⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀⡲⢷⠷⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⢠⣣⡓⡉⣧⠎⠋⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣻⣷⡦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣔⠦⣤⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⣙⣯⣡⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⢹⣧⣢⠀⠀⠀⠀⡇⠀⠀⠀⣤⠂⡟⡟⣈⡳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠸⣻⡘⠀⡀⡀⣜⣇⡄⠀⠀⣧⡧⣿⣿⣿⣻⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠂⠐⢓⣶⢾⡿⣵⣖⡓⣒⢈⠛⣁⣞⣭⣏⣿⣿⣿⣦⣿⡕⣘⣥⡀⢠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠂⠑⠋⠉⣳⣭⣿⡋⡹⠉⠠⠷⣿⣿⣶⣲⠓⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠟⣞⡌⠗⠀⢺⣞⢯⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣋⣂⣀⠀⠰⢷⠿⠁⠀⠀⣤⢺⢋⣁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠛⠉⠀⣔⠛⣶⡟⡲⠀⠀⠀⢈⠸⣿⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠂⠀⠀⠀⡨⢭⢿⠋⡱⣀⡀⠀⢸⠀⡿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠉⠀⢳⣧⡛⠉⠉⠳⡘⠀⡽⠈⡄⠀⡀⠀⢀⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠜⢼⡤⠀⣠⠰⠳⠠⣸⢀⠃⠀⠀⠀⢏⣗⡑⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠀⠀⢸⠔⢄⡀⠀⠀⡇⡻⠋⠀⠀⠉⠉⢹⣋⠇⢀⢀⠀⠀⠀
⠐⠂⠒⠒⠒⠒⠒⠛⠓⢫⠛⢻⡱⠛⠫⣺⢽⣧⡧⢾⠈⡈⠈⠉⢻⢸⢵⣈⠺⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡄⠀⠀⠸⣲⡌⢿⣾⡰⡃⢀⡤⠼⣽⣮⢣⠅⠤⠄⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠥⡍⣿⠟⠱⣒⣬⣤⡃⠼⣥⡤⠄⠊⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠁⠀⠚⠀⠀⠈⢻⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠤⣤⣀⠀⠀⠠⡀⠀⣀⣹⣦⠀⠀⠀⠀⣠⣶⣉⡀⠀⠀⠀⢀⣀⣠⡤⠤⠄⠀
⣀⣀⣤⣿⣿⣶⣄⡈⢳⣿⣿⣿⣷⣦⣢⣴⣿⣿⣿⣶⢋⣠⣴⣿⣿⣧⣄⣀⣀⡤
⢈⡙⠛⠏⣀⠈⢙⣿⣾⣿⣿⡿⣄⠹⢹⢀⣾⣿⣿⣿⣾⡿⠙⠀⢈⢛⣟⡉⠀⠀
⠀⠈⢩⣻⡖⠒⠦⣥⣎⣩⣿⡿⣮⣆⢀⣼⣿⣿⣿⣓⣨⡤⠒⠲⣿⣉⠉⠀⠀⠀
⠀⠀⠀⠀⠉⠒⠠⠀⢻⢉⠈⠉⠑⠻⡿⠓⠋⠁⠈⣹⠁⠀⠐⠊⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢈⣁⠆⡀⠀⠀⠀⠀⣄⠀⠀
⠀⠀⠀⢳⢹⠁⠀⠱⡀⠀⠀⢈⠆⠀
⠀⠀⠀⠠⢾⣆⠀⠞⠁⠀⣠⠮⡤⡀
⠀⠀⠀⠀⠐⠹⢦⡀⠀⠰⠁⡀⢰⡁
⠀⠀⠀⢔⠞⠛⠶⣟⣦⣀⠀⠀⠛⠀
⠀⠀⠀⠌⣤⡴⠀⠀⠀⠉⠳⡰⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢄⠙⢀⢷⢁
⠀⠀⠀⠀⣀⣄⡀⠀⠑⠀⠀⠊⣸⢰
⠀⠀⠀⡔⠁⠠⠗⠀⠀⠀⠀⠀⡭⠄
⠀⠀⠀⢣⠀⠀⠲⣄⣀⣀⢤⡾⠁⠀
⠀⠀⠀⠀⠑⠢⠀⠀⢠⣴⣟⠍⠀⠀
⠐⠄⠄⠤⢐⡢⣀⡼⡾⠋⠀⠀⠀⠀
⠀⠀⢀⠔⣡⣞⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠔⢡⠞⠁⡎⠀⠔⠒⡄⠀⠀⠀⠀
⡎⢰⠃⠀⠀⡗⠄⠁⣀⠆⠀⠀⠀⠀
⠀⠁⢀⠃⠀⠣⡀⠀⠀⠀⠀⣥⠀⠱
⠀⠀⡂⢧⡀⠐⢌⣀⠀⠀⢀⡠⢠⢀
⠀⠀⠂⠀⠁⠀⠀⢐⠩⣏⣋⡸⠗⠊
⠀⠀⠀⠀⠀⠈⠉⡆⢡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⠤⠔⠁⣸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣒⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠒⠒⠒⠐⠢⢤⣀⠐⢄⣀⢰⡀⠿⢀⡆⣀⡠⠂⣀⡤⠴⠂⠐⠒⠒⠁
⠀⠀⠉⠻⠭⣙⡠⢼⢷⣤⠯⠼⣵⠿⣮⠧⠽⣤⡾⡧⢄⣋⠭⠟⠉⠀⠀
⠀⠀⠀⠀⠀⠠⠤⣾⢻⢫⠚⢜⠍⣿⠩⡣⠓⡝⡟⣷⠤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠉⢇⠀⠀⠿⠀⠀⡸⠉⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⢄⠀⡠⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀