⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠉⢳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠟⠉⢩⠋⠉⠉⠳⡄⠀⠈⣤⢠⠶⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⠀⠀⠀⢣⣀⢤⣾⣌⢱⣤⠴⠮⡀⡜⠀⣼⡐⢠⡴⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠠⠠⣀⡔⢹⡀⠀⡀⣠⣚⠉⠱⢄⠀⠀⠀⠀⢀⠖⠊⣽⠁⠀⠀⠈⣢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡁⣾⡀⢄⡤⠇⢄⡜⠁⠸⠸⣯⣿⣟⠋⠃⠀⢢⡵⠚⠿⣿⣿⢥⡀⢨⠄⠀⡴⠊⣖⢄⠀⠀⠀⠀⠀⢰⢋⢰⣇⠂⣴⡷⠀⢀⣷⣥⣴⣿⡀⠄⠂⢸⠀⠀⠀⠀⡞⠡⢀⣽⣆⡌⣴⡾⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠖⢿⣿⣿⣉⣠⠞⠃⢲⠔⢣⡟⣟⡧⢽⠄⠁⠊⢇⡀⠐⡛⠝⠟⢙⡈⠀⢸⠀⡴⠙⢳⢻⠄⠀⠀⠀⣨⠖⠻⣿⣿⣿⣱⣤⠔⠺⡿⣿⡿⣯⡅⠲⡌⠀⠀⠀⠀⡩⠒⠛⣽⣿⣿⣿⣀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠰⡿⠹⢟⠷⢠⣤⣿⣷⡀⣹⠀⠀⢸⠠⠤⡁⢀⣈⢽⠕⡀⢒⢳⠀⠀⢹⢼⡐⢂⡸⠋⠀⠀⠀⠀⠸⣄⠀⣚⠷⠓⠙⣇⠠⠁⠠⠿⠡⠙⠀⢀⡝⠀⢀⡀⡈⣇⠀⠈⢆⣿⡏⢿⠶⢑⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠑⠤⢤⠀⢷⣾⢿⣆⠂⢨⠃⡤⣿⣧⢆⣴⣿⠐⠀⠀⠳⡜⠋⣩⢋⠉⠸⡉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⢄⣾⣾⡦⠤⡀⢼⠢⠤⠔⠋⢰⡊⣀⡎⡠⠙⢦⡞⠁⢀⢹⡉⠑⢰⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡁⢀⣹⢠⠞⢒⠓⣿⣿⣿⣿⣏⡐⠄⠀⡔⠛⢻⣿⣦⠿⠃⢧⠀⠀⠀⠀⣔⠒⢠⠀⠀⠀⢸⡀⠀⢽⡟⣿⠗⣤⠃⠀⠀⠀⢰⡏⢁⢿⣿⡾⠏⠝⠓⢸⣶⣷⡿⠦⠼⡆⠀
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣧⠀⠄⠓⡠⣼⡽⠳⣧⡉⢳⡀⠱⣀⣓⠿⢿⢶⣀⠟⠀⠀⠀⠀⠣⠒⠁⠀⠀⠀⠀⠑⠤⠚⠄⣀⡴⠋⠀⠀⠀⠀⠈⢧⣈⡟⠻⡝⡆⢆⠀⢿⡿⠻⢦⠁⢠⡇⠀
⠀⠀⢠⢚⠀⠀⡈⡗⢩⡗⠊⠉⡍⠀⠀⠀⠀⠀⠑⡄⢀⡴⠢⡤⢄⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠠⠀⣭⠐⠂⠀⠁⠀⡝⡶⠇⢸⠤⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡃⠀⠀⠀⠀⠀⠀⠀⢀⡵⣢⠖⠃⠈⠉⢍⡀⢀⣸⠀⠋⠀⠀
⠀⢀⡼⠇⣤⣂⣴⣽⡧⠁⠀⢠⣧⡈⠍⡂⣢⡔⠓⢁⠺⡇⣴⠏⢻⠒⢦⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠘⠦⠥⠤⠴⠉⠢⣀⠀⢹⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢰⡗⣇⠀⠀⠀⠀⠀⣠⠶⢇⠕⠁⢀⣠⣄⣄⠀⠈⠁⠀⠀⠀⠀⠀
⠀⡎⠀⢸⣬⣿⣿⣻⡀⠀⠘⢼⡿⣝⡲⣾⣿⠃⠄⠀⠀⠙⡅⡠⠞⠉⢿⠄⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡰⠉⠀⢀⡠⡔⠿⣨⠜⠁⣠⠎⠋⠁⠀⢠⠲⣀⠀⠀⠀⠀⠀⠀
⠀⢙⣄⢀⣻⡏⠉⣻⡟⠉⡍⢱⣿⣿⣿⣿⣯⣐⣰⠀⡄⢠⡟⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣡⣴⣾⣿⣅⣤⠊⢡⣤⣎⣤⣶⡞⠙⠛⢳⣦⣽⠀⠀⠀⠀⠀⠀
⠀⢿⣹⠎⡁⠀⠀⢿⠘⢀⠙⢇⠆⣿⣿⢿⣷⡙⠻⢆⣰⠞⠀⠀⠀⢀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢳⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⢶⠶⣶⠛⡟⠹⠋⡟⠋⡏⠀⠈⣻⣶⣏⢸⣉⣏⡀⠀⠀⠀⣾⠟⢳⠀⠀⠀⠀⠀⠀
⢸⡙⣧⣀⡀⢑⠾⣽⣄⡀⠀⡈⠒⣉⠡⠄⠉⠁⠀⢘⡄⠀⠀⠀⡐⠁⠀⢢⣱⠤⡀⠀⠀⠀⠀⠀⠀⠑⠒⠾⠂⠀⠀⠀⠀⠀⢸⠀⢰⠇⣀⣠⢤⠖⠒⠋⠉⠃⠀⣁⣀⠠⠤⠔⠒⠚⠘⣄⣐⣿⣶⡟⡀⠈⡎⠉⠉⠓⢦⣩⠉⠁⠈⣿⡿⠁⠀⠀⠀⠀⠀
⠀⣧⣀⣉⣩⠭⠛⠕⠚⡿⠊⠈⢩⠗⠒⠤⡀⠀⡴⠊⠁⠀⠀⢰⢃⢀⠞⠉⠙⡑⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠹⠋⠈⠀⠀⣀⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢽⡟⣿⠑⡄⠃⠀⠀⠀⠀⠈⠛⠂⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠁⠀⠀⠀⢀⠜⠙⣄⡄⣿⣊⣀⣀⠋⡟⡆⠀⠀⠀⠀⠸⡄⣎⠠⢄⠀⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠏⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠚⠄⣀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠘⣆⠀⡹⢿⢿⡟⡿⠈⣱⠸⢱⠔⠉⠙⡔⠲⢌⣓⠬⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠤⠃⠄⠀⠀⠀⢽⠀⠀⠚⡩⣁⡠⠋⠘⠯⠂⣴⣾⣿⠤⢌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠛⢁⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠍⠄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⠒⠒⠁⠀⠀⠀⠸⡀⡸⣿⠿⣧⡌⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠄⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠸⣁⣀⣨⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠉⠀⠚⠒⢒⡲⠂⠀⡰⠊⠒⠢⡠⠧⣾⣇⣦⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠥⠘⠆⠀⠀⠀⠀⢱⠀⡜⡄⠀⠀⠀⠀⠀⠀⠀⢀⢴⠋⠁⡠⠒⠒⠀⠉⢹⣀⢠⣴⣗⠰⢄⣀⣣⣀⣾⣿⣣⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠋⠀⠀⠀⠀⠀⢇⠰⢹⡀⠀⠀⠀⠀⣠⡶⠇⠈⣠⠞⠀⠀⠀⠀⡸⠁⢠⠹⣿⣿⣿⠟⢁⣎⣠⣎⢤⣘⣶⣊⣉⡉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠔⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠃⣇⠀⠀⣠⡞⠘⠁⢀⠔⠁⠀⠀⠀⠀⠀⢣⡀⡀⠲⣿⣿⣏⢮⢸⠀⣽⢿⣯⠘⣇⠐⠀⣸⡮⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣼⣠⣾⠇⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡿⠉⡉⣷⠹⣷⢏⣿⣌⣥⠇⠀⠱⢨⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠜⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢩⠋⠈⠀⣠⠟⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⡸⠇⣇⣽⣿⣄⣈⡏⢻⠫⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠣⡈⠀⡿⠀⠀⠸⡀⠸⣾⡿⣯⡐⠀⡭⠸⣧⠘⢗⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⡞⠀⠀⠀⡠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠓⣉⠀⣀⡧⢚⠁⠀⢱⠇⠀⢫⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠋⠸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠉⣧⡀⢈⢷⢀⣘⡮⢄⣸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠇⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣄⠼⠣⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠡⠃⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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