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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⠉⡉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠤⣇⡀⠐⡈⢄⣁⣂⣄⡡⠈⠄⠠⢈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣞⣤⡴⠤⠬⢷⣡⣰⣞⣉⣀⡈⠙⣦⠈⡐⢀⠂⡄⡘⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⡔⢧⣈⢁⡴⠒⠛⠄⠸⡆⠚⠂⠉⢙⡟⠋⠙⡉⢉⠉⡉⠛⠹⣄⠀⠀ ⠀⢀⡴⠃⠀⠄⡈⠙⣧⡀⣌⡄⠁⡉⠓⢒⣚⠋⠚⡙⠓⡀⢂⠐⡀⠂⠄⠹⡆⠀ ⠀⡼⠀⠠⠁⢂⣾⡭⢤⡭⢥⠴⠶⠶⠓⠚⠉⡉⠄⠐⠠⠐⢀⠂⠠⢁⠈⠄⢳⠀ ⠀⡇⠠⠁⠌⡀⠙⣆⠀⠄⠂⠠⠀⠄⠂⡁⠂⠄⡈⠄⢁⠂⠄⡈⠐⠠⢈⠐⢸⡀ ⠀⡇⠄⡁⠂⣤⠷⠛⠠⠈⠄⠡⠈⠄⡁⠐⡈⠠⠐⢈⠠⡆⠐⡀⢁⠂⠄⣺⢸⠄ ⠀⢹⡀⠐⡈⣧⠀⠂⡁⠂⣌⠠⠁⡐⠀⢥⡀⢁⠂⠄⠂⣧⠐⢀⠂⡐⢠⡟⣸⠀ ⠀⠀⠳⣄⠐⡙⢦⣅⣀⣢⡼⣄⠐⡀⠡⣸⠇⠀⠂⠌⠐⠈⠳⠦⠴⠴⠋⣰⠇⠀ ⠀⠀⠀⠈⢓⣦⣄⠀⡉⠀⠄⡈⠛⠛⠋⠁⠄⠡⢈⠐⢈⠐⡀⢂⠐⢠⡱⠃⠀⠀ ⠀⠀⣠⡞⡯⢞⡭⣟⠷⣾⡴⣤⣦⣔⣈⣴⣬⡴⣤⣬⣀⡐⢀⣢⠼⠊⠀⠀⠀⠀ ⠀⠀⠘⠯⣵⣫⣞⣜⣯⣖⡽⠵⣿⢫⢟⡼⡲⣝⣣⠯⣝⡻⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠷⠮⠷⡽⠶⠭⠾⠓⠛⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠁⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⣤⣴⣶⣿⠦⠤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡒⢾⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⠟⠋⢉⣀⡠⠤⠤⢄⣉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡀⠠⣄⣠⣾⣥⣄⠹⣼⠀⠀⠀⠀⠀⠀⣤⣾⠟⢁⡤⠚⠉⣀⣠⠤⠤⠤⢤⣉⡻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣿⣷⡿⠋⠁⣈⣻⣧⡏⣆⠀⠀⠀⣠⣾⡿⠁⣰⠋⢀⡴⢋⣡⣤⣶⣶⣶⣦⣤⣙⣮⣳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⠀⣰⡿⣿⡁⠈⣇⡿⣾⣶⣿⣿⡿⠁⣰⠁⣰⣿⣾⠿⠛⢉⣉⣠⣀⣉⠙⢻⣿⣿⣷⣟⣡⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⡏⣼⣿⣿⣿⣿⢷⣈⠉⠉⠉⠀⣰⠃⢠⣿⣿⠁⢀⣴⠟⣁⣤⡞⠉⢻⣆⠙⢿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠸⣧⠹⣿⡿⠛⠉⠀⢈⣙⢦⣠⠴⠃⠀⢸⡿⠃⠀⣼⠁⣾⣿⣿⣷⣶⡞⢹⡆⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢘⣷⠁⠀⠀⠀⠀⠀⠹⠄⠙⢦⡀⠀⠸⡇⠀⠀⢻⡄⢿⣿⣿⣿⣿⠇⢨⠇⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢹⡀⠀⠈⠿⣦⡉⠛⠛⢁⡠⠋⠀⢀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀ ⠀⠀⠀⠶⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⢿⣗⡲⣦⣄⣀⡀⠀⠀⢀⣠⢶⡟⣧⠀⠳⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⡾⢹⠀⠀⠀⠀⠀⠀⢀⡀⢠⡇⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠐⠊⠉⢩⠳⠤⣄⡀⠀⠀⢀⡤⠚⠉⠀⠸⣿⠙⣿⣿⠁⢋⣽⠿⢁⣴⠟⠀⠈⢷⡀⠘⠲⢄⣀⠀⠀⠀⣀⣠⠖⠋⢠⣿⡀⠀⠀⠀⢀⡔⣡⣹⡎⡇⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⢀⡴⠙⣦⠖⠁⠀⠀⠀⠀⢀⣿⠀⣏⣿⠷⠋⣁⡴⢫⡟⠀⠀⠀⠀⠙⢦⣀⠀⠈⠉⠉⠉⠁⠀⣀⣴⣏⢸⠁⠀⠀⢰⢋⣾⢣⣿⢰⠀⢠⡣⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⡀⠈⢀⠞⠁⠀⠀⠀⠀⠀⠀⢨⣿⣦⣤⣤⣶⣯⣥⣶⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣶⣶⠶⢟⡟⠁⢻⣼⠀⠀⢰⠋⣼⢃⣿⡇⠀⢀⢯⠇⠀⠠ ⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠉⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣃⣿⡿⠿⣶⢿⠁⢀⠏⢰⡟⢨⡏⡷⠀⡞⡞⠀⠀⠀ ⠀⠀⢠⣖⠻⡶⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡍⢹⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⡇⠠⣿⡼⡄⣸⠀⣾⠃⡾⢳⠇⣸⣹⠁⡼⠀⠀ ⠀⠀⠒⢠⡉⡳⢵⣄⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⣼⣿⡿⠙⢦⣴⣿⡅⠊⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣯⠞⠙⡇⡇⡷⣴⣟⣸⡇⠀⢠⣧⡏⣼⠃⠀⠀ ⠀⠀⣈⣒⡺⠥⠤⠛⣆⠀⢀⣠⣿⣿⣷⣶⣶⣿⣿⠿⣿⠤⠞⢻⡿⠉⢷⡒⠹⣆⢻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⢩⣿⣷⣄⣉⣏⣟⠟⠻⣿⣄⣤⣼⠾⢶⣧⠀⠀⠀ ⠀⠀⠠⠤⠭⠭⣍⠉⠘⣤⢟⣵⠟⢻⣿⣏⡿⠋⣁⣤⣾⡀⠀⣾⠇⢳⢀⣿⡖⡺⠻⣿⣿⣷⣦⣀⡐⣶⣾⣿⣿⣿⣿⣯⣦⣿⡟⠁⢹⠹⡇⢷⡀⢀⣬⡛⠉⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣈⣹⣡⡴⣾⣿⠋⠉⣽⡟⠀⢧⡀⠙⠀⢈⡿⡟⣟⠁⠀⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⣿⠀⣾⣄⠙⣴⣿⣇⠀⠀⠟⣇⡆⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡿⠋⣏⣽⠟⠁⣼⡟⢹⡄⠰⡟⠀⠀⣴⣻⣖⠞⠁⣿⠡⡌⢦⣄⣀⣠⡿⢻⡿⡿⣧⡁⠙⢁⣴⢿⣿⣿⣦⣩⣾⡟⣏⡍⠻⡎⢹⡭⠶⣄⠉⠫⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣽⣨⣬⣾⣿⡇⠀⣰⡟⠐⡆⣷⣤⡤⠴⢋⣧⠃⢿⠀⠐⡿⠀⢹⣴⣿⣧⠼⠁⢸⣟⢳⡛⣿⣿⣯⠁⠀⢻⣏⢿⣿⣿⣿⣿⣿⣧⣤⠾⡿⢦⠈⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⡍⣰⡿⠁⡉⢷⠂⢿⠀⢀⣷⣫⢿⡇⠀⢸⡏⠘⡎⢧⡀⠁⢒⠾⢹⡇⠸⣆⠀⠘⢻⣠⣷⢿⣿⢿⣷⣦⡄⣛⣮⣿⠁⠙⣷⢸⣿⣿⣧⣽⣦⠴⠟⠛⠚⠳⠆⠀⠀ ⠀⢀⣾⣿⣿⣤⠛⣀⣠⣵⡿⣿⢺⠲⢉⣯⠇⢄⢧⠞⣲⠁⠀⣸⣿⣹⢻⡀⠀⠘⡇⠀⠹⣵⣦⣴⡟⠀⠈⣿⡴⣭⣿⣿⣿⣿⣿⣷⣷⣾⣾⣿⠿⠋⠉⠙⠿⢿⠟⠺⠾⣧⣄⠀ ⠀⠘⣿⣿⡿⣿⣿⣿⠿⢹⣻⢹⣍⠄⣼⡏⢰⢸⡈⣷⣧⠠⠞⠁⡏⡇⢦⣷⡄⠀⠁⢡⣴⠏⢻⣏⣝⢦⣀⡌⠛⣎⢿⣿⣿⣿⣿⣿⣿⣿⡟⡁⣀⠀⣠⠀⣤⣿⣀⡀⠀⠀⠈⠀ ⠀⣼⣿⣿⣿⣿⣿⣣⠀⣿⢇⠈⢧⣀⡟⠀⢸⣬⣾⠇⢻⡀⠀⢀⣿⢁⢀⢫⣯⣷⣾⣹⠃⢀⢸⢫⠘⣞⣿⣿⣧⡛⡌⠿⣏⣳⣿⣿⣿⣿⠿⠟⠛⠻⢿⣿⠋⠘⠽⡯⠭⠬⡏⠉ ⢠⣿⣿⣿⣿⣿⣿⣧⡐⡿⡜⣼⣼⣿⣷⡿⠋⢸⡾⡄⠈⢿⣄⠀⢿⠸⣼⣼⣻⠫⠘⢿⣤⣾⠘⠈⠀⣼⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⠐⠲⢤⣀⠒⣿⢠⡾⡄⡼⣃⡴⠃⠀ ⢼⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⡿⢿⡿⠿⣧⡀⠀⠃⢳⢀⣾⣿⣷⣷⣔⠋⠉⠸⠹⡄⢸⣿⣿⣲⣶⣞⠉⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠠⣀⣾⡿⠷⣷⡿⠛⠋⠁⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠋⠈⢨⡇⠀⠈⢇⣲⣶⡾⠿⠙⠛⡏⠀⠛⣶⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⢤⣘⠙⠳⣶⣦⣄⣔

ִֶָ𓂃 ࣪˖ ִֶָ🐣་༘࿐

⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣠⣫⡟⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡃⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠁⠀⠀⠀⠀⠀⠀⡁⡃⣎⠀⠀⠀⠀⡘⡆⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⡀⠐⠀⠀⠀⠀⠀⡃⣇⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⣐⠁⢄⠀⠀⠀⠀⠁⡃⢆⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀ ⠀⠠⠢⡅⠀⠀⠀⠀⠀⠂⠅⡃⡀⠀⠀⠀⠀⡻⠄⠀⠀⠀⠀⠀ ⢀⠉⢂⠁⠀⠀⠀⠀⠀⢔⢁⠃⡀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀ ⠆⠌⡘⠀⠀⠀⠀⠀⠀⢜⢸⠀⠠⠀⠀⠀⠀⡶⡂⠀⠀⠀⠀⠀ ⡂⢠⠃⠀⣀⣠⣤⣀⣀⢭⢸⠀⠀⠅⠀⠀⠀⡯⠂⠀⠀⠀⠀⠀ ⠁⠀⢠⢯⡿⠋⠁⠹⠽⡿⣾⣧⡀⠑⢀⡀⠤⡏⣧⡄⠤⡀⠀⠀ ⠀⠀⢸⡇⡅⠀⠀⠀⢠⠃⠀⠉⢋⣷⠁⡠⣢⡯⠀⠉⠉⠲⡀⠀ ⠀⠀⢘⡷⠀⠀⠀⠀⠀⠀⠀⠀⣐⡧⡟⠁⠁⠂⠀⠀⠀⠀⠫⡀ ⠀⠀⠈⣿⣄⣀⡀⠀⠀⠀⠀⢀⢲⣽⠇⠀⡃⠀⠀⠀⠀⠀⠨⡅ ⠀⠀⠀⠑⢇⡉⠉⠋⠋⠶⢖⣒⣣⡳⡀⡌⠀⠀⠀⠀⠀⠀⢨⡃ ⠀⠀⠀⠀⠀⠁⠙⠓⠒⠂⠊⠿⣟⣪⠕⣧⡀⣀⠀⡄⠀⢀⡗⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠍⠭⠝⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣤⣤⣤⣬⣻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⡟⠀⠀⠀⠀⠀⢀⡴⠦⣄⠀⠀⠈⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣖⣚⡁⣀⢠⢠⣠⣖⣉⣤⣤⢞⡆⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣤⣬⣭⡻⣏⣿⠝⠓⠊⣉⣹⠃⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢘⣯⣉⣴⣿⣿⣿⣷⣿⣿⣿⣿⣷⠤⢤⣄⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⡀⠀⠀⠈⠙⠻⠿⠿⠿⢛⡋⠀⠀⠀⠙⣆⠀⠀⠀⠈⠑⠦⠤⢄⡀ ⠀⠀⢸⢻⠀⢠⠊⠀⠀⠀⠀⠀⣀⣠⠴⣞⠉⠙⢯⡉⠙⢢⢘⡆⠀⠀⠀⠀⠀⠀⢤⡞ ⠀⠀⢸⡜⡀⠀⠀⠀⠀⢀⣴⡛⠙⢦⡀⠈⠳⡀⠀⠓⣄⢈⣧⡟⠀⠀⠀⠀⣀⣀⡀⠙ ⠀⠀⠈⢧⠀⠀⠀⢀⡔⠋⣠⠽⠶⠤⠬⠦⠴⠿⠶⠒⠛⠋⣾⡅⠀⠀⠀⠀⠈⠳⣍⠉ ⠀⠀⠀⠹⣦⠀⠀⡎⠀⠀⠙⠓⠦⢤⢄⣀⣀⣀⣀⣤⣴⣾⣿⣷⣦⣀⠀⢠⢤⣤⣄⣣ ⠀⠀⠀⠀⠉⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⡇⠀⠀⠀ ⠀⠀⣠⡴⠴⠤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀ ⠀⢰⠃⠀⠀⢀⡴⠟⠲⢤⡀⠀⠀⠠⣏⣴⣿⢀⣿⣿⣿⣿⠛⠉⡽⠋⠉⠙⠒⢤⡀⠀ ⢀⡼⠓⠦⣄⡟⠀⠀⢀⠀⣳⠀⠀⠀⠉⣸⢻⣠⠟⢿⡇⠉⠀⠘⠃⠀⠀⡴⢃⡼⠧⡀ ⢸⠀⠀⠀⢸⠁⠀⠀⣴⠀⡗⢆⡀⠀⣠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢳ ⠈⡗⣤⡀⠸⣆⠀⢠⡏⠊⠀⠀⠑⢋⣹⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓ ⠰⣇⠀⠉⠉⠉⠳⢾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠦⢤⣀⡤⢞⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀

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⠀⠢⠐⠠⡀⠄⡀⠀⣟⠀⢆⠡⢂⠔⡀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠄⠀⠂⠠⠀⠀⠀⠈⠀⠉⠀⠉⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡳⡜⣬⠳⣌⢣⣓⣮⣵⣢⣶⣤⣦⣴⣦⠳⣌⢆⡣⡝⣆⢣⡓⡼⣌⠳⣌⢧⢣ ⠦⣡⢆⣁⡐⢠⠀⡁⢎⡘⠤⢁⠊⡔⠁⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢧⡝⡾⡽⣜⠶⣭⣛⢿⡹⣏⢿⡹⣏⢯⡷⣝⣎⢷⣹⢬⡳⣝⡶⣭⢻⣜⢯⢧ ⠀⠀⢚⠀⠉⠣⠓⢦⢣⣴⣂⠤⠡⠈⠅⠐⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣻⣵⢻⣭⡟⣶⣫⢾⣱⣏⣾⢳⡝⣮⢻⡝⣮⠷⡽⣎⢷⣫⢾⣱⢯⣾⡹⣎ ⠀⢀⢻⠀⠀⢀⠀⠀⠀⠀⠉⠉⠓⠹⠦⢴⣠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣷⣞⡿⣶⣻⢳⣯⣟⣧⠿⡼⢯⠾⣽⣛⠾⡵⠻⠳⡭⠟⠼⠳⠏⠾⠓⠛⠱ ⠀⠀⢬⠀⠈⠠⠈⠐⡀⠂⠀⠀⠀⢠⠃⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠁⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠖⡩⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢬⠀⠀⢁⠂⠐⠠⠀⢀⠁⠀⢀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠑⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡈⠼⠀⢀⠀⠀⠌⡐⢀⠂⠀⠀⣀⡇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠟⡛⢭⠩⡍⢭⠱⣉⠯⡜⢣⢏⠷⣚⠶⣳⠲⣖⠶⡶⢶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠒⠳⠲⡤⠦⣄⢤⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣦⣤⣤⣠⣤⣦⣄⣤⣄⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣼⣿⡿⠃⡜⠰⡉⢆⠳⡘⢦⠹⣌⠶⣉⠗⣮⡙⣎⠷⣣⠟⣬⢳⣝⡳⣎⢷⡹⣏⣟⡿⣻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⢀⡁⠀⠀⠀⠈⢹⡿⠻⠿⠿⠿⣿⣦⣤⠀⢰⣾⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣻⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⣠⠑⡌⠱⢌⠢⢣⠙⣆⠳⡌⠶⣉⠞⡴⡹⢬⡳⣍⡻⡜⣧⠞⣵⢫⣏⣷⢫⡾⣝⡯⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠛⠋⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠌⠐⠀⠁⠢⢹⡃⠀⠀⠀⠀⠀⠈⠁⠀⠈⣿⣇⢺⢿⣷⣿⡟⠊⠛⠙⠉⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⣿⠃⡜⣀⠣⢌⡑⡊⠥⡃⡍⢆⠳⣌⢣⡹⢜⡱⣍⢧⣓⠮⡵⣛⡴⢻⣜⡳⣞⡼⣻⢼⣏⡾⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⠈⠠⠀⠠⠀⢸⡁⠀⠂⠄⠀⠁⠂⠈⠀⠐⣿⡉⢢⣷⢎⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠣⡘⠰⡄⢃⠆⡌⠥⠓⡌⡜⣌⠳⣌⠲⡱⢎⡵⣊⢶⡩⣞⡱⢧⢫⢗⡎⣷⡹⣞⡵⢯⣞⣽⣳⢿⣿⣿⣿⡇⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠐⠡⠀⠠⠀⠀⠸⡁⠀⠀⠐⠀⡐⠠⢀⠀⠠⣿⣷⣦⣏⢛⣿⠇⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⣿⡟⢠⢁⠓⡌⠒⣌⠰⡉⠖⡡⠎⡔⢣⡌⢳⢩⠞⡰⣍⢖⡳⢬⠳⣍⠯⡞⣼⠲⣝⢮⣝⣳⡞⣧⢯⢿⡽⣿⣿⡅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣄⠠⣀⠀⡄⣀⠀⠸⡀⠀⠀⠀⠀⠐⠀⠂⠀⠀⢨⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢀⠣⢌⡘⠰⡉⢄⠣⠜⡡⠱⣉⠜⡡⢎⡱⢎⡚⡵⣊⢮⠵⣫⠝⡮⣝⡵⢣⡟⣼⢳⣎⡷⣽⢫⣟⡾⣽⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠱⠈⠉⠘⠂⠙⠃⠙⠣⠎⠀⢷⡦⢶⡖⠀⠀⢨⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⡌⡘⢤⣈⣱⣈⣆⣣⢎⣑⣣⡜⣬⣑⣎⡵⣊⡵⣱⡍⣎⡳⣥⢫⡵⣚⣼⢣⣟⣬⡳⣎⢷⣫⣟⡾⣽⣫⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⣿⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠰⠁⠀⠀⠀⠀⠁⠈⠀⢂⠀⢘⣿⠀⠀⠀⠹⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⢈⠅⠀⠀⠀⠀⠈⠀⢀⠂⠀⢨⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣦⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⠆⠀⠀⠀⠐⠀⠈⠄⠀⠠⢘⣿⠀⢆⡀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⣶⠾⢿⡛⣛⣛⣛⡛⢶⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠒⠎⠖⠲⠒⠦⠲⠜⢦⠳⠌⠶⠑⠎⠻⠶⣿⠆⠀⠙⠓⠀⠀⠀⠠⠄⠀⠠⠶⣦⣾⡟⠭⣉⠦⣙⢦⣹⡵⣞⣶⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⠿⣟⣻⡛⢿⣩⠯⡵⢣⡞⣬⣻⣿⣿⣜⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄ ⠀⠀⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢿⣿⣬⣆⢡⠚⠤⢃⢣⠙⣙⢋⡛⢛⣿⡟⣻⠻⢟⠿⣻⢟⣿⣻⢿⡻⢟⠿⢻⠟⠿⣻⢛⡟⣛⢛⠻⡹⣍⠯⡹⢍⢧⡙⢦⢣⣇⡳⣔⣳⣌⣻⣴⣣⣽⣮⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠁⠀⠀⠁⠐⡆⠀⢈⠀⠀⠂⠄⢸⣧⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠛⠻⢿⣾⣶⣧⣦⣱⣌⣦⣱⣊⣥⣘⣍⣓⣌⣦⣡⣎⣴⣉⣎⣹⣌⣣⣧⣙⣲⣥⣣⣜⣦⣭⣶⣵⣾⣶⣿⣾⣶⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠋⠋⠙⠻⠟⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠄⡀⠂⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣬⣉⠉⣻⣟⣛⣛⣛⣛⣛⣛⠛⣛⠿⢿⠛⠿⠛⠻⠿⠻⠿⠻⣿⠿⡿⠿⣿⠟⢛⠛⠛⠛⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠌⠐⢀⠐⠀⠈⡅⠀⠀⠀⠀⠀⠀⠄⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⢨⣿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣤⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠒⠲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⣀⢄⡠⢄⡤⢢⠜⡴⢢⠞⠐⠓⠶⠑⠺⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣷⢰⣿⣿⣿⡿⠛⠋⠉⠉⠉⠁⠈⠀⠉⠉⠙⠛⠛⠛⢿⣿⣼⢫⡟⣽⢻⡿⢯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⢿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⢀⣤⣴⣿⣟⣤⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣴⣦⡀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠉⠉⠉⠒⠈⠙⢻⣶⡿⠟⠋⠙⣿⣟⣩⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣹⣿⡗⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⢀⡀⠉⠛⠛⠛⠋⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠁⠀⠀⠀⠀⣽⣿⡇⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠀⠀⠀⠀⣰⡾⠁⠀⠀⣤⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠀⠀⢠⣀⣀⡀⡀⢠⣿⣿⠁⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣤⣾⠟⠀⠀⠀⢀⣿⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⣐⣆⠀⠀⠀⢀⣺⣿⣿⡟⠁⠀⠉⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣯⠀⠀⠀⢀⣸⣿⡃⠀⢀⣀⣰⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢶⣶⣮⣽⣿⣿⡀⠀⢀⡀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣷⣾⣿⣯⣿⣿⣿⡿⠿⠛⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⣿⣾⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣤⣤⣤⣾⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣠⣼⠉⠁⢈⣿⣷⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠒⠲⠐⠆⠐⡽⠲⠶⠤⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠧⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠗⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠈⠁⡟⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣿⣿⣿⠻⣿⣿⢻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠻⠛⠿⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠇⡇⠈⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣾⣀⣧⣿⣿⣿⣷⣾⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⠸ ⡄⣿⢻⠀⠀⠀⡄⣿⣿⣿⣿⣝⣷⣿⣿⣿⣿⣿⣿⠿⡿⣶⣷⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿ ⠀⣧⣿⠹⠀⠀⠇⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣠⠰⡀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣷⣿⢿⠙⠀⣿⣿⢻⣽⣿⣿⣻⢛⡔⣤⣦⢀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼ ⠀⠀⠀⣆⣷⣹⣮⣷⣿⣭⣭⣭⢋⡚⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣯⣿⣯⣿⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⣄⣦⠶⡲⣶⣒⢒⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣟⢿⣿⣿⣿⣿⣿⣿⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣿⣿⣿⣿⣿⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣟⣿⣻⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣯⣿⣿⣿⣿⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣴⣻⣷⣞⣨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⢾⡇⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀ ⠀⢀⣴⠋⠁⠀⣼⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀ ⠘⠳⣤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀ ⠀⠀⠀⢉⣽⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀ ⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀ ⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀ ⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⠀⣀⣴⣿⣷⣄⣀⠀⣀⣴⣿⣷⣤⣀⠀⣀⣴⣿⣷⣤⣀⡀⣀⣤⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢛⠿⠿⠟⠛⠁⠉⢛⠻⠿⠟⠛⠁⠉⢛⠻⠿⠟⠛⠁⠉⠛⠻⠿⠟⠛⡁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠚⠉⠶⣈⠀⠃⠚⠘⠇⠋⠨⠌⠠⠀⠇⠉⠟⣏⣏⢄⠓⢏⡹⠁⣾⠙⠹⠰⣽⠿⠣⠁⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⣀⡀⢀⡀⡀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⣿⣧⣿⣿⣿⣾⣶⣉⣀⣠⣅⣦⣿⣷⣳⣿⣞⣄⣾⣿⣿⣿⣿⣿⣿⣷⣤⣶⣽⣄⣦⣿⣷⣿⣿⣿⣿⣷⣧⣻⣿⣟⣯⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢞⠫⣔⡺⣿⢀⠀⠁⠏⡿⠿⡼⠰⠊⡷⢱⣺⣾⢼⠡⢛⣿⣶⣿⣿⣿⠻⣹⠍⣯⣽⡿⠟⡽⣉⣿⣴⣡⠄⠤⣷⡿⣿⣿⢶⣿⣿⣿⣿⣿⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⣛⣯⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿ ⣾⢳⣽⠯⢾⠔⠤⡿⣿⣿⣠⢈⠁⢀⠀⡿⠄⢀⠃⣿⣰⠀⠀⠀⠁⣯⣿⣼⠘⣇⣿⣯⣿⣮⣠⢀⡤⢖⠷⡿⣿⣷⣿⣶⡿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣻⣿⣽⢾⣿⣿⣿⣿⣿⣿⣞⣽⣿⣯⣾⣟⣞⡿⣽⢿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿ ⠊⡕⢫⡟⠛⠉⠀⡇⣿⢡⠀⠀⠙⠈⣿⣿⢹⠀⣷⣼⠀⠋⠛⠛⡄⢫⣵⡞⣤⢻⡟⢹⠀⠀⠀⠀⠃⠚⠃⠛⠛⣾⣤⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣽⣾⣷⣿⣿⣿⣾⡟⣯⡏⣿⣿⣾⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣾⡟⣿ ⣶⡶⣲⣿⣿⣫⢯⡍⣿⣳⠉⡞⣟⢶⣿⣿⣿⠿⡿⣿⡿⣞⣡⢚⢬⡻⡴⠀⠄⠪⡄⣏⣸⣤⠏⠾⣫⡖⣠⣉⠛⠟⡴⣿⣯⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⢿⣿⣟⣿⣿⣽⣾⡟⣱⣺⣷⢟⣻⣶⢿⣿⡿⣷⣟⡾⣿⣿⣿⣿⣿⣿⠿⣻⣿⢿⣷ ⢫⠽⡧⣯⣿⣠⢀⡓⣿⣿⣿⣄⣽⠍⣿⣿⣿⣿⣿⢽⣫⡑⢼⠫⢟⡼⠀⠀⡭⢈⡅⣿⢈⠇⣿⢀⢁⠟⣿⣛⣘⣛⣗⣏⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣷⣟⣯⡞⢿⡿⡟⣯⣻⢶⡿⢿⡿⢯⣿⣟⡾⣿⡿⣿⣿⣻⢿⣫⣿ ⢿⡻⢿⣿⣹⠂⠄⡿⣿⣻⣤⣩⣷⣿⣿⣽⣿⣧⣿⣿⠿⣻⣟⣿⣿⣿⠿⣿⣿⣿⡿⣽⣤⣤⢦⠛⣿⣿⣿⣿⣏⡿⣴⣫⣛⣿⡿⢿⣿⣿⣿⣿⣿⡿⣟⣯⣾⠻⣷⣋⣷⣽⡿⣽⠻⣟⢿⣾⣻⣷⣯⣿⣿⣿⣷⣯⣽⣚⢿⣿⣿⣯⣽⣾⣟⣿⣞⣿ ⣿⣿⣿⣿⣿⣤⣡⣧⣿⣴⣀⠀⠃⣿⣿⣿⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢈⠀⠀⠋⣨⠋⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣷⡷⣟⣽⣿⣽⢿⣫⢿⣿⡿⣟⣯⣿⣿⣾⣻⣟⣿⢿⡾⣟⣧⡾⣟⣼⣷⣟⣧ ⣾⣿⣷⣮⣿⣹⡘⢄⡀⠤⠈⠁⡟⣿⣿⣿⣿⣾⣧⣔⢠⡟⣿⣿⣿⣿⣿⣿⣿⢹⠀⠁⠉⠉⠉⡈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣽⣯⣿⣾⢿⣷⣾⣏⣽⣿⣟⣯⡿⣟⢯⣿⡿⢏⣾⣽⣯⢿⣰⣛⡾⣟ ⢟⣹⠷⣍⡶⣼⠋⠙⠛⡛⢿⣿⣶⣿⣿⣻⢞⢡⣠⡑⡏⣿⣿⣾⣾⣾⣀⢧⣿⣿⣆⣿⣻⣴⠦⠙⠀⡀⣤⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣳⣿⣷⣽⢾⣿⣯⢷⣯⣷⣿⣿⢿⣯⡾⣿⣯⣿⣿⣍⡭⢭⣯⡷⣟⣿⣻⡷⡿⣿⣿ ⠈⣀⢆⡷⠂⢀⣻⣀⣐⣤⣤⣷⠿⣿⣿⣿⢿⣏⠼⡿⣿⣾⣿⢼⢠⢀⠀⣇⢀⡄⢸⡐⡄⢸⠀⣄⣳⢟⠛⡛⡽⣦⣿⣿⣿⣿⣿⡵⢿⣾⣿⣯⣷⣿⠿⣻⣽⣾⡟⣿⡿⢾⣽⣯⣻⣿⣾⣙⣯⣿⣿⣟⣯⣿⣏⡼⣡⣟⣿⣳⡽⣻⢿⣽⡾⣽⣟⣿ ⠶⣳⠿⡟⢵⡼⢤⠻⠘⠣⠴⡚⣞⣧⣿⣿⣿⡿⢸⡄⣿⢈⣾⢸⠄⠘⠁⡍⠈⠀⠀⠀⠀⠀⠈⣻⠀⡴⣦⠽⡀⣷⠻⣥⣿⣿⣿⣿⣻⣿⣾⣿⣿⣳⣿⣽⣻⣿⢯⣽⡿⣯⣿⢿⣿⢿⣿⣿⣟⢾⣽⣿⣻⣷⢿⣿⣿⣻⣿⣿⣟⣿⣾⣿⣿⣷⡾⣿ ⠠⡀⡀⣘⣿⣿⢿⣧⣿⣾⠙⠾⢟⢫⣿⠿⠛⢧⢻⠈⡇⠘⢀⢠⠀⣆⡿⣿⠀⠀⠿⠈⠀⠟⢸⣞⢷⢺⠑⡃⢮⠐⣀⢳⡛⣭⣷⣿⣿⣿⣿⢿⣻⣿⣽⣻⣿⢿⣽⣾⣿⣿⣿⣯⣟⣿⣷⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣟⡽⠿⣿⣿⡿⣾⣿⣟ ⢿⠻⠻⠟⣿⣿⢳⣬⣥⢦⠉⣤⣷⣔⣿⣿⣾⣽⣦⣌⠴⢦⠲⠙⠈⠀⡄⣹⠘⠘⣷⢸⠀⡇⣮⠐⡀⢧⡆⣿⠛⠓⠈⡇⠚⣷⣭⣾⡿⣿⣿⣾⢿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣽⢿⣯⡷⣟⣮⡿⢟⣿⢿⣿⢿⣿ ⣧⣟⣿⣿⣽⣾⡻⢄⡙⠿⣻⠘⡍⠡⣿⣯⢿⣉⠠⢃⠄⠀⠛⣶⢘⠀⠀⣯⢚⢿⡄⢿⠀⡆⢌⠃⠀⡀⠹⣈⣇⡹⢈⡁⢈⡀⣄⢦⣧⣿⣿⢿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⡷⣿⢿⣻⣷⣿⣿⣿⣿⣿ ⣤⣞⣷⣶⣻⣵⢲⣍⡿⣿⣿⣛⠝⠩⣷⠘⣇⣼⣦⠦⣛⡴⣨⠀⠀⠀⠀⡄⢱⡄⢠⡃⢸⠀⢠⠀⢘⠀⠀⠀⡀⢧⠉⡆⢀⠈⢄⠻⠀⣧⣻⣿⣿⣾⣿⣿⣶⢿⣿⣿⣿⣿⣳⣿⣟⣾⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⠡⠘⣋⠏⣻⣽⢮⡟⣿⣻⣵⢢⠃⡹⡿⢸⣦⢷⠻⠟⢲⠙⡀⠤⠀⠀⠀⠀⡄⠳⠀⠀⢆⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡆⣝⡲⣿⣻⣿⣿⢿⣿⣿⢇⣿⣯⣿⣷⣿⣯⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿ ⡂⡕⣾⣾⣶⣾⣵⣠⣉⣤⡽⣦⣿⡿⣿⣿⣔⠧⡢⣍⢾⣠⣦⣉⠄⠲⠙⠀⠀⡄⠌⠘⠆⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣏⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿ ⢿⠻⢏⣘⠐⣷⠣⣌⡛⢯⢰⡦⣿⣿⣿⣿⠀⢋⣼⣩⠛⡟⣿⢿⠻⠛⠙⠉⠀⠀⢃⠌⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⣬⣷⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢶⣏⣼⣄⡒⣑⢾⣏⡿⣭⡿⣴⣙⣜⣈⣷⣿⣿⣶⣈⣐⣁⣶⣿⣿⣿⣿⣿⣿⠿⠻⢛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡇⣿⣿⣾⣿⡟⣿⡿⣛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⢐⡀⣄⠒⡃⢯⣞⠿⣿⢹⠈⡄⠿⡏⠸⣠⣦⢿⡟⠛⣱⠾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣡⠰⣈⠱⣞⠄⣩⣖⣉⣶⣿⣿⣿⢓⡿⣙⣠⡾⣀⠒⠙⠩⠟⣿⣿⣿⣷⣿⣙⣏⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡐⠊⢅⡠⢀⡍⡘⢢⡵⠚⠡⣀⣤⣤⠴⡈⠁⢆⠜⠉⠈⣅⣿⣿⣻⡽⣻⣟⣳⣽⡿⣿⣿⣵⣾⣾⢷⠙⠀⠀⠀⠀⢰⠀⠀⠀⣇⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣸⠐⠠⠀⠄⡙⢶⡨⠐⡁⢆⠷⣿⣿⡟⠛⢹⠿⣟⢾⣿⢯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⠨⠁⠀⠀⠀⢀⡟⣿⣾⣿⣿⢛⡟⣿⣽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⠀⠟⡀⡿⠘⡄⡄⣿⢻⢠⡿⣿⣿⣿⢿⣧⣿⣟⣿⣿⢿⣻⣿⡼⣿⣟⡿⣿⣼⣿⣻⣿⣼⢿⣿⣿⣿⣟⢿⠻⠀⠀⠀⠀⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢻⠷⠿⣿⣧⢍⠀⢂⣝⡱⠿⣿⣽⣻⢿⣿⣶⣿⢿⣿⢿⣿⣿⣽⣿⢾⣽⣿⡿⣟⣻⣽⣻⣿⣿⣯⣿⣿⣷⣿⣟⢿⠻⠙⠉⡆⣾⢡⠟⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣾⢻⡽⠟⢯⡜⡛⣧⣿⣿⣽⢶⡀⠱⢂⠀⣟⡽⣻⢿⣽⣻⣿⣽⡿⣽⣻⣿⣷⣯⣽⢾⣿⣻⣿⣿⡿⣿⡿⣿⣿⣿⣿⢿⡿⢧⣿⣿⣿⣿⣾⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣜⢾⣫⣵⣞⣍⣮⣿⣿⣿⣾⣭⣿⣿⡾⡱⣞⠉⢱⡬⠟⣯⣟⡾⣟⣯⣟⣯⣿⣻⣷⣟⣿⣿⣾⣽⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣫⠿⣛⢷⣟⣿⣿⢷⢊⡱⣵⣎⣿⠜⢯⡳⣟⢿⣮⣟⣽⢾⣻⣽⣿⢯⣿⣾⣻⢷⣿⣯⣿⣟⣻⣿⣷⣾⣿⣿⣽⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⣻⣜⡙⠧⢏⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣯⣟⣿⣿⣏⣿⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠒⠒⠀⠀⠀⠐⠒⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠚⣿⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⡘⠈⠉⢻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡤⢯⣱⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣼⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣰⠏⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⢸⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠉⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠐⠛⡿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀ ⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⣴⣾⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠄⠠⠔⠒⠒⠉⠀⢀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠣⡀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠂⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠄⠂⠁⠁⠀⠀⠈⠉⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠈⠐⡀⠀ ⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠄⠀⠂⠈⠀⠈⠀⠁⠀⠁⠀⠂⠠⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠ ⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⡐⠀⠀⠀⠀⠀⡀⡀⡀⣀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⠀⢰⠒⠉⠑⠢⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⢂⡑⡐⠔⢲⣄⠨⣧⠀⠀⠀ ⠐⠄⠀⠀⠀⠀⠘⠆⡀⠀⠀⣢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡣⠏⠱⠍⢬⠺⣑⠗⠉⠝⠀⠀⠀ ⠀⠈⢂⠀⠀⠀⠀⠀⠈⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣈⣉⡈⣀⢉⠄⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠁⠒⠂⠒⠂⠅⠀⠀⠑⠂⠂⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠐⠉⠁⠉⠂⠂⠒⠐⠂⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⠂⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠆⡤⠐⠀⠀⠀⠀⠀⠛⡖⠒⠒⠂⠒⡹⠃⠀⠀⠀⠀⠀⠀⠒⠒⠒⠤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⡀⣠⠄⠐⠀⠀⠀⠀⠀⢳⠄⠠⠀⡔⠃⠀⠀⠀⠀⠀⠀⠐⠐⠄⡀⠠⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠒⠔⠀⠀⠀⠀⡀⠂⠁⠀⠀⠈⠀⠄⠀⠀⠀⠀⠈⣇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⠦⣀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⠀⠀⠃⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⡀⡀⣈⣁⡀⡀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⢣⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠑⠢⠤⠠⠠⠠⠠⢢⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠈⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠑⠂⢄⠀⠀⣀⣀⡀⡀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢁⠀⠀⠀⠀ ⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠠⠀⠀⠀⠀ ⠢⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⠄⡀⣀⡸⠨⠀⠀⠀⠀⡄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠨⠀⠀⠀⠀ ⠈⡂⠀⠀⠀⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣠⠚⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠱⡄⡀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀

⢏⣮⣛⣽⠿⣳⣿⢯⣾⡳⣿⡮⣝⣽⢯⣟⡿⣿⣿⢿⣿⣯⣿⣿⣿⣯⣿⢻⣽⣟⡴⠙⣵⣼⣯⣿⡷⣽⡿⣯⣵⣿⡼⣾⣛⣾⣞⠷ ⢟⣭⠶⣝⡳⣜⠿⣣⡵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⡿⣿⣼⣛⣧⡙⣲⡝⢟⡻⡹⣌⠷⣫⣵⠻⣧⣜⢻⣮⢗⣯ ⠼⣚⡵⣚⢯⡖⢹⣳⡿⣿⣯⣿⣾⣟⣶⣟⣿⣽⣻⣽⣻⣶⡾⣽⣳⢿⣼⢻⣦⠛⢦⡹⣤⣜⣱⢎⡝⡶⠧⢔⣫⡼⣛⡯⢗⣮⣹⢷ ⢎⣩⣵⠮⣙⣶⡟⣮⢿⣵⢾⡯⣞⣽⣷⢯⣳⣼⢿⣭⢳⣣⢭⣒⢭⡴⢎⡱⢦⡙⢄⠃⢆⡌⡘⠂⡁⣬⣑⠤⢃⣥⢟⣺⡽⢾⣟⣯ ⣎⡜⠳⣍⠳⣽⣺⣟⢖⣹⣵⢻⣦⡝⡷⢎⣹⡾⢻⣾⡬⢠⠁⠚⢣⣌⡔⡁⠤⠐⠡⠶⡡⠅⠈⠜⢂⠌⠢⣘⠰⡉⢶⣿⡷⣟⢾⣿ ⢯⡌⢳⣍⡿⣮⣷⢋⣯⡟⢿⡿⢿⣻⢯⣋⢶⣌⢐⢢⢄⠀⡁⠄⢢⡐⠌⠋⣒⠛⢠⠆⣡⠚⠆⠁⢀⡀⢀⡃⢀⠀⠄⡿⣻⣟⣯⣿ ⢋⣤⣘⡏⡣⢏⢿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣘⠀⠀⢀⠛⡾⠿⣾⢿⣯⣷⣞⡿⣿⣽⢻⣽⣋⢇⠈⠀⠀⡀⠀⠀⠀⠀⡉⣿⣟⣿⣿ ⢏⣭⠦⣿⡿⣿⣿⣽⣿⡿⣿⣿⢿⣵⣿⢗⢫⠛⠻⣿⣾⣽⣿⣟⢿⢷⣾⣽⣿⣞⡿⣽⡽⢻⢭⡜⠌⠀⠀⠀⠀⠀⡀⠀⣇⣽⣿⣿ ⠻⣛⢿⣯⣿⣻⣷⡟⢿⣷⢾⣏⣯⡻⣧⡞⣿⡟⣿⢟⣯⣷⣿⡽⣟⡻⢮⣼⠿⣏⢵⣾⡽⢷⣩⢷⠼⠛⠉⠈⠀⠀⠀⠀⣷⣿⣿⣿ ⠀⠀⡟⣿⣧⣿⣭⣮⣿⡾⢯⣹⣛⡥⡲⡕⢟⣼⣿⡿⢧⡴⢃⡴⠝⢶⣧⣛⢣⢵⣸⢷⣭⣳⣭⡶⡛⣞⡟⣛⣿⠘⠀⠀⠀⣁⣿⣷ ⠀⠀⣿⣶⣶⢿⣇⢷⣹⡶⢿⡇⠷⡆⡉⢆⡾⢷⢱⣹⣆⡸⣷⡈⠎⣰⣰⡸⣆⡸⡾⢱⣸⡿⣸⣿⠿⣿⣾⣏⣿⠀⠀⠀⠀⡏⡹⣿ ⠀⠇⣺⣻⢧⣷⡦⣁⣳⢦⢞⣭⡚⢇⡅⠎⢑⣩⠦⡉⢖⣌⢋⡥⢊⡜⡍⡌⣜⡭⢖⡩⡾⢗⣮⢿⣩⣣⠟⣿⣻⢃⡍⠸⠄⣀⣀⣀ ⠀⡆⣿⡘⣵⡗⣕⡖⡁⢿⣲⢸⡵⢺⢯⠡⢠⠸⢆⡈⠷⢄⠺⣡⠗⢆⢣⣌⡚⢍⡢⣖⣌⢚⣤⠛⡿⣿⣽⢾⢻⡠⢼⢹⠈⠀⠀⠀ ⠀⠀⣇⣎⣊⡹⣗⡔⣭⠘⢭⣿⡜⠶⣋⢱⡡⠔⢂⠌⢃⡡⠆⣁⠰⣣⢆⠌⠢⠐⣡⢢⢎⡱⣜⡿⢼⣪⡿⣎⢛⢲⣻⣿⣿⣿⠻⠀ ⠀⠀⠀⢆⣌⡙⡥⡚⣟⡇⡇⣥⡜⡶⢞⣽⠣⠡⢁⡁⠐⠌⡊⠄⡘⢂⢤⡐⢂⣀⡲⢆⣥⣎⣠⢞⡳⣾⢜⣼⢹⣾⣽⢿⣿⢧⣠⠀ ⠀⠀⠀⠁⡿⡙⢀⢇⢗⣨⢵⣮⣟⣃⢦⣖⢢⢿⢺⡘⠔⠀⠀⢈⠀⠌⠠⡀⠡⢄⡡⢂⣈⠖⣈⠝⢠⡓⢮⣸⡿⢮⣞⣻⣽⣾⢸⠀ ⠀⠀⠀⡆⣟⣿⢿⣙⠣⡔⡽⠇⣡⡓⣄⣹⣗⢙⣿⠴⢀⠁⢈⠀⠂⠂⠉⢀⠨⣐⡐⠸⣅⠢⢌⠑⡤⠛⣬⡟⣾⣺⣼⣞⣞⣇⢸⠈ ⠀⠀⠁⠉⣏⣿⣿⣿⢾⡿⡏⣣⡯⠥⣸⢟⣆⡤⢤⠤⠐⡛⠌⢃⢄⠊⠩⢀⠐⡀⠌⡂⡐⢌⡑⠌⢣⡴⣟⣹⢿⣧⣹⣗⠋⣿⢸⠀ ⠀⠀⠀⢇⣯⣿⣿⣿⢿⡶⣚⣵⠮⡴⣀⠀⠀⠀⠀⠀⠄⢎⡝⠆⡑⢌⠰⠒⠉⠠⠑⢈⠬⡎⠅⡑⢫⣾⢷⣋⠧⣾⢩⣿⡲⣭⢋⠒ ⠀⠀⠀⡄⣷⣿⢿⠝⠀⣭⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡯⡡⢈⠥⢕⠠⠖⠢⡂⠂⠐⢒⠤⣐⡣⣄⡘⠤⠃⣿⢇⣷⢞⡥⣿⢹⡿ ⠀⠀⠀⠀⡀⣇⣰⣱⣧⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡙⠤⠁⣐⠴⠙⢀⠀⠃⠐⠌⡡⠆⠠⠉⠾⣴⢋⠳⣼⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠛⠈⠀⠁⣈⠅⠢⠐⠈⠂⠂⠴⣰⢍⡊⡻⡵⠟⣿⣿⣿⣸⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣀⣀⣶⣶⡽⣭⠣⠉⣀⣄⢡⠌⠉⠛⠿⡿⣰⠭⢛⣛⠏⣿⣿⣿⢸⠀ ⠀⠀⠀⠉⠉⠉⠓⠒⠙⠛⠿⠛⠟⠻⠿⠇⠝⠞⠿⠿⡿⣿⠀⠀⣿⣿⣿⣿⣿⣿⢿⡛⠉⢫⣉⡙⢛⠿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠼

⢄⠀⠤⠤⠄⠄⠀⠠⠀⠀⠀⠀⠀⡂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⢂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠂⠂⠉⠋⠐⠀⠀⠈⢤⠫⠉⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⠁⠀⡀⠀⡀⠀⢀⠀⠂⢲⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤

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⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣦⡀⠀⠀⠀ ⠀⠀⣠⣶⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀ ⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡁⣽⣖ ⡇⠀⠀⢠⣶⣶⣖⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⠰⣿⠛⠆⠐⢆⠀⠃⢠⣤⣤⣤⣤⣴⣦⣦⣤⣬⠁⢸⠙ ⡇⠀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⠀⠀⠀⢈⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⢘ ⡇⠀⡏⢸⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⡏⣿⠀⠀⠀⢸⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸ ⡇⠠⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⣿⠀⠀⠀⠈⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣸ ⡇⠈⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⡄⢸⠭ ⡇⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⣿⠀⠀⠀⠀⠀⡗⢸⣿⣟⣿⣶⣶⣿⣿⣿⣿⠂⢸⢰ ⡇⠀⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⣴⣋⠀⠀⠀⠀⠀⢀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⣿⠀⠀⠀⡀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⠨ ⡇⠀⡇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢀⠀⠀⠀⠀⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣿⠀⠀⠀⠅⠀⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⢐ ⡇⠀⡇⠐⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢨⠈ ⡇⠀⡇⠀⡟⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⣿⠀⠀⠀⡆⠀⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢀ ⡇⠀⡇⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠛⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣿⠀⠀⠀⡇⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡍⢠ ⡇⠀⡇⠀⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⣿⠈⠀⠀⡇⠀⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀ ⠇⠀⠇⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠂⡄⠀⡇⢰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡁⠀ ⠀⠀⠀⠀⠳⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⡛⢛⢛⣛⣛⣛⣻⣿⣟⣛⣛⣛⣛⣃⡻⣿⠀⠃⣴⡇⢨⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣛⣷⢏⣳⡼⣯⡞⢯⣳⣼⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣟⡷⣯⢻⣽⢿⢯⣳⡿⣞⣻⣽⣿ ⡽⢮⣞⡷⣏⢳⣮⢟⣫⡽⢯⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣷⣻⡌⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣷⣻⢻⣽⡿⣞⣻⣾⢿⣯⢷⣻⣷ ⡯⣞⣟⣯⡟⣻⣷⢯⣽⡿⣯⣿⣿⣿⣿⣿⠿⡿⢿⣿⠿⡿⣹⣿⡯⣿⣿⣿⣿⣮⣷⣿⣿⣻⣿⣻⣿⡿⣽⣾⣟⣧⣽⢾⣽⣾⡽⣿ ⢏⣮⣛⣽⠿⣳⣿⢯⣾⡳⣿⡮⣝⣽⢯⣟⡿⣿⣿⢿⣿⣯⣿⣿⣿⣯⣿⢻⣽⣟⡴⠙⣵⣼⣯⣿⡷⣽⡿⣯⣵⣿⡼⣾⣛⣾⣞⠷ ⢟⣭⠶⣝⡳⣜⠿⣣⡵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⡿⣿⣼⣛⣧⡙⣲⡝⢟⡻⡹⣌⠷⣫⣵⠻⣧⣜⢻⣮⢗⣯ ⠼⣚⡵⣚⢯⡖⢹⣳⡿⣿⣯⣿⣾⣟⣶⣟⣿⣽⣻⣽⣻⣶⡾⣽⣳⢿⣼⢻⣦⠛⢦⡹⣤⣜⣱⢎⡝⡶⠧⢔⣫⡼⣛⡯⢗⣮⣹⢷ ⢎⣩⣵⠮⣙⣶⡟⣮⢿⣵⢾⡯⣞⣽⣷⢯⣳⣼⢿⣭⢳⣣⢭⣒⢭⡴⢎⡱⢦⡙⢄⠃⢆⡌⡘⠂⡁⣬⣑⠤⢃⣥⢟⣺⡽⢾⣟⣯ ⣎⡜⠳⣍⠳⣽⣺⣟⢖⣹⣵⢻⣦⡝⡷⢎⣹⡾⢻⣾⡬⢠⠁⠚⢣⣌⡔⡁⠤⠐⠡⠶⡡⠅⠈⠜⢂⠌⠢⣘⠰⡉⢶⣿⡷⣟⢾⣿ ⢯⡌⢳⣍⡿⣮⣷⢋⣯⡟⢿⡿⢿⣻⢯⣋⢶⣌⢐⢢⢄⠀⡁⠄⢢⡐⠌⠋⣒⠛⢠⠆⣡⠚⠆⠁⢀⡀⢀⡃⢀⠀⠄⡿⣻⣟⣯⣿ ⢋⣤⣘⡏⡣⢏⢿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣘⠀⠀⢀⠛⡾⠿⣾⢿⣯⣷⣞⡿⣿⣽⢻⣽⣋⢇⠈⠀⠀⡀⠀⠀⠀⠀⡉⣿⣟⣿⣿ ⢏⣭⠦⣿⡿⣿⣿⣽⣿⡿⣿⣿⢿⣵⣿⢗⢫⠛⠻⣿⣾⣽⣿⣟⢿⢷⣾⣽⣿⣞⡿⣽⡽⢻⢭⡜⠌⠀⠀⠀⠀⠀⡀⠀⣇⣽⣿⣿ ⠻⣛⢿⣯⣿⣻⣷⡟⢿⣷⢾⣏⣯⡻⣧⡞⣿⡟⣿⢟⣯⣷⣿⡽⣟⡻⢮⣼⠿⣏⢵⣾⡽⢷⣩⢷⠼⠛⠉⠈⠀⠀⠀⠀⣷⣿⣿⣿ ⠀⠀⡟⣿⣧⣿⣭⣮⣿⡾⢯⣹⣛⡥⡲⡕⢟⣼⣿⡿⢧⡴⢃⡴⠝⢶⣧⣛⢣⢵⣸⢷⣭⣳⣭⡶⡛⣞⡟⣛⣿⠘⠀⠀⠀⣁⣿⣷ ⠀⠀⣿⣶⣶⢿⣇⢷⣹⡶⢿⡇⠷⡆⡉⢆⡾⢷⢱⣹⣆⡸⣷⡈⠎⣰⣰⡸⣆⡸⡾⢱⣸⡿⣸⣿⠿⣿⣾⣏⣿⠀⠀⠀⠀⡏⡹⣿ ⠀⠇⣺⣻⢧⣷⡦⣁⣳⢦⢞⣭⡚⢇⡅⠎⢑⣩⠦⡉⢖⣌⢋⡥⢊⡜⡍⡌⣜⡭⢖⡩⡾⢗⣮⢿⣩⣣⠟⣿⣻⢃⡍⠸⠄⣀⣀⣀ ⠀⡆⣿⡘⣵⡗⣕⡖⡁⢿⣲⢸⡵⢺⢯⠡⢠⠸⢆⡈⠷⢄⠺⣡⠗⢆⢣⣌⡚⢍⡢⣖⣌⢚⣤⠛⡿⣿⣽⢾⢻⡠⢼⢹⠈⠀⠀⠀ ⠀⠀⣇⣎⣊⡹⣗⡔⣭⠘⢭⣿⡜⠶⣋⢱⡡⠔⢂⠌⢃⡡⠆⣁⠰⣣⢆⠌⠢⠐⣡⢢⢎⡱⣜⡿⢼⣪⡿⣎⢛⢲⣻⣿⣿⣿⠻⠀ ⠀⠀⠀⢆⣌⡙⡥⡚⣟⡇⡇⣥⡜⡶⢞⣽⠣⠡⢁⡁⠐⠌⡊⠄⡘⢂⢤⡐⢂⣀⡲⢆⣥⣎⣠⢞⡳⣾⢜⣼⢹⣾⣽⢿⣿⢧⣠⠀ ⠀⠀⠀⠁⡿⡙⢀⢇⢗⣨⢵⣮⣟⣃⢦⣖⢢⢿⢺⡘⠔⠀⠀⢈⠀⠌⠠⡀⠡⢄⡡⢂⣈⠖⣈⠝⢠⡓⢮⣸⡿⢮⣞⣻⣽⣾⢸⠀ ⠀⠀⠀⡆⣟⣿⢿⣙⠣⡔⡽⠇⣡⡓⣄⣹⣗⢙⣿⠴⢀⠁⢈⠀⠂⠂⠉⢀⠨⣐⡐⠸⣅⠢⢌⠑⡤⠛⣬⡟⣾⣺⣼⣞⣞⣇⢸⠈ ⠀⠀⠁⠉⣏⣿⣿⣿⢾⡿⡏⣣⡯⠥⣸⢟⣆⡤⢤⠤⠐⡛⠌⢃⢄⠊⠩⢀⠐⡀⠌⡂⡐⢌⡑⠌⢣⡴⣟⣹⢿⣧⣹⣗⠋⣿⢸⠀ ⠀⠀⠀⢇⣯⣿⣿⣿⢿⡶⣚⣵⠮⡴⣀⠀⠀⠀⠀⠀⠄⢎⡝⠆⡑⢌⠰⠒⠉⠠⠑⢈⠬⡎⠅⡑⢫⣾⢷⣋⠧⣾⢩⣿⡲⣭⢋⠒ ⠀⠀⠀⡄⣷⣿⢿⠝⠀⣭⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡯⡡⢈⠥⢕⠠⠖⠢⡂⠂⠐⢒⠤⣐⡣⣄⡘⠤⠃⣿⢇⣷⢞⡥⣿⢹⡿ ⠀⠀⠀⠀⡀⣇⣰⣱⣧⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡙⠤⠁⣐⠴⠙⢀⠀⠃⠐⠌⡡⠆⠠⠉⠾⣴⢋⠳⣼⠻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠛⠈⠀⠁⣈⠅⠢⠐⠈⠂⠂⠴⣰⢍⡊⡻⡵⠟⣿⣿⣿⣸⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣀⣀⣶⣶⡽⣭⠣⠉⣀⣄⢡⠌⠉⠛⠿⡿⣰⠭⢛⣛⠏⣿⣿⣿⢸⠀ ⠀⠀⠀⠉⠉⠉⠓⠒⠙⠛⠿⠛⠟⠻⠿⠇⠝⠞⠿⠿⡿⣿⠀⠀⣿⣿⣿⣿⣿⣿⢿⡛⠉⢫⣉⡙⢛⠿⣿⣿⣿⣾⣿⣿⣿⣿⣷⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⡀⡁⠁⢆⠹⣄⠀⠀ ⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⠈⠀⠀⠀⠀⠠⢐⠁⠐⠘⡎⡀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠒⠀⠀⠀⠀⡀⠐⠀⠈⠀⠀⠀⡀⠄⢹⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⣀⠤⢆⡁⠀⠀⠈⡇ ⢸⡇⠀⠀⠀⠀⢀⠄⠁⢀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢣⠀⠀⠀⡇ ⠈⡇⠀⠀⠀⠀⠓⠐⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⣀⠀⠀⠀⠀⠀⢰⠇ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠂⠀⠁⠈⠀⠀⠠⠀⠀⠀⠈⠹⠀⠀⠀⡼⠀ ⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠄⠁⠀⠀⡼⠁⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠐⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⢅⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⠀⣀⣡⣄⣠⠤⠗⡋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⡀⠀⣄⠶⡙⣈⣆⠲⡙⠧⠟⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⠿⠛⠈⠀⣄⠦⠑⠀⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢳⡰⣀⣤⢴⡂⣔⣦⣶⢿⠻⠉⠀⣗⠲⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⠻⣝⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣆⣿⣿⣿⣿⢹⡀⠀⠀⠁⠀⠈⠀⠀⠀⠀⡜⠣⠀⣆⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⠹⠀⠀⡄⠀⢀⠀⠈⠀⠀⠀⠀⠣⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡆⣿⣿⣿⣿⣧⠘⠀⠀⠀⠈⠀⠀⠁⠀⠀⠻⡜⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣤⣤⣤⣤⣤⣀ ⠀⠀⣧⣿⣿⣿⠉⣧⠉⠈⠀⢀⠀⢀⡄⠹⠀⣣⢰⠂⠄⣿⣿⣤⣦⣀⣀⠀⠁⠋⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⠀⣇⣎⠘⠀⠀⠀⠀⣆⢹⠀⠡⢸⠀⣷⣿⢸⠀⠀⠁⠟⣴⣠⠀⠀⡀⣧⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⢸⠙⣄⠀⠀⠀⠀⠀⠀⣆⢻⠀⢹⠃⡇⣿⣻⠀⠀⡗⢺⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⠂⡀⠲⠀⠀⠀⠀⠀⠀⡇⣼⢸⣄⣿⢸⣿⣾⠅⢳⣏⢸⠀⠐⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠠⠀⢹⣿⠀⣿⢻⣿⢼⠅⣿⣴⢀⢄⡙⠗⠈⢀⠸⡿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⣿⣿⣿⠘⠀⠀⠀⣄⠠⡘⢠⡆⣿⣿⠀⣇⣿⣿⢻⡾⢠⠙⠈⠦⠘⢄⣄⠠⢶⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⢻⠀⠀⠀⠁⠍⢯⠟⠿⣿⣿⠿⣿⣿⣿⣿⢀⠀⠀⡄⠱⡀⢥⠿⠛⠞⣤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣴⣤⣥⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⢨⢠⠀⠀⠀⢾⡀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡧⣿⣿⢰⠀⠀⠀⡄⣶⣿⣿⣿⣿⣿⣿⣼⢀⣢⢌⠸⠀⠀⢸⠀⠉⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣾⣞⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣷⠹⠈⠀⡇⢰⡐⡄⢲⢏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⡀⣑⣬⣿⣿⣜⢀⠀⠀⠁⡴⠀⠛⠀⢏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠋⣼⢪⢴⠀⠀⠀⠃⣰⠀⠞⢣⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⡝⢞⣠⠞⠠⠀⠀⠀⠀⣸⠁⡴⢏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣿⢀⠀⠀⠀⠀⠀⠂⣀⠦⡀⠀⠀⠀⠀⠉⠆⢶⢋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠟⠿⣵⣟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⢰⠀⡏⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡎⣯⢀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢰⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠞⢠⠃⡿⣿⢿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢔⡤⠀⠋⣾⣀⣀⣤⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠏⣿⢠⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣦⣶⣿⣿⣿⢿⠿⠻⠛⠉⠈⠀⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠁⠐⡇⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣶⣶⣿⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢻⡰⠀⡁⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣏⣾⠀⠀⡁⣿⢿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⣾⢠⠀⠂⡿⣿⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⣿⣰⠀⠇⣿⣿⣧⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣰⠁⠟⣿⣿⢣⣼⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⡴⢩⠟⣿⣿⣾⢇⣤⡏⣧⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠊⠖⡶⣷⣿⢂⣵⢋⣿⠔⢀⡎⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠤⣀⢀⠉⠚⠄⣠⠋⠟⣴⣫⡰⠀⠋⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠋⠒⠤⣴⣩⠛⡴⢀⠀⠊⢳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣀⢀⠁⠋⠟⡢⣪⣠⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠔⡠⣊⡠⢀⠀⠀⠀⠀⢉⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠃⠤⡡⣚⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠉⠈ ⠀⠀⠀⠀⢇⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣶⣀⣀⠀ ⠀⠀⠀⠀⠀⠸⢆⠛⠘⠀⠀⠀⠀⠀⠀⠀⠃⢣⣿⠾⠀⠀ ⠀⠀⠀⠀⠀⢇⠘⢄⠘⠀⠀⠀⠀⠀⠀⠃⢠⢿⠘⡀⠱⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠈⠁⢰⡏⠂⢠⠀⡎⠀ ⠀⠀⠀⠃⣠⣀⠤⠐⣯⠰⠁⠚⡠⠀⠀⠀⣃⠒⠤⣀⠀⠀ ⠀⠀⠀⡅⠀⢇⠈⠀⡀⠠⣠⠀⠁⠊⠄⠤⢀⠀⠀⠀⠀⠀ ⠃⠚⠀⡠⠏⢀⡀⠩⠙⠈⠉⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣄⣤⣤⣮⠀⡎⢁⡽⣼⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠆⢀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠰⠀⢻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠈⠃⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⣀⢄⡤⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢢⠀⠂⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠟⡷⣯⣷⣟⣾⣻⢿⣷⣞⣻⣷⠿⠛⠈⠀⠉⠟⠿⣽⣿⣟⡷⣽⢿⣯⣽⣿⢾⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⣿⣞⣿⣿⣽⢿⣯⣽⡿⣿⣿⣿⣷⢯⣿⣯⡿⣟⣯⢿⣷⣟⡿⣿⣿⡾⣽⡿⣷⣽⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣽⣾⣿⣯⡷⢿⣯⢷⣻⣽⡾⣽⣻⢷⣾⣟⣿⢾⣻⣿⢯⣽⣻⢾⣽⣾⣟⣿⡷⣻⣷⣿⠸⠀⠀⠀⠀⠀⠀ ⠃⠚⣿⣿⣟⣯⢾⣽⣾⡿⣟⣿⡿⣞⣿⣯⣞⣿⣷⣿⣷⣿⣻⢿⣻⣽⢾⣿⣯⣟⣽⣿⣾⡿⣳⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣿⣼⣦⣿⣟⣯⢷⣾⣿⡷⣯⢷⣻⣿⣳⣿⣾⣿⣿⣟⣻⢿⣷⣯⢷⣻⢾⣽⣻⣿⣳⣿⣿⢩⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⢿⠙⡈⣄⣦⣷⣷⣟⣯⣳⣿⢯⣻⣽⢿⣯⣷⣞⣿⣽⡿⣯⣞⣿⡽⣾⣻⢷⣻⣿⣾⢠⠀⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣶⣿⠛⠉⡅⣿⣽⣾⣿⢳⣿⣿⣽⣿⣯⣷⣿⣯⡟⣽⣿⣯⢻⣽⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⣿⡿⣿⣟⣻⣷⢿⣷⡽⣿⣯⡷⣽⡾⣿⣿⣟⡿⣾⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠞⡤⣀⠀⠉⡀⣄⣦⣿⡿⣳⣽⢾⣿⣯⡽⣾⣻⣿⣼⢀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢈⠀⠁⡼⣀⠀⠀⠻⡀⣷⣽⣻⣷⢿⣯⣳⣿⣞⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣸⣀⢺⠛⠛⠍⣦⣼⡏⣾⣻⣿⡿⣿⣿⡿⣟⣯⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⣹⣿⣿⣿⣿⢻⣿⣾⣟⣿⣼⢀⠛⡀⣿⡿⣞⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣴⣧⣿⢯⣷⣟⣿⠛⠟⢿⠿⣿⣻⣽⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣼⢀⠀⡇⣿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣽⡿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣿⣿⣾⠀⠀⠀⡇⣿⣯⣿⣿⣿⣯⣷⣟⣯⣷⣿⢿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠿⠿⡿⣿⣿⢯⣿⣿⣾⣷⣿⡿⣿⣶⢿⣻⣷⣿⠿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⢷⣿⣿⣿⢿⠀⣇⣿⣿⠹⡀⣷⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣹⠀⡁⣿⣿⣬⠈⡇⣿⢸⡀⣄⣤⣶⣿⣿⣴⣯⠶⠓⠛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣟⣿⣿⣿⣴⠀⡟⣿⣿⢲⡠⡟⣿⢠⠀⠀⠀⠀⡀⣧⡼⢂⡝⣀⣉⣈⣧⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣟⢯⣿⣿⠿⡻⣽⣿⣻⠛⡿⣿⣸⠀⠀⠀⠀⠀⠀⡆⢿⠁⡼⣀⣀⣀⣄⢧⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣽⡿⣳⣿⣽⣾⣿⣯⣷⣿⣾⣿⣾⠀⠀⠀⠀⠀⠀⠀⡇⣸⠃⣼⡠⣀⣄⠦⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣿⣷⣯⣿⡿⣞⣿⣯⣟⣷⡾⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣌⢦⠛⠟⡿⠿⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣼⣟⡼⢿⣧⡟⣧⣿⢿⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⠀⡄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣽⡾⡽⢾⣟⣳⡽⣳⣻⣷⣽⣟⣯⢯⣟⣧⢾⠙⠀⠁⠋⣿⠙⠉⠀⠀⠀⢹⠀⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣻⢷⣳⣟⢳⣻⣳⣽⡟⣳⣿⡽⢯⢷⣫⣽⣞⣿⡀⣀⣦⣿⣠⣇⠸⠀⠀⣄⠤⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡿⣻⣿⡟⣳⡽⢾⣳⡽⣳⣿⡼⣻⡾⣝⡾⣟⣼⠀⠀⠁⢢⠋⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⡄⣿⡟⣭⣻⣳⣿⣳⣼⢻⣾⣛⣿⣰⠀⠀⠀⡀⣄⣶⣿⣿⣾⣤⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⠀⡀⢦⣷⡟⣯⣻⢷⣮⢻⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠛⠉⠉⣻⣝⡿⣟⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣶⠞⠋⢉⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⠿⢿⣿⣶⣤⣀⠉⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣄⣀⣀⣀⣀⣙⣿⠿⠿⠿⢿⣿⣦⣤⣄⠈⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠹⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⣴⣿⣷⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⣀⡼⠿⠛⠁⢀⣤⣤⣤⠀⠀⠀⠀⠀⠈⠉⠛⣿⡿⢿⣿⣿⣿⡿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠁⠀⠀⡉⠀⠀⣠⣶⠿⠛⠁⠉⢷⣄⡀⠀⠀⠀⠀⠀⠈⣷⣶⣽⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣠⣿⡿⠃⠠⣄⣀⣠⡼⠃⣠⣾⠋⠁⠀⠀⠀⢀⡸⠛⠻⣶⣄⡀⠀⠀⢀⠀⠿⠿⠷⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⣰⣿⡿⠻⡆⠀⠉⠉⠁⠀⣴⡉⠁⠀⠀⠀⠀⠀⣸⣿⣦⣤⣬⣿⣿⣶⣿⡿⠀⢠⣶⣦⣾⡿⣿⣿⡇⠀ ⠀⢀⣾⣿⠋⠀⢀⣼⠁⠀⠀⠀⣴⡿⠟⠋⠀⠀⠀⣀⡀⠋⠙⠏⠉⠙⠛⢿⣿⣧⣀⣴⣿⣿⣿⣯⣤⣿⣿⡇⠀ ⢰⣿⡟⡇⠀⠀⠘⠁⠀⠀⠀⣸⣿⠃⠀⠀⠀⢠⣾⡟⠃⠀⠀⠀⣠⣦⣴⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀ ⣾⣿⡄⠀⣴⡆⠀⢠⡄⢠⡾⠟⢛⣀⡄⠀⢠⣿⣿⣦⣤⣴⣦⣾⣿⣿⡿⢡⣾⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣇⠀ ⢸⣿⣧⣀⢻⡇⠀⠀⠀⠉⠀⢰⡿⠿⣿⣶⣿⠋⣸⣿⣿⠟⢿⣙⣿⣿⡿⠋⠙⠿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣦ ⢸⣿⡏⠻⣿⣧⠀⠀⣠⠀⣴⣿⠁⢠⣿⡟⢁⣾⣿⡏⠀⣀⣼⣿⣿⡟⠀⠀⢀⣀⠈⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⢸⣿⡇⠀⠀⠀⠀⢰⣇⣀⣿⣟⣠⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠈⢿⣧⡀⠀⠀⠀⠀⠁⢸⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⢀⣀⣾⣿⠏⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠻⣿⠀⠀⢀⠀⣰⣿⣿⡿⠿⠟⠃⠀⢀⣾⡆⠀⢘⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⢀⣿⣷⡆⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠺⠟⠁⠀⢸⣿⠟⠻⣿⠀⠀⠀⠀⠀⣸⣧⢹⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⠁⣀⣿⣿⣯⠀⠀⢠⡄⠀⠀⠠⠀⠀⠀⠀⠙⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠉⠻⣾⣿⣿⣿⣇⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⡀⢀⣛⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣸⣿⣏⠀⠀⠹⠿⠿⠿⡷⠀⠀⠀⠀⢸⠋⠉⠉⠉⠙⠿⡿⣉⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠙⢿⣷⣄⠀⠀⢀⠀⢰⡄⠀⣰⡿⠃⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠙⢿⣷⣶⣿⣷⣤⣁⣴⣿⠃⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⣿⠿⠿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠛⠤⣤⡆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣄⠀⠀⠈⠇⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠐⣶⣶⠀⠀⠀⢙⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⠀⣈⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣇⣠⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣷⡿⠛⠉⣿⣿⣿⣿⠋⢙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠀⠸⣿⠋⠛⠿⢿⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣾⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠁⠀⠘⠛⠋⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣻⠿⣶⡄⣰⡿⠿⣿⠿⢿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠝⣿⣾⣿⣾⣿⣾⣷⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⣫⡾⣻⣿⣟⣯⢧⣎⢻⣹⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠊⠛⡿⣿⢾⠯⠚⠈ ⠀⠀⠀⠀⠀⠇⢷⢫⣿⣶⣛⢮⣱⣿⢞⣟⡽⡾⣟⠛⠛⠛⠟⠟⠿⠿⣻⣿⣿⣿⢿⣿⡿⣷⣾⣟⣧⣞⣿⣟ ⠀⠀⠀⠀⠀⡇⡏⣏⡲⣽⡷⣏⣿⣣⣽⣿⡶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣷⣾⣟⣷⣯⣳⣼⣛⢧⣥⠾⣿ ⠀⠀⠀⠀⠁⡿⡿⣿⣷⣯⡱⣞⡯⣶⣝⡳⣏⣶⣟⣿⣾⣿⣾⣳⢷⣬⣻⣽⣫⢷⣮⣾⣹⢻⣬⢛⢳⣦⡝⣿ ⠀⠀⠀⠀⡧⣯⣿⡿⣿⣦⢚⢱⢭⡼⡓⠲⣈⣿⣏⢽⣮⣽⣛⢥⡹⣌⠳⣌⡞⢷⣽⢞⣫⠷⣎⠑⡸⢯⡷⣿ ⠀⠀⠀⠀⡄⡾⢿⣯⢲⢭⡌⠐⠁⣊⡑⢫⣟⢁⣯⡑⢿⣎⡙⣢⠵⣌⡹⢦⣁⡼⣎⡷⣌⠲⣍⡲⡙⢞⣠⠀ ⠀⠀⠀⠀⠀⢣⢯⣯⣿⣻⣝⠦⣄⠏⠳⢒⠈⡂⢁⣩⠑⠜⡡⢞⡡⣜⠉⢧⡐⡜⢋⢂⠗⠫⢝⣾⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⣿⣿⠾⣙⣹⢳⢋⣀⠖⡈⢀⠁⠋⠠⡜⠡⡴⢊⡡⢌⠚⡡⠵⠊⣥⠞⡤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⣿⢿⣯⣝⡲⢽⣁⡘⠣⠆⡉⣱⡜⢊⡑⣊⣐⢤⡒⢎⡙⢲⡩⢖⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠛⠿⡿⣿⣿⣞⡹⢿⣂⡰⠃⢙⡮⣙⣷⠞⣙⠷⢋⣰⣇⠌⢭⡧⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⡟⣿⣿⣿⣿⣿⣞⣽⣛⣦⢼⡻⢎⡳⢦⡲⢸⣵⡜⡻⠞⣃⠳⢉⢟⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⡿⣿⣾⣿⣼⣻⢵⣎⡳⢸⣏⠶⢎⣓⠬⢷⡆⡏⣅⠳⣍⣹⠶⠻⣚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣧⢻⣷⣛⣶⣎⡱⡌⡔⣎⢦⣬⣳⢖⡜⢫⣥⣈⣽⠮⣱⡟⢪⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣲⣬⣷⡽⢫⢳⡈⠁⡌⠐⢩⢦⠹⣣⢞⣩⠶⣌⡹⣾⣘⡶⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠦⣑⢮⠹⠏⡋⠔⡪⢖⠤⠓⢫⠒⣉⣽⢎⠳⣜⡏⢀⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⡿⢿⣿⡿⢚⢩⣡⠦⠞⣯⢺⡷⢎⢧⡓⣌⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠋⠛⠽⢿⣿⣿⣿⣿⢿⢮⣙⡚⣝⢧⣋⣤⢳⣈⢉⠳⠙⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣫⣿⢽⣾⣿⣷⣿⣿⣷⣿⣽⣎⡷⣜⣋⢡⡾⣗⢧⣬⡙⠖⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⢿⣯⣞⣱⣾⣟⣻⣳⢦⡸⢍⣴⣭⢂⠸⠖⣊⠴⣚⣱⡽⢮⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡾⢋⣵⡮⠞⠳⣆⣬⢳⢽⠂⣤⠚⢥⡒⢨⠄⣉⣋⡖⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣞⣳⡽⢳⣍⠢⢊⢐⡀⡏⠐⣄⠒⢣⡆⠐⢢⡖⣏⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⠦⣾⡟⠣⢮⢒⣹⣄⠡⡆⠀⠄⠠⢉⣊⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣑⢯⡙⠻⡙⢚⠹⠉⢋⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠚⢉⣙⠻⠟⢏⠙⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⢀⡒⠊⢽⠁⡢⠑⠤⢀⠄⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⠉⠁⡤⠠⢈⡨⠃⠢⡀⢄⠆⡇⢀⠄⢄⠤⢄⣳ ⠀⠀⢀⡠⠔⠒⣉⢉⣀⠀⡴⢄⡁⠜⢱⠪⡑⠄⢅⣆⠀⡀⠘⠀⠅⠂⠀⠀⢸⠁ ⠀⢠⣿⢄⠒⠬⢂⠔⠂⢺⠀⠢⡑⠴⢈⠀⢈⣰⠂⠀⠈⠂⠀⠁⠀⠀⠀⡠⠃⠀ ⣠⠊⠉⢂⠢⣀⠸⠈⠆⢚⡰⠒⠨⠒⢓⡐⠑⠒⠂⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀ ⣇⠤⠀⢀⡓⢠⠖⠒⠒⠈⠡⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠀ ⠙⢆⣀⢈⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠳⣄⣀⠀⠀⣀⣀⡠⠤⠖⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠂⠓⠝⠭⠻⠛⠞⠬⠿⠯⠿⠛⠛⠤⠧⠻⠛⠈⠁⠚⠒⠒⠓⠛⠉⠉⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣟⠀⠁⣧⣿⣽⠧⠂⣿⣿⣿⢻⠪⣟⣿⣿⢋⡛⣹⣘⡊⣗⣿⣿⢼⡺⣿⣿⣿⣿⣿⣿⢿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⡵⣱⣦⣧⣿⠉⠇⣿⣿⣿⣽⣯⣿⣾⣧⣿⣿⢹⣀⢉⡿⣿⣿⣸⣯⣾⣷⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⢮⡿⣿⣹⣷⣿⣿⣩⣿⣾⡼⠀⠀⣿⣿⣤⣄⣿⣿⣾⣫⠟⣿⡾⣥⣾⣶⣤⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣾⢳⠚⣷⣿⣿⣾⣠⠀⠀⠀⡄⣷⢿⠒⣗⣿⣿⣿⣿⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⢀⣏⡟⣿⣿⣿⠀⠀⠀⠀⠀⠇⣃⢠⠀⠇⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠴⢀⡂⣧⣿⣿⣿⢸⠀⠀⠀⠀⡇⠺⠀⡔⢞⣷⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⢀⠀⠗⡄⣿⣿⣿⢸⠀⠀⠀⠀⣿⢠⠀⡀⠀⡃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠌⠄⠀⢄⣿⣿⣿⢸⠀⠀⠀⠀⣺⠀⠀⠧⠿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠪⠀⠁⡏⣿⣿⣿⢸⠀⠀⠀⠀⢷⢹⠉⠉⢏⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣌⡅⣾⣿⣿⣿⢸⠀⠀⠀⠀⡎⣴⣠⣇⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠿⠷⣿⣿⣿⢿⠈⠀⠀⠁⡾⢿⠿⢾⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣭⢀⠀⠀⢀⣿⣿⣿⢹⠀⠀⡿⣴⣄⡐⢒⡿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠼⡀⢁⢠⠉⡿⣿⣿⣿⠀⠀⣿⠐⠀⠀⢀⡊⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠚⠛⠚⠓⠛⠈⠀⣾⢑⠟⡿⡿⡿⣿⣿⣿⣿⠀⠀⣿⣻⠝⠊⠓⠥⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⢹⣾⣠⡇⣽⣇⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⢿⡻⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠧⢂⠁⡷⡠⡟⣷⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⢪⠨⠀⠈⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠜⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣣⠤⠁⢸⢁⣟⣿⣷⣿⣿⣿⣿⣿⣴⡤⣠⣄⣤⣤⣧⣷⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⣋⢟⢿⡟⠿⣾⢀⠀⡄⣯⣾⣽⢗⢀⠀⠀⠀⠀⠀⠀⠁⠊⡟⣫⣿⣿⣿⣿⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣄⣥⣷⣷⣿⣿⠘⠀⠇⣿⢹⡻⡟⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣢⠀⠀⠊⣷⣿⣿⢸⠀⣿⣿⣄⣝⣷⠀⠀⠀⠀⠀⠀⡈⠐⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⡺⣖⣦⢿⠻⠈⠀⠀⠀ ⣸⢲⠀⠠⣧⣿⣿⣿⢸⠇⣿⣾⣓⣿⣗⠀⠀⡀⠀⠀⠀⢀⡂⡷⡋⡿⣿⣿⣿⣿⣿⣿⠘⠀⡜⣤⣤⢿⡿⣿⢸⠀⠀⠀ ⢡⠃⠀⠂⠂⣿⣿⣿⢠⡇⣿⢺⢴⣣⣞⠈⠀⠀⠀⠀⠀⠀⠀⠊⡋⣿⣿⣿⣿⣿⣿⣿⢸⠃⣤⢦⠻⡟⣿⣿⢿⠻⠈⠀ ⡄⠑⠫⠑⡇⣿⣿⣻⠈⡀⣿⠅⢔⠨⠙⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⣿⣿⣿⣿⠋⢯⠻⠙⡟⣷⣾⣿⣽⣯⣿⠹ ⠀⠁⠊⣤⣦⣵⣷⣿⣿⠻⣿⡹⠁⠈⠑⣗⠀⠀⠀⠀⠀⠀⠋⠛⠛⣿⣿⣿⣿⣿⣿⣾⢆⡶⣿⣿⣿⢵⡿⣯⣿⡿⣿⣿ ⠀⡀⡸⠁⠀⠁⠎⣖⣿⣿⣿⣿⡹⢃⠁⣈⢣⠀⠀⠀⠀⠁⣮⣷⣿⣿⣿⣿⣿⣿⣿⢠⠋⡟⣿⣿⣿⣿⣨⣌⣠⣏⣷⣼ ⠀⠀⡆⣳⠘⡀⣄⢂⣯⣿⣿⣿⡿⡘⠀⠑⢁⠹⠀⠀⠀⠁⠿⡿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠾⣠⠀ ⠀⠀⠀⢣⠓⠀⡀⠁⣖⣷⣿⣿⣿⣿⠀⠐⣹⣋⢻⠙⠈⠁⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣇⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⢢⠍⠰⠄⠀⣩⣿⣿⣿⣿⢿⢻⡶⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣯⣿⣿⣿⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣲⣭⣎⣗⣯⢙⠩⣿⣿⣿⢿⣷⣀⠀⠀⣿⣿⣿⡓⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⣏⣿⣰⣮⢎⣁⠉⠛⠓⡿⣿⢩⠑⡛⣿⣿⣿⣿⣝⣶⣠⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣾⡗⣾⣠⣖⣤⣆⣾⣿⣿⣄⣾⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣭⣦⢙⠁⠰⡾⡴⠀⡧⣿⡀⠀⡇⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠊⢁⣄⠎⣷⡟⢋⠉⠋⡟⣻⠟⡿⢻⣝⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣗⣺⠣⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⡟⡌⠈⠀⣍⣯⣿⣿⣿⣴⡝⣿⣿⣿⣿⣿⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣻⣷⢰⡀⣤⣧⣷⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⣿⣿⣿⣼⠽⠗⠸⠈⠀⠀⠀⡝⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⡀⢤⠿⡿⢯⠿⠿⣿⣿⣿⣼⣠⠀⡀⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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