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