⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣶⡤⣤⣤⣀⡀⠀⠀⠀⠈⢣⡀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣀⣤⠤⢴⣶⣤⠀
⠈⠻⣿⣷⣶⠦⣍⡙⠓⠦⣄⠀⠀⢣⠀⢀⠎⠀⢀⡠⠖⠛⢉⡤⠶⣶⣿⣿⠟⠀
⠀⠀⠈⠻⣿⣦⣀⠈⠀⣁⠠⣹⡦⡀⢃⡎⣠⣔⡽⠐⡀⠀⢀⣠⣾⣿⠋⠁⠀⠀
⠀⠀⠀⠀⠘⣿⣯⡉⠡⠀⠩⣞⣿⣿⣾⣿⣿⣟⡮⠉⠤⠌⣉⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣄⡀⣀⣀⣤⣬⣿⣿⢿⣿⣥⣤⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠋⡹⡟⣿⢻⢸⣿⢗⠌⠛⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣀⡠⠐⠀⠌⢸⢸⢸⠎⠀⠀⠢⢄⣠⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢻⣿⣀⣀⣼⠀⣼⠈⢸⣇⠀⣦⣀⣨⣿⡛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⡿⠀⠀⢿⣿⠿⢿⣿⡿⠃

⣾⠛⠛⠲⣤⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢻⡆
⣿ ⠀⠀⠀ ⠙⢦⡀⠀⠀⣠⠞⠁ ⠀⠀⠀⢸⡇⠀⁺⊹
⢿⡄ ⠀⠀⠀⠀ ⠹⣄⡼⠁ ⠀⠀⠀⠀⠀⣼⠇
⠘⢷⣄⣀⡀⠀⠀⠀⠙⠁⠀⠀⠀⣀⣀⣴⠟
ㅤ⠀⣼⠛⠉⠉ ⠀⠀⠀⠀ ⠈⠉⠙⢻⡄
ㅤ⠘⣷ ⠀⠀⠀⠀ ⡞⣦⠀⠀⠀⠀⣰⡟
⊹⠀⠈⠻⣦⣤⡶⠋⠀⠈⠳⣦⣤⡾⠋ ⠀

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⢿⣄⡀⣀⢻⣿⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠀⡭⠛⠻⢆⠹⡆⢸⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⢰⣶⠦⣄⢦⠃⠜⠊⣀⣠⣥⣤⣤⣤⣄⣀⠀⠀
⠀⠀⢀⣠⣤⣽⣿⡢⣘⣿⣾⡴⠬⠤⢄⣨⠏⠁⠀⠈⠉⣻⠆
⢀⡴⠿⣿⣭⠤⠔⡺⣿⣿⡯⢍⠙⣶⠀⢻⣦⣀⣀⣤⠞⠁⠀
⣏⣀⣠⣟⠡⠞⠊⠰⠋⠏⡎⢿⠿⣛⣡⣃⡠⠝⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⢸⠊⣇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠟⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⢿⣿⣿⡿⢦⡐⡀⠀⢀⢂⡴⢿⣿⣿⡿
⠈⣿⣮⡓⢄⢙⢦⣄⡲⡋⡠⢚⣿⣿⠁
⠀⠻⣷⣀⣈⣡⣿⣿⣿⣌⣁⣀⣾⠟⠀
⠀⢀⣿⢯⣝⡥⢚⣿⡓⣬⣫⡹⣿⡀⠀
⠀⠀⢷⣧⡠⡈⡌⠛⢡⢁⢎⣬⡾⠀⠀
⠀⠀⠀⠉⠛⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠄⣺⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⢚⠄⠊⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣔⣤⢲⣋⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⡔⠻⣿⢡⠼⢧⠀⠀⠀⠀
⣾⣷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠋⠀⣙⣀⣰⣽⡀⠀⠀⠀
⠙⠻⣤⠐⢺⡗⠤⡀⠀⠀⠀⠀⠇⢀⢃⣴⡿⢋⠤⠾⠯⢽⣄⠀⠀
⠀⠀⠀⠙⠢⢄⠀⠐⠴⣄⠀⠀⣰⣻⡿⢛⡉⠉⠀⠀⠐⠀⢿⡀⠀
⠀⠀⠀⠀⠀⠀⠙⢴⠁⣠⣵⢶⣿⣾⢭⡭⠤⣀⠀⠄⢀⠁⠀⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠈⠫⠻⣷⣝⡢⢄⠀⠀⠀⠈⠱⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⠻⢿⣶⣤⣄⣀⣀⣴⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⡄⠹⣦⠈⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠽⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀
⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⠀
⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀