⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⣟⢻⠻⡿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⡙⢦⢃⡇⣣⠝⣸⢛⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠻⡌⠶⡙⠦⣍⠲⡅⡞⣡⠎⡴⢹⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡿⢫⡱⢋⡼⢱⠩⢞⡰⢍⡲⢱⡡⢞⡡⢏⡜⡜⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⢫⡜⢣⠜⣣⠜⣡⠛⣤⢋⢖⡩⢖⡱⣊⡜⢲⡘⣜⢢⡋⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⡫⡜⢥⣊⠧⡹⢄⡛⡔⢫⡔⣩⢆⠳⡜⡰⢥⠚⣥⠚⣤⠓⡼⢡⡚⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡛⣬⢑⠮⡱⢌⡖⡍⣎⠱⢎⢣⡜⢆⡎⢳⡘⡕⣪⢙⡤⢛⠤⡛⣔⢣⠹⡌⡞⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢏⠖⣱⢂⢏⡲⢍⡲⢜⢢⠍⡞⣡⠧⣘⠎⡜⡥⢚⢬⡑⢮⢰⢋⡼⠱⣌⠎⡵⢊⡼⢌⡽⢿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⢣⢎⡹⢤⢋⢦⠱⢎⡱⢪⠱⢎⡱⢆⡣⢇⢺⠱⣘⡍⢦⡙⠦⡍⠶⣨⢓⢬⠚⡥⢋⡴⢃⠞⣰⢻⣿⣿⣿⣷⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⢫⢔⠣⢎⡲⢥⢋⠦⡛⣌⠶⣉⢳⢊⡕⢎⡱⢎⢥⢋⠖⡬⢣⠜⡳⠸⡅⡇⠞⣌⢣⡍⣣⠜⣩⠚⣥⢒⠼⣻⣿⣿⣿⣦⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢟⡱⢋⡬⡙⢦⠱⢎⢎⡱⡱⢊⡖⡍⢦⢋⡼⡘⠦⣍⠦⣋⠼⡡⢇⢫⠜⡣⡕⢎⡝⡬⣒⠜⣡⠞⣡⠫⣔⡩⢖⡡⢟⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢋⢦⢃⡏⢴⡙⡬⢓⢎⡜⢢⢓⣍⣲⣩⣖⣣⣒⣍⠳⡌⣖⠩⡖⡹⡘⢎⣜⣱⣬⣣⣜⣔⢣⡙⢦⡙⡴⢓⠦⣱⢊⠵⣊⡜⣻⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡟⢥⡚⢬⡒⣍⠦⡓⡬⣍⠲⣬⣷⣿⠿⠛⠛⠛⠛⠛⠿⣿⣶⣬⣓⣼⣵⣿⡿⠛⠛⠛⠛⠛⠻⢿⣿⣦⡓⡬⢓⡜⣢⠍⡶⢡⢎⡱⢛⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⢏⢎⡱⡜⣡⠞⡤⡓⡥⣓⣬⣿⡿⠋⠀⢀⣴⣶⣿⣿⣶⣦⡀⠙⢿⣿⣿⠟⢁⣤⣶⣾⣿⣷⣶⣄⠀⠈⠻⣿⣶⣉⠖⣡⠏⡴⢋⢦⠱⣍⡚⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⣼⣿⣿⣿⣋⠮⡜⢢⡕⢣⡚⡔⡣⡕⣳⣿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⣿⣧⠞⣡⠞⣡⢋⢦⢋⡴⢱⠩⣿⣿⣿⣷⡀⠀ ⠀⣰⣿⣿⣿⢳⡘⢦⡙⡥⢊⠧⡜⣡⠳⣼⣿⡟⠀⠀⠀⢺⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⢹⣿⣏⠦⣙⠦⡍⢦⢋⡴⢋⡕⢪⢿⣿⣿⣷⠀ ⢀⣿⣿⣿⣏⠦⡙⢦⡙⠴⣋⡜⢲⡡⣓⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⢬⡑⠮⡜⣡⠞⡰⢭⡘⡥⣛⣿⣿⣿⡇ ⢸⣿⣿⣿⡇⡞⣩⠦⣉⠗⣢⡙⢦⢱⢊⣿⣿⡇⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢠⣿⣿⠦⣙⢲⣉⠦⣍⢓⠦⣙⠴⣡⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⣶⣡⠎⡵⢊⡵⢨⠇⡮⣑⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⢖⡩⢲⠌⡶⢡⢎⠳⣘⣼⣼⣿⣿⣿⡇ ⠀⢻⣿⣿⣿⣿⣿⣿⣶⣯⣶⣧⣹⣔⣣⣎⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢩⣆⣝⣦⣯⣴⣯⣾⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠈⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢻⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⣀⣠⣶⣿⣿⡿⢥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⡢⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⡘⣾⣿⣿⡋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢋⡼⣉⠟⡻⢿⠿⡿⢿⢟⡻⢍⡳⢌⠧⡙⢦⣙⠻⣛⠿⡿⢿⢿⣛⠻⣑⢣⡱⣹⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡞⡴⢱⠪⣕⠪⡕⣍⠎⢦⢃⡳⢸⡸⣘⡱⣊⠴⢣⠍⠶⣉⢎⠖⡌⢧⢩⢖⣱⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⢳⡡⠳⣌⢳⣘⠦⣙⠎⣥⢣⠓⡴⢃⡾⣹⢞⡥⢋⠧⡩⢎⡚⡍⢖⠣⣎⠷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠥⣃⠞⡱⢬⡳⣭⢻⡜⣘⢆⡣⢝⠲⣉⠾⡵⢫⡜⢣⡚⣵⢫⡞⣵⢊⠳⡌⢞⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢧⡳⣉⠮⡱⢃⠿⡜⢧⡙⡲⢬⡱⡾⢷⣭⢒⡱⢣⠜⣣⢙⣮⡳⣝⠶⣉⠳⡜⣼⣚⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣧⠳⣌⢣⠕⣋⢖⣩⢆⠳⡱⢆⡟⣭⢳⣻⢬⡑⢏⡜⢆⡣⡜⣵⣩⠲⣉⠳⣜⢧⡝⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⣌⠳⣌⢧⡚⢥⢪⣿⢬⣳⣵⣊⡜⢣⢏⣿⠦⡙⢎⠼⣌⡱⠜⣽⣇⢳⣉⠧⣙⢮⡝⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣬⢓⢮⡳⣝⢎⣿⣿⣧⢗⡮⣝⢮⡑⣎⣿⡥⣙⢮⡗⣦⢙⡜⣿⣿⣧⣛⠾⣥⢊⣽⣾⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣾⣌⢳⣭⣿⣿⣿⣿⣎⢷⡹⢮⡱⣾⣿⣷⣍⢞⡹⢆⡫⣼⣿⣿⣿⣯⣽⢲⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣾⣉⣷⣾⣿⣿⣿⣿⣦⣱⣮⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⣻⢿⣿⡿⣋⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⡿⠃⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘⡓⠂⠀⠀⠀⠀⠈⠛⢿⠿⠛⠁⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀