Cactus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⣷⠀⣼⢀⡴⠎⠀⠀⠀⠀⢐⢺⡏⠄⠀⢀⠉⢲⠀⠀⠀⠀⠀⠙⠛⢶⣄⠀⢰⠟⠀⠘⣆⢣⣈⣴⢀⡔⠀⠀⠐⣿⣄⠀⠀⠀⢀⣹⣧⣤⣤⣤⣾⠟
⠀⠀⠀⠈⢷⣼⣼⣷⢟⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠻⣦⠓⠀⠐⡖⣲⠀⢟⢃⣿⡵⠂⠀⠀⢸⣿⣤⣶⣿⠿⠟⢛⠉⠉⠉⠁
⠀⠀⠀⣀⠀⠙⠿⠟⠛⠉⠁⠀⠈⢻⣏⡀⠨⣧⠄⠀⢆⢀⡀⠀⠊⠵⠀⠀⠀⠲⠀⠀⣟⠀⠀⠀⠐⠈⡖⣆⢨⠄⠁⠀⠀⢀⣼⣿⡿⠋⠀⣀⣤⣬⣷⣷⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⡠⠐⣷⠄⠘⣾⣫⠄⠀⠉⠐⣀⠀⠀⠀⡆⠀⠀⠈⠡⠀⠀⠘⠿⠿⢃⠀⠀⠀⢴⣿⣿⠏⠀⠀⣀⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⢁⠄⠀⢀⠀⠀⠁⠀⠀⠀⠠⠿⣬⣿⠊⢱⡿⠄⢀⠀⠀⠀⠉⠀⠤⠀⠈⣀⠠⠲⠀⠀⠀⠰⠖⠚⠟⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣹⠛⠂⢠⡉⠦⡒⠤⠄⠀⠐⡸⠐⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⣀⢀⡀⡀⠀⠀⢱⡄⠀⠇⠀⠀⠈⠿⠉⠁⠀⠰⢐⠣⠼⠀⠆⠠⠈⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠛⣿⡇⠀⣴
⠀⢀⣀⡀⠀⢀⡀⠁⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⣀⣤⣄⡀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣀⠀⠀⠀⠐⠂⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡀⠸⣿⣾⣷⠀⢨⣶⢾⣭⢴⡍⠀⢀⣛⣓⣉⣵⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠠⡄⠀⠐⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠⠀⠄
⠀⢹⣿⣿⠇⢠⣿⡿⠃⠀⠀⢰⣿⡿⡦⠀⠀⠘⣿⠿⠷⠾⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⠿⢀⡤⠁⠀⠀⠀⠀⠀⣭⣻⡰⡞⠁⠀⢰⠶⢖⣻⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣿⡇⠀⠀⠀⠀⠀⠎
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠏⠋⠀⠀⠀⠘⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠃⠀⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⣶⣾⣷⣀⠀⢀⡀⠴⢃⡄⢀⣠⡄⠀⠦⠀⠀⠀⠐⣄⠀⠄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠑
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⡇⠀⡆⠀⠀⣿⣿⣿⣿⡀⢲⡙⡘⣆⣃⠀⡁⡦⢀⡃⠈⠀⠀⠠⡀⢂⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢶⠘⡁⠈⠁⠀⠘⡛⡴⠁⣠⣶⣤⠀⠈⠆⣡⠀⠠⢀
⠀⢠⣭⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⡏⠀⣀⠈⠁⠀⠈⠀⠀⠁⠀⢸⣿⣿⣿⡇⠀⠀⠈⠛⠟⠋
⠀⠈⠖⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⠀⠀⢹⣿⣿⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄
⠀⠀⠍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠠⠄⠀⢸⣿⣿⣿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⣼⣦⠀⠀⠀⠐⠀⠛⡛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣤⢀⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⢠⠰⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⣸⣿⡼⠇⠀⠀⢸⣇⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡆⠉⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣀⡏⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠸⣿⣿⡯⠀⠀⢀⠀⢨⣷⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠖⠀⠀⠀⠸⣄⣧⢰⡄⣿⠃⡏⣤⠀⠀⠀⡄⢀⡠⠂⠀⠀⢀⣤⢄⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⢷⣘⣏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡄⣇⣿⢠⡇⣿⠀⠀⠀⢃⠀⢀⠀⠀⢀⠿⠇⡋⢿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣶⢿⠃⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⣇⠰⠄⠀⠀⠀⢣⢹⣿⣸⣇⠇⠀⠀⠀⡎⡀⣻⠀⠀⠈⡆⠃⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣌⡁⠀⢫⡔⡮⠁⠀⠀⠀⢻⣿⣿⠞⠀⠀⠀⠀⠰⣃⣿⠀⠀⠀⠑⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠠⠀⢀⡿⡿⢗⢐⡱⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣻⣿⠀⠀⠀⠀⠱⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣇⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠻⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠒⣦⣵⣸⡟⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢆⡁⢂⠘⠈⡌⠘⢀⠠⠆⠀⠀⠀⠀⠔⢁⠄⠊⡁⠄⠂⢘⠻⣜⣻⠶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤⡀⠙⢦⡸⣿⡤⠋⠀⠴⡳⣖⠠⣄⡎⠠⢂⡤⠊⠀⡠⠊⠁⢠⢹⣮⣳⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⣢⣌⡙⣿⣿⣿⣾⠧⠒⢖⠾⠎⢣⠀⠱⣧⠊⠀⢀⠜⠀⠀⢀⠃⠈⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢦⡤⠀⣡⢚⡟⢇⡉⣗⠢⡎⡄⠀⢡⠀⠘⣤⠐⠁⠀⢀⠀⠁⡰⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠃⡼⡵⠛⠁⡎⢁⠈⠁⣾⠀⠀⠰⠀⠀⢣⠀⠰⠄⠄⠀⠁⡠⠞⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠭⠭⢉⡚⠀⠀⢡⠀⠲⠀⠈⠟⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⣶⣤⣢⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠤⠤⠀⠀⠀⡅⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠂⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢫⡁⠒⠠⠤⠄⢚⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣁⡂⠐⢒⡩⡆⠇⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠈⠀⠀⢸⠀⠀⠸⠀⠀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⠰⡀⠠⠀⠀⠀⠇⠀⢸⠀⠀⡄⠀⢠⠁⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣄⣥⣀⣆⠀⡀⢰⡀⢨⠀⢀⣇⣀⣼⣤⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠷⣧⣭⣩⣍⣿⣍⣏⣉⣋⣍⣩⣥⣤⠴⠟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠔⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⢰⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣧⢸⣿⣇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣶⡄⢀⢰⡇⢠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡄⢰⢀⡇⡇⠀⠀⠀⢿⣿⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⡇⣼⠈⣷⣼⠀⣶⣦
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣧⢸⣸⣿⠃⡇⠀⠀⠈⠛⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⣿⡏
⠀⠀⢸⠀⠀⢰⣿⠁⠀⠀⢸⣿⣿⣿⠏⠸⠇⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣾⣾⣦⣼⣿⡇⠀⠰⣸⣿⣿⣿⠀⢤⣼⠀⠀⠀⣸⣿⡿⡇⢸⣿⣇⢀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡓⣿⣿⡖⣿⣿⣿⣿⣿⣿⣾⣿⣷⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⢟⣷⣿⣿⣿⣿⡿⢯⣬⢄⡹⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⣭⠞⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡬⣯⣡⣽⠂⡽⠏⠟⣟⣷⣾⣇⡀⠀⢹⣿⠛⠻⣿⡿⢋⣹⣿⡁⠁⠐⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⢻⠅⣈⣥⠹⡇⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⢾⣻⣿⣿⣿⣷⣾⡶⢶⡿⠿⠿⢿⠿⡿⠿⠿⠿⣿⣿
⢸⣿⠷⠀⠈⠉⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿
⠰⠆⠒⠤⠤⠠⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠿⢷⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⠀⠀⢸⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⣿⠀⠀⠸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⠋⢿⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡇⣿⠀⣷⠀⣿⠀⣴⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠈⠃⢸⡷⠘⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡂⡼⠀⠛⠀⣻⡄⠀⠀⣠⣾⣮⣴⣆⠀⠀⢰⠀⣿⡀⢰⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⡇⢹⣾⠆⣼⠛⡇⠀⢀⣛⣹⣿⣿⣿⣤⠀⠈⢠⠏⠃⠈⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡇⢹⣇⣼⣡⣤⣀⣶⡄⠀⢹⣿⣿⣿⣿⣠⣿⢠⡀⢸⠀⠆⢸⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⢻⣿⡿⢿⠞⣷⠀⣆⣿⢹⣿⢻⡉⣿⠿⠁⠸⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⣼⡏⣧⣸⠁⠈⠀⠆⢾⣿⣿⢸⣿⢹⣷⣿⡀⠀⡾⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⣿⠃⠟⢹⠀⠀⠀⢰⠸⣧⡏⣸⣿⣸⣧⠿⠧⢘⡇⢠⢠⡿⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⠀⡀⢙⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣶⣿⡿⣦⣸⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⠀⠁⢸⠀⡄⢰⡆⠀⢸⣇⣿⣿⡧⡻⢇⣿⡛⡧⠙⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⢸⡀⠀⠈⠇⠇⢸⣿⣿⡟⠁⡇⢈⢸⠁⡇⠸⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠃⠸⡇⢠⠀⡆⠀⢸⢻⣿⡇⢀⠃⠘⢌⠀⠁⠘⢸⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠁⠀⡇⠀⠀⢿⠀⢸⣿⣿⡇⠸⠀⠀⠈⠀⠀⡆⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠐⡄⢿⠀⠀⣼⠀⠸⢿⣿⡟⠀⠂⠀⡜⠀⠀⢸⣿⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢱⠸⡇⠀⢸⠀⢸⣿⣿⡇⠈⠀⢸⡇⠀⣀⢰⣿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⡆⢰⠀⢸⠀⠸⣿⣿⣧⠈⡀⠐⡆⠀⢉⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠁⠘⠀⢮⠀⣸⣿⣿⣿⠀⡇⢰⣇⠀⡄⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⡄⢀⠟⣸⠀⢿⣿⣿⣿⡆⡗⣸⡏⣰⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣿⣿⣿⣿⠈⣐⢻⣥⣾⣿⣿⣿⣿⣴⣿⣷⣿⣿⣿⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⡾⠟⠟⠯⠬⠭⠍⠿⢭⠭⠍⠉⠉⠙⠛⠛⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡙⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠦
⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣽⣿⡿⠿⠧⣽⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣦⣤⣤⣄⣽⣿⣷
⠛⢻⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠶⠶⠀⠀⠀⠀⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀
⠀⠀⠀⠈⠚⠉⠳⠀⠀⠀⠀⢀⢪⠉⠋⠄⠀⠀⠀⢠⣵⠌⠦⢡⠸⠀⠀⠀⠀⠊⢠⠀⠀⠀⢠⡾⣿⢆
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠗⠁⠀⠀⠀⣸⡑⡆⢰⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⢠⠁⡍⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡴⠀⠂⡄⢚⣧⣥⣬⡴⡏⠀⠠⠀⠁⠀⠀⠀⠀⠀⠂⡅⡇⣷
⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⢰⠀⡠⡀⠀⡃⠀⢠⠃⠀⠀⠉⠉⠀⠀⠀⠠⠀⡀⠀⠀⡀⠀⡀⠐⣡⣇⡇
⠀⠀⠀⠀⢱⠀⠇⠀⢠⠃⠀⠀⠑⠤⠒⠒⡌⠀⠀⠀⢀⣠⣶⣀⠀⠀⠀⠐⠄⠀⠀⠏⠀⠀⠀⠹⠿⠁
⠀⠀⠀⡀⠙⠀⡤⠠⠃⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⡜⢡⠊⠉⠑⠙⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⢀⠞⠁⠉⠢⠀⠀⠑⠌⣄⣀⡠⠖⠁⠀⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠈⣦⠃⠀⢀⡠⢅⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠙⠀⠀⠐⡤⠊⠉⠈⠑⡄⠤⠚⠀⠀⠀⢠⠂⠢⠀⠀⠀⠀⠉⢀⠀⢀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠆⠀⠬⠇⠀⠀⠀⠀⢆⠀⠀⣰
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⢄⡀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣩⣴⡀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠟⡀⠀⠀⠀⣀⠴⣈⡷⠖⡢⡄⠀⠀⠲⠃⠀⠈⡋⠀⠀⠀⠀⠐⠂⠀⢠⡀⠜⠄⡀
⠀⠀⠀⢠⡌⣷⡄⠃⠀⠀⡜⠁⠂⠀⠁⠀⠈⠸⠀⠀⠀⡠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠠⡀⠺⡇⡼⣂⠂
⠀⠀⠀⠘⠹⠇⡅⠀⠀⠀⡇⠀⠀⠀⠈⠀⢀⢀⠃⢀⡠⣷⢣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠁⠛⠋⠉⠁
⠀⠀⠀⠀⢰⠀⠇⡀⠀⠀⠰⡀⠂⠀⠀⠀⡌⡜⠀⠃⠀⠈⢣⢠⠀⠀⠀⣀⠀⣀⠀⣀⠴⡶⡄⢀⢠⠒
⠀⠀⠀⠰⣎⠀⢸⡷⠀⠀⠀⠑⢄⢆⢐⣰⠜⠀⠀⢃⠀⠀⢸⠸⠀⠀⠸⣇⢀⠾⡖⣇⡄⡇⢇⣸⢨⣱⠄
⠀⠀⠀⠀⠚⣧⣸⠃⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠠⡀⢙⡆⠀⠀⠀⢀⠀⣄⣦⣀⠀⠄⢀⠀⡠⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠋⡝⠁⢹⠉⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡘⢠⠀⡎⠀⡈⡻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠻⠛⢷⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠇⠀⣇⠈⢰⡇⠀⠁⠱⢈⣷⠀⠀⠀⠀⠀⣤⡿⡼⠀⠀⡆⢸⠛⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡇⠃⢸⡇⠀⢠⠰⡏⠸⡷⠁⠀⠀⠀⣾⠁⡇⢰⠀⢁⠀⡇⢹⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⣄⡇⠀⢸⡇⠀⠎⢠⡆⠀⣿⠀⠀⠀⠙⣿⠐⣧⠀⠀⢸⠰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢸⡀⠉⡇⠀⢸⡇⠀⡆⢐⠇⠀⣿⠂⠀⠀⠀⣿⠀⢸⠀⠈⠸⠀⠘⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⢶⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠃⠀⡇⠃⠀⠃⠀⠀⢀⡇⠀⢹⠀⠀⠀⠀⣿⠀⠻⡀⠀⣀⠇⠘⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠃⢸⡆⠹⢳⡔⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⡇⠀⠀⣴⠇⠀⢸⠇⡔⣸⡇⠀⠀⠀⢹⡄⠀⡅⠠⢫⠀⣼⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢾⡁⢰⡄⣿⣄⡤⠀⠀⠠⣼⡇⠈⠀⢰⡇⠰⠀⡇⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⣸⡗⠀⡆⠀⢸⠀⣯⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⡘⠁⢸⠇⡏⣿⠀⠀⠀⠀⢸⡇⡀⠀⠀⡇⠀⠀⡇⢀⠆⠀⠀⠀⣾⠀⠀⠀⠀⢸⣇⠀⡝⠀⢸⢀⡗⢠⡗
⠀⠀⠀⠀⠀⠀⢠⣯⠀⢹⠀⠇⡠⢟⠀⡇⣿⡀⠀⠀⠀⢸⡇⡇⠲⠀⡇⢀⠀⡀⠀⠀⠐⠀⢀⣿⠃⠀⠀⠦⣸⠏⢶⠀⠀⡜⢻⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⡃⠀⠸⠀⡷⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠈⠀⡅⠀⠀⢰⡀⠀⣿⠀⠀⠀⣨⡟⠀⡜⢀⣴⠃⡬⢠⡿
⠀⠀⠀⠀⠀⠀⠰⣧⠀⢸⢢⠙⡆⢀⣄⡆⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠓⠀⠃⠀⠀⣸⠇⠐⣿⣀⣤⠾⠋⣠⡎⠀⣠⠃⡰⢁⣾⠁
⠀⠀⠀⠀⠀⠀⠰⣿⠀⢰⠀⢰⡀⠘⡇⠆⣿⠀⠀⠀⠈⢺⡇⡿⢆⠀⡇⠀⢠⡄⠇⠀⣧⠀⢠⡿⠭⠼⠒⢉⡳⠤⠚⣃⠟⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣆⠘⣱⠀⠇⢰⢿⡄⠀⠀⠀⢸⡇⡇⠀⠀⡇⠂⢸⡇⠀⠀⣿⠀⢸⡟⠒⢻⠋⣉⡹⠶⢺⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⢻⠀⢸⠘⡜⢷⡇⢠⣠⣸⡇⡇⠀⢠⣇⠀⢸⡇⡄⠀⣻⡄⢸⣏⣹⣯⣥⣴⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣇⠘⢦⠈⢧⡈⠫⠿⠿⠿⢹⡇⡇⠀⠀⠏⠀⢘⠃⠈⠀⣿⠁⢸⡭⠍⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⡗⠈⠳⢄⣉⠚⠳⣆⡉⠨⣷⡇⠐⣄⠀⠀⠀⠀⠀⠀⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠘⠷⣤⡤⢉⣉⣉⡩⠴⣲⣿⡇⠀⢹⠀⠀⠈⣦⠂⠀⡹⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣄⣀⣀⣀⣴⠶⠛⠁⢸⣿⠀⢸⠀⡄⠸⠏⠀⠀⢷⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢿⢸⠀⢀⠀⠁⠰⠀⢠⠀⠼⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠀⠸⢦⠀⡀⠙⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠐⠈⠀⣷⠀⢰⠸⡆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⢸⠀⠀⠿⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢘⠀⠀⢰⡄⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣀⠀⢸⠁⠀⢸⠀⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠰⠈⠆⠘⠀⠘⢸⠀⣿
⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⡀⠀⠿⠀⠀⣈⠀⣿⠆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⢾⣿⠀⢸⠃⠀⣟⠀⡔⡏⠀⡿⢶⣤⢤⣤⣀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠚⠋⣩⡀⠀⠁⢸⣿⠀⠈⠀⡄⣿⠀⠀⡇⢸⡇⠀⠰⠄⠠⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠀⠒⠂⠻⢿⡷⠂⡆⠀⡿⢀⣀⣷⠟⠀⠠⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠙⢻⡷⠶⠿⠟⠋⠀⡀⠀⠙⠀⠰
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⢀⡀⠀⠈⠥⠤⠀⠀⠀⠤⠄
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠆
⠀⠀⠀⠲⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆⡼⢠⠆
⠀⢀⠀⠢⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⠇⠀⠉⠁
⠀⠀⠀⢆⠆⠀⠀⣸⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⢠⠀⠰⡄⠀⢀⢀⡎
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡆⠀⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⢣⡄⢠⡀⠀⠘⠆
⠀⠀⠀⢤⣠⡄⠧⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣰⠀⠀⠀⠀⡿⠛⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠈⠻⡄⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⢦⠀⠀⠈⠁⠀⠀⢀⣠⠁⠀⢸⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡇⢠⡆⠀⣰⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣆⠀⠀⠀⡈⣤⣀⣰⠇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠱⣌⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠙⠓⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠋⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡺⠋⠋⠛⢂⠀⠀⠀⠀⠀⢠⢡⢋⠉⠇⢡⠣
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠐⢸⠀⡇⠁⡄⠀⠀⠀⠀⠀⠀⠐⢀⠁⡆⠀⢰⠘⠀⠀⠀⠀⠀⠆⡆⠘⢰⠸⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠈⢠⢸⠀⡇⢀⢠⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⠀⠈⠀⡆⠀⠀⠀⠘⢠⠀⠀⠘⠀⡀⠇⠆
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠈⢸⠀⡇⠸⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⢸⠀⠀⢀⠀⡇⢠⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠄⡄⢀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⡇⠘⠀⡇⢸⢸⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠘⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⠃⠸⠀⠇⠀⠀⠀⠀⢸⠀⠇⡁⢠⠀⢸⢸⠀⠀⠀⠀⠰⠹⠀⢁⢩⠣
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⡇⢸⢠⠀⠀⠀⠀⠀⠀⠀⠂⠘⢠⠀⠃⠸⠀⡄⠘⠀⠀⠀⠀⡇⠀⢨⢸⠈⠀⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢰⢸⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⡄⠀⠀⠀⡄⡆⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⢸⠀⠀⠇⠀⠀⠀⠀⠀⡀⢁⠈⡀⠆⠸⠀⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠃⡄⠈⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⡇⠈⠀⠀⢠⠀⠀⠀⠀⠀⠆⠸⠀⢁⢸⠀⠇⠠⠀⠀⢸⢰⠀⡇⠀⠀⢸⠀⢠⠀⡄⠀⠀⢠⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠃⠀⠀⠃⢸⠀⠀⠀⠀⠀⠰⡀⢣⠸⡀⠆⠸⡀⠣⡀⠀⠀⠀⠃⠀⡇⠀⡄⠈⠀⡇⠀⠀⠸⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⢠⠀⢰⠀⡄⢸⠀⠀⠀⠀⠀⠀⠱⡀⢆⠱⡈⢆⠑⢄⡈⢣⠀⠀⢠⠀⠁⠀⡇⢠⠀⡆⠀⠀⡄⢀⠀⠸⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠂⢀⠀⡇⢸⠀⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠱⣄⠑⠠⠌⣹⠀⠀⢸⠀⠀⠀⡇⢸⠀⡇⠀⠀⠇⢸⠀⡆⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢌⡑⠢⠄⣸⠀⡆⠀⠀⡇⠀⡇⢈⠀⠀⠀⢠⠀⡆⢠⠀⡆⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠘⠀⢸⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢈⡐⠂⠰⠀⡇⠀⠀⡇⠀⠀⢸⢀⠀⢠⠃⡘⠀⡆⠀⠁⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡆⡇⢠⠀⠃⠀⠂⢸⢀⡦⠁⡰⠃⡘⠀⡐⠀⠇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⡸⠊⢀⠎⢀⠜⠀⡰⠁⡜⢠⠃
⠀⠀⠀⠀⠀⠀⡀⢠⠀⢠⠀⡇⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢸⠀⠀⢀⠖⢁⠔⠁⡠⠋⠀⡔⠁⡸⠀⠎
⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢁⠊⡔⠁⡠⠊⠀⢠⠊⠀⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠾⡘⢀⠎⠀⢀⠔⠁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⡀⣧⢂⡠⠒⢁⠠⠊⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⡝⠻⡄⣉⠠⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⡇⢰⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡄⢸⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠃⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⡻⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠶⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢇⡄⠀⣰⠆⠀⠀⣺⠁⠀⡀⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠹⠿⠦⢤⣴⡞⠀⠙⠉⠁⠀⠀⢸⠃⡆⠘⣷⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢸⣇⣧⠐⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢢⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣶⣧⡟
⠐⠀⠀⠀⠀⠀⠀⣿⣁⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠗
⣸⠇⠠⠄⠀⠁⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡦
⠁⠀⣧⠀⠋⠀⡀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣀⠀⠦⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⡀⠀⠀⠈⠉
⠀⠀⢸⡖⠂⠈⠀⡼⠀⠀⠀⠀⠀⠀⠰⢼⣦⠀⢸⡇⠀⠀⢀⠇⠀⠀⠀⢨⠁⢢⢠⠀⠀⠀⢸⣀⠀⠀⠸⠶⠃
⠀⠀⠀⠀⠰⢪⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⢾⣧⣼⠷⠃⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡤⠚⠋⠀⠀⡆⢠
⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠘⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⢛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⢸⠀⠀⠀⠈⠋⢀⠠⠀⠀⠰⣄⡴⠀⠓⠂⢀⣀⣀⠰⠁
⠸⡤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⣆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢰⠀⡀⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⡄
⡀⠀⣀⡀⠀⠀⠀⢠⠂⠀⠀⠀⣠⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠧⢀⠈⣇⠀⠘⠠⡇⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⢦
⢷⣸⠀⠹⠃⠀⠀⠁⠀⠀⢠⢏⡆⢰⡞⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢀⠠⡁⠀⠀⠀⠀⠀⡀⠀⢸⠇
⢀⠹⠀⢠⡄⠀⠀⠀⠀⠀⣹⣼⡆⣾⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⢡⠀⣇⡿⠀⠀⠀⠀⠀⠀⣘⠟⠀⢀⠠⠀⠀⠙⣿
⠾⠃⠀⡾⠛⠀⠀⠀⠀⠀⠻⣿⣷⣷⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠳⠷⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈⠀⣀⠀⠂⠀⠀⢻
⡅⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠀⠀⢠⡜⠀⠀⠈
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣥⠞
⠐⠀⠚⠛⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⠑⢀⠔⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠑⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠈⠇⠀⠀⠿⢸⡇⠀⠀⣄⠀⣷⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠞⠀⡇⠀⠀⡁⢠⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡄⠑⣤⠀⢀⠀⢰⠀⠀⠀⠀⡇⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠛⠀⠈⠀⢠⠀⠀⠀⠀⠁⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠂⠀⣿⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⢤⡀⠀⠀⠀⠀⡄⠀⡇⠀⠠⠀⡇⠈⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⣈⠀⠇⠀⠀⠀⠀⠀⠀⢀⠀⣠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠸⣇⠀⠀⢿⠀⠄⠀⠀⠀⠀⣆⠀⠀⣠⡟⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⣄⡈⠃⠤⣈⡲⢀⡀⠀⠀⠀⠁⠀⠾⢋⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣌⣀⣀⣀⡀
⠀⠀⠀⠐⠃⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣾⠿⠿⠿⠿⠟⠿⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡿⠾⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⣲⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠋⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀⠊⠀⠈⠙⢦⡀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠰⠀⠀⠀⠀⣾⣿⡏⣴⡆⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⡧⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡶
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡿⢀⠀⠀⠀⠀⣿⡟⢡⣿⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⢸⠀⠀⠀⠀⣿⠀⢹⣿⠀⠀⢿⣿⠟⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⢀⠀⣿⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⣿⠀⡄⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠆⠀⠀⣿⣧⣿⣇⠀⠈⣿⡇⠀⠘⠀⠀⠀⣿⡀⠸⣿⠀⠈⣿⠇⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡃
⡄⠀⠀⢻⣿⢿⣿⠀⢁⢻⣧⠀⢸⠀⠀⢰⡟⠃⢸⡟⠀⢰⡟⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⡀⠰⠀⠀⠀⠀⢰⡇
⠰⡆⠁⣸⣿⣆⠙⣧⠘⠀⣿⡀⢸⠄⠀⢸⡇⠀⣿⠃⠀⢾⠁⣴⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠸⣄⠛⢿⣿⣧⡈⢣⠀⠸⢧⠈⠀⠆⢸⡇⢰⡟⠀⠀⠀⣴⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠂⡀⠙⢿⣦⠠⠖⠀⠈⠀⠠⠀⠀⠁⡞⠃⢀⣠⡾⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠈⢦⣀⠙⢷⣄⡀⠈⢤⠀⠀⠰⠂⠀⠀⠛⠉⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠁⠐⠒⠈⠉⠱⠦⣬⠻⠷⡄⠡⠀⠰⠀⢀⣤⠶⠚⠁⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣶⣿⣶⣤⣤⣤⣼⣿⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⣿⣀⢀⣀⣨⣿⣿⣷⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠻⠿⠿⠿⠿⠿⠿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠓⠘⠛⠈⠉⠃⠐⠀⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢾⣄⣱⠖⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⣄⡠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡖⢠⠚⠑⠶⠚⣯⣹⡖⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⢢⠜⠉⠀⠈⠀⠀⠠⠀⠀⠈⠁⠐⠠
⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⡐⠈⠀⠁⠠⠎⣿⠙⣏⡉⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠰⠃⠀⠈⠀⠰⠁⠈⠁⠀⣉⠰⡏⠘⠃⠈⠱⠞⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠆
⠀⠀⠀⠰⠂⢰⡁⠀⠸⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⢠⡆⠀⡉⠛⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⢧⡤⠐⠇⠐⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⢠⡄⠀⠀⠀⠀⢠⠀⠆⠀⢢⠀⠁⠀⠈⡀⠐⠂⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⢁⠀⠰⠏⠀⠈⢃⠀⠀⠀⢀⠀⠀⠀⠱⠀⠀⠀⠀⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠦
⠀⠀⠀⠘⠃⠀⠰⡶⠀⠈⠡⣄⠀⠀⠃⠀⠀⠰⠀⠶⠘⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡄⠈⠂⠀⠀⠘⢄⡀⠀⡄⠀⠰⢀⡀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠰⡷⠀⠀⠀⠀⠀⠀⡇⠀⡀⠈⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠻⠀⠈⠻⠀⠀⢀⣁⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣾⣿⣷⣶⣷⣶⣿⣿⠿⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠀⠀⠉⠉⠁

⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠘⢿⣿⣤⣀⡀⠀⠀⣿⡇⠀⠙⣿⣯⣄⠀⠀⢸⡀⢠⡄⢠⣶⡄⣿⡇⢀⣤⣿⣿⢠⣿⣿⡆⣴⡆⢰⣷
⠀⠀⢾⣿⣿⣿⠋⢰⣧⣿⡇⠸⣦⣹⣿⣇⣰⡦⠘⣇⢸⠅⠀⢿⣷⣿⠀⢸⣿⣿⡏⠀⠀⠈⢷⣿⡇⢸⣿⣶⣦
⠀⠀⠈⠛⢛⠃⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠿⠼⠀⠀⠸⣿⠟⠀⠸⣿⡿⠁⣠⣄⡀⣸⣿⡇⠸⣿⣿⡇
⠀⠀⠀⠀⣾⡇⠀⠘⠛⠉⠁⠀⠸⣿⣿⣿⡇⠀⠀⣜⡞⣇⡞⣠⠀⢀⣀⣀⣀⠀⢺⣿⣿⠁⣿⣿⡇⠀⠉⡉
⠀⠀⠀⠀⢻⡇⠀⢰⣧⢰⣿⡄⣠⠈⠙⡉⡀⢀⡄⠀⣿⣿⣿⡄⠀⣾⣿⣿⣿⡇⢸⣿⣿⡄⠈⢋⣀⠀⢸⡇
⠀⠀⣸⡄⣼⡇⠀⣀⠙⢿⣿⣿⡿⠀⢱⣿⣿⣾⣠⠀⢻⣿⣿⠁⠀⠙⠿⠿⠿⠁⠈⣿⣿⣿⡀⢸⣿⡄⢸⡇
⠀⠀⢿⡇⣿⣇⠀⣿⡇⠸⣿⠀⠀⠀⠲⣿⣿⣿⠃⢀⠀⠙⠁⡴⣿⣳⠄⢠⣤⣤⣀⠸⣿⣿⠇⠘⣿⡇⣿⡇
⠀⣀⢸⡇⣿⣿⠀⣿⡇⠀⢀⣤⣤⡄⠀⠈⢉⠁⠀⣿⣷⣶⠆⠈⠁⠋⠀⢿⣿⣿⡗⠀⠉⢁⠀⢳⣿⣧⣿⠃
⠀⢻⡏⢿⣿⣿⠀⣿⠇⠀⠘⣿⣿⡛⣀⡀⢿⠇⢀⣾⣷⠁⢰⣿⣿⡆⠀⠘⣿⣿⠇⠀⠀⣾⡇⣎⢻⣿⡿
⠀⠘⣿⣼⣿⣿⡾⠟⢠⣾⡆⠁⠀⠀⠿⠷⢾⣦⢸⣿⡟⠀⠀⠛⠉⠡⡄⠀⠘⠃⠀⣿⢠⣿⣿⣿⠀⠀⣤⣤⡄
⠀⠀⠀⢸⣿⣿⠀⠀⣼⣿⣿⡆⠀⣴⣷⡄⠀⣿⣿⣿⡄⢠⣴⣧⠞⡀⣴⣾⣷⣦⡀⢸⣿⣿⢿⣿⠀⠀⣿⣿⡁
⠀⠀⠀⠘⣿⣿⠀⠀⠸⣿⣿⠇⠸⣿⣿⡿⠀⢿⣿⣿⠃⠰⣿⣿⠏⠐⣿⣿⣿⣿⡅⠘⣿⣿⣼⠏⠀⢠⣿⣿⡇
⣀⣀⣀⣀⣉⣁⣀⣀⣀⣈⣁⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣉⣁⣀⣀⣈⣉⣁⣀⣀⣀⣉⣉⣀
⣿⣟⣟⣛⣝⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡄⠀⠀⠀⠲⡦⠀⢠
⠀⠀⢀⠀⠀⠀⢀⡆⣰⠃⡀⠀⠀⠀⠀⠀⢠⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⢼⣣⢀⡓⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠈⠳⠥⠅⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢠⣉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠁⠀⠀⠀⢙⣋⠠⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠂⠀⠀⢀⠠⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⢢⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠌⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⡴⠀⠀⢰⣿⠃⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⢀⠠⠋⠀⡈⠈⠀⠀⢁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⡀⠀⡇⠀⠀⢀⣸⣀⠀⠀⣱⢶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠎⠀⠀⠀⠀⡀⢠⠸⡇⢀⡇⠀⠀⠀⠉⠉⠀⠀⢹⢸⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇⢐⣠⡗⠚⠁⠰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠆⡄⠀⢄⠀⠀⠜⢀⠄⠈⢺⢸⠁⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠽⠿⠟⠀⠀⠀⠁⠁⢀⠁⠀⠀⠸⢼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⣙⡁⠀⠸⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡤⠿⠤⠤⢮⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⠿⠲⠶⣄⠀⠀⠀⣴⣠⠞⡋⢀⡄⠠⠀⠀⠀⡈⢻⡍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⡁⢠⠀⡆⢼⠃⣀⣀⡾⢁⡜⢀⡞⢠⠁⠐⠘⡆⢱⠀⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⡆⠀⡇⢸⠀⢀⡿⢀⡞⢰⡞⠀⡏⠀⡇⠀⣇⠘⡇⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⡇⢰⣇⡇⠀⣼⢀⡞⠀⡾⠀⡸⠀⢸⠁⠀⣷⠄⣿⠀⢸⠉⠁⠀⠀⠀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⢿⠈⢸⠁⢳⡇⣸⠁⢰⠃⣤⠇⠀⡘⠀⠀⣿⠀⢸⡄⢸⡇⣰⠂⠀⢀⣠⠿⠟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡆⢷⡘⣧⢸⡀⣾⢀⡏⠀⡾⠀⡞⠀⠀⡇⠀⠀⢸⠃⢸⡇⢨⡟⠁⢀⡴⠋⣀⣀⡴⠄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠈⢷⣌⡁⠳⡟⢸⡇⢸⠃⣸⠃⠀⢸⠇⠀⠀⢸⠀⠘⡇⠀⡷⢀⡞⣠⠞⣵⠋⠀⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣉⣉⣠⡇⣼⠀⡾⠀⡿⠀⠀⣸⠀⠀⠀⢸⠀⠀⡇⠀⡇⣼⢳⠏⣰⠃⣼⢁⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⢉⡇⣿⠀⡇⢰⡇⠀⠀⣿⠀⠀⠀⣿⠤⣼⣇⣸⠁⡇⣸⠀⡟⣰⠏⣼⠃⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡏⢸⠁⣼⡇⠀⢸⡏⠁⠀⢠⣟⠀⣒⠮⢭⣽⡷⣏⣼⡵⠋⣴⠋⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣿⡇⢸⠀⢻⡇⠀⢸⠃⠀⠀⢺⡍⠀⠈⠉⢒⣒⣾⠿⢋⣠⠞⢁⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡇⢸⠀⢸⡇⠀⢸⣤⠄⠀⢸⣆⠒⢦⣭⣉⣭⡴⢖⣫⡵⠞⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⡇⠸⡇⠀⣾⠁⠀⠀⣾⠈⢉⡏⠛⠛⠛⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⡇⠀⣷⠀⣿⠀⠀⢰⡇⠀⣸⠁⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣇⠀⣿⠀⣿⠀⣿⠀⠀⡾⠀⢠⡏⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⡄⢸⡇⣿⠀⣸⠃⠀⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠲⠶⠚⠻⡇⣿⠀⠘⡇⠘⣇⠻⢠⡏⠀⡼⠁⣾⠭⠦⣄⣀⡤⠖⠒⠛⠛⠓⠒⣦⠀⢀⣀⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠃⢸⡦⠀⣿⠀⣿⠀⣾⠀⡼⠁⣸⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠦⣄⡀⡧⠀⣿⠀⡿⢠⡏⣼⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⢦⣼⠇⣸⠃⢸⠇⡟⢀⣉⡤⠤⠤⠤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠤⠴⠶⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙



⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣧⢙⣍⢋⣿⣿⡇⠀⠀⠀⠻⢧⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡿⣯⣿
⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠘⣿⣿⢧⣿⣿⡸⠿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣼⡇⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠨⣿⢿
⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣭⣭⣽⣫⣽⣭⣭⣶⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠰⢶⡶⠿⠿
⡇⠀⠀⠈⣻⡋⠀⠀⠀⠀⠀⢀⣾⢯⣿⣽⣟⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢿⣿⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⣿⣟⣿⣿⣽⣿⣽⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠘⠿⠿⠿
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢿⡧⣿⣿⣼⣿⣺⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣿⣺⣟⣻⣗⣛⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣬⣀⠚⠂
⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣟⡛⠋⠀⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⡍⢰⣿⣿⠂⠁
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⢸⣿⣿⠅⣉
⠀⢀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣇⣸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠂⢺⣿⣿⠂⠆
⠀⠀⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⠋⣿⣿⣿⠃⠀⣼⣿⡿⠃⠀⠀⠀⠀⠖⢺⣿⣿⡉⡁
⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣾⠟⠉⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣧⣤
⠀⠀⠀⠻⠿⠿⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣀⣈⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠹⠿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⣤⣤⣤⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢠⣶⣷⡆⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⢹⣿⣽⣭⣽⣿⡏⠉
⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⡇⠀⢸⣿⣿⠏⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⢠⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣶⠀⠀⠀⠀⠀⣶⣶⣘
⣭⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣿⣿⣟⣯⢷⡄⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠟⣿⣿⠀⠀⠀⠀⣀⣀⣈⠻⠿⠿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣷⣿⣿⢿⣟⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣯
⣿⣷⣷⣿⡇⠀⠀⠀⠀⠿⢿⣿⣛⣛⣛⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⢿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⣿
⣯⣭⣭⣽⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠰⠀⣠⡀⠀⠀⢠⣾⣷⣿⣿⣾⣯⣽⣽⣿⣦⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢰⣾⣿⣭
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣿⣶⡀⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⣿⠄⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⢿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⣈⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⣁⣸⣿⣿⡑⡂⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣶⣿⡆
⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⡂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⢀⡀⣿⠃⠀⣼⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿
⣿⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡶⣶⡆⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠃⠀⠀⣶⣶⡙⣿⣾⣿⢠⣤⠀⠀⠀⢻⣿⣷⣠⣶⣯⡻⠟⠀⠀⠀⠀⣿⣻⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠒⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠐⣢⠄⡄⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⢀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢈⡼⢹⣷⢤⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠄⡀⢰⣾⣿⡁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⡈⢀⢩⡟⡾⠇⢡⠔⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣞⠉⡟⣿⠋⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠲⠿⣿⡏⢸⡇⠀⡆⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠁⢸⡇⠀⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢺⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⠀⠘⠃⠀⠻⠀⠧⣼⠀⠀⠀⠀⠢⠀⠢⠄⠀⣀⡠⠉⠀⠠⣤⡌⠀⢀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠒⠞⠓⠚⠛⠚⠒⠻⠿⠷⠶⢿⣶⣝⣈⠄⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣼⣶⣀⣬⣿⣦⣷⡀⢂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠉⠡⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡁⠈⠉⠉⠉⠙⠛⠫⠶⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣀⣀⣀⣀⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⣤⣤⡄⠀⠀⣠⣤⣤⣄⠀⣤⣤⠀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠈⢻⣷⠀⢠⣿⢻⣷⠀⢸⣿⣅⠀⠉⠀⣿⣿⠀⣿⣏⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠀⣾⣏⣘⣿⡆⠀⠙⠻⢿⣷⡄⣿⣿⠀⠉⠛⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣾⠟⢰⣿⠏⠉⢻⣷⢠⣦⣤⣼⣿⠃⣿⣿⢠⣦⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠈⠉⠀⠈⠉⠉⠀⠀⠈⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠐⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡈⠁⠘⠀⠀⠀⠀⠱⢑⡧⠀⠀⡀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡙⠢⠀⠀⣦⡀⠠⢄⠀⠒⠀⠀⠀⠀⡆⠠⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡀⣉⠀⠄⠀⠀⣧⠈⣀⠈⠀⠀⠂⢀⠟⠀⢠⡀⠀⢸⠀⠀⠇⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢦⡀⠀⠈⠄⠀⠀⠠⣴⠈⣿⡀⢙⠂⠀⣸⠂⠈⡀⠀⡘⠀⣀⠈⠄⡀⠀⡰⠁⠀⠈
⠀⠀⠀⠀⠀⠲⡄⡀⢀⡀⢸⡃⠐⠀⣀⠘⡃⠠⠄⠀⡀⢙⠂⡉⠲⣄⠛⠀⠁⠀⠁⠀⠃⢀⠋⢀⡴⠐⣠⠀⠀⠊
⠀⠀⠀⠀⠀⠀⣈⣻⣤⡨⣏⢀⠤⣀⡀⣠⡆⠀⠠⡄⠂⠀⡀⠈⠢⠀⠈⡿⠀⣀⠊⠀⠨⠼⡀⠈⠀⠀⠕⠀⠀⢠⢠⢀
⠀⠀⠀⠀⠈⠙⠀⢀⡼⠇⠘⡇⠰⡀⠙⠄⠁⡔⠰⠠⢴⡀⠘⡀⠈⢀⣀⠈⣋⠀⠄⢈⠀⠀⠀⠠⠈⠀⠉⢒⡒⠃⡉⠼⠓⠁
⠀⠀⠀⠀⠀⠀⠁⠞⠁⡖⠀⠿⠀⠹⢄⠀⢘⡆⠀⣰⣫⣎⠄⠃⠀⢸⡁⠀⠈⠀⠀⠀⠀⡄⢀⠀⠀⠀⣯⣈⢁⡾⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠬⠁⠠⢱⡄⠂⠀⠀⠇⢡⣀⠀⠀⠎⠀⠖⠀⠀⠂⠀⠀⠦⢀⠀⢀⠀⠈⡀⢠⡈⠀⠀⡽⡹⠃⡀
⠀⠀⠀⠀⠐⠂⠻⢄⠀⠀⠢⠋⠀⠈⣀⡀⠌⠃⠈⢁⠁⢠⠔⠁⠐⠦⣰⠁⠀⠀⠐⣰⣄⡦⠐⠀⠀⠈⠢⢮⡥
⠀⠀⠀⠀⠀⡀⢢⡀⠀⠀⠖⣧⣀⠀⢀⡀⠄⠀⡄⠀⠀⠀⠶⠄⠰⠃⡁⠀⠑⠂⠸⡛⠆⠀⠘⠐⢶⠃⠀⠈⡂
⠀⠀⠀⠀⠀⠀⡍⣅⠀⠠⠒⠊⠃⡉⠡⡀⠀⠑⠋⠀⠀⢴⡀⣀⡋⣤⢃⣀⠀⠀⠀⢈⡆⠀⡰⠀⠨⠤⠀⠠⠃
⠀⠀⠀⠀⠀⠀⢒⡘⠀⠀⠠⠐⡂⠅⠀⠈⠈⠀⣀⡀⢀⠀⢈⡐⠛⣭⠨⡅⠀⠐⠒⡀⣀⠖⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⢬⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠣⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⣆⠆⢠⠀⠂⢠⠀⠀⠄⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠙⠀⠸⠀⠠⠘⠄⠀⠏⠀⠇⠃⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⡠⡀⠀⠀⢀⠄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⠋⠀⡀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣴⠟⢠⡾⠛⠋⠋⠉⠓⠦⣄
⠀⠀⠀⠀⣰⠐⠂⠒⢄⠳⡅⡔⠁⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠏⢠⠎⠀⠀⠀⠁
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠇⡠⠀⠐⠂⠀⠀⠤⣀
⠀⠀⠀⠈⠀⠀⠀⢀⡤⢤⣀⠰⣿⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⡿⠪⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⣇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠸⠒⠂⠂⡄⠀⠀⠀⠀⠰⡀⢧⣆⠄⠀⠀⠀⠀⠀⠀⠀⠸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡽⠁⠉⠉⣧⠀⣾⠀⠀⠐⠛⠉⠙⠒⠀⠀⠀⠀⠈⠉⠀⠃⠾⠇⠀⠀⠸⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠔⠋⠀⠀⠀⠀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⢸⡷⠖⢊⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢤⡀⠀⠀⣀⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⣀⣿⠤⠤⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⠀⣀⣠⡤⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠉⠐⠒⠀⠀⠄⣀⡀⣠⠴⠒⢒⠒⢚⡩⠒⠚⠉⠀⠀⡄⠀⡴
⠀⠀⠀⠀⣀⢀⣀⣷⠀⠀⠂⠀⠀⡀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠣⢸⠃⢀⠜⠁
⠀⠀⠀⡔⠁⠀⠀⠉⣄⣀⡴⠀⢀⡘⡐⠻⠰⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠃⠛⠱⢓⣢⠤⠆
⠀⠀⠀⠙⠶⠤⠤⠐⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢦⠂⠠⡀⠄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⡂⢄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢀⡘⠀⡀⠀⢀⠀⠀⠀⠀⠀⡧⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢼⣧⣤⠄⠀⠀⠰⠒⠤⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⣧⣤⣤⠤⢽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠘⠂⠀⠈⡏⠀⠀⠀⠀⠆⠀⠠⠿⠏⠉⠙⠳⡒⠶⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⡀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠉⠀⠈⢤⡀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠰⠦⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⢿⣹⠆⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⢸⠀⠐⠓⢀⡛⠛⠉⠰
⠀⠀⠀⠳⠛⠛⢇⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⢀⣴⡎
⠀⠀⠀⡜⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰
⠀⠀⠀⢱⡀⡘⠣⡄⠀⠀⠀⠀⠐⠂⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠐⠲⠀⣀⣠⠤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠦⠚⠁⠀⠀⠠
⠠⠀⠀⠀⠂⠀⠀⠀⠚⠀⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⡀
⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢂⠀⠁⠐⣠⡀⠀⢀⠀⠐⠂⠉⠁⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⣴⠁⠀⠈⡏⠀⠀⠀⢠⠆⠀⠀⠀⠈
⠀⠀⠈⠁⠀⠠⠔⠂⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠘⡷⠒⠂⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⢠⣈⣻⡇⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠉⢀⡀⠒⠈⠉⠓⠂⡈
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⠘⣋⡛⣹⣿⣿⡂⠀⠀⠈⠻⢧⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⣯⣿
⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠘⣿⣿⣏⣾⣿⡇⠿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⢸⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣛⣛⣛⣟⣛⣛⣚⣣⣤⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⣤⣤⣼⣷⣿
⣷⠁⠀⠀⢦⡶⠀⠀⠀⠀⠀⠀⠀⣴⣞⣿⢺⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣾⣿⣿⣷⣦⠀⠀⠀⠀⠉⣾⣶⣶⣶
⡟⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⣾⡿⣼⣿⢻⣿⢻⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⣿⣗⣿⣿⢻⣿⣿⣿⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⡯⣿⣿⣻⣿⣷⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠀⣠
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⣾⣷⣾⣶⡆⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⡌⣸⣷⣆⠡⠄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠐⠀⣿⣿⣯⠠⡄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⠀⢠⣴⣦⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠉⠀⣻⣿⡷⠰⠆
⠀⠀⣤⣽⣿⣽⣯⣤⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣤⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠈⣻⣿⣿⣘⡃
⠀⠀⠛⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠘⠃⣻⣿⣿⠄⠁
⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⣤⣥⣽⣭⣽⣤⣤
⠀⠀⠀⠸⠿⠿⠃⠀⢀⣶⣿⡄⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⣤⣤⣌⣿⣿⣿⣁⣀⣠⡀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣶⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠐⣿⣿⣷⡀⠀⠀⠿⢿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⢠⣤⣤⣬⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢠⣶⣶⡄⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⣭⣭⣭⣭⣭⣭⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⡇⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣽⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠃⢀⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⣤⣦⠻
⠟⠿⣸⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣿⢺⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⢈⣹⣭⣉⠁⠀⠀⠀⠀⢰⣿⣿⣇
⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣼⣿⣹⣿⣻⣧⢿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⡟
⣿⣃⣶⢻⡿⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣾⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣹⣿⣯⣿⣺⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⢿
⡿⠿⠿⠸⣃⡀⠀⠀⠀⠀⠉⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣹⣗⣻⣿⣽⣿⠻⠿⢾⣏⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣭⣤⣤⡀⠀⢀⣻⡿⠿
⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠲⢠⣅⡀⠞⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⣾⣿⡷⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠸⣿⣿⣿
⣿⣿⠿⠛⠁⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢤⠈⣿⣿⣟⢘⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⠠⣿⣿⡯⢨⡁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⠠⣿⣿⡷⠰⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀
⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠠⠠⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⡿⠃⠀⢸⣿⣿⡿⠀⠀⠀⠀⣠⣾⣿⢿
⣿⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⡷⠶⢶⡆⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠂⠀⠀⣶⣷⡘⣿⣾⣿⡇⣤⣄⠀⠀⠀⢿⣿⣷⢠⣶⣾⣿⠿⠁⠀⠀⠀⢸⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣼⡄⠀⣦⣹⠟⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢏⣥⠟⠛⠀⢹⣿⠀⡞⠁⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⡸⠁⢠⣴⣾⡀⢈⠙⢣⣔⢏⡈⠸⠗⢤⡀
⠀⠀⠀⠀⠊⠉⠙⠑⡉⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠇⢀⣼⠇⡸⣷⡀⣰⣷⠾⠮⠁⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⢠⣾⣷⣟⡇⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣾⠏⠎⣻⡟⣧⢉⣿⢷⣄
⠀⠀⠀⣀⣠⣤⣿⣾⠞⠋⠛⣤⡞⢉⣻⠛⣭⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠠⣿⠀⠛⣾⡆⠰⣻⡆
⠀⠀⠚⠛⠏⠻⠏⠀⠀⠀⣶⡇⠀⠀⠁⢀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⢀⣠⢄⡀⠀⠁⠀⠘⣿⠀⠀⢹⣿⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣱⠀⠀⠀⠀⠈⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣀⣿⣎⣷⣀⡀⠀⠀⠀⠀⠹⠀⠀⠀⠘⠆
⠀⠀⠀⠀⡄⠀⠀⠀⠀⣸⡟⣿⡄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⡟⢠⣿⣿⠑⠻⢦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡐⣿⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠐⣮⢖⡄
⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠰⠶⠀⠀⠀⠄⢠⠎⢀⣀⡀⠀⠀⠀⠀⠀⢀⠠⠔⠺⣷⡤⢋⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠛⣡⡄⠀⢱⣟⠃
⠀⣹⣿⣷⣤⣤⣀⡀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡁⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠠⠞⢋⣼⡦⡀⢪⡏
⠀⠈⠉⠀⠋⠉⠛⠅⠀⠋⠁⠀⢆⠀⡎⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢷⡀⠈⠟⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣦⠸⣴⡇⢀⡾⡠⠀⠀⠀⠀⢀⣀⣀⢀⣤⣶⣴⣶⣶⣦⣦⣾⣿⣾⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠒
⢀⡠⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⢑⣿⣟⣾⣔⣀⣤⠶⠚⠛⠋⠉⠉⠁⠈⠉⠋⠛⠛⠛⠻⣿⣿⡿⠿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣴⠿⢿⣿⢛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⢹⣿⡧⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣤⣤⣀⠀⠁⣠⡞⠛⠛⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⣙⣿⣶⣏⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡴⡎⠿⠽⠉⠙⠉⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⣿⡿⠧⠤⠄⠀⣝⣄⠄⠀⠀⠀⠀⠳⡄⠀⢙⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⠀⡈⠁⠀⠉⢠⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⣁⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠠⠤⠀⠀⠀⠀⠀⢰⣏⠁
⣤⣤⣴⣬⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣵⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⡠⠚⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠉⠀⠀⣠⡘⠄⠀⠀⠀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⡄⠀⠠⠊⠀⠈⠗⠀⠀⠀⠀⠘⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠃⠒⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠈⠀⢀⠀⡀⠀⠀⠀⠀⢙⣤⢦⣁⠈⠁⠀⠀⠀⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⢍⠀⠀⠀⠀⢀⢸⠅⠀⡆⢰⢂⣀⢌⢀⠀⠠⠄⠀⢀⠄⡪⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠘⠁⠈⢥⠉⠑⢠⡸⠌⠸⠟⠂⣠⡀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⠴⢤⠦⠠⠖⠋⡸⠈⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠓⢦⠆⠁⠀⠀⠀⠀⢠⡄⣠⣄⡖⠀⠀⠀⠀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠿⠑⠤⢀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠀⠀⠀⣀⡡⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⢀⣤⣄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠟⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⢸⣇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⣤⣄⡀⠀⠀⠀⠀⣀⣈⣉⣀⣀⡴⠋⠉⣷⠀⠀⠀⠀⡿⢩⠭⣍⠓⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠤⠤⠤⡀⢻⠋⠉⠉⣉⣉⠉⠉⠀⠀⠘⠂⠒⠉⠉⠉⠉⠙⠃⠸⣀⣠⠀⣏
⠀⠀⠀⠀⠀⢠⡞⠩⢬⠀⣁⠤⠔⠇⢸⠉⠉⠋⠀⠀⠱⠊⠉⠙⠲⠒⠛⠲⠞⠛⠒⠉⠉⠳⢢⣀⣠⠌⢉⡧
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠉⠙⠒⠚⠘⠦⠤⠤⢄⣀⣀⣀⣀⣀⣀⠤⠤⠤⠴⠖⠒⠒⠚⠉⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡒⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠒⠒⠤⢌⣉⣑⡒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⢒⣒⣚⣉⠭⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⠒⠒⠒⠒⠂⠉⠉⠉⠉⠉⠁⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠙⠒⠲⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠒⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⡀⠀⣾⢱⡏⣾⡀⠀⢀⠀⣾⠃⣾⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢳⢸⡟⢸⡇⠈⠛⠷⣇⢰⡏⢀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠹⣷⣸⠘⠷⠊⠓⠀⠘⠐⠋⠘⠃⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⢢⣰⣠⠄⠀⣀⡀⠀⠀⠈⠓⠤⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⣷⣸⡆⣴⢰⠤⠀⡠⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣿⣏⠀⢪⣿⣿⣋⠀⠀⠀⠀⠀⠀⢬⣿⣿⣖⠀⠀⠀⠀⢾⣿⣿⣿⣯⣼⣿⣅⡤⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⢻⠛⠄⣼⢿⠿⡇⠁⠀⠀⢴⣦⠀⠊⢿⠟⠧⠀⠀⠠⠾⠟⢿⣿⡿⠃⢼⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⢸⠀⠀⠀⣀⣇⣸⣏⠀⣄⢸⣃⡀⢠⣀⠀⠀⠰⡋⣻⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣦⣼⣾⣆⡆⣸⠆⠿⠞⠻⠟⠛⠛⢚⡛⠛⠛⠃⠳⠿⠷⢦⣀⣇⣿⢀⡀⢸⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣿⣹⣿⣿⡏⠉⠘⢻⠆⠈⠁⠈⠛⠀⠀⠀⠀⠘⠀⠀⠒⠀⠒⠀⠙⣛⠿⢿⣿⣼⣇⣴⣷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠈⠀⢿⠻⠿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢻⣦⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⡀⡀⠀⠀⡀⠀⢠⣠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠁⠀⠀⠴⠤⣄⣀⠠⣀⣄⠀⠢⡀⢸⣰⣀⣞⣠⣾⣵⣧⠔⢂⣿⣟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠀⠈⠙⠛⠓⠻⠚⢛⣿⣿⡛⠟⠛⠓⠐⠛⠻⠋

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣆⡀⠀⠀⠀⠀⣿⡇⠀⠙⣿⣿⣁⠀⠀⠀⢿⠈⢠⡄⠀⣤⡄⢸⣿⠀⣀⣰⣿⣿⢀⣾⣿⣧⢠⣤⠀⣾⣦
⠀⠀⢸⣿⣿⣿⡟⠃⣴⣆⣿⡇⢰⣦⢙⣿⣿⠀⣤⡀⢸⡆⢸⡃⠀⢿⣿⣾⡏⠀⣿⣿⣿⡗⠀⠉⠉⣧⣾⣿⠀⣿⣿⣤⡄
⠀⠀⠘⠿⠿⠿⠁⠀⣿⣿⣿⡇⠀⢉⣿⣿⣿⣿⠋⠁⠘⣇⣾⠀⠀⠸⣿⣿⠃⠀⣿⣿⣿⠁⠀⡀⠀⢸⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⠀⠀⣿⣿⠿⠇⠀⢸⣿⣿⣿⣿⠀⠀⠀⢡⡠⡄⢠⠀⠉⠋⠀⠀⠘⠛⠁⣴⣾⣿⡖⢸⣿⣿⠀⠘⠿⠿⠁
⠀⠀⠀⠀⢸⣿⠀⠀⢠⡀⢀⣤⡀⠀⠻⢿⣿⠟⠀⠀⠈⠓⣧⣷⣦⡞⠁⢠⣶⣿⣶⣦⡀⣽⣿⣿⡀⠸⣿⠏⠀⠀⢰⡆⠄
⠀⠀⢀⡀⢸⣿⠀⠀⠸⣷⣼⣿⣇⣾⡆⢀⢠⣰⣆⣴⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠇⢸⣿⣿⣧⠀⠀⣶⡄⠀⣾⡄
⠀⠀⢸⡇⢸⣿⠀⢀⣤⠈⢻⣿⡿⠟⠀⠈⢿⣿⣿⣧⡖⠀⠻⣿⡿⠁⣀⣀⠉⠛⠛⠋⠀⠀⢿⣿⣿⣦⠀⣿⣿⢀⣿⡁
⠀⠀⢸⡇⢸⣿⡆⢸⣿⡇⠘⠿⠁⠀⠀⠘⢿⣿⣿⡟⢀⣤⡀⠈⠀⢾⣿⢿⡧⢀⣶⣾⣶⡄⠙⣿⣿⠏⢀⢻⣿⢸⣿⠁
⠀⣠⡘⣧⣸⣿⡇⢸⣿⠀⠀⢀⣶⣶⣄⡀⠀⢀⣀⠀⠘⣿⣿⣿⠇⠀⢉⠈⠀⠐⣿⣿⣿⡍⠀⠀⢀⡀⠸⣿⣿⣾⣿
⠀⢸⣇⢻⣿⣿⡇⢸⣿⠀⠀⠘⢿⣿⡟⢁⣀⠸⣿⠂⢠⣾⣾⠀⢰⣿⣿⣷⠀⠀⢻⣿⣿⠃⠀⠀⣼⡇⣴⠙⣿⣿⠏
⠀⠈⣿⣆⣿⣿⣷⡿⠟⢰⣶⡆⠁⠀⠀⠻⠿⢦⣷⡄⣿⣿⡿⠀⠀⠛⠋⠉⣤⡀⠀⠛⠁⠀⣿⠀⣿⡇⣿⡇⠀⢠⣤⣤⡀
⠀⠀⠈⠉⣿⣿⡇⠀⠀⣾⣿⣿⡄⠀⢠⣶⡆⠀⢹⣿⣿⣿⡄⢠⣠⣇⡴⠂⢈⣶⣾⣶⣄⠀⢻⣷⣿⡇⣿⡇⠀⢸⣿⣿⠁
⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⡏⢠⣿⣿⣿⡆⢸⣿⣿⣿⠇⢠⣿⣿⡷⠋⢼⣿⣿⣿⣿⡀⠸⣿⣿⣻⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠛⠛⠃⠀⠀⠈⠛⠋⠀⠀⠙⠛⠋⠀⠀⠙⠛⠉⠀⠀⠛⠛⠁⠀⠈⠙⠙⠛⠋⠁⠀⠙⠛⠛⠁⠀⠀⠙⠛⠛

⠁⢀⠤⠜⠓⠐⠀⠀⠀⠰⡇⣦⡔⡉⠤⠠⢾⠀⠀⠀⣀⠃⠀⠀⠈⠈⣡⠃⠀⠈⠀⢀⠤⠚⠃⠒⢀⠀⠀⠸⡑⣤⢐⠩⠄⠠⡎⠀⠀⠀⡐⠁⠀⠀⠉⢈⡔⠁
⢿⡃⠀⠀⠀⣠⣾⣄⠀⢀⠜⠁⢀⠤⠄⠀⣨⢀⡠⢴⡉⠡⠖⠊⠉⠈⠉⠉⡹⠶⣾⠁⠀⠀⠀⣠⣿⡀⠀⣠⠋⠁⢠⠤⠀⢀⡌⢀⠠⢞⠉⠰⠒⠊⠉⠉⠉⢉⡵
⠀⣱⠖⠦⠐⠋⠈⠉⠙⡿⠓⠒⠛⠓⠢⣤⠼⣏⠀⠀⠀⠀⠀⠴⠶⠦⠐⠾⠀⠀⠀⡶⠖⠆⠘⠉⠉⠉⢙⡟⠒⠒⠛⠒⢦⡤⢿⡅⠀⠀⠀⠀⡠⠶⠶⠆⠰⠮
⠨⢂⠀⣀⡴⠤⢤⣤⠜⠁⢀⣠⠄⣄⣀⣀⣠⠌⠉⠟⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⣀⠀⣀⡴⠤⢤⡤⠞⠀⣀⣠⠤⣄⣀⣀⣠⠈⠉⠟⠉⠀⠀⠀⣀⡀
⠛⠋⢉⣼⣄⠀⣀⣠⠀⠉⠈⢂⠀⠀⠀⠀⠴⠞⠀⢀⣀⡤⠔⠋⠉⠉⠀⠀⣨⠚⠛⠋⣁⣼⡀⠀⣀⣠⠂⠁⠙⢄⠀⠀⠀⠀⠴⠇⠀⢀⣀⡤⠒⠉⠈⠉⠂⠀⡥
⢴⡊⠀⠀⠈⠉⠁⠘⣦⠤⠐⠈⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢀⡠⠐⠒⠚⠳⠦⣴⠊⠀⠀⠉⠉⠀⢹⣄⠄⠒⠋⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⣀⠤⠒⠒⠛⠲
⣀⣧⣀⡀⠀⢀⠠⢘⣻⠶⠟⠋⠀⠀⡠⠴⠦⣾⡤⠾⠿⠛⠞⠉⢿⠀⠀⠀⢀⣀⣈⣧⣀⡀⠀⢀⠤⣚⡷⠶⠚⠁⠀⢀⡠⠴⢴⣦⡴⠾⠟⠳⠞⠙⢗⠀⠀⠀⣀
⠀⠀⠀⠈⡹⡡⠞⠛⢦⡤⠖⠙⠒⠋⠀⠀⢀⡏⠀⠀⢀⡴⡀⠀⠀⠈⣻⠋⠁⠀⠀⠀⠀⠈⡟⡴⠚⠛⢤⡤⠊⠙⠒⠉⠀⠀⢰⠃⠀⠀⢀⠜⡀⠀⠀⠙⡿⠉
⢄⠀⢀⡴⠗⠁⠀⠀⣠⠗⠊⠀⢀⣀⠀⣠⠞⠀⢀⣄⢀⡈⡤⠖⢉⠚⠧⠤⣠⠄⠄⠀⢀⠼⠊⠀⠀⠀⣸⠗⠁⠀⣀⣀⢀⣠⠋⠀⢀⡆⢀⠀⡤⠚⢁⠛⠧⢄⣠
⠔⠛⡋⠀⠀⣀⡤⠚⠁⣀⠔⠈⠀⡘⠉⠛⠦⠒⠋⠉⠠⠀⣸⣤⣾⡀⠀⠀⠀⡠⠚⠛⡃⠀⠀⣀⠄⠛⢁⣠⠀⠁⢀⠘⠉⠓⠄⠚⠉⠉⡤⠀⣧⣤⣆⡀
⣠⣒⠁⠐⠈⢿⠆⠉⠀⠉⢧⠀⡸⠁⢀⠔⠀⠀⣀⡀⠤⡦⠋⠁⠀⠈⡣⠐⠔⢁⣴⣒⠥⠐⠉⡿⠊⠁⠈⠙⣆⠀⡞⠀⣠⠄⠀⠀⣀⡠⢤⠜⠉⠁⠀⠉⡦⠂⠊
⠀⠀⠀⢀⡤⠻⣀⣀⣀⣤⣊⠴⠁⣲⣁⠄⠚⠉⣡⣴⠊⠀⠀⠐⠥⠺⠤⣤⠔⠉⠀⠀⠀⢀⠔⢧⡀⣀⣠⡴⣣⠾⢐⣞⣁⠔⠚⠉⣠⣴⠃⠀⠀⢀⠕⠺⠤⣤⠞
⠀⠀⡠⠊⣀⡔⢹⠁⠀⠀⣠⠖⠋⠉⣡⠤⠒⢈⡡⠋⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⡐⠁⣀⡌⢹⠁⠀⠀⡤⠚⠉⠉⣠⠔⠂⢉⡵⠋⠀⠀⠀⠀⣀⣤⡾⠃
⢠⠞⠀⡈⠘⠁⣼⡀⠀⣠⡧⠀⠲⢔⣡⢶⣯⠥⠤⠤⢤⣀⠠⠊⠀⣠⢧⡠⢤⡄⡠⠎⠀⡁⠙⢀⣾⠀⢀⣼⡤⠒⠦⢎⡠⣶⣯⠤⠤⠤⢤⣀⠔⠈⢀⡼⢇⡠⢤
⣴⣀⣘⣀⡴⣚⣀⣉⣉⣙⣦⣐⣚⣋⣠⣮⣌⣿⣀⣀⣀⣠⢂⣐⣉⣀⣤⣠⣞⣁⣄⣀⣚⢠⡖⣋⣀⣉⣉⣻⣤⣒⣛⣉⣴⣧⣬⣟⣀⣀⣀⣸⣂⣚⣉⣀⣄⣰⣊
⣿⢿⠿⠿⢿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣛⣿⣟⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⢷⠀⣼⢀⣴⠞⠀⠀⠀⠀⢐⣺⡯⠄⠀⠀⠉⠲⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⢰⠟⠀⠘⡆⢡⣈⡴⢀⡆⠀⠀⠐⣿⣆⠀⠀⠀⢀⣹⣧⣤⣤⣴⣾⠗
⠀⠀⠀⠈⢷⣼⣼⣷⢏⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠀⠻⣄⡋⠀⠀⠖⢢⢀⠟⢃⣯⡵⠂⠀⠀⢸⣿⣤⣶⡾⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠙⠿⠟⠛⠉⠁⠀⠐⢺⣏⡀⢬⣧⠄⠀⢆⢀⡀⠀⠈⡬⡀⡀⠀⠔⠂⠀⡿⠀⠀⠀⠀⠀⡇⡆⢰⠂⠁⠀⠀⢀⣼⣿⡿⠉⠀⣀⣤⣤⣷⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⠀⣷⠄⠘⣾⡫⠀⠀⠉⠔⣐⠄⠀⠀⡀⡀⠀⠀⡅⠀⠀⡈⠿⠟⠁⠀⠀⠀⢴⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠷⣤⣿⠒⢰⠿⠄⠀⠀⠀⠐⠋⠀⠤⠀⠤⡀⢄⠔⠀⠀⠀⠐⠖⠒⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣹⠟⠒⢠⡉⠶⠒⠤⠀⠀⠀⢠⠒⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢱⡄⠀⠇⠀⠀⠉⡿⠉⠀⠀⠰⢑⠣⢍⠀⠆⢀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠓⣿⡇⠀⣴⠀⠀⠈
⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⢀⣤⣄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠂⠀⣠⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡄⠸⣿⣾⣷⠀⢨⣴⢾⣯⣴⡍⠀⢀⣋⣛⣊⣵⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠
⠀⢹⣿⣿⠇⠠⣿⡿⠏⠀⠀⢱⣿⡿⡦⠀⠀⠰⣷⣬⠿⠿⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⡿⠀⣀⠉⠀⠀⠀⠀⠀⣭⣻⣠⡾⠁⠀⠠⠴⢶⣺⣭⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣻⡇⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠋⠀⠀⠀⠘⢟⣻⡿⠟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠢⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣲⣞⣦⡀⠀⠀⡀⠰⠂⡀⠀⢂⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⢀⠀⠀⢸⣿⣿⣿⠀⢠⡙⠰⡆⣁⠀⢠⠅⠀⠂⠀⠀⠀⠠⠀⠆
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢦⠘⡃⠘⠁⠀⢐⣒⡺⠀⣠⣴⣤⠀⠀⠂⢁⠀⠠⣀⠀⠀⠀⠀⠀⠀⠠
⠀⢠⣍⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⡀⠈⠁⠀⠈⠀⠀⠁⠀⢰⣿⣿⣿⡇⠀⠀⠈⠻⠾⠋
⠀⠂⠦⣯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠕⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⠀⢸⣿⣿⣿⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣄⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠛⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⢸⣿⣼⠏⠀⠀⢸⣖⢀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠆⣈⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡀⡗⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠸⣷⣿⡟⠀⠀⢀⠀⢘⣧⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠱⣄⣧⢠⡄⣿⠃⡟⣠⠀⠀⠀⡄⣀⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⣷⣘⣛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡀⣇⣿⢠⡇⣿⠀⠀⠀⡇⠀⡉⠀⠀⠀⡟⡇⡟⢧
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⠿⠆⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⣁⠀⠀⠀⠀⠀⢧⢹⣾⢸⣇⡇⠀⠀⠀⣠⠀⣿⠀⠀⠀⡇⢁⠠⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⡀⠘⢋⣄⡜⠁⠀⠀⠈⢻⣿⣿⡞⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠱⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢠⣿⠿⠄⠈⢡⡿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠰⡄⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⢊⠖⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢀⣴⢃⣤⠶⠘⠖⠲⠤⣄
⠀⡰⠄⠒⢄⠺⣆⡴⠊⠀⠀⠉⠁⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢿⢁⡜⠁⠀⠀⠂⠀⠀⠀⠁
⢰⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⢘⡞⡠⠄⠐⠂⠐⠠⢤⡀
⠀⠀⠀⢀⠤⠶⢴⡐⡷⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡆⠀⠀⠀⢣⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠃
⠀⠀⠀⠀⠀⠀⢠⢬⡁⠀⢰⠀⢐⡄⠀⢈⣦⣿⣖⡁⠀⠀⠀⠠⠄⢀⠇⣾⠀⠀⢀⠄⣀
⠀⠀⠀⠀⠀⠀⠈⢯⣀⣀⣠⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⢸⣾⣡⠤⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠉⠩⠶⠒
⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⢀⡠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⢨⠃⣾⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⡆⠀⠀⢄⣤⠶
⠀⠀⠀⠀⠀⠀⠘⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⡷⠤⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠀⢠⣀⡀⣀⠀⠀⠀⠀⠀⣐⣂⣀⣠⠴⢖⣫⠆
⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⢰⠀⢠⠂⠀⠀⠀⠈⠒⠒⠒⠋⠉⠀⠉⠑⠋⠉⠀⠀⠀⡇⢠⠇⠀⡤
⡠⠒⠐⠺⠇⠀⢀⠆⠀⢢⡸⡆⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡟⡾⣠⣎⣀⣀⡀
⠷⣄⣀⣀⠜⠉⠁⠀⠐⠚⠀⠈⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⠀⠀⠀⠀⢈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢕⠄⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠑⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠈⠁⠀⢄⠀⠈⠄⢇⠀⠀⠀⠀⠀⣀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢄⢰⡈⠀⠀⠀⡴⠋⠀⠀⠀⠀⠐⠄⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⠔⠂⠀⠑⠢⣀⠀⠀⠀⠠⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡈⣧⠀⠀⠔⠿⣿⠀⡀⠀⣀⡤⠠⢄⢀⡈⠀⠄⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠦⣤⡈⠀⠀⠀⣄⠀⠀⠁⠀⠐⠀⢠⡎⠀⠀⠀⠙⢦⡈⠀⠘⡆⢀⠜⠁⠀⠐⠀⠙⡄⠀⠀⠀⠀⠀⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠀⡀⠀⠀⠀⡁⠀⢀⡜⠀⠠⡑⡄⠀⠀⢻⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠂⠀⠑⠤⣀⠀⠀⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⡰⠁⠰⠁⠀⠀⢀⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠀⠀⠠⠀⠀⡀⠀⠀⢡⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠑⠦⠀⡼⠁⠀⠀⠠⠀⠀⠀⢀⣠⣄⣀⣤⠶⠚⠉⠁⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣀⣀⠉⠀⠛⠛⢉⣡⡀⠀⠀⠀⠑⠤⣄⠀⠀⢀⡠⠛⠀⢤⣄⡒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⠀⠀⠀⠉⠁⠈⠀⣀⠀⠘⠒⠀⠐⢈⢋⠉⡉⠁⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠱⡖⢄⠀⠀⠀⠀⢀⣠⠄⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⠀⠀⠀⠈⡀⠀⠀⠉⠙⢦⡀⠀⣀⡔⠉⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢳⠦⠤⠒⠋⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠂⡀⡀⠀⢀⠿⠐⠉⠀⠀⠀⠐⠢⠀⠠⠄⠚⢡⣀⠀⠀⠀⠀⢀⠀⠀⠀⡜⠒⠒⠂⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠞⠓⠒⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠉⠛⢧⣄⣀⠀⢀⡠⠞⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠄⠐⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠚⠑⢬⡂⠀⠀⠀⠀⢈⡳⣀⠀⠤⠔⢊⡼⡱⡄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠐⠀⠬⠉⠠⡾⠉⠙⠒⠒⠉⠀⠁⢟⠲⣄⠀⠀⠀⢈⠔⠁⠠⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠀⠀⠈⠢⡐⠀⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠀⡂⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⢣⠀⠓⡄⢸⠀⢀


⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓
⣦⠤⠦⠤⠤⠤⢤⡤⢤⡀⠖⠒⠶⠤⠦⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠒
⠀⠶⠶⠶⠦⠠⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠦⠤⠤⠄⠀⠀⡀⠠⠄⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⢀⠀⣤⣤⣄⣀⣀⣀⣀⣀⡀
⣦⣿⡿⠛⠿⠯⠿⠿⣿⣿⣿⡟⠛⠒⠒⠛⠙⠛⠉⠉⠉⠉⠉⠛⠛⠉⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠍⠩⠛⠛⠓⠀⠛⠉⠛⠛⠛⠛⠛
⣿⣿⣿⡿⠶⠶⠶⢶⡶⣖⣀⣠⣀⣀⠀⠀⠀⠀⠤⠄⠀⣠⣤⣀⣀⡀⢀⡀⠀⠄⠀⠠⡄⠀⠠⠄⠀⠤⠤⠄⠀⢀⡀⠤⠠⠤⠤⣤⠄⢀⣀⡀⣀⣀⣀⣀⣀
⢠⣤⣤⣄⣀⣀⣴⠔⠀⠀⠀⠤⠤⣤⣤⣤⣠⣤⣤⣄⣠⣄⣠⣄⣀⣀⡀⣀⣀⠀⣀⣀⡚⠛⡛⠚⠛⠒⠒⠂⠲⠤⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠬⠷
⠀⠀⠀⣀⣈⣱⣶⠶⠶⠶⠶⠶⠆⠀⠐⠶⠄⠀⠠⠩⣭⣴⣶⡦⢤⣭⣯⣍⣭⣉⣉⣉⣙⣛⣛⣛⠛⠓⠒⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠘
⠀⠀⠶⠿⠿⠟⠉⠉⢉⡙⠙⠋⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⢀⠀⠀⠈⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⣿⡟⠒⠶⠦⢤⡄⠀⠈⣄⡁⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⠐⠂⠈
⠐⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠄⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠠⠤⠒⠀⠠⠤⠤⠤⠤⢤⠀⠒⠒⠒⠀⠠⠤⠄⢠⣄⠀⠀⠲⠴⠀⠠
⠤⠄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠁⠀⠀⠀⢀⣀⠀⣀⣀⣀⣐⣒⣶⣶⣦⣤⣄⣹⡟⠛⠙⠀⣐⣒⣲⣶⣶⣶⣶⣦⡴⠀⣀⣠⣄⣘⣓⠀⠠⠬⢤⣭⠙
⠀⣀⣀⣀⣀⣀⣀⣲⣤⣤⣤⣤⣤⣤⣤⡶⢷⣾⣿⣻⡿⢛⠛⠛⠶⠶⠶⠶⢤⣤⣄⣀⡛⠛⠛⠛⠿⠃⠠⢤⣤⣤⣤⣍⣉⣛⣉⠉⠙⠚⠛⠻⠗⠒⠒⠂
⣭⣭⣭⣍⣉⣙⣛⡛⠿⠿⠶⠶⣶⠿⣿⣿⣶⣾⣯⣭⣭⣭⠽⠽⠿⠐⠒⠶⠶⠶⠾⢯⣭⠉⠉⠙⠿⠶⠶⠶⠶⠶⠾⠍⠉⠉⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⢀
⠆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⣄⣤⣤⠤⠶⠶⠷⠿⣿⣿⣟⣛⣛⠛

⠀⠀⠀⠀⣀⣠⡤⣢⣆⡄⠀⠀⠀⠀⢀⡴⣶⣦⡦⣦⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⡀⠀⠀⠀⢀⡴⣤⣀⡠
⠀⠀⠀⠀⣴⠿⣾⣿⡧⣯⣷⡆⠀⠘⣷⢿⣷⠹⢷⣷⠀⠀⢠⠀⠄⣈⠳⣀⡀⠁⡧⠀⠀⠰⣯⡹⣽⣨⣃⣤
⠀⠀⠀⠀⢽⠻⠟⣻⣟⡓⠌⠀⠀⠀⠉⠛⠻⠛⠚⠁⠀⠀⠀⢑⡤⣙⣤⢻⣇⡴⢫⠀⠀⠀⡉⣽⠤⠿⠈
⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠵⣬⣟⣫⢿⡴⣿⡓⠀⢀⠄
⠀⠀⠀⠠⢶⣤⢤⣄⣤⠄⠀⣀⣴⢶⠑⢤⠷⣺⣼⣴⢦⡄⠈⡭⢉⣴⠟⠹⣾⡷⠠⣽⠄⠀⠀⠀⣠⢀⣸
⠀⠖⠀⢫⣽⣿⣶⣇⣼⠎⠀⢸⡭⣝⡳⢏⠴⡨⢏⢽⣽⡧⠈⠉⠁⠁⣠⠴⡇⠀⠐⠸⠀⠀⠦⢤⢿⡟⣃
⠀⠈⠾⢿⣍⣻⡿⠿⢉⡂⠀⠀⠙⢛⣻⠳⣾⣧⠾⡞⠋⠀⠀⠀⠀⠐⠁⠀⠐⠆⠀⠀⠀⠀⠢⠤⠀⠉⠁
⠀⠀⠃⠉⠛⡋⣸⠖⠛⠁⠀⣀⠀⠀⠀⢠⠀⠈⠉⠀⠀⣀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡀⡠⢤⢢⣀⣲⡀⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⣠⣻⣷⣴⣾⡞⢀⡄⠀⠀⠀⠈⢿⠶⢾⡎⢹⠇⠄⠀⢀⠤⣼⢷⢼⣣⠟⣶⢷⣾⣀
⠀⠸⡇⣶⣶⠯⢀⠀⠠⣤⣿⣽⣏⣿⣿⣿⣿⣧⠞⠀⣠⡔⣾⣶⣿⣤⠷⠤⣄⠀⢾⣶⡿⣾⣿⣿⢿⢻⡿⣿⡟
⠀⠀⠓⣾⢻⠶⠛⠁⠀⠨⢽⠯⡭⣷⣿⠗⠛⠀⠘⠹⣯⠶⢿⣯⡏⣱⣆⠀⠉⠀⠈⠛⢿⣷⣽⠍⣾⠓⠶⡟⠁
⠀⠀⠰⠻⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠉⠀⠀⠘⠎⠢⡀⠀⠀⠀⠀⠛⠘⠦⠜⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⢤⣄
⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣴⡄⠀⠀⠀⠘⣤⣀⣰⠇⠀⢀⡯⡀⢠⠈⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⢴⣾⠁⠈⠁⠀⠀⠀⣸⢱⡂⢸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣸⣿⣇⢸⢹⡏
⠀⠀⠀⠀⠀⠀⢠⠆⠄⠐⠀⠀⠀⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣶⠞⠀⠀⢀⣤
⢠⡄⢀⠀⠠⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⣰⢾⡀⠀⠘⠃⠀⠀⠀⠀⠀⠠⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠋⠀⡆⠠⠄⠀⠁⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⡅⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠙⠳
⠀⠀⢫⡠⠀⠂⢠⠇⠀⠀⠀⠈⠉⢁⣠⡀⠀⣟⠀⠀⠀⠇⠀⠀⠀⠓⢀⠉⡀⠀⠀⢠⢀⠀⠀⢢⠔
⠀⠀⠈⠁⠀⣲⠞⠀⠀⠀⠀⠀⠀⠀⢸⣥⣶⣇⣠⣶⠎⠀⠀⠀⠀⠀⠀⠷⠁⠀⢀⠼⠋⠀⢠⡀⡀
⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠓⠇
⠘⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⠀⠀⠸⠀⠀⠀⠈⠉⠀⠄⠀⠈⢦⡴⠆⠓⠂⢀⣀⡀
⠘⠶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢠⠀⠸⣤⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠚⠀⠌⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⠀⠀⠀⠀⠀⠰⠆
⡄⠀⢦⠀⠀⡄⢠⠃⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠀⠀⠀⠲⠛⢀⠀⠀⠀⠀⠀⢀⠸
⡍⢶⠀⣧⠀⠀⠹⠀⠀⠀⡤⡈⢁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡑⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈
⠙⠷⠀⢀⠀⠀⠀⠀⠀⢸⣸⠁⣾⣰⠂⠀⠀⠀⠀⠀⠀⢸⡧⡄⡀⢠⢱⡆⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠠⣤
⣼⠀⠀⡾⠄⠀⠀⠀⠀⢺⣿⣧⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢥⡼⠚⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠠⠀⠀⢸
⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⣰⠂⠀⠈
⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣨⡴⠋
⠐⠀⠚⠋⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣀⣼⠀⠀⠙⣋⠁
⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣤⣤⣤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣹⡿⢋⡽⠋⠀⡟⠉⢿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡜⣀⠀⢰⡇⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⣤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠸⡇⢸⡄⢸⠁⠀⣶⢸⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⠁⢸⡇⠈⣿⣿⡋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠇⠀⠸⢣⠀⠀⣫⠀⠀⠀⠈⡆⢨⣿⡀⠀⡀⠀⠀⠀⠰⣴⡟⢷⡏⠀⠀⢣⠀⢸⠉⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣼⠈⣷⠀⡇⠀⠀⢠⡄⣿⠆⠘⣷⠞⠀⠀⠀⠀⠀⣿⠃⢸⡇⢦⡀⢸⠀⠈⣧⠸⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⡀⣿⠀⠀⠀⡇⠀⠀⣼⠁⣿⠀⠀⣿⠀⠀⠀⠀⠐⢶⣿⠠⣼⡇⠈⠁⠸⡀⢰⣇⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡇⣿⠀⠳⣿⠀⠀⠀⡇⠀⠈⣀⠀⣯⠀⠀⢿⣆⠀⠀⠀⠀⠈⣿⠀⠹⡇⠀⢠⡄⣷⠈⢹⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⣿⡄⠀⣿⢀⠀⠀⢧⠀⠀⠿⠀⡿⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⡄⣱⠀⠘⠃⣿⠀⢸⡆⢠⣿
⠀⠀⣀⠀⣼⣶⠶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⣿⠁⠀⣿⠈⠷⠀⢰⠀⡀⠀⠀⣟⠀⠀⢸⡇⠀⠀⠀⠀⣀⣿⠀⠙⣿⠀⠀⠀⣿⠀⢸⡇⠘⣿
⠀⠀⢸⣿⣿⠁⠰⡇⠈⢿⢷⣄⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⡟⢴⠀⣿⠀⠀⠀⢸⣄⠇⠀⠀⣿⠃⣰⠸⣧⡀⠀⠀⠀⠈⢿⡆⠀⢸⠀⢠⡞⣧⠀⣸⡇⠀⣿
⠀⢴⡿⠁⡇⠀⠀⡟⠀⢸⠘⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⣷⠀⠀⣿⠀⢀⡀⢸⡏⠀⠀⠀⣿⠀⠃⢸⡏⠀⠀⠀⠀⠀⢸⣷⠀⢸⠀⠈⠀⣿⠠⢿⠁⢸⣿
⠀⣾⡧⢀⡇⠀⢻⣇⠀⢸⡇⢹⣷⣤⠎⠀⠀⠀⠙⢾⣿⠀⡿⠀⠘⢿⡀⠘⠃⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠐⢾⡏⠁⢸⢠⠀⠀⡏⠀⡞⠀⢸⡇
⠀⣿⠀⢸⡇⠀⣾⠀⠀⢸⠃⢸⢹⡇⠀⠀⠀⠀⠀⠸⣿⠀⡇⠀⠀⢸⠁⠀⠀⢸⡇⢀⡟⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⠀⢸⠈⠃⢀⠇⢰⡇⢀⣾⠇
⣸⣿⠀⢸⡏⠀⣿⢀⣴⠿⠀⢹⢸⣷⠀⠀⠀⠀⠀⠐⣿⠀⡇⢶⠀⢸⠀⠀⡆⢸⡇⠈⠀⠀⣿⠀⠀⣸⡟⠀⠀⠀⠠⡄⢸⡏⣇⣸⠀⠀⢸⠘⢯⠃⢨⡿
⢸⣧⠀⢸⡇⠀⣼⠈⠀⢰⠀⢸⣸⣿⠁⠀⠀⠀⠀⠸⣿⠀⡅⠀⠀⢸⠀⠸⠇⢸⠁⠀⠀⠀⡇⠀⠀⢻⡇⠀⠀⠀⠀⢱⣿⠁⢠⡟⠀⢀⡜⠀⡿⠀⣼⡇
⢸⡟⠃⢸⡇⠀⢹⡄⠀⢸⠀⢸⢹⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣾⠰⡀⠀⢸⠀⠀⠀⠀⣷⠀⠀⣿⡇⠀⠀⢠⣤⡾⠃⢀⡞⣡⠴⣿⠁⢸⠇⣺⡟
⠸⣿⡄⢸⡏⡆⢸⠱⠀⢸⡄⢾⢸⡿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠛⠀⢸⠀⡀⠀⢠⠿⠀⠈⣿⣥⣤⣴⠾⠋⣀⣴⡏⠀⢀⡞⠁⣠⠏⣰⣿
⢤⣿⠀⠸⡇⠀⢻⢀⠀⢸⠃⢸⠸⣿⠀⠀⠀⠀⠙⢶⣿⠀⡿⣄⠀⣹⠀⠀⠀⣼⠀⡇⠀⢸⠀⠀⠀⣿⣯⣥⡼⠗⠊⠁⣚⣤⠶⠛⢊⡽⠃⣰⠟⠁
⠀⢻⡆⠀⣧⡀⠀⡟⣧⠘⡆⢸⣴⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠀⣿⠀⣶⠀⡡⠀⠁⠀⢸⠀⠀⢤⣿⠤⠤⣴⠶⠒⠻⢯⣤⣤⡞⢉⣤⠾⠋
⠀⠘⣷⡀⢸⡳⠄⢷⡉⠀⢿⠈⡇⢻⡄⣀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠁⠀⡇⠀⠀⠀⢸⠀⠀⠸⣿⣀⣀⠴⠤⠖⠛⢋⣁⣴⡿⠛⠁
⠀⠀⢻⡇⠀⢳⡀⠘⣟⠀⢸⡇⠱⡌⢿⣯⣀⣦⣴⣤⣿⠀⡇⠀⠀⣿⡄⠀⠀⣧⠠⡄⠀⢸⣼⠃⢸⣿⣤⣼⠷⣶⠶⠟⠻⠏
⠀⠀⠘⣧⠀⠈⣧⠀⠹⣄⠀⠻⣄⠉⠲⠿⠛⠿⠛⠛⣿⠀⡇⠀⠀⣿⠀⠀⠀⡏⠀⠉⠀⢸⠏⠀⢸⣇⡤
⠀⠀⠉⢻⣆⠀⠘⣷⠀⠘⢦⣀⠙⠳⠦⠶⣴⠒⠚⢉⣿⡆⡇⠰⡀⣿⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⣾⡏
⠀⠀⠀⠀⢻⣿⠅⢘⣦⡀⠀⠈⠓⠒⠒⠆⠛⠒⢊⣩⣽⡇⣿⠀⢷⡎⠀⠀⠀⡗⣠⠀⠀⢸⢠⡆⣿⠁
⠀⠀⠀⠀⠀⠙⣧⡈⠉⠙⠲⠧⠥⠤⠤⠤⡖⢛⣩⡴⢿⣷⣗⠀⠀⠇⠀⠀⠀⣧⡙⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣈⡻⢶⣦⣄⣀⣠⣄⣀⣴⡿⠟⠉⠀⢸⣟⣿⠀⠀⡇⠰⡄⠀⣿⠀⠀⠀⢸⡆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠉⠀⠀⠀⠀⠀⢺⡟⢏⡀⢀⣧⠀⠋⠀⣇⢀⣀⠀⣸⣧⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡀⠀⠉⠀⠀⠚⠋⠀⠙⢁⣿⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢹⡇⠠⠶⠶⠄⠲⠆⠀⢠⠼⡿⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⣶⠀⠀⢰⡄⠀⢴⠀⣤⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢈⠀⢠⣏⠀⠀⢸⠀⠀⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠘⠀⠀⡇⠀⠀⢸⡄⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⢰⣿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠳⣄⠀⢸⠇⠀⢠⢸⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣿⡇⠀⠀⡇⠈⠃⢸⠀⠀⠈⢰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠰⣇⠀⠀⢸⠀⠀⠀⢸⠇⢸⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⡀⠀⢸⠀⠀⢠⡿⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠟⠛⠛⣿⡇⠀⠀⡏⠀⠀⢸⠀⠐⠃⣿⠀⢸⡏⠛⣛⠛⠻⠶⢶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⣠⡤⠀⠀⠁⠀⣿⡟⠀⠀⣧⠘⠇⢸⠀⠀⠀⣿⢀⣾⠃⠀⠐⠲⠂⠰⠄⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠄⠀⠀⠒⠀⠻⣿⣿⡵⠆⣿⠀⠀⢸⠀⠀⠀⣿⡾⠃⠀⠠⠔⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⠄⠙⠷⣤⣿⣀⣀⣼⣤⣾⠿⠋⠀⠀⠀⠤⠄⢀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠩⠥⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢀⣄⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⡇⣀⣴⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣧⡠⢼⣿⡀⠀⠀⠀⢒⣦⣄⠀⠀⠈⠡⣷⣾⣿⣿⣷⣴⣤⣾⣅⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠁⠜⡏⠀⠀⠀⠀⢸⠋⠙⢄⠀⠀⢀⡾⠛⣿⣿⡏⡿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⡇⠀⢠⣠⡀⠀⠀⣀⠈⣆⡄⠈⠹⠈⠀⡇⠘⠁⠈⢸⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣿⣷⣤⣇⢸⣤⣿⣷⣠⣤⣬⠥⠭⠯⠁⢛⡀⠀⣿⠀⣀⠀⠈⡇
⠀⠀⠀⠀⠤⠤⠤⠿⢷⣿⣿⣿⡋⣉⡉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣠⢸⣴⡄⠇⢠⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⣀⠀⣀⣀⣄⠀⠀⣀⣀⣠⡄⣦⣷⣿⣿⣿⣿⣿⣾⣿⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⣄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡦⠠⠄⠀⠀⠀⠁⠦⢄⢁⠃⣠⠀⡔⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⢄⠰⠂⠀⡄⢀⡂⠀⠀⣈⡂⠀⡛⠀⠀⠄⢁⣀⠀⠚⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡆⠀⢲⠀⢠⠇⠁⠇⠈⢀⠁⠳⠀⠈⠁⠀⢦⡉⠣⡄⣦⠱⠃⠈⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠘⠑⠃⠀⢀⠀⠀⠉⡁⠐⠁⠄⠺⠄⠀⢋⡢⢌⡛⠄⡇⠈⣀⠔⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠑⠀⠀⠑⡤⡀⢀⠖⡔⠁⠀⠤⠘⠀⠀⣌⠀⠀⢀⠠⢶⠕⢤⡀⣠⠀⠂⠅⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠐⣆⠠⣀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⠀⠈⢢⠓⣀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠝⠑⠀⠤⠀⠙⠉⠀⠈⡀⢀⠆⠐⠂⣄⠀⠀⠀⡀⠚⠙⠾⣦⠒⠙⠒⠲⠂⠀⠉
⠀⠀⠀⠀⠀⠣⠐⠢⠄⠀⠀⡀⠀⡠⠙⠂⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡔⠒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⠂⠊⠀⠀⠄⠀⠙⠂⣀⠀⢠⠔⠈⠑⠄⠀⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢀⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠒⠉⠀⠀⠰⠴⠀⠀⠢⠀⠀⠠⡜⠁⠀⠀⠀⠀⠀⡀⠀⠀⠨⢴⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡀⠐⠀⠀⢂⠀⠀⠀⠈⠐⡺⠀⠀⠀⠀⠀⠀⠀⠂⠐⠆⢀⠀⠤⠂⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠑⠀⣀⠀⠀⠈⠟⠀⠀⠀⠀⠋⠉⠀⠀⢀⠀⠀⠈⠤⢀⠄⠀⠀⢀⠤⣀⢀⠠⠀⠀⠀⡀
⠀⠀⠐⡄⠀⠁⠀⠂⠀⠀⠀⢁⣌⣱⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⡄⠀⠁⠄⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⢨⠄⢀⡂⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠍⠢⢁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⢀⠒⠂⡁⠀⢀⡠⠒⠄⠁⠀⠉⡄⢁⠒⠤⡀⠀⠝⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠉⠐⠀⠀⠰⠊⠑⠊⠚⠀⠀⠐⠁⠉⠀⠠⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⡀⠀⠀⠀⠠⠴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡻⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⣤⣄
⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⣾⡄⠀⠀⠀⠘⣤⣀⣰⠇⠀⢀⡯⠀⢀⠈⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⢶⣾⠁⠈⠉⠀⠀⠀⢸⢱⡃⢸⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣸⣿⣇⢸⢹⡏
⢀⠀⠀⠀⠀⠀⢰⡆⠄⠐⠀⠀⠀⠛⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⠞⠀⠀⢀⣄
⢠⡄⢀⠀⠠⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠘⠃⠀⠀⠀⠀⠀⢠⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡁
⠛⠁⡆⠠⠄⠀⠁⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢅⠀⠐⠀⡇⠀⠀⠀⠀⢀⣀⠀⠈⠛⠣⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⢫⠠⠀⠒⢠⠇⠀⠀⠀⠈⠉⢁⣠⡀⠠⣟⠀⠀⠀⡇⠀⠀⠀⠓⢠⠉⡀⠀⠀⢰⠀⠀⠀⢦⡴
⠀⠀⠈⠁⡴⣲⠞⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⣇⣠⣶⠎⠀⠀⠀⠀⠀⠀⠷⠁⠀⢀⠼⠋⠀⢠⡀⡀
⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠓⠇
⢛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⠀⠀⠸⠇⠀⠀⠈⠋⠀⠄⠀⠈⢦⡴⠄⠓⠂⣀⣀⣀⠄
⠸⠶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⠀⠸⣤⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠾⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⠀⠀⠀⠀⠀⠰⡆
⡄⠀⢧⠀⠀⡄⢰⠃⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⡀⠀⠀⠀⠀⠀⠲⠟⢀⠀⠀⠀⠀⠀⢀⠸
⣟⣴⠀⣧⠀⠁⠹⠀⠀⠀⡤⡈⣁⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠁⠀⣠⠀⠀⠀⠈⠁
⠙⢳⠀⢀⠀⠀⠀⠀⠀⢰⣱⠁⣾⣸⠂⠀⠀⠀⠀⠀⠀⢸⣣⡄⠀⢢⢱⡄⠀⠀⠀⠀⠂⢤⡿⠀⠀⠀⠀⢠⣤
⣴⠄⠀⡾⠄⠀⠀⠀⠀⢺⣿⣧⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣥⡼⠚⠁⠀⠀⠀⠀⠀⠋⠠⠀⠀⢀⠀⠀⢸
⡃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⢀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⣰⠂⠀⠈
⠁⠀⢹⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⢀⡴⠋
⠐⠤⠚⠋⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣰⠀⠀⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢂⠀⠀⠁⠂⢂⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠐⢤⡏⠈⠡⠂⠠⡂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠈⠀⣹⠀⠀⡀⠘⠀⠀⠀⠀⠀⣀⠀⢈⡘
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⡀⠤⠀⠀⠀⢐⠀⠀⡄⠀⢠⡤⠂⠉⠁⠀⠀⠉⠀⠔⠄⠀⠀⡢⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠂⠐⡜⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣵⡴⡄⠈⠀⠈⠀⢣⠀⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⡈⢀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠀⠘⢰⠓⠄⠊⠀⠍⠀⡀⠀⠒⠀⠆⡗⢢⠔⡠⠂⠠⢈⡒⠡
⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⠃⡀⢄⡀⠒⠀⠀⢠⡟⡜⡀⠀⢠⠄⣡⠫⠐⠍⠀⠴⢆⠖⠁⠀⠠⣈⡬⠀⡛⠠⠂⢁⠰⠀⡜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢠⣄⡢⠀⠠⠠⠀⢢⣄⣀⣠⠋⢉⠀⠉⡒⢡⠚⣋⠤⣄⠈⢤⠲⠧⠤⠤⣤⣈⣼⢡⠨⢥⠈⡁⠡⠤⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⡋⠙⠂⠀⠁⡤⣄⣀⣈⣸⠆⠀⠉⢈⣉⣀⢀⠀⠐⡀⠀⣢⠂⢀⢹⣴⠃⣾⠷⠧⣔⡁⠁⠐⡀
⠀⠀⠀⠐⠐⠀⡀⠀⠀⠈⠀⠙⠢⡄⢀⣾⡁⠶⠛⡦⠀⢀⡀⠴⠊⠈⠙⠲⠖⠁⠛⠊⢈⡇⠀⠀⡀⠀⠍⣀⠀⢀
⠀⠀⠀⠀⠂⠀⠈⠀⠁⠀⠁⠀⠁⠈⣑⡄⢠⣖⣟⣁⣀⠨⣁⡴⠖⡀⢉⡐⠂⠁⢀⠠⢀⠀⠀⠐⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠂⠄⠀⠈⠘⠀⠂⢐⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠄⠉⢁⠄⠴⠿⠍⠒⠛⠀⢀⠀⡐⠀⠂⠀⠀⠉⢉⡉⢀⢀
⠀⠀⠘⢀⠀⡨⠘⣯⠁⢂⠀⠀⡠⣞⠀⠁⠀⠀⢐⠃⣼⣫⡝⢀⡀⠀⠔⠀⠑⡄⢁⠀⠆
⠀⠀⠀⠘⠐⠻⢿⡁⠀⠈⠉⢉⠐⠀⠀⠀⠀⢓⠡⠊⠁⠀⠀⠀⠀⠀⠀⠈⢀⠁⠨⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⣇⠀⠀⠀⠃⠛⠀⠄⠐⠈⠁⠀⠰
⠀⠀⠠⠀⠀⠀⢀⢈⡷⡂⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠠⣀⠼⢋⢛⢂⠀⡀⠀⠁⠀⠤⠔⠸⠄⢐
⠀⠀⠀⠀⠚⢿⠨⠐⠂⡐⠂⠀⠄⠀⠀⠀⠀⣀⠒⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣢⣆⠰⠦⠤⠀⠀⠀⠀⠀⠀⠀⡐⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⢀⠈⢀⠐⠰⠃⠀⠀⠀⠀⢴⣠⠭⡁⠄⠐⢢⣴⠀⡀⠀⠀⡁⠀⠆⡀⢇⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠰⠄⠠
⠀⠀⢀⠀⠀⠰⠀⢉⠈⠀⠜⠀⠀⠀⢀⠀⠨⠼⠂⠐⠄⠍⢋⣑⠂⠀⠠⠀⠐⠦⠒⡈⠂⠁⠒⠈⠀⠀⠀⠐⠐⠀⢈⠀⢁⡀⠐⠠
⠀⠀⠀⠀⠀⠸⠈⡠⠔⠂⠂⠐⠀⠀⠀⢀⣆⠋⠣⠠⡉⢾⠳⢇⠀⠀⠀⠂⠀⠚⠂⠀⠄⠱⠀⠂⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠾⠒⡤⠀⠀⠀⠀⠀⠀⠈⠀⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠦⠈⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠂⠀⠀⢂⠐⠈⠀⠄⠀⠀⠀⠄⠀⠀⡀⠰⠀⠆⠀⠀⠀⠀⠄⣁⡀⠒⠄⠀⠌⠀⢀⠣⠀⠀⠀⠘⠀⠂⠀⠀⡑⠀⠁⠠
⠀⠀⠀⠁⠁⠀⣶⣷⡄⠀⡀⠀⠀⠀⠀⠐⠀⠁⢀⣅⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠢⡘⠀⡀⠂⠂⠄⠀⠈⠢⠅⡠⠠⠵⠂⠈⣀⠈
⠀⠀⠀⠀⢀⠈⠀⠑⠀⠀⠀⠄⠀⠀⠀⠤⠉⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⠀⠐⠁⡀⠀⠈⡤⠂⠀⠀⠡⠐⠀⠄⢒⠈⠉⡁⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⣀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠧⠰⠁⠔

⠀⠀⠀⠀⡀⠆⠠⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠐⢀
⠀⠀⠀⠀⠐⢴⠂⠀⠀⢀⠈⠂⠀⠀⠀⠀⠀⢀⠐⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠠⠔⠈⠠⡀⠀⠀⠀⢄⠠⢀
⠀⠀⢀⠄⠐⡤⢠⡉⠉⠌⠅⠐⠀⠀⠀⠐⢠⠀⠎⡱⠀⢀⠀⢀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠜⠯⠀⠁
⠀⠀⠀⠄⣀⠔⠲⠞⠠⠀⠄⠀⠀⠀⠀⠀⠄⠀⠂⠂⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠩⣀⠀⠀⠀⠈⠀⠂⠀⠠⠀⠐
⠀⠀⠀⠘⠁⠜⡋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⠈⠃⠀⠀⠆⠜⢗⡢⠀⠀⠀⠒⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡄⠀⢠⠀⢀⢠⠀⡐⡂⡔⠂⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣀⠸⡀⠘⠄⠀⠉⠀⡇⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⢈⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠠⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠐⠀⢰⡄⠰⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠸⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧⠀⠀⠀⠁⠸⠀⠀⠜⠀⠁
⠀⠀⠀⠀⠀⢀⠸⣄⠀⠆⠀⠀⠀⠀⠄⠀⣴⠃⠀⠁
⠀⠀⠀⠀⠀⠈⣤⣬⣤⣬⣥⣤⣤⣀⣠⣾⣥⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣴⣤⣦⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⢼⡿⣱⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡇⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠁⣼⡏⠀⠀⠀⣼⠁⣿⠁⢤⣿⠇⠀⢀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⢠⢰⣮⠈⣿⡇⠀⠀⠀⣽⠀⣿⠀⢸⡏⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢸⣿⣿⠀⢼⡇⠀⠀⠀⣿⠀⡿⠀⣼⢁⣿⡿⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⢸⣷⡙⣆⠀⣷⠀⠀⠀⡏⢸⡇⠀⠏⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇
⠀⠀⠀⠐⡌⠻⣷⡈⠢⠉⠆⠀⠀⠇⣼⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠰⣌⠻⣦⡀⠢⠀⠀⠀⠀⠘⠋⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣝⣣⠈⠀⢀⣤⡖⠯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣞⣀⣀
⠀⠀⠀⠀⠀⠒⠀⠀⠚⠛⠻⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠘⠛⠛⠗⠚⠛⠛⠛⠛⠚⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠰⠆⠀⠑⠒⣯⣽⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠋⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠂⠀⠂⡖⠰⠀⢈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠰⠀⣆⠀⠄⠀⠀⠈⠁⠀⢀⠘⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠒⠀⣈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠅⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⣄⠀⠁⠀⠆⠀⠀⡀⠁⠈⡀⠒⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠉⡀⠀⠄⠀⠀⡀⠀⠀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣄⠁⢀⠈⠃⡀⠀⠀⡉⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣉⣄⣉⣀⣠⣴⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⢀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠛⠛⠛⠛⠋⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣒⡒⠖⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⡌⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⠀⠀⠀⠒⠒⠠⠤⣀⠀⠀⠀⠀⠸⠀⠀⠙⢄⠀⢠⣚⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⣲⣦⣤⣤⣤⣀⣀⠀⠀⠀⠈⠑⠤⡀⠸⠀⠀⠀⠈⡆⠉⣠⡴⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⣻⠿⠛⠛⢿⣿⡶⢦⣄⣀⠈⠑⣄⠀⠀⠀⢡⠀⠀⠈⠓⠊
⠀⠀⠀⠀⠀⠀⣄⠀⢸⡆⢀⡆⠀⠀⠀⢸⠁⠀⠈⠀⠉⠀⠀⠀⠀⠀⢠⢝⡛⠛⢢⣌⢆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠙⠂⠈⠁⠘⠃⠀⠀⠀⢸⠀⠀⠞⢹⠄⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⢿⣿⣆⢠⠁
⠀⡤⠒⠒⠒⠀⠀⠠⠤⢤⣤⣤⣤⣤⣄⣬⡀⠀⠀⠀⢀⡄⠀⠀⠀⠘⠁⠱⠀⠀⠀⢸⣿⡟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠻⠙⢿⣿⣿⣟⠲⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⢸⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠁⢸⣿⠀⠰⠒⣹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠊
⠈⠢⠤⠤⠤⠄⢀⣀⣠⣿⣄⠀⠀⠀⠀⣾⡯⠊⠉⠋⠥⣀⣀⣀⣀⣀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢢⠀⠀⠀⢡⡤⠴⡖⠛⣿⣧⣀⣀⣠⣤⣾⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡆⠀⠀⠀⢳⡈⠸⢠⣼⠿⣛⣛⢍⠩⡍⠙⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⡀⠀⠀⠀⠙⠛⠉⣷⢋⠰⠀⠀⣀⠈⠂⣼⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠓⡄⠀⠀⠀⠀⠀⢸⡎⡇⣀⣈⢙⣡⡾⢋⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⣶⢶⠒⡛⣷⣭⣵⠾⣛⡉⠊⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠙⠉⠁⠀⠀⠀⠁⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣶⢀⣤⡴
⠀⠀⠀⠀⠀⠀⠠⢀⣄⣃⠔⠠⠠⠀⠀⠀⠀⠈⢉⣛⢚⠫⠆⣀⢀⡠⣄⣤⡄⠀⠀⠀⠀⢠⠠⡄⠀⢀⡴⠀⠄
⠀⠀⠀⣾⣯⣶⡋⣓⡯⣽⢿⣃⢀⠄⠀⠀⠀⠀⢤⣔⣷⢫⢾⡷⣿⣷⡊⣇⡃⡀⠀⠀⠠⣤⣄⣿⣅⡀⢟⠻⠛⠀⢀⡄
⠀⢠⣠⣷⣚⣿⣟⣻⣿⣿⣶⣭⣄⡀⠀⠀⠠⠀⣳⠿⣿⠟⡊⢿⣽⣛⠟⣿⣿⡁⠀⠀⠀⣨⢽⣾⢾⢿⣀⣶⠈⡿⢋⡀
⠀⢸⣿⠿⣧⢿⣽⣿⣾⣟⣿⣿⢿⡿⠀⠀⠠⠼⣍⣻⣋⣭⣽⣷⣯⣹⡾⣿⣿⣦⠀⠀⠠⢿⢻⠧⢟⠻⢏⠹⠃⢛⠿⠖
⠀⠀⠠⣿⣛⡿⣿⣿⣟⣿⡻⠈⠉⠀⠀⠀⠀⠲⠿⢹⠘⢾⣻⣿⣿⢧⢟⣻⡿⠟⠗⠀⠀⠘⠙⢿⣋⡤⠀⠱⣮⣹⡇
⠀⠀⠀⠀⠈⠿⣿⠧⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢾⠯⠙⠊⠼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠤⡤⠄⣀
⠀⠀⠐⠀⠈⠁⠄⠀⠀⠀⠀⠨⠀⠂⠄⡄⠀⠀⠀⠀⠀⠀⠋⠀⠁⡄⠌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⠀⠌⠁⠀⢨⠠⡆
⠀⠀⠃⠄⠈⠈⡀⠆⠀⠀⡀⠀⠄⠁⠂⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠐⠈⠃⠀⠈⡀⢠⡄
⠀⠀⠀⠁⢀⠀⠀⠐⡀⢀⠀⡀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠗⢲⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠀⠠⠄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠐⢠⠅⣈⠀⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠚⠀⠂⢁⠘⠆⠀⠀⠀⠀⠀⠀⠈⣀⠘⠂⠀⣀⡀⠀⢘⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠡⢈⠘⠀⠀⠀⠀⠀⠀⠀⠠⠆⠘⠃⠀⠐⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠠⡄⠀⡁⠐⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠄⠀⠠⠆⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡀⠀⠀⡄⡁⢠⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢦⠀⠈⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠒⠀⠨⠁⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⠀⠒⡇⠇⣀⠀⠀⠀⠀⠀⠀⠋⠁⠄⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⡆⠀⠉⢠⠁⠀⠀⢐⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⡴⠛⢛⠦
⠀⠀⠀⠀⢠⠀⠇⠞⠆⠀⡀⠼⢁⠊⠀⢠⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⢈⠀⠁⡀⠀⠈
⠀⠀⠀⠀⠀⣄⠸⣄⠰⠨⠀⠀⠑⡠⠂⣸⠜⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠃⠁⠀⠄⠀⠀⠀⠀⢡⠇
⠀⠀⠀⠀⠀⠘⠁⠠⠁⠀⠀⢠⠠⢣⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠇⠀⡀⠀⠄⢰⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢐⣘⡇⠀⢗⣄⢠⠾
⠀⠀⠀⠀⠀⠠⠠⠀⠀⢀⠀⢀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⢀⢀⢀⢠⢀⠠⢠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣁⠀⠁⠁⠁⣈⣁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⠀⠘⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡔⠀⠀⢠⠄⢈⠐⠀⢀⠀⠘⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣇⣾⡇⠀⣠⠏⠀⠀⠀⠀⠀⠐⠊⠁⠔⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣄⡀⢀⠀⠀⠀⠀⠀⡀⢠⣿⡿⠃⢸⣏⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊
⠀⠀⠀⠀⠀⠼⢳⣞⠀⣤⣀⣠⣾⣷⢋⣵⣦⡴⠚⠋⠀⠀⠀⠀⠀⠀⠉⢱⣄⠀⠀⠀⠀⠀⠘⠁⠀⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣼⣿⣿⠟⠻⢣⣿⡟⠉⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖
⠀⢠⣤⡄⠀⣼⣿⣿⡏⠙⣿⡙⣷⣿⣏⣤⣾⣿⠀⣀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠓⢺⣯⠭⠛⠂⠿⠇⠸⠯⠿⠟⠛⠋⠿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠒⠒⠉⠤⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⣙⣷⡑⢿⡀⣆⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠈⠙⠟⢮⡁⣺⣿⣿⠀⠀⠄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⣆⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⠃⠈⢻⣿⣿⣾⢠⡿⠂⠀⠀⠀⠀⠀⠀⠘⡀⠐⡗⡀⠀⠀⠀⠀⠀⠀⡀⣜⢷⣿⣿⡁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣎⣧⠀⠠⣿⣿⡇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⣼⡷⡄⣠⣀⢀⣿⣿⠗⣾⠟⣁⡀
⠀⠀⠀⣤⡤⣠⣀⣠⣶⣿⢿⣿⣷⣄⣿⣿⡄⢻⣿⣷⣤⣐⡤⣄⠀⠀⢠⣤⡄⢻⣿⣿⣍⢫⡿⠟⢱⡷⣸⣯⣞⣁⣠⠀⢀⠤
⠀⠀⠀⠙⠺⠭⠍⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢙⣛⡋⠁⠉⠀⠀⠀⠉⠓⠋⠉⠉⠛⠛⠛⠛⠛⠛⠋⠭⠭⠛⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣽⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⣿⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⣽⡿⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⢀⣀⣀⣿⠃⢀⠄⠈⠀⠀⠀⠀⣀⣠⣤⡀⠀⣹⣿⣿⣿⣿⣿⡿⣝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠠⠤⢬⣿⣿⣷⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⠳⠘⢹⢿⣿⣿⣷⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⣀⣤⠶⠚⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⠊⠉⡿⡿⡻⠀⠀⢸⢸⡇⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠀⠀⠘⠋⣼⡿⢿⠀⠀⠀⠀⠈⠀⠀⠀⠀⣇⠁⠀⠀⠈⠈⠇⠘⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣱⣿⠃⠀⠀⠀⠀⣶⣴⣾⣿⡷⠀⡀⠀⠠⠤⠤⠤⠀⠀⢀⣿⡀⢀⣆⡀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⡀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⡏⠀⢀⡠⠤⠔⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠣⠀⠀⢰⣶⠀⠸⣧⡀⢀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣽⣷⣎
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠃⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠻⡿⠉⠉⠉⠉⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠀⠀⠠⠄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠼⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⢤⢔⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠙⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠅⣃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢄⣰⣦⣶⡤⠀⠀⠀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠿⠄⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⡏⢠⠌⡌⢶⡀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠐⢅⡎⡜⠘⣄⢳⠀⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠀⢰⠀⠀⢡⡇⠀⠈⠢⡷⠀⢀⡄⠨⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠄⢤⡀⠐⠀⢸⠀⢀⡜⠑⢄⠀⠀⡣⢸⠜⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆⠈⠐⢧⡸⣤⠎⠀⠀⠀⢣⠎⠀⢸⠀⢠⡶⠣⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠘⡆⠀⠀⠙⡟⠀⢀⠀⠀⠄⠀⠀⠀⡖⠉⢀⣥⡆⢀⠆⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠢⡡⡀⢳⡀⠀⠀⢰⡀⡈⠑⠶⣀⠀⠀⢀⣧⠖⠉⠀⠀⢂⠄⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢀⠀⠈⠻⡦⢷⡀⠀⠀⡿⠁⠀⠀⠈⠑⢦⡟⠁⠀⠀⢀⠞⠁⢀⠌⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⢐⠦⠤⠀⠀⠡⣄⠀⠈⢢⠈⠑⠲⣇⠀⠀⠀⠀⠀⠈⡄⢀⣀⣠⠎⠠⠤⠂⡀⠄⠀⠀⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠦⠤⣀⡀⠈⠒⠮⣧⠀⠀⠈⠳⣄⡀⢀⣠⠴⠛⠉⠀⠀⡰⠋⠀⢁⣀⡠⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠈⠑⢦⣀⠈⠓⢦⣄⣲⠈⠛⠩⢄⠀⠀⢀⡠⢊⡠⠔⠋⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢓⣦⣄⣀⠈⠙⠛⠋⡹⠃⠀⠀⠀⠀⣻⡛⠛⠛⠉⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠛⠈⣏⣏⠉⣻⢿⣷⣦⣤⣤⡴⢾⡿⡛⠓⣶⣖⣛⠿⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠁⠀⠘⠛⠒⠂⠛⠙⠃⠛⠛⠂⠀⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠲⠤⠤⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠤⡤⠴⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⠀⠀⠀⠀⠀⠠⠄⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⣼⡿⠁⠈⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣧⣾⡿⠁⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠟⠋⠉⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣆⠀⣴⣼⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠓⣷⠞⠙⠀⠈⢿⢠⡞⠁⣀⠀⣀
⠀⠀⠀⠀⣀⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢠⠃⢀⣮⠿⣆⠀⠉⡱⣾⢡⡀⠘⠁⢦
⠀⠀⠀⠀⠁⠀⠉⣠⢹⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⣶⡗⣤⣿⡄⣼⣿⡛⠒⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡾⡽⣿⣽⠀⢀⡤⣼⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠏⠘⢼⡏⣷⣠⠟⠻⣆
⠀⠀⣠⣴⡶⣿⡿⠋⠁⠈⡲⠟⠀⠼⠁⢳⡁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠻⠀⠀⣿⠁⠉⢿⣇⠐⠼⣆
⠀⠀⠈⠀⠀⠉⠀⠀⠀⣿⣿⠀⠀⠀⠐⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢴⡂⠒⠀⠀⠀⠀⢻⠀⠀⠘⢿⡀⠀⠘⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠠⣿⣿⡇⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠫⡷⢛⣾⡷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⠁⠀⠀⠀⠘⠏⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣾⠿⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣄⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⣼⣇⢰⠏⠀⠹⠄⠀⠀⠀⠀⠀⠀⢀⣴⠞⠃⠀⢫⡮
⠠⢶⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠈⠟⠃⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⣤⠖⣻⣅⠀⢝⡇
⠀⠙⠛⠙⠛⠻⢟⠀⠸⠛⠀⢤⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣧⠀⢸⡗
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣄⣈⣅⡯⢀⡼⡡⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣾⣯⣬⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡡⠄
⢀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠑⣽⣷⣾⡕⣀⣠⠴⠖⠛⠉⠉⠁⠉⠉⠛⠛⠛⠛⠿⣿⣿⠿⠿⣇⡀
⠈⠀⠀⠀⢀⠈⠁⠀⠀⢀⣤⡿⠿⣿⢛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⣴⣦⣀⠀⢠⣴⠛⠛⠒⠂⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣀⣹⣷⣾⣥⡀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠶⠆⠿⠟⠁⠉⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠿⠿⠿⠶⢦⠀⢨⣡⡄⠀⠀⠀⠀⠳⠄⠀⡉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠨⠉⠀⠀⢀⣾⡿⠛⠁⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢸⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣿⣧⣴⡷⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⠀⠀⠰⣷⣤⣿⣧⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠋⠀⠀⠀⠀⠀⣠⣿⠟⠁⠙⢿⣧⡀⠀⠀⠀⠀⠈⠻⢿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣆⠀⠀⠀⢸⣿⡀⣿⣧⡀⠀⠀⠀⣼⣿⠀⠀⠀⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠈⢿⣧⠀⠀⠀⢻⣷⣌⠛⠁⠀⢀⣴⣿⠃⠀⠀⢰⣿⠏⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⢸⣿⡇⠀⠀⠀⠙⠻⠿⣿⠿⠿⠋⠁⠀⠀⠀⣿⣏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠋⠉⠛⠛⠿⠿⠿⠛⠛⠉⠛⠛⠿⠿⠿⠟⠛⠋⠙⠛⠻⠿⠿⠟⠛⠋⠉⠛⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⢀⣀⣤⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠋⠉⠙⠛⠿⠿⠿⠛⠛⠉⠙⠛⠿⠿⠿⠟⠛⠉⠙⠛⠻⠿⠿⠛⠛⠉⠉⠛⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⢿⣧⠀⠀⠀⣰⣿⠋⢻⣷⡀⠀⠀⢠⣿⠏⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⢀⣸⣿⠀⠀⠀⣿⣧⡀⣠⣿⡇⠀⠀⢸⣿⡀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠈⠻⠿⠟⠋⠀⠀⠀⠀⠙⠿⠿⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⢀⣀⠀⠀⠀⢀⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢫⠀⣼⠇⡏⢺⣄⡀⡠⢰⡿⢰⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠈⡇⣿⢠⣇⢀⢉⠛⡦⢸⣇⠜⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠙⠷⠇⠙⠃⠈⠁⠈⠉⠁⠈⢡⠤⠞
⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠰⢦⡰⠂⠀⠀⠀⠀⠂⠄⠀⣀⢀⡀⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢌⣾⣾⠁⣰⣾⣤⠄⠀⠀⠉⠁⠀⠠⣧⣦⡀⠀⠀⠀⢘⣷⣿⣾⣷⢃⣦⡞⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢽⣿⢷⡀⣹⣿⣿⠒⠀⠀⢀⣀⠀⡹⣿⣿⡗⠀⠀⢀⣤⣿⣿⣿⡷⣹⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠁⠋⢻⠈⠀⠀⢠⠈⣿⠃⠀⢸⡇⠁⢀⠀⠉⠁⡴⢻⡏⠀⠘⡏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⣶⣄⡆⣼⣠⣦⠾⣿⠿⠿⠧⠿⠾⠷⠟⣾⣷⣦⣄⢸⢸⡇⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣳⣿⣿⡟⠛⠲⣯⠄⠒⠀⢻⠃⠀⠀⠀⠸⠀⠀⠶⠀⠤⠉⠻⠿⣿⣿⣾⣇⣤⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠟⠋⠙⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⢽⡿⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⣦⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⡀⠀⢀⠀⢠⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠂⢠⠀⠴⠤⣄⡀⢤⣢⣀⡰⢄⠸⣰⣤⣎⣴⣾⣼⡤⠂⣸⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠉⠙⠓⠛⠟⠋⡿⠿⠻⠋⠛⠃⠈⠙⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⡀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⡂⠨⠀⠠⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢃⡇
⠀⠀⠄⠁⡠⢘⠆⠄⠀⠀⠀⠀⠀⠀⢀⠈⠰⣎⠐⡀⠀⠀⠀⠀⠀⠁⢄⠰⡲⠄⠈⠄⠀⠀⠠⡁⠁⣁⠀⠀⠄
⠀⠀⠀⢁⠁⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠡⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠠⣠⡀⢢⠴⠡⠔⠣
⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢀⡀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⣀⣶⣦⣿⡿⣿⣴⣦⠀⠀⠀⠀⢸⣿⣾⣿⣿⣻⡇⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣧⡄⠀⠀⠀⢰⣄⣧⣴⢀⠄
⠀⠀⢹⣿⣿⣟⢻⣿⣿⣾⡟⠀⠀⠰⣿⣯⡿⢿⣟⣿⣿⠆⠀⠀⢾⣿⣿⡿⣛⣿⣿⣿⣷⠀⠀⣄⣦⣿⣿⣿⢿⡼⢀
⠀⠀⢀⣿⣽⣿⣿⣿⡿⠟⠉⠀⠀⠘⣿⣿⣭⣮⣿⣿⣿⠄⠀⠀⠘⢿⣿⢿⣽⣿⣿⡟⠁⠀⠀⠚⠿⣞⢿⢟⣿⣷⣋
⠀⠀⠈⠁⠋⠻⠟⠿⠇⠀⠀⠀⠀⠀⠉⠉⠹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠻⠟⠙⠁⠉⠁⠀⠀⠀⠀⠈⠉⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠲⣄⠀⠀⢸⠀⠀⠘⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⡄⢹⠀⠀⢸⠀⠤⠀⠈⢠⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⢸⠀⠀⢸⠃⠀⠀⠀⢰⣠⠠⢻⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢸⠀⢴⠷⠄⠀⠀⠀⠸⠁⢀⡜⢀⡞⠉⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⢈⠀⠈⠧⠀⠀⠀⠀⢠⠒⠁⠀⢸⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⢰⢶⡄⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠠⠀⠂⢸⠀⠀⠜⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢈⡀⠀⢠⠀⠀⢘⠀⢨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢀⠀⠈⢧⣀⣳⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⢀⠉⠁⠀⠀⠈⠀⠸⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢰⠀⢰⠀⠀⢀⠎⠀⠀⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⠀⢸⠀⢸⣤⠴⠚⠁⢀⠊⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⠀⠸⠀⠀⠀⠀⠠⠀⠁⠀⠠⢢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠠⠀⠐⠀⠀⠀⢀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠸⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⡁⠦⡃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⣿⡿⣛⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣦⣴⣶⣶⣦⣤⣤⣦⣶⣶⣦⣶⣦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢟⣩⣥⣭⣙⢿⣿⣿⣿⣿⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣭⢅⣾⣿⣿⣿⣿⡆⢩⣭⣭⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⡜⣿⣿⣿⣿⣿⡟⠸⠿⠿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣷⣜⠿⠿⠿⢟⣵⣶⣶⣶⡇⠀⠸⠿⢛⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣷⣦⣝⡻⠿⠿⠿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⡀
⠀⠀⠀⠤⢀⠤⠀⠀⠀⠀⠀⠀⠠⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠃⠖⠂⡐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⡁⠀⠡⠏⠉⠙⠀⣀
⠀⠀⢠⠀⠀⠄⠨⠁⡀⠀⠀⠐⠄⠁⠠⠀⠁⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠠⡄⠀⠸⠂⠉
⠀⠀⠀⢈⠀⠂⠀⠄⢁⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣤⠀⠀⠀⠀⠀⠀⣦⠀⠗
⠀⠀⠀⠀⠀⠅⠐⠈⠈⢆⠐⠆⠄⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣋⠙⠛⡙⢂⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐⠂⠀⢀⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠉⠰⠂⠤⠀⡁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠁⠀⠉⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠀⠀⡠⠄⠀⢠⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠠⠈⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢘⠀⠀⠐⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠀⠂⠐⠀⠀⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⡈⠐⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⠀⠀⠀⣦⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀⠀⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠐⠂⠅⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⢠⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠁⠐⠲⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠱⠀⠀⠀⠀⣃⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠂⠠⠀⠀⡁⠀⠞⠋⠙⠓
⠀⠀⠀⠀⠀⠄⠘⡀⠏⠇⠀⣀⠢⠃⡐⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⢀⡀⢵⡀⢠⢀⠁⠀⠈⢄⠰⠊⣸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠈⠀⢠⠀⠀⠁⠀⡂⠁⡄
⠀⠀⠀⠀⠀⠀⠻⠂⢈⠀⠀⠁⠀⡀⡸⣤⠞⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠈⠈⠀⠐⠇⠀⠀⠀⡁⢀⡅
⠀⠀⠀⠀⠀⠀⠒⠃⠲⠶⠆⠀⠰⠂⠰⠓⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢸⠀⠀⡦⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠈⠈⠀⠀⠁⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠐⠀⠀⠀⠀⠈⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⠂⠁⠂⠂⠐⠘⠐⠊⠁⠃
⠀⠀⠀⠀⠀⠀⡅⡀⠁⠈⠈⠀⠈⢈⠈⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⡀⢠⢀⢀⢀⠀⠄⡀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⣀⣠⠄

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣨⣭⡶⡦⢤⣤⡴⠶⠛⠉⢉⣁⣭⣭⡽⠶⠦⣤⣤⠴⠶⠛⠉⢉⣠⣤⣬⡭⠷⠦⠤⣤⣤⠴⠞⠛⠉⣁⣠⣤⣭⡭⠶⠦⠤⠤⠴⠞⠛⠉
⠀⠀⠀⠀⢀⣠⣤⣴⠦⠴⠶⠶⠶⠿⠛⠋⠁⢀⣠⣤⡴⠶⠶⠶⠶⠶⠿⠛⠋⠁⢀⣠⣤⡶⠶⠶⠶⠤⠶⠾⠟⠛⠉⠀⣀⣤⣤⡶⠶⠶⠶⠶⠾⠛
⠀⠀⠀⠀⢉⣉⣠⡤⠴⠖⠒⠒⠶⢤⣔⣒⠛⠛⢉⣁⣤⠶⠒⠒⠒⠶⢤⣐⣚⠛⠛⢉⣁⣤⠴⠒⠛⠓⠲⠦⣤⣒⠚⠛⠋⣉⣠⡤⠖⠒⠛⠒⠶⠄
⠀⠀⠀⠀⢉⣉⣀⠒⠛⠛⠻⢶⣦⣤⣈⣉⣙⣋⣉⡁⠘⠛⠛⠿⢶⣦⣤⣈⣉⣉⣉⣉⣁⡀⠉⠛⠻⠷⣶⣤⣀⣉⣙⣛⣉⣉⣀⠈⠙⠛⠿⢶⣦⣄
⠀⠀⠀⠀⣈⡉⠛⠻⠷⣦⣤⣤⣄⣉⣩⣭⣍⣉⡉⠛⠻⠷⣶⣤⣤⣄⣈⣭⣭⣭⣍⡉⠙⠻⠷⣶⣤⣤⣤⣈⣉⣭⣭⣭⣉⡉⠛⠻⠷⢶⣤⣤⣀⡀
⠀⠀⠀⠀⣈⠙⠓⠶⠤⠤⠴⠞⠫⢥⣤⣤⣄⣉⠙⠓⠶⠦⠤⠶⠒⠩⠥⢶⣤⣤⣈⡉⠛⠶⠦⠤⠤⠶⠚⠭⠤⣦⣤⣄⣉⠙⠛⠶⠶⠶⠖⠚⠩⠤
⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⢶⣦⣤⣀⡀⠉⠛⠛⠓⠲⠒⠒⠲⠶⣶⣤⣄⡀⠉⠙⠛⠳⠶⠶⠒⠒⠶⢶⣦⣤⣀⡀⠉⠙⠛⠛⠒⠒⠒⠲⠶⣶⣤
⠀⠀⠀⠀⠴⠒⠚⠛⠛⠲⢦⣤⣀⣉⣙⣛⣻⠽⠒⠛⣛⣛⠓⠶⣤⣀⣈⠉⢛⣛⡯⠕⠒⠛⣛⡛⠲⢦⣤⣀⣉⣉⣉⡩⠽⠒⢛⣛⣛⠳⠶⣤⣀⡁
⠀⠀⠀⠀⣴⠾⠛⠋⠉⣉⣀⣀⣍⣉⣉⣡⣤⣴⠾⠛⠋⠉⣉⣁⣠⣬⣍⣉⣉⣤⣤⡶⠟⠛⠉⢉⣉⣀⣤⣬⣉⣩⣤⣤⡶⠿⠛⠉⠉⣉⣁⣠⣬⡁
⠀⠀⠀⠀⢀⣤⣴⡶⠿⠛⠉⢉⣀⣤⣤⣤⣤⣀⣤⣴⠶⠿⠛⠉⢁⣀⣤⣤⠤⣤⣤⣠⣤⣴⠾⠟⠛⠉⢁⣠⣤⣤⢤⣤⣤⡤⠶⠾⠿⠛⠉⣁⣠⡤
⠀⠀⠀⠀⠠⠄⠒⠶⠶⠶⠞⠛⣉⣤⣴⠶⠶⠬⠍⠓⠲⠶⠶⠞⠛⣉⣤⣴⠶⠶⠆⠤⠐⠲⠶⠶⠶⠛⢋⣡⣤⡶⠶⠶⠬⠉⠓⠲⠶⠶⠛⢋⣩⣤
⠀⠀⠀⠀⠶⠶⠖⠒⠒⠒⠚⠛⠋⠁⣀⣠⣴⡶⠶⠚⠒⠓⠚⠛⠛⠋⠁⣀⣠⣴⡶⠾⠛⠛⠛⠒⠒⠛⠛⠉⢀⣀⣤⣶⡶⠟⠛⠛⠛⠛⠛⠛⠉⡁
⠀⠀⠀⠀⣠⣤⠶⠖⠛⢛⣉⣙⠛⠻⢉⣉⣁⣀⣤⡴⠾⠛⣋⣉⡙⠛⠫⢉⣉⣁⣀⣤⡴⠞⠛⣉⣉⣉⡛⠛⠋⣉⣉⣀⣠⣤⠶⠟⢛⣉⣉⣙⠚⠉
⠀⠀⠀⠀⠠⢤⣶⣊⣉⣉⡉⠉⠛⠷⢶⣤⣍⣩⣤⣴⣄⣉⣉⠉⠙⠛⠷⢶⣤⣭⣭⣤⣴⣬⣭⣁⡈⠉⠙⠻⠶⣤⣬⣉⣥⣤⣴⣬⣅⣀⡉⠉⠛⠗
⠀⠀⠀⠀⢤⣤⣀⡀⠉⠙⠻⠷⢶⣤⡤⠤⢤⣤⣤⣀⡈⠉⠛⠻⠷⠶⠦⠤⠴⠶⢶⣤⣄⣀⠉⠙⠛⠿⠶⡶⠤⠤⠴⠶⣦⣤⣀⣈⠉⠙⠛⠷⠶⠦
⠀⠀⠀⠀⢤⣤⣉⠛⠻⠶⠖⢂⠠⠴⠶⠶⠶⣤⣌⣉⠛⠛⠶⠒⡂⡄⠴⠖⠲⠶⢦⣤⣉⡙⠛⠶⠶⢒⣀⠤⠶⠒⠶⠶⣤⣌⣉⡛⠛⠛⢚⣂⠤⠆
⠀⠀⠀⠀⣀⣈⠉⡛⢛⡛⠛⠛⠛⠿⠶⣦⣤⣀⣈⣉⣛⣛⣛⡉⠙⠛⠛⠿⣶⣦⣄⣀⡉⠛⣛⣛⣋⠉⠙⠛⠻⠷⣶⣤⣄⣈⣉⣙⣛⣉⡉⠙⠛⠓
⠀⠀⠀⠀⠉⣉⣉⣉⣉⡙⠛⠷⢶⣤⣄⣀⠈⠉⣉⣉⣉⣉⣉⠛⠻⢶⣦⣤⣀⣈⠉⡙⠛⠋⠉⠉⠙⠛⠳⠶⣦⣤⣠⠌⢉⣉⣭⣭⣉⣙⠛⠿⢶⣦
⠀⠀⠀⠀⠛⠉⣉⣠⣬⣭⡕⡲⠦⢤⡤⠴⠖⠛⠉⣁⣠⣤⣬⠽⠶⠦⢤⣤⡤⠶⠞⠋⠀⣀⣤⣤⣤⠴⡶⠦⠤⠤⠶⠞⠛⢉⣠⣤⣤⣭⣿⡶⠦⡤
⠀⠀⠀⠀⠶⠿⠛⠉⠁⣀⣤⣤⡶⠶⠶⠶⠶⠶⠟⠛⠉⠁⣀⣠⣴⡶⠶⠶⠶⠴⠶⠾⠓⠃⠀⢀⣀⣤⣶⠶⠶⠶⠶⠶⠞⠛⠛⠉⢀⣀⣤⣶⠶⠖
⠀⠀⠀⠀⠰⢤⣞⡛⠛⠛⣉⣠⣤⠶⠞⠛⠒⠶⢤⣚⣛⠛⠋⣉⣠⣤⠶⠚⠛⠛⡲⢦⣔⣛⠛⠛⢋⣁⣠⡴⠖⠛⠛⠓⠶⢤⣝⣛⣛⣉⣁⣤⡴⠖
⠀⠀⠀⠀⠙⠓⣈⣉⣙⣋⣉⣁⣠⣴⡶⠿⠛⠛⠁⣈⣉⣉⣉⣉⣁⣤⣴⡶⠿⠛⠉⠉⣀⣉⣉⣙⣋⣉⣀⣤⣶⠾⠟⠛⠉⢀⣀⣉⣉⣉⣉⣀⣤⡦
⠀⠀⠀⠀⠾⠟⠛⢉⣉⣉⣭⣍⣉⡠⢤⣤⣴⡾⠟⠛⢉⣉⣩⣭⣍⣉⡠⢤⣤⣴⠾⠟⠋⢉⣉⣤⣭⣭⣉⣁⠤⣤⣤⣶⠾⠛⠋⢉⣁⣤⣭⣅⣀⡀
⠀⠀⠀⠀⠴⠖⠛⠫⠭⢤⣤⣤⣈⡉⠓⠶⠤⠤⠶⠚⠫⠥⢤⣤⣤⣉⠙⠓⠲⠤⠤⠶⠚⠫⠥⠴⣦⣤⣄⡉⠛⠲⠤⠤⠴⠶⠛⠭⠥⢤⣤⣤⣈⡉
⠀⠀⠀⠀⠰⠶⠶⣶⣤⣄⡀⠈⠙⠛⠷⠖⠶⠶⠶⠶⣦⣤⣀⡀⠉⠙⠛⠓⠒⠒⠒⠒⠶⢶⣤⣄⣀⠈⠙⠛⠻⠶⠒⠒⠒⠲⠶⣦⣤⣄⣀⠉⠙⠛
⠀⠀⠀⠀⠲⠶⣤⣀⣈⣙⣛⣻⠷⠞⠛⠛⠛⠲⠶⣤⣀⣉⣉⣛⣻⠷⠛⠛⠋⠛⠛⠶⣤⣄⣈⣉⣛⣛⣻⠶⠛⠛⠛⠛⠳⠶⣤⣄⣈⣉⣉⣩⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠖⠂
⠀⠀⠀⠀⡀⣀⡀⠀⠖⢋⠐
⠀⠀⢠⠠⠀⠠⣁⡬⠴⣅⡀
⠀⠀⠚⠀⢀⠞⠹⠀⠓⢄⠈⠳⡄⠀⡀
⠀⠀⠀⢀⠁⠀⠂⠀⢢⠀⢂⡀⣀⠀⠉⠁
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠑⠸⠀⠢⠀⠀⠀⠀⢀⡀⠈⠻⠟⠃
⠀⠀⠀⢙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢐⣳⠺⠿⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⡒⠀⠔⢀⠀⠈⢂⠙⣍⠓⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠸⠗⠁⠀⠁⠀⠀⠀⠠⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠶⠄
⠐⠳⡰⠀⠀⠀⠀⠀⠀⣀
⡄⢰⣈⠆⠀⠀⡀⢈⡄⠽⠀⠄⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠁⠍⠳⡈⠂⡀⠀⢀⠀⠄⠀⠀⠀⠡⠉⠃⠘
⠀⠀⠀⡑⢙⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀
⢰⡖⡈⠁⠙⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠀⠠

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

⣿⣄⣤⡾⣿⣿⣿⡿⠷⢤⡀⠀⠀⢈⣷⠀⠀⡞⢀⣦⡀⡏⡀⡇⠀⣿⣼⠀⢾⣷⡇⠀⠀⣿⣿⠇⠀⠀⠀⣼⠃⠀⠀⠀⢸⣷⡆⣇⡀⠠⢸
⣿⣯⠟⠀⡔⠰⠀⠀⠀⠠⠙⣦⠀⢠⣿⣸⣴⣴⣿⣿⣣⣿⠿⠻⢾⣿⣿⣉⣾⠿⠛⠒⠚⠿⢧⣖⢀⣀⡸⣿⠀⠀⠀⠀⢸⣿⣿⣟⣛⣶⣿
⣿⣿⣾⡀⣶⣶⣠⣴⣆⣄⢱⣾⣷⡿⠋⠉⠉⠉⢻⣿⣯⠴⢤⣀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣯⣹⣿⣿⣤⠴⢦⣤⣼⣿⠛⣿⣿⠋⢸
⣿⣿⠛⠛⣿⠋⠉⠉⠉⠛⢿⣿⣿⢠⠀⠀⠀⠀⣷⣿⣧⣠⠖⠋⠉⠉⠲⣆⡀⠀⠀⣀⣤⣤⣤⣀⢾⣿⡿⠋⠀⠀⠀⠈⣿⡇⠀⢸⣿⣀⣸
⣿⡇⠀⢺⢹⡄⠀⠀⠀⠀⠀⠹⣷⣾⠀⠀⠀⠀⡏⣿⢸⡟⠀⠀⠀⠀⠀⢸⡷⠶⢴⣿⠃⠀⢸⣿⣿⠏⠀⠀⣠⣤⣶⣤⣿⣧⠶⠛⠉⠙⣿
⣿⡇⠀⠸⣆⣿⡄⠀⠀⠀⠀⠀⢘⣿⣴⣰⠀⣤⣇⣿⣿⣷⣤⣠⣠⣤⣶⣾⣿⣷⣄⣿⠀⠀⢰⣿⡏⠀⢠⡾⠋⠁⠀⠈⢻⣧⣀⡀⠠⣰⣿
⣿⡇⢶⡛⠛⠛⠛⠓⠶⠶⢤⣶⡿⡿⠿⢿⣿⣿⣿⡟⠉⠉⠉⡙⠿⣿⢘⣿⢻⢹⣿⢹⣿⣦⣼⣿⣇⣠⣾⠃⠀⠀⠀⠀⡀⣿⡉⠙⠛⠿⣿
⣿⣷⣠⣽⣦⡀⠀⠀⠀⡄⣾⠃⠀⠀⠀⠀⢻⣻⡿⠡⠄⢠⢠⢠⢀⡇⢸⢸⢸⢸⣿⡇⣷⣿⣿⡿⠋⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⣀⣄⣠⣿
⣿⠟⠀⠀⠈⠳⣄⣧⢲⣿⠇⠀⠀⠀⠀⠂⢀⢿⣧⠀⠀⢸⠸⡜⣾⡇⣿⢸⢸⢸⣿⡇⣿⣿⣿⣧⢀⣀⣿⠀⠀⠀⠀⠁⠀⢸⡇⠀⠉⣽⣿
⣿⣆⣀⣀⣤⠴⠿⠛⠻⣿⠀⢰⢸⠀⠀⠀⠄⣾⣿⡌⢸⠘⡆⣇⣿⣷⣿⢸⢸⢸⣿⣇⠏⠈⣿⣿⣿⣿⡿⣶⣄⠀⠀⡄⠀⢸⡇⢀⣼⠟⢸
⣿⡟⠋⠁⠀⠀⠀⠀⠠⣿⠀⠘⠸⠀⠀⠀⠀⣿⣿⣷⠸⡆⣿⢻⠋⠻⣼⢸⢸⢸⣿⣿⠀⠂⣿⡟⠁⠀⠀⠀⠙⣷⡆⡇⠀⢸⣷⠟⢁⣤⣿
⣿⣿⣤⡖⠂⣀⣄⣠⣼⣯⠀⡄⠀⠀⠀⠀⡇⣿⣿⣿⣧⣿⣇⣸⡀⠀⢻⣸⢸⢸⣿⢻⣇⢸⣿⡇⠀⠀⠀⠀⠀⠈⣿⣇⡆⣿⣥⠶⠛⣉⣿
⣿⡿⠞⣿⠉⠘⣧⠀⣾⣷⠆⡇⡄⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣏⣇⠀⢸⣿⣿⣿⣿⢸⣮⣿⣿⣿⣶⣦⣤⣤⣀⡀⠘⣿⣿⣿⣥⣶⣿⣛⣿
⣿⡿⢦⣜⣷⣄⣽⡾⢿⣿⠀⡇⡇⠀⠀⡇⡇⣿⣿⣿⣿⡏⣉⢻⡾⣿⢾⣿⡇⡇⣿⢸⣿⠟⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⡿⠛⠙⠛⠻⣿⣿
⣿⣿⡷⢮⣍⣻⡇⠡⠀⣿⡆⡇⡇⠀⠀⡇⡇⣿⣿⣿⠟⠓⡹⠛⢦⣸⡏⣿⡇⡇⣿⣼⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠹⣧⠀⠀⠀⠀⠈⣿
⣿⡷⠟⠒⠀⠙⣿⠄⠀⢸⡇⡇⣇⠀⢀⡇⡇⣿⣿⣿⠦⢴⡇⠀⢸⣿⣧⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⢸
⣿⣇⣠⣴⣷⣼⣽⣿⣦⣿⣇⠁⢋⠀⠸⡇⡇⣿⣿⣇⠀⠀⢝⣦⣼⠁⢀⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠠⢸
⣿⣿⠿⠋⠀⠛⠁⠀⠙⢿⣿⣸⢸⢸⠀⡇⡇⣿⣿⣿⣿⣿⠋⠁⠈⢹⣿⣟⣫⡿⠟⠛⠛⠛⠻⢷⣤⡀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣾
⣿⡁⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣾⣾⣧⣿⡿⠿⠿⠿⢿⣇⡀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⡇⠀⠀⠀⢰⡟⠀⠀⠀⢀⣾⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⢿⣷⠿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⢀⣾⠃⠀⠀⢀⡾⠋⣻
⣿⠟⢦⡀⠀⠀⠀⠀⣴⡞⠛⢻⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣛⢻⠀⡀⣄⣤⢀⡇⠀⠀⠀⠀⠀⣽⡈⣿⡀⣼⠃⣀⢠⣴⢿⡿⢿⣿
⣿⠀⠈⣿⡇⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣿⣆⣦⡏⠟⡾⣴⣠⠄⠀⠠⢀⣻⣟⢾⣿⣹⣶⣻⣏⢹⣿⣦⡈⣹
⣿⠀⠀⣿⡇⠠⠀⣸⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢻⣽⣽⣮⠷⠾⣿⣙⠉⡰⢲⡟⠺⡿⣿⣿⣿⣿⣿⡿⢸⣨⣿⡿⢷⢻
⣿⠀⠀⣿⡧⢀⡼⠋⠉⠀⠉⠍⢻⣧⡆⠀⠀⠀⠀⠀⠀⢀⢠⢸⣿⡟⠁⠀⠈⢷⡀⠈⠻⣖⣿⠺⢷⡈⢧⠙⠿⡜⢿⡼⠥⣾⣛⣋⣴⠟⣻
⣿⣤⡴⠛⠛⠛⠛⢦⣀⠀⣠⠴⠾⣿⣧⠄⠀⠀⠀⠀⢀⢠⢸⣸⡇⠁⠀⠀⠀⠈⣧⢀⠄⣿⡟⢷⣤⣬⢾⠟⠋⠀⡟⠀⠀⠈⣧⠈⠙⠿⣽
⣿⡏⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠈⠻⣷⣴⣴⢀⣦⣸⣼⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⡗⣿⣿⣻⠏⢰⡏⠀⠀⢸⡧⠀⠀⠀⢸⡆⠀⡠⢹

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣾⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⣿⣆⠀⠀⠀⠀⠀⣸⣷⣾⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⢹⣿⡧⣷⣿⠀⠀⠀⠀⢀⡟⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣏⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⡟⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⢸⡿⣿⢿⡇⣿⣿⠀⠀⠀⠀⣾⣿⡿⣿⢼⣿⣇⣿
⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣸⣷⡿⣿⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⢸⣿⡿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣿⢻⣇⣿⠀⠀⠀⠀⣿⣿⣿⣧⣿⣼⣏⣿⠀⠀⠀⠀⢸⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⣿⣽⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣾⣧⣿⡆⠀⠀⢀⡿⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⢹⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠸⣿⢹⡟⣧⣿⣹⣧⠀⠀⢸⡇⡿⣿⣽⣿⢻⣿⣿⡄⠀⠀⠀⣿⣼⣿⡏⣟⣇
⠀⠀⠀⠀⠀⢸⣿⢻⡇⣿⢻⣿⣿⣼⡇⠀⠀⠀⠀⠀⢿⣟⣷⢿⣽⣟⣿⣄⠀⣼⡇⣷⣿⣿⣿⣼⣿⣿⡇⠀⠀⢀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⢻⡇⠀⠀⠀⠀⠀⠈⢿⡿⣞⢷⣻⣞⢿⣦⣿⡧⣿⢹⡿⣿⣿⣿⣿⡇⠀⠀⢸⡏⣿⣿⣧⣟⡟
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣼⣇⠀⠀⠀⠀⠀⠀⠈⢿⡽⣯⢷⣽⣻⠾⣿⣇⣿⣾⣿⣿⣿⡟⣿⡇⠀⠀⣼⣧⣿⣿⢻⡿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡳⣯⣛⣿⣿⣷⣿⣿⣿⣿⣿⡇⣿⡇⠀⢀⣿⣿⣧⣿⣾⢿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣯⣽⣿⣿⣿⣿⣟⣿⣿⡇⣿⠀⠀⣼⢿⡿⣽⣇⣿⣼⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣼⣇⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⣿⣠⣾⢯⣾⣳⣿⣽⣏⡿
⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣧⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⡿⣿⣿⣏⣴⣟⣵⡿⣵⣿⣳⡿⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣻⣷⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣟⣿⣡⣿⣯⡾⣫⣾⡿⣷⡿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣸⡿⢻⣯⣿⣫⣾⣿⢿⣾⣿⣽⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣇⡘⣿⣽⣿⢟⣵⡿⣫⣾⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⣿⣿⣇⠙⢯⣷⣻⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡟⣿⢸⡧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⣿⢹⣧⣿⣭⣯⠉
⠀⠀⠀⠀⠀⠀⣿⣧⣿⢸⡇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣼⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢻⡧⣿⣸⡇⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⡿⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠸⠇⠿⠻⠛⠇⠿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠻⠸⠗⠿⠻⠇

⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿