20 Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⡤⢤⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⢿⣿⣿⡄⢀⣾⣿⡿⠛⠛⢿⣿⣿⡄⠀⠓⠚⣽⢏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢸⣿⣿⠁⠀⠀⠀⣿⣿⣧⠀⠀⣼⠏⢿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⢸⣿⣿⡀⠀⠀⠀⠉⢁⣀⣀⠀⣀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣤⣤⡀⠈⢿⣿⣷⣤⣤⡄⢰⣟⠉⢹⡆⣿⠤⠄⣿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠙⠛⠛⠟⠃⠀⠛⠒⠛⠀⠛⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣟⣽⣭⣤⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⣭⣍⣛⣿⣿⣿⣿⡿⠛⢛⠂⠐⣀⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣟⣛⣿⣿⣿⢿⣿⣻⣿⣿⠿⡿⠿⢿⣿⣧⣄
⠀⠀⠀⠀⢀⣾⣿⡿⣿⡟⢻⣿⣿⣿⣷⣿⣿⢿⠿⣿⣷⣮⢿⡷⣦⣍⠻⢿⣿⣇
⠀⠀⠀⠀⣼⣿⣿⡇⣴⣿⣿⣿⣿⣿⠿⠛⠻⠿⡿⠛⠛⠑⠒⠿⠿⣯⡿⣦⡻⣿⣷⡄
⠀⠀⠀⠀⢹⣿⣿⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠈⠹⣿⣿⡜⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣄⠀⠀⠀⣿⣿⠇⠀⠀⢰⣤⠀⠹⣿⣿⣻⣿⡁
⠀⠀⠀⠀⢿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠸⣿⣷⠀⠀⠈⢿⣇⠀⠀⢸⣿⣇⠀⠸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣯⡿⣿⣿⣿⡇⠀⠀⠀⠹⠃⢀⣄⡀⠘⠟⠀⣶⡄⢻⡿⠀⠀⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠈⣿⣷⣻⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⠄⠀⠀⣿⣿⠈⠋⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⢺⣆⠀⠹⣿⠀⢤⡀⢹⣿⠀⣤⡀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⡆⠀⢸⣿⣆⠀⠁⠀⢸⣿⣌⢿⠀⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⢿⣇⡀⠂⠈⢸⣿⣿⠀⠘⣿⣿⣾⣿⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠂⡄⣷⡄⢀⡘⢿⣿⣆⠀⠘⠋⣿⣿⣿⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣗⠱⠀⣿⣿⠆⠀⠼⢻⠟⢸⣯⣐⣿⣾⣿⣶⣾⣵⣤⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣥⣤⣬⣄⣀⠈⡉⠀⠀⠀⠈⠔⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⢿⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣶⣶⡶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣦⠈⠛⠃⠸⡘⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠛⢻⣿⣿⣿⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣯⣿⣿⣿⡟⠛⠻⣿⣿⣿⠛⣿⣻⡀⣀⣠⢧⣶⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣯⣻⣿⣿⣧⡀⠀⣿⣿⣿⣶⣿⣿⡿⢙⣿⡿⠿⠿⡟⠻⠋⠣⠶⠶⢤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣶⣤⣙⣿⣿⣿⣛⠗⠺⠻⠶⣤⡀⠀⠁⠀⠀⠀⢀⣀⣀⡈⢳⣴⣀⣀⣀⣀⠀⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⠀⢀⣀⣈⣽⣷⣿⡟⠛⠉⠉⠀⠀⠈⠉⠙⢿⣿⠟⠋⠁⠉⢻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⡟⠉⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣴⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⣿⣿⣿⣦⣀⣹⣷⣶⣦⣴⣾⣤⣠⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣱⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠈⠻⢿⣷⣿⣿⣿⣿⣿⣯⡄⠀⣼⣿⣿⣿⣻⣿⣿⡿⣿⣟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠘⠿⠿⠻⣿⣿⣴⣰⣼⡿⢿⣿⣿⡿⢧⣴⡿⠿⠿⢿⣿⣆⣿⡿⠁⠈⠁⢀⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠀⠀⠀⠀⠈⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣷⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣼⣿⣿⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠋⠙⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⣩⣾⠋⠀⠀⠀⠀⠙⣷⣍⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⢀⣼⠟⣁⣀⡀⠀⠀⢀⣀⡈⠻⣧⡀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢛⡉⠀⠀⢀⣴⠟⠁⠾⠋⢉⣿⠀⣼⡏⠉⢻⣆⠈⠻⣦⡀⠀⣠⠍⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⢁⡔⢹⠣⠂⣰⡿⠋⠀⠀⢀⣴⠞⠁⠀⢿⡇⠀⠸⣿⠀⠀⠙⢿⣎⠉⢶⠦⣄⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣤⣄⡀⠈⠠⠟⣡⡾⠋⠀⠀⠀⠰⠿⠷⠶⠶⠀⠈⠻⠶⠾⠋⠀⠀⠀⠀⠙⢷⣄⠻⠏⠀⢀⣠⣤⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⡉⠛⠷⣦⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣴⠾⠛⡉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢨⠟⡔⠀⣾⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣷⠀⢉⣥⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⠋⢠⠇⣸⡟⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢻⣇⠸⣄⣧⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠞⣾⢠⡿⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣾⣿⠁⠈⣿⣷⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⢿⡄⠉⣹⠄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠘⣿⣶⣴⣿⠃⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠘⣿⠀⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⡏⠀⠀⢀⣀⡀⠀⠘⢿⡄⠀⠀⠀⣾⡟⠁⠈⢻⣷⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⡿⠀⢠⣶⠟⠉⢹⡆⠀⠈⢿⣄⠀⠀⠻⣷⣤⣤⣾⠟⠀⠀⣠⡿⠁⠀⠀⢶⣦⡀⠀⠀⠀⢿⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⠃⠀⢸⣅⢀⣠⣾⠇⠀⠀⠈⢻⣆⠀⠀⠀⠉⠉⠁⠀⠀⣰⡟⠁⠀⢀⣀⣀⠉⠻⢷⡶⠀⠘⣿⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⠀⠀⠙⠛⠉⣀⣤⣶⠇⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⣴⠋⠉⣿⢷⡄⠀⠀⠀⠀⠸⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠐⣿⠋⠁⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⣼⠟⠀⠀⠀⠻⢶⠶⠋⣠⠏⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣄⣀⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣠⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⣍⡉⠛⠛⠛⠿⠷⠶⢶⣶⣦⣤⣤⣤⣹⣷⣾⣏⣤⣤⣤⣤⣶⡶⠶⠾⠿⠛⠛⠛⢉⣩⣽⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⠀⠀⠀⣠⡶⠀⣌⠉⠉⢹⡏⠉⠉⣡⠴⣦⣀⠀⠀⠀⠀⣀⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡘⠋⣠⡤⠶⠟⠂⢸⡇⠀⠾⠁⠚⣉⠟⢁⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⢸⡇⠀⠀⠀⣉⣥⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⣸⣇⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠒⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⡠⢛⡽⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⢀⢀⡤⠒⠀⠀⢀⣀⣀⠄⢚⠕⡉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢁⠄⠈⠀⠀⠀⠀⠀⠀⢉⣀⣄⠶⠶⠿⣋⣀⣀⠄⠀⢀⡰⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣰⠟⠀⠀⠀⠀⠉⠑⣚⡿⠟⠛⠛⠓⠒⠈⠀⡀⠤⠀⠁⢉⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠺⣦⣧⡟
⠀⠀⠀⠀⣤⣤⣾⣀⣀⣀⣀⣀⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠬⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⢠⠔⠒⠀⣢⣖⠋⠉⢀⠈⠉⠁⠋⠀⠀⢀⠀⠂⠀⠆⠀⠀⣉
⠀⠀⠀⠀⠈⠀⣰⢛⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠠⠆⠀⠀⡀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⣀⡀⠀⠀⠀⠰⠀⠀⠀⢁⠰⠒⡄⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠆⠀⠔⠁⡐⠀⠘⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡀⢀⠀⠀⠀⢀⣎⠤⠀⢀⠀⠀⠐⠃⠀⠀⢀⣿⠶⠄⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣷⣤⠤⠊⠀⠐⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣷⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⡀⣹⠃⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠂⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⡄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠒⣀⠠⣼⣷⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠃⠀⠀⡸⢁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠔⠉⠀⠀⠀⠈⠃⡤⠤⡒⠠⠄⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⢀⡟⠑⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠐⢶⣌⡆⠀⠠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠈⣆⡆⡜⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠔⠒⣿⣿⡆⢀⠈⠁⢀⡆⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⡸⡆⢻⣇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠔⠋⠉⠃⠈⠀⠀⠀⡄⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠛⣿⣿⢃⣾⣿⣿⣿⠟⠛⠛⠛⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⢀⣼⡇⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡄⣿⣿⣿⣇⠀⠂⠀⠃⠂⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇⠸⣿⣿⣿⣆⡀⠀⠀⠀⢀⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⠻⢿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⣭⣽⣶⣶⣿⡿⣿⢿⡿⣯⣟⢛⡻⠿⢻⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠿⡿⢿⣟⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⣿⣯⣭⣽⣉⡩⢭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⠦⠁

⣿⣿⣿⣿⢹⣧⠙⢧⣹⣷⡙⢦⡙⠻⢶⣶⣦⣿⣿⣿⣿⣾⣿⠋⣴⣿⣿⠿⣋⣵⣿⣴⣿⡿⣃⣴⣯⡾⠃⣠⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠻⣷⡀⠙⣿⣿⣿⣿⣷⣦⣀⠉⠻⣿⡌⢻⣿⣿⣼⣿⣿⣷⢟⣭⣽⣿⣿⣿⣿⣿⣿⢋⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠻⣿⡄⢸⡿⣠⣈⡉⠛⢿⣷⣄⣿⣇⣿⣿⣿⣿⣿⣿⣵⣿⣿⠿⠛⢉⣡⡄⣿⣧⣿⡿⠋⣰⡿⢱⣿⣹⣿
⣿⣿⣿⣿⢿⣷⡄⢹⣷⣾⠇⡿⣬⡝⠳⣄⠈⠻⡿⠟⠛⠛⠛⠛⠛⠿⢿⠟⠁⣠⠞⣩⡣⣿⢸⣿⠏⣠⣾⠟⠁⣾⢣⣿⣿
⣿⣿⢿⡿⣧⡻⣿⣆⢿⣿⢸⡇⡏⢯⣽⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⣽⣿⡿⢸⢸⣿⣾⠟⠁⣠⣾⣷⣿⣿⣿
⣿⣿⡎⣿⡌⢻⣾⣿⣿⣿⣾⣇⠿⢫⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠿⣸⣼⣿⣃⣤⣾⣿⡿⣋⣽⣿⣿
⣿⣯⣿⣾⣿⣦⡙⢿⣿⣿⣿⠿⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⢿⣿⣿⣿⣿⣿⣵⣾⡿⣫⣿⣿
⣿⣭⠛⠻⢿⣿⣟⠳⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢟⣿⣿⣯⣾⣿⣿⢿
⣿⠶⢖⣒⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⡞⠋⢹⡶⣄⠀⠀⠀⠀⠀⣤⢾⡏⠙⢧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣶⣾
⣿⣿⣿⣿⣿⡿⠿⠒⠒⠉⠀⠀⠀⠀⠀⣇⠀⣾⡇⠘⡇⠀⠀⠀⢸⠁⢸⡇⠀⡸⠀⠀⠀⠀⠀⠀⢒⠚⠿⣿⣿⡿⢿⣿⣾
⣿⢋⣴⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠦⣼⣃⡴⠃⠀⠀⠀⠘⢦⣸⣧⠜⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣗⠮⣽
⣿⣟⣥⣾⡿⢃⣠⠴⣶⣶⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠊⠯⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⣶⡶⢤⣄⠙⣿⣿⣿⣷⣾
⣿⣻⣿⣿⣷⠟⢡⡾⠋⠁⢀⣼⣿⠉⠛⠶⣤⣀⠀⠀⠀⢀⣦⠀⠀⠀⠀⣀⣤⠶⠛⠹⣿⣧⠀⠈⠙⢷⡈⠻⣼⣿⣯⣿⣿
⣿⣿⡟⢻⣿⢠⡟⠀⠀⠠⠚⢁⣾⠀⠀⠀⠀⠉⠉⠛⠻⣽⡿⣭⠛⠛⠉⠉⠀⠀⠀⢠⣧⠈⠓⠄⠀⠀⠑⠀⣿⣿⣿⡟⣸
⣿⣿⡇⠘⣿⠈⠀⠀⠀⠀⠀⢈⣼⣆⠀⠀⠀⠀⠀⠀⣰⠃⣧⠹⡄⠀⠀⠀⠀⠀⠀⣷⣧⡀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⣿
⣿⣿⣿⡄⠹⣇⢸⣄⠀⠤⠶⢛⣽⣿⢀⠀⠀⠀⠀⣰⠃⡼⡟⢦⠹⡄⠀⠀⠀⠀⡀⣿⣯⠛⠒⠀⠀⣰⠆⣼⠃⠃⣼⣿⣿
⣿⣿⣿⣿⣦⡈⠈⢿⡓⢒⣶⡿⠋⢻⣿⢀⠀⠀⢰⢃⡞⠁⡇⠈⢧⡹⡄⠀⠀⡀⣷⡏⠙⢿⣖⡒⣛⠟⠐⠁⣀⣼⣿⣿⣿
⣿⢿⣿⣟⠻⠿⠿⣿⣿⣿⡿⠶⣦⡈⢿⡎⠀⠀⣯⡎⠀⠀⡇⠠⠀⢳⣿⠀⠀⢱⡿⢀⣴⠶⢻⣿⣿⣿⠿⠿⠟⣿⣿⠿⣿
⣿⣷⡙⢿⣆⢠⣾⣿⣿⡿⣿⣷⡌⣷⢸⣧⡀⠀⣿⡇⠀⠄⠛⠀⠀⣼⣿⠀⢀⣾⢁⡿⣡⣾⣿⢿⣿⣿⣷⡄⣸⡿⢡⣾⣿
⣿⣿⣷⠈⢿⣿⣿⣇⣿⣧⣿⡟⣿⣾⣾⡇⠙⢆⢹⣿⠀⠀⠦⠀⠀⣿⡇⡴⠃⢻⣾⣷⣿⢿⣿⣾⡏⣸⣿⣿⡟⠀⣿⣿⣿
⣿⣿⣿⡄⠸⣿⡨⢻⣿⠟⣿⣧⣿⣿⡿⠁⠀⠈⣾⣿⡄⠆⠀⠀⢸⣿⡿⠁⠀⠸⣿⣿⣯⣼⣿⠻⣿⡟⢸⣿⠁⢸⣿⣿⢹
⣿⠹⣿⣧⡀⢿⣿⣾⢛⡀⣫⣭⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠇⠀⠀⠀⢸⣿⣿⣭⡍⣪⣻⣷⣿⠟⢀⣾⣿⠏⣸
⣿⣷⣾⣿⣷⣦⣭⣛⣛⡿⢿⣿⣿⣿⣧⠀⠀⠀⠈⣿⣇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⠿⢟⣛⣩⣥⣴⣿⣿⣷⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⣸⡀⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢉⣤⣤⠀⢈⣹⣉⡀⠀⠀⢈⡙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⡵⠆⠠⣿⡿⠗⣀⣈⣽⣍⣁⣀⠐⠛⠶⢶⣤⡍⣓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠆⣀⣋⣠⣦⠴⠖⠚⢋⣉⣰⠏⢳⣈⣉⡛⠒⠾⢦⣄⣀⣍⠀⢬⡙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⣫⣥⡴⠿⠗⠛⠉⠉⠁⠰⠀⠀⠉⠉⣹⠃⠀⠀⢻⣍⣉⣋⠀⠰⠦⠈⠉⠙⠓⠿⠷⣤⣽⣷⢦⣄
⠀⠀⠀⠀⠀⠀⣴⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠠⠆⠀⠀⠚⠛⠋⣽⠃⠀⠀⠀⠀⠻⡍⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠙⠛⠻⢶⡄
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⠶⢦⡾⠁⠀⠀⠀⠀⠀⠀⠹⡖⠛⠃⠈⢡⣄⣨⡿⠖⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠀⠀⣰⠟⢹⡇⢀⡴⠀⠀⢀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠖⠂⠀⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠙⠂⠸⣷⡟⠁⡀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠂⠀⡀⠀⠀⢿⡛⣋⠀⠀⠀⢀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠘⣹⡀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢳⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠚⠁⠀⠀⠾⢿⡉⠀⠀⠀⣸⠉⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠙⣧⠀⠀⠀⢠⡀⠀⠀⢠⣤⡟⠀⠀⠀⡾⠋⠙⣧⠀⠀⣰⠟⠛⢶⡀⠀⠘⣷⠞⠀⡀⠀⠀⠀⠀⠀⢠⡏⠃⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠘⣀⢸⡄⠀⢀⠀⠀⢠⡀⢠⠏⠀⠀⠀⠀⠀⣠⡾⠃⠀⢠⡟⠀⠀⢸⡇⠀⠀⠈⢷⠞⢁⠈⠁⠀⢴⠀⣼⠃⠘⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣠⣼⡆⢷⠀⠈⢀⡀⠀⣹⠏⠀⠀⠀⠀⢠⣾⣁⣀⣀⠀⠀⢿⣀⢀⣸⠇⠀⠀⠀⠈⢷⡋⢰⠇⢠⡀⢰⡏⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⢻⠀⣁⠸⡇⢀⠈⢳⣴⠏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⢳⡟⠀⡾⠀⣾⡁⣼⢻⡸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⣰⠟⠀⢻⡈⣇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⠃⢸⠁⠁⠙⢻⠑⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠛⠂⠀⠟⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡟⠇⠀⠀⠈⢸⡇
⠀⠀⠀⠀⠀⠀⡿⢠⠀⢀⣀⣠⠿⢷⡶⣶⠶⠶⣶⠶⠶⡶⠶⢶⡶⠶⣶⠶⢶⡶⠶⣶⠶⢶⡶⠶⢶⡶⠶⢶⡶⢶⡿⢧⣾⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣷⣏⡴⠿⢯⡀⠀⠘⠻⣌⠳⣄⠉⣀⠀⠹⠄⠀⠁⠀⠛⠀⠀⠀⠀⠋⠠⠞⠀⢰⠏⢀⡴⢋⡴⠋⠃⠸⠉⠙⡿⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠻⢿⣗⠆⠀⢠⡴⠶⢤⠘⠳⣌⠃⠈⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⢠⠀⠀⠀⠀⠀⢈⡴⠿⠀⠤⠴⠞⠃⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡙⠲⠞⠁⠀⡈⠷⣄⠀⠀⠀⠀⠀⠻⣤⣤⣤⡟⠀⠀⠀⠀⠀⢀⡴⠛⣠⣤⠤⣤⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣿⠟⠛⠂⠈⣷⣄⠀⠀⠀⠸⢯⣤⣬⠗⠀⠀⠀⠀⣴⠟⠃⠸⠷⢋⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣴⡿⢦⡀⠀⠀⠀⠀⣠⠾⣗⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣦⡀⣠⣾⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⣿⢿⠿⠿⡿⣟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢆⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⡘⠀⠄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⠉⣴⣿⣿⡿⠗⠉⢋⠉⠙⠁⠀⠉⣡⣤⣄⢀⡀⠈⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⢇⣬⣥⣭⡹⣄⠹⠿⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⣿⡿⠃⣹⡷⠀⣿⢾⣿⣿⣿⣟⣷⣶⡄⠀⠀⡈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⣸⠁⡀⠀⣩⣷⡏⣰⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣶⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⢸⡟⢾⣿⣏⣠⣥⣼⣿⣛⣟⣛⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⡀⢹⣿⠋⠁⠀⠂⠙⠀⠉⡛⢿⣷⣦⡄⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⠐⣥⡾⠃⠄⠈⠛⠀⠀⠀⠀⠐⠰⡦⡉⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣙⢤⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⣿⠀⢰⣦⡀⠀⠈⠀⣀⡀⠁⠀⠀⠀⣀⠀⠆⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⢸⣿⣃⠀⠀⠀⠈⠙⠲⠖⠂⢹⣿⢷⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠁⢸⣿⣋⡓⣶⡶⠦⣀⡀⢀⣸⡿⣿⣆⠀⢊⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⣿⡿⣿⣿⣿⣿⣗⣀⣛⢋⡿⣿⣿⣿⢿⠀⣘⠧⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠛⠻⠷⠛⠋⣿⡻⣿⡋⠉⢉⣿⣿⣿⣿⢿⡀⠑⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢻⣷⡷⢠⣇⢨⡦⠂⣠⣄⡀⠀⠉⠉⠘⢣⡱⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⣟⡀⢀⣀⣀⡴⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⡿⠾⠿⠶⠀⠀⠀⠸⢦⣿⠿⢿⢟⠁

⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣤⣤⣤⣤⡄⠀⠀⠠⣤⣤⣶⣶⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠨⠤⠀⠤⠬⠄⠀⠠⣤⣤⣭⣥⡤⠀⠀⠀⣤⣬⣭⣥⡄⠀⠀⠤⢤⣭⣭⠭⠀⠀⠀⠠⢤⣬⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠠⣤⣤⣤⡄⠀⠀⠀⣤⣤⣤⡤⠤⠀⠀⠠⢤⣤⣤⣤⠄⠀⠀⢤⣶⣶⣶⣶⠀⠀⠀⠐⠶⢶⣶⡖
⠀⠀⠐⠶⠶⢶⡦⠀⠀⠀⠤⠴⠶⠶⠖⠀⠀⠠⠶⢶⣶⡶⠆⠀⠀⠠⢤⣶⣶⣶⠄⠀⠀⢦⣤⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠐⠶⠶⢶⠆⠀⠀⠐⠲⠶⠶⠶⠆⠀⠀⠠⢤⣴⣶⣶⠀⠀⠀⠚⠲⠶⠿⠋⠀⠀⠀⠒⠶⠶⠶⠦
⠀⠀⠘⠓⠶⠶⠶⠀⠀⠀⠒⠶⠶⠶⠶⠀⠀⠐⠲⠀⠲⠾⠆⠀⠀⠒⠶⣶⣶⠿⠀⠀⠀⠑⠒⠶⠶⠶


⠀⠠⠶⠶⠶⠖⣒⠀⠀⠈⠛⠛⠛⠛⠃⠀⠈⠻⠿⠛⠛⠒⠀⠀⠀⠚⠿⠿⠿⠇⠀⠀⠀⠶⠶⠿⠷⠆
⠀⠀⠛⠛⠛⠋⠉⠁⠀⠀⠛⠀⠛⠛⠛⠀⠀⠘⠿⠿⠿⠿⠖⠀⠀⠐⠛⠛⠿⠿⠇⠀⠀⠙⠛⠛⠛⠋

⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡟⣿⠇⠀⠀⠀⠀⠀⢀⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⡇⠋⠀⢄⠀⢘⡿⠿⣿⣿⣿⣿⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⢀⡀⢀⡔⠂⠉⠞⡸⠎⠀⣶⣤⣀⠙⣿⣷⣤⠀⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣦⠈⠂⡌⠀⠠⠀⠂⡀⠈⠄⢌⡙⠛⠋⠏⠉⠉⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⡯⠂⣀⡑⠄⠀⠘⡧⣀⠠⢆⡸⢨⣄⠀⠆⠀⠠⢛⣽⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠭⢤⠰⣶⣙⣷⣼⡆⠀⡕⠁⠀⠀⠀⡀⠉⠑⡄⠀⠈⠙⢿⡷⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢠⣸⠀⠠⢋⠟⢫⣁⠉⢁⠢⡈⠃⣀⣬⠀⡀⡈⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢘⣆⠀⠃⠀⣠⠽⠜⠃⠀⣎⣰⠝⢃⠚⠄⡨⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣆⠸⣄⠈⠋⠈⠁⠰⢃⡠⠈⠀⢀⣀⠻⡫⢰⡔⢈⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣾⠁⠓⠀⣈⠀⠀⡇⠈⠃⠛⠋⠀⢣⠊⠀⢺⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢰⠀⠘⠟⠟⠀⠀⢀⠠⠀⠸⠇⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠏⠉⠉⠉⠉⣉⡉⠉⠉⠹⣿⣿⣿⠋⠉⠉⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢁⣀⡀⠀⠀⣾⣿⣿⡆⠀⠀⠈⠉⠀⠀⢠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠅⠀⠀⡀⣀⣴⣶⣶⠄⠄⠊

⣿⣿⣷⣀⠀⠈⣳⡸⣴⡛⠒⢛⣴⠨⢙⡮⠿⣯⣾⣿⣿⡿⣿⣎⣻⣯⣭⡝⠃⠀⠸⡏⠠⡇⠈⣿⠈⠻⠇⠙⠻⢯⢶⣆⡿⠃⠡⡾⠃⠀⡛
⣿⣿⣿⣿⣿⣿⣥⣠⣘⠛⠐⠀⠓⢦⠀⢻⢦⣿⢯⣼⢿⣷⣽⢿⢻⣩⣿⣧⡔⠘⠂⡶⠀⠐⠀⣄⠀⠀⠀⠀⠀⠘⡿⠁⠀⢦⠀⠁⣀⡠⢿
⣿⣿⣿⣿⣿⣏⢛⣧⣌⢶⣦⣠⣀⠀⠠⠉⢀⣆⣽⠾⢾⣿⠷⠾⢷⣭⣝⠰⠁⢠⣴⣿⣿⣷⣷⠀⠀⣀⠀⠀⢀⡀⠃⠀⠰⠀⠈⣧⠉⣠⣶
⣿⣿⣋⣉⣉⡽⠋⣿⡇⣬⣥⡏⠀⢀⠀⢀⡸⢯⠉⠓⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⢃⠀⣿⢡⠋⠂⠠⠍⠒⢠⠀⠉⠐⠀⠀⠠⢾⡟⠋⠉
⣿⣿⣿⣿⣿⣧⣾⣿⣛⣋⣡⣶⡯⠧⣄⣮⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠏⠀⠁⠀⠀⠺⠇⢠⡄⠀⡙⢸⡖⠀⠂⠀⠚⠁⠀⠐⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⡬⠇⠋⠀⠀⠈⠛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣁⣧⢰⠃⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⡇⣤⣤⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣤⡤⡟⣝⣰⣟⣟⡦⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣇⣤⡀⣠⡀⠀⠀⠀⠠⠴⠒⠒⠀⠀⠀⠀⠀⠐⠆⠀⢀⣩⠤⠃⣟⢩⠾⣼⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠀⠀⠀⠀⠐⠶⠠⠀⠀⠀⠀⠃⢀⠀⠐⠦⠀⠀⠀⢛⣀⢔⡇⠀⠐⠂⠀⠀⠀⢶⣆⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣥⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⢡⣤⠰⣌⡐⠘⠁⠀⠀⠀⠀⠀⠀⠤⠻⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⢎⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠶⢠⡔⠁⠀⠀⢀⠀⠀⠐⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡵⡛⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠆⠈⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢯⣾⠁⠀⠀⠀⠀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣸⠶⠀⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⢎⠟⣷⡶⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠋⠠⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⠷⠦⢠⢀⠀⠀⠀⠀⣠⣭⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠺⢫⣦⣧⣀⢀⢹⡚⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠙⢩⣤⣸⠥⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣳⡟⢠⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢰⢉⣼⣧⡖⠀⠈⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢘⠠⢤⣀⣸⡾⣇⣙⣿⡧⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⡐⢄⣶⡿⠏⣋⣿⡟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠾⡅⠀⠺⣪⣿⠏⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠴⣓⡛⠂⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢙⡻⠛⠛⢿⣷⣤⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠀⠻⣿⣷⣾⣷⣤⣤⣶⣽⣧⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⠼⡄⠀⠀⠈⢪⡹⣓⠶⢿⣿⣭⣛⣹⣿⡏⠘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠖⠤⠔⠛⠈⠀⠀⠀⠀⠀⠀⠀⠙⠢⣑⣄⠈⣩⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢦⡀⠀⠀⠀⠈⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠄⢀⢸⡅⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⢠⡽⣶⠤⣄⠸⣟⠕⠋
⠀⠀⠠⢒⣴⣾⣥⡃⡀⠀⠀⠀⠀⠀⠠⣠⠾⠋⠁⠀⠀⠀⠀⣠⣶⠿⠋⠀⣠⣮⠋⠁
⠀⠀⠀⠙⠻⢯⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⢀⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⢄⡀⠀⠀⠀⠤⠾⠋⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠐⢢⢈⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⡸⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣏⣽⣇⠻⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⣽⣛⣛⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⣾⡿⠁⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢾⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣖⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣆⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⡞⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡄⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣥⣿⣽⣿⡌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⡹⠿⣿⣿⣿⠦⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⡜⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣾⡟⠛⠛⠛⠛⠛⠛⠋⠓⠒⠒⠒⠒⢶⣶⣶⣶⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⢀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠔⢺⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠢⠠⠬⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠁⠀⠀⠀⠀⠀⣠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢸⡇⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢋⣥⣤⡀⠀⢸⡇⠀⠀⠀⢀⡝⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣩⠖⠠⣾⣿⠟⢀⣀⣸⣧⣀⡀⠀⠛⠷⠶⣤⣌⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⢋⣁⣤⠤⠶⠒⠛⠉⢡⠟⠻⡌⠉⠛⠓⠶⠤⣤⣀⡀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣛⣁⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣌⣙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠙⠛⠻⠷⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣄⣀⣽⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣾⢻⡀⠀⠀⠀⢠⡟⠙⣇⢀⣴⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠙⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿
⠀⠀⠀⠀⠀⠀⣿⠈⣧⠀⠀⠀⠘⠃⠀⣿⡾⠁⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢲⡟⢛⠁⠀⠀⠀⣸⠁⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢹⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠰⠿⣏⠀⠀⠀⢠⡏⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣴⠟⠙⣷⠀⠀⢠⡾⠛⢳⡄⠀⠈⢳⡀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢀⠸⡆⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠁⣀⡴⠏⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⣠⣼⡇⢿⡀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣼⣋⣀⣀⡀⠀⢻⣄⠀⣠⡟⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⢻⡀⣁⠘⣇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⠃⢠⡟⣇⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠂⢻⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⡟⠀⠈⠛⡏⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠻⠆⠀⠈⣧⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣸⠁⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⡼⢷⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣾⠧⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⣀⡤⠖⠋⠁⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⠳⢤⣀⣻
⠀⠀⠀⠀⠀⠀⠻⢯⣀⠀⠀⠀⡴⠶⢤⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡤⠶⠟⠀⠀⣀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡙⠶⠾⠃⠀⡈⠳⣄⠀⠀⠀⠀⠀⠸⣧⣤⣠⡿⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⡤⢤⡀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣾⠞⠻⠆⠈⠳⣄⠀⠀⠀⠀⢿⣥⣬⡿⠀⠀⠀⠀⣠⠞⠁⠠⣯⠞⣡⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡘⢧⡀⠀⠀⠀⠀⢀⡼⢋⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢽⣦⡀⢀⣴⡯⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣿⡋⣿⣿⣿⡗⢰⣤⣤⠀⡀⠀⢀⣴⠶⠟⠡⢄⡐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⡶⠒⠀⠀⠀⠀⡄⠀⣶⠀⠀⠀⠀⠀⢨⣷⢸⡇⠈⢿⡿⠁⠸⣿⡇⠀⣿⣶⡏⠁⠀⠀⠀⠀⢹⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠿⠆⠀⠀⠀⠀⠎⢀⣴⠟⠂⠀⠀⠀⠀⠈⢛⢸⣧⢠⡘⣿⠀⠀⣿⠐⢸⣿⠉⢀⡴⠄⠀⠀⠀⠈⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣿⡿⠸⠀⠀⡀⠀⠀⠀⠀⢾⣿⡶⢶⣿⣀⣀⠀⠀⣾⢸⣿⡆⢡⢻⡇⢐⣿⢁⣾⣿⣴⣿⣀⡴⣂⣀⣀⢠⡖⠁
⠀⠀⠀⠀⠀⠀⡀⣌⠓⠦⢸⡇⠐⠀⠋⠀⠂⠀⣠⡴⠚⠁⠀⠀⠀⠄⠈⣧⡌⣿⣿⣯⣿⣆⣯⣷⣼⣿⣿⣏⣹⢹⡍⣿⣿⣿⠛⠉⣾⠇⡀
⠀⠀⠀⠀⠀⠠⠁⠤⠈⣀⣦⡇⢰⠀⠀⠀⣠⡾⠁⣴⡀⣀⣤⣤⣤⡠⠞⠓⠂⠉⣿⣿⣿⣿⣷⣿⣿⣿⡿⠧⠷⡾⠧⣝⣿⣿⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⣂⣤⣴⣿⣿⢸⡄⢠⣾⡟⢠⣧⠛⣿⢻⣟⠿⠹⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢜⣿⣤⣎⣹⣿⣿⣿⢀
⠀⠀⠀⠀⠀⣆⣤⡹⣿⣿⣿⣷⢸⣇⣿⣟⢀⡏⢿⠀⠘⠀⣅⡆⠀⡀⠀⠀⠈⠁⠈⢻⣿⣿⣿⣿⣿⣿⣯⣷⣼⣏⣼⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣷⡝⣿⣿⡟⢸⣿⣿⣿⡘⡛⢿⡄⣤⠀⢸⡇⡼⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡜⣿⣷⢸⣿⣿⣿⣦⣧⡀⠁⣿⠀⠈⣿⠃⡄⣠⠁⠀⠀⢹⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣦⣥⡴⣿⣿⣿⣿⣿⡇⠀⡄
⠀⠀⠀⢴⣠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣥⣿⣆⢰⣿⢸⣵⣧⠀⢀⣠⣼⣿⠟⠏⠄⠀⣀⣠⣄⣈⣙⣛⡛⠛⠿⣿⣿⣿⣿⠃⠰⠁
⠀⠀⢀⠈⣹⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣥⣶⣿⡿⢿⣷⣾⣾⣿⢯⠿⠋⠋⠀⠒⠻⣿⣧⡀⣿⣿⣿⣟⣀
⠀⠀⠸⣈⢿⣿⣿⣟⡡⠊⢀⡴⠟⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣦⣌⠛⣿⠃⠀⠀⣀⠀⠀⠀⠀⢸⡿⠁⣿⣿⣿⣿⣯⣀
⠀⠀⠀⠻⣿⣿⣿⡟⢡⣾⠟⠑⠊⢡⢃⣅⠎⣿⡿⢹⣿⣿⠉⠛⡷⢈⢀⠈⣷⠻⣿⣝⠿⣿⡄⠀⠠⠀⠀⠀⢀⣴⡿⠁⣼⣿⣿⣿⣿⣏⠌⠃
⠀⠀⠀⠀⠀⣿⡿⢁⠸⡏⠘⠀⡀⠁⠀⠈⣤⣿⠁⠙⢩⢹⡿⢿⣱⣜⠃⠀⣦⠀⣻⣿⡷⣦⣉⠛⠓⠲⣶⣮⡟⠉⣠⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣸⣿⣿⡉⠀⣧⣀⣼⣇⠀⡀⢘⣿⡇⡸⢈⣰⡾⠿⠋⢻⣿⣷⣤⣿⣿⡿⠿⢧⡀⠙⣿⣶⣿⣿⣿⣿⣟⡩⣀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⣿⣿⣟⣿⣾⣿⣤⣣⣿⣿⣂⠀⡤⢀⣿⣿⣷⣿⠷⠍⠶⠀⠙⣦⡈⣻⣿⣿⣿⣿⣿⢛⣏⣿⣿⣿⣿⣿⣿⢿⡆
⠀⠀⠀⠀⣿⣿⣿⣯⣔⣴⣶⣿⣿⣿⣿⣽⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⣠⣄⡀⠀⠈⠉⣻⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣽⣿⣿⣷⣆⣛⣠⣮⣭⣾⣿⣿⣽⡽⣿⡿⣿⣿⣿⣯⣶⣶⣶⣶⣆⠀⠀⠀⠉⠛⠈⠙⢦⣾⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡟⠏⢿⣿⣿⣿⣿⡿⠿⠟⠻⠷⣷⣤⠀⠀⠀⠀⣾⡿⢟⡉⢉⠟⠉
⠀⠀⠀⢠⣾⣿⣿⣿⠿⠟⢀⣯⠯⢿⣽⣿⣿⠛⠿⠻⢿⣿⣤⣴⣶⣿⠟⠋⡝⢨⣿⠦⠦⠐⠀⢀⠙⣿⣤⣤⣾⡯⠚⠉⠀⠂
⠀⠀⠀⡾⠉⠈⣿⡃⠀⠀⠀⠀⠀⠀⠨⠿⣅⡠⠙⠂⠄⠉⣍⣩⣄⠴⠶⡁⣰⣿⣇⠀⠀⠀⡉⠙⠛⠛⠛⠋⠁⣀⣤⣤⣄⣀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠙⢷⣦⠄⠀⠀⠀⠀⠀⠀⠟⠉⠰⠶⠦⣤⣤⡤⠴⢶⠒⠋⠉⠁⠈⠂⠀⠀⠀⠠⣤⠤⠴⠒⠛⠋⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀⠀⣀⡴⠀⠀⠀⠀⠀⢀⣠⣦⣄⡀⠀⢄⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⣴⣆⠀⠀⠐⠀⣤⠀⠀⠐⠀⣶⡀⠀⠀⢸⣷⡤⠤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠿⠏⠡⠴⠛⠂⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠑⠾⠿⠿⠓⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡴⠛⣤⠎⠱⣤⠛⣦⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠓⣲⣶⠐⣲⣖⠒⠒⣲⠚⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠋⠵⣋⢘⣿⡯⠶⣾⣷⠶⢤⣉⣛⠲⠈⠝⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣩⠶⠴⠚⠚⠩⠉⠐⠒⡺⠃⠈⢟⣒⡒⠈⠭⠛⠓⠾⠶⣍⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠋⠉⠁⠀⠀⠀⠐⠂⠀⠘⠉⡽⠁⠀⠀⠈⢯⣉⣀⠀⡀⠀⣄⡀⠀⠈⠉⠙⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⡴⢦⠀⣀⠀⠀⠉⡝⠁⠀⠀⠀⠀⠈⢫⣠⡄⠐⣖⠛⠁⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠘⠃⢸⡶⠃⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢀⡀⠀⣶⣚⠀⠀⠀⣏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⣇⠀⠀⠀⠀⠁⠀⢉⡟⠀⢀⣠⣄⠀⠀⢀⣀⡀⠀⢻⣉⡀⠀⠛⠯⠀⠀⢸⡅⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡿⣾⡀⠀⠘⠀⡀⢈⠟⠀⠀⠘⢁⡼⠃⢠⡏⠀⢹⡆⠀⠹⡤⠂⠐⠀⢠⢀⡗⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣤⣿⢧⠈⢁⡀⢨⠏⠀⠀⠀⢰⣯⣤⡄⠈⢧⣀⡼⠃⠀⠀⠹⡎⡴⢀⡀⣼⠃⡀⢸⡄
⠀⠀⠀⣤⣴⡦⢤⣄⣀⠴⠛⢬⣿⠟⠺⢦⣄⣱⣏⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡸⢠⠷⠸⣽⢸⠞⡄
⠀⠀⠀⣘⣾⣿⣶⢿⣯⡀⢀⡈⣯⢴⡺⠭⠒⠒⠀⠉⠐⠀⠊⠉⠿⢶⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡾⠆⠀⠘⢸⠚⣇⠀⠀⢠⣄⣀⣀
⠀⠀⠀⢻⡾⢏⣳⠚⠙⠛⣶⢟⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢕⠶⣶⠒⣲⠒⡲⢒⣞⢳⣇⣠⠀⢸⡏⣀⡹⢖⣟⡽⢷⡟
⠀⠀⠀⠀⠑⠺⡽⣄⣀⣨⣿⡁⡫⠂⠀⢀⡀⠀⠠⠤⠤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠁⠨⡛⢅⣚⣵⠃⣀⣨⡴⣛⠛⠫⠍⢁⡀⣼⢭⠗⠊
⠀⠀⠀⠀⠀⠸⡇⠈⢹⠋⢈⣻⡵⢠⢖⣩⡶⠞⠋⣿⢯⣉⠙⠓⠦⣕⡢⢄⠀⠀⠀⠀⠀⠀⢝⡶⣤⣄⣠⣿⣴⣩⡍⠥⠄⠀⢿⢸⠇
⠀⠀⠀⠀⠀⠀⢈⣩⠿⠚⠟⡿⣷⣰⡏⢻⣽⣾⣯⣹⡄⢈⠑⢆⢀⡼⠛⠲⢍⡢⣀⠀⠀⠀⠀⠈⠓⠉⠛⡻⠶⠶⢭⡧⠔⢀⠈⢛⣦⣤
⠀⠀⠀⠀⠀⠀⠉⠙⠷⣆⠐⠵⣨⠿⡲⠶⢿⣿⠿⠿⠷⣄⠑⣼⠉⠹⣄⣾⣠⠟⠺⣕⣤⡀⠀⠀⠀⠀⠐⠠⠬⠉⠽⣯⣤⣶⣟⣉⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠒⠠⢒⣁⣫⠗⠤⣌⣙⣛⣛⣇⢀⣹⣇⠀⣸⣏⡀⣸⣛⣺⣕⡦⠄⠀⢀⠀⠩⠭⠁⣾⣿⢿⡳⠈⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⡴⠖⠋⠉⠉⢧⣀⣠⠏⢠⠋⠔⣉⣟⠀⠋⣿⠙⠂⣹⣉⠳⠝⡿⣍⣓⡶⠤⢤⣭⣭⠥⡞⠉⠈⡗⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠋⠁⠈⠓⠒⠉⠲⠚⠁⠈⠙⠲⠿⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⡶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⡏⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣋⣍⠀⠀⠀⡇⠀⠀⢀⣍⡑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠩⠳⠝⢀⣇⠈⠇⠿⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⢙⠽⢃⡤⠚⠉⠲⣄⠻⢽⡟⠈⠳⡀⠀⠀⠀⠀⠀⡴⠛⠓⠒⠚⠋⠉⠉⡽⠹⡍⠉⠉⠛⠒⠒⠚⠲⡄
⠀⠀⠀⠀⠀⠀⣴⣁⡀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠙⠢⣄⠀⣀⣹⡄⠀⠀⠀⠀⡿⡀⢰⣿⣷⡆⠀⡜⠀⠀⠘⣄⠀⣤⣼⡆⠀⡼⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠉⢻⠀⠀⠠⣶⡆⠶⢶⣦⠀⠀⢨⠏⠁⠀⡇⠀⠀⠀⠀⡇⢳⠀⠈⠉⢀⠞⣤⣄⢀⣤⣈⢆⠈⠃⠀⢠⠃⡇
⠀⠀⠀⠀⠀⠀⡇⢠⡶⠈⣇⠀⠀⢸⡇⣠⣞⡃⠀⠀⡜⢀⢀⠀⡇⠀⠀⠀⠀⣿⡎⣇⠀⢠⠎⠀⣴⣟⢸⣇⣿⠈⢦⠀⠀⣎⡲⡇
⠀⠀⠀⠀⠀⠀⢧⠈⣤⡦⠸⡄⠀⠈⠁⠉⠉⠉⠀⣸⠁⠹⡾⢀⠇⠀⠀⠀⠀⡗⠋⠸⣠⠋⠀⠀⠉⠉⠀⠉⠁⠀⠈⢣⡼⠙⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠳⡈⠀⠀⡣⠤⠤⠤⠤⠤⠤⠤⡇⠀⠀⡠⠋⠀⠀⠀⠀⠀⢧⠔⠚⠙⢍⠉⠉⢉⡉⠉⡉⠉⠉⢉⠝⡙⠒⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡞⠁⠀⠀⣥⣶⡂⠀⠀⠘⣦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢾⡞⠳⣄⠸⠿⠃⠷⢀⡴⠛⣻⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢍⣉⠥⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣷⡀⠀⣰⡫⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣠⠔⠊⡽⠁⠱⡉⠒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⢰⠉⣠⠇⡜⠁⠀⠀⠹⡄⢷⣮⢱⠀⠀⠀⠀⠀⢀⡴⠥⠤⠤⠾⠿⠥⠤⣤⠊⡇⠀⠀⠀⠀⠀⠀⠀⢀⢎⣤⠙⡄
⠀⠀⠀⠀⢸⠘⢁⠞⠀⢰⣟⣿⠀⠘⣎⠘⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⢠⠏⠚⠿⠇⠘⣆
⠀⠀⠀⠀⢸⢠⠎⠀⠀⢸⣏⣿⠀⠀⠈⢆⢸⠀⠀⠀⠀⠀⣿⠀⠀⢰⣟⣉⠁⠀⠀⣧⣾⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢸⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⠀⠀⠀⠀⠀⣿⠀⠀⠸⣧⣸⠇⠀⠀⡏⠀⡇⠀⠀⠀⠀⡰⣡⢤⣧⠀⠀⠀⣼⣡⢈⢧
⠀⠀⠀⠀⠀⠙⠲⢄⡀⢀⣼⠃⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠁⠀⠀⠀⠸⠥⠽⠤⠤⠤⠤⠤⠤⠭⠭⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⣠⡴⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⠒⣲⡖⣒⡶⢦
⠀⠀⠀⠀⠀⠀⣰⢋⡇⠀⢶⡄⠉⠉⢓⠲⠦⣄⠀⠀⠀⢀⡴⠋⠴⠂⡠⢖⡠⠞⠁⣠⡘⣇
⠀⠀⠀⠀⠀⣰⠃⠘⡇⠀⣀⠀⢶⣦⠘⠛⠀⣿⠀⢠⣾⣥⣈⠭⠤⠭⣵⠋⢀⣄⠀⠻⠁⠸⡄
⠀⠀⠀⠀⢰⠃⡖⢀⣧⣀⡛⠃⠀⠀⢠⣄⠀⢸⠀⠘⣆⠀⢀⡀⠀⠀⠸⣆⠘⠛⠀⠀⢠⡄⢱⡀
⠀⠀⠀⠀⢿⠀⢀⡞⠁⠈⠉⠙⠓⠲⠤⢭⣀⣸⠀⠀⠸⡄⠘⠿⠀⠀⠀⢹⡄⠀⣤⡀⠘⠋⣨⠇
⠀⠀⠀⠀⢸⢀⡜⠀⠀⠀⣀⣀⠀⢴⣶⠀⣸⠏⠀⠀⠀⢱⡀⠀⠀⠰⣶⠀⢷⠀⠙⢁⡠⠞⠁
⠀⠀⠀⠀⢸⡟⠀⠶⠶⠀⠙⠋⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢷⣀⣀⣀⣀⣀⣘⣧⠴⠋
⠀⠀⠀⠀⠈⠉⠓⠲⠦⣤⣄⣀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠞⠛⠏⠉⠍⠉⢉⠋⠉⠻⢹⣲⡶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠏⠀⢁⣀⠀⠀⠘⢣⣤⡄⠀⠀⠈⢊⡓⠾⢻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠙⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣋⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣴⣰⡜⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣼⣠⣿⣧⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠞⠁⠀⠤⠤⠀⠀⠀⠀⠀⠀⣰⠀⠀⢀⡄⢸⣧⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡍⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡧⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣟⣡⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠿⣿⠿⢛⣫⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡶⢛⣿⣿⠿⠛⠩⣠⢀⣾⣷⣶⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⠀⠀⣠⡞⠑⣹⡏⡼⠀⠀⢰⡇⣸⣿⡿⢻⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡆⠀⡿⣿⣿⣿⠀⠁⠀⠀⠈⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣧⣽⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣷⡟⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣿⣅⣏⣿⣿⣸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡦⢻⣿⣿⣿⣿⡛⠛⣿⣭⣝⢿⣿⣶⡗⠆⠀⠀⠀⠀⠀⠿⢯⣵⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⣿⣿⣿⣷⣸⢿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⡄⣤⡤⣀⡀⠀⢾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠋⠘⠻⠃⢠⣭⠀⢯⠀⠺⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠶⠦⠂⠘⠻⣤⡄⠈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣤⣄⡀⠠⠀⠬⡿⢿⣿⣿⣿⣏⣿⣿⣿⡇⢿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣛⡛⠿⠛⠛⠛⠇⠐⠄⠊⢩⣿⣿⣿⣿⣷⢺⣿⢿⣙⣾⡟⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠂⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢠⣤⣤⣬⣽⣳⣾⣿⣿⣿⣿⡋⠻⠛⠿⠙⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣴⠶⠾⠿⢻⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⣷⣦⣴⣙⣹⣯⡹⣄⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣾⡝⣻⡏⢘⢛⣟⣻⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⣶⣿⣿⣿⣾⡿⢿⣿⣿⣼⠁⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣼⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⡿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⣸⣇⠀⠈⠙⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢉⣀⣀⠀⠀⠛⢻⡟⠓⠀⠀⠀⠀⢉⡛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣋⡅⠀⣰⣿⣿⣿⠁⠀⠶⢻⡟⠛⠂⠀⠀⣴⣾⣁⣤⡈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⣠⡾⠋⠀⠘⠻⠗⣛⣉⣴⣦⠶⣾⣷⠶⣤⣶⣄⣀⠈⢉⡉⠻⠿⠆⢠⣍⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⢋⠁⠚⢁⣈⣁⣠⣼⡷⠶⠟⠛⠋⢉⣀⣀⣼⠃⠘⣷⣤⣀⣉⡉⠛⠻⠷⢦⣤⣄⣴⣄⠀⢦⣌⠙⠳⢦⣄⡀
⠀⠀⠀⠀⣀⣤⠶⢛⣭⣀⣴⣿⠷⠶⠛⠛⠉⠁⠀⠴⠄⠀⠘⠛⠋⢉⣽⠃⠀⠀⠘⣿⡉⠉⠛⠛⠀⠀⢶⣤⠈⠉⠛⠛⠶⠿⣿⣦⣄⣩⣿⣶⣤⣀
⢀⣠⣴⣾⣿⠶⠶⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⣤⡴⠶⢶⡾⠁⠀⠀⠀⠀⠈⢿⡟⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⣽⣿⣦⣄
⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⠀⢠⡄⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠉⠀⠀⠀⣤⣠⣤⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⢸⡛⣧⠀⠀⠀⠀⠀⢠⣾⠋⢹⣧⠀⢠⣴⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠶⠶⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛
⢸⡇⣿⡄⠀⠀⠀⠀⢸⣧⠀⢸⣿⣰⡿⠁⠀⠀⠀⠘⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣤⠀⠀⠀⠀⠀⠀⣤⣶⠶⠿⠂⠀⠀⠀⠀⢠⡟⠙
⢸⢁⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⢦⣄⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣀⣤⠄⠀⠀⠙⣿⣤⣶⠀⠀⠀⠀⠀⣼⢷
⢸⠁⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⠚⠛⢿⡄⠀⠀⠀⠀⢰⣿
⣸⠀⠀⠉⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⣀⣼⠋⠀⠀⠀⢠⣾⠛⠉⢻⣆⠀⠀⠀⣴⡿⠛⠻⣶⡀⠀⠀⠘⣷⡾⠛⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠙⠃
⣻⠀⠿⠀⠸⣇⠀⠀⠀⠀⠉⠀⢀⡀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠁⠀⣀⣾⠇⠀⠀⢸⡟⠀⠀⠀⢹⣷⠀⠀⠀⠘⣷⣠⡾⠋⠀⠚⠀⠀⢀⡦⠀⣸⠿⠀⢶
⣿⠀⠀⢷⡀⢿⡀⠀⢰⡄⠀⠀⠈⠻⣦⡾⠃⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⢿⡀⣴⠆⢠⡀⠀⠘⠁⢀⣿⡆
⣿⢠⡶⢾⣧⠘⣧⠀⠀⠀⣤⡀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢼⣿⣤⣤⣤⣤⠀⠀⠘⢿⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⠈⢿⡅⢀⡿⠀⢠⡆⠀⣸⣇⠀⢀⡀
⣿⠘⣧⠀⣉⠀⢻⡆⠀⠀⠈⢷⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠃⠀⣾⠁⢠⣯⡀⢠⡟⣻⡄
⣿⠀⠉⢀⡿⠧⠈⣷⠀⢷⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡏⠀⣾⠉⠃⠘⠷⣿⡇
⣿⠀⢀⣾⡁⠀⢀⣿⡇⠘⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢰⣿⡀⠀⠀⠀⣾
⣿⠀⠀⠉⠁⠀⠘⠁⢿⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡿⠈⣃
⣿⠀⣤⠀⢀⡀⢀⣠⡾⢿⣶⠶⣶⡶⠶⠶⣶⠶⠶⠶⣶⠶⠶⢶⡶⠶⠶⡶⠶⠶⣶⠶⠶⢶⡶⠶⠶⣶⠶⠶⠶⣶⠶⠶⢶⣶⠶⣶⡿⢷⣤⡟⠀⠀⡀
⣿⣼⠏⣠⣾⣿⡋⠁⠀⠀⠿⢷⣌⠻⣦⡀⠙⠃⠀⠀⢻⣆⠀⠈⠃⠀⠀⣿⠀⠀⠉⠀⠀⠾⠃⢀⣼⠋⠀⣠⡾⠁⢀⣴⠟⣡⡾⠛⠇⢠⡿⠙⠳⣶⣟⡀
⣿⣿⣿⣉⡀⠉⠙⠃⠀⣀⠀⠀⠙⣧⡈⠻⡆⠘⠷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠞⢁⣴⠋⠀⠀⠀⢀⣴⡄⠀⠛⠉⠛⢶
⠈⠙⠷⣬⣉⠀⠀⠰⣟⠉⠛⢷⡄⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⠿⠿⢷⣄⠀⠀⠟⠀⠀⠀⠀⠀⠀⢀⣴⠏⠙⠀⠀⠛⠛⠋⠉⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠉⠛⢶⣤⣈⠛⠻⠛⠁⠀⢀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⣠⣴⡶⢶⣤⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣶⣶⠾⢷⡄⠈⢻⣦⡀⠀⠀⠀⠀⠀⢾⣏⣉⢉⣹⡇⠀⠀⠀⠀⠀⢀⣴⠿⠇⠀⣾⣡⡟⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠈⠉⢻⣦⡀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⢀⣰⣿⠁⠀⠀⠀⣉⣥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡈⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣚⠿⠷⣄⠀⠀⠀⠀⠀⠀⣠⡾⠟⣛⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣼⣷⣄⠀⠀⣠⣾⣫⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢲⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠫⣥⠄⣻⣃⠀⢼⣷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠚⠉⣜⢁⣚⡤⠦⡾⡦⠤⣄⣲⡟⠈⠹⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡵⠦⠚⠚⠩⠉⠐⠒⡿⠁⠹⣟⣒⠊⠩⠝⠛⠺⠷⣬⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠁⠀⠀⠀⠀⠂⠀⠈⢉⡝⠀⠀⠀⠘⣌⣀⡀⠄⠀⠀⢀⡀⠀⠉⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠛⣆⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠘⣦⠤⢀⣀⣠⠴⠛⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣇⠀⠁⠀⠈⠳⠄⢀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠈⢖⢀⠻⠀⠀⢼⢉⡇⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⡀⠀⢀⣀⠏⠀⠀⠀⠀⣤⡆⠀⠀⠀⠈⢧⡤⠘⠒⠛⠉⠁⡸⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⣀⠁⢠⣠⠏⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⢷⢋⠈⠀⠰⢠⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⠈⡇⠀⢦⣠⠃⠀⠀⠀⠀⠀⠀⠴⠷⠀⠀⠀⠀⠀⠀⢫⡼⢠⠆⡞⡈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠃⢹⠰⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⢰⠃⢿⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠀⠉⣷⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣏⡅⠈⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡥⠷⡉⠈⠳⣝⢆⠁⡀⠳⢀⣁⣘⣀⣈⣀⣃⡸⠁⠜⢁⢞⡵⠛⠸⠓⢾⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡤⠤⠖⠒⠚⠋⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠶⢤⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢺⡷
⠀⠀⠀⠀⠀⠀⠀⠻⡧⢂⣠⡤⠴⢾⡉⠉⠀⠀⠀⠉⠛⢽⣦⡀⣠⣾⠕⠋⠁⠀⠀⠉⠉⣹⣶⠦⣤⡀⡢⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣾⣤⣦⢿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⣴⢧⣦⣴⣷⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⠀⠫⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠢⠃⠀⠈⠹⢦⡀
⠀⠀⠀⠀⠀⠀⣀⣼⣡⡤⠤⡄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡤⠤⢤⣙⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢣⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢰⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋

⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣀⡄⢀⠈⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠡⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠀⢠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻⣾⣷⣷⡆⢃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡄⣸⡄⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠤⠤⣴⣦⣴⣦⣤⣀⠀⠀⠘⢿⣿⣷⣼⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⢰⣿⡇⠀⠀⢙⡿⣩⠟⢋⠤
⠀⠀⠀⠉⠉⠛⠿⣿⣿⣦⡀⠀⢻⣿⣿⣣⠘⡄⠀⠀⠀⢀⠌⠀⠀⠀⢸⣿⣿⡁⣠⣴⣫⢞⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣤⡹⣿⣿⣧⣃⠀⠀⠀⡆⠀⠀⠀⠀⣦⣿⣿⣿⢟⣿⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡀⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡎⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⣠⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠬⢉⣉⣉⠁⠀⠒⠒⠒⠠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠁⠉⠁⠀⠁⠀⠀⡂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡘⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣈⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠤⣀⡀⠀⠙⠓⠢⢄⣀⠀⠀⠀⢀⠀⠀⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠂⠀⡈⠓⠲⠤⣀⡀⠀⠉⠲⠤⣀⡀⢀⠇⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⡠⠈⠁⠒⠼⠄⣼⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⢀⠤⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡀⠐⠁⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠓⢤⣀⠀⠀⠀⣀⠐⠁⠀⠀⠀⠀⠠⠊⠀⣠⠶⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡰⢀⠃⢨⠁⠢⣄⡀⠀⠂⠌⡀⠐⠀⢀⠴⠋⠘⡀⠄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠂⠀⡆⢠⠁⠆⠈⠒⢤⣀⢀⡠⠖⠁⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠂⠌⠀⡸⠀⠀⠰⠀⠀⠀⢸⠀⠉⡁⠀⠀⠀⠀⠀⠁⠸⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠁⠀⠄⡐⠀⠀⣅⠀⠁⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⢰
⠀⠀⠀⠀⢠⠇⠀⡈⠐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡜⠀⢰⠀⡆⠀⠀⠀⠀⠀⡄⢀⠀⠈⡀
⠀⠀⠀⠀⢎⡀⠐⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⡇⠀⠀⠀⠀⠀⠠⣘⣀⠤⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢹⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢺⠇⡝⣁⣸⣀⡈⣛⡍⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⡩⠤⠒⠒⠉⠉⣠⠋⢣⡈⠉⠑⠒⠠⠬⣑⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠁⢀⡀⠀⠀⠀⠀⡰⠁⠀⠀⠳⡀⠀⠀⠀⢠⡄⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⠏⠙⢄⠀⠀⡰⠁⠀⠀⠀⠀⠱⡀⢲⠖⠉⡤⣄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⠀⠀⠀⠀⠁⡜⠁⠀⠀⣠⡄⠀⠀⠱⡄⠐⠶⠓⠋⡸⠀⣆
⠀⠀⠀⠀⠀⠀⢀⡟⡇⣀⢇⠀⠀⠀⡜⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡄⠀⠀⢀⠇⠀⡟⣇
⢀⣀⣀⠀⠀⠀⣸⡗⡟⢏⡘⡀⢀⠞⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⣄⠀⡜⣆⡀⡗⣿⡀⠀⠀⢀⣀⣀
⠹⡷⠧⣹⠲⡎⠁⠙⡇⠚⠀⢣⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣦⠃⠑⠋⡟⠁⠉⡶⢺⡡⠷⡿
⠀⠈⠺⡭⠽⠷⡖⢦⣧⠤⠊⢉⣹⣄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣜⣉⣙⠢⢤⣧⠶⣶⠿⠭⡽⠊
⠀⠀⠀⣇⠀⣴⡷⢒⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣖⠲⣷⡆⢀⡇
⠀⠀⠀⠈⢩⠟⢱⡇⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⠤⠤⣤⣤⢤⣤⣀⣀⡀⠀⠀⠀⢈⡷⡟⢯⠉
⠀⠀⠀⠀⠈⠢⢬⠿⢄⡤⠒⠉⢻⣭⣝⣿⠛⠻⣧⢀⠀⣿⠞⠻⣟⣩⣽⠋⠓⠢⣀⠾⢿⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠉⠉⠉⡿⠘⢧⣀⡀⣬⣾⣾⡥⠀⣀⠟⠸⡋⠉⠉⠙⢅
⠀⠀⠀⠀⠀⠀⢀⣴⡥⠤⡄⢀⡜⠳⣤⡔⠋⠩⢿⣿⣿⠯⠉⠓⣤⡤⠓⡄⠀⡤⠤⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⠀⠀⠀⠱⢄⠤⡟⠈⠈⡷⢄⡠⠃⠀⠀⢸⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢿⡀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⣧⠀⠀⠀⠀⠀⣴⠞⠳⢶⡄⠀⠀⠈⠉⠙⠛⠳⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢠⡄⠀⠀⢹⡄⠀⠀⠀⠀⠙⠀⠀⠀⣷⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣤⡽⠿⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⢀⣀⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠉⠀⣀⣠⡴⠞⠛⠉⠁⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠞⠛⠉⢉⣴⠖⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇
⠀⠀⠀⠀⠀⢀⣼⠟⣿⣤⠆⣠⡶⠋⠀⠀⠀⠀⠀⢻⠄⠀⣀⣤⡴⠖⠛⠉⠀⠀⠀⠀⠀⡴⠶⣤⡀⠀⠀⠀⠀⠀⢸⡇⢻⡄
⠀⠀⠀⠀⣠⡿⠋⠀⠀⣴⣞⠉⠀⠀⠀⣀⣤⡴⠶⠂⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀
⠀⠀⢀⣴⡟⠁⠀⠀⠀⣀⣡⣤⠶⠞⠛⠉⠀⠀⠀⢠⡆⠀⠛⢦⣄⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠟⠁⣴⠟⠛⢶⡀⢸⡇⠀⠘⣧
⠀⣠⣾⣋⣠⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠙⠳⣄⡀⠀⠀⠙⢿⣄⠀⠀⠀⣼⠃⠀⠀⣸⠇⢸⡇⢴⣄⣹⡆
⣰⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠉⠓⠀⢸⡇⠀⠀⣰⠏⠀⢸⡇⠀⡙⢿⢿⡄
⣿⣇⠀⠀⠀⠀⠀⠀⣠⡶⠦⣤⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠘⠷⣤⡴⠋⠀⠀⢸⡇⠸⣿⡀⠈⣷
⢻⣿⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠙⣦⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⣧⠀⠸
⠀⢻⣿⣿⣆⠀⠀⠀⠈⠛⠶⣤⣄⣀⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⢸⡇⠈⠋⠻⠂
⠀⠈⢿⣿⣿⣷⡀⢰⣦⣄⣀⠀⠉⠉⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⢸⡇⠀⠀⠀⢀⣴
⠀⠀⠈⢿⣿⣿⣿⣆⠛⠈⠉⠛⠶⢦⡄⠀⠀⣿⠀⠀⠀⠀⠀⣠⠶⠿⣦⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄⠈⠃⢀⣠⣾⣿⠋
⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⣇⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⠀⢸⡿⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⣸⣧⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡾⣿⠟⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡤⠶⠿⣯⠞⠁⠀⠀⠈⢷⣀⠀⢀⡴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠁⢁⣰⡶⠶⣦⠀⠀⠀⢀⣤⣠⡴⠛⢁⠁⠱⠀⠒⢠⡄⠀⠀⠀⠀⢈⠻⠋⠀⠼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠻⣦⠐⠠⠐⠏⠤⠀⠈⠀⣰⡄⠀⣼⣿⠀⠀⢀⢴⡿⠒⠀⢀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠔⠂⣠⠆⠀⣹⣿⣰⣿⣿⡦⠊⠑⠀⠀⢈⠰⢏⣨⣿⡆
⠀⠀⠀⠀⣰⣄⡀⠀⠐⣡⠞⠀⠀⠀⠀⠀⠀⠀⣻⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡤⠀⠀⢀⣡⣴⠟⠉⠁
⠀⠀⠀⠀⠉⠙⠻⢿⣼⣱⣶⣄⡀⠀⠀⠀⠀⣠⣿⠄⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆⣡⣄⡀⣾⣶⣷⡇
⠀⠀⠀⠀⠀⠀⠀⢤⡙⠛⠁⠁⠉⢷⣄⣤⣾⡿⠋⠀⢰⣿⣄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣿⠿⠛⠋⡉
⠀⠀⠀⠀⠀⠀⠀⢈⡙⠓⠤⣄⡀⠀⠉⠙⠛⠒⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⢠⣴⣿⣃⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣠⣴⠶⠊⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠘⠓⠲⢤⢀⡀⠙⠿⣄⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⣰⣮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠳⣿⣦⣾⣿⣿⣿⣿⣿⠿⠻⠟⠻⠛⠉⠀⠀⢀⣄⣀⡠⠀⠀⢀⡴⠟⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢁⣾⣿⣿⠿⠛⠛⠀⠀⠀⠀⠐⠀⢠⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠷⠶⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⡎⠀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠣⠶⠶⠤⠤⠤⠤⠤⠤⣤⣄⣀⣀⣰⠇⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠊⠓⠒⠒⠒⠲⠶⠤⠤⠤⠤⣤⣤⣼⠀⡌⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡋⣲⠒⠒⠒⠶⠤⠤⠤⣤⣀⣀⣀⣀⡇⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡏⠉⠉⠛⠓⠒⠒⠶⠤⠤⣤⣀⣈⣹⡇⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⡏⠉⠑⠒⠒⠦⠤⢤⣀⣀⣀⠀⣸⠀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⢀⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡧⣘⡠⠅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠤⢤⣀⣀⡇⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠴⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣍⣀⠂⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⡩⠄⣶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⠉⠓⠲⠤⣍⣑⡒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢊⣥⠴⠊⠁⢀⡀⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡟⢰⡤⢄⣀⠀⠈⠉⠓⠲⠦⣬⣉⡑⠒⠖⠒⣉⡤⠖⠚⠉⠀⣠⣴⣞⣉⡇⢘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠘⡇⠀⠀⠉⣓⣶⡤⢄⡀⠀⠀⢹⠛⢻⠋⡏⠀⣀⡴⠶⣉⣀⠀⠈⠉⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠊⠓⠶⢶⣟⠉⠀⢀⡤⠜⠋⠓⢺⡀⢸⠀⣿⠉⠁⠀⠀⠀⠈⠉⠑⢲⣧⣤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣀⠀⠀⠉⠉⠛⠳⢤⣤⣀⠀⢸⡇⢸⠀⣿⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⣿⠉⠑⠢⢄⣀⠀⠀⠈⠙⠛⢻⡇⢸⠀⣿⠀⣀⣤⡶⠋⠁⠀⢀⡤⡆⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠀⠀⠀⠀⠈⠉⠒⠦⣄⣀⠠⡇⠸⠀⣿⠞⠋⠁⠀⣀⠴⠚⠁⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠈⠀⣿⢀⣠⠔⠋⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⡆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⣀⢀⠀⠀⠀⠄⢠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢻⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣉⡀⠀⢸⠀⠀⠀⢙⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠗⠀⠾⢿⣃⣠⣼⣤⣀⣀⠛⠒⢦⡬⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣀⣠⠥⠶⠒⠛⠉⠁⣰⠃⠻⡄⠈⠉⠛⠒⠦⠤⣄⣀⡉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠾⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⣀⣘⣷⠄⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⣰⠋⢿⢀⡴⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⠏⠀⣀⣀⠀⠀⠀⢠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠈⠀⠸⠟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠘⣯⡭⠀⠀⠀⡾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⠶⣤⠀⠀⣠⠤⣄⠀⠈⢧⠀⠀⠀⠉⠃⠀⠀⢰⠃⢘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⠿⡄⣧⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢁⣠⠞⠀⢰⡇⠀⠘⡇⠀⠈⢧⡀⠀⠀⠀⠀⠀⡟⠀⠸⣇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣴⣿⠸⡄⠀⠀⠀⢠⠏⠀⠀⠀⠠⣾⣥⣤⠀⠈⢧⣀⣰⠇⠀⠀⠈⢳⡀⠀⠀⠀⣸⠁⣀⢸⡇⣸⡇
⠀⣀⣴⣶⣶⠤⣄⡀⢀⡤⠿⢤⣿⣿⠷⢤⣷⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⡏⠰⣿⡇⡟⢩⡇⠀⠀⠀⠀⠀⠀⣀⣀
⢿⠿⣽⣾⣿⣦⣼⣿⡏⠀⠀⠀⣿⢃⣠⠤⠞⠓⠚⠛⠛⠛⠒⠒⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡼⠀⠀⠸⠃⣷⠋⠉⠛⢦⣠⢴⡞⠉⣿⡽
⠈⢻⡋⠙⣻⣯⡥⠾⠿⢦⣄⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⡽⢇⡀⠀⠀⠀⡇⠀⠀⠀⢠⣇⣸⣷⡛⢉⣻
⠀⠀⠉⠛⢧⣼⡇⠀⠀⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⣠⠞⠁⢀⡉⠓⠦⣄⣧⡞⣀⣴⢿⣿⣶⣿⠟⠋⠁
⠀⠀⠀⠀⣾⠀⠙⠒⣶⠟⢧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣠⠞⠁⠐⠚⠋⢁⣠⡴⠾⠷⠿⠟⠛⠋⢡⡏⢸⡆
⠀⠀⠀⠀⠹⣤⣀⣠⣇⣀⡤⢾⡆⠀⢀⣤⣖⣻⣍⣩⣤⢦⠉⢯⡉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⣙⣧⣖⣽⡇⠀⠀⠀⠀⠀⠀⠀⣼⣠⡼⠁
⠀⠀⠀⠀⠀⣠⣼⡛⠉⠁⠀⠀⢧⣰⠋⠈⢿⣯⠉⢽⣷⣦⣄⠀⠙⢦⡀⠀⣩⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣭⣏⠛⠒⠲⣄⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠈⣏⣳⡄⠀⠀⠈⠛⠒⠒⠢⣿⠶⠶⣾⢸⣿⡟⣶⣤⣙⢾⠁⠀⠀⠙⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⣿⠀⠀⠀⣀⣨⡽⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠈⢙⡇⠀⠀⠀⠀⠀⠀⣀⡼⠀⠚⢩⡷⣶⡞⠁⠀⠉⢻⡆⢠⡄⣰⡿⠋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣾⢻⣯⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⠴⠖⠚⠉⢻⣍⠀⣀⣴⡟⠀⠛⣇⡀⠀⠰⢦⣽⠾⠷⣏⡤⠄⠀⠀⣸⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣟⠒⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠸⡇⠀⠀⣠⡽⠿⠗⢺⣇⢿⡿⣸⠶⠶⠶⣯⡁⠀⠀⣿⠉⠛⠲⠦⠤⠤⠤⠴⡞⠁⠁⢹⠳⢤⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢾⡃⠀⠀⠘⢋⡽⢳⠾⣏⠙⠂⠀⠀⢹⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀⡤⢿⠃⠘⠁⢹⡷⣄⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢿⡀⠀⠀⢠⠇⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡿⠱⠂⠖⠰⢢⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣽⣯⣿⡽⢫⣦
⣿⣿⣿⣿⣋⣚⠐⠃⠖⡴⠋⠘⠀⢿⣿⣟⠋⣭⠉⣰⠉⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣯⣿⣽⣯⡝⣱⣿⣼⣆⠀⡀⢶⡖⣶⡿⣳⣦⡀
⣿⣿⣿⣿⡍⣭⠉⠉⠛⣇⠀⠘⠀⣸⡇⣌⠳⣄⠰⠯⠀⣓⣈⣿⣿⣿⣿⡇⠀⠀⠀⠰⡖⢶⣶⣶⡜⣿⣯⣽⡿⢀⡟⣦⡙⢿⣓⣿⣧⠽⠆
⣿⣿⣿⣿⣿⣄⠀⠀⢀⡘⣆⠚⣰⣿⢁⡀⠰⡌⡿⠛⠉⠉⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⢿⡜⣯⡟⠁⢸⢿⣿⣹⡆⣭⣶⣶⣿⡟
⣿⣿⣿⣿⣿⣿⣶⣶⣦⣥⣼⣾⣿⣿⣦⡀⣤⢠⠇⠀⠒⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠈⠀⠀⠈⢻⡟⣿⢡⣿⣯⣽⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣀⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠾⠿⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⡠⠐⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠴⢊⣥⠄⠀⠀⠀⢈⣑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⡠⠖⠉⢛⣛⠿⠾⠶⡾⢷⡶⠤⣬⣥⣤⣭⡶⢤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠕⠒⠊⠉⠀⠀⠀⠀⡴⠁⠀⢣⠀⠀⠀⠀⠉⠐⠒⠪⠵⣦⣄⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢣⠀⠀⢤⠼⠓⠀⠀⠀⢀⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠃⠸⡶⠀⠀⡜⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣴⣂⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠞⠀⣰⠲⡆⢀⡴⢦⠀⠱⡀⠐⠛⠁⠀⢠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡄⠀⢸⠀⠀⠀⢀⠎⠀⠀⢀⡼⠁⢸⡁⢸⠇⠀⠱⡄⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠺⠈⣁⢆⠀⢠⠊⠀⠀⠀⠉⠉⠁⠈⠓⠋⠀⠀⠀⠘⡄⠀⢠⠁⣴⣼
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⠀⠁⠘⠀⠸⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡆⠀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⢶⣤⣖⣛⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⢁⠞⠳⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⣀⠠⣜⢩⠻⣝⠛⠓⠒⢲⠶⢶⡤⠤⢤⣤⣤⣔⣁⡖⠓⣀⠬⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠢⢴⡖⠎⠢⡀⠀⠠⣟⣹⠀⠀⢀⠔⠑⢿⣩⣝⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⣈⠢⡀⠀⠀⢀⠔⣁⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⣀⣙⠻⢦⡴⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣛⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⢈⠉⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠄⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣀⠠⡌⢀⡠⠀⢐⡂⠤⠠⠄⠋⠐⠚⠻⠤⠤⣀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣁⣀⣤⠀⠁⠀⠀⠀⠀⠀⠠⠤⠴⡶⠂⠀⢠⣤⢏⣁⠒⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡠⠤⠄⢀⠀⠀⠠⠀⠀⠀⢀⣀⠾⠀⠀⠀⣀⢀⡬⠔⠢⢤⣠⢄⣀⢤⡐⠂⠀⠠⠍⠀⠊⡀⠤⠀⠃
⠀⠀⠀⠀⠂⠀⠀⠤⠇⡀⠠⠀⣀⣀⢀⣀⢴⡉⠓⡒⢼⡗⠏⠉⠹⠓⠢⠍⠛⣉⠒⠁⠂⠠⠖⠛⠋⠂⡀⠀⢠⠀⡀
⠀⠀⠀⠐⠃⠤⢴⠞⠋⠭⠱⠀⠀⠀⠀⡀⢠⣆⠀⠠⢼⠶⠦⠦⠠⠤⣤⣦⣤⣤⣀⠀⠠⠤⠔⣒⣢⠭⠵⠒⠛⠈
⠀⠀⠀⠀⠀⠀⠘⠂⠴⠤⠼⠦⠄⠄⠤⠤⠟⠉⠙⠉⡝⡂⠘⢀⣀⢀⠀⠀⠉⠉⠙⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⣀⢀⠂⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣚⡉⢼⡧⠉⣓⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢊⠟⢨⠟⣁⣺⣗⣀⠀⣟⣮⠙⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⣍⣣⠤⠼⡒⠛⡭⢥⠎⠹⡬⠭⡛⢓⡦⠦⣔⣭⡓⢦⣀
⠀⠀⠀⠀⠀⢠⠴⠿⠓⠋⠉⠁⠀⠤⠀⠠⠖⢲⠏⠀⠀⠹⡖⠂⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⡄
⠀⠀⠀⠀⠀⢸⡆⠀⠀⡴⣆⠀⠀⠀⠀⠒⢲⠋⠀⠀⠀⠀⠘⣏⣁⠈⠀⠀⣠⠷⠂⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢸⣽⠀⠘⠁⠈⠳⣄⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⣧⠈⢳⠋⠁⢠⠖⣆⠀⣞⡇
⠀⠀⠀⠀⠀⢸⠩⣇⠀⠀⠀⠀⠀⠈⡹⠃⠀⠀⠀⢀⣄⠀⠀⠀⠈⢞⣀⠰⠤⠼⠖⠃⢸⡍⡇
⠀⠀⠀⠀⠀⢸⠂⢸⡀⠀⠘⢀⡀⡹⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠈⢧⠖⡐⠀⢠⢀⡗⠀⡇
⠀⠀⠀⠀⠀⢸⣰⠦⢧⠈⢠⡀⡽⠁⠀⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠈⢿⣱⠃⡄⡸⡑⠀⣇
⠀⠀⠀⠀⠀⢸⠉⡴⠘⡔⣆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⢠⠏⢷⢦⣿
⠀⠀⠀⠀⠀⢸⠘⠃⠘⢳⡞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⡜⡃⠈⠋⣿
⠀⠀⠀⠀⠀⣼⣎⡴⣖⠉⠹⣝⢯⡙⠉⠹⡍⠙⠉⠏⠙⠉⠝⢩⠋⡩⢋⡽⣫⠟⠹⠓⢴⣀⣿
⠀⠀⠀⠀⠀⠙⠿⣆⡀⢀⣀⡬⡳⣅⠀⠀⠀⢰⡋⠳⠈⣿⠁⠀⠀⠀⣨⠞⢡⠤⠖⢀⣠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢿⣃⠘⠈⢳⣄⠀⢸⡃⣠⠀⣿⡄⠀⣠⠾⠁⠤⣖⡦⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡘⠳⡄⠉⠁⠀⠉⢀⡜⢃⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣦⡀⢀⣴⡭⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠦⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠘⢦⠀⠀⣤⣤⣄⠀⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣤⣄⠀⠳⡄⠙⠻⠿⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉⠀⢠⠇⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢸⣿⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⡀⠈⠻⣦⣠⡶⠞⠋⠉⠀⠀⠀⠀⠀⢀⡏⠀⣤⡘⣧⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠉⠁⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢿⣿⣿⡆⠈⠻⣄⠀⣠⣶⣦⠀⠀⠀⢀⡞⠀⠘⣿⣿⠈⢷⡀
⠀⠀⠀⠀⠀⣴⠏⣠⣤⠀⠀⠀⠀⠀⠀⣤⣤⠀⠘⢦⣀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢦⠻⠿⠋⠀⠀⠀⡼⠁⠀⠀⠈⠁⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣏⠀⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⠇⠀⢸⠽⠋⣉⠋⠉⠉⣩⣿⡉⠉⣻⠀⠀⣀⣀⣤⣞⣧⠀⠀⠀⢀⣾⣦⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠻⣆⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⡴⠋⢀⣿⣿⡇⠀⠸⣿⡿⢃⡾⠷⠚⠋⠉⠁⣀⠈⠙⣆⠀⠀⠀⠻⠟⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢠⣤⡀⠀⠀⢀⡞⢁⣴⣦⠙⠉⢰⣾⣷⠀⣴⣫⣀⠀⠀⠀⠀⣿⣿⣿⠀⠈⢳⡀⠀⠀⣠⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⣿⣿⡇⠀⣠⠋⠀⠸⣿⠟⢀⣤⡙⠛⣡⡞⠻⣿⣿⠃⠀⠀⣀⣌⡉⠁⠀⠀⠀⠹⣄⠀⣿⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠉⢀⡼⠁⣴⣿⡗⠀⠠⣿⣿⢃⡼⠋⠻⣄⠀⠀⠀⠀⠐⣿⣿⡟⠀⠀⢀⣀⡀⠘⢦⠈⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣠⠏⠀⢀⣙⣋⣤⣤⠴⠾⠟⠋⠀⠀⠀⠘⢷⣄⠀⢠⣴⣦⡄⠀⠀⠀⢿⣿⡿⠀⠈⢳⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠿⠿⠃⠀⠀⢀⣀⣉⣠⣤⣤⡴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣮⣭⣽⣿⣽⣿⣿⣿⣿⣽⣿⣷⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠿⠭⣽⣛⡷⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⢶⡶⠶⣶⠶⢶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⠀⠀⠈⠉⠙⠛⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠦⣀⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠻⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠖⠛⢿⣤⣼⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣄⣹⠀⢸⡇
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣾
⢀⣼⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⢊⣡⣿⡏
⠸⣷⣄⡀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⢋⡤⠖⣩⡿⠋
⠀⣿⠉⢻⣶⣄⡀⠀⠀⠀⠈⠙⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠞⣉⣴⡞⠙⢳⣄
⠀⣿⠀⢸⡇⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣩⣴⠾⠋⣡⣴⠟⠉⠈⢻⣆⠀⢿⡄
⠀⣿⠀⢸⡇⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣡⡴⠟⠉⣠⡴⠟⠉⠀⠀⠀⠀⠀⢻⡇⠸⣷
⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣠⠞⠁⣠⠞⢉⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⢀⡾⠋⣠⠞⣡⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⣼⠃⣰⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠸⣧
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠶⠃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⡆
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣇
⢸⡷⠶⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢹⡄
⣿⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠞⠁
⠛⠶⣶⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⣸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⢠⣶⣶⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠗⣠⣶⢿⣽⢾⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣤⣾⢻⢸⢻⣿⡿⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣀⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⢹⢼⢸⣸⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣸⢸⣈⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡟⡃⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣗⣿⡏⡇⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣯⡟⡇⡇⡇⡵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠏⡇⣿⠇⡷⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⡇⠀⡇⣴⣶⣿⡧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⡇⣻⣿⣿⡷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⡇⣣⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⢾⣿⣿⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣼⣺⣿⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢠⣴⣾⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⡿⣟⣿⣿⣿⢿⣿⣾⣿⣿⣽⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣗⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⡶⠶⢶⡶⢶⣶⣶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠾⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠉⠉⠉⠉⠒⢤⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠃⠀⠀⠀⠀⠠⠀⠀⢦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡆⠀⠀⠸⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠙⠦⠶⠞⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠲⣃⠀⠀⠀⣘⠶⠂⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠚⠛⠓⠀⠀⢠⠈⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠈⠛⠛⠛⠣⠤⠄⣠⡤⠐⠉⠀⠀⠀⠀⠙⠠⢄⡀⠀⠘⡀⠀⢀⡀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⢀⠤⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⢸⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⣀⣀⠠⠼⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⢀⡀⠀⠀⠀⠀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⣀⠀⠢⣄⠀⠔⠈⠁⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠓⠐⠂⠀⠀⠀⠄⢤⠤⠀⠀⠐⠂⠀⠈⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣨⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⡍⠉⢉⣀⠀⣉⡈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠲⠖⠒⠂⢤⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠄⠀⠀⢀⡍⠢⠾⠆⢉⠉⠉⠉⠁⣶⠋⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡋⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠠⡌⠀⠀⠀⠀⠀⢀⠦⠤⡤⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢠⡆⠀⠀⠀⡐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣀⠤⠛⠁⠀⠀⡄⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⣃⣹⣯⣹⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⠤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠒⠛⠲⠾⠾⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡉⠐⠒⠒⠶⠦⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠐⢈⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠗⠐⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣮⣵⣬⣮⡓⢒⣫⠯⠉⠛⠛⣛⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠮⡭⠤⠀⠀⢠⢖⡪⢺⠆⠰⣍⣉⣛⡻⠷⠿⣶⡒⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠒⡼⠀⡠⢖⠕⡡⠖⠉⠉⠉⠉⠀⠀⠈⠉⠓⢲⠼⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢰⢗⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⡋⡩⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⣤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢿⡏⠈⣭⣝⠓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡜⢋⣠⠜⣩⠖⠋⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢠⠏⢸⡇⠀⠉⠋⢀⣀⠀⢶⣆⠈⣷⠀⠀⢀⡴⠋⠴⠆⠁⠴⢆⡴⠚⠁⠀⢰⣷⠀⢷
⠀⠀⠀⠀⠀⣠⠏⡀⠀⡇⠀⣴⣤⠈⠛⠃⠀⠀⠀⣿⠀⠐⡟⠛⠓⠀⠉⠙⠉⢻⡀⠀⣿⡆⠀⠁⠀⠘⣇
⠀⠀⠀⠀⢀⡏⠰⠃⣠⠿⠶⢤⣍⣀⡀⠀⠿⡦⠀⢸⠀⠀⢹⡀⠀⣴⣄⠀⠀⠈⢷⡀⠈⠀⠀⠀⣾⡆⢸⡄
⠀⠀⠀⠀⠀⡇⠀⣰⠏⠀⠀⠀⠀⠈⠉⠙⠓⠲⢤⣿⠀⠀⠀⢳⠀⠈⠋⠀⠀⠀⠘⣇⠀⢰⣶⠀⠈⢁⡴⠃
⠀⠀⠀⠀⠀⡇⣰⠋⠀⠀⠀⣠⣤⡀⠰⠿⠷⠀⣼⠃⠀⠀⠀⠈⢧⠀⠀⠀⠸⣿⠀⢹⡄⠈⠁⣠⠞⠉
⠀⠀⠀⠀⠀⣿⠃⠐⠿⠷⠀⠈⠉⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣿⡴⠛⠁
⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠁

⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠧⡄⠀⢀⣀⣀⣀⣀⡀⣀⣀⣸⠀⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠁⠒⠒⠒⠂⠤⠤⠤⠤⠬⣿⢠⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠼⠧⠬⢉⣉⣁⣒⠒⠒⠒⢴⡇⡄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢺⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣺⠀⠐⠒⠠⠤⠄⣀⣀⠀⣸⢠⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠂⠂⠐⠐⠦⠤⣤⣀⣀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠇⡀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⡁⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠒⠒⠬⢄⣒⠂⠤⢀⡀⠀⠀⠀⣀⠤⠐⣀⠥⠒⠉⣀⡀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢈⢹⠒⠢⠤⣀⡈⠉⠐⠲⠤⣍⣉⣩⡤⠒⠉⠀⠀⠐⠺⢤⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡤⢆⣀⡤⠶⠋⠁⣒⠤⢄⡄⠀⠀⡧⠔⠊⠉⠐⠂⠤⢀⡇⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠆⠀⠀⠁⠂⠶⡯⣁⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⣀⡤⠖⠉⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡟⠀⠂⠤⣀⠀⠀⠉⠓⢿⠀⠀⡇⢀⣠⠴⠊⠁⢀⡠⠆⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⡇⠀⠀⠀⠀⠈⠐⠢⢄⣸⠀⠀⠿⠋⠁⣀⠤⠚⠁⠀⢧⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⡟⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣀⣀⣠⣧⣀⣀⡉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⢀⣿⣀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⢰⡾⠟⠛⠛⠛⠉⠉⢩⡿⠹⣏⠉⠉⠛⠓⠿⠿⢷⣤⠀⠀⣤⡾⠿⠷⠖⠛⠛⠋⣹⠿⣯⠙⠛⠲⠶⠿⣿⣦⣄
⠀⠀⠀⠀⢸⣿⠀⡐⠻⡄⡀⣰⠟⠀⠀⠙⣧⠀⠔⠊⠀⠀⣸⣿⠀⢠⣿⡄⢀⠞⡄⠀⢀⣼⢃⣀⠘⣧⠀⣠⠔⠂⠀⢀⣿⠁
⠀⠀⠀⠀⢸⡿⣇⠀⠀⠏⣴⢯⠤⣄⢀⡤⣜⣧⠀⣹⠔⢢⡟⣿⠀⢸⡟⣧⠁⠀⠳⢀⡾⠁⠀⢽⠀⠘⢷⡀⢀⣋⡅⣼⣿
⠀⠀⠀⠀⢸⡇⢿⡀⢀⡼⠃⠀⢠⠏⢸⠀⢸⠘⢷⡀⠀⣾⠁⣿⠀⢸⡇⢹⡄⠀⢠⡟⠁⠀⠀⣿⠀⠀⠈⢷⡀⠀⢰⡏⣿
⠀⠀⠀⠀⢸⠀⠘⣧⡾⠁⠀⠰⠷⠆⠘⠦⠞⠀⠈⢷⣼⠇⠀⣿⠀⢸⡇⠈⣷⣰⠏⠀⠀⠀⠀⠛⠂⠀⠀⠈⢷⣄⡿⠀⣿
⠀⠀⠀⠀⢼⣶⠞⠛⣿⡛⠛⠛⠛⡛⣛⠛⠛⠛⢛⣿⠿⢦⣤⡇⠀⢸⣧⣤⠾⣿⡒⠒⠲⠶⠶⠶⠶⠶⠶⠶⢶⡿⣧⣀⣿
⠀⠀⠀⠀⠀⠙⠳⢦⣌⠻⣦⡀⠘⡧⣼⠁⢀⣴⠟⣁⣤⠶⠛⠁⠀⠈⠛⠶⣤⡈⠻⣦⡀⣣⠀⠀⡇⠀⢠⡴⠋⣀⣤⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⣎⠃⢊⣴⣿⡵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣷⣌⠀⠀⢁⣴⣫⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⣛⣳⣤⠖⢶⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣹⣏⣷⣾⣿⣩⣟⣻⠟⣿⣦⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⠷⣾⣷⣒⣶⣾⣛⣶⣶⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⢰⡟⣒⣛⢤⠂⠻⢗⠶⠶⣶⣴⣿⢤⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡧⢘⣿⡟⠉⠒⠱⡶⡿⠃⡠⢺⣷⣿⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡍⢀⡿⠔⢳⢚⡼⠳⠟⠪⣴⡿⣻⣿⣨⢼⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣌⢸⣇⣁⡻⣽⢣⠜⣍⢉⡸⡏⠿⡟⣫⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣿⡋⢸⠏⣿⡟⡟⡀⠛⠙⠏⠴⣿⣭⡼⠇⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠟⠋⠿⠿⢿⣿⢭⣿⣇⡊⢻⣶⡔⠂⡤⣸⠟⢿⣶⣟⣭⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡷⠴⠀⠂⠁⠀⠀⢸⣟⠂⣿⡿⣗⣿⡟⣿⠏⣸⣏⢾⣿⣟⣼⣯⡉
⠀⠀⠀⠀⠀⠀⠈⢿⣠⠝⣿⡇⠀⠀⠀⠀⠀⠀⢸⡧⡅⡿⠶⠶⠼⠾⠶⠶⠿⠷⠬⣋⣿⡟⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡥⢠⣏⣩⣩⣡⣁⣀⣁⣀⣀⣀⣹⣿⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢀⣀⣀⠤⣴⣚⢛⠟⠓⠛⣓⡶⠂⠐⠒⢲⣀⠀⣿⣿⡷⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⣭⣶⣛⣱⣶⣞⣂⣶⣢⡀⣈⣉⠀⣀⣀⣀⣈⣀⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⣽⣿⣿⣻⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣛⡛⠛⠛⢾⡏⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⢛⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⡼⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡇⠀⠀⠀⠀⠀⠀⠁⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⣀⣴⣾⠇⢨⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣹⠄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⣇⣀⣤⣶⡿⠛⠉⠘⠐⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣱⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⢽⡟⠛⢛⣿⠿⠍⣤⠀⠒⠠⠤⠀⢀⣀⠀⠀⢀⢸⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸

⠀⢀⣠⣴⣾⣒⣶⣶⣶⣦⠤⣤⣤⣄⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⢀⣤⣶⣖⣶⣶⣖⣿⣿⣿⣷⣦⣀
⢰⣿⣿⣷⣾⣿⣿⣿⣭⣽⣿⣿⡿⣿⠀⠀⠀⠀⣴⡏⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⡿⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣏⠀⣹⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⡞⣻⡇⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⠉⣿⣿⣿⣿
⢸⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⡏⡇⠀⠀⠀⠀⡟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⠇⠀⠀⠀⠀⣷⣿⣿⡿⠉⣽⣿⣿⡿⠛⣻⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿
⠈⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠛⠿⠿⠤⠿⠿⠿⠯⠥⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⣿⡿⠿⣿⣿⣿⡿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀
⢸⣿⣦⣤⣿⣿⣿⣦⣤⣿⣿⣏⣿⡆⠀⠀⠀⠀⠀⣾⣿⣿⣧⣠⣾⣿⣿⡟⠛⣿⣷⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⢿⣿⣿⣷⣄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠉⣻⣷⣶⣿⡏⠀⠀⠀⣠⣿⣿⣿⠟⢷⣤⣼⣿⣿⣿⣿⣿
⣾⣟⠉⢹⣿⣿⣟⠉⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣏⠈⣻⣿⣾⡿⠿⣿⣿⠁⠀⠀⢸⣿⣿⡿⠻⣤⣴⣿⣿⣿⡟⠉⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⡟⠀⠀⠀⠀⠙⢿⣧⣤⣿⣿⣿⣿⠉⠙⣶⣿⠋
⠈⠻⣿⣭⠿⢭⡽⢯⣭⠿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣶⣾⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡏⠉⣷⣾⠟⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣛⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣷⡀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣴⣿⠛⠟⠛⠁⠒⠀⢀⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠀⠀⠀⠀⠀⠀⣀⡒⣒⠚⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣀⣠⡄⠀⠀⠀⠨⣥⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣤⠀⠀⠁⠈⠀⠀⠒⣂⣿⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠂⠀⠀⠀⠀⢦⣹⣃⠀⠀⠀⠀⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡌⠀⠠⠀⠐⢾⣻⡷⠀⠀⠄⠰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡄⢀⠀⠀⢙⣷⣄⡀⠄⠀⣹⣿⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠙⢄⠀⠶⠻⣿⣿⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠆⠻⢶⣿⣿⣿⠃⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⡀⠈⠉⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⠓⠚⡶⠿⢋⡶⣯⣷⣟⣣
⠒⠒⡾⠿⠿⠻⠿⠻⠿⠻⢟⠳⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⡛⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡲⠡⣾⣇⣸⣗⣀⠰⠬⡓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡪⠬⠖⠚⠋⠩⢲⠎⠹⣖⡋⠙⠖⠢⠶⢍⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠀⠀⠀⠀⢈⣩⠏⠀⠀⠘⡤⠄⠀⣀⣤⠀⠀⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠰⠏⣧⠖⠀⢠⠃⠀⠀⠀⠀⠘⣆⠀⠉⢀⡤⠄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠹⡀⠀⠀⠉⠀⣱⠃⢀⣤⡀⠀⣀⣀⠈⢞⡁⠐⠻⠀⠀⡏⢡⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡿⣧⢧⠀⠀⠠⡸⠁⠀⢈⠴⠃⢸⡁⢸⠆⠈⢶⡁⡁⠐⣸⠁⢺⢵
⠀⠀⣀⣀⡀⠀⢸⢏⣻⡿⢙⡄⡐⡴⠁⠀⠀⠈⠉⠁⠀⠙⠋⠀⠀⠈⢳⢡⢃⡇⣶⣼⢾⡇
⢿⣫⣯⣿⣼⣿⡁⢀⢻⣤⠖⠛⠙⠛⠛⠉⠉⠲⢦⣀⣀⠀⠀⠀⠀⠀⠀⢻⡼⠀⠘⢹⠊⠉⢲⡴⣞⣹⣟
⠀⠓⢶⣛⣷⠉⠉⣾⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⡫⣏⠽⢩⣯⠟⠹⣣⣆⣸⠤⠒⣿⠷⣛⡶⠚
⠀⠀⠀⡇⠘⠲⡞⠳⣖⠅⡠⣂⡤⠶⠾⣷⠤⣄⡤⣀⠀⠀⠀⠈⠑⣶⣁⡈⣹⣣⣔⠈⡀⠀⡇⠀⢸
⠀⠀⠀⠙⢒⡾⠗⠿⣿⣨⠟⣷⠓⣻⣍⡈⢣⡄⠈⣓⣵⣢⡀⠀⠀⠈⠙⠙⠛⢾⡿⣿⠀⠀⣙⡶⡏
⠀⠀⠀⠀⠹⣍⣳⠈⢃⠛⣛⢻⡗⣺⣽⣿⡷⢾⣿⠀⠀⢹⣿⢷⣄⡀⠀⠀⠀⠀⠀⢽⣶⣿⡥⠶⡃
⠀⠀⠀⠀⠀⠀⢹⢀⡠⠤⢶⠚⢁⣵⠋⢏⠀⠀⣙⣦⣧⣟⡀⠀⢹⠛⣧⣤⣀⣈⣑⣼⠛⠹⣄⣠⠇
⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠈⠉⠉⢯⡀⣠⠽⠒⣺⣿⣿⣿⡒⠶⣅⢀⡽⠉⠉⠁⠀⠘⠢⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡀⢀⣴⠋⠏⣦⡀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢢⣀⣀⡼⠈⠉
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣻⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣋⣽⣿⣿⣿⣿⠟⠛⠛⠻⠿⢿⣿⣭⡙⠛⠻⢿⣿⣿⣿⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣥⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠹⣿⡟⢿⣷⡝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣿⣆⠘⣷⡀⢻⣿⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠻⣧⢹⣇⠈⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠰⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢠⡏⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣷⣼⣷⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣾⣿⡇⣼⢣⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣭⣿⡿⠿⠟⠻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣷⣇⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣤⣶⣿⣯⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⢿⣿⣭⣛⡻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⠛⠳⢗⡶⣦⣌⠻⢿⣷⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠶⠾⠟⠛⠛⠛⠛⢿⣿⣶⣿⣶⣌⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⣿
⠀⠀⠀⠀⢀⣀⣠⣶⢶⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⡿⢠⣿
⠀⠀⠀⠀⣀⡙⠶⣄⠀⡰⣾⣶⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢣⣿⠃⣼⡏
⠀⠀⠀⠀⠙⢿⣶⣌⢻⣧⡸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣾⠏⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢠⣾⠏⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⣿⠏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣹⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣫⣿⣿⠇⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⠻⢿⣿⣿⣿⣶⣶⠶⣶⣶⣶⣶⣿⣿⣿⣶⣿⣿⣟⣥⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣄⡈⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⠿⢛⣋⣩⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠖⠚⠛⠛⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡞⠋⠛⠟⠉⢻⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⠀⠀⢧⣀⠀⠀⣠⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠈⠙⠻⠃⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠳⠶⠦⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣤⡴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣙⣿⡿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣛⡳⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⠶⣚⣫⡽⠖⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠉⠛⠒⠶⢭⣍⣛⡓⠶⠖⣛⣭⠵⠖⣋⣩⣤⡶⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⣿⠛⠶⠶⣤⣄⣉⠉⣿⢋⣩⡴⠶⠛⠉⠁⠘⡇⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⡿⠀⠀⠀⠀⠈⣿⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣧⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢻⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⠀⣼⠃⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡆⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠻⣾⣇⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣤⡾⠃⠀⠀⠀⠀⠀⠀⢻⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣼⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣴⣾⣷⣦⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠿⠟⠛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠟⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⣠⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣷⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⣀⣬⠙⠻⢿⣿⣿⣿⠃⠀⠘⣿⣿⡆⠀⠀⠀⣸⣿⣿⡀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣿⣿⣿⣤⣤⣾⣿⣿⠏⠀⠀⠀⠹⣿⣿⣦⣤⣶⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⢀
⡄⠀⠀⠀⠐⢿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣞⣿⠿
⣿⣶⣄⠀⠀⣺⣿⣯⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⢿⣿⡇⠀⠀⠀⠈⢹⣿⣿⣶⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⣷⠀⠀⠀⢐⣶⣶⣿⣿⣿⣿
⠈⠛⠧⠀⠀⠀⠀⠸⢿⣿⡟⠁⠉⠻⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠙⠁⠀⠀⢀⣼⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⡗⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⣸⣇⣀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣪⠭⠴⠒⠋⠩⢱⠎⠱⡞⠍⠑⠒⠢⠾⣕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⠀⠀⢈⣩⠏⠀⠀⠙⡥⠄⠀⠀⠀⠀⠀⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⣎⠀⠀⠀⠀⠀⠀⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠹⡆⠀⠀⠀⠀⣱⠃⠀⠀⠀⠀⠀⠀⠘⢎⠀⠀⠀⠀⢠⠏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢾⠀⢸⠀⠄⠠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⠄⡀⠂⡮⠀⡷⢧
⠀⠀⣀⣀⠀⠀⠀⠀⡟⢾⠀⠀⢇⡈⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠸⢰⠅⠀⡷⢻⠀⠀⠀⠀⣀⣀
⠀⠘⣿⠿⣙⡖⡖⠉⢹⣿⢦⠀⠚⣼⡁⢀⡀⣀⢀⣀⣀⣀⢀⡀⣀⣀⡀⣀⢣⣟⠀⠀⡿⠉⠉⢲⢲⣋⠿⣻⠃
⠀⠀⠈⠲⣎⡽⠷⣄⣸⢻⣾⣶⠍⠙⢿⣮⠁⠙⠈⠁⠃⠈⠘⠁⠋⠜⢥⡻⠋⠙⠲⢆⣧⣆⣠⠿⠯⡵⠖⠁
⠀⠀⠀⠸⣿⣯⣷⡎⠀⢹⣇⡤⠷⠖⠛⠛⠐⠒⠦⣤⣀⠀⠀⠁⠀⡠⠊⠀⢀⡠⢶⣿⣿⣿⡒⡀⠀⡷
⠀⠀⠀⠀⠈⢻⠊⠙⣳⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⢤⠎⣀⣴⡮⢛⠟⠁⢋⣯⠷⢿⢯⠉
⠀⠀⠀⠀⠀⠀⠳⡶⠻⣤⠁⡠⣀⣠⡶⣶⣦⣤⣀⠄⡀⠀⠀⠀⠋⢻⣿⢟⠛⣏⡉⠽⠀⠀⣧⠜
⠀⠀⠀⠀⠀⢀⣠⠗⠚⣿⣤⡞⢇⣀⣴⠃⠻⣀⠀⢽⣾⣄⣄⠀⠀⠈⠙⠓⠒⠯⡭⣵⡆⠀⠑⣤⡄
⠀⠀⠀⠀⠀⠈⠉⠑⡌⢃⠛⣓⠺⡇⠸⣄⡠⠚⠉⠽⣿⣿⠿⠿⣦⣀⠀⠀⠀⠠⠤⠼⣷⣾⡯⢤⡂
⠀⠀⠀⠀⠀⠀⠀⢠⢃⡠⠴⠒⠚⠁⠀⠀⠹⣄⣠⢾⠁⠃⢷⢄⣠⠟⠛⠤⣀⣀⣉⣢⠟⠛⣄⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠛⠛⠋⠛⠛⠛⠻⠟⠳⠶⠶⠾⣿⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠛⠉⠺⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠛⠉⠶⠶⠾⠿⠛⠻⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⢻⣷⣄⣠⣤⣴⡶⠾⠟⠉⠀⠀⠀⣠⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢦⣤⠀⠀⠀⠉⠙⠿⣶⣤⣤⣄⣀⣠⣾⠏
⠀⣀⣤⣶⡶⠞⠋⠈⢹⡇⠀⠀⠀⣀⣀⣤⡴⠞⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠉⠹⠷⢦⣤⣀⠀⠀⠀⠈⣿⠉⠁⠛⢶⣦⣤⣤⡀
⢶⣏⣁⢀⣠⣠⡄⠂⠘⠿⠶⠾⠚⠋⠉⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠚⠛⠀⠀⠀⠀⠀⠀⢙⣻
⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣿⠟⢿⡆⠀⠀⠀⠀⢸⡟⠉⠛⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣤⣼⡇⠀⠀⠀⠀⢸⣷⢶⣶⣶⣆⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣿⠀⠀⠀⠀⠀⣿⠋⢻⡇⠀⠀⠀⠀⢸⣿⣿⠛⢻⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠆⠀⠀⠀⠀⣿⠀⢸⡷⠀⠀⠀⠀⢸⣿⣿⡄⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣧⠐⣿⣿⡆⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠠⣿⣿⡏⠀⠀⠀⠀⣿⠀⠀⣶⠀⠀⠀⠀⢸⣿⣿⠃⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⢈⣿⠀⠀⢻⠀⠀⠀⠀⣸⣿⣿⠀⠰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⢻⣿⡇⠀⠀⠀⢸⡟⠀⠀⣿⠀⠀⠀⠀⣿⠿⣿⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⡇⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⣸⣿⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠸⣿⣟⠀⠀⠀⣸⡏⠀⠀⢹⡃⠀⠀⠀⣿⠁⣿⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣽⠀⠀⠀⢿⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠻⠷⠷⠶⢿⣇⠀⠀⠘⢿⠶⠶⠾⣿⠀⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⠀⠀⠀⠀⢈⣿⠀⢀⠀⠀⠀⠀⠀⣹⡇⣿⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⠚⠛⠛⠛⠛⠙⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⣊⡁⡆⡘⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠂⠉⠁⠀⠀⠤⠽⠚⢁⠜⢡⡖⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡉⠁⣠⢄⡠⢀⣲⠂⢀⢔⣲⠆⢀⠎⠀⡘⣧⡼⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣈⡛⠋⠁⠘⠚⠉⠁⣀⠈⠭⢐⠲⢭⡀⠀⠀⠈⠀⢰⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⣨⡶⢃⡀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⡀⢡⠀⠀⠀⡞⣬⠇⠡
⠀⠀⠀⠀⠀⠀⢀⢔⡀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠈⠀⠂⠀⠀⣷⢼⠂⢠⢃
⠀⠀⠀⠀⠀⠀⡾⠁⠄⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢦⠀⢸⢷⣴⠆⡅⠈⠈⠆⠀⢙⠉⠀⠘⣼⠄⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡴⡒⠲⢄⠀⠀⣿⣦⡄⡠⠀⠈⠙⠒⠉⠀⠀⠀⠘⡀⢘⢀⡀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣶⡵⣃⠌⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡏⢃⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡤⡀⠀⢋⠱⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⡀⠀⢰⡿⢿⡆⠸⠀⠀⠇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⣞⢶⢆⠀⠀⢸⡿⢵⠆⡀⠀⠀⠙⠛⠓⠁⠀⠀⢸⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢿⠶⠍⢠⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠊⠩⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡀⠠⠀⠀⢂⡀⠤⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠄⠠⢂⠄⠀⠔⡠⠀⠠⢀⠄⡠⠀⠠⡀⢀⠄⡀⢀⠀⡠⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢀⠄⡊⠀⠠⠂⠐⠈⠄⠈⠔⡡⠂⠡⠊⠐⠠⠊⠀⠠⢊⢔⠅⠈⠔⡡⠊⢀⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠡⠂⡠⠊⠀⢀⠔⡠⠂⡔⡀⠀⠠⢊⠀⠑⠡⠂⠠⠊⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⣀⣀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣊⡡⠤⠔⠒⠉⢉⠎⠱⡉⠉⠒⠢⠤⢌⣑⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠉⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠀⢱⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡎⠀⡿⢧
⠀⠀⢀⡀⠀⠀⠀⠀⡟⢾⠀⠈⡆⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢰⠁⠀⡷⢻⠀⠀⠀⠀⢀⡀
⠀⠘⣟⠿⣙⡶⡔⠋⢉⣿⣆⠀⢹⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡇⠀⠀⡿⠉⠙⢢⢶⣋⠿⣻⠃
⠀⠀⠈⠲⢎⠽⠷⣴⢾⢿⣼⠔⠊⠙⢍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡩⠋⠑⠢⢄⣇⡶⢦⡾⢯⡱⠖⠁
⠀⠀⠀⠐⣿⣇⣶⡟⠉⢹⣏⡩⠷⠐⠒⠓⠂⠀⠤⢄⣀⠀⠀⠀⠀⣠⡎⠀⠀⣨⣟⣾⠅⠠⢾⡄⠀⡷
⠀⠀⠀⠀⠈⠛⠝⠛⣢⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⡾⣫⣧⡶⢟⠿⣿⢷⣤⡤⢾⢯⠋⠁
⠀⠀⠀⠀⠀⠀⠣⣤⠾⣄⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠙⠿⣛⣭⠟⡏⠉⠉⠀⠀⣧⠜
⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⣄⠔⢇⣀⣴⠋⢿⡀⠈⢵⣦⣀⠀⠀⠀⠀⠈⠑⠲⠯⠍⣲⠀⠀⠑⣤⡄
⠀⠀⠀⠀⠀⠀⠉⠑⡄⠀⠙⠒⠚⡇⠸⣀⡠⠚⠛⡽⣿⣿⢿⠦⣀⠀⠀⠀⠀⠀⠀⠈⢶⣶⡯⢤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠤⠐⠒⠁⠀⠀⠱⣄⣠⢾⠁⠋⣷⣄⣀⠟⠒⠤⣄⣀⣀⣠⠞⠙⡆⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠁


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣻