Snack Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠚⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠛⠀⣿⡁⢘⣀⣀⡤⠢⡀
⠀⠀⠀⣀⠤⠤⠄⣀⠀⠀⠀⡰⠊⠀⢀⡤⠤⢄⡀⠈⣧⠀⠀⠀⠀⠀⡖⠲⣄⠇⠀⣸⣆⢀⢧⡏⠈⠀⠸⠁⡜
⠀⠀⡼⠁⠀⠀⠀⠀⠉⠲⠎⠀⢀⡔⠁⠀⠀⠀⢻⠀⢸⠀⠀⠀⣠⡉⠣⡈⠻⡅⠀⢩⢿⣏⠀⠛⡄⠀⠀⢰
⠀⢰⡇⠀⡔⠉⠙⠓⠦⡄⠀⢠⠯⡀⠀⠀⠀⠀⡸⠀⢸⠀⠀⢮⡈⠿⡆⠀⠀⠀⠀⠀⠜⢿⠀⠀⠃⠀⠀⠈⡇
⠀⠈⡇⠀⠱⡀⠀⠀⠀⢇⠀⠊⠀⡃⠀⠀⠀⠀⠇⠀⣼⠀⠀⠀⠈⠢⣄⠀⢀⠠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠹⡀⠀⠱⡀⠀⠀⣨⠂⠀⡰⠦⣀⠀⠀⡸⠀⢠⡇⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠙⣄⠀⠙⣤⠞⠁⢀⡞⢦⠀⠈⠑⢶⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠣⣀⠀⠀⢠⡎⠀⠀⠑⣤⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠹⠤⢖⠁⠈⠓⠒⠊⠀⠀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣀⡠⠴⠶⠊⡉⠉⠉⠩⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⣠⠔⠚⠉⠉⡉⠉⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⣹⠓⠒⠒⠂⠒⠒⠂⠂⠒⠒⠒⠒⠀⠒⠒⠀⠀⠀⢧⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠸⡇⠀⠀⠀⠀⠑⠁⠀⠈⠐⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄
⠀⠀⡠⠏⠀⠉⠈⠁⠁⠀⠀⠂⠀⠀⠀⠔⢎⠐⠂⠁⠀⠀⠘⢲⠀⠀⢳⡄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠈⡷⠈⠓⠀⠀⠄⠄⠀⠀⠄⠂⠄⠀⠠⠐⠄⡀⠂⠀⡢⣤⡼⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠉⢻⡐⠒⠉⠑⠠⠔⠀⠄⢀⣀⠖⠒⠠⠴⠐⠐⠊⣠⠎⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠙⠒⠦⠤⢦⣄⣠⣤⣀⣀⣠⣀⣠⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠊⠉⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⢁⡌⠀⠀⠀⠀⠀⠀⣈⡶⢀⠀⡀⠀⠀⠀⠀⠀⠰⣩⢹⡑⡒⠀⠀⠀⠀⠀⠀⢀⠀⣩⠏
⠀⠰⠀⠤⠀⠰⠌⠰⠀⠀⠀⠀⠸⠁⢀⠀⠈⠥⠀⠀⠀⠀⠀⠰⡃⢱⣢⢠⠀⠀⠀⠀⠀⠀⠉⠙⠚⠉⠅⠀⠀⠀⠀⠀⠴⣤⠚⠕
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊

⠀⠀⠖⠒⢒⠒⠒⠆⠀⠀⠀⠀⠀⢀⠠⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡄
⠀⠀⠀⠂⠤⢤⠀⠀⠀⠀⠀⠀⢀⠚⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⣔⠙⢄⡙⠈⠀⠀⠀⠀⡱⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢠⠪⣩⠷⢱
⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠘⠉⣉⡉⠙⠀⠀⠀⠀⠀⢠⡐⢆⠱⠄⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⠙⢬⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠚⠒⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠠⠒⠢⡈⠂⠀⠀⠀⠀⠐⣁⠄⡄⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⠀⠀⠀⠀⠞⠀⣀⢀⣀⠐⠷⠀⠀⠀⠀⠠⡮⡖⠿⠶⢄
⠀⠀⠈⢂⡂⡂⡊⠁⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⢾⢠⠤⠘⠀⠀⠀⠀⠀⠈⠀⢤⠤⡄⠂⠀⠀⠀⠀⠨⣀⠅⠀⠀⠀⡠
⠀⠀⠀⠨⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡸⠜⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠈⣄⠀⡠⠊
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢱⠊⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠦⠭⢴⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡱⠀⠀⠀⠀⠀⠘⠚⠛⠚⡃⠀⠀⠀⠀⠀⠐⠛⠄⠎⠈⠆
⠀⠈⠅⠈⠁⠉⠉⠆⠀⠀⠀⠀⠀⠠⠀⠀⠴⠀⠀⠀⠀⠀⠀⡀⠊⢥⡤⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠂
⠀⠀⢾⡦⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⡁⠀⡁⠀⠀⠀⠀⠀⠈⠢⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⡉⠉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⡽⠛⠋⠛⠛⠓⠶⢤⣄⣀⢀⣀⣠⣤⠶⠶⠶⢦⣄⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣰⣦⠀⠀⠙⢦⠀⠀⠀⠙⢷⣄⣀⠤⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡿⠀⠀⠀⢸⣾⡿⠀⠀⠀⣄⢠⡄⠀⠀⠈⠛⠛⠀⠀⠀⠈⢷⣄⢀⡤⣾⡁⢠⣤⡄⠛⠉⢀⣠⡍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⡯⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠿⠗⢈⣥⡄⢀⠾⠶⠀⠾⠿⠀⠰⠿⠉⢢⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠞⠃⠀⣀⣠⣤⣤⣤⣴⠶⠦⢤⣄⠀⠀⠨⣧⠀⡼⠁⠰⠶⠆⢡⣗⠀⠶⡶⢀⣴⡌⠛⠓⠰⣿⠀⢳
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⣡⡴⠚⠛⠉⠉⠙⠛⠲⢬⣳⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⢷⡀⢸⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⢀⣀⠈⠃⠘⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢸⡇⠀⣾⠀⠀⠚⠛⠉⠀⠀⠀⠹⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣶⠒⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠁
⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠀⠛⠳⠆⠘⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠨⡆⠘⠤⠊⠉⠓⠤⠤⢤⡀⠀⠀⠀⣠⠖⠦⣀⠀⠀⡰⠋⢸
⠀⠀⠀⠀⠸⡆⢿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⣤⠤⠶⠋⠁⠀⡀⣣⠀⠀⠀⠀⠀⣠⣀⠀⢧⡀⢀⡴⠃⢀⣄⡀⠉⠉⠀⠀⡎
⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠈⠻⠂⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠛⡿⣿⠀⠀⢦⠀⠘⢷⡿⠀⠀⢌⡤⠀⠀⢿⡿⠇⠀⢰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⣴⠇⠀⠀⠀⠘⠷⠀⠀⢸⠇⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠙⠲⠶⢤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⣆⢀⣀⡀⢀⡟⠀⠀⢹⡀⣈⣄⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠙⠾⠤⣴⠚⠺⠏⠉⠉⢧⠀⠸⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣝⣓⣲⠒⠚⠋⠁⠙⣦⣀⠀⢀⣠⠾⢦⣀⣀⣀⡴⠛⠒⠒⠀⠤⠤⠤⠀⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁




⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠦⠀⠀⠀⢀⠀⠀⠀⠐⠂⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢢⠀⠀⠀⠀⠀⠈⠀⠅
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢋⠀⢱⢸⡆⠀⠀⢀⡆
⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠤⠬⠼⠥⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠠⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢁⢠⡀⠀⠀⠀⠀⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠠⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⡀⠐⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠄⡄
⠑⠄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡴⡆⠰⣊⡥⠎⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠃⣀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣤⡄
⠀⠀⠀⠀⠀⡀⣇⠣⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣤⠾⠉⠻⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣟⣻⡿⢾⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣵⣁⣼⠀⠀⠀⠀⠀⠀⠀⣭⣤⣤⣥⣤⣤⣤⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣷⣽⣛⣿⣥
⠀⠀⠀⢀⣼⣿⣉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣤⣤⣤⣤⡀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣟⣯⣿⠉
⠀⠀⢀⣺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠙⠛⠛⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⣈⣙⣿⡇
⠀⠀⠈⠉⠙⠷⠿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠾⢯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⡴⠛⠻⠋⢓⣦⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⠀⠠⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⣋⣭⣴⣾⣿⣿⠄
⠀⠀⠀⣾⠛⠀⣶⢀⣨⣭⡇⠀⠀⠀⠀⠀⠀⠘⠳⠤⣄⡀⠀⠀⠀⢀⡴⣚⠁⠀⠀⠀⠀⠀⣴⣭⣶⣾⠿⠟⠋⠁⠈⠹⡏
⠀⠀⠀⠻⣾⠂⣴⡏⢥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⣶⣍⡲⠤⢞⣭⣾⣿⡄⠀⠀⠀⠀⢺⣿⣿⠁⠀⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠙⠳⠾⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣻⠿⣛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠰⢿⣶⣤⣉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢲⣄⣿⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡈⠛⠁⠀⠀⠀⠀⠀⠀⠰⡖⢾⠸⡇⣿⢸⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣶⣶⡄
⠀⠀⠀⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣬⣶⣷⣷⣾⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⠀⠀⡟
⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣾⣿⣦⣶⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⠟⢻⡇
⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡶⠶⢿⡟⠛⠛⠉⢻⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢿⠛⠋⠉⠹⣇⠀⠀⠈⣧⣀⣠⣤⣼⡷⠾⠿⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠟⠛⢿⡁⠀⠀⠘⡇⠀⣀⣠⣿⡶⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⢀⣤⣴⡶⢿⡟⠋⠁⠹⡆⠀⠀⢘⣧⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠸⣿⠀⠀⠈⢧⠀⣀⣠⣿⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠶⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠹⣧⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⠁⠈⠻⠀⠀⠀⣀⣠⣤⠴⠖⠛⢿⣆
⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠈⢿⡆
⢰⡟⢹⣧⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣾⡇⠀⣿⡆⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⣿⠀⠀⠸⣷⠀⠀⢻⣧⠀⠀⠀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⣿⡀⠀⠀⢿⡆⠀⠀⢻⣶⠚⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢻⡇⠀⠀⠘⣷⠀⠀⠈⢿⡄⠀⣠⡾⢁⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⢸⣧⠀⠀⠀⢻⡆⠀⠀⠘⣷⡀⠉⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⢹⣧⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣠⣶⠆⠀⢿⡆
⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣤⡷⠀⢿⣤⣀⠀⠘⣿⡀
⠀⠀⣿⡆⠀⠀⠘⣿⡀⠀⠀⠈⣿⡀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠈⣿⣷⣄⠀⠉⠹⣷⠀⢹⣧
⠀⠀⠸⣷⠀⠀⠀⢹⣇⠀⠀⠀⠸⣷⠀⠀⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣦⡀⠀⣿⡀⠀⠀⠀⠘⣿⠙⠃⠀⠘⠋⠀⠀⢿⡆
⠀⠀⠀⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⢻⣇⠀⠀⠀⠉⠻⢶⣄⡀⠀⡀⣀⣄⡀⠀⢰⡟⠀⠀⣿⣧⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠘⣿⡀⠀⠀⠸⣷⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠙⢿⡌⣿⡟⠙⢷⡄⠘⢷⣤⣴⡿⠙⠃⠀⠀⠀⠀⠀⢀⣠⡤⠶⠂⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢹⣇⠀⠀⠀⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣿⡀⠀⠀⠀⢹⣇⠀⠀⢀⣀⣀⣸⡟⠀⠉⠁⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⣰⠀⣀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠈⠙⠛⠋⠀⠀⢀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⣿⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢻⣆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⢿⡄⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠘⣷⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠹⣧⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢻⣇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡆⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⣿⡀⠀⠀⢿⡆⠀⠀⣀⣠⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠸⣧⠀⠀⠸⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣇⠀⠀⣿⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⢿⡟⠋⠉⣷⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⣿⡄⠀⢻⡇⠀⠈⠳⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠻⣏⠉⠀⠀⠈⣷⣠⣴⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⣷⠀⢸⡇⠀⠘⠳⢮⡻⠆⠀⠀⠀⢀⣠⣤⣴⣶⠟⠛⠉⠙⣧⠀⠀⢀⣹⣦⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⢿⡇⣾⡇⠀⠀⠀⢀⣀⣤⣴⠶⢿⡟⠋⠉⠀⠸⣇⠀⠀⣀⣼⣶⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣁⣤⣶⡾⠛⢻⡅⠀⠀⠀⢻⡄⠀⣀⣤⣿⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉⠁⠘⣧⠀⢀⣻⣤⣤⣴⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⣶⠿⠿⠛⠛⠉⠁

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⢀⠀⣀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠤⠤⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⣰⣦⠀⠀⠀⠀⠀⠀⢐⠀⠄⢂⠈⢀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⣠⠐
⠀⠀⢀⣠⣤⣴⣶⡆⠀⠸⠀⠈⠹⠀⠀⣠⠀⠐⣥⣤⣤⡄⣤⡄⠀⡂⠀⣀⠄⠁⠀⠀⠣⠀⠀⠠⠰⠀⠀⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠐⡐⠈
⠀⢸⡿⢟⡿⣱⣼⡇⠀⠠⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠁⠀⠀⠀⠄⠀⠀⣠⣴⠀⡄⣐⡥⠤⠄⣀⣤⠀⠆⠐⢀⣀⠐⠓⠒
⠀⢸⡷⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⣻⠀⠃⠀⠁⠈⡛⠛⠁⠠⠀⠀⢿⢸⠠⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠸⠂⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣹⡴⠛⠁⠀⠀⠀⠀⠙⠃⠄⠈⠀⠀⠈⠈⠉⠀⠀⠁⢰
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣞⣁⣀⣺⣆⠀⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡿⠋⢀⡄⠀⠀⠀⢄⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠀⢼
⠀⠸⢯⣿⣿⣽⠻⠇⠀⠀⣾⠙⡋⣩⡇⣜⡷⠀⠀⠀⠠⡰⠖⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠺
⠀⠈⠂⠤⠠⠄⠐⠁⠀⢀⠈⠒⠻⠟⠛⠛⠁⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣄⠐⠑⠄⠀⠐⠐⠁⠀⠀⠐⠀⠀⠀⢐⡹⢄⠀⠀⢘⠀⠀⠀⠀⠀⢰
⠀⠀⢀⡀⠀⠀⠒⠨⠊⠀⠁⠂⠀⠀⠀⠐⠈⠀⠈⠐⠀⠀⠀⠐⠊⠀⠀⠀⠈⠁⠐⠓⠈⠀⠀⠐⠊⠁⠂⠢⠀⠀⡐⢃⡄⠀⠐⠀⠀⡀⠀⠀⠄
⠀⠀⠈⠉⠀⠀⠄⠲⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠄⠀⠀⡀⠀⠀⠈⠄⠂⠀⢞⣘⠀⢈⠒⡆
⠀⠀⠃⠂⠀⠀⡀⣀⡤⠖⠉⠀⠀⠀⢸⡿⠛⠛⡃⠀⠀⠀⠀⠀⠀⣷⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠰⠾⠃⠁⠀⠀⢀⡀⠠⠤⠄⠠⠄⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠃⠀⠀⠀⢸⣧⣀⠘⠓⠒⠰⠆⠂⠲⠂⠙⠀⠈⣹⠃⠀⠀⠀⠀⠀⠀⠀⡰⢂⣀⠀⢰⡀⠀⢀⠀⠀⠀⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣀⣄⣀⣀⣀⣀⣀⣈⣙⣀⣀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠑⣆⡠⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⣜⢁⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠆⠀⢀⡁⠀⠐⠉⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⣾⡶⡎⠁⢸⠀⠀⠨⠀⠒⠀⠀⢒⣀⣠⣴⣶⣖⡒⠂⠒⠆⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠀⠤⠤
⠀⠀⠄⢀⠀⠀⢾⡏⠀⠐⠁⠀⠀⢜⠀⣠⠶⠿⠟⢋⡙⢫⣼⠰⢜⡆⠀⡁⠀⠀⠀⠀⢰⠰⣴⠀⡄⢀⠅⢸⡇⣇⡿⠀⣼⡟⠁
⠀⠀⡀⠀⠀⠉⠉⡀⢀⣀⠀⢀⠀⠀⠀⢧⣛⣣⣦⣦⣵⣷⣶⠿⠋⠀⠀⡇⠤⠠⠤⠠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠄⡈⠀⠉⠀⠀⠀⠀⠀⠀⣼⠂⠐⠀⠈⠉⠛⠛⠋⠉⠁⠰⣯⣩⡿⠀⡆⡠⠀⠀⠐⠀⣀⡀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠐⢠⠤⡄
⠀⢈⣈⣁⣀⣀⣈⣉⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣰⠺⡄⠅⢔⠐⠊⡀⡆⠀⠀⠀⢀⠀⠀⠀⠈⠄⠣⠀⠰⠂⠃
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⣄⠔⢨⡅⠖⡄⠀⡆⠔⠀⠑⡆⢦⠀⠣⡀⠁⠀⠀⠀⠈⠁⡐⢀⠠⠀⠈⠀⠈⠁⠂⠀⣠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠉⠀⠀⠁⠁⠀⠁⠁⠂⠐⠉⠉⠀⠀⠈⠢⠄⠀⠀⠔⠊⠀⠀⠀⠁⠒⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡈⠐⠁⡀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢰⣀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⣀⣤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⠿⡿⣷⡄⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸⣿⣥⣭⣿⢈
⠀⠀⠀⠀⠓⠲⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⣶⣷⣿⣇⡀⠀⠀⠀⠈⠀⢠⣤⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠠⠀⡀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠀⠀⠀⠀⠴
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠃⠀⠀⠂⠀⠄⠀⠐⠁⠀⠈⠉⠀⠒⠈⠀⠀⠀⠀⠈⠀⠂⠐

⠀⠀⠀⠀⠠⠠⠀⠐⢄⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠑
⠀⠀⠰⠀⠀⠀⠀⠈⠀⠆⠂⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢀⢀⢀⡀⠀⡔⠓⣀⠰⠃⠀⠀⠈⠀⢀⡈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈
⠀⠀⠀⠀⢀⠄⠀⠂⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢱⠠⢍⠉⡠⡀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⡉⠀⠀⠑⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠐⠒⠑⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠤⠠⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠓⠒⠶⠼⠧⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠡⡀⠀⠀⠀⠠⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠀⠀⠀⠘⠄⠁⠁
⠀⠀⠀⠨⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⡌⢐⠨⡟
⠀⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠸⠄⠤⠀⠠⠄⠼⠀⠀⠘⠈⠠⢄⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⡇⠀⠀⠀⠠⠐⡈⠄⡐⠣⡀⠀⣔⠂⠉⠉⠉⠉⠉⠉⠁⠐⡄⠧⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣤⣤⣴⠀⠀⠀⠀⠀⢻⣄⡀⢘⠀⠠⢌⣁⣀⣄⢈⣡⡀⠀⠆⠀⠀⡤⠉⠀⠀⠸⣁⠀⠐⡄⢨⠉⠁⠐⠒⠒⠒⠂⠉⠉⠁⡇⠀⠀⠄⠤⢠⠘
⠀⢰⡾⣿⢿⠏⣯⣽⠀⠀⢠⢀⠈⠀⠀⠉⠙⠀⠁⠈⠉⠉⠉⠈⠉⠀⡀⡇⠀⠛⠀⠀⠀⢄⠀⠀⠀⢀⡄⠀⠀⡠⣊⣀⣀⠁⣢⠀⢰⠀⠇⠀⠀⠴⠮⠅
⠀⢸⣧⣏⡾⠾⠛⠛⠀⠀⠈⠈⢉⣉⣁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠠⠀⠀⠀⠀⣠⣾⡟⣧⠀⠀⡏⠇⠰⠮⠿⠟⠀⡄⠀⣰⡏⣇⣐⣒⡂
⠀⠘⢋⡁⠀⠠⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⢈⡃⠀⡏⠉⡍⠨⡅⠨⠀⠀⠀⠀⠀⠀⠀⢰⠾⡿⣤⠟⠋⠀⡃⠃⠀⢿⣿⣀⠀⢁⠁⠀⡇⠿⠏⠁⠠⠄
⠀⠀⠀⠍⠁⠀⠄⠀⠀⠀⠀⠀⣤⠬⡉⣩⡅⠀⠁⢠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣻⠟⠁⠀⠀⠀⢠⠈⠨⠀⠀⠥⠌⡘⠀⠀⡇⢀⠀⠐⠤
⠀⢰⡦⣤⣤⣤⣤⣴⠀⠀⢀⣴⣷⣷⣿⡿⣻⣦⠁⢸⠀⠄⠀⣀⣠⢰⣆⠀⠀⡄⠀⠀⠀⠘⠁⠠⠚⠆⠀⠀⠀⠑⠠⠀⠀⠠⠐⠁⠀⠀⡇⠄⠀⠀⠀⠀⡁
⠀⠘⡛⠛⠚⠓⠒⡹⠀⠀⠘⢿⣸⣖⣾⣷⣯⡟⠃⠘⠀⠀⠱⠋⠁⠀⢸⠀⠀⡇⠀⣀⠀⠀⠀⠃⣠⠀⡀⠀⢀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠈⠉⠉⠁⢀⣀⡀⠠⡀⠉⠉⠉⠉⠁⢀⠆⠀⡄⡃⠀⠀⠀⠀⡸⠀⠀⠷⠁⣀⠑⣀⢀⠩⠐⠈⠀⢀⢠⡀⠀⠀⢸⠖⡓⠄⠀⢰⠅⠀⠀⠀⠀⠀⢽
⠀⠀⢠⣄⡀⠄⠚⠁⡚⠀⠀⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠄⠂⠉⠀⠀⠀⠘⠀⠀⢤⡭⢞⠀⢈⡉⣀⠤⣀⠀⠀⠊
⠀⠀⡄⠀⢀⠤⠔⡊⢓⢠⢤⡄⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠣⠀⠁⠐⠀⢀⣠⡄⡂⠀⠀⠒⠉⠀⠸⠥⣇⠀⣨⢹⠆
⠀⠀⠏⠐⠐⠄⠄⠠⣴⠶⠃⡀⠀⠀⠀⢸⣿⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣿⡇⠀⠀⠀⠄⠉⠀⠀⠸⠛⠓⠁⠇⠀⠀⠀⠀⠠⠠⠄⠀⠈⠄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠈⡇⠀⠀⠀⢸⣿⣄⠈⠛⠒⠒⠖⠂⠐⠒⠂⠙⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⢣⢠⠄⠸⡤⠀⣀⣀⡀⠀⢀⣀⣀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣏⠈⢀⣤⣀⡀⣄⣀⣀⣀⣈⣹⣀⣀⣈⠃⠀⠀⠀⡇⠀⠀⠀⠀⣐⣇⡠⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣠⡛⢀⠄⡄⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢤⣈⠀⣀⢁⡠⠖⠉⠀⠀⠈⠲⣀⠀⠀⠃⠀⠃⡠⠊
⠀⠀⠀⠀⠀⠀⢰⣿⣥⡟⠁⡇⠀⠀⢰⠀⠒⠀⠀⠒⠀⣀⣀⣀⣐⡒⠂⠀⠐⡄⢀⢀⣀⣀⣀⣀⣀⣀⣉⣁⣀⢀⣀⢀⢀⠀⠀⡀⢁⣀⣁⢀⣁⢀⣀⣀⢤
⠀⠀⣀⠀⠀⠀⢨⣿⢏⡠⠔⠃⠀⠀⡸⠀⢀⣬⣴⡾⡿⠛⠿⣫⡏⢥⢱⡄⠀⡇⠀⠀⠀⠀⠀⡄⣄⣔⢰⠠⢠⠀⢰⡆⣆⢲⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⠀⠀⠨⠀⣾⢰⢷⢠⣠⣛⣰⣭⣽⡶⠞⠁⠀⡇⣀⢀⣀⡀⢀⠃⠈⠃⠘⠀⠛⠀⠘⠃⠉⠋⢠⣿⡏⠀⠀⠈⠀⠀⠀⣀⣀
⠀⣐⠩⠅⠱⠎⠀⠉⠀⠉⠉⠉⣰⠀⡨⠀⠘⠳⠿⠿⠿⠿⠛⠋⣽⣶⢖⣦⠀⡇⠀⠀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⡀
⠀⠠⠼⠤⠤⠤⠤⠤⠼⠥⠬⠼⠏⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠛⠛⠃⠂⠃⡈⢥⣤⡃⠾⢚⡭⣤⢦⢱⡀⠀⠀⠀⠀⢤⠀⠀⠀⡏⣹⠑⠄⣹⣸⡆
⠀⢰⠒⠒⠒⡒⠒⠒⣒⠒⠒⠒⢶⠀⠀⢀⢀⠤⠤⣀⡀⠀⢀⡀⢀⠤⢄⡀⡀⠈⡇⠚⠭⠹⢩⠭⠢⠭⠘⢸⠁⠀⢀⠠⠔⡠⠤⢀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⢿⢩⡘⠃⠬⣸⠀⢸⣨⣅⠀⢀⠇⠽⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⡖⠊⠄⣀⠀⠀⠀⠨⠀⡐⠛⠁⠈⠈⠛⢂
⠀⠀⠀⠀⠀⠒⡆⣲⠖⠀⠀⠀⢸⠀⠀⣤⣀⡀⠁⡀⠀⠀⠀⠀⠈⠉⠁⠀⣤⡄⠀⢀⡈⠡⠭⠭⠍⢁⠀⠀⠁⠀⠀⠉⠀⠀⡀⠀⠀⡇⠈⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠤⠀⠁⠤⠐⠀⠀⠸⠀⠀⠃⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂⠀⢸⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠃⣠⢶⠶⣶⣄⢰
⠀⠀⠀⠀⡀⠀⠠⡀⠠⢀⠀⠀⠀⠀⠀⠇⠀⢀⣾⣿⠻⢛⡿⢻⢻⣿⡆⠀⠀⠄⠀⢸⠀⠒⡄⡈⠁⠸⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⡆⠻⢷⣶⡶⠿⢸
⠀⢠⠀⠀⠉⠉⢦⣈⠴⠊⠀⠀⢰⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⡅⠀⢸⠀⠀⣴⣶⠂⢰⠀⠀⠀⠠⠀⠸⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠰⡇⠀⢸⠀⠠⠄⢤⠀⢸⠀⠀⣀⠐⠀⠐⠀⢀⠠⠘⠀⢣⠀⠀⠀⠀⠀⡜
⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠃⠀⠈⠐⠂⠠⠀⠒⠈⠀⠀⠈⠉⠀⠛⠈⠁⠀⠀⠀⠀⠉⠀⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣠⠤⠒⠂⢼⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠑⠦⠤⣤⡯⠤⠖⠁⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣤⣤⣀⣀⣤⣤⡴⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠤⠤⣀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⡀⠀⢠⠀⠀⠁⠀⢀⠀⠀⠉⠲⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀⠤⠀⠀⠉⠀⠘⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠤⠤⣤⣄⣠⣤⣤⣀⣠⣤⣤⣤⣀⣀⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠳⢶⣤⣭⣿⣍⣀⣀⣀⣠⣴⢦⣤⣤⡶⠂⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡀⠉⠉⠉⠉⠉⠉⠁⣉⣠⣴⠖⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⣿⡀⠀⠉⠉⠛⠓⠚⠛⠛⠛⠉⠁⢀⣠⠄⠀⠀⠀⠈⠻⠷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⠶⠞⠋⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣠⠤⠒⠛⠋⠉⠉⠉⠉⠛⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣁⣀⣀⣀⠠⢤⣤⣄⣀⣀⡀⠀⠀⠀⣸⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣀⣈⣙⠛⠛⠛⠉⠻⢶⣄⡈⠉⠉⠁⠀⠀⢠⣿⣿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢶⣶⣤⣈⠉⠛⠿⣷⣦⣄⠀⠀⠉⠻⠷⠄⠀⠀⢀⣾⣿⠇
⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⣴⠟⠁⠘⠳⢦⣄⡉⠛⠿⢷⣦⣄⡉⠛⠿⣶⣄⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠈⡙⠷⣤⣀⠈⠙⠻⢷⣦⠈⠙⠋⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠇

⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⢖⢢⡵⠦⠶⣂⢆⣠⢀⠀⠀⠀⠀⠶⠤⠈⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠠⠄⣐⣇⣬⣥⣽⠖⣃⣿⣿⡾⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣶⣬⣍⡣⣛⣯⣾⡷⠖⠛⠉⠀⣠⡴⠎
⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⣦⠀⠀⠈⠘⠛⠋⠉⠁⣀⣠⡄⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⣀⠀⠄⠈⠀⠀⠀⢠⠀⠀⠀⠈⠛⠳⢤⡀⡀⣶⠾⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠀⠆⠀⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠡⣀
⠀⠀⠀⠠⠀⠑⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢇⠀⠃⢄⠁
⠀⠀⠘⠢⢀⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠤⠆⠘⠃⠀⠀⠠⠄
⠀⠀⠀⠀⠘⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠁⠀⠒
⠀⢀⠄⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠠⢄⡀⠀⠈⠀⠤⠀⠀⠐⠒⠃⠀⠀⠠⢀
⠀⠃⣔⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠃⠒⢄⠀⣠⢄⠀⠀⠀⠀⢀⡠⠄⠠⠂⠁
⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠈⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠎⠀⠰⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⠀⠀⠀⠀⠈⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠁⠀⣠⣤⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡜⠁⠀⠀⠻⠋⠀⠀⠀⢸⣷⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⣶⡆⠀⠀⠀⠈⠉⠀⠀⢀⣦⡀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢣
⠀⠀⠀⠀⠀⢀⠞⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⡠⠷⡀
⠀⠀⠀⠀⢠⣿⣷⣄⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⣀⣴⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⣀⠈⠉⠑⠒⠒⠒⠠⠤⠤⠤⠔⠒⠒⠒⠊⠉⠀⣀⣤⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠇⢹⠈⢣⠀⠀⠀⣴⠈⠀⠀⠀⠀⠀⠀⣰⢫⣞⡳⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠰⠲⠷⠀⢣⣴⢸⠀⠀⣬⣯⣉⡤⠄⠀⠀⠸⣧⠸⠃⠀⡷⠀⠈⡈⣥⡠⢀⠀⠀⢠⢎⡽⣷⡯⠋⠀⠀⠀⠀⠀⢰⡎⢹⡆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠞⠁⠀⠀⠀⠀⢀⠤⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠑⠉
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⢀⠀⠐⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⢀⠀⡠⣤⠀⠀⠀⢀⡐⠶⠙⢀⠆⠀⠈⠙⠻⠿⠋⠁⠀⠀⠁⣠⠈⠀⢤⡀⠀⠀⠸⠿⣿⡿⠓
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠣⠰⠏⠀⠀⠀⠀⠈⠉⠀⠔⠁⠀⠀⠀⠂⠀⠀⠀⢠⡀⢀⡾⠃⠰⠂⠀⠁⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠢⠈⠀⠀⠀⠀⠁⠀⠐⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠚⠛⠛⠃
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⠀⠀⠒⡶⢀⡀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠖⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠈⠀⡀⠀⠶⡄⠈⠛⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⠿⠆
⠀⠀⠀⠀⢺⡷⣶⠀⠀⠓⠀⢀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣦⣴⣶⠆⠀⠀⠀⠁⠠⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢶⠄⠀⠀⠀⠀⡀⢢⠀⣣⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠈⠁⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢺⠀⢀⣐⢀⣡⠔⠋⠁⠀⡂⢀⠀⠁⠀⠀⠀⠀⢏⠉⠉⢉⡤⠝
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠈⠁⠀⠈⠙⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⡿⠃⠀⢀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠔⠀⠀⠀⠀⠀⢆⠀⠠⠄⠀⠀⠀⠀⠀⣀⢀⠐⣦
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠙⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠧⠟
⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⡈⠀⠀⠀⠀⠀⡀⠀⢰⣾⢛⡛⢿⡄⠀⠀⠀⣠⢄⠀⠀⠀⠀⠖⠆⠀⠰⠚⠆⠀⠀⡰⠀⣘⡄⢀⣀⠀⢀⣴⠶⢦⡆⠘⠂
⠀⠙⠿⠶⠶⠾⠟⠀⠀⠈⠙⠚⠛⠛⠁⠀⠐⣄⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⢎⡿⠉⣿⣈⠗⠈⠋⠓⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⣶
⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢴⠆⠀⠀⠀⠘⢻⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⠄⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠰⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣴⣃⠀⠀⠀⠀⠀⢠⣀⠀⢀⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠤⠈⠀⠈⠄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⣘⠫⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠠⠆⣀⠴⢇⠀⠀⠔⠠⠄⠉⠅⠀⠀⠠⣆⣿⣧⣌⠁⠀⠀⠀⠀⡄⠐⢳⠀⠀⠀⢀⡀⠈⠉⠁⠀⠀⠀⢴⠔⠶⠰⠖
⠀⠀⠐⠂⠙⠠⠘⠀⠀⠀⣀⣀⡀⠀⠀⠀⠦⠍⠹⠄⠺⠃⠀⠀⢀⣂⠃⣸⠀⠀⠀⠀⠛⢡⣤⠐⠦⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠲⠶⠖
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠤⠀⢠⡄⠀⠀⠀⠠⣤⣤⠀⢀⠀⠀⠀⠿⠆⠀⢀⡤⢤
⠀⠀⢠⣴⡶⠆⠀⠀⠀⠂⠀⠀⠙⠀⠀⠀⡴⠟⠋⠁⠀⠀⠀⠀⠁⠠⢼⣦⠀⠀⠀⣀⡀⠀⢠⠠⡌⠀⠀⠀⠁⠐⠀⠐⠃⠚⠁
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠚⠁⠀⠀⠠⠿⠟⠙⠛⠉⠀⠀⠀⠀⠐⢁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣤⣿⣦⣾⣤⣼⣦⣴⣿⣵⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠃⠠⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠞⠁⠣⠢⠄⠀⠀⠀⠠⠀⢀
⠀⠀⠂⠀⠉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠆⠃⠈⠔⠁⠀⠀⠀⠀⠁
⠀⠰⠀⠀⢀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⢀⠀⡀
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⢃⣌⢏⢀
⠀⠀⢠⠀⠀⠌⠀⠀⢀⡘⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠀⠊
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡃⠦⠀⠒⠀⠈⣀⠤⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⢇⢵⠄⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠏⣻⠇⠀⢀⠃⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡠⠄⠒⠙⠠⠤⠐⠁⠀⠀⠀⠀⠀⢿⣿⣯⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⠒⣸⣿⣯⣐⠒⠂⢰⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣀⠔⠊⠁⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⢀⠆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡟⠀⠀⠀⠈⢛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣿⣿⠏⠀⠀⡠⠃⠀⠀⢠⣶⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠾⠋⠀⠀⠀⠀⡠⠁⠀⠈⠙⢿⣿⣿⣷⡀⠀⠀⠙⠿⠄⠄⠊⠀⠀⠀⠀⢺⡟⠁⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠐⠢⢄⣴⣿⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⡤⠖⢐⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⣠⣿⠟⢡⣿⠁⠀⣾⣿⣿⡟⠀⠈⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢰⣿⣿⡿⠁⠑⠢⢤⣤⡾⠆⠀⠈⠉⠉⠉⠉⠀⠀⠘⠛⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⢦⠀⠀⠀⣿⣿⣿⠁⠀⢠⣶⣶⠀⠀⠙⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣴⣾⡿⠷⣆⠀⠀⣾⣇⠀⠀⢠⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⡆⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⢠⣿⡟⠁⠀⠀⣰⣶⣤⡹⣿⣦⣠⠃⠀⠀⠀⣿⣿⠁⠀⠀⡆⠻⣿⣀⡠⠀⠀⠀⢘⣿⣷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⣿⠿⠃⠙⣿⣿⣦⣄⠀⠀⢻⣿⠀⠀⠀⠃⠀⠈⠉⠀⠀⡠⠒⠁⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠃⠈⠉⠁⣼⣿⠟⠁⠀⢀⠌⠀⠛⢿⣿⣷⣄⠈⢿⣇⠀⠘⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⠂⠀⠀⠀⢰⣿⠃⠀⣀⠔⠁⠀⠀⠀⠈⠻⣿⣿⣷⡀⠙⠒⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠐⠁⠀⠀⠀⠀⠈⠃⠄⠊⠀⢀⠤⢤⣄⡀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢹⣿⡄⠀⠀⢹⣿⣿⣧⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠋⠉⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠁⠂⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⣠⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⡀⢠⠀⠀⢄⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠠⠐⠀⣀⢡⡀⠆⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⡄⠀⠸⠀⠔⠘⠘⠊⠄⠀⠉⠀⠀⠡⠀⠀⠀⠀⠀⡀⡀⣧⡄⣧⡗⡠⡐⠳⡘⠆⡅⠄⣦⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⠁⠀⠀⠀⠀⠀⠁⠆⠋⣁⠘⡰⢇⠉⠆⠙⢸⠀⠄⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠾⣄⣅⠣⠈⣤⠆⣻⡼⢢⡄⢠⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⡀⢠⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠴⠥⡌⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣷⠀⠀⠀⠀⢸⠀⠐⠠⠄⠀⠔⣠⠀⡄⣶⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠀⠐⠲⠶⠶⠞⠴⠟
⠀⠀⠀⡈⠓⠠⠤⢄⠀⣀⣀⣀⠀⠀⠰⠞⠃⣈⣾⠀⠀⠀⠀⠀⢇⠀⠁⠀⠁⠈⠉⠉⠁⠒⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⡖⠒⢤⣀⡀⢀⡀⠀⠀⠀⠀⢀⡄⠉⠭⣲⠆⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢠⠉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣰
⠀⠀⠀⡗⢦⡈⠉⡀⠀⠀⠁⠈⠉⠊⠉⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⢀⠘⠷⠤⠀⠀⠀⠠⠴⠔⠒⠀⡠⠖⠁⠀⠀⠀⠀⠀⡄⠈⡀⠀⠀⠄⣄⠀⠠⠃⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠠⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠃⠂⠘⠂⠒⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠄⣠⣄⠐⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⠙⠲⠄⠀⠢⠴⠀⠀⢫⣙⢃⠀⠑⠒⠶⠆⠀⠀⠢⠐⣦⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠋
⠀⠀⠀⠀⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠂⠈⠠⠔⠠⠄⠩⠗⠠⠔⠰⠒⢠⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠊⠀⠒
⠀⠀⠀⠀⠀⠀⠉⠾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠐⠁⠀⠀⠀⠠⠘⠁⠀⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⠃⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡄⡨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣦⡌⠀⠸⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠚⠈⠀⠈⠂⠐⠂⠈⠑⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣐⣻⠿⠟⠓⠁⢻⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⡀⠀⠀⣀⣀⠘⠉⢑⠠⠠⠄⣄⣀⣰⡂⠉⠁⠀⠀⠀⠁⠈⠀⠀⢀⡀⠀⣄⣤⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣷⣶⣷⡎⠸⢦⣶⣾⣷⣶⣷⣶⣷⣤⣿⣯⣭⣄⡨⣉⠀⢂⡰⢦⠒⣊⣥⣾⣾⣿⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣄⡼⠿⠛⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣧⣿⣤⣸⣶⣿⠿⠿⠛⠋⠉⠀⠀⢀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⣀⠄⠀⠖⠒⢀⡉⠙⠤⠤⠥⣱⠀⠀⣀⠈⠐⠒⣒⠂⠀⣀⣊⠈⢧⡈⢢⣽⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⣀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄⢀⡬⠩⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢰⠁⢠⡄⣀⡤⠂⠒⠀⠤⢄⠀⠀⠀⠀⠈⠃⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠥⠔⠋⠁⠀⠀⠀⠀⠀⢀⠱⠢⢀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⢀⡠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⡀⠱⠒⠤⠤⠤⠤⠄⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡤⠖⢚⣋⣉⣉⣉⣉⣀⣠⣤⣤⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⣷⣶⣤⣀
⠀⠐⣏⠛⢛⣻⣿⣿⡿⠿⠿⠿⠿⠿⢯⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⠥⠤⠤⠤⠤⣤⣬⡉⢧
⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠟
⠀⠀⠀⠈⠲⠿⠶⠒⠒⠒⠶⠞⣶⣄⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⣶⢄⡠⠶⢶⠻⠋
⠀⠀⠀⠀⢀⠀⣨⠿⢟⣿⠿⠿⢿⡿⠯⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⠝⠋⠀⠂⢸
⠀⠀⠀⠀⡾⡜⢡⠖⠉⠀⠀⠀⢸⣷⠃⣀⡬⠓⢦⠀⠀⠀⠀⠀⣠⠔⢋⣩⠽⠋⠁⢠⣤⢀⠀⢸⡷⣄⡀
⠀⠀⠀⢰⢇⣷⠃⠀⠠⠴⠶⣦⢼⠿⠋⠀⠀⠀⠈⢳⡀⠀⠀⣴⣧⠴⠋⠁⠀⠀⠀⠈⠁⠘⠃⠘⡇⠀⠙⢆
⠀⠀⠀⣸⢸⡇⠀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠚⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠃
⠀⠀⠀⡏⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⢸⣠⠾⠃
⠀⠀⠀⡇⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡤⣴⡄⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡦⢾⣿⡆
⠀⠀⢰⡇⡏⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣹⣍⡉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣠⣿⣤⣼⢸⠁
⠀⠀⠈⢧⢧⡀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⣿⢯⣙⠓⠒⠚⠛⠛⣉⣭⣿⣟⣛⠻⢧⣤⣄⣸⣺
⠀⠀⠀⠈⢳⠬⣝⣛⣛⣓⣒⣒⣒⣒⡿⣺⣥⣄⡏⠈⠳⠈⠙⠓⣖⣚⠉⢁⡾⣍⣛⣿⢻⡽⢯⣉⡏⡧
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠉⠉⠉⢹⣿⠁⠘⢾⣶⣠⣶⣤⣴⣚⣁⣘⣞⣉⣀⣉⣩⣯⠬⠤⠚⡽
⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣄⣀⣀⣘⣋⣀⣀⣀⣀⣉⣀⣀⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠄⡀⠀⣤⣠⡦⢴⣏⣳⣀⡤
⠀⠀⠀⠀⠠⠔⣟⡨⠛⠁⣇⠀⡿⡄⡇⢰⡇⣾⢈⠟⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠴⠾⡷⢒⡲⠖⣇⣠⠃⢱⡇⠘⠃⢈⣁⣰⡀⢠⠀⢀⣞⢕⡅
⠀⠀⠀⠀⢀⡤⡟⠉⠀⠀⠉⠀⣴⣀⢸⣤⡞⣾⠓⠛⠉⠁⠀⠈⠁⠁⠀⢠⣀⣀⡤⡄
⠀⠀⠀⠀⠁⣀⠀⣀⣀⣤⣦⠛⣿⠿⠺⠖⠀⣀⣀⣠⡤⠶⢖⡈⢉⠑⠢⢇⠁⠁
⠀⠀⠀⠀⢀⢸⠟⡿⠋⠈⠏⠁⠁⣀⠤⠔⠁⠀⠘⢾⣶⣞⢨⡓⡄⢱⡤⣄⠑⠢⡀
⠀⠀⠀⠀⢇⠞⠀⠁⢀⡠⠔⢺⠿⣆⡐⠀⡀⠤⠀⢄⠞⠉⠙⢭⢇⣎⡑⡈⣇⢤⣈⠓⢄⡀
⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⢀⠠⠀⠁⠌⠒⢤⣦⡀⠈⠀⠀⣀⡀⢛⡲⠻⢜⠕⡼⠡⣄⠀⡌⠢⡀
⠀⠀⠀⠀⢰⡗⠾⣆⠀⠄⠒⠁⠀⠀⠘⡐⠀⠈⠛⢄⣸⠀⠀⢰⠊⠀⠀⠀⢻⣡⡔⡡⣺⡢⠗⡇
⠀⠀⠀⠀⢸⠑⢦⣸⠨⠤⠀⢔⢨⠢⠑⠈⣠⡟⢛⠧⠨⢟⢧⡃⢰⢁⣀⠈⣀⠧⠗⠋⠁⠀⢠⠇
⠀⠀⠀⠀⢸⠀⠀⠈⠲⣄⣐⢬⠞⢳⠞⠉⠀⢉⠋⡤⠠⡀⣆⣈⡺⠞⠛⠉⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠉⠲⢄⣜⣠⡊⣱⣸⡼⠤⠒⠋⠉⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠩⠉⠁⠀⠀⠀⠈⠀⢀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⢀⠀⣄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠚⠉⠁⠀⠀⠀⠀⢰⠻⠆⠟⠙⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣀⣰⠋⢳
⠀⠀⠀⢀⡼⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⣠⢬⣇⢀⣏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⢀⣠⠴⠒⣆
⠀⣠⢦⣉⣻⡁⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠉⣵⠒⣯⣛⣻⢷⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⣉⣀⡀⠀⢸⡀
⠴⠧⡞⠁⠉⠳⣄⡀⠀⠈⠙⠒⢲⢲⠀⠀⠀⡿⢷⣯⣏⣉⣹⡼⠃⠈⣇⠀⠀⠀⠀⠀⠙⣦⠀⡞⠁⠀⠈⣧⠀⠙⢦⡀
⠀⠀⠳⣄⠀⠀⠀⠙⠓⠶⠶⣖⣉⡛⠀⠀⠀⢱⡀⠀⠌⢉⡝⠡⠀⠀⠸⡄⠀⠀⠀⢀⠔⠃⠀⢧⣀⠀⣀⠏⠀⠀⠀⡇
⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⣰⣏⡇⠀⠀⠀⠀⠳⡀⢀⡞⠀⠀⠠⠀⠀⢳⠀⠀⠀⣏⠀⠀⠀⠀⣈⣉⡁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠒⠖⠚⠉⠁⠈⠉⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⡆⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈⠣⣄⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢣⣴⠲⣇⣸⣁⣀
⠀⠀⠀⣀⣀⣀⣟⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣎⣈⣧⡄⠀⢰⡇⡖⠀⠀⠀⣠⣾⠀⠀⢠⣄⣹⡏⢩⢿⢙⣇⠙⣽⠂
⠀⠼⣭⠭⠭⠭⠤⠤⠤⠤⢤⠿⠀⠀⠀⠀⢀⡷⠲⠒⠶⢇⡀⠀⡇⠃⡞⠛⠾⡟⠁⠀⠀⠘⠒⢦⡍⠻⣼⢸⠟⣆⠘⣆⡀
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢹⠀⡵⠒⢿⣦⣤⠇⠀⠀⠀⠀⢻⡛⠻⠦⠼⠿⠾⠛⠊⡽
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣸⣤⣷⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣷⣀⠈⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢾⠁⠈⠙⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠒⠒⠒⠒⠚⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠛⠒⣲⡾⠷⠥⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⠤⡤⢤⣤⣄⣠⣄⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠉⠉⠛⠲⠤⣄
⠀⠀⡰⠛⠉⠍⠉⠲⢼⡒⣿⢶⡲⢤⡀⠀⠀⠀⠀⣠⠖⣋⡉⡉⠫⢙⡳⢤⡀⠀⠀⠀⠀⠀⣿⡚⠲⠤⣞⡀⠀⠈⠙⢦⡀
⠀⢸⠁⠀⠀⠀⠓⠀⡀⠙⣍⢳⣗⡦⢳⠀⠀⠀⢸⡃⠖⠀⠁⠉⡠⠈⠤⠆⢳⡀⠀⠀⠀⠀⣿⡙⣦⠀⠤⠉⠻⢤⣠⠄⠙
⠀⠈⠣⣁⠀⠂⠀⠀⠀⠰⠘⣎⢹⣿⢺⠀⠀⠀⠀⣟⣓⣒⡒⠒⣒⣲⣒⢒⣾⡃⠀⠀⠀⠀⣿⠕⠃⡴⣫⣭⣿⣳⣽⠶⠒
⠀⠀⠀⠈⠓⠦⣀⠈⠀⢠⠀⢸⣼⢼⡏⠀⠀⠀⠘⢯⣭⡤⠭⢿⣥⡤⠬⠭⢴⡏⠀⠀⠀⠀⡧⢄⠘⣏⡷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⣧⠎⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣙⣶⡤⠞⠀⠀⠀⠀⠀⡧⠞⠋⠁
⣾⣷⠿⠿⠾⣿⣿⣿⣿⣾⣶⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠏⠐⠂⠒⢄⡀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢢⡀⢀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⡀⠂⢀⠀⠈⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⢀⠀⠀⡫⠵⠀⢤⡔⠌⠀⠀⢱⣦⡈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢼⠡⢠⡶⠋⠀⢀⣀⠀⡀⠀⠁⠀⠀⠀⣸⠃⣝⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢄⠑⠃⠈⠃⠠⠄⣠⡖⢀⡴⣻⠟⠂⠀⣀⣀⣼⣿⠎⣩⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠈⠁⡤⠛⠀⢘⣇⣴⣀⣤⣾⣿⣿⣿⠃⠀⡟⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⠹⠿⢿⠿⠟⠛⠉⠀⠀⠀⣇⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⠀⢀⠰⡀⠀⠀⠀⠀⠀⠀⡏⠀⢢⠈⠉⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡠⠴⠄⡁⠀⠀⢀⠀⠀⠀⡠⠀⢸⠀⢆⠸⠀⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣂⣤⠖⠁⠀⠀⠀⠁⠀⠀⠶⠀⠊⠀⠈⠢⡁⠈⠂⠀⠀⠸⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣘⠁⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠀⢀⢱⣀⣀⣀⠀⠁⡀⠁
⠀⠀⠀⠀⠀⠀⣠⠃⢃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⡀⠀⠀⠀⢔⠛⣻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⡐⠸⠀⠀⢀⡝⢶⣄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢒⣒⠒⠒⠒⠀⠀⠀⠀⠒⡒⠞⠋⠉
⠀⠀⠀⠀⡜⠀⠀⠀⠸⠀⠀⡐⠀⡀⡧⠀⠀⠑⣄⠙⠿⣦⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠃⡉⠛⡋⠉⢩⡍⠀⠡
⠀⠀⠀⠰⠁⠀⠀⠀⠀⡆⠰⠁⠀⡇⠱⣄⠐⢄⣀⠁⠀⠈⠛⢿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢒⠃⠠⢾⡇⠀⠀⢣
⠀⠀⠀⡧⠀⠀⠀⠀⠀⠱⠃⠀⠸⠁⠀⣨⠗⠸⠁⢀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⣀⠠⡄⠀⠀⠀⠄
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡠⠖⣿⠐⢉⡤⠛⣧⠀⠀⠙⠳⣦⡀⠀⠉⠒⢄⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠘
⠀⠀⣜⣀⡀⠤⠤⢴⠖⠉⠀⠘⠁⡠⠋⠀⠰⠁⠀⠸⡀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢤⢚⠀⠀⠀⢀⠆
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠈⠒⠦⠠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠐⠉⠁⠈⠈⠁⠀⠒⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣀⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⡉⣉⣁⣀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠛⠛⠛⡿⢿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠻⢲⣄⠀⠀⠈⠙⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢢⣄⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠳⣶⣶⣤⣄⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⠏⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠶⠚⠉⠁⠀⠀⠀⠈⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠖⠀⠀⠊⢹⣦
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣚⡏
⠀⠀⠀⠀⠀⠀⠛⠿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠋⢀⡤⠀⠀⠀⠀⢴⡇
⠀⠀⢰⣄⡀⠀⠀⠀⠀⠉⠛⠺⠿⢏⣻⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠢⠄⠀⠀⠈⠀⣀⡠⠎⠀⠀⠀⣞⠀⠀⠀⣾⠇⠀⠀⠀⢀⣾
⠀⠀⠸⠿⣽⣲⢤⣄⣀⣀⠀⠀⣦⣀⣠⣬⣤⣿⠋⠉⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠈⠁⠀⠀⣀⣠⡤⠒⠋⠁⠀⠀⣠⠺⠇⢳⣤⢀⡤⠂⠀⠀⠀⠀⣰⠏
⠀⠘⣦⣤⣀⠀⠉⠁⠘⠻⠁⢀⣟⠀⠀⠘⠉⠀⠀⠀⠀⠀⠒⠒⠦⠄⠀⠀⠀⠀⠀⡀⠴⠒⠉⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠉⢾⠁⠀⠀⠀⢀⣰⠁
⠀⠀⠈⠙⠛⠿⠇⢰⢦⣤⠀⠼⠃⠀⠀⠀⢀⡀⠀⠉⠉⠓⠀⠀⠀⢀⣤⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⣠⠖⠂⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢹⡞⠸⡇⠀⠀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⢀⣴⡾⠓⠂⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⠀⠀⠀⠀⠀⠹⣹⡧⠀⣀⣠⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣦⣄⣀⠀⠀⠀⠀⡀⠀⠐⠛⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠉⠛⠿⣷⣶⣌⣉⡳⠶⠂⠈⠀⣀⣠⡾⠃⠀⠀⠀⠀⣀⡀⠺⠋⠀⠀⠀⠈⠙⢆⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣤⣴⠷⠚⠁⠀⠀⠀⠀⠀⢀⠚⠁⠀⠙⣶⣤⣄⣀⣀⣠⠞⠛⢧⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠊⠉⠁⠽⣍⣹⡥⠀⠀⢘⡇
⠀⠀⠀⠘⢦⣄⣀⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣴⠋⠀⠀⠀⠀⠀⠓⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣠⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⣤⣈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢤⣄⡀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡀⠀⢀⡀⠓⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠉⠉⠉⠈⠉⠉⠐⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠉⢉⣙⠛⠷⢶⣤⣀⠀⠀⠈⠑⢄
⠀⠀⣤⢠⣄⣤⣤⡄⠀⠀⠀⠀⡠⠊⠀⠀⣠⣴⣿⠕⠊⠉⠉⡉⠉⣒⢄⡰⠁⠀⠉⢦⡀⠈⠙⠳⣦⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡴⢄
⠀⠀⢽⣿⣿⣿⢹⡇⠀⠀⠀⡜⠀⠀⢀⣴⢟⠟⠀⠀⠀⠀⠘⠜⠈⠊⠈⢟⠀⠀⠀⢠⠊⠙⢷⡖⢁⠙⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⡇⠀⠱⡀
⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⡞⠀⠀⢀⡾⢃⠎⠀⠀⠀⠀⠀⠓⠀⠚⠐⠗⡟⠀⠀⠀⠀⠑⡬⠷⢵⡦⠼⠚⠿⡄⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⢱
⠀⠀⠈⢿⠻⢛⡟⠀⠀⡸⠀⠀⢀⣾⠁⡎⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⣇⣀⠤⠄⠠⢄⣥⠒⠀⣷⡛⡤⠔⢻⣆⠀⠀⢱⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⢹⡇⠀⠀⢀⠃⠀⠀⣸⠇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⢤⠀⡯⠇⡒⡌⢉⠛⣿⡟⠃⠀⠀⢻⡄⠀⠀⡇⠀⠀⡇⠀⡠⠃
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡿⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⢌⢉⡸⠝⠀⡬⡠⠚⠓⠖⠓⠒⠒⢄⠘⣧⠀⠀⢰⠀⠀⢧⡔⠁
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡀⣨⢇⣰⡎⡤⡔⠋⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⣯⠜⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⣘⠚⠉⢉⢕⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⠀⠀⢸⠀⠀⡘⡇
⠀⠀⠀⠀⢸⢰⠀⠀⠈⡄⠀⠰⣁⣄⠀⠀⠀⢠⠊⢀⠤⣄⠸⡡⠀⠉⢢⡈⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠀⠀⡆⠀⠀⡇⡇
⠀⠀⠀⠀⠸⢸⠀⠀⠀⢱⠀⢀⣸⡟⢢⠖⠤⠃⢀⠓⠀⣈⠀⡱⣮⢄⣀⠗⠀⣘⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣾⠃⠀⢰⠁⠀⠀⡇⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢣⢇⣀⡀⠘⡄⠀⠀⢸⠀⠀⣼⢸⠄⠉⡆⠀⢰⡩⢃⠵⠈⣉⣢⣀⠀⠀⢀⠔⢁⣾⠃⠀⢠⠃⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠣⡀⠑⠚⢷⣄⠀⠘⠮⠔⠁⠸⡠⠈⡇⠀⠘⢾⡴⠞⠋⠑⣬⢧⠉⠉⠀⣴⡟⠁⠀⡠⠃⠀⠀⠀⢸⠀⠁
⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⢷⣄⡀⠀⠀⠀⠑⠜⠁⢠⠻⡄⢙⡆⠛⠭⠿⠃⣀⣴⠟⠉⠀⢀⠔⠁⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠈⠺⣬⡖⣁⣠⣤⡶⠟⠋⠁⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠉⠉⠛⠛⠛⠓⠚⠛⠉⠉⠀⠀⢀⡠⠔⠊
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⡤⣼⠟⣱⣛⣆⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠴⠚⣫⠝⠁⠀⠀⠀⠀⡾⣠⡆⡰⣹⢠⡏⣹⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢹⣠⣴⠯⠴⠒⢶⠀⢰⣿⡾⣿⠫⡿⠁⡿⠀⠉⠁⠀⡆⢀⡿⠀⠀⢀⡀
⠀⠀⠀⠀⣠⣖⣫⠔⠋⠀⢸⠁⠀⠀⣀⡴⠃⠐⠻⠜⢁⠁⠀⢀⠀⣀⠀⣇⡶⣼⣧⢞⡇⠀⠰⢋⡁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⣆⣤⠞⠁⠀⠀⠀⠀⠀⣼⠀⣾⢾⡵⣿⣰⠻⡴⢻⠃⠸⠇⠀⠀⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡏⠀⠀⠀⢀⣀⡄⠀⠀⡟⠀⣉⠈⢡⡏⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠈⠁⠀⠀⠈⢩⢿⠀⠀⠰⠷⠛⠁⠀⠈⠁⠀⠀⢀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⢉⣹⠁⢄⣑⡢⣍⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠀⠀⠀⠀⢀⣀⣤⢶⡚⠉⡕⠁⠀⠀⡄⠂⢣⣀⡀⡀⡇⠈⠂⠀⠆⣙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⢀⢄⣰⠛⠶⠃⠈⠉⠱⣈⡛⠦⣐⠚⠉⡠⠊⠁⠀⣀⠨⢃⡐⡠⠞⢉⠤⣖⣂⡌⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠙⠊⠀⠁⠀⠀⠀⠀⠠⠢⠄⢆⠀⣀⢙⠾⢤⠐⠒⣉⠕⢂⡩⠭⢕⠢⡈⠂⠇⠊⣀⡤⠞⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠒⠀⠀⠀⠀⠀⣀⣸⠉⠀⠀⡔⠊⠀⠁⣳⠐⢍⡺⢥⡐⠥⣘⣈⠼⢃⣨⠷⠒⠋⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡟⠦⣀⠀⠀⠀⢀⠤⠒⠛⠯⡀⢀⢀⢁⡠⠖⠚⠻⡇⠀⠐⡇⢈⣳⡦⠖⠚⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠙⠲⢴⣡⠀⠀⠀⣠⠞⠛⠛⢯⡀⠀⠀⢀⣸⠤⠖⠛⠉⠀⡠⠄⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠉⠓⠦⣴⣁⣆⢀⣀⣠⠷⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠭⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠀⣠⡴⠶⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡂⢄⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠠⠆⢩⠁⠀⠀⠀⢠⣴⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⢀⠈⡄⠀⠀⠀⠠⢠⣉⣩⠝⠀⣤⠤⠛⠂⡀
⠀⠀⠀⠈⠃⠁⠀⠀⠀⠗⠀⠁⠀⠀⠀⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠻⣶⣦⣟⣀⣴⡾⠃⠀⠀⠤⠾⢖⡽⠇⠀⠌⠇⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃

⠀⢀⣤⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣡
⠀⠈⢯⣽⣿⠏⣹⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣤⡁⣤⠀⣴⡀⢠⡤⣄⢠⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢫⠸⠀⣾⣿⡏
⠀⠀⠈⢻⠙⠛⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡷⣿⠻⣿⣰⠿⢷⠻⣤⡤⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢹⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢺⢿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⡀
⠀⠀⠀⠀⠈⠁⣀⣀⢤⣶⣀⠀⠀⠂⢀⡤⠀⠐⢯⠿⠀⠶⡆⠀⠀⠀⠘⠛⠈⠉⠉⠃⡀⠈⠓⠢⠬⠅⠀⠀⠠⠄⠐⠀⡀
⠀⠀⠀⠀⢸⠯⠛⢟⠋⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠀⣠⣤
⠀⠀⠀⠀⠘⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠄⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢘⡃⠃⠙⠈
⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣠⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣍⣀⣀⣩⡄
⠀⠀⠀⠂⠀⠓⠒⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢀⡉⣤⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠄
⠠⢄⠑⠈⢡⡀⠀⠁⠀⠀⠀⢀⠀⠈⢀⠀⠀⠠⠄⠆⠀⠅⠐⠀⠀⠀⣅⠀⠀⠐⠀⢽
⠠⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡀⠠⠂⠀⠀⠀⣿⣹⡟⣿⣿⣽⡇⠀⠀⠀⢠⠀⠀⡤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣷⣶⣼⣿⣿⠇⠀⢰⡀⠀⣴⠈⠁⡀⠰⢎⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠀⡀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠉⠉⢠⠀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⡄⠀⠃⠀⢠⠄⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠉⠀⠀⡀⠀⠀⠲⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠈⠃⠀⠤⠀⠀⠀⠈⠀⠈⠣⠀⠠⠂⠀⠠⡄⠤
⠀⠀⠈⠀⠀⠀⢀⢏⠂⣈⢢⠄⠒⠈⠄⠐⠸⠘⢪⠐⠀⠀⠀⡀⢀⠄⠠⠤⠀⠀⠀⠀⠀⠖⣥⠧⡀⠀⠀⠀⠀⠉⠁⠔⠦⠀⣀⠀⠀⠁⠂⠰⡇
⠐⠄⠀⠀⠀⠀⢸⡀⠈⠁⠈⠀⠇⠀⠀⠐⠀⠁⠀⠀⠀⠠⠃⠀⡤⠀⠂⠠⡄⠘⠆⠀⠈⠳⠛⡈⢤⠐⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠙
⠀⠈⠀⠀⠀⠀⠀⠀⠐⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⢁⠀⠀⠂⠀⠀⠀⠀⡄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢘⠀⠀⣈⠀⠀⠀⠠⠀⡔⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠇⢠⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠃⣀⠀⡀⠀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⠀⠀⠀⠠⣄⡀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠒⠀⠀⠀⢀⣄⣤⡄⣄
⠠⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⠐⠂⠀⠀⠀⠀⣘⣤⠛⠦⣙⡤⠙⡄
⠀⢀⢀⠀⠀⠀⠀⠀⡞⠡⠤⠀⠀⠀⠀⡀⠀⠀⣼⡿⠋⠀⠀⠀⢈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⢁⡄⠉⣤⠛⡄
⠀⣀⣀⡀⠀⠀⠀⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠊⠤⠰⠀⠃⠈⠀⠀⡀⠀⠀⠀⠀⢀⠴⡆⠀⠀⠀⠐⢃⡠⠠⣄⠜⢣⡜⢣⡄⢻⠇
⠀⠀⠁⠀⠀⠀⠀⡉⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠰⢎⡀⠶⣀⠰⢆⡠⡞
⠀⠀⠰⠀⠀⠀⠀⠘⣸⠁⠀⠀⢀⠠⠶⠆⠈⠁⠤⠴⠂⠀⣀⠔⠊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⡠⡎⢑⡄⠉⣤⠊⣰
⠀⠀⠀⠀⠀⠀⠘⠇⣹⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢂⢄⡇⠀⠀⠀⠸⢄⠘⢃⡘⠋⡀⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⣀⣠⣄⣀⠀⡤⠀⠀⠀⢀⣊⠀⠀⠂⠈⡀⠀⠀⠀⢈⡋⠇⠀⠀⠀⢘⢀⠶⠀⠰⠆⠁⣤⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠠⠬⠭⠀⠈⠃⣀⡷⢄
⠀⠀⠀⣀⠤⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⠁⠀⠀⠀⠀⠅⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⣨⠖⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢙⠀⠀⠀⠀⠀⣃⠘⠀⠀⠀⠀⠀⠆⠐⠂⠀⠀⡀
⡴⠉⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⢰⠾⠀⠀⠀⠐⠂⢀⠀⠐⠀⠐⠀⠐⢄
⡃⠀⠀⢦⠀⠐⠈⠠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢤⡀⠀⠢⢀⠀⠰⠒⠈
⡇⠀⠀⠀⠀⠀⢍⠰⠄⠀⠀⠀⠀⢘⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠀⡠⠔⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠀⠀⠀⠁⠠
⠁⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢰⣶⢿⣿⣿⣟⣿⣿⢻⠿⣿⣇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠀⠐⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠐⢂⠈⠁⠀⠀⠀⠀⠈⣿⣯⣿⣿⣿⣻⣯⣿⣾⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡅
⠀⠀⠀⠀⠀⠀⠂⠈⡑⠀⠀⠀⠀⠀⢻⠿⠿⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡂⠀⡇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠂⠂⡁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⠦⡀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠠⢀⠤⠠⠤⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢈⡀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⢀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣑⡄⠀⠈⠢⡀⠀⡜⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡇⢰⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⢀⠥⠠⠤⢀⣀⡀⠤⠔⠋⠉⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⢀⡼⡆
⠀⠀⠀⠀⠀⠀⢈⢀⣀⣀⠀⠀⠀⠀⠀⢀⡠⠓⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣼⠊⡡⠔⠁
⠀⠀⠀⠀⠀⢠⣿⣁⣀⠀⠈⠉⠉⠉⢉⣁⣀⣠⣷⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣘⣾⣳⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⢠⣀⠀⠈⠉⠉⠉⠉⠉⠀⣀⣠⣽⠀⠀⠀⠀⠀⠀⡘⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢿⠀⠀⠀⠀⢠⠊⠉⠐⠒⠒⠒⠒⠒⢒⣒⣒⠒⠒⠀⠭⠴
⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠏⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠩⠁
⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⡞⠂⡤⡤⢤⢄⡀⠀⣠⢤⢤⡤⠐⢣
⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⢀⡸⠄⠠⠤⠄⣤⣤⠄⠤⠦⠤⣅⡁⢸⠀⠀⡄⢻⢸⠘⠃⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⣒⠂⠙⠉⠰⣿⣷⣿⡧⠈⠉⠁⢒⣷⣸⠀⠀⡇⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⠀⠉⠉⠀⠚⠛⠛⠛⠋⠀⠉⠉⡀⢸⢀⠈⠣⡇⠐⠘⠀⠀⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⢄⣀⡠⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡜⠚⡇⠐⠗⠒⠒⠘⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠒⠊⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡠⠃⡸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠣⡀⢀⡤⠚⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣉⣀⡴⠥⠤⠄⠐⠒⢚
⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠈⣋⠀⠀⠀⡋⠢⣀⠀⠀⠀⠀⠀⢀⡠⢚⠇⠁⠀⢘⠂⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠢⠌⣀⠈⠁⠒⠀⠭⠭⠭⠉⠐⠂⠁⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠒⠒⠒⠒⠀⠈⠉

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

⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠄⠠⢈⡐⠁⠷⢀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠡⠄⢘⠑⠂⠗⢸⠁⠀⠀⠀⠁⠛⠋⠘⠛⠛⣮⣂⠀⠀⠠⠀⣀⠀⠀⠀⣀⠀⠴⠃⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠘⠁⠘⢆⡈⠡⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡇⠰⢆⡆⢠⠀⠤⢤⠤⡄⢠⡄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠂⠌⡃⠛⠉⡀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠈⠙⠻⠶⠧⠴⠦⠛⠊⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢄⡘⣆⠀⠀⣠⣿⣿⡿⠀⠀⠀⠠⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣞⣿⣿⣿⠃⠀⠀⠰⠀⠉⠉⣠⠀⠀⡘⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠰⠊⠹⣶⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠲⠤⠤⠊⠀⣰⠁⠀⢰⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⢰⢦⠀⠀⠀⠀⣶⣀⣀⣠⣶⢀⡀⠀⠀⠀⠐⠛⡇⠀⠀⠀⠑⢶⣴⣿⠾⠟⠁
⠀⠀⠀⠀⠃⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⢟⣣⠞⠁⠀⢀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⢸⡏⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⣠⡀⢰⠀⢠⣦⡏⢀⠄⢦⣶⣹⣧⣤⣄⠀⠀⠀⣸⠁⠀⠘⢷⣀⠀⠀⠀⣠⣀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠛⠛⠋⠁⠀⠄⠊⠙⢻⠉⠀⠈⠻⣧⠀⠁⠹⡄⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⢤⡆⠀⠈⠢⣀⣀⣀⣶⣶⠾⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠰⠶⠛⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣄⣀⣠⣶⠀⠀⢰
⠀⠀⠀⠀⠀⣴⣾⣶⣶⣶⣶⡊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⡸⠀⠀⠀⠀⠠⠛⠃⠹⠀⠇⠠⠄
⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⡛⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣦⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣀
⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⢻⡿⠇⠀⠀⠀⠀⠀⢠⡞⢋⡿⣿⠛⣦⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⠀⠀⠀⠀⠀⠀⠘⣧⠀⣳⡏⢠⡿⠀⠀⠀⠀⠀⣴⡿⢿⣿⡿⢿⣦
⠀⠀⠀⠀⠀⢸⢿⢿⢿⠿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣬⢊⡵⠁⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⠟⡄⠀⠀⠀⠀⠀⠀⢸⡿⣿⠅⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣧
⠀⠀⠀⠀⠀⠠⡾⣿⣿⡷⠊⠀⠀⠀⠀⠀⢰⡷⣶⣶⣛⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠺⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻


⠀⠀⠀⠀⠀⠀⣠⣶⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆
⠀⠀⠀⠀⠀⣼⣷⣿⣻⣿⣻⣇⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⢻⣯⣿⢿⣽⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢿⠆⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⠿⠶⠂⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢴⣦⣀⣠⣶⡆⠀⠀⠀⠀⠀⠀⢠⢩⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠷⠽⠳⠽⠻⠼⠄⠀⠀⠀⠀⠀⠸⣿⡋⣻⣿⠀⠀⠀⠀⠀⠀⢀⣻⣿⡧⠐⠉⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠈⠉⣹⣋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⣀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢐⣀⣩⣤⠤⠄⣤⣀⣀⠀⠠⡄⠤⢤⣀⡙⢅⠢⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⡤⠖⠋⢩⠏⠁⠀⠀⠀⠀⠀⠈⠉⠒⢼⡳⡄⠈⠉⠓⠧⠀⢠⡄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢨⠁⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠙⡆⠀⠀⠀⠀⠀⢸⠋⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣄⡀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠑⠲⠦⠴⠖⠋⡁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠄⣤⣠⡤⡤⠼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠒⡈⠃⠛⢐⠒⠂⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡀⠀⠀⠻⣄⡔⠁⠀⠀⠀⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⣀⡴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡔⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢧⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡉⠂⢀⠠⠒⠈⠁⡴⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⢁⡠⠤⠗
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡀⡄⠤⠴⠒⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⣡⢄
⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡵⠊
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠤⠤⠤⠤⠶⠶⠒⢻⡉
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠉⠙⠒⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⣤⠤⠼⢰⣤⣤⡤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⣸⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠘⠢⠚⠡⠀⠀⡘⠀⠙⠋⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⣀⠀⠀⣀⣀⣀⣤⠴⠖⠒⠃⠀⠑⠦⣤⣀⡀⠀⠀⠀⠈⢢

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠤⢀⠀⠀⠀⠀⠀⣀⣴⣎⣩⣶⣦⡀⠀⠀⠀⠀⠀⣀⢆⠁⠀⡌⢆⠀⠀⠀⠀⠀⡠⣶⣬⣿⣷⣴⣿⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠂⠁⠀⠀⠉⠛⣿⣿⡄⠀⠀⠀⢰⠌⡁⣈⢁⠡⠄⠇⠀⠀⠀⢠⣴⣿⣿⡁⠀⢀⣹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣟⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠙⠓⠍⣁⠀⠠⠁⠀⠀⠀⠀⠐⠤⣄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠭⠹⠿⠋⠍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠢⠊⡀⠤⠈⡄⠀⠀⠀⠠⠆⠀⠉⠿⠛⠁⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠷⣽⣿⣛⣛⣛⣫⠭⠇⠀⠀⠀⠀⠀⢄⠀⠠⢄⢁⠄⠀⠁⠀⠀⠀⢸⠓⠲⠶⠤⣤⣀⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠠⢀⡈⠃⠀⢃⡦⠂⠀⠀⠀⠀⠘⠉⠙⠛⠒⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠀⠈⠐⠄⠀⠀⠀⠀⡼⢿⡟⠁⢹⡟⠻⣷⠀⠀⠀⠀⠀⣰⣾⣿⣛⣻⣷⣶⡀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠞⠙⢢⠈⣷
⠀⠀⠀⠀⠘⠠⠶⠀⠀⡤⠀⠀⠰⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠛⠉⢃⠀⠀⠀⠀⠀⠀⠘⣄⠸⣦⣐⣁⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡤⡠⢤⠀⠁⠀⠀⡠⠂⡍⠀⠀⠀⠀⠀⠀⠀⠘⡅⠠⠀⠀⠀⠀⠀⠈⡷⠆⠉⠉
⠀⠀⠀⠀⠀⠢⡀⠈⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠞⠀⠀⠀⠣⡀⠐⠢⠤⢤⣀⣤⠤⠴⠎⠁⡠⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠆⠙⣿⣿⣿⣿⡿⠃⡓⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⣀⠐⠁⠑⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣋⠌⠀⠀⠀⠀⠀⢠⣾⣻⢻⣟⣞⣻⣿⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣿⣿⣷⣯⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⣰⢶⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⢣⡾⢅⡠⠷⡶⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠸⠷⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛

⠀⣀⢀⡀
⠀⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠈⠉⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣄⠀⠀⠀⠀⢀⣀⣤⠄⠀⠠⠔⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠈⠛⡶⢶⠶⢞⣁⣀⣀⣠⡴⠊⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡤⣶⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡷⠖⠂⠀⠀⠀⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⠶⠆⠀⠠⠄⠘⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠟⠀⢒⠶⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⠆⠈⠀⠈⠀⠛⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⣠⣤⣴⣶⡿⣿⣷⡀⠀⠈⠀⠈⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠲⢼⣷⣌⠛⣄⢠⣤⠴⢪⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⢅⣠⡆⠁⠀⠈⠓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠀⠾⠿⠃⠀⠀⠀⠀⠀⠙⠶⣤⡀
⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡀⠀⠀⢀⡀⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠙⡆
⠀⠀⠀⣠⠞⠀⠠⠤⠤⣄⡀⢻⡄⣀⢀⢶⣈⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣶⡄⠀⢹
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢷⣼⢃⣿⠶⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠸⡆
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢻⡎⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⢻⡆⠀⢰⠀⠀⠀⠀⠀⠹⣦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡟⠘⠁⠀⠀⡧
⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣨⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠐⠂⠀⢀⣾⠁⠀⠈⠳⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⡀⠀⠠⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⢀⣾⡇⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠒⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⠇⠀⡀⠠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⢦⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠤⢄⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣠⣤⣼⡇⢸⡀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢀⡀⠀⠀⢡⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠅⠸⣇⢸⣿⣦⠀⠀⠀⠰⢶⣤⡶⢢⡟⣱⡦⡄⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠦⠂⢈⣎⢻⡄⣿⣍⠐⡰⠟⡉⠄⣈⡜⠢⠗⢸⣾⣶⠏
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠻⢛⣥⣠⣦⣄⡈⠙⢷⣌⢿⣿⣧⡁⠈⠛⠳⣽⠿⠷⠾⠿⠿⠿⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠋⡹⠀⠀⠛⢷⣝⠻⢿⣦⡀⣀⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠸⣿⣿⣦⣍⣉⣾⣿⣷⣿⣾⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣇⠈⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠾⠞⠛⠛⠛⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⣿⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠛⠛⠛⢻⣿⡟⠛⠛⠛⠀⢸⣿⠀⣿⣿⠛⠛⠛⠻⠛⠀⠀⠀⠀⣼⡿⠛⠛⠿⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣟⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣟⠀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⢠⣤⣄⣀⣤⣾⡿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢸⣿⠀⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠙⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠉⠉⠙⠋⠉⠛⠉⠉⠛⠛⠛⠉⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠿⣿⣦⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠙⣿⣆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠙⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠹⣿⣆⣀⣀⣀⣤⣾⠟⠉⠀⠀⠀⠸⠿⠃⠀⠀⠘⣿⣧⣄⣀⣀⣠⣾⣿⠇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣦⣴⣶⣶⣦⣤⣦⣤⣴⣶⣴⣶⣶⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠤⢄⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠠⠤⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⢸⠁⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⢧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⢀⡈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠟⠃⠀⠰⠟⠛⠛⠦⡈⠐⣄⠃⠀⠀⠂⠠⠆⠀⠀⠀⠀⠀⠞⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠽⠀⠀⠻⠥⠀⠀⠀⠀⢹⡆⠀⠀⠀⡨⢄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⢀⠁⠄⠀⢀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⢠⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⠄⢁⠀⠀⠸⠀⠀⠐⠿⢿⣛⣛⢻⡷⠖⠀⠀⠀⢸⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠀⠀⣠⠜⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠚⠀⢨⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⢦⣤⡤⠔⠊⠀⠀⡠⠋⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⣾⡇⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠙⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⢊⠁⡘⠃⠀⠉⠿⠦⣤⣀⣀⢐⣐⠧⠀⢀⡴⠊⣴⠁⠀⠀⢉⢑⠖⠦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⢋⡜⠁⠀⠀⣠⠀⠀⠀⠀⠀⠉⣉⠉⠉⠆⠁⣸⠏⠀⡆⢰⠃⠏⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠐⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⣦⡿⠀⠈⢀⡟⣀⣔⢀⡀⠀⢰⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣸⣿⢣⡇⢠⢾⠇⣿⠟⠀⠀⢠⣤⠑⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠰⠙⣧⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢡⠏⠞⢸⣠⠇⡜⠸⢻⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠀⢸⠁⠀⠀⢸⡟⠀⠃⠀⢿⠀⣠⠄⢠⣤⠀⠈⠢⠀⠠⠂⠈⣁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠐⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣸⠃⠀⠀⠀⠈⠣⡄⢰⡿⠋⡁⠀⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⢸⠇⡀⠳⡄⠘⠧⡀⠀⠀⡈
⠀⢀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠘⡷⠸⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢀⡄⠀⡇⠀⠀⠘⠀⣰⠀⠀⠀⠀⢠⠂⠀⠁⠷⠄⢁⡀⡀
⠀⡇⠠⠀⠀⠀⠀⢀⠔⠠⠁⡤⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⢐⡅
⠀⢱⠐⠀⠀⠀⡰⠃⠀⡴⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢼⡇⠀⠀⠀⠘
⠀⠀⢣⣄⠀⠈⠀⣠⡌⠔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁
⠀⠀⠀⠐⠢⠔⠊⠁⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠆⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠘

⠀⠠⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⣠⣤⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢐⠂⡨
⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⠀⣀⣀⠀⣉⠁⣀⠀⢀⣀⡄⠆⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠘⠀⠈⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⢄⡠⠞⣀⣄⠀⠦⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠄⣀⣀⣀⣀⠀⠄⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠃⠀⠁⠀⡰
⠀⠐⠀⠀⠀⢁⠁⠠⠀⠀⡌⠀⠀⠀⠀⠤⠀⡠⠊⠑⡄⠔⠁⠀⠀⠀⠀⠉⠆⠀⠀⠃
⠀⠀⠀⠀⠀⠘⡀⠀⡃⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠃⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⠂⠀⠀⠀⠀⠀⡌⠉⠐⠤⠕⠀⠀⠀⣄⣀⣊⠁⠀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⢣⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢟⠀⠀⡕⠄⢱⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠀⡠⠈⠑⠉⠈⠲⢅⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠀⠉⠁⡰⢢⠼⠴⠁⡀⠠⠔⢁⠔⠋
⠀⡠⠄⠠⠩⠁⠠⠁⠄⠀⠜⠩⠉⠑⠢⣄⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⠀⢠⠈⠀⠂⠠⠈⠄⠀⠀⠀⠔⠁⠰⠂⠁
⠀⡄⢠⠁⠄⠀⠅⢐⠀⢀⠃⠰⠀⠀⠈⣹⠀⠀⠀⠐⠁⠀⠣⡀⠀⡤⠀⠀⠀⠀⠀⠒⠣⠤⣀⣀⣅⠔⠀⠀⠀⢀⣀⣀⣀
⠀⠋⡒⠷⠤⠼⠤⠄⠀⠠⠤⠤⠤⠤⢚⠏⠀⠀⠈⡄⠑⠳⠤⠼⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⡶⣺⣭⠻⣷⣮⣧⡀
⠀⠀⠈⠁⠒⠂⠀⠀⠀⠀⠐⠒⠒⠉⠁⠀⠀⣰⠛⢄⠂⠄⠰⠒⡪⢺⠄⠀⠀⠀⠀⠀⢀⡀⠔⠒⠉⠙⠈⣣⠑⠽⢟⣛⠕⠃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡐⢆⠈⠉⠉⢀⠤⡚⡸⠀⢀⡀⠐⠈⠀⢀⣀⣀⣀⣀⡅⢨⠤⠤⠤⠤⠤⠤⠤
⠀⠀⢀⠀⠀⠂⠀⠀⡈⠁⠀⠒⠲⢄⡀⠀⠀⠀⠁⢲⠆⡄⣈⡀⠠⠺⠁⠀⠃⠉⠉⠉⠀⠀⠒⠂⠀⠀⠁⠈⠀⠀⠀⠈⠉⠉⠉
⢀⠂⠀⠀⠀⢊⡀⠀⢀⡀⠁⢢⠀⠀⠙⢆⠀⠀⠘⡦⠈⠀⠜⢂⢆⡆⠀⠀⢒⣀⣒⣀⣀⡀⠀⠠⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠰
⡆⠀⠀⠀⠈⠃⠠⠤⠀⠤⠔⠃⠀⠀⢀⣈⡇⠀⠀⠹⠂⠁⠴⠧⠸⠀⠀⠀⠘⣄⠀⠁⠀⢀⢀⠉⠩⣁⠙⠙⡙⠋⠔⠀⠐⠊⣹
⢣⠁⠠⣀⠠⢄⢀⡀⠤⡀⣀⠔⠢⠴⠃⠀⡇⠀⠀⠀⠡⡀⠀⢀⠃⠀⠀⠀⠀⢃⠀⠉⠉⠉⠈⠉⠉⠍⠩⠭⠭⠄⠀⠈⢐⣒⡞
⠀⠳⠄⣀⣀⡀⠁⠀⠀⠈⢀⣀⣀⣀⠤⠚⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠈⠀⠒⠒⠒⠒⠂⠀⠴⠄⠤⠤⠤⠤⠄⠀⠀⠇

⠀⠀⠀⢠⣴⣾⣿⣶⣼⣿⣿⡀⠀⣬⣤⢼⠿⠸⠟⣠⣤⠄⠀⠀⠀⠠
⢰⣷⣦⣿⣿⣿⣿⣿⠇⠙⠛⠃⠀⢝⠋⠿⠻⠷⢀⡉⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣄⡀
⠘⣿⡿⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠠⢸⣷⣤⣤⠻⣋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠁⠈⠙⠿

⠀⠀⢀⢀⣠⠤
⠀⠀⠈⡃⢉⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⡄⡘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠛
⠀⣿⠋⠉⠀⠈⢀⡤⠶⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⣴⡆⣀⡀
⠀⠻⣦⣀⢀⠼⣿⣁⠀⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢤⠉⠁⠼⠳⣆⠘⠛⢿⣿⣿⣷⢀
⠀⠀⠈⠉⠁⠀⠙⠿⢿⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠠⣦⣀⠶⠂⠘⢻⡆⠀⠈⠙⠛⢻⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠉⠀⠠⠔⠆⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠰
⠀⠀⠀⠀⡄⠀⠠⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⣀⡄⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠑⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣀⢀
⠀⠀⠀⠀⠐⠒⠃⣀⡩⠀⠀⠂⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⡀
⠀⠘⢀⡃⠀⠂⠰⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⢉⡀⠉⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⢀⠀⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠋⠉⠀⠀⠀⡂⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠠⠀⠣⠄⢶
⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠆
⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠒⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠁⢀⠀⢐⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢠⠀⠤⠀⠠⠠⠀⠀⠀⠀⠀⡀⠀⠞⠉⠱⠆⢀⡀⠀⠀⠀⠀⠀⠔⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠐⠂⠀⠐⠁⠀⠀⠀⠀⢰⠈⠁⢉⠉⡍⠉⠉⠱⠀⠀⠀⠀⢀⢠⠀⠨⡤⠀⠀⠀⠀⠀⠀⠐⠉⠀⠠⠐⠈⠑⢢
⠀⠀⠀⠐⠆⠀⠀⠀⡠⠀⠀⠈⠂⠈⠈⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣀⡁⠈⠈⡰
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠢⠤⠤⠔⠊⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⡀⠀⡜⠉⠶⠄⢖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡰⠐⡄⡀⠀⣔⠓⠊⠀⠄⢤⠁⠋⠳⡐⣰⡆⡀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⢦⠀⡴⢶⡛⡉⠛⠛⡙⢟⢶⣸⠌⠋⡕
⠀⢱⠦⠑⠚⠫⠤⡳⣀⠀⠑⠊⡠⠤⡲⢿⠉⡀⠤⠜⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠠⠦⣬⠡⠀⢣⢡⠀⡇⠀⢸⢸⣧⡀⠀⢳
⡰⠋⠀⢀⣀⣠⡞⠉⠓⢀⢀⠀⠳⠴⠃⣼⠓⢦⠀⡞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡀⢠⢤⣸⢶⡁⡸⣸⢀⣷⣆⣼⡼⠙⢥⠋⠁
⠣⢄⡴⠛⠳⡀⠉⢳⡒⡜⣀⠜⡠⢊⡼⠁⠓⠤⠴⠃⠀⠀⢀⣤⠔⠒⢆⡁⣋⡵⠒⠒⠤⣄⠀⠈⢩⣇⡷⠈⠁⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠈⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣈⣀⠒⠋⠋⠙⠓⢌⢑⣾⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⡋⠉⠉⢩⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠀⡇⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠆⠱⢒⡠⡀
⠀⠀⠀⠀⠀⡠⠤⠊⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠑⠄⢬⣀⣀⣀⣇⣀⣀⡸⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠄⠀⠀⠰⣁⡨⠊⢢
⠀⠀⠀⠀⢀⡇⠘⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠤⠃⠸⣀⡵⠀⠀⠰⡈⡂
⠀⠀⠀⠀⠀⡗⢄⠈⠳⢄⡀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢀⡀⠀⠤⡀⣆⣉⠇⠈⠁
⠀⠀⠀⠀⠀⠳⡀⠑⠢⠄⣈⠉⠐⠒⢉⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⣠⠤⠉⠑⠒⠤⠤⣀⠀⠀⠘⢦⡇⠐⠒⠁⢀⣀⡾⢅⡀
⠀⠀⠀⠀⠀⠀⠈⡦⢄⡀⠀⠈⢉⡩⠟⠀⠀⠀⠀⠀⠀⠀⣀⡠⠐⠈⠀⠀⠀⠤⡀⠀⠈⠁⠀⠀⠀⢀⠠⠒⠉⡄⠀⠀⠀⠈⠁⠈⠲⣋⠃⡜⡖⠚
⠀⠀⠀⠀⠀⠀⢠⠃⢀⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⣉⣈⡋⠻⣀⠀⠀⠀⠀⠀⠀⠈⠙⢂⡠⠊⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠈⠉⠀⠉⢃⠘⡆
⠀⠀⠀⠀⠀⢀⠞⢀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠀⠀⠀⠀⢉⠝⡫⠦⣀⣀⣀⡠⢦⡐⠁⠸⡇⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠘⡄
⠀⠀⠀⠀⢀⡞⢀⠎⠀⠀⠀⠀⠀⠀⠀⠮⣁⠢⢀⠀⠀⠀⡀⣐⠑⠀⠀⠀⠀⠠⠘⠱⠄⠘⡀⡠⠗⠁⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⢦⣸
⠀⠀⠀⠀⡞⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⡈⠑⢢⠉⠉⠹⠊⠁⠈⢱⠊⠉⠙⠆⠀⠀⢆⣸⠇⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠊⠙⢦⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠆⠂⢼⠄⠒⠒⢾⠤⠒⠢⢤⠠⠒⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡠⠴⢤⣄⠠⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢌⣠⣠⠋⣠⢤⠅⣺⠁⠐⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣇⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢇⠀⢈⡦⠔⢋⢂⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢖⠛⣍⠉⠙⣇⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠫⣔⠛⠲⣅⠂⠀⣸⠼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⢊⠙⢄⠀⠀⠀⠱⡘⡄⢠⠿⢧⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠋⠉⠈⢂⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠛⢭⡀⢄⠀⠀⠐⠄⠇⠀⣀⣠⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠳⡀
⠀⠀⠀⢀⠁⠈⢏⠒⠤⠧⠄⠈⠳⠀⠙⡌⣆⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠙⢆
⠀⠀⠀⠈⡗⠒⠈⠱⠒⡦⠺⢅⣀⠤⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠃
⠀⠀⠀⠸⣄⠀⣾⠗⠚⠁

⢰⡇⢀⣀⠀⢂⢀⠀⠀⠀⣀⡈⢢⡀⠀⠀⠐⠄⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠠⠀⠀⣠
⠌⡞⠁⠀⠇⠀⠀⠀⠀⢺⣅⡷⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠐⠂⠈⠀⠄⡀⣐⣠⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⢀⢌⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠂⢣⠐⠉⠉⠀⠁⠈⠁⠀⠈⠁⠐⢰⠰⡀⠀⠀⠀⠀⠀⠀⡇⠄⠂⠒⠀⢄⠀⠃⠂⠀⠤⡀⠀⠈⠐⠀⠁⠒⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠑⠄⣠
⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠔⠁⠀⢀⡀⠀⠁⠀⠙⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠢⢄⡀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⣀⠁⠈⠉⠂⢄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠀⠀⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠂⠂⠀⠀⢁⠀⠀⠄⠀⠀⠀⠈⠀⠁⠐⠀⠠⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡀⠀⠠⠌⠀⠀⠀⠄⠠⠄⠂⡐⠂⠀⡀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡁⠤⠂⣀⣀⣀⡠⠴⠖⠒⠊⠉⠀⠀⠀⠅⠈⠀⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠆⠀⠁⠂⠤⠀⠀⠠⠂⠀⠀⠐⡀⠀⠑⠀⠀⠀⠀⠄⠀⠜⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠃
⣀⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠐⠀⣈⠡⠏⡴⢀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠈⠦⣀⡀⠀⠀⠀⠀⠀⢀⣀⠴
⢇⠀⠀⠀⢀⡠⠄⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠰⢁⡀⠃⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⠐⡀⠀⠈⠑⠀⠀⠀⢉⠉⠁⢀
⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠄⡀⠀⠐⡈⠒⠄⠒⠂⠉⢀⣀⡀⠤⠐
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠠⠐⠀⠀⠀⠠⠁⠀⠀⠀⠀⠢⠀⠐⠒⠀⠰⢴⣉⣉⠄⠄⠐⠚
⠀⠁⠀⠀⠀⠀⠀⠀⠖⠁⠀⠌⢠⠃⠀⠀⠀⠀⠀⠈⠂⢄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠃
⠀⠣⣀⡠⠤⠄⠀⠀⠀⠇⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠤⠀⠀⠀⠐
⠀⠀⠉⠂⠤⠀⠀⠤⠄⠒⠁⠀⠀⠀⠂⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⣠⠂⡠⢀⠤⠤⡀⠀⠐⢄⠀⠀⠁⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡞⠁⠀⠁⠀⣀⢀⡸⠀⣀⡀⠱⣄⠀⠀⠀⠈⠒⢌⠂⠄⠀⠀⠀⠀⠀⢠⠎
⠂⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⡸⠀⠀⠀⠀⢳⠊⠀⠱⠀⠈⠈⠁⠘⣧⣽⠂⠈⠂⠀⠀⠀⠀⠈⣆⠀⠂⠀⠀⠀⢠⠂⠀⠂
⢠⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢀⠀⡇⠀⠀⠀⠁⠐⠤⠀⠂⠀⠀⢀⠂⡔⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠁
⠀⠀⢀⠜⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣤⠀⠑⢄⠀⣰⡤⠰⡄⡚⠚⠀⠈⠉⠉⠀⠀⠉⠉⠀⠇⢱⠀⠀⢀⡀⠤⠠⡄⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠁⠒⠢⠤⠤⠤⠄⠒⡈⠁⢀⠤⣛⠄⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠐⠠⠤⠤⠰⠐⠁⠀⠀⠀⡀⢨⠁
⢀⡤⠀⠂⠀⠁⠐⠀⠀⠀⠔⠂⠀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠘⠀⠀⠀⢀⠄⠠⠀⠀⠀⠢⠜
⠠⠃⠀⠀⠀⠐⠄⣀⠈⠀⡰⠊⣋⡄⡢⠐⠊⠀⣀⡀⠤⠤⠀⡄⠀⠰⢊⠠⠤⠔⠀⢀⠊
⠠⡇⠀⠂⠀⠀⢈⡀⠀⠈⠉⠉⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠄
⠀⢀⡔⠁⠄⠠⠤⠤⡁⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠸⠂⠰⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠠⠠⠤⠤⠄⠤⠤⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠂⠈⠌⡁⠀⠰⠀⠀⠐⠋⠉⠈⠀⠀⡤⣀⣄⡀⢔⡂⠚⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠠⠀⠋⠀⠀⠀⢄⠀⠘⠛⠀⢀⠀⣐⡷⠘⠋⠀⠀⠄⣈⣄⡈⠉⠁⠀⡀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠲⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⠀⡀⠌⣈⢡⢶⠅⠘⠟⠛⠁⠘⢶⠂⠑⠉⠀⠖
⠀⠀⠀⠀⣴⡄⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢰⠈⢋⣁⣀⣰⣚⡉⠛⠁⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠠⠀⠁⠀⠁⠀⠐⠾⢃⡁⠒⠃⠀⢄⠀⠀⠀⠀⠀⠊⠁⠀⠈⠁⠀⠀⠀⢉⠀⢀⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⠠⠁⠐⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠈⠁⠀⠀⠈⠀⠠⢄⠄⠀⠐⠁⢈
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢅⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡏⠉⠉⠛⠛⠲⠶⠶⠶⣶⣤⣤⣤⣤⣤⠄⠀⠰⠀⠦⠀⠐⠶⢶⣶⣶⠒⠒⠲⣶⣶⣶⢶⣶⣶⣶⣶⣴⣤⣦⡴⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠤⡁⣀⠀⣈⣩⣨⡶⠿⠛⠛⠉⠏⠀⠀⠠⠀⠀⠀⢚⠁⢘⣄⣄⣀⢠⣌⡇⢀⣀⢠⣿⣍⡉⠉⠉⠉⠈⠉⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠉⢛⠙⠀⠀⠁⠐⣤⣤⣄⠀⠆⠐⠙⢄⣩⡤⢯⡟⢢⠉⣉⣉⣉⣿⣿⣓⠒⠒⠤⠤⠤⠤⠄⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⣴⡧⡖⠀⠂⠃⠀⡀⠀⠰⠚⢿⣿⣿⡷⠊⠀⡀⠀⣤⣬⣏⣆⣩⣈⣁⡀⠈⠉⠉⠉⠁⠉⠀⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠈⠀⢁⠉⠀⠀⠠⣴⣿⣈⠁⠐⠊⠥⢷⢳⡞⢛⣻⣿⣿⣿⣧⣾⣇⣀⣼⣆⣭⣏⣛⣛⣻⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡀⠀⠈⠁⠀⠠⢟⣳⣌⣹⡿⠏⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠉⠉⠉⠀⠀⣀⠵⢿⠫⠹⣟⣿⢿⠶⠒⠂⠀⠐⢉⠃
⠀⠐⠿⠏⠰⡀⠀⠢⣈⡇⢫⣫⠀⠀⠁⢀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢺⡄⠀⠃⠀⣞⠿⡉⠀⠀⠀⠀⢀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠻⢣⠍⠏⠐⠀⢀⣰⣶⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠏⠡⡶⠅⠐⠀⠄⠱⢂⡀⡀⠀⠐⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢁⣀⡅⠀⣯⢹⠻⡟⢦⡀⠀⠀⠀⠀⡠⠎⠁⠀⠉⣒⣀⣀⡀⠲⡆⠀⢨⠶⠤⠟⢀⣘⣚⡳⠆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠛⠿⠷⠜⠁⠀⠀⠆⠑⢄⠀⠀⠀⢴⠄⠑⠋⠀⠀⠀⠨⣉⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠂⠀⠀⠠⠁
⠀⠀⠀⠀⠄⠀⠀⣰⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⣶⣶⣶⣶⠲⠴⠖⠒⢲⢶⣦⣤⣠⡄⠤⠐⠠⡆⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠐⠈
⠀⠀⠀⠀⠀⠈⠒⠼⢤⣀⡀⣀⣀⡠⣄⠀⠀⣀⠉⢚⣛⣓⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⣰⢀⣀⡀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠒⠒⠛⠁⠁⠒⠒⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠒⠈⠉⠁⢀⣈⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠿⠋⣉⣭⠶⠛⣋⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⠉⠛⢛⠟⠛⠭⢠⡄
⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⣢⣀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠓⠒⠦⢤⣄⡀
⠀⠀⢀⠴⠊⠉⠀⢔⣮⡅⠻⢮⣿⣿⣿⡶⢤⣤⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣌⣬⣵⢦⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣭⠵⠶⠛⠋⣉⣉⣿⠿⠿⢿⣯⣯⣷⣒⣶⣧⣄⣀⣀⣿⠛⠉⠁
⠀⠀⠈⠢⢄⡀⠀⠈⠐⠀⠀⢴⣿⠿⠖⠒⠛⣩⣽⣛⡥⠴⠟⠛⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣄⣀⣤⢤⡤⢶⣤⣀⣀⣀⣤⠤⠤⡶⢤⣤⣄⣀⣠⣤⣴⠶⠦⣤⣀
⠀⠀⠀⢀⡴⠋⠀⠀⠳⠤⣤⣤⠤⠞⠀⠘⢆⡀⠀⣀⣀⡤⠞⠁⠘⢦⣀⡀⣀⣠⠜⠀⡤⡀⠈⠳⣄
⠀⠀⠀⣼⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠀⠀⠀⠈⠉⠉⢀⣀⣀⣀⣀⣀⣀⣹
⠀⠀⣴⠛⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⢲⠲⠒⠒⠒⢒⡒⠒⠛⣉⣭⣍⡉⢉⣭⣍⣉⣉⣉⣀⣠⣤⣉⡗
⠀⠀⠈⣛⣿⣙⣲⣒⣉⣶⣖⣟⣶⣖⣉⣉⣓⣶⣫⣭⢯⣉⣭⡤⠤⠤⠽⠧⠤⠤⠤⠤⠤⠧⠤⠖⡟⣶
⠀⠀⠀⣏⠓⠒⠊⠓⠤⠴⠒⠲⠒⠊⠓⠒⠒⠛⠒⠒⠛⠉⠉⠈⠙⠋⠙⠋⠉⠙⠋⠉⠑⠒⠊⠉⢀⡏
⠀⠀⠀⠙⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣤⠖⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢐⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠤⠄⣨⡅⢀⠀⢠⠠⠄⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠄⠊⠤⠂⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠂⠤⠐⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠄
⠀⢀⠀⠄⠀⠀⠀⠐⠀⢈⠁⠀⠀⠀⠀⠀⢀⠄⠄⠀⠠⠐⠀⠐⠂⠄⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⡄⠀⠡⠀⠊⠀⠀⠀⠀⠈⠐⠃⠀⠸⠨⠀⠀⠀⠀⠀⠀⠱⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡀⠀⠀⠀⠀⠀⡐⠂⢄⠘⡄⠀⠀⠀⠀⠤⠂⠀⠄
⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠰⡀⠌⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⡸⠉⠉⡢⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⢀⠐⠑⠚⠐⠬⣁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠤⡨⠤⠆⡀⠀⡔⢁⠼⠉
⠀⡠⠄⠜⠈⠀⠌⠠⠀⠠⠉⠉⠑⠢⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠉⠀⠂⠔⠡⠀⠀⠀⠄⠁⡰⠂⠁
⠠⣄⢤⠀⠀⠨⠀⠌⠁⠙⠀⠅⠀⢁⣽⠀⠀⢠⠋⠀⠘⢄⠈⠢⠀⠀⠀⠀⠀⠘⠂⠀⠀⡡⠔⠀⠀⠀⢀⣀⠀⡀
⠀⠨⣘⠃⠀⠇⠤⠠⠤⠴⠬⠠⢐⡫⠃⠀⢀⡰⠈⠘⠒⠐⢂⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡖⠉⠤⠘⣖⠈⢂
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡮⠑⠌⢐⣐⡉⠡⢺⢆⠀⠀⠀⠀⡀⠠⠐⠈⠁⠀⡄⠱⠀⠘⠢⠌⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⣈⡂⠄⠀⠄⠐⢉⠜⠀⡤⣤⡤⣤⠄⠀⠀⠀⠀⡖⢰⠒⠒⠒⢒⣒⡀
⠀⡀⠀⠀⢀⠀⠀⠠⠤⠄⡀⠈⠑⢄⠀⠀⠀⣄⠋⡔⠀⡆⢘⡹⠀⠀⡀
⡀⠀⠀⠀⢦⠐⠂⠐⠂⢀⡼⠀⠀⠀⢳⡀⠀⠘⣅⠤⢘⡠⢃⠇⠀⠀⢑⠒⠒⠒⠈⠁⠭⠽⠉⠩⢭⠭⠍⣉⢉⣉⠭
⡗⠀⠀⠀⠀⠀⠉⠉⠈⠀⢀⣀⢀⠖⠒⡇⠀⠀⠠⡀⠈⠉⡘⠀⠀⠀⠈⡗⣀⣀⣂⣂⡢⠤⠶⠥⠴⠦⠤⠤⠤⠀⢠
⠘⢄⡈⠈⠉⠐⠂⠉⠑⠒⠁⠀⠁⣀⡴⠁⠀⠀⠀⠑⠄⠔⠀⠀⠀⠀⠀⠰⠤⠤⠤⠄⠀⢀⣀⣀⣉⡉⠀⠈⠉⠉⢹

⠀⠀⠀⠀⣴⣿⣿⡿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⢸⡟⠛⠛⠃⠈⢿⡇⠀⠀⠀⠀⠀⠀⡠⢸⠁⠀⠀⠀⠀⠀⡍⢰⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣿⡆
⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠘⠀⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠋⠀⠙⢿⠇
⠀⠀⠀⠠⠠⠙⠋⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠆⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⣀⣀⡄
⠀⠀⠀⠠⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣅⠎⠀⠀⡀⠂
⠀⠀⠀⠀⠚⠀⠀⠀⠒⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⣀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠠⠜
⠀⠀⠀⠠⠈⠉⠑⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡁⣠⠤⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠐⠐⠒⠠
⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⣶⣄⠀⠀⠀⢀⣠⠖⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠁⠘⣿⠀⠀⢀⢸⠡⠤⠀⠀⠀⠀⡉⢲⠀⠀⢰⣿⣿⣿⡿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠀⠀⠸⠘⠀⠀⠀⠀⠀⠈⠃⠸⠀⠀⠻⠟⠙⠛⠁⠘⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠒⠒⠒⢦⠀⠀⠀⠀⠀⢀⠶⡆⠄⠰⡀⠀⠀⠀⠀⠀⢂⣀⢀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⠀⢃⠀⠀⠀⠀⠮⠄⠀⠀⠀⠑⡀⠀⠀⠀⠠⣨⡰⠁⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠢⡭⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠃⠀⠀⠀⠐⠀⠁⠀⠀⠃⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠑⠒⠠⠤⡆⠀⠀⠀⡄⣈⡁⣀⠤⠠⠁⠀⠀⠀⠀⢈⠄⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠾⠿⠶⠶⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠀⠀⠀⠀⠰⠖⠀⠂⠀⠀⠈⠉⠛⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⣀⣀⠀⠀⠈⠈⠙⣷⡄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣧
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⢄⣀⣀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣀⣤⣤⣤⡠⠀⠄⠀⣿⡆
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠅⠀⠀⢸⣧
⣠⣤⣸⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉⠂⠀⣰⣾⣿⣿⣿⣿⣿⣿⡿⢟⠃⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⣾⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⣤⡀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⠀⣀⡀⠀⠀⠀⡁⣼⡇⠀⠀⠀⢰
⣿⣿⣿⣿⣷⡀⠀⠀⢰⣧⣼⣧⣾⡆⣰⣿⡄⢰⣿⢿⣿⠌⣿⣆⣿⡆⣿⢸⣿⣆⣿⢠⣿⢛⣻⡆⠀⠀⢰⡿⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⡿⢀⣿⠿⣿⢸⣿⠛⣿⡄⣿⠹⣿⡇⣿⠸⣿⠹⣿⡌⢿⣬⣿⡇⠀⢠⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠁⠈⠁⠈⠁⠀⠉⠁⠉⠀⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢘⣰⡿⠁⠀⠀⠀⠀⠀⢸⣧⣴⣶⣿⣿⣶⣦⣄⣀⠀⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣥⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣮⣷⣶⣶⣶⣿⣿⣿⡽⣿⣿⣿⣿⣏⣁⣀⣀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠋⠙⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡯⣕⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢹⡏⢠⣤⣤⣄⡀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⡍⠉⣩⠉⠉⠁⠙⡀⠸⠿⠛⠉⡵⠾⠛⠛⢛⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⡄⡷⣀⢁⣰⣇⡤⠀⢀⡶⣀⣀⣐⣈⣀⡀⠀⢙⠏⢉⣉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠂⠀⣠⣶⣶⣾⣦⡀⠀⢀⣀⣸⣅⣠⢴⠟⢿⠉⠉⢳⠉⠠⠀⣴⡆⡉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣀⣴⣽⣿⣿⣷⡹⢷⣾⣿⣿⣿⢩⠁⡄⠀⠈⣿⢠⣆⡞⠃⠀⣾⣧⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣉⡀⠙⠛⠟⠛⣇⣀⣀⣾⡿⠛⠉⠒⠧⣀⣤⠾⠺⠴⠁⣉⠥⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⢲⣶⣤⠤⣤⣤⣤⢤⣤⣤⣤⣤⣴⣶⣦⣭⣅⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⢿⠛⠉⠉⠛⠶⡀⠉⣿⣺⣿⠉⠆⢽⡏⠉⠙⠛⣼⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠸⣗⣂⠰⠃⠉⠁⠀⣠⣇⢀⣈⣉⣁⣀⠒⢛⣛⣛⣉⣭⣭⠭⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣉⠁⠀⠂⠂⠐⠠⢌⢹⢿⣿⣿⣿⡍⢿⡏⠙⠛⠟⠉⠘⠛⢛⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⢂⠤⠴⠯⡁⠒⠀⠒⠒⠒⣿⠾⣿⣿⣿⣿⣷⡼⠓⠠⢠⣤⡶⠗⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠚⠶⠶⠮⠭⣤⣤⠬⠍⠉⠩⠙⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠋⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠤⠀⠀⠀⠀⢀⣠⣴⠛⠓⠒⠚⠙⠨⢧⣴⣶⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠩⠏⠟⠛⠛⠃⠬⠴⠾⠿⠛⠛⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡄⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣀⣀⢨⡤⣀⣀⣖⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⡀⠀⠀⠀⠳⠇⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠘⠋⠋⠈⢀⠲⠘⠚⠁⠈⠙⠃⠀⢠⠈⠀⣤⣤⠀⠓⠦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠤⣤⠄⠤⡤⠤⠰⠦⠄⠀⢀⢀⣤⠀⠙⢀⢷⠀⠰⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠙⢱⠀⠀⠈⠀⠄⠀⢀⠀⠀⠸⠀⠀⠀⠀⢉⢠⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠯⠉⠉⠉⠉⠋⠉⡋⠁⠀⢀⠀⠲⠟⠀⠸⠆⠰⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣤⣀⣀⡀⣀⣀⣩⡀⠀⠘⠓⠒⠂⠚⠁⠀⠀⠀⠄⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⡀⢀⠀⠀⠀⠀⠀⢀⣠⡀⠠⡜⠋⠀⠠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⠶⠤⠤⠤⠮⠧⠤⢒⠄⠀⢈⠉⠀⣀⡉⠈⡧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠞⠀⡀⡀⠀⠠⠖⠀⠀⠀⡐⠬⠀⠈⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠐⠂⠉⠁⠀⠀⠐⠒⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠶⠐⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣾⣯⣻⣷⡀⠀⠀⠀⠀⠀⠀⢠⡤⢋⡀⣤⣔⣶⣶⣾⣯⡱⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣺⣻⣿⣹⣯⠭⢟⣽⣿⠄⠀⠀⠀⠀⠀⡚⠄⣽⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡰⣾⣻⣯⡶⠿⣟⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣀⠐⣽⡿⢻⣯⣿⠿⣥⠶⠏⠻⠞⠀⠀⠀⠀⠀⢠⣯⡿⣿⣿⣿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠰⠟⣿⣿⣷⣾⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠴⠆⠼⠖⠛⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⢿⣏⣽⡞⣫⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠟⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡍⢻⡟⢻⣷⠹⡿⠁
⠀⠀⠀⠀⠘⢫⣿⣿⣿⡿⠿⣿⣟⡿⢛⡛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢊⣽⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣦⡉⢾⡇⣿⣷⣽⣶⡟
⠀⠀⠀⠀⠘⠻⠿⣾⣿⣿⣷⣟⣻⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠁⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣛⣻⣷⡄
⠀⠀⠀⠀⠀⣰⣿⡏⣿⣿⣿⡻⣸⣟⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣿⣿⣾⣿⠟⡁⢀⣿⣿⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣿⣶⡹⢾⣶⡿⠻⢯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⠿⠟⠕⠚⠁⠛⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣷⣶⡾⣿⠶⢶⣞⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡻⣛⣯⣽⣟⡀
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣟⣻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠛⢻⠿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢈⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣀⢸⣿⣯⣈⣯⣿⡿⣰⣿⣿⡏⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠐⣿⣿⡿⢿⣿⣛⡿⣃⣝⣛⣫⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠠⣄⣼⣷⢣⠃⠀⠀⠀⠀⢀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠊⢄⠈⠂⢸⡄
⠀⠀⣠⣤⣶⠛⠋⣀⣾⣀⡀⠀⠀⡠⢿⣤⣀⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠐⡇⠀⠘⣄⠐⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡰⣆⣀⡤⣶⠏⠀⢀⣠⣄⡀
⠀⠀⠀⠈⠉⠉⣻⠋⢀⡼⠙⢲⣼⡥⠶⠶⠿⢯⣛⠛⡇⢠⠞⠋⠉⠙⢳⣦⡹⣄⠁⠀⠀⣀⣴⣣⠴⢲⡖⠒⢶⣤⣠⠃⠈⠁⠸⣧⣀⡴⠋⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢠⡇⡰⠋⠀⣴⠋⠁⣠⡤⠶⣤⡀⠙⢷⣷⠏⢀⣤⠶⠚⠉⠀⢻⣼⢻⠟⣫⣿⠋⠀⠀⣸⠁⠀⢸⠀⠙⣶⣤⣀⣀⣾⡟⠳⠶⣤⣀⡀⢹
⠀⠀⠀⠀⠀⠈⣟⠁⠀⣼⠃⠀⣸⠁⢀⣀⠈⢳⠀⠈⣿⠚⠉⠀⠀⢀⣠⠖⠋⢹⣞⡼⢁⣏⠀⢀⣀⣿⣀⣀⣘⣀⣀⣿⣀⣈⣽⣏⣁⣀⣀⣤⣭⣽⣿⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣿⡶⠶⠿⠶⠶⠿⠶⠟⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⢶⡆⢾⣿⣦⣄⠀⠘⢿⡇⢰⡿⠛⠿⠀⢹⣧⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⣧⠈⢻⣷⠀⢸⡇⠸⣧⠀⠀⠀⠸⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡿⢾⡏⠁⠀⢸⠇⠀⠙⠧⣤⠄⠠⠇⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⢿⡆⠛⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡟⠀⣿⢀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣼⠃⠀⠿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡁⠀⠀⢀⣀⣀⣀⡀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣆⢾⣷⣦⣀⠀⠀⣿⠿⠿⠆⠀⢺⣿⣦⠀⠘⠋⣿⠉⠃⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⣿⠉⢻⣧⢠⣿⠋⠀⠀⠀⣾⠶⠿⡇⠀⠀⣿⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢶⡟⠁⠀⠻⣤⡴⠀⠰⠃⠀⢠⠇⠀⠀⢸⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⢤⠀⣤⠑⢦⠀⠀⢧⣀⡅⡴⠢⠊⠀⢀⠴⠒⠀⠺⣠⠀⡘⠄⠀⠒⡄⠀⢠⠋⣧⠀⢰⠋⠙⠲⢍⡉⠓⠦⢤⣀⣀
⠀⠀⢀⢁⠨⣧⣽⡤⠊⣀⠠⠤⣀⠀⠑⠀⠊⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠩⢨⡆⠈⡷⠃⢠⠏⠀⠀⠀⠀⠈⠉⢳⡄⠀⢠⠇
⠀⠀⠀⠐⢋⠙⢀⠔⠉⠀⠀⠀⠀⠉⠒⢤⡀⠀⢸⢏⠉⠐⠒⠀⠐⠒⠀⠒⠂⢙⡆⠀⠁⣠⠏⠀⠀⠀⠀⠀⠀⡤⢺⠃⢀⡏⡄
⠀⠀⠀⠑⠁⡔⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⡆⠘⠳⠭⢀⣀⣀⣀⡀⠀⢂⣀⠹⠂⠀⢸⡁⠀⠀⠠⠀⠀⢀⡞⡔⠁⠀⢸⡸
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠉⠉⠳⡄⠀⡽⢀⡴⠶⣦⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠈⠻⢵⣲⣤⣀⠀⡜⣸⣁⣀⣠⠇⡇
⠀⠀⣰⢤⡀⠘⠦⣄⠀⠀⢷⡀⣀⡠⢢⠇⢠⠇⢸⠀⢀⡾⠀⢰⠊⠓⢦⠀⠀⢈⣧⣀⣀⣀⣀⣀⡙⠪⢿⠕⠛⠒⠒⠒⠚⠁
⠀⢰⡇⠀⠘⠢⡀⠈⢢⡀⠀⠙⠒⠚⠉⣠⠎⠀⠈⣉⣉⣀⡀⠈⠳⠤⢾⠀⢸⠿⠼⣧⠤⠶⠒⠚⡃⠀⠀⠀⠀⣠⠊⠉⠳⡀
⠀⠈⣿⡀⠀⠀⠈⠓⢤⡑⠢⠤⠤⠴⠞⣡⠖⠋⠉⠉⠀⠉⠉⢙⡆⡀⠀⠀⢸⡄⠀⢹⡄⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⢠⢃
⠀⠀⢸⣧⠀⢰⠋⢓⢦⠈⠳⡀⠀⢀⡜⠈⣇⠰⠀⠀⠀⠀⠀⣸⠀⠈⠳⣄⠀⣷⠭⣭⣿⡭⠭⠿⡇⠀⠀⠀⡟⠦⠤⠤⠤⠜⡃
⠀⠀⠸⡌⣇⠈⢦⣀⣹⠇⢀⡇⠀⢸⣔⠄⠘⡆⠀⠤⠄⠀⢀⣇⠀⠐⣡⠻⡀⢱⠀⠀⠈⣧⠀⢰⠇⠀⠀⠀⠙⢾⣤⣀⣠⠞⠁
⠀⠀⠀⠳⣌⠳⢤⣀⣀⣠⡾⠁⠀⣇⢊⡷⠴⠛⠋⠉⠉⠉⠉⠈⠙⠚⣅⣀⡇⠘⢆⣀⣀⣘⣀⡼⠀⣏⠹⡀⠀⣀⡬⠉⢤⣀
⠀⠀⠀⠀⠈⠙⠒⢚⣛⣉⣠⢤⣀⠈⡩⢄⠀⠀⠀⢻⡲⣦⣄⠀⠀⠀⠀⠁⢀⣴⣦⣍⣉⣁⣀⣀⣀⠈⠛⠧⣌⣓⠒⠒⠒⠋
⠀⠀⠀⣮⠐⣾⢍⠁⠤⠤⠀⠀⠈⠻⡀⠸⡀⠀⢀⠴⡛⠛⠿⠴⠒⠒⢦⡀⠸⣯⣝⣻⠶⠦⣥⣤⣭⣭⣓⠦⣀⠀⠉⠲⣄
⠀⠀⠀⣹⡆⠈⢳⣿⢶⣤⡀⠂⠀⠀⠱⡀⣇⠀⡏⠈⠀⠀⠀⠀⠀⠀⠂⢳⠀⢈⣛⠻⠿⠿⠿⠶⠶⣾⣭⡳⣮⠇⠀⠀⠸⡆
⠀⠀⠀⠻⣉⢝⡂⠻⠦⢯⠛⠷⣦⣄⡀⠘⢎⠀⢳⠀⠀⠀⣰⠠⡄⠀⠀⡜⠀⢸⣯⣭⣉⣒⣒⣒⡒⠤⢍⠛⠃⠀⢠⠶⠚⠣⡄
⠀⠀⠈⠲⡈⠙⠪⣗⢤⡈⠒⢢⠈⠙⠫⢕⠞⠀⠈⢧⣠⡀⠀⠀⢀⠀⣰⠃⠀⠸⢾⣭⡭⣤⣤⡭⠍⡑⢢⡇⠀⢀⡾⡤⠤⣼⡇
⠀⠀⠀⢺⣷⣤⡤⢤⠑⠮⡓⢤⣁⣉⠖⠀⠀⣀⠀⠀⠑⠚⠒⠲⠶⠚⠁⢀⣠⡤⠤⠤⠭⢭⣉⠉⠳⢤⣸⡄⠀⠸⠵⣦⣼⣟⡇
⠀⢀⣴⡿⠋⠉⠐⠉⠀⠀⠈⠑⠒⠁⣠⠔⠋⠀⠉⠓⠦⣄⡀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠨⠳⡀⠀⠀⢀⣀⣀⣀⣀⠀⠁
⠀⠀⣀⣴⣒⣒⣠⣤⣴⣶⣒⣤⠀⢸⣓⠒⠒⠒⠲⣒⡶⠤⢬⣑⣢⠀⢿⢄⠀⠀⠀⠀⠀⠀⠰⡔⠁⣠⠞⣹⠃⠈⠀⠈⠑⣄
⠀⠘⡄⣧⢹⠉⠉⠉⠉⠉⠀⡔⠀⢀⡼⠃⢠⢤⡀⠀⠀⠀⠀⠀⡜⠀⠈⠪⡝⣆⠀⠀⠀⠀⠀⡆⢰⡇⢘⠆⣴⠋⢻⣆⠀⠘⡄
⠀⠀⠈⡻⣆⠀⠀⠀⠀⠀⣴⡁⠀⠈⡷⠀⠀⠉⠀⠀⣏⣿⠀⠀⢸⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⢳⠘⡇⡇⠀⠙⠦⠾⢃⡤⣸⠁
⠀⠀⠀⠙⠺⢷⣶⣶⣶⠾⠓⠁⠀⠀⠷⠤⠤⠤⠤⠔⠦⠤⠤⠤⠼⠀⠀⠀⠘⢮⣇⣀⣀⣀⣀⡼⠀⠙⠮⣍⣙⠒⣉⣻⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠋⣼⠟⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠀⠀⣼⠏⠀⠀⣼⣿⡍⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡟⠀⠀⠀⣸⠏⠀⠀⢰⣿⠀⠛⠶⢶⡾⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠃⠀⠀⠀⣿⠀⠀⠀⠘⣿⣀⢀⣀⣀⣀⣀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⡆⠀⠀⠀⢻⣧⠀⠀⠀⠈⠙⠛⠉⠉⠉⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣼⣧⡀⠀⠀⠀⠙⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠘⣿⣷⣦⡀⠀⠀⠀⠉⠙⠻⠿⠿⠿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠘⣿⠉⠙⠻⢷⣦⣤⣤⣤⣤⡄⠀⠀⠀⠀⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⠀⠀⠀⢻⣧⠀⠀⠀⠀⠙⢿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣆⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠉⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣌⢿⣦⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣹⡟⠷⣽⣷⣤⣀⠀⠀⠀⠈⠙⠛⠿⠶⠶⠶⠶⠶⠿⠿⢷⣦⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇⠀⠀⠙⢿⡿⠻⠶⢶⣤⣤⣤⣤⣶⠶⠒⠂⠀⠀⠀⠀⠈⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠸⣿⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣶⣤⣄⠀⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠘⢿⣄⠀⠀⠀⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⠲⣤⣽⣷⣄⡀⠀⠀⠀⠉⠻⠷⣦⣤⣀⡀⠀⣀⣤⣶⣿⡿⠟⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣭⣉⣛⠛⠷⠶⠶⢶⣶⣶⣶⠿⠿⠿⠛⠛⣛⣉⣥⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⣄⠙⣿⣙⡿⠟⠷⣶⡶⣶⣶⠶⠶⣶⣾⣿⡟⠛⡉⠛⠏⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡘⣿⣷⠈⠋⣠⡶⢦⡌⠻⠏⢠⡶⢶⣄⠙⠋⣠⡞⢻⡇⣀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⢷⠙⠏⢀⣄⠻⣧⣠⡟⢀⡀⢻⣧⣴⠟⢀⣀⠙⠶⠟⢰⠟⢡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⠈⠛⠇⠈⠉⠠⣾⣿⣶⠉⠉⠰⠿⠿⠗⠀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⣶⠟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠉⢠⣴⠾⢷⣤⡉⠛⠛⣁⡴⢶⡄⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣴⣦⡈⠙⢷⣶⠟⢃⣤⡀⠛⢷⡾⢃⡀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣈⣿⠆⠀⠀⠰⣏⣀⣿⡆⠀⠀⣿⡍⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⠛⢡⡴⠛⢷⣄⠈⠛⠁⣠⢶⣄⠈⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⡈⠻⡶⠟⣉⣤⣄⠈⢷⡾⢋⡀⢨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⡿⠀⠀⠸⣿⠀⢹⡇⠀⣠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣷⣄⣹⣷⣿⣥⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣋⡥⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢲⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠛⠁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠾⣇⢀⣀⣤⣤⡿⠓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⢀⡶⠛⠛⠳⢦⡀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⢶
⢸⠁⠀⠀⠀⠀⣙⣃⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠹⡀
⢸⠀⠀⢀⡴⠋⠁⠀⠉⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢣⡤⠒⠠⣀⠀⠀⠀⠀⡠⠞⠙⡆⠀⠀⢀
⠈⣇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠆⠀⢠⠞⠀⠀⠀⠇⠀⣠⡟
⣠⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠞⢠⣧
⢇⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠈⢻⠆⠈⠉⠐⠒⠤⠤⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠖⠊⠉⠀⢴⠞
⠀⢸⡆⢠⠒⠂⠤⠄⣀⣀⣿⠀⠀⣼⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⣷⠀⢰⣏⡠⠤⠔⠲⡄⢸
⠀⠈⡇⠘⡀⠀⠀⠀⠀⠀⠉⠲⠖⠋⠀⠒⠲⠶⠖⠒⠖⠒⠒⠒⠖⠒⠒⠛⠛⠉⣿⠀⣼⠁⠀⠀⠀⢰⠁⢸
⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⠀⡏
⠀⠀⠸⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡏⢰⠃
⠀⠀⠀⢻⡀⢷⠀⠀⣠⠔⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠹⠆⠀⠀⠀⣼⢁⡟
⠀⠀⠀⠈⢷⡈⢧⠀⠘⣄⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢀⢰⠇⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠈⢷⡈⢳⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠻⣆⠙⣄⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠈⠳⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣌⡑⠢⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⢖⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣷⠀⠀⠉⠉⠉⠉⠉⠁⠠⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣍⣒⣠⡤⠦⢤⣤⠤⠤⢤⡤⠤⠤⠤⠶⢶⣒⣫⡽⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⢈⡀⠀⠀⠀⢀⠁⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⡠⠀⡂⠅⠀⠀⠀⣀⡀⠀⠀⠨⣐⠀⢄⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⡡⠀⠡⠐⡀⠬⠀⠀⠀⠀⠀⠅⠀⠀⢌⠀⢌⠢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡐⠡⢊⠔⡡⢀⠡⠐⠈⠀⠀⠀⠀⠀⠀⠂⠌⠀⢄⠢⡑⠈⢂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠁⢁⠊⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⠐⡈⠄⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢀⢁⠃⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⠀⡀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡠⠃⠉⠞⠈⠙⡴⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠉⠑⠖⠁⢣⡨⠤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠂⣠⠄⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢠⡀⠀⠀⣤⠀⠀⠈⠂
⠀⠀⠀⡀⠖⢐⡀⠀⠀⠀⠀⠀⠀⡀⢠⠤⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⣀⣀⣀⣀⣀⡀⢢⠀⠐⢀
⠀⠀⠀⢆⣀⡄⠀⠀⠀⠀⠀⠀⠀⠓⡀⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢉⠒⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠐⢤⠐⠒⠢⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠂⠀⠈⠁⠂
⠀⠀⠀⠀⠚⠘⠃⠛⠔⠲⠒⠘⠑⠲⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢠
⠀⠀⠀⠀⢠⠀⠀⠖⠀⠀⠰⠆⠀⢀⠓⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠂⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠄⠰⠀⢂⠄⠱⠊⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⡠⠄⠆⠀⠀⠀⠀⠈⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⡀
⠀⠀⠀⡄⠀⠀⢀⡀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠂⠐⠒⠀⠀⠀⠀⠀⢀⠀⢀⠆
⠀⠀⠀⠘⠄⠀⠁⡀⠀⢙⠐⠋⠁⠈⢢⠀⠀⠀⠀⠀⠀⡠⠠⣄⠀⠀⠀⠀⣠⠄⠤⢀⣀⡀⠄⠒⠂⠐⠋⠒⢤⡀⠀⠀⢠⠎
⠀⠀⠀⠀⢸⣀⠧⡀⠄⠈⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢰⠑⠂⠀⠑⠄⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⢀⢐⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⠀⠆⠀⠀⠀⠀⠈⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠄⠶⠀⠁⡣⠜⢹⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠄⢀⣠⠤⠒⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠂⠤⠤⠤⠤⡄⠀⢀⠠⠤⠤⠤⠔⠒⠚⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⠏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣏⣀⣀⣀⣀⣀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⢈⣠⣄⠀⠈⠉⢳⡀⠀⠀⠀⠀⠀⢸⠗⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠹⣏⣁⣈⣽⠃⠀⢸⡇⠀⢀⡞⠋⠉⠉⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣶⣤⣤⣤⣼⢁⡄⠀⠙⣦⣴⣯⣴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢻⡀⠁⠘⢠⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠋⣠⠖⠒⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠶⢤⡤⠤⠤⣤⠤⠤⠤⢤⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣧⠀⠀⣿⠀⠀⠀⢸⠃⣾⠷⠶⢶⡶⠶⠶⡶⠶⠶⠶⢶⡶⠶⢶⡶⠶⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡄⠀⢻⠀⠀⠀⣼⠀⢹⡄⠀⠈⣇⠀⠀⣧⠀⠀⠀⣸⠀⠀⣼⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⣧⠀⢸⡀⠀⠀⣿⠀⣸⢿⡀⠀⢹⡀⠀⣿⠀⠀⠀⣿⠀⢠⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡄⢸⡇⠀⠀⡇⠀⡟⠀⣷⠀⠈⣇⠀⢸⠀⠀⠀⡏⠀⣼⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣧⠈⡇⠀⢰⡇⣸⠃⢰⠟⣧⠀⢹⡀⢸⡆⠀⢰⡇⢠⡇⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠘⣆⣘⣇⣸⣇⣀⣸⣇⣼⣁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠂⠈⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢢
⠀⠌⠠⠀⠀⠀⠁⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠁⠀⣀⣠⠄⠈⠑⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢤⠂⢋⠐⠠⠄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢂⠰⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠤⠴⠾⠛⠃⠀⠀⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⢀⠀⠀⡏⠀⢇⠀⠓⢀⠀⢀⠈⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠃⠑⠒⠒⠤⠶⠯⠤⠆⠤⠖⠒⠋⢩⠀⠀⠀⠀⠀⠀⠀⠢⣤⡀⠀⠀⠀⠐⡄⠀⠂⠑⠀⢈⣤⠶⠁
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠓⠒⠆⠉⠤⠐⠇⠐⠙⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠈⠛⠤⠤⢤⣤⠬⠠⠴⠦⠜⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⡐⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⢀⣀⡆⠀⠀⠀⠀⠉⠀⠒⠐⠀⠈⠉
⠀⠀⠄⠐⠒⠒⠒⢀⣁⡉⠁⠀⡎⠀⠀⠀⠀⢀⡀⠀⢀⠔⠐⡄⠀⡔⠊⠉⠀⠀⠉⠑⢦⡐⠀⠀⠱⠈
⠀⠀⠠⠀⠀⠀⢸⠀⠀⠧⠄⠒⠃⠀⠀⠀⠠⠀⠀⠐⠋⠄⠀⡙⠨⡀⠀⠀⠂⠀⠀⠀⠀⢱⣀⠀⠀⠈⣢
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣰⠃⠤⠄⡀⠀⠠⠀⠀⠁⠀⠴⠤⣀⠀⢮⡀⠀⠀⠀⠀⠂⣀⡤⠀⠀⡈⠐⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⢠⠎⠀⠀⠐⠁⠀⠀⣨⠂⠀⠀⠑⠒⠁⠀⠀⠀⢦⠤⠤⢄⠀⠰⡀⠀⠀⠀⠀⡈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠙⠀⠙⣤⠃⠀⠀⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠏⠀⣒⠠⣓⠄⠼⡁⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢁⡀⠀⡠⠐⡡⠋⠉⠈⡶⢅⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠑⠀⡤⢌⣩⣠⡚⠀⠤⢀⠔⠁⣴⠗⠁
⠀⠀⣀⠀⠰⢒⠂⢀⠏⢘⠉⠉⡹⢓⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡠⢂⠃⠀⠀⠀⠀⠠⠚⠀⠄⢀⡠⢊⠀⠀⠀⠀⢀⠝⠐⣠⠄⠊
⠀⠞⠉⠉⠁⠌⠂⠄⠀⡬⠥⠤⡅⢨⠄⠀⠡⠬⣆⠀⠀⠀⢀⡔⠡⠀⡏⠒⠠⡀⠀⠀⠉⠐⠠⠄⣀⣠⡉⠀⠐⠀⡔⠁⡠⠊⠁
⠀⡿⡄⢪⠈⠀⣀⠁⠐⠒⠒⢒⠃⢈⠀⡒⢒⣰⡇⠀⠀⠠⡆⢂⠠⠀⠘⢆⠀⡸⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠⠖⠉⠀⠀⠀⣀⡤⠄⡖⠒⣄
⠀⠐⠤⣉⠑⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⢒⣉⠔⠁⠀⠀⢁⠧⡀⠉⠛⠒⠚⢉⠇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢺⠉⡀⡶⠈⢫⣝⢮⠣⡀
⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⠀⠀⠀⠀⡼⡉⠢⣈⠒⠂⠒⠛⡡⠚⠧⡀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠁⠀⡆⠈⡆⠑⠼⠶⣤⠡⠊⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠜⢦⡀⠉⠉⠉⢁⡠⢾⢀⠇⠀⢀⠠⠐⠊⠁⠀⠀⢀⣀⣀⣀⣹⣀⣸⠀⢤⡤⠤⠤⠤⠤⠬
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠒⠒⠂⠀⠰⠤⣄⠀⠀⠀⠀⠀⠓⠲⡮⢉⠈⠉⢁⣠⠴⡎⠀⠸⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠓⠀⠓⠐⠂⠒⠒⠒⠒⠒⠈
⠀⡠⠂⠁⠀⢀⠄⠂⠀⠀⠒⠒⠢⡀⠀⠀⠑⢄⠀⠀⠀⠰⡆⠁⠎⠈⠸⠅⡬⣸⠀⠀⠀⡄⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠
⡰⠁⠀⠀⠀⢣⡔⠀⠀⠀⠒⠒⢠⡜⠀⠀⠀⠀⢳⠀⠀⠀⢹⡁⡤⢌⢁⠖⢓⡇⠀⠀⠀⢓⢰⠒⠲⠒⠒⠒⠲⠖⠶⠂⠠⡭⣭⢥⡤⢀⣀⣀⣠⠤⢼
⡷⣀⢀⠀⠀⠀⠈⠉⠐⠐⠀⠉⠁⠀⠀⠀⣠⠢⠼⡇⠀⠀⠀⢫⠁⠀⠛⠉⡹⠀⠀⠀⠀⠘⡶⠤⠤⠤⠤⠤⠰⢄⣀⣤⣇⣈⣴⣆⣀⣈⣀⣀⣐⡀⣾
⠱⡄⠈⠣⠠⠒⠦⣀⡤⠒⢦⣀⡴⠋⠑⠒⠃⠀⢠⠇⠀⠀⠀⠀⢣⡀⠀⡠⠁⠀⠀⠀⠀⠀⢩⠈⠉⠉⠉⠉⠀⠀⠐⠒⠒⠒⠒⠒⠂⠀⠤⠤⠤⠤⡇
⠀⠙⠲⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠖⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠃

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢹⠀⡶⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡉⠀⠀⠂⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠠⠘⠀⠐⠖⠂
⠀⠀⠀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠒⠃⠤⣄⣠⣨⣠⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣿⣭⣿⣿⣿⣿⣻⣿⣯⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡉⣙⠛⡒⠻⢿⡿⠿⣷⣏⣽⣴⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠸⣿⣿⠓⠋⠈⠉⠉⠈⠉⠁⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠖⠀⠀⠀⠄
⠀⠀⠀⠀⢀⣆⣠⣄⣐⠲⢶⢤⣤⢤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣇⢰⣄⣀⣰⢠⠆⠐⡀
⠀⠀⠀⠀⢹⣾⢣⣛⢢⠁⠈⢛⡩⣭⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢄⡀⢀⣀⡜⠉⠂⡰⠐⠊⣱⠒
⠀⠀⠀⠀⠰⣇⢈⡙⠰⣏⠉⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⣭⠈⠁⢠⣌⡀⠿⣠⡬⣡⡀⢠
⠀⠀⠀⠀⠀⢸⡃⠠⣀⡴⠏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣏⠙⣿⣣⣌⠿⡎⠹⣿⣉⣹⠓⡟
⠀⠀⠀⠀⠀⠀⠣⡀⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠿⠞⣳⠧⡼⣿⡬⢽⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠈⠑⠂⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⢤⣤⡤⠴⠒⠈⣨⠤⢆⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⡦⢰⣯⡤⠴⠒⠋⠁⠈⣉⣛⣳⡄⢦⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠛⠉⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠛⠶⠶⠦⡠⡖⠛⠉⣙⣉⣁⣹⡌⢣⣬⣉⣭⡙⣦
⠀⠀⠀⠀⠀⡠⡶⠛⠉⠁⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣍⣛⣛⣛⠛⠛⠛⠻⣿⣿⠯⠭⢶⠋
⠀⠀⠀⠀⠀⡄⠈⠓⠲⠶⠤⣴⣎⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠙⣇⠀⠀⠠⠤⠤⠤⠤⠤⠤⠔⠂⡾
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠶⠲⡒⠋⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣁⣀⣀⣀⣀⣠⠴⠚⠹⡇⠀⠀⠤⠤⠄⣤⠾⠛⠓⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⣳⡶⠛⠉⢁⢄⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⣟⠛⠶⠶⠦⢤⣼⣥⣄⣀⣀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠈⢦⠱⡄⠀⠀⠀⠀⠀⠀⢀⡴⢻⣀⣤⠶⠶⣾⠒⠒⠶⢬⡉⠉⠉⢓⠦
⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢳⡝⣆⠀⠀⣠⠴⢚⣩⣶⡟⠋⠀⠀⠁⠲⠚⠀⠀⠀⢹⣦⠴⠋⢸
⠀⠀⠀⠀⢠⡾⣏⣁⣹⣤⣈⣉⣙⡛⠛⠛⠲⠶⠶⠶⠶⣿⢌⡄⢪⡵⠚⣛⣿⡏⡰⠁⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⠶⠶⣶⣶⣶⣿⣿⣟⣁⣼⣞⣣⡼⡇⠁⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⠉⣍⢳⡄⠀⠀⠀⠀⢀⣈⣉⣉⠉⠛⠛⠳⠷⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼
⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢠⠚⠁⡼⠁⠈⠀⠀⠀⠀⠀⢀⡔⠐⣼⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠙⠶⠤⣤⣰⢡⠀⠘⢇⣀⣀⣀⣀⠀⢀⣠⡞⠁⣰⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣒⣒⣀⡀⠀⠀⠉⠉⢁⣠⡾⢃⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠋⠁⠀⠀⠉⠉⠙⠓⠒⠒⠒⠋⠉

⠀⠀⠑⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠁⡆⠡⠤⠂
⠀⠀⠀⠰⡅⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠙⠓⠄
⠀⠀⠀⠀⠘⠡⢀⠔⢀⠀⠀⠀⠀⠀⠀⢨⠀⠘⠰⠗⠒⠀⠌⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠞⠃⠶⢲⢀⠒⠀⠀⠀⣤⠀⠐⠒⠓⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠈⠤⠈⠁⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠔⣹⠔⠑⠄⢀⡠⡔⠈⠉⠀⠀⠀⠀⠈⠀⠘⠂⠈⠓⠀⠈⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤
⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠱⢄⣀⡀⢤⡤⠄⠀⠀⠀⠀⠀⢀⠄⠁⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠈⠀⠒⠚⠄
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡤⠃⠔⢂⡌⠀⠀⠀⠀⠀⣬⠀⠂⠁⠤⠀⠘⠁⠀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⠀⠀⠀⠀⠀⠀⠁⡄⠓⠠⠂⠴⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠶⠢⠀⠀⠀⠀⠐⠲⠆⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠖⠀⡁⠀⠀⠠⠴⠀⡄⠀⠀⠀⠀⢡⣇⠀⠀⠀⠀⠀⠀⣨⡌⠀⠀⠀⠀⠈⢀⠀⡀⢀⠀⡀⡁⠀⠀⠀⠀⠀⢜⡁⢒⠀⣀⡀⣐⢈⡃
⠀⠀⠂⠀⠀⠀⠀⣤⢤⠂⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠈⢨⠈⠁⠈⠁⣨⠁⠀⠀⠀⠀⠀⢈⡥⠄⠤⠄⠤⠄⢬⡁
⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠤⡈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠦⠄⠲⠀⡈⠁⠀⠀⠀⠀⢀⠀⣤⣀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⡁⠠⠀⠤⠓⠘⠁⠀⠀⠀⠀⠀⠈⡀⠛⠁⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡤
⠀⠀⠀⢀⠂⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡶⣆⡹⠀⠀⠀⠀⠀⠀⠀⠜⣠⡀⠚⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠘⡠⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠰⣚⣳⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⠀⠀⠀⠀⠀⠀⠀⢠⠠⢤⣄⡄⢠⠀⠄
⠀⠀⠀⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠭⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠀⠀⠀⠀⠀⠀⠈⠀⠲⠒⠶⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀
⠀⠀⢀⡈⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠑⢀
⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠆⠠⠤⠄⠤⠀⠠⠀⠀⠀⠀⢀⡀⠶⠂⠠⠴⠅⠂⠀⢀⠀⠀⠀⠀⢂⠀⡁⠀⡀⢀⡑⢈⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠀⠀⠀⠤⡤⠔⠂⢈⠀⠀⠀⠀⢨⠀⠙⠀⠒⠒⠒⠙⠁⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⡀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠱⠂⠒⠒⠒⠀⠂⠌⠉⠀⠀⠀⠀⠈⠄⠐⢉⣁⣉⣉⠉⠀⠷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⣠⣤⠂⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢐⠂⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⠀⣀⡀⢀⣉⠉⢀⠀⢀⢀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⢄⡠⠖⣀⣄⠀⠦⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠲⠄⣀⣀⣀⣀⢀⠄⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠁⠀⠀⡠⡰
⠀⠐⠀⠀⠀⢀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠤⠀⡠⠊⠑⡄⠔⠁⠀⠀⠀⠀⠁⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠘⡀⠀⡃⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠃⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⡠⠂⠀⠀⠀⠀⠀⡌⠉⠐⠤⠵⠀⠀⠀⣄⣀⡊⠁⠀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⢢⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢃⠀⠀⡕⠄⢰⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⡀⠀⡠⠈⠑⠉⠈⠲⢅⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠐⠈⠁⡐⢢⠼⠴⠁⡀⠠⠔⢁⠴⠋
⠀⠠⠄⠠⠡⠁⠠⠁⠄⠀⠼⠩⠉⠑⠢⡄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⡈⠀⠂⠠⢂⠄⡀⠀⢀⠔⠁⡰⠂⠁
⠀⡅⠀⠁⠄⠀⠅⢐⠈⢀⠃⠰⠁⠀⡁⣹⠀⠀⠀⠰⠁⠁⠣⡀⠀⠄⠀⠀⠀⠀⠀⠂⠃⠄⢀⣈⣁⠄⠀⠀⠀⠀⣀⣀⡀
⠀⠋⡐⠷⠤⠼⠄⠄⠀⠀⠄⠄⠤⠤⢚⠏⠀⠀⠈⡄⠑⠶⠤⠼⠐⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡔⢊⣭⠹⣶⢬⢦⡀
⠀⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠒⠒⠉⠁⠀⠀⢰⠛⢌⠂⠄⠐⠒⡊⢺⠄⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠹⠀⣣⠑⠽⢟⣛⠁⠃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⢄⠈⠉⠀⢀⠠⡚⡸⠀⢀⡀⠐⡈⠀⠀⣀⣀⣀⣀⡅⣨⠀⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢄⡀⠀⠀⠀⠁⠲⠆⡀⣈⡀⠤⠺⠁⠀⠃⠉⠉⠉⠀⠀⠒⠒⠂⠀⠁⠈⠀⠀⠀⠀⠉⠉⠉
⢀⠀⠀⠀⠀⠂⣁⣀⣀⠀⠁⢢⠀⠀⠙⢆⠀⠀⠘⡦⠈⠀⡜⢂⢆⡆⠀⠀⢒⣀⣀⣀⡠⠄⠀⠤⢄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴
⡆⠀⠀⠀⠈⠃⠠⠀⠀⠠⠔⠃⠀⠀⢀⣈⡇⠀⠀⠹⠀⠁⠤⠧⠼⠀⠀⠀⠘⣄⠀⠁⠀⠀⠈⠉⠩⠀⠉⠙⡉⠃⠐⠒⠒⠊⣹
⢧⠀⠠⡀⡠⣄⠀⣀⢄⡀⢀⠔⠢⠤⠃⠈⡇⠀⠀⠀⠡⡀⠀⢀⠃⠀⠀⠀⠀⢃⠀⠉⠀⠈⠉⠉⠉⠉⠭⠭⠍⠀⠐⠚⣒⣒⡚
⠀⠓⢄⣀⣀⡀⠀⠀⠀⠀⠁⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠀⠀⠄⠠⠤⠤⠤⠤⠀⢀⣀⠇

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠙⢦⣀⣀⣀⣀⣤⣤⣤⣶⣶⣶⡿⠿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠳⣀⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣶⣶⣶⠶⠶⠾⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣎⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠙⠛⠿⢿⣿⣶⡀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⠠⠤⠀⠀⠀⠈⣿⣿⠂⠀⠀⠀⠀⠀⠁⠈⠉⠻⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣼⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣀⡾⠃⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⢴⠟⠁⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠤⣄⠃
⠀⠀⠀⠀⠀⠀⠴⣱⣤⡄⠉⠀⠐⠀⡰⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠩⠀⠀⢇⣀⡸⠀⠂⡠⠄⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⠑⠤⠜⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢲⡁⠀⠄⠀⠐⠈⠒⠠⠢⠀⠂
⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⣀⢀⠀⠀⠂⡀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠁⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⡿⠃⠋⠉⠘⠈⠁⠁⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠴⠀⢀⣐⡀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠈⠁⢈⣡⡀⣠⠤⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣚⢪⡟⠐⡋⠩⠄⠂⠄⢄⡀
⠀⠀⠀⠀⠀⠀⡜⢗⣘⡤⠌⡉⣤⡤⣖⣯⣷⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠌⣒⣒⠒⠈⠑⠂⠀⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠀⠁⠷⠧⠼⠚⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡦⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣖⡀⠀⠀⣤⠈⠐⠊⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⢀⢀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣣⠄⠀⠀⠁⠈⠉⠃⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢒⠶⣶⣶⠶⠒⣢⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⣷⠿⠯⠽⠛⡿⣿⡿⠟⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠐⠀⠀⠦⠀⠀⠀⢰⠁⠀⠈⢁⠔⠀⠀⠀⠈⠟⣉⡆⠀⠀⠀⠀⠀⠀⣴⠤⠀⠀⠠⠀⠀⠀⠀⡀⠔⠿⢧⠄
⠀⠀⣌⠑⠓⣾⣛⣷⠀⢰⣿⡿⢿⣆⣠⡄⠀⠀⡀⠀⠀⠀⢰⣦⠀⠀⠀⣿⣶⣬⣷⡖⣰⣆⠀⠀⠀⢰⣿⠓⠒⠊⠑⡆
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠈⠀⡈⣇⡏⡟⠀⠚⠀⠀⠘⠿⠅⠀⠙⠷⠠⣠⠄⢠⣷⢶⡤⠀⢰⡇
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠙⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠛⠛⠁⠀⠀⠂⠀⠀⣀⣀⠀⢀⣤⢤⣤⠄⢀⣇⣀⣁⠀⢈⡁
⠀⠀⠀⠀⢀⢐⠀⠠⢀⡢⠀⠀⠀⠀⣼⣟⣙⣻⠟⠁⠀⠀⠀⠀⠀⠀⠠⢭⠀⠿⠜⠶⠲⠶⠶⠶⠂⠀⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠸⣟⣟⡶⢶⠤⣥⡁⠀⠀⠐⠀⠤⠍⣉⣿⠀⠀⢀⢄⠂⠀⣠⣴⣲⠄⠀⠀⠀⠀⢀⣘⣃⡚⠛⢗⠂⣀⡆
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⣝⠀⠀⠯⣉⡓⠒⢤⣉⠁⠀⠈⠀⠀⠀⠰⣾⡟⠀⠀⠀⢠⣀⢈⣉⡉⢁⣀⡤⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠈⠙⠒⠟⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠙⠓

⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢤⢄⡀⠀⠀⠀⠀⣠⣄⠀⠀⢠⡀⠀⢀⡠⠤⢄⡀
⠀⠀⠀⢀⠔⡉⠀⣈⠭⠭⣀⠀⠙⢦⡀⠛⠀⡤⠤⣼⠀⠪⠒⠒⢄⡀⠈⠁⠀⠀⠀⠀⢠⠏⠀⠈⠀⠑⡤⠤⠤⣄
⠀⠀⠀⡮⢤⠀⠀⣏⠉⠙⠲⣕⡄⠀⢳⠀⣨⠆⠁⠘⡄⠀⠀⠀⠀⠈⣇⠀⠀⣎⣳⠀⠸⡞⢙⠆⠀⢀⡀⠀⠐⠆⢣
⠀⠀⠀⡇⡜⠀⠀⠈⠓⠤⠤⠜⠁⢀⢸⠀⢧⣀⣠⠔⠁⠀⠀⠀⠀⠀⠋⡆⠀⠈⠀⠀⠀⢣⠈⠦⠴⠋⠱⡤⠢⣠⠏
⠀⠀⠀⠱⡧⠭⠤⡄⠀⣀⠀⠀⣠⢬⡞⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⣠⠃⠀⣀⡴⠉⢢⠀⢳⣀⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠈⠢⢄⣑⠊⠈⣣⣼⠕⠋⠀⠀⠶⡖⠀⠘⢄⣓⣂⣀⡤⢚⠅⢇⢸⡁⠀⠀⡸⠀⡜⢠⠏⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠶⠀⢀⡤⣉⣉⡠⠤⢄⠀⠀⠛⠚⢁⣀⠔⢦⡀⠈⠑⠦⣁⠒⣸⡀⠈⠉⠉⠁⡸⠁⡞⠀⠰⡳⠀⠀⠊
⠀⠀⠀⠀⠀⢰⠃⠉⠀⠉⠀⠈⠁⡇⠀⠀⢀⣗⠀⠀⡸⠙⢲⡄⠀⠈⠑⠦⣧⠀⠀⡄⢰⠃⡼⠀⠀⢀⣀⡤⢤⣀
⠀⠀⠀⠀⠀⡞⢣⡀⠀⠀⢀⡄⡴⠁⡠⠞⠛⠀⠉⠉⠉⠒⠊⠉⠓⠦⡀⠀⠀⡠⠚⢁⠇⢰⠁⡴⠮⢥⡀⠀⠀⡈⡆
⠀⠀⢀⢖⠉⠁⠀⠉⠲⢤⠴⠊⠀⠀⡗⢆⡠⢦⠀⠀⢀⡀⠀⠈⠁⠀⠌⠳⡄⠀⠀⡞⢠⠇⢸⢠⠐⢰⡃⠀⠀⠁⡇
⠀⠀⠈⢦⡀⠀⠠⢄⣀⠞⠀⣠⡀⠀⣟⠒⠤⢼⣤⣠⠃⠸⠴⠛⡆⢀⡴⢻⠁⠀⡼⢀⡎⠀⣼⢦⡀⠂⡑⢒⠉⢢⠇
⠀⠀⠀⠀⢈⡩⣩⠉⠀⠀⠀⠙⠁⠘⠧⣉⡓⠲⠬⠭⣉⣑⣒⡒⠛⠚⢳⡇⠀⢰⡁⡜⠀⠀⠈⣇⣉⡲⡥⠤⠔⠁
⠀⠀⠀⠀⠀⠀⣛⣀⣀⣴⠋⠳⠖⡲⡄⠀⠈⠉⠒⠒⠤⠤⠬⠭⠭⡭⠽⠀⢀⠀⠉⠀⠀⠀⣀⢄⡀⠉⠁⠀⡠⢄
⠀⠀⠀⠀⠀⣎⣀⠁⠀⠘⣄⠀⢀⣴⡃⠀⠀⠀⠏⠲⣀⡴⠒⠤⡀⣀⣀⣀⠀⠉⠉⠀⡤⠶⠁⠁⢳⠄⣀⠀⠓⠚
⠀⠀⠀⠀⢀⠿⣼⠀⠀⠀⠈⠉⠁⠀⠉⡢⡀⢸⠀⠰⣿⠀⠀⠀⠈⠀⠐⠈⣧⠴⠒⡆⠣⣄⣀⣠⠇⠀⠀⠹⢤⡀
⠀⠀⠀⢀⣎⠳⣜⠮⠴⣉⢧⠤⢤⠀⠀⠈⢹⠘⠶⠊⠙⢆⠀⠀⠀⣀⠄⣰⡟⠀⢐⠄⢠⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⢤⡑⠦⣙⠢⢬⣉⡒⠚⠮⠾⡟⠁⠀⢀⡤⠤⡈⠳⢤⡤⠕⠋⠀⠙⠤⠋⠀⠘⡤⠀⠀⠀⠀⠀⢀⡜⢇
⠀⠀⠀⠈⠢⣉⠢⢌⡙⠒⠤⠭⣍⣉⡟⠀⡎⠉⣩⣀⠖⡿⠀⠀⠀⢴⡦⠀⣔⠓⠲⠒⢦⠳⢤⣀⡠⠤⠚⠁⠀⢸⡄
⠀⠀⢠⡖⣦⠈⠑⠢⢌⣉⣒⠒⠒⡾⠁⠀⠙⢿⣁⣀⡰⠃⠐⠆⠀⠀⠀⠀⠹⣍⠑⣲⠏⠀⠀⠀⠙⢦⣀⣀⠴⠋
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⡛⠙⠛⠛⠻⠿⠟⠋⠉⠉⠙⠿⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠛⠛⠿
⣿⣿⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠧⣄⡀⠀⠀⠂⠐⠠⠴⠀⠀⠀⠀⠀⠀⠀⢀⡠
⣿⣿⣿⡦⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠓
⣿⣧⡉⠛⠂⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⢰⣤⣤⣄⣀⣀⡀⣀
⣿⣿⣭⣀⡀⠀⠀⠀⠀⠀⠈⢳⣤⣄⣉⣈⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣯⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣄
⣿⣿⣿⣦⣤⠄⠀⠀⠀⣰⠁⠀⣴⣿⣿⣿⣿⣿⢿⣯⠻⠶⠿⠟⠛⠙⢻⠿⠶⠶⢦⣤⣴⣿⣧
⣿⣏⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⠿⠛⠋
⣿⣿⣿⣿⣿⣿⣏⣠⣀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣠⣤⣼⣯⣮⣄
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣷⣤⣾⣶⣿⣿⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣥⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡠⢖⡛⣈⣀⣉⠀⠁⣀⣁⣈⣁⣉⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠚⠀⠧⠭⠤⠧⠬⠥⠼⠼⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⠀⠀⢀⠴⢄⡠⠒⠢⡔⠁⠀⠀⢰
⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠁⠈⠉⠉⠛⠛⠲⠶⢦⣤⡤⠄⠀⠀⠐⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢘⠛⠷⢦⡄⠤⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣤⠞⢦⣤⣄⣀⣀⣒⡒⠀⠀⠀⠀⢀⣒⣒⣒⣒⣨⣥⣤⠚
⠀⠀⠀⠀⠀⠙⠐⡚⠆⠐⠤⠀⡿⠛⠓⠲⠾⠛⠛⡃⠐⠲⢐⠈⠩⠽⠏⠉⠉⣯⠉⠁⣀⣈⠤⢬⡁⠤⠭⠀⠀⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⡃⠈⢁⡀⡀⢢⠀⠠⠇⠀⠉⠠⣄⡭⣗⣖⣒⢶⣢⠶⣀⡉⠉⠉⣁⠰⠒⠒⠒⠚⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠚⠍⠑⠌⠾⠀⢨⠂⠒⠒⠞⣂⠎⢉⣳⣁⢋⣠⣄⠀⠙⠀⢀⡠⠄⢀⠬⠄⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠐⠀⠀⠖⢹⠆⠉⡄⠉⠀⠄⢸⣽⠡⠦⣌⢙⠐⠛⣛⣁⢉⣙⢀⣤⡠⢿⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⣼⡄⠸⢀⣠⠤⠔⠂⠉⠀⠳⠤⣄⣀⡉⠚⠟⢩⡟⠛⠉⠘⠉⠀⢒⣒⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⡒⡒⠍⠍⠉⠉⠙⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⡠⢒⠡⠐⠀⠰⡳⠄⠀⠀⢰⣒⡄⠀⣠⠉⠋⠟⡲⢦⠔⡊⠅⠂⠃⠱⠵⠀⠀⠀⠀⠀⢰⣒⡦⠀⠀⠈⠕⡦⡀
⠀⠀⠀⡠⠊⢀⠀⢠⢢⠄⠀⢀⢠⣰⣠⢀⠀⠀⠀⠀⣠⡀⢀⣞⡀⠂⣤⡄⣀⢠⠠⡄⡄⡐⠰⢠⢀⠀⠀⠀⠀⠐⠿⠂⠈⣽⣳⣄
⠀⠀⡔⣡⠁⡛⠁⠀⠀⢴⡴⡘⡸⣣⣾⣸⣸⢰⢠⢀⢉⢠⠋⠉⠀⠀⠨⡙⣬⠖⡇⡇⡄⣇⣀⣸⣘⣸⣰⢠⢠⢀⠀⠀⠀⠓⠻⠭⠷⡀
⠀⠰⠘⠋⠉⠋⠀⠀⢌⢆⡧⠛⠉⠉⠀⠈⠉⠛⠾⠼⣼⣸⠘⠝⠀⠀⣐⢜⣜⣽⣽⠛⠋⠉⠉⠉⠉⠉⠉⠙⠳⢌⠳⡀⡤⡄⠀⢭⣭⢿⣆
⢀⠃⠀⠸⠭⠵⢤⡙⢪⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⢠⣾⣽⠿⠏⣓⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡎⠈⠀⠀⢰⢚⣝⡺⡆
⡈⠘⠃⠀⠀⠀⣐⠪⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⡴⠛⠁⠐⠽⢖⢪⣟⢶⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢣⠁⣀⠀⠀⠩⣓⢌⢻
⡇⠀⣠⣀⠀⠀⠬⢑⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⡀⠈⠃⠀⠀⢰⢮⡢⣹⣯⡎⠀⣎⣹⠏⠲⣄⠀⠀⠀⠀⢸⠀⠓⠃⠀⢸⣮⠱⣝⡆
⡇⠀⠉⠁⠀⣶⡍⢯⣽⠀⠀⠀⠀⢀⡴⠚⠱⠶⠄⠀⡀⡘⡛⡄⡆⡎⢏⢂⣱⣽⢹⡸⡌⡔⢠⣀⠀⠛⠋⠳⡄⠀⠀⣾⠀⠀⠀⠀⢙⡻⡱⡘⡇
⢠⢀⠀⠀⠀⠀⠩⠭⢽⣆⠀⠀⡠⠋⣂⠀⡀⡄⠆⢳⢿⢣⣡⣥⠧⠿⠚⠉⠀⠉⠉⠉⠓⠣⢮⡟⡖⡀⠀⠀⠈⠢⣼⣗⠀⠀⠀⡠⢧⡱⡔⣜⠃
⠘⡠⡀⠀⢀⡄⡈⠥⣠⣭⣧⠞⠁⡀⢻⢹⡼⠗⠚⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣡⡀⠶⠍⠂⠉⠢⡀⠀⢝⠺⡑⡘⣼
⠀⢱⠠⠀⠈⠒⠃⢈⠶⠚⠁⠠⠀⣁⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣗⣤⠀⡀⣀⢤⢧⠀⢢⠱⡱⣰⠇
⠀⠀⢳⢰⡀⠀⢰⠃⢀⢀⠂⠡⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠟⠋⠙⠛⣹⢯⡙⣆⢷⢳⡿
⠀⠀⠀⠣⡑⣆⢈⠢⣍⣈⣂⡵⠿⠛⠫⠋⠓⠦⢄⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠤⠴⠒⣚⡀⠀⠀⠀⠊⡙⠀⠀⢈⡩⡝⣦⣷⡸⡌⣷⠁
⠀⠀⠀⠀⠙⢬⢿⡆⡀⠀⠀⠀⠀⠰⣋⣇⠀⠈⠂⠀⠨⡭⠉⠉⠉⠛⣁⡀⠀⠀⡤⣄⠀⠑⠃⠀⠰⠶⠀⢀⠀⡐⡄⢳⡘⡍⡏⢣⡽⠁
⠀⠀⠀⠀⠀⠀⠑⢞⡧⠁⡆⡄⠀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⡀⠀⠉⠉⠀⠀⠈⠀⢀⢀⠀⡀⡀⢄⢢⣜⣱⢧⠘⡄⢇⢱⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢧⣇⡇⡇⠆⢠⢠⢠⠀⣠⡄⡀⠘⠒⢃⢀⠀⡄⡆⣟⣹⠻⠘⡌⡆⢳⠘⡌⢆⢣⢹⠈⢇⣳⠼⠊⠁
⠀⠀⠀⠀⢔⠤⣒⠤⣀⠴⢀⠬⢛⠾⣼⣜⡜⡌⡎⡏⢃⢣⢹⠘⡜⡆⣇⢣⢱⡸⡌⢇⢣⠱⡈⢆⠳⡙⡜⣎⣧⠗⡋⠁
⠀⠀⠀⠈⠀⠊⠐⠊⠐⠊⠡⠊⠡⠊⠕⢋⠝⣻⠞⡾⢮⣮⣧⣳⣱⣘⣜⣮⢣⣱⣘⣌⣦⡵⣽⢆⠗⡫⢋⢕⡥⡪⢊⠕⣡⠞⡡⢢⠖⡰⢠⢄⢄⢔⡤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⡀⢤⠀⠴⢦⣴⡀⠄⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⡤⠦⠀⠀⡰⢀⡀⠐⢠⠊⠱⠗⣠⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣂⠼⡁⠀⢈⡩⣼⡵⣼⡷⣐⢀⡣⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠘⠁⠨⡽⠀⠉⠛⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠕⠁⠒⠀⠀⣰⠄
⠀⠀⠀⡀⠀⠈⠢⠀⢄⠀⢠⠊⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⣀⣀⠀⠴⠚⢱⠞⠒⠞⠦⠤⠖⢠⣆⣶⢿⡦⠀⣀⣀⡤⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠈⢡⢦⠀⡠⠐⠉⠁⠀⢈⡖⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢙⠘⢂⣀⡉⢙⣛⣚⣉⡷⢏⠉
⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⣀⠒⠣⠀⢀⠠⢠⢾⣼⠄⠀⣀⡆⠀⢀⣴⠮⠲⡚⠀⠀⠀⣄⣙⢢⢴⢉⠩⠀⠈
⠀⠀⠀⠀⠀⠰⠔⠀⠁⠚⠀⠀⠀⠀⠀⠐⠒⢋⠁⣐⡬⠖⠁⠀⠈⠠⢰⣐⣇⣧⡴⠆
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠼⠓⠋⠁⠀⠀⠀⠀⠀⠠⢀⠈⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⢤⡀
⠀⠀⠀⢀⠔⠂⠉⠀⠄⠂⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠈⢀⠀⢀⠀⠀⠀⠀⠀⠐⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣆
⠀⠀⠀⠰⠀⠀⠀⠀⠡⠀⢀⢀⠀⠀⡚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⣊⠀⠛⠁⡇
⠀⠀⠀⠀⢃⠀⢀⠖⠤⡠⠂⠀⠱⣀⡁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠘⠒⠒⠚⠉⠢
⠀⠀⠀⠀⠈⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡠⡴⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢩⠊⡜⠀⠰⡈⠒⠧⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠁⢰⠀⠀⠀⠘⢦⠀⠀⠙⡝⢯⠇⡖⢦⣀⡠⢄⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀⠤⠔⠚⣇⠀⢰⠀⠘⡄⠀⠀⠀⠀⡇⠀⢀⣌⠑⠤⢇⡀⢑⣤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡧⣰⡉⠑⠄⠣⠄⣈⠦⠄⢠⠔⠓⠒⠉⠓⠙⢍⠁⠙⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣈⣁⠸⡉⠐⠹⢶⠁⠙⠔⠉⠑⠔⠉⢑⠉⠑⠖⢙⣫⠭⠙⠴⠃⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠇⠙⡅⠙⡄⠀⢡⠀⠀⠀⠀⡌⠀⣸⠔⡁⠀⠄⠀⠁⣀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠸⡀⢱⠀⢰⠀⢸⠀⠀⠀⠀⠇⡰⠁⠀⠀⡠⣴⠭⠪⠄⢅⡢⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⢀⠄⠀⢤⡥⠠⡤⠂⠷⠊⠉⠘⡆⠀⡆⠀⠀⢸⢀⠁⠀⠈⠄⡘⠅⣀⣀⡀⠤⢃⠀⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⠀⠀⠀⠀⠀⠯⠄⠀⠀⠠⠄⠀⠷⡑⠐⠢⡀⢀⡈⠀⠀⣈⢀⠔⠃⢀⠌
⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⣀⠞⠤⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠉⠁⠈⠑⠊⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⡤⢤⣀⢀⣀⣀⣀⣀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠚⡵⠓⢄⣈⠓⢤⣀⠀⠈⠉⠓⠦⣄⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠎⢠⠊⢰⣓⠒⢮⡳⢄⠈⠑⣦⡀⠀⠀⠀⠑⢆⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⡴⠡⣞⡡⣞⠒⠺⢭⠉⣀⠞⣠⠞⣠⠟⠀⠀⠀⠀⠀⢳⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⠇⠸⢍⡑⠨⢉⠪⢕⡒⢚⡽⣡⠞⣡⠎⡝⡟⣩⣉⣉⣉⣑⣚⠓⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣿⣥⠢⢍⡲⢝⣋⡔⣡⠜⠁⢀⢁⡇⡇⢀⡖⣶⡄⢹⢱⠃⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⢠⢏⣴⠃⢰⠦⣍⠓⠿⠔⠁⠀⠀⢸⢸⢀⠇⠀⣙⠋⠁⡜⡞⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠹⡜⣎⢻⡀⠀⢣⡀⠩⣒⡒⠒⢲⠆⡞⣸⢨⠀⠸⣙⣿⠆⡇⡇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠛⠙⢦⣀⠉⠒⠒⠒⠊⣁⡄⣇⣿⣘⠒⢤⡤⠤⠤⢇⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢮⡉⢉⣩⣉⡜⠁⠛⠓⠬⠭⢭⣭⣭⡍⠩⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣈⡉⠉⠉⠉⠉⠙⠛⠉⠉⠉⣀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⢘⢿⣿⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣫⡶⢃⣞⣼⡟⢮⣝⠦⡈⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡩⡆⠀⢩⡴⠺⠋⠀⣷⢸⣷⠀⣽⡄⢻⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣷⡶⠿⠥⣶⠶⢚⣁⣼⣟⣠⣿⠁⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⢉⣡⠤⣶⠶⠚⠛⠿⠍⠁⣀⡀⠠⠚⡿⢂⣼⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠴⠚⠉⠀⢀⣀⣤⣴⣶⣶⣿⣧⠤⠤⣤⡴⢶⡿⢻⣿⡿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⣶⠾⠟⠛⢻⢏⣁⣀⡠⠴⢶⠞⢉⣴⢟⠧⢸⣿⣿⡜⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣀⣴⠞⠉⢀⣠⠴⠒⠈⠁⣀⡠⠴⠒⠊⠉⠉⠠⠋⣠⡿⣿⣿⠃⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢰⡟⠀⣠⠴⠋⠀⢀⣤⠖⠋⠁⢀⣀⡤⠤⠒⠚⠛⢋⣡⡾⠛⣁⣼⣿⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠘⣿⣇⢰⡏⠀⠀⣰⠋⠀⢀⣠⠖⠉⠁⢀⣠⡤⠶⠲⢋⣩⠐⠋⠉⠈⣠⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠈⠻⢌⣧⡀⠠⡇⠀⢠⡟⠀⣀⣴⠞⠋⠀⠀⣠⣶⣿⣥⣤⣤⣴⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣛⠳⠤⣄⣠⡉⠙⠲⠷⠤⣿⣥⣴⣿⣯⣤⣴⡶⣿⠛⣻⣷⣴⣾⣿⣿⢿⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠄⠀⠀⠀⠉⠙⠙⠒⢶⠶⡶⠶⣦⠽⡶⣿⡿⢿⡟⢻⠙⡏⣿⢸⡇⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠷⠀⡏⢰⡇⢸⡇⣼⣿⢀⡇⣼⢳⣿⣿⣿⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡄⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⢸⠀⣏⢸⡁⢸⢀⡇⣼⣸⣷⡏⡸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⢸⡄⣟⢠⠀⣿⢸⡁⠦⡟⢸⢣⣷⣿⡿⣿⣶⡄⡀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢸⡄⣇⢝⢾⠐⡀⢠⠘⠀⡇⢟⢼⢰⡇⣼⣿⢲⡏⣿⣾⣿⣿⣿⣟⣿⣿⣿⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⣯⠿⡜⣾⣇⠱⠘⡅⡇⣿⣿⣿⢸⣧⣯⣿⣿⢵⣿⣿⣿⣿⣿⣿⣿⣮⠛⢃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⢿⣬⣧⣃⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠙⠻⠷⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣀⣴⣶⣦⣴⣄⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⢀⣀⠠⠤⠤⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣉⡴⢞⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣠⣞⡽⠞⠉⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣆⣀⠀⠀⠀⠙⢻⣶⣶⣶⠾⠿⠿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣷⣿⣿⣿⡆⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡀⠈⢰⣤⣶⣦⣼⡗⠀⠀⠀⠀⠘⢿⣿⣇⣀⣠⣴
⠀⢰⣿⣷⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⡿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⣿⣿⣿⣿⣿⣦⠀⢠⡀⠀⠀⠉⠙⠋⠉
⠀⠀⠙⠿⢿⠿⢿⣟⢾⣿⣿⣿⣿⣿⠃⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⠀⡇
⠀⠀⠀⠀⠀⠀⡿⠀⡾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠿⠛⠛⠛⠿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⠀⠀⠀⠀⢘⣿⣿⣿⣿⣧⣹
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⢿⣶⣦⣤⣶⠂⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢨⣤⣤⠤⠶⣶⣾⣿⣿⣿⣿⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⠀⠀⢀⣀⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣾⣿⡟⢿⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣾⣦⣤⣤⣤⣤⣶⣿⠏⣼⠟⠃⠀⢀⡼⢋⣠
⣀⣀⣀⣀⣀⠀⠀⠀⠐⢌⣦⣄⠀⠀⠀⠀⣀⣴⣿⠏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⡿⠁⠀⠃⠀⡀⡠⠊⠾⠛⠉
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠻⣝⠻⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠻⡤⠊⠀⠀⠀⠀⡠⠃⣀⣠⠄⠀⢀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠓⢦⣉⠉⠁⠠⠐⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡷⠊⠀⠀⠀⠠⠖⢈⣰⣤⢀⡀⢁⣰⣿
⠀⠀⠀⠉⠉⠉⠛⢃⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢬⣤⡀⠀⠀⠀⠀⠀⠻⣿⣿⢁⢀⣤⣤⠀⣀⣴⣿⡿⢟⣫⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣤⣤⣶⣾⠟⠀⠀⠐⡁⣤⣿⡿⠋⢠⣰⣿⣿⣿⣿⣿⡿
⣀⣀⣀⣀⣴⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣼⡟⣼⣿⣶⣾⣿⣿⣿⣿⣿⣯⡿⢿
⡿⠋⠉⠉⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⣠⣾⣿⣽⣿⣿⣿⣿⣿⡿⠛⠸⡿⠟⡁⣨

⠀⠀⠀⠀⠀⡀⠄⠤⡀⠀⢀⠄⠀⠐⢒⠒⠤⡀⢠⢄⢀⠒⠂⠐⠀⠐⢦⠀⣀⠀⢀⣤⡶⠶⣀⠄
⠀⠀⠀⠀⢰⠁⠀⠀⢸⡐⠁⠘⢀⠤⠨⡁⡄⠑⠘⠉⠀⠍⢣⠲⠢⢴⡞⠀⠓⠀⣺⡿⡯⠑⣶⡇⡁
⠀⠀⠀⠀⠀⠑⠀⠔⠃⢃⠀⡄⠈⢄⠀⡐⠀⡐⢠⠁⢉⠈⢐⠈⡼⢮⠤⡀⣄⠀⣿⣯⣚⣎⣿⣷⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢠⠈⢆⠀⠠⠀⠀⢚⠐⠁⠸⣀⡒⢠⠏⠀⡇⠀⠀⠸⣸⠀⠙⠛⠓⡿⠟⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⢁⡀⠀⠈⠀⠀⠤⡄⠀⠀⡀⡀⠈⠮⠶⠴⠮⠟⠀⢖⠀⠀⡇⢰⠓⠇
⠀⠀⠀⠀⠀⡡⠴⠖⠒⠦⣤⠘⠀⠀⠀⠀⠀⠀⡗⠒⡌⠣⡀⠡⠀⣂⣆⠀⣤⠠⢠⡄⠀⠇⠈⠈
⠀⠀⠀⠀⠘⠆⠀⠀⠈⠀⠇⠸⡉⠥⢀⡁⠄⣀⡃⡰⢰⠀⠈⠁⣏⣀⣉⣉⣁⢈⣧⣶⠘⠄⢀⢄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⠁⠁⢣⠀⠀⠀⠀⡜⠁⠐⢁⠀⢀⡀⠙⠉⠋⡉⠉⠉⠛⠁⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠤⠠⠀⡀⡀⠉⠀⢀⡅⡆⣄⠀⡴⠤⠤⢤⣭⢀⠁⣦⠑⠂⡍⠑⠀⠀⡤⠤⢄
⠀⠀⠀⠀⠀⢴⡀⢰⠢⠀⠀⠒⠁⠀⠀⢥⠼⢿⣼⠀⠑⠢⠀⠐⠁⡈⡀⣄⠀⡘⠁⡜⠀⠀⣟⣻⠁
⠀⠀⠀⠀⠀⠑⠀⢐⠉⢄⠀⠶⢧⣈⠐⢌⠑⠉⢠⡂⠐⠒⠀⠐⣂⠀⠑⠄⠀⠡⢊⢄⠀⠀⡃⢰
⠀⠀⠀⠀⠀⠀⢱⠀⡁⢠⠠⠈⠢⣉⠛⣦⠆⠀⢀⠀⠀⠉⠉⠁⢸⡒⠢⠀⢠⠊⠉⡷⠃⠀⡇⢨
⠀⠀⠀⠀⠀⠂⠘⠀⠃⠁⢐⠍⠵⠀⡠⡀⠀⠀⠸⠀⠀⠀⠀⠀⣠⣬⡠⠠⡊⠀⢈⠁⠀⠀⠯⠽⠄
⠀⠀⠀⠀⠐⣧⣴⣦⣆⣇⣈⡒⠀⠊⠀⠈⠢⠠⠀⠑⠠⠤⠤⠐⠁⠀⠀⠀⡌⠲⡁⠀⠀⡠⡄⢤
⠀⠀⠀⠀⠀⠇⠀⠀⣀⡃⡆⡅⠀⢁⣈⡀⣨⠤⢄⠀⠈⠚⠋⠟⢋⠂⣰⠁⣋⢉⣋⡂⠀⠈⣿⡊
⠀⠀⠀⠀⠀⢈⠉⠘⠉⠟⠒⠀⢸⠀⠀⠀⡁⢐⣼⡇⠆⡞⡇⠷⢾⠀⠇⢀⠀⠀⡈⡑⢀⠎⠀⠱⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠉⠁⠉⠉⠈⠀⠀⠐⠙⠑⠛⠈⠀⠈⠒⠄⠀⠐⠁⠈⠂⠠⠬⠁

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