Butterfly wings Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⠒⡐⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠔⠒⠉⠓⠢⡀⠀⠀⠀⢂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣶⣶⣾⠿⠰⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⢉⣤⢴⢆⡰⠀⠀⠈⠃⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣤⠈⣈⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣵⢿⢸⠁⣁⣠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢀⠄⡀⣀⠤⠟⠋⠉⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⡀⠀⠀⠠⠴⠔⣦⠰⡎⠀⠀⠀⠀⠉⠀⣀⡄
⠀⠀⠀⠀⠀⢀⠤⠒⠋⠞⠁⢀⣴⡯⠀⠀⠀⠀⡠⣦⠊⠉⠀⠀⠀⠀⠀⠀⠀⡀⠤⠃
⠀⠀⠀⢠⠆⠀⠀⠁⠐⡇⠀⠺⠷⢾⠧⠘⢗⡊⣽⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠶⠒⠒⠚⠉⠉⡁⣀⠁⢈⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠳⠤⣄⡐⠀⠄⠀⠀⢐⠠⠀⠀⠀⠁⠳⠴⡇⠀⠀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠒⠀⠤⠤⠤⠚⠀⡀⠑⢛⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢀⣤⡄⠀⠀⠀⣤⡦⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡤⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣏⣿⣿⠿⣷⠀⠀⠀⢹⣯⡅⠼⣿⠗⣤⠀⠀⠀⠀⣠⡶⢯⡷⠠⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡟⢩⡟⠉⠉⢠⣾⠀⠀⠀⠀⢿⡇⠀⠈⠒⠀⠑⣄⣀⠞⠁⠐⠊⠀⠈⣿⠃⠀⠀⠀⠀⣀⡤⠖⠒⢻⣿⠑⠒⠦⣄⡀
⠀⠀⠀⢀⣴⣶⠿⠾⣧⡀⢀⠋⣿⠀⠀⠀⠀⠈⠓⣶⠖⢻⠖⠒⣿⣿⠗⠒⡟⠳⣦⡖⠃⠀⠀⠀⡴⢿⡿⠄⠆⢠⣿⡿⣧⠀⠂⠼⣿⠷⡄
⠀⠀⠀⣾⣿⠅⠀⡄⠨⢷⠈⢠⠇⠀⠀⠀⠀⠀⢸⣟⠀⠢⠖⡁⢾⣿⠠⠑⡴⠀⢘⣟⠀⠀⢠⣿⣗⣤⡄⠀⢀⣿⢠⣇⢸⣇⠀⣀⣴⣔⣿⣧
⠀⠀⠀⢹⣿⡯⠭⢉⡓⣼⣷⡾⠂⠀⠀⠀⠀⠀⠀⢿⣮⣬⣐⣰⠃⠁⢣⣱⣰⣴⡾⠃⠀⠀⠈⠉⠉⠛⠻⣿⣿⣶⠖⠘⢶⣿⣿⡿⠛⠋⠉⠉
⠀⠀⠀⠀⠉⠛⠛⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣶⡆
⠀⠀⣼⣧⠋⣭⣿⣆⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⢸⣟⢷⣶⣤⠟⢟⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⢐⡿⠁⠀⠘⡌⠙⣇⠀⣠⠴⣿⠇⣽⠏⠀⠀⠀⠸⣍⣌⠉⣿⣷⠀⠉⢿⡀⠀⠀⠀⢠⣾⡳⢉⠿⠿⢀⡉⠉⢙⣶⣷⣞⠉⠉⡁⠽⠻⠉⢿⣷⣦
⠀⠈⢓⣶⠶⢦⣤⣠⣽⡟⠁⠒⠀⢨⠏⠀⠀⠀⠀⠀⢻⡏⢳⡏⠨⠀⣀⣼⣁⡀⠀⠀⠀⠉⠻⣿⣆⠀⢀⣴⢞⠍⢻⡿⠉⡓⢦⡀⠀⢀⣾⡿⠉
⠀⠀⣞⠃⠠⣨⠄⣹⣿⢋⠙⠻⡖⠋⠀⠀⠀⠀⠀⠀⠀⠻⣌⡇⢀⣾⣏⠈⠉⠹⡄⠀⠀⠀⠀⠈⠙⣶⠞⠁⠊⢠⢸⣇⠀⠙⠊⠙⢶⠞⠉
⠀⠀⣷⣆⢀⢔⡔⠟⢀⠀⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠒⠋⢄⣸⡗⠀⠀⠀⠀⠀⠀⠘⢷⣴⣴⣼⠌⠘⢤⣦⣴⡼⠏
⠀⠀⠈⠛⠓⠋⠀⠀⠈⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠠⠭⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠐⣿⣯⡉⠳⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠞⢉⣿⣿⠂
⠀⠀⠘⢿⣿⣄⣘⡆⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢰⣃⣠⣿⡿⠃
⠀⠀⠀⠀⢻⣿⠀⡇⣠⣶⣷⣮⠳⣄⠀⠀⠀⠀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⣠⠞⣵⣾⣷⣄⢸⠀⣿⡟
⠀⠀⠀⠀⢸⣿⡦⢷⡘⣿⠿⣟⡙⠢⡑⣄⠀⠸⣄⡸⠀⠙⢆⠀⠀⠀⠀⡰⠋⠀⢧⣠⠇⠀⣠⢊⠔⢋⣻⠿⣿⢃⡾⢴⣿⡇
⠀⠀⠀⠀⠘⣿⡇⠀⡇⢇⠘⠷⠏⢀⡇⠈⠳⡄⠀⠀⠀⠀⠘⡆⠀⠀⣰⠁⠀⠀⠀⠀⢠⠞⠁⢸⡀⠹⠾⠃⡸⢸⠀⣸⣿⠃
⠀⠀⠀⠀⢀⣿⡷⢴⡇⠈⠓⠒⠒⠉⠉⠲⣄⠘⢦⠀⠀⠀⠀⢸⡀⢀⡇⠀⠀⠀⠀⡴⠃⣠⠖⠉⠉⠒⠒⠊⠁⢸⡦⢿⣿⡀
⠀⠀⠀⠀⢸⣿⠁⠘⢦⡀⠀⣠⣶⣿⣶⠦⢌⠳⣄⠳⡀⠀⠀⠀⡇⢸⠀⠀⠀⢀⠞⣠⢞⡡⠖⣶⣿⣶⣄⠀⢀⡴⠁⠈⣿⡇
⠀⠀⠀⠀⠈⢻⣷⠒⠒⡇⠀⣿⣿⣅⣈⠇⠀⠙⢮⢦⡹⡄⠀⠀⣇⢸⠀⠀⢠⢋⡔⡵⠋⠀⠸⣅⣨⣿⣿⠀⢸⠒⠒⣶⡟⠁
⠀⠀⠀⠀⠀⣸⣿⠀⢰⡁⠀⠘⠻⢤⣀⣀⣀⣀⠀⠱⣵⡜⣆⢀⣷⣾⡀⣰⢣⣮⠎⠀⣀⣀⣀⣀⡤⠟⠃⠀⢘⡆⠀⣿⣇
⠀⠀⠀⠀⠀⢻⣿⡍⠉⠳⢄⡀⠀⠀⣴⣿⣿⣿⣿⣖⣮⣿⣾⣎⣿⣿⣱⣷⣿⣵⣲⣿⣿⣿⣿⣦⠀⠀⢀⡠⠞⠉⢙⣿⡟
⠀⠀⠀⠀⠀⠀⠙⠿⢦⣶⣋⣭⣑⣶⣬⣿⢿⡯⠭⠭⠵⣶⣶⣿⣿⣿⣿⣶⣶⠮⠭⠭⢽⡿⢿⣥⣶⣊⣩⣝⣶⡴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢪⠟⠋⢉⡽⣋⠥⠖⠚⣹⢫⠏⠀⣿⣿⠀⠹⡙⢏⠓⠲⠬⣙⢯⡉⠙⠻⡕⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠹⠤⠴⣫⣾⠃⠀⠀⡜⡽⣿⠀⠀⣿⣿⠀⠀⣿⢯⢣⠀⠀⠘⣷⣝⠦⠤⠏⠀⠸⣿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡄⠀⠀⠀⢿⣿⣧⣄⡼⡟⠀⢯⣇⠀⣿⡿⠀⣸⡽⠀⢻⢧⣠⣼⣿⡿⠀⠀⠀⢠⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡄⢀⠔⠪⡙⠛⠉⠀⢧⣀⡼⢻⡀⠘⠃⢀⡏⢧⣀⡼⠀⠉⠛⢫⡗⠑⡆⢠⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠈⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣄⣠⣤⠀⢀⣤⣄⢀⣿⣶⣴⣿⡇⠀⠀⢸⣿⣶⣶⣿⡀⣠⣤⡀⠀⣤⣄⣠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⢿⣿⣷⣿⢿⣿⣿⡿⢿⣿⡿⠁⠀⠀⠈⢿⣿⡿⢿⣿⣿⡿⣿⣾⣿⡿⢿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠙⠛⠁⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠛⠋⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟

⠀⠀⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠙⣿⣦⣌⠑⠦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢋⣤⣾⡟⠁
⠀⠀⠀⠹⣎⡀⠀⠀⠁⠀⠈⠉⠲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠚⠉⠀⠀⠀⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠈⢻⡷⠦⢤⣄⠀⠀⠀⠈⠻⣿⣿⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣾⣿⡿⠋⠀⠀⠀⢀⣤⠴⠶⣿⠋
⠀⠀⠀⠀⠀⠈⠿⣷⡦⢬⣭⡀⠀⠀⠀⢈⣿⣿⠷⢮⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⠶⢿⣿⣏⠀⠀⠀⠀⢨⣭⠤⣶⡿⠟
⠀⠀⠀⠀⠀⠀⢠⣌⠉⠛⣷⠦⠄⠀⠀⠈⢻⣿⣿⣾⣿⣿⣿⢧⡀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣾⣿⣿⠋⠀⠀⠀⠤⢶⡖⠋⢉⣤
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠿⣖⣂⣀⡀⠀⠈⠿⣦⣼⣿⣿⣯⣷⣿⡄⠀⠀⠀⠀⣼⣷⣯⢿⣻⣿⣤⡾⠏⠀⠀⣀⣀⣲⡾⢧⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠋⠉⠉⠀⠀⠀⠀⠈⠿⣦⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⣧⡾⠏⠀⠀⠀⠀⠉⠉⠉⠛⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣀⡴⢆⡀⠀⠀⢀⣠⣼⡷⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⡷⣿⣤⣀⠀⠀⠀⢀⠶⣄⣰⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠷⠔⢈⣤⠞⠁⠀⢠⠞⠋⠉⠛⠇⠀⠠⠟⠋⠉⠛⢦⠀⠀⠙⢦⣌⠐⠶⠟⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠝⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡾⢁⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⣄⠹⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣱⣿⢧⣀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⣠⢿⣷⣹⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡟⠀⣹⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⡁⠘⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⡏⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡈⣷⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣯⣿⡇⢀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠀⣿⣯⡿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣆⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣾⠏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣋⡡⢼⣿⣿⣥⠠⣐⠖⢁⣴⠟⠋⣸⣿⣧⡾⣧⢿⣿⣿⣟⣷⣔⢦⣌⡙⠲⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠠⠚⠁⣀⣼⣿⣿⠅⠈⣠⣾⠟⢁⠄⣰⣿⠟⠀⡇⢹⡄⠘⢿⣿⣷⡝⢷⣝⢿⡶⢤⡀⠈⠁⠐
⠀⠀⠀⠀⠀⡠⠞⠁⣴⣷⣤⠀⠀⠻⣿⣿⢋⣠⡾⠋⠀⡰⠋⣰⣿⠏⠀⢸⠀⡄⣷⠈⢦⣻⣿⣿⣄⠙⢦⡉⠲⣝⣳⡦⣤
⠀⠀⠀⣠⣾⠀⠀⠀⢀⣿⣿⠀⠀⢀⡼⠟⠋⡟⣀⣤⡾⠁⣰⣿⢏⣴⠀⣼⠀⣷⠸⣇⠈⢿⣿⣿⣿⣧⡀⠹⣆⠘⣿⣷⣄
⠀⢀⣾⣿⠁⠀⠀⠀⠈⢻⠟⠉⠉⠉⠀⠀⢸⢱⣿⣿⡆⡼⢻⡏⠈⠁⠀⡇⢸⡟⡇⢻⡄⠀⠻⡽⣿⣿⣷⡄⠈⣿⠺⢅⡀
⢀⡞⢻⣿⡟⠀⠀⠀⢀⣶⠀⢀⣾⡄⠀⢀⡄⠀⣽⡟⣰⢁⣿⠀⠀⠀⢰⠃⢸⣃⡇⠀⢿⡀⢻⣿⠻⣿⣿⣿⡄⠸⡆⠀⠙
⢸⣿⠀⢹⣧⡀⠀⠀⡾⣿⡀⠻⣿⡇⣰⣿⡆⠀⠈⢠⣧⣿⡏⢺⣿⠀⣸⠀⣸⠙⣿⣶⢸⠟⢦⣀⠀⠹⣿⣿⣿⣦⣿⡄
⠘⣿⣿⡋⢏⢹⡖⠀⠀⣸⠃⠀⠀⣿⠉⠻⣧⡀⠀⣼⣿⡏⡁⠈⢁⠜⠙⡟⠙⡆⢹⠀⢸⡇⠀⠈⠳⣦⣙⣿⣿⣿⣿⣿⢀
⠀⠘⠿⣷⣿⡆⢻⣷⡆⢈⣶⣶⡄⠋⣀⣄⢿⣷⣴⡟⣿⠁⠃⢠⠏⠀⠀⢹⣀⡇⢸⡄⢸⣧⣀⠀⠀⠈⠛⠘⣿⣿⣝⣿⡎
⠀⠀⠀⠘⠻⠿⣅⣸⢹⡇⢈⡟⢣⡜⢿⣿⣸⣿⣿⣧⠇⠀⢸⡏⠀⣿⡦⡸⠙⢷⣤⣷⡟⠀⠙⢿⣗⠰⣿⣧⡈⠛⢙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠸⣇⣸⣇⣻⣧⠿⠋⠀⠀⠀⢿⣷⣀⣀⡇⠀⠀⡟⠉⠹⣦⣀⣠⣌⠓⢄⡀⠀⠀⠹⡟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⠃⢿⣷⢿⢀⣀⡙⣍⠛⠿⠆⠀⣙⣾⣿⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣹⣦⡈⠁⣸⡌⢿⣿⠈⢦⠀⢀⠀⢻⡟⠛⢷⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢻⣼⣿⣷⣀⡀⠀⣿⣷⣿⣿⠺⢷⣤⣈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⡄⠈⣿⡟⠷⢿⡄⠈⢻⣦⣄⣹⡿⠃⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣴⡟⠛⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠻⣿⡛⠛⣿⡄
⠀⠀⠀⢻⣦⣀⣿⠃⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⣽⣷⣾⡟⠁
⠀⠀⠀⢸⣏⢹⣿⢦⣤⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⢀⣠⣴⠶⠟⣻⣏⣰⠇
⠀⠀⠀⠀⣿⡿⣿⣤⣈⠙⠷⣦⡀⠸⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢰⣿⣠⡾⢛⣉⣤⡴⠾⣿⢛⡿
⠀⠀⠀⠀⢹⣧⣿⣄⡉⠛⠶⣬⣻⣷⣿⡀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⣠⡾⠿⣿⡾⠋⣉⣠⣤⣾⡿⣾⠁
⠀⠀⠀⠀⠈⣿⣿⣿⡛⠳⢦⣌⣿⡟⠙⠷⣤⡀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣠⡴⠟⠁⠀⢰⣿⠿⠛⣉⣩⣿⣿⣾⡏
⠀⠀⠀⠀⠀⢻⣍⢹⡟⠳⢦⣌⡛⣷⠀⠀⠈⠻⣄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣡⡾⠋⠀⠀⠀⢠⣿⡷⠞⠋⠉⣡⣿⣠⡾⠁
⠀⠀⠀⠀⠀⢸⡟⠿⣿⣤⣀⡈⠙⢿⣧⠀⠀⠀⠈⢳⣌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡾⠋⠀⠀⠀⠀⣴⣿⣡⣤⠶⠶⣿⡿⠉⢹⡇
⠀⠀⠀⠀⠀⠘⣷⣶⣾⣧⣍⣙⠓⠶⣿⣧⠀⠀⠀⠀⠙⢷⣹⣆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⢠⣾⣟⣯⣥⡶⠶⠿⣿⠟⠛⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣄⠈⣿⠉⠙⠛⠷⣦⣽⣷⡀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⢀⣴⡿⠟⠋⠉⠀⠀⢀⣴⣏⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⣧⣤⣀⣀⠀⠉⠛⢿⣆⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣴⣿⠀⠀⣠⣶⣿⣿⡶⠶⠶⠶⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣿⣭⣍⣛⣛⣛⣿⣿⣷⣄⠀⠀⣼⡇⠀⠀⠀⠀⢠⣿⣿⣶⣿⣿⣿⡛⠛⠛⠛⠛⠛⠻⠿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠉⠉⠉⠙⠛⢛⣻⣿⣿⣦⣿⣧⠀⠀⠀⠀⠘⣿⣿⣟⠛⠿⠿⠿⠶⢦⣤⣤⣀⣀⠀⠈⠛⢶⡄
⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⣀⣤⣤⣴⠶⠶⠶⠶⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠘⣿⡙⠳⣦⡀⠀⠀⠀⠀⠈⠙⢿⣟⠷⣶⣤⣙⣦
⠀⠀⠀⠀⠀⢸⡿⢿⡟⣯⣉⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⡿⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠻⢦⡄⠀⠀⠀⠀⠈⣿⣶⣿⣿⠙⣿⠇
⠀⠀⠀⠀⠀⣼⣇⣸⣷⠟⣿⡇⠀⠀⠀⠀⢀⣤⠞⠋⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢿⣦⣄⣀⣀⣠⡿⣧⣹⡿⣶⣿⡆
⠀⠀⠀⠀⠰⣿⠛⢷⣽⡾⠛⣷⣦⣤⣤⣶⡿⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣿⣿⡿⡟⢻⣆⣨⡿⣾⡁⣽⠇
⠀⠀⠀⠀⠀⣸⣧⣿⡉⢻⣶⠋⣸⣯⣿⣿⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢹⣿⣿⣿⣴⢿⣯⣴⠟⢷⡿
⠀⠀⠀⠀⠀⠘⣿⣀⣿⣿⣝⣿⣿⡿⣽⠇⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣴⣼⣿⣿⣿⣿⠟⠛⣷⣴⡟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣏⠀⣹⠟⣾⢱⣿⡶⠶⢶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣿⡜⣧⣴⣿⣿⣿⣤⡀
⠀⠀⢀⣴⣿⣿⣿⡟⢻⣾⣯⣼⣇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠻⠿⠟⠈⢻⣿⣿⣿⣆
⠀⠀⠸⣿⣿⡿⠋⠀⠈⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⠿⠟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠛⠹⠿⣿⣿⣆
⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠢⡀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣠⢔⣁⠀⠀⠀⠀⠀⠺⣿⣿
⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⣀⠋⠛⢮⡢⡀⠑⠀⠀⠀⠀⠀⠠⠊⢠⢞⡵⠋⠙⣄⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠩⡀⠀⠀⠙⢾⣦⠀⠀⠀⠀⠀⢀⣴⠕⠁⠀⠀⢠⠇⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠹⣏⠁⠀⠀⠀⠀⠀⠀⠦⢄⠀⠀⠙⢷⡀⠰⠆⢠⡾⠁⠀⢀⠠⠖⠀⠀⠀⠀⠀⠀⠀⣹⠏
⠀⠀⠀⠀⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣿⠀⢸⣿⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠏
⠀⠀⠀⠀⠀⠀⠀⢈⡽⠶⠒⠠⠤⠤⣤⠤⠶⠖⠒⣿⣿⠄⢸⣿⣿⠛⠒⠒⠲⠶⠒⠒⠒⠒⠚⠯⣅
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢐⠀⠀⠀⠀⠀⠠⠚⠉⣹⠀⠘⣧⠀⠑⠄⠀⠀⠀⠀⠈⣃⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⡀⠀⢠⠇⠀⠀⠸⡄⠈⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠀⠀⠁⠋⠀⠐⠁⠀⣸⠀⠀⠀⠀⣇⠀⠀⠃⠀⠉⠈⠀⠀⠀⠀⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢠⠁⠀⠀⠃⠀⣠⠃⠀⠀⠀⠀⠘⢆⠀⠘⠀⠀⠈⠆⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⣀⡀⠀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁



⠀⢀⡀⢀⢀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣖⣾⣛⣿⣻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠚⠉⠙⢻⣿⣿⣤⣿⣤⣽⣯⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⣠⣶⢉⣿⡟⢻⣦⠀⠀⠀⠈⠹⠿⢿⣿⣽⣻
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⠿⡿⢿⣿⣿⣧⣀⣀⡀⠀⢀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⢀⣤⣾⣯⣥⣌⣹⣿⣧⣀⣸⣧⡾⡝
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣴⡿⠋⠀⢀⣠⣴⣾⣯⣁⣀⣀⠀⠀⠈⠉⠻⢿⣟⣛⡗
⠀⠀⠀⠀⠀⠀⠐⢸⡆⣼⣋⣤⠶⠛⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠓⠲⢶⣿⢯⡟
⠀⠀⠀⠀⠀⠀⢃⢸⣿⡿⠗⠲⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⡟⡞
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⡛⠻⠾⢿⣿⣿⣿⡿⠛⠛⢿⣿⡿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⢐⠸⠏⢀⠙⢷⣄⠀⠀⠈⢫⣉⠐⢺⣿⣿⣿⣿⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠣⡀⠙⢷⣄⠀⠀⠩⣉⠛⠻⠷⣬⣹⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢆⠱⡄⠀⠻⣿⠛⢿⡟⠳⢦⣄⠀⠙⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠹⡄⠀⠹⣧⡀⠻⣦⡀⠉⠻⣶⣿⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⣄⠀⠘⣷⡀⠈⢿⣤⣴⣿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣆⣀⣽⢷⡖⣻⡽⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣥⢷⣚⣿⡽⠒⠉

⠀⢺⡃⠦⣀⠤⠆⣻⠂⠀⣂⢤⠀⠀⢀⡀⠀⠀⠶⣦⠀⠀⠀⡈⠛⢓⠀⠀⣦⠄⠀⠀⠠⣴⠀⠀⡀⠀⠀⠀⣀
⠀⠘⢳⠖⢺⠐⡶⠋⠀⠀⣿⠀⣠⠀⡼⠁⠀⠀⠐⢿⡄⠀⠐⣄⡀⠘⠀⠀⠑⠠⢰⡆⠠⠚⠀⠀⠳⠆⡖⠰⠃
⠀⠀⠀⠙⠁⠙⠁⠀⠀⠀⠙⠂⠱⠊⠀⠀⠀⠙⠂⠘⠃⠀⢆⡀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠐⠦⠀⢀⠀⠀⠀⠀⡀⠀⢸⠰⣄⣀⡴⢺⠁⠠⠀⠀⠀⠐⠒⠀⢾⣖⢠⣀⡄⣶⡗
⠀⠀⢱⡷⡿⢿⣷⡇⠀⠀⠀⠀⢱⠀⠘⠢⠰⡆⠔⠃⠀⠈⡏⠈⠏⠈⡇⠀⠀⢠⠼⠖⠲⡄⠀⠘⢛⣸⠻⣓⠛
⠀⠀⠈⠇⠀⠀⢛⠁⠀⠀⠑⠀⠉⠀⠀⠓⠀⠀⠚⠀⠀⠀⢹⠉⠀⠙⠁⠀⠀⠀⠓⠘⠛⠃⠀⠀⠛⠀⠀⠘⠋
⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣗⠀⢀⠀⢐⡇⠀⠸⡞⠂⠀⠀⠱⣀⣠⣶⣄⣀⠂⠀⠄⠀⠀⠠⠀⠀⠀⠀⠰⠸⣶⠀⠀⠠⣀⡀⠀⢺⣼
⠀⠀⢀⡡⠜⠔⣁⠀⠀⠀⠑⢂⠆⠀⠀⢋⣀⠉⢀⡙⠀⠀⠀⠀⡘⠆⢊⠄⠀⠀⣤⠀⠍⡂⠀⠀⠈⢤⢻⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⢠⠄⠀⠀⠀⠀⢤⠀⡤⡀⠀⠀⠀⠀⢄⢠⠀⠀⠀⢠⠠⠄⢐⣶⣄⠀⢀⡤⠀⠀⠤⡄⠀⢠⠀⢄⠀⠀⢀⡀⢠
⠀⠸⣀⣉⢠⢈⣅⡸⠀⠃⠀⢀⠀⢀⠒⠘⢧⠄⢽⠄⢴⠟⠀⠈⡳⠼⣿⢿⠃⠀⢩⠁⢹⠀⠈⢻⠙⢒⣶⡚⢛⡟
⠀⠀⢸⠦⠛⠣⢾⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠄⠈⠀⠄⠀⠀⠀⠳⠖⠠⠆⠀⠀⠘⢏⣲⡄⠀⠈⡇⡄⠀⢀⣎

⠀⠀⠰⣶⠂⠀⠀⠀⠀⠀⠀⠀⢲⡶⠀⠀⢠⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⢶⢠⡦⠀⠀⠀⠀⠀⠀⢰⣆⠶⠀⣶⡖⠂⢄⠀⠀⠀⠀⠀⠒⣶⠆
⠀⠀⠀⠈⢧⡀⠀⠀⡄⠀⠀⣠⠏⠀⠀⠀⣾⢠⠞⡄⡀⣜⢢⠘⡇⠀⠀⠀⠘⡇⠀⠀⢀⡀⠀⠀⢰⡏⠀⠀⠈⡦⠀⠀⢑⣤⡄⠀⠀⢠⡏
⠀⠀⠀⠀⢠⡍⠁⠀⡇⠀⠉⣥⠀⠀⠀⠀⢛⣸⠘⣇⣿⡿⢸⣅⠃⠀⠀⠀⠀⢀⠀⠀⠸⡇⠀⠀⡀⠁⠀⠀⠀⠻⣤⢄⣠⢿⢤⡀⢤⠞⠁
⠀⠀⠀⠀⠘⣧⣄⣠⣥⣀⣤⠟⠀⠀⠀⠀⠘⣿⣆⠈⡏⠀⣼⡿⠁⠀⠀⠀⠀⠻⣧⣀⡀⢁⣀⣴⡿⠀⠀⠀⠀⠀⣇⠸⢣⠘⢈⠿⣸⠇
⠀⠀⠀⠀⢀⡼⠉⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢨⠛⠁⠈⠛⣧⠀⠀⠀⠀⠀⠀⠈⠳⠛⠀⠘⢺⠉
⠀⠀⣀⣀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠸⡇⠀⠀⠀⠀⡀⠀⠀⠀⢨⡟⠀⠘⣧⢨⣸⢦⣄⣠⡴⣇⡅⣴⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣧⣤⡀⣀⠀⣠⣴⡏
⠀⠀⠀⠹⣆⡀⠀⠸⡇⠀⠀⣠⡾⠀⠀⠀⠸⣆⡀⢠⣸⣇⡄⢀⣰⡇⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠙⠉⠀⢹⠀⠉⠙⡀
⠀⠀⠀⠀⢻⣦⡀⠀⠃⠀⣠⣿⠀⠀⠀⠀⠀⠧⡳⢤⠈⠁⡤⢞⡼⠀⠀⠀⠀⠉⣇⠀⠀⠹⠀⠀⢰⠏⠀⠀⠀⠈⣦⠀⠀⠈⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠙⠛⠃⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠐⠚⠃⠀⠀⠀⠀⠀⠈⠛⠒⠀⠘⠻⠋
⠀⠀⠰⡆⢀⠄⡀⠀⠀⠀⡀⡄⢀⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠹⣄⠈⠀⢀⡄⠀⠉⢠⡞⠀⠀⠀⣀⠀⠀⠀⢿⣿⠀⠀⠀⢀⠀⠀⠀⠈⢰⡇⠋⢠⡄⠑⢸⡆⠁⠀⠀⠀⠀⢀⡐⣿⡇⡀
⠀⠀⠀⠀⢨⡃⠀⠸⡇⠀⠀⣋⠀⠀⠀⠈⠛⠀⠀⠀⠸⠇⠀⠀⠀⠚⠁⠀⠀⠀⢠⠁⠀⠸⠇⠀⢈⡄⠀⠀⠀⠀⢠⣌⡛⣛⠛⣫⣄
⠀⠀⠀⠀⠈⠳⠴⠄⠁⠦⠶⠃⠀⣤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⢀⠞⠀⠀⠀⠀⣠⡶⠭⢍⣱⣏⠭⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠋⠀⠀⠀⠀⠀⠈⠁⠈⠋⠋⠛⠋⠈⠉
⠀⠀⣴⡶⢂⣄⠀⠀⠀⠀⣀⡀⠶⣦⠀⠀⣴⣤⣀⡀⠀⠀⠀⢀⡀⣴⣄⠀⠀⣶⣦⣄⠀⠀⠀⢀⣴⣶⡄⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠹⠁⢸⡏⠀⢀⡀⠀⠈⣿⠀⠟⠀⠀⢹⡁⠋⡸⠳⣤⠾⡏⠛⢸⡏⠀⠀⣿⠀⠀⠡⡀⡐⠁⠀⣿⠁⠀⠀⢻⡎⠀⠀⣠⠀⠀⢉⣿⠁
⠀⠀⠀⠀⠘⢷⡀⢸⡇⠀⣰⠇⠠⠀⠀⠀⠈⠧⠠⡿⠁⠟⠘⣿⠠⠞⠀⠀⠀⠹⣄⡀⠀⣿⠁⢀⣀⡝⠀⠀⠀⠈⢳⡄⠀⢿⠀⢠⡼⠃
⠀⠀⠀⠀⢰⣌⠛⠛⠙⠛⣁⣴⠀⠀⠀⠀⠀⠸⣆⣀⠀⠀⠀⣀⣴⠃⠀⠀⠀⠰⡆⢀⡄⠘⠠⡀⢀⡇⠀⠀⠀⠀⠸⣇⢠⡞⣄⢀⡿
⠀⠀⠀⠀⠈⠛⠿⠁⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠉⠛⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠢⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⡀⠑⢄⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀⢰⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠑⢄⣱⣄⠀⠈⢆⠀⠀⠀⢁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⣀⠊⡀⢿⡇
⠀⠒⢒⣶⠤⠤⣀⡀⠀⣼⠧⢄⡀⣹⢌⠳⡐⠄⢂⠀⠃⠠⠢⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⢀⠴⡯⠂⠈⣀⠜⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠘⠉⣽⣤⠀⣢⡙⠓⠺⠤⣀⠈⠳⣇⠀⠈⢪⢪⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⢀⡀⠀⠾⡩⠴⢿⠁⠀⣀⣠⡤⠤⠒⠚⠛⠗⠠⠄
⠀⠀⠀⠀⡇⠀⠀⢒⢩⠄⠒⠠⢙⣻⢾⣉⠢⣱⣷⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣔⢻⡡⠐⢈⣆⠤⢚⠊⠉⢀⡐⢈⠁⠀⠘⣿⠃
⠀⠀⠀⠀⠛⠻⣍⠉⠡⠋⠀⠀⠒⢿⢸⠀⠉⠻⢏⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠟⠒⠛⡏⣏⡉⠠⠄⠀⡌⠡⠌⢀⣀⣠⠋
⠀⠀⠀⠀⠀⠀⠹⠶⣖⠛⣞⡉⠭⠽⣼⠀⠀⠀⠀⠑⣤⣿⣇⠀⠀⠀⠀⠀⣼⣿⣴⠀⠀⠀⠀⢀⣶⠓⠂⡤⢀⣉⠈⠨⣠⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⢀⣠⠄⠼⠇⣀⠀⠀⣠⣻⣿⣿⡦⠀⠀⠀⢸⣿⣿⣧⡄⠀⡀⠴⠞⠉⠈⠀⠲⢄⡠⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡰⠤⠀⣚⠅⠀⣠⠟⡽⠉⠃⠀⠀⠀⠀⠈⠈⠘⡏⢣⠀⢹⠦⠰⢂⠙⢦⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⡌⣰⡠⠔⢣⡵⠊⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⣞⠓⢀⠽⠒⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠰⢂⣁⢤⡞⠁⣎⡣⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢤⢉⠑⢄⡙⠤⡀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣃⠤⠚⠉⢠⠋⢳⠘⢰⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡊⠢⡸⢏⠓⢄⡐⠲⣿
⠀⠀⠀⠀⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⡞⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡃⢸⠁⠀⡇⠀⠈⠐⠬⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣯⠿⣭⣿⣳⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣴⣿⣶⣿⡿⠏⠁⠈⣉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣯⣿⡿⠛⠇⠀⠀⠀⢀⣾⣟⢙⣿⣀⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢧⠀⠀⢠⣤⣤⣾⣿⣿⡿⠿⠻⢿⣿⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢷⣾⣦⣀⣼⣿⣯⣤⡤⠽⠿⣦⣀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⣹⡿⠏⠁⠀⠀⣀⣀⣠⣤⣽⠷⢶⣤⣀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣿⠷⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⣍⣷⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣄⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣾⠖⠒⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⢻⣿⣿⠛⠛⢻⣿⣿⣿⡿⠿⠛⢋⡽⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣸⣿⣿⣿⣿⣗⢉⣉⡼⠁⠀⠀⣠⣴⠋⡀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣏⣥⠾⠟⠛⣉⠝⠀⠀⣠⣾⠟⠁⡔⠁⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⠋⠀⣠⣴⠞⢛⡿⠛⣻⡟⠁⢀⡞⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⣿⣶⠟⠉⢀⣴⠟⠁⣼⠏⠀⢀⠎⢠⠃⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣿⡦⣤⡾⠃⠀⣼⠏⠀⢠⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⢯⣿⢲⣾⢿⣀⣠⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢏⣿⣓⡾⣭⣟⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⢍⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡩⠐⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠠⡕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠈⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⣀⠁⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡟⠀⠀⠀⠈⣀⡀⠀⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠢⡈⠢⢄⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣟⡠⠐⢁⠔⠈⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠤⠀⢘⡄⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⣰⡁⠠⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⢻⣆⠀⠀⠀⠀⣰⡟⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠲⣄⠀⢻⣆⠀⠀⣼⡟⠀⡠⠖⠃⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⡑⢬⣿⡄⢠⣿⡴⠊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠲⣄⡀⠉⠀⠈⠙⣀⡠⠆⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⢀⡴⢿⠟⠀⠀⠀⠀⠻⢟⢦⡀⠀⠑⠄⣁⠀⠀⠀⠠⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠖⠈⠁⢀⣀⡤⡔⠡⠂⠄⠀⠄⠀⠀⢐⠀⠀⠠⡙⢦⢄⣀⠀⠉⠐⠢⢀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠁⠀⡠⠔⢊⠕⠃⠌⡰⠁⠀⢀⠌⠀⠀⠀⠀⠢⠀⠀⠀⠌⢢⠑⢍⠑⠢⣀⠀⠈⠂⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⢀⠐⠁⠀⠐⠁⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠑⣀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⢀⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠂⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⢄⠀⠀⠊⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⡀⠃⠀⠀⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦

⠀⠀⣾⣟⣲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣿⡆⠀⠀⠀⠀⢠⣶⡶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡄
⠀⠀⣿⡿⣟⣉⣩⣽⣦⠀⠀⠀⠀⢀⣶⣭⣉⣙⡿⣿⡇⠀⠀⠀⠀⢸⣿⠥⣴⢟⣟⡦⡀⠀⠀⠀⠀⠀⢠⢶⣻⡻⣦⠭⣿⠇
⠀⠀⣿⣶⠛⠃⠈⠀⠉⢳⡀⣀⣰⠟⠁⠈⠀⠛⢳⣾⡇⠀⠀⠀⠀⠀⣿⣏⠉⠒⢧⡁⠘⢦⠀⠀⠀⡴⠃⢈⠽⠒⠉⣹⣿
⠀⠀⠘⠧⣄⣀⣀⠀⠀⠀⢹⣿⡃⠀⠀⢀⣀⣀⡤⠟⠀⠀⠀⠀⠀⠀⠹⣏⣉⣁⣉⣙⠒⠄⣱⣷⣎⠤⠒⣉⣉⣈⣉⣹⠋
⠀⠀⠀⡾⠍⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣥⡞⠋⡯⠍⢉⢻⣿⢏⡉⠩⢝⠙⢷⣌
⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠈⡯⢀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⢸⣟⣈⢴⠵⡲⠣⢰⣿⡄⡝⢖⠼⡮⣁⣻⡇
⠀⠀⠀⠻⣇⡀⠀⠀⣠⠊⠀⠁⠈⢢⡀⠀⠀⣀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⣁⡎⣰⢣⠃⠟⠸⡘⣄⢣⣘⣦⡿⠁
⠀⠀⠀⠀⠈⠛⠶⠛⠁⠀⠀⠀⠀⠀⠙⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠁⠀⠀⠀⠙⠛⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿
⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠹⣿⣿⣿⣿⢋⠽⠶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠯⠙⣿⣿⣿⣿
⠹⣿⣷⡙⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠛⣡⣿⣿⠁⠀⣿⣿⣟⣂⠐⢄⠀⠈⢣⡀⠀⠀⠀⢀⠞⠁⠀⡠⠂⣐⣻⣿⡿
⠀⠹⣿⣷⣆⠙⣿⣷⣄⠀⠀⠀⠀⢀⣴⣿⡟⠁⣲⣿⡿⠁⠀⠀⠸⣿⣿⣯⠄⠈⠁⠄⡀⠱⡄⠀⢠⠏⢀⠤⠈⠁⠬⣽⣿⣿⠃
⠀⠀⢻⣿⣿⡄⠘⢻⣿⣷⡀⡄⣰⣿⣿⡛⠀⣼⣿⣿⠃⠀⠀⠀⠀⢻⣿⣶⡶⠂⠀⠀⡈⠠⢽⣿⡧⠄⣀⠀⠀⠐⢶⣶⣿⠟
⠀⠀⠈⢿⣿⣿⣅⠀⢻⣿⣿⣿⣿⣿⠃⢀⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⢨⣿⠿⠛⠋⡛⠓⠀⣸⣿⣇⠀⠚⣛⠙⠛⢿⣿⡅
⠀⠀⠀⠀⠉⣩⣿⣆⡀⠘⡏⡏⡟⠀⣀⣼⣯⡉⠁⠀⠀⠀⠀⠀⠀⢐⣿⠛⢀⡠⢐⠧⠐⠃⡜⣿⢣⠐⠢⠜⠂⢀⡀⠛⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣧⠜⡇⡇⡟⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢁⡀⠁⠀⢀⡜⠁⠛⠈⢦⡀⠀⠀⢀⡈⢻⣿⠇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣴⠇⠀⢻⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣏⣠⠀⣀⡞⠀⠀⠀⠀⠀⢣⣀⠀⣄⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠙⣟⣿⡏⠀⠀⠀⣿⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⢳⡄

⠀⠀⢀⢤⡽⣿⢷⣶⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣶⣾⢯⠿⣥⠄
⠀⠀⠸⣿⣿⠿⠟⠋⠀⣴⠾⣗⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢰⡿⣶⡀⠉⠛⠿⣿⣿⡿
⠀⠀⠀⢿⣿⡄⠀⣤⡼⠿⣿⠛⠻⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⠛⢻⡿⠷⣤⡄⠀⡾⣿⠃
⠀⠀⠀⠈⢿⣿⡾⠛⠋⢉⣉⣙⣦⣄⡀⠙⢷⡄⠀⠀⠀⠀⠀⣴⠟⢁⣀⣤⣞⣉⡉⠙⠛⠻⣾⣿⠍
⠀⠀⠀⠀⠈⢿⡟⠛⠉⠉⠁⠀⠀⢀⣉⣙⡲⢽⣼⡇⠀⣷⣾⠕⣚⣉⣀⠀⠀⠀⠉⠉⠙⢻⣿⠏
⠀⠀⠀⠀⠀⠈⠻⢶⣿⢿⣿⠿⢿⣿⣿⡿⠷⣺⣿⡇⠀⣿⢷⡲⠿⣿⣿⣿⠿⢿⣿⢿⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⣮⣿⢿⣿⣯⠤⠋⠀⣠⠞⡁⠘⠃⠀⠛⠀⠙⢦⡀⠈⠦⢭⣿⡿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⡟⢉⣡⠖⡷⢲⡞⠁⡄⠀⠈⠀⠀⠁⠀⡐⡀⠹⣖⢶⡶⢤⣉⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢺⣷⡋⣠⠞⢡⡟⢀⠌⡄⠀⠀⠀⠀⠀⠀⠰⡐⡄⠙⣆⠙⣆⠉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣤⢿⣀⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⣄⣸⣦⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠚⠛⠋⠉


⠀⠀⠀⠀⠠⠀⠏
⡀⠀⠀⠀⠀⠂⣦⠀⠀⡀⢸⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣄
⣿⠀⠀⠀⠀⡀⠉⠀⢺⣷⢸⣿⣿⣿⣿⣽⣿⣿⡇⣤⣴⣶⣆⣠⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡠⠐⢲⡆⠀⠀⣾⠏⠀⠀⠀⢀⠤⠒⢪⣀⠀⢀⣾⠏⠀⠀⠀⠀⡠⠀⠲⠛⠛⠛⣻⡏⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠛⠁⠀⢴⡿⠀⠀⠀⠐⠁⠀⣤⣛⠒⠂⢰⡿⠀⠀⠀⠀⠈⠀⣀⠚⠛⠛⢿⣿⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠠⣽⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⣬⣿⠃⠀⠀⠀⠀⠐⠛⠛⠛⠿⣷⣿⠃⠀⠀⢠⣾⡿⠛⠁⠀⠀⢀⣲⡟
⠀⠀⠀⣦⠀⠀⠀⠀⠀⠠⡀⠟⠋⠀⠀⣦⠀⠀⠀⠀⠀⠠⡄⠞⠋⠀⠀⣦⠀⠀⠀⠀⠀⠀⡀⠾⠋⠀⠀⢰⡟⠁⠀⠀⠀⠀⣀⠸⠟⠁
⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⢿⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠁⠀⠀⠙⠿⣷⣶⣿⣄⠀⠀⠀⠘⠻⣿⣷⣄⡀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠲⠶⠗⠀⣻⣿⠀⠀⠀⠀⠀⠀⠂⠒⠗⠀⣹⣿⠀⠀⠀⠀⠀⠀⠲⣄⢶⣄⣹⣿⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠳

⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣄
⠀⠀⠀⠀⢰⣿⣿⠋⠁⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠈⢉⣿⣿⡆
⠀⠀⠀⠀⢸⣿⡋⠀⠀⠀⠀⠠⠶⣌⠢⡈⠢⡀⠀⠀⠀⠀⢀⠔⢉⢔⡵⠶⠄⠀⠀⠀⠀⢘⣿⡇
⠀⠀⠀⠀⢾⣿⠋⠀⠀⠀⠀⣓⠀⠀⠑⢜⢆⠀⠀⠀⠀⠀⢀⣴⡵⠋⠀⠀⡟⠀⠀⠀⠀⢘⣿⡷
⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠁⣄⠀⠀⠙⢷⡀⠠⡄⢠⡾⠉⠀⢀⡠⠌⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⠄⢸⣟⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⢈⡹⠶⠂⠦⠤⠤⡤⠴⠖⠒⣿⣿⠆⢸⣿⣟⠒⠒⠒⢶⠖⠒⠒⠒⠺⢯⡀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣐⠀⠀⠀⠀⠀⠐⠁⣹⠂⠘⣇⠨⠑⠀⠀⠀⠀⠀⢅⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢿⠀⠀⡀⠄⠀⠀⡀⡀⠀⠠⠂⠀⡇⠀⠀⢸⡀⠀⢄⠀⢀⢀⠀⠀⠀⢄⠀⠀⡿
⠀⠀⠀⠀⠀⠘⡅⠈⠀⠀⠀⠀⠀⠀⢀⠁⠀⣸⠀⠀⠀⠀⣇⠀⠈⡀⠀⠠⡀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠌⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠡⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠤⠤⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠐⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢫⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡽⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡤⠤⠈⢇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡰⠁⠤⢤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⢄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡠⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣤⣤⣤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⣤⣤
⠀⣿⡷⢾⣉⣉⣹⣿⠷⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⠾⣿⣏⣉⣉⡷⢾⣿
⠀⢹⣵⠾⣥⡤⠴⣯⣁⠾⣷⣟⡲⣄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⢖⣻⣾⠷⣈⣽⠶⢤⣬⠷⣮⡏
⠀⠀⠻⡶⣿⣦⢤⣾⠟⠓⠺⠛⠛⠚⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠓⠛⠛⠗⠚⠻⣷⡤⣴⣿⢶⡟
⠀⠀⠀⠙⣿⣧⣤⣿⡀⠀⠀⣀⣀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣀⠀⠀⢀⣿⣤⣼⣿⠋
⠀⠀⠀⠀⢻⣿⡶⢿⡏⠁⠀⠀⠀⠑⢀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡀⠊⠀⠀⠀⠈⢹⡿⢶⣿⡟
⠀⠀⠀⠀⠀⣿⣷⡞⣧⡄⠠⠤⠄⠒⠛⠒⠠⠀⠀⠀⠱⣄⣤⣤⣠⠎⠀⠀⠀⠄⠚⠛⠒⠠⠤⠄⢠⣼⢳⣾⣿
⠀⠀⠀⠀⠀⢹⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⢈⣿⣿⡁⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⡶⠿⠿⠿⣿⠿⠶⠶⠶⠶⣾⣿⣿⣷⠶⠶⠶⠶⠿⣿⠿⠿⠿⢶⣶⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢠⡟⣻⣏⠀⠀⣀⡀⡀⠁⠀⠀⠁⢀⠴⢹⢻⡟⡍⠦⡀⠈⠀⠀⠈⢀⢀⣀⠀⠀⣹⣟⢻⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣽⠋⠉⠀⠀⡠⠀⠀⣀⡤⠚⠁⠀⠀⣾⣷⠀⠀⠈⠓⢤⣀⠀⠀⢄⠀⠀⠉⠙⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⠄⠐⠚⡡⠘⠉⠁⠀⠀⠀⠃⡄⢹⡏⢠⠘⠀⠀⠀⠈⠉⠃⢌⠓⠂⠠⣤⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠸⠇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣷⣤⣤⣴⠀⢀⠎⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⠱⡀⠀⣦⣤⣤⣾⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣷⣿⣭⣿⣿⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣿⣿⣯⣿⣾⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⠉⠋⠘⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣴⣿⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⡿⠋⢈⡽⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣼⣠⠞⠉⣀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣰⡏⢀⣴⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣴⣿⣿⡣⠔⣋⠤⠝⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠋⠁⣿⣿⣿⣷⣷⣶⣶⣦⣤⣀⢠⣦⣽⣿⣿⠿⠛⠉⢁⣀⣴⣒⣛⠛⣻⡷
⠀⠀⠀⠀⠀⠸⣿⣿⣿⠗⢀⣬⣿⣿⡿⠤⣤⣤⣬⡿⠿⣿⣿⣿⣿⣿⠓⢒⣛⡛⠛⠷⢶⣮⣍⣙⣿⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣤⣿⡟⢁⣠⠖⠉⣀⣤⣶⣿⣿⠟⡝⡉⠻⣆⠀⠀⠩⢍⡓⠲⢤⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⠋⢀⣴⣿⡿⢛⡿⠏⠁⣼⢁⠃⠀⠘⢆⠀⠀⠀⠈⠑⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠟⢋⣿⠗⢋⠄⣠⢞⣿⢸⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⢁⡞⣹⢸⡏⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣀⣿⣈⣷⣼⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠻⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠉⣷⢶⡞⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢅⠺⣯⡿⢗⣃⣤⣤⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠻⠯⠉⣝⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠈⠁⣀⣀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡆⢰⣿⣿⣿⡗⠀⠛⠛⢛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠃⢘⠿⠿⠿⠑⠠⢄⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢄⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡄⠑⢀⢄⠀⠀⠀⠀⢀⠂⠐⠘⠃⠃⠄⠀⢈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠞⠀⢠⠄⢠⠟⠑⠊⢹⠁⠁⠸⠇⢀⡀⠛⠀⢻⠉⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡼⠀⠉⠀⣀⠀⠸⠀⠈⢰⡆⠀⠀⠈⠃⢀⠀⡀⠀⢤⠈⢆⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣀⣐⠃⠀⠄⢰⡇⠀⠀⠀⡇⠀⠀⠘⠃⠁⣀⣤⣴⡇⠀⠀⡶⢤⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⢶⣶⣶⡖⠒⢒⡒⠈⠉⣍⠙⣿⣿⣿⣿⣄⣠⣤⡼⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⢠⠄⠀⠀⠀⠸⡄⠘⢿⣿⣿⣯⣿⠋⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⠀⠈⢸⠀⠀⠀⠀⠹⡄⠈⢿⣿⣸⣷⣷⣿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠐⣡⠟⠁⠀⢀⡿⠀⣷⣬⣴⣶⣶⣾⣿⣿⡄⠘⡏⢁⠃⠇⡉⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢰⣏⠀⠀⠀⣸⡇⢠⠋⠙⠛⠛⠛⠻⠏⢻⣿⡄⠀⢸⣿⣿⠈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⢸⡏⠀⣿⣿⣹⠀⠠⢠⡀⠀⠀⠀⠀⠀⠊⣿⣷⠀⠜⣿⣿⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⢸⡇⢀⣿⣿⡏⢀⠃⢠⠀⠀⠀⠀⢁⠀⠀⢹⣿⡇⢠⡙⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡀⠈⢄⣼⣿⡟⡃⠃⠀⠀⠀⠀⠀⠀⠧⠀⠀⠈⣿⣿⠸⡅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⠃⠀⠀⠀⠀⡠⠉⣁⣉⣤⠀⢿⣿⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣼⣤⣤⣤⣤⣁⣤⢤⣤⡤⡤⣿⢾⣿⣧⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⢁⣿⡗
⠀⠀⠀⢠⠴⠂⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⢁⣷
⠀⠂⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣤⣀⣀⠀⠘⣷⢿⠿⣩⣄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠃⠀⠀⢰⣿⣿⣿⣿⣿⣶⣧⠺⠠⠤⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠎⠀⠀⠀⢘⣿⣿⣿⣿⠋⠉⠹⠇⠠⢁⠀⢀⠀⢠⣾⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣿⣿⡽⠁⠀⡀⠃⠚⠐⠀⢹⣾⣧⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢈⣻⣧⠀⠽⡀⠀⠄⠡⡀⣸⡿⢷⣿⣿⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣾⣿⣿⣄⠀⠁⢤⠠⡀⣸⣿⣽⣿⣿⣧⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣿⣿⣿⣿⣷⣤⣴⣾⠟⠹⣿⣿⣿⣻⠻⡿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢻⢿⣿⣿⣿⠿⠃⣶⣿⣿⡃⠀⠀⠀⢀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⢆⠀⠀⢠⣧⣀⢀⠠⠀⢀⣤⣶⣾⣿⣿⣥⣠⣀
⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣈⣉⣛⣒⣒⣛⣛⣛⣛⣛⣙⣛⣛⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢺⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢋⣩⠼⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡧⢿⣏⡤⠴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢾⢿⣾⣿⣤⡾⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣰⣷⠗⢳⡞⠁⢀⣸⣿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠁⠀⣼⠴⠚⠉⠀⢸⣿⣷⡆
⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣰⢃⣀⡤⠔⠚⠉⠻⣿⡇
⣶⣯⡽⢋⣉⣿⡧⠿⣯⣿⠷⣰⣦⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡼⠉⠁⠀⠀⠀⠀⣀⣴⡷⠃
⠙⢿⣻⣍⡤⠴⢿⣾⣿⢭⣿⡁⠉⠉⠉⠛⠻⠶⣤⣀⠀⣤⣄⡞⠀⡠⠋⠀⠀⣀⣤⣶⠾⠿⢿⣛⡦⣀
⠀⠈⠛⣿⣷⠶⣿⡁⢀⣀⠤⠽⠲⠤⣄⣀⣀⣀⠀⠉⠙⣿⣿⣧⣊⣤⣴⣶⢿⣛⡉⠤⠤⠒⠚⠛⢻⣿⣧
⠀⠀⠀⠀⠸⣻⣟⣿⠉⠀⠀⣀⠤⠒⠉⠀⠈⠉⠉⣉⣭⡼⢿⣿⡍⡀⠀⠀⠀⠈⠑⠒⠶⡒⠒⠒⠛⢻⣟
⠀⠀⠀⠀⠀⠘⣽⣿⣷⠚⠉⠀⠀⠀⣀⣠⣤⣶⡾⠛⠁⢀⢺⣿⡿⠢⢍⠒⠲⠤⣤⡤⠖⠛⠦⣄⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠘⢽⡿⣤⣤⣤⣶⠿⠛⢋⡁⠾⠁⠀⢠⠎⡄⢸⣿⣧⣄⠙⠢⣀⠈⢻⣶⡀⠀⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢹⣏⣿⡤⠒⢁⣴⠃⠀⣠⠃⢀⠇⢸⠙⣿⡈⠳⣄⠈⠓⢄⠀⠙⣦⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡏⢀⠔⠁⢧⠔⠊⣿⠀⢸⠀⢸⠀⢸⣷⡀⠈⠳⣤⣀⣿⣺⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠁⠀⠀⡇⠀⠘⡿⠀⡌⠀⣼⠀⠀⢿⡇⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⢷⣦⣼⣄⡀⢀⣇⣀⣧⡠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣯⣿⣾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣟⣿⢛⠃⠹⢹⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⡄⠀⠀⣼⡟⠋⢿⠉⠙⣿⠛⣇⣸⣧⣇⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠙⢫⡉⠹⡛⢻⣷⣆⣿⡇⠀⢸⠀⠀⡏⢀⠿⣯⣬⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡝⠓⢦⡀⠡⠀⠇⠘⡇⢻⣿⠃⠀⢸⠀⢀⣤⠾⢾⣩⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠤⣄⡉⠲⡏⠚⢄⡃⣼⣿⠀⠀⠀⣰⠋⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠦⢄⡈⠛⠷⣥⠀⠀⢹⣹⡏⠀⠀⡼⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡈⠛⢦⡈⠳⣄⠀⣿⡇⠀⠈⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠐⣬⣣⣿⣧⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠓⠿⠿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⢀⡠⠐⣩⠟⣿⡏⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣁⡤⠞⠋⣠⠞⠁⢠⣿⡇⠀⢀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢀⣤⡾⢋⠅⠀⣠⠾⣸⡇⠀⠀⢣⡀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⠏⠉⣀⠔⢻⠆⠚⢡⠀⢿⣇⠀⠀⠀⠳⣄⠀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣷⡞⠁⢠⠂⢰⠃⣸⣠⣿⣿⠀⠀⡄⠀⢈⠙⠶⢾⢹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⣶⣧⣤⣿⣶⡿⠟⢹⣿⠀⠀⡇⠀⢸⡄⢸⣾⡏⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠀⠀⠀⣿⣦⣴⣧⣀⣼⣧⣼⡋⣻⢻⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣧⣧⢀⡄⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⣿⣾⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⠷⣖⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣊⠙⠛⠻⣿⢛⣿⣦
⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣷⣶⣶⣿⣿⡻⢕⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣞⢑⡫⠿⣿⣶⣿⣮⣭⢻⣏⡻⠆
⠀⠀⠀⠀⠀⠈⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣛⣷⠄⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡾⠇⢻⣯⣴⣺⣯⡽⢿⣷⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠹⡿⣛⣿⣿⣿⣿⣿⣟⣿⡿⣦⢈⣓⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢨⣎⣀⣠⢽⣿⣩⣿⣿⣿⣮⠿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣿⣿⣭⣿⣮⣽⣿⣿⣝⣿⢦⡀⠀⠀⠀⠀⣠⣻⢫⣮⣿⣿⣒⣿⣷⢾⣷⣆⡻⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣃⣿⣿⣿⣿⡛⢛⣻⣿⠻⢿⣿⣿⣷⡄⠀⠀⣼⡟⣵⡿⢟⣹⣷⣤⠈⣽⣿⣽⣿⢧⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⣾⣉⣿⠿⣷⣾⠿⢿⣿⣷⣯⣻⣧⢁⣰⣶⡡⢚⣵⣾⠿⢷⣿⠻⣷⣿⡻⢷⡹⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢉⣩⣽⡹⣿⣇⣿⡿⠉⢛⣾⣿⣿⣗⣪⡥⢿⣇⣻⣿⣰⠶⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣷⣷⣄⠿⣯⣥⡴⣾⠟⡋⡴⢹⡏⢮⣟⠿⣿⢶⣶⣞⢣⣜⣿⡎⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢽⣿⣾⣹⣿⠝⣋⡹⢏⣥⡜⡜⠀⠀⡇⠊⢎⢳⣾⢿⣋⣍⣫⣿⣌⣿⣿⢛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡛⢫⣬⣽⡏⣝⡉⡍⡙⢣⠀⠍⡹⠀⠀⠀⡇⠀⠈⢇⢩⠘⡟⣃⣃⢨⣢⣭⣿⢶⡟⣭⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⣣⣾⢙⣛⠿⡿⠧⢾⡿⠎⣾⠦⠁⠀⠀⠐⠇⠀⠀⠈⡜⡿⢑⡻⠟⣝⡿⠋⣯⡔⠿⢯⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣴⡦⡨⢟⡃⢾⡾⠇⠺⠿⣍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠝⣠⠻⠛⣘⡻⡟⣀⣉⣁⡰⡆⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠟⠹⠋⣴⡌⠿⠸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠻⠱⠷⠈⠋⠙⠃


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢣⡜⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠤⠶⢤⣤⣀⣤⣤⣦⣼⣾⣿⡟⢹⡏⢻⣿⣷⣦⣴⣄⣤⣀⣤⡤⠶⠤⠶⠤⠤⡄
⠀⠀⠀⠀⠀⠀⣀⡀⠛⣡⠤⠒⠚⠛⠛⠉⠻⣿⡿⠿⠟⣛⣵⣿⠏⢀⣾⣷⡀⠹⣷⣮⣛⠻⠿⢿⣿⠟⠉⠛⠛⠒⠲⠤⣌⠛⢀⣀
⠀⠀⠀⠀⣀⠈⣩⡖⠋⠀⠀⠀⠒⠀⠈⠀⠀⢀⣠⣴⣾⣿⡿⢃⣠⣾⠻⠟⣷⣄⡘⢿⣿⣷⣦⣄⡀⠀⠀⠁⠀⠒⠀⠀⠀⠙⢶⣍⠁⣀
⠀⠀⠀⠀⠋⣴⠋⠀⠀⣀⣤⣴⣶⣶⣶⡶⠖⣯⠀⢸⣿⣿⣾⢿⡿⠃⠰⠆⠘⢿⣿⣷⣿⣿⡇⢀⣽⠲⢶⣶⣶⣶⣦⣤⣀⠀⠀⠙⣦⠙
⠀⠀⢀⡮⢠⠇⠀⣼⣿⡿⠿⠛⣻⡿⠋⣀⠀⠀⣰⡿⠏⠁⠁⢸⡇⠀⠺⠗⠀⢸⡇⠈⠈⠙⢿⣆⠀⠀⣀⠙⢿⣍⠛⢟⢿⣿⣦⠀⢸⡄⢰⡀
⠀⠀⠀⡇⢸⠀⢀⣿⡗⠀⠀⠀⣾⠃⠀⠉⢀⣾⠏⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠻⣧⡀⠉⠀⠘⣧⠀⠀⠀⢻⣿⠀⢀⡇⢸
⠀⠀⢠⡆⢸⡇⢸⡿⠀⠀⠀⢠⡇⢠⡦⠀⢸⡇⠀⠀⠀⠀⠀⠀⣷⠀⢰⡆⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⢴⡄⢸⡄⠀⠀⠠⢿⡇⢸⠇⢸⡄
⠀⠀⠈⢣⠀⣷⠈⣇⠀⠀⠀⠀⡃⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠸⠀⠀⠀⠀⣸⠁⣼⠀⡜⠁
⠀⠀⠀⢸⡆⢹⡄⠘⡆⠀⠀⠀⣇⠸⠇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠺⠇⣸⠀⠀⠀⢰⠃⢠⡏⢰⡅
⠀⠀⠀⠈⢣⠀⡇⢠⣰⡄⠀⠀⠹⡄⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢨⠃⠘⡅⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⠏⠀⠀⢠⣆⡄⣸⠀⡜⠁
⠀⠀⠀⠀⣾⣠⣿⣞⢻⣿⣄⠀⠀⢣⠘⠃⠀⠀⢷⡄⠀⠀⠀⠀⠀⡼⠀⠀⢧⠀⠀⠀⠀⠀⢠⡾⠀⠀⠘⠃⡞⠀⠀⣰⣿⡟⣷⣿⣄⣷
⠀⠀⠀⠀⠈⠉⠙⢏⣈⣹⣿⡿⢷⣌⣷⣀⣄⠀⣞⣿⣦⣤⢀⡀⣴⣷⣶⣶⣾⡦⣀⣀⣠⣴⣿⡳⠀⣠⣀⣾⣡⡾⣿⣿⣏⣀⡹⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢭⣍⣉⠙⠛⠛⠻⠿⠿⠶⠾⠿⠿⠿⠿⠿⠤⠿⠋⠙⠿⠥⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠛⠓⠛⣉⣉⡭⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡦⠌⢭⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣭⠡⣤⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢞⠻⠭⣤⣀⣠⠄⠀⠀⠀⣩⡟⠛⢿⠅⠀⠀⢀⠖⠲⡀⠀⠀⠸⡿⠛⢿⡝⠂⠀⠀⢠⣄⣀⣤⠭⠟⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠨⠭⢁⣀⠀⣠⠾⠿⠶⠟⠀⠀⠀⠘⠦⠴⢃⡀⠀⠈⠿⠶⠿⠷⢄⠀⣀⡈⠭⠅⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁

⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣴⣯⣍⣽⣏⡉⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⢋⣉⣿⣉⣭⣷
⠀⠀⠀⠀⢸⣿⣤⣿⣿⡈⠙⡛⠉⠁⣐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⡈⠉⠛⡋⠉⣸⣿⣥⣼⡟
⠀⠀⠀⠀⠀⣿⡇⢼⣨⣧⠀⠁⠀⣼⣿⡆⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠠⣿⣷⡄⠈⠁⣸⣇⣻⢄⣿⠇
⠀⠀⠀⠀⠀⢸⣧⢸⡄⢿⡀⠀⠤⣉⠁⣠⣾⣿⣿⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⢸⣿⣷⣦⠀⢉⡥⠀⠀⣿⢇⡿⢰⣿
⠀⠀⠀⠀⠀⢸⣇⢠⡇⢸⣧⠀⠀⠀⠀⠙⠿⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠻⠟⡀⠀⠀⠀⢠⡷⠸⡇⢠⣿
⠀⠀⠀⠀⠀⠘⣷⡀⣗⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⣸⡏
⠀⠀⠀⠀⠀⠀⢹⡇⢸⠀⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⣀⠀⠀⢀⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠁⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢿⡈⢧⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣄⢰⣿⣷⢀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠣⠸⠧⠀⠀⢀⣀⣀⣀⢀⠀⠀⢚⣿⣿⣿⣿⣏⡉⣩⣿⣿⣿⣿⣟⠀⠀⠀⣀⣀⣀⣀⠀⠀⠰⠟⠰⠡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢲⡌⠉⠛⠟⠛⠛⠛⠟⠛⢛⣿⣿⣏⣄⣼⣿⣿⣟⠛⠛⠟⠛⠛⠛⠟⠋⢩⣶⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣏⡀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠳⣫⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠈⣿⣁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣌⠛⣁⡼⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⠇⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠤⣾⡁⣿⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢣⣈⠛⣉⢴⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⠀⣿⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⢻⡀⢿⣄⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠸⣖⠤⢖⡿⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⢀⣾⠆⣿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠺⣧⠈⢿⣤⣀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠻⠀⠀⣀⣠⣾⠃⣤⠟⠠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⣸⣧⣄⠋⠙⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠉⢡⣤⣿⡀⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣀⣈⠛⢷⣄⣉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢉⣡⣴⠟⢇⣀⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠉⠉⠻⣦⠀⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⣠⡞⠋⠉⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⢷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠀⣤⣿⠟⠋⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⡿⠏⡂⢀⣠⣀⣲⡾⠃⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢽⣻⣿⡾⣶⣧⣴⣤⣴⡞⠀⠀⠀⠀⢉⣿⡏⠀⠀⠀⠀⠀⠀⣻⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢠⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣯⣀⣰⠀⠀⠙⠾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣻⣿⠀⠀⠀⢀⡄⠈⣹⠋
⠀⠀⠈⢿⠇⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣽⣿⣄⣠⠆⠁⢀⠞⠁
⠀⠀⠀⠘⣟⡀⠀⠀⠈⡀⠀⠀⠀⠀⠒⠂⠀⢀⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣼⣿⣿⣿⣿⠉⠀⡤⠋
⠀⠀⠀⠀⢹⡄⠀⠀⢰⣿⣶⡖⠀⠀⠀⠀⣄⣾⠏⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡐⠃⠀⣺⡃⠀⣿⣃⠀⠙⠈⢒⡟
⠀⠀⠀⠀⢸⣏⠀⠀⠀⠼⡏⠉⠀⢀⣀⣰⠞⠁⠀⠀⠀⠈⠙⢶⣋⠐⢄⠀⠀⢰⠁⠀⠀⠈⡧⠀⠘⠋⠀⣤⠔⠋
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠃⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠛⢦⣾⣁⡀⠀⣸⣧
⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⢤⣠⡴⠟⠁⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠙⢶⡞⢿⡿⠁⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⢿⡄⠀⠀⠀⠀⠀⠈⠻⢿⣅⠀⢤⡾⠁⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣤⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠄⠀⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠀⠀⢨⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣏⠁⠀⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧⡀⠀⡸⠃⠀⠑⢆⠀⠀⠀⠀⠀⠀⣾⠉⠩⠀⠓⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢤⣤⣼⣿⣿⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠃⠀⠀⣀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡛⠛⠃⠀⠠⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠖⠤⣄⣀⣄⣀⣤⣤⠞⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⠤⠤⠾

⣴⣿⢯⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣖⣻⣷
⢻⣿⣿⣿⡿⢻⣿⠍⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⡿⠩⣿⠿⢾⣿⣿
⠀⢻⣯⣿⣿⣉⣹⣶⣿⠻⣽⣯⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⡽⠛⣿⣿⠉⣻⣟⣿⡿
⠀⠀⠙⣿⣭⡿⡍⠀⠉⠙⢿⣉⠉⠛⢿⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⢻⡿⠛⠉⢉⣹⣿⣯⣿⠟
⠀⠀⠀⢸⣿⣻⡋⠉⠉⠉⠉⠛⠳⣤⣀⠈⠻⣦⡀⠠⡀⠀⠀⢀⣴⡿⢋⣀⣤⡾⠛⠉⠉⠉⠉⢻⣟⣿⡏
⠀⠀⠀⠀⢿⣷⡿⠒⠒⠓⠒⠚⠉⠉⠉⠙⠳⣬⣿⣄⣿⣷⣠⢋⣥⠞⠋⠉⠉⠉⠙⠛⠛⠒⠾⣿⣿⡿
⠀⠀⠀⠀⠘⢿⣷⣤⣶⣴⣶⣶⣤⣤⣶⣶⡶⠾⣿⢫⡟⢿⡗⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣮⡿⠃
⠀⠀⠀⠀⠀⠀⠉⣩⣭⠋⠉⣉⣉⣙⣵⠖⠛⠉⡹⢿⣿⣿⡿⡉⠙⠲⢶⣟⡛⠉⠉⠉⢻⣍⡉⠉
⠀⠀⠀⠀⠀⢠⢾⣿⠷⠚⠋⣉⣤⡾⠃⠀⣠⠞⢱⣿⣿⣿⣷⡘⢦⡀⠀⠹⣯⣉⠓⠶⢤⣿⣿⣦
⠀⠀⠀⠀⠀⠿⣯⣅⣠⠔⠋⣩⣆⣠⣴⡾⠁⣠⢣⠏⣿⣿⢡⢳⡀⠙⣦⣤⣈⣯⡓⠦⣄⡈⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣇⣠⠞⢩⡟⠁⡾⠁⣰⠃⠈⠀⢼⡇⠩⡆⢳⡀⠸⣧⠙⢏⠛⢦⡀⢙⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⡏⠀⣸⠃⢠⡏⢠⠆⠀⢸⡇⠀⢳⠀⢷⠁⠹⡆⠘⣆⣀⣽⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠁⠀⠈⢦⣼⣧⣶⣿⣶⣿⣿⠟⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣯⣽⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤⣶⡟⠛⣿⠷⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⢿⡟⠛⣷⣦⣄
⣾⣿⣟⣿⡟⢻⣶⣾⣿⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣾⣿⣶⣾⠛⣿⣟⣿⣿
⢷⢿⣿⣟⣻⡟⠁⠀⠀⠀⠀⢿⣿⡛⠻⢿⣷⣄⡀⠀⠲⣤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⣀⣴⣿⠿⠛⣻⣿⠇⠀⠀⠀⠀⠙⣿⣛⣿⣿⢷
⠘⣿⢿⣿⣿⣶⣤⣤⣄⣀⣀⠀⢻⣷⡄⠀⠈⠙⠿⣦⡀⠀⠙⢆⠀⠀⠀⢀⠔⠁⠀⣠⡾⠟⠉⠀⠀⣴⣿⠃⢀⣀⣀⣤⣤⣴⣾⣿⣿⢿⡟
⠀⠘⣿⢿⡏⠉⠉⠈⠉⠉⠉⠉⠙⠛⢿⣦⡀⠀⠀⠈⠻⣦⠀⠀⢣⠀⢠⠊⠀⢠⡾⠋⠀⠀⠀⣠⣾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⣿⢿⡟
⠀⠀⠸⡿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠈⢷⡀⢀⣷⣇⠀⣰⠏⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⡿
⠀⠀⠀⣷⣿⡿⠿⠿⠿⠟⠛⠛⠒⠒⠶⠶⠶⠾⠿⠶⣄⡀⠀⠻⣴⣿⣷⡼⠃⠀⣀⣴⠾⠿⠶⠶⠶⠖⠒⠚⠛⠻⠿⠿⠿⠿⣿⣷⡇
⠀⠀⠀⢻⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣿⣿⣿⣧⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⠃
⠀⠀⠀⠈⢿⣼⣷⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⡶⠶⠶⠶⠓⠒⠚⣿⣿⣿⡟⠒⠒⠲⠶⠶⠶⣶⣶⣤⣤⣤⣄⣀⣀⣀⣠⣴⣿⣼⠏
⠀⠀⠀⠀⠀⠉⠻⠾⢿⣿⣿⠿⠿⠿⠯⠥⣤⣤⠴⠶⠒⠛⢋⣩⣿⣿⣿⣯⣉⠛⠓⠲⠶⢤⣤⡤⠭⠿⠿⠿⢿⣿⣿⠿⠾⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣤⣤⠤⠤⠤⣴⡿⠀⠀⠀⣠⡴⠋⣡⢿⣿⣿⢧⡉⠳⣤⡀⠀⠀⠸⣷⡤⠤⠤⣤⣤⣬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣾⣾⠁⠀⢀⣀⡤⠤⣾⣉⣀⣤⣶⠟⠁⠀⣴⠃⢈⣿⣇⠀⢳⡄⠀⠙⢷⣦⣄⣈⣹⡦⠤⣄⣀⠀⠀⢹⣾⡆
⠀⠀⠀⠀⠀⠀⢿⢿⡶⠟⠉⠀⣀⡴⠊⠉⢁⡼⠁⠀⢠⡾⠁⢀⡜⣿⡟⣆⠀⠹⣦⠀⠀⠹⣄⠉⠉⠲⣄⡀⠉⠙⠷⣾⢿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⢧⣀⣤⠞⠉⠀⠀⢰⡿⠀⠀⣰⠟⠀⢀⠞⠀⣿⡇⠘⢆⠀⠘⢷⡀⠀⠸⣷⠀⠀⠈⠛⢦⡀⣠⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣇⠀⠀⠀⣰⠏⠀⢀⣼⠋⠀⡠⠋⠀⠀⣿⡇⠀⠈⠣⡀⠈⢻⣄⠀⠈⢷⡀⠀⠀⢈⣿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣴⣏⣀⢀⣾⣃⣤⠞⠁⠀⠀⠀⢹⡇⠀⠀⠀⠘⢦⣄⣻⣆⠀⣈⣷⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⣏⣿⣯⡿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣏⣿⣷⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣉⢀⣴⠛⠉⠉⠉⠙⠛⠶⣤⣿⣿⣿⣿⣤⠶⠛⠋⠉⠉⠉⠛⣦⡀⣉⠻⣆
⠀⠀⠀⠀⠀⢀⣀⡀⠀⡏⠰⡿⢸⡇⠀⠀⠀⢀⣀⣀⠤⠀⣿⠀⠀⣿⠁⠤⣀⣀⡀⠀⠀⠀⢸⡇⢿⠆⢹⠀⢀⣀⡀
⠀⣴⡿⢛⡿⠿⠛⠛⠛⢿⡀⣤⡘⣷⠛⠛⠛⠋⠉⠀⠀⠀⡿⢸⡇⢿⠀⠀⠀⠉⠙⠛⠛⠛⣾⢃⣤⠀⡿⠛⠛⠛⠿⢿⡛⢷⣦
⣴⡏⢰⡏⠀⠀⠀⠀⠀⠘⣧⠘⠃⠹⣆⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⣰⠇⠘⠃⣼⠃⠀⠀⠀⠀⠀⢹⡆⢹
⠻⡇⢸⡄⠀⠀⠀⠀⠀⠀⠈⢷⡘⣷⡘⣦⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⣴⢃⣾⢃⡾⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸
⠀⣿⡌⢧⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢠⡌⢷⡀⠀⠀⠀⠀⡇⢈⡁⢸⠀⠀⠀⠀⢀⡾⢡⡄⢠⡞⠁⠀⠀⠀⠀⠀⠀⢀⡼⢡⣿
⠀⠙⠿⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠛⠀⢳⡀⠀⠀⠀⡇⢸⡇⢸⠀⠀⠀⢀⡞⠀⠛⣱⠏⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠿⠋
⠀⠀⠀⢿⣦⠹⡄⠀⠀⠀⠀⠀⠀⠀⢹⡄⢿⡄⢳⠀⠀⠀⠀⣨⣅⠀⠀⠀⠀⡞⢠⡿⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⡿
⠀⠀⠀⠀⠙⢧⠙⢀⠀⠀⠀⠀⠀⠀⠀⠇⢈⣤⣌⠇⠀⠀⢾⣿⣿⡷⠀⠀⠸⣡⣤⡁⢸⠀⠀⠀⠀⠀⠀⠀⡀⠋⡼⠋
⠀⠀⠀⠠⡶⢾⡟⠿⠳⣦⠀⠀⠀⣴⣶⢀⣘⣻⣫⣤⡀⣶⣶⣾⣷⣶⣶⢀⣤⣝⣟⣃⡀⣶⣦⠀⠀⠀⣴⠞⠿⢻⡷⢶⠄
⠀⠀⠀⠿⠷⣼⡟⠛⠛⠧⣶⣷⠀⣾⡿⠛⢃⣿⣷⣛⠁⣈⣿⡿⢿⣿⣁⠘⣛⣾⣿⡘⠛⢿⣷⠀⣾⣶⠼⠛⠛⢻⣧⠾⠿
⠀⠀⠀⠀⠀⢿⣷⣦⢠⣶⣄⣙⡲⠿⠿⠿⠯⠼⠧⠽⠿⢿⢿⢥⡬⠿⠿⠿⠯⠼⠧⠽⠿⠿⠿⢖⣉⣠⣶⡄⣴⣾⡿
⠀⠀⠀⠀⠀⠀⢯⣿⣷⣶⠒⣾⣿⣋⣿⡿⢿⣏⣹⡿⢿⣏⣹⠟⠻⣏⣹⡿⢿⣏⣹⡿⠻⣿⣙⣿⣶⠒⣶⣾⣿⡽
⠀⠀⠀⠀⠀⠀⢸⣏⠀⢹⣿⣯⣼⡿⢿⣄⣠⡿⢻⣷⣾⡟⢻⣦⣴⡟⢻⣷⣾⡟⢿⣄⣠⡿⢿⣧⣽⣿⡏⠀⣹⡇
⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠷⣚⣛⣓⣚⣛⡛⠛⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠿⠛⢛⣛⣓⣚⣛⣓⠾⠿⠿⠿⣇
⣶⣶⡶⣶⣶⣶⣿⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣿⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⡿⣿⣙⡶⠿⠿⡶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⠿⠿⢶⣋⣿⢿
⠀⢿⡯⣭⡗⠒⢚⣻⡿⢈⣿⣵⣦⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣮⣿⡁⢿⣟⣓⠒⢺⣭⢽⡿
⠀⠈⢷⣏⣹⡏⠉⢙⣿⣮⣉⣻⣷⣮⣑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣵⣾⣟⣉⣵⣿⡋⠉⢹⣟⣹⡾⠁
⠀⠀⠈⢿⣽⣾⠛⢻⡟⠁⠀⠉⠂⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠐⠉⠁⠈⢻⡟⠛⡷⣯⡿⠁
⠀⠀⠀⠀⢹⣿⡶⢾⣷⣄⡀⠀⠤⠦⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⠴⠤⠀⢀⣠⣾⡷⢶⣿⡏
⠀⠀⠀⠀⠘⣿⢿⠛⢿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⡿⠛⡿⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣛⣦⠄⠐⠒⠒⠚⠉⠉⠐⠂⢀⠀⠀⠙⣄⣶⣶⣠⠋⠀⠀⡀⠄⠂⠉⠉⠓⠒⠒⠂⠠⣴⣛⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢈⣿⣿⡁⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⠿⠿⢿⢿⡿⠿⠶⠶⠶⠶⣿⣿⣿⣿⠶⠶⠶⠶⠾⢿⡿⡿⠿⠿⣶⣶⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⡏⠀⠀⠀⠀⣠⠊⠀⠀⠈⠀⢀⠔⢹⢿⡿⡏⢢⡀⠀⠉⠀⠀⠑⣄⠀⠀⠀⠀⢹⣿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⠟⠉⠉⠉⢁⠁⠀⠀⢀⡤⠒⠁⠀⠃⣾⣷⠘⠀⠈⠓⢤⡀⠀⠀⠈⡀⠉⠉⠉⠛⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⣀⣀⠠⠴⠃⠰⠖⠋⠉⠀⠀⠠⠃⡄⢿⡿⢠⠘⠄⠀⠀⠉⠙⠲⠆⠘⠦⠄⣀⣀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡏⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢹⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣏⠀⠀⢀⡄⠀⢀⠄⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⠠⡀⠀⢠⡀⠀⠀⣹⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣟⣿⣟⣻⡿⣦⢴⡏⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⢹⣦⣴⢿⣟⣻⣿⣻⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠽⢿⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡿⠯⠿⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⣟⣶⣄⠀⠀⠶⢀⣤⣫⣤⣴⣿⡿⠉⠩⠿⣿⠃⠀⠀⠀⣴⣾⣿⣿⠗
⠀⠀⠀⠀⠀⢠⣿⣟⠍⢻⣶⢾⣿⣏⠁⠀⠀⠀⠀⠀⠀⣀⣾⣥⣤⣀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣦⣷⣀⣽⣧⣽⣯⢷⣦⣄⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⠒⠍⣿⣿⣿⡄⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣌⣡
⠀⠀⠀⠀⣴⣿⣿⣷⣦⣿⠈⣿⡻⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠅
⠀⠀⠀⢀⣿⣿⣿⡌⠻⣿⣇⢻⣿⣿⡿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠶⠤⠄
⠀⠀⠀⢸⣿⣓⣿⣇⠀⠸⣿⣾⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡽⣿⠿⠿⣛⠓
⠀⠀⠀⠘⣿⡧⣿⣿⣻⣷⣿⣿⣿⣿⠻⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⠂
⠀⠀⠀⠀⠙⢿⣿⣿⣋⣥⣾⣿⣿⣿⣟⡷⣿⣿⣿⣡⣺⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⣿⣿⣿⣵⡂
⠀⠀⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣦⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⢟⣿⣛⣿⣿⣟⣻⢿⣿⣾⣼⣹⣿⣧⠙⠙⣿⡉⠙⢿⣿⣿⣿⣿⣿⣿⡿⡿⢷⣝⣻⣿⡇
⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣾⣼⣭⣟⣿⣻⣿⣦⣆⣿⣇⡘⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣯⡟
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠉⠉⠛⠻⠟⠛⠛⠉⠛⠛⠛⠛⠿⠿⢷⠿⠻⠿⠿⠟⠻⠏⠓⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠶⠶⠖⠶⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣤⣶⣾⠋⡉⠀⠀⠀⠀⠀⢀⣀⡀⠀⣄⡵
⠀⠀⠀⠀⠀⠀⡆⠄⠀⡀⢀⣀⡀⢀⣀⢀⠔⠒⠘⠿⠷⣦⣄⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣀⡴⠿⠋⠉⠀⠀⠐⣠⠜⠒⠀⠉⠉⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠉⠀⠀⠈⠙⠀⠀⠀⠀⠀⠈⠉⠛⣷⣄⡀⠀⠈⡀⠀⠀⣠⡾⠋⠀⠀⠀⢀⠠⡴⠖⠄⠚⠳⠢⠤⢀⡀⠀⠀⠚⠙
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠁⢄⠤⠀⠐⠚⠉⠀⠘⠁⠐⣂⣀⣀⣤⣐⣿⣿⣦⡞⡿⣷⣾⣯⣄⡤⠤⢂⣘⣻⡀⠀⠛⠒⠤⠤⢀⡀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⡀⠀⠀⠀⠀⠔⠚⠊⠉⢀⢀⡶⠶⠒⠒⠙⠛⡿⡟⣿⠟⠉⠤⣄⣂⡀⠀⠈⠉⠒⠄⠀⠀⠀⠀⠉⠙⠒⠁⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠚⠁⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⣀⣠⣭⠄⡇⠀⢸⣤⣠⣤⣀⠀⠀⠁⠒⠀⠀⠀⠈⠒⢦⣄⠀⠀⠦⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡰⢀⡤⠂⠁⠀⠀⠀⣀⠄⣦⠿⢋⡵⢢⠂⣴⣔⣯⠲⡙⢯⠛⢟⡶⠤⣀⠀⠀⠐⢦⣀⠈⢃⣀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠤⠆⠀⢀⣤⠖⠉⠠⠚⢁⡴⠁⡴⠁⢸⣿⠀⢻⣇⠑⣄⠱⣄⠈⠀⠄⡙⠲⢤⣄⡈⢣⣠⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠛⡏⢡⡤⠂⠀⡠⠈⠀⠜⠀⢀⠆⢸⡀⡧⢘⠀⠈⢆⠀⠃⠀⠀⠀⠈⠒⡌⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⠁⠀⡠⠊⠀⠀⠈⠀⠀⡌⠀⠈⢧⠃⠀⢀⠀⠀⠒⡀⠀⠑⠤⡀⡂⢦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠁⠌⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠈⢲⡀⠀⠈⠢⣀⠠⢨⡄⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⡀⠀⣀⠀⠀⡀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠀⢘⡁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠚⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⠁








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄
⠀⠀⢀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢠⡿⣧⡀
⠀⠀⢻⣿⡀⢿⡾⠉⠛⠳⠶⣄⡀⢀⡀⢀⡤⠶⠞⠛⠙⢿⡇⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡞⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠙⢿⣬⠃⠀⠉⠀⠀⢀⣹⣾⣷⣏⠀⠀⠀⠁⠀⠸⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠑⠀⠹⡄⠀⠀⠀⢀⣠⣴⣾⡏⢻⡗
⠀⠀⠀⠀⠈⠻⣷⣤⣤⠶⠛⠉⢨⣿⣿⡄⡙⠓⠶⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢶⣤⢤⣀⡀⢻⣠⣠⠖⠋⠁⠀⠹⢡⡾⠁
⠀⠀⠀⠀⠀⠀⣿⡀⠺⡄⠀⠁⢸⢿⢻⡇⠈⠀⣰⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡞⠁⠀⠀⠙⣿⣿⡷⢤⡀⠀⠀⣨⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣄⡹⢀⡠⠋⠘⠀⠳⣄⠰⡃⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⡗⠀⠒⠀⣾⢻⡿⠀⠀⢸⠷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠓⣀⣠⠞⢁⡿⡇⠈⢀⡜⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠈⠁⢣⡠⠞⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠛⠁
⠀⠀⠀⠀⠀⢀⣾⢟⣿⡿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⣿⡆
⠀⠀⠀⠀⢀⣾⣯⡾⠏⣠⣴⡇⠀⠀⠀⠀⠀⠀⠸⣷⢀⡿⠞⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠳⢿⡀⣾⠇
⠀⠀⠀⢀⣿⣿⡿⠙⠉⠙⢳⡇⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠁⠄⠀⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄
⠀⠀⣀⣤⣿⢽⣄⠀⠀⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣀⣀⣀⣀⣸⣶⣶⣇⣀⣀⣀⣀⣠⡿⠇⠀⠀⠀⠀⠀⠀⣴⣶⣾⣥⡈⢿⣆
⢀⣼⡟⢉⡠⠞⠛⢦⡀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣽⠁⠀⠂⢉⣿⣿⡉⠐⠀⠈⣯⠱⣄⠀⠀⠀⠀⠀⠀⠈⣯⣀⣙⢿⣿⣑⠛⣷⡄
⢸⡿⢀⡞⠁⢄⡀⠂⢷⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⡄⠐⠁⣸⢻⡟⣇⠈⠂⢠⡗⢨⣿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⠉⠉⢻⣇⡼⠁
⠈⢿⣬⣀⣀⣀⣴⠶⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡓⣀⡴⠋⠘⠃⠘⢦⣀⠞⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⠀⠀⣼⣋⣛⠛⢷⣦
⠀⠈⠙⠉⠉⠉⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡜⠁⠀⠈⠳⡄⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠙⢿⣾⣇⣀⠐⠁⠀⢈⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠙⣇⠀⠀⠀⠀⠀⠀⠉⠛⢯⣉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⠧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⣶⣦⣄⠀⠀⠀⠀⡟⠠⠀⠩⣧
⠀⠀⠀⠀⢀⣠⣴⣶⠛⢋⠉⠀⢠⣿⣿⡀⠀⠉⡛⠓⡶⣤⣄⡀⠀⠀⠀⠹⣦⡹⡏⠈⡛⠲⢄⣤⡇⠀⣀⣴⢋
⠀⠀⠀⠰⣿⣅⣙⠧⡀⠀⠀⣰⠛⣿⣿⠻⣄⠀⠀⢀⠞⣋⣨⣷⠀⠀⠀⠀⠈⢳⣇⠀⠀⢀⡠⣿⣿⡏⠀⠈⣌⢳⡀
⠀⠀⠀⠀⠈⠙⠛⣿⣷⣶⡞⠃⢠⡿⢿⡀⠙⣶⣶⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⠓⡚⡇⠀⡀⣿⢿⠣⡁⠘⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣬⡴⠋⠀⠀⠱⣬⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢆⡁⠘⠈⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠄⣠⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢰⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠚⠃⣰⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠗⢀⣉⣃⡀⠻⠀⢶⠆⢰⡄⣴⡄⠙⠛⣛⠋⠤⣶⢠⣆⢰⡄⠰⠶⠘⠗⠐⠓⠠⠷⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⣴⠟⠛⠛⠓⠦⠈⠀⡀⣶⣶⣶⡇⠘⢠⣭⠄⢷⣶⣤⠀⠀⠀⣀⠀⠀⠠⠽⠿⢷⣦⡀⠉⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠶⠀⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⢡⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠶⠂⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣛⠁⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢰⣊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢄⠀⠀⠀⠀⢤⡀⠀⠀⠀⣐⢄⠉⢉⣴⡏⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⣴⠃⠀⠀⡞⣫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⡷⡄⠀⠠⠀⠗⣀⣄⠀⣉⠛⠀⢈⠋⠀⣿⡂⠤⠀⠀⠗⠂⢤⣠⣾⠃⠤⢠⣒⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣿⠈⢳⡄⢻⣳⣞⢺⣿⡙⠀⣶⡶⠸⠇⢶⣤⣿⡷⠀⠼⢷⡾⣿⣿⣿⠁⠠⠃⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣴⣶⣿⡦⣳⣥⣤⣽⣯⣭⠭⡶⠶⠶⢬⢭⣭⣭⣥⣦⣤⣻⣿⣿⣿⣿⢆⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣬⢵⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⢉⣿⣟⣿⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣛⡍⠤⠀⢀⣀⣤⠀⠐⠀⠘⠒⠒⠚⠀⠉⢀⣁⣍⣉⣉⣏⣉⣹⣻⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠈⠁⠉⠙⠻⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠒⣒⣁⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⢤⣲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⢿⡟⣙⣿⣻⣿⣿⣿⣿⣿⣿⣶⣦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠷⠭⠮⣬⣷⣽⣮⣭⣽⠿⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢚⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣉⣭⡗⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⢿⣏⣁⡤⣟⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣼⣷⣾⣿⣥⣴⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⣽⠧⣯⡼⠋⠉⢈⣿⣾⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡿⠃⠀⣼⣡⠴⠚⠉⠙⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⡟⠀⠀⣰⠏⠀⢀⣀⡤⠶⢿⣿⣻
⣠⣴⢲⡶⠶⢶⣖⣲⣶⢲⣤⡤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⠿⠒⠋⠉⠀⠀⠀⢀⣿⡹
⢻⣯⣯⡴⠚⢋⣻⣥⣿⡟⢣⡽⠛⠛⠿⠴⣶⣤⣀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠞⠁⠀⠀⠀⣀⣤⣴⣾⣿⣏
⠀⠙⢶⢟⣟⣉⣡⡿⠛⠋⠛⠻⣤⣀⠀⠀⠀⠀⠉⠛⠲⢤⣾⣿⣞⢀⠔⠁⣀⣀⣤⣶⠿⠛⠉⢁⣹⣶⣿⣵⣦
⠀⠀⠀⠙⢿⣏⣽⣷⣤⠖⠚⠉⠉⠉⣙⠷⠒⠶⠦⠤⠤⠤⠼⣿⣿⡷⠾⠟⠛⠛⠛⠲⣄⣉⣉⣁⣀⣀⣨⣿⣾
⠀⠀⠀⠀⠀⠱⣿⣿⣇⣀⣀⠤⠖⠋⠁⠀⠀⠀⠀⣀⣤⡾⠟⢙⣿⣿⣂⠤⣀⣀⠀⠀⠀⠈⢙⣦⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠱⣿⣿⡏⠀⠀⠀⢀⣠⣤⣶⠾⢿⡟⠉⠀⢀⠆⠿⣿⣋⡑⠂⣉⠉⠙⢿⣏⡉⠀⠙⠲⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣳⣶⣶⣾⡿⠛⢉⡠⠖⡹⠀⠀⢠⠎⢸⠀⡿⣿⡗⢄⠈⠒⢦⡀⠘⠿⣆⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣤⡷⠖⠉⡠⣾⠁⢀⣴⠃⠀⡏⠀⡇⠹⣧⠀⠑⢤⡀⠙⠢⣀⢈⡷⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣅⡠⠊⠀⠳⠒⠁⣼⡀⢠⠇⠀⡇⠀⢻⣧⠀⠀⠙⢦⡤⣿⣫⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⢀⡇⠀⠀⡿⠁⢸⠀⢰⡇⠀⠘⢿⡇⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣶⣾⣄⣀⣀⣧⣀⣼⣤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣷⣿⣶⡿⠋

⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄
⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⣆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⣶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢹⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⠶⠶⣤⣤⣀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣀⣠⣤⠶⠶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠹⣿⣿⠟⠁⠀⠀⠀⠀⠀⢉⡙⠶⣬⡓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣥⠶⢛⡉⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣮⡙⢦⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⡴⢋⣵⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⣻⠃
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡙⣆⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⣰⢋⣴⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣯⡻⣮⢧⡀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⡼⣱⢟⣵⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣜⢷⣳⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣞⡾⢣⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠀⠀⣀⠠⡄⠀⠀⠻⣎⢿⢧⠀⠀⠀⠀⠙⡄⠀⠀⢠⠊⠀⠀⠀⠀⡼⡿⣱⠟⠀⠀⢠⠄⣠⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡟⠁⠀⠉⠓⢦⡘⢦⣝⠳⣝⠢⡀⠀⠹⣜⣎⣧⠀⠀⠀⠀⢈⣤⣤⡁⠀⠀⠀⠀⣸⣳⣣⠏⠀⢀⠴⣫⠞⣫⡴⢃⡴⠛⠉⠀⠈⢻⣿⡇
⠀⠀⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠉⠳⢭⣛⠮⣝⣾⣷⣄⠹⣿⣾⣆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣰⣷⣿⠏⣠⣾⣷⣫⡵⣛⡭⠞⠉⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣧⣄⠀⠀⠀⠠⢤⣀⠉⠛⠾⣽⣛⡿⢿⢎⡻⣿⣦⡀⠀⣸⣿⣿⣇⠀⢀⣴⣿⢟⡱⡿⣿⣿⣯⠵⠛⠉⣀⡤⠄⠀⠀⠀⣠⣴⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⠲⠦⣤⣌⣉⣛⠛⠒⠲⠒⢛⣷⣿⣿⣿⣿⣿⡛⠒⠖⠒⠚⣛⣉⣡⣤⠴⠖⠋⠁⢀⣀⣤⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣉⣉⣉⣉⣥⣴⢿⣿⣿⣿⣿⣿⣿⡽⣦⣬⣉⣉⣉⣉⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣟⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁⣠⣾⣏⣿⢿⣿⣿⡿⣿⣹⣷⣄⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠋⠉⢁⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⢏⣞⡟⠘⣿⣿⡇⢻⣷⡹⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣀⡈⠉⠙⠻⢿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣿⣿⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⢞⡼⠁⠈⣿⣿⠃⠈⢷⡳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠙⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣥⢞⣩⠟⠀⠀⠀⣿⣿⠀⠀⠀⠹⣌⡳⣬⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣥⠶⣛⣭⠶⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠶⣭⣛⠶⣬⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⢟⣫⠶⢛⣭⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣭⣛⠶⣍⡻⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢋⣴⠟⣡⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⠻⣦⡙⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⡾⠁⡼⠋⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠘⢧⡈⢷⠀⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠘⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠃⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣬⣝⣶⣦⣤⣤⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣴⣶⣫⣥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣹⣯⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣽⣯⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠦⣤⣀⡀⢸⣿⣿⣿⣿⡏⠀⣀⣤⠴⠶⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡆⢼⣿⡆⠀⠀⢰⡝⢿⣿⣿⡿⢋⡄⠀⠀⢠⣿⣷⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⢿⣿⣿⣦⢸⣿⣿⣿⣿⣷⣿⡇⣰⣿⣿⣿⢿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣼⣇⠈⡟⢸⡿⢛⣿⣿⣏⠻⡇⢹⡇⣠⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣴⡾⠿⣛⣶⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⢿⣛⡛⠿⡶⢄
⠀⠀⠀⠰⠶⠁⣀⡛⠋⠀⠀⠈⠛⠙⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠝⠁⠀⠀⠈⠙⢣⡄⠀⠚⠆
⠀⠀⠀⢴⡶⠀⠩⣥⣀⡀⠀⠀⠀⠀⠐⠦⣉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢊⣭⠖⠂⡀⠀⠀⠀⢠⣴⡖⠀⠰⠶⠂
⠀⠀⠀⠀⠰⣶⣶⣬⡍⠀⣀⣀⡀⠀⢀⣀⣀⠀⠈⣦⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣨⣤⣀⠀⢀⣠⣤⡄⠀⠲⣾⣿⠟
⠀⠀⠀⠀⠀⠈⣡⣼⣄⣸⣿⠿⠗⠀⣀⣿⡿⠷⣄⠈⠙⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠁⡴⠿⢿⣯⣀⠘⠿⠿⠿⢠⣴⣤⡍
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠗⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠠⡀⠀⠳⣄⠀⠀⠀⠀⠀⠠⠊⠀⡀⠀⢈⠄⠀⠀⠀⢠⣶⣶⡄⠸⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⣤⣤⣤⣀⠉⢉⣀⡀⠀⠐⠒⠚⠂⠀⠀⠀⠘⢦⢠⣄⠀⠔⠀⠀⣈⠄⠚⠁⠀⠀⢀⣀⣀⠈⢩⣤⣶⣦⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢛⡁⠀⠸⣿⢿⣟⣀⠀⠐⠒⠠⠤⠀⠂⢌⣿⣿⡾⣠⢔⣋⠠⠐⠒⠀⠀⠐⢿⣿⡿⠂⠀⢍⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠞⠛⠉⡉⠁⠄⠀⠀⠀⢉⡓⠲⠔⢚⣿⣿⣿⠁⠈⠉⠉⢉⡡⠤⠤⠄⠀⣀⠈⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠀⠸⠿⠃⠀⡀⠀⠈⠡⠄⢀⠴⠋⠸⣿⣧⠙⠢⡀⠠⠤⠀⠀⢄⡀⠈⠻⠇⠀⠻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣀⠀⢴⣶⠀⠀⢀⣶⣷⡖⡀⠄⡸⠁⠀⠀⠘⣿⡷⡙⠄⢌⢳⡢⢀⣻⣿⣿⡍⠐⠐⠿⠆⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠾⠿⠃⢠⣤⠄⠠⠛⠛⡹⠋⢀⠔⡕⠀⠀⡜⠀⣿⡇⠱⡌⢎⢣⡱⡄⠈⠻⡉⢁⣀⡀⢶⡦⠀⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⣠⣤⠘⠋⢰⣿⡇⢀⣀⢀⠊⠜⠰⠁⠌⠀⠀⣿⡇⠀⠙⡌⢣⡹⡜⠆⢠⣕⠜⢿⡿⠀⠁⠰⣷⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⣥⠀⣤⠀⠉⠀⠻⠏⢰⠎⢰⠃⠀⠀⠀⠀⢹⡇⠀⠀⠈⡄⢳⡘⣾⠈⠛⠂⠀⠀⢴⡄⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⠐⢛⡀⠀⣶⠀⣀⠈⢠⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠀⢣⠀⢠⠀⠸⣦⢀⣤⡉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠨⢡⣎⡽⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊⠤⠷⠄⠈⠛⠁





⡿⠿⠿⠻⠿⠻⠟⠿⠿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⡇⠀⠀⣾⣿⡇⢀⠀⠂⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉
⠀⠀⠀⠈⠳⣖⠢⠀⠀⡀⠀⠀⢱⠀⢠⣿⣿⣿⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⢀⣤⣿⠆⢠
⠀⠀⠀⣰⠆⠈⠳⣌⣳⣧⠄⠀⢻⠀⠸⡥⠀⠁⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣀⡾⠋⠀⠀⣾
⢤⣠⠞⠁⠀⠀⠀⠈⠷⣟⠀⣠⠞⠀⠀⠁⠘⠁⠀⠀⠀⠿⣶⣶⢦⣆⣄⣤⠞⠀⠀⠈⣻⡏⠀⠀⠀⡾⠿
⡠⠃⠀⠀⣶⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⠆⠀⠙⠛⠀⡾⠃⠘⠃
⠀⠀⠀⠀⠹⣷⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠢⠀⠀⠀⠀⢀⠀⢀⡈⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣦⣤⠀⠀⠀⢀⡾⠏⠀⠀⠀⡾⠀⠀⢨
⠀⠀⠀⠀⠀⣾⠿⠶⠤⢴⡿⠋⠀⠀⢀⠀⠀⠀⣏⠀⠀⠸⠉⠀⠠⣄⠞⠁⠀⠀⠀⣠⡇⠀⢀⡎
⠄⠀⠀⠀⠀⠻⠶⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣦⠀⠀⠀⢀⣴⠁⠀⠀⠀⠀⡜⠁⠃⢠⣾⣤⡤⠤
⠀⣀⣤⣷⠄⠀⣀⠀⣦⣦⡿⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢠⡁⠀⠀⠛⠛⠉⠁
⠋⠉⠀⠀⡀⠈⣿⠀⠀⠀⠀⠀⠀⠈⠙⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠆⠀⠀⠐⡦⠤⠶
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠰⠒⠚⠋⢲⠶⠂⠉⠉⠁⠉⠙⠛⠁⠀⠀⢀⣤⣶⣿⠏⠀⠢⠤⠐⠊⠁
⠀⠀⣠⣦⠀⠀⢾⡁⠀⠀⢀⠀⠀⣀⣄⣀⣀⣀⣠⠄⠂⠀⠀⢀⠴⢿⣿⣾⠟⠁⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠉⠳⠀⠀⢀⡇⠠⡌⠀⠀⠀⠹⢿⣏⠀⠀⠀⠀⠀⠀⠀⠋⠁⠐⠟⠛⠒⠀⠠⠀⠀⠀⠀⠘⠻⠦⣄
⠻⣄⣀⠀⠀⠀⠚⠀⠀⠁⠤⣀⣼⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠁⣒⠊⠃⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠈
⠀⠈⠉⣩⡀⠀⢠⡶⣦⡀⠀⠀⠙⢦⣀⠀⠀⠁⠀⠹⣦⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⣰⣟⠉⠀⠈⢠⡾⢷⢤⣄⣀⣀⡉⠲⣤⠀⡀⠀⢻⢧⡄⠀⢠⠇⠀⠀⣠⣤⢶⡖⣋⠉⠅⠂
⣠⣾⠋⠉⠀⠠⣶⠁⠀⠀⠈⠈⠙⠛⠿⠀⠙⠿⠁⠀⠀⣿⠟⠍⠙⡆⠀⢨⡅⠈⢻⠻⠅
⠋⠁⠀⠀⠀⠀⣿⠆⠀⠀⢀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠹⡄⠀⠠⠃⠀⠈⠣⣄⣄⠀⠀⠀⡄⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣸⣿⡆⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⣦⣤⡀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⡀
⠀⢀⣿⣿⣻⣴⣾⣿⣿⣶⣦⣤⡀
⠀⠀⣿⣿⣻⣿⣛⣛⣛⡏⠀⢸⣷⣼⣷⡆⢀⡀
⠀⠀⠈⢿⣯⣿⣿⣅⣀⣽⣿⣿⣟⡛⣤⣽⣿⣿⣆⣀⡀
⠀⠀⠀⠀⠙⣿⣯⣽⣿⡉⠀⠀⠉⠉⠻⣏⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠸⣿⡟⣾⡟⠋⠉⠉⠉⠉⠉⠓⢦⣀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣤⡤⠤⠴⠶⠶⠒⠚⠛⠛⠲⢤⣀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠁⡀⠀⣻⣦⣤⣾⣷
⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⢨⣿⣷⣀⡬⠽⠛⠛⣯⡤⠤⢤⣤⠤⠒⠂⠀⠀⢰⣿⣿⡿⠋⢿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⣀⠔⠋⠀⣠⠔⠋⠀⠀⡀⠀⠀⢀⣿⣿⡟⠡⠀⢸⡏⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠁⠀⣠⠞⠁⠀⢀⠴⠋⠀⠀⣴⡿⣻⡟⢀⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣾⡁⠀⢠⠞⠁⠀⠀⢀⣾⢟⣴⠏⠀⢺⠀⢀⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣿⣽⣞⡁⢀⡴⠇⠀⢟⠁⣿⠏⠀⠀⠘⡷⢏⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠙⠉⠀⠀⠀⠀⣾⠋⠀⠀⠀⢠⣦⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣾⣁⡀⣀⡌⣠⠿⣇⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣀⡺⣿⣿⣫⡯⢻⢁⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠟⠁⠙⠃⣽⠿⣿⣾⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢟⡤⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⢠⣶⣿⣿⠈⣩⣔⡀⡄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡀⠀⣨⣵⣦⣰⣿⣿⣿
⠀⢸⣿⣿⣙⣿⣿⣿⡃⢉⣶⣶⣄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡄⠉⠿⣿⣿⣤⣿⣿
⠀⠈⣻⣿⣿⡿⠿⣷⣶⣾⣿⣿⠃⠉⠲⢄⡠⡈⢀⣴⣄⢀⣤⡤⠊⠁⠀⣿⣿⣿⣿⡾⠛⢙⣿⣿⠇
⠀⠀⠈⣽⣿⣷⡶⠾⣿⠟⠉⡁⢴⣤⣤⣤⣽⣿⣼⣿⣯⣾⣿⣶⣶⣶⡾⠁⠀⠈⢻⡋⠛⣿⣿⠟
⠀⠀⠀⠀⠿⣿⣷⣶⣿⡇⠀⢀⣸⣿⡿⠿⠛⢙⣿⣿⣿⣏⠙⢿⣿⣿⡷⠄⠀⢰⣿⣿⢟⣿⡏
⠀⠀⠀⠀⠀⠉⠳⠿⠟⣷⣤⣄⠀⠘⠻⠁⠀⣼⡿⣿⡿⣿⡀⠈⡏⠁⠀⢠⣶⣾⣟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⢻⡟⠀⢀⣼⣦⣼⣿⠁⡿⣇⢿⣷⣶⣷⣄⠀⠙⣟⢹⣏⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⠀⠀⠊⠻⠉⡟⠉⠀⣯⡟⠘⠙⡅⠙⠀⠀⣄⠘⣾⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⢿⣿⣦⣤⡀⢀⣀⣠⠀⠙⠁⣴⣤⣥⣀⣧⣤⣿⣟⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣿⡿⣿⣿⠟⠀⠀⠀⠘⢿⣟⣿⣻⣿⡵⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠃

⣴⣿⣿⣳⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣴⣻⣿⣷
⢹⣿⢶⣿⣭⣭⣍⣻⣍⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣏⣽⣋⣭⣥⣽⣷⠾⣿
⠘⣿⡾⣯⠤⢬⠧⣮⣤⣿⣿⡟⠻⢷⣄⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣴⠿⠟⣿⣿⣧⣬⡦⢭⠤⢤⡽⣾⡟
⠀⠈⢿⣿⣶⣼⣾⠾⠿⠿⠭⣙⣾⣿⣿⣿⣦⡀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣠⣾⣿⣿⣯⣞⡩⠽⠿⠿⢾⣾⣴⣾⣿⠟
⠀⠀⠈⢿⢷⣯⣤⣤⡀⠀⠀⠀⢳⡀⠀⠉⠻⣿⣦⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⣾⡿⠋⠁⠀⣰⠋⠀⠀⠀⣀⣤⣬⣷⢿⡏
⠀⠀⠀⢸⣿⣏⣿⠋⠉⠉⠉⠀⠈⠙⠢⣄⠀⠀⠙⢿⣦⡀⠈⠢⡀⠀⠀⡠⠊⠀⣠⣾⠟⠁⠀⢀⡠⠒⠉⠀⠁⠉⠉⠉⠹⣟⣻⣿
⠀⠀⠀⠀⣿⣿⣿⣦⣄⣀⠀⠀⠀⠤⠤⠬⡳⢄⡀⠀⠙⢿⣄⠀⣼⠀⢸⡄⢀⣴⠟⠁⠀⢀⡴⡻⠤⠤⠄⠀⠀⢀⣀⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠲⢄⡀⠙⢷⡌⠀⠈⣴⠟⠁⣀⠤⠚⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⡿
⠀⠀⠀⠀⠀⠸⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⠀⠀⣉⣓⣲⠀⠀⠀⢹⣒⣋⣁⠀⠀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⡽⠿⠿⠿⠿⢟⣛⣛⣋⠭⠅⠚⢉⡄⠀⠀⣌⠙⠒⠬⢍⣛⣛⣛⠿⠿⠿⠿⠿⣭⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣥⠤⠴⠖⠒⢒⠏⠁⠀⠀⢀⡤⠚⣹⣿⠂⢺⡷⠉⠢⢄⠀⠀⠀⠉⢷⠒⠒⠶⠤⢤⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⣀⣤⠤⢒⠞⠁⠀⠀⣠⠖⠁⠀⡰⢡⡟⠀⠘⣧⠡⡀⠀⠑⢦⡀⠀⠀⠙⢖⠲⠤⣄⡀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠋⠁⣀⡤⢏⡤⠔⠒⡾⠁⠀⢀⡜⢁⡾⢡⠀⢠⠙⣆⠘⢄⠀⠀⠙⡖⠒⠤⣄⠧⢄⡀⠉⠳⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣧⣴⠋⠁⣠⠋⠀⢠⡞⢀⠄⣠⠏⢀⡾⠁⠘⠀⡈⠀⠹⣆⠈⢣⡀⢄⠘⣦⠀⠈⢣⡀⠈⠳⣤⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⣰⢃⠂⢠⠏⣠⠏⡴⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠱⡌⢳⡈⢣⠀⢢⢳⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣯⣶⣾⣶⢣⠞⢁⢄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢆⢘⢦⢳⣼⣶⣮⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣻⣯⣟⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣳⣟⣿⣽⣻⣿⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⡏⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⢸⠋⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⡇⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⢹⡄
⠀⠀⠀⠳⡖⢾⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡷⢲⠞
⠀⠀⠀⠀⡇⠀⢳⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢀⡜⠀⢸
⠀⠀⠀⠀⢻⠀⠀⠳⡀⠀⠀⢀⡎⠀⠀⡤⡄⠀⠀⠹⡄⠀⠀⢠⠏⠀⠀⢀⣤⡀⠀⢳⠀⠀⠀⢀⡞⠀⠀⡏
⠀⠀⠀⠀⡼⢦⠀⠀⠱⡄⠀⡞⠀⠀⠀⠓⠁⠀⠀⠀⠙⡄⢠⠋⠀⠀⠀⠈⠚⠁⠀⠀⢣⠀⢀⠎⠀⠀⡠⣇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⣙⣾⣠⠤⠤⠤⠤⠴⠖⠒⠒⠒⠚⠓⠒⠒⠶⠦⠤⠤⠤⠤⣄⣈⣧⡋⠀⠀⠀⣹⠃
⠀⠀⠀⠀⢀⠷⠒⠋⢉⣀⣀⡤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠲⠶⠶⠦⠤⠤⠤⢄⣀⣉⡉⠓⠲⢧
⠀⠀⠀⠀⠸⣤⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⣠⠇
⠀⠀⠀⠀⠀⠀⢧⠀⣀⣀⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠒⠒⠒⠒⠒⠒⠒⠦⠤⠤⢤⣀⣀⠀⡏
⠀⠀⠀⠀⠀⠀⣼⢋⣡⠤⠤⠒⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠲⠤⠤⣌⡙⡇
⠀⠀⠀⠀⠀⠀⠘⠣⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⡀⣴⣶⣶⡿⠠⣭⣦⣤⣰⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⣠⣤⣤⡅⠠⣴⣶⡆⡠
⠀⠀⠀⣾⣿⣿⡏⠠⠀⣿⣿⣻⣿⣧⠀⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣾⣿⣽⣿⣧⡀⠈⣿⣧⣯⡟
⠀⠀⠀⢾⣿⣿⣥⠂⠠⢿⣿⣽⣿⢏⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⠈⠿⣿⣭⣿⡟⠀⠀⣾⡿⣿⡇
⠀⠀⠀⠈⣿⣿⣏⠃⠀⡀⠙⠋⠁⠐⠀⠘⣷⠱⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡜⣸⡇⣠⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠉⠉⠛⡈⠁⠈⣿⡿⡍
⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⢀⠂⠀⠀⠀⢰⣿⣇⠀⠉⠀⠀⠀⠀⠀⣁⣾⣿⣯⣾⣷⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠐⠀⠀⠈⠀⠂⠀⣸⣿⡶⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣤⣄⠃⣀⣀⣾⣿⠁⠀⣀⢠⡀⠀⢀⣰⣴⣿⣿⣍⣿⣿⣿⣿⣷⣶⣤⠄⠀⠀⠀⠀⠀⢈⣻⣇⡀⠀⡀⣠⣂⣴⣾⣿⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⣟⣟⡿⣟⡿⣟⣾⣷⡷⠛⠁⠴⠙⣿⠟⣽⣿⠋⣿⣿⠹⣿⣍⠹⠃⠠⠠⠁⠘⣶⣦⡸⣽⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣿⡾⢋⠭⠂⢀⣆⠒⠙⢠⡾⣽⠁⠀⠿⣿⠀⠘⢿⢷⡀⠀⠢⡐⠠⡀⢻⢿⣿⣟⣦⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⡛⠞⠉⠉⣶⡄⡄⠠⡖⠡⠈⢂⠏⠀⠀⠖⣿⠀⠀⠘⡄⠇⠘⡆⠐⠄⣀⣺⠃⢌⠙⠿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡟⢛⡀⠀⣀⠀⠙⣿⣯⢹⣦⠳⠚⠄⠀⠀⠀⡄⣷⠀⠀⠀⠀⢔⡀⣸⠛⣾⡟⠀⠀⠀⠀⠀⠈⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⢾⣿⣧⣤⣄⠀⠘⠀⢸⣯⠱⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⣙⣿⠆⠈⠃⠀⣨⣁⣸⣿⡇⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⣿⡅⠀⠉⠻⣷⡿⣼⣿⣷⣿⣗⠁⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠙⢿⡦⣶⣶⡴⢿⣽⡃⡥⠀⠘⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⢛⣿⣄⠀⢀⣤⠈⠛⣽⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢍⡋⢠⣄⣀⣄⣴⣶⡻⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠹⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠝⠍⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣾⡟⣶⣿⣿⠻⣟⡲⢤⡀
⠀⠀⠀⠀⠀⠀⢸⣯⣟⡒⣾⡛⠫⢍⡻⣟⢶⣄
⠀⠀⠀⠀⠀⢠⣯⡼⣷⣤⣌⣉⡓⣦⣽⠛⢿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⣼⣋⣻⣿⣅⣀⣀⡉⠳⣼⠓⠾⣶⠛⣷⡄⠀⠀⠀⡔⠀⢀⠤⠀⢀⣤⣶⣯⡛⣳⣯⠽⣿⢶⠇
⠀⠀⠀⠀⠘⣟⣹⡏⠁⠀⠀⠀⠈⠉⠻⡄⠀⠀⠙⢿⣷⠀⠀⡎⢀⠔⠁⣠⠾⣯⣜⡹⡧⠔⠒⠫⣽⡿⠋
⠀⠀⠀⠀⠸⣯⠛⠉⠉⠉⠒⠒⠒⠒⠲⠿⣆⡀⠀⠈⢿⡇⠰⢀⠂⣠⡾⠛⠉⢉⣽⣓⣉⠉⣻⣾⣷⠇
⠀⠀⠀⠀⠘⣿⣶⡒⠒⢒⣒⣤⣄⣀⠀⠀⠀⠙⢦⡀⠘⣿⣶⣦⡾⠋⠀⣀⣴⡋⠀⠀⠈⠙⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠉⢙⣛⣿⡿⠿⠿⠿⣿⣶⣦⣤⣤⣝⣦⣿⣿⣋⠤⠒⠉⠀⠀⠈⠉⠒⠢⣴⣯⠟
⠀⠀⠀⠀⠀⠀⣾⣻⡿⠋⠉⠙⠒⣲⠖⠒⠛⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣖⠲⢤⣀⡼⠋
⠀⠀⠀⠀⠀⣴⣻⠛⠋⢉⣉⣭⠋⢁⣀⣠⠤⠖⣻⣿⣿⣿⠳⣄⠈⠱⡶⠭⢙⣿⡛⠛⠛⠁
⠀⠀⠀⠀⠀⣿⣷⠖⠉⢁⡠⠞⣩⠝⠋⢀⡤⣪⣾⣿⡟⣟⢧⠘⣦⣀⣙⠒⢄⣹⣻⠄
⠀⠀⠀⠀⠸⣷⣯⣤⡔⠉⢠⠞⠁⣠⠖⣩⢖⢿⣿⠟⠀⡟⡘⡆⢸⡈⠇⠑⡄⢹⣻
⠀⠀⠀⠀⠀⢼⣛⣿⣤⣴⠃⢀⡾⢁⣔⣵⠋⠘⠋⠀⠀⣧⡁⣧⠀⡇⢸⡀⢸⢿⠃
⠀⠀⠀⠀⠀⠀⠻⣧⣿⢻⣶⣋⣠⡾⠟⠁⠀⠀⠀⠀⠀⢹⡇⢿⣠⣧⣼⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⠧⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣊⣤⣶⣾⣿⣿⣿⣿⣥⠈⠉⠒⠚⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⣫⣴⣿⣿⠿⣻⡿⠛⠋⠉⠉⠉⠛⠢⠀⠀⠀⠈⠐⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢥⣾⣿⡶⠛⠁⠞⠁⠄⣒⠒⠒⠂⣀⣀⢀⠀⠀⠀⠀⠀⠈⠃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⣾⣿⣟⠁⠀⠀⣠⡴⠟⣛⣻⣶⣜⢿⣿⢎⠳⡷⠀⠰⠶⣷⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡀⢸⣿⣿⠃⠀⣠⣿⠋⣰⠟⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⣿⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣇⠈⠐⣶⣆⣰⠃⢡⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢷⣿⣿⣿⠋⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠈⠻⠻⠷⣾⡷⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣷⣄⣷⣦⣾⣟⠁⠀⠀⠈⣀⣀⣀⣉⠙⠛⠃⠀⠀⠀⠴⣛⣉⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣮⣿⣿⡇⣙⢿⣷⣪⠂⠀⠀⠙⠻⣟⣿⠏⠳⠄⠀⠀⠀⡴⠻⡟⠉⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⡿⡟⠱⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣅⢻⣄⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠙⣿⣿⣷⣦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⡠⠞⠙⣿⣿⣿⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠶⠾⡦⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠩⠷⠶⠖⠀⡰⠁
⠀⠀⠀⠀⠀⠀⣸⣿⡄⢀⡴⠞⠀⢰⣯⣾⣿⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠘⣿⣏⡀⣨⣿⠁⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣻⣿⠃⢀⣨⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡿⢷⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠟⡀⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠛⠋⡀⠀⠀⠁⠘⠢⠤⣀⠀⠈⠂⠀⠈⠻⠮⡳⣌⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠻⠧⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠑⠀⠀⠈⠪⡓⡙⠛⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣁⠤⢾⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠾⣏⣡⠤⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢶⣿⣶⣿⣥⣤⡾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⣦⠧⢾⡴⠋⠁⢀⣿⡿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠋⠀⢸⣃⠴⠒⠋⠉⢻⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢠⡟⠁⠀⣀⡠⠴⠻⣿⣟⡇
⢀⣤⡖⣶⠶⠶⣶⣒⣶⡖⢤⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣠⠿⠖⠚⠉⠁⠀⠀⠀⣸⣟⠇
⠸⣿⣿⣥⠖⠚⢛⣯⣩⣿⠿⢤⠷⠻⠿⠧⠴⣦⣄⣀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡔⠁⠀⠀⠀⢀⣠⣤⣴⣾⣟⡉
⠀⠙⢷⣾⣲⡚⢉⣹⠿⠛⠛⠛⠦⣄⠀⠀⠀⠀⠈⠉⠓⠶⣄⣼⣿⣾⢀⡴⠋⠀⢀⣠⣴⡾⠟⠛⠉⢉⣷⣾⣟⣦⡄
⠀⠀⠀⠐⠿⣿⣙⣿⣤⡤⠴⠒⠋⠉⠉⣓⡶⠤⠤⠤⠤⡤⠤⠼⣿⣿⡯⠶⠿⠟⠛⠛⠳⣆⠀⠉⢉⣉⣀⣈⣻⣷⣷
⠀⠀⠀⠀⠀⠙⣽⣯⣿⡀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⣠⣶⠟⢛⣿⣷⡀⢀⣀⠀⠀⠀⠀⠉⠙⢯⡀⠉⠁⠈⢹⣯
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠁⠀⠀⠀⣀⣠⣤⣶⢾⡿⠋⠀⠀⡌⢿⣿⣯⠒⢤⡉⠉⠒⢶⣖⠊⠉⠙⠢⣄⣀⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠈⢾⡿⣦⣤⣤⣶⡿⠟⠋⣁⠄⡾⠀⠀⢀⠞⢰⠀⣿⣿⡷⣄⠉⠲⣄⠀⠹⢷⣄⠀⠀⢈⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣿⣹⣧⠴⠊⣁⡴⠁⠀⣠⠋⠀⡞⠀⡇⠹⣧⠈⠳⣄⠀⠑⢤⡀⠈⢳⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⠁⣠⠞⠁⣧⠤⠊⣻⠀⢀⡇⠀⡇⠀⢿⣧⠀⠈⠳⣤⣀⣹⡖⣿⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠁⠀⢀⠇⠀⠀⣿⠁⢸⠀⢠⡇⠀⠘⣿⡇⠀⠀⠈⠛⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣀⣼⠀⠀⠀⣇⠀⣸⣀⣸⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣟⣿⣿⣶⣾⣟⣿⣯⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣒⣒⣒⣲⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⡖⢾⡟⢿⣿⠿⢏⣿⢹⣿⣿⣿⡿⠟⢿⠛⡟⠛⢿⣇
⠀⠀⠀⣠⣄⣀⣀⣤⣴⣿⣿⣿⣿⢏⡅⢘⡧⠐⣷⠀⢟⣧⠘⣯⣀⢻⣆⠹⠧⠈⣿⣹⣿⣿⠆⠈⠳
⠀⣀⣠⣟⣻⡿⣿⠿⣁⢻⣯⠊⡏⢸⠆⠨⡵⠀⣽⡃⢘⣿⠊⣷⢉⢸⣟⠸⣷⠁⢽⡜⣿⣹⡄
⠀⠁⠼⠁⠀⠀⠀⠀⠙⠘⠁⢸⡷⢼⡃⠠⣟⠀⠺⡅⠨⠯⠅⠹⡻⠪⣿⠀⢿⠇⢸⣟⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⢨⡅⢐⣯⠀⣩⠗⢈⣳⣂⢘⠁⡀⣿⡅⢺⣿⢈⣯⢹⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣸⠆⠀⣷⠀⠸⣞⣀⡭⣥⠀⣄⡀⢻⡃⢹⡧⠈⣷⣶⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⣇⠀⢼⡃⠐⣫⡄⠘⣳⠀⣯⣇⢸⡇⢸⣗⠀⣿⢳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠠⠀⠀⢯⠀⢑⡆⠘⡽⠂⢾⡳⠸⣇⢸⡏⠀⢿⢦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⠃⠐⣻⠄⠀⡶⠀⣈⠃⢸⢦⠘⣇⢸⡇⢀⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⡀⠠⢗⠀⠙⠈⢃⡃⠠⠆⢄⡟⢸⡅⢠⠇⣺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠱⠄⠘⠧⠘⢃⠈⣤⠀⢒⢨⡇⢸⠁⣬⣙⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⢠⠀⢣⠌⡆⠹⡥⣾⠰⠁⡟⣸⣧⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣡⠀⠋⠀⢮⡇⢹⡂⣴⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⣆⠙⠎⠃⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⣀⡿⠋

⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠐⣢⣬⣤⣂⡄⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠣⣂⣄⣓⡰⢡⡈⠀⠹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣿⣿⣟⣛⡛⣿⣶⣭⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⢄⣠⣴⡶⠿⠿⢿⣿⣿⡆⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡃⢿⣿⣷⠤⠤⢿⣝⣿⠻⣷⣴⡀⠀⠀⠐⣀⠀⠀⣐⢂⠃⢀⢁⣢⣾⠿⣽⣙⣿⠭⢉⣽⣿⣿⠰⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⡋⠉⠂⢷⠉⠛⢿⣦⡀⠸⣟⠀⠀⣿⠪⢆⣴⡿⠛⢉⡿⠙⠛⠳⣴⣿⣿⣿⠣⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠉⠀⠈⠳⣄⠀⠈⠻⣆⢻⡠⣠⣏⣴⠟⠁⠀⣠⠞⠁⠐⠊⠙⢿⣿⣿⠁⢃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠓⠒⠀⠀⠀⠀⠉⠂⠀⠈⢿⣷⣾⡾⠁⠀⠔⠋⠁⠀⠀⠐⠒⠶⣿⣿⡇⢈⠤⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠻⠿⢶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣴⡿⠟⠐⠀⠈⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣲⣿⡯⠅⠀⢩⠟⠓⠉⡩⢻⣿⣿⠫⡉⠙⠛⢯⠉⠥⢙⣿⣧⠀⠒⠅⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢸⣿⡧⠖⠒⣸⣁⢀⡴⠊⡤⠁⣿⡇⠀⡈⠢⣄⣀⢑⡀⠤⢬⣿⣿⠄⠁⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠸⣿⡤⠒⢁⠔⢡⡾⢡⡞⢀⠄⣿⡇⣄⠘⣆⠹⣦⠩⡀⠐⢄⣼⣿⠀⠊⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣶⣏⢀⡟⢀⠏⣠⡏⡐⣿⡇⠘⣧⠘⣆⠘⡆⠈⣦⣴⣿⡗⠤⠂⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⢿⣿⣿⣿⡶⠛⠈⠀⠉⠁⢁⠘⠷⣾⣾⣿⣿⡿⠿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠁⠀⠠⠱⠀⠀⠀⠀⠠⠀⠢⠌⠁⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠉⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⣤⣴⣶⣶⣿⡿⠋⢻⡇⠀⢀⣤
⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣿⡇⠀⢾⣿
⠉⠛⠿⠿⣿⣿⣿⣿⣿⣷⣽⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢸⣟⣀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠻⠿⠿⢿⣿⣏⡁⠀⠈⢻⣷⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣾⣃⣔⣀⣼⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠉⠛⠛⠋

⡉⠀⠀⠀⠀⢀⠀⡶⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⡁⢠⡶⢀⠂⠀⣐⣽⣿⣿⡟⠀⠀⢀⡀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢿
⠙⠟⢟⢻⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠿⠤⠤⠾⣿⣿⣿⡷⢤⣾⣿⣇⣸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣇⠉⠃⠀⠀⣀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⣠⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠖⣠⠈⠛⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡄⠙⠀⠿⢡⠗⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢯⣠⠗⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠗⠀⠀⢀⣀⣹⣤⣶⣠⡤⠴⢴⠂⣶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠺⠃⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢤⣴⣶⡖⠺⢿⣿⣿⣿⠆⠀⠌⠐⠋⠀⠾⢁⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣧⠈⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠛⠋⠀⠀⣾⣿⢿⠃⢡⣦⡀⠐⠿⠃⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⢳⡄⢈⡀⢹⡄
⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠡⢿⣄⠀⠀⠀⠟⠁⠀⠀⠸⠿⠛⣦⠦⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠉⠄⠀⠛⠃⢘⡇
⠀⠀⡺⠁⣤⢦⡀⠀⠀⠀⠀⠀⠀⠈⠽⢳⣄⡀⠀⣀⡀⢀⣀⣠⡖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⣿⣶⣢⠤⣶⣴⡖⢻⡄
⠀⡴⢉⣀⠁⡰⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⠚⡟⠉⢉⣽⣿⣿⣿⡿⠄⠙⠛⠁⢸⠭
⠐⣏⠈⠛⠀⠀⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠹⣥⠈⠃⠀⠀⢉⣞⠉⠙⢿⣿⠀⠀⠀⢀⡞⠆
⣿⢋⣷⣶⣄⡲⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⣤⡀⠻⠃⢀⣿⣿⠀⠀⠀⠈⠀⠀⣠⠋⠉
⡇⠈⠙⠉⠉⢹⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⢻⣦⣅⣀⣀⣠⡤⡴⠄⠁⠁
⣇⠀⠀⠀⣴⣿⣿⣿⡟⠏⠉⢓⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠘⠈⠃⠁
⢿⡆⠀⠈⠋⠉⠐⠉⣨⡄⠐⠨⠤⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢤⣶⣴⣀⡄⡄
⠀⠐⡦⣀⠀⠀⠀⢾⣿⡇⠀⣶⡦⠀⠶⠋⡆⠀⠀⠀⠀⠀⠀⠀⠠⣌⠗⠋⠁⠀⠀⠀⠀⠈⠙⠳⣗⡄
⠀⠀⠀⠨⠓⡦⢠⠤⣤⠿⠦⣤⣴⠴⠶⠷⠛⠀⠀⠀⠀⠀⠀⣀⡷⠁⠀⠀⠀⢠⣷⡄⠀⠀⣶⣶⡼⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣅⣾⣿⡆⢰⣼⣿⣷⣀⣠⠿⠋⠀⣠⣌⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢍⣀⠀⠉⠑⢒⣿⣿⣿⣿⠓⠃⠀⡀⣤⠀⣤⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠘⠛⢠⠈⡅⢀⡼⠋⠿⠉⠙⠓⠾⠧⠼⠥⠾⠀⠊⠁
⠀⠀⠀⠀⠀⢀⢴⡊⠩⠇⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⣗⡀⣻⠤⠛⠉
⠀⠀⠀⠀⡔⠳⠀⠇⣠⣤⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⢠⣄⣾⣁⠀⠁⠀⠈⠉⣘⠋
⢛⣿⣿⣿⣷⡜⠙⣿⣿⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠧⠼⠤⢧⣄⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⡖⢻⠛
⣣⠟⠛⣿⣿⡝⠀⠈⠁⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠎⠳⢯⣠⣤⠀⠀⠀⠀⠀⠐⢯⣆⡄⠀⠀⠀⠀⠀⣾⠀⠷⠆⠙
⣿⠀⠀⠈⠻⠆⠀⠀⣀⣎⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⡁⠰⣿⠆⠈⢿⠟⠀⡄⣠⣶⠂⠀⠀⠻⣶⠂⠀⠀⠀⠀⠈⠛⠶⣀⠛⠃⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠖⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⣒⣶⣤⣤⣀
⣿⣶⣦⣤⡤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠔⣶⣶⡞⠉⠉⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠉⠁
⡟⠻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠁⠀⢀⣠⣤⣶⣶
⣧⠀⠈⠻⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣴⣾⠟⠋⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿
⡿⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⢀⣠⣾⠿⠋⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛
⡇⠈⠻⣿⣦⣀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣷⡿⠛⠁⢀⣤⣾⣿⣿⣿⣿⣿⡿⠛⠉
⣇⠀⠀⠀⠙⢿⣷⣦⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄
⣿⣿⣷⣶⣦⣤⣬⣿⣿⣷⣦⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⡇⢰⣒⣶⠀⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿
⡇⠀⠉⠙⠛⠛⠛⠛⠟⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⢱⢶⢾⡷⣿⢶⢶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⢻⣟⣿⠛⣚⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⡆⠞⠉⠙⡀⣿⣿⣿⣛⡋⠉⠙⠻⠿⣿⣶⣄⡀⠈⠉⠉⠉⠛⠛⠿⢿
⡏⠉⠙⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠛⣋⣉⣉⣉⣙⡛⠣⢵⡤⣴⠤⠛⣛⣉⣉⣉⣉⣓⠢⢄⡈⠙⠿⣿⣶⣄
⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⢡⣶⣿⡿⠋⠁⣠⣿⣿⣟⣢⡄⣤⣒⣿⣿⡟⠿⢿⣿⣿⣷⣦⡙⢦⣀⠈⠙⠿⣿⣦⣀
⡇⠀⠀⠀⢀⣠⣤⣾⣿⣿⡟⢰⡿⠟⠁⣀⠴⠚⠉⠉⠁⠀⠀⡇⡇⠀⠈⠉⠑⠒⠤⣈⠙⠻⢿⣷⡈⣿⣿⣦⣄⠈⠛⢿⣷⣄
⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⠃⡏⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⡇⢹⣿⣿⣿⣷⣦⡀⠙⢿⣷
⣻⣿⣿⣿⣿⣿⠿⠛⠁⢸⡀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⡇⢸⣈⣙⣿⣿⣿⣿⣶⣄⠙
⢿⡿⠛⠋⠉⢀⣠⣴⣾⠿⡇⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⡎⠀⠀⠀⠈⠉⠉⠙⠛⠷
⠀⠈⠉⠑⠚⠛⠿⠯⠤⠤⢽⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡄⣀⣤⣄⡀⠀⣀⣤⣄⡀⡇⡇⣀⣤⣄⡀⠀⣀⣤⣄⡀⡰⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⣴⠛⣷⠙⠎⣴⠛⣷⠙⠃⠋⣾⠛⣷⠙⠎⣼⠛⣷⠙⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠛⠋⠀⠀⠘⠛⠋⠀⠀⠀⠙⠛⠋⠀⠀⠘⠛⠋⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠒⠛⠢⣄
⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⢀⡞⠉⢀⢰⣶⣠⡀⠀⠀⡰⢅⠀⠀⢀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣼⠀⠀⠀⠀⠀⢙⣿⣀⣤⣶⣀⠲⡠⠁⣠⣢⠤⠀⠀⠀⠀⠘⠳⢦⣄
⠀⠀⠘⣄⠀⠀⠐⠋⠋⠉⠉⣙⣻⣿⡷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠶⣄
⠀⠀⢀⡞⠱⠦⠤⠒⠊⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠝⠳⡄
⠀⡰⡯⠐⠲⣆⠀⠀⠀⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⡄⠀⢀⡃⠒⠀⠀⠀⣈⣴⡶⠶⠶⠾⢤⡄⣠⡤⣴⢂⠠⠲⠆⢀⠀⠀⠀⠀⠀⠀⠃⠠⡌⢳⡶⠾⠟⠒⠦⠴⢿⡓⣦⣄⣀
⠀⠙⣺⠛⠳⠶⢒⣋⣉⣉⣀⣀⢀⣤⣴⠿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠘⣷⣆⢸⠀⠀⠀⠬⢷⠁⠍⠏⠉⠓⠲⠦⢤⣤⣤
⠀⢀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⡔⠀⠘⣉⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣋⢸⠀⠀⠀⢀⣸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠻⣧⣸⣠⣄⣀⢀⣐⠀⡉⠠⣩⣴⡼⠟⢫⣤⡙⢿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡧
⠀⠀⠀⠈⢹⡋⠛⠛⠛⠛⠒⠛⠛⠛⢩⠀⠀⣼⡯⠔⠉⠉⠓⠆⣤⣶⣤⣀⡀⠀⠄⢄⡀⢀⠀⠀⠀⡞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢷⣦⣀⡀⡀⠀⠀⣄⣀⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⠀⠀⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠁⠈⠙⠿⢼⣐⡜⣁⢀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣠⣀⠀⠀⢠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠿⢧⣤⣥⣶⠾⠶⠛⠛⢶⣙⡀⡏⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⠀⠀⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣄⣀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⡟⡇⡀⡄⠀⠂⠀⠂⠀⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣱⣹⡡⡐⣐⡀⡀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣵⣿⣿⣿⣟⡙⠐⢡⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠮⢼⣔⣐⣃⣩⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣉⣷⣄⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣾⣿⣷⣟⣆⠀⠀⣰⡿⢿⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⢷⡈⣧⠹⡛⣆⣰⡟⣷⣾⣿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷⣾⠉⠢⣿⠻⣷⣿⡏⢹⣿⠻⡄⢻⠙⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢹⣷⣿⣷⣄⣽⡾⠿⣿⣻⣿⠈⢣⡿⢻⣦⣇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⣿⣿⡇⢈⣿⠻⣷⣶⣿⡿⢿⣧⠀⢷⠀⠇⢹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⡅⠀⠀⣸⣛⣿⣶⠋⠙⠻⣇⠀⠙⣇⠸⡆⢸⢸⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠁⠀⠙⢦⣼⡿⠉⠉⠻⡄⠀⠀⠈⢧⠀⢸⠶⣷⣾⣾⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠦⣄⠀⠀⣯⣽⣄⠀⠀⠹⣄⠀⠀⠈⣇⣸⣤⡟⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣈⣿⣶⢿⣷⣄⢹⣧⠈⢧⡀⠀⠘⢦⠀⠀⢸⡿⠁⢻⣾⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣿⡽⣿⣩⣿⣷⡾⠿⣽⣷⣿⣷⣄⢳⡀⠀⠈⢳⡀⣸⠁⠀⠸⡏⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣷⣾⠛⣷⣿⡁⠀⠙⢦⡀⠈⠳⡈⠻⣿⣧⣳⠀⠀⠀⢻⡏⠀⠀⠀⣧⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⣿⣟⣿⠉⠉⠉⠳⢦⡀⠙⢦⡀⠙⣆⠘⣿⣿⡆⠀⠀⢸⡇⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⡟⢻⣿⣦⣤⣄⣀⠀⠉⢲⡤⢵⣄⣘⣧⡈⣿⣷⠀⠀⠀⡇⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢺⡏⣻⣿⡿⣿⡋⠀⠀⠀⠈⠉⠓⠾⣦⡀⠀⠉⠉⠳⡜⣿⣇⠀⢀⡇⠀⢠⣿⠇⠀⢀⠠⠄⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣤⣼⣿⣶⠶⠶⠶⠶⠶⠶⢬⣿⣦⣀⠀⠀⠙⣿⣿⣆⢸⡇⢀⣾⣏⣤⢊⠡⠤⠰⠶⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣿⣿⣉⣿⠁⠀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠘⣿⣿⣶⣇⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⠤⠤⢭⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣷⣶⣶⣶⣒⣚⣛⣛⣓⣒⣒⣶⣶⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠙⠛⠛⠛⠉⢩⣿⣿⠿⠟⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠒⠂⠒⠒⠲⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⠚⠛⠖⢊⠟⡱
⠀⠀⠀⠀⠀⠀⠀⠄⠤⡤⠤⣄⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢤⡀⠉⠙⠢⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣠⠖⠋⠀⠠⠖⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢕⠀⠀⠀⠐⠂⠀⢀⠀⠀⠈⠢⡀⠣⡀⠀⠀⠀⠀⢀⠎⠀⣠⠎⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠃⠉⠲⢤⡀⠑⢴⣀⠀⠱⡀⠱⡀⠀⠀⠠⠃⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠀⠀⠀⢀⠇⠠⠤⠄⠁⠀⠒⠉⠳⣄⠀⠀⠀⠙⡄⠐⢾⡗⠁⢀⠊⠀⠀⠀⠀⠀⣀⡤⠔⠒⠂⠀⠀⠝
⠀⠀⠀⠀⠀⠐⡇⠀⠀⠂⡀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠰⡘⠐⠈⠃⠂⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠉⢲
⠀⠀⠀⠀⠀⠀⠣⣈⣠⣠⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⢀⢀⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠒⠒⠀⠒⠂⠉⠀⠈⠄⠀⠀⠐⠂⠐⠂⠒⠀⠤⠤⠤⠒⠲⢉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⡐⠈⠀⢢⠀⠀⡈⠀⠢⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢜⡀⠀⠀⠂⠀⠀⠀⠀⠐⡰⠁⠀⠀⡸⠀⢰⡇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⠁⠄⠀⠘⡀⠀⠈⢣⡀⠀⠀⠀⠀⠐⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⡴⠁⠀⠀⡰⠁⠀⠀⠀⠀⠸⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠓⠢⡀⠀⠀⠁⢀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠳⠄⡀⠈⠂⠀⠀⡠⠤⠐⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⡄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣀⢰⡞⠾⠋⠙⢿⠶⠶⠶⠶⠄⣠⠤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠁⠼⣧⠌⠻⡆⠀⠀⠀⠀⣾⠃⡀⠘⣿⠄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢂⣴⣦⡾⠃⠀⠀⠀⠀⠻⢉⣥⣤⡌⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⡄⠀⠀⣠⣤⣤⣄⣀⠀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣘⣆⠀⠀⠘⠆⠀⠷⠂⠀⠶⠀⠈⢉⣵⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⢋⣈⣉⣉⣉⣉⣉⣀⣁⣀⣀⢀⣒⠂⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠉⢩⣤⣤⣤⣄⠀⠀⠀⠈⢉⡉⠉⠙⢶⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠨⣯⣭⠥⣦⡄⠀⠀⢀⠐⢨⡆⢠⠾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠘⣿⠒⠀⠀⠀⠀⠸⠃⠘⣡⠃⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⠀⠀⠈⠀⠀⠀⠀⠀⢰⣆⣼⠇⣰⠁⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣅⣀⣈⠂⢄⡀⠀⠀⠀⢘⣿⣿⣰⠃⣴⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⠈⠉⢀⠀⠁⠀⠄⠘⣸⣿⠙⣷⠞⣠⠖⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣯⠈⢹⠀⠸⠀⢂⠘⠈⣰⣿⠟⠀⠈⢿⣽⣾⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣜⣧⠈⢃⡄⠸⠊⢀⣾⡿⠋⠀⠀⡤⢢⡟⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣴⠟⠀⢸⠁⢠⣾⡿⠋⠀⠀⠀⣌⣶⣄⠬⡠⠒⠈⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣄⣠⣤⣾⠿⠋⠀⠀⠀⢀⠸⠏⠁⢭⠃⠀⠀⠀⠀⢁⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⠀⠀⠀⠀⠈⠇⠀⠻⡌⠀⠀⠀⠀⠀⠈⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢰⣀⠃⠀⠀⠀⠀⠀⠀⠃⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⢣⡏⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⢸⡇⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡅⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢮⣿⣿⣿⡇⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠃⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣿⣿⣿⣿⣿⡇⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⡈⢣⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⠀⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣻⣶⣘⣿⠻⣿⣿⣿⣿⣿⣿⣿⢿⠀⢠⡄⠀⠀⠀⠀⠀⢷⡀⣠⡾⠃⠀⠀⢀⠀⠀⠀⠀⠀⣿⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠉⠉⠉⠙⠋⢄⡑⣌⣿⣿⣿⣿⣿⡿⣾⠀⠈⢿⠀⠀⣀⢀⣶⠾⢿⡉⢄⠀⠀⢆⠈⢣⡀⠀⠀⢰⡇⣸⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡟⢀⠁⡌⢀⣴⠾⠟⠉⠉⢉⣉⡹⠛⠙⠛⢠⡿⠒⠲⠖⠉⡙⠋⠁⠀⠀⠀⠙⣆⠱⠀⠈⣤⠀⠣⠀⠀⣾⢹⡇
⠀⠀⠀⠀⠀⠀⠸⢷⣼⣄⣠⣿⣤⣤⣀⣀⣌⡛⣁⡐⠊⢠⠶⠋⣩⠟⠁⡞⢡⢀⠀⡤⠀⢀⣀⡀⣻⠀⠡⠀⢠⡄⠀⡇⢸⡿⣾⡇⠂⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠛⠻⣿⣛⢿⣟⡻⠿⢿⠿⣷⣦⣴⡟⠀⢠⡇⢰⡇⢸⡁⢰⣟⠀⠉⣿⠀⡐⠀⣠⡇⠀⣧⣿⣿⣿⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⡀⢠⣽⠉⠉⠀⠉⠁⠀⠀⠀⠀⠉⠙⠻⠿⢿⣧⣸⣰⡀⡇⢸⣿⣶⣾⣿⢀⣵⣾⣿⡅⢀⣿⣿⣿⢿⡌⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣾⡏⢸⡿⣄⢠⣄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠉⣻⠿⣷⣾⣿⣿⣛⣻⣾⣿⣿⣿⣷⣿⡿⣿⡟⠇⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⣼⢧⠀⣠⡝⠃⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣀⠄⣪⡗⠃⠐⢝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣽⣿⡝⠀⠀⣶⠀⡃
⠀⠀⠀⠀⠀⠀⣾⠛⣧⣹⡇⠀⣿⣿⠁⠀⠀⠀⠀⡆⠀⠀⠀⢀⠔⢡⠞⠁⠚⠀⣠⠊⠁⠀⠗⣩⠿⠛⠛⠉⢀⣠⣿⡯⠋⠀⠀⣴⢫⣄⡇
⠀⠀⠀⠀⠀⣰⣿⡇⣸⣿⠀⢸⣿⣿⡀⠀⠀⠀⣾⠀⠀⠀⣰⡿⢀⠁⠶⠀⠀⣼⡟⠀⢀⡴⠚⠁⢀⣤⣶⣵⠿⠛⠉⠀⠀⠀⠼⠟⠛⠋
⠀⠀⠀⠀⠀⣿⣿⢠⣿⡇⢀⣾⣿⡇⠁⠀⠀⣰⡇⠀⠀⡄⣿⠇⠘⣠⡄⠃⣸⠏⠀⢠⡿⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠀⠀⠰
⠀⠀⠀⠀⢀⣿⣿⢸⣿⠁⢸⣿⣿⡇⢸⠀⢀⣿⠀⠀⢸⠇⣿⠀⠀⠀⠹⢰⡿⠀⠀⣴⠁⣰⣿⠃⠀⠀⢠⡤⠔⠒⠟⠛⡉⣉⠉⢁⣤
⠀⠀⠀⠀⢸⣿⡿⣿⡟⠀⣼⣿⠋⡇⠘⠀⢸⡇⠀⠀⡆⠀⠟⠀⠀⣿⠀⢸⡇⠀⡆⠸⢀⣿⣿⠀⠀⠀⣿⠀⣶⠀⣎⣀⡉⠉⠃⠘⠉
⠀⠀⠀⠀⢸⣿⡇⣿⡇⠀⣿⣿⡇⠁⠀⠀⣿⠀⠀⠀⣏⠀⠃⠀⠀⠀⠀⣿⡇⠠⠇⠀⢸⣿⣿⠀⠀⠀⣿⢀⡌⠃⠉⢄⡀⢀⠀⠠⠉⣷
⠀⠀⠀⠀⣿⣿⣟⣿⡇⠀⣿⢸⣇⠀⡆⢰⡏⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⣿⡇⠀⠀⡇⢸⣿⣿⠀⠀⠀⣼⠁⡼⠣⡀⢠⠁⠌⡀⠃⠀⢹
⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⣿⠀⢻⠀⠃⣼⡇⠀⠀⣸⠀⠀⠀⡆⠀⠀⢀⣿⡇⠀⠀⠀⠘⣿⣿⠀⠀⠀⣼⠀⠀⢰⠙⠆⠀⠀⣀⠀⠀⢸
⠀⠀⠀⠀⠈⢻⣿⣿⠀⣶⡟⣄⠸⡄⢀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠘⡇⢸⣿⡇⡇⠀⠀⣷⣿⡟⠀⠀⠀⠿⠀⣀⠘⡷⠀⡠⢀⠉⢄⠀⢸
⠀⠀⠀⠀⠀⢀⣿⣿⣧⣸⣷⣿⣀⣇⣸⣿⡇⠀⠀⣿⠀⠀⠀⢀⠀⡇⢸⣿⠀⣇⠀⠀⣿⣿⡆⠀⠀⠀⢸⡀⠰⠤⠁⠰⠰⠎⡄⠈⠀⣸
⠀⠀⠠⠶⠾⠛⣹⡿⠻⣿⣭⣭⣁⠉⣿⣿⡇⠀⠀⣿⠀⡀⠀⠈⠀⠀⣿⣿⠀⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠠⠀⡴⠃⠀⢸
⠀⣀⣀⣤⣤⣾⣿⣷⣦⣭⣉⠈⢿⣾⣿⣽⣧⡀⠀⣿⠀⡇⠀⠀⠐⢡⣿⣿⠀⣿⠀⠀⣾⣿⠀⠀⠀⠀⠀⠠⠦⠀⠙⠂⠀⠐⢀⣀⠀⠾
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣆⠙⠓⡿⠀⡇⠀⡆⠀⣿⣿⣿⠀⠋⠀⠀⣿⣿⠀⠀⠀⠀⣤⠀⠠⠤⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣦⣿⣾⣿⣶⣅⣤⣿⣿⣿⣀⣤⣶⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠻⣿⣦⣤⡴⠶⠶⠶⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⣶⡄
⠀⠀⠀⠀⠀⢀⣴⢿⣿⡀⣠⡾⠉⢩⣞⣿⡇
⠀⠀⠀⠀⢠⡾⠁⠙⣾⡟⡿⢄⣀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠠⢖⡶
⠀⠀⠀⠀⣾⡷⡤⣶⢯⠟⢲⡏⢽⡞⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡆⠂⣸⣓⡿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠿⣗⣟⠐⢐⣶⣿
⠀⠀⠀⢰⣿⣛⣷⣻⠚⠙⠏⠀⠰⢯⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡽⡜⠓⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⠚⠓⡾⣥⣿⡿⠃
⠀⠀⠀⢘⡞⠉⣿⠃⠀⠀⠁⠀⢀⠼⢯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣳⠀⠀⠀⠀⢀⠀⠙⢦⠀⡄⣠⠞⠁⢀⠀⠀⠀⠀⢾⣳⠟⠁
⠀⠀⠀⠸⡇⠀⣿⠀⠀⡤⠐⠈⠀⣀⣠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⠒⠂⠁⠀⡀⠀⠤⢹⣿⠡⠄⢀⡀⠀⠀⠂⢲⣷⠏
⢀⠀⠀⠀⢹⡀⣿⠀⠀⠀⣤⣒⣽⣥⠤⠾⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⠴⠞⡩⠀⢀⠐⣾⣿⡂⢀⠀⢬⡑⠦⣤⣾⠏
⠀⠀⠀⠀⠀⠳⣸⢀⡔⠋⣉⠠⠮⢄⠀⠀⠘⠋⠻⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⡀⢁⠔⠁⠀⠉⡏⢀⢀⠱⡄⠁⡀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⣿⣿⣔⡏⠀⠤⠤⢤⣀⠈⢱⠄⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠘⠖⠀⠠⠀⠁⠀⠀⠀⠂⠀⠠⠰⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⡀⠀⠒⠀⠄⡀⠂⠄⡐⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣠⣠⣦⡶⠀⠀⠀⠀⠀⠀⠰⣤⣆⣄⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠠⠶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡠⢞⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠸⣽⡇
⠀⠀⠀⠀⠀⢠⡼⢻⣧⠀⠀⢀⣾⡽⢎⣠⢚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡣⡴⢸⣿⠁
⠀⠀⠀⠀⠀⣸⡁⠘⣾⣧⠀⡼⢿⠛⣯⠽⡞⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⣩⠗⢺⣩⡏
⠀⠀⠀⠀⠀⣿⣏⡖⢢⠿⣧⡽⠋⠙⠁⠀⠼⣭⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⠀⠘⢗⣇
⠀⠀⠀⠀⠀⢿⣣⢼⠁⠹⢿⢷⣄⡀⠁⠀⢀⡸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣯⠓⠒⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡀⠔⠻⣿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⢀⡽⢿⣷⠐⠈⠁⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢷⣷⣁⢴⠾⣭⡟⠒⠦⣄⠀⠀⡀⢸⠁⠀⠊⠀⠀⠀⣴⠿
⠀⠀⠀⠀⠀⠀⢷⠀⢀⡔⠉⠀⠀⣿⣇⣠⣤⣤⣾⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡿⣀⠀⠀⠀⠀⠉⠂⢹⣾⠀⠀⠀⠒⣛⠛⠃⠐⣶⣦
⠈⠀⠀⠀⠀⠀⠘⣇⠀⠀⣠⡴⡾⠛⠻⣿⣿⣦⡈⠓⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣇⠀⡠⠊⠁⢀⠀⢿⣦⡆⠀⠀⢄⢀⢠⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡄⠄⢉⠴⠤⠀⣀⡀⠈⠉⣷⡄⠀⠰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⣰⠃⠀⠀⠛⢿⡀⢐⠄⠀⠈⠀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣇⠠⠤⢤⠤⠘⠡⠠⣿⡇⣁⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⡏⠀⠁⠂⠀⠈⠁⠀⠀⠰⠾⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡔⠀⠄⠀⠉⣹⡿⢣⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣅⠈⠃⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⣼⡶⢾⡤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⣤⣼⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠡
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣄⣀⠐⢄⠀⢀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⣠⣶⣿⡿⠟⠛⠋⠉⠉⠙⠛⠛⠿⣿⣿⣶⣿⣿⣶⣿⣿⠿⠟⠛⠋⠉⠉⠙⠛⠻⢿⣿⣶⣄
⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣛⣿⣿⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⢀⣿⣿⠃⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠀⠀⠀⠀⣿⣿⠀⠀⠈⠉⠁⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣼⣿⡇⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⢸⣿
⣿⣿⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⣿
⣿⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⣿
⢿⣿⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⣿
⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿
⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠘⣿⣷⣀⣴⡶⠷⣶⣦⡀⢀⣴⣶⠾⣶⣦⣀⣿⣿⣠⣶⠶⢶⣶⣄⠀⣠⣴⡶⠷⣶⣤⢀⣾⣿⠃
⠀⠀⠀⢸⣿⣿⡏⣾⣿⡎⣿⣿⣿⣟⢴⣿⣦⣻⣿⣿⣿⣿⢡⣿⣷⢹⣿⣷⣿⡏⣾⣿⡎⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣮⣭⣵⣿⣿⣿⣿⣮⣭⣵⣿⣿⣿⣿⣿⣷⣭⣭⣾⣿⣿⣿⣷⣬⣭⣼⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⠀⠙⢿⣷⣦⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠙⠻⣾⠟⠻⡿⢿⣷⡈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣄⡀⢸⠗⠂⠀⣜⠛⢇⣀⠘⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢶⠀⣠⢟⣴⣿⠟⠁⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣵⣿⠋⠁⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠉⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠈⢿⠀⢠⡄⠀⠀⠀⠐⣆⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡃⠀⠀⠀⢀⠁⣿⣿⡄⠀⠀⠀⣿⣇⠀⠀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠘⣷⡜⢿⣿⡀⠀⠀⣿⣿⠀⠀⠙⠉⠉⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣭⣝⣈⢿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣿⣿⣿⡜⠇⠀⢰⣿⣿⠐⣿⣿⡇⣶⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⠛⠛⠛⢸⣿⣿⣿⡇⣦⠀⠈⠁⠀⡄⣿⣿⣇⣿⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢇⣿⡇⠀⠀⢸⡇⣿⣿⢸⡇⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⢀⣀⠀⠀⢸⣿⣿⣿⢸⡟⠀⠀⢀⣿⡇⣿⣿⣸⡇⠀⠀⠀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⢸⣿⣷⡦⢸⣿⣿⡇⡾⠁⠀⢀⣾⣿⢧⣿⡇⣿⢁⣠⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⠃⣾⣿⣿⡇⠁⠀⣠⣾⣿⡏⣾⣿⣧⣿⠈⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⢀⣼⣿⣿⠃⠀⢿⣿⣿⣴⣶⠆⣨⣭⣭⣼⣿⣿⢸⡟⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠸⣿⣿⡈⠛⠛⠿⠿⣿⣿⠼⠇⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠻⢿⣷⣶⣤⣝⡋⠀⠀⣀⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⡀
⢰⣶⣶⣶⣶⣶⣶⣶⣿⣋⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠚⠿⠿⣿⣿⣿⣿⣆
⣾⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠛⠙⠛⠛⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⡀
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠙⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠄
⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠀⠙⢿⣿⣿⣿⣷⣦⡀⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠻⣿⣿⣿⡿⠃⢹⣿⣿⣿
⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠁⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠖⠁⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢀⣶⡪⠤⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⡾⠀⣤⣶⡶⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡈⠺⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⠀⢄⢠⠤⣶⣢⠀⠀⠠⢀⠀⠀⠀⠀⠀⣄⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣈⠛
⠀⠀⢀⣴⣿⣕⠄⡀⢀⠺⠿⡻⢉⡤⣤⣐⢦⠰⠀⢀⡟⢉⣺⣿⡆⠀⠀⠀⠀⠀⠀⠻⢟⣻⣆
⠀⠀⠀⠛⠿⣿⣾⣶⣄⠀⢒⡿⠈⠙⣿⠄⠻⠈⠀⣻⣷⡈⠉⡻⡶⠒⠲⣄⠀⠀⠀⠀⠐⢿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠠⣾⠏⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠙⡀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡁⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⢍⠵⠀⠀⠘⡀⠀⠀⠀⠀⣴⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⣠⡄⠀⠀⠀⠘⠀⠀⠀⠀⡆⢣⠁⠀⠁⢀⣴⣤⣿⣯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⣏⠙⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⣴⣦⣼⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠟⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣻⣿⣧⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⡟⡏⠋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⣶⣶⣄⠀⢸⠋⠙⡏⠉⡟⢹⣤⢧⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⠈⠂⠘⡆⢻⢳⣾⠇⠀⠃⠀⠁⣘⡿⣞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣀⡑⠠⡦⢤⠈⢠⣿⠀⠀⢀⠔⠋⢁⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠦⢄⡙⠳⢥⠀⠉⣿⣿⠀⢀⠊⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠈⠓⠄⠑⢄⢸⡏⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣠⣬⣶⣿⣷⣶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠈⣻⢿⡟⠛⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣁⠴⠚⣡⠞⠁⣸⡇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⡤⠶⢋⡅⣀⠴⢻⡇⠀⠈⢆⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡤⠊⠁⢉⠅⡀⣸⣿⠀⠀⠈⠳⢤⣈⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣴⣁⣼⣤⡷⠟⣿⠀⢰⠀⢠⡀⢣⡷⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠀⠀⢿⣤⣾⣄⣼⣧⣞⢹⠻⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣾⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⡿⠁


⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣽⣿⣷⣤⡎⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣏⢹⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣴⣿⣿⣿⣿⠟⠛⣸⡿⠛⠙⠻⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠶⠶⢤⣀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⡿⠛⠁⣤⣶⡉⣶⣄⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡡⠀⠀⡰⠋⠀⠀⠀⣈⣭⠓⢒⣾⠏⢉⡿⠛⡋⠁⠀⢠⣾⣿⡇⠉⣦⣀⣱⣀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⡈⠀⠀⣰⡔⠀⠀⠀⠀⠀⠁⠐⠋⠁⠀⠜⠀⡞⠀⠀⠔⢋⡀⢸⣇⣴⣯⡿⣏⠃⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢸⡄⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⡟⠀⣿⡟⠛⢦⣏⠈⢀
⠀⠀⠀⠀⠀⠒⠶⣾⣿⣿⣿⣿⠀⣇⢸⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠁⠀⣼⡟⢀⣼⠏⠀⠀⠀⠙⣦⣛⣷⡞
⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣧⡈⠀⣿⣧⠈⠻⢦⡐⢤⣄⣠⣾⠃⠀⣧⠀⠀⠀⣼⡿⢡⡟⢁⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠁⠁⠘⣧⢠⠾⠿⢷⣄⠀⠈⠑⠈⠉⣿⠀⣠⡞⠳⣤⡀⠹⠵⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣱⣶⠇⠈⢳⣶⣶⣤⣤⣿⣾⢿⡇⣰⡿⠧⢀⣐⡺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⣿⠋⠀⠀⡼⡿⢻⠋⠙⢻⠁⠀⠹⡿⠷⠻⢿⣟⠓⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣻⡇⠀⠀⠀⠹⣼⢿⡀⠀⠘⣧⡄⠐⡇⠀⠀⠀⠉⠻⣆⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠈⠻⡹⣄⡀⠘⣿⡄⢃⠀⠀⠀⠀⠀⠘⢿⡦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣆⠀⠀⠀⠀⠀⠙⣿⣷⡀⢸⡅⠈⡆⠀⠀⠀⠀⠀⠀⠹⡜⣦
⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⢷⣿⣇⠀⠀⠀⠀⠀⢹⣿⠛⣸⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡈⣷
⠀⠀⠀⠀⠈⠙⠓⠀⣈⣛⠛⠛⣓⠒⠒⣾⡟⠛⡆⠀⠀⠀⠀⢠⡾⣏⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠙⠊⠉⠛⠁⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠘⠶⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⠛⠛⠓⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣒⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠛⣳⣦⣤⣄⠀⠀⠀⣀⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠐⠿⠿⣿⣿⣿⣿⠿⠟⣰⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⢿⠉⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣌⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣠⣿⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠱⢶⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⠀⠀⠈⢿⣿⣶⣤⣀⡀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢻⡄⠀⠀⣰⠟⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠃⠀⢠⡟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠛⠶⣤⣀
⠀⠀⠀⢀⣿⣿⠿⠿⠛⠻⠿⠁⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠤⠄⠀⠀⠐⠒⠒⠛⠛⠛⠂⠉⠉
⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠚⠓⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⠀⢀⢀
⠀⠀⠀⠀⠀⠰⣧⣴⡛⣶⢖⣊⠛⣀⠁⣀⣧⣤⢀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠘⠀⠀⠈⠭⡧⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠺⠖⠛⣿⠉⢀⠀⢰⣠⣤⣿⠁⠀⢸⠀⠀⢘⡿⠿⣿⣿⢇⣨⣿⣦⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡿⡄⠹⣿⠏⣻⡦⠵⣿⣉⣀⠠⡥⣬⣀⣤⡤⣤⣷⣄⣒⣚⡷⠀⠘⢉⠁
⠀⠀⠀⣀⣤⣴⠛⢣⠀⣸⡥⠀⠷⠂⠢⠿⣦⠗⠀⠈⠡⢻⣏⠁⠂⠨⢉⠛⠛⠉⠌⢛⡛⢿⡿⢂⣈⠲⢄
⠀⠀⠀⠠⣀⣰⢚⡂⠛⠋⠀⠀⠀⠀⠀⠀⠿⠀⡀⡀⠀⢔⣿⣿⡯⠁⠈⠀⠀⠘⠃⠀⠐⢙⣿⣿⡿⠛⠦⠛⢲⡄
⠀⠀⠀⠀⠈⠀⠚⠛⠐⠂⠀⣼⠀⠀⠀⠠⢐⣻⣀⣀⠠⠯⠽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠛⠋⠁⠀⠀⣹⠂
⠀⠀⠀⠀⠐⠤⠴⠶⠴⠶⠶⣒⠻⠋⠉⣤⡰⣶⠤⠀⢀⣀⠀⠀⠀⠰⠀⠈⣠⠄⢀⠀⢀⣠⣢⡤⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠲⠞⢳⠈⠉⠀⠀⠀⠠⠀⠀⠀⠁⠘⠉

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣷⣾⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢻⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡼⠿⢛⡟⣻⣟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⡿⣿⣿⡗⢲⣶⣄⡀⠀⡼⣰⢧⡾⣶⡡⢿⣏⣻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⢿⠹⣇⣇⡛⢹⣯⣿⡋⣻⣿⢿⢁⠊⣰⠋⣀⣼⣯⡿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⢸⡟⡏⢸⠁⣼⠟⢻⡿⢿⡇⣧⡏⣴⢁⡼⠋⠙⣿⣷⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡇⢸⠀⡏⠀⡼⠁⣿⣿⡏⣹⢙⡏⢀⡴⠋⠉⠉⢹⣶⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣾⢾⡟⢧⢀⡇⢰⣧⣨⣷⠛⣿⡴⠋⠀⠀⢀⡴⠋⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣄⣿⠻⣷⡀⢸⡏⣹⠃⠀⢸⠁⠀⣠⠞⠁⠀⢀⡤⣞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡼⢿⠀⠈⢳⣼⣿⠇⠀⠀⣸⡴⠊⠀⠀⣠⠞⣉⣴⠟⢁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⡄⠀⠀⢻⣿⠀⠀⢠⡏⠀⠀⢀⣞⣵⣾⠿⢿⣿⣽⣟⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⢸⣿⠀⠀⡼⠀⠀⣠⣿⡿⠋⣡⠔⠉⢀⣠⠼⠛⠣⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⢀⠻⣷⡄⠘⣿⠀⢰⠃⢀⣴⡿⢋⣴⣞⣁⡴⠚⢁⣀⠤⠤⠴⢿⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠐⠀⠠⣑⢊⣻⣦⣿⠀⣏⣴⣿⣿⠖⠁⠀⠀⠀⣈⣿⣁⣀⣀⠀⠀⢀⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣋⣀⣀⣤⣤⢶⣿⣭⣄⣀⡀⠀⠈⠉⢿⣟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣯⠭⣄⣀⣀⣀⡀⠀⠀⠉⠙⠳⣦⣴⣾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣖⡦⢭⣉⡉⠙⠳⠶⣤⣀⣈⡟⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡳⢦⣬⣑⣦⣄⣀⣉⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠙⠛⠛⠛⠋⠉


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣷⡄⠀⠀⠀⠀⠉⠉⠛⠶⢶⣦⣤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠚⠉⢀⣿⣿⣿⣿⣦⠀⠀⠐⠶⠀⠠⣤⠀⠙⠷⣿⠯⣽⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⣿⠟⠁⠀⠀⠀⣸⠟⣿⣿⡇⠙⢷⣄⠀⠀⠀⠀⠀⠁⠀⠀⠙⡗⢯⡉⢢⣽⡾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⡟⠁⠀⡴⠀⠀⢀⣿⠀⢹⣿⣷⠀⠀⠻⣷⣄⠀⠀⢀⡀⠀⣦⣶⡿⣾⣶⣿⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢷⣿⣟⣽⢠⡔⠀⠀⠀⠀⣼⠏⣆⠀⣿⣿⠀⢸⠀⠈⢻⣷⣦⣤⣿⣿⣿⣽⣿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⢦⢾⡟⠀⠀⠀⠀⠀⠀⣰⣿⠀⠘⠆⠘⣿⠀⠈⠀⠁⠋⠙⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡤⢿⣰⢁⠶⣾⣇⣀⡀⠀⡀⠀⣠⣿⠏⠀⠀⠀⣀⣽⣄⣄⣀⣀⣀⣤⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣻⣿⣿⣷⣾⣿⣾⣿⣿⣄⢀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠛⠛⠉⠙⠛⠻⠿⢿⡿⣿⣿⠟⠋⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠁⠀⠀⢀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣿⡀⠀⠀⠀⢀⣶⠿⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⢀⠟⠃⠀⢠⣤⡾⠃⠀⠀⠀⢸⣷
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠳⢷⣾⠋⠀⠀⠠⣰⡿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠠⡶
⠀⠀⢻⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⣽⣻⣷⠀⡀⠊⢁⠞
⠀⠀⠈⣷⠀⠀⠈⡀⠀⠀⠀⠐⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⡿⣿⣿⠟⢁⡴⠃
⠀⠀⠀⢸⡄⠀⠀⢿⡷⡂⠀⠀⠀⡼⠋⠀⠀⣤⡄⣀⠀⠀⠀⠀⠊⠀⢹⡀⢸⣥⠀⠁⢉⠏
⠀⠀⠀⢸⣇⠀⠀⠚⠁⠀⠀⣶⠞⠁⠀⠀⠀⠀⠙⢦⡙⢠⣀⣰⠀⠀⢨⡇⠀⠁⠐⠂⠁
⠀⠀⠀⠀⠙⠦⠀⠀⣀⣀⡴⠃⠀⠀⢠⣤⠀⠀⠀⠀⠙⢦⡽⣷⡆⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠹⣧⠀⠀⠀⠀⠀⠻⣾⡀⢠⠜⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠷⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡄⠀⠸⠋⠑⢄⠀⠀⠀⠀⠀⡾⠛⠇⠤⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢤⣤⣽⣿⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⣀⡸⠁
⠀⠀⠀⠀⠀⠀⣤⣄⢀⡀⠀⠀⠀⠀⠀⣈⠉⠉⠀⠐⠂⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠚⠻⢥⣀⣀⣀⣠


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣥⢲⠴⠶⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠾⢻⢾⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠦⠤⠴⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⠾⢶⠲⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣦⢰⢢⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠠⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣒⠆⠀⠀⠀⢑⢒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⠀⠀⠀⠀⠀⠢⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢈⢡⢸⠖⣓⣶⡈⢁⡀⡀⢀⡤⡞⠻⡦⠲⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠠⠸⡿⢿⠹⢿⠻⠹⠿⠿⠿⠿⡟⢿⠇⠠⢒⡔⠀⡰⠹⠷⡿⠿⠾⠾⢾⡷⠇⠠⠤⠄
⠀⠀⠀⠀⠀⠀⢠⣶⣺⣶⣶⢲⢶⣶⣷⣶⣶⣿⢸⢼⡷⣇⡇⣟⢻⢼⠼⢿⡿⢧⢤⠤⣦⢤⣦⡄⣬⡥⠐⠒⠒⠂
⠀⠀⠀⠀⠒⠒⠒⠶⠀⠂⠶⠆⠲⠒⠶⠶⠶⠠⠶⠖⠶⠶⠦⠆⠶⠶⠲⠶⠒⠈⠰⠶⠖⠰⠶⠠⠶⠖⠶⠆

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠾⠶⢘⣿⣀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡠⣦⢀⣸⣿⣧⡀⠀⠀⢀⡴⠾⠗⠒⢳⣦
⠀⠀⠀⠐⢶⡄⠀⢸⣿⣿⣧⡀⠀⢠⣤⣤⣿⣿⣿⠶⣤⠀⠀⢠⡞⢋⣿⠉⢷⡄⠀⠀⢸⣿⣿⣾⣿⠛⢿⡶⠄⠀⢈⡿⣰⣺⡆⢸⡇
⠀⠀⠀⠀⣾⣵⠃⣿⢯⣅⡀⠀⠀⠀⠀⢘⢿⣿⣿⣀⡀⠀⠀⠈⣷⠟⠁⢀⣾⠇⠀⠀⣼⠿⠿⢸⣿⣿⣿⣧⠀⠀⢸⡇⠻⠿⠇⢸⣿
⠀⠀⠀⠀⠻⠛⠛⠁⠀⠙⠿⠆⠀⠀⠀⠿⢷⣭⣽⡯⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠁⠀⣿⠀⠀⠀⠸⠇⠀⠀⠰⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠒⠒⠒⠛⠃⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠈⠙⡇⢀⣠⣤⣤⣤⣤⣴⡶⠶⢶⣦⠄⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣶⣶⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠋⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⢆⣶⡄⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠴⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⠃⢸⡆⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⡏⠀⣤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣧⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡶⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣇⣼⠏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠘⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠓⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⢦⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⡀⢀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠙⠻⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣀⣠⣀⠀⢿⡛⢿⣿⣿⡿⣿⣿⣿⢿⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡞⠉⠀⠼⡇⠀⠙⠿⣧⣴⣟⡩⠴⠶⠚⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⣈⣷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠈⠳⣤⣤⣤⣿⡇⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⢸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⢹⣿⠟⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠰⠚⢧⡍⠁⢙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠀⠀⣙⡋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣩⣆⣤⣾⡡⠖⣩⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠛⠿⣿⣿⣶⣶⣶⣶⣶⠶⠿⠛⢻⣿⣿⣿⡿⠃⠈⠋⣠⠴⠋⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⣤⣾⣿⣿⠿⠿⠿⣿⣿⣷⣄⡤⠿⣿⣿⣿⣧⣀⡴⠚⠁⠀⢀⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠿⠛⠁⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣿⡿⠟⠁⠙⢦⣄⣀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣤⣀⣀⣀⠀⢀⣄⠀⣀⣀⡀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣝⡻⣧⣜⠋⠙⠃⠛⢻⣿⣿⣿⠛⠃⠛⠙⢻⣤⡾⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣶⣌⠡⢹⣿⠃⢀⣴⣶⣿⣿⠿⠋⠉
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠙⢾⣹⣿⡄⠁⣶⣿⣻⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⣏⢹⠳⣄⣀⣀⡴⢾⢛⣿⠀⠀⠘⣿⡿⠃⠀⠻⣿⡗⠀⠀⠀⢻⣧⠀⣶⣤⣤⣴⣿⣿⣿⠃
⠀⠀⠈⠻⣧⣾⣿⣿⣿⣿⣦⡾⠋⠀⠀⠀⠹⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠙⣧⢺⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠰⣗⣿⡿⠘⠹⣟⣷⡿⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠻⠷⠟⠛⠳⠾⠋
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⢰⣶⣶⣶⣤⣄⣷⣠⣤⣶⣶⣶⠂⣰⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⢿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⣿⠿⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣙⣻⣦⡻⣿⣿⡟⣿⣿⣿⣿⢋⣶⣿⣿⠷⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣙⠻⢮⣿⡇⠉⢿⣿⣵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⠀⠉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡮⠙⠀⠀⠀⣶⡄⠀⠀⠈⢀⣿⠿⠟
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⣤⣞⣿⡿⠶⣶⣶⡿⠟⠀⢠⣄⣀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⢓⠠⡀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣵⣿⠄⢠⣤⣤⡷⠀⠀⠀⠰⣾⣿⣿⣶⣴⣾⣿⣿⡟
⠀⠀⠀⠈⠑⠴⡷⣿⣷⡗⠀⠀⠀⠀⠀⠀⠿⠋⠙⠀⠀⠐⠾⠧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠤⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣤⣤⣀⣀⠀⠀⢀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣴⣾⣿⣿⡀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⠟⠀⠀⠀⢀⣼⣿⣿⣷⡄
⠀⠀⠀⠀⠘⠻⣿⣿⣿⣷⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⠀⢀⣠⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣆⠀⠈⠙⣿⡿⠻⠻⣿⡿⠋⠉⢹⣾⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣤⣴⠟⠀⠀⠀⠈⢷⣤⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠄
⠀⠀⠀⢀⢢⣶⢛⡾⢺⣿⣿⡖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢲⣿⣿⡟⣷⠛⣾⠜⡆
⠀⠀⠀⢹⣿⣿⣾⣿⠟⠛⠃⠀⣠⣼⣷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣾⣧⣄⠀⠘⠛⠻⣿⣷⣿⣿⡇
⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⢰⣿⣤⣿⣶⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⣶⣿⣤⣿⡆⠀⠀⠀⠉⢙⣿⣶⡇
⠀⠀⠀⠀⠿⣟⣻⠀⠀⣶⡶⠟⠿⣿⡛⠉⠻⠻⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠛⠉⢛⣿⠿⠻⢶⣶⠀⠀⣟⣻⠿
⠀⠀⠀⠀⠘⣹⣿⣷⣾⡿⠷⠚⠛⠛⠻⢦⣀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⣀⡴⠟⠛⠛⠒⠾⢿⣷⣾⣿⣏⠃
⠀⠀⠀⠀⠀⠈⡶⣿⣏⣀⣀⣤⣤⠶⠖⠚⠛⠻⠶⣤⣀⠻⣧⠀⣠⣄⠀⣼⠟⣀⣤⠶⠟⠛⠓⠲⠶⣤⣤⣄⣀⣹⣿⢾⠁
⠀⠀⠀⠀⠀⠀⠹⣻⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⣉⣓⢾⣧⣿⣿⣼⡷⣚⣉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣟⠏
⠀⠀⠀⠀⠀⠀⠀⠩⣵⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣿⣿⣿⣿⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣮⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣟⣽⣿⣉⡉⠽⣿⠟⠛⠋⢉⡴⠻⣿⣿⡟⢦⡉⠙⠛⠻⣿⠯⢉⣨⣿⣯⣻⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡿⠿⣿⣯⡤⡤⠁⠀⢀⣴⠟⠀⠀⢙⡋⠀⠀⠹⣦⡀⠀⠈⠦⢤⣽⣿⠿⢿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⡷⠞⠋⢁⣴⣀⣠⣤⡿⠁⡠⠁⠀⢸⡇⠀⠈⠄⠈⢻⣤⣄⣀⣦⡈⠙⠳⢾⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠀⣠⡾⠋⣰⠏⣱⠟⠀⠠⠁⠄⠀⢸⡅⠀⠠⠘⠄⠀⢻⣌⠹⣆⠙⢷⣄⠈⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⠁⢀⣾⠃⢰⡟⠀⢠⠃⡜⠀⠀⠸⠇⠀⠀⢣⠘⡄⠀⢻⡆⠘⣷⡀⠈⣿⣟⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣷⣾⡁⢠⡿⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡄⠀⢿⡄⢈⣿⣾⣿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡟⢾⣝⡟⣷⣤⣇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⣤⣾⢻⣫⡷⢻⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⠭⠗⠾⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠷⠺⠭⠷⠈⠁

⣴⣶⣶⣶⣶⣶⣤⣀⡀⢀⠶⢢⡠⣠⠄⡤⡀⡤⠠⢰⠄⠀⣯⢦⠀⡰⠐⠂⡤⠠⠸⢸⢠⡀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣤⣀⠈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⡩⠎⠁⠀⠁⠁⠀⠐⠈⠖⠁⠀⣠⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣛⣿⣿⣿⢿⣟⣿⣷⣦⡀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⣿⣾⣿⣿⠉⠙⠛⠛⢿⡛⠋⠹⢿⣦⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣠⣶⡿⠛⠉⢙⡿⠛⠉⢉⣉⣿⣿⣿⣿⠏
⠀⠀⠸⣿⣿⣿⠟⠛⠛⠛⠚⠷⣄⠀⠀⠿⢻⣷⣄⠀⠑⣄⠀⠀⠀⢀⠔⠁⣠⣾⠟⠁⠀⢀⣤⠞⠛⠛⠛⠉⠉⣿⣿⣿⡟
⠀⠀⠀⢻⣿⣿⣄⣀⣀⣠⣤⣤⣬⡿⣦⣄⡀⠈⠹⣷⣄⠈⣰⣶⣷⠁⢀⣴⡟⠁⠀⣠⣴⢿⣷⣶⣦⣤⣤⣤⣤⣿⣿⣿⠁
⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣜⣿⣦⣹⣿⣿⣤⣿⣋⡤⠖⠋⠁⠀⠀⠤⣈⣈⣉⢀⠀⢨⣿⣿⡏
⠀⠀⠀⠀⠸⢾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠛⢓⣛⣻⣿⣿⣿⠛⠛⣫⢿⣿⣿⣿⣿⣯⡙⠙⠛⠛⠿⣿⣛⣛⣛⡛⠳⣶⣦⣄
⠀⠀⠀⠀⠀⢠⣿⣿⡧⠔⠚⠉⣉⡽⣯⡾⠛⣳⣶⠟⣱⣿⣿⣿⣿⣯⢂⠙⢶⣤⡀⠀⠈⠳⢬⣉⠉⠛⠺⣿⣿⣧
⠀⠀⠀⠀⠀⢺⣿⣿⡠⠔⠚⣩⠋⠀⣉⣴⣿⣿⢁⣼⣿⣿⢻⣿⣿⢇⠀⢡⡀⠈⠻⢦⣄⣀⠀⢫⡙⠓⠦⣼⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣏⠀⢀⠴⢳⠞⠋⣽⡿⠙⢁⣿⢻⣷⠃⢸⣿⣿⠀⢢⣄⢱⡄⠀⠈⣿⡉⠛⢾⠳⢦⡀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣶⣁⢠⠏⠀⣸⠛⠀⢀⡾⠃⣾⠃⠀⢸⣿⣿⠀⠀⢿⡄⠹⣄⠈⠈⢧⡀⠈⢧⣀⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣴⣏⠀⢀⡞⠀⣼⠏⠀⠀⠈⠛⠃⠀⠀⠈⢿⣄⠘⢆⠀⢈⣧⣤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⡶⣾⣟⢿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⢰⣿⡇⢿⣿⡈⠛⢿⣿⣿⣿⣿⣭⣉⣙⣉⣉⣉⣉⣤⣴⣶⣾⣿⣿⠿⠟⢛⣛⣷⣄⡀
⣰⡘⣿⣷⡜⣿⣿⣤⡀⠈⠙⠛⠿⠿⠿⣿⣿⣿⠿⠿⠿⠛⠛⢉⣡⣤⣶⣿⣿⣿⠿⠿⠿⢆⡀
⣿⣷⡙⢿⣿⣮⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⡿⢟⣛⣩⣥⣴⣶⣶⣾⣿⣿⣷⡄
⢻⣿⣿⣶⣽⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⣉⣉⣉⣉⠛⠛⠻⠿⣿⣿⡆
⠀⠹⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣿⡄
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⣠⣴⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠴⠶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⠛⣛⣩⣶⡶⠒⠓⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣴⣶⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠟⠋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠻⠇⠀⠀⢠⣤⣤⣶⠿⢋⣿⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠘⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡏⠉⠀⠀⠸⠃⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⣿
⠀⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠸⣇⡀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠛⠛⠛⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⣠⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠉⠀⣠⣴⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠀⣠⣶⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠃⠀⠀⣼⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣤⡖⠒⣲⠶⠒⣶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣶⠒⠒⢶⡖⢲⣦⡄
⠀⠀⠀⠀⠀⢻⣥⠀⠿⠆⠈⣷⠀⡟⠘⠛⢶⣤⣀⣾⣆⣤⠞⠋⠀⡟⢀⡼⠁⠀⠻⠃⠰⣿⠃
⠀⠀⠀⠀⠀⠈⠱⢶⠀⣠⣤⡀⠁⠀⢀⡤⠤⣾⣿⣿⣿⣿⠶⠄⠐⠒⠀⢠⣶⣶⠀⣈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣥⠈⠉⠀⢀⣨⣵⡶⠛⠿⣿⣿⣿⣿⡭⠖⢦⣤⡀⠀⠉⠉⢤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡖⢿⣿⣾⠃⠀⠀⢻⣿⣿⠨⠆⠀⣯⣾⡿⠓⣾⡷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⡈⠉⠁⠀⠀⠀⠸⣿⠃⠀⠀⠀⠈⠉⠁⣠⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⢳⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⠋⣿⢲⣤⣤⠀⡤⡴⠶⠒⣯⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠃⠋⠀⠁⠛⠀⠁

⡖⠒⣶⣲⣶⣖⣶⣶⣲⣶⡖⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶