⡀⠀⠀⠀⠀⠀⠀⣾⡳⣼⣆⠀⠀⢹⡄⠹⣷⣄⢠⠇⠻⣷⣶⢀⣸⣿⡾⡏⠀⠰⣿⣰⠏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡹⣟⡪⢟⣷⠦⠬⣿⣦⣌⡙⠿⡆⠻⡌⠿⣦⣿⣿⣿⣿⣦⣿⡿⠟⠚⠉⠀⠉⠳⣄⡀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣟⠛⠛⠙⠛⠉⠻⢶⣮⢿⣯⡙⢶⡌⠲⢤⡑⠀⠈⠛⠟⢿⣿⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠯⣙⠛⢉⣉⣙⣿⣿⡳⢶⣦⣝⢿⣆⠉⠻⣄⠈⢆⢵⡈⠀⠀⢰⡆⠀⣼⠓⠀⠀⠀ Nah, ⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠖⠉⠻⣟⡿⣿⣭⢽⣽⣶⣈⢛⣾⣿⣧⠀⠙⠓⠀⠑⢦⡀⠹⣧⢂⠀⣿⡇⢀⣿⠺⠇⠀ ⠀I'd⠀ ⠀⣿⠀⠀ ⠀⠀⠀⠀⠐⠈⠉⢛⣿⣿⣶⣤⣈⠉⣰⣗⡈⢛⣇⠀⣵⡀⠀⠘⣿⡄⢻⣤⠀⢻⡇⣼⣧⣿⠀ win ⠀⡿⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⢍⡉⠛⠻⣷⡆⠨⣿⣭⣤⣍⠀⢹⣷⡀⠀⠹⣿⡄⠈⠀⢿⠁⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⣇⠀⠀ ⠀⣿⣇⣠⣾⣿⣛⣲⣿⠛⠀⠀⢀⣸⣿⣿⣟⣮⡻⣷⣤⡙⢟⡀⠀⠙⢧⠀⠀⠎⠀⠉⠁⠰⣿⠀⠀ ⠀⢀⡿⠀⠀ ⠀⠈⢻⣿⣿⣽⣿⣿⣿⣴⡏⠚⢛⣈⣍⠛⠛⠿⢦⣌⢙⠻⡆⠁⠀⠀⠀⣴⣦⠀⠀⠀⠐⢳⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠀⠀⠀ ⠀⠀⠈⠙⣿⣧⣶⣿⠿⣧⣴⣿⢻⡉⠀⢀⣠⣴⣾⡟⠿⠃⠁⣠⣤⡶⣾⡟⠅⠀⣀⡄⠀⣾⢸⣿⣏⢻⢶⣦⣤⣤⣄⢶⣾⣿⣡⣤⡄⠀ ⠀⠀⣠⣞⣋⣿⣿⣾⣿⡿⡛⣹⡟⣤⢰⡿⠟⠉⣀⣀⣤⣤⡠⠙⢁⣾⡿⠂⠀⣿⠟⣁⠀⣹⠀⣹⣿⡟⣼⣿⣿⣌⣿⣞⣿⣿⠁⠀⠀⠀ ⠀⢠⡿⢛⢟⣿⣿⣿⣿⣿⣿⡟⣼⣿⣟⢓⠛⣿⣏⣿⣵⣗⣵⣴⣿⢟⡵⣣⣼⣿⢟⣵⣶⢻⣶⣿⠀⠀⣈⢻⣿⣿⣿⢿⣾⢿⣧⠀⠀⠀ ⠀⠘⠃⢸⣿⡾⣿⣿⣿⣿⣯⣿⣿⣿⣶⣿⣿⣟⣾⡿⣫⣿⣿⣿⣽⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣴⡆⣻⣿⡏⣿⢻⣧⣿⡿⣿⡆⠀⠀ ⠀⠀⠀⠜⣿⣾⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣭⣿⣖⣿⢿⣿⡿⣿⣿⣿⡿⢡⢯⣿⣿⣿⣿⣿⣿⣿⣧⡿⣾⣷⣿⣿⢿⣿⡇⠉⠁⠀⠀ ⠀⠀⠀⠀⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⡇⣭⣿⣿⣿⣿⠃⠞⠟⣸⣿⠏⣸⣧⣀⠿⢿⣿⣿⣟⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢶⣦⣄⣿⠏⠀⣿⣟⣿⣶⠾⣿⣟⣋⣛⣿⣿⣿⣿⡇⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠛⠫⣿⣿⣿⣿⣿⡿⣧⠛⣿⠛⣿⣿⣿⣷⡌⠹⡟⠀⠀⠉⡟⠋⢠⣾⣿⣿⣿⡟⣿⣿⣿⣿⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⣾⣷⣿⣿⣧⠙⠀⠙⢣⠝⠛⠋⣽⣷⢦⠇⠀⠀⠘⠁⣤⣾⣿⠝⠛⠉⠘⢻⣿⣿⢿⣼⣷⡟⢻⣷⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣾⠟⠀⢸⣷⣿⡇⠀⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣆⠀⠛⠁⠶⣶⣶⣶⣶⣶⣶⡶⠆⠘⠋⣠⡾⢫⣾⡟⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠙⣷⡀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⢀⣴⠋⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣰⣦⡀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡄⢺⣿⡄⠹⣿⠻⢦⣤⣤⣤⣤⣶⣿⡟⢀⣀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡀⠹⡷⣦⣀⡀⡀⢸⣿⠏⢠⣾⣿⠀⠀⣾⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣷⣻⡟⠀⡼⠁⣴⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢆⠠⡀⠀⢃⠑⢦⣰⢁⠆⡀⠀⣷⣢⠀⢈⡐⠀⢀⠀⠀ ⠀⠀⠀⠀⠄⠒⠐⠦⢘⢀⡨⢈⠐⢉⠂⠂⠜⢶⡗⠸⠐⠈⠀⠀⠀⠀⠠ ⣀⠠⢀⢀⠹⠖⠐⢠⠔⢌⠛⠀⠀⢄⡁⠀⢠⠀⡜⡄⠀⡗⢼⡯⢽⡧⢼ ⠐⠕⠭⣉⠑⠢⠨⠁⠆⠀⠀⠀⢥⠀⡁⠀⠈⢀⢁⡆⠀⠀⣹⣏⠃⣏⠆ ⠠⢌⡈⢁⠃⢀⠐⠄⢠⡀⠱⠀⠈⠁⠀⠀⢁⠀⣫⡅⠀⣧⣼⣹⣏⡗⢼ ⠀⢀⠘⠀⣀⠘⠃⡧⣀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠫⠋⣀⠰⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠂⣀⣀⣀⠀⡤ ⢄⠠⣋⢅⠔⠐⡘⢉⢀⢀⠀⠀⢀⡴⠊⠀⢡⠀⠈⡀⡈⠀⡂⢇⣄⡆⠐ ⠌⠜⣠⠉⣔⢂⣀⣤⢢⠀⣠⠾⣐⢡⢗⡏⢡⢒⢣⣆⠇⡄⡸⠌⡷⠈⡇ ⢂⣩⡿⡌⢏⣯⠫⢝⣗⢈⠔⡝⠫⡫⠈⠐⣥⢯⣡⠛⠀⣇⢠⡔⣑⢢⠇ ⣛⣽⣷⢝⣤⡅⡼⡿⢿⠲⢀⢄⡏⠁⣑⣲⡠⠏⠂⡓⡄⣰⡝⠨⣚⢺⠀ ⠀⠼⣽⣿⢸⢃⠸⡉⠝⠗⢢⠈⠅⠀⠱⠁⢰⠚⠚⠉⢲⣱⠃⠘⠾⡉⠀ ⠀⠀⠒⡽⢬⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠘⠈⠁⠀⠁⠘⠈⡘⣽⠀⠃⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⢺⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢚⢆⠀⠈⠐⠭⠽⠶⠊⠁⠀⠀⢡⡓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡇⣮⠸⣷⣄⠀⠀⠀⠀⢀⡔⠀⠀⠉⡃⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣾⣿⣿⣷⡼⢷⡘⢯⢅⠒⠒⢲⠗⢁⢄⠀⢸⣿⣦⣄⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⣎⢿⣳⠃⠬⣠⣗⣧⣴⣾⣿⣿⣿⣿⣶⣦⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠘⣿⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠈⢿⡆⠀⠀⣿⠙⠛⠷⣶⢟⣷⡿⠱⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢻⣧⣴⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠸⣿⡀⣶⣿⠀⢠⣾⢋⣾⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢻⣧⠀⠀⠀⣀⣀⣄⣀⣠⣀⣀⣀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀ ⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢹⣷⠸⣿⢠⡿⢁⣾⡟⢹⣧⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⢿⣖⠛⠉⠉⠉⠈⠉⠉⣛⡻⠦⠔⠶⢬⡛⠀⣾⣷⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢰ ⣄⡀⠸⣷⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⣿⡄⣿⣯⢀⣾⠟⠀⠘⣿⡄⠀⢻⣆⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠰⠖⠛⠉⠉⠉⠉⠉⡛⠛⠿⣷⣦⣄⡀⠙⠻⣷⣄⠀⠀⠀⠀⠈⣿⣇⠀⢻⡿⠀⠀⣀⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠈⠓⢿⡇⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢠⣿ ⠙⢿⣦⣻⣇⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢹⣿⡇⢿⣞⠋⠀⠀⠀⠹⣿⡄⠀⢻⡄⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⣀⣤⣶⡶⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⢃⡆⠀⠀⠉⠛⠿⣶⣄⡈⠻⢷⡄⠀⠀⠀⢸⣿⣄⡸⠟⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣸⣿⠁⠀⠀⢀⣿⢿ ⡄⠀⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⣿⡄⠀⢿⣆⠀⠀⠀⠀⠈⣿⡆⠈⣧⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⢄⣴⡾⠋⢰⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢰⡇⠈⠙⡁⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣠⣿⡏⠀⠀⠀⣼⡿⢸ ⣷⡄⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠸⣷⣄⠈⢿⣆⠀⠀⠀⠀⢸⣧⠀⠈⠁⠀⠀⠀⣿⠘⣧⠀⠀⠀⠀⢠⣾⠟⢁⣼⣿⠟⠉⢀⣤⣿⠇⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⣇⢸⣆⠀⠀⣴⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⢠⣿⠇⣼ ⣿⣿⡄⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠈⢻⣆⠈⢿⣆⠀⠀⠀⠈⣿⠀⢠⡄⠀⠀⠀⣿⠀⡷⠀⠀⢀⣴⠟⠁⣰⡟⠁⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⡇⣸⠁⠀⠀⠀⠸⣿⡀⢿⡄⠀⠸⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⣸⣿⠀⢾ ⣿⠹⣿⡄⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠹⣧⡀⢻⣆⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⢹⠀⠉⢀⣴⠟⠁⠀⠀⠛⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢻⣧⠘⣷⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⡄⠀⢠⣴⡆⠀⣰⡄⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡇⠀⢿ ⣿⡇⢹⣿⡄⢈⣿⡄⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠹⣿⣦⣻⣧⠀⠀⣿⡇⢹⡇⠀⠀⠀⠀⣠⡀⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⣸⡟⣿⠇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠃⠃⠀⠀⠀⠀⠀⠈⢿⣦⢸⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⢀⣿⠁⣰⡟⣿⡇⢠⣿⣥⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡇⠀⣻ ⢸⣿⠀⢿⣿⡛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⠀⠀⠹⣿⣷⣻⣷⡀⣻⠇⢸⡀⠀⠀⠀⣰⡏⠀⠀⠀⣠⡖⢀⣄⣾⠃⠀⣰⡿⢹⡟⠀⠀⠀⠀⠀⠀⡿⠀⣀⣀⣀⣀⣸⣀⣀⣀⠀⠀⠀⠀⠀⠈⠛⠃⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣿⣾⢃⣾⡿⠾⣿⣇⣾⠛⢉⣿⠃⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⣟⣿⠃⠀⣽ ⠀⣿⡆⠈⣿⣧⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣧⠈⠳⣤⡀⠘⣿⣻⣽⣷⡿⠀⢸⡇⠀⠀⢠⣿⠁⠀⢠⣾⡏⢠⡞⣾⡟⠀⢠⣿⠃⡿⠁⠀⠀⠀⠀⣀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠹⠋⠺⠃⠀⠀⠻⢸⠏⠀⠘⠏⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢾ ⠀⢹⣷⠀⠸⣿⡆⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⠻⣦⣌⣛⠹⣎⢿⣦⠀⣷⠀⠀⢸⡏⠀⢀⣿⡟⢠⡟⢸⣿⠁⠀⣾⠇⡸⠃⠀⣀⣤⣶⣿⣿⠿⠛⠁⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⢿⣿⣿⣶⣄⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⢀⣤⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢺ ⠀⠈⣿⡆⠀⢻⣿⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠻⣿⣷⣽⣇⠙⢷⣿⠀⠀⢸⡇⠀⣼⣿⠀⣞⡴⣿⡏⠀⣸⡟⠀⣠⣴⣿⣿⡿⠟⠋⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡏⢹⡿⠁⢸⡿⠉⢉⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡆⠀⢸ ⠀⠀⢹⣷⠀⠈⣿⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠈⢻⣿⣿⣦⡀⢿⡃⠀⢸⡇⢠⣿⡇⢸⣿⡇⣿⡇⢀⡿⢀⣰⣿⠿⠋⠁⣾⡇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣀⠀⠀⢀⣾⣃⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠘ ⠀⠀⠘⣿⡆⠀⠸⣿⡆⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠙⢿⡽⢿⣦⣻⣆⠘⣇⢸⣿⠀⣿⣿⠀⣿⠇⢸⣱⣿⣿⠇⠀⠀⢸⣿⠁⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣷⡄⠀⠀⣀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠛⠀⠀⠘⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⠀⠀ ⠀⠀⠀⢹⣷⠀⠀⢹⣷⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠸⣿⡂⠹⣿⣿⣦⡈⠘⣯⢸⢹⣿⠀⢿⣠⣿⡟⣼⡟⠀⠀⢀⣿⡇⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⢸⣿⡇⠀⢸⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡆⠀ ⠀⠀⠀⠈⣿⡇⠀⠀⢻⣧⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠙⣷⡄⠈⢿⣮⠻⣷⣏⠀⢸⡇⠀⣸⣿⡟⣰⡿⠁⠀⠀⣸⡟⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡇⠀⠀⢷⡞ ⠀⠀⠀⠀⢻⣷⠀⠀⠀⢿⣷⣄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⠀⠘⢷⣄⠀⠻⣷⡈⢻⣦⣸⡇⢠⣿⡿⢡⣿⠃⠀⠀⠰⣿⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⠛⠀⠘⣿⣿⡆⠀⠀⠀⢠⣾⣿⡇⢰⣿⠿⠛⢻⣿⠂⣴⣿⣷⠀⠀⣾⡟⢛⣿⣷⠸⠛⢻⡿⠛⠛⠁⠐⡇⣀⣠⡟⠀ ⠀⠀⠀⠀⠈⣿⡇⠀⠀⠈⣿⡻⣧⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⣿⣦⠀⠈⠉⠀⠹⣿⣇⣿⣿⠁⣾⣿⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⣴⣿⣥⣿⠁⣼⠇⢀⣴⡿⢁⣾⣯⣼⡿⠀⢠⡿⠛⠛⠛⠁⠀⢀⣿⠃⠀⠀⠀⢠⡿⢫⡟⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣧⠘⢿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠸⣿⡿⠃⠀⣿⡇⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢠⣶⡆⠀⠀⠀⠉⢏⠁⣼⠟⠉⢹⣿⢰⣿⡾⠟⠉⢠⡿⠛⠉⣽⡇⠀⣾⠃⠀⠀⠀⠀⠀⣾⠇⢀⣴⡶⢠⠏⠀⣾⠁⠀⠀ ⡄⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢿⡆⠈⢻⣮⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣽⣧⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠈⠛⠁⠀⢀⣀⣠⡾⠣⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠃⠀⢸⠇⠀⣀⣴ ⣧⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠘⣿⡀⠀⠻⣧⡈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⣄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠙⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢾⣠⡾⠟⠁ ⣿⡄⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢻⣧⠀⠀⠙⣷⣄⠀⠈⠛⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠍⠉⠉⠉⠉⠁⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠁⠀⢀⣴⡿⠋⠀⠀⠀ ⢿⣷⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠘⣿⡆⠀⠀⠹⣿⣄⠀⠀⠙⢿⣿⡻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⢠⠀⠀⠀⠀⣼⡟⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⢶⣶⡆⣠⣤⣤⣤⣤⣤⡴⠶⠆⠛⠛⣿⠟⠁⢀⣴⣿⠟⠁⠀⠀⠀⠀ ⠸⣿⣧⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⢹⣷⣄⣀⠀⠘⢿⣶⣶⣦⣄⡙⠇⠀⣨⣿⡿⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⠀⢸⡇⠀⠀⠀⠉⠀⢸⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡃⠀⣠⣻⣾⠁⣿⣵⡿⠋⠁⠀⠀⠀⢠⣾⠏⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⡆⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠉⠛⠿⢿⣷⣦⣅⠈⠉⠻⢿⣶⣾⣟⣯⣤⣤⣤⣭⣽⣻⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣿⠏⢀⣸⡇⠀⠀⣀⠀⢀⣿⣷⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⣿⠁⢰⣿⣿⣯⣶⠿⠁⠀⠀⠀⠀⠀⠀⣾⣯⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠈⠙⠿⣿⣆⡀⠀⠙⢿⣿⡛⠉⠋⠉⠙⠻⢿⣿⣆⡉⢿⣿⣶⡀⠀⠀⠀⠸⢟⣶⡿⢀⣾⠆⣀⣾⠏⣾⣿⡿⠀⣿⡟⠃⠀⣸⣿⢀⣿⡿⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢸⣿⣿⣾⠟⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣰⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢀⣀⣬⣽⣿⣦⣤⣤⣭⣿⣦⣀⡀⠀⠀⠀⠈⠛⢿⣿⣿⡛⢿⣶⣤⣦⣄⠀⠀⠀⠈⠁⠾⠋⠁⠾⢡⣿⠃⣸⡟⠁⠀⠀⣿⡏⠸⣿⡁⠈⠿⠟⠁⠀⠀⠀⠀⣀⣤⣶⡾⠛⠁⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟ ⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠘⠛⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠙⠻⢷⣦⣤⣀⡀⠈⠛⢿⣶⣌⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⣠⣾⠿⠋⣰⡿⠁⠀⠀⠀⠻⣿⣄⠙⢷⣄⣀⠀⠀⣀⣤⣴⠟⠛⠉⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣄⠘⣿⣇⠀⠀⠉⠛⠿⠿⠶⢞⡿⠟⠁⠀⣰⡿⢿⣷⠀⠀⠀⠀⠉⠻⢷⡄⠉⠙⠛⠳⠛⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣾⣿⡄⠀⠀⠀⠀⢀⣴⠿⢿⣿⣷⣰⣿⡅⠸⠿⠀⠀⠀⢠⡆⢀⡾⢃⡦⠀⠀⢠⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠁⠀⠄⠀⠀⠀⠀⠀⠀ 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