Coffee cup Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⢀⣐⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣈⣥⣴⠆⣝⠙⠀⢩⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣴⣿⣿⣟⣪⣕⣶⣬⡁⠀⠀⣀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠎⣆⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⢿⣿⣿⣿⣿⠿⢿⣤⣶⣄⠶⢄⠺⠉⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣩⠇⣸⡇⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠶⢽⡻⢿⣿⣿⣶⣾⣿⣿⣶⣻⣿⣦⣤⣌⡠⠀⡀⠀⠀⠀⢠⣀⣴⣤⡾⢞⣡⠾⢹⡏⣰⣦⠾⢦⣶⣈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠑⠂⠭⢙⠛⡛⠻⠿⠷⠿⠿⠿⠿⠿⠷⠾⢛⣚⣛⣩⣭⡭⠴⠚⣋⡩⣂⣽⣿⡏⠀⠀⠀⠈⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢈⡅⠰⠶⣖⡻⣯⡷⢝⣫⣿⣿⣇⡀⠀⠀⠀⡸⢟⡇
⠀⠀⠀⠀⠀⠀⢀⢀⣤⣖⣘⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠶⢬⣝⣲⣭⣶⣿⣯⣿⣿⡯⣫⣷⠞⢡⣾⠁
⠀⠀⠀⠀⡠⠂⠵⣗⡽⣌⢽⣷⣾⣧⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠿⣟⣻⣿⣿⣷⣿⣿⣿⡿⠟⣋⣴⣾⣿⣷⣏⢂
⠀⠀⠀⡐⢰⠳⠺⡋⣾⠃⡸⡿⢻⣿⢆⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢁⣚⠻⢿⣛⣾⣿⣿⣟⣋⣥⣶⣿⣿⣥⢪⠁⠻⠀⡇⠃
⠀⠀⠀⡅⠁⠇⢇⡜⠊⠈⠈⠘⠓⠩⠻⣧⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣷⣾⣿⣿⣿⣿⣟⡿⠟⢻⡟⠾⠛⠛⡛⣁⠁⠀⡠⠁⠆
⠀⠀⠀⠱⡈⠆⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⠓⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠚⡻⣭⣍⢺⣉⣿⣿⡿⢠⠄⠁⠀⠀⡀⠄⠀⠀⠀⠔⢁⠎
⠀⠀⠀⠀⠈⠢⡑⠤⣝⡣⡀⠀⠀⠀⠀⠀⠀⠈⠲⡅⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⣈⣃⣤⣹⢴⣿⠿⠃⠀⢀⠠⠄⠀⠀⠀⢀⠠⠊⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠠⣉⠂⠁⣀⠀⠀⠀⠀⠀⠀⠱⣈⠁⠀⠒⠒⠀⠐⠛⠂⠛⠙⠛⠋⠉⢁⣠⠞⠁⠂⠀⠀⠀⠀⠀⠠⠔⢊⡤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣀⡐⠂⠀⠀⠀⠀⠀⡉⠓⠲⠶⠶⠤⠤⠤⠤⠶⠶⠒⠛⠉⠀⣀⠀⠀⠠⠀⠀⢀⡤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠥⢀⣒⠂⠀⠤⠤⠀⠀⣉⣈⣀⣀⠀⠀⠈⠩⠤⠄⠐⣂⡀⠥⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠂⠐⠒⠂⠀⠀⠐⠒⠒⠀⠈⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⠆⠀⠀⠀⠀⠴⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢶⣭⣼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣬⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠻⢦⣄⣀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣼⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠶⠦⣤⣌⣉⣉⣙⣛⡛⠓⠒⠒⠛⠛⣛⣋⣉⣉⣩⣤⠴⠞⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣦⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣯⣝⣓⡒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⣟⣿⡿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡟⣟⣿⢙⡖⠒⠒⠂⠉⠉⠉⡛⡛⣽⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⣿⣿⠇⠟⠯⠘⠁⠀⠀⠀⠀⠀⠀⠅⠤⠟⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠶⠶⠶⠖⠒⠚⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢤⡀⣤⡘⢯⠻⡀⠀⡀⠒⢢⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠒⠛⠺⠇⠘⣆⢻⡸⠹⠦⣠⠆⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣽⣿⣷⣶⣶⣶⠤⠨⠤⠥⠤⠤⠶⢶⡶⠚⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⣿⠢⣿⠐⠀⠀⠀⠀⠀⢸⢿⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⣿⣿⣞⣿⠀⠀⠀⠀⠀⠀⢘⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠌⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡞⣼⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠏⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⢿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⡇⣿⣤⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣶⣶⣦⠤⠤⢤⠤⠤⠴⢶⢶⠒⠛⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣘⣯⣤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣤⡄⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠜⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠒⠒⣾⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣈⠲⢍⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠛⢦⣬⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⡟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⠴⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠋⠁⠀⠀⡀⡸
⠀⠀⠀⠀⢲⠀⠀⠀⠒⠂⢄⢀⢬⠢⡐⢄⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⣤⡤⢊⡵⠛⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠑⢄⡉⠉⠂⢤⠙⣦⣅⣈⡒⣬⣖⡖⣰⣀⡀⠀⠀⣔⣚⣁⠔⠋⠀⠀⣀⡀⠤⣐⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢐⢢⡤⣽⣿⣦⢜⣶⠚⣅⠭⠷⣉⠯⢭⣭⣭⣭⠭⠤⠭⠭⠁⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣽⣾⢻⣛⢯⡿⡯⢽⠵⣪⣞⢴⡒⣤⡟⡳⣧⢸⡄
⠀⠀⠀⠀⠀⠈⢁⣌⠁⢯⢀⣷⠶⡪⢷⣸⣟⣛⣻⣦⣜⣸⡿⠷⠿⠿⠟⠁⠲⠼
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠢⠤⠒⠚⠁⢱⠇⠎⢤⣺⡳⢖⣙⡃⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠠⠄⠀⠀⣀⣀⠀⢁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⣀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⡠⠤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠔⠉⠁⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢈⠀⠤⡁⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠰⠊⠉⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣌⡒⠂⠤⢄⡀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠪⠐⠠⠔⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⡶⢂⠚⡃⠈⠖⣠⣀⢲⠶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⣀⣠⣭⣧⣼⣄⣧⣌⣼⣾⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⡴⣼⡉⢦⣤⣙⣻⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢛⣛⣯⣵⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⣟⠀⠘⣇⢸⣿⠯⠍⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡙⢄⠀⢻⡄⢻⡄⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣑⡂⠿⣄⠛⢆⢠⡻⢿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣟⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠾⣷⣌⣉⢡⣼⣿⣷⣄⠀⠀⠀⢀⡴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡶⠶⠚⢭⣿⣿⣭⣭⣛⣛⣛⣛⣺⣛⣛⣼⣓⣂⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⣿⣿⡃⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⠿⠿⠛⣛⣿⣿⣿⠖⠈⡂
⠀⠀⠲⢼⣿⣿⣶⣶⣽⠿⣿⠿⣿⣿⣦⣤⣉⣙⣛⠛⠛⠛⠛⠒⠶⠆⠀⠀⠀⠀⠛⢉⣉⣡⣴⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢤⣄⣒⠀⠁⠉⠉⠉⠛⠛⠛⠿⠿⠷⠶⠿⠶⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⢦⣤⣤⣴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣭⣤⡽⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⠁⠲⣾⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⢠⡔⠂⠀⢀⣀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢀⢺⣶⣶⣾⣿⣿⠿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣷⣶⣶⣿⣥⣴⣾⣯⣭⣯⡙⠿⠿⣿⣷⣦⣄⠀⡸⢀⡆⠀⢀⡠⠤⠄⠠⣄
⠀⠀⠀⠀⢸⣦⠙⠿⣟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣯⣿⣿⠟⣡⣾⣧⣶⢛⡀⠀⠀⠠⢤⣷
⠀⠀⠀⠀⠘⠿⠀⠂⠚⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣫⣴⢞⣿⣿⣿⣷⡏⠁⠀⠀⠀⠀⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢛⣛⣛⡛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠍⠡⠖⠀⡰⠊⣿⣿⣿⠍⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣿⣿⢁⣿⠛⠋⠀⠀⠀⠀⠀⡄⢀⠆
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢿⣿⢻⡏⠀⠀⠀⠀⢀⡠⠊⡠
⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡟⠀⠀⣀⠠⠖⢋⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠋⣁⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⣾⣼⠿⠟⡫⡶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣶⣤⣠⣤⣤⣄⣤⣤⣤⣤⣴⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠁⠈⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⢀⡴⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⣠⡶⠚⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡾⠃⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠸⣧⡀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⣿⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢠⡾⠋⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⠞⣀⣠⣤⣴⣶⣶⣾⣟⣛⣛⣛⣛⣛⣛⣓⡒⠶⢦⣤⣀⡀⠲⣄⠙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡾⠃⣿⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⣠⡟⠛⢲⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠃⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠿⢻⠏⠀⣠⠞⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⢠⣯⡤⠞⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⢷⡄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⣠⠟⢉⡟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠛⠛⠻⣅
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢰⡏⢀⣞⡴⠟⢛⣋⣉⣿⣶⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⣄⡞⢹⣿⣯⣭⣭⠴⢞⡟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣝⣛⡛⠛⠦⣤⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠶⠶⠶⠦⠤⠤⠤⠴⠶⠶⠶⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠛⠻⠛⠛⠒⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⢀⣀⣤⠴⠶⠶⠖⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢠⡾⠛⠁⣀⣤⠶⠖⠛⠛⠛⠶⣄⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣿⡄⠀⠀⢿⣅⣀⣠⡄⠀⠀⠀⢈⡇⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠈⠛⠷⣦⣄⣀⣉⠀⢀⣀⣀⣤⠾⠁⠀⢀⣴⡿⠃⠐⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⣶⣤⣄⣀⡀⠀⠉⠉⠉⠉⠉⠉⣁⣠⣤⡾⠟⠋⢀⡆⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠀⠀⠈⡇⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⢸⡇⠒⠶⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣀⣄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢿⣿⣷⠆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠐⠚⠋⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢠⣖⣂⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠻⠿⠛⠀⠀⠈⠙⠷⢤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣀⣈⠙⠛⠛⠛⠛⠛⠉⠀⠀⣀⣀⣠⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠒⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠠⠀⠀⠀⣀⢀⠏⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠉⠒⠊⠁⠉⢀⠄⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠀⠐⠂⠀⠠⠀⠠⠄⠀⠉⠭⠀⠀⢸⠀⢀⢀⡴⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡟⠛⠩⠵⠖⢂⡀⢀⠀⠀⠄⠠⠬⠭⠤⠤⠀⣈⠐⡂⠈⠀⠩⢠⣖⣮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⡿⣿⣿⣷⠶⣶⣶⣬⣤⣀⣈⣉⣉⣉⣁⣀⣨⣥⣴⣶⣶⣶⣶⣶⣭⡵⠋⠁⣠⠴⠒⠛⠙⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡃⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠀⠈⡛⠛⣛⠛⠻⠯⣽⣿⣿⣿⡇⢸⡣⠀⣯⠄⢀⣠⠴⠶⢤⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⣐⣒⣛⣻⣭⡭⣖⡂⠠⢒⢠⣇⡴⠋⠀⠀⠀⠀⢹⡄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠠⠍⠉⠒⢚⣛⣋⡭⠴⠀⡵⢨⡏⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠐⢒⡂⠈⣉⣭⠭⠶⢒⡋⠠⠆⢸⠇⠀⠀⠀⠀⠀⠀⡼⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠬⠄⠠⠤⠴⠶⠖⢚⣛⣩⠀⢒⠁⢸⠀⠀⠀⠀⢀⡠⠞⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠂⣐⣛⣩⣭⠥⠖⢀⡉⠀⢸⠀⠄⠐⠊⠉⠀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠅⠠⠬⠵⠶⢒⣚⣁⠀⢒⠀⡾⠉⣀⡤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠐⣚⣛⣭⡭⠵⠖⢈⠅⣸⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⢠⣴⣶⣾⠏⣑⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣤⡤⠤⠬⢷⣄⠒⠀⠀⠀⠀⠀⡄⢨⣤⠈⣥⣤⣭⣽⣿⡟⠳⢀⣴⣿⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⣠⠴⠖⠚⠉⠉⠙⠒⠀⠀⠠⠤⠤⠒⠒⣛⣻⠶⠥⠀⠀⠀⠈⠄⢩⣀⣼⣿⣿⡿⠧⠽⢶⣿⣛⠲⠿⠿⠿⠤⣤⣭⣉⡉⠉⠛⠳⣶⣦⣄
⠀⠀⠸⣅⢤⣠⣆⠀⠀⠪⠅⠀⠀⠀⠀⠀⠣⠀⠀⡈⠒⠠⠤⣤⣀⣀⣀⣀⣂⣀⣶⣿⣿⣧⡷⠞⠁⠠⠤⠂⠀⠠⠄⠀⣀⣨⠽⠂⣀⡄⣈⠵⣸⠇
⠀⠀⠀⠈⠛⠾⣭⣛⡓⠲⠶⠦⠤⢤⣭⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣨⣥⣤⣀⣀⣀⣰⣶⣶⣶⣾⣥⡤⠴⠶⠶⠒⢛⣉⣭⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⢤⣤⣤⣄⣀⣀⣀⣀⣉⡉⠉⠉⠩⠉⠉⠉⠭⠉⠉⢉⣉⣉⣉⣉⣀⣀⣀⣤⣤⡤⠶⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⠦⠀⠀⢸⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡷⠀⠈⠃⣿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠁⠀⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄
⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⢠⣾⣷⣾⡟⠁⠀⠀⣐⣂⣨⣥⣤⣀⠐⠶⣻⣿⡇⡄
⠀⠀⠀⠀⠀⠻⣄⠳⡀⠀⠀⠀⠉⠙⠛⠛⠻⠧⠦⠬⠉⠿⠧⠌⠻⠓⢊⣻⣥⣾⣷⡟⠞⠐⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠍⣻⣿⣿⡿⢻⠋⠀⠐⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠹⡇⠀⢀⠄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢴⡾⢱⢿⠟⠁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢂⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⠷⠖⠊⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠻⠧⣕⢽⣦⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣿⣿⣿⣷⡒⠢⣀⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⢔⡀⠙⢿⣷⡀⠠⣤⣤⣀⣠⣿⣷⣾⣿⣿⣿⡿⠟⠊⠀⠈⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠀⠈⠠⢄⠀⠓⠞⣐⡔⠀⠹⡌⠀⠀⠀⠌⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⣤⣄⣀⡀⠷⠦⠄⠀⠀⠀⠀⠀⡠⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠙⠛⠛⠿⢟⠗⠛⠛⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠈⠠⠄⠄⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡴⠚⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⡀⠀⠈⠉⠙⠒⣤⠂⠀⠀⠀⠀⠀⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⣶⡇⡻⢿⣿⣿⣷⢆⡀⠈⠁⠈⣥⠀⡘⡄⣴⠄⠙⣿⡆⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡙⢾⣿⣿⣷⣦⠉⣿⢿⣿⠀⠐⣬⠠⢄⣢⣴⣷⣿⣿⣦⣷⡿⠃⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣬⣙⡛⠿⠿⢶⣶⣾⣷⣶⣶⣾⣿⣿⣿⠿⠿⠛⠋⠁⠀⠐⠒⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣮⣇⠘⠍⠛⠛⠛⠓⠶⠶⣤⠬⡭⠥⠤⠔⠒⠀⠀⠈⠀⠀⠀⣠⠀⠀⠠⠄⠈
⠀⠀⠀⠀⠄⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⠢
⠀⠀⢀⠀⠈⣻⠟⢽⣷⡿⣿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠛⣎⠂
⠀⠀⡄⠸⡀⠈⣷⣾⢿⣾⣏⣿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⣿⣿⠀⠈⣿⡿⡷⣶⣤⣤⣀⣀⣀⠠⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣤⣶⣤⣿⣿⣷⣶⠟⢂⡄⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⣤⣤⡤⠀⠀⠀⢠⠖⡐⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠻⠿⣿⠶⠀⠙⠛⠃⠉⠀⠀⠀⠀⠀⠀⠛⠿⠃⠀⠀⠹⠛⠿⠓⠀⣠⠔⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣖⠯⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢠⣖⣚⣛⣋⣉⣉⣉⣭⣭⣭⣭⡭⠭⠭⠭⠭⠭⠭⠭⠭⢭⢭⣭⣉⣉⣉⣛⣛⣓⣶
⠀⠀⣼⣉⠟⠉⣉⠟⢙⣟⡖⠒⢒⡶⢶⢲⡖⠒⡶⢲⢶⠖⠒⢒⡶⢒⣿⡟⠉⣹⢋⡟⢹⡆⠀⠀⠀⢀⣀⣀⡀
⠀⠀⣿⣻⠒⢚⡷⠶⣿⡿⠶⠾⠯⠦⠾⠯⠴⠾⠥⠾⠧⠶⠾⠿⠶⠾⢿⣶⠾⢷⡟⠺⣿⡇⣠⠶⢯⠉⠙⡏⢹⡟⢦⡀
⠀⠀⣿⠁⢠⠟⢿⠞⠁⢀⡴⠒⠚⠛⠒⠲⣄⠀⠀⢀⡴⠚⠉⠙⠓⢦⡀⠈⢳⡿⠻⡄⠈⡟⢻⣄⡼⠷⠾⠧⣼⡁⢀⡿⡆
⠀⠀⣿⠀⣾⢷⡏⠀⢰⠋⢀⣠⠤⢤⡀⠀⠈⣧⢀⡏⠀⠀⣠⠶⣄⠀⠹⡄⠀⢻⣋⣿⠀⣧⡞⠁⠀⠀⠀⠀⠀⠹⡟⢀⣿
⠀⠀⣿⠀⣿⣺⡇⠀⢸⠀⠈⢧⡀⢀⡟⠀⠀⣼⣼⡇⠀⢸⣁⠀⣸⠆⠀⣿⠀⢸⣏⣻⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡞⢸
⠀⠀⢻⢀⣿⣺⣇⠀⠘⢧⠀⠀⠉⠉⠀⢀⡴⢛⣛⢷⡄⠀⠈⠉⠁⠀⢠⠏⠀⣼⡉⡿⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣾
⠀⠀⢸⢸⡈⢧⣼⣦⡀⠈⠙⠶⠤⠤⣴⢋⡜⣡⣌⠳⡝⣶⠤⠤⠤⠖⠋⢀⣴⣿⡽⠁⡇⡇⠀⠀⠀⠀⠀⠀⠀⣰⣋⣀⣸
⠀⠀⢸⡆⢧⡈⠻⣄⣿⠶⣤⣤⣤⠴⡏⢸⠈⢧⡸⠃⢷⢸⡦⣤⣤⣤⠶⣿⣤⠞⠁⡼⢡⡇⠀⠀⠀⠀⠀⠀⡴⠛⠛⢻⠏
⠀⠀⠈⡟⢦⡑⢦⣈⠙⡷⢋⡤⢭⡳⣷⠸⡄⠀⠀⢀⡟⣸⠟⡩⠥⣍⢳⡋⣁⡤⢊⡴⢻⠇⠀⠀⠀⠀⣠⠾⢧⡀⣰⠋
⠀⠀⠀⣇⠀⠉⠲⢬⣙⡇⢿⡀⢦⠗⠈⢳⡙⢆⣠⠎⡴⠃⠸⠴⠆⣽⢸⣏⡥⠖⠋⠀⢸⠀⠀⢀⣠⠞⣿⠀⣨⠟⠁
⠀⠀⠀⢻⠀⠀⣠⠴⢮⡻⣄⠓⢦⣀⠀⠀⢹⣌⢡⡾⠀⠀⢀⡤⠞⣡⠞⡵⠲⣄⠀⠀⣾⣠⡔⢻⡇⢀⡼⠟⠁
⠀⠀⠀⢸⣆⠀⠙⠦⠼⠃⠘⣗⣦⣈⠳⣄⠀⣿⢻⠃⣠⠞⣉⣤⣺⡇⠈⠧⠴⠚⠀⣠⡏⢸⣇⡤⠟⠉
⠀⠀⠀⠀⣿⣓⠦⠤⣤⣴⠊⠉⠀⠈⠑⢮⢳⣸⣟⡴⣡⠞⠁⠀⠈⠙⢦⣤⡤⠴⣚⣽⠗⠋⠁
⠀⠀⠀⠀⢹⡈⠉⠛⢺⡇⠀⠀⡴⠒⠦⣄⢳⣿⣿⡟⣡⠴⠒⢦⠀⠀⠈⡗⠛⠉⢁⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⢧⡀⠀⠳⣄⡀⠈⢧⢿⣿⣰⠃⠀⣠⠞⠀⠀⡼⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⢻⠶⠤⣤⣀⣙⣦⣄⣀⠉⠓⢮⣿⣿⡧⠖⠋⣀⣠⡴⢚⣀⣀⣤⠴⡏
⠀⠀⠀⠀⠀⠘⣇⡴⠋⠁⠈⠉⠉⣩⠿⠛⠛⠛⢻⠛⠛⠛⢯⡉⠉⠉⠉⠙⢦⣼⠃
⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⢤⣤⣾⣁⣀⣀⣀⣀⣾⣀⣀⣀⣀⣹⣤⠤⠴⠖⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⡾⣛⢿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡸⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⣿⣿
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠧⠚⠁⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣘⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⣻⢿⢿⣿⡿⣻⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠒⠒⠒⠒⠶⠶⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣚⣭⠥⠶⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠛⠒⠲⠦⢭⣙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠽⠛⠉⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠈⠙⠲⢬⡑⣆
⠀⠀⠀⠀⠀⠀⡞⡿⠁⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣀⠀⠀⠀⠉⠙⠲⢤⣀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢷⣠⠞⠁⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠴⠋⠀⣠⣄⠈⢧⠀⠀⠀⠀⠀⠀⠈⡷⢋⣼⡇⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡍⠦⣙⠲⣄⡀⠀⠀⠀⠀⣏⠀⠀⠀⣤⠤⠤⠾⠁⠈⣧⢸⠀⠀⠀⢀⣠⠴⣋⡵⢋⡼⠗⠋⠉⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠈⡇⠀⠈⠓⠦⣍⣓⠲⠦⢤⣼⣦⣀⣀⣻⣄⣀⣀⣀⣠⣯⣾⠴⠖⢛⣉⡴⠚⠉⠀⣏⠀⢀⡤⠖⠛⠉⠙⠲⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⠤⣭⣉⣉⣉⣉⣉⣉⣥⠤⠴⠖⠚⠉⠁⠀⠀⠀⠀⠉⣻⠉⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠉⠛⠒⠒⠒⠒⠋⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⣀⡴⠚⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⠤⠤⠤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠛⣆
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢧⡙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⣿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣍⣙⡛⠒⠒⠒⠶⠶⠒⠚⠛⣉⣉⡤⠴⠋⠁⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠈⢿⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠳⠯⣝⣒⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⣒⡯⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠬⠭⣭⣝⣛⣛⣛⣛⣛⣛⣛⡭⠭⠵⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠄⣀⣐⡲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣠⣌⣀⡛⣀⣂⡀⠀⠠⠄⣠⡄⠉⠻⠶⣿⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠁⠠⠰⢆⣤⡙⣿⣹⣦⡀
⠀⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡈⠋⠑⢘⣿⣿⣧⢀⡀
⠀⠀⠀⠀⠀⢸⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣨⣛⣿⣿⠏⣸⡄⣠⡶⠛⠛⠳⣆⠀⡀
⠀⠀⠀⠀⠀⠸⣷⣤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣿⣿⠋⠀⠀⠀⠀⣿⣧⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣍⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠄⣼⡏
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣽⡦⡁⠠⡍⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢜⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡬⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⠘⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⣌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣾⣿⡀⠀⢦⣄⣀⡀⠀⠀⠀⠀⠀⡀⢤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⠶⠿⣿⠷⣼⠤⠤⠶⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣣⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠁⢁⠃⠀⠈⠉⠉⠙⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⢀⣀⣠⣤⣤⣼⣤⣤⣤⣤⣤⣀⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⢹⣤⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⣀⡤⠒⠹⡇⠀⠙⠻⢯⣟⣻⡿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣻⡯⠷⠋⠁⠀⡟⠑⠢⣄⡀⢨⣿
⠀⠀⢀⡠⠞⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⣹⢏⡟
⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣠⡤⠖⣋⡴⠋⠈⢦⡀
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣩⡤⠖⠋⠁⠀⠀⠀⠀⢷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢶⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢀⣠⠴⠃⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⣠⠞⠋⣡⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠈⢳⡄⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⣴⠇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡞⠁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣫⠖⣀⣠⣤⣴⣶⣶⣶⣞⣛⣛⣛⣛⣒⣒⠶⠦⣤⣄⡀⠲⣌⠙⣆⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡾⠃⣟⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠁⢀⣠⡟⠙⢳⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣿⠁⠀⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣹⠃⣀⡼⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠚⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠙⣧⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠥⣤⣴⠖⠋
⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡾⠁⡼⣡⣿⠧⠴⠤⣤⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⡇⡼⢿⣷⣖⣒⣛⣭⣿⠧⠴⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣌⣻⠷⠾⢯⣍⣉⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⠤⢤⣤⣤⣤⡤⠤⠤⠴⠶⠒⠛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠠⠀⢀⡀
⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣿⣻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡔⢵⠄⠀⠒⠒⠒⠒⠒⠒⠒⠂⣤⢱⠄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠁⠀⠐⠙⠒⠒⠒⠒⠂⠈⠀⢸⠑⠈⡆
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠌⡸⠁
⣿⣿⣿⣿⣿⣯⣝⢿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡠⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠶⡈
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢄⠘⢄⡈⠑⠒⠠⠤⠤⠒⠁⡠⠃⢀⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠒⠁⠄⠈⠠⠶⠊⠑⠂⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⢀⣠⠤⠴⣒⣚⡭⠭⠭⠭⢭⣉⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⣠⠴⢚⡩⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢆⢸⡆⢒⠢⢤⣄
⠀⠀⠀⠀⠀⢀⣤⡤⠀⢀⣤⣶⣶⣶⣿⣷⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠉⠛⢮⡹⣄
⠀⠀⠀⠀⠀⠈⠙⠃⠀⠻⣿⠛⣹⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠳⣄⠀⢻⢸
⠀⠀⠀⠀⢀⣤⣶⣃⠀⢰⠃⣼⠁⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⢹⠀⠀⡸
⠀⠀⠀⢀⣿⡿⠛⠉⠀⠸⣄⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⠚⠉⠉⣉⡿⠊⠀⠀⠀⠀⢸⠀⢀⡟⢀⡴⠁
⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠘⣷⣄⡉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣧⠴⠞⠉⠀⠀⠀⠀⠀⠀⢸⡷⢋⣴⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢦⠉⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⢸⡇⢈⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢉⣉⡉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⣨⠇⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠓⠦⣤⣄⣀⣀⣀⣠⣤⠴⠞⠋⠉⠀⣠⡴⠛⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⢀⠔⠀⣴⠋⠀⠀⠀⠀⠁⠀⠀⢀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠃⢄⠀⠙⠳⠶⠶⠶⠶⠒⠛⠛⠉⠉⠀⣀⠀⠀⠀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠭⠁⠒⠒⠒⠒⠀⠀⠀⠀⠂⢊⣉⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠲⠶⠖⠒⠒⠚⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⢤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣋⠥⠔⠒⠒⠒⠐⠒⠒⠒⠤⠭⣙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣴⣶⣶⣚⣽⣿⡿⢣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣮⣭⣛⣛⣛⠛⠿⠿⠿⠛⢛⣛⣛⣭⣵⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡛⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠚⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⣀⣤⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⡉⠛⢦⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣠⣤⡇⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢀⡞⠁⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠸⡇⠀⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠹⣄⡈⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠈⠙⠓⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢻⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⡤⠤⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⣀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠁⠀⠀⣀⡀⣠⣤⢠⣤⠤⠤⠤⣤⢤⣤⣤⣌⣀⠀⠀⠀⠀⢰⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠉⠀⠄⠁⢠⡤⠀⠀⠀⠀⠀⡶⠿⠿⠟⠿⣿⣿⣿⣶⣧⣄⡈⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠦⠀⠀⠀⠀⢠⠀⠰⣖⣀⣠⣤⣤⡶⠂⠀⢀⠀⠉⠉⠙⠃⣭⠉⠻⣿⣿⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢦⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢁⠀⠁⢙⠂⠔⠚⢛⣻⣦⣀⠀⠙⢀⣀⣿⣿⠇⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡙⠒⠤⣀⣀⠀⠀⠀⠛⠁⠈⣉⠑⢀⡀⠀⠀⠶⠿⠿⡶⢶⡯⠟⣁⡴⢳⣾⠃⢀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢶⣦⣮⣍⠁⠀⠀⠀⠀⠠⠶⠿⠷⠤⠰⠿⠒⢛⣍⣡⠀⠀⣿⣿⣰⣿⡟⠉⠉⠻⣖⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⢀⣰⢶⠗⠀⠈⠉⠛⡀⠘⠃⣿⢿⣿⠁⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣼⣏⣀⣠⣴⠿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⣅⣉⣉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠷⠊⠙⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣟⠿⠿⢷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠠⠃⠀⠀⠀⠀⠀⠴⣻⣷⣵⣆⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⣰⠽⣿⡿⣋⡬⣿⠀⠈⠀⡈⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⡁⢹⣧⣠⣹⣿⣆⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⢀⣩⠾⣿⡾⣥⣾⣷⠤⡀⠀⠐⠀⠘⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⣹⣭⣿⡋⠥⣺⠏⣻⣷⣷⣦⣄⣀⡀⠀⣀⠀⡂⢀⣉⣀⣴⣾⣿⣱⢊⣽⣓⣺⣿⣾⡷⠏⠀⠁⠀⢀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣡⠀⢀⠉⠉⠛⠻⠿⠿⢿⣿⣿⠿⣿⡿⠿⠿⣿⣻⢍⣫⡙⣌⠛⠉⠀⠀⠀⠀⢀⠠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣥⠬⠋⠀⣴⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠋⠛⠉⠀⠀⢀⣥⢴⢊⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⣀⣀⣀⠠⣄⣀⠀⡀⠤⣶⢎⢃⠈⠿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠂⠀⠂⠁⠁⠀⠀⠀⠘⠓⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⡄⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠸⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⢰⠇⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢃⡞⠀⢸⢻⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣼⠁⢀⠃⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⣰⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠛⢛⣉⠹⡄⠉⣻⡀⣀⣀⣀⠒⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣾⣛⠉⠉⠁⠀⠈⠁⠀⠑⠀⠈⠉⠉⠉⢒⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠛⠛⠛⠒⠶⠶⠶⠶⠶⠖⠒⠒⠛⠋⠉⢁⣸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣤⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠔⣫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⠊
⠀⠀⠀⢀⣠⣤⡴⠶⠞⠛⠛⠋⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⡾⠋⠉⠀⠀⣀⣠⣤⣤⡶⠶⠖⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦
⠀⢿⡄⠀⠀⢰⡾⠋⠉⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⠀⠀⠀⢠⠃
⠀⠈⠻⣦⣀⠘⠷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠉⠛⠷⢶⣬⣭⣙⣛⡛⠛⠷⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⠒⠒⠛⢉⣉⣀⡠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣽⣿⣽⣭⣿⣯⣭⣽

⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⡀
⠀⣰⣾⠿⢟⣛⣫⡭⠭⠭⠭⠒⠒⠒⠒⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠉⢛⣛⡻⢿⣶⡄
⠀⣿⡟⠻⠧⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠿⠟⣿⡇
⠀⣿⡇⠀⠀⠁⠀⠂⠉⠿⠭⠭⠽⠿⢿⣛⣛⣛⣛⣛⣛⣛⣻⠿⠿⠯⠭⠭⠿⠛⠚⠃⠀⠁⠀⣿⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠛⠉⣉⣉⣉⡉⠛⢿⣶⡄
⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⠿⠟⠛⠛⠿⣷⣄⠙⣿⡆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣾⡿⠁⠀⠀⠀⠀⠀⠈⣿⣇⢹⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢠⣿⡇
⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣸⣿
⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢰⣿⠇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⣰⣿⠋
⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣴⣿⠟⣡⣾⡿⠁
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣠⣴⣾⠿⠋⣡⣾⡿⠋
⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠟⠛⠉⢀⣤⣾⠟⠋
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⣾⡿⠋⠁
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⣿⣷⣶⣶⣶⣶⣾⣿⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣠⣄⠀⡀⠀⣀⣀⡀⣀⣤⣴⣤⣤⣤⡤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣮⡬⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠛⠛⠛⠛⠛⢛⣛⣶⣶⣶⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⢠⣟⡀⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⣼⣿⠡⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣠⡿⠃⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣟⢠⡿⠁⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣯⣾⠟⠃⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡂⢠⣄⣠⣤⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣾⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⢖⠒⠷⠘⠚⡛⠛⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣬⣤⣤⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠠⠿⣴⣊⠁⠀⠈⠉⠛⠿⠿⠿⠿⠭⠽⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣤⣄⠶⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣤⣤⡭⠽⠟⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠀⠀⠀⣀⡽⢷⠲⠾⡋⠁
⠀⠀⠀⠀⢀⣀⡾⠤⣀⣀⡀⠤⠤⠔⠒⠊⢉⣁⠤⢊⣠⠔⠛⡄
⠀⠀⠀⢠⣏⠀⠓⠤⠤⠤⠤⣄⣒⣒⠪⠭⠅⠒⠉⠁⠀⣀⡤⠃
⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⡠⠤⠶⠒⠉⢹
⠀⠀⠀⠀⠁⠒⡖⠒⠒⠒⠓⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠔⣒⡩⠔⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⢸⠤⣬⠭⠭⠭⠭⠥⠤⠶⠒⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠠⢦⠢⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⡇⠸⡄⢰⠀⠀⠀⠀⠀⢁⣀⡤⠔⠒⠛⠉⠉⠉⠉⢉⠉⠉⠓⠒⠢⢄⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠄⣧⠌⠀⠀⠀⣠⠔⠋⡀⠀⠀⠀⠁⢀⡀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠑⢤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣀⣀⣀⡠⠤⠤⠔⢒⠟⢁⠀⠈⠀⢀⠀⠀⠀⠀⡀⠀⢀⢤⡀⠀⠀⠀⠐⠀⠀⠤⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠉⠀⠑⡀⠀⠀⠀⠀⡀⢀⡀⠀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠘⠀⠀⠂⠀⠀⠀⠀⠈⠉⢉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠁⣀⣈⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠸⣇⠉⢢⠀⠠⠀⠀⠀⠈⠀⠠⡀⠀⠀⠐⠀⠀⠈⠀⢠⠤⢦⠘⡅⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠐⠐⠒⠒⠊⠉⠙⢅⠀⠙⠒⠒⠊⠉⠳⣔⠄⠀⠀⠀⡠⠊⠉⢢⠀⢹⡄⠙⢾⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⣀⡀⠀⠈⠑⠒⠒⠋⠀⠀⠀⣈⣶⠾⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⢒⡚⠛⠛⠉⠉⠉⠉⠛⠛⠓⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣤⣼⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⠀⠉⣳⣀⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠫⠀⢀⣀⣀⡀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠈⢣⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡶⠞⣋⠔⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠘⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⣤⡒⠊⠁
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠈⠢⣝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠂⢄⠈⠓⢄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⡒⠠⠤⠤⠤⠤⢤⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣁⣐⠂⠀⠀⠤⠀⠀⠀⠀⠀⠠⠄⠀⠀⠒⣀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠤⠤⢴⣾⣷⣤⣤⣤⣤⠤⣤⣽⣿⣽⣿⣿⣦⣀⣐⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⣾⣿⣿⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⣿⣟⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⣸⡟⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣟⢠⡟⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⡿⠋⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣀⡤⢰⣢⣴⣤⣶⣴⣶⣿⣷⣧⣤⣀⠀⠀⠀⠄⢠⣼⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⢰⣝⡛⠯⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⣤⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣻⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠶⠶⠦⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣀⡠⠤⠒⠒⠉⠉⠁⠀⠀⠀⠀⣀⣀⣤⠤⠶⠚⠉⢸⣋⣁⡈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠲⠶⠶⠶⠶⠖⠒⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⡿⠀⠀⡽⠀⣼
⠀⣠⣄⠤⣄⣠⠤⢤⣀⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣠⠞⠀⡴⠃
⡼⠁⠊⠀⣏⠀⠈⠀⢀⡼⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⢁⡴⠊
⠳⣄⣀⡼⢭⣉⠉⢉⡡⠴⠒⠢⢄⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠖⠁
⠀⡞⡡⠂⠀⡸⢲⣋⡔⠂⠀⢀⡼⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠓⠒⠋⠁⠀⠈⠳⠶⠒⣋⡤⠖⠒⠛⠉⠉⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠤⠤⠀⠀⠀⠄⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠐⠀⠀⠀⠀⠈⠓⠶⠶⠤⠤⠴⠶⠶⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠴⠒⣊⣩⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠯⢭⣽⣓⣒⣒⣒⣒⠒⠒⠒⠒⣒⣒⣛⣉⣉⣉⣩⡭⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣵⠟⠋⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠐⢄⣀⣠⠾⠟⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣧⡹⣆⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⢷⣄⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣝⢷⣄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢶⣝⢷⣿⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⢹⡇⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣤⣀⣀⠀⠀⠀⢿⠐⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⣿⠿⠶⢒⣂⣄⣀⠘⣧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣭⠿⠿⣿⣷⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣼⡁⠀⠀⠈⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⡀⠀⠈⠑⠀⠀⢀⡿⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢤⣤⣀⠀⢸⠃⠈⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠐⠀⠘⠀⠀⠡⠴⠶⠶⣬⣝⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣠⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⠖⠀⢹⣧⡙⠀⠀⠀⣄⠀⠀⠀⠀⠐⢶⡄⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⣧⡟⠀⠀⠀⢸⠈⢟⡳⠶⣤⣍⣛⠛⠻⠤⠶⠟⠁⠀⣠⡿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣄⠀⠀⠘⡆⠀⠉⠛⠶⢦⣭⣭⣓⡢⠄⠀⠠⢊⣵⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⢦⡄⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⠐⠋⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡾⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⢡⠖⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠰⢤⣉⠳⣄
⠀⠀⠀⠀⠀⠀⣿⠀⢾⡀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⡼⠃⡀⠀⠀⠹⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠘⣧⡈⠻⢦⣄⡀⠀⠀⠳⣤⣈⠙⠻⠶⠶⠶⠶⠟⠋⢀⣠⠇⠀⠀⣰⡏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣭⣛⣻⡶⣦⣤⣍⣛⠻⠶⠶⠶⠶⠶⠛⠋⠁⠀⢀⣴⢟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣷⣶⣤⣀⠀⠀⠀⠀⣠⢞⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣄⠀⠰⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⠇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢠⡏⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡾⠀⢀⡾⠀⠀⣰⠏⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿⠀⣸⠇⠀⣼⠃⠀⣰⠏⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠛⢹⡇⠀⣿⠀⢠⡏⠀⢠⡏⠀⢀⡞⠘⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣩⡴⠞⣋⣁⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡃⠀⢸⠇⠀⠀⠒⠤⣌⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣿⣾⣟⣭⣤⣴⣾⣇⣶⣿⣰⣾⡇⣶⣾⣧⣦⣾⣠⣄⣈⠙⠲⣦⣝⠂⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠖⠀⣀⣴⠟⢸⣛⡷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠙⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⣁⣀⣠⣤⠶⠟⣫⣴⡇⣚⣛⠲⢤⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⢋⣉⣩⣥⣴⡾⠿⣛⣥⠀⠉⠉⠙⢷⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⠃⢹⣟⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣉⣉⣭⣴⣶⠿⢛⡅⠀⠒⢂⣠⢿⢏⠄⣾⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠾⣛⡭⠔⣀⠀⠀⠀⢿⡛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⣛⣋⣩⣥⣶⠾⡛⢡⡶⢞⣫⣵⡿⢋⡾⢣⣄
⠀⠀⠀⠀⢀⣴⠏⣡⠞⢫⡴⢋⣡⠔⠀⠀⠈⢿⡷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⣛⣋⣭⣵⣶⠿⢡⣾⣿⠿⣛⣭⠾⠋⠀⠠⡉⢳⣄
⠀⠀⠀⠀⣼⠃⣸⡏⢰⡏⠠⡟⠁⣴⠉⠀⠀⠈⢻⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣛⣋⣩⣭⣶⠞⣡⣿⣷⣶⣿⣿⣷⡄⢦⡘⢦⢹⡄⢻⡆
⠀⠀⠀⠀⢹⣆⠸⣧⡈⠷⣄⡻⢦⣌⠳⠤⠀⠀⠀⠙⢿⣖⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣩⣭⣭⣶⣾⣴⣿⣯⢿⣿⠹⣿⡌⣿⠈⡧⢸⠀⢁⣼⠃
⠀⠀⠀⠀⠀⠙⢦⣝⠻⣶⣌⡛⠶⢬⣝⡓⠀⠀⠀⠀⠀⠙⠿⣷⣶⠦⢤⣤⣤⣤⣬⣭⡭⢷⣿⣿⣿⣿⠿⣣⣿⡟⣸⣿⢀⣿⢣⠏⣰⠃⢈⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠰⠿⠷⢦⣍⣛⠷⠶⣤⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⢖⣛⣛⣛⣭⣥⡶⠿⢛⣩⣾⠟⠡⠞⠁⢀⣠⣤⣾⣿⡿⠯⠍
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣿⣷⣶⣦⣬⣅⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣭⣭⣭⣭⠵⠶⠶⣛⣛⣉⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣯⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠶⠶⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣋⣉⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢉⡛⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⡗⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⣠⠔⠒⠋⠉⠉⢉⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⢁⡴⠋⠀⠀⠀⠀⠀⡾⠋⠉⢳⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠶⠾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⣿⠁⢀⣴⠟⠛⠳⣄⠀⠙⢦⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⢸⡇⡞⠉⠇⢸⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢿⣇⠘⣇⠳⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢿⡆⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢸⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⣤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣈⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠺⣿⡁⢀⣠⠤⠶⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⢀⣽⠇⢀⣿⣄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⠤⠤⠤⠶⠒⠒⠒⠛⢉⣡⡴⠟⠉⣿⣯⣥⣌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠉⠉⠀⠀⠀⢸⠟⠁⠀⠘⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⣴⡃⠀⠈⠓⠠⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣲⠄⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠈⠛⠦⠤⠀⡀⠀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⢤⣤⣀⣀⣀⣀⣀⣀⡀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣂⠀⠀⠀⠀⠒⠀⠛⠈⠀⠉⠀⠀⠀⢀⠂⢀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣂⡴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⣀⡀⠀⠀⠀⠉⠙⠒⣤⡐⠠⠀⠀⠀⠀⠀⠀⢤⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠋⠀⢀⣠⣴⠀⢾⣶⢾⣷⣿⣶⣤⠀⠁⠐⠃⠄⢙⣁⠀⠰⢆⢀⣤⠀⠙⢷⣦⡀⣤⡀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣧⣰⣿⣿⣿⣄⠉⢴⢿⣿⣿⣿⡇⠙⡀⠰⡄⠀⢈⠋⣀⣲⣼⢶⣿⠀⢦⢸⣿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣌⠛⠿⣿⣿⣿⣧⣄⡰⣛⠩⠛⣇⠐⠐⠟⣈⣫⣴⣾⣭⣿⣿⣿⣿⣷⡿⠟⠃⠀⠀⣠⠆⠄⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⢿⣶⣤⣈⣉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠋⠉⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣽⡄⠘⡌⠙⠛⠛⠛⠛⠷⢶⣶⣦⡤⢤⠤⠤⠤⠴⠒⠒⠀⠈⠀⠁⠀⠀⠀⢀⠀⠀⠀⢀⣠⠒⠁
⠀⠀⠀⠀⠀⢀⠀⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠈⠀⠠⢄⡐⢄
⠀⠀⠀⠀⠐⠡⢪⣿⣿⢟⣭⣹⣿⣿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡑⢤
⠀⠀⠀⠐⢀⠀⠱⢫⡁⣻⣿⠛⣛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢁
⠀⠀⠀⠁⠸⠆⠀⠹⣿⣿⠻⣿⣿⣥⣟⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣿⢿⣿⣿⠀⠀⠨⣿⣿⡿⢶⣦⣤⣄⣀⣀⣀⣀⣀⣠⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⢉⣣⣀⣸⣿⣷⣿⣤⣽⠷⠶⠌⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣱⠌⡐⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠠⡀⠀⠀⠀⠰⣿⣿⣿⣿⣛⠛⢻⣿⣿⣄⠴⠋⠀⠀⠀⠀⠀⠀⠠⣶⣖⣦⠀⠀⢠⣾⣿⣿⣿⣭⠀⠀⡀⢀⡼⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⢉⡁⢀⡠⢞⡩⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⢖⣺⠥⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠉⡉⠡⠀⠂⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠛⠛⢛⡛⠻⠯⣶⣢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣻⢟⡭⠚⢁⠠⠤⠀⠠⣄⠈⣉⠉⠑⠲⠬⣙⠪⣝⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣩⢞⣟⡵⢋⠔⡨⠔⠊⠀⠀⢈⡫⡠⠀⠀⠀⠀⠐⠪⡙⠦⡙⢿⣮⣙⡦⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠋⢠⢯⠞⡀⣠⠊⠀⣠⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠈⢢⠘⢎⢫⣧⠀⣀⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠋⠀⢀⡏⡏⡜⠰⠃⠀⠀⠴⠄⠠⠀⠐⠀⠀⠀⠠⠆⠀⠁⠄⠀⠀⠀⠈⠈⡏⣿⠋⠀⢠⢧
⠀⠀⠀⠀⠀⠀⢠⡟⡰⠁⠀⠀⢸⢸⠁⠃⠃⠀⠀⠀⠀⠈⣄⠀⡀⠘⠇⢀⠆⠰⠀⠇⠀⢸⠀⠀⠀⠀⢸⢸⣂⡴⠛⠒⠧⠤⠀⣀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣾⠸⡆⡆⢀⠀⡄⢂⠀⠁⠈⠓⠠⠦⣴⡅⠊⢀⠘⢀⠁⡎⠀⠀⠀⠀⢸⢸⣿⣶⣤⣄⡀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⢸⠇⠄⠀⠀⠀⠀⢻⡆⢧⠰⡈⢆⢘⣄⡢⣀⠀⠀⠀⠀⡈⢀⡼⢋⠔⡡⢊⠀⠀⠀⢰⢃⡟⣼⣿⡋⠋⠧⠙⢿⡖⠦⠤⠜
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷⡘⣆⠀⠀⠀⠙⠻⣶⡛⠷⢶⣤⡙⠈⣴⣵⠟⠊⠀⠀⠀⡰⢃⡞⣰⣿⠙⢃⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⣿⠰⠀⠀⠀⠀⠀⠀⡟⣷⣌⢧⡀⠐⢤⡀⠀⠈⠙⠲⢌⠻⢸⠟⠁⠀⠀⠀⡠⠞⣡⢏⣴⡿⠁⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣝⠲⣄⡈⠑⠢⠤⣄⠀⠐⠘⠀⠀⠀⢀⣠⡴⢋⣵⣾⡿⠃⠀⠀⠈⠘⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡳⠮⣍⣓⠲⠦⠤⠤⠤⠤⠴⠒⣚⣩⡤⠞⣋⡴⠏⢀⢀⠂⠀⢀⠆⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠙⠟⢷⣤⣈⡍⠛⠛⠛⠛⠛⠛⠋⢉⣠⡴⠞⠋⠀⠀⠡⢂⠄⢀⠌⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢢⠣⡈⠲⣍⠛⠻⠿⢷⠶⠶⠷⠛⠛⠋⠉⠀⠀⠀⡀⠜⠁⡁⢠⠊⡔⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⢑⠢⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢐⡨⢐⡡⢊⠔⣡⠎⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡐⠀⣀⠈⠁⠐⠂⠒⠂⠐⠀⡀⠤⠒⡡⠒⡡⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠨⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡠⢖⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣳⡶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢖⣊⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠾⢭⣭⣭⣽⣭⣭⣭⠭⠶⠖⠛⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠄⠀⠒⠶⠶⠶⠶⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠑⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣩⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢬⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣎⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠐⠲⣶⠶⣶⢶⣦⣤⣄⡀⠀⠀⠀⡁⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠳⢄⠀⠈⠲⣄⣀⣴⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⢀⣤⣿⣷⣿⣿⣿⣿⣿⣿⣷⡤⠚⠀⢀⡠⠚⣧⠖⠛⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠲⠦⣄⣉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⣁⣤⠴⠚⠉⠀⠀⡇⠀⠀⢀⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⢤⣭⣍⣉⣁⣀⣀⣀⣀⣈⣉⣉⣭⣭⠭⠴⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⢀⡧⠀⡜⠙⠻⡁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⠃⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠉⠀⠀⢀⡜⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⣠⠴⠚⠁⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠉⠀⠀⠀⣀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡀⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⡊⠑⠓⠦⣤⣀
⠀⠀⠀⢀⡠⠔⠛⠉⠁⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠓⠚⠁⠀⠀⠀⠀⠈⠙⠦⣄
⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠳⢄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⢀⠀⠙⠶⣤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠶⠋⠀⢄⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠙⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠄⣀⣀⡀⠉⠑⠛⠫⠭⠿⠿⠿⠝⠛⠛⠉⠀⠀⣀⣠⠴⠄⠒⠁⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⡤⠤⣰⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢝⡛⠳⠶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣿⡿⠿⠟⣫⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣉⣉⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⢉⣉⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠒⠒⠉⠉⠉⠉⠁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠶⠦⢤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠶⠦⠤⣤⣤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠬⢥⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣭⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠚⠭⠿⢿⣛⣛⣛⣛⣛⣿⣿⡿⠛⠿⠍⠑⠁⣠⠤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⢠⠥⠒⢲⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠃⠀⠤⠶⢚⣡⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⢒⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⣼⠶⠞⠫⠥⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⢈⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠀⢀⡀⠀⠀⠀⠀⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠈⠀⠰⢔⣤⣌⣓⣦⣤⣤⣤⣤⡤⠤⠴⠒⠁⣠⠴⠓⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⠤⠤⠴⠶⠶⠒⠛⠋⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⢀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣦⣦⣤⣼⣘⣶⣾⣿⣆⣿⣿⣷⣰⣶⣶⣶⣶⣦⣤⣨⡂⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉






⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⠶⣄⡀⠀⠀⠀⣠⠴⠒⠋⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⢰⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢀⣠⠤⠴⠖⠒⠛⠛⠋⠉⢉⣉⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣛⣛⣓⣒⣲⠦⠤⢄⣀
⣿⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⣿⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⢸⡇
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⠤⠤⠤⠤⣄⡀
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡀⠀⠀⠙⢦⡀
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠔⠋⠉⠀⠉⠳⣄⠀⠀⢳
⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢀⣤⣤⡀⢰⡷⢰⣿⢠⣿⣴⢏⡼⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢀⡜
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣾⢷⣼⣧⣾⢃⣾⠛⠛⢧⡴⠟⠁⠀⠀⠀⠀⠀⢀⡾⠁⢀⣀⣀⡤⠴⠒⠋⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣀⣿⣠⠟⠁⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠁⠀⢀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠠⣿⣷⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⠤⠴⠖⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⢀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


⣿⢿⠿⡿⡿⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠶⣖⡒⠒⠓⣟⣛⣷⣶⢦⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠟⠋⠉⠴⠞⠁⣾⡶⠊⠉⠻⠋⠁⠹⣮⣿⣿⣿⠿⣙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠁⠀⡜⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⣠⣿⡿⠛⠁⠀⢸⣯⡝⠻⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⢣⠀⠀⠀⠀⠈⠛⠻⢦⠀⣴⠿⠋⠁⠀⠀⢀⣠⣾⠏⠀⠀⢸⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⡟⠀⠀⠈⠢⠐⠠⠔⠒⣒⠠⡀⠀⠋⢀⣤⣤⠶⠶⠛⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⠏⣄
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠠⣀⣠⣤⣤⣠⣠⣭⡻⣤⣶⠟⢉⣀⣤⣤⣤⣴⣾⣷⣿⣿⣿⣿⣿⠿⡫⣾⣿⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣴⣭⣭⣯⣉⣉⠉⠛⣿⣾⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠈⠛⢻⣿⠁⡀⠴⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠄⠠⠀⠀⠀⠀⠀⠐⣾⠆⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡏⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡟⠀⠀⠀⠀⣠⠔⢋⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡏⠀⠢⠐⠚⠉⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠎⠀⠀⣀⣀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⠦⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠿⡖⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣶⠶⠟⠛⠋⠉⠉⣙⡛⠻⠽⣖⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣯⢟⡵⢊⡡⠤⠆⠀⢀⣤⠀⠄⠀⠉⠓⠦⢍⡓⢽⣷⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⢞⡽⡵⠋⢐⡡⠚⠉⠀⠀⠠⢝⡔⠒⠀⠀⠀⠈⠲⣍⠢⡝⢿⣦⡽⠖⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡱⠊⢀⣾⡟⡠⢠⠋⠀⠠⠖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠈⢢⠙⡎⢿⣧⣠⡴⠆⢹
⠀⠀⠀⠀⠀⠀⠀⡴⢃⠞⠀⠀⡼⡸⢰⢁⠃⠀⠀⠰⠣⠀⠂⠀⢀⣄⠠⢐⠁⠘⠀⡆⡀⠀⠀⠀⠘⡟⣿⠁⣠⣞⣆
⠀⠀⠀⠀⠀⠀⣼⠁⠋⠀⠀⠀⡇⡇⢸⠈⠀⡄⠀⠀⠀⠳⣄⠀⡈⠁⡔⠁⠘⢠⠀⠇⡄⠀⠀⠀⡀⡇⣿⡴⠉⠉⠉⠒⠀⠀⠠⣀
⠀⠀⠀⠀⠀⢰⡇⡄⠀⠀⠀⢰⡇⢻⠸⡈⡄⠰⡐⡄⠀⠀⠈⠉⠚⢾⠊⢠⡦⢀⡔⡰⠃⠀⠀⢠⠃⡇⣿⣿⣿⣶⢦⣤⣀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠂⢻⡘⣆⠣⠘⠌⢿⣬⣲⣤⣀⡀⠀⢤⡠⢏⣔⡩⡊⠑⠀⠀⢠⠎⡼⢱⡿⣾⡄⠘⠀⢩⣿⠉⠛⠋
⠀⠀⠀⠀⠀⡟⠰⠀⠀⠀⠀⠀⠸⣷⡘⣆⠀⠀⠀⠉⠛⠯⢭⡛⠷⣦⢠⡾⠟⠉⠀⠀⠀⡰⢋⡼⢡⡿⠃⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⠳⣄⠈⠲⢤⣀⠀⠀⠑⠎⢻⠃⠀⠀⠀⠐⢊⡴⢋⣴⣿⠁⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣳⣮⣛⠦⣤⣈⡉⠒⠂⠀⠀⢀⣀⣠⠴⢚⣩⡶⣫⡞⠁⢀⠂⠀⢠⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠿⣶⣍⢛⠲⠮⢭⣭⣭⣭⣭⣭⠴⠶⠚⢉⣥⠞⠋⠀⢂⠊⠄⠀⠄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠘⢌⠻⢷⣷⣤⣤⣄⣠⣠⣤⣤⠶⠞⠋⠁⠀⠔⡠⠁⠊⢀⠎⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⢄⠙⠢⣈⠀⢊⠉⠁⠀⠀⠀⠀⠀⠀⠠⠐⡨⢀⠔⡠⢃⠌⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢑⠬⡂⠅⠒⠄⠍⠉⣀⡀⠀⠀⠐⢂⠥⢚⡥⢊⠔⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢅⡂⠤⠄⠀⠀⠀⡀⠂⠈⠀⢀⠡⠒⠁⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⣗⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢖⣫⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⢯⣿⣛⣒⣒⣶⣶⣒⣚⣛⣭⡭⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠤⠤⠀⣒⢒⣒⣒⣀⣀⡀⠀⠀⠀⠀⢄⢐⣒⠒⡒⡒⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣬⣤⣶⠒⠀⠅⠁⠩⠚⠉⠈⠁⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠁⠀⠈⠘⢶⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡙⠿⢿⣡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠠⠄⣀⣪⡵⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠟⠿⠷⠶⣿⣥⣤⣤⣠⣄⣀⣠⣤⣤⣤⣭⣥⣬⣶⢶⡶⠶⠛⠛⠋⠉⡴⢒⡸⠁⣀⣤⠄⢀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠋⣿⠀⠠⣄⣀⡠⢈⣡⡭⣫⣖⣡⠴⠒⠒⠒⢦⡌⢻⣅⢲⣆⡒⠋⡁⠘⠼⠂⠇⢹⢫⠀⠀⠐⢕⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠉⠀⠀⠀⠈⠽⠿⢯⠘⠉⠑⠃⠀⠀⠶⡄⠀⠈⠀⠻⣶⠳⠍⢢⡝⡄⠐⢤⡆⠈⠆⠀⠀⠀⠀⢩⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠄⢦⠄⣠⡌⣄⢆⣠⡄⠋⠋⡠⠛⢲⡗⠻⠗⠀⠓⢈⣆⡗⢷⡄⢴⠇⠓⡈⠈⠁⠀⠀⠀⠀⠀⢽⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠁⠖⡨⣀⠹⢿⡉⠀⡠⢶⡄⠷⢴⡀⢛⣂⠀⠀⠈⡏⠁⠀⡇⣽⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡄⠀⣷⠀⢸⡇⠰⡦⢼⣿⡿⣸⡛⢤⣿⣷⠄⠀⠇⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⣧⠀⢸⡇⠀⠱⡏⡳⢖⡉⣡⠾⠀⠰⣶⣦⣴⣦⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠄⡸⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠇⠀⣭⣄⠸⣧⣄⣀⠀⠙⠉⠈⢀⣹⣿⡶⠟⣍⠉⣯⢄⣷⡾⠀⠀⡥⢄⠀⢀⠠⠊⠈⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠀⠀⢀⣃⣀⣻⠜⠛⢿⣻⢹⢶⡐⣤⣤⣻⡿⣺⣷⣇⣏⣼⡿⣯⣸⣤⠀⠀⣦⠀⢀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⡀⠤⣀⣀⣐⡒⢨⣶⡀⠀⠀⢨⡻⣟⢡⣶⣄⠉⢻⣼⢢⠇⠘⠻⣿⠳⢾⡻⢶⡧⠤⢀⣴⣎⠁⠀⠀⣿⡩⣤⡴⠶⢯⣑⠢⣄⣀⡀
⠀⢄⣬⣵⡾⡛⠯⣍⡭⣺⢿⣕⡶⢁⠀⠠⡬⢟⣿⠚⢯⡝⣠⣞⢻⣻⣄⠀⣻⣿⣶⣾⡇⣈⣙⣢⣴⡯⠙⠀⠀⡠⠱⣚⣱⠾⠶⠶⡉⣏⡶⠾⠭⣝⢢
⠄⣼⢟⣇⡹⠀⠀⠀⡯⠉⠠⠤⠀⠈⢣⣀⠠⢧⣾⣿⣦⣧⡈⢁⡼⣻⣯⡀⠉⠉⢈⣧⡻⣿⡿⣿⠉⠁⠀⢀⠞⠁⠈⠁⠀⠀⠀⠈⠵⣃⠚⠻⡗⢾⡇
⠀⡻⠜⣏⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠉⠳⣦⡀⢹⣯⣽⣿⣿⣿⡏⠛⠓⠀⠲⢿⣸⣍⣾⣷⠋⢀⣠⠞⢁⢄⢄⡄⠀⠀⠀⠙⠒⠠⠛⢈⣀⠴⢋⡴
⠀⠈⠒⠮⢭⣥⣀⣢⠤⡀⢀⣀⡂⠤⠨⠄⠀⠀⠈⢢⣍⢻⡿⠋⠛⠧⠀⠀⠹⣿⣻⣽⣟⣿⡿⠾⠧⠃⣀⣐⠌⣐⡤⠈⠲⢖⣀⣢⡠⠌⣃⠴⠃⠁
⠀⠀⠀⠀⠀⠢⢉⠛⠳⠾⠭⠭⠶⢶⠶⢶⠴⠭⣭⣬⣭⣭⣥⣄⣒⠰⠄⣂⣀⣙⣐⣤⢠⣤⣬⣥⣶⣶⣶⣶⣶⣶⣶⠾⠟⠋⣉⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠟⠛⢉⣉⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠬⣄⣁⣐⠒⠀⠀⠠⠠⠤⠤⠤⠀⠀⠠⠤⠤⠄⠐⠒⢒⣂⣀⣩⡭⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠸⢷⣄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⠛⢶⠹⡊⡴⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⣶⢏⢹⣿⡐⠢⣜⠐⠀⣣⠔⢒⣿⡏⡹⣖⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠁
⠀⠀⠀⠀⠘⣿⣏⣾⣺⠁⠙⢽⠻⡟⠑⡼⠂⣰⢿⡟⣧⠙⢿⣦⡑⠂⠘⢊⣴⡾⠋⣾⢛⡿⣆⠐⢤⠊⢹⠿⡯⠋⠉⣗⣷⣻⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣡⣿⣭⣒⡬⢄⡁⠠⣕⣻⠃⢾⠧⠟⣤⣦⡍⠛⢦⡴⠛⢩⣴⣤⠷⢾⣷⠘⢟⡫⠄⢈⡠⣥⣖⣽⣿⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣉⡽⣿⡿⣷⣌⠄⠩⢙⡲⠛⠉⢰⣿⣿⡏⠀⠘⠋⠀⢹⣿⣿⡆⠹⠛⠖⢏⠌⠐⣡⣾⢿⣿⢧⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⢟⡄⢙⣿⡌⢠⡆⢀⡀⠰⠄⢸⣿⡇⣤⣠⣆⣤⢸⣿⡃⠰⠄⢀⡀⢰⠄⢁⣿⡋⢠⡻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢰⣷⡇⠀⠁⡿⡏⢠⢒⡟⢢⢹⣾⠳⢞⣷⡏⡔⢳⡒⡆⢹⣿⠈⠀⢸⢿⡄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣗⡇⠀⠀⡇⢠⠌⠉⢸⡟⣸⠛⠃⠘⠛⣇⢿⡇⠉⠡⡄⠺⠀⠀⢸⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⢿⣳⣶⣾⣧⣿⡀⠀⠀⢀⣿⣼⣷⣦⣞⡿⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣽⣆⣸⢿⢧⡀⢀⡼⡿⣅⢰⣯⣾⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣖⣾⣷⣿⣿⣿⣿⣿⣶⣾⣭⣖⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⠊⣇⡿⠿⠟⠛⠛⠛⠛⠛⠻⠿⢿⣿⣷⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⠃⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⢣
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣶⡆⣼⡟⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⡿⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢉⡛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣁⠴⠒⠉⠁⠀⢀⣀⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⡞⠁⠀⠀⠀⠀⢰⠏⠁⠉⣧⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣴⡏⠀⠀⣀⣀⡀⠀⠸⡄⠈⠛⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢰⣿⠀⢠⡿⢉⣍⡙⣆⠀⠙⠶⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⣿⡀⢸⡁⡇⠀⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣧⠈⢧⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⠀⠋⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⣴⡞⠋⠁⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⣦⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠙⠓⠀⠚⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⠾⠋⣠⡾⢿⣶⠖⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠒⠋⠁⠀⣸⠟⠋⠛⣦⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢠⡖⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⣦⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⡀⠀⠀⠈⠛⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠛⠁⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⢤⣄⣀⣀⣀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⢤⣄⣀⣀⣀⣀⣀⣀⡀⠠⠄