Una Emojis & Symbols

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⡞⠻⣟⢛⡻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⡛⣻⠟⢳⡀
⠀⠀⠀⠀⣼⠁⠀⠈⢷⣽⣿⣿⣏⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣹⣿⣿⣿⡾⠁⠀⠀⣧
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠹⣧⢹⣿⣿⡷⣝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣻⢾⣿⣿⡏⣵⠏⠀⠀⠀⠀⢸⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡘⢷⡻⣿⣿⣶⣟⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡷⣿⣾⣿⣿⢟⡾⢃⠎⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠐⡈⢷⣸⣿⣿⢿⣿⣷⣯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣟⡿⣿⣿⣇⡾⠁⠂⠄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢣⠘⣿⢿⣟⣾⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⣷⣻⡿⣾⠃⡌⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠄⢃⢹⣆⣿⣿⣿⣿⣿⡧⡽⠚⢻⢖⣐⢖⣨⣆⣰⣁⡲⣊⠲⡟⠓⢭⢾⣿⣿⣿⣯⣿⣴⡏⡘⢠⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⡘⡈⡌⣿⢷⣿⠟⢹⠃⣶⣇⣾⡿⣼⣟⣾⠟⣰⣌⠻⣷⣻⣷⢿⣷⣸⣶⠘⡏⠻⣿⣾⣿⢡⢁⠃⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠰⠱⢹⣿⢊⣽⢺⣿⢸⣿⣻⣿⣱⡿⠿⢗⣴⣿⣿⢷⡙⠷⣿⣞⣿⣿⣿⡇⣿⡇⣯⡑⣿⡜⡆⠆⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢡⣣⢏⣵⢸⣿⢸⡟⢾⣓⣛⣭⠿⠶⠀⣿⣿⠟⠻⣿⣷⠀⠖⠯⣭⣛⣚⡷⢻⡇⣿⡇⣮⡹⡜⡜⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢺⡏⣼⣿⡟⣫⠴⣺⣿⣿⠛⢶⣫⣭⣗⢾⡇⣸⣇⢸⡷⣺⣭⣝⣶⢛⣿⣿⣟⠦⣽⢻⣿⣵⢹⡇⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⢱⣽⢏⡿⣱⣿⣿⣿⣿⡿⠿⠟⠿⣿⣷⣷⢸⡇⣾⣾⣿⠿⠛⠿⢿⣿⡿⣿⣿⣬⢷⡹⣯⡎⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢉⣻⣿⣾⣿⠧⠖⠚⠉⠉⠈⠀⠀⠀⠀⠙⢿⡞⢳⡿⠋⠀⠀⠀⠀⠀⠉⠋⠓⠶⠼⢿⣷⣿⣟⡙⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣠⣟⠡⠠⠒⠐⠀⠀⣀⣠⣤⣤⣀⣀⣀⣀⣬⣽⣿⣿⣯⣥⣀⣀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠐⠀⢈⣻⣄⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣀⣤⣾⣿⣿⣿⣿⡟⣫⢿⣿⣫⣾⣿⢿⡿⣿⣷⣝⢿⡻⣽⢻⣿⣿⣿⣿⣶⣤⣀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⣿⡿⣫⢟⣽⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣯⡳⣝⢿⣿⣿⣿⣿⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡿⣱⢫⣾⠟⠋⠙⠛⠋⢹⣯⣽⡏⠛⠛⠋⠙⠻⣷⡹⣎⢿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣾⣿⣯⡿⣿⢱⢏⡞⠁⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠈⢳⡹⡄⣿⣿⣽⣿⣷⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣷⣿⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢾⣿⣿⣾⣿⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣮⠻⣿⣯⢹⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣽⣿⠟⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⣿⣷⣌⢡⠾⣀⡀⠀⠀⠀⢀⣀⠴⡋⢀⡾⢷⡀⢙⠦⣀⡀⠀⠀⠀⢀⣀⠷⡌⣡⣾⣿⡿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣉⣽⡿⣤⣃⠹⠉⠽⠉⠍⢀⣠⢴⡿⣣⣘⢿⡦⣄⡀⠉⠉⠭⠉⠏⣈⣤⠿⣯⣉⣬⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠉⠉⠛⠒⠛⠛⢉⣵⠛⣵⡟⢻⣦⠛⣦⡉⠛⠛⠒⠛⠋⠉⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠶⣺⣭⣞⣣⣦⢡⡌⣴⣜⣷⣭⣗⠶⠤⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣾⣯⣵⣻⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢀⣀⣀⣤⡤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⢤
⣶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠘⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⢿
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠂⠀⠉⠀⠀⠀⣠⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⡾⠿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠐⠂⠀⠀⠁⠀⠀⠀⢀⡀⠠⠄⠒⠚⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⢠⣤⠏⠀⠀⠀⠀⠀⠀⡠⠀⢠⡞
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⢀⠄⠀⠄⠐⠂⠀⠉⠀⠀⠀⢀⢠⠠⠀⠀⠉⠁⠀⠀⠀⢳⠀⣀⡿⡿⠀⠀⠀⠀⠀⢀⣼⠇⠔⣹⠃
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠀⠁⠀⠀⠀⢀⣀⠠⠔⠒⠀⠀⠀⠘⣶⣿⠁⠀⠀⠀⠀⠀⣠⠿⠃⣠⠞⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⡀⠀⠠⠄⠐⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⡐⠀⠈⠁⠀⢙⡟
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠒⠂⠉⠁⠀⠀⠀⠀⢀⡀⠤⠐⠒⠈⠁⠀⢀⣀⠀⣷⡀⡇⠿⣿⠀⡰⠁⠀⠀⢀⣠⢿⠇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠⠤⠐⠒⠈⠁⠀⠀⠀⠀⢀⡀⠤⠔⠒⠀⠈⠀⠀⡇⠹⣇⠀⡇⢠⠁⠀⢀⠔⡽⢣⠏
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠐⠒⠀⠉⠁⠀⠀⢀⡀⠀⠤⠀⠄⠀⠒⠈⠉⠀⠀⢀⣀⠠⠤⠖⠚⠉⡇⠀⠀⠀⢡⠃⠀⠀⠁⢀⣰⣯⣴
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠉⠀⠀⠀⣀⣀⣴⢀⡇⢀⠀⠀⠎⠀⠀⠀⠀⠉⢁⡼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠀⠈⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠂⠀⠀⠀⠀⡿⣿⠇⢸⠀⠈⠀⡴⢁⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠤⠀⠒⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠂⠉⡇⠉⢸⡞⢀⠀⣞⣴⠋⠀⣰⢋⡴
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠄⠀⠐⠒⠈⠉⠀⠀⠀⠀⣀⡀⠤⠄⢹⡀⠀⠃⠄⠼⠋⠁⠀⠀⢟⡿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠈⠳⡄⠸⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣠⣿⢃⡖⠒⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠉⠈⢸⣧⡜⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠇⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠤⠶⠖⠒⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⠤⠴⠖⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠶⠶⠶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣉⢸⠒⠇⣗⠸⣁⢸⢯⠀⣇⢸⠌⣣⠨⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣇⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡞⠋⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠠⠤⠤⠄⠀⠠⠤⠤⠄⣾⣿⣿⣿⡛⠛⢻⣿⣿⡿⠃⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⢻⡿⠁⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠛⠋⠉

⣿⠿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠿⠛⠛⠛⠻⢷⣦⣤⣀
⠀⢰⣿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄
⠀⢸⣿⠀⠈⠻⢿⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀
⠀⢸⣿⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣿⠃⠀⠀⠀⠀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠋⠁
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢹⣿⣧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⣦⣄⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣶⣶⣶⡿⠿⠿⠛⢻⣿⠇⠀⣴⣷⣶⣶⣦⣤⣤⣤⣤⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣛⠛⠛⠛⠿⢿⣿⣶⣿⡿⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠁⣶⣆⣀⠀⠀⠀⣻⡇⠀⠀⢸⣿⣅
⠀⠀⠀⠀⣠⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣆⣼⡟⠀⠀⢰⡿⠻⢿⣷⣄
⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠙⢿⣆⡀⣰⡿⠁⠀⠀⠙⢿⣷⣄
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠛⠛⢿⣦⠀⠀⠹⣿⣏⡀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⣰⣿⠃⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⣿⡇⠀⢰⣶⡄⠈⣿⡇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠈⢻⣿⡄
⣿⡿⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠙⣿⡆⠀⠀⢿⣇⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠹⣿⣄
⣿⡇⠀⠀⠀⠀⣾⡟⠀⠀⣾⣿⠀⠀⣿⣷⠀⠀⠈⠻⢿⣶⣶⣿⠟⠃⢠⣆⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠸⣿⣆
⣿⣧⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢷⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠘⢿⣄
⢹⣿⠀⠀⠀⠀⠀⠙⠻⣷⣶⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠋⠀⠀⠈⠁⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠘⢿⣄
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣸⡏⠀⠉⢻⣿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣇⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⢻⣿⣿⡁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⢹⣧⡀⠀⠙⠻⢿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣠⣿⠿⢿⣦⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⡏⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⡀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠁
⣶⣶⣤⣴⣶⣦⣤⣶⣶⣶⣶⣶⣦⣶⣶⣶⣤⣾⣿⣿⣿⣷⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣤⣤⣤⣤⣴⣶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣦⣤⣤⣶⣶⣶⣦⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠋⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣶⣄⡀⠀⠀⠀⠀⢀⣠⣾⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠉⠉⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠉⠙⠛⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⢀⣿⣿⠛⣷⣀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣠⡞⠙⣿⣷⡀
⠀⣼⣿⡇⠀⠀⠙⠻⠷⠟⠛⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⠟⠉⢉⣠⣴⣮⣽⣿⣦⡀⠀⠀⣀⣴⣿⣭⣷⣤⣄⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⢠⣿⣟
⠀⢰⣿⡟⠁⠀⠀⢽⡒⣶⣿⡏⠀⠐⠋⠿⠿⠿⠧⠀⢸⣿⠩⠟⣿⠁⢨⣿⡿⠿⠏⠑⠄⠀⣿⣿⡶⣒⡶⠀⠀⠈⢻⣿⡆
⠀⠸⣿⣧⣤⣄⣀⣺⣽⣿⡇⠹⣄⠀⠀⠀⠤⠦⠀⢀⣼⠃⠀⠀⠹⣆⠀⠀⠴⠴⠄⠀⠀⡰⠃⣿⣿⣉⣀⣠⣤⣤⣼⣿⠇
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠳⠄⡀⠀⣠⠴⠞⠁⠀⠀⠀⠀⠙⠳⢤⣄⠀⣠⡴⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣇⣀⠀⠀⠀⠀⣀⡼⢦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⢿⣧⠀⠀⢠⣤⠶⠋⠀⠀⠉⠛⠶⠶⠛⠉⠀⠀⠙⠶⣤⣄⠀⠀⣾⡿⠻⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣾⣿⡀⠀⠀⠀⠀⡆⠀⠤⢤⣤⣶⣤⣤⡤⠤⠀⢰⠀⠀⠀⠀⢰⣿⣷⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠛⢿⣷⣤⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣾⡿⠟⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠻⢿⣷⣦⣤⣀⣀⣀⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣴⣿⣿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣦⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠟⢿⠋⠈⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠄⠿⣄⠀⢀⣴⠻⡄⠀⠀⡀⠀⠀⠀⠀⠀⠼⣲⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠀⠀⠴⠦⠀⠀⠀⢀⣠⠄⠚⠑⠦⠞⠸⣇
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⡤⠤⠶⠶⠛⠫⠀⡄⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⠗⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠁⢘⣧
⠀⠀⠀⠀⠀⠎⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢸⣠⣿⠿⠖⣄⣠⣤⣤⣄⣀⣐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠉⠉⠙⢛⠿⠅⠛⠛⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣧⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣿⡄⠀⣀⣄⢴⣾⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠀⢀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⠛⠛⠋⠀⠈⣸⣇
⠀⠀⠀⠀⠀⠀⠀⣆⠀⣸⠀⠀⠀⠀⡠⢊⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⡆⠀⠀⠈⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠸⢈⣽⠁⠀⠀⡠⢫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⠀⠀⠊⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠋⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡀⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⣻⣧
⠀⠀⠀⠀⠀⠀⠀⣴⣛⠀⣴⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⠇
⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠹⣿⣿⡄
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⢀⢻⣿⣇
⠀⢀⣠⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠈⣠⣿⠽⠂
⣶⠻⠻⢿⠇⠀⠀⠀⠀⠀⡘⠈⠟⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣿⣏⣠⣆⣱⡟⣁⠀⠀⠠
⠈⠳⠀⣿⠀⠀⠰⣤⣤⣤⣴⣿⠿⠿⠾⢿⣿⣤⣶⣶⠶⠶⠶⠦⠤⠤⠀⠠⣶⣒⣁⣤⣜⣻⣷⠺⠿⠿⠛⠶⠦⠬⠍
⠀⠀⠳⣽⣾⡍⠻⠀⠀⠁⠉⠙⠉⠉⠀⠀⠀⠠⠤⠀⠈⠉⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⣼⣆⠀⠀⠀⢀⣷⡀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⢰⣶⠀⠀⠀⢠⣶⣶
⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢸⣿⡿⠀⠀⠀⠐⣿⣿⠀⠀⠀⢸⣿⣷⠀⠀⠀⢊⣿⡿⠆⠀⠀⠀⢻⣟⡇⠀⠀⠘⣿⡟
⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣸⣿⡆⠀⠀⢰⣿⣧
⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⠀⢸⠁⢧⠀⠀⠀⢰⠇⢻⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⡏⠹⡀⠀⠀⠀⡏⢸⠀⠀⠀⢸⠃⢧
⠀⠀⠀⠀⡎⢀⠞⠀⠀⠀⠀⡘⠀⠰⠀⠀⠀⢸⠀⠸⠀⠀⠐⠁⠐⡂⠀⠀⠀⠀⢰⠀⡱⠀⠀⠘⠀⠘⠀⠀⠀⠸⠀⠸⡀
⠀⠀⠀⠒⠋⠉⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠀⠑⠷⠀⠀⠀⠀⠉⠛⠦


⣿⣛⣻⣻⣛⣻⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃
⠀⠀⠀⡀⠀⠀⢄⠈⠃⠀⠀⣾⣶⠄⠀⠀⣾⡁⠂⠀⠀⠐
⠀⠈⠀⠒⠈⠀⠀⢀⠀⠀⠀⠈⠉⠂⠀⢰⠟⠁⣀⣀⡈⠈
⠀⠀⠀⠀⠀⢀⣿⠆⠠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠇⠀⠀⣠⣷⡤⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠁⠀⣀⣤⠀⢠⣆⠀⠀⠀⠀⢐⣾⣷⡆⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠨⠀⠀⠀⠀⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢧⠀⠀⡈⠁⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠁⠀⠚⠁⠀⠀⠀⠀⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠈⢀⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⣤⠄⢀⠼⠋⡐⠀⠀⠀⡀⠀⠀⠠⢀⡀⠀⠛⠀⠀⠈⠣⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠏⠀⠀⠀⠀⠀⣼⡶⠇⠀⠰⠖⠀⢀⠓⢤⣭⣤⣿⣄⣀⢀⠀⡀⡀⠉⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠘⠁⠀⠠⡤⣤⣤⠶⣿⢿⡙⠹⣓⣤⡂⢠⣤⣵⣏⡔⠫⣿⣭⣯⣻⣽⣇⡀⣠⣴⡌⣂
⠀⠀⠀⠀⠀⠀⡈⣅⡶⢖⣦⡴⢻⣿⣯⣠⠙⡶⠤⣛⠿⠿⣿⣿⣿⣏⡇⢀⣨⣿⡳⣟⣳⢷⡀⠉⠙⣦⣥⠏⠈⡄
⠀⠀⠀⠀⠀⢠⡀⠈⠀⢺⣀⠀⣸⠟⢷⣘⢹⣧⣂⡘⣷⡾⢛⣿⡟⣾⣩⢯⣶⣼⣥⡀⠘⠆⢽⣧⠘⡝⠸⠀⠀⢙⢀⡀⠄
⠀⠀⠀⠀⢠⣜⡆⠀⠈⡎⠧⣀⣿⣶⣬⣄⣸⢱⠙⣯⠟⠆⢻⣼⣿⣆⠙⢦⣿⠁⢁⣳⣬⣠⣾⣷⣽⡧⢾⢲⣄⢼⠛⡇
⠀⠀⠀⠀⠀⡏⠻⢦⡾⡹⣵⣿⣋⢣⠀⣈⢻⡿⢰⣼⣳⣶⢉⠣⢿⠑⠻⣾⠿⣿⡈⢿⠇⡀⢈⡙⢛⣿⡧⠩⡝⣧⡄
⠀⠀⠀⠀⠀⠀⠐⣾⠑⡆⢺⣿⣿⡌⢧⡜⠘⣧⣹⡃⠙⢿⡍⣶⢿⣄⣦⣿⡔⠢⢿⣞⡴⠈⣏⢁⡽⢿⣿⣤⠂⠈⣷⠁⢀
⠀⠀⠀⠀⠀⣀⠘⣇⠀⠙⢿⣿⡇⢸⡀⣿⠄⡿⣿⡛⠤⠀⣿⣿⣿⣿⣷⡿⢄⣁⣾⣸⣷⣈⣟⡜⢧⡾⣿⡏⠐⢤⡟⠀⠎
⠀⠀⠀⠀⠀⠘⠂⠘⢶⣠⢈⢿⡟⢯⡸⠿⣦⡧⢾⠙⣶⣾⣥⣿⣿⣹⣿⣻⣿⣻⡟⠽⣯⢷⣿⢓⢼⢃⡾⣄⢘⣿⣃⠴
⠀⠀⠀⠀⠀⠀⠀⠂⠨⣿⣄⣺⣷⣴⣟⣧⣿⣷⣿⡿⠶⡻⣿⣼⣿⣿⣿⣏⣿⣿⠦⣹⣿⣿⣿⣿⣿⡿⠻⢽⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡀⠉⣛⣿⣯⣿⣿⣿⣦⣍⣙⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠟⠟⢚⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣮⣽⣮⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣁⣠⠶⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⠞⠷⠿⠿⣿⣿⣿⡿⢿⠛⠋⢉⠁⠉⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠹⡛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠛⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠋⠙⠁⠀⢀⡤⠁⠈⠙⠿⠛⡲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣁⡤⠖⠂⠀⠀⠙⠒⠀⠀⠀⠰⠬⠭⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣻⣿⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣠⣹⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣼⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡧⠋⠀⠀⠚⠀⠀⠀⠀⠀⠘⠀⠀⣴⢠⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢋⣾⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣽⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠿⠟⣻⠟⢫⣽⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⡏⢽⡿⡏⠉⢀⡖⢼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⠑⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⡀⢰⣿⣤⣿⢰⠁⠀⠘⠃⣿⣿⣸⣿⣿⣿⣿⣿⠴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣹⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣼⣿⣿⣸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⣀⡀⠀⠀⠀⠀⣼⡿⢟⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠐⣹⣿⣿⣿⣷⡟⣿⣿⣿⣶⣾⣿⡷⠿⠟⣋⣁⣀⠀⠀⢠⣭⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠂⢉⢿⣿⣿⣿⣷⣿⡿⣿⣿⣿⠛⠔⠖⢀⣘⠡⠏⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡂⠐⠒⡀⠙⢧⡤⠨⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠐⠐⢺⣿⣿⣿⣿⡽⣿⣿⣇⣻⣿⣯⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⠟⠛⡛⠛⠿⠿⠿⠿⠶⠮⠉⠉⡁⠡⢬⣅⣤⣾⣿⣿⡿⣯⢿⢽⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣻⣾⣿⣿⣿⣿⠦⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠸⠀⢠⠄
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠄⠀⢠⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡀⠀⢠⠁⠀⠀⠀⢉⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠑⠂⠁⠀⣀⠐⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠐⠀⢄⠀⠀⠀⠀⠈⡀⠀⢠⠀⠀⠀⡀⠘⡃⠀⠀⠀⠰⠄⠄⢀⡤⠪⠁
⠀⠀⠀⠀⠀⠈⠀⠀⡈⠁⠉⠀⢠⡀⠈⠁⠀⠀⠀⠀⠁⠀⠈⢷⢄⠀⠈⠀⡀⠀⠀⠀⠀⠅⡠⢊⠂⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠸⠀⠀⠁⠀⠀⠀⠐⡂⢄⠀⠀⠀⠈⠳⢐⠄⠀⠇⠀⠀⠀⠀⢸⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠌⠖⠀⠐⠄⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠄⠓⠢⡖⢄⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠈⠙⠲⠄⡄⠀⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢅⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠂⠂⠀⠈⠈⠀⠀⠀⠀⠈⠀⣀⠤⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠢⠈⠸⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠘⠐⠙⠀⠀⢲⢊⣀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠇⡆⠀⠀⠀⠀⠠⡀⠀⡀⠙⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡌⡌⠀⠀⠉⠙⠁⠈⠀⡀⠀⠀⠠⠂⠒⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠣⠄⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠀⠠⢄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⠀⠰⠀⠠
⠀⠀⠀⠀⠀⢀⠊⠀⢀⠄⠀⠠⡀⠀⠄⠀⠂⠀⠊⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⢀⡀⡠⠢⠈⠢⠀⠀⠀⡁⠀⠀⠄⠠⠀⠂⢁⠀⡀⠀⠉⠀⠀⠀⠀⠠⡀⠀⢃⠀⠀⠀⡄⠂⠀⠀⠀⠁⠐⢀
⠀⠀⠀⠀⢰⠀⠃⠀⠋⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⠀⠰⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⢀⠀⠀⠉⠐⠀⠔
⠀⠀⢀⠀⠀⢧⡀⠀⣠⣂⡀⠃⠀⠀⠖⠈⠀⠀⠀⠀⠁⠀⠀⢀⠤⠂⠠⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠒⠐⠀⢄
⠀⠀⠀⠠⠀⠐⠬⢉⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⡆⠠⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⢂⠀⠈⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢄⠀⠈⠂⠀⠀⡠⠔⠒⠒⠒⢄⠂⠀⠀⠁⠀⠀⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⣀⣈⠀⢀⣀⡀⠀⠀⠁⠀⢡⠔⠒⠀⠤⠤⠤⠄⠀⣑⣌⠂⠠⠀⠀⠀⠊⡀
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠂⠐⡁⢄⠨⠁⠩⠀⠈⢙⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠠⡀⢱⠘⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠡⣀⣆⡂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠤⠔⠀⠀⡠⡀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠤⢀⣒⣀⣀⠖
⠀⠀⠀⠀⡰⠊⠄⡁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠊⠀⠀⢀⠘⠂⠀⠁⠀⠀⠈⠊⢔⡤⠠⡀⠀⠀⠀⠈⠒⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⢿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠉⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠠⠀⣀⣤⣶⣾⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⠊⠀⢀⠄⠑⢀⣴⣿⡿⢟⣯⣿⣿⡿⣿⣿⣟⡁⠘⠻⠿⣷⣄⡙⠻⢿⣄⠈⠿⣿⣿⠛⢶⣦⣄⡀
⠀⠀⠀⠀⠐⠀⠀⡔⠁⢀⣴⣿⢟⣭⣾⣿⣿⣿⣇⣀⠉⣙⣛⣛⣓⣒⠶⠦⢬⣉⡓⠦⣌⡛⠦⣈⠻⣦⡈⢿⣿⠛⢷
⠀⠀⠀⠀⠀⢀⠊⠀⣠⡿⢟⣵⣿⣿⡿⠁⠛⠛⢛⣋⣩⡭⠭⠭⠭⠭⠭⠍⠓⠒⠭⣝⡲⢭⡳⢬⡓⢌⠓⣄⠙⣧⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⣾⣿⡿⣿⣷⡶⠖⢛⡩⢅⣒⠦⢁⡒⠀⠐⣃⡩⠔⠒⠬⣀⠈⢑⠮⣓⢝⡦⣕⢌⠳⣌⢳
⠀⠀⠀⠀⠀⠀⠀⠃⢰⢿⣿⣿⠁⠉⣁⡴⢚⡵⣺⠕⠒⢉⣀⣤⠴⠿⢭⣽⣫⢖⣂⠀⠈⠒⠄⠪⡳⣝⢮⢧⡱⣌⢦
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⡿⣿⣷⠟⢉⡾⡫⡪⠒⢅⡤⢓⠋⢀⠀⠀⠀⠀⡀⠉⡛⠕⠢⠀⠀⠀⠈⢪⠣⡱⡝⣎⢦
⠀⠀⠀⠀⢰⠀⠀⣸⠀⠇⡇⠉⢁⣴⢋⢞⣜⡕⡕⡩⢪⢔⡩⠔⣚⡯⠭⠽⣞⡻⢾⣷⣦⣀⠀⠀⠀⠀⠱⡐⠜⣞⢎
⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⣿⣶⡟⢁⡎⡼⡞⡞⡜⣱⢡⡏⢰⣿⠁⣰⣶⠛⠓⠾⣷⣮⡻⣿⣦⡀⠀⠀⠀⠐⡄⠘⡎
⠀⠀⠀⠀⢸⠀⠀⢧⠀⠰⡈⠉⢀⡾⢰⢿⣿⣷⡇⡇⠸⣧⡈⠻⣆⠘⣷⠀⣼⡿⠶⣝⣿⣮⢻⣷⠀⠀⠀⠀⠰⠀⠸
⠀⠰⠀⠀⠸⡀⠀⢸⡄⣧⠻⣶⣾⠇⣼⠈⡟⣇⢧⡻⣦⣈⣙⠳⣌⢣⡸⡆⣿⠃⢀⣤⡹⣿⠩⣏⠀⠀⠀⠀⠀⠇
⡇⠀⡆⠀⠀⢃⠀⢈⣷⣿⣷⣌⡁⠀⣿⡆⢷⡘⢦⡙⠦⣤⡉⠻⡌⡇⣧⣷⣿⠀⣿⠟⠻⡜⠆⢹⠀⠀⠀⠀⠀⠸
⠸⡀⠰⡀⠀⠀⢂⠩⣿⣎⢻⣿⣟⠾⠿⠃⢸⣷⠀⢻⣦⠈⣿⢀⡇⡏⡿⡟⡟⣸⠃⣠⣤⠙⠀⢸⡇⠀⠀⠀⡀
⢧⢣⠠⠱⡀⠀⠀⠂⠘⠻⣷⣭⡻⢿⣲⠶⠾⠛⣀⣼⠟⣠⢏⠜⡰⡱⢣⢳⢡⠇⣼⠟⠻⡇⡀⢸⡇⠀⠀⠁⠅
⣎⢧⢣⡱⡑⡄⠀⠀⠀⠀⠉⠛⠿⡻⢶⡯⠭⠭⠭⢒⡫⢕⡫⣊⠔⠑⡁⡡⢣⠞⢁⣠⡄⣷⡅⣸⠀⠀⠸⠀⠆
⣎⢧⡳⡵⣜⢎⠢⡀⠐⢝⡢⣈⠐⠦⢄⣀⡀⠀⠀⠀⣌⣔⠪⢑⠅⡪⢞⠕⣁⡴⠿⢿⣷⣿⢣⠇⠀⠀⠆⠘
⡌⢧⡳⣜⢮⡳⣕⢬⡢⢐⠬⣒⠭⣒⡦⢬⣍⣉⣉⣛⢙⡢⢅⣒⡭⣚⡵⠚⣉⣠⡄⣼⣿⣿⡟⢀⠀⡜⠀⠂
⠘⣦⠙⢌⠳⣝⠮⣕⢮⣲⢤⣂⠉⠒⠒⠭⠔⠂⣀⠐⠒⠩⣙⣓⣩⡵⠶⠛⠻⣿⣿⣿⣿⠏⢠⣎⡌
⣧⠈⢷⣌⠳⣌⠓⢬⡑⠮⣕⡺⢭⣒⡲⠬⠭⣥⣤⣉⣩⣭⣭⣤⣴⣶⣶⣄⣼⣿⣿⢟⣱⣾⠯⠊⠀⠀⠀⠠
⠻⢷⣾⣿⣦⠈⢳⣦⡉⠳⣤⣉⠓⠦⣭⣙⡓⠒⠲⠶⣦⣤⣤⡀⢀⣿⣿⣿⡿⣫⣵⣿⢿⠕⠕⠅⠀⠀⡔⠁
⠀⠀⠙⠉⡛⠷⢾⣿⣿⣆⣈⣿⣿⣦⡀⢙⣿⣿⣦⣀⣼⣿⣿⣿⣿⣿⣯⣷⣿⣿⠿⠁⢕⠕⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠿⠿⠛⠉⠄⠪⠊⠁⠀⠠⠞⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢶⣿⣿⡈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠳⠀⠉⠛⣿⡄⠀⢤⣄⣤⡄⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣿⣿⣷⣾⣿⠳⢄⡀⠀⠘⠛⠀⠈⠙⣿⣌⠾⠛⠿⠦⣄⠀⠀⢀⣴⣿⣧⣀⠀⠀⠀⠀⣰⣿⣷⡀
⠀⠀⠀⢴⣶⢾⠻⢿⣿⣿⠿⢻⣿⣿⡟⠂⠀⠙⠀⠀⠀⠀⠀⡀⠈⠛⠳⠀⢀⠀⠈⠻⠛⠿⠛⠋⠈⠙⣻⣶⣤⡞⠁⠀⠈⠛⣠⣄⠀⠀⡀⢀
⠀⠀⠀⠀⠁⠘⣁⣀⡙⠃⢴⣿⣿⡿⠟⠀⠀⠀⠀⢠⣶⣶⣿⣿⡔⢦⣄⠀⠀⠀⠱⣶⣤⣤⣀⣀⡴⠟⠛⢟⡇⠉⠀⡀⠀⠀⠀⠈⠛⠘⠉⠉⠑⠦
⠀⠀⠀⠀⠀⠘⠿⠛⠻⣄⠈⠛⠿⣃⣄⠀⠀⣤⣾⣿⣿⣿⣿⣿⣯⠀⣉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⠿⣿⣿⣿⠿⡿⢋⠜⠛⣿⣿⣻⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⡜⠀⠐⢋⣾⡿⠛⢻⠀⠀⠀⠀⠀⠀⢶⣿⣿⣏⠁⠀⠀⠀⠀⣼⣿⣿⡇⠀⣀⠐⡋
⠀⠀⠀⣶⣶⣦⡀⣀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰⠀⣀⢠⠟⠀⢠⣤⣠⣰⣄⠀⠀⠀⠀⠀⠈⠻⣽⣦⣦⡀⠀⢠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢹⣿⠿⠿⢾⣷⣶⣆⣠⣄⠀⠀⠀⣼⣧⠀⠀⠀⠀⠁⠀⠴⢪⣿⣿⣿⣿⡿⠷⡀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠠⣶⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠠⡀⢸⣿⣿⣿⣿⣿⣶⣾⣆⣿⣿⡇⣼⣷⡀⠀⠀⠀⢀⡉⠛⠿⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⠆⢀
⠀⠀⠀⢠⣄⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⢠⣿⣇⣴⡀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣶⠄
⠀⠀⠀⠀⠉⠉⠛⠋⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣷⣴⡄⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠙⠛⠈⠋⠛⠛⠛⠉⠙⠿⠿⠿⢿⣤⣾⣿⡂⠀⠀⢀⣴⣄⣼⣿⠿⠛⠿⠿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⢀⣀⣤⠶⠖⣛⣫⣭⠥⠶⣒⣒⣶⣯⡭⢓⢦⣀
⣋⣥⡴⠞⣛⣩⡥⠶⢚⣩⡭⠶⢚⣫⡭⠷⣒⣫⢷⡠⣄⢤⡀⢀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⣛⡛⠛⠛⠛⠿⠶⠶⣦⣤⣤⣤⣤⠴⠶⠛
⣩⡤⠶⢛⣩⡥⠶⢛⣩⡥⠶⣛⣩⡴⠖⣋⡭⠶⣚⣷⡈⠷⠙⣊⣃⡤⠴⣚⣫⡭⠶⠚⣛⣛⣉⣉⡛⠛⠛⠻⠷⣶⣦⣤⣤⣤⣤⣴⣶⡾⠿
⠵⢖⣛⣭⠵⣖⣛⡭⠴⣒⣫⡭⠶⣚⣫⠵⣒⣯⠵⣚⣩⣭⡭⠥⠶⣚⣋⣭⠶⠖⣛⣋⣉⣉⣉⣙⠛⠛⠿⣶⣦⣤⣀⣉⠉⠉⣉⣀⣀⣠⣤
⣍⡩⠷⠮⠽⢓⣒⣚⣭⡭⠶⣚⣫⠭⢖⣫⠵⣒⣋⣉⠉⠛⢿⣟⣭⣭⡥⠶⢚⣛⣉⣭⣭⣍⣉⡛⠛⠷⣦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛
⣉⣉⣉⣉⣉⣉⣭⣥⠴⠖⣛⡭⢖⣪⠽⢒⣋⣉⠙⠻⣿⡆⢸⡟⢰⢒⣒⣛⣩⡭⠤⠶⠦⢤⣭⣙⠻⢶⣄⠙⠻⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠛⠛⠛⠛⣋⣉⣥⠴⢞⣫⠵⣚⠽⣒⣛⣉⠙⠻⣿⡄⢸⡇⣸⠃⡏⣮⡲⠿⠶⣒⣛⣛⣛⡒⠦⣍⠳⣦⡙⢿⣦⣀⠉⠙⠛⠛⠻⠿⠿⠿⠿
⠿⠿⠟⠛⣋⣩⠴⣚⡭⣶⢟⣚⣋⣉⡙⠻⣷⠀⣿⠁⣿⠀⣿⠀⢷⣬⣭⡭⠭⠶⠶⠶⣬⣉⠳⢮⡙⢦⡹⣦⡈⠻⢿⣶⣦⣤⣤⣀⣀⣀⣀
⣤⡶⠾⣛⡭⢖⡯⣷⣟⣯⠭⠥⣬⡙⣷⢀⡟⢰⣿⠀⣿⡀⠙⠷⠶⢶⣒⣛⣛⣛⡛⠶⣦⣉⠳⣦⡙⣎⢳⡌⠻⣦⣀⠉⠙⠛⠿⠿⠿⣿⣿
⣤⠶⣻⢽⣺⣿⠿⠛⠉⠉⠀⠉⢸⡇⡏⢸⡇⠸⣿⣄⠙⠛⣛⣛⡯⠭⠭⠷⠭⢭⣍⡓⢦⣝⠳⣌⢳⡌⢧⡹⣦⡈⠻⢿⣶⣤⣄⣀⡀
⣖⣭⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⢸⠘⣧⠘⢿⣤⣈⣙⣛⡭⢽⣒⡾⢭⣭⣭⠭⢟⣲⢭⡳⢍⠳⣝⢦⡹⣌⢳⡌⠻⣦⣄⠉⠛⠻⠿⣿⣿⣷
⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⢷⣤⣬⡭⢽⣒⠯⢗⣺⡭⠽⠷⠶⠯⠭⣗⣛⡯⠷⠽⠮⠶⢕⣌⠣⡙⢦⣌⠛⠿⣶⣤⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣛⣒⣒⣒⣫⠭⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠈⠳⢍⡳⢦⣌⡉⠛⠿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⢝⠳⢦⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⣠⣼⣧⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⢀⣴⣷⡄
⠀⠀⠈⣿⣿⠙⠀⠀⠀⠰⣻⣿⠇⠀⠀⠀⠀⠘⢏⣿⣯⠟⠀⠀⠀⠐⣯⣿⣿⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⢫⣿⣯⠇⠀⠀⠀⠀⢾⣼⣿⠟
⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⢨⣿⣿⡆⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⡿⠻⡇⠀⠀⠀⠈⣻⠛⣇⠀⠀⠀⠀⠀⣼⠛⡟⠁⠀⠀⠀⠀⢹⠋⢿⡀⠀⠀⠀⢨⡟⢻⡀⠀⠀⠀⠀⢸⡟⢻⡀⠀⠀⠀⠀⠈⣿⠙⣧
⠀⠀⠀⠇⠀⢳⠀⠀⠀⠀⢹⠀⢹⡄⠀⠀⠀⣸⠃⢀⡇⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⠀⠀⢸⠁⠈⡇⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⢹⠀⠘⡆
⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠉

⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠰⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀⣾⠃⠐⠄⠀⢿⡇⠀⠘⡀⢠⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⢀⠴⣿⡇⠀⠀⢤⠀⣿⠀⠀⣼⡋⠻⠈⠠⡴⢾⡿⠀⠐⠀⠀⣀⡄
⠀⠀⠀⠠⠀⢊⣡⡴⠻⠦⠴⡿⠀⣩⠞⠀⠀⠉⠂⡏⢈⣥⡾⠡⡄⠀⡄⠀⠙⢧⠀⠀⡀⠀⠈⠳
⠀⠀⠀⠆⠚⠋⠛⠷⢀⠀⠀⠀⠀⠋⣴⣤⠀⢀⣴⣡⢿⣿⠁⠀⠈⢠⣄⠀⠀⠈⣇⠐⣇⠀⠀⠀⣄
⠀⠀⠀⠀⣦⠰⠤⠄⠨⢿⣄⠀⣀⡀⢈⣿⠀⠀⠉⠐⣿⠋⠦⠀⠀⠀⠈⠳⢄⠀⠈⠂⠙⢦⣼⣧⡿⠚
⠀⠀⠀⠀⠁⠀⠀⠀⣄⠀⣈⡴⠟⠃⠉⡿⠠⣄⡀⠀⠻⢦⠀⠀⠦⠀⠀⠀⠀⠀⢀⣄⠶⢘⡧⠏
⠀⠀⠀⠀⠀⣶⡤⠄⠛⠊⠁⣠⢀⡄⢀⠁⠒⠄⠀⠉⠈⠛⠆⡀⠀⠀⠀⢀⡠⢴⣋⡡⠖⠉
⠀⠀⠀⠀⠈⠁⠀⣤⠀⢀⣤⣿⣾⣿⣾⣆⢀⠀⠘⠓⠆⠈⠉⠁⠒⠩⢖⣡⠖⠋⣵⡄⠀⠀⣤⣀⣶
⠀⠀⠀⠀⠀⠀⣸⣿⣶⡼⠿⠿⠿⠿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠉⢴⠂⠉⠀⠀⣸⣿⡿⠔⠛⠉⠁
⠀⠀⠀⠀⠀⠤⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠰⠂⠀⠀⠀⠀⠀⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⢰⠀⠀⠀⢰⠀⠀⢠⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⠐⣀⡸⠁⠀⠀⡘⠃⠀⠀⠀⣀⠀⠀⠈⠷⠀⠀⢠⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠆⠀⠀⢸⣀⢁⠁⠀⠀⠀⠁⠄⠀⠀⠀⡽⡇⠀⠀⢠⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⢆⡇⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⢎⡵⠋⠀⠀⠀⠀⢀⠞⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠃⢈⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⡸⠔⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠀⠀⠀⢄⠻⠀⠀⠀⠀⠴⠀⠀⠀⢆⡀⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⡇⠀⣷⡀
⠀⠀⠰⠘⡀⠀⠀⡸⠅⠘⠀⠀⠀⠈⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⣴⡧⠧⡖⠴⠆⠀⠀⢰⡇⠀⠀⠀⢤⠁⣸⣅⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠤⣀⡀⣠⠀⢀⡄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡬⣿⠀⠀⠀⢸⡉⠋
⠀⠀⠀⠀⡱⢿⣿⠷⣴⠮⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡝⣿⡗⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⡉⠲⣈⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⡇⠀⠀⠀⡇⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⢈⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠁⠄⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠔⢩⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢱⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢧⠀⠀⠀⡐⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣇⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⡁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⠌⠀⢤⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⣉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠠⠰⠗⣼⣧⡀⠊⠀⢀⡒⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⡋⠛⠃⠀⡤⠈⠁⡗⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠓⢀⠀⠀⠀⠷⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠤⠤⠈⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⡄⠠⢦⠀⠀⠈⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⣴⣄⢆⠀⠀⠀⠢⠀⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢣⠐⡇⠀⠀⣀⡀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⢢⢰⠀⠖⠀⢸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⡨⠐⠂⠀⠀⠩⢣⣄⠈⣷⡘⢧⠀⠀⠀⠀⠀⠘⢧⡤⠌⠰⢷⣄⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⠀⠀⠀⠄⠀⠀⠈⠉⠷⣬⣷⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡂⢀⠄⠀⢿⣳⣴⠀⠀⠈⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠠⢊⠤⠀⠻⢿⠞⠄⠀⠀⠒⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⡤⠀⠀⢀⠀⠀⠀⢤⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣩⢷⡱⠾⢿⣽⠁⠀⡾⢛⡛⢶⡀⠈⣿⣿⠿⢆⡷⣍⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢩⣿⣿⣿⣿⣿⣿⠟⠾⢷⣾⣷⡾⠷⠻⣿⣿⣿⣿⣿⣿⡍⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⣰⣿⣿⣿⣿⡿⡷⠀⢀⠘⣻⣝⠃⡀⠀⠾⢿⣿⣿⣿⣿⣆⣀⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠐⣿⡀⠈⣹⡏⠀⠙⣯⣿⣿⣿⣿⢫⡿⢟⡻⢿⡝⣿⣿⣿⣿⣿⡋⠀⢹⣏⠁⢀⣿⠂⡀
⠀⠀⠀⠀⢀⣄⡞⣀⢀⣸⡷⠾⡿⠛⣈⣺⣛⣿⣿⣿⣿⡼⠧⠊⠑⠼⢯⣿⢿⣿⡿⣛⣗⣃⠙⣿⠷⢾⣇⡀⣀⢳⣤⡀
⠀⠀⠀⢠⢻⣞⣿⣿⣿⣿⣁⠀⣐⢸⡟⣩⢙⡷⠞⣉⣥⣶⣶⢛⡓⢶⣦⣬⣙⠲⢾⣋⣍⢻⣇⣂⠀⣀⣿⣿⣿⣿⣳⡞⡄
⠀⠀⠀⠈⣱⡎⣿⣿⣿⣿⣿⣾⣿⡼⢷⡼⢫⣶⢿⠿⢿⡟⠀⢹⡇⠀⢻⡿⠿⡿⣶⡍⢧⡾⣧⣿⣷⣿⣿⣿⣿⣿⢱⣦⠁
⠀⠀⠀⢰⣟⣷⣿⣿⢿⡏⣿⣿⣿⣿⡼⢡⣿⡟⢻⣶⡠⣿⣿⣦⣬⣿⣿⣄⣶⡟⢺⣿⡄⢳⣿⣿⣿⣿⢸⡿⣿⣿⣿⣻⡇
⠀⠀⠀⠏⠁⠀⣻⡅⠀⢀⡿⣛⣛⡿⢁⣾⣿⠷⣤⣮⣴⢟⣻⠿⠿⣿⣻⣦⣵⣤⠾⣿⣿⡈⢿⣛⣛⢿⡀⠀⢨⣿⡀⠈⠙
⠀⠀⠀⢀⣾⢋⣹⣷⣶⣤⣿⢏⡩⠃⣼⢛⣀⣀⠻⢿⣿⡞⣵⢟⡻⣦⢳⣿⣿⠟⣄⣠⡙⣧⠸⢍⡹⣷⣄⣶⣾⣏⡙⣷⡀
⠀⠀⠀⠀⢻⣌⣹⡿⠿⠙⢿⣆⣑⡆⢻⣬⠋⠉⣤⣿⣿⢧⡻⣮⣵⢟⡼⣿⣿⣦⠉⠉⣡⡟⢠⣊⣱⡿⠋⠾⢿⣏⣡⡿
⠀⠀⠀⣆⡀⠈⣽⡃⠀⠈⣿⣭⣯⣷⡈⣿⣿⡶⠛⢿⠫⣺⣽⣶⣶⣯⣵⠛⡿⠛⢶⣿⣿⢁⣾⣽⣭⣾⠃⠀⠘⣯⠁⢀⣠
⠀⠀⠀⢸⣯⡿⣿⣿⣾⣇⣿⣿⣿⣿⢷⠘⣿⡧⣼⠿⠑⣿⣿⠟⠻⣿⣿⠋⠿⣧⣼⣿⢃⡜⣿⣿⣿⣿⢸⣷⣿⣿⣿⣽⡏
⠀⠀⠀⢀⡹⢇⣿⣿⣿⣿⣿⣿⣿⢣⡾⢳⡜⠿⣾⣶⣶⣧⠀⢸⡇⠀⣼⣷⣶⣷⠿⢣⡞⢷⣞⣿⣿⣿⣿⣿⣿⣿⡸⢟⡀
⠀⠀⠀⠘⡾⢯⣿⣿⣿⣿⠋⠀⠽⢸⣧⣙⣨⡷⠤⣉⡛⠻⠷⣬⣭⠾⠟⢛⣉⠴⢾⣍⣋⣸⡇⠝⠁⠙⣿⣿⣿⣿⡽⢷⠃
⠀⠀⠀⠀⠈⠋⢧⠉⠈⢹⡷⢶⣶⣄⠩⢹⣭⣿⣿⣿⣿⢳⡖⢄⡠⢲⣞⣿⣿⣿⣿⣭⡍⠍⢠⣶⡶⢾⡏⠁⠩⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⠁⢀⣹⣇⠀⣠⣽⣿⣿⣿⣿⣜⢷⣮⣵⣾⣣⣿⣿⣿⣿⣿⣅⠀⣸⣟⡐⠈⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠉⠹⣿⣿⣿⣿⣶⡶⠀⠈⢠⣽⣫⡄⠁⠀⢾⣾⣿⣿⣿⣿⠏⠉⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣘⣿⣿⣿⣿⣿⣿⣦⢶⡾⢿⡿⢷⡶⣤⣿⣿⣿⣿⣿⣿⣃⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣹⡾⡱⣶⣾⣿⡀⠈⢷⣬⣥⡾⠁⢀⣟⣿⣶⢎⢷⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠓⠀⠀⠈⠁⠀⠀⠚⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠏⠀⢠⣤⡴⢋⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀⣴⣃⣀⡿⠀⠀⠈⣻⣧⢸⡏⠀⠀⢢⡥
⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠄⠈⠛⠿⣿⣿⣁⠀⠀⠀⠑⠙⣻⡗⠀⠀⠈⣦
⠀⠀⠀⣠⣶⠟⠀⠈⠓⢠⣄⢀⠀⠀⠀⠙⠽⡄⠀⠀⠀⠀⢻⣷⠄⠀⠀⠈⠃⠀⠀⠀⠠⣤⠂⠀⣴
⠀⠀⠙⠛⠻⣄⠀⠀⠀⠀⠉⠛⢦⣤⡀⠀⠀⠀⠀⠀⢀⡀⠘⠹⢾⣷⣄⡀⠀⠀⠘⢧⣤⣄⠠⠞⠋
⠀⠀⠀⠀⠀⠈⢳⣢⡀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⢀⡼⠃⠀⠀⠊⠙⣿⠣⣄⠀⢀⡀⠀⠀⠤
⠀⠀⠀⢀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠀⠀⠀⢰⡀⠈⠡⠶⠟⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣰⡷⠀⣄⣴⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⡆⠀⠀⣼⡄⠀⠀⠁⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠐⣪⠞⠀⠒⠛⠁⠀⠀⠀⠀⠀⠚⠛⠷⢤⣄⣿⣷⠀⠀⣿⡇⠀⣠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⣼⣿⡇⠀⣿⡇⣼⣇
⠀⠀⠀⠀⠤⡤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠼⣿⢟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⣿⣦⣀⣈⡧⢳⣟⠓⢧⠆⠉⣾⠻⣷⣿⣿⣿⣷⣽⣯⣯⠉⠀⠸⠏⠰⠀⠻⠈⠛⠈⠋⢿⣶⠼⠃⠀⡟⠀⢸
⣿⣿⣿⣿⣿⣶⠮⢍⡀⠈⠙⠆⠸⠛⠻⣚⣻⣿⣟⣝⡶⢿⣳⠉⠁⣯⣤⣀⠒⠀⠀⠀⠀⠈⡏⠀⠘⠠⡄⠔⢋
⣿⣿⠟⠛⣳⢾⣿⢸⢟⠖⠂⠀⠁⢸⡟⠯⠉⠛⠉⠉⠛⠃⠀⠰⠏⠛⡿⡻⡡⢀⠂⠄⠀⠢⠠⠀⢁⣠⡷⠖⠛
⣿⣿⣿⣿⣧⣼⡿⣛⣋⣴⠶⢀⣘⡓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡞⠀⠋⠁⠰⠆⣠⠀⠑⢰⡄⠠⠀⠸⠁⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠟⠘⠁⠀⠙⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡅⣿⢸⠃⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣴⡶⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⣶⠞⡿⣵⣿⢿⡇⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣷⠀⠀⠀⠈⣅⡀⠀⠀⠀⠄⠈⠁⢄⠒⠋⠸⡆⠉⡟⠁⢀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢀⣄⢤⠋⠁⠃⠀⠀⠀⠀⠀⡽⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡴⣢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠴⠠⠄⠀⠀⣀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣾⠁⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠈⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣰⣿⣅⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠏⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⡟⠃⣄⡀⠀⠀⠀⡶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠿⠶⠀⣷⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⠏⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⢉⣶⣴⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢤⣼⣿⣭⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⣨⠚⢻⣣⣾⠿⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⡠⠬⠍⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠒⢀⠀⠀⠒⠂⠀⠠
⠀⠀⠀⠀⠁⠀⠈⠀⢀⡀⠐⠀⡀⠀⣀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠠⠀⠁⡀⠉⡄⠀⠀⠀⢅⠀⠁⠀⠄⠀⠀⠠⠊⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠄⣀⣁⡀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠘⢀⡀⠀⢀⠀⢀⠀⠙⠉⠁⠀⠠⠛⠀⠀⠀⠀⠘⠣⠄⠀⠀⠄⠀⠄⠀⡀
⠀⠀⠈⠀⠁⠀⠀⠁⠁⠤⠤⠐⡀⠡⡔⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠌⠀⠒⠀⠀⡀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠠⢆⠀⡀⠐⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢠⠎⠀⠁⢈⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⠄⢗⡌⠀⠐⠀⠰⠂⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣡⠀⠊⠀⢉⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠘⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠐⡀⠤⢀⠀⠴⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⣀⠔⠓⠀⠐⠁
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⣶⣶⠶⢶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⡀⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⣿⡛⡁⠀⢐⣇⣤⠾⠃⢤⠀⣀⢀⠠⡌⠀⠀⠀⠉⠀⠀⠈⠛⠛⠃⠀⠇⠐⠘⡤⠄⢀⡄⣀⠁
⠁⠠⣄⠐⠂⠀⠀⠀⢿⣦⢸⣾⣿⡟⠃⠀⠸⠅⠀⠀⠀⠈⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠄⠀⠀⠀⠀⠻⠀⢁⠀⡈
⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⢸⡿⠏⠁⣀⣠⠄⠀⢸⣷⡄⠀⣀⣀⠀⠀⠰⠌⣰⠀⠀⠀⠙⠀⠆⢰⠀⠠⣀⠀⠁⢘⠀⠁⠀⠰⠆
⠀⢤⠀⡤⠀⠀⠀⠀⠘⣿⡝⡆⢠⠞⠋⠁⠀⠀⣶⣿⠿⣿⣿⠏⠀⠀⢈⠓⣙⠃⠀⢠⠄⠹⡆⠺⠆⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⣷⣤⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠉⠀⠶⢀⠾⠀⠙⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉
⠀⠀⠀⠛⠃⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⡀⠀⠈⢆⣠⠀⠀⠄⢁⠐⡄⡶⠘⢀⠘⠳⠄⠀⠀⠀⠠⠀⠀⡀⠀⡀
⠀⠀⢄⡀⠀⠀⠈⠰⠀⠀⠀⠰⠆⠀⠀⠀⡀⠀⣙⢀⣤⠀⠀⠈⠀⣄⠈⠃⡀⣸⠀⠙⠃⠀⠀⠦⠈⠙⠀⠀⠀⠀⠀⠀⡀⠀⠅⠠⠄
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣘⡁⠌⠀⠄⠀⠀⠉⠉⠸⠟⣧⠐⢻⣅⠁⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠰⠀⣤⢠
⠀⠈⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡴⠶⣶⠀⠀⠛⠃⠉⠀⠀⠉⠈⠀⣀⠀⠀⡀⠀⠀⠀⠲⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠻⣿⠧⣦⠀⠘⠀⠀⠀⠀⠀⠀⣈⠀⠈⠝⠂
⠀⠀⡀⠈⠇⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠐⢀⡄⠀⠀⣀⠀⠀⠀⠀⠀⢹⡼⠃⠀⠀⠐⠀⠁⠀⢁⠀⠀⠀⠀⠤
⠀⠀⠙⠀⠀⠀⡀⠀⠴⠛⣧⠀⠐⠢⢀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡆⡘⠀⠈⠠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⡀
⣀⣀⣀⠀⠀⠀⠀⠀⢀⡘⣼⠆⢀⡀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠈⠀⠀⢸⠀⢸⠟⣠⣷⠇⠀⠄⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠁⠀⠘⠃
⣻⣽⣿⡇⠀⣴⠀⠐⠀⠀⠀⡐⠉⣅⠀⠀⠀⠁⠰⠄⠀⣤⠄⠀⠀⠀⠘⡇⡇⢀⢸⡏⢰⠁⢀⠀⠀⠀⠩⠱⠀⠀⠰⣿⣽⠂⣸⡆
⠉⠉⠉⠀⡼⠃⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⢰⡿⣄⡹⣡⠞⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⡈⠻⠀⢩⣷⡀
⣀⠀⠀⡾⠃⠀⠀⠀⠁⠰⠀⠀⠁⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⢹⡀⣧⢹⣤⡥⢀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠹⣄⠡⠈⣿⠄
⠟⠀⡾⠃⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠁⠀⢸⡀⠘⢺⠃⢠⠞⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠐⠻⣦⡑⢄⢘
⢀⠞⠀⠀⠀⠀⠘⠁⡈⠇⠘⠂⠀⠄⠀⠀⠠⠀⠀⠀⠀⣁⠁⠂⠀⠀⠀⠱⣄⣟⠴⠋⠀⠀⢀⠱⡆⠀⠀⠀⠀⠀⠀⣠⣄⡈⠛⢶⡙
⠀⠀⠀⠀⠀⠈⣐⠀⠈⠄⠁⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠈⠰⡠⠀⠀⠐⢲⣿⡥⠤⠄⠀⠀⠈⢇⠁⠀⠀⠀⠀⠀⠀⠙⠋⢀⡤⣤⣌
⠀⢠⣶⠀⠀⠀⢀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⣠⣄⡀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠘
⣀⣾⣿⣄⠀⠀⠐⠉⠀⠀⠀⠀⠂⠀⠈⠀⠐⠀⠀⠂⠀⠀⠐⠀⠀⢀⣤⣴⠄⠀⠀⠘⢯⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⠛⠙⠋⠀⠀⢀⡀⠀⠀⠀⠠⠄⠀⠀⡄⡀⠠⠄⠀⠀⠀⠀⡀⠀⠈⠁⠃⠀⠀⢀⣈⣉⠠⡀⠾⡮⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛
⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠴⠉⡱⠛⠁⠀⠀⠀⠀⡄⠀⠁⣀⠃⠀⠠⡀
⡐⠀⠰⠀⠒⠀⠀⠐⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠠⠀⠐⠋⠀⢀⣡⡇⠀⢠⡄⠀⠂⠀⠰⡎⠱⠂⠀⣸⡄⣠⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣴⡀⠀⠀⠀⠀⠒⠄⠀⠠⠀⠀⠂⠀⠀⠀⠜⠙⡿⠧⣄⣻⣿⣆⠀⠀⠐⡀⠐⠦⢀⡤⢀⡤⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⠀⠀⠀⠀⣤⠞⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠙⢉⡇⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣠⠆⠓⠀⠀⠀⠀⢸⣿⠻⣿⣶⣄⠀⠀⢸⠀⠘⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⣿⠀⠈⠻⢿⣿⣶⣼⣤⣤⣴⣿⣿⣧⣄⣀⣠⣤⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠈⠛⠻⠟⠛⠋⣽⣿⠃⠀⢠⡤⠤⠶⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣦⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⡀⠀⠘⣧⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⣠⠞⠋⠁⠀⠀⠀⠉⠓⣶⣿⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠃⠀⠀⣿⡇⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⣼⠀⠈⣿⣏⠀⣠⣴⣶⣶⣦⣄⣼⣯⣼⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠾⠟⠛⠛⠲⠦⣄⣿⡱⡛⢦⡀⠀⢀⡏⠀⠀⠘⣷⢲⡟⠁⣶⠚⠉⠉⠁⠀⣿⣿⠀⠀⢻⣤⣄
⠀⠀⢀⡀⢀⡄⠀⠀⠀⠀⠈⠙⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⠈⠳⣄⢸⠇⠀⠀⠀⠹⣞⣧⡀⢻⣄⣤⡄⠀⠀⣿⣿⠷⠒⠻⣆
⠀⠀⠈⡯⠁⢙⠀⠀⠀⠀⠀⠀⢠⣿⡷⡄⣴⡾⠟⠻⢷⣦⠀⠀⠸⣧⠀⠀⠈⠿⠀⠀⣤⠀⠀⢹⣎⠙⠛⠛⠉⠀⢀⣴⠇⣸⣇⣀⣀⣿⠿⠷⠶⠒
⠀⠀⠈⠉⠑⠎⠀⠀⠀⠀⠀⢀⣼⣿⣿⢼⡏⠀⠀⠀⠀⠹⡇⠀⠀⣿⢸⣦⡀⠀⠀⠀⣿⣆⠀⠀⢻⣤⣄⣀⣤⣴⠿⢫⡾⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣻⣧⡀⠀⠀⠀⣠⠇⠀⠀⣿⣷⣿⢿⣦⡤⣸⡇⢻⣦⣶⣾⡟⢛⡛⠉⠀⠀⣿⡀⠀⠀⠀⠀⠀⢤⣄⣠
⠀⠀⠀⠀⠀⠤⠴⠾⠿⠿⠿⠿⢿⣿⣿⣿⣭⠛⠶⠶⠞⠋⠀⠀⡤⢉⠈⢙⠈⠛⠛⠋⠁⠈⠉⠁⠀⠘⢦⣙⣦⣤⣤⣬⣷⣄⡀⠀⠀⠰⢾⣄⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢈⠿⣿⣮⣵⡀⠀⠀⣀⣠⣾⣿⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠻⡎⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⡴⠋⠀⠀⢹⡿⠿⠿⠿⠛⠋⢝⡻⣿⣤⠀⠀⠀⠀⣠⣤⢤⠶⡀⣤⣠⡄⢀⠘⣤⡀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⢿⡄⠀⢠⡞⠉⠈⣉⣭⣄⡁⠙⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⢘⡇⢠⡏⠀⣠⠟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠀⢈⡺⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠴⢦⣼⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡄⠻⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣀⣰⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦
⠀⠀⠢⡀⠁⠀⠰⠀⠀⠀⠀⠀⣀⠸⠆⡀⠀⠀⠀⢨⢋⣽⣶⡛⠲⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠾⠄⡆⠘⠿⠞⠀⠀⠀⠀⠀⢀⣶⣾⣿⡄⠀⠀⠀⢀⣤
⠀⠀⠀⢹⠀⠀⠀⢠⠄⠀⠀⠀⣠⣌⢨⡂⠀⠀⠀⢨⡁⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⠛⡀⢠⣤⣤⠀⠀⠀⠀⢸⣿⣾⣿⣧⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠉⠀⠨⢍⠆⠀⠀⠀⢳⡀⠸⡇⠀⢀⠀⠀⠀⠀⢾⡧⠀⠀⠀⠀⠀⠠⣿⡞⠋⠉⠀⠀⠀⢀⣿⡏⢻⢁⣿⣷⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠒⡶⠀⠀⠀⠀⠈⢷⠀⠀⢠⠎⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠘⠢⣈⠙⠁⢸⡀⠙⠃⢠⠏
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡂⣿⠄⡇⣐⣔⠄⠀⠀⠀⠸⣷⣤⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡼⠑⠄⠀⠀⠀⠀⠙⣢⠀⢸⡏⠀⢀⡟
⠀⠀⢀⡀⠀⢳⢼⠃⠀⠀⠀⠁⣈⢭⣀⠀⠈⠇⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠐⡇⡘
⠀⠀⠀⠃⡐⢘⠛⠀⠀⠀⠀⠀⠀⠠⠈⢒⣀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣴⣾⡿⣯⡉⠛⠂⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠐⠯⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠋⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠃⠀⠀⠀⠀⠀⠀⢹⡇⣦⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣢⢄⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠤⠳⠂
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢶⣾⢢⠤⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⣶⣶⣤⡀⠀⠀⠀⠀⠸⡟⢿⡿⠂⠀⠈⣿⡏⠀⠀⠀⠀⠀⠂
⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠠⠈⠃⢫⡀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠟⢋⣤⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠠⠀⠘
⠀⠄⠀⠀⠘⣿⣟⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠛⣀⠀⠀⠀⠀⠐⠆⠀⠆⠀⠀⠘⠁⠀⠈⠈⠋⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠠⡄⠀⠀⠋
⠀⡀⠀⣠⣀⣁⡀⠉⠀⠀⠀⠾⠄⡀⠀⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠠⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠉⠉⠀⠀⠀⠈⠏⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐
⠀⠄⠀⠻⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠂

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣠⣶⣟⣥⣶⠖⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⠿⠛⠛⢛⡛⠛⠿⢿⣥⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⣆⡿⠋⣤⠀⠾⠀⠻⠟⠀⣶⠀⠈⠳⣿⠟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⣿⣾⠋⠰⠆⠉⠀⠀⠀⠀⠀⠠⠀⠘⠿⠀⠘⡿⠟⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣤⣿⠸⠟⠁⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢸⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠌⢁⠈⠠⠀⠁⠀⠀⠀⠀⠀⣄⣠⣀⣀⠀⠀⠀⠀⢈⠁⢸⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⡏⠠⠄⠙⡀⠀⠁⢻⣶⣤⡿⠿⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠋⠀⠒⠂⠁⠘⡙⢦⡐⠀⢁⠀⠀⠘⢹⡏⣿⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢸⠢⠙⢦⣸⡄⠀⠀⠀⠀⠿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠰⣤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠀⠀⠀⠀⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣤⠄⠀⠀⠀⢀⣀⣠⣴⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⢲⣾⣿⣿⠀⠙⠈⠙⠃⠀⠐⠂⠀⠀⠐⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠉⣼⣿⠷⠠⡀
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠁⠏⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿
⢠⠆⠁⠀⠈⠁⠆⠀⠀⠀⠀⠶⢆⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠂⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡘⣠⣾⡯
⡉⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠒⠂⠰⠉⠀⠀⠈⠢⠀⠀⠀⠀⠢⠀⠀⠀⠂⠉⠀⠐⠀⠀⢀⡀⢀⣤⣀⣰⣤⣤⣀⣴⣿⣿⣏
⠀⠀⠀⠀⡁⠀⠀⢀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠓⢦⡔⠙⠉⠃⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⢿⣿⣿⣿⣥⣤
⣄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠘⠖⠦⠀⠀⠀⢀⡀⠀⠀⠠⢿⣿⡏⠻⡿⢿
⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠁⠀⠀⠀⢀⣿⡏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠠⠄⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣿⣧⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡆
⠀⠀⠀⠀⢸⠒⠤⠤⠀⠀⠡⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡆⠀⣸⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠊⠉⠹⠦⠠⠀⠀⠀⠀⠠⠤⣼⣿⣿⡇⠀⣿⣅⣠⡤⡀⠐⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⢤⡼⠿⢿⣿⣼⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢡⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠃
⠀⢁⠀⣦⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣒⡾⠛⠋⠿⣇⠐⠂⠀⠀⠠⢤⡀⠀⠀⠅⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠉⠉⠷⠀⢀⠐⠁⠀⠀⠀⠀⠀⠂⠤⠤⠤⠐⢢⠟⠉⠔⠃⠄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠓⡄⠀⠀⠀⠀⣀⣠⣀⡀⡃⠀⠀⠀⠀⢀
⢀⡤⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠛⠿⠿⠤⢄⣀
⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠒⠣⢤⠠⠤⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⣤⠀⠆⠀⣠⣶
⠀⠀⠀⠐⠆⠢⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⣧⢀⣽⣶⣶⣾⡟⠋
⠴⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠰⠃⠀⠀⢀⣠⠎⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⠁⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⣀⠀⠀⠀⠈⢻⣿⣧⢘⢀⠀⢀⣠⣿⣿⠋⠀⠀⠀⠀⠀⢀⠀⢐⠟⠩⠙⢢⡀⠄⢀
⠤⠀⠐⠁⠀⠃⠀⠀⢄⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠙⠢⡀⠀⠈⠻⣿⣿⠻⠀⣸⣿⣟⡡⠊⠁⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠈⠑⠒⠠
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣬⣉⡀⠢⢜⣿⣟⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠹⠛⠛⠛⢻⡿⢿⠁⣠⡔⢫⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠤⠀⠀⢀⡀⣀⡀⠀⠠⣠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠺⠀⠶⠤⠄⠀⠰⠂⠑⠐⠂⠀⠈⠁⢀⣱⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠒⢆⠀⠒⠒⠒⠒⠒⠀⠈⠉⠀⠐⠢⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣙⠐⠀⠀⠤⢼⠀⠠⠤⠤⠖⠒⠒⠀⠀⢈⡷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠬⢈⡓⠒⠒⠺⡆⠐⠒⠒⠒⠂⠉⢉⣀⣀⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⣉⡉⠉⡁⠀⠀⠀⠀⠈⠉⣀⣀⠿⠄⠀⠆
⠀⠀⠀⠀⠳⣄⡀⠀⠖⠀⠀⢅⡲⠀⠈⢡⣉⡃⣀⣀⣉⣉⣉⣭⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⣀⠀⡈⠀⢀⠀⢀⡀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠘⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⢁⠈
⠀⠀⠀⠀⠀⠀⠀⢺⡇⣰⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⠃⠛⣃⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣸⣧⡆⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠘⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣠⡟⢠⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠜⢁⠂⠤⢂⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⢷⣾⡿⠿⠋⠀⣠⠉⠾⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⢀⠀⣸⣧⣩⣤⡌⠉⠃⠀⢽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣴⢫⣟⠰⢆⣿⡟⠋⣩⡀⠗⠂⠀⠃⠀⠐⣰⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⡿⠃⠂⠀⠁⢻⣈⢉⠉⠀⢠⣽⣀⠾⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣃⢲⣀⡀⠀⠸⡿⠇⠰⠀⠀⣰⣥⡆⠁⣶⣄⣈⣹⠀⠀⢠⠉⠉⠀⠀⠀⠀⠀⠀⣼⠏⢘⠁⠀⠀⠀⢶⣟⠛⡉⠁⠡⢀⡿⠟⠛⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⡴⠻⣇⡙⠀⠀⠄⠀⡀⢠⡌⢻⠁⠶⠄⢀⡉⢻⠆⠀⡜⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⢠⡄⢀⡾⡇⣾⣧⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⣴⠾⠧⠀⣤⣄⣾⣧⡈⠀⢸⠀⠀⠀⠨⠑⠼⠀⠀⠁⠀⠀⠀⠰⡋⢙⡄⢀⡤⠀⠀⠀⢊⣱⡁⠀⠑⡶⠚⢁⡾⠉⢳⣿⣧⣶⣄
⠀⠄⠠⣄⢀⣀⡀⠀⣶⠃⠀⢴⣟⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⢠⠃⡀⠀⠀⠆⠀⠀⠀⠀⢀⠏⠀⢰⣴⡆⣾⣾⣧⣜⣿⡇⠿⣙⡆⡈⠀⠀⡾⠁⣰⣶⣶⡯⣿⣥
⠀⠀⠀⢨⠛⠻⣇⡀⠁⠀⣡⣶⠒⣻⣶⢀⣺⣿⡿⠀⠂⠀⢰⡇⠀⠹⣦⠀⡄⠀⠃⠀⠀⠸⠆⠀⢘⣿⣧⣾⡿⣿⣿⣷⣄⠀⠼⠏⠿⢀⡞⠀⣠⣬⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠻⠄⣠⣶⠟⢸⠏⠈⢻⣾⣿⡟⠧⠀⢲⡀⢼⠃⠀⠀⠨⣧⠀⣀⣀⠀⠀⠒⠀⠀⠋⢹⣿⣿⣿⡟⢹⣿⣿⣷⡄⠀⢀⡼⢶⣰⠿⠇⠀⠁⣿⡀⠔
⡀⠶⠀⣀⠀⠀⠀⣹⣿⠁⢀⡿⠀⠀⠋⢦⠽⠀⠀⠆⢀⣁⣾⠀⠀⢀⣤⣌⡠⣿⣇⣴⡄⠀⠙⢀⣰⣿⣿⣿⣿⡇⠛⢹⣿⡟⢻⣀⣾⣻⠿⠁⠀⠶⠠⠀⣩⣴⡇
⠀⠃⣘⣡⡄⠀⠠⠙⢻⣆⡠⣄⠀⠀⣠⣴⣶⣶⣤⣾⣝⣿⣿⠓⠀⠘⠛⢻⣅⢘⡘⣿⡇⠐⠶⢾⣻⠻⠿⣿⡿⢯⣤⣿⢘⠁⢘⣿⢿⣿⠶⣀⣴⣧⣴⣾⡿⠛⣷
⠀⠀⢸⡿⡉⠶⠦⣤⣾⣧⠀⣼⣿⠁⠀⣾⡇⠈⠙⠻⡿⢿⣿⠀⠀⠀⠀⠺⡿⢚⢠⣿⣷⣄⠀⠀⠟⠓⠘⠋⠀⠘⣿⠋⠀⣰⢟⣵⣾⣞⣳⣿⣿⣿⣿⣿⡿⢿⡿
⠀⠀⠀⠘⠀⡇⠈⢢⣿⡟⠸⣿⣿⠀⣾⣿⠁⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⠀⡶⠋⣡⠆⠹⠋⠀⢸⠀⠀⠀⠀⡀⠈⠁⠀⠀⢡⡾⠛⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣺⣿⣿⣷⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢠⢮⡾⠛⠉⢟⡻⠉⠛⢷⡷⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣦⣤⡶⠶⠚⠻⠿⣧⣠⢔⡾⢷⡢⣄⣼⠿⠟⠒⠶⢦⣤⣴⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⣶⣄⠁⠀⠀⡸⡳⠁⣨⣅⠈⢞⣇⠀⠀⠈⣠⡲⡟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠄⠙⡻⢎⣤⡶⢽⡷⢋⣉⣉⡙⢾⡯⠶⢤⣱⢟⠋⠠⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣿⡆⠀⠀⣠⡯⡮⣿⡟⡔⣵⢚⡓⣮⢧⢻⣿⣽⢿⡄⠀⠀⢰⣿⣲⢄
⠀⠀⠀⠀⠀⠀⢀⣞⣾⠋⠉⣻⢶⡪⢷⡷⢛⡭⡁⠀⣑⡃⢘⣊⠁⢈⠭⡛⢾⡾⢗⡶⣟⠉⠙⣷⣳⡀
⠀⠀⠀⣀⣀⣀⣾⣾⣧⢄⣐⡵⡁⣠⡏⢰⡱⢛⠵⠼⢿⣷⣾⡿⠇⠮⡛⣎⡆⢹⣄⢈⢮⣂⡠⣼⣷⣷⣀⣀⣀
⠀⠀⠀⠉⠉⠉⢿⢿⡟⠊⠹⡳⡁⠙⣇⠸⡹⣬⡲⢰⣾⡿⢿⣷⡆⢖⣥⢏⠇⣸⠋⢈⢾⠍⠑⢻⣿⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢯⢿⣄⣀⣽⠾⢵⡾⡷⣭⣲⡁⢀⡩⡅⢨⣍⡀⢈⣖⣭⣾⠷⡮⠷⣯⣀⣠⡿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⣿⠇⠀⠀⠘⣇⣗⣿⣧⠧⡻⢬⡥⢟⡜⣼⣾⣻⣺⠃⠀⠀⠸⣿⠽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠂⣠⣵⢎⠛⠷⣺⡷⣌⣉⣉⣡⢾⡟⠶⠚⡳⣮⣄⠐⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⠾⠋⡀⠀⠀⢱⡵⡀⢙⡋⢀⢮⡎⠀⠀⢀⠙⠷⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠟⠛⠷⠶⢤⣴⣶⡟⠙⠪⢳⡾⠗⠋⢻⣶⣦⠤⠶⠾⠛⠻⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠘⢞⢷⣤⣀⣮⣵⣀⣤⡾⡳⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢽⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠂⣽⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢮⡀⠸⠹⣆⡀⠀⠀⣀⣼⠿⠈⢻⣆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠨⢿⣦⠀⠱⢄⠀⠈⡇⠀⠠⣿⠋⠀⠇⢸⣿⣷⣄⠀⠐⣄
⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⠀⠘⢻⣧⡄⠀⠀⠀⠳⠀⡼⠁⢰⡦⠀⢷⣸⢻⡌⢧⠀⠈⠂⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⢀⡟⠻⣿⡄⢀⠶⠊⠀⠠⠋⠀⠀⠸⣧⣸⢿⠀⠱⠄⠂⠈⠁
⠀⠀⠀⠆⠀⠙⣿⣿⣿⣇⠀⢰⡄⣿⣄⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣾⠃⠀⠀⠑⢦
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⣸⣿⣿⣽⣿⣿⢤⣧⠀⠑⢄⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠂⠀⠉⠳⣄
⠀⠀⠀⠀⠠⠽⠿⢿⡿⡿⠛⠛⠛⠻⠿⠿⠿⣿⣿⡆⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⣦⡿⣹⡟⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣦⠔⠛⠿⠿⠾⠋⠀⠀⠀⠀⠺⢧⣀⡀⢀⡾⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⣠⣾⡷⢷⣄⠀⠀⠀⠀⢀⣤⣠⡤⠞⠉⢀⠁⠱⠀⠒⠂⣴⡄⠀⠀⠀⠀⠀⢈⠿⠋⠀⠰⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⡼⠋⠁⠀⠀⠙⢻⣦⠀⠦⣉⢱⡏⣀⠄⠀⠋⠐⣠⡄⠀⢀⣿⣷⠀⠀⠀⢀⣴⣯⠖⠀⠀⠀⢀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⣀⡀⠂⢀⡀⠀⣻⣿⠀⣼⣿⣿⡀⡤⠚⠥⠋⠀⠘⢀⣼⠠⣻⣿⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠋⣠⠆⠠⠀⠀⠀⠀⠀⠀⢦⣼⣿⠞⠁⠀⠔⠉⠀⠠⣾⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⡠⠌⢉⣠⡾⠿⠋⠁
⠀⠀⠀⠀⠠⣿⣧⣤⣀⡐⢡⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠃⠀⠀⠀⡀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⡀⢀⠴⠶⠟⢁⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣮⣼⣿⣦⣤⣀⠀⠀⠀⠀⣤⣿⡷⠀⠀⣀⠀⠂⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣷⢀⣴⣦⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣌⠙⠛⠁⠀⠀⠹⣷⣄⣤⣿⡿⠋⠀⠀⢰⣿⣆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣿⣿⠿⠛⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣤⡀⠀⠀⠈⠉⠻⠿⠦⢶⣤⣶⣾⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠐⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣀⣠⣄⠖⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠑⣷⣄⣀⠀⠀⠈⠓⢶⣤⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠐⠋⠟⠋⠀⠀⠀⠀⠀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠛⢦⣦⢀⣄⠙⠷⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠻⣿⡷⢿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠁⠙⠁⠀⠀⠀⢀⣴⣧⣠⡴⠂⠀⠀⣠⠞⠋⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢁⣾⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠔⠀⢀⠾⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠚⠉⠉⣉⣛⢦⡒⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⢟⢱⠁⢀⣀⣰⠋⠠⣤⡙⡔⠁⡠⠛⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⢟⠇⠆⠸⣄⠸⠇⠈⣷⡞⠁⠀⠙⠘⠀⠻⠤⠂⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡜⣿⡿⢸⡀⠘⣄⠈⣳⣶⣿⣶⣷⡀⠀⠀⡆⠀⠌⠀⡠⠒⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣾⣿⣿⢻⣶⡇⠀⠳⡀⠀⢙⣿⣿⣿⣿⣿⡗⠛⠂⠁⠀⠀⢸⠀⡴⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠋⣴⣶⣎⢻⣧⠀⠀⠈⠛⢏⡹⢿⣿⡿⠿⡧⣠⠜⠦⡀⠐⡸⡀⠻⠓⠀⠺⣁⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⣦⣬⣿⡟⢹⣿⣆⠠⣄⡀⢿⡀⠀⢹⠆⠀⠸⢄⠀⠀⠈⢐⣈⠙⠶⢤⣀⠀⠉⠲⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⣭⣹⡟⠻⣿⣿⣷⣤⣉⣉⣉⡠⠮⢀⡠⠔⢈⠝⢉⠔⣠⠂⠀⠀⡠⠄⠙⢦⡀⠰
⠀⠀⠀⠀⠀⠀⢰⣻⣿⡿⣣⣥⡹⣿⠗⢸⣿⣿⢸⣷⠦⣤⣄⣀⣘⡇⢀⡆⠀⡆⠀⢻⣠⡤⢾⡁⠐⣶⠦⡱⡀
⠀⠀⠀⠀⠀⠀⢸⣯⢳⣥⣭⣿⢧⣶⣶⡇⣿⡿⣾⣿⣾⣿⢋⣿⣿⠿⠿⣷⣮⡇⠀⠀⣯⣀⠀⡿⢺⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠈⣿⣷⣽⣻⢶⣿⣿⣿⠵⣯⣞⣛⣺⣯⣿⣿⡟⣴⣿⠛⣛⡿⣿⣦⡀⠈⣉⠴⠛⠛⢧⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢠⡝⢻⣿⣿⣶⣌⢛⢿⣟⣿⣿⡿⢞⢿⣿⠆⢿⣿⠇⣽⣿⣷⣿⣧⠀⡏⠀⠐⢶⣄⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⣽⣯⣃⢻⡏⣿⣿⣳⣭⣾⣿⠀⠀⠀⠀⠀⢛⣬⣙⢿⣿⣿⠀⠙⣦⠤⠞⢻⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣥⣿⢇⣿⣿⣿⢿⣭⣩⠀⠀⠀⠀⠀⣈⡻⣿⣷⢹⣿⣥⣎⠁⠀⠀⡏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣯⣷⣿⣟⣿⣿⣼⣿⣿⣧⡠⢄⣤⣤⣛⢿⣎⣿⣿⡿⠁⠘⠆⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣽⣦⣽⣿⣟⢿⠿⢫⣬⡸⠿⢀⣿⡎⣿⣿⡜⠁⠀⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⡿⢻⣎⠷⡶⠿⣱⣿⣿⣿⣳⠿⠋⣀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠻⠿⠿⠛⠛⠑⠀⠁

⠀⢀⣀⣤⣀
⠀⢹⣟⣿⠿⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠉⣠⣭⣿⣿⠿⣖⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠀⠔⠈⣩⣈⢿⣿⣀⣿⡥⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⣀⣄⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡾⠻⢩⠟⠀⠩⠛⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⣷⡁⠉⠀⠀⣠⡄⠐⠀⠀⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⡎⠒⠋⠀⠀⢠⣄⣤⠀⠀⣀⠀⠀⠀⠀⠛⠀⠀⠀⣀⠅⣤⠄⠀⢐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠦⢻⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣅⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠓⠉⣁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⣴⣦⣴⡆⠀⠀⠀⠀⠀⠈⠁⠉⠙⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⡍⠢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣍⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠈⠁⢤⠽⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⠏⠀⠀⠉⠘⠂
⠀⠀⠀⠀⠨⢁⠀⠀⠀⠨⢳⡌⢂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⠀⠀⠀⠚⠁⢀⠀⢀⡤⠀⠀⠀⠋⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⣘⠃⠰⣂⠀⠀⠀⠈⠶⡀⠈⠉⠀⠀⠀⠛⠁⠀⠀⠂⠠⣀⠀⠀⠀⠀⢉⡤
⠀⠀⠀⠀⠛⡓⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠈⠛⠁⠰⠄⠀⠀⠀⠀⠃⠉⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⢤⡄
⠀⠀⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⢶⣶⡶⠿⠟⠋⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⣠⠖⠀⠀⠀⠀⠉⠙⠛⠛⠷⣦⡀⢰⡀⣴⠀⢀⣴⠞⠛⠛⠉⠉⠀⠀⠀⠀⠢⣌⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⠁⢀⣤⣴⣶⣶⣶⣶⣦⣄⡀⠈⠃⠘⠃⠋⠀⠘⠁⢀⣤⣶⣶⣶⣶⣶⣦⣄⡀⠈⣧⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡄⣀⡀⢦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠋⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠋⣸⢡⣿⣿⡸⠆⠙⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣾⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣀⠀⠀⠀⠀⣰⢃⣾⣿⣟⣿⣿⣧⠹⡄⠀⠀⠀⠀⣀⣀⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⣿⣿⣿⡆⠀⠀⠣⠈⠻⠿⣿⡿⠿⠟⠠⠇⠀⠀⢰⣿⣿⣿⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠸⣿⣿⢻⠶⢷⡤⣆⣴⣀⣀⣀⣀⣦⣰⢤⢷⢼⠓⣿⣿⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠹⣿⣻⢻⢼⣇⡇⢸⠁⢸⡅⠸⠁⣇⣸⢼⢾⣻⣿⠏⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠹⡏⢶⣄⡉⢝⢻⠒⢾⡶⢺⠛⡏⢹⣸⠞⢹⠏⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⠁⠀⠈⠑⠺⢬⣇⣸⣇⣼⠤⠗⠋⠀⠀⠈⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠐⢦⣀⣀⡀⠀⠀⢀⣀⣠⠴⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣈⣉⣠⣤⣤⣀⣉⣁⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠙⠉⠉

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⣶⡶⠶⡶⢶⠶⠶⣶

⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡶⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠒⢲⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣆⣈⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣦⣠⣼⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣶⣾⣿⣿⡇⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⢛⣿⣿⣿⣿⣯⠟⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⡇⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣁⡠⢸⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣏⢩⡿⢫⣿⣿⣄⠈⢊⣿⣿⣿⣿⣿⡄⣼⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣼⣅⣿⣿⣼⣿⣿⣿⣿⣾⣿⣿⣿⡿⢹⡇⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣻⣷⣿⣿⣿⣿⣿⣿⢽⣺⣿⣿⣿⡇⣿⡇⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿
⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣧⣿⣼⣿⣿⡾⣫⡿⣿⣼⢿⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡆
⠿⢉⠉⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠘⠿⠿⠾⠿⠷⠶⠾⠒⠳⠷⠚⠟⠻⠗⠛⠟⠃⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠠
⣿⣿⣯⣤⣤⣤⣤⣥⣤⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣶⣤⣦⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠴⡶⠶⡦⢴⠶⠶⠰⠦⠦⠴⠶⠴⠶⠆⠦⠶⢦⠴⣦⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⢶⣶⣶⡶⢶⡖⡲⢶⣶⣶⣿⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⢫⣿⣠⣽⣽⣿⣿⣿⣿⣿⣿⣯⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣟⣹⣿⣿⣿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⢀⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠄⠀⠀⠀⣾⠆⠀⠀⠀⠀⠄⠈⡀⠴⠘⡄⠁⠄⠀⠀⠀⠂⣰⠈
⠀⠀⠀⠀⠀⣠⣤⣾⢿⣧⣤⠜⠀⠀⠀⠀⠀⠠⠀⠀⠀⢘⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠀⣴⠁⢌⡱⢐⠀⠀⢀⢈⠇⠈
⠀⠀⠀⠐⠀⢙⣿⣅⣏⣿⡟⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠈⠀⠀⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡉⢀⠒⠢⢀⠀⠀⠀⢀⠚⡆
⠀⠀⠀⠐⠀⠈⠟⠛⠛⠟⠇⠄⠂⠀⠀⢀⡨⠇⠂⢠⡈⢄⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠈⠀⠠⠈⠃⠀⠀⠀⠀⠀⠐⢧⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠐⠀⠀⠀⠀⣤⠼⠀⠀⠀⠈⢁⠀⠀⢰⣿⠛⠁⠀⠁⠀⠀⢄⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢻⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⣾⠁⠀⠀⠀⢀⣰⢠⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠁⠦⠘⠘⠸⠁⠀⠀⡀⠀⠀⠀⠀⢀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢄⠂⠐⣀⢆⠄⠀⠀⠀⣀⣸⣄⠂⠀⠠⠐⣾⡂⠀⠀⠀⠀⠁⠰⡶⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⡀⢀⠀⠀⠀⠀⣰⠇⠂⠀⢌⢄⠂⠤⡩⣚⠌⡄⠀⠈⠔⡷⠾⠉⠂⠀⠀⢸⡇⠁⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⣠⠁⠀⠀⠀⢀⡴⠂
⠀⠀⠄⢢⠼⢦⠂⠀⠀⠅⠀⠀⠠⠂⢌⠦⠐⡖⠀⢂⡱⡁⠀⠀⠀⠀⠀⠀⠀⠐⠸⣇⣀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡏⠀⢀⠀⠁
⠀⠀⠨⠜⠓⠋⠁⠀⠀⠀⠀⠀⠠⠎⠎⡜⠨⡰⢁⠃⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢏⠀⠀⠀⠀⢠⡆⠀⠈⠁⠘⠁⠀⠄⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠈⠚⠱⠱⠑⠂⠉⠀⠀⠀⠀⠀⡐⠈⡄⠀⡀⠀⡀⠈⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠙⠁
⠀⠀⢀⣀⠀⠈⠋⠈⢠⡦⠀⠀⠀⣤⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢥⢀⡖⠀⠀⡀⠁⠀⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠗⣀⠀⢂⠠⠀⢀
⠀⣠⡌⠋⢶⢆⡄⣁⢠⡀⠀⣠⡀⠉⢀⠀⠀⣁⠀⡄⠀⠀⠈⠢⠄⡠⢿⣿⠗⠃⢀⠀⠀⠚⠋⠀⠀⠀⠀⡀⠀⠀⢀⣄⠀⠊⠓⡌⠀⡄⠙
⠀⠀⠁⠨⢄⠈⠁⡄⠈⠳⡶⠙⢁⡀⠀⡔⢆⠉⠀⠁⠜⠠⠀⠀⢠⠀⢀⠋⠠⠀⠀⠄⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣄⠀⠈⡗⠋
⠀⠀⠘⠓⠀⢒⠀⢼⠀⠸⠆⠇⠘⠁⠀⠀⢀⣀⠤⠤⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⠖⠀⠀⠀⠀⠈⢈⠑⡼⠂⣀⢰⠆
⠀⠀⠀⣀⡀⣘⠃⠐⢦⠀⠋⠘⠓⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠴⠏⠀⠀⠄⠀⠟⢠⠀⠀⢹⠄⠒⠉⠀⠀⡀
⠀⠀⢠⡝⠃⡛⠀⠛⢀⢡⠀⠿⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣸⠛⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣇⠄⠀⠀⠀⢀⠇
⠀⠀⠈⠁⠀⣤⠁⠉⠉⠀⢳⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⠀⢸⡀⠀⠀⠄⠀⢀⠋⠉⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠧⠀⠐⠀⠀⡘⠀⠀⠀⠈⠸⡟⠋⠀⠂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢴⡗⠃⠀⠀⠀⠀⠀⢰⣶⡴⣾⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢸⠀⠀⠀⠀⠘⣤⢧⡤⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣾⣯⣝⣿⡷⠤⠂⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠻⢅⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⠤⠦⢤⡀⠀⠀⠀⠀⣠⠖⠒⠒⢆⡀⠀⠀⢠⡦⡴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣰⡇⣴⠚⠛⠻⡄⠀⣰⢋⣓⣢⣤⣴⣞⣉⡷⠀⠸⢵⣠⣿⠬⠽⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠤⣄
⠀⠀⢺⢸⡇⠘⠲⠶⢺⠁⠀⠈⡽⡟⢹⣅⢀⣈⡇⠀⠀⡞⢻⠉⢧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⣼⠻⣄⠀⠀⠀⠀⠀⠀⢀⡏⣾⡷⠀⠀⠀⠀⢠⠾⠶⢦⡀
⠀⠀⢸⣸⡆⠀⠀⠀⢸⠀⠀⠀⡇⡇⠀⠈⠙⢹⠀⠀⠀⡇⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠷⠤⣞⣦⠀⠀⠀⢴⣋⣋⣠⣭⡗⠀⠀⠀⠀⣸⠦⢤⢾⡄
⠀⠀⠀⠹⣇⣠⠿⣇⣼⠀⠀⠀⠳⡇⠀⣤⡄⢸⠀⠀⠀⠙⢾⠀⢠⣤⠀⡿⠀⠀⠀⠀⢀⣤⡏⢰⡋⠉⠉⣳⠀⣀⣼⠁⣞⠉⠉⢳⡄⠀⢀⣴⡇⢼⠉⠉⠙⡆
⠀⠀⠀⠀⠈⠁⢀⣈⡀⠀⠀⠀⠀⠙⢚⣁⠙⠋⠀⠀⠀⠀⠘⢒⢋⡘⠛⠃⠀⠀⠀⠀⢸⠀⡇⠀⠙⠒⠛⡇⠀⡇⢸⠀⠘⠓⠒⢻⠀⠀⢸⢸⡇⠈⠓⠚⢻
⠀⠀⠀⢀⢴⡉⢀⣤⣜⠀⠀⠀⠀⡴⠯⠼⡓⣦⠀⠀⠀⠀⡴⠯⠽⠼⢷⠄⠀⠀⠀⠀⠸⣆⡇⠀⠀⠀⠀⡇⠀⢧⣸⠀⠀⠀⠀⢸⠀⠀⢸⣸⡇⠀⡀⠀⢸
⠀⠀⢠⢾⡎⢿⡉⠀⣈⡇⠀⠀⣀⡟⢳⠟⠛⠛⣆⠀⠀⠀⣽⠋⣻⠿⢿⡄⠀⠀⠀⠀⠀⠈⣧⣀⡟⢿⣠⠇⠀⠀⢹⣀⣸⠻⣄⡟⠀⠀⠀⠸⣇⣠⠟⣇⡼
⠀⠀⢻⢸⠀⠀⠉⠉⢹⠀⠀⢸⠉⡇⠈⠳⠤⠶⡏⠀⢠⡖⡏⠘⣇⣀⣀⡼⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄⠀⠀⠀⠀⠀⣀⠤⢤⡄
⠀⠀⠸⣼⡇⠀⣀⡀⢸⠀⠀⢸⡄⡇⠀⠀⠀⠀⡇⠀⠸⡇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⣆⣀⡼⠀⠀⠀⢀⡞⡡⠖⠞⠦⡀⠀⠀⠀⠉⢻⣏⠳⣤⣤⡄
⠀⠀⠀⠘⠧⠼⠛⠧⠞⠀⠀⠀⠙⣇⢀⡾⣆⣰⠇⠀⠀⠷⣇⠀⣤⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⣿⣄⠀⠀⠀⠸⢴⡃⠠⡶⠰⢿⡄⠀⠀⠘⢿⣿⢓⣚⣿⡄
⠀⠀⠀⢀⣤⡀⠀⣠⡀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠀⠀⠀⠻⠶⢋⡙⠞⠁⠀⠀⠀⠀⠀⠀⣰⠋⡤⠬⠷⣄⠀⢠⢼⡏⢻⡛⠋⠉⡧⠀⠀⡤⣿⠀⡏⠉⠈⣹
⠀⠀⠀⠘⡶⠛⣚⣳⣞⠀⠀⠀⠀⢠⠖⢒⣲⣤⠀⠀⠀⠀⣠⠚⠉⠉⠙⣆⠀⠀⠀⠀⢀⡞⣿⠘⢧⣀⣠⡼⠀⢸⢸⡇⠀⠙⠛⢹⡇⠀⠀⡇⣿⠀⠈⠙⠉⡇
⠀⠀⢠⢼⡇⢾⠁⠀⢉⡆⠀⠀⡤⡟⠰⡟⣖⣪⡷⠀⠀⣈⣷⢿⣟⣛⣽⣿⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⡇⠀⢸⣼⡇⠀⣀⠀⢸⡇⠀⠀⢧⣿⠀⢀⣀⠀⡇
⠀⠀⢸⢸⡇⠈⠉⠉⢹⠀⠀⠀⡇⡯⠀⠉⠉⠉⡇⠀⠀⡇⣿⠀⠛⠯⡴⢿⠀⠀⠀⠀⠀⠳⣿⠀⣤⣤⠀⡇⠀⠀⠘⣇⣠⠟⢧⡼⠀⠀⠀⠀⠻⢤⠞⠻⠤⠇
⠀⠀⠸⣼⡇⠀⣀⡀⢸⠀⠀⠀⢧⣗⠀⣀⣀⠀⡇⠀⠀⣇⣻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣙⣶⣋⠙⠚⠁⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⣠⡤⣄
⠀⠀⠀⠘⠧⠴⠛⠧⠞⠀⠀⠀⠀⠻⠤⠎⠻⠴⠁⠀⠀⠈⢻⣀⣸⢻⣀⡏⠀⠀⠀⠀⠠⣎⡴⠠⡞⠀⠀⠀⠀⠀⠘⣏⡙⠾⢁⡟⠀⠀⠀⢀⡽⠏⠉⠚⢷
⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⡤⠒⢄⠀⠠⠚⢢⠀⠀⠀⠀⢉⡴⢦⠀⠀⠀⠀⠀⠀⠀⠉⢳⡴⠛⠒⢦⡀⠀⠀⠀⢠⠟⠛⠓⣦⠀⠀⠀⠈⠛⡶⠲⣤⣷⡄
⠀⠀⠀⡽⢶⣲⣺⣿⡆⠀⠀⠀⡗⣧⡼⠒⠳⢾⠊⠀⠀⠀⠀⣮⠑⠺⡄⠀⠀⠀⠀⠀⠀⣠⣾⠀⡟⠉⠉⢱⡄⢀⣤⡟⢰⡋⠉⠉⢳⠀⠀⣠⢼⠃⢾⠁⠀⢹⡆
⠀⠀⢀⣸⡏⣵⠛⠛⠳⡄⠀⠀⣨⣿⠀⡟⠉⠉⢳⠀⠀⠀⢰⠋⣩⠯⠿⣄⠀⠀⠀⠀⠀⡇⣿⠀⠙⠒⠒⢻⠀⢸⠀⡇⠀⠙⠒⠚⡏⠀⠀⢹⢸⠀⠈⠉⠉⢹
⠀⠀⢸⢹⡇⠘⠲⠶⢺⠁⠀⠀⡇⣿⠀⠙⠒⠚⣏⠀⠀⡞⣿⠀⢧⣀⣀⣼⠁⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⣿⠀⠘⣇⡇⠀⠀⠀⠀⡇⠀⠀⠸⣼⠀⢀⣀⡀⢸
⠀⠀⢸⣸⡆⠀⠀⠀⢸⠀⠀⠀⣇⣿⠀⠀⠀⠀⡇⠀⠀⡇⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢿⣀⣸⢻⣀⡟⠀⠀⠈⣧⣀⡿⢿⣠⠇⠀⠀⠀⠘⣦⡼⠙⢧⠞
⠀⠀⠀⠹⣇⣠⠿⣆⣼⠀⠀⠀⠈⢿⣀⡼⢿⣠⡇⠀⠀⠓⣿⠀⢠⣤⠀⡟⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠘⠲⠋⠘⠚⠃⠀⠀⠀⠀⠀⠀⢠⡞⠉⠓⡄⠀⠀⠀⠀⢠⡴⣿⣿⣷⠀⠀⠀⠀⠀⠀⢯⣤⡗
⠀⠀⢀⣀⣠⠖⠦⣀⠀⠀⠀⠀⢀⡴⠶⠚⠃⣠⠇⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡸⠷⠘⡄⠀⠀⠀⠸⢧⣧⣤⣼⡀⠀⠀⠀⠀⠀⡼⠀⢳⡀
⠀⠀⠘⢶⡷⣦⣖⣚⣩⠆⠀⠀⣸⣧⢿⠟⠛⠻⡄⠀⠀⠀⠀⡿⠒⠲⣄⠀⠀⠀⠀⠀⠀⣀⣼⠀⡷⠞⠙⢾⠀⠀⠀⣀⡞⢠⠖⠒⠛⣦⠀⠀⠀⣸⠓⡶⠶⠿⣄
⠀⠀⢰⢺⠀⢧⣀⣀⡝⠀⠀⢸⢩⡇⠘⠦⠤⢶⡃⠀⠀⢠⢼⠁⣏⠉⢉⡧⠀⠀⠀⠀⠀⡇⣿⠀⠙⠖⠒⣿⠀⠀⢸⡏⡇⠈⠳⠶⠶⡏⠀⢠⡞⡇⠈⢧⣀⣠⡞
⠀⠀⢸⢸⠀⠀⠀⠀⡇⠀⠀⢸⣀⡇⠀⠀⠀⢸⠁⠀⠀⢸⢸⠀⠈⠉⠉⡇⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⡏⠀⠀⠘⡇⡇⠀⠀⠀⢰⡇⠀⠘⡇⡇⠀⠀⠀⠀⡇
⠀⠀⠘⢺⠀⢰⣶⢀⡇⠀⠀⠀⠙⣇⢀⡶⣆⣸⠀⠀⠀⠘⢾⠀⢠⣤⢀⠇⠀⠀⠀⠀⠀⠈⢿⣀⣸⢿⣀⡇⠀⠀⠀⠉⣇⣀⡿⣇⣸⠇⠀⠀⠓⡧⠀⣴⣤⢀⡇
⠀⠀⠀⠈⠙⠁⠈⠉⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠀⠀⠀⠀⠈⠓⠋⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠙⠒⠃⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⣰⠂⠀⠀⠀⠀⠀⠒⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠈⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠄
⠐⠀⠀⠀⡤⠀⠌⠹⣄⡤⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠒⠄
⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠘⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⡜⢀⡖
⠀⠀⢱⠀⢠⠀⠀⠀⠀⠀⠀⢣⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠠⠀⠀⠀⠙⠋
⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠘⣦⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠁⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠘⠢⡀⠀⠉⠀⠈
⠀⠀⠀⠀⠃⠀⠈⠲⠚⠀⠈⢆⠀⠀⡀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡎⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⢀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠀⠀⢰⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠠⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠒⠁⢠⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠒⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⠊⠀⠀⠀⠀⠸⣄⢀⡄⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠱⠔⠁⠀⠀⢀⠤⠤⠀⠈⠉⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⢄⡀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄⠂⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⠀⠸⣤⣴⠃⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡆⠀⠀⡄⠀⠀⡀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠞⢀⠀⠐⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⡤⠠⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⣀⡐⢠⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⣼⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢣⠀⠀⠀⠀⠀⠀⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠘⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠂⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⣀⣀⣢⣤⣀⠀⠀⠀⠠⠄⢉⣉⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣤⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠠⡀⣶⣿⣿⣷⡴
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢿⡆⠈⢁⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠹⣀⠀⠀⠀⠻⠀⠀⠐⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠴⠶⠷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠲⣤⣤⣄⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⡀⡀
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠙⣋⠈⠛⠙⢶⣄⡀
⠀⠀⠀⠈⠐⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⡄⠀⠀⠀⠀⠀⠐⢂⠺⠄⠈⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠄⠀⠀⢀⠀⡠⡾⠎⠙⢷⣧⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠻⠀⠀⠀⠀⣸⣼⣗⠀⠀⠀⠀⠈⠃⠀⢀⠀⠀⢄⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠄⠉⠉⡆⢠⠇⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠻⢷⡾⣿⣿⣿⣷⣶⢀⠀⡀⠀⠿⡟⠀⠀⠀⠀⠀⣼⣿⣴⡶⠴⠞⠀⠂
⠀⠀⠀⠀⠐⢤⡀⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡌⠀⠀⠉⠙⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⣿⠟⣻⣟⠀⠀⠀⠀⠁⠀⠋⠻⣷⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠙⡧⠀⠀⠐⠀⢰⣿⢛⣿⣿⡦⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀⠀⠀⠀⢺⣿⣿⣿⣿⣷⣾⣄
⠀⠀⠀⠀⠀⠀⠈⠵⢷⣄⣀⣀⠀⠀⣀⣀⡑⡀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠐⠀⠄⠈⠁⠨⣽⠿⡿⢳⣯⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠤⣿⣿⠉⢯⡄⠈⢻⣷⣦⡄⠀⠀⢀⠤⠛⠓⣸⠓⠀⣀⠴⠂⠀⢄⣁⢈⡗⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠁⠈⠁⠀⠈⠁⠙⣿⡌⠂⠀⠈⠀⣀⣉⠄⠀⠉⠓⠀⠀⠀⠀⠀⠉⠓⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⢹⣟⠂⠀⠐⠋⠉⠛⢻⡆⢀⣀⣤⡄⠸⢤⣴⣤⣤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⠛⣦⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣛⣙⣻⣉⡟⢻⡟⣹⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠿⠋⠙⠉⠉⠉⠉⠛⠛⠂⢻⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡟⠋⣁⣤⣤⣄⣀⡀⠀⠀⠀⠲⠶⣤⡄⠀⠀⠀⠀⠈⠙⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⢀⣾⡿⠿⠏⠉⣁⣀⠀⠀⠰⠆⠀⠀⠀⠀⢠⣤⡆⠀⠀⠈⠛⠁⣀⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⣼⡿⠋⣀⠀⢒⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣧⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣿⣷⣾⡇⠀⠈⠑⢿⣧⠔⠖⠀⠀⠀⠀⠀⠀⠷⠀⠈⠀⠀⠀⡀⠹⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣀⡀⠈⠁⣰⣶⠂⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⣴⠇⠀⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣾⣻⣿⣧⡄⠀⠙⣿⣿⠶⠂⠀⠈⠀⠀⠀⣤⣼⢿⠁⣴⡴⣿⣿⡋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣩⠟⢷⣼⣿⣿⣆⠁⢀⣀⣤⡀⣾⡿⠟⢀⣸⣿⡶⠿⠯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿⡶⡾⣷⣿⣿⣿⣶⣯⣿⣿⣿⠎⠃⢰⣿⢹⣿⣷⢶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣮⣤⡤⣽⣿⣿⣿⡿⢯⠙⠀⢠⡄⣿⡏⣾⣿⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⢀⣴⣏⣸⣿⢽⡛⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡼⢠⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡦⠉⠉⢻⣿⣅⠈⣛⡿⠿⠾⢛⠙⢻⡿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⢢⣄⡈⠛⣿⣷⣮⣿⣦⣾⣧⣼⣿⣧⣾⣿⠿⠼⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣤⣴⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠈⠙⢷⣬⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠙⠿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢷⣄⠙⠿⠿⠋⣿⠃⢼⣿⠇⠀⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢼⣿⣿⣧⡶⠀⢰⣟⡴⠟⠛
⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣤⣤⣄⣀⠀⢳⣄⣀⡀⠀⣀⣿⣿⣿⣷⢶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠘⠛⠛⠛⠟⠿⠶⣾⣿⣿⣭⣁⠀⣹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠹⠶⠀⠀⠀⠀⠈⠻⣿⣿⣿⡯⠈⠉⢉⣿⡿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⠀⠀⠀⠀⣼⣿⠼⠿⠿⠇⠀⡀⢰⣶⠈⢻⡿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠈⠛⢿⣶⠃⠀⠀⢉⣥⣶⣶⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠿⠿⠟⠃⠀⠀⠉⠠⣴⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⣠⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡄⢰⡟⢿⣿⣿⠇⠀⠴⠶⠒⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⢼⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⣾⣿⣿⡇⠀⢠⢩⡝⠛⠛⣿⣿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⣿⣿⠟⣽⣿⢁⡵⣾⣿⡗⢦⡀⣿⣿⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⢁⣾⣿⡏⣀⣙⣛⣛⣩⠵⠄⠛⠛⠛⠻⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣻⣿⣿⠟⡥⠶⣿⣿⣿⠃⠀⠋⠈⠁⠀⠊⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⡔⣰⣿⣿⠏⠈⢧⣀⢨⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⡜⣰⣿⣿⡟⢠⠞⠉⠉⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡼⢠⣿⣿⣿⠃⠘⢦⠤⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢰⠃⣼⣿⣿⣿⠀⠀⣸⠀⣼⣿⡇⠀⠀⠀⠀⡴⠚⢲⣄⡤⠖⠶⢤⡐⠲⣶⠒⠒⠒⠲⠛
⠀⠀⠀⠀⣼⠀⡏⣿⣿⣿⡄⠀⡏⠀⣿⣿⣷⠀⠀⠀⠀⠷⣖⣚⣛⣒⣒⣒⡒⠿⢸⢻⡄
⠀⠀⠀⠀⣇⠀⡇⢿⣿⣿⣧⠀⢳⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⡜⠀⢷
⠀⠀⠀⠀⢻⠀⣇⠸⣿⣿⣿⣄⠘⣇⢸⣿⣿⣿⣷⣦⣄⣀⣀⣀⠀⠀⠀⠀⢀⣠⡃⠀⠘⣇
⠀⠀⠀⠀⢸⡀⢹⡀⢻⣿⣿⣿⣦⠘⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⢹⣿⣿⣇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⣇⠈⢧⠀⠹⣿⣿⣿⣷⣌⢾⣿⣿⣿⡇⠙⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠹⣄
⣀⣀⣀⣀⣀⣈⣀⣈⣧⣀⣈⣙⣿⣿⣿⣷⣝⣿⣿⣀⣀⣘⣿⣇⣀⣀⣀⣸⣿⣿⣿⣇⣀⣀⣀⣙⣦⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠈⠛⠻⠿⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⠋⠈⠁⠀⠀⠀⠀⠀⠀⣄⣠⣤⣤⠶⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠁⠀⠀⡟⢤⠀⠀⢀⠀⠀⠀⢠⣤⠾⢛⠏⠀⠑⠁⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠹⣿⣿⣿⡿⣯⣶⣶⣿⣇⣀⡤⠊⠀⠀⠀⠀⠀⠈⠁⢀⡞⠁⣴⠁⠓⢄⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠉⠻⣿⠿⠿⢷⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠁⣀⣼⣿⣥⡀⠩⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠓⢄⠀⠬⠷⡆⣅⣹⣵⠤⠤⣶⣶⣤⠤⠤⠖⠛⠻⠉⠿⢝⠋⠢⠅⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠃⣴⠔⠛⠀⠀⠀⠠⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠃⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠄⠀⠄⠂⠀⠈⠈⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⣀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⢿⣧⢏⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⣀⣐⣂⠀⠉⠁⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡⠫⡺⠊⣽⠃⣰⠶⠂
⠀⠀⢠⣘⠛⣿⢫⣏⠀⠀⢀⡠⠤⢤⠄⠀⠀⣶⠶⠒⠆⣠⠦⡄⣠⣌⣀⡐⠀⠀⠄⠀⠠⠡⢼⡆⠀⠀⠀⣀⡜⢋⡴⢾⣷⣞⣧⣼⠋⣴⢋⢱⡄
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠛⣄⠀⠀⡀⠃⠀⠈⠙⠓⠾⠧⣤⣉⣑⣀⡉⠙⠻⠿⠶⠶⢶⠀⢠⠃⠀⢠⠰⣋⣠⠞⠁⣰⣏⡼⠏⠀⡼⣡⡾⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢬⣉⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠛⠒⠒⠚⠃⠀⠀⠀⠀⠳⢩⡁⠀⡀⡼⠛⠓⠄⣢⡽⢏⡴⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⡙⠙⠁⠀⠀⠠⠃⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⣷⣄⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡤⢶⠎⠀⠀⠀⠀⠈⣥⣤⢀⡀⠀⠀⠀⠀⠀⠀⢈⠑⠉⠁⠀⠀⠀⠈⠁⠦⠀⡀
⠀⠀⢠⠶⠺⠏⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⢺⠂⠄⢠⠤⣀⣀⣀⠀⡀⠀⠀⠁⠀⢤⣀⠀⠀⠀⠀⠀⠠⠒⠈⠉⠉⠒⠢
⠀⠀⠀⠠⣀⣄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠈⠛⠑⠀⠀⠀⣸⣷⣶⣤⣤⣄⣈⣀⣀⠁⠁⠉⠈⠁⠁⣉⠀⠀⠀⠀⠀⣦⣀⣀⣀⣀⣀⣠⡆
⠀⠀⠀⠀⠀⠉⠙⠒⠀⣃⠀⢀⡧⠀⠠⠤⠧⠤⠛⠂⠉⠀⠀⠀⠛⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠈⠿⣟⣛⣛⣛⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠶⠶⠶⢤⣶⣤⠶⠾⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣆⣾⣿⠶⣶⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢛⠉⠙⠋⠈⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀⠀⣀⣀⠀⣀⡠⠤
⠀⠀⠰⠮⣏⣹⣽⠇⣿⣚⣏⣹⠧⣿⢻⣇⣰⣤⡀⠀⠀⠀⠀⡀⡀⣋⡀⣀⣘⣁⣀⣶⣀⣀⠀⠀⠀⠀⠀⢠⡄⣩⣼⠛⣤⠿⢁⣼⡛⢁⣜⠋⠆
⠀⠀⠐⠀⠀⠨⠙⠛⠫⠼⡗⣾⣛⣿⣙⣯⡜⠣⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠠⡾⠊⡵⠺⠁⡶⠋⢠⠎⠇⣴⡏⡀⡨⡃
⠀⠀⠘⠂⠠⠀⣀⡀⠀⠀⠀⠈⢉⡉⠁⠀⢀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠾⠇⠰⠋⠁⠰⠷⠂⠶⠲⠠⠖⠂⢀⠴⠁
⠀⠀⠀⠁⠂⠤⢀⠀⠉⠒⠠⠀⣀⣀⠴⠂⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠿⠁⠚⡛⡀⣚⣛⣀⣟⣋⠸⠿⢤⡠⡂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠤⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⠿⠿⠛⠁⠀⠈⠑⠐⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠹⠈

⠀⢀⣀⣤⢤⢤⢤⠴⠦⠴⣤⡴⠤⢶⠀⠶⡄⠀⢦⡤⢤⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠴⠆⢀⠴⠤⠦⠤⠤⣤⣤⠤⠄⣀
⠰⡏⠍⡾⠊⣡⠤⡤⣤⡀⠀⠙⣦⢎⢧⡐⠘⡦⠐⣇⡀⢇⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⠢⠐⢠⠖⢤⠆⠰⠄⡏⣞⠐⠻⣷⠈⡷
⠀⠙⢏⣃⢸⠁⢠⠄⡈⢳⠀⠀⠸⣸⢸⠹⡞⠃⣀⠼⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠐⠨⡔⠀⠢⣀⣠⢾⣣⢌⡗⠶⢋⡼⠃
⠀⠀⠀⠙⢿⡄⠠⣐⠐⠋⢀⡴⣣⢃⡧⠀⡱⠵⢋⠠⡤⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⠁⣑⡴⣞⠿⠛⠉⠐⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠹⣶⡢⠌⠠⠄⣊⡤⠋⠑⠤⡔⠢⣒⡴⠗⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣴⣳⠞⣁⠔⢁⡴⣺⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣙⠻⠛⣉⠵⡀⠀⠀⢍⣦⠋⢀⠔⠊⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣞⡾⠁⠐⠁⣴⢻⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣖⠉⢐⡀⠄⢋⣡⡞⠁⡝⠁⣠⠋⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡺⣼⠡⠀⠀⡼⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣁⠤⠚⣉⡼⠀⡜⠀⣰⠁⢠⠋⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠥⡇⠐⡇⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠲⡙⡽⡏⠀⡇⠀⠻⠀⢃⢰⢁⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣏⣰⡇⡁⢂⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠹⡌⢷⠀⢡⠀⠘⡠⠙⣄⠑⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠤⢼⡃⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⡌⢏⠀⠢⡀⠘⢦⡀⢩⠒⢂⢱⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⠒⣺⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⣎⢣⡀⠌⠒⠤⣀⣉⢉⣉⡠⠴⠀⠀⠀⠀⠀⣰⠃⠀⡄⣟⣈⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠹⡔⠤⣀⣀⣀⣀⣀⣀⣤⢷⡀⠀⠀⡼⠛⣦⠀⡄⣇⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⣦⡀⠪⣉⣀⠤⠭⢬⣀⠀⢀⠵⣤⠞⠑⢲⣆⠜⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢯⡱⢟⣏⣏⡙⢢⣜⡦⢸⠀⢰⡀⠂⠐⠁⢆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠁⠋⣠⣄⢹⠄⢼⡄⡠⠀⠢⡑⠄⠈⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⢇⡑⣨⢧⡏⢸⠃⠡⣈⡀⡠⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠒⠌⠃⣼⠇⡺⡄⡀⢀⠑⢲⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠉⢠⣟⣰⠇⠁⢠⠛⠄⠰⠃⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣞⢢⠟⠘⠀⠌⠄⠁⢴⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠈⠣⣄⠤⠼⣎⡀⠐⡈⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⣘⠎⠉⣕⢌⠂⢈⢃⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠤⠻⡄⠀⣠⠔⠲⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢣⠀⢀⣵⠊⠉⡂⢀⡎⠀⠄⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣼⢸⡞⠁⠀⡰⠚⠉⡋⠉⢣⠤⢈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠏⣸⢁⠤⠾⡒⠲⠶⢥⣤⠊⠀⠠⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣠⣯⠞⠉⢐⡠⠴⠒⠒⠲⠤⣈⠙⢦⡄⠀⠈⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣴⢾⡟⠁⣨⠖⢉⠤⢒⡂⣱⣐⠢⣄⠑⡄⠹⣆⣡⠄⠂⡝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢅⣧⡞⠈⡰⠁⣰⠃⡴⢉⡤⠠⣌⠳⡌⢆⠘⣄⢹⡇⠨⠥⠾⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠾⠷⠶⠷⠶⠷⠾⠶⠾⠶⠶⠾⠖⠷⠺⠶⠷⠶⠓⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠘⠛⠀⠀⠀⠀⢀⣺⣿⠄⠀⠀⠀⠀⢀⡦⣶⣦⠀⠀⠀⠀⢨⣅⣀⠀⠀⠀⠀⠀⠘⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡬⠄⠂⠀⠀⠀⠀⠉⠉⠀⠀⢰⢂⡀⠀⠳⠞⠻⠄⠀⠀⠠⣼⣿⣷⠆⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠐⠀⡀⠀⠐⠦⡜⣻⡄⠀⠀⠀⠀⠀⠀⠀⠲⣷⣮⠦⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡂
⠀⠀⠀⡀⠠⠁⠀⠀⠈⠁⠈⣤⣦⠀⢀⡀⠀⠀⣄⠀⠉⠙⠀⠀⠀⠀⢀⠀⠘⠷⣴⠁⠀⠖⠀⠀⠀⡀⠀⠀⢸⡳
⠀⠀⠀⠨⠀⠈⠀⠀⠒⠴⠂⡈⠁⠀⠈⠁⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠈⠃⠀⠀⡄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡤⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠤⠈⠀⢀⠤⠀⡀
⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠴⠷⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⠀⠸⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⡀⠛⠀⠀⠀⡀⠀⠊⠁⠂
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢬⠔⠀⠀⠀⠀⠀⢤⠀⠀⠀⠒⠀⠱⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⣳⢜⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⡀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠙⠒⣄⠀⠀⠀⠀⢠⡬⣷⠂
⠀⢘⠀⠀⠀⠤⢹⡈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⡘⠀⠀⠀⠂⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⡃⣠⠀⠀⠀⠀⠀⠐
⠀⠸⠀⠀⠀⠀⠀⠁⡄⡀⣘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⡁⢰⠁⡄
⠀⠀⠄⠀⠈⠂⠀⡌⠀⣷⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡈⠁⢰⠇⢀
⠀⠀⠀⠀⠀⢀⢀⡈⠙⢁⠀⠰⢧⠄⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠈⠑⠉⢀⡜
⠀⡀⠀⠀⠀⠐⠝⠈⠀⠘⢁⠘⣀⢀⢎⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢁⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠠⠋⢀⣀⠄
⠀⠀⠠⠀⠀⢁⣠⢀⠑⢦⠊⠀⠟⠣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠠⡀⠂⠀⠐⠀⠀⠀⠀⡀⠀⠈⠉⠑⡐⡠⢀⡐⠉
⠀⠀⠀⠈⠀⠢⡅⠁⠀⢸⠀⠀⢰⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢧⠂⠀⠀⡐⠂⠁⠀⠣⠐⠙⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠐⢺⣤⡄⠀⠀⡄⠀⠀⢙⢁⠖⢢⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⣷⡤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⣡⠤⠀⠀⠀⡀⠚⠀⢠⡆⣈⠀⠛⠋⠠⠈⠀⠀⠠⠁⡄⠀⠒⠛⠢⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠤⣤⢡⠤⠖⠀⠀⠀⠀⠀⠀⢣⡄⢠⢁⠀⡴⠐⣆⠀⣰⠤⠘⠀⢀⠀⠀⠀⠀⠀⠀⣄⠱⠵⠄⠀⠀⠀⠀⠂
⠀⠀⠀⢸⠇⠀⠀⠀⠀⢢⡭⠥⠀⠀⠀⠀⡀⡀⠁⠀⠠⡤⠀⠀⠀⠠⠶⠦⠄⣁⢤⡴⠃⠐⠃⠌⡏⠀⠁⠀⡀⠀⠀⠀⠀⢀⡄⠈⠳⠒⠂
⠀⠀⠀⣸⠂⠀⠀⠠⣄⠻⢚⣁⣀⠀⠀⠈⠉⠉⠃⠀⠁⠀⡀⠀⠀⠀⠀⠀⢵⠆⢚⠀⠰⢶⡈⢤⣤⣅⡀⠁⠂⠀⠀⠀⢀⠈⠀⠁⠠⠐⠐
⠀⠀⠀⡿⠀⠀⠠⣀⠈⠛⣉⣅⡤⠂⠐⠀⠀⠀⠀⠀⢰⠐⠁⠀⠀⠀⠀⠂⠀⡘⠙⠛⣤⠌⠤⠊⡇⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⢆⡰⠿⠓⠤
⠀⠀⢰⠃⠀⠀⣀⡘⠷⠿⠗⣀⣀⣀⡀⠈⠙⡢⡠⡀⠂⠒⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⡉⢂⠀⠃⠀⠷⡈⡈⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⢲⣷⡾⢙⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠑⠀⠀⠠⠈⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡩⡿⠟⠿⠿⠿⠿⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⡒⡂⠄⠀⢀⡐⡠⠰⠥⠒⠚⠁⠉⠚⠣⡄⣰⢴⡆⡦⣶⡆⡆⡖⣒⢺⢲⡒⡖⣖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠐⠘⣻⡹⢩⣰⠋⡌⠖⠊⠁⠀⠄⠀⠀⠂⠀⠐⠤⢈⡟⡈⠈⠓⠓⠛⠓⠇⠷⢸⠸⠰⡆⠧⢶⠼
⠀⠀⠀⠀⠀⠀⡎⢬⡡⢹⡅⡚⠉⠈⠀⠸⠀⠠⠁⠀⡂⠈⠀⠠⡔⣆⠠⠀⠉⠀⠂⢀⠀⠂⠉⠉⠀⠈⠸⠄⡇⢇⢸⢸⠀⡆
⠀⠀⠀⠀⠀⡄⠈⠐⠙⠋⠁⠄⠶⢦⠐⠀⠀⡀⠈⢡⠀⠀⠠⢀⡌⢁⢈⠀⢀⠠⣀⠤⢒⠒⠺⠛⠛⠛⠓⠨⡋⠛⣸⡿⡗⡇
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⢺⡄⠈⠀⠰⡄⡀⠱⠎⡊⠡⣉⡴⠯⣶⣛⠥⠒⠂⠉⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠡⠀⣘⡋⠇⠇
⠀⠀⠀⠀⠀⡇⠸⠀⠄⢊⠴⠤⠄⠠⢀⡀⠤⠒⠈⠁⠀⠀⠀⠀⠈⠁⣀⠀⢀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠠⠀⠒⢻⠀⠆⠁
⠀⠀⠀⠀⠀⠀⡀⠑⠀⢀⢢⡀⠀⠈⡏⠀⠀⠀⠀⡀⠤⠀⠠⡀⠀⠀⠀⠲⣤⠐⠄⢠⠍⡄⠈⠀⠀⠀⠀⠀⠀⠐⡧⢈
⠀⠀⠀⠀⠀⣀⠧⡀⠔⢀⠤⠀⠀⠀⣿⠀⠀⢊⠤⠴⢢⡄⠀⢀⠀⠀⠀⠀⠀⠚⡀⢘⠅⠆⢠⡄⠣⠙⢀⣁⠅⠀⠷⡠
⠀⠀⠀⠀⠀⠃⠈⠀⠄⣈⠊⠀⠀⢸⣿⠀⠀⠁⣀⠷⠨⠄⡀⢸⠀⡀⢂⣒⣂⠄⠈⠢⡉⠀⠀⠉⠀⠋⠉⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⣠⢸⠀⡠⢊⠴⠀⠀⢸⣿⡆⠀⠘⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠇⠀⠐⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠄⠀⠘⠠⢈⣲⠀⠀⣸⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠄⠀⠈⡠⠀⠀⢼⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠈⠀⡀⠃⠘⠀⠲⠀⠀⣻⡇⢹⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠊⠸⠁⠑⠠⠀⠀⡿⡁⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⢀⠄⠂⡀⠁⠀⠀⠂⠘⢇⣀⣠⠤⠀⠀⠀⠀⠀⠀⢸⢄⣀⠀⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠐⣀⣠⠤⡂⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠈⡀⠀⢨⠀⠂⠀⠈⠀⢈⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠅⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⠀⠀⠀⠀⠉⠁⠂⢊⠈⠁⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢄⠀⠀⢀⠀⠀⠀⠀⠀⡎⠙⠁⠓⠀⠀⠀⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠈⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠃⡤⢠⠤⠤⠤⠶⢆⡒⠀⠐⢠⢄⠀⠀⠀⡄⠀⠀⠀⡤⡀⠀⠐⢂⡟⡄⠀⠀⠀⠀⠀⠀⣠⣂⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⡂⠘⠁⠀⠀⠁⠀⠀⠈⠑⠶⠁⠈⠓⠤⠏⠀⠳⢤⠜⠀⠈⠶⠤⠎⠀⠀⠉⠓⠒⠒⠒⠁⠐⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣒⠖⣀⣤⣶⠾⡇⠉⠀⣠⣦⣴⣄⠀⠉⠹⠷⢶⣤⣄⢖⣲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣮⣳⣌⣛⣛⣟⣟⣀⠀⣼⡏⢰⡆⢹⣧⠀⣀⣻⣻⣛⣛⣥⣟⣵⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠣⣼⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣷⣿⣿⣾⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⠌⠛⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢧⠀⠀⠄⠛⢿⣟⠛⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⢉⠛⢻⣿⠟⠋⠻⢿⣫⣷⣶⣶⣶⡮⣣⣾⣿⣿⣷⣼⢷⣶⣶⣶⣾⣝⡿⠟⠉⠛⣿⡿⠛⡉⢹⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠘⠀⠘⣿⣀⣰⣾⣯⡄⢠⣠⣿⣿⣿⣿⣿⣿⢱⣿⠃⡰⢆⠙⣿⡎⣿⣿⣿⣿⣿⣷⣆⡄⢀⣼⣷⣤⣀⣾⠃⠀⠃⣤
⠀⠀⠀⠀⠀⣠⠶⣾⣋⣦⣠⣴⣾⠛⠋⠻⠁⣠⣴⣶⣮⣝⠻⣷⣟⡿⠖⠛⠉⣁⣈⠉⠛⠲⢿⣻⡿⠟⣯⣵⣶⣤⣄⠈⠟⠉⠛⣿⣦⣄⣴⣉⣷⠶⣄
⠀⠀⠀⠀⢰⢣⣮⣻⣿⣿⣿⣿⣧⡀⠀⣺⢰⣿⠁⣤⣀⡿⠟⢋⣁⣤⣴⣾⣿⣛⡛⡿⣷⣦⣤⣈⡙⠳⢯⣀⣤⠈⣿⡆⣖⡀⢀⣼⣿⣿⣿⣿⣟⣽⡬⡆
⠀⠀⠀⠀⠘⢣⣦⢹⣿⣿⣿⣿⡿⣳⣿⣿⣎⢿⣄⡼⠋⣴⣾⣿⣿⣿⣿⠃⠀⢽⣧⠀⠘⣿⣿⣿⣿⣷⣤⡙⢦⣤⡿⣱⣿⣿⣞⢿⣿⣿⣿⣿⡏⣴⣄⠃
⠀⠀⠀⠀⢠⡿⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⢿⣖⡾⢁⣾⣿⢰⣷⣔⠀⣿⣶⣶⣈⣁⣦⣶⣿⠀⣠⣾⡦⣿⣷⡈⢷⣰⡿⣿⣿⣿⡏⣿⣿⣿⣿⡇⣿⢿⡆
⠀⠀⠀⠀⡾⠇⠛⢻⣿⠛⠉⠃⢸⣿⣿⣿⣿⡽⠁⣼⣿⣿⠀⠙⡿⢋⢿⣿⣿⢷⡾⣿⣿⡿⠙⢿⠛⠀⣿⣿⣧⠈⢯⢿⣿⣿⣿⡇⠙⠉⠛⣿⡏⠛⠸⢷
⠀⠀⠀⠀⠁⠀⣀⣤⣿⡀⠀⠄⠾⣯⣵⡶⣼⠁⣸⣿⠿⠋⢻⣿⣿⣷⣻⣮⠿⣛⣛⠻⣷⣟⣾⣿⣿⡟⠙⠿⣿⣇⠈⣯⣶⣾⣽⠷⠠⠂⢀⣿⣤⣀
⠀⠀⠀⠀⢠⣾⢋⣉⣽⣿⣿⣦⣾⣿⢉⡠⠇⢰⣿⢃⣀⣤⡔⠻⢿⣟⣿⢣⣾⢛⡟⣷⡌⣿⣻⡿⠟⣲⣠⣀⡜⣿⡄⢸⢄⡙⣿⣷⣄⣻⣿⣯⣉⠙⣷⡄
⠀⠀⠀⠀⠐⢿⣄⣉⣻⣿⣿⠕⢿⣿⣌⠑⡆⠘⣿⡜⠉⠛⠫⣴⣾⣯⣿⡘⢿⣽⣥⣿⢣⣿⣽⣷⣧⠍⠙⠙⢥⣿⠃⢰⠊⣁⣾⡿⠃⣿⣿⣟⣉⣡⡿⠃
⠀⠀⠀⠀⡀⠠⠉⠛⣿⠁⠀⠀⢶⣟⡻⠿⢻⡀⢹⣿⣶⣄⣼⣿⣿⡿⣵⢟⣦⣭⣭⣴⡻⣮⢿⣿⣿⣧⣤⣶⣿⡏⢀⡟⠿⢟⣫⡶⠀⠀⠈⣿⡛⠉⠄⢠
⠀⠀⠀⠀⢷⡆⣤⣼⣿⣤⣀⣤⢸⣿⣿⣿⣿⣳⡀⢻⣿⣿⠀⣠⣵⣌⣾⣿⣿⣾⢿⣿⣿⣷⣠⣾⣄⠀⣿⣿⡟⢀⣾⣾⣿⣿⣿⡇⢠⣀⣤⣿⣧⣤⢰⡾
⠀⠀⠀⠀⠸⣷⣿⢹⣿⣿⣿⣿⣸⣿⣿⣿⣾⠯⢷⡈⢿⣿⠺⡿⠻⠀⣿⠿⠻⣩⡉⠟⠿⣿⠀⠙⢿⠗⣿⡿⢁⣞⠹⣿⣿⣿⣿⣇⣿⣿⣿⣿⡟⣿⣾⠇
⠀⠀⠀⠀⢠⣝⠟⣼⣿⣿⣿⣿⣷⡽⣿⣿⣏⣾⠃⠳⣄⠻⢿⣿⣿⣿⣷⡄⠀⢺⣗⠀⢠⣾⣿⣿⣿⡿⠟⣠⠞⠛⣿⡹⣿⣿⢿⣾⣿⣿⣿⣿⣇⠻⢋⡄
⠀⠀⠀⠀⠸⡞⢟⣽⣿⣿⣿⣿⣟⠁⠈⠽⠘⣿⡀⠛⠉⣳⢦⣌⡉⠛⠻⢿⣶⣭⣥⣷⡿⠿⠛⢉⣡⢴⣚⠁⠛⢀⣿⠇⠯⠀⠈⢻⣿⣿⣿⣿⣯⣻⢳⠇
⠀⠀⠀⠀⠀⠙⠦⢿⡍⠟⠙⠻⣿⣤⣀⣴⡀⠙⠻⠿⢟⣫⣴⡾⣯⣷⡦⣤⣀⣉⢉⣀⣠⠴⣺⣽⣷⣧⣝⡻⠿⠛⠋⢀⣦⣀⣤⣿⠟⠋⠻⢉⡿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⡟⢀⠠⢠⣿⠩⠙⣿⡟⠁⠘⠙⣿⣿⣿⣿⣿⣿⡸⣿⣄⠱⠎⢠⣿⢇⣿⣿⣿⣿⣿⣿⠏⠃⠈⢻⡿⠏⠉⢿⡄⠄⠄⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣈⣤⣼⣿⣤⣀⣴⣾⣝⡿⠿⠿⠿⢗⡝⢿⣿⣾⡿⢫⡺⠿⠿⠿⢿⣻⣷⣦⣀⣤⣿⣧⣄⣁⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠋⠛⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⣤⣽⣭⣤⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠛⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⢿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⢂⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡿⢟⣽⢋⣭⣭⣭⣯⠉⠀⢻⣇⠘⠆⣸⡟⠀⠉⣿⣭⣭⣭⡙⣯⡻⢛⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⠤⠝⠻⠷⢶⣇⡀⠀⠙⡿⠻⠋⠀⢀⣰⡶⠾⠟⠋⠶⠭⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⡀⣉⠀⠀⣠⠀⠂⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡈⠀⠁⠉⢠⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠠⠄⡄⠀⡩⠄⠁⠐⠂⠀⠀⠀⠀⠠⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠈⠳⣄⠘⠀⣠⠄⢒⠀⠁⠀⠀⠀⠀⢀⠄⠄⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡈⠀⠈⡁⠤
⠀⠀⠀⠀⠀⠻⠂⠀⡀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⢃⠀⠭⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠓⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠠⣀⠰⡌⠁⣀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡅⠊⠤⡶⡱⢄
⠀⠀⠀⠀⠀⠁⠀⢰⠄⠀⠀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠐⡈⠛⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠄⠣⠀⠀⠉⠁
⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠢⠀⢠⡀⠀⣀⡀⠤⡀
⠀⡇⠲⣦⡷⠒⡒⢶⠒⡒⡗⣾⠒⡒⢢⠖⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠆⠘⠂⠁⠀⠀⠒⢀⡇
⠀⡞⢶⠄⣷⠸⠜⢸⢸⠓⡇⣿⢸⢹⢸⡘⠟⢸
⠀⠈⠒⠚⢃⢰⠚⠉⠛⠀⠙⠋⠊⠙⠺⡍⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠿⠿⢿⣿⣿⣿⣿⡿⠛⠋⣉⠉⠉⠉⠙⠻⢿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠈⢻⣿⡏⢠⡾⠋⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠹⡇⠸⡁⢠⡦⠠⡐⢤⡈⠳⡄⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢠⠇⠀⢻⡄⠹⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢀⠕⠒⠄⢸⣿⠀⠇⢸⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠒⠂⠀⣾⣿⠆⠀⠸⣿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡗⠀⠾⣿⣿⡄⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⣿⣇⠀⢠⣿⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣿⣿⠈⡇⢸⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠘⣿⢰⠃⣸⣿⡇⣿⠀⠀⠀⣄⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡞⠀⣿⣿⠀⠑⠀⡶⠀⣿⣆⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⡠⠞⠀⢸⣿⡏⢠⡀⢠⠇⢰⣿⣿⣆⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⣿⣿⠁⠉⢁⡞⠀⠚⠿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡄⣸⣿⠇⠀⠀⣼⠗⠲⡶⠆⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠁⣿⡟⠀⢀⣾⠃⢀⣠⡤⠀⠉⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⢰⣿⠃⠂⣼⠇⣴⠏⠀⠀⠀⠀⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠘⠀⣿⠀⣿⠀⢸⠿⠀⢀⡼⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡿⠀⠀⣿⠀⠘⠆⠀⢙⡛⠋⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢻⡄⠀⢠⡞⠉⠉⠙⢦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⠄⠘⢤⡄⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣦⡈⠛⠷⠶⠶⠶⠶⠛⢉⣠⣦⣄⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣀⣡⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⡀⠀⡀
⠀⠀⠀⠀⠀⡀⡴⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢹⠤⠃
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠦
⠀⠀⠀⠀⠀⠿⠀⠀⢰⠂⠀⠀⠀⠀⠀⢴⣆⣀⣀⡀⠛⠂⢄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⡀⣀⡜⠀⠀⠀⠀⠀⠀⣀⠟⠋⠈⠛⣦⡀⠘⠇⢸⠙⠁⠀⠀⠀⠀⠀⠈⠉⢁⡄
⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠈⠟⠃⢀⡴⠆⠈⠃⠀⠰⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠃⢉⣄⣀⣀⣤⣤⣄⠙⠁⠀⠀⠀⠀⠀⠀⣄⠒⡟
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⣴⠦⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢲⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⢷⣤⣿⡿⠂⠀⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⣠⠊⠈⣿⠿⠠⠀⠀⠈⢷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠄
⠀⠀⠀⠀⠀⠈⠿⣇⣀⣀⠀⠀⠀⠀⠀⠈⣿⣷⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⢀⣾⠃⠀⠀⢸⣿⡉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⠟⠁⠄⠀⠀⠈⣿⣿⣶⣶⣾⣇⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⣾⡿⣿⠛⠋⠛⢿⣿⣶⣦⣤⡄⢀⠐⠀⠛⠟⢻⠿⠿⠿⠿⠷⠶⠿⠛⠚⠓⠓⠶⠶⠶⠶⠦⣤⣀
⠀⠈⢟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡠⠀⣀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⣯⣀⠈⢣⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⢿⣿⣿⣷⣴⠆
⠀⠷⠠⣀⡀⠀⠀⠘⠋⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡄⠀⠀⠀⣀⡉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣎⢫⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⣿⣿⣤⡄⠀⠀⠀⠀⠉⠙⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣿⠟⠻⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⠿⠿⠛⠁⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠛⠟⣛⣋⠭⠝⠛⠫⠤⠭⠙⠛⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡔⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡏⠒⠂⠀⠛⣷⣤⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣧⣀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣶⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣁⠉⢩⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠿⣿⣦⠎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠤⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡏⠀⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠰⢿⣤⣀⡄⠀⣭⡉⠉⠉⠉⢻⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠀⠿⠟⠀⠀⠀⠘⠿⢿⣿⣿

⠀⢐⣾⣳⡞⣿⣻⡃⠀⠀⠀⠀⠀⠀⢀⡔⠒⠢⠒⠒⠔⠂⠐⠢⠒⠢⠤⠀⢄
⢠⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⡐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒⠒⠈⠉⠉⠁⠐⠒⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⣀⠀⣀⠠⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠐⡄⠀⠘⠁⠀⠀⣾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠠⠠⠤⠔⠙⠂⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⢀⠳⠄⠠⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⢀⡀⠀⠀⢀⠃⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⡀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠂⠁⠉⠳⠤⠤⡤⠔⠢⣄⣀⣠⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣆⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣇⠙⣿⣷⣤⣤⡆⡾⠉⣦⠄⢸⣶⡄⠀⠀⠤⣾⣿⡄⠀⠀⡀
⠀⠀⠀⠀⠀⣄⡀⠐⠀⠀⠀⢸⡆⢘⣿⠹⣿⢹⠁⠀⠀⠀⣼⡈⡀⢶⡀⢭⣿⣿⣗⠀⢰⣧
⠀⠀⠀⠀⠀⠸⣛⣤⡀⠀⠀⢸⠇⢾⡌⠁⢹⡴⠋⠀⢠⣿⠈⠀⠓⢸⣿⣶⣾⣷⣿⣅⣺⣿⡄
⠀⠀⠀⠀⠀⠐⠙⢿⣿⣶⣄⡉⢀⠬⠓⠀⠍⠀⠀⠀⣼⠃⡀⠀⠀⢸⣿⣿⣿⣿⣿⣐⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣎⢻⡻⣽⣇⠀⠈⠀⠀⠠⠄⠀⠀⠢⠀⠀⢀⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠹⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠠⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⠉⠉⠛⠿⢿⣿⣿⣶⣤⣀⠀⢐⣿⠿⣿⠿⡿⣿⣿⣿⣿⣿⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣦⣤⣤⣀⣉⣬⠽⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⡙⠿⡛⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠠⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⠀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣶⣦⣴⣿⢿⠿⣿⣦⢟⣿⣶⣦⣄⣀⣤⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣸⣿⠿⠿⠿⣿⣛⣛⣛⣻⠿⢧⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣟⣛⣻⢻⣍⣭⣽⣼⣿⢿⡿⢾⣿⣿⣿⣿⣿⣿⣹⣿⣷⣄⡀⢀⣶⣿⣿⢻⣽⣶⣶⣿⣿⣿⠿⢏⠿⣿⡿⠿⣷⣮⣿⣦
⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣯⠿⣏⣯⣽⣤⣶⣿⣿⡿⣿⣾⣷⣾⣯⡝⢛⠿⣿⣿⣁⣾⣿⣿⣾⣿⢏⣼⣍⣽⣶⣶⣾⣛⠷⢷⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⡟⢻⠿⢛⣷⣤⣦⠿⢶⣜⣿⣿⣛⣻⣽⣙⠿⣿⡿⠞⢉⡙⢻⣭⠵⢞⣋⡰⣧⣤⠉⠙⢿⣿⣶⣝⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣙⣷⠿⡿⠋⠁⠀⠈⠉⠉⠉⠙⠛⠛⢏⡑⢄⡀⠈⠉⠁⠀⠠⠾⠟⣯⣿⣧⡹⣶⣆⠀⠉⠉⢹⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡙⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣮⣿⠆⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⢘⣷⡶⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣥⣴⣾⣆⠀⠀⠀⠸⣯⣾⣮⠿⣧⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⣷⣏⣡⢴⣿⣦⣾⠿⣿⣥⣿⠿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣅⣿⣷⡾⠛⠋⠀⠚⠉⠉⠙⠒⠀⠀⠈⠙⠛⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣖⣤⣴⣿⣾⣷⣴⣶⣾⣿⣶⣟⣿⡻⣦⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢰⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣥⡈⠭⢉⣿⣿⠿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣞⣿⣿⣿⣿⣬⣿⣿⣿⣿⡄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣾⣿⠃
⢠⣾⣿⣷⣤⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⠁
⠈⠻⣿⣿⣿⣷⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠿⠛⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧
⠀⠀⠈⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⣀⡤⣰⡶⣾⣶⣦⡈⠙⠻⡿⠛⠛⠛⠛⠛⠿⠛⣉⣡⣤⣤⣤⣄⣀⠈⠉⠉⣿⡇
⠀⠀⠀⣿⣿⡿⣿⣿⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡻⣯⢳⣽⣿⣶⡀⠠⢄⣀⣈⣤⠄⢠⣾⣿⣿⣿⣿⢿⣿⣿⣷⡘⢿⣿⡇
⠀⠀⠀⢸⣿⣷⠿⣿⣾⡿⠛⢁⣠⣤⣴⠚⠃⠀⣿⡿⣴⣾⣿⣿⣾⣿⣿⣿⣿⡄⠈⣿⣿⣿⣿⠀⣿⣧⣶⣿⣿⣿⣾⣿⣿⢿⣷⠘⣿⠁
⠀⠀⠀⠀⢿⣿⢶⢿⣯⠀⣤⣾⣿⣿⣿⠐⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡀⢿⣿⣿⡻⠟⠻⢿⣿⣿⣿⣿⠀⡿
⠀⠀⠀⢰⣿⡫⢂⣤⣻⣿⣿⣿⣿⣿⣿⡀⠀⡀⠈⠛⠛⠛⠀⠀⠀⢨⣿⣿⡟⠀⣼⣿⣿⣷⣾⣷⠈⢀⡉⠁⣀⣀⣴⣿⣿⣿⠃⣼⡇
⠀⠀⢰⣿⣿⣍⣾⣿⣻⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠲⠶⢾⣿⡿⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣇⠀⠉⠛⠿⠿⠿⠟⠛⢡⣾⣏⣷⡀
⠀⠀⢸⣿⣿⣿⣏⣿⣿⣿⣼⣿⣿⣿⣯⣾⣷⣶⡿⣿⣿⣶⣶⣶⣦⣤⣖⡿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣶⣦⣴⣶⣿⣿⣿⣿⣿⣯⡙⣿⡀
⠀⠀⠀⠻⢿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣬⣿⣿⣿⣿⣶⣍⢩⣍⣻⣿⣿⣿⣿⣿⣏⣛⢿⣾⣣
⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣹⣿⣿⣿⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣿⣻⣧⣴⣿⣿⡻⠿⣿⣿⣿⣿⣿⣯⣿⡿⡆
⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⣿⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣛⣿⣾⡿⣿⣿⣯⠇
⠀⠀⣼⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣎⣹⠟⠛⣻⣋⣻⣛⣭⣭⣷⣿⡟⠁
⠀⠀⢻⣿⣿⣅⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⣼⣭⣷⣶⣿⣶⣿⣷⣿⣿⠟⠻⠿⣦⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣄⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣼⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⠻⣿⣿⣥⣶⡾⠟⣿⣿⣯⣻⣿⣿⣿⣟⣻⣷⣼⣷⣿⣿⣤⡿⣿⣿⣿⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣼⣋⡀⠀⠈⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣻⢿⣷⣷⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⡤⣡⢅⠀⢀⠀⠀⠀⠀⠀⠀⢠⢁⠀⠀⠀⠀⠀⢰⣦⣀⡰⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠠⠤⠀⠈⠀⠀⠺⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠱⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠙⣯⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠴⠰⠆⠀⠠⠤⠀⠠⠄⠰⠄⠀⠀⡀⠀⠀⠄⠀⠠⠀⠀⢼⡴⣦⡄⢄⡰⠀⠀⠀⠱⠷⠀⠀⡐⠀⠀⠠⡄⣶⣄⠉⠁
⠀⠀⠀⠀⠀⠀⣀⢒⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡄⠒⣠⠐⢦⡤⠀⠀⠀⠉⠁⠀⠀⡄⠀⠀⠀⠀⢠⢞⣁⠑⠄⠀⠠⠖⠈⠀⠲⠶
⠀⠀⠀⠀⠀⢄⡩⡄⡍⢰⣿⠇⠀⢠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⢀⠰⠠⠄
⠀⠀⢠⣶⡄⠈⠙⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠁⠠⠀⢀⠀⡀⢀⠈⠀⠀⣤⠀⠀⡀⢀⠀⢀⡐⣨
⠀⠀⠀⢂⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠆⠀⠀⡤⣶⠆⢃⠀⣀⡀⠀⠀⠀⠀⠘⠿⠀⠸⡿⠁⠀⠈⠀⠀⠙⠎⠀⠀⢱⠇
⠀⠰⠶⣷⠶⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣬⡄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡀⢠⣤⡴⠀⠀⠀⡀⢀⡀⠀⠀⠀⣤
⠀⣄⠀⠀⢀⡀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⡊⠉⢠⣀⡦⣴⡂⡄⠀⢠⠀⢠⠴⣄⠀⢾⢟⠀⠈⠁⠀⠀⠻⠂⠈⠀⠀⠀⠀⠀⠏
⠀⣽⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠈⠀⠃⠙⠁⠙⠉⠉⠋⠉⠉⠁⠀⠀⠀⠂⠀⠀⢤⣆⠒⢸⠴⣪⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠈⠀⠉⠀⠀⠤⠀⠀⠀⡶⠶⠎⠀⠀⠀⠀⠢⠀⠀⢀⣺⣭⢸⠷⢺⢶⣂⡆⡶⢤⡦⣖⣡⠀⠐⠂⠀⠀⠀⠠⡐⢾⠀⠓⠃⠄⠀⠀⠀⠋⠀⠀⠁
⠀⢠⡈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⣹⣉⡱⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⢰⣿⣿⠂⠀⠀⠀⠀⢠⡄⠀⣠⠂⠀⠀⠱⡀⠀⠀⠀⠾⠂
⠀⢀⣟⣛⣧⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠿⢀⣤⣄⠉⠉⠀⠀⠦⠀⠀⡾⠀⠀⠐⠰⣿⣾⢾⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⣄⡄
⠀⠀⠿⠿⠏⠀⢠⣠⠤⣄⠀⢀⣀⡀⠀⢠⣾⣿⣿⣶⡀⠘⣾⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣌⣠⣦⠄⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⠀⡄⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢛⠄⠀⠀⠘⠘⠚⠙⠉⠀⠀⢰⣦⣀
⠀⣰⠀⡠⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⣤⣄⠉⠛⠟⠃⠀⠀⠀⠐⠂⠀⠆⠀⡿⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠸⡟⠀⠃⠚⠒⠂⠀⠙⠑⠂⠈⠛⠉
⠀⣿⢰⠃⠐⢃⠌⠀⠀⠠⣿⣿⡇⠀⠛⠋⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⣤⣤⠄⠀⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠃⠀⠀⠀⢀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⢠⠀⡤⡤⠖⣦⢠⣠⡅⣰⡀⣀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢰⣀⣰⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣀⠀⠀⠀⡇⠐⠀⠰⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠈⠀⠌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⡃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣹⣿⣿⣿⣿⣿⣧⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠐⠛⠉⢉⣽⣿⣿⣿⣿⣿⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⠎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠩⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⡀⢠⡞⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡽⠛⣿⢹⢿⣿⣿⢿⣇⢿⡽⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠘⠘⡏⠹⠹⢿⠟⠋⠱⠆⠠⠄⠸⠀⠄⠀⠀⠀⠘⠃⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠄⠘⠸⠿⠃⠈⠋⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠋⠀⡰⠣⡀⡐⢾⣿⡿⢾⡿⠿⠀⠀⠀⠀⠴⡃⠀⠀⠀⠀⢰⣇⠀⠀⠸⣿⠿⠃⠀⠀⠀⠠⢎⠀⠀⠀⢀
⣦⡼⠀⢸⢆⠈⠀⠉⢙⡀⠀⠀⠀⠀⢀⠀⠐⠛⠃⠀⢸⣿⡛⣻⣶⣦⡃⠀⠀⠀⠀⠀⡀⠀⠚⠚⠀⠀⠛⠂⠀⣀⣤
⣯⣽⠬⡀⠐⠼⢠⠈⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠱⢰⣿⣿⣿⣿⣿⣿⣁⢀⠄⢀⡄⠴⠋⠀⣀⣀⠀⠀⢀⠀⠀⠙⠙
⡿⠛⠊⣨⣬⠇⢂⢀⣠⣴⣤⣈⡀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣿⣿⠋⣰⣶⣦⣤⣥⣀⣀⠀⠀⠈⠂⡠⠀⠀⠠⠀⠀⠀⠦
⠀⠀⠀⠈⠁⣿⣷⣿⣿⣿⣿⣿⣿⣆⠀⢈⣀⡄⣀⠀⢻⣿⣿⣿⣿⣀⠋⠀⠉⠙⠛⠿⣿⢿⣦⡀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⠯⢐⠇⠆⠸⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠈⠉⠃⢰⠃⠀⣶⣶⡎⠀⠀⣰⣿⣿⣿
⠁⠦⠐⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣼⠖⠀⣠⣿⢻⡿⢿⣤⣀⣠⠙⠛⠛⢿⣷⢶⣤⣀⣀⣜⠀⢂⠙⣭⣥⡌⢀⡻⢿⣿⡷
⠐⠀⠁⠀⣙⣻⣿⣿⣿⠟⢿⠛⠻⠿⠿⠿⠻⢟⣸⣾⣿⣿⡿⠀⠠⠀⠋⠹⣄⠀⠀⠀⡀⠀⢹⢿⠟⠙⠃⠀⢢⡉⢿⣡⣸⣿⡯⠄
⠀⠲⠀⣾⣿⠟⠋⠿⡿⠆⠘⠃⢈⣥⢶⣤⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠉⠛⠛⠀⠀⠉⠓⠺⠋⢠⣿⠍⠂⣬⣿⣶⣿⣯⡥⠄⠀⢀
⡟⠠⡆⠀⠁⠀⠀⠀⢀⣤⡤⠤⣾⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠈⠀⢠⣤⣿⢙⣴⣿⣿⢟⢵⡟⣿⣿⡔⠂
⠀⢀⠠⠄⠰⠄⢲⣦⣿⡇⠈⢀⢁⣸⠋⠙⢈⡙⠻⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣤⣠⣾⣿⣧⣛⡛⠉⠐⠋⣼⣍⡈⢿⣿⡄⣻
⣷⠀⠖⢀⢀⡘⢾⣿⣿⡿⠶⠋⠂⠰⠦⠀⠀⠁⠀⢈⣿⣿⣄⠈⠀⠀⠀⠙⠟⠃⣿⡏⢹⣿⣿⣿⣿⡏⠃⠈⢃⣼⣿⣿⡿⡀⣙⡓
⠀⠀⠀⣾⡆⠀⢨⢙⣏⣴⣿⣿⠉⠁⣀⡀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣾⣶⣤⣀⣰⣿⣿⣿⣿⣿⣿⣿⣷⠂⢀⡾⡁⠉⢽⣶⣿⣤⣺⣿
⠀⠀⠀⢸⣷⠀⠀⠁⠀⣿⡏⠀⣀⣄⠙⠀⠤⠋⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠋⢀⣅⠈⠢⠙⠓⠄⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿