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

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

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