⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠿⠇⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀ ⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣾⡿⠟⢿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠁⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀ ⠀ ⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⣿⣧⣄⡀⠀⠀ ⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣷⣄ ⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢹⣿⡄⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠻⣿⣦⣀⠀⠀⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⣀⣤⣾⠁ ⠀⠀⠈⠛⠿⣿⣷⣶⣾⡿⠿⠻⢿⣿⣶⣾⣿⠿⠛⠉⠀𓂸

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠿⠇⠉⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀ ⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣾⡿⠟⢿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠁⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀ ⠀ ⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⣿⣧⣄⡀⠀⠀ ⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣷⣄ ⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢹⣿⡄⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠻⣿⣦⣀⠀⠀⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⣀⣤⣾⠁ ⠀⠀⠈⠛⠿⣿⣷⣶⣾⡿⠿⠻⢿⣿⣶⣾⣿⠿⠛⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠓⠲⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢹⠀⠈⡢⢆⡈⠐⡂⣅⢦⠷⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠋⠙⠛⠋⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⢬⠔⠃⡰⠠⠀⠐⡀⠒⠀⡀⡐⣢⣵⠾⠻⠛⠉⠈⠁⠈⠑⠩⠛⡷⣾⣿⣶⣍⣤⣱⣎⣂⣌⢒⣬⣣⣖⡾⣕⢣⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠇⡠⢀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⣀⣣⣿⣻⡼⢧⣇⡿⣼⡘⣀⠇⡀⠛⠀⡜⠃⡀⡜⠀⢣⡄⠘⢠⡜⡃⠧⣜⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢂⠜⠱⠀⠀⠀⢀⠠⠈⠀⠀⠀⠂⠁⠀⠀⡦⣝⣿⣿⣿⣾⢀⠀⢀⠡⠄⠂⣁⠂⢁⡄⠐⣈⠱⠎⡁⢌⠘⢡⠲⣍⡗⢫⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠙⡀⠀⡀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⣯⣿⢴⢈⠀⠀⠄⠀⡈⠁⠠⠌⠀⠰⡈⠐⠡⠐⠠⠘⠤⡐⠔⡋⠻⣿⠀ ⠀⠀⠀⠀⠀⠑⠏⠛⢿⠿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠂⡷⠻⠯⠀⠀⠀⡀⠀⠀⠀⠉⠁⢉⡈⠄⡀⠡⡀⢁⡁⠐⣀⡝⡮⢟⡰⠀ ⠀⠀⠀⠁⠏⠾⣫⣤⣹⣆⣉⡴⣜⣯⡭⣰⣾⣇⠿⣿⡿⣿⣿⠿⡛⠙⠙⢀⠐⠂⡉⣟⣿⣿⣿⠻⠉⠠⠀⠤⠤⠤⠤⠤⠤⠤⠴⠒⠂⡒⠴⠲⠵⣁⠓⡩⠀⠀⠀ ⠀⠀⠏⣪⣹⢦⠐⣨⠓⢆⡉⡒⠇⢖⡑⡍⣷⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣯⣿⣽⣾⣟⣯⣷⣟⣾⣿⣿⣿⢻⠼⠯⠿⠿⠿⠻⠛⠛⠚⠛⠓⠿⡠⣵⠺⣌⠫⠈⠀ ⠀⡜⡿⢤⡘⠧⣊⡝⠡⢒⡙⠡⣳⢧⣋⣛⣿⣿⣿⣿⣿⣿⣿⣝⡾⣽⣾⢧⣼⡽⣵⢮⣯⡼⣼⣷⢷⣶⣟⣷⣍⣿⣿⣿⣿⣿⣧⣸⣟⣾⡤⣻⠳⡡⢋⣾⢘⢿⠀ ⠇⣬⠛⣡⡜⠎⢣⡨⢔⡮⣻⢰⠢⣩⠟⣿⣿⣽⡾⣿⣷⣿⣿⣿⠿⣏⡬⣱⠶⣊⡰⢖⢣⣤⡜⢣⡰⢞⢣⡿⣿⣿⣿⣿⣿⢣⣱⡏⣿⠄⣢⡗⢨⡞⣗⣧⠉⢃⢸ ⡇⣸⢸⡱⢉⣆⠿⢿⡏⢇⢶⡿⠿⣿⣿⡎⢸⣹⣆⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢇⡇⣿⢰⡏⢇⣾⡏⠈⡾⣿⠈⡿⢀ ⠀⢦⣌⠱⣆⡻⢠⡧⢸⡁⣆⡙⣧⢻⣿⣿⣽⠮⣍⠟⡿⣿⣿⣿⣿⣾⣶⣷⣿⣶⣷⣾⣿⣾⣿⣿⣿⣿⣿⡷⣾⣡⢓⡫⠃⢳⡿⣠⠋⢃⣛⠞⢢⠡⡋⠼⢿⣔⠀ ⠀⠀⡄⡓⢤⢆⠙⠸⠛⡉⠸⣁⡐⣦⣿⣯⣿⣿⣿⣿⣿⣾⣴⣡⢛⠿⣿⣿⣿⣿⣿⣿⠿⢯⠽⠾⠿⠦⣞⢠⣔⠫⠙⣏⣷⣲⢙⡘⢧⣯⢠⡔⣄⡣⢚⠉⣰⠀⠀ ⠀⠀⠀⠀⡀⡠⡄⢠⡒⢅⡠⡡⣄⡄⠊⣌⣦⣵⣿⣶⣔⡠⣄⢤⣯⡿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣜⢋⢿⢎⣧⡹⡛⣼⣤⢃⠏⢋⡷⣺⣶⠚⣤⣥⢈⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠋⡿⣿⣾⣿⣶⣿⣯⣿⣯⢎⠳⢟⣧⢴⣫⠟⢿⡴⢁⠞⣠⢉⣞⣶⡅⢊⢢⣠⠒⢐⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡯⣟⣯⢿⣶⣘⣷⡌⢾⣛⣵⣮⣵⣓⠿⢶⣠⡁⠖⠠⡆⠗⡼⣀⢃⠐⣈⠂⢪⢤⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢯⣼⢿⣮⠙⣽⡛⡅⢳⢚⣏⠡⠟⠾⣄⠀⠈⣮⢠⠋⡼⣠⢀⠂⣤⢃⡊⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣷⢯⢋⢏⡺⣤⠆⡤⢶⢎⣰⣁⠀⠰⠛⠞⣴⣠⢀⠆⠁⠚⡠⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⠙⣥⢲⣽⠒⠙⡏⠛⣷⠂⠒⠈⡄⠀⠀⠀⠁⠀⢠⠈⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡟⡨⣶⠉⠞⡱⣱⢉⡀⠁⠚⣀⠀⠋⠔⠀⠊⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣌⣠⡘⢀⡐⠊⠘⡤⣀⠂⠡⡈⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠤⡤⢤⠀⡄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀