Sonic the hedgehog 2 Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⢁⠛⠈⠀⠀⠀⠀⠀⠀⠓⢁⠀⠀⠀⠀⠀⠈⠁⢹⡆
⠀⠀⡇⠀⣗⣶⣦⣴⣿⣷⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⣄⡀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⡀⠰⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⢄⠀⠼⠃⢀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠀⠈⠀⠈⠀⠈⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠄⠀⢐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⡄
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠛⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⢀⡇⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢁⡀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡤⠀⠀⠀⠈⠀⠀⠀⢸⡀⠀⠀⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡌⡰⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡤⠤⡤⢴⢤⢤⡤⢮⢠⠤⠤⢤⠤⠤⢤⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣄⠳⠀⡇⠀⡘⢸⠀⢰⠶⡈⠁⣿⠘⠀⠀⣫⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠨⠆⡅⡆⢁⠃⢳⡔⠘⡆⠐⠦⡆⡿⠘⢤⠂⢹⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⡇⣹⢸⠆⠀⡓⠆⢘⡇⠃⡀⡇⠀⢘⢺⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠧⠇⠈⠤⠐⠓⠄⠓⠀⠒⠧⠗⠤⠚⠢⠚⢸⡇
⠀⠀⢦⣀⣀⣀⣄⣠⣄⣠⣠⣠⣀⣄⣀⣠⣀⣀⣄⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠁⠈⠀⠀⠁⠀⠈⠀⠁⠀⠀⠈⠀⠉⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⢀⣤⠴⠒⠛⠐⠒⠐⠦⣄⡀⠀⢀⣤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠈⠲⣌⢂⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣲⠝⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⢃⣤⠶⠶⢄⠀⠀⠀⠀⠀⣀⡤⠶⠶⠶⣤⡀⠀⣶⢧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡿⠋⣠⠤⠤⣀⠁⠀⠀⠀⠈⠀⡠⠤⠴⢤⡀⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡿⢠⠎⠀⠀⠀⠀⠁⠀⠀⠀⠴⠉⠀⠀⠀⠀⠘⢦⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡞⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣇⠀⠀⡇⠀⠀⠀⠀⢿⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣂
⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠉⢻⡄⠀⢱⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢰⠉⠉⠱⣷
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢾⣀⢧⣀⠀⠀⣿⣧⣄⣀⣀⣀⣁⠀⠀⠀⣀⠤⢴⣄⡄⠀⠉
⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣇⠀⠈⠁⠀⠈⠙⠋⠀⠀⠈⠉⠩⠁⠀⠀⠀⣀⡿⢀⡴⠞
⠀⠀⠸⠀⠀⠀⠀⡀⠐⢆⠀⠀⠀⠀⣀⣡⣿⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣰⠏⠀⢀
⠀⠀⢆⠄⠀⠀⣀⢣⡀⠈⢷⣀⢀⡜⠁⠈⢱⡄⢈⣯⡽⢷⣶⡶⠶⠶⢶⣴⡶⣖⠚⠉⠀⠀⠀⣽⠀⡴⠃
⠀⠀⢸⠀⠀⢠⠟⣄⢦⠀⠀⢀⣀⣀⣠⣶⠟⠋⠉⣁⣤⡾⠁⠀⠀⠀⠀⢸⢷⡸⢷⣄⠀⠀⠀⡹⣿⠅
⠀⠀⠀⠀⠀⠿⣉⣤⡈⢛⡒⢾⣿⣿⣿⠁⠀⣔⡋⠀⡆⠀⠀⠀⠀⠀⠀⢸⠀⢳⡄⠻⣦⡀⢠⠀⠙⢧⣘
⠀⠀⠀⡀⢠⡖⠹⠘⣷⠀⠉⠙⣿⡏⢻⣤⠚⠁⠀⠀⢿⠀⠀⠀⠀⠀⢀⠇⢠⡏⠙⠢⡀⠉⠀⢀⠀⠀⠘
⠀⣀⣬⣁⣘⠀⠀⠰⡟⢀⠲⠺⣄⠑⣄⡇⠀⠀⢀⠄⠘⡄⠀⠀⠀⠀⠂⢠⡾⢄⠀⠀⠉⠙⠐⢂⠁⠂⠐
⣌⠀⠀⠀⠈⠀⠀⢸⠁⡼⠁⠀⠹⡆⠘⢧⡄⡔⠁⠀⠀⣿⠄⠀⠀⠀⠀⢾⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢆⠀⠀⡟⠀⠷⠦⣄⠀⢻⠀⢸⠀⠀⠀⠀⠀⢸⠀⢸⠒⣆⠀⠸⣇⠀⠀⠁
⡆⠀⠀⠀⠀⠁⢄⡤⠀⠀⠁⢸⣦⠼⠀⢸⡄⠳⠀⠀⠀⢸⠀⢸⡆⠈⡆⠀⢻⡐⠤⡀
⡇⠀⠀⡌⠀⠀⡴⡟⠷⣦⡄⢸⣿⡀⠂⠐⢰⡆⠀⠀⠀⢸⠀⢸⡇⠀⢻⠀⠘⣇⠀⠈⠁
⠱⡀⠀⠳⣄⣬⢼⣀⣤⠈⠀⣿⠇⠀⢉⣀⡰⢧⡀⠂⠀⢉⠀⠈⡇⠀⠈⡆⠀⢹⡀
⠀⠈⠲⠄⠼⠁⠀⠀⠈⠁⢰⣿⠀⠀⠈⢡⠤⠄⠛⠲⢄⡐⠀⠀⣧⠀⠀⢡⠀⠀⢧
⠀⠀⠀⠀⠀⢤⡀⠀⣀⣤⠟⠀⢻⣄⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢿⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⣀⣀⣾⠀⠀⢸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠤⠤⠀⠀⠨⠄⢹⡀⠀⠐⠒⠚⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠆⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠰⡎⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠐⠂⠐⠄⡈⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠂⠠⠌⠀⠀⠀⠀⠀⡁⠀⢂⢤⠌⠈⠗⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⣄⠐⠀⠀⠀⠻⢷⡦⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠑⠂⠄⠄⠀⣀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⠀⣀⠀⠀⠀⠀⣀⡀⢤⠀⢀⡈⠉⠑⠸⠀⠈⠐⠂⢀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⢀⡴⠄⠤⣀⡀⠀⣼⠧⡠⠟⢋⢀⡎⠀⠀⠣⣉⡠⡔⠂⡀⠔⠁⠀⠒⠂⡁⠢⡀
⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠈⠑⣄⠹⡶⠔⠣⠬⠐⠊⠹⡆⠀⠀⠀⠀⠀⠈⠈⠀⠠⢀⡠⠁⡠⠁⠀⡇⠀⠠⠀⠐
⠀⠀⠀⡀⠀⠀⠑⠂⠶⠶⠶⠶⠻⢾⣃⠔⢂⡰⠂⠱⠌⡉⠤⠀⠀⠀⠀⠀⠠⠄⠀⠂⠘⠉⠋⠑⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿
⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⣿⣷⠦⠀⠀⠀⠀⠀⠉⠁⣠⡼⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⠤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠠⠀⠀⠦⠊⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⢀⠾⠀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠈⠁⠈⠠⠀⠀⠀⠀⠀⠠⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⣠⠴⠒⠐⠦⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⠤⠖⠀⠀⡠⠁⠀⠀⠀⠀⠀⣽⣿⣿
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢦⠀⠸⡤⠆⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠈⠒⠋⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠌⡜⠂⠄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣏⠀⠀⠀⠀⠀⢴⠉⠀⡈⢠⠀⠀⠠⠀⠀⠀⠙⠀⠀⠀⡟⠂⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠐⠤⣈⣀⠴⠋⠀⠀⣇⠀⠀⢀⡤⠛⡄⠀⠈⠁⠀⠀⠰⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠘⢤⡤⠚⠉⢦⠀⠈⢆⣀⠀⡠⠒⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣑⠒⠤⣀⠠⠆⣉⣈⡑⡄⠀⠀⠀⠀⣀⠤⠒⣊⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠑⠬⡑⢶⠊⣀⠈⢻⡄⠀⡠⢚⡥⠊⠁⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⡆⠀⢀⠔⢛⣣⡾⠋⢉⣒⡏⠉⠁⠛⠢⣄⠀⢠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠰⡔⠁⠀⠋⡰⢀⡔⠉⠈⠁⠀⠀⠀⠀⠈⢣⡌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠁⠀⠀⢠⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣌⣀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⠀⢈⣳⢦⠀⠀⣤⡴⠃⠀⠘⡄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠀⡅⠀⠘⠿⣿⠀⠀⣿⣿⡉⠀⢠⠁⣘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠈⠉⠐⠒⠓⠛⢒⡒⠛⠚⠒⠂⠉⠁⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣗⡀⠀⠀⠀⠀⢠⣀⡀⠙⠛⠀⡀⠀⠀⠀⠀⠀⢀⣘⠍⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠐⠒⠢⠤⣀⡈⠙⠛⠛⠋⠁⣀⡤⠔⠒⠂⠼⠂⠀⠀⣠⠋⡇⠀⠀⡠⠖⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢉⠝⠛⠛⠙⠛⠫⡍⠐⢦⡀⠀⠀⠀⠀⣰⠃⠀⢣⡠⠋⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠶⠀⠀⠀⠀⠀⠀⠰⣄⠀⠈⠳⢄⠀⢠⠃⠀⠀⠈⢇⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡜⠁⠀⡰⠊⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢦⠀⠀⢳⣞⡀⠀⠀⠀⠈⢦⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠉⠓⢾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡳⠚⠉⠁⠙⡄⠀⠀⠀⠈⢧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠿⢤⣀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢱⠀⠀⣀⡤⠼⣄⠀⠀⠀⠀⠳⣘
⠀⠀⠀⠀⢀⡠⡎⠁⠀⠀⠀⠙⢎⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠄⠀⡇⠀⠀⠀⢱⠋⠀⠀⠀⠀⢑⣤⡀⠀⠀⠹⡄
⠀⠀⢠⢒⡩⢊⡜⣰⠀⡠⠒⢆⠘⡄⠀⢀⠏⠀⠀⢠⡴⠶⢄⠀⠀⠘⡄⠀⢠⠇⢠⡖⢄⠀⢦⠳⡑⢬⡓⡄⠀⢳
⠀⠀⠰⣏⣤⠋⢠⠃⣰⠁⠀⠘⢄⡅⢀⠎⠀⠀⢠⠋⡇⠀⠈⡆⠀⠀⠸⡞⢹⣠⠃⡇⠈⢆⠈⣇⠘⢦⣉⠇⠀⠈⡇
⠀⠀⠀⠀⠃⠒⡇⣰⠃⠀⠀⠀⠀⠀⡸⠀⠀⠀⡶⠀⡇⠀⠀⢸⠀⠀⠀⢷⠀⠀⣰⠃⠀⠈⢆⢘⠓⠘⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡴⠒⠳⠤⠤⠤⢇⠀⢳⠀⠀⣠⠧⠤⠤⠞⠓⢺⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⣰⠃⠸⡄⠈⢇⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣶⡦⣤⣀⠀⠀⣹⠀⠀⢳⡀⢎⠀⠀⣀⣤⢤⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⠙⠋⢝⡳⠋⠉⠉⢷⠀⠀⠀⠳⣼⠉⠉⠙⢶⡫⠝⠋⠉⠉⠉⠒⢦⡀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⣸⠀⠀⠀⠀⢂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢱⠚⠁
⠀⠀⠀⠀⠀⡧⠄⣀⣀⣀⣀⣀⡀⠤⠴⣒⣘⠥⠟⠀⠀⠀⠀⠸⠬⣇⣀⠲⠤⠀⣀⣀⣀⣀⣀⠠⢴⠅
⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⡠⠒⠉⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠒⠉⠉⠉⠉⠉⠉⠐⠒⢤⡀
⠀⠀⠀⢀⣠⠃⠀⡬⢛⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⢦⡠⠤⡀
⠀⠘⢍⢀⠃⠀⠘⠥⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⠔⢡⡂⡰⠈⠳⡀
⠀⠀⠀⢹⠀⠀⢀⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠘⠣⢄⡀⡠⠚⡦⣀⢈⣆⠜⢠⡃
⠀⠀⠀⠘⡀⠀⠃⡔⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡤⠜⠃⠙⠓⠒⠓⠁
⠀⠀⠀⠀⠑⣄⢼⡃⠀⢀⠧⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢠⣬⠋⠁⠈⡁⠀⠀⣸⠤⠄⠀⠀⠤⡤⠄⣀⡀⠀⢁
⠀⠀⠀⠀⠀⠈⠒⠶⣋⡁⣤⠊⠀⠀⠀⠂⠠⠀⠱⡀⠀⠈⠑⠚
⠀⠀⠀⠀⠀⣀⠤⢊⡡⠒⠹⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡰⠮⢐⠢⡀
⠀⠀⠀⠀⠀⣁⠰⣅⡀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠘⢮⡜⠀⠀⠀⠀⠀⣴⣂⠚⠗⠢⡀⠑⣬⣄
⠀⠀⠀⠀⠰⡅⠠⠒⠉⢀⡒⡄⠀⠀⠉⢲⠦⢄⠀⢀⠀⠀⠈⠑⠢⣄⡤⠊⠁⠀⢡⠀⠀⠁⠀⡃⠙⣕⢢
⠀⠀⠀⠀⠀⠱⠁⠀⠠⢀⢱⠜⠀⠀⢠⠃⠀⢀⡴⢋⡉⢒⠤⣀⡀⠀⠀⠀⣀⣤⠜⣰⣠⠇⡐⠀⢀⠋⠱⣡
⠀⠀⠀⠀⠀⠀⢆⠠⣑⣢⠏⠀⠀⢠⠃⠀⡠⠿⡐⡯⡉⢢⠱⡀⠉⠒⠒⠉⠀⠀⠀⠀⠈⠙⠤⡠⠂⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢎⡀⠀⠁⠀⡇⠀⠁⠀⢣⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢗⣚⣀⣄⣄⠔⠁⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣀⠠⠒⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⣿⣿⣿⣿⣿⡿⠁⠀⠀⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⣯⣽⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⢹⣿⠆⢠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠂⠀⠀⢀⠀⠀⠀⣿⣦⣤⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠘⠀⠀⠀⠀⣀⠀⠈⠀⠀⣠⠊⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⢀⠔⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠉⠛⢿⣿⣿⣿⣿
⠀⠀⢄⠰⠄⠀⠀⠀⠀⠀⠀⠌⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠶⠤⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⣰⡟⠀⠀⠀⢰⡿⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠻⠆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠃⠀⠙⠁⠀⠐⣧⣀⢀⡄⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣿⣇⠀⠀⠀⠀⠈⠀⠀⠒⠂⠚⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⡆⠀⠀⠀⠀⢀⡤⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠹⣦⣄⣘⢁⣴⣆⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢹⣿⣿⡄⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠆⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠄⠀⠸⠿⣿⣧⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠛⢦⣄⣠⣄⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣷⣶⣶⣶⡾⠛⠉⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣀⣠⣤⣌⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠻⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣸⣿⣿⣿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡾⣿⣏⡈⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢙⡀⢁⣭⣿⡿⠃⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣹⣆⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠁⠈⠙⢢⣄⣀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⣉⠀⠀⠀⢠⣄⣬⣀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠁⠀⠀⠀⢈⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⢀⠀⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠁⠈⠛⢛⠂⢀⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠶⣄⠀⠀⠀⠈⢧⣤⠾⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⢰⠞⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠈⠀⠀⠄⠀⠈⠀⠀⠘⠋⠉⠉⠩⠿⠶⠦⠤⢤⣀⣀⣀⣴⣄⡀⠀⠀⡀⠀⠀⠘⠙⡄⣠⣴⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣻⣿⣦⡀⠀⢄⠀⠀⠀⠀⢠⣿⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⡀⠀⠀⠀⡎⠁⠀⠈⠛⢷⣦⣤⠦⣀⣠⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊⠀⠆⠀⠺⠀⠀⠀⠀⠀⠂⢹⠃⠀⢸⡇⠁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⠀⠀⢠⠎⠀⠀⣸⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢈⠢⠐⢦⣀⡀⢀⡠⠊⠀⠀⣠⡟⠻⠿⠛⠛⠁⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠀⢠⠀⠀⡰⠛⠉⠉⠉⠀⠀⢀⣶⣟⠀⠀⠀⠀⠠⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⠀⢀⣧⡀⣀⡀⣀⣠⠤⠚⠉⠉⠀⠀⠀⠀⠰⠷⠀⠘⠣⠄⠀⠀⡴⠋⠀⠀⠀⠊⣦⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢿⣄⢘⠋⠉⠉⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠐⠊⠀⠀⠈⠠⠖⢶⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠴⠀⣾⠐⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠌⠅⠀⠀⠀⢀⣀⠶⠀⠐⡁⢺⠑⠻⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠛⢋⣅⠀⡛⠈⠁⣘⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣠⢔⡎⢹⣇⡤⠔⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠀⠐⠀⠀⠀⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢾⣅⣈⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⠆⠀⠀⢀⠈⠃⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⠈⠠⠀⠀⣀⣀⣀⣀⣤⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠩⠉⠁⢘⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⡔⠁⠀⣤⠀⠀⠀⠀⠀⢄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⢀⡼⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⢠⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⡇⠀⣿⡟⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢰⠀⠀⠀⠀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⡜⠀⠀⣿⡇⠀⠀⠀⢀⠎⠀⠀⣀⡀⠀⠀⢀⣿⣿⠀⠀⠀⡆⠀⠀⣠⣾⡿⠋⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⡠⠊⠀⠀⠀⣿⣇⠀⠀⡠⠊⠀⠀⠸⣿⡿⠀⠀⢸⣿⡏⠀⠀⡜⠀⠀⢰⣿⡿⠁⠀⡔⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⣿⣿⡠⠞⠀⠀⠀⠀⠀⣿⣿⣀⠔⠁⢀⠀⠀⠀⢀⣀⠀⠀⢸⣿⡇⠀⡜⠀⠀⢠⣿⡿⠁⡠⠊
⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠠⠊⠀⣿⠀⠰⣿⣿⠀⠀⠀⣿⣇⠜⠀⠀⠀⣼⣿⡧⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⠜⣿⣿⡃⢀⣾⡿⠀⠀⢿⣿⠀⠀⠀⣿⡏⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⠎⠀⠙⠿⠃⣾⣿⠃⠀⠀⠀⠻⢧⠠⠚⠹⣿⠀⠀⡰⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⠎⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠊⠀⢸⣿⠀⠀⠀⠀⠐⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠤⠔⠁⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢀⣴⠾⠛⠳⠀⠀⠀⠀⠀⣠⣼⣿⣶⣶⣶⣤⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⢠⣤⠀⢻⣆⠀⢀⣿⡏⠀⠀⢀⠀⠀⠀⠠⠋⠁⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢢⠀⠀⢡⠀⠘⡄⠀⠀⣠⣤⡅⠀⠀⠈⠉⣼⣿⠀⠀⠀⡌⠀⠀⣀⣤⣄⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠆⠀⠀⠀⠑⠲⡦⠒⢸⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⠀⡘⠀⠀⣴⣿⠋⢨⠀⠀⠀⢿⣷⡀⡌
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡏⠀⠀⠀⠀⠀⣿⣿⢀⠜⠀⠀⠀⣿⣏⠤⠃⠀⠀⠀⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⡔⠹⣿⣇⠀⠀⠀⠀⠀⢀⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠊⠠⢤⡤⠔⠻⣿⡀⠀⠀⢀⡠⠂⠁⠙⢿⣷⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢻⣿⡄⠀⠀⠀⠀⡌⠀⠀⠈⢿⡇⠀⠀⠀⠀⡠⢿⣿⡆⠀⠀⠃⠀⠀⠈⠉⠀⠉⠁⢀⠔⠂⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠠⠁⠀⠀⠀⠈⠻⠤⠤⠔⠉⠀⠈⢿⣧⠀⢀⠇⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⡠⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠒⠒⠓⠒⠒⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⡤⠖⠛⠛⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢀⣀⠀⢀⡴⠚⠉⣺⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⢀⡤⠞⠁⠀⠉⠺⠀⢀⡜⠁⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣹⡄⢧⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⡄⠀⠀⠀⠀⠈⠀⠀⠸⣄⠘⠿⠿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠲⢤⣄⠀⠀⠀⢹
⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⣀⣤⠊⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠙⢦⡀⢸
⠀⠀⠙⠒⢤⣄⠂⠀⠀⠀⠠⣇⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⣼
⠀⠀⠀⠀⠀⠈⠣⣄⣠⢤⡀⠈⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⡰⢉⡳⣦⠀⠈⢻⠳⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠋⢹⡄⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⢠⡏⠀⠈⢧⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⢧⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⡀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢳⡀⠀⢀⠀⢴⣳⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣧⠀⠘⡏⠒⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠃⠀⠙⠇⠀⠸⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠤⠄⠒⠒⠊⠉⠁⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢀⠀⠀⡀⡀⠀⡀⢀⠀⢀⡀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠊⠁

⣠⣴⣶⣾⣿⣿⣦⠡⠀⠀⠀⠀⠈⠀⠀⣞⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⠑⢄
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠁⠀⠀⢀⡤⠋⡇⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠈⠣⡀⠀⣠⣾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡒⠒⠒⠉⠀⣼⡃⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⢀⠀⣀⣾⣿⡿
⣶⣟⡻⠿⣿⣿⣿⣿⣿⣧⣙⢂⣀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣾⣥⠯⠙⠛⠛⠛⠛⠛⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⣏
⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⢀⠈⡄
⠀⠀⢀⣀⣠⣤⣤⣤⣤⣶⣦⣦⣤⣤⣿⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠻⡧⠇
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⡆⣀⣒⣊⣢⡀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣷⣯⣿⣾⣿⣿⡟⠀⡀⠀⠀⡇⢸
⢄⠀⠀⢹⡟⠙⠛⠻⢿⣿⣿⣿⡿⠿⠟⠻⣿⡄⠀⠀⠀⢿⣿⣿⣿⠋⢁⣀⠙⠘⠀⠀⣰⡇⠄
⣄⠙⠒⠞⢧⡀⠀⠀⡠⠈⠉⠀⠀⢀⣠⣴⣿⡇⠀⠀⠀⠘⣿⣿⡏⢠⣿⣏⠀⠀⠠⠈⣸⠇
⠈⠳⢾⡇⠀⠙⡶⢊⣀⣤⣤⣶⣾⣿⣿⣿⣿⣷⣤⣤⣤⣴⣿⣿⡇⠘⣿⣿⡄⠀⠀⠀⠀⢠⣤⣤⡄
⢦⣄⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣀⠈⠙⠁⠀⠀⠠
⠀⣹⡷⣴⡟⠛⠋⠉⠉⠻⢙⣻⣿⣿⣿⣿⣿⣿⠟⣥⠌⠀⠀⠀⠀⣧
⠀⣽⠁⠀⠈⢻⣦⡀⠀⠀⠛⠿⣿⣇⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡍⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣿⣽⣿⡻⣿⡀⠀⠀⠀⠀⠀⢀⢴⡇⡀⠄⠀⠁⠀⠀⠀⠉⠉⠀⠐⢰⡾⠋
⣾⠃⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⣿⣿⣿⣿⣿⡄⠀⠀⢀⡠⠂⠡⠈⠁⢀⣠⣴⣾⣶⣶⣦⣤⣤⣀⣰⣿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣿⣿⣿⣿⣿⣿⣤⣴⠿⠐⠁⣀⣴⣾⣿⡿⠛⠉⠈⠉⠛⠻⢿⣿⣿⣿⠀⢀
⡇⠀⠀⠀⠀⠐⢦⣄⣀⣀⡀⢀⣿⡯⠟⠛⠻⣿⡿⢃⣠⣴⣿⠿⠟⠉⠀⠸⡄⠀⠀⠀⠀⠀⠀⢈⢹⣷⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⡿⠋⣁⠀⠀⣀⠀⠀⢹⡄⠀⠀⠀⢴⣷⣤⣿⣿⣿⣿⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡄⠀⠀⠀⢹⡁⠙⠀⣿⣴⣿⣿⡀⠀⠀⢳⡀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿
⣦⣤⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢳⡀⠀⠈⢻⣿⣿⣷⣦⣤⣈⣧⣤⣤⣶⣿⠟⠈⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠱⡄⠀⠀⠙⢿⣿⡟⣹⠿⠿⠿⠿⠛⠁⣠⣾⡿⠛⠋⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠘⢦⡀⠀⠀⠙⠃⠱⢦⣤⣀⣀⠄⣮⡿⣿⣡⣤⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣴⡀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠙⢦⡀⠀⠀⠘⢾⣿⣿⠿⠟⠓⠊⢻⣿⣫⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠙⠲⣤⣄⣀⡁⢀⣤⣶⣤⡀⠀⠈⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠘⠻⣿⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣶⣄⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠙⣿⠟⠛⣍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⣀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠟⠀⢿⡇⠀⠀⠀⠀⠠⣤⣤⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣟⣋⠁⠀⠀⣿⡇⠀⠀⠀⠘⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠉⠛⢛⡛⠻⠳⣦⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣿⡉⠆⢀⣠⡶⢛⡥⣌⡁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣻⣿⣤⣾⡟⡝⠉⠀⠀⠹⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⠆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⡿⠀⠀⠀⢀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣄⠀⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⣡⠇⠀⠀⢸⡄⠀⡿⡇⠀⢠⣶⡅⠀⠀⠀⠀⡀⠀⢠⡉⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠋⠀⠀⠀⠸⣧⠘⠁⠀⠀⣹⡿⠋⠀⠐⠙⠿⣿⣿⣶⣤⣶⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣧⣀⡀⠀⣀⡤⠦⠄⠒⠊⠁⣀⣀⣤⣤⣤⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠹⠿⠟⠁⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣷⣮⣤⣼⣿⣿⡯⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡶⠿⣄⣀⠀⡀⠀⠀⠀⠀⢀⣴⣗⠄⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠻⣤⣈⠙⣿⠛⣻⣿⠇⠲⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⣾⣿⣿⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠈⢿⣿⣿⣇⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⡉⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣇⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣤⣶⣾⣿⣿⣶⡀⠀⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠻⠿⠿⠿⠿⠇⠀⠀⠀⠈⠛⠿⠃⠀⠀⢠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⢿⣿⣿⣶⣤⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⡅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢴⣤⡈⡇⢸⡇⣿⠋⠁
⠀⠀⠀⠀⠀⠠⡀⠐⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢍⡉⣈⢹⡏⢈⡷⢸⡄⠉⠳⠀⠃⠈⠓
⠀⠀⠀⠀⡄⠠⠄⠀⠀⠀⡉⢈⡀⠐⠀⠰⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠉⠉⠀⠀⢄⠀⡄⢠⠀⠆⠲⠀⠋
⠀⠀⠀⠀⣵⣶⡀⠁⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠂⠆⠐⠆⠀⠃⠉⠀⠀⠀⠈⠀⢲⠄
⠀⠀⠀⠀⣿⠿⣢⣤⣤⣴⡆⠁⠀⠀⡀⠠⠀⠄⠀⡀⠀⢈⠀⠉⢕⠃⠀⠆⠀⡤⢶⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠷⢿⡀⢀⠘⠃⠀⣄⠂⠄⢀⣀⣦⢤⣤⣦⣤⣤⣀⣠⡁⢸⡇⠀⠀⢀⠜⣹⣷⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠉⠀⠀⠴⠆⠀⣀⠗⠉⣁⣤⣶⣿⣿⠟⣫⡍⠉⠉⡁⠀⣿⢲⡴⠋⣰⠟⠁
⠀⠀⠀⠀⣿⢿⣙⢻⣿⣶⠂⠂⠀⣠⠔⠋⠁⣠⣾⣿⣿⣿⣿⣿⠉⢡⣵⠞⠁⡵⠀⠘⠋⠀⡔⠋⠓⢦⣠⣤⠄
⠀⠀⠀⠀⣏⣸⣵⣾⠁⠈⢀⣴⣿⠟⢠⡾⠋⡤⢹⣿⣿⡿⠋⢨⣿⠿⠥⠤⠜⠁⠀⠀⠀⢈⣭⣤⠤⠴⠾⠋
⠀⠀⠀⠀⣿⣻⠉⠉⠀⣴⣿⣿⢋⣤⣿⣄⢀⡴⠛⡿⠋⠣⢶⡀⠙⠿⢤⡤⣶⣀⢤⣀⣀⣀⠙⢤⠠⢄⡀⠀⠀⢀
⠀⠀⠀⠀⢓⡏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣀⠄⠁⠀⢰⡟⠉⣀⡀⠀⠀⠻⠀⢀⣚⠟⢃⣙⣢⣖⠀⠉⠳⣄⠀⠃
⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢏⣿⣿⣿⣿⣿⣿⢣⠀⠀⡈⣿⠃⠀⠁⠀⢀⠀⠀⠀⣿⠳⢶⣿⣿⣿⣿⣿⣷⣦⣈
⠀⠀⠀⠀⣿⠃⠀⠘⠛⠛⠘⢿⣿⣿⣿⡿⣁⢀⣼⠆⠸⣿⣷⣀⠀⠀⠀⠒⠀⢰⣯⣄⣀⡀⠉⠃⠀⠀⠀⠈⠙⠷⣄⣠
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠆⠀⢨⠿⠟⠻⠻⡷⠿⣿⣦⡀⠈⢤⡽⠀⠀⠀⡄⢠⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣦
⠀⠀⠀⠀⣿⣇⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠿⣦⡀⢈⠀⠁⠀⠀⣿⣿⣿⣯⡉⠛⠻⢿⣿⣧⡀⠀⠀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣿⡼⡀⠀⠛⣰⡏⢀⢠⡔⠀⠀⠀⠀⠰⢋⢠⠈⠻⣦⡳⠄⠀⣠⣿⣿⠛⠻⢷⡄⠀⠀⠉⠛⣷⡄⢠⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣷⡄⣰⡿⠗⠚⠃⠐⠀⠀⢀⣠⣧⡌⣰⣦⡶⠚⠿⣶⣎⠁⠈⠻⠇⠀⠀⠉⠀⠀⠀⠀⠘⣇⢸⣿⣿⣻⣿⣿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⡉⠘⠛⠛⠉⠀⠀⣼⠃⠉⠑⢠⠐⢶⣶⢸⣷⢀⠀⠀⠀⠀⠃⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣤⣤⣤⣤⣐⠖⢰⡆⣐⠀⣤⡀⢠⣼⣷⣶⣶⠇⠀⣤⣾⣿⡇⣿⣠⣦⠒⡀⠐⣸⣿⣿⣿⣿⣿⡇⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣠⡮⣙⣿⣯⣯⣿⣿⣾⣿⣿⣿⣿⣠⣶⡟⠙⠛⠈⣿⣷⣿⣿⣷⣞⣿⣿⣿⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⣦⣼⢠⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⠟⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠡⠤⣤⣶⣧⣴⠀⣀⣤⣄⣀⢤⠈⠙⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⡀⢠⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣾⣿⣿⣶⣤⣈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠿⢋⢀⠀⠀⢀⣀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣦⠀⣸⣶⢸⣀⣴⡆⣁⣴⠟⢩⣿⡇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠉⣿⣿⢴⣿⠁⡘⢸⣿⣀⢸⣏⡀⠉⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢠⢾⣿⡟⠈⠿⠞⠀⠈⠙⣥⠘⢋⡴⢲⠈⠛⠁⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⢡⢾⣿⠇⣰⣿⣶⢲⠀⣴⡆⢀⣾⠐⡁⠀⢀⣴⠒⠘⢶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣾⡟⠀⣿⣿⠀⢹⢹⣿⠁⢸⣧⠊⢹⣷⣸⣧⠀⢀⢢⠚⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⠟⠀⠀⢻⣿⡠⠃⠘⠿⠤⢻⣿⣜⣸⠟⠈⠛⠒⠁⠘⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡔⠲⣄⠀⠀⡀⠀⣠⣤⡀⠉⠀⣰⢎⠕⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡆⢸⣀⣾⣿⡜⠀⣿⡇⠀⣸⡟⠀⣠⣿⠂⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠉⢸⠁⢿⣿⡇⢸⣿⠁⣼⣿⠁⢠⢹⣿⠀⡜⣿⡷⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢠⠎⠀⠸⣿⠇⠘⠿⠞⠘⣿⣤⠏⠀⠛⠛⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠒⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠴⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠢⣅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣂⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣧⣿⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡆
⠀⠐⠐⠂⠀⠉⠉⠀⠀⠉⠉⢑⠆⠀⠀⠀⠀⠰⠉⠉⠙⠂⢀⡀⠀⠀⠀⠀⠀⢀⠀⢸⣋⡤⢾⣦⠀⠀⠀⠀⠀⡀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢃⠀⠠⢶⠀⠀⠈⠁⠒⠒⠒⠉⠀⠀⠸⠿⠶⠟⠁⠀⠀⠀⠀⠈⡗⢁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⣠⠀⢆⣀⡸⠀⠐⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⢠⠴⠀⠀⠊⠉⠅⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠉⠀⣠⠍⠀⢻⣉⠝⠛⠀⠀⠉⠛⠆⢄⠀⠀⠀⠀⣄⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠀⣀⠤⢪⠏⠀⠀⠀⠀⠀⠀⠀⢢⠈⠐⠒⠁⢈⠷⠄⡠⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣾⠉⠀⢰⠋⠣⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣆⠀⢱⠀⠏⠋⠀⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠸⠗⠁⠀⠀⡘⠀⠀⠈⡆⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠂⠤⣀⣀⠔⠁⠀⠀⠀⡖⠒⣒⣲⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠟⠠⠄⠀⣀⢼⠁⠈⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠈⡀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠄⠀⠀⠀⣧⠀⣻⠆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠜⠓⠀⣃⠀⠉⠁⠀⠀⠀⠈⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⢀⣀⠀⠀⣠⠄⠀⠠⠄⠀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⠀⠀⠈⠀⡀⠀⠀⠀⢀⣀⣸⣄⣘⣂⣈⣁⣀⣀⣀⣀⣐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠤⠊⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠁⠀⠀⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠢⣄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢴⠖⠻⠛⢭⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⢀⡤⠀⠤⢄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡼
⠀⠀⠀⢀⠼⠃⠀⠀⠈⠉⢆⢘⡄⢰⡄⠀⠀⠀⠀⠀⠀⠄⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣔⠋
⠀⠀⠜⠉⠀⠀⠀⠀⠀⠄⠬⣍⡒⠦⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⠀⢀⣀⣙⡍⢲⠆⠭⠈⠉⠢⡀
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠒⠒⠋⠉⢀⣠⢤⡀⠀⠀⠀⠀⠀⢖⠒⠢⠽⡄⣡⠇⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠉⠉⠢⣀⡀⠀⠀⠀⠄⡤⠤⠔⠒⠊⠁⠀⠀⠙⠢⣀⠀⠀⠀⠘⠖⣒⠞⡫⠃⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⣀⣤⡀⠈⠣⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⡴⠉⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣠⠔⠋⠁⠀⠈⠓⠤⣀⣀⠴⠦⠤⢦⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⣀⡴⠋⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢰⠁
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡎⠁⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣠⡴⠃
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⢣
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠃
⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠐⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡄⠀⠀⢀⣀⣀⠄⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⣿⢀⣾⣿⡿⣿⡆⢠⣿⡿⢻⡇⠀⢸⣿⡿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⣼⣿⡿⠁⣿⠁⣼⣿⠃⢸⣿⠀⢸⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⣿⣿⠃⢠⣿⠀⣿⣿⠀⣼⡇⠀⣿⣿⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠐⢶⡞⠀⣿⣿⠀⣼⡏⠘⣿⣏⢠⣿⠃⠀⣿⣿⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠾⠁⠀⠙⠿⡿⠛⠁⠀⠻⠿⠾⠋⠀⠀⠿⡿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢰⡆⢠⣶⣤⠀⢰⣶⢤⡄⠀⣴⣶⣦⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⠁⢸⣿⡟⠀⣿⣿⢸⠇⠀⣿⡇⠀⠀⢸⣿⡏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⢸⣿⡇⠀⣿⣿⣇⡀⢠⣿⣇⡀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣸⣿⠇⠀⣿⣿⣸⡇⢸⣿⡏⠁⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠹⠿⠀⠀⢿⡿⠟⠀⠸⣿⣅⡀⠀⢷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⡀⠀⣠⡀⠀⠀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⡆⠀⣿⣿⡆⢸⡇⠀⣿⣿⠀⠀⣿⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⣿⡿⣿⢸⡇⠀⣿⣿⠀⠀⣿⣿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⡏⢀⣿⡇⢸⣿⡇⢀⣿⡏⠀⠀⠈⠛⠷⢾⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡿⠁⢸⣿⠇⠀⠻⠀⠸⣿⣧⡀⠀⠀⢠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠛⠋⠉⠉⠁⠀⡠⣄⡀⠀⠈⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠀⠀⠀⣸⠐⠀⠨⣑⢦⡀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡇⠂⣀⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣎⠉⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠗⠀⠀⠃⠈⠁⠀⢀⠔⠊⠉⠑⠢⣄⠀⠀⠀⠀⠈⢳⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⡀⠀⠈⢆⠀⠀⠀⠀⢈⡙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠸⡆⠀⠀⢠⠏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢳⡀⢀⡏⠀⣸⠁⠀⠀⠀⠀⠀⣀⡤⣄
⠀⠀⠀⠀⠀⠀⢠⣞⣤⡤⠤⠤⠤⠤⢤⣤⡀⠀⠀⠀⢀⡤⠦⢦⣀⠘⠋⠀⠀⠀⠀⠀⠉⣿⠃⣠⡇⠀⠀⠀⠀⢀⡜⠁⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣟⠀⢀⣤⠈⠳⠦⣤⣤⠤⠖⠚⠉⣷⣯⣿⠟⠀⢠⠞⠛⣮⠔⣚⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠹⣆⠀⠘⠢⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣊⠰⣀⢹⣎⠭⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢈⣓⣦⣄⡀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⢀⠼⠉⠀⠈⠻⣁⠠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⠴⠚⠋⢉⣽⠯⠖⣦⡩⠛⠙⠉⠉⠻⣦⣄⡀⠀⢀⣿⠀⠀⠀⠤⣤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠚⠉⠀⠀⢀⠔⠋⣠⠴⠚⣙⠀⠀⠀⠀⠀⠀⠈⣆⡉⠛⢉⣠⠗⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⢸⠲⣄⡸⠉⢳⠀⠀⠀⠀⠀⠀⣹⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡜⢣⡸⠀⠈⡇⠀⠛⢤⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠔⠷⣀⡀⠀⣰⠇⠀⠀⢸⠇⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡿⢥⠀⢀⣰⢻⠒⣆⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢲⡏⠁⡏⠀⢸⡄⠸⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣼⠀⢸⣅⠀⣠⣇⠀⣻⠍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠳⠤⠞⠀⣹⡅⠉⠉⠁⠀⠈⢹⣦⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⠀⠀⠀⢘⡇⡏⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠈⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠫⡙⠓⢶⠶⠒⣯⠀⣹⠓⠚⠉⠁⢸⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠘⢆⠀⠂⠀⠘⡇⣏⠀⠀⠀⠀⠈⣀⣀⣤⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠸⠀⢐⣀⡴⠏⠻⠤⠶⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡤⡆⠐⠒⣤⢠⡒⠄⠐⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⡟⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠞⡇
⠀⠀⠀⠀⢤⠈⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠁⠀⠀⠀⠈⢆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡌⢠
⠀⠀⠀⠀⠸⡀⠈⢦⡀⠑⠂⠀⠀⢀⡤⢃⠈⡐⠄⠀⠀⠀⠀⠀⠈⢧⠀⢠⠏⠀⠀⠀⠀⠀⠀⠐⡀⢀⠣⣄⠀⠀⠀⠐⠁⣠⠎⠀⡸
⠀⠀⠀⠀⠀⢇⠀⠀⠑⢄⠀⠀⠀⠈⠇⠀⢀⣤⣴⠶⠶⠀⠀⡀⠀⠀⠱⠁⠀⠀⡀⠈⠰⠶⠶⣤⣄⠀⠀⠛⠀⠀⠀⢀⠔⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠑⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠐⡌⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠆
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠈⢨⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠈⡿⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢰⣄⡟⠀⢠⠀⠘⣇⣰⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⢾⡍
⠀⠀⠀⠑⡙⢦⡲⢄⡀⠀⣀⣀⡄⠀⠀⠀⠀⢦⡀⠀⠀⠀⠸⢿⠇⠀⣿⡇⠀⢿⠿⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⣄⣀⡀⠀⣀⠴⣢⠚⡑⠁
⠀⠀⠀⠀⠘⣄⠉⠂⢌⣉⠉⠀⠒⠀⠀⠀⠀⠀⠙⢗⠢⠀⣀⢢⣀⡀⢿⠇⣀⣠⡂⠀⠠⢒⠟⠁⠀⠀⠀⠀⠐⠃⠈⢉⣉⠄⠊⢁⡜
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣓⡤⢄⣀⡀⠀⠀⠀⠀⣀⣀⠤⣔⡁⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⡀⠀⠑⢍⠁⢀⡀⢋⠕⠃⠀⡀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠜⡠⠀⠘⢉⡉⠀⢀⠆⢂⠀⠈⣉⠛⠁⠠⡐⠄⠂⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⡁⠀⠀⠀⠔⠀⠠⠀⠠⠀⠐⠌⠀⠀⠀⢡⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⡟⠀⠀⠳⡀⠂⡴⠣⡄⡤⠳⡄⠂⡰⠃⠀⠘⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⠀⠀⠀⠀⠙⡄⠀⠀⢡⠁⠀⠀⠜⠁⢀⠀⠀⠰⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡁⠹⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⣤⠏⠀⠀⠀⡼⠀⣥⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⡌⠙⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠠⠶⠐⠙⣄⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠴⡄⠀⠀⠀⠀⠘⠀⠀⡠⡀⠀⠰⠀⠀⠀⠀⠀⡴⠞⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠈⠂⠌⠀⠀⠀⠀⠀⠀⠰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠃⠀⠀⢃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡆
⠀⠀⠀⣠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⢀⡀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣁⠈
⠀⠰⠾⢯⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠄⣤⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⢠⡄⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⡘⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠻⡛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡻⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⡒⠚⢢⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠚⠒⡒⠓⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠄⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠄⠀⣚
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣡⡴⠶⠶⣦⣌⠻⣦⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣀⣤⣀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠐⠟⠉⣸⣧
⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠋⠀⢹⡆⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣠⡞⠉⢿⡀
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡏⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⣰⠏⠀⠀⢸⡇
⠀⢀⣾⠃⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⡇⠀⢠⡿⠀⠀⠀⠀⠈⢷⡀⣀⣠⡾⣿⠀⠀⠀⣸⠇
⠀⠘⠛⠛⠋⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⢛⣷⠆⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠻⢿⣤⡛⠶⠟⠁⠀⠀⠀⠀⠀⠈⠙⢻⣇⣠⣿⡶⢦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⢀⣠⣤⣀⠈⠙⠳⢦⣤⣀⣀⣀⣠⣤⠶⠶⢿⡟⠁⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠋⠙⣧⡉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠙⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣉⣷⣦⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣠⣴⠶⠞⠛⠋⠉⠉⣩⡴⠟⠋⠉⠉⢙⣿⠳⠶⣦⣤⣤⣤⣤⣤⠶⣾⡛⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣤⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⠷⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠹⣏⠉⠻⣶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣀⡿⠀⠀⢸⡇⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠙⢷⣄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠉⠀⠀⢀⣾⠁⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⣠⣴⠟⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠙⣧⡀⠀⠀⠀⣠⣿⣤⣤⣤⣴⡶⠛⢿⣶⠶⠟⢋⡁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣜⣃⣠⣴⠞⠋⣰⡏⠀⠀⠘⣷⡀⠈⢿⡷⢿⣿⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡏⠀⢠⡿⠀⠀⠀⠀⠘⣇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⡇⠀⢸⣧⡀⠀⠀⠀⣠⣿⠀⠀⣿⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢾⣇⣀⣸⣧⢿⡄⠀⣾⣯⣿⣀⣠⣿⠖⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠁⢸⡇⠀⣿⡀⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣄⡀⠀⠀⠀⠀⣠⣾⡁⠀⢈⣷⣤⣀⣀⣀⣀⣤⡾⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠙⢷⣌⠛⠛⠛⠛⠛⠉⠘⣷⠀⣼⠃⠈⠉⠉⠉⠉⠁⣠⠞⠋⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠻⣦⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣾⠃⠀⣴⠟⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠘⣧⠀⢹⡆⠀⠀⠀⢀⣠⠟⠀⠻⣦⡀⠀⠀⠀⢸⡇⠀⣼⠇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⢘⣧⣠⡴⠾⠛⠁⠀⠀⠀⠈⠙⠳⢶⣤⣿⡀⢠⡿⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⠶⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠠⠀⠀⠀⣠⠄⣸⡇⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇⣶⠇⠠⣶⡆⢀⢴⡏⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⣿⠇⣿⠀⠀⢿⠀⠀⠸⡇⠘⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⢀⣤⠦⠀⠀⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢾⠀⠀⢀⣾⠁⠀⠀⠀⠈⠀⢰⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⡖⠀⢡⠀⢸⡏⢀⡀⠀⢀⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣧⢠⡿⠀⣿⡅⠁⣿⣰⡏⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠸⡇⠀⣿⠁⢰⡿⠸⡇⠰⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠑⠀⠙⠀⠚⢁⡤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢲⡄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠠⠀⣼⠇⢸⡇⠀⢠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢰⡇⠀⠎⢹⡇⠀⣿⠀⢸⡇⠀⣿⠀⣾⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⡠⠀⠸⠇⠀⣿⠀⢸⡇⡸⠻⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⠀⡀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠁⠀⠀⢀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠒⠒⠂⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠂⠤⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⡠⠄⠒⢦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠛
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢁⠞⠁⠀⠀⠀⠀⠀⢀⡠⠔⠒⠢⢄⠀⠰⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠃⠈
⠀⠀⠀⠀⠀⡦⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁⡀⠤⡤⠀⡀⠁⠀⠀⠈⠑⢄⢠⠀⡀⠀⠀⠀⠀⠀⡠⠒⠉
⠀⠀⠀⠀⠀⠠⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⡠⢀⡴⠋⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠈⠃⠀⠇⠀⠀⠀⠠⣎
⠀⠀⠀⠀⠀⠀⠾⠁⠀⠂⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⡀
⠀⠀⠀⠀⠀⢠⠀⡐⢠⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⡧⠀⠀⢂⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣧⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢻⣷⡄⠠⠊⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⢀⣴⣦⣄⡀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣠⡠⠤⠀⢄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⡄⠐⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠀⠀⠀⠀⡇⠀⠀⢀⠁⠠⡄⠒⠒⠀⠀⠀⠀⠐⠒⠂⠤⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠛⠃⠀⠀⠀⠀⠁⠐⠒⠒⠀⠁⠀⠀⠀⠀⠀⡹⡃⠀⠀⡇⠀⠀⠈⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠊⠀⠁⢀⠔⠀⢀⠆⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠨⢤⡦⠤⢀⡀⠀⠀⣀⠀⠠⠀⠂⠁⡴⠚⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠀⡀⠀⡀⢃⡄⠊⢁⡀⠤⠬⠧⠤⠀⢠⡔⠁⠀⠀⢸⠄⠀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠃⢀⠀⠈⠀⠀⠐⢿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡔⢁⠀⠀⠀⠈⠑⠤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠑⠰⠶⠘⢆⡀⠀⠈⠑⠛⠄⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢰⠀⠣⠀⠀⠀⠀⠀⠈⠢⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠕⠢⢄⡀⠀⠠⠙⠆⠄⠀⠀⠨⢦⡤⠀⠀⠁⠀⠘⠀⠁⠀⡘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⣠⢀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠈⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⢁⠖⠊⠀⠊⢀⠄⠒⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠄⣀⣀⣀⠠⠔⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢠⠤⢄⠀⠀⠰⠃⠤⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠈⡀⠀⠀⡆⠀⠈⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⢐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠈⠀⠀⢉⠀⠐⢰⡄⠀⠘⡦⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⠉⠉⠉⡩⠒⠉⠀⢰⠀⠀⢡⡔⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠘⡀⠀⠀⠒⠛⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠱⢄⡀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠰⡀
⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠢⡀⠀⠙⠒⠒⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠸⡀⠀⠘⠀⠀⠀⠀⠱⠤⠄⠀⠀⢀⡀⠠⠤⠴⠎⡉⢂
⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠈⠻⡆
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⣠⡇⠀⠀⠐⠁⠀⠰⠉⠀⠀⠉⠲⡄⢰
⠣⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠼⠤⠤⠓⠒⠈⠀⢃⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⣼⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢳⣶⡆⠀⢰⡏⠀⠘⡇⠀⢠⡏⠀⠈⡇⠀⠀⣴⡟⠑⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⡞⢹⡇⢀⣾⣿⠀⠀⡇⢀⣾⣿⠀⠀⡏⢀⣼⡿⠀⠀⣿⠏⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢀⡞⠁⢸⣿⠾⣿⡏⠁⣾⠟⠋⣿⡏⠑⢶⠟⠋⢿⡇⢀⡴⣿⡄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣠⣾⣿⠀⠻⢧⡴⠋⠀⠀⠹⢧⡴⠏⠀⠀⠈⠛⠛⠀⠙⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣸⡇⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣿⠃⠀⢠⡄⠀⠀⣼⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠀⠾⠁⠀⢰⣿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⣰⡆⠀⠀⣼⡿⠀⠀⢸⣿⡞⢀⡴⣦⡀⠀⠀⢠⣾⢟⡦⠀⣾⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡿⠳⠤⢴⣿⡇⠀⠀⣼⣿⢀⡏⠀⣸⡇⠀⢠⣿⠗⠚⠁⠀⣸⣿⡀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠇⠀⠀⢸⣿⠁⠀⣰⢿⣿⡼⢀⣤⣿⡧⠖⠛⣿⠀⠀⠀⣼⡧⢽⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠴⠏⠀⠀⠀⠀⠻⣦⡴⠃⠈⠿⠇⢯⣼⠟⠀⠀⠀⠙⠦⡤⠞⠙⠧⠼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⢷⠀⠀⣶⣦⠀⢠⣶⣦⠀⠀⣿⣇⡾⠁⠀⣶⡄⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢸⡇⢀⣿⡯⢀⡏⣽⣿⠀⢀⣿⡟⠁⠀⢸⣿⡇⠀⡼⢻⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⢤⣾⠶⠛⣿⡇⣼⠀⣿⡇⢀⡾⣿⡇⠀⢀⣾⣿⠁⢰⠃⣿⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣴⠃⠀⠀⢿⣿⠇⠀⢿⣧⡾⠁⠙⢿⣴⠟⠘⣿⣤⡏⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⢆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠳⠛⣀⠀⠀⠀⠀⡾⠁⠘⣧⠀⠀⠀⠀⡠⠻⢲⠀⡄
⠀⠀⠀⢠⡤⠤⢤⣀⣀⡀⠀⠇⢸⣄⠲⠿⡻⣶⣤⣸⡷⠀⠀⢿⣆⣤⣶⠋⠓⠴⣠⠀⠀⠀⢀⣀⣠⡤⠤⣤⠄
⠀⠀⠀⠈⣷⢇⣂⡢⠄⠉⠉⠙⠺⣿⣦⠐⠃⠘⢿⣿⡇⠀⠀⢸⣿⡿⠁⠂⠀⣴⡿⠓⠉⠉⠉⡠⢔⣒⡙⡿
⠀⠀⠀⠀⢻⢰⡸⠙⠳⣦⡲⣄⠀⢀⠃⠤⡀⠀⠀⠙⠃⠀⠀⠉⠋⠀⠀⢀⡴⢛⠀⢀⣤⣶⡴⠞⢫⢧⢷⠇
⠀⠀⠀⠀⠈⣇⢧⢂⠀⠈⢿⣾⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣫⣿⡟⠀⠀⣎⡎⡞
⠀⠀⠀⠀⠀⠈⢮⢧⢢⠀⠘⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢊⣿⣿⠀⢀⢎⢎⡞
⠀⠀⠀⠀⢀⣴⣾⣷⣢⢳⣴⣙⠗⠀⠀⠀⠀⠀⠛⢻⠀⠈⠁⠀⢙⠂⠀⠀⠀⠀⠀⠟⣻⣲⢯⣮⣾⣷⣦⡀
⠀⠀⠀⣠⠿⠿⣿⡿⢿⠛⠛⢒⣠⣤⣄⠀⠀⠠⠄⠀⠁⠀⠀⠈⠁⠐⠒⠀⠀⣠⣴⣤⠒⠛⠛⠿⣿⣟⠿⠻⢦
⠀⠀⠀⠑⢢⠜⢁⠀⣘⣿⡿⠿⠟⠻⠿⣿⣔⣢⡤⠀⡀⠀⠀⠀⠀⢂⣤⣤⣿⠿⠿⠿⠿⣿⣧⣀⡀⡌⢣⡔⠈
⠀⠀⠀⢠⠎⠀⣠⣿⡛⣻⣄⠀⠀⠀⠀⠀⠉⠳⣖⣀⣾⢀⡀⣳⣠⣾⠿⠉⠀⠀⠀⠀⠀⣠⠟⢛⣷⣀⠀⠱⡄
⠀⠀⢠⢃⣤⣤⣄⡈⢷⡅⠙⢆⠀⠀⠀⢠⠀⠀⠈⢹⣿⣬⣥⣿⠋⠁⠠⠀⠀⠀⠀⢀⡴⠋⢠⡿⠁⣠⣦⣤⡘⡄
⠀⠀⠈⢹⡿⣿⣞⣷⣾⢿⣤⣤⣙⣦⣀⠰⣦⡄⠀⣈⠛⠛⠛⢻⡀⠀⢠⡾⠀⣀⠴⣋⣤⣴⡿⢧⣞⡻⣿⢿⡏⠁
⠀⠀⠀⠘⠁⣽⣿⡿⢧⣿⡅⠀⠈⠉⠒⠭⣍⡁⠚⠉⢀⣖⣶⡀⠙⠂⠉⣃⡭⠒⠋⠉⠀⢨⣿⣞⣿⣿⣷⠀⠃
⠀⠀⠀⠀⣷⣿⣿⣷⣤⣈⣻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣏⣁⣆⣰⣿⣿⣾
⠀⠀⠀⠀⡏⢸⣿⣿⣿⢿⢿⣿⡿⣷⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇⠹⠆
⠀⠀⠀⠀⠀⠨⢻⣿⣿⣷⣿⠋⠀⠀⠙⠷⢮⣝⣒⠶⠶⠶⠶⠿⠶⢒⣪⡵⠾⠋⠁⠀⠙⣧⣿⣷⢹⡟⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠈⠩⠿⠛⢷⡶⠿⠻⠛⠍⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢻⡟⢹⠹⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⡏⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡄⠉⠈⢿⣷⣦⣄⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⣴⣾⠟⠉⠀⢠⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡦⢰⣾⣿⣿⠟⠉⠙⠳⢦⣴⣇⡼⠟⠋⠉⠻⣿⣿⣶⡆⡇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣼⡿⠛⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠻⢿⣡⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢀⣠⡤⢄⣀⣠⣤⣴⠶⠛⠉⠀⢠⣄⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣟⣩⣶⣿⠿⢟⣫⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠤⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢌⠛⠉⠀⠺⡿⠿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠁⠀⠀⠛⠻⣦⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⣀⣀⣼⠁⠀⠐⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⡉⠉⠛⠲⣤⣀⠀⠀⠀⠀⠂⠘⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⢀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⡀⠀⠠⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢶⠃⠀⠀⢀⠀⠈⠀⣀⣈⣉⣙⢶⣄⡀⠀⠀⠀⠈⠉⠉⠙⠛⠦⢄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒⠶⠖⢉⣴⠀⠀⠀⢻⣿⣿⣿⠿⣿⠄⠀⠀⠀⠂⠀⢄⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣴⣃⣤⠔⠂⠀⠹⣧⠀⠀⠀⠋⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄⣀⣻⡿⠁⠀⠤⠤⠤⠴⠀⠀⢀⠀⠨⡋⠩⠿⠶⡄⠀⠀⠀⠀⠀⠀⠙⢠
⠀⠀⠀⠀⠀⠀⠘⢋⠠⠂⠀⢀⣠⠟⠉⠉⠀⠐⠔⣶⣦⣉⣍⠓⠀⠘⠛⠒⠀⠀⡸⢀⣰⣖⠚⠃
⠀⠀⠀⠀⠀⠀⡠⢋⠀⢠⠞⣽⠟⠀⠀⠀⠀⠀⠀⠙⢿⠟⣹⣿⡆⠀⠀⢀⡠⠖⠐⠿⡉⠑⠢⠆⠀⠂⠈⠒
⠀⠀⠀⢀⠴⠚⣓⠿⠖⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣭⣾⣷⠀⢰⡉⠀⠀⠰⡄⠘⠗
⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠸⡿⣟⠋⠂⠀⣷⡄⠀⠐⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠰
⠀⠈⠀⠒⠄⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠉⠾⣿⣯⣁⣀⠉⠄⢠⣀⠀⠶⠿⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⡄⠉⠛⠿⢿⣶⣶⣧⡀⠀⠀⣻⣿⣿⣄⠀⢠⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣶⣬⡛⢿⡄⠦⠀⡸⣿⣿⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠠⣾⣿⣿⣷⣦⣀⡀⢁⣸⣿⣿⣷⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⣠⡄⠀⣠⣈⠻⢿⣿⣿⣿⣿⣷⣮⣉⠙⣻⠀⣴⠀⠀⠀⠀⡄
⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠇⠤⠉⡉⠀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠃⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡉⠓⢄⠀⠑⠀⢠⠀⠆⠀⡆⠸⠀⡄⢀⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠖⠛⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠀⠱⡄⢡⠈⡇⠀⡠⠴⠦⣄⠀⠌⢠⠂⢀⠂⠀⠀⠀⠀⠀⡴⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢹⠁⠀⠀⢳⠀⠣⢁⣾⠁⠈⠁⢸⠖⠒⠲⡄⠁⡴⠃⢀⠔⢠⠞⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢸⡇⠀⠀⢸⠀⢠⢞⠇⠀⠀⠀⡏⠀⠀⠀⡼⠒⡒⢤⠀⡰⠃⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄⢸⡇⠀⠀⠈⢷⠋⣨⡴⢒⠒⣒⠲⣤⣀⠸⠁⠀⠀⢨⠟⠀⠈⢂⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⠀⠀⠉⠀⢠⠞⡥⣤⡏⣿⡏⣷⡖⡌⣧⡀⠀⡰⠋⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⡀⠀⠀⠀⡸⡀⣷⡾⣧⠟⢷⡋⠏⣥⠬⡁⠼⠁⠀⢲⡼⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⣇⠀⠀⠀⡗⢨⣓⣒⣒⡬⡅⣞⠙⢯⠀⣿⠀⠀⢀⠞⠠⠤⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠔⠒⡀⢸⡄⠀⠀⠹⡌⢿⢹⣿⡿⣧⡟⠸⠾⣡⠃⠀⢠⠏⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⢁⠄⡞⠈⠂⠀⠀⠙⠲⣜⡛⠷⠛⣛⡡⠟⠁⢀⡴⠃⠤⡈⠑⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠄⢧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⡴⠋⢄⠀⠢⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⠒⣲⠞⠉⢄⠈⢀⠑⠄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⠉⠲⠤⣄⣀⣀⣠⠔⠁⡀⠡⠀⠣⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡄⠀⠀⢰⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠤⣄⣀⢀⣀⡤⠴⠒⠒⠂⠀⠀⠐⠀⠀⠀⠈⣉⠳⠴⠒⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣽⡂⡲
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠰⠯⠤⠤⣤⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠝⠁⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡸
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠢⢄⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⢉⡭⣍⣿⣀⣀⣠⠴⠲⡤⠔⠒⠲⢤⡀⠀⣼⠀⠀⠐⠀⠀⣨⠟⠛⣛⡴⠚⢓⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⣏⠀⠈⠁⠀⠀⠑⡄⠀⢹⡤⠖⠛⠢⢌⠆⠈⠳⡶⢖⡚⠉⠀⡴⠋⢅⢀⡴⠁⣠⠈⢧
⠀⠀⠀⠀⢀⠴⢋⠤⠂⠘⡧⠀⠀⠀⠀⠀⠀⢰⢀⣬⠷⡄⠀⠀⠀⠀⠀⠀⡟⠢⣍⣉⣉⣇⠠⣀⠿⢤⠊⣁⠔⣸
⠀⠀⢀⡴⡡⠊⠀⠀⠀⠀⢹⢦⣀⣀⣀⡤⠶⣯⠭⠤⠔⠁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠉⠉⢦⣀⡬⠞⠛⠥⠞⠁
⠀⠀⡞⡌⠀⠀⠐⢄⢀⠞⠁⡀⠀⠀⣨⠃⠀⠀⠉⠁⡲⠂⠀⠀⠲⢏⠁
⠀⢰⣧⠁⠀⠀⢀⡤⢿⡀⡜⠀⢀⣴⠋⠓⢦⣀⣠⠞⠁⣠⠞⠲⣄⠀⠙⢦⡀
⠀⢸⣿⠀⠀⢠⠏⠀⠀⠉⠧⠴⠋⠈⠙⠲⢤⣀⣀⣠⠞⠁⠀⠀⠈⠳⣄⠀⠹⣄
⠀⠘⣧⣂⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⡤⠶⡄
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡦⠚⠁⠀⠀⢳⣄⣀⣤⡴⠖⠚⠉⠉⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢀⣠⠴⠋⠉⠀⢀⡤⠒⢆⠀⣼⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠉⠀⠀⠀⠀⢸⠁⣂⡱⢈⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⣀⡠⠵⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⣉⣩⣤⣶⠋⠡⢀⢀⢤⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⠀⠈⠈⠈⠉⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⣷⡄⠀⠀⠀⠀⠀⡠⣀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⡀⠀⢀⠘⠓⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣤⣄⣀⣀⣀⣀⣘⠀⢸⡇⠀⠀⠀⢀⠜⢉⣿⡷⠀⣿⣿
⣿⣿⣿⠀⠚⠋⠀⠀⠀⡤⠀⢀⣠⠴⠒⠚⠉⢉⣡⣶⣾⣿⣿⠟⠛⠛⠋⠉⠛⠀⠘⣷⣦⣄⡴⠋⢀⣿⠟⠁⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠁⢀⣴⣿⣿⣿⣿⣿⣯⠤⠒⠉⠀⣠⡄⢸⠀⠀⢻⣴⠟⠀⢠⡾⣧⡀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣠⣶⠟⠁⢀⣠⠶⢻⣿⣿⣿⣿⣿⡿⠁⢀⣠⣶⠞⠋⠀⣼⠃⠀⠀⠀⠀⣰⣏⠀⠀⠙⠳⢒⣿⣿
⣿⣿⣿⠐⠂⣠⣾⣿⠟⢀⣾⠟⢁⡴⠈⣿⣿⣿⡿⠋⠀⢤⣿⡟⠁⠠⠤⠞⠁⠀⠀⠀⠀⠀⣬⣤⣴⠶⠶⠾⠟⣿⣿
⣿⣿⣿⣠⣾⣿⣿⠁⣠⣾⣇⠀⠀⣠⠞⢻⡿⠋⠂⠀⡄⡎⠉⣿⣦⣀⣤⣤⣀⢀⣀⠀⠀⣀⠈⠳⣄⠠⣀⡀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡾⠃⢀⠘⠁⠀⠀⣴⡇⠇⠠⠀⠀⠈⠀⣻⡏⠁⠈⣿⣿⡟⠓⠶⣌⣑⠄⠉⠳⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠃⠀⠀⠠⣼⣿⠀⢂⠴⠒⠀⠀⠀⠈⠑⠀⣶⡶⣉⣠⣶⣶⣶⣿⣶⣤⣄⣿⣿
⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⡿⠠⠇⠀⠀⣄⣿⡇⠀⠈⠀⢀⠀⠠⠤⠀⠀⢸⡿⠙⠿⠿⣿⣿⡿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⠛⠘⢿⣿⣿⣿⣿⣿⠟⡀⠀⣰⡷⡄⠸⣿⣿⡆⢰⠀⠀⠀⠀⠁⠀⢀⣿⣥⣤⡀⠀⠀⠉⠃⠀⠀⠀⠀⣿⣿
⣿⣿⣿⡄⠀⠀⢹⣿⡿⠻⡿⣿⣷⣾⣿⣷⣀⠀⠈⢓⡉⣫⠀⠀⠀⠀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠉⠈⠀⠀⠀⠈⠁⠀⠉⠛⢿⣷⣄⠈⠉⠃⠀⢤⠀⠀⠁⣼⣿⣿⣟⠻⠿⠿⣿⣿⣿⣿⣦⡀⠀⣿⣿
⣿⣿⣿⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠉⠻⣷⣄⢠⡀⠀⡀⠀⠀⣽⣿⣿⣿⣷⣄⠀⠀⠉⠛⠿⢿⣷⡄⣿⣿
⣿⣿⣿⣸⡇⠀⡀⣠⡄⠃⠀⠀⠀⢦⠀⠏⢀⢰⡆⠘⢿⣷⡝⠖⠁⢀⡴⣿⣿⡏⠉⠙⠻⢦⠀⠀⠀⠀⠀⠙⣿⣿⣿
⣿⣿⣿⠿⠷⠂⠋⠀⠀⠀⠀⠀⠀⠠⣿⣀⠏⣼⣦⣴⡶⠛⢿⣦⣶⡀⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠫⠿⠾⠿⠛⠁⠀⠀⣰⡟⠉⠛⠂⠀⠀⢀⣠⣤⠰⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⠀⠘⠁⠈⣽⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣼⣾⣿⣿⡇⣿⡇⠀⠗⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠠⢶⣿⠉⠙⠻⡇⢿⣧⣤⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠘⠃⡀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣄⣸⡇⣿⣿⣷⠃⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣀⣀⣀⣀⡄⠀⣠⣤⢴⣦⡀⢀⡖⡫⠻⣶⡄⠀⢀⡴⢿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠰⣿⡟⠁⢉⣿⣁⣴⠟⣏⠀⣿⡇⡞⠀⢧⣠⣿⣇⣴⡟⠀⠀⡿⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠈⠉⠉⣿⠏⠀⣯⠀⠈⣹⡿⠋⡇⠀⢀⣽⠟⠁⢾⣇⢀⣼⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠞⠁⠀⠀⠙⠤⠾⠋⠀⠀⠙⠶⠛⠉⠀⠀⠘⠿⠟⠁⠳⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢸⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢸⣿⡆⠀⣴⡿⠀⠀⠀⣿⡡⠋⠀⠀⠀⣠⡤⡄⠀⠀⣿⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⠀⠀⠀⡿⠖⢪⣿⠁⠀⠀⣸⣿⠒⣷⣄⢀⣾⣟⡴⠃⠀⠀⡹⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⣿⣄⣀⡼⠁⠀⠸⣯⠀⢀⡴⢻⡇⠀⣼⡇⣸⣿⡏⠀⢀⠀⠊⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠙⠓⠛⠁⠟⠻⠶⠟⠒⠁⠉⠛⠛⠁⠀⢰⣷⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⣿⠿⠲⣄⠠⠀⠀⠀⠉⢻⠉⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣴⣿⣿⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⠇⠀⠀⠀⠋⠀⠀⣀⡀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢈⣴⣶⡶⣄⠀⢁⣴⣶⡶⡄⠀⠀⣀⣤⣤⣿⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠀⠀⠀⣹⣧⠀⢰⣿⣿⡏⠀⡟⢰⣿⣿⡏⠀⡿⢀⣾⡿⠁⢸⣿⣿⡟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣿⡇⠀⢀⣴⣿⣿⡇⢸⣿⡏⠈⢳⠷⢾⣿⡇⠈⢳⠷⣾⣿⠁⣰⠻⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⣿⣿⣶⠟⠩⣿⣿⡇⠀⠙⠳⠒⠁⠀⠈⠙⠳⠒⣁⠄⠘⠛⠛⠁⠀⠙⠛⠓⣋⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⢀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿⠋⣱⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣸⣿⣟⣠⠏⠀⠀⠀⠀⠀⠉⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⡙⠿⠆⠀⣀⣿⣿⡟⠁⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⢇⢸⠀⢀⣿⣷⠀⠀⢀⣿⣿⣃⡤⣤⡀⠀⣠⡶⠓⣦⠀⣴⣾⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢈⡟⠒⢺⣿⣿⠀⠀⢸⣿⣿⠏⠀⣸⡷⢸⣿⣇⡼⠋⢀⢿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣇⠞⠀⢀⠸⣿⣿⣄⠴⠻⣿⡿⢀⣴⠟⠁⠘⢿⣯⣀⡴⠋⡜⢻⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⣦⡄⠀⠀⠀⠀⠧⡼⠿⠛⠊
⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣾⣿⠛⢧⠀⠀⣿⣿⡆⣠⠶⣶⠀⠀⣿⣿⡏⠀⠀⢲⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⢧⣀⣸⣀⣰⣿⣿⣿⠃⢸⣿⠀⠀⣿⣿⡇⠀⠀⣿⣿⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣿⣿⠀⢈⡟⠉⠙⣿⣿⡇⠀⣼⡿⠀⠀⣿⣿⡇⢀⡴⢿⣿⣠⢾⣿⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡛⠓⠉⠀⠀⠑⠄⠉⠀⠀⠸⢧⡠⠞⠀⠉⠉⠁⠀⠀⠉⣀⣼⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣿⣿⢇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡄⢀⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠁⠘⢾⣿⠇⠆



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠶⠖⠒⠒⠶⠶⠶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⢤⣀⣤⠴⠖⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠛⠋⢉⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢸⣏⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠐⠐⠉⠀⠙⣅
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣋⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡹⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠲⠶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⠳⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣁⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⣾⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⣀⡀⠀⠸⣿⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡤⠤⠤⠶⠶⢶⡾⠁⠀⠀⠀⣠⣀⠀⢀⣠⣤⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⠚⢣⣤⣤⣶⠄⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠛⢳⠾⠷⠶⠶⢶⠛⠁⠙⣮⠉⠀⣀⣈⠙⠦⣄⠀⢷⡀⠀⠀⠘⣀⣠⠴⠋⠀⣠⡴⠞⠁⢀⡴⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⣸⠇⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⡷⠚⠉⠈⠙⠢⠼⠀⠀⡩⢻⠻⢭⣉⠀⢀⣠⡟⠁⠲⣄⡠⠎⠀⣠⠆⠈⣧
⠀⠀⠀⠀⠀⢀⣤⠞⢁⠤⠒⠁⢹⠤⡀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⡿⢦⡀⠀⠀⠀⠀⠀⠰⠁⢸⠓⢦⣈⣉⡉⢹⡄⢢⣀⣸⠧⡤⠚⢁⡠⠂⡼
⠀⠀⠀⠀⣰⢏⡵⠊⠁⠀⠀⠀⠘⢷⡠⠄⠀⠀⠀⣀⣠⣶⣛⣋⣀⣠⠞⠀⠀⠀⠀⠀⠀⠁⣠⠋⠀⠀⠈⠉⠉⠉⠻⣄⠈⠀⣲⣬⣶⣋⣠⠞⠁
⠀⠀⠀⡾⡡⠋⠀⠠⠀⠀⠀⢀⡴⠋⠉⠙⠛⠛⢻⡍⠀⠉⠓⠲⠤⢄⣀⠀⠀⠀⢀⣠⠥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⢸⢣⡃⠀⠀⠀⠀⠑⢠⠎⠀⢠⠎⠀⠀⢀⣾⣀⠀⠀⠀⠀⢀⡴⠃⠀⣄⠀⠀⠙⠢⣄
⠀⠀⣿⢼⠀⠁⠀⠀⣠⡴⠻⣆⣠⠏⠀⢀⣴⣏⠀⠉⠳⢦⣤⡴⠋⠀⢀⡴⠋⠙⢦⣀⠀⠈⠳⣄
⠀⠀⣿⢸⠀⠀⠀⣴⠋⠀⠀⠀⠙⣦⡴⠟⠁⠈⠛⠶⣤⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠉⠳⣄⠀⠘⢷⡀
⠀⠀⢿⢸⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⢦⡀⢀⣀⣄
⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⣨⠟⠋⠁⠨⣇⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣨⣷⠴⠶⠚⠛⠉⠁⠀⠀⠀⡼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⣠⡴⠛⠁⠀⠆⠀⣠⠴⠛⠙⡄⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣞⠋⠁⠀⠀⠀⠀⠀⡏⠡⠒⢉⠆⢘⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢘⣆⣉⣥⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠂⠤⠤⠤⠒⢊⣩⡤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⡤⠶⢺⣿⢱⠐⢐⠠⡆⣾⡱⠀⠂⣆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⣒⣒⣊⣩⣭⣭⣭⣭⣍⣉⣐⣒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣄⣀⣠⣴⣺⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣶⣦⣭⣙⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⠿⠶⢯⣝⠻⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣮⢻⣿⣿⣿⣿⣿⡵⠋⠁⠀⠀⠀⠈⢷⡹⣿⣿⣿⣷⣾⣡⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠘⣾⣿⣿⣿⣯⠞⠀⠀⢀⡄⠀⠀⠀⠈⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠟⣿⡿⣻⠃⠀⠀⠀⣸⢻⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡷⠋⠀⠀⠀⠀⢿⣾⠁⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢷⣤⡹⠃⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠏⠉⠑⠦⣄⡀⠀⠀⠀⠀⢀⣠⠴⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢳
⠀⠀⠀⢠⠞⠉⢭⡑⣲⠖⠲⢄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠙⠛⠛⠋⢩⣥⣤⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠇
⠀⠀⣴⢿⡀⢀⡴⠋⠁⠀⠀⠈⠀⠀⠀⠀⠳⣄⠀⠀⠀⢠⣄⣀⣀⡤⠞⠁⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠙⠻⢿⣿⣿
⠀⠀⣿⢄⡉⢻⣄⠀⣠⠇⡠⠊⢑⣦⣄⡀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠸⣄⣈⣉⣨⡟⠁⡜⠀⠀⠀⢀⣠⣿⠀⠀⢀⣠⠜⠛⠛⠳⢶⣶⡞⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠳⣤⡠⠼⣁⢸⡇⠀⠀⢠⡏⠉⠛⠛⠉⢩⠃⠀⠀⠀⠀⠀⠙⣿⣶⣶⣤⣤⣀⠀⠈⠻⡿⠟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⣄⠘⣹⠗⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠻⣿⣿⣝⠲⠎⠀⠀⠉⣠⠜⠛⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠉⠙⠺⣤⠀⢀⡼⠁⠀⠀⠀⠀⠀⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀⣀⣤⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠦⣼⠁⠀⠀⠀⠀⠀⢢⢸⠆
⣾⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⣤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⢃⠀⠠⡄⠀⠀⢧⣠⠟
⠙⣷⡙⢿⣿⣿⣿⣿⠗⠢⢤⡤⢾⠁⢠⣼⣿⣯⡴⠿⠿⠿⣿⣿⣟⠉⠁⠉⣛⣛⢓⣀⣤⣾⣿⣷⣦⠙⠛⠅⣀⣠⠞⠋
⠀⠈⢻⣄⠙⣿⠟⠁⠀⢀⣴⠀⠈⠂⠈⢿⣿⢻⡄⠀⠀⠀⠹⣿⣿⣷⣤⣎⣁⠈⠛⠀⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠙⢷⠀⠀⠀⣠⣾⣿⣧⠀⠀⠀⣀⠉⠀⡇⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⡿⠿⢦
⠀⠀⠀⠀⠈⠓⢄⣤⣙⠿⣿⣿⣿⣦⣤⣬⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⠛⠀⠀⠀⠀⡾⠋⠁⠀⠀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡤⠶⠤⢾⠀⢀⣠⣶⣿⣿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣇⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢒⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⡠⠊⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠚⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠒⠒⡲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢠⠊⠉⠉⠀⠀⠈⠢⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢀⠆⠀⠀⠀⠀⠀⠀⠀⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠔⠒⠉⠉⠉⠑⢄
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⠃⠀⠀⠀⠀⠀⠀⠀⢱
⠈⢓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠢⠄⠤⠤⠠⢄⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠑⠠⡄⠀⠀⠈⠁⠀⢠⣿⡇⠈⠁⠀⠀⠀⣀⠄⠒⠉⠁⠁⠂⠉⠑⠤⠠⠄⣀⡠⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡴⠀⢣⠀⠘⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠜⠁⢀⡼⠀⢐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⠀⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡤⠤⢈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠄⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⡀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⣀⣉⣀⣀⡠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠚⠋⠉⠉⠉⠉⢉⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠡⢄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠲⢄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⠤⠤⠬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢶⣫⡏⠁⠉⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣔⠉⠉⠓⢄⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜
⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠈⢣⣨⠦⠘⠆⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⣁⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⠧⣛⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠌⣫⡉⡹⠂⠂⠀⠈⠑⢄
⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠓⠒⠊⠉⠀⣀⡤⢤⡀⠀⠀⠀⠀⠀⢳⠐⠒⠠⢧⠀⡼⠀⠀⠀⠀⠀⠀⢈⢣
⠀⠀⠀⠈⠉⠳⢄⣀⠀⠠⠐⠀⠄⣠⠤⠔⠒⠚⠉⠁⠀⠀⠙⢤⡀⠀⠀⠀⠈⠖⢒⡸⢛⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠢⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⣀⡀⠈⠣⣄⣸⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢠⠒⠊⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⠤⠒⠉⠀⠉⠢⢄⡀⠁⢀⡤⢀⢠⡄⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡋⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠱⠀⠀⠀⠀⢀⡟
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⡀⡔⠒⠈⠉⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⡴⠁
⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠂⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠉
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠈⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡆⣴⠀⢸⡆⠀⣰⡏⢐⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⠚⡇⠀⠸⠇⠀⠸⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⡁⠀⠀⢀⡴⠒⠀⠘⠇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠣⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⡇⢠⡇⢰⡏⠐⢦⢀⡴⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠃⢸⠃⢸⡇⢀⣾⢻⡇⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠘⠃⠰⢃⣀⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠐⡆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠄⢰⡇⢸⡇⠀⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠃⣿⠀⢸⡇⢸⡇⢀⡏⠰⣧⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠀⢸⡇⠸⠧⠈⠑⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠒⠒⠂⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⢀⡀⠰⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠓
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⡱⠞⠁⠀⠀⠀⠀⠀⢀⡠⠀⠒⠠⣄⠀⠠⠎⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠉
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣀⣀⡀⠈⠃⠀⠀⠉⠢⡄⢀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠈⡀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠁⡰⠊⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠈⠞⠀⢸⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠀⠀⠀⢡⠎⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠒⠠⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠆⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⣧⠁⠀⢡⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢃⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣷⡀⠀⣠⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣿⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⢀⠁⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣄⡈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠀⠁⠀⠑⡄⠀⠀⠀⠃⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠀⠀⠈⠁⠂⠀⣀⣀⡀⠀⠄⠀⠉⠀⠀⠒⢠⡄⠀⠀⡁⠀⠀⠰⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠅⠀⢀⠃⠀⢀⠂⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠋⠀⠀⠀⡠⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⣀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠒⢟⠓⠒⡤⠄⠐⠀⢤⠀⠒⠂⠁⢀⠞⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠋⠀⡠⠀⠠⢈⣴⠁⠀⡠⠀⠀⠈⠁⠁⠀⠐⠆⣀⠀⠀⡰⠃⠀⠀⠄⣀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡎⢘⠀⠀⠈⡀⠀⠀⠙⢦⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠣⡀⠀⠀⠀⠀⠑⠢⡀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠛⠃⠙⠦⡀⠀⠀⠀⠙⡀⠀⠀⠀⠐⡄⠀⢄⠀⡄⠀⢸⠀⠈⢆⠀⠀⠀⠀⠀⠈⢆⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠒⣤⠀⠀⠂⠙⠂⠄⠀⠀⠜⢳⠆⠀⠀⠀⠀⠘⠀⠀⠀⠜⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠰⣁⠀⣀⠄⣫⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⢀⡴⠠⠎⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠉⠀⠀⢠⠄⠐⠂⠠⠄⣀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠀⡀⠀⠠⠐⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠑⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⡤⠤⢄⠀⠀⠸⠑⠤⣀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠈⡀⠀⠀⡄⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⢃⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⡈⠀⠁⠀⠀⡉⠀⠒⣼⡀⠀⠘⡤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠉⠉⠀⠈⡉⠆⠉⠀⠅⠀⠀⢣⡄⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢨⠀⠀⠐⠒⠛⠒⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠣⡀
⠀⠀⠀⠀⠀⠀⢀⠐⠊⠉⠢⡀⠀⠙⢶⠂⠀⠀⠠⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⡄⠀⠀⠆⠀⠀⠀⠘⣤⢀⡀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠄
⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠑⢴⣄
⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⡰⠃⠀⢀⠔⠀⠀⠒⢤⡀⠉⡀
⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⣸⠠⠤⠒⠻⠀⠀⠰⠀⠀⡐⠁⠀⠀⠀⠀⠀⠙⢀⠃
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠱⣀⠆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⢀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠉⠙⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⡶⣆⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⠶⠋⠀⣿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠒⠛⠛⠛⠛⠃⠚⠉⠀⠀⠀⠀⡿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢧⣤⣀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣾⠂⠈⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⠀⠀⢸⡏⠀⠀⢸⡄⠀⠀⣠⠎⠁⢻⡷⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣏⠛⣷⣄⣳⠀⠀⣿⠇⠀⠀⠈⠳⣶⠿⠁⠀⠀⢸⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⢥⣬⣽⠳⣄⣿⡀⢀⣀⠠⠤⣤⡀⢀⡀⠀⣼⣟⣾⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣯⢱⣮⣭⣍⠉⠁⠀⠐⢿⣿⣯⡿⢞⣛⣭⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠈⡆⠘⣿⣿⣸⡏⠙⣷⣄⡀⠀⠀⠈⣉⣴⣿⡿⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠞⠋⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⠀⢻⣿⣿⣧⣠⣿⢈⣿⠓⣶⢋⣿⡾⢡⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣿⣿⣿⣿⣿⣾⣷⣾⣿⣾⡿⢱⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⠀⠀⠀⠀⢸⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠘⢿⡄⠀⠸⡀⠀⠀⠀⠈⡇⢸⣿⢿⣿⣿⣿⣿⣿⣿⢃⠎⠳⣄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⣧⣴⣶⠶⠾⣷⢸⡏⣸⢿⣿⣿⣿⣽⡏⡞⠀⠀⠈⠉⠁
⠀⠀⠀⣀⣤⣤⠶⠶⠞⠛⠚⣷⠀⠀⠀⡄⠀⠀⢣⠀⠀⢹⢻⡛⠛⠛⣿⢸⡿⠁⣾⣿⢻⣆⡿⢰
⠀⣴⠞⠉⠁⠀⢀⣀⣤⣤⣤⣽⡇⠀⠀⣝⢦⣀⠘⡄⠀⠘⡼⠙⠶⣤⣽⢸⣿⣶⡇⣿⣸⣿⢃⣷⡀
⢸⡇⡠⠀⢠⣾⣿⣿⣿⣿⣿⠟⠛⢳⣞⠙⠿⣝⡛⢇⠀⠀⢣⡴⠶⠚⠻⣆⡈⠛⠻⠟⠛⣡⡞⢨⡇
⢹⡆⠳⠄⠈⠛⠿⣿⣿⣏⣁⢀⠀⠈⣿⣿⠀⠈⣿⢸⠀⠀⠈⣧⣴⡄⠀⢿⠙⠲⣶⡶⠚⠙⣧⠞⠁
⠈⠳⣬⡑⠀⠀⠀⠀⡈⣩⢉⢻⣆⠀⣸⣿⣀⣀⡿⣾⡇⠀⠀⢸⡆⢷⣤⣾⣧⣤⢿⡧⠀⠀⣿
⠀⠀⠈⠙⠛⠶⠦⣤⣤⣄⣀⣁⣉⣛⣋⣠⣽⣿⣥⣼⡇⠀⠀⣸⠷⣶⡾⠋⢙⡻⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⢩⠟⣽⠋⢀⣠⣤⣽⠃⠀⢰⡇⢰⢱⡇⢰⣿⡿⠟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⢸⠇⠀⣿⣿⠏⠁⠀⢀⡿⠻⣾⣸⡇⠘⣿⣇⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣆⠀⠙⠿⠷⠶⠖⣻⠃⠀⠈⠻⢷⣄⣙⣻⣛⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠲⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣄⠙⣿⡆⠟⢁⣴⣾⣿⠿⢿⣿⣶⣤⣀⠀⠀⠀⣤⣶⡿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⢸⣿⡇⠘⠃⠰⣿⠟⣉⣀⣀⠀⠈⠙⠛⢿⣿⣶⣴⣿⣯⣤⣴⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⠇⢀⣀⣀⣀⠀⣡⣶⣿⣷⣆⢠⣼⡿⠛⣿⣧⠀⠀⢀⣠⣈⣽⡿⠛⠛⠛⠋⠁⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠹⢻⣿⠟⠁⢿⣿⣀⣿⡿⠀⣿⡇⢠⣿⡟⢀⣾⡿⠛⣿⣿⠃⢠⣴⡆⢠⣿⡄⠈⢀⣴⠆
⠀⠀⠀⠀⠀⠀⣶⣱⡀⢻⡇⠀⠘⣿⣧⠀⣾⡿⠀⠀⠘⠻⠟⠛⠁⠐⠻⣷⣾⡿⠁⣾⣿⣠⣾⡿⣿⣦⣾⡟⠁⢸⡟⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠉⠀⠀⠘⣿⣷⣿⠃⠀⣠⣄⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠉⠋⠋⠀⠀⠚⠤⠞⠛⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⠋⢀⣄⡀⠈⠙⠁⣰⣿⡿⠋⠀⢸⣿⠛⠿⣿⣆⠀⠀⠀⣀⣀⡀⠀⠀⣀⣶⡿⣿⣦⠀⠲⢦⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠘⢻⣷⡀⠀⢰⣿⠏⢴⡶⠀⣸⣿⠀⠀⢸⣿⡆⢰⣾⡟⢻⣿⡄⠀⣿⡟⠀⠘⣿⡇⠀⡀⢻⣷⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣤⣼⣦⡀⠈⢿⣷⢠⣿⡟⠀⣴⣦⠀⣹⣿⠀⣠⣾⡿⠁⣾⣿⣶⣾⣿⠃⠀⣿⣇⠀⠀⠛⠁⣾⣿⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⢿⣷⡀⠘⣿⣿⣿⠁⠀⣿⣿⠀⢸⣿⣿⣿⣿⡄⠀⣿⣿⢉⣽⡁⠀⠀⢿⣿⡄⠀⠀⣼⡿⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠈⠁⠀⠹⣿⡇⠀⠀⣿⣿⠀⢸⣿⣤⣴⣿⡇⠀⠸⣿⣿⡿⠁⢠⣾⡞⣿⣧⠀⠠⣤⣦⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⣠⣦⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠛⠋⠙⠁⠀⠀⢀⠈⠉⠀⠀⠸⢿⣧⣿⡟⠀⢰⣦⡙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⠀⢠⣾⡿⢿⣷⡄⠀⣴⣆⠀⣀⣀⠀⠀⢰⣿⡇⠀⢠⣴⡄⠉⠉⠉⠀⠀⠀⣿⡌⡄⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠘⣿⣦⣿⣟⣀⣼⣿⣿⠀⢹⣿⣴⣿⢿⣿⠀⢸⣿⠇⠀⣿⣿⠀⠀⠀⠀⣠⣤⡄⣿⣷⡇⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣞⡢⡀⠀⠈⠛⣿⡿⠿⠻⣽⣿⠀⠹⣿⡿⠁⣼⣿⠀⢸⣿⠀⠀⣿⡇⠀⣠⣴⣿⣿⡿⠀⣿⣿⠇⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠐⢿⣷⡀⣰⣿⠇⠀⠀⠛⠁⢀⣿⡟⠀⢸⣿⠀⠀⠻⣿⣿⠟⢫⣼⣿⠃⠀⠻⠋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣦⣄⠈⢿⠿⠿⠋⢰⣦⠀⠀⠀⠸⠿⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⠃⢀⣴⣶⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⢀⣠⣴⢀⡄⠰⠂⣀⣤⣶⣶⣶⣤⣄⣀⠈⠉⠀⣤⡀⠀⣠⣿⡿⠁⠀⠉⠀⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡿⠃⣾⡇⠀⢲⣿⠋⠉⠉⠉⠛⠻⢿⣿⣶⣤⣉⣠⣾⣿⠟⠀⣰⣶⡆⢹⣦⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠔⠁⠀⣿⣧⠀⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⣹⣻⣿⣿⣿⣷⣶⣾⡿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠈⠙⠿⣿⣷⣶⣶⣶⣿⠿⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢶⡋⠉⠁⠀⠀⠀⡴⠒⠠⣄⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢀⠃⠀⡀⠴⠑⠀⠀⠀⠀⠈⠓⢤⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠝⠀⠀⠀⠉⠀⠠⠐⠀⠐⢤⡀⠀⠀⠀⢳⡀⡼
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠱⠀⠀⠀⢠⣼
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⢇⠀⢰⠃⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣰⣃⡠⠤⠤⠤⣄⣀⠀⠀⠀⡠⠤⣄⠘⠟⠀⠀⠀⠈⢲⡟⢀⡇⠀⠀⠀⢠⠞⢁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢸⡁⠠⡤⠙⠲⠤⠴⠒⠊⠹⢿⡿⠋⠀⠞⠙⡷⣚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠱⢄⡈⠒⠀⠀⠀⠀⠀⣀⠜⠁⠀⣰⠌⠢⡽⠒⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡠⠤⠖⢒⣶⠭⣓⠶⠶⠖⠶⣏⡁⠀⠀⡎⠁⠀⢀⣈⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠊⠁⠀⡠⠒⡩⠔⢊⡃⠀⠀⠀⠀⠘⣌⣓⣋⡽⠢⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⡗⠢⠏⢸⡀⠀⠀⠀⠀⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣇⠓⠁⢀⠇⠀⢹⡄⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣹⣶⢏⠀⢀⢾⠰⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⠁⡎⠀⢣⠘⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢊⣇⣰⡗⣤⠺⠤⠜⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠰⣏⡆⠀⠀⢀⡴⠋⠉⠉⠛⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢝⠒⠶⠒⢾⠀⡗⠒⠋⠁⡆⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠂⠈⠀⠈⣧⡇⠀⣀⣀⣤⠤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣠⡤⠖⠋⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠙⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠉⠁⠒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣤⠶⠚⠋⣉⠹⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⠉⠛⠓⠲⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠑⡇⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉⡜⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⡁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⣄⠀⠌⣼⠛⢦⡄⠀⣠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠑⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠙⡄⠀⠋⠀⠀⠹⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠐⠁⣴⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠅⠀⠈⢣⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠸⠀⠀⠈⢳⡀⠀⣀⠀⣠⠎⠀⡆⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢃⠀⠀⠛⠉⢂⣩⣒⡁⠀⠀⠋⠀⠠⠤⡄⠀⠀⠀⠀⢹⡗⠦⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⠓⠂⠒⠈⠈⠛⠃⠀⠀⠀⠁⡰⠀⣠⡷⠒⢶⣤⡀⠀⡇⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣏⠈⠀⢾⠀⠙⢢⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠙⠢⡤⢀⠀⠀⠀⠀⠀⣽⠲⠖⠲⠶⠒⠒⠛⠉⣤⣀⠀⠙⠲⢬⣀⠀⣀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠂⠉⠢⡄⠀⠀⣷⠀⠀⢀⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⣌⠛⠢⣄⡀⠈⣻⠉⠛⢉⣿⡉⠉⢶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠠⠔⢠⠀⠀⡴⠉⣳⠚⠁⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢴⠀⠀⢙⡶⠁⠀⠐⠁⢸⡄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢨⡛⠛⠁⠀⢸⡤⠞⠉⢣⠀⠀⠀⠀⠀⠀⠀⢸⡟⢢⡀⠀⢠⡋⠀⡄⠀⠀⠀⠀⣹⠶⢟⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣀⠇⢀⠀⣚⣨⠇⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⡾⠤⢀⣡⠀⠈⠉⠻⢦⡄⠀⢀⠴⢧⡀⠀⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠖⠻⠚⠉⠁⠀⠀⠀⠀⡸⠉⣰⠶⠶⢶⡀⠱⡀⠀⠈⠀⠀⠀⠀⠀⢹⡏⠙⡆⠀⠉⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠇⠀⠀⠈⢇⠀⢱⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠂⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠎⠀⠀⠀⠀⢘⡄⠀⢳⡤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⠎⠀⠀⠀⠀⡐⠉⣷⠀⠈⣷⡈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣼⣀⠀⠀⠀⠀⣧⡘⣾⠆⠀⢹⡼⠂⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠩⣿⢀⡰⠧⠎⣱⠀⠀⢠⢎⠓⠈⠉⠉⠉⡀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⠀⠀⣀⣀⡤⠺⡁⠀⠀⣸⢄⠑⢦⣬⣤⣤⡴⠞⣡⠋⢉⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠖⠺⠆⠲⠦⣤⡤⠶⢶⠁⠀⠀⡧⠆⠑⡄⠀⠀⠁⢀⠬⣀⡼⠋⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠙⠶⣤⠜⠲⠄⠀⠀⢸⡄⠀⠀⠑⢤⣀⠀⣄⠀⠀⣌⢀⡟⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢻⡄⠀⢀⡇⠀⠀⠀⠀⠈⠙⠋⠳⣄⡋⣻⠁⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⣼⠋⠐⢄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡧⢶⡛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠆⣥⣄⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠈⠁⠐⠀⠤⠀⠀⢸⠷⢸⠇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⣀⣀⡀⠀⠀⢀⣄⣾⡳⠿⠾⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⣤⠞⢋⣤⠞⠃
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠠⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣶⣏⣥⣾⣏⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⡛⢦⣌⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠈⠛⠆⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⢀⣤⣶⣄⠀⢀⣴⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠙⠁⠀⠀⣰⣾⠿⠛⢿⡇⠀⢀⣴⡿⠟⠛⣿⡆⠸⠟⢻⡏⠉⠉⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢀⣀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⠀⣼⡿⠀⠀⠀⢹⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⣿⣿⡄⠀⣿⡇⠀⠀⠀⢸⡟⠀⣿⠇⠀⠀⠀⣾⡇⠀⠀⢸⣿⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⣸⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠘⣿⡄⠀⠀⢠⣿⠃⠀⠀⠈⣿⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣰⡿⢿⡇⠀⢹⣿⡀⠀⣼⣿⠀⠀⢿⣧⠀⢀⣾⡟⠀⠀⠀⠀⣿⠆⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⠁⢸⡇⠀⠀⠻⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀⠀⢰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣤⡄⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢸⣿⠀⠐⠿⠿⣿⡟⠃⠀⠘⢿⣿⠉⠉⣿⠀⠀⣼⡿⠛⠋⠉⠀⠀⢀⣾⡿⠛⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⢀⣼⡏⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣿⡿⣿⡆⠀⢸⣧⣤⣴⣶⠀⠀⠙⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣿⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⢸⣿⠛⠋⠁⠀⠀⠀⠈⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣿⡄⠀⣸⡏⠀⢸⣯⠀⠀⣀⣄⠀⢸⡷⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⣶⣾⣿⡿⠃⠀⠀⠀⢿⣷⣾⠟⠀⠀⠸⣿⣶⣿⡿⠋⠀⠸⣿⣶⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣿⡀⢐⣿⣿⡄⠀⠀⠀⢰⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⢿⡇⢸⣿⡿⣷⡀⠀⠀⢸⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣿⡇⢸⣿⠁⢻⣷⠀⠀⢸⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣿⠃⢸⣿⠀⠈⣿⣧⠀⣸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟
⠀⠐⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⣼⡟⠀⢸⣿⡇⠀⠘⣿⣆⣿⡇⠀⢸⣿⠀⠀⢀⣠⣤⡀⠀⠀⠀⢰⣿⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠸⣿⣦⣾⡿⠁⠀⠘⠿⠀⠀⠀⠹⣿⣿⠇⠀⠈⣿⣷⣿⣿⠿⠛⠁⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣄⡀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣌⡙⠶⣌⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠳⣦⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⢈⡿⠖⣺⡿⠖⣻⡿⠖⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠒⠲⠲⣷⠀⠀⣉⡿⠆
⠀⢀⠀⠀⠀⠀⢀⣴⠞⣋⣴⠞⣩⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠓⢞⣖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠂⠀⠀⠥⠀⣰⠋⠰⠀⠀⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢀⣉⡐⠉⠀⣀⡀⠀⠉⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⣰⡿⠯⢽⣶⡾⠯⣽⣶⡟⣿⠁⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣠⣴⣿⠹⣇⢀⡞⢻⣇⣠⠏⣿⣠⢧⢀⡻⠖⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣿⣀⣬⣭⣄⣀⣉⣁⣀⣈⣀⣤⣭⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠋⣿⢉⠉⠉⡉⠙⢛⣋⠉⢉⡉⢉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢹⠘⡇⢰⠃⡇⢸⣠⠇⣿⡀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⣸⠀⢳⡏⠀⣷⢸⠀⣱⣿⠀⢀⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁⠀⠈⠃⠀⠛⣨⢭⡁⠈⠉⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⢢⡀⣀⠀⣀⠀⢸⣇⡼⢡⣤⠀⢰⡄⠺⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠓⠴⠖⣿⢿⣿⠋⢷⢸⣿⠁⣼⣿⠀⢿⠁⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⡿⢹⡏⠀⢸⡞⣿⣸⠹⣿⠀⣼⡇⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⡼⠃⠈⠃⠀⠀⠀⠈⠁⠀⠈⣩⡼⡏⠉⠺⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡉⠉⠀⣄⠶⠠⠚⠓⠄⠀⠀⢠⡾⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⣹⠬⠥⢤⣀⣈⣁⠔⢁⣿⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠆⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠤⠂⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠉⣩⣿⡿⠙⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡦⠤⣤⡾⠋⠀⠀⠀⠀⠀⢺⣀⢀⡿⠲⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠶⣄⠀⠀⣄⠀⠀⣴⡏⢸⣷⠘⢦⣀⣀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⢣⣀⢻⣀⡾⣿⣇⣼⡟⠀⠀⠉⠻⣍⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⣤⣨⣿⢿⡿⠶⠞⣫⣼⠇⠀⢀⣠⣄⡘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠳⢤⣀⣀⣀⣠⣾⣟⣡⣾⣿⡟⠛⣄⠹⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢰⡏⠁⢹⠈⢧⣹⡟⠻⣄⠘⢆⠈⠃⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢸⡀⠀⢻⣿⡄⠘⠂⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢀⣾⣧⣀⡼⠃⢰⡞⣿⡄⣀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⢧⡈⣷⢶⣏⡾⣿⠠⣤⣄⢸⣮⣛⠙⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⡞⣫⡿⣷⣄⣹⠆⡇⢸⡇⢻⡈⣏⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣸⡏⢲⣿⠟⠁⢠⡇⢸⡇⠘⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸⡇⢸⠃⠀⢿⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣾⠁⢸⣦⣄⢸⡄⠸⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢽⡛⠉⠡⣿⣿⠧⠤⠿⠋⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⢲⡦⠤⠴⣿⣿⠛⠛⣂⣋⣽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⣦⠀⠀⣧⠀⠀⣿⣸⡿⠛⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢸⠀⠀⣿⣠⣴⣿⣿⢃⡴⠒⠛⠓⠲⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣦⣴⣶⣺⣿⠿⠟⠋⠉⠀⣿⡞⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⣿⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣤⣤⣤⣾⣿⣿⣿⠟⠟⠁⠀⣿⠀⠀⠀⠠⠴⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠙⠛⠿⠷⠶⢦⣤⣿⠆⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⠿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⡋⠄⢀⣠⡾⣋⣁⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⣿⣴⣿⠏⠋⠁⠀⠙⣶⡆⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⡏⠄⠀⠀⡀⠀⣹⠇⠀⠀⢀⠀⠀⠀⠀⠈⠛⢷⣄⣠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡼⠀⠀⠀⣦⢀⡿⠆⠀⣾⣿⠄⠀⣀⣐⣤⣄⠢⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣧⡄⠀⠀⠀⠛⣀⠀⣀⡰⠟⠁⢀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡥⠟⢷⣶⡖⠋⠉⠁⠀⠀⢶⣾⣿⣿⣿⣶⣤⣠⣙⣿⣿⣿⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡴⠁⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣏⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡶⢿⣀⠀⠀⠀⠀⠀⠀⢀⣴⡆⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣉⢹⡟⣻⣿⠇⠲⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⡀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠸⣿⣿⣷⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢿⡇⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣶⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣾⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠁⠀⠀⠀⠉⠉⠣⠀⠀⣾⣿⣦⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣠⡤⠤⣴⠀⣴⡖⢷⡄⡜⡉⢹⣇⢀⡴⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠃⢰⠟⢸⠁⠑⣾⠷⠁⠈⣾⠟⢻⡁⣰⡇⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠖⠋⠀⠀⠲⠚⠁⠀⠑⠚⠁⠀⠘⠛⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡞⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢴⡄⠀⣤⠀⠀⢸⡣⠃⠀⠀⣀⡀⠀⣼⢻⠃
⠀⠀⠀⠀⠀⠀⣀⢼⡇⠀⢸⠗⢸⡏⠀⢀⣿⠓⣦⢀⣾⡵⠃⠀⠹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡴⠃⠀⠸⣧⡴⢫⣧⣠⡟⠜⠿⡤⠔⠀⣀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⠀⣀⡀⠀⣰⡧⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⡀⣿⡆⢼⡾⣿⠃⢠⡟⠀⢰⠃⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣸⠟⠀⣾⠁⠯⠀⣿⢀⡠⢻⣶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠛⠉⠀⣠⡤⣾⠗⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠦⡀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡀⣁⣴⠟