Watering Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠀⠒⠢⢤⡂⡀
⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠀⠐⠐⠂⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⣠⡴⢛⢇⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠄⠀⠀⠀⠀⠀⠠⢀⠐⠄⠀⠀⠀⠀⠂⠠⠄⠠⠤⠤⢂⡀⠀⠀⠈⡄⢀⣔⣽⡻⠟⡁⠂⠂⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠤⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣷⠟⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⠊⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠱⠃⢀⣀⣠⠵⠄⠀⠀⠀⠀⠄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⠀⠀⠀⠀⠀⢀⠌⠐⢀⠀⠀⠀⠀⢀⢄⠂⠐⢢⡥⠴⠒⠊⠉⠭⠀⠀⠀⠀⠐⠄⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠤⠄⠊⠁⠀⠀⠀⠀⠀⣀⠚⠄⠑⢝⣶⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠂⠀⠀⠀⢀⠁⠐⡈⠐⢠⡍⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠠⢀⡀⠀⢀⢀⠠⠀⠄⠀⠀⠀⠀⠀⠄⠁⣐⣢⠄⠃⠆⡀⠀⠀⠀⠠⠈⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠒⠒⠐⠂⠐⠀⠐⠐⠊⠂⠀⠀⠀⠐⠐⢾⡿⢢⠘⢐⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢹⡀⠄⢳⡿⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⢰⠸⣇⡴⠊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠈⡙⢍⢀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠧⢸⠈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⣀⠀⠀⣀⣀⢀⠀⠀⠸⢶⠀⣜⠀⢠⡿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠒⡄⠄⢀⠈⠀⣀⠀⠀⢀⠉⠈⡈⠁⠀⠰⠟⠰⡯⠄⠀⠤⠄⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠁⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠙⠘⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠉⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⣛⣛⣛⣛⡓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡵⠞⠋⠉⠉⠉⠉⠙⠛⠶⣭⡛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣻⡆⡀⠀⠀⠀⠹⣦⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣡⠞⣩⠿⣧⡆⠀⠀⠀⠘⣧⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡏⠀⠀⠀⠀⠀⠀⢀⣴⠏⣡⠞⣡⠞⣡⡾⠋⠻⣦⡀⠀⠀⠸⣇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢀⡴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠈⠻⢦⡀⠀⢿⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣇⠀⠀⢀⣴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡸⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⣀⣴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⡞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣩⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣛⡛⠶⠶⠶⢦⣤⣤⣤⣀⣈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡴⠟⠁⠉⠙⠛⠶⢦⣤⣀⡀⠀⠀⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣤⣀⡀⠈⠻⣦⡀⠀⠀⠀⢀⣴⢏⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠾⣿⣦⣀⣴⢟⣵⠟⣡⡾⢋⡴⠋
⠀⠀⢸⣟⣯⡉⣿⢶⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⡟⣡⡾⢋⡴⠋
⠀⠀⠀⢻⡍⠙⢿⣀⣿⠀⠀⣀⣴⠞⣋⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣋⡴⠋
⠀⠀⠀⠀⠙⠶⠶⠟⢧⣿⢰⡏⣿⡾⠛⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⡿⣯⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⣴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠙⠳⣶⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠞⠋
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣤⣬⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠤⢿⣋⣛⣛⣛⣙⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣈⣍⡭⠭⠽⣴⣒⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠀⠀⢀⢔⣒⡲⡤⢄⣀⠀⠀⠀⠀⠘⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠇⠀⠀⣰⣷⣿⣿⣗⠇⠀⠉⠉⠲⢦⣤⣀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⢰⢹⣿⣿⣿⢫⠀⠀⠀⠀⠀⠀⠁⠐⠳⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢇⠀⡇⠀⠈⠙⢫⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢄⣀⡀⡰⡣⡢⣪⡗⡐⡄⠄⡄⡀⡀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠮⣥⣮⡪⠢⣾⡮⡪⢊⢎⢌⢔⠜⡔⣰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠛⠺⣶⣵⣕⡫⡪⣪⡾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣀⠔⣋⡵⠛⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡾⢊⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠠⠤⢤⢚⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⣷⠑⠔⣿⡇⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⠐⡀⢀⠚⢦⡊⢎⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢁⠀⢀⠁⠃⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠈⠄⠘
⠀⠀⠀⠀⠀⠀⠈⡀⠀⡁⡄⠠⠀⢈⠀⢀⠃⢈
⠀⠀⠀⠀⠀⠐⢀⠀⢀⢀⠀⠀⠄⢈⠀⠠⢁⠀⠄
⠀⠀⠀⠀⡀⠄⡈⠀⢀⠠⠀⠀⠄⢠⠀⠀⢈⠀⠄⠀⠀⢠⡆
⠀⠀⢦⣼⣅⠂⡠⣀⣀⢠⠀⣀⣢⡀⣸⣷⡦⢀⠀⢀⠠⣿⢟⠇
⢀⠔⠲⢋⣤⣀⣀⣤⡤⢀⡭⢧⣧⣄⣠⣭⡅⢀⣀⣁⡁⠙⠓⠴⢒⠠⡀⣀⢀⢀⢄⠀⡠⡠⢄⢄⠠⡠⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠏⢁⠌⡁⠀⠀⠀⠀⡠⠂⢁⡤⠔⠒⠒⠢⠤⣉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡂⢉⢸⠀⠀⣀⠠⣁⠔⠀⠀⠀⢀⠊⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠤⢀⠦⣼⠻⠇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡀⣄⢀⠀⠀⠀⠀⠀⠂⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠄⢀⠑⢿⠍⠐⠋⣷⢯⠀⠀⠀⠀⠐⠀⠈⡄⢀⢴⢿⡿⠀⠀⠈⠉⠐⠢⢄⣀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠫⡁⠫⣔⣵⣞⠿⣯⠆⠀⠱⠭⠢⡀⠀⠀⢟⢆⠛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣄⠀⡀
⠀⠀⠀⡠⠐⣄⠀⠄⡀⠙⢻⢩⢹⠞⡿⠀⠀⣅⣠⣤⡇⠀⢠⢤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⠁
⠀⠀⢊⡀⢺⠗⠃⣂⠁⠀⠸⣌⣣⢀⠂⠀⢻⣔⣿⠙⠂⠀⠈⠓⢦⡀⠀⠀⠂⠂⠀⠄⡀⡀⠀⠀⠀⡀⠈
⠀⠨⡞⠀⢠⢷⡾⡟⢻⢂⡌⠀⠙⣧⠀⣶⣼⣛⡟⠋⠀⠀⠀⠀⠀⠈⡿⢧⡀⢀⣀⡀⠊⠀⠀⠀⡹⡝
⠀⠀⠀⠀⠈⠈⠹⣥⢾⣷⡿⠀⠀⠙⡾⠁⠀⣂⣼⡄⣶⠆⠀⠀⠀⢰⠃⠀⡙⠁⠀⢈⣵⣔⣡⡺⠊
⠀⠀⠀⠀⠀⠀⠀⠘⣉⣉⣻⡄⠀⢼⠀⠀⠰⣯⣟⣿⠃⠸⠍⠁⢀⡏⡠⠊⢀⡠⠖⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⡄⣠⠾⠥⠚⠉⠘⠒⠀⠀⣼⠋⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⢠⣧⠏⠀⠀⠀⠀⠀⠀⠀⢊⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣳⢰⡗⠃⠀⣠⡤⠤⢔⣣⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠊⠀⠀⠀⢄⠀⠑⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡰⠈⠒⠤⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣸⣋⣥
⠀⠀⠀⠀⠀⠀⠀⠠⡔⠐⠀⠀⢠⡄⣹⢛⡼⡁⠇⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠈⠉⡭⠹⠃⠒⠀⡩⠉⠿⠛⢑⠀⢠⠙⠋⠃⠊⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠡⡯⣞
⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡤⢸⣷⡿⣣⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡛⡉⠉⠀⠸⣿⣿⣿⣟⣰⢚⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣶⣯⣿⣿⣷⣯⣬⣽⣿⣿⣿⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣟⢿⡛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣁⢶⠊⠜⠉⡉⢹⠽⣯⠻⣽⣳⣿⣿⣿⣿⡅⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠙⢦⡀⠀⠀⠀⠀⠀⠀⣿⠿⣼⣥⣬⣥⣬⣉⣌⣩⣭⣬⣿⣿⣷⢿⣟⣿⡇⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢦⡀⠀⠀⠀⠀⣿⣿⣛⠷⠶⠶⢶⠿⠶⢶⠶⡶⢾⣿⣿⣯⣿⣿⣧⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠙⢷⡀⠀⠀⣿⣿⣽⣛⣛⠓⠾⡟⡿⣟⢛⣻⣻⣯⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⢿⡷⢯⣭⣍⣙⣛⣛⣛⣛⣿⣯⣿⣿⡿⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠙⢿⣿⠶⠶⢬⣭⣭⣭⣽⣽⣯⣿⣶⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⣿⣿⣟⣛⡶⠶⠶⠶⠶⠶⣾⣟⣻⣽⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣿⡶⢿⣭⣽⣛⣛⣛⣛⣛⣯⣯⡿⣶⣟⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣝⣓⣒⣶⠾⠯⣭⡽⠷⠶⡷⣟⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠩⠟⠻⠛⢛⣻⢛⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⠤⢼⣭⣤⣾⡿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦⡀⣰⣿⠏⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠛⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣤⣀
⠀⡸⠀⠈⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣡⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤⣄⠈⠙⢷⡀
⠀⡇⠀⠀⢀⣀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷
⠀⡇⠀⣤⣿⠿⠛⠢⠙⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣳⣿⠇⠀⠄⠐⠂⠀⠈⠀⣀⣤⣤⣤⣦⡔⢢⣤⠉⠒⢄⠀⠀⠘⣧⠀⣿
⠀⣿⣴⡇⡩⠒⠋⠓⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠿⢧⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠁⠀⠀⠈⠁⠀⣸⠇⠀⣿
⠀⠸⠟⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠈⠑⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⢤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠀⠂⠀⠀⠀⠀⠀⣰⠃⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠔⠂⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠶⠖⠒⠒⠚⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠐⠢⠤⠤⣀⣀⣀⣀⣀⠀⠠⠤⠤⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡛⠉⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠋⠀⠙⢿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠴⠶⠒⠒⠒⣲⣶⡄⠀⢀⣠⣾⣛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠀⣀⣀⣤⣤⠶⠾⠿⣯⣤⠿⣶⣿⡿⠋⠉⢳⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣴⡶⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠦⣤⣤⣄⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠘⣿⠃⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠈⠉⠉⠙⠛⠛⠶⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⣈⡙⠁⢀⡀⠀⣤⣶⣾⣿⡆⠀⠀⠀⠀⢀⡿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢛⠁⠈⠃⢀⣀⠉⠙⠉⠁⠀⠀⠀⠀⠸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⢰⣶⡌⠻⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⣠⡄⠀⠸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⢠⡿⣷⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⣦⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣼⠇
⠀⠀⣀⣤⣤⣄⣀⣸⡏⠀⢀⣾⠏
⣠⡾⠋⠉⠀⠉⣻⣿⣷⡾⠟⠁
⠙⠛⠷⠶⠶⠿⠛⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟
⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣠⡞⢳⡾⣤⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣴⣾⠿⠛⠛⠻⣿⣶⡀
⠀⠀⠀⠀⣼⣙⣿⣿⡋⣻⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡻⠭⢭⣛⣛⣛⣛⣛⣛⣫⣭⢷⣿⡟⠁⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⣼⣏⣿⣧⣼⡟⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠚⠿⠁⠒⠒⠒⠒⠒⠒⠊⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⣿⣹⠷⣾⣛⣿⣟⡭⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠘⠻⠷⠟⠋⠀⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠈⡇⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢸⠀⠀⠸⣦⣀⠀⠀⠀⠀⣠⡶⠋⡇⠀⠀⢷⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⢿⣦⡀⠀⠀⡼⠀⠀⠰⡜⠮⣑⢆⠀⣜⡟⠀⢠⠃⠀⠀⢸⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠉⠪⡷⣄⡇⠀⠀⠀⠙⢦⣈⠻⣾⡟⣀⠴⠃⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠀⠀⠀⠀⠀⠀⢿⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡟⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡣⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⣤⣤⣤⣀⣀⣠⣤⣤⡤⠤⠶⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⠭⠙⢋⠭⠿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⠤⠕⠀⠀⠀⠀⠀⢀⠀⠀⢠⠜⡖⠂⢱⢾⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠛⠋⠀⠀⠃⠋⢃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠁⣀⠀⢀⡉⠀⠈⠣⠢⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠫⢊⠃⠹⠉⠞⡑⢗⠠⡀⠀⠀⠀⠀⢀⢄⡻⢈⠏⠡⠉⠏⠘⣗⠄⠀⠀⠀⠀⠀⠲⢈⠣⠤⣄⠛⣂⡁⣉⡉⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠂⠆⠄⠠⠴⠐⠐⠈⠈⠀⠀⠀⠀⠉⠑⠀⠀⠤⠀⠦⠌⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠂⠄⠀⠐⠁⠈⠂⠀⠀⠀⠀⠀⠖⠂⠴⢴⠦⢶⠴⠆⠒⠂⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠈⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣀⠀⣉⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⢰⣆⣶⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠿⡥⢼
⠀⠀⠀⠀⠀⠀⠀⢨⠅⠰⠤⠂⠄⡲⠤⠀⠭⠭⠅⠀⠀⠀⠀⠠⢤⢤⣀⣈⣁⣍⡀⣠⢤⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣸⣇⣸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⢒⠐⠖⠘⠒⠘⠐⣒⡀⠀⠀⠀⠠⣾⢟⡽⠁⡏⢸⠈⡇⠹⣝⢿⡦⠀⠀⠀⠀⠀⠐⠛⡐⠖⣂⠻⢎⡺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠳⠐⠘⠖⠠⠙⠆⠀⠒⠀⠀⠀⠀⠀⠐⠁⠁⠈⠠⠈⠂⠈⠀⠈⠐⠀⠀⠀⠀⠀⣀⣴⢀⢱⣗⣉⣰⡌⢉⣦⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡇⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡋⠀⠀⢙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠄⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢺⠒⡄⠐⣿⠇⠀⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⢶⡇⢵⠇⠸⣹⠱⡀⣆⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠖⠀⠈⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⠀⠀⣎⡆⠀⠀⢳⠆⠀⠀⠀⠀⠀⠀⣆⠙⡋⡘⠋⢈⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠈⠋⠃⠈⠁⠂⠘⠁⠀⠒



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠈⠙⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠆⠀⠀⠀⠀⠀⠈⢆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠀⠀⠀⠀⠈⠆⠣
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⣿⣿⠶⠿⢿⣿⣿⣿⣿⣶⣷⠀⣦⣤⣄⡀⠀⠠⠤⣄⣀
⠀⠀⠀⠀⠀⣠⡾⢟⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠁⠀⠀⠀⠐⠀⠀⠈⠉⠛⠿⢿⣿⡀⣿⣿⣿⣿⣿⡖⠀⠀⠉⡷⡄
⠀⠀⠀⢀⣼⣯⣷⢟⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠻⢿⣟⢿⠁⠀⠀⠀⡄⣿
⠀⠀⠀⣼⣟⣯⠷⣿⣬⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⠉⢉⡙⠻⠤⠈⠁⠘⠛⠛⠻⠿⠿⠿⠦⢽⠋⠉⠉⠹⡏⢸⠀⠀⠀⢠⠀⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠈⢢⡀⠄⢐⣂⣀⣠⣤⣴⣶⣶⠾⡯⠧⢴⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣷⢸⠀⠀⣠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠻⣛⠉⠉⠉⠀⠀⠀⠀⠀⢘⠲⢼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⢾⠀⡰⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢉⠑⢻⣥⣉⡉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⢉⣀⡠⠴⠿⡾⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠳⢤⡀⠀⠀⠀⢸⠙⢻⠧⣄⠉⠉⠁⠒⠒⠒⠒⠒⠒⠚⠉⠉⢉⣀⣤⣴⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠘⠦⣄⠀⢸⠀⡼⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠒⠈⠉⠁⠀⠀⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠺⣝⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠈⠛⢿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠈⠉⠃⠀⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⣰⠚⠉⠙⢢⡀⠀⣰⠄
⠀⠀⠀⠀⠀⣄⣤⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠛⣶⠒⢲⡞⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⢠⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⢀⠀⠀⠀⢀⣀⣿⣀⣸⣇⣀⠀⠀⠀⢀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⢸⠉⠉⠉⠉⠉⢹⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠓⠶⣄⠀⠀⣠⠴⠚⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⡟⠓⢦⡀⠀⠀⣠⠖⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⢧⡴⠃⠀⣠⠇⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠹⡄⠀⠙⣆⡼⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣸⣇⡤⠞⠁⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠙⠲⢤⣸⣧⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⢰⡖⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂



⡏⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⣀⡀⢀⠀⢀⣀⠀⡀⠀⣀⡀⠀⣀⠀⣀⡀⢀⡀⠀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⡇⢸⠀⡌⢧⢸⠾⡁⡇⠀⠇⠀⠀⠣⡄⢸⠁⡷⢼⢸⠀⢸⢸⢮⠀⡇
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣿⣾⣶⣷⣾⣶⣶⣾⣾⣿⣶⣿⣶⣷⣶⣶⣾⣷⣾⣶⣷⣾⣶⣿⣷⣾⣶⣷⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⢿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣠⡅⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠋⠐⢉⠉⠉⠀⠀⠈⠻⣿⠉⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠹⣄⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⡹⢻⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠉⠀⠀⠈⠓⣤⣀⣀⠀⠀⣀⣀⣴⡚⠁⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⣠⠴⠒⠉⠁⣸⣭⠽⠛⠉⠁⠀⠈⢦⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣾⡉⠀⣀⣀⡤⢯⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣴⣏⢷⡫⠵⠚⠛⠉⢁⣀⣀⣸⣆⣀⣠⠤⠶⠒⠚⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⡽⣭⡽⣀⣴⣶⣒⣿⡉⠉⡽⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⡿⠧⠋⠉⠁⢀⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠉⠉⠙⠓⣲⠶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣳⡤⠴⠒⠋⠁⠀⠀⠀⠀⠹⣖⠒⠒⠒⢒⣖⡒⠒⢖⣒⠖⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⣄⠀⠀⠀⠀⠈⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠘⠴⠃⠀⠀⣀⣄⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⢶⣄⣠⣴⣿⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⡔⢦⠀⠀⠀⠳⠜⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣇⣸⠟⠛⠒⠲⠤⢭⣍⣙⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡙⠉⠀⠀⣏⣳⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⠀⠀⠀⠀⠀⣀⡴⠯⢤⡯⠼⠦⢤⠤⠬⢤⠴⠿⠦⠿
⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠋⠁⡇⠀⢸⠃⠀⠀⢸⡆⠀⢸
⠀⠀⠀⠀⠀⠐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣾⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⡴⠒⢶⣋⣉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠁⠀⡇⢀⣀⣀⣀⡏⠉⢹
⠀⠀⠀⠀⣨⠤⢤⡖⠒⣲⣵⠒⠙⣒⠋⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢀⣀⣠⠤⠴⢺⡟⠉⠉⢀⣀⣀⡤⠼⠃
⠀⠀⠀⠀⢱⠦⠘⠭⠜⠩⡭⠟⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠈⠓⠚⠉⠉⠁
⠀⠀⠀⠀⠈⠒⠒⠉⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣊⣁⣀⣀⣙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠢⠭⢗⠀⠀⠀⠀⠀⠀⠀⢸⠨⠭⣒⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⠐⡉⠀⠀⠒⠓⠒⢶⢶⠒⠒⢶⠒⠚⠉⠒⠂⠙⠢⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠄⡴⡪⠀⢀⠖⠁⠀⠀⢸⢸⠀⠀⡈⠀⠒⠦⡀⠀⠀⡀⢄⠳⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⢣⠎⡜⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡇⠀⠀⠀⢱⠐⠀⠈⢢⠣⡱⠘⡄
⠀⠀⠀⠀⠀⠀⢀⢣⢂⠏⠐⠀⡸⠠⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠣⢳⠀⢱
⠀⠀⠀⠀⠀⠀⢸⢈⡜⢠⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠇⠀⢃⠀⠀⠂⢇⠀⡆
⠀⠀⠀⠀⠀⠀⡌⠀⠇⢸⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⢰⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⢰⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠸⠀⠀⢸⠀⠀⠸⠀⠈⢀⡄⠸⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢇⣀⠔⠒⡇⠀⡜⠉⡉⠑⠦⠀⠤⠤⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠢⠤⢤⣤⠒⠒⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⡹⠶⠒⠪⢍⡑⢦
⠀⠀⠀⠀⡰⢁⠔⠁⠀⠂⠀⠀⠀⠀⠙⠂⡀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⡁
⠀⠀⠀⠐⡠⠃⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠑⠥⠤⠄⠤⠤⢀⣀⣁⡀⠤⠤⠬⠄⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⡀⠀⢀⠀⢀⣀⠀⠀⠀⠀⣣




⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⡀⠀⢀⢄⠂⡄⠁⡠⠒⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢄⠘⣷⢡⣴⡡⣛⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠼⢄⣤⠑⡀⠢⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢀⣂⡇⠐⠀⡠⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢋⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠢⡀⠐⠈⢛⠘⠩⠠⠐⠉
⠀⠀⠀⠀⠀⠀⡂⠈⢷⡎⡰⠉⠄⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠼⠿⠦⠔⠃⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠸⡀⠢⣽⡡⠬⢖⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠳⠴⡶⠤⢤⠖⡫⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⣦⠖⠜⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣤⢴⢠⡶⢆⠠⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡱⢤⡌⣦⢀⠐⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠈⢦⣴⢃⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠘⣡⣶⠁⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣠⠁⠀⢢⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢂⢨⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢠⣯⠀⠀⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠄⢙⠇⠠⢸⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠃⣼⠔⠀⡐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠡⣸⠗⠗⢓⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠳⠏⣀⠊⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⣼⠁⠐⠀⠀⠀⠀⠀⠀⠀⠉⠐⢔⢆⠣⣿⢄⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠠⣨⡅⢀⣠⠊⠀⠀⠀⠀⠀⠀⠃⠄⠈⢺⣞⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢄⠉⠃⢭⡄⢠⣤⠌⢀⠀⠀⠀⠘⢄⡀⢀⡜⠁⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢌⠄⢺⠀⣀⠠⠔⡁⠀⠀⠀⢖⠂⠈⢙⡃⠜⠉⠃⠆
⠀⠀⠀⠀⠀⠈⠂⢅⠈⠁⢈⣯⠀⠈⠐⠁⠀⣀⠀⠲⢱⣢⡿⠁⠚⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠇⠀⠀⠀⠀⠀⠠⡀⢐⠣⣆⡤⢖⠋⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠸⣿⡄⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠛⠛⠛⠛⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⢀⣤⣴⡶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣞⣛⣫⠭⠭⠭⠭⠭⠭⣍⡽
⢀⣤⢞⡝⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢶⣄⣠⣴⣾⡿⠿⠛⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⣀⡴⣡
⣿⣧⢍⣔⣂⣀⣐⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠬⠤⠒⣾⡯⠓⠉⠁⢀⣤⣶⣾⡿⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠋
⢸⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⡿⠛⠉
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢞⡿⠋
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣾⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠘⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁
⠀⠹⣮⡻⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠈⠙⠷⢧⣴⣂⣤⠩⠭⠍⠀⠀⠀⠀⠀⠀⠅⢀⣀⣠⣤⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⢉⣉⡉⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡴⠚⠋⠉⠉⠉⠉⠓⠶⣄⡀⠈⠛⢦⡀
⠀⠀⠀⡶⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠳⡄
⠀⠀⠀⠛⠒⠶⢤⣀⠀⠉⠳⢤⡀⠀⠀⢰⠇⢠⣞⣀⣤⣤⠤⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢳⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠳⣄⠀⣼⢦⣈⠉⠀⠀⠀⠀⢠⠖⠒⠒⠒⢯⡝⢦⠀⠀⠀⣧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⣆⣿⠀⠉⠙⠒⠶⠤⣤⣈⣙⣒⣒⣒⣺⠷⢻⡇⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢰⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣤⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⣰⠟⠁⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠰⠆⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄
⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡏⣇⡂⡀⡃⠄⠀⠀⠀⠀⠀⠜⣶⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎
⠀⠰⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡇⡟⡇⢱⠁⠀⠀⠀⠀⠀⠀⠀⣙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⢀⡔⠁
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠟⡇⡅⡇⡄⠀⠀⠀⠀⠀⠀⠀⢜⢰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣠⡤⠤⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡀⠀⣄⠁⡇⠘⠂⠀⠀⠀⠀⠀⠀⠀⢈⡃⢐⣠⠀⢀⡀⠀⠀⠀⠐⠈⠻⣾⣷⢋⡠⠄
⠀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡟⠀⡇⠉⡇⠀⡀⠀⠀⠀⠀⠀⠀⠱⡙⠃⠀⠀⠈⠀⠀⠀⠀⠛⠙⢿⡷⠋
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⡄⠀⢀
⠀⢀⠀⠀⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⢀⠸⡄⠀⠁⠼⠃⢠⡞⠀⠀⠀⠀⢀⢠⠠⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂
⠈⣇⠁⠀⠅⢔⢠⣿⡾⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣰⡈
⠀⢙⡈⠀⠘⡁⢚⠟⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⡀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠠⢤⣿⢃⡠⠊
⠀⠈⣁⡰⢺⡶⠖⠋⠀⠀⠀⠀⠀⠤⡒⢔⠋⠀⠀⠂⠁⠀⠒⠁⠀⠀⠀⠀⠀⠀⠛⠻⠛⢛⣧⣧⣤⡶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣟
⠀⠀⠈⣣⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡗⠀⠀⠄⠀⠒⣤⠀⠀⠀⠁⠀⠀⠰⢿⣿⢆⡈⢿⣿⣿⣗⣾⣿⣿⣿⣶⡄⠀⠀⠀⠩⢕⣷⣆
⠀⠀⠀⠬⠿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠀⠻⠿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⣛⣿⠏⠀⠀⠂⠀⠀⠈⠉⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠈⠀⠀⠐⠇⠀⠀⣀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠜⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⢀⣀⡴⠖⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣶⣶⣤⡂
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⢸⣿⣿⣿⣿⡯⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠈⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⢰⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋
⠀⣾⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⣿⠻⡿⠿⠿⠟⠁
⢠⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏
⣼⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣦⡀⠘⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠂⠀⠌⠙⠻⠿⠿⠿⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⣀⣠⡠⢀⠤⡤⢤⠄⡠⢀⢀
⠀⠀⠀⠀⠀⠀⠀⣤⢴⢾⣷⡒⠢⢶⣖⣿⣿⣲⣢⣄⡄⠀⠋⠉⢈⢎⣎⠳⢣⠚⠋⠏⠞⠱⠁⠏⠸⠅⠷⠹⠜⠣⠱⠛⠜
⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⡀
⠀⠀⠀⠀⠀⠷⠀⠺⠿⠻⠷⠀⠀⠀⠀⠶⢄⣀⠀⠀⡀⠀⢀⣀⠀⢀⣤⡀⠀⢀⡀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠈⠛⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢾⣿⠖⠒⠒⠚⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡀⠀⡄⠢⡁⠀⠔⠈⢀⡀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢀⠀⠑⠈⣄⠄⠇⠀⣰⠡⣤⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢗⠢⢄⠹⡟⢰⣾⢅⠬⠡⠌⡒⢌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡕⡼⠀⣴⡀⠚⡀⠒⢬⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢄⠠⡀⡎⢁⠆⠀⠀⠠⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠈⠐⠳⣧⠥⠤⠔⠓⠒⡲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⡠⠂⣡⡴⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢄⠑⠤⡀⠈⠀⣀⢀⠐⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡑⠤⠙⣽⡇⡘⠁⡠⠊⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠢⡀⠈⠒⠲⠟⠺⠖⠋⢀⡠⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢬⠂⠠⣈⣿⣁⢄⡵⠪⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠱⣌⣦⡀⠴⣅⣠⠶⠣⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡒⠒⠈⡁⣠⠀⡠⠪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢔⡂⢉⠠⡀⢌⣅⡊⠐⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠛⠲⢺⣋⠄⠠⠃⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⠛⠁⢚⢉⠅⠊⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠛⣮⡢⢿⠒⡀⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠑⠌⠫⢶⠯⠠⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⢤⣾⡆⠠⢈⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠊⠀⢀⢤⡩⠍⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠢⡌⠉⡁⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠃⢀⣿⠁⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡠⢈⢠⢤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠄⠘⠋⡀⠤⢒⠀⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠌⡐⢠⣄⢀⠁⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⡀⢇⢤⡧⠊⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⢤⠟⡫⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⠸⠥⡀⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡢⠀⣰⢊⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⡑⡆⠡⣰⣧⡌⠀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⠺⠏⠡⠐⢂⡐⠃⠀⠀⠀⠀⠀⠀⠐⢆⡐⢄⠐⢼⣀⠏⠀⠉⡁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⡀⣴⠧⠀⠒⠇⠤⡄⠀⠀⠀⠀⠀⠄⠠⠠⠈⠄⢰⠜⠓⢂⢀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⢲⡶⠀⣻⠶⠊⢀⠄⠀⠀⠀⠀⠈⠢⢕⢀⣘⡁⠀⠁⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⣈⢺⡄⢈⡀⠤⢐⡁⠀⠀⠀⠀⠐⡀⠀⠀⠉⣛⠡⠄⠭⠉⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠅⡀⠀⠀⠐⡀⠟⡁⠠⠦⢀⠌⠀⠀⠀⠀⠰⡌⡂⠀⣰⡟⢁⠒⠒⠊⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⠁⠸⢷⡷⠡⠐⠁⠀⠀⠀⠙⢌⠢⠑⣈⣂⢻⠀⢁⢀⣤⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠣⡐⠢⠠⣹⠾⠃⠡⠒⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢻⣷⠥⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠿⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣉⣉⣉⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣴⣿⣶⣤⣰⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠷⢦⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢿⣿⠋⠉⢻⡿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠻⣤⣄⢸⡇⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⢸⡏⠀⠈⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣻⣿⣿

⠛⠛⠃⠀⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠐⠛⠛⠛⠛⠀⠀⢰⠏
⠚⠛⠃⠀⠛⠓⠒⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠒⠛⠛⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢦⣄⠀⠀⠀⣀⣀⣛⣛⣀⣀⠀⠀⠀⣠⡴⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠿⠿⠿⠿⠿⠟⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⢰⣶⣄⡀⠀⠀⠀⣠⣴⣶⠀⠀⠀⠀⠀⣹⣿⣿⣇⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⣠⣴⡶
⠀⠀⠀⠀⠻⣿⣿⡄⠀⣼⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣷⡀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠛⠗⡘⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠻⢇⡸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣀⣀⣀⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⠙⣛⣛⠋⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣱⣿⣿⣮⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡀⠀⠀⠈⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⡒⢬⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠄⠀⠀⠠⢭⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣧⣉⠇⠀⠀⢀⣌⡂⠀⠀⠀⠀⠂⣁
⠀⠀⠀⠀⠀⠰⠒⣀⠀⠀⠀⠀⠀⠤⠀⠀⢐⠂⠀⠀⠐⠖⠁⠀⠀⠀⠀⠀⢰⡀⢒⢀⠀⢾⣿⡁⠀⠀⠠⢵⠣⠄⠀⠠⠄⠀⢈⣁
⠀⠀⣂⣀⠀⢈⣩⣡⢀⡠⠠⠀⠀⠒⢄⠀⠤⠀⠀⠀⠘⠒⠀⢠⠤⢀⠀⡐⠒⠀⠀⠒⢠⡄⣠⠄⠀⠀⣉⠈⠀⠡⣦⣍⠀⠀⢀⣀
⠀⠀⠐⠒⠀⡤⠤⢴⣾⣌⠙⠀⢂⡙⢄⢰⣤⡓⢀⠀⢈⡁⠂⠐⢚⡭⢀⢈⡩⠥⠀⠈⠁⣿⠦⠈⡁⠀⠨⠀⠀⠐⠓⠖⠀⣀⠠⡀
⠀⠀⠀⠉⣹⣒⠒⠾⢧⢤⣓⠀⡉⠻⣿⡜⢣⠀⢒⡲⢀⡤⠉⠀⠚⡴⠬⣂⡴⠒⣂⡀⠀⠃⠶⠂⠀⣀⠂⠠⠀⠀⠈⠁⠴⡟⠲⠐
⠀⠀⠠⣜⠉⠓⢶⡣⣬⣶⣀⠈⠁⠀⣀⢉⠁⠀⠶⠄⠀⠀⣀⠀⢀⣤⡦⠠⠐⠉⢀⠄⠀⡀⢀⢀⡄⠡⠍⣀⠀⠀⠀⠀⠂⠈⠒
⠀⠀⣤⡈⠉⠂⠍⢀⣠⠊⠀⠀⠀⠀⣈⣉⠀⡑⠂⠀⠀⠀⠀⠠⢜⠧⡄⠀⠀⠀⠅⣠⠞⢁⣀⠀⠀⡤⠚⠍⠀⠷⠅⠀⠒
⠀⠀⠀⢩⠁⠒⠀⠀⠆⠄⠀⠀⢀⠀⠄⡘⠢⠥⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⡀⠄⠎⠁⠀⠀⠂⠐⠀⠀⠄⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⡋⠙⠎⠀⢻⠇⠵⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡛⢼⠀⠆⡰⠀⠀⠠⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⢳⣄⡀⢸⠒⢈⠓⣤⢤⣶⣟⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣁⠈⣩⠧⣀⢾⣧⡜⠃⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣼⠁⠠⣽⠉⠰⠈⣷⠦⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⢺⣙⣆⠀⢁⠟⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢄⠀⠀⠉⣿⡗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢤⠳⡄⠀⣿⡇⠀⠀⢀⡤⠒⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢦⠙⣄⣿⡇⢀⠴⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡂⢸⣿⣧⣮⡀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⠀⣀⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⠲⣾⣿⣻⣿⣛⣿⣿⣟⡏⡝⠙⢸⣻⣏⢉⠉⡉⠉⡉⠉⠉⠉⠛⠛⠛⢛⣿⡗⡆
⠀⠀⠀⠀⠀⠀⢹⠑⠒⠒⠒⠢⠤⠤⠤⠭⠍⢥⣉⣉⣉⣉⣉⣉⣉⢉⣭⣭⣭⡭⢭⡭⡭⡤⢶⡻⠁
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢠⠆⡄⢰⢁⡞⡜⡰⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⢄⡄⡄⡔⡰⢡⢏⡞⡰⢃⠎⡜⡰⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠹⣻⢲⢶⠤⡴⣥⢥⠥⡬⣬⣤⢤⡥⣭⠾⡴⢳⠿⡾⢻⠟⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠈⠀⠁⠊⠘⠰⠱⢃⠞⡠⢃⠜⡡⢋⡞⢡⢏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⡡⢋⠞⡡⠋⡰⠃⠊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡱⢋⠞⣡⠎⡠⢣⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⢋⡴⢁⢜⡵⣣⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⣡⠎⡴⣣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠜⣡⢊⡜⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⠞⡱⣫⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠄⠀⡀⢀⣨⠞⠡⠾⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢄⡤⢂⠤⠀⡠⢀⡀⢀⠄⣀⠄⡠⠀⡀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠑⠋⠔⠁⠐⠂⠔⠡⠖⠡⠊⡠⠊⡤⠊⡔⣡⠜⡵⣡⢢⠆⠔⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣍⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠸⢄⢢⡅⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠙⠿⣿⣇⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⢞⢚⠿⡻⢆⠂⡀⠀⠀⠀⠀⠀⢀⠀⢀⢶⣀⠀⠐⠠⡀⠀⠀⠀⠀⠘⠂⠘⠀⢈⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠏⢘⢣⣧⡡⢾⡈⠓⠌⠤⡚⠀⠀⠎⡊⣀⣀⢤⡈⡉⡁⠠⡀⠁⠂⣄⠀⠰⢤⡀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣟⠽⣀⠿⡗⡇⠀⡰⢆⠀⠀⡠⠚⠉⠀⠀⠀⢱⡛⠋⠂⠌⡐⠄⣼⠀⠀⠿⠀⠀⣩⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⢸⠅⠀⠪⠿⢦⡀⠉⠉⠢⢉⠁⠀⠀⠀⠀⠀⠀⡗⠂⠄⡀⠀⠀⠐⠀⠯⡧⠙⠉⠀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⣀⠀⠔⠊⠀⠀⠀⠀⠈⠐⠠⢀⠀⡆⠀⠀⠀⣀⠄⠀⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⢀⡀⢙⠁⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈⠁⢀⠀⠙⠀⢰⡞⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠘⠃⡠⠈⠀⢘⠃⠸⡗⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠰⠂⠀⡌⠀⢿⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠀⠀⠆⠀⠀⠀⠸⣆
⠀⠀⠐⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⢀⡄⠀⢺⠀⠀⠒⠉
⠀⠀⠀⣉⣻⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣦⡤⣴⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⠗⠀⠘⠀⠀⠀⠀⡆⠀⠀⠐
⠀⠀⢀⡀⢛⢽⡆⠈⣸⡆⠀⢰⡦⣠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠈⠄⢉⣱⡵⡆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠖⠀⢘⠂
⠀⢀⡈⠱⠸⢟⡿⣏⢺⡔⢀⣏⡼⢋⠈⣰⣴⡖⠘⠂⠈⠷⠈⢀⢤⢄⢼⡿⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂
⠀⢀⡹⣦⣀⣿⣿⣃⠰⢶⣼⣾⡟⢃⣴⠟⠡⣐⠖⠀⠆⢈⠴⠄⡀⠋⣻⠹⠿⠁⠡⠀⠈⠁⠀⠀⠀⠀⠀⠣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠴⠋⠈⢪⢿⣿⣿⣿⣶⣿⣿⣿⡾⣯⣶⣔⢾⣄⠠⣀⡷⠀⠰⠈⠉⠀⢹⠰⠆⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣹⡉⠉⠉⠉⣯⣴⣾⣷⡄
⠀⠀⠠⢡⠋⠛⣻⣷⣷⡻⠛⠻⡗⡞⡿⣯⣟⠃⣀⡨⣮⢊⠐⠷⢀⣧⣞⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⡴⠀⠀⠀⢻⠏⠈⠺⠿⠷⠳⠘⣰⠌⠀⠀⠈⠀⣻⡌⠃⠀⠀⢡⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣽⣿⣿⡿
⠀⠀⠃⠀⠘⡄⠋⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⡠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢶⡶⠶⣶⣶⣦⡤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢙⢆⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠈⡌⠣⡀⠀⠀⠀⢠⠞⠀⡇⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠘⡄⠙⣄⢀⡔⠁⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⣀⣴⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠹⡄⠘⣾⠀⠀⣰⢃⡴⠃⠀⠀⠀⢀⣠⠴⠊⡽⠈⡆⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡇⠀⠀⠀⢹⡀⠸⣆⢰⣷⠋⠀⠀⢀⡠⠖⣹⠃⠀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠀⠀⠀⢣⠀⢹⡘⡏⠀⠀⣰⠋⠀⢰⣃⡤⠞⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠘⡄⠀⣇⣷⢀⡜⠁⠀⠀⡏⢁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠀⢱⠀⢸⣏⡞⠀⠀⠀⠀⡏⢉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⢶⣒⡒⠲⢬⡆⠘⡇⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⡿⠓⠒⢤⡀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠢⣕⢝⣄⢹⡀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡴⡏⠒⠒⣚⠁⢂⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡖⠒⠒⣒⠒⠲⢤⣈⢺⣎⢦⣇⠀⠀⠀⢸⠀⢀⡇⠀⢀⡤⠊⢰⠛⠛⠛⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⢛⢯⡉⠙⠳⣽⡌⢿⡄⠀⠀⡆⠀⣼⡠⠖⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢄⠁⢙⠦⣀⠘⡏⠛⢷⡀⣰⠁⣰⡏⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣍⣒⣥⣮⣿⣿⡄⠀⠳⡗⠚⠁⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⢦⡀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣳⠈⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢸⢀⣶⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠇⢻⡆⢡⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⡇⡀⢸⡾⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⡇⠀⠀⠀⢣⢸⣇⢸⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⡇⡇⡇⣜⡇⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⡇⢫⠀⢸⠑⣼⠀⣿⢸⡶⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠘⢀⠇⡇⡇⣿⠁⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢃⢣⠈⡆⠈⠳⡜⢧⠁⡼⡇⡿⡸⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣿⠀⠇⢴⢿⡸⢠⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⡆⢸⠀⠀⠈⡆⢠⢣⠃⢣⡧⢊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣇⢸⣄⠇⣿⠀⡇⠸⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⠀⡇⠀⢠⢃⣮⠎⢀⡮⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣧⡘⣮⠻⡆⢹⢰⡇⡆⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⣠⠃⡜⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡵⡜⠃⢹⢸⠀⡼⡜⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢠⠏⡜⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣛⡀⣿⢸⠀⠟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣼⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣜⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⡀⢠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡇⠀⡿⢿⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⢆⠀⠀⣿⠈⢆⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠐⠈⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡏⣼⠀⠀⡇⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡇⢸⡄⠀⡇⢸⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠠⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⢸⠁⣠⠇⣼⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⢸⠰⢁⡜⢹⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⢘⠈⢁⠎⢀⠎⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡸⣰⠁⢀⠜⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡁⡇⡰⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⡷⠃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣇⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡃⠂
⢺⣷⣶⣦⣄⢀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⡑⠀⠀⠀⢁
⠚⢯⠏⠉⠉⡟⣀⠀⠀⠃⢀⣓⠂⠒⠐⠐⠂⠐⠒⡓⠒⢒⡒⣿⣶⣶⣄
⠀⠀⠀⠀⠡⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠃⠀⠈⠁⣟⡹⠉⠁⠀⠢⡀
⠀⠀⠀⠀⠀⠈⠡⠒⡲⠂⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠄⠀⠀⣀⡄⣀⠀⠀⡀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⢠⠟⢻⣯⡇⡀⠁⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠄⠀⠈⠶⠠⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣁⣤⡁⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠈⢿⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡒⠀⠋⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠁⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡄⠀⡠⠎⠹⣷⣦⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠓⡒⣾⡅⠤⠄⠒⣨⢋⠳⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⠋⠀⠀⠀⠀⠶⣀⡎⠸⠀⠀⠀⢀⡜⠃⠀⠀⠀⢷⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠞⠐⠒⠒⠒⠊⠉⢙⢁⡀⠆⠀⣠⠏⠸⠂⠀⠀⠀⢸⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠤⠚⠁⢠⠃⠀⠀⠀⢠⡟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢀⡌⠀⠀⠀⠀⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡖⠉⢛⣦⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠤⠁⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⢣⡤⠈⠀⠘⠀⠒⠲⠖⠒⠛⠛⠛⠛⠃⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠤⠴⢶⡉⠉⠙⠒⠶⢤⣄⣀⡀⠀⠀⠀⢀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠁⠿⠀⠀⢸⠆⠀⠀⠀⠀⢰⠆⠉⠉⠛⠛⠛⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠂⠚⠁⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢸⡀⡠⠞⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⣸
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠒
⠈⠓⠀⢀⡀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⡼⠁
⢀⠈⠀⠸⠈⢆⠀⢸⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠓⠚⢅⠸⠂⠀⣇⢀⠠⠐⠀⠂⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⡇⠀⣀⠤⢤⡀⠀⠀⣠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⠀⠀⠀⠀⢧
⠀⠀⠐⠉⠈⠉⠉⠰⠋⠀⠀⠀⣹⠪⡁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⢸
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⢸⠆
⠀⠈⠀⠀⢃⠀⢀⠃⠀⡜⠃⠀⠀⠀⠀⠀⣠⡴⠛⠙⢳⠄⢠⠀⠀⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠂⠈⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠒⣤⡄⠀⠉⠉⠉⠉⠈⠁⣼⠃⠀⢀⡰⠏⠀⠘⠀⠀⠀⡎⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠠⡎
⣀⠀⠀⢀⡀⠘⠀⠈⣂⠀⠀⠠⠀⠀⢰⠇⣠⠖⠋⠀⠠⠀⠛⠛⠓⣤⠁⠋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠰⠁⠀⠈⠁⠀⠛⠊⠀⠀⠐⠃⠜⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⠠⡤⠴⠊⠁⠀⢀⣠⡤⠞⠁⠀⠀⠀⡇⠀⠀⡝
⠀⠀⢤⡠⠔⠂⢀⠔⠓⡀⠤⠀⠀⠁⠀⠀⢀⠤⠒⠛⠓⠈⠁⠀⡄⢀⠔⠋⠉⡢⢀⣠⠖⠈⣷⣉⣁⣀⣀⠠⣴⡶⣾⠁⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⡁⠀⡠⠖⠒⠲⠦⢠⡀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠉⠀⢾⠁⢀⡴⠛⢦⣤⠀⠌⠉⠀⣰⠏⠀⠀⠈⣿⠀⠀⠀⠀⠀⢀⠴⢄
⠤⠤⢄⣀⠀⠀⡄⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠔⠁⠀⢱⠀⠀⡰⠋⠀⠀⢀⡾⠟⣀⠤⣄⠀⢰⡏⠀⢸
⠀⠀⠀⠉⠙⠂⠶⡀⠀⠀⠈⠳⠤⢄⡀⠤⠶⠚⠀⡔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠀⢀⡴⠃⠀⢸⢆⡠⠦⣰⠞⡡⠊⠁⢀⣼⠃⠀⠀⢀⡞
⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣭⣴⣤⣤⣤⣭⣭⣭⣤⣮⣤⣴⣶⣿⣮⣥⣤⣴⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡀⠀⢀
⠀⠀⠀⣀⢴⣾⠉⠋⠓⠒⢤⠀⠐⡠⠀⣀⢀⡀⣀⣀⣀⣠⣀⣀⣀⣀
⠀⢀⡜⢁⠯⠁⠀⠀⠀⠀⠀⠁⢶⣶⡿⠋⡰⠋⠍⡱⡍⢹⡻⠋⢙⢝⣝⢝⢝⢹⠟⢖⣦⣅
⢠⡮⢨⡆⠃⠀⠀⠀⠀⠀⠀⠀⠠⠍⠓⠚⠓⠶⠴⠴⠭⠾⠥⠤⠴⠷⠴⠵⠼⠵⠗⠛⠉⠑⠂
⢼⠭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡫⠤⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠺⡗⡸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠄⠐⠀⠠⠁⠂⠄
⠀⡟⠪⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠆⠀⠐⠀⠠⠄⠃⠀⠠
⠀⠜⡄⠀⢧⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠆⠁⠈⠠⠄⠀⡄⠁⠀⢄
⠀⠈⠻⡆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⡠⠈⠀⠀⡀⠠⠀⠒
⠀⠀⠀⠳⡄⠆⢧⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⢀⠐⠂⠀⡀⠁⡈
⠀⠀⠀⠀⠘⣆⠀⢱⡀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠠⠤⠖
⠀⠀⠀⠀⠀⠈⠆⠁⠛⠦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢆⢁⡙⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠊⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡾⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠠⠋⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠐⠶⣤⡀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠐⠀⠔
⠀⠀⠀⠀⠀⠀⠈⠳⣕⢀⡇⠀⠀⠀⢀⣁⠀⠀⢀⢱⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠈⢧⡁⠀⠀⠉⢀⣹⣧⡂⠘⢸⡇⡆⠔⠂⠀⠂⣠⣾⠃⡂⠀⠀⠀⠀⠀⠈⠔⠁
⠀⠈⠛⠻⠷⠶⠶⠶⣾⣜⣽⡖⢪⡶⢳⡞⠯⢵⡘⠆⣜⠣⢄⠀⣰⣾⣿⡿⠟⢀⡠⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠌⣯⣓⣬⠚⣷⠷⢯⠜⣒⣱⣶⠉⠙⣸⡄⠛⣿⠩⢆⣔⣯⡒⣏⣤⣦⣏⠀⠈⡠
⠀⠀⠀⠀⠀⡰⢗⡲⠣⠚⢶⣊⡟⣷⡽⠇⡀⠁⣌⠙⢆⢀⡙⠀⠈⣉⣫⣴⣿⣏⣛⣽⡿⢇⣿⣶⡼⠁⠀⢠⡔⠁
⠀⠀⠀⠀⠀⠈⠠⢤⣴⣶⣦⣭⡝⠛⠶⢶⣷⣤⢬⠅⢞⠉⢘⠒⣉⢉⡱⢲⣎⢹⣇⣨⡧⢈⢛⡛⣁⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣺⣀⣨⣤⣶⡚⠙⡉⢀⣤⠖⢉⡏⢹⢦⡈⠻⠁⣕⣳⣿⣩⣯⡒⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠉⠊⢁⠴⢲⣿⣄⠜⠲⠂⠀⠀⠹⠱⡏⣾⣼⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠈⠐⠀⠊⠀⠀⠀⠀⠀⠐⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢫⣟⢹⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⡏⠘⠉⡇⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⠀⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣏⢿⡆⢀⠀⢳⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⠀⢿⣏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡟⢸⡇⢸⠆⢸⡇⢠⡇⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠙⠀⣿⠆⢸⡟⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢼⠃⠘⠋⠈⣷⠀⠀⠀⣠⣾⣶⣥⣆⡀⠀⠀⡆⢸⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⠈⣶⡷⢀⡿⢻⠃⠀⢀⢛⣹⣿⣿⣿⢣⡄⠀⠁⣼⠙⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⢸⣏⣠⣍⣠⣀⣠⣆⡀⠀⢻⣿⣿⣿⣿⣉⣿⡇⣄⠀⣿⠠⠄⣼⠇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⣿⡟⣿⣿⡿⣿⠟⣧⢀⡈⣿⢻⣿⢻⡏⢿⡷⠏⠀⡿⠀⠀⣿⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢼⣠⣿⢻⠉⡟⠀⠏⢠⠉⣾⣿⣿⢸⣿⢻⣷⣼⡇⠀⢠⡆⠀⠀⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⡿⢸⠻⡇⠀⠀⠆⡀⢻⡏⡟⢸⣿⢸⣿⣹⣷⡀⢾⠀⡀⢠⡟⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠸⣿⠇⠀⠰⠇⠘⠀⠀⠁⠘⣿⡇⣻⣿⣾⣿⣦⣤⣤⣿⣤⡃⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣿⠀⠳⠀⡆⠀⠀⢠⠀⠀⢿⡇⣿⣿⣟⢹⡿⢻⣿⣿⠙⢷⣿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⡇⠀⠀⣇⠘⠀⢸⠀⡄⢹⣷⣿⣿⡏⣼⠁⠚⡷⢸⠁⣼⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡆⢰⠀⣿⠀⠀⢸⠀⠁⢸⣿⣿⡇⠀⡿⢠⡄⠇⠸⠀⡇⣿⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢨⠀⢹⠀⠃⢸⣆⠀⢸⣼⣿⣷⢠⡅⠀⠉⡆⠀⠀⡁⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⡀⢸⡅⠀⠈⣿⠀⢸⣿⣿⣇⠈⡃⠀⠀⡀⠀⠸⣇⣿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢳⠘⣇⠀⠀⣿⠀⣘⣻⣿⣿⠀⡁⠀⣴⠁⠀⠀⢻⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⡆⢹⠀⠀⣿⠀⢿⣿⣿⡟⠀⠀⠀⠿⠀⢀⡄⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⢳⠀⣷⠀⡿⠀⢸⣿⣿⣷⠀⣀⠀⣿⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠉⠰⣇⠀⣾⣿⣿⣿⠂⣨⠀⣿⡀⢴⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⠈⣰⠇⣸⠀⢿⣿⣿⣿⡇⣿⢠⡿⢁⣾⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⣿⣿⣿⣇⠁⡼⢿⣡⣾⣿⣿⣿⣷⣥⣾⣷⣾⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⡾⠷⠞⣋⣉⣩⣛⣿⣟⣛⣋⠛⠛⠛⠛⠛⠿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢶⣦⣀⣠⡤⢤⣤⢤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⣿⣟⢙⡓⢺⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣿⣿⣇
⠉⠹⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢛⣛⣛⣛⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⠶⠛⠉⠉⠉⠉⠉⠛⠶⣮⣙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣇⢀⠀⠀⠀⠘⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⢋⡿⢿⣤⠀⠀⠀⠈⢻⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡶⢋⡴⢋⡴⠋⠙⢶⣄⠀⠀⠈⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣠⠞⢡⡼⢋⡴⢋⡴⠛⠀⠀⠀⠀⠙⢧⣀⠀⠸⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⠞⣁⡶⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢹⡄⣠⠞⢁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⠟⢁⡴⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⣯⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣗⠲⠶⠶⢦⣤⣤⣤⣀⣀⣈⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠞⠉⠉⠛⠳⠶⢤⣄⣀⡀⠈⠉⠉⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⡀⠀⠙⣦⡀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣿⣦⡀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⢰⣿⣯⡉⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⢿⡉⠙⢿⡀⣿⠀⠀⢀⣤⠶⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⣡⡾⠋
⠀⠀⠀⠀⠻⢦⣤⠿⢧⣾⢠⡟⣿⣴⠿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠈⠉
⣴⠞⠓⠚⠛⠛⠛⠓⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⢶⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠟⠁
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢀⡟⠀⡄⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣴⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠈⣧⡀⠻⣤⠀⠀⣠⠇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠷⣄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⢰⠇⢀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⣆⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣬⣥⡤⠞⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⠴⠶⠶
⠀⠀⠀⠀⠀⠛⠛⠓⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⣄⡀⠀⣀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠒⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠘⠲⠶⢤⣤⣀⠀⠀⠀⠀⠀⣀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢆⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠈⠉⢓⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣷⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⡀⡿⠁⠀⢸⣿⡀⢀⣀⣀⡿⡏⢰⣤⣟⡬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣿⠂⣼⢀⡭⠿⠟⠓⠲⠿⢏⡇⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢳⡙⠞⠁⡸⢤⡀⠀⠀⠀⠀⣼⣿⣉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢥⡳⣬⠇⣰⠋⠉⠛⠃⢰⣦⠀⣸⢣⠟⣾⣣⡄⣶⢻⣤⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣸⣏⠣⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⣁⣀⡐⣇⠀⢠⡶⣤⣸⡿⣤⠏⡞⠀⣿⢹⡥⠋⣘⣿⣥
⠀⠀⠀⠀⠀⠀⠘⠲⠖⠲⣅⠸⡄⢀⡶⡄⢀⣤⣀⠀⠉⣩⣄⠈⠹⣌⢧⠀⠉⠓⢮⣄⠀⢸⣷⣻⠿⠒⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠇⠙⠞⢸⡁⠈⣛⡿⠓⠚⠋⢧⡀⠀⠘⡎⢧⠀⠀⠀⢘⡇⡴⠋⠀⢀⣤⣶⠀⡶⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⠉⠓⣦⢉⣉⠉⣰⠚⠉⠳⢤⡙⠓⠦⠟⠸⣆⠰⢿⣚⠃⣧⢀⣠⠞⢻⣥⡄⣧⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⣿⠛⣫⠟⢋⣩⠇⠹⣄⠀⢠⡴⣣⠴⠶⠶⢤⣌⠳⡄⠈⣧⠛⣿⠞⠉⠉⠉⣰⠟⣛⡿
⠀⠀⠀⠀⠀⠀⠀⢙⡿⣻⡿⡇⢸⠁⠀⠻⠞⡧⣶⠚⠁⠀⠉⠁⢀⣠⡀⠀⢈⣳⠙⢦⣸⠀⡇⠀⠀⢠⣞⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⠛⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⢈⣿⠙⠒⠋⣉⣄⡀⠛⢰⠇⣴⣄⡞⢾⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢭⣭⠉⣠⠖⠛⢷⡇⠀⢳⠀⣾⠀⡏⢋⡴⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⢶⢿⠀⠀⠀⠀⢀⡼⠀⠹⠴⠃⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠘⣻⠖⠋⠉⠉⠻⡄⠀⠀⠀⠀⠘⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇⠀⠀⢠⡴⠚⠛⢲⣄⣀⣴⠋⠉⠈⠙⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠿⣄⣀⣀⡤⠏⠁⠘⠶⠤⠶⠚⠁




⣿⣏⢹⣟⠻⣿⣛⠟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⡲⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⡇⠀⠀⠀⠀⠀⣠⢊⠜⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⡀⠀⠀⠀⠀⠀⠀⡸⢸⠁⠀⠘⢄⠀⠀⢀⡔⣡⠏⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠫⡲⣄⠀⠀⡠⠚⠁⢸⠀⠀⠀⢸⡏⠉⠁⣰⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢮⡳⣄⢱⡀⠀⢻⠀⠀⠀⠀⡇⠀⢰⠇⣠⡦⡀⡸⠀⠀⠀⣀⣤⠖⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠙⣎⠉⠈⢆⢸⡄⠀⡤⠜⠀⢀⣏⢔⡟⢠⠃⠳⣄⡠⣪⠗⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⢳⡀⠘⣜⡇⠀⡆⠀⠀⣸⢏⡞⢀⠎⣀⠔⣩⠞⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢶⣄⠀⠹⡄⠈⠙⢢⠱⡀⢀⢏⡞⠀⠘⢎⢀⡾⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠫⡳⡄⠹⣄⠀⠘⡔⠁⠁⡼⠁⠀⢸⣴⠟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠳⢶⢄⡀⠀⠀⠘⡄⠙⢎⠢⠿⣆⢰⡽⠀⣸⠁⠀⠀⣸⠏⠀⠀⡠⠔⠊⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⠮⡓⢤⡤⣇⠀⠈⢳⡀⢸⡾⠇⢀⡇⠀⠀⠀⢙⠀⢀⣨⠦⣒⠽⠋⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⣄⢘⠄⠀⠀⢳⡀⠳⢤⣸⠀⠀⠀⣠⠞⠉⣡⠴⠋⠁⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢾⣄⠀⠀⠀⢳⡀⠀⡇⠀⠀⢸⠁⣠⠞⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣄⠀⠀⢳⡍⢢⠀⠀⢳⠀⡇⠀⢀⣴⠟⠁⠀⢀⣀⣀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢤⣀⡀⣹⡗⣄⡀⢈⣷⣅⡔⣻⡃⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠄⡈⠓⢄⠀⠀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣇⠀⠈⠢⣠⠇⠀⠀⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⡤⣑⢦⣸⣷⣦⣀⣀⣦⠎⢻⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠘⠛⢬⣯⠈⢿⣿⠇⠘⢿⡟⠁⠀⢠⢀⣤⠌⠀⠀⠀⠀⠀⠀⢠⣀⠀⠴⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠘⠀⠀⣹⠀⠀⠘⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡖⢸⢃⠀⠀⠴⠛
⠀⠀⠀⣀⣀⣀⢡⡀⠈⠀⠁⠀⠠⣧⣃⡟⠀⢀⣄⣠⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠏⠰⠀⠐⣯
⠀⠠⠟⡉⠉⠉⠉⠉⠓⠐⠢⠤⣤⣤⣼⠷⠶⣿⠷⠤⠤⡀⠀⠠⠴⠂⠀⠀⠀⠀⣻⣴⢣⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠂⠄⢂⡤⢦⡴⠎⠁⠀⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢾⣷⣶⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣴⠃⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠚⠀⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠀⠀⠀⠃⠀⠀⠀⢀⠀⢢⠀⡀⠂⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠩⡶⢿⣷⣱⣶⣴⠦⠀⠀⠚⠂⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡄⠂⠀⠀⠀⠘⠁⠶⠺⢧⠩⡭⣝⠀⠠⠀⠐⠖⠶⠤⢄⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⠃⠀⠐⢤⠀⠀⢀⣒⠐⠂⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠀⠀⠀⠻⣟⠣⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠄⠀⠀⠀⠈⠙⠲⢴⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠰⢂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠋⠚⠛⠲⠤⠬⠦⠤⠵⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡘⠃⠀⠀⠀⣰⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣠⣆⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⡌⢳⣄⣀⠀⠀⠀⣴⡶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠖⠻⡄⢻⡉⠛⣆⡜⡟⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢿⠀⠀⢻⡈⣧⡴⠋⠻⡁⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠈⠳⣦⣼⠟⠋⠀⠀⠀⠙⢾⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇
⠀⠀⠀⠀⠀⠀⣤⠤⣈⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⢰⠃⡏⠠⣤⣄⣀⣀⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠸⣴⣇⡠⠖⠤⠤⣈⡉⠉⠉⠛⠚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⢠⠞⢀⠀⢠⠂⢠⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣌⣧⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⢺⠀⠈⠀⡏⠀⠈⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠒




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢶⡦⠠⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣦⣼⣷⣿⣶⣾⣧⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡀⢀⣤⣿⣿⣁⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿
⠀⠠⠶⢶⢶⡴⣶⣦⠴⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣤⣤⣤⣤⢈⡙⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣴⣆⡷⣀⣠⣴⣠⣤⣤⡤⣶⣯⣠⢙⣛⡟⡿⣿⢿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣨⣸⣇⣷⣽⣞⢧⣿⣿⣿⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣯⣻⣷⣟⢿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠸⣿⣧⠙⣿⣦⠙⢿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣧⣿⣿⣎⢿⣿⣿⣆⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⡙⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣎⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡇⠆⠋⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣾⣿⣿⣿⣿⠻⡾⠯⢹⠿⢿⣿⣿⣿⣿⢿⢦⠙⠟⠀⠠⢿⣿⣿⢿⡿⣿⡿⠄⠀⠂⠉⢻⣿

⠀⠀⠀⠀⠀⠀⢁⣴⠖⠂⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣥⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠈⠀⣠⠀⠈⠀⠄
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠉⠂⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣿⠀⠀⠂⡼⣇
⠀⠀⠀⢠⢇⣼⣿⡀⠀⠀⣄⠉⠖⢢⠀⠀⠀⠀⠀⠀⠀⡏⢝⣿⣽⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢟⢠⢀⡀⣇⣿
⠀⠀⠀⡰⣿⣾⠯⠗⠖⢦⡐⠀⣿⡏⠀⠀⠀⠀⠀⠀⢸⡆⠐⣿⠇⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡐⣁⢿⡟
⠀⠀⠀⠈⠉⠙⡱⣯⣋⠹⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣀⠠⢝⣳⠛⠏⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠈⡘⣷⠟⠁
⠀⠀⠀⠂⠄⠀⠚⠿⢛⣷⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⢉⡽⠃⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠈⢸⡟⠁
⠀⠀⠀⠀⠘⡆⡁⠐⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⣿⡇
⠀⢀⠀⠀⠀⠀⡀⠐⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡇⢠
⠀⠐⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⢰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣵⢾⣿⣾⡽⡀
⠀⠀⣠⠖⠾⣷⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣦⣿⣯⣛⡛⢅⣾⣥⣄⡀
⠀⠸⠁⠤⠈⣹⢦⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣽⣧⣿⣏⣻⣟⡹⢿⣯⣽⠝⢧⠀⢠⠀⡀
⠀⢸⡆⠈⣧⣾⠙⢓⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠦⢟⢰⣥⡉⢻⡿⣽⠌⣿⣿⠗⠀⠀⠀⠀⠁
⠀⠀⠙⠾⢿⣾⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢊⠘⣻⠇⠸⡇⠙⢷⣑⣸⠖⠃
⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⢀⣰⣿⣶⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡓⢹⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⡆⠂⢰⣿⠿⠇⠀⠀⠀⠟⠹⠹⠂
⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠸⣗⣨⡆⠀⠀⠀⠀⠀⠀⠀⠠⠛⠉⡙⠀⠈⠁⢸⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⢀⢹⡀⠘⣯⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣰⣿⣴⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⠀⠀⡇
⠀⠀⠀⠐⢿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢘⠀⢀
⠀⠀⠀⠉⣛⣘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⢀⠀⠻⠀⠆
⠀⠀⠀⠈⠉⠁⣄⣀⡀⠀⠀⢠⣾⣿⣿⣄⠴
⠀⠀⠀⠈⠓⡔⡜⠉⠀⠀⠀⢺⣿⣿⣱⣟⠀⠀⠀⠀⠀⠚⢓⣠⢤⣒⡶⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡖
⠀⠀⣉⡛⠆⡹⠁⠀⠀⠀⠀⠘⣿⣿⣾⠏⠀⠀⠀⠀⠀⢠⣶⣶⣿⣷⣟⣙⣦⠀⠀⠀⠀⠀⢠⣤⠿
⠀⢤⢬⡉⣿⠷⠚⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⢀⣤⣿⢿⣿⠿⢿⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣄
⠀⠀⠤⢤⢏⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⡁⠀⡞⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠉⢩⣾⡐⢆
⠀⠀⠐⠶⠞⠓⣷⢄⣀⣸⣀⡀⣤⡤⢠⡀⠀⠀⠀⠀⠈⠄⠸⠁⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠁⠀⠁
⠀⠠⠄⠀⠀⣰⠋⠈⢿⠉⠛⠳⠤⠤⠞⠉⠐⠀⠀⠀⠀⠀⠰⠀⢠⠁⠀⠀⠀⠆⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⡀
⠀⣠⡴⠶⠛⠋⠉⠉⠉⠈⠉⠉⠉⠙⠛⠷⣦⡀⠀⠀⠀⠸⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⡁⢈⣉⣭⣹⡷
⠺⠿⣀⠒⠒⠛⠛⠛⠶⠶⠦⢤⣀⣠⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⢀⣠⣴⠶⠟⠛⠉⢡⡼⠋
⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⠐⠈⢻⡄⠀⠀⢹⣿⡄⠀⠀⢀⣴⠟⠁⠀⢀⣶⠿⠟⠋⠁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠐⠒⠒⠛⠿⣧⡀⢿⡀⠀⠀⣿⡇⠀⢠⡾⠁⠀⣠⡾⠟⠁⢀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⣿⡇⢠⡟⠀⣰⣾⠿⠗⠛⠉⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠾⢿⣦⠀⣿⠁⣼⢁⣴⠟⠁⠀⠀⠀⣀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⠀⢻⣾⣣⡴⠶⠶⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⣿⣿⠷⠿⠿⠿⠿⠿⠷⠶⠶⢶⣦⣤⣤⣀⣀
⠀⠀⠀⢀⣀⣤⣴⠾⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢦⣤⡀
⠀⠀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷
⠀⠀⣿⠻⢶⣤⣄⣀⣀⣀⠀⠀⢀⣀⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⣿⢿⡷⠶⠶⠶⠶⠦⠤⢤⣤⣀⣀⠀⣀⣀⣠⣤⡾⠛⠉⢹⡀
⠀⠀⢿⡄⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⢶⠶⣶⣶⠿⠾⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⣿⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏
⠀⠀⠀⠀⠈⠉⢿⠓⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠚⢻⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⠀⠃
⠂⢠⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠉⠀⠄⢀⠀⠀⠀⠉⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠈⠁⠀⠀⢀⠀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠲⠀⣀⠀⠀⠒⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠂⠀⠀⡀⠰⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⠈⠀⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠈⢠⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣬⣿⣿⣿⣯⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠮⢍⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡰⠉⠑⡀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⢱⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠀⠀⠀⠈⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠓⠒⠀⠈⡝⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣠⠆⠁⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⠄⠀⠠⠤⢀⡀
⠀⢀⢊⠐⠀⢀⠎⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⡅⠀⠀⠀⣏⣈⣉⣀⡲⠊⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠠⠁⠀⢀⠔⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⠇⠀⠀⠀⢠⠀⡠⠒⠉⠀⠉⠑⠢⡀⠀⠈⢆
⢇⣀⠐⠁⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⠉⠐⠒⢢⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠉⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡠⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠊⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢉⡐⠂⠤⠤⠄⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⠀⠤⠤⠔⠒⣉⠤⠊

⠀⠀⠀⠀⡀⠀⣖⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠄
⠀⠀⠄⣊⣴⠇⣌⠳⠶⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠲⠔⣠⡮⣭⡘⣯⡸⣼⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠠⠄⡀⠀⡔⠔⡌⠀⠀⠀⡂
⠀⠛⠿⢽⣒⠲⢸⢣⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢧⣴⣾⠷⣀⣡⣴
⠀⠀⠀⠀⠋⠓⠛⠛⠉⠀⠀⠀⠀⠀⢁⠰⠀⢹⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⢿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢀⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢠
⠀⠀⠹⠠⠷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡈⠀⠀⠀⠀⠀⠈⡄⡁⠀⠃⢀
⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠇⠀⠀⠀⠀⠀⢳⡿⠻⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡰⡎⡔⠀⠀⠀⠀⠀⠘⠃⠀⠀⢡
⠀⠀⠀⡰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢈⠀⠉⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣳⡁⠀⠀⠀⠀⠀⠀⢶⡇⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠠⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⣀⠀⣤⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠣⠀⠀⠂⡠⠁
⠀⠀⠀⠀⠈⠆⡼⠃⡴⠋⣑⠈⣅⡀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⠙⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠉⠀⠀⠈⡉⡉⠘⢭⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠛⠛⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⡴⠒⠚⠛⠛⠲⠶⢤⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡇⠀⢀⡠⠖⠒⣒⣶⠶⣶⣦⡤⢿⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⡄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠀⢀⣾⣤⣀⡘⠳⠶⠶⠖⠊⠀⠸⠇⠀⠘⠐⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⠀⠰⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡏⠈⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢻⡄⡄⠀⠖⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠞⢋⡾⠷⠾⣧⡰⠆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⡤⣤⡾⠁⢠⡞⠁⠀⠀⠀⠉⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⢉⡽⠋⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⡴⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠊⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⠶⠦⣤⣤⣤⣤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢣⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠙⢦⠀⢃⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢉⠉⠒⢦⠀⠀⠀⠛⠀⠀⠀⠀⠓⢬⣼⡦⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇⠀⠀⠀⠀⡀⠤⠒⢒⡶⠿⠿⠯⢍⣉⣉⠑⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠃⠀⠀⢀⠌⢀⠜⠀⠀⢀⠔⠉⠀⠀⠔⠁⠀⠀⢡⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠓⠊⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠰⡆⢄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⣼⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⢿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠲⠤⠀⣀⣀⠀⠒⠠⠄⣀⠀⠀⠑⢄⠱⡄⠀⠀⡄⠀⢀⠅⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⣧⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠛⠶⣄⡈⠢⡘⡄⠀⡇⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠀⠈⠳⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡓⠸⣷⡀⣃⠇⠀⠀⠀⢠⠀⠀⠀⠀⣀⡤⠔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠤⠙⠚⣻⣯⠀⠀⠀⠀⣼⠆⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⢣⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠁⢙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠀⠋⠀⢨⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠑⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⣀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠚⠋⠉⠀⠀⠀⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣍⢢⡀⢀⡤⢒⡦⣄
⠀⠀⠀⣠⢴⣶⢤⠸⡄⠸⠤⠴⠃⢸⠀⠻⣍⡼⣀⠤⣄
⠀⠀⢰⡃⠸⠬⠼⠀⡨⠗⠒⠋⠉⠙⠓⠢⢄⣸⠁⡴⢦⢳
⠀⠀⠀⠳⠤⡤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⠂⠋
⢀⡔⡺⢲⠀⢰⠁⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠈⢄⠔⢒⡲⡄
⠸⡀⠑⠋⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡇⠟⣹
⠀⠉⠓⠊⠁⠘⡀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡤⠞⢀⡞⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⠉⠉⠉⠉⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡶⠶⠶⠖⠒⠚⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⡠⡖⠉⣀⣉⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⠒⠤⠄⠊⠁⠈⠖⠛⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡠⠊⠑⠒⠂⠄⣸⠀⠀⢀⣄⡄⠠⠆⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⢢⠤⠜⠹⠄⠀⠐⠀⠠⠀⠀⢀
⠀⠀⠀⢀⡴⠒⠻⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠤⠚⠤⠆⠀⠠⠀⠀⠀⠂⠀⡀
⠀⠀⠀⢯⡠⠾⠴⢣⣧⡄⠀⣤⣄⠀⣠⠀⠰⠆⠀⠉⠘⡆⠀⠙⠲⠤⠤⣀⣀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠉
⠀⠀⠀⠀⠀⠀⠰⣇⠤⠤⠄⠐⡶⠒⠊⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⢳⠀⠀⢠⠖⢢⡤⠠⣡⡖⠲⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡜⢲⡏⠉⡞⠙⢣⠚⢄⢤⣧⠗⡔⢢⠴⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⡍⠈⣻⠑⡖⠈⣠⣁⡴⠻⣄⡽⠋⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡄⠀⠀⢀⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡟⠋⠁⠀⠙⠚⣷⠀⠀⠀⠀⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢆⠀⠘⢆⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⣻⣿⡿⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣧⢹⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠻⣧⡀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠿⠃⢀⣿⠷⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⣀⣤⡶⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡆
⠀⠀⠀⢠⣾⠋⠁⢾⣿⣿⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠷⢶⣬⣿⠀⠀⠉⠛⠻⢿⣿⣿⣛⣻⣶⣶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⢛⣋⣭⡶⠟⠋⢹⣇⣉⣉⣉⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣋⣭⣀⣀⣀⠀⣾⣏⣽⠟⢋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⡉⠉⠉⠙⠛⠛⣋⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⠛⠛⠛⠶⠶⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠁
⠀⢠
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠐⢦⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠀⠀⠈⡐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⡀⠀⡐⠀⠀⠈⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘⢠⠀⠀⠀⠀⡾⠁⢀⠄⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠠⡀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⠧⠶⠤⠤⣀⠘⠀⠠⠊⡠⠂⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠈⠆⠀⠠⡄⠀⠀⢀⠗⠋⠉⣠⡢⢐⠓⢘⡦⣮⢕⡖⠀⠀⠀⢀⠀⢀⡍⠀⠀⠀⢀⣀
⠀⠀⠀⠰⢢⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠘⠄⢰⠈⠀⠁⠈⡸⠃⠀⠈⠁⡀⠠⣪⢿⡇⠀⠀⢀⡠⠜⢀⠠⠄⠒⠉⠀⠀⢹
⠀⠀⠀⢐⠀⠡⠀⠣⣀⣀⠁⡀⠀⠀⠀⢠⠖⠂⠀⢀⠠⠀⠈⠀⠀⠀⠀⠔⠊⡵⡿⠀⢀⠴⢋⡠⠊⠁⠀⢀⣀⣤⢤⠾⠇⠀⠀⡆
⠀⠀⠐⡁⠀⠀⠈⠐⢌⠉⠛⠺⠤⡀⠀⢘⠀⢘⠤⠈⠀⠀⠀⠀⠀⠠⣢⠈⠀⣰⢁⡔⣡⠔⠉⠀⢀⢄⣢⡿⢿⠟⠁⠀⢀⣤⠞
⠀⠀⠀⠁⠀⠀⠐⠦⠀⠈⠢⢄⠀⠀⠈⠻⡄⠀⠀⠁⠀⠀⠐⢁⣠⠴⠟⠓⢛⣉⣈⣥⣭⣷⣶⠶⠛⣉⠕⠂⣀⣀⣴⡾⠟⠁
⠀⠀⠰⡀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠢⣠⣦⣬⣓⠐⣒⡐⠒⣂⣉⣥⣴⠾⢛⠭⠓⡉⢋⡼⠋⣀⠔⠊⡀⡤⠞⢡⡾⣻⠊
⠀⠀⠀⠉⠙⠛⠛⠲⠾⠷⢄⠤⡦⢤⢤⣍⠙⣻⣿⣙⣛⡛⠻⠟⠋⠁⢉⠀⠀⢈⣴⣋⠔⠟⣡⣶⣯⣮⡮⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠮⠤⢤⣼⣦⣀⣠⣤⣀⣭⠙⠻⠦⣭⢀⡠⠄⠘⢋⣴⠚⠉⠛⠋⠛⠁⠒⠀⠀⠒⠐⠒⠂⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠛⠒⠒⠒⠒⠒⠂⠠⠤⠄⠐⠀⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣰⡿⡯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⣽⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡟⢿⣥⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣾⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣦⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⣾⣿⢿⣏⣼⡿⣿⣿⣿⣿⣷⣯⢻⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡿⢋⣿⣿⠟⣿⣽⣿⣿⠹⣿⢿⣿⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⠞⠁⣾⠿⡏⢠⡿⢀⣿⢿⠀⢻⠀⣿⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠉⢰⠃⠋⣀⣿⠏⡽⢀⡟⠀⠀⠡⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠀⠀⠃

⣶⡖⢲⡶⢶⣶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠉⢊⠊⢻⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢢⢀⢿⡆
⠀⠀⠀⣠⣾⣟⠟⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⡚⣾⣿
⠀⠀⣾⣿⡿⠙⣢⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣷⣷⢷⢿⣧⣤⣀⣀⣠⢤⣶⣶⣶⣄⡀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠉⠀⠉⠛⠛⠻⠿⠿⢿⣻⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠈⠉⠉⢻⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⣿⣽⣟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡝⣆⠀⠀⠀⠀⠀⠀⣠⣴⢿⣷⣶⣭⣉⣉⣋⣃⡀⢀⡀⣈⣈⣟⣋⣿⠤⠴⢒⣿⣿⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⢧⡀⠀⣠⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡍⡏⠁⠠⠿⠔⠛⠀⠀⠀⣽⣿⢀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢳⣾⣿⣥⡾⣯⢛⣿⣿⣿⣿⣿⣿⣿⣿⣫⣴⠂⢀⠄⠀⠀⠀⠀⠀⢈⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠙⢯⣧⣿⡽⣹⢿⣿⣿⣿⣿⣿⣿⣟⣿⣶⠿⢈⠀⠍⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡜⢿⣽⣿⣿⢻⣿⣿⣿⣟⣿⢿⡿⠿⠭⠤⠠⠤⠤⠐⢐⣀⣬⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠾⠿⠛⠛⠚⠉⠉⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡘⣿⢾⣿⣿⣿⣿⣿⣿⣿⣱⣡⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡞⠫⣿⣿⣿⣿⣿⣿⣟⠟⡒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣿⣿⣿⣿⣿⣿⣿⣧⡰⡅⠄⠀⠀⠀⠀⠀⠀⢸⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡅⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⣝⡇⡃⠀⠀⠀⠀⠀⠀⢠⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢿⡎⠇⠀⠀⠀⠀⣀⣀⠤⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣄⢀⣾⠟⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠋⠁⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⢄⠀⠀⠀⠀⠀⡰⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⢆⠀⠀⠀⢠⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠑⢄⠀⡇⠀⠀⠀⠈⠆⠀⠀⡂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠊⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠢⣁⠀⠀⠀⠀⠘⡀⢀⠃⠀⡀⠀⠀⢸⢀⠔⠉⠀⢹⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⠀⠠⡀⠀⠀⢡⢸⠀⠀⠁⠀⡀⢰⠋⠀⠀⠀⢸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⡄⠀⠈⠁⠰⠈⣮⠀⠀⢀⡐⢡⠃⠀⠀⠀⠀⣬⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠒⢆⡴⠢⣄⠈⡆⠀⢹⠀⢠⢸⢀⠇⠀⠀⠀⠀⠀⠇⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡅⠀⠈⢧⣡⠀⠘⡄⠀⣆⡈⠀⠀⢨⢀⠄⡸⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢃⠀⡀⠀⢻⣀⠄⡷⠀⣴⠁⠀⠀⠎⠁⢠⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠈⢲⠈⠏⠀⡀⢁⡏⠀⠀⡞⠀⢀⡇⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⡄⠓⠆⡸⠀⡿⢰⡇⠁⠰⠕⢂⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣜⣔⣼⣀⣿⣧⣸⣁⣠⣁⣠⣶⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠁⡏⠀⠀⠈⢻⣿⡇⣿⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⢰⠇⠀⠀⠀⢸⣿⡇⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⡄⢀⣵⠆⣛⣛⡛⢲⣤⡀⠀⠀⠀⣴⣶⣄⣸⣿⣯⣀⣼⣀⣀⣀⣀⣼⣿⢸⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧⣿⢣⢲⣿⣿⣿⣰⡝⣷⠀⠀⢀⣨⣭⣬⣿⣿⣿⣄⠀⡇⠀⠀⠀⢸⣿⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⣦⢩⢈⣛⣛⣛⢉⡅⣴⠂⠘⢋⣩⣤⣴⣮⣍⣝⠿⣷⣧⣤⣤⣶⣿⣿⢸⣼⡇⣿⣎⠿⠦
⠀⠀⠀⠀⠀⠀⣀⣀⣼⡇⢸⡇⢿⣮⡋⢿⣿⡿⢘⣼⠟⢀⣼⠟⣩⠤⢆⠀⠉⠛⢷⣎⢻⣿⣿⣻⣿⣿⣜⣛⣵⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⢠⢞⣝⣿⣿⣿⣾⡇⠀⣍⠓⠸⠶⠇⢛⡅⢀⣿⢃⡞⡵⠋⠉⠉⠳⡄⠈⢿⡆⣿⣿⣿⣿⣿⡿⢿⣍⣉⣉⡛⢿⣿⣿⡅
⠀⠀⢀⡄⡑⣫⢋⠞⠉⣿⣿⣿⠿⠿⠀⠀⠀⠀⢸⡇⠘⣿⠈⠸⡅⠰⣿⡗⠀⡗⣤⢸⣧⢹⣿⣿⣿⡟⠀⣴⢛⣭⣭⣍⠳⡜⢿⡇
⠀⠀⠘⣿⡅⠀⠃⠀⠀⠉⢩⣶⠿⢿⣦⡻⠿⠿⠿⠿⠎⢿⣆⠀⠑⢤⣀⡠⢞⡱⢃⣾⠇⠛⠛⠛⠛⠃⢸⡇⢿⠡⡦⢹⠇⣿
⠀⠀⠀⠛⣷⣷⠀⠀⠀⠀⢸⣿⣘⣣⣿⠇⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣚⣩⣴⡿⠁⠀⠀⠀⠀⠀⠀⠈⢧⡈⠒⠖⠊⣠⠟
⠀⠀⠀⠘⠟⠉⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢷⡄⠀⠀⠀⢸⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢻⡆⠀⠀⠀⢿⡀⣿⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⠀⠀⢸⡇⣿⣀⡼⠃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⢹⠀⣧⠀⠀⠀⣸⠃⠈⠉⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⡀⠀⠀⠀⢸⡄⣿⠀⢀⡼⠃⢀⣴⠞⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢧⠀⠀⠀⠘⣧⠘⣶⠟⠀⠀⣼⠁⠀⠀⠀⠘⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠑⢦⡀⠀⢹⡆⠋⠀⢀⣼⠃⠀⠀⠀⠀⢰⠀⢻⠀⠀⠀⠀⠀⣠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠀⣿⠀⣠⡞⠁⠀⠀⠀⠀⢀⡜⠀⢸⡇⠀⠀⠀⠀⡏⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⠶⠟⢰⡏⠀⠀⠀⠀⣴⠛⠉⠀⣀⡾⠀⣠⣤⠀⠀⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠻⣦⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⣴⠞⣫⡴⠞⠁⣼⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣷⠀⠀⠀⠀⠀⠸⣧⠀⢸⡇⠀⠀⠀⠀⢻⡄⠛⠛⠉⢀⣠⠾⠃⣀⡴⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠈⣷⠀⣠⡞⢋⣵⠾⠛⠉⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⣤⠀⠀⠘⣷⠀⠙⢦⡀⠀⠀⠀⠘⣧⠀⠈⢷⡄⠀⠀⠀⢹⡄⣿⢀⡿⠁⠀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠀⠀⠀⢳⠀⠀⠀⠀⠈⢷⣄⠀⠹⣆⠀⠀⣼⠀⣿⠸⡇⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⢧⠀⠀⠀⠀⠀⠹⣦⠀⢻⠀⣰⠏⠀⢸⡆⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣴⠶⠟⠛⠉⠉⢿⡄⢸⡆⠀⠀⠀⠀⠀⢹⡇⢸⣧⡏⠀⠀⢸⣵⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣷⢸⡇⠀⠀⣀⣤⣤⣀⣇⠀⠛⠀⠀⣠⠟⠁⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⣷⠀⠀⣿⠀⠻⠶⠚⠉⠀⠈⠛⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣤⠾⠋⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣠⠖⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⣀⣀⣤⣴⠾⠋⠁⠀⠉⢳⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣉⣉⣩⣤⣤⣤⣤⣤⣤⣈⣇⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠉⣉⣭⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠈⠁⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⠤⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢠⠀⠋⢐⡀⠁⠀⠀⠀⠘⡄⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⡀⠀⠙⣄⠲⡆⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⠀⠁⠀⠀⠈⠳⢄⣀⣀⣀⠠⠊⠀⣀⠄⠸⡀⠀⢛
⠀⠀⠀⠀⠀⢔⠢⠀⢒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢬⡉⠁⠀⠈⠉⠈⡄⠀⢧⠀⢸⡄
⠀⠀⠀⠀⢀⠈⠠⠐⠀⠀⠀⢠⣐⠀⠀⠒⠀⠀⠀⠀⠀⡀⠠⡈⠁⠑⠀⡀⠀⠸⢻⡀⠸⡄⠈⡇
⠀⠀⠀⠀⠀⠘⠀⠀⢡⡠⠂⠰⠇⠔⠁⠀⠤⠀⢀⠞⠀⠁⠀⠹⡟⠀⠀⠁⢠⡏⠀⢧⠀⢳⡀⢹⡀
⠀⠀⠀⠐⠀⠑⠀⠀⣄⡃⡆⢠⡤⠃⠴⠂⠀⠀⣊⠉⠀⠀⠀⠀⠑⠌⠄⠀⠊⠐⠀⠈⢂⠀⢷⡀⢇
⠀⠀⠀⠀⠐⠁⠀⢦⠈⠁⠛⠀⠀⠀⢠⠠⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠘⠄⠀⢀⠀⢠⠘⡤⢄⠳⣌⢆
⠀⠀⠀⠀⢀⠔⠀⠈⠥⠴⠤⠠⠤⠤⡄⠀⠢⡃⠀⠀⠈⠢⡀⡠⠀⠀⠀⠘⠉⠸⠀⠈⠉⢡⠀⠉⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⣠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠠⠤⠀⠀⠀⠒⢒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣬⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣏⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⣿⣿⣿⣷⣦⣀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢿⣷⡶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡄⣴⢣⣀⢰⠀⡇⢢⠀⡄⣸⡈⡄⡈⣆⣀⣆⢰⡆⣂⣦⠐⡀⣷⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⣀⣀⣀⣠⣤⣽⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣏⣥⣤⣴⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⢀⣶⣶⣶⣶⣤⣤⣀⢀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣤⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣀⠠⠘⣼⢹⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⣰⣀⡀⠀⠀⠀⡄
⠀⢠⡀⢨⠄⢰⡀⡠⢤⠀⢶⣄⠀⣿⡯⢀⡗⠀⠀⣿⠘⠳⣽⢘⣶⠞⠀⠀⠀⡁⠀⠀⡇⠐⠀⠀⢾⣿⣿⣷⠀⠀⣾⠅
⠀⠀⠰⡈⣇⠀⡥⠁⠎⠀⠘⣿⣿⡟⣀⣾⠇⠀⠀⢈⢾⣄⠉⣿⢃⡞⠀⠀⠀⢡⠀⢠⡷⠁⠀⠀⠈⠉⠋⠁⠀⢈⣧⡀
⠀⠀⠀⢅⡪⢤⡿⡠⠀⠀⠀⢿⣿⣯⣿⠃⠀⢠⡀⠀⠳⠬⣷⡿⠞⠋⠀⠀⠀⠀⠱⣞⢇⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣖⡄
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠈⠁⠉⠁⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠰⢰⡀⠀⣷⡁⠀⠨⡬⣞
⠀⠀⢲⣾⡄⠀⠀⣸⢁⡀⠀⣤⠀⠀⠀⣆⠀⣿⡿⠀⡀⠀⠀⠀⣀⠄⠀⢠⢀⠀⢀⠀⠀⠀⢠⢲⣼⣳⠂⠛⡢⢤⣀⢨⡷
⠀⠀⠸⡇⢷⠀⢷⣸⡸⡄⢸⠁⠀⠀⠀⣿⣾⣿⢃⣼⡇⠀⢐⠃⠌⠳⣤⣘⢺⠃⣠⠀⠄⠀⣎⢣⢻⣇⡂⠀⠀⠅⢸⡞⠂
⠀⠀⠀⠙⢮⣷⣼⡇⡇⢷⢸⡀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠈⠿⠾⣿⡷⠏⠁⠀⠀⠀⠈⠺⠿⠟⠁⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠙⢿⣧⣸⣾⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⢀⠀⢀⠀⠀⠿⠛⠛⠁⠀⠀⠀⠀⠀⠰⠊⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣼⣿⠀⣾⣿⡗⢰⣶
⠀⠀⣿⡆⣸⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠋⠐⠑⠃⠃⠂⠘⠁⠚⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿⣿⡇⣼⣿
⠀⢠⣿⠇⣿⡟⣷⠀⠀⠀⠀⢠⣄⡄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⣌⢿⣧⢻⣿⡇⣿⡇⣠⣶
⠀⠈⣿⣆⣾⣿⡟⠀⠀⢸⣾⣿⣿⣷⣦⣾⣷⠃⠀⠀⠰⡀⠘⡄⠀⠆⠀⠀⠀⠀⣄⠾⣃⠀⠘⣿⣦⢻⡜⣿⢱⡿⣵⣿⠃
⠀⠀⢸⡟⢿⡟⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠄⡃⣾⠐⠀⠀⠀⢐⠢⠜⣳⡆⠀⠈⠙⠓⠅⠙⠫⠞⠛⠁
⠀⠀⠘⠇⢸⠿⠋⠀⠀⢴⣮⣿⣿⣿⣿⡿⠟⠁⠀⠀⠰⠀⠘⣇⣟⡤⠀⠀⠀⢈⣗⠰⢛⣁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠄⠂⠲⣿⣋⠔⠀⠀⠙⠾⠿⣧⠚⣫⡄⠈⢦⡀⠸⣧⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢠⡾⠀⠀⠀⠙⢶⣿⠗⠊⠀⠀⠀⠛⠃⠋⠀⠀⠀⠀⠘⣿⣆⠉⢀⣾⡏
⠀⠀⢀⡀⠀⡾⠀⡄⠀⠀⡆⠀⠀⢸⣯⢀⣿⡇⢀⠀⡀⠀⠀⣿⠀⠀⠘⡆⠀⢠⠀⠀⠀⡀⠀⠀⠀⠻⣿⡄⠈⠹⠇⢀⡀
⠀⠀⠸⡆⠀⠺⠀⣇⠀⢰⠀⠀⡆⠸⣿⡌⣿⣇⢹⡀⣽⠀⠀⠉⣀⣭⣷⣾⣆⣸⣰⢞⣋⡁⢠⣀⡀⠀⠈⠀⠀⢀⣾⡏
⠀⠀⠀⠹⣆⠨⠀⠇⠐⠃⠀⠀⠻⣧⠹⣷⡜⣿⣾⢣⡿⠀⠀⢀⠤⠖⣒⢾⣿⣿⣿⠶⢦⡀⠀⠈⠛⠀⠂⠀⡆⠀⠙
⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠀⠀⠀⠘⢳⣌⢿⣹⡦⠛⠁⠀⠀⠀⠀⠈⠰⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁