Crying Face Dot Art

⠀⠀⠀⠀⢀⣞⣵⡕⢋⡥⣾⢛⡞⠀⠀⠈⢷⢸⢻⡄⢿⡄⢳⠘⡌⡄⢳⠀⠀⠀ ⠀⠀⠀⠀⣾⢟⣏⢴⣿⡼⠃⡟⠀⠀⠀⣇⠘⣇⡄⢻⣄⢿⡌⣧⠸⡘⡜⡄⠀⠀ ⠀⠀⠀⠀⡡⢺⡟⡼⣹⢡⣶⡷⠶⠶⢶⡇⠀⠙⣧⣤⣽⣀⢳⡹⣧⡜⣮⣇⠀⠀ ⠀⠀⠀⠀⢸⠾⣇⠁⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠹⢿⡇⢹⣿⣼⡛⠄⠀ ⠀⠀⠀⠀⢸⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡈⠓⠄⠀ ⠀⠀⠀⠀⡏⡧⣀⡄⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⡀⣸⠋⠀⠀⠀ ⠀⠀⠀⠌⠸⢱⣿⣿⡄⠀⠀⠀⠀⠀⠘⠂⠐⠇⠀⠀⠀⠀⠀⢠⡫⢿⠀⠀⠀⠀ ⠤⠴⠿⢿⠟⠉⠟⠟⡇⢄⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⣰⣿⣧⠿⠷⠶⠤⠤ ⠀⠀⢀⠁⠀⠈⠢⠀⢀⠀⠱⣖⠢⠠⢀⠠⢐⠕⣤⣤⠔⠸⠋⠀⠉⠳⡄⠀⠀⠀

⠀⣗⡠⠂⠀⠀⠀⠀⢀⠔⠡⠀⠀⠀⠀⢃⠀⠑⡀⠀⠀⠀⠀⠑⡀⠘⡇⠀⠀⠁ ⠀⠼⡑⠀⠑⠁⠀⡠⠋⠀⡠⠄⠀⠀⠀⡘⠀⡧⡸⡀⠀⠀⠀⠐⡱⡀⠣⠀⠈⠀ ⠀⠃⢀⠎⠀⠀⡔⠁⢀⠚⠀⠐⠀⠀⠀⢀⡇⡇⠈⠻⡄⠀⠀⠀⠰⣡⠘⡄⡢⠀ ⠀⢠⡿⠄⠀⡜⠀⡔⢁⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠈⢢⡄⠀⠀⢡⠆⢣⡇⠀ ⠀⢹⡇⠀⡘⢀⠌⠀⣀⣳⣄⣀⣀⡡⠀⠀⢸⣄⣀⣠⣴⣋⠈⠢⡀⠀⡆⢸⣷⠀ ⠀⣿⡇⢠⠀⡎⢠⡞⣯⣿⣿⣿⣧⢀⠱⡀⢸⣅⣴⣿⣿⣿⡻⣦⠑⡀⢰⢸⡟⡀ ⢰⠙⡇⠀⠘⡇⣿⢨⣼⣿⣿⣷⠇⠡⠖⠑⡀⡇⢡⣾⣿⣿⣧⢹⡄⡗⡈⢸⡇⢁ ⣷⣾⣿⠀⠘⡇⠻⡜⢖⠭⢟⡒⠁⠀⠀⠀⠘⠃⠛⡢⠭⢝⠎⡾⠀⡇⡄⣾⣿⣶ ⣿⣿⣿⣾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠤⠀⠤⠠⠤⠤⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢀⡀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⡨⢝⡙⢅⡐⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⡾⡝⡞⠁⠀⢻⡑⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⣿⡿⢡⣇⢀⡠⢬⣗⠹⠻⣿⡗⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣧⡧⣿⢣⡼⡗⠖⠒⡢⡋⣆⡞⠨⣷⣷⠎⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⣸⣿⡟⢟⠓⠰⠀⠀⠀⠀⠚⠀⠀⢸⠁⠀⠀⠀⠘⠖⢄⠀⠀⠀⠀⠀ ⠀⣰⢿⡇⣿⡿⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠿⠛⣷⣄⠀⠀⠀ ⡼⠃⢸⣟⣿⡇⢱⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠐⠀⡿⡎⢧⡀⠀ ⣧⠀⠰⣟⣇⣿⠀⢆⠀⠀⠀⢀⢤⣀⣀⣀⣴⣶⣶⣂⢄⠀⠀⠀⠸⠁⡇⠸⠏⢢ ⣿⣷⣥⡀⠸⢿⡆⢰⠀⠀⣴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⢀⠃⢀⠀⡘⠀⠀ ⣿⣿⡿⡟⢷⢾⣷⡈⢂⠀⡟⢹⠁⠀⠀⣇⡄⢱⡾⡆⠙⡄⡇⡈⠀⣼⡔⠀⠀⠀ ⣿⡿⠉⠀⠘⠎⣿⣷⡀⢂⠑⡘⢆⠀⠀⡽⡀⢾⠇⣄⠜⠔⡐⢁⣼⡿⠀⠀⠀⠀ ⣿⠃⡠⢴⣲⠶⠛⣹⡏⢢⣂⠈⠂⠄⠀⠀⠀⠀⠀⠐⢀⠔⡠⠂⣿⠇⠀⠀⠀⠀ ⣿⡔⢠⠋⠀⠀⠚⢹⣷⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠠⡢⠚⠀⠀⣏⠊⠀⠀⠀⠀ ⢹⠀⠆⠀⠄⠀⡠⠊⢸⡀⠀⠀⠀⠁⠂⠤⠤⠄⠒⠁⠀⠀⠀⢠⠃⠀⢀⡀⠤⠄ ⠈⠄⣄⠌⠀⠘⠀⡠⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⡶⠋⠁⠀⠀⠀

⡁⠀⣠⠂⠀⠀⠀⠀⣰⢡⠊⠥⡆⡘⢿⣧⠀⠀⣿⣼⡄⠀⢸⠹⣦⣻⣿⣿⢿⣿ ⣵⣾⣿⠀⠀⣰⠀⢠⣿⡞⠛⡲⣴⣧⠘⣾⣄⠀⡗⠈⣧⡀⣘⡕⢘⣹⢿⣯⣽⣿ ⣿⣿⠇⠀⢰⠵⠀⡼⠿⢀⣿⣿⠜⠣⢀⡿⢸⣦⠟⣹⣿⡍⠙⢿⡜⡿⡾⢱⣿⣿ ⣿⣿⠁⠠⠊⢦⠞⢀⣿⡎⠂⠋⠀⠀⠀⠁⠈⠄⡀⡿⣿⠟⠀⢸⢹⡇⣿⣶⣿⣿ ⣿⣿⠇⡇⢠⡇⠀⣾⣧⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⠖⠠⢅⡾⡇⣿⣿⣿⣿ ⡏⡟⢸⠇⢸⡄⠀⣿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡌⡼⢡⣷⠋⢀⣼⣿ ⢀⡇⣾⠐⡞⠉⠑⢹⣿⢃⠀⢠⣤⠄⢀⠀⠀⠀⠀⠔⠍⠁⣱⢁⣜⣇⣴⠾⢛⣿ ⠈⢿⣿⠈⠀⠀⠀⠈⡿⡼⡄⠀⠀⠈⠲⠇⠀⠀⠀⡎⠀⣸⣼⣿⡿⠛⠁⣠⣾⣿ ⠀⠀⠩⢄⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⢠⢎⠌⠀⠀⠏⠁⠁⠀⢀⣶⣿⣿⣿

⠀⠀⠀⠠⢁⡃⢃⠜⠁⡜⡈⠁⢀⠉⢳⠈⢃⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣦⡟⢡⠂⢀⣮⡡⠵⠀⠖⠠⠁⣧⣸⡄⠀⠟⡆⠀⠀⠀⠀⠀⠀ ⠀⠂⠉⢿⡏⣠⠴⣿⣶⡤⣄⡓⠀⢠⠴⣾⣿⢷⡄⡀⠻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢳⡋⠀⢿⣿⡣⡙⠁⠀⠀⠘⣿⣻⢀⠁⣿⡄⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⡤⣽⡆⠁⠀⠀⠁⠀⠀⠀⠀⠀⠊⡾⡄⡟⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⡆⠙⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⢹⡗⢦⡌⠀⠀⠀⠀⠀ ⢠⠴⡪⣇⠡⢤⠎⠢⡀⠀⠀⠀⠀⠀⠀⢂⠜⠁⡺⠰⠀⠟⡄⠀⠀⠀⠀ ⠸⣷⠀⡇⣑⢍⠀⡀⡍⠐⠄⡀⢀⠠⠂⠩⣄⢠⠟⡀⡄⢌⣅⠀⠀⠀⠀ ⠀⠨⡠⡟⣗⣤⠋⠁⡇⠀⠀⠀⠀⠀⠀⠸⠡⠻⠌⡪⢋⡏⢸⡆⠀⠠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⢀⡀⠀⠀⠀ ⠀⠀⡆⠀⠀⢠⠎⠀⢁⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡇⠨⡄⢸⢡⠀⠀⠀ ⠀⠀⠀⡀⢔⣋⡀⢀⣈⣤⣧⠀⡄⠀⠀⠀⢰⠀⠸⠀⡈⠰⠀⣧⢣⠀⠀ ⠀⢸⢈⠔⠁⠀⠀⠀⠀⠱⡇⠆⠱⠠⠠⠀⠘⣐⠃⢦⠇⣀⠡⢡⢹⠀⠀ ⠀⣘⣁⣤⣄⣐⣂⣠⣄⡀⠙⡈⢴⣥⣣⣳⣄⢇⢠⡏⠀⠀⠀⠑⣏⠀⠀ ⠀⠈⠃⢻⢿⡿⣉⡍⠛⠢⠀⠑⠀⠙⢮⠪⢙⣻⢧⣤⣤⣤⣤⣰⡏⠁⠀ ⠀⠀⢀⢄⠉⠁⠉⠀⠀⠐⠀⡀⠄⠈⠀⠀⠀⠀⠸⣿⠿⢦⣄⠏⣇⢠⠇ ⠀⢰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⠁⡜⠀ ⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⠃⠸⢰⠁⠀ ⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣦⠇⠀⠀ ⣇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢰⡍⠀⠀⠀ ⠘⢆⠀⢻⣷⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⡾⠀⠀⠀⠀ ⠀⠈⢦⠈⣏⣷⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⡿⠁⢀⠜⠀⠀ ⠀⠀⠀⠳⣼⣿⣿⣿⡧⡑⠠⡀⠀⢀⡀⠄⠂⣉⠤⣺⡟⠁⠔⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠀⠀⠈⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⠀⠀⠠⠤⠄⣀⠀⢠⠆⢀⡤⠒⠂⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠠⠔⠢⠄⠀⠀⡀⠀⠀⠔⠋⢁⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⢀⣤⠶⢦⣤⣑⠲⢄⠃⠀⡠⣔⣾⣵⣶⣤⡀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠁⠢⢤⣈⡙⢷⡔⠲⢊⡴⠛⠥⠔⠂⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣠⣎⣓⣒⣒⣖⡇⠀⠻⡠⣾⠿⠿⣷⠖⢲⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠘⡍⠓⠐⠒⠉⠀⠀⠀⠣⠀⠉⠉⠁⢠⠋⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡃⠀⡘⡀⠀⣰⡔⠀⠀⠀⣀⡢⣆⠀⠀⠎⣇⣠⢞⠒⠢⠤⣀⡀⠀ ⠀⠀⣠⠴⠺⣿⣦⡁⡔⡾⠉⠙⠳⠠⠚⠛⠀⠙⡆⢸⢠⣿⡟⠓⢦⠀⠀⠀⠙⠦ ⠖⠋⠀⠀⠈⠙⣽⣷⡇⢧⣠⣖⠒⠒⢒⣒⣒⢼⠁⢣⣬⠿⡇⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⠸⣷⡈⣿⡟⠿⣿⣿⠿⣿⢻⠀⣸⢯⣡⠇⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⣽⣷⣻⣿⠀⠘⠃⢠⡿⡸⣬⡿⠋⢁⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⡪⣍⠉⢉⣉⠴⣿⡟⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣧⣩⣭⢥⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⡿⠸⢉⠃⠀⠀⢰⠀⢀⣧⢃⢸⠀⠀⠀⣼⢰⠀⠈⢂⠐⣇⢦⡀⢸⠀⠀⠈⠀ ⠀⢀⠇⢸⠀⠀⡆⢸⡀⣿⢻⣸⡌⠀⠀⢠⣿⣿⢠⡐⡜⠀⡏⣸⣷⣸⡆⠀⠀⠀ ⠀⠸⠀⠸⣠⠀⣧⢻⢳⡗⠸⣿⣷⣄⠀⣿⣿⣿⣾⠀⠸⣶⠙⣿⠛⣿⡇⠀⠀⢀ ⠀⠀⠀⠀⣿⡀⣿⢿⠀⣃⡀⢹⢻⣿⣾⣿⡟⠿⠃⢀⣀⣏⣀⢸⠐⣿⡇⠀⠀⢸ ⠀⠀⠀⠀⠘⢻⣿⡴⠛⠉⠛⠓⠮⠙⢿⠏⠀⠈⠞⠛⠉⠉⠛⠁⠀⢹⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⡇⢸⣤⣿ ⠀⠀⢇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣺⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣠⠤⣲⣤⠀⠀⠀⠞⢫⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠢⣀⠀⠘⠯⠍⠉⠁⠤⠜⠀⢀⡠⠀⢩⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀ ⠀⢀⣿⡿⠁⠀⠘⠳⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠶⠃⠀⠀⢻⣿⡆⠀ ⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀ ⠀⣿⡿⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⣼⠏⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⣿⠀⠈⢿⢿⣷⡄⠀⠀⠀⠀⢸⣿⡇ ⠸⣿⣇⠀⠀⠀⠀⠀⠙⢁⡏⠀⢀⣿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢹⡇⠀⢸⡏⠉⠁⠀⠀⠀⠀⢸⣿⡇ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⣼⣿⠃ ⠀⢹⣿⡇⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇⠀⠀⠀⢀⠖⠉⠁⠀⠉⠓⣄⠀⠀⠀⠀⣷⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⡿⠀ ⠀⠀⢿⣿⡄⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣼⡆⠀⠀⠀⣿⠀⠀⢿⡆⠀⠀⠀⢀⣾⣿⠃⠀ ⠀⠀⠘⢿⣿⣄⠀⠀⢠⣿⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⢀⣾⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣿⣦⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⠀⠀⢸⡇⠀⣠⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣼⡇⠀⠀⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣿⠀⠀⢸⣧⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⣿⠇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡶⠶⠟⠋⠀⠀⠀⠈⠻⣦⣤⣀⣤⣤⣤⠴⠶⢶⣤⣤⣀⣠⣴⠟⠁⠀⠀⠀⠈⠛⠷⠶⣤⣄⠀⠀⠀ ⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣤⣤⣬⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣤⣴⠶⠛⠋⠉⠁⠉⠻⣦⣄⡀⠀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡜⠁⡰⠃⠀⠀⠀⡴⠉⢀⠎⡾⠋⢀⣴⣿⠃⠀⣰⡟⠁⣼⠆⠀⠀⠙⡆⠀⠇⠀⢇⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⣠⢿⢡⠂⣜⠞⠀⣠⠇⠆⠀⠀⣰⠁⢀⠏⡼⠁⢠⡟⢡⠃⠀⡜⡿⠀⢰⣿⠀⠀⠀⠀⡇⠀⡀⡇⠸⡀⠀⠘⡄⠀ ⠀⠀⠀⠀⢠⠃⣧⠏⢸⠏⠀⣰⡟⡼⠀⠀⢠⠃⠀⡞⣼⠃⣠⣟⣀⠆⢀⣮⣼⠁⢠⢿⡏⠀⠀⣸⢸⡇⠀⡇⠃⠀⡇⠀⠀⣷⠀ ⠀⠀⠀⢀⡿⢸⡘⢠⠋⠀⢠⣿⢃⠃⠀⢀⡟⠀⡼⣰⠇⡴⣉⣩⠍⣴⣭⣽⠇⢠⠃⢸⡇⠀⢀⣇⣇⡇⢸⡇⡆⠀⡇⠀⠀⢿⡆ ⠀⠀⠀⣸⡇⢸⡷⠁⠀⣠⣿⢟⣾⠀⠀⡎⡁⢠⣷⣵⡞⢛⣿⣿⣾⣿⡟⢻⢠⠃⠀⢸⠀⢀⣾⣿⠀⡇⡾⣧⡇⠀⡇⠀⠀⣯⢣ ⠀⠀⠀⡿⡇⡜⠁⠀⡰⢟⡟⢸⣿⠀⢸⠀⣇⣾⡇⠘⡆⠈⠀⢀⣈⡭⠥⣿⠁⠀⢀⡟⢠⢫⡟⢻⣿⣿⣄⣾⡇⢀⡇⠸⠀⡿⣾ ⠀⠀⠀⢃⡟⠀⠀⡴⢁⣾⠃⠘⣿⠀⣾⠀⠿⢻⡀⠈⡷⢤⠀⢸⠉⠓⠼⠃⠀⠀⢼⣧⠋⡎⠀⢿⡻⢿⣛⣿⠇⡘⡇⡀⢰⠁⡿ ⠀⠀⢀⠏⠀⢀⡜⠀⣼⣿⠀⣴⣿⡇⣿⡀⠸⠈⠀⢀⠁⠀⠀⡎⠀⠀⠀⠀⠀⠀⠘⠁⠀⣥⠀⠀⢱⣤⣬⠟⣰⣷⣧⣧⠏⢀⠇ ⠀⢀⡎⠀⢀⡞⠀⣰⡏⠀⠸⣇⡿⡽⣿⣇⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡼⠛⢀⣿⣿⣿⣿⠏⠀⠘⠀ ⠀⣼⠃⣰⠏⠀⢠⢻⠁⢸⡟⣌⣷⠀⢹⡿⠾⠀⠂⡟⢣⠀⢠⡴⠒⠊⠉⠁⠒⠂⠤⣀⡀⠀⠀⢠⠁⠀⢸⡿⣠⢏⡏⠀⠀⠀⠀ ⢰⠃⢠⠏⠀⣶⡏⠀⠀⢸⠃⠘⣿⣤⡞⢁⠇⠀⡄⡇⠀⣄⣮⣴⣶⣿⣿⣿⣿⣶⣦⣤⣀⣱⠀⡈⠀⠀⣾⢱⣇⢸⣡⠀⠀⠀⠀ ⡟⠀⣼⠀⠀⣿⡇⠀⠀⠈⣆⡤⢋⠞⠀⡞⠀⢠⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣏⣠⡟⠀⠀⠀⢀⢿⡸⠈⣦⣿⠀⠀⠀⠀ ⠀⢰⣿⠀⠀⢿⠁⠀⠀⡴⠁⠀⡎⠀⢠⡇⠀⢸⠀⠀⠀⡟⠁⠀⠀⠈⠉⠉⠛⠿⠿⣿⣿⠃⠀⠀⢀⡼⣸⠃⠀⠈⣿⠀⠀⠀⠀ ⠀⡞⣿⡄⠀⠸⣶⠀⠀⢡⠀⠀⢧⠀⠈⣧⠀⠘⣤⠀⠀⡿⠶⠶⠒⠂⠤⠤⢀⣈⡉⢹⠏⠀⢀⡴⠋⣱⣃⠀⢰⠀⡿⠀⠀⠀⠀ ⠀⡇⢸⣧⠀⠀⢹⣇⠀⠈⡆⠀⠸⡄⠀⢸⠀⠀⠹⡇⢠⣹⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⣠⠔⢋⠵⠚⠁⠀⠀⢸⢀⠃⠀⠀⠀⠀ ⡀⢳⠈⡿⣧⠀⠀⢿⡄⠀⢰⠀⠀⢧⠀⠀⠁⠀⠀⠀⠀⠀⡧⣤⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀ ⢧⠈⡆⠱⡜⣧⡀⠈⢻⡄⠘⣄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠰⣌⠉⠒⠤⣤⠊⠁⠃⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣆⢸⡔⠛⢎⠻⣦⡀⠹⢆⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠄⢠⡇⠀⠀⠀⠀⠀⣀⣀⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠙⣆⠳⣄⠘⣷⢮⣿⣦⡈⠣⡸⣿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠏⢣⣠⣤⣄⣴⠛⠉⠻⠟⠉⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠧⠘⡗⢯⣧⣉⠛⢿⠦⡙⣿⡀⠑⢄⡀⠀⠀⠀⢀⣠⠴⠓⡦⠀⢻⡁⠀⠙⠋⠀⠀⠀⢘⡄⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠻⣷⡀⠀⢀⣰⠛⠺⠳⣼⠈⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⠀⢈⡇⠰⠈⢯⣀⠀⠀⠈⠳⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⢺⣧⠀⠀⢦⠈⠳⢄⡀⣠⡌⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣃⣀⣀⠀⢠⠞⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣿⠀⠀⠸⡄⠀⠀⣏⠁⠘⢆⢣⠀⠀⠀⠀⠀ ⠀⠀⢰⡿⠁⢀⠟⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢠⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡟⢧⡀⠀⢣⠀⠀⠸⡄⠀⠈⢳⣷⡀⠀⠀⠀ ⠀⢀⡏⠣⠤⠏⢀⠎⠀⠀⠀⠀⢠⡾⠁⠀⠠⡇⠀⢸⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⢿⣦⣇⠀⢳⡀⢸⣆⠀⠀⢧⠀⠀⠀⠻⣷⡀⠀⠀ ⠀⣸⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⢧⠀⠸⠀⢱⣤⣾⠁⠀⠀⠀⠀⠀⠈⡇⡏⠉⠉⢻⠙⠙⣄⠀⢸⡀⠀⠀⠀⢹⣧⡀⠀ ⠀⡎⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡟⠀⠀⢠⣇⠸⡦⡖⠒⠉⣇⠈⢧⠀⠀⠀⠀⠀⠀⢹⡥⠂⣀⣤⣿⡀⠘⡄⠀⡇⠀⠀⠀⠈⡟⢷⡀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⣹⣧⣀⣀⣈⣇⠘⡷⡄⠀⠀⠀⠀⢸⢰⣿⣿⣿⣛⠻⣷⣼⡄⡇⠀⠀⠀⠀⠷⠀⠁ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇⠀⢰⢁⣤⣾⣿⣿⣿⣿⣻⠿⣆⢣⠘⢦⡐⣆⠀⠈⡄⢻⠁⢀⣿⣷⡈⢿⣷⡷⠀⠀⢸⠀⢰⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⢠⣧⣾⡿⢹⠋⠀⢸⣿⣿⣷⡌⠻⠀⠀⠙⢮⣷⣄⡇⢿⣿⣿⣿⣿⣿⠘⠁⣇⠀⠀⣼⡆⠀⠀⠀ ⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡿⢹⡿⠀⢸⣶⣾⣿⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠛⠶⠟⠀⠀⡿⠀⣠⠇⢳⠀⠀⠀ ⠀⠀⠀⡆⢸⡀⢳⠀⠀⠀⠀⠀⠀⢹⡜⠿⠀⠸⣿⣿⣯⠟⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⡇⠸⣇⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢣⠀⣿⣆⠀⢡⣀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠘⣦⡿⣟⢧⠀⢯⠓⠤⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⣤⠤⠤⠤⠀⠀⡀⢤⣤⡀⠀⠀⠀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⡇⠙⠶⣷⣌⢇⠀⠀⠉⠑⠒⠒⠛⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠄⠀⣠⠾⣧⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠈⠉⠛⠒⠒⠒⠛⠳⢤⣀⠀⠀⠀⢾⣤⣄⣀⣀⠤⠖⠒⠒⠋⠉⠁⢀⣠⠞⠁⠀⢸⡄⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠛⡏⠒⠢⠤⣀⣀⣀⣀⣀⣀⣀⡀⢤⣴⣾⣯⣀⠀⢀⣨⠏⠘⢆⡙⡄⠀⠀⠀⠀ ⠿⠶⠄⠀⠀⠀⡾⣇⠀⠀⢀⣀⠀⠀⠀⣀⣾⠋⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢹⢧⡀⠀⠀⠀⠀⠉⠻⣿⠙⠫⡀⠀⠀⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⣹⣆⠀⠈⠟⢷⣤⣴⠟⠁⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠑⣄⡀⠀⠀⠀⠀⠹⣧⡀⠈⢢⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣼⡇⡇⣾⣿⡤⣼⡡⣤⣧⡾⠔⠊⡇⠀⠀⠀⡃⠠⠃⠃⠀⠻⣽⡒⠾⣶⠾⡾⢿⢦⡬⣷⠀⠀⠈⢸⠀⠀⠸⡇⢹⡄⢰ ⠀⠀⠀⠀⠀⡀⡟⡇⡇⣯⠇⡇⡇⠀⠀⢱⠃⠀⠀⢰⠀⡀⠀⡇⠀⣤⠀⠀⠀⠹⣇⠀⠈⢆⢳⠈⢧⠱⣻⣇⠀⢰⠀⠀⠀⠀⡇⢺⢣⠘ ⠀⡄⠀⠀⡜⠀⡇⢰⡷⢿⠀⢹⠀⠀⠀⠸⠀⠀⠀⠀⢣⢰⡀⡇⠀⢹⡄⠀⠀⠀⠘⠂⠀⠀⠻⡆⠈⢧⢹⠹⡀⡼⠀⡇⢀⠀⡇⢸⠘⣄ ⠀⡇⠀⢰⠁⡄⡇⠈⣇⣿⠀⠈⠀⠀⠀⢀⠤⠤⠔⠀⠈⢻⣧⢸⠀⢹⢷⠀⠀⠐⠒⠀⠤⠄⠀⠀⠀⠀⢻⡇⣇⠇⠀⡇⢸⠀⣧⢸⠀⢻ ⠀⡇⠀⣸⠀⣇⣇⠀⢻⣿⠶⠶⢶⣶⠶⣶⣶⣶⡞⠃⠀⠀⠻⣿⡆⢸⠸⡄⠀⠚⢻⠿⠻⣶⣶⣶⡶⠶⠶⡇⡿⠀⠀⡇⡌⠀⣿⡾⠀⠈ ⠀⡇⠀⣿⠀⢹⡽⠸⣼⣿⠀⠀⣿⣀⣰⣿⡿⣿⡇⠀⠀⠀⠀⠀⠻⡈⡇⠀⠀⠀⣼⣤⣼⣿⣿⣿⣷⠀⢸⣵⠃⠀⢰⢡⠃⢸⣿⡇⠀⠀ ⠀⢣⠀⣿⡇⢸⢳⠀⢽⣿⠀⠀⢻⣿⣟⠿⢗⣛⠃⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⢹⣿⣜⠿⣯⠿⠇⠀⣿⠏⠀⣴⣿⣾⠀⣾⣿⠁⠀⠀ ⠀⢸⣄⣿⣷⢸⠈⢧⠸⣿⢧⠀⠈⠿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠛⠛⠛⠿⠀⡼⣻⠀⣼⣟⠏⢸⣸⣿⣿⠀⠀⠀ ⠀⠀⠙⠛⠛⢻⠀⠈⣧⣿⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣿⣿⠀⣷⠋⠈⠉⠀⠀⠀ ⠀⡀⠩⠉⣮⣿⠀⠀⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⡿⠈⡿⠶⢶⠶⡆⠀⠀ ⠀⠩⡿⠯⠿⣿⠀⠀⢹⠸⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⡿⠀⠀⡇⢸⡿⠿⢾⠶⠟⠀⠀ ⠀⠓⡒⠒⠒⢻⠀⠀⢸⠀⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢸⠀⢸⠗⠒⠒⠒⠒⠀⠀ ⢰⣶⣶⣶⣖⣾⢰⠀⠈⡆⢸⣄⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⡎⢀⢸⣀⣀⣀⣀⣀⣀⠀ ⢸⣿⣿⣿⣿⣇⣿⠀⠀⣷⡈⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡇⢰⣾⠁⡜⣾⣿⣿⣿⣿⣿⣿⡆ ⢸⠿⢿⠿⠿⢿⣿⡄⠀⢸⣧⢹⠿⠿⢿⣿⣿⣷⣦⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⢤⣶⣿⣿⣿⣿⣿⣿⢃⣿⡟⢀⠃⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢰⠀⠀⠀⠀⢻⡆⠹⡆⠀⠀⠀⠀⠆⠀ ⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣷⠀⠀⠈⡆⡀⠀⠀⠘⣷⠀⢳⠀⠀⠀⠀⠀⢀ ⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⣼⢰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢻⣇⠀⠀⣿⡹⡀⠀⠀⢹⠀⠘⡀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⣿⠀⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⣻⠀⡞⣶⠀⢼⣿⡆⠀⣿⣧⣷⡀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⡼⠂⢻⡄⠀⠇⠀⠀⠀⠀⠀⢀⣿⢰⠀⢹⡄⠈⡿⣷⠀⡟⠸⣿⡏⠀⠀⣇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠀⢀⡠⣴⣿⠊⢉⣏⠀⡇⠘⣇⠀⠸⠀⠀⠀⠀⢠⣿⣿⣿⠀⠈⣧⠀⡇⣟⡀⠁⠀⡏⠰⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠁⠀⡸⢸⠀⠸⡏⠀⢱⡆⢹⡆⠀⠀⠀⠀⢀⣿⣿⢻⠏⠀⠀⢿⣻⣿⣽⣿⣧⣤⣇⣀⠀⠠⠃⡆⠀⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣇⠈⡆⢰⣿⣀⣘⢃⠈⡟⣆⠀⡀⠀⣼⣿⠇⠏⠀⠀⢠⣾⢿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣄⡟⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢿⣆⢀⣿⣶⣿⣿⣿⣿⣿⣿⣦⡈⠈⢧⣧⣰⢣⠏⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⠿⢿⣿⠉⢻⣷⡇⠀⡇⠀⠀⠀ ⡀⢦⡀⠀⠀⢸⣿⠈⣿⡿⠛⣿⣿⡿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠤⡠⡀⠰⠋⡴⠁⣾⡇⠀⢇⠀⠀⠀ ⡇⠘⣧⠀⠀⠈⣿⡟⢻⡀⠀⠻⠉⠁⣠⠄⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣰⠇⡇⠀⠘⡄⠀⠀ ⠘⣄⣿⣧⠀⠀⣿⣷⡄⠉⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⡃⠀⠀⠸⡀⠀ ⠀⠈⠛⣯⢆⠀⢿⠙⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡟⣄ ⠀⠀⠀⠘⣮⡧⡸⡇⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡆⠀⢀⢻⣷⠿ ⠀⠀⠀⠀⢿⡇⢿⠛⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣾⡇⠀⣼⣿⡍⠀ ⠀⠀⠀⠀⢸⣿⠀⣧⠈⢯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡇⣰⡿⣿⣷⣶ ⠀⠀⠀⠀⣾⣿⣦⣿⡄⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣷⣿⠁⢿⣿⣿ ⠀⠀⠀⠀⣿⣿⣻⣿⣷⡀⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠤⠤⠄⠀⠀⠤⠤⠤⠔⢁⣀⠤⠤⠄⠒⠒⠒⠲⢾⣿⠃⡸⠀⠸⣿⣿ ⠀⠀⠀⢠⣿⣿⣿⡿⠿⠟⠀⠛⠋⠉⠉⠉⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣁⠀⠤⠤⠒⠊⢀⣀⠀⠀⠈⠙⠣⢄⣠⣿⣿ ⠀⠀⡆⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⠋⢀⠤⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿ ⠀⢠⣷⡿⠋⠀⠀⠀⠀⠀⠀⠐⠒⠠⠤⠤⠴⠦⣄⡀⠈⠹⡶⢤⣀⠀⠀⠀⠀⣠⣷⡡⠖⠁⠀⢀⣀⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⣀⣀⣀⠀⠈⠻⣦⣀⠘⢆⠈⠙⠷⣶⣿⢿⠏⠀⢀⠴⠊⡩⠚⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⡀⠙⠢⡀⠈⢫⠉⠻⣴⣶⠿⣿⡭⠏⠀⡰⠁⠀⡜⠀⢀⡴⠒⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠒⠢⠤⡀⠈⢦⠀⠘⠦⣀⣱⡄⠹⣷⢴⡟⠓⠒⠋⠀⢠⢊⣀⠔⠋⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠈⠢⣄⣑⣆⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣰⣳⣿⣥⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣥⣿⢿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠙⢿⣿⣿⣿ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⡜⠀⠀⢀⡴⠶⡄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣞⠀⠀⣰⠋⠀⠀⡇⠀⠑⠢⣀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⡇⠈⠀⠀⡇⠀⢀⡼⢡⡀⠀⠀⠀⠑⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠹⣷⡀⠀⠀⠙⠶⠋⠀⠀⠈⠲⣄⠀⠀⠀⢸⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣸⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠑⠓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⠀⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⡰⢫⠂⠈⢢⣿⣀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡆⢠⡞⠉⢹⠀⠀⠀⠀⣀⣠⣣⠃⠀⢀⡞⢙⡛⠿⠿⠿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⣦⡄⠈⢧⡟⠀⢀⣜⡠⠔⠊⠉⠀⠀⠀⠁⣠⠛⠛⡅⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿ ⠀⠀⠀⠀⠢⣄⠀⠀⠻⣿⣿⣿⣿⣿⣿⡀⠈⠳⣄⣸⣓⠶⠊⠁⠀⢄⡀⠀⠀⠀⣀⠞⠁⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣦⣅⠀⠀⠈⠙⠿⣿⣿⣿⣿⣦⣄⣨⣻⣿⣷⣤⣀⣀⣀⣉⡢⠔⠊⠁⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠊⠔⠂⣒⢦⡤⠉⠙⠛⠿⠭⠭⠍⠻⠿⠷⠴⠋⠓⠢⠤⠥⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣯⢧⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣼⣿⣿⣿⣿⡇⠈⡛⠛⢹⠿⣿⠏⠀⠀⠀⠀ ⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡻⣿⣿⡿⠃⠸⠙⠀⢻⣄⡎⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡗⣶⣦⣤⣀⣽⣿⣿⣿⣿⣿⡏⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣤⣄⣀⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠖⣛⣉⣛⠳⣤⡀⠀⠀⠀⠀⠀⢀⣤⡾⠗⠲⢤⣀⠘⣿⣿⣿⣿⣿⠛⢿⠇⠀⢠⣾⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⢧⠎⠉⣿⣿⣷⣼⡟⠀⠀⢀⠀⡴⢻⡷⠋⢻⣿⣶⡝⣦⣿⣿⣿⣿⣿⠙⣼⡆⢀⣿⣿⣿⠟⠛ ⠀⢸⣿⣿⣿⣳⠿⠓⠒⢿⢿⣿⣿⣿⣿⢸⡷⢾⣿⡟⢻⣇⡇⠀⢼⢏⢞⡄⡎⣧⣠⣾⣿⡿⣿⢸⣿⣿⣿⣿⣿⣀⣸⢥⣼⣿⠟⠁⠀⠀ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠘⠜⢿⣿⣿⢿⡆⠻⠶⢯⡷⢟⡽⠀⠲⢣⢊⠎⢈⠱⡸⣦⣽⣿⣤⠟⢘⣿⡿⠋⠁⠀⠀⠉⠛⠻⢤⡀⠀⠀⠀ ⠄⠀⢺⣿⠁⠀⠀⡀⠀⠀⠀⠀⠙⢿⣎⠋⠀⠀⡰⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⡍⠉⠁⠀⣼⡟⠁⠀⡀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀ ⠉⠀⠠⡿⡄⡆⠀⡇⠀⠀⠀⠀⢰⠀⢫⡁⠀⠀⣧⠤⠤⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⢣⠀⠀⢀⣿⠁⠀⡘⠁⢠⠇⠀⡄⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠹⢷⣿⡒⢷⠒⢻⠒⢒⣽⠾⠋⠙⠢⠄⣹⡀⠉⠉⠁⠀⠉⠙⠛⠛⠛⠩⠭⡽⠀⢀⡼⢿⣦⠤⣇⣀⡎⠀⡘⠀⠀⡜⣡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢩⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⢐⡖⠒⠒⢒⠒⠒⠒⠒⠁⠀⠈⠀⠀⠈⠓⠓⠤⠿⠿⠧⠴⣾⠿⠿⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠉⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢬⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠘⡇⠀⠈⡏⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⣰⡿⠁⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⠀⠐⢳⠀⠀⣇⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢞⠟⠀⠀⠀⠀⠘⡆⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡼⢸⠀⢸⠀⢇⠀⠸⣆⠹⣄⠀⠀⠀ ⠀⠀⠀⡌⢀⡰⠚⣡⠛⠒⠒⠂⠀⠒⠒⢻⡟⡿⢇⠀⢿⡀⠀⠀⠀⠀⠠⢤⣇⠀⢠⠇⢸⠀⡆⠀⠘⡆⠀⡝⢆⣸⠀⠀⠀ ⠀⠀⠀⡏⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣱⠘⡄⠀⢳⠀⡀⠠⡀⠀⠀⢯⠉⡟⠒⢼⣴⣁⡀⠀⠘⣄⢱⠈⣧⠀⠀⠀ ⠀⠀⢸⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠱⡀⢈⢧⠐⡄⢳⡄⠀⠘⡾⠀⠀⣼⠇⠀⠈⠉⠐⠚⢞⢷⡟⠀⠀⠀ ⠀⠀⢸⣠⣤⣶⣶⣦⣤⣤⣀⣉⣙⣋⣉⣃⠀⠀⠱⡀⠘⢞⣾⣇⣹⣦⡻⣦⡀⢣⣀⣰⡋⠀⠀⠀⠀⠀⠀⠈⢺⣧⠀⠀⠀ ⠀⠀⢸⠙⢅⢸⣯⣿⣿⣿⡙⠛⡛⠛⠿⢦⡀⠀⠀⠱⠀⠀⠻⢿⡌⠳⣌⠛⠿⣾⣯⣅⣀⣀⠀⠀⠀⠀⠀⢀⣿⡟⠃⠀⠀ ⠀⠀⢸⠀⠀⠀⠹⢏⣻⣛⣿⡶⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠙⠦⠈⠐⠒⠛⠛⣿⣿⣿⣿⡿⠿⠿⢿⣾⣿⡃⠀⠀⠀ ⠀⠀⢸⠀⠀⡠⢄⡄⠀⠀⠁⠀⠀⠀⠀⠀⠊⢁⡠⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⣦⣴⢨⠋⢻⣂⢀⣴⠇ ⠀⠀⠸⡀⠈⢕⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠛⢁⡿⠀⡞⠁⢀⡏⠀ ⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⡇⠀⡼⠁⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢸⠁⣰⠃⠀⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⡟⠀⠀⡘⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⡇⡾⠀⠀⠀⠀ ⢠⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⣿⠃⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀ ⠀⠻⣆⠀⠀⠸⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⢻⣿⣿⡟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇⣸⣾⡟⠁⠀⠀⢀⡄⠀⠀ ⠀⠀⠀⠙⣦⠀⠈⣧⣹⣿⣶⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⣿⣿⡟⠁⠀⠀⡰⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡄⠸⣿⣿⣿⣿⣿⣿⣏⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⣠⣟⣿⡟⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣿⣿⣿⡏⢦⠀⠙⠢⣄⠀⠀⢀⣀⠤⠔⠊⢁⣀⣠⠴⠊⣡⣿⡟⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⠀⠀⢀⣀⡴⠶⠒⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠂⠀⠚⠁⠀⠐⠛⠁⣀⣤⣄⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠖⠛⠛⠒⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣄⣀⡀⠰⠦⢤⣄⡀⠠⠇⠀⠀⠀⠀⣀⣤⣶⣛⣁⣀⣀⡀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⣴⣾⠛⠛⠛⠛⢿⣷⣦⣄⠈⠙⠂⠀⠀⡠⠖⢋⣵⣿⣿⠿⠿⠿⠿⠿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠲⣤⣀⠀⠈⡛⢿⣷⡄⠳⣶⠖⢃⣴⡿⠛⣭⣤⠴⠶⠋⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣭⣭⣭⣥⣄⡙⣷⠀⠀⢠⣿⠋⠀⣤⣶⣶⣤⣤⣤⣠⣤⣤⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣾⣧⣤⣤⣤⣀⣨⣽⣭⡞⠀⠀⠀⠳⡄⠳⣿⡛⠻⠿⠿⣷⠾⠉⢹⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⢯⠙⠻⣤⣠⣤⠶⠞⠋⠀⠀⠀⠀⠀⢻⡀⠀⠉⠙⠛⠛⠁⠀⢠⡞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⢀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡼⢇⠀⠀⠀⣴⣲⠇⠀⠀⠀⠀⠀⠀⢈⡷⢶⡄⠀⠀⠀⡿⠁⣷⢀⣰⣿⡟⠛⠛⠲⢦⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣖⡀⢰⠃⠘⣆⣀⣼⠛⠻⣶⣦⡀⠀⣠⢶⣿⡿⠁⠙⣿⡄⠀⢀⡇⢀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠛⢷⣤⡀ ⠀⠀⢀⣤⠶⠛⠉⠘⣿⣿⣿⣶⠇⢸⠋⣿⠃⠀⠀⠀⠈⠋⠘⠃⠀⠀⠀⠀⠀⢨⡿⠀⣸⠇⣸⣿⣿⡧⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠈⠻ ⣴⠾⠋⠀⠀⠀⠀⠀⠁⠸⢹⣿⣷⣿⠀⢻⡀⢠⣴⠶⠖⠒⠒⠒⠒⠒⠒⠲⣤⣼⠃⠀⣯⢀⣸⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢻⣿⡄⠸⢷⣿⣿⣷⣦⣤⣤⣤⣶⣾⣿⣶⣦⣹⠀⠀⢸⣘⡿⢇⢨⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠘⣿⣷⡆⢸⣿⣿⡟⠻⢿⣿⣿⣿⡿⠟⣿⡟⣹⠀⠀⣾⡿⣧⣀⣾⠃⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣿⣻⣷⡄⣿⣿⣷⠀⠀⠹⡿⠋⠀⢠⣿⠃⣿⣀⣿⣿⣷⠿⠋⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣷⣿⠻⣯⣀⣀⣀⣀⣀⣠⡽⠋⣰⣇⣿⣿⠟⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠷⣮⣍⠉⠉⠉⠉⠁⢀⣴⣿⣽⡏⠃⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⣏⠓⠒⠶⠶⠟⠋⣤⣾⠟⠟⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣇⣶⣼⣶⠿⢿⠛⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⣿⣾⠟⠁⠀⠈⢿⣿⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢁⡞⠀⠀⠀⠀⠈⣿⡀⢸⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡟⣿⣿⠁⢸⡗⠀⠐⠒⢤⣤⣼⢿⢁⠼⠋⣿⣿⣿⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⣹⣧⣷⣿⠇⠀⣼⣟⣉⣈⣉⣀⡀⠹⣍⢇⠀⢀⡟⠹⣿⡄⣻⣁⡬⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠗⣿⣻⣿⡟⢰⡾⡟⢻⠉⠋⠀⠰⠿⢿⡠⠬⣦⡟⠀⠚⢿⣯⣿⠅⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡏⢸⣿⣿⣿⠟⡿⣿⠧⠘⡄⠀⠀⠀⠈⠀⠀⢠⠟⠁⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠘⣷⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⠁⣿⣿⣿⡿⠀⠐⠁⠀⠀⢱⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢯⡇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⢿⣿⢠⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠸⢸⠹⣿⣦⡀⠀⠀⠀⠀⠀ ⢀⣾⠟⠁⢾⣿⢾⣿⣻⡇⢿⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⣿⣏⠙⣦⡀⠀⠀⠀ ⣿⠋⠀⠀⢾⣿⣾⡛⣿⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⡟⣿⠀⢹⣿⣦⠀⠀ ⣿⡄⠀⠀⢸⡟⢻⣇⢻⣷⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⢀⣀⣒⣶⣶⡚⠦⣄⠀⠀⠀⠀⠀⠀⢸⡿⠁⢸⠀⠀⣏⡏⠳⣄ ⣿⣷⡀⠠⡃⠙⠚⢿⣿⢿⡀⠀⠙⠀⠀⠀⠀⠀⣠⢊⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡵⣄⠀⠀⠀⠀⣸⠁⠀⡘⠀⠐⡾⠀⠀⠘ ⣿⣿⣿⣷⣬⣁⠀⠚⡿⣿⣇⠀⣸⡀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⠃⠀⠀⡇⠀⢰⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣦⣇⣹⣿⡄⠈⢧⠀⠀⢰⣿⠟⣿⠟⠉⠉⠉⠉⣏⢉⠉⠙⣧⣼⣦⡀⠙⣿⡍⢹⡆⠀⡜⠀⠀⢰⠁⢠⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⢳⠏⠀⣿⡏⢻⣿⣷⡀⠀⢣⠀⢸⡏⠀⣿⠀⠀⠀⠀⠀⣿⣌⠄⠀⣿⡿⠙⡇⠀⢈⡇⢰⠃⣰⡁⠀⢠⣿⣴⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠸⢳⠈⣿⣿⣷⡄⠀⢃⠀⠙⡄⠻⣦⠀⠀⠀⠀⡇⣷⠀⢰⣿⣿⠀⣷⢀⠞⡠⠃⠰⠛⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⢂⣏⣿⢿⣿⣦⡀⢢⠀⠈⢦⡈⠒⠀⠀⠐⠓⠚⠒⠐⠛⠓⠒⠛⣁⠔⠁⡰⠁⢀⠜⠛⣹⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⢀⡔⠚⣯⣽⡿⠛⠉⠁⣸⣿⡄⢱⣤⡣⡀⠀⠉⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⢀⠎⢀⡴⠃⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⣠⠃⢀⡾⠋⠁⠀⠀⢠⠾⢿⣿⣇⠀⠙⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡴⠊⠀⠀⠀⣿⢇⡜⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠔⠉⠀⠀⠀⠀⠀⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⢸⠀⠀⢀⠖⠀⠀⢀⠴⠋⠀⣼⡆⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⡤⠤⠤⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⣀⡠⠤⠀ ⠀⡇⠀⠀⠀⢀⠎⠀⠀⣠⠃⠀⠀⣰⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣠⣤⠖⠊⠁⠀⠀⠀⠀ ⠀⠘⠀⢰⣠⠞⠀⠀⠀⠁⠀⢀⡐⠁⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⣞⡽⠻⠁⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⡀⣹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢀⡾⣉⣀⣸⠄⡾⢹⣴⣧⡀⠀⠀⠀⣸⢳⣸⡄⠀⠀⠀⢸⠉⣻⣆⢏⢿⣿⣿⣿⣿⣿⣿⣿ ⡆⠀⢠⣾⣷⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⣯⣀⡀⠉⢹⡀⡇⠀⢻⢻⣧⠀⠀⠀⢸⠛⢳⣿⠒⠒⠀⠼⣇⠈⢻⣿⣼⣿⣿⣿⣏⣿⣿⣿ ⣷⣶⣾⣿⡏⠀⠀⠀⡀⣰⠀⠀⣄⣼⣿⡾⠛⠛⠻⢷⣮⡇⣧⠀⠸⣿⣿⣀⠀⠀⣸⠒⠒⠿⢧⣀⣀⠀⢿⠑⠀⣿⢸⠻⣿⣟⣼⣿⣿⣿ ⣿⣿⣿⣿⠇⠀⠀⢠⢇⡏⠀⠀⣿⣼⡿⠀⢀⣶⣽⣷⡘⣿⡏⢧⠀⣿⡏⢻⡆⢀⣏⣶⣾⢿⣿⠻⠷⣿⣼⣦⣄⣻⢸⣀⣟⡿⣽⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⠀⢸⡼⢻⠀⣴⠟⠛⡇⠀⢸⣿⣿⣻⡇⠈⠳⡀⢹⣿⠀⠘⣿⡾⠋⠁⣴⣥⣿⣷⠀⠀⠻⣿⣆⢸⠟⣿⠟⠀⣿⣿⣿⣿ ⣿⣿⣿⡏⠀⠀⣠⠞⣠⣯⣰⣃⠀⢸⣷⣄⡘⣬⣽⡋⠀⠀⠀⠈⠈⠁⠀⠘⢡⡇⠀⢸⣛⣿⡟⣿⠃⠀⠀⢹⠉⣾⠀⢸⣷⣶⣾⣿⣿⣿ ⣿⣿⣿⡇⠀⢰⠁⠀⢸⡿⠋⠀⣠⣾⡿⣦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣜⣦⡨⠟⠃⢀⡀⢀⠞⢰⣿⡆⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠃⣿⠀⢀⣟⠀⠀⠸⣿⣿⣇⠈⠳⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠳⠒⡻⠒⢭⢩⡀⣿⢻⡇⢻⣿⣿⣿⣿⣿⣿ ⡿⢹⣿⡇⣸⣿⠀⢸⣿⠀⠀⢸⣿⡏⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⠀⢹⠏⢸⣧⣸⠟⠉⠉⣿⣿⣿ ⡇⠸⡿⠀⣿⠇⠀⢸⣿⢀⡀⢸⣿⣇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣀⡟⢐⡟⠀⣾⣿⠁⠀⠀⣰⣿⣿⣿ ⢠⠀⡇⢠⣿⣠⠔⡾⠙⠉⠙⠎⢹⣿⣿⣧⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡞⠉⠉⣽⡾⠀⣸⢳⡇⢀⣰⣶⣿⠿⢿⣿ ⠘⡄⣧⣼⣿⠀⠰⠃⠀⠀⠀⠀⠈⣿⡿⠸⣆⠀⠀⠿⠯⢽⣒⠓⠢⡀⠀⠀⠀⠀⠀⡜⢡⠟⠀⠀⡴⢱⣇⣾⣥⣿⣿⣿⠟⠋⠈⣄⣿⣿ ⠀⢣⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣠⣿⡄⠀⠀⠀⠀⠈⠙⠶⠿⠀⠀⠀⠀⡼⢀⡏⠀⠀⢸⣥⣾⣿⣿⣿⠿⠛⠁⠀⢀⣼⣿⣿⣿ ⠀⠈⢎⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⡞⠀⠀⢀⣿⠟⠛⠛⠛⠁⠀⠀⠀⠰⣾⣿⣿⣿⣿ ⢀⢀⠈⠒⠒⠦⣀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣡⠞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⡽⠉⡩⠉⡹⠋⠉⢩⠋⠉⠉⠉⠉⢩⠋⠻⣏⠉⠙⡏⠉⠉⠙⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣸⣥⠊⣀⠜⠀⠀⢠⡿⢀⣷⠀⠀⢠⠿⠀⠀⢻⡄⠀⢰⡄⠀⡄⠺⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⡟⠁⢠⠏⠀⢀⣰⣫⣧⠮⡿⠀⡀⡿⠓⠠⠤⢀⣿⣄⢘⣧⠀⡇⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢻⣼⡧⠠⢺⠋⣩⣟⣉⣈⠊⠀⡇⢀⣿⠁⠀⠀⠀⢀⣈⣻⣏⣿⡑⠧⠄⡇⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⡇⡤⣾⠞⢋⣿⣿⣿⡟⢧⠁⣼⡏⠀⠀⢀⡾⢛⣿⣿⣿⡟⠷⣧⠈⣧⣼⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⢀⣧⠹⠀⢸⣿⠿⢿⠗⢈⢎⡟⠀⠀⠀⠀⠀⢹⡿⠿⣻⡃⢰⠋⠀⣿⢻⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣸⢼⡄⡇⢈⡿⠛⠛⠔⢡⠞⠀⠀⠀⠀⠀⠀⠈⠛⣛⢫⠇⣼⠀⠀⣿⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣷⣄⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢰⣿⠀⢀⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡁⢻⣝⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡼⣹⡇⢸⣤⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡗⠒⠓⢻⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢡⣿⣇⣿⡄⠙⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡴⣻⠛⡀⢣⠀⢀⡿⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣠⠟⠁⢿⡏⢹⠀⠀⢛⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠟⠘⡘⠹⡄⣱⡈⢇⡼⠃⠀⠈⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣼⡇⠀⡆⠀⢸⡼⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡸⣆⠃⠀⢿⠁⡟⣌⣇⠀⠀⢀⢸⠀⠑⠢⣄⠀⠀⠀⠀⣠⠔⠊⢀⠧⢄⠀⢰⠿⠱⡀⠇⠀⡸⢡⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣣⡙⡆⠸⡘⣶⠋⠀⠉⣳⠖⠓⡾⡆⠀⠀⠀⠉⠑⠒⠁⠀⠀⠀⢸⢠⠎⢣⡏⠀⢣⠱⣆⡴⢗⡟⢸⡄⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠈⠁⠀⠑⢬⡲⡷⣘⣍⣽⡿⠃⠀⠀⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠴⠋⢟⢿⢈⣷⠁⣠⢻⠀⢸⢿⡉⠀⠐⠢⠤⣀

⡟⠀⢠⡇⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⣹⠞⠁⠀⠀⠸⣿⠀⢹⡀⠀⠈⠀⣾⡀⠘⡇⠀⠀⠀⠀⠱⠑⠸⡍⠙⠲⢤⣄⡀⠀⠀⠀⠀ ⠁⢰⣿⠂⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠣⢄⣀⠀⠀⠀⣿⠀⠀⢳⡀⠀⠀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⠒⠤⣀⡉⠓⠀⠀⠀ ⢀⣾⡇⢰⣿⣿⠀⢀⠀⠀⠀⠀⡀⢀⡿⠁⠀⠀⠀⠉⠑⠒⢿⠶⠦⠈⣧⡀⢀⡇⠘⣇⠱⡄⠀⠀⠀⢀⢰⠀⢸⠀⠀⠀⠀⠉⠑⠂⠄⠀ ⣼⣿⣇⣿⣿⡗⠀⣼⠀⠀⠀⠀⣧⣼⢡⠴⠒⠛⠛⠒⠲⣤⡀⠀⠀⠀⠸⣧⢹⢇⠀⠸⣦⢹⡄⠀⠀⢸⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⡇⢰⣿⠀⠀⠀⠀⢻⣿⡀⢠⣄⣀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠸⡟⠀⠙⠢⢿⡀⣇⠀⠀⡸⡸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢱⡇⢼⣿⠀⠀⠀⢸⠀⢹⡟⠚⠀⠀⠈⠫⢿⠶⠖⠀⠀⠀⠀⢰⠉⠉⠑⠢⡄⢸⣿⠀⢸⢇⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢸⡇⣸⣿⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠸⢿⣿⣧⡏⣼⡟⠳⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢷⣿⣿⠀⠀⠀⠈⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⣦⣀⣿⠋⠈⠁⣇⢀⡄⠀⠈⡇⠐⡟⠶⢶⣄⣀ ⣿⣿⣿⣿⣿⠘⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⣿⠉⠁⠀⠀⡇⠈⠁⠀⠀⠀⠉ ⣿⣿⣿⣿⣿⡆⣿⣿⠀⠀⠀⠀⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⣿⠀⠀⠀⠀⡇⢰⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⢻⣿⡄⠀⠀⠀⣼⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣷⠀⢠⣿⠀⠀⠀⠀⠃⢸⡇⠄⠀⠀⡄ ⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⣿⡁⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⢁⣰⣯⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣷⣄⢠⣄ ⠛⠉⠉⠉⠀⠈⣿⣿⣿⠀⠀⠀⢹⠳⣄⣀⣨⠗⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡟⢻⣇⠀⣿⣿⠀⠀⠀⠀⠀⢸⣷⣾⣿⣭⣿ ⠀⠀⠀⠀⠀⠀⠘⠸⣿⡀⠀⠀⢸⡇⠀⠉⠀⠀⢒⡶⣾⣿⣿⣷⣶⣶⣿⡿⣼⣿⣿⣿⣿⠁⣸⣿⢰⡿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⢸⠁⠀⠀⠀⢀⣾⠀⠈⠫⠹⢿⣿⣿⡿⢃⣿⣿⣿⣿⠃⣰⣟⣿⣿⣇⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⠔⢀⠞⠁⠀⠀⢠⡶⠁⠀⡄⠠⠀⠀⠀⠀⠀⠀⠄⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⡰⠃⢀⡞⠀⢠⣿⠇⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠘⡔⣀⠀⢃⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡴⠁⢀⣾⠁⠀⡞⢸⠀⠀⡏⠀⢀⢰⠀⠀⠀⠀⡎⠀⠀⢱⢹⡄⠸⣆⠀⠀⢱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⡸⠁⠀⣼⡇⣀⣼⣀⣸⣄⣀⣷⠤⢿⠘⠳⠑⢤⣰⡇⠀⠀⠀⣧⣣⠀⢻⣆⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠃⠀⢰⢿⠁⢀⡃⠀⢹⡇⠸⣏⡅⠈⡆⢧⠀⠀⢹⡟⠒⢤⡀⢹⣿⣧⠀⢻⡄⠀⠀⠳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⣾⠀⠀⡿⢸⣤⣼⣿⣿⣿⣿⣦⣧⢰⠀⢱⡘⡇⠀⠿⢧⠀⠀⠈⠙⡿⣽⣷⣄⠳⡀⠀⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢰⡟⢸⢛⣻⣼⠿⠟⠻⢻⡟⠛⠄⠘⣟⠜⡄⢸⣾⣿⣶⣷⣄⣱⠘⣷⡙⢷⣧⡀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⠁⣼⠸⣿⠉⠀⠈⠈⠉⠀⠀⠀⠀⠹⢆⠈⢀⢥⣿⣿⣿⣿⣿⣧⣺⣷⡄⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣸⠀⠈⣏⢻⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠁⠘⠺⠿⠯⠤⣌⣁⣿⡏⡙⣿⠄⣽⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⢞⣿⣾⠀⡏⠻⢦⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⣍⠁⠠⢬⠃⣠⠞⡀⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⡴⠁⡜⢈⣿⣾⡇⠀⠀⠑⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⣺⠞⢁⢾⢡⣶⠇⠀ ⠀⠀⠀⠀⢠⠚⣯⡜⠀⢠⠇⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⠉⣾⡿⠟⠂⠀ ⠀⠀⠀⠀⠀⣹⡟⠀⢀⣾⠀⢸⠀⠀⢱⠀⠀⠀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⠞⠁⠠⠾⠋⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠎⢸⡄⠸⣇⠐⣄⢣⠀⠀⠉⠉⣉⠙⠛⠭⢉⡒⣦⣀⠀⠀⠀⠀⢠⠋⡿⠧⠀⠀⠀⠐⣶⠶⡎⠀⢲ ⠀⠀⠀⠀⠀⢿⣱⡜⢀⠃⠱⡄⢻⠳⣌⠛⢧⠀⠀⠀⠀⠉⠑⠂⠀⠀⠉⠉⠀⠀⠀⢀⠇⠎⠀⡠⠚⠓⠢⢤⣥⡔⠊⠻⡅ ⠀⠀⠀⠀⠀⠈⢇⡇⢸⠀⠀⠈⠓⣳⣄⡉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡴⠋⠀⠀⠀⠀⢸⠀⢻⡄⠀⠈ ⠀⠀⠀⠀⠀⠀⠈⢣⡘⡦⠒⠊⠉⠀⠀⠙⠧⠤⣵⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡿⣏⠀⠀⠀⠀⠀⠀⠈⢇⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⡠⠔⢋⠓⢝⢤⡀⠀⠀⠀⠀⠀⠀⢀⠏⠒⠒⠒⢲⣿⣿⣿⣿⣿⠿⠉⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⢦⡼⠁⠀ ⠀⠀⣀⠴⠊⠀⠀⡌⠀⠀⠑⠬⡒⠤⣀⠀⢀⠔⠁⠀⠀⠀⢠⠋⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⢀⡠⠊⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⢸⠁⠀⠀⠀⣴⡏⠑⠦⡉⠛⢦⡀⠀⠀⠀⠀⠀⡘⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠓⠣⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠎⠀⠀⠀⠈⢳⢤⡈⠳⢄⠀⠀⠰⠁⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠏⠀⠀⠀⠀⠀⢸⠀⠑⢄⠀⠑⣴⠀⢀⠎⠀⠃⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢀⡟⠀⠀⠀⠀⠀⠀⣸⢀⡴⡟⢢⠀⠘⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢪⠞⣱⠿⠞⠈⣠⢞⣿⠿⣹⠏⠁⠀⢸⡀⢹⣧⠀⠘⢿⣧⠀⢹⣧⡀⠈⣧⡀⢱⡀⢳⡀⢺⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣯⡾⠃⢀⣴⡟⣡⡿⠃⣾⠇⠀⠀⠀⠸⡇⠈⢿⣇⢸⠈⢿⣧⠘⢿⣷⡀⢸⣧⠀⢳⡈⢷⠀⡹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣱⢟⣟⣠⡾⣿⡿⣱⡟⠁⢸⡏⠀⠀⠀⠀⢀⣧⡄⠘⣿⡌⡆⠀⢻⣧⡄⢻⣷⡀⢿⣧⠘⣷⡈⢇⢱⣃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠋⣡⣾⣿⡏⢰⡿⢳⡟⠀⢀⣼⣥⣤⣤⣤⢤⣄⣹⠀⠀⠘⣿⣧⠈⠓⢿⡇⠀⢻⣧⠸⣿⡆⢃⢳⡜⣆⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡼⠋⣽⣿⢀⡿⢡⡟⠀⣿⣿⡿⠶⠿⠷⠿⠿⠿⡿⠂⠀⠀⠘⢿⣶⣶⡦⢿⣄⣀⢻⣇⢸⣿⣸⡆⢻⣾⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⢀⣿⡇⣸⠁⡸⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠓⠾⢯⣿⣼⣿⡄⢽⣿⣿⣎⢿⠻⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⡸⠁⣴⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠿⡇⢸⣿⣿⠻⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢿⢠⢸⠟⠳⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣷⡙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢃⣿⡟⣦⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⢸⡟⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠔⠒⠲⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⢀⡟⣁⣸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣺⠇⢸⡆⠀⠀⠀⠀⠀⠀ ⡶⠶⠾⠿⠿⢿⣿⠟⠉⠉⠇⠻⡏⢿⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⠿⠿⠿⠶⠦⠤ ⠀⠀⠀⠀⠀⡼⠁⠀⠙⢦⡀⠀⠙⠘⢶⠀⠻⣦⣀⣤⣄⡀⠀⠀⢘⡩⠤⢬⡱⣦⠀⠀⠀⠀⢀⡠⣾⣿⠟⠛⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠙⠦⠀⠐⠜⠆⠀⠈⢻⣏⣙⡿⠠⢚⡡⠔⠢⢄⠙⠎⣳⣾⣥⠖⠋⢠⡏⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠠⠄

⠀⠘⡧⠀⣠⠎⠀⠀⢀⠔⠁⠀⠀⠀⠀⣠⠞⣇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⣿⡴⠃⠀⠀⡰⢣⠆⠀⠀⠀⢀⡴⠁⠀⠸⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⡄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⡈⢧⠀⠀⢻⡀⠀⠀⢠⠀⠀ ⠀⠀⡿⠁⠀⠀⡜⡰⠁⠀⠀⠀⣰⠋⠀⠀⠀⣠⠿⡀⠀⠀⠀⠀⠀⡀⣧⠀⡟⠲⣄⢳⡀⠀⠀⠀⠀⠀⠀⠱⡘⣇⠀⠈⣧⠀⠀⠸⠀⠀ ⠀⢠⠃⠁⠀⡜⡜⠁⠀⠀⢀⡼⠁⠀⠀⣠⠞⠁⠀⢱⡀⠀⠀⠀⠀⠀⢸⡀⢳⠀⠈⠳⣿⡄⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠸⡄⠀⡄⠀⠀ ⠀⠀⠀⢀⡞⡰⠀⠀⠀⢀⠞⠀⠀⢠⠞⠁⠀⠒⠀⠀⢣⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⢣⢹⠀⠀⢷⠀⣆⠁⠀ ⠀⠀⢠⣿⡇⠇⠀⠀⢀⡞⠀⠀⡴⠃⡄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠈⡌⣇⠀⢸⡆⡇⠀⠀ ⠀⢠⣿⣿⠐⠀⠀⢀⡞⠀⢀⡜⠁⠀⠙⣆⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢻⢸⠀⠀⠀⠀⠀⢀⣤⠎⠑⢄⠀⠀⠀⠰⢸⡀⠀⣿⣷⠀⠀ ⠀⠀⣾⣿⠀⠀⠀⡼⠀⢀⠞⠀⠀⣀⣠⣬⣿⣦⣤⣤⣤⣤⠞⢦⠀⠀⠀⢸⣺⣦⣤⣤⣴⣶⣯⣥⣀⡀⠈⠳⡀⠀⠀⠃⣇⠀⢻⣿⡄⠀ ⠀⢠⣿⣿⠀⠀⢰⠃⢀⡎⠀⣰⣾⢟⣫⣽⣿⣿⣿⣿⣷⡄⠀⠈⢦⠀⠀⢸⣿⢀⣤⣾⣿⣿⣿⣿⣿⢿⣦⡀⠙⡄⠀⠀⢹⠀⢸⡇⣇⠀ ⠀⣼⢹⣿⠀⠀⡾⠀⣾⠀⣸⡿⢡⠞⢻⣿⣿⣿⣿⣏⢿⠓⡔⠀⠨⢣⠀⠈⣿⠿⢻⠋⢻⣿⣿⣿⣿⣆⢹⣿⠀⢻⣄⠀⠸⡇⣸⡇⢹⠀ ⢀⡇⠀⣿⡄⠀⠇⠀⣿⠀⣿⡇⢸⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠾⠂⠀⠳⡀⣿⠀⢸⣶⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⠙⡆⠀⡇⣿⡇⠀⠀ ⣼⣤⣶⣿⡇⠀⠀⠀⣿⠀⢻⣧⠸⣿⣌⡙⠻⣿⣯⡼⠄⠀⠀⠀⠀⠀⠀⠱⡇⠀⠾⣧⣄⡛⠛⣻⣯⡼⢰⣿⠀⢸⠀⢹⡀⣿⣿⣷⣦⣄ ⣿⣿⣿⣿⣿⠀⣠⠀⣿⠀⠀⠙⠃⠑⠢⠭⠭⠥⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠭⠭⠥⠚⠁⠛⠁⠀⢸⠀⣠⣧⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⣿⣷⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠊⠉⠉⠉⠓⠒⠒⠉⠉⠉⠓⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡍⠒⠒⠠⠤⣠⣤⡤⠄⠐⢒⠊⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠧⣄⣀⡤⠚⢥⡤⠹⠦⣘⢁⡴⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀ ⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡄⠀⠀ ⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⡞⠉⠀⠀⠀⡰⠀⠀⠀⠀⢸⠀⡄⠀⠀⡆⡆⠀⠀⠀⢰⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⢀⠔⢁⣜⣾⠁⠀⠀⡀⣸⠁⡀⠀⣸⠀⢸⢰⡇⠀⡼⢰⠁⠀⠀⠀⠀⠇⠀ ⢸⠀⠀⠀⠀⠀⠀⢀⣾⣰⠋⢠⢻⡿⢸⡇⠀⢠⢣⠃⡇⣇⣠⡿⠀⣿⣾⠀⡼⠁⡜⡀⠀⡀⡆⠀⠀⠐ ⢸⠀⠀⢀⠆⠀⠀⣼⣷⣧⣦⣿⢾⠇⠀⢇⠀⢸⡞⠀⢿⣥⠛⣧⣼⡟⣽⠞⠁⣸⠁⠁⠀⡇⡇⠀⠀⠠ ⢸⠀⠀⣾⠀⠀⢸⣿⠋⣿⠼⠘⣾⠀⠀⠘⡆⢸⣧⠀⠸⠃⣀⣭⡁⠸⠓⠒⢾⢻⠀⠀⢸⢡⡇⠀⠀⠀ ⢸⠀⢰⣿⠀⠀⣎⢙⣶⣿⣿⣿⣿⣿⣆⠀⠘⣄⢿⣆⠀⣾⣿⣿⠿⠿⣷⣦⣭⣼⠄⢀⠇⣸⠁⠀⡀⠀ ⢸⠀⣸⢹⠀⢠⣏⣟⡩⠟⠉⠀⠈⠀⠙⠃⠀⠈⠛⠬⠷⣿⠉⣯⠀⠀⠀⠉⠻⣏⢠⠎⢀⡿⠀⢠⠃⠀ ⠀⡇⣿⣿⠀⠈⡟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⣿⡄⠀⠀⠀⢰⣿⠏⠀⣸⠃⣠⡏⠀⠀ ⠀⢧⡏⢿⡇⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡇⠀⠀⠀⠀⢠⡿⣿⠀⡜⡝⣼⡟⠀⠀⠀ ⠀⠸⡇⠈⣿⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⣿⡀⠀⠀⠀⠀⠀⣏⡜⣰⣹⡟⠀⠀⠀⠀ ⠀⠀⠱⠄⠸⣷⣿⣷⣀⡀⠀⠀⠀⢠⣿⣷⣶⠶⠶⠶⢶⣶⣿⣷⡄⠀⠀⠀⣸⣿⢴⣳⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡙⢿⡀⠀⠀⠀⢾⣟⠉⠀⠀⠀⠀⠀⠈⢙⣿⠃⠀⠀⠀⣿⢁⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⠦⡀⠀⠈⠙⠻⠶⠶⠶⠶⠶⠟⠋⠁⠀⠀⡠⠊⢁⣨⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣴⣶⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣼⣯⣾⣔⢠⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣛⣿⣿⣧⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢟⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣦⣀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⢁⣼⣿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⠙⢍⣒⣒⠤⠤⢄⣀ ⠀⢠⢾⢁⣾⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠙⣿⡟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡀⠠⠙⠫⣵⠦⢄⡀ ⢠⠊⢸⣼⡞⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠋⣁⠹⠿⠒⠹⠏⠿⣿⡌⢷⠉⠿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡀⠙⢕⠄⡙⠢⠄ ⠇⠀⢸⣽⡇⢻⣿⣿⣿⣿⣿⣿⣿⣟⣥⣾⣷⣾⣦⣔⡒⠒⣶⠒⠂⠈⠁⣰⣿⣿⣿⣷⣖⠿⣿⣿⣿⣿⡸⣿⣿⣿⣾⣷⣴⡀⠉⠪⢅⡂ ⠀⢀⣿⢯⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠁⠀⠘⡇⠀⠀⠈⠉⠸⣿⣿⣿⡿⠟⢿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀ ⠀⣼⡟⢸⡇⣿⣿⣿⣿⣿⣿⡧⡏⢣⡠⣛⣋⣩⡩⠶⠀⠀⠀⠁⠀⠀⠀⠀⠾⠮⠮⠴⢴⣤⢻⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣷⡉⠛⠦ ⠀⣻⠃⢸⣧⣿⣿⣿⣿⣿⣿⣇⢱⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠑⠄⠀ ⠀⣿⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠠ ⠀⣿⡄⠘⡜⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⣸⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠄ ⠀⠈⡟⢦⡃⢻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⢣⠀⠹⡌⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢣⡀⢱⣹⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠑⢄⣳⣿⣿⣿⣿⣿⣿⣿⣧⣝⣿⣿⣮⣙⠓⠶⠤⠄⠀⠀⠀⠀⣀⠤⠚⡏⠱⡵⠄⠀⠀⠀⠀⠀⠀⠙⣷⣝⡿⣿⢿⣿⣿⣿

⠀⣰⣿⠃⡜⠉⢹⠃⠀⠀⠀⠀⠀⡇⠀⠀⢸⢠⠻⡰⠀⡇⠀⠀⠀⠀⠀⣼⡀⡄⠀⢸⠀⢳⠀⠀⢸⡄⢰⡄⠀⠀⢽⡄⠀⠀⠀⠉⠀⠀ ⠘⠟⠛⢰⠇⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⢰⣾⣾⡀⣧⠀⡇⠀⠀⠀⠀⢠⣿⡇⣿⠀⢸⠀⠈⣇⠀⠀⣷⡀⣿⣆⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⡀⡀⠀⠀⡶⠀⢠⡇⠀⣾⡇⡟⣇⣿⡆⠙⠀⠀⠀⠀⣼⣿⣧⣿⠀⡌⢰⢂⢸⡀⢰⡏⣇⢻⣿⣧⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⡇⡇⠀⠀⣿⠀⣾⣹⣀⣿⠃⢸⣿⣾⣷⠀⡀⠀⠀⣸⣿⣿⣿⣿⣰⣇⣇⣘⣌⣇⣸⢠⣸⣼⣿⣿⣷⣿⠀⠀⠀⠀⠀⢀ ⠀⠀⢸⠀⠀⠀⢱⣿⠀⢰⣿⡆⢹⡏⢏⣿⠉⠉⢿⣿⣿⣧⣧⠀⢠⣿⣿⣿⠇⣿⣟⡟⠀⠀⢃⢹⡏⠘⡌⣿⡇⢻⣿⣿⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⠀⠀⠀⢸⣿⡆⢸⣿⡻⣾⡇⠘⢿⠀⠀⠘⢿⢻⣿⣿⣧⣿⣿⣿⣏⡴⣿⡟⠀⠀⠀⢸⣸⠃⠀⢣⢻⠰⡘⣿⣿⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠈⣧⢷⢸⣿⣇⠙⢅⣤⣬⡤⣄⣀⠨⢆⠻⣿⣿⣿⣿⣿⠟⠘⢉⡠⢔⣲⣤⣼⠗⣶⣤⣼⡜⠀⢇⢻⡏⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠘⠟⢿⣿⣿⡴⠋⠉⠉⠉⠙⠛⠿⢶⣄⠙⢿⡏⡸⠁⠀⠀⠀⡾⠟⠛⠉⠉⠉⠉⠉⠃⠀⠀⢸⣼⡇⠀⠀⠀⠀⢀⣾ ⠀⠀⠀⡆⠀⠀⠀⠀⠠⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠀⡿⠀⠀⠀⡀⠀⢜⣿ ⠀⠀⠀⠇⢠⡀⠀⠀⣶⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣾⠃⢰⣷⣦⣾⣿ ⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⣞⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣺⣵⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡤⠴⠖⢦⣦⡀⠀⠀⠀⠀⠴⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⠓⠒⠛⠉⠉⠛⡇⠀⠀⠀⠀⠀⣠⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⣦⣄⣀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠚⡁⠀⢀⣠⠴⡊⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠾⠿⠛⠛⠛⠛⠛⠻⠿⠷⠶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢠⣄⠀⢠⣤⡀⠀⢀⠀⢸⣧⠀⠈⠹⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⢀⣤⣤⠀⠀⠀⠀⣠⡀⠀⢠⣦⠀⠀⢸⣿⡄⠀⢸⣿⡄⢸⣿⡇⠀⣿⣧⢸⣿⣇⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠁⠀⢀⡾⠻⡏⢀⣤⡀⠀⣿⣿⠀⢈⣿⡆⠀⢸⡟⣷⠀⠀⣿⣷⣸⡇⢿⣼⠇⠹⣿⡇⠹⣧⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠁⠀⢠⡿⠁⠀⣇⣸⢿⡇⢀⡿⢹⡆⢸⠋⣿⡀⣸⠃⢹⣧⣼⠇⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⣼⡇⠀⢀⡿⠁⠀⠀⣿⠇⠘⠿⠟⠁⠈⣷⣾⠀⠘⠓⠛⠀⠀⠉⠁⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠀⠀⠹⣧⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⣾⢁⣄⣄⣀⣀⣀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⢸⡇⠀⣸⠇⠀⠉⠉⠉⠉⠙⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇⠀⠀ ⠀⠀⠀⣸⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡆⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⢀⣠⡾⠂⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⡇⠀⠀ ⠀⠀⠀⣿⣤⡟⠀⠀⠀⠀⠲⠶⠦⣤⣄⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⡇⠀⠀ ⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠰⠶⢛⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀ ⠀⣠⣤⣿⠇⠀⠀⠀⠀⠀⠰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⡀ ⣼⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⡿ ⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣠⣿⠁⠀⠀⠀⠀⣀⣀⣴⡿⠁ ⠀⠈⠛⠻⢿⡇⠀⠀⠀⠀⠘⣿⣀⣸⣷⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⡟⠛⠋⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⣠⣶⡿⠛⣿⡉⢹⣿⠛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢻⣇⣀⣽⣷⣾⠿⠿⠛⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠐⣿⣤⣴⠶⠶⠾⠛⠛⠛⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢷⣶⣶⣶⣶⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣟⣀⣀⣤⣤⣤⣤⣴⣶⣶⣖⣿⣿⣿⣿⣿⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⣠⣤⣄⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⡞⠀⠀⠀⣰⠟⠁⠀⢸⡆⠀⠠⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣧⡴⠻⠆⠀⠀⣸⠇⠀⠀⢀⡾⠀⠀⠀⠀⠙⠢⣀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣇⠀⠀⠀⠀⣿⠀⠀⢠⡾⠃⠤⣄⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢻⣿⡀⠀⠀⠀⠘⠳⠾⠋⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⡏⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣿⡆⠀⠹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡇⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠲⠤⣤⣞⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⠀⠙⢄⢸⣿⠀⠘⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣷⠀⠀⢀⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏⠀⠀⢠⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⡆⢠⡟⠁⠀⢸⠇⠀⠀⠀⠀⣀⣀⣼⣧⣏⠀⠀⢀⡾⣁⣉⡉⠿⠛⠛⠿⠿⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠀⠸⣇⣾⠀⠀⠀⡼⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⣠⠟⠿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣷⣄⠀⣿⡼⣄⣠⠞⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠙⢷⣿⣷⣦⡀⠀⠀⠀⠀⠙⠦⡀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣼⣿⠶⣤⡀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣶⣦⣾⣽⣿⣿⣿⠷⠦⢤⣤⠤⠤⠔⠚⠉⠀⠀⠀⠀⡠⠤⠴⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⢀⠀⠉⠓⠃⠂⣘⠷⣲⠆⠀⠈⠉⠛⠛⠳⠤⠤⠬⠭⠿⠟⢒⠒⠋⠈⠉⠓⠒⠒⠦⠤⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⠀⣾⣿⣇⣀⣞⣁⣀⣠⣤⣿⠤⠔⢺⡅⠀⠀⠀⠀⡏⠀⡜⡗⠀⠀⠙⢿⢻⠦⠼⣧⡤⣬⣷⣿⣿⣦⣀⣿⡆⠀⠀⠀⠉⢲⠀⠀⠀⢺⡆⢹⣇⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣼⢠⣿⡏⣏⢈⡏⠁⠈⠉⣭⠇⠀⠀⠀⢧⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠈⢿⣇⠀⠀⠳⡄⢹⠀⠹⡌⢻⣹⣿⡄⠀⠀⡀⢸⠀⠀⠀⢸⡄⣸⣿⡀⢸ ⠀⠀⠀⠀⠀⢀⡖⢸⡏⠁⣿⢸⣿⠁⢸⣼⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡆⠸⡀⠀⣇⠀⠰⣇⠂⠀⠀⠀⠈⢻⡄⠀⠀⠙⢦⣇⠀⠹⣄⢳⣿⣧⠀⠀⡇⠀⡄⠀⠀⠈⡇⢸⠀⢇⠀ ⠀⢰⠀⠀⠀⡼⠀⢸⡇⠰⣿⠜⣻⠀⠈⡿⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠸⡄⣧⠀⣯⠀⠀⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⡄⠀⠘⣆⢹⠸⡆⢸⠃⠀⡇⠀⡄⠀⡇⢸⡇⢸⣠ ⠀⢸⠀⠀⢠⠇⢠⢸⡇⠀⣿⡄⣿⠀⠀⠘⠀⠀⠀⠀⣠⠤⠤⠴⠚⠀⠀⠹⣿⣧⢸⠀⠀⣿⣿⠀⠀⠀⠈⠓⠒⠒⠤⠤⠀⠀⠀⠀⠀⠘⣿⡄⢧⡟⠀⠀⡇⢀⡇⠀⣧⢸⡇⠀⣿ ⠀⢸⠀⠀⢸⠀⢸⡄⡇⠀⠸⣷⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠆⠀⠀⠙⢿⣿⡇⠀⣿⠸⡄⠀⠀⠚⠿⣷⡶⣶⣶⣶⣶⣤⣤⣤⣤⣼⡇⣾⠃⠀⠀⡇⢸⠁⢰⣿⣸⠁⠀⠘ ⠀⢸⠀⠀⣿⡀⠘⣷⢿⢠⣄⢿⣿⠀⠀⠀⣿⠋⠀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠙⢿⡆⢹⡀⠃⠀⠀⠀⣸⡃⠀⣼⣿⣿⣿⣿⣇⠀⠀⣼⢡⡏⠀⠀⢰⠃⡟⠀⢸⣿⣿⠀⠀⠀ ⠀⢸⠀⢠⣿⡇⠀⣿⡏⠀⢹⣾⡏⠀⠀⠀⣿⣶⣶⣿⣿⡏⣽⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⡇⠀⠀⠀⠀⢹⣿⡟⣿⣿⣿⢹⣿⡿⠀⢀⣿⣾⠁⠀⢀⣾⣸⡇⠀⣾⣿⡇⠀⠀⠀ ⠀⠘⡇⢸⣿⣷⠀⣿⢻⡀⠐⣿⣿⡀⠀⠀⢿⣿⣿⣟⣻⣋⣉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠘⣿⣷⣌⣛⣿⣞⡛⠃⠀⣼⣿⠃⠀⣰⢿⣿⢿⠁⢰⣿⣿⠀⠀⠀⠀ ⠀⠀⣷⣸⣿⣿⡆⣿⠀⢷⡀⢻⣿⢷⡀⠀⠈⠿⠿⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⠏⠀⣠⢏⣟⠀⣴⡿⣻⠏⢸⢠⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠉⠿⠿⠿⢿⣿⠀⠈⢷⡘⣿⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣼⣿⣵⡏⠀⣿⡟⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠤⠤⠤⢤⢤⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⡿⢻⡇⢰⣿⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⢠⣀⣈⣀⣹⣿⣿⠀⠀⢸⡟⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣷⠟⠀⣸⠁⢠⣟⣉⣉⣙⣉⣯⠀⠀⠀ ⠀⠀⠼⠿⠿⠿⢿⣿⠀⠀⠈⡇⠘⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣿⠇⠀⠀⡟⠀⢸⡟⠛⠛⠛⠛⠛⠀⠀⠀ ⠀⠐⠒⠒⠒⠒⠚⣿⠀⠀⠀⣷⠀⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⢰⡇⠀⣸⠷⠒⠒⠒⠒⠒⠂⠀⠀ ⠀⣇⣤⣤⣤⣤⣤⡟⢠⠀⠀⢹⡀⢸⡇⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⣼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣾⡇⣾⠀⠀⠸⣇⠀⣿⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠰⠦⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠁⢀⢠⡇⢀⡇⣿⣶⣶⣶⣶⣶⣶⣶⣦⠀ ⠀⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⣿⡆⢹⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⢀⣿⣿⠁⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⢀⡿⠿⢿⠿⠿⠿⢻⣿⡆⠀⠀⢸⣿⡘⣿⠿⠿⠿⣿⣿⣿⣿⣷⡶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⠏⠀⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⢀⣶⣿⠃⢰⠋⠘⢻⠇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⡾⢣⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⡇⠈⢳⠀⠀⠀⢸⡇⠀⣦⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠘⠁⠀⠀ ⣾⣿⣿⠀⡟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣼⣧⡇⠸⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣷⠀⠀⡇⠀⠈⣇⠀⠀⠈⣷⡀⢸⣷⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢸⠃⠀⠀⡏⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⣿⡟⣿⣷⡀⣿⠀⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⢠⡇⢀⡀⢸⡄⠀⠀⡏⢷⠈⣿⣿⣆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⡇⣄⠀⠀⠀⣾⠁⠀⣸⣧⠀⢸⣿⡇⢻⣸⡧⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⠀⣸⠀⡼⢹⠀⣷⠀⢸⡇⠸⡆⣿⣿⣿⣆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠀⠰⡇⢿⠀⠀⠀⣿⡄⢰⣿⣹⣄⢸⣿⠃⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣏⣸⣁⣈⣇⣹⣄⣸⢸⣄⣷⣿⡿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢸⠀⠀⠀⠀⣷⣼⡄⠀⢰⣿⣇⠈⣿⡟⢿⠙⣿⠉⠉⢻⣿⣿⣿⣷⣸⣇⠀⠀⣼⣿⣿⣿⣿⢹⣿⣿⢿⠏⠉⠉⢹⠙⣯⡟⠀⣇⢸⣿⡇⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠘⠀⠀⠀⠀⢻⣿⣧⠀⢸⣿⣿⣆⣿⡇⠘⣷⡿⠀⠀⠀⢿⣟⣿⣿⣿⣿⡆⣰⣿⣿⣿⣿⠇⣼⣿⣿⠏⠀⠀⠀⠈⡇⢿⠇⠀⢸⡈⣿⠣⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⡀⢸⣿⣇⠹⣿⡇⠀⠘⢧⠀⠀⠀⠀⢻⡘⣿⣿⣿⣿⣿⣿⣿⣿⣏⡞⣹⣿⠏⠀⠀⡀⠀⠀⣿⠘⠀⠀⠀⡇⣿⠀⢧⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⣧⢸⣿⣿⡄⠙⣦⣴⣶⣾⡖⣶⣤⣄⡐⠧⡈⢿⣿⣿⣿⣿⣼⣿⠏⠀⠁⢡⠴⣚⣩⣴⣶⣾⣟⣙⣿⣶⣶⡷⠇⠀⠸⡄⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠾⣿⣿⣿⣷⣸⠋⠉⠉⠉⠉⠉⠛⠛⠿⢷⣦⡀⠙⢿⡿⢀⡟⠁⠀⠀⠀⢀⡾⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣧⢻⡇⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠴⠂⢹⣿⢠⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⡇⠀⠘⠀⠀⠀⣀⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣠⡶⠀⣀⣄⣀⢈⣿⣿ ⠀⠀⠀⢳⠀⣷⣄⣠⣤⣾⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣶⡿⣁⣀⣽⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡵⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣠⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣞⣛⣉⣥⡤⠼⢿⣿⡆⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⣠⠾⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢳⣦⣄⣀⡀⠀⠀⠉⠓⠒⠋⠉⠉⠉⠉⠉⠓⠒⠚⢉⡀⠀⠀⣀⣠⠶⢋⠁⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠞⣠⠏⣠⠿⣾⠁⠂⣠⡴⣫⣾⡿⢱⡿⠋⠀⠀⢸⡇⠀⢻⣿⡀⠀⡿⢿⣿⡄⠀⢻⣷⡄⠀⠘⣷⡄⠀⢳⡀⠺⣄⠃⢺⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⡞⣡⡾⠋⠀⢀⣠⡾⢋⣴⡿⠃⣤⡿⠁⠀⠀⠀⠀⣿⠀⠘⣿⣷⠀⢱⠈⢿⣿⡄⠸⣿⣿⣆⠀⠸⣿⡀⠈⣧⡀⢿⣆⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢡⣿⣿⡟⠁⣠⣴⣿⡿⢁⣾⡟⠁⢸⣿⠁⠀⠀⠀⠀⠀⢻⡇⠀⢸⣿⣇⢸⡀⠈⢿⣿⡀⠁⢿⣿⡆⠀⢿⣷⡀⠘⣧⠈⢿⡄⢢⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣥⠟⣹⣏⣴⡾⠟⣿⣿⢃⣾⠏⠀⠀⣿⠇⠀⠀⠀⠀⠀⠠⢼⣷⠄⠀⠹⣿⡄⡇⠀⣀⢻⣷⡆⠈⢻⣿⡄⠘⣿⣷⠀⢹⢷⡀⢳⠈⣧⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⢀⣴⣿⣿⡟⠀⣸⣿⢋⣾⠏⠀⢀⣠⣯⣤⣤⣤⣤⣤⢤⣤⣀⣳⠀⠀⠀⠹⣿⣼⠀⠈⠻⢿⣿⠀⠀⢻⣿⡀⢻⣿⣧⢸⡈⢿⣌⢧⠸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠾⠋⣿⣿⠇⢰⣿⠃⣾⠏⠀⣾⣿⣿⣯⣬⣿⣯⣽⣿⣾⣿⣿⡿⠀⠀⠀⠀⠹⣿⣧⣤⣤⣤⣿⣇⡀⠀⢻⣷⡀⢻⣿⡆⣷⡈⢿⣮⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢸⣿⣿⢀⣿⠃⢰⠏⠀⠀⠙⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣬⣿⡿⣷⢠⣿⣏⠈⢿⣷⣿⣷⡈⣿⡿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠟⢻⣸⠓⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠈⠉⠛⠿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣜⣧⠈⠛⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡏⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⠀⣿⣿⣿⠙⢿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⣟⠀⠄⡿⠙⠷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣸⣿⣦⡀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⣿⢉⣿⣶⣬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠋⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⣿⠃⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠋⠉⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢩⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⡾⠃⠀⢻⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢺⠏⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⣤⣴⣿⣿⣿⣿⣿⣿⠿⠛⠙⣇⠻⣿⡏⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀⣀ ⠉⠉⠉⠉⠉⠉⠉⣹⠟⠀⠠⣄⠀⠈⠀⠙⣇⢹⣄⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠶⠛⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣛⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠹⡇⠀⠘⢿⣶⣼⣷⣶⣤⡄⠀⢀⣠⠤⠒⠚⠻⣦⡘⢷⡀⠀⣀⡀⠀⣀⡴⠚⣿⠟⠟⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢦⠻⠀⠀⠀⠙⢿⣇⣉⣹⠇⠴⢋⣠⠔⠊⠳⢤⡈⠛⠆⣹⣿⣿⣷⠞⠉⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠬⢿⡆⠀⠀⠀⠐⠀⠒⠂

⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢀⢸⡀⠀⠀⠀⠀⢹⡀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡴⣰⡏⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⠀⢀⡇⢸⠁⠀⠀⣼⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣠⠞⠁⣴⢣⢿⡁⠀⠀⠀⡀⢰⣧⠀⡄⠀⢀⡞⠀⢸⠁⣾⠀⠀⣰⠃⣸⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⣴⠋⢀⡞⣹⡟⢸⡇⠀⠀⢰⠃⡞⢸⡆⣇⠀⡼⡇⠀⣼⢰⡿⠀⣰⠇⢀⡏⡄⠀⢀⠀⣇⠀⠀⠀⠠ ⡇⠀⠀⠀⢀⡆⠀⠀⠀⡾⡟⣼⢣⠀⣾⣤⣿⠃⠈⣧⠀⠀⢸⢰⠁⠈⣧⠏⡻⢥⡇⢰⢯⢿⣇⡼⢻⠀⣼⠀⠇⠀⢸⠀⣗⠀⠀⠀⠠ ⡇⠀⠀⠀⣼⠁⠀⠀⢸⣣⣷⣿⡾⢾⠛⡉⡏⠀⠀⢸⡄⠀⢸⣼⠀⠀⢻⡼⠁⢸⣹⠿⢯⣼⡟⠀⢸⢰⡇⠀⠀⠀⣼⢀⡏⠀⠀⠀⠈ ⡇⠀⠀⢰⡇⠀⠀⠀⡿⣽⠃⣿⡧⠞⠀⣷⣇⠀⠀⠀⢳⡀⢸⣿⡀⠀⠾⠀⣠⣬⣤⡀⠰⠃⠉⠉⢻⡏⡇⠀⠀⢀⡇⢸⡇⠀⠀⠀⠀ ⡇⠀⠀⣾⡇⠀⠀⢰⡇⡿⣶⣿⣿⣷⣶⣿⣿⣿⡆⠀⠀⢳⡀⣯⣧⠀⠀⣾⣿⣿⢿⣿⣿⣷⣶⣤⣉⣠⣇⡀⠀⡼⠀⣼⠁⠀⠀⠀⠀ ⣇⠀⢸⡏⡇⠀⠀⣼⢷⣿⠿⢻⡿⠟⠛⠛⠋⠛⢷⣶⠀⠀⠳⣼⡙⠳⣄⣿⡽⢿⡟⠀⠀⠉⠙⠿⣏⣿⠋⠀⡼⠁⢰⡿⠀⠀⢸⠀⠀ ⢸⠀⣸⣇⣇⠀⠀⣿⡼⣧⠖⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠃⠙⢻⡇⠸⣧⠀⠀⠀⠀⠀⠈⣿⣆⡼⠁⠀⣼⠇⠀⢠⠇⠀⠀ ⢸⡆⣿⣾⢻⠀⠀⣽⠣⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠸⠰⣿⡄⠀⠀⠀⠀⢸⣟⣿⠁⠀⣰⡟⢀⣤⡟⠀⠀⠀ ⠸⣇⡏⠹⡿⡆⠀⣿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⡴⢳⠃⡾⡾⠀⠀⠀⠀ ⠀⢹⡇⠀⢹⣷⠀⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠘⠃⢹⠇⡼⢁⡏⣼⡿⠁⠀⠀⠀⠀ ⠀⠈⣷⠀⠈⣿⡆⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠓⣾⣿⡀⠀⠀⠀⠀⠀⠀⣿⡼⠁⡼⣸⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠘⠦⠀⠘⣿⡜⡾⣿⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠶⠶⠿⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⣿⡥⢺⣱⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣵⠻⣿⡃⠀⠀⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠀⠀⠀⠀⠀⣿⠏⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠑⢦⡀⠀⠀⠀⠻⢽⣦⡤⣀⣀⣀⣀⣀⡤⣴⣲⠿⠋⠀⠀⠀⢀⡼⠛⠐⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣰⣿⣼⢻⣿⡭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣴⣟⠁⠀⢀⡇⢠⡿⠻⡔⣾⣆⠀⠀⠀⠀⠀⢰⡿⣆⢻⡀⠀⠀⠀⠀⢸⡏⠙⣿⡆⢸⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⡄⠀⠀⢀⣠⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣠⡿⠁⠈⠙⠛⠻⡇⢰⡇⠀⢿⣿⣿⣆⠀⠀⠀⠈⢹⡿⢿⣼⣧⣤⣄⣀⣀⣀⣷⠀⠻⢿⣾⣇⣻⣿⣿⣿⣿⡿⣸⣿⣿⣿ ⣟⣀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣿⣇⣼⣿⣷⣶⣤⡀⠘⣇⢸⡇⠀⠘⣇⢻⣿⠀⠀⠀⠀⢼⡇⠀⠙⣿⣆⠀⠀⠀⠈⢿⡦⣄⠘⣿⡛⢷⣿⣿⣿⣿⢡⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⢀⡿⠀⠀⠀⣦⣿⣿⣿⠋⠁⠈⢉⣙⠻⢿⣿⣼⣷⠀⠀⢻⣾⣿⣆⡄⠀⠰⣾⠋⠉⠉⣛⣻⣦⣤⣤⣀⡘⣧⠈⠁⢹⣿⢸⠙⣿⣿⣷⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡾⢸⡇⠀⠀⠀⣿⣼⣿⢿⠀⢀⣼⣭⣿⣷⡄⢻⣿⡏⢧⡀⢸⣿⡇⢻⣿⡀⢀⣟⣴⣿⣿⢿⣿⠛⠻⠿⣿⣷⣾⣦⣄⣸⣿⢸⣀⣼⣻⠯⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠁⠀⠀⠀⢰⣇⡿⣿⠀⣠⣴⡿⠿⣿⠀⠀⣼⣿⣿⣿⢿⡷⠈⠙⣧⠀⠑⣾⣿⠀⠀⣿⣷⣾⠟⠋⢁⣴⣋⣽⣿⡄⠀⠀⠙⢿⣿⣆⠈⣿⠺⣿⡿⠋⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⠏⢠⡏⠀⣼⠃⠀⢠⣿⣀⠀⢻⡙⠛⣿⠾⠁⠀⠀⠈⠓⠀⠻⠃⠀⠀⡟⢸⠃⠀⠀⣾⢿⣿⣿⣿⣿⠀⠀⠀⠘⣿⠻⣦⣿⠀⢻⣦⣄⣈⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⢠⡞⠁⠐⣿⣷⣾⠷⠂⠀⣸⣿⣟⠳⠤⠽⠯⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠀⣷⠾⠿⣿⣨⠟⠀⠀⠀⠀⣸⠀⣸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⡀⠀⡾⠀⠀⠀⣿⠟⠁⠀⢀⣴⣿⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⣼⣦⡴⠟⢁⠀⠠⣄⠀⡴⠃⢰⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣵⣿⠋⣸⣇⠀⠀⣼⡇⠀⠀⠀⣿⣾⣿⣷⡀⠙⠷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⢛⡿⠒⢬⡩⣄⠀⣿⡟⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⢿⡟⢀⣿⣿⠀⠀⣿⡇⠀⠀⢀⣾⣿⡟⢿⣿⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡇⠈⢷⡿⠀⣿⡇⢸⣿⠟⠛⠛⣿⣿⣿⣿ ⣿⠀⣿⣾⠁⢸⣿⡇⠀⢀⣿⡇⠀⠀⢸⣿⣿⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣼⠃⣐⣾⠃⢠⣿⣷⠟⠁⠀⠀⠀⣿⣿⣿⣿ ⠟⠀⠹⡇⠀⣿⡟⠀⠀⢸⣿⣇⡤⢤⡘⡏⣿⣿⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⡤⢴⣿⠀⣼⠃⠀⣾⢻⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿ ⠐⡆⢰⡇⠀⣿⣤⠴⠚⣿⠃⠉⠀⠀⠙⠁⢿⣿⢿⡿⣇⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡾⠁⠀⠀⣸⣿⠇⠀⣼⠏⣾⠇⣀⣴⣿⣿⡿⠟⢛⣿⣿ ⠀⣇⢸⣇⣸⣿⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⣿⣾⠇⢻⡄⠀⠀⠸⣿⣯⣍⣓⠒⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠟⠀⠀⠀⣴⢃⣿⢀⣾⣣⣾⣷⣿⣿⣿⠟⠁⠈⢡⢸⣿⣿ ⠀⢹⡘⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣼⡇⠀⠀⠀⠀⠀⢠⠏⢠⡟⠀⠀⠀⣼⠃⣸⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣰⣿⣿⣿⣿ ⠀⠈⢧⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣴⣿⠟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣰⡏⢀⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿ ⠀⠀⠈⢇⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢀⡞⠁⠀⠀⠀⢾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⡀⠈⠉⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⣀⡜⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣴⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣠⠟⠁⢠⠏⠀⠀⠀⠀⢀⡜⠋⠀⡰⢃⣾⠋⠁⢠⣾⣿⠟⠀⠀⣰⡿⠁⠀⡿⡆⠀⠀⠘⠘⡇⠀⢸⠀⠀⢻⡀⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣠⠀⡴⣴⠋⠀⠀⡎⢠⠀⠀⠀⢀⡞⠀⠀⡼⢁⡾⠁⠀⣰⡿⢫⠏⠀⠀⣼⣿⠃⠀⣰⢿⠀⠀⠀⢰⠀⡇⠀⠀⠁⡇⠈⡇⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⡼⢠⠃⢰⣳⠃⠀⢰⣾⢃⡇⠀⠀⠀⡼⠁⠀⣰⠁⣾⠃⠀⣴⠏⠀⡎⠀⢀⡜⣹⠃⠀⢠⢿⡜⠀⠀⠀⢸⢠⡇⠀⢰⠀⡇⠀⢹⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⢰⢃⡏⢀⡷⠁⠀⢠⣿⡏⡼⠀⠀⠀⣰⠃⠀⢠⠇⣼⠇⢀⣼⣯⣤⡼⠀⣠⣾⣲⡏⠀⢠⢟⣿⡇⠀⠀⡀⡇⡼⡇⠀⢸⡀⠐⠀⢸⠀⠀⠀⢰⢳⠀⠀ ⠀⠀⠀⠀⠀⣾⠇⡞⡼⠀⡼⠁⠀⢀⣾⡿⢠⠇⠀⠀⢰⡿⠀⢠⠏⣼⡏⢠⢞⣉⣀⡈⢁⣼⠥⢤⣾⠀⢠⠋⠀⣽⠃⠀⠀⣹⢀⣇⡟⠀⡼⡇⡀⠀⢸⡄⠀⠀⠈⡞⡆⠀ ⠀⠀⠀⠀⢰⡟⠀⣷⣇⠞⠀⠀⢠⡞⣼⡇⣾⠀⠀⢠⡏⡇⠀⡾⣰⣳⢡⠿⢶⣶⣿⣰⣿⣿⣿⢿⡇⢠⠋⠀⠀⣿⠀⠀⣰⣏⡞⠐⡇⢠⣇⡇⡇⠀⢸⡁⢠⠀⢰⡟⣇⠀ ⠀⠀⠀⠀⣿⣿⠀⣿⠏⠀⠀⢠⣿⣹⠏⡇⣿⠀⠀⡼⠀⡇⢸⣧⠟⢿⡋⠠⠾⠿⠿⠿⠿⠿⠖⢸⣰⠃⠀⠀⢰⡏⠀⡴⢻⣿⣷⣤⣇⡜⠉⢿⡇⠀⢸⠀⢸⠀⢸⢧⢸⠀ ⠀⠀⠀⠀⡏⡟⣰⠃⠀⠀⢠⠏⢡⡟⠀⣿⣿⠀⢰⡇⠀⣇⣿⡟⠀⣉⣳⠀⠀⠀⠠⣤⣶⠚⢉⣿⠃⠀⠀⢀⣿⠇⡼⢁⠟⠈⢹⣿⣿⣶⣤⣿⡇⠀⣼⡇⢸⠀⢸⠚⣼⠀ ⠀⠀⠀⠀⠃⡿⠁⠀⠀⣰⠃⢰⣿⠁⠀⢻⢻⠀⢸⡇⠀⣿⢻⣇⠀⠈⡟⢦⣄⠀⢸⠁⠉⠳⠾⠃⠀⠀⠀⢼⣿⡼⠉⡏⠀⠹⣍⠛⠿⣏⣙⣿⠇⢰⢻⡇⡏⠀⡿⠀⡿⠀ ⠀⠀⠀⢐⡞⠁⠀⠀⡴⠁⢀⢯⣿⠀⢀⣼⣿⡇⢸⡇⠀⢿⠈⠁⠀⢀⠃⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢣⠀⠀⠈⢷⣀⣀⣹⣻⢀⡞⣼⣡⡇⡸⠁⢀⡇⠀ ⠀⠀⢀⡞⠀⠀⠀⡼⠁⠀⣼⡏⡏⢀⣾⣽⣿⢱⣹⣿⡀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣈⡿⡏⠁⣇⣾⡟⣿⣿⣰⠃⠀⠸⠀⠀ ⠀⠀⣼⠄⠀⣀⡾⠀⠀⢰⡿⠀⣇⣸⠱⣼⡟⠊⢿⣷⣇⢀⡴⡆⠀⣄⡀⠀⠀⠈⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠁⣸⣿⠿⣷⣏⡿⠃⠀⠀⠂⠀⠀ ⠀⢰⡝⠀⣸⡟⠀⠀⢠⡏⡇⠀⢿⡏⢧⣸⡗⠀⠈⢿⠟⡟⠀⠃⠀⡏⠹⡄⠀⣴⡾⠛⠉⠀⢀⣀⠉⠙⠒⠲⠤⣄⣀⠀⠀⠀⡼⠀⠈⠁⣹⠇⣶⢻⣸⡀⠀⠀⠀⠀⠀⠀ ⢀⡗⠀⢰⡟⠀⢰⣾⢻⠀⠀⠀⢸⠇⠀⣿⣿⣀⣴⠏⢠⠃⠀⡄⠀⡇⠀⣇⢠⣋⣰⣶⣶⣿⣿⣿⣿⣶⣶⣦⣄⣀⠉⢹⡄⢀⡇⠀⠀⢠⣿⢠⡏⠀⣇⡇⠀⠀⠀⠀⠀⠀ ⣼⠃⠀⡾⠀⠀⢸⣿⢸⠀⠀⠀⠸⡀⠀⣨⠟⡹⠃⠀⡎⠀⠀⡇⢀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢉⣿⠀⠸⠀⠀⠀⢸⡇⢸⠙⡆⢹⡇⠀⠀⠀⠀⠀⠀ ⠏⠀⢸⡇⠀⠀⠸⡟⡏⠀⠀⠀⠀⡧⠞⠁⡼⠁⠀⢸⠀⠀⢰⠀⢸⠀⠀⡿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡏⠀⠀⠀⠀⢀⡞⢳⡏⠀⢸⣼⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢸⠀⠀⠀⡇⢹⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⣾⠀⠀⢸⠀⢸⠀⠀⢧⡁⠀⠀⠒⠀⠀⠀⠀⢀⡉⠻⠿⣿⣿⣿⠀⠀⠀⠀⢠⡞⢡⡾⠀⠀⡈⢸⡿⠀⠀⠀⠀⠀⠀ ⠀⢸⠿⣼⡀⠀⠀⢻⡸⡀⠀⠀⢧⠀⠀⠸⣧⠀⠀⢹⡇⠀⠈⣧⣸⠀⠀⢸⠽⠶⠾⠟⠒⠠⠤⢄⣀⣀⠈⠉⠉⣻⠇⠀⠀⣀⠔⠁⢁⡞⣀⣀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⣷⢧⠀⠀⠈⢧⢧⠀⠀⠘⡄⠀⠀⢿⠀⠀⠀⣧⠀⠀⠹⣿⡄⠀⠘⡆⠀⠀⠀⠀⣠⠖⠀⠀⠀⠉⠙⠒⠃⠀⣠⠾⠟⣄⠴⠚⠉⠀⠀⢸⡁⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⣿⡄⢹⣯⣆⠀⠀⠘⡞⡄⠀⠀⢳⠀⠀⠈⣇⠀⠀⢸⠀⠀⠀⠹⠃⠀⠳⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠴⠖⠉⠁⠀⠀⠀⠀⠀⣸⠆⠊⠀⠀⠀⠀⠀⠀⠀ ⡄⠁⣇⠈⣟⢿⣆⠀⠀⠘⡽⡀⠀⢸⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⢶⣀⠀⠀⠀⠀⠀⢀⡤⣺⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⡀⢸⡀⠘⣎⢻⣧⡀⠀⠸⡽⡄⠀⢧⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠈⠙⠲⠤⢤⠞⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⣧⣠⠜⢧⡙⢷⣄⠀⠘⢿⣄⠀⢳⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢀⡸⣇⠘⣧⠀⠀⢿⣦⡙⢷⣤⡀⠙⢆⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⡼⢧⠀⠀⠀⠀⠀⣠⣶⠟⢻⣿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠘⣧⡘⢷⣄⢸⡿⡛⢶⣽⣷⣆⠀⠳⡜⣿⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⠃⣨⣶⠶⠒⣲⢾⣏⠀⠀⠈⠉⡍⠀⠙⣗⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠵⠄⢻⡛⢷⣽⣦⡈⠙⢟⡷⢦⡙⣾⣇⠀⠙⢦⡀⡀⠀⠀⠀⠀⣀⡤⠖⠋⢻⡼⠀⢙⣧⡀⠀⢉⠉⠀⠀⠤⠄⠀⣛⣆⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢡⣾⣿⣷⣦⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⣽⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⢿⣿⣿⣿⣿⣿⠟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡞⣿⣿⣿⣿⣿⣿⠇⡀⣭⠉⠁⣿⠛⢿⡟⠀⠀⠀⠀⠀⠀ ⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡝⢿⣿⣿⡿⠏⠀⠻⠊⠁⠈⣿⡄⡼⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣶⢶⣦⣤⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⣀⣀⠀⠀⣀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣶⣶ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⢀⣀⣀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⡾⢋⣡⣤⣤⣭⡙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣛⣛⡛⠳⣦⡀⠈⣿⣿⣿⣿⣿⣿⣏⠙⢿⠃⠀⠀⣴⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⠋⠀⢹⣿⣿⣿⣆⣿⠛⠀⠀⠀⠀⠀⣴⠿⣿⡵⠋⢻⣿⣿⣷⣎⢻⣆⣿⣿⣿⣿⣿⣿⡏⢳⢸⡆⠀⣼⣿⣿⣿⡿⠟⠛ ⠀⠀⣿⣿⣿⣿⡿⣵⣶⡶⠦⢼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣦⣤⣾⣿⡿⢿⣿⢹⡀⠀⢠⣿⢏⡼⣡⢰⣿⡁⠀⣰⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠇⠈⣸⣁⣠⣿⣿⡿⠋⠀⠀⠀ ⣶⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⡘⣿⣿⣿⣿⣿⣧⠸⣿⣄⣹⢿⣃⣼⣿⡞⠀⡀⡼⢡⡞⡴⢡⠞⡇⢿⡝⢿⣿⣿⠃⣹⡇⢿⣿⣿⣿⡿⠟⠛⠛⠒⠿⣭⣿⡍⠛⠀⠀⠀⠀⠀ ⠛⠛⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠃⠘⢿⣿⣿⡹⣿⡆⠈⠙⠛⠛⣛⡩⠞⠁⠈⠈⠀⠋⠼⠁⡡⠂⠹⣌⠻⠿⣿⣿⠿⠋⠀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⠀⠀⠀⠀ ⠂⠀⠀⠻⣿⡇⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠉⢻⣧⡈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢰⣿⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀ ⠉⠁⠀⢰⡟⡇⢸⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⢹⡝⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⣿⠀⠀⢀⡎⠀⠀⡞⠀⠀⡤⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣷⣤⣧⠤⣷⡤⠴⣷⠤⠤⠔⣷⣴⡾⠉⠢⣀⠀⠘⡷⠒⠒⠒⠒⠊⠉⠛⠛⠿⠿⠶⠤⣀⣓⣒⣲⡇⠀⠀⢰⣿⣿⣄⣀⣼⠀⠀⡸⠁⠀⡼⠁⠀⢀⡾⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠦⠼⢧⡤⠽⢤⣴⠾⠋⠁⠀⠀⠀⠈⠉⠑⠛⠦⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣭⠀⠊⠠⠋⠉⠛⠳⣌⣻⡓⠚⣧⠤⣴⡇⠀⣀⣞⣤⣾⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠈⣉⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠿⣟⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⢰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⡞⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⣹⠉⠉⡉⠉⢩⡟⠉⠉⢉⡟⠉⠙⠉⠉⠉⠉⢉⡏⠙⣿⡍⠉⠉⢻⡉⠉⠉⠉⢩⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠃⡠⠊⠀⣰⠋⠀⠀⠀⣼⠃⢸⡄⠀⠀⠀⣀⣾⠀⠀⠘⣷⡀⠀⠀⣇⠀⠀⠀⠀⣽⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣿⡿⠀⢰⡼⠁⠀⠀⢀⣼⡟⢀⣾⣿⠀⠀⢀⣿⡉⠀⠀⢠⠹⣧⠀⠀⢹⣇⠀⢸⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⡿⠁⠀⠀⣠⣞⣱⣧⡾⢾⡿⠀⣸⢸⠟⠉⠒⠢⠤⣤⣽⣧⣀⣸⣿⠀⢸⠀⠀⢿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢻⢉⣿⡄⢀⠤⡗⠒⢉⣽⠋⠉⠁⠞⠀⢨⡇⠀⡇⡏⠀⠀⠀⠀⠀⠀⠈⢹⣿⣉⣿⡗⢺⢄⡀⢸⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⢸⣿⣾⡇⠀⣀⣧⣴⡿⢿⣿⣿⣿⢶⣦⢸⠀⢸⢳⠃⠀⠀⠀⢀⣴⡾⣿⣿⣿⣿⣿⣷⣴⠀⠰⢾⠀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡟⠁⡟⢿⡏⠁⢰⣿⣿⣿⣿⣧⠈⡏⣠⣿⡏⠀⠀⠀⠀⠞⠁⣰⣿⣿⣿⣿⡟⠘⣻⡟⠀⣿⣸⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢰⣿⠈⢃⠀⢸⣿⡿⠿⢿⡟⢀⡱⢻⡟⠀⠀⠀⠀⠀⠀⠀⣹⣿⠿⠿⣻⠁⠀⡟⠀⠀⣿⠟⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠇⡼⢼⡆⢸⠀⣈⣻⡿⠿⠟⣠⠋⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠶⢿⠆⢰⡇⠀⠀⣿⣿⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡇⠊⢳⡈⡇⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡞⠀⣾⣇⠀⠀⣿⠏⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⢻⣷⢾⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⢨⡏⣽⠀⢰⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠹⣷⣽⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣿⠀⣾⣧⣤⣀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⠖⠒⠛⠾⢷⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣿⣿⡄⣿⡇⠉⠻⣷⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠘⡆⠀⠀⢰⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣾⠟⠁⣷⡿⢹⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡿⢡⢿⡁⢣⠀⢡⡄⠀⣾⠇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠁⠀⠀⣿⡇⠸⡇⠀⠀⢸⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠏⢸⢡⠇⢸⡇⢀⢧⠈⢧⣸⠏⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⢰⣿⡄⠀⢹⠀⠀⠀⣷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠸⡌⠸⠀⠀⣷⠏⠀⠷⣌⢯⠀⠀⠀⠀⢀⣷⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⣯⣀⠀⠀⠀⣾⢇⢱⠀⢸⡀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣧⠀⢤⠸⣇⣰⠞⠉⠳⢷⣄⣠⣶⢍⣽⠀⠀⠀⠀⠙⠲⠤⣀⡤⠖⠋⠁⠀⠀⢠⡇⢠⠛⡄⣸⠇⠘⡆⢣⣀⠇⢠⣞⣴⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠤⠤⠼⢦⠙⢄⠘⣆⠹⣧⣀⣀⣤⣤⡾⠉⠀⡼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠎⠀⣸⣧⣄⣀⣘⣆⢹⠖⠛⣩⡞⠀⢸⣧⣀⣀⣀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⠳⣯⢦⣻⣀⣾⣿⠟⠀⠀⠀⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠠⠞⠁⢹⡛⣏⣐⣹⠇⠀⣼⢉⠂⠀⢸⢿⡇⠀⠀⠉⠙⠒⠤⣄

⠀⠀⠀⠀⠀⠀⢀⣾⣟⡾⣣⡆⢠⣿⣿⣿⢿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣾⣿⣿⣿⣻⣿⡿⣿⣿⣿⣧⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡿⣿⣵⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠋⣸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢻⡗⠲⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⢀⣴⣿⣿⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠢⣤⣯⣍⡙⠒⠒⠤⠤ ⠀⠀⡼⢻⠁⡞⣿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇⢻⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢌⠙⢦⣽⠶⠤⣀⡀ ⠀⡼⠁⣮⣸⣼⠏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⢿⣿⠗⠆⣻⣿⢿⣿⣿⡘⢿⡉⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢷⡦⣈⠓⠦⣄⡀ ⡼⠁⠀⣿⢿⡟⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣿⣡⣤⣚⣁⣈⣀⣀⣀⣀⣀⣤⠬⠽⠥⠬⣷⣶⣶⣿⣦⣬⣙⣻⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣯⢿⣦⠰⡀⠙⠮⣝⠲⠤⠀ ⠃⠀⢀⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠈⢿⡀⠀⠀⠀⢠⣾⠿⣿⣿⣿⣿⣿⣶⣍⣻⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠈⠙⠲⠄ ⠀⠀⣼⣿⠃⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⣛⣿⢿⠿⢿⠟⠋⢻⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀ ⠀⢰⣿⡏⢈⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠳⣠⣞⣛⣋⣈⣍⣵⡶⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠲⠿⠦⠾⣤⡦⣞⣤⠎⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣿⣷⡈⠙⠳⠦ ⠀⢸⣿⠀⢸⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣇⠀⠙⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠹⣄⠀⠀ ⠀⢸⡇⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀ ⠀⣾⡇⠀⠸⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⢁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁ ⠀⠛⣷⡀⠀⡇⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⢀⡿⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠆ ⠀⠀⢹⠙⢦⣹⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤ ⠀⠀⠘⡆⠀⠹⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⡄⠀⠹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠙⣄⠀⢹⡸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠓⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣿⣿⣿⣦⣍⠙⠛⠒⠶⠤⠄⠀⠀⠀⠀⢀⣠⠔⠋⢹⠀⠹⡝⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣬⣻⢿⣿⣿⣿⣿⣿⣿

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⣿⠃⠀⢠⡟⠀⣠⣿⣿⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢛⡶⠋⠀⠀⠀⠀⢿⡟⠀⠘⣇⠀⠀⠈⠉⠠⣾⡀⠀⢿⡇⠀⠀⠀⠀⠀⢹⠘⠆⢻⡉⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⣤⣿⠅⣀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⡆⠀⠀⠀⠠⣿⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⠤⣄⡈⠉⠛⠶⢤⡀⠀⠀⠀ ⠀⢈⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠈⠉⠒⠦⢤⣀⣀⣈⣧⣀⠀⠀⢻⡆⠀⠀⠀⡏⢻⣇⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀ ⠀⣿⣿⡇⣸⣿⣿⡏⠀⢀⡄⠀⠀⠀⠀⢀⡆⢀⡾⠃⠀⠀⢀⣀⡀⠀⠀⠈⠉⠻⠛⠛⠃⠈⣷⡠⢀⣼⠃⠀⢹⡄⡟⣧⠀⠀⠀⠀⠀⡆⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠀ ⣼⣿⣿⢡⣿⣿⣿⠃⠀⣸⡇⠀⠀⠀⠀⢸⣇⣼⢁⣴⠞⠛⠋⠉⠙⠛⠲⢶⣄⠀⠀⠀⠀⠀⠘⣷⡈⣿⣆⠀⠀⢻⡇⠸⣇⠀⠀⠀⠀⡇⡟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⡆⢰⣿⡇⠀⠀⠀⠀⠀⣿⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠘⣿⡇⠈⠙⠦⣈⣇⠀⣻⠀⠀⠀⢰⠇⡇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠏⣼⠁⢸⣿⡇⠀⠀⠀⠀⣤⠙⢫⡷⢤⣞⠀⠉⠓⢒⡒⣤⣤⣬⡭⠁⠀⠀⠀⠀⢀⡼⠗⠲⠦⣄⡀⠙⢀⣿⡆⠀⢠⡾⢸⡇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⣿⠀⣹⣿⡇⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠙⣦⣼⣿⣧⢀⣼⠃⣾⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⣿⠀⣿⣿⡇⠀⠀⠀⠀⡷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⠀⠙⠻⣿⣿⣾⢃⡼⢿⠏⢻⠒⠶⢤⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⢲⣿⣿⡇⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡷⣦⣀⣾⡟⠃⠈⠁⣾⡀⠀⡄⠀⠀⠘⡇⠀⢻⠻⠷⢶⣦⣀⣀ ⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠘⣿⡇⠀⠀⠀⢸⣿⠛⠃⠀⠀⠀⡇⠀⠙⠀⠀⠀⠈⠉⠉ ⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⡇⠀⠀⠀⠀⠀⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⠀⠀⢸⡿⠀⠀⠀⠀⠀⡇⠒⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣧⠀⠀⠀⠀⢠⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠁⠀⣿⠐⠀⠀⠀⠠⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠁⢀⣾⡇⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⡀⢠⣄ ⠿⠟⠛⠛⠛⠉⠉⠹⣿⣿⣿⡗⠀⠀⠀⠈⣿⣧⡀⠀⠈⢙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⢿⣿⡇⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⣿⣗⣻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⡇⠀⠀⠀⠀⣿⡄⠙⠳⠶⠛⠁⢀⣉⠙⠳⣶⣤⣤⣄⣀⣀⣀⣤⣴⡟⣿⣿⣿⣿⣿⣿⠏⠀⣿⡇⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣽⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⡟⠀⣰⣿⣇⣸⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠙⠄⠙⢿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⡟⢀⣴⣿⣭⣿⣛⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀ ⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀ ⠀⠀⣾⣿⡿⠁⠀⠀⣄⡀⠀⠀⣀⣀⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣄⣀⡀⠀⠀⣀⣄⠀⠀⢹⣿⣿⡄⠀ ⠀⣸⣿⣿⠁⠀⠀⠀⠉⠛⠻⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⢿⣿⣷⡀ ⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇ ⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠛⢻⣿⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣟⠛⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⣹⡇⠀⠀⣸⡏⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠈⣿⠀⠀⠈⣿⣹⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⢁⣿⠁⠀⠀⣿⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⡆⠀⠀⣿⡇⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏ ⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠘⣿⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃ ⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⡇⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡄⠀⠀⠀⠀⣿⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀ ⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣧⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀ ⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣾⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠘⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠿⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠹⢷⣦⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⠾⠿⠿⠟⠛⠛⠛⠛⠻⠿⠷⠶⠶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⡆⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣤⣤⣴⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⣤⣴⡾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢀⣀⣤⣴⡶⠟⠛⠉⠉⠉⠙⢿⣦⣀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠷⠶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢠⣤⣤⡤⣀⣀⣤⣀⡀⢀⡀⡀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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