Cytoplasm Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠁⠘⠀⠁⠁⠁⠈⠉⠀⠀⠀⠁⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⣂⣠⣠⣤⣆⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠰⢸⢀⣀⣆⣱⣴⠼⠶⠶⠓⠛⠛⠩⠉⠍⠀⠀⢈⠙⢧⡂
⠀⠀⠀⠀⠀⠀⠀⢀⢢⣰⡼⠦⠶⠚⠚⢻⠋⠉⠁⠠⠀⠆⠌⡐⠀⠄⠉⠀⠐⠀⠀⠀⠸⢀⠀⣿⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⡐⣶⠋⠡⠀⠀⠁⠀⠨⢉⠛⠵⠶⠐⠄⠰⠀⠀⠂⠀⠈⠀⠊⡀⠀⡉⠀⠌⢀⡯⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠠⠤⡇⠐⠒⡂⠀⠀⠀⢸⣠⢷⡴⠐⣠⠀⡀⠀⢠⠀⠀⠀⠂⠰⠀⠂⣁⣀⣴⢟⠢⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠭⢧⡰⢂⠀⠂⡉⠀⠀⢀⠀⠀⠀⠀⢐⣀⣁⣬⣤⠴⠶⠶⠺⠋⠏⠍⢋⣀⣠⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠐⠩⠻⢦⣤⣤⣥⢤⢶⠶⠖⡞⠟⠏⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠀⠉⠉⠉⠉⠉⢀⢒⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢆⠀⠄⠄⠀⠤⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⢘⠮⢠⠠⠀⠤⠄⠠⠀⡄⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠒⣶⡶⠂⠄⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠁⠀⠈⠐⠒⠒⠠⡴⠋⡴⢠⠳⣈⡄⣤⠦⡜⠳⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢋⠃⠚⠀⢋⡗⢱⠋⣥⠖⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠒⠢⠵⠒⢣⡨⢰⠘⡆⢣⣤⢫⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠦⡀⢒⠠⢤⣈⠗⢟⠀⠚⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⣤⠏⠊⣜⢀⡉⢠⠏⢡⣷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠨⠂⠤⢁⡈⣇⣈⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠄⠀⠀⠈⠔⠠⠀⠀⠀⠀⠀⠀⠀⢃⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠐⠦⡂⠄⢠⡄⠠⠀⣄⠠⢠⠀⢀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⢀⣀⡀⣀⣀⣠⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣁⣐⣂⣤⣤⣴⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠉⠓⠂⣼⡏⠘⠋⠀⠁⠈⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠔⠀⣀⠀⢁⠈⠁⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣤⣐⣮⠁⢸⣚⣿⠴⠒⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣄⠙⢦⠐⣃⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣿⣆⣉⣳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢿⢧⡼⠿⠶⠆⠀⡠⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠆⠀⠀⠐⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠿⠱⢧


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⡀⣀⡀⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠉⠉⠁⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠖⠒⠲⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠉⠁⢀⡀⠀⠀⣀⣠⢄⣀⡀⠀⠈⠙⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢊⣁⡀⠀⠀⣀⡴⠋⢹⠀⢾⣉⠘⡜⡅⢋⠷⡀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢏⡯⠜⢱⢦⡈⣇⠀⢸⠀⢀⣨⣍⠓⠓⠛⠊⣤⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠈⠳⢏⡗⣮⣵⠈⠛⠋⠀⢺⣀⣠⠇⠀⢠⣶⡇⠀⠰⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢀⡖⠙⢢⠀⠠⣄⢀⣙⠓⠊⠲⠄⠀⠀⠀⠈⠁⡄⢄⠘⠙⠀⠀⣉⣦⠟⣿
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠓⠔⠋⢀⡄⣬⣙⣿⡍⠿⠬⠾⡥⡔⠀⠀⠀⢹⣿⡄⠀⢀⣄⢺⣿⢀⡏
⠀⠀⠀⠀⠀⠀⣼⠁⣀⣝⡢⠀⠀⢠⣩⠟⢋⡵⠚⠛⠛⠲⢮⡘⠀⠀⠀⠀⠉⠀⣔⣾⣿⠿⠃⣼⠁
⠀⠀⠀⠀⠀⠀⡏⢸⣿⡮⠊⠀⠀⠀⠗⣲⠋⠀⠀⢠⡏⢙⣧⠹⡄⠀⠐⠶⠀⠘⠓⠉⠐⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡇⠈⠻⢃⡖⢢⡀⠀⠀⣏⠀⠀⠀⠀⠙⠛⠉⠛⡷⠀⠀⠀⣠⡒⣲⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⠴⡩⢾⡀⠀⠹⡄⠀⠀⠀⠀⠐⠶⣰⠃⠀⢀⣞⠳⡰⣼⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢏⡥⠩⢇⠀⠀⠈⠲⠤⢤⡤⠴⠚⣥⠀⠀⣞⢮⢡⡽⢃⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢴⠛⠧⠂⠀⠠⢀⡂⠄⠀⡂⠄⢀⣀⡀⠀⠈⠉⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠴⠋⠉⠁⠈⠐⠀⢏⠀⢸⠆⢀⡼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⢶⡖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠄⠀⢐⣷⣀⢀⣀⠐⠂⠀⠂⠶⠶⠶⠶⣶⣦⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠠⠀⠹⣧⠈⠀⠟⣿⢿⠟⢻⡆⠸⣷⣀⡀⢠⣥⠞⠙⣻⡏⣛⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⡸⠻⣆⢤⣤⣤⣤⠟⡀⠀⠀⢀⣟⣒⣾⣡⠞⠋⢸⡗⣾⣇⣠⣶⡛⣿⠛⠉⢻⣿⣯⠠⡀
⠀⠀⠀⠀⠀⣾⣋⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡭⠻⣥⣤⣐⣸⡟⠫⡉⠡⣹⣯⣿⣴⣾⣿⣿⣿⣷⣎⠳⡀
⠀⠀⠀⠀⠀⠉⠡⠀⢀⣀⡀⠀⡀⠀⠠⠀⠀⠀⠆⠈⢉⣤⣄⡄⠉⠉⢿⠀⠀⢸⡉⠟⣛⣻⣿⣻⣿⢛⣿⣿⣷⣼⣾⣦⣄⡀
⠀⠀⢨⡀⠀⠀⠀⣴⠏⠉⠙⣦⠀⠁⠀⠀⠀⠁⠀⠀⠘⠣⠘⠀⠀⠀⣀⢀⣥⡾⠶⢶⣯⠖⣴⠻⣟⣈⡿⣿⣿⡏⢿⣿⣿⣿⣶⡀
⠀⠀⠈⠧⣄⠀⠸⣇⠀⠀⠀⢸⡆⡴⢦⡀⠀⠀⠀⠀⣀⣀⣶⢠⣙⡢⠅⡈⢿⡁⠀⠰⡿⣤⠼⣿⣟⠉⢀⣿⣿⠃⢸⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠿⡦⠐⠿⢾⣄⣀⡾⣽⠁⠈⠳⣄⠀⢠⡞⠉⠛⣟⡛⢿⣍⣇⠆⢈⠳⡶⠶⠛⢷⡀⠠⣯⡀⡟⡹⠁⠀⢾⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠈⠙⠘⢷⣦⣜⡉⠀⢹⣦⣀⣀⡟⠀⠘⠷⢿⣄⢀⣝⣛⣻⣿⠠⣠⠀⠀⠀⠠⠻⣇⣀⡽⡷⠁⠀⠐⠠⠟⠒⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣭⣈⣹⣄⡀⣦⠀⠒⠭⠉⠉⠉⢙⠀⡈⠁⠄⠀⠀⠂⠐⠂⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠛⠉⠉⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⠿⠿⠀⠀⣠⣤⣦⣠⡇⠀⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣿⣷⣶⡶⠀⠧⠙⢻⣾⣿⢟⠀⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⣿⣿⣷⣄⠀⠀⠻⣿⣷⡾⠖⠀⠹⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⣻⣿⣿⣿⣿⣦⣤⠀⠉⠁⠘⠃⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠂⡻⣿⣿⣿⣿⣿⣷⣄⡀⢀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣃⠀⠀⣀⢀⠄⠀⠀⠀⠀⡀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⢿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠋⠉⣁⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡈⠙⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢁⣠⣤⣶⣶⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣶⣤⡀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⣠⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⢿⣷⣦⡀⠀⠀⠀⣀⡀⠀⢀⣴⣾⡿⢿⣶⡄⠀⠀⠀⠻⣿⡄⠘⣿⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣧⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠈⠹⣿⣆⠀⠸⠿⠃⠀⣼⣿⠁⠀⠀⣿⣷⠀⠀⠀⠀⠹⣿⡄⠘⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⠀⢻⣿⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢹⣿⡄⠸⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠸⣿⡇⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠻⣿⣦⣾⡿⠃⠀⢰⣶⠀⠀⠀⢿⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣧⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠿⡷⠀⠀⠈⠉⠉⠀⠀⠀⠘⠋⠀⠀⠀⠸⣿⡆⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢹⣿⠀⠀⠀⠀⠀⠙⢿⣷⣄⣀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⣿⣷⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⣿⡄⠀⠀⠀⣀⡀⠀⠉⠛⠛⠛⠉⠀⢠⣤⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⡀⠈⠉⠀⠀⠀⢹⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⣴⡿⠟⠋⠉⠀⠀⠀⠉⠻⣿⣦⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⢸⣿⠁⠀⠀⠀⠀⣀⠀⠀⠠⣶⣆⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣾⡿⠀⠀⠀⠀⠸⡿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠇⢠⣿⡇⠀⢀⣄⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠈⠉⠀⣾⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⠁⠀⠿⠟⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢰⣿⠆⢠⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⡿⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⣾⡿⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⢠⣾⡿⠛⠛⣿⣧⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⣸⣿⠃⢰⣿⠇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⢀⣀⣤⣴⣿⠟⠁⠀⠀⣰⣿⠃⢠⣿⡟
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⠀⠀⠘⣿⣧⡀⢀⣿⡟⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⣴⣿⠃⢠⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣷⠀⢻⣿⡀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣴⣿⠆⠀⠀⠀⠀⠀⣀⣴⡿⠋⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠙⠿⣷⣦⣄⣀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⡈⠙⠛⠿⠿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠿⠛⠁⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣀⣀⡉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣶⣶⣶⣶⣾⣿⠿⠿⠟⠛⠉

⠀⠀⠀⣀⣤⣤⠤⠤⢤⣤⣤⣤⡤⠤⠤⢤⡤⠤⢤⡤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠒⠛⠛⠛⠛⠛⠛⠛⠛⠉⠲⢆
⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢰⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⢠⠀⢀⠀⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣀⢀⣂⣩⣥⣴⣶⣷⡿⢷⣿⣷⣿⣶⣶⣭⣶⣤⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣏⣽⣿⠻⣿⡇⣸⡟⠉⣿⣿⣿⠻⣿⣿⣿⣷⡄
⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣾⣿⠱⢾⡿⠉⢻⣿⠻⠃⠀⣶⠿⣧⡆⢰⣿⣿⡀⣻⣿⣏⣸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣼⣷⣤⣾⣿⣤⣦⣰⣿⣶⠛⣷⣼⣿⣿⣿⢿⠟⠛⠋⠀⠠⡀⠉
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠛⠻⡿⠟⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠏⠁⡀⠀⠀⠀⠀⠀⠁⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⡀⠀⠀⣀⠀⢀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠆⠛⠸⠀⠿⠀⠺⠃⠀⠟⠀⢻⠛⠀⠃⠙⠁⠇⠸⠇⠙⠘⠗⠗⠐⠇⠀⠿⠀⠿⠃⠀⠻⠀⠛⠻⠃⠀⠀⢠
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣇
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⡏⠀⠀⠀⠀⠀⠀⠘⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⢠⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣣⣤⣤⣤⣀⢀⢠⣤⣤⣄⢠⣤⣶⣤⣤⣶⣶⣴⣶⡿⣦⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⣿⣿⣿⠉⢹⣿⣿⡁⠈⣿⡇⠀⣿⡇
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠹⣿⣿⠉⢀⣿⣿⠀⢺⣿⣿⡏⠀⣿⣿⣷⠀⣿⣿⢿⣦⣿⣧⣾⠟⠁⠀⠀⠀⠁
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣰⣿⣿⣄⣸⣿⣿⣶⣿⡿⣿⣧⣀⣿⣿⣿⣷⣿⣿⣾⡿⣿⣿⡁⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠿⡿⣿⣿⣷⣿⣿⣿⠿⣿⠿⠟⢉⠛⠻⣿⠿⠛⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠂⠉⠛⠉⠡⠋⠐⠀⠀⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⢸⡇
⢸⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢦⣤⡄⢠⣤⣤⣤⡄⠀⠐⣀⣀⠘⠀⠀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠉⠉⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡟
⠀⠀⠙⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠄⣤⣠⣤⣤⣤⣤⣤⣤⡴⠞⠋
⣤⣤⣤⣤⣭⣿⣷⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠐⠒⢳⣄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠒⡆⠀⣀⢠⡤⠀⠀⠁⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⢶⣞⣡⠨⠶⠟⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠡⠀⠀⠔⢢⣄⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⢢⠜⣃⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠛⠑⣲⣶⡮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⢞⣯⡉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠐⠦⣄⡀⠐⠏⠀⢀⠀⢁⠀⠂⡀⠀⠐⢩⣮⡙⠓⣄⠀⠱⡆⠀⠶⢲⠋⠁
⠀⠀⣀⠀⣄⠀⠀⣽⣷⣦⣿⣷⣆⠈⠫⡳⣄⠀⠀⠠⡌⣾⡿⠫⡄⠂⠀⠛⠳⣀⠀⠀⢀⠶⢸⣃⠙⡀⠠⠤⡀
⠀⠄⠃⠈⠠⠄⠸⠉⣧⣞⠛⠋⠄⠀⠀⠐⠘⢦⢀⠀⠁⡔⠰⠃⠀⠀⠐⠂⠀⠨⢧⣂⠈⠐⠀⡋⢀⡩⢀⠚⡁
⠀⠂⠸⠂⢁⠀⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠠⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡃⢀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠂⠀⠠⣶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠤⡢
⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠻⢦⣀⣤⡀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢨⢝⢆⠠⠄⠈⠉⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠻⣦⣛⠘⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠞⣤⠁⣀⡀⠀⠀⢘⠆⠀⠀⠀⢸⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠱⢴⠺⢿⣽⣷⠺⠓⠀⠀⠀⠀⣸
⠀⠀⠀⣢⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⠀⠀⠀⠈⠒⠒⠏⠁⠀⠀⠀⠀⠀⢈⡏
⠀⠀⠆⠻⢇⠑⢀⠀⠀⠀⠀⢰⣦⡤⢿⣦⠂⠀⠀⠀⠀⠀⠀⠈⢦⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣦⠘⠁
⠀⠀⠈⠑⠀⠑⠈⠂⠀⠀⠀⠈⠈⣱⣾⣧⣀⣀⣤⣤⣀⠀⠀⠀⠀⠙⠦⠔⡄⠀⠀⠀⢀⣦⣄⣿⣿⣿⡆
⠀⠀⠀⠀⢀⣤⡄⠀⠁⠀⠀⠀⠐⠹⠿⠋⠀⠀⠀⢀⠀⡍⠀⠀⠀⠀⠈⣊⠀⠀⠀⠀⠙⠚⢳⣴⣿
⠀⠀⠀⠀⠀⠻⠁⠀⢰⣦⣅⠀⢠⡀⠀⠀⠉⣦⢐⣺⡹⠁⠀⠀⠀⢴⡟⣋⡍⠉⣉⡽⣇⠈⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣒⡿⠞⠀⠀⢉⣉⠉⡘⠫⣦⡀⠀⠠⣶⠤⠀⠀⠠⣅⣀⣨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠊⢀⡀⣀⡀⠀⢰⡶⢤⣙⠩⠁⠙⠓⠒⠐⠶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⠃⠘⠓⠒⠄⠐⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⢀⡠⠋⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⡠⠑
⠊⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⠚⠛⠋⠀⠀⡠⠋⠀⠀⠐⠁⠀⠀⠂⠀⠀⠀⠀⠀⡀⠠⠛⠛⠁⠀⢀
⠀⠀⠀⡀⠘⢏⠀⠀⠀⠂⠀⠀⠀⠈⠩⠂⠠⠐⠀⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠄⠀⠀⠀⠐⠱⠂⠠⠐⠀⠁
⠀⠀⠀⠐⡀⠘⢶⣼⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⣦⣼⠄
⢀⠀⠀⠀⠈⠢⣄⣀⣯⣢⠃⠀⡠⠐⠒⠁⠈⠀⠀⠀⠠⡀⠀⠀⠀⠐⠦⣄⣰⢷⡢⠀⠀⠠⠐⠐⠉⠁
⠀⠑⢄⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣠⠤⠈⠐⠐⠀⢀⠈⠢⡀⠀⠀⠀⠀⠉⠈⠀⠀⠈⠀⠀⣤⠤⠀⠂⠂
⢍⢦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠠⣕⠄⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⣶⠟⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠒⠶⢤⣴⣾⠿⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠒⠦⣤
⣀⣤⡽⠋⠀⠀⡀⠄⠠⠤⣤⣀⠀⠁⠠⡀⠀⠀⠀⠀⢀⣀⣄⡷⠃⠀⠀⠀⠀⠄⠤⣤⣀
⠛⠉⠀⠀⠀⠈⠀⠀⠀⣤⡐⠸⡇⠀⠀⠀⠉⠐⠒⠒⠚⠋⠉⠀⢀⠔⠀⠀⠀⠠⣤⡀⢹⡆⠀⠀⠀⠉⠒⠒⠒
⠀⠀⠀⡈⠀⠀⠀⠀⢠⠿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡰⠣⠀⢸⠇
⠀⠀⠀⠁⢀⣶⡦⠖⠁⠀⢠⠎⠀⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⣠⣷⡴⠂⠀⠀⡠⠋⠀⢀⠄⠀⠀⠄
⠀⠀⠀⢔⣤⠀⠀⡀⠠⠂⠁⠀⠀⠈⠀⢴⠀⠀⠈⢂⠀⠀⠀⠀⢄⡀⠁⢀⠀⠄⠊⠀⠀⠀⠂⠀⡴⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣆⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣄⣀⡀⠈
⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⡈⠛⢻⣀⡀⠀⠀⢀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠈⠛⣇⣐
⠀⠐⠁⠀⢀⠀⠄⠄⠀⠀⠀⠢⡀⠀⠀⠀⠉⠛⠛⠓⠁⠀⠀⠁⠀⠀⠄⠄⠠⠀⠀⠑⢀⠀⠀⠀⠀⠙⠓⠛⠊
⠀⠆⠀⠐⢯⠀⠀⠀⠀⠈⠓⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠀⠀⠀⠈⠲⣄⠱⠄
⠀⠠⠀⠀⠈⠑⠤⣀⣀⣀⣈⣦⡇⠨⡆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠓⢤⣀⣀⣀⣸⣬⡆⢸⡀
⠀⠀⠑⠄⠀⠀⠀⠀⠉⠉⠛⠉⡠⣲⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠛⠁⣠⡾⠀⠀⠀⠀⠀⢀
⠙⢶⠀⠀⠀⠐⠠⢄⣀⣰⡶⠷⠛⠁⠀⡠⠀⠀⠀⢀⡉⠹⣦⠀⠀⠁⠂⠤⢄⣀⣠⡾⠟⠋⠀⠀⠀⠂⠀⠀⣈
⣂⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣹⣓⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⣛⡛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⠟⠟⠇⠸⠁⢸
⣿⢰⡦⣧⣶⣤⣤⡄⢰⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠗⠷⠂⠀⠀⢸
⣿⢀⣤⡀⡁⣈⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠘⠷⠛⠛⠿⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢰⡯⣤⡦⣆⣥⣇⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠉⠈⠁⠁⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢠⢤⢀⢀⡀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠈⠈⠉⠉⠉⠟⠁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠰⠼⠳⠶⠲⠶⠲⠰⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢰⠦⣦⣠⡤⡄⣤⢠⣠⡀⣤⢠⢰⣄⡤⢠⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣻⠭⠥⠒⠒⠒⠒⠒⠠⠤⠤⣍⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢏⠞⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢯⠎⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠉⠒⢄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣿⣿⣿⣿
⣿⣿⣿⣿⢯⠋⠀⠀⠀⠠⠀⡜⠀⠀⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⠀⠸⠸⣿⣿⣿
⣿⣿⣿⢏⡎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠦⣀⣀⡤⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡇⢻⣿⣿
⣿⣿⡟⡸⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⣿⣿
⣿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⡄⠀⢹⢸⣿⣿
⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⢸⢸⣿⣿
⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿
⣿⣿⣧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⣿⣿
⣿⣿⣿⣆⢣⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠜⠑⢀⠀⡐⠀⠀⠀⠀⠀⠒⠀⠀⠀⢂⡎⢰⣿⣿⣿
⣿⣿⣿⣿⣆⢣⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡳⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠃⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡓⢄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⣑⣒⠒⠂⠀⢀⣒⣒⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⠀⠀⠀⣠⣶⣤⡄⠀⠀⠀⢀⣶⣾⢺⡷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⣾⣿⣷⡄⠀⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⢀⣴⣲⡶⣤
⠀⠀⠐⣇⠙⠃⡧⠀⠀⠀⠀⠴⣷⠚⣿⠅⠀⠀⠀⠰⣯⢯⡧⠀⠀⠀⠀⠀⠩⣍⣉⠀⠀⠀⠀⣴⠚⠛⠛⣿⠀⠀⠀⢈⣭⣭⣭⣭
⠀⠀⠀⠉⠋⠋⠀⠀⠀⠀⠀⠈⠹⠛⠛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣸⣿⡧⠀⠀⠀⢀⣴⣿⣷⣦⠀⠀⠀⢸⣿⣶⡿⠿⠶⠀⠀⠀⣠⣴⣶⡶⢦⠀⠀⠀⢻⣶⠶⣶⠶⠉⠀⠀⢀⡦⣵⠟⡂⠄
⠀⠀⠠⣾⣿⡿⠃⠀⠀⠀⠸⣇⠛⠛⣺⠁⠀⠀⠈⣽⣿⠷⠟⠃⠀⠀⠐⣇⣩⣁⣰⡞⠁⠀⠀⢸⣧⣻⣼⡀⠀⠀⠀⣰⣿⠽⠻⠿⠆
⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠟⠁⠀⠈⠱⠆⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⢀⣶⡿⢻⣆⠀⠀⠀⢀⡴⣴⠚⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⢾⣿⠷⠂⠀⠀⠀⢸⡏⠉⠀⠀⠀⢦⣴⣿⣄⡆⠀⠀⠶⢳⠾⣅
⠀⠀⠘⣏⠀⢀⡿⠀⠀⣀⡤⠛⠋⠀⠀⢠⣤⣤⣴⡿⠀⠀⢐⣲⣾⣿⣷⣾⠀⠀⢠⡟⠁⠀⠀⠀⠐⢲⣿⣿⡷⠂⠀⠀⠀⠈⢧⠁
⠀⠀⠀⠈⠩⠉⠀⠀⠀⠻⠿⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠀⠀⠀⠙⠻⠏⠉⠁⠀⠈⠻⠦⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣭⣙⣫⠅⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⠁⠻⡅⠙⡷⠈⢣⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⣒⢢⣀⠀⠀⠀⠀⣇⡇⠀⠀⢘⣴⠁⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡈⢄⡁⡈⢃⠰⠠⠈⢱⠀⠀⠀⠱⣜⠢⣠⠼⢋⠣⣤⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⣳⠁⡢⠂⠉⠐⢄⣧⠀⠀⠀⠈⠢⠬⣀⣀⡤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣰⣿⣠⠃⠀⠀⠀⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⣿⢫⣃⢌⢀⣀⣄⡴⣳⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠵⣒⣚⣛⣯⠭⠚⠁⠀⣀⠄⠐⠋⢡⠀⠉⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢲⡤⠤⠒⠒⢢⢤⠲⠈⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡔⠁⠀⠀⠀⠀⠠⣻⡟⢎⠐⠃⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡀⣇⠀⠀⠀⠀⡴⠊⣀⣼⣼⡎⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁⡌⣉⠓⡈⢏⠔⠋⠀⠀⠈⣉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣈⠒⠆⠎⠀⠀⠀⠀⢈⡟⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⡀⠂⢄⡀⠀⠀⣠⠞⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠭⠭⠭⠒⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⢿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣾⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠻⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡷⣧⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠒⠐⠂⠐⠀⠒⠂⠂⠐⠒⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠷⢦⣤⣤⠴⠶⠾⠟⠛⠻⠏⠉⠙⠛⠛⠳⠶⣦⣤⣤⡤⠖⠚⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⡃⠀⠀⢤⡀⠀⠀⠀⠙⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢹⡐⠀⢻⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⠎⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡴⠋⠉⠉⠙⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⢀⠗⡄⣠⡄⠀⠀⣴⠚⣀⠖⢁⠄⠀⠀⡦⣔⡼⢲⡆⠠⡦⡖⣦⡦⡆⣶⠤⡄
⠀⡖⢰⡤⡆⣦⢔⡤⡖⠀⣴⠀⣔⡄⡤⢰⣴⢦⡆⢀⣄⣠⠞⠓⠾⢱⢺⠘⣄⣟⡽⠴⠎⠑⢄⠚⣀⠞⢉⠴⠃⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⠀⠀⠀⣸⣷⣿⢙⡁⠀⠀⠀⠀⢇⢡⡖⢋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⡠⠖⠁⢹⡜⡿⠋⠒⠒⠠⠤⠼⡆⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢣⡴⡎⣴⢚⡇⢸⡇⡃⠺⣷⣄⠀⡴⠚⠓⠦⣄⡤⡄⢰⡄⣤⢠⠤⣢⢴⢴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡰⠃⠀⠀⠀⠀⠹⠃⠏⣧⣼⡇⣇⠎⠉⠻⠟⠉⠀⠀⠴⣡⢶⠃⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠄⠀⠀⠀⠀⠀⢀⡴⠉⢻⡁⢻⡀⠀⣀⣤⡀⡀⣠⣠⣀⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣀⠤⠤⠒⠊⠁⠀⠀⠈⡇⡏⠣⡀⡾⣄⠤⠤⣤⢤⡦⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣵⠀⠈⠑⠠⠤⠀⠀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣍⣉⣩⣭⣍⣉⣉⣉⣩⣽⠃⠸⡉⡉⠉⣉⣩⣍⣉⣩⣭⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠡⣴⣶⠋⣉⣹⡯⢞⡧⠀⢮⠄⠀⠙⣍⣉⡑⠻⢶⡍⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢒⣿⠟⢫⠟⢩⣿⣱⣣⡀⢻⣁⠀⠠⣽⣦⣶⣦⠀⠁⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡿⣻⣿⢦⣼⣅⡀⠀⠀⠉⠀⠉⠀⠀⡴⡴⣲⢶⢴⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠈⣥⡿⢻⣼⣇⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢋⣉⣉⣤⣤⣤⣤⣉⣉⡙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⣁⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠉⠻⢷⣦⡈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⢁⣴⡿⠋⠀⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⠀⠀⠀⠀⠙⢿⣦⡈⢻⣧⡀
⠀⠀⠀⠀⢀⣾⠏⢠⣾⠏⠀⠀⢀⣿⣿⣷⠶⠓⣠⣤⣤⣄⠀⠀⠹⣦⣼⠋⠀⢀⣤⣤⣤⡀⠙⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣾⡏⢠⣿⠃⠀⠀⢀⡿⣹⡏⠀⠀⠀⢻⣆⣀⣹⢷⣴⠾⠋⠙⠷⣦⡾⣃⣀⣼⠇⠀⠘⣿⡄⢹⣷
⠀⠀⠀⣸⡿⢀⣿⠇⠀⠀⠀⣼⢷⡟⠀⠀⠀⠀⠀⠉⠋⠙⣷⠀⢈⣀⠲⠂⠀⣾⠋⠉⠁⠀⠀⠀⠸⣿⡀⢿⣇
⠀⠀⠀⣿⡇⢸⡿⠀⠀⠀⢰⣏⣾⠃⠀⠀⠀⠀⠀⣀⣤⣤⡿⠀⣏⣍⣳⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⢿⡇⢸⣿
⠀⠀⢀⣿⠀⣿⡇⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⣼⠏⠀⣱⡟⠻⢾⡍⣥⡶⠛⢷⣍⠈⢹⡆⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⣸⠇⢻⣄⠀⠀⠙⠛⠛⠁⠀⠀⠀⢸⡿⠀⣿
⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⢸⡟⢿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣾⡏
⠀⠀⠀⠀⢿⣇⠘⣿⡄⠀⠀⣿⣼⡇⠀⠀⠀⠐⣶⣼⡷⢦⣤⣤⠶⠾⠛⠛⠛⢷⣴⡟⠀⠀⠀⢠⣿⠃⣸⡿
⠀⠀⠀⠀⠈⢿⣆⠘⢿⣆⠀⢸⡇⣿⠀⠀⢘⣻⡏⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠃⠀⣰⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣧⡈⠻⣷⣌⠛⠛⠀⠀⠉⣹⣷⣬⣀⡐⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⣠⣾⠟⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⢷⣦⣀⠀⠀⠉⠰⠟⢹⠟⠛⠛⠉⠉⠁⠀⠀⣀⣴⡾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⢉⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣌⣉⣉⠛⠛⠛⠛⣉⣉⣡⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⣅⠤⠠⠤⣀⠠⠀⠀⣉⣁⠀⠀⠀⠀⢀⢀⢀⣠⠀⠀⡀⢀⠒⡆⠀⠀⠐⠐⠴⠚⢲⠛⠃⡦⠤⠀⠀⠀⠦⠖⠐⠂⠀⠐⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⠁⣀⣀⣀⠈⠤⠤⢁⡀⠠⠴⠔⠲⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠁⢉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠅⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠈⠀⠀⠂⠀⡈⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⡶⠶⠾⠛⠛⠛⠻⣶⣄⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⠠⠀⠈⠀⠀⠀⠰⠀⠰⠀⠀⢁⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠁⠀⠀⢀⠤⣤⣄⠀⠀⠙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⣅⡠⠆⠘⠀⠀⠀⠀⠀⢂⠀⠀⠠⠀⠀⠀⠀⠀⢀⣾⠏⠀⠰⡀⠀⠀⠀⠉⡂⠙⠗⠀⠀⠈⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡙⡜⠱⠂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠰⠆⠀⠈⡂⡐⠄⠀⡀⠀⠀⢁⣀⠀⠀⢹⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠒⠀⠐⠀⢃⣯⠁⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⣻⢀⡥⣶⣆⡥⢙⡋⢂⡄⠀⠀⢠⡏⠀⠀⠀⠀⡿⣦⣀⠈⠁
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢀⠀⡈⠑⠀⡀⠈⣒⣬⣭⠗⠠⠀⠀⠁⠀⠠⠤⠀⠀⠀⠀⠀⣿⡄⠀⡀⢂⠂⠑⢀⠎⠲⠄⠀⣀⠀⠀⠀⠀⠀⠀⢌⡹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡰⠊⢀⠀⠀⣀⠱⡋⠿⣥⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⡀⠀⡂⠀⠄⢛⠨⠡⠔⠀⠀⠲⠀⠀⠀⠀⣼⢹⡗⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠜⢦⠀⠠⠀⠀⢠⠚⠁⠀⢀⡀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢦⡙⠃⠃⠎⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠙⠋⠐⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠰⠋⢲⡀⠀⠐⢀⡄⢀⠐⠲⣤⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡟⠦⢤⣄⣃⠀⠀⣠⠇⠐⠀⠀⠂⠀⠙⣄⡴⣿⠃
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠃⠀⠀⠈⠙⠣⠔⠓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠙⠶⠀⢼⣍⣁⣹⡀⢉⡉⢉⢈⣉⠭⠕⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠁⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣇⠀⢨⠀⠈⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠁⠀⠀⠀⠀⠣⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣤⣀⡀⡀⣠⢄⢠⡤⣠⢄⢀⣤⢀⣀⢠⡀⡀⣤⢀⠀⡀⡤⠀⡠⡀⡀⡠⡀
⠀⠀⠀⡤⠞⠉⠁⠀⠀⠈⠙⠲⣄⠀⠋⠁⠋⠃⠳⠼⠀⠇⠳⠼⠁⠽⠂⠏⠸⠙⠇⠓⠸⠉⠇⠯⠄⠯⠇⠇⠭⠃
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⣤⡀
⠀⣸⠀⠀⠀⢠⣀⡀⣤⣄⠀⠀⠀⠸⡆⠀⡦⢔⠴⣴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⣤⡤⣤⡤⠤⠙⡢⣬⣿⡇
⠀⢹⠀⠀⠀⠈⠉⠉⠉⠈⠀⠀⠀⢰⢇⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢠⣺⣼⣽⠏⠁
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡈⢁⠁⠉⠉⠀⠛⠘⠀⠀⢀⣀⣀⣧⢞⡻⠆⠀⡴⠚⠓⠒⠢⣤⣞⣽⣿
⠀⠀⠀⠙⢦⣀⡀⠀⠀⣀⣠⠴⠫⣄⢬⠉⡇⠀⠀⠀⠀⠀⠀⠀⠺⠗⠺⡟⡏⠀⢀⡼⢏⣉⣉⠉⠒⠮⠽⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⢏⢈⡆⠀⠀⠘⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣤⣯⣄⠀⠈⠉⠙⠛⠚⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣈⠒⠢⣄⡀⡗⠚⡠⠴⣶⣤⡀⠀⠀⠀⠀⠀⡇⢿⡟⠀⠙⣧⣞⣉⠓⢦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠈⢩⣞⣋⣉⣡⡽⠉⠛⠲⢦⣄⠀⠃⡾⡇⢠⠜⠟⠿⠉⠀⢨⡟⠉⠉⠀⠉⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡁⡏⠈⣀⢀⡄⠀⠀⠀⠙⡷⡆⠁⡇⠸⡄⠀⠀⢀⣠⠞⡉⡖⢒⣖⢊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠙⢎⠁⠘⠢⢄⠀⠀⠀⢱⡉⢀⡇⠀⠈⠙⠛⡉⣀⠀⠋⠘⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⠛⢢⠀⣧⠀⠀⠘⡇⢈⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠲⠐⠸⠆⠦⠚⢆⡰⣃⡤⠋⠀⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⢤⣄⢄⢤⣩⡛⠉⠁⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠉⠈⠀⠀⠀⠀⠀⣀⣄⣀⡇⢀⣇⣀⡀⠀⠀⠀⣀⠀⠀⢀
⠤⠤⠤⠤⠖⠒⠒⠒⠓⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠔⠋⠉⠁⠀⠀⡇⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢀⣄⣄⣀⣀⣀⣻⡗⢄⣠⣄⡤⡪⠑⡆⢰⠓⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠉⢁⡈⠉⣉⠉⣽⡣⠾⣧⣿⠋⠀⢀⠀⢸⠀⠀⠀⠹⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣈⡭⠖⠀⠧⠝⠘⠞⢠⢤⠠⡲⠘⢛⣴⡶⠫⡄⢨⠭⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣖⠒⣲⠀⠀⠮⠗⠠⣖⡄⠀⠥⠀⣴⣾⢟⢺⡄⣤⢷⣏⠀⣸⡏⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⡒⣲⠄⠆⠆⠸⠹⢀⣘⠊⠈⡁⢸⣻⠒⣿⡯⠄⠀⠀⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠘⠋⠟⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⢶
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⣦⣯⣥⣯⣥⣯⣥⣶⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣾⢀⣀⡘⠃⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⡏⣧⡌⣧⡆⢽⡏⣿⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⠀⠀⠀⠙⢮⣙⣁⡴⣋⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤
⠀⠀⠀⢴⡧⣤⢤⡤⣤⠀⠀⠀⠀⠀⣇⣙⣃⣙⣃⣘⣃⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠁⠉⠈⠁⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣢⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹
⠀⠀⠀⠀⠋⢽⣿⣯⠢⠄⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⣶⢿⣏⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠸⡀
⠀⠀⠀⠀⣴⠿⠿⢇⠀⠑⠀⠀⠀⠀⠀⠈⠌⢿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣟⣾⣻⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⠁


⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡰⠊⠉⢀⣭⠑⢆⠀⠀⠀⠀⢀⠔⣉⣁⡄⠉⠲⡄⠀⠀⠀⠀⡴⢫⠉⠀⠉⠓⣄⠀⠀⠀⠀⠀⢳⣝⢫⡆⠀⠀⠀⠀⠀⠀⢀⣾⣏⣀⣤⡀
⠀⠀⢸⢡⣶⡄⠘⠛⠁⠈⡆⠀⠀⠀⡞⠰⣿⣿⣷⡖⠀⢹⠀⠀⠀⢸⠀⠈⢦⢢⡴⠉⠸⡄⠀⠀⠀⠀⡀⠬⠍⢳⠀⠀⠀⠀⠀⠀⠘⠛⠉⢉⡟
⠀⠀⠘⣆⠉⠁⢴⣿⡷⣰⠃⠀⠀⠀⠹⡀⠛⠙⣿⡿⢂⡞⠀⠀⠀⠘⣄⠀⢸⡋⠀⠀⡸⠀⠀⠀⠀⠀⢑⡬⢅⡀⠀⠀⠀⠀⠀⠀⠴⣦⣴⠟⠁
⠀⠀⠀⠈⠓⠦⠤⠵⠚⠁⠀⠀⠀⠀⠀⠉⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠈⠓⠤⠭⠔⠊⠀⠀⠀⠀⠀⠀⠚⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⠄

⠀⡁⠈⡃

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠢⡄⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡤⠒⠒⢤⡈⠢⣀⠠⠚⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⣠⠊⡠⠊⠀⠀⠀⠀⠈⠒⠤⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡀⠀⠀⠀⢀⢨⠀⠀⠀⡠⠔⠒⢉⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⠐⢄⠀⢀⠀⢱⢰⣀⣤⣤⡇⣮⡀⡰⠋⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠆⠀⠀⠠⢀⢣⣤⠔⠺⣼⠁⠀⠀⠙⠯⠙⢃⡀⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⢈⠮⣒⢤⡶⠛⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣴⠐⠢⠤⠌⢩⡁⠐⢦⠀⠀⠀⠀⠀⠀⠀⠔⢒⣒⡲
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⣤⢆⣡⠞⠋⢤⠅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⡀⠱⡀⠀⠀⠀⠀⡜⢠⠋
⠀⠀⠀⠀⠀⠀⢣⡄⡀⠠⢀⡼⠘⢅⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⡖⣴⠁⠄⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠀⢀⡜⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡨⡎⢶⠋⠀⠀⠉⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢨⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠭⣁⡠⠊
⠀⠀⠀⠀⠀⢀⠄⣰⠛⠢⠟⠀⠀⠀⠂⠄⡐⠒⠂⠀⠀⠀⠀⠀⢀⣄⠀⣠⠞⡀⠀⠀⠇⡀
⠀⠈⠅⠁⠀⣄⣠⠁⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣝⠣⠄⠀⠀⠀⠀⢰
⠀⠑⠀⠀⠘⠲⡖⠒⠁⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣏⢲⠋⠡⠈⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠨⠰⠋⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⢄⣀⡴⠛⠁⢆⠇
⠶⠦⠀⠀⠀⠲⣙⠟⣹⣀⣤⣄⡀⣀⣶⢲⡤⠞⡘⠅⠂⠀⠀⠈⠪⠦⡀
⠀⠀⠀⠀⠀⠀⢉⠎⠈⡉⢹⢸⠉⠉⢡⢸⠂⠀⠈⠀⠐⢦⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠀⠀⠀⠀⠑⠄⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠒⠂⠀⠂⠒⠀⠂⠒⠂⠒⠂⠀⠒⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉⠀⠀⠩⠄⠀⠥⠉⠥⠉⠀⠬⠈⠡⠤⠭⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⡀⢤⠀⠀⠀⠠⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠘⠔⢂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠁⠈⠀⠨⠵⠌⠠⠄⠩⠤⠍⠠⠬⠄⠡⠈⠭⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣀⡄⠧⠤⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡄⢀⠀⠀⣀⣀⣀⡀⠀⠀⡀⣀⡠⠀⢀⡀⢀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠖⡀⠸⢤⠀⠐⠌⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠒⠀⠂⠐⠒⠀⠒⠒⠂⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠁⡄⠀⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⡀⠀⣀⢀⣀⠀⢀⠀⠀⣀⣀⣀⡀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⡐⠲⠶⠶⢄⠐⠄⠤⠁⠀⠠⠄⠀⠠⠴⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡔⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠀⡈⠀⠁⠉⠁⠈⠀⠉⠀⠉⠀⠁⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠎⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠈⠥⠁⠌⠡⠄⠩⠠⠉⠉⠉⠈⠁⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡄⢄⠡⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣤⣄⣀⣄⡀⠠⠤⠀⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠁⠐⠚⠀⡄⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠂⠀⢐⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠩⠍⠉⢡⠀⠨⠍⢭⠡⠄⠄
⠀⠀⠀⠀⠀⠠⠤⠲⠖⠀⠓⠀⠀⠐⣛⠂⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣀⣀⠂⢀⡀⢂⣀⡒⢀⣀⢀
⠀⠀⠀⠀⠀⣘⡂⣒⣀⡀⢁⠀⡀⠀⢩⣉⡉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠀⣀⠂⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠙⢿⢟⡉⠀⠀⠐⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠉⠉⣦⠈⢜⣠⢴⠾⠃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠒⠀⠀⠀⠀⠐⣌⣩⣾⣿⠶⡗⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠘⠟⣻⡔⡈⠉⡀⢐⠅⣟⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⣸⡂⣿⣽⠒⠀⠀⢀⡄⠈⢉⡀⠀⠀⠀⠀⡀⠀⠀⠸⡿⢧⠀⠂⣪⠴⢶⣿⠋⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⢻⡇⠀⠀⠁⡤⠀⠀⠀⢤⠀⠁⠀⠀⠰⡤⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠃⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠈⠊⠀⢸
⠀⠀⠀⣶⡄⠀⠈⠁⠀⠄⠀⣴⣭⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡟⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢀⣀⣀⣔⣦
⠀⠀⠀⣿⣷⠀⠀⠀⠀⢡⣴⠟⠋⠏⠀⠀⠀⠟⢀⡀⡀⠀⠀⠀⣎⠈⠛⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣿⡿
⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⠐⠀⠹⠗⠁⠀⠀⠐⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡄⠀⠀⡆⠀⠀⠐⠀⣰⠁⠉⣹⣄
⠀⠀⠀⣿⣿⡄⠀⠀⠈⠳⠦⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣾⣿⣆⠀⠀⢉⣱⣄⡾⣱⠋
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏⠀⠀⠰⣛⡻⢰⡇⢀
⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠰⠆⢙⠋⠀⣀⣤⣈⣧⣤⣤⣄⣠⠇⠀⣾⣶⡣⠀⣼
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⡆⢀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠹⢄⣸⣛⡀⠛⠻⣿⡿⢿⠇⠀⠨⣿⣿⣧⣰⠃
⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢣⡞⠀⠶⠔⢓⡀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⡀⠈⠋⠃⠨⣤⣁⣤⣬⣷⣷⣾⣿⣿⣿⡿⢼⣦
⠀⠀⠀⠚⣿⣿⣿⣿⣷⣰⣄⠀⣠⣦⣾⡄⠀⣸⣿⡿⡇⢀⡀⣀⣿⠇⠀⠀⠀⢀⣰⣾⣶⡄⢀⡀⠀⡴⠀⠀⠀⠀⢻⡟⠛⠛⢿⠿⡿⠟⠛⢋⡡⠲⠋
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣡⠍⠄⠀⣿⣿⠁⣁⠘⠛⢛⣿⣯⢀⠀⡔⡍⠁⠀⠙⠇⠀⣣⡖⠃⠀⠀⠀⠀⣾⡇⠀⠀⢴⣦⡄⠙⠒⠁⠠⠂⠀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⢻⣆⣸⡟⣿⡇⠀⣸⣿⠿⠋⠉⠈⠈⢻⣿⠀⠀⠀⠀⡀⢸⣿⣷⣿⣶⣦⠀⠀⣿⣧⡰⣶⡼⠷⠀⠀⠀⠀⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠛⣭⣿⣿⣿⠻⠟⣾⣿⣯⣤⡿⠀⠉⠙⣿⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⣄⡇⠀⡀⣿⡽⡿⠧⠘⣶⣿⣿⣿⠿⣿⣧⡀⠀⠀⢰⠋⠀⣀⠊
⠀⠀⠀⠀⠀⠀⠀⣻⣿⡟⠉⠀⠀⠀⠙⣿⣿⡇⢠⡀⠀⡿⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠋⡇⠀⣿⠿⠀⠱⣤⡤⢋⣉⣛⣀⠀⠻⠙⠧⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⢦⡀⠀⠰⢐⣿⣿⡇⢸⣿⣾⠁⠀⠀⠀⠀⠀⠀⢸⠉⠐⠋⠁⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠷⠀⠋⠉⠓⠲⠶⢶⣶⠾⠟⠋⠀⠂⠀⠀⠀⠚⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⡾⠋⣁⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀⡄⠄⠀⠈⢿⡄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠁⠀⠀⠰⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠂⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇
⠀⠀⠀⣿⠀⢸⠀⢀⠔⠊⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⢠⠏⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠘⣶⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢠⢸⡀⠀⠈⠚⠘⠓⠀⠀⢸⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠘⠁⠡⢄⣻⠛⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⢣⡀⠀⠀⠀⠀⠀⣠⠦⣈⠍⠉⠀⠉⠁⠀⣀⡤⣶⡺⠂⢀⣂⣁⣐⢢⣼⣾⠁⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠉⠒⠆⠠⠖⢚⠁⠀⠂⠀⠀⠀⠀⠀⠀⠉⠈⢹⠀⣰⠋⠐⠶⠤⢥⠬⠿⠷⠂⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠤⠘⠀⣀⣰⠐⣀⡠⣄⠀⠀⠀⠀⠀⣿⠉⢛⣤⣒⠢⡄⢀⣀⡀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢠⠿⡤⠴⠊⠉⠙⠳⣄⡀⢹⠀⠊⠙⠁⠀⡿⠀⢀⡀⠕⠀⠀⠀⠇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠶⠂⠘⢀⠀⠀⠘⡅⢸⠀⠓⠀⠐⠋⠐⠐⠺⠐⠂⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠂⠀⠑⠀⠀⡇⢈⠀⠀⠀⠈⠉⠉⠉⠀⠁⠈⠙⠁⠀⡆⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠉⡤⠂⠐⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⡀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇
⠀⠀⠀⣿⠀⠰⠒⠒⠂⠀⠉⠁⠀⠀⠈⠀⠐⠒⠒⠒⠒⠈⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⠀⠀⢠⡄⠀⡀⠠⠤⠁⠨⠦⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠉⠉⠹⠧⠾⣿⠃⠀⠄⢇⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⣀⠐⡒⠊⡈⡈⢀⠁⢀⠀⣂⣤⣞⠉⣀⠊⢹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠉⠀⠁⡄⢠⠠⠈⠀⠄⣐⠋⠃⢸⡧⢿⡇⠈⠁⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡇
⠀⠀⠀⣿⠀⠀⠠⠀⡆⠠⢀⠠⠀⢄⠚⢀⠀⠀⢀⢄⣀⠤⡀⢤⠠⠄⡐⠑⡄⠠⢄⠠⠠⢀⠠⡀⡐⢆⢠⣀⠀⢸⡇
⠀⠀⠀⢿⡀⢀⠐⠈⢀⢸⢐⠀⠉⡸⠀⡬⠘⠂⠬⠦⠁⠀⠃⠈⢨⢀⠠⠨⣄⢈⠸⠀⠳⠮⠶⡍⡆⡠⠦⢉⠀⣸⡇
⠀⠀⠀⠈⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⢀⠀⢀⠀⡀⢀⣀⣀⢀⡀⢀⡀⡀⡀⠀⡀⢀⢀⡀⡀⠀⠀⠀⠀⣀⠀⠀⡀⢀⣀⢀⣀⣀⣀⣀⣀⣀⡀⢀⡀
⠀⠀⠀⡏⠉⠉⡉⣉⠉⣉⠉⠉⠉⣉⡉⡉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⠦⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⡇⠀⢀⡁⠈⠀⠉⠀⠉⠈⠈⠁⡈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣄⠠⠃⡆⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⠎⢤⠘⢆⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢈⠠⡁⠀⠀⠀⠀⡰⢀⣀⡙⠒⠤⠤⠴⠒⠋⠅⠤
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠐⠄⠀⠴⠋⠀⠀⢱⠔⠐⢂⠐⠂⢄⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠃⠀⠈⠃⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⡈⡐⠀⠀⣜⠀⣒⠂⢁⠠
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣤⠅⠐⠈
⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⠀⠀⠄⢈⠀⠀⡀⠐⠀⠀⡅⠁⢄⡀⢁⠈⠀⠂⡠
⠀⠀⠀⡇⠀⠈⠀⠀⠈⠀⠀⠁⠢⠀⠄⠀⡀⠈⠂⠀⡆⠦⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⠀⠀⠃
⠀⠀⠀⡇⠀⠠⠄⠁⠐⠀⠄⠐⢂⠔⠀⢈⡀⠍⢀⢄⠀⢀⠀⠠⠀⠐⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠁⠔⠀⠀⢀⡀⠤⠤⠐⠀⡄⠀⠐⠈⠀⠐⠁⡀⡑⠀⠀⠀⠀⡖
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠉⠀⠀⠀⠀⠘⠀⠀⠁⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡟⡀⠀⠀⠠⠀⠄⠀⠄⠀⠀⠀⠀⠤⠀⠐⣦⠂⠂⠀⠄⠀⠤⠀⠒⠰⠇⢠⡀⠀⠤⠀⠄⠀⠠⠀⠄⠀⠤⡦
⠀⠀⠀⣧⠄⠄⠡⠄⠐⠀⠄⠀⢀⠂⠄⠐⠐⢒⣞⠈⢚⣱⡦⠀⠄⠠⠄⠤⠠⠀⠀⣀⣀⠀⠠⢤⠤⠀⠧⠀⡁⢠⣤
⠀⠀⠀⡧⠈⠄⠀⠀⠁⠀⠠⠑⠠⠀⠀⠀⢠⠠⠎⢁⡉⣀⠀⠠⣄⠀⠠⠤⠀⠀⠀⠉⠉⠐⠂⠄⠐⠀⠄⠀⠀⠀⠶
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠂⠁⠁⠀⢆⠀⠐⠀⠻⠈⠉⠠⠈⠀⡀⠂⠁⠀⢂⡘⠚⠠⠀⠀⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠒⠁⠀⡀⠀⠀⠐⠄⠖⠈⠁⢈⠷⠔⢠⠈⠀⠓⠈⣆⠀⣊⠀⣄⢁⡇⠀⠀⠀⠐
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠄⠀⠇⠀⠇⠀⢇⡀⠀⠠⠈⠀⠈⠀⠈⠉⠁⠀⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⣀⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡋⠀⠈⠁⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠾⠿⠁⠀⠈⠀⢠⡀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠧⠀⠀⣀⠀⢀⣶⠀⠹⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣠⡾⠛⠻⢿⣯⠀⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢾⡏⠀⠀⣠⣾⣿⣧⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢸⡇⠀⠰⣿⣟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⡇⠀⢀⣾⣙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⣾⣏⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠓⠲⠛⠿⠿⠿⣿⣿⣀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣤⣀⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠗⠀⢠⡾⠉⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢸⡇⢠⣶⠄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠰⠂⠀⠀⠁⠀⠰⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⡀⠀⢀⡄⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠋⠁⠀⠈⠁⢀⣾⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃⠀⠀⠀⢀⣴⣶⡞⢿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠸⠿⠀⠀⣿⠃⠈⠀⠀⢹⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢱⣦⠀⢶⣶⣄⠀⢾⡇⢠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠃⢀⠁⠀⠀⠀⠙⣦⣄⣶⡿⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣀⣾⣶⡀⠙⢋⣠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠒⠀⠸⢿⣿⣿⣷⣶⠟⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠀⠀⠈⠉⣻⣿⣤⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣶⠄⠻⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⣽⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠀⢠⣿⡿⠉⠁⢈⣹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⡟⠁⢰⣿⣏⠀⠀⠀⢿⡏⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣼⣿⣦⠟⠁⠀⠈⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠻⣿⣦⣤⣤⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠆⠀⢀⡀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠉⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠋⠀⠀⠀⣈⡁⠀⠀⠀⠉⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠠⣶⡆⠀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠰⠛⠃⡀⠀⠠⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⡀⠀⠀⡇⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠙⠃⢀⡄⠀⣴⡿⠃
⢀⣾⣿⠇⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⢀⡄⠀⠚⢠⣀⠀⠀⠀⠀⠿⠆⠀⠻⡿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣾⡟⠀⠉
⠿⠿⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠋⠀⣀⣀⠀⠹⡇⢀⣄⠀⠀⠀⣴⣶⠄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏
⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⣿⠆⠀⢠⣾⠛⢁⣀⣴⣿⣷⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⠻⠿⠁⣸⣿⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡅
⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠈⢀⣄⠀⠀⠀⢀⣴⣿⡟⠐⠒⢶⣾⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣿⣟⠛⣷⣤⠄⢈⣿⣷⣼⣿⣿⣿
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠦⠀⠀⠉⠀⠀⠙⠉⠰⣿⣧⠀⠘⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢸⣿⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣈⣁⣠⠟⣻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣤⠀⠀⢠⠄⠀⠀⠀⠠⠀⠈⠉⢻⣿⣶⣿⣿⣿⡿⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠉⣿⣷⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠘⢻⣷⣤⣄⠉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣈⡉⠰⣾⣏⠙⠛⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢀⣤⡼⠛⠃⠀⢿⣏⣰⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⣴⣶⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣦⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈⠙⢿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢾⣿⠆⠈⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⣤⣤⠀⠀⠀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠁⠀⠀⠀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠉⠻⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⣶⣆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠔⠒⠒⠒⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⣀⣤⣠⣀⡀⠀⠀⠀⠀⠠⠉⠓⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣆⣥⣍⠹⢲⣀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠺⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢆
⠀⠀⠀⠀⠀⢠⠞⡀⠀⠀⠀⠀⠀⠀⠔⠡⠤⠀⠂⣁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⡀
⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⢂⠐⠀⡁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⡀⠈⣤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⢇
⠀⠀⠀⡏⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡁⡐⢦⣡⢈⣵⣀⢋⢂⡀⢰⢎⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⣀⡜⠅⠉⡬⠹⠘⡀⢅⡈⢼⡀⠐⠄⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠐⡌⠙⠂⣊⣡⡟⢭⡟⡃⡪⣘⠡⠁⢁⣒⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣆⢔⣢⠉⡝⠈⢩⠈⡓⣰⢶⣅⠈⡎⠠⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⡇⠀⠀⠀⢬⠰⠠⡂⠀⠀⠀⠠⠋⠡⠚⢠⢫⠇⢾⢀⠣⢎⣒⣢⡔⠐⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⢹⠈⠀⠀⢊⠰⠚⠀⠀⠀⠀⠀⠁⢈⠚⡠⡠⢅⣣⢎⠶⠈⢗⢀⠔⡃⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠄⣂⠊⢋⠀⠎⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠠⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣡⢃⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⢁⠘⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠗⢵⠎⠂⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⡨⢅⠏⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠄⠀⠀⠀⣞⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠃⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠙⡏⡇⠗⡤⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠈⠥⣅⣸⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣊⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣐⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⣀⡀⠂⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⣂⣈⡤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣿⣤⡤⣄⣠⣼⠇⠸⠶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣶⠾⠛⠉⠉⠀⠘⠋⡿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⣰⣽⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢺⡌⡆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⡿⠃⠀⠀⠀⠀⠙⠛⠀⠀⠀⢀⠀⠀⡾⡙⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⡦⠠⢤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡁⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠶⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡽⡆⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠠⣴⡄⠀⣸⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⢀⡀⣘⠌⠀⠀⠀⠀⠀⠐⣿⡟⠃⠀⠀⠀⠀⠀⠁⢸⣹⡟⠁⠀⠀⠘⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠏⠀⠀⠀⠀⠀⢀⡾⢋⠁⠀⠀⠀⠀⠘⠑⢢⡾⠿⠳⠦⠀⠀⠀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣠⣴⠞⠄⠀⠀⠀⠀⠀⣾⠻⡔⠡⠄⠀⠀⠀⠀⠀⣠⢟⡵⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢯⠁⠀⠀⠀⠀⠀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣘⢍⠋⠉⠛⠓⠀⠀⠲⠶⠶⣶⡆⠰⡦⠀⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣾⢃⠆⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠀⣤⠀⠀⠀⠘⣿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢈⠿⡟⠁⠀⠀⠁⠀⠀⣯⠙⠗⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠉⠀⠀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣶⣉⠀⠀⠀⠀⠀⠀⣶⢿⠙⠂⠀⠀⠀⠀⠀⢀⣴⠿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠳⡄⢀⡸⡑⠝⠀⠀⠀⠀⠀⠀⣄⣅⠁⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠑
⠀⠀⠀⠀⣦⢠⣀⣈⣿⣯⠛⠀⠀⠀⠀⠀⣶⣿⠷⡏⠀⠀⠀⠀⠀⢠⣼⡏⠁⠙⢦
⠀⠀⠀⠀⠀⠉⢰⣿⡿⠃⠀⠀⠀⠀⠀⠻⣿⡾⠃⠀⠀⠀⠀⠀⣰⣿⠙⢦
⠀⠀⠀⠀⠀⣀⣶⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠁⠀⠈
⠀⠀⠀⠘⠛⠟⣿⠶⡖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡛⠻⣆
⠀⠀⠀⠀⠀⠀⣿⣷⣇⠀⠀⠀⠐⠿⠷⠄⠀⠀⠀⢀⣴⢿⣇
⠀⠀⠀⠀⢀⣤⡿⣯⠷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡱⠁⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢋⣶⣤⣀⣀⣀⡀⣤⡾⢋⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠓⠷⣯⣭⣩⣧⣿⠞⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡙⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠕
⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣎⣀⣠⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢹⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠈⠀⠀⠀⠈⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⡀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣧⠀⠨⣿⡿⠿⣷⢾⣿⠴⡷⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠾⣿⣦⣄⣀⣀⣀⡀⠀⢀⣀⣀⣤⡾⠟⠁
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠭⠭⠭⢯⣭⣿⠛⠛

⣀⣀⣀⠀⡀⢀⢀⠀⠀⠀⡀⡀⢀⠀⡀⣀⣀⠀⣀⡀⢀⣀⡀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⣿⣿⣿⣿⣿⡏⠍⠋⢻⣿⠋⢻⠉⠿⢩⡉⣽⡟⢩⣙⠋⠭⡏⢻⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣧⣾⣧⣬⣥⣴⣬⣤⣦⣼⣤⣿⣷⣌⣥⣤⣭⣧⣬⣧⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⢀⠠⠤⠄⠐⠒⠒⠊⠉⠉⠁⠀⠀⠈⠉⢉⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⠉⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠈⠐⠀⠀⠀⢠⣢⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⣝⠆⠀⠀⢸⣿⣆⠀⠀⠀⣂⣬⡦⠈⠙⠤⠒⠂⠄⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠆⠉⠀⠀⠀⠀⢻⠿⠀⠀⢈⣍⢋⠔⠁⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠀⢠⠖⠀⠀⠀⠋⠀⠀⠀⠀⡜⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡆⢞⠉⠀⠀⠀⠀⠀⠀⠀⠂⢔⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢼⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡱⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠄⠠⡆⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠒⢒⠁⡾⠋⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣧⠠⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠅⠀⣴⣜⡀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡞⠀⠀⠱⢘⠣⠁⠀⠀⠛⠋⠀⢊⣉⠆⠀⠀⠀⠀⠠⠹⠀⣸⣿⡇⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠶⠶⠶⠦⠤⠤⣤⣀⣀⠀⠙⠛⠀⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠉⠙⣛⡛⠛⠉⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠱⣄
⠀⠀⠀⡜⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⢆
⠀⠀⢰⠃⠀⠄⠀⠀⠀⠒⠠⢽⣷⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⢸⡆⠀⠄⠀⠀⠀⠀⠀⠀⠈⠣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣇
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠀⡏
⠀⠀⠀⠈⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠑⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⣀⡀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢠⡄⢤⣤⢤⣤⡄⣤⣤⢠⣄⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣇⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⠀⠀⠤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣿⡿⠀⠀⠀⠀⠀⠀⢰⡆⠈⣿⠀⢻⠇⠘⡟⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣠⣾⣿⣷⣄⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡡
⠀⠀⠀⠀⠀⠀⢠⡿⣟⠽⠋⢹⣿⣿⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⡂
⠀⠀⠀⠀⠀⢀⡿⢊⠁⠀⢀⣿⣿⣿⠃⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢀⡤⠒⠒⣀⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠐⠻⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⢰⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠸⣇⡁⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⡷
⠀⠀⠀⠀⠻⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣤⢠⣀⡄⣀⣠⢀⡀⡄⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠰⠇⠎⠼⠰⠡⠆⠮⠠⠠⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⣶⣿⣶⣦
⠀⠀⠀⣰⣋⡘⣘⣁⢋⡋⣘⢁⢀⢀⠈⠀⠐⠁⠀⠀⢀⡔⠄⠠⠁⠀⠀⠀⠉⠀⠠⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢰⠆⡴⠰⠤⠆⡶⠴⠠⠀⠄⠤⠠⣀⠁⠀⠀⠀⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠐⢀⠘⠀⠀⠀⢃⠰⠀⠀⣎⠁⠀⠀⠉⠑⠢⠄⠠⠄⠊⠈⠋⠑⢤⠀⠀⢀⡦⢓⠃⠛⢢⠀⠀⠀⠀⡌⠒⠂⠐⠤⢀⠀⠀⠠⢠⡀⣠⢃⠀⠄
⠀⠒⠂⠀⠀⠀⠀⠀⠂⠂⠀⠈⠑⠉⠐⠦⣀⠀⢀⣀⡤⠤⠤⠀⡠⠜⠀⠈⢴⡄⠀⠈⠀⣘⠂⠀⠀⣉⠀⠀⠀⠀⠀⠅⠀⠀⠀⡜⠃⠈⠰
⠀⠰⠐⡄⠀⠀⢀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠒⠦⠴⠆⠋⠀⠀⠀⠈⡀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠐⣞⠀⠀⠂
⠀⠀⠈⠀⠘⠀⠈⠁⠀⠀⠐⠀⠈⠡⠔⠠⠀⠀⠀⠀⠀⡈⠀⢈⠁⢑⠀⠀⠀⠀⠀⠀⣀⣠⠄⡀⠀⠀⠀⠁⠚⠉⠀⠂⠀⠀⠂⠀⠀⣹⡄
⠀⠀⠀⠠⢄⠀⠀⠁⠀⡀⠀⡂⢀⠄⠀⠁⠀⠂⢀⢀⡀⠉⠅⢀⠀⠀⡀⠀⠀⠖⠀⠐⡂⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠈⠀⡀⠁⠀⢠⠀⠀⠀⠄⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠈⣀⠀⠐⠀⠁⠀⠀⠀⠈⠁⠞⠘⠀⠀⢳⣄⡈⠛⠲⢦⣄
⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡀⣠⠠⠔⠒⠒⠄⠀⠀⠀⢀⠈⣿⠀⠀⠀⠹⡢⠀⠀⠀⠄⠀⢀⠄
⠀⢘⠀⠀⡈⠀⢀⠊⠉⠂⠀⠀⠀⢀⠰⠂⠀⡄⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⣠⠾⠀⠸⡄⠀⡿⠀⠀⠀⠀⠀⠈⠀⠈⡀
⠀⠈⡦⠂⠀⠀⡄⠀⠀⠎⠀⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣀⠀⠤⠐⠉⠀⠬⠋⠀⠀⠀⠀⣰⠍⠀⠀⠀⠐⠀⠀⠨⡴
⠀⠀⡁⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠀⠀⠄⠈⠁⠀⠀⠂⠀⠄⠀⠉⠑⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉⡀⠘⠀⠀⡫⡈⠀⠀⠁
⠀⠀⠅⠀⠀⠀⠣⡀⠜⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⢿⣷⣦⡄⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠘⠀⠤⠀⡀⠀⠀⣰⡿⡟⡉⠉⠩⠉⡉⢏⠁⣀⣛⡛⢷⣄⠌⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⡴⠚⢢⠄⠈⠁⠀⢰⣿⠀⠃⣧⢠⡀⣌⣙⣌⣃⣸⣍⣁⣴⣿⣿⢿⠁⠹⣷⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠤⠀⠀⠱⠦⠴⠁⠈⠂⠀⢸⣿⣦⣼⡿⠻⣿⠋⣙⣯⡉⣽⠉⠤⠧⠐⢀⡄⠇⣆⣿⡀⠀⠀⡁⠈⠀⠌⠀⠈⠀⠈⠚
⠀⠀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠐⠁⢀⡄⠀⠃⠀⠀⠈⢿⡔⣀⠧⢠⡌⠃⠻⠟⢿⡘⣇⠰⠾⢇⢀⢓⢀⣿⣿⠀⠀⠀⠐⠀⠈⠈⠃⡀⠊⣑⣂⠕
⠀⡜⠀⠀⠀⠈⡆⠀⢀⠀⡠⠀⠀⡄⠀⡀⢀⡀⠀⠀⠀⠹⠮⣤⣦⣿⡶⠷⡶⠿⡷⡿⡶⣶⣾⣿⣿⠿⠛⠁⢀⡀⡠⠤⠀⠀⠀⠒⠂
⠀⠙⣄⣀⣀⡰⠃⠀⠀⠀⠀⠐⠂⡤⠤⡀⢈⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢍⣰⠡⣄⢀⠀⠀⠀⠀⢀
⠀⢀⣀⡀⠀⣀⠤⠠⠤⡀⠋⠀⠈⠧⡄⠞⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠐⣶⣄⡽⠞⠋⠉⠁⠀⠀⠀⠀⠂
⠀⢏⠀⡹⢰⠃⠀⠀⠀⠘⡄⠀⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡜⠁⢹⠀⠀⠀⠈⠣⠚⠉⠀⢀⣀⣀⡀⠀⣀⠐⠀⠁
⠀⠀⠁⠀⠘⣄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠈⠒⠁⠀⠀⣠⠒⣶⠶⣞⢹⣧⢎⡇⠙⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠘⠀⣀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠾⠃⠿⠉⠁⠀⠁⠀⠄⠀⠀⠀⢀⢀⡀
⠀⠀⢀⠀⡄⠒⢀⠆⠤⠤⠋⡄⠐⡀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⡠⡪⡐⠀⠂⡕⡄
⠀⡐⠂⠔⠒⠒⠓⠐⠊⠈⠀⠂⠲⢅⡆⠀⠀⠀⣠⠤⠲⠐⣆⠀⠀⠀⠀⡠⠄⡀⠀⠀⠀⠀⠆⠀⠀⢐⠺⠀⠀⠀⠑⠐⠀⢐⠉⠀⠀⢀⠈⠀⠈
⠀⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠁⠀⡰⠊⢁⣀⣠⠴⠏⠀⠀⡠⠊⠀⠀⡉⠀⠀⠠⠀⠀⠀⠀⢘⣁⠀⠀⠀⡚⠀⠀⠈⠐⢄⠀⠈⢀⢄⠌
⠀⠑⡊⢂⢆⢀⠀⠤⠀⡐⣈⠄⠡⠌⠀⢸⣠⠞⠉⠀⠀⠀⡔⠊⠁⣀⡀⠴⠊⠀⠀⠀⠤⠀⠀⠀⠀⠀⡹⠐⠒⠘⠀⠀⠀⢀⠀⠀⠀⠐⠂⠁
⠀⠈⠁⠈⠠⠰⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⡀⡀⡠⡀⣀⢀⢀⢀⡀⣀⡀⡀⡀⣀⢀⢀⢀⠀⣀⡀⣀⣀
⠀⠀⢀⠴⠋⠁⠀⠀⠈⠙⠢⡀⠛⠁⠋⠋⠃⠋⠃⠘⠘⠑⠙⠘⠀⠋⠃⠃⠘⠙⠘⠁⠊⠓⠓⠙
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⣷⡆
⠀⢸⠀⠀⠀⠢⢆⠶⠶⠀⠀⠀⡧⠀⠓⠋⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠒⠖⠒⠒⡸⣰⣿⠿
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠖⠒⠶⠒⢲⡖⠆⠀⠀⠀⢠⣀⢤⡀⠀⢀⠤⠤⣄⡀⡨⣾⡿⠋
⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⡴⣏⣙⠚⡆⠀⠀⠀⠀⠀⠀⣴⡿⢿⢷⠋⠁⣰⡗⠒⠒⠦⢝⣻⣿⣇⡀
⠀⠀⠀⠀⠈⠉⠛⠛⡏⢹⠄⠀⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣠⣾⡁⠈⠉⠓⠒⠲⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠮⣉⠒⠤⣀⣳⢚⡤⣖⣦⣄⠀⠀⠀⠀⢸⠸⣿⠁⠙⣦⣎⡙⠢⡀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠃⣡⡿⣭⠤⠴⠋⠉⠛⠶⣄⣸⠰⠋⢠⠋⠛⠏⠀⢀⣿⠀⠀⠀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣴⣇⠤⠤⡖⠀⠀⠀⠹⡿⠀⠀⠈⢦⣀⣀⠤⠊⢬⢍⣭⣯⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠈⠣⣤⢌⠑⢄⠀⠀⢱⠀⡇⠀⠀⠀⠀⠤⠤⠤⠤⠄⠤⠠⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣤⢤⢄⢄⠤⠁⡸⢀⠜⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⣒⠛⠂⠁⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠈⠉⠉⠀⠀⠀⢀⣀⠄⣸⠀⣧⣀⣀⠀⠀⣀⡀⠀⣀⡀
⠠⠤⠖⠒⠒⠚⠉⠉⠑⠒⠉⠉⠒⠒⠤⠤⠤⠖⠒⠋⠉⠀⠀⢸⠀⡇⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⠜⠀⣱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠓⠖⠲⠶⠶⠶⣿⢉⡖⣶⡮⠊⠹⢠⡇⠉⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢠⡀⢴⣲⠠⡲⣈⡉⡉⡛⠿⢀⣤⣚⠀⣣⣤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡤⠬⢍⠁⢠⡲⠀⡤⡀⠑⡅⢈⣤⡞⢽⣀⣸⣰⠁⢸⡟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣤⢒⡄⠔⠆⠰⠰⢀⡛⠉⠈⢼⡷⢾⣿⠇⠈⠀⠟⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣉⣁⣈⣉⣁⣙⣙⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢸⡁⡇⢸⠤⢼⠀⡎⠉⢱⠀⠹⠁⡜⠁⠑⠀⠪⢌⠀⢣⠞⠀⢷⣐⠇⠈⡏⠀⡧⠤⡇⢸⠠⠀⠢⢌⠀⡇⠸⠌⡀
⣀⠀⣀⠀⠘⠀⠀⠘⠀⠘⠀⠙⠒⠊⠀⠘⠀⠈⠒⠊⠀⠑⠚⠀⠘⠀⠀⠃⠘⠁⠀⠁⠀⠃⠀⠃⠘⠒⠀⠑⠊⠀⠃⠘⠒⠁
⠈⠉⠈⠒⠒⣄⣀
⠉⠉⠑⠒⢤⡀⠈⠦⣤
⠀⠀⠀⠀⠀⠈⠢⡀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠈⢹⡶⠋⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠺⣧⣀⣤⠼⠧⣄⡀⣠⣿⣤⣀
⠀⠀⠀⠀⠀⣠⠜⠁⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣏⠀⠀⠘⡇
⣀⣀⠤⠴⠚⠁⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠶⢾⠁⠀⠀⠀⠀⠀⠀⢸⣤⣠⡼⠃
⢀⣄⣀⠤⠤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡾⠀⠈⢳⡄
⠉⠀⠁⠀⠀⠀⠀⠰⡉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⡾⠋⠓⠦⣤⠤⠶⠻⣦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣠⣿⠀⠀⠀⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢡⠂⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢹⡏⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠑⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠔⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣆⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣤⠶⠶⠶⠶⠶⠶⠶⠶⠞⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠈⠛⠷⢦⣤⣀⠀⠀⣼⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⣇⠀⠀⠀⠀⠀⠙⢳⣄⣿⣴⣏⡴⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⣼⠙⢧⡀⠀⠀⠙⠳⢦⣹⣿⡿⠋⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠁⠀⠀⠀⠙⢶⣤⣀⣀⣀⠹⣿⠁⠀⠉⠛⠶⠶⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡷⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣴⣶⠶⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⣀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⣁⣒⣉⡦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠲⡎⠱⢠⡔⢤⡔
⣧⠍⠈⠀⠔⢲⣆⡀
⠛⠳⢄⡂⣰⠟
⠀⠀⠞⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⢀⣀⣤⠀⡀⠀⢀⡀⠀⣀⢀⣄⣄⢀⡀⠀⢀⢀⣄⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⣄⣿⢸⣧⠤⢸⡇⠀⢸⡇⠀⣿⢸⡧⠄⢸⡿⣆⣸⠀⣠⡟⠁⢠⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠈⠟⠘⠇⠀⠘⠷⠦⠈⠳⠾⠃⠸⠷⠦⠸⠃⠈⠛⠐⠿⠶⠀⠟⠁⠙⠇
⠀⠀⠀⡀
⣰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡀
⠎⢳⣿⢲⡆⣠⠎⠀⠀⠀⠀⠀⠀⠙⠋
⠠⠈⢀⡁⢠⣿⡄⢀⡤
⠠⠄⠈⣀⠉⠉⣘⣡⠄

⡆⠠⡄⠀⠀⠴⣯⡅
⠀⠠⡄⠀⠑⢆⢀⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢲⠀⣄⠀⣴⣠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⣤⣄⣹⡰⢿⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡄⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠙⠃⠸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⣠⣜⠓⠂⠀⠀⠀⠀⠐⠶⢤⣴⢧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠿⢹⡈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣷⣶⠾⣶⣶⠜⠀⠀⠀⠀⠀⠀⠠⣄⠈⢛⠀⢸⠃⢰⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠋⠁⠈⣦⡄
⠐⠾⠇⠀⠀⠀⠀⠀⠙⣹⣧⣤⣿⡛⠳⠆⠀⠀⠀⠀⣤⠀⣘⡶⠾⠛⠛⣟⠿⠃⢴⡎⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⡿⠟⢋⠀⠀⠀⠀⠠⣄⣩⠾⠇⠘⢗⠀⠀⠉⠀⠀⠰⠞⠛⣶⡞⠉⠀⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠀⣀⡀⠀⢨⡟⠘⠳⡄⠈⢀⠀⡿⠁⢀⠴⠃⠶⠟⢷⠖⠛⠁
⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢙⣋⠀⢈⡁⠈⠳⠈⠀⠰⠂⢀⣄⠰⠶⠿⢶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⣨⣄⣠⣃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⠀⡈⣁⢀⡀⠀⠷⠀⡀⠀⠀⡀⠀⠠⣴⡇⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⡭⢱⡄⠀⠀⠀⠈⠷⠘
⢻⣌⠁⠈⠀⠿⠄⡶⢀⢀⡤⠚⠁⠀⠀⠀⢠⣤⠄⢿⡴⠟⠉⠀⠀⣠⠀⠀⢁⠐⠶⡉⠳⣶⡾⠷⠄⣠⠄⠀⠀⠀⠀⠀⠈⠳⠴⠛
⡀⠙⠀⢀⡔⢀⠘⣧⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⣰⡆⠀⠉⠀⣤⠀⣧⠄⠀⣦⡸⠷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠲⠀⠈⠀⠀⠀⠀⢤⠿⡞⠁⠀⠀⠀⠀⠀⠀⠚⠋⠀⣘⡿⢅⣠⣜⣇⠀⢀⣼⣀⠴⢾⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠛
⢀⠤⠀⠀⠀⠉⠛⠰⠖⢀⡷⠄⠀⢤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠉⢻⠛⡛⠙⠇⠀⠀⠻⠖⠀⠀⠀⠀⣿⢀⠤⢤⡄⢻⡁⠀⠀⠀⠀⠀⠘⢋⡰⠖
⠋⠠⠄⠸⡏⠐⣤⠔⠶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠀⠷⠀⠀⠐⢷⣆⡀⠀⠀⠀⠈⡷⢠
⡄⠦⠀⣤⠤⠦⡁⢠⠤⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢀⠁⠀⠀⠀⠀⠀⣠⠀⠠⢈⣡⡞⠃⠀⠈⠁
⠱⠶⢆⡻⠀⠄⠉⠲⠀⠈⠣⡤⠀⠀⢠⣄⠀⣱⣄⡄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠳
⠇⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣁⢈⡁⠶⠈⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠓⠻⡧⠌⣠⠀⠴⠒⢴⣧⣀⠀⠀⠠⠼⠃⠀⠀⠀⠀⠘⣭⠀⠀⠴⠀⠀⠀⠰⠆⠀⠀⠈⠀⠄⡴⠀⠀⠀⠋⠓
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣶⡀⠰⠂⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠁⡴⢤⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⢧⠄⠐⡦⠀⣀⠀⢠⠿⠾
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡬⠁⠐⠈⠁⢡⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠
⣰⢦⡗⢀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣧⠸
⠉⠉⠁⠁⠩⠶⠒⢄⣰⠃⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠐⢢⡄⠀⣀⢨⡄⠈⠀⠉⠀⠙⣿⠶⣆⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠘⠆
⠀⠀⢌⠁⠀⠀⠈⠙⣃⣢⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠋⢠⡀⠁⠀⠐⡂⠀⠀⠁⠀⠉⣱⣖⠁⠀⠀⠀⠀⠀⠀⣀⡱⠀⠀⠈⠉⣻⡉⢁⡄
⠀⠀⠀⢀⠈⠋⠀⠀⡡⠙⡶⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡯⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣦⣤⣶⣤⣴⣶⣶⣶⣶⣾⣶⣤⣶⣶⣶⣶⣶⣶⣶⣴⣾⣷⣶⣷⣶⣿⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣦⣶⣿⣦⣶
⣿⣿⣿⠻⠍⠛⠟⠉⠙⠛⢻⡟⠏⣹⡿⢻⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣖⣒⣒⣶⣴⡴⠿⠭⣭⣕⠂
⠀⠀⠀⠀⢀⢴⣽⠞⠋⠉⠁⠠⠉⠁⢠⡄⢀⣤⢬⡀⠙⣦⠣⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⡛⠉⢙⣓⠒⡚⠛⠉⠉⠉⠛⠲⢤⣀
⠀⠀⠀⢀⢣⠟⠀⠀⣠⡷⠾⠿⢷⣶⣄⠀⡘⢯⡝⢳⡄⠘⡇⠄⠀⠀⠀⠀⠀⢀⡞⠉⠘⠀⠰⢀⣀⣠⢮⠤⣚⣁⡇⠀⡀⠛⡤⠤⣄⠉⠳⣄
⠀⠀⠀⠰⣮⣴⣲⣼⡏⠀⠀⠀⠀⠙⢻⡇⠀⠀⠻⣷⠇⢀⡇⠀⠀⠀⠀⠀⠀⡾⢠⠞⡿⡇⡀⠈⡋⣠⢶⣶⡉⣁⡴⠞⠁⠢⣞⣟⢾⢷⢀⡈⢣
⠀⠀⠀⣰⡇⡭⡻⣻⠅⠀⠀⠀⠀⢀⣼⠇⠄⠘⢀⠐⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⣜⡝⣌⠈⣻⠠⠯⣾⣿⣿⣷⣷⣿⣥⣆⠀⣾⣿⡈⢦⣇⠀⠈
⠀⠀⠀⣼⠸⠿⢆⡿⠀⠀⠀⢀⡴⠛⣡⡤⠄⣙⢞⡂⢰⢇⠃⠀⠀⠀⠀⠀⢠⡇⠿⠮⣻⣾⡇⠀⣨⢗⡿⢛⣿⣭⣍⡉⠹⣛⣬⣬⣟⣦⢻⡇⢀
⠀⠀⢸⡇⢠⠀⣼⠃⠀⠀⢀⣾⠁⣾⣡⡶⠞⢹⡗⡏⢸⢘⠀⠀⠀⠀⠀⠀⢸⡇⠺⡶⡿⣧⣷⡇⠀⠋⡼⠋⠛⢀⠉⢻⠀⢙⡻⠈⠋⢾⠔⡇⢠
⠀⠀⣾⣀⠀⢸⡇⠀⠀⢠⠞⠁⠺⡥⠋⣀⣈⣳⣯⣟⢸⢸⠀⠀⠀⠀⠀⠀⠈⣇⢸⡤⢡⣣⣶⣿⡿⣿⡷⠰⣿⠇⠐⢹⠣⡍⢁⠠⢄⣾⠋⠀⡾
⠀⢴⠇⠀⠀⣾⠀⠀⠀⢸⡄⠀⠀⣴⢿⠋⠉⢹⡉⢹⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣎⠙⢬⡉⣾⣾⡽⢦⣷⣆⠀⢁⣨⢯⢾⣤⡯⠀⠆⠀⠘⢠⡇
⠀⣿⣰⣿⣆⢿⡆⠀⠀⣸⠇⢠⡀⣿⠄⠒⣀⢸⡥⠞⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠹⠃⡃⠯⢫⡏⠂⠉⢙⣹⢛⡝⢛⣾⠁⠂⠞⢳⡎⢸⠁
⠀⢻⠸⣿⢿⣆⠻⢿⡿⣋⡤⣾⡌⢿⡄⠙⠿⣏⣧⡆⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⠹⠆⠀⢳⣼⠞⣷⠛⡩⠔⠻⢫⠟⣸⠎⢐⡏⣼
⠀⡘⢦⠙⠿⠿⠃⠑⢲⣵⣿⣿⠷⠈⣻⣿⣿⣯⣾⣡⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠈⠀⢀⡈⠛⣀⡥⡞⡶⠃⠸⣯⡀⠉⣰⠇
⠀⠘⠈⠳⣄⠀⠀⠁⠘⢳⣛⣁⣀⠐⠓⠾⣛⣫⢟⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠤⣬⣁⣀⠋⠘⠋⠀⠉⢀⣀⣩⠼⠃
⠀⠀⠀⠐⠬⠛⣛⡛⠿⠭⠭⠿⠭⠭⠉⠉⠭⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣀⡀⢀⣀⣀⣀⣀⣀⣀⡤⠤⠄⣀⣀
⠀⠀⣠⠴⣶⡾⠾⢿⠿⠚⠚⠛⠛⠓⣛⠛⠛⠛⠛⣛⡉⠉⠛⠓⠒⠒⠾⠷⢴⡆⢀
⢠⣾⡔⣋⣄⣀⠐⢫⡤⠶⢦⣥⡀⢈⣥⣤⠚⣳⢦⣍⢁⣀⡀⢀⡤⣤⣬⣥⡀⠙⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣬⡞⢰⣿⣿⣿⣀⡿⣽⡒⣯⣿⣇⣯⠞⣿⡿⣷⣖⣿⣸⣭⣿⢸⣷⣯⣿⣾⠇⠀⣼⣭⣤⣤⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⢳⡀
⡏⣇⠈⡻⠿⣿⠿⠿⠉⠹⣿⣿⣶⣫⢾⣿⣷⡟⠙⠟⠟⢓⠛⠿⠿⠋⠁⢉⣁⡴⠃⡰⠀⠀⠸⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠘⣮⠣⣄⣀⡀⠘⠀⠀⠀⠈⠉⠉⠀⣀⣈⣤⣤⠤⠤⠤⠤⣔⣖⣒⡛⢫⠭⠥⠒⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣀⣠
⠀⠀⠙⠲⠬⣭⣍⣉⣉⣭⣭⠭⠽⠿⠟⠛⠋⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠐⣶⢠⢦⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⣤⣴⣿⠂⠀⠰⠿⠿⠷⠐
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠓⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠿⠿⠟⠁⠀⠀⠀⠀⠒⠦⠠
⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⢰⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⡿⠀⠀⠀⠻⣿⣭⣽⣿⡆⠀⠀⠳⢦⡝⠛⣋⡀⠀⠀⢼⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠠⠥⠾⠄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠚⠛⠉⠁⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠀⢀⣿⣶⣴⠆⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠷⠀⠀⠻⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠛⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⣤⣾⣷⡄⠀⠀⠀⠀⣠⣤⣶⣶⣄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠈⠂⢠⣶⣦⡜
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣠⡾⠻⠿⠋⠀⠀⠃⠹⣿⣿⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠄


⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡟⢉⠙⠛⣿⣿⠛⢿⠛⢿⢛⡋⢛⣿⠟⣉⠛⠋⣙⡟⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣇⣰⣶⣄⣛⣃⣤⣘⣀⣆⣸⣇⣸⣿⣄⣛⣡⣀⣒⣇⣙⣃⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⣉⣉⣀⡤⠤⠤⠀⠀⠀⠠⠤⠤⠀⠀⢉⣀⣀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠶⠖⠒⠒⠒⠀⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠈⠁⠀⠀⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡶⠀⠀⠀⣤⣤⠀⠀⠀⠀⢀⠀⡀⠰⢟⡻⠅⠀⠁⠀⠀⠀⠐⠼⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣦⠁⠀⠀⠀⢻⣿⣇⠀⠀⢀⡡⣾⡞⠠⠁⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠒⠈⠀⠀⠀⢀⣈⠻⠛⠀⠀⢨⣦⢨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡀⢠⣖⠉⠀⠀⠈⠀⠀⠀⠀⠀⠮⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⢼⠉⠀⠀⡀⠀⠀⠀⠀⠈⠐⢄⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⣠⠸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢣⢃⠆⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢀⠄⠠⡦⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠑⠢⠤⠤⠤⠐⠁⠔⠞⠁⠁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠋⠐⠃⠀⠀⢀⢄⠀⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣷⠀⠤⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⡀⠀⠀⢸⣾⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠈⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢜⠯⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠄⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠈⡀⡀⠀⠀⣶⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠐⣁⠘⣷⠠⠀⠀⢹⣿⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣶⣶⠀⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⠀⠀⠘⠃⠌⠂⠀⠀⠀⠉⠁⠀⠣⠠⠇⠀⠀⠀⠀⠀⠣⠜⠀⣼⣿⡏⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠳⠶⠶⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠓⠳⠶⠶⠶⠶⢤⣤⣄⣀⣈⡉⠀⠀⢀⡿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣛⣛⠛⠉⢀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠚⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⡀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⡁⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠑⠒⠁⢀⠖⡄
⠀⠀⠀⠀⠀⠐⠂⠀⡀⠈⠀⠀⠀⠄⠀⠈⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠂⠈⠁
⠀⠀⠀⠀⡒⠊⡀⢀⢐⡘⢠⡀⠀⠀⠀⠀⠀⢑⠀⠀⢠⠀⠀⠀⠀⠀⠄⠒⠁⡐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⡀⣶⣤⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⡚⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠤⠤⠤⠤⠄⢀⠤⠤⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠰⢀⠘⡀⠈⢀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⢁⠀⠐⠃⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢨⠐⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡠⣀⣀⣀⣤⣀⣀⣤⠀⠀⠀⡁⠀⠀⠀⢀⣤⡤⡀⡀⠐⠂⡀⡀⡀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣈⣴⡅⢠⣟⣧⣿⣷⡶⡢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣥⢩⡿⣯⣿⣿⣳⣯⣧⣾⠿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠍⠛⣽⢛⡿⣾⣟⡏⣧⡼⣗⠷⠆⠰⡀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠘⡋⣎⠻⣷⡝⣃⢈⠀⠀⠀⠈⠊⠂⠈⠀⠨⠄⡀⠄⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠁⠁⠀⠐⠀⠀⠤⠵⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠂⠀⢀⠰⠧
⠀⠀⠀⠀⠀⠀⠀⠐⡸⣀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⡀⠾⠀⠀⠰⠀⠙⠃⠀⠰⢀⡤⠀⠀⠖⠀⠉⠁⠶⠀⠀⢦⡈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠊⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡟⢀⠀⠈⠁⢠⠂⡄⠠⡠⠀⢀⡐⠲⡈⣤⢶⠖⢢⡀⠀⢠⠀⡀⠘⠃⠀⣈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⡃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⠓⠖⠀⠓⠄⠁⠚⠻⠴⠓⠙⠤⠘⠊⠂⠰⠱⠛⠴⠺⠐⠀⠀⠀⠀⢉⣿⣿⣿⡏⠓⡄⠀⠀⠀⡇⠀⡃⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⢀⣤⠴⠀⠠⣤⠀⠆⠀⠛⠡⠆⠀⠀⠠⠆⠀⠀⠂⠨⠀⢀⣾⣿⣿⡿⠁⠀⠐⡀⠀⢀⠁⠀⡇⠀⡈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡿⠁⠀⠀⠀⢃⠀⡈⠀⠀⢃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢰⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⣽⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢓
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⢄⠰⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠛⠐⠢⠈⠣⣀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠠⠈⠀⠀⠀⠀⡖⢀⠀⡈⠑⠒⠂⠒⠒⠉⠁⠄⠶
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢁⠀⠀⠞⠈⠀⠀⢠⡄⠂⠀⢀⠚⠢⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡏⠀⠀⠈⠃⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠁⠠⠀⠀⠀⠀⠀⠄⠀⠊⢀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠘⡀⠐⠂⣀⠒
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠳⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠀⠀⠀⠀⠈⡀⠀⠰⠀⠈⠐⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⠄⠀⠉⠀⢀⠘⠒⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠰⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⢸⠀⠀⠤⠀⠠⠐⠀⠠⠈⠘⡠⠒⠀⠉⡀⠁⢀⠠⡀⠀⠠⠀⠀⠀⠐⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠀⠈⠀⢀⠀⠄⠠⠀⠂⢠⠀⠀⠒⠈⠀⠒⠂⠀⢀⠣⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠓⠂⠉⠒⠈⠁⠀⠀⠀⠆⠈⠐⠂⠠⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠀⠀⠀⠀⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⢀⢀⠠⢀⢀⣀⣠⠜⠄⡤⣄⡀⠀⠀⠉⠐⠀⠀⠀⠐⠘⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⠁⠄⠁⠉⠡⠀⠀⠈⠀⠀⠂⠈⠀⠀⠀⠐⠒⠄⠠⠒⠚⠃⠀⠁⠈⠑⠉⠀⠁⠀⠠⠤⠦⠀⠈⠉⠉⠈⠀⠡⠈⠂⠉⠛
⠀⠀⠀⢸⠂⠀⠂⠀⠂⠒⠀⠀⠁⠈⠂⠀⠀⠉⠁⠈⠉⠐⠢⠐⠖⠀⡝⠂⠭⠉⠋⡁⠀⢈⢀⠐⠒⡈⠉⢉⡄⠈⠒⠀⠐⠀⠀⢋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣀⠀⢀⠀⠁⠀⣀⠀⡂⠀⡠⠁⠀⢀⠀⠄⢄⢈⠀⠀⠀⠘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡠⠃⠀⢰⠀⠀⠈⠀⠱⡀⠈⡄⠀⢄⠀⡔
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠨⠀⠈⠄⠈⢓⣀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⡠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠠⡀⠀⠠⠀⢂⣁⠶⠒⠲⢤⡀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠐⠈⠀⡴⠋⠰⠀⠀⠀⠀⠙⢦⣈⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⡒⠬⢻⠆⠀⠀⠁⠀⠀⠀⠀⠀⠻⢆⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠄⡈⣿⠸⡄⠀⢴⠆⢺⣿⣷⣶⢄⠀⠀⠓⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢽⣇⢱⡀⠀⠀⠻⣿⣿⣿⣿⣖⣀⠀⠈⠳⡀⠁⢠⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢀⣿⣧⣱⣄⠀⠈⡘⣿⣿⣿⣿⣷⣷⡆⠀⠘⢣⡀⠂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡀⠘⠿⣷⡜⢦⠰⠛⡱⠿⣿⣿⣿⣿⣿⣦⣤⠀⠙⢦⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠂⠤⠀⠚⠭⣿⣦⠱⣜⠵⠶⠻⣿⣿⣿⣿⣿⣿⠟⣄⣦⣱⣖⠈⠤
⠀⠀⠀⠀⠀⠀⠠⡪⠒⠈⢝⣻⡇⣸⣦⠀⠀⠉⠹⣿⣿⣿⣿⣯⣽⠟⢳⡘⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⣀⣰⣿⡿⢀⠀⠀⠀⠚⠻⣿⣿⣿⣿⡧⠀⠁⠘⣇⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠿⡗⣮⠃⠰⣄⠀⠀⠀⠛⣿⠏⠀⠀⠀⠀⢹⠉⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣷⣌⠳⣤⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠠⢫⣿⣿⣥⣁⠒⠤⢤⠤⠤⠿⣯⣿⡓⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠎⠋⠘⡿⣿⣿⣶⣶⣶⣿⠟⠛⠉⠉⢏⠙⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡈⠀⠉⠁⠈⠀⠀⠀⠀⠀⠘⠦⣬⠿⠶⣶⢶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣏⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⢻⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠚⢶⣤⢤⡒⢦⣠⢤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠓⠓⠾⠛⠛⠈⠃⠸
⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⠖⠻⣗⣶⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢿⠁⠰⣆⡀⠈⡉⠀⢹⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠉⠉⠀⠀⢳⡬⠛⠉⠠⠘⣧⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⢠⢦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⡖⢤⡀⢀⣄⡈⠀⢀⠉⣏⠁⠀⠀⠰⣒⡋⡷⠖⠓⠚⣇⣩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡛⣅⠀⣸⠎⠀⣸⡤⠚⠛⣂⣰⣧⡀⣤⡀⣴⠉⠉⠁⠀⠀⠀⠈⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⢦⣤⢀⠄⠛⠀⢀⣴⣧⠎⠀⠀⡱⠙⣯⠀⢀⡤⠜⡇⠀⡼⡂⠀⢬⠶⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠟⠣⢵⡖⠚⠋⠉⠛⠀⠀⠚⠊⡿⠁⣠⣄⡈⠙⠁⠀⠓⠚⠃⢸⡟⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠸⣅⠌⣱⡼⠀⡰⣩⠵⠆⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡤⢼⣢⠉⡼⡳⠦⣄⠀⢠⡄⠀⠀⠀⠘⠷⣍⣄⠄⢙⠁⣠⣰⠻⢥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⡏⠀⢊⡁⠙⠀⣀⠀⡑⣷⠎⠧⣀⡀⠀⠀⣴⡫⡸⡋⠉⠉⠉⠸⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠋⠁⣀⡜⢹⠀⢰⠙⢦⡄⠈⡺⣯⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡏⠀⠀⠉⠑⠋⠀⠀⠉⠁⡄⠠⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢈⡽⠀⠾⣁⢒⠄⠀⡔⢒⡦⠀⠀⣤⠿⡲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⣤⢠⡈⠚⠀⠀⠷⠁⠀⠃⠀⣿⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠚⣦⣄⠀⣊⣵⢶⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢣⡇⠉⠉⠉⡝⡤⠽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⣀⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢠⠄⠀⠀⠀⠈⠉⠓⠒⠤⣀
⠀⠀⠀⡔⠁⠂⡀⠀⠀⠀⣀⡀⠀⠁⠀⡀⠁⠀⠘⠘⠀⢀⡀⠀⢠⢲⣲⢦⣤⡄⠉⠳⢄⡀
⠀⠀⢸⠁⡀⠀⠀⢠⢎⣯⣽⣽⣽⡗⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢟⡿⢺⣵⣻⡄⠀⠀⠙⢦⡀
⠀⠀⡇⠀⠀⠀⠀⠈⠺⠿⠇⠿⠿⠚⠁⠀⠄⠀⠀⠀⠀⠠⡔⢠⠀⠀⢑⠫⠿⠽⠎⠀⠀⠀⠀⠑⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠀⠀⣉⠌⠦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⢇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠄⠠⠀⣃⠤⠒⠒⠒⠤⣀⠀⠀⠀⠀⠈⢦
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡈⠀⠘⠀⡜⠁⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠱⡄⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠄⠘⣉⢸⠀⠀⠀⠀⠀⢀⣤⣄⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⢦⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣨⠂⠄⠀⢸⡀⠀⠀⠀⠀⠈⠛⠋⢁⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⢄⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣍⠁⠒⠀⠀⠳⡀⠀⠀⠀⠀⢀⣀⠞⠀⠀⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠷⣞⡆⠀⠈⠀⠀⢠⡚⣯⣷⢿⡿⠐⠀⠁⠀⠀⠈⠑⠒⠤⠒⠊⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⣗⢿⣻⡮⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠑⠒⠒⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⣿⣿⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠈⠉⠈⢉⣉⢹⣾⠁⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⣿⡿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⡶⢸⡟⢸⡟⠀⠀⠀⠀⣿⠉⠉⣿⠀⣀⡀⠀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠇⠘⠇⠸⠇⠸⠇⡀⠀⠀⠀⠿⠿⠿⠿⠼⠿⠿⠦⠿⠿
⠀⠀⠀⠿⠿⠟⠛⠃⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⣼⡫⠋⠁⣼⣿⣿⠋⢉⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣹⠟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⣿
⠀⠀⠀⠀⣸⣷⣶⣶⣶⣿⣿⣇⣀⣾⣿⡏⠀⠀⠀⠀⢠⣮⣴⣶⣶⣬⣳⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠋⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢯⣈⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣟⣀⣀⣗⣀
⠀⠀⠀⠘⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠠⣤⡄⠀⠀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⣀⣀⣀⣀⣠⢀⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⣐⢒⢒⢂⢂⢂⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣶⣿⣶⡆
⠀⠀⣰⢂⢂⢆⢆⢆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠟⠛⠻⠃
⠀⠀⠉⠈⠈⠈⠈⠈⠉⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⠿⠿⠿⠿⠿⠿⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⠉⢁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢻⣷
⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⢸⣿
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠘⣿⣆⠀⣀⣠⣤⣤⣤⣼⣿⣤⣄⣀⡀⠀⠀⣼⡿⠁⠀⠀⠀⠀⣿⣇
⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⣷⣾⣿⠁⠀⠀⠀⠀⠀⠈⠉
⠀⢠⣿⣏⡀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣾⡟⠛⠿⣷⣦⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⢻⣷⣀⣀⣤⣤⣶⣿⣿⡄
⢸⣿⠁⠀⠀⠀⠉⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠋⠉⠁⠀⠘⠋
⣼⡏⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⡇⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⣄
⣿⣇⠀⠀⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⣀⣠⣤⣾⠟⠋⠉
⣿⡿⠿⠿⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣶⣦⡀
⢹⣷⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢘⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠘⣿⡄⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠹⣿⣄⣀⣀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⢻⣷⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢻⣇⠀⢀⣴⡿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠈⢿⣶⡿⠋⠀⠀⠀⠈⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⢿⣶⣶⣶⣶⣾⠿⠿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⢀⣈⣻⣷⣦⣤⣶⡾⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⠛⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⡐⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⢀⡤⣄
⠀⠀⣠⠄⣠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣀⡀⠀⠀⢳⠀⡏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⣸⠛⡇⢠⢼⣀⡼
⠀⠘⣇⣀⢿⣀⡿⠀⡄⠈⠁⠀⠀⠄⡀⠐⠞⡁⠀⡀⠈⠙⠲⡄⠈⡇⠁⠀⠀⣠⡴⢶⠖⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣠⠞⠂⡀⠀⠠⠀⠠⠀⠀⠘⣄⠀⢀⡤⠊⠁⢀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠐⠀⠀⠀⢠⠀⠀⠀⠈⠁⠋⠀⠀⠙⠄⠀⠀⠁⠘⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠒⠄⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠒⠒⡶⠀⠀⠀⠀⠑⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠑⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⠀⣟⡁⡆⢰⣧⡞⣋⠀⡾⡆⢸⣻⠦⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠁⠀⠀⠀⠘⠃⠓⠞⠉⠓⠞⠘⠋⠛⠘⠘⠂⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠂⢠⠠⠄⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⡠⠈⠀⠀⠀⠀⠀⠈⢳⡀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⢠⡀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⡁⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⡆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⢀⡁⠁⠉⡈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠑⡈⠋⠈⣑⠋⠙⠊⠚⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠃⠘⠃⠃⠓⠃⠛⠚⠓⠋⠃⠒⠁⠚⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡿⢽⣿⣿⣿⠿⡿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⣚⣉⣉⣀⣀⣀⣀⣀⠈⠉⠙⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣭⠴⠒⠋⠉⠉⠁⠀⡀⠀⠀⠀⠉⠉⠉⠙⠓⠲⠦⢤⣈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⡀⠁⠂⠐⠂⠀⠀⡀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠙⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡰⢣⠏⠀⠀⠈⢀⡀⠀⠀⢀⡠⠖⠋⠁⣀⣀⡀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⢧⢹⡄
⠀⠀⠀⠀⠀⠀⡰⣣⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡴⠋⠁⠀⠉⠳⡄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣧⢳
⠀⠀⠀⠀⠀⣰⢱⠃⠀⠀⠁⠀⢀⠈⢀⡞⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⢈⡀⠀⠐⠸⡎⣇
⠀⠀⠀⠀⣰⢣⠇⠀⠀⠤⠀⠀⠀⠀⣸⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠉⣁⠀⠄⣧⠸⡄
⠀⠀⠀⢰⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠓⠶⠶⠊⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢰⠈⡄⠐⠁⢸⡀⣧
⠀⠀⢀⡏⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀⠀⠆⠠⠘⡇⢸
⠀⠀⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠋⠀⢠⠀⠄⠈⡇⢸
⠀⠀⢸⠀⣇⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠈⠁⡌⢁⠈⠀⡇⢸
⠀⠀⢸⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢄⣀⣀⣀⡤⠴⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⢸⡄⢸⡀⠀⠀⠈⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼
⠀⠀⠀⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠁⢐⠛⠂⠣⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠁⡞⢀⡇
⠀⠀⠀⠘⡄⢳⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠠⠬⠀⡀⠀⢀⠟⣂⠀⠈⠢⠄⠀⠀⠁⠀⠀⢀⢀⡀⠀⠀⠀⠀⡀⣸⠁⢸⠁
⠀⠀⠀⠀⠹⡌⢧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠛⠁⠀⠋⠀⠁⠘⠀⠢⠀⠀⠀⠀⠀⠐⠀⠂⠀⠈⠆⠀⠀⢠⠃⢀⠇
⠀⠀⠀⠀⠀⠹⡌⢧⠀⠀⠀⠀⠈⠀⡀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⣰⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠘⢦⠳⣄⠀⠀⠀⠐⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠤⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⢀⠄⠀⡰⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠔⠁⢀⡞⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⣄⠀⠈⠀⠁⠀⠀⠀⠐⢄⠢⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠏⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠳⢤⡀⠀⠀⠀⠀⠀⠀⠲⡀⢂⡀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⢀⡠⠞⠁⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⠳⢤⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣈⠙⠒⠶⠤⣤⣀⣀⣀⡀⢀⣀⣀⣠⠤⠶⢚⣉⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠭⠭⠭⠴⠶⠒⠒⠉⠁

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⣿⣿⣿⡶
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⣿⠟⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡆
⣯⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡋⠙⡯⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⡎⠉
⣿⡟⠿⢗⣤⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇
⣿⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣡⣿⣡⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⡇⣾⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣇⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡤⠤⠤⠄
⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢿⣿⡹⠋⠟⢙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⣠⣴⣾⣶⣶⣄
⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⢀⣿⣷⣶⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧
⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⢀⣀⣤⣶⣯⣭⣿⣶⡀⠘⣫⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⣟⡘⠛⣤⣹⣿⣴⠚⢯⡉⠉⠉⢋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠄⠀⠙⠀⠋⠁⢙⣿⣷⡿⠀⠀⠉⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⡀⠀⠓⠀⠀⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⡀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣤⣿⡉⢂⣴⣀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠂⢠⣾⡿⠋⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢻⣇⡈⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠓⣀⠀⡖⠀⠌⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣁⠀⢠⣭⣃⣿⣀⡀⠀⡂⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡿⣝⠀⠉⠻⡀⡄⣻⠍⡫⡄⠀⠚⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣧⣬⡙⠂⠛⣻⣻⠶⣍⠴⣿⢀⠚⠣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢭⡀⣾⣫⠹⣅⢪⡍⠋⠆⠴⠂⠤⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠤⠐⢡⣲⠛⡏⣨⡹⠟⣬⡍⠀⠂⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠖⠙⠻⠄⠘⠻⢃⡐⠟⠁⠈⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⡀⠐⠀⠀⢈⠵⠐⣃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⣤⣤⣀⣀⣠⣠⣤⠤⠴⠖⠒⠉
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠠⠀⠂⡄⢀⠀⢀⠔⠒⠒⠤⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⣠⠠⣄⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠒⠂⡀
⠀⠈⠀⠀⠀⠈⠤⠄⠘⠂⠄⠤⣀⠀⠀⠈⡀⣀⣀⠀⡸⠀⠀⣌⠀⠀⠀⢃⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⢀⠇⠱⠄
⠠⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠦⠠⠄⡃⠀⠀⠀⣀⠀⠀⢠⠂⠀⠀⠀⠐⢶
⢀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⠈⠁⠉⠁⠂⠀⠐⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠈⠀⢈⠄⡀⡐⠀⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠨⠠⠀⠀⠀⠄⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠈⠢⡀⠈⠓⢦⠀⠀⠀⡀
⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⠀⠀⠀⠠⠀⢀⡴⠀⠇⠀⠰⠀⠁⠀⠀⠀⠂⠈
⠈⠤⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠤⠐⠁⢠⠞⠀⠀⠈⢀⡗⠀⠀⠀⠀⠀⢀⢠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠉⡁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⡶⣶⠶⠶⣾⣿⡟⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⡀⡀⠁⠠⠀⠀⣾⢹⢡⠀⠈⠰⠎⠦⢰⡶⠎⣻⣮⣼⠟⢿⡆
⠀⠀⢠⠀⠀⠀⠀⡀⠀⠘⣀⠸⠀⠠⠀⢸⣿⣀⣼⠦⣶⠗⢾⡒⢺⠛⣻⡏⠍⡈⠆⣼⡇⠀⠀⠈⠈⠀⠂⠐⠀⠀⠄
⠀⡀⠤⢄⠀⠀⠀⠀⠀⠄⢀⡀⠐⠂⠀⠈⢯⠀⡹⠀⡌⠘⠿⢿⡜⣇⠰⠶⠀⡓⢀⣿⡏⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀
⢐⠀⠀⠀⢱⠀⢀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠓⠧⠶⠿⠾⠷⠾⠿⠿⠶⠶⠿⠿⠟⠋⠀⡀⠀⢢⠀⠀⠐
⠈⠢⠄⠤⠃⠀⠀⠀⡀⠁⡐⠒⡄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡐⣰⠈⠾⠄
⠀⠀⡄⢠⠊⠉⠁⠢⠀⠤⠈⠂⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠄⢠⠂
⠈⠒⠁⢂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠑⠀⠀⠀⠘⠠⠜⠀⠀⡠⣤⣠⡔⢶⢰⡖⠢
⠀⠂⡀⠀⠑⠒⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠝⠛⠀⠁
⠀⠠⠠⠔⢀⠀⠀⠆⡡⡀⡂⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠢
⢄⠁⠊⠁⠈⠀⠈⠀⠀⠈⡢⠅⠀⢀⡤⠒⠉⢑⡄⠀⠀⡀⠒⢠⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⢈⠀⠀⠀⠀⠄⠀⠀⡀
⢂⡀⣀⠀⠀⠀⠀⠀⢀⠈⠐⠀⡰⢃⠤⠒⠂⠈⡀⠠⠂⠀⣀⠜⠀⠀⠈⠀⠀⠀⠀⠂⢠⠀⠔⠀⠀⠀⠈⠀⠄⠀⠂
⠀⠂⠂⡁⡉⠂⠊⠀⠁⠀⠁⠀⠈⠁⠀⠀⠀⠈⠒⠒⠂⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠀⠐⠀⠀⠀⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⢀⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⣄⣁⠘⢃⣭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⠛⣿⡧⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⠻⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣄⢸⡇⠀⠀⠁⠦⣀
⠀⠀⠀⠀⢀⡴⠊⠁⠀⣇⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠙⣿⠟⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⠛⢁⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⣿⣴⣦⢹⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⢸⣿⠀⠘⠻⠊⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⣿⠻⣥⡘⣿⡇⠀⠀⠀⠀⠀⢠⣶⣶⣶⠲⣾⣿⣭⣭⢿⣤⣤⣴⣿⣀⡔⣁⣠⣿⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⣷⣄⠈⠳⣿⣧⠀⠀⠀⠀⠀⠐⣿⣿⣿⣀⣿⡗⠒⠒⠲⠿⠿⢿⣿⠿⢻⢟⠓⣿⡄⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢨⡇⠘⡀⠀⠀⠀⠀⣿⡿⣦⡀⠈⠻⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠙⠒⠊⠁⠀⢀⣴⢇⡰⠯⠂⠀⢹⡇⠀⠀⠀⠀⢘⣠⠏
⠀⠀⠀⠈⢳⣬⡇⠀⠀⠀⠀⣿⣇⠯⣉⣦⣄⠈⢦⣀⣤⡴⢶⡶⣖⠒⢲⢶⡶⢶⣶⠤⡶⠟⣧⠞⢁⡀⢀⣴⣿⣧⠤⠀⠀⢒⡯⠉
⠀⠀⠀⠀⠀⠹⠏⢙⣒⣚⢺⣿⣿⣶⣄⡀⠻⣧⣌⠉⠉⠙⡇⢸⠗⠒⠒⢟⠚⡏⢀⣠⡤⠖⣿⣀⣽⠛⠛⠛⠋⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡷⡶⠶⠇⣸⣤⣤⣤⡶⢤⠟⠚⣙⣷⣶⣿⣿⣿⣿⠿⠿⣶⣦⣄⣤⡤⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣧⡹⢦⡄⠲⠦⠍⠉⢁⣠⣴⣾⣿⣿⠟⠛⠉⠀⣀⡤⢶⣛⣭⣵⠶⠶⠾⠷⠶⣦
⠀⠀⡀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣿⢹⣿⣝⠳⠦⣀⣠⣴⣾⣿⣿⠿⠛⠉⠀⠀⣀⢔⣪⣵⣾⣿⣿⣤⣤⣄⡀
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⠴⣚⡽⣾⡙⠻⣿⣿⣿⣿⣿⡿⣿⡿⠋⠁⠀⠀⠀⡠⢊⣴⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠒⠀⣀⡤⢴⡾⢋⣵⡞⠉⢰⣿⣿⣷⣤⣭⡽⢟⣩⠞⠋⢀⣀⣀⣀⡠⢊⣴⣿⠏⡠⠒⠁⣀⠔
⠀⠀⢀⣤⣴⣚⣉⣀⡔⢁⠞⡵⠁⢠⠞⠉⠀⣠⣿⣿⢿⣶⣛⡛⢩⡍⠉⠩⠡⡼⢡⣾⣿⠟⢉⡠⠔⠊⠀⣡⣀
⣠⣴⠟⠁⢀⣡⣤⣯⣴⠿⠾⠶⢶⠿⠚⠛⢋⣿⠟⡵⠯⠶⠒⠒⠐⠊⠉⠀⣩⠁⣾⣿⠏⡲⠋⣡⡴⢶⣿⣿⣿⣿⣷⣦⣤⣀⠀⠄
⣼⣏⣠⣞⣋⣡⠏⣴⣿⠀⠀⢠⠇⠀⠀⢀⠞⣡⠾⢶⣤⣒⣒⣆⣈⣉⣉⡉⡍⢸⣿⠟⡸⠃⠈⣤⣤⡜⠲⢬⣝⡛⠯⣽⡿⠁⠀⠐
⠏⣽⠋⠈⠁⡟⢰⣿⣿⠀⢀⡟⠀⠀⡠⢋⠜⠉⡏⠉⠀⡝⠀⠀⡈⠀⠀⡍⣧⣸⣃⣈⣀⣠⣾⣛⣛⠁⠀⠠⣤⣬⣍⡊⠀⠀⠀⡠
⣤⣯⣤⣤⣴⠃⣿⣿⣿⠀⣸⠇⢀⡜⣡⣮⣀⣸⣁⣤⣴⣥⣤⠖⢿⣿⣿⢹⣩⠟⠿⠃⠀⠀⠛⠹⠋⠉⠐⠢⢤⣀⠀⠈⠀⢀⠔⡠⠊
⠀⣿⣴⣿⣿⣀⣿⣿⣿⣷⣿⣠⠏⣰⣯⣴⣤⡭⢴⢻⠏⡴⠁⢻⣿⣿⣇⣾⠁⢾⠇⠀⠲⢶⣶⣦⣤⣄⣀⡀⠀⠀⢡⠀⡠⢈⠄
⣾⠛⠛⣻⡍⢉⣭⣿⠯⢭⡽⠿⠿⣧⣿⡉⠁⠀⣼⢸⢠⠃⢶⣿⣿⣿⡙⡇⣤⡄⢄⣀⡀⠊⠠⠊⣹⠿⣭⡙⠛⠋⢁⠊⠔⠁
⠋⣰⠻⣿⣯⣭⣥⣼⠇⣾⡇⠀⢸⣿⢻⠇⠀⢠⠇⠸⣼⣄⣴⣿⡿⣻⣱⠃⠉⠁⠀⢈⡹⠻⡶⣄⡁⠀⠀⠙⢦⡄⡠⠊
⢀⣽⡄⠈⠙⠛⠛⠁⠀⢿⡇⠀⠀⣿⡜⡇⠀⣸⠀⠀⠹⡝⠛⠋⠈⠁⢿⡆⠺⢶⣦⣤⣀⠈⠠⠈⠙⠷⣄⠀⠀⠙⡄
⣾⠻⣿⣄⢻⣄⠀⣿⣦⡀⣷⠀⠀⢿⢿⡹⡄⢿⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⠰⡩⠓⢭⡛⠶⣤⡀⠀⠘⢿⠶⠄⠂⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⠀⠀⠃⠀⠈⠀⢸⡇⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠀⠀⠀⠀⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢘⣇⠤⠒⠂⠉⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⢀⠀⢀⠀⠀⠈⠉⠒⠢⢄⣈⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠠⠔⢹⡇⠀⠀⠀⠀⣀⠠⠄⠒⠀⠁⠂⠓⠠⠄⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⢳⠠⡀
⠀⠀⠀⠀⠀⢀⡴⠚⢈⠀⠘⠇⠀⣴⠔⠉⠀⠀⠀⠀⢀⣀⠀⣄⠠⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠳⣄
⠀⠀⠀⠀⣠⠊⡔⠊⠉⠉⠉⠈⠉⠉⠁⢲⠴⠇⠉⠁⠀⠀⠈⠈⠈⠀⠀⠀⠀⠉⠀⠀⠀⢀⠔⠊⠉⠀⠉⠐⢢⡌⢣⡀
⠀⠀⠀⡰⠁⠀⢎⠑⠒⠒⠒⠒⠒⠒⠚⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡀
⠀⠀⢀⠇⠀⠀⢯⣉⠉⠒⠒⠒⠒⠉⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢣
⠀⠀⢸⠀⠀⠀⡣⢄⣉⣉⣉⣉⣉⣉⡠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸
⠀⠀⢸⠀⠀⠀⠑⠤⠤⠀⢀⣀⡠⠤⠤⠚⠂⠤⣤⡀⡀⠀⢠⡆⠐⢰⠀⠀⢀⠀⠀⠰⠂⠣⢄⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⡇⠁⠢⢄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠉⠁⡀⠈⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠒⠰⠦⠀⢂⡀⢆⠀⠀⢠⠐⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠒⠠⠄⣀⣸⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⢀⣄⢀⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠊⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⣴⣶⣿⣿⣿⣧⣄⠐⠐⠂⠐⠤⠄⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⣀⢼⡇⠀⠀⡜⣿⣟⣼⡽⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣠⣤⣴⣿⣿⠂⠀⣤⣴⢤
⠀⠀⠀⠀⠀⠀⠈⠦⣌⠁⠐⣶⣷⣾⣯⣗⣚⣟⣿⣿⣿⡿⠋⠶⣿⣿⣿⣿⣟⣿⡿⠀⣶⣬⣭⢄
⠀⠀⠀⠀⠀⠀⠱⡤⢀⡈⠀⠶⠙⣿⣿⡿⠿⠿⠛⢉⡉⠀⠀⠈⠻⠷⣶⣿⡿⡿⠋⠛⣋⣡⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣠⠟⠋⡀⠠⠤⣄⣀⣀⣀⢀⠈⠉⠉⠀⠀⠀⠀⠀⢀⠀⣰⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣑⠤⠁⠂⠀⠉⠉⠉⠁⠀⠀⠉⠉⠀⠘⢀⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢁⣀⡀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⢀⠀⡀⢀⡀⡀⠀⢀⠀⣀⠀⠀⢀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠌⠸⠃⠐⠑⠈⠃⠘⠀⠢⠁⠀⠀⠃⠤⠀⠣⠀⠇⠘⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢋⡉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⡀⢀⢀⠀⡀⢀⡀⡀⠀⣀⢀⣀⢀⠀⣀⠀⢀⡀⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠹⠿⠻⠼⠻⠧⠼⠳⠼⠏⠹⠹⠤⠃⠧⠸⠿⠤⠀⠧⠸⠧⠾⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⠀⠉⣡⣀⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠐⠀⠀⠀⠱⠀⠀⠐⠂⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠿⠶⠶⢴⣦⣦⡤⠶⠿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⠒⢀⡀⠡⠒⢀⣦⣄⣀⣃⣰⣆⣾⣿⠈⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠢⠰⢆⠀⠛⠿⠿⠿⠿⠿⡿⠟⢿⢿⠇⣸⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⣄⣀⣀⣀⣐⣀⣀⣂⣈⣴⢏⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠉⠉⠁⠉⠁