Toys Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡴⢋⣩⢭⡙⢦⠀⠀⢀⡴⠊⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⡆⢳⠦⣀
⠀⠀⢠⡶⣼⠃⡏⠀⠀⡽⢸⠇⠀⠀⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⢹⠈⡆⠈⠑⢄
⠀⣠⠴⠷⠀⠀⠑⠒⣚⣡⠞⠀⠀⠀⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⡀⠀⠀⢇⢸⡀⠀⠀⠱⣄
⣼⢡⠞⠉⠙⡆⣤⡙⢯⡀⠀⠀⣀⣀⣀⣧⠀⠠⠬⠦⠤⡤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠠⣾⣿⣟⣦⣈⣳⣄⣸⣄⣧⣀⣀⣀⣈⢦
⢷⠸⣄⣀⡼⢡⠏⠉⠢⣭⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠦⢤⣀
⠈⠓⠶⠶⠞⠋⠀⠀⣴⣛⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣓⣲⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡾⠭⠭⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣎⠍⠀⣀⣤⣴⣶⣶⣶⣦⣄⡀⢣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠇⢀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⢸⢸⡭⠭⠭⢽
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⣾⣿⡿⢛⣛⣙⣛⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⣛⣉⣛⠻⢿⣿⣷⡄⠀⠀⠈⠒⠨⠭⠭⢽
⠀⠀⠀⠀⡎⠀⠈⠈⠃⢀⣿⣿⢋⠔⢁⠤⠤⢄⠑⠌⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⡐⠉⡠⠄⢄⡉⢦⢻⣿⣿⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠓⠤⠤⠤⠖⢺⣿⣿⢸⠀⡃⠀⠀⠀⡇⢸⢸⣿⣿⠒⠒⠒⠂⠀⠀⠀⠀⠈⠉⠙⣿⣿⠀⠁⢘⠀⠀⠀⡁⠀⠆⣿⣿⠓⠒⠒⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡌⢦⡘⠢⠤⠚⣠⠎⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠣⡈⠂⠤⠐⢁⠜⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣌⣐⣒⣈⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣬⣑⣒⣊⣥⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁


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

⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⢹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠟⠉⠉⠘⠮⡝⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡴⠂⠈⠉⠉⠁⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠒⢦
⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠠⢗⠒⠀⠈⠓⠀⠀⠀⠀⠀⠀⣤⠊⠉⠁⠈⠉⠉⠀⠐⠢⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢂⡤⢤⠀⠀⠀⠀⠀⠈⠀⠀⠛⠉⠓⠊⠉⠥⡄⠲⠊⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇
⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠆⢠⠟⠃⠈⢹⠏⠉⢹⠏⠉⠙⡖⣷⢀⡀⠀⠀⠀⢠⢻
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⢀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⢀⠀⣿⠀⠉⠛⠛⠒⠛⠈⢀⢀⠐⡠⠖⠒⠒⠂⠀⠀⠠⠤⠤⢠
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠘⠆⠀⡄⠀⠀⠸⡀⠀⢸⠄⠀⠨⡄⣿⠀⠀⠀⠀⠀⠀⠀⠈⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⣰⣀⣧⣤⠤⠴⠇⢠⡘⠷⠖⠶⠗⠿⣶⣦⣤⠤⠤⣤⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⣸⠏⠉⠀⠀⠀⠀⢠⠚⠀⠈⠑⣦⠀⢠⠊⠁⠀⠈⢳⡀⢸⡧⠴⠷⠤⠤⠤⠤⠀⢀⣀⣀⡀⠀⣘⠃
⠀⠀⠀⠀⠀⠉⠒⠤⡤⣤⠤⠤⠒⠉⠀⠀⠀⠀⡠⢊⠸⡆⠀⠀⠀⠀⠀⣯⠀⠫⠉⠁⣉⡁⢛⡀⠂⠀⠀⣠⡇⠈⠉⠙⠉⠉⠉⠉⠉⠁⠀⠀⠐⠀⠉⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠂⠀⠀⠀⠀⠠⣥⢎⣴⡁⠦⠃⠀⠀⠀⠀⠀⠙⢦⣤⣤⣴⠟⠀⠈⠻⢦⣤⠶⠋⠀⠀⠰⢀⡠⠈⢄⣀⠄⠀⢄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠉⠁⠀⠀⠈⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠖⠛⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠁⢀⠼⠤⣄⡀⠀⠈⠑⠄⡀⠑⢄⠀⠀⠀⣠⠴⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡾⡤⠰⢏⠀⠀⠀⠙⠦⡀⠀⠀⠈⠠⠈⢧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠷⠚⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢦⡀⠀⠀⢃⠘⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠑⢄⠀⠀⠀⠹⣄⠀⠈⠀⠇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢂⡀⠀⠀⠀⠈⠳⣄⠀⠀⠘⣆⠀⡸⠀⠀⠀⣧⠀⠀⢠⡄⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⢻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠳⡀⠀⠀⠀⠀⠈⢦⠀⠀⢘⣾⠃⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⡶⠛⠳⡄⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠙⠢⢄⡀⠀⠀⠀⢑⣤⠞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⣉⡛⠳⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠘⣧⠀⠀⠿⠶⠶⠖⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠁⠀⠒⠙⠓⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣤⠤⠖⠚⠉⠀⣀⠤⣀⠠⠤⠤⣄⣠⠖⠢⡄
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡰⠁⠀⠀⠀⠈⠀⠙⣤⠇
⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣄⠀⠈⢱⡀⠐⠛⠛⠃⠀⠀⢐⠀⡔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨⡄⠀⢀⠱⢦⣀⡀⠀⢈⣤⠊⠀⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⣀⢈⠞⠁⠀⠀⠈⠁⠀⠀⠙⣦⠔⠀⢀⠜
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠉
⠀⣀⠔⠂⠀⠀⠘⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠃⡀⠐⠲⠤⣀⠐⠀⠀⠀⠉⠛⠓⠀⠤⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠈⢧⠀⠐⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠶⠶⠦⣤⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣺⠀⠀⠀⡀⠀⠀⠙⣄⠀⠀⠀⠊⠄⠐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠛⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠃
⠀⠀⠀⠀⠐⠒⠒⠊⠀⠀⠁⠠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢀⣠⠖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⣀⡹⠉⠒⠒⠒⠲⡖⠒⠉⠀⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡌⠉⠉⠙⠻⠅⠀⣀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡀⠀⠀⠀⠀⠀⠑⠶⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⣆⣶⠀⡴⠀⢸⠀⢰⠀⢰⡄⠐⠇⠀⡧⠀⠰⠀⠸⠀⢰⡆⣼⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣤⣀⣤⣄⣤⣄⣠⣄⣠⣤⣴⣎⣀⣴⢠⣶⣦⣴⣆⣰⣿⣿⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣐⠲⠂⢀⠐⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠁⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡀⠀⠀⣀⣔⠈⠙⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠒⢄⠀⠀⢀⠀⢀⠀⠑⡀⠔⡟⠔⠆⠁⠘⠢⠀⠀⠀⠀⡀⢔⡡⠦⢋⠡⣐⠏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠢⠄⠘⠀⠀⠈⠈⠠⠀⠠⠐⠔⡸⢀⠀⠐⠹⠀⠀⠉⢑⠀⠀⡸⡀⠀⢄⡴⣛⠜⡊⢧⠗⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠀⢀⣀⠀⣀⠘⠃⠀⠀⠱⠚⡙⣀⠥⠷⣵⢊⠖⠈⠚⠹⢂⠤⠽⡂⠁⠌⠾⠦⠵⠛⠈⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠺⣿⠟⠀⢀⠈⢢⠃⠀⠄⢖⠛⣹⡇⠰⢤⣠⠅⠎⠷⣰⣜⣠⠊⠉⠈⠥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠤⠠⠄⠀⠀⠀⠘⠀⠐⢆⠂⠩⡡⠾⠦⠈⠀⠀⠀⠜⠅⢈⠃⣀⡒⠀⣴⢄⠀⠉⠐⣠⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢉⠔⠀⠀⠀⠀⠀⢀⡀⠰⢦⣤⣥⣔⡀⡖⠀⠀⠀⠤⠀⠀⠈⠁⠈⢯⣿⠄⠙⢀⠀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠁⠀⠉⠀⠠⠀⠐⠀⠰⠦⠀⢀⠀⣨⡀⠀⠈⡇⠀⡀⣀⠀⠤⠄⠀⠀⠐⠋⠁⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⢀⠊⠀⠀⠀⠠⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢀⢀⠀⠄⠀⠀⠀⠀⠁⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢢⠀⠜⡐⠉⠁⠖⢂⠠⡀⢀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢈⠀⡃⠅⠀⠠⢠⠀⡑⢄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠈⠁⠀⠀⠂⠁⠑⠂⠐⠥⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠂⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠆⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠤⠤⠀⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠐⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⡦⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⡦⠀⠀⠠⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠰⡈⠀⠀⠀⠀⠈⠀⠀⠐⠄
⠀⠀⠀⠀⠤⠀⡀⠀⠀⡀⡀⠠⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠠⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⡒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⣀⣀⠤⠐⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠄⠠⢀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⠀⠀⠀⡐⠐⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠋⢉⡀
⡄⠀⠐⠂⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⣈⠀⠀⢤⡒⠀⠀⠀⠀⢨⠀⠀⢰⠚⠓⢠⠀⠰⠃
⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠘⠧⠄⠇⠀⣈⠁⠀⠀⢀⠁⢀⠁⠚⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠣⡀⠁⠀⠀⠁⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣠⠤⠦⠆⢇
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⠡⠤⠶⣖⠁⠀⠐⢄⠚⠏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠚⠘⠅⢧⡘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⡄⠠⠀⣄⠀⠀⢴⡐⠀⢠⣄⠁⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠙⠀⠀⠈⠁⢀⠋⠁⠀⡜⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠈⠉⠀⠀⠀⠀⠀⠀⠁⠢⢄
⠀⠀⠀⠀⠂⠀⢰⠀⠀⠠⠄⠀⢀⡀⠀⠀⠌⠀⠀⢐⠀⠀⢀⠁⠀⠀⠂⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠀⠀⠀⡅⠀⡐⠁⠀⠀⠆⠀⠀⡀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠀⠂⢣⣀⡴⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠆⠀⠐⢐⡀⠃⠀⠑⠂⠈

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣀⠉⠑⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⣀⢠⠂⠁⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠈⣄⠘⠛⠁⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⡇⠀⠰⢀⡐⠀⠘⠀⡰⡄⠂⠀⠀⠀⢊⠁⢀⠀⢀⣀⡆⠀⢠⠔⠉⠑⠂⠀⠺⣀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠊⡜⠁⠀⣀⢀⠀⠧⢴⣀⡀⠈⠁⠀⠘⢀⡁⠀⠀⠀⢀⠀⡈⡔⣡⣶⠀⣴⡄⢆⠁⠀⠀⠀⠀⠀⠀⠘⠔⢈⡀⡔⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠣⡀⠑⠂⢈⡠⢷⠚⠠⢄⠀⠀⠀⠀⠀⠈⢏⠐⠂⠀⠡⠈⡇⠈⠉⣂⡉⠁⢨⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠙⢩⠦⠤⣧⣤⣆⡠
⠀⠀⠀⠀⢀⠌⠉⠉⠙⠦⠜⣤⡀⠀⠁⡄⠀⠀⡀⠀⠸⠄⢀⠀⠀⠀⠈⠂⠄⠉⠠⠔⠁⠡⠒⢀⠄⠒⢀⠀⠀⡼⠋⠁
⠀⠀⡀⠂⡌⠀⠀⠀⠀⠀⢦⠉⢈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄⠀⠀⠸⠄⠀⠋⠀⠀⠀⠈⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠸⣄⣠⠅⠌⠀⠀⠈⠀⠸⡵⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠠⠔⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣀⠆⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠀⠡⠀⠀⠈⠀⠀⠄⡀⠠⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣂⠀⠀⢠⠂⠩⠀⠁⠘⠂⠀⠀⡀⠀⠙⠢⠤⡀⣀⠀⠀⠀⣀⡀⠔⠁
⠀⠀⢔⠀⠁⢠⠤⠤⠴⠺⠄⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠈⠀⠁⠈⠀⡃⠀⠠⠄⠀⠠⠀⠀⠄⠀⠀⠑⠤⣄⣀⠤⠂⠀⢀⠏⠁⠀⠄
⠀⠀⠀⠉⠉⠁⠠⣀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠠⠤⠸⠀⢐⡃⠀⠀⠀⠀⠂⡀⣀⣠⡄⣀⢠⠀⠀⠃⠀⠀⠔⠃⢀⠰⠆⠀⠀⠈⠳⠶⠆⠶⠎
⠀⡐⠁⠀⢀⡠⠐⠂⡀⡀⠀⠀⠀⠀⠁⠀⠣⢔⠃⠁⠀⠀⢰⠐⠒⠆⠀⠐⢃⡀⡀⢀⠀⡠⠀⠀⡅⠀⢘⡄⠰⠾⠀⢰⣷⠀⠠⠄⠠⠀⡀
⠰⠀⠀⡠⠋⠀⠀⠀⠀⠰⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠉⠁⠀⠀⠈⠣⣀⣴⣄⠨⡵⠤⠤⢴⣠⠄⠀⠀⠀⠄⡠
⠈⣄⡐⠀⡠⠂⠀⢀⠀⠘⠂⠀⠀⠀⠀⠀⡀⠀⠠⠠⠀⠰⠁⠀⠀⠠⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠒⢀⠀⠐⢢⡀
⠀⠘⢦⣀⠀⠀⠄⢂⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠈⠎⠄

⠀⠀⠀⠀⠀⠀⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠂⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠄⢀⢀⡤
⠀⠀⠀⠀⠀⠀⣀⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⣠⠴⠒⠚⠢⣀⡀⠀⠀⠀⠀⠁⠀⡼⠃⠀⠀⢸⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡜⠀⡄⠀⢀⡡⠠⠉⠉⠀⠀⡀⠀⠀⠀⠀⢰⠃⠀⣠⠊⠁⠀⠀⠀⢀⠏⠐⡀⠀⠀⠀⠀⡜⠀⠀⣦⡐⠇⠀⠀⠐
⠀⠀⠀⠀⠎⠀⠀⡈⠀⠐⠟⠠⠤⠤⠀⠀⠄⢀⠄⠀⠀⢸⠀⣰⠃⠀⠀⠀⠀⢀⠞⠀⢀⡇⠀⠀⠀⠀⠁⠀⠁⠁⠔⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠈⡵⠉⠀⠀⡌⠠⠔⠒⠀⠔⠀⠐⠆⠀⠀⠀⠠⡇⠀⠀⢀⣠⠔⠉⠀⢀⡜⠀⠀⠀⠀⠀⣠⠖⠀⠀⣁⡈⠐⠚⠁⠠
⠀⠀⠀⠀⠀⡔⠀⠀⠏⢉⡁⠀⠀⠀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠑⠐⠋⠉⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠠⠴⠋⠀⠀⢠⠀⠀⠀⠐
⡔⠃⠀⢀⡜⠀⠀⠀⡠⠈⠀⠀⠀⠈⠁⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠚⠉⠁⠐⠄⠀⣠⢆⣠⡴⠐⠂⣠⠆
⠀⠊⠀⠍⡇⠀⡾⠁⠀⠀⠀⠐⢀⣠⠍⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠀⠀⢠⠎⠁⠀⠀⠀⢸⡆⢀
⠀⠏⡉⠙⠢⠈⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣤⠤⠶⢢⡀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡠⠔⠚⠃⠀⠀⠀⣠⡟⠀⠁
⠀⠀⠚⠁⠐⠠⠄⣀⢈⣉⣉⣀⣀⣈⣉⣉⣁⠤⠔⠒⠉⠀⠀⡠⠊⠁⠐⠒⠒⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣀⣀⣀⡀⠈⠊⢀⡄⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠠⡀⢀⡠⠤⠖⠉⠀⠀⢏⡇⠀⢀⠀⠀⠀⡧⡰
⠀⢀⠄⠀⢀⠄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⠀⠎⠀⡌⠀⠀⣨⠁⠃
⠁⠈⠀⠈⠈⠐⠉⢀⡼⠀⠀⡤⠂⠀⢀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⠀⠀⠃⠐⠀⠀⡍⠀⠀⠀⢀⣀⡀⠀⠀⠉⠀⠁⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⢀⠤⠀⣠⠤⠲⡆⠈⠁
⠀⠀⠀⠀⢀⡨⠃⡇⠀⠀⠀⠎⠀⠀⣄⠀⠀⡔⠊⠀⠀⠀⠄⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡜⠁⢂⣸⣁⡴⠛⡄⡀⠀⢀⠔⠁
⠀⠀⢀⠋⠉⠀⠀⠇⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⢀⡴⠚⠉⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡽⣠⡾⠒⠲⡧⠀⠀⢰
⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⢀⡇⠀⣠⠜⠀⠀⠐⠁
⠀⠀⢈⠀⠀⠀⡀⡀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠊⠀⣡⠀⠀⠒⡇⡠⠀⠀⠄⠀⠀⠀⢀⡔⠋⠀⠀⠁⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠄⢀⠀⠈⡀⠀⠐⣊⠀⠀⠊⢸⠀⠀⠀⡔⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠓⠘⠷⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⡀⠀⡆⠀⠀⠀⠇⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠐⠄⡀⠀⠀⢀⠄⠁⠤⠀⠠⠊⠀⣶⠁
⠀⠀⠀⠀⠀⠀⢂⠔⠂⠀⠀⠐⠁⠀⡅⠀⠀⠀⠀⠡⠐⠚⠀⠀⡰⠂⠒⠀⠀⠄⣀⡤⠖⠀⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⢺⣅
⠀⠀⠀⠀⠄⠤⠊⠀⠀⠀⠀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⡀⠀⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡆⠀⠀⠤⢤⡔⠒⡆⠀⠀⠀⡠⠐⠉⠣⢤
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣀⡌⢰⣴⠾⡓⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⣦⠀⢰⣃⠀⣀⠀⣰⠀⠀⢀⠸⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠈⢁⠠⣤⠆⠐⠚⢂⡞⠊⣁⡈⣿⣆⠀⠀⠀⠀⠀⠀⢠⣅⠊⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⢰⡒⠃⠀⠀⠘⠒⠀⠀⠃⠀⠀⠸⠤⠒⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠈⠥⣄⠤⠒⠊⠣⡰⡎⠩⣆⢹⣿⡆⠀⠀⠀⠀⠀⡋⠒⡭⠟⠱⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⡴⠤⠝⠀⠀⠀⣀⢠⢶⡄⢀⣤⡀⠀⠰⡏⢧
⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠀⠀⣀⠱⡐⠔⣋⣭⣽⣷⠀⠀⠀⠀⠀⢧⡀⡄⣀⠴⠀⢠⡄⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⣻⠹⡬⠇⠙⣩⡤⠟⡴⠓⠷⠘⣄⣀
⠀⠀⠀⠀⠀⠀⠘⢯⣷⣄⢴⣿⣂⣥⡵⠿⠿⠿⣿⣾⡆⠀⠀⠀⣰⠓⠚⠛⠓⠒⠘⠃⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣠⠤⣆⢈⡧⠀⣤⠞⠀⠀⠀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣿⡿⠀⠀⠀⠀⠀⠈⠁⠀⢀⡔⠉⣢⠤⠔⢶⠒⠈⠡⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠘⠦⠶⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠣⣀⠤⠚⠀⠀⠀⣂⠄⠀⢀⡴⠶⡛⢋⡿⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⣀⡀⠀⣀⣀⣤⣄⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠐⠢⠴⡄⡇⠀⠀⡗⠀⠉⠁⠀⣴⡥⠤⢤⣼⠻⣤⠒⠉⠉⢦
⠀⠀⠀⣿⣛⡿⠋⠁⠀⠀⢀⡈⠻⣹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⢸⠁⡤⠚⠉⡹⠻⣅⠉⠑⢦⣸
⠀⠀⠀⠙⢻⠁⠘⢟⡤⡤⢜⠃⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢠⠃⠀⠈⢣⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⡞⠋⡙⣶⠴⠶⣄
⠀⠀⠀⠀⠘⢧⡀⠸⣴⣷⡬⠃⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⡀⣀⣤⣄⠀⠀⠀⠀⠀⠘⢆⠀⣼⠀⠀⠀⠈⣇⣠⠃⠀⠀⠀⠀⣠⠖⠚⢇⡃⠀⡇⡀⠀⢨
⠀⠀⠀⠀⠀⣠⠟⠓⠒⠖⠒⠺⡅⠀⠀⠀⠀⠀⠀⣠⣤⣄⠹⠦⠈⣿⠋⢤⣼⠃⠀⠀⠀⠀⠀⠀⠙⠻⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⢿⡀⠐⠛⢡⣤⠀⠩⠍⠙
⠀⠀⠀⠀⢰⡏⠀⣠⠶⠲⣤⣀⣽⡄⠀⠀⠀⠀⢰⡏⢀⣈⠳⣤⡞⣧⣠⠴⠞⠛⢦⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣻⠛⡆⢠⣁⢈⠙⢦⣠
⠀⠀⠀⠀⢸⡉⠉⣹⡇⢾⣉⣁⣠⡇⠀⠀⠀⠀⣴⠃⣼⠏⣷⡟⢹⠟⣡⡶⣷⣴⠋⠀⣠⠖⢉⣁⡤⠤⡤⠶⢶⠶⠶⢤⡀⣈⣉⣙⢶⡀⠹⣄⣀⣨⢯⡀⢀⣸⠁
⠀⠀⠀⠀⠈⠻⡿⠛⢷⠒⣻⠛⢻⡇⠀⠀⠀⠀⢻⣤⡽⠟⢻⢧⡟⢷⡙⢦⡗⢹⠀⠀⡇⢰⠉⢸⠀⠀⡇⠀⢸⠀⠀⠀⡇⡏⠉⢍⠓⠋⠀⠈⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠉⠛⠉⠀⠀⠀⠀⠀⢠⡏⣴⣿⣸⠾⡇⣶⡙⡶⠶⠛⠀⡴⠃⠈⠒⠞⠶⠶⠓⠶⠞⠓⠒⠚⠁⠓⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⠟⠁⠀⠳⣼⣧⠇⠀⠀⠀⠉⠒⠦⣴⡿⣷⡶⠶⠶⠶⠶⠶⣶⡶⣶⡔⠃
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠘⢿⣿⠿⠁
⠀⠀⢸⠁⢤⣬⣽⠳⢤⡴⠒⢦⡼⢳⣾⡯⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣣⣀⣀⣚⠛⣛⡳⣦⣶⡲⣄
⠀⠀⠘⡇⠠⣿⡷⠶⢾⣇⣀⣠⣧⠤⢭⣿⣂⣼⠀⠀⠀⢀⡴⠚⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢱⡿⢿⠁⠻⢀⠸⠋⡻⢧⡙⡟⡆
⠀⠀⠀⢹⣾⠁⣀⣤⡾⢩⣿⠈⠻⣟⠒⠶⠾⠃⠀⠀⠀⢸⡁⠀⣏⣹⠄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⢁⣈⣧⣘⣊⣚⡰⠃⢸⣿⣇⣷⡀
⠀⠀⠀⠀⠙⠋⠉⣼⠃⢸⠻⡄⢀⣘⡆⠀⠀⠀⠀⠀⠀⠈⣷⢀⣤⣤⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣚⠥⣺⣧⠈⢳⠞⡋⢙⡧⣈⡛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠿⠒⠾⠀⠙⠋⠉⠀⠀⠀⠀⢀⣠⣤⣼⡇⣾⠀⠀⢹⠎⠷⢛⡓⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢀⡏⠙⠰⠂⣁⣏⠑⠦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢡⡴⣤⠀⠈⣛⠒⣋⡀⠀⢯⣹⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣙⡃⠾⠆⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠳⠋⢀⡞⠉⠉⠉⠙⠦⣄⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢹⠛⢛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣛⡾⠀⢸⣚⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⡽⣾⡽⠿⠚⠺⢽⣾⡖⣆⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠞⠁⠀⡀⠀⠀⠀⠹⠉⠰⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊⠀⢃⠀⠁⠀⠀⠀⠀⢘⣡⠟⠀⠀⠀⠀⠀⡀⠤⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠂⣄⡐⠂⠈⠰⠏⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠊⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡰⠆⠀⠀⠀⠂⠀⠀⠀⠨⠀⣀⣀⡠⠄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠐⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⠀⠤
⠀⠰⠀⠠⠂⠀⠀⠁⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠁⠀⠁
⠀⠀⠀⠀⢀⠀⣀⠤⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⡀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊⠁⠀⠀⠀⠀⢀⣋⣙⠒⠓⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠒⠶⠶⠤⠤⠤⠤⠤⠀⠀⠂⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠴⠀⠀⡜⠁⡀⣀⠠⠀⠀⠀⠋⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄⠰⡆⠀⠐⠂⢘⠀⠐⠺⡀⠁⠘⠚⠂⠀⠀⠀⠘⡄⠀⠐⠷⠂
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⡀⢀⠀⠄⠀⠀⠀⠀⠉⠁⠀⠀⠙⠒⠂⠂⠀⠀⠀⠀⠉⠚⠒⠀⠀⠀⠀⠀⠀⠈⠠⣄⣀⠀⠀⠀⠀⣀⠠⡀
⠀⠀⠀⠀⠐⢠⠀⡐⠀⠀⠸⡄⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⢡⠉⠋⠛⠊⠉⠠⠒⢼⡄
⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠓⠦⠚⠀⠀⠘⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⣀⣀⡀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡄⠀⠈⡄⢀⠀⠄⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⠐⠀⠀⠀⠳⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⠃⠀⠐⡀⠂⠐
⠀⠀⡠⢀⠀⠀⠀⠐⠄⠀⠁⠈⠀⠀⠀⠀⠀⡀⢀⡣⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉
⠀⡠⠐⠈⠀⠀⠀⠀⢀⠒⠀⠂⠀⢀⠀⠀⠈⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢌⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠒⠚⠲⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠻⣏⠁⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⠀⣠⡞⠁⠀⠀⠀⣀⣀⣀⣀⠘⣧⡀⠀⢀⣸⠇⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠉⠉⠉⣿⠀⠀⠀⢠⣎⠖⠉⠉⠑⢿⢎⠙⠛⠛⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣧⠉⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣤⣤⣀⢀⡟⠀⠀⠀⠀⠡⣿⣄⠀⠀⢀⢴⡹⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣰⠟⣰⠏⠉⠛⠁⢀⣀⣀⠀⠀⠈⠫⠶⠶⠍⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⡼⠃⠀⣠⠞⠁⢰⢏⣤⣠⡴⠞⠋⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⢀⡾⠁⢠⡾⠃⠀⠀⣸⢿⣄⠙⢦⡀⠀⠀⣠⠇⠀⠀⢀⣀⣤⠴⢶⡾⠋
⠀⠀⠠⣟⣀⡴⠋⠀⠀⠀⣸⣇⠀⠙⢷⣄⠙⢦⣰⠏⠀⠰⣟⠉⠁⠀⠀⠀⣧
⠀⠀⠀⠈⠋⠀⠀⠀⠀⢸⣇⠈⠳⣄⠀⠙⠷⣄⣹⠆⣀⣠⢿⡄⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠳⣤⠈⢳⣤⡴⠛⠳⠛⢉⣤⠞⠁⠀⠀⠀⣀⡼⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣤⠞⠻⠋⠁⠀⠀⢀⡴⠋⠁⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠰⣏⣠⠞⠋⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡾⠋⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡴⠞⠋







⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⣿
⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⢛⠉⠀⠠⠀⠀⠐⠆⠀⢨⡻⣿⣿⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠈⠀⠀⠀⠐⠀⠀⠀⠄⠀⣌⠀⠀⣝⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠈⢻⠃⠀⠈⠁⠐⣇⠀⠀⢀⣀⠈⠛⣀⠁⠀⠚⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠀⠸⠂⠀⠂⠈⡇⠀⠈⠋⠀⠀⠙⠀⠀⠀⠂⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠠⠀⣀⣠⡀⣤⣄⠀⡀⢤⣠⣾⠆⠀⠂⠐⠂⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠈⠀⢙⣽⣥⣄⡁⠈⢿⣿⣷⣦⣴⡆⡴⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠐⠿⠧⠿⠋⠋⠛⢿⠛⠋⠁⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠊⢀⣤⣶⣾⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠆⠀⠀⠀⠀⢠⠞⠛⠀⠀⠀⡼⠁⣰⣿⣿⡿⠿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⣤⡀⠀⠀⠀⢸⠃⢰⣿⡟⡏⠀⠀⠀⠉⠁
⠀⠀⠐⠲⣄⣀⡀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⡸⠿⠣⠇⠀⠀⠀⠀⠀⠤⠶⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⡘⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣦⣘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠲⣿⣿⣿⣿⣿⣋⣀⣀⠀⠀⠀⠹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣧⠀⠤⠶⢦⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣶⣤⣤⣤⣤⣤⣤⣤⣼⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠛⠛⠿⠿⠿⠿⠿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠳⢶⣶⣶⣶⣶⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠢⣄
⠀⠀⠀⠘⠂⢀
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠘⠐⠚⢒⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⣢⠆⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠠⠖⠊⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠐⣠⠀⠀⢠⡔⠐⣄⠀⠒⠂⠀⠀⠀⠂⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠶⠊⠀⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⣀⢀⢀⢠⠐⠀⠦⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢌⠃⠂⠀⠀⠀⠀⢋⠐⠁⢆⠀⠀⠀⠚⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⡀⠀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣶⣿⣾⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⠿⣿⣦⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢤⣾⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠷⠬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠻⠿⡶⠄⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣠⣤⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⢿⣿⣿⣮⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⣤⣼⣿⣻⣿⣿⣏⡿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⣷⡿⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⠙⢿⣿⣧⢀⣾⣿⡿⢻⣿⣿⣾⠟⠋⠻⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⢀⣼⣿⠟⠸⡇⢿⡃⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⣠⣾⡿⠋⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠶⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠀⠈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⢃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠀⠀⠀⢀⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠠⢔⠕⠁⠀⠀⠀⠠⠄⢤⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⣀⢀⣃⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⢄⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠤⢤⠤⠴⡀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡐⠂⠤⠔⠒⠁⠀⠀⠀⠀⠀⠑⠀⠠⠠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⠤⢒⣒⣉⡩⢭⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠚⠄⠄⠴⠀⠀⠀⠀⠀⡗⣋⠉⣈⣤⠔⠊⠡⠄⠉⣙⡛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠀⠀⠀⠀⢠⡴⠚⠁⠈⠉⠀⢱⡀⠀⠀⣀⣸⡵⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⡞⠀⠀⠀⠀⢸⡃⢀⣾⣭⣵⣤⠤⠓⠊⠉⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠃⠀⡉⠈⠉⡰⠄⠀⠀⠀⠙⠋⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⠀⢈⣠⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠐⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⡀⠘⠀⠀⠀⠊⠀⠀⠀⢀⠀⠀⠐⠒⠐⡸⢂⣀⠐⠠⠠⢺
⠀⠀⠀⡠⠤⣎⠜⠁⠂⠢⡀⡠⠚⠄⠤⡈⠀⠁⢀⠄⠠⠦⢼⣰⣥⠒⠐⡪⠛⠅⢸⠀⢀⠀⡺
⠀⠀⢸⠀⠦⠁⠄⠂⠀⠀⢀⡀⢀⡤⢄⠈⡄⠀⣁⠄⢒⡷⠞⣖⣹⢿⣻⣁⣀⣠⠧⠬⡬⠖⡀
⠀⠀⠈⠷⠀⠁⠀⠂⠀⠀⠀⠀⠘⢄⣚⠔⢳⡞⠁⡔⠁⠒⠀⡨⠁⣀⠩⡀⠈⢲⣄⢀⡈⢦⠈⠂⢴⠆
⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠠⢠⠃⠀⠀⠀⡠⡇⠀⢠⡎⠰⣻⣿⠀⠀⠈⠹⢏⢳⠐⠀⠳⣖⣋⡠⢺
⠀⠀⠄⠀⠀⠀⠀⠸⠠⠔⢆⠀⢀⡜⠀⢀⠀⠡⠀⢈⡒⢷⠃⠐⠀⠁⠀⡠⠀⠀⠈⢯⠆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⡛⠦⣀⣀⣀⠈⠫⠀⣤⠃⢠⠪⠀⠀⠀⠀⠀⠞⠢⢄⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡠⠤⠤⡶⠧⣀⠀⠄⠀⠙⠆⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⢠⠀⢄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⢖⡡⠴⠒⢛⠛⠾⢫⠳⣼⠀⠀⢀⢼⠀⠀⠀⢀⡀⠀⠸⢄⠈⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⡵⠋⠀⡠⠊⢉⠩⠭⢿⠟⠉⠉⠀⠀⠸⠀⠀⠀⠀⢠⢠⠇⠀⠙⡏
⠀⠀⠀⠀⠀⠀⠀⢀⢖⣡⠟⠀⠀⣰⠁⠰⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠂⢀⡆⠀⡸⠁⡄⠀⢀⠁
⠀⠀⠀⠁⠀⣀⡈⢉⡩⠟⠀⠀⡠⠋⠢⠴⠄⡇⠀⠁⠀⢀⠜⢀⠙⠉⠀⠀⠁⠀⠃⠀⠀⢀⠂⠀⢄
⠀⠀⠀⡀⠡⠙⢍⡰⠂⢀⡠⠜⠁⠀⠀⠀⣀⠀⠐⡦⠐⠁⠂⠁⠀⠠⢒⠁⠀⠌⠀⠀⡰⠁⠂⠁⠀⠁⠂
⠀⠄⠂⠈⠒⠔⢄⡠⠋⠉⠐⡞⠉⠝⠂⠈⠃⠀⠜⠁⠔⠀⠀⠒⡄⠣⡘⣤⢌⣢⡤⠊⠀⠀⠀⠄⠂⠐
⠀⠀⠄⠀⠠⠀⣀⠧⣀⠗⠀⢣⠊⠑⠂⠀⢀⢾⠀⠘⠀⠰⡒⠀⡐⢀⠬⡄⠀⠀⣸⠒⢦⡞⠁
⠀⠀⠀⠀⠀⠐⣅⠀⠠⠢⡀⠸⡀⣄⡀⠔⠁⢈⠃⠀⠀⠀⠈⠉⠀⠌⠮⠀⠐⠀⠡⢖⠠⠋⠑
⠀⠀⠀⠀⠀⠀⠘⠤⣠⡔⠁⠀⠀⠀⠀⠈⡳⢁⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⢀⠤⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣒⣀⣚⣒⣊⣀⣀⣀⣙⣒⣒⣉⣁⣈⣑⣒⣒⣊⣁⣈⣉⣁⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠰⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠈⡀⠡⡀⠍⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠀⠀⣀⠀⠀⠰⣆⣷⡄⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠀⠀⠀⠉⠋⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠠⠄⠀⢰⡆⠂⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢀⢀⠃⠀⠄⠈⣢⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠡⠀⠀⠀⠀⠇⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠘⠀⢀⡀⠈⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⠀⠀⠲⠀⢁⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠀⡀⠀⠂⢀⠀⢀⠒⡁⠄⠀⠀⡠⠀⠀⠠⠮⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡀⠀⠀⠑⢀⡇⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⢀⠠⠂⠈⠀⠀⠂⠀⠀⠀⡀⠀⠐⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⡀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⢣⠀⠁⡀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠅⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⣍⣉⣶⢰⡂⠀⣢⣀
⠀⠀⠀⠀⠀⠀⢀⠴⡅⣁⣫⡉⡕⠒⢻⡛⠛⣽⡇
⠀⠀⠀⠀⠀⡠⠿⣈⣻⡛⢩⠐⠳⠿⠛⢃⡞⠹⠁
⠀⠀⠀⠀⣴⠂⠙⢻⣛⠅⠺⢴⣶⡿⣠⡟⠀⢲⣇⣀
⠀⠀⠀⣎⡈⠛⠛⠿⠙⣗⣦⣶⡇⣰⣗⣀⢀⡟⡶⣭⣿⣭⠑⠲⡂⠠⣤⣄⣀⡀
⠀⠀⠀⡆⠂⠈⠉⠁⠒⠒⠂⠠⡾⢹⡣⣀⡾⣿⣛⣻⣋⡹⢵⡶⠏⢿⣤⣨⣦⡜⠛⣓⠒⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠇⣧⣟⢮⡷⢿⣛⠚⠵⣶⣿⢴⢉⣉⣯⣉⠿⢿⠟⣼⠟⠀⠀⠀⠀⠀⠀⣤⢰⢀⣰⣶⣦⣬⣯⣟⣤⣿⠿⣾⣷⢄
⠀⠀⠀⠗⠠⠄⣀⠀⠀⠀⠀⠀⢷⣿⠣⡿⢑⠀⠀⠀⠈⠁⠐⠀⠂⠭⠟⣋⠙⠶⠾⣿⡇⣷⣀⣀⠀⠀⠀⠀⡏⢆⢹⢥⣭⣾⣧⣤⣷⢷⣬⣷⣿⣤⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⣫⢇⢃⣿⡂⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢙⡝⣤⠿⣶⣶⡷⣶⡀⣀⣃⠀⣳⠛⠛⠛⢟⢍⢝⠝⠍⡡⠉⠈⠀⢨⣗⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⡶⢿⠫⡫⠑⠒⠢⠤⢄⣀⡀⠀⠀⠀⠀⠈⠸⣡⡟⢀⣿⣷⠶⠯⢿⣤⣈⣷⢷⠔⢕⠔⠀⠑⡡⠠⢊⢀⢔⣀⣴⣸⣏⣀⠍
⠀⠀⠀⢶⠂⠒⣄⣀⡀⠀⠀⠀⣏⡾⠀⢸⠕⢌⠂⠀⠀⠀⠀⡆⠀⠉⠉⠒⠒⠤⠼⣯⡐⢟⣫⣽⡆⡔⣈⢛⣏⢡⢿⡛⠋⠛⠛⠘⠙⠉⠉⠉⠉⠉⠉⠁
⠀⡠⠁⠼⢽⠿⠏⢹⣢⣤⣾⣶⠛⡁⡈⢿⣤⣔⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠵⢿⣿⣳⡿⢹⡍⡁
⣔⠀⢷⣦⣴⡇⢰⣅⣉⣳⣴⠃⡸⠀⣱⠟⠅⡩⠉⠉⠉⠒⠒⠧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⢂⢀⣀⡀
⡏⠉⠐⠒⠂⠠⠬⠽⢟⣿⠃⢰⢡⡷⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⠀⣀⡀⠀⠀⠀⠀⡆⣹⡼⠃
⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣱⠎⠉⠁⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠉⠣⠿⠁⠀⠩⠠⠄
⠙⠢⠄⣀⣀⠀⠀⠠⠀⣆⡾⠃⠐⠒⠠⠀⠀⡠⠤⣁⣐⣾⣣⣤⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⡠⠤⣤⣆⣐⣾⣯⣭⡿⢆
⠀⠀⠀⠀⠀⠈⠉⠉⠒⠛⠂⠀⠉⠉⠉⠀⠀⠈⠻⡛⣯⣉⣱⡿⣶⡼⠧⣄⡀⠀⠀⠀⠀⠀⠀⢮⠹⣣⣤⣼⠿⣶⡶⣟⠚⡿⠓⢌⣽⣉⣺⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠫⡉⣏⠉⠐⣗⣤⣼⣧⣌⡀⠀⠀⠀⠀⠀⢣⠠⡯⣉⣹⠾⣢⣴⡾⢧⣿⣿⢽⠿⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠘⢎⠻⢿⡟⠁⠽⣄⣀⣹⣆⠀⠀⠀⢆⠀⢧⠬⠿⢷⠖⢞⠟⢉⢍⠕⠁⠀⠀⠀⣽⣒⣒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⣌⠧⣶⠾⠛⣛⢫⢞⡇⠀⠀⠌⢆⣸⢀⠔⠁⠀⠅⠔⡁⢠⣪⣨⠦⠾⠛⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠣⠤⠖⢛⡬⢢⣾⡏⠅⠠⠄⠈⠷⣥⠦⠶⠶⠺⠮⢙⣉⣁⠀⠐⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢐⡇⢄⢐⣐⣭⠿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⡷⠛⠁⠀⠐⠒

⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⣃⢻⡇⠀⠀⠀⠀⠀⠸⣿⣻⡿⠀⠀⠀⠀⠀⠀⢠⣼⣤⠀⠀⠀⠀⠀⣾⣗⠀⠀⢰⣿⡆⠀⠀⠀⠀⣴⣤⡄⠈⠃
⠀⣤⡤⣿⣯⣿⡧⣤⡄⠀⠀⠶⢿⣿⣿⣿⠷⠆⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⣟⣿⣀⣀⣸⣿⡇⠀⠀⠇⠈⠻⠟⠃⠀⣤⠄
⠀⣿⣇⣸⣿⣿⣚⣿⡇⠀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⡟⠛⣿⣿⡇⠀⠀⠀⢠⣤⣄⠀⠘⠛
⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉
⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢤⡤⣤⠀⣤⢤⡄
⠀⡏⠉⠉⡇⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⣿⣿⡁⠀⠀⠀⠀⢰⡏⠈⣷⠀⠀⠀⠀⠠⣿⠭⢿⡅⠰
⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣿⣾⣿⣿⠇⠀⠀⠀⠀⢀⣿⣾⣏⠀⠀⠀⠀⢸⡿⠿⢽⡧⠀⡇
⠀⠻⣀⠟⠛⠛⠛⠿⠇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⡿⠛⠛⠙⠃⠀⠀⠀⠀⠸⠹⡿⠹⠀⠀⠀⠀⢽⠯⠭⠭⣿⠄⠇

⢰⠦⠤⠤⠤⠄⠀⠠⢶⠀⠀⠀⠀⠀⢀⣤⣆⠀⠀⠀⠀⠀⠀⢠⣶⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤
⢸⠒⠒⠂⠀⠐⠒⠒⢳⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⡀⠀⣀⣼⣿⡿⠛⠂⠀⠀⢀⣤⣤⣤⣤⣤⣴⠀⠀⠀⠀⣰⡇⣿⣷⡄
⢸⡉⣉⢉⢉⣀⡈⠉⢫⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⢿⠀⠀⠀⢠⣾⡿⠛⠋⠀⠀⠀⠀⠀⠀⢼⣿⣇⣿⣿⣿
⠼⠥⠤⠤⠤⠤⠤⠤⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠷⠛⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣤⡞⣿⣩⡟⣳⡄⢠⠀⠀⠀⠀⣼⣿⣧⣄⠀⠀⠀⠀⢀⡤⣤⡤⣄⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⢸⣿
⢸⣍⣿⣿⣿⣿⣉⡇⡾⠀⠀⢰⣿⣿⠿⣿⡿⠀⠀⢀⣠⣮⣤⣼⣤⣼⣄⣀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣷⣷
⠀⠙⣿⠋⣻⣧⡜⠁⡇⠀⠀⠀⠙⠋⠀⠁⠀⠀⠀⣼⡟⠻⣿⣿⣿⡿⠛⣿⡄⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣶⡄
⠀⠀⠘⠛⠛⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⠏⠙⣿⡟⠈⣻⡇⠀⠀⠀⢀⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠰⢏⠀⠀⠀⢸⣽⢿⣧
⠀⣿⠶⠲⣾⣷⢷⣿⡇⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠿⠛⢚⣖⣦⣀
⠀⣿⡀⢀⣼⣇⣸⣿⡇⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⣀⣜⠉⠉⣙⣄⠀⠀⠀⠀⣰⣄⣀⣀⣀⣼⡄⠀⠀⠀⠀⠀⠾⣿⣿⠟
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⠀⠀⠀⡏⠀⠀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⠀⠀⠀⠁⠀⡼⠐⠀⠀⢀⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠁⠀⠀⠠⢠⠎⣀⠔⠈⠀⠀⠔⠉⠁⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠐⠁⣰⣴⣏⣼⠏⠀⠀⠀⠀⡰⡴⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⢀⠄⣠⠚⠁⢠⡟⢡⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠨⠀⣮⡾⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⢀⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⡿⢱⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣦⣈⣒⣄⣄⠀⠀⠈⠇⠀⡔⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠛⢩⠝⠛⢍⠓⠂⠤⡈⠢⡁⠀⡀
⠀⠀⠀⢦⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⠀⠀⠀⠈⠓⠒⠉⠁⠊⠀⡰⢩⠊⡄⠀⠡⠤⠀⠀⠠⡉⢻⢱⢀⢀
⠀⠀⢸⠃⢁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⢀⠄⢀⡀⠀⠰⡌⠈⠇⢀⡄
⠀⠀⢸⠳⠈⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠒⠒⠐⠒⠀⠀⠀⢰⠀⠀⠀⢼⠀⠄⡤⠉⠀⢰⠙⢻⠀⠀⠞⡇
⠀⠀⢸⡆⢁⡇⠀⠁⠀⠄⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠂⠂⠀⠠⣀⠔⠋⠀⠀⠀⠘⣸⠖⠁⠀⠀⠀⠃⠘⢰⡏⢀⡇
⠀⠀⢸⣇⣸⢠⠆⢠⢠⠈⣁⡀⡀⠀⠀⠀⠀⠒⢄⡳⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⡙⠀⠀⢀⢀⠀⢰⠀⠸⠁⢸⠇
⠀⠀⠀⢿⡿⠀⠀⣸⡤⣮⣅⠃⠀⠀⠀⠈⣀⣤⣽⠶⠿⠚⠧⣠⡆⡀⢀⠁⠀⠠⢠⠀⠃⡀⠈⠀⠠⠀⢠⡆⠀⡄⡾
⠀⠀⠀⠸⣿⣀⡴⠋⢼⡓⠉⢸⢀⠰⠀⠀⢸⠈⠃⠀⠀⠀⠀⠸⡟⡀⠈⠀⢤⠀⢠⡑⡿⣿⣄⡠⠀⢠⠚⢱⡀⣿⠃
⠀⠀⠀⠀⠹⣿⠃⢸⠸⠑⠌⠸⠄⠀⡴⠒⡼⢠⠀⠂⠀⣀⠀⠘⠙⠁⠀⠠⠤⣄⠲⣍⣿⣽⣷⣇⡴⠁⠐⢠⢳⠏
⠀⠀⠀⠀⠀⠙⠄⠈⠄⠀⠀⠀⠀⠊⡠⠢⢁⠼⠡⠤⢀⠂⠀⠀⠀⠀⠀⠀⠠⠄⠝⠘⠉⢙⣟⢋⣄⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠰⣄⠈⠢⣀⣀⠀⠈⢀⢢⠂⠀⠠⠀⡠⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⣨⢸⠀⢱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠀⠉⠀⠀⠰⠃⢀⠠⣔⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢁⠁⣸⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡴⣄⠴⠚⣈⢦⡙⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣐⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠉⠀⠮⢤⣜⣁⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣟⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠂⠺⡿⠟⠉⠛⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡠⣼⡁⢢⣤⠀⠠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣽⠀⠀⠀⠀⠀⢨⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⡄⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠤⠀⠀⠀⠈⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠰⢤⠄⠀⠀⠀⠀⡠⡆⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⣤⡴⣶⢀⣀⠀⣠⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣛⣷⣯⣙⠛⢡⡙⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣝⣳⣾⣿⣷⣦⣀⣰⣯⣝⣷⢉⣼⣿⣯⣭⠿⣦⣌⣠⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣋⣿⡟⢻⣿⣾⣿⣿⣯⣿⣯⢸⡏⣾⣿⣿⣮⣽⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣬⣹⣾⣿⣿⣿⣿⡼⢻⣟⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣷⣿⣸⣿⣷⣾⣗⣿⣦⣽⢿⣝⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣿⣽⡷⠿⣯⣿⣿⢻⣯⣽⣾⣯⣿⣻⣶⡻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣽⣶⣶⣿⠿⠋⣼⣟⣿⡿⢿⡿⢿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢻⣿⢦⣽⣿⣛⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣳⣤⣟⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣝⣷⣦⣄⣀⣠⣤⣶⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣧⡀⠀⠀⠀⠀⣼⣧⣿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣏⣿⣟⣹⣿⣿⣆⣀⢀⣴⣿⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣏⣿⣿⣿⢿⣿⣿⣿⡿⣯⡝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⢀⣼⣿⣿⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣾⣿⣿⣾⣿⣿⡿⠿⠛⠿⠿⣻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠛⠻⠿⣿⣿⣛⣛⣛⣿⠾⠟⠋

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣋⢿⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋⠙⡛⠁⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣦⡀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣷⣦⠈⢳⠆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠆⠁⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⢀⣴⡌⠳⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⠀⠀⣀⣴⣿⣿⣷⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣞⢒⠖⠀⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡿⠛⣍⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⡼⠁⠀⠈⡀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣥⡔⣠⡀⢹⣆⠘⢿⣿⣿⣿⣿⣿⢷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣭⡿⠉⣽⡇⠘⢛⡃⠀⠈⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⢠⣴⠆⣋⠳⣽⣿⣅⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠓⠳⠊⠺⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣤⣴⣆⠈⢀⠁⢰⠆⣤⡄⠄⠀⠀⠀⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠆⣤⠀⠯⠀⠁⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠄⢳⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣠⠔⣶⣂⠐⠶⣤⡀⠀⣦⣠⡆
⠀⠀⠀⢀⣡⠈⠀⢰⡖⣶⢀⡀⠄⠀⠀⠀⢻⡜⣟⠋⢿⣆⠾⠵⠚⣶⣤⣤⣵⡆⠀⠀⠀⠀⠈⢀⢀⡀⠀⠀⠀⡠⡆⠰⠈⡀⢀⢀
⠀⠀⠀⣯⡽⠷⡶⢛⣳⠏⠀⠁⡀⠀⠀⠀⠀⠐⣿⣄⣈⣿⣦⡒⠀⠉⡌⠋⡈⢁⠐⠸⡤⢀⡀⠀⠠⡋⣳⠀⠁⠄⠉⠇⢠⠄⣬⡀
⠀⠀⠁⠈⠛⠛⠛⠋⠁⠀⠀⠔⢂⠀⠀⠀⠈⠡⢾⣯⡙⠄⠓⠙⠣⢀⠂⡤⠃⡔⠉⠂⠐⢤⡍⠢⢄⡓⠀⠠⠃⠀⠀⠀⢈⠀⠰⠱⡀
⠀⠀⢳⣶⣶⡄⡀⢀⡀⠀⠚⢃⡎⠠⣀⠀⡆⠀⢸⠃⢀⠐⡀⡓⡪⢂⡔⢰⠀⢔⠀⠁⣮⡠⠙⠲⣬⠂⢀⠂⠀⠀⠠⡀⢰⠂⠀⡇⡀
⠀⠀⠘⣏⠀⢩⠰⠈⢤⡀⠓⠁⢀⠀⡄⠈⢳⡡⡀⠃⠐⡀⠈⠀⠀⡀⠄⠿⢆⡘⠀⠐⠂⠙⠦⣄⠘⡃⠠⡄⢀⠀⠀⠠⠈⠀⡴⠠
⠀⡤⠈⡈⠀⢀⠂⠑⢀⠱⠛⠸⠂⢸⡉⠀⣰⡿⢅⠑⢈⣈⡐⠦⢘⠀⠐⠽⣬⣥⠀⣼⣦⡑⠀⣄⠀⢸⣦⣇⡄⠀⠄⢁⢀⣮⡰
⠀⠀⠀⠀⠀⠀⠈⢐⠀⠀⠱⡶⣭⢥⣼⣾⠟⠡⠤⠙⢻⠒⠕⠃⠈⡷⠶⡓⣃⡛⣴⢿⣱⣿⣦⡼⠶⠚⠯⡀⠛⠓⠚⠙⡊⠓⡞
⠀⠀⢀⡀⢀⡀⠠⠸⠓⣄⠀⠐⠀⠀⢘⣁⡠⣾⣅⣡⡗⢪⢠⠀⡦⠀⢄⠀⣂⡦⠹⡄⠁⡸⠉⠛⠛⡛⢻⣿⡐⠀⠈⠘⡷⠴⠓
⠀⠀⠀⠃⠀⣤⠤⠒⢣⣀⠈⠀⢂⡚⣿⠓⠂⠉⠹⣗⡧⣪⠈⢿⡥⠋⠀⣀⡧⠄⢾⡁⠀⡇⠀⠀⠀⠀⠁⠐⢩⡤⠀⡤⠀⠀⠁
⠀⠀⢀⠀⠀⢡⡶⣖⣿⣿⠖⣫⡋⠀⠙⣆⠀⠀⠀⠘⠛⠛⠃⠈⠁⠀⢀⡏⢱⣦⣾⠀⠐⣷⡅⢸⠀⠸⠄⡄⠂⢈⠩⠴⣀⠄⡘⠁
⠀⠀⠀⠀⠀⢀⣟⣫⣹⣏⠛⡟⠢⠀⠀⠈⠙⠛⠓⠄⠀⣠⣾⠀⠹⡕⠘⠃⢨⡭⣻⡁⠀⢿⣟⢂⡜⠃⡄⠉⠐⣤⡶⠟⠛⠛⢦⡌
⠀⠀⠀⠀⠀⢹⠂⠋⠅⠀⣤⡼⣘⠙⠀⣠⣀⢀⢀⡀⡀⢞⠻⣧⠈⢯⡁⠻⠄⣦⢺⡏⠀⠈⢷⠆⡀⠆⣀⠓⣎⣹⣶⠄⣀
⠀⠀⠀⠀⠀⡜⠐⡒⠢⠌⠘⠤⠦⡁⠀⢀⢀⠀⠁⣀⠼⣩⠂⢻⡄⠸⡦⢙⡆⠰⡞⠉⡐⠄⢬⣆⠃⣶⠉⠰⣾⡿⠀⠀⠻⢃⣄
⠀⠀⠀⠀⠄⠁⠂⠀⠀⠀⢀⠈⢶⢈⣔⢒⣲⠀⢎⠇⡀⠀⠀⡀⠼⡀⠡⠐⠇⠀⢇⡀⠀⠀⡀⠽⠓⠀⠸⢶⣿⠇⣀⠀⠀⠈⢛⣂
⠀⠀⠀⠀⢸⡀⢀⣦⣴⣤⣶⢶⠞⢛⡤⢊⠁⣆⠐⠀⣉⠀⡀⠀⠀⠁⡦⠥⠶⠦⣄⣈⠈⠛⡔⠀⣴⠖⠠⠀⠻⠀⠻⢣⣄⠀⠀⠛
⠀⠀⠀⢰⡎⢡⠀⣆⠀⣤⢸⣷⣴⠋⠀⣴⢞⡉⠀⠂⡉⡀⠀⠀⠀⠎⠀⣴⡦⡄⠀⡎⣽⠁⠱⣤⢿⣦⣠⡇⠈⣤⠀⠄⠙⣧
⠀⠀⡉⠀⠑⣆⡈⠁⢤⣄⠹⠐⡇⠰⠋⣀⠞⡉⠀⢧⣱⠂⢰⠆⡘⠀⣸⡅⠂⢃⢠⢧⠴⠁⠠⢤⣼⣝⠁⣼⡀⢸⣤⠴⠫⢾⢅
⠀⠀⠇⣐⠂⠦⠸⡝⣤⢔⠶⠀⡄⠘⢊⡡⠞⣃⣤⠘⢫⡷⠃⠐⠠⠛⠏⣏⠏⠩⠃⠀⠀⠀⢠⠀⢙⣿⠀⠈⡆⠀⣿⣟⡤⠤⠭⢆
⠀⣚⣤⢉⠸⠆⢲⢬⣉⣁⢠⠢⣷⣀⣅⠶⠈⠁⠈⠀⢈⡷⢤⣴⠦⡔⠘⠰⠀⠠⠀⠀⠐⠖⢤⣅⢀⣻⠈⠆⢻⠀⠹⢷⡂⠬⠩⠥
⠀⠹⠆⡜⠓⢰⣦⠀⣤⢨⠽⣭⠤⣤⡈⣠⢍⠀⠀⠀⠊⠓⠶⠷⠞⢉⢗⠘⡀⠈⠄⠀⠀⠈⠄⢉⣙⣿⣞⡀⠞⢣⢈⢧⡑⢬⠙
⠀⠀⠘⢟⠀⣦⠀⡀⢸⠃⢰⢃⣂⣈⠓⡌⠲⡀⠀⠀⠀⠀⠀⠀⠀⡈⣈⢁⡑⢤⠀⠀⡀⠀⠀⣸⣿⠏⠈⠙⠲⢶⣠⣌⣈⠃⡀
⠀⠀⠀⠀⠙⢄⣀⣬⢏⡰⠁⢾⡅⣭⠆⠈⣣⡇⠀⢄⡀⠛⠇⣉⠞⢀⡉⠀⡀⢄⠼⢶⡌⢦⢿⣟⡍⠈⠠⠔⢀⠀⡀⠀⢀⢀⠄
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠁
⡶⣶⢶⢷⣷⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠀⠀⠀⠀⠀⠀⠀⡁⠠⠆⠚⣆⠀⠲⡄⢄⡠⢔⡒⡒⡆⠀⠀⠀⠐⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢈⠄⠄⣑⠊⠰⢺⣧⠀⢨⡦⠤⠧⠌⠀⠁⢀⡡⠃⢀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡾⡀⠀⠀⠙⠢⢭⡸⢴⠀⠀⠘⡏⠉⠄⠀⠀⠠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠈⠓⠂⠠⠤⠶⠒⢋⣀⡀⠀⠸⡄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣾⡆⠀⠀⠀⠀⠀⢠⣮⣿⣿⡛⠀⡇⠀⠈⠙⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢻⠇⠀⠀⠀⠀⠀⠸⠙⠛⠋⠀⢠⠇⠀⣀⡺⠀⠀⠀⠀⠐⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠸⠁⠂⠀⠐⠀⠀⠀⠀⠀⠀⠂⢀⡞⠀⡄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠸⡄⠠⢤⡤⠊⠀⠀⠀⠀⢀⡴⠋⠀⠀⠢⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠑⠒⢲⠔⠒⠒⠒⠈⠁⡅⠀⢀⣂⠀⠀⠀⠀⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠠⠀⠹⣄⣈⣉⠈⠑⢢⡔⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢳⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠰⢠⡶⠁⢀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢠⠀⠀⠀⠀⡬⠀⠀⢸⠀⠣⡀⠀⡀⠀⠀⢀⠀⠀⡰⠰⠠⠀⣼⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠅⡀⠐⠆⠀⢙⠒⠼⠀⠀⢸⠖⠚⠱⠀⠀⢀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⠀⠈⠀⠀⠇⠀⢸⡄⡅⠀⢃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⠂⠁⢀⠇⠉⡇⠀⠀⢰⠠⠸⡇⡇⠀⢸⠀⢀⡄⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠄⠀⡸⠀⠀⠇⠀⠀⢸⠀⡀⠧⠚⠀⡎⠀⠈⡇⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠒⠄⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠠⢖⠉⠀⢀⠸⠢⣀⠀⠀⢸⣿⣿⡿⠟⠻⢡⣉⣿⣿⣿⢨⠁⠀⠀⠀⢀⠉⠃⠀⠀⠀⠉⠉⠉⠳⢦⡀
⠀⠀⠀⡀⠀⠀⣆⡀⠨⠨⠑⠀⠀⠀⣿⡷⣺⠲⡊⠐⠁⠋⠉⡶⠂⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠐⢀⡂⠎⢁
⠀⠀⠀⠀⠀⣠⠀⠀⠐⠁⡗⠁⠀⢀⣿⣷⣬⣌⠀⠀⠀⢀⠌⠀⠀⡴⠂⢈⠀⢰⠀⠀⠀⠀⠈⢣⡠⢂⠊⠀⠘
⠀⠀⠀⣦⣤⡇⠀⠀⣂⡈⠀⠀⠀⠈⣉⣉⠀⠀⠁⠀⠐⠃⠸⠥⡄⠁⢰⠘⠙⠃⠀⠀⠀⠀⠀⠈⢏⠂⠠⠔⠨
⠀⠀⠸⣿⣿⣿⡀⡍⠀⠀⠀⠀⢠⠊⣁⡘⠲⠀⠀⠀⠀⠀⠀⢄⢀⠀⡄⢀⠀⣀⡠⠀⠐⠰⠛⠋⠉⠀⠀⠀⠠
⠀⠀⠀⡿⠿⠛⢃⠀⠀⡀⠤⠒⠃⠀⠈⠳⠀⠈⣠⠀⠀⠀⠀⠊⠍⠇⠀⠀⠈⠉⡇⠀⠀⣦⠀⠀⣀⠀⠀⠓
⠀⠀⠀⡀⠠⠂⠈⠀⠋⠀⡀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠀⢀⠀⢀⠀⠀⡜⠈⠛⠛⠛⠂⠀⠂⣠
⠀⠀⠀⡄⠄⠈⠉⠰⠀⢰⠐⠂⠀⠀⠀⠀⠚⠃⠀⠀⢀⣶⡇⠀⠀⣀⣀⠀⠀⠼⠀⡐⠀⠀⣤⠄⠀⠀⠀⠀⠿
⠀⠀⠀⡔⠂⠀⢀⣠⣦⠈⡒⠠⠄⡉⠐⠀⠐⢁⣄⣀⢀⣁⠀⠄⠘⠛⠟⠀⠠⡯⣭⠁⠰⢄⠉⠄⠀⠀⠿⠀⠔
⠀⠀⠀⣦⠔⠋⠁⠠⠄⡀⠀⠀⣆⠂⠀⠀⠀⠈⠉⠉⠉⠛⠃⣀⡀⡀⠀⠀⠀⠀⠀⢰⠅⠀⢠⣀⡀⠈⠒⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠰⣂⢀⣤⡀⡀⠈⠠⠄⢐⠒⠀⠍⡁⠀⠴⠖⠂⠠⠀⠀⠑⠈⠐⣉⡀
⠀⠀⠀⡁⣀⠀⢀⠀⠀⠠⠉⠅⠊⠀⠀⠐⠀⡃⢴⠀⠊⠐⠑⠩⠆⢰⠀⣄⠀⠀⠀⢠⡌⠉⠐⠰⠉⠀⠀⠀⡔
⠀⠀⠀⠏⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠩⢂⠠⠦⠀⠂⠀⠖⠀⠛⣄⠀⣤⠀⠸⣏⠀⢢⣄⠀⠀⠀⠂⢠⡅
⠀⠀⠀⠀⠠⠿⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠐⠛⠋⠀⠀⠀⠒⠟⠒⠒⠚⠉⠉⠈⠉⠉⠉⠉⠊⠛⠛⠛⡀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠤⢀⠀⣄⠠⠀⣠⠟
⠀⢀⠄⢱⣄⡴⠂⠀⠀⣀⣤⣴⠆⠀⠰⣿⣾⠤⣄⢀⠶⠏
⠀⠈⠀⠙⠋⠁⠀⠀⢸⣿⣿⡟⠀⣠⡟⣿⡃⠀⣹⣷
⠀⠀⢀⣀⣀⣤⣤⣶⣿⠟⢸⠀⣀⢿⡇⣿⡿⠋⠙⠓⠰⢄
⠀⠀⠀⠉⠙⠛⠛⢻⡟⠀⢸⡆⢹⡧⠇⣿⡄⠀⠙⠶⢦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⣸⣇⠸⠃⣶⣿⣿⡄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⡿⠃⠀⣿⣿⡿⢹⠄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠠⠋⠀⠀⢠⢻⡿⠁⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⡇⠀⡋⣠⡶⢢⠀⢤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠉⢻⣄⡹⠠⣤⠁⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⢹⡆⠀⢹⣃⣸⠷⣴⣏⣰⠃⠸⠆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡿⠀⣿⠃⣼⡇⠀⠀⢻⣟⣶⣯⣤⡏⠁⠶⠚⡀
⠀⠀⠀⠀⠀⢁⣾⣿⣿⣷⣿⢨⣧⡾⠟⠀⠀⠀⠀⠙⠿⣶⣟⣁⡾⠃⡚⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣁⡟⠃⠲
⠀⠀⠀⠀⠀⠀⠹⣿⣆⢻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣛⡄
⠀⠀⠀⠀⠀⠀⠁⠹⣿⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠚⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠛⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⡇⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣧⡸⡄⢹⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣷⡜⢦⡉⠻⣯⣟⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⣿⣿⣎⠻⣦⠘⣿⣿⣶⣝⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣡⣿⣿⣿⣿⣿⣷⡘⣷⡌⢿⣿⣿⡷⣦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⣿⢻⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⡇⠈⢻⣦⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⠿⢛⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢿⣄⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡡⣶⠟⣿⠁⠀⢸⡿⠀⠸⣿⣿⣿⣿⡟⢻⣿⣿⣿⡇⠀⢰⡟⢸⣿⡆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⠖⠁⡴⢁⣺⡇⠀⠀⢻⡇⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⠁⠀⣼⠃⣾⣿⠇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡞⠀⢸⠃⡇⠀⠀⢸⡇⠀⢰⡆⣿⣿⠻⡇⢸⣿⢿⡇⠀⣰⠏⣰⣿⠟⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⡞⠀⠀⣾⠀⡇⠀⢀⣿⠃⠀⢸⡇⡿⠶⠴⠟⠛⠁⣏⠀⣴⠋⢠⡟⠁⠀⡰⠂
⠀⠰⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⡜⠀⠀⢠⠇⠀⣱⠀⣾⣯⠤⡀⠈⣷⠁⠀⠀⠀⠀⠀⡠⠛⠁⢀⠏⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠃⠀⣠⡟⠠⠊⠉⠛⠛⠃⠀⠈⢶⠏⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⡴⠋
⠀⠼⠁⠀⠀⠀⠸⣿⠀⠀⠀⠀⢿⡶⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣠⣾⠋
⡄⠰⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣾⡟⠁
⠆⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⡟
⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⡀⢀⣀⣠⣤⣀⡀⠀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣠⣼⣿⣿⣿⣿⣿⣏⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡁⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁

⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠻⠟⠻⠿⠿⠿⠿⠿⢿⡿⠿⢓⣠⡽⠿⠿⠟⠿⠿⠿⠟⠻⠏⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠄⠂⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠋⠁⠙⠀⠀⠀⠀⠐⢇⢀⣀⡀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠟⠃⠙⠓⠀⠛⠀⢳⢲⢀⡀⠀⠀⡇⠀⠀⢀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢢⠀⡄⠀⠀⡄⠀⠀⠀⢸⢸⠀⠀⠈⠉⠁⢠⡐⠁⠀⠀⠀⠀⠁⠀⠰
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣀⢠⣀⡀⠧⠀⠤⠤⠼⠴⣤⣤⡀⣀⣸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠑⠀⡀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠸⡏⠀⠀⠀⢠⠆⡈⠈⢢⢠⡎⠀⠀⠱⡀⠿⠘⠃⠀⠀⠀⠀⠀⠤⢀⡇
⠀⠀⠀⠀⠀⠱⠛⠂⠉⠀⠀⡀⡠⣂⣀⡇⠀⠀⠀⠸⣄⡁⢀⡴⠂⢦⣀⣁⡼⠁⠀⡀⠀⠄⠀⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡳⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠒⠋⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⡄⠀⠉⠢⣄⠀⠀⠀⠘⡄⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠈⠳⡀⠀⢡⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠢⡀⠀⠘⢄⠀⢠⠀⠸⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡤⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠢⡀⠀⠀⠈⠢⠀⠘⣴⠃⠀⠀⣇⠀⠈⠀⢀⡴⠦⡄⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⢄⠀⢀⣡⠔⠁⠀⠀⠀⢹⠀⠀⠀⢸⡀⠀⣿⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⡀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⡆⢀⣀⠬⠇⠀⠉⠉⢉⡉⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢘⡸⠁⢀⣀⠉⠓⡤
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠱⣀⠙⠉⠀⠀⡂⠀⠐
⠀⠀⠀⠀⢨⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢠⠂⠉⠁⠀⠀⠻⡀⠌
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠱⠄
⢠⠂⢁⣀⠈⠁⠀⠀⠤⡤⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡠⠠⠀⢀⡇⠀⠀⠀⠀⢰⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠊⠓⢤⣀⡀⠀⠀⢀⣠⠶⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⢈⠧⠠⢤⣄⠊⠀⡀⠀⠀⠀⠀⠀⠀⠑⠠⠒⠀⠈⠉⠘⢅⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠌⠀⠀⠀⠀⠀⠁⣷⣠⠀⠄⢰⠀⡄⠠⠀⠰⠀⠄⠀⠀⠆⢠⢀⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⣧⣴⣴⣦⣶⣤⣦⣴⣶⣧⣴⣴⣷⣴⣦⣼⣿⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿
⣿⣭⣭⣯⣽⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣾⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠖⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡟⠆⠀⡆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢀⠃⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢉⠀⠀⣑⠄⠀⠐⠀⠀⠐⠀⠀⢄⠁⠀⢈⠐⡑⠄⠀⠀⠀⠀⡄⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠰⠠⢀⠀⠀⠀⠈⠄⠀⠀⠰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠁⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⠀⢊⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠃⠀⠀⠀⠀⡆⠀⠀⢰⠊⠁⠐⣀⠀⠀⠡⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠄⠀⣩⣍⡀⠀⠀⠚⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠠⠛⠄⠀⠠⠃⠀⠈⠁⠉⡄⠳⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣿⠇⠀⢰⠀⠀⠀⠀⠘⠂⠐⠒⠒⠂⠚⡖⠀⠂⠀⠒⠒⠒⠒⠂⠀⠀⠂⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⢀⠀⠾⠧⠂⣀⠄⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠠⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊⠓⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠊⢄⠈⠐⠢⠀⠀⠀⡧⡼⠁⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠂⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⢂⠀⠀⠀⠁⢢⡁⠐⠡⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠠⠁⠀⠀⠀⡰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠈⢔⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠉⠐⠀⡀
⠀⠀⠀⠡⡀⠀⡠⠊⠰⠀⠀⠈⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⣈⠀⠡⡄⠀⠀⠀⠀⠈⠞⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠤⢀⠀⠑⡀⠀⠀⠀⠀⠈⢀⠠⠤⢀⠀⠈⢠⡔⠒⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠠⠁⠀⠀⠀⠐⡀⠸⠓⠄⠀⠀⠀⠐⠁⠀⠙⠁⠀⠙⠿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠠⣄⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠡⣀⠀⠀⠀⢀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣀⣤⡸⠀⠀⢢⣤⣀⣤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠀⠀⠀⠀⠀⠉⠙⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠈⠛⠛⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡟⢦⣠⠟⡆⢀⣤⠖⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣷⡟⠉⢰⡿⢋⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠂⡾⢋⣭⣭⣭⡛⢿⣿⠿⣶⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠄⠀⠀⠳⠌⠁⠀⠀⠉⠂⢹⣧⠀⢉⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡏⡜⣏⠀⠀⢀⡤⠀⢠⡀⢀⣠⠀⠀⣿⡆⠀⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣧⣀⠀⠀⡀⠘⢷⣤⣤⣛⣫⣥⠆⣰⡿⠁⠐⠦⣤⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠛⠧⠄⠀⠀⠀⠈⣓⣒⣺⣛⣟⣭⣴⠿⠋⠁⠀⠀⠀⠀⠉⢻⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⢀⣠⣴⠶⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠘⠉⢋⣴⠟⣩⡶⠃⠀⠀⠀⠀⠀⢀⣀⣉⣉⣒⠦⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣴⠦⢠⣿⢋⣾⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠉⠃⠀⠀⠀⣶⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⢸⠁⣿⣀⡙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⣿⡜⠰⣌⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢿⣿⣿⣄⠉⠋⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⢿⣯⠙⠻⠿⠿⠃⡀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠲⠂⠈⠻⣷⣌⠲⣦⡴⠋⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢧⣀⢈⠛⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⡫⠉⢀⡀⠨⣝⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡻⠶⠞⠁⠀⠈⢿⣷⡝⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠘⣿⢿⣼⡗⢦⣄⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⠃⢸⣿⠁⠈⣿⣆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢻⡄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠚⣣⢸⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⠿⠿⠿⠿⢟⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣟⣿⣿⣟⣛⣻⣿⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠤⠀⠀⠐⠋⠀⠀⠀⣠⣿⡃⠀⠀⠘⢿⡟⠿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠙⠿⠿⣦⣤⣠⡄⠀⠀⠤⠀⠰⠟⣿⣿⠃⠀⠀⣤⠾⠁⠀⠙⣿⠿⣿⣶⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⡇⠀⠀⠀⣀⣠⣾⣿⣿⠀⠀⠀⠁⠀⠀⠀⢠⡀⠀⠀⠹⣧⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠤⠀⠀⠀⠀⠀⠠⢤⠤⢶⣿⣅⠀⢠⣤⣿⡾⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣶⠏
⠀⠀⠀⠀⠀⠀⣀⢔⣻⣤⣤⠄⢀⣀⣴⠶⠾⠿⠿⠿⠶⢿⣿⡿⠀⢀⠀⠀⢀⣿⠏⠀⠀⠀⡀⠀⠀⠀⢀⣭⣿⣿⣴⣸⣿⢣⡶
⠀⠀⠀⠀⠀⠀⢁⣾⠛⢡⡴⠾⠟⠛⠁⠀⠀⠀⡀⠀⣴⣿⣿⣀⣾⣏⠀⠴⣿⡏⠀⠀⠀⢸⣿⣤⠀⣼⣿⡋⢀⣿⠏⣿⣿⠏⠁
⠀⠀⠀⠀⠀⢀⣿⣿⣶⡿⠤⠶⣤⣤⣶⣦⡤⠀⢁⣼⠿⢸⠟⠛⠘⣿⡀⣶⡿⠀⠀⠀⠀⠈⠛⠻⠀⢿⣿⡀⢸⣿⠰⣿⡋
⠀⠀⠀⠀⠀⠸⣿⣟⠀⠀⠀⡴⠛⠛⠋⠁⠀⣀⣿⣿⣆⢠⡀⠃⢠⡈⠁⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠻⣧⡀⢀⣴⠂⠀⠀⣠⠶⣶⠟⠁⠸⡏⣿⣷⠂⣼⣿⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡙⣿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢻⣇⣰⡿⣾⣿⣶⣏⣠⣤⡞⢙⣿⣫⠞⠋⡁⠴⠉⣴⢞⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢣⠟⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢋⣵⡾⢋⡝⢂⣴⣉⣐⣥⣴⠓⠁⢀⡼⠃⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠠⠟⢉⡜⣡⣴⣿⡿⢋⣿⣿⠉⠀⠀⣠⣴⣶⡿⠟⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢶⣀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⢳⣆⣸⣿⣾⠿⠟⠁⠶⣬⣽⠿⣤⡰⢾⠯⠉⠛⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⡟⠳⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⢀⣾⢂⣈⣡⠴⠊⣡⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⣿⠿⠟⠛⠁⠀⠀⠟⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⢶⡆⢠⠄⣴⠆⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠘⠓⠲⡜⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢆⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡉⢉⣤⡈⣳⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⠞⡣⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠁⢿⣧⣼⡿⢀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡅⣷⡀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠟⢿⣿⣇⣸⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣤⣿⣅⠀⠀⠄⠀⠀⠀⠀⠑⠄⢸⣼⡿⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣛⠃⠀⠀⠙⠿⠻⣆⠀⠀⢀⠀⠀⢀⢀⣤⠿⠏⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢣⣤⣄⠈⢶⣤⡄⠀⠘⢿⣆⠀⠀⠚⠐⠛⠻⡈⠡⠀⠀⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡈⠓⠈⢏⣸⣇⡀⠀⠿⣷⣴⣀⢰⣶⠐⠁⠀⢀⡞⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⠿⠃⠀⠀⠈⡁⣾⣿⠦⠀⠛⠉⣨⠟⢀⠟⢀⠴⠟⠀⡟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠂⡿⠂⠀⠀⢰⣿⠀⣿⡟⣠⡆⠀⠘⠁⢠⣤⠒⢁⡴⣧⡿⣀⡀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣶⠃⠀⠀⠀⣸⣿⣴⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⢪⡵⠊⠚⠛⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⡇⠀⠸⣇⠻⣬⣛⣿⣿⢳⡄⣖⡀⣀⣡⠤⠛⣧⠦⢀⣻⣦⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⣼⣧⠀⡄⢸⣆⣩⣿⣿⣿⣿⡿⣿⣿⠛⢁⣠⠖⢁⣰⠯⠛⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣦⢿⣄⣿⣿⣿⣿⠟⣡⣾⣿⣿⣶⣿⣧⡴⠞⠋⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢿⣷⡿⢸⣿⣼⣿⡟⠋⣼⣯⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣾⣿⣧⣿⣿⣿⡟⠁⣾⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣿⣏⢷⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⣻⣿⣿⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠈⠁⣀⠈⢠⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣙⢿⣷⣦⡀⣠⡄⢘⠂⣀⣶⣌⣇⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢴⣦⣽⣧⣐⣫⣤⣌⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣛⣛⣛⣛⣋⣛⣛⣃⣈⣙⣛⣟⣛⡉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣯⣬⣭⣭⣭⣭⣭⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣍⣭⣭⣉⣭⣿

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠡⠀⡀⠄⠀⠀⠀⣀⠀⠤⠤⠤⢀⡀⠀⠀⠀⠀⡀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⣀⠀⠡⡶⠤⠭⢀⠀⠀⠉⠉⠃⢔⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠉⢆⡀⠀⠋⠀⠀⠀⠀⠀⠀⠐⡀⠀⢁⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⡘⠀⠀⠙⣆⠀⠀⡈⠀⠀⢰⠖⠰⡆⠁⠀⠁⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠰⢡⠀⠀⠈⠢⠀⠀⠀⠀⠀⡨⠀⠀⠁⠀⠀⠸⢸⠀⠁⠀⠠⣄⣤⡤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⡆⠀⠀⠆⢰⠏⢢⡄⠀⠘⡆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠒⠀⠀⢹⠀⠀⢀⠌⠀⠀⠜⠀⠰⠀⠘⠁⠀⢀⡆⢁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⡀⢂⠀⢀⣸⠀⠔⣀⣀⠀⠈⠀⡐⠁⠀⠀⠀⠀⡼⠔⠙⡖⠈
⠀⠀⠀⠀⠀⢀⠀⠠⠈⡀⡐⡄⢀⠴⠊⠁⣀⠠⠑⠎⠁⠀⠀⡐⢀⡞⢆⠀⠀⢠⠁⠀⡰⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣐⡾⠊⢉⠃⢀⠔⠊⠀⠀⠀⠀⢀⣶⠀⠀⠀⡇⠈⠓⢦⡬⠉⡎⠉⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠐⠀⠈⣡⣀⠂⠀⠁⣀⠀⢀⣀⡠⢔⡕⠃⢡⡀⠀⠄⢀⠟⠉⢱⠊⠙⠆⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠈⢀⠁⢠⠖⠁⠉⠈⡹⠁⠀⠀⠁⠀⠐⠀⠩⡀⠀⠈⢀⠴⡋⠠⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⡀⠁⠠⠀⠅⠂⠀⠁⠀⠀⠀⠀⠀⠈⠂⠎⠀⠀⠐⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⣿⠛⠛⠻⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠇⢠⠀⢀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠀⠀⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⢦⣬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡆⠀⠀⢰⣀⠸⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠸⣿⡶⠛⡀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢠⣽⡀⠀⠀⠉⠀⠀⠘⠷⠤⠄
⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⢰⣿⠇⠀⠀⠂⡀⠀⢠⠄⣠⣄⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡌⠐⠀⢁⡙⢶⣧⡀⠀⠀⠻⣾⣻⣿⣾⣿⣿⣧⣦⡀
⠀⠀⠀⣠⣄⠇⠌⢹⠒⣅⣿⢷⣶⣯⣿⣦⣄⠀⠈⠻⠿⠛⠛⠿⠻⣿⣿⣦⡀
⠀⠀⢾⣏⡴⣿⣦⣼⣷⢽⣿⣷⣯⣿⣿⣿⣿⠿⠖⠀⢀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⢐⡉⠀⠀⢈⣟⣏⢞⢹⡻⢇⣧⣷⣯⡈⢩⣿⣀⠀⠁⠀⠀⡀⠀⠀⠀⢻⣿⡀
⠀⠀⠈⠙⠒⠚⣿⣿⣿⣿⣿⣿⠛⡛⠋⠱⢛⣟⠋⠀⠀⠀⠐⠀⠃⠀⠂⠀⠸⣿⣧⠈⠀⠀⠀⠀⣠⣶⣤⣀
⠀⠀⠀⠀⠈⠛⣿⣯⣹⣿⠋⠀⠁⠉⠂⠀⠀⠉⠀⠀⠀⠀⢰⣦⢤⣶⠂⠀⠀⠀⢿⣧⡁⠀⠀⠀⠘⠟⠻⠄
⠀⠀⠀⠀⠀⠐⠛⠛⠙⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣯⡿⠟⢃⠀⠀⢀⠙⢷⣶⣄⣀⠀⢀⣠⣤⣤⡀⠀⠀⠠⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠈⠙⠻⣿⣿⣿⣿⣿⡯⠀⣰⣾⣿⡾⢍⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠳⣋⠉⠉⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠀⣀⣼⣿⣿⣷⡖⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⠛⠁⠁⠸⠿⠟⢏⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣴⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠉⠉⠛⠓⣦
⠀⠀⠀⣠⣴⡾⠋⠀⠀⠛⢟⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢹⡟⠁
⠀⠀⠀⠙⣿⣧⠀⣀⣀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⠛⠓⠊
⠀⠀⠀⠀⠙⠻⠾⣿⡟⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣂⠄⠀⠀⠀⣼⠛⠃⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢠⣼⣿⡄⠀⠀⠀⠀⠀⣴⠒⠺⠿⠿⠟⠓⡄
⠀⠀⠀⠀⠀⡔⣻⠆⢹⣿⣿⣿⣦⣤⠀⣿⠀⠀⠀⠀⠀⢀⣾⡗⠀⠀⠀⠀⠀⣀⣈⣄⣿⣿⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡀⠛⠋⢠⠀⠉⢻⣿⣿⣿⡇⠙⢧⣄⣀⣀⣀⣼⡿⠃⠀⠀⠀⠀⠈⠻⣧⣬⣿⣿⣿⣀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⡇
⠀⢀⣠⡄⢀⡶⣦⡀⢀⣴⣿⣿⣥⡏⠁⠀⠀⠙⣿⡟⠉⠁⠀⠀⠀⠀⢀⠄⣷⣄⣠⣤⣿⢿⣿⠿⣀⠀⠘⢿⣤⣤⣤⣤⣤⣶⡧
⢰⡿⣧⠟⠘⢷⡾⢃⣿⣿⣛⡷⠎⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢀⠈⡾⠛⢿⣯⣉⣿⣤⣿⠷⣇⣤⡀⠀⠀⠀⣿⡇⠀⠈⠁
⠈⢧⣄⠘⠛⠀⣠⣾⠿⣿⡝⠁⠀⠀⠀⠀⣀⠀⣿⣷⣄⡀⠀⠀⠀⣿⠀⣠⣦⠈⠋⣁⣿⣿⣿⡇⣸⣬⣷⠀⠀⠀⣿⡃
⠀⠀⠙⢦⣀⣾⣿⣿⡾⠃⠀⠀⠀⠀⠀⠚⠁⣞⣿⣿⡟⢿⣶⣄⡀⠈⠀⢿⣹⣷⣿⠟⣿⣿⣿⣼⣿⠟⠋⠀⡀⠀⠿⠃
⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⢀⡄⢠⠀⣠⡀⣿⣿⣿⡒⠈⠀⠻⡆⠀⠀⠈⠙⠛⠿⠿⠟⠛⠉⠀⣠⠖⠁⠀⠀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⢀⡀⠉⣀⣿⣿⣿⣿⡇⠠⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠠⣶⡧⠀⠈⠋⣫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠣⣾⣿⣿⣿⣿⣿⣿⣾⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣭⣅⣀⣀⣀⡈⣫⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⣿⣿⣿⣿⣿⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⢉⢿⣿⡯⠁⠛⣿⣻⣟⠈⢹⣿⡿⠙⣻⣿⣿⡿⠉⢹⡇⠀⣴⣤⡀⠀⢴⣦⣶⠀⠀⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠿⠴⠦⠾⠻⠷⠼⠿⠿⠻⠴⠾⠿⠝⠷⠾⠷⠿⠻⠿⠶⠿⠇⠈⠙⠛⠃⠀⠘⠉⠋⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠁⠀⡠⠂⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠒⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡋⠒⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡘⠁⠀⠠⠌⠣⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠘⠁⠢⠀⠠⢄⠠⢌⠊⠉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠑⠀⠀⠄⢀⠈⠀⣀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠨⠀⠐⢠⣧⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⠀⡃⠀⠀⠀⠠⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⣀⣠⠤⠐⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠐⢠
⠀⠀⠀⢀⠀⢀⠄⡀⠀⠀⠀⠀⠀⢂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠀⠀⢀⡀⠀⠀⢐⠂⠂⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠛⢉⡁⠉
⡔⠈⠀⠂⠈⡡⠈⠁⠀⠀⢨⠀⠀⠈⠁⠢⠁⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠈⠂⠀⣧⠒⢀⠀⠀⠀⠀⡀⠉⠉⢰⠚⠒⢀⡀⠠⠜
⠁⠄⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠀⢌⡡⠀⠀⠀⠀⢸⢾⡉⣇⠄⠈⠉⠈⠀⠀⠐⠁⠘⠒⠒⠋⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠙⢶⠀⠐⠀⠀⠘⠁⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣄⡔⠃⠀⠛⠒⠀⠀⠰⣿⠆⡖⠀⠀⠀⠀⢀⣶⣦⣤⣾⠽
⠀⠀⠀⠀⢀⠀⠀⠑⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⣴⣧⣤⣴⣶⣾⣿⣟⡿⢱⣾⠟
⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡏⡏⢉⡍⢰⠻⠊⠉⠀⠙⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡄⠠⢄⢱⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠉⢘⡄⠉⠀⠧⠄⠀⢺⠆⠀⠁⡗⠂⠀⢰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠄⠐⠒⠲⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢠⠃⠀⠀⡸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠁⠀⠀⣏⠐⠀⡕⠀⠀⢈⡄⠀⠀⡆⠀⠀⠠⡅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢄⣀⡜⡁⠠⢀⠞⠀⡀⢠⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠘⢄⡠⠇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠤⠤⠤⠄⠀⠐⠀⠀⢀⡠⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠉⠰⠂⠀⠂⢜⡤⠁⠀⠉⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⢀⠐⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣝⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠰⢨⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠙⠉⡁
⠆⠀⠈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⡠⠁⠀⠰⡍⠀⠀⠀⡀⢤⠀⢀⡏⠉⠀⠄⠐⠃
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠈⠓⡘⠀⠤⠀⠀⠀⢠⡀⠀⠉⠁⠀⠀⢀⡀⢀⡠
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⣠⣴⡾⡿⢋⣿
⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⢻⢛⠉⡩⡯⠋⠈⠑⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠣⠈⠀⠓⠂⠀⠗⠀⠀⠓⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠂⠀⠐⠂⠐⠠⢄⡀
⠀⠀⠀⠠⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠎⠀⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠓⠀⠰⠄⠀⠈⡂⠀⡼⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠤⠔⠱⡀⢠⢥⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠆⠀⠐⣐⡐⠀⠘⠄⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣤⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣰⢶⣽⡯⠇⠗⢯⣷⣽⠶⠄⠀⠀⠀⠀⠀⠀⠂⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢮⠋⠀⠀⠀⠀⠀⠈⢣⠙⢥⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡖⠀⠀⠀⠀⠀⠈⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢦⡀⠠⠤⠄⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠰⠂⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠀⠁⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠁⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠤⠄⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⣒⢒⠠
⠀⢀⠂⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⢃⠤⠀⠠⠁
⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⢰⣀⢔⣁⡆⠀⡀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠈⠉⠀⠀⠀⠀⠀⠀⠥⠤⠄⠉⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⠀⠀⠈⠛⠛⠓⠒⠒⠒⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⣀⣀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⡤⢀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⡐⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⢀⠄⢼⠀⠀⠨⠅⠐⠀⠐⠼⡀⠀⠀⠳⠖⠀⠀⠀⠀⠰⡀⠀⠀⢶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠐⠐⠀⠀⠈⠣⠤⠄⠀⠈⠀⠀⠀⠙⠲⠦⠂⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⣞⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢃⠀⠂⠀⠀⠈⠑⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠐⠂⠁⠀⢠⠀⠀⠀⠀⠐⠀⠀⠙⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠈⠈⠀⠀⠀⠒⠒⠂⠐⠂⠀⠀⠈⠀⠄⠀⠀⠀⠀⢰⡀⠀⢘⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠂⢁⠀⠀⠀⠓⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠈⠀⢀⠀⠂⠀⠀⠁⠀⠁
⠀⠀⠐⢢⠀⠀⠀⠀⠀⠐⡀⠀⡄⢂⠀⠀⠀⠀⠀⠀⠠⡀
⠀⡐⠀⠁⠀⠀⠀⠀⠀⠨⠁⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⢯⣾⣿⠛⠁⣠⣴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣱⣿⣿⡟⢿⠿⢿⡿⠁⣾⠟⠃⢀⣤⣷⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⢋⣼⠦⢉⠁⠤⠀⠠⢤⡖⠋⠀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⡋⠀⣛⠀⠀⠠⠏⡤⠀⣀⡹⠛⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠦⠀⠰⣼⠃⠛⠚⠓⣦⣾⠋⠀⣅⣠⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣈⣅⡀⠀⢿⠇⠀⠀⠀⠀⣿⠇⣰⣿⣾⡟⢁⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣸⣯⣉⠁⠒⣾⠀⠀⠀⠀⠈⣷⣾⣿⣶⣥⣶⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠧⢀⠀⡻⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣥⠤⠀⣠⣴⡾⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠿⠻⡟⠛⠉⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣷⣶⣶⡆⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⠿⢃⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠻⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⡉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠘⣆⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣻⣟⣿⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⠀⠉⠋⠛⣶⣤⣤⠤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⣸⣇⠱⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠀⠀⠠⡀⠀⠀⠀⠀⣾⡉⣿⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠸⣷⣼⡆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣛⣿⣿⣿⣿⣿⠇⠹⠄⢀⠀⢀⠀⢹⣿⣧⣀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⠟⠀⢀⠘⢆⠙⢦⣿⣓⣿⣯⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⢸⡛⠛⢁⣤⡤⠀⠀⠁⠀⠀⠘⡗⣦⣽⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⣟⣿⣯⣉⣤⣄⣛⠁⠀⢀⠢⠂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣽⣿⣿⣿⣿⡟⠋⣀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠻⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠊⠀⠀⠈⢢⠄⠄⠴⠉⠀⠀⠁⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢸⢩⣀⠀⠀⢀⡼⢤⠠⠧⡀⠀⠀⢀⣌⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⡞⢲⠀⢾⠁⡈⣉⡀⠙⠢⠼⠍⠒⠋⢁⣈⢹⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢇⠘⡀⢀⠃⠙⠃⠀⠀⠠⡀⠀⠀⠈⠋⠈⡄⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢣⡅⡰⡀⠀⠸⡙⠋⠉⠈⠙⢋⠇⠀⠀⠴⠘⠀⠀⣠⠔⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡰⢠⠧⣑⠤⡀⠈⠑⠂⠐⠒⠉⢀⡠⠊⠀⢆⢣⡰⠁⠀⠀⢨⠀⣀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢡⢃⠎⠀⠉⡸⡻⠓⢄⡀⣾⢫⠖⠀⠀⠀⠬⣄⢣⠤⠤⠤⠼⠔⠡⢼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡀⠙⢄⡠⣪⠂⠀⠀⢀⡔⡱⠁⠀⠀⠀⠀⠠⠀⠉⠀⠀⣀⡤⠒⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣤⣊⠔⠻⠀⠀⡠⢊⠎⠀⠀⠀⠓⠒⢂⡐⠷⠦⡔⠋⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠛⠙⡇⠀⡨⠄⣀⡉⣉⣐⡐⠷⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠅⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⣰⣀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠧⠴⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠒⣈⣁⣉⠀⠀⠀⠀⠀⠀⢀⣈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠌⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡆⠀⠇⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠂⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠉⣰⣖⡳⠞⠛⠒⢄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡎⠀⠃⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢀⡆⠀⠀⠀⠀⠀⠀⠀⠳⠄⠐⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⣿⣷⠒⠂⢤⣤⣤⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⣬⣽⣿⣶⣤⣽⣿⣮⣙⢄⡁⠺⠉⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⡀⠀⠀⠀⠘⠃⠳⠤⣤⣀⣄⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠙⠻⣆⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿
⣿⣿⣿⣋⠀⠉⣠⣴⣿⣿⣿⣿⣧⠀⠀⠀⠘⠛⠿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⡿⠁
⣿⣿⣿⣿⣷⣔⡛⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⡟
⣿⣿⢿⣆⠙⠻⣿⣿⣿⣿⣿⣿⣾⣿⠿⢃⣀⣤⣤⡶⠛⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣄⣴⣿⡟
⣿⣿⡄⠉⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠉⠀⣀⡀⠀⠑⢦⡀⠈⢿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡒⠉⠉⠀⠀⠀⠀⠙⢿⣶⣿⠟⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣰⣶⣄⡀⠀⠀⠀⠀⠈⢛⣿⣼⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⡀⠘⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣌⣻⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⡇⢿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡿⠀⠘⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⡄⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⣻⣿⣿⣿⡿⠀⠀⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠃⢀⠀⠘⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢘⣷⡀⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⡿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣤⣴⡶⢦⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⣶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠈⢁⠞⠀⢀⡟⣤⠋⣠⢶⣀⣤⢳⡾⢃⣤⡶⢰⡟⠀⠀⠉⡴⠁⠀⣸⢀⣴⡄⣤⣤⣤⣄⣄⣤⣴⡟⣠⣴⣄⣤⣶⢀⣤⣴⠏
⠀⠀⠀⠀⠀⠀⢿⠤⠖⠋⠘⠧⠺⢷⡿⠻⠷⢾⠖⠻⠾⠷⠿⠔⠀⠀⢸⡧⠶⠚⠁⠻⠾⠻⠷⠿⠛⠻⠿⠷⠿⠔⠧⠟⠻⠶⠷⠺⠗⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠠⠴⠂⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣠⠈⠀⠀⠀⠀⠀⠀⣴⠂⣤⣠⡞
⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣇⣼⢿⢇⡖⣻⡆⠀⠀⣼⢃⡿⢣⠟⣠⡾⠃
⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠟⣵⠛⠋⠉⣩⠟⠁⠀⢰⣻⠏⠛⠉⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⢶⡤⣍⠀⠀⠀⠀⠈⠁⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠸⠇⠈⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⡾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢦⣈⣃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠸⣇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠐⢆⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠈⠱⣆⠀⢀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠃⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠛⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠦⡀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⣔⢃⠀⠀⡈⠄⣅⠀⡐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣆⠀⣤⡀⠈⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣤⣄⠀⢁⠐⠦⣼⠿⢯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠘⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣨⣅⠈⠉⠀⠀⢂⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⡋⠀⠀⠐⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⣀⡀⠀⠀⡰⢶⣴⠛⠛⠲⠂⣠⣴⣟⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡩⠛⢛⡶⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣷⣀⣀⡠⠎⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⣿⣿⡇⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠜⠛⠛⠁⢠⣦⠉⠉⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠳⠁⠐⢄⠀⠀⠀⠁⢀⠄⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠠⠁⠀⠀⠀⠑⠢⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠢⠄⣀⠀⠀⢀⣀⠔⠁
⠀⠀⢀⠔⡡⠔⠒⠠⡈⠆⠀⠒⠂⠐⠒⠂⠴⣁⠄⠒⠢⢌⠢⡀⠀⢀⡀⠤⠤⠠⠤⠀⠒⠒⠛⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠇⠎⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠱⠰⣀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡄⢆⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡰⢠⠋⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠈⠢⣽⠀⠀⠀⠀⢶⣖⠀⠀⠀⠀⣲⡶⠆⠀⠀⠀⣫⠔⠃⠀⢆⠀⠁⠀⠀⠀⠀⠐⠊⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠨⠀⠀⠀⠀⢙⡫⢴⣶⣶⡦⢝⠋⠀⠀⠀⠀⡇⠀⡀⠀⠈⠑⠐⠒⠒⠒⣤⡖⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡀⠀⠀⠰⠋⠀⠀⠉⠉⠀⠀⠙⠄⠀⠀⢀⠃⢀⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠐⢄⠀⠀⣀⠀⠄⣀⣀⠠⠀⣠⠂⠀⡠⠂⢀⠈⠢⡀⠀⠀⠀⠀⠀⣴⠏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⡠⠔⠈⠑⠄⣈⠑⠢⠤⠤⠔⠊⢀⡠⠊⠉⠲⢎⠀⢀⠌⠀⠀⢀⡀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠘⡄
⠀⠀⡠⠊⠀⠀⠀⢀⠔⠁⠈⠉⠀⠀⢉⡁⢀⡣⡀⠀⠀⠀⠑⢎⠀⠀⠀⡇⠀⠉⠁⠒⠒⠒⠒⠒⠒⠀⠉⠁⠀⠀⡆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠠⣏⠁⠀⢻⠈⢆⠀⠀⠀⠀⠣⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠄⠀⠀⡐⠈⠒⡀
⠰⠀⠀⠀⠀⢀⣃⣀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠉⣀⣈⣄⡀⣠⣴⣶⣧⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢄⢀⠇⠀⢀⠁
⡆⠀⠒⢒⠖⣡⠤⠤⣍⠒⢄⠀⠀⠀⠀⡠⠒⣩⠤⠽⣄⢿⣿⣿⣟⠉⠢⠤⠐⢺⠁⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠒⠈⠉⡩⠋⠀⢀⠎
⠣⡀⢀⠃⡜⠁⠀⠀⠀⠙⣌⢢⠀⠀⡔⣡⠋⠀⠀⣶⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠢⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠔⠊⠀⠀⡠⠋
⠀⠈⢙⠀⡇⠀⠀⠀⠀⠀⠘⡄⡇⢰⢠⠃⠀⠀⠀⠹⠛⠉⠁⠀⠀⠑⠤⠤⡤⠤⣤⣊⡀⠀⠀⠀⢀⣀⣀⠀⠤⠄⠒⠊⠁⠀⠀⣀⠔⠋
⠀⠀⠈⡄⢧⠀⠀⠀⠀⠀⢀⠇⡜⢳⠸⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠐⠒⠉
⠀⠀⠀⠘⢌⠳⢄⣀⡠⠔⡫⠜⠀⠀⠳⢜⠢⢤⣀⡠⠞⣧⡀⠢⡀⠀⠀⠀⣣⠴⠛⠀⠀⠒⠒⠒⠀⠀⠂⠈⠉⠁
⣤⣤⣤⣤⣤⣵⣶⣶⣶⣥⣤⣤⣤⣤⣤⣤⣬⣶⣶⣶⣮⣤⣽⣶⣷⣶⣦⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢢⣀⡇⠀⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⢹⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡑⠦⠖⢧⠀⠀⠀⠀⢠⠂⠐⡀⠀⠀⠀⠀⠀⢸⡆⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⠉⠒⠼⡄⠀⡀⠀⠈⠙⠋⠀⠀⠀⠁⠀⠀⢸⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠹⣄⠑⢄⡀⠀⠀⠀⠀⡠⠃⠀⢀⠟⠀⣀⣀⡤⠤⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣠⠤⠄⠀⠈⠓⠦⣌⣉⠉⠉⠁⢀⣀⡴⠟⠊⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢠⣀⠀⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⠉⠉⠉⠁
⠀⢀⡤⠒⠐⠒⠦⠤⣀⡠⣜⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣾⠈⠑⢆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⢿⡀⠀⠈⡄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠈⠳⢦⣴⣁⣀⣀⣠⡤⠾⠋⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠑⠦⢄⣀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠒⠛⠋⠉⡇⠀⠀⠀⠀⠀⢀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⡔⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢜⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

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



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⢀⣀⣿⠦⣤⣤⡤⢾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⣀⣠⣽⠗⠛⠋⠉⠉⠻⣤⣄⣀⣤⠾⠉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠚⠛⠉⢿⣄⣉⣉⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠉⠛⣷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⢦⣄⠀⠈⠉⠉⠉⠀⣠⠶⠚⠛⠓⢦⡄⠀⠀⠀⠀⣟⠛⠒⠚⠛⣻⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣿⠳⠶⠶⠶⢻⡇⠀⠀⠀⠀⠙⠳⠶⠶⠚⣋⣀⣠⣤⠴⠶⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠙⠷⠤⠤⠴⠞⣁⣀⣠⣤⡤⠶⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣟⣉⠀⠈⣉⣷⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢰⣶⠛⠋⠹⣏⠉⠉⠉⢉⡿⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠈⠻⣦⡀⠈⠙⠛⠛⠉⠀⣠⠶⠶⠶⠿⣷⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠚⣿
⠀⠀⠀⢸⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⣿⠶⢤⡤⠴⢿⠀⠙⠷⣄⡀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠻⢦⣤⣤⡤⠞⠀⠀⠀⢈⣻⣾⣧⡤⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⣀⣠⣤⡤⠶⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠖⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣿⠀⠀⠀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠖⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣯⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⣽⡿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡼⠋⠀⠀⠉⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⡼⣻⡿⣿⣿⠛⢵⠄⠀⢀⣄⢠⠀⠀⠀⠐⠛⢷⣆⠀⡴⢶⣄⣰⣿⡿⣻⡿⣱⠋⠁⠀⠈
⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠀⠀⠀⠀⢴⡟⢤⣴⠆⣤⣤⣾⣏⣀⣤⣴⣿⣿⡿⣱⡿⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⣼⢻⢻⣿⣿⠿⠀⠰⠶⠿⢿⣟⠦⠀⢊⣿⣿⣯⣿⣿⣿⣿⣯⣵⣞⣫⠞⠁⢀⠀⠀⠀⢠⣖⡄⣰⢢⡟⠁
⠀⠀⠀⠀⠘⠸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣛⣋⣁⠀⢀⣸⠇⠀⢠⡟⡞⣸⢁⣯⣤⠴⠦⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⣃⣒⣦⢞⣥⡄⠀⢸⣿⣿⣛⡷⣦⣭⣛⣿⣿⣿⣿⣿⣯⣍⡉⠉⠉⠁⠀⠀⣼⢹⣡⢯⣾⣥⣶⣲⣿⣿⣶⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠵⠊⠛⠛⠂⠀⠈⠁⠀⠀⠙⠮⣳⠿⢿⣿⣿⣟⡉⠉⠉⡷⠀⠀⠀⠀⢀⠟⢛⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣈⠉⠉⠉⠙⠛⢿⡄⠀⠀⠀⠀⠀⣰⣧⡔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠙⠋⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⢀⣀⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⡴⠶⢦⡄⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠙⢿⠀⠀⠀⣿⠛⠉⠉⠉⠉⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⢹⠀⠀⠀⣿⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣤⣤⣤⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⢀⣀⣤⠤⣦⠀⠀⠀⣴⢤⣤⣀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⡴⠞⠋⠁⠀⠀⣿⠀⠀⠀⣿⠀⠀⠉⠙⠳⣄⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣸⣆⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠒⠛⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠷⠶⠶⠦⣄
⠀⠀⠀⢠⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃⠀⠀⣠⠴⠶⣄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠶⠦⣄⠀⠀⠘⣧⠀⠀⠀⠀⡿
⠀⠀⠀⠈⠳⢦⣤⣤⡏⠀⠀⢸⡃⠀⠀⠈⡇⠀⠀⢸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⢹⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠳⣤⣤⠞⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠳⣤⣤⠞⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠑⡆⢄⠀⠄⡆⠀⠖⠠⢀⠀⡔⠁⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠘⢄⠀⢀⠀⠀⠴⠀⠀⠳⠀⠐⢂⢀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢨⠘⠀⠀⠐⠚⠋⠉⠀⠀⡤⠀⠀⠀⢃⠀⠰⢠⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄⠣⠀⢘⠀⠀⠀⠠⠀⠀⠀⠀⡗⠚⢨⡀⡠⠀⠓⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠂⠁⠁⠀⠀⡀⠀⢁⠀⠆⠀⠧⡤⠤⠫⠂⠀⠴⢅⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠠⢀⠀⢀⠄⠠⠊⠀⠸⠆⡀⠜⠀⢢⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣆⣤⣶⣶⣦⡣⣑⣀⡼⠗⢁⠔⠁⠀⠀⠀⡄⠐⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠈⠻⡏⢙⣿⣿⣷⠒⠀⠐⠂⠁⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠂⠂⢆⠻⢿⣧⠽⠋⠀⠀⠀⠀⠰⢲⢶⢶⢞⠣⠁⠀⢀⠀⢀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠢⠀⢀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⡌⢀⠂⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⢋⡶⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠠⠂⢀⠌⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠓⡦⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⠁⡠⠊⠀⠁⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⢰⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⢡⢀⡞⠱⡄⢀⠖⠉⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠈⠀⠀⠁⠀⠐⡀⠀⠆⠀⠀⠀⠖⠄⡀⠀⢠⠁⠈⠃⠘⠀⡰⢌⠓⠠⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⢀⡀⠠⠚⠍⣁⠦⠤⢤⠀⡖⠀⠀⠀⠊⠀⢴⢉⠁⠲⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡈⠀⣰⠁⡀⠀⠀⢁⠇⠀⠀⠀⠐⠄⡀⠴⠀⠀⠁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣙⢲⠁⢀⡰⠐⢄⠘⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢇⠀⢀⠄⠀⠀⠉⠁⠘⠦⣀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡠⢄⡀⢤⣠⣲⢿⡿⠶⠾⠟⠳⠼⣯⡍⣛⢦⡄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣘⢿⣿⠓⠀⠁⠀⠀⠀⠀⠀⠈⠛⢥⡿⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡍⠉⠀⠀⢀⠐⠦⣀⠀⠀⠀⠀⠀⢨⢷⣔⣸⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢾⠗⠀⠀⠂⠁⠀⠀⠀⠀⢰⠀⣯⣥⠂⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⠀⣿⡈⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⢸⠃⠀⠀⠀⠀⠀⠀⠀⣿⢱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⣲⢁⡇⠀⢀⠔⠀⠀⠀⡠⠄⠻⡾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣾⠲⠃⠁⠤⠴⠤⠀⠀⠀⠀⢻⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠔⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡀⠀⢠⡌⠘⠀⠊⠀⠀⠀⠀⠀⠤⠔⠁⠀⠈⠁⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠱⡀⢀⠀⢤⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⡠⠊⣡⠈⠃⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⡄⠀⡊⠉⣿⠇⠂⠀⠚⣉⣷⣄⠀⢀⢥⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠰⠀⠤⠡⢀⢀⡄⠀⠀⠁⠁⠀⠀⠀⠉⠲⡄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡸⠀⠀⠀⠀⠀⠀⠹⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⣀⣀⣀⡀⠀⣠⠎⡉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⢯⣳⠒⢦⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣀⡀⢱⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⢾⣹⣿⡿⡶⣿⡄
⠀⠀⠀⠀⢀⠀⣤⣄⣠⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠙⢾⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡜⠀⣼⣿⡷⢰⣼⠘⣧
⠀⠀⠀⠀⣆⠀⠬⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⡄⠀⠀⠀⠀⠩⠝⢩⠔⠋⠀⢸⡏⣬⡇⡼⣻⢀⡿⣆
⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⣄⠀⠀⠀⠀⢣⡀⠀⣀⢸⣷⣿⣿⣷⣥⢪⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⣳⡦⣄⠀⠀⢑⠤⣍⣾⡯⣿⡽⣡⣡⡟⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢁⣀⠈⠔⠁⠈⢱⡀⠈⠓⡌⢣⣾⡿⢟⣿⣥⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢰⠛⠉⠀⠀⠀⠀⠀⡜⠀⡠⠊⣰⡿⣫⣞⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⣀⢀⡆⠀⠀⠀⠀⠀⣀⠞⢠⠏⠀⢰⣿⣱⡿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⠐⡞⠻⠿⠷⠤⠤⠂⣠⠜⠁⠀⠆⠀⠀⢸⡈⣿⣧⡔⢰⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣠⢦⣼⡀⠀⠀⡀⠳⣝⣯⣽⣿⠟⠩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠬⠉⠙⠛⠛⠛⠊⠀⠀⠀⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡄⠀⠀⠀⠀⠀⢀⠀⢀⠤⠀⢀⢠⠄
⠀⠀⠀⠀⠠⠊⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡴⠊⠉⠉⢢⠤⠀⠀⠀⠀⠰⠋⠀⠀⡄⠀⠠⠃
⠀⠀⠀⠰⠁⠘⠀⠰⡆⠀⠀⠀⠀⠀⡀⠀⠀⡇⢠⠏⠀⠀⠀⢀⠎⠀⡆⠀⠀⠀⠃⠀⠚⡁⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠜⠀⠀⡀⠀⠂⠀⠄⠀⠄⠀⠀⠀⡏⠀⠀⣀⠴⠋⠀⡰⠀⠀⠀⠀⡠⠀⠀⣀⠀⠒⠚
⢀⠀⠀⢀⠊⠀⠉⠩⠀⠀⠀⡀⠀⢲⠀⠀⠀⠀⠈⠈⠉⢀⡀⠤⠚⠁⠀⣀⡀⠀⠁⠀⠊
⠃⠄⢠⡆⠀⡤⠐⠁⠀⠀⠀⡄⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠜⠁⠀⠈⠀⠀⢢⠖⠋⠈⠐⡉
⢠⡖⠐⠇⠐⠁⠀⠀⠀⠀⠈⠁⣀⣀⣀⡠⢀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠐⣀⠠⠇⠀⠀⠀⣰⠁⠊
⠀⠀⠃⠀⠠⠈⠀⢀⣀⣀⣀⣈⠉⠩⠄⠒⠉⠀⡠⠊⠀⠀⠐⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠤⠄⠈⢁⠄⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠐⢀⠖⠈⠁⠀⠀⢸⠄⠠⠀⠀⠌⠌
⠂⠂⠀⠐⠰⠂⢰⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁
⠀⠀⠀⠐⠀⠸⠁⠀⠈⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠸⠀⠀⠀⠀⣠⠄⢠⠀⠁
⠀⠀⢀⡠⠈⠰⠀⠀⠀⠀⢀⡆⠀⠐⠉⠀⢀⣀⠤⡊⠀⠀⠀⠀⠀⠀⠀⠐⣾⣥⣷⢿⣶⠛⡦⠤⣠⠞⠁
⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⢒⡖⠀⣸⠋⠓⠚⠓⠒
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁
⠀⠀⠀⠀⠊⢈⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠖⠁⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠘⠀⠀⠌⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠌⠀⠛⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⡃⠀⠀⠀⠄⢠⠌⠀⢠⠀⡀⠀⠀⢀⣁⠄⠐⠀⠀⠐⠁⠈⠁⠀⠀⡜
⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣩⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠢⠞⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢖⡄⠀⠀⡸⢰⣜⠏⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣫⠔⠊⠁⠀⢀⠎⣧⠀⠀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢰⣤⠀⢀⡠⢫⠎⠀⣇⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⡠⠚⠣⣑⢦⡀⣀⠠⠤⣐⣯⢟⢅⠀⠀⠋⢱⡄⠈⠳⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢣⠹⡔⠂⠉⠀⡀⡌⢑⣝⠢⡀⠈⠸⠳⣦⣹⣿⡦⢄⣀⣀⣀⠀⠀⢀⣀⡀⠌⠈⡆⠀⠀⠀⢀⡠⠤⣤⡀
⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⣈⠤⠗⠀⠐⠒⠇⠒⠉⠆⠱⢌⠑⠤⢀⡀⠬⠋⡠⠚⡷⡶⠦⢤⣤⣤⣤⣤⡴⠊⠁⠉⠉⢰⡁⣀⡀⠈⠈⢑⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠑⠦⢄⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠉⠹⣱⡄⠀⠀⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠸⡀⠀⠀⢀⣤⣤⣄⠀⠀⣿⠀⠀⠀⣏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡰⢡⠒⡌⢻⡄⠀⠀⡀⠦⠤⠄⠀⠀⠤⠓⠀⠀⠃⡒⡢⠹⡇⢠⠉⢿⠀⡀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠃⠀⠉⠀⡿⠀⠀⠀⠈⠁⠀⠒⠒⠒⠒⠉⠀⠀⣇⠈⠀⠀⢿⡎⠀⠀⠣⣽⡒⠤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣰⠧⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⡰⢀⣀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⠐⣷⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠉⠚⠥⣲⣇⠺⠬⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠤⠃⣽⠶⠞⠋⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡠⠞⠑⠢⢄⡈⠑⠒⠛⠑⠢⠤⠴⣦⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠦⠤⠖⠚⠓⠂⠉⣀⠤⠒⠙⠤⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⡏⡄⢠⢱⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠄
⠀⠀⠀⢶⣵⡤⣤⣿⡶⠀⠀⠀⠀⢾⣏⣿⡇⠀⠀⠀⠀⠀⢿⣿⡊⠀⠁⠁⣾⡿⠀⠀⠀⠀⢰⣿⣦⠀⢀⣤
⠀⠀⠀⣾⣿⣗⣾⣿⣷⠀⠀⠀⢺⣿⣿⠿⡿⣿⢿⡟⠀⠀⠰⣿⢟⣛⣛⡻⣿⡆⠀⠀⠀⠀⠘⠛⠋⢁⣾⠇
⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠩⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⢤⢄⣀⠀⠀⠀⠀⣠⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⣰⣏⢨⣷⣾⡱⣹⣆⠀⠀⣠⣲⣎⠿⢘⣣⣷⣿⠀⠀⠀⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⢆⣀⣀⠀⣿⣿⡷
⠀⠀⣿⣿⠇⠈⠁⠸⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⢸⣿⣶⡦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⣼⠿⡿⠋⠛⠀⠀⠀⠀⠀⠸⠉⠉⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠦⠀⠀⠀⢀⠔⠀⠀⠀⠀⣷⣾⠿⣿⡁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡉⢛⢳
⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠹⣿⣴⡿⣿⠀⠀⠀⠀⢠⢨⠛⢻⠠⢠⢠⠀⡀⠀⠀⠀⡖⢀⣠⠘⡆
⠀⠀⠰⠦⣤⣄⣠⣤⠼⠀⠀⠀⠀⠘⠛⠉⠘⣆⠀⠀⠀⠰⢾⢿⣿⢏⢺⢿⣾⣷⠇⠀⠀⠈⢁⣿⣿⣇⠁
⠀⠀⠀⠸⠁⠇⠘⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⣜⣹⣿⣷⠀⢀⣀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⣽⣿⣆⣀⣀
⠀⠀⠀⠀⢐⣦⣄⠀⡼⠁⠀⠀⠹⣿⣿⡿⢰⣥⣿⣷⠀⠀⠀⢀⣰⣾⣿⣦⡀⠀⠀⠀⠀⣠⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⠋⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⢶⣿⣿⣿⣭⣿⣿⡷⠀⠀⠀⠙⠛⠛⠿⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⢀⡀⠀⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠌
⠀⠀⠀⠀⠀⢠⠁⠀⠀⣄⢹⠀⢀⡀⠐⠀⠀⠈⠠⠀⠀⠀⠃⠄⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⡀⠀⠇⢸⠀⠀⠈⠀⠀⠀⠀⠀⢈⠀⠀⠀⠄⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⣇⣀⢀⢠⣤⢾⣴⡦⠀⢰⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢙⡉⠈⠀⠀⠀⣀⣤⣄⡀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠰
⠀⠀⠀⡀⠀⢈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠹⠗⠀⠀⠀⠙⠛⠀⠐⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⡄
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡟⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢀⠀⠃⠀⠠⠀⠀⠀⣞⠆⠃⠀⠀⢁⠌⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⢩⠀⠀⠀⣺⣁⠀⠀⣠⠀⠀⠀⢱⢄⠀⠈⢒⠃⠀⡂⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢀
⠀⠀⢀⣀⠀⠠⠑⠁⡀⠀⠌⠀⡀⠙⠂⠠⡴⠉⠂⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠀⠀⠠
⠀⢀⠀⠈⠀⠀⠀⠈⠁⠈⠂⠀⠵⠘⠁⡂⢀⠀⠀⡀⠀⡌⡀⠁⠀⠀⠀⠀⠀⠋⠀⢠⠀⡀⠊⠀⠀⠁⠀⠈⠄
⠀⠊⠀⠀⠀⠀⢂⠄⠀⠀⠁⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⠀⠀⠀⢠⠀⠋⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠄⠉
⠀⠀⠀⠀⠠⡔⠓⠀⢀⠶⢤⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠤⠘⠂⡜⠀⠄⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠢⠀⠈⠒⡈⠀⢠⡅⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⠰⢤⠈⠁⠀⠀⠀⠀⠀⠤⠀⠆
⠀⠀⠀⢀⠴⠀⠂⡀⠆⢢⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠁⡂⠢⠆
⠀⠀⠀⠒⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⢁⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆
⢀⠀⠀⠀⣠⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠂⠊⠀⠀⠐⢄
⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠘⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣉⣿⣉⣗⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠸⠉⠁⠀⠙⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⠁⢸⠂⠀⠀⠘⣸⠜⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⠀⠀⠴⢲⡋⠁⠀⠈⠉⢹⠙⠀⠤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢀⣿⢡⠐⠀⠄⠀⣾⣁⠀⣀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡅⠈⠀⠀⠀⢉⠙⣿⠓⢪⠒⠁⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠳⡀⠀⠀⠀⠀⢙⠯⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢔⡌⠇⠀⠀⠀⠈⠤⢂⡴⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠈⠀⠇⠀⠀⠀⠀⠀⣤⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠊⠳⠀⠀⠀⠀⠀⠀⠘⠒⠒⣀⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠀⠂⠈⠣⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣂⡠⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣖⣀⠀⠠⠄⡨⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠘⠁⠈⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣟⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠃⢸⠁⠀⢱⠈⠉⠉⠃⠇⠀⡀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⠄⠀⠀⠈⡄⠀⠀⠀⢄⠀⠀⠀⠃⠡⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠸⡄⠘⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠳⡀⠙⠀⠀⠀⠀⡀⠀⠀⠈⠣⠀⠄⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠚⠛⠛⠻⠛⠲⢤⣂⠀⠀⠀⡎⢦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠋⠀⠀⣠⠖⠛⠙⠳⣄⠀⠈⡆⠀⠀⠇⠈⡇⠀⠀⠀⡀⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠁⡸⠁⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠔⠁⠀⢀⡴⠀⠀⠀⠀⠑⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠁⠀⠀⣠⠔⠂⠁⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣀⠲⠄⠀⠐⡀⠀⠀⠀⠀⠀⡄⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠀⠀⠀⠀⠈⢆⠀⢁⠀⠀⠠⠞⠃⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠉⠛⠒⢒⡡⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡼⠎⠈⠂⠀⢢⡀⠠⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠘⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⢀⠒⠋⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡊⠀⢠⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡤⠊⡀⠀⡠⠒⡁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠁⢀⣀⠤⠖⣱⠀⠀⠀⠀⡀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣾⡅⠀⠀⣼⠁⠀⠀⡠⠂⠀⠈⣧⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠣⠈⠁⠠⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢰⠃⠀⠀⠀⢻⠀⠀⠀⠠⡀⠀⠈⢧⠀⠀⠘⡏⠀⠀⠀⢀⠀⢀⠁⡀⢀⣈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠺⠤⠀⠐⠁⠀⠂⢸⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢆⠀⠸⡆⠀⡞⠁⠀⠴⠁⠈⠅⠛⠘⠃⠈⠉⠁⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢦⠀⠂⠈⠀⠀⡇⠀⠀⠀⢀⠤⠤⠆⠰⡴⠤⠀⡃⢯⠴⠓⠢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠶⠀⢼⠇⣆⠀⠀⡀⢠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⢀⡴⠏⠀⠘⠄⠓⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⢰⠆
⠀⠀⠀⢸⡆
⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠃
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⢀⣠⠖⠀⠿⢿⣧⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⣀⠀⠠⣿⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡌⠉⡀⠀⣹⣿⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣿⣄⠛⠁⠘⠋⠈⢿⣿⡏
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣷⠀⠀⠀⢀⣼⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡉⠁⠀⠀⠺⢿⡿⠛⠓⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⣿⡀⠀⣠⣤⣾⣷⣶⡾⠆⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⢻⣿⣧⣴⠟⠛⢻⣿⣿⣆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⣼⣿⣿⣿⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣰⣦⣀⠀⠿⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢻⣧⣽⣿⣷⣴⣷⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⠉⠙⠛⢻⣿⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣉⣀⠀⠀⠀⠀⢾⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⢻⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡿⠁⠀⠙⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡁⠸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠈⣠⣀⠙⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣿⣿⡷⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⣬⠻⠟⠀⣰⣏⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣠⣤⣭⣿⣿⣷⠀⠀⠀⠰⣄⣼⠇⠀⠀⠘⣿⡀⠀⠀⠘⠻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠿⠀⠈⠁⢀⡿⠏⠀⠀⠀⠀⢻⣿⣶⣄⣀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⠁⢀⣠⣶⣶⡟⣁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣶⣾⠟⠋⠀⠸⠋⠀⠀⠀⣀⠀⢻⣤⡀⠀⣿⣇⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠟⠁⢀⣽⣿⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇⢸⠇⢀⣿⣿⣿⣿⣧⠀⠀⣠⣶⣦⣄⣤⣧⡄⠀⣶⣶⣾⣿⡇⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠰⡆⠀⠈⠻⢿⣾⣿⣿⣇⠀⠹⣿⣿⣿⣿⣿⠇⠀⣿⠛⠛⠉⠀⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⠟⢹⣿⡀⠀⠻⢿⡟⠹⡟⠀⠀⢿⣦⣾⡷⣦⣶⣄⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠠⠀⠀⠀⠀⠈⠟⠀⢸⣿⡇⠀⠀⣸⣇⠀⣶⣄⢀⣤⠛⠛⣶⡾⣿⣿⣷⢸⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⡿⠋⢻⣿⣿⠁⠀⠀⣤⣄⠻⣿⣿⡟⠋⠁
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠿⢇⣤⡀⠀⠀⢀⣀⡀⠀⠀⡿⠃⠀⠐⠈⠀⠀⠀⠻⠿⠇⠀⠀⠈⠁⠀⢸⣿⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⣿⣿⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⡼⣦⡀⠐⣿⣿⣧⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⠀⣈⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠉⠀⣈⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣤⣿⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣠⣿⣿⡋⠈⠉⢿⣿⣿⣿⠇⠀⣦
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠒⣤⡜⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⡿⢿⣿⠀⠀⡏
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠒⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠀⠀⠀⠀⢰⡇⢸⣿⠇⠠⡿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠰⠟⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣷⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣴⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢹⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡠⠈⢻⣾⣷⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⠉⣤⡴⠂⠈⠉⢹⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⣿⣿⣶⣦⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⣞⠉⣿⡇⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⡀⠀⠀⠀⣿⠀⠹⠟⠉⠀⠀⠀⢀⣶⣤⣿⣶⣿⠇⠀⠀⠀⠀⣀⢸⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⠀⢠⣾⠿⢿⣷⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣤⣤⣼⡿⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⢻⣷⠀⠀⠻⡿⢧⣀⣼⡿⠛⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠛⠻⠗
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⠰⠿⠀⠀⠀⠀⣼⣿⡿⠁⠀⠿⠀⢹⣿⣿⣿⣿⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠛⠋⠉⠀⠀⠀⢠⣄⣀⣠⣴⣾⣿⣿⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠚⠁⠈⢻⣶⣠⣿⡿⠟⠛⠉⣹⣿⠁⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣧⣼⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢿⣯⣽⣿⣿⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⠿⠟⠻⡿⠛⢻⣿⠷⣤⣄⣀⣸⣧⣀⣀⣀⣀⣇⣀⣼⣄⣈⣿⠿⠿⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⢠⡄⠀⠀⠀⠀⠀⠀⠈⢻⠟⠉⣿⣿⠉⠹⣿⣿⣿⠟⢿⣿⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⣹⣿⣧⠀⣼⡇⠀⠀⠀⢀⣠⣤⣶⠁⢠⠀⠈⢻⣦⠀⠈⠻⣿⣀⣼⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣃⣀⣸⣿⣟⠛⠋⣠⣤⣶⣶⣦⣤⣽⡧⠀⠘⠟⠁⠉⠀⡀⢠⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠻⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠛⠿⠀⠙⠛⠀⠀⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣬⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⠀⠘⠃
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠧⠀⣰⣦⣠⣾⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠁

⠀⠀⠀⢠⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠋⠉⠻⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢣⠀⡀⠀⡀⠊⠩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣆⠀⢡⠀⠌⠀⢂⠄⠾⠁⠧⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠂⣱⣤⠔⣻⠆⢲⡇⠀⡀⠀⡎⠠⢀⠢⢀⣀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠠⠐⠂⠉⠀⠘⣄⠠⢀⣸⡘⡀⠀⠀⠀⣀⡘⣥⠀⠈⠃⠀⠀⠸⣄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢁⣲⡿⠵⣄⠀⢠⡄⡀⠉⠐⠀⡀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⢨⢀⠆⠀⠀⠀⠀⢀⡠⠒⠀⠀⣠⢿⣏⣿⠀⠀⠉⠙⡛⠃⠀⠀⠀⠈⡄⠀⠀⠀⣠⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠔⠹⡀⠀⠀⠀⡇⢀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠐⠖⠂⠤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⡀⡆⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⡀⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠇⠀⠖⠉⠀⠀⠀⢀⠘⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡨⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠏⠷⣔⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡀⠐⢃⠀⣠⣲⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠲⠴⠾⡿⡁⢜⢀⠀⣀⠀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢉⡆⠀⢠⠀⢧⣹⣁⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢣⣥⣰⢰⡄⡴⠮⠟⠤⠐⠟⡠⣜⡀⠀⠄⠀⢴⣀⠤⢾⡄⣸⣛⡠⡄⣽⠙⠋⠁⢀⣀⣗⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠀⢐⣋⠼⢏⠠⡈⡄⠈⡀⠠⢲⡍⠀⠈⠀⠠⡈⠠⠀⢈⠻⠗⠙⣀⠒⠻⠿⡦⡞⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠴⠄⠀⢄⠀⠀⡀⠉⠠⠎⠑⠀⠀⠀⠐⠀⠈⠥⣄⠀⠁⠂⠐⠔⡂⠻⠞⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⣶⠖⠂⠈⢀⣴⢾⠃⡀⠀⡈⠀⣁⠀⠀⢀⣀⠀⠀⠂⣀⠀⢀⣠⣉⡩⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢱⣾⠀⣾⡤⣤⠈⢀⠁⠀⠈⠁⠉⠩⠁⢈⣱⠿⠅⢀⣿⠑⠹⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠘⠁⡸⢦⠀⠀⠐⠲⢒⠀⠀⠀⠘⠻⣾⡉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⠀⠀⠘⠃⠀⠈⡁⠚⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣀
⣿⣏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⡤⠴⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠙⣷⠖⠛⠉⠉⡴⠋⠀⠉⠉⠙⠻⢦⣀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠎⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢠⠏⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⣿⣂⣠⣤⣀⣀⣾⡷⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠚⢹⠋⠉⠉⣱⠈⠉⠲⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠁⠀⠀⠉⠋⠉⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠸⡄⣀⠀⠐⣄⢀⢀⣠⠆⠀⡼⠀⠀⠀⢀⡴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠳⣬⣲⣭⠭⠤⠤⠤⠤⠖⢚⣁⣠⠴⠚⠉⠀⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠉⠉⠉⢉⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢰⡟⠓⣤⠶⣄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢠⡇⠀⠀⠀⠈⢷⡄⣡⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣤⣄⡀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀⠈⠙⠷⣦⡾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡴⠖⠛⠛⠛⠛⠿⣤⡀
⠀⠀⠀⠀⢠⡟⠀⢀⣤⣤⣄⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣀⣀⡀⠀⠈⠻⣆
⠀⠀⠀⠀⢸⠁⢠⡏⠀⠀⠈⠙⢷⣄⠀⠀⠀⠈⢷⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⠞⠋⠉⠉⠙⠻⣦⡀⠀⢹⡆
⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠸⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⠁⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇
⠀⠀⠀⠀⠘⣇⢹⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠹⣜⣧⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡾⠁⣀⡀⠀⠀⠈⠳⡄⠀⠀⢀⣘⣷⣸⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠘⢮⣷⣦⣄⣀⣠⠾⠃⢀⣠⣾⠵⠚⠁⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠙⢿⣿⡶⣤⣤⣤⡴⠾⣋⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⡊⡄⢠⠀⠔⠀⠀⢤⠄⣀⣄⠀⢃⠐⡤⢤⠄⣲⢠⠀⡆
⠀⠀⠀⡄⠠⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⣤⣤⠔⠀⠀⠀⢀⣀⡀⠀⠀⠀⠐⠌⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⢀⠄⠘⠂⢠⠀⠀⠀⠂⠉⠑⠀⠀⠀⠀⠀⠀⠃⠀⠃⠄⣀⠀⠀⠈⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⠀⠠⢄⠀⠀⣫⢞⣠
⠀⢀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⡄⠄⠀⠀⠀⠈⠱⠛⠁
⠐⠨⠁⠂⠀⠀⠐⠈⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠔⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⢠⠀⠈⠁
⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡡⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠄⠀⠀⠐⠁⠀⠀⠀⣐⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠅⠀⠀⠀⠀⠀⠠⠄
⠀⠀⡴⢋⠂⣠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠑⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⠐⠒⠂⠀⠀⠀⠀⠠⠔⠁⠀⡀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠆⠀⠀⠀⠀⠀⠑
⠀⠐⢀⠐⢠⡶⡄⠀⣴⢦⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⢤⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄
⠀⠘⠛⠀⠈⠛⠁⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠉⠉⠉⠉⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣠⣤⣶⣶⣶⠶⠶⣶⣤⣀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⢀⣴⠟⠋⠁⠀⢸⡷⠀⠀⠀⠈⠙⢿⣦⡀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣴⡟⠁⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠙⣿⡄⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣸⡟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠿⠀⠀⠻⠿⠿⠶⠶⠶⠶⠶⣿⣿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠃⠀⠻⠷⢶⣶⣤⣄⣀
⠀⠀⠀⣠⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⢻⣧⡀
⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠻⢷⣦⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⡟⠋⠉⠛⢷⣄⠀⠀⠀⠀⢀⣼⡟⠃
⠀⠀⠈⢿⣤⣤⣤⣤⣤⣴⣿⠃⢀⣤⡀⠀⢹⣷⡶⠶⠶⠶⠿⠿⠶⠶⠾⠿⢿⣿⠀⢰⣶⠄⢈⣿⠿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠙⠁⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣴⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁