Bastard sword Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢿⡿⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠒⣾⣷⠒⠀⠀⠀⠀⢾⣷⠀⠐⠀⠠⠀⠀⢺⣷⠀⠀⠠⢠⡄⠠⠐⠒⣿⡖⠂⠀⢠⡄⠀⠀⠀⢼⣷
⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣽⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣸⣯⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⢰⡶⠶⠶⠶⢾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣈⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⡛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⢿⡏⡌⢉⣛⠋⠉⠉⠛⡻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⣛⣛⣛⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠦⣿⣿⣾⠟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣾⣛⣛⣛⣛⣓⠐⢛⢺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⣿⠋⠛⠻⠶⣄⢀⣀⣠⡿⠉⠿⣷⣶⡾⢏⣩⡭⠉⠠⠁⠀⡈⠍⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⠭⠂⠐⢷⣾⡉⣍⣧⣨⢴⡀⢬⣿⣯⣵⠞⠀⠤⠰⠐⠫⠖⠠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⣂⡄⠛⢿⣿⣝⠻⣶⣽⣿⡿⢟⡡⣾⡀⠉⠁⠀⠀⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣣⣾⠟⣅⠐⣶⠶⣿⣿⣿⣿⣿⣯⡽⠛⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣯⣆⣼⠏⠴⣶⣾⣿⣿⣿⣿⢿⡃⠀⣠⠶⠋⠀⠀⠀⢶⣼⣁⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣇⡀⣏⣀⣰⣾⣿⣿⡿⠉⠁⢸⣧⠀⣿⡀⠀⡀⣘⣥⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡹⢿⡿⠿⡏⠒⢺⣿⣿⣿⠗⠀⠀⣸⣦⢈⣿⣶⣶⣿⣏⡿⢿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠤⠙⢤⣿⡴⢋⣘⣿⣟⠀⠀⠀⣿⣿⣯⣾⣿⣿⣿⣿⣧⣄⣱⣎⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠢⢸⡓⢿⡻⣿⢟⣴⢀⢸⣻⣿⣻⠷⠟⠿⣻⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣣⣼⣋⠀⣸⠃⢺⡭⠁⢠⣷⣽⣾⣿⣿⣝⢾⢿⡟⣿⣿⡗⠈⡟⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⢡⣿⠖⡋⢶⢛⣸⣙⣙⣻⣋⣵⣾⡷⠘⢇⡻⣿⣿⣦⢧⡜⣇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢃⣿⡷⠆⢠⣿⣿⣿⣿⣿⣿⠻⠛⢿⡇⠱⣟⣱⣽⢿⣿⣯⣀⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢃⣾⣁⡀⠐⠿⠿⣿⣿⣿⣿⡇⢰⠀⢼⡇⠠⣿⣿⣿⠎⢿⣿⣿⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣶⣦⠀⢸⣿⣿⠻⠷⠦⠶⢾⡇⠀⣨⣿⣿⣆⡘⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣱⡽⠟⢉⡀⠚⢿⠑⣤⣄⠠⢰⣬⣇⡝⢻⣿⣿⣿⣄⠐⠢⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢛⡿⠋⠀⢠⢿⣇⣁⠀⢀⣿⣿⣠⣨⣾⣿⣿⡟⠋⢙⡿⣽⣧⣦⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⠳⡀⠀⣿⣾⣿⣾⣿⠿⣿⣿⣿⣿⡟⣨⣽⣷⢿⣯⣴⡣⢛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠈⠀⠀⣀⣀⣼⣯⣴⣿⣿⣭⡿⢟⣿⣿⣿⡿⢋⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⣿⣿⣿⣿⣶⡶⠄⠰⢿⣿⣿⣿⣿⣽⣾⣿⣿⣿⠿⠯⠄⠵⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⢀⢀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢀⠄⣰⠊⣁⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠉⠀⠁⣴⣏⠁⠉⠳⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣄⠀⣯⠙⠀⠠⠀⠰⣔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡷⢿⣿⡿⢃⡲⣤⡀⢠⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣆⡚⠁⠱⠖⠀⠈⠁⡀⠈⣶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡀⠉⠉⢃⣀⠐⠀⠂⡎⢀⡀⠀⠐⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢠⠀⠀⠖⢋⡀⠀⠀⠀⠀⠢⢁⠀⡈⠅⡀⠀⡀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⢻⣿⢿⡀⠀⠀⣴⢶⣆⡀⠀⠿⠉⢀⡄⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡐⣾⢿⠆⢈⣂⠐⢁⡄⠀⠙⠀⠀⣨⣦⠀⠀⠀⢀⠤⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⣠⢾⣾⣿⠿⠕⠊⢁⣤⠭⢩⣄⠀⠰⢂⠈⢺⣤⠄⢀⠓⢀⣤
⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠀⢀⡖⢀⣠⣷⣧⠔⠀⣽⣿⣶⣶⣷⣶⣀⠿⠋⣭⠄⣀⠈⠀⣀⣿⡷⢎⣀⣹⠃
⠀⠀⠀⠀⠀⣠⣤⠀⢢⠸⣇⡀⣊⠀⠈⠉⠉⠁⢤⣀⣿⣿⡥⣾⣙⡟⢁⣈⠀⣤⠠⡌⠏⠀⠸⢣⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠴⢃⡄⠘⢿⡛⢠⡀⠀⢀⣤⠞⢹⣿⡿⡇⠙⣿⣿⡟⠀⣀⣴⣾⠁⠀⠀⠀⠟⣷⡴⠖⠉⠀⠀⠀⠀⠀⠐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⢃⡀⠻⢦⡷⠿⢥⡿⠀⢸⠀⠃⣀⣠⡙⠁⠀⢺⣄⣿⣄⠑⠂⠀⠁⢤⣏⡁⠀⠀⠐⠒⢶⣖⠒⢚⣯⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⣈⠄⠀⣸⠁⠀⡟⠀⠀⢻⣿⠾⡶⠀⠀⠻⢾⣿⠷⠄⠀⠊⢸⣿⣶⠤⠄⠐⢒⣿⢧⠐⠾⡅⠙⡛
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠸⠀⠀⡇⠀⠀⣼⠃⡘⠀⠀⠀⠀⠀⢹⠀⡀⢀⠀⢸⠛⠇⠀⠀⣄⠁⠄⠀⠐⢆⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⢠⠁⠀⣼⠃⠀⠀⠀⡸⢣⡄⠀⠸⡀⢉⠀⠀⢸⡆⠀⠀⣨⠀⠙⠃⢒⡠⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢠⡿⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⣼⣥⠀⠀⠘⠀⡄⠘⡇⠀⠦⠿⠛⠲⢦⡅⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣿⠀⢸⣷⣤⡔⠀⠀⢀⡾⣿⠀⡇⠀⠀⠀⡇⠀⣀⢐⣧⠆⣐⣀⠟⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡀⠀⠰⠿⠖⢀⢉⡀⠀⣼⣶⠟⠀⠃⢠⡇⠀⠀⠀⠀⠀⣿⠛⢿⠀⠈⢻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠔⠁⢰⠶⠤⣶⣿⠋⠙⢀⣵⡿⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠀⠀⠲⣶⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢹⡖⢸⡅⢀⣿⠋⢹⣿⠃⠀⠀⢀⠉⠁⠀⠀⢸⠀⡿⠿⠿⣿⡂⠈⠛⠿⢶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠲⡄⠀⠀⠲⠜⠉⠿⠇⠀⠸⠏⠀⠀⠀⠤⠈⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⡀⠈⠲⣤⣤⣴⢆⣠⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠸⠀⢈⣻⡶⠄⠀⠀⠀⠠⢄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠁⢀⡄⢹⡟⠂⠈⠿⠿⠿⠦⠀⢤⣀⡀⠀⠠⠦⠀⠀⠀⠀⣀⢀⣸⡄⠠⡀⣰⣶⣶⣮⣿⣄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢸⣷⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣟⣙⣿⠟⢛⡁⠰
⠀⠀⠀⠀⣀⡠⠴⠂⠉⠁⣴⣶⣿⣧⠀⠀⠀⠘⡴⠀⠀⠀⠀⠉⢹⣷⠦⠴⠧⠀⠀⠀⠀⠀⣀⢿⣦⠀⣀⣿⣿⠛⠓⡀⡌⢻
⠀⠀⠀⠀⠀⠀⣤⣴⣧⠀⠀⡈⠀⢹⡀⠀⠀⠁⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣈⣙⣷⣷⣿⣿⠿⠛⠋⣀⠸⠻⠃
⠀⠀⠀⠀⠀⠴⠿⠿⣿⠷⠦⠴⢖⣛⠛⠋⠀⠀⠉⠈⠉⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⣿⣿⠏⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠚⠓⠒⠟⠙⡿⠟⠀⠐

⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⠆
⠀⠀⠈⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖
⠀⠀⢠⣤⣀⣀⣠⣀⣀⣀⣼⣧⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠘⠛⠉⠉⠙⠉⠉⠉⢻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⣿⡷⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣠⣶⠃⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢰⣿⡇⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⣿⠀⢠⣿⠀⠀⠈⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⡏⠀⠀⢸⣿⣇⢸⣿⡄⠀⠀⠘⣧⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢸⣿⡇⠀⠀⢸⣿⣿⡆⠻⣿⣦⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣤⣾⡿⣿⡇⠀⢹⣿⣧⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠸⣿⣷⡙⠛⠛⣵⡿⠁⠀⠀⣿⣿⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢿⣿⢀⣾⡟⠁⠀⠀⢀⣿⣿⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣾⣿⠀⠀⠀⠀⣼⡿⢹⣿⠏⠀⠀⢰⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣦⣴⣏⠀⠀⢀⣿⣿⣿⣤⣀⣤⠞⡉⢀⣿⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠾⣿⣿⣦⣤⣾⣿⢻⣿⣿⣿⣿⠀⡇⢸⣿⡿⣶⣾⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡛⢿⣿⠀⠻⣿⣿⣿⠀⡷⠄⢀⣴⡿⠉⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣧⣀⠁⠰⣆⠙⠛⠋⢰⠁⣴⣿⣿⡀⢀⣠⡿⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⣠⢀⣿⣿⣷⣦⡈⠻⣶⣶⣿⠀⠻⣿⠟⣿⡿⠋⠀⠀⠀⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢹⣿⣧⠀⢹⣿⣿⠷⠖⠀⣰⣿⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡙⠛⠋⠁⢸⣿⡏⣴⢿⡟⠁⢀⣴⣾⣿⣿⣀⠀⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣄⠀⠘⠋⢸⣿⠘⠀⠀⣿⣿⣿⠟⠛⠛⠋⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠘⡆⠀⣿⡀⠀⠀⠈⠉⣡⠖⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣰⣿⠇⢀⣵⠀⣽⠹⣦⣤⣤⣾⣿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡟⠀⣾⣿⢾⣿⡀⢻⣿⠏⣿⡿⢸⣿⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠄⠘⠿⠄⢉⣤⠆⠁⣰⠟⠡⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠴⠒⡒⠒⢤⡀⠀⠀⠀⠀⡤⠼⠥⣄⠀⠀⠀⠀⠀⡟⣟⠀⠀⠀⠀⢀⡤⣒⣶⣿⠶⢝⣆
⠀⠀⢰⡥⠤⠤⠤⠤⠤⣽⠀⠀⠀⢺⡭⠭⠭⣭⠇⠀⠀⠀⢸⣓⠻⡄⠀⠀⢠⢫⣮⣅⡿⡿⣟⡯⡅
⠀⠀⠸⣏⣙⠾⠭⢞⣉⡿⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⢻⡸⢂⡇⠀⠀⢸⢸⢉⣏⠛⢽⣆⡇⡇
⠀⠀⠀⠓⠚⠢⣠⠞⠓⠃⠀⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⣸⠀⠸⡇⠀⠀⠀⠣⣙⠭⠾⠶⣊⠜⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢀⡴⡟⣇⡟⡷⣄⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⢀⡠⠤⠦⠤⡀⠀⠀⠀⠀⢀⡴⠋⠻⣷⡄
⠀⠀⠸⡍⠉⠉⠉⠉⣹⠀⠀⠀⠀⢸⠛⠛⠛⢳⢤⡀⠀⠀⢯⠤⡤⠤⡠⢬⠇⠀⠀⠀⡞⠀⠀⢀⡼⠁
⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⢀⣀⣸⣄⣀⣀⣿⣊⡀⠀⠀⠘⡆⢇⢠⠇⡞⠀⠀⣠⣴⡹⠶⠒⠉
⠀⠀⠀⠘⠒⠒⠒⠚⠁⠀⠀⠀⠓⠶⠶⠶⠶⠶⠚⠁⠀⠀⠀⠙⠚⠚⠚⠁⠀⠀⠙⠚⠀⣠⣄⡀
⠀⠀⠀⠀⠀⣀⠴⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⢠⣞⣓⣞⣳⡄
⠀⠀⠀⡼⠭⠤⠤⠽⡄⠀⠀⢰⠋⠉⠛⠉⠙⠉⠉⢳⠀⠀⠀⠀⠀⣀⡞⠑⠺⡀⠀⠘⡟⢛⡻⢿⠃
⠀⠀⠀⣟⢲⡚⢲⠛⡇⠀⠀⣿⡯⢽⡯⠟⢭⣿⠽⣿⡇⠀⠀⢀⠴⣅⠈⠓⢼⠁⠀⠀⢸⡥⢒⡟
⠀⠀⠀⢸⡀⡇⡟⣸⠀⠀⠀⠙⠛⠿⠭⠭⠭⠽⠟⠛⠀⠀⠾⣙⣆⣈⣧⠴⠋⠀⠀⠀⠀⢟⣹⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⢒⣟⣲⡀⠀⠀⣠⠒⢄⣠⠒⣄⠀⠀⠀⣾⢿⠆⣜⣳⡄⠀⠀⠀⠀⠀⣴⣽⡷⠦⡀
⠀⠀⠀⢀⡴⠋⠀⡯⢽⣻⠃⠀⢸⠁⡸⠈⡇⡹⠈⡇⠀⠀⣿⠸⣤⠏⠘⢦⠀⠀⢀⡤⣪⣾⠞⠀⢀⡗
⠀⠀⢰⠋⠀⣠⠞⣠⠞⠁⠀⠀⠈⢦⠃⡰⢧⠃⡴⠃⠀⢸⠁⠀⢹⠀⠀⢸⠀⠀⢗⡿⠚⠁⠀⡠⠊
⠀⠀⠀⠑⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⢸⣀⣀⣸⣀⣀⣸⠀⠀⠈⠳⠤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢋⡏⡄⠀⠔⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡰⠁⠀⠐⠀⢠⠇⠀⡡⢢⡄⢀⡴⢊⠭⢍⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡴⢡⠀⡇⡆⡆⡿⠀⠸⣇⠀⠀⠘⠀⣇⣶⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣇⠰⡀⢧⢸⠸⣿⡀⢆⠉⠳⣄⠐⡄⠻⣝⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠁⠈⠢⣳⡈⢆⢣⠻⣿⣌⢧⢀⠘⣷⠸⡄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⡅⠀⠀⠉⡡⡄⢱⣌⢿⣾⣷⣧⠹⣿⠘⣾⣦⣿⠇⡇⣈⠀⢸⡆⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣺⢩⣛⢦⣿⣿⣿⣶⣿⢀⣿⡿⣫⠞⠁⡡⢀⣼⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠠⡸⠖⠀⢸⠂⠹⣿⣿⣿⣇⣾⣯⡟⢁⣴⣿⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⠀⠀⢤⠀⢿⡄⢆⠹⣯⣿⣿⣿⣿⣷⣿⣴⣆⡀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⠍⢹⠒⡟⣰⠺⢿⣶⣷⣿⣿⠟⠛⠋⠉⠉⠁⠱⠉⠃⠙⠒⣶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠿⠃⣼⠀⠀⠁⠐⣠⠼⠛⠁⠁⠀⠠⠀⠀⠀⠰⢆⠀⡀⠀⣼⢡⢺⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠷⠶⠶⣧⠤⢤⣞⣭⣀⡀⠀⠀⠀⢀⡴⣋⠀⢤⠶⢦⠶⢾⣧⣷⡘⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡗⠀⣤⡤⡀⢀⢸⡀⢀⢮⣹⡆⠀⣨⣾⠛⢿⣃⡏⠠⠄⠀⣼⣿⡍⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡇⢀⡛⡇⠀⣀⣸⣧⣐⣊⣿⢷⣿⡁⠠⠀⠘⣿⡷⢦⠤⠼⠋⢙⡃⢁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠲⠶⢒⣻⠿⢛⠅⠈⢛⢽⠞⠻⢿⣴⣶⠟⠃⠐⠀⠁⠀⠃⠀⠀⠴⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢉⣛⠻⠿⢰⡖⡠⠹⠆⢀⣈⠛⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢻⣼⠇⠶⠂⠉⠑⠒⠀⢿⣽⠇⠀⠰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡉⡴⢦⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠙⣛⡴⠇⠉⠀⠀⠀⠀⠀⠀⠀⠄⠙⢷⣼⠞⢃⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣥⣄⢻⣿⠇⡀⡀⢠⡀⠀⣠⠀⠐⢄⡈⢿⣿⢃⣼⡛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣜⠷⠞⣸⣿⣎⣤⠁⠀⠀⠀⠀⠀⣰⣷⣽⣿⣷⡾⠷⠟⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⣈⡛⢿⣿⣿⡿⠷⡄⠀⠠⠾⠻⣾⣿⣿⣿⣀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⢯⡽⢠⣿⣿⣥⠀⠀⠀⠀⠠⣤⣻⣿⡿⢿⣽⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⡄⠁⢸⣿⣷⡀⠀⣠⣾⣿⣿⠏⢀⣴⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⢸⣿⡏⢇⣰⣛⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⣿⣿⣧⣼⣽⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⡆⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠾⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⣊⡑⢢⠀⠀⠀⠀⠀⣀⢤⡤⠤⣄⣠⠤⡄
⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⣠⣖⣂⣁⣀⣲⣄⠀⠀⠀⠀⣞⣁⢀⣹⣌⢱⡄⠀⠀⠀⣈⠞⠀⡞⠺⣡⡞⢾⣽
⠀⠀⠀⠀⣢⣤⠤⢤⠤⡤⠤⢤⣤⣼⡀⠀⠀⠀⠀⢧⠒⠒⠒⠒⢲⠞⠀⠀⠀⠘⢧⠶⣖⣒⠶⢲⠋⠀⠀⠀⢸⡒⠼⠼⢄⠿⠼⠚⡏
⠀⠀⠀⠀⢱⣊⣉⡲⠮⠭⢷⠭⣙⣤⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⣎⢉⣱⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠣⠤⠍⠮⡇⢙⡴⠵⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣦⠙⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⠔⢋⠤⡤⠤⠤⣉⢆⣴⠒⣆⠀⠀⠀⠀⣠⠔⠊⠻⡍⠙⢏⠐⠢⡀⠀⠀⡤⠒⠉⠉⠉⠙⠒⢄⠀⠀⠀⠀⠀⡴⠊⠉⠉⠲⣄
⠀⠀⠀⠀⠎⡞⢙⣚⣁⣡⢞⣕⣋⡀⣇⢸⠀⠀⠀⣜⠁⠀⠀⠀⠘⣄⣸⠦⠤⠜⠀⠘⡤⠤⠤⢤⠤⠤⠤⡞⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡆⡘⠨⠈⠁⠹⢉⠟⢲⢲⠉⠉⠀⠀⢠⠋⠣⡀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠸⡀⢇⠀⡇⢸⢠⠇⠀⠀⠀⠀⠇⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠰⡌⠳⡉⣉⣢⣀⡴⢁⡞⠀⠀⠀⠀⢸⠲⢄⣨⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣘⡀⢃⣁⡜⠀⠀⠀⠀⣀⠇⣹⠦⠔⠋
⠀⠀⠀⠀⠀⠈⠓⠢⠤⠭⠔⠒⠉⠀⠀⠀⠀⠀⠸⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠯⣅⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡆⢠⣆⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢠⣴⡒⢒⣖⠲⠦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⣃⣀⣀⠀⠀⠀⠀⠀⠀⢩⠩⣇⡼⠼⡄⠀⠀⠀⠀⢀⠴⢄⡀⣠⠔⢄⡀
⠀⠀⠀⠀⢰⢛⡥⠞⠓⠦⠥⠭⡻⢄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣾⡻⣹⠀⠀⠀⠀⡈⠀⣍⠖⠒⢦⡀⠀⠀⡰⠋⠈⡆⠙⢇⢸⡀⠙⢦
⠀⠀⠀⠰⣏⡜⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⣀⢀⣱⣄⣀⣀⣤⠞⡛⢩⡁⠀⠀⠀⡞⠁⠨⠁⠀⠀⠀⢹⠀⠀⡇⠀⢠⠁⠀⢸⠀⡧⠀⢸
⠀⠀⠀⢠⣋⣀⣀⣀⣀⣀⣀⣀⣀⡸⠀⠀⠀⠘⠢⢤⣤⣄⣀⣤⠤⠴⠊⠀⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⢸⠀⠀⠱⣄⠸⠀⣀⢮⡀⠇⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⡇⠀⠀⠀⢈⠀⠀⠀⠀⠑⠎⠁⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣿⡒⢢⠀⠀⠀⠀⠀⢸⢾⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⢱⢦⡀
⠀⠀⠀⠀⠀⣀⡠⠤⣐⣵⢿⡿⠊⠉⢣⠀⠀⠀⠀⡜⣈⢘⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⣹⣳⣲⡹⠀⠀⠀⡴⠲⡤⠒⠒⡤⠐⠲⡤⠤⢤
⠀⠀⠀⢰⡯⣒⡲⣩⣓⠵⠊⠀⠀⢀⡜⠀⠀⠀⠸⡩⢍⠉⠈⡆⠀⠀⠀⠀⡰⠗⠒⠉⠁⠀⣠⠇⠀⠀⢸⣄⣈⣁⠠⠄⣁⣀⢀⣁⣀⣠⡇
⠀⠀⠀⠺⣈⠞⠉⠁⠀⠀⠀⠀⡡⠊⠀⠀⠀⠀⠀⢱⢀⠇⠸⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢮⣽⣚⡈⣉⣐⣒⢒⠮⣉⣳⢯⡽
⠀⠀⠀⠀⠘⢆⡀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠸⡄⠀⠀⠑⠤⣄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠢⠤⠒⠒⠠⠤⠁⠂⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⠤⠃⠀⠀⠀⠀⠈⠳⠴⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠄⠀⠀⠘⢌⠢⠀⠀⠰⠀⠠⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠊⠀⠘⡠⠀⠀⠀⠠⠑⠀⠀⠀⠐⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⠀⡰⠁⠀⢹⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠁⠄⠘⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠐⢀⠁⠳⠉⢦⣠⠁⠀⠀⢸⠀⠲⢀⡶⢱⠀⢀⠀⠸⠎⠀⠀⡄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⡉⠀⠀⠹⡀⠀⠀⠸⠀⠀⠰⠁⠀⡇⠈⠴⠃⠐⡆⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢾⠣⣄⣠⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠀⡇⠂⠀⠀⢠⠃⠀⠀⣀⢀⡀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⢇⠀⠀⢠⢃⣄⣀⣤⡔⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⢈⠼⠊⢰⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠙⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⢀⠔⢠⠀⠀⠱⠁⠀⠰⠁⡾⠁⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣅⣀⠀⠀⠀⠀⠀⠀⠃⠄⠂⠖⠄⠀⡀⠈⠠⠄⠂⠀⠀⠠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⢐⡖⣻⣉⣉⠉⣩⣽⠶⣀⠀⠀⣀⣠⠤⢤⣀⡄⡦⠀⡠⢦⠐⠠⣤⢄⠂⠠⠾⠿⢷⣿⡂⡀⢰
⠀⠀⠀⠀⠀⠀⠹⠷⠼⠷⠶⠚⢧⡇⢠⣾⣶⣛⡻⣄⣵⢠⣼⠃⣓⢲⠀⢘⣧⡂⠚⢺⣇⣀⡀⡶⡞⣮⣭⠴⣾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠙⠛⠛⠁⠀⠙⠶⠖⠛⠉⠙⠳⠚⠋⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⠚⢀⠘⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣶⣤⠀⠀⠀⠀⠀⠉⠢⣤⢦⢄⣠⣤⠈⣄⣤⣤⣬⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠏⢿⠀⠀⢀⠇⠴⠆⠀⠠⢀⡴⠒⠳⡎⢁⠈⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⣘⣁⡴⠆⣀⣈⣆⢠⠀⠿⣟⠷⢾⡇⠸⡆⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣸⣏⣉⠳⢾⣩⣾⣤⠋⠵⠈⢷⣤⣾⡇⠀⠻⣼⣦⡐⣦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡍⡧⠤⡑⢦⣿⠟⠁⠀⠀⠀⠘⠿⡿⠁⠀⠀⠙⣿⡃⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⡇⢏⠠⢭⣿⣿⡀⠀⣠⡄⠀⠀⢠⠁⠀⠀⠀⣸⠿⣠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⢰⣅⠈⠐⣿⢿⣿⣧⠀⣩⣥⣤⣤⣼⣠⣀⠀⣠⣯⠺⡇
⠀⠀⠀⠀⠀⠀⠀⢩⢁⣿⡿⠉⠓⠂⠁⠀⣡⣏⠛⠉⠉⠨⠍⠭⣿⣿⣿⣽⠿⣀⠁
⠀⠀⠀⠀⠀⠀⠐⣯⠇⠘⠎⠀⠀⠀⢰⣎⡅⠉⡙⠀⠀⠀⠀⡛⠛⡟⢿⣆⠑⢦⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣯⠜⠀⠈⠀⠀⠀⢸⠀⠉⠹⠀⠄⠀⠀⠀⣇⠀⡏⠙⣿⠑⠀⠈⣳⣾⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡀⠀⠀⠀⣻⠀⠀⠀⣂⣠⣄⠀⢀⣿⡧⠀⠀⢻⣄⠀⢠⢷⡟⣡
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⢀⣴⣶⣾⠀⠀⠀⣸⣿⠛⠠⣿⣿⡆⠀⠀⠘⣿⣶⣿⡏⠗⡏
⠀⠀⠀⠀⠀⠀⢸⠀⣰⢏⣴⣿⣿⡿⡇⠀⠁⠀⣸⡏⠀⠀⠘⢿⣧⡐⠀⠀⠘⣿⠿⢤⠸⠃
⠀⠀⠀⠀⠀⠀⠈⠺⣿⡿⠛⣿⠋⠀⡇⠀⠀⠀⣿⡁⠀⠀⠀⣨⣝⣧⠡⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⡇⠀⠀⢿⠓⢶⣶⢿⣿⠀⠀⡰⣿⢟⠻⡟⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠀⠀⢸⠏⣺⣿⢼⡏⠠⣴⣷⣁⡞⢡⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣠⣼⡎⠛⢹⣾⣿⣶⣯⡭⣽⣀⣾⣶⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣴⣾⣿⣿⣿⣿⣠⣯⠽⣿⣿⣿⡀⠀⠉⠈⢿⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⣤⣖⣿⣿⣿⣿⣿⣿⣿⠿⠈⠉⠀⠀⢹⢟⣿⣇⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣤⣀⣸⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣠⣴⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠛⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣿⣿⣿⡿⠿⠟⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡴⢂
⠀⢰⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⣶⠁
⠀⠘⣿⡇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠧
⠀⢠⣀⣆⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣦⣤⡶⠁
⠀⠀⠙⣿⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣿⣿⡟
⠀⠀⠀⠹⣿⣦⡠⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢰⣦⡂⢧⣼⣷⣿⠟
⠀⠀⠀⠀⠈⢿⣷⣷⠀⠀⢸⠀⠀⠀⢠⠀⠀⢀⡀⣐⢀⣄⣘⢿⣟⣾⠟⠛⣁
⠀⠀⠀⠀⠀⠀⠙⢿⣶⣁⢸⡄⠀⢠⣼⠀⠀⢴⢄⠸⣿⠁⢻⠖⠋⠁⣀⡼⠥
⠀⠀⠀⠀⠀⠀⡀⠈⢿⣿⣿⣇⣴⡹⣿⠀⠀⣤⢠⢀⠛⢀⡎⠀⢀⡶⠟⠀⠀⠀⢲⡶⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠹⡿⣿⣾⣿⠄⣥⡇⠀⢆⠄⠸⠁⠀⣸⡁⠀⣦⣀⠀⢀⠀⠀⠀⣀⣴⠟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠤⢈⠻⣿⣷⣼⠇⣴⢸⠀⠀⠀⢰⠋⠀⠀⠘⠻⠿⠿⠷⠚⠛⠉⠁
⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠙⢿⣷⣥⣼⠀⠀⠀⡇
⠀⢱⡄⠒⠻⠿⠷⢶⣶⣶⠶⠤⢠⣀⡀⠀⠀⠨⡻⣿⡆⠀⢸
⠀⠀⡡⠀⠀⣀⣠⣄⣈⡀⠀⠀⠐⣦⣌⣤⣀⠀⠈⠛⢧⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⢀⣀⣀⣀
⠀⢰⠃⠀⠀⠨⣽⣿⣿⣿⣶⣶⣲⣾⠟⢀⣽⣷⣆⣠⠾⠲⠃⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠿⠿⠟⠉⠉⠉⠉⠁
⠀⠈⠙⢣⣴⡟⠀⠤⠞⠛⠉⠉⠁⠀⠀⡀⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠿⢿⣉⠉⠉⠁
⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠽⠒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⣤⡶⠀⢀⣼⣿⣿⡿⠂⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⡌⠅⢨⡁⠀⣈⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢀⣤⣬⡤⠄⠉⢣⣄⠀⠀⠀⠀⢀⠀⠀⠀⡠⠖⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠞⠛⢣⠀⠀⠀⠉⠀⠠⣄⣀⡘⠇⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠂⠀⠀⠀⣣⠀⠀⢉⠀⢀⣾⠟⠛⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡇⠀⠀⠀⢸⡀⠀⠘⠀⢸⣿⣦⣴⣿⣿⣿⣷⡤⠤⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⣼⠃⠀⠀⣷⠀⠻⣿⣿⣿⣿⡟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡿⠀⠀⢄⠉⠀⠀⠀⠛⠀⠀⠀⠉⡉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠻⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⣄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠦⠀⠀⢄⠈⠰⠤⠀⠒⢐⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⡁⢀⠄⠀⢀⠀⠀⠀⢀⠐⠀⠀⠀⡐⠊⠀⠈⠸⡀⠀⠀⠀⠀⠐⠀⠈⡀⠄
⠰⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⠃⠀⠋⠀⡎⣉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠑
⠀⠀⠐⠒⠒⠚⠁⠀⠀⠀⠀⠀⠊⢲⠂⢑⠤⠘⠁
⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⠀⣀⡀⣀⡀⢀⡀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢰⣷⠘⣇⠁⢹⠀⣇⡀⡏⢹⢸⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠼⠻⠴⣬⠇⢸⠀⡇⠀⢧⡼⠸⣼⠃⣧
⠀⠀⢠⡀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠌⠸⣧
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠷⠴⠆⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⠁⠁⠀⠉⠈⢲⡀⠀⠀⠀⠘⠟⠛⠲⢴⠿⣠⡒⠶⢅⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠦⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⡎⠱⣄⡀⢐⡀⠕⠒⢬⡧⠃⠀⠀⠀⠀⠀⠀⠀⢄⡐⠢⠀⣀
⠀⠀⢛⠀⠀⠀⠠⠈⠀⠈⠀⡀⡉⠀⠀⠀⠀⣤⠀⠐⠃⠐⠓⠒⢬⡀⢂⣤⠈⣠⠀⠀⠐⠀⠀⠀⡀⠄⠉
⠀⠀⠀⠈⠀⢁⠂⠀⠐⡀⠖⠃⠀⠀⠀⠀⠃⠠⠤⠦⣀⠐⢁⠝⢊⠀⠀⠈⠈⣀⣢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣷⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠻⣿⣧⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣼⠀⠀⠀⠀⢻⣿⡇⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡆⠀⠀⠀⢸⣿⠇⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣄⣀⣠⣿⡿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠈⣿⣿⣿⣿⠃⠀⢀⣾⣿⠏⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣿⣿⣷⣶⣿⣿⡟⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸⣿⣿⡻⣿⣿⣿⣿⡇⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⢀⣼⣿⣿⡇⠸⣿⣿⣿⣿⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠘⠛⠁⢰⣿⣿⣿⣿⣿⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⡄⠀⢰⣿⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⣿⣿⠃⠀⠈⠛⠀⢻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣸⣿⠀⠀⠀⡀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣻⠀⠠⡄⢏⢧⠐⡀⠙⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠀⣶⣿⣿⡇⢀⡀⠀⠀⠀⠣⠀⢸⡄⠈⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⢹⣿⣿⣿⣿⣇⠁⠀⠒⠒⠒⠒⠒⠛⠉⣁⡤⠒⠀⠈⠉⠉⢀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⢳⠒⠓⠂⠀⡀⠀⡸⢦⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠈⣦⣤⣄⠀⠀⢀⡏⣠⠈⢙⡳⢦⡤⣄⣀⣀⣀⣤⡤⠤⠆⠒⠃⡀
⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣶⣤⣾⣧⡇⢸⠸⣡⣼⢇⡐⠂⠐⠀⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡼⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠙⠿⠿⠿⣿⠻⠿⠿⣿⣿⣼⣿⣇⣀⡀⣠⢼⣋⣴⡡⠇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⠀⠀⠠⡀⠀⠈⠛⠪⠿⠭⠬⠭⠭⠿⠖⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠉⠐⠒⠒⠂⠘⠑⠒⠀⠤⠤⠤⠤⠤⠤⠀⠤⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣥⡶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⣤⡦⣰⡄⠀⠀⢰⡦⢦⣰⣤⣤⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⠀⣶⠓⣦⠀⠀⠀⠀⠀⣤⡀⢀⣠⡀⢠⣄⡀⣀⡀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠀⠙⠒⣿⡄⠀⠀⣿⠀⠑⠾⠟⠛⠃⠚⠻⠟⠘⠛⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⢀⡿⠁⢈⠀⣯⠀⢰⠀⣤⢀⠀⡾⢀⣄⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠟⠀⡇⠀⠋⠀⢿⢹⢠⡇⢸⡇⠀⡁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠑⠈⠁⠁⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢓⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠂
⠀⠀⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀
⠀⢀⠤⠠⣤⣠⣇⡔⠇⠀⣀⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠤⠤⠤⣄⡀⠀⠀⢀⡠⠤⠀⠒⠂⠀⠀⠉⠀⣠⡴⢿⡀
⣤⣯⣤⡚⠀⠀⠈⡟⠉⠲⡀⠀⠀⢱⠀⠀⠀⣀⠤⢄⠀⠀⠀⢠⠖⠊⠉⠁⠀⠀⠀⠉⠘⠒⠢⣄⡙⣦⠀⡸⢤⣂⡀⠀⠀⠀⠀⣤⡼⢟⣴⣾⠇
⡇⠠⠀⠙⠶⢤⠴⠖⠒⠲⠿⣤⣤⣞⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠒⠄⠀⠀⢀⡐⠀⡂⡀⠂⠘⠏⢹⡆⢰⠆⢤⣿⣋⠐⠒⢚⣩⡴⠟⠋
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢻⠶⠇⠀⠀⠀⠀⠀⡀⠀⠀⣸⣦⣤⣄⣄⣠⣄⣠⣦⣠⣦⣶⣶⣞⣿⠀⠀⠒⢄⠉⣁⠴⠟⠋⠁
⢸⠀⡆⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣧⠀⠀⠨⣀⠀⠀⡇⠀⢾⢀⡙⠓⠛⠳⠶⠛⠷⠞⢛⣋⡭⠖⣻⠏⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠛⢆⡀
⠘⡄⠁⠀⠀⠀⠀⠀⡔⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⣭⡭⣭⣭⣭⣭⣭⠭⠴⠖⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠸⠀⢀⠨⡸⡄
⠀⠉⠛⠛⠛⠓⠒⠺⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣈⠀⠀⠈⠇⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡘⠲⠂⠠⢀⠉⠛⢦⣄⠀⠀⠀⠀⢷⠀⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣠⣴⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠰⠞⠃⠀⠘⠀⠀⠀⠀⠀⠀⢀⡞⠱⠀⠀⠀⠀⠐⠢⡀⠈⠳⣄⠀⠀⠘⠇⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⢋⠉⢊⠈⢉⡏
⠀⠀⠀⠀⠀⢀⣘⠃⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡀⠀⠀⠀⠀⠈⠢⡀⠈⣆⠀⠀⠀⠃⠀⢀⡀⠸⠀⠀⠀⠀⠀⠠⡐⠠⠑⢨⠅
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠁⠀⠀⢀⣠⣶⠶⠛⠚⠋⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡏⠰⠀⠀⠀⢠⣀⣴⠾⠿⠋⠁⠀⠀⠀⠀⠀⢰⠀⠀⡈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⢀⠢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠂⠀⠀⠀⢀⡿⠀⡀⢈⣤⡶⠛⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⢰⢬⠁
⠀⠀⠀⠀⠀⠀⠀⡆⢉⣻⣦⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⢸⣃⣴⠾⠛⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⡠⠦⠴⢤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡤⠶⠛⠿⢫⡥⠅⠀⠦⢤⡀⠀⠀⠀⠀⢀⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢀
⠀⠘⠀⢤⠀⠈⡇⠀⠀⠀⠀⠀⣀⠠⣤⡄⢠⠶⠤⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⠚⠀⠀⠀⠀⣀⠀⢀⣿⠀⠀⣠⣤⢴⣤⣤⣤⢴⡄⢠⠀⠀⠀⠈⢳⣿⣄⠼⠶⣤
⠀⡆⠘⡆⠀⠀⣿⠀⠀⠀⣠⣾⠟⢁⡽⠓⠉⠉⠛⠛⢴⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣫⣽⠀⠀⠈⣽⡇⠉⢉⢻⡸⡇⣸⣤⠀⠀⠀⠀⠋⠀⠈
⠀⠃⣴⠃⠀⠀⣿⠀⠀⢰⠻⠏⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⡀⠀⠁⣀⡠⢤⣶⠿⡿⣋⠁⣴⠼⠃⣤⠀⢸⣏⣤⣸⣄⣧⣷⣿⠃⠀⠀⠀⠀⠘
⠀⢸⠋⠆⠀⠀⡟⠀⠀⠘⢾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⠿⡏⠉⢀⣬⠥⠌⣻⣯⣭⠶⡞⢻⠃⠀⠘⡆⠀⠉⠉⠉⠀⣼⠁⠀⠀⠀⠀⠀⢢⠤⠬⠉
⠀⢸⣠⡇⠀⢰⡇⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠀⠒⠒⠒⠁⠀⠀⠀⣳⣟⠦⠴⣤⣾⡿⠛⠋⠀⢀⡷⠋⠀⠀⠀⢷⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⡂⣀⠰⠊
⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⣄⣀⣀⣉⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⣆⣰⠇⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠋⠀⠀⠀⠀⡀⠔⠄
⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠⡄⠲⡀
⠀⠀⠀⢈⢧⠀⠀⠀⠠⡤⠤⠤⠤⢤⡄⣀⣀⣀⣀⣈⣐⣄⠀⠀⠀⠀⡤⢀⣤⣤⣴⠾⠿⠛⠉⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣣⠀⠈⣢⡀
⠀⠀⠀⠘⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢉⡀⠀⠙⡀⠀⠀⠔⠉⠝⠉⠁⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⢀⣀⣀⠤⠼⢧⡽⢤⣾⠿⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⢦⠀⠀⠀⠀⣀⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡆⠀⠀⠀⠀⠀⠀⢰⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⣴⡟⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⡀⠀⠀⢠⣿⠃⢀⡞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⣷⣄⠀⢸⣿⡄⢸⡄⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣗⣤⣀⠀⠀⠀⠀⠀⠈⠻⢿⣧⠈⢻⣧⣼⣥⣼⣷⣦⡀⣸⡆⠀⣀⡄⠀⡠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⠒⢦⣀⣀⠀⠀⠙⢷⣼⣿⣿⣭⣿⣿⣯⡱⣬⡥⠔⠉⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢷⣶⣤⢿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⠿⠒⢛⣛⠻⠿⣿⣿⣿⣿⣿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠄⠘⠛⠋⠉⠀⣴⢿⣭⣄⣄⣾⣿⣿⣿⣿⣿⣿⣏⠙⠛⠿⢿⣷⣆⠢⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⣶⡿⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⠉⠉⠉⠙⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠀⠛⠛⠛⠛⠚⠛⠒⠤
⠀⠀⠀⠀⠀⢠⣷⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢟⣁⠀⠀⠀⠀⡨⣿⣿⣿⣿⣹⣿⡄
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣷⡈⠿⠓⣤⣤⠠⣧⣿⣿⣿⣿⣷⢻⣿⡄
⠀⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡋⠺⢃⣉⣙⣠⣿⣿⣿⠟⠀⣿⣯⢿⣿⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⡿⠋⠀⠀⢸⡿⣾⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢠⣷⢄⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢩⠓
⠀⠀⠀⠀⢀⡤⠊⠁⠀⠠⢄⠘⢶⠂⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣫⣴⠾⠃⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⢠⣾⡄
⠀⠀⠀⠀⢸⡀⡀⠀⠓⠒⡢⠤⠤⠾⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠾⡋⢻⡴⠏⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢿⡾⠇⠿⣤⣤⣦⠉
⠀⠀⠀⠀⢸⣿⠩⣀⡴⠊⠀⠀⠀⠀⠀⢮⣀⡀⠀⠀⠀⠀⣤⠂⣰⣟⢻⣅⡦⠟⠉⠀⢀⣰⡿⠃⠀⠀⠀⠀⠀⣆⠚⢧⣼⡇⠨⣶⡄⠒⠉⠉⠛
⠀⠀⠀⠀⠀⠙⠢⠿⠇⠀⠀⠘⠷⠜⠀⠈⣬⡃⠀⠀⠀⠀⠙⢀⣷⡜⠋⠁⢀⢀⣶⣿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠹⣿⣯⡀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⠀⡀⠀⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠻⣀⣴⣷⣉⣴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⡉⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠶⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢾⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠦⠀⠀⠃⡀⠂⣨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡆⠀⠀⢾⠆⡠
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⢀⣀⣐⢃⣠⣴⠾⢃⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⢿⡀⢻⣇⠀⠀⠰⢺⠃⣾⣷
⠀⠀⠀⠀⠀⣾⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⣮⣽⣿⣿⣧⣬⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⣿⡖⠏⠉⠓⠀⠀⢼⣯⣥⠂
⠀⠀⠀⠀⠀⢉⠀⠀⠠⣿⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣿⣏⣉⣙⣛⣭⣼⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠈⠳⢀⣰⡙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⣤⡿⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣠⣴⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠⡄⠀⡀
⠀⠀⠀⠀⠀⢠⣧⣤⣴⠶⢠⣾⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠲⠦⠟⢿⣻⡆⠀⠀⠀⠀⠀⠀⠀⢠⡶⣾⣷⣶⡿⣿⣿⣿⣗⠂⡄⠐⡀⠁
⠀⠀⠀⠀⠀⠘⢩⠟⠳⠶⠷⣬⣭⣵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠒⠂⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣹⣯⣷⣿⣛⣻⣿⣷⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⣴⣶⡖⢢⣾⡏⠀⠀⠀⠀⠀⠀⠀⠛⢶⣌⠙⢳⣤⣿⣿⠿⣋⣽⠃⣸⢳
⠀⠀⠀⠀⠀⠀⠀⣧⡐⢿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⠬⠁⠼⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⣿⠸⣦⣾⣿⡇⠀⡿⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢷⠀⠉⠀⣉⠹⠟⠃⠘⠃⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠛⠶⠾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⣶⣬⠓⣯⣾⡻⠛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣹⡧⠀⠀⢀⣼⣅⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢹⢻⡄
⠀⠀⠀⠀⠀⣠⠊⣿⣶⣶⡉⣭⢳⣾⣿⣖⣠⡇⠀⠀⠀⠀⠀⠀⠀⣿⡗⢩⣭⡧⠀⢠⣿⠧⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⣮⣤⡿
⠀⠀⠀⠀⠀⠛⢶⣿⣛⠻⣿⣶⣿⣤⢒⣽⡿⢋⣆⠀⠀⠀⠀⠀⠀⣶⠀⠀⢸⡇⠀⠈⡇⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⢃⠲⣼⠷⠆
⠀⠀⠀⠀⠀⠤⢂⠈⠙⠻⢿⣍⣙⠿⠼⢿⣤⡾⠛⠀⠀⠀⠀⠀⠀⣿⠀⣤⣼⡇⠀⠀⡟⢰⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡘⣟⣓⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⡠⠈⠙⠿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠉⢹⣷⠀⠀⣷⠈⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢫⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⣸⣯⠀⠀⢹⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣦⡜⣷⣷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠲⠤
⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⢡⣷⢸⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠂⡀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣇⣸⡟⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⣡⠔⠃⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠚⠛⠻⠿⣿⣿⣴⣶⡀
⠀⠀⠀⠀⠀⠐⣷⠿⠿⠿⠿⠿⢧⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠐⠊⠁⢀⣴⣿⣿⣿⡟⣻⠀⠀⠀⠀⠀⠀⠰⢖⣀⣀⠐⠠⠔⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⢀⡐⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⡁⠤⣳⡿⢻⣿⣽⡿⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢷⣦⣄⡀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣷⠾⣿⡿⠶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡻⢶⣬⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠈⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⢹⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⡟⡆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣦⢸⢸⠿⡆⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢰⢿⠇⡇⣴⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣿⠀⡼⠹⠘⢸⠀⣷⠀⠀⠀⠀⣶⡰⣭⡆⠀⠀⠸⠈⡇⣇⠏⢣⠀⣿⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣡⣾⢸⣧⣙⣡⣧⠸⣤⣿⠀⠀⠀⣰⣿⣷⣜⠃⠀⠀⣷⡆⡇⣼⣌⣋⣼⠉⣧⣜⣷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣼⡟⣷⢧⡄⡇⢹⣥⣨⢣⣿⣾⠀⢀⢴⣿⡏⣿⢻⡦⡀⠀⣷⣿⡜⣅⣬⠋⢸⢰⡹⡿⢿⣧⢿⡇
⠀⠀⠀⠀⢠⡄⠀⢸⣦⣹⣷⠏⣿⠀⣿⣷⢻⡏⣿⠇⡿⢀⠎⣼⢹⡇⣿⢼⢃⣵⡀⢿⠸⣳⢹⡏⣾⣿⠘⣷⠻⣾⣿⢬⡇⠀⢠⡄
⠀⠀⠀⢠⡿⠀⠀⢸⣟⣹⡏⢆⡏⢸⡏⡏⡌⠑⡎⡀⡇⢸⡟⣿⠘⣇⢹⣧⣸⣿⡇⢸⢀⣿⠸⢡⣿⢻⡆⢣⢁⢹⣏⣾⣇⠀⠀⢿⡄
⠀⠀⢠⠏⣧⠀⣠⠇⡻⣿⣱⡟⣾⢸⡇⢣⢻⣄⠁⡇⢿⡜⣧⡇⣶⢻⡀⣿⣿⣼⣣⡟⣼⠈⣰⡟⡏⢸⡇⣧⢿⡆⣿⣿⠹⣄⠀⡸⢹⡄
⠀⠀⢸⢠⡘⣿⣡⣞⢠⡿⠿⢹⢿⢸⡇⣼⣆⠛⠆⢿⢸⣙⣿⢡⢿⣾⡇⢹⡇⣿⠉⡇⡿⠸⠋⣰⢧⢸⡇⣿⠘⠃⢿⡈⣣⣎⣿⢃⡌⡇
⠀⢠⣼⢼⡇⣹⡶⡽⣾⣷⣇⢸⡿⢸⡇⡟⡿⡜⡟⡌⣼⣿⢃⡿⢸⢸⣇⣼⡇⣏⠿⣏⢃⢿⢱⢿⢸⢸⡆⢿⠀⣼⣾⣇⢯⢶⣏⣼⢱⣧⡄
⢀⡾⢻⡏⣱⠏⣀⡰⣻⢿⡟⣧⢿⣸⠃⠀⠁⡇⡷⣱⢋⣿⣏⣷⡼⢸⡿⣿⢱⢟⣄⠹⣎⢾⢸⠈⢀⠘⡇⠿⣾⢹⡟⣿⣆⣀⠻⣟⢸⡟⣿
⣼⡷⣾⡿⣱⢇⣿⠾⣇⣾⠣⢻⣄⡿⢸⣧⢠⠃⣼⠃⢸⣿⡜⠘⢁⡾⢁⡏⡿⣾⠙⣦⡹⣦⢸⣠⣼⡆⣿⢰⡟⠸⣧⣼⠧⣿⡼⣞⢿⣗⢾
⡏⢻⣿⢣⢻⡘⣯⠘⡿⢣⡶⣸⣿⠇⣦⣿⢸⡾⡏⣶⠸⢀⡖⣸⢹⣧⣾⡗⣧⢣⡆⣼⢣⣿⢿⡇⣿⣰⠸⣿⣇⢶⡘⢯⠃⣽⢣⡟⡜⣿⡞
⢷⡟⢸⡸⠞⠄⣩⢞⣡⡞⣰⠿⡏⢸⣇⢻⠘⠀⡇⠙⠘⠏⡟⢉⠘⠛⡏⢣⠉⠘⠃⠛⠈⣿⠀⠁⡇⢸⡇⢻⠻⣦⠷⣌⠳⡍⢠⠳⢷⡇⣷
⠈⢿⡈⢧⠻⣷⣯⣞⣠⡾⢃⢸⠁⢸⡘⡏⣴⡄⣿⠀⡆⠀⢰⠞⠀⠀⠀⠈⠟⣧⠐⠑⠀⣿⠀⣆⢱⢙⡇⠘⡇⡘⣷⣌⢳⣽⣦⢟⡞⢀⡿
⠀⢬⣳⡌⢳⣿⢋⡞⣿⢣⣿⢸⣸⣇⠻⢠⡏⠀⡿⡄⠀⢸⡄⢶⠀⠀⠀⠳⠀⢹⡄⠎⣸⢿⠀⢹⡌⠟⣼⣇⡇⣿⡘⣟⢿⡙⣷⡞⢠⣞⡤
⠀⢸⣿⠇⢾⡻⣟⠠⣿⢸⣻⠸⣿⠘⡆⢸⢰⢰⡇⢰⣸⡿⡇⣾⢷⡆⢾⡆⢸⠂⣷⢰⡇⠸⠀⣌⡇⢸⠁⣿⢣⣟⡇⣿⢤⣿⢿⡁⣸⣿⡇
⠀⢸⡏⢧⡾⡁⣧⠃⣿⣸⢻⡇⢡⡄⣷⢸⢃⡟⢰⢸⡿⣦⢃⡟⠸⣳⢢⣿⠸⠁⡘⣿⢳⡄⢷⡘⡇⣿⢰⡅⢸⣿⡇⣿⠘⣾⢈⢧⡽⢹⡇
⠀⢸⣷⡜⢱⢃⣿⢷⡟⣿⡟⡴⢛⠃⣿⣴⡟⣠⢿⢸⡇⡿⣸⣇⢠⣏⡎⣿⣴⢸⡇⣿⡞⢳⣌⢻⣦⣿⠸⡛⢆⢻⡇⢿⡾⣿⡸⡎⣡⣾⡇
⠀⢸⡟⣸⠀⣼⣿⢀⡁⣿⢸⢱⡏⢸⢫⢏⣾⡟⡘⣼⠉⣵⡿⡏⣾⢏⡗⢹⡅⣼⠇⡿⢧⠎⣿⣦⡹⡝⡆⢹⡞⡇⣿⢈⡀⡿⣧⠀⣇⢻⡇
⠀⠀⢧⠻⢸⠇⣿⢘⢣⠈⣤⣾⠃⡾⠃⣎⢸⢱⢣⡇⣼⠹⡇⢳⡿⢠⢗⡟⡼⠁⣸⣧⠸⡜⡜⢂⢳⠘⣷⠘⣧⣥⢁⡞⡃⣿⢸⡆⢏⡾
⠀⠀⠈⢷⣼⡆⣿⠸⡾⣇⢿⡘⣸⢃⠸⡹⠘⣿⢸⡿⣏⣆⢳⡀⣷⠺⣬⢡⣽⣼⠋⣿⢿⡇⣿⠸⢾⠀⡘⣇⢇⡟⣸⣣⢇⣿⢸⣧⡾⠁
⠀⠀⠀⠀⠉⠃⠈⢧⡹⣿⣮⢡⡏⣷⡀⣧⡄⢻⠘⠁⣿⢙⣦⠳⣌⠷⠏⢣⡿⣱⡏⣿⠘⢠⡇⢠⡼⡄⣧⢻⡈⡿⣿⢋⡾⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠐⣦⡻⣍⣮⣾⡇⢿⣿⠘⠇⢸⠀⣷⠸⡎⣿⡆⠹⣷⣴⠏⢐⣯⣹⠇⣧⢸⡇⡞⠃⣿⡹⢸⣧⣽⣱⠟
⠀⠀⠀⠀⠀⠀⠀⢫⣳⡹⡏⢿⠀⡟⢸⣠⢰⣾⢰⡏⡄⣿⠘⣷⠀⢻⡏⢺⣘⠃⣿⢰⢹⠸⣇⠇⣄⠃⣷⢸⡇⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣥⢻⣾⡄⡇⣾⡿⡄⢿⡘⣧⡇⣿⠃⡁⣾⢸⣷⠸⡏⢸⣿⢾⣸⢰⡟⢸⣿⢰⣶⢸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣏⣣⢷⠉⡇⢷⢰⣄⠻⠇⣿⢠⣿⡏⣾⠛⣧⢻⢹⣿⠸⠏⣨⡄⣷⢸⢀⡏⣜⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠳⣏⢸⠸⣘⢧⠀⣿⠸⢹⣧⡟⢀⢹⣦⡟⣿⠀⠾⢹⠀⡇⣸⠟⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡻⠄⢿⡀⡆⣿⡼⣼⢹⡇⡿⢸⣿⡕⡿⢸⣠⡟⠰⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣍⣃⠘⣷⡉⢾⡕⣣⡟⣩⣼⢃⣉⣭⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣾⣷⡟⢞⣵⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠸⠇⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢻⠀⠀⠀⠀⡇⣸⠃⢀⠀⢠⡈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠁⠀⠀⣰⠃⠀⠀⡞⠀⢈⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠸⠁⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠚⢸⡆⠀⢰⡆⠀⠀⣠⠀⢀⡀⠀⠈⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣞⠀⠀⠀⢻⠀⠀⢸⠆⠈⠁⠀⠀⣇⡔⢰⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠋⢠⠀⡄⠀⠀⠀⣀⠀⠀⠀⣼⠀⢉⠀⢸⣧⡇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣼⠃⠀⡠⠀⢀⡀⠆⠀⢀⢉⠀⠀⣧⠁⠀⠈⠀⠏⠏⠀⢰⠀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣇⠐⡇⠀⠀⠁⠀⢸⣷⠀⠃⣾⠀⠀⠂⠈⠀⠀⠁⠆⠀⠀⠀⢸⢃⡁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁⣸⡆⣦⢠⠀⠀⢠⠀⠁⠀⠀⠛⠀⢀⢰⠀⡄⠀⣆⠀⠁⠀⠀⠀⠸⠃⢸⠆⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⡀⣠⠠⠈⡃⠞⠀⠀⠁⡀⠀⠀⢀⠀⢀⠸⠆⣆⠁⡞⠑⠀⡀⣤⠀⠀⣠⠀⠊⠀⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⢳⣉⠀⠁⠑⠰⠓⣠⣷⠇⠀⠰⡌⠂⠰⠀⡄⠉⠀⠇⠐⠾⠁⣸⠀⣶⠀⣶⠄⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠋⡤⠛⠐⣷⡀⠜⠿⣿⡏⣻⣧⡐⠁⢀⠀⢸⡇⠀⠀⠀⠀⢠⣘⡧⣶⠛⣷⣤⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡀⠘⠄⢀⡀⠀⣄⣀⠈⡄⠙⠉⣿⡄⠉⠀⡠⢁⡯⠀⢠⠀⣸⡟⠁⠇⠞⠟⢁⣀⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡄⠙⣻⡆⢨⢉⣠⣿⣾⣏⢀⣔⢃⠈⣁⠀⡀⠇⠋⠛⠀⠀⠀⠋⠅⢡⣴⡀⢸⡇⢦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠓⠉⠙⠛⢾⡌⠙⣿⠇⠁⠈⠛⠙⢷⢈⣤⣅⠀⣄⢂⣼⣷⡀⢰⣾⠆⡿⠃⣾⣿⠆⠘⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⢠⣿⡿⠂⠉⠁⠒⢶⡄⠀⣤⣼⡿⠋⠁⠀⠈⠙⢿⣿⡆⠀⠀⠆⠉⠘⠳⣦⣤⡠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⡒⣶⠞⣻⣟⡀⢀⠀⣀⣼⣮⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⣸⣆⠀⠀⢀⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠯⢉⣛⣛⡽⣿⣦⢠⠞⣿⣿⠦⡀⢀⡀⣰⡿⠿⣿⣿⣯⣾⣽⣷⣀⣫⣾⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠦⠤⠔⠒⠊

⠀⡀⣀⢀⣀⣠⣀⠠⣤⡀⣠⣀⢀⣠⣀⣀⣀
⠀⠀⠀⠈⠉⠀⠋⠀⠈⠈⠁⠈⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⢻⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⡑⡄⡈⠀⣴⠁⠀⠀⠀⢀⣀⣀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⣿⣧⠏⠀⣰⡆⠀⣠⡞⠿⡹⢡⣯⠶⢿⠋⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣳⣿⣿⣴⣿⣇⣸⢻⣡⣧⣿⣛⣃⡤⠊⠀⠀⠀⠀⣾⢉⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠺⢿⡟⢻⡿⢿⣿⣿⣾⡟⣧⣌⡵⠊⠀⠀⠀⠀⠀⢀⠙⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣬⡉⣍⢦⠈⠱⣾⣿⣾⣧⠘⢿⡿⠿⢛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣿⣿⣾⣇⣇⢻⣿⠋⠉⣦⣶⣞⣩⡻⣿⠁⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢷⣾⣿⣿⣾⣿⡂⠀⣿⢙⢿⣿⣭⠿⣷⠿⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣾⡶⢷⣿⣷⣧⣠⠋⠘⠙⢿⣿⣜⠠⠖⢸⠋⡟⢰⢣⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣄⣨⣶⣿⣿⣿⣏⠀⠀⠀⠀⢉⡟⢻⢀⡟⣸⣥⣿⣟⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠁⢠⣿⣿⠃⡿⢯⢰⡧⢄⣠⣿⣇⣿⣾⣿⣯⣿⣻⣟⠞⠁⠀⣴⣿⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡋⠄⠀⢸⡀⣷⠿⣿⡿⠿⠿⣿⣧⣽⣯⡕⠁⠀⠀⠀⢿⠷⠶⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⠲⡖⢶⡶⢤⣄⡀⠈⠀⠀⣤⡾⣇⣯⣞⣥⠀⢠⡶⠂⢠⡄⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠤⠖⠾⠷⢿⣺⠷⣾⣦⣹⣄⢳⡝⣷⣀⣨⣿⣳⣿⣿⣭⡿⣿⠚⠛⠛⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣍⠴⠟⢛⣿⣷⣼⡏⢹⡯⠙⣿⣏⢻⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠿⠶⢛⣿⣿⣤⣁⣀⠇⠙⠾⠿⣿⣁⣤⢶⣶⠤⢀⣀⠀⠀⠀⢠⣿⣿⣿⡿
⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⠀⠀⢐⣟⣿⣶⣾⣿⣿⡿⡿⢯⠙⣷⣦⠶⢶⣿⡟⣠⡾⣡⣴⢋⣉⣱⣤⠀⠀⠙⠓⠛⠁
⠀⠀⠀⠈⣛⣢⣤⠘⡔⠂⢤⡀⠈⠙⠋⣿⣿⣿⡁⠃⡭⠖⡟⢑⣫⣶⢾⣿⣿⡿⢿⡿⢿⡿⢿⣷⣾⣧⡀
⠀⠀⠀⠀⢩⣭⣽⣷⣷⢸⠠⢱⣄⠀⠀⡟⠁⠀⠀⠀⠀⣼⣦⡽⠿⢿⡛⣧⠀⢳⡀⠑⣄⠙⢆⠑⣈⡿⠿⠆
⠀⠀⠀⠀⠀⣷⣶⠶⠿⢿⣤⡄⡏⡷⣤⣴⣤⣀⠀⣠⠞⠻⣅⣠⣤⣀⠈⠑⠻⠶⣿⣶⡬⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠻⣗⣛⣛⣛⣿⣿⣥⠿⣿⣿⣷⡄⠉⠀⡼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⠉⢰⣮⣽⣶⡎⣧⠹⠁⠀⢸⣾⣷⣿⣿⣿⢷⡇⠀⠀⠀⠀⠀⠀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠥⣴⡏⡇⢸⣸⣾⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣻⠃⠀⠀⣠⡼⡇⠀⠛⢸⠀⠁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣰⣿⡷⠿⠋⢸⡇⠀⠀⠀⠀⠹⣿⣻⢿⣿⡿⠃⠀⠀⠘⠓⣄⣀⣀⡤⢨⠄⣠⡀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⠉⠻⡟⠀⠀⠀⠀⠀⠀⢻⣮⡤⡇⡀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⣠⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣷⣀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⢀⢈⡇⢐⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣫⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠈⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⣤⣤⣶⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡞⠂⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠉⠛⠉⠀⠀⢀⡤⣦⡀⠿⢿⡿⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠀⠀⠀⢠⣟⠁⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣶⢟⣽⣧⢰⣶⣿⣇⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⢀⡼⠇⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⢀⣴⣿⠟⣡⢟⣾⣿⣿⡟⣯⢹⡟⡄
⠀⠀⠀⠀⡀⠀⠂⠉⢛⡓⠀⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠠⣾⡿⢁⣼⢫⣾⡿⢿⣿⣧⢹⣼⢑⡶
⠀⠀⡀⠀⣀⠒⠉⠘⠥⣿⠷⢄⣞⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠉⢠⡿⢡⣿⣿⡅⣿⠵⡹⠂⠟⢾⡅
⠀⠀⠛⡀⢭⣤⡔⠐⢠⠄⢷⣼⡁⠁⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣿⠀⠀⠀⠀⣰⣿⣿⢟⡁⣿⣿⣿⠀⠀⢸⣿⡄
⠀⡠⠋⢔⢘⡏⠁⠀⢀⣭⠉⠐⣇⠂⠀⣀⢀⢀⣤⣰⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⣹⡿⢿⣿⣿⣿⣿⡝⢦⡀⢸⣿⣇
⠀⡀⠐⠛⢋⣄⡞⡔⢻⡿⣤⠰⡿⣙⡟⢿⣻⣬⡻⣟⣷⣷⣿⣿⣿⡏⢁⣀⠀⠀⣿⣥⠿⠿⣿⣿⣿⣿⠘⡇⠈⠻⠛
⠀⠀⡀⡔⢡⣿⣇⠘⠈⠁⠉⠉⢵⣿⣮⣾⣬⣷⣷⣼⣿⡿⠿⠟⣩⡶⠋⠻⠛⠂⠀⠀⠐⠀⠘⢿⣿⣿⢸⡇⠀⠀⠀⠀⢀
⠀⣠⣿⠀⢛⢋⣟⡀⢀⢰⣠⠀⠀⢹⣿⣿⣿⡿⢿⣿⣿⣷⣖⡟⠁⠂⠀⠀⠀⠀⠀⢀⡘⠀⢀⣸⣿⣿⣸⠃⠀⠀⠀⣠⠎
⠀⠉⢻⡶⡌⠛⠙⣧⡷⢻⡿⠦⠀⢸⣿⣿⠋⠀⠀⠙⠛⠟⠋⠀⠀⡁⠀⠁⠴⠀⠂⠈⠀⠀⠀⢹⣿⣿⡿⠀⠀⠀⠀⡔
⠀⠐⢸⠛⣦⠆⠀⣿⡇⠱⠞⡄⢠⠀⢿⡏⠀⠀⢀⣤⣄⣤⣴⣷⣦⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠃⠀⠀⠀⠐⠁
⠀⠠⠈⢻⡅⠀⣧⡷⠟⣶⠀⡟⠁⠀⠈⢧⠀⠈⠉⠉⠉⠉⠉⠉⠃⠛⠛⠛⠀⠀⢀⣠⣷⣦⣀⠀⠄
⠀⠀⠠⠈⣿⢼⣘⠘⠚⠁⠳⣆⠀⠀⠀⠈⣧⣀⣀⠀⠀⠀⠀⣀⣄⢠⡄⠀⣠⣤⣘⢿⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣶⠀⠳⠴⣌⠳⣦⠀⠀⠈⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⡾⠯⣬⣄⣀⣀⣉⣉⣼⣼⣿⣿⣗⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠘⠢⢄⠀⠑⠀⠹⣏⣰⠆⠸⣦⣀⠀⠀⠀⠀⢀⣷⡆⠀⢀⣀⣿⠉⠁⢠⡈⠒⣤⠾⡁⠉⠉⠀⠀⠀⢀⠀⠴⠋
⠀⠀⠀⠀⠀⠙⢷⣄⠀⢢⠁⠁⠀⢸⠟⠻⡿⠶⠿⠿⠿⠛⠉⣿⢿⡿⢶⣶⣿⣄⣠⣞⣀⠤⠤⠴⠂⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⡾⢦⡄⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⡁⠈⢻⣿⣿⣿⣻⣱⡆⠀⠀⣄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠀⠀⣌⣒⢤⣤⣤⡄⣸⢤⡤⡀⠀⢠⡉⠉⠉⠉⠙⠉⠉⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠚⠳⣟⢑⠆⠙⠦⡛⠡⠼⠆⠀⠈⠁⠀⢤⣠⡶⣄⠂⡸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⢨⠿⠛⠃⠀⠀⠆⠠⠀⠋⠁⠀⠈

⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⡀⢀⡁⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠲⢤⣀⡐⠒⠂⠀⡀⠀⠄⠒
⠀⠀⠀⠑⣂⣾⢛⣻⠗⠶⣽⢳⣖⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠎⣰⣌⣩⢥⡓⢒⡦⣟⣩⠇⢀
⠀⠀⢰⣿⢻⣿⠿⠿⢿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢳⣶⣩⠵⠲⢿⣿⣶⣾⣷⣆⣻⠇
⠀⠀⠀⣁⠩⢵⣶⡆⠈⠁⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣄⣀⣀⣂⣤⠀⠀⠀⣠⣠⣤⡤
⠀⠀⠀⠉⠉⠉⠛⠛⠛⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢤⣖⠚⢿⣤⠿⣿⣶⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣞⠃⢿⠿⡇⢡⣜⠉⢀⣼⣿⠜⠥⣆⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⣉⡀⠴⠰⠀⠀⣐⣚⣙⣀⣐⣔⣀⣀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⣱⣿⢻⣧⠀⠀⠀⠀⠀⠀⢀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿
⠀⠀⠀⠀⢸⣿⠘⣿⡀⠀⠀⠀⠀⠀⠐⢠⠘⣏⢻⢿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢁⣾⡏⠀⠀⠀⠀⠀⠰⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣦
⠀⠀⠀⢰⣼⠀⣤⠛⡇⠀⠀⠀⠀⠀⢰⢿⣿⢃⡀⢸⣶⠂⠀⠀⠀⠀⠀⢸⡇⠋⢀⢸⣯⣔⡇⠀⠀⠀⠀⣾⠉⡀⢸⡇⠀⠀⠀⠠⢠⣠⡾⣿⢠⡌⠹⣷⡀
⠀⠀⠀⢈⣏⠃⡝⣆⣷⠀⠀⠀⠀⠸⣿⠆⢁⡞⣇⠀⢛⡟⠀⠀⠀⠀⠀⠘⢿⣄⢼⣦⣿⡟⠀⠀⠀⠀⠀⣾⠄⣧⣈⡇⠀⠀⢀⣴⠛⢛⣄⣁⣼⣧⡆⡹⠁
⠀⠀⠀⠀⠉⠛⠓⠋⠁⠀⠀⠀⠀⠀⠈⠑⠂⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠚⠃⠀⠀⠀⠀⠀⠈⠑⠛⠉⠀⠀⠀⠘⠛⠀⠛⠈⠉⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⢃⣴⡎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠴⠀⠠⠀⠀⠀⠀⣶⣄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠄⢀
⠀⠀⠀⠀⢾⡟⢿⣷⡈⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠀⣠⣴⣶⡿⠀⠀⠀⠀⠀⠀⢿⣿⠿⣷⣆⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⠁⠀⢀
⠀⠀⠀⠀⣸⡇⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣆⡿⠋⣜⣥⣠⡌⠀⠀⠀⠀⠀⠻⣆⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢃⡴⣿⠠⣶⡿⢻⣿⢀⡴⣯
⠀⠀⠀⠀⠿⣟⢸⡄⡿⠀⠀⠀⠀⢀⣠⣰⣶⠏⣸⠟⢡⠜⠙⠻⢛⡵⠆⠀⠀⠀⠰⡶⣿⢠⡄⢸⣦⠀⠀⠀⣠⣴⣤⡴⠋⣸⡿⢚⡉⣠⢿⡿⠋⣴⠏⡀
⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠠⣿⢋⣛⣡⢦⣠⠶⠻⠴⣦⣤⣀⡶⣧⡀⠀⠀⠀⢹⡦⣾⡁⡸⠃⠀⠀⠞⡋⡉⣩⣞⣀⡀⢴⣋⣈⣥⣠⡄⠚⠟⣻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⣟⣻⣦⢀⠀⠀⠀⠀⠀⣀⠂⢀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠃⠘⣿⡏⢻⣆⠀⠀⠀⢸⣿⣷⣄⡠⢀⣁⣀⣒⣠⣤⣌⡁⠀⠀⠀⠀⠀⠀⣿⡿⣦⣤⣇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣧⠈⡀
⠀⠀⠀⣠⣦⡿⡁⠘⠉⡇⠀⠀⠀⠻⢿⣟⠛⠟⠛⠻⠿⣿⣿⠛⣿⣤⡀⠀⠀⠀⠀⠹⣧⠈⠙⠻⡿⣦⣷⣦⠀⣂⠀⠀⠀⠀⠀⠀⠀⣿⠻⣷⣿⣦⣤
⠀⠀⢼⡏⠋⣼⣧⠄⠸⣿⠀⠀⠀⠀⠐⠉⢻⣷⣶⡄⢲⣤⣈⡆⠙⢿⠇⠀⠀⠀⢀⢳⣾⢷⡄⠰⣤⣤⣍⣉⠻⡟⢷⠀⠀⠀⠀⢀⣗⠾⣆⢉⡛⠈⠻⠿⣆
⠀⠀⠈⠻⠦⠿⠸⠧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠧⠼⠷⠽⠷⠦⠟⠀⠀⠀⠰⠾⠿⠋⠁⠠⠶⠾⠧⠉⠉⠳⠤⠌⠦⠀⠀⠀⠸⠿⠆⠠⠾⠟⠓⠛⠲⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠶⠂⠀⢀⡄⠀⠀⠀⠘⢏⡴⢛⣯⠉⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣠⣵⡌⢡⠀⢀⣤⢎⠿⣧⡈⠀⢂⡀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣤⣿⣮⡀⠀⢻⡈⠔⠛⡽⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠁⣦⠟⢸⡾⠃⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣾⡀⠀⣠⣴⣾⡟⠛⠛⠛⡻⠖⠒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣖⠲⠞⠛⠻⠒⢶⣄⠀⠀⠀⠀⢈⡟⠀⡄⣈⣿⢁⣘⡛⠊⣡⣉⣨⣤⠤⠤⣶⣤⡄⢈⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣉⠻⠤⢦⡀⠙⢧⣀⣄⣀⢀⡀⠀⢻⣹⣿⣜⣽⢿⡟⠛⢏⠀⠈⠰⠄⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠷⣮⠵⣦⣀⣿⠟⠛⢻⡅⠀⠀⠙⢿⢿⣶⠐⠚⠳⠤⣤⣄⠠⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⠀⠀⢨⠛⢦⠀⣿⠀⠀⠀⣰⠟⠹⠛⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣻⠀⡟⣈⠁⠁⠀⠈⣆⡿⠀⠀⣼⠋⠀⠀⠠⣘⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⡛⣀⠙⠏⠀⠀⠀⠀⢻⠇⢀⡞⠁⣷⡀⢀⣤⠈⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⢘⣁⠀⡀⢨⠀⠀⠀⠀⠀⠀⣾⣤⠂⠀⢀⡮⠁⢀⡁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣦⣄⠀⠀⠘⠟⠀⠻⡾⠀⠀⠀⠀⠀⢠⡿⠈⢤⣈⣿⢼⡀⣴⣤⣀⠜⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣇⣈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣀⠉⠛⣻⡿⡟⠋⠉⠄⠀⠀⣴⢓⡟⢦⡀⠀⢀⡀⠀⢰⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢿⣽⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⣿⠋⠰⡉⠛⠐⠄⣀⠀⠀⣼⠁⠸⠀⣸⠇⠀⡛⠛⠑⣇⠈⡙⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢽⡆⡄⠀⢠⡙⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢣⡞⠀⠀⠈⠀⠀⠛⠋⠀⠜⠃⠰⢋⣿⣦⣿⣿⣿⣗⡲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠹⣧⠀⢰⠁⢸⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣤⠞⠁⠀⢀⣼⠀⣬⠀⣸⢧⡄⠈⠻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣿⣴⡏⠀⠀⡟⠀⠀⠀⢠⠤⡦⠲⢲⡶⠀⠀⣾⠀⣠⡴⠛⠓⠽⠛⢳⠀⠰⠟⠀⠉⠋⠉⣨⡿⢷⣴⣯⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⠀⠀⡅⠰⠀⣼⠀⡸⠂⡠⡞⠀⢘⣤⣿⡼⠷⢤⣀⠀⠘⣐⣧⣶⣶⠓⠄⣀⡀⠀⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠦⠆⠀⠙⣷⣦⠀⠀⡶⠛⣿⠀⠘⠁⠆⠀⣸⡿⠋⠀⠀⠰⣟⠁⢀⡝⣻⡁⠙⣦⣬⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡀⢢⣀⣐⣿⣷⠀⠐⠂⢨⡿⠀⠻⠄⢀⣴⠋⠀⠀⠀⠀⠀⠀⢰⣧⣀⠰⠑⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠫⢍⡙⣿⡿⠀⡧⠀⡇⠀⠀⣠⠞⠛⢷⠀⠀⠀⢀⣴⡶⢾⣧⡿⢀⣤⠀⠉⠃
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⡼⠁⢠⠁⢠⡜⠁⠀⠀⢨⣇⠀⠀⢘⠻⠇⢰⠀⠈⠋⢸
⣴⠋⠹⠿⣿⡷⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠘⠠⡍⠀⠀⠀⢰⡟⢹⡄⠀⠈⠠⣜⣿⣤⣟⠤⠊
⠿⢹⣧⡤⠟⠀⠀⡀⠿⣿⡟⠛⢳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⣾⢆⡑⠀⠀⠀⣰⠏⢀⡼⣇⠀⠀⠀⠀⣿⠁⡏
⠀⠀⠀⠀⢀⣠⡶⣧⣠⣼⡸⣦⡞⠙⣷⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣧⡏⠁⠀⢠⠺⠯⠀⡬⠁⡉⠀⠀⠀⠀⢻⣨⡃⠂⠒⢶⣶⡶⢶⣦⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢀⡾⢩⣄⠹⠏⡈⠁⠀⡟⠀⣹⠀⠀⠀⠀⠀⠀⠀⢈⡇⣿⣿⠀⠀⢰⡇⠀⡀⠀⣧⣤⡟⠀⢀⠴⠀⠈⣟⠀⠀⠀⠀⣹⣟⣹⣷⠳⠖⠊⢉⠇
⠀⠀⠀⠸⣧⣸⡟⠂⡘⢿⣤⡾⠁⠘⠛⠀⢀⣤⢤⣄⡀⠀⠀⢹⣙⡃⠀⠀⠸⣷⠞⠁⠀⠉⠁⠀⡐⠀⠀⠇⠀⢩⣄⣤⠶⠚⠛⠁⠀⢠⣦⣼⠿⠋
⠀⠀⠀⠀⠉⢹⣇⣰⡇⠈⠉⠀⠀⠀⠈⣠⠞⣧⢀⡍⠙⠆⠀⢘⡏⠙⠀⠀⠀⠀⡤⢀⡀⠀⣦⠒⠀⠀⣡⣤⡖⠛⠀⢀⣀⣀⡀⠠⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠋⠀⣀⣀⣀⡀⠀⠘⣇⠀⠀⢹⣄⠀⠀⠀⢸⠳⠄⠀⠀⢠⠎⠀⢰⠆⠰⣬⡁⢀⡴⠆⠀⠀⠀⠀⠀⠘⠋⠁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣸⡋⠙⢦⠀⡇⠀⠳⣦⠘⠳⠃⠀⣿⠀⠀⠀⠀⣾⠐⠀⣯⠀⡠⢢⡶⠛⠀⠀⠉⠁⠂⣢⡀⣽⣤⡾⠁
⠀⠀⠀⠀⠀⠀⣾⠃⠺⠆⡮⠛⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠀⢀⣿⠈⡴⠟⣿⣤⣀⣀⣠⣤⢊⣱⡾⠾⠋
⠀⠀⠀⠀⠀⠀⣿⣄⣴⠀⢷⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢐⣷⣞⣴⣏⣀⠀⠀⢀⡀⠑⠆⢤⣻⡟
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠈⠉⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⠀⠀⡘⢣⣞⣋⣈⣉⡛⠶⣾⣿⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⣰⣰⠟⠁⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢃⠀⠀⠀⠀⠀⠸⣿⡇⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢦⠀⠀⠀⠀⠀⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢃⠀⠀⠀⠀⢹⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⡀⠀⠀⠀⠘⣷⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣠⠄⠴⡉⠉⢣⠀⡝⠛⢲⡀
⠀⠀⠀⢀⡤⢧⡀⣠⣿⣶⣿⣿⣿⣿⣿⣷⣤⡤⠤⣄
⠀⠀⢰⡋⠀⢀⣾⣿⣿⠿⠿⣿⠛⠛⢯⠀⠙⡆⣀⣠⠃
⠀⠀⢠⠟⠒⣿⣿⣿⡇⠀⠀⠈⡆⠀⣼⡤⠞⠫⡀⠀⢱
⠀⠀⠱⡄⠀⣿⣿⣿⠗⠤⣀⣠⠞⠉⠀⣇⠀⣠⠗⢴⠋
⠀⠀⠀⠙⠂⢿⣿⡿⠀⡀⠀⠑⠤⠤⠜⠁⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠉⢆
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠙⠂⠀⠀⢄⢤⣀⠴⢂⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠈⢁⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠤⠤⣀⣠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠰⠀⣠⠀⡄⢸⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠝⠉⠙⠶⠤⣤⣤⠤⠚⣦⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⠀⠀⠀⠀⠈⠲⠤⣠⣀⣀⣀⣀⠴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⢰⠓⠦⡤⠶⠦⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⢩⠀⢸⡉⠑⠦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠙⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠇
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠒⠒⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠋⠁
⠀⠀⠀⠀⡠⠊⠡⠀⠀⠀⠄⠀⠀⠒⠀⠠⡈⢳⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⣧⠉⠒⠲⠦⡤⠤⠄⠔⢶⠒⢋⣽⡞⣽⡄
⠀⠀⠀⠀⣿⣙⣓⣚⣺⣦⣤⠤⢶⡧⢾⠛⠒⢏⡹⡀
⠀⠀⠀⠀⢼⠀⣉⢹⠀⢸⠉⠉⡉⠚⠐⢅⠠⢃⡵⢇
⠀⠀⠀⠠⡛⢦⣄⣙⣤⣼⣉⣉⣥⡤⡴⠖⠚⣹⣤⡏
⠀⠀⠀⠀⠸⡖⠢⠤⢤⣌⣀⣀⣠⣤⣏⡴⢾⠉⢠⠃
⠀⠀⠀⠀⠀⠱⢄⣁⠀⠀⠉⠁⠀⠠⠂⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⢀⠀⡀⣀⡀⠀⣀⠀⢀
⠀⠀⢀⡗⠀⠀⠀⠀⢀⣴⣿⣾⡆⠀⣼⣿⣷⠀⠀⠀⢀⡀⡀⠀⠀⠐⣾⣿⣷⣿⣿⣿⣾⣿⣿⡿⢀⣉⡇⣨⡽⢃⡀
⠀⢠⣾⣿⣴⡄⠀⠀⣸⣿⣿⣿⣿⡀⠁⠹⠏⠀⡐⡜⣨⡵⣿⣷⣤⡠⠙⠛⠛⡛⠛⣛⣛⣛⣋⠀⡸⣿⣜⡿⢳⡞⣖
⢀⣿⡟⠉⢿⣷⠀⠀⠻⣿⠿⢿⣿⠇⠀⠀⣠⣾⣷⣿⣿⣿⣿⣯⣿⣿⣦⣄⢼⣿⣙⢺⣟⡋⠛⠁⠘⠿⠻⣷⣾⠟⠋
⠀⠛⠄⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣼⣿⣿⠋⠀⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢰⣠⢼⡰⢠⢠⣀⠀⠀⠁⠊⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠀⠢⠀⠀⠰⡄⣠
⠀⠀⠐⡄⠀⢰⣺⣽⣿⣿⣾⣽⣼⣿⣿⠀⠀⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⠐⠀⠈⠼⠷⠁⣨⢷⣿⢕⠗⠀⢀⣘⡆
⠀⡄⣾⢁⠀⠈⠙⠛⡉⠉⠉⠙⠛⠛⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⠀⣠⢞⢢⡇⠀⠀⢀⣈⣿⣿⣏⣀⠰⣞⣮⣷
⠈⢷⣙⣾⣦⠀⠀⣴⣻⣶⡄⠀⢀⡺⣿⣎⠠⣄⠈⠻⣿⣿⣿⣿⡿⢠⣶⣿⡏⣿⣷⡇⠀⠉⠉⠉⠉⠉⠉⠀⣤⣿⠇
⢀⣾⣼⣿⡏⠀⣼⡏⠹⢿⣿⠀⢢⣹⣯⣟⣵⡝⡄⠠⣿⡿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣗⠀⠀⢀⣠⡄⠀⠀⠈⠻⣧⣄
⠀⠛⠿⠟⠃⠀⠈⠓⠀⠘⠃⠀⠘⠛⠛⠛⠛⠛⠋⠀⠘⠇⠸⠋⠀⠰⠿⠿⠿⠿⠿⠟⠀⠶⠿⠿⠿⠷⠶⠀⠶⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⣼⡟⠁⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⢀⣼⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⣼⣿⠁⣸⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⣠⣾⠇⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⢀⠃⢰⣿⣿⢀⡇⢸⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⢀⣼⣿⡏⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⣿⠀⢸⣿⡟⠸⡇⠋
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⣰⣿⣿⡏⠀⣠⣾⣿⣿⣿⣿⠋⢠⠂⠀⢰⡿⠀⢸⡿⢁⡆⠁
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⡇⣸⢿⣿⡟⢀⣾⣿⣿⣿⣿⠟⠁⡰⢃⠆⢠⣿⠇⠀⡞⢁⡾⢱⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⠟⠁⢸⢻⡿⢰⡏⣸⣿⣰⣿⡿⢋⣾⡿⠋⠄⡼⣡⠟⣴⡿⠃⠀⠀⣰⣟⣷⠏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⠏⠀⠀⣼⠈⡇⣿⠀⣿⣿⣿⡟⢀⣾⣿⢃⡏⣼⣷⣯⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⣀
⠀⠀⠀⣶⠀⣼⢿⡀⠀⠀⢸⣿⠀⢠⠀⡟⠀⠃⠟⢸⣿⣿⠛⠀⣾⣿⠇⣾⢡⣿⣿⣿⡟⠀⣰⣿⣿⠟⠁⠀⣠⣴⣿⠇
⠀⠀⠀⣿⠀⠸⣟⣧⠀⠀⢸⡇⠀⣾⣴⡇⠀⠀⠀⢸⣿⠇⠀⢸⣿⡿⢸⣿⢸⣿⣿⣿⡇⣼⣿⣿⠃⢀⣴⣾⣿⡿⠃⢀⠆⢀⠄
⠀⠀⠀⣿⡄⠠⢹⣿⡆⠀⢸⠃⢠⣿⣿⠃⠀⠀⠀⢸⡏⠀⠀⣿⡿⡇⣿⣿⢸⣿⣿⣿⣷⣿⡿⠁⢀⠼⡫⠓⢉⣠⡶⣋⠔⠋
⠀⠀⠀⣿⣧⠀⣧⣻⣷⠀⢸⠀⣼⣿⡿⠀⠀⠀⠀⢸⠃⠀⢠⡿⢰⢱⣿⣿⠸⣿⣿⢹⣿⣿⡇⢀⡾⠋⣠⣶⣿⡿⠛⠁
⠀⠀⠀⢻⣿⣧⢸⣿⣿⠀⡀⢠⣿⣿⠃⠠⠀⠀⠀⣎⠀⠀⢸⢇⡟⣼⣿⣿⢸⣿⣿⠸⣿⣿⡇⢸⠇⣰⣿⣿⡩
⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⢃⣾⣿⠃⠀⢰⠂⠀⠀⠋⠀⢸⣿⡼⢡⣿⣿⢇⣾⣿⡟⣸⣿⣿⡇⠀⢰⣿⣿⠋
⠀⠀⠀⠀⠀⢻⣻⣿⡟⠀⣾⡿⠃⡀⠀⣸⠃⠀⠀⠀⢠⣿⣿⢃⠟⣸⢏⣾⣿⣟⣵⣿⣿⡟⠀⣴⣿⠟⠁⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠈⢿⣿⠃⣼⡿⠁⣼⠃⣰⣿⠀⠀⠀⠀⣾⣿⢃⢂⢠⣫⡾⣻⣿⣿⡿⠟⠋⡠⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡟⣸⡟⠀⣼⠃⣰⣿⡏⠀⠀⢀⣼⡿⠁⢂⣾⣰⣟⣽⣿⠿⠋⠀⢀⣠⠄⠀⢀⣠⣴⠾⠟⢉⣴⠋
⠀⠀⠀⠀⠀⠀⢀⢱⡟⠀⣸⢃⣼⣿⡿⠁⠀⢀⣾⠟⠁⠀⣼⡇⣏⣿⡟⠁⠀⣠⡾⠋⠀⣠⡶⠟⠉⠀⣴⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⣿⣿⣿⡟⠁⠀⢀⣾⠋⠀⠀⣼⣿⣇⢻⡟⠀⢠⣾⡿⠀⢀⠾⠋⠀⢀⣴⣾⢿⣿⡏⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⣿⣿⠋⠀⠀⠀⡾⠁⠀⠀⣼⣿⡟⢻⢸⡇⣰⣿⣿⠃⠀⠁⠀⠀⣰⣿⣿⣳⣿⡟⠀⡜⣯
⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⠃⠀⠀⠀⠀⠁⠀⢀⡾⢋⣿⡧⣀⣼⣠⣿⣿⠏⠀⠀⠀⢀⣼⣿⡿⣷⣿⠟⠀⡰⠁⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣰⠏⣴⣿⣿⡇⣿⣿⣿⣿⠋⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⡰⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡰⢡⣾⣿⣿⣿⣼⣿⠿⠋⠁⠀⠀⠀⣰⣿⣻⣿⡿⠋⠀⢀⡔⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡄⠀⠀⢀⣴⢟⣽⣿⡿⠛⠉⠀⠀⠀⠀⠀⣠⣾⣿⡷⠛⠁⠀⣠⣴⣿⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⣼⠁⠀⢀⠞⣱⡿⠋⠁⠀⠀⣀⣤⣔⣀⡴⠞⠛⠉⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⣳⠏⠀⠀⢊⡞⠁⠀⢀⣤⡾⠿⠋⠁⠉⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⠏⠀⠀⠀⢋⠀⢀⡴⠟⢁⡀⠀⠀⠔⢊⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢀⡴⢃⠤⢊⣠⠞⠁⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⣼⡿⠋⠀⣠⣴⣾⠟⠀⢀⣴⡿⠁⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⣼⠋⢀⣴⣿⡿⠟⠁⣠⡴⠿⠋⠀⠀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠚⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢈⡟⠁⠀⡀⠀⠀⠀⠈⠁⡀⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⡀⠀⠀⢀⠀⣄⠀⡀⠀⠂⠄⠀⠀⠀⠦⠔⠂
⠀⠀⠀⠀⠀⠀⠠⠖⡐⠀⠈⠀⡈⠀⠀⠀⠀⣀⡴⠚⠀⠀⠀⠉⠃⠀⠰⢣⣴⡀⠀⡁
⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⢁⡈⠀⠀⠀⢀⣀⡸⠐⣤⠔⠁⠀⠀⢂⠔⠁⠁⠀⠉⠈
⠀⠀⠀⠀⠐⠂⠐⠀⠀⠉⠀⠅⠁⠀⠀⠀⠈⠀⠀⠁⠸⠀⢀⠘
⠀⠀⠀⠒⠁⠐⠐⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⢤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢀⡀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠁⠠⠀⠁⠙

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢈⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠁⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⠀⠀⠀⠀⣆⠀⢃⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⡏⠳⢄⠐⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡈⠀⠀⠀⠀⠹⣀⠄⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠌⡇⢀⡄⠀⠀⠀⠐⢤⠀⠀⠙⢆⠀⠀⠀⠀⣠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡏⢸⠱⡀⣀⠀⠀⠀⠑⣄⠀⠈⣇⠀⠀⠌⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠤⠐⡇⠀⠑⠹⡌⣏⢢⡀⠀⢹⢀⠈⢸⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠲⡀⠻⡄⠀⠀⢀⡇⠐⡧⢠⠏⠸⠀⢸⠀⢠⡾⡀
⠀⠀⠀⠀⠸⡗⢄⡀⠀⠀⢳⠀⠡⠈⠢⡈⢢⣀⠞⢠⠀⠿⠁⡐⢀⠀⡜⠀⢸⠁⢇
⠀⠀⠀⠀⠀⠑⢄⠈⢦⠀⠀⠱⣄⠡⠀⠈⢄⠛⡐⠁⠃⡠⠊⠀⠌⡸⠁⣠⠏⠀⢹⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠐⠲⡤⣍⠀⠀⠀⠘⡆⠑⠀⠈⣤⠁⠀⠞⠀⠀⠌⣰⠵⠚⢁⡄⠀⣼⠀⠀⡠⢊⡾
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠉⠢⡀⠀⢸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡁⠔⠂⡑⠀⣰⠃⠀⠨⠐⣉⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⢆⠹⡄⡞⠠⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⡎⢀⡔⠁⣠⢀⡴⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠂⠛⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡞⣰⢾⢃⡎⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠘⡀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⡿⢨⢸⣼⠰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢁⠈⡄⠁⠁⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠀⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠀⠀⣀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠨⠀⠄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠠⠊⠁⠀⠈⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠠⡀⠀⠀⠀⠀⡀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠈⡠⠀⠀⡀⠶⠁⠰⡘⢃⣂⠀⠃⠀⠀⠈⠀⣀⢄⠀⠤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⣡⣤⣶⠿⠛⠛⡛⠛⠛⣛⣻⣿⣿⣿⢷⣤⣄⣀⠑⠐⠁⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠿⡏⠧⠘⣀⡰⠆⠈⠉⠁⠙⠻⠿⠿⢷⣾⣯⣭⣙⡛⠛⢻⡟⠉
⠀⠀⠀⠀⠀⢀⡀⠀⢀⠄⠀⢀⣠⣾⣧⣶⣴⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⢠⣌⠛⣿⣿⣿⣷⣎⡉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⠔⡠⠈⢿⡿⣾⣿⣤⣶⣴⢶⠾⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣸⣦⣾⣿⣿⢿⣦⡀⠚⠂⣘⡇⢀⣿⡀⠁⠀⡀⠀⠀⠹⣿⣯⣉⣉⠛⣷⡿⠋⠈⠻⣿⠖
⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⢻⣿⣿⣟⠷⡀⠂⣠⠙⢈⢻⡇⠚⠀⠉⠂⢀⣴⣿⣿⣿⣏⣁⣉⠀⠀⠀⢠⣴⣄
⠀⠀⠀⠀⠀⠀⢩⣤⡀⢠⠀⠙⢻⣿⣷⣿⣀⠁⠚⠀⢺⣽⣶⣤⣶⣾⣿⣿⣿⣿⣿⣫⣽⣰⡄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⡌⠃⠀⣄⠀⢹⣿⣿⡏⣿⣿⣿⣷⠛⢋⣉⠉⡍⢩⠡⠡⠈⠀⣿⣿⣿⣿⣿⡄⠘⠁⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣦⣷⢀⣤⠟⠁⣽⣷⣿⣿⡟⠛⢀⢤⣁⡐⡛⠛⠻⠿⠷⠾⠿⠿⣿⣿⠿⠃⢀⡿⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠈⠉⠀⢀⠼⣿⣿⣿⣿⡇⢰⡿⠆⢿⣿⣿⣿⣿⣿⣿⠘⣷⠀⢹⠁⠀⠀⠛⣇⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣾⣏⡀⠀⢀⢠⣼⡄⣝⣻⣿⣡⣾⢀⣶⡟⢿⠿⠿⢿⢿⣿⣿⣆⠛⠀⣾⠀⠀⢀⠀⠈⠻⢦⣤⣶⣯⣤⣄⡀⠠⣾⠣⢦
⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⡿⠸⢿⡵⠛⡻⢿⣿⣿⠘⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⢸⡀⠀⠀⣷⣦⣤⣀⡈⠙⠛⠛⠛⠁⠀⠀⠀⠚
⠀⠀⠀⢠⣤⠀⠛⠋⢡⣾⠏⡌⠰⢮⣆⠐⢼⣿⣿⠀⣿⠿⠯⠿⠰⣯⡵⢸⣿⣿⣿⣇⢸⣿⣶⣶⣿⣿⣿⡟⠿⠅
⠀⠀⠀⠀⢿⡀⠀⣀⣾⡿⠀⠀⠂⠀⠉⠁⢌⣿⣿⠐⣿⠄⠀⡞⠀⢆⠀⣸⣿⣿⣿⣷⢸⣿⣿⣿⠿⣿⣿⣷⡜⢇⢀⡐⠀⠀⢀⠀⠉⠒⣦
⠀⠐⠄⠀⠉⠷⡄⠹⣿⣇⠀⠀⡄⠀⠀⠀⣼⣿⣿⠀⣡⣴⡈⢤⣤⡀⢠⣿⣿⡁⠤⠉⢼⣿⣿⡆⠀⠻⣿⣿⣿⠄⠉⠈⠇⢠⣉⡀
⠀⠀⠀⠀⢧⠰⠎⠛⠻⣿⣿⣀⣃⣀⣀⣤⡿⣿⣿⡀⠿⠿⠷⠄⠀⠰⠿⣿⣿⣿⡄⠓⢸⣿⣿⠇⠀⠀⠸⣿⣿⣧⡀⠀⠀⡀⠀⠉⠉
⠀⠀⠀⠀⠀⢈⡉⢒⣐⣂⣉⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⢗⣦⣴⢲⣶⣶⣶⣶⣶⣾⣿⣿⣿⡖⣤⣴⣿⣿⣿⢿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠛⠋⣌⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣭⣤⡸⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣠⡶⢸⣿⣿⣿⣿⣿⠀⠠⣾⣷⢀⣶⣀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⣈⡉⠙⢧⡁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠃⠀⣾⣿⣿⣿⣿⠏⠀⢉⡿⠁⢸⠯⠀⠀⣾⣿⣿⣿⣦⣉⡀⠘⠻⠋⠀⠀⣈⠁⣀
⠀⠀⠀⡐⢁⣿⠏⣿⣿⣿⣿⣿⣷⠀⢡⣾⣿⣿⣿⣿⣿⠀⣠⠜⠐⠇⢸⠀⠀⢰⣿⣿⡿⠟⡿⠉⠁⢠⣄⠀⠀⠈⠁⠈⠉⠳
⠀⠀⠀⠁⢸⡟⣼⣿⣿⡯⢁⡜⠃⠀⠀⠛⠛⣻⢿⣿⣿⣷⣄⠘⠿⠀⠈⢁⣠⣼⡿⠋⣰⠏⢡⠀⠀⠀⣿⡟⠒⣶⣫⠂⠀⠀⠀⢀⡴
⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⠛⠿⡄⠀⠀⣠⣾⡇⠀⢿⣿⣿⣿⣦⣤⣴⣿⣿⣿⡿⠁⠐⠃⠐⣿⡄⠀⠀⢹⠀⠀⢸⣿⠀⣠⡄⠀⠊
⠀⠀⠇⠀⠘⣿⣿⣿⣿⣿⣤⣤⡘⠶⢾⣅⣀⣿⡆⠸⣿⣿⣿⣿⡿⠋⠀⠈⢿⢀⠀⣤⠀⠀⠹⡇⠀⠀⠘⠀⠀⢺⣿⣿⡿⠗
⠀⠀⡇⠀⠀⠘⢯⠻⣿⣿⣿⣿⡆⠀⠀⠉⣻⣿⣧⠀⣻⣿⣿⡏⠁⠀⠀⠀⡄⠋⣰⢟⠀⡈⠢⠘⡀⠀⠰⠀⠀⢹⣿⠋
⠀⠀⠑⠀⣀⠐⢈⣳⣾⣿⣿⢹⡿⠗⠒⠋⠉⣿⢃⣴⣿⡇⠀⠐⠒⢁⢠⡆⠠⠊⠁⠀⢀⠑⠴⠶⢥⡀⠀⠉⠒⠘⠿⠆⣀⠀⣾⡂⠄
⠀⠀⠀⢦⡈⢀⠀⢀⡙⢿⡏⣸⣿⠀⠀⠀⠘⠁⠾⣿⣿⣧⡀⢨⠂⢸⡀⡠⠀⠀⠀⠀⠀⠰⠄⠠⢶⠄⡈⠉⠲⠄⠀⠀⠄⠀⠈⢁
⠀⠀⠀⠀⠱⣄⠀⠁⠆⠀⣈⠛⠛⢦⡤⢤⣤⠤⠴⠟⠛⢩⡇⠈⡁⠃⡜⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⡄⣀⠆⠀⠀⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠈⠓⠄⠀⠠⠤⠇⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⡀⠒⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣤⣽⣤⣦⣤⣿⣬⣼⣯⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⢛⣛⣁⣀⣀⠀⠀⠀⠉⠉⠘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠤⠀⢰⠂⠀⠀⣀⢀⡀⠀⢀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⣀⠀⠀⣿⡀⠏⢢⡿⣿⡟⢠⡎⠀⠀⠀⠘⣷⢹⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⢇⢹⠀⠀⣿⣿⠀⠀⠀⢸⡇⠨⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⣄⢹⣇⣾⡄⡅⡀⢹⡏⠀⢸⣷⣿⠁⢠⡀⠀⠀⠀⠀⢻⡗⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣻⣧⡀⣷⢸⠇⠀⣼⣿⠇⠀⣼⣧⣤⠄⢰⡄⠚⠓⠼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠷⠛⠛⠉⢻⣿⣿⣾⡰⢠⣿⣿⣶⣦⣿⣿⣿⣴⣀⣤⣐⣴⣦⡀⠘⠿⡃⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠻⠿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠛⠉⠉⠁⠀⠀⠀⠉⠉⠙⠟⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠉⠁⣀⡤⠴⠶⠶⣶⠶⡶⠖⠲⠦⠤⠤⠴⠃⠈⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢦⡨⢛⣩⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠐⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡈⠉⠘⡿⠿⣛⣋⣻⣍⣉⡋⢉⡉⠙⣛⣻⣛⡛⠛⠃⠲⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⢁⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⢶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⣈⠻⢿⣍⣍⡀⠀⡀⠆⠁⠈⠀⠀⠀⠈⠈⠉⠑⣢⣦⣠⡴⠏
⠀⠀⠀⠀⠤⠤⠶⣶⣾⣿⣿⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣴⠿⠶⠞⢛⣟⣓⣛⣛⣻⣟⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣻⣟⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣾⣿⠿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠛⠿⠿⠿⠿⠟⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡌⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠘⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠹⣷⠀⢀⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⣿⣦⣾⣿⠏⠉⣣⡄⠀⠀⠀⢠⣶⢴⣿⣿⣿⡁⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⣿⣿⣿⠀⠀⣴⣿⠓⡄⠀⠀⣿⣿⡾⠛⠉⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣌⠙⣿⣿⣀⢸⣿⢿⠛⢧⡀⠀⢸⣏⡰⢷⣾⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣯⠈⠃⠸⠀⠀⢹⡆⠋⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡟⢡⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⣄⣤⣶⣾⣿⣿⠉⠿⢛⠁⠀⠀⠀⠀⢰⡀⢀⣠⣼⣻⣾⣿⣅⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣍⢠⣼⣿⣧⣤⣶⡟⠁⠘⠀⠀⠀⣸⠟⠈⠉⠀⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠻⣏⣜⠛⣡⣼⣿⣅⠀⠲⠦⡤⢆⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⣤⣤⣀⠙⠛⠿⢿⣿⣿⣦⣀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣄⣀⣀⣠⣴⣶⣶⣿⣶⣉⡛⠛⠛⠂⠀⠀⠉⠉⠻⣿⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣝⣿⡟⠛⠿⣟⣥⣽⣿⣿⣦⡔⠛⠛⠛⢶⣤⠹
⠀⠀⠀⠀⠀⠀⢀⢄⡀⢻⣿⣿⣿⣿⣿⡖⣧⠰⠿⣿⣯⣈⣤⠟⠁⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠙⠎⠹⣶⣿⣿⣿⣿⣿⣿⣯⣼⣿⠟⢻⡿⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣻⣿⡿⠛⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠻⢿⣿⠿⠛⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣥⣭⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣠⣶⣿⠟⣋⣉⣽⡽⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠱⠿⠛⠻⢿⡉⠙⠻⡿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣧⡈⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢁⠀⢀⣾⡏⢠⡙⣿⣿⣿⣿⣿⣿⡟⠛⠆
⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢸⣿⠀⡾⠃⣿⢿⣿⣿⣿⣿⣧⣴⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡧⣿⠃⠀⠀⣿⡄⢻⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣻⣷⠀⣠⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⣣⡤⠂⢠⠛⣧⡀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⣻⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⡼⣏⠙⣿⣿⣿⣿⣿⠁⣠⣿⠀⠘⢷⣿⣿⠟⠉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣧⣀⣾⣿⣿⡮⠓⡼⢻⡆⠀⣼⣿⡿⠀⢰⣿⣯
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⣴⠁⠀⠻⠀⢻⣿⠃⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠻⢁⠻⣿⣿⣤⡀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢹⣿⣹⣿⣿⢡⡾⠿⠀⠀⠀⠀⠘⣿⡇⢠⠟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⣿⣿⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⢻⠉⠃⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢉⣿⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⣾⡇⠸⢄⣠⣄⠙⠃⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⢀⣀⣀⣀⣀⣠⣤⣤⣄⡈⠉⠁⠀⠀⠻⠏⠁⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠛⣿⣿⣿⣶⣿⣿⣿⡿⢿⣋⣉⣉⣉⣉⣁⠉⠁⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣏⣀⣠⣄⣀⣈⡉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠹⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⠀⠙⣿⡿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣷⡛⠻⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠷⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠙⠻⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠻⢆
⠀⠀⠀⠀⠀⠀⠸⣿⡻⠟⢢⡀⠙⠛⠳⠌⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣌⠉⠛⠃
⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠦⠄
⠀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠆⠰⠄⠀⠀⠦⠠⠶⠤⠤⠴⠆⠶⠠⠖⠀⠀⠴⠆⠶⠠⠀⠶⠆⠰⠶⠶⠶⠀⠦⠠⠖⠠⡶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠀⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾
⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠄
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡀
⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠐⡀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠈⠁⠈⠁⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠘⢻⣼⠉⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⡰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡀⠀⠀⠀⠀⠀⠀⠀⣸⢳⡀⠀⠀⠀⠀⠺⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⢀⣰⣷⡄⠀⠀⢀⢰⣧⠀⠀⠀⠀⣾⣧⠀⠀⠀⢀⣼⣧⡄⠀⠀⠀⣾⣄
⠀⠀⢾⠿⡹⣿⠀⠀⢰⣿⣿⣿⠀⠀⢾⠟⠙⣿⠀⠀⢸⣾⣯⡤⠀⠀⢰⣿⣿⡆⠀⠀⣽⡟⠻⣷⠀⠀⣿⠏⢻⣶
⠀⠀⠈⠘⠃⠉⠀⠀⠈⠛⠛⠁⠀⠀⠈⠃⠐⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠐⠃⠉⠀⠀⠈⠀⠀⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣄
⠀⠀⣰⣾⣿⣧⠀⠀⠀⣼⣿⠀⠀⠀⢀⣿⣷⡀⠀⠀⢀⣿⢷⣄⠀⠀⢠⣾⢿⡆⠀⠀⣠⣿⣿⡀⠀⠀⢠⣶⢿⡄
⠀⠀⠻⢿⡽⠟⠀⠀⠰⣿⣿⠟⠀⠀⠸⡏⠘⠟⠀⠀⠸⣧⣆⠟⠀⠀⢸⡇⠸⡇⠀⠀⢻⣿⣿⡟⠀⠀⢸⣣⡌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣰⣷⡄⠀⠀⠀⢰⣦⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⢰⣶⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⣾⣆
⠀⠀⢴⠟⡈⣷⠀⠀⢨⡟⢹⣶⠀⠀⢰⡿⠹⣧⠀⠀⢀⣿⢿⣀⠀⠀⣰⣿⣿⡇⠀⠀⣤⣿⢿⣧⠀⠀⣤⡟⢹⣧
⠀⠀⠘⠚⠃⠋⠀⠀⠘⠃⠀⠋⠀⠀⠘⠃⠀⠃⠀⠀⠈⠃⠈⠃⠀⠀⠘⠻⠿⠋⠀⠀⠙⠋⠈⠋⠀⠀⠙⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⣴⡾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢷⣦
⠀⠀⠀⠀⠸⣯⢠⡄⠀⢼⣷⡄⠀⠀⠀⠀⠀⠀⣠⢞⡵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡀⠀⠀⠀⠀⠀⠀⢠⣾⡧⠀⢠⡄⣽⠆
⠀⠀⠀⠀⣠⡿⠛⠀⠀⢸⠋⠻⣦⣀⠀⠀⠀⣰⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣱⡄⠀⠀⠀⣀⣴⠟⠙⡇⠀⠀⠛⢿⣄
⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⡀⠀⠙⠳⢤⣀⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢳⣀⣤⠞⠋⠀⢀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠒⠞⠛⠉⠉⠙⠻⣷⣦⣄⡀⢹⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣠⣴⣾⠟⠋⠉⠉⠛⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡇⠀⠔⠒⠶⢄⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⡤⠖⠒⠄⠀⢸⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⣤⣤⣀⠙⠲⠄⠀⠈⠋⠀⠠⠚⠉⢀⣠⣄⡀⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠭⠛⠋⠁⠀⢠⣾⣿⣄⠈⠉⠛⠛⠻⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⡿⣦⡒⠀⠀⢀⣀⠀⠀⣿⣿⢿⣿⠆⠠⢀⣀⠀⠀⣀⣴⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢀⣠⠤⠤⣤⣤⣤⣴⣾⡿⠿⠛⠉⣀⣨⠿⡟⢿⣿⠄⡀⡀⢀⠀⡀⡀⠀⠀⠐⢻⡿⣿⠿⣥⣀⠉⠛⠿⢿⣷⣦⣤⣤⣤⠤⠤⣄⡀
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⢻⠀⣿⣶⢤⢤⢪⠠⡅⡤⠤⠴⢶⣾⠀⡏⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⢸⣠⡶⠛⠁⠀⠀⠀⠀⠀⢸⡆⠨⣟⡻⢾⠾⢤⢧⠷⠶⢾⣫⠙⢰⡇⠀⠀⠀⠀⠀⠈⠛⢶⡄⠇⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠉⠙⡛⠒⠂⠒⠋⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡠⢄⡀⠀⠃⠀⠤⢂⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠛⠛⠛⠛⠉


⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠉⠉⢻⣿⣿⣿⠉⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠶⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠠⠆⠀⠀⠀⣄⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⢀⣀⡀⠀⠀⣀⡀⠀⠙⢀⠀⡀⠈⠑⢄⢠⠀⠁⠀⠒⠲⠖⠒⠒⠒⠒⠀⠐⠲⠲⡂⡀⠀⠀⠤⡩⠎
⠀⠈⡉⠛⠛⡻⠛⠁⠀⠀⠀⠐⣀⣀⣀⣀⣥⡤⠤⠐⠂⣀⢂⣀⠃⡀⠃⢀⠢⠄⠘⡅⠁⢠⠈⠇⠉⣂⠀⠀⠒⠒⠒⢻⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠐⠄⠀⠀⠁⣼⠁⠲⡅⠺⣿⠐⠂⠀⢠⡖⢸⠀⣠⡆⠀⠀⠀⠀⠒⡂⠸⡇
⠀⠀⠀⠀⡀⠀⠈⠀⠠⠀⠀⠀⠀⢠⠿⢧⡀⠀⠀⢀⠀⠃⣛⣠⠌⣁⣘⡈⢧⣄⡆⠸⣤⡘⣄⡴⣇⡄⣤⠄⢐⡉⠀⢠⡇
⠀⢈⠀⢀⡇⠀⣀⣤⣥⣀⣀⣀⠀⠃⡼⢡⣙⣦⡀⣎⡤⠐⡈⠁⢄⡀⠀⡇⠈⢻⣟⡀⠀⠋⢹⠁⢡⢈⠁⡶⠁⠂⢠⢸⡇
⠀⢸⠀⣸⣷⠐⡁⠈⠉⡈⠙⣟⣷⣴⢻⣶⣾⣻⣿⠋⠀⡀⠛⣄⠧⡀⢀⡇⠀⠀⠙⢦⣼⠀⢸⠟⣡⣘⣼⣷⣀⢀⠄⢸
⠀⢸⢰⣿⣿⠀⠘⠀⠉⠀⠀⠀⠤⠀⠀⢿⣿⠋⠋⠀⣸⣧⠚⣹⠃⠈⠜⠯⠆⡉⠰⠌⠺⠿⠋⢉⣼⣿⡟⣿⡙⠈⢁⢸
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⡄⢸⠀⣿⡿⠶⣶⡒⠛⢛⣞⣣⡤⠤⢤⠄⠐⠒⠒⠒⢒⣶⡖⣾⡿⢻⠀⠙⠁⠀⢸⢸
⠀⢸⣿⣿⣿⡀⡇⠀⢘⢀⣀⣰⣅⣸⡄⡷⠿⢶⡦⠤⠤⠴⠂⠤⢶⠖⠲⢷⡒⠂⡴⠛⠾⠻⠶⡏⠀⣼⠀⣸⠀⠀⢸⣼
⠀⢼⠟⠉⠑⠂⠁⠉⠉⠈⣉⡉⠈⠀⢁⡁⠀⠸⠩⣭⣭⠉⠁⠉⣭⠀⠀⠀⢀⣀⣀⠀⢠⠀⠀⣀⡀⠛⢒⣻⡴⠦⠜⣿
⠀⠿⠤⢤⣤⠴⠶⠶⠶⠶⠿⠿⠿⠿⠿⠷⠶⠾⠿⠿⠿⠾⠿⠿⠿⠶⠶⠾⠿⠿⠿⠿⠿⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠟
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⡰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢄⠀⠀⡆⠀⠀⠀⠀⠀⢀⡄⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⣠⡤⢠⠀⠃⠀⣘⠀⢀⡏⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⠦⠂⢠⠊⡜⠁⠈⠀⢡⡀⠘⠦⠚⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⢧⣀⠄⠀⠀⡇⠀⢀⢻⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸⣆⠀⠀⠇⠀⠀⠀⠀⢰⡥⠔⠁⡸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⡌⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⢃⠀⠈⠓⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⠟⣠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢀⡈⠑⠊⠿⣶⣲⠤⠶⠦⠖⠶⠭⠐⠋⠁⠀⠒⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠂⠀⠀⠩⣒⡦⢤⣀⡈⢉⠥⠔⠒⠈⠁⠀⡀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⣄⣀⠀⢀⠀⠀⠐⠊⠉⠀⠀⠀⠠⠂⢀⡀⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠚⣁⠄⠀⢀⡀⠠⠀⠀⡀⠀⠒⠊⠉⣁⠒⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⡰⢚⡑⢂⠀⠀⠀⠀⣀⡠⠤⠒⠊⠁⠤⢀⣐⡦⠤⢀⠀⠀⠀⢀⠞⠩⣁⢀
⠀⠀⠀⠀⠀⠀⠳⣎⣁⣾⠠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡀⢸⠀⠄⣰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠘⠈⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠄⢀⠄⣤⠀⡀⠠⡀⠀⠀⣀⡀⢀⣀⡀⠀⣀⡀⢀⣀⠀⠀⠀⢀⠀⣄⢀⢀⢀⡄⢀
⠀⢾⠉⠃⠉⠀⠉⠀⠁⠋⢱⠆⠘⠞⠄⠘⠓⠀⠒⠃⠀⠛⠃⠠⢽⠻⢿⣿⢁⡀⢿⣿⠿⠹⠅⠀⢠⡎⠐⡛⠐⡴⡴⡻⠎⢲
⠀⢻⡆⠀⠀⣤⣤⣸⢄⠀⣾⠀⠀⢀⠀⠀⠘⠋⡗⠀⠀⠀⠀⠠⠒⠒⠤⡀⠘⠛⠀⡤⠔⠐⠆⢀⣾⠁⢰⡎⢳⣎⠰⡬⠀⢈⣧
⠀⢈⠁⠀⠀⠀⢸⣧⢸⠀⢉⠀⢠⡄⠀⠛⠚⠀⣷⠀⠀⠰⡆⠀⣳⠃⡄⢀⡀⢀⣀⠠⠈⣷⡁⠀⠟⠀⢀⡀⠈⠋⠀⠀⠰⠞⠋
⠀⣽⠆⠀⢀⠀⠈⠠⠀⠀⢿⡄⠈⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢰⣿⡲⠆⠈⠽⠎⠍⢀⠗⣷⡧⠀⡟⠃⠀⠀⣤⣢⠄⠀⠀⠘⣏
⠀⢸⡃⠀⠀⠠⡂⠀⠀⠀⣟⠀⢠⠾⠸⡗⠒⣤⠔⠚⡏⠷⠆⠘⢦⠀⠤⠛⢦⠢⠟⠤⠄⢰⠃⠀⣶⠆⠀⢀⠘⣛⣀⠀⠀⢰⡆
⠀⢸⡃⠀⠀⠀⠁⠀⠀⠀⣿⠀⢠⠀⠀⢱⡂⠈⠐⡺⠀⠀⡆⠀⣄⢈⠂⢠⠘⡇⢰⠐⢂⢀⡄⠀⢛⡀⠀⠘⢿⣿⡏⠀⠀⢘⠃
⠀⠸⢗⣤⣴⠾⠻⣶⣤⣴⠷⠀⠈⢹⡴⠄⢭⠀⡠⡠⢦⠏⠁⠐⢩⡟⢀⡒⠲⠲⠴⡀⠚⡅⠁⠀⠀⠡⡿⠃⢼⠿⠐⠺⡧⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣤⣦⡴⣴⣤⢤⢤⣤⡴⣤⣦⣄⠀⠀⠀⠠⣠⢴⡖⠂⠀⠀⠒⣲⠦⣄⡀⠀⠀⢀⣠⡄⣀⣤⡔⠒⠒⢢⣤⣀⢠⣄⡀
⠀⠀⢀⡌⠙⠋⠈⠑⠂⠒⠉⠈⠛⠉⣅⠀⠀⢀⣰⠂⠛⠛⠒⠃⠚⠜⠛⠛⠺⣏⡀⠀⢉⣹⠈⢈⡉⣽⠟⣿⣯⡉⠁⠁⣟⣏
⠀⠀⢘⣟⠀⠒⠀⢠⠶⠰⠀⠠⠀⢈⣯⠁⠀⠩⠄⠀⠀⠀⠀⠂⠺⠶⣆⠀⠀⡧⠅⠀⢸⣤⠀⣤⢀⣤⠄⠉⠽⡇⠀⠀⣿⡏
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠴⠠⢤⠀⠀⣿⡁⠀⠘⡟⠀⠀⠀⢠⠴⠃⠠⡥⢸⠀⣟⠁⠀⠈⠸⠀⢀⠈⠀⠀⠀⠀⠈⠐⡀⠇⠁
⠀⠀⠘⠀⠈⠂⠁⠨⠀⠠⠀⠀⢱⠀⠨⠁⠀⢸⣋⣤⣤⠤⡄⠀⠔⢠⡌⠈⠀⣹⠆⠀⢰⢋⡀⠀⠀⠓⠛⠂⠉⠁⠀⢀⡐⡦
⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢾⡁⠀⢸⡟⠈⢀⡀⠀⢀⠠⠈⠀⠁⠀⣻⠀⠀⠐⣼⠁⠀⠀⠀⠀⠀⠀⠀⡀⠈⢥
⠀⠀⠹⡽⠧⠦⠟⢿⣟⣿⠟⠧⠯⠾⡽⠁⠀⡐⣿⠧⢀⡥⠶⠦⢶⠶⢤⡠⢾⣿⠂⠀⢀⢺⣷⣆⠒⢰⣖⣶⡆⠐⣠⣶⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⡇⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠃⠀⢀⣾⠟⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣌⠀⠀⣠⣿⡏⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣠⡾⢻⡿⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⣾⡿⣡⣿⣧⠆⠘⠁⢸⣿⠀⡀⠀⠷⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣟⣵⣿⣿⣇⠀⠀⣠⡾⣿⣿⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣦⡾⣽⣿⣹⣟⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣾⡟⣱⣿⣿⣿⣿⡟⣱⣿⣿⣧⠻⣯⠜⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⢣⣿⡟⣼⢿⣯⣿⣿⣽⢣⠟⣿⣿⠹⣦⠙⢧⣀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡀⡆⢸⣿⠃⣿⡿⢰⡟⣿⡿⣿⣿⣏⠸⡆⢸⣿⣿⣿⡄⡈⢻⣧⡈⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣼⣿⡇⣿⢱⣿⣿⣿⣿⡿⠇⠁⣾⡈⣿⣿⣧⢰⡀⢻⣿⣆⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⠀⢿⣰⡇⡿⠁⣘⡇⢀⣼⣿⠇⢸⢻⣿⢸⡇⠀⣿⣿⠆⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⢻⣿⣿⣀⢸⣿⡇⠀⠀⣧⣷⠘⢿⡏⠀⣿⢹⡏⣸⣇⡀⢸⣿⡇⠀⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⣿⣿⣿⣌⣿⣧⣀⠀⠻⣿⠆⠈⣿⣰⢃⡾⢡⣿⣿⡁⢸⣿⡇⠀⣿⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠻⣿⡿⠿⣧⣼⡻⣷⡄⠉⠀⣰⣯⣿⡾⢡⡞⢹⣿⠁⣸⣿⡇⠀⣿⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣙⠓⠪⡿⠶⣿⣷⣿⣮⡻⣦⣬⣿⡿⠋⠐⠋⠀⣼⠟⣰⣿⡿⠁⢠⡏⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢽⣿⣿⣿⣷⣬⣉⠉⠁⠀⠀⠴⠊⣅⣼⣿⠋⠀⢠⠟⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡏⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⠟⢀⡴⢋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣿⣿⣿⣿⣿⣿⠿⢛⣋⣤⠶⠋⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣷⠶⣿⠶⠶⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡟⠿⡿⠛⡿⠿⣿⠿⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣾⣶⣷⣶⣿⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠇⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣇⠀⡠⠼⠔⢣⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⣠⠔⠚⢆⢫⠀⠀⠘⡆⢰⠀⠀⠸⠀⡎⠉⠑⢢⢀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⣈⡮⣆⠀⠀⠱⠘⠀⠀⠀⡿⠀⠀⢀⣃⠏⠀⠀⢹⠂
⠀⠀⠀⠀⢀⣀⠤⣤⣴⠦⠤⠶⢾⠀⠷⠶⠦⢴⣦⣤⠧⣀⣧⠀⠸⡀⠀⠀⢻⡂⠀⢀⠇⠀⠀⡘⠉⢓⠄⢠⠃
⠀⠀⠀⢰⣅⠰⢍⣀⠀⠀⠀⠀⠘⠖⠁⠀⠀⠀⠀⣀⡩⠆⣨⡄⠀⠇⠀⠀⢸⡇⠀⠸⠀⠀⠀⡇⠀⡞⠀⡏
⠀⠀⠀⠘⡓⠮⠭⠭⢛⣛⣛⣓⣒⣓⣚⣛⣛⣛⡛⠭⠭⠵⢺⠹⡀⢸⠀⠀⢸⠇⠀⡇⠀⠀⢰⠀⢠⢁⣼
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⢇⡀⡆⠀⢸⠀⠀⡇⠀⠀⢸⢀⡼⠋⡌
⠀⠀⠀⠀⢰⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣶⠀⠀⠈⠑⠒⠚⠤⠴⠇⠐⠒⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠘⡀⠀⠀⠚⠁⠘⢃⣤⣤⣤⠘⠃⠈⠃⠀⠀⢀⠿⠀⠀⡴⠛⢶⠄⠀⠀⠀⢠⠞⠳⡦⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡿⢿⠇⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠻⠦⠞⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣅⡢⡖⢈⡉⠭⠶⣞⡢⢤⣤⣤⣤⣈⡉⣀⡀⠀⠀⠠⠼⡤⢤⣐⡲⠶⠍⣉⣑⠦⠄⣤⣄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠱⣹⣉⣐⣲⣖⣂⡉⠉⣉⣒⠢⣍⡙⠛⠛⢛⣛⡻⠟⣋⣒⡢⢤⣴⣶⣊⡕⠊⠉⠁⠈⠆
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⢇⡀⣠⠞⠉⠀⠶⠀⠬⠍⣁⠙⣃⡐⢛⣒⠛⠓⠒⠚⣛⠚⠋⢻⠉⢉⣍⢀⣄⠀⠈⠙⢦⡀⢀⠆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠋⠀⠀⠀⠙⠂⠈⠶⠀⠁⠗⠈⠃⠠⡏⠰⠃⠘⠃⠴⠂⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠤⠤⢀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⠠⠤⠤⠤⠄⠒⠒⠊⠁



⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠦⣄⠈⢷⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠻⣎⠻⣦⣀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠸⣆⠀⠀⠀⠀⢹⡆⠈⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⣦⠀⠹⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠁⠀⠘⣇⠀⠘⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡀⢀⡾⠃⠀⠀⠀⠘⢧⣀⣸⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⣇⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡼⠃⣾⡁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢦⡀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⠀⠀⠈⠻⢦⣄⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠹⣦⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠀⠀⠈⠉⢿⠓⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡟⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠃⠀⠀⠀⠀⣠⠞⣿⠇⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⡆⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⠞⠁⠀⢀⣤⠶⠛⠁⣠⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⡇⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠐⣇⠀⣤⠞⠋⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡇⢸⡇⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡀⠀⡼⠃⠀⢀⡼⠁⢸⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⡄⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⡇⠊⠀⠀⠀⣾⠤⠒⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⡄⠀⠰⠾⣡⣶⣟⣯⣤⣦⠀⠀⠈⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣦⡀⠀⠀⠀⠀⢀⡀⠛⢿⣷⣦⣤⣠⣴⣿⣷⣿⣿⠟⠃⠀⠄⠀⠂⠈⢁⣤⣶⡆⠀⠀⠀⠀⠀⣠⡟⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠶⠾⠿⣶⣤⡀⠰⠄⠠⣤⠄⢈⣩⣥⣾⠿⠿⠛⢉⣤⣄⡀⠰⣶⡿⠿⣿⣛⡉⣁⡀⠀⠀⢀⣤⡾⠛⠛⠛⠛⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠛⠛⠋⠉⠉⢛⣿⣶⣦⣤⣤⣿⡿⠛⠿⣶⣶⣦⣬⣽⣿⣿⣿⣶⣄⠈⠙⠛⣛⣩⣷⡶⢾⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⠶⠶⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⣿⡿⠿⢿⣿⣿⣛⣛⣻⣛⡻⠿⢿⣶⡶⠶⠦⠬⣭⡉⠛⠛⠓⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠋⢁⣚⡯⠟⠛⠉⣀⣤⣄⠀⠀⠀⠉⠁⠉⠉⠙⠒⠲⠤⣀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣻⣅⣤⡤⠶⠚⠋⠉⠁⠀⠰⠞⠛⣁⣀⣘⠛⠉⠙⠛⠒⠒⢦⣤⣤⣤⡶⠒⠾⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠋⠉
⣀⡀⣀⣀⡀⣀⣀⣀⢀⣀⢀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢤⠀⡀⠀⡀
⠀⠀⠀⣀⣰⡨⠄⠲⠌⢠⣠⡀⠀⠀⠀⠀⠈⡒⣼⣇⢀⡀⡀⣸⡧⢛⠁⠀⠀⠀⠀⠠⢴⣶⠲⡆⠒⢠⠖⣲⡶⠆⠀⠀⠀⠀⠐⠾⠠⠬⠣⠄⠔⠣⠤⠳⠂
⠀⠀⢄⢹⡅⠐⣀⣄⢌⡤⣯⢀⠄⠀⠀⠠⢖⠂⠀⠁⢀⠠⣟⡈⠀⠀⣲⠆⠀⠀⠐⠴⡆⢠⡀⠈⣀⡁⠀⠀⢀⡶⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠶
⠀⠀⢀⣺⡝⡻⠁⠸⢇⠇⣙⡄⠀⠀⠀⠀⠶⠀⠀⠀⢀⡠⠀⣘⠠⠀⠶⠀⠀⠀⠀⢾⡇⠀⠀⠀⠈⡁⢀⠁⢸⡧⠀⠀⠀⠀⢠⡆⠄⠒⠾⠀⠰⠀⠀⠰⡆
⠀⠈⡀⢿⡧⢉⠀⠀⠊⢸⡿⠂⠁⠀⠀⠀⣞⣀⣠⣄⡀⢠⠀⣀⠀⠀⣺⠀⠀⠀⠀⠛⠁⠣⠐⠈⠀⠀⠀⠠⠀⠙⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⡀⢸⡗⠘⠀⠁⠃⠌⣷⠀⡀⠀⠀⠀⣿⠋⢀⡀⠀⠀⠀⠁⠀⢂⢻⠀⠀⠀⠀⣱⣒⢀⢀⡀⣀⣀⡀⢀⣐⣊⠁⠀⠀⠀⠀⠖⠓⡟⠒⢤⡔⠚⣿⠣⠄
⠀⠀⢀⠞⠿⠶⠾⠛⠶⢾⠟⢆⠀⠀⠀⠀⢼⡷⢠⢴⠶⣖⠶⠦⢤⠺⠯⠀⠀⠀⠀⠈⠋⠘⠈⢛⡿⠛⠁⢓⠙⠋⠀⠀⠀⠀⢰⣆⠀⢹⣂⠈⠀⣸⠁⡰⡆
⠀⠀⠀⠀⠀⠁⠀⠠⢈⠄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⠟⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠣⠹⡁⠯⠝⠷⠇
⠀⠀⠀⠐⠀⠈⠉⠈⠉⠀⠐⠀⠀⠀⠀⠀⠄⠠⠔⠒⠐⠂⠠⠠⠠⠄⠀⠀⠀⠀⠀⠀⠠⠂⠄⠠⠄⠠⠄⠐⠖⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢽⠷⣾⣿⠁⡀⣿⣷⠾⢹⠄⠀⠀⠀⠀⡶⣧⠐⢽⠀⠀⢄⢿⠖⡜⠳⠄⠀⠀⠀⠀⢰⠃⢂⡉⠐⠴⠔⣳⠆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠠⡙⠾⠛⠏⡠⠖⠒⡆⠀⠀⠀⠀⣶⠅⠐⠈⠀⠀⠀⠱⠐⢀⣴⠂⠀⠀⠀⢰⣏⠀⠴⠞⣹⣧⠒⠦⠀⢈⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡠⣀⡀⢀⣀⢠⣈⣶⠀⠀⠀⠀⠀⠃⡆⠛⠐⠂⠀⠀⠐⢤⣸⡇⠀⠀⠀⠀⠀⣁⡀⠲⠀⠀⠀⠀⠀⠘⢋⡉
⠀⠄⠀⠀⠀⠀⠀⠰⡿⡛⢂⣬⠙⠋⢩⠀⠟⢻⡇⠀⠀⠀⠀⡄⢃⠈⠀⠤⠤⠀⠀⠀⠁⢠⠀⠀⠀⠀⠐⠋⠀⠀⠐⢦⡴⠂⠀⠀⠈⡑
⠀⡀⠀⠀⠀⠀⠀⠀⠲⣀⡓⠈⢖⡶⠉⠒⣃⠴⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢸⠌⠀⠀⠀⠀⠀⣟⠀⠀⢠⣤⣤⡌⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡥⢃⣠⡸⢃⣔⡈⢥⡠⡄⠀⠀⠀⠀⠀⠿⣦⠀⢰⣤⡆⠀⣰⡟⠂⠀⠀⠀⠀⠀⠐⠀⢶⠌⢾⡟⢡⢰⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠩⠵⣼⡚⠮⠬⠩⢦⠁⠀⠀⠀⠀⠈⠇⠽⠀⡰⠒⠂⡁⠼⠐⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠙⠋⠀⠈⠝⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡘⡛⠛⠳⡁⣀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠤⠀⠀⠀⠠⡄⢠⡄⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⣄⠀⣀
⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⡰⠟⡗⠚⠎⡛⡹⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢀⣄⢠
⠀⠀⠒⠚⠋⠉⠉⠀⠀⢠⡌⠈⠀⠀⠀⠐⠀⠈⠃⠀⠀⣠⣴⡶⠂⠀⠀⣀⡠⠂⣑⣀⠔⠡⣬⠀⢇⠎
⢠⣀⢄⠈⢉⣆⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠠⢾⡿⠗⠁⠀⠀⡘⠲⡇⠀⣝⡏⠀⡰⡾
⠈⠲⠃⠀⠈⢀⣀⡀⠀⠠⠀⠀⠀⠀⠃⣀⢀⡀⠀⠀⠀⠀⠀⠰⠀⢠⣅⣙⡃⣰⢾⠁⢠⣿⠁⠠⠂
⠀⠀⢀⢄⠀⡆⠄⠔⠁⠀⢠⣍⡆⠀⢘⢖⠉⠃⣠⠠⠻⣀⠠⠀⠀⢸⠃⠀⠉⠈⠉⠋⠒⡇⢀⢄⣠⡄
⠀⠒⢁⢈⠀⠃⡡⠴⠀⢀⢃⠭⡸⠀⠈⣲⠍⡆⠀⡙⣎⡁⢠⠶⣦⢸⠘⠂⠉⠐⠥⠀⣾⠀⠀⠀⠕⡁
⠀⠀⠀⢻⠈⠂⠃⠀⠀⠘⠊⠀⠓⠃⠀⠑⠒⠁⠀⠑⠐⠃⠈⠋⠁⠈⠓⠒⠒⠂⠲⠀⠃⠀⠀⢠⢰⠟
⠀⠀⠠⠒⢣⡀⠃⡑⠀⠀⠠⠫⡷⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⠞⠁
⠀⠀⠀⠀⠁⠈⢙⢤⡄⠀⠀⠁⣂⡀⡀⠀⠀⠹⠒⠇⠀⠀⠠⠀⠀⢠⡔⠀⠀⣀⡀⠠⠀⠀⠰⣿⠴⠂
⠀⠀⠀⠀⠀⠀⠣⠜⠁⠀⠀⢸⠔⠒⠊⢀⢎⢭⢳⠀⡔⡒⠄⠀⠀⠠⡀⢀⠞⠉⠙⢦⠀⢠⠶⢦⡀
⠀⠀⣼⣷⠀⠀⠠⠀⠀⠀⠀⠘⢨⠴⠂⠸⡘⠐⡸⠰⠐⠝⡘⢰⠸⠵⡘⠘⡀⠀⠀⢸⠀⠃⠀⢸⠃⠁
⠀⠀⢳⣿⡇⠀⠀⢀⣀⠠⢀⠘⠚⠀⠀⠀⠉⠉⣠⠤⢵⡮⣀⠘⠒⠈⠠⠀⠘⠢⡤⡎⠀⣀⠔⠁⠀⠸
⠀⠀⠀⠉⣴⣖⠈⠙⢷⣄⠈⣆⢤⠀⠐⠈⢀⠼⠢⡖⠚⠳⡤⣇⠠⢰⡅⠀⠀⠀⢧⠥⠀⠿⠀⠠⡂⠢
⠀⠀⠀⠀⡍⢮⣦⣠⠾⣿⠊⠡⠀⢠⣤⠀⢸⠑⠾⠛⠓⠛⠓⠺⠀⠈⠀⠀⠀⠠⡀⡄⠀⠀⡄⠀⠜⠤
⠀⠀⠀⠘⡄⠀⠈⠀⠀⣿⠀⠀⡇⠀⠉⠀⠀⡀⡆⠀⠉⠊⠀⠸⠀⠀⠀⠀⠀⣀⣥⣤⣠⡀⠁⠀⢱⡎
⠀⢀⣀⡀⠙⠂⠂⠒⠘⠛⠂⠉⠀⠀⠀⠀⠀⢟⠿⠚⡟⠛⠛⡇⠦⠀⠀⠀⠀⢠⣉⣉⣉⡁⠀⠀⢅⡸
⠀⢠⡸⣈⡵⡆⢠⣶⡐⡎⢱⠀⢔⣉⡱⠀⠀⡘⠲⠐⠓⠒⠒⠃⠀⢰⣉⡕⠀⠸⠶⠴⠴⠇⠀⠀⡔⢢
⠀⠠⠳⣦⣄⣈⣋⣀⣉⡥⠋⠀⠀⠀⠀⠀⢼⣽⠰⣿⠠⠴⠦⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠼⠇⣀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠐⣧⡤⠀⠀⠀⠀⢻⠒⠀⠀⠀⠠⢾⡄⠀⠀⠀⠤⢸⡤⠄
⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠩⡇⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⠀⢻⡇
⠀⠀⠀⢾⠀⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⣿⠀⠀⢸⠀⠀⢠⠀⠀⢸⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⢹⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠐⣿⠀⠀⠸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⠘⡇
⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⠃⠀⠀⡇⠀⠀⠈⠀⢠⣿⠀⠀⠃⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠁
⠀⠀⠀⢸⡇⠀⠈⠀⠀⢾⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠀⠀⠘
⠀⠀⠤⣸⡧⠄⠀⠀⠀⢸⡇⡀⠀⠀⠀⢀⡧⠤⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⣸⣤⡀⠀⠀⠀⣸⠦⠄
⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘
⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⡙⢿⣷⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⠀⢹⣿⣿⣷⡌⣿⡆⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⣦⠀⠀⠀⠀⠀⣿⣿⣿⡇⠸⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠙⢶⣦⡀⠀⠀⠀⠀⠸⠀⣾⣿⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠋⢻⡀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀⣤⣴⣿⣿⣿⠁⠀⠘⣷⣦⡀⠀⠀⠹⣿⣷⡄⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣆⠀⠀⢿⡇⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⢠⣿⣿⠃⢀⡀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀⠈⠇⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⡏⠀⠈⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡄⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠤⠤⠀⠛⠿⠣⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣬⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣭⣽⣅⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠿⠤⣿⣿⣿⣽⡿⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣸
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢀⡀⠀⣿⣿⣿⠄⢀⡔⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣿⣿⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠨⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠰⠠⠐⠀⠀⠐⠀⢺⠄⠐⠀⠠⡂⠐⠀⠉⠉⠀⡀⠀⠰⡍⠕⡀⢤⡀⠀⠀⠀⢳⠂⠀⠀⠀⠣⠘⠀⠶⠀⠀⠀⠀⢀⠀⠠⢀⡀⠘
⠀⠐⡀⠀⠀⡀⠅⠀⠀⢠⠠⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡠⣌⠉⠃⠊⢀
⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠐⠏⠝⢀⡄⢲⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠎⠙⠃⠀⠀⠀⠺⠆⠁
⠀⠀⠀⠀⠄⠈⠁⠀⡠⠚⢁⠤⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠎⠕⠀⠀⠀⠉⠁⠀⠀⠠⠀⠀⠀⠂⡀⠐⢠⣀⠀⠀⠀⢀⠀⠀⢀⡠⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠈⠣⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠘⠀⠀⠀⣀⠀⠀⠂⠈⠙⠃⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠇⠀⠐⡔⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠂⠰⠂⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠑⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠠⠀⠚⠀⣄⠀⠂⠀⢀⠀⠀⠀⠉⠀⠀⠀⡋⡜⠃⠀⠀⠂⠀⠐⠀⣤⣄⣁⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠈⠀⠀⠢
⠀⠗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠃⠀⠄⠀⢀⠧⡀⡮⠸⠃⠀⠀⠀⠀⠤⡁⠉⠛⠃⠀⠒⠶⠃⠀⠀⠀⠀⠢⠲⠁⠲
⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢀⠀⠐⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⢼⠁⢀⠎⡁⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⡀⠀⠠⠈
⠀⣀⠀⠠⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢀⠘⠄⠄⠀⣤⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠂
⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠆⠀⠀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠀⠚⠠⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡂⠠⠄⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣅⣤⣦⡤⣤⣌⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⢿⣿⠿⠺⠿⣿⣿⣧⡄⠑⢄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣌⡂⠲⠠⣀⠙⢾⣿⣧⠀⠁⣄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣷⣦⠀⠳⡌⠻⣯⣞⡤⡀⣁⠀⣀⡤⡾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢀⡀⠌⠙⢻⡇⠀⣷⠀⠈⠻⢟⡿⣻⣼⣿⢿⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣶⠘⣳⣿⣿⣤⣄⣉⣠⣼⠇⠀⠀⠀⠀⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡴⠆⢠⣹⡛⡋⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡆⣷⠀⣀⣩⣶⣿⣧
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠶⣾⣧⣾⡇⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⡞⢀⣤⣈⢢⣤⣿⣻⣿⣿⣷⣶⣯⣿⣿⠿⠃
⠀⠀⠀⢸⣧⡀⠀⠸⣯⠉⠓⠙⣾⣿⠿⠋
⠀⠀⠀⠈⣿⣿⣄⠀⢻⡧⣤⣼⣾⠃
⠀⠀⢀⠔⠙⢿⣻⣷⣯⣀⣠⠟⠁
⠀⠐⠁⠀⢠⣼⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠿⣻⠟
⠀⠀⠀⠀⠈⠁

⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠛⠉⠉⠀⠉⠉⠛⠛⢿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⠿⡿⠟⠀⢰⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠳⢠⢀⢀⠀⠀⠀⠀⢀⠠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡀⠀⠀⠀⠀⢠⣾⣿⣷⡄⢠⠀⠀⠀⠈⠛⢼⡃⣠⠀⠢⢠⡶⢩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣧⠈⠻⢷⡄⠸⠿⠿⠿⠃⢸⣇⠀⠐⡄⠀⠀⠤⠿⣦⣰⣿⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢹⣧⠀⠀⢻⡄⠀⠀⠀⠀⣸⣿⣷⣄⠉⢰⣿⡆⣶⣿⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⣷⣄⢈⣿⡀⠸⡆⢀⣿⣿⣿⣿⣷⣬⣉⣼⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣻⣷⣶⣨⣸⣿⣿⣿⣿⣿⣿⣯⣌⣿⣿⣿⣿⣿⣿⡶⠂
⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣀⣤⡀
⠀⠀⠀⠘⣿⣿⣿⣶⣤⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠉⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡉
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣗⠀⠶
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠱⠆⢉⢠⡁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠉⢻⣿⣿⢡⣄⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠹⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⠿⠋⠇⡠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣹⣯⣿⣿⣷⣶⣾⣿⣿⠁⣹⣿⣿⣿⣿⣿⣿⣿⠠⡄⠀⠉⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⢐⡋⣡⣿⣿⣿⣿⣿⣿⠋⠉⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⢋⡍⠈⢠⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⢰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠋⠀⠈⢀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣏⠀⠀⠀⠀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡀
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠛⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠉⢹⣿⣿⡏⠉⠀⠀⠀⠉⠀⠀⢻⣿⡟⠁⠀⠈⠀⠐⠚⠉⠉⠀⢹⣿⣿⠀⠈⠉⠓⠂⢴⡄⠐⠒⠛⠉⢹⣿⡏⠉⠙⠒⠒⠠⣦⠀⠛⠛⠛⠛⢻⣿⣿⠛⠛⠛⠛
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠐⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣾⣿⣶⣶⣷⣿

⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⢀⠤⠀⠠⢤⡈⣧⡀⠀⣀
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠲⡀⠀⢀⠀⡴⡾⢉⣧⣟⢵⡱⡤⣾⠾⣀⠀⠀⠀⠀⣀⡔⠂⣄⣶
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠑⢿⢴⡞⡼⡏⣼⡸⡜⡟⢸⠟⠁⠀⠀⣈⠀⢈⢶⣿⡿⢄⡀
⠀⠱⢅⣀⣀⣀⣀⣀⣀⠠⣥⠜⡶⠀⠀⠈⠉⠁⠛⠘⠿⠇⠓⠊⠹⠀⠀⠔⠁⠀⠉⠀⠤⠭⠤⠤⠤⠙⢲
⠀⣿⣷⣾⣶⢾⣯⣿⠶⣲⣗⡿⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢘⡉⠒⠡⠌⠣⠎⠳⠉⠞⢳⡻
⠀⠳⡿⠓⠛⠪⠭⠿⠿⠿⣿⠇⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠏⠛⠛⠛⠛⠭⠭⠭⠽⠯⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢢⠅⠉⠐⠢⠤⠤⠒⡩⠡⢀⠄⢱⣀⣀
⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⢎⠉⢇⠀⠀⠤⠀⠀⠁⢉⢀⣀⠁⠤⠂⣠⠞⣠⠛
⠀⠀⣒⣓⣒⣒⣀⣀⡈⠉⢭⠭⢭⣭⣭⣭⣭⢭⠄⠀⠀⣝⣚⡳⢶⣖⣒⣒⣒⣒⣲⣦⣶⣶⢟⣒⡽⡄
⠀⠀⠖⢒⣟⣛⣿⡛⠻⠒⠛⠲⠒⠋⠍⠍⠁⠬⠇⠀⠀⠀⠣⠌⣉⣛⣁⣵⣓⣚⣛⣻⣛⠫⠽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡰⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⠀⠀⠀⠀⠀⣠⠒⢚⢙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹
⠀⠰⠊⢰⡓⢤⡀⠀⠀⠀⠀⡠⣬⡄⠠⡊⡞⠀⠀⢀⣀⣀⢠⡝⣿⣥⣄⡀⠀⠀⢀⠤⣄⠀⡴⢾⣿⡷⠾
⠠⣝⡺⠒⠺⣛⡽⢄⠀⡰⠂⠓⠐⠓⢢⡸⡇⠀⠀⣿⠦⠤⠤⠩⠥⠤⠤⢿⠇⠀⣵⣁⠙⡇⢣⣷⡟⠠⠄
⠣⣤⣀⣉⢉⣵⡤⠎⠀⢗⠚⠂⠑⢊⣾⣠⢹⡆⠀⠈⣥⠔⢲⣐⠒⠂⣌⡏⠀⠀⠀⢀⣴⣡⡞⣁⠁
⠀⠰⣞⡡⢏⡞⣹⠁⠀⠈⢍⠁⠛⠉⠈⡠⠊⠀⠀⠀⢫⠌⢹⠉⢙⠀⣸⠀⠀⢸⠶⠈⠛⠏⠅⢚⡷⠐⠄
⠀⠀⠹⣿⣷⠾⡇⠀⠀⠀⠀⠈⠈⣉⡁⠀⠀⠀⠀⠀⠘⠀⣕⠈⠄⠀⠇⠀⠀⠈⠇⠒⠒⠒⠒⡹⠷⠤⠃
⠀⠀⠀⠡⡀⡸⠁⠀⠀⠀⠠⡉⠀⠈⠉⡹⠀⠀⠀⠀⠀⢠⣆⡖⢺⡞⠀⠀⠀⣤⠚⠓⠆⠲⠚⠙⢓⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠁⣸⡏⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢠⣿⣇⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣸⣿⣿⣦⠀⢸⠆⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠹⣷⡀⢰⣿⣿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⢿⡀⣿⡇⢸⣿⣿⣧⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡇⣼⠃⢸⠇⢹⣿⢸⡏⣿⠻⣷⠀⠀⢸⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣼⣿⠏⡠⠀⠀⢸⣿⡾⠁⢿⢠⡿⣠⢇⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⢀⣼⡿⠋⠀⢃⣄⡆⣼⠟⡠⠀⣫⣾⡿⠿⠿⠃⣿⡇⣼⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣿⠀⣰⡿⠋⢀⠆⣠⡞⠀⣸⢃⡞⠁⣼⣿⢏⣀⠀⠰⣣⡿⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣿⣯⣾⣯⠔⠀⠀⣴⡟⢀⢠⠇⣸⢁⢸⣿⣿⡟⣡⣶⢶⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡿⠋⠀⠀⣸⡿⠀⡞⠀⠀⠇⠸⡈⣿⣿⣸⡟⣰⠏⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣿⡿⠁⠀⠀⠀⣿⣇⠀⢿⡀⠁⠀⠀⡁⠘⣿⣿⣷⡇⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢿⣿⡇⠀⠃⣄⢰⠹⣿⡀⠈⡁⣇⠘⢦⠀⢠⡘⣿⣿⣇⠈⡀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣸⣿⣧⠀⠀⢻⠸⠄⠻⣷⡀⡱⣿⡤⠌⣧⠀⡇⢸⢿⡇⠈⣴⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⢹⣆⠀⠘⣧⠀⠠⡘⢷⠀⢹⣷⠀⣿⠀⣷⡇⣸⣇⣾⣿⣇⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⣿⡜⠉⠳⠀⠘⢷⣄⠹⠘⠂⢸⣿⢀⣿⢀⡿⢡⣿⡿⠻⢹⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢳⡈⠓⡀⠳⡄⢀⠈⢿⣷⣆⠸⢸⡏⣾⡏⠀⡰⠟⢁⡤⢂⣿⡏⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⠀⠁⠠⡐⢮⣷⡼⣿⢹⣦⣿⣿⢏⣠⠔⢂⣠⣴⣶⠿⠋⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣦⡈⣿⣧⣿⣿⣿⡟⣱⡿⣡⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣸⣿⣷⣿⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠙⠂