀⠼⠀⠀⠀⡞⠀⠀⢀⣿⠀⠀⠀⠀⣸⡅
⠀⠀⠼⢿⣗⡦⣄⣀⣀⡀⠀⣤⣀⣠⣭⣥⡿⠋⠁⠀⠀⠀⠀⠀⠤⢄⡀⠀⠉⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⢠⠾⠇⢣⣤⢀⠔⠀⠀⠀⠀⢀⡿
⠀⠰⣤⣄⣀⠀⠉⠈⠛⠃⢀⣿⠀⠀⠘⠁⠀⠀⠀⠀⠐⠒⠲⠤⠀⠀⠀⠀⣀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠁⠿⠀⠀⠀⢀⣠⡏
⠀⠀⠈⠙⠛⠛⠤⠶⣶⡄⠸⠃⠀⠀⠀⢀⣀⡀⠉⠉⠀⠀⠀⢀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⢀⢀⡴⠚⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢞⡘⠇⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠈⢂⣾⡿⠉⠁⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠈⠹⢿⣤⣤⡶⠶⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠀⠀⠙⠻⢿⣾⣽⣛⠳⢦⣄⣀⠠⠔⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠦⣄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠛⠻⡷⢶⣏⠉⢠⣄⠴⠒⠛⠁⠀⠀⠀⡠⠂⠂⢬⣀⠀⠀⠀⠀⢈⡶⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠴⠛⠋⣿⠿⣶⡉⠀⠘⣇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡄⠀⠀⠀⠙⣾⠟⠀⠀⢠⡏
⠀⠀⠀⠀⠉⠻⠿⣶⣶⣀⣐⠲⣶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠘⢤⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠶⠿⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢿⠓⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢠⣟⠆⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⡶⢀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠁⠀⣤⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠀⠀⠀⢰⣿⡵⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣆⠀⠀⠀⢼⡿⠗⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠙⠛⣶⠟⣷⠆⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢻⣧⠀⣤⢀⠄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣧⣴⢛⣿⣶⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠸⣿⣿⡟⣻⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⢰⣿⡿⢁⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⣿⣿⢃⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⢂⣾⣿⡏⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⣿⡿⠠⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⠃⢾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢰⠰⣿⣿⡏⣀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⢹⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠒⠀⠒⠒⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠀⢸⢻⣿⣿⡇⠀⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣇⠀⢻⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠙⠉⠉⠃⡀⢿⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠘⠂⠐⠒⠒⠐⠀⠀⠀⠀⠀⠀⠐⠆⠴⠄⢀⡀⣠⣤⣦⣾⣿⣷⠞⠂⠚⠁⣴⣶⣶⣦⣤⣤⣤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠏⠀⠀⠀⠰⠶⠀⠉⠉⠉⠁


⣶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⡇⠀⣯⣹⠃⠘⣏⡟⠀⢻⣩⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠖⠶⠶⢖⡶⠶⡲⠶⡖⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠸⠻⠀⠯⠟⠀⠇⠘⠇⠸⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠶⢶⡄⣴⠶⢶⡄⣴⠶⠶⡄⠀⣿⠒⠒⠒⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⣀⣸⡇⣿⣀⣸⡇⣿⣀⣀⡇⠀⣿⠤⠤⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢺⡇⠀⣈⣉⣁⡀⣈⣉⣉⡀⣀⣉⣉⡀⠀⣿⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠀⢸⡇⠀⡏⠀⢸⡇⣿⠀⢸⡇⣿⠀⢨⡇⠀⣿⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠚⠚⠁⠛⠒⠚⠃⠙⠒⠚⠃⠀⣿⠛⠒⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⢸⡇⠀⠀⠀⢠⡤⠤⠤⠤⠤⣤⠀⠀⠀⠀⣿⠤⠤⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠉⠉⢹⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⢸⡇⠀⠀⠀⢸⡃⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠠⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠟⠛⠛⠛⠙⠛⠛⠛⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣴⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣉⣉⣈⡴⢫⣝⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⡴⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⠟⣩⠶⢠⡷⣬⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⣼⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⣾⣰⠏⢸⠀⣇⠘⣧⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠿⡇⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣴⡞⡧⡶⣲⣆⠀⠹⣿⠀⠘⣷⣿⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢦⣄⣙⠁⠉⠳⠄⠀⠀⠀⠀⣸⣏⣵⢾⢉⡦⣽⢻⠀⠀⠘⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠙⣿⣿⣶⡶⠆⠀⠀⠀⠀⣿⡿⢣⡏⢆⢱⡌⠻⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⣰⣿⢟⣛⡻⣿⣶⣄⡀⠀⠀⠹⠀⢿⣇⠈⢿⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢻⣿⣸⣍⣿⢘⣿⣿⣿⣦⡀⠀⠀⠀⠈⠀⠈⣇⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠉⠛⠛⠋⣸⢡⣶⡄⠙⢷⣄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣿⣿⣗⡢⢴⣾⣿⣷⡾⠁⠀⠈⢿⣆⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢸⡇
⢀⣴⠾⠿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⣿⠟⣛⣻⣦⠹⠟⢫⣴⣶⣦⣄⠈⢿⣆⣀⣤⠴⠊⢿⠀⠀⠀⠀⣿
⢺⠁⠀⠀⢹⣿⡿⢟⣛⠿⣦⡀⢠⣤⢀⣴⣾⣿⣿⣶⣤⣀⠘⠂⢈⡁⠀⠉⢀⣏⠘⣲⢨⣻⡷⡀⣿⣋⢻⣿⣿⣷⡄⠻⣅⠀⠀⠀⢸⡇⠀⠀⢰⡿
⠈⠓⠤⠀⢸⡏⢘⣭⡉⢛⢿⡿⣄⠀⢼⡿⠛⠛⣿⣿⣿⣿⣷⡀⠈⠁⠀⣠⣾⣿⡿⠃⢸⣿⣿⡝⣾⣭⣾⣩⣌⠙⣿⡄⠈⠑⠂⠀⢸⡇⠀⢀⣿⠇
⠀⠀⠀⣤⣿⣧⣤⣴⠇⢸⣷⣝⢮⢻⣮⣛⣛⣠⡿⢉⡉⠙⢿⣿⣄⠲⠿⠿⠟⠋⠁⢴⣿⣉⣽⠫⡪⢝⡻⠿⠋⠀⠈⠛⠶⠤⢀⣀⣈⠀⠀⠈⠉
⠀⠀⠀⠈⠙⢛⠋⡅⠀⣸⣿⣿⣯⡳⣝⠻⣿⣿⣧⣿⣽⠀⠀⠙⠿⣷⣤⣄⣤⠤⠤⠤⢤⡍⠀⠀⠀⠀⠈⠉⠒⠒⠀⠀⠈⠉⠉⠁⠙⠒⠒⠋⡙⠦⠄
⠀⠀⠀⠠⣶⠀⠀⠀⢾⣿⣧⣀⣶⠙⠲⣝⠲⠬⣍⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠄⠉⠉⠉⠉⠙⠒⠒⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠛⠒⠒⠚⠛⠉⠙⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡎⢠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⣀⠤⠀⠀⢀⠀⠀⠀⠘⠄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠉⠠⠀⠘⠓⠁⠀⠀⡐⠂⠾⡐⢄⡀⠀⢠⡘⠀⠄⢼⣷⡤⠅⢷
⠀⠀⠀⠀⠀⠠⠄⢰⡀⠀⠂⠠⠀⠀⠀⠀⣰⡿⣣⣾⣧⣁⣈⠀⣇⠉⠀⠀⠀⡀⠱⡄⠈
⠀⠀⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⠀⠈⠆⠠⠄
⠀⠀⢳⡀⠀⠈⠛⠿⠿⠷⠾⠲⠶⠶⠶⢶⣶⣒⣛⣛⣛⣛⣛⣉⠉⣿⠀⡸⠃⠀⠀⠀⠀⠂
⠙⠛⣉⣉⣐⣛⣛⣛⣋⣁⠀⠀⠈⠛⠿⠯⠭⢥⣤⠀⠀⠀⠀⠀⠀⢹⡗⠰⠀⠀⠀⢱⠀⠀⠁⠀⠀⣠⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣦⣬⣭⠉⠁⠀⡀⢠⠀⠀⠀⠬⣤⣴⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⡉⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⢰⡀⠀⠀⠛⠁⠀⠀⢰⡀⠐⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠁⠠⠄⠀⠀⠀⠀⠀⠀⠁⠐⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡓⠀⠀⠀⠄⠈⠛⠉⠓⠄⠀⠠⠀⠀⠐⠊⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠽⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣀⣀⣤⣤⣶⣦⣀⣀⣀⣓⣠⣤⣤⣤⡀⠀⠀⠶⠿⠿⠛⠛⠉⣉⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠉⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠠⠤⠐⠒⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⢀⣤⣶⣤⡤⠀⠀⠚⠛⠻⠆⠹⣿⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣿⣿⣷⣶⠄⠀⠈⠀⢤⣤⠃⠀⠀⠀⠰⠶⠀⠀⠙⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠸⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠋⢡⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠁⠀⢀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⢃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢤⡀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡀⠀⣀⣀⣀⣀⣀⠼⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⢄⣡⠊⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣿⡏⠛⠛⠉⠉⠉⢉⠉⠀⠀⠀⠛⠀⠤⠄⠀⠀⠀⠀⠀⠀⠆⠀⢀⡠⣌⠁⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠁⠠⢤⡈⠠⠖⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢸⠄⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠁⠀⠀⠈⠉⠠⢄⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠰⠆⢀⡴⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⢀⠆⠀⠻⠖⠐⠶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠽⠀⠀⠀⠀⠀⠀⢀⣤⠞⠳⠋⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠐⢢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⢃⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣽⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⣄⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠻⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡈⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⠄⢀⣀⡀⡀⠀⠀⠀⠀⣀⣀⣀⡠⠆⠈⡹
⠀⠀⠀⠔⢉⠀⠀⠤⠄⠈⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠁⡀⠊⠀⠰⡖⠒⣦⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠣⠀⡜⠁⡋⠈⡟⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠠⢀⠀⠀⠠⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠈⢦⠀⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠆⢀⠀⠃⠀⠀⠐
⠀⠘⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡇⠀⠀⠀⠈⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⣤⣶⠟⠁⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠉⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠒⠤⠤⡤⠤⣤⡤⠟⠀⠀⠀⠀⠘⠦⠤⠘
⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⢠⡇⠀⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤
⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂
⠀⠈⠳⠄⣀⣀⣀⣀⣠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠳⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢱⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁
⠀⠀⠀⠀⣿⠃⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⢀⣄⠀⢁⣤⣄⡀⠀⣤⡀⢠⣄⠀⣤⡀⢠⣄⠈⢩⡍⠁⢀⣤⣀⡀
⠀⠀⠀⢰⡟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠋⠀⣿⠀⣿⠀⠘⠇⠀⣿⠀⢸⡇⠀⣿⠁⠸⣿⡄⢸⡅⢠⡟⠀⠘⠇
⠀⠀⠀⠸⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣴⠀⠀⣿⠀⢿⣦⣀⠀⠀⣿⣀⣸⡇⠀⣿⠀⢀⡻⣇⢸⠇⣾⡷⣆⣀⣀
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠛⠀⠀⣿⠀⠈⠙⢻⣷⠘⣿⠉⢹⡇⠀⣿⠀⠰⡆⢻⣼⡅⢿⡇⠀⢸⡏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣆⠀⠀⣿⠀⣿⠀⢸⡇⠀⣿⠀⢰⡇⠘⣿⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣃⡀⠀⢐⣟⣀⠛⣳⣖⠁⢀⣿⣆⢸⣷⡀⣿⣇⣸⣧⡀⢹⡀⠀⠙⣳⣞⢿
⣿⣿⡿⠿⣿⡿⠿⠿⡿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣟⣷⣼⣿⣿⣿⡿⢟⣯⣽⡟⠟⡴⢋⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢷⣶⣿⣿⣿⣿⡿⠋⠑⢋⡽⢛⡅⣠⢿⠟⡉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠻⠿⣿⡘⣿⡇⡄⠀⠀⠀⢉⡞⠟⢸⣴⣷⣦⣿⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⠀⣘⣶⣶⣝⠻⡧⢳⣄⣀⢀⣼⣤⡄⣨⡭⠭⣂⣀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠽⣿⣿⠀⢷⣆⠛⠛⠛⢛⡭⠀⢰⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣷⣤⠙⠿⠶⣟⣫⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠩⢭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣠⠴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣣⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⡏⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠈⢻⣷⣄⠀⠀⠰⠿⣧⣀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠉⢿⣿⡟⠋⣉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⣦⡄⠈⠿⠟⠙⠻⣷⣤⣤⣾⣟⠳⣌⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⢻⡝⢳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢂⠀⠀⠐⠀⠁⠀⠀⣈⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠈⠀⠀⠀⠚⠃⠀⠀⢈⡀⢸
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⢸
⠈⠛⠋⠁⢀⣀⠀⠀⠀⠀⠀⠀⢠⣐⣆⣀⠀⠄⢶⡆⢀⠀⢀⡀⠀⠈⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠚⠂⠙⠀⢸
⠀⠀⠀⠈⠾⠯⠁⠀⠀⠀⠀⠀⠀⠰⠾⠏⠀⠀⠛⠂⠐⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠮⠳⠦⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣦⣗⣀⣇⣿⣼⣥⣭⣤⣇⣼⣀⣿⣶⣶⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡏⣿⢹⠏⢻⠉⡟⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⡿⡿⢿⠿⡟⠿⢻⢛⣟⣟⣹⡿⠿⡿⡿⢿⠿⢿⠿⡿⢿⠿⣿⣉⣟⣻⢛⡟⡿⢿⠿⡿⣿⢿
⠀⠀⠀⠀⠀⢰⡷⣷⢾⠿⡿⡿⢻⠛⡟⣟⣹⣯⣤⣷⣿⣾⣷⣾⣶⣷⣾⣤⣿⣙⣟⢻⠻⠟⡿⢿⢿⡷⣷⣾
⠀⠀⠀⠀⠀⢠⣷⣶⣾⢶⡿⡿⢿⠿⡟⣟⢻⣟⣉⣇⣟⣸⣃⣺⣀⣇⣸⣈⣿⡛⡟⢻⠻⡿⡿⢿⢾⡷⣷⣾
⠀⠀⠀⠀⠀⢠⣷⣷⣾⣶⡷⡿⢿⠿⡟⡿⢻⡟⠛⡟⣿⢻⠟⢿⠛⡟⢻⠛⣿⠛⡿⢻⠿⡿⡿⢾⢶⣶⣷⣾
⠀⠀⠀⠀⢠⣤⣧⣧⣼⣶⣷⣷⢾⢾⡷⡿⢿⣿⠿⡿⠿⢿⠿⢿⠿⡿⢿⠿⣿⠿⡿⢿⢾⡷⣷⣾⣶⣧⣧⣼⣤⡄
⠀⠀⠀⣀⣼⣭⣧⣭⣼⣴⣷⣷⣶⣶⡷⣿⢾⣿⣤⣷⣿⣾⣷⣾⣶⣷⣾⣤⣿⠷⣷⢾⢶⣷⣷⣾⣼⣧⣯⣽⣭⣇⡀
⠀⠀⠀⣹⣹⣩⣯⣯⣼⣬⣧⣭⣼⣶⣷⣶⢦⣶⣾⣿⣯⣼⣤⣼⣤⣷⣶⣶⣿⣲⣷⣾⣾⣥⣡⣼⣬⣧⣯⣽⣹⣏⣇
⠀⠀⠀⣿⣽⣭⣯⣯⣽⣭⣻⣿⣿⡿⣤⣷⡼⡟⢹⡿⢃⠀⠀⠀⠀⠿⣿⡁⣟⣦⣧⣼⣜⣿⣿⣿⢯⣭⣯⣽⣽⣯⣏
⠀⠀⠀⢻⢹⠙⡏⡟⢹⠉⡇⡮⣹⠈⡏⡏⢸⣷⢸⡇⢈⠀⠀⠀⠀⡇⢸⠀⣿⠁⡏⢹⠩⡆⠏⢹⠸⡏⡟⢹⠹⡟⡏
⠀⠀⠀⣾⣾⣾⣷⣿⣾⣾⣷⣿⣺⣶⣷⣿⣾⣫⣜⣡⣤⣤⣤⣤⣄⣥⣜⣇⣿⣶⣿⣿⣾⣷⣶⣾⣾⣷⣿⣾⣾⣷⣷
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠀⠉⠉⠉⠉⠉⠉⠉⠁





⣿⣿⠛⢿⢛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠐⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⡂⣄⠀⠀⣸⠀⡈⠁⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⣀⠀⠀⠀⢀⡶⠀⠀⡄
⣀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠤⠀⡰⣄⠀⠸⠇⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⠐⢶⠗⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠰
⠶⠦⠛⠉⠹⣋⢛⣴⣦⣤⡆⠄⣐⠀⢣⠰⠛⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠔⠊⢁⠀⠀⡀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠙⠂⠘⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠮⠡⡀⠀⠀⠈⠉⠉⠻⠂⠀⢠⣄
⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⠄⣀⣀⡄⠔⠂⠈⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠉⠑⠖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠰⠿⡓⠡⠆⠂⠤⣥⣖⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠦⡖⠀⠀⠀⠀⠀⠀⠀⠃⠐⢠⡼⠉⢝⠲⠀⢀⣶⠠⠔⠀⠁⠀⠀⠆⠈⠁
⠀⠀⢠⢤⡤⣶⢏⡌⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠙⢤⠤⣶⢺⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢄⠚⣶⡄⠀⠀⠀⣆⡁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠙⢤⡆⡀
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⠌⠠⠋⠀⠉⠀⠀⣰⢃⡃⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⠀⠀⠘
⣤⣤⣦⣜⣀⡛⠀⠈⠈⠀⠐⢀⠊⠀⠀⠀⢰⡾⠞⠁⠎⠀⠀⠐⠀⠀⠀⡆⠐⠀⠈⠐⠁⠒⠀⠉⠀⢀⣠⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤
⠈⠁⡉⠀⠐⠃⡤⠀⠤⠠⠞⠁⠀⠀⠀⠀⠛⠁⠈⠂⠀⠀⠀⠀⠀⠀⠍⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣀
⠠⠐⢀⠄⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⡀⢄⠀⠠⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⡀⠀⠘⠿⠃⠂⠀⢈
⠟⠀⢁⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠈⡴⠀⢀⡀⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢀⡀⠢⠠⠈⠓⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡄⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢄⠀⠀⠀⠀⠀⠀⡂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠆⠀⠀⠀⠀⠀⠘⡂⠀⠀⠠⢾⡿⠈
⠀⠀⠀⠀⡨⠣⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢣⠹⠌⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠈⠀⠀⣠
⠀⠀⠀⠘⠀⠀⠂⠀⠄⠀⠀⠀⢀⣰⠆⠀⠀⠀⣀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣀⡔⠁
⠈⠀⠀⠀⠀⠄⠤⠊⠈⠀⢣⡀⠠⠁⡆⣀⠖⠉⠀⠁⠀⠈⢋⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⠈⠀⢀
⠀⠈⠐⣄⠀⠀⠀⠀⠀⢈⠄⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢰⡵⠂⠉
⠺⠃⠀⠁⠐⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠠⠀⠉⠊⠉⢳⠂⠀⢄⡰⢾⠀⠀⠚
⢂⠒⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈⠺⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠖⣠⣾⣿⣷⣦⠰⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡏⣰⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠃⠈⣻⠛⠛⠛⠛⠛⠛⠛⠛⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⣀⣀⣀⣀⣀⣀⣀⣰⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣧⣀⣀⣀⣰⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣆⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣶⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢋⡄⠀⠀⠀⠀⢲⡴⠋⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢃⠀⠿⢿⣿⣿⣦⡾⠁⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⡥⢾⠀⢠⣶⡇
⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠈⠳⠀⠘⠟⠁⣿⠇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠙⠻⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣷
⠀⠀⠀⠀⣰⠿⠁⠀⠈⠉⠀⠀⠀⠀⠈⠈⠓⢀⡀⠤⠤⠄⠻⠀⠀⠀⠸⠹⡤⠀⠀⡐⠀⠔⠈⡇⠀⠀⠀⠀⠀⠲⠈⠀⢀⣀⡀⢻⡆
⠀⠀⠀⢠⠏⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢰⡆⢛⠶⠄⠀⠀⠀⠀⢀⠑⠀⠀⣶⣄⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⠠⣍⠡⣦⡁⣀
⠀⠀⠂⠈⢢⡈⠛⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠰⠋⣠⡎⠀⠀⠀⠘⢿⡀⡠⠖⣁⡠⣴⠊⠀⠀⠀⠀⠀⠀⠙⢶⣾⣿⣶⣶⠟
⠀⠀⠐⠗⠤⣅⣀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣯⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠓⠆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢃⣠⡀⠀⠀⢁⣄⡀⠀⠀⠀⢠⣀⠀⠀⠀⠈⣂⡀
⠀⠀⠀⠀⠑⠄⠀⣤⣩⠟⠘⠤⠀⠨⡥⢏⠽⡄⣠⢍⡽⡸⢤⡀⡈⣩⠇⠹⡄⠀⡬⢉⣆
⠀⠀⠀⠀⢑⣣⣾⣦⣵⡓⣶⣴⣿⣢⣝⠛⠿⣴⣷⣮⣟⣹⣥⣺⣦⣰⠓⢻⡡⣶⣮⣸⡇
⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⡒⣒⠲⠆⡀⠒⣒⡒⠒⠒⠒⠐⠒⠒⠒⠐⢒⡒⠒⠒⠒⠚⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠀⡇⢹⠉⠙⡞⠛⣶⠙⢡⢺⣭⠋⢸⠁⠀⠀⢀⠄
⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⢤⣿⠀⢤⡇⠨⠧⠴⠁⠠⣿⠄⢠⣘⣥⠷⣈⣥⣾⠀⠀⠀⢀
⠀⠀⠀⠀⠉⢩⣽⣍⠉⢭⣭⡭⠉⢭⣭⠉⢩⣭⣍⢩⣭⣯⢩⣷⣮⠙⣽⣷⡎⢡⣶⣿⠋
⠀⠀⠀⠀⠀⢹⣹⣿⠀⢻⡋⣇⠀⣶⣾⡇⢸⣟⣿⢸⢛⣹⢸⢃⢻⠀⢸⣹⣧⢸⣇⣟⠇
⠀⠀⠀⠀⢠⣈⠉⠉⠀⠈⠁⠉⠀⠉⠉⠁⠈⠉⠁⠈⠈⠉⠈⠉⠉⠀⠈⠉⠉⠈⢉⡉
⠀⠀⠀⠀⠈⢰⠦⣬⠁⣬⣬⡉⢩⣭⡭⠉⣉⠉⣻⢍⠟⠉⢨⣌⣯⠉⠭⠽⡏⠩⠭⣭⢩
⠀⠀⠀⠀⠀⢸⣿⡟⢀⣿⣿⠇⢸⣻⡃⢈⡤⠞⠓⠒⢤⡀⢸⣿⣿⠀⣿⣜⡇⢸⢿⣿⡸
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⢉⣀⣈⣉⣹⣷⣥⣥⣤⣆⣡⣸⡎⠁⠈⠀⠀⠀⠁⢀⣀⣁⢀
⠀⠀⠀⠀⠀⢿⡟⣿⠈⣿⣿⠁⢻⡏⡙⠡⠄⠁⠤⠄⠼⠇⠞⢻⡏⠉⣿⣿⡏⢻⢿⣿⠋
⠀⠀⠀⠀⢀⠘⠛⠋⠀⠛⠛⠀⠘⠃⡗⠀⠀⠀⠿⢂⠀⢀⢰⠙⠃⠀⠛⠛⠃⠘⠛⠛⡀
⠀⠀⠄⠀⠨⠤⠬⠥⠤⢤⠤⠤⢬⠭⡥⠤⠦⠤⠶⠤⠴⠤⠄⠤⠤⠤⢤⠤⢄⣄⡤⢀⡷⡤⠤⢠⠠⡠⢤

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⢠⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢑⠔⢰⣃⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠘⠀⢼⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠲⠂⠀⢰⣷⡀
⠀⠀⠀⠀⢀⣀⣄⠀⣡⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⢤⡄⠀⠀⡀⠀⣦⢁⡂⠂⢠⣤⣾⣿⡘⡷
⠀⠀⠀⢠⣿⣿⣿⣿⣦⣿⣿⡃⠀⡀⢀⠀⣀⡀⣀⢀⠼⡿⠿⡻⣦⡏⠀⠀⢧⣤⣽⣴⡟⠻⠿⠛⠉⠑⢀⣤
⠀⠀⠀⠀⠻⣿⣿⣻⡙⢻⣉⠉⢀⡀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠀⢈⣀⡲⠤⠤⠩⠽⠭⠠⡆⠤⢴⠶⢠⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⠓⢀⣀⠀⠀⠀⠒⠉⣉⣡⣤⠤⠤⠤⠤⠤⢄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠋⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠦
⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⣀⣠⡤⠤⠤⠶⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠒⠤⠀⠀⣠⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠰⣿⡆⢠⣾⠁⠀⠈⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠄⠠⠿⠛⠃⠀⠀⠀⠀⠀⠘⠀⠀⠠⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠉⢀⡀⠤⣿⣤⡌⠐⠠⠀⢀⣤⣤⣀⡀⠠⢤⠀⠙⠢
⣠⡤⠶⠶⠀⢀⡁⠀⠘⡉⢀⡠⢶⣦⣤⣐⣂⠈⠛⠇⠠⠤⠼⢿⣿⣿⣿⠿⠿⠶⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢂⡀
⠻⢶⣄⡀⠀⠀⠹⢷⡒⠂⡏⠉⠃⠀⠀⠀⠀⣀⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡥⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠳⢯⣀⢀⣾⣿⣿⠀⠀⠀⠀⢀
⠀⠀⠈⠙⠳⢦⣤⣸⡉⠀⠰⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⣶⣦⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⠻⠟⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢻⠷⢦⣵⣄⣀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣵⣿⣿⣿⣿⣻⣿⣦⡬⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡬⠵⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⡍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣟⣿⣿⣧⣠⣦⣤⣤⡤⠤⠶⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡄⠿⠆⠈⣝⢿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣧⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠈⠀⠒⠠⠄⢬⣖⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣮⣙⣤⣬⣩⣯⣵⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀
⠀⠀⢀⢤⡯⠴⠚⠛⢿⠄⠀⠀⠀⣀⠋⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⡠⢤⡀⠀⣤⣀⢀⠀⠀⠠⣤⣤⡄
⠀⠀⢸⡅⠉⠈⣀⣀⠈⣧⠀⠠⠊⠀⠀⠀⠀⠀⠀⢢⢣⠀⠀⢀⠔⠲⡢⡀⠀⠀⠀⢸⡆⠸⠀⠘⡇⠀⡻⢯⡟⠀⠀⠀⡇⠀⡆
⠀⠀⠀⢷⠈⠥⠀⠒⢂⠺⡄⠀⢄⠀⠀⠀⠀⠀⠀⢘⡼⠀⢠⠊⡀⡀⠘⢴⡄⠀⢐⠀⡇⠀⢑⠊⠀⠀⠑⡔⠁⠀⠀⢀⠇⠀⡇
⠀⠀⠀⢫⠔⣈⠉⠩⢤⡸⠇⠀⠀⠙⠀⡆⠒⢐⠘⠉⠀⠰⠁⠀⠈⠉⠀⠈⢳⠀⠘⢲⠚⠀⠀⢘⠀⠀⠃⡄⠀⠀⢠⠊⠀⠀⠸⢢
⠀⠀⠀⠈⠍⠀⠬⠅⠒⠂⠁⠀⠀⠀⡖⠒⠲⠖⢲⡆⠀⠁⠛⠛⠛⠛⠛⠋⠊⠁⠀⠀⠒⠀⠐⠊⠀⠀⠑⠁⠀⠀⡘⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠭⡭⡭⠭⠭⠭⠭⢭⠭⠭⠭⠕⠀⠀⡇⠀⠟⠑
⠀⠀⠀⢀⠔⡉⠤⠒⠨⢕⠢⡀⠀⠀⠀⠀⢀⡠⠐⠚⠓⠂⢄⠀⠀⠀⠀⢰⠸⠷⠃⣠⡤⣄⡹⠿⢤⠆⠀⠀⠀⠀⠋⠈⠉⠈⠁⢩
⠀⠀⢠⢡⢊⠤⡀⠀⠀⠀⠱⠰⡀⠀⠀⠰⡑⠁⡎⠀⠀⠀⠀⠑⠄⠀⠀⢸⠈⠀⡾⣥⡄⡀⣿⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⢈⢰⡃⠀⢟⠸⢸⣳⡇⠇⠅⠀⣀⣃⣀⣈⣁⣠⣤⣤⣤⣤⣸⣀⠀⢰⠀⠀⠙⣿⣁⣻⠟⠀⢸⡇⠀⡎⣤⣠⣤⢠⡄⣤⠠⢼⡆
⠀⠀⠈⢌⠓⡔⠁⠘⣍⣩⠞⡸⠀⠘⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠃⠸⠴⠤⠄⠉⠀⠈⠀⠤⠎⠇⠠⠁⠉⠀⡁⠉⠈⠈⠈⠵⠒
⠀⠀⠀⢀⠁⠯⠐⡂⠇⡀⠊⣠⣖⡒⢦⠀⠀⠀⣀⣀⣀⡀⠤⢀⠢⡄⠀⠀⣠⠀⠐⠒⢂⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠜⠀⠀⠀⢅⠅⠀⠟⢶⠲⠽⠀⠀⡎⢠⢢⢀⠠⡀⠑⢁⠿⠀⠀⣇⣤⠬⢤⣤⣴⠀⠀⡠⣴⣡⣤⣤⣤⣤⣤⣤⣌⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠀⠀⡄⠀⠀⣧⢄⣈⣘⣀⣡⢰⡩⠋⠀⠀⢸⠇⣀⡾⠿⡾⠀⠀⢠⠊⣠⠲⣠⣦⢴⠂⣦⣤⠙⢺
⠀⠀⠀⡤⠀⠒⠀⢠⡀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠚⠚⠂⠉⠁⠀⠀⠀⠀⠘⣎⠛⣃⣠⡇⠀⠀⡌⠣⠙⠚⠙⠁⠘⠂⠃⠋⠴⢺
⠀⠀⠠⢉⡀⠠⢀⣈⡅⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⡀⢀⠀⠀⠀⠀⠀⡠⡀⠈⠉⠈⠉⣀⠀⣀⡈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁
⠀⠀⢰⠜⠉⠉⠁⠨⡄⠀⠀⡇⡧⣒⣒⣒⣒⣓⣒⣚⣓⣚⣒⣒⣒⣒⡂⡇⡇⠀⠀⣊⡉⡤⠁⠀⠨⠍⡂⠳⢢⣀⠀⠀⠤⠤⢄
⠀⠀⠀⠪⣂⠄⣐⠕⠁⠀⠀⡇⠧⠤⠤⢄⠀⠀⠀⠀⠁⠀⠀⢠⠤⠠⠤⠇⡇⠀⢰⠉⠂⡇⢸⠈⢨⠀⡌⢑⡞⠉⠀⢸⣁⣀⡌⡇
⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⡇⡏⠉⢹⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡇⡇⠀⠰⢗⠤⣇⣈⣈⣈⠤⣐⠇⠘⠦⠀⢘⠀⠇⠃⡇
⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠧⠇⠀⠸⠼⠀⠀⠀⠄⠆⠀⢀⡸⠼⠀⠀⠣⠇⠀⠀⠀⠉⠑⠂⠐⠊⠈⠀⠀⠀⠀⠀⠘⠦⠤⠦⠃
⠀⠀⡀⡀⡀⠀⣀⠀⣀⣤⣤⠦⠖⠀⠀⠀⣀⠠⠤⠤⣤⠄⢮⠘⠀⠀⠀⠀⠀⠀⢀⣠⣤⢄⠤⢒⡸⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⣘⣀⣘⣙⣀⣀⣋⣀⠀⠀⠀⠀⡠⢊⠔⠆⠀⡜⠀⠀⡰⢢⠀⠀⠀⠀⠀⠀⠀⣻⣷⠜⠀⠀⠀⠀⠀⠀⠀⢠⠒⠯⠽⠒⢤⡀
⠀⠘⡀⡄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡁⢸⠈⠦⡄⠈⠒⢋⠔⡸⠀⠀⠀⠀⡠⣶⣲⣾⣷⣖⣶⣄⠀⠀⠀⠀⠀⣮⠤⠒⢊⡍⠴⡆
⠀⠀⣸⠮⡂⣀⠀⡠⠴⡅⠀⠀⠰⡀⣓⣀⣓⣒⡃⣐⣈⣐⣚⣀⠄⠠⡄⠴⠿⠿⠻⠿⠿⠞⠿⠿⠦⠤⡤⠀⢸⡒⣒⣉⡩⠄⠒⠁
⠀⠀⠀⠁⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢤⠀⠀⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠠⠒⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠶⠒⠒⠒⠚⠒⠒⠛⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡏⠉⠉⠉⡇⠀⢠⠤⠴⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣇⣀⣀⣀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⡧⠤⠤⠤⠐⡒⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠇⠀⠀⠀⠀⠀⠀⠘⠀⣀⠃⠀⠒⠀⠁⣤⠤⠒⠊⠁⣀⢀⡇
⠀⢀⡀⡠⣄⢰⡖⠒⠛⠁⠀⠐⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⠴⠀⡏⢸⢸⠇
⠈⡇⢁⢡⠘⠉⣧⠀⢀⡤⠤⠤⠤⡄⠀⢰⠒⠒⠒⠒⠲⠀⠐⠂⠈⠉⠉⡇⢸⠀⡇⠀⠀⡇⡘⢸
⠀⠸⡈⢁⡀⠧⢽⡀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⡇⢸⠀⠧⠔⠀⠁⠀⢸
⠀⠀⠧⠔⢐⣂⠘⡇⠘⡄⠀⠀⠠⠇⠀⠘⠄⠐⠒⠒⠒⠃⠀⠓⠒⠐⠈⠁⣼⠀⠀⠀⠀⠀⣀⢸
⠀⠀⢰⠉⠌⠍⣗⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣿⢀⡤⠐⠀⠋⠀⢸⡀
⠀⠀⢸⠀⣄⡸⢉⢻⠀⠤⠤⠤⠀⢠⠀⠰⠒⠀⠀⠀⢸⠀⠠⡅⠀⠀⠀⡇⣿⠀⠀⠀⠀⢁⡠⢸⡇
⠀⠀⠀⢣⡤⠤⠎⣸⠀⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⡃⠫⠀⡄⠤⠀⠀⠀⠘⡇
⠀⠀⠀⠘⠰⠀⠖⢹⡇⠠⠤⠤⠀⠸⠀⠀⠒⠒⠒⠒⠚⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠴⠂⡇
⠀⠀⠀⠀⣀⡓⠡⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡆⣦⠀⡆⣷
⠀⠀⠀⠀⡄⠒⡞⠙⡇⠀⡠⠤⠤⠤⡀⠀⡠⠒⠒⠒⠒⡆⠀⡚⠀⠉⠉⡇⢸⠀⡇⠀⠇⠰⠒⠁⢹
⠀⠀⠀⠀⢆⢈⣉⠶⡇⠀⡇⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠃⠘⠀⢧⠔⠃⠀⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠓⠀⢸⡇⠀⣇⣀⢀⣀⠀⠀⠠⠤⠤⠤⠤⠃⠀⠓⠒⠊⠉⠁⠀⡄⠀⠀⢀⣤⡀⠀⠸⡇
⠀⠀⠀⠀⠘⡀⢒⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢠⡞⢠⠏⠀⠀⣇
⠀⠀⠀⠀⠀⠁⠀⢸⡇⣠⢤⠤⠀⠀⠒⠒⠒⠒⠒⠒⠐⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⢇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⠒⠲⠒⠒⣦⢸⣟⣠⠔⠉⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢸⠐⡏⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⡿⠀⡇⡇⠀⢀⠄⠀⠀⠀⡠⠀⠀⠀⡇⠀⡇⠀⡄⠀⢤⠈⡆⡇⠀⠀⠀⢀⡴⠋
⠀⡀⠀⠀⠀⠀⢀⡇⢰⠀⡁⢀⣀⡀⠀⠀⠤⠤⠤⠀⢰⡇⢀⡇⠀⠀⠀⠀⠀⣇⢸⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠇⠘⠒⠐⠒⠒⠒⠀⠀⠉⠉⢁⣉⣁⣀⣸⣇⣠⣤⣤⠤⠤⠾⠶⠟⠁
⠀⠀⠀⠀⠀⠀⢼⠤⠤⠶⠶⠖⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠠⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠆⠰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠐⠉⠀⠈⠋⡀
⠀⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠁⠁⠒⠦⠴⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠐⢿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⣤⢬⣉⡅⡉⠽⠉⠿⠯⠶⠷⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠽⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢄⠀⠁⡀⢠
⠀⠀⠀⠐⢪⣷⣻⠯⡑⠀⠳⠟⣓⡃⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠹⠧⠃⡁⠤⠚⡤
⠀⠀⠀⠀⢸⡋⠚⠧⢵⠒⢲⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⣒⠙⠉⣀⢐⠸⡆⣀⡚⡀
⠀⠀⠀⠀⠀⣷⠋⠠⢈⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡟⠻⡶⢄⠻⣯⠑⣾⡟⢘⡟⣾
⠀⠀⠀⠀⠀⠘⣆⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢛⢯⠟⣾⣠⣿⣯⣽⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠚⠾⠉⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠂⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⣖⡄⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠠⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠈⠉⠙⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠙⠛⠻⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⣉⡑⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠠⠴⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠀⠀⠀⠛⠇⠀⠀⠀⠀⠠⣏⡿⠂⡗⠾⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠁⠁⠒⠒⠦⠤⢄⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡋⣀⣅⣀⣸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⡠⠀⣠⣰⣮⣽⡿⠿⠿⡟⠛⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⡿⠛⣿⡉⠭⠑⠒⠈⠃⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡵⠶⠓⠉⠀⠀⢀⣀⣤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠋⠁⠀⠀⠀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣤⣤⣴⣧⠄⠊⡀⢰⣦⡄⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⡿⠛⠻⠋⠳⠟⢀⣈⣽⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴
⠀⠀⠀⢀⣀⣀⣀⣀⣠⣬⠤⠶⠶⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁



⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢀⣤⣤⡀⠀⣤⡤⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠠⣼⡅⣿⡃⠀⣿⠄⢾⡇⢀⠀⢸⣧⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠃⠈⠓⠚⠋⠀⠛⠓⠚⠀⠚⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠀⡀⠄⠒⠄⠠⠀⠂⡴⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠁⠀⢀⠁⠀⠀⠤⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⢀⠀⠁⠀⠀⠀⠀⢸⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡁⣛⡣⠀⠀⠀⠀⠀⠘⠀⢰⠙⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠠⠀⡐⢂⠇⡴⠒⠴⢍⡀⠀⠀⠀⠀⠀⠀⠀⣔⠆⠀⡌
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⠄⠀⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⡖⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠚⠀⠈⠁⠀⠁⠀⠀⠀⠈⠀⠈
⠐⢤⣠⡀⠐⠤⠔⠀⠀⠀⠤⠀⠠⠁⢬⠠⢴⣄⣷⡥⢀⠀⠐⢄⣢⣐⠐⠀⡢⠨⢀⢠⡠⠀⠀⠀⡀⣑⡀⢄⢀⠀⡀⠀⠄⡄
⠀⠀⠈⠘⠈⠀⠀⠀⠀⠁⠁⠁⠁⠉⠁⠀⠀⠀⠀⠈⠲⠂⠙⠃⠀⠐⠘⠐⠃⠀⠀⠀⠈⠀⠀⠀⠁⠉⠀⠁⠀⠑⠀⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠞⠁⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⢴⠾⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠘⢈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⣀⠄⠐⠀⠀⠉⢁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠠⠴⠒⠈⢘⡉⠀⠀⠀⠐⠂⠈⠉⠉⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡠⠄⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡠⠀⠀⡄⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠰⡀⢢⡀⠀⣀⢀⠤⠐⠂⢘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠤⠀⡂⠀⠀⠀⡆⠀⠠⠤⠐⠴⠂⠆⠐
⠀⠀⠀⠐⠄⠀⢀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡡⠀⠀⡇⠆⠀⠀⠃⠀⢀⣴⠄⠀⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠋⠡⠀⠀⠠⠀⠀⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠂⠀⠀⠀⠚⠉⠁⠀⠀⠤⠄⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⢘⢈⢸⡬
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠉⠀⠀⠁⠈⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠜⠐⠂⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⠀⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⢐⠀⠀⠀⠀⡂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⡀⠁⡄⢀⢈⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡞⡉⢳⡄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠤⡄⠴⠦⠀⠄
⠀⠈⠑⠤⠁⠀⠠⠔⠀⠀⠇⠀⠀⢀⠈⠒⠀⠂⠶⠒⠒⠚⠛⡆⠀⠀⠀⠀⠐⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⢁⢀⠁⠒⠤⡀
⠀⠀⠀⠀⣀⡂⠂⠀⠀⠀⠀⠀⠀⠘⣄⠋⠄⠴⠌⡃⠉⠀⢠⡇⠀⠀⠀⠀⠐⠁⢇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠌⠀⡤⠤⠀⢠⠀⠄⠄⢸
⠀⢠⠀⠀⣘⠑⠀⠀⠀⠔⡃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠒⠒⠀⠀⡠⠊
⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠂⠀⠀⠀⠀⠀⠀⠀⢤⡀⠉⠑⠒⠚⠊⠉⢀⡠
⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠁

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⣿⣼⣿⣻⣟⣩⣿⣾⣀⢴⡿⣿⠯⢀⣩⡐⢺⠦⣿⠙⣽⣾⢻⣟⣹⡯⣿⢻⠤⠦⢀⣶⣂⠤⣤⣤⣄⠀⠃⣶⣴⡄
⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠉⠀⠀⣩⣿⣿⡿⠻⠙⢷⣄⡙⠀⣇⣼⡞⣯⣿⣷⣿⣨⣧⡏⠈⠁⠝⡘⣯⡿⢹⠋⢰⢞⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⢋⣠⣤⣦⣿⣿⣿⣀⠈⠭⠵⠯⠌⠸⠟⠟⠇⢤⡤⠙⣿⣿⠇⠀⣴⣗⠼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢸⡧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣯⣿⣻⣿⣿⢟⣻⣿⣿⣷⣯⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⡇
⠀⠀⠀⠀⢀⡀⣴⢿⣿⣿⣿⣿⣿⣿⡛⠩⡽⠎⠈⠓⠊⠁⠉⠙⢼⡽⠃⢘⣿⡯⣵⠉⢻⣿⣷⣄⡀⠀⠀⠀⠀⠉⠛⣻⡷⠇
⠀⠀⢰⡾⣏⡿⢋⣿⣿⡟⣿⣿⣿⠁⠂⠀⠀⢀⣀⠀⠀⠀⠀⢠⡶⠁⠀⠈⠉⠁⠀⠀⠈⠴⠬⠻⣧⡀⠀⠀⠘⠳⠾⠙⠇
⠀⢠⢤⣷⡽⣤⣿⣿⣿⣴⣿⡿⠉⠀⠀⠀⣀⠜⢿⣦⠙⢷⣤⣸⣿⠳⠤⠀⠀⠀⣀⡔⠀⣀⣤⠴⠒⣬⣶
⠀⢹⡄⢿⣷⣿⣿⣿⣿⡿⣿⡇⠀⠀⠘⠋⣁⡈⠀⠙⠃⠘⠻⠿⠌⠳⣄⠈⠶⠬⠄⡁⠈⠙⢁⣴⢋⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⣿⣷⠙⣿⣻⣿⣿⣿⣿⣷⣤⠶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣽⣿⣦⣤⣤⣬⣷⣤⣥⣈⣙⣳⢦⡆⠀⠀⠀⣿⣿⠋
⠀⢀⣿⣿⠀⠛⢿⣿⠻⣿⣿⣾⣧⢀⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣿⠿⣻⣯⣥⣼⡿⣿⣦⢈⠉⢭⡿⠎⠀⠀⠀⠀⠈⠉
⠀⠈⣽⣿⣧⢀⣠⠙⣷⡌⠛⠚⢿⣿⣿⡇⣾⣿⣿⠷⠾⣫⣾⣿⣿⣿⣿⠿⠋⢉⣿⣿⠇⠀⠀⠀⠄
⠀⠀⠸⣻⣿⣦⡈⢁⣙⠻⣦⣀⠈⠉⢻⡇⢸⣿⣯⡿⠟⣵⣿⡿⢃⣴⣶⣶⠏⢉⠛⠉
⠀⠀⠀⠹⣿⠿⠿⢦⣝⣄⠀⠉⠳⣀⣠⣇⢸⣿⠏⢀⣠⣷⣻⠿⠋⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠸⠟⠙⠋⢂⠰⡶⠾⣿⡧⢿⡇⠀⣰⣶⣦⣤⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠵⣮⠓⠉⠁⢾⡇⠀⠀⠀⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡤⢚⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣾⣾⣿⣿⣿⣶⣤⣤⣾⣍⣴⠋⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱
⠀⠀⢀⣠⣤⣶⡾⢿⣿⢿⣿⠿⠿⣿⡿⡿⢿⢿⡟⣻⣿⡿⣿⢿⢿⡿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⣰⠋⣰⠁
⠰⢾⠋⠩⣽⣿⠃⠀⠉⢷⣶⣶⠶⠾⠿⠷⠚⠳⢶⣷⡌⠀⠁⠉⠚⠁⠉⠁⠋⠙⠛⠛⢛⣿⣾⣾⣿⣿⠃
⠲⢦⣧⡶⠈⠁⠀⢀⡄⣾⣸⣄⣀⠄⠒⠒⠒⣈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠋⠉⠉⠙⣿⠿⢇
⠀⠀⠈⠉⠛⠲⢦⣼⣿⣟⣻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣶⣶⣶⣾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠿⡿⠛⠛⠛⠛⠋⠉⠉⠉⠙⠯⣉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠉⠉⠁⠀⢀⣄⡀⠀⠀⢠⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡗⠺⠰⣻⠄⠹⠸⣟⠃⠸⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠱⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⡴⠒⠲⡀⠀⢾⠉⠁⢹⠀⠀⡏⠉⠙⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠳⠒⠚⠁⠀⠈⠉⠉⠉⠀⠀⠓⠒⠚⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠤⠤⢤⠀⢰⠒⠒⠐⡄⠀⡴⠂⠐⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠦⠤⠼⠀⠈⠓⠒⠒⠃⠀⠓⠤⠴⠃⠀⡾
⠀⠀⠀⠀⠀⠀⡤⠶⡄⡴⠲⡄⠀⢀⣀⣠⣇⠀⣠⠤⠤⡄⠀⡶⠒⠒⡄⠀⡴⠶⢤⠀⠀⣇
⠀⠀⠀⠀⢴⠓⣓⠀⣉⡥⠔⠛⠉⠉⠀⠀⢸⠀⢱⣀⣠⠇⠀⠧⠤⠤⠇⠀⠧⠤⠼⠀⢠⡏⠉⠑⠒⠤⣀⣀⢤⡀
⠀⠀⠀⢀⠤⠇⡵⠊⠁⠀⢀⣀⠤⠔⠒⠈⠈⡇⠀⡤⠤⢦⠀⡔⠒⠒⡆⢠⠒⠒⡆⠀⣼⠉⠙⠒⡦⢄⡀⠉⠳⣼⣰⠒⣄
⠀⠀⠀⢈⡷⠀⢳⡠⠔⠊⠁⢀⣀⠤⠔⠒⠈⢳⠀⠧⠤⠼⠀⠳⠔⠒⠃⠘⠦⠴⠃⢀⡏⠁⠓⠲⠤⣜⣈⡗⢰⠁⠁⢾⢥
⠀⠀⢸⡟⠁⡆⠀⢧⠴⠒⠉⠁⢀⣀⠀⡔⠲⣸⡀⠀⢠⡖⠒⠒⠒⠒⠒⢲⡄⠀⠀⡼⠉⡖⠢⠤⣄⡀⠈⢠⠃⠀⠀⠀⡎
⠀⠀⠈⠧⠤⣤⠀⠈⣇⢰⠒⡄⠣⠤⠇⠙⠚⠉⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⢠⠋⠘⠒⠮⠤⣅⡼⢠⠇⠀⠀⠼⠀⠳⡀
⠀⠀⠀⠠⡖⠃⠀⠀⠘⡌⢉⣀⡠⠤⠤⠤⠒⠒⠓⠒⠚⠉⠉⠉⠉⠉⠓⠚⠒⠒⠾⠤⠤⣄⣀⡀⠀⢀⠎⠀⠀⢀⠀⣠⠤⠇
⠀⠀⠀⠀⣣⡤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠤⣀⣈⡤⠼
⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡈⠙⠻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠉⠻⢿⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡿⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠈⢿⣧⠉⠛⠻⢿⣶⣄⡀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠈⠙⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠉⠻⢿⣦⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢀⣠⣴⡿⠟⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⢀⣿⣟⣠⣴⣾⡿⠟⠋⠀⠀⠀⠀⠈⠙⠿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⢾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⣀⣤⣾⡿⠛⠛⠛⠿⠿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠛⠛⠂⠀⠀⣰⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣦⣤⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⠿⠛⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠻⣿⣿⣿⣶⣄⣠⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡾⠋⠀⠀⠀⠀⠀⠈⣿⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣼⣷⣄
⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄
⠀⠀⣠⣴⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⣿⣿⣿⣿⣷⡄
⣤⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣰⣿⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣿⣿⢿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢀⣾⡇⠀⠀⠀⠀⠁⠀⢰⣿⡇⢸⣿⣿⣿⡇
⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⢀⠀⢸⣿⠁⠈⣿⣿⣿⣿
⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⢀⡿⠀⣼⡟⠀⠀⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⢠⣾⠇⢰⣿⡇⠀⢀⣿⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣴⣿⡏⣠⣼⣿⠀⠀⣸⣿⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⣿⡏⣰⣿⠏⠋⣰⡆⣿⡟⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣴⣿⡿⠀⣼⣿⣿⣿⠁⠀⢠⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣼⣿⡏⠻⠃⣶⠀⢸⡇⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⣿⣀⣾⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡉⠉⠉⠛⠋⠀⠀⠀⠀⣼⣿⢋⣿⡿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣸⣿⠁⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣦⠀⠀⠰⠛⠁⠀⢰⣿⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⢛⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣶⣾⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣯⡄⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠇⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠛⢿⣿⣷⠀⠀⠀⠀⣿⣿⠇⢨⣿⣿⣿⡇⠘⢿⣆⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⢀⣿⡏⠀⢸⣿⣿⣿⣷⠀⣈⠉⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⣾⣿⣿⣿⣿⡄⢻⣷⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⣿⣿⣿⠟⠻⣷⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⣿⣿⡟⠀⠀⢹⣧⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⠇⠀⠀⠈⠻⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠻⣿⣿⣿⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⡟⠀⠀⠈⠻⢿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⣀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⢿⣿⡟⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠀⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⢉⣡⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣆⠉⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠋

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⡀⠀⠀⣀⠘⠻⢛⠛⠋⠉⠉⠉⠉⠁⠐⣒⡄⠀⢄⣀⡀
⠀⠀⠀⠀⠸⣷⡴⠾⠳⠦⠾⠛⠉⠉⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⠑⠿⢿⡯⠝⣚⣩⢠⠄
⠀⠀⠀⢀⡀⢽⡇⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠃⣀⣉⡴⢀⣤
⠀⠀⠀⠸⠟⠛⠋⠀⠀⣠⣌⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠠⢐⠁⠀⠈
⠀⠀⠀⠀⠀⠐⢠⠤⢿⠀⢦⠀⠀⠀⠠⣲⡦⠤⠄⠀⠀⠀⠀⣰⡠⠟⠓⠁⣰⠄⡿⠤⡄⠂
⠀⠀⠀⠀⡠⠒⠁⠀⠸⠖⠉⠁⠀⠀⠲⠀⢀⡀⠀⠀⠀⢀⡀⠀⠔⠂⠀⠈⠉⠲⠇⠀⠈⠐⠄⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣥⡉⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⣿⣟⠛⠿⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠈⠙⠶⣔⠂⣿⠙⢃⡶⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⣷⣄⠀⠀⠈⠆⠀⠤⣜⠁⣰⡟⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢰⠃⠉⠳⣦⣠⠀⠀⠀⠀⠉⠛⢄⡀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⡀⠒⠉⠓⠠⠀⠤⠀⢿⣀⢦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⣀⣰⢢⠀⠀⠀⠙⣿⣷⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠃⠀⠀⠀⠀⠠⢿⠇⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠰⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠿⠷⣶⣶⣦⣴⣶⣶⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠈⠉⠉⠉⢻⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⠀⣿⡆⠀⠀⠀⠀⢻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠰⣼⡇⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⠀⠀⠀⠰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢸⣿⠀⠀⠀⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣿⣧⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡿⣆⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⠁⢻⡄⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡏⠀⠀⠹⣆⠀⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⡇⠀⣿⡇⠀⠀⠀⢨⠃⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣧⠀⠀⠀⠀⢳⡀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⣿⡆⠀⠀⠀⠈⣿⣄⢠⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⣿⡇⠀⠀⠀⠀⢹⡟⠎⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⣧⠀⠀⠀⠀⠈⣳⣶⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠗⣾⡷⢿⣤⣴⣤⣀⣀⣿⣿⣿⣠⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠠⠴⠞⠉⠉⠉⠛⠻⠛⠛⠋⠉⠙⠋⠀⠉⠉⠉⠉⠉⠁⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠸⢼⠇⠀⠀⠀⠀⢠⣶⣦⡀⠀⢰⠀⠀⠁⠀⠀⠀⢘⣈⠁⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠧⠀⠀⠀⢸⡇⠈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹
⠀⠀⢠⠀⠀⠀⠀⠀⠚⡀⠁⠀⢠⡥⢿⣄⠀⢻⣶⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⢸⡀⠀⠀⠀⠀⠠⠁⡄⠀⠈⠀⠈⠙⣧⢸⡆⠀⠤⣀⢒⣾⣿⣀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢀⣀⣀
⡿⠋⠉⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⢀⣿⡥⣾⡿
⠃⠀⠀⣸⠏⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣧⠀⢀⡀⠀⠀⠰⣶⣦⣼⡄⠀⠀⠀⠀⠈⢧⠀⠈⢿⡇⠀⠃
⠀⠀⠀⢫⠾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠐⠂⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⠈⢇⠀⠀⠈⢀
⠀⡠⠀⠀⠀⠀⠉⠀⣀⣀⣤⣶⠛⠛⡐⠂⠀⠀⢤⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡼⠶⣶⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⠏⠉⢛⡷⣾⣛⠉⠉⠀⠀⠀⠈⠈
⠀⠀⢤⡀⢀⠠⠖⠉⠀⢀⠈⠉⠀⠀⡠⠀⢤⡀⠀⠀⠀⠁⠀⠀⠱⡍⠢⢭⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠐⠓⠀⠀⠐⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⡶⣧⡇⠀⠀⠀⠉⠉⠛⠛⢷⡴⠞⠁⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠀⣀⡘
⢙⣀⢀⠀⠀⠀⢀⡦⠀⠀⠀⢀⣀⣀⡦⠀⠀⢀⠀⠀⠀⠀⢀⠎⠲⣀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠐⣾⠐⠉⠳⠒
⠋⡏⣸⠧⠤⠖⠋⢀⣶⢟⡺⢯⣍⣭⡄⠀⠀⠠⠀⠀⠀⢠⡟⣗⠀⠈⠑⠂⠀⠀⠀⢻⠀⡔⠻⠆⡠⠚⠐⠟
⢀⡁⠀⠀⠀⠀⠀⢸⡟⢸⣋⣐⡤⠄⠀⠀⠀⠀⠳⡀⠀⠈⡤⠚⣀⠀⠀⠀⠀⠀⠀⢈⣾⣱⡁⢀⡷⠤⣴⠋⢰
⠘⠀⠀⠀⠀⠀⠀⣠⡿⢛⠿⡿⣿⢯⣧⣠⡀⣰⠀⡗⠀⠀⣹⡉⠱⠆⠀⠀⠀⠀⠀⢸⣬⡉⠙⣿⡀⠠⣟⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠏⠐⣾⠚⠇⠈⣷⡦⣤⣴⡇⠘⠀⠀⠀⢹⡖⠆⢛⠀⠀⠀⢀⡜⡀⠠⠿⣤⣯⣤⣟⣁⣠⣀
⢶⡄⠀⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣿⣼⠛⢿⡸⡆⠀⠀⠀⠘⣷⠬⠋⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠉⠈⠉⠉⠉
⠉⠀⢀⡴⡞⢯⠉⠳⠄⠈⠀⠀⢀⣿⡇⠀⠰⣇⠁⠀⠀⠀⠀⠿⡂⠴⣢
⠀⠀⢸⠀⠀⠀⠀⣄⡗⠀⠀⠠⠞⡿⠁⠠⠴⠋⠀⠀⠀⠀⠀⠈⠣⠿⠟⠀⠀⠀⠀⠀⢀⡔⠛⠛⠐⠒⢠⡀
⣀⣀⣰⣛⣆⣀⣂⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣄⣀⣀⣀⣀⣸⣀⣘⣛⣀⣀⣀⣘⣄
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣿⣵⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢦⡟⠈⢻⣿⣿⣿⡀⢚⡠⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢿⣿⣷⣾⡿⣶⡜⣿⣿⣿⣃⢛⣷⣿⣯⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣾⢻⣿⣿⣿⣫⣿⣯⣥⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠿⣿⣻⣿⣾⣻⣿⣿⣆⣾⠉⣧
⠀⠀⠀⠀⢠⣦⣀⠀⠀⣀⡉⣿⣷⢻⣿⣿⣿⣿⣿⣫⢻⢫⣾⣿⣿⣿⣿⣷⣯⣾⣽⣿⣿⣧⣿⡆⢀⣠⣦
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣽⣇⣘⣿⡇⠻⣿⣿⣬⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⡇⢿⣷⣟⣟⣿⣷⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣷⢶⣿⣯⣿⣵⣭⣭⣭⣭⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⠯⣻⣹⣹⢿⢹⣟⣿⣯⣿⡯⣿⣋⣷⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠋⠉⠉⠁