My Little Pony G1 Emojis & Text

Copy & Paste My Little Pony G1 Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡽⠟⣛⣛⡓⠢⣤⣤⠜⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢹⢠⣴⣧⣫⠖⠃⠈⢱⣮⡑⠪⠯⠴⢻⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢽⣸⡘⣼⢸⠛⠿⠈⠉⠑⢪⣿⢹⣍⠩⢴⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡾⠃⡑⢧⠾⠀⠀⢀⣤⣶⣞⣥⠿⠈⠻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⢠⢁⠏⠀⠀⠀⢹⣿⣿⣶⣄⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆⠃⠸⣼⣄⡀⠀⠠⠿⣿⣿⡿⠃⠀⠀⠀⠀⠰⡆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢳⡀⠀⢌⣙⣛⣋⣠⠤⣈⠉⠀⠀⠀⠀⢀⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡢⣙⣆⡀⠀⣀⣀⡈⣉⢙⣷⠀⠀⠀⠀⡈⠝⢳⣶⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣮⣛⡿⠷⢦⣖⡿⠀⢸⣇⡠⠴⠾⣯⣍⣉⣁⣠⢿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢦⠉⠽⣖⡦⣝⡛⢶⣄⠀⠀⠀⠈⠘⢖⠒⠩⠯⠽⠿⠶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⣌⢻⠢⣄⠀⠀⠉⠓⠈⠑⢥⢣⠀⠀⠀⠀⠈⢧⣄⣤⠔⢀⣠⠼⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡤⠬⣆⡙⣦⢌⣑⠀⠈⠑⢦⠙⣏⠀⠀⠀⠀⠀⠸⣆⣠⣴⣋⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣿⠼⣷⣮⢹⡶⣄⣆⢳⢸⠀⠀⠀⠤⠤⣀⣇⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢤⡶⠶⢆⠉⠁⢺⣷⡏⡀⠀⢹⣫⢈⣯⠉⡾⡄⡼⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣀⠀⠀⢛⢆⠀⠀ ⠀⠀⠀⠀⣠⡾⢣⠎⢠⠴⠚⡷⡤⣾⣞⣀⣸⣿⣿⣭⡞⠉⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠈⢦⠀ ⠀⠀⠀⢰⡟⠀⢎⢠⣧⠀⡎⡇⠈⠻⣢⡈⠛⠉⠘⠃⢃⠞⣲⡀⠀⠀⠀⠀⠐⠦⣄⣀⣀⠀⠀⠀⠀⠀⠈⠳⣄⢈⡆ ⠀⠀⠀⢸⠁⠀⠘⣼⣾⡀⢇⠘⢆⠀⠘⢷⠋⢙⣆⡔⠙⡌⠇⠃⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⢆⠀⠀⠀⠀⠀⠘⢾⠃ ⠀⠀⠀⠘⡅⠱⣤⣈⠓⠷⣜⣦⡈⢣⡏⠙⠉⠻⠏⠉⠟⠃⠀⢀⠀⣠⣤⡞⠁⠀⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⢀⣈⡧ ⠀⠀⠀⠀⣿⡦⣀⡉⠉⠓⠒⠮⠭⢐⣾⣄⠀⠀⠀⠀⠀⠀⠀⣾⠋⢉⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⣠⡟⡡⠀⠏⠙⣟⢏⠑⡲⡰⡞⡿⠦⠀⠀⠀⠀⢀⡾⠁⠀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢠⠇⢠⠇⠀⣸⠈⡇⢱⡜⡜⠁⠀⠀⠀⠀⣴⠟⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣿⠗⢁⣠⠔⣁⠴⠋⢠⠇⡿⠀⠀⠀⠠⣾⢹⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⠋⢁⡤⠔⠒⠋⠁⠀⠠⠔⢋⡰⡇⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⢀⠞⢁⡤⠀⣀⡠⠤⢔⡲⣊⣩⣜⡇⠀⠀⠀⠀⠢⡆⢷⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡟⠀⣏⠀⢾⡉⠰⡊⠉⠀⣨⠇⠙⡇⠀⠀⠀⠀⠀⢹⠘⡆⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡀⠨⣀⠀⠉⠉⠁⠈⠉⠁⠀⠀⣡⠀⠀⠀⠀⠀⠈⡆⠉⠒⠦⠤⠤⠤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠤⢭⣓⡒⠒⢒⣚⣉⠥⠞⠙⠦⣀⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Related Text & Emojis

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

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣴⣶⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣸⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⠷⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⢿⣿⣿⣿⣿⢿⠀⢠⣿⣿⣿⠟⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⠟⠘⠀⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠻⠿⠿⠟⠋⠀⠀⢸⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⡏⠄⢲⢁⠂⡌⢐⠡⢒⠈⣌⡰⠔⡚⠡⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠀⡂⢼⠃⢌⡇⠂⡔⠐⣂⢰⠬⡚⢁⠆⠡⡐⠡⢉⠔⣊⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⡿⠊⢄⢂⠱⠀⢾⠡⢼⠠⠑⣨⢖⢕⠃⡐⢠⣡⠬⠒⠎⡩⢉⠂⡔⣀⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠈⠱⣌⠂⠆⠌⡑⠠⡗⢸⠀⣃⡵⢁⠊⣰⠜⠍⠠⠌⣈⠐⠡⣈⣒⠐⠤⢈⡁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⠀⡀⠀⠀⠑⢿⠈⠉⠉⠉⠉⠛⠲⠼⣀⢢⠟⡁⠌⣀⠃⢰⡤⢺⡉⠥⠉⣙⣦⣡⠄⢣⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⡿⣧⠀⢡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡘⡐⣠⣼⣫⣤⣴⣿⣾⣿⣿⣿⣿⡎⠄⡃⢾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⢀⢿⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣇⠎⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⠣⠈⠜⣇⠀⠑⡀⠀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡯⣐⠡⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⡎⢡⠈⠜⣆⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡾⣟⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣽⣿⣿⢇⠉⢗⡸⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣵⢀⣊⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣾⢏⠞⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣷⣿⣿⣿⣿⢿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡿⠀⠀⠀⠘⠋⠹⡟⠫⠕⠁⠀⠀⠀⠀⢚⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠢⡘⢧⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠒⠂⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⢫⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡠⠐⠌⢧⡀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠉⠀⠀⠀⠠⠤⠴⡲⡝⢠⠘⣧⡀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣝⢄⠳⡠⢁⠊⠄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠮⡊⠔⡡⣸⠡⢙⣦⡀⠀⠀⠀⠀⠀⠑⡿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⢣⡙⢆⡈⠤⠁⠜⢳⡀⠀⠀⠀⠤⠤⠤⠤⠖⠒⢺⠛⠩⠐⣀⠒⠠⣱⠣⠑⣠⣞⠟⢦⡀⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⣌⠱⣆⠉⡄⠡⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣇⢃⠡⠄⠌⢢⣧⠶⠟⠉⠀⠀⠀⠈⠀⠀⢀⣴⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢈⠲⡈⠳⣌⠤⢉⠰⠈⠷⣄⠀⠀⠀⠀⠀⠀⠙⢧⣢⠼⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣮⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⡑⢆⠄⠳⣌⠢⡁⠆⡉⠷⣄⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⣀⢤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢦⢀⠉⠳⡐⢠⠓⣔⢂⠰⢀⠉⠷⣄⠀⠀⠀⠀⠀⠈⢻⢤⡤⢶⣮⣿⣿⣿⢿⣡⣦⣀⠙⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⢝⡈⢧⡈⠤⠙⣢⡒⢈⠳⣔⠈⠤⠑⡘⢦⡀⠀⠀⠀⠀⠀⢛⡆⣸⢿⣿⣿⣯⣿⣿⣿⣿⠈⠆⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡃⠀⢇⠀⠻⣄⠥⢀⡑⣆⠂⠌⡳⣂⠡⠐⣈⠳⣴⠀⠀⠀⠀⠀⢿⡸⡘⢿⣿⣿⣿⣿⣿⡟⢈⠐⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⡀⠘⡄⣰⠟⢦⡂⡔⢈⢮⠐⡄⡙⣆⠥⢀⠡⠹⣧⠀⠀⠀⠀⢸⢇⢇⢂⠙⠻⠿⠿⢋⠐⡀⢺⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⢠⡟⠁⠀⠀⠳⣌⠂⢂⢳⠠⠁⠌⢧⠊⠰⠁⢻⡆⠀⠀⠀⠈⢼⠸⡌⠂⠡⠘⠠⠃⣢⣼⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⢀⠀⠠⢀⠀⠄⡀⠠⢀⠀⠄⡀⢀⠀⠀⢀⣤⣶⡟⣟⢯⡻⡝⣯⣛⢟⡷⣶⣄⠀⠀⠀⠀⢀⠀⡀⠄⡀⠠⢀⠀⠄⡀⢀⠀⡀⠀⠀⡀⢀⠠⢀⠀⠄⡀⠠⢀⠀⡀⠀⠀⢀⠀ ⠀⠀⠄⠂⢁⠠⠀⢂⠠⠐⠀⡀⠂⢀⠀⢠⣴⡿⣻⢧⡻⣜⢧⣛⡽⣲⡝⣮⢳⣭⣻⣧⡀⠁⠀⠠⠀⠄⠠⠐⠀⠄⠂⠠⠀⢂⠀⢀⠀⠐⢀⠠⠀⠄⠂⠠⠐⠀⠄⠂⢀⠐⠀⠠⠀ ⠀⠠⠀⠌⠀⠄⠂⠠⠀⠂⢁⠠⠁⠀⢠⣿⢏⡞⣯⢳⡝⣮⢳⡭⣖⢧⡻⣜⡿⣎⢷⣹⣇⢠⠀⠁⠂⠈⠀⠂⠁⡀⠈⠀⠁⠀⠈⠀⡀⠀⠂⢀⠂⠐⠈⠠⢀⠡⠀⡁⠠⠀⠀⠐⡀ ⠀⢀⠀⠂⢁⠐⠈⡀⠁⠌⠀⠄⠀⢄⣿⡳⣏⡞⣯⡳⣝⢮⡳⣝⢮⣳⣽⢾⠿⣜⢧⣏⣿⢀⢀⣀⣐⣀⣁⣀⣤⣤⣤⣦⣬⣤⣤⣁⡇⠀⠐⠀⠠⠁⡈⠄⠠⠀⢂⠐⠠⠀⠀⠀⠄ ⠀⠀⠠⠁⡀⠂⢁⠠⠈⠠⢈⠀⠠⢸⣯⢳⡝⣾⣹⢿⡼⣧⣟⣾⣻⡷⢯⣾⣹⢎⡷⣎⣿⡾⣛⢯⡿⣯⠟⣯⢽⡹⣎⢷⡹⣞⡽⡻⡽⢿⣶⣄⠀⠄⠀⡐⠀⠡⠀⢂⠐⠀⠀⠈⡀ ⠀⠐⠀⠂⠀⠁⠀⠀⡀⢄⣀⠀⡀⣽⢧⣻⢾⣭⢷⡿⣛⡵⣫⢖⣧⢻⡝⣮⣛⢿⣞⡵⣫⢞⣽⣟⡳⣭⢻⡜⣧⢻⡜⣧⣛⢶⡹⣵⢫⠷⣭⢻⢿⣄⠀⢀⠈⠄⠂⡀⠂⠈⠀⠀⠀ ⠀⠐⠀⠁⢀⣨⣴⡾⣟⢯⣛⠿⡷⣞⡿⣭⢳⡾⣟⡼⣣⢟⣥⢻⣬⢳⡝⣶⡹⣞⡼⢿⡵⣿⠳⣎⠷⣭⢳⡝⣮⢳⡝⣶⡹⣎⢷⢣⣏⠿⣜⠯⣞⣻⣧⡄⠀⠐⡀⢀⠁⡈⠀⠀⠂ ⠀⠠⠐⣴⡿⣫⢷⡹⠎⠷⣭⢻⡵⣻⣟⡼⣟⡿⣜⡳⣝⠾⣸⢳⣎⢷⡹⢶⡹⢶⡹⣏⢿⣱⢻⣜⡻⣜⢧⡻⣜⢧⣛⢶⡹⢮⣭⢳⣎⠿⣜⡻⣼⣱⢻⣵⡠⠀⠐⠀⢂⠀⠄⠀⠄ ⠀⢠⣿⢏⡷⣹⢂⠔⠉⠐⢍⢳⡝⣶⣻⡵⣯⠷⣭⢳⣭⠻⣵⢫⡜⣮⡝⣧⣛⢧⡻⣜⢧⡏⡷⢎⡷⣹⢎⡷⣹⠮⣝⢮⣝⡳⣎⠷⣎⠿⣜⡳⡵⣎⢷⣫⣇⠀⠌⠐⡀⠀⠂⠀⠀ ⢀⣿⡟⣮⢳⢁⠆⠀⠀⠀⠀⢂⢻⢶⡹⣷⢫⣿⣜⡳⣎⠿⣜⢧⣛⢶⡹⢶⡹⣎⢷⡹⢮⣽⣹⡯⢾⡷⣻⠾⠷⢻⣼⣳⣎⠷⣭⢻⣜⡻⣜⡳⣝⢮⡳⣭⣿⡄⠀⢂⠀⠡⠀⠀⠀ ⢸⣿⡜⣧⠛⢨⠀⠀⠀⠀⠀⠀⡆⣯⢳⢻⣿⣿⣬⢳⣭⢻⡜⣧⠛⣮⡝⣧⢻⡜⣧⣿⡟⠈⠁⠀⠂⡍⢹⠀⠀⠀⠈⠁⠛⣿⣮⢳⡎⣷⣭⢳⡝⣮⢳⣧⡟⡆⢠⠀⡌⠀⡄⠀⠀ ⣾⢇⡿⣜⠇⡆⠀⢰⠀⠀⠀⠀⠐⣹⢮⢃⠅⠺⡿⣮⡝⣮⢳⣭⢻⣜⡳⣝⢮⡷⠟⠁⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠏⠚⣿⣜⡳⣎⢷⡹⣎⠷⣎⣿⠃⠀⠄⠐⡀⠠⠀⠀ ⣟⢮⡳⣽⠰⠀⠀⡟⠀⠀⠀⠀⠀⢊⠔⠁⠀⠀⠙⢷⣽⢎⡷⢎⡷⢎⡷⣹⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡆⠀⠈⢿⡵⣫⢞⡵⣫⢻⣼⣻⠀⢈⠀⠂⠄⡀⠄⠀ ⡿⣎⢷⣹⢸⠀⠀⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⣾⣝⢾⡹⣞⣽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⣼⠀⢠⡁⠀⢠⠸⣿⡱⣏⢾⡱⣏⣾⠇⠀⡀⠂⠁⠄⠀⡀⠀ ⣿⣜⣻⣼⠰⠀⠀⠐⡄⠀⢰⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠧⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠙⢾⡏⢀⣶⠇⠀⢨⢠⣿⢳⡝⣮⢳⣽⡾⠀⠐⠀⠠⠁⠂⠁⠀⠀ ⣷⢎⡷⣎⣇⢃⠀⠀⢮⠀⠘⣧⣠⡾⠋⠉⠉⣙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠩⠘⠢⠅⡢⡀⠈⢻⡟⠁⢀⣆⢆⠎⣿⢣⡟⣼⢳⣾⠁⠀⢠⡆⠀⠂⡁⠐⠈⠀ ⢯⣟⡼⡳⢾⡐⡀⠀⠘⢷⣀⣨⡟⠀⠠⢂⠱⣀⠎⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡇⠀⠀⠀⠈⢒⡀⠀⢳⠞⠋⢄⠞⠀⣿⢣⡟⡼⣟⠏⠀⣴⡿⡆⠀⠂⠄⡀⠁⠀ ⠸⡿⣼⡹⢧⣳⠐⡀⢦⡀⠉⣿⠀⢠⠁⢊⣶⣏⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⠲⠀⠀⢠⠊⡋⠀⠄⣿⣏⠾⣽⣋⣴⡿⣫⡿⠀⠐⠈⠠⠀⠂⠀ ⠀⣿⣷⡹⢧⣏⠷⣌⠀⠙⠛⠏⠀⠆⡈⣿⣿⣿⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠙⢦⣄⡀⣀⠆⠃⠀⡇⡆⡇⢀⠂⣿⣎⢿⡹⣏⢷⣹⡯⠃⠀⠌⢀⠡⠀⠂⠀ ⠀⣿⣎⠿⣷⣎⠿⣜⣳⣅⢠⢠⠀⠇⠀⣿⣿⡋⠙⣦⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣼⣿⣿⣿⢀⡀⠀⡃⡇⣷⣶⣶⣟⡿⣎⣷⣹⣞⠗⠁⠀⢂⠐⠀⠄⠂⢁⠀ ⠀⢸⣯⣻⢼⡹⣟⢮⡳⣞⢈⠀⠀⠸⡀⣿⣿⣧⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢀⠂⠀⠗⡗⣟⣶⣓⢮⡳⣏⢿⣹⡶⣄⠀⠈⠀⠄⡈⢀⠂⠄⠀ ⠀⠀⢻⣯⢷⣻⣼⣧⠿⣾⣅⣦⣥⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠤⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⡁⠈⠀⢘⠻⢹⢿⣣⢟⡯⣷⣽⢎⡷⣹⢻⣦⠀⠁⠠⠐⠀⠠⢈⠀ ⠀⠀⠀⢻⣷⡳⣎⢾⡹⣞⣽⡼⠤⢄⠀⠠⠘⢿⣿⣿⣿⣿⡿⢁⠀⢀⠀⠀⠀⠀⠀⡆⠀⠈⠦⠿⠛⠻⠻⣅⠌⠀⢀⠈⣻⣸⢧⣛⢮⡳⢧⣛⢿⡜⣧⢻⡽⡇⠀⠐⠠⠁⢂⠠⠀ ⠀⠀⠀⠈⢳⡿⣽⣎⠷⣭⢻⣦⢡⠏⢀⠀⠐⠀⡩⡻⠋⠉⠀⠁⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠐⣰⡯⣞⡭⣞⣭⢳⡝⡾⣏⢷⣫⢾⣿⠀⠀⠡⠐⠀⡀⠂ ⠀⠀⠀⠀⢰⡙⠷⣽⡟⣷⣯⣞⣮⠡⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣂⢄⠀⠀⠀⠀⠀⠀⡐⣡⣟⡳⣭⢞⡼⢎⡷⣹⢳⣿⢣⡟⣾⡏⠀⠈⠀⠂⠁⠠⠀ ⠀⠀⠀⠀⠘⣿⢦⣌⣙⠷⣮⣽⢭⢧⡁⠄⠀⠀⠀⠀⠀⠀⠰⢎⠁⠠⠤⠤⠀⠐⠒⠊⠁⡀⡘⠀⠀⠀⠀⠀⠀⢌⣴⢿⣱⢻⣬⢻⡜⣯⢞⡵⣫⢷⣫⢾⣳⣥⣤⣤⣆⡀⠈⠀⠄ ⠀⠀⠀⠀⠀⠸⣿⣭⣛⣟⡻⣞⡻⣎⠿⣦⡁⠆⡀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠈⠀⠀⢀⠠⡠⠅⣾⣏⠷⣭⢳⣎⢷⡹⣖⢯⢾⡟⣧⢿⣫⢟⡼⣹⢮⡝⡿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠘⢟⡾⣜⡳⣭⢳⣭⣛⣾⡇⢣⠐⠅⡂⠄⡀⡀⠀⠉⠐⠀⠀⠀⠐⠈⠁⡀⠀⢄⠰⠑⠀⠰⣡⣿⢎⡿⣜⡳⣎⢷⡹⣞⣾⣻⣜⣳⣎⢷⣫⢞⡵⣣⢟⡵⣫⢟⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⣽⣞⣷⡾⠽⠚⠀⢁⢆⠀⠀⠁⠀⠒⠡⠔⠂⢠⣀⡐⠂⠤⠅⠂⠁⠁⠀⠀⠠⠂⡎⣿⡺⣵⢫⡵⣫⢞⡵⣫⢞⡵⣫⢳⣝⡻⣮⡻⣜⢧⡻⣜⢧⡻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠐⠤⢲⢰⠀⠀⠀⠀⠡⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠓⠃⡇⢹⣷⡹⣎⢷⣹⣎⣷⣹⣎⠷⣭⢳⣎⢷⡹⣷⣏⢾⡱⣏⢾⣱⢿ ⠀⠀⠐⢂⠀⠀⠀⠀⠀⢇⠊⡔⡇⡆⠀⠀⠀⠀⠰⢩⠁⠊⣂⡠⢀⡀⠀⠀⠀⠀⠀⣀⠀⢄⢐⠥⠐⠀⠀⡁⠆⠈⣫⣷⡻⣏⢷⡹⢮⡝⡾⣿⣜⡳⣎⢷⡹⢾⣏⢾⡱⣏⢾⣽⠇ ⠀⠀⢠⡀⠈⠢⡀⠀⠀⠘⡡⢂⠄⡃⠀⠀⠀⠀⠀⠏⡄⠀⠀⠈⠁⠒⠀⠁⢨⢰⠰⠂⠉⠀⠀⠀⠀⠀⠀⠀⣃⣾⢟⡼⣛⡾⣧⣛⣧⣻⣵⠿⣜⡳⣝⢮⣝⡿⣎⢷⡹⢮⣟⠎⠀ ⠀⠀⠀⠸⢀⠀⠀⢀⠀⠀⢇⠄⡄⡃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⡿⣸⢇⡿⣸⢻⡜⣧⡜⣿⡸⢧⡻⡼⣼⡻⣜⢧⣻⡿⠇⠀⠀ ⠀⠀⠀⠀⠈⠠⡀⠈⠂⡀⠀⢎⢣⠡⠀⠀⠀⠀⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⢘⠀⠀⠀⠀⠀⠀⠀⢼⡟⣮⢳⡝⣮⢳⣭⢳⡝⣶⡹⢶⡹⢧⣻⡟⣧⣻⣞⠯⠋⠁⠀⠄⠁ ⠀⠀⠀⠀⠀⠀⠈⢄⠀⠐⡀⠀⠣⢆⡒⠄⣀⡀⠠⢀⡉⡄⠀⠀⠀⠀⠀⠀⠠⢸⡹⡀⡄⠀⠀⠀⠀⠀⠀⣾⡟⣼⢣⡟⣼⢳⣞⣧⢿⡶⡽⢷⡻⣏⢷⡹⣝⢷⣧⠀⠐⠈⠠⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠄⠀⠑⢎⡒⢒⠒⡚⠍⢧⠀⠀⠀⠀⠀⠀⢀⠆⣮⠕⣧⡑⢀⠀⠀⡀⠄⣈⣿⡻⣜⢧⡻⣜⡳⣎⢿⣎⢷⡹⢧⡻⣜⢧⡻⣜⢧⢿⣇⠀⠄⢁⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⡄⠀⠀⠑⠨⣢⠑⡸⢈⠳⢬⣁⣒⣒⣂⣡⠞⣥⠛⡴⡹⣒⢖⡲⢴⣋⢧⢻⣷⡹⣎⠷⣭⢳⡝⣾⡟⣮⡽⣧⣻⡜⣧⢻⡜⡯⢾⣻⠀⠐⡀⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⠀⠀⠀⠀⠀⠑⠂⢍⣚⠤⢃⠎⡴⣉⠶⡙⣤⠛⡴⢣⢍⡲⢩⠖⠱⠚⠁⠙⣷⣭⢻⡜⣧⣻⢟⣼⣹⡽⢮⡝⣿⣜⢧⡻⣭⢿⡏⠀⠐⡀⠄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠐⠑⠊⠑⠂⠛⠐⠋⠂⠉⠀⠀⠀⠀⠀⠀⠀⠛⠿⣾⣟⡽⣚⠶⣭⢻⠷⣽⣮⣽⢷⣻⠝⠃⠀⠠⠁⡀⠐⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠠⠀⠀⠀⠀⠉⠛⣻⡿⣞⢯⡻⣜⢶⣹⡿⠀⠀⠠⠈⡀⠐⠀⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠀⠀⠁⠀⡀⠀⢀⠠⠀⠀⠄⠀⠀⠀⣾⣟⡼⣹⢎⣷⣽⡾⠛⠁⢀⣴⠂⠐⡀⠁⢂⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢹⣷⡹⢧⢯⡝⡷⣶⢶⡿⡿⠃⠀⠂⢀⠡⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⢀⠀⠁⢀⠈⠀⠐⠈⠀⠀⠀⠐⠀⠀⠉⠻⠿⣞⣿⣳⡟⠾⠋⠀⠀⠄⠡⠀⠄⠂⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⢀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⢠⠗⠠⠄⠀⡆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠉⠉⠂⢄⡔⠁⠀⠀⠀⠀⢀⣴⣒⡒⢤⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⡀⠀⠀⢁⣀⣠⣞⠀⠀⠘⣞⢹⢮⡳⡱⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⠘⣄⠀⣰⡫⢶⡢⡁⠀⠀⠘⢽⡾⢿⣷⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⡀⠁⣇⡧⣼⣻⣶⠠⢂⠉⢀⡩⠛⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢿⣵⣟⣻⠏⢠⡤⠚⠁⠀⠀⠀⣠⢇⡀⠀⠀⢀⠤⠒⠐⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⣁⡀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⢦⡴⠁⠀⠀⠀⠀⢡ ⠀⢀⠤⠤⢄⡀⠀⠀⠔⠁⠀⠈⠓⠒⠒⠂⠉⠀⠈⢆⠀⠀⠀⠑⠀⠀⠀⠀⢀⡠ ⠠⠁⢠⠃⠀⠈⢢⡌⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡠⠊⠁⠀ ⡇⡠⠁⠀⠀⠀⠀⠧⠀⠀⠀⡠⠺⡀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠤⠔⠋⠀⠀⠀⠀ ⠈⠒⢄⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠒⢄⡀⠀⡠⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠋⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠋⣽⣿⣿⣿⣿⣿⡿⣿⣿⠟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⠟⢱⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⠟⢡⡆⣡⡾⠛⠉⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⣇⠀⠀⠀⠀⢀⣴⡆⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡿⠛⣡⣾⣿⣷⠏⠀⣴⣿⠟⠙⠻⣿⣿⣿⣿⣿⣿⢰⣿⠀⠀⠀⢀⣾⡿⣴⣿⣿⡟⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠋⠁⠀⠸⣿⣿⣿⡟⠀⣸⣿⣿⣆⠀⠀⣿⣿⣿⣿⣿⢃⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⠏⢀⣴⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⣿⣧⣹⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⡇⠀⠰⣫⣦⢹⡿⣡⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⠿⢋⣴⣿⣿⣿⣿⠃⠀⣸⣿⡟⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⡬⢩⣿⣿⣿⣿⣿⠀⢀⣿⡿⢑⣥⡼⢟⣡⣤⣤⣤⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⣻⣿⡿⢡⣿⣿⣿⣿⣿⠇⠀⢸⣿⣵⣿⠟⣼⣿⣿⠿⠋⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣾⡿⢋⣿⣿⡟⢀⢠⣿⣿⠟⠥⠞⠯⣽⣾⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⠟⡄⣼⣿⡿⠁⣴⣿⣿⣷⠆⣿⠿⡁⠋⠛⠛⢿⣯⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠈⣼⠁⣿⣿⠁⣾⣿⣿⣯⣥⣷⣶⡿⠁⠀⠀⠀⢼⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣿⠀⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⡀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡹⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢿⣿⣿⡆⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⡄⠀⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⢿⣿⣟⠻⢿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣠⣤⣄⣐⣒⠒⠒⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⣶⣶⣤⣄⣀⡴⠋⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣱⠶⠖⠛⠉⠁⠀⠀⠈⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠛⢿⡇⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠘⣇⠘⣿⠀⠀⢠⣤⣄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⣀⣤⡤⠤⠤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠘⠛⠋⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣡⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⢰⣿⣿⣧⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢠⣾⡵⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠸⡄⠀⣀⣤⣯⣶⣇⠀⠀⠀⠀⠈⠻⠟⠃⠀⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⣷⠞⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡃⣠⠴⠟⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠛⠉⣉⡥⠞⠛⠛⠳⢶⣤⣀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⣼⢳⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⡞⠃⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠃⠠⡏⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠼⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⣆⠀⠀⣀⣠⣴⡶⢿⣿⣿⣿⣾⣷⠀⠀⢷⠀⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠹⠛⢹⣿⣿⣇⣴⣾⠿⠿⠿⢿⣿⡆⠀⢸⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣛⣋⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠋⠁⠀⠀⠀⠀⡿⠉⣿⣿⣋⠀⣀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢹⣿⣾⠿⠋⠉⠉⠉⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣧⣼⣻⡟⠿⢯⣉⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⣼⡿⠁⠀⠀⠀⠀⢰⡇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⡽⣿⣿⡿⠿⠿⢰⠛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠿⠆⠀⣾⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣷⡂⠀⠀⠀⠀⠀⠀⢻⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣀⣴⠿⠛⡙⠃⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣿⣿⣶⣄⡀⠀⠀⠀⠈⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⢀⠖⣼⠃⠀⠀⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⡛⠿⠷⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⡏⠀⠀⠀⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⠿⠭⠤⢦⣄⡀⠀⠀⢀⣤⣿⠟⠁⢠⠇⠀⠀⢠⡇⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣶⣄⡀⠠⢀⡀⠀⠀⠼⠋⠀⠀⠀⠀⠀⢀⣀⣤⣾⡽⠟⠁⠀⠀⢸⠀⠀⠀⣼⠀⠀⣏⡟⠛⠿⠿⠶⠶⠤⣤ ⡀⠀⠀⠀⠂⢻⣵⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⡬⠍⠛⠶⠶⠶⠂⠀⠀⠈⣥⠞⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡏⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣻⣿⠿⣿⣿⣿⣿⣿⡁⠛⠳⣄⣀⣀⡤⠤⢤⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠁⠀⣾⣿⠹⢷⣄⠀⠀⠀⠀⠀ ⣥⣀⣀⠀⠀⠀⢹⣟⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡧⣹⣿⣿⣿⣿⡿⠛⣧⡀⠀⠈⢩⡁⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⢠⡟⣿⡀⠀⢹⣧⡀⠀⠐⣋ ⠀⠉⠉⠛⠿⠶⢮⣿⣷⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢹⡘⢻⡏⢉⡿⠃⣰⣿⣷⣤⣀⠀⠑⣄⠀⢀⢾⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⣼⠀⠈⠿⣄⢠⡏⢀⠶⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡇⢈⣷⡟⠀⢰⡿⢽⣷⠈⠙⠻⠶⢾⠉⠉⢿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠌⣷⡇⠘⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢷⢸⣹⡇⠀⣿⠇⠀⣿⡆⠀⠀⠀⠈⢱⣤⣸⡇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡞⠀⢠⢿⡆⠀⠀⡀⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠦⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠓⣷⢸⣿⡂⠀⢹⣿⣄⠀⠀⢀⡾⠘⣿⡇⠀⠀⠀⠀⠀⠠⡇⠀⠀⢰⡇⠀⢸⣾⡇⠀⠀⢠⡏⠿⠀⠀⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⠀⠀⠀⠀⠀⣴⣶⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠙⠻⣿⣗⣶⣤⠀⠀ ⠀⠀⠀⢀⣤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣄⡀⠀⠉⣽⣽⣵⡄ ⠀⠀⠀⠛⣿⡯⣻⢟⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⣄⠀⠛⠙⠙⠁ ⠀⠀⠀⠀⠈⠳⡌⢩⣶⣭⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣆⠈⠓⠎⢯⣻⣿⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡾⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⢻⣻⡇⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠇⠚⡧⠀⠀⠀ ⠀⣤⡴⠶⠶⠶⢖⠒⢚⣆⠀⠀⠀⢯⢳⡀⠀⠉⢿⣄⠀⠀⠀⠀⠀⣀⠔⠒⠁⠀⠀⠉⠉⠉⠙⠲⢤⣄⡀⠀⠞⠀⠀⣇⠀⠀⠀ ⢰⣿⡷⡄⠀⠀⠀⠱⡄⢹⡀⠀⠀⠸⣽⣷⡀⠀⡼⠙⣦⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⡈⡟⠀⠀⠀ ⢸⣇⠀⣟⢦⡀⠀⠀⠘⢆⣇⠀⠀⣳⣿⠏⠹⣌⠀⠀⡏⢧⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀ ⠈⣿⠀⢿⣦⠵⡀⠀⠀⠘⣿⠀⠀⢻⡟⠀⠀⠘⢦⡘⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠸⡄⠸⡾⣄⠹⡄⠀⠀⢸⠀⠀⢾⣇⣀⠀⠀⣾⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⠆⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠹⡜⣦⡹⠀⢀⣼⡧⣄⣠⣷⡏⠙⠛⣿⣀⠀⣼⡝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣤⠤⣤⠄⠀⠀ ⠀⠀⠀⠙⢄⠙⢌⠻⠖⠁⢸⡇⠘⣿⣿⣷⣀⣀⠘⡇⠀⠈⠉⣼⠉⠉⠛⠓⢒⠲⣛⣛⡛⣟⠀⠀⠀⠀⢠⣿⣏⡼⠀⢘⡇⠀⠀ ⠀⠀⠀⠀⠈⠳⡈⠳⣄⠀⢸⠇⢀⣾⡇⠑⠿⢷⣾⣷⠀⠀⠀⣿⢀⡀⠀⠀⣀⣀⣭⣴⣶⣿⣶⣶⣶⣤⣿⢉⠞⠁⠀⢼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢬⣓⣾⠤⠚⠀⢧⠀⠀⠐⣮⠇⠀⠀⠀⠋⠙⠿⠿⠟⠛⠁⠒⠚⠋⠉⠉⠀⣠⡿⠟⠁⠀⠄⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⣠⣤⢤⡀⢀⣀⣀⣤⠖⠋⠁⠀⡠⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠙⠓⢚⣿⣿⣟⣿⠟⠁⠀⢀⠴⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⢉⠟⠁⠀⠀⠐⠁⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠏⠈⣠⠋⠀⠀⡤⠤⠒⠒⣤⠀⢀⡜⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⡴⠁⠀⣰⠃⠀⣠⠋⠀⢠⠀⢰⣿⢀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⡠⠊⠀⠀⢰⡇⠀⢀⡇⠀⠠⢻⡀⣼⠟⡏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⣿⡆⠀⢸⣇⡟⠀⢹⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠇⢻⣧⣠⣾⠟⠀⢀⣾⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢲⣔⠋⠉⠁⣀⠴⠋⡼⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠈⢷⡛⠛⠓⠒⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⡀⢀⣀⡠⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠫⠭⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣷⣿⠟⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣶⣤⡀⠀⠂⠠⣾⠟⠉⠉⠀⠀⠙⣿⣇⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠛⠋⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀ ⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀ ⠀⢠⣿⠟⣀⣤⡶⠶⠿⠿⠿⠷⠶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀ ⠀⣻⣿⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀ ⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣤⣾⡿⣵⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠶⢶⣤⣤⣄⣀⣀⣀⣤⣤⣴⣶⣾⢿⣿⣷⠟⢸⡿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⣠⣶⣿⠟⠁⠀⣾⠁⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡜⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡟⠋⢸⠃⠀⠀⢼⡂⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢷⣶⣶⣦⣤⣶⣶⣶⣶⣾⣿⣟⡛⠉⠙⠛⢶⣾⠀⠀⢶⣾⣷⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⣧⡀⠀⠀⠉⠉⠈⠀⢀⡿⠻⣿⣏⠙⠶⣄⠀⠉⢳⣄⣸⣿⠻⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⣿⣿⣦⡈⠳⡄⠀⠙⣇⠀⢲⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣿⣿⣿⣆⠙⡄⠀⠈⢇⣌⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠙⢿⣷⣤⣼⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣇⠸⡄⠀⠸⡿⡈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢀⣤⣶⠿⠛⣻⣿⣿⣿⣿⣶⣤⣄⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠸⢷⠀⠀⢀⣿⣿⠛⢿⣿⣿⡀⢇⠀⠀⢿⡇⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⠏⠁⢠⣾⠟⠁⠀⠈⢿⣿⣿⣿⣷⣄⠈⠋⠀⠀⠀⠀⠀⠀⠘⠺⣄⣠⣾⣿⣿⣄⣸⣿⣿⠇⢸⠀⠀⠸⣿⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡿⠁⠀⢀⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⣿⣷⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠃⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⠰⠧⠒⠲⠒⢻⡏⡇⠀ ⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⢻⡆⠀⠀⠀⠀⢀⣿⣿⡀⠘⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⠻⣟⠿⠃⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⣤⣤⣴⠿⠀⠀⠀⠸⡆⠳⣄⠀⠀⢀⣾⠿⣿⣿⣾⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡇⠀ ⠠⠀⠀⠀⠸⣆⢳⡄⠀⠀⠀⠀⢼⡀⠀⠀⠀⢳⡀⠙⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢀⡇⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠀⠀ ⠀⠈⢦⡀⠀⠹⡄⢻⡀⠀⠀⠀⠀⢷⠀⠀⠀⠈⢳⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣗⣿⠇⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠿⠀⡀⠀⠀⠀⠀⢀⣿⣻⣿⠀⠀ ⠀⠀⠀⠙⢲⣄⠹⠄⢳⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠹⣄⠀⠙⠿⣿⡿⠟⠿⠉⠀⠀⣠⠁⠀⠀⢠⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣾⣿⡛⠻⠄⠀ ⠀⢠⣤⣉⣻⣿⣷⣤⡀⠙⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⢢⣶⠞⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⣾⣷⣟⣻⡆⠀⠀ ⠀⠈⠻⣿⣿⣿⡛⠛⠛⠳⠘⢳⡄⠀⠀⠀⠈⢦⣀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⢀⢀⣠⣶⣿⣿⠁⠀⠀⢀⣾⡟⠉⠉⠉⠛⠀⠀ ⠀⠀⠀⠈⠻⣿⡟⣿⡷⣤⣽⣦⠙⢦⣄⠀⠀⠀⠨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢛⡋⣱⣿⠁⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠈⡿⢿⣿⣦⣍⠛⠻⢦⣍⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣤⠾⠿⣿⠉⠀⣀⣴⠟⠿⣷⠀⢸⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠓⠀⠙⠻⢿⣷⣶⣤⡙⠳⣬⣙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣤⠔⢋⣠⣾⣿⠍⠇⠀⠸⠀⢸⡇⠀⣼⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠯⠟⠿⢿⣷⣶⣧⣴⡆⠉⠻⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠞⢋⡿⠋⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⡾⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠒⡉⠿⣻⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⣅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠶⠒⠲⠾⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣻⠷⠀⠀⠒⠲⠶⠒⠀⠀⠴⠃⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠓⠶⢶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣿⢿⣫⣧⡑⡌⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣇⣿⢈⠁⢳⠱⠘⣀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠑⠒⠂⢠⠶⠶⣖⡒⣮⣿⢩⣽⠉⢉⢯⣹⡝⡠⠄⠀⣤⣤⣀⣀⣀⠤⠤⡀ ⡨⠶⠀⠀⠘⠒⢤⠄⠈⢷⢿⣿⣿⠀⢸⣿⣿⡟⡠⠊⢁⣀⠨⠕⠀⠀⣀⠔⠁ ⠙⠢⠤⣀⠀⠀⠥⠤⡄⠀⠺⣑⡤⠷⠧⣴⡿⠓⢁⣄⣈⣱⠀⠀⠀⠀⣈⠅⠀ ⠀⠀⠸⠤⠔⣖⣁⣠⠉⢉⠒⡛⠇⠀⠀⡝⡗⡙⣿⢃⡀⠰⡄⣈⣙⡍⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣒⣧⣻⣄⣴⣧⣧⡈⡸⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣒⢧⡈⡳⢋⣸⡿⡫⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡿⣯⣘⣿⣟⣹⢶⣾⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠿⡘⠐⠘⠀⢿⣌⢿⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⡊⠔⡇⠀⠀⠀⢸⣜⣌⡊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠞⠒⠛⠒⢺⢴⡿⣶⢾⢺⡏⡧⠩⠦⠵⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠃⠬⠔⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⣿⣿⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣦⣿⣿⡟⢿⠛⢏⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢻⡏⢻⢯⢳⣾⠷⡀⠱⡀⠀⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⠀⣸⣿⠘⠈⡆⢻⡆⠱⠀⢱⠀⠘⡧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣷⣇⣰⣀⣇⣸⣿⣄⣧⣼⣶⣾⠃⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡅⠀⠉⠉⠓⠒⠒⣶⣿⣿⣭⣭⣉⠉⠙⣦⣿⣿⠁⣶⣿⡇⠀⠀⣸⠷⣌⢻⣿⠃⣠⠴⠒⠒⠲⣦⣤⣤⣀⣀⣀⣀⣠⣤⠤⠤⣄ ⠈⠻⣦⣀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠈⠙⢦⣏⣹⣿⣶⣿⣿⠇⠀⠀⣿⣾⣿⣿⣯⡞⠁⣠⡴⠚⠛⠉⠉⠛⢳⡌⠉⠁⠀⠀⠀⢀⡿ ⠀⣶⠛⠉⠁⠀⠀⠀⠀⠀⠉⣹⠖⠂⠀⠀⢻⡿⣿⡿⠿⠿⢈⠉⣁⣿⡿⢿⣿⣿⢁⡾⠁⠀⠀⣤⡤⠶⠚⠋⠀⠀⠀⢀⣤⣖⠋⠀ ⠀⠙⠷⣄⣀⡀⠀⠀⠀⠀⢸⣁⣀⣀⣀⡄⠀⠱⢻⡓⢦⣀⣻⣧⣟⣠⣤⣾⣿⡇⠎⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢉⣷⠀ ⠀⠀⠀⠀⢈⡽⠛⠁⠀⠀⣀⠈⠉⠁⢿⣀⣤⡆⠈⣷⣾⠋⠉⠉⠉⠀⣿⣿⡿⣆⣄⣸⢸⡟⠒⠒⠛⠁⠀⠀⢠⣤⡤⠴⠚⠋⠁⠀ ⠀⠀⠀⠀⠘⠳⠖⠒⠚⣿⣁⣀⣠⡴⠈⠀⠀⣙⠛⢻⠻⡄⠀⠀⠀⠀⡿⢻⠳⡈⠛⣿⡏⢄⡀⠀⠘⣶⣤⣀⡀⢉⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠓⠒⢺⡟⣁⣠⣾⠐⣿⣄⠀⢀⣼⡅⣸⡄⠈⠛⢹⡧⣬⠟⠓⠲⠞⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⣥⠤⣿⢷⣮⣿⠶⣿⢿⣷⣿⣼⣦⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⠖⣻⡀⠈⠙⣶⠛⠉⢸⣿⣟⠯⣄⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠴⣶⣊⣹⠟⠯⣽⣩⣇⡴⢿⣟⣌⠓⠦⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⣿⡿⡿⣆⣀⣻⣿⣟⡁⣸⠿⡿⣿⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⣻⡟⠁⣇⠀⢀⣏⣉⣉⣿⡄⠹⣾⡿⢤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡟⠛⣾⠀⠀⠀⡇⠀⠀⢽⢿⡶⠛⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠘⢊⣠⠞⡿⠀⠀⠀⡇⠀⠀⢸⣆⠙⣆⡘⠖⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⣠⡖⠋⡀⣠⡇⣠⢦⢀⡇⣠⣄⠀⣯⢧⣿⠙⠦⣀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⠉⠉⠉⠉⠉⣿⡟⣰⡟⣿⣿⢳⡦⢻⣿⣈⡿⠓⠒⠛⠛⠶⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣈⣇⣹⣏⣈⢉⣀⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠂⢉⣩⠭⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠒⠉⠈⠉⠐⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠱⡀⠀⢀⠴⣊⠤⠐⠒⠉⠉⠑⠒⠢⠄⡀⠀⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⢀⠎⠀⠀⡆⠘⡴⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⡞⠀⠀⠀⡽⠀⢸⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⢠⠇⠀⠀⠀⣧⠀⠀⡦⣶⣂⣤⡀⠀⠀⠀⠹⡙⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⢳⠀ ⢸⡄⠀⠀⢰⠁⠃⠸⠁⡠⠄⠀⠉⠙⠲⢤⡀⢱⠀⢀⣼⣀⡈⢟⠢⣄⠀⠀⢸⠀ ⣸⢳⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠢⡇⣾⠃⠙⣷⡸⡄⠀⠑⢄⢈⠀ ⡇⠀⢣⡀⠀⠀⠀⠀⠈⢲⣾⠟⠻⣦⣄⠀⠀⠀⠁⣿⠀⠀⠘⠿⢇⣀⡀⠈⢾⠀ ⢣⠀⠀⣇⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠙⠂⠀⠀⠑⠚⠛⡄⠐⠊⠲⣎⠁⠀⠀⠀ ⢸⡀⠀⢸⡄⠀⠀⠀⠈⠻⢃⣀⣀⠀⠀⠀⢠⣇⠀⠃⢀⠇⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⢧⠀⠈⢟⢄⠀⠀⢠⣊⠡⠔⠋⠀⡠⣺⠉⠙⠷⣶⠋⠀⠆⠀⢀⡼⠁⠀⠀⠀ ⠀⠈⢧⠀⠈⠢⣙⠢⢄⣀⣀⣀⣀⡠⢀⡇⠀⠀⠀⠙⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠉⠀⣀⣤⠊⠀⠈⠧⣄⡀⠀⢀⡤⠒⢫⡀⠀⣀⣀⠀⣀⠀ ⠀⠀⠀⠀⣙⣦⣀⣈⡉⠉⠀⠀⢧⠀⠀⢀⣀⡤⠤⠾⠭⢽⡶⠻⣿⣭⣿⠴⠷⠊ ⡠⠖⠛⠉⠁⠀⠀⠀⢹⠀⠀⠢⣘⡤⠚⠉⠀⠀⠀⠀⠀⢈⠏⣉⣉⣡⠤⠤⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⠠⠤⠤⠒⠉⡀
⣿⣿⡟⢰⠃⢀⣴⣫⣾⣿⣿⢿⡏⠉⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠁⠀⠀ ⣿⣿⣇⡏⣠⢯⣾⣿⣿⣿⢃⡟⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢡⠏⢀⣴⠃⠀ ⣿⣿⢈⡶⣷⡿⠿⠿⠛⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠙⠓⣢⡤⠤⠤⢤⢤⡤⠤⠤⠤⠤⠤⣴⢶⡄⢸⠏⠀⠀⡴⠋⣠⠟⠁⠀⠀ ⠛⠋⠘⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢷⡾⠀⣠⠞⣡⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣴⡿⠿⣿⣿⣿⣿⠳⣶⣤⣤⣄⣀⣤⢴⠏⠀⠀⢸⢃⣜⣥⡾⠛⠉⠉⠉⠙⠻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⠏⢤⣴⣿⠟⠀⠀⢹⣿⣿⣿⡆⠘⣿⣦⠀⠉⣰⠏⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⣃⣠⣾⣿⡟⠀⠀⢀⣿⣿⣿⣏⣡⠀⠘⢿⢆⣴⠋⠀⣠⣾⠟⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡾⢁⡼⠋⢻⣹⣿⣷⣤⣾⣿⣿⢿⣿⡇⠀⠀⣠⠟⣡⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⢁⡞⠁⠐⢾⣿⣿⣿⠛⢿⡿⠏⢸⡿⠀⢠⡾⠗⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣧⡟⠀⠀⠀⢸⠙⠇⢻⣄⡀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣽⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⡟⠀⠀⠀⠀⣿⠠⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣴⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠀⠀⠀⢰⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⠀⠀⠀⣿⠁⠀⢠⣧⡀⠀⠀⠀⠀⠀⢀⡴⢁⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡟⢿⠻⢿⠿⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⢸⡇⠀⢀⣐⠚⢳⣦⣄⣀⣠⡤⠼⣿⠉⠉⠀⠀⠈⡉⠁⠀⠀⠀⠀⠻⣤⣀⡀⢀⣸⠟⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠃⠀⠀ ⣄⣉⣩⠿⠿⠶⠤⢤⣄⣀⠀⠀⣀⣴⣞⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⣀⡤⠶⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠛⠁⠀⠀⠀⠀⠀⢀⣩⠷⠛⠉⠁⠙⣧⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢀⣠⠾⠋⠀⣠⠀⠀⠀⠀⠸⣧⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡴⠊⠉⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠘⠲⠤⣀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢧⡀⠀⠀⠀⠘⣦⠉⠛⠶⣤⣄⣀⡀⠀⠉⠓⠚⠋⠁⢀⣀⣀⣤⠶⠒⠋⠀⢠⠆⠀ ⠟⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⣷⠀⠀⠀⠀⠘⣇⠀⠀⠹⡄⠉⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⢸⣷⡄⠀⠀⠀⢹⣤⠀⠀⢻⡄⢸⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣀⡴⣋⡠⣶⠂⠀
⣿⣿⣿⡟⢰⡟⠀⠀⣤⢞⣵⣾⣿⣿⡿⣽⠏⠉⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠋⠀⠀⠁ ⣿⣿⣿⠃⡿⠀⣠⡞⣥⣿⣿⣿⣿⡿⢰⡏⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢫⡟⠀⢀⣴⠀⠀ ⣿⣿⣿⢸⠃⣴⢫⣾⣿⣿⣿⣿⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣶⠞⠛⠉⠀⣠⠏⠀⣰⡿⠁⠀⠀ ⣿⣿⡇⢨⡟⣵⡿⠿⠿⠛⠛⠛⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⣉⣾⠿⠟⠷⠦⠤⠤⠤⠤⠤⠤⠶⠿⠟⠛⣿⠿⣷⠀⣸⡇⠀⠀⢀⡾⠃⣠⣾⠟⠀⠀⠀⠀ ⠛⠛⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠸⡆⣿⠀⢀⣴⠟⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢀⣴⣿⣿⣿⣿⣷⣶⣦⢤⣤⣀⣀⠀⠀⠀⠀⢀⡀⣼⡏⠀⠀⠀⣿⠃⢠⡞⣁⣶⡿⠟⠛⠛⠻⠿⢶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢀⣴⣿⡟⠉⠙⣿⣿⣿⣿⣿⡄⠘⣿⣿⡙⠛⠷⠶⠛⣹⠏⠀⠀⠀⠀⣯⡴⣣⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢠⡟⠁⢳⣶⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠘⣿⣷⡀⠀⢀⣼⠏⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣟⠀⣠⣾⣹⣿⡏⠀⠀⠀⢠⣿⣿⣿⣿⡍⢉⡀⠀⠈⢿⠧⢀⣾⠋⠀⢀⣤⣾⡿⠋⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⣼⠏⢉⣽⠋⢿⠛⣿⣽⣦⣀⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢈⣴⠟⢁⣠⣶⠿⠋⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣰⠏⢠⡾⠁⠀⣸⣴⣿⣿⣿⣿⣿⣷⣿⣿⠏⣿⣿⡏⠀⠀⣠⣞⣥⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢰⡟⣠⡟⠁⠀⠉⢹⡏⣿⡹⣿⠃⠈⠛⠛⠃⠀⣹⡟⠀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠈⢻⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡿⣠⡟⠀⠀⠀⠀⢸⡇⠹⠇⠻⣧⡀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⢷⡿⠀⠀⠀⠀⠀⣼⠇⣂⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣸⣿⠁⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣄⣠⣾⣿⣿⣿⣿⣿⣏⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⠀⠀⠀⣼⡏⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠤⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢣⠀⢸⣯⠻⢯⠻⠿⠿⢟⣵⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡰⠾⠛⣷⣄⣀⣀⣀⣀⣀⡨⣿⡟⠋⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠟⠳⠤⠴⠋⠀⠉⠉⠉⠉⠁⠀⢹⡇⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠿⠥⠤⠤⠄⠀⠀ ⠲⠶⠦⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣀⣤⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣄⣠⡴⠟⠛⠛⠛⠛⠿⢦⣤⣀⡀⠀⣀⣤⣾⣯⡁⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠶⠟⠋⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⠟⠋⠁⠀⠘⢿⣦⣈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⣯⠉⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡴⠾⠋⠉⠻⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣤⡀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⢰⠟⠁⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⣇⠀⠀⠀⠀⠀⠈⢷⡉⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠙⠓⠲⠒⠚⠋⠁⠀⠀⠀⢀⣠⣤⣶⠖⠒⠀⠀⣠⠃⠀ ⣴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣆⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠙⢯⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠟⠋⠉⠀⠀⠀⢀⣼⠏⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣇⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠸⣿⣷⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⢸⣇⠀⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣴⢋⣁⡤⢶⠟⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠓⠢⣀⣀⣀⣀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠞⢻⠁⠀⠀⢠⠞⠁⢀⡤⠟⠛⢢⣴⢁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠁⠀⢸⠀⠀⢠⡏⣠⠞⠉⠀⠀⠀⢰⡇⡾⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠛⢿⡇⠀⠀⠘⡆⠀⣸⡴⠃⠀⠀⠀⣀⣀⠾⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢮⠳⣄⠀⠀⢱⡀⣿⠃⠀⢀⡴⢾⢍⠀⠀⠀⠗⠀⣼⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠘⣦⣈⣙⣲⠶⠒⣿⣤⣾⠃⠰⣿⣟⠟⠓⠀⠀⠘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡼⠁⣰⣿⣿⣄⣴⡏⢹⣏⡇⠀⢬⣽⣾⡲⣶⣄⠀⠘⣌⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⢠⣿⡋⠿⠞⠁⢧⡸⡏⠁⠀⠏⢠⣇⢸⡿⣿⡷⡄⢹⣆⠀⢱⣄⠀⠀⠀⠀⠀⣠⠴⠒⠋⠓⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⡾⣼⣾⣿⣷⣤⡈⠓⠓⠀⠀⠀⠈⣯⣿⣿⡿⠃⠁⠀⢻⢧⣀⣿⠀⠀⠀⢠⡜⢁⡤⠞⠛⠛⠓⢄⡈⢣⡀⠀⠀⠀⠀⠀⠀ ⠘⣿⢰⡇⣿⡇⣽⣽⣿⣿⣀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⢸⣼⠟⠁⠀⠀⠀⡼⢠⠏⠀⠀⢀⣀⠀⠀⠙⢦⡱⣄⠀⠀⢰⣦⡀ ⠀⠹⣼⡁⢻⠧⣘⡿⣿⣏⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⢸⠃⡞⠀⡠⠞⠉⠈⠙⠲⣄⡀⠈⠚⠦⢤⠼⣿⡇ ⠀⠀⠙⠇⠸⡇⠀⠀⠀⠻⣅⣀⣤⣀⣾⡿⣿⠀⠀⠀⠀⢀⠾⡇⢸⠀⠀⠀⠀⢸⡀⡇⣰⠁⢀⡤⠖⠒⠒⢮⣝⡢⠤⠤⠼⠚⣽⠇ ⠀⠀⠀⠀⢰⠿⣆⡀⠀⠀⠀⠙⢿⣿⣿⢈⡿⠀⠀⢠⣾⠉⣸⠁⡾⠀⠀⠀⢀⣀⣷⣷⣿⠰⠋⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀ ⠀⠀⠀⢀⡇⠀⢨⡟⠓⠤⣤⣀⣀⣈⣛⣋⡀⠀⠀⠀⢿⡴⣣⠞⠁⠀⣠⠖⠋⠁⠀⢀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠁⠀⠸⡇⠀⢸⠇⠀⠉⢹⠉⠉⠀⠀⠀⠀⠈⢿⠁⠀⣠⣾⣁⣀⣠⠤⢤⡏⣴⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⢧⠀⢸⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠳⠿⣓⣲⠞⠋⠀⠀⠀⢻⡻⠟⠓⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠈⢧⡘⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⢦⠀⠀⠀⠀⠀⢷⠀⠀⠀⣧⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠶⢽⡾⠦⠤⣴⣇⠀⠀⠀⠀⠀⣀⡴⢛⡵⠋⢳⠐⢷⠀⠀⠀⠀⣈⣇⠀⠀⠃⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢛⡟⢹⣏⠙⠒⠒⠒⠛⢉⡴⠋⠀⠀⠘⡇⠈⡇⢀⣤⢞⡽⠋⠀⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠦⠯⠴⡯⢿⡉⠒⠒⠒⠋⠁⡀⠀⠀⠀⠀⣧⣀⣇⡿⣾⡏⠀⠀⠀⣠⠏⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸⢫⣧⡴⡏⠙⠓⠒⠚⢹⠂⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣷⣤⠤⣖⠋⠙⠢⣤⣀⡼⠁⠀⠀⣶⣴⡿⠛⠁⠀⣧⣄⠀⠀⠀⣼⣴⠀⠀⢀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢿⣻⣿⠯⠿⠦⣤⣄⡾⠀⠀⠀⢸⠁⠀⠹⣆⡀⠀⠀⢸⠀⠀⠀⣿⢱⠀⢡⡀⣷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⣯⣷⣦⠖⢋⡞⠀⠀⠀⢠⡏⠀⠀⢀⡞⠀⠀⠀⡏⠀⠀⠀⠻⣯⠤⠟⠚⣡⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡞⠀⠀⠀⠀⡾⠀⠀⢀⡞⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⠶⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⢀⠘⠓⠀⣤⠚⡇⠀⠀⣸⠁⠀⠀⠀⢰⡇⠀⢀⡞⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠈⣿⠂⢀⡟⢰⠇⠀⠀⡏⠀⠀⠀⠀⠈⡇⢀⡞⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠾⢭⣁⣀⠎⠀⠀⢸⠃⠀⠀⠀⠀⠀⣧⢞⡄⢀⠀⡀⢰⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢻⡖⠃⢮⣷⣿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⢷⠤⠤⠬⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⢀⠀⠀⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠄⢠⣀⣠⠖⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠒⠠⠤⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠈⣗⣄⣀⠠⠄⠒⠀⠀⠀⠀⠒⠒⠂⣤⠀⠤⠤⠄⢀⡀⠀⠀⠀ ⢀⠁⠈⠑⠢⡀⡠⢺⠤⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠑⢤⠀ ⠈⠀⠀⠀⢀⠎⠀⠀⢣⠒⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠡ ⡇⠀⡇⠀⠎⠀⠀⠀⠈⢆⠠⠜⢀⠇⠀⠀⠀⡄⡘⡘⠐⠒⠀⠤⠤⠤⠤⠀⠒⠀ ⣧⠀⢡⢸⢠⠂⠀⠀⠀⠈⣄⠄⠂⠀⠀⠀⠰⡰⠋⢀⢤⣒⣀⣈⣄⠀⠀⠀⠀⠈ ⢸⡀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣴⠋⠁⠀⠘⣽⠹⣀⠀⠀⠀⠀ ⠈⢧⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠣⢂⡀⠀⡠⢣⠂⢹⠀⠀⠀⠀ ⠀⠀⠓⢤⣸⡀⠀⠀⠀⠀⠀⡀⣀⢜⣁⠀⠀⠀⠀⢀⣈⠙⠂⠁⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠡⡀⠀⠀⢀⣥⣴⠛⠁⠀⠁⠠⡂⠉⠀⠆⠀⡀⠀⢰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⡀⢀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠤⣀⣀⡀⠀⠀⢀⡠⡀⠆⢱⡿⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢡⠀⠀⠀⠀⢰⠀⠀⠀⠁⠒⠈⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣀⠀⠙⢦⡀⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢢⠭⠦⠤⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⢏⡟⠁⣾⢧⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⡆⣰⣿⢣⡏⠀⠀⣇⠀⡟⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣿⢹⢳⠃⡼⠀⠀⠀⢻⣸⡇⠀⠹⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠈⢏⢇⠀⠀⠻⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⢳⣸⠀⡇⠀⠀⠀⠀⢸⠘⡄⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣠⠿⠚⢯⣇⢳⠀⠀⠀⠀⡼⠁⢻⡀⠀⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢾⣁⡀⢀⡀⠻⣞⣇⠀⢀⣴⣁⣀⣾⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣷⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠼⠟⠻⢷⣭⡤⠈⠛⠒⠋⠁⠀⠀⠈⠙⠛⠉⣉⡨⠭⠽⣗⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢆⠙⢎⠳⣤⡀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣤⡈⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣦⠈⣧⣳⡙⣦⡀⠀⠀⠀⣼⠃⢹⣿⣿⡟⣦⡄⠀⠀⠠⣄⣀⣀⠀⠀⠀⠀⠐⡆⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠿⠹⣧⣘⡽⣦⡀⢠⡇⠀⠀⠉⠛⠛⠟⠁⠀⠀⠀⣽⣿⣟⣛⠷⣄⡀⣸⠛⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀ ⠀⠀⠀⠀⢹⡳⡟⢾⡿⡇⠻⢱⣌⣧⠀⠀⠀⣄⠈⠉⠉⠒⢆⣸⣿⣿⣴⣟⣿⠟⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠁⠀⠀ ⠀⠀⠀⠀⠈⢿⠃⠘⡇⠹⠟⣿⠛⣮⢧⡀⠀⢸⣷⣦⣤⣀⠐⣀⡀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢁⡼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⢻⠒⢶⡏⢢⣉⣯⡳⣤⡀⠛⠦⣭⣿⠟⠋⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠖⣉⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣌⠧⠀⠓⠀⠃⢻⡽⣄⣹⠦⢤⣀⣀⣀⣀⣀⣠⠤⠞⠁⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠡⠒⠛⢹⠆⠔⠚⠉⣻⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠲⣟⠛⢮⣿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⡡⠐⠒⠒⣶⣀⣤⣞⢑⣶⡤⠔⣻⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠲⢤⡀⡾⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⢀⡴⣞⠁⠖⠋⢉⣹⣆⣀⡀⠀⢀⣠⠜⠭⠤⠴⣶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠙⣤⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠖⠛⠋⠩⠗⠢⢤⠀⠀⠀⣠⠝⠚⢙⡿⠀⢤⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⣆⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⠶⠋⠀⢈⡿⠀⣀⡾⣭⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡿⠁⠀⢧⠀⠀⠀⠀⢰⠇⠀⢸⠀⠀⠈⠙⠻⠥⠤⣤⣹⣡⣶⣒⡒⠚⠯⣄⠙⢦⡀⠀⠀⠀⠀⢀⣀⡸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠹⣦⠀⣨⣧⡀⠀⢠⠏⠀⠀⡜⠀⠀⠀⡄⠀⠀⠀⠈⣹⡏⢙⣿⣍⠲⡄⠈⢦⡀⠉⠒⠒⢒⣶⠿⠛⣱⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠘⠏⢿⠁⠀⠙⢦⠏⠀⠀⢸⠇⠀⠀⠀⠙⢦⡀⠀⠀⠉⠀⠈⣏⢻⣧⠈⢦⡀⠙⠢⣄⣀⣀⣀⡴⢚⣟⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡚⠀⡆⠘⢾⡖⠠⣼⠃⠀⢠⠏⠀⠀⠀⡟⠒⠒⠲⣖⠒⠋⠛⢦⡀⠀⠀⠀⢹⡄⢻⣣⡀⠳⣄⠀⠀⠉⠉⠁⠀⣿⣽⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢡⣄⠐⣶⡶⠃⠀⠀⡏⠀⠀⠀⠸⣇⣀⠀⠀⠈⠓⢦⣤⠀⢹⠶⣄⡀⠀⠹⢦⠙⢷⣄⡈⠓⠶⠤⠤⢴⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠭⠽⠛⠁⠀⠀⢠⡇⠀⠀⠀⠀⠙⡎⢳⣄⠀⠀⡸⠀⠀⠘⡇⠀⢹⠀⠀⠈⣇⠀⠙⠛⠒⠦⠒⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢳⠀⠏⣇⢰⡇⠀⠀⠀⣿⣢⡘⡆⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⡤⠀⢹⣾⠀⠀⠀⠀⡁⠘⡗⡇⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣤⠀⡀⠀⠀⢰⡿⣿⣤⠀⢀⣰⠁⢠⡿⡇⠀⠀⠀⠠⠼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⢹⠯⢥⢾⡿⠁⠹⣿⡀⢈⣛⣠⠟⠀⣇⡀⠀⠀⠸⠗⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠀⠀⠀⠈⠻⢿⠟⠁⠀⠀⣇⣹⠀⣖⡂⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣀⡀⣼⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⣠⡿⡿⠁⢸⠉⠻⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⣽⢻⢡⠃⠀⠘⣆⡇⠈⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣿⠇⢸⠀⠀⠀⠸⣧⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣸⠿⣾⡸⡀⠀⠀⢠⠂⢇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣮⣁⢀⣈⠳⣧⠀⣠⣊⣠⣏⣴⣿⣁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡶⣦⢄⠀⠀⠀⠀⠀⠀⢠⣟⠛⠉⡿⡾⠀⠈⠉⠁⠀⠀⠀⠉⢀⠤⠘⠛⠿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡈⢮⢻⢦⡀⠀⠀⢀⡿⢻⣿⣶⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⡸⠹⣇⣻⣦⡀⢸⠀⠈⠙⠛⢿⠀⠀⠀⣹⣿⣓⡶⣀⣠⠗⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀ ⠀⠀⠀⢿⡏⢻⠿⣙⣳⣼⡄⠀⠰⣄⠀⠉⠒⠼⠿⠷⠾⠿⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡿⠀⠀⠀ ⠀⠀⠀⠘⣇⠈⣦⣁⡯⡙⢿⣦⡀⠻⣟⣳⣦⠴⠂⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⢞⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⡱⠈⠃⠹⠹⣿⣙⡦⢄⣉⣁⣀⣀⣠⠴⠊⠀⠀⠀⠀⢀⣠⠤⠖⠊⠕⠒⡦⠠⠖⢛⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣾⠋⠻⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⣠⠔⢊⣁⡐⠂⠹⠆⠤⢌⡱⠤⠒⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠉⠑⢴⠃⠀⠀⠀⠀⠈⠣⣄⣴⠾⣤⣈⡀⠐⠓⠂⡄⠤⣶⠉⢒⣸⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣇⣀⢾⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⢠⡤⠛⠀⣲⠋⢠⣶⣡⡴⠋⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⠁⠘⡄⠀⠀⢀⡆⠀⡐⠀⠈⠙⠛⠶⢤⣭⣴⣖⡓⠻⢄⠑⢄⠀⠀⠀⢀⣀⢾⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣷⣤⠟⢆⣀⡞⠀⢠⠃⠀⠀⢄⠀⠀⠀⠟⠠⣿⣯⠢⡀⠣⣀⠉⠉⠻⠛⣡⡟⠀ ⠀⠀⠀⠀⠀⠀⣷⠄⠀⠠⣤⢀⡳⠀⢀⡟⠀⠀⡾⠤⠤⡤⠤⠳⢄⠀⠀⠀⢣⠹⣧⠈⢆⠀⠉⠒⠂⠈⣻⡿⠁ ⠀⠀⠀⠀⠀⠀⠙⣦⣠⣀⣲⡴⠃⠀⡞⠀⠀⠰⣧⣀⠀⠈⠲⡤⠀⢹⠦⣀⠈⠳⡜⢷⣄⠑⠢⠤⢤⡶⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⣇⠀⠀⠀⠘⡈⢦⡀⢠⠃⠀⠸⣄⢸⡀⠀⠹⡀⠈⠉⠑⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢁⠈⢳⡜⠀⠀⠀⠋⣷⡇⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⣀⡀⠈⢠⣾⣧⠄⢀⣴⠀⣼⡇⠀⠀⠠⠼⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⡟⢶⡟⠁⠹⣇⣠⣥⠜⠁⡧⡀⠀⠘⠃⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⢳⡃⠘⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⡯⠍⠀⠀⠈⠉⠓⠢⣄⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢉⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣣⡴⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃⠀⢠⠀⣧⡀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⢹⠁⠀⠀⠀⠀⣠⠄⣠⠞⠉⠀⠀⠀⠀⣸⠀⡏⢹⠀⠀⣠⢤⡴⠋⢀⡎⠀⣠⠴⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⢀⡴⠞⣿⢞⣵⣖⠓⠲⣎⣀⠔⠁⣠⣁⡎⡰⠋⢀⠎⠀⢀⣎⡴⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣀⡤⣶⣩⡇⠐⣿⣿⠋⢻⣧⠀⠹⠷⠀⢰⡿⣿⠎⠀⢀⣞⣤⣤⡟⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⣿⣿⠁⠀⣿⣿⣧⣴⣿⠀⠀⠀⠀⡼⢀⡇⠀⢀⣾⠋⢀⠏⠀⢀⣴⣋⡀⢀⣠⡤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡛⠁⠀⠀⠈⠿⣿⡿⠃⠀⠀⣠⠞⠁⣸⣷⢶⠋⣹⠀⣼⠖⢳⡎⠀⠀⠀⣀⠼⠛⠛⠳⣦⡀⠉⠳⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣤⡊⠀⠀⠀⠀⠀⢀⡶⠟⢷⠆⣰⣿⣿⡜⣠⠇⠀⠁⢀⣞⡠⠔⠊⠉⠀⠀⠀⠀⠀⠈⠻⣟⢶⢬⣳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠊⢉⡏⠀⢠⢏⣼⣿⡿⣿⠼⠟⠀⠀⠰⡏⠉⢙⡖⠢⢤⡀⠀⠀⠀⠀⠀⠀⢹⣆⢧⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠃⡏⠀⠀⠀⣀⣠⣧⠖⡏⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣿⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣿⡟⢻⡇⢀⠇⠀⠀⠉⠁⠀⣿⠀⢳⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⢹⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢿⠁⠸⡄⢸⠀⠀⠀⠀⠀⡐⠸⠀⡟⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⡀⠀⠹⣾⠀⡄⠀⢀⡴⠃⠀⢠⠃⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⢺⠈⠃⢹⣾⡉⠹⡀⠀⠸⠲⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢸⣿⡸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠇⢣⠀⢣⠀⠀⠀⢳⠀⠀⠀⠀⠋⢸⠀⡄⠀⠀⢸⣿⢿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢸⢸⠀⠸⡆⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⣿⡄⠀⢸⣿⡄⠻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡎⠀⠀⠀⢸⣠⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⢷⣾⠙⣄⠘⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡇⠀⠀⠀⢸⡿⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⡄⠈⠳⣿⡿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣼⠀⠀⠀⠀⢸⠃⠀⡼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠂⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⢶⠃⠀⠀⠀⠀⣸⠋⢹⣃⡀⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡠⠴⣖⠒⠒⠲⣶⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠊⠁⠀⠀⠀⠉⠒⢄⡘⢷⡀⢰⡆⠙⠢⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠒⠒⣾⠓⡦⣤⣄⣀⠀⠙⠪⣷⡈⡇⠀⢀⠞⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣉⡬⡶⠒⠻⣁⡜⠑⣤⣉⠶⠒⠛⠋⠙⠒⠎⠀⠀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡔⠉⢇⠹⡄⠀⠙⣦⣰⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡓⠦⡈⢦⠈⠢⣼⡉⠃⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⡼⠀⢸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠈⠢⡑⢴⡇⠈⡄⠀⢀⠎⠀⢀⡀⡀⢈⣶⡞⢀⣀⣏⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣲⣄⠱⡼⣿⣶⡆⠀⠈⠀⣀⣼⣷⡓⢺⣿⡿⠋⣸⠘⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢻⣦⣤⣷⣧⢿⣿⠇⠀⠘⡟⣿⣿⣟⣷⣺⠿⠀⢀⡟⡂⠰⡼⡇⠀⠀⠀⠀⠀⣀⡤⠔⠒⠛⠛⢶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⠭⠿⠟⠁⡴⠋⠀⠀⠀⠧⠜⠛⠻⠗⠁⠀⠀⡸⠃⢣⡴⠃⡇⠀⠀⢀⡴⠊⢁⡠⠐⠒⠤⣄⠀⠈⢢⡈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢤⣠⠂⠀⠀⠀⠀⠀⣀⠤⠀⢀⡇⣸⣟⣁⢰⠃⠀⡴⠋⡠⠊⣁⠠⠤⠲⠤⣀⠑⢄⠀⢳⡀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠖⠉⠉⠁⠀⠀⢀⣾⣿⣛⠉⠀⡞⢀⡞⢀⣾⠕⠋⣀⠤⠤⠤⠤⣌⠳⡀⠱⡀⡇⠀⠀⢸⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠉⠲⢄⡀⡞⠀⠀⠀⠀⢀⡴⡿⣿⣯⡍⣹⡾⠁⡼⢠⡟⠁⡴⠊⠀⠀⠀⠀⠀⠀⠑⡝⡄⢹⡇⠀⠀⡟⡿⣧⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣾⡘⠀⢳⣋⡿⢫⡗⠰⣧⡎⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⠟⠀⠀⡜⢀⠇⣿⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢷⢤⣀⡇⠀⠀⠀⠀⠘⣏⣉⣉⡡⠔⢁⣷⢡⠀⠙⣅⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠜⠁⠀⣠⠞⠀⡜⠀⣟⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⠈⢻⠀⠀⢄⠀⠀⣯⠀⠀⢀⠔⠋⣽⠿⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡤⠚⠁⢀⡜⠀⣸⣿⡆⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠘⡄⠀⠈⢣⡀⢸⡖⣉⣠⣶⠿⠛⠀⢰⣼⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡠⠊⢀⣴⣿⠏⣷⡀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⡸⠁⠀⡇⠀⠀⠈⡏⠲⢍⡉⠁⠀⢢⡀⠄⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠁⢀⣴⣿⠟⢁⡾⢹⠁ ⠀⠀⠀⠀⠀⠀⠙⠤⠴⠁⠀⠀⠃⠀⠀⠀⢹⠀⠀⠈⠙⠒⡶⠿⢦⡀⠀⠀⠉⠉⠑⢄⠀⠀⠀⠀⠀⣼⣿⣿⣶⠿⠋⠁⡰⣻⢁⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠈⠑⡦⢄⠀⠀⠈⠳⡄⠀⠀⠀⠘⠿⣉⣀⣠⠔⠋⡴⣡⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠈⢣⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⢣⣀⠴⢋⣴⠃⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⢳⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢳⡞⡟⢹⡸⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀⢣⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠳⡱⣈⣹⠟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠃⠀⠀⠀⠀⠀⣷⣤⣤⣴⠁⠀⠀⠀⠀⣸⣤⣄⣀⣈⡇⠀⠀⠀⠀⠹⡄⠀⠀⠘⠢⠬⠽⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣷⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!
AI Story Generator - AI Chat - AI Image Generator Free