Pasta Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣀⣞⣿⣿⡷⣶⢿⠋⢀⡀⠈⠉⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⣫⣭⣋⣩⣽⠋⠀⠠⠾⡼⠾⣁⣀⣠⣴⠛⢟⣆⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣾⠋⠁⠠⠜⠏⠀⡉⠐⠒⣈⡉⢲⠆⢈⠀⣻⡎⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣦⠠⢧⡀⠱⠆⠈⠶⠀⣀⡁⢐⠰⢘⣾⡿⣣⡎⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣈⠙⠓⠲⠭⢽⡷⠷⠦⠠⠒⠚⠹⠛⠋⠉⠟⡐⠇⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠏⠿⣿⣿⣻⢶⣧⣤⣤⣤⣤⣤⡖⠒⣛⣁⠄⢀⢀⣄⣼⠕⠀⢀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⢙⠻⢽⠭⣿⣿⣿⣿⣦⣄⣀⠈⠑⠒⠈⢀⢥⡟⠉⠀⠈⠈⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠘⠛⠛⠛⠛⠛⠛⠛⠷⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⢠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠏⠑⠛⠒⡿⠚⠙⠋⠊⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡨

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣿⣹⣆⣀⢀⣰⣦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡆
⠀⠀⢸⣿⢻⣏⣿⣾⣽⣷⡟⣿⠀⠀⠀⢀⡤⠊⠀⠀⢀⠀⠀⠀⠴⡖⢀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⠛⠈⠋⠉⠙⠋⠋⠋⠉⠀⠀⠀⡎⠀⠀⠐⡀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢊⣁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠤⠀⠀⠀⠀⠏⠀⠀⠀⡆
⠀⠀⠀⠀⢀⣀⠐⠐⠪⠿⢮⡄⠀⡶⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⠬⠌⠧⠄⠀⠀⠆⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠤⡁⠀⠐⠢⠀⠈⠉⠁⠀⠀⡀⠆⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠛⠘⠣⡠⠒⠊⠀⠀⠀⡰⠀⠀⢀⡤⠒⠚⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠄⡀⠀⠀⠀⠀⠀⠙⠀⠀⣀⣠⠊⠀⠀⢰⡇⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⡲⠀⠑⠆⡺⠷⣋⣀⣐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⠂⢰⡀⠠⠊⢄⡈⠈⠉⠤⠜⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⠈⠋⠀⢂⠄⠠⡄⠀⢐⡋⠀⢠⠇⠁⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠈⠥⣡⡘⡒⠤⢐⠖⠈⡕⡱⠶⠄⠉⣥⡄⠂⠀⢀⠌⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠚⠁⠒⠾⠴⠦⣶⣶⠍⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⣒⣋⣩⣤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠂⢀⡬⠅⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠭⣼⡪⣆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣇⣿⣷⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⣼⡧⣿⣖⠋⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠈⠉⠧⣩⡟⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆⣀⣰⡿⢫⡱⣦⣤⠊⠈⠓⠚⣤⣤⡰⠇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡒⢒⡺⣿⠟⠋⠉⢟⡘⣼⠁⠁⠙⠁⠀⠀⠀⠀⣚⠓⠿⢴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣾⢷⠤⠾⣿⠂⠀⠀⠀⠀⠿⡏⠀⠀⢈⣰⠲⠄⠀⠚⣏⠀⠀⢰⡟⠚⠦⠤⣤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⡸⠦⣀⣀⣠⣤⠴⢛⠕⢦⣙⣙⠁⠀⠂⠀⢈⠷⣦⠊⠀⡒⠀⠀⣛⡶⠀⠝⡆
⠀⠀⠀⠀⠀⢀⡴⠊⠉⢏⠀⠀⠠⠀⣈⢰⣿⢿⢿⢜⣧⣀⡄⠚⠒⣻⣿⡶⠤⢄⡤⠃⠨⡈⠢⠤⡔⠃⠤⠙⠃⠀⡠⠃
⠀⠀⠀⠀⠀⠎⠀⡀⠀⢸⡃⠢⡐⠲⣗⣦⣴⣾⣿⣿⣯⣻⣧⣌⡚⠁⠋⠓⠄⣨⣭⣆⣠⣸⢦⡸⠉⠚⠔⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠈⠒⢭⣆⣀⠙⠒⠒⠀⠲⢶⣏⣓⣠⠭⠿⢿⣥⣭⣷⣀⣐⡦⢿⠟⠉⠒⠋⠀⠀⠀⠀⣀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡒⠀⠒⠂⠉⠭⠁⠉⠺⠶⠭⠝⠋⠁⠉⠀⢁⣀⣀⡠⠤⠤⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠖⠂⠠⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢒⡄⠰⢐⡱⠀⠀⢀⠁⠁⠈⠊⠉⠒⠀⡀⠔⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⢁⠀⣘⣌⣛⣓⠁⠥⠠⢄⡂⠀⠐⠴⢈⡁⠂⢤⢠⠤⢈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡔⠮⡤⠾⢐⣁⣃⡐⠄⣀⡁⢠⡀⡁⢂⠁⠀⢉⢁⠅⣀⣀⠀⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠬⠀⠀⠬⠁⢆⡀⢄⠠⢀⠠⣧⡐⠁⠈⠐⠚⠅⠀⡧⠀⣤⠌⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠑⠀⠠⠄⡚⠰⣃⠌⠓⠢⠭⠥⣈⡩⠴⢎⠭⠒⠖⠆⠔⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢘⡊⢠⡀⢁⠋⠂⠉⢀⡂⡸⠶⠭⢀⡩⡤⠌⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠓⠓⠈⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢴⡷⣤⢄⣴⡆⣶⢏⡴⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠿⠞⠿⠺⠽⠟⠿⠺⠗⠿⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣴⣦⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⡇⢸⣧⡄⠀⠀⠙⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠀⡇⢸⣯⡄⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣄⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠀⣧⢸⣯⣥⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⣇⢻⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣼⢋⣿⡘⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⠟⣡⠟⠉⢷⡹⣦⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢧⠾⠋⠀⠀⠈⠳⣌⠷⣌⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣳⣬⣙⡲⠮⣭⣛⡻⠶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⢛⣻⠿⣿⡿⢟⣻⡿⠿⣛⣶⡮⣭⣛⠶⣭⡛⢿⡿⣿⣿⣿⣿⡛⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⢀⡴⢛⣵⠟⣩⡶⢛⣥⠶⣛⣭⣶⣿⡿⠿⠿⣦⡙⢦⡙⢶⡙⢿⡻⣿⢷⣄⠀⠀⠈⠉⠛⠳⢶⣄⡀
⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⠀⣰⠟⣴⠟⣠⠞⣁⣴⡿⠗⣛⣋⣭⡴⠶⠖⣛⣛⣩⣿⣆⠹⣦⠹⣦⠻⣌⢷⡹⣆⠀⡀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢷⣯⣼⣣⡼⠟⣛⣭⠴⠖⣛⣩⣥⠴⠶⢛⣛⣩⣭⡤⠶⠿⣇⠘⣧⠸⣇⢻⡌⣷⣽⡾⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠹⢦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣶⣿⣿⣽⣷⣶⣿⣿⣯⣭⣷⣶⣶⣟⣻⣿⣤⣿⡶⠿⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⡶⠶⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡤⠴⠶⣶⣾⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠙⡀⡎⠀⠀⢀⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣷⣓⢷⡰⣾⡃⠐⢲⣿⣽⠻⣯⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⢹⡿⣻⣌⢻⡛⣺⣷⣾⣦⣴⣷⣿⣿⣷⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢃⠻⢗⣶⡞⣷⠙⣷⣤⣧⣿⣿⣿⣿⢿⣿⢣⡿⡽⢷⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠛⣤⡠⠤⣼⡛⢓⣾⣧⡇⢾⣧⠝⣫⡟⣻⣼⣾⣟⢼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠢⠶⠖⢋⣑⣒⡊⢷⠹⣾⣿⠎⡿⢃⡍⠀⢛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠞⠳⠀⠛⡃⠸⠇⢀⣀⡀⢒⡋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣉⢉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠶⠒⠒⠒⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢲⠀⠻⡇⠁⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠙⠀⠐⢠⠀⠀⠇⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠐⡧⠀⣀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠂⠠⠣⡃⠀⠉⠈⠀⠀⠀⠐⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⣆⠀⢀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣠⠐⡀⠀⠃⡁⠨⠀⡾⡛⠒⢧⡠⠥⠖⡂⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⡌⠀⠀⠀⠀⢨⠀⠄⠽⠄⠠⠆⠨⣺⢀⡧⡐⠠⣙⡴⣤⣀⡀⠀⠂⠄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠁⠀⠀⡰⡀⠀⡠⠚⠛⠂⡠⠏⠕⡡⡔⠀⡰⡀⢀⣀⠀⠙⠟⠓⠩⢤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⡆⠀⠀⠀⡄⢈⠄⣀⠀⠐⡸⠤⢀⣤⠴⠊⠁⠈⢲⠀⠀⡄⠔⡠⠾⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡀⠀⠸⠈⠚⠘⢁⠔⠤⠠⠔⠃⠈⡛⠶⠠⡴⠿⡈⠀⠀⠀⠂⠀⠘⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠠⢴⠃⡀⢀⠀⠄⠀⠈⠁⠀⠰⠔⠓⠂⠖⡶⢂⣄⠂⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠑⠰⣅⠀⢀⠐⢀⠐⣳⠄⠀⠀⠀⠊⠀⠈⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⣧⣿⣟⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣏⣉⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣴⣶⣾⣿⣿⣷⠿⣿⣛⣛⣛⡛⣛⣻⣿⣟⣻⣿⡿⢿⣿⣷⣶⣦⡤⣄⣀
⠀⠀⠀⠀⣀⢤⣒⣯⠷⢟⣋⣭⣵⣶⣾⣿⣿⣯⣿⣿⢮⣣⣿⣵⣿⣽⣭⢿⡭⠿⣽⣯⣲⣈⣭⣝⣻⠾⣽⣖⠦⣀
⠀⢀⡴⣫⣶⢟⣿⣶⡞⣻⣿⣟⢭⣿⣿⣿⣿⣿⣿⢏⣿⣿⣧⣿⣿⣪⣽⢿⢿⣟⣒⠿⣾⣽⣿⣟⣿⣟⣆⡉⠻⣦⣝⢦⡀
⢠⢏⣾⠟⣵⣿⣟⣻⣿⣯⣺⡵⣿⣿⣿⣿⡿⣟⣿⣼⣹⣱⣷⣿⡽⣧⣻⣾⣟⣷⣏⣿⣾⣷⣿⣿⣿⣿⣧⣞⡦⡈⠻⣷⡹
⡏⣼⡟⢎⣿⣽⣯⣟⠻⣿⣿⣾⣿⣿⣏⢿⣿⣿⣗⡏⣧⣿⣿⣿⣇⣿⠾⣯⡻⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⢟⣽⣽⣦⢿⣧
⢧⢹⣷⡀⠉⣷⣿⣿⢿⣿⣿⢿⣿⣿⡿⣷⣾⣫⣿⣧⣿⣿⣳⣿⣷⣿⣾⣾⣷⡿⣻⣭⣭⣿⣼⣿⣽⣿⣿⢿⣿⣿⣟⣾⡏
⠈⠣⡙⢷⣄⠈⠙⢻⣫⣽⣿⠽⣾⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣏⣿⣟⣾⣿⣹⣿⣿⣿⣿⣿⣾⡿⠛⣩⡾⢋⠜
⠀⠀⠉⠲⣍⡻⢦⣌⡛⠽⠶⢿⣿⣾⣝⣿⡿⢿⣿⣿⣷⣺⡶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠲⠿⢛⣩⡴⢟⣩⠖⠉
⠀⠀⠀⠀⠀⠉⠓⠮⢝⣛⠶⢦⣤⣄⣙⣻⢿⣿⡿⠿⠻⠭⠾⠿⢿⠿⠿⠽⠿⠿⣿⣛⣩⣭⡴⠶⣛⡫⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠭⠭⢽⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡯⠭⠭⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡔⠡⠔⠤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢊⣤⠂⢒⠎⢠⠓⢄⠀⠁⢈⡀⠠⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⠴⠖⠒⡤⣍⠱⠒⣃⡉⣀⠓⠪⡎⠔⠶⢁⠴⠳⣔⠄⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⢡⠡⠐⢚⣋⣀⣚⠛⠥⣀⣀⠙⢢⠘⡿⠃⠺⠳⢒⠠⡉⠰⣲⢬⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢗⡡⢂⡔⣉⡔⣺⣩⣛⣲⣌⠑⡖⢬⠇⣸⠀⡯⠵⡢⢌⠪⡲⡈⢦⠰⡌⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢊⣡⣤⠤⡤⣭⡑⠶⣒⣬⣙⡳⡌⡊⠰⢷⣰⣟⠲⢄⠠⠡⠐⡹⡌⡄⢠⠘⡆⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣴⢻⢁⠃⠊⠜⡴⢊⡱⣌⠳⡴⡶⢊⢴⡶⢦⡈⢣⣚⡙⠦⡆⡇⢻⠁⢠⠀⢄⠹⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⢹⡇⢸⠈⠘⠘⢰⢯⣑⠁⣧⠘⣇⠸⣼⠇⡄⢸⡀⣧⡌⢢⠐⠇⡏⡄⡈⠀⠠⢳⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⡆⢰⠀⣰⠠⠸⠘⣗⠨⡄⢯⢳⡈⢳⡤⣉⣁⣺⢀⠷⡿⢘⡀⣻⠡⢠⡇⠀⠃⠆⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠙⠁⣾⣆⠉⠀⠑⣑⠬⢙⣓⣈⢫⡜⢢⢈⣑⣊⠥⡾⠳⢸⣏⠡⡜⡡⢎⠒⠸⢸⠄⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⡗⠉⢆⠀⢑⢌⡱⠂⣉⢉⣀⠙⢧⠾⣟⣁⣜⠛⣻⠆⣿⡄⣹⠁⠀⠗⠃⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠠⠀⠈⠕⢦⡍⢠⠮⠭⠤⠭⢧⠀⡷⠲⡆⡤⠖⡡⢡⣏⣴⠏⣰⣛⠋⣉⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢃⠡⡈⠢⣀⡟⡛⠳⠶⣨⠟⣰⠅⠠⡇⣟⣩⡴⠏⠑⠖⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢂⠁⡈⠑⢬⣁⠀⠙⢋⡡⡞⠉⢷⡙⡴⠇⠲⠈⡙⠦⠈⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠄⡑⠠⣄⣄⠀⢀⡰⠤⢒⡡⡆⡀⠐⡌⠤⡇⣐⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠥⠤⠲⢎⣯⣙⠪⠀⠀⠀⢂⠄⠡⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡢⠀⠀⠀⠀⠀⣀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⠁⣤⣤⡄⢀⣤⢤⡤⢀⣤⢤⡄⣾⣿⣥⢀⣤⣤⢠⣾⢥⣾⢇⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠈⣿⣿⠏⣼⣧⣟⣱⣿⣱⣟⣱⣿⣹⡏⣼⣃⣾⠓⣋⣾⣇⣾⣇⣼⣃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⡟⠛⠋⠉⠋⠁⠋⣩⢋⡽⠃⠋⠀⠙⠁⠉⠋⠁⠈⠁⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠊⠀⠀⠀⢀⡗⠀⣇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢤⡄⠒⠀⢈⣱⡟⠀⠄⠈⢷⣁⡃⢙⠂⠒⠒⠠⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠈⢁⡀⠠⠀⣈⡇⢆⢾⣵⢎⠚⠓⢂⡐⡊⠜⣓⣠⡭⡷⠀⡀⠄⠤⡀⠀⢈⠁⠐⠂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠃⠀⣀⠀⢤⡄⢀⣰⣯⡼⣷⣮⠻⢏⠘⠪⠭⠍⠀⠄⡰⠿⣿⣿⣿⣵⣱⣿⡿⠁⡄⠚⠗⠀⠀⠀⠀⠑⡠⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⣀⠥⠴⠃⠀⠁⣼⣇⢸⣿⣾⣿⣶⠿⢏⡉⠀⣠⢿⠄⣜⣿⠹⣿⡿⣷⠻⢌⡄⣉⠥⣙⠀⢄⠤⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢁⢃⠆⢤⠀⣼⣿⡿⣷⣿⡙⠻⠴⠭⠁⠚⢉⣁⡱⢄⡟⠏⣗⣿⣟⣿⡷⢾⠻⠄⡒⠁⡼⠛⡆⠀⠀⠀⠀⠁⣹⡄
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠔⢀⢚⡂⠁⣸⣷⡟⣷⣣⣿⣿⣟⣗⢠⡝⣳⠰⠞⣫⣿⣴⣿⣯⡟⣩⣆⠈⢢⣦⠁⠀⠝⠔⠋⠃⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠁⠀⠉⠁⠀⡅⠙⠳⢷⣩⣿⣿⣿⣻⣈⠕⡻⢶⢾⣿⣿⣟⢿⠿⡿⣿⡿⡟⠒⠒⠒⠀⠀⡦⠀⠊⠀⠀⠤⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⢀⣿⡉⠁⢀⠀⣀⢙⣻⣿⣟⢻⣿⣿⣿⣿⣟⣻⣾⡿⣿⣽⢾⠿⠋⢁⠃⢈⣵⡂⢂⡊⠁⠀⠀⢀⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣄⠀⠑⠒⠂⠙⡊⠀⠈⢊⡃⠙⢿⡟⠓⢍⡇⣁⠉⣁⡢⠊⠀⣢⢭⠔⠨⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣤⣀⣀⣈⡀⠀⠉⠁⠉⠉⠑⠀⠈⠀⠉⢈⡉⣁⣀⣩⣀⣤⣤⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠙⠓⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠲⠶⠶⢤⡄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡝⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠼⠦⢦⡆⡮⣽⠋⠁⢻⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠳⣄⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⠚⣀⣠⢿⣻⠄⢠⡼⠥⠇⣐⠀⠀⠀⠀⢰⣀⡀⠉⠀⠀⠀⡱⢦⡈⠳⡄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⣀⡶⢽⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠞⠛⠀⠀⠀⠀⠱⡄⠀⢀⠀⠀⠱⡄
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⢐⢟⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠲⠀⠀⡀⠀⠘⠋⣘⢦⡀⠘⣆⠈⠧⠀⠀⠹⡄
⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠜⠃⠀⠀⠀⡰⠛⠢⡑⠂⠍⡉⠨⠤⠀⠀⠀⠀⠀⠀⠄⠁⠄⣨⠂⠈⢧⢳⡀⠸⡆⠀⢠⠀⠀⢹⡀
⠀⠀⢠⠇⠀⠴⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠃⠜⠱⠛⢓⠤⣉⣉⣂⠉⠲⠃⠠⠀⠀⢆⠀⠈⠁⠀⠁⠈⢇⢣⠀⢹⡀⠈⣇⠀⠀⢧
⠀⠀⣼⠀⢠⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣠⣄⣀⠀⠀⠁⠀⢈⠄⠀⣠⢂⡵⢦⣤⠶⣍⢳⡅⡃⠁⠚⠜⠐⠦⡀⠀⠀⠀⠀⢸⠘⣆⠀⡇⠀⢹⡄⠀⠸⡆
⠀⢀⡇⠀⡏⠀⠀⠀⠀⠀⣀⣀⡀⢀⠖⠒⠦⢤⡁⢨⠀⠀⠀⠌⢰⢩⣍⠻⣿⠈⠘⠭⣧⠷⣋⡵⢢⡄⠀⠀⠀⡀⠀⢀⡄⣲⣲⢎⡣⡀⠀⠀⠇⠀⠀⣧
⠀⢸⠃⠀⡇⠀⠀⠀⡀⣼⡹⠴⢌⣷⣹⠉⠓⠲⠄⡀⠙⠆⠀⠈⠰⢽⣎⡌⠙⣧⣤⠟⢡⠞⢁⠔⣁⡀⠀⠈⠀⠡⣦⣺⣾⠉⠙⣷⡇⠀⠀⠀⠀⠀⠀⢹
⠀⢸⠀⠀⠁⠀⠀⠘⠧⡾⢳⣤⣀⣱⡚⢱⣴⠀⠀⣄⠐⠒⢭⣙⣛⢛⡧⡳⣄⠹⠋⡤⠋⣤⠇⠐⢸⠀⠆⣀⡞⠀⠘⣏⣡⣦⣞⠷⠃⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⢠⢀⡀⠀⠀⠙⠷⠶⠷⡿⣿⠀⡍⠀⠀⢡⡀⠀⠀⠁⠈⠀⠑⠈⠛⠳⠾⢻⢛⠸⢊⡇⠀⠣⠸⡇⢀⡈⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⢸⡀⣇⠀⡄⠈⠉⠈⡉⠀⠈⠄⠸⠀⠀⠘⡈⢤⡀⠀⠀⠑⠒⠤⠤⣠⠃⠀⠀⢄⠀⠂⠀⠀⠃⢇⡼⠁⠀⢾⡤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠈⡇⠀⠈⣇⠸⡀⠠⡠⠀⠠⠀⢀⠀⢰⣄⢀⠀⠀⢳⣄⠀⠀⠄⠀⠀⠠⣄⠈⣠⠤⠒⡬⠀⠀⠀⣀⠠⠋⠀⠀⠀⢀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⢻⠀⠀⠹⡄⠃⠀⢀⡀⠁⠀⠾⠀⠐⠛⢜⠢⡀⠀⠉⠳⢅⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⡴⠀⣠⣾⣏⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠈⣇⠀⠀⠱⡀⠀⠀⠙⠛⠟⣦⠄⠀⠀⠈⠻⢤⠀⠦⣄⣀⠀⠉⠻⢭⠤⠤⣄⠐⠚⠃⠀⣂⠥⡤⣴⠡⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣆⠀⠀⠙⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⢀⣻⣦⣠⠝⠛⢀⠀⡈⠳⢤⡀⡈⠁⠁⠀⠀⠈⣐⣯⡵⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⢟⡝⣠⣵⢿⡞⣁⠴⠷⠦⠐⠛⠖⠀⠀⠀⠉⡄⢫⢯⡄⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣅⣍⡴⣪⡉⠙⣶⡇⠃⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⡋⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠳⢄⡀⠀⠀⠀⠀⠙⢾⣽⣲⢈⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠉⠙⠓⠒⠶⠤⠤⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠒⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣦⣤⣶⣦⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀⠀⣸⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⠿⢷⠀⠀⠘⢻⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠈⠙⠛⠋⠈⠛⣿⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡏⠛⠁⠋⠀⠉⠀⠀⠈⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠃
⠀⠀⠀⠀⠀⢰⠷⡞⠛⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⢇⡟⠀⠀⠀⠀⠉⠀⢀⠀⡀⠈⠀⠈⡄⠀⠀⠀⠴⠀⠀⠀⠀⠴⠀⠀⠀⠈⠸⠛⠃
⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⡁⡀⠁⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠿⠍⠀⠀⠀⠇⠀⡁⠀⠀⢰⡂⢐⠆⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠂⢉⠅⠛⠅⡘⠦⡤⢀⣀⠀⠀⢀⠀⣀⠤⠺⡐⠤⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢢⠀⠠⠂⠰⠊⠀⢀⠔⠁⠀⠀⠀⠀⠉⠋⠂⠀⠃⠀⢃⠀⠀⠀⠀⠀⠑⠄⡉⡗⠄⡓⡄⢠⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢎⠐⠩⣤⠂⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠂⠤⡄⠀⠀⢏⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢄⡔⢄⢻⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⡷⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠑⢌⡢⢠⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠀⠀⠀⠀⢡⢂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢮⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛⠶⡇⠀⠀⠀⠀⠀⢀⠌⠀⢀⡔⠀⠀⠀⠀⠀⢸⣇⣢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠠⠄⢀⠀⢀⠠⡇⠀⠓⠄⣀⣀⡠⠐⠁⡀⠔⠈⠁⠀⠀⣀⠀⠈⡇⠀⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠂⠀⠱⠐⠛⣱⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠠⠄⢀⣀⠠⠊⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠔⠁⠀⠀⠢⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⠀⡄⢀⡃⠀⠀⠀⠀⠀⠀⡆⠀⠔
⠀⠀⠀⠀⠀⠀⠰⡙⢶⡇⠀⠀⠀⠀⠀⠱⣂⣱⣂⠶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠇⠀⠧⢠⣇⣀⠀⠀⠰⡉⠻⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠛⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠍⠐⠋⠀⠀⠓⠒⠒⠀⠃⠀⠀⠀⠁⠂⠁


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢲⠀⠸⡇⠈⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⠁⠀⠈⠄⠀⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠃⠀⠀⣳⠀⢀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠠⠢⡉⠀⠈⠁⠉⠀⠀⠀⠂⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⡇⠀⢀⡀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡐⡄⠀⠙⣁⠈⠅⠼⠟⠒⠢⣀⢬⠔⢂⡀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⠄⠄⠸⠄⠤⠲⠀⣵⠁⡬⢀⠀⡌⡶⢦⣄⠐⠀⠐⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠁⠀⠀⢰⢀⢁⠀⠚⡛⠒⡠⠞⠹⠁⠔⠉⢠⣆⠀⡀⡀⠜⡏⠓⠊⢀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠈⣬⢈⠄⢀⠀⠘⡺⠦⠠⣤⠤⠊⠁⠀⢰⠆⠀⣐⠀⣠⠴⠀⢀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡄⠀⠐⠈⠛⠈⠁⡰⠠⠄⠔⠂⠈⣛⠲⠧⢴⠾⣂⠀⠀⠀⠆⠀⠀⠁⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠂⢤⠂⡀⠀⠀⠤⠂⠈⠁⠀⠰⠔⠓⠂⠔⢶⠂⣠⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠁⠠⢄⠐⠀⡐⠂⡀⢶⠂⠀⠀⠀⠀⠁⠈⠁⠀⡀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡄⢐⣦⣤⡀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟
⠀⠀⢠⣾⣤⠀⠸⠿⢿⣿⣆⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠈⣿⠀⠀⠀⠀⢸⣿⡇⠀⣾⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣆⠰⠀⠀⠀⠀⣠⠊⣡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠁⠀⠀⠀⣿⡄⠀⠀⠀⢸⣿⡇⣶⡏⠀⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⡄⠀⠀⠀⢰⢁⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⣿⡇⣿⡇⢸⡿
⠀⠀⠀⠀⠙⠛⠓⠒⠈⠁⠀⠀⠀⡸⠙⣿⡀⠀⠀⠘⢿⡝⢤⣀⣀⣇⡀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠈⢛⡿⠦⣀⠀⠀⠘⣿⡆⠀⠀⠛⣿⣥⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⢹⣿⠀⠀⠀⠀⠙⠿⣍⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡄⠉⣧⠀⠀⢻⣎⠀⠀⠀⣿⣸⣿⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡔⠀⠀⢼⡿⡀⠈⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣾⡆⠀⠈⢿⣆⠀⠀⢹⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣆⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢠⣴⣇⣿⣿⡿⠃⠀⠀⠈⢿⣧⠀⢸⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣶⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠞⠓⢻⡿⠋⠀⠀⠀⠀⠀⠈⡿⣦⠀⣿⣿⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢻⣧⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⣶⣶⣿⣏⠀⠐⠀⠀⠀⠀⠀⠀⢰⡈⢲⣿⡟⢠⠆
⠀⠀⢀⠢⢈⡠⣤⣄⣀⡤⠀⠀⠀⠀⠸⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡏⠀⠀⠀⠀⠉⠉⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⡇⡟
⠀⠀⠀⡐⣶⣿⣿⣧⣹⣶⣶⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⠂⢳⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟
⠀⠀⠈⠈⠁⠈⠻⠋⠿⠿⠟⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⢀⣴⣮⡀⠀⠀⠏⠁⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⠇
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡟⠀⠀⠶⡞⠠⠀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠘⡿⣍⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠀⠀⠠⢠⡇
⠀⠀⠀⠀⠀⠁⠈⠂⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⡀⠀⠀⢀⠎⠀⠀⠈⠀⠀⠀⢀⡄⣰⠀⠗⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠠⠄⣤⡴⠟⠁⠀⠀⢀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠴⠤⠓⠃⠤⠂⢾⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡝⣰⠁⢿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡀⠐⠋⠈⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡿⠀⠀⠀⠀⠀⠀⠁⠀⠈⢰⣀⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠿⠓⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡀⠀⠉⠛⠂⠀⠀⠘⠉⢋⠀⠀⠀⠀⢠⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠃⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⣀⠤⠄⠠⠄⣢⡀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⣰⡧⠀⡆⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠈⢠⠖⠂⠾⣤⣷⣀⣄⠀⣀⣤⣆⣰⣰⣦⢀⣤⡎⠁⠀⠀⠀⠀⠀⠹⣶⠤⠄⠀⠀⠀⣀⣠⠀⠀⣠⣾⠟⠁⢀⠟⠂
⠀⠀⠀⠀⠄⣀⠀⠀⠈⠀⠀⠈⣫⣽⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣾⡷⠞⠛⠋⠉⠉⠁⠀⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣨⣿⠋⠉⠉⠛⢿⣿⣿⡇⠀⠀⢄⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⡄
⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠘⠟⠛⠁⠀⠐⠂⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣇⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠘⠿⠃⠀⠀⢿⣷⡄⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠄⢤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠤⠠⠄⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⡂⢀⡴
⠀⠀⠀⢠⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠉⠉⠃⢈⠐
⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠚⠤⠈⠉⠒⠒⠄
⠀⠀⠢⡈⠢⣁⡄⠛⠁⢠⠀⠁⠐⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠇
⠀⠀⡀⠈⠓⠀⠀⠖⠉⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠀⠠
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠡
⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠁⠘⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⢀⡔⠉⠲⠂⠉⠉⠙⠛⠶⣷⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢠⠁⢠⡤⠄⠠⠤⠤⠒⠒⠉⢀⣠⣾⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠰⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠗⠠⠄⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠙⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠘⣩⠏⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠉⠁⠒⠒⢊⡁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⢾⣅⣀⡀⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣠⣤⡤⠶⠛⣁⠰⠌⢣⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢹⢄⠀⣤⠀⠈⠐⠃⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠀⣀⣀⠀⠠⠖⠋⠀⠀⠀⠘⣴⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡄⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣤⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠓⠒⢁⡖⠀⢀⠇⠀⠀⠀⠀⠀⠀⣀⠩⠴⠚⠉⠈⠳⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠛⡀⠰⠿⠤⠤⠤⠐⠐⠛⡏⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⢤⣀⣀⡴⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⣀⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⣿⠟⠉⠀⠀⠀⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠾⠛⠛⢿⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣾⣷⣶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣧⠀⠀⠀⠈⣇⠀⠀⢀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⠀⣠⣿⣷⡀⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠋⠉⠛⠲⢄⠀⠙⠀⢸⡇⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡀⠀⠘⠀⣠⠏⠀⠀⠀⠀⠀⣀⡤⠶⠻⢇
⠀⠀⠀⠀⣴⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢻⢿⣦⣤⡴⠶⠛⠋⠀⠀⠀⠀⠘⡆
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢈⡿⠁⠀⢀⡀⣠⠀⠀⠀⠀⢀⠇
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣹⢋⣀⡀⠠⠬⠝⣹⣶⣶⣶⠖⠁
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⡀⠄⠤⠒⠛⠉⠁⢀⣀⡀⠤⠐⠀⣰⠃⠘⣿⡇
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣴⠶⠶⣄⠀⠐⠂⠀⠀⠀⠀⣀⠀⢂⣴⠇⠀⠀⣸⠁
⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣠⡟⠀⠀⠀⠈⠉⠉⠉⠀⣢⣿⢿⣤⣤⠶⠋
⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢌⠡⡉⠳⠶⣤⣤⣤⣤⠶⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠄⠀⠄⠀⡀⠀⠀⠀⠽⢮⣕⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣹⣿⡀⢜⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⡸⠁⢸⡇⠈⠢⣹⡷⢤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⣧⠀⠀⠙⡿⣦⠙⠢⡈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡾⠁⠀⠀⢸⣿⠀⠀⠀⠈⢾⣇⠀⠈⢷⡄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⢀⣾⠃⠀⠀⠀⢈⣿⠀⠀⠀⠀⠘⣿⡄⠀⠈⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⢠⢰⡿⠀⠀⢺⣿⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⠀⠀⠻⣿⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⢿⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⡄⠀⢰⣿⡆⠀⡀⣄⣦⣿⣿⠀⠀⠀⢀⣾⢇⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣦⣺⣿⣿⣇⣿⣼⣿⣿⣿⡠⠐⡆⣼⣿⣦⣾⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣾⣿⣿⣿⣿⣿⡟⢻⡟⣽⣼⡡⣼⣰⣏⡐⠶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢙⢻⢿⣿⡿⣿⣿⣿⡷⣞⡞⣇⢻⠿⠇⢡⡝⣉⣡⣴⠛⠊⠉⠉⠉⠉⠉⠙⠒⠂⠶⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠿⠿⣻⣼⣢⣿⠧⠤⠄⠐⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⡀⠈⠁⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣄⣀⡀⣀⣀⣠⣴⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠿⠻⠿⠟⣿⣷⣾⡿⢟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⣿⡟⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠿⢿⣿⣿⣶⣦⣄⣈⡇⣿⢹⣿⠃⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣟⢿⣿⣿⣧⢿⣸⣿⣿⡿⣟⣻⣭⣭⣭⣍⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⠿⢿⣶⣝⡿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣟⣾⣿⣟⣽⣾⣷⢻⣿⣿⣿⣶⣽⡻⣮⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣼⢟⣽⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣮⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡇⡿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣧⠸⡇⠀⣀⠀⠀⠀⠀⣰⠃⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⡹⡋⠉⠒⠉⠙⢦⠀⠀⣸⡆⢻⡏⣨⠇⠀⢀⡴⠃⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣀⠾⣤⡀⠀⡰⠁⡠⢀⣠⡤⠤⣿⡿⢹⡇⠘⡿⢧⣠⠚⣡⠂⠀⠀⠀⠘⡄⠀⢄⠱⣄
⠀⠀⠀⠀⠀⠀⠰⡁⠄⠀⡹⠒⡳⠎⠈⠁⠂⢉⡽⠋⠀⠈⡇⠀⣯⡀⠈⡛⢧⡀⣼⠀⠀⠀⢱⡀⠈⢆⠈⣦
⠀⠀⠀⠀⠀⠀⠸⡔⠨⠐⢣⣒⣃⣤⡀⠀⣠⡟⠀⠀⠀⡇⣷⠀⢸⡴⠀⠀⠀⠘⢧⠀⠀⠀⡎⣧⠀⠘⡎⣾⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠸⡆⠀⢠⠪⠉⢇⢊⠋⠳⡏⡅⠀⠀⠀⠇⢹⡧⠀⡷⠀⠀⡇⠀⢸⠂⠀⢰⣰⣿⠴⠞⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢿⠀⠀⡘⢦⡑⠢⣇⣵⣄⠀⠀⠘⠈⣿⠀⣧⢃⢀⠇⢀⣾⣄⢀⣹⢧⣀⡀⠀⠀⣀⡴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣬⠶⠟⠓⠚⢮⣻⣷⣤⣄⣀⣼⡄⠸⣆⣈⡤⢞⣈⣉⡋⠻⣆⠄⣈⣉⡉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠒⠈⠛⡽⢚⡩⠭⠲⠭⣷⣮⡑⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣋⣀⠠⠤⠀⠀⢉⣿⠶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠥⠶⠤⠤⠔⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣄⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⣦⠀⠀⢙⠿⣤⣤⣬⣍⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⢧⡶⠿⠟⠻⢷⣤⣥⡀⠋⠉⠉⠓⢮⣿⣶⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣟⠓⠒⠶⠶⠦⢾⣿⡿⢶⣾⡶⠾⠿⠛⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡀⠀⠀⠀⠐⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠲⠀⡀⠀⠠⢾⣧⣴⠛⠋⠐⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣷⡀⢂⣾⣄⡀⠀⠑⠖⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡡⠐⠒⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠆⣀⣳⣇⡠⠀⠈⠒⠈⠀⠀⠀⠒⠟⢿⣿⣳⣤⣄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢤⣀⠠⡿⢀⠈⠐⠃⢄⡀⠀⠀⠀⠀⠙⠓⢾⡟⠛⠉⡦⡌
⠀⠀⠀⠀⢀⡄⠀⢀⣠⠔⢟⠀⡇⠀⠈⠉⠀⠁⠀⠀⠸⠀⣀⠀⠀⠈⣧⣤⣀⡶
⠀⠀⠀⠀⠀⠄⠰⢂⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣼⣧⣀⡠⢯⠿⠟⠀⠂⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠠⠰⠖⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⢟⠉⠀⠀⡀⠉⠁⠈⠀⢂⠾⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⠀⣸⡇⠀⠈⠀⠆⠀⠉⢣⠿⡤⠓⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⣾⡽⠀⠀⠁⠀⠀⠀⠀⠀⠠⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠿⠟⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠓⢶⣤⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣡⡀⠀⠀⠘⠁⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠄⠀⢻⡌⠦⡰⠀⢼⣟⣀⣀⣀⣀⣀⡀⣀⣀⣠⣤⣤⡤⠶⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠻⣧⣀⠀⢿⣴⡇⢨⣾⣷⣡⡤⠴⠚⢛⣩⣵⣖⣻⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⣠⣤⡤⠤⣤⣌⣻⣷⢽⣿⡀⣾⣿⣴⣦⣶⣿⣿⣟⡛⠋⠉⠉⠉⠛⠂⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠉⠉⠉⠙⣻⠷⠶⣾⣯⣿⣯⢽⣿⣿⣿⣾⣷⣿⣿⣷⣾⣿⣷⣶⣶⣷⣴⣠⣌⢠
⠀⠀⠀⠀⠀⠠⠊⠜⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠛⠉⠁⠀⠀⠀⠙⣿⣷⡄⠀⠉⠙⠈⠀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣷⡶⡤⠄
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠉⠹⢷⣷⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢧
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣷⣃
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣿⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣯⣿⡆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣿⣿⠃
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⢀⣷⣿⡄
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⢳⠁
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⡟⡞
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣩⡿⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣠⣘⣿⣿⣟⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣾⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⣠⣔⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢬⣀⡀⠁⠀⠀⠀⡀⠀⡀⠀⠐⠀⡀⠁⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠶⠴⠶⠶⠶⠷⠶⠦⠷⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡟⢦⠶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡠⠳⣄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢃⠞⢁⡴⠃⣰⣦⢾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠋⡠⠔⠁⡰⠋⠀⡴⠃⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠀⢠⠊⠀⢠⠞⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⡰⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⠃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⠎⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠋⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠞⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⣀⡴⢋⠔⠉⢀⠔⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠤⠤⠴⢿⣿⠛⣁⡠⠖⠁⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢥⣄⣴⠀⣀⡠⠴⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠉⡉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⣿⡿⢿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣸⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣼⢇⢼⣷⣇⢸⣀⣀⡀⢥⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠬⠿⠿⠿⠿⠏⢹⣿⣿⠈⡡⣿⣿⠿⠿⠷⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣄⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡋⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠧⠔⠊⣩⠿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠁⣷⡀⠀⢰⡒⠀⠀⡴⠶⠖⡀⠒⠐⠤⠀⠀⠨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⠬⠁⠀⢘⠁⠀⠉⡰⠿⣿⣷⠤⠤⠴⠆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⣶⣤⡼⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠐⠘⡀⠀⠈⣤⠞⠉⠀⢀⡆⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣧⡀⢰⡀⠀⢀⣾⡷⠋⠀⢋⣄⣀⣰⣆⡠⡯⠀⠀⢿⣥⡴⠞⠋⣷⢀⡟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡛⠳⣀⢹⣉⡝⣉⣤⣨⣿⣞⡏⢀⠜⡡⠂⠈⡿⠉⢖⡘⣿⡃⠀⢻⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⠀⠀⠻⠈⢻⣏⣷⢨⣾⣿⣧⡤⠚⠐⠉⡰⠁⠀⠈⠈⣴⠐⣄⠚⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠿⠀⠒⠒⠚⠒⣲⣿⣿⣿⣿⠟⠁⣤⣰⣦⠔⢲⡤⡤⠀⠀⢋⠁⠉⠉⠓⢦⠀⠶⠄
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⢀⣠⢀⡔⠁⠴⠶⠖⠲⠦⠤⠇⠀⠀⣥⠂⢀⣞⣟⢓⣺⣏⣾⣷⢤⠆⡀⠀⠐⠠⠄⠸⢑⣤⠆⠦
⠀⠀⠀⠀⠀⠴⠉⠁⠀⠀⠀⠈⠀⠢⠤⠤⠤⠤⠤⠀⠀⠤⠤⠠⠤⠤⠤⠄⠀⠉⠉⠉⠀⠀⠒⠊⠀⠀⠀⠐⠒⠛⠉⠉⠁⠰⠠⠤⠤⠔⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠑⠂⢄⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠔⠂⠐⠢⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢢⠀⠀⠀⠘⠀⡌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠃⠀⠀⠀⡐⠀⠡⠀⠀⠈⢆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠣⣀⠄⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠱⡆⠀⠀⠉⠀⠀⣀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢳⠀⣀⣀⡀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⡴⠖⠋⠀⠙⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡼⠀⠀⠀⠀⢠⠞⠋⠀⠈⠉⠙⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠙⣛⠉⠀⠳⣄⠀⠀⠸⣄⣀⣀⣀⣀⣀⣹⠆⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⢉⡁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⡤⠤⣄⠀⠀⣀⠀⠀⠀⠀⢿⠉⢦⢰⡏⠀⠈⡇⢠⠎⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡄⢺⠀⠀⢸⢆⡞⢁⡇⠀⠀⠀⠈⢧⡸⣆⠓⠦⠖⢁⠯⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠿⣄⣙⣛⣁⡼⢤⡼⠀⠀⠀⠀⠀⠘⣆⠈⠉⠉⠉⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡾⡄⠀⠀⠣⠴⠖⠒⡏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⣦⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇⠀⠀⣞⠀⠹⣄⡀⢀⣀⣠⠤⠿⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣼⠈⢷⡀⠀⠹⡄⠀⠀⠀⠀⠙⣄⠀⠈⠳⡀⠀⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡇⠀⠀⢳⡀⠀⢹⡀⠀⠀⠀⠀⠈⢳⡀⣠⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠳⣀⡤⠷⣄⠀⠀⠀⠀⠀⣟⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣉⣑⡇⠀⠀⠀⠀⠀⢯⡴⠚⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠃⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⡄⡀⠠⡄⢀⡄⠀⡄⡄⡀⠀⡤⠀⠀⠠⠀⠠⡄⢠⠀⡄⡄⠠⡀⡄⡄⠠
⠀⠀⠀⠀⠀⠀⠀⣋⡀⣀⣀⠆⡂⢀⡁⡞⠰⢀⣉⡇⣃⡀⣏⣀⠀⣈⡳⠀⡃⢸⠘⡌⢄⣀⠃⡏⢆⣈⣀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣴⡠⢀⡀
⠀⠀⠀⠀⠀⣠⠶⢛⣽⣳⢄⣾⢿⡛⢶⡀⠀⠀⠀⣴⣾⢿⣟⣣⣀⣿⣿⣿⣦⡀⠀⠀⠀⣴⠶⣶⣶⣿⣯⣭⣽⣶⣦⡄
⠀⠀⠀⠀⢠⡏⣴⠈⠁⠀⠀⠛⠀⠀⢢⣿⠀⠀⣸⡏⠀⠊⠁⠀⠘⣿⣿⣿⣿⢷⠀⠀⢰⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠈⣸⠀⠀⢻⣧⠀⠀⠀⠀⣠⣿⣿⣿⡿⠘⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢻⣜⠆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠘⢿⣿⣶⣶⣾⣿⣿⣿⠟⢁⠎⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣯⠥⠒⠁⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣜⣂⣿⣚⣠⡴⠁⠀⠀⠀⠀⠀⠀⠠⣤⢤⣶⣤⠄
⠀⠀⠀⠀⠀⢠⡴⠿⢹⡿⣿⣿⣭⠶⣄⠀⠀⠀⠀⣠⡶⠾⠛⠛⠛⠿⢿⣷⣦⡀⠀⠀⠀⢀⠀⢠⣞⠧⢴⡿⠦⠀⢀
⠀⠀⠀⠀⢰⡏⠀⠀⠘⠀⠈⠃⠈⠃⠘⣧⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⢠⡏⠀⠈⠀⠀⠀⠃⠀⠀⠈⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⡤⠴⠞⠋⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠙⠿⢿⣷⣶⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⢀⣤⠤⡴⢲⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣄⡇⡄⢀
⠀⠀⠀⠀⢠⣶⢿⡿⠗⣀⠀⣙⢲⣶⣦⡀⠀⠀⠀⠀⡀⠀⢰⠟⢿⠻⣄⠐⣦⣄⠀⠀⠀⠀⣀⡤⠙⠷⣾⣿⠶⠋⢤⣄
⠀⠀⠀⢠⣿⢤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣶⡹⡆
⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⡗⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢹⣿⣿⣦⣤⣤⣤⣶⣿⣿⣿⠇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡾⣱⠇
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣬⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢶⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢾⡀⡏⢸⣉⡉⠛⠛⢳⡶⠖⢛⣛⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣯⢭⡤⣄⣸⡇⢡⠞⢑⠏⣠⠶⢃⡤⠚⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢉⡥⠤⠤⠴⠶⢍⠲⢍⣠⠃⠀⡾⢞⡅⣠⣏⡀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⣑⡄⠀⠀⢰⡏⠀⠉⠀⠠⢍⡓⢤⡀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠀⠀⠀⠀⠀⡠⠎⢁⣀⣤⡀⠡⠐⠂⠋⠓⠒⠶⣌⡂⢹⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡞⠄⡼⠉⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡜⠀⠀⣀⣤⠶⠛⠛⠛⠛⠛⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣷⡜⠁⠀⠀⠀⢱⣰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⢀⠞⠁⠀⡀⠀⠠⠤⢤⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣀⡠⠤⠤⣿⣊⠜⠀⠀⠈⠀⠐⠀⠀⠀⠙⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠞⠁⢀⠀⠄⢀⠀⠀⠀⠔⠀⡔⢅⠶⡀⠒⠄⡘⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡜⠁⢠⠖⠁⢀⠐⡂⠑⢄⠀⣄⠀⡄⠀⢙⣃⠔⢊⡀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡼⠀⢠⠗⢉⠁⢠⠜⠉⠱⢬⠇⠈⠈⠀⠀⠈⢄⡔⠉⠁⢤⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣝⠋⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⠀⢸⠄⣂⠐⠓⢠⡄⠀⠀⡠⢄⠀⡖⠐⠄⢀⣼⠢⠀⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣂⣈⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢣⠀⠀⢧⣀⡈⠵⢊⣠⡄⠀⣠⢼⡆⡻⡤⡈⠟⠈⠠⢠⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡉⠩⣤⢭⣓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣹⡆⠀⠈⣆⠀⠀⠀⡴⠈⠈⠊⠱⠒⠣⠀⡣⠁⠘⠦⠴⠒⠓⣉⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢶⡌⠉⠛⢛⠃⠈⣙⠛⠃⠈⢉⠩⠝⠛⠉⠉⠉⠀⢹⣆⠀⠘⣆⠀⠀⠳⡜⠠⠠⠀⡅⣠⠖⠁⢀⣠⣤⣴⣶⣟⣉⣙⣛⠛⡷
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠞⠋⠁⠀⠀⠀⣀⠀⠀⠙⠒⠋⠀⠀⢀⠄⣀⡤⠶⠒⣾⠈⠳⣤⡈⠣⡀⠀⠉⠒⠢⠴⠖⠁⢀⣴⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⣠⠞⢉⡀⠤⠒⠒⠈⠉⠉⠙⠁⠀⠀⠀⠀⠌⣠⠄⡰⣡⠞⠁⠀⠀⣠⠏⡀⠔⢹⠙⢳⡾⣷⣤⣄⣀⣤⡤⠶⠋⠁
⠀⠀⠀⣴⣧⣬⡥⠤⠤⢤⣤⣤⣀⣀⣀⣀⣤⠖⣃⣠⠞⣯⣼⠞⠋⠀⢀⡴⣛⣥⣤⠀⠀⡦⠀⡀⠳⣄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢼⠷⠛⠉⠀⠀⠉⠀⠀⠀⠀⠘⢋⡵⡚⣁⠀⠩⠁⡀⣿⠳⢼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣹⠏⣠⢋⣼⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡷⠛⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢝⡶⠶⢲⣛⣈⣠⣛⠀⡳⠿⠿⣥⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣄⡽⢛⢁⠀⠀⠀⠀⢀⣹⣏⠛⠀⠀⠀⢶⣘⠟⠁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣿⡘⠗⠊⠀⢀⠉⢋⢠⡄⠀⠀⢸⡆⢙⢷⣀⣠⠁⣸⢿⣤⠄⣔⠚⢱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠊⣹⠟⡟⠀⠁⠀⠘⢷⣄⣡⣷⣀⣀⢃⣿⣾⠟⠋⠉⠛⢷⡾⢿⣖⣺⣿⣦⣼⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢛⣭⡿⣦⣇⢀⠐⠠⢤⣾⠟⠉⠀⢀⣩⡝⢯⠁⡀⢀⠀⠠⠘⣻⣷⢨⠉⢸⣿⣿⣯⣯⡀⠀⠀⠀⢠
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢌⡐⡄⠈⠃⠉⢿⣗⡢⠽⠏⣇⠀⠀⠀⠈⢿⢧⢲⡆⢩⠀⠀⢀⣆⣿⣿⠄⢀⣿⣿⠛⠂⠎⡁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡪⠴⠋⡈⡩⢙⣷⣦⣴⣍⠃⠀⠀⢀⡴⣺⢚⣗⣰⣦⣤⡿⣣⢿⣿⣾⣿⠙⢢⠶⣦⠚⠭⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠻⠐⢟⠈⠰⠉⠉⢖⣯⡭⣷⣤⣶⣮⣭⠶⣫⣲⣤⣧⠾⢿⣟⣛⣛⣋⣙⣅⠅⠁⢈⣀⣈⠄⠀⡰
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠧⠀⠠⠀⢀⢨⡞⠻⠀⠈⠁⢡⡚⡛⠯⠥⣙⠉⡥⡈⠑⠙⠻⠿⠄⢈⠎⢚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣾⠏⢊⡥⣄⠸⢀⠚⢡⣍⣛⣠⠶⡌⢹⣟⠵⠲⠚⠆⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠒⠊⠈⠉⠀⠈⠉⠀⠐⠋⠀⠁⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠲⠙⠂⡤⠤⡑⠀⣤⡄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⣂⠈⡕⠦⢻⡀⠀⠀⠀⠈⠂⠃⠐⠣⠇⠋⠠⠀⠀⠠⡁⠤⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡼⠡⠚⢳⡀⣥⣆⣂⡠⠀⠤⠈⠂⢀⠀⠀⠁⡀⢀⠠⠤⠈⢃⠔⠀⠀⠀⠠⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠐⠀⠄⣅⢦⣱⠦⡤⣤⠂⣀⠛⡏⠓⢠⢉⡈⠁⠐⢛⠁⣢⣀⠁⢘⠎⣶⠂⠉⠅⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢢⡑⠤⣥⣦⠯⠔⣂⣈⣁⣐⠶⢀⣈⡁⠆⣅⠀⠀⠙⠁⠀⠀⠀⠠⢁⡄⠀⠀⠁⡀⠈⢃⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣄⠑⠤⡀⠒⣀⠋⡔⠐⠈⢘⠀⡈⡀⣀⣵⡌⢁⠌⠀⠙⠄⠤⠖⣣⢀⢏⣈⢁⡉⠐⠚⠁⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⡋⡡⠤⢤⠍⣠⠉⠑⣢⠘⣢⡁⠵⢌⡙⠩⢦⣀⣐⠀⠤⠄⢉⣠⠤⠚⣂⡀⠻⠉⡠⢐⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠣⣄⣘⠁⠖⠒⢐⡉⡍⠘⢡⠔⠊⠁⢈⡒⠒⠒⣲⣢⡔⡺⣛⠤⠊⡉⠔⠈⠃⠘⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠌⠙⠆⠑⣀⠀⠁⡘⠈⠕⠨⠁⠄⡚⢐⢿⣦⣭⠄⢘⡉⢤⡬⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠦⠭⠀⠀⠀⠤⠮⠵⢌⠒⠠⠴⠒⠛⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠟⠈⣻⠆⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠴⢖⣿⢖⣶⠆⣴⣲⠆⣲⡟⢢⡶⢓⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢾⣧⢾⣯⢾⡌⣿⠖⣿⡵⣿⡥⢿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠠⢊⡆⠀⣤⠀⠤⢤⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡶⠚⠁⠀⣴⠠⠁⢸⠀⠀⣿⠀⠀⣼⠃⣼⡁⢹⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⠴⠂⣷⠂⠀⢸⡄⢀⡿⠀⠈⠃⠀⢋⡤⣾⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⢔⠁⠀⠀⠀⠀⠀⠀⡳⢢⠇⠀⠀⠀⡰⠋⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⡟⠀⠀⠀⠀⠀⠀⡌⠀⡞⠀⠀⠀⢰⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠐⢰⡧⢻⢠⡟⡐⢀⡸⣀⠞⠁⠀⣀⠀⣨⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣘⠃⠸⠯⠁⠀⣾⠁⠀⠊⠉⢩⡏⠙⡟⠀⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡿⠿⠿⢿⠆⠀⠀⢰⡇⢀⠔⢸⠂⣼⠀⢰⡇⢸⡇⣼⠏⢠⠁
⠀⠀⠀⠀⠀⠠⣾⣿⠿⠛⠉⢁⣿⠁⠀⢠⡖⠀⠀⠀⠀⢸⡧⠂⠀⠸⠀⠿⠀⢸⡇⠘⠇⠻⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡏⠀⠀⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠸⡇⠀⠀⠀⠀⠀⣀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⠇⡠⠀⣷⠀⠀⠔⣽⠂⢠⣇⠎⢠⡟⠀⢀⣠⡾⣷⠄⠈⠯⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠰⠁⠀⣿⢀⠎⠀⣿⠀⢸⠇⠀⣾⢁⡴⠁⢘⢓⡟⠀⢠⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠈⠁⠀⠀⠙⠊⠀⠀⠉⠀⠀⠀⠀⠻⠋⠀⠠⠁⣼⠃⠀⠧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⣉⣉⣁⣀⣉⣉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢄⡀⠀⠀⠒⢍⡲⣄⠈⠓⠐⠂⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠈⠓⢝⣦⣀⠢⣀⠀⠀⠀⠀⠢⢷⡤⠤⠀⠀⠀⠀⢀⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⣆⠀⠀⠀⠀⠀⠙⠺⢝⡲⠥⣤⣄⣀⣀⣀⣒⣀⣀⠀⠠⠔⣊⢴⣗⡒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠕⡀⠀⠰⠺⡆⠀⠀⠀⠀⠀⠀⠀⠨⢉⠒⠒⠋⠭⠭⠍⠛⠒⠒⠋⠉⠁⠈⠀⠈⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⢬⠀⠦⠄⠹⡴⡀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⡠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠠⠋⠁⠀⠀⠹⣌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠦⠐⠒⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠳⣕⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠧⠥⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⠀⣤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣔⣠⠖⢆⠀⠀⠡⡀⠀⠀⠀⠀⠀⡠⠀⣼⢁⢀⣀⣀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣢⣀⠀⠀⠀⠀⠉⡠⠞⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠜⣁⠀⠀⡀⣀⠀⠀⢀⠀⡀⠀⡼⢀⠄⠀⠀⠀⠀⠓⠦⡄⢀⠀⡀⠀⡀⢀⠀⢀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠃⠊⠸⠃⠋⠎⠰⠁⠸⠅⠺⠀⠋⠐⠀⠀⠠⡀⠠⠀⠀⠇⠚⠅⠚⠀⠏⠰⠃⠀⠎



⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠐⢰⠀⠀⡀⠁
⠀⠀⠀⢀⣿⢈⣿⣐⣀⠐⣀⣸⣿⣀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣾⠀⠀⡇⡇
⠀⠀⠀⠰⣿⠚⢹⡏⣿⢀⣿⢹⡏⣾⢻⣿⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⢀⠀⠤⣄⢦⠞⠀⠀⠀⠀⠀⢸⠀⠸⠐⡟⠀⠀⠁⠁
⠀⠀⠀⠈⣿⠀⠹⡷⠿⠾⣾⠿⠧⠿⡾⠿⠀⠀⠠⠀⢰⠏⠀⠀⠀⡤⢐⣮⡍⠤⠀⠀⠀⠘⠀⠝⠀⠀⠀⠀⠘⡀⠀⢠⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⡏⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢸⡇⠀⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠶⣬⣥⡄⠀⠀⠀⠀⢨⢸⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⢉⡣⢤⣌⠢⡀⡁⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠐⠠⣆⠁⠀⠀⠀⢠⡘⢃⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠴⠄⣀⠀⢒⡊⠙⠚⠷⢂⣰⡬⠃⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠈⠉⠁⠉⠒⠒⠓⠚⠛⠀⠀⠀⠀⠃⡞⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠠⠐⡨⠴⣂⠀⠁⠲⡩⠦⡀⠈⠁⠀⠀⠀⠀⢠⣀⠆⠃⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡇⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠄⡟⠑⡶⣈⢀⣶⣶⠻⠃⠀⠀⠀⢰⠘⠋⡰⠂⣦⣲⠦⠾⠿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠉⠀⠜⠁⠀⠀⠐⠾⠊⠀⣴⠼⠶⠋⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⣁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢋⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠠⣀⠀⢤⡀⠀⠀⠀⠀⠀⠐⠖⠘⠂⠀⢀⠀⣠⡞⠁⠀⠀⠀⣾⠃⠀⠀⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢦⡌⣐⡢⡔⢲⣶⡭⠛⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⣀⢶⣞⠉⣁⡬⠑⠂⡩⡏⠀⣇⠶⡺⠟⠑⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠌⣛⠚⢂⣈⣛⡖⠀⠉⠄⠱⢤⡀⠐⠀⣉⡱⠋⡍⠃⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠔⣦⡀⠥⠉⢐⢶⣠⡇⠀⣖⡀⠁⠐⢊⠁⠀⢰⡨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠈⠒⡈⠂⠰⡦⢮⣍⠠⣬⠤⢜⡂⣍⣥⣦⣉⠙⠉⡥⢀⢠⠌⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢸⠈⣇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠉⠻⠧⢶⣴⡁⡠⣦⠀⣀⠡⠔⢉⠡⣄⠀⡐⢿⠏⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠙⠩⣯⡿⠿⢂⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢥⡰⣬⣩⠐⠂⢄⣀⣤⣤⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣄⡨⣏⣊⡴⠯⠷⠓⠚⠓⠿⠗⠛⠁⠒⠾⢯⡭⢄⣙⢎⢲⣲⡤⡀
⠀⠀⠀⠀⠀⠀⣄⠶⣢⢦⡭⠟⠂⠁⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⠛⠾⣶⣯⣄⡰⠤⠦⣄⢄
⠀⠀⠀⢀⡞⡽⡽⢪⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠂⠀⠀⠀⠘⣷⠝⢿⣿⡎⣁
⠀⠀⡀⠶⠕⠟⣿⡾⣷⠀⠀⠀⢄⠀⠦⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⢤⡐⣻⡆⣠⡀
⠀⠺⣴⠖⣓⣃⣒⢕⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢳⠟⠚⠻⣟⣯
⠀⣨⠷⢉⣫⢵⣩⣬⣓⢤⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⣯⣞⡜⢈⢝⢣⠘⣽
⠀⣯⡤⢬⡽⣦⣺⣻⣭⣤⣽⣆⠀⠀⠨⢇⣀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⡴⡿⠟⣝⡆⣸⠟⢀⢇⠈
⠀⠙⢗⡿⢖⡢⣍⣛⣋⡭⢡⡞⢳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡠⢋⢜⣗⣞⡛⢅⣿⠴⠫⡪⠂
⠀⠐⢶⠈⠝⣓⠭⠷⣮⠿⢊⡾⣶⢫⢺⠭⠍⠰⠶⢖⢀⣤⡀⠀⠀⠀⣠⠾⣫⢲⡴⢻⡶⢫⢵⡾⡐⡷⠞⢉⣢⠔⠈
⠀⠀⠀⠀⠺⠿⢸⡐⣲⢯⣝⣾⢡⣿⢸⠹⠵⡥⣣⠶⢶⢆⠯⡛⢦⡛⣹⢟⡌⣰⣖⡚⢠⡏⡬⠵⢝⡺⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠳⠾⠭⣝⣛⠭⢶⣃⠫⠶⠽⢷⢎⣬⠽⢳⢛⡔⢁⣫⢞⣉⡙⠑⡫⠞⠂⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠙⠋⠉⠵⢂⣊⢏⡚⠯⠊⠉⠣⠍⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠜⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠠⠂⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⣄⠠⠀⣀⣨⢶⠤⣄⡀
⠀⠀⠀⢀⠥⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠋⠄⠄⠘⠊⠀⠀⠈⠙⠀⡒⠒
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠐⢊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠊⠀⢀⢼
⠀⠀⠈⣀⠑⠄⠐⠀⠂⠉⠀⠀⠀⠜⠀⠀⣠⠎⠜⠀⠀⠀⢀⠀⢈⡆
⠀⠀⠀⠉⠐⠠⠙⠀⠀⠀⠀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠉⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠁⠀⠀⠀⠀⠄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠆
⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣰⣜⠃⠀⠀⠀⢀⠃
⠀⠀⠠⠌⠙⠣⣄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⠉⠀⠀⠒⠂⠈
⠀⠀⠀⠠⠀⠀⡎⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠆⠀⠀⠀⠀⠀⣠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣴⣞⣠⢶⡆⠶⡶⣰⢋⡴⢋⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠟⠁⠈⠉⠉⠈⠉⠈⠁⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀
⢺⣿⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⢻⣿
⢼⣿⠘⠛⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠿⠿⠟⠋⢸⣿
⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢺⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿
⢠⣿⠟⠛⠿⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠟⠛⠻⣿
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣦⠀⠀⢸
⣿⡇⠀⠀⣿⡏⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⢹⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣟⡷⣦⣤⣤⣶⣿⣿⣿⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⣿⣟⣿⣿⢛⡁⠘⠛⣛⡈⠛⣻⣯⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠿⣿⡽⢿⣿⣴⠾⠋⠛⠷⠾⠿⠿⠃⠀⠀⠀⠉⠛⠻⣷⣤⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⣿⡇⠀⠀⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠏⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣾⡿⠿⠟⠋⠉⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠈⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠾⠒⢒⣂⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠉⢀⠀⠀⠘⡉⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⡻⣿⣷⣾⣢⠀⠠
⠀⠀⠒⠠⣾⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣠⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣮⣿⣿⣿⣿⣿⡀
⠀⠀⡆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠿⢷⣶⣆⠀⡀⠀⡀⠀⠀⠀⠀⠀⢷⣿⣽⣿⣿⣿⣿⣿⣿⡷⠀⠈
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣿⡾⠇⠀⠀⢀⠂⣻⣷⣿⢟⣻⣾⣿⣿⣿⠃
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡄⠀⠀⠀⠣⠃⠉⠻⠿⠵⠛⠛⠉⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣩⠯⣑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠠⠆⠀⠀⠀⠀⠀⠁
⠀⢀⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣟⣛⠿⣦⣼⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀
⠀⠸⠉⠙⣿⠀⠀⠀⢨⠀⢀⠀⠀⠀⠐⡖⡮⣻⢿⢷⡞⢫⣼⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣻⣿⣿⣷⡆⠀⠀⠠
⠀⢘⣀⣶⣿⠀⠀⠀⢰⠀⠀⠑⠤⣀⡀⠘⠙⠎⠻⠛⠿⠟⠿⠿⢿⠿⠓⠀⡠⠔⠀⠀⠀⠀⠀⠈⠀⡀⠀⠿⢿⢿⣿⡿⣿⣿⣿⠄⠀⡠⠄
⠀⠘⠸⠪⠿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠴⠶⠴⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠲⠶⠶⠒⠒⠋⠀⠐

⡅⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠈⠂⠑⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠀⠂⠔⠁⠀⠁⠈
⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠈⠢⡂⠀⠘⠀⠀⠢⠀⠀⠀⠀⠀⢁⠀⠐⠀⠀⠀⠀⠀⠊⠀⠀⠀⡠⠊⠀⠠⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠄⠀⠑⠤⡀⠀⠂⠀⠀⠈⠢⠀⢁⠀⠀⠐⠤⠃⣀⠀⠼⠘⠂⠀⠠⢄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⡈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⠄⠈⠁⠀⠈⠁⠐⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠠⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⡇⢀⠁⠀⠀⠀⠀⢀⠅⠀⠀⠈⠢⡀⠀⠀⠀⠀⡨⠂⠀⢀⣤⠤⠤⢤⣄⡀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠲⢄⠀⠀⠀⠀⢀⠂⠀⠀⢀
⡇⠀⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⠐⠁⠀⠚⢉⣀⠀⠙⠀⠀⠀⢠⠎⠀⣠⣍⡑⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠀⠀⢀⠔⠁⠀⠀⢀⠠
⡇⠀⠀⠀⠘⠢⠀⠀⠂⠀⠤⠀⠀⠀⠀⣑⠂⠠⡠⠀⠀⠀⠀⢰⠋⠉⢷⠀⠀⠄⠀⡜⠀⠸⠁⠈⣷⠀⠀⠀⠀⠀⡴⠄⠐⠀⠀⠀⠀⠐⠀⣀⠠⠒⠈⣀⠠
⡇⠀⠀⠐⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠞⢄⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⢀⠒⠃⠀⡀⠂⠀⠐⠉⠀⠀⠈⠁
⡇⠀⠀⠀⠀⠠⠄⢈⣁⠒⠂⠁⠀⠄⡌⠀⠴⠈⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠙⠁⠀⢀⣠⠔⠋⠈⠀⠀⠀⠀⠀⠀⠁⡖⠀⠑⠀⠀⠒⠥⠁⠀⠀⠀⠀⠴⠂
⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢷⠀⢃⣄⠀⡀⡤⢠⠄⠾⠇⠶⠽⠻⠟⠻⠟⠛⠐⠃⠖⠏⠻⠚⠇⠆⣠⣀⠈⢴⡗⣠⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠱⠐⠃⠔⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠸⠓⡷⢠⢄⢴⡰⠀⡀
⡇⠀⠀⠀⢤⠠⠷⠒⠎⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠴⠀⠀⠀⠉⠁⠀⠀⠐⠁⠀⠀⠀⠀⠄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠑⣰⣦⠰⣄
⣇⡔⣖⠨⠆⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⢠⠠⠠⠀⠀⢐⣄⢀⣈⠀⠀⠀⠀⠀⠀⠲⢦⠀⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠄⠁⡒⡀⠀⠀⠀⠀⠀⠀⠈⠑
⡧⠉⠀⠀⠀⠠⣂⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠊⠈⠈⠀⠀⠀⠒⠬⢨⠀⠉⢀⠀⢀⣁⠀⣂⠐⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠂⠸⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠋⣀⡉⠁⠀⠄⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣂⣤⡆⡠
⡞⣣⠄⠈⠡⠀⠀⠀⠀⠈⠄⠁⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠀⠩⢄⣀⣀⠀⢠⣀⣠⢖⢀⡀⠀⠀⠀⠀⢼⡦⢀⣀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢈⡀⡷⢆
⢇⡀⡬⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢠⢰⠆⠀⠀⠀⠀⠘⠷⠅⡼⣉⠛⠋⠉⣷⠕⠊⠀⠀⠀⠀⠀⠝⠳⢺⠗⠂⠀⠀⠔⠂⠪⠐⠀⠀⠀⠀⠠⠘⠂⢀
⡇⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⠦⠄⠀⠀⡃⠈⠰⠆⠀⠀⠀⠀⠀⠂⢀⠇⡴⠶⠶⠶⠲⡄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠰⠄⠀⠀⢄
⡇⠀⠀⠘⠀⠀⠀⠘⠀⠙⠀⠠⣤⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠺⠃⠀⠀⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡈⠦⠂⠀⠀⠀⢄⠀⠉⠀⠈⠒⢄
⡳⣄⠀⠀⠀⠀⠀⢘⠐⢃⠁⢀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢦⡀⠃⠶
⡇⠘⣎⠀⢀⠄⠀⠈⠀⠈⣤⠀⠒⠀⠀⠀⠀⠂⠠⠀⠀⠄⠀⠳⠙⢇⣴⣄⠀⠀⠀⠀⣠⡆⡹⢋⠞⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠨⠀⠀⠠⠀⢛⠳⡈
⠅⠐⠺⣆⠞⠀⣠⠀⣠⠀⠀⠘⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠓⠀⣀⠐⠉⠠⡄⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠹⡄⢸⡆⠀⠀⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆⠀⡇⠘⡇⠀⠀⡇⡇⡠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣏⡛⠒⠲⠶⣻⠄⡟⠉⡇⠹⠛⠓⠶⢁⡏⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠁⠉⠢⣁⢿⡰⡡⢠⠀⡦⠀⠈⣡⠾⡛⠍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⠀⢠⠜⠊⠉⠉⠈⠉⠛⠻⠚⠉⠉⠉⠉⠛⢣⢤⠀⠘⢛⢦
⠀⠀⠀⠀⠀⠀⣼⠓⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱⡀⠪⣮⣧
⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠂⡀⡔⢔⢅⠀⣹⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡇⠀⠀⠀⠀⠺⠱⠰⢈⣎⠃⢿⣿⣷⠀⠀⢀⣀⣠⠤⢦
⠀⠀⠀⠀⠀⢸⡏⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣠⣀⡤⠼⠶⠶⠴⠶⠗⠒⠚⠛⠛⠋⠉⠉⠐⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⠋⠁⠀⠀⠀⠒⠒⠀⠄⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠹⣤⠀⠘⠀⠀⢀⣤⠀⠸⠀⢰⠏⢀⡀⠠⠀⠐⠒⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣶⡷⠄⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⢄⠃⡜⣿⡀⡶⠄⣿⠀⠠⠰⡀⠀⢀⡀⣟⢛⡬⠇⣴⢦⡄⣤⢄⠠⡰⣶⣦⠏⢰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡉⠂⢷⢟⢽⡇⠂⣿⠀⠀⠣⠳⣄⠀⠙⢮⡚⠲⠊⠊⢸⡁⣿⣾⠘⣷⢘⡷⢠⠊⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣘⠒⠁⢈⡾⣇⠀⢑⠵⡜⢮⡓⢀⠙⠲⢦⣜⣁⠙⣉⣠⣛⣉⠥⠚⠁⠰⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣬⣧⣀⢈⠚⣷⣿⣦⣀⠰⢦⠀⠈⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢭⣛⣿⣿⣿⣽⡶⣤⠶⠀⠴⠦⢀⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠛⠛⠚⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠐⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⠀⠀⠀⠀⠸⠈⠋⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡀⠀⢾⡻⣶⣷⣇⠀⠀⣄⠀⢀⡏⠎⢦⣼⡇⠀⠀⢶⡎⡇⠀⠀⠀⠀⢲⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠃⡙⣿⣿⣷⠀⠇⡀⡞⠁⢠⢀⢿⠙⡆⠀⢛⣿⣸⠀⠀⠀⠀⢸⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠐⡆⠀⠀⢶⡌⠻⣿⡄⠞⢡⢃⠠⠃⠌⠈⣷⠙⡆⢸⣿⣏⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠟⣦⡙⣷⢰⠈⠾⠀⠘⢀⢠⠇⡀⣷⢀⣿⣯⢣⢳⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⣯⣷⣌⢷⡄⠀⠃⢀⠃⠈⣆⢳⢺⣸⣿⢃⣿⣼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠙⣇⠀⠀⢸⣽⢫⣆⠁⡆⠀⠈⠰⠀⣠⢀⠚⣿⣹⠀⢸⣇⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⠀⢹⡀⠀⠈⡷⢸⣹⡧⡨⣦⠀⢠⡆⠁⡾⠰⣾⢿⡆⠰⣿⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠰⠡⠙⢷⡟⢎⣳⡄⠐⢀⢡⡄⠁⡈⣷⠀⡟⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢂⠆⠈⠻⣫⡷⣥⣡⡇⢸⢇⠀⡀⣿⡄⣧⡇⠀⠀⠸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠀⠈⠌⡀⠀⠹⣻⡝⢦⠸⣇⡿⠀⠇⡼⣧⢈⣿⡄⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠐⠐⠀⠀⢙⣷⣎⠱⡜⣷⡀⠂⢧⣿⡈⢹⣷⠀⢠⡇⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠀⢸⢺⢫⣷⡘⢮⡻⢷⠀⣿⡇⠌⡜⡇⠈⢷⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢁⠀⠀⠘⠆⠻⢷⣎⡳⡱⡅⣽⢻⣄⠇⢹⠀⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡄⠐⠘⡆⠀⠘⣿⣷⡽⢮⠺⣣⡻⡐⣧⢇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡘⡀⠀⢁⠀⠀⢻⡷⢳⡎⠱⡙⡷⡇⣿⡼⡇⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠐⡡⠀⠀⡆⠁⡘⣡⢱⣟⢗⠙⣎⠿⢿⣣⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠃⠀⠁⠸⢸⠸⢸⡝⣾⡂⢋⣧⡈⡳⣽⡇⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠘⠀⡀⢠⠀⡇⠀⣿⣏⢻⣿⡀⡟⣔⠜⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠄⠀⠀⠘⡄⢠⠀⣼⡜⢿⣿⣿⣤⣿⢆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀⠐⡀⣠⠆⢣⡜⡄⠹⣠⠀⡟⡜⢟⢿⠸⠷⢔⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢷⠀⠱⣩⠆⠈⣶⣀⢸⣿⡈⣻⢱⡨⠋⣳⣼⣼⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⡆⠀⠉⣟⢤⢻⣷⢂⣿⡧⠏⡆⣧⣸⡗⠹⣿⠇⠐⢝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⠀⠀⠘⡄⢘⢹⡎⣸⣧⢼⣇⠸⣞⢃⠘⣟⢦⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠈⣷⠈⠹⢷⠽⣯⡞⣿⠀⢉⢋⠀⠁⠸⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆⢸⣴⢻⡄⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⡄⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠈⡆⢡⠀⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠜⠀⠚⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠌⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠤⡅⠀⠤⢤⠁⢀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡁⣄⠈⠐⡁⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⠔⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⡄⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠤⠤⢄⣀⠀⢀⠎⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠠⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⢆⠀⠀⠈⠙⢮⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢄⡴⠚⠉⠀⠀⡀⠀⠀⠈⠉⠓⠬⡆⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠋⠀⠉⠁⣀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠐⣲⢤⡀⠈⢦⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⣾⡏⠀⠁⠀⠀⠙⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡇⠀⠀⠨⣭⣁⣀⣈⣉⣉⣤⣶⣿⣿⠁⠀⠀⠀⢰⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠹⣿⣿⡿⠟⠟⠉⢙⡿⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠈⠛⠧⠤⠠⠔⠋⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⣀⣀⣁⣀⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠈⠉⠉⡹⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠⠤⡀⠶⢀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠘⣄⠀⠀⠌⠢⡀⠀⠀⠘⠀⠀⠈⠃⠀⠑⢄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠈⢢⡀⢄⠀⠈⠲⢤⣠⢄⠀⠀⢀⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠙⢦⡑⠠⣀⡐⠁⠀⡇⠀⠈⠑⠢⢄⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠤⢀⡀
⠀⠀⠀⠀⠀⠈⠒⠬⣀⣀⣀⡆⠀⠀⠀⠀⠀⠈⠁⠒⠠⠄⣙⠲⢤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠞⠉⠀⠂⠀⢁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡈⠙⠓⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠦⣄⠀⠀⠀⠈⠢⣐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⡀⠀⠇⠈⠳⡀⠀⠀⠀⡙⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⡟⠂⠀⠀⠠⠐⢀⠜⠀⠀⠀⠙⢆⠀⡰⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠌⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⣤⣤⠀⡎⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⣹⣷⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⡀⢽⡄⢀⠆⠀⠀⡤⠄⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⢀⣂⣫⡾⣶⡋⠀⠀⠁⢠⠀⠀⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⢹⡿⠟⠿⣟⠉⠀⠀⣾⣷⣎⠁⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠈⠂⢠⠀⢈⢹⠧⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⡀⢸⡇⢀⣽⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⣀⣴⠏⠀⢧⡾⠉⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⣉⣰⣼⣾⣡⡦⢈⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣨⠠⠵⢔⣢⡀⠀⠀⠀⠉⠛⠻⢿⣷⡼⠇⠀⠰⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢂⡠⠠⠔⠀⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠉⡷⠹⣶⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠙⠛⠓⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠛⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⣤⡀⣀⡀⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣪⣗⠓⠚⡏⠤⢔⣍⣀⡛⠿⠳⡶⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣆⢀⡤⠼⢩⣡⠀⠀⠀⠀⢤⠿⣭⡁⠀⠀⠈⣷⡜⠉⠑⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣐⣽⣧⠙⡉⠀⠀⣄⠉⣔⣦⠀⠀⡘⣇⣸⣷⣤⣎⣠⡟⣶⣞⠲⣯⡁⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣌⢰⡏⢹⠀⠀⠀⠀⢹⣧⣼⠿⠦⠤⣡⣿⡿⠉⠀⠀⠙⣿⣟⠿⣭⡽⣿⣶⡿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠴⣿⠻⣿⣄⡀⠉⣱⣿⠋⠀⠀⠠⣴⡎⠓⡀⡄⠔⠀⠈⢨⣿⡇⠖⢠⣿⣿⣿⢿⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣔⠂⣈⡀⠬⢿⣾⡋⠃⠣⡄⠀⠀⠄⠹⡙⣿⡇⢐⡀⢀⣼⣞⣿⣟⣠⣾⡟⢇⣀⢉⡴⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡎⣩⡔⠔⡨⠿⢛⣾⠷⣄⠀⣀⡠⢮⣛⣵⡓⠾⡟⣿⣯⣾⣿⣿⠿⡧⢨⠻⠑⠅⠘⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠁⠸⣧⠀⠁⠀⠉⠚⣏⣽⡛⠻⠟⠟⣩⣾⠿⠿⠿⠩⠽⠶⡳⢶⣶⡞⢊⢄⣄⣴⠴⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣀⣐⣤⢰⠇⠀⢠⡄⣤⠞⠦⢤⠍⣙⠦⣴⡽⢂⣀⣠⡉⣉⠤⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠄⠋⢩⠭⠐⠢⠘⠻⠖⡊⠩⠅⠪⢊⠁⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⡲⣔⡇
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⢸⣷⡴⣿⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠠⣦⠶⠦⠀⠀⡀
⠀⠀⠀⠀⠀⢐⡏⣠⢀⡀⠆⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⣠⠀⠛⡗⢆⣤⠀⠀⠀⢠
⠀⠀⠀⠈⠀⠚⣅⢀⠘⠙⣦⣤⡤⣾⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⠀⠐⠀⠈⠌⠙
⠀⠀⠈⢂⠀⠀⠀⢸⡀⢈⡸⠋⢠⡾⠀⠂⠾⠦⠀⠀⠀⠀⡀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠀⣠⠂
⠀⠀⠀⠈⠰⢄⣀⣸⣃⣾⡁⠀⠀⠘⠀⠂⠀⢄⠃⠀⠀⠀⠀⠈⠈⠉⠀⣀⣤⣀⠀⣀⣄⣜⡠⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢡⠀⠀⠀⠀⣼⠀⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⠤⠿⠰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠙⢇⠀⠀⠠⠀⢿
⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡄⠀⠀⠊⠈⢧
⠀⠀⠀⠀⠀⠸⡄⡀⠀⠀⠀⠀⠀⡀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢳⣄⡀⡀⠄⠸⣷
⠀⠀⢀⠀⠰⠊⠁⠘⠲⢤⣀⡀⠀⠀⠀⣼⠋⠠⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠉⠻⢷⣄⣰⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠈⠆⢹⡇⠀⠀⠀⠀⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠩⣿⡿⠃
⠀⠀⡀⣾⠀⠀⠀⠀⠀⠃⢸⣷⣦⡀⡈⢷⡇⢀⣿⠄⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠈⠻⠀⢀⣠⣤⣮⡴⠟⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⡠⣦⣀⢀⣶⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣸⠅⠄⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢠⡀⠊⠀⠀⣠⠉⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠂⠌⢷⣆⠰⡍⢧⡴⢚⠁⣠⣾⠀⢠⡀
⠀⠀⠍⠀⠀⠗⠀⡀⢣⡀⠀⡀⢰⣆⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠁⠁⠁⠘⠁⠛⠄⢻⠁⠌
⠀⠀⠀⠀⠀⠊⢉⠀⠀⠉⠉⠈⠁⠀⠀⡔⠈⠁⠆⠀⠀⠀⠀⠱⠤⠤⢧⣄⣠⡴⠀⢀⣀⠀⠀⣄⣀⢁⡄
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠉

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾
⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⢀⣀⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⡀⣤⣴⣾⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠛⠀⠸⠷⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣶⣶⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⠒⢲⢀⡆
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣿⣿⣷⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢯⢳⣺⠀⢸⢊⠧⣀⣀⡀
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⠶⣖⣚⡀⢸⢀⡇⠮⢔⠽⠛⢦⡀
⠀⠀⣰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠀⣀⢎⠤⡉⣄⠐⠥⣀⣀⡀⢳⡀
⠀⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡸⢰⠁⠀⠐⠛⠛⠁⠀⣷⠀⠉⠑⠒⠋⠁⠀⣇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢳⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⣈⣁⣤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣀⡭⠴⠖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠂⡡⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡣⢿⢢⣉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣫⡵⡃⠈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠘⠘⠃⢿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠂⠀⠀⠀⠀⠀⠀⠀⠉⠤⢸⠊⠠⢾⡿⡟⣇
⠀⢀⡠⠐⠀⠀⠀⠀⠀⠄⠀⣤⢞⣽⠿⠛⠉⣳⡌⣛⡛⡦⣤⣤⡀⡰⢽⠄⠃⢹⡀⠀⢠⠄
⠀⡆⠀⠀⡄⠛⠀⠀⢠⠶⢀⣻⣻⠷⠞⠉⣉⢿⣶⣞⣛⣷⣿⣿⣶⡧⠀⠁⠾⠀⠀⠟
⠀⠡⡀⠠⡀⠀⢀⣀⠧⡽⠛⢻⣻⣿⡓⢻⢛⡐⢒⢼⣛⢿⢾⠿⣿⠿⠿⢾⢳⡀⠈⠅⣂⠀⡀
⠀⠀⠀⠠⠌⠁⠐⢷⣽⢿⣁⣡⡻⣮⠕⣓⣿⣤⠟⠞⣩⣾⣋⠳⢅⠁⠈⠉⠉⢷⣠⡀⠀⠈⠒⢕⠠⡀
⠀⠀⠀⠀⠀⠈⠒⠠⣈⠙⠻⡜⣚⠿⣦⣌⣉⣉⣉⣤⠭⠭⠵⠌⠂⠁⣩⣉⣉⣍⣭⡇⠀⠈⠀⠀⠡⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠅⢒⠠⠁⢈⠓⠿⠅⣂⣤⠿⠶⠶⣒⡴⢾⣩⠟⠣⠀⠁⠨⠯⠂⠀⠀⠔⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⠭⢀⢀⡀⠉⠠⠄⠀⠀⡛⠁⠁⠀⠀⣀⣀⠀⡀⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠒⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢌⠒⢄⡀
⠀⠀⠀⠀⠀⠜⠮⣙⠦⢭⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠍⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠒⠢⢄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠷⣄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠙⠢⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠒⢲⣤⠤⢄⣠⠒⠲⣤⢀⡠⠔⠒⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⡫⢎⠥⠂⠁⠀⢸⣿⠆⢌⣙⢯⣋⣍⢀⣤⠶⢿⠿⡧⠦⠤⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⡬⠴⠐⠆⠐⣛⡻⠿⠋⠉⢆⣀⣀⠈⠭⣙⠲⠤⣄⣀⠀⠀⠩⠭⢅⡘⠻⢿⣦⡀
⠀⠀⠀⠀⠀⣠⠴⠖⡻⠟⡫⢕⣠⡴⢀⠴⢋⠥⠒⠂⠉⣁⡤⢤⣤⡤⡤⣤⣬⡱⢶⡩⢓⢦⣤⣀⠀⢙⡳⣦⠻⣜⢿⣛⠲⢦⣄
⠀⠀⠀⠀⡾⣅⠐⠏⠐⠠⠖⠡⠋⠀⠂⠀⠁⠀⠂⠁⠈⠐⠈⠝⠓⠀⣈⠄⣱⠘⡆⡩⢑⠢⠭⣙⠻⠶⣤⣬⠁⢀⣼⠏⠀⢀⣸⡇
⠀⠀⠀⠀⠘⢎⡉⠓⠲⢦⡤⢤⣤⣤⣀⣉⣉⣁⣐⣒⣒⣊⣁⣀⣐⣈⣁⣈⣀⣀⣘⣁⣀⣈⣒⣒⣚⣋⣠⣤⣤⣤⡶⠒⠚⣩⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠑⠴⣤⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⣤⣼⡿⠿⠋⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡗⠛⠻⣿⠷⠶⠶⠦⠤⠤⠤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠤⠴⡶⣿⡷⠟⠓⠚⣻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣈⠛⠷⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⢾⠟⢃⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠭⢽⣶⣤⣤⣤⣀⣄⣂⣽⣭⣭⠭⠵⠾⠓⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣯⡿⠋⣀⣭⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣾⠋⢀⣾⣿⣿⣿⣿⣿⢉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⢀⣾⣿⡿⠁⠀⠀⠈⢻⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡿⣷⣶⢪⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣾⣟⡽⠃⣾⡟⠲⠤⣄⠀⠀⠀⠀⣿⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠟⠀⣼⠟⠈⠙⠒⠄⠀⣴⣚⣹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡍⣶⣾⠉⠀⠀⠀⠀⠀⢀⠇⢠⣿⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣇⠀⢀⣀⣐⣊⠊⣴⣿⡀⢿⢸⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣡⣾⡟⢹⡏⢢⠀⢉⣙⣛⡿⠻⡇⣳⣜⣇⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⡉⠉⠉⠀⢸⠁⢈⣛⣉⡍⢀⠠⠤⠤⠤⣤⡛⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠈⠀⠋⠁⠀⠀⣃⠂⠀⠀⢰⠟⣀
⠀⠀⠀⠀⠀⠀⠀⡔⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠊⣉⣩⣭⣱⢤⡀⠀⠈⡑⢾⠀⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⠴⠉⢠⠎⣉⣩⣅⣀⠀⠉⠲⣟⠂⠘⡄⠀⠀⡰⠁⠀⡆
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⡠⠋⣀⠔⢁⠎⠉⠀⠉⠉⠀⠀⠀⡇⠀⠜⠀⠀⢰⠁⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠔⠁⠀⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡺⢦⣤⣼⢛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡡⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡁⠀⠰⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠊⠰⢠⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣶⣖⠚⠁⠀⠀⠀⠘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⢀⡠⠖⠋⢡⠞⠟⠋⠉⠉⠳⣤⣐⠙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠐⠠⢊⣴⢋⠀⠐⣰⠇⠀⠀⠀⠀⠀⠀⣹⠉⠉⠳⡈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⡼⠁⠀⠐⢠⡞⠁⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡄⠀⠹⣟⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡏⢰⡇⠀⠀⠀⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢻⠀⠀⢈⢦⠻⡄
⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⠀⡀⢸⡿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠸⣇⠀⠀⠈⡆⠹⣦
⠀⠀⠀⠀⠀⠀⢻⣴⡈⢧⠀⢇⠈⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠹⡅⠈⠳⡌⠀⢿⣆⠀⠐⡀⢸⠀⠀⠂⠀⢀⠀⢰⠇⠀⠀⠀⠀⠀⢀⡾⠀⠀⢰⠇⠀⡿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣕⠘⢦⠈⠻⣦⡀⠀⠈⣇⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠏⠂⢠⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣑⢤⣈⠻⣦⠀⠘⣆⢀⠀⠘⣸⡇⠀⠂⠀⠀⠀⡰⠃⠀⡠⠋⠀⢠⡿⠘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⣾⣷⣶⣎⣷⣁⠤⣿⡇⢈⠀⢀⣠⠞⠀⣨⠞⡡⢀⡴⠋⠄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠻⢿⣿⣿⢿⣿⣷⣶⣿⣿⡵⠞⠉⣀⣠⡴⠋⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⢙⠕⠋⠛⠻⠻⠻⠟⠯⠥⠤⠦⠒⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢲⠀⠠⢀⠀⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣾⠀⠀⢲⡆⢸⡄⢸⡇⣾⠀⠐⢸⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⣀⠀⢿⠀⠀⠸⠁⢸⡇⢸⡇⠻⠀⠀⠈⠃⠈⣿⠈⠆
⠀⠀⠀⠀⠀⠀⢠⠖⠀⢸⠇⠀⣼⠁⠈⠀⠀⠀⠀⠀⠈⠓⢈⣇⠀⠀⠀⠀⢠⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⢀⡧⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢠⡄⠀⣾⠀⠀⠀⠀⠠⠊⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⣷⠀⣿⠀⠀⠀⠀⢀⣀⣿⠀⣀⡀⠀⢀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⡆⢻⣀⠙⠦⠃⠀⢰⡏⢸⡇⢰⡇⢰⡇⣸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠃⠀⠁⠐⢤⡀⠀⢸⡄⠸⣇⠸⠇⢾⡀⢻⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⢱⠀⠀⠉⠀⠉⠀⠀⠀⢥⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢄⠉⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠠⠀⠰⠷⠟⠃⠀⢄⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⢐⣦⢀⣀⢠⡄⣴⠑⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢢⠛⠀⠀⡘⠁⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠠⣮⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⡜⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⢀⠔⠀⠔⠁⠠⠀⠀⢠
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⢀⡤⣸⣧⡀⣀⣤⣶⡯⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣸⣵⠋⠀⠀⠚⠧⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢠⣀⠻⣇⠀⠄⠀⠀⠀⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠜⠋⡁⠀⡀⠀⠀⠀⢈⠣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠾⢬⣀⠀⠄⠀⠁⠀⠀⠀⠈⢹⠀⠀⠀⡀⠆⠁⠄⠀⠀⡉⠂⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢛⣋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣠⢴⡿⢃⡴⢞⣿⠇⡾⢻⠟⣸⠟⢁⡴⠇⣠⠞⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣡⡾⠛⠉⠓⠋⠿⠊⠀⠛⠊⠹⠖⠉⠷⠊⠙⠖⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⡄⢼⣿⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⢿⢸⣿⣿⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠀⠀⠀⠀⠀⠚⠁⠋⠀⠋⠈⠀⠀⠀⠀⠀⠁⠂⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠡⣅⠴⠀⡤⠟⠁⠀⠀⠀⠀⢀⡔⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⣤⣤⠆⢀⣼⣾⣿⣗⠶⢤⣀⠀⠀⢸⠃⠀⠀⢠⣀⡀⠀⠀⠀⠀⢀⠀⢀⡀⣼⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠉⢀⣴⣻⣿⣿⡇⢾⡁⠄⠀⠑⠀⠘⢦⡃⢀⣾⣿⣿⣦⣄⣀⣀⡈⡿⣏⠉⠃⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣱⡿⣿⠟⠻⡄⠑⠈⣳⡀⢰⡄⠈⣷⣿⣿⠀⢿⣿⣿⣿⠏⠅⢙⡄⠀⠄⣺⠏
⠀⠀⠀⠀⢠⡾⢁⠀⠀⠀⠀⢀⡼⠿⢀⡿⠀⣘⣿⣦⠰⣿⣿⡟⡧⠀⠘⣿⣷⣆⣈⣿⡍⢈⢀⣀⣼⠖⠛⠋⠁
⠀⠀⠀⠀⠀⣷⢺⣶⣄⣄⣴⣯⠏⠀⢸⡃⠀⣿⣿⣿⣆⣿⣿⡿⠃⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠉⠘⢿⣿⣿⣳⣿⣂⣠⡿⣇⢰⣿⣿⣿⣿⡯⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⣿⠹⣿⠟⢁⡟⠬⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⠃⠀⠀⠀⢀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡙⠘⠦⠶⢮⣽⠟⠋⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⡀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠳⡦⠤⣴⣾⠉⣠⢰⡦⣼⡧⠤⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠒⣶⣒⣒⡚⠛⠉⠉⠛⠋⠛⢶⣄⡴⣻⡥⠼⠟⡠⠀⠈⠀⠀⠀⣞⢠⢿⠀⡇⠀⠈⠳⢤⣶⠆⠀⠘⣦
⠀⠀⢀⠔⠁⠀⠀⠈⠉⠛⠓⠶⣶⣶⡷⢢⠋⠸⣤⡤⢤⣴⡃⠀⠀⠀⠀⠀⢯⠊⠈⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⢀⡤⠋⢳⠀⠈⠹⠷⣌⡻⡄⠀⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠰⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡤⠚⠉⠀⠀⠘⡆⢰⠀⠀⠘⢧⣻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⠑⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠈⠀⠀⠁
⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⣀⣀⠤⠤⠶⠒⠒⠒⣒⣒⣲⣦⣤⣤⣀⣀⠀⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠤⠒⠏⠁⣀⡠⠴⢲⠞⣳⠾⠥⠤⢽⣼⣿⣒⣉⡏⡻⣖⠦⣀⠐⠪⣗⢄
⠀⠀⠀⠀⢀⡜⠁⠀⢀⠞⠳⢄⣠⠴⠺⣥⠞⠭⣽⣯⢥⡬⠥⣥⢼⣤⣤⡜⠲⠷⡑⢈⣳⡌⠳⡄⠈⢀⠳⡀
⠀⠀⠀⠀⡼⠀⠀⢠⠇⠀⡠⢪⠘⢡⣞⣡⡴⠒⢳⣤⡬⠵⢚⡋⠉⡼⣄⣙⠮⡒⠌⡳⣧⣙⠆⢸⡄⠀⡄⢧
⠀⠀⠀⠀⣷⠀⠀⢸⡀⡜⠉⡦⢖⣋⡡⢈⡳⠶⡏⣰⣁⡉⠤⢴⠮⣱⣄⣝⢷⡨⢓⣼⣏⠙⣦⢉⡇⠀⠃⣾
⠀⠀⠀⠀⠸⡀⣀⠀⢧⡷⠾⠤⢬⡖⠫⠵⣀⡤⠛⢙⠤⣤⣴⣊⣲⡶⠦⣬⡏⢹⣿⣿⣿⣿⡍⡼⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠳⡘⣄⠈⢿⡉⠲⡞⠓⡶⠟⠓⡆⢂⣤⣖⡭⠒⡩⢔⡩⢶⣯⡿⣿⡽⣎⣛⣻⠟⠁⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠙⢮⡠⠄⠙⠶⣧⠼⣥⠤⠴⠿⣟⣉⣉⣭⣽⣊⣭⠤⠴⣿⢙⣷⣿⡯⠛⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠈⠙⠓⠮⠭⣐⣂⣀⣞⣉⣉⣱⣨⣇⡤⠽⠟⠋⠁⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣤⣀⣀⣀⣀⠈⠉⠉⢀⣀⣀⣀⡤⠤⣖⡪⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠺⠭⠭⠭⠭⠭⠥⠶⠒⠚⠉⠁





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿