Grocery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠖⠁⠈⡀⠀⠀⠀⢀⡤⠕⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠚⠉⠁⠀⠀⠀⡸
⠀⠀⢀⡴⠒⠒⠒⠒⠒⠒⠚⠛⠒⠛⠒⠓⢒⡲⠷⠚⠉⠁⠀⠀⠀⣀⡤⠔⠚⠻⢄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀⡠⠔⠒⠉⠀⠀⠀⠀⠀⣸
⠀⠀⠘⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣒⣉⣁⣀⣀⣀⡀⣠⠤⢦⠤⢾⣟
⠀⠀⠀⠀⠀⢧⠀⠀⢸⠁⢸⠀⡇⠀⡇⢸⠀⢸⠀⡇⠀⣇⠜⠡⠊⠀⡔⠁⠀⠀⠊⠳⠠
⠀⠀⠀⠀⠀⠘⡄⠀⢸⠀⢸⠀⡇⠀⡇⢸⠀⢸⠀⡇⠀⠏⠠⠁⠀⡘⠀⠀⠀⠀⡄⠀⠃⠡
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⢸⠀⡇⠀⡇⢸⠀⢸⠀⡇⠈⠀⡂⠀⠠
⠀⠀⠀⠀⠀⠀⠘⡆⠸⣄⡸⠀⢧⣀⠇⠸⣄⡼⠀⢧⣰⠀⡀⠀⠆⠀⠀⢰⠖⠚⠲⠀⠁⠀⠉⠉⠁⠀⠍⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢱⣀⣠⠊⠉⠑⢆⣀⣀⣀⣀⣀⣀⠔⠣⣅⠀⠀⠀⠀⠀⣎⢔⢀⠑⠤⢀⣀⡀⠤⠊⠄⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡸⠀⠀⠀⠀⠀⠸⡄⠀⠈⢳⢤⣀⣠⠊⡠⠕⣕⠠⠂⠰⠀⠂⡀⣅⠢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠀⠉⠍⠢⣄⣀
⠀⢀⣀⡤⠤⠴⢞⣡⠔⠂⠀⣄⠀⡀⠈⠡⣠⠆⠀⡀⢀⡠⣀⠈⡇
⠀⣏⠀⠀⣠⡔⠋⠑⣤⠀⠀⢈⠿⣅⠠⠀⠀⠀⠠⠈⠁⣀⣠⢴⠇
⠀⠘⡶⠦⢤⣌⣳⣉⡀⢈⣂⣀⣀⡠⠴⠒⠛⣋⣉⣉⣉⡡⠴⠋⢀⣀⣤⣔⣪⣿⣯⣵⣖⡒⣒⢤⡀
⠀⠀⠈⠷⣤⣀⣀⣈⢉⣉⠉⣉⣁⡤⠴⠊⠉⠁⠀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⡿⣛⣁⠛⣿⣎⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠤⣒⣯⣵⣶⢶⢟⣳⣦⣼⣷⣿⣾⣿⣿⡕⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠟⣷⠫⣝⣾⠿⢯⣭⡭⠿⠭⢿⣿⣿⣿⣟⣸⡿⢥⡾
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣞⢠⣿⡇⠀⣿⣿⡇⠀⠀⠀⢹⣿⡦⢀⣀⡠⠟⠁
⠀⢀⡴⣫⣶⣦⢰⣍⠒⠤⢤⣄⣀⣀⣀⣀⣈⣉⠁⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠋⠉⠉
⠀⣾⣴⣿⣿⣿⠸⣿⣿⣿⠿⢃⣶⣶⣶⣶⣤⣍⣙⠢⣄
⠀⡇⣿⣿⣿⣿⣆⠠⣭⣀⠒⠛⠛⠛⠛⢛⣉⣭⣭⣶⢘⡆
⠀⣇⠹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣥⣾⡇
⠀⢹⣦⣝⡛⠟⠃⣸⣿⣿⣿⣿⣿⠟⣫⠴⠋⠁⣠⠴⠛⠀⣀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢿⡄⠉⠛⠒⠬⢭⣭⣭⣭⣶⣿⣿⣤⠔⠋⠀⢀⡔⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠊⠁⠀⠈⠓⠤⡀
⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠓⠤⣀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠀⣀⣠⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⠀⣶⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠁⣐⡂⠀⠀⠐⢒⢖⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣈⢣⠒⡟⠘⣇⡖⡄⠀⠀⠀⠀⠀⠀⡜⠠⣀⠔⢂⠀⢈⣦⠴⠓⡄⠀⠳⣄⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⢱⣠⡄⡂⢀⡸⢹⣠⡆⠀⠀⠀⠀⢰⡧⠀⠙⣦⡴⠚⡍⠀⢱⣤⠞⠣⡀⢈⠦⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠾⠞⣹⡻⡁⣄⠙⢉⠘⡿⡄⠀⠀⠀⠸⢈⠀⠈⠉⢶⣀⠝⢿⡁⢈⣧⡔⠉⠣⡀⡨⠶⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣧⣿⣿⣿⣯⠾⡍⢐⡀⢸⣦⠀⠀⠈⠃⣱⣀⠀⠋⠱⣄⡠⠓⣏⠀⢙⣦⠐⠉⠂⣠⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠿⠛⠋⠃⡀⠀⢻⠚⠓⠊⠘⠂⠀⠈⢿⢁⡃⢄⣀⣉⠃⠀⠬⠓⠉⢀⣠⠴⠋⠀⠈
⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁⠀⠀⠀⣶⢉⡓⣚⣹⠃⠀⠀⢐⠀⠀⠀⠁⠀⠀⢈⡉⢋⠉⠉⠉⠉⡉
⠀⠀⠀⠸⠉⠉⠉⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣦⡃⠀⠀⠘⠀⢱⣦⡦⠘⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀
⠀⠀⠀⠀⣤⣤⣤⣴⠷⠤⣤⣀⣠⣤⣤⡄⢀⣀⠀⠀⠘⠝⠙⠀⠀⠀⠀⣪⡙⣷⡴⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣡⠶⠺⣕⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣟⣦⢄⡒⣛⣸⠑⢦⣄⡐⢝⣀⡠⣄⡀⡈⠓⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣧⠈⡀⠈⠹⣿⠘⣇⡀
⠀⠀⠀⠀⠀⠀⢀⡙⠏⠞⠃⠢⠀⡁⠰⡵⣸⡏⠀⣷⢟⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢋⠴⣊⣬⢿⡮⡅⠀⠀⠉⠀⢇⠄
⠀⠀⠀⠀⠀⠀⠠⠙⠲⠽⣟⡳⢀⣺⣡⣎⠉⠀⠀⢡⡼⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠷⣾⢛⣼⡿⠉⠈⠱⡄⠀⠀⠀⠾⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢻⡿⠺⢖⣤⡀⣠⣬⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢁⣴⠾⣓⡯⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠙⠮⣭⢱⣎⡀⠄⠚⠁⠀⠀⠀⠀⠀⣀⣤⠔⠋⣉⠠⢚⣩⠔⠛⢉⡴⠀⠀⠌⠀⠀⠀⠈⠀⠀⢀⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢀⣀⣤⣶⡷⠷⠒⢒⣩⡴⠞⠉⠀⠀⠀⢸⣿⣄⠀⠀⢶⣀⠂⠈⠐⠀⠁⠀⠎⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣧⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⠓⠀⠀⠀⢹⣇⠀⠀⠀⣨⢀⣴⠇
⠀⠀⠀⠀⠀⣠⠖⠀⠂⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀⣀⣀⣰⣿⣯⣻⣿⡶⠦⣦⡄⠀⠄⠠⣀⣺⣟⣾⡿⢷⡄⠀⣀⣼⣟⢃⣠⠜⣡⠞⡟
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠭⠿⣾⠿⠿⣭⣉⣉⣙⣙⠿⢿⣦⣭⣠⣡⡤⠶⣊⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠿⢶⣭⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢦⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⣬⣿⣦⣧⠀⠀⠀⠀⠋⠀⠈⠐⠓⠒⠒⠉⠉⠁⠀⠀⢱⣄⡀
⠀⢲⡻⣷⣿⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⢸⣾⣇⣿⣼⣅⣿⡾⠀⠀⠴⢄⣀⣀⡀⠀⢀⣀⣀⣠⣴⡆⠀⣾⠇⠁
⠀⢻⣭⣻⣢⡦⢰⡲⣯⡳⣽⡏⠀⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠈⠙⢿⣇⢸⡿⠿⠿⣿⣦⠸⡟
⠀⠀⠙⠻⣿⣷⣶⣿⣮⣽⠟⠀⠀⠀⠈⢢⡻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢺⠹⣸⠀⠀⠀⢌⡏⢠⠇
⠀⠀⠀⠀⠈⠻⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣩⡭⡯⠍⣹⡄⠀⠀⠀⠀⠀⠈⠈⠢⠋⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⡘⠀⢤⠀⠀⠀⠀⢰⠋⠛⠤⡷⠞⠋⢳⠀⠀⠀⢀⢾⢀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣧⠀⠀⠸⡧⠀⢠⡿⡟⣿⡄⠀⢠⡴⣻⣭⣵⡽⢿⣷⡆
⠀⠀⠀⠀⣀⡄⡰⠁⢀⢂⣤⣀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠘⠷⣷⠷⠃⠀⣵⡞⣿⣿⡟⣿⣯⠻⣿
⠀⠐⣿⣶⣌⣿⡇⠀⠀⣹⣏⣠⣶⡷⠀⠀⢀⠀⠀⠀⢆⡀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢠⣁⣾⣿⣧⣿⣻⢄⡿
⠀⠀⠈⠉⠋⢻⣿⠀⢠⣿⠏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠾⣼⣿⣷⣠⡀⠀⢸⡿⣽⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠘⣿⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⡀⠀⠀⠤⢤⣴⡏⠀⠀⢠⡷⣱⡿⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠱⣥⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⣭⠄⠀⠀⠀⠀⢸⡇⠀⠀⠸⣟⣫⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠚⠉⠓⠢⣄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠔⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣧⡀
⠀⠀⠀⠀⢀⡴⠋⡠⠒⠀⠐⠈⠍⣻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣷
⠀⠀⠀⠀⣼⠁⡎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡶⠦⣤⣤⣀⣠⣤⣤⣖⡯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⢠⡿⠀⢧⠀⠀⠀⠀⢀⡴⠖⢒⢶⡄⠙⢢⡀⢀⡤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⢸⣇⠡⠘⢆⠀⠀⠀⡞⠀⠊⠉⢳⣿⠀⠀⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⣿⡀⢁⠘⢆⠀⠸⡇⡆⠀⢀⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼
⠀⠀⠀⠀⠸⣧⠀⠣⡈⢣⡀⠳⣝⣒⣋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⣿
⠀⠀⠀⠀⠀⠙⣧⠀⠈⠢⡱⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎⢰⡟
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠪⣳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠚⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠈⠓⢌⡉⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢚⡡⠔⠉⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠑⠒⠨⠵⣲⡶⠶⠶⠶⠶⠖⠖⠒⠒⠚⣉⡥⠔⠚⠁⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⠁⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⠟⠛⠛⠛⠛⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⡴⠟⠻⣦⣤⣤⡀
⣼⠀⠀⠀⠁⠀⠈⢻⣄⣀
⠻⣤⣤⣄⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠈⠻⠦⢦⣤⡀⠀⠀⠀⠀⠈⢙⡷⠶⠾⠿⠷⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠶⠾⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⣉⣤⠤⠶⠶⠶⠒⠒⠲⠦⢄⣉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣤⢾⡄⡀⠀⠀⠀⢀⡴⠋⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠙⢦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢿⡀⠀⠉⠀⠀⠀⣠⢏⡴⠉⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠟⠁⠀⠀⠸⡇⠀⠀⠀⠀⣴⢣⠏⠀⠀⠀⣠⡤⠶⠶⢤⣀⠀⠀⠀⡴⠊⠉⠀⠀⠈⠉⠙⠢⡀⠀⠀⢸⡆⢿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⢣⠆⠀⠀⣴⠟⠁⠀⠀⠀⣠⠈⢳⠀⢸⡁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡇⢸⡀⠐⢯⣄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡆⠀⢠⢇⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠴⠃⠈⠧⣄⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⢸⠁⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣿⠃⠀⠀⢸⣇⠀⡟⣸⠀⠀⡼⠁⠀⠀⠀⠁⠀⢠⠎⢁⡤⠶⢤⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠃⠀⠀⠀⠀⣿⢰⠇⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⡏⠀⢸⠁⠀⠀⡿⠀⢹⠀⠀⠀⠀⠀⠀⢀⡟⠀⡼⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢰⡇⠀⢸⡀⠀⠀⠀⠂⠀⠀⢧⠀⠘⠦⠤⠞⠁⢠⡆⠀⠀⠀⠀⠀⢀⡞⠀⡼⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⠋⢀⡼⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⣧⠀⠀⠘⢦⣀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⠞⠁⣠⠎⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠁⢀⡴⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣉⣙⠒⠒⠶⠶⠶⠒⣒⣊⣩⣥⠴⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣫⣽⣶⣶⠒⡠⣔⣫⠽⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣭⣾⡿⠛⠛⠛⢁⣦⡉⣓⠾⣭⣿⣓⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⠏⠁⡰⣜⢮⡿⣷⣽⣾⣧⠈⠻⢿⣓⣶⠾⢤⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣉⡁⣴⣿⣿⣮⣳⣝⡮⣷⣿⣿⡬⣧⣄⠺⣭⣽⣛⡂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⣮⣳⡜⢿⡯⣟⢮⣗⢿⣚⠩⣿⣣⢿⣾⣦⠙⢳⢯⣟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠻⣿⣧⠈⢿⣮⣟⡮⣝⡾⢈⣓⠾⣽⣲⠏⠀⠈⣓⢏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠻⠃⠄⣶⣝⡲⣝⡛⣭⣐⠮⣝⡆⣬⣛⠂⣐⢎⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃⣼⠀⢿⣿⣝⡲⣽⡷⢮⣙⠾⣱⢰⣝⡷⠌⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⣿⠀⣷⣽⡻⣽⣻⢏⡳⣭⣳⣇⡻⣮⠃⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⡿⢠⡹⣿⣿⡳⢍⡳⣝⢮⡻⣯⡻⠀⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⢃⣺⣷⣝⢟⢿⡳⣝⢮⣳⡽⠎⢁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡾⠏⡰⣝⢮⣿⡇⠠⠅⠈⠀⠁⢀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣶⠁⣰⣿⣾⣯⠗⠀⠀⠀⠀⣀⣴⢸⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠟⡃⣾⣯⣿⡿⠃⠊⠀⣠⣴⡇⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⡙⠙⠛⢋⣀⣠⡆⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣇⣷⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⢶⣳⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠠⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⡞⠉⣩⣆⠈⠛⣿⣄⠀⠀⠀⠀⠀⠀⠓⢄⠀⣑⡈⣳⣤⣶⡛⠋⠁⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣨⠇⠀⠎⠛⠁⠀⠀⠀⠛⡆⢀⠀⡀⠀⠉⠻⣅⢠⣶⠟⣉⠙⡛⠛⠉⠈⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣶⣄⣀⠀⠀⠉⠲⣄⠀⠀⢲⣄⣼⠦⠶⠃⠄⠀⣈⠀⠀⡀⠈⢉⡟⠉⠛⠉⠙⠋⠀⠐⠋
⠀⠀⠀⠰⠂⠀⠀⠀⠆⠀⢾⣿⢁⠹⣜⢦⠀⠀⠙⠶⣽⡮⠹⣿⣍⣷⠶⠶⠟⠿⠿⢷⣬⡤⠀⠁
⠀⠀⠀⠀⣨⠥⠀⠀⡤⠀⠈⢿⣟⣷⡜⢿⡇⠀⢀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠐
⠀⠀⠐⡤⠿⠔⠀⠀⢅⠀⠀⠸⣿⣿⣿⣛⣣⡄⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡦⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠡⣀⠀⠄⠀⠀⠀⢄⡀⠈⠻⠿⣿⠟⠁⠀⠁⠀⣀⠤⠀⠀⠀⣠⠠⢲⠇⢰⡆⢀⠀⠀⠀⠀⠀⠈⢶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⢠⠊⠀⠀⠀⠄⢀⠘⣠⣷⣤⣼⣿⣿⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⣀⠀⣈⡄⢦⣤⠀⢄⡀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣷⡦
⠀⢀⠀⣀⡿⠟⣹⢧⣭⣶⣛⣳⠛⡆⠀⠀⠀⠋⢒⠘⠃⡀⣿⣿⣷⣿⡿⣟⠙⠙⠏⠙⠢⣅⣾⠁⠀⠀⠀⢀⠔
⠀⠘⣿⢿⠳⢞⢧⢺⣿⣟⠻⡿⣷⢤⣀⠀⠀⠐⠚⠒⠶⠚⠛⠛⣁⣈⠉⠻⡗⢲⠖⣢⣴⣯⣿⣦⠒⠆⠀⠁⠐⠶
⠀⠀⢰⣾⡖⣸⢋⡧⠌⠹⠇⢰⡜⣧⣌⣧⣄⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⠓⠴⠼⠿⠟⠁⠀⠀⠀⠂
⠀⠀⠈⢛⣿⣽⡿⢶⠐⣆⡀⢈⡷⣼⠟⣿⣟⣆⠀⠀⢀⣄⣴⠰⣾⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡤
⠀⠀⠀⠨⠙⢛⣛⣛⠁⣬⣿⣟⣿⣯⣯⣿⣿⠷⠂⠀⠀⠙⢿⠂⢩⠃⠈⠉⠉⠀⢧⣤⣡⣶⣿⣿⣧⣄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠈⠁⢲⣍⢡⠀⡀⠀⠀⠿⢻⣧⣽⣷⢾⣤⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⡓⢸⠂⠀⠀⠀⠼⡦⠀⠁⠀⢀⡄⠈⣿⣿⣿⣸⣯⡐⠀⠀⠀⢠
⠀⠀⣀⠀⢀⡤⠴⠶⠚⠓⣒⠈⢉⠀⠀⠀⠀⠀⠸⣿⣷⠲⡤⣤⡤⠀⠁⠲⠂⠀⠀⠐⢃⡟⣿⣯⣿⣷⣷⡖⠀⡐⠀⡀
⠀⢠⣏⢳⣛⡅⠶⠾⠿⣷⡎⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠤⠂⢉⡭⣿⣇⠀⠀⠀⠩⡰⠛⣿⣿⣿⣿⣷⣵⣤⡟
⠀⠀⣿⣿⢽⣷⣿⣾⣿⡟⠑⠁⠀⠀⡠⠞⠀⠀⠂⠘⠂⠀⡰⣯⣿⠿⠷⠛⠁⢀⠀⠀⠀⠠⠾⣛⠛⠿⢿⣛⠷⠚⠁
⠀⠀⠘⣿⣵⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠈⠐⠀⠒⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢷⠀⠀⠀⠀⠾⢥⣶⣴⠟⢿⣦⡀⠀⢀⠀⠀⠀⠀⢀⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡒⢉⣡⢤⡾⠀⠀⣴⣤⣀⠂⢤⡀⠀⢾⠿⣿⠟⠻⣷⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⢰⣏⢱⠍⠐⠋⠀⠀⢶⡶⢶⣿⢿⣦⣈⠿⠛⠳⢤⡀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⢤⣉⠂⠠⠊⠀⣠⠶⣯⣵⡿⠟⠋⠀⣀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣳⣦⡀⠙⠧⠀⠈⠀⠤⡉⠻⣿⣶⡆
⠀⠀⠀⠀⠠⢌⠲⢠⣰⡾⣱⣾⡽⠋⠀⠀⠀⢀⠀⠈⢰⣶⣾⣿⡷⠤⡀⠀⠀⠀⠀⠈⠙⠛⠦⠘⢦⠀⠀⣀⣀⡁⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠒⠿⠾⠛⠁⠀⠀⠒⠂⢀⣷⣮⣓⣞⣟⣛⣻⣥⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠈⠻⠲⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣯⣒⠚⠛⠛⠛⠻⣿⣿⣿⣿⠟⠎⢀⠀⠀⠀⠀⡄⡠⠀⠀⠈⠓⠠⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⣾⣿⣷⣷⡶⣞⣾⣶⣾⠗⡶⠁⠀⠀⢀⣻⣴⡌⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠛⠿⠇⠒⠋

⢀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠂
⠐⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠄
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⣄⣤⠛⠁⢠⡴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⢄⠀⠀⣁⠔⠀⠀⠀⠀⠀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠅⠀⠄⠈⠈
⠀⠀⠀⠀⠅⠀⠸⠒⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠁⠀⠀⡀⠀⢀⣼⠉⡪⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⡀⠀⠀⢄
⠀⠀⠉⠀⠀⠄⠀⠠⠀⠀⠁⠀⡰⠋⠑⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠘⠀⢠⡀⠊⠀⠀⠀⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸⣿⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⠀⠸⣿⠀⠀⣧⡈⠳⣄
⠀⠀⠀⠐⡄⢀⡤⠖⠉⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⢞⡥⣸⡷⠀⠀⠀⢿⠀⣄⣿⣧⡄⠈⣳⡄
⠀⠀⠀⠀⠘⠾⡀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣤⡴⠋⢠⢸⡇⣿⡇⠀⠀⣠⠀⢰⣯⣿⡟⢃⢞⠝⠁
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⡑⠈⢿⣧⠹⡄⢸⢸⡇⣿⡇⠀⠀⣿⠀⢸⠛⣃⢔⠕⠁
⠀⠀⠀⠀⠀⠀⣈⡆⠀⢐⠆⠰⡁⠘⣆⠈⡿⠛⠛⣆⢼⡇⢹⠀⠀⠀⡟⢀⣠⡾⠗⠁⠀⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢳⡀⢹⣄⣸⠖⠃⠀⠀⠈⢆⠁⢸⠀⢀⣠⡶⢟⣋⠴⢒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡾⠛⠉⠀⢘⠇⠀⠏⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡎⠀⢀⣸⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⢤⣤⣄⣀⣠⡤⠶⠒⠚⢛⣒⣚⠛⢧⠀⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣥⣤⣍⡉⠉⣤⣤⣄⠲⣶⣶⣶⣶⣶⣿⢃⣾⣿⡿⣋⣴⣿⢀⡟⣷⠇
⠀⠀⠀⠀⠀⠀⣼⠁⠾⣿⣶⣯⣽⣿⣦⡘⢿⣿⣷⣮⣿⣿⣿⡿⠃⣚⣻⣻⣿⣿⣿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠶⣿⠗⠲⠶⠤⣭⣛⠿⣿⣿⣌⡛⢋⣭⣭⣭⣍⠐⢋⣭⣭⣭⣭⡭⠀⢀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠆⡖⢩⣛⠶⣌⡙⠻⠶⣦⣭⣭⣭⡴⠿⠟⣋⣉⣥⠴⠞⡻⢟⣼⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡲⠶⣾⣿⣑⠈⠉⠛⠒⠶⠶⠶⠖⠚⠋⠉⠉⠀⠰⠖⣋⡵⢛⡁⠦⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠁⢀⠍⠙⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠛⠋⠇⠀⠢⠀⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠙⠛⠉⠉⣉⠁⠁⠀⢀⠠⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠉⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠖⠒⠒⠒⠒⠒⠛⠋⠙⠛⡒⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠀⠀⠉⢀⠉⠓⠲⣄
⢀⡤⠴⠖⠚⠛⠉⣥⡴⠞⠉⠀⠀⠳⣄⢀⡔⠀⠀⠢⡴⠋⠀⠢⡀⢀⠴⠃⢄⠀⣼
⢸⠀⠀⠀⣡⣴⠛⠁⠈⢢⣤⠀⠀⠀⡨⠻⣄⠠⠖⠁⠀⠀⠀⠤⠈⠁⢀⣀⡤⢾⡇
⠈⣷⢤⣤⣀⡈⠙⢦⡚⠁⠈⠑⠄⠀⠀⠀⢈⣡⡤⠖⠒⠒⠒⠒⠚⠛⠉⣁⡴⠏⠀⠀⢀⣀⣠⠔⣫⣽⣭⣓⣒⠤⠤⠤⢄⡀
⠀⠈⢳⣄⣈⠉⠉⠛⠓⠶⠖⠲⠖⠒⠚⠛⠉⢀⣠⠴⠖⠒⠚⠛⠋⠉⠉⠁⠀⢀⡴⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠆⣿⣶⣌⠳⣄
⠀⠀⠀⠙⠛⠷⠴⠤⣴⣤⣤⣤⣀⡴⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣘⣻⣿⣛⠿⠿⣛⣛⣿⣛⣡⣶⣶⡆⣹⣿⣷⣜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⣫⣽⡶⢿⡿⠿⣟⣩⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣿⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠿⡗⠮⣍⣲⣟⣿⣯⣭⣭⠭⠽⣯⣼⣟⣛⣛⣛⣿⡿⣃⣿⣋⣥⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡄⠀⡿⠀⣾⣿⠁⠀⢸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣧⡉⠉⠉⠁⢠⡿⠃
⠀⠀⢀⡴⢒⣛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠚⠳⠶⣿⣿⣥⣤⣼⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠧⠶⠒⠚⠉
⠀⣴⢋⣾⣿⣿⣇⢸⣧⣄⣉⠓⠲⢶⠶⠶⠶⠶⠶⠶⠦⣤⣀⡀
⢸⢃⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⠿⠋⣰⣿⣿⣿⣿⣶⣶⣤⣉⣙⠶⣄
⣿⢸⣿⣿⣿⣿⣿⡄⠈⣉⣉⠁⠴⠾⠿⠿⠿⠿⠟⠛⠋⣉⣉⣩⣤⠘⣆
⣯⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠋⣠⣿
⢹⣆⠹⣿⣿⣿⣿⡟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⠤⠶⠞⠻⣿⡏
⠀⣿⣷⣬⣉⡛⠋⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣡⡖⠋⠁⠀⣠⡴⠞⠋⠀⣀⡤⠔⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠸⣿⡀⠈⠙⠓⠲⠬⣭⣉⣉⣉⣭⣴⣾⣿⣿⣧⣠⠖⠋⠁⠀⢀⡴⠊⠁⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠛⠉⠁⠀⠀⠉⠓⢄⡀
⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⠞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣤⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⠉⠓⠒⠚⠛⠉⠉⠀⠀⢀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⣠⡤⠴⠒⠚⠉⠁

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡤⠤⠄⠀⢤⣤⡤⠀⠤⢤⡶⠚⠉⣁⣴⣶⣿⠟⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣠⣶⣯⣴⠶⠞⣿⠟⠁⠀⠀⣰⣿⣡⣴⡾⠿⣽⡿⠁⠊⠀⣀⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠶⣶⠟⠛⠉⠁⠀⣠⡾⠁⠀⣀⣤⣶⠿⠟⠋⠁⠀⣰⠋⢀⣠⣶⣿⡿⠋⢀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡾⠃⠀⠀⠀⣠⣾⣿⡴⠾⠛⢻⡟⢁⡤⠀⠈⣠⣾⣧⡶⠿⠛⣡⡟⠁⠈⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡋⣀⣠⠤⣶⠾⠋⡁⠀⠀⢠⣼⠏⢐⣁⣴⣶⠟⠛⠛⠁⠀⠀⣼⣿⣥⡶⠶⠶⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⣠⠞⠁⠀⠀⠀⣠⣞⣩⣴⠞⠉⣼⠟⠁⠈⠀⢀⣨⣤⠞⠉⠡⠀⠀⢀⡾⠃⣀⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠻⣄⠀⠀⣀⣠⠞⠛⢩⠄⠂⣠⡜⢁⡠⠔⠒⠋⢉⡼⠃⠠⠄⠂⠈⣠⠎⢀⣠⣾⣿⠀⠈⠲⠦⠞⠀⠴⠺⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣪⡟⠁⠀⠀⠀⣠⣾⣿⣾⣿⣗⣶⣶⣶⣿⣤⣤⣄⣐⣦⣾⣧⣶⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⣿⣧⣠⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣑⣟⣹⠟⣿⣷⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⣿⣧⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⠆⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣸⣻⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣐⣚⣍⠴⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠚⠋⠉⠉⠀⠈⠉⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠁⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⢀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠄⠐⢲⠒⠉⢹⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡭⣽⣿⣆⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠀⣠⡄⠤⢼⠒⠂⠛⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⡿⣻⣛⡃⣿⣽⣥⣿⣿⣿⡿⢟⡅
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠀⢸⣀⣀⣤⠤⠀⠂⢀⠴⠊⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⡿⠿⠿⠇⣿⣿⣿⣿⢟⣭⣾⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡴⠃⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⢟⣵⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠑⠦⢄⣀⣀⣀⣀⡤⠔⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣻⠿⣿⣿⣿⣿⠿⣛⣵⣿⠟⠁
⠀⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⡗⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠀⠀⠀⠀⡇⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⢁⠠⠀⠀⠒⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⠉⠀⠀⠀⠀⢄⠉⠀⡀⠀⡰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡠⠤⢒⡈⠅⡰⠀⠈⠇⠠⠀⠀⢂⡀⠂⢠⠠⠠⠆⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠋⠸⡈⢀⣀⢂⣸⣀⣀⣂⣀⣀⣁⡁⠤⠤⠤⠤⠰⠒⠒⠒⠚⠉⠉⣩⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣀⡡⠤⢤⡴⠊⠈⠑⠢⢄⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⠔⠉⠀⢀⡴⠋⠀⢀⣀⡂⠀⠀⠉⠑⠢⢌⣂⡀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠄⠀⡔⠂⢢⠀⡇
⢠⣎⠡⠤⠤⠔⢉⣀⣀⣀⣈⣀⣁⣀⣀⣀⣀⣤⣤⠌⠩⠭⠭⠭⠭⠭⠧⠔⠒⠒⠉⠉⢹⠀⡇⠀⠀⠀⠀⠀⡇⠀⠨⠀⡇
⠈⠉⠉⠉⠉⢹⡄⠀⠒⠒⠂⣶⠒⠒⢢⠀⠀⠀⡶⠂⠂⠐⡆⡖⠒⠒⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⠀⠀⠀⠀⡇⠀⢰⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⢿⠈⠀⢸⠀⠀⠀⣇⠀⣶⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠄⠀⡇⣀⠼⠀⡇
⠀⠀⠀⣀⡠⠼⠿⠿⠿⡿⢺⢸⠀⠀⢸⠀⠀⠀⣧⣴⠤⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⢀⡠⠄⠀⠉⠀⣀⠴⠃
⠀⠾⠭⣤⣀⣀⠀⠀⢁⡹⠿⠿⣿⡷⠾⠂⠤⢠⣈⣤⡆⠠⣅⣣⢀⣤⢀⡀⠤⠀⣀⡇⢸⠀⠓⠊⠁⠀⠀⣠⠔⠊
⠀⠀⠀⠀⠈⠉⠙⠛⠯⠄⣠⣔⡈⠀⢀⡠⠒⠻⠷⢞⡷⠿⠓⠸⠾⠯⠵⣮⣂⠝⠉⡇⢸⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠫⠤⣀⣀⠐⠈⠀⠀⠉⠁⠒⠢⠤⠄⣸⠠⢐⡡⢚⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣀⣀⠀⠀⣀⠄⣊⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠪⠿⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣦⡀⠀⠀⣈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⢈⢿⣿⣿⣷⣄⠀⠀⠀⠂⠈⠑⢄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠈⢢⡈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡒⠲⡄
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠐⠐⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⣹
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠐⠘⢦⣀⠀⠀⠀⠀⢀⣠⠏⠀⢰⣏
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢀⡤⣄⠀⠀⠀⢀⣿⣿⠀⡀⠀⠀⡠⠀⠀⠀⡀⠈⠈⠉⠓⠒⠚⡿⠀⠀⠀⠘⠈⠳⡄
⠀⠀⠀⠀⠈⣿⣿⡄⠀⢠⡏⡞⢢⢳⠀⠀⣸⣿⡏⢀⠇⠀⠀⣇⠀⣠⠀⣇⡤⠂⠀⠀⠀⣀⣽⠤⠤⣄⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠘⣿⣷⡀⠘⣇⢧⡼⡸⠀⣠⣿⡟⠀⡼⡠⠊⠀⣿⠞⣁⡴⠿⠒⠚⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠉⠉⣁⣴⣿⠟⢀⣠⠏⢁⡠⢚⣧⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⣟⠥⠒⢁⣮⣔⡫⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⣠⡆⠀⢀⠆⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠒⠒⠀⠁⣹
⠀⠨⢰⣤⢠⠀⠀⠒⠐⡭⠛⠀⠀⠘⠃⠒⠈⠀⠀⠠⠀⠀⠀⢠⡾⠛⠛⠚⠀⠀⠊⠀⠀⠲⠆⠀⠀⠀⠊⠉⣀⡁⠼
⠀⠀⠙⠁⠘⠀⠐⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠴⡮⠁⠁⠀⠀⠀⢀⡀⠀⢀⢠⠔⠆⠀⠀⠀⠀⠀⠤⠄⢒
⠀⡤⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣷⠸⠁⠀⠀⠰⠀⠐⠀⠀⠐⣂⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⢤⣤⣀⣀⠀⠀⠀⠀⠔⠸⠂⢸⠀⣆⠀⠀⠙⠳⠤⠗⠀⠀⠀⠀⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠉⠈⠻⠛⠀⠀⡒⠂⡃⠘⠂⢸⣴⣿⠀⠀⠀⠀⠀⠀⢠⢋⠔⠡⠈⡠⠊⡠⠂
⠀⠀⢰⣄⠀⠀⣀⣀⣀⣀⡄⠀⠁⠠⡀⠀⠀⠀⠉⠉⠉⣋⠈⣣⣞⡧⠁⠀⠀⠒⠷⣶⡄⠈⠟⠶⣣⢆⣀⠞⢠⠊⢠
⠀⠀⠈⢿⣯⠁⣯⣹⠁⠣⠃⠀⠀⠀⠈⠁⠀⠀⠈⠻⢷⣾⣮⠿⠈⠀⣤⡄⠀⠀⠐⠁⠙⠃⠀⠀⠈⠈⠛⠛⢷⡶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣶⣶⣾⡿⠟⠛⠿⠿⠟⠻⡿⡿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⣠⠊⠉⠟⢋⣿⠿⡿⠿⠿⠻⢻⣿⠉⠀⠀⠀⠀⠀⠀⣈⠥⠀⠒⠛⠉⠁⠀⡀⢀
⠀⠀⢸⣷⣿⣿⣳⣿⠋⡞⠁⣠⠆⣴⠎⢠⠆⣠⣂⠀⠤⠒⠈⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠉⠛⢿⣿⣿⣶⣄⣼⣇⣪⣼⣶⣿⣿⣿⠟⠁⢀⡀⢰⢋⣄⠄⠀⠀⠀⠀⠀⠀⡰⠁⠀⣃⣆⡃⢂
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠀⠼⣏⠁⡄⠀⠀⠀⠀⠀⠀⠰⢃⣄⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⠀⠠⠀⡀⣰⠆⠁⠀⠑⠀⡴⠆⢉⡀⣤⣤⣀⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⢿⣀⠀⣨⡴⢷⡀⠁⢀⡤⠀⠀⠛⡛⠷⠾⣿⣿⣉⣀⣀⣠⣄⡀⠤⢶⣤⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣫⡍⢙⢻⡄⠀⠷⢡⣷⡟⢩⠧⢴⡖⢈⢁⠠⠔⠀⠂⢉⣫⣙⣷⣾⣿⣟⡋⣴⣴⠦⠓⢒⠼⠀⢠⡟⠿⢶⡄⠀⢦⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠙⣿⣷⣄⡈⠺⠿⠿⣿⠻⣜⠖⣬⡾⣿⣛⡯⣝⠻⣤⣅⠀⠒⠂⠂⣁⣠⣶⣏⡄⡈⠎⢀⣰⣿⡿⡾⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠀⠙⠫⢿⣓⣀⣁⢀⣀⣴⡙⠯⠾⠾⠾⠛⠋⠉⠉⣀⣠⣴⣶⣿⠏⠹⠚⠋⢁⣠⣴⡿⠧⠒⠋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣉⣁⣀⣀⣤⢤⣴⢶⠾⠿⠿⠻⠛⠛⣉⣁⣠⣤⣤⣶⣶⠿⠟⠛⣉⣡⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠘⠶⠤⠴⠶⠖⠒⠚⠛⠋⠙⣯⣉⣉⣡⣬⡤⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣶⡶⣿⠛⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠈⠁⠀⢰⠃⢠⠊⠁⠈⠑⠦⡈⠑⢄⡀
⢠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠈⡆⠀⠙⢆
⡏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠂⠀⠀⠀⢀⠞⢀⠞⠓⣄⠑⡄
⢻⣄⠀⠀⠾⠷⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠙⠲⠤⣤⠏⣠⠋⠀⠀⠈⢦⠘⣆
⢀⡟⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠉⠒⠢⠤⢍⣉⡐⠒⠒⠚⠀⠘⡄
⣾⠀⠀⠀⣼⠛⠛⠻⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⡀⢳
⠘⠷⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠱⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡦⢄⣀⠀⠀⠀⠀⠙⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠀⠀⠀⠈⢣⡘⢦⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠙⢦⡙⠦⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⣦⣤⣀⣀⠙⢦⡈⠓⠦⣄⡜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢿⣷⣤⣀⣠⠏

⡗⢺⣆⠧⠔⠀⠀⠀⢀⡜⡏⣿⠋⢀⡴⢾⣟⣭⣿⣿⣿⣧⠀⠀⠀⢹⣧⣄⠀⠉⢳⡄⠀⠀⡇⠀⡃⠀⣇⠀⡃
⠟⠊⠁⠀⠀⠀⠀⠀⠈⢷⣿⣯⣤⢻⠽⣴⣻⣮⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢿⣿⡇⠀⠀⢧⣄⢰⡀⠱⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠓⠒⠚⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⣴⣶⣾⣭⣴⣟⠙⢫⡿⠀⠀⠈⠂
⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⣴⣿⣥⠙⢦⣭⣏⡘⣆⠀⠀⠉⠻⠏⠿⠯⠽⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣠⣾⣧⣿⣷⠀⠀⠀⠀⠀⢰⣿⣟⢿⣧⡄⢸⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡀⠀⠀⢀
⢠⡞⢹⣿⡯⢞⠛⠀⠀⠁⠀⠀⢸⣏⠛⠊⠉⠸⠿⠁⠀⠀⠀⢀⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⡿
⣇⢨⡴⠋⠂⠀⠀⠠⠁⠀⠀⢠⣟⢁⡀⣠⡼⠃⠀⠄⠀⣠⣬⣶⣤⡾⢳⡖⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢮⣾⠃⠀⠀⣾⡜⢻⡿⠉⠢⠀⠀⠀⢰⡟⠀⠿⠋⣼⣷⣶⣏⠽⣷⠄⠀⠀⠀⠀⢠⠏
⣠⣤⠖⣦⠠⣾⠇⡏⠀⠀⠐⢯⢕⡈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⢻⣿⡏⠷⠴⣯⠘⢦⣀⠀⣰⠏⢀⣀⣤⣤
⢏⠁⠀⣀⣠⣡⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢢⡀⠀⠉⢯⣀⣘⣃⠛⢻⣯⣄⣘⠿⣷⡒⣨⣿⠋⢠⣾⡟⠛⠻
⡄⢀⢈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠈⠛⠯⣽⣏⣚⣷⣶⣿⡿⠟⠁⢠⣿⡅⣳⠆⢂
⣶⡿⣫⣿⠏⠀⠀⢆⠀⠘⡄⠀⢢⠀⢃⠘⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣿⣱⡀⣠⣼
⣸⣿⠟⠁⠀⠀⠀⢠⣡⠀⣇⡀⣸⡆⢨⡄⣱⠀⠀⠀⠰⡈⠿⣷⠶⣦⣄⣀⣀⣀⣀⣤⣤⡀⠀⠀⢿⣿⣆⣩⡌
⠋⠁⠀⣤⡀⠀⣶⡛⢿⣶⡉⡙⡋⠙⣋⣻⣿⠿⠇⠀⠀⠈⢷⣍⠓⢮⣭⣭⣭⠷⣶⣶⣈⣿⣦⠀⠈⣙⣛⣩⣵
⠀⠀⣴⣹⡿⠀⣻⣧⠀⠛⠿⠷⠲⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠙⠳⣔⣏⠉⠈⠒⠈⠛⠻⣿⢿⣶⡄⡀⠈⠉⠉
⡼⠋⢉⣽⠁⣰⠋⠋⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⠀⠀⠀⠀⠛⠀⣰⡏⣿⡄
⣤⡶⣼⡇⠀⣿⡒⠠⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠈⢳⡀⠀⢀⠐⣊⣼⣶⡿⠁⠀⠀⣴
⣸⢿⣿⠁⠀⠘⢿⣄⣉⣈⠻⢀⣄⣠⣠⡭⡴⠾⠋⠀⠀⢠⣶⡜⠺⢿⣷⡦⠀⠹⣗⣧⣌⣤⠾⠟⠀⠀⠰⠘⣿
⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢉⡀⠀⠀⠀⠀⠀⢀⣇⠁⠀⠈⠁⠁⣝⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙
⠄⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣖⣴⣾⡿⢻⣿⣿⣷⡶⣄⠈⠋⠙⢹⣄⡀⠔⢦⡾⠇⠀⠀⠀⡠⠂⡠⠀⡀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⡏⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⣀⠀⢀⠀⠀⡇⠀⠀⠀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠀⠀⡄⠀⠁⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢂⢩⠅⠰⠀⡀⠈⠀⠀⠐⡀⠀⡄⠈⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢰⠉⢇⠈⣉⠀⣰⣄⣐⣀⣀⣀⡈⠡⠤⠤⠤⠀⠂⠒⠒⠒⢈⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠄⠄⠄⡰⠊⠈⠑⠢⢄⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡠⠚⠁⢀⡴⠊⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣀⣀⠀⠄⠠⡔⠁⠀⢀⣀⣀⠀⡄⠀⠒⢲⠀⡂⠉⡇⢸
⠀⠀⠀⠞⠒⠤⠬⠭⠀⠀⠀⠀⢀⣒⣀⠐⠒⠒⢒⣒⠒⣒⢒⣂⣀⣁⠉⠁⠀⡀⢸⠀⡇⠀⠀⢸⠀⠇⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢏⠀⠀⡇⠀⠀⣿⢀⡄⠸⠨⠀⠀⠀⠀⠀⠀⠇⢸⠀⡇⠀⠀⢘⠀⠆⠀⡀⢸
⠀⠀⠀⠀⠀⠀⢀⣼⠶⣶⣦⠤⢸⠀⠀⠁⠀⠀⣿⣀⡉⠀⢀⠀⠀⠀⠀⠀⠀⡀⢸⠀⡇⠀⠀⡨⠀⠒⠈⢀⠜
⠀⠀⠀⠰⢮⣍⣀⡀⠀⠀⣘⠴⠿⢶⡶⠦⠀⢀⣉⣠⠀⢄⣰⣀⣠⠀⠀⠀⠀⡄⢸⠀⠇⠂⠁⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠥⢠⣄⣈⠀⣠⠔⠋⠻⢾⠖⢛⠚⠓⠿⠵⠬⡠⠋⠁⢸⠀⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠠⠤⣄⣁⠀⠀⠈⠉⠐⠂⠀⠄⡀⠅⡫⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡀⡀⢐⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⡤⠤⣀
⠀⠀⠀⠀⠀⡀⢤⠒⠋⢹⡖⠂⠈⢳⡌⢂⠙⣿⠣⡀⠀⠀⠐⡟⠡⠔⣛⣫⣶⣦⠀⠀⢀⠎⠀⣀⠤⠜⠀⠧⣀⠀⠡⡀
⠀⠀⡠⠒⣭⢄⠸⡍⠳⡈⢳⡀⠀⠀⢻⡌⡄⠘⣄⡇⠀⢸⠀⠃⢠⠊⠉⠉⢉⣈⣁⠀⣸⡀⠚⠀⠀⡄⢠⠀⠀⠱⠀⡧
⠀⠰⠁⠀⢿⠀⠂⠹⣆⢱⡈⢷⡀⠀⠘⡇⣧⣶⠟⠀⠀⠘⢧⡀⠐⠔⠒⠉⠉⢉⡟⠀⢿⣧⡀⠀⠀⠸⠂⠀⠀⣀⣴⠇
⠀⢠⡀⠀⠈⠓⠄⣦⣘⢦⣧⣀⣷⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⠴⠚⠁⠀⠈⠻⣿⣷⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠉⠛⠓⠒⠛⠛⠛⠛⠛⠋⠉⠀⡠⠒⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⡩⠭⠟⠫⢤⣀⣀
⠀⠀⣠⠒⠫⣅⠉⠉⠱⣶⢤⠀⠀⡌⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠀⠀⠙⡿⠉⠱⡀⠀⠀⢀⣴⡙⠀⠀⠀⠀⢨⠀⢨⣉⠵
⢀⣞⠣⠄⢈⢮⡀⠀⣠⡇⢠⠳⡄⡇⠁⠀⠀⠀⠀⠀⣸⠀⣸⠶⢦⣄⡰⠁⠀⠀⣷⠀⣰⡋⠀⠘⢎⢂⠀⠀⣸⠀⠊⠁
⠠⠁⠀⠉⣷⣿⣿⡾⠛⠶⠾⢤⠁⠘⢄⣀⣀⣀⣠⠴⠃⠀⡇⠀⠀⠘⡇⠀⠤⠞⡿⠠⠀⠬⢷⣤⠼⠿⠶⠛⠁
⠘⠦⠒⠛⣉⣁⠀⠄⡠⠠⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠰⣄⠀⠚⠀⠀⠀⠀⠤⠶⠾⠥⣄⡀⠈⠙⠲⣄
⠀⠀⣴⠍⠁⠀⠀⠀⠀⠀⠛⣯⠀⠀⠀⠀⠀⠀⠀⠤⡤⢤⣤⣤⣭⣉⠉⠁⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠈⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⠈⠢⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡱⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠀⢹⠁⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣸
⠀⠀⠀⠙⠢⠤⠴⠄⠂⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠘⠓⠢⠤⠤⣄⣀⡀⠀⡼⠖⠉
⡶⠒⢶⢶⡶⠶⠶⣶⢶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⠶⠶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠒⡂⠐⠒⠦⠤⣋⣉⠉⠩⠉⠙⠒⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣚⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⢄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠌⠠⠒⠔⠲⠈⠍⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡀⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡴⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣀⢈⣥⣤⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⢠⡈⠛⠀⡠⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠽⠚⠁⠉⠀⠀⠐⠉⠍⠉⠉⠙⣛⠓⠚⠣⠦⣄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠨⢆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠑⠫⣢⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠅⢪⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠤⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⢈⡹⣷⣌⠂⠄⠀⢁⠀⠀⠆⠄⠆⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⡀⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⠀⠀⠀⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠻⣦⠀⡀⢂⡴⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⣴⡋⠐⠂⠠⠀⢀⡀
⠀⢀⣴⡾⠛⠉⠉⠉⠨⠉⣉⠉⠈⠛⠀⠛⠷⢶⢤⢬⣀⡀⠁⠀⠀⠠⠀⠐⠂⠀⠀⡀⢂⠂⠠⢳⡧⠐⠃⠀⠀⠐⠀⠂⠀⠀⢀⢀⡨⠞⢁⣀⠀⠐⠀⠀⠉
⢠⣨⠁⠀⡀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠍⠐⠛⠿⢶⣤⡀⠀⠀⢀⠀⠀⠀⡩⠂⣾⠷⠔⠐⠶⠳⠶⠾⠶⣶⣷⣶⣾⣿⣶⣶⠶⣶⣶⣶⣷⣶⠖⠂
⢺⠉⠙⠳⢦⣤⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢛⢶⡀⠈⠡⠀⠀⢀⣴⡽⠲⠲⠒⢒⠳⠶⠖⠛⠛⠻⠿⠏⢻⣿⣿⣿⣿⣿⠟⠋⠉
⠈⠉⠁⠶⢄⡀⠉⠛⠶⢤⣀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠄⢳⣿⡻⣷⠖⣞⣿⢫⠾⠟⠛⠛⠿⠏⣛⣛⠛⠛⠛⠒⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠈⠉⠓⠶⣠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⣀⣎⣼⠤⠩⠀⠀⠉⠑⠒⠒⠢⠥⠒⠒⠠⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣀⣙⠣⠗⠶⠒⢒⣲⣖⣼⡿⡛⣡⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠶⠤⢴⣂⣲⣧⣴⠟⠛⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡿⠃⠀⠀⠀⠀⢸⣿⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⢺⠂⠀⠀⠀⠀⠀⠐⡗⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⡔⠉⠉⠉⠉⢉⠍⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠩⡉⠉⠉⠉⢢
⠀⠀⠀⠀⠀⢇⠀⠀⡀⠂⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢄⠀⡸
⠀⠀⠀⠀⠀⠀⠹⠊⠀⡀⡖⠑⡂⡆⠐⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⢠⠁⠀⠠⡊⠀⡇⠀⡇⡇⠀⠀⡇⢀⠀⠀⠀⠳⠀⠀⠀⠀⠀⡇⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢣⠀⡄⠀⡃⡇⠠⠀⠇⠈⠀⠀⠀⢅⠀⠀⠀⠀⠀⡤⠼⠦⠧⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⡀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠰⠢⠤⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠠⣆⠔⡦
⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⣭⠅
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⠀⠀⠀⠘⠀⠑⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣍⣍⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⡓⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣒⡦
⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⡄⠀⠀⠠⡇⠀⡠⢀⠀⠀⠀⠠⣞⣶⡂
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣁⡀⠀⠀⠀⠠⠊⠁⠀⢱⠀⠀⠰⣇⣘⡧
⠀⠀⠐⠀⠘⠲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⣴⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠀⠈⠆⠀⠖⠈⣉⠀⠀⠈⠃
⠀⠀⠀⠀⣄⡄⠈⠉⠀⠀⠀⠀⠠⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡤⠀⠀⠀⠀⠁⡀⢤⣤⣄
⠀⠀⠀⠈⠁⠏⠀⠀⠀⢀⠀⠀⠀⢀⣶⠀⠀⠐⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠲⠃⠀⠘⠁⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡠⠶⠂⠀⠀⠀⠀⠀⠀⢠⣧⠆⠀⠀⠀⠀⠀⣠⠤⠀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠈⠣⠄⠠⡆⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢠⠀⠀⠐⠦⠀⠀⣷⠀⢀⠀⠀⠘⠁⠀⠐⠋⠀⠀⠙⡆⠀⠀⠀⠀⢸⣠⠂⠀⠀⢀⠀⢀⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⠀⠀⠛⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠐⠁⠀⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡀⢀⡤⠀⠀⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⢀⡄⡀⠀⠰⣦⡤⠊⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⡆⠀⠀⢿⣇⣀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⢤⡠⠄⠀⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠐⢄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠠⠀⠀⠰⠆⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡀⣠⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢛⠿⠛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⠀⠀⢀⡀⢀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⠀⢀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆
⠀⠀⠀⠀⢠⠀⠀⠐⠦⠀⠚⠉⠊⠃⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⠁⢣
⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠆⠀⠒⠀⠒⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠴⢠
⠀⠀⠀⠀⠀⢀⣉⣀⣀⣂⣀⡀⢀⠀⡀⣀⡔⢈⢀⣌⠀⡀⡀⣀⢀⡀⣠⡁⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⡔⠉⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠠⡀⠀⠀⠀⠉⢢⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠤⠤⠤⠤⠤⠴⡁
⠀⠀⠀⡀⠀⠀⡠⠀⠁⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠀⢄⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⠶⠊⠀⠀⠴⡧⠀⡤⠠⠄⢠⠄⡤⠀⡤⢠⠄⢠⠄⡤⠀⡴⠦⡀⠀⠑⠶⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠔⠁⠀⡠⡆⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⡇⢸⠀⢸⠀⡇⠀⡇⠀⠈⢠⢀⠀⠈⠢⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠐⠐⠈⠀⢣⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⡇⢸⠀⢸⠀⡇⠀⡇⠀⠀⡏⠀⠑⠠⠄⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡆⠀⡃⠀⡇⠀⠀⢸⠀⠀⠀⡇⢸⠀⢸⠀⡅⠀⡇⠀⠸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠑⠐⠃⠈⠢⠞⠀⠐⠴⠃⠈⠢⠞⠀⠐⠰⠃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠉⠛⠛⠳⢾⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠶⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣽⣶⣿⣭⣭⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡊⠉⠉⠉⠢⡈⡏⠉⠉⠉⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠏⢹⢻⠛⣟⢹⠛⡟⡏⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡰⣼⣨⠾⡼⣄⣇⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⢏⡹⠂⠀⢫⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠁⠉⠃⠘⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⢸⠁⠀⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣠⣄⢀⡀⢀⢀⠶⠶⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠶⠾⣀⣀⣀⡀⣠⣄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠲⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠖⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⢖⣳⢲⡒⠒⠲⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠶⢖⣒⣒⣒⠶⠶⠶⠶⡒⠒⠒⠒⢺⣲⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠭⡭⠭⠭⠍⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠅⠀⠀⠀⠀⠀⠬⠭⠭⠭⠭⠭⡭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀⠄⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠑⠊⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡠⠴⠒⠐⢄
⠀⠀⠀⠀⠀⠠⠔⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣠⠤⠒⠉⠁⠀⠀⢀⡀⠞
⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡩⠟⠋⠁⠀⠀⢀⡠⠄⠂⠚⠉⠛⢆
⠀⠀⠀⠀⢸⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠰⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣀⠤⠐⠈⠁⠀⠀⠀⠀⠀⡐⡠
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠆⠐⠂⡶⠀⡆⢶⠀⠶⢰⠂⢶⢰⠆⢰⠰⠆⠰⠶⠈⢀⣠⠉⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⡇⢸⠀⡃⢸⠀⢸⢸⠀⢸⠀⠀⠘⠃⠀⠼⡏
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠇⠈⠀⠁⢸⠀⢸⢸⠀⢸⠀⠀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⠇⠀⠀⢀⠀⠀⡠⠐⠈⢲⠊⠑⠆⠀⠾⢁⠀⠀⠀⠀⠈⠀⡸⠸⡀⡸⠀⢄⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠈⠳⡆⠛⡖⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠖⠁⠊⢰⢰⡄⣀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠉⢲⠊⠱⠄⠙⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⢣⠀⠀⡀⠆⠧⠁⡾⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠔

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠈⠀⠀⠀⢀⣀⠀⠐⠠⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣾⠃⠀⡠⠔⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡠⠀⠑⢄⡀⠒⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠈⢢⠀⠀⢠⣿⠠⠊⣀⠔⠊⢀⡠⠊
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠄⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠙⣆⡀⠀⢀⡼⠊⠉⠙⢿⠒⠛⠒⠂⠉⠁
⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠙⠛⠻⡇⠀⠀⠀⢨⠤⣠⣤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣤⠴⠟⠋⠉⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠠⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠋
⢀⡴⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⣩⡭⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠉⠉⠙⢦⡀
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣀⡠⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠈⠙⠲⢶⡶⠶⠶⠶⠶⠶⡶⠶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠶⠶⠶⠶⢶⡶⠖⠋⠁
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⣸⠁⠤⠐⠀⠀⠂
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠠⠀⠀⠛⠐⠒⠒⠒⠒⠉⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠁⠄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⣇⣀⣀⣸⣀⣀⣇⣀⣀⣸⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣇⠀⠀⣸⠀⠀⣇⠀⠀⣸⠀⠀⣇⠀⠀⣸⡤⠚⢏⠀⠘⢄⠀⠑⣄⠀⠑⢄⠈⠢⡀⠈⠣⡉⠑⠦⡀⠀⠰⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠓⠚⣁⣀⣀⣈⠓⠚⠁⠀⠀⠈⠓⢺⠋⠀⠀⠀⠱⣄⠀⡱⠀⠈⠣⡀⠀⡡⠀⠙⢆⡀⡸⠀⠀⠘⡄⠀⠀⠈⠛⠓⠐⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣠⠞⠉⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⡏⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠚⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⠆⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠁⠈⠐⠒⠒⠂⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⡏⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⣀⠀⢀⠀⠀⡇⠀⠀⠀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠀⠀⡄⠀⠁⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⢂⢩⠄⠰⠀⡀⠈⠀⠀⠐⡀⠀⡄⠈⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢰⠉⢇⠈⣉⠀⣰⣄⣐⣀⣀⣀⡈⠁⠤⠤⠤⠀⠂⠒⠒⠒⢈⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠄⠤⠤⡴⠊⠈⠑⠢⢄⡀⠈⢄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡠⠚⠁⢀⡴⠊⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣀⣀⠀⠄⠠⡔⠁⠀⢀⣀⣀⠀⡄⠀⠒⢲⠀⡆⠉⡇⢸
⠀⠀⠀⠞⠲⠤⠬⠭⠀⠀⠀⠀⢀⣒⣒⠐⠒⠒⢒⣒⡒⣒⢒⣂⣀⣉⠉⠁⠀⡀⢸⠀⡇⠀⠀⢸⠀⡇⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢏⠈⠀⡇⠀⠀⣿⢀⣄⠸⠨⠀⠀⠀⠀⠀⠀⠇⢸⠀⡇⠀⠀⢸⠀⡆⠀⡀⢸
⠀⠀⠀⠀⠀⠀⢀⣼⠶⣶⣦⠤⢸⠀⠀⠃⠀⠀⣿⣀⡉⠈⢠⠀⠀⠀⠀⠀⠀⡀⢸⠀⡇⠀⠀⡨⠀⠓⠈⢀⠜
⠀⠀⠀⠰⢮⣍⣀⡀⠀⠀⣘⠴⠿⢶⡶⠦⠀⢀⣉⣠⠀⢄⣰⣀⣠⡀⠀⠀⠀⡄⢸⠀⠧⠂⠁⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠥⢠⣄⣈⠀⣠⠔⠛⠻⢾⠗⢛⠚⠛⠿⠵⠬⡠⠋⠁⢸⠀⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠠⠤⣆⣁⠀⠀⠈⠉⠐⠂⠀⠄⡀⠅⡫⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⡄⣠⢐⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢿⠀⣸⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠉⣧⠀⠂⣈⠀⠘⡇⠠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡞⠀⡿⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠡⡀⠘⠃⠈⠢⠀⠀⡗⠀⠾⡄⠀⠀⠀⢀⠠⠤⠒⠢⠤⡀⠀⡇⠀⠰⠃⢸⠃⡠⢪⠋
⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠐⠀⠄⠀⢀⢀⣘⠇⠀⢠⠎⠁⠀⠀⠀⠀⠀⢱⡀⠇⠀⡀⢀⠆⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠘⠢⠠⠀⠈⠆⡀⠀⢈⡼⡇⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠀⡼⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⠀⠐⠀⣇⠖⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⢡⡟⡸⢡⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⢍⠙⢶⡂⠉⢈⡭⠓⠘⠛⢦⡄⢰⠃⠀⠀⠓⠂⠀⠤⠦⠀⠀⣿⠁⡜⡰⢡⢃⠜⣡⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠈⣏⠃⠀⠁⠈⣧⠀⠸⠀⠀⠀⠐⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⡼⡠⢡⠟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢹⡄⢸⠀⠈⠀⠀⢠⡿⠁⠀⠉⠉⠁⠚⠛⠓⠂⠀⣿⡟⡱⡵⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠔⠒⠦⣀⣹⣾⣀⡀⠀⣀⣸⡃⢀⠠⡀⠀⠀⢀⠀⢀⢀⣼⣏⣜⡼⠵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠈⠀⠉⠉⠉⠉⢙⠉⠈⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡐⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠀⠀⠀⠀⢰⠃⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠊⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠔⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠀⠀⠀⡇⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⡂⠀⢠⣇⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡤⣤⣀⡀⠀⣀⣠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡾⠍⣀⠀⠀⠀⠐⢮⡛⣿⣅⠀⠈⠉⡲⡄
⠀⠀⢀⣠⡶⠞⠛⠉⠙⠛⢿⣦⠀⠀⠈⠃⣼⣿⠅⠀⠀⠡⢱⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⣾⡍⠀⠀⠈⢠⠞⣠⠴⠿⡶⢶⠶⠻⠋⠁⠀⠀⠀⣘⣼⠀⣀⡴⠖⢋⣭⠭⠴⠶⠀⠀⠉⠃⠈⠉⠛⢅⠈⠉⠙⠲⢦⡀
⠀⠀⢷⣷⡀⠀⠠⢂⣎⡀⠂⠀⠀⠀⠀⠐⠀⠀⠀⣠⣤⣷⠿⠟⠛⠛⠛⠓⠲⠦⣄⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⠀⠀⠈⡻⡆
⠀⠀⠈⠷⣍⣀⣀⣈⣯⡡⣤⣤⣀⣀⣤⣴⣶⣶⡿⢟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⢀⠀⠀⡀⢀⠀⡀⢃⠄⢀⢠⡇
⠀⠀⠀⠀⢹⡯⠝⠉⠈⠙⠓⠚⠚⠛⠛⠉⠉⢳⡌⢸⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠐⢸⠢⢠⣩⣼⣶⣇⣼⣴⣿⡿⠁
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡆⠟⣿⠗⠒⠛⠳⢶⣶⣄⡄⠄⡂⠀⢰⣿⣼⣾⣿⡿⠿⠟⠛⠛⠉⠉⢠⡇
⠀⠀⠀⠀⠀⣿⡀⡇⠀⡀⠀⠀⢀⠟⠚⠋⠙⠛⠻⢿⣅⡰⠄⠀⠀⠀⠉⠻⣿⡆⠠⣰⠟⠉⠁⠠⠀⠂⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⣿⣷⣼⣿⣼⣷⡏⠀⠀⠀⠀⠉⠀⠀⠙⢿⣷⡀⠆⢀⠀⡀⠟⡷⢰⣿⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿
⠀⢀⣰⣿⣿⣿⣷⡾⠿⠿⠿⢿⡇⠀⠀⠠⠀⠈⠀⠀⠀⠈⠏⡇⠀⢀⣠⣼⣤⠇⢸⡟⣽⡆⠆⠀⠀⡄⢀⣠⣠⣦⣴⣾⣿⠿⠁
⠀⠀⠈⠙⠛⠯⢭⣽⣿⡻⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⠞⠁⢠⠟⢻⠟⠁⠀⠈⣿⣾⣧⣧⣼⣶⣯⣿⣿⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠁⠀⠀⠀⠀⠀⢠⠟⣿⠁⠀⠀⢸⣤⣯⣀⡀⠀⠠⢿⣿⣿⡿⠿⠿⠿⠯⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠐⠀⠀⡀⣼⣶⣷⣤⣤⣵⣿⣿⢿⠯⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⡾⠿⠟⠁⠀⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿