23rd Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢤⠀⣴⣇⠀⣿⣇⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠁⠀⠀⠀⠟⠂⠁⠀⠑⠋⠁⠈⠛⠁⠈⠛⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢀⠿⠰⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣰⡍⠁⠈⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠍⠰⠤⠃⠀⠀⣀⠀⣻⡈⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠰⠙⠀⠀⠌⢀⠀⠁⠀⠀⠀⠻⠁⠐⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⡆⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠁⠀⡇⢀⠀⠀⠀⠀⠀⡆⢆⠀⠀⣔⣀⣐⣃⣒⠆⡐⠒⠀⠀⢀⣄⢀
⠀⠀⠀⠀⠀⠀⠄⠈⠱⠠⠐⠀⠐⠁⠰⠊⠀⠀⠀⠀⠉⠠⠀⠋⠀⠐⠀⠀⠘⢘⠀⠋⠑⠀⠴⠄⢀⡁⢀
⠀⠀⠀⠀⠀⠀⠪⠢⠡⠀⠀⣰⠀⠀⠀⠸⠐⠒⠒⠂⠤⡀⠀⠀⠀⠀⠀⠀⢠⢸⢈⠐⠀⠢⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⢄⠉⡀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢂⡀⠀⠀⠀⠂⠸⠸⠀⢀⣰⠀⠀⠀⠊⠪⣁⠈
⠀⠀⠀⠀⠀⣴⠃⡀⠁⠠⠀⠳⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⡀⠈⢢⠀⢆⠀⡰⠄⠀⠀⢃⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠩⡀⠀⠐⠀⠢⠀⠰⠀⠄⢠⡝⢒⠀⠀⣀⠉⠈⠠⠀⢸⠀⠔⠀⢀⠀⠀⠀⠀⠐⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠉⠀⠈⠁⠁⠁⠀⠁⠘⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠤⠀⢴⠰⣆⠀⣶⠲⣄⠀⠀⣠⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢰⡆⠁⠀⣿⠀⠀⠘⡷⠂⠀⢸⡟⣧⠀⣿⢺⡇⠀⡠⢿⡄⠀⣸⠇⠀⢠⡏⢀⣤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⠀⡄⠸⠇⠒⠀⠋⠈⠁⠈⠉⠁⠀⠉⠀⠉⠈⠀⠘⠃⠀⠻⠀⠀⣾⠁⢸⠃⢀⡿⠀⠸⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠲⢦⣄⣀⣀⣀⣀⣤⠶⠛⢁⠙⠳⢦⣄⣀⣀⣀⣀⣤⠴⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣠⣶⣤⣄⣉⣉⣉⣁⣤⣴⣾⣿⣿⣶⣤⣄⣈⣉⣉⣁⣠⣴⣦⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢹⡆⢸⣿⣿⡿⠟⠋⠉⠙⠛⢿⣿⣿⡿⠟⠋⠉⠙⠛⢿⣿⣿⡿⣿⠀⣾⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⣡⠄⢸⡇⢸⣿⡿⠀⢠⣶⣶⣶⡀⠀⣻⣿⠁⢀⣶⣶⣦⡀⠈⣿⣿⣛⣿⠀⣿⠀⢤⡙⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⢟⠀⢸⠇⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⡀⢹⠀⣘⠷⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠟⠀⣿⠀⣿⣿⣿⣿⣿⣿⡟⠁⢀⣼⣿⣿⣿⣿⡏⠀⠀⠰⢾⣿⣿⣿⣿⡇⢸⡇⠘⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣴⡏⢀⡇⢀⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣷⠀⣇⠈⣷⣅⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⣫⡖⢸⡇⢸⣿⣿⣿⠟⠁⢀⣼⣿⣿⣿⣿⡏⠉⠹⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⠀⣿⠀⣮⡏⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠻⢿⡅⢸⠀⢸⣿⣿⡏⠀⠀⠈⠉⠀⠉⠉⢹⣿⣦⣀⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⠀⢸⠀⣽⠿⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡇⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣽⣧⠸⡇⠸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣷⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡿⢀⣿⣥⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣿⣇⡹⣄⣙⡿⠿⠿⠛⠛⠛⠛⢋⣉⢉⡉⣉⡉⢉⡙⠛⠛⠛⠛⠿⠿⣟⣁⡼⣡⣿⣏⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠉⠉⠛⠳⡏⠁⣤⡀⣶⣧⣿⣿⢿⢸⣿⢸⡃⣿⣧⣸⡏⣼⣟⢸⣷⠠⣤⠄⠉⡷⠛⠛⠉⠉⢳⣀⡀
⠀⠀⠀⠀⠸⡉⠊⠉⠁⢩⠀⠀⠀⠀⠀⣦⠀⠻⠓⠈⣉⣈⣈⣤⣄⣤⣤⣤⣤⣄⣄⣤⣄⣁⣉⣋⡘⠃⠀⠀⡄⠀⠀⠀⠀⠨⠁⠉⠉⠚⣹
⠀⠀⠀⠀⠀⠙⢢⡄⠀⠸⣀⣤⣤⣤⡀⠣⠐⠚⠻⣿⠉⠉⠓⠦⣤⣉⠛⠿⠟⠋⣡⡤⠖⠋⠁⢹⡿⠛⠒⠠⠃⣠⣤⣤⣄⡸⠀⠀⣤⠚⠁
⠀⠀⠀⠀⠀⢠⢏⣠⠤⠶⠶⠿⠾⢿⣿⠶⣄⣀⣀⣼⠁⠀⠀⠀⠀⠉⠓⠶⠖⠋⠁⠀⠀⠀⠀⠸⣄⣀⣀⡴⢾⣿⠭⠶⠶⠶⠦⢤⣈⢣⡀
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃


⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣠⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣆⣠⣴⣶⣿⡄⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⡿⠟⠛⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⢿⣿⣿⡟
⣀⣴⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠁
⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣿
⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣹⣿
⣉⠿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⣿⣏⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢲⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠈⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣯⣿⡶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⠀⢸⡿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣾⣽
⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⠻⢿⣿
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⡀
⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡄⠀⠘⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⡇
⣰⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠁
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⣿⡟⢿⣿⣧⠀⠀⠀⢤⣤⣤⣤⣀⠀⠀⠀⣀⡀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣨
⠉⠀⠀⠙⠋⠀⠀⠀⠀⠛⢿⠛⣿⣶⣾⣿⣿⣿⡄⠀⢰⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⣴⡿⠛
⡀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣆⣘⣿⣟⣛⣋⣁⣀⡀⣸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣛⡛⠛⣂⣄⣈⣀⣀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣌⠑⠀⠀⠀⢰⡤⠀⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠋⢻⣷⡄⠀⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠄⠀⣉⣧⣤⡄⠀⢴⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠛⠿⡇⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠐⣻⠀⠀⠀⠀⠉⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⡀⣞⣇⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⡀⢰⡴⠀⢸⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣇⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣶⠁⠘⡇⠀⢸⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠀⠿⣄⠼⠋⠀⠀⠀⠀⠀⡀⠀⠀⣼⠀⢀⡇⠀⠘⢸
⠀⠀⠀⠀⠰⠶⢀⣀⠀⠀⠀⠀⠀⡥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣿⠀⣸⡇⠀⡀⢸
⠀⠀⠀⠀⢘⠛⣿⣿⣟⡶⠦⠴⢠⣷⣆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠚⠻⠻⠶⣿⣷⡦⢇⣸⡀⡀
⠀⠀⠀⠀⠸⠟⠋⠉⠁⠀⠀⠀⢸⠋⡿⣶⣶⠀⠆⠤⣴⢷⣶⣶⠏⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢯⣝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠟⡿⠀⠀⠀⣏⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡟⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣿⣶⣆⣀⠐⣳⡄⣼⣁⣀⡤⠴⢂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⡁⣉⣉⣉⣉⠛⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠋⠉⠛⠛⠋⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⣶⣤⠃⣾⡇⢫⣴⡶⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣮⠻⡧⢉⠰⡿⠋⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⢚⣥⡆⡀⠀⠀⠀⠰⠂⠀⠀⠀⢀⢰⣬⡓⢀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡇⡉⣴⣿⠁⣿⠟⢈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠻⣿⠈⣿⣧⢉⢸⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠙⢁⠁⣿⡏⡤⣀⠖⡡⢊⣴⣶⣦⡀⢠⠶⣶⣆⠑⢌⠳⣄⢤⠹⣿⠀⡈⠋⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠹⠇⠦⢸⡇⠀⣠⠞⡡⠊⠀⠈⠀⠈⣿⠇⠀⠀⣸⡏⠀⠀⠑⢌⠳⣄⠀⢸⡇⠴⠸⠏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣤⣈⠁⣞⢡⡊⠀⠀⠀⠀⠀⡼⠋⠀⠀⠈⠻⣿⠀⠀⠀⠀⢑⡌⣳⠈⣀⣤⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⠛⠿⠯⡷⠌⠢⣙⢦⡀⠀⢀⣾⣷⣶⡆⣤⣄⣀⠟⡀⡄⢀⡴⣫⠞⠡⢞⠽⠿⠛⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣷⡆⠀⢦⣌⠢⡙⢦⡀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡴⢋⠔⣡⡴⠀⢰⣾⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣤⣶⣶⣶⣶⠦⠈⠢⠈⠀⢶⣤⢰⡇⣠⡶⠀⠁⠔⠡⠴⢶⣶⣶⣶⣤⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⢁⡈⠋⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣦⣤⠈⠁⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⢀⣁⠀⢀⣀⢀⣀⠀⢉⢉⣉⠉⡁⠀⣀⠈⢉⣉⠉⢉⣀⢀⡀⠀⠀⠀⡀⠀⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣨⡟⠀⢸⣿⠀⢸⣿⣀⡿⠂⠀⠀⣿⠀⠁⠀⣿⣀⢸⣿⠀⢸⣿⠀⢹⡆⠀⠸⣷⡀⠀⢻⣆⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⡿⠂⢸⣿⠀⢸⣿⠙⢷⡄⠀⢀⣿⠀⠀⢀⣿⠀⢸⣿⠀⢸⣿⣀⡼⠃⣐⠁⠙⣷⡀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⢀⣤⣤⣤⣄⣀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠛⠛⠋⠁⠂⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⢹⡆⠀⠀⣠⡖⠉⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢠⣿⡇⠀⢰⣿⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠄⠀⠀⢀⣴⣿⡿⠁⠀⠀⠉⠀⠀⣾⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⣿⣦
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⣤⣄⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⣿⣇⣠⠤⠶⠶⠶⣶⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⣠⡴⠖⠒⢢⠀⢠⣿⡟⢀⡠⠤⣤⡍⢉⣀⣀⣀⣀⣀⣀⠈⠀⠘⢿⣄⠀⠀⠀⣀⣼⠿⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢠⣾⠟⠀⠀⠀⠘⢀⣾⡿⠋⠁⢀⠄⢻⡏⠀⠀⣀⡀⠀⠀⠈⠉⠓⠶⢤⣌⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢠⣿⡟⠀⠀⠀⣀⢴⣾⡿⠁⠀⡔⠁⢠⡿⠁⣠⡾⢡⠂⠀⠀⠀⢦⠀⠀⠀⠈⠙⠻⠶⣤⣄⣀⠀⠀⠀⠀⣀⣤⠞
⠀⢺⣿⣧⣤⠔⠊⢡⣾⣿⠃⠀⠘⠧⠔⠋⠀⢰⡿⢡⠃⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⠛⠋⠁
⠀⠀⠉⠁⠀⠀⢀⣾⣿⠇⠀⠀⢀⡴⢂⠄⠀⣿⡗⠁⠐⣦⠀⠀⣼⡏⢀⡀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡤⢄
⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⢠⡟⠀⠈⠀⠠⣿⡀⠀⠀⡿⠀⣰⣿⠁⣿⠇⠀⢀⣼⠏⠀⣤⠀⠀⠀⠰⣿⠀⠀⠀⠿⢅⠶⣾⡇
⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠘⠓⠒⠀⠀⠀⠙⠓⠀⠊⠀⢠⣿⡇⠀⠛⠂⠀⠀⠛⠃⠀⢻⡄⠂⠀⠀⠻⠄⠚⠄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠚⠛⠛⠓⠒⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⣤⣤⠀⠀⢰⣶⡄⠀⢀⣤⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠰⣟⡀⠀⢸⣿⡇⠀⢸⣿⠁⢀⣾⣿⠀⠀⢺⡶⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠰⣆⠀⠀⢹⣧⠄⠈⠛⢃⣀⣈⣈⣁⡈⠉⠛⠀⢰⠏⠀⢀⣴⠂⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢠⣶⢀⠀⠘⢷⠆⢀⣠⣴⡾⠿⠛⠛⠛⠛⠛⠛⠿⢷⣦⣄⡀⠠⠞⠁⢀⣴⣆⡀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠙⢿⣴⠄⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠐⣿⡿⠋⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⣿⣂⣤⡀⢀⣴⡿⠋⠀⣠⣤⣶⣶⣤⡀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠈⢻⣦⡀⢀⣤⣶⣿⠆⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠙⠛⢁⣾⠟⠀⠀⢰⣿⣿⠟⠻⣿⣿⡄⠠⣿⣿⠟⠛⢿⣿⡆⠀⠀⠹⣷⡀⠛⠋⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠀⠀⣾⡟⠀⠀⠀⠈⠉⠁⠀⢀⣿⣿⠇⠀⠀⠉⣀⣀⣼⣿⡇⠀⠀⠀⢹⣷⠀⠀⣤⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣯⡀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⡶⠶⠂⢸⣿⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⢹⣿⣷⠀⠀⠀⠀⣿⡇⠐⠲⢶⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠀⠀⠸⣿⡀⠀⠀⠀⣾⣿⣿⣯⣤⣤⣤⡄⠸⣿⣿⣤⣤⣾⣿⡟⠀⠀⠀⠀⣿⠇⠀⠀⠘⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢿⣧⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠖⠁⠀⠀⠈⢿⣆⠀⠀⢤⣠⠄⢠⡤⠄⠀⣤⡄⠀⣠⢤⡄⢠⣤⡄⠀⠀⣰⡿⠁⠀⠀⠀⠒⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢠⡆⠀⠈⢻⣷⡀⠘⡟⠀⢸⣯⡀⢰⡿⣷⠀⢿⢿⠁⠠⣿⡷⢀⣴⡟⠁⠀⢠⡆⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⣀⣤⣾⠂⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠠⣽⣆⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠟⢁⣴⣷⠆⣈⠙⠿⢷⣦⣤⣤⣄⣠⣤⣤⣴⡾⠿⠛⡁⠐⣿⣧⡀⠉⠃⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⠿⠃⣰⣿⠏⢰⠆⣄⢉⠉⣉⡉⢉⣍⠀⣴⡆⠘⣿⣦⠈⠻⠋⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣈⠙⠏⢠⡏⠀⣿⡟⠀⣿⠁⢸⣿⠂⢹⣿⡄⠘⠋⣁⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣀⣙⡀⠀⠛⠂⠈⢋⣃⣀⣥⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠻⣿⣿⣿⡆⢰⣿⣿⡿⠛⠛⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⢠⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣛⣁⣀⣀⡀⣴⣦⣶⡄⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⠉⠛⠛⠛⠛⠛⠉⣠⣤⣶⣶⣶⣶⣤⣀⠉⠛⠛⠛⠛⠛⢉⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠆⣀⠀⠀⣈⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠠⠂
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢒⠉⠀⠈⢁⡄⠐⣏⡀⢀⢦⠂⠀⠀⡄⠀⡘⣱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠴⢛⣶⢏⡁⠀⠀⠘⠂⠀⠠⡀⡠⠀⠂
⠀⠄⠀⠀⠀⠁⠀⠀⢠⣶⠀⠀⠀⡀⠒⠈⠋⠠⠏⠀⢂⣤⣀⠀⠈⠈⠁⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠈⠁⠠⠀⢀⠚⠄⣠⢖⡲⠆⠠⠀⠀⠀⠀⢴⣣⣦⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡀⠀⠀⡬⠘⣀⠀⠄⠚⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠉⠁
⠀⢀⠊⠀⠀⠀⠀⠀⠉⠉⢋⡐⠀⠀⢀⠈⡱⠄⣀⣰⠁⠀⠀⠀⠀⢁⡀⣄⠀⠁⠒⠒⠒⠀⡐⠀⡀
⠀⠙⡢⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡤⠴⡀⠘⠉⠉
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠤⠄⠐⢒⠒⠀⠤⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢨⢄⣗⠓⠊⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠙⠵⣆⣨⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⣞⡾⣥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣽⢿⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣥⣽⢯⠵⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢀⠀⣸⠀⠐⠾⠽⣶⣱
⠀⠀⠀⠀⠀⠀⢸⣒⣾⣑⡤⠀⠀⠀⠀⠀⡞⠉⢳⠀⠘⠀⢈⡇⠀⠉⠼⣖⣂⠀⠀⠆⣹⡧⠴
⠀⠀⠀⠀⠀⠀⡄⣽⠟⠠⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠐⠻⣄⠀⠉⠉⠀⠀⠀⠀⠠⡔⣻⣟⣀
⠀⠀⠀⠀⠀⠀⠳⣿⢏⡁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢰⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠈⢝⡿⠂
⠀⠀⠀⠀⠀⠀⡆⣻⡼⠂⠀⠀⠀⠀⠀⠀⣼⠥⣤⠤⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡰
⠀⠀⠀⠀⠀⠀⢘⣻⣿⠇⢠⠚⡆⠀⠀⠀⠀⠀⡀⣤⢀⢴⢰⠒⡆⠸⡅⣸⢹⢸⠉⣇⡎⣸⣀
⠀⠀⠀⠀⠀⠀⠘⠴⢿⠂⡎⢀⡀⡴⡄⡏⡇⡇⣇⡜⠙⠥⠞⠀⠓⠓⠉⠉⠉⠁⠀⠄⢚⠋⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡗⢹⠁⡇⠧⠇⠙⠉⠁⠀⠀⢀⢀⠀⠀⠀⠂⠂⠀⠀⡄⣓⢁⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡀⡰⠀⠈⠀⢠⡀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠂⠀⠀⢠⠄⣰⣷⡻⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠼⢳⠼⣆⣰⣆⢠⠀⠀⠀⠀⠀⢠⠀⣄⣃⣼⣟⠟⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠩⢍⣿⠦⠿⠄⣀⣀⠸⠷⠶⡍⢉⠈⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠐



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⢀⣠⠀⣠⠀⢀⡏⡃⡆⠀⡀⣠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⡴⢤⢄⡈⠛⠿⣀⣷⡗⢤⣵⣺⡏⣿⣿⣿⠷⡀⣾⡄⡠⣴⠀⠀⢼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠿⢀⡟⣾⣸⢇⣶⣄⣭⡛⠒⠦⣽⣿⣿⣿⣿⣻⠀⣿⢠⠇⣿⠀⠸⣽⣿⣿⣿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣗⣶⣦⣬⣅⣼⡼⣿⣽⣰⣿⡿⣷⣦⣍⡙⢿⣿⡏⢻⣿⣤⣇⣿⠀⠨⣽⣿⣏⡻⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⡗⠲⠿⢿⣿⣟⣿⣿⣷⣾⣽⣵⣻⣟⠿⣿⣿⣿⡙⠖⢤⣉⣉⠙⠀⠀⣿⣿⡏⢱⣾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡇⢻⠋⠛⠛⢿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣯⣘⣛⠶⣭⣛⣳⡾⢿⣿⡇⢸⣿⠃⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⣿⣿⣿⡧⣾⠀⠀⣀⡄⠤⠤⠤⠶⠃⠓⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⡳⠿⠯⣽⢸⣿⣧⢼⣿⣼⣧⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣷⣿⠸⠋⠁⠀⠀⠀⠆⠲⠐⠐⠀⢸⣿⣿⣿⣿⣿⠛⣿⣿⠋⠀⠰⠆⣰⠘⣿⠙⡏⠈⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⣿⠰⠀⢀⠀⡄⠀⣄⣀⣀⡀⠀⣼⣿⣿⣿⣿⣃⡈⠻⠋⠀⠀⠀⠀⠻⠈⠻⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⢁⡈⠁⠁⠀⠉⠑⠉⠃⠀⣿⣿⣿⣿⣿⢿⢿⣇⠀⠀⡤⠀⢦⠀⠐⠀⣀⢸⣶⡄⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⡘⢦⣸⡦⠃⡜⣆⢲⣄⢶⣿⣿⣿⣿⣿⣀⣿⣯⢠⠀⡟⢀⠠⠀⠒⠀⠉⢠⢹⢃⣆⢸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣿⣿⣿⣿⣿⠀⠉⠏⡌⢁⣀⠁⠈⠀⠀⠘⡿⣿⣿⣿⣿⣏⣹⢿⣿⣠⡗⡜⠀⠀⠂⢰⠂⠈⢼⣽⣧⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⢷⢶⣦⣾⣷⣴⣗⣴⣶⣶⣤⣥⣿⣿⣯⣌⣿⣭⣿⣿⣿⣧⢦⣤⡤⠀⢸⠂⠁⣾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣯⣵⣯⡾⢛⠝⣳⣶⣛⣻⣿⣿⣿⣦⣿⣿⣿⠻⠿⣿⣿⣿⡟⡿⠀⠀⠀⠁⠈⣖⠀⣿⣿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⡏⠻⠿⢷⠞⣿⣿⣿⣿⣏⣈⣛⣛⣡⣿⣿⣿⣿⢰⣿⣿⣿⠉⠇⢂⣄⠰⠀⠀⠛⠰⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣿⣿⣿⣿⠸⡷⠀⢽⡄⠀⠸⢀⡆⠀⠀⠀⠁⢹⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠘⣿⣼⡿⢹⣀⣣⣤⠾⠃⠀⠘⡗⣾⠀⢀⡀⣠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⣿⣿⣿⣿⠿⢿⠗⠛⡇⠀⠀⣀⣹⣿⣗⠃⠸⠇⠀⠀⠀⠀⠀⠃⠋⡄⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢿⣿⠿⡿⠷⢖⣻⣿⣿⣿⣿⣿⢛⣋⡤⠆⠉⠀⠀⠀⠁⠀⠀⢀⡳⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⢶⠿⣿⣿⠟⢋⠡⠿⡏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣶⣄⡀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣷⢴⣷⣶⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡙⣷⡀⠀⠈⠉⠙⣿⣿⡏⠉⠁⢸⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠛⢿⣿⣿⣾⣿⠀⢰⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣾⣇⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣶⣆⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠋⠀⠀⣸⣿⣿⣿⣿⠀⠈⠿⣿⣿⡿⠀⠀⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠋⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣤⣶⣿⣿⣿⣿⠏⠀⠀⠀⠀⠁⠀⣶⣶⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠈⠻⠇⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⢿⡏⠉⠉⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢹⣿⣁⠀⠀⢀⣤⣶⣤⠀⠀⠀⣿⣿⣿⢸⣇⡀⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣹⣿⣿⣿⣿⣿⣋⣹⣷⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠉⠁⠁








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⣶⣶⣶⣶⣶⣶⣦⣤⣄
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢰⣿⣿⣿⠟⠻⣿⣿⣧⠀⠀⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣷⠀⣿⣿⣿⣿⠛⠻⣿⣿⣿⣷⡀
⠀⠀⣼⣿⣿⡏⠀⠀⠀⢻⣿⣿⡄⠀⠈⠛⠛⠃⠀⣰⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⠁⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣆⠀⣿⣿⣿⣿⠉⠻⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⠀⣠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠀⠀⠀⠀⢰⣶⣷⡄⠀⣠⣾⣿⣿⡟⠀⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣆⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣾⣿⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⢿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠿⠏⠛⠻⠟⠛⠛⠛⠛⠋
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠉⠉
⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢀⠀⢀⣀⡀⠀⠔⠠⠴⠦⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈⢀⢨⡄⠁⠀⠀⠀⠀⠀⠤⠤⠶⠂⢀⣍⣍⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠄⢠⠀⠀⠀⠀⠀⠀⠴⢃⡀⠀⣄⣠⢕⡢⠤⠤⣄⣤⡀⡀⠀⠀⠀⢂⡠⠄⠒⠃
⠀⠀⠀⡀⠀⠀⣐⡠⣀⠂⠤⠤⠤⠔⠇⠉⠀⢺⠙⠀⠈⠉⠁⠀⠩⠌⠀⠁⠐⠋⢉⢁⠄⢀⡆⠠
⠀⠀⠀⠀⠁⢘⠁⠀⠁⡁⠀⠀⠀⢀⡿⠄⠤⢼⡉⡌⠁⠂⠛⠓⠷⠶⠄⠐⠪⠭⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⣇⠀⠀⠒⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⢔⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢔⣴⡂⠎⠉⠯⠉⠽⢿⠿⡟⠇⡟⡫⢾⠶⠾⠿⠿⠛⠟⠘⠘⣊⡉⠃⣿⣻⡇
⠀⠀⠀⠀⠀⠀⡠⡴⠉⠀⢀⡀⠀⠀⠀⡐⣠⡾⣠⢳⣾⠀⢠⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡆⢹⣻⡇
⠀⠀⠀⠀⢀⠪⠊⠀⠀⠀⠑⠁⠂⠀⠀⣿⣿⠅⡴⣾⣿⠆⡘⠀⠀⠘⠛⠛⠋⠀⢀⡀⡐⣀⢿⣿⡏
⠀⠀⠀⡠⣰⣧⣤⡤⠰⠠⣰⢐⢢⣤⣤⣾⢏⢜⡇⣿⣭⣮⣤⣀⣁⣀⡀⡁⣼⡿⠍⠷⣴⣏⣾⠟
⠀⠀⠀⣷⣶⣿⢛⣛⣻⣿⣶⣶⣶⣾⣭⣿⣾⣴⣷⣿⣿⡿⠿⢿⣿⡿⠿⠷⣖⣚⣛⢛⣿⣿⡟
⠀⠀⠀⣯⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠭⠽⠷⣶⣶⣶⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁

⠀⠀⠀⢈⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⢀⣿⡹⣯⡀⠀⠀⠀⠀⠀⣤⣤⣼⣷⣿⣂⠀⠀⠀⠀⠀⣿⣴⣂⣀⡦⡄⠀⠀⠀⣴⣿⣿⠿⢻⣿⠶⠀⠀⠀⠀⢰⣿⣿⣿⢿⡀
⠀⠀⠘⠿⠶⠿⠃⠀⠀⠀⠀⠀⠛⠛⠷⠶⠋⠁⠀⠀⠀⠀⠤⠿⠿⠽⠿⠧⠤⠀⠀⠀⠀⠙⠿⠾⠿⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠾⠁

⠀⠀⢠⣶⣶⣶⡀⠀⠀⠀⠀⠀⢀⣠⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⡄⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖
⠀⠀⢸⣿⣿⣷⢲⡄⠀⠀⠀⠀⠾⢀⣞⠹⣿⠓⠀⠀⠀⠰⣟⣿⠀⠀⢸⣏⡷⠀⠀⠀⠀⣶⣒⣚⣛⣓⡂⠀⠀⠀⠀⠀⣰⣟⢽⣦
⠀⠀⠈⠙⠛⠙⠚⠁⠀⠀⠀⠀⠦⠌⠏⠠⠟⠁⠀⠀⠀⠀⠈⠁⠳⠶⠂⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⠯⠇⠀⠀⠀⠀⠀⠙⠿⠾⠋

⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⢾⣿⣾⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣤⣤⠀⠀⠀⠀⠀⢀⡴⣤⡐⢀⠇⠀⠀⠀⠀⠀⣿⣿⣽⣭⣿⡛⠋⠀⠀⠀⢰⠀⣺⠀⢨
⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠘⠯⠿⠃⠁⠀⠀⠀⠀⠘⠛⠛⠒⠚⠓⠛⠁⠀⠀⠀⠀⠀⠂⠤⠄⠙⠁

⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⢤⣤⣄
⠀⠀⢰⣿⡿⣿⣿⡿⣆⣀⣠⣿⣾⣿⢿⣿⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⠿⠷⠂⠀⠀⠀⠒⠿⢿⠇
⠀⠀⢸⡏⢀⠙⠛⣿⣿⣿⣿⣿⠛⢋⠀⣹⡇⠀⠀⠀⠀⢛⣛⣾⣿⣿⣿⣷⣿⡛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣦⣀⣠⣤⣤⣤⣄⣀⡴⠁
⠀⠀⠈⠛⠚⠁⠀⣿⣻⣿⣿⣻⠀⠙⠚⠋⠀⠀⠀⠀⠘⠛⠋⣿⣿⣿⣿⣿⡍⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠬⢿⣿⣿⣿⣿⣿⠯⡥⠚
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠁⢘⡯⢻⢿⣿⠿⣟⢭⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⢺⣿⣿⣿⣿⣷⣤⣤⣄⠀⠈⠀⠻⣄⠀⣠⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀⣾⠏⡀⠀⠉⣉⡛
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⢿⣿⢿⣿⣧⢠⣦⣤⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⢈⣁⢀⣀⡠⠖⠁
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣞⣻⡷⠂⠀⠀⠀⠀⠹⠟⠋⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣄⣀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠏⠀⠀⠀⢲⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠋⢺⠙⠁⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠘⠋⠏⠛⠿⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡁⠀⠀⠀⢩⠀⠀⠀⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢴⡷⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠻⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠺⠛⣳⣿⣿⣿⣿⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢶⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⢀⣤⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⢻⣿⣿⡃⠀⢤⡄⠀⢀⣿⣧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣷⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠈⣿⡟⠀⠀⠙⠉⠀⣾⢿⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⠿⠿⠿⠛⠉⠉⠉⣹⠇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢻⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠉⠉⠛⠂⠀⠀⠀⠄⠀⠀⣤⣶⣶⣶⠖⠁⠀⠀⠀⠀⠀⠘⣶⡶⠶⠶⠖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⢠⣶⠀⣸⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠾⠻⠿⠛⠻⠿⠛⠷⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡿⠏⠉⠀⢹⡄⠀⠀⠴⠌⠰⠀⠀⠀⢸⠇⠀⠉⠿⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠫⡀⠄⠐⠄⠀⠈⢇⠀⣀⣀⣠⣄⣀⣀⣀⡟⠀⠀⠀⠀⠀⡀⠟⠻⣦⣄
⠀⠀⠀⠀⠀⣠⡾⣏⠀⠀⠀⠃⠈⢁⣴⠶⢚⠋⠉⢁⠀⠀⠀⠀⢈⠉⠙⠓⠦⣤⡀⠀⠀⠀⠀⢈⣽⢷⣄
⠀⠀⠀⢀⣴⠟⠀⠈⠳⣄⠀⣠⠟⠉⠀⠀⠀⠀⠄⠈⠁⠀⠘⠀⠈⠀⡄⠀⠀⠀⢉⠲⢄⠀⡴⠋⠀⠈⢻⣦⡀
⠀⠀⢀⣾⠛⠰⠀⢀⠀⣨⠋⠀⠀⠐⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡙⢄⢀⠀⠠⠋⠙⣷⡀
⠀⢀⡿⠑⠡⠁⠡⢂⡜⠁⢀⠁⠀⠠⠄⠆⠀⠐⠀⠀⠀⡅⠀⠀⠠⠄⠀⠀⠀⠀⠒⠀⠀⡀⠈⢻⣄⠂⡈⠠⠝⣷⡀
⠀⣾⠃⠀⠁⠠⢅⡞⠀⠀⠀⢀⠁⠀⡀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⢠⠀⠉⢀⡀⢻⡖⠀⠀⠀⠘⢷
⢸⡿⠶⠦⣄⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠶⠐⣄⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢧⡤⠴⠖⠛⢻
⣾⠃⠀⠀⠀⢨⠇⠀⠂⠀⠀⠀⠀⠐⠃⠀⢀⠀⠁⠈⠶⠀⢸⠀⠀⠈⠆⠉⠀⢀⠀⠐⠂⠐⠀⠐⠃⠸⡄⠀⠀⠀⠸
⣿⠀⢀⠠⢀⢸⠀⠀⡀⠀⠀⠖⠀⠀⡄⠀⠈⣉⠀⠠⡅⠈⠱⡄⠁⠀⠀⢀⣀⠈⠀⠀⠀⢠⠄⠀⡄⠀⣷⠘⠁⢂⢠
⣿⣇⠘⠂⠀⢻⠀⢀⠀⠤⠀⠀⠁⠀⠀⡀⠀⠂⠀⢀⠰⣄⢀⡇⠀⠠⠃⠈⠁⢀⠀⠄⠀⠀⠠⠀⠀⠀⡟⠈⠌⣄⠸
⣿⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⡠⠀⠀⠈⠉⠀⠀⠘⠀⠀⠋⠀⠀⠀⠀⠚⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰
⢸⣧⣤⠶⠖⠚⢳⠠⠀⠀⢀⠓⠁⠄⠀⠀⠀⠀⠘⠂⠀⠐⠀⠀⠘⠃⠀⣀⠀⠁⠀⠀⠀⠂⠀⠐⢂⡞⠉⠓⠲⢶⣬
⠀⢷⡀⠀⠠⠀⢈⢧⠀⠌⠀⠀⣤⠀⠂⢤⠀⠀⠀⠈⠀⠀⠀⠐⠒⠀⠀⠉⠀⠀⠀⡀⢴⡏⠘⠃⣾⣣⣤⡀⠀⢰⣿
⠀⠘⣷⡀⠨⢀⢀⢊⢧⡀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠂⠀⠀⢠⡄⢀⡾⢓⠻⡍⠓⢀⣿⠃
⠀⠀⠘⢿⡄⠀⠁⠀⠀⠙⣆⡐⠃⠀⠀⡀⠠⡆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⣠⠋⠀⠁⠀⠀⢰⡿⠁
⠀⠀⠀⠈⢻⣆⠀⠀⣠⠞⠁⠙⣦⣀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠃⠀⢰⠄⠀⠰⠀⣀⠴⠋⠀⠙⢦⡀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠙⢷⣞⠁⠀⠀⠈⠉⣉⠙⠲⠤⣄⣀⣀⠀⠀⠁⠀⣀⣀⣠⠤⠖⣿⡃⡤⡖⠀⠀⢈⣻⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⣰⣱⠋⠀⠀⡼⠀⠉⣍⣛⢛⣉⠉⠀⢳⠀⠀⠀⠱⡝⢜⣦⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣧⣆⠀⢰⠇⠀⠀⠑⠈⠠⠐⠀⠀⠸⣇⠀⣀⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠿⠶⢦⣤⣤⣔⣖⣤⣤⡶⠶⠿⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠁⢀⣀⠀⠀⠀⢀⣶⡿⠟⠙⢿⣶⡀⠀⠀⠀⣀⡀⠀⠙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢰⣿⣿⣿⡆⠀⣿⣿⣅⡛⠸⢿⣿⣿⠀⢰⣿⣿⣿⡆⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⠿⠿⠟⠁⠀⢻⣿⣛⠛⢘⣠⣿⡟⠀⠈⠻⠿⠿⠃⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠼⠿⠋⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡤⡤⣤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣿⡿⠿⢿⣿⣿⡿⠉⢀⣼⣧⡄⠉⢿⣿⣙⣛⠻⢻⣿⣶⣤⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡏⠀⠀⠀⢻⣿⠀⠀⠻⢾⣧⡀⠀⠈⣿⡟⠀⠀⠀⢸⣿⡧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣷⣄⣀⣠⣾⣿⡄⠀⠦⣼⡧⠟⠀⢠⣿⣷⣄⣀⣠⣾⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣦⣄⣘⣃⣠⣴⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⣳⣧⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⢉⡱⠀⠀⠀⠀⡀⠀⠦⠄⠠⢒⣼⠒⢐⢚⣺⠀⣻⡃
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠥⠤⠄⠒⣒⢲⡂⢎⢫⣻⡦⠭⢯⠟⡖⠋⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⡐⠀⡄⠀⠂⠀⣀⠀⠀⠀⠀⠓⠂⠋⠉⠉⠉⠁⠹⠀⠚⠚⠁⠀⠀⠖⠀⠀⠐⠨⢍⣀⠀⠀⢄
⠀⠀⠀⠤⢶⡤⠀⠀⠀⣠⠐⣲⣾⡞⠨⢵⣶⠅⠐⣖⣈⢥⡀⠶⢁⠁⠀⠀⢀⠀⠀⠀⢈⡐⢁⡢⣀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣈⣤⠴⠧
⠀⠀⠑⠤⡐⠀⠐⠀⢄⠙⠒⢋⣜⣿⣀⢘⣻⠤⢀⣰⣏⡿⣥⡀⠀⠁⢂⡐⠀⠌⣃⢠⠐⠀⠦⢄⠠⠑⠤⣏⣀⣈⣟⣶⡞⠉
⠀⠀⠀⠀⠈⠁⠠⡀⠀⢢⠄⠀⣠⠤⢉⣉⠩⢅⠀⠒⠾⣟⠉⠤⠴⠂⢀⡌⠀⢠⠈⠃⠄⢀⣀⡀⣰⡄⠴⠄⠵⢤⠶⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢡⣒⡶⠃⠀⠐⠁⠄⢬⡼⠿⣾⠷⣀⠀⠀⢉⡁⠀⡀⢀⣀⡀⣀⣠⣠⣜⣠⠒⠡⢶⡄⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡛⠉⠁⠀⠈⣿⣦⠟⠋⠛⠛⠋⠉⠀⠉⠁⠈⠀⠁⠀⠀⠌⠠⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣢⣀⡰⠆⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠴⠖⠚⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢔⡲⠈⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⣥⣾⡷⠛⠁⠀⠀⠀⠀⣠⣭⡒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠙⠲⢿⡛⠻⢥⡀⠀⠀⠀⢀⣤⣮⡥⢋⡴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢐⣠⣭⣿⣶⣤⣀⠀⠀⠀⠈⠙⠲⢽⣦⣴⣾⠿⣛⣥⣺⢵⣚⣭⣶⡆
⠀⠀⠀⠀⠀⠀⣀⣠⢤⢲⣻⠿⠟⠋⠉⠘⢦⡉⠛⢦⣄⡀⠀⠀⠀⠈⣉⢲⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠐⠠⢉⡛⠋⠁⠀⠀⠀⠀⢀⣠⣤⣿⣷⡶⣞⣻⣷⡆⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢄⡀⠀⠀⣊⠕⡢⢄⡠⢶⣯⡥⢞⣛⣭⣶⣿⣿⣿⣽⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⢷⣶⣍⡂⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⡿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠑⢤⡀⠨⡛⢿⣷⣤⣀⢸⣿⡿⢿⣻⣭⣷⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠈⢹⣾⣭⣶⣿⣿⠿⣛⣭⣷⣿⡿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠢⣀⠈⡳⢦⣸⡿⢟⣛⣭⢶⣻⣿⣿⣿⡿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡂⠙⠿⣟⣭⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢸⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡾⠿⠿⠿⠿⢷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⢁⣀⣠⣤⣤⣤⣤⣄⣀⡈⠉⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣠⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⡈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢸⣿⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣾⡏⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣸⡿
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡈⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⡈⠉⠙⠛⠛⠛⠛⠋⠉⢁⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢷⣶⣶⣶⣶⡾⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠙⣟⣁⠀⡀
⠀⠀⢀⡴⠖⠛⠋⠙⠿⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣡⠌⢉⡀⣼⠇⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠙⠻⠷⢁⣄
⠀⠠⣏⣠⠄⠀⣠⠴⠒⢀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣰⠸⠖⢫⣿⣜⠁⠀⠣⡀⢉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯
⠀⢀⡏⠛⠗⣰⡇⠀⢋⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⣠⠀⠀⠉⢣⠙⣿⠂⢿⣮⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠰⣿⣧⣡⡤⢭⡝⠂⢤⣰⢾⡿⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠲⣤⡿⣠⡇⣼⢘⢬⣥⣾⡇⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⠉⠉⠁⣰
⠀⠉⠋⠁⠀⠀⢀⡴⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠺⣏⢴⡟⢀⠡⣽⢆⡠⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠟⣷⣮⣽⡿⠃⡀⠀⠠⠤⢤⣶
⠀⠀⠀⠀⠀⠀⣿⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡸⢈⠁⣈⠛⠀⣋⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠦⠔⠃⠹⣦⡤⠤⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⠻⣦⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠟⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢛⡿⢿⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠲⠶⠶⠶⠶⣄⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣙⡋⠸⠏⠀⠀⢻⠑⢛⣛⣦
⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢀⠠⠆⠀⣠⡄⠀⠀⠀⠀⠐⢆⠀⠿⢐⡀⠂⠀⠁⠔⢀⣼⣿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⡅⠷⠖⠶⠶⠲⠾⣀⠙⡁
⠀⠉⠁⠀⠀⠀⠀⣹⣇⠀⡀⠀⠐⠂⠀⠘⠂⠀⠀⠀⠀⠀⠉⠁⠤⢊⣁⡀⢀⠀⡀⠈⠁⢀⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⣺⣠⡀⠢⢀⡄⠐⢀⣸⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠻⡭⠃⠀⠀⠞⢠⣿⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣵⠟⠤⠞⠳⡼⠻⣮⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠛⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣳⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⡀⠘⠃⠰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠀⠀⠆⠀⠀⢦
⠀⣀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡘⠛⠳⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣷⠏⠀⠂⠀⠆⢳⡘⣧
⠀⢻⣄⣿⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⣀⣤⡤⢿⡄⠀⠈⠉⠱⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢰⠄⢶⡇⠀⣦⣰
⠀⠀⠫⡙⠣⡁⢀⢠⣼⣷⠆⡤⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠃⠀⠀⠐⠈⠻⣦⡄⠀⠀⠀⠀⠒⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢖⢒⡧⢐⠷⠺⣦⠠⢶
⠀⠀⠀⠀⢀⡜⠁⣀⠀⢁⣸⣗⡛⠶⣙⠟⢶⣀⡀⠀⠀⠀⠀⣶⠀⠒⠢⢄⢢⡀⠁⢉⠀⠀⣀⠀⣀⡐⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⡷⣌⠲⡆⣩⢾⣫
⠀⠀⠀⠀⠘⠳⠇⠀⠀⢻⠇⣨⣽⣀⠴⢟⣦⣭⡀⠀⠀⠀⠀⠹⣷⠶⠄⠀⠙⣷⣦⣀⡹⠾⠿⠿⣉⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠠⠿⡘⢦⡁⠈⠛
⠀⠀⠀⣠⡄⡀⣠⠶⠶⠃⢀⡀⣭⡴⠟⣉⡈⠁⢻⡄⠀⠀⠀⠀⠈⠛⣋⡙⠛⠀⠀⠉⠳⠶⠶⢶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡘⠁
⠀⠀⠀⠻⠧⠘⠀⠀⢠⡖⠉⠉⠀⠀⠀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠘⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⠀⠇⠀⠀⠀⠀⠘⠀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢼⡁⠆⠀⣄⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣾⠲⡦⢀⡀⣶⠺⣧⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡖⠉⢶⡃⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⣌⡀⢞⠳⣀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢹⣢⣤⠎⠥⣤⣴⡋⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠁⠈⢙⢿⡧⣿
⠀⠀⠀⠀⠀⠀⠘⠉⣿⣴⣧⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠿⠛⠁⢻⣦⣼⠛⠉⠛⢯⣤⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡿⠦⣴⠛⢛⡃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡾⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣿⣧⣀⠀⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢏⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⡄⢡⡼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠊⠛⣿⠋⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠱⡄⠀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⢃⡀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠀⠄⠐⣋⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠠⠐⠂⠈⠁⢀⠁⠀⠀⠀⠀⢄⠠⠂⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠢⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⡀⠘⢀⠀⠀⠀⠀⢀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠱⡄⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠔⡀
⠀⠀⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠀⠀⠀⠀⠤⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⢂⣈⣀⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⣀⣘⣤⠄⠀⠀⡀⠀⠈⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢻⣿⠟⡡⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠄⠀⠀⠁⠄⠀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠂⠀⢀⠠⠄⢈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄
⠀⠀⠀⡀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⡀⠀⠀⠈⠁⢀⠀⢀⡐⠈⠀⡀⠀⠀⠀⠂⣀⠀⠀⠀⢀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠏⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣂⠀⠀⠀⠀⠂⠀⠀⠀⢀⣼⠟⠡⠀⠀⠀⠠⠀⢀⠘⢄
⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⣴⠯⠉⠀⠀⠀⠀⠀⠈⠀⠐⠁⠈⠡⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠸⢿⢿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠐⣨⣤⣬⣄⣀⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠥⠭⠛⠗⣐⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠂⠉⠀⠲⣤⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⠴⠓⠠⠀⢀⢤⠄⢸⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⢰⠀⠀⠀⠀⢄⡀⠛⠿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⠀⠀⠂⠘⣯⠙⠀⠐⠯⠙⠂⠁⠔⠀⣿⣧
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢸⣿⣿⡀⢀⠠⠼⠁⠀⠀⠀⠀⠄⠰⠀⢠⡾⣿⣿⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⢸⣿⠿⢧⢸⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠋⠋⣿⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠇⢷⣼⣏⠛⠛⠳⠀⠀⢘⠁⠀⠐⡁⠠⡀⠀⠆⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⠀⠀⠀⠀⢀⠒⠀⠀⠏⠀⡀⡠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⡀⠑⠒⢀⡠⠦⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠶⠖⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡴⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠭⠴⠟⠉⠉⡽⢲⠎⢩⡯⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⣉⣀⡀⠀⠀⠀⠀⢛⠈⣢⢋⣴⣟⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠺⠑⠒⠀⠈⠉⠒⠚⠷⢦⣀⡀⣠⣾⣿⣻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡼⢛⠗⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⡽⠧⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠭⠒⠉⠀⠘⢄⡠⠀⠐⢉⡫⢛⣶⡦⣄⢠⢂⢆⣿⣿⣿⡿⠏⣎⣠⣷⣿
⠀⠀⠀⠀⠀⠀⣀⠠⠔⣊⣥⠖⠙⠓⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⢈⡥⣪⣾⣿⠀⢊⣾⣿⡟⠝⢉⣶⢿⣿⣻⢻⡇
⠀⠀⠀⠀⠀⢀⣿⢴⣢⣍⡁⢮⣀⡑⠒⡀⠀⠀⠀⠀⠀⢀⡠⣒⢵⣾⣾⣿⣿⢁⢿⣿⡿⠟⠚⠻⣿⣝⡕⣵⠏
⠀⠀⠀⠀⠀⠀⡏⠑⢶⡬⣉⡛⠶⣭⣕⣲⠚⣩⡽⢛⡩⢕⣺⣷⣿⣿⣿⣿⣯⡖⠛⠀⠀⠀⣀⡆⣿⣾⣾⠋⠱⠶⢤⣀
⠀⠀⠀⠀⠀⠠⡏⠀⠀⠙⣑⠪⢝⣒⢻⣾⣽⣓⣖⣿⣶⢿⣿⣿⣿⠿⠿⠏⠓⠒⣶⣤⣄⢮⡟⡄⣿⡿⣉⣑⣦⠀⠩⢃⣩⡕⢲⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢭⣍⡲⠬⣅⡂⠭⢙⢻⣿⣶⣿⡧⡟⠓⠈⠤⠤⠖⡩⣫⣯⡟⢾⠑⣹⠟⠋⠉⠀⠺⢕⡳⢜⣨⣶⣷⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⠳⠦⢭⣙⠫⣼⠿⣟⢉⠬⠍⠀⠀⠀⢀⢜⣴⢿⣿⡏⢇⡿⡓⠀⢀⠔⠁⠀⠀⠈⣉⡚⠿⢿⠷⢇⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⢉⠤⠉⢰⡁⠒⠂⢭⣙⡋⠨⠁⠀⢀⣀⣀⣀⢔⣕⣞⣷⣿⣿⣦⠏⠄⠐⠒⠁⠀⠀⠀⠀⠤⠄⠀⠀⠜⠂⢔⢨⠉⣳⡆
⠀⠀⠀⠀⠀⠀⢐⡯⠬⠥⠉⣁⣀⠐⠊⠭⠭⠶⢢⡠⠤⠊⢁⠞⣃⢴⡿⡫⣾⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠒⠀⣸⢄⣠⠴⣊⠥⢻⠄
⠀⠀⠀⠀⠀⠀⠀⣿⠅⢃⣒⣒⠒⠂⠭⠭⠤⠀⢀⣀⣈⢉⡭⠭⠔⣫⣺⣿⣿⣏⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠠⢔⡒⠭⢒⡩⣴⣫⣵⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢅⡒⣒⣂⡰⠯⠭⠭⠥⠔⢛⣒⡂⢬⠍⡭⡯⣿⣿⠟⡏⠙⠿⣿⠤⣐⠓⢭⠕⠲⣒⣂⠭⣔⣺⣵⣶⣿⢿⣿⠿⠛⣋⢭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢕⠮⣛⢜⡙⠫⢛⢟⡹⣋⢟⠰⡫⢛⠕⡲⢛⢷⣜⡦⠀⠀⠀⠹⣦⢽⡖⠺⠿⠿⠟⢿⣾⣿⣿⢿⣛⣭⣴⣾⣿⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠀⠉⠢⢤⣄⡀⢁⣉⣈⣀⡃⠈⣈⣰⣧⣿⣿⣄⠀⠀⠀⠈⠃⠖⡶⠶⠶⢶⠚⠫⠟⠚⠿⠟⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠨⣟⢥⡠⠶⠚⣋⣭⣾⢿⣿⣿⡿⣟⠝⠒⠄⡀⠀⠘⣟⣛⣿⣿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠸⡩⡉⠹⢿⣻⣷⣟⣿⡿⠟⠊⠀⠀⠀⠀⠈⠁⠒⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⡀⠘⡇⢰⣿⣿⠗⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠔⡠⠐⠄⠂⠔⡠⠀⠔⡠⠂⡠⢀⠄⡠⢂⠄⡠⢀⠤⢀⠄⠄⠀⡠⢂⠔⠀⠄⡠⢀⠄⡠⢂⠔⡠⡠⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠊⠔⠡⢊⠔⢈⢔⡠⢊⠔⣊⠔⡠⢂⠕⡈⠐⠥⢊⠔⡡⢂⠄⡠⡢⢊⠄⡀⢐⡕⡨⢂⡵⢃⠔⡡⢪⠊⠔⠱⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠁⠐⠁⠊⠁⠊⠐⠁⠊⠔⠡⠊⡠⢊⠔⠡⠪⠎⠐⠁⠊⠐⠋⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡚⠛⠉⠉⠉⠉⠒⠤⣔⣲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⣉⣉⣽⡶⠆
⠀⠀⠀⠀⠙⠛⠿⣯⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣽⣗⡢⢄⣀⠀⠠⢀⡀⠈⠉⠓⡓⠤⢤⣀⣴⣾⣯⣷⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⣿⠒⠦⣌⡙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣈⣉⣲⣤⣤⠝⠒⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⢸⡷⠦⣄⡉⠙⠲⢤⣉⡛⢒⣛⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⡀⣻⡿⠿⠿⠿⠿⠯⠅⠀⠐⠒
⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣟⡒⠤⣀⠀⠀⠀⠀⣹⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢍⡓⠦⢍⣀⠒⠠⠄⠙⣩⠵⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠈⠁⠀⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣍⣙⠒⠒⠖⠋⣱⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⠒⠛⢣⣄⡀⠀⠈⠐⠛⠷⠆⠀⠀⠀⣀⣠⣤⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⢟⠂⠤⣀⠀⠀⠀⠀⠀⠈⠙⢋⣉⣐⢤⡶⠒⠋⠀⣻⣿⣿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣤⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠉⠒⠲⠶⣾⣿⣿⣿⣿⣿⣽⡇⢀⣀⣤⣿⣿⣯⣴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⣉⡒⠾⣿⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠤⣀⠀⠈⢿⣿⣿⣿⠿⠟⢛⣳⣯⠛⠉⢁⣼⣿⣯⡽
⠀⠀⠀⠀⠀⢈⡀⠠⢤⣴⣿⠢⠬⣭⣿⣿⣿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠿⢤⣀⡈⠀⠒⠛⠉⢀⣴⣾⣿⣿⡿⠒⠚⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠬⢭⣛⣿⣊⣁⡒⠺⣿⡿⣿⡀⠤⢤⣴⣿⡆⠀⠀⠀⠀⢸⡏⠑⠒⠤⢍⣀⡐⠀⠀⢼⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢀⣑⠒⠶⣿⡟⠢⢬⣽⣿⣿⣿⠌⣙⣻⣿⣛⣧⠄⠀⠀⠀⠈⠣⠄⣀⠀⠀⠀⠉⠉⣒⣭⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠬⢉⣛⣿⣛⡁⠒⠲⢿⣯⣿⡓⠲⢾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠒⠶⠚⠁
⠀⠀⠀⠀⠀⠐⠓⠶⢾⣿⣧⠬⢐⣒⣶⣿⣿⡅⠙⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⢾⣿⣿⠿






⡿⢿⡿⠿⣿⡿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣟⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣶⣒⣚⣓⣒⣲⡶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣻⣭⣽⣷⣿⣿⣿⣿⣿⣿⠿⢿⣿⣛⣿⣷⣿⣷⣭⣝⡳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣫⣵⣾⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⡳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣫⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢻⣿⣿⣿⣿⣿⣿⣿⣿⢷⢳⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣷⣾⠷⣄
⠀⠀⠀⠀⠀⢀⡼⣫⣾⣿⣿⣿⢿⣾⣷⣾⣿⣿⣽⣿⣿⣿⣷⢋⣿⣿⣋⣿⣿⣿⣿⣿⢎⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣜⢧⡀
⠀⠀⠀⠀⣠⢟⣼⣿⣿⣿⣿⣯⣷⣝⢿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠹⠟⢛⡛⣛⠛⠻⠳⢺⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣫⣾⣿⣿⣿⣽⣧⡹⣄
⠀⠀⠀⣰⢯⣾⣿⣿⣿⣿⠛⣿⣿⣾⣷⣽⢿⣿⣶⡿⠛⢩⠀⠀⠀⠀⠘⢹⠟⠁⠀⠁⠀⢠⡉⠛⢿⣿⣿⡿⣿⣫⣾⣿⣿⣿⣿⣿⣏⣿⣷⡙⣆
⠀⠀⣰⢏⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣔⠛⠋⠀⠹⡞⠧⠀⣠⣤⣤⣬⣤⣤⣄⣄⠀⢾⡽⠉⠀⠈⠋⣪⡾⢿⣿⣿⣿⣿⣯⣿⣿⣿⠛⣷⡘⣆
⠀⢠⡟⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡀⣡⣶⡿⢿⣿⣾⣿⣿⣤⣿⡟⣿⣷⣄⣀⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⢹⡄
⠀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢡⠏⡶⠀⣸⣿⣽⣿⠿⠿⢿⡴⠲⣄⠀⠉⠻⢿⣯⣿⣷⣅⠠⣴⣻⣄⢻⣶⣿⣿⣿⣿⣾⡿⣿⣿⣿⡿⡾⢷
⢰⡏⣾⣿⣿⣿⣯⣗⣋⡽⣟⠿⡿⣿⠁⠈⠘⠁⣼⣿⣽⣿⣷⣿⣧⣤⡠⠀⠙⡆⠀⠀⠈⢻⣿⣷⣿⣧⠙⠁⠀⠀⠿⠿⠛⢛⣙⣯⣽⣿⣷⣿⣿⣿⢸
⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⡆⠀⠀⠐⣲⣿⣿⣯⣤⡈⠉⠀⡜⠁⢨⡍⡇⢨⡁⠀⠈⣿⣬⣿⣿⣗⡤⠀⠀⠰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎
⢸⢸⣟⣿⣿⣿⡿⣿⣿⣿⣿⣶⣿⠀⢀⣤⠀⣿⣏⣹⣿⢿⣷⡶⠶⡇⠀⠀⠀⣥⠀⠀⠀⠀⣿⣿⣿⣽⣿⢰⠶⣶⡀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇
⢸⢸⣿⣿⣿⣿⣷⣿⣿⣿⠿⣿⣿⠘⠛⠀⠁⣿⣽⣿⣿⣌⣉⣀⠀⠘⣦⡀⠀⢹⠀⠀⠀⣰⣿⣼⣿⣿⣿⠈⠻⠲⠃⣿⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢇⡀⠀⠒⠾⣿⣅⣽⣿⣿⡿⠷⣚⣛⠾⠥⠋⠀⣀⣴⣿⣿⡟⢻⣿⡯⠁⠀⠀⢰⡿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢇
⠸⣇⣿⣿⣿⣿⣿⣿⣿⢽⣓⣮⣷⣿⡀⣠⡄⡀⢻⣿⣿⣿⣛⣿⣾⣿⣿⣿⣶⡶⣿⣿⣿⣿⣻⣿⣿⡿⢠⣄⠀⠀⣶⣾⣮⣵⣞⡭⢿⣿⣿⣿⣿⣿⢸
⠀⢿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡙⠙⠋⠀⢙⣷⣿⠿⣿⣿⣿⣧⣼⣿⣷⣿⣿⡟⢛⣿⡿⡋⠘⠙⠯⠇⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠘⣇⢿⣿⣿⣿⣿⡏⢙⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⣙⠿⣿⣯⣽⣿⡟⣿⣿⣯⣿⣿⠿⠋⠉⠀⠀⠀⣠⣾⢿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⡿⣰⠃
⠀⠀⠹⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡼⡟⣠⣄⠀⠀⣼⣦⠀⠙⠙⠙⣛⣛⡋⠛⠃⠀⢞⣶⣷⠄⣀⣄⢙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⠏
⠀⠀⠀⠹⣎⢷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣿⣿⣦⣝⡋⠀⠀⠀⠀⣟⣸⠃⠀⠀⠀⢀⣉⣵⣾⣿⣿⣷⣟⢿⡿⣿⣿⣿⣿⣿⣿⣦⡿⣡⠏
⠀⠀⠀⠀⠙⣮⢻⣿⣿⣿⣿⡿⣫⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢲⣶⣦⣤⣤⣤⣶⣾⢸⣿⣿⣯⣠⣿⣿⣿⠿⣷⣝⢿⡿⣿⣿⣿⣿⡟⣱⠋
⠀⠀⠀⠀⠀⠈⢳⣝⢿⣿⣿⣾⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣡⣿⣿⣿⣻⣿⣿⣿⣿⣣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⡿⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢻⣯⣿⣿⣿⣿⣿⣿⣿⣯⡞⣿⣿⣿⡟⣻⣿⣻⣿⡿⣿⣿⡿⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣝⠿⣿⣿⣿⣿⣿⣿⢉⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⣝⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⣫⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢮⣝⣻⢻⡿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣬⣿⣿⢿⣟⣛⣫⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠾⠭⠭⣭⡭⠭⠭⠷⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠓⢃⣮⡛⣍⠚⣳⡲⠶⣄⣀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣢⠖⠋⠉⠀⠀⠀⠀⠀⠘⡟⠁⠉⠉⠉⠋⠛⠷⢾⣽⠒⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣩⣴⣀⠀⠀⠀⢰⣶⣶⡄⠈⣿⠀⢀⣀⡤⢀⠀⠀⡾⠏⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡖⡢⠞⠉⠀⠹⣧⡄⠀⠘⠿⠉⠀⠀⢸⠀⠈⠉⠀⠙⠀⡐⠋⠀⣠⣀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡬⢃⣾⠗⢀⡴⠆⠀⠈⠻⣦⡀⣤⣶⡶⠿⠿⢷⠿⠿⠧⣶⣠⢁⠀⠀⠁⠼⡇⠁⠀⢀⣌⠳⡙
⠀⠀⠀⠀⢞⡺⢡⡾⠃⠐⠏⠀⠀⠀⣀⢖⡿⠚⢻⣅⠀⠄⠀⢸⠀⠀⠀⢠⡟⠻⢿⣦⡀⠀⢀⣤⡾⠛⠛⣷⠐⡆
⠀⠀⠀⠀⡼⠁⠉⠛⠶⣄⡀⠀⠀⢔⣴⠋⠀⠀⠀⠻⢆⣠⡤⠼⠦⢤⣀⠏⠀⢀⠀⢙⣿⣲⠗⠁⣀⣤⣄⠘⣦⠹⣀
⠀⠀⠀⢰⠇⠀⠀⠠⠀⠀⠙⢣⣿⡿⠛⠳⢦⣀⡴⢋⡱⠖⠊⠋⠋⠐⢮⣝⢦⠠⠞⠋⠀⠱⡷⡐⠿⣿⠿⠃⠘⡇⠫
⠀⠀⠀⣻⠀⠀⠀⠀⠂⠀⠀⣾⡿⠀⠀⠀⢰⠟⡴⠁⠀⠀⢀⢀⡀⠀⠀⠈⠵⡱⣄⠀⠀⠀⢹⣱⠀⠈⠂⠀⠀⢲⢘⡆
⠀⠀⢠⡏⠀⠀⠈⡄⠐⠃⢰⣿⡃⠀⢀⠀⡟⠼⠁⠀⠀⢠⣾⠿⢷⣤⡀⠀⠀⢱⢹⡞⠛⠛⠻⣿⣤⠶⠶⠶⠿⠛⠁⠅⠇
⠀⠀⡀⡇⢀⣀⣀⣀⣠⢀⣌⢻⠋⠋⠉⢸⣇⣃⠀⠀⠀⣹⣇⠀⣀⣿⠅⠀⠀⢸⢸⡇⠄⡘⠀⣿⠇⢀⣀⠀⠀⠀⠀⡋⠄
⠀⠀⠓⠧⠙⡏⠉⠉⠈⠀⢰⣺⡇⠈⠀⠸⣿⡸⡄⠀⠈⠈⣻⡿⢿⠃⠀⠀⠀⠍⡼⠱⣤⡀⢸⣿⠅⣮⠉⠀⠀⠀⢀⡵
⠀⠀⠀⢸⠀⣃⠀⠰⠏⠁⠈⣧⢻⡀⢁⣤⠟⢧⡐⢤⡀⠀⠀⠁⠀⠀⠀⣰⢎⢼⠃⠀⠈⠙⡿⡋⠀⠹⢦⠀⠀⠀⡸⠃
⠀⠀⠀⠀⣧⠻⣄⠐⠚⠀⠀⠈⢨⣛⡏⠀⠀⠀⠙⠦⣅⣓⣒⣆⠖⣒⣩⢼⠟⢧⡀⠂⢀⡾⡐⠓⢦⣄⡀⠀⠀⠰⣋
⠀⠀⠀⠀⠘⣆⠻⣄⠀⢀⣠⡶⠃⠛⣿⣦⣀⠀⠀⣴⠏⠛⠛⠛⢘⡍⠀⠀⠀⠈⣻⡶⢋⠜⠡⠦⠀⠈⠙⡲⢂⢯⡄
⠀⠀⠀⠀⠀⠸⢆⠛⠟⠋⠁⢀⣀⣤⠀⠻⢿⣷⣾⣏⡀⠂⠀⠀⠸⠇⣀⣠⣴⣾⡿⠇⠉⢴⠂⢀⡀⠀⡴⢣⠞⠈⠁
⠀⠀⠀⠀⠀⠘⠊⢳⣀⠀⠀⠸⡿⠿⠇⠀⢀⡔⠚⠬⣍⣻⣛⡛⣛⠻⠟⠿⠙⠁⠈⢣⡀⠀⠀⠁⣠⠞⡱⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢲⣀⠀⠀⠀⠀⢀⡞⠀⠀⡀⠀⠀⠀⠀⢿⠀⠀⠀⣄⠀⠀⠀⠑⢦⡴⢋⣀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⣾⣁⠀⠈⢁⠀⠁⠀⠀⢸⠀⠀⠜⠛⠃⠀⠀⠀⠀⣖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡵⠶⡭⣝⢓⠶⠤⠤⠤⠤⠾⠀⠀⢀⣀⣤⡤⠺⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠙⠊⠒⠙⠎⠽⠍⠓⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣤⣤⣤⣶⣾⣿⡟⢉⣥⡌⠙⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⠛⠋⠉⠀⢀⣴⠚⠿⣶⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠸⣯⣤⡄⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣏⠀⠛⠻⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠰⣎⢿⣿⣿⣿⣿⣿⣄⠀⠴⢾⠃⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⠙⡆⠀⠀⠀⠀⠀⠹⣿⣟⣉⢰⡿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⢹⡞⣿⣿⣿⣿⣿⣿⣷⣶⣶⡾⠿⠛⢉⣁⣀⣤⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀⠈⠉⠛⢉⣀⣤⣶⡾⠿⠟⠛⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⡜⠻⠿⠿⠿⠟⠛⢉⣁⣤⣶⣾⣿⡿⠿⠿⠿⠿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⢹⣤⣀⣀⣀⣤⣤⣶⡾⠟⠋⠉⠀⢀⣀⣀⣤⣄⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣾⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠉⠙⠛⠉⠉⠁⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠀⠀⡴⠀⠀⠠⠁
⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⢠⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣯⣤⢿⡆⠠⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠆
⠀⢀⠀⠠⠀⠔⣤⢸⣇⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠈⠃⢞⠀⠁⠀⠀⢰⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠐⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠠⠄⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠆⠀⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠆⠐⠀⠀⠀⠀⠂⠀⠀⢤⠤⠄⠀⠀⠘
⠀⠊⢳⡎⠁⢈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣴⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⢰⣠⡀⠀⠂⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⣸⠇⠀⠀⠀⠐⠂⠒⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⡀⠄⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠈⢺⡆
⠀⠀⠀⠀⠀⠀⣫⡔⣮⡂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠸⠃⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⢜
⠀⠀⠀⠀⠂⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠓⣊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠆⠠⠂
⠀⠄⠀⢈⠃⠀⠀⠡⠀⠀⢄⠀⢀⣀⡀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠖⢆⠀⠀⠀⠀⠀⣀⣄⣤⡀⢀
⠀⠀⠠⠈⠀⢀⠀⠀⠀⠀⣀⠀⠿⠽⣉⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠸⢆⠇⠀⠀⠀⠀⠀⠹⠘⢈⡁
⠀⠀⠀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠑⠚⠒⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⠀⠀⠀⠠⠀⠂⠰⠤⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡊⠇⠀⠀⢠⠂⠀⠀⠀⠚⡰⠄⠣⠔⠂⠜⣂⠀⢀
⡄⠀⠀⠀⠀⠀⡆⠀⠈⡀⢀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣐⡶⠃⡄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢉
⠁⠉⠀⠀⠀⠀⠁⡀⣀⠀⠉⠀⠰⠀⠀⠁⠀⠈⠄⠀⠀⠤⢀⠀⠀⠈⠋⠰⠟⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠃⠀⠀⠀⠀⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⢀⡘⠀⢀⣀⣄⣠⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⡀⠀⡀⠀⢠⡘
⠀⠀⠀⠀⢠⠛⢣⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠥⠀⠀⡅⠀⠀⡏⠈⠀⢃⡀⠀⠀⠀⠀⢀⣀⠶⠀⠀⢀⠁⠈⡁⠂⠁
⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⠚⠁⠀⠠⠤⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⢄⠖⠓⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢈⠆⠒⡃⡐⠁⠀⠈⠉⠃⠀⠀⠀⠀⠰⣉⢭⣓⡃⠀⠀⠀⠀⠀⠛⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⡀⠀⠀⠀⣀⡋⠉⠂
⠀⠀⠘⣡⣄⣵⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠉⠀⠀⠀⠀⠀⠐⠀⣰⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡞⠁⠡⠀⠀⡠⠀⠙⡆
⠀⠀⠀⠀⢈⠅⢀⠀⠀⠀⠈⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠘⡀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠶⠧⠀⠀⠀⠀⠠⠶⢆⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠘⠂⠀⠀⠐⠀⢀⠀⠆⢀⠀⠀⠀⠀⡀⠏
⠢⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⡀⠀⠀⠀⡀⢠⠀⢀⠀⠀⡀⠀⠀⠠
⠀⠃⢸⣗⡄⠘⠂⡄⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⢻⠃⠀⠁
⣀⣀⣀⣀⣀⣐⣂⣉⣀⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣈⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⢀⡀⠠⡆⠀⠀⠀⠈⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣿⣸⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠡
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⢻⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠹⡷⠈⠉⢀⢐⠂⠀⠀⠀⠀⢀⠀⠺⠇⠀⠀⠂⠀⠀⠀⠈⠉⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠒
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡔⠀⠀⠀⠀⠆⠀⠀⠀⠺⢠⣠⠔⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣐⠂⠁⠐⠚⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠂⠂⠐⠒⠁⠀⠀⢀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠳⠜⠜⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⡆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈
⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠲⠒⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠠⠶⠀⠀⠀⠀⠀⡀⠀⣠
⡿⠋⢁⡄⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢠⠜⠀⠀⠀⠐⣠⣴⣿⣿
⠁⠀⠺⡤⠀⠀⢸⣿⣿⣿⡿⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡄⠀⠀⠤⠄⠀⣼⣿⡿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣶⣤⣤⣴⣾⡿⠋⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠄⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠈⠀⠁⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡐⠠⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡿⢋⠀⠀⠀⠑⠀⡀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠀⠀⢀⠄⠀⠀⠀⠀⠀⢿⣿⣿
⠁⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠈⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠲⠄⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢄⣀
⡠⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⠖⠐⠀⠁⢀⠤⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲
⠀⠀⠀⠁⠀⠀⠀⡀⠀⣄⠀⠈⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⢓⡆⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡖⠀⠘⡅⠀⠀⠀⠀⠀⢉⠂⠐⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⠀⠉⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠒⠢⡁
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠿⢤⡀⣀⠠⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⣀⠫⠀⠀⡀⣀⡴⡃⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣠⡾⣿⢻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠛
⣇⠀⠀⠐⠀⠀⠀⠀⣀⣤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣀⣿⢸⣷⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘
⠀⠄⠀⠀⠀⠀⢠⣿⣯⢿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣾⣿⣶⣄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⡟⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠶⠶⠶⠤⢴⡷⠀⠀⠀⠀⠸⠾⠷⠶⠶⠶⢶⣄
⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⢋⣰⡇
⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠚⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⠶⢶⡇⠀⠀⠀⠀⢸⠀⣾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣧⣤⣀⣠⣤⣤⣤⣤⣤⣶⣶⡶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠶⠶⠶⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⣤⡀⠀⠀⣠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠙⢶⡴⠋⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣞⣡⡾⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠿⠛⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢙⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢀⡾⢁⣙⠳⢤⡀⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⢻⣶⣛⣛⣋⣩⣭⣭⣭⣥⣤⣤⣤⣤⣶⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⣰⠏⣴⠟⠛⠷⣦⡉⠳⠶⢋⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⢦⣤⠞⢁⣾⠋⠀⠀⠀⠈⠻⢶⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠒⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⣠⠒⠛⢐⣤⣀⠀⠀⠀⢠⣴⣾⣿⣿⣶⡤⠀⠀⠀⠀⢀⣤⠤⢤⠠⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢻⣾⡿⣷⣿⠃
⠀⠀⠀⢾⣹⡇⠀⣿⣧⣿⠆⠀⠀⠀⢹⠀⢸⠀⢸⠀⠀⠀⠀⢰⣿⣷⣬⣿⣠⡾⠀⠀⠀⠀⢰⠾⣧⡿⢷⠀⠀⠀⠀⠀⢸⣯⡿⣯⣿
⠀⠀⠀⠀⠙⠄⣄⠬⠋⠉⠀⠀⠀⢀⣾⣄⣾⣄⣼⣄⠀⠀⠀⠘⠟⠛⠻⠻⠋⠀⠀⠀⠀⠘⠛⠒⠛⠓⠚⠛⠂⠀⠀⠀⠺⣿⣿⣿⣿⠆

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⣴⠹⡍⢩⠏⢦⡀⠀⠀⠀⢾⢉⢹⡄⢤⡄⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠈⣃⣜⢉⢟⡖⢤⠀⠀⠀⠀⢠⣤⠯⢧⣀
⠀⠀⢺⡇⣻⡇⣿⣿⠀⢸⡧⠀⠀⠀⢨⣧⣯⣵⣼⡄⠀⠀⠀⠑⣺⣿⣿⠀⣿⡒⠁⠀⠀⢺⠋⠀⢹⠺⠤⡎⠀⠀⠀⢶⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠉⠻⣰⣣⣞⣆⠞⠀⠀⠀⠀⢸⣿⣿⣿⣽⡇⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠈⠒⠐⠻⣄⡛⣤⠀⠀⠀⠀⠙⣿⠿⢿⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣤⣤⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣸⣷⡆⠀⠀⠀⠀⠀⠀⢠⡿⠛⠿⣦⠀⠀⠀⠀⢠⠻⡈⢹⠐⢒⡆⠀⠀⠀⠀⣴⣶⣶⣶⣶⣤
⠀⠀⠀⣯⣽⣿⢺⢺⠾⡷⡇⠀⠀⠀⠂⠙⠛⡉⠛⠶⠄⠀⠀⠀⢘⠗⠀⠐⢟⠀⠀⠀⠀⠙⠒⠃⢸⠀⣎⣘⡄⠀⠀⠀⠘⢿⣿⣿⡿⠁
⠀⠀⠀⠛⠛⠛⠛⠿⠿⠋⠀⠀⠀⣠⣶⣶⡄⠂⠀⠀⠀⠀⠀⠠⣿⣿⣶⣾⣿⡧⠀⠀⠀⠀⠀⣀⣸⣀⡈⠁⠀⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠻⠛⠻⠂⠀⠀⠀⠀⡇⢴⡦⠀⣿⣻⣿⡇⠀⠀⢠⢝⢿⣿⡿⣆⡀⠀⠀⠀⢀⣀⣴⣒⣲⣆⣀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣷
⠀⠀⠀⠀⠀⠘⠂⠊⠀⠀⠀⠀⠀⣥⣤⣤⡄⠛⠛⠛⡁⠀⠀⠇⠀⠑⠀⠛⢩⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣦⢸⡇⢿⣼⡿
⠀⠀⠀⠠⣾⣿⣾⣼⣿⡆⠀⠀⠀⣿⣯⣸⡇⠐⠟⠀⡇⠀⠀⠈⠢⢤⡄⢴⣿⣿⠂⠀⠀⠀⠿⠿⠷⠿⠿⠇⠀⠀⠀⠀⠉⠈⠁⢿⣾⠟
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠻⣿⠿⠟⣛⣃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣀⣤⡶⠟⠛⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣴⠿⠋⠁⠀⠀⠀⣀⣙⣛⣉⣛⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⣴⠟⠋⢀⣀⣤⣴⠶⠿⠛⠛⠛⠋⠛⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⢐⣋⣭⣤⡶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠀⢀⣤⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⡃⣍⣹⣿⣿⣿⠀⠀⠀⠀⣴⣿⣷⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠘⠇⠿⢿⣿⣿⣿⠀⠀⠀⠀⠙⠻⠟⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣶⣦⡀⠀⠀⠀⢸⣿⣿⣿⣷⡆⣶⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠘⢿⡿⠃⠀⠀⠀⠘⣿⣿⣿⣄⣁⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠀⣀⣠⣤⣴⣶⡶⠶⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣤⣤⣤⣶⡶⠾⠛⠛⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡻⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠈⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣴⠶⠿⠿⠿⢿⣤⡀⠀⠀⡀⠀⠀⠀⠀⣉⣉⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⢿⡿⢋⠀⠰⠄⠀⠀⠒⣈⣉⣤⣤⣴⣶⠶⠿⠟⠛⠋⢿⣇
⠀⠀⠀⠀⠀⠀⣈⣤⣴⣶⠿⠛⠋⠁⠀⢀⣉⣉⣥⣤⣶⡶⠾⠛⠛⠿⢿⣭⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⠉⣡⣤⣤⣶⡶⠿⠿⠛⠛⠉⣹⡟⡁⠀⢐⣦⣀⠀⠀⠈⢻⣆⠀⠀⡀⢀⣀⡀⡀⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣩⣥⣤⣤⣤⣤⣤⣬⣭⣬⣤⣤⣭⣭⣬⣥⣤⣤⣥⣭⣤⣤⣥⣭⣭⣥⣥⣭⣭⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⣟⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠛⠉⠉⡉⠉⠙⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠀⠀⢀⡀⠀⠀⠀⣼⠋⠀⠀⣠⠾⡗⣦⠀⠀⠈⢿⡄⠀⠀⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣿⡟⠀⢠⣶⣦⠀⠀⢸⡏⠀⠀⠀⠻⣶⣇⡉⠀⠀⠀⠘⣷⠀⠀⢠⣶⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⣷⠀⠈⠛⠋⠀⠀⢸⣧⠀⠀⠀⣤⡌⡟⢻⡆⠀⠀⢠⡿⠀⠀⠈⠛⠋⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠙⠲⡷⠛⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣀⣀⣀⣀⣀⣀⣀⣹⣷⣦⣄⣀⣁⣀⣤⣾⣟⣡⣄⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠛⣿⣿⣿⣿⡟⠡⣾⣛⠛⢿⣿⣿⣿⣿⢿⣿⣷⣦⣄⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡷⠠⣾⣿⣿⣿⣿⣶⡶⣿⣣⣾⣿⣿⣿⣯⠘⠿⢿⣿⣿⣿⣮⡲⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣿⣴⣷⣿⣿⣿⠿⢿⣿⣛⣻⣻⣿⡿⣿⣿⣿⣦⣴⣼⣿⢏⣿⣿⣿⣌⢦⡀
⠀⠀⠀⠀⢠⣾⣏⢛⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⠿⢿⣿⣧⡱⡄
⠀⠀⠀⢠⣿⣿⣿⠀⠉⠛⢻⣿⡟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⢠⠀⠀⠙⣿⣷⡹⡄
⠀⠀⢀⣿⣿⣿⣿⣦⣶⣶⣾⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡀
⠀⠀⣼⣿⣿⠿⠿⠿⠿⣿⢯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⣾⣿⣿⡎⣇
⠀⠀⣿⣿⣿⣿⢻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠟⢹⣿⠙⢿⣇⢹
⠀⠰⣿⣟⠛⠯⠀⢿⣿⣧⣿⠟⣻⣿⠟⣿⡿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠎⠋⢾⣿⣿⢸
⠀⠀⣿⣿⣶⣦⣤⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⡿⢸
⠀⠀⣿⣿⣿⣿⠿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣛⣿⣿⣿⣿⡇⣼
⠀⠀⢹⣿⣿⣷⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⢁⡇
⠀⠀⠈⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣯⣤⣽⣿⣿⠇⡼
⠀⠀⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣣⣾⣝⡿⣿⣿⣿⣿⣿⠏⡼⠃
⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣯⣶⡟⠛⣿⣿⣻⣿⣿⣿⡿⢋⡼⠁
⠀⠀⠀⠀⠀⠑⣍⢿⣿⣿⣵⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣶⠀⠀⣹⣿⣿⣿⠟⣡⠞
⠀⠀⠀⠀⠀⠀⠈⠳⣽⣻⣿⣿⠿⢿⣿⣟⠟⣿⣿⣿⣿⣿⠇⢾⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⡝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⣩⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠮⣍⣛⡛⠿⠿⠿⠿⠿⠿⠿⠟⢛⣋⣩⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠒⠛⠛⠉⠉⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣀⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣈⣹⣿⣷⣌⢻⣷⡄⠀⠀⠀⠀⠀⢀⣤⣿⣿⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣨⣟⣿⣿⣿⣿⣧⢻⡇⠀⠀⠀⢠⣶⡻⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢀⣾⠟⠋⠉⠻⣿⣷⡀⠀⢠⣾⣿⠏⠉⠛⢿⣦
⠀⠀⠀⠀⠀⣾⠃⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠸⠃⠀⠀⠀⣿⣿⣿⡾⠿⠿⠍⠉⠉⢿⣿⣦⣤⣄⠀⠘⣿⣀⠀⣠⡷⢹⣿⣷⣤⣿⣿⠁⣧⡀⠀⣸⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠙⣿⡁⠀⠀⠀⠀⠀⠀⣹⡋⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠈⠛⠻⠛⣱⣾⣿⣿⣿⣿⣿⣷⡝⠛⠛⠛⠁
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⣀⣈⣁⠀⠀⠀⠀⣠⣴⣿⡇⡀⠀⠀⠀⠀⠀⢀⣠⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⣿⣿⠟⢻⡇
⠀⢀⣴⢶⣾⣿⣿⣿⣿⣿⣿⣄⠸⡏⣹⣿⡇⠀⠀⠀⠙⠛⢻⣿⣧⣄⣀⣘⣿⣶⡻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣿⣿⣿⠟
⠀⢸⣯⣿⣿⣿⣿⢿⣧⢨⣿⣿⣷⣾⡿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⣛⡿⠃
⠀⠀⠙⠛⠋⠀⠙⢷⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣠⠄⠤⡀⢀⣴⣾⣿⣿⣷⣄⠀⢠⠄⠠⡀⠀⠀⠀⠘⣶⣄⣸⣦⣷⣼⣷⣼⣧⣾⣠⣴⡗⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠘⣧⡲⠴⣣⣿⣿⣿⣿⣿⣿⣿⣷⡸⠤⢂⡿⠀⠀⠶⣶⣿⣿⡿⢿⣿⣿⣿⣧⣿⢿⣿⣿⣷⡶⠂⠀⢸⣿⣷⣤⣤⣀⣤⣤⣤⣤⣄⣠⣤⣴⣿⣿
⠀⠀⠉⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⡟⠻⠛⠛⠁⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⠄⠀⠀⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⡿⢿⣿⣿⡿⠿⣿⣿⣿⣯⣥⣀⠀⠀⣴⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠈⢙⣻⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⡋⠁⠀⠸⠿⠃⠘⣿⠛⣿⣿⣿⣿⡿⢻⡿⠀⠙⠿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⡟⠁
⠀⠐⢤⣊⣀⣤⣿⣯⡉⣿⡟⣩⢿⣯⣄⣀⣠⠄⠀⠀⠐⠛⢛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠈⠉⠁⠸⡀⣠⠟⢧⡀⡀⠃⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋
⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⡀
⠀⠀⣾⡇⠘⣦⠀⠀⡀⠃⠘⢀⠀⠀⣴⠁⢸⣷⠀⠀⠀⠀⠀⣀⣤⠶⠟⠻⡏⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⠞⠋⠙⠛⣿⣄
⠀⠀⠛⢧⡾⠋⠀⠀⣃⠀⠀⣘⠂⠀⠙⢷⡸⠛⠀⠀⠀⣠⠞⠉⠀⠀⠀⢠⡇⠀⠀⠀⠈⠛⢦⡀⠀⠀⢠⣾⣯⡉⠀⠀⠀⠀⢿⡏
⠀⠀⠀⢹⣏⠀⠀⠸⣿⣶⣶⣿⠇⠀⠀⣸⡏⠀⠀⠀⠀⢁⠀⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡿⠿⡃⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢿⣦⣠⣾⣿⣿⣿⣿⣷⣄⣴⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣷⣦⣤⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠙⣋⢿⣿⣿⣿⣿⡿⣙⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣷⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠛⠋⣟⠳⣦
⠀⠀⠀⢀⡴⠊⡡⠖⢉⠻⢿⡉⠒⢌⠑⢤⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⣼⣿⡀⠀⠀⠙⠿⠿⠟⠀⠀⠀⡞⠁⡽⠛⣿⠿⣿⡁⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠣⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠃⠀⠘⢿⣤⣖⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣄⡁⠀⣁⣸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠻⣧⡄⠀⠀⠀⠀⢀⣤⡻⠃⠀⠀⠀⠐⢉⠉⠉⠉⠉⠙⠛⠿⣿⣶⣄⡀⢀⣠⡴⠂
⠀⠀⠀⠀⠀⣼⣿⣿⣁⡄⠀⣄⣹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢫⣿⣷⣶⣶⣾⣷⣿⠁⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⢀⡛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⠛⠙⣿⣿⣿⡇⠀⠀⠀⢀⡤⢾⣿⣿⣿⣿⣿⣿⣿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣆
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⠉⠙⡇⠀⠀⢰⣿⡇⣾⣿⠻⣿⣿⡟⣻⣿⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠃⠀⠀⠸⠟⠃⠈⢻⣿⣿⣿⣿⡟⠁⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⢠⠞⠉⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⢦⣀⣀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡼

⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀
⠀⢸⣷⣦⣀⠾⣉⠉⠉⠉⠉⠉⠉⡋⠉⠭⣭⡛⠩⠍⡉⠉⠉⢐⠶⣲⠷⠒⣚⣛⡒⠲⠶⡢⢄
⠀⣿⣿⣿⣿⣿⣦⣅⡒⠀⠤⣀⣀⣀⣁⣒⣬⣭⣧⣤⣼⣀⣠⠺⡦⡵⣶⣤⣘⣛⣃⣠⡤⠚⣈⠉⢉⡐⠢⡀
⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⡞⢶⠾⢶⣾⠊⡔⠉⢀⣤⡀⠈⠢⡈⠄
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢭⣏⣹⣏⣹⡏⢠⠠⠀⠘⢿⡉⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣯⣟⣚⡗⢺⡖⢺⣿⡀⢖⢄⠘⠿⠏⠀⢠⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠯⠽⠭⠽⠭⠑⢄⡑⠂⠤⠄⠊⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢠⠀⠀⠀⠀⠀⢠⠄⠀⢀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢤⡀
⠀⠈⣿⣿⣶⣦⣤⣤⠂⠀⠀⠠⣾⣿⣿⣿⣷⣄⠀⠀⠀⢰⠱⠎⢉⢽⠿⠂⠀⠀⠀⠀⠓⣶⣿⡖⠃
⠀⠀⠈⣿⠋⣹⣹⠁⠀⠀⠀⠀⠈⠟⠏⠉⠛⠋⠀⠀⠀⠀⡼⢀⠿⡀⢠⡀⠀⠀⠀⠀⢀⠀⠉⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣤⣄⠀⠀⡤⠀⠀⠀⠀⢀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⣀⡠⢤
⠀⠀⠋⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠠⢠⣿⣿⠀⠀⠀⠀⣠⢶⣴⣿⣿⣷⠘⠀⠀⠀⣾⣷⣀⠘⠻⣷⡆
⠀⠀⠠⠃⠙⠛⠫⣀⠀⠀⠀⠀⠀⡰⠋⠀⠹⡄⠀⠀⠀⢠⢹⠉⠙⡻⡧⠀⠀⠀⠀⠀⠉⠹⡤⠖⠛

⠀⠀⢠⢶⣶⣿⣦⡀⠀⠀⠀⠰⣾⣽⣄⠀⠀⠀⠀⠀⠀⠰⠆⠀⣀⠀⠐⠶⠀⠀⠀⣰⣄⢀⣶⣶⢴⠂
⠀⠀⠀⢀⣽⢿⡅⠁⠀⠀⠀⢀⡛⣿⣿⣦⣲⠤⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡻⡆
⠀⠀⡴⠏⠀⠀⠙⠢⠀⠀⠀⠸⠼⠫⠉⢿⡿⠂⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠤

⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠒⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⢀⣄⡈⠀⢀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⣠⣴⣾⣿⣧⡀⠻⣿⣶⣦⣤⣀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⣾⣿⣿⡿⣫⣭⠇⣿⣷⣿⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣿⠏⠀⡎⣶⣧⣻⢹⣻⣷⢻⣨⣿⣿⣿⣿⣆⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠀⠀⢠⣿⣿⣿⠟⠁⠀⠙⢏⣉⠛⣿⣿⠿⠟⠋⠉⠉⠉⠙⢿⣿⣧⠀⠀⠀⢢⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⢀⡤⠞⠛⠋⠈⠴⠤⡄⠀⡀⠀⠀⣸⣿⣿⡆⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠀⢸⣿⣿⣿⣿⡀⠀⢠⡏⠂⠀⡆⠀⠐⠂⠓⠀⠀⠻⣦⣶⣿⣿⣿⣿⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠁⠀⢀⠇⠀⠀⢸⣿⣿⣿⣿⠷⠤⣰⣧⣄⡀⠉⠀⠢⡄⠀⠀⠀⠀⢢⠀⠉⠛⣿⣿⠀⠀⠀⢆⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠘⣿⣿⣿⣿⡄⡠⠉⠀⠡⢀⡄⠤⠐⣡⠎⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠨⡄⠀⠀⠹⣿⣿⣷⡆⡄⠀⠀⠐⠉⠀⠀⠈⠀⠀⠀⠀⢱⣿⣿⣿⣿⡿⠀⠀⠀⡬⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠹⣿⡿⣿⠆⠀⢆⡀⡤⠀⠀⠀⠀⠀⡀⠀⠠⣿⣿⣿⡟⠁⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠻⣦⣤⣾⠇⢙⣽⣿⠇⠀⠀⠀⠈⢀⣴⣿⠿⠋⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣾⣿⣶⣦⣴⣶⣾⡿⠿⠛⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠠⣤⢤⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⢉⡁⢰⣶⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠋⣉⡠⠤⠖⠒⠋⠉⠈⢇⠀⠿⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠚⣉⣁⠤⠤⠶⢊⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠘⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠂⣉⣉⡤⠤⠔⢂⠟⠋⠁⢀⣤⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧
⠀⠀⠀⠀⠀⡔⠒⢈⠉⢠⡤⠤⠒⠊⠉⠁⠀⠀⠀⡔⠁⠀⠀⣴⣾⣿⡿⣷⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀
⠀⠀⠀⠀⠀⢱⠀⠘⣢⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⣿⡁⢹⣷⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠘⡆⢀⠥⠔⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠻⣿⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹
⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⢻⣷⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠀⠏⡇
⠀⠀⠀⠀⠀⠀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠰⡇⠀⢧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠿⣷⣶⣿⣿⡿⠋⠀⠀⣠⠋⠀⠀⠀⠀⣀⣠⠤⠄⠓⠀⣉⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠛⠁⢀⣠⣞⠥⠤⠒⠒⢉⣁⠤⠤⠖⠒⠈⠉⠀⣳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡲⠶⠶⠒⠊⣉⣁⠤⠔⠒⢺⠋⠁⠀⠀⠀⠀⠀⢀⠞⢁⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢴⠀⠙⡆⠀⣀⣀⠤⠄⠒⠚⢉⣁⠠⠤⠶⣶⣿⣿⠟⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⢸⡄⠈⡳⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⠇⠀⢉⣉⡁⠤⠔⠒⠋⠉⠓⢤⣀⠀⠀⠀⠈⠉⢀⣀⣴⣋⡠⠤⠤⠒⠒⠂⢋⣉⣉⡡⠤⠤⠰⡖⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠧⢲⠊⠙⡍⠀⠀⠀⠀⠀⣀⣀⣀⠠⠬⠽⠛⠒⠊⢉⣉⣁⡠⠤⠤⢲⠖⠂⠉⠉⠉⠀⠀⠀⠀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡷⠀⠻⠒⠒⠊⣉⣁⣤⠤⠤⢤⠒⠒⠊⠉⠻⠟⠉⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠦⠤⠖⠲⠶⠬⠭⠥⠤⠤⠤⠤⠤⠤⠭⠶⠦⠤⠤⠤⠤⠶⠮⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠨⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⡤⠄⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠦⢤⡤⡤⠀⢀⡾⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⣳⠀⠀⠀⠂
⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⡀⠀⠀⢀⢔⠏⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠴⠋
⠀⠀⠀⠀⠸⠄⠀⠀⣸⠀⠀⡀⣴⠀⠀⣝⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢸⠀⠐
⠀⠀⠀⠢⠤⠤⠤⠴⠉⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⢐⠈⠀⠀⠀⠀⠀⢤⡀⠀⠠⣀⠀⠀⣀⡞
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡁⠀⠀⠈⠙⠛⠃⠀⠀⢠⡶⠂⠀⢹⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠈⠀⠀⠀⣠⠀⢸⡇⠀⠀⠤⠤⠦⠀⠀⠀⠄⠀⠀⠈⠉⠉⠁⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣷
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⣦⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢅⠉
⠀⠀⠀⠀⠐⠰⠤⠄⠀⢠⡴⠧⠀⠀⠁⠀⠀⢀⣤⠖⠛⠀⠀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠤⠀⠐⠤⠖⠒⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠾⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⠠⡀⠀⠀⠉⠀⠉⢉⠉⠁⢀⠀⠀⠀⠀⣐⠀⠒⠀⣠⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠤⠀⠑⡀⠀⠀⠀⠯⠉⠁⠀⡿⠀⠀⠀⠀⠐⠖⠐⠀⢐⡇⠀⠀⠀⠙⠒⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢀⠀⠀⡇⠀⠈⠢⢤⣀⡤⠠⠁⠀⠀⠀⠀⠀⡀⡀⠀⢊⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡊⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⣀⣠⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⢠⠴⣄⠀⣤⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠠
⠀⠀⠀⠸⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡎⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⣥⡤⢤
⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠸⠥⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠁⠈


⠀⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠐⠳⡖⠳⡖⢳⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠦⡄⠀⠀⠀⠀⠀⠀⠚⢶⠚⣶⠛⡆
⠀⣠⠖⠲⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠸⡏⡷⠀⠀⠀⠀⠀⢸⡅⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⡇
⠀⠻⣄⣀⠟⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢁⠀⠀⠀⠀⠀⣉⣥⣤⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠑⠑⠂


⠀⠀⠀⠈⠒⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠀⠀⠀⠀⠀⠀⠀⠴⠒⢦⣀⣠⠖⠲⠄⠀⠀⠀⠀⠀⠀⢠⡀⢠⠂
⠀⠀⠀⢤⡞⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠐⢤⠀⠀⠀⠀⠀⠀⣠⢤⣀⠉⢁⣤⢤⡀⠀⠀⠀⠀⠀⠀⢺⡷⢿⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂

⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠐⠀⠁⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠉⠋⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈

⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⠀⠉⠐
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠃⢀⠀⠀⡂⠁⠀⠈⡀⠅⠀⠀⠀⠀⠀⠛
⠀⠀⠉⢀⠈⠉⡁⠀⢉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠆⠀⠀⠐⠀⠈⠤⠀⠀⠊⠀⠀⠀⠀⠀⡀⡅
⠐⡘⠄⠀⠀⠀⠙⡀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠶⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠻⡁⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠂⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢠⠦⢸⡀⠀⠀⠀⠋
⠀⠘⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⣀⠈⠁
⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠓⣾⠎⠀⠀⠀⠠⠈⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⡄⢠⡆
⡌⠀⡀⠀⠀⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠠
⠀⠀⠈⠀⠀⠈⠀⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⡆⠀⠀⢀⡄⠠⠀⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⣂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠉⠀⠀⢀⠒
⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠀⢄⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⢀⣀⠈⠁⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⡀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⢤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠎⠐⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠄⢈⢤⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⠀⠀⠀⠂⠂⠂
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠠⡆⠀⠀⠀⠈⠈⠉⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡆⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⡀
⠀⠀⠈⡁⠀⢀⠀⠀⠠⠄⠐⠀⣠⠀⡀⠀⠞⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢄
⠐⠀⠁⠢⣤⠋⠀⠀⠀⢠⠸⠈⠉⠀⠩⠄⠀⠐⠐⠚⠀⠀⠒⠀⡀⠀⢀⠘⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀⢀⠀⠀⠑⡄
⠀⠀⢀⢀⡄⡀⠀⠀⠀⢰⡀⠀⠄⢃⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠄⠠⠀⠀⠈
⠰⠀⠃⠀⠀⠀⠄⠠⠂⠀⠁⠀⠀⠀⢃⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠂⠀⠃⠀⣠⠄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⢡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⡀
⠀⠶⢤⣦⠂⠀⠀⠀⡈⠐⠲⠒⠂⢸⠀⠀⠀⠀⠁⠀⡠⠀⢀⡄⡀⢀⠉⠀⠠⠄⠀⠀⠀⠀⠒⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠂⠀⠀⠄⠀⠉⠐⠀⠀⠓⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀
⡠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠐⠀⣠⠀⣀⠀⠀⠀⠀⠩⠕

⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠈⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠅⠀⠀⣠⠂⠀⠀⠠⠎⠀⠈⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠐⠁⠀⠀⠁⠀⡠⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠄⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢄⡤⠀⡀⠈⠀⠀⠀⠀⠐⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠀⠀⡀
⠠⡀⠀⠀⠀⠐⠈⠁⠀⠄⢠⠀⠀⠀⡄⢰⣉⣃⣘⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⡄⣶⣹⣁⣛
⠀⠀⠀⢀⠤⢠⡄⠀⠀⠀⠈⠃⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡃⠀⢠⠤⢠⠄⠀⠀⠀⠈⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠉⠀⠀⠌⠀⠼⠀⢠⡄⠀⠂⠀⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠰⠃⠉⠁⠀⠀⠌⠠⠼⠀⢠⠄⠐⠂⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⡀⠀⠀⠀⠀⠄⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⣀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢢⡀⠀⢠⠄
⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠂⠰⠀⠊⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠂⡀⠄⠀⠀⠀⠀⢀⡐⠒⠢⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠠⢂⠐⠀⠂⠀⠀⠀⠀⠀⢀⠐⠒⠂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠄⢂
⠀⠠⠠⠞⠀⠀⠀⠈⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠉⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠈
⡀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟
⠀⠀⠀⠀⠉⠁⠐⠂⠀⢀⡀⠀⠀⠀⡀⢠⢰⡄⢲⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠁⠔⠀⠀⢀⡀⠀⠀⠀⠀⣠⢰⠄⡦
⠈⢢⠀⠀⡀⠀⡀⠀⠀⠀⠘⠆⠀⠀⠃⠜⠃⠒⠒⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠚⠄⠀⠀⠃⠟⠐⠒⠂
⠒⠊⠀⠠⠉⢩⠁⠠⠔⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠀⠀⢀⡂⠒⠒⠀⠀⠠⠉⢨⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⣠
⠀⠀⠀⠉⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⢂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠁⠀⠀⠰⠐⠈⣄⠃⠀⠘⠁⠀⡀⢀⠀⡄⠀⠀⠀⠀⠁⢁⠀⠀⠈⠁⠀⠀⠔⠀⠀⡌⠁⠀⠈⠀⠄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢿⡿⣿⣿⣶⣶⣦⣤⣤⡄⢠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⣯⣲⣦⠀⠀⠀⠀⢀⠄⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⣧⠀⠀⢠⣿⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⢿⣿⣿⣆⣿⡇⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣽⣿⣿⣿⣿⣿⠷⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣩⣿⣿⣿⣾⣶⡶⢲⣾⡑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⣾⣿⣿⣿⣿⠟⣸⠃⠈⠻⡿⣄⠁⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡀⠋⢠⡄⣤⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣽⣯⠀⠀⣿⣿⡟⡇⣿⠿⠛⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⠀⢿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠛⢹⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠀⢠⣤⣿⢸⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢈⣹⣻⣿⣿⣷⡶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⠠⠀⠀⠀⢀⣿⣿⣼⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣷⣂⣀⡤⠖⣾⣿⣏⢻⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢷
⠀⠀⠀⠀⢶⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣿⠿⢛⣁⣀⣀⣿⣿⣷⡬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠛⠛⣿⣯⣍⣉⣉⣉⡙⠛⠛⠻⠿⡯⠔⠚⠋⠉⠉⣙⡻⣿⣿⣧⢀⡀⢰⣁⠀⠀⠀⡆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⣿⣿⣻⣻⣶⣶⣦⣤⣄⣀⡀⠐⠉⠁⣀⣿⣿⣿⣧⡬⠙⠿⠿⡿⠀⣂⣠⡤⠞⠋⠁
⠀⠀⠀⠀⢸⣶⣦⣤⣀⣀⡀⠊⠉⠉⠛⠛⠻⠿⣿⣯⡤⠴⣚⣉⣽⡿⠿⣿⣿⣿⣿⣿⣻⣟⠁⡿⠟
⠀⠀⠀⠀⠙⠿⠷⠾⣯⣿⣿⣿⣶⣶⣦⣤⣀⣤⠼⠗⠊⢉⣉⡠⠼⠁⠀⠀⣌⠁⠀⠀⢠⡿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣧⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⡼⢽⡧⠀⠼⣏⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣻⡗⢀⡚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠷⢦⣯⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⡤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣒⣢⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠄⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡴⠖⠒⠒⠒⠓⠒⠒⠒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣁⠤⠔⠂⠀⠀⠉⠉⠉⠉⠀⠀⠐⠢⠄⣈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⡠⠐⠉⠀⠀⢀⡴⢤⡀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠁⠂⢄⠈⠲⣄
⠀⠀⠀⠀⠀⣠⠞⢁⠔⠁⠀⠀⠀⠀⠀⠈⢦⣸⠇⠀⠀⠀⠀⠚⢋⡟⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⣄
⠀⠀⠀⢀⡜⠁⠔⠁⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢦⠀⠈⠂⠈⠳⡀
⠀⠀⢀⡞⢠⠊⠀⠀⠀⠛⠝⠙⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠔⠊⠀⠀⠀⠱⡄⠳⡄
⠀⢀⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠹⡀
⠀⡼⠀⠄⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢢⡀⠰⠀⢳
⢠⡇⠘⠀⠀⠏⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠁⠀⠄⢂⡀⠀⠀⠀⠀⠀⠀⠀⢸⡻⠹⠁⠀⠇⠘
⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠋⠀⠀⠀⠀⠁
⢸⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⢺⣿⣷⣶⣶⣄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘
⢸⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠻⣿⣿⣿⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡰⢀⡀⡀
⠘⡇⠰⠀⠀⢲⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠉⠉⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⢰⠃⠀⠆⢰
⠀⢳⠀⢃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡘⠄⡜
⠀⠈⢧⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡰⠁
⠀⠀⠈⢆⠈⢂⠀⠀⢠⡈⠳⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣞⠉⡦⠄⠀⠀⡔⠁⡰⠃
⠀⠀⠀⠈⠣⡀⡑⢄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⡠⠊⢀⡜⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠑⢄⠀⠀⠀⠀⠀⠀⡸⢴⠁⠀⠀⠀⠀⠀⠘⡆⢠⠀⠀⠀⠀⠀⡠⠊⢐⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠈⠒⠄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠒⠁⠉⠀⢀⠠⠖⠁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⣀⠉⠀⠂⠠⠄⠀⠠⠄⠀⠤⠄⠐⠂⠉⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢻⡍⠁⢠⣤⣄⠀⢀⣤⣄⠀⠈⣟⠛⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⢁⣤⠀⠀⠀⣧⠀⠐⣿⠻⣿⣿⢻⡿⠀⢸⠇⠀⣴⣄⠀⠉⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣀⣀⠸⣿⣤⡆⠄⢹⡄⠀⠀⠀⣿⠣⠀⠀⠀⡟⠀⢀⣼⣷⣦⣄⣁⣀⡈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣄⠀⠀⠨⣉⣿⡿⠿⣧⣄⠀⢇⠀⠁⠀⠙⠀⠰⠀⢸⠃⠀⣿⡟⠉⢹⣿⠟⠋⠀⣠⡾⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⡀⢈⠳⣄⠀⠛⡘⣿⠀⠆⢀⣀⣼⣶⡶⠶⠶⠶⠶⢶⣦⣄⣀⠙⢷⡶⢾⠟⠀⢀⠞⠉⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⣰⡿⠃⣀⣻⠋⣤⡤⠈⠳⣄⠀⢁⣤⡶⢟⣫⣥⣶⣶⣾⣿⣿⣶⡶⣦⣭⣙⠷⣦⣄⠀⢀⠔⠁⠀⠂⣈⣻⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣰⡿⠁⣤⣿⡉⣶⠿⠂⠀⠀⢈⣷⠟⣩⣶⣿⣯⣿⣿⡟⣿⣷⣼⣿⡷⣿⣭⣿⣷⣦⡙⢷⣅⠐⠻⣶⡾⠋⣁⣼⣷⡀⠹⣷⡀
⠀⠀⠀⢠⣿⠃⠀⠘⠇⢿⡟⠀⠐⠀⣠⡿⢫⣾⣯⣿⣿⣽⣧⣽⡿⠛⠉⠉⠉⠙⢛⠿⣼⣿⠿⣿⣦⡹⣦⡀⠘⣷⡾⠋⠁⠙⠛⠀⢹⣧
⠀⠀⠀⣾⡿⢤⣤⣁⡀⠘⠇⠀⠀⢰⡿⣱⣏⣙⣿⣿⡿⠋⠉⠉⠑⠞⠋⢳⣄⠀⠀⠉⠪⡻⣶⣿⣿⣷⡘⣷⠀⠀⠷⠆⣀⣠⡤⠶⠞⣿⡆
⠀⠀⢠⣿⠁⠀⠀⠉⠉⢉⠒⠲⢤⣿⢡⣿⢻⣿⣿⡿⠧⣄⣶⠀⢀⢠⠐⠀⢹⠀⠀⠀⠀⠐⢽⣿⣼⣿⣷⢹⣷⠒⠈⠉⠀⠀⣀⡀⠀⢸⣇
⠀⠀⢸⣿⠀⠄⠀⢠⡶⣆⢀⠀⢸⡏⣸⣿⢻⡿⠁⠀⠀⠀⠀⠀⠸⠁⢂⣩⡙⠆⣼⢅⡢⠀⠰⢻⡿⢿⣿⡆⣿⠀⠀⣴⡏⣾⣏⣿⣤⠸⣿
⠀⠀⢸⣿⠀⣤⣶⣾⠷⠿⢶⡄⢸⡇⣿⣿⣿⣿⣤⡥⠄⠀⠀⠀⡑⠀⠈⠁⣹⢀⡈⠉⠀⠀⢀⢸⣿⡿⢿⡇⣿⠀⠀⣿⣇⣬⣉⠉⣿⠀⣿
⠀⠀⢸⣿⠀⣿⠿⠾⠂⠁⠀⠁⢸⣧⢹⣤⣾⣟⣯⠀⠀⠀⠀⠀⠹⡄⠀⠠⡄⣿⡠⠀⠀⠀⠀⣿⣿⣷⣾⢇⣿⠀⠀⠫⣿⣭⡿⢰⠛⢸⣿
⠀⠀⠈⣿⡀⠁⠀⠀⣀⣀⡤⠴⠚⣿⡜⣿⡟⣿⡿⣦⣤⡤⠀⠀⠀⠘⠀⠀⠀⡯⠀⠀⠀⠰⣼⣟⣉⣿⡟⣸⡟⠒⠢⠤⣄⣀⣀⠀⠀⢸⡏
⠀⠀⠀⢻⣷⠶⠛⠋⠉⠄⠀⠀⠀⠘⣷⡜⣿⣿⣷⣿⣿⡀⠈⠀⢀⣀⢎⠁⠀⠁⠀⢀⣠⣾⣿⣛⣿⡿⣱⡟⠀⠀⣠⣤⡀⡈⠉⠛⠻⣿⠃
⠀⠀⠀⠘⣿⡄⢀⣀⣠⣞⣀⣸⣆⠀⠘⢿⣌⢿⣶⣿⣿⣿⣶⣾⣏⣿⣷⣶⣶⣶⠾⣿⣿⠛⣿⣿⢟⣴⠟⢠⠂⡸⣯⣽⣇⡀⠀⠈⣼⡟
⠀⠀⠀⠀⠸⣿⡈⠙⠻⣏⠙⣿⠛⠷⠀⠈⡻⣷⣍⡻⣿⣿⣽⣿⣿⢻⣿⣿⣿⣿⣶⣿⣿⡿⢟⣵⡿⢇⠀⠿⠋⠻⣦⠉⠙⣧⡄⣰⡿
⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⢉⠀⢀⡴⢊⣀⡀⠙⠿⣶⣭⣛⡻⠿⠿⠿⠾⠿⠿⣛⣫⣵⡾⠟⠁⠀⠀⠳⣄⠉⠀⠉⠿⠿⠟⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⢀⣴⠏⠀⠈⢉⡷⠀⠀⠀⠉⢙⠟⠛⠿⠿⠿⠿⠛⢛⠉⣱⣦⠄⠀⠀⢠⡀⠈⠳⣦⡀⠐⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣴⠟⠁⠀⢁⣴⠋⣡⠀⢄⠀⠀⡜⢀⣤⡄⢢⣀⣀⣠⠌⡆⠛⣇⣿⠈⣧⡀⣿⣶⣀⠈⢻⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⢿⣾⣇⣠⠿⠀⢰⠇⠹⢾⣷⢋⣻⣿⣵⠆⢿⡀⠈⠙⢷⣼⠟⠛⠉⣁⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⡀⠙⢻⡄⠀⡿⠀⠀⢺⣧⣀⣨⡿⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣴⣇⣀⠀⠀⠙⠛⠛⠂⠀⢀⣀⣿⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⠀⡠⠀⠀⠀⠄⡠⠄⠒⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠅⠀⠀⢰⢠⣀
⠠⢊⠷⠲⠄⠀⠀⠀⠀⠀⠀⢦⡀⠀⠐⢄⠠⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡦⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠢⡀⠀⠀⠀⠀⠀⠐⢒
⠉⠊⠛⠛⠅⠔⠅⠲⠄⠀⢀⠐⣠⠞⠁⢀⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠄⠄⣀⣤⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠊⠍
⠀⡠⢤⣄⠀⠀⠀⠘⠀⠀⠈⠘⣅⠀⠔⠁⠙⢦⣀⠔⠀⠀⠀⠀⠄⡀⠈⠀⠊⠁⠀⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠈⣜⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠶⠦⢄⠀⠀⠀⠄⣀⡀⡀⠂⠐⠔⠤⠤⠦⠄
⠀⠈⠁⠐⠈⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⢲⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⡠⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢀⡀
⠀⠠⠀⠐⠤⠤⠐⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⠐⠒⠠⠠⢄
⠀⠀⠀⠀⠀⡠⡄⠀⢤⢐⡪⠭⠤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⠀⠃
⠀⠀⠒⠅⠐⠃⠀⠈⠀⠀⠀⠀⠀⠂⠀⠈⠝⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣰⣄⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⠀⠙⣴⠀⠀⣧⠁⠀⠑
⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠒⠒⠒⠚⠂⠀⠀⠀⠁⡀⠀⠉⠀⠀⠀⠘⠆⢀⠠⠇⡆⠀⠈⠢⡄⠔⠀⠀⡀
⠀⠀⠢⠠⠂⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡲⠶⢄⠀⠀⠁⠀⠀⠀⠀⠄⠂⠀⠀⠰⠐⠤⠄⠀⠀⠀⠅⡇⠀⠀⠀⠀⠀⠀⠀⠲
⣳⠄⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡇⠀⠀⠀⠈⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣄⠀⠁⡀⠀⠀⠀⠐⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢩⠔
⠂⠁⠈⢧⣀⠠⠀⠀⠀⠢⡀⠀⠁⠑⠂⠤⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡰⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠐⠢⠀⠠⠀⣄⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢧⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠂⡐⠁⠀⠀⠀⢀⠆⢀⡀⠀⠀⠀⠉⠉⠁⠓⠀⠀⠀⢃⠀⠈⡄
⠀⡀⠀⠀⠅⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠖⣄⡀⠀⠙⠢⠈⠀⡠⠁⠀⠀⠀⠒⠒⠰⠭⠡⠰⢠⣐⣒⠐⠀⠀⠀⠘⡄⠀⢸
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠉⢂⠀⠀⠀⠀⠈⠉⡶⣄⠀⠀⠪⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⡀⠀⠉⠀⠀⠀⠀⠐⠀⠀⢣
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⢊⡔⠁⠀⣄⣄⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⡀⠀⠊⠀⠉⠓⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀
⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⣄⣀⣀⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⣄⣀⣀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠁⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢮⠀⠀⣸⢤⡀⠀⠐⡄⢸⠀⡖⠀⢀⣠⢼⡀⠀⢨⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠉⠀⠀⠈⠓⢄⠀⠀⠀⢀⡔⠋⠀⠀⠉⠉⠁⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡴⢾⠉⡏⠉⡏⠉⠉⢩⠉⣉⣉⡉⣉⠉⢹⠲⡄⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⡇⠀⠀⢸⠀⠀⠒⠒⠂⠀⢸⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⠟⠙⠇⠀⠀⢸⠀⠠⠄⠤⠤⠄⢸⢀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⢸⠀⡀⢀⣀⣀⠀⢸⠀⠀⠶⠶⠶⠆⢸⢐⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣀⣀⡀⢀⠀⢸⠀⠒⠒⠒⠀⠂⢸⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠁⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⢰⡿⠻⣦⢀⣴⠟⣷⡄⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠻⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠿⠿⠷⢶⠄
⠀⠈⠛⠀⢻⣿⡇⠐⠟⠀⠀⠀⠀⠀⠀⠀⢈⣿⡶⢾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠉⣻⡇⢠⡾⠿⣶
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠋⠀⣘⣷⣶⡿
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠟⠛⠛⠻⠷⣦⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁


⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⡶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⢶⡶⣶⡶⣦
⠀⠀⠀⣾⡏⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⢷⡄⠀⠀⠀⠀⠀⠀⣠⣍⣉⡛⠛⣋⣉⣥⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿
⠀⠀⣴⢿⣧⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿⣸⡏⠀⠀⠀⠀⠀⠀⠈⢹⡿⠁⠀⠹⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿
⠀⠀⠿⣶⡿⣾⡇⣠⡤⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠁⣿⣤⣄
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣠⡄
⠀⠀⠀⡀⠈⢉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢿⣾⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣦⡿⣦⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢸⡟
⠀⠀⠈⢻⣶⡟⠁⠘⠗⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡿⠛⣷⡆⠀⠀⠀⠀⠀⠉⢉⣤⣉⣤⣈⣡⣌⠁⠀⠀⠀⠀⠀⠀⠐⠾⢿⡿⢿⡿⠿⠂
⠀⠀⣴⠟⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣼⠟⠿⠛⠁⠀⠀⠀⠀⠀⠶⠾⠛⠿⠋⠻⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠
⠀⠀⠀⠀⡧⠄⢀⠀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠤⢺
⠀⠀⠀⡾⢧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞
⠀⠀⠀⣇⣀⣀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠀⡀⣠⡼⠀⠀⠀⠀⠠⠐⠂⠀⠈⠀⠀⠀⠁
⠀⠀⠀⣇⠀⠉⠉⠉⠉⠉⠈⠀⠈⠉⠉⠈⣉⠔⣺⠷⠖⠒⠒⠶⢤⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠠⣎
⠀⠀⠀⠀⣽⠉⠀⠂⠒⠒⠒⠒⠒⠒⠲⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⡀⠀⠀⣀⣀⣀⣀⢠⡤⠿⡆
⠀⠀⠀⡆⡈⠁⠐⠂⠐⠄⠠⠀⠤⠠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠂⠐⠂⢄
⠀⠀⠀⣇⣀⠀⠀⠁⠈⠉⠉⠁⠈⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠈⡳⠤⠀⠀⢀⢀⡀⠀⡀⠀⡀⢀⠀⠀⠤⢰
⠀⠀⠀⣇⠀⠈⠉⠉⠀⠁⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞
⠀⠀⠀⢸⡛⠉⠀⠐⠐⠦⠂⠤⠂⠲⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢿⣄⣀⡀⢀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣼⠂
⠀⠀⠀⢸⡃⠤⠤⠠⡄⢠⠀⢀⠀⠀⠀⣜⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢷⡀⠈⠉⠉⠉⠉⠈⠁⠀⠁⠈⠉⠁⠀⡸⠃⡄
⠀⠀⠀⠘⠣⠤⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠈⠹⠶⠤⠤⠤⠤⠄⠒⠉⠀⠀⠀⠀⢸⠉⠁⠈⠐⠂⠒⠒⠒⠒⠒⠛⠋⠉⠈⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠠⡀⠀⠀⠀⠀⠁⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡵⠋⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡺⠛⠛⠓⠶⣤⠀⠀⢸⡟⠲⠦⠤⠤⠴⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⠀⠀⠀⠀⣀⣼⡇⠀⣿⣝⠷⠶⠤⠤⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⣉⡙⠛⠛⢋⣹⡿⠃⠀⢻⣍⡙⠛⠛⠛⠋⣿⡟⠀⠀⠀⣀⣤⠴⠚⣋⣥⣙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣥⣍⣉⣛⣫⣽⣿⠀⠀⠀⠀⠈⠙⠛⢛⣛⣫⣥⣤⠶⠚⠋⠉⠀⠀⠉⠁⠀⠉⠓⠌⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣀⣀⣤⠾⠛⢀⣀⣀⣤⡤⠶⠒⠛⠻⣿⣿⣿⣷⣄⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⣿⣿⣷⣄⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠈⠻⣿⣿⣿⣿⣦⡛⠀⠀⠀⢀⣠⡴⢚⣩⡴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡛⢦⡀⠈⠳⣄⡀⢄⡀⠀⠀⠀⠉⠻⠷⣦⣬⠙⢿⣿⣿⣿⣦⡴⢞⣫⡵⣞⣫⠵⢶⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡛⢦⡙⢦⣄⠈⠛⢦⡙⠶⣤⣤⠤⠤⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⢛⣋⡭⠶⣚⣻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢦⡙⢦⡙⠷⣄⠀⠙⠶⠶⠶⣒⣛⣯⠽⣷⣿⡿⢿⣿⣿⣿⠶⣛⣭⠵⠖⠋⢩⡴⣞⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢦⣙⢦⣈⠳⠶⠖⢛⣋⣭⠵⠖⣛⣭⠴⢖⣻⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣜⣃⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⣝⠷⠶⢚⣋⣥⠴⢞⣫⡭⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⢻⣤⣉⠙⠛⢋⣉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⣚⣫⡥⠖⠛⠉⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⣿⠦⣤⣍⣉⣩⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠒⠁⠀⠀⠈⠙⣆⠀⠙⠶⣤⣤⣤⣤⡤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⢤⣤⠤⠶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⡤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⡞⠡⡼⣹⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⣽⢿⡍⣹⣿⣷⣸⣆
⠀⠀⠀⠀⠀⡠⢚⠙⢿⣿⡇⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣇⠉⠈⢿⣪⠟⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠃⣚⡠⣼⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡲⢍⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣔⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠒⠠⠤⠞⢡⣤⠀⠀⠀⠀⠀⠀⢰⡶⠒⡲⣒⣒⡲⡒⠲⣶⠀⠀⠀⠀⠀⢀⣾⠃⢸⣿⡦⠄⠛⠉
⠀⠀⠀⠀⠀⢠⣅⠐⣿⡇⣶⡆⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⠶⡹⣯⢜⡷⡱⠆⢸⠀⠀⠀⠀⠀⠘⠛⠃⠉⠈⡆
⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠸⠷⠤⣱⡯⠭⠷⠥⠴⠿⠀⠀⠀⠀⠀⠀⠀⡔⢪⠖⣩⡒⣴⢢
⠀⠀⠀⠀⠀⠈⠩⠤⠉⠡⠉⠡⠌⠩⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡺⣄⡞⣠⣟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣄⡤⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠽⣋⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣶⣄⠁⣠⠟⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⢶⣿⣦⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠦⡝⢻⣿⣿⠃⠀⠀⠀⠀⣠⡞⠁⡘⠷⡧⣯⠞⠁⠻⣧⡄⠀⠀⠀⠀⣿⣿⣿⣿⡀⣫⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⣄⣁⣠⠞⡅⣿⣦⣴⡿⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠱⠚⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠉⢳⡀⠤⠤⣄⣉⠑⠢⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡰⠓⠦⠤⠤⠤⡄⣧⠀⠀⠀⠈⢙⡆⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠉⠉⢉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣠⠊⡝⠁⢹⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣄⣀⠴⣏⠀⠀⠀⠀⠀⠀⢀⣡⠴⠧⠤⠼⠦⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠘⢇⡀⠀⣀⠞⠓⠦⣄⠀⠀⠀⠙⡞⠉⠉⠉⠉⠉⠑⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⢦⠀⠀⢣⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢳⢄⡀⣠⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡤⡖⢻⡀⠉⠁⣸⠃⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢣⠀⠉⠛⠋⠁⢀⠇⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠣⣀⡴⢦⣠⠞⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠈⠦⣤⡇⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⣅⠀⠀⠀⠀⠀⠀⡧⠤⠤⢸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⠤⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠦⣌⠙⠒⠤⠤⠤⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⠶⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡍⢠⣤⣤⣤⣤⡄⢨⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣀⢤⣒⠮⠑⠓⠈⠉⠠⡤⢤⢤⣈⡀⠉⠁⠚⠋⠽⣒⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⣔⠽⡂⢍⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡗⠃⠀⠀⠁⠀⠀⠀⣈⣒⠯⣲⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡴⡻⠚⠁⠀⣇⠀⢓⡄⠀⠀⣀⠀⠀⠀⡀⠚⠀⠀⠀⣀⠀⠀⠰⣹⠁⡨⠂⠈⠑⢝⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⡫⠛⢀⠀⠀⠀⠁⠊⡁⢄⠀⣀⡨⠤⠄⠐⠒⠛⠂⠠⠤⢅⡈⠀⠠⠀⠸⠴⠀⠀⠀⡠⠛⢝⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⢮⠎⠀⠀⠀⠁⠄⠀⠐⢀⡠⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⡀⠀⠀⠠⠊⠀⠀⠀⠱⡵⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⢳⢃⡔⠤⣀⣄⢀⠀⢑⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡊⠠⡀⠀⡀⢎⠗⢾⡞⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠃⠮⣉⠒⠀⠀⠠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢘⠀⠱⣴⣲⠘⠘⡟⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢏⠃⠀⠀⠀⠁⠰⠒⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠀⠀⠀⠀⠀⠘⡹⡀
⠀⠀⠀⠀⠀⠀⠀⢘⡙⠀⠀⠀⠀⢠⡁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⡄⠀⠀⠀⠀⢋⣃
⠀⠀⠀⠀⠀⠀⠂⣉⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⣩⠐
⠀⠀⠀⠀⠀⠀⠀⣯⠀⠟⣅⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠐⡦⠀⡔⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠱⠆⢀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠒⠉⠉⠙⠂⣿
⠀⠀⠀⠀⠀⠀⡀⣉⡄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⣉⠠
⠀⠀⠀⠀⠀⠀⢀⢩⣡⠀⠄⠀⠀⠘⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠃⠀⠀⠀⠀⣌⡍
⠀⠀⠀⠀⠀⠀⠀⠈⡏⡆⠀⠀⡤⣄⠀⡀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠆⠀⠀⠀⠀⢠⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡄⡠⠛⣉⠀⠀⠝⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠈⠊⣟⢙⡦⡼⢧⣿⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡼⡗⣎⠀⠀⠀⠈⠂⡨⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢅⡀⠁⠀⠈⠉⣳⣠⣿⠃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⢆⠀⠀⠀⠠⠂⠁⠂⠈⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡀⠐⠀⠑⢄⠀⠀⠀⡰⡳⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡕⣤⠊⠀⠀⢠⣀⠀⠀⠊⠇⠈⠑⠒⠂⠠⠤⡤⠄⠐⠒⠊⠁⠀⠀⢨⡄⠀⠀⠀⠀⠑⣤⣪⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣕⢄⡀⠑⠪⢍⡒⠀⠀⠀⠉⠀⠀⠀⡄⢈⠁⠀⠀⠉⠀⠀⠀⠀⡏⠳⠬⢂⡠⣪⠞⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡑⠯⣲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠀⠀⠀⠀⠀⠀⠈⠒⣃⠤⣖⠝⢊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢉⠚⠭⢖⡠⡤⢀⣀⠀⠀⠂⠐⠀⠀⣀⡀⢤⣄⣲⠭⠓⡉⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⡃⠘⠛⠛⠛⠛⠃⣘⠃⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣦⡀
⠀⠀⠀⠀⢀⣠⣤⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⠖⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠹⣶⣴
⠀⠀⠀⣰⠋⡁⠀⣀⣠⢀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⣀⢪⡴⢲⣮⠅⠠⣀⠔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡇
⠀⠀⠀⡙⠻⠶⠠⡇⠐⠪⠀⣽⣇⡀⠀⠀⠀⠀⠀⠀⠈⠓⢏⣠⠂⠉⢻⡒⣾⠘⣾⡘⣇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⢸⣿⣡⠤⠥⡛⠤⣤⢾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⢢⣼⢃⡇⣼⣀⠭⢼⣿⠀⠀⠀⠀⠀⠀⠘⣝⠋⡉⢀⣠⠂
⠀⠀⠀⠉⠁⠀⠀⡠⢞⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠱⡝⠀⣜⠿⡠⣺⠇⠀⠀⠀⠀⠀⠀⠈⠻⠷⠾⠿⡃⢄⠀⠂⠶⠾⣲
⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠣⣴⡍⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠈⢷⣶⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢠⡔⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢛⡿⠿⣛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⢛⠛⠛⠛⠦⢤⣇⢤⠀⠀⠀⠀⠀⠀⠀⠀⢿⡭⢁⡹⠀⠀⠙⡉⢭⡽
⠀⠀⠀⠄⠀⠀⠀⢠⣷⠀⠀⠐⣚⠁⠠⡇⠀⠀⠀⠀⠹⠄⠉⡰⠇⠈⠐⠀⠰⠟⢻⣳⡄⠀⠀⠀⠀⠀⠀⢀⡴⢀⡚⢉⠉⠉⢉⠁⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡶⣖⠶⠃⠀⣤⣸⣿⣟⠀⠀⠀⠀⠀⠀⠈⠳⠻⣿⣎⡸⢆⣱⢾⡛⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢪⣤⣤⡵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠒⠠⠤⡍⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⢀⠀⣠⡘⣧
⠀⠀⠸⣆⣿⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣀⣷⡜⠋⠰⠆⣵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠃⢀⡄⣄⡀⢹⢸⡇
⠀⠀⠀⠹⣟⠯⡀⢀⣠⣿⠄⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠋⠉⠡⠌⡻⣦⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠰⠡⡾⣠⠿⣴⣄⣬⡄
⠀⠀⠀⠀⠀⢀⡞⢁⡰⢉⣸⣿⡛⢮⡛⠳⣄⠀⠀⠀⠀⢸⡆⠒⠂⠘⡄⠀⢁⠀⢀⡀⢀⡀⠛⠃⠀⠀⠀⠀⠀⠀⠐⣽⡿⣌⠠⢬⡽⣿⠅
⠀⠀⠀⠀⠀⠈⠙⠃⠀⢸⠇⠴⡦⢔⡻⠷⡶⡄⠀⠀⠀⠘⠿⣒⣀⣀⡹⠶⣤⡙⠛⠛⣣⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⠌⢢⠀⠈⠁
⠀⠀⠀⠀⢰⡗⣂⠚⠉⣁⡄⠤⠞⠛⠑⡂⠀⠘⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡜⠁⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠠⠋⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠘⠀⠀⠀⠀⠋⠰⠟⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢊⣀⠦⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣟⠻⣠⢄⠟⢹⡆⠠⡀⠀⠀⠀⠀⠀⠀⢸⣷⠇⡸⣧⣨⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣰⢤⡚⡝⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⣤⡾⢻⡅⢨⡿⢷⣤⢶⡁⠀⠀⠀⠀⠀⠀⣾⣿⣄⢀⣠⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡞⠛⢿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠴⣻⣟⠲⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⡉⠉⠇⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢟⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⢉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠜⠛⢿⡺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠷⡀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠴⠧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⠿⢿⣿⠟⣣⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⣵⣶⣶⣶⠞⣢⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣡⣾⣿⠿⣋⣵⣾⣿⠟⣋⡛⠿⠿⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣋⣼⡿⢋⣵⣾⣿⠟⣋⣴⣿⣿⣿⣿⣿⣷⡌⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⣡⣾⣿⣿⣿⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢟⣩⣶⣿⡿⢛⣥⣿⣿⠃⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢠⣾⠟⣫⣴⣿⡿⢟⣡⣶⣿⣿⣿⣿⣄⠙⠛⢉⣉⠙⢿⣿⣿⣿⣿⣿⠿⣋⣴⣿⡿⠟⠉
⠀⠀⠀⢀⣴⡿⢱⣿⣿⣿⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠿⣋⣵⣾⣿⠟⠉
⠀⠀⠀⣾⣿⣿⡘⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⡀⢺⣿⣿⣾⣿⠟⠋
⠀⠀⠀⠻⣿⣿⣿⣌⢿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⠿⠋
⠀⠀⠀⠀⠈⠙⢿⣿⣦⡹⣿⣷⡜⢿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡜⢿⣿⣮⣥⣤⣭⡛⣩⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠁⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⡠⠒⣶⠀⠘⡄⠀⠀⢀⠄⠊⠢⡀⣠⡶⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠉⢉⢤⠾⠋⠄⡰⠁⠀⠀⢿⣦⡀⠀⢈⠁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⢠⡤⠤⠛⠃⠀⠀⠀⠈⠈⠩⠍⡇⠀⠀⠀⢺⡇⠀⠀⢂⣀⠀⠤⠄⠠⠇⠀⠀⠀⠀⣰⣕⠁⢀⡴⠊⠀⠀⠀⠀⠀⣨⡟⢀⠀⠀⠀⢪⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⡇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢙⣣⠤⠌⠀⠀⠀⠀⠀⠠⢾⡁⠀⢀⠤⣦⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠹⣧⡠⠤⣶⡆⠀⠁⢸⠉⠉⠁⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⡀⠈⠀⠜⠀⠀⠀⠀⠻⣁⡂⠆⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠈⠛⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠈⢣
⠀⠀⠀⠀⠀⢰⡟⠹⢑⡄⣴⣻⠋⠐⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣸⡇⠀⣶⠶⠒⡄⠀⠀⠀⠀⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠑⠒⢋⣴⡷⠁⠰⢀⠜⠀⠀⠀⠀⠀⠀⢀⣄⡤⢤⠴⠶⠒⠚⠛⠛⠛⠓⡄⠀⠸⢇⣀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⢸⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⢎⠞⠀⠀⢠⠊⢀⡀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣼⠟⠀⣠⡐⠑⡄⠀⠀⠀⠀⠀⠈⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡴⡳⠋⠀⠁⡔⠁⠠⡟⠭⠳⡄⠀⠀⠀⠀⠙⠒⠒⠒⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠲⠊⠈⠻⠒⠁⠀⠀⠀⠀⠀⠀⠙⣒⣒⠁
⠀⠀⠀⠀⠀⠀⠻⡁⠀⢤⠎⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁
⠀⠀⠀⢀⣠⣤⠤⢀⠀⠀⠀⠀⠀⠀⡴⡒⠀⠀⢠⣴⡂⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⢆⠀⠀⠀⣾⡏⠁⠂⠤⢀
⠀⠀⢠⢛⠋⠀⣠⡀⠙⡆⠀⠀⠀⢳⡇⠀⡁⠀⠀⠉⢹⡆⢸⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠄⣠⠖⠁⠀⠀⠀⠈⠁⠒⠤⢔⡀⠀⠑⢐⠄
⠀⠀⣇⡎⠀⠌⣸⣿⠀⢸⠀⠀⢀⢾⠋⢐⠁⠀⠀⠀⢅⡄⠸⢄⠀⠀⠀⠀⢠⣾⠟⠁⠀⢠⣋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⡮⠟⢁⡴⠋
⠀⠀⣿⡇⠸⣴⡿⠃⢀⡎⠀⠀⠀⢀⣣⠘⡆⠀⠀⠀⠜⠟⠀⡎⠀⠀⠀⠀⠀⠉⠓⠦⢅⣀⠈⢉⠓⠶⢤⠀⠠⣴⡿⠛⠙⢀⡴⠋
⠀⠀⠈⠳⣄⣀⣀⡤⠊⠀⠀⠀⠀⢸⡟⠰⠇⠀⠀⣤⣤⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣤⠞⠀⠀⠘⢆⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠤⠃⠀⠙⠃⠥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡔⣤⣐⢦⣄⡰⣥⣄⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠠⠤⠄⠐⠊⠀⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣣⠶⣿⡦⠾⣷⠶⣿⣤⡽⠞⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠁⠀⠆⠀⠀⠀⣁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢠⡿⠀⣼⠃⣰⡟⠀⠀⢀⣀⠀⠈⢙⣟⣂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠂⠀⠀⠀⠉⠀⠈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⣼⠇⣼⠇⣰⡟⠀⠀⠀⢟⣿⡇⠀⠀⢳⣍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠀⠀⠆⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⢴⣿⣴⡿⣶⡿⠐⢀⣀⠓⠀⡀⠀⠀⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⠇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣿⣵⣿⣶⣿⣴⣎⡍⠉⠙⢦⠈⠄⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠀⣤⠤⡤⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣽⢿⠿⣿⡇⠻⠿⠻⣿⣸⡇⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠄⢠⣠⣨⡜⠂⠑⠀⠀⠀⠀⠀⠀⢠⣻⣟⡯⣿⣿⣿⠏⠀⢻⣿⣦⣀⣘⣩⠟⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⡄⠈⠀⠇⢀⠐⠀⡄⠀⣀⠀⠀⠀⠒⢿⡿⠿⠿⣿⠃⠀⠀⣈⠉⠃⡄⠄⠀⣸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠊⠀⠀⠀⠀⡇⢠⠈⠀⢠⡆⠀⠀⠘⢉⠍⠉⠈⠱⠴⠅⠉⠉⢈⣭⠍⣭⡍⠉⠈⠉⠉⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠙⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠠⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⢠⢃⠀⠠⠀⡀⠀⠀⠀⠀⢠⣎⢊⣄⠈⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠨⠀⠆⠐⢠⡄⠀⢠⢠⠀⠀⡀⠀⠀⠀⡄⣄⠀⢠⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠰⡄⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⡄⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠂⠡⡂⠀⠀⠀⢘⠀⠀⢂⠀⣰⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⡇⠀⠀⠀⢈⡀⠀⠀⠀⡆⠀⠀⠀⠤⠀⠀⠤⠀⠄⠀⠀⠀⠠⠠⠀⠤⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠁⠡⠀⠀⠀⠁⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠒⠒⠂⠒⠀⠂⠒⠐⠂⠐⠒⠒⠒⠀⠓⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠁⣉⢀⡉⠀⠈⡀⢈⠈⠉⢈⠀⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⠀⠀⠀⠀⢀⣆⣀⡀⠔⢠⣀⠀⠀⣀⠀⡀⠀⢀⡀⢀⢀⠀⣀⠀⡇⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠔⠀⠀⠀⠀⠘⠂⠀⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠


⣾⣿⣿⣶⣶⡷⢿⣾⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⢷⡿⠿⡿⢶⣶⣿⡿⠶⠶⢶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡶⠿⣿⣿⣿⣶⣶⣦⣤⣤⣄⡀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣆⡱⣿⣯⠳⣯⡉⠉⠀⠀⠀⢀⠍⢉⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣧⠈⢳⡀⠀⠀⣴⡧⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⢹⣧⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣻⣾⣿⣿⣿⣾⣿⣄⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⢛⣿⣿⣿⣏⣏⣉⣉⣤⡖⢐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣅⣀⣴⣿⣿⣿⣿⣿⢏⡏⠀⠻⣿⣆⠑⠝⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⡿⠃⠸⠃⣀⠀⡙⠈⠂⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠃⠀⢀⣀⣿⣼⣧⣀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⢻⣿⣿⣷⡄⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣿⣿⣟⢀⠀⢿⣿⣿⣽⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣿⣿⣿⣟⡎⠀⠈⢿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⣿⣿⣿⣯⡀⠀⠈⠀⣿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⢠⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠐⢷⣿⡇⣿⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠠⠽⣿⣿⣽⣿⣿⡃⠛⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⡠⣼⣿⣷⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢀⡀⠙⢛⣿⣿⣷⣿⣶⣿⣿⣷⣾⣿⣿⣿⣤⡴⠶⠚⢹⣿⣷⠈⣿⡟⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⣟⣿⣿⣿⣿⣿⣶⣽⠿⢛⣉⣠⣤⣤⣼⣿⣿⣗⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠉⠉⢿⣿⣯⣭⣭⣩⣉⣉⡉⠉⠛⠻⠧⠂⠉⠉⠀⠀⣉⠙⢻⡿⣿⡄⢀⠱⣦⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⠟
⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⢿⣯⣿⣿⣿⣶⣶⣤⣤⣤⡤⠚⠉⢀⣀⣺⣿⣿⣿⣴⢞⣓⠻⢿⡇⠐⣀⣶⠶⠛⠉
⠀⠀⠀⠀⢘⣷⣶⣤⣄⣠⣀⡒⠈⠀⠉⠛⠛⠻⠿⣿⣯⡤⠖⣛⣉⣽⣿⠻⣿⣿⣿⣿⣯⣿⣿⣏⢩⠿⠋
⠀⠀⠀⠀⠘⠻⠷⠶⣮⣿⣿⣿⣷⣶⣶⣤⣤⣀⣤⠼⠗⠛⠉⣉⡠⠤⠃⠀⠀⢀⡀⠀⠀⠀⣸⠧⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣇⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⢸⠯⣿⡅⠠⠾⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⣿⠂⢐⠾⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣽⣥⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⡄⣄⠀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠥⠤⠌⠁
⣦⣶⣤⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠈⠉⠀⠰⠀⢀⠂⠀⢶⡔⠡⠐⡄⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠁⣀⠐⣄⠈⠲⣦⠀⠀⠆⠀⠀⠀⢀⠈⠀⡐⠀⠈⠂⠀⠀⠄⢮⣱
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠘⠂⠀⠈⠁⢀⣀⠀⠀⠄⠡⠀⠀⠀⠁⠀⠐⠀⠀⢀⠈⠱⡃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⠑⢐⣀⣀⠠⠀⢠⠁⠁⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠱⡄⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⣀⣁⣤⣼⡶⠂⠀⠀⠀⠈⢐⡄⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠉⠘⠿⠋⠊⣀⠀⠘⠀⣄⠀⠁⠀⠀⡀⠀⠀⠀⢠⠐⠀⠤⠀⠀⠀⠀⢐⠀⠀⢀
⠀⠀⠀⠀⢐⠀⠀⠀⡄⠀⠀⠀⠀⠒⠃⠉⠀⠀⠀⠁⠐⠡⠀⠀⠀⠀⠂⠀⠈⠘⡤⢔⡊⠁⠘⠠⠀⠀⠀⠂⠀⠀⠈⠠⡀⠘
⠠⠀⠌⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠁⢈⣦⠞⠡⠀⠉⢦⡀⠀⠈⠁⠀⠀⠠⠑⠂
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢈⣠⠄⠀⠀⠀⢠⠈⣂⠀⠀⠀⠀⠀⠀⠀⣴⡟⠣⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠒⠂⣤⣀⣀⣀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠂⠀⠀⠁⠀⢀⣴⣾⡏⠁⠀⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⢀⠀⡄⠀⠤⢀⠠
⠀⠀⠀⠀⠈⠙⠛⣿⣿⡆⠀⠀⠀⠀⠐⠠⠄⠂⠀⠐⠒⠠⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣰⣶⠶⣶⣶⣦⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠉⠛⠓

⠀⣴⠀⠀⠀⠀⠀⠀⣀⡄⢀⡢⢀⣠⠀⣰⠀⠀⠀⠀⠠⣤⠀⣐⣶⠖
⠀⣶⠀⠀⠀⠀⢀⡈⠁⠈⠁⠀⠁⠀⠉⠀⠉⢀⠀⠀⠠⣦⠀⠘⠁
⠀⣶⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣁⠚⠀⠠⣦
⠀⠶⠀⠀⠀⠐⡹⠁⠀⠀⠀⣰⠄⠈⠀⠀⠀⠈⠘⠀⠰⡶
⠀⠶⠀⠀⠀⠀⢲⠀⠀⠀⠐⣧⠄⠺⠂⠀⠀⠉⠔⠀⠐⠶⠀⠀⠇⢀⡀
⠀⠀⣀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠠⠄⠂⠀⢠⣆⠀⡆
⠀⠁⠀⠀⠊⠀⠉⠈⡁⠆⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⢸⡏⠀⡅
⠀⠀⠀⠀⠀⠚⠀⠀⢀⡐⠁⠀⠀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠐⠇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡀⠀⠒⠂⢀⣀⠐⠂⠀⢀⣀⠂⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⡃⠀⠀⣀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⢇⠀⠀⠀⠀⠙⢬⡴⠀⢛⢟⠀⠀⠀⠀⠁⢂⣀⠈⠐⠀⠀⠁⡂⠀⠈⠐⠀⠀⠁⠂⠀⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣿⠆⠀⠀⠀⠀⢤⠈⠀⢴⣶⠄⠀⠐⡀⠀⠛⠶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠲⠀⠀⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀
⢀⡆⠀⠀⠀⠀⠀⠀⠙
⢀⡉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠙⢿⣦⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣠⣀⣀⣠⣤⣀⣨⣿⡿⠛⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢠⡞⠁⠈⠉⣡⣴⡿⠛⠁⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢀⡴⠋⠀⣀⣴⡾⠟⠁⣠⠴⠛⢦⣤⡤⣄⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠏⢀⣤⡾⠟⠉⣀⡴⠛⠁⠀⠀⠀⠀⠀⠈⢷⡀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣀⣤⣾⠟⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣤⣾⠟⠋⢀⠀⠰⣆⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⠟⣡⣶⠿⠋⢁⣤⠞⠉⠀⢠⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⢁⣠⠖⠋⠀⠀⠀⠀⠈⠻⠶⠾⠿⠿⣶⡀⠀⠀⠀⠀⣀⡴⠛⢁⣠⣾⠟⠋
⠀⠀⠀⣠⣿⢿⡟⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣿⠇⠀⢀⡴⠞⢁⣠⣶⠿⠋⠁
⠀⠀⢰⣿⠁⠘⢿⣆⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⡄⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠻⣷⣄⡈⢻⣧⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠈⠙⢿⣦⡹⣷⣄⠈⢧⡀⠀⠀⠀⠀⢀⣠⠖⠋⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⠀⠛⠉⠉⠳⠶⠋⢁⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡀⠀⠀⢀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡷⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠄
⠀⠀⠀⠀⠀⠀⠀⡄⢤⡐⣮⢱⣆⡲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣘⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠰⡠⠀⠀⠈⠱⢾⠿⠉⠯⡉⠁⠀⠸⡄⠀⠀⠀⠄⠀⠀⠋⠀⢉⡇⠈⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠃⠀⠀⠀⠀⣀⠘⣷⠀⠀⠀⠠⠆⠁⠀⢀⠀⠆⠀⠀⠀⠀⣼⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠄⠟⠁
⠀⠀⠀⠀⠄⠐⠀⢿⡀⢂⠉⠀⠀⠐⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⣠⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡍⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠐⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⠏
⠀⠀⡸⠀⠀⢹⠀⡁⢱⠀⣿⠁⢸⣿⡆⠀⠀⠀⠀⢀⢊⣾⣷⢢⣤⡤⠔⠀⠄⠄⠔⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠈⠀⡠⠋
⠀⠀⢻⡀⠀⠘⠀⠐⠋⠀⠷⠖⠘⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢵⣢⡀⢀⠜⠁
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⣠⠋
⠀⠀⠀⠀⠈⠙⠛⠶⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⢄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠅⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠂⡐⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠠⡀⠀⣖⠀⠹⠆⠀⠀⠀⠀⠀⠁⠀⠀⠈⣏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠁⢠⡖⠆⢱⣀⡉⣡⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣶⣦
⠀⠀⠀⠀⠀⠈⠣⣌⠁⣀⠞⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⣰⡯⠥⠤⠤⠰⠆⠤⠤⠬⢽⣔⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣩⡄⠂⠉⠀⠀⢀⡀⠀⢸⡇⠀⠀⢀⣀⠀⠉⠐⢠⣍⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠖⠊⠀⠹⡄⠀⠀⠊⢸⣿⠀⠠⠀⠀⠒⠿⡧⠀⠀⢠⠏⠀⠑⠦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢫⠜⠁⢠⠀⠀⣠⠈⠄⠀⠠⠋⠹⠀⢠⡄⠀⡠⣴⠀⠀⠠⢁⣤⡀⠀⠀⠈⢢⡙⢄
⠀⠀⠀⠀⠀⠀⡜⣠⠊⠀⠀⠀⢰⡦⠀⠀⠀⢦⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⡴⠀⠌⣏⣷⡦⠀⠀⠀⠑⣄⢣
⠀⠀⠀⠀⠀⡼⡠⠉⠓⠦⡀⠀⠀⠃⠀⠀⠀⣈⢶⠂⠩⠀⠀⠀⣀⡉⠐⠾⣁⠀⠀⠋⠙⠣⠄⢀⠴⠚⠉⠄⢡
⠀⠀⠀⠀⡰⢵⠃⠀⠀⢀⠀⠁⠠⣄⡀⢠⠊⣀⠀⠣⡈⠁⠠⠄⢈⢀⠜⢀⠀⠑⡄⢀⣠⠄⠈⠀⠀⠀⠀⠘⣆⢃
⠀⠀⠀⠀⣏⡌⠀⣰⣤⣾⣷⠀⠀⠀⠹⠓⠤⡀⠠⠂⢱⣦⣾⠷⠤⣮⠐⢄⢀⠄⠚⠇⠀⠀⢺⣥⣦⡵⠀⠀⢹⣸
⠀⠀⠀⢸⠘⡆⠀⠀⠉⠙⠿⠀⠀⠀⠃⠂⠀⠈⠑⣿⣿⣿⡏⠠⠄⠈⢳⠎⠅⠰⠒⠘⠀⠀⠀⠀⠁⠀⠀⠀⢰⠁⡇
⠀⠀⠀⢸⠰⠆⠶⠶⠀⠂⠀⠶⠶⢸⠆⠀⠀⠆⠾⣿⣿⣶⡟⠀⠀⠆⢸⡷⠰⠀⠀⠠⡇⠶⠶⠀⠀⠀⠶⠶⠰⠆⡇
⠀⠀⠀⢸⡀⡇⠀⠐⣿⣤⠀⠀⠀⠀⡄⠀⠀⢐⡰⠿⣿⣿⣧⠀⠂⢀⣼⢄⡂⠀⠀⢠⠀⠀⢜⡓⢰⣷⠀⠀⠸⠀⡇
⠀⠀⠀⠀⣷⢇⠀⠠⢼⡿⣷⡗⠀⠀⢰⡤⠒⠁⠐⢄⡻⠛⢿⡗⠺⢇⠠⠂⠈⠒⢠⡆⠀⠀⠀⠛⡾⣇⠀⠀⡸⣿
⠀⠀⠀⠀⢸⣌⡄⠈⠉⠀⠉⡁⠐⠊⠁⠘⢄⠀⠀⡔⠁⠁⠐⠂⠀⠈⢢⠐⠀⡤⠃⠈⠑⠦⣤⡀⠀⠀⠀⢠⠷⡇
⠀⠀⠀⠀⠀⢋⠑⣀⡤⠖⠁⠀⠰⣾⣆⠀⠀⢉⠾⠄⣀⠀⠀⠀⠈⣁⠠⢷⡀⠀⠐⣶⣀⣀⠈⠙⠳⢦⣠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⢣⠙⢄⠀⠀⠀⣠⠿⡄⠀⠀⠞⠀⠀⠀⠀⢩⡍⠀⠀⠀⠀⠻⠀⠈⢻⠿⡿⠀⠀⠀⡠⠋⡝
⠀⠀⠀⠀⠀⠀⠀⠑⣮⠣⡀⠀⠁⠀⠈⢀⠂⣰⡖⢹⣤⣀⠘⠃⣀⣴⣷⣦⡀⠐⡀⠈⠀⠁⠀⢀⢜⣥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢎⡢⢄⠀⣰⠃⠀⠛⠿⣆⣽⠟⠀⠀⠉⢻⠛⠻⠏⠀⠘⣆⠀⡠⠖⡱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣙⠃⠄⣀⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠠⠘⣋⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠴⢾⣱⡖⠒⠒⠰⠆⠒⠂⢒⣨⠥⠆⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⡟⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⢻⣿⡟⠛⠛⠛⢻⣿⡟⠛⠛⠛⠛⢛⣿⡟⠛⠛⠛⠛⣿⡟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣾⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣾⣿⡇⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣾⣿⡇⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⣦⢀⣀⣀⢀⡀⣴⠀⠀⠀⠀⢰⢩⣭⣭⣭⣍⢳⠀⠀⠀⠀⣰⠲⠲⠲⢶⡄⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣼⠭⡭⡭⡝⡆
⠀⠀⣿⣩⣭⣭⣉⣉⣿⠀⠀⠀⠀⢸⢨⢩⠭⢍⣅⢸⠀⠀⠀⠀⣿⠀⣒⣒⢸⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠉⠭⠇⡇
⠀⠀⣿⢬⡧⠭⢤⡦⣿⠀⠀⠀⠀⢸⢘⣒⣒⣒⣷⢸⠀⠀⠀⠀⣿⠠⠤⠤⢸⡇⠿⠀⠀⠀⠀⢠⣋⣋⠏⠋⣉⣱⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⡇
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠂⠀⠂⠂⠐⠋⠀⠀⠀⠀⠙⠒⠒⠒⠚⠁⠋⠀⠀⠀⠀⠘⠛⠛⠒⠒⠛⠛⠃⠀⠀⠀⠀⠘⠒⠒⠒⠒⠃

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢀⡞⠉⠉⠉⠳⡄⠀⠀⠀⠀⢀⡞⠋⢩⠉⠳⡄⠀⠀⠀⠀⢀⡴⢋⡉⣉⠳⡄⠀⠀⠀⠀⠀⡴⠋⢩⠍⠻⣆⠀⠀⠀⠀⠀⡴⢋⣉⣉⡙⣆
⠀⠀⢸⡀⠒⠒⠒⢀⡇⠀⠀⠀⠀⢸⡅⠒⢿⠒⠀⡟⠀⠀⠀⠀⠸⡇⢠⠿⢧⠀⡿⠀⠀⠀⠀⠸⡇⠐⢒⡒⠂⣿⠀⠀⠀⠀⠀⣇⠨⡭⣭⠅⣸
⠀⠀⠀⠳⠦⣤⡴⠞⠁⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠙⠦⣬⡤⠞⠁⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠃


⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤
⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⡶⣎⠀⠀⠀⠀⠀⠀⢠⡟⢛⣻⣟⠛⢻
⠀⠀⢸⣷⣘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⡘⠁⠺⣆⠀⠀⠀⠀⠀⢸⡇⠘⢧⡼⠃⢸
⠀⠀⠘⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⡀⣀⢀
⠀⠀⢠⢚⠄⢸⠜⠓⡄⠀⠀⠀⠀⠀⣆⣠⠀⣆⢀⡄⠀⠀⠀⠀⠀⢀⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢊⡽⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒
⠀⠀⠸⠈⢢⢸⡰⠁⢇⠀⠀⠀⠀⢀⡜⢳⡀⠘⡾⠁⠀⠀⠀⠀⠀⠈⣿⠁⡀⣀⠀⠀⠀⠀⠀⠀⠙⣧⡟⠁⠛⠂⠀⠀⠀⠀⠀⠛⣦⡼
⠀⠀⠘⢦⡃⢘⢠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⢇⠀⠀⠀⠀⠀⠀⣴⠋⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⢐⣒⣓⣲⠇⠀⠀⠀⠀⡄⠒⠂⣀⣀⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⣇⠈⠉⠉⠉⣉⣠⢤⠤⠀⠀⠀⠳⣄⠀⢈⣭⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣛⣧⣀⠀⡉⡉⣉⣽⡗⠒⠐⠒⠚⢊⣿⠀⢨⢤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⢨⣩⣿⣈⠉⡉⣋⣉⢥⣯⠁⠀⢙⣙⣩⡟⠀⠤⠾⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⣰⣧⠀⠉⠋⠀⢂⣹⣿⠀⠉⠉⣋⣹⣓⠂⠲⠶⢾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⢠⣤⣼⣤⣨⣽⣷⣀⠀⣉⣉⢉⣱⣿⡀⠀⣉⣉⣿⢟⠂⠒⢚⢻⡶⠒⠶⢼⠂
⠀⠀⠀⠀⠀⢠⣤⣐⣊⢿⠉⢔⠦⠤⠆⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⢉⠭⠷⣄⣀⣭⣤⣿⢛⠀⠒⠚⢩⡟⠐⣟⣿⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠈⠉⠙⢛⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣛⣉⠁⠀⠠⠄⠀⢀⣡⣶⠭⠿⡶⠲⠻⠿⢿⢚⣯⣿⣼⣖⣀⣶⣦⣶
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⢹⣟⡿⢶⣤⣤⣹⠦⠴⣊⣻⣥⠴⣷⡖⣒⡖⠒⢒⣶⣿⣉⣿⠿⢿⣧⣨⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠈⠿⠯⠽⢿⣿⣷⠐⠀⠀⠀⠀⠀⠀⢸⠒⠄⠀⠀⠁⠀⠉⡷⠚⠝⠚⠝⠛⠛⣻⡟⠛⠛⠯⣝⠛⠀⠤⠤⣽⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⡀⠀⢸⣦⣍⣀⠉⠀⠀⠀⡇⠀⢀⠁⢀⣀⡤⢼⣷⣂⣀⣀⣉⠲⠶⠶⠞⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠛⠛⠿⠻⠶⣦⣤⣷⣶⣶⣾⣿⣞⣛⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡁⠀⠀⠀⠀⠀⠀⢀⣴⣴⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⢦⣤⠀⢰⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⣿⣷⣜⣧⣾⣵⠀⢠⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣤⣶⣾⣿⣿⢿⠟⠛⠷⣤⣿⣶⣦⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢉⣾⢻⢏⡇⠞⠈⡠⡀⠀⠆⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠸⣿⠛⠘⠀⣴⠀⠀⡀⣤⣾⣤⣤⣤⣤⡔
⠀⠀⠀⠀⠀⢀⣤⣲⣖⣂⡖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠈⠀⠀⢿⡷⠖⠋⠉⠅
⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⢠⣶⡀⢀⡀⢰⣿⣀⣤⣤⣤⡾⠁
⠀⠀⢸⣿⡿⢿⣿⣿⣿⡇⡇⠈⣄⣀⡀⠀⠀⠀⠀⣠⣼⠏⠀⠀⢀⣴⣿⣿⢿⠿⠟⡩⣥⠀⠀⠀⠀⠘⡄
⠀⠀⢘⠛⠀⠈⠈⢠⢸⡇⡇⠀⢻⣀⣀⡀⢠⣴⣿⣿⠋⠀⠀⠀⠸⣿⣅⣿⢰⣄⡀⣠⣿⣤⣤⣤⣴⣶⡇
⠀⠀⣼⣀⣧⣧⣼⣾⣿⣇⢳⠀⠸⣿⣛⣿⣭⣽⣿⠇⠀⠀⠀⠀⠀⠙⢿⣿⣼⣟⠙⠉⠉⠉⠉⠉⠉⠉⢱
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⢻⣿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢧⠀⠘⡇⠀⠀⢸⡃⠀⠀⠀⠀⠀⢠⣶⡄⣿⠀⣿⢘⣿⡄⠀⠀⠀⠀⢤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡸⣄⠀⠙⠀⠀⢺⣵⣄⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀⠀⠀⠀⣄⣿⣿⣿⣶⡄⠀⠀⠀⠀⠻⠉⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠆
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣦⣤⣤⣤⣄⡀⣀⣀⠀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣾⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠤⠤⠄⠀⠀⠤⠤⠤⠤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣧⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⡠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⡿⢀⠀⠀⠀⠀⠐⠒⠂⣶⢋⡙⠃⢸⣀⣀⣀⠁⠁⠀⠀⠀⠀⠀⢀⠀⠘⡩⢆⠀⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠴⣾⣔⣡⣀⣠⣀⣠⣠⣀⣾⢧⠏⠠⣼⣿⣟⠀⣠⠀⠀⠀⠀⡀⠄⢊⠠⠐⢀⡠⢞⡧⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐⠠⠀⠀⠀⠉⢰⠋⣝⡍⠙⠉⠘⢋⡛⠛⣯⡝⠽⣻⢿⡿⠿⠞⠙⠀⡀⠐⠈⡠⠀⢀⡤⢚⠭⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡦⣌⢤⡜⢀⠏⠰⠿⠀⢰⡔⠀⣿⠃⠠⠿⣽⢶⣿⣿⠁⠠⠀⠖⠈⠠⠂⣁⠤⢊⠧⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠐⢰⡾⠠⢁⡞⢀⢠⠄⠀⠀⠀⠀⠀⢠⣅⢀⣀⣾⣾⡇⡠⢏⠀⠀⣡⠔⣚⠤⠚⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⡞⠀⠾⠏⠀⣼⡛⢹⠀⠀⠼⣷⡷⣻⣿⣏⡎⠀⠀⢺⡧⠖⠊⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠁⠁⠀⠦⠴⠇⠀⠀⣀⣰⣟⣀⣯⠀⠈⡀⠀⢰⣿⡿⠛⠯⣼⡡⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠒⠒⠀⠴⠄⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠉⠉⠁⠙⠛⠓⠐⠜⠀⠀⠠⠐⠤⠂⣄⣀⣸⠃
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠉⠉⠩⡹⠋⠒⠂⠄
⠀⠀⠀⠈⠙⠒⠢⠦⢤⠤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠈⠙⠁⠂⠒⠒⠒⠖⠴⠠⠠⠤⢤⢤⣤⣤⠞⠨⠆⠁

⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠒⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⢀⠀⢀⠀⠁⠀⠈⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠉⠀⠾⠒⡂⠈⠙⠉⠁⠀⠀⢠⠆⠠⠀⠃
⠀⠂⠈⠀⠚⠀⠉⣀⡀⠐⣦⠀⢀⣠⠀⠦⢰⢰⢄⡄⢀⠀⢀⢃⠀⡀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢀⠈⠀⠂⠀⢰⢛⡇⠀⣾
⠀⠀⢀⠔⠑⣄⠘⣯⣹⠇⣿⠀⠀⡇⠐⠃⠘⠘⠈⠆⠎⢩⠾⢸⢰⠧⠀⠂⠀⠀⠀⡇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⡇
⠀⠀⠎⠀⠀⠸⡆⠈⠉⠀⣿⠀⣤⣄⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠂⡃⠀⠀⠀⡀⠀⠀⠀⣬⠛⣿⠁
⠀⡟⠀⠀⠀⠀⢳⡠⠊⠀⢻⡄⢿⡿⠇⡀⡀⠈⠀⠀⠀⠀⡀⠀⡱⡁⠀⠀⡴⡔⠂⠀⠀⠀⠀⠀⠀⣇⠄⠀⠀⠀⠀⢀⠀⢧⣴⠇
⠀⡇⠀⠀⠀⠀⡜⡇⠀⢀⠘⠃⠀⠠⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⠌⠀⢁⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠃⠀⠩⠄⢀⡀⠀⢠
⠀⣆⠀⠀⠂⠼⠀⠐⠐⠖⠀⢰⠌⠠⡄⠀⢄⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡰⠀⠐⢈⠀⠼⠀⢰⡛⠒⠂⠠⠤⡜
⠀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢀⠡⠄⠀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣶⡶⠇⠀⠀⠄⠀⢒⡐⠀⠀⠈⢃⠤⠀⠢⠈⢁⣁⠒⠠
⠀⠋⠀⠀⠰⡄⠀⠐⠀⠀⠀⡴⠀⠈⢀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠐⠃⠀⠀⠀⢢⠆⠀⠄⠑⠀⠀⠀⠀⠶⠁⠀⠀⠓⠐⠀⠀⢀
⠀⠀⠀⠀⡀⠉⠂⠀⠀⠐⠄⠀⠀⠀⣠⣦⠀⡆⠀⢀⣤⣄⢀⣀⣁⠀⠐⠀⠀⣠⣈⠀⠀⣰⣆⠀⠒⠊⠰⠀⡀⠀⣀⡀⠀⠀⠠⠄
⠀⢀⠰⠀⠀⠀⠀⠰⠄⠀⠀⣀⠀⢠⡏⣿⢸⡇⠀⣸⠃⠘⢺⡇⠉⠃⡟⣷⠀⣿⢹⠀⢰⡏⢿⠀⡤⠄⠀⠊⠀⠀⠚⡁
⢀⡀⠁⠀⠀⠀⠰⠀⠀⠀⣰⠃⠀⣾⣠⣿⢸⡇⠀⣿⠘⣶⢸⠦⡄⠀⣷⢯⡀⣿⣏⠀⣾⠷⢾⡄⠰⠎⠀⢠⠖⠀⠐⣁⠤⠀⠐
⠐⠃⠄⠂⢸⠂⠠⠄⠀⠀⢘⠁⠠⡏⠀⣿⢸⣇⣀⢿⣀⡏⢸⠀⠀⠀⡇⠀⣷⣿⠘⣇⣿⠀⢸⡇⠐⡒⡂⠀⠀⠁⢀⠀⠀⠀⠀⠀⢂
⠀⡀⠄⠀⡀⠀⠀⠀⠀⠀⠧⠆⠀⠁⠀⠁⠀⠀⠀⠀⠉⠀⠈⠛⠛⠉⠓⠞⠁⠛⠀⠋⠉⠀⠀⠀⠀⠄⠀⢠⠀⠀⠈⠀⠂⠀⠀⠀⠉
⠀⠂⠒⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⡠⠐⠂⠀⠀⠀⠀⣴⠛⢶⠊⣳⠈⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢠⠀⢰⠀⠀⠘⠿⣅
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠄⡀⠀⠸⠀⠀⠀⠀⠀⠀⡆⢘⠁⠀⠀⠀⠠⢤⡄
⠀⠀⠠⠀⠀⠐⠋⠣⠀⠀⠨⠀⠀⠀⡐⠁⢀⠀⠀⠁⠀⠈⠩⠁⣆⡼⢧⣠⠖⠀⣄⣈⣡⠤⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠠⣄⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠠⠄⠠⠄⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠂⠈⠘⠁⠀⠈⠀⢁⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠔⢢⠀⠡⠊⠈⠀⣠⠖⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⣤⠶⣢⠦⣀⣠⡼⠀⠀⠀⠀⠀⢀⠈⠅
⠀⠫⡉⠉⠉⠀⢀⠀⠀⠀⠈⠔⠂⠀⠠⠃⠀⠀⠀⠀⠊⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠁⠉⠀⠀⠀⠀⠀⠆⢀⠙⠋
⠀⠀⠜⠀⠀⠀⠀⠱⡐⢋⠔⠂⠑⠄⠈⠀⠀⠀⠜⠀⠆⠀⠀⠀⠀⠲⠃⠀⢀⠔⠃⢀⠀⠤⠞⠁⢬⣧⠖⠀⠀⢹⠀⠀⠸⠀⢨⠉⠃
⠀⠒⠀⠀⠠⠂⠀⠀⠐⡘⠜⠠⠰⡄⢀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣉⡷⠂⠀⠘⠠⠢⢁⣠⠀⠀⠀⠀⡀⠀⠀⠀⠈⠣⠠⠃⠀⠀⠉⠒
⠀⠀⠄⣠⠈⠀⠀⠇⠀⠈⢌⣀⠠⠊⠁⠘⠀⠂⠘⠀⡆⠀⣠⣞⠋⢀⠀⢀⢀⠀⠀⢀⡁⠐⠁⡴⠋⠡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣁⣀⣀⣀⣐⣁⣉⣀⣀⣀⣘⣉⣙⣓⣚⣃⣀⣈⣀⣀⣐⣃⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠙⠒⠦⣀
⠀⠀⠀⡴⠋⢀⠴⠚⠉⢉⣩⠙⠢⡄⠈⢣
⠀⠀⡼⠀⣰⠃⠀⠀⢸⡉⠉⠂⠀⠘⡆⠀⣇
⠀⠀⡇⠀⡇⠀⠀⠀⠀⠱⡄⠀⠀⢀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣚⣋⣉⣉⣉⣛⡒⠲⢤⡀
⠀⠀⢣⠀⠹⣄⠀⢳⠖⠚⠁⠀⣠⠎⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⡞⠭⣴⣀⣠⠖⠛⢳⠾⢙⡆⠘
⠀⠀⠈⢷⣄⡈⠙⠒⠲⠖⠒⠋⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣈⡙⠒⠒⠒⠒⠒⠒⠚⣉⣤⣾
⠀⠀⠀⠀⠙⠿⣷⣶⣶⣶⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⠤⠤⠴⠶⠶⠤⠤⢤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢩⠔⣒⡏⠉⣩⠭⠿⣗⣲⢤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡈⠺⠭⢿⣟⣁⣀⣤⠥⠴⠚⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣀⣀⣀⠉⠙⠿⣿⣿⣿
⠀⢀⣠⠤⠖⠒⣒⣒⡒⠒⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠋⠁⠀⠀⠉⠲⣄⠈⢿⣿
⡔⠁⡔⣊⣩⠉⢉⡽⠛⢯⡭⠖⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⣠⠄⠀⢀⣠⣀⠈⢆⠈⢿
⣷⣄⡙⠒⠮⠭⠭⠤⠤⠤⠖⠚⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠈⠹⣄⣠⠎⠀⣸⠶⢸⠀⢸
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠣⡀⠀⠀⠀⠀⠁⢀⡞⠀⡸
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠉⠉⠛⠋⠉⠉⠉⠀⠘⢿⣷⣄⠉⠒⠤⠤⠤⠔⠋⠀⡴⠃
⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣤⣤⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠄⠂⠒⠲⠀⠠⠤⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠛⠉⢧⡜⢂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢭⡙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡏⠀⠀⠀⠀⠀⠈⠇⠈⣖⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⡔⠁⠃⠀⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⡰⢃⣤⣶⠖⣓⠚⠢⢤⡀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣹⣿⣿⣿⣿⣆⠀⠤⡒⠬⠂⣴⠻⣷⠸⢂⠙⡆⠀⠀⢡⠀⠁⠐⠠⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣡⣾⠿⣩⣽⡿⢟⠉⠂⠁⠀⠀⠀⣼⡶⢿⣧⣿⡶⠷⠔⠃⢴⡇⠀⠀⠀⠀⠀⠐⠨⠂⢀⠀⠀⠀⢀⡴⢣⠦⡝⢆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⣥⣾⡿⠋⠂⠀⠀⠀⠀⠀⠀⠈⢿⠰⣿⠏⠯⠀⡀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠉⠔⢡⠞⠀⠀⠳⡀
⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⢿⢠⠀⠙⠻⢠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⠙⣄
⠀⠀⠀⢠⠃⠀⠉⠛⠿⣿⣿⢏⠈⠀⠀⠀⠀⢀⡠⡶⢛⣉⡛⣏⢸⡇⠈⣇⡠⢧⣈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⠣⠀⠀⠀⠀⢀⡴⡛⠭⠀⢁⠻⢝⣿⣶⢿⣤⠀⡈⢩⢙⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠆⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡟⠠⣄⡀⠀⠀⢀⠢⠁⠀⠀⠀⣴⢟⠛⣉⣈⡙⢶⣷⣾⣻⢟⣿⣿⢷⣶⣶⡾⣻⣿⣿⣿⣃⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⢀⠀⠀⢹
⠀⢸⠁⠤⢬⣏⠈⠁⢠⠁⠀⠀⠀⣠⣿⡿⠋⠉⠉⠙⠻⣿⣵⢣⣿⡓⣬⣿⡿⣫⣾⣿⡟⢍⣷⠷⠤⢀⣀⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠋⠙⡆⡇
⠀⡎⠀⠀⠀⠀⠑⠀⠆⠀⠀⠀⣰⢿⡟⠀⠀⠀⠀⠀⠀⣿⢧⣿⠳⣼⣿⢏⣾⣿⣟⢣⣼⢟⠉⠩⣈⢷⣳⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠹⠉⠀⢸
⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⣾⣧⣽⣿⢯⣿⣿⠿⣬⡿⠇⡃⢢⢶⣽⠟⢉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘
⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⣟⣼⣷⠀⠀⠀⠀⠀⠀⣸⣼⣿⣿⠟⣿⣿⠯⣙⡿⢟⠥⡰⣯⡿⠉⢋⡼⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠈⠁⠁⠀⠀⠀⠀⢸⠀⠀⢠⡾⡇⣿⣿⡇⠉⠓⠀⠀⠀⣿⠏⣿⣿⣼⣿⣿⣓⣾⢻⠱⣸⣻⡿⠖⢰⡏⣬⠼⢝⣳⠦⢠⣠⠀⡀⠀⠀⠀⠀⠀⠐
⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⣿⡅⢸⡟⢸⣇⠀⠀⠀⠀⠀⢸⡎⠹⢎⣯⣻⣗⣸⠇⡇⢆⣷⣿⡠⢐⡏⠡⣖⡈⣴⠃⠀⡝⠀⣼⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀
⠀⢧⠒⠁⠀⠀⠀⠀⠆⠀⠛⢻⣿⡇⢸⣹⠀⠀⠢⡀⠀⠀⣿⠻⣮⡳⢾⣿⣿⣾⣼⣸⡽⠏⠱⠜⠛⠚⢿⠾⡃⠀⢠⠇⣸⣿⡏⠀⠀⠀⠀⢠⠁⠀⠤⢀⣀⡀⢸
⠀⢸⠈⣉⠔⠛⠋⠀⠘⡀⠀⠀⢿⣧⡄⢻⣧⠀⠀⠁⠀⠀⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⠛⠀⣴⣿⣄⡸⠀⡿⢛⠀⠀⠀⠀⠀⠄⢠⣄⣛⡒⠦⠏⡇
⠀⠀⣷⢅⠤⠀⠀⠀⠈⡠⡀⠀⣦⣿⣿⡎⣿⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣤⣤⠶⠿⢿⣿⣿⣤⡞⠷⡀⠀⠀⠀⠀⠈⠂⠀⠈⠢⠽⠋⢹⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⡔⠀⠈⢻⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⢻⣿⡟⠀⠀⢀⠛⠀⠀⢌⠂⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⢻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣁⣤⠴⡚⠵⠋⠍⠠⢀⡀⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠙⡄⠈⠀⠀⠀⠀⠀⠁⢡⠀⠀⠀⠀⠛⠛⠉⠀⠀⣄⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠀⡄⠈⣡⡔⠀⠈⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⡔⠛⢢⠑⢀⠀⠀⠀⠀⠀⠀⠄⡇⢠⠀⡇⣰⢰⢀⠀⡓⢰⠆⢹⠀⡆⡴⠀⣌⠀⠀⠀⠉⡩⠁⣀⡰⠄⣵⣀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣔⠒⠚⢧⣀⠴⠀⠀⠀⠣⠢⢀⠄⠀⠀⠁⠈⢸⠁⠉⠉⠈⠉⠁⠈⠀⠉⠀⠁⠁⠁⠀⠀⠄⠆⠈⠀⠈⠀⠙⢆⠀⢈⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢰⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⡉⠉⠐⠒⠒⠒⠒⠒⠀⠉⠁⠠⡔⠒⠂⠤⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⣸⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⡰⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡒⠂⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢂⣉⡥⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠢⠤⠤⠤⠤⠤⠦⠤⠤⠔⠒⠒⠉⠉
⣶⣶⣶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣿⣿⣶⣾⣷⣶⣷⣿⣶⣶⣶⣾⣿⣷⣿⣾⣶⣾⣶⣶⣶⣶⣶⣶⣷⣾⢷⣶⡿⢷⠶⢾⣷⡶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⢰⣶⣶⣦⠀⢰⣦⣰⣦⠀⠀⣦⠀⠰⣶⣄⣶⡄⠀⢶⣴⠖
⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢁⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⢻⣿⠀⠀⣿⠀⠀⣿⠙⣿⡇⠀⢸⡟⢷
⠀⠀⠘⡰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⣰⠞⠛⠀⢶⡆⠀⠀⡠⠒⠒⠦
⠀⠀⠀⠑⠄⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⡰⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠛⠃⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⡄⠀⢠⠀⠀⠀⡀⢠⠀⠀⡄⠀⢀⠄⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⠈⠁
⠀⠉⠀⠴⠄⠉⡄⠀⢰⠀⠙⠀⠀⠸⠀⠀⡇⠀⢺⠀⠉⠶⠂⢸⠀⠀⡇⠀⠸⡇⠀⢸⠀⠏⠉⠀⡇⠈⠹⠖⠸⡀⠀⠳⠆⠀⠀⠠⠘⠃
⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⡈⠀⢸⠀⠀⡇⠀⢀⠙⢢⡈⠀⢸⠀⠀⡇⠀⡆⠀⠀⢸⠀⠤⠆⠀⡈⠓⣄⠀⠀⠉⠲⡄⠀⠀⢠⡄⠀⡀⣠
⢀⡄⠀⠀⠀⠂⠀⠀⢸⣀⣈⡠⠀⢨⣀⣈⣁⠄⠹⣀⣈⣠⠀⢸⣀⠀⢁⡀⠹⣀⡀⢸⣀⣀⣀⠈⢇⣀⣁⡠⠘⣄⣈⣁⡄⠀⠀⠁⠀⠀⠉
⠀⣷⡶⠄⠀⢀⡀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣱⠀⣿
⠀⡇⠀⠀⠀⠀⠉⠄⠀⠉⠈⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠂⠀⠈⠀⠀⠂⠠⠀⠀⠠⠀⠀⠞⠁⠀⠿
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣅⡠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠈⠀⠀⠈⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠰⠶⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⢁⠄⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠃⠀⢸⠃⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠉⠀⠈⠡⠀⠀⠀⠀⡃⢠⠀⡆⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⢀
⠀⠀⠱⠖⣂⢖⡂⡎⠀⠀⠀⢀⣀⠀⠀⠀⢠⡀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠠⠄⠀⠘⠀⠁⠀⡈⠁⠀⠉⠁⠀⣶⣶⣶⣶⠖⠀⠈⠀⠀⠀⢀
⠀⠀⢒⣚⣒⠳⠞⠃⠀⠀⠀⠘⣟⠀⢀⡀⢸⡇⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡀⢰⠆⠂⠀⠀⢻⣿⠟⠁⠀⢀⠄
⠀⠀⠌⠀⠀⠀⠀⠂⠀⠀⠀⠀⠿⠀⠷⠄⠘⠇⠻⠾⠙⠥⠴⠿⠀⠨⠨⠅⠸⠀⠄⠀⠀⠠⠤⠸⠄⠄⠀⠀⠀⠁⠂
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠑⠄⠀⠀⠀⠀⡔⡨⢭⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⢇⠂⡀⠨⢀⣀⠈⠀⠜⡄⠀⠄⠀⠰⣀⠀⢤⡠⠤⠤⠤⣄⠀⠀⠀⢫⠙⡀
⠀⡠⢂⠊⠈⠀⠂⠖⠚⢀⠎⠌⠀⠐⠬⠉⡞⢁⠔⠁⠀⠀⠀⠀⠀⠱⡄⠀⢀⣆⢱⠤⢤⡀
⠔⣑⡃⠠⢄⠀⠉⠁⠀⠄⣈⣀⡀⡤⠀⠀⣇⠌⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠈⠺⠀⠀⠛⢢
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡤⠤⠤⠤⢤⣴⡋⠀⠀⡞⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⣞⠁⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢒⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡤⠞⠁⣶⠉⠉⠉⠉⠉⠉⠹
⠀⢀⣀⣀⣀⣀⣀⣀⣠⠋⠀⡀⢀⠎⠀⠀⠀⠀⠐⠀⠀⠐⠒⠲⢼⠀⠀⠀⠈⣇⣀⣀⣀⣧⣤⣤⣤⣀⣄⣀⣼
⠀⠀⢀⣀⣀⣀⣀⣀⣘⣆⠀⠘⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⢠⠇⡀⠄⠀⠀⠀⢲⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠈⡏⠀⠀⠀⠀⠀⣸⡀⠀⢀⣀⠴⡁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠙⠳⠤⣤⣤⡤⢴⠚⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⣴⣀⣠⣀⠵⠀⠀⠸⢄⣤⣀⣀⠦⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢸⠄⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢸⠁⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢰⣿⠉⠻⠇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠷⣦⡄⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⣷⣤⣼⠇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢼⠀⢸⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢸⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⡤⠴⠶⠦⠤⢤⣖⠢⣤⣀⡀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣾⣶⣾⣾⣷⡀⠀⠀⠀⠀⠀⣠⠴⠶⡿⠷⠦⣄⡀
⠀⠀⠐⠦⠀⠀⠀⠈⢳⣀⣈⣉⢀⠞⠀⠀⠀⣀⠴⠚⠁⠀⠈⠉⠉⠉⠉⠀⠙⠢⣄⠀⠀⠀⠈⢦⣀⣀⣀⣀⡜⠁⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢿⠿⢿⠿⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠿⢿⡿⠿⠿⢷⡀
⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢀⡤⠶⠧⢤⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⡴⠁⠀⠀⠀⣠⠤⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠦⡄⠀⠀⠀⠈⢢⡀
⠀⠀⢸⠁⠀⠀⠀⠀⢧⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣅⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⣇⢀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⡏
⠀⠀⠘⡄⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠛⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠩⢞⡦⢄⣀⣀⣀⣀⣀⣀⣀⣠⣼⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⡯⣀⡀⠀⠀⠀⠀⢀⣠⡔⣋⣀⣀
⠀⠀⠀⠀⠀⠞⠁⠼⠋⡽⢋⠜⢋⠔⢁⠔⢁⠞⣩⢟⡿⢛⡿⠋⣹⠟⣹⠋⡹⢋⡽⠁⠎⠰⠋⠞⠙⢫⠟⡽⠁⠞⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠈⠀⠀⠁⠀⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠆⠀⠀⠉⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠉⠻⣦⠀⣸⠃⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠘⣧⡿⠀⠀⠀⠀⣠⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠉⠙⠛⠿⣿⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⣀⣠⣾⣿⣏⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠘⠛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢀⣀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠘⠛⠻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⣀⣀⣀⣀⣤⣶⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁


⣿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⢤⡰⠄⠴⠦⠴⠦⠰⢄⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡴⠒⠋⠉⠀⠀⠀⠀⣰⣿⠿⠾⢤⣤⠶⣦⢬⣝⣊⡢⠶⣉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠉⠋⢻⣶⠎⠙⠺⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠕⣁⣴⣄⣀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠘⣯⠀⠀⣀⣀⡶⠀⠀⠀⠀⡾⠏⠀⠀⠀⠀⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⣠⠎⠙⠁⠙⢧⣠⡀⠀⠀⠻⣿⠛⠁⠀⠀⠠⠀⠀⠙⠉⠀⠘⠀⠀⠴⠗⠀⠀⣀⠂⠀⠀⠀⠉⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⣡⣾⡅⠀⡠⣄⠀⠀⠛⣷⣄⠀⠀⢀⣀⣤⣤⣴⣾⣦⣐⣒⣠⠆⢀⣀⠘⠂⠀⠀⠚⠉⢻⡆⠘⠀⠀⠀⠘⢖⡀⢦
⠀⠀⠀⠀⠀⢠⣄⣨⠅⢰⡿⠋⣠⠾⠁⠁⠀⠀⠀⢈⣷⢗⣨⣿⡟⠋⠋⠉⠉⢹⡏⠉⠉⠉⠛⢶⣧⣶⣄⠀⠀⠈⠉⠃⠀⢀⣠⣶⣿⣎⠁⡀
⠀⠀⠀⠀⠀⠛⡭⢂⡜⣻⠀⠀⠉⠋⠀⠀⠂⢀⡴⣫⡴⠋⠁⠻⣧⠀⠐⠀⠀⢸⡇⠀⠀⠀⢠⡟⠁⠙⠻⣿⣦⡀⠀⣠⢶⡶⠋⠁⠈⢸⡇⢸⡅
⠀⠀⠀⠀⠀⡴⠃⠀⠈⠑⠻⢦⣀⠀⠀⠀⠰⢫⡾⠋⠀⠀⠀⠀⠹⠗⣀⣤⡤⠼⠷⠤⣤⣄⡟⠀⠀⢀⠀⢈⣿⣿⢨⡗⠁⢀⣠⣶⣄⠀⢹⣦⠸⢀
⠀⠀⠀⠀⠠⠌⠀⠀⠀⢀⠀⠀⠈⠻⠦⣸⣿⡟⠻⢷⣤⡀⢀⣴⡿⢋⣭⠲⠔⠆⠛⠐⠢⢌⡓⢦⡀⢠⡴⠛⠁⠈⢧⡳⡀⣬⣿⣿⣿⡷⠀⠻⡆⢟⡀
⠀⠀⠀⠀⡼⠁⠀⠖⠀⠙⢄⠀⠀⠀⣰⣽⡞⠀⠀⠀⠈⣱⡿⡡⠾⠑⠀⠀⠀⠀⢀⠀⠀⠈⠙⠣⡙⢄⡀⠀⠂⠀⠈⢧⢓⡀⠈⡽⢮⠀⠀⠀⣷⠀⣠
⠀⠀⠀⠰⣏⠀⠀⠀⢄⠀⠀⣀⠀⢠⣿⡿⠁⠀⠅⠀⢀⡟⣼⠍⠀⠀⠀⢀⣰⣰⣮⠀⠀⠀⠀⠈⠹⢎⢷⣀⣀⣀⣤⣼⣇⠇⠀⠀⠀⠀⢀⣠⣼⡄⢏⢠⡀
⠀⠀⠀⠰⠇⠀⠀⠀⠰⠇⠀⠁⠀⣸⣿⣇⣀⣀⣀⡀⣿⠰⠇⠀⠀⠀⢠⣼⡿⠛⠛⣿⣖⡀⠀⠀⠀⣻⢙⡇⠉⠉⠁⠈⣿⣷⠾⠛⠛⠛⠛⠓⠈⠁⢄⡘⠃
⠀⠀⠀⠘⡁⢀⢀⣀⣀⣀⣀⠀⢠⣌⢹⡟⠛⠉⠉⢠⣷⢘⡁⠀⠀⠀⠐⣻⣇⠀⠀⣸⣿⠍⡁⠀⠀⢰⢰⡇⠠⢀⡘⠀⣿⡿⠀⠀⣀⡀⠀⠀⠀⠀⠞⡀
⠀⠀⠸⠼⡁⠸⠿⠛⠋⠋⠈⠁⠀⢷⢸⡇⠀⠡⠀⠸⣟⡆⢗⡀⠀⠀⠈⠹⣿⣿⡿⡟⠄⠀⠀⠈⢀⡟⣸⢇⣄⡀⠀⢀⣿⣟⢠⣼⠛⠃⠀⠀⠀⠀⢆⡤
⠀⠀⠀⠀⢲⠀⢘⠀⠀⠀⡄⠀⠀⠸⣂⢿⡀⠀⠀⠀⣹⣝⡘⢥⠀⠀⠂⢀⠟⠇⠀⠁⠀⠀⢀⣀⠖⣱⠏⠀⠉⠻⢶⣸⠿⠆⠀⢧⡀⠀⠀⠀⠀⢰⡚
⠀⠀⠀⠀⠻⡄⢰⣇⠀⢘⣋⡄⠐⠀⢫⠜⣷⣠⣴⠟⠋⠘⢿⣄⠙⢤⣀⡀⠀⠀⢀⢀⣐⣤⢖⣫⣚⠞⠁⠔⠀⠀⣠⠏⡲⠀⠀⠈⠙⠂⠀⠀⠀⢘⡄⠂
⠀⠀⠀⠀⠀⢳⠈⢻⡄⠀⠉⠀⠀⠀⠀⢠⣮⣿⢄⠀⠀⠂⠀⠈⠻⢶⡬⣭⣙⣓⣘⣋⣩⡴⠮⠞⠛⢷⡄⠁⠀⣴⢏⡤⠉⠙⠷⣤⣄⠀⠀⠀⢘⡩⠄
⠀⠀⠀⠀⠀⠘⢖⠈⠷⣄⠀⠀⢀⣤⣶⠗⠘⢻⣿⣷⣄⠁⠀⠀⣰⡟⠉⠛⠓⠒⠂⣩⠉⠀⠀⠀⡀⠈⢻⡶⠞⢡⠞⢠⡶⠄⠀⠀⠉⢳⡷⢀⣧⣀
⠀⠀⠀⠀⠀⠀⠈⣖⠀⠻⣶⠶⠛⠉⠀⠀⢀⡈⠩⠟⣿⣗⡦⢼⡟⠀⢠⠄⠉⠀⠀⣿⡆⠀⠀⣁⣤⣞⣿⣿⠈⠁⣴⠤⠁⢀⠒⠀⢀⠞⠀⠭⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢮⡱⣀⠀⠀⠀⠀⢘⣿⣿⣿⠀⠀⠁⠛⢉⡟⠛⠷⠶⣤⣤⣤⣤⣭⡗⣾⣿⡿⣿⠛⠣⡅⠀⠀⠉⠀⠰⠈⢀⣴⢋⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⡀⠀⠀⠈⠛⠙⠋⠀⠀⢀⡾⠁⠈⠙⠐⠂⠶⠴⠆⢴⠄⠘⠋⠉⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⡴⠊⠑⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣄⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡴⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣴⣄⠀⠀⠀⠀⠙⢷⠌⢋⣀⣬⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣂⡀⠀⢀⣾⣃⠀⠀⠈⠁⠀⠈⠁⠀⠀⠘⡃⠀⠀⡴⠛⠻⠀⠀⠀⠀⠀⢀⡖⣘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢊⢦⡨⡙⠃⠶⢦⣤⣄⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⢀⡀⢀⢠⠒⠒⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠘⠈⠧⠐⢆⠺⣍⠩⢉⢭⣍⠥⣄⠶⣤⠂⠚⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠐⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢻⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣷⣌⡻⣆⠀⣀⠠⠄⣀
⠀⠀⢄⠀⠀⡠⠄⢸⣿⣷⣏⢷⣽⣿⣮⡇⠀⠀⠀⠈⣷⠞⠉⠑⠢⣄⠀⢀⡀
⠀⠀⠀⠑⠄⣈⠀⣸⣿⡟⣟⣸⢿⠇⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣼⠋⠁⠉⠑⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣶⡿⠄⠛⠠⠤⠄⣀⠼⠄⣄⡀⠀⠀⡏⠀⠀⠀⠀⣸⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠙⠛⡟⠀⠀⠀⠀⠀⠸⠁⠀⠀⠠⠁⠀⢸⠁⠀⠀⠀⢠⡏⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⠀⠲⡀⠀⠀⠀⠀⠰⠧⣀⣴⢇⡜⠀⡟⠀⠀⠀⢀⡞⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠲⣤⣀⣀⣀⣤⣴⠋⠀⢸⡇⠀⠀⢠⡞⠀⠀⠀⣴⣷⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⣿⡿⡟⠹⡿⢶⢶⣿⣷⣴⢶⣯⣀⣀⣠⣾⣽⣏⢻⣾⣿⡿⠋⣡⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠞⠁⠃⠀⠀⠈⡇⠛⢿⡀⠀⠉⢍⣍⠙⢿⣯⣻⣫⣾⡿⠀⣮⡈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢻⢢⠈⠻⣿⣿⣿⡇⢸⣿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⡄⠀⠀⠀⢡⡀⠙⠹⣿⠀⠘⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣀⡀⠀⢀⣀⣼⣣⠀⠈⠀⠀⣀⠀⣟⠦⣀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠙⠛⠛⠛⠋⠥⢤⣤⣤⣤⡼⠋⠦⠖⠚⠙⠓⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡉⠙⠛⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠋⢉⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣤⣶⣶⣾⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⣠⣾⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⡿⠋⠉⠀⠉⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣄⣀⣉⣉⣉⡉⠀⣼⣿⣿⣿⣿⣿⠀⢰⣿⠀⣷⡀⣨⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣄⠀⠉⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣀⣉⡉⠉⠙⠛⠃⠘⣿⣿⣿⣿⣿⣿⠿⣿⣷⠀⣤⡀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣧⠀⠘⢿⠀⡿⠃⢀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⡉⠉⠛⠛⠛⠛⠛⠃⠀⢻⣿⣿⣿⣿⣷⣤⣀⠀⣠⣤⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣄⠙⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠷⠀⠈⠙⠛⠿⠿⠿⠿⠿⠛⠋⠁

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⢀⣄⢠⡀
⠀⠈⠻⢬⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⢆⣀⠀⠀⠀⠀⣀⠀⢀⡀⠉⠃⠀⠀⠀⠀⠉⠀⠀⠀⢀⠄⠀⠀⣏⣩⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠢⣄⡄⢐⠀⠀⠀⠀⠀⠉⠀⠀⠀⡤⣰⡃⡿⠁⢠⣤⠆⠀⠀⠀⣠⣼⣲⣆⡀⠀⠁⠀⠈
⠀⠀⡠⠒⢰⠄⢨⣤⡾⠛⠃⠞⠃⢄⠀⠀⠀⠀⢀⠠⣀⠀⢽⠟⠁⠀⠀⠀⠀⡀⠔⠚⠉⠈⠉⠻⣷⢀⣦⠀⢰⡐⡄
⠀⢠⣠⠏⠈⠀⠘⠔⠀⠀⠀⢤⣄⡀⠈⠲⡄⠀⠀⠓⠂⣴⠿⢀⠀⠀⠀⡔⠀⢀⣠⣤⣀⠀⠀⠀⠀⠻⢦⠃⠈⠛⠃
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⢾⣿⠛⠀⠀⠈⠀⡀⠀⠈⠁⣨⠟⠁⠀⢈⣀⣾⣽⣋⣉⣁⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠻⢿⣿⠶⡀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠘⢻⣸⡓⠓⣚⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣌⣷⢿⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⣇⠀⠀⠛⠭⠭⠼⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⠟⠀⠀⠀⠠⠃⢀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠈⠛⠲⠇⠀⠀⠀⠙⠢⠄⣀⣀⠤⠄⠀⠀⠤⠐⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛
⠀⠀⠀⣞⠱⠆⠀⠀⠻⣥⠀⠀⠀⡠⠀⠀⡞⠀⠘⠀⠀⠀⠀⠀⡁⠀⠀⢀⡀⠀⠀⢢⡄⠀⠀⣄⢄⣀⣀⡀
⠀⠀⠀⠙⢄⣀⣀⠀⠀⠀⠀⠀⠀⠁⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡇⠀⠀⠀⢿⠀⠀⢿⣆⠌⠿⠂⠋
⠀⠀⠀⠀⠀⠉⢹⠆⠀⠀⠀⠀⠀⡴⠋⠀⡀⠀⠀⠀⣠⡤⣰⡄⡇⠀⠀⠀⡇⠀⠀⠀⠘⠷⣄⣀⠘⠓⠂⠀⢰⣦
⠀⠀⠀⢸⣡⠄⠃⠀⢀⡤⠀⣠⠞⠀⠆⠀⠿⠀⡇⠀⠷⠖⠉⠀⡇⠀⠀⠀⡇⠀⠀⢠⡀⠀⠀⠉⠓⢦⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⣤⠀⠀⠀⡍⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠈⠃⠀⠀⠐⠀⠀⠉⠳⠶⡦
⠀⠀⠀⠀⠀⣤⠞⠁⠐⡆⠀⠀⣿⠀⠀⢠⡁⠀⡇⠀⠻⣙⡀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⡆⠀⠂⠀⠀⢳⡄
⠀⠀⠀⢀⠔⠁⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⡇⠀⠀⠈⠀⠀⡇⠀⠆⢀⡆⠀⡄⢰⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠱
⠀⠀⠀⣉⠠⠤⠧⠤⠶⠧⠴⠷⠛⠒⠖⠾⠷⠖⠇⠀⠀⠀⠀⠀⠛⠛⠉⠋⠙⠛⠛⠛⠛⠒⠛⠒⠓⠂⠀⠄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⣤⠀⠀⠀⠀⠀⠚⠶⢤⡀⠀⠀⣀⠠⡄⠀⠘⣃⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢸⣷⠀⢸⣤⣴⣶⡆⠠⣤⢐⣏⠁⠀⠀⠋⣰⠃⠀⡰⠣⠁⠀⠀⠤⠤⠚⠃
⠀⠀⠀⠀⠀⣄⠳⠊⢁⡐⣛⠒⢕⣫⣾⢿⡏⠀⣼⠏⠉⠿⠀⠀⠀⠙⠉⠀⠀⠈⠉⠀⢀⡜⠁⠀⢀⠀⢦⠀⠀⠀⢀
⠀⢉⣈⣐⣒⡏⠀⠐⣟⣛⡂⠈⣿⠅⠀⠜⢉⣷⠶⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⡄⠰⡏⠁⣸⠂⠀⠀⢠⡀
⠀⠘⢂⣀⠀⣿⣀⣀⡿⠖⢀⠀⠹⡄⠋⣀⠈⠛⠐⠉⠁⠀⣀⣈⠀⠀⠀⡀⠀⠀⡉⠁⠀⠀⠈⠂⠤⠴⠋⠀⣠⡎⠈⠁
⠀⠐⠊⠁⠀⡴⢿⣧⢿⡶⠀⠀⠑⢠⡎⠀⣀⠀⠐⢀⣠⡞⢹⢿⣐⢰⡻⠏⡙⠿⣆⠀⠀⠀⢌⠀⠀⢠⠴⢚⢧⠠⣄⠈
⠀⠀⠀⠲⡄⣀⡢⠥⠀⠀⢀⣚⠫⠓⠛⠉⠀⠀⠠⠄⠈⠫⠛⢲⣬⣿⣏⣈⣧⠴⠀⠀⠝⠓⠀⠀⠀⢐⠒⠀⠾⠀⠉
⠀⠀⠀⠀⠈⠉⠛⠒⠒⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⠶⢧⣿⠖⠖⡂⠢⠀⠀⠀⠀⠀⠀⠈
⣠⣠⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣛⣿⢉⡛⣛⡛⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠖⢋⢝⠛⠓⣲⢦⠒⠻⣤⠀⢹⡮⠖⠣⣹⠖⠚⠦⠠⠖⢊⢌⡿⠐⠲⠾⣕⣭⠀⠩⣕⠸⣀⡿⠀⠀⠠⢮⡁
⠰⡈⡍⠳⢶⠞⢻⠛⣃⡀⠈⡇⢸⡃⠀⠀⠱⢾⠬⣉⡉⣉⣡⣾⠤⠒⠒⣦⠈⢻⠇⣴⣨⠵⠹⡄⠄⡙⠓⣎
⠀⠈⠀⠀⣺⠿⠷⢤⠋⠛⠂⣠⣿⠛⠲⠎⣷⣯⠦⠦⠈⠁⡩⠐⠘⣿⢣⡽⠀⣼⣨⠾⠡⡉⢲⡉⠀⣌⡹⠂
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠀⠀⠁⠒⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠊⠀⠀⠀⠈⠉⠐⠋⠒⠁
⠀⠀⢸⠀⠀⠴⠦⠴⠦⠴⠶⠆⠀⢈⠀⡇⠀⠐⠠⠴⠤⠤⠴⠰⠀⠀⠁⢸⠀⠤⠦⠦⠶⠦⠤⠤⠖⠆⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⠐⠒⠲⠶⠶⠲⠲⠲⠀⢘⠀⡇⠀⠀⠖⠶⠲⠶⠲⠂⠀⠀⠁⢸⠀⠰⠴⠒⠲⠶⠰⠶⠲⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠀⠘⠙⠉⠉⠙⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠂⠐⠒⠒⠒⠒⠀⠀⠀⠀⠘⠀⠂⠀⠂⠒⠒⠒⠂⠀⠐⠀⠀⠃⠀⠒⠐⠒⠒⠒⠂⠀⠀⠂⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠀⠑⡎⢡⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠉⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣨⠃⠂⠀⠀⣀⠀⠀⠀⠠⠟⠅⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢠⠄⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⡴⠃⠠⠔⠁⣠⠂⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⡄⣰⢄⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱⣬⢦
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠋⠠⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠃⠈⠘⠐⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⠔⠁⠀⠱⡄
⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⠀⣴⢂⠂⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⡲⡄⠀⠀⠘⠆⠀⠀⢀⣸⡄
⠀⠀⣰⠁⠀⠀⠀⠀⠰⠅⠠⠖⠿⢳⡦⠤⣀⣀⡀⠤⠲⠉⠈⢋⣰⣮⠉⠈⠹⠂⠄⣀⣀⡠⠤⣶⠻⠟⠦⠀⠈⢀⣤⣾⣿⣿⣿⡄
⠀⢀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⠀⡜⠀⢠⣏⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⡇⣧⣵⢝⣧
⢀⠃⠀⠀⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣴⣾⣿
⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠈⠛⠛⠛⠛⠛
⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠈⠤⠒⠀⠀⠀⢠⢀⣦⣤⣶⣶⣷⣶⣶⣶⣾⣶⣶⣤⠆⠀⠀⠉⣾⡜⠀⠀⠀⣰⣤⣴⣶⣾⣶⣶⣶⣶⣾⣶⣦⡴⡄⡌⠀⠤⢀⣀⢠
⠀⢃⢈⠔⠉⠉⠀⠊⠻⣿⣯⣍⡉⠙⠛⠉⠉⠉⢁⡀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠘⢿⣿⣯⣉⡉⠉⠉⠉⠉⠁⣀⠄⡑⠠⢦⢉⣐⣞⡞
⠀⠈⡗⠒⠀⠀⠀⠐⠀⠀⠉⠛⠛⠛⠟⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⢀⠂⠀⠀⠁⠉⢰⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠙⡄⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠀⡔⠒⠀⠡⠀⠀⠀⠀⠀⠀⣠⢤⣤⣶⣿⣿⣿⣮⣶⣤⡢⡀⠀⠀⠀⠀⠀⡀⠄⣀⡀⢁⣄⡀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠳⣔⠈⢣⠤⠊⠀⠀⠀⠢⡀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⢀⠔⠄⠁⠀⠁⠘⠦⣀⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⠀⠀⠀⠀⠀⠀⠀⠁⠑⠂⠤⢀⡀⠀⠀⠀⠀⢀⡀⠠⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⢈⠇⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠩⠁⠀⠀⠀⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⠀⠼⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠒⣀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠊⠉
⡶⢶⣶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⡶⠶

⠀⠀⠀⠀⢀⣤⢖⣻⣶⣦⡀⠀⠀⠀⠀⠀⠀⠏⠳⣤⣀⣤⠀⠀⠀⠀⠀⣀⣴⡂⣴⠀⠀⢤⡀⠀⠀⣠⢴⠖⠀⡀⠲⣦⣄
⠀⠀⠀⠠⢊⡅⠿⣏⣦⡙⣿⡄⠀⠀⠀⣘⡣⠰⢶⡚⣿⡀⠀⠀⠀⢀⣴⠟⠏⠀⠈⢻⣶⣦⢹⠀⠀⠙⡞⢢⡆⠰⢰⠟⡏
⠀⠀⠰⣀⣠⣴⣾⠟⢻⣷⢙⡇⠀⠀⢰⡿⠀⠘⠭⠄⡟⠁⠀⠀⠀⢸⣿⠦⣄⠀⠀⠈⢛⣾⢺⠁⠀⠀⢄⣸⣇⢸⡄⣧⠁
⠀⠀⠀⠙⣻⡿⠓⠐⢋⡼⠘⠁⠀⠀⢸⡇⢸⠉⠁⢤⡧⠀⠀⠀⠀⠸⣟⢿⣧⣀⠀⢀⣽⡿⠉⠀⠀⠀⢸⠗⢹⡼⠸⠻
⠀⠀⠀⠀⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⠘⠣⠼⠀⠀⠘⠗⠚⠳⠀⠀⠀⠉⠁⠉⠙⠃⠘⠁⠀⠀⠀⠀⠀⠐⠀⠐⠓⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⣄⡠⢼⣧⠤⣀⡄⠀⠀⡀⠒⣿⠕⡄⠀⢀⣀⣀⡀⠀⠀⠀⠀⢰⠤⣤⡤⡿⣧⡤⠄⠀⠀⠀⣰⡷⢸⡇⢾⡆
⠀⠀⠀⠀⠘⠀⢠⡇⠀⠘⠀⠀⠀⢰⡖⣫⡴⠇⠀⠀⠉⢀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠷⣏⠀⠀⠀⠀⠀⠸⣇⣼⡇⣼⢇
⠀⠀⠀⢼⣤⢶⢼⣧⢼⡴⢶⡄⠀⠈⢿⣡⣦⢠⢶⣿⣧⡀⠀⠀⠀⠀⢀⡞⢀⣦⣤⣦⢷⣺⠀⠀⠀⠀⢚⣶⣿⣷⣷⡗
⠀⠀⠀⠈⠉⠉⢸⡷⠈⠉⠉⠀⠀⠀⢀⡿⢹⡆⠀⢹⠀⢹⠀⠀⠀⠀⠈⠁⡜⠹⡇⠀⠚⠀⠀⠀⠀⠀⠉⠋⣿⣿⠙⠍
⠀⠀⠀⠀⠀⠘⠋⠁⠙⠀⠀⠀⠀⠀⠛⠑⠛⠁⠐⠛⠀⠛⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⢠⡄⠀⣤⣤⠀⢠⡶
⠀⠀⠀⠀⠀⠐⣋⣁⠸⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠰⢆⠄⠦⠇⠀⠀⠸⣿⣷⣭⢨⣼⣿⠇
⠀⠀⠀⠀⣴⡶⡈⠁⠀⢰⠤⡀⠀⢀⣤⠴⣮⠛⢉⣩⣴⣾⣧⡀⠀⠀⠰⡆⣠⣀⣀⢠⣴⠇⠀⠀⠀⠀⠈⠙⢹⣬⠙⠁
⠀⠀⠀⢀⡾⠻⣿⡷⢦⣼⠑⠃⠀⠉⠀⠀⠈⠛⣿⠿⣟⢯⠳⠄⠀⠀⢀⡴⣿⠋⣙⢸⡿⠀⠀⠀⠀⠀⠀⠀⠘⡿
⠀⠀⠠⠾⠀⠀⡸⠃⠀⠙⠇⠀⠀⠀⠀⠄⢶⡶⠚⠀⠋⠈⠀⠀⠀⠀⣿⠀⠸⣦⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣀⣀⣀⣘⣆⣀⣀
⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋