Hands tied Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣂⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠈⢻⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⡗⠉⠉⠰⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡇⠣⠤⠤⠞⠈⢶⢭⠢⡀⠀⠀⠀⠀⣴⠁⡇⢸⠳⣄⣀⡤⠃⡷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠇⠀⠀⠀⠀⠀⠈⢦⠱⡜⡄⠀⠀⢸⢸⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⠙⢏⠓⢄
⠀⠀⠀⠀⠀⠀⡠⡾⠋⡠⠀⠀⢀⡸⡄⠀⠀⠀⠀⠀⠸⠀⢹⢸⠀⠀⣼⠈⡆⢳⠎⠀⠀⠀⠀⢠⠇⠀⡀⠀⠰⣸
⠀⠀⠀⠀⠀⠀⡿⠁⡜⠀⠀⠈⢸⡇⡿⡄⠀⠀⠀⠀⠘⡀⢸⠞⠀⠀⣿⡄⢱⠎⠀⠀⠀⠀⠀⣼⠖⠊⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠙⢄⠈⠀⢀⠀⠀⠛⡇⠘⢆⠀⠀⠀⠀⢷⠋⢧⢀⣤⣸⡼⠁⠀⠀⠀⠀⠀⠜⠙⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢿⠝⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡆⢸⠒⣹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⡇⠀⠀⠀⠀⡸⠁⣸⢒⣿⠀⠸⡄⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠑⠀⠀⠀⠀⠀⢠⣋⣡⡞⢄⠀⠙⠀⠀⠀⠀⠈⠂⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢙⡦⢄⣀⣀⣀⣀⣀⣏⡴⢮⠼⢢⣳⡀⣀⣠⠴⡖⢚⠋⢹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⣧⣘⣇⠀⢣⠀⠣⣸⣳⡜⢳⣭⡾⢹⣁⣸⣴⡥⢾⠖⡫⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⢋⠉⠉⢻⡂⡟⢧⣹⢧⡼⢳⠯⠼⠥⠼⠤⠾⠖⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠘⠓⠈⡉⢙⣹⡉⠱⢤⡞⢙⡿⡄⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠇⢸⠕⡳⠦⠟⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠐⢸⠋⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣

⡶⢦⣠⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢻⣄⡴
⡇⠀⢹⢧⡀⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢳⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⡼⡏
⢿⠀⢸⠀⢳⣨⠷⡄⠀⠀⠀⠀⠀⠘⣇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⠃⠀⠀⠀⠀⠀⢠⠾⣅⡞⠀⣇
⠘⣦⣿⠀⣸⠋⠀⡿⢦⡀⠀⠀⠀⠀⠹⣄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⠀⣠⠏⠀⠀⠀⠀⢀⡴⢿⠀⠹⣇⠀⣿⣴
⠀⠈⣿⠀⣿⠀⢰⣇⡀⠉⠳⢦⣄⠀⠀⠈⢳⡆⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡞⠁⠀⠀⣀⡴⠞⠉⢀⣸⡆⠀⣿⠀⣿⠁
⠀⠀⣿⠀⣿⠀⢸⡇⠙⠶⣄⡀⠈⠙⠳⠦⣄⣳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣟⣠⡴⠖⠋⠁⢀⣠⠶⠋⢸⠇⠀⣿⠀⣿
⠀⠀⠹⣄⣿⠀⠀⡟⠦⣄⠈⠙⠚⠁⠀⠀⠈⠉⠻⣦⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣴⠟⠋⠁⠀⠀⠘⠓⠋⠁⣠⠶⢻⠀⠀⣿⣠⠏
⠀⠀⠀⠘⢿⡀⠀⠻⡄⠈⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠋⠁⢠⠟⠀⢀⡿⠃
⠀⠀⠀⠀⠈⢧⠀⠀⠙⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢷⡾⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⡀⠀⠀⠀⣰⠇⠀⠀⠀⢸⡇⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠘⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠃⠀⠀⢺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣷⠶⠶⣶⠶⠶⢶⡶⠶⢾⡷⠶⠶⣶⠶⠶⣶⠶⠶⢾⠷⢦⣠⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣾⣷⣶⣞⣛⣒⣖⣛⣒⣒⣻⣷⣶⣟⣓⣒⣾⣓⣲⣚⣻⣶⣻⡶⢿⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢯⣤⣯⣥⣤⣿⣥⣤⣾⣥⣤⣼⣯⣤⣴⣯⣤⣤⣿⣥⣤⣾⣥⡽⠙⠻⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣧⡟⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣻⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣉⣧⡜⢳⣀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⢇⣠⠛⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣉⣳⣸⠋⠀⠉⢹⡄⠀⠀⣴⠚⠉⠙⢾⣷⠋⠉⠓⢦⠀⠀⢠⡞⠉⠉⠻⡇⡼⠛⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⢿⡆⢠⠀⣼⠗⠋⠉⢣⡀⠀⣀⢸⡇⢀⠀⢀⡼⠛⠓⢼⡇⠀⠀⢠⡿⠗⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⠚⢻⡛⢷⡀⠀⠀⢦⣽⢾⢶⣯⢤⡔⠋⠙⠛⠦⣽⢾⡷⣯⡴⠟⠛⠛⢦⣌⣻⣼⣧⣟⣡⠀⠀⠀⣷⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⠛⣻⠟⣻⠿⠟⠛⣻⣗⠿⢇⣿⠺⡇⠀⠀⠘⣛⣧⡻⢟⣽⣛⠃⠀⠀⢸⠯⣟⣾⣷⣻⠤⢶⣶⣾⠤⣾⠥⣴⡯⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⣇⠀⠀⠈⣡⡟⣿⠻⣎⠁⠉⠓⢺⠟⠉⡼⢹⡟⢧⠙⢿⡖⠒⠉⠛⣹⢶⡾⣏⠓⠀⠀⠈⡶⠼⠦⠼⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⣿⠀⠀⠀⢻⠳⢤⠤⣏⠀⠀⠀⣸⣇⠀⠀⠀⣹⣀⡠⢾⠇⠈⠁⠹⡧⣄⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣄⣠⠞⠀⠀⠀⠈⠳⠶⠞⠁⠙⠶⠴⠚⠁⠀⠀⠸⣄⠀⢀⣰⠃⠀⠉
⣶⣶⡶⠶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⢠⠤⡖⠁⠈⠒⢤⡄⢄⡀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⣄⡀
⠀⠀⠀⢦⡃⣀⣀⣤⡀⠀⠀⠀⠀⠙⢦⣀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣿⣿⡿⠟⠛⠁
⠀⠀⢠⠏⠀⠛⢍⠉⣿⡶⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠟⠳⠄⣤⠖⡒⠻⢎⣩⣵⣿⡿⠍⠃⠒⠁
⠀⠀⠈⣧⠀⠀⡨⢋⠅⠁⠁⠀⠀⠀⠀⠀⠀⠹⠿⣿⣏⣚⠷⣤⡜⣉⣠⡟⠉⠁
⠀⠀⠀⣿⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡠⢿⣠⡎⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⡅⢦⣀⠉⣉⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡈⢀⠞⣲⣤⠙⡱⣄⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠙⣦⣤⣤⣤⣤⣴⠦⣤⣀⡀⠀⠀⠀⠀⡘⢡⣆⡼⠋⠻⣦⡌⠻⣦⡘⢤⣄⣤⣤⣤⣴⣤⣴⣴⣦⠶⠚⠁
⠀⠀⠀⠀⠈⠳⠖⣿⣶⣶⣶⣦⣤⣭⣿⣶⣶⣤⠐⣼⢋⣤⡤⠴⠾⢷⡤⣄⣙⣧⢸⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠃⠀⠀⢀⠀⢠⡟⢀⡾⣿⡤⢴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⢜⠁⣾⡀⢸⣇⡘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠄⡀⡀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⣿⡇⠺⣿⡅⠨⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣆⠀⠤⣼⠡⣤⣤⣤⣶⠚⠁⠀⠀⠀⠀⣿⡏⠠⣿⣿⡇⠘⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠘⢇⠸⣇⠬⡷⢤⡀⠀⢀⡼⠿⡗⢀⡟⠉⢑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠙⠓⢦⣉⣎⡇⠘⠀⡔⠙⠓⢀⠏⠀⠀⢠⢀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣠⡏⠉⠉⡜⠀⢸⡁⠀⢸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠖⠑⠒⠊⠉⠉⠁

⠀⠀⠀⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀
⠀⠀⠀⡇⢹⢆⢣⠀⠀⠀⠀⡴⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣆⠀⠀⠀⠀⡜⡰⡏⢸
⠀⠀⠀⠱⣸⢈⠏⢱⣀⠀⠀⠸⡄⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⢠⠇⠀⠀⣀⡎⠹⡁⣇⠎
⠀⠀⠀⠀⢹⢸⠀⡷⢄⡙⠢⢄⡈⢇⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡸⢁⡠⠔⢋⡠⢾⠀⡇⡏
⠀⠀⠀⠀⠘⣼⠀⢗⠢⣉⡒⠀⠈⠙⠣⢄⡈⠣⡀⠀⠀⠀⠀⢀⠜⢁⡠⠔⠋⠁⠀⢒⣉⠔⡺⠀⣧⠃
⠀⠀⠀⠀⠀⠈⢆⠈⠦⡼⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⡄⢠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⢧⠴⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠀⢠⠃⠀⢸⡇⠀⠘⡄⠀⢀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⣀⣁⣀⣀⣨⣅⣀⣀⣈⣀⣸⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡷⢾⡷⢾⡷⢾⡷⢾⡶⢾⠶⢿⢾⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠹⡏⠉⠉⠉⠉⠉⡏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⡎⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⡜⠀⠀⠀⠀⣠⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠓⡀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠠⠞⠱⣆⡔⠊⠉⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠲⢤⣀⠳⣄⠀⠈⢂⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⣀⣴⣏⣀⠤⠴⠈⢿⡀⠀⠀⠀⠀⠀⠀⡴⢢⠄⠀⡀⠣⣀⢀⠈⠳⣿⡀⠀⠀⢆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡸⢹⡾⠁⠀⣀⣀⣠⠾⣄⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠈⠑⠮⣿⡀⠀⠈⢷⡀⠀⠈⡆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣇⡜⠀⠀⢀⣟⢹⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠈⢳⠈⢠⡞⠁⠀⠀⡏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⣇⠀⠀⠙⢿⣸⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⢣⠞⠁⠀⠀⡰⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠘⣆⠀⠀⠀⠻⢤⣈⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣞⣈⣧⠀⠀⠈⢣⠀⠀⡰⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠢⡘⠀⠀⠀⠀⠀⠈⢳⣉⠓⢦⡀⠀⠀⠀⡴⠞⣩⡴⡿⠁⠀⠀⠀⠀⠱⢀⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡐⣀⠀⠀⠀⠀⠀⠉⠓⢦⣿⡄⠀⣾⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠜⣩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠳⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠋⠀⠀⠀⠀⠀⠀⠀⡠⢖⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠆⠤⢶⣛⡷⠤⠠⠔⠴⡲⢖⡶⠻⠜⠆⡠⢠⠤⡤⠤⠾⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⢤⣤⠋⠙⠉⠟⡘⢋⠑⣉⢛⣁⡉⢈⣁⣠⣨⣧⡵⡶⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⣈⣭⣏⣭⣭⣍⣭⣥⣾⠵⠷⠚⠚⠛⠛⠻⢶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠂⣩⡁⠀⠀⠀⢸⡏⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠸⣇⣴⠁⠀⠀⠀⢸⢠⡏⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠰⠿⠏⠀⠀⠀⠀⠀⢸⡇⢹⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠠⢀⡴⠉⣯⡇⠀⠹⡅⠀⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡅⠀⣸⠁⠀⡏⡟⠑⢤⡠
⠀⠀⠀⠀⠀⡚⠁⠀⢠⠃⢸⡀⠀⣷⣀⣡⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⣇⣠⡇⠀⢰⠇⠳⡀⠀⠉⣣
⠀⠀⠀⠀⠀⣇⠀⠀⠷⠒⠚⠛⠛⢿⠭⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠭⠿⠛⠛⠓⠒⠯⠀⠀⡇
⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠲⣤⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣠⣤⠄⠀⠀⢲⣧⠘⠢⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃
⠀⠀⠀⠀⠀⠐⢤⡈⠓⠤⠄⣀⠀⠀⠈⠀⠀⠀⢹⣬⡶⡽⠷⠄⠀⠀⠈⡰⢦⣿⠃⠀⠀⠈⠀⠀⠀⣀⠤⠔⠊⣁⠔⠂
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠸⡄⠀⠀⠀⠀⣀⡜⠀⣇⡇⠀⠀⠀⠀⠀⣣⣾⠈⣆⡀⠀⠂⠀⠀⢸⠁⠀⠀⠈⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⠤⡞⠁⣇⣸⠟⡿⡄⠀⠀⠀⢸⢻⠻⣄⣊⠘⡦⢤⡀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⠫⠏⣠⣃⠜⢉⠇⢠⡇⠀⠀⠀⠀⠀⣼⠀⢻⠙⢦⣱⡀⠻⠙⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⡏⢩⣟⡽⣡⠇⢀⠾⠰⠊⠀⠀⠀⠀⠀⠀⠈⠓⠈⢧⡀⢣⡉⣍⢫⠍⠓⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠗⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠓⠣⠼⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠄⡀⠀⠀⡴⠖⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡹⢆⣤⣀⣀⡀
⠀⠐⠐⠀⠀⠀⠈⠀⠘⢷⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⡎⣰⠃⠀⡀⠉⠑⢩⡹⢄⣀
⠀⠁⠀⠀⠀⠈⢂⠀⠀⠀⠳⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢂⣀⣼⠔⠀⠀⠀⡁⡠⠀⠀⠉⠑⢎
⠀⣤⠀⠀⠀⣠⠼⣶⠁⠀⠀⢰⠀⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢜⣁⠀⠀⣸⠓⢄⡀⠀⠘⠄⠀⠀⠀⠀⢀⢻
⠀⢠⠀⠀⠀⠀⠀⠈⠧⠀⠀⣾⣇⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠁⠉⠙⢷⡤⠟⠓⠢⠀⠀⠀⠈⠀⠀⠀⠀⢏⠜
⠀⣿⠀⠀⢀⠀⠂⠀⠀⠀⠀⠙⠛⠛⢭⡅⠭⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⣠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠊
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⠀⠊⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠁
⠸⣆⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢰⣯⡶⠛⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⢀⡿
⠘⢦⡑⠌⠓⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠹⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢰⣶⡿⠃
⠀⠀⠙⠳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣰⡾⠋⠁
⠀⠀⠀⠀⠀⠙⠻⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣁⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡎⡀⡀⠄⠀⠀⠠⠤⠀⢿⡧⣽⣌⣐⣰⣀⡂⠀⠤⠀⡀⣘⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣷⠷⠶⢾⠶⠶⠷⣶⢿⣻⡗⢸⣽⣹⣹⣛⠛⠻⠶⢴⢤⣤⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⡾⠶⡶⠶⠶⢾⡏⢰⣿⣿⣾⣿⣭⡛⠿⠿⠿⠶⠷⠶⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣾⣶⠶⠷⠶⠶⣿⠣⣿⣿⠿⠛⣿⣿⣿⡄⠷⠶⠳⠷⠚⠓⠾⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⡯⢸⠀⢉⠀⠀⢹⡟⠀⢿⠤⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⣒⠀⠸⠀⠀⠸⡇⠀⢸⡯⡀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⡧⠔⠀⠀⡀⠀⠀⣷⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢸⡅⡃⠀⠀⡇⠀⠀⠹⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢸⣅⠄⠀⠀⢃⠀⠀⢰⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣗⢥⠀⠀⢸⠀⠀⠸⠇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠇⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠿⠖⣦⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⣤⡿⢛⣧⣬⣏⡙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣛⣥⣾⣷⡞⢠⣞⡙⠳⠦⣍⡲⢼⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣹⡷⠶⠛⠛⠋⠉⠁⠀⣽⣀⡿⢦⣉⠓⠦⡼⢩⡗⠯⣷⣄⡀⠀⣠⡴⣿⣁
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠈⣙⣾⢁⡟⢿⣦⡈⠻⣿⡟⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡷⣄⠹⡟⠒⠋⠀⢤⠀⠀⠀⠀⠻⣄
⠀⠀⠀⢰⠟⠀⠀⠀⣠⡷⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣤⣿⠋⡛⠁⠀⠀⠀⠈⠳⣧⡀⠀⠀⠘⢷⡀
⠀⠀⢠⠟⡄⠀⢀⡿⠯⣍⣀⣀⣀⠤⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠐⠤⢄⣀⣀⣀⡭⠿⣇⠀⠀⡜⢧
⠀⢰⣟⠊⣀⣴⡯⣄⡴⡶⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡀⣤⡶⠶⣄⡬⣷⣄⡈⢚⡷
⠀⣠⠞⠋⠙⠁⣸⡟⠠⠤⢸⠏⠩⢹⡶⠶⡄⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⡴⠶⣾⠩⠉⣿⠠⠴⠘⣿⡀⠙⠉⠛⢦⡀
⠠⡇⠀⠀⠀⣠⠞⠀⠀⣰⠋⠑⠒⡜⠀⠄⡿⠀⠀⢀⣴⠟⢷⡄⠀⠀⠘⡇⠀⠘⡔⠒⠉⢳⡀⠀⠘⢦⡀⠀⠀⠀⡧
⠀⠙⠦⢴⡞⠁⠀⠀⣰⠏⠀⠀⣸⠁⠀⠀⡇⠀⣹⠟⠁⠀⠀⠙⢿⣁⠀⡇⠀⠀⢹⡀⠀⠈⢳⡀⠀⠀⠙⣶⠤⠞⠁
⠀⠀⠀⠘⣇⣀⣀⣴⠇⠀⠀⢀⡏⠀⠀⢀⣿⠿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠀⠈⣇⠀⠀⠀⢷⣄⣀⣀⡟
⠀⠀⠀⠀⠀⠉⠉⠸⢦⣀⣠⠞⠻⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠛⢦⣀⣠⠾⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠙⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠐⢶⣦⡄⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠃⠀⠀⠀⠀⠀⢿⡇⠀⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⣔⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣾⣿⣿⠿⠛⠛⡏⠀⠀⢀⡠⠄⡂⠀⠈⠑⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⢳⣶⠖⠉⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⢸⡏⠀⠀⠀⠀⠀⢰⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⣇⠀⠀⠀⠀⠀⠘⣿⣧⣀⣷⣄⡀⠀⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⣻⠇⠀⠀⢀⣠⣾⠿⢿⡟⣿⡟⠁⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠀⢀⣴⣻⠏⠁⠀⠀⡇⣼⠁⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⠾⣿⣿⣿⣿⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠉⠀⠀⠀⠸⡿⣿⣧⣀⠀⢠⣾⣿⣿⣟⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈⢪⣿⣿⣾⣿⣿⣿⣿⡇⢸⣿⣏⣀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠛⡩⠾⢶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡟⠙⢷⣦⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠛⠛⠛⣻⣿⡿⠿⠀⠀⠀⠈⠉⣡⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠟⠋⠁⠀⣀⣤⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⢪⠟⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠁⣀⣤⣶⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣿⡿⣁⣠⣾⣿⣿⣿⣿⠿⠿⢿⣿⣶⣶⣾⣟⠊⠉⢀⣠⣴⣾⡿
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣼⠟⢠⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⣰⣿⣿⣿⡿⠉⢀⠟⣿⣿⣿⣀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣾⣿⣍⡉⠉⣁⡴⠒⠢⣄
⠀⠀⠀⠀⢿⣿⣿⠏⠁⠀⠰⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠉⠉⠛⠻⠿⣿⣧⡀⢀⣸⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡀⠀⠣⣀⣹⣿⣿⣿⣿⠯⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡶⠶⠚⠓⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⢦⣤⣿⡿⠿⠿⠯⠤⠤⠤⠐⠚⠉⠁⠉⠉⠙⠓⠶⠶⠶⠶⣶⡿⠿⠍⠁⠀⠀⣀⣀⣠⣼⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⢀⠄⣤⠊⢻⢲⠀⠈⣎⠀⢈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡉⠀⢹⠋⠀⡐⡿⠙⢦⡠
⠀⠀⠀⠀⠀⡜⠋⠀⢀⡜⠘⡄⠀⢸⡄⢘⡤⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡇⢀⡏⠀⢀⡇⠹⡀⠀⠉⢳
⠀⠀⠀⠀⠀⢳⠀⠀⡿⠤⠒⠛⠲⢾⡯⡉⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢉⢽⡿⠖⠚⠓⠦⢼⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⠀⠀⠬⢽⡏⠱⢄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠠⢄⡉⠢⢄⣀⠀⠀⠀⠐⠂⠀⠀⠀⣏⣹⣍⣿⣦⠀⠀⠉⠑⣬⣤⣷⠇⠀⠀⠀⠂⠀⠀⠀⣀⡠⠔⠋⣠⠄
⠀⠀⠀⠀⠀⠀⠢⠙⠂⠀⠀⠘⡇⠀⠀⠰⠀⠀⢀⠞⢸⢨⠇⠀⠀⠀⠀⠀⡇⡟⠹⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣠⡞⢹⠀⣼⢿⢦⠀⠀⠀⠀⣰⠻⢿⡀⡟⠳⣄⣀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡷⡲⠃⡸⢀⠜⢻⠃⢸⡈⠀⠀⠀⠀⠉⣿⠈⢟⠳⡄⢳⠈⢷⠲⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠓⣲⢄⡞⣩⠃⢀⡏⡠⠎⠀⠀⠀⠀⠀⠀⠙⢄⡸⣄⠈⢏⠳⡆⢗⡚⢧⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢰⠠⠓⠋⠒⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠙⠘⠇⣌⢸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑

⡖⢦⡏⢢⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠊⣧⠖
⡇⢸⠛⡎⣧⡀⠀⠀⠀⠀⡇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡇⠀⠀⠀⠀⣠⡇⡞⢻
⠹⣼⠀⡽⠁⡷⢄⡀⠀⠀⠹⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠁⠀⠀⣀⠴⡇⠹⡅⢸⡼
⠀⢸⠀⡇⢰⡧⣄⠉⠲⢤⣀⠈⢧⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⠏⢀⣠⠴⠊⢁⡤⣷⠀⡇⢸
⠀⠸⡄⡇⠀⡧⣌⠙⠢⠄⠈⠉⠚⢧⣀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢀⣠⠞⠚⠉⠀⠤⠚⢉⡤⡇⠀⡇⡼
⠀⠀⠘⢧⠀⠱⡀⢙⡞⠀⠀⠀⠀⠀⠈⠑⠆⠈⠳⢤⡀⠀⠀⣠⠴⠋⠀⠞⠉⠀⠀⠀⠀⠀⠈⣞⠁⡴⠃⢠⠟
⠀⠀⠀⠈⣆⠀⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⢀⡞
⠀⠀⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⢀⡆⠀⠀⢻⠃⠀⠀⣆⠀⠀⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠊⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣻⣛⣻⣟⣛⣿⣛⣿⣛⣻⣟⣛⣿⣛⣻⣛⣶⣶⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣻⣛⣻⣟⣛⣿⣛⣻⣛⣻⣟⣛⣿⣛⣻⣛⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⢠⣤⣿⠃⠀⠀⠀⠉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠐⢸⡏⠀⠀⠀⠀⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠊⢁⣠⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢶⣧⡈⡇⠀⢀⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⢠⡎⠹⣿⣄⡀⠀⠀⠀⠀⢰⣤⣆⣸⣛⣿⣏⣀⣽⡁⠘⠒⣫⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣶⣿⠘⠉⠀⠀⠘⠿⠿⣶⣀⠀⠘⣇⠹⣿⣿⠧⣿⣿⣿⣿⣿⣿⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡈⠈⠀⠀⡀⢀⠸⡏⠰⠀⠁⠀⣽⠇⠀⠙⢛⠻⢋⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣤⡆⠀⠉⠀⣰⣿⡇⠀⢀⣾⡏⢿⠛⠷⢼⣷⡍⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢹⣾⡇⣦⣤⣴⡏⣿⣷⣴⣿⣿⣧⢸⠀⠂⢸⠋⣿⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢿⡇⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⠈⠀⢀⡇⣼⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢩⣀⣤⣸⣿⣿⠀⢿⣿⠟⠛⠃⠘⠃⠀⡾⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢿⡼⣿⣿⣿⡁⢸⣿⡦⠀⠀⠀⠀⠈⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠇⢸⣿⣿⣧⣈⣿⠃⠀⠀⡀⢢⣀⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡿⡄⠘⠋⠹⠿⠻⡟⢂⣈⣶⣶⣿⠏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣶⣿⡟⠛⠉⠀⠟⠀⠁⠀⠀⠀⠀⠀⠀⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣟⠋⢉⣁⣶⡆⡀⢻⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣶⣄⠀⠀⠀⠀⠀⣶⣦⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠁⢸⣿⣿⣿⠃⠹⣿⣿⡷⠄⠀⠀⠀⠘⢿⣿⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢹⣿⠀⠀⠀⠙⠇⠀⠁⠠⣀⠀⠀⠈⠛⢧⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠙⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣦⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⠉⡏⣩⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣠⡞⢹⡄⣸⡴⢿⢋⠜⣡⣊⣟⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡇⢹⠀⣷⣿⠷⠷⠟⠛⠋⠉⠉⠉⠉⠛⠛⠓⠲⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢻⠀⢇⣸⠊⠉⠛⠛⠛⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠠⣄⠀⢀⡔⣹⢏⠹⣸⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢷⡄
⠀⠀⠀⠘⢶⣎⢹⣇⠈⢢⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣯⣻⣄⠑⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⠙⢦⡀⠘⢧⡀
⠀⠀⠀⠀⠀⠙⠿⣧⣝⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠘⠻⢷⣦⡀⠀⠅⠁⠀⢙⣦⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⡯⢝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⡈⢻⣣⡀⠀⠰⣏⠀⢹⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠢⣿⣦⠀⠀⢤⡀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠁⠀⢙⠿⣶⣤⣌⣭⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣍⢆⣽⠈⢷⡀⠀⠑⢄⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⣇⣀⣼⡿⠁⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇⠀⠀⢻⡄⠀⠀⠑⢀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣾⣿⡅⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠲⡀⠈⠣⡀⠀⠀⠈⠀⠤⣤⣤⣀⣀⠀⠀⠀⣠⠏⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠻⣤⣠⣤⡦⣄⣠⡤⣴⠞⠛⣻⠋⠛⠛⢿⣏⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⢧⣤⠽⢤⣤⡽⣦⣤⡴⠞⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣀⣠⣤⡾⠋⠀⠙⠶⢤⣀⣀⣀
⠀⠀⠀⢠⣋⠸⠃⠈⠃⠀⠀⠀⠀⠘⠉⠀⠈⠳⣄
⠀⠀⠀⠀⣹⡦⢤⣤⣬⠿⣷⣄⣀⠀⠀⠀⠀⠀⠈⠳⠦⣄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⣠⢤⣤⠴⠶⢋⣻⣷⣤⣄⡄⠠⠤⠂⠈⠁
⠀⠀⠀⢰⠏⠀⠈⠙⢢⡀⣹⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢰⡏⣉⠝⠓⠺⣟⣡⠄⣉⣉⡶⠾⠿⠟⠛⠛⠃
⠀⠀⠀⠘⣦⠀⠀⠉⢉⠝⢉⠸⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣤⣏⣜⡹⢷⣦⣤⢩⣤⣴⡿⠁
⠀⠀⠀⠀⣿⡆⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⢀⣼⡃⣠⠎⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⡟⠇⠀⠀⠤⢶⣦⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⡼⣅⠀⠻⡿⣧⡀⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⣧⠺⣦⣄⡀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡞⢡⣼⣿⡇⠈⠈⣿⡀⠉⢳⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠈⢳⣤⣤⣤⣤⣤⣄⣰⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⡏⠁⣼⣡⡾⠃⠉⠿⣶⡆⠘⠿⣆⣉⠳⢶⣲⣶⡾⠷⠾⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣮⣭⣭⣭⣶⣶⣧⣤⣤⣉⣙⣛⣶⣶⣤⣄⣠⢧⣠⡿⢉⣠⣤⣤⣤⠿⢷⣤⣦⡈⠛⣳⡀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢠⡿⠀⠉⠉⠁⢀⠄⢀⣿⠋⢈⡿⣟⡙⣁⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠉⠀⠀⠀⠀⠐⠃⠀⢸⡇⢀⡟⠙⣻⣟⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⣝⠀⣼⢷⡀⢙⡿⣄⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣇⢸⡁⠸⡅⢿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠉⢳⠷⠀⠀⠀⣀⣀⣠⡴⠂⠁⠀⠀⠀⠀⢸⠌⡇⢀⡇⠈⢳⡆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣷⠀⠘⠚⠿⢍⣿⠿⢿⣿⠿⣥⡀⠀⠀⠀⠀⠀⢀⣾⠀⣇⠀⢳⠀⠘⣇⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣇⠀⠀⠀⠀⢀⠙⣄⠼⣧⠤⠼⡷⠶⣤⠀⠀⣄⡞⠁⠀⡏⠀⢎⠀⠀⣸⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠟⠓⠛⠶⣤⡋⢁⢸⡆⠸⠀⠀⡟⠛⠛⡆⢠⡏⠀⠀⠀⣹⠀⣸⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⢀⡾⠛⠯⠚⣰⠃⠀⣸⠁⠀⠀⣷⡞⠀⠀⠀⠀⣇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠴⢾⣧⠀⠀⢠⣏⣀⣀⡿⣦⣤⣤⠏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠈⠉⠉

⠀⠀⠀⠀⠀⠀⡀⢀⡴⠲⡶⡄⠉⢳⡋⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠉⡴⠁⠐⡖⡖⠢⣀⢀
⠀⠀⠀⠀⠀⢠⠖⠋⠀⢠⠇⣇⠀⠀⣧⠀⢂⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣘⠀⢰⠃⠀⢰⠁⣇⠀⠉⠲⢇
⠀⠀⠀⠀⠀⢸⠀⠀⢰⣋⣠⠼⢦⣤⣿⠖⠊⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠙⠒⣿⣦⣤⠾⢤⣈⡦⠀⠀⣼
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⢽⡗⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠶⢖⠲⣏⡀⠀⠈⠙⠳⠀⠉⢦⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⡙⠢⡄⠉⠒⠂⢄⠀⠀⠀⠀⠀⠀⠈⡷⢯⢳⡟⠛⠀⠀⠀⠀⡜⢹⢻⡃⠀⠀⠀⠀⠀⠀⢠⠄⠒⠉⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⣼⠁⣸⣼⡀⠀⠀⠀⠀⠀⣱⣼⠀⢳⢄⡀⠈⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢀⣠⠔⣾⠁⣸⣠⡟⢹⢳⠀⠀⠀⠀⢸⢹⠙⣧⣸⠀⢳⠲⣄⣀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡐⠡⠋⣠⣃⠔⠉⡜⠀⣼⠆⠀⠀⠀⠀⠈⢼⠀⢹⡉⠳⣌⣆⡘⢎⠃⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠃⢩⢟⡹⢁⡎⢀⡴⠡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠓⠄⠧⡀⠘⣌⠫⡙⡭⠈⡇⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠇⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠒⠅⢽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣼⣦⣵⣦⣤⣦⣴⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠛⠛⠛⣛⡛⠲⣶⣾⣟⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣠⣠⣤⣶⣿⣉⡉⣻⠋⠉⠙⠓⢦⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠉⢉⣿⣧⡀⠈⣹⠋⠓⠶⢄⡀⠀⠀⠈⠙⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣀⣠⡤⠶⣟⠀⠈⢙⡿⠤⣀⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠉⠀⠀⠀⢸⣦⡐⠋⠀⠀⠀⠀⢢⡀⠀⠀⠀⠈⠑⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⢀⣠⣴⡶⠟⠛⠛⢦⣄⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠈⠉⠉⠉⠀⠠⢄⡀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠳⠀⠀⠀⠈⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⣆⢀⣠⠟⠙⠛⢿⣿⣿⣷⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⣽⣦⣤⡀⠀⠀⠀⠉⠻⣿⣿⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠐⢾⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⣀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠻⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⣿⣿⣿⠗⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣄⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⠻⣿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⡙⠳⠶⣍⣙⠻⣿⣷⣄⠀⠀⠀⠀⠀⣀⣴⡿⠿⠖⢋⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣝⠻⢷⣦⣉⣓⣦⣌⡙⠛⠶⠶⣶⣿⣯⣭⣤⣴⣾⣭⣴⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠉⠉⠛⢶⣦⣤⣉⠉⠛⠛⠻⠶⠶⣤⣤⣤⣤⣤⣤⣴⣾⣥⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⢿⣿⣿⣿⣭⣽⣭⠽⠿⠟⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⣖⡄⠀⡔⣦⢲⠀⢀⢶⢄⠀⠀⢀⣀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⡿⡽⠉⠉⣻⡏⠟⠓⢺⡟⠺⠒⠲⣾⡿⡾⠤⣾⡼⣼⠤⣴⣽⣽⣄⣠⣖⣶⣆⣠⣶⣖⡄⠀⡠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣾⣿⡇⠀⣾⡿⣿⠀⢠⣾⣷⡇⠀⣠⣿⣟⠀⢀⣿⣵⠁⠀⣾⣇⠆⠀⣨⣎⡜⠀⣋⡟⡹⠉⢩⣹⢛⣟⡐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠉⠀⠀⠈⠉⠁⠀⠈⠙⠛⠁⠀⠙⠛⠋⠀⠘⠿⠟⠀⠘⠿⠿⠂⠀⢿⣿⠇⠀⣿⣿⡇⠀⣾⣿⡆⠀⢃⣿⣿⣦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠋⠁⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠩⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡯⠌⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣏⡉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⠍⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⢂⢄⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣁⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⣇⢫⣲⣊⡀⠈⣱⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣓⣒⣒⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣳⣿⣮⣿⢏⠀⠀⠀⠀⠩⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣒
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣡⢃⢆⡄⠀⠀⠀⠈⠐⠨⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣆⡎⠞⡵⢀⠀⠀⠀⠀⠉⠂⡙⠢⣄⠀⠀⠀⠀⠀⠀⣸⣷⣿⡍⠉⠩
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⣴⡰⢡⢂⢄⡠⠀⠀⠀⠀⠁⠂⠙⠦⡀⠀⠀⢀⣿⣻⡿⠭⠭⠁
⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠛⢧⣁⢊⠔⡡⢂⠀⠀⠀⠀⠈⠀⠨⠓⢤⣸⣿⣿⠧⠭⠤
⠀⠀⠀⠀⢠⠃⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢼⣠⢣⠎⡡⢂⠀⠀⠀⠀⠀⠁⢈⠻⢿⠥⠤⠁
⠀⠀⠀⠀⡎⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⣜⡐⢡⢊⡴⣀⠀⠀⠀⠀⠀⠀⠙⢯
⠀⠀⠀⡜⠀⢀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠱⢧⣎⡰⡡⢋⠔⡠⢀⠀⣠⠒⠉⠲⢤⡀
⠀⠀⡼⠀⢀⡪⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⠱⢧⣜⡰⢡⢋⣞⠭⠓⣠⠞⡿⠃
⠀⡔⠀⠠⣂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢩⢭⣿⣿⣞⣿⣇⣾⣿⣟⣡
⣜⠀⠐⠥⣂⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢇⣀⣈⣃⣐⠲⠬
⠀⡽⠗⡶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣿⣿⠇⠒⣒⠒
⠈⢱⠶⢤⣤⣈⣘⠉⠛⠙⠓⠖⢲⠶⡤⢤⡤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢰⢀⣿⣿⣟⣒⣒⡂
⠀⠀⢹⣒⠦⡬⣍⣉⣙⡓⠒⠶⠦⢤⣤⣄⣈⣁⠘⠉⠋⠝⠩⠛⠳⠒⠖⣲⠖⣶⠖⡤⢤⡤⣤⣀⣀⣀⣀⣀⢈⣈⠂⣈⣸⣿⣿⡗⠒⠒
⠀⠀⠀⠈⣛⢛⡒⠲⠾⠭⠭⣟⣙⣛⠒⠶⠮⢬⢭⣟⣙⣛⣖⡶⠲⠶⠶⠶⠦⢴⠤⡤⢬⢤⡥⣬⣤⣭⡬⣥⣭⡭⣭⣩⣩⣿⣿⡧⠭⠭⠁
⠀⠀⠀⠀⠠⠤⠬⠭⠭⠭⢍⣉⣉⣉⣙⢛⣛⡛⠛⠚⠒⠓⠚⠿⠿⢽⣽⣿⣷⣶⣲⣖⣖⣖⣶⣳⣶⡶⢲⣖⣶⡶⣲⢲⣖⣞⣻⠭⠭⠍
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠒⠂⠤⠬⠭⠭⠭⠭⠭⠍⢈⣛⣃⣀⣐⣛⡓⣒⣩⣭⠭⠍⠙⠉⠉⠉⠉⣛⣛⣛⣛⣛⣓⣒⣒⣒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⢀⠀⠀⡕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⠀⢀⠀⡇⢰⣁⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠘⣧⠀⠀⢄⣼⠏
⠀⠀⠀⠀⠀⠀⠸⠁⢰⡞⠛⠉⠁⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⠋⠀⢻⡄⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⡀⢸⢠⡆⠐⠋⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠘⠃⢀⠀⢸⠃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠀⠰⢤⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠈⠑⠊⠉⠀⣼⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢡⡀⠠⠎⠀⠐⢄⠀⠀⠀⢀⠈⠀⠀⠄⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠉⠀⠀⠀⠀⠀⠑⢄⠀⠆⠀⠀⠀⠀⠀⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡢⣤⡀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠙⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣦⡀⠀⠀⠀⡇⢀⡀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⡇⠀⠀⢀⣿⣿⣿⣆⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣀⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠈⡏⠀⠀⠉⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠃⠀⠀⠀⢰⢹⠀⠀⠀⠀⠀⢹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠉⠓⠢⣄⠀⠀⠀⢀⡤⠖⠊⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⡞⢦⡏⢱⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⣰⠋⣧⠞
⡇⢠⠟⣆⣳⡄⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣰⣃⡞⢏⢀
⠹⣼⠁⣸⠃⢹⢄⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⢼⠁⢻⡀⢺⡼
⠀⢸⠀⡇⠀⡧⣄⠉⠲⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⠊⢁⡤⡇⠀⡇⢸
⠀⠸⡀⡇⠀⣧⣈⠙⠦⣤⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡤⠞⢉⣠⡇⠀⡇⡸
⠀⠀⠙⢧⠀⠹⡌⠑⣶⠂⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢲⡖⠉⡼⠁⢠⠟⠁
⠀⠀⠀⠘⣆⠀⠙⠦⠇⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠧⠞⠁⢀⡞
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⡄⠈⠑⢤⠔⠈⠁⡄⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⠹⡄⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣧⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣶⣾⣶⣶⣳⣶⣿⣶⣾⣷⣶⣿⣶⣞⣷⣺⣽⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢄⠀⠘⢲⠟⠖⠚⠗⠒⠓⠒⢺⠖⠒⠓⠒⠛⠒⠚⢷⠚⠉⠓⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⢯⣹⡄⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⢚⡶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⣣⡼⠉⠉⢢⠀⣀⡴⠚⠓⢾⡖⠛⠲⡄⠀⢠⠖⠚⢲⣉⠟⣲⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡞⠀⠈⢻⣠⣄⡾⠋⣈⣣⣀⢠⣸⣠⠄⣠⣋⡉⢺⡄⡄⣸⠟⠉⠳⡀
⠀⠀⠀⠀⠀⢰⡮⣧⠬⡧⢵⣦⡬⣽⣿⡿⣾⣿⠀⠀⠭⣿⣽⣽⡮⠅⠀⠘⣶⣿⣿⣷⣂⣀⣴⣋⣟⣲⣦⣄
⠀⠀⠀⠀⠀⠀⠉⠓⠚⠳⡇⠀⠐⣹⢻⠺⡝⠚⠲⣲⠞⠹⢳⠻⠙⢶⠦⠚⢟⡿⡽⣟⠆⠉⠙⡬⠧⠽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⡏⠀⠀⡏⠲⠴⣇⡀⢀⡾⡄⠀⣀⠧⠴⢺⠁⠁⢸⠦⢤⠜⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣚⣁⣀⣀⣀⣉⣉⣀⣈⣉⣁⣀⣀⣘⣦⣤⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢚⠉⣠⣬⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠬⠛⠛⣛⣉⣉⣩⣿⣿⣷⣌⡑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣀⣠⣤⣾⡿⣭⣍⣽⡃⠀⠀⠈⠙⠛⠻⠷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠷⠂⠉⢉⣹⣧⣀⠀⣸⠏⠉⠛⠷⣤⣀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢀⣀⡤⢾⡇⠀⠉⣷⡶⣤⡀⠀⠀⠀⠉⠛⠷⣤⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠸⠛⠁⠀⠈⢿⡷⠾⠋⠀⠀⠈⢳⣄⠀⠀⠀⠀⠈⢷⡄⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣀⣤⡶⠿⠛⠳⣄⡀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠀⠙⢆⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢤⡴⠞⠋⣁⣀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⢸⣇⡈⣹⠿⠿⢷⣆⠉⠹⣧⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠁⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠈⢻⣍⣉⠀⠀⠀⠙⠷⣦⣿⣿⡀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠠⠾⣿⣿⣿⣦⡀⠀⠀⠻⣿⡟⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠠⠝⠻⣿⠛⣿⡆⠄⠀⠀⠙⢯⠃⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠐⠀⠙⠩⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣕⡄⠀⠀⠀⠀⠀⠀⠘⣿⠷⡄⠀⠀⠀⠀⠀⠀⣠⠀⠸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠠⡿⠁⠀⢰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⠀⣀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⣿⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣷⣥⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡛⠛⠻⠷⣽⣟⡛⣿⣶⣤⣀⣀⣤⣴⣿⣿⣿⣿⣽⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠿⣿⣛⡷⣶⠶⣿⣿⣷⣦⣤⣍⣉⣉⣉⣛⠛⣉⢉⣭⣴⣯⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠙⠻⠿⣶⣶⣤⣤⣤⣤⣿⣿⣿⠿⢿⢛⣛⣻⡶⠟⠿⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠛⣿⣿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡟⠀⠀⠈⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠃⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢤⣄⠀⡤⠤⣄⠀⠀⡀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠆⠁⠉⣾⠃⠄⠘⠀⣠⠮⠬⠿⡀⡜⡉⢙⣇⣀⡰⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⢠⣿⣷⠀⠀⠀⣿⣶⠄⠀⣻⣤⡁⠀⠀⣿⣥⡁⠉⠁⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠀⠈⠙⠁⠀⠀⠈⠛⠋⠀⠀⠿⠿⠃⠀⠐⣿⣿⠃⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡘⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠲⠥⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢖⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠁⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣜⣿⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠇
⠀⠀⠀⠠⡐⠀⠀⠈⠀⠊⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣑⡟
⠀⠀⠀⠀⢌⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡾⡻
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠈⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣔⢄⣭⠃
⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣌⠀⠀⠂⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠠⠤⣤⢊⣌⣢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠒⠒⠲⠆⠀⠀⠀⠀⠠⠀⢤⣄⢀⣀⡨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠠⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠀⠀⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣟⠁⢉⣩⠷⠋⠉⠉⠛⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⡕⠋⠀⠀⠀⠈⠒⢤⡀⠀⠉⠉⣙⣷⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢿⣿⡯⠿⠛⠻⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢢⡤⠆⢁⣾⠍⠁⠙⣷⡀⠀⠀⢈⣉⠶⠶⠚⠛⠉⠈⢹⣟⣉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣟⡋⠸⠃⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⣾⣿⣧⠴⠛⠉⠁⠀⠀⠈⠐⠠⠀⢸⣈⣯⣽⠿⠟⠛⠙⢿⡿⣿⣿⣿
⣿⣿⣿⠟⢿⠲⣦⡀⠀⠀⠀⠀⠀⡠⠀⠀⠉⠀⠀⠖⠀⠀⢠⣤⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠤⠶⠚⠉⠛⠦⣬⣀⡀⠈⠂⠀⣰⣿⣿⣿
⣿⣟⡇⠀⢀⣀⠠⠬⠛⢷⠟⢯⣀⡀⠀⠀⠀⠀⢀⠀⠀⠂⠉⠁⠀⠉⣿⣿⣿⣿⣿⣿⣆⡤⠶⠲⠊⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠉⢉⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠄⠀⠀⠈⠀⠀⣠⠽⠷⠶⠶⠇⡀⠀⠀⠀⢀⡠⣴⣾⣿⣿⣿⣿⣿⣿⣏⣀⢀⠀⠀⠀⠀⠀⠐⠀⢠⣠⣤⠄⠐⢐⡛⣿⣿⣿⠿⣿⣿
⣿⣿⣿⢯⡄⣡⣀⠀⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠂⣿⣼⡧⠏⢛⣿⣿⣿⣿⡿⠉⣹⡸⢀⠄⠀⢄⢀⠀⠀⠀⠀⠀⠈⠙⠺⡿⣿⣛⡿⢾⣿⣿
⣿⣿⣿⠓⣈⡝⠀⠀⠀⢰⡆⠀⢀⣀⣠⠀⢀⣀⠀⠀⠀⠀⣿⣿⣿⣃⣸⣹⣿⣿⣿⠂⢐⣿⡇⠠⣀⣀⠀⠀⠀⠒⠀⣀⡀⠀⢰⣦⠀⠂⣿⣾⣿⣿⣿
⣿⣿⣿⣠⢨⣧⣄⣿⠷⠿⣷⡞⠋⠛⠛⠏⠉⠉⠉⠉⠉⠁⣻⣿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡁⠀⠂⠉⠀⠀⠀⠀⠀⣀⣉⣁⡬⠗⠖⠶⠿⣿⣿⣿⣿
⣿⣿⣿⣒⣻⠉⡿⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⣿⣿⣿⣿⡟⠀⠻⡿⣿⢏⠀⢀⣀⠤⠤⠖⠚⠟⠉⠁⠀⠀⠀⠀⠄⡀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠀⣽⣿⣿⣿⣿⣟⣘⣇⣿⣿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿
⣿⣿⣏⣿⠋⢽⢸⢛⣿⠿⠿⡷⠦⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⢿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣴⠀⠀⢀⡀⠀⣤⣤⡄⠀⠀⠀⠀⣤⠆⠿⠟⠛⠿⣿
⣿⣿⣿⣿⣤⣾⣿⠋⠁⠀⠀⢷⠆⠀⠈⠉⠲⣶⣤⣴⠚⠉⠀⠙⣿⣷⣮⣝⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠃⠀⠈⠁⠀⠐⠀⠀⡀⠀⣼⡆⠠⠀⠸⣿
⣿⣿⣿⣿⣤⣾⠠⡧⢀⠀⠀⢀⣀⡠⠤⠖⠛⠉⠉⠉⠉⠉⠒⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣷⣦⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢙⣿⣿⣴⣶⣼⣿
⣿⣿⣿⣿⣸⣙⣳⡦⣤⣶⣶⣉⠁⠀⠀⠀⢰⡀⠀⣀⣠⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣷⠀⠉⠱⠶⠤⢤⣀⣀⣁⣠⣾⣿⣿⣟⢿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣇⠀⠈⠰⠹⠛⣒⣤⣤⣜⠛⢙⢫⡄⠀⡏⢿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣆⣿⣿⢀⣀⣀⣤⡖⢲⠋⢻⣿⡷⢬⣿⡿⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣧⣬⣸⣿⣤⡶⡶⠛⠉⠉⣀⠀⠈⢙⡻⣷⣦⣼⣧⣼⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⠻⣷⡵⣬⡄⠸⠁⠠⢹⡇⣿⣯⣿⣗⣾⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⢋⣠⣆⣰⣨⣴⣤⠾⠛⣛⡋⠚⢻⠉⣿⣿⣿⣿⠶⣾⣿⣿⣿⣿⣿⣯⣹⣷⣿⣦⣚⣽⣿⣶⣷⣿⣿⣻⣿⣿⣿⣋⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⢿⠏⠈⢉⣛⡋⠀⣨⡭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠘⠂⢀⠈⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠈⠀⠀⣈⣄⡁⠈⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⣦⣠⠀⠂⢀⠈⠉⢠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣗⢦⣀⠈⠉⣹⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⡛⣩⣟⣻⠿⣮⣳⣤⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⢿⣿⣿⡵⠛⢿⡣⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣧⣿⣿⢼⣾⢙⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣽⣿⣿⣷⣷⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⣟⡟⣧⣟⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⢈⣿⣿⢿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⢿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡂⢀
⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣟⣿⣿⡟⣡⣾⣿⣽⣭⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈
⠀⠀⠀⢀⣴⣯⣢⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⢪⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢘⡿⢿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣨⣿⣿⣿⣿⣾⣿⣿⣿⣫⣷⣿⢿⣻⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⡨⠁⠨⠚⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠌⠀⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡿⠿⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠰⣤⠀⠀⠀⢨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠋⠘⠿⠿⠟⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠹⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠻⣿⡿⠛⠁
⠀⠀⠀⠀⠹⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠔⠊⠁⠀⣀⣽⣦⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣈⣥⡞⣩⠔⢲⡶⣾⣟⠋⠉⠀⢀⣀⣀⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣽⠟⠛⢳⣴⡃⢀⡾⠉⠙⡟⠉⠉⠀⠀⠀⠀⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡾⠁⠀⡴⠃⠀⢉⠟⠷⠤⢠⣷⣤⣴⠶⠶⠖⠋⠀⠈⠉⣶⡄
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⡜⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢀⠄⠠⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠞⠀⠀⠀⡆⠀⠀⠀⣾⣧⣠⡴⠓⠦⢂⣷⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⡞⠀⠀⠀⢠⣿⣿⡟⠀⠀⢠⣾⣿⣿⡟⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⡟⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣤
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⣼⣿⢿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠻⠦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠛⠿⣿⣶⣾⣿⢏⡼⢃⡿⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠦⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⠎⣴⠟⣼⠟⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣴⣯⠞⣡⡾⠃⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⢿⣶⣦⣤⣤⣤⣴⠞⢁⡼⠛⣡⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣉⣉⣩⣵⠾⢋⣥⣶⣭⣴⡾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣶⣞⣭⣴⡾⢟⣫⡽⠿⢿⣷⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣶⣾⠿⠛⠋⠉⠀⠀⠀⠀⠹⣇⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠤⠤⠤⠴⠶⠾⠛⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠛⢷⣤⡴⠶⠟⠷⠶⣶⣶⣶⣶⡶⠿⠿⠿⠛⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⣠⠀⣠⡆⠀⢀⡾⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠈⠓⠀⠀⠀⠀⠀⣰⡏⣰⡟⢀⣴⠟⢀⣤⡴⠾⠛⠛⠛⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢻⣦⣰⣿⣴⣯⣴⢿⣿⣾⠟⠁⠀⠀⠀⠀⢀⣨⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⡷⢞⣋⡙⠛⠛⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠿⠿⠿⠿⠟⢛⣻⡿⠟⠋⠉⢀⡼⣯⢤⣀⠀⠙⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣴⣿⠃⢿⣄⠈⠛⠶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣴⡶⣿⡿⠃⠀⠈⣿⣧⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣴⡿⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣯⡁
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣽⠂
⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄
⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣤⣄
⠀⠀⠀⠾⠿⠛⠛⠛⠛⠋⠉⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⣄⠀⡄⡀⢀⡀⢀⡀⠀⡀⠀⣀⠀⢠⠀⢠⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⣿⣷⣿⣷⣿⣿⣾⣿⣾⣿⣾⣿⣷⣿⣷⣿⣷⣾⣿⣾⣿⣾⣿⣶⣿⣷⣿⣷⣿⣿⣾⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣰⢿⣰⡎⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣾⣿⣯⡝⠅⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢻⣿⣿⣿⣿⣿⣳⣴⣷⣿⣻⣟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⡿⣟⣻⣫⣾⡗⣿⣄⠀⠀⠈⠙⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣧⣾⣿⣿⣿⠆⠀⠀⠀⠀⢹⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣙⠻⢿⣿⡟⠛⠿⣿⣯⣴⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠚⠋⡩⡞⠁⢦⡀⠀⠀⢸⠋⠙⡿⠉⢹⡟⠣⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡜⠀⠀⢀⠀⠉⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃