Untrustworthy Emojis & Symbols

⠀⠀⢠⠖⣩⣭⠉⠒⣄⠀⠀⠀⢀⠔⠋⢩⠉⠑⢦⠀⠀⠀⠀⡰⠊⠩⣉⠙⠢⡀⠀⠀⠀⣠⠒⠉⣉⣉⣲⡄
⠀⠀⡇⠀⡙⣟⣰⡄⠘⡀⠀⠀⡞⠀⢰⣾⣶⠀⠀⡇⠀⠀⢸⠀⢸⣴⡋⠂⠀⢱⠀⠀⠠⠃⠀⠈⣭⠉⠉⢸
⠀⠀⢣⡿⠿⠿⠿⠿⡼⠀⠀⠀⠱⡀⠀⣿⡟⠀⣠⠃⠀⠀⠘⣄⠛⠋⢼⡩⢂⠎⠀⠀⠀⢧⡶⠷⠶⠂⢀⡜
⠀⠀⠀⠙⠒⠀⠒⠊⠀⠀⠀⠀⠀⠈⠒⠂⠐⠚⠁⠀⠀⠀⠀⠈⠓⠂⠐⠒⠁⠀⠀⠀⠀⠀⠑⠒⠄⠒⠋

⠀⠀⢀⠔⠚⠉⠑⠢⡀⠀⠀⠀⠀⡤⢒⣉⣙⠲⢄⠀⠀⠀⠀⣠⠖⢋⣉⣒⢤⠀⠀⠀⠀⢀⠔⠊⠉⠓⠢⡀
⠀⠀⡎⢠⣠⠬⣤⣤⠸⡀⠀⠀⡜⠀⣿⣿⣿⡆⠈⡆⠀⠀⢰⠁⠀⠻⡿⠿⠁⢣⠀⠀⠀⠇⣠⣤⢰⢖⢦⢹
⠀⠀⢇⢸⣿⣷⣿⣿⣰⠀⠀⠀⢳⡀⠘⣿⡿⠇⢀⠇⠀⠀⠸⡄⣶⣷⣶⣶⢀⡞⠀⠀⠀⣆⢧⡠⠋⠒⠊⡸
⠀⠀⠀⠑⠤⠤⠤⠚⠁⠀⠀⠀⠀⠙⠢⠭⠤⠔⠁⠀⠀⠀⠀⠈⠫⠭⠭⠝⠋⠀⠀⠀⠀⠈⠓⠤⠤⠤⠊⠁

⠀⠀⢀⡤⠒⠒⠒⢤⡀⠀⠀⠀⠀⡠⠔⠒⠒⠦⡀⠀⠀⠀⠀⢀⠔⠒⡒⠢⣄⠀⠀⠀⠀⢀⡤⠒⠒⠒⢤⡀
⠀⠀⡎⣠⣤⣤⣤⣤⠹⠀⠀⠀⡼⠁⣾⣿⣷⡇⠘⡆⠀⠀⢰⠃⠀⢿⣽⠀⠈⢧⠀⠀⠀⠏⣀⠀⡆⠀⠀⢱
⠀⠀⣇⠈⠻⠿⠛⠉⢰⠁⠀⠀⢣⠀⢿⣿⣿⡇⢀⠇⠀⠀⠸⡀⣴⣦⣵⣦⠀⡜⠀⠀⠀⡆⠉⢀⣧⡐⠒⣸
⠀⠀⠈⠢⢤⣀⡠⠔⠁⠀⠀⠀⠀⠓⠬⣉⣩⠵⠊⠀⠀⠀⠀⠑⠯⣍⣉⠭⠚⠀⠀⠀⠀⠈⠢⢌⣉⡥⠔⠁

⠀⠀⠀⣠⠤⠀⠤⢄⠀⠀⠀⠀⠀⢀⠤⠄⠠⢄⡀⠀⠀⠀⠀⢀⡤⠄⠢⠤⡀⠀⠀⠀⠀⠀⡠⠤⠀⠤⣄
⠀⠀⡜⢁⣶⡆⠀⠀⢱⠀⠀⠀⡰⠁⢸⣯⣿⡀⠙⡄⠀⠀⢠⠋⣘⣃⢀⣇⠈⢆⠀⠀⠀⡞⠐⠂⣤⠀⠈⢣
⠀⠀⡇⣈⣋⡀⠙⠒⢠⠃⠀⠀⢧⠀⠈⢻⠛⠀⠀⡇⠀⠀⢸⠀⣻⡏⣻⡿⠁⡸⠀⠀⠈⡄⠀⣤⣿⣄⠀⢸
⠀⠀⠘⠯⣉⣁⣀⡤⠋⠀⠀⠀⠈⠢⣄⣈⣀⡠⠞⠀⠀⠀⠀⠱⢌⣉⣋⣩⠔⠁⠀⠀⠀⠙⠤⣉⣉⣁⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⢀⣤⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠶⣈⢉⡭⠤⠶⠶⠶⠶⠮⣭⣍⣓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⢡⠶⠋⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠛⠶⣍⡳⣤
⠀⠀⠀⠀⠀⠀⢀⣰⢋⡄⠈⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠻⣦⡻⣄
⠀⠀⠀⠀⠀⢠⡜⣱⠏⠀⢀⠀⠀⠀⢀⣠⠴⠒⠐⡀⠏⠓⠒⠦⣄⡀⠐⠿⠂⠀⢈⣻⣎⢳
⠀⠀⠀⠀⠀⡞⣼⠃⠀⠀⠻⠃⢀⡖⢣⠰⠐⡀⡄⠰⠐⡈⠀⠄⢀⣙⣦⣴⣶⡿⡿⢻⣿⣦⢻⡀
⠀⠀⠀⠀⡻⢰⠁⠀⠀⠀⠀⣰⢃⢁⠠⠀⠃⢡⠠⢐⣀⣥⣶⣾⣿⠟⢛⡉⣇⢳⡈⢸⣿⣿⡆⢧
⠀⠀⠀⢨⠇⡏⠀⢀⣀⠀⢰⢡⠨⠀⣂⣡⣴⣶⣾⣿⢿⢋⠻⡀⡄⢳⡈⣷⠀⡄⢿⡄⣿⣿⣿⢸⡄
⠀⠀⠀⢼⢸⡇⠀⠘⠛⢀⣧⣴⣶⣿⠿⠟⠋⣩⠑⠈⠈⡄⢇⢱⠠⡌⢷⣘⣧⣽⣾⣿⠿⠛⢻⡎⡇
⠀⠀⠀⢼⠸⣧⣤⣶⣾⠿⠛⡏⢣⠹⡐⠾⣧⠸⣧⠀⠀⢹⣌⣠⣧⣿⣾⠿⠟⡟⠁⣤⡄⠀⢸⢇⡗
⠀⠀⠀⠸⡆⣿⣿⣥⠐⣦⠑⠸⡌⣆⢛⠢⢘⣇⣹⣷⣾⡿⠿⢛⢋⠉⠄⢃⢱⠇⠀⠉⠁⠀⣾⢸⠃
⠀⠀⠀⠈⢳⠹⣿⣿⣇⢹⡆⢣⣱⣤⣼⣷⣿⠿⠛⠋⠁⠀⠘⠈⡀⠄⢀⢨⠎⠀⠀⠀⠀⢰⠇⣎⠁
⠀⠀⠀⠀⠈⣧⢻⣿⣿⣶⣿⠿⠟⢿⣫⠱⠐⠀⡀⠡⠰⠈⡀⡄⠀⢨⠼⠁⢠⣦⠀⠀⢠⠟⡼
⠀⠀⠀⠀⠀⠈⢧⡹⣏⠉⠀⠠⣴⠄⠈⠁⠡⠥⣥⣰⣀⣥⠥⠔⠊⠁⠀⠀⠀⠁⠀⣠⢎⡜⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣌⠡⣄⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢰⣶⠄⠀⠀⢀⣠⠞⣡⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢮⡛⠶⣤⣀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣀⣤⠶⣋⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢭⣛⡓⠶⠶⠶⠶⠶⠶⣚⣋⡭⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠙⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡤⠤⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠶⠶⣶⣤⣦⣄⣀⠈⠐⠲⠂⢻⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣠⡀⡀⢀⠠⠐⠊⠁⠒⠒⠒⢒⣒⣒⡦⠀⠀⠀⠀⣰⣛⣛⣛⣉⣀⣀⣀⣠⡆⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠋⠀⠀⠠⢴⣾⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠑⠺⢿⣿⣿⠿⠿⠿⢿⠁⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⣶⣶⣶⣤⣤⣥⣬⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠓⡿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣧⣀⡟⠛⠛⠉⠛⠿⠟⠉
⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⣾⣿⣦⠉⢻⣿⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠙⣿⡃⠀⠘⢿⣷⣦⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⢀⣼⣿⣿⡄⠀⠈⠻⣿⣟⠿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠿⢿⡬⢥⡿⣿⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⢸⡇⢸⡆⠀⠀⠀⠀⠛⣻⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠉⠁⠈⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠁
⠀⣠⢀⡀⣀⡀⣀⣠⣀⢀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣦⡀⠀⠀⠀⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠒⡱⡀⠀⠀⠉⠀⠠⠀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⣰⡷⣏⠃⠀⣤⢴⡷⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠈⠀⠀⠀⠡⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⢾⣷⣼⡇⠀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣿⣿⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⡥⠯⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⢲⠀⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠲⠥⠴⠮⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠃⠀⠀⠀⠀⣛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠻⡏⣻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⡿⣃⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡾⣿⣿⣿⢫⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠛⠑⣴⢾⣿⡟⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡎⣫⣿⣝⣿⣯⣻⢸⡇⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣼⣷⣿⣿⣿⣤⣧⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣻⡛⢿⣿⣿⠛⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⠀⠀⠐⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣩⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠛⠶⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣫⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣵⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠻⣿⣿⣿⣿⣿⡿⠀⠀⠤⣤⡀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣭⣿⣿⣯⣙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢿⣿⠛⠉⠿⠅⠀⠘⢿⣶⡍⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠁⠀⠈⠈⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⢶⣶⣶⢀⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡀⣀⠀⠀⢰⠤⣇⠀⠀⠀⠀⣴⣶⣶⣟⠀⠀⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⢿⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠖⡿⠀⠀⡞⠀⢻⡄⠀⠀⠀⠛⠋⣭⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡇⠀⢤⣤⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⣸⠇⠀⠀⠙⢶⣤⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣾⣿⣿⡿⢿⣿⣤⡐⢂⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⣿⠀⣀⣤⠶⣛⣉⣩⣿⣿⣧⡀
⠀⠀⠀⠀⣠⡾⠋⠉⠀⢰⣯⡴⢻⣇⠀⣈⡿⣏⣹⡷⣽⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⠿⠛⠋⠉⠉⠉⠀⠉⠙⠳⢦⣄
⠀⠀⠀⣼⠏⠀⠀⣀⡀⢰⡏⠀⠀⣿⡾⠛⣦⠿⣿⡇⠈⢳⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⢰⡏⠀⠀⢨⡿⣷⠀⢳⡀⡸⣸⣇⣸⠉⣇⣿⡰⡀⡼⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⢀⣾⠇⠀⢀⣼⢇⡟⢀⢪⢷⣱⣱⣿⡿⠀⢸⣿⣷⣽⠁⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢐⣺⣿⣆⢷⡄⠀⠀⠀⠀⠀⠀⡜⣄⣀⠀⠀⠀⠀⠀⣿⡇
⢀⣾⠁⠀⢀⣽⣿⡿⢡⣮⣿⣿⣷⣿⣿⠿⣻⣿⣿⡿⠃⢰⣿⢸⣷⡟⢻⣆⣀⠀⠀⠀⠀⣸⡟⠀⢐⣒⣾⣿⣿⢸⣿⠀⢀⢀⢀⢣⣣⣷⣿⣿⣶⣦⡄⣔⣾⣿⠃
⢸⡇⣴⣿⣿⡿⠿⠿⢿⣿⡿⠛⠉⠀⠀⠘⠛⢿⣿⣇⠀⣾⣷⣼⠿⢧⡀⠉⠉⢻⣆⢀⣠⣿⠁⢀⣒⣿⣿⣿⣿⢸⣿⣿⣾⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⡘⠉⠀⠀⣀⣀⢸⡿⡇⠀⠀⠀⠀⠀⣍⡒⠢⢿⣶⣿⠭⠤⠖⠘⠃⠀⠀⠀⢹⢟⣿⡏⠀⠠⠭⣽⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡇⣾⣀
⠸⣿⣿⣴⣼⣿⣿⣿⡜⣧⣿⣷⣶⣤⣤⣜⣒⣬⣽⡾⢿⣿⣖⣘⣃⠀⠀⠀⠀⢀⡏⣾⣿⠇⠀⣉⣛⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⠟⠛⣉⣩⡤
⠀⠈⠛⠶⣿⣿⣿⣿⣿⣿⡿⣟⠯⠁⠈⣿⡟⠉⠉⠀⢸⣿⡷⢶⣶⣶⣶⣶⠶⢾⣇⣿⣿⠀⢐⣲⣾⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⠁⣀⣷⣟⣩⠟
⠀⠀⠀⢰⣿⣿⣿⣿⣟⣿⠛⠂⠀⠀⠀⣿⠀⠀⠀⣾⠻⣿⣷⠘⣿⠀⠀⠀⠀⠈⠛⢻⣿⠀⠀⣲⣿⡿⢋⣼⣿⣿⠿⠿⠿⠿⣿⢿⡇⠀⠀⢀⣯⠥⣄⡉⣻⠄
⠀⠀⠀⣿⣿⣿⣿⢿⡓⠛⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⢴⣿⣯⠄⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠉⠁⠚⠉⡁⣆⢲⢰⢰⣸⡄⡽⣆⢻⠀⠀⠘⠦⢴⡄⢙⡇
⠀⠀⢸⣿⣿⣿⣯⣓⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣗⠀⣿⠀⠀⠀⠀⠀⠀⠸⣇⢿⣶⣦⣦⣦⣧⣿⣿⣾⣿⣿⣿⣷⡗⣿⣸⣦⣄⣀⣀⣤⣴⠟⠁
⠀⠀⣾⣿⣿⣟⡒⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⣓⣠⡿⠀⠀⠀⠀⠀⠀⠀⠹⣮⣛⣛⠛⠿⠿⠿⠿⠿⠿⢿⣛⣛⣥⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡏⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⢿⣿⣭⣅⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣀⡀⠀⣸⡇⣰⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠛⠛⠛⣿⣷⣿⣦⣏⣀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⣰⡿⢻⣿⣿⡏⠀⠀⠀⠀⢹⣷⣶⣯⣥⣭⣍⣻⣷⡆⠀⠀⢰⣿⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⡇⠀⠀⠀⢰⡿⠁⠀⢻⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⡟⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣠⣀⢀⣀⢀⣄⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣿⡇⠀⣿⠉⠉⠉⠉⠉⠉⣿⠶⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⢸⡏⣽⠍⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠹⢷⣦⡀⠙⣦⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⣸⣿⣦⠹⣿⡀⠸⡆⠛⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⢸⡇⣿⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣿⡇⠀⠿⠶⢦⣤⡀⠀⠋⣼⣿⠃⣿⠇⢀⡟⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⢸⡇⣿⢡⡴⠶⠶⠶⠶⠇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣿⣷⣤⣤⡛⠈⢿⣿⣦⡀⢋⣡⣾⠏⠀⣼⣅⣤⡀⠀⣀⢀⣿⠀⣿⠀⣿⠀⠀⢸⡇⣿⢸⠁⠀⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⠸⣧⣤⣤⣤⣀⣀⣀⣀⣖⣈⣻⡇⢸⣏⣑⣂⣀⣀⠀⣿⠀⡀⣿⠛⠋⠀⣿⠀⣿⠀⠒⢸⡇⣿⢸⠀⠸⡇⠀⣤
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠷⠿⢿⡍⣿⠀⣿⠀⣡⡿⣠⢸⠛⢃⣤⡍⠛⠛⢻⡇⣿⢸⠀⢰⡇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆⠁⠀⠀⠀⠀⠁⣿⠀⢻⡿⠋⢀⣴⣾⠀⠀⠉⠀⠀⠀⢸⡇⣿⢸⠀⢰⡇
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣿⢸⡇⠀⣾⠶⠷⠿⠿⢾⡆⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠛⠁⣰⡿⢋⣴⡆⠀⠀⠀⠀⠀⢸⡇⣿⢸⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣀⢸⡇⠀⣿⢸⡇⠀⣿⠀⠀⠀⠀⢸⡇⢨⣧⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⣿⡇⣿⣯⡹⠆⠀⢀⣀⠻⠄⡀⣿⢸⠀⢸⡇
⠀⠀⠀⠀⠀⢨⣌⣼⡇⠀⣿⢸⡇⣤⣿⣄⣀⣀⣀⣼⡇⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡹⣷⣌⠛⠇⣀⣴⣿⠟⠛⠻⡇⣿⢸⠀⠀⡇
⠀⠀⠀⠀⠀⢈⣀⣀⣀⣀⣿⢸⣇⣀⣈⣉⣉⣉⡉⢉⣀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠈⠁⣨⠛⢻⠀⣿⠛⠁⣠⡌⠩⡇⣿⢸⡇⠰⡇
⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣥⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡝⣿⠀⠈⠄⢸⠀⣿⠒⢸⣿⠇⢸⡇⣿⢸⡇⠐⡇
⠀⠀⠀⠀⠀⢸⠒⠒⠒⠚⠒⠓⣒⠒⣶⣶⣶⣶⣶⣶⠒⠶⡄⢩⣶⡄⠉⠀⠀⠀⠈⠉⣿⣄⠲⠂⢸⠀⣿⠀⢸⣿⠇⢸⡇⣿⢸⡇⠀⣧⡀
⠀⠀⠀⠀⠀⢸⠶⠶⣦⠀⢀⣀⣩⣾⠟⣡⣶⣶⣌⠻⣷⣤⡇⢸⣦⡇⠀⠀⠀⠀⠀⢠⣬⡛⣿⡄⢸⠀⣿⠀⣀⣀⣀⣘⡇⣿⢸⡇⠀⢸⡇⣠
⠀⠀⠀⠀⠀⢸⠸⠆⣿⠀⣻⠉⠉⠉⠘⠛⢯⡽⠛⠃⣉⣉⠘⠧⣹⣇⠀⠀⠀⠀⢠⡞⣻⣷⢸⣿⢸⠀⣿⠀⣿⠉⠉⠉⠁⠛⠈⣿⠀⢸⣧⣬⣤⡀
⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠋⡇⢸⡏⠉⠉⢻⣿⣄⠀⠸⠿⢋⣼⡟⢸⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢸⡿⢛⡁⠀⡇⢸⡟⠓⣦⡀⠙⢿⣿⠀⣾⠿⣋⠂⢸⠀⣿⠀⣿⠀⠀⠀⠀⠀⠿⢀⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢿⣤⡄⢠⣤⣤⣤⣼⡇⠈⠁⠀⡇⢸⣇⡸⣏⠹⡦⣄⣿⠀⣿⠀⠋⡀⢸⠀⣿⠀⢿⣤⣤⣤⣤⣤⣦⣾⠁⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣀⠀⢸⡇⢸⡇⠀⠀⠀⣀⠘⢃⣠⡇⢸⣯⡁⠉⠻⣇⠀⣿⠀⣿⠀⣀⠀⢸⠀⣿⠀⢀⣄⣠⣀⣀⣀⣀⣤⣄⣸⡿⢩⣝
⠀⠀⠀⠀⠀⢸⠁⠂⠉⣿⡇⢸⡇⢸⠆⠀⠀⠀⢉⣴⣿⠟⠃⣬⣙⢻⣷⡀⠉⠛⣻⠀⣿⠀⠛⠁⢸⠀⣿⠀⢸⡏⠉⠉⠉⠉⠉⠉⠭⢭⣥⣮
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇⢸⡇⢸⡇⠀⢸⠟⠛⠛⠃⠀⣤⠛⣿⡆⣿⡟⠛⠛⢋⣤⡝⠛⣷⠀⢸⠀⣿⠀⢸⡇⠺⠄⠀⠀⢀⡀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⢸⠀⢠⣅⣿⠇⢸⡇⢸⠇⠀⢸⠃⠀⠀⠀⠀⠈⣿⠿⢡⣿⡇⠀⠀⠀⠉⠀⠀⣿⠀⢸⠀⣿⠀⢸⣧⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⢸⠀⠀⡅⣿⡆⢸⡇⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⢠⣶⠿⢻⡇⠀⠀⠀⠀⠀⠀⣿⣀⣼⠀⢿⣄⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⡀⡈
⠀⠀⠀⠀⠀⢸⠀⡀⠀⣿⠁⢸⡇⢸⡀⠀⢸⣁⣀⣀⣀⣀⣀⣸⡇⣶⢸⡇⣷⣤⣤⣤⣴⣧⣬⣭⣥⣾⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⠀⠀⠀⠀⠀⢸⠶⢅⣵⠟⠰⢾⡇⢸⡁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠘⠛⣶⠀⣶⠒⠲⡖⠒⠒⠒⠒⠖⠒⣶⢸⡇⡶⢒⣶⡆⢰⣖⠒⠖⠶⠶
⠀⠀⠀⠀⠀⢸⠶⠞⠁⣠⣾⣿⠇⠘⠿⣷⣄⠈⢿⣿⣿⡿⠿⠿⠟⢀⣴⣿⠿⢀⡛⢿⣶⡉⠀⣦⡶⢶⣦⠀⣿⢸⡇⣿⡿⢛⣡⠘⠿⣿⣦⠸⠆
⠀⠀⠀⠀⠀⢸⣀⣿⣴⣿⠟⠀⢀⣿⣷⡜⣿⡆⠘⣷⣽⡇⢀⣿⢤⣾⡿⠃⠀⡸⣿⣦⠹⣿⡀⢸⡆⢰⣿⠀⣿⢸⡇⣿⢠⣿⡿⣄⠀⠙⠿⠷⢶
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣴⣿⠇⣿⡇⢀⣿⢿⡇⠀⣿⠀⠀⠀⠀⠘⢷⣾⡿⢠⣿⠃⢸⣇⠸⣿⠀⣿⢸⡇⣿⡘⢿⣷⡏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢛⣩⣾⡟⠁⣼⠇⣿⡇⠀⣿⠀⠀⠀⠀⠀⠘⣋⣴⣿⠏⢀⣾⢃⢌⣿⠀⣿⢸⡇⣿⢿⣦⡍
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⢛⡉⣠⡾⣋⡄⢿⡇⢰⣿⠀⠀⠀⠀⠀⠀⣿⣋⢀⣤⠟⣡⣜⡻⣿⠀⣿⢸⡇⣿⢠⡭⣗
⠀⠀⠀⠀⠀⠸⠿⠦⠴⠶⠶⠶⠶⠾⠉⠐⠿⠐⠙⠂⠿⠇⠘⠿⠶⠶⠶⠶⠶⠶⠟⠉⠸⠇⠒⠈⠘⠛⠿⠀⠿⠸⠇⠿⠀⠈⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣏⡄⠄⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠋⠻⣌⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠉⠛⠻⢿⡆⢤⡀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠃⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣀⣀
⠀⠀⠀⠀⠀⠠⠤⠤⢤⣤⣽⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣬⣧⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⣿⣿⣿⣿⠉⣿
⠀⠀⠀⣠⣶⠄⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⠋⣠⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠉⣁⣴⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠁⢴⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢸⣿⣿⠀⢉⣉⣉⡉⠀⣿
⣀⣠⣴⣾⣿⣿⣿⠟⢁⣄⠀⠀⠀⠀⠀⢀⣤⠀⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣿⣿⡅⢸⣿⣿⠀⣿⣿⣿⣿⠀⣿
⢻⣿⣿⣿⣿⣿⠃⠀⠿⣿⣷⣄⠀⢀⣴⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⣿⣿⠄⢸⣿⣿⠀⣿⣿⣿⣿⠀⣿
⠀⠙⠿⣿⣿⠁⠀⠀⠀⠘⠛⢁⣴⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠃⣤⣾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⣿⣿⣿⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠀⣤⣤⣤⣀⣈⣉⣉⣁⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⣿⣿⣿⣿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⡙⢋⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠃⠘⠻⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠘⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣦⠀⢶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠀⣤⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠙⢆⠀⠃⢠⡎⠀⠙⠀⠀⢸⠁⠀⠰⡇⠀⠈⢣⠘⡇⠀⠀⢸⠂⢸⠁⠀⠃⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⡃⠀⠉⠐⠦⡀⠀⢸⠀⠀⢀⡶⠂⢶⠃⢠⡇⠀⠀⢸⠀⠀⠉⠰⢄⠀⠀⣹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣠⣄⣐⣃⣀⣃⡐⣢⣤⣤⣃⣀⣸⣀⣀⣐⣂⣀⣀⣃⣀⣁⣤⣤⣊⣀⣐⣤⣤⣜⣁⣀⣛⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢲⣿⡿⣄⣀
⠀⠀⠀⠀⣠⠴⣿⣿⠒⢦⡀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⡀
⠀⠀⠀⠀⠋⢀⣿⢿⣤⡀⠀⠀⠀⠀⢾⣿⣿⠧⣄⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣀⡖⠀⠀⠀⣿⣈⣷⣄⡀
⠀⠀⠀⠀⢀⡿⠁⠀⠈⢻⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢠⣿⣧⠤⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠓⢒⣶⡌⠉⠉⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣼⠃⣷⠀⠀⠀⢾⣿⣇⠀⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣀⡀
⠀⠀⢰⣶⡉⠁⢀⣶⡆⠀⠀⢠⣶⡄⠀⠸⢿⡀⠀⠀⠀⣠⣤⠀⠀⣴⣦⠀⠀⠀⣰⣶⠀⠀⠀⣸⣼⣶⡆
⠀⠀⢸⣿⣿⠀⣿⣿⡧⠀⠀⢸⣿⣿⠆⢀⣸⣿⠀⠀⢠⣿⣿⡇⣾⣿⣿⡇⠀⠀⣿⣿⠳⢤⡀⠈⡹⣿⡋
⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠉⢸⡟⠀⠀⠸⣿⣿⠇⠘⣿⣿⠁⠀⠀⣿⣿⡧⠶⠚⡏⠁⠫
⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢠⡏⢹⡆⠀⣗⠛⣇
⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠈⠁⠈⠁⠈⠉⠉⠉⠁

⠀⠀⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣤⡄
⠀⠀⢀⣴⣿⣣⡄⠀⣀⣤⣤⣤⣤⣀⠀⠴⠛⢻⣿⡗⠒⢦⠀⣠⣽⣥⡀
⠀⢠⢞⣿⣿⠋⠀⠈⠁⠀⣿⣿⠀⠈⠁⠀⠀⢸⣿⣦⡄⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣿⢻⡀⠀⠀⠀⠀⢸⡇⠸⠃⠀⠀⠉⣿⣿⠁⠀⠀⢀⣤⣶⣶⣴⣿⣿⣿⠛⡄
⠀⠀⠘⠿⠿⠀⠀⠀⠀⠰⠏⠸⠇⠀⠀⠀⠀⠚⠡⠤⠤⠄⠀⠀⠿⠿⠀⠀⠀⠀⢠⡾⠿⠟⠛⠋⡿⠉⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠛⠛⠛⠛⠛⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣄⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣠⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣼⠟⠁⣠⣴⡾⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠁⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠛⢷⣤⣼⠏⢠⣾⣋⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⣿⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠿⠛⠉⠉⠉⠀⠀⠀⠉⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣿⣦⠈⠻⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠈⠙⣿⠟⠛⠛⠛⠻⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⣿⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⠾⠿⣦⡀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⢀⣤⣿⣷⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠀⠀⣀⣴⣿⡇⢸⣿⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⣠⣾⠟⠁⠙⠁⣾⡏⠀⠀⠀⠀⠀⠀⢿⣟⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢠⣼⠟⠁⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠿⠗⠀⠀⠀⣴⡏⢠⣴⠟⠁⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡀⢀⠀⠀⣿⣷⡿⠃⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠛⣻⣿⣿⠋⠀⠀⠀⠀⢀⣴⡿⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣅⢀⣴⠾⠿⠿⣿⣶⣤⣤⣴⣶⣏⣉⠴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣶⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣁⣀⣀⣴⡟⠁⠈⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⡿⠋⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣴⡟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⣼⡟⠁⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⣇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⡇⠀⠀⠀⠀⣾⡟
⣤⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣿⠀⠀⢀⣾⡟⠁
⠻⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣿⣤⡾⠟⠁
⠀⠈⠛⠿⢶⣶⣶⡶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡇⣿⡇⠀⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣼⡟⢀⣿⣇⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣦⣤⡀⠀⠀⠀⠀⣸⡿⠿⠿⠿⠿⠟⠋⠀⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⠉⠉⠙⠿⠆⠀⠀⢹⡇⠀⢀⣤⣤⠶⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠸⣷⡞⠛⣤⣴⢀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣇⠀⣠⡿⣡⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣧⡀⠀⠀⢀⣿⡿⠋⠶⠁⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣄⠘⢧⣄⣰⠿⠋⠀⠀⢀⣼⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢹⣷⣼⡿⢋⣴⣤⡀⢠⣿⠁⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⣥⢠⣾⠻⠏⢠⡾⠋⠉⠻⣟⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢀⣶⠋⣶⠉⢀⣰⠟⠀⠀⢀⣴⠛⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣠⣾⣁⣰⡟⢀⣼⠃⠀⠀⣠⡿⠁⠀⢀⣼⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢷⣶⡿⠛⠉⠙⠻⠿⣿⡁⠀⢠⡾⠏⠀⠀⢀⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣓⠈⠉⠛⢷⣦⣄⠀⠀⠈⢿⣷⣿⠃⠀⠀⣠⣿⠁⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⡿⢶⣿⣿⣷⣄⠀⠈⢻⡿⢷⠄⣴⡿⠃⠀⠀⢸⡟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⢀⣽⡿⠻⣦⡀⢸⡇⠀⣶⡟⠀⠀⠀⠀⠈⢁⡸⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⡿⠁⠀⠈⠻⣾⣅⣼⠏⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠾⠛⠉⠁⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠻⠿⠿⠷⠶⠶⠶⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠛⠛⠿⢷⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⢹⡏⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡖⠛⠛⠛⢋⣉⣁⠀⣾⣇⠀⠈⠻⠤⣴⣦⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠾⠛⠋⠁⠀⠉⠷⠶⠶⠞⢉⣉⡉⠶⠾⠿⠟⣉⡰⠶⢄⣀⣼⠿⠛⠳⠶⢶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠖⠉⠉⠁⠀⠀⠀⠀⠉⠁⠲⠞⣉⣁⠀⠀⠀⠀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⣤⣤⠶⠾⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⢦⣤⣤⡀⠀⠀⠀⢹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⣿⢟⣿⣿⣿⠟⢛⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣠⣾⣿⡿⢡⠞⣵⡿⠟⠋⢀⠔⡫⠟⣯⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣤⣼⠏⠀⠠⢀⠔⠀⣠⣾⠿⣛⣽⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⣿⢟⣽⢟⣵⡾⣋⣴⠿⣫⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡁⢀⣴⡿⢛⣥⣾⣿⠟⣻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⡾⢡⢋⣵⠟⣡⡾⢛⣥⡾⣫⠞⠋⠗⣛⣭⠶⣻⣿⣿⣿⣿⣿⣿⣿⣏⣴⡿⠟⣫⣴⡿⢟⣭⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣾⠿⡏⠛⠻⣿⣦⣾⡇⡼⢋⣴⠟⣡⡞⣡⢊⣴⠿⣋⣵⣾⡿⢟⣻⣿⣿⠿⣿⣿⣿⣿⣶⠟⣋⣥⣾⢟⣫⣿⣿⣿⣿
⠀⠀⠀⢀⣾⡟⠻⡇⠁⠀⠀⠀⠙⢿⣿⣧⣿⣥⣾⣿⣴⣷⣿⣿⣾⡟⣩⣴⡾⢟⣋⣥⣶⣿⢿⣿⣿⣿⣿⣿⣟⣭⣶⡿⢟⣩⣾⣿⣿
⠀⠀⣠⡿⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠉⠉⠙⠛⠻⢿⣷⣾⣿⠿⣛⣥⣶⢟⣫⣿⣿⣿⣿⣿⣯⣥⣶⣿⣿⣿⣿⣿
⠀⢰⡿⢇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣯⡶⢟⣫⣽⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⣫⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿
⢀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣩⡴⢞⣻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⣿⠤⠁⠀⣠⣤⣤⣦⣄⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠈⢿⡷⠛⠋⠩⠕⣒⣻⣭⣿⣿⡇
⠀⣿⠶⠶⠄⠀⠈⠉⠛⣿⣿⠃⠀⠀⠘⣷⣦⣤⣀⣠⣤⣶⣶⠿⠿⠟⠋⠉⠛⢻⣷⠀⠀⠀⠸⣿⡄⢀⣒⣫⡭⠽⣿⣿⣿⡇
⠀⣿⣦⣤⣤⣤⣤⣤⣾⣿⠃⠀⢀⠀⠀⠈⠛⠛⠻⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⣿⣏⠉⣩⣤⣴⣿⣿⣿⣿⠇
⠀⢸⡷⣬⣩⣟⣹⣿⣿⠇⠀⠠⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⠿⠿⣿⣿⣿⣿⣿
⢀⣿⠀⠈⠛⠿⢿⣿⡏⠀⠀⠆⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢰⡿⢋⣤⠀⠛⠣⢹⣿⣿⠇
⢸⡇⠀⠀⠀⢀⣿⣿⠁⠀⣆⠀⠀⠀⠀⠙⠷⣬⣙⠛⠿⢶⣶⣶⣶⣶⣶⡿⠛⠋⠁⠀⠀⠀⠙⢱⣿⡧⢂⣄⣠⣿⣿⠏
⣿⠁⠀⠀⠀⢸⣿⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣼⣿⡇⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⣰⣿⣿⡿⠋
⣿⠀⠀⠀⢠⣿⡿⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣼⠿⠛⠁
⣿⡆⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁
⢹⡇⠀⣠⡿⣿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠘⣷⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⢻⡇⠙⣦⣿⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠈⣿⡆⠙⣿⣧⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⢹⣷⠀⠀⠹⣧⣀⣴⣿⣅⠘⢿⣷⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⣿⡄⠀⠀⠘⢿⡟⠳⡙⢦⡀⠙⢿⣬⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠻⠄⠀⠀⣉⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣶⣶⣿⡇⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣾⡿⣿⢿⣿⣿⡿⠻⠋⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⢿⣿⣿⣿⣾⠿⠛⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠇⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠻⣤⣀⣠⣴⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣠⠤⣤⣤⣤⡤⢤⣶⣶⡶⠂⢠⣤⠤⠤⡤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣖⣻⣷⣿⣿⣿⣥⣽⣷⣏⣁⣈⣀⣀⣁⣘⣓⣖⣀⣀⣓⣤⡰⠆⢴⡦⠀⠸⠷⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⢿⣿⣽⣿⡿⣿⣿⣟⣿⡿⣿⡿⢶⣶⣶⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠛⠟⠚⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠷⠿⢿⣿⣏⣿⣷⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣿⣿⣿⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣽⣿⣿⣿⠃⠀⠀⠢⣀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⣿⣟⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢘⣿⣿⣿⣿⡋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠉⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⣽⣿⠉⠀⠁⠀⠀⠐⠂⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⡏⣿⠛⠛⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠵⡶⠴⠶⠆⠀⠀⠈⠢⠟⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⢂⣤⣔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠞⢴⣶⣷⣴⡶⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠁⠀⠀⠈⠙⠋⠈⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠈⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠛⠒⠒⠲⢶⣦⣀
⠀⠀⠀⢀⠴⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⢀⠐⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠴⠄⠀⠀⠀⠀⠙⣦⡀
⠀⡜⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠈⣷
⡄⠁⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠈⣷
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⣀⣀⠀⠶⠖⠂⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⡿
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡤⠄⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠼⠧⠾⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⢀⡀⢀⠀⣠⣠⣤⠀⣶⢤⣴⡆⢰⣦⡄⢰⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠈⠋⠉⠁⠙⠀⠁⠀⠈⠉⠉⠀⠀⠈⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⡀⡀⠀⢀⣄⣠⣤⣤⣀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣇⠀⠈⠛⠛⠛⠛⠛⠀⠀⠀⠙⠻⠛⠛⠛⠂⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠤⠈⠓⠒⠒⠒⠒⠒⠂⠀⠀⠠⠤⠤⠤⢤⣤⣤⡤⠤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⣇⣸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⢢⡾⠷⡶⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣤⣤⣤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗
⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠛⠋⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆⠀⠀⢹⣿⡀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⠀⣼⣿⠀⢸⣿⡄⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠈⣿⣧⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠘⣿⣧⡀⠀⠀⠉⠁⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⡀⢀⣀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⡀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠟⠋⠀⢀⣠⣴⣶⣶⣶⣦⣀⠈⠛⠻⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠋⠁⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠛⠛⠉⠁




⣿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣛⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠉⠄⠀⠀⠀⠀⠀⠀⠉⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠀⢀⡀⠀⠀⠀⢀⣀⡀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠀⠠⢬⠕⠀⠊⠥⠄⠁⠂⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣈⠁⠀⠀⠓⠐⡂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⠋⢀⠀⠀⠀⠀⠀⠚⠄⠀⠀⢁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⡀⠠⠤⣔⠊⠁⢀⡀⠀⢀⣀⡄⠊⠉⠒⠦⢤⡀⠀⠀⢙⡄⠈⣙⡺⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢒⢡⣲⣦⠀⠀⢠⡀⢠⣭⠽⢁⣙⡐⢢⠀⢀⡀⠀⠈⠑⣴⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡈⡧⣀⠢⠀⠀⠀⠀⠲⣿⠀⠈⠀⡀⢆⠄⠀⢂⣀⣀⠀⣽⠂⣀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠁⠠⠒⠀⠀⠀⠨⣿⠀⢡⠛⠡⠀⣭⢹⠂⣷⡄⠀⡼⠻⠶⠢⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡠⠀⠀⠀⠀⣸⠆⠀⢀⠁⠀⡸⢠⠌⠛⠯⠛⣟⡫⠂⠹⠀⠀⢬⣀⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠁⠁⠀⠀⠂⠀⠍⠰⠄⠀⠀⠀⠀⠀⢀⠀⠂⢰⣦⣛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⣰⡷⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⠨⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠶⠴⠾⠿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠤⠀⠸⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣦⣄⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣠⣴⣿⣿⣿⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠉⠻⣿⣿⣆⡀⠀⠈⣿⣿⣿⣿⣿⣿⠁⠀⢀⣠⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣽⣿⣿⣿⣷⣄⣿⡿⠁⠈⢿⣿⣠⣶⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣿⣆⠀⠈⣡⣤⣤⡙⢿⣿⣿⡇⢰⡆⢸⣿⣿⡿⢋⣤⣤⣌⠁⠀⣰⣿⣿⣿⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⠰⢿⣿⣿⣿⡌⣿⣿⣷⣿⣿⣶⣿⣿⢡⣿⣿⣿⡿⠆⣰⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠈⢻⣿⡇⢸⢻⣿⣿⣿⣿⡏⡏⢸⣿⡟⠁⠀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⣸⣿⣿⡄⠸⠻⡇⢸⠏⠇⢀⣿⣿⣇⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠛⢻⣿⣷⣶⣴⢸⡇⣦⣶⣾⣿⡟⠛⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣶⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠹⣿⣿⣿⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁







⣿⣿⡿⠿⣿⡿⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢆⣉⣉⣩⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⠶⢛⣫⣥⡴⠦⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⡴⠞⠋⣉⣤⡶⠶⠟⠛⠛⡿⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠞⠋⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⡇⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⢀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠙⢿⣿⡆⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⡀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣸⣅⣠⣤⣤⣼⣿⡿⠿⣿⣿⣿⠿⢿⠟⣿⠟⠛⢿⣿⡿⠟⠋⢻⡟⠋⠀⠀⢀⡿
⠀⠀⠉⠉⠉⢹⠁⠁⠀⢉⠀⠘⣧⡀⠈⠉⣁⣴⠏⠀⡟⣧⡀⠀⠉⠉⣀⡴⢻⡇⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠉⠛⠉⠀⠀⠀⠰⢄⠙⠛⠚⠛⢉⡴⠋⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⣼⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠁⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢹⣿⡛⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣠⣤⢤⣾⣿⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠘⣿⣷⠶⣦⣀⠀⠙⢿⣦
⠀⠀⠀⣤⠟⠋⠉⣀⣠⣿⣿⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⢻⣆⠀⠀⢿⣇
⠀⢀⣾⠏⠀⣠⡿⠋⢹⣿⡏⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢈⣿⠀⠀⢸⣿
⠀⢸⣿⠀⠀⣿⠀⠀⣾⣿⠃⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣤⣴⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣸⡟⠀⠀⣾⡟
⠀⢸⣿⠀⠀⢿⡄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⠟⠀⢀⣼⡿⠁
⠀⠀⢿⣇⠀⠈⠻⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣠⣴⣿⠟⠁
⠀⠀⠈⢻⣧⣄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠉⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⣶⣴⡾⠋⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⣀⣀⢀⣀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⢴⣶⡆⠀⣤⣤⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⠒⠀⢀⠀⠱⠉⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣿⡿⠀⠀⠀⠀⠈⢁⠔⠁⠀⠀⠀⠀⠀⠸⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣽⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢰⣿⠄
⠀⠀⠀⢠⠖⢋⠍⠙⠢⡀⡟⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⢀⠄⣀⣀⣀⣀
⠀⠀⢀⡈⠀⡏⠀⠀⠀⣇⡅⢠⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠒⠓⠚⠒⠁⠀⠈⠀⠓⠒⠒⠒⠒
⠀⠘⠁⠀⠀⠑⠦⡔⠎⠀⠉⢳⡄⠉⢦⡀⠀⠀⠀⠀⠀⢀⠠⠊⠀⢸⠀⠀⠀⠐⠐⠂⠂⠐⠐
⠀⠔⠀⠀⠀⠀⠀⠈⠲⡄⠀⡜⠱⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⢸
⡅⠀⠀⠀⠢⣄⠀⠀⢀⠇⠀⢧⣄⠑⠚⠉⠀⠤⠠⠠⠄⠀⠀⠀⠀⢾
⠰⡀⠀⠀⠀⠈⠑⢊⠳⣄⣀⠎⠀⠀⠀⠀⢀⠀⠃⢂⠀⠄⠀⠀⠀⢸
⠀⠈⠑⠤⣤⠤⠞⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⠀⢈⠙⠛⠻⠿⠿⣿⣿⣿⡿⠿⠟⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣎⣱
⠀⠀⠀⠀⠀⠑⠂⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣇⠀⢰⣧⣶⣶⣶⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠈⢻⣿⣿⣿⠟⢀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⢸⡇⠉⠀⠀⢸⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠟⠀⢸⣷⣷⣴⢀⡈⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣭⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣿⣯⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠏⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⢀⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣾⡿⠃⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⣠⣴⣶⣌⣯⣴⡾⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⣠⣮⣻⢿⣼⣾⣷⣿⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣹⣯⣴⣦⣄
⠀⠀⠀⠀⢸⡟⠙⠋⢹⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡿⣿⣽⣿⢿⣿⣿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠐⢃⣭⣶⣿⣿⣿⡛⠻⠛⠃
⠀⢀⠀⠀⠀⠁⠀⢿⣿⣿⣿⣿⣿⡇⠀⢠⡄⠀⢀⣤⣔⡷⣝⣻⣿⡿⣵⣯⡄⣨⣷⣿⣿⣿⣿⣿⡇⣠⣄⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣷
⢠⣾⣗⡀⠀⢦⣀⣠⡿⣿⣿⣿⢏⣤⣶⣿⠇⠀⣈⣿⣿⣿⣿⣿⣿⣷⣟⠻⣧⡿⠛⡿⣿⣿⣿⣷⣯⣷⡾⠂⠀⢠⣿⣤⣍⢿⣿⣿⣿⢿⣧⣤⣶⠆⠀⣰⣿
⢘⣿⣿⣿⣦⣜⡻⣿⠿⠦⣅⢹⣨⠟⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣃⣜⣵⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣯⣿⠿⡄⢹⢉⡥⠿⠿⢿⣣⣴⣿⣿⣿
⠘⠛⠛⣿⣿⣿⣿⣶⣦⣄⡈⣾⡇⣸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢋⣽⣿⣿⣧⡀⢻⣿⠏⢀⣤⣶⣿⣿⣿⡛⠛⠋
⠀⠀⢸⣿⠋⡾⠛⠻⠿⣿⣷⣼⣧⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣟⠻⠿⢿⣷⣿⣿⣇⣿⢁⣴⣿⣿⠿⢮⣿⢹⣿⡆
⠀⠀⠘⠛⠀⠀⠠⡾⢿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣄⡙⢿⣿⣿⣿⣛⣭⣿⣦⠀⢥⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣈⡽⣿⢿⡿⣿⣿⣷⣿⣿⣌⣿⣷⣼⣿⣿⣾⣿⣁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣯⣸⣿⣧⣙⣻⣷⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⣿⢿⣿⠇⢻⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣧⡼⠿⠿⠿⣿⡿⠿⢿⣿⣧⣤⡀⣿⣿⣿⡿⣤⣼⣿⣸⣿⣿⣿⣿⡿⠿⠿⣮⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣶⡆⠀⠸⣿⡷⠀⠘⠟⠿⠿⠃⢹⣿⣿⡁⠙⠿⠟⠇⠀⠸⣿⡿⠀⠀⣶⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣿⣿⣿⣿⣿⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠿⣿⡿⠈⠛⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⢿⡀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀⠉⠙⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣶⣤⣀⡀⠀⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡶⣿⣿⠿⠿⠿⠿⣿⡟⠲⢧⡀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠉⠁⠀⠀⢰⣿⡡⠤⣤⣤⣤⣈⣿⡄⠀⠙⠓⠾⣆⠀⠀⠀⠀⠛⠦⣤⣤⡀
⠀⠀⠀⣠⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠛⠿⠃⢀⣿⠃⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⣤⠞⠁
⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣦⣴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⠳⣄⡀
⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠉⠉
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⣿⣷⡄
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⢻⣿
⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣠⣾⡟
⠀⠈⠙⠿⢷⣶⣶⣤⣤⣤⣤⣴⣶⣶⢶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠛⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⣀⡤⠴⠶⠶⠒⠒⠒⠒⠒⠶⠶⠶⢾⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⡀⠀⠀⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡟⠀⠀⠈⢉⣿⡏⠉⢉⡽⡿⢯⠉⢉⡿⣏⠉⠉⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⢸⡿⠀⠀⠀⠀⢸⠇⠻⣤⠞⢠⠇⠈⣷⠞⠁⣿⠀⠀⠀⠀⣤⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠙⢦⣬⡤⠞⠁⠀⠀⢿⠀⠀⠀⠀⢻⡀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣴⠟⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡏⠰⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢰⣿⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⠀⠀⣸⡀⠀⠀⠀⢀⡇⠈⠁⠀⣀⣀⣸⣇⣀⣠⣤⣤⣴⣿⣾⡇⢐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠛⢻⣿⠛⠛⠋⠉⠉⠉⠹⢷⣶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠙⠉⠙⠛⠛⠿⣄⠀⠀⠀⠀⠀⠀⣠⠟⠛⠋⠉⢙⠛⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠶⢿⣀⣹⡆⠀⠀⠀⠀⢰⣏⣠⡷⠶⠦⣼⣤⡴⠿⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⣦⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀
⠀⠀⠀⠀⠀⢀⠀⢊⣀⡂⢱⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡀⣈⡀⠌⠠⡀
⠀⠀⠀⠀⠀⠢⠀⠈⠁⠂⠊⠉⠉⢣⠀⠀⠀⡆⠀⠄⠐⢀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⢢
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠢⠄⣀⠠⠊⠀⠀⠀⠁⢸⠀⠀⠀⡀⠀⠀⠘⠤⠤⠤⠀⠒⢁⠄⠀⠀⢈
⠀⠀⠀⠀⠀⢾⠀⠤⠦⠤⠖⡇⠀⠀⠀⠀⠀⠐⠘⡄⠀⠀⡆⠇⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡀⠼
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⠀⠀⡀⠀⢸⠀⠈⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⢐⠀⠈⠐⠁⠀⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡀⠐⡤⠠⢤⠔⠃⠀⡄⠀⠀⠀⠘⠢⡤⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠢⣀⣀⣀⣠⠄
⠀⠀⠀⠀⠑⠀⠠⠴⠀⠢⠀⠀⠘⠀⠀⠀⠀⠀⠂⠠⠬⠥⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⡄
⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠤⡀
⠀⠀⠀⠀⢐⡄⡄⠈⡀⠀⠀⠀⢀⢀⠠⠀⠀⣠⠖⠀⠾⡀⠀⠀⢀⠀⡂⠀⠀⠀⠀⡐⠡⣤⢠⡄⠘⡀
⠀⠀⠀⠆⠀⠈⠁⠀⡅⠀⠀⠀⠀⠀⠀⠀⢀⢉⠀⠤⠐⠋⡄⠀⢀⠁⠀⠀⠀⠀⠀⠅⡈⠉⠈⣣⠀⡇
⠀⠀⠈⠀⠀⠘⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⢈⠘⣷⣶⣶⡇⡇⠀⠁⠀⠀⠀⠀⠀⠀⡄⠈⠈⠍⢤⡀⡇
⠀⠀⢠⡀⣠⠂⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠄⠠⡇
⠀⠀⢰⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠄⢘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⢀
⠀⠀⠀⢠⠤⠤⠤⡔⠀⠀⠀⠀⠀⠀⠀⠁⠀⢦⠄⠀⠠⠤⡇⠠⠐⠀⠀⠀⠀⠈⠀⢒⢢⠤⠤⠤⢔⠃⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠐⠄⠊⠀⠀⠀⠀⠂⠀⠀⠤⠃⠀⠂⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⡀⢠⠀⡄⢠⠀⠆⢠⠀⠀⢠⠀⡄⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣤⣤⣤⣤⣤⣄⣶⣴⣤⣤⣴⣦⣦⣸⣿⣆⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡀⢀⣀⣀⣠⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠉⠻⡍
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢻
⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡼
⠀⠀⠀⠀⢠⠏⠀⠀⠀⣿⠀⠀⠙⠦⣀⠀⠀⣀⡠⠖⠛⠉⠉⠓⢦⡾⠁
⠀⠀⠀⠀⢸⡄⠀⠀⣸⠏⠣⣀⠀⠀⣈⡷⠚⠁⠒⠀⠀⣀⣀⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠻⣤⣤⡏⠀⠀⠈⢉⡽⠋⠀⠀⣠⠤⠤⡀⡤⠒⠦⡀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠋⠀⠀⠀⢸⠁⣶⣂⣿⣥⣞⡄⣣⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠘⠦⣬⠿⠃⠙⣯⡴⠃⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡤⠶⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⣦⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠘⢦⡀⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⠀⢠⠏⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠛⢦⣀⢸⠀⠀⠀⠀⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣽⠴⠛⠁⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠶⢤⣄⣀⣀⣀⡀⠈⠙⢋⣁⣀⣀⣠⣤⡶⠞⠻⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡆
⠀⢀⡤⠤⣄⡀⠀⢸⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⠀⠀⢹⡀
⡼⠁⠀⠀⠀⠙⢦⡿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⢀⡠⠶⠒⠓⠲⣄⠀⠀⠀⠀⠀⢀⠂
⣇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡷⠋⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⠔⢁⡞
⠸⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡟⣀⠔⠁⣠⠊
⠀⠙⣆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⠞⠁
⠀⠀⣈⣳⣄⣀⠀⠀⠀⠸⡆⠀⢀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⣀⡴⠒⠳⢤⡀⠀⠀⠀⠀⣠⠞⠋⢀⡤⠞⠁
⠀⡾⠁⠀⠀⠉⠉⠑⠂⠀⣷⠞⠙⠓⠀⠀⠀⠀⠛⢦⡀⣠⠖⠛⠀⠀⠀⠈⠛⣦⠀⠀⠀⠙⣦⣴⣚⣫⡥⠖⠚⠉
⠀⠻⠤⣇⠀⠀⢸⣇⣀⣰⢿⣄⣰⠂⠀⠀⢰⡄⠀⢸⡟⣟⠀⣴⠀⠀⢠⠀⠀⣿⢀⡄⠀⠀⣸⠏⠁
⣀⣀⣀⣉⣉⣉⣉⣉⣉⣀⣀⣀⣙⣓⣒⣒⣚⣋⣉⣉⣁⣉⣙⣻⣶⣶⣟⣛⣋⣉⣙⣦⣶⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⢠⡶⠿⢷⣦⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠃⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠒⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⠴⠒⢦⡄⢀⡴⠛⠛⠳⣄⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠠⡷⢤⣤⣤⣿⢸⡧⣤⣤⣤⢽⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⡉⠀⠀⠀⠀⢳⣌⣉⣽⠃⢈⣧⣌⣛⣻⠟⠀⠀⠀⠀⠘⢛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡙⠀⠀⢀⣴⠞⠋⠉⠁⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠸⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠋⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⡇⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣾⠿⠛⠁⠀⠀⠀⣿⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⡇⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠀⣼⡆⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢷⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠋⢰⠏⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢻⡞⢩⠗⡞⠉⢷⠳⣄⣠⡤⠤⠤⢤⣄⣀⣀⣀⣠⠏⠀⢀⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣼⠀⡟⢀⡇⠀⢸⠀⣿⠀⣀⡤⠖⠋⠉⠀⠀⠀⠉⢀⣠⣾⠙⢎⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢿⣀⡇⢸⡆⠀⣼⢀⡿⢾⣥⣤⣤⣤⠶⠶⠶⠟⠛⠋⢹⡿⢦⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠙⠛⠳⠶⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡟⠀⠀⠉⠉⠉⠉⠉⠉⠙⣟⠉⣿⠁
⡴⢦⣀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠶⢶⣾⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠶⠿⠶⣶⣤⣄⡀
⢳⡄⠉⠛⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆
⠀⠙⠳⠶⠤⣤⡴⠶⠶⠶⠶⠶⣦⣤⣤⣤⣾⠇⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⢀⣀⣠⣼⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣾⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⡼⠹⣿⣟⣹⣿⣿⣿⣿⣹⣿⡏⣟⣠⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⡼⠃⠀⠘⣿⢿⣯⣿⣿⡟⢻⣿⣷⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠽⠟⡿⢁⣀⠀⠀⠘⠨⠭⠁⠩⠝⢘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢰⣿⣿⠁⠀⢀⣶⣶⡀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣤⣄⠘⠛⠛⠛⠂⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣔⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣐⣿⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠤⣶⠿⠿⠶⢿⠍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢛⣡⣤⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠉⢿⣿⣿⠀⠀⣿⣿⣿⠋⠁⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠿⠟⠉⠀⠀⣀⣀⣀⠀⠉⠻⠿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠈⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⡄⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣤⣆⣀⣉⣉⣉⣉⣰⡖⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠀⢠⠀⠈⠁⢠⡄⠻⣿⣿⠏⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⣀⡀⠂⢁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡂⠀⠀⢈⠜
⠀⢀⠀⠀⠀⠀⠀⡄⠀⠓⠀⠀⠀⢠⠀⠀⠀⠸⡟⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⠢⣄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠑⠦⣀⠀⠀⢀⠔⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠀⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣿⡿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠛⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡀⠌⠀⠐⠒⠂⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⠲⣄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠀⢀⡐⠀⠀⠀⠀⠀⠠⣄⣀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠰⣄
⠀⠀⠀⠀⠀⢠⠒⠒⠈⠐⣁⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠉⠠
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⡤
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣷⣿⣿⣿⣷⣦⣍⣼⣿⡿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠉⠛⠀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣷⡿⢠⣿⣿⡿⣀⠙⢿⣯⣿⠿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣴⡿⠋⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢿⣿⣿⣿⣻⣿⣿⣯⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⠀⠀⠀⠻⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⣀⣀⣀⣀⡀⠀⠀⣠⡴⠶⠶⢾⡽⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣿⣿⣿⣿⠉⠐⠊⣁⣈⣉⣻⠇⠀⢰⣧⣶⣿⠿⣿⠃⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠄⢸⣠⡟⢿⣿⠇⠘⢛⣿⣿⠟⣛⡧⠀⠀⢻⡿⠿⠖⠉⢧⠀⠀⠀⠠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⠈⢻⣇⠸⣿⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠑⢄⠀⠀⠘⡇⠀⠀⠐⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠃⠀⠈⢿⢳⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠞⠀⠀⢰⡇⠐⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⢺⡀⠀⠈⣷⣍⢻⣄⠀⢸⡄⠀⠀⠀⠀⣀⣴⣿⣾⣷⡦⡼⠀⠀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣯⣷⡄⠀⠈⢿⣿⣟⢦⡀⠁⠀⠀⠀⠀⠉⠛⠻⠛⠋⣰⠃⠀⢰⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣿⡇⠀⠐⠶⠽⣿⡀⠙⣳⣦⣀⡀⠀⠀⠀⠀⠀⢰⠏⢀⡄⣽⣿⠇⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣴⡄⠀⠀⠀⠀⣿⠃⠀⠀⣹⣟⠛⠿⣶⠶⠶⠶⠟⢀⣿⣗⣿⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⡿⠻⠂⠀⢀⣀⣿⠀⠀⠀⠈⠁⠀⠀⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠁⠀⠀⢀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⢹⣿⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⣠⣶⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢇⣀⣿⠛⢿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣶⣿⡿⠃⠀⠉⢓⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣶⣤⣧⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠠⠀⠀⠒⠈⣥⣤⣬⡽⠿⠾⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣘⣛⣛⣉⣉⣠⣽⣿⣻⣟⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⡀⠄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠀⠿⣿⣿⡓⢤⡀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣀⠈⠓⢜⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠳⠄⣀⡄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢠⠀⠀⠀⠀⠠⠄⠀⡿⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡌⠀⠀⠑⢄⠀⠀⠀⠀⢀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢷⠀⠀⠀⢨⢦⡤⡄⢀⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣀⠀⠘⡇⠀⠰⠋⣄⢹⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠳⠢⣥⡞⠀⢠⡏⠠⠉⢿⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⡀⠀⠈⠁⠀⠈⠆⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢛⠁⢠
⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠡⡀⠀⣇⢸⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠳⡀⢹⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣳⡀⠀⠀⢠⣷⣼⣧⣾⣯⣠⠴⠂⠠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣈⠛⠛⠁⣠⠀⠹⢤⣤⢬⣿⠿⠃⢰⣾⣿⠀⢌⣦⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠋⣵⣀⣼⡿⣶⣶⣦⣄⣈⣽⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠛⠲⠶⠖⠋⣭⣽⣯⣯⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡉⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⢀⡟⠰⠶⠆⢠⣤⣤⣴⣶⣴⢶⡆⣸⡿⠛⠯⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠚⠛⠓⠒⠐⠀⠀⠀⠀⠀⠀⠀⠛⠸⠿⠀⠀⠀⠈⠉
⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠺⠆⠒⠚⠿⠷⡗
⠀⠀⠀⠀⣲⣿⡦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡀
⠀⠀⠐⠂⠉⠈⠉⠓⢚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠠⠶⢤⡆⣭⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡤
⠀⠀⠀⠁⠀⣤⠀⠁⠀⠀⠀⠁⠀⠀⡀⣀⣀⣠⣤⠄⠀⢸⣶⣾⣿⣯⣃⡦⠀⠁⠿⣿⠿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡁
⠀⠀⠀⠀⢈⣽⣿⣤⣤⠴⠶⣾⠿⠿⠿⠿⠿⠿⠏⠀⠠⢁⣬⢃⡉⢸⠀⣧⣹⣼⠆⠞⣷⣈⣿⡿⡿⢿⣿⡿⣿⣷⣶⣷⣶⣦⣄⠀⠲⡢⣿⠟
⠀⠀⠀⠀⠀⢛⣿⡿⠿⠟⠁⢀⣀⣀⡤⠄⠀⠀⠀⠀⠈⣿⠦⣽⠥⢾⣯⣷⠾⠧⠊⡛⢈⣒⠷⠶⠤⣶⣦⣶⣾⡿⢿⣿⣿⣽⣿⣿⣿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠐⣩⣵⠺⢯⣦⠄⠀⢠⣾⠁⠈⢁⣀⣀⢠⣨⣅⣀⣴⠶⣾⣭⣹⣛⣒⠒⢤⡼⠵⠿⠥⠴⢶⣿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠹⠟⠁⠌⠉⠉⠤⠭⠽⠿⠟⠳⠶⠦⠭⠿⠿⠿⠿⠿⠦⠤⠘⠓⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⢁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠻⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢸⣿⡆⢠⣿⡏⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠘⣿⡇⢸⣿⡇⠀⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⢠⣿⡇⢸⣿⡇⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣸⣿⠃⠈⣿⣇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣶⣶⣾⡿⠛⠁⠀⣀⣠⣤⣄⣀⠈⠛⢿⣷⣶⣶⣶⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣠⣾⡿⠛⠛⠛⠿⣷⣄⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⢿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⢀⠀⠀⠈⠛⠋⠙⢿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⡻⣿⠛⠃⢶⣿⡿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠉⠁⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⡄⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⢶⠲⡋⠁⠀⠙⣁⣂⠐⠟⠛⠓⡤⢄
⠀⠀⠀⠀⠀⠀⣠⣴⣉⣈⠀⣀⢀⡃⡀⠀⠀⠱⡄⠒⠶⣼⣤⣧⠦⠬⣿⠲⡤⣀
⠀⠀⠀⠀⠀⣸⠉⠛⠙⠛⠛⠛⠻⠛⠟⠟⠛⠛⠁⠀⠉⢡⠀⡇⠀⠀⠈⢳⡀⠈⡆
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠂⠀⠀⠠⢼⣠⣧⣀⣀⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠁⠀⢀⡤⠴⠲⠖⠺⠒⠒⠲⠋⠀⠀⠀⠀⠛⠉⣿⠙⠻⣿⣦⠀⠙⣦⡀
⠀⠀⠀⠀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⢹⠀⠀⣿⣿⡆⠀⢹⠇
⠀⠀⠀⠀⡏⡀⢀⠀⣀⣁⣠⣀⣤⢀⣄⣤⠀⢄⠁⠀⠒⡇⢠⢸⠀⠀⠀⢻⣿⡄⢸
⠀⠀⠀⢰⣏⡁⡀⠀⠠⡦⠠⠤⠿⠠⠶⡇⠀⠀⠀⠀⠀⠐⡂⢺⡆⢤⣴⠸⢿⣧⣸
⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠄⣡⠸⡇⠀⢸⡀⠘⣿⣷
⠀⠀⠀⢰⡏⣉⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠱⠀⠀⠄⠀⠀⠈⢤⡇⠀⢸⣟⠠⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣼⣏⠙⠚⣿⡆
⠀⠀⠀⠈⣧⣀⡀⣀⠀⠄⢤⢠⡦⣤⠤⡤⣤⠄⠐⠂⠀⠀⠠⠄⡆⠸⠉⣿⣠⡀⢿⡁
⠀⠀⠀⢀⡏⠉⠉⠋⠛⠁⠉⢘⠃⠛⠛⠏⠈⠁⠀⠀⠄⠂⠀⠀⠆⠀⠀⣁⠈⢿⣦⡃⠀⡀
⠀⠀⠀⢸⣶⡒⣶⢂⣺⣀⣀⣸⡀⣄⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢿⠠⣾⠈⢳⡀⢱
⠀⠀⠀⠘⠉⠀⠁⠀⠀⢀⡀⣨⢀⣅⢠⡅⢈⣁⠀⣀⠀⠀⢀⠀⠈⡐⠂⠁⠀⣿⠑⠦⠉⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠁⠀⠀⠁⠈⠀⠈⠉⠃⠀⠀⠀⠀⠀⣄⠈⠳⣇

⢠⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣦
⢸⠀⠀⣤⣶⣶⣶⣶⣄⠀⢰⣶⣶⠀⠀⢰⣶⣶⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⣶⣶⣶⣆⠀⢰⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⣶⠀⢸
⢸⠀⠘⣿⣿⣦⣤⣍⡉⠀⢸⣿⣿⣤⣤⣼⣿⣿⠀⠀⢀⣿⡿⢹⣿⣆⠀⠀⣿⣿⢿⣿⡀⣾⡿⣿⣿⠀⢸⣿⣿⣤⣤⣤⣄⠀⢸
⢸⠀⢀⣠⣍⠛⠛⣿⣿⡆⢸⣿⣿⠛⠛⢛⣿⣿⠀⢀⣾⣿⣥⣤⣿⣿⡆⠀⣿⣿⠈⣿⣷⣿⠇⣿⣿⠀⢸⣿⣿⠉⠉⠉⠉⠀⢸
⢸⠀⠈⠻⢿⣷⣾⡿⠟⠁⢸⣿⣿⠀⠀⠸⣿⣿⠀⣼⣿⠟⠉⠉⠹⡿⣷⠄⢿⠿⠀⠸⣿⡏⠀⢿⠿⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸
⠘⢦⣤⣤⡤⣠⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠞
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡄⠀⠀⠀⠸⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣸⣿⣿⡿⠿⢷⣀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⣾⡿⠿⠿⣛⣛⣛⣿⣯⣽⣿⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣛⣯⡽⣶⡚⠿⠭⠙⠒⠒⠉⠉⠁⠀⠀⣀⣮⡡⣿⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣫⠽⣒⡮⣽⠶⣺⢭⣤⢄⡀⠀⠀⠀⠀⢀⡤⠖⢚⡩⠜⢽⣞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⣿⣿⣦⡏⠉⠈⠙⡲⢦⣠⣓⠀⠀⢰⣙⣠⠜⡋⠀⠀⢸⣿⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠊⣙⡇⡇⠀⢠⡤⠠⡤⢈⡟⠀⠀⠸⢿⠁⣤⠀⡶⠀⢼⣱⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⢻⡇⠀⠈⠑⠂⠀⠛⢀⠀⠀⢸⠺⠑⠀⠊⠀⠀⣾⡏⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣻⡀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣀⠀⠀⠀⠀⢠⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⣧⣇⡀⠀⠀⢰⡉⠁⠀⠀⠈⢉⣄⠀⠀⣰⣃⡸⣅⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⡻⡟⣻⣿⠽⠷⣄⣀⠴⠿⠷⠖⠻⠻⢛⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⣿⣧⣤⣿⠀⡎⠑⠄⠤⠄⠀⠠⠴⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⢿⡿⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⡈⠀⠁⠂⠀⠤⢀⣀⠠⠤⠖⠊⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠤⢾⣿⡷⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠿