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