Golden hamster Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠚⢷⡄
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠋⠀⠀⠈⢿⡄
⢰⡟⠛⢿⣟⠻⠶⣦⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⡶⠟⠋⣱⡟⠁⠀⠀⠀⠀⠸⣷
⢿⡇⠀⠀⠹⣷⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢨⡿
⠈⢻⣆⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠹⣧⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠦⠀⢀⣾⢷⣤⣀
⠀⠀⠀⠹⣧⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠈⠙⠻⢶⣤⣄⣀
⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⢸⣿⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⢸⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣆
⠀⠀⠀⠀⠀⣿⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⢸⣯⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠻⣾⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⢷⣄⠀⣠⡆⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⣷⡀⠀⠙⢿⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣷⠈⠻⠶⣶⣿⣻⣶⣤⣤⡶⠾⠋⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⢠⡿⢷⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢠⡿⠁⠘⢷⣄⣀⣀⣀⣀⣀⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡿⠁⠀⠀⣠⡿⠋⠉⠛⠋⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠁⠀⠀⠀⠙⠛⢿⣧⣴⣦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠈⠙⣷⡀⠀⢠⡾⣻⣦⣤⡄⢰⣦⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣷⡄⣾⠛⠷⠾⠃⠀⠻⠷⢿⣿⡿⢷⠿⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠊⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⠀⣀⣼⣷⢖⠶⡤⣤⢤⡄⢀⡄⢠⣴⣾⡖⢁⠀⠉⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⣸⡟⠙⠋⠀⠁⠀⠅⠀⠁⠀⠀⠸⡿⠛⣨⢁⣀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡿⣃⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠀⢀⣿⣿⠂⠀⠀⠀⠀⠀⡀⣴⣿⣶⠆⣤⠀⠈⠈⠙⢷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠀⠀⢾⡿⠛⠀⠀⠀⠀⠀⠐⣗⣿⣷⣿⠁⠀⠀⠀⠁⠀⢠⣭⣿⡂
⠀⠀⠀⠀⠀⠀⠀⣤⣟⠧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⢟⠀⠀⢀⠁⠂⠀⢐⣿⣿⢗⣃
⠀⠀⠀⠀⠀⠀⠷⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠍⠀⠈⠛⣓⣀
⠀⠀⠀⠀⠀⠠⡀⠀⠫⠄⠀⠀⠀⠀⠀⢀⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠄
⠀⠀⠀⠀⠀⠚⠁⣀⠀⠶⢆⡀⠀⠀⠀⢶⠀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣒⣷⡦
⠀⠀⠀⠀⠀⣉⠁⠀⠀⠚⣻⣧⣘⠢⣄⣤⠽⣤⣀⣀⣀⡠⠀⣀⣀⣤⡾⠸⠂⠀⠠⠀⠀⣀⠀⢀⣺⣿⡄
⠀⠀⠀⠀⠀⢓⠂⠉⠀⠀⠉⠉⢙⣿⣿⣿⣶⣶⣶⣮⢸⣶⡷⠝⢻⡟⠇⠀⡀⠀⠀⠀⠀⠈⠕⠚⣿⡿
⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⡀⠀⠈⠀⣽⣿⣥⠉⠉⢋⠀⢫⠃⠠⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣹
⠀⠀⠀⠀⠀⠀⠩⢟⣀⠀⠀⠀⠀⠀⢉⡷⣸⣷⠀⠈⠀⠀⠀⢀⣀⡰⡆⠀⠀⠀⡆⠀⢀⠱⣼⡿⢿⡏
⡀⠀⠀⠀⠀⠀⠀⠙⣡⣤⣀⣴⣤⣘⢙⣡⣿⡴⢦⡀⠀⠀⠀⠻⠽⡿⢃⠀⢦⡀⢀⣰⣬⣿⣿⢧⡶
⡀⠢⡀⠀⠀⠀⣀⣀⣈⠩⡾⣿⡿⣿⠟⠻⠿⢷⣆⣈⣧⣴⠀⢀⣮⣴⣿⢧⣠⡁⣾⣿⡟⣿⣿⣿⠧
⠀⠀⠒⠶⠀⠀⠒⢀⣘⣛⣛⣿⣶⡸⣦⢖⡴⣬⠏⠹⠿⠿⠗⠛⣛⣿⢡⣄⣏⣻⠿⠛⠿⠿⠷⠾⠿⠂
⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠂⠀⠀⠀⢀⣀⣀⡤⠤⠴⠷⠞⠂⠉
⠀⠀⠀⠁⠄⠀⠉⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢉⡀⢀⣽⣼⠶⢠⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢾⠃⣾⠃⠰⠀⠁⠐⠒⠈⠛⠃⣶⣾⣶⡶⢒⣿⠉⡉⢲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⡦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣵⡟⢡⡚⢈⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠁⣶⡄⠀⠀⡀⠀⠀⠀⠀⠀⠂⣠⡀⠀⠛⣧⣿⣿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠛⠀⠀⠄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠺⣿⠨⣿⠿⢃⣀⠀⠘⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠀⠈⠁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠟⣀⡹⠋⠁⠀⠀⠤⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⠘⢡⣾⡄⠠⠀⠀⠀⡀⠀⢠⡄⠀⣤⡴⠃⠀⠀⠴⠂⠀⠆⠀⠀⠀⠘⢛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠀⠀⠀⠀⠀⠘⠛⡤⠀⠀⠀⠀⠀⠀⢨⣾⡿⠟⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠀⢉⠱⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠓⠀⠀⢀⠀⠀⠀⢠⢀⠀⠀⠀⠀⡘⠀⠈⠉⠁⠊⠀⠀⠀⠀⠀⠠⣽⡆⠀⠀⠈⠑⠀⠀⠹⠀⠾⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣴⡄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⣀⢎⠁⠀⠀⠀⠀⠀⠀⣀⡀⠘⠚⣢⣄
⠀⠀⠀⠀⠀⠀⠀⣬⡭⢷⣮⣿⣆⣠⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠄⠀⢘⡳⠈⠁⣀⣿⡏⠀⢠⣤⡀⠀⠀⠀⠀⠉⠀⢀⡏⠙⣇
⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠈⠿⢿⣿⡆⠀⠈⢠⡀⠀⣀⠘⠀⠀⠀⢀⣶⣶⣿⣠⣤⣾⣿⡏⠃⠀⠀⠘⣻⠀⠀⠀⠐⠂⠀⢀⡙⠃⡽
⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠠⠽⣿⣶⣦⣤⣿⣾⣅⣀⣀⣀⣤⣿⡿⣿⠟⢻⣿⣿⣿⠀⠀⠀⠈⡂⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣦⢴⣡⠀⠀⠀⠘⡿⢉⣉⣹⣿⣿⡿⠿⣿⣿⠛⠻⠓⠿⠀⣼⡿⠃⠉⠀⡀⠀⢴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠡⣾⣥⠀⠀⠀⠀⢧⢈⣭⣉⣶⠶⠄⠀⠹⠟⢁⡀⢀⠀⠈⠉⠀⠐⠅⠀⠀⠀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡰⠀⣆⠀⠀⠘⣄⠲⠾⣿⡆⢀⣤⠞⠀⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⣴⡴⠈⠙⠣⠾⢻⣾⣷⣀⡀⠀⡄⠀⠀⠀⠠⠄⢠⡀⣦⣆⠈⠃⠀⢓⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢀⣴⣴⣤⣼⣿⠟⢿⣿⡏⠚⠷⠖⠾⠿⠇⠀⠈⢁⠀⠩⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠿⣿⣿⠀⢸⢿⣷⣦⣀⣤⣠⣀⣀⣄⣤⣼⡟⠀⠀⠀⠀⠄⠀⠀⠀⠘⣤⣷⣼⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⡷⡀⠀⠀⠘⠀⠂⠀⠀⠀⠻⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢿⣧⣾⣾⣿⣿⣿⣿⣇⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢪⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠀⣉⣥⡤⣶⡿⠟⠻⠟⠻⠛⣿⣧⣼⣤⢀⡀⠀⡀⠀⠀⢀⡀⣠⣽⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣐⣒⠂⠀⠀⠀⠀⠉⢻⣿⣿⣟⠀⣴⣏⡄⢀⣨⣾⣿⠿⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠙⠟⠿⣿⣿⣿⣿⣿⡿⠿⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⣽⠉⠙⣿⠁
⡨⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢐⢀⡾⠀⢨⡿
⠔⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣎⣤⢠⣤⡆
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡽⠟⠋⠅
⠀⠀⠈⠁⣀⠀⣀⠂⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⢲⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⡏⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣛⡇⠀⠀⢸⣿⣿⣿
⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⠀⢀⣤⣀⡀⢸⣿⣿⣿⣿⣶⣦⠈⣿⣿⣿
⣶⣤⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⣿⣿⣿
⣿⣿⣂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣤⣤⣀⡀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⣿⣿⠋⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿
⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿
⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⡿⠛⠱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠿
⠀⢠⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀

⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠎⠈⣧⣤⣠⡤⠤⠶⠶⠶⡶⠦⠤⢄⣤⠟⠁⠈⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢤⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⠀⠀⠀⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣰⢷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⠀⢸⠇⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢊⡆⠀⠀⠀⠀⠀⢽⣷⣄
⠀⠀⠀⠀⠀⣰⢿⡄⠀⠈⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⡀
⠀⠀⠀⠀⣼⠏⠘⣴⡆⠀⠀⠠⡀⠀⢠⣾⣟⡏⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⢼⠏⠀⠈⡟⠀⠀⠀⠀⠈⠃⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⡟⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⢀⣀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢰⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢳⠀⠀⠀⠀⡸⠀⢸⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠸⣄⡄⠀⠈⢳⣄⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠘⢶⡤⠞⠀⠀⢠⠇⠀⢀⣴⠏⠀⣾⠀⠀⢀⣀⠀⠀⣰⠃
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠙⠻⣦⣀⠀⠈⠛⠢⠤⢀⣀⣤⣾⣄⣀⣀⡠⠋⡀⠔⠋⠁⠀⣸⠇⠀⠀⠉⠙⣇⣰⠃
⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣆⡀⣀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⢱⡷⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠘⠟⠉⠙⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡄⠀⢀⡈⠀⠀⠀⠀⣴⡶⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⣯⣆⡤⣶⡴⠳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠉⠉⠐⠂⢄⡀⠀⢀⣀⠠⠤⠄⠠⠤⠄⣀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠔⠀⠀⠀⠐⢄⡀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠀⡀⠔⠀⠀⠀⠂⡀⢡
⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠘⢄⢂⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢠⢢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡴⠕⠁
⠀⠀⠀⠠⠤⢀⣀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠄⠂⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠤⡀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠠⢤⡀⠀⠀⠆⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⡁⠀⠀⠀⣨⠄⠒⠈⠁
⠤⠐⠂⠂⠀⠀⠀⠀⠀⠒⠂⠸⡄⢑⠂⠈⠒⠀⠒⠁⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠁⠐⡊⠡⡤⠐⠒⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⣀⠠⠄⠐⠒⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠂⡞⠁⠀⠀⠒⠂⠠⠄⢀⡀
⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠲⢄⠀⠀⠀⠑⠀⠊⠓⠐⠃⠀⠀⠀⢀⡴⠋⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠄⡍⠁⠀⠀⠀⠉⡅⠄⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠉⢐⠦⠄⢀⡀⢀⡀⢀⣀⠠⠤⢖⠉⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡒⣠⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⠀⢠⡘⡖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠒⠲⠶⢄⣐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠓⠚⠛⠒⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢮⣷⣦⣄⡀⣠⢈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢛⣀⡌⠃⢙⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠂⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠘⢆⠸⢿⡿⠁⠉⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡞⠀⠀⠸⢤⠈⠂⠀⠀⠀⠢⠀⠀⠲⠤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣰⣅⠀⢻⣀⠀⠀⠾⣤⣀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠲⣿⣷⣆⠀⠀⠀⠀⠰⣷⣮⡗⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⠿⣄⠀⣹⣦⠀⢀⡀⠈⢻⣄⣘⣚⠛⠒⠶⣄⡀⠀⠈⠻⢯⠙⢧⣤⣤⣀⠉⢡⡀⠦⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣛⡿⣛⠋⠙⣎⣀⣦⣼⣟⣻⠿⠿⠿⠿⣿⣿⣦⣤⣶⡶⠶⢌⡛⠻⠛⠟⠇⣅⣀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣾⣿⡿⠞⠁





⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣦⡀⠀⠀⠀⠁⠁⠁⠀⠘⠀⠤⢶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣶⠟⠉⣿⣿⣿⡣⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠑⢦⣤⣤⡄
⠀⠀⠀⠀⢠⡴⠾⠋⠀⠀⠀⠘⠿⢿⣿⣂⠀⠀⠀⢠⢀⡆⠀⠀⠀⠀⠀⢸⣿⣗⠄⠀⠀⠀⣿⣆
⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠀⠀⢇⠈⠈⠃⠀⠀⠀⠀⠀⠀⢏⠁⠀⠁⠀⠀⠈⣳⠆
⠀⠀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡇⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⢺
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⣷⣤⡀⢠⡀⢀⠀⠀⢀⣀⣴⡞⠀⠀⠀⠀⠀⠀⢻⣗
⠀⠀⢹⣂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⢂⠀⢻⣿⣿⣾⣇⠈⠀⠔⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣻⠆
⠀⠀⠂⢾⠆⠀⠀⠀⠐⠈⢧⣷⡶⠾⠥⡀⠙⠙⠛⠻⠿⠿⠀⠀⠰⠿⠟⡳⠋⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠈⠃⠠⢤⠄⠀⠀⢤⣷⠋⠍⢄⣬⣽⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡄⠆⠀⣀⣀⣀⢀⣛⠿⠄
⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠈⠀⠈⠍⠙⠁⠐⠂⠀⠂⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣞⣳⠄
⠀⠀⠀⠀⠀⣰⣿⣿⣤⣄⣀⣤⣴⣤⢀⣠⣶⣤⣀⣀⢀⣀⣀⣀⣠⣀⣴⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⠿⣿⣿⢿⡿⡻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠛⠻⠛⣿⣿⢿⡿⢏⡜⠁⠀⠀⠀⠀⠀⢀⣤⣤⣌⠃⠙⠛⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⢳⣿⣿⢓⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣇⠀⠀⠀⠀⢐⠀⣼⣿⣿⠏⠀⠀⠸⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣌⢀⣽⣿⣿⣷⣄⠀⠀⠀⠈⠉⠁⠻⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⠿⠟⠁⠘⠻⠿⠿⠟⠛⠓⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠⠤⠀⠀⠀⠀⠀⠠⠣⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣤⣤⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣭⡐⠤⠂⠀⠂⠀⠀⣸⣉⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⣦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠋⠀⠀⠀⠀⢻⡿⠶⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⢃⣤⣌⢂⠀⠀⠀⠀⠀⡻⢿⣿⣿⣏⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠈⢿⡿⠈⠀⠀⠀⠀⠀⡁⠀⢰⣿⣿⣿⡿⠬⠀⠀⠘⠛⠛⠛⠉⣃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣆⠀⢠⠀⠀⠀⠀⣠⠃⠀⠻⣟⡻⢿⣧⡀⠀⠀⠀⠀⠀⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠆⠀⠀⠀⡏⠉⠂⠀⠀⠈⠉⠉⠁⠔⠉⠒⣤⣤⡀⢀⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⠢⠠⠀⠀⠀⠀⠀⠀⠠⡀⢀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠸⠿⠟⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣯⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣷⣶⣿⣿⣿⣷⣶⣤⣴⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡙⢻⣿⡿⠟⠉⠿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣴⣤⣤⣀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣿⡏⠿⠿⠦⠤⢠⣤⣤⣴⠞⣿⣿⠻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠹⠇⠀⠀⠀⠀⠀⠀⠈⠫⡄⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣶⣆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠟⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠛⠃⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠐⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⡿⠀⠀⣄⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢦⡀⠀⠀⠙⠾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣖⣛⠛⣷⡖⠚⠲⠤⡀⢤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣍⡙⠓⠂⡼⣏⡒⠀⠊⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢀⠉⢛⣦⡤⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣤⣀⡄⠀⣠⡀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣦⡈⠿⢷⠶⣿⡀⢀⠄⢀⡀⢀⣔⠀⢀⠀⠀⠲⢄⠀⠀⢀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣄⢀⠐⣹⣿⣏⣀⡡⠔⢪⡿⣦⠺⡄⠀⠀⠀⠁⠀⢸⡀⢀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡏⣩⣷⣶⣽⣆⠈⠀⠀⠀⠀⠀⠀⢠⣾⣟⢻⡇⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢀⣶⣿⠏⠃⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣴⣾⣿⣿⢛⣆⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⠿⢿⡏⠀⠀⢀⣠⣿⣿⣿⣿⣄⣼⣥⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣺⣿⣿⣁⢠⡿⣄⣠⣗⠋⠉⢉⣉⡻⡟⣛⢫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠧⢶⣤⠦⠿⠉⠈⠁⠈⠉⠉⠙⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠠⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠠⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠉⠉⠉⠀⠁⠈⠉⠉⠉⠛⠛⠛⠻⣿⣿⣿⡿⠟⠉⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⠈⣷⣌⠐⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⢿⣿⣿⣌⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣰⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⠀⣿⣼⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⣿⣿⣿⣄⣠⣴⠄⠸⣶⣿⣿⣿⣿⣾⣿⣿⣿⡿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⠃⠊⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⠏⠀⠀⠀⠀⢫⣿⢿⣿⣿⣿⣿⣧⣤⣴⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡿⠋⢻⣿⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠙⠋⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⣀⣬⠍⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠈⠳⠀⣰⣶⣿⣿⡇⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⡄⠀⣁⣦⡀⠀⠀⠀⠀⠀⣤⠀⠀⢻⢿⡿⠋⣀⣤⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣘⠿⣿⣷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⠙⢿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⢻⣿⢿⣿⡿⡝⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠉⠙⢛⣸⣷⣼⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⢿⣤⣿⠟⢃⣀⣀⠀⠀⠀⠀⣈⡉⠛⠻⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣧
⠺⣷⣦⣼⡿⠋⠁⠒⠉⠙⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠉⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣊⠛⢋⡉⣧⠉⠀⠐⢃⣰⣿⣿⣿⣿⠿⢉⣠
⣤⣿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠋⢹⣿⣿⣿⢼⣿⣁⣥⣤⣥⣾⠟⠁⠘⠀⢤⣶⡿⠉⠉⠙⠃⠙⠴⣎⣿
⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇⢻⣿⣁⠈⠙⠿⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⡻⠇⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣄⠀⠀⠐⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡃⠂⠀⠁⣾⣿⣿⣿⣿⠻⡦⠂⠀⠀⠀⠀⠘⡁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⠃⠀⠀⠀⠛⢿⣿⣿⣿⠇⢸⡿⠃⡚⠁⢠⠈⡃⠀⠀⣠⠄⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠦⠄⠐⠶⣶⣶⣿⡆⢬⢿⠹⡟⠛⠁⠀⠀⠀⢰⣶⣿⣿⣿⣧⢘⣿⣿⣿⣤⣌⣈⠁⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⠐⢶⡶⠛⣿⣿⣃⡀⠈⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⡿⢿⡂⠁⠀⠘⠁
⠀⣠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⣀⡿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣶⣶⣷⣄⣠⡀
⣼⣿⣤⣿⣿⣷⣶⣤⣤⣄⣀⠀⠛⣁⠀⠀⠈⣿⣿⣶⣶⣦⣤⣀⠀⣠⣿⣿⣿⣿⣿⡿⠏⢿⣿⣿⣿⣿⣿⡟⠉⠁⠘⡃
⠿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠉⢳⡀⠈⠶⡆⠀⠙⠿⢿⣿⣿⣿⣿⣷⡿⣿⠟⣿⣿⣿⡇⠀⠈⢻⣿⣷⡶⠤⠵⠞⠀⠀⠁
⣠⣤⣧⣤⣿⣿⣿⠏⠉⠑⠀⠚⠁⠀⠀⠀⠀⠀⠀⠙⢿⣷⣬⣷⣾⠓⠂⠾⠿⢿⠿⡟⢀⣰⡿⡏⠁
⣿⠛⢿⡟⣿⣿⢹⡦⠀⢐⠀⠉⡁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢋⠀⠀⠍⢳⡀⣧
⣿⣦⣤⣄⣿⠿⠈⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠐⠀⠴⢻
⢉⢉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢑⠤⠖⠤⠂⠤⡀⢄⠀⠀⡠⢒⠁⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⠄⠀⣠⠒⠉⠀⠀⠀⠆⠀⠀⠀⠈⠘⠒⣅⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠞⠀⡴⣩⠢⠀⠀⠈⠀⠀⢠⢒⢢⡀⠈⡆⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⠆⠿⢹⠀⠀⠀⠀⠀⡇⣿⢛⠁⠀⠺⣐⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⢀⢾⣖⣡⠀⠀⠀⣄⠀⢘⡤⠊⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⡠⠀⠀⠀⠀⠀⡇⢰⡀⠘⢬⡀⠕⠁⠉⡉⣩⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⢀⠀⠁⠀⠀⠀⠀⠀⠘⡄⠑⠂⢒⠣⠄⠠⠜⢀⡉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠒⠤⢀⣀⣀⠠⠔⠊⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠄⠠⠈⠈⢁⠀⠀⠀⠀⢀⠀⣀⡠⣀⠤⠂⠀⠨⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠉⠰⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⡴⠁⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⣣⢰⡇⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⢱
⠀⢀⠎⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠏⠉⠁⠁⠀⠀⠑⠀⠀⠀⠀⡠⠃⠀⠀⠀⢣
⠀⢸⠄⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠉⠒⠒⠢⠤⢤⠤⠤⠔⠃⠀⠀⣀⡠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⡑
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡸⠀⣠⠆⠐⢠⠖⠉⠀⠐⣴⢰⣰
⢠⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠁⠀⡴⠁⠀⠀⠀⠀⠀⠉
⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡠⠂
⡇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠋⢀⣀⠤⠊
⠸⠀⠀⠙⠒⠀⠀⠀⠀⠀⠒⠉⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⢠⢞⡤⠊⠁
⢠⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠀⠀⠤⠔⠉⠀⠀⠀⠀⡠⠔⠉⠁
⠪⠀⢣⡐⣄⠀⠀⠀⢀⣀⠜⠁⠀⠀⠀⠀⠀⡠⣀⡠⠶⠋⢲⡤⣄
⠀⠲⠔⠤⠽⠛⠲⡊⠁⠈⠙⢉⢒⡒⠒⠒⠊⠉⠓⠀⠠⠄⣒⣭⠪⠂
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡐⠪⣑⢕⢮⡦
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣿⣾⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⡲⢦⣀⣠⠤⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⣠⠴⢚⣛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⢙⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡋⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⣴⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢦⠀⠀⠈⢯
⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠸⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠇⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢺⡏⡏⡗⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠀⠀⠒⠒⠦⢤⣄⠤⢄⠀⠀⡠⠤⣠⡤⠶⠒⠒⠀⠀⠘⠛⡹
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢸⣆⣼⠇⠸⣧⣰⡇⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⠴⠋⠈⠀⠀⠀⠀⠁⠙⠦⣤⡀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣭⡷⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⢾⣭⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡴⠄⢾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠘⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠖⠈⠉⠀⠠⠀⠀⠀⠀⠸⣿⣖⣶⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣌⠀⠘⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠶⠈⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡌⠀⠀⠀⡐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡬⠝⠣⠄⡀⠀⢹⡋⠙⠂⡤⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠳⠀⣙⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢶⣲⣆⡀⢀⡀⠖⠈⠉⠘⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠠⣤⠭⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠃⣹⣿⣿⣉⠀⠀⠀⠀⠀⠁⠈⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠸⣷
⠀⠀⠀⠀⠀⠀⠈⡰⠋⠁⠈⢻⡄⠀⠀⠀⠀⠀⢀⡰⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁⢛⡆
⠀⠀⠀⠀⠀⠀⢾⠁⡀⠀⢀⣼⠁⠀⠀⠀⠀⡈⣫⡄⠚⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢬⣿
⠀⠀⠀⠀⠀⠀⡞⠳⣇⡯⣘⣿⠀⠀⠀⣠⣼⢤⡬⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⡂
⠀⠀⠀⠀⠀⠀⣰⠃⠨⠛⠿⠏⠀⠀⡞⠁⠀⠀⠀⢰⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿
⠀⠀⠀⠀⠀⠀⠁⣠⠁⠀⠀⠀⠀⣘⡟⡄⠀⢠⣴⣾⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠼⠛⠐⠴⢻⡿⠛⡵⣠⡀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠄⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠊⠀⢠⠠⠛⠂⠀⠀⣠⣄⠀⠀⠀⠀⠀⢸⢿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡠⠘⠀⠀⠀⢀⣴⠁⠀⠀⠀⠀⠀⠉⢼⠀⣬⠀⠃⠀⠀⠆⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠁⠀⠀⠀⠀⠈⣩⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡀⡔⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠳⢧⡇⠀⢀⡇⠀⠀⠀⠀⠀⠦⢀⣿⠀⠸⠀⣴⣀⡜⣿⣹⣏⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⠶⣯⣷⡀⢠⣯⡀⢠⡴⠋⠀⠀⠀⢁⠃⠉⣀⣽⣠⠿⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣠⣠⡶⠿⠛⢒⣺⣿⣃⠟⠚⠓⣰⣤⣶⠿⠶⠾⠿⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠠⠰⠻⠯⣧⣀⢀⡠⣾⣝⣋⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⢉⣍⣚⡻⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⢉⣉⣒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠉⠙⠲⣄⠀⣘⡦⠴⠒⠒⠒⠒⠒⠦⢤⡞⠀⡠⠚⠉⠀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠇⠀⠀⠀⣼⡿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⢱⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠀⠀⠀⠀⣿⣷⣿⣿⠀⠀⠀⠀⠀⢸⣿⣷⣾⡇⠀⠀⢸⡗⢆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠥⠞⠒⠤⢤⡀⠘⠻⠿⠋⠀⠀⠀⠀⠀⠀⠻⠿⠟⣡⠤⠒⠚⠓⠬⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢀⡠⠤⣾⠒⠋⠉⠉⠉⠉⠉⠒⠒⠂⠀⢀⡠⠤⠤⠤⡀⠀⠀⠤⠒⠒⠒⠒⠒⠒⠒⠒⢺⢷⣄⡀
⠀⠀⠀⠀⠀⢰⠉⣇⣀⡤⠔⠒⠚⠋⠉⣁⣀⠀⠸⣄⠀⠀⢀⡼⠀⢀⡀⠒⠒⠒⠒⠤⢤⣀⢀⡞⠈⡇⠈⠁
⠀⠀⠀⠀⢀⡼⠒⠉⠣⣄⠀⣀⠴⠒⠉⠁⣀⠀⠀⠈⣙⣏⠉⠀⠀⠀⣈⠉⠒⠦⣄⠀⢀⡠⠋⠓⢤⣸
⠀⠀⠀⠔⠉⡇⠀⠀⠀⣨⠟⠓⠲⠤⠖⠊⠉⠹⣍⠉⠁⠀⠉⣉⠟⠉⠈⠑⠒⠒⠒⠛⢯⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⢠⠃⣀⠀⠠⠃⢀⣠⠤⣄⠀⠀⠀⠀⠀⠉⣉⣍⡉⠁⠀⠀⠀⣀⡤⠦⣀⣦⣀⣧⠔⢫⢷⡴⣧⡀
⠀⠀⠀⠀⢸⠀⠸⡀⠀⣴⡛⣤⡵⠶⠧⠤⠤⠤⠒⣋⠴⠢⢬⣉⡉⠉⣉⣡⠴⠚⠲⠤⣥⡤⠔⠋⠺⢴⣧⢷
⠀⠀⠀⠀⢸⠀⠀⠉⠒⡾⠉⠋⠙⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠑⢆
⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⣇⠀⠀⠀⣇⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠈⠿⠟⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⢦⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣤⡽⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣀⡇⢸⣭⠇⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⣀⠴⢖⡎⢙⣓⣖⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠔⠊⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣄⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀⠀⠘⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠙⢻⣿⣿⣿⣿⣿⣿⡟⠉⠈⠉⢻⣿⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⣨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⣿⡆⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⠆⠀⣿⣿⡀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⣼⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿
⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿⣶⠀⠘⣿⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⡟⠉⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠻⢿⣿⣿⣿⡟⠙⠻⢿⣿⣿⣿⣶⣿⣿⣿⠀⠰⣶⡶⠀⢸⣿⣿⠏⢀⣴⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⣿⣿⣿⣿⣶⣤⡀⠈⠛⠻⠿⢿⡿⠿⠷⠀⠀⠀⠰⠿⠛⠁⣠⣾⣿⠃
⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣶⣤⣤⠀⠀⣤⣤⣶⣷⠀⢠⣤⡴⠺⣿⣿⣯
⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠻⠿⠿⠛⠉⠀⠈⠙⠉⠉⠉⠀⠈⠉⣀⣴⣾⣿⣿
⢻⣿⣿⣿⣿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⣴⣿⣿⣿⣶⡄⠘⣿⠃⢠⣿⣿⣿⣿⣿⡏
⠘⣿⣿⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠻⣿⣿⣿⠟⠀⠰⠏⠀⣼⣿⣿⣿⣿⠟
⠀⢻⣿⣿⣿⣿⣿⣿⣷⣤⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃⠀⡈⠉⢁⣠⣤⡀⠀⠘⠻⠿⠟⠛⠁
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⠿⢿⣿⣷⣶⣦⣤⣴⡄
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⢿⠿⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⡿⠋⢀⣠⣄⡀
⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣤⣤⣴⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣸⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⠿⠋⠈⠁⠴⠐⠛⡱⠻⠴⣆⣤⣄⣀⠀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠜⠑⠋⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠰⣥⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⠀⠰⠿⡯⠀⠀⠀⠀⠀⣰⣿⣿⣇⠄⠠⠂⠀⠀⠒⡶⠌⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠙⠛⠟⠋⠀⠀⠉⠀⠈⠍⢂⡀⠀⠀⠈⣒
⠀⠀⠀⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠘⢇⠀⠀⠘⣀⡉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠴⠿⠢⣶⣮⣭⣶⣦⣴⣶⡀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡄⠈⠈⠋⠉⠉⡿⣭⣟⠛⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠶⠶⠶⠶⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⡴⠖⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠫⡛⠳⣦⣤⣤⣤⣤⢶⡶⢛⣉⣉⡙⠲⢶⠾⠿⠶⢦⣤⡘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡎⠰⠟⠛⢛⣿⡷⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠀⠈⠳⢀⡀⠠⠤⠀⠀⢣⣌⠛⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⠋⠁⠀⠀⠀⢈⣐⠀⠀⠀⠀⠀⠈⠎⠹⣦
⠀⠀⠀⠀⠀⠀⣼⠏⡠⠁⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢰⡟⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⠓⢄⡀⠀⠀⠉⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣿
⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠋⢰⠃
⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣠⣴⡦⣰⠃
⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡄⢀⣀⡀⠀⡀⠀⢀⡠⠶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠠⠀⠈⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⠲⣤⣤⣤⠾⠒⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣵⣤⣤⡀⠀⠀⣠⣀⣠⡦⠦⠤⠖⠚⠛⠿⢿⠿⠾⠶⠶⠾⢶⣄⢀⡀⠀⠀⠀⠉⠑⠲⣆⠠⠀⠉⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠽⣷⢿⣍⣤⣤⣤⣤⣤⡴⠦⣤⡤⡼⠇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠾⠶⠤⠶⠾⠛⠛⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣭⡐⠒⢶⣄⡀⠀⠀⣀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠿⣿⣿⣶⡌⢉⠈⢦⡸⢫⠻⠟⣿⢢⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⡄⠟⠛⠉⢀⠈⠀⠃⠃⠀⠀⠀⠘⠂⠉⠿⣿⣤⣄⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣷⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⠉⠀⠀⠀⠀⠀⠀⢀⡴⢶⡀⠀⠀⠀⠀⠀⠀⠀⣘⠡⡈⠉⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠻⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢼⠓⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠠⣄⡀⠀⠀⡀⠀⠀⠀⢀⡤⠱⠀⠀⠐⠀⠀⠀⠀⠀⢻⡇⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⢣⠀⠀⠀⣠⣾⣿⣿⠁⠀⠀⠰⢤⠀⠀⠀⠀⠀⢐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⡰⣀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠈⢦⣧⡘⠀⠀⣰⣿⣿⣿⣿⣇⢀⠄⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡖⠀⠀⢸⣿⣀⣤⡄
⠀⠀⠀⠀⠁⠒⠂⠠⣤⣄⣰⡄⠀⣼⣿⣿⣿⣿⣿⣿⣯⡊⠄⠀⠀⠀⠦⠐⠛⠀⠀⠀⠀⢠⣷⠄⠀⣀⣈⠔⠀⠀⣼⣿⣿⣿⢷⡀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⢿⣿⡟⢹⢉⣟⢹⣿⡿⠿⠷⢦⣶⣆⡀⠀⢺⣷⣦⣀⣈⣹⣿⠷⠛⠁⢀⣠⣼⣿⣿⡏⣨⠀⡄⣾⣿⣭⣭⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣾⣧⣾⣿⣷⣿⣿⣿⣿⣿⣿⣧⣌⠻⣿⠿⠙⣻⣿⠿⣾⣿⣿⣿⣿⣿⣿⣧⣽⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⢻⣍⣝⢻⣿⣿⠼⣿⣿⣿⣿⣷⣌⣙⢚⣋⣴⣾⣿⠟⠻⣟⣿⣿⢿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⢙⠇⠈⢻⣇⡛⠉⠁⣼⣿⣿⣿⣿⣿⣿⡟⢧⡀⢤⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⠁⣿⠀⠉⠈⠙⠃⡠⠐⠈⠡⠞⣿⣠⣀⢰⡾⠃⠀⢤⣄⢸⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣝⡻⠛⠛⠛⣿⡅⠀⠘⠃⠐⢡⡂⠸⠉⠃⠙⠃⠀⠀⠀⣴⣿⡛⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣁⣤⡌⠠⠄⡉⡁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢈⠙⢳⢾⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢙⣿⣄⠀⢠⡾⠂⠃⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⣾⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⣖⠛⡛⢁⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣄⠀⠀⢀⣀⡈⠋⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⢯⡄⠀⠈⠀⢘⠀⠰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠽⢑⠉⠀⠷⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⢉⡩⢀⡀⣨⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠐⠀⢦⣴⠂⠺⣤⡀⠠⠼⢯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠭⠁⢠⣤⣞⣀⣿⠁⠀⠀⠀⠎⠀⠀⠰⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⣘⣶⣄⠨⠟⠁⠘⢶⣟⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠤⠀⡀⡀⣰⣏⠁⠛⠀⠆⠐⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠔⠀⠀⠀⡬⠉⣯⡀⠁⠀⠀⠀⠈⢿⣧
⠀⠀⠀⢠⡀⠀⢠⣿⣏⠀⢠⣾⠋⠃⠙⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⢷⣶⣶⡀⠐⠒⠺⣟⡀
⠀⠀⢒⠜⠣⠨⢿⣭⠂⢘⢡⣇⣀⡔⠀⠄⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡂⣫⢻⣷⣦⠀⠠⣿⡇⠀⡀
⠀⠀⠈⡂⠀⠖⠒⢉⢿⡁⣤⣰⣿⣾⣣⣤⣗⣤⣧⡀⠂⠀⠀⠀⠀⢠⣆⡆⠀⠄⠀⠀⠀⠀⢀⣀⠀⠚⣻⢋⠠⣎⡔⣿⣂⢲⠁⠃⢢⢧⡄
⠀⠀⠐⠃⠂⠤⢄⣤⣴⠟⠁⠈⠁⠈⠙⠛⠿⠿⢿⣑⣶⣁⣄⠀⠀⢠⣿⠁⠀⣀⠀⠀⠂⡠⢾⣿⣤⣥⣾⣿⣾⣿⣿⣿⡏⠀⠀⣐⢤⡼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⣷⠈⡃⠘⣿⠀⣴⣃⣾⣿⣶⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠘⠻⠤⠴⠆⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⣾⣻⣦⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣰⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⡿⠛⠿⠿⠿⡟⢿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣷⣶⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣷⣶⣄⡀⠀⠈⢻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠛⠉⠀⢀⣤⣶⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣏⠻⠟⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⣛⠛⠛⠉⠁⠀⣴⣶⣦⣤⣤⣄⣀⣠⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢛⣥⣶⣦⡙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣶⣝⠻⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣝⠿⣿⣿⣿⣷⣄⡀⠀⢀⣴⣾⣿⣿⣿⠿⣋⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⠟⠋⣴⣿⣿⠿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⡤⣤⡀⢤⡀⠀⠀⠀⠀⢴⣠⡞⠁⡿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢐⣿⠇⠈⣿⠏⠑⠸⣿⣌⠃⠈⡟⢧⡄⡄⢹⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⡘⠋⠀⠀⠘⠈⣻⠀⠦⡟⠔⢻⡇⡼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⣸⠐⠂⠀⠸⡀⣿⠶⡆⠀⢰⡄⣿⠹⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢿⡉⠂⢠⠐⠁⠈⠹⣧⢰⣿⡀⢿⣆⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⣯⠂⢰⣾⡄⢠⣴⡀⠛⡮⢿⣿⠀⠙⣦⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠐⠂⢀⡀⠋⠁⠈⠁⠟⣧⠀⠠⢾⣷⠆⣈⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠠⠤⠒⡊⠀⠀⠀⠀⣸⡄⠀⠀⠹⠛⢪⣄⡨⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢖⣠⠀⠀⠀⠀⠉⠁⠀⠀⠀⢈⣁⡀⠀⢀⡈⣀⣹⣿⣍⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠠⠶⣶⣤⣦⣤⣆⣤⣤⣉⣁⣤⣶⣾⣿⣿⢿⣿⡿⣷⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠸⠟⠛⠃⠻⣿⠟⠛⠻⢿⣿⠿⠻⡟⢻⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠝⢠⠁⠀⠀⠈⠀⡄⣀⢀⣿⣀⠠⢢⠜⡇⠐⠄⢁⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⢣⣀⠀⢀⣠⣼⡿⠋⠉⠋⠺⣧⣼⣁⣀⢠⣤⣿⣿⠃⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⢀⠈⠛⠻⠿⠿⠛⠋⠀⠀⢸⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠄⠐⠀⠀⠀⢀⠞⠀⠀⠀⢀⡀⠀⠄⠀⢀⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢠⠀⠀⠀⢸⠄⠀⠨⡼⠀⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠈⠈⠀⠀⠀⠠⢁⡞⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣟⣒⣺⣶⣷⣾⣿⡿⠒⠛⠏⣠⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠦⠷⠿⠿⠿⠿⠻⠿⠁⠰⠓⠗⠚⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠀⠀⠀⠀⢀⡞⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢀⡴⠁⠀⠀⡴⠋⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢀⣤⢞⣭⣤⣀⠘⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⣴⡟⠑⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢳⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⢀⣠⣤⠤⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢀⠴⠶⠶⠶⣾⣿⡿⢦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠴⠋⠀⠀⢾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣤⣀⡀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡿⠈⠉⠛⠛⠛⠛⠓⢒⡒⠈⠛⠿⠿⠿⣦⣀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⠟⠛⠁⠀⠀⠀⠀⠀⠞⢫⠟⠛⠛⠻⠿⠶⠶⠶⠦⠄⠀⠀⠀⠠⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠋
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠛⢿⡄⠹⣷⣄⢠⡀⠀⠀⠀⠀⠀⣠⡄⣠⣶⡏⠀⣴⠿⠿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⣿⠃⠀⣿⡿⠆⠹⣿⣶⣶⣿⠙⠋⡼⠻⣿⠀⠘⣿⡆⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠀⣿⡄⠀⠋⠀⠰⠠⠀⠶⠈⢁⡁⠘⠀⠀⠃⠀⠀⣿⡇⠠⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣆⠙⠁⠀⡀⠡⢰⠀⣆⠀⢾⢡⣠⠄⣧⣴⡆⠀⠀⠛⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣏⣃⠠⠆⣿⡏⠁⠀⠙⡷⢄⠸⡅⠀⠉⢡⡎⠔⠀⠀⢸⣓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡶⣦⣆⠰⠞⡷⢦⠀⠻⢱⠆⠐⡐⡇⠰⢶⡅⠃⠦⠄⣶⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠘⠙⠈⠁⣱⣿⣶⠀⢠⡄⢀⣰⢃⠀⢶⣿⢟⠀⠨⠯⠭⠵⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠂⠀⠀⢀⡀⠙⠋⠁⡰⣎⡅⠹⣇⢾⣀⡀⠈⠛⠀⠀⠀⠀⠛⠛⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⡘⠋⠀⠉⠀⢀⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠀⠀⠀⠀⠀⠀⠤⠄⠤⠤⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠒⣒⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢇⡀⡀⠀⠉⠛⠷⠟⢰⣤⣄⣀⠐⠚⠓⠂⢀⣠⡤⣴⡿⠿⠛⠃⠀⢀⠀⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠘⠟⢿⣴⣤⣤⣀⣄⣀⠀⣈⣇⣌⡈⢀⣠⣯⣍⣁⡀⣠⣤⡶⠖⠉⠁⠀⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠊⠘⠁⠋⠉⠛⠻⣿⠿⠿⠿⠿⠟⠉⠙⠻⠿⠇⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡷⢒⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠙⣲⣿⣿⣷⣶⣍⣁⡀⠁⠀⠀⠠⠀⠀⣠⣶⣶⣏⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣬⣽⡆⣜⠄⠀⠀⠀⠀⠁⢀⣄⣾⣿⣿⠻⠋⠙⢿⠿⢿⣿⣿⣷⣶⣤⣤⣴⣾⣿⡿⡀⠋⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡿⠀⠈⢿⣧⣤⣶⣾⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠰⠀⠁⠀⠉⠙⢟⢻⠿⢿⣿⡭⠘⡀⠆⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠆⠀⠀⢸⣟⣿⠋⠈⠃⠈⠀⢀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠘⡇⢺⡏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢃⠆⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠰⡄⠀⠀⠀⠀⣄⠀⠄⠀⡞⠀⠀⣸⡧⣤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣥⡿⠀⠀⠀⠈⢣⣦⢀⡄⠀⡄⠀⠀⠰⡇⠀⠈⠀⠀⠀⠀⢠⠀⠀⠄⢸⠋⠁⠀⠀⢟⣂⢤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡴⠆⠀⠀⠀⠀⠀⠺⠀⠆⠀⠀⠀⡀⢫⡀⠐⠁⠀⠀⠘⠸⢣⡖⠀⠀⠀⠀⠀⣸⠆⢀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⡰⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠟⢃⠀⠒⢾⣷⣶⣦⣶⣤⣶⣶⣶⣿⡟⠈⢉⠃⢴⣷⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠀⠓⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠃⠘⠆⠘⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠄⠠⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⠀⠀⠂⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡐⠁⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢠⢜⡂⠈⠁⠆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⡖⠠⡆⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠐⠢⣠⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠁⠀⠀⢴⡤⠖⠓⡦⠄⠠⠀⠘⠀⠚⢃⡤⣀⣀⠀⠀⠀⣟⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣀⠒⡐⢆⠀⠀⠀⠈⡆⠀⠀⠀⠘⡶⠁⠀⠀⢀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠂⠀⠸⣇⠀⠀⠀⢸⡇⠀⡄⠀⠐⠀⢁⠈⠀⠀⠀⠀⠀⠉⣇⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠠⠀⠀⠐⠂⣨⡀⠀⠀⡄⣿⠀⠀⠉⠘⣷⡐⠁⠆⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡏⠰⠀⢀⠀⢸⡁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡂⠐⢼⡇⠀⠀⠐⠚⣧⠀⠀⠀⢀⠀⠀⠀⠠⠀⠂⠘⡾⠀⠀⠀⠀⢬⢸⡗⠁⠰⠉⢐⠁
⠀⠀⠀⠀⠀⠂⡀⠈⠹⣤⠀⠀⠉⢀⢸⡏⠀⠀⠀⠀⠘⠳⣅⠀⣸⠀⠀⠀⠀⠆⣠⠞⠁⠀⠀⠀⠀⠀⣻⣠⠀⠀⡷⠈
⠀⠀⠀⠀⠐⠀⠀⠂⠠⠷⢄⣀⡀⠈⢹⡷⠀⠀⠀⢈⠀⠄⣌⠿⢧⣄⡀⢤⣰⠟⠁⠀⠀⠀⠂⠠⠂⠈⣿⠀⣠⡾⢁⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠉⢳⣼⡇⠀⠀⠀⠀⠁⠀⠁⢀⢀⣩⡿⠿⣧⣞⣀⠀⠀⠼⠀⠁⠀⣸⣧⡾⠋⠀⠈⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢹⡇⠀⡀⠃⠀⠀⢦⣠⡾⠛⠁⠄⠀⠀⠉⠙⠿⢿⣦⣀⡄⠀⣿⣿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢙⢀⣴⠟⠛⠲⠀⠂⠰⠁⠀⠀⠀⢤⡀⡬⠻⢿⣦⣿⣿⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠘⠀⠀⢻⣆⠐⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠈⠀⠀⠹⣿⣿⡇⠀⢀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠁⢀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠰⠀⢠⣿⣿⡇⠀⠀⠀⡵⠚
⠀⠀⠀⠀⠀⠀⠉⠑⣮⡀⠀⠀⣜⠁⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⠋⠠⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠹⣆⡀⣾⠁⡄⠀⠀⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠾⣯⠈⠀⠈⡄⠂
⠀⠀⠀⠀⠀⠀⢀⡰⠆⠈⠉⠛⠛⠻⢷⣤⣿⣿⡇⠀⠀⠀⠀⠀⣠⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⣼⣿⣧⠈⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢻⣿⡟⠁⢹⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠈⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡇⠀⠀⢀⣿⢸⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⡆
⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠶⠾⠿⠿⠷⠶⠶⠶⠾⠿⠿⠟⠛⠛⠿⠿⠛⠛⠳⠶⠶⠤⣤⣄⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢠⠃⠳⣄⣄⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⠀⣀⣴⠖⠁⢻⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠀⠀⠀⠀⠈⠉⠀⠀⢉⣿⡆⠀⠀⠈⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠴⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢀⠄⠀⢸⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣢⢄⡟⡀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠸⠀⠀⠀⠀⠀⠀⠘⠿⣷⠄
⠀⠀⠀⠀⠀⢀⡾⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡀
⠀⠀⠀⠀⢠⡿⠁⢈⣴⡇⠀⠀⠀⢢⡀⠀⢰⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡄⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⣿⠁⠀⢀⡟⠀⠀⠀⠀⠀⠙⠂⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢰⠇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠚⠙⠀⠀⠈⢣⠀⠀⠀⠀⠀⡾⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⣇⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⣦⣀⣀⡄⠀⠀⠀⡇⠀⠀⢀⣰⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠸⣼⠁⠀⠀⠈⢳⣦⣄⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⢈⡟⠉⠀⠀⠀⡰⠃⠀⣠⠾⠋⠀⢰⡏⠀⠀⠤⠶⣤⠀⢠⠏
⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠉⠉⠀⠒⠾⠿⠟⠒⠢⠖⠚⠁⠐⠈⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢸⡴⠋
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣷⣃⣄⣠⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠉⠀⠘⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣴⡀⠀⠀⡀⠀⠀⠀⠀⢠⣶⡖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣮⣄⣠⢴⣆⡾⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠀⠈⠋⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⡼⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣫⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⠁⠀⢹⣾⣶⣤⠶⠶⠒⠛⠛⠛⠻⠿⠖⠲⠶⢤⣶⢟⠁⠀⠀⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣀⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⣸⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠰⠾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⡔⠀⠀⣿⠉⠉⠙⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠹⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣖⡤⢀⡏⡄⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠋⣼⠀⠀⠀⠀⠀⠀⠀⠒⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⢯⡆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⡄
⠀⠀⠀⠀⠀⢀⣾⠋⠠⢃⣤⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⣷⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠆
⠀⠀⠀⠀⢠⣾⠇⠀⠠⣿⡿⠀⠀⠀⠀⠘⢦⡀⠀⢿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢹⠏⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠅⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢰⣇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠚⠒⠆⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⣼⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢠⡇⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣇⣠⠆⠀⠀⠘⣦⣄⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠈⠻⣶⡶⠞⠁⠀⠀⢀⡇⠀⠀⠀⣴⡿⠃⠀⣼⠇⠀⠀⠀⣀⡀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠹⣾⡄⠀⠀⠀⠀⠹⢿⣶⡄⠀⠀⠀⠛⠷⢦⣀⡀⠀⠀⣀⣠⣯⡀⠀⠀⠀⢀⠞⠁⢀⡤⠞⠋⠀⠀⢰⡟⠀⠀⠐⠛⠛⢷⡆⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⣄⡀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠙⠓⠋⠁⠀⠊⠁⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⣰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡞⣀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠸⠿⠋⠉⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⡀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣄⠀⣠⠎⠀⠀⠀⠀⣀⡀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣯⡴⠚⣿⣴⠋⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢉⡀⠀⣧⣾⠦⣴⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠃⡼⠋⠰⠀⡈⠀⠲⠘⠛⢣⣶⣾⡶⠦⢒⡟⠁⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⢦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣴⡟⣳⠂⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠁⣶⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢛⣤⣿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣧⠸⡿⠿⣂⡈⠀⠊⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠀⠈⠀⠀⠀⠀⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠓⣀⠛⠋⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡖⠀⠀⠀⠘⣠⣾⡀⠀⠀⠀⢀⠈⠀⢠⠀⢀⣀⠞⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠙⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠄⠀⠀⠀⠀⠹⠛⡄⠀⠀⠀⠀⠀⠀⣠⣾⡞⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⣫⣭⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠰⠠⠘⠋⠀⠚⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠂⠀⠘⠆⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⣴⡀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣨⡍⢤⣬⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢠⡄⠀⢈⠶⠈⠀⢠⣷⡏⠀⣤⣅⠀⠀⠀⠀⠀⠁⠀⣘⡉⢻⡀
⠀⠀⠀⠀⠀⠀⢀⣯⡀⠀⠘⠿⣿⣿⡀⠀⠘⢠⡀⠀⠀⠘⠀⠀⠀⢠⣦⣴⣿⣀⣤⣾⣿⡛⠁⠀⠀⠺⡇⠀⠀⠀⠐⠀⠀⠈⠛⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠎⠄⠀⠀⠀⠈⠿⣿⣦⣤⣬⣷⣾⣃⣀⡀⣀⣰⣿⣿⣿⠟⣿⣿⣿⡗⠁⠀⠀⠐⡀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣦⢴⣠⠄⠀⠀⠚⡿⢋⣉⣻⣿⣿⠿⢿⣿⣿⠟⠿⠻⠟⢀⣼⡟⠋⠁⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢫⣾⣡⠀⠀⠀⠰⡇⢈⣩⣙⡴⣤⠁⠀⢿⠝⠁⡀⠀⠀⠘⠉⠀⠰⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡹⠀⣆⠀⠀⠀⡀⠦⠾⣳⡄⢠⣠⠆⠀⠙⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢰⣧⡤⠉⠓⢃⡿⢳⣾⣇⣀⠀⢀⡄⠀⠀⠀⢀⠀⣠⠰⣠⡄⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢠⣴⣤⣠⣸⣿⠟⣿⣿⠇⠾⡧⠦⢾⠷⠀⠀⠉⠀⠈⠃⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⡇⢀⡼⣿⣷⣄⣀⣀⣀⣀⢀⣀⣤⣾⡇⠀⠀⠀⢀⠂⠀⠀⠀⢣⣸⣦⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⣿⡧⠀⠀⠀⠃⠀⠀⠀⠀⠀⢿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡿⣿⣅⣮⣾⣿⣿⣿⣿⠇⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢲⣦⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⡏⠉⢉⣩⣀⣬⡿⠿⠿⠿⠿⢿⣿⣇⡼⡀⢀⠀⠀⠀⠀⠀⠀⠀⣒⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⣄⣃⠀⢄⣹⣶⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣼⣿⣿⣷⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⠙⢋⣿⠀⠀⠠⠤⠄⠤
⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⢰⡏⠀⢸⡏
⠑⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣋⡀⣀⢨⠁
⡔⠢⡀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣷⠿⠙⡀
⠘⠡⠘⠀⠀⠀⠁⢦
⣤⣤⣤⣤⣤⣤⣭⣤⣴⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢻⡿⢿⢛⣿⣛⡛⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣛⣿⣿⣛⣛⣻⣿⣻⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠠⠒⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⠤⠴⠶⠦⠴⠦⠄⠀⠀⢃⠔⠁⠀⠀⠀⠀⠀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠠⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠈⠀⠚⠒⡀⠀⠀⠀⣠⣯⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠐⠊⠀⢠⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠛⠶⠶⠛⠁⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⢀⠄⣀⣄⠀⠀⠀⠀⠀⢀⢔⣢⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⢀⢾⣯⣼⠂⠀⠀⠀⠀⠸⣾⣯⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠉⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠐⠃⢀⡴⠃
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⡤⢿⠀⣧⠀⠈⢳⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠈⠶⢧⡀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢛⡟⠉⣹⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡿⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠘⠀⠘⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹⡄⠀⠀⠀⡄⠀⢠⡄⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠱⣄⠀⠀⡇⠀⠀⠈⠒⠒⠤⠀⠀⢰⡀⠀⠀⠀⢀⣀⣤⠴⠋⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣆⠀⠈⠉⠈⠉⢉⣽⡃⠀⠀⣠⠤⠠⠞⠁⠂⠚⠛⠉⠉⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠙⢦⣀⠀⠀⠀⢀⣤⠏⠀⣤⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⢳⠒⠒⠚⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⣀⣤⡶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠸⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⢀⠠⠄⠒⠒⠒⠒⠒⠚⠛⠂⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⣈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⡶⠦⢤⣤⣄⣠⣤⠴⠂⠉⠉⠁⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠙⣿⡤⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣩⠚⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣤⡀⠀⣀⣀⣀⠀⢀⣴⣿⡿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠙⢿⣿⠟⠋⠁⠀⠀⠀⠈⠉⠻⢿⠇⠀⠀⣿⣿⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠒⢤⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣴⣆⡀⠀⠈⢢⡀⠀⠀⠉⠢⡈⢢⡀
⠀⠀⠀⠀⠀⠀⡰⠋⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⢸⠋⠉⢳⣄⣹⠀⠀⠀⠱⡀⠀⠀⠀⠘⢦⠙⣄
⠀⠀⠀⠀⠀⡜⢁⠞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠤⠼⠁⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢳⡈⢆
⠀⠀⠀⠀⡜⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠀⠀⠀⠀⣰⣀⠀⠈⠙⠛⠀⠀⡇⠀⠀⠀⠀⠀⢳⠈⣆
⠀⠀⠀⢸⠁⡎⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢇⢸
⠀⠀⠀⡏⢸⠁⠀⠀⠀⢀⠼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢢⡀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⡇⠘⠀⠀⠀⢠⠎⠀⠀⠈⠉⠒⠢⠤⠤⡀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠒⠊⠁⢀⠄⢀⠱⡀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⡇⢠⠀⠀⢠⠇⣰⠁⠀⠉⠐⠂⠤⠄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠤⠔⠊⠁⠀⠈⢆⢣⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⣇⢸⠀⠀⡌⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠿⠿⢇⠈⠁⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⢸⡈⢇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⢀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡜⢰⠃
⠀⠀⠀⠀⢳⠘⢦⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣍⢓⣖⣋⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣰⢁⡞
⠀⠀⠀⠀⠀⠳⡈⠳⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜
⠀⠀⠀⠀⠀⠀⠙⢦⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡜⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠤⣀⣀⠀⠀⠀⠀⢀⣀⣠⠤⠒⣉⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠭⠉⠩⠭⠤⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢿⡄⡷⢦⣀⣀⣀⣄⣀⣀⡤⠔⢰⠿⠿⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠸⡇⣿⣛⢟⡟⠙⡿⣿⢹⣷⠆⢰⠖⠂⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣿⣷⢯⡄⠉⠀⠁⣋⢀⣍⡤⢮⡆⠀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣩⠆⢸⠁⠁⠀⠀⢼⢣⣤⡡⢾⢅⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⣰⣿⠟⣀⢠⠀⠀⡄⢸⠻⣾⣷⠈⠚⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢠⣾⣿⣾⠟⠉⣮⣼⠃⠓⢹⢗⣠⠙⠳⠀⠈⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⢽⣯⣿⠁⠀⠀⣿⡼⡇⠀⠀⠘⣿⣿⣛⣷⠂⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡄⠈⢗⡀⠀⠀⠉⠉⠀⠀⠀⠀⣿⠿⠍⠋⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣤⣄⡀⠐⠚⠓⠒⠀⠐⠚⠳⣄⢠⣴⢮⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠈⠘⠏⣿⣿⢷⡿⣿⢦⣶⣾⡶⣿⡿⠆⠉⠀⠀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡀⠀⠀⢁⠀⠑⠁⠛⠀⢠⠀⠿⠀⠁⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣏⡀⠄⠐⡃⡔⣀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢙⡦⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠣⠉⠈⣿⠀⠀⠀⢈⠝⠿⣶⣄⠀⠀⠀⠀⣸⡿⠉⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡁⠀⠀⠿⣧⠀⠐⠚⠂⡤⠘⣿⠀⠀⢀⣾⠟⠀⠀⠂⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⡇⠐⢀⡀⢰⣤⣄⠀⢀⡃⠂⠘⡇⠀⡘⠁⠈⠁⢀⣧⣼⡟⢉⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣹⠃⡀⠀⠀⠀⠙⢿⣿⣿⣧⣀⣀⣴⣾⣥⣤⣴⣾⣿⢟⠁⠀⠠⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣷⢾⠅⠀⠀⠀⠀⠀⠛⠛⠻⠛⠋⠁⠡⠈⠉⠩⡉⠀⠀⠀⠀⠀⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⣿⡐⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠃⠀⢩⠀⠀⠀⠀⠀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡦⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠂⡀⠀⠏⠀⠀⠀⠀⢀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⡀⡀⠀⡀⣂⠀⡀⠀⢀⣀⡁⠘⠀⠀⢀⣀⣶⠿⠁
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠋⠁⡀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠙⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⠴⣄⠀⠀⠀⠀⢀⣤⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣠⠏⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⡾⠀⠀⢠⠶⠒⢦⠖⠲⢦⡀⠈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⠖⠋⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠶⣄⠀⠈⠳⣄⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣤⠀⢹⡆⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣳⣼⡟⠓⠒⠶⠶⢦⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢦⣤⡟⠁⠈⠳⢦⣄⣀⣀⡼⠃⠀⠀⠀⠀⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠳⢤⣀⠀⠀⠈⠉⠙⣦⠀⠀⠀⠀⠀⡿⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡟⠓⠶⠦⠶⠃⠀⠀⠀⠀⠀⡇⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⣄⣠⣤⣤⣠⣤⣀⣠⡇⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡗⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢠⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⢸⡇⠀⣀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠙⣟⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠛⢾⡷⠛⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠿⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠾




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠄⠀⢠⠀⢀⠀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⡀⠂⠒⠀⡆⠒⠀⠂⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠧⠤⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⢀⣀⣀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⢀⣀⡀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠐⠁⠈⠃⢸⠀⢸⠀⢰⢻⡀⢸⠤⡇⢸⠀⠀⡇⠀⠀⠀⠧⡀⠀⢸⠀⢸⣀⠇⡜⠀⠈⡆⣧⡜⠀⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣥⣤⣈⣤⣤⣃⣸⣀⣸⣀⣏⣈⣁⣸⣤⣏⣸⣤⣄⣧⣤⣀⣀⣤⣜⣀⣸⣀⣸⣀⣇⣘⣤⣔⣁⣇⣈⣆⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠲⠶⢦⣄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⡾⠁⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠉⠲⣄⠈⠛⢦⣀⡴⠛⠛⠋⠉⠐⢛⡭⠿⠿⠿⣶⣄⣠⠞⠋⠀⡴⠊⠁⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠐⣾⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⢸⣖⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣋⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⣴⣾⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣄⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣈⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⣁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⣰⣾⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⣦⡀⠀⠀⠀⠘⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⠇⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠀⠤⠄⣀⡀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⣀⡀⠠⠤⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠠⠄⠀⠀⢰⡋⠉⠙⡶⠀⠀⠠⠤⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠐⠒⠒⢐⣿⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣈⠀⠀⠀⠀⠉⢳⠋⠁⠀⠀⠀⢈⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢿⡆⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣴⠀⠀⠀⣀⠠⠄⠂⠈⢀⡀⠄⠂⠀⠀⠀⠀⣸⠀⠀⠀⠀⠐⠢⠄⡀⠉⠑⠂⠤⢀⡀⠀⠀⢰⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡦⠂⠉⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠸⢤⡴⠛⠧⣤⠞⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠑⠢⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠛⣷⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠙⣷⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⠴⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⢐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⡀⠀⢀⣤⣴⠏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣙⣿⡄⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄⠀⠀⠀⠠⣾⣋⣁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣿⣠⡆⣰⢰⣆⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣀⣆⢰⣀⡆⣹⠟⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠾⠋⠋⠛⠟⠋⠋⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⡆⠀⣀⠀⠀⡀⢈⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣿⢠⡔⠀⠋⠁⠀⠀⠀⠈⠁⠀⣼⠁⢈⠇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠿⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠈⠹⢀⣼⣿⡄⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⡀⠀⠜⠢⠀⠀⢀⠀⠁⠀⠀⣠⠀⠀⢱⡄⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢽⠁⠄⠀⠀⠀⠠⠀⠀⠀⠀⠈⠋⠀⠘⠀⣷⠛⠄⠀⠹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢨⠄⠀⠀⠀⠷⠄⠀⠀⠀⠼⠾⠀⠘⠀⠠⠤⠬⠱⠂⠃⠐⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠸⠡⠀⠀⠒⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⠀⢀⡟⠀⠐⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⣁⠐⡀⠀⡀⣄⠐⠠⣶⣖⣲⡾⠏⠀⠀⠀⢀⣀⠂⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⠂⡀⣤⣿⣿⣷⣤⡬⠃⠀⠺⣿⣿⣿⡿⠛⠒⠀⠀⣼⣿⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⢻⡄⠘⣹⠋⡙⣣⣄⠀⣶⠛⠛⠫⠁⠁⠀⢀⣰⠟⠃⢐⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠹⣆⠀⠀⢡⡐⣿⣾⣧⣀⣤⣴⣦⣶⡿⠟⣉⡶⢿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⣒⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡝⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⣛⣁⠹⠾⠿⠟⠿⠿⠿⠿⠟⠛⠻⢿⣡⢀⡀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉






⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡘
⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠑⠄⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⡀⠀⠈⢆⠀⡔⠁⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠻⡀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢤⡀⠀⠀⠀⠑⢄⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢳⣄⠀⠀⠀⠈⣇⠐⠄⣠⠤⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⡂⢄⠀⠀⠀⠈⢆⠀⠀⠀⢫⠢⡄⠀⠁⠘⡄⠀⠁⠀⡄⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠘⡄⠣⡀⠀⠀⠈⢆⠀⠀⠀⢣⠻⣄⠀⠀⠰⠀⡇⢠⠁⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⡀⠐⡄⠀⠀⣸⡄⠀⠐⠉⡄⠈⢂⢀⣀⡇⠈⠪⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⡇⠀⠀⠸⠱⠀⠀⠀⣱⢖⢜⠀⢀⡦⣀⠀⠀⠑⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⠁⠰⠁⠀⢀⠃⠀⠃⠀⠀⢸⡌⠛⣼⣡⠃⢸⠑⠤⣀⡀⣈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡌⠀⠀⡆⠀⠀⢀⠘⢄⠀⠀⠑⢄⢆⡰⠁⠉⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠘⠀⠀⠀⠇⠤⠤⡎⢢⣈⠑⢤⡤⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠀⠀⢣⣣⡸⠑⠮⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⣻⣦⠤⠶⠶⠶⠒⠒⠒⠲⠶⠶⢤⣴⠋⠁⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⡀⢀⠀⠄⠀⠀⠀⣠⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠸⢾⠟⠀⠀⠀⠈⠛⠞⠃⠀⠀⠀⠸⣶⡟⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⠒⠑⠊⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣼⡁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣴⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠤⣀⠀⠀⣀⡤⢤⣀⢀⠆⠀⠀⠀⠀⠀⠁⠀⠘⣧
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠈⠇⢰⠁⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣠⠴⠓⠦⠴⠃⠘⠦⠴⠞⠦⣄⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⡤⠀⠀⠀⠈⠑⢦⣤⣤⡤⠤⠤⢤⣤⣤⣀⣠⠖⠉⠀⠀⠀⠀⢶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⠠⠒⠉⠀⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⣡⡠⠤⠐⠒⠒⠒⠒⠒⠂⠀⠈⡄⠁⠀⠀⠀⠀⠀⡄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⠀⠀⠀⠐⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠺⢦⠀⠀⠀⠀⠈⠉⢥⠀⠀⣠⠾⠓⠲⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠀⠀⠀⠌⣶⠞⡆⠀⠀⠀⠀⢰⣱⡞⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠵⠀⠀⠀⠀⠫⠿⠿⠃⠀⠀⠀⠀⠈⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠶⠀⣠⠇
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠓⠊⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢋⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡠⠞⡇⢸⠀⠈⢳⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠉
⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣄⣀⣀⣀⣠⡤⣴⠞⠉⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡟⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠠⠂⠄⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⡀⠀⠀⡇⠀⠉⠦⣤⣄⣠⠆⢰⡄⠀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠒⠒⠒⢒⠀⠀⠀⠀⡀⠀⡈⠀⠤⠤⠶⠚⠛⠉⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⢦⡀⠀⠀⢀⣉⡴⠆⢠⡴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⢲⠖⠶⠛⠀⠀⠀⣤⣀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢙⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢹
⠀⠀⠀⠀⠀⠀⠈⡙⠀⠀⠀⠀⠈⠛⠶⠤⣤⣤⣤⣤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟
⠀⠀⠀⠀⠀⠀⠀⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⣷⡼
⠀⠀⠀⠀⠀⠀⠀⢀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁
⠀⠀⢀⣀⣀⣀⣀⣈⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠒⠂⠠⠼⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠾⡤⠀⢀⣄⡀⢤⠤⠤⠤⠤⠤⠴⠶⠒⠊⠁⠈⠉⠉⠉⠻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣎⣀⣀⣠⠤⠤⠤⠶⠒⠒⠒⠒⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠈⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⠀⠀⠀⣀⣠⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠑⠠⠁⠰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣑⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⠀⠀⣼⣿⠟⠉⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣦⣴⣿⣿⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠇⡀⠀⠀⠀⠻⣿⣿⣿⣿⠁⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠈⠿⠿⠛⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠸⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠐⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠛⠫⢍⠀⠈⠓⢄⠀⠀⣠⡠⠤⠖⠲⠶⣀⠀⢀⠴⠊⠁⠈⡩⠛⠛⠢⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⢳⡀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠐⣸⠑⠃⠀⠀⢀⠞⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠠⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠦⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶⢷⣦⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⢸⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⡇⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⢈⡫
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉
⠀⠀⠀⠀⠀⠀⠀⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢣⠁
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠈⠉⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠒⠋⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠡⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡰⠁⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠑⢄⣀⡠⠧⠀⠀⠀⠀⠀⠀⠀⠠⠧⣀⣀⠔⠁⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡎⠀⠀⢘⣄⣀⣀⣀⣀⣀⣀⣀⣀⡎⠀⠀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀⠀⣿⣿⠇⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢾⣿⣿⣿⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⠟
⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣏
⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣾⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣹⣿⣿⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣴⣿⣿⡄⢺⣿⣿⣿⣿⣿⣿⣿⣿⠇⣀⣀⡀⠸⠿⠿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣽⠃⣸⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣽⣿⡆⠀⠀⢻⣿⣿⣿⡅
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⡟⠀⠀⠐⢻⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠿⠏⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⢷⣗⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢫⡀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣟⠿⣿⣧⣄⡀⠀⠒⢹⣷⣯⡉⠡⠖⠀⠀⣠⡜⠀⢠⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣦⣌⣛⣻⣿⣿⣟⣖⣈⣓⣲⣶⣶⣿⣏⣀⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⡿⢟⢿⡿⠟⢋⣉⡁⠀⠀⠀⠀⠀⠀⠀⢙⡍⣻⢿⢻⠛⠀⢾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠉⠀⠸⠚⠇⠁⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢻⣆⠀⠀⠀⠀⠀⢀⡞⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣿⢀⢀⡀⣀⣀⣼⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⣾⠁⡈⢻⠏⠟⢱⠏⠀⢀⢠⣏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢿⡈⠇⢈⢆⢬⣸⠀⣠⡆⡾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠜⠀⠇⠘⠇⢠⣯⣸⠠⠿⠱⢫⠁⡴⠃⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢷⡇⠀⠀⢸⣿⠁⡏⠀⢀⠀⠟⣯⡆⠀⣸⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡍⠁⢡⣼⢰⠻⣿⠰⣿⡄⣿⣖⠁⠛⠠⢴⣿⠃⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠾⠃⢸⣶⡏⠠⢠⢸⢰⡿⣿⣯⣼⣷⠀⠀⣽⡏⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠙⠋⢠⠀⣸⡄⠸⡟⡇⠙⠻⠿⠆⠀⢿⣧⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠀⠀⠐⠄⠀⢰⣿⢿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠩⠖⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠈⢂⠀⠀⠀⠀⣀⠬⠍⠁⠀⠀⠀⠀⣲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⡀⠀⠀⠀⠀⠙⣝⠀⠀⠀⣀⠀⠁⠀⠀⠀⣠⣦⢴⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣶⣦⣄⡀⠀⠉⠀⠀⠉⣀⣀⣴⠾⡟⠫⠉⢓⣭⣭⠕⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⠉⠛⠷⣶⠶⠟⠛⠉⠉⠉⠛⠾⠀⠱⠜⢿⣽⣄⠄⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢠⡆⠀⢠⣭⠀⠀⢰⡄⠀⠀⠀⣨⢟⣨⣷⣾⣏⠱⠞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠐⠷⢿⢿⠆⠇⠀⠞⠰⠿⣷⣴⣶⣴⣾⡾⠟⠁⣸⣿⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢠⣾⣿⠏⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⠘⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠟⡉⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠋⠁⠉⠉⠀⠉⠉⠑⠶⠶⠂⠒⢰⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣏⢹⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢉⡉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡡⠄⠁⠀⠀⠐⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⣆⡠⠤⠤⠐⠒⠒⠒⠠⠤⠀⡉⣰⠉⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠘⠁⣲⠀⠀⢀⡴⠷⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⠃⠀⠰⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⢀⣴⢦⡀⠀⠀⠀⠀⠰⣡⡶⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⡅⠀⠀⠀⠠⣼⣧⡾⠁⠀⠀⠀⠀⠰⣿⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢤⣀⠀⠀⠀⠉
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⢀⡄⠀⢈⡇
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠴⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧⡀
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⡇⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠘⠋⠁⣄⣇⠀⠀⡈⠉⠛⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢻⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠖⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⠶⠶⠶⡶⠛⢻⠉⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡾⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⣰⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠎⠐⠀⠈⠁⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣇⠀⠀⠀⢠⠀⠇⡀⠀⠀⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢦⡀⠀⢸⠀⠀⠐⠢⠐⠀⠐⠀⠰⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⠀⠉⠐⠋⢉⣩⡗⠀⠀⡀⠤⠤⠰⠖⠒⠒⠊⠉⠁⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠳⣄⡀⠀⠀⢀⣡⠟⠀⣤⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢹⡖⠒⠒⠁⠀⠀⠘⢇⡀⠀⠀⢀⣀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠳⠶⠶⠤⠤⠤⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⢸⣴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣸⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⢠⣂⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠽⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⢤⣅⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠋⠉⠙⠒⠒⠒⢶⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠖⠀⠀⢀⣀⣀⣀⡤⠤⠤⠴⠶⠶⠶⠶⠖⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣈⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣶⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣭⣍⢿⡄⠀⠀⠀⢠⣿⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣟⣽⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣴⡆⢹⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣷⣦⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠘⢿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣷⣭⣛⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⡿⠋⠉⣉⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⢸⣿⣿⡇⠀⠸⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⣼⣿⣿⣧⣀⣳⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠋⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠻⠿⢿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠲⠶⠤⢄⡀⠀⠈⠟⠹⠋⠋⠀⠀⠀⠀⠀⠛⠘⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣴⣶⣶⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢋⣭⣭⣥⣭⣍⣉⣩⣭⣭⣭⣭⣭⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣜⡿⠓⢿⣯⣿⣿⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⣿⣭⣿⠸⣿⠇⣿⣭⣿⠸⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣫⣷⠶⣾⣍⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣶⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣶⣶⣬⣭⣭⣭⣥⣴⣶⢸⣿⢰⣶⣬⣭⣭⣭⣭⣭⣶⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠂⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠟⠸⠿⠿⠿⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⣃⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠢⡀⠀⠀⠀⢀⣀⡄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢀⠈⠲⢼⣻⡾⠛⡉⠀⠁⠘⠃⠊⣴⣢⠖⠁⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠈⠓⠓⠀⠸⠀⠀⠀⠀⠀⠀⠉⣣⠄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠻⡀⢦⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠂⣀⠀⣽⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠂⠄⠀⢤⠆⠀⠀⠀⢰⣿⣧⠀⡂⠀⠀⠀⠂⣰⣆⢰⡈⢻⣟⠻⣇
⠀⠀⠀⠀⠀⠀⠀⡲⢃⡀⠀⠀⠰⡞⠀⢀⠀⠀⠙⠛⠛⠂⠀⠀⠀⠀⠘⠻⢿⠀⣅⠈⠹⡬⠙⣖
⠀⠀⠀⠀⢀⣤⣞⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠁⢠⠼⡖
⠀⠀⠀⠀⣩⠋⡁⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡑⠀⠒⢆
⠀⠀⠀⠀⣠⠆⠀⠀⠒⠂⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢈
⠀⠀⠀⠀⠞⣉⠀⣀⠀⠀⠀⠀⠠⢶⣀⣀⠀⠀⠀⠑⢠⣄⣐⠫⣘⢀⣀⣠⠔⠀⠀⠤⠀⠈⠁⠀⠠⢠⣾⠇
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⣴⠉⠠⠂⡖⢺⣿⣿⠿⠿⠿⢿⣟⢿⠋⠃⠀⠀⠀⠀⠀⠀⣀⠰⣯
⠀⠀⠀⠀⠀⠹⠀⠀⢪⣤⣤⣀⠀⠈⡕⠀⢠⡄⣷⠟⠉⠁⠀⠀⠀⠀⠀⠙⡏⠳⣗⣤⣀⣰⡀⠀⠛⢲⣿
⠀⠀⠀⠀⠀⠘⠷⢀⢈⡙⠉⠉⠀⢲⡷⡷⢇⠻⡃⠀⠀⠀⣀⣀⣀⠀⠀⠀⠷⠂⠸⢿⠛⠛⠁⠀⢢⣧⠁
⠁⠄⠀⠀⠀⠀⠀⠸⢿⣷⣶⣤⢀⣤⣷⣿⣄⣙⢂⠀⠀⢼⣿⣿⣿⣷⠀⣄⢙⣧⢰⣆⠙⠀⣦⣴⠀⠁
⠀⠀⠑⠤⠀⠀⠐⠲⢾⣿⣿⣿⣾⣟⣟⣿⢿⡿⠷⠤⣶⣾⣿⣿⣿⡿⠿⢿⣽⣟⣟⣟⣜⣾⣿⣗⣀⡀
⠀⠈⠄⠀⠑⡀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠛⠒⠚⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢋⠠⠒⠉⠀⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⣡⡠⠤⠐⠒⠒⠒⠒⠒⠂⠀⠈⡄⠁⠀⠀⠀⠀⠀⡄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⠀⠀⠀⠐⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠺⢦⠀⠀⠀⠀⠈⠉⢥⠀⠀⣠⠾⠓⠲⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠀⠀⠀⠌⣶⠞⡆⠀⠀⠀⠀⢰⣱⡞⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠵⠀⠀⠀⠀⠫⠿⠿⠃⠀⠀⠀⠀⠈⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠶⠀⣠⠇
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠓⠊⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢋⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡠⠞⡇⢸⠀⠈⢳⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠉
⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣄⣀⣀⣀⣠⡤⣴⠞⠉⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡟⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠠⠂⠄⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⡀⠀⠀⡇⠀⠉⠦⣤⣄⣠⠆⢰⡄⠀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠒⠒⠒⢒⠀⠀⠀⠀⡀⠀⡈⠀⠤⠤⠶⠚⠛⠉⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⢦⡀⠀⠀⢀⣉⡴⠆⢠⡴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⢲⠖⠶⠛⠀⠀⠀⣤⣀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢙⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢹
⠀⠀⠀⠀⠀⠀⠈⡙⠀⠀⠀⠀⠈⠛⠶⠤⣤⣤⣤⣤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟
⠀⠀⠀⠀⠀⠀⠀⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⣷⡼
⠀⠀⠀⠀⠀⠀⠀⢀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁
⠀⠀⢀⣀⣀⣀⣀⣈⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠒⠂⠠⠼⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠾⡤⠀⢀⣄⡀⢤⠤⠤⠤⠤⠤⠴⠶⠒⠊⠁⠈⠉⠉⠉⠻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣎⣀⣀⣠⠤⠤⠤⠶⠒⠒⠒⠒⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣴⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢻⣿⠀⠛⠛⠛⠙⠛⠛⠿⠛⠁⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⠴⠶⠋⠁⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⣸⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠻⣿⣉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⢀⡟⠀⠘⢷⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣠⠶⠛⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠉⠛⢦⣀
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠙⠶⢶⣞⡉⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⢀⣠⡤⠿⢿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⢹⡛⣿⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶
⢠⠞⠉⡝⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠈⡇⠘⣇⠀⢹⡆⠀⠀⣠⣄⠀⠀⠀⠀⠀⠉⠉⠁
⡇⠀⠀⣏⠀⠀⠀⠀⢳⡀⠙⠿⣿⣿⣿⣿⣿⣿⡄⠀⡇⠀⢹⡄⢸⠃⠀⣴⠃⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢧⠀⠀⢿⠀⠀⠀⠀⠀⠳⣄⠀⠹⣿⣿⣿⣿⣿⡇⢀⡇⠀⠀⢳⣼⠀⠀⡇⠀⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⢸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⢾⣿⣿⣿⣿⣿⣡⠞⠀⠀⠀⠘⣏⠀⢰⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢰⡇
⠀⢹⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏⣰⠏⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾
⠀⠈⣧⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠞⠁⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠀⠀⡴⢇⣹⣦⠶⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡾⢁⡼⠋⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⡆⠘⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠛⠓⠚⠚⠛⠛⠋⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠂⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠖⠊⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⣀⣠⣤⠤⠶⠶⠖⠚⠛⠛⠉⠉⠉⣽⣄⡴⠃⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⣨⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣿⣦⡀⠀⠀⠀⠀⠀⣠⠞⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠳⣄⡀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⠓⠶⢶⡶⠛⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣈⡽⠛⢻⡛⠋⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣤⠞⠁⠀⠀⠈⣷
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡾⠁⠀⠀⠀⠀⣀⡼⠗⠋⠉⠉⠉⠁⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⠁⠀⠀⠀⣰⢟⣡⠤⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢴⣞⣉⢉⣁⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠤⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡾⡛⢷⣄⣄⢀⠀⣿⣆⣄⢀⠀⣤⣶⡀⠀⣀⣤⣴⠣⠏⣵⡿⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠴⠀⠙⡃⢨⣿⡿⠙⣿⠾⣇⡟⠃⠘⠋⠙⠿⣿⡇⢼⢹⣇⡄⠛⠃⠈⠃⡞⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⡁⠀⢾⣿⢿⡷⣇⢿⡆⠸⠀⢠⠐⢔⡦⣀⠀⠀⠀⢀⣽⣠⠆⠀⢠⣤⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣅⠸⣿⣿⣷⡁⠀⢀⣷⢜⣰⢿⡄⣿⡁⡇⠀⠀⢀⡴⣻⣿⡆⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠂⣿⠉⣣⣬⡆⠚⠓⠚⢽⠚⠃⣿⡇⠠⢸⣤⣌⠉⠀⣿⠖⢠⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣽⣟⠁⣼⣧⣼⠃⡄⢀⣷⠀⢰⡾⠁⢰⠄⢸⣡⣘⣷⠀⣦⡴⣪⡿⠓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠷⣆⣸⣿⡿⢋⢻⡧⢤⣩⣀⠀⢰⠗⠙⣵⡘⢿⣿⣻⡇⢀⡴⠆⣀⣀⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠛⠁⠀⠀⠲⣽⣦⡰⡏⠀⠀⢸⡇⢻⣠⡄⠀⠀⠉⠛⢫⡭⠽⣢⠤⠖⠛⠁⠈⠁⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠅⠀⢀⣥⣿⣷⣼⡟⠛⠢⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠋⣤⣶⠶⣶⣶⣦⡀⠀⠀⠘⣥⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠄⠀⠐⣻⠟⣿⡛⠉⠁⠈⠀⠀⠀⠀⠉⡟⠁⡀⠀⠀⠀⠀⠈⣈⠉⣉⡻⠯⢼⠿⠖⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠁⠈⠁⢀⡀⠀⠀⠀⠀⠀⠈⠀⣷⡈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠓⠍⠀⠀⠀⠀⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠘⢳⠹⠀⠀⠀⠀⠀⢀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⢼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⠀⠀⠀⠀⠀⠀⠐⠃⠶⣶⠄⠰⠶⠿⠷⣦⠄⢰⣠⡞⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣦⠙⠿⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣱⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣴⣶⡶⠘⠉⠛⢷⣶⣤⡀⠀⠀⠀⠀⣀⣴⣿⣿⣟⣝⡚⡀⢀⡿⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣼⣿⣾⣿⠿⣿⣿⣿⣧⣤⣉⠉⠁⠈⠀⢀⠀⠂⠀⠇⠁⢿⠁⢀⣴⣾⣿⠛⠿⠺⢁⠸⠎⠑⠾⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⢻⣿⣵⣟⣏⡤⣛⣿⣿⣿⣿⣧⡀⠀⠀⠈⢳⡄⠀⠀⢀⣤⣾⡿⠟⠉⢀⠀⢦⡼⠋⢩⣈⠂⠓⢀⣳⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠉⢱⣿⣯⣴⣶⣿⠛⣛⣿⣿⣿⣿⡓⢄⡀⣼⡏⠀⠶⢿⣽⠳⢀⡀⠒⠊⠋⠓⢀⣀⡐⠈⠀⠀⣠⠿⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣵⠀⠠⡾⣿⣿⣵⣶⣿⣿⣷⠀⢸⡍⠀⠀⣸⣿⣏⠀⠘⣥⠀⢰⣭⣁⡲⣤⡚⣬⣧⣴⣛⠀⠀⣨⣥⣄⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣎⢿⣦⡀⠀⢫⣿⣿⡿⣿⣿⣿⣄⠈⢳⣼⣷⢿⣿⣿⣶⣰⠏⠀⣸⣿⣿⣽⣷⣾⣾⣿⠿⠛⢡⣤⣬⠿⡽⠖⢌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢃⡈⢙⢦⣆⠀⠀⠀⠚⠛⠿⠛⠛⠛⠘⠛⠉⠀⣿⡈⠉⠛⠘⠿⠟⠻⠿⢿⠿⠿⠋⠉⣀⣴⣾⣿⣿⡧⠒⣹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⢫⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢱⣤⢠⠀⣿⣧⠀⣤⣼⣆⠀⠀⠀⠀⠀⠠⣴⣶⣶⣿⣿⣿⣟⢺⣿⣽⠮
⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⠄⢀⣴⣶⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⢿⣿⣇⢻⡏⠸⠿⢻⣿⠀⠀⠀⡀⢰⣶⣿⣿⣿⣿⠿⣶⣦⣁⣻⡻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢀⣽⢾⣿⠟⢛⣿⣦⡀⠀⠀⠈⢻⠾⢠⣧⣠⠈⢸⡟⢀⠀⢰⣿⡼⣿⠿⠿⣧⣤⡭⠀⠈⠒⠛⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠚⠿⠀⠈⠀⠻⠛⣾⣄⣷⣄⠀⢸⣯⠘⢀⣠⣶⣿⡀⡿⠋⡠⢈⠒⠻⠓⠋⠀⠀⠀⠀⣰⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣄⠀⠀⠀⠀⠀⠀⠐⡀⠘⠛⣿⣯⢳⣼⣏⣴⣿⡿⠛⠋⢈⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⢠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣦⣄⣀⣀⣀⣀⣹⣷⣄⣨⣉⣻⣿⣿⣿⣉⣁⣄⣀⣎⢀⡀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⡀⠀⡀⡀⡠⠀⢐⡂⠀⡴⠠⢂⠄⢠⢄⡀⠀⡀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⡄⠀⢙⠊⠉⠀⠁⠀⠁⠀⠀⠀⠈⠈⠑⠉⣿⡁⣠⣶⠟⠉⠁⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⣿⣿⡧⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠘⢿⣷⠖⠀⠀⢀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢰⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣻⣦⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣻⣿⡟⠀⠀⠀⠀⠀⢠⣾⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢦⡀⠀⠀⠘⢻⣦⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⠀⠀⠀⠀⠀⢺⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣬⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠁⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⡀⠐⡂⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠓⠦⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢢⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠹⣧⣏⣴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠐⠒⠶⠶⠂⠈⠀⠀⠀⠀⡀⠀⠀⢠⣠⣼⡇⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⢿⠛⢦⣦⣀⣀⡀⢀⣠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⢠⣆⢀⣴⡾⡿⠙⠉⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠀⠀⠀⠁⢦⡌⠉⠙⠉⠉⠉⠉⠛⢿⣶⠿⠟⠿⠻⠿⣶⣞⡛⠃⠉⠙⠉⠁⣠⠃⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡧⠀⠀⠀⠀⠌⠳⣄⣀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⣀⡴⠃⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠈⠛⠓⠶⢶⣿⡀⡄⢦⡧⠀⠀⠀⠀⢸⢃⠀⠀⢀⠟⠉⠀⠀⢸⠇⠠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠘⠧⢴⠴⠎⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣶⣤⣤⠴⠾⠳⠦⣄⣀⣀⣤⣤⣤⣤⣾⣟⠛⠛⠉⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡿⠗⠀⠀⠀⢸⣿⡿⠛⠛⠛⠛⠛⠿⣀⠀⢀⢠⢈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠠⣇⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⠆⠀⠀⣠⣤⣤⣶⣶⣦⣦⣤⣄⣀⣀⡀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⡀⠀⠀⢿⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⡿
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⠀⠀⠘⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⠇
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⡋
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣾⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣽⣿⣧
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢠⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⡀⠛⠛⣿⣿⣿⡿
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⡿⠃⣼⣿⣿⣿⣿⣿⣿⡏⣿⣷⣿⣿⠀⠀⢸⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⠟⠀⠀⠀⢿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⢿⣿⣿⣿⣿⠿⡅⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣯⣻⢿⣶⣄⣀⣉⣸⠿⣯⠁⠚⠀⣀⣴⠂⢀⣴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣮⣭⣽⣯⣭⣥⣬⣭⣿⣿⣿⣧⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⡿⠿⠟⠉⠉⠉⠉⠛⠛⢿⠿⣿⣿⣿⠛⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡞⠉⠀⠏⠠⡴⡞⠂⠀⠀⠀⠀⠀⠀⠞⡵⠋⢳⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⢶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣛⠀⣹⡆⣄⣄⣤⢤⡤⢀⠠⣾⡟⣠⣄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿⣧⢿⣡⣿⣬⡡⣮⡀⢁⣤⠙⠁⢻⣿⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⣠⣁⡻⠋⠀⣼⣿⡇⠈⠑⢀⢀⢸⡿⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢙⡥⡆⢠⠿⠻⢇⠀⡤⠄⠘⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⣼⣿⢇⣈⡘⠁⣸⡀⢿⣿⡀⠈⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⣼⡋⠃⠈⠛⠁⠀⠃⠃⠀⠙⢿⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢄⣾⣷⠀⠀⠀⠰⣄⢀⡀⠀⠀⠀⢻⠿⠧⢀⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣯⣤⡄⡀⡀⠀⠀⠈⠻⢋⠀⠀⠀⠀⣈⢍⣰⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡡⢛⡽⣶⣯⣄⣀⡀⠲⠶⠀⠀⡰⣦⡉⣐⠟⠍⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆⡰⠙⠛⠻⠿⣿⣿⣿⣿⡿⠟⢟⠉⢆⠀⠰⢦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢡⣇⡀⠀⠀⢀⣄⠀⢀⠀⣀⠀⠀⠌⠀⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⢈⡈⠈⠙⠷⢶⣾⣿⠀⠇⠀⠈⠀⡀⢀⡆⡀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠘⠿⣷⣦⣄⣀⢸⠇⠀⠀⠁⣸⡧⠡⠌⠀⠈⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠠⠀⠀⠀⠀⠉⠛⢿⡆⠀⢼⡷⠛⠁⠀⠀⠀⠀⢀⣼⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠿⣿⣷⣄⠀⠀⠠⣄⠀⠀⠻⣰⡟⠀⠀⣀⠀⠀⣀⣴⡿⠁⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣟⠀⠀⠻⣿⣿⣶⣶⣿⣤⣄⣄⢹⣼⣴⣼⣿⣶⣿⠟⠋⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢁⡀⠀⠀⠈⠛⠟⡿⢿⡿⠿⠟⠘⠻⠛⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⡿⠛⠈⢭⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢐⣿⣯⣶⠯⢾⣿⡃⠃⠀⠢⠌⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠶⣿⢿⣿⢯⣿⣷⠈⠉⠀⠀⠂⠠⠄⠀⠀⠀⠈⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⣰⠶⠚⠀⠁⠀⠀⠀⠠⣀⠀⣸⣏⣸⣿⣏⠀⠀⠀⠀⠀⠀⣠⣤⣔⣄⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠀⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣠⣿⣯⠾⠁⢄⠀⠀⠐⠁⠸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠃⠀⠀⢀⠭⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠃⠀⠠⠀⠀⠁⠀⠀⠐⠈⠋⠀⠀⡀⠀⠀⠀⠀⠑⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣤⣤⣠⡄⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⡁⠿⣾⣧⣄⣀⡀⠐⢠⣀⣀⣀⣀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠉⠛⠛⣿⣷⣿⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣁⢀⠛⠿⣏⣀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣔⡦⢴⢿⣟⠃⣀⡀⠈⠩⠜⠋
⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⢀⡜⡻⠉⠉⠀⠀⣆
⠀⠉⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠕⠿⠛⠲⣜⡧⠔
⠲⠀⠀⠘⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠊⠀⡀⠀⢀⠂⡀
⣶⣶⣶⣶⣶⣶⣶⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣯⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣯⣿⣿⣿⣿

⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠐⢶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠂⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣄⣀⣴⣿⠟⠉⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠋⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⢀⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣶⣄⡀⣠⣾⣿⠏
⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣤⣴⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠘⠗⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠟⠁⠁⠙⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠹⠟⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠟⡿⢿⣿⣿⣿⣿⣷⣶⢾⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⣿⣿⣿⣿⣿⡾⠟⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⡟⢻⡿⠃⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⢙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠺⠟⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠁⠉⠀⠀⠀⡀⠈⢹⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⡗⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡀⢀⣠⣿⣿⣿⣿⡇⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⡿⠷⣿⠛⠛⠿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⣿⣻⡛⠛⣛⣟⠛⢛⣻⢻⣛⠛⠛⢛⡛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣟⠋⢀⣴⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠛⠿⠟⠀⣼⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣆⣶⢲⡯⠤⣠⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠲⢄⢠⡄⠼⠁⠻⠀⠀⠀⠈⠀⠚⠳⢦⣀⡤⠒⠒⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠖⠛⢷⡄⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡋⠓⢢⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢐⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡜⠁⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣶⡶⡄⠀⠈⠑⢄⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠰⠄⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠴⠧⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢱⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠑⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠋⠈⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠙⠢⠷⠦⠽⠶⠒⠛⠶⠒⠶⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢠⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠘⢄⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡴⠃⢀⣴⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠑⠦⣀⡙⣒⠦⠗⠃⠀⠀⠀⠀⠀⠀⠑⠧⢴⣔⣉⣀⡴⠞⣛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠘⣅⣄⣀⡝⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣇⣀⣀⡸⠑⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡠⠐⠂⠉⠀⠀⠀⠉⠒⠄⡀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠀⠀⠀⠁⠀⠀⠀⠠⠄⠒⠀⠀⠀⠈⠣⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⣠⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠘⢠⠀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⠀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⠀⡖⠀⡜⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⢀⣤⡄⠀⠈⢦⡀⠀⠀⠀⠁⠄⠀⠀⢀⠞⠀⢀⠀⠀⠀⠀⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢀⠌⠀⠀⠑⢄⠀⠉⠲⠀⠀⠀⠀⠀⠀⠈⠀⠠⢃⠄⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠈⠀⠀⠚⠀⠈⠂⡠⠃⠀⠀⠀⠀⠀⢀⠔⡐⢁⠊⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠘⡀⢰⠀⠒⠈⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠡⡠⠀⠀⢀⠊⠦⠀⠀⠀⠀⠀⢀⠄⡇⠈⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠇⢇⠀⠀⠓⠤⠀⠀⠀⠀⠀⠀⢰⡷⠒⣄⠞⠃⠀⠳⡀⠀⠀⠀⢀⢘⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠱⡀⠀⠀⠀⠀⡠⠔⠒⠰⢝⡾⢷⠞⠢⡀⢀⠜⠁⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠑⢶⠲⣴⠂⠀⠀⠀⠀⠔⠛⠁⠀⠀⢘⡁⢀⡀⠀⠞⠉⢫⣠⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠼⠀⢧⣄⠀⠀⡀⠀⠀⠀⠀⢀⠴⠛⠒⠒⠉⠙⠢⠀⢸⢀⡇⠀⠀⠀⠀⢀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣆⢃⢳⠉⠛⡒⠒⠒⡞⠁⠀⠀⠀⠀⠀⠀⣀⣠⣣⠞⠀⠀⠀⠀⠀⢸⡜⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢪⠂⠐⡄⠣⡠⠊⢇⠀⠀⠀⠘⠛⢞⠻⡇⠁⠀⠀⠀⠀⠀⠀⠀⢹⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢱⠀⠀⣀⣀⠀⠀⠀⣀⠤⠛⠀⠐⢄⠀⠀⠀⠀⠀⠎⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠀⠈⢻⠹⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠲⣖⣁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠤⠤⠤⠤⠤⠒⠒⠚⠉⠈⠑⠂⣴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿