⢀⣠⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⢤⠤⠤⣿⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡞⠓⣶⠒⠿⡉⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣠⢴⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠉⠀⠀⠀⠀⠀⢈⢽⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡤⢖⣛⣭⠖⠋⠉⢧⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡇⠀⠀⠀⠀⠀⢀⣀⣀⣠⣫⣋⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⢸⡟⠛⢮⡙⣿⡞⠡⠋⠀⠀⠿⣟⣦⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠋⠑⠀⠀⠀⠀⠀⠀⡰⡵⠁⠉⠉⠉⠙⠛⠙⠲⠶⢮⣽⣷⣦⣄⡀⠁⠀⠀⠙⣮⡳⣄⠀⠂⠀⣀⣬⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡽⠀⠀⠀⢲⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠦⢤⣤⣾⡿⣌⢷⣾⡿⠋⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⢠⣳⠁⠀⠀⠀⠀⡇⢈⡓⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣫⠟⡠⢸⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡇⡜⠉⠒⠮⢍⣛⣉⠉⠉⠉⣉⣉⣴⠮⠗⠉⠀⠀⢿⢹⡀⠀⠀⠀⣀⡴⠖⢋⣉⣥⣶⣶⣶⣿⣶⣦⣤⣄⣀⡤⠶⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡼⢀⡇⠀⠀⠀⢀⡠⠼⣋⣉⠭⠥⢶⣶⣶⣶⣶⣤⣄⡈⢆⠻⣄⡰⣎⣩⣴⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣽⢷⣄⠙⣄⠀⠀⠀⠀⠀ ⠀⠀⢘⣇⡀⠀⠀⠠⣸⠀⢀⣀⡴⠊⠀⡼⠀⣀⡴⢞⣩⣶⠿⠽⠛⠛⠉⠉⠈⡟⢿⡟⢿⣿⡿⢿⣷⠬⣍⣙⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣠⡶⠟⠉⠀⠘⣯⠳⣌⠻⣷⣶⣄⡀ ⠀⠀⠹⡿⣿⣉⣉⠙⠊⢉⣉⣡⡴⠾⣋⣴⢟⣭⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⣠⣤⣿⡻⠴⠲⠦⣝⣷⡄⠳⡀⢀⡟⡟⢻⠋⠉⠛⢻⣿⣿⣿⣤⣄⡀⠀⠀⢿⡄⠈⠳⣌⠻⣿⣿ ⠀⠀⠀⢹⡎⣏⠉⠉⠉⠉⠁⢀⣤⠞⣫⠶⠛⠁⠀⢀⡄⠀⠀⠀⡰⠃⠀⣴⡟⠀⠈⡙⣷⣄⠐⡂⢹⣀⣭⣿⡿⡿⠋⠱⣼⣠⡺⠚⣉⣠⢭⣁⡀⠈⠛⢦⡀⠸⣧⠀⠀⠘⠷⡜⢿ ⠀⠀⠀⢸⣿⡜⡄⠀⠀⢀⣴⢛⣥⣾⠕⠔⠁⣠⡴⠋⠀⠀⢠⠞⠁⢀⣾⠟⠀⠀⠒⣿⠻⣟⢦⡐⣿⠛⠀⠀⡸⠀⠀⣴⣾⣿⢝⣉⣀⡀⠀⠀⠈⠳⡀⠀⠈⠢⣿⡄⣀⣠⠤⣚⣧ ⡀⠀⠀⢸⡇⢳⣳⢀⣴⢛⣴⣿⠟⠁⣠⣴⠞⠋⠀⣠⢤⠼⠋⠤⣤⡾⢿⣠⢄⠀⠈⢨⠟⠆⢀⣿⠃⠀⠀⢰⠃⠀⢰⠇⡀⠀⠀⠀⠈⣇⠙⢦⠀⠀⠙⣄⠀⠀⠚⠻⣯⡉⠀⠀⠀ ⠈⢣⡀⢸⡇⠀⣿⠟⣵⠟⢁⣤⡤⣿⣭⡤⢆⡴⠛⠟⠁⠀⣠⣾⠯⠤⠤⣌⠛⠀⠀⠈⡤⢠⣴⣿⡀⠀⢠⡇⠀⠀⢸⡶⢧⡤⠀⠀⠀⠸⡄⠀⠳⣄⠀⠈⠓⢤⡀⣀⠀⠙⢦⡀⠀ ⡠⠀⣳⣸⣧⡾⠋⡼⣏⡤⣺⢿⣿⠟⢉⡴⠋⠀⠀⠀⣠⣾⣿⣴⣶⣶⣶⡁⠀⠀⢀⠞⣀⣀⣾⢿⣧⡀⡌⣇⠀⠀⠘⢧⠏⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⣄⠀⢠⡟⠛⢝⢆⠀⠻⢄ ⠑⢶⣾⡟⠋⣠⠶⡿⣫⣾⣽⠟⢀⡴⠉⠀⠀⢀⣴⣾⣿⢿⣼⣽⣽⣏⢹⡦⠀⠀⣎⣴⣥⣴⣿⣿⡟⢷⣵⡸⡄⠀⢀⠀⡀⠀⢀⣤⣤⣀⣀⠙⢆⠀⠀⠈⠳⢶⠭⠔⠋⠈⡇⠀⠈ ⢦⡀⠙⢿⣶⣄⣰⢱⠏⢸⠃⡠⠋⣠⢖⣵⣾⢋⣿⠋⠈⠿⣵⢀⠀⠈⠉⠀⠀⢿⣿⣯⣟⣀⣿⣿⣧⡶⠟⣷⡿⣦⣼⣄⣹⣠⣽⡟⠓⠻⢯⡉⠈⢷⣦⡀⠀⠀⠀⠀⠀⡸⠁⠀⠀ ⠀⠙⢦⡄⠻⣮⡿⣿⣦⡟⠀⢀⣾⣣⣿⡿⠁⣼⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢳⠀⠉⣿⣹⣿⡿⣷⡀⠈⡿⣎⢸⠉⣱⢏⣴⣾⣷⣦⠌⢻⡄⢸⣄⢿⣶⣶⣤⣶⢪⡁⠀⠀⠀ ⠀⠀⠀⠱⣦⡿⠉⢀⢟⣿⡀⡾⢣⡟⣰⠁⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣳⠀⠛⣾⣿⡁⢘⡷⠲⠛⢋⣷⠇⢷⠿⢧⣷⣯⣟⣷⣶⣷⣸⣿⣦⡹⢿⣿⣿⣧⣻⡄⠀⠀ ⠀⠀⢠⡾⠋⢑⢶⢋⣾⣪⣿⠀⣸⢀⠏⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⢠⡤⣤⣀⠙⠉⠀⠀⢠⣿⣿⣿⡿⠁⠀⢀⡞⠀⠀⠘⢧⣄⠈⠉⠋⢀⣼⣿⣿⣿⣿⣿⣦⡙⢿⣿⣷⡘⡄⠀ ⠀⠀⢉⡀⢀⣸⣷⡿⣧⢋⡿⢠⣿⣾⠀⠀⠀⠘⢮⣻⣷⣄⠀⠀⠀⠈⠳⣄⣀⣭⠷⠀⣤⠟⢿⣿⣿⠀⠀⢀⡜⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣷⡜⢆ ⠀⢀⡥⢖⣽⠟⠙⠿⣿⣋⣤⡿⠛⢻⣧⠀⠀⠀⠀⠙⠻⠿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣾⣧⠀⣀⢱⢿⡀⢰⣄⡉⠓⠀⠀⣀⣀⠀⠀⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣷ ⠀⢩⣴⡿⠽⠵⢋⣤⡾⣿⠝⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣤⣴⠿⣇⠈⢯⣇⢫⡌⡈⣷⡀⠙⣟⢏⣱⣻⠞⠃⠀⠀⣻⡽⢻⡿⣿⣿⣿⠿⠛⠛⠚⠽⠿⠷⠞⠛⠿ ⠀⠀⠉⠀⠀⠀⣠⡟⣰⠃⣠⣴⣾⠛⣻⠿⠋⠛⢿⡿⠶⣦⢤⣄⡀⠈⢳⡰⠿⠃⠈⢳⡘⣿⠀⢹⡇⡿⣷⣄⠈⠉⠉⠀⠀⢀⣤⠞⠋⣠⡟⣠⣟⡩⠴⠒⠋⠉⠙⣦⣀⣠⣤⣤⣀ ⠀⠀⠀⠀⢀⣼⠏⠀⣿⢠⠟⡻⣷⡾⠋⠢⣄⠀⠀⠉⠶⣄⠉⠪⠉⢳⡄⠹⡄⠀⢀⡞⠀⣿⠀⣼⢃⣷⣷⣿⡷⣦⠤⣶⡾⠟⠁⠀⣼⠟⣰⣿⠋⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠀⣹ ⠀⠀⠀⢠⣾⠏⠀⣠⢟⣾⣦⣶⠋⠀⣤⣄⡈⠑⠢⣀⠀⠈⠑⢄⡀⠈⢿⡄⢳⣠⣾⣇⠀⣿⡞⢡⣾⠻⠟⡵⢹⣿⣇⣹⡇⠀⠀⢠⡟⣴⣿⡏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡠⣶⢾ ⠀⠀⣰⣻⠃⠀⢠⠃⡞⣨⡿⢃⣴⡶⠊⠈⠉⠓⠶⣬⣑⢄⠀⠀⠙⢦⣸⡇⣼⡟⠉⣿⣾⢋⣴⣿⠁⠀⣼⠃⠈⠹⢿⣿⡇⠀⠀⠈⣼⡿⠉⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢞⠝⠁⣀ ⠀⡼⣹⠃⠀⠀⡏⣼⣾⡿⢡⣾⠋⠀⠀⠀⠀⠀⠀⠈⠙⢳⡷⠒⠂⢀⣟⣴⡟⣇⣶⡿⣱⣟⠉⡎⣷⡀⠏⠀⣤⣤⣾⣿⣇⣠⠴⠾⣿⣤⡀⠀⠀⠀⠀⡔⠁⠀⣀⣠⣴⣶⣾⣿⣿ ⠘⠁⠃⠀⠀⢸⢀⢧⡿⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠷⠦⡴⢟⣩⡶⢷⣟⡟⡴⢻⣟⠀⣹⡹⢿⣶⣾⠿⣛⣻⣿⡏⠀⠀⠀⠀⠀⠻⣆⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⢋ ⣀⢀⠀⠀⠀⡎⣸⣿⢃⣻⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⣿⣀⡿⣸⢰⠳⡘⣿⣿⣟⣷⡴⣶⣻⡏⠉⢰⡟⣀⣀⣀⣀⠀⠀⠀⠙⣆⣴⣿⣿⣿⣿⣿⣿⣿⡿⣫⡾⠛ ⠀⠀⠀⠀⠀⡇⣿⣿⢏⠃⠁⠀⠈⠀⣁⣀⣤⡾⠿⠗⢒⠛⡻⡯⠋⣭⠉⠿⣿⠛⢛⠷⣧⣿⠿⣿⣿⠇⣿⡇⢿⣦⡟⠋⠀⠀⠀⠈⠛⢦⡀⠀⠹⣿⣿⣿⣿⣿⣿⠟⣡⡾⠋⠀⠀ ⠀⣄⠀⠀⠀⢹⣸⣿⡾⠤⣒⡾⠿⡽⠗⢻⣻⠏⠙⢠⢡⠀⢣⢧⠉⢻⠃⠀⡽⣳⠘⡶⡝⠋⠙⣿⣿⣼⣿⡇⣸⠏⢀⣤⣤⠤⠴⡿⠦⣤⣽⣀⡀⢿⣿⣿⣿⡿⢃⣴⠟⠀⠀⠀⠀ ⢂⣚⣛⠻⠭⢴⢾⢫⡍⠉⢳⢤⠀⠣⡵⠀⢏⡆⣀⢬⣟⡆⣀⣙⡷⠿⠷⠾⠾⠵⣾⣻⡀⢀⣶⣩⡇⣿⣿⡵⣯⠖⠋⣀⠤⢤⣬⣤⠤⢦⣈⢟⣿⣞⣿⣿⡿⠁⣾⠋⠀⠀⠐⠃⠀ ⠀⠹⡶⡇⠀⣾⠃⠀⣤⠀⠀⡏⠄⢠⢃⠇⣸⣟⡫⠽⠓⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⠇⡟⠀⣿⡿⠁⢈⣫⠟⠋⢉⣉⡀⠤⠴⠒⠆⠀⠀⠈⠻⣿⡻⠦⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⢱⡄⣿⠠⢞⣁⠟⠂⣧⠖⣋⡯⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢧⣴⠏⠀⢴⡋⢀⡠⠖⠁⢀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠈⠻⡆⡈⢷⣄⠁⠀⠀⠀ ⠀⢀⣎⠞⠀⢹⣆⣠⣿⣒⣽⡿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⠁⠀⠀⠈⠉⠿⢤⠴⣞⣩⠭⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣧⡀⠀⠀ ⠀⢩⣭⣭⣭⣿⣿⠿⠛⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣤⣀⡀⠀⠀⠰⣍⣀⣠⡤⠤⠤⠤⠤⣤⣀⠀⠀⠀⣿⠀⠀⠀⠩⢳⣄⠀ ⠀⠈⠉⠁⠀⠀⢸⡆⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡷⠉⠓⢶⣤⣿⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢠⣿⠀⠀⢀⣤⣤⡠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⢄⡤⠤⠄⠀⠀⠀⠀⠀⠇⠀⠀⢸⡆⣿⠀⠀⠀⠀⢀⣤⡟ ⠀⠀⠀⠀⠀⠀⠀⢹⣦⢠⣿⢈⠀⠀⠘⠁⠀⠈⢳⡂⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠽⣿⠀⠀⠀⣰⠏⢀⣼ ⠁⠀⠀⠀⠀⠀⠀⠀⢟⢿⡁⢸⠀⠀⠀⠀⠀⢀⡾⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⣿⠀⠀⡸⠁⠀⣼⠀ ⠀⢧⡐⠄⠀⠀⠀⠀⠀⠀⠙⠾⣦⣄⣤⣤⠴⠋⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄⠀⡀⢸⠀⠀⠀⢸⢀⣿⠀⢀⡇⠀⣼⡏⠀ ⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠀⠂⣿⢹⣿⠀⠀⣯⣲⣿⠁⠀ ⠀⠀⡏⠛⠽⣿⣶⣶⣠⣄⣀⣀⣀⣀⠤⠖⢿⡉⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠋⢠⣿⠈⠀⠈⢹⡏⠁⢁