Camp fire Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⠴⠁⢀⣦⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⣤⡇⢀⣶⣽⡦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣘⣰⠚⢁⡴⡻⠋⢸⣿⠹⢲⡼⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⢝⡀⣿⠐⠃⠀⠘⣯⢴⣤⣧⡄⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢹⢸⡆⢸⡏⠛⡇⠀⣼⣤⡁⠀⢹⢠⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣠⣮⠷⣼⣟⢢⢀⡞⠁⢸⡇⠀⡯⣶⢸⠼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡏⣾⢧⠀⠛⢠⠾⣄⠀⢼⠛⣦⡀⣻⢿⡄⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢏⠻⡆⢀⣆⣇⠀⡉⠀⠀⠇⢸⠁⠁⣸⣷⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢜⢷⡈⠺⣅⠃⠀⡗⠀⠀⠐⠉⠃⠴⠟⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⡠⠺⠛⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢉⡉⠒⠂⣡⢀⠀⠀⠀⣠⣄⣤⣀⣤⣴⣶⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢛⠩⠾⠛⠋⢁⣀⣤⣤⣤⣬⣍⣩⡭⠭⠿⠤⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣦⣶⣷⣊⣛⡏⣴⢻⣿⣿⡿⣧⣶⣦⣶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠉⠛⠛⠁⠉⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣿⣿⣿⡏⢻⣿⣿⣿⠀⠀⢹⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⣿⣿⣷⣼⣿⣿⡟⠀⢸⣿⣿⣿⠀⠀⠈⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⡄⠀⠀⠸⣿⣿⠀⠘⣿⣿⣿⣿⠀⣿⣿⡆⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢸⣿⣿⠛⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣧⠀⠀⠀⣿⡿⠀⠀⣿⣿⣿⡏⠀⣿⣿⣁⣿⣿⡇⠀⠀⢀⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⡿⠀⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⡄⠀⠀⣿⡇⠀⠀⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⢻⣿⡿⢿⣿⣷⡀⠀⠈⣿⣿⡇⠀⢰⡟⠀⠀⢠⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣃⣾⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣶⣄⠀⣿⣿⡿⣿⣿⣷⠀⠘⣿⣷⠈⢿⣿⣷⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⣼⣿⠃⠀⣸⣿⣿⡟⢸⣿⣿⣿⡟⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⡇⠘⣿⣿⡀⠀⢹⣿⣧⠀⠹⣿⣇⠀⠀⣿⡿⠀⠀⠀⠀⢰⣿⠃⠀⢠⣿⣿⠏⠀⢸⣿⣿⡿⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠘⣿⡇⠀⠀⢹⣿⣇⠀⠸⣿⠀⠀⣿⠇⠀⠀⠀⢀⠾⠁⠀⠀⣾⣿⡏⠀⠀⣿⣿⣿⠃⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⢸⣷⠀⠀⠀⣿⣿⡀⠀⣿⠀⠀⠋⢀⣀⣠⣄⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⡿⠀⠀⠀⢸⣿⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢹⡇⠀⠀⠀⣿⣿⡏⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠹⣿⣿⡆⠀⠀⠀⠀⠀⣸⠏⢀⣴⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣷⡄⠀⠁⠀⠀⠀⢹⣿⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠹⣿⣿⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⢦⣍⢻⣷⣌⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⢻⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⢿⣟⠻⣦⡙⢷⡈⢿⣷⣬⣿⡟⢿⣿⣿⣄⠀⠀⢠⡟⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣦⡙⢷⡈⢿⣌⠻⣾⢷⣌⣻⣿⣦⡙⢿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⣿⠃⠀⠀⢀⣴⣿⢻⣿⣿⣏⠻⣦⣹⣶⣿⣿⣿⣦⡹⣿⣿⣦⠻⣦⣙⣿⣿⣦⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⢀⣴⡿⢫⣿⠟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣷⡈⢻⣿⣿⣿⣷⣄⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣄⣠⣾⣏⣴⣿⣷⣾⣿⣿⠿⣛⣥⠾⢛⣡⣼⣿⣿⣿⣿⣿⣷⡜⣿⣦⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠟⠛⣉⣩⣴⡿⠟⠋⠠⠞⢋⣩⡶⠿⢛⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠟⢋⣥⡶⠞⠛⠛⠉⠁⠀⣠⣴⡾⠟⣛⣭⡴⠞⣉⣼⣿⣿⣿⡿⠿⠿⠷⣶⣤⣉⡉⠛⠿⣿⣿⣿⠿⢷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⣀⣤⣶⠿⣿⡿⠟⢉⣠⡾⠟⢋⣠⡴⢞⣁⣄⠀⠞⢋⣄⢀⣾⣏⣡⣴⡿⠟⣻⣿⣿⣿⣇⠑⠶⢦⣤⣉⣙⡛⠳⠶⢶⣤⣽⣿⣶⣤⣭⣿⣿⣿⣷⣦
⠀⠀⣀⣴⣾⠟⢋⣤⣾⣯⣴⠟⠛⢩⡴⠞⢋⣥⡾⠟⠋⣡⣶⠾⣿⣷⣞⣩⣽⢟⣫⣴⣾⣿⣿⣿⡿⠛⠛⠿⢷⣦⣬⣉⣙⣃⣀⠀⠀⢈⡉⠙⠻⣿⣿⡿⠛⠻⣿
⣠⣾⣿⣿⣿⣿⣿⠟⠋⢉⣠⡴⣀⣤⡶⠞⠋⢁⣤⣶⣿⣯⣵⡾⠟⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠋⣀⣀⠘⠿⣶⣤⣽⣿⣿⣿⣿⣟⠓⠉⠛⠿⢶⣾⡿⢡⣆⡀⢸
⣿⡿⢋⠉⠻⣿⣧⣴⡾⠛⠉⢀⣬⣶⡴⠗⢀⣿⣿⡿⠛⣋⣡⡶⠟⣋⣥⣾⣿⣿⡿⢿⣿⣁⠀⠀⠈⠙⠿⢶⣤⣄⠉⠙⠻⣿⣿⣿⣿⣶⣶⣦⣼⣿⠇⣾⣿⢃⣿
⢻⣧⠘⣾⣷⠘⣿⣯⣤⣴⣶⠾⣿⣉⣴⣾⡿⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡛⣿⡷⢦⣽⣿⣿⠶⣤⣄⣀⠶⣤⣭⣀⣻⣷⣿⣧⡈⣿⣧⣤⣉⣿⣿⣧⣼⠏⣼⡿
⠈⢿⣧⠹⣿⡃⢸⣿⣿⣿⣴⣾⡿⠟⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⣷⣦⣌⡉⠛⠶⣦⣭⣛⡁⠀⣉⣙⣻⣿⠋⠙⣿⣿⣭⣍⣿⣿⣄⠙⣁⣼⡿⠁
⠀⠈⠻⣷⣌⠻⡿⠋⣻⣿⣿⣷⣴⣾⣿⣿⣿⡿⠟⠋⠙⠛⠿⢿⣷⣦⣌⣙⠻⢿⣷⣤⣽⡟⠷⢶⣼⡟⠻⢿⣿⣿⣿⣿⠃⢸⣧⣿⡿⠿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠙⢿⣷⣶⣾⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣏⣛⢿⣶⣤⡿⠿⣷⣶⣤⣹⣿⡇⢶⡾⣼⡟⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣶⣦⣌⡉⢻⣿⣧⣠⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣉⣹⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣴⠇⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢠⣿⣿⠀⣿⣿⣿⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡀⠀⡀⢸⣿⣿⡆⢻⣿⣿⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡇⢠⣿⡄⣿⡏⡇⢸⣿⣿⠛⣿⠇⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⢀⣾⣿⠁⣿⢱⠃⢸⣿⡇⣰⢋⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⣰⢃⡏⠀⢸⣿⢰⠃⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⣿⡖⠃⢸⠁⢀⡾⠃⢺⡀⣸⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠁⠀⠀⠁⠀⣸⡷⠋⠁⢀⠀⠉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⣀⣀⣀⣞⢣⣀⣻⠃⠀⢀⡀⠀⠰⠋⠀⠀⢠⡜⡆⠀⠀⣰⡿⠷⠒⠒⠒⠒⠒⠚⠒⣦
⠀⠀⠀⢀⡾⠛⡇⠉⠉⠀⣉⠙⢧⠀⢸⡷⢄⠀⠀⠀⠀⣼⡗⠁⣀⣴⣯⠤⠤⠀⠒⠂⠀⠀⠀⠠⢼
⠀⠀⠀⢸⡇⠁⡇⠀⠀⣤⣤⣄⣨⣵⣦⣷⣾⣧⠀⢀⡼⣿⣵⡚⠿⣷⠦⣤⣬⣭⣭⣥⣥⣤⠀⢀⡼
⠀⠀⠀⠘⣇⣳⣷⣤⠴⠚⠛⠫⣭⣿⠿⠉⠁⠉⢷⣿⣄⠉⡀⢄⡀⠀⠀⠀⠈⠙⠛⢯⣍⣉⠉⠉⠁
⠀⠀⠀⣴⠋⠉⠳⣄⠀⢀⣠⡄⠄⠀⢀⡠⠄⣀⣸⣟⠌⠛⢿⣷⢮⣁⠀⠐⢤⣤⠞⠋⠀⢍⣧
⠀⠀⠀⡧⡄⠐⡘⢸⡆⠀⠀⠀⢠⣴⣶⣿⣿⠭⠞⠉⠙⢻⢠⣬⣙⢊⠁⠀⢺⣯⠂⢰⡇⠈⡿
⠀⠀⠀⢷⣯⠢⠠⢡⡇⠠⢔⣚⠭⠖⠋⠁⠀⠀⠀⠀⠀⠈⠓⠃⠉⠓⠯⣄⣸⢿⡦⠼⢀⡼⠁
⠀⠀⠀⠈⠻⣕⣠⡾⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⠶⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⣠⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠱⠋⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁⠀⢀⡄⠀⢸⣜
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣴⡠⠚⢭⣆⣠⡏⠓⢄⡩⢳⣍⣂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⡤⠐⣉⣠⠐⠉⣽⠛⢻⡀⠀⠙⣀⡀⢈⣷⣌⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢟⣿⣿⡀⠀⣡⣠⣮⣿⣄⠀⠈⣻⡿⠿⠟⠛⠿⠈⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣁⠈⠉⠉⠙⠛⠛⠉⠛⢷⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⡆⢠⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣴⠏⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡇⢃⢸⡇⠀⠀⡄⠈⣧⠀⢆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣰⡇⠘⠈⡇⠀⣼⡇⠀⡟⠀⠈⢧⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⣿⠀⡇⠀⢰⠀⣿⣧⠜⢀⠄⠀⠀⡄⢘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡇⢀⠀⢻⡄⠁⠀⠀⠀⣽⠋⢠⡞⠀⠀⢀⡇⠈⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⡇⢸⡆⠈⠇⡀⠀⢀⣼⡇⢠⡟⠀⠀⠀⣼⠃⠀⡇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢳⠀⡇⢀⠀⡇⠀⠈⣿⠀⢸⡇⠀⠀⣸⡇⢀⣼⠃⢠⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸⠀⠀⡜⡼⠁⠀⠀⢸⠀⠀⠁⠀⠀⣏⢣⡾⠁⢀⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠈⠀⣠⠁⢰⠀⡟⠀⠀⠀⠀⠀⠛⢸⡇⠀⢸⠁⡇⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣠⠏⠀⣴⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⡄⢃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣿⠀⠰⡇⠀⢿⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠸⠂⢹⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢻⡄⠀⢁⠀⠸⣇⠀⢀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⣴⣄⣘⠳⡀⠈⣧⠀⢹⠀⣼⡇⠀⠀⣧⠀⢠⡏⠀⡄⣰⣣⣤⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣶⣯⣤⣤⣤⡤⠴⠄⢸⣷⡄⠀⣿⣇⠀⣰⠇⣴⣿⡄⢸⢰⡯⠤⢴⣶⡶⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠦⢈⠉⠉⠀⠈⠉⠀⠀⢀⡤⠜⠻⢿⡴⠋⠉⢳⣿⠿⠉⠁⠀⠙⠛⠦⣤⣤⣄⡀⠈⠃⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⠂⣀⣒⣦⣴⠶⠛⡉⠀⠀⠀⣰⡇⣠⠀⣀⣻⣷⣀⠄⠀⠀⠀⢱⡆⠙⠛⠻⢿⣿⣿⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣼⠿⠿⠩⢱⠓⢤⠄⠀⣀⣴⣏⠁⠁⠀⠀⠈⠉⠻⣾⣷⠃⡠⠀⢆⣈⢀⠔⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠐⠀⣶⣾⢿⡏⠉⠓⢠⣄⠀⠀⠀⠀⢿⡇⢼⠀⠀⠟⠋⠘⠊⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠴⠛⠁⠈⢆⢀⡅⠀⠩⠊⠀⠃⡜⠙⢧⠾⠞⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠀⠟⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⣿⣷⡄⢠⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡗⢠⠿⠋⡷⠚⣧⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡜⠋⠀⡠⠋⠀⠀⠇⠀⢹⡄⠟⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠞⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡼⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡟⢧⠀⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⡶⡝⣼⣿⡘⣿⠀⠀⠀⠀⠀⠀⣤⡜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣬⡿⠋⠀⠚⠀⢻⣇⣽⡀⠀⡆⠀⠀⠀⡿⣿⢶⣀⢰⡦⠀⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⢻⣿⣄⡴⢃⣴⣇⡐⠀⣰⡇⣹⠉⢷⣄⣏⠀⠀⢠⣷⠌⠃⠝⢿⣷⢠⡿⠒⠙⢢
⠀⠀⠀⠀⠀⠀⠀⢀⣮⣴⡖⠢⡀⠀⣈⣿⠋⣠⣿⡟⡟⠀⢠⣿⠀⡟⠀⢸⡟⠟⢦⣵⣿⣿⠳⡄⠀⠰⢝⢿⠁⠀⢀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠙⠳⠷⢾⣿⣥⡾⢻⡟⡾⠀⢀⡟⣿⢠⠇⠀⢛⣿⣿⠘⡄⠘⡽⣇⢻⣦⣠⡼⣾⣎⠂⠌⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠂⠋⠀⠀⠀⠀⡘⣭⡿⢛⣛⠺⢧⠤⠾⠷⠷⢾⢶⡀⡠⠿⢿⣧⡷⠤⠾⢿⣞⠛⠁⢀⣀⠍⢳⣆⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⢀⣿⠃⠁⠀⠀⠀⠀⠀⠀⠈⣿⢸⡟⠀⣀⣀⠀⠀⠀⠀⠈⢿⠀⠚⠉⠀⠀⠈⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⢀⠇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣹⡇⠚⠁⠀⠀⠀⠀⠀⠀⠸⠧⢤⣀⡀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠼⠵⠖⠇⣀⡀⠀⠀⠀⠀⠀⠀⢼⠀⢺⠇⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡼⠁⢹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠋⠉⠉⠑⠒⠒⠒⠒⢒⡒⣻⢀⣀⣜⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⣀⣴⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⣸⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠁⡇⠀⠈⣷⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⠀⢷⠀⠀⠘⣧⠀⡞⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⢸⡆⠀⠀⢹⡄⢧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠲⣄⠀⠀⠀⢿⠀⠹⣆⣸⠇⠀⠀⠀⣧⠘⣧⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣇⠀⠀⢸⡆⠀⠈⠁⠀⠀⠀⠀⣿⠀⣿⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢻⣴⠏⠀⢸⠇⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡟⠀⣷⣄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡇⠀⣿⠈⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢠⡿⠀⢸⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡾⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢴⣟⡉⠙⠳⣄⠀⣿⠀⠀⠀⠙⠋⠀⠀⠸⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢀⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⢹⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⠀⢠⣄⠀⢸⠸⣦⡾⢡⡇⠀⠀⠀⠀⠀⠀⠈⣿⢿⡀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠷⠞⢻⠀⣸⠀⠀⠀⣼⢣⢶⠀⠀⠀⠀⠀⠀⢹⡼⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡴⠋⠀⠀⠀⢿⡾⢸⠀⠀⠀⢠⠀⠀⠸⣿⠃⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⣆⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠹⢦⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠋⢸⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣼⠇
⠀⢀⣴⠶⡦⠤⠤⣀⣹⣧⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡾⠀⠀⠀⠀⣠⣾⡧⠤⠤⠴⢶⠶⢦⡀
⠀⢸⡇⠀⢸⠀⠀⠀⠀⣈⠻⣦⣀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠞⠁⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⣬⠀⢸⡇
⠀⢸⡇⠀⡙⠀⠀⠀⠀⠀⠀⣀⣉⣛⣶⣤⣄⣙⡳⣦⣤⣀⠀⠀⠀⠀⣀⣀⣠⣤⣖⣋⣡⣤⣶⣟⣉⣀⣀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇
⠀⠈⠻⠾⠟⠛⠛⠛⠛⠛⠋⠉⢉⣩⠿⠛⠉⠉⠉⠙⣻⢿⡟⠛⠛⢻⡟⠻⣯⡉⠉⠉⠉⠳⢦⡈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠚⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⡠⠄⢀⡴⠟⠁⣾⠁⠀⠘⠘⣇⠀⠈⠻⣄⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠶⠟⠩⡄⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡏⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣄⠀⠀⠀⢤⡀⣙⢳⣤⡀
⠀⠀⠀⠀⠀⣼⡁⠊⠀⠀⠜⠀⠀⢀⡴⠋⠀⠀⠀⠀⣼⠃⠀⡰⠀⠀⣿⡀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣽⡉⠀⠊⡙⣦
⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⢀⣿⡾⠋⠀⠀⠀⠀⠀⠀⡟⢀⣀⣀⡀⠠⢹⡇⠀⠀⠀⠀⠀⠀⠙⢦⣼⠁⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠈⠻⠶⡶⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⡟⢫⠍⠉⠉⠛⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣄⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢁⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣥⣤⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⢀⣟⡘⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡇⠀⠀⠀⠀⡼⢸⠀⠠⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⢷⠀⠀⢀⡼⢁⠎⡀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢠⠈⠓⠒⠋⠠⠊⡸⠁⠘⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⢤⡀⠀⠀⠘⣿⡸⠀⠘⡄⢰⠁⡴⢁⡀⠐⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢳⡀⠀⡇⣇⠱⡀⠃⠈⡜⣰⣿⠁⠀⢸⠁⠀⠀⡟⢦⡀
⠀⠀⠀⠀⠀⠀⢰⠇⡅⠸⠈⣧⣠⠇⡟⢀⡤⣶⠆⣿⠃⢿⠀⠀⢸⡀⠀⣸⢣⠀⢳⡀
⠀⠀⠀⠀⠀⢀⡟⢠⠁⠘⠀⠀⠁⢀⢣⠏⣰⠃⠀⢻⠀⠘⣆⠘⡀⠓⠚⠃⠘⡀⠈⡇
⠀⠀⠀⠀⠀⣼⠀⡆⢰⠀⠑⢄⠀⠘⢸⡀⣏⠀⠀⣼⠀⠀⠘⡇⠁⠠⢰⣷⠀⡇⢸⠇
⠀⠀⠀⠀⠀⣿⠀⡇⠸⠀⢀⡀⠡⠀⠈⢧⠈⠳⠞⠁⠀⠀⢰⠇⠐⣱⠋⡏⢀⢃⡟
⠀⠀⠀⠀⠀⠸⡄⢣⠀⢇⢸⣧⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢯⠴⠞⠁⢸⠃⡜⠸⣇⣀⣤⡦
⠀⠀⠀⠀⠀⠀⠻⡄⢂⠘⣾⡌⠳⢤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠐⠀⠀⢈⢍⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡳⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣲⡿⡣⢔⡵⠋
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⠦⣅⡳⢤⣀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⣉⡤⠖⠋⢀⣀⣠⣄
⠀⠀⠀⢰⠏⢉⠉⠓⠶⢤⣀⡀⠉⠓⠿⠽⢿⣿⣯⣭⡭⠭⠤⢖⣚⣫⠥⠶⠒⠛⠉⠁⠀⠈⣧
⠀⠀⠀⢸⠀⢀⠉⠑⠂⠀⠠⠉⡛⠲⢤⣄⣀⡀⣀⣤⠴⠒⠛⠉⡁⠀⠀⠐⢀⡠⠄⠂⠀⣀⡾
⠀⠀⠀⠘⠷⣄⡀⠉⠐⠢⠄⠀⢀⣉⡤⠶⢛⡉⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈⣀⣤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⣲⡶⠶⠚⠉⠀⠀⠀⠁⠀⡀⠠⠔⠒⢀⣀⡤⠴⠶⢯⣁⡀
⠀⠀⠀⣀⣠⠴⠖⠋⠁⠤⠒⣀⠠⠐⠀⠁⠀⣁⣠⠤⠖⠛⠉⠀⠀⠀⠒⠠⢀⢉⠙⠒⠦⢤⣀⡀
⠀⢠⡞⣁⠬⡙⣆⠀⠐⢈⡀⠤⣤⣤⠴⠒⠋⠉⠉⠓⠲⠤⣤⣀⡀⠀⠐⠀⠀⠀⠀⠀⢠⢞⠭⠍⠙⢦
⠀⢸⡹⣍⡣⢧⣏⣀⣨⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢬⣁⠂⠀⡟⢀⢶⠐⡄⣼
⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠿⠤⠥⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠋⠂⠀⠀⠀⡄⠀⠀⠀⠀⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⣸⠀⢰⠀⠃⠐⢡⣊⡁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠘⡆⡞⣿⡀⡈⠳⣄⠠⠘⢿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⢱⡘⣜⡙⣷⡼⡄⠈⣷⢱⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠀⠠⢲⡼⣦⣻⣿⣷⣸⡿⢻⣷⡟⡸⠠⠀⢸⠀⠰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠉⢳⠙⣿⣿⣿⢇⣿⣯⠚⣡⣦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⢀⠀⣾⠠⡙⣿⣿⣿⣿⣧⣾⣭⡁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⡉⠟⠺⡱⠘⠷⣿⡾⠿⠛⠉⠉⠉⠀⠊⠁⠑⢲⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣡⠇⠀⢀⠠⠚⠉⠀⠀⠀⣀⠀⠀⣉⢀⣢⡠⡏⡌⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢉⡉⠉⠹⠃⠛⡲⡆⠀⢠⣾⣷⡆⡏⢉⠉⣹⣿⠓⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠺⠇⢀⣨⣇⣐⣸⣧⣶⡉⠅⠀⣿⡷⣤⠤⠟⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⢚⠽⢛⡅⠈⡻⠟⠛⠷⠶⠞⠉⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠢⠀⠀⠀⠀⡄⢈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⡄⠠⠂⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⣀⠀⢀⠎⠀⠸⠀⠀⠀⣀⠀⠀⠀⠀⠄⠑⠄⠘⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢘⠉⠢⡘⠀⠀⠀⠆⠐⢠⡎⢣⠀⡀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠨⠀⠀⠹⠀⠀⠀⡃⠀⡈⠀⢸⠀⠐⠃⠀⡇⠀⠀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠘⡉⠑⢾⡀⠀⠀⠀⠀⠀⠰⡄⠀⠀⢸⠀⠀⠀⡰⠀⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠆⠀⢰⠁⢓⠒⢻⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡄⡀⠀⢱⠌⠁⣠⠃⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣀⡀⠀⠀⠀⠀⠁⠐⢀⠀⠤⡀⠀⠀⠂⡁⠤⠀⠀⢀⡤⠚⠂⠈
⠀⠀⠀⠀⠀⢀⡖⣗⣒⡒⢈⣩⠥⢀⠒⠀⣀⣤⣤⣀⡀⡤⠠⡠⡄⠠⢤⣀⠀⠠⠶⠶⣶⣆⠀⢀
⠀⠀⠀⠀⠀⠘⠷⠾⠗⠖⠻⣜⣠⣾⡶⠛⢿⣨⡆⣬⠇⣗⢲⠀⣻⣄⠘⢢⣧⣄⣐⣶⢳⡽⠴⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠚⠛⠃⠈⠙⠚⠃⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣿⡅⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⠀⠹⣿⣷⠀⠀⠀⠀⠙⣿⡟⢻⣿⣿⣿⣿⣿⡿⠀⠀⣄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡆⠀⠀⠀⠀⢸⠇⠀⢻⣿⣿⣿⣿⣷⣀⣠⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⣿⢿⣦⡀
⠀⣰⣿⣿⡟⠋⠉⠉⠛⠛⠛⠻⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣛⣛⣋⣉⣉⠉⠁⠀⠀⠒⠚⣿⡀⣿⡇
⠀⢻⣯⣿⣴⣶⣶⣶⡾⠿⠿⠿⠟⠛⢛⠛⠋⠉⣹⡿⠶⣶⣤⣴⣶⡆⠛⠛⠿⣿⣟⣛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣧⣤⣀
⣰⡟⠻⣯⡍⠁⠀⠀⠀⠒⠀⠀⠀⠈⠉⣡⣴⠞⡋⠀⠀⢸⣿⠀⠙⣷⡀⠀⠄⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣻⡿⠛⣿
⣟⠡⣠⢻⣆⡠⠄⠀⠀⠀⠀⣀⣤⣶⣿⡟⠁⠘⠁⠀⢀⣿⡇⠀⠀⠸⣷⡄⠀⠑⢄⠀⠈⠙⢿⣿⣶⣤⣀⠀⠀⠀⠈⠉⢰⣿⡘⠀⣿
⢻⡄⠩⢸⣿⠀⠀⣀⣤⡶⠟⢋⣽⡿⠋⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⢹⣿⣄⠑⢄⠀⠀⠀⠀⠙⠿⣯⡉⠛⠶⣦⣶⣦⣽⣟⢇⣨⡿
⠀⠻⢷⣾⡿⠿⠟⠋⠁⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠆⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠈⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠠⠂⠀⠀⠀⠀⢀⣾⠏⣿⡟⠀⠀⠀⠀⠀⢻⡆⢻⣷⡀⠠⡀⠀⢀⠀⢀⠙⢽⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠁⠀⠀⠀⢀⣾⠏⠀⣿⡇⠀⠀⠀⠀⠀⢸⣧⠀⠻⣿⣄⠀⠀⠀⢑⣤⡿⠛⢻⣿⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣦⣔⠀⡰⠃⠀⠀⢠⣾⠏⠀⢸⣿⣧⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⢿⣷⣔⢦⣾⢿⡎⠰⢨⣹⡇
⠀⠀⠀⠀⠀⢹⣏⠀⠈⢭⡛⣷⣆⠀⣠⣿⠏⠀⠀⢸⣿⢻⠀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢿⣿⡇⣄⣃⣴⣷⡟
⠀⠀⠀⠀⠀⠈⠻⣦⣌⡐⠤⠸⢻⣷⡿⠃⠀⠀⠀⢸⣿⣿⠾⡿⡿⠷⢷⣾⣿⠀⠀⠀⠀⠀⠀⠉⠛⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠷⠿⠋⠀⠀⠀⠀⠀⢸⣏⢦⡐⢀⠛⠂⡱⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢯⣭⣤⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠝⣶⡀⠘⠃⠀⢴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣲⡦⣤⣀⠙⠮⣵⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣞⣭⠼⣻⣦⡈⠛⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢻⣛⡭⠷⣒⣻⣦⡀⠀⠀⠀⢀⣴⡫⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣰⡿⣇⠀⠀⠈⣗⡂⣬⡉⠴⢚⣷⠀⠀⠀⢼⠋⠖⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡴⣿⠀⣴⠗⢚⣛⣦⠀⢀⡿⠄⣿⢹⡄⢩⡽⡇⠀⣤⡘⢧⡘⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢰⡇⢠⣟⠋⠩⢵⣺⣇⣼⡛⢀⡏⠀⣷⠐⡒⡷⠀⢸⡽⢦⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⣇⢸⡧⢰⣆⠉⠵⣿⡉⠁⣼⢁⡄⣿⢨⢽⡇⠀⡼⠖⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⢻⡽⢯⠳⢮⡁⠒⣼⢃⡕⢂⡇⣚⡿⢀⡼⢛⠉⣠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢶⡦⣄⡀⠀⠀⢿⡍⢧⠀⠙⣶⡇⠰⡋⢸⠃⣽⣇⡞⣛⡉⠀⠴⣺⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣄⠹⣯⠛⣆⠀⢸⣿⠸⡇⡄⠘⠃⢘⠅⣾⠀⢚⣿⣫⠅⠀⠖⣶⠋⣠⢟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⣹⣫⢽⣦⡯⠴⢰⠇⡴⡁⠀⡥⠀⢹⡄⠡⠊⣥⠀⢒⡟⠁⠀⣿⠡⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣿⡖⢻⡭⠖⢂⡟⣠⢞⡁⠀⠀⠀⡈⢷⡀⡾⢻⠐⣿⠁⣷⢦⡈⢳⣸⠇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣾⠁⡿⣆⠫⢩⠞⠠⣶⡯⠀⠀⠀⢰⣣⠀⠻⠇⢸⣈⣿⡀⡿⢚⣻⡄⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣴⠿⠂⡼⠁⣻⣰⠋⠀⣨⠵⠀⠀⠀⠀⠀⠘⡏⡄⠀⠘⣧⢚⣷⣛⡭⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⢋⡾⠁⠀⣿⠃⠀⠀⢶⡃⠀⠀⠀⣀⠀⠀⠈⣷⣧⠄⢸⡇⢛⡥⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠄⡾⠀⢔⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠁⠀⠀⡅⢶⡷⠋⠰⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠠⡇⠐⣯⠆⠀⠀⠀⠀⠰⠃⠀⠀⠀⡠⢋⠀⠀⠀⠀⠀⣼⣻⣿⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠶⠤⣤⣼⡯⠂⢷⠈⠑⣫⠀⠀⠀⠐⣚⠅⠀⠀⠀⢘⡱⢂⠀⠀⠀⠠⡏⠾⣏⣀⣀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⣴⢠⢀⠀⡀⠀⠀⠙⣷⢘⣇⡀⠀⠀⠀⢀⡽⠇⠀⢀⣠⡀⠈⠖⣡⠄⢀⣠⣄⣿⣚⣧⠉⠉⠉⠁⠀⠀⠈⠉⣧
⠀⠀⣀⣀⣀⣤⣇⡇⣿⢸⣼⣷⣚⡛⠛⠉⠉⠀⠹⣆⡀⠀⣩⣴⣞⣛⡉⠁⠙⠲⣮⠡⢾⡏⠀⠀⠀⠈⠉⠓⣶⣧⣶⢸⡄⡆⣆⢸
⠉⠽⠿⢓⣒⣲⣿⠿⣿⣿⣚⣧⡴⣍⢣⡀⣀⡀⢀⠈⠉⡿⠉⡴⢖⠎⢉⡛⢶⣦⢹⣶⠋⡄⡰⣴⢀⣄⢀⣾⣟⣖⣽⣾⢧⠇⡏⣾⣖⣂⣀⣀⡀
⠀⠀⠀⠉⠀⠒⠚⣉⣿⢻⡘⡆⡽⢈⡿⡇⡟⣿⣸⣶⢸⡇⡞⣽⣿⠯⢤⢻⡈⣿⣾⠿⠿⣷⣧⡇⡾⡏⣸⣿⣏⢻⣿⡿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⢒
⠀⠀⠀⠀⠀⠀⠤⠤⢿⣾⡧⣽⡷⢛⣼⣿⣥⣿⣷⣿⣾⣧⡳⢬⣙⣓⣋⡞⣠⡿⡯⠍⠉⠉⠽⠷⢿⣇⢿⠻⠛⣿⣿⣒⣀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢚⣩⣭⠬⠿⢛⣓⣛⣟⡓⠒⠒⠂⠀⠶⠒⣛⣲⣦⣤⣴⣾⠛⠓⠃⠀⠀⠀⠀⠉⠉⠽⠿⠷⢶⣿⣗⣒⣒⣾⣷⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠭⠿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠠⠭⠶⠖⠒⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⣿⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⠀⠘⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⣧⡀⢀⣿⣿⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠈⠻⠿⡿⠿⠃⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⢻⣿⠀⣀⠀⠀⠀⢰⣿⠀⢸⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⢸⣿⠀⣿⢦⣤⣴⠏⣿⠀⢸⣿⣿⡿⠻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢸⣿⡀⠀⠀⠀⣾⡿⠀⣿⠀⠀⠀⣰⠏⢠⣿⠟⣿⡇⣀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢻⣷⣀⣀⣼⡿⠃⢰⡏⠀⠀⢰⡏⢠⣿⡏⣸⡿⢀⡿⣧⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣀⠙⠿⠿⠋⢁⣰⠏⠀⠀⠀⣿⠀⠘⠿⠿⠟⠁⣸⠇⢹⡆⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⠷⣤⣤⠶⠛⠁⠀⠀⠀⠀⠸⣆⠀⠀⠀⢀⣴⠋⠀⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠛⠁⠀⠀⣸⠇⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠙⠀⠀⣀⣠⣤⣤⡶⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⢠⡟⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣁⣠⡴⠶⠛⠉⣁⡴⣾⣧⠀⢠⡟⣿⢶⢦⣤⣀⡀⠀⠛⠀⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠯⠿⠦⡉⠉⣹⠟⡱⢃⣿⠀⣞⡴⢿⣮⣦⡱⣍⠙⠛⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡻⠿⠶⠶⢖⠒⡄⢀⣇⡾⠧⣚⠵⠋⣸⣾⡾⢀⣸⡏⠙⢿⣗⠯⠷⢶⣶⣤⣬⣽⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠷⣄⠀⠀⣸⣔⣡⣿⢟⡿⠝⠢⡄⣰⠿⣿⣷⠏⠈⣷⠀⡰⠛⠳⣶⣒⠒⠒⠢⣼⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣘⣇⣴⠿⢻⡿⣋⡡⠤⣀⠀⣿⠃⠀⣿⣿⠀⠀⢻⣦⡇⢠⠚⠙⠻⣟⠳⠶⣿⣤⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⣰⣟⣉⣀⠀⠀⢈⡾⠃⠀⠀⢻⣿⠞⠛⢾⡟⢷⣼⠀⣠⠶⠾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⠛⣦⡾⠁⠀⠀⠀⢸⣏⣀⣀⣀⣿⠀⠹⣧⣟⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠞⠛⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠠⢠⠥⢠⡀⠀⠀⠀⢀⡀⢐⠀⠀⠀⠀⠀⢇⣠⠆⠀⠀⠀⠠⣀⣸⣇⠀⠀⠂⡀⠀⢂⠎⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⡼⠻⠹⠀⠄⠀⠀⠐⠚⠛⠃⠀⠀⠀⠈⠉⠉⠐⠀⠀⠀⠀⠀⠀⠌⠒
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢤⣄
⠀⠀⠀⢠⢲⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢉⡟⢂⣮⠖⣶⡖
⠀⠈⠸⠛⢲⠚⠑⠈⠄⠰⠀⠐⠁⠐⢄⠂⠀⠀⠐⣂⠁⠓⠥⠔⠀⣾⢉⠺⠁⠀⠀⢠⣴⣀⣀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠸⣯⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣄⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣿⣿⣿⣿⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣤⣿⣿⣿⣿⣷⣿⠃⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠙⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢀⣴⣶⣮⠋⠿⠃⢙⣩⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⡘⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡂⢹⣿⡿⠿⣿⣿⣿⣿⣧⢁⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠈⠉⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⡄⠀⠀⠀⢀⠜⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⣇⣠⠤⠴⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣄⠀⢠⡟⠀⠀⠀⠀⢀⡜⠀⠀⡀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠢⣼⡇⠀⠀⠀⢀⡎⠀⠀⣸⠇⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⢀⠔⡙⠀⢰⠀⣀⠴⠂⠉⠉⠉⠉⠉⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⡀⠀⠀⠘⢦⠏⢀⠇⠀⢸⠞⠁⠀⠀⠀⠀⢀⡤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠑⠲⢤⡀⠀⢣⠀⠀⢀⠀⢇⠀⠀⠀⢸⠀⠀⡇⢠⠏⠀⢠⢠⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠱⡄⠀⡇⠀⢸⡄⢸⠀⠀⠀⢸⠀⠀⠑⣼⠠⡀⢠⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⢀⠇⠀⢠⡟⢦⡀⠀⠀⠈⡄⠀⠀⠈⢇⠱⠘⡆⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡏⠀⠀⢀⡇⠀⠈⠳⡄⢠⠁⠀⡀⠀⠈⡄⡆⣇⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡁⢀⡄⠀⠀⡆⠀⣾⠀⢀⡄⠀⢸⠀⠀⢾⠇⡀⠀⣇⣠⠟⠏⢘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡇⢸⡇⡄⠀⣃⡞⢹⠀⡎⠀⠀⡎⠀⠀⢶⢀⡆⢠⠙⢇⠔⠉⡠⠊⠵⠒⠒⠂⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣆⠘⣾⡻⡀⠀⣿⢀⠘⡄⠃⢀⠈⡇⠐⢦⡸⡼⣧⣼⠀⡞⠀⢸⠀⠠⡀⠀⣠⠊⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢦⡀⠙⢷⡀⢿⠸⡄⢱⠸⠼⡆⢧⠀⠘⣷⡙⢹⣿⣮⡇⠀⢸⠀⢷⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡏⠒⠦⣝⠺⣷⠀⠘⠂⣸⠃⠀⣀⡼⢡⣇⠿⢟⣿⠀⠀⠀⡆⣸⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠹⣆⡘⣌⢳⡈⠦⠀⣴⣿⢠⠞⠁⠀⡞⠹⡄⠙⠁⠀⣤⡀⡃⢡⣤⣾⣄⣶⡤⢒⠶⣠⣄
⠀⠀⣀⣤⡄⢤⣖⣶⡶⢒⢺⡛⣋⣉⡙⢦⡈⠙⠪⠳⡇⠀⢸⠘⣿⢸⠀⠀⠀⢻⢃⠆⣴⣾⣼⠟⣠⣿⣿⣿⣿⣛⣯⠭⠼⢞⣽⣯⡃
⠀⢼⠁⢻⣿⣷⠲⠷⠿⠰⠚⠙⠁⠀⡩⠟⠉⢑⡒⣾⠁⠀⠀⠣⠹⠉⠖⠀⠀⣫⢵⣬⣯⣭⣴⢾⣯⣭⠥⣈⣭⡋⠀⠀⠀⠀⠙⣿⠇
⠀⠀⠙⠋⠦⠶⠶⠶⣶⢶⣶⡶⠖⠋⣀⣤⣶⡿⠟⠇⠀⣴⠋⠙⠦⣘⠉⠉⠳⠭⠽⠯⠭⢿⣟⣛⣓⠧⢺⡁⢸⣷⡶⣶⢾⠋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣵⣄⣤⣾⣿⣟⣥⠴⣮⣿⠷⣦⣿⡓⣤⡈⠑⠢⢄⣀⣀⠀⠀⠀⠀⢀⣈⡉⠉⢣⣘⠙⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⠒⣿⣿⡿⠟⠹⠶⢾⣿⠿⣥⠿⣿⣿⣝⣿⣦⡀⠀⠉⠻⢿⣿⣿⣿⡛⠂⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠻⣽⣿⣿⣿⣶⣴⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢫⠟⠞⢳⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⣿⣷⡀⠀⠀⡀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡿⣷⣄⠀⠏⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣿⠈⢿⣆⢠⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡿⢿⡄⣾⣿⠘⣿⣿⣿⣧⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⢠⡿⠁⢸⡇⢸⣿⡀⣿⢸⣿⢻⣧⠀⠀⢠⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢠⣿⣾⠃⡠⠀⠀⢸⣿⣴⠏⠸⣿⢸⡿⢠⠇⣾⣿⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⣠⣿⡿⠃⠰⢃⡄⡄⣸⡿⢋⡀⠐⣣⣿⣷⣿⣿⠏⢸⣧⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⣿⠀⢀⣼⡿⠋⢀⠀⢀⡾⠈⢡⡟⢡⠎⢀⣴⣿⠟⠁⠀⢀⡞⣼⡏⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⡟⣰⣿⢋⡄⠀⠉⣰⡿⠁⢀⡟⢠⡏⠀⣾⣿⣯⡶⢒⣠⣀⡾⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿⡿⠋⠀⠀⣼⡿⠁⡴⠘⠁⣸⠀⡆⣿⣿⣿⢠⡿⢛⣭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⡟⠀⠀⠀⢰⣿⡇⢠⣇⠀⡄⠁⠀⢣⠸⣿⣿⣾⢁⡾⠁⣠⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⣿⣿⡟⠀⣠⠀⠀⢸⣿⡇⠀⢿⠀⡀⢠⡀⠢⠀⠹⣿⣿⣿⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣿⣿⡇⠀⠉⢸⢸⡆⢿⣷⡀⠀⡀⣧⠀⠳⡄⠀⢤⠘⣿⣿⣧⢀⡄⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣿⣿⣇⠀⠀⢸⡄⠇⠈⢿⣧⠀⡹⣾⡆⡄⢻⡄⢸⡆⡟⣿⡇⠈⣴⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢻⣆⠀⠀⢿⡄⠀⢄⠙⣧⠀⢹⣿⠀⢸⡇⢸⣧⡇⣿⣇⣼⣿⣿⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣷⡙⠋⠳⡄⠈⢿⣄⡈⢧⠹⠀⠘⣿⠂⣼⡇⢸⡟⢠⣿⡿⢿⢻⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣆⠙⠧⠀⢲⡄⠀⠀⢻⣿⣦⡀⢰⢰⣿⢰⣿⠃⠈⣰⠟⠉⣀⠄⣼⣿⢁⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡙⠷⠀⠃⣀⠩⣌⣳⡠⣻⡏⣿⡀⣾⣷⣿⠋⢀⡨⠁⠀⣈⣥⣾⡿⠃⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣶⣬⣓⠈⢿⣿⢹⣿⣾⣿⣿⠟⣡⡞⣉⣴⣾⡿⠟⠛⠉⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⣼⣿⣿⣿⣿⣿⢋⣾⣿⣰⣿⠟⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⣼⡿⠿⢿⣧⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣈⡁⠉⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡁⢱⠀⠀⢀⡿⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠀⠀⣨⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣠⡄⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⠀⠀⠀⠐⠠⠄⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⢉⡙⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠉⠁⠘⢣⠀⠀⠀⠀⠀⣶⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇⠀⠀⠀⠀⠈⢂⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢙⣿⠏⠀⠀⣿⠀⠀⢠⡏⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠑⠖⠛⠰⢷⣶⠶⠈⢄⣴⣿⣴⠞⠁⠀⣠⡄⠈⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⠀⢀⣀⠀⠀⠀⡀⣄⣀⠈⠉⠁⠀⠴⠞⠿⠇⢠⠃⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢿⣦⡀⣩⣿⣅⣊⡉⠹⡟⠛⠛⠂⠀⠐⢢⡤⠐⠁⠀⠀⠀⠀⠀⣇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠐⠈⠛⠁⡠⠋⠀⠀⠀⠈⡤⠖⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢈⣿⣿⠀⠀⣴⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠴⠛⠁⠀⠀⠀⠀⠘⣷⣀⣠⠤⢶⣻⡿⠶⡄⠀⠀⠀⠀⠀⡟⠀⠀⢸⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢒⣿⣫⣥⡶⠞⢋⠉⠀⢀⠹⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⣰⠿⠟⠋⠉⠁⠀⢸⣬⠇⠀⠀⠀⢣⠀⢀⠶⣿⣇⡀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠁⠀⢶⡿⠀⠀⠀⠀⠁⠀⠀⡄⠄⠈⣧⣿⡶⠶⢎⠉⠙⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠎⣼⠇⠀⠀⠀⠀⠀⡠⢠⡀⠀⠀⠀⠉⠁⢀⠸⣏⡇⢿⠘⡇⠠⣄⢹⣿⣀⣀⠀⠀⠀⣀⣀⣐⣺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣼⠋⣴⡴⠈⠀⠀⠀⠻⠟⠃⠀⢀⣀⠀⠐⣿⡁⣾⠇⢁⣀⣿⢀⡭⣰⣿⠿⠿⠾⠟⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢷⡀⠙⠃⠀⠀⠀⢀⠠⡀⠀⠀⠘⠟⠀⣀⣀⠐⢃⠴⠛⠛⢉⣈⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣙⣋⡽⠟⠳⡄⠘⠖⠀⣀⣤⣤⡶⠟⢉⠡⠐⢋⣩⣤⣾⣿⣿⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣉⣠⣤⣡⣿⣦⣤⠾⠛⠉⡀⠀⢈⣠⣴⣿⠿⠛⠋⠋⠙⢿⣇⢹⡞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⡩⠞⣋⡵⠾⠟⡋⠁⠐⠊⣉⣥⡴⠶⠛⢉⠤⣤⣤⣀⣀⣀⠀⣀⢹⡆⢹⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⣙⠉⠁⠀⠐⣈⣤⣶⣾⡟⠋⢉⠀⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣧⠘⣷⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡉⠙⣠⣶⣾⡿⣿⣿⣶⣿⡦⠉⠙⠁⠀⣿⣿⣿⣿⣛⣉⣿⣿⣿⢻⣿⡆⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠱⣿⡟⣋⣿⠇⠀⠀⠀⠃⠁⢻⣮⣿⠿⢛⠻⣟⣿⢰⡏⠧⢈⣿⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⣿⣿⠇⡄⢿⣟⢿⡇⣤⣴⣄⠀⠀⠀⠙⠉⠛⠷⠮⣤⣬⡴⠋⠳⠄⢺⣿⢯⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡘⢻⡞⣇⠀⠙⢻⣷⣿⣿⣿⣆⠀⢀⠁⠀⠀⠁⠀⠰⠶⠂⠒⠂⠀⠙⠀⠄⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢂⢿⣿⡄⠀⠀⠘⣿⠿⡏⠛⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⢶⣭⢴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⠻⠶⣄⢠⣿⡆⠁⠛⠋⠀⠀⠀⠀⠀⣀⠀⢠⣌⣡⣼⣿⢿⡾⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⡍⢿⣆⠉⠐⠂⠀⠀⠀⠀⠄⠀⡀⢡⣤⣏⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⣇⢰⣄⡀⣰⣤⣠⡾⣤⢶⡇⢿⠹⣿⣿⡏⠏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣻⣿⡋⢸⠟⣇⢹⣇⣿⣼⣤⣧⡼⡛⣿⠛⠁⡂⣏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡿⡟⢻⠻⠟⢻⠙⣍⣧⣼⢤⠧⠛⠋⡠⢈⢃⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠢⠼⠞⠋⠀⠀⢀⣀⣴⣿⣿⣯⣶⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣖⣤⣾⡿⠿⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠚⡦⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⣄⡀⠷⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠉⠀⢺⡆⣴⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡄⢂⢠⣦⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠠⠂⢀⡿⠀⠀⠀⡘⠃⠈⠀⢻⡆⢀⡡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⣇⢺⡀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠈⠁⣀⠈⠀⠴⠁⠀⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠄⠀⠠⠻⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠁⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠈⠀⢠⡟⠀⠀⠀⠀⠀⠀⣤⡴⣣⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠓⠄⠀⠀⢂⡴⠉⣴⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠇⢀⣠⠏⢡⡎⢶⣄⠀⠀⢙⢦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣿⣿⣣⣷⣿⠕⣠⣻⣿⣄⢹⣄⠀⡼⢤⣙⠶⣤⣰⡟⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣤⣿⠉⣿⣿⣿⣯⣾⣻⠥⣎⠉⠹⠥⢈⡽⠿⣦⡀⣀⣽⡷⠶⢄⣨⣯⣡⡀⠑
⠀⠀⠀⠀⠀⠀⠘⠛⢻⣋⣡⣌⣉⣙⠛⠿⠤⠿⠿⣠⠤⠾⠷⠦⠼⠿⠻⣉⡐⣢⡏⠥⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠉⠓⠒⠀⠶⠶⠶⠖⠒⠒⠌⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣉⡜⠛⠠⠤⠀⠀⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⢀⡔⡉⠙⠢⠀⠀⠠⠀⠀⠀⠀⠈⢢⠁⠒⢠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣦⠂⠀⠀⠀⠀⠀⡇⠀⢸⠈⠢⢀
⠀⠠⠴⣗⣾⠤⠤⠴⢿⣥⠽⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠀⠀⠈⠈⠉⢹⣿⡿⣬⣧⠤⠤⡇⠀⠀⡇⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢯⡱⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠴⠚⠛⠋⠁⠙⠛⠁⠀⡇⠀⠀⡇⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠓⠲⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣶⣷⣶⣾⣄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⠿⠿⠿⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠰⡆⠀⢫⠀⡄⠀⡄⠀⠸⠀⢠⠀⠃⠀⠆⢀⠸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡀⠃⣄⠀⠃⢸⢸⠀⠀⡸⠱⠀⠀⠀⠎⡆⠠⣆⣠⣿⠀⡀⣼⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡄⠑⠑⠛⠸⠲⠴⠤⠀⠞⠉⠁⠸⠿⠋⠾⠀⠁⠀⠀⠀⠀⠆⡰⢰⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠂⠀⠂⠢⠔⣲⠐⢰⣤⠞⠀⣶⣖⠨⣩⠇⠠⠤⢤⣄⣈⡬⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⢀⣤⢀⠈⠀⠀⠀⢀⡠⠖⠁⣀⡴⠁⣰⠃⠀⣨⣿⠀⠀⣿⠻⣤⡈⠰⢄⡀⠀⠀⠀⠈⠐⡢⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⢸⡜⣣⣄⣴⣶⠟⠋⠀⠀⣴⠞⠁⡼⠃⠀⢂⣿⡟⠀⠀⣹⣕⠈⢿⡄⠀⠈⠻⣶⣦⣤⡜⡷⣵⠀⠀⠀⠀⠀⡇
⠀⢠⡼⣷⣿⠄⠀⠈⢦⠽⣿⡿⡡⠤⣀⣠⣴⠏⠀⣼⠃⠀⠞⣾⣿⠁⠀⠀⢹⣿⡄⠈⢿⣾⠆⠀⠈⠻⣿⠧⡼⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⢂⡿⠿⣿⣇⢻⠇⠐⠶⣷⣿⡿⡶⢠⡄⣼⣿⡷⣦⢬⡿⠿⣦⢤⠰⣾⣢⠀⠀⠀⠀⠀⠀⣤⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠙⠜⠢⠜⠁⠈⢸⠧⡆⠆⠊⠀⠳⠋⠄⠃⠀⠈⠓⠽⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⡆
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣿⣧
⠀⠀⠀⠀⠀⣰⣿⡿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⣆
⠀⠀⠀⠀⢠⣿⡿⠁⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢿⣿⡆
⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢶⣝⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠈⢿⣿⣆
⠀⠀⠀⢠⣿⣿⠀⠀⣼⡀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⣯⠻⣿⣷⣦⣄⡀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠈⣿⣿⠀⠀⣿⣧⡀⠀⠈⠻⣿⣷⣄⡀⠀⠀⣰⣿⣿⡆⢻⣿⡆⠀⠙⢿⣿⣿⣆⠀⢀⣼⣿⡿⠀⠀⣰⠀⠈⢿⣿⡄
⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣷⣶⣿⣿⣿⠃⢸⣿⣿⡄⠀⠀⠙⢿⣿⣷⣿⣿⠟⠁⠀⢠⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠸⣿⣇⠀⠸⣿⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣄⠀⠀⠈⢻⣿⠟⠁⠀⠀⢠⣿⣿⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣧⠀⠹⣿⣿⣿⣿⣷⣤⣀⠀⠀⠙⠻⠋⠀⣠⣿⣿⣿⣿⣿⣧⠀⠀⠈⠁⠀⢀⣠⣾⣿⣿⡿⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⡿⠃⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠄⠀⠸⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⢴⣿⡿⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⠀⢀⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠂⣸⠱⡄⠈⠈⢳⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⢦⢄⡀⠂⠄⠀⣤⣀⠀⣠⠗⠊⢺⠀⠀⠌⡢⡈⠀⠀⡰⡅⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⣇⠉⢦⠀⠀⢸⠈⣶⠇⠐⠃⢸⠀⠊⣠⠥⢹⠀⠀⠁⢃⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡧⣒⠀⠀⣼⠀⠈⢇⠀⢸⠁⠆⠌⠀⠆⢸⠀⡰⠁⠀⢀⠁⣰⢀⠌⠀⢱
⠀⠀⠀⠀⠀⠀⠈⠀⠱⣌⢉⣳⣿⠂⢀⡈⠢⣜⠘⢄⠀⠀⠠⠈⢶⢃⠀⠀⣜⡴⡽⠀⢀⢦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢧⡀⠤⢀⡈⠂⢈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠐⠟⡞⢁⠔⠉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢱⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠈⡤⢰⡔⠁⠔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢵⣸⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠰⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢠⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠁
⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢉⣝⠁⠀⢀⡤⡤⢄
⠀⠀⠀⠀⠀⢻⣡⣀⣠⣠⡤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠤⠶⠲⠶⠶⣿⣿
⠀⠀⠀⠀⢀⡏⠉⠉⠀⢀⠀⢀⠖⡎⠙⢦⡀⠠⣴⠅⠂⠺⡦⣷⡄⠀⠈⠉⠩⠉⠒⢦⡄⠀⠀⣸⢉⣸⡆⠀⠀⠀⡀
⠀⠀⠐⠒⠤⠆⢾⡆⠀⣉⣨⣿⡀⠁⠀⡂⡅⢀⡷⠀⠀⢵⠚⠉⢷⡐⠷⣤⣀⡂⠀⣾⡷⠛⠛⡿⢎⡼⠁⠁⠀⠁⠈
⠀⠀⠀⠀⢀⡘⠶⠓⠛⠉⠉⠉⢻⣀⣢⣴⡧⠛⢛⣉⠠⠛⣢⡒⠛⢦⣰⠀⠹⡁⠿⡿⠷⠤⣤⣶⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠹⠷⠶⠿⠁⠀⠀⠈⠙⠲⠆⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢄⠀⠀⠀⠀⠀⡄⠀⡇⢀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⢷⠀⠀⠀⢰⡿⣄⠐⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠜⠀⠀⠀⠈⡧⢈⠑⢄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣧⠀⠀⠀⠀⠀⠘⢖⠁⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⢸⠀⡼⠀⠀⠀⠀⠀⠑⣤⠂⢀⠙⣆⠀⠀⠀⢀⠞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⢀⠨⣸⠀⢇⠳⡀⢤⣀⠀⠀⠈⢢⠀⢐⡘⡆⠀⢠⢁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⡂⠑⠄⢳⠀⠀⠁⠺⠌⡮⠳⡄⠀⢸⠂⡁⠁⢵⠀⠘⣡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡇⠀⠘⢄⠈⠢⡀⠀⠀⢠⠇⠂⣻⢠⠏⠀⠇⠠⡍⠀⢰⢻⡀
⠀⠀⠀⠀⠀⢯⠢⣄⡀⠀⠀⢳⠅⠘⡀⠑⢄⠙⣆⣠⠋⣠⠀⠿⠉⡠⠁⠂⢠⠃⠀⡼⠐⣇
⠀⠀⠀⠀⠀⠈⠢⡀⠙⡄⠀⠀⠱⡄⠑⡀⠀⠳⡈⠃⡐⠀⡄⢀⠎⠀⡐⢠⠏⢀⣴⠇⠀⢻⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠰⣤⣅⡚⠀⠀⠀⠘⣦⠐⡀⠀⠱⡐⠀⠀⡖⠁⠀⡐⢠⣮⡴⠛⢁⡀⠀⣼⠀⠀⢀⠜⣹
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡌⠓⢤⠀⠀⢸⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠛⣀⠄⠒⡉⠀⣴⠏⠀⢐⡡⠞⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⡀⢳⡀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⢀⠎⢀⡤⠁⠀⠀⢈⠔⢫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡄⢷⠟⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘⠀⡜⢁⣴⠏⡴⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠐⠀⢠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠘⣵⠯⢹⢰⠃⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠃⢦⢘⠟⡌⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠈⢦⡰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠀⣀⣀⠀⠠⠌⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠡⠐⠈⠐⠠⠀⠠⠀⠤⠂⠄⠂⠀⠠⠀⠠⠤⠆⠑⠀⠀⠁⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠈⢻⠀⠀⠀⠀⣦⡀⠀⠀⠀⢨⡏⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣬⢳⣤⡶⠟⠀⠀⠀⣸⣿⣿⣄⠀⠀⠘⠷⣦⣤⢫⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠈⠛⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠈⠙⠉⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⣿⣿⣿⡄⣤⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⣹⣿⣄⠀⠀⠀⠀⠀⠀⣰⣿⣁⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⣀⠀⠈⠉⠛⠳⠤⣀⣠⠴⢚⡋⠉⠠⠒⠊⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣤⣅⡀⠀⠠⢄⠀⠒⠭⡙⠳⠤⣤⣴⣶⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡚⠉⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⢈⡙⣲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢱⣮⣥⣶⣿⣿⠿⠛⠿⢶⣤⣍⡒⢦⣼⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠞⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠁⠠⡄⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⣃⠀⠂⢸⠀⣼⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠰⡀⢀⡀⠁⠀⠃⠞⠤⢷⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡱⢀⡈⠉⠿⢇⡀⠀⠀⣀⠈⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣁⠛⢦⢸⡱⠔⠒⠚⠁⣀⠐⢅⣀⢪⠐⢅⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢯⣀⠈⠙⠛⢤⠀⡠⠒⠉⠀⢶⠒⣚⠡⠋⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠤⠽⠀⠀⠀⠀⠑⠢⣤⠀⢀⠙⠃⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣤⣾⡏⠉⠁⠐⡈⠁⠰⣯⣄⣰⣥⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣷⣷⣬⣿⣷⣶⡶⢾⣧⠀⣾⡿⢿⣿⡇⠉⢫⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠃⢸⣿⡟⠁⠙⡄⠈⠻⠿⣿⠇⠀⠉⠻⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⣤⡶⢶⣄⠈⠀⣦⣴⡃⠁⣠⣶⠶⣦⣀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣸⣿⡏⠂⠘⢹⣿⣷⣿⣿⣷⣿⣟⠘⠐⢻⣿⣿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢉⠛⠻⠶⠶⠿⠿⠯⣄⣤⡼⠿⠿⠷⠶⠞⠛⢋⢁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⢂⣀⣠⣤⡀⠒⠀⣠⣿⢿⣆⠀⠐⠂⣠⣄⣀⣀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡈⠻⡍⠈⠚⢿⡟⠸⣿⠟⠁⢨⡿⢋⣤⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢿⣦⡤⠤⡤⢠⠤⡴⢤⣾⠂⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡆⠻⠗⡶⡤⡧⡶⡾⠟⢁⣄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⠀⠘⠙⠃⠉⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢦⣀⢀⣠⠶⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠂⠀⠀⠀⠀⠀⠀⠆⢸⢢⡀⠀⠉⠳⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⣀⡁⠱⠄⠀⠀⣀⡀⠀⠀⢠⡯⠔⢹⠀⠀⢠⢃⡀⠠⠀⠀⣠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣟⠓⢄⠀⠀⠈⡏⠳⣠⠏⢀⡄⢸⠀⠰⠂⡸⠙⡆⠀⠀⠃⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⡅⠀⠀⢹⠀⠈⣆⠀⠀⡿⠔⡛⠰⠁⡅⢸⠀⠀⡼⠋⠀⢹⠀⢠⠁⠱⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠘⡟⠲⢤⣀⣻⠂⠂⠘⢆⠀⡏⡀⢀⠀⠀⠁⠘⡄⡼⠁⠀⠀⡔⢠⣿⠐⠁⡀⣀⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠤⣠⠾⠛⠣⠀⠦⡈⠳⠇⠈⠂⠀⠀⠈⢄⠹⠃⠆⠀⢰⡴⣣⠃⠀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠐⡂⢤⠀⠑⠠⡀⠂⠀⠀⠀⠈⠄⠠⠀⡀⠙⢹⢃⡴⠋⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡀⠸⡄⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠂⠀⢠⠆⢸⠊⠄⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢙⣄⡇⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠘⠘⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠌⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣣⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢰⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡵⠁⠀⣀⡀⣀⢀
⠀⠀⠀⠀⠀⠸⡟⣄⠈⠉⣁⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠮⣁⣤⢤⣤⣀⣀⣠⡆
⠀⠀⠀⠀⠀⢰⠛⠛⠋⠉⠉⠁⠀⡠⢴⠪⣦⡀⠀⢀⣰⡂⠄⢴⣄⣦⡀⠀⠀⠒⠒⡲⢦⣤⣀⡀⠀⠀⢀⡎⠎⣧
⠀⢀⣀⣀⡀⣉⢀⣤⡀⠠⠂⠒⣼⠀⠺⠐⠄⢑⠀⢹⡏⠄⠠⣂⠩⠳⣿⠠⣄⡀⠀⢠⡁⠀⣿⣧⣤⣦⣼⣴⢛⡟⠠⠀⠤⠊⠒
⠀⠀⠀⠀⠈⠉⣄⣻⣥⡤⠾⠛⠿⣦⠀⡀⠠⣸⢠⣾⣥⠆⠀⠜⠀⣀⣯⣇⠈⡙⠳⡶⢂⢼⣿⣃⠀⠀⡏⣕⣿
⠀⠀⠀⠀⠀⠒⠊⠉⠀⠀⠀⠀⠀⠘⠳⠷⠟⠛⠁⠀⠱⣾⣈⠀⣾⡦⠀⠉⠳⢧⣄⣑⠎⢹⠏⡉⠉⠛⠛⠛⠁⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡄⠀⠀⢀⠜⠀⠀⠀⣄⠀⠀⠀⠘⣆⢀⡇⠱⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠢⣄⠎⠀⠀⠀⢀⠛⡄⠀⠀⠀⠸⠞⠀⠀⢧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⡄⠀⠀⠀⠀⠀⠀⠘⣴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣸⠀⠀⣄⠀⠀⠀⠀⢰⠃⠀⠀⢱⠀⠀⠀⢰⡆⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⠀⠀⡏⠱⣄⠀⠀⡎⠀⠀⠀⠈⡇⠀⡰⠃⢱⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣄⡇⠀⠈⢣⡀⡃⠀⠀⠀⠀⣧⠊⠀⠀⢸⠀⣠⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡏⠃⠀⠀⠀⠙⠇⠀⣷⠀⠀⠁⢀⣶⠀⠘⠋⢸⠟⡈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠹⡄⠀⠀⢶⣀⠀⣰⠁⢣⣠⠞⠁⢸⠀⠀⡰⠧⣪⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡹⡄⠀⢸⠈⠳⠇⠀⠘⠁⠀⢀⡼⢀⡴⢥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠻⠤⠬⠦⣤⠔⠒⡒⠒⠲⢾⠒⢭⡰⢄⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡴⠊⠀⠀⣠⠔⢑⣦⡈⠳⠄⠀⠀⠰⢍⠂⠉⠲⠌⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣷⡦⡜⢁⠄⣠⠔⠋⠀⣠⠵⠚⠉⠲⢄⡐⢦⡀⢄⠙⠆⡴⢊⠵⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣟⠷⡜⠀⡠⢖⡩⠖⠉⠀⠀⠀⠀⠀⠀⠉⠲⣌⠳⠁⡞⡰⣟⡼⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣒⣱⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣧⣠⠭⠒⠁


⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⣄⠀⢶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠦⣈⡇⠀⢧⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⡄⠈⠁⠀⢸⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢳⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⠀⠀⢠⠏⠀⠀⢸⠇⠀⢸⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡟⠀⡴⠃⠀⠀⠀⣸⠀⠀⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢸⢃⠞⠀⠀⠀⠀⢠⠇⠀⠀⠉⢀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢸⡼⠀⠀⠀⠀⠀⣸⠀⢀⡴⠚⠉⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠸⡇⠀⠰⣆⠀⠀⢸⣠⠏⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⠛⠀⠀⣴⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠏⣸⠀⠀⠀⠀⢀⡴⠙⡆⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠹⣄⠀⠀⡞⠀⢻⠀⠀⡤⠚⠉⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠀⠈⠳⣤⡇⠀⠀⠳⠞⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡶⠚⠉⣱⠶⠤⢤⣤⠤⠤⢶⣊⡥⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠧⣄⢀⣼⡏⠀⠀⢸⠛⣄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠼⠋⣼⢤⣤⣀⡏⠀⠈⢦⣠⠔⠚⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁⠀⠀⠈⠓⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⣦⡹⣿⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠂⡀⠀⠀⠀⢿⣿⣷⢹⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠐⢦⣄⠀⠀⠀⠸⠃⣼⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠋⠇⠀⠀⠀⢸⣿⣿⣦⣤⣴⣿⣿⡏⠀⠸⣷⣄⠀⠈⣿⡷⠈⢷⡄
⠀⠀⠀⠀⠀⢀⣆⠀⠀⢸⣿⡇⠀⠀⠀⠘⣦⣸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣇⠀⠸⡇⠀⣼⡗
⠀⠀⠀⠀⠀⢸⣿⣶⣴⣾⣿⠁⠸⣦⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡄⣼⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠈⢻⠀⠀⠀⣤⡀⠀⠀⢸⠋⠀⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢎⣦⡴⠋⠀⠀⣰⣿⣷⡄⠀⠈⠳⣤⣎⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⢻⣿⣷⣿⡄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠈⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠍⠙⠚⠻⢦⣄⠀⢀⣠⠾⠟⢊⠭⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣅⡀⠀⠄⠐⠩⢝⠲⠥⣀⣤⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⡙⠓⣶⣤⣄⡀⠀⢀⠀⠈⣙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣷⣾⡿⠟⠛⠉⠙⠻⠶⣭⣵⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⡿⠋⠉⢳⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠈⠛⠛⠻⠿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⠉⠀⠀⢀⣀⣠⣤⣤⠆⠀⠀⡀⠀⠀⣤⣤⣀⣀⠀⠀⠈⠙⠻⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠁⠀⣀⣤⣶⣿⣿⣿⣿⣿⠏⠀⢀⣼⡇⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⣠⣾⣿⣿⣿⣿⠉⠉⠛⢿⣿⡟⠀⠀⣾⣿⣿⣿⠀⠀⢻⣿⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣼⣿⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠃⠀⢰⣿⣿⣿⣿⡆⠀⠘⣿⠏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⣻⣿⣿⡄
⠀⠀⢀⣾⣿⡟⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣦⡀⠀⠀⢸⣿⠁⠈⢻⣿⡀⠀⠉⠀⠀⣶⠀⠀⢻⣿⣿⠿⠋⠁⠀⢀⣤⣾⣿⣿⣿⣿⣆
⠀⠀⣼⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡆⠀⠈⣿⡆⠀⠘⣿⣷⡀⠀⠀⣼⣿⡇⠀⠈⠋⠀⠀⣀⣴⣾⣿⡿⠟⠉⠀⠙⣿⣿⡄
⠀⣼⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⠀⠀⣿⣷⣄⠀⢸⣿⣷⣦⣾⡿⠛⠁⠀⢀⣠⣴⣿⣿⡿⠛⠉⠀⢀⣠⡄⠀⠸⣿⣿⡀
⢀⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢀⣤⣶⣿⣿⠿⠋⠁⠀⢀⣠⣶⣿⣿⣷⠀⠀⢻⣿⣧
⢸⣿⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⡟⠉⠻⣿⡟⠉⢻⡿⠋⠉⠁⠀⣀⣤⣾⣿⡿⠟⠋⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿
⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⣿⡇⠀⢸⣿⡷⠄⠈⠀⠀⣠⣴⣾⣿⡿⠟⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿
⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣧⠀⠀⠁⠀⢀⣠⣴⣿⣿⠿⠛⠁⠀⢀⡤⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿
⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⠋⠁⠀⢀⣤⣾⣿⣿⠟⠋⠀⠀⠀⠀⢸⡟⠁⠀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿
⢿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⣀⣴⣾⣿⡿⠟⠉⠀⠀⠀⣴⣾⠀⠀⠈⠀⢀⣴⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿
⢸⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣠⣴⣿⣿⡿⠛⠉⠀⠀⢀⠄⠀⢀⡿⠃⠀⠀⣀⣴⣿⡿⠋⠻⣷⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿
⠈⣿⣿⡆⠀⠘⣿⣿⠿⠛⠁⠀⢀⣠⣶⣿⣿⠿⠋⠁⠀⢀⣤⣶⠟⠉⠀⢀⣾⠁⠀⣠⣾⣿⡿⠛⠁⠀⣰⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⡏
⠀⠹⣿⣿⡀⠀⠉⠀⠀⣀⣤⣾⣿⡿⠟⠋⠀⠀⡀⠀⠀⠾⠛⠛⠓⢤⣶⣿⣿⣶⣾⣿⣿⣿⣄⣀⣤⣾⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⣸⣿⡿⠁
⠀⠀⢹⣿⣷⣀⣠⣴⣾⣿⡿⠟⠉⠀⠀⠀⠰⣿⡇⠀⠀⠀⣀⣀⠀⣠⣿⣿⠋⠉⠉⠙⠛⠻⢿⣿⣿⣏⠀⠈⠀⠀⣸⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⠃
⠀⠀⠀⢻⣿⣿⣿⡿⠛⠁⠀⢀⣤⣶⣷⡀⠀⠙⠀⠀⣴⡿⠋⠁⠀⣸⣿⠿⣦⣤⡤⢤⣄⡀⠀⠈⠻⣿⠇⠀⠀⣴⣿⣿⣿⣿⡟⠁⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠺⠟⠛⠛⠻⠷⠀⠀⠀⠘⠛⠁⠀⠀⠈⠛⠏⠀⠈⢿⠀⠀⠈⠿⠶⠀⠀⠀⠀⠀⠾⠛⠉⠙⠻⠋⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⡤⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠈⠙⠿⣿⠁⠀⠈⠀⠈⣟⠁⠈⠙⠓⠶⠶⠠⣶⣿⡟⠛⠛⠛⠛⢻⣿⡿⠟⠉⠀⢀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣀⠀⠈⠑⠒⠶⣶⣾⣿⡇⠀⠀⣀⣀⣀⣀⣼⣿⣧⣤⣤⡄⠀⠘⠁⠀⢀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣤⣀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢀⣠⣤⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣶⣶⣿⣿⣿⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠔⠁⠀⠀⠀⠘⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠣⡀⠀⠀⠀⠀⠀⠘⢆⠀⠣⡀⠀⠰⠀⠇⠀⠂⠀⡁⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢀⠜⢠⡀⠠⠀⠘⠀⠈⢣⠀⠈⠢⣄⠀⠀⠀⠀⠀⠣⡈⠢⡀⠀⠃⢠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣆⠈⠢⠀⠀⠀⠀⠀⢹⠀⢡⠀⠀⠀⠈⠁⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣸⠻⣆⠀⠀⠀⠀⠀⢀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠑⠄⠀⠀⠠⣤⣀⠀⠀⠀⢀⣴⠏⡪⢚⣇⠀⠀⠀⠀⢈⠀⠃⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠳⡄⢠⢛⠅⠋⠈⠡⢺⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡰⢀⠎⠀⠊⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢠⠀⠀⠀⠻⡳⣄⠀⠀⢸⡗⠹⣗⠅⡠⣾⠀⡪⠼⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⠀⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢇⠘⣄⠀⠀⠀⢻⠝⠆⠀⢰⡫⠂⠁⡜⠁⠺⠈⠕⡃⠀⠀⣸⡄⠀⠀⢀⣾⡇⠀⢠⠀⠳⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⢢⠀⠀⡖⠐⣺⡄⢸⢗⠁⡼⠀⠀⠸⡀⠪⠅⠀⢠⠖⡹⡄⠀⣸⣻⠁⢀⢎⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⡰⠁⢰⡫⢊⡀⢷⣼⡻⢀⠃⠀⡀⠀⢣⠘⣧⠀⡾⡊⣣⢾⠀⡿⣺⣴⢟⠅⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡛⠔⡬⠱⡄⢙⡞⢸⠀⠀⢀⠀⠀⢣⠘⣶⡋⢰⡀⠹⢠⡋⠞⢑⡡⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⠁⡆⠀⠈⠳⣌⢸⠀⠀⠀⡠⠀⠈⣇⠹⠃⣼⡀⣽⡿⢋⡄⡩⣪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡵⠀⡃⠀⠀⠀⠈⢾⡄⠀⢀⠔⠁⠀⢩⢈⠞⡸⢸⡿⣠⢺⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⡵⣿⡄⣇⠀⠀⠂⠀⠈⠃⠀⠀⡫⠂⠀⢸⡏⠀⣆⢀⡔⠁⢸⠨⣧⢔⡽⠛⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢦⡼⠆⠀⠐⡡⠀⠀⠀⠠⢖⠄⠀⠈⠁⡆⠈⠁⠠⠂⢸⠐⢱⠎⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⣀⣀⣀⣉⣲⣌⠦⠀⠈⠔⡡⠀⠀⠀⠁⡁⠀⠀⡬⠂⠀⠀⠚⠀⡼⢸⡇⣀⣀⡀⠀⠀⢀⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣔⣍⢈⡶⢳⡲⡶⠈⢣⠀⢀⢀⡠⢄⣶⠤⡀⠀⢀⢀⠈⠀⠐⣲⢖⡺⣅⣞⣙⠀⠀⢳⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠒⣀⢹⢟⠕⠜⡰⣁⠄⡏⡐⠕⠇⣉⣘⣆⡤⠣⢪⢀⢀⡧⡜⣈⣸⡣⠡⠣⢢⢸⡤⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢋⡹⠷⣤⡷⢾⡿⠾⢛⠋⠝⢛⠳⢤⣲⠈⠡⢂⡿⠐⡛⠿⣚⠾⣕⣒⣹⡟⠿⠻⠟⠛⠿⠊⠕⠂⠝⠂⠭⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠉⠀⠒⠁⠠⠛⠉⠵⠊⠁⠀⠉⠔⠊⠽⠋⠡⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢁⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢸⣿
⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣿⣿⣾⣿⣦
⠀⠀⠀⠀⠘⢿⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⡀⢰⣿⠏⠀⣤⠀⠹⣿⣿⣿⣿⡇⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⠇⠀⠀⢿⣷⣾⣿⣿⣿⣿⠇⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⡄⢻⣿⣿⣷⡀⠀⠀⡀⠀⢰⣧⠀⠀⣸⣿⡟⢀⡀⠀⠈⢿⣿⣿⣿⣿⢏⣴⣿⣿⡟⠀⠀⢤
⠀⠀⢦⣀⣴⠏⢀⠙⣿⣿⣷⠀⢀⣿⠀⣿⣿⣿⣾⣿⣿⡇⠀⣿⣦⡀⠀⠙⢿⡿⣋⢼⣿⣿⣿⣷⣤⣤⣿
⢠⠀⠈⣿⡏⠀⠸⣿⣿⣿⣏⣴⣿⠋⢀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣧⠸⣿⣿⣿⣿⣿⣿⡿
⣿⣷⣾⣿⣀⣷⡄⠘⠻⣏⣾⣿⣿⣦⣾⠆⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⣦⢿⣷⣿⣿⣿⣿⣿⡟⠁
⠈⠿⣿⣿⣿⣿⡇⠀⢠⣿⣼⣿⣿⣿⠏⣾⣆⣀⣸⣿⣿⣿⣿⣿⠃⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣤⣿⣿⣿⡏⣀⣤⣾⣿⣿⣿⣿⣏⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠙⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠆⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗
⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⡄⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⢶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⠊⡈⠀⠀⠀⢀⡆⠀⢀⡀⠀⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⣀⣼⠀⢰⡁⠉⠀⠎⠰⣋⡈⢪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⢳⢸⢸⣿⠀⡌⠳⢦⡀⢄⠸⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠂⠣⡱⡌⢆⢣⠻⣷⡙⡄⠀⢻⡌⣆⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠈⢀⢩⠑⣌⢻⣾⣷⣇⠹⣷⢹⣴⣼⡿⢸⢀⠀⠈⡇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢑⡏⣝⡳⣿⣿⣿⣶⡿⢸⣿⣟⡵⠋⡈⠀⣸⠇⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠠⠓⠂⢀⡇⠘⣿⣿⣿⣧⣿⣿⡋⣰⠾⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣀⣀⡀⢐⡄⠸⣧⠰⡘⣿⣿⣿⣿⣿⣿⣷⣷⢄⡀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠀⠟⠹⢭⠏⠛⢿⣿⠿⡿⠋⠉⠁⠀⠀⠀⠃⠈⠈⢉⡶⡲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣠⠇⠀⠀⣀⠴⠊⠉⠀⠀⠀⢀⡀⠀⠀⠉⢀⣦⡄⣾⢰⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠛⠂⠙⡟⠲⢖⢦⡀⠀⢠⣰⣯⣦⢀⠏⠙⠋⢹⣿⠾⢦⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⣿⡅⠀⠀⣧⠀⡌⣿⣇⣤⠞⠛⠈⢿⣾⣄⣉⣀⣿⠻⡇⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣷⣀⣨⡥⢴⣿⠟⠛⢲⢿⣿⢿⣧⣈⣠⡼⠏⡉⠫⠁⠀⠀⠂⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠷⠀⠐⠈⠁⠀⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⣼⢀⡜⠀⠀⠀⠆⢀⡀⠀⠀⠀⠐⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣡⢘⣭⣿⠃⠀⠀⣀⠄⠀⠈⣦⠀⠀⠀⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⢏⣰⠳⢡⢸⠁⢰⠇⠀⣿⠀⠀⣀⠤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢃⣎⣿⣿⣀⡞⣠⡞⠿⢠⣾⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢏⣯⡿⠟⠋⣾⣯⣿⣿⣾⠟⢣⠁⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⠄⠁⣀⠟⢁⣰⣶⣿⠏⢻⣿⣿⣷⣯⡼⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣈⣤⣶⡿⢃⣴⣿⣿⡟⣿⠀⢨⣿⣌⢿⡿⠟⠿⢿⣃⣢⡀
⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋⣹⣻⣾⣿⣿⡏⢠⣿⠀⢻⣷⢿⣮⡻⣶⣦⣈⡛⠿⢿⠁
⢠⣤⣤⣴⣾⣿⣿⣿⣇⣺⣾⣟⣯⣿⣿⣿⣛⣿⡿⢠⢼⣿⣷⣬⣷⣬⣿⣿⣿⣷⣴⣟⣶⣶⣰⣖⣶⣀⣄⣀
⠀⠉⠁⠉⠉⠉⠉⠙⠅⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠒⠉⠈⠉⠈⠉⠉⠙⠉⠉⠉⠉⠉⠙⠛⠁⠈⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣴⡀⠀⠀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣦⣿⣿⣧⣴⣶⣶⣾⣥⣾⣮⣿⣷⡄⠘⠓⣦⠀⠛⣒⣶
⠀⠀⢀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣧⡀⢸⡻⣿⣿⡇⠀⢀⢀⠐⣾⢈⢦⣠⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣶⢟⡤⣿⡋⢐⡆
⠀⠀⣼⣿⣿⣷⣷⡀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣇⠀⠁⠘⠋⠀⢠⡌⣎⢠⢦⡟⣿⣯⣾⣦⡰⠀⠉⠉⠉⣉⢉⢉⣉⣉⣉⡭⣁⡀⢀⡻⣿⣬⣽⠟⢻⣟⣾⡋
⠀⣼⣿⠟⠁⣿⣿⣧⠀⠀⠘⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⢀⢰⣾⣧⣿⣿⣾⢻⣿⢿⣼⣟⣷⣷⣤⡀⣜⣿⣏⠻⠬⣟⠚⠋⠛⠃⠀⠻⣷⠾⣷⣴⣿⡿⠟⠃
⠀⢻⣯⠀⠀⢨⣿⡿⠀⠀⠀⠈⠉⠁⠀⠉⠉⠀⠀⠀⠀⠺⠿⠿⠛⠿⠻⠿⠻⠟⠛⠛⠛⠟⠛⠿⠛⢸⣿⣿⣿⠿⠇⠛⠆⠀⠀⠀⠀⠀⠀⠟⠛⠃
⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠀⡄⠠⠀⠀⠀⠀⢀⠀⡀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡆⣱⣸⠸⣄⡏⢴⠀⣆⡄⠀⠀⠐⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠿⠟⠛⢁⠀⠅⠆⠀⠀⠘⢧⣀⡴⠀⠀⠀⠀⢀
⠀⠀⠀⠸⡄⠀⠀⣸⢸⣭⣏⣷⣿⣾⣧⣿⣼⣿⣥⣧⠀⠀⠀⠀⠀⠀⠀⣰⣆⣄⣀⡀⠀⠀⠀⠀⠀⠰⠄⠄⠸⢸⣿⠏⠃⣨⢿⡿⣿⠴⡿⠀⠀⢀⡈⣲⡄
⠀⢀⠄⣼⠇⠀⠀⠘⠿⠿⠿⠟⠟⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⢀⣰⣺⣷⣿⣿⣿⣿⡀⠀⠀⠀⢀⡵⣴⣠⡆⠀⠀⠀⠀⠙⣿⣿⣶⡞⠁⠀⣠⠬⡝⢿⡄
⠀⣾⠘⣯⢰⡇⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⢠⡠⣄⠠⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⢰⢿⡐⣤⢿⣄⡤⠀⠀⠶⠶⠿⠿⠿⠷⠴⠆⠙⠓⣿⣿⠏
⠀⠸⣷⢸⣿⣻⡆⠀⢀⡴⣫⣿⣿⢧⠀⠀⢠⣌⢿⣾⣡⡘⢶⡄⠐⠉⢻⣿⣿⣿⣿⣿⡟⠠⣏⣿⣼⣏⣼⣾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿
⠀⣼⣏⣸⣿⣿⠁⠀⣼⡿⠁⠿⠿⣾⡇⠀⢢⣹⣿⣸⣟⣹⣤⠇⡄⠀⣼⣿⡿⢿⣿⠗⠀⠀⢹⡿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠘⣄⠄⠀⠀⠀⠘⠿⣷⣤⡀
⠀⠻⣿⣿⣿⡿⠀⠀⠙⢷⡀⠀⣰⠟⠁⠀⠸⣿⡿⢿⢿⠿⢿⣾⠟⠀⠈⢻⠃⢹⡿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⠀⢠⣴⣾⣿⣿⣶⣦⣤⡄⢀⣤⣾⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢦⡀⠀⠀⠀⠀⢠⠂⠈⠀⠀⠀⠀⠀⠀⡀⠓⠀⠀⠀⠀⠀⠀⠰⣦⣳⡜⢡⣀⠀⠀⠀⣤⡀⢀⣀⣀⡤⣀⡠⣀⡀⠀⣸⣿⡻⠽⣟⣛⠉⠁
⠀⠀⣤⣤⡽⠂⠀⠀⣐⡛⣦⣰⢞⡀⠀⠀⠀⢀⡴⠣⢆⡼⠀⠀⠀⡀⢶⣽⠻⣾⢦⠹⡇⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠀⣹⣿⣿⡟⠃⠈
⢠⣖⠲⣌⣻⣆⠀⢠⡜⣿⠻⡷⢻⠟⠀⢠⢠⡿⣧⠳⣜⣷⣠⠆⠀⢸⣶⣿⣾⣷⣾⣿⣱⣇⠈⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠸⣿⣿⡿⠂⠀⠀⣄⡑⡀
⠀⠉⠛⣿⣿⠋⠀⠈⢹⣿⣿⣿⠋⠀⠀⣾⣸⣷⣿⣡⣿⡿⣿⠀⠀⠈⠙⠋⠙⠙⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠛
⠀⣴⣿⡿⠟⠀⠴⠶⠿⠿⠿⠿⠶⠶⠆⢘⣿⢻⣿⣿⣿⣷⣿⡎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⣄⠐⡇⢦⣠⡟⢀⡆⢀⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠻⢿⣦⣤⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⡷⠀⠀⢠⣾⠁⠀⠀⠀⢠⢠⡷⡿⣴⡟⣼⣁⣷⢸⡄⢣⣄⣿⢴⠁⠀⠀⢀⣾⣦⣆
⠀⢀⣠⣾⣿⡷⠀⠀⠀⠀⣰⣿⣷⡆⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⣎⣿⣧⣰⡀⠀⣿⢸⣧⣿⣼⣿⣿⣿⣿⣾⣷⣼⣿⣷⣾⣧⠀⢰⣿⣿⣿⣿⡄
⠀⠈⠉⠉⠉⠁⠀⠀⠀⢸⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⠄⠀⢠⣿⣿⠃⣿⣿⣧⠀⠛⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⢿⣿⠿⠏⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠻⢶⡀⠺⢗⣶⠄⠸⡌⠻⣿⠿⠃⠀⠀⢠⠀⠀⣆⢿⣰⠀⢸⣿⠁⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⠋⠋⠛⠛
⠀⣠⣶⡞⣡⢾⡏⠁⣶⠀⠀⠀⠋⠀⠀⣼⠁⠀⡀⠀⣸⣺⣿⡇⠀⠉⠁⠀⠘⠋⠁⠀⣤⢠⡁⠠⠀⠀⠀⠀⠀⢀⣔⣿⣿⣿⣦⠀⠀⠀⢀⣶⡄⡀
⠀⡘⢿⣦⣽⡿⢹⣿⢱⣏⠀⠀⠀⢀⢃⡈⣦⣼⠁⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠐⡘⢀⢋⣶⣿⣧⣆⡀⡀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣠⢯⣽⣿⣿⡄
⠀⠹⢿⠶⢿⣦⣾⡿⠿⠋⠀⢰⣴⣼⣾⣷⣿⣻⣄⣆⣀⣀⢰⠀⠀⠀⠀⢠⣼⣇⣿⣾⣼⣷⣷⣿⣻⢿⣤⣄⡀⠀⢸⣿⣿⣿⡏⠀⢠⣿⠋⠸⠟⣿⣷
⠀⠀⠀⠀⠸⠛⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠰⣷⡿⠿⠿⠿⡿⠾⠿⠿⠿⠿⠿⠿⡿⠀⠈⠻⠈⠟⠁⠀⠀⠻⢦⠀⢀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣾⣿⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⡇⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⠟⠀⠀⠘⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⠀⠰⠟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣤⣤⣤⣤⣶⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⢸⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡄⡀⣿⢷⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢸⢻⠀⠁⣤⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣿⡆⢠⢟⡑⡇⡿⠸⡂⠀⠀⠀⠀⣆⢠⢣⡀⠀⠀⡞⢸⠀⣧⢛⡤⠀⣿⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣰⡏⣤⠏⣷⡐⠎⣱⢡⡇⡄⡇⠀⠀⠀⣸⣿⣦⠻⠃⠀⠀⡇⡌⣤⢣⡘⢞⣰⠇⣇⡘⣧⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⠻⣀⣿⠸⡼⡄⣿⠙⣯⣉⠳⣹⣇⡇⠀⠀⣼⣿⠃⡏⡷⣄⠀⠀⡇⣯⠣⢋⣹⡟⢹⢠⡸⡸⢺⣇⡸⣇
⠀⠀⠀⠀⠀⡀⠀⢸⢠⡹⣿⣼⣱⡇⣽⣶⡟⣿⢣⢧⢸⡇⢠⡇⡿⢹⠀⡗⢹⠌⣧⠀⣿⢫⣇⢻⡟⣶⣿⠘⣷⢳⣼⡟⡀⣿⠀⠀⡀
⠀⠀⠀⠀⣼⠃⠀⢸⣧⢳⣿⠣⠱⠀⣿⢿⡇⠿⢸⡃⢸⠀⣶⣼⡇⢸⠰⢻⡝⢸⣇⡆⢹⠈⣿⠸⡇⣿⢻⡄⢣⢣⢻⡇⢲⣇⠀⠀⢻⡄
⠀⠀⢀⡾⣿⠀⠀⡼⢹⣿⡇⣦⢣⠆⣿⢸⠟⣇⠘⢰⢸⣆⢻⣸⡇⡄⣇⡎⣿⣏⣹⢁⡾⣰⠙⢀⡟⢹⢸⡇⣆⢧⡤⣿⣿⠹⡄⠀⢸⡻⣆
⠀⠀⢸⡇⠹⣶⢞⣡⠇⣿⢹⡏⣿⠀⣿⠘⣇⠹⣇⢸⡇⡟⢾⡿⢀⣷⢹⠀⣿⡙⣿⠚⡇⣿⢰⡿⢠⡇⢸⡇⡿⡜⡗⣽⠁⢆⣝⣶⡞⡀⣿
⠀⢀⢸⡟⡧⢹⣬⢎⢠⣏⣤⠀⡿⡀⣿⠃⣻⡆⢦⡌⡇⣿⣾⢣⡞⡻⢸⠀⣾⢣⡿⣴⡇⡟⣴⢠⣿⡁⢼⡇⣧⡇⢰⣬⣧⣎⢬⣼⠰⡏⣿⢀
⠀⣼⢿⡇⢇⡼⠋⢋⢞⣿⡛⣦⢷⡇⡏⠈⠃⢻⢸⡔⣸⢻⣧⣻⡄⡿⢸⣿⣿⣨⣷⠈⢷⡡⣟⣾⠁⠉⢸⡇⣿⢠⠟⡿⣿⡌⠋⢻⣼⠃⣿⣿
⢰⠏⢸⣧⠞⡁⣼⣨⡞⢰⣧⡟⡏⢸⠇⣶⡀⣾⠘⣽⠃⣮⣗⡯⢿⠃⡿⢡⡇⡿⣵⢰⠈⢷⡍⢸⠀⣰⡄⣧⠁⡿⣸⣧⢹⣷⢸⡤⡹⢦⡟⠘
⡌⢄⣾⡏⣼⠁⡟⢈⢿⡿⢡⡄⣧⡿⠀⣽⡇⣯⣼⡇⡄⡏⢙⡅⡴⣸⢃⣸⢸⠣⠇⡌⢹⡜⣷⣼⡇⣿⠡⢹⣦⡇⣄⠹⣞⠏⡈⡇⣿⡌⣿⣄
⣇⣼⢻⡅⣧⡇⠷⣠⠎⣀⠋⣼⣿⠃⣶⢹⡇⠟⢹⢠⡇⣧⣾⡇⡇⣿⢸⣽⡼⡇⢸⣷⡿⠁⣿⠹⠇⣿⢡⡄⢿⣷⡉⢃⡘⢦⠰⠇⡇⣾⣿⢻
⠹⣿⠸⣇⢣⡇⡴⣣⡆⣩⡾⢋⡎⠸⡿⢸⠀⣴⢸⡆⣷⠙⠘⣇⣧⢻⢸⢣⢿⣴⡆⣸⢦⡇⣿⢠⡄⢻⢸⡇⠸⡌⠻⣎⠓⣎⢳⡀⣯⢡⡏⢸
⠀⠹⣆⠙⣎⣹⢳⢯⣾⡿⣡⠀⡇⣄⢧⡞⣸⣿⢸⣇⠛⠀⣆⢻⡘⠘⡀⢊⡌⠉⣷⢸⡔⣰⣿⢸⣷⠘⣤⢣⡄⡇⣦⠹⣿⣮⢷⢷⣩⠞⢠⡟
⠀⢰⣾⡇⢘⣿⣴⠏⣼⢡⣿⡄⣿⡿⡌⢁⡏⣿⣸⠻⡄⣾⣿⣸⣷⣄⡇⣦⠁⣤⢹⡎⢃⡟⢿⢘⡾⡇⢁⡞⣷⡇⣿⡇⢿⡈⢧⣼⡏⠀⣿⣶
⠀⢸⣿⡇⢸⡏⢟⡆⣿⠘⣏⡇⠻⠁⢻⠈⣷⢠⡟⠀⣷⢿⢹⣿⡇⣿⢃⢻⡆⢹⠀⢷⣼⢇⠸⣆⢣⡇⣼⠀⠻⢡⡏⡇⢸⢡⢸⠋⣦⢰⣿⣿
⠀⢸⡇⢹⡟⡔⣺⡌⢸⢸⣇⡏⣠⡗⢸⡞⢣⡾⢡⡷⢸⢸⡆⣹⠃⠈⡎⡼⡧⠋⢠⠈⣿⢸⡆⠹⣮⠃⣿⢸⣦⡘⣇⣷⢹⢈⣾⠰⡜⡿⢁⣿
⠀⢸⡎⢃⡐⢂⣿⠙⡿⢸⡏⡼⢁⠇⣾⣶⠟⣱⡞⡀⡿⡸⢣⣿⡆⣸⡼⣄⣿⠏⢸⡇⣿⡜⠰⣦⡙⣷⣿⡄⢆⢳⡜⣿⠸⠟⣿⡆⠃⣰⢯⣿
⠀⠘⡇⢸⠁⡾⢹⠀⣄⠺⣸⢳⡮⢠⣣⢋⠞⣿⣠⢱⠇⣰⣿⣿⢳⡿⠰⡁⡸⢠⡟⢠⡟⢷⢆⢹⡗⡌⢣⣃⢸⣇⢳⡽⢀⡄⢿⠹⡄⣹⢈⡟
⠀⠀⢻⡎⢸⡇⣾⢸⡹⡆⢱⡞⠇⣼⠃⡎⣴⢱⡇⣾⣰⡏⢹⡄⢾⡇⣼⠱⡁⡹⢠⣾⣧⣸⠸⣹⣃⡟⡄⢻⡀⡟⣾⠁⡞⣱⢸⡄⣷⢉⡾⠁
⠀⠀⠀⠙⢾⡇⢸⡎⢧⣳⡈⡷⢠⢳⠀⡟⠉⢸⡇⣿⢻⡸⣌⢷⡘⢧⠃⢣⡱⣵⢟⡀⡟⢻⠀⣿⠈⢳⠃⣄⢃⢡⠏⣰⣁⢁⡾⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠉⠀⠹⣌⢿⣹⡄⡾⣸⣠⢹⣶⠸⣇⠈⡘⣇⢼⡦⠻⣌⠻⢈⣼⢫⡾⢇⡇⡈⢰⡇⣰⡿⣴⢻⢸⡄⣞⣿⢣⡞⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢿⡌⢷⣹⣦⡇⢃⣿⠈⢰⡄⡇⢸⡇⢻⡘⣷⠇⠹⣷⡾⡁⢮⡗⣾⢱⣧⢸⡇⡛⠀⡿⡞⠘⡇⣼⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠸⡝⡌⢧⢹⡇⢸⠀⣴⡘⢡⡇⢸⢸⢸⣧⢸⡆⡀⣿⡁⢻⡜⢳⣏⡸⢸⠸⣷⢈⣴⡇⢳⠀⡇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣧⠸⡿⣇⢸⠇⣿⠧⠘⢇⢸⣸⢸⣿⢀⣰⡇⣸⣧⠻⠁⣸⡟⢷⡸⢰⠏⡼⢿⠳⢸⢰⡷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠳⣹⡸⣄⡟⢸⡇⣦⡈⠟⢸⡇⣸⣿⣄⡿⠹⣇⠿⣼⣿⠸⢃⣴⢀⣧⡘⣀⡏⣜⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡙⢷⡸⡇⢠⠛⠆⢸⣧⠀⣿⢸⡇⡄⢻⣴⡏⣿⢠⢻⢸⢨⡇⣼⠟⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣙⠓⠸⣇⢸⠸⣧⢿⡝⣾⠀⡇⣾⡿⢼⡟⣸⣨⠟⠸⢋⣵⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣬⣍⣁⢻⣧⠁⣿⠘⣴⢋⣄⣾⢁⣉⣥⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣴⠃⢛⡼⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡁⢈⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣿⣷⡄⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠠⡄⢸⠃⠀⠘⢟⡿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠁⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡜⠀⠀⠀⠀⣿⣿⡂
⠀⢠⣶⡶⠄⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⣼⡟⣨⠀⡀⣀⠀⣿⡂⠀⠀⣰⣾⣦⣀⡰⣦⣿⡻⣿⣿⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣡⡄⠀⠀⣰
⠀⣿⠇⣿⣰⡿⣯⡆⢹⡇⠀⠰⣿⡟⠛⢋⣄⡋⢹⢶⣿⣿⣿⣿⣿⣇⣤⠄⢠⣿⣿⣿⣿⣧⠀⣠⣿⡀
⠀⣿⣿⣿⣿⡾⠋⠶⠀⢿⡆⠘⣿⣥⡿⢬⣀⣀⣸⣃⡴⠻⣿⣿⣿⠟⠃⢰⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⡔⢿⣿⣹⡟⠀⠀⠀⢲⣼⣿⣄⠘⢿⣷⡀⡿⠛⢻⣿⣥⠀⢠⣾⣷⡶⡾⠟⠉⠀⠛⣿⣷⣟⡟⠛⢿⣟⠀⠀⢀
⣿⣼⣿⣿⠇⠀⠀⠀⢨⠾⣨⠛⠶⠄⢉⣬⣽⣷⢚⡉⢫⡄⠈⠛⣿⣷⠄⠀⠀⠀⠀⠘⣿⣿⡟⠁⠈⠛⠀⡠⠋
⣿⣿⣿⣿⣦⠀⠀⣥⣾⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣧⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⡗
⣿⣿⣿⣿⣿⢸⣯⣇⣸⣟⣿⡄⠀⠀⠀⠘⢿⣧⣿⣿⠹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⡇
⢿⣿⣿⣿⣿⣿⣷⣿⣼⣿⣿⣧⣄⠀⠀⠀⠀⠉⠀⠀⠀⠹⣿⠈⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⣸⢻⡇
⠘⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠻⣿⠷⣀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣄⣾⡇⡿
⠀⠹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣶⣾⣦⣌⡁⠀⠄⠀⣠⣠⡄⣾⠻⢿⣷⣦⣤⣤⣶⠿⠁⠻⠿⣿⢿⣿⣴⠃
⠀⠀⠘⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡀⠠⠾⢿⣂⣤⣌⣿⣋⣍⣀⠀⠀⠈⠠⣤⣿⠟⠁
⠀⠀⠀⠀⠙⢿⠟⠙⠟⠻⡿⢿⣿⣿⣿⣿⣿⣗⠈⣿⣠⣴⡟⠋⠉⠁⠀⠈⠉⠛⢷⡄⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠛⡿⣿⣿⣿⣿⠀⣿⣿⠁⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠓
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⢀⡀⠀⠁⠙⣿⣿⣿⣿⡟⣿⣦⣿⡀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡦⡁⠀⡰⢢⡘⣀⠈⣿⣸⣿⣇⣹⡿⠋⠉⠁⠀⠠⢀⣾⡿⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠐⢷⣮⠳⣼⣳⣴⢂⣠⠈⡄⠈⢹⣿⡏⢿⠀⠀⠀⣠⣠⠆⢸⣿⡧⠀⠀⠀⠀⠀⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣿⣬⣿⣽⣿⣧⡀⠠⣿⣷⣿⣶⣠⣾⣿⠃⠀⢻⣽⠃⠀⠀⠀⠀⠀⣧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡆⣿⣿⡿⠷⡟⠋⠁⠀⠀⢿⡿⣂⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⢿⡿⣿⣿⣿⡟⠁⢻⣰⠀⠀⠀⠀⠘⣿⣿⣤⣠⣆⣤⣿⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢶⠀⢰⣿⣿⣦⠹⣯⢻⡤⠻⡏⣇⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠛⠀⣀⠻⣿⣿⡆⢿⡐⠇⠀⢱⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⣄⠨⣑⣿⡝⢿⡬⣧⢡⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⡁⠛⢈⠳⣿⡆⢷⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠈⠓⣻⣿⡈⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⢄⠀⠀⠹⣿⣇⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣹⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠀⠄⠀⢀⠀⠀⢸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠁⠀⢸⡇⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠃⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⣿⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠸⡇⠀⠀⠹⣧⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡿⠀⣿⠀⠀⠀⢹⣇⠀⣾⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇⠀⢹⡇⠀⠀⠀⢻⡄⢻⡀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⣿⠀⠘⣷⠀⢸⡇⠀⠀⠀⠘⣧⠘⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢻⣆⠀⠀⠀⢹⡀⠀⠙⠷⠾⠃⠀⠀⠀⠀⣿⠀⢸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡿⠁⠀⢸⡇⠀⣠⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠀⢸⣷⣄⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠈⣿⠙⣷⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⡏⠀⢠⣿⠀⢸⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⢸⡇⠀⠀⠈⣷⣤⣾⠃⠀⠸⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠟⠁⠀⠀⣿⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠿⣯⣅⡀⠈⠻⣦⠀⢸⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣴⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢹⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣾⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡇⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⢺⣿⡇⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢷⡀⢀⣷⡄⠀⢸⡇⠿⠾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣧⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⠻⠾⠋⣿⠀⣼⠃⠀⠀⠀⣿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡌⣿⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣧⣼⠏⠀⠀⠀⠘⣷⣼⢸⡇⠀⠀⠀⠀⡀⠀⠀⢻⣿⡟⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣷⣦⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⡇⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⠹⣧⡀⠀⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣤⡾⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⡇⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⣤⣤⣤⣤⣤⣀⣀⣘⣿⣄⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣣⣴⠂⠀⠀⠀⠀⠀⣠⣿⣃⣤⣤⣤⣤⣤⣤⣤
⣼⡯⠒⢿⣆⣀⣈⣉⠉⠉⠻⣷⣄⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣽⠏⠀⠀⠀⢀⣤⡾⠛⠉⠉⠉⠀⠀⠀⣿⠀⠘
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠙⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠁⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇
⢻⣆⠀⣾⠁⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣷⣦⣤⣽⣿⣷⣦⣤⣤⣀⣠⣠⣤⣤⣶⣾⣿⣿⣥⡶⣾⡿⠿⠿⠶⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⠐⣷⠢⣺
⠀⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⣀⣤⡶⠟⠋⠀⠀⠀⠈⢉⡽⢿⡿⠛⠉⠛⠙⣿⠉⠙⢧⡈⠀⡀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⣠⠔⠀⣠⡾⠋⠁⣼⡇⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡈⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⣁⠄⠀⠀⠀⠔⠉⠀⣠⡾⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⡀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣾⢏⡥⠖⠠⠈⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡏⠀⠀⣠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣄⢀⠀⠀⠈⢳⠞⣉⣉⡻⢷⣄
⠀⠀⠀⠀⢸⣿⠸⠀⠀⠀⠈⢘⡇⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⣿⠃⡀⡀⠃⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣰⡏⠓⠀⠀⠙⣎⣿⡄
⠀⠀⠀⠀⠈⢿⣄⠁⢰⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣟⣠⣧⣥⣤⣄⣀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡀⠀⠀⠀⠀⢉⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠷⢾⡷⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣉⠢⠀⠚⠀⠙⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣾⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣬⣓⠀⠀⢈⣩⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⣻⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠠⠀⠐⠄⠀⢉⡃⠀⢾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⣺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⢼⣷⣀⠀⠀⠀⣸⡇⠀⠀⡀⠈⣽⣏⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢀⡾⠁⠐⠀⠀⣴⡿⠁⠀⠀⢸⡄⠁⠙⠦⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡁⠉⣰⠄⠀⡆⢸⡿⠁⠀⠀⠀⣾⡇⣾⠀⠀⢨⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠦⠚⠁⠀⢰⠇⢸⠇⠀⠀⠘⠀⣿⠁⢸⡄⠠⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⡐⠀⠀⣿⠀⠈⠇⠀⡆⠀⠀⢹⡇⠸⣿⠀⡀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣏⠀⠀⠟⣿⠀⠀⠀⠀⠱⣦⠀⠋⠀⢸⡿⠀⠀⣿⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⣿⡇⢀⠀⠀⢻⡀⠀⠄⠀⠀⢹⣇⡠⠀⢸⠁⠀⡀⢸⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣚⣿⣟⢸⡆⠀⠀⠁⠀⠀⠰⠀⢸⠋⠀⠀⠀⠀⢠⡇⣽⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⠿⠾⢿⣄⠸⣄⢰⡇⠀⣴⠀⠀⣸⠀⠀⣠⣾⠷⢿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣬⢻⣷⣿⣶⣿⣶⣿⣷⣶⣿⣾⣿⠟⠁⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣹⢟⢁⡽⠋⢛⠉⢻⡋⠙⢯⡈⣻⣿⣥⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⣿⣧⡶⠉⢂⡠⠊⢷⠀⠑⢌⡀⠈⢶⣼⣇⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢈⣿⢷⣤⠮⣤⣄⡼⢦⣠⣤⣵⣦⣾⠏⠉⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣷⣤⡿⠃⠀⠉⢳⣾⠿⢦⣶⡟⢉⠉⠙⣇⠀⠀⣸⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠈⠛⢯⣤⣤⡔⠛⠡⠀⢀⠉⣣⣀⣁⣠⣾⣶⡶⠋⠀⢴⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠙⠶⠶⠶⠾⠛⠋⠉⠙⠉⠉⠁⡀⠴⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠖⠄⢠⡄⡄⡄⡀⠀⡄⠀⠤⠒⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⢻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠤⣤⣄⣀⡀⢀⣠⡴⠿⠷⠶⠶⠶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⠀⠀⠀⣾⠟⠛⠋⠉⠉⠉⠁⢀⣀⣀⣀⣀⣠⣤⣬⣽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡄⠀⠀⠀⠀⣿⡀⠐⢶⡄⠀⢀⡴⠟⠋⠉⠉⠉⠉⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢸
⣿⡨⠻⣦⣤⡀⠀⠙⢷⣤⣾⡁⣠⡞⠁⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣠⣬⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣸
⣿⡇⣀⡀⢹⡇⠀⠀⠈⠉⠉⠻⣿⠀⠀⢶⡄⠀⠀⣼⠃⠀⠀⠀⠘⠁⠀⠈⢻⡄⠀⠀⠀⢸⠁⢰⣾⡴⡿⠀⠀⠈⢷⡀⠀⠀⣿
⣿⠇⠀⠁⠘⣇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣷⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡇⣸⠏⠀⡇⠀⠀⠀⢸⣇⠀⠀⣿
⣿⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠙⢷⡾⠿⠟⠛⠒⢻⣄⠀⠀⠀⠀⠀⠀⠀⣰⢇⠀⠀⠀⣬⠙⠟⠀⢸⣧⠀⠄⠀⠀⣿⠀⣴⣿
⣿⡈⠋⠉⠁⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⠤⢤⣤⣴⠞⠁⠀⠀⠀⣠⡇⣀⠀⠀⠘⠟⣿⠀⠀⢰⡏⣴⡏⣿
⣿⣧⠤⠤⠔⠲⠦⠙⠻⢶⣶⣶⣤⣤⣤⣶⣶⣶⣶⠶⢿⡇⠀⠀⠀⢀⣀⣤⡀⠀⢀⣶⣯⡼⣿⣧⡀⠀⠀⣹⠀⠀⣼⣿⠏⠁⣿
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣷⡀⠀⠀⢸⠃⠀⣀⣴⡿⠋⠁⠀⠈⢻⣿⡄⠀⣻⠀⣸⣿⡟⠈⠀⣿
⣿⣧⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠙⢿⣶⣤⣼⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠹⣿⣄⣧⣾⠿⣯⣄⣀⡀⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣹⣿⠏⠉⢀⣀⣀⠀⠀⠀⠀⠄⠰⠌⢾⢿⡛⠛⠂⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠘⠿⢿⠄⠀⢸⣿⣿⠀⠀⠀⢸⣿⣷⠊⠉⢻⢖⠒⠂⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠸⠿⠿⠀⠀⠀⣾⣿⡟⠀⠀⢸⣿⣏⣀⡀⠲⢦⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡜⠈⠁⠀⠀⣀⣀⢸
⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠈
⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⡋⠿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⡞
⣿⣿⠖⠒⠒⠒⠛⠛⠻⠿⠟⡿⠿⠿⠿⠷⠶⠶⢾⣶⣤⣤⣀⣠⡿⠂⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⢀⣼⠓⣂⡀⠀⢀⡀
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀⠀⢀⣤⡄⡀⣿⡀⢁⠀⠉⠛⠛⠿⠷⠾⢿⣿⣟⣛⣤⣤⣤⣼⡯⣀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠜⢿⣤⢸⣿⣿⣇⡟⢃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠷⠶⣤⣭⣀⣀⣀⣤
⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠿⠾⠟⠀⢸⡀⠀⣀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠨⢍⢻⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠈⡇⠀⠹⣷⣼⣿⣾⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⠀⠀⠙⣧⢻⠿⠛⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⣿⠀⡀⠀⢹⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢰⡀⠀⣠⠀⣿⡀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣥⣼⣿⣶⣿⠛⠀⠀⣾⠇⡀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣿
⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠹⣿⡇⠀⠀⢸⣿⣔⡃⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿
⣿⣿⣿⣇⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡄⣿⠇⠀⠀⠈⣿⠋⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣯⣼⣷⣶⣶⣶⣿⣿⣶⣶⣶⣶⣯⣤⣤⣤⣾⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣤⣤⣄⣀⣀⣀⣀⣻
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡀
⠀⠀⠀⣦⣿⣿⠉⠻⣿⣠⡀⠀⠀⢠⣄⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣤⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣿⡄
⠀⠀⠸⣿⡟⠃⣠⡀⠿⣿⡇⠀⠀⢸⣿⣿⠃⠘⣿⣿⣾⠆⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣜⣿⠟⠀⢹⣿⡇⠀⠀⠀⢸⣦⣿⠋⠀⢸⣿⣿
⠀⠀⠀⢻⣇⢰⣿⡇⢠⡟⠀⠀⠀⠈⢿⡇⠀⠀⠘⢻⡟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⠉⣠⣷⡀⣹⠇⠀⠀⠀⠸⣿⡇⠀⠀⠈⢹⡟
⠀⠀⠀⠀⠉⠓⠈⠒⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠀⠁⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣶⣸⣿⣷⣰⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣄
⠀⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠰⣦⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⣆⣿⣿⢿⣿⣄⣤⠀⠀⠀⠀⠀⣷⣻⣿⣿⡄⡤
⠀⠀⠀⠀⣿⣿⣿⣿⣠⣧⠀⠀⠀⢀⣿⣿⠟⠘⢻⣿⣷⡇⠀⠀⠀⣾⣿⣿⠃⠸⣿⣿⡄⠀⠀⠀⣿⣿⣿⠟⠀⢻⣿⣿⡇⠀⠀⢰⢸⣿⣷⣿⣿⢿⣷
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⢿⡿⠀⣴⡄⢸⡿⠁⠀⠀⠀⢻⣿⠁⠀⢸⢿⣿⠁⠀⠀⠀⠹⣿⠈⢀⣦⠈⢹⡿⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠙⠻⠿⠿⠋⠁⠀⠀⠀⠀⠈⠙⠈⠿⠏⠈⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠀⠻⠿⠁⠈⠀⠀⠀⠀⠀⠈⠛⠾⠛⠿⠋⠁

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⣟⣸⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⣰⣷⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⡀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣶
⠀⠀⠀⣿⣿⡿⠃⠙⣿⣿⡄⠀⠀⢠⣿⣿⣾⣿⣏⣠⣶⠀⠀⠀⠀⣷⣼⡿⠃⠈⢿⣿⡆⠀⠀⠀⠀⢸⣿⡿⢿⣯⣠⣄⠀⠀⠀⣰⣦⣿⣿⠿⣿⣿⣤⡄
⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⠁⣴⣧⠀⣿⠃⠀⠀⠀⠸⣾⡿⠧⢁⣿⣿⡟⠀⠀⠀⢹⣿⣿⡟⠀⠹⣿⣿⠁
⠀⠀⠀⠀⠙⠦⠤⠴⠛⠁⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠙⠷⠿⠿⠞⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠠⠋⠀⠀⠀⠀⠀⠙⠏⠉⠀⠀⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠀⠀⠒⠀⠀⠀⠰⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⢠⢠⠀⠀⠀⠀⠀⡀⠀⠀⡠⢠⠄⠀⠀⢦⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡳⠀⠀⠀⠀⣸⡌⢎⠳⡄⠀⠀⢠⡝⢆⠀⢇⢇⠀⠀⠀⠖⣽⡄⠀⠀⠀⠰⠂⢀
⠀⠀⠀⠀⠀⠒⠄⢳⠈⡇⠀⠀⢀⡄⣿⠇⢸⢀⠏⢠⡆⢿⡌⢈⠆⢈⣮⠀⡷⡘⢆⡽⠁⠀⠀⠀⠀⠀⠁⢀⠄
⠀⠀⠀⠐⠄⠀⠀⡌⡜⠀⠀⢀⡮⠳⡀⢠⢻⠃⢼⡻⢧⡀⠹⠏⠀⢀⣠⣚⠧⢘⡲⡄⠀⢀⠀⠀⠀⣸⡄⠀⠠⠔
⠀⠀⣀⡀⠀⠀⠀⢣⣹⠀⣤⠘⢿⡃⡱⠘⠌⣜⠭⢒⠭⠳⡀⢀⣴⠏⢉⡴⡇⠠⠶⢿⢠⣿⠀⠀⢠⠫⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⢠⠀⠁⣼⠭⠳⡈⠓⠁⣄⠀⠘⢮⢔⡊⠀⡇⡾⡒⡰⠋⠀⢣⠀⠪⡽⢸⣸⠇⣦⢹⠈⡾⠀⠀⠀⠐⠂
⠀⠘⠂⠀⠀⠀⡼⡇⢸⢗⡏⠀⠱⡀⠀⣹⢳⠀⣼⠁⠀⢰⠀⢿⡂⢇⠀⠀⠀⢳⢸⠃⠀⠉⡰⠟⣆⠙⢀⣴⠂⠀⠐⠂
⠀⠂⠀⠀⠀⢰⣏⢸⠸⣗⠥⠀⢰⠀⢠⡟⡿⢸⡃⢠⠻⣌⢣⣌⣷⡈⢆⠀⢈⢼⠘⢧⣀⡞⢁⠈⢚⡇⡏⢻⡄⠀⠀⠂
⠠⠄⠀⠀⢸⢧⡣⠞⠀⠹⡭⣄⡘⢦⡿⣥⡙⠮⣿⡌⡄⠀⠙⠺⢬⣁⠎⠀⠀⠊⡳⡄⠛⣰⠉⢣⢐⡾⢘⣸⢡⡀⠐⠂
⠀⠀⠀⠀⡀⠻⣿⢗⢤⡀⢰⣚⠛⢎⢹⡇⠉⠒⠦⠥⢬⠆⢲⣌⡐⠄⢀⡆⡘⣦⢰⢸⣠⠇⢠⠇⡾⠁⠛⢁⡏⢧
⢀⡀⠀⠸⡗⠦⡈⢷⡫⢷⣞⡸⠁⠘⠒⠓⢠⣤⣄⠈⠈⠘⢀⢧⢷⡴⢯⣄⠁⣺⢀⡄⠀⢰⢣⡏⠀⢀⢔⡫⠔⠃
⠁⠀⠀⠀⠙⣦⢸⢸⢒⠮⡴⠁⠀⢀⣠⠴⠊⠑⢮⡳⣤⣄⠂⢠⠃⠀⠫⣻⠀⡎⡽⡇⠀⠘⣾⣟⡦⣌⠈
⠀⠒⠀⡀⠀⠈⠋⡞⢸⠀⠀⢀⡴⠚⢁⡴⢚⢱⣄⠙⠺⣻⣦⡘⡆⠀⠀⣋⣇⠀⠀⣻⡶⡠⣿⣿⣿⣯⡓⢄⡀
⠀⠀⠉⠀⠀⠀⠀⢷⡈⣦⠔⠉⡠⠞⢱⢄⣤⣤⣭⣷⣄⡈⠷⣟⠯⢦⠀⣰⣯⡜⢧⣜⠷⣿⣮⡓⢧⣻⢮⡢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡨⠋⣀⡴⡏⠇⠀⢸⡝⣿⣿⣽⣺⠱⢹⢦⡨⠳⢶⡳⠯⡻⣿⡲⣌⠛⢼⡻⣎⡳⢌⣳⣿⢮⣷⣽⠂
⠀⠀⠀⠀⢀⡴⢋⣤⠞⠇⠀⠀⠀⠀⢸⠿⢿⣯⣿⣿⠀⠀⠺⠽⣦⣿⢱⢦⡈⠻⣟⣶⣕⢦⣽⣾⣿⠾⣿⣿⣫⣾⣇
⠀⠀⠀⠐⢥⣴⠛⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⠿⠿⡿⠀⠀⠀⠀⠀⠀⡰⣀⠀⡢⣄⣧⣀⠋⠀⢁⣂⢺⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⢀⠀⠀⢰⣦⣤⣤⡤⠤⡀⠀⠀⠀⣠⢀⣀⣀⣀⣀⡀⠀⠁⠉⣿⡪⣛⣏⣸⣻⡼⡱⣵⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⡯⡍⠉⡇⡇⠀⠀⠀⡁⣾⣟⣚⣿⣳⢽⠀⠀⠀⢹⢜⣿⣽⣟⣧⢎⢜⡴⢟⡿⢿⣿⣯⡭
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡯⢋⣿⠙⣇⠁⠀⠀⠀⡅⣿⣾⡿⣧⠽⠸⠀⢀⢰⢸⢮⣽⣿⣷⣿⢮⡏⢠⢎⣾⣷⣿⢋⡗
⠀⠀⠀⠀⠀⠈⠀⠀⠸⣗⣷⣷⡖⣻⠤⠀⠀⡆⡆⣇⣜⣏⣼⡧⡆⢠⠈⢸⢸⢫⣞⣿⠿⡾⣹⡿⠛⢺⣿⡱⡱⡣⣿⠦⠤⠤⠒⠀⠄⠠⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠈⠇⠀⡇⡉⠛⠛⢓⠒⠚⠁⠰⠄⠸⢸⡡⢣⢊⢞⣾⢫⣿⡯⣸⣏⢜⢔⣵⣿⠭⠭⠭⠭⣭⣭⣥⣬⡥⠤
⠀⠀⠀⠀⠀⢀⡄⠦⢿⢰⢀⠀⠀⠀⠀⠀⠀⡇⡃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡕⡵⡵⡿⡱⣡⣿⠀⣇⣧⣮⠾⠿⠏⠉⠩⢥⣀⣀⡒⠒⠂
⠀⠀⠀⠀⠀⠛⠧⢤⣤⣤⣈⣈⣀⠀⠀⠀⠀⠁⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢸⣾⢎⢎⠞⣔⣵⣿⣚⣋⣂⣒⣚⣛⣛⣛⣓⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠳⠶⠦⠤⠶⣖⣂⣤⣤⣤⣀⣸⣷⣧⣿⣿⣿⣗⣒⣒⣚⣚⡾⠯⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡿⠀⠙⠛⠀⠀⣰⠀⠀⠀⠀⠀⠘⠻⢻⣆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣻⡇⠀⠀⠀⡀⣾⠇⠹⣧⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⡟⠓⠀⠀⢰⣷⣻⡇⠀⠈⢿⣄⠀⠀⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣿⡙⢿⣷⠀⠀⠀⢻⡆⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠸⣧⡀⠀⠀⠀⠀⣸⡇⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⠿⠒⠀⠀⠚⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠀⢸⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠘⢼⠄⡸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠁⠋⢸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢠⡼⠀⠀⠀⠀⢀⠀⡄⠂⠀⠀⠈⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⢰⡋⠁⠀⢀⡦⠀⢸⣿⡟⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠀⠀⣴⣒⡶⣛⣷⡀⣰⣟⠷⣄⢈⠽⣯⣑⡦⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⣀⣀⡥⢛⡡⣠⠖⢛⣻⣿⣿⡀⠈⠻⡾⠉⠉⠙⣦⣙⠢⣄⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⢿⣧⣶⣿⣿⠃⠀⠸⠇⢠⣼⣷⣀⠀⣌⠻⣿⣿⣿⣿⣦⣶⣟⠓⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠦⠀⠀⠀⠉⠹⠿⠿⠷⢤⡴⣿⣾⣿⣿⣿⣧⣹⣴⣿⡏⠉⠁⠀⠀⢁⡀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠞⢋⣩⠉⠉⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣡⣶⡞⠁⠀⠀⠀⠰⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⢋⣠⣦⣴⣶⣤⡄⠘⠛⠛⠻⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣭⣹⣿⣿⣿⣿⣯⣀⣤⣄⣤⣄⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠋⢳⣦⣿⣿⣿⣿⣈⣿⣿⣿⣯⡭⣭⣿⡃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠹⣿⣿⣿⡿⠛⣿⣿⣿⣟⣭⣽⣼⣿⢦⡀⠀⣠⣶⣿⡿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠸⡿⣷⣼⠋⣸⣿⣿⣧⣼⣿⣿⣿⣿⣿⡀⣿⣿⣿⣟⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠇⠀⠀⢸⣃⣿⡿⢴⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⢿⣿⣯⠙⠋⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠀⢀⣀⡀⢨⣭⣷⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⣾⣫⣭⣭⡡⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢫⣟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠻⠷⣿⣌⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣏⣼⠉⣿⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠸⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⢙⣿⠛⣄⢤⠄
⠀⠀⠀⠀⢀⠀⣾⠂⣨⣿⣄⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣽⡆⠀⣠⣼⣿⣤⡿
⠀⠀⠀⠀⢸⠄⣱⢠⣾⣿⣿⣿⣿⣯⣿⣛⣻⣭⣽⣿⣿⣿⣿⣿⣯⣿⣿⠏⠀⢀⣿⣷⣿⣿⠿
⠀⠀⠀⠀⠈⠀⠛⠁⠈⣭⣿⣿⣿⣟⡛⣿⣿⣿⣿⣿⢻⡿⣿⣛⣿⣿⣇⠀⢀⣾⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠿⢿⣯⡿⡷⣾⣿⣾⣿⣿⣷⣶⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠃⢙⣿⣿⣿⣿⡾⢻⣿⣿⢿⣷⡊⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠘⠁⠀⠙⣾⣿⣟⡿⣱⣾⣾⣿⣸⣿⣽⣗⣾⡿⢽⣿⡏⣧⡙⠻⡷⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⣽⡟⢱⣿⣿⣿⣿⢿⠉⠁⢻⣿⣿⣷⣾⣿⣿⣿⣖⣧⣸⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣴⣿⣿⠃⣾⣷⣾⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡟⡟⠉⠙⠉⠙⠋⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⢸⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣾⡇⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠛⠋⠉⠉⠙⠛⠁⠀⠻⠿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣄⣀⣀⣀⡀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⡂⠀⡀⠂⢧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⡇⢀⠀⡇⠀⢃⢠⡼⡀⡀⠀⠟⢹⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⠂⠠⠃⠀⣧⡌⣸⠇⠀⠀⠈⠃⡇⠘⠀⠄⠈⠃⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠇⠀⡀⠀⡴⠀⢀⠀⠿⠀⠋⠀⠀⠀⠸⡆⣇⡇⠀⠀⠀⠈⠀⠆⠈⢆⢰⠀⠈⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⢰⠃⠀⡖⠀⠀⠀⠀⢰⢃⡼⠀⠁⢿⡇⠀⢰⢀⠈⠀⠘⣄⠈⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡆⠀⠈⠀⠀⠇⠀⣼⠀⠀⠘⢸⠇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠗⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠈⣀⠐⣑⣄⡀⠀⣀⢀⢀⣸⠀⠀⠀⣀⠰⡀⢠⡾⠀⠀⠀⢀⡠⡤⠔⢂⡄⢠⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠗⣚⣒⢒⡧⠾⣷⠗⡧⣭⣿⣤⠄⣤⡹⣢⡖⠉⠃⣠⠤⠼⠋⠊⡀⢀⠺⠁⠈⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡡⠔⣁⣀⡄⢢⠖⠁⠀⢀⣸⣛⣂⢀⣼⠥⠤⠤⢧⣵⣒⡙⠯⠍⠛⠛⣹⠚⠒⣀⣈⠤⠤⠒⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀⢔⡩⠴⠿⠓⠢⠞⠻⢋⠯⡠⠅⠞⣁⣤⣤⡆⣰⠎⡀⡏⠙⣟⠒⡲⠒⠄⠽⠒⣀⢀⣘⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⣀⠜⠃⢀⡤⠈⠀⠚⠁⠀⠊⠀⠓⢌⡃⠀⠉⠀⠃⠀⠀⠀⠀⠙⠷⢖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠶⠀⠀⠀⠀⠀⠀⢠⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠃⠀⠀⠀⠀⠀⠀⠈⠦⣀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⢸⠀⠀⠀⠀⠀⣴⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⠃⠀⠀⠀⠀⣼⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⣇⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠈⣧⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠙⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢸⠆⠀⠀⠀⠀⠀⠀⢠⡏⢹⡀⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⣴⡀⠀⠀⠀⠘⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡰⠋⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⢳⣄⣰⠇⡀⠀⠀⣸⠁⠀⢠⠏⢧⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠃⠀⠀⠀⡾⢹⠀⠀⠀⠘⣇⠀⠀⠈⠁⠀⡿⡀⠀⣿⠀⣰⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢰⡇⠈⢧⡀⠀⠀⣹⠀⠀⠀⢀⡞⠀⢃⠀⠈⠉⠁⠀⢀⡞⠀⡀
⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠙⠒⠚⠉⠀⠀⡰⠋⠀⠀⠸⠀⠀⠀⢀⣤⠞⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡇
⠀⠀⠀⠀⢸⠈⢳⠀⠀⠀⠀⣿⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⠇⠀⠀⢠⡟⠀⠀⠀⡾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇
⠀⠀⠀⠀⡎⠀⡜⠀⠀⠀⠀⡇⠹⣄⠀⠀⠘⠲⡄⠀⠀⢠⠃⠀⠀⠀⠀⡘⠀⠀⠀⢸⡄⠀⢀⡼⠃⢸⡇⠀⠀⠀⣠⡀⠀⠀⠀⡌⢀⡽
⠀⠀⠀⠀⠑⢄⡆⠀⠀⠀⠀⢣⠀⠈⠓⠶⣤⡀⠙⣦⠀⡌⠀⠀⠀⠀⠀⠃⠀⢷⡄⠀⠙⠲⠋⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠈⢧⡀⠀⠀⠀⡙⢦⣸⠆⡇⠀⢀⡀⠀⠀⠀⠀⢸⠈⢦⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠏⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠙⢦⡀⠀⡛⡄⠁⠀⢀⠀⠀⡿⣄⠐⢇⠀⢸⠀⠈⢇⠀⠀⠀⢠⠏⣀⡤⠞⠁⣰⠇
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢧⡀⠀⠀⠹⣆⡇⠈⢢⡀⣸⠀⢠⠁⠘⢆⠈⠲⠃⠀⠀⢸⠀⠀⢠⡿⠚⠁⠀⠀⣰⠏
⢋⠳⡄⠀⠀⠀⠀⣄⠀⠀⠻⡀⠹⣦⡀⠀⢸⡱⠀⠀⠉⠁⢠⠏⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠚⢁⣤⠄⢀⡞⠁⠀⢀
⠈⠢⣘⠆⠀⠀⠀⡿⣄⠀⠀⢳⡀⠀⠙⠶⠞⠀⢣⠀⠀⢠⠃⠀⠀⢠⠏⠀⠀⣠⠄⢀⡎⠀⢀⠞⠁⡟⢠⡏⠀⣀⡴⢻⡇⠀⠀⠀⣀⣀
⠀⠀⢩⡆⠀⠀⠀⣇⠈⠛⢦⡀⢳⡄⢀⡷⡄⠀⠀⢧⠀⡆⠀⠀⠀⣶⠀⣠⢞⠏⠀⡞⠀⢠⠋⠀⡼⠁⣼⣠⠞⠋⢀⡼⠃⠀⠀⠀⠩⡍⠳
⠀⠀⠈⠁⠀⠀⠀⢹⡄⠀⠀⠙⢦⠹⡌⠇⠈⠢⣀⠈⡀⢃⠀⠀⠀⣿⢰⠁⡎⠀⠐⣄⡠⠃⠀⡰⠁⠀⠼⠃⢀⡴⠋⠁⠀⠀⠀⠀⣼⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠳⠟⢰⠀⠀⠈⠉⠀⠘⡄⠀⠀⠹⠆⢠⠀⠀⠀⣀⡤⠀⢰⠁⠀⢠⡶⢀⡞⠀⠀⠀⠀⠀⠀⠀⠙⢄⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡿⡄⠀⢇⠀⠘⢳⡤⣄⣱⠀⠀⠀⠀⢸⠀⡴⢋⡍⠀⢀⠃⣀⠔⠁⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠘⢦⡈⢆⠀⠀⠱⠀⠙⠇⠀⠀⠀⠸⠜⠀⠨⠀⠀⠈⠉⠀⠀⠘⠇⢸⠋⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⡇⠀⢋⠀⠀⠉⠒⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠾⠀⢸⠀⠀⣰⠆⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢻⠀⠈⣇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡸⠃⠀⡼⠀⢠⠈⡁⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢷⡀⠘⣆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣰⠃⢀⡾⠁⠠⡧⠜⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢿⣄⡀⠀⢀⣀⣤⡴⠿⢦⡈⢣⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⣡⠴⢋⣠⠄⠀⠀⣀⣠⣤⠶⠞⠋
⠀⠀⠀⢀⣠⠤⠶⠿⢟⣉⠁⠀⠀⠑⠂⠽⠶⢷⣄⡀⠸⠦⠤⠀⠒⠒⠒⠠⠤⠴⠇⣀⠤⠾⠟⠓⠂⣉⡤⠴⢚⣋⡭⠷⢦⣄⡀
⠀⢀⡾⠉⠀⢀⡀⣀⠀⠀⠙⢦⡀⠀⠀⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠀⣠⠞⠉⠀⢀⣀⡀⠀⠉⠳⡄
⢀⡞⠁⠀⡔⠉⠀⠀⠙⠢⡀⠀⢷⡄⠀⠘⢅⣀⠘⣦⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⣼⠇⠀⡰⠊⠁⠀⠉⠳⡀⠀⢹⡆
⢸⠁⠀⠸⠀⡖⠉⠙⣆⠀⢃⠀⠀⣷⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠛⠳⠤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠁⢠⠞⠉⠲⡄⢱⠀⠘⣧
⠸⠦⢤⣦⣤⣤⣄⣀⣸⣆⣸⣀⡀⣹⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣀⣸⠀⠀⣸⣀⣆⣀⣀⣀⣥⣬⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣠⠚⠒⠒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⣿⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢳⣴⡟⠀⠀⢻⣰⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⠀⠉⠀⣷⣄⠘⠉⠀⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⠿⡇⠀⢠⣄⣿⠻⣦⠀⠀⣿⠟⢷⣠⣄⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⡿⢤⡀⣿⠀⠀⠀⣸⡏⠃⠀⠙⣧⠀⠉⠀⠘⡇⢀⠽⢆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠉⣿⠀⠀⠀⡿⠀⠀⠀⠀⢻⡆⠀⠀⢀⡟⠀⣀⠌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡓⠿⣆⠀⠀⢿⣄⡀⠀⣀⡾⠁⠀⢀⣼⠳⠊⣡⡶⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣦⣝⠷⣤⣀⡉⠙⠋⠉⣀⣠⣴⣟⠻⣶⡛⠁
⠀⠀⠀⠀⠈⠋⠀⠀⠀⣀⣠⠴⠋⢁⡼⠛⢦⣍⡻⣟⠻⣟⣛⠉⠓⠎⠳⠄⠙⣳⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢦⡐⠊⠉⣠⠖⢁⠼⠛⢮⣝⠂⠉⡉⠓⠀⢀⡴⡾⠭⢭⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣤⡙⣆⠈⡤⠒⣡⠾⠋⠉⠉⠳⣤⡙⠶⣤⡟⢸⣀⣦⣞⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣁⣿⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠉⠳⠮⣧⣀⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢄⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡈⠀⠀⠀⢠⠇⠀⡠⣠⠀⡠⢖⡨⢒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢰⢰⢠⣾⠀⢸⣄⠀⠀⠁⣎⣶⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⢢⠸⡜⡜⣿⡄⢆⠉⠳⣄⢂⠘⠯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⢀⠠⠌⡢⣧⡱⣼⡘⣿⣎⣇⡀⢹⡎⣇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⢎⡦⢾⣜⢿⣿⣷⣘⣿⢸⣿⣿⢃⡟⠔⠀⣸⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠙⡎⢻⣿⣿⣿⡇⣾⣟⡵⢋⣤⣢⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇⠀⠀⠀⡀⢠⡇⢀⠻⣿⣿⣿⣿⣿⣴⣯⣍⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡛⢳⠶⡗⡤⢿⣦⣷⣿⣿⠿⠛⠛⠛⠉⠩⠑⠂⠫⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⠇⣸⠀⠈⠁⢂⡼⠛⠁⠁⠀⠄⠀⠀⠠⠆⠀⡀⢀⡞⡐⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠿⠧⠀⣶⠯⣥⣄⠀⠀⠀⢠⣞⣅⢠⠖⠶⠖⣾⣮⣧⣑⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⡖⠄⠀⣷⠀⠘⣮⡇⣀⠼⠛⠙⣯⣼⠀⠂⢠⡿⣿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⣈⣃⣠⣴⣿⠶⢦⣾⣟⣿⣆⠘⣀⣼⠟⠙⠏⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠚⠉⠶⠀⠀⠘⠋⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣧⢤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⢸⡿⣇⠀⠀⠀⠀⠀⠀⡔⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣼⣿⣿⠁⠀⠀⠀⠀⢀⢷⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣶⣴⡄⠀⠀⠀⠀⠈⡏
⠀⠀⠀⣾⠿⠿⣿⣰⠀⠀⠀⢠⡾⠿⠿⠷⠆⠀⠀⠀⠀⠀⠈⠛⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠲⠦⠠⠖⠂
⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠏⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢾⣦⡏⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣴⣿⣿⣼⡯⠀⠀⠀⠀⠀⣾⠱⢀⡤⠀⠀⠀⠀⠀⠀⣇⣿⡰⣤
⠀⠀⠀⢀⣶⣶⣶⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⣾⢿⡿⣿⣿⠟⠁⠀⠀⠀⣴⣿⣷⣿⣿⠘⠃⠀⠀⢀⣰⣾⣿⣼⣷⣿⣄⣀
⠀⠀⠀⠘⠛⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⣈⠙⠀⠁⠀⠀⠀⠀⠘⠛⠛⠿⠟⠋⠀⠀⠀⠀⠚⠛⠛⠟⠛⠛⠛⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡄⡏⠀⠀⠀⠀⠀⠳⢻⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⠀⡜⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢻⡀⡇⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⢇⣠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠁⠀⠀⠀⢸⠁⢱⠀⡀⠀⠀⠀⠘⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⣀⣯⠀⠀⠀⠀⠀⡜⠑⠃⠀⠈⠛⠹⡀⠀⠀⠀⠀⢱⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡶⠇⠀⠀⠀⠀⠀⠀⠀⠸⠊⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠈⠒⠤⣄⣀⡠⠴⠊⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣟⠒⠤⢄⣀⣀⡤⠤⢄⣀⣀⡠⠤⠒⣾⡵⢮⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣯⠟⣿⡀⠀⢀⣰⠁⡆⡞⢝⡟⣄⣀⡀⠀⡿⣝⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠯⠼⠒⠋⠉⠘⢄⠧⣉⡽⢃⠇⠀⠈⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡇⠀⠈⠀⢠⡀⢸⡆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⣡⠀⠀⠀⢠⡇⠼⠃⢠⠀⠀⣷⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠾⠀⠀⣸⠀⠸⡁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⡀⠀⠀⢀⠀⠻⠆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⢸⡇⠀⠀⢸⡀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣼⠁⠀⠀⠈⡿⠀⠀⢸⡆⠀⠀⠀⠀⢰⡀⡆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠐⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠘⢁⠀⢸⣇⡷⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣻⠇⡆⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⢸⠘⠁⠀⠸⠀⠛⡟⠃⠀⡀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢠⡋⢠⡟⠀⠀⠘⠀⠀⣶⡄⠠⡄⣾⠈⠀⠀⠘⠃⠀⠰⠀⡄⠀⠀⠀⢸⡇⠘⠁⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⣷⠀⡁⠀⠀⠀⠀⠀⠹⠃⠀⠀⠻⠀⠀⠀⡄⠀⠀⢠⠀⠀⠆⠀⠀⠐⠁⣾⠀⣆⠘⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠀⠀⠛⢣⡟⢸⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢠⡀⡇⠸⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⠠⡇⢀⢀⡅⠈⠠⠀⠄⢰⠀⠀⠀⢀⠀⠠⠀⠃⢻⠆⢸⡇⠈⢠⡆⢺⠄⢀⠰⢃⡀⠀⢠⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⢠⠌⢇⡄⠀⡀⠀⢀⣈⣥⣾⣯⢠⠀⢸⡄⠁⠐⠀⡼⠀⠀⠈⠀⠘⠛⢀⡄⢀⢸⣆⠘⠃⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡈⢠⡀⠁⠘⠿⠄⠌⠛⢿⡿⢘⣿⣦⡘⠀⣠⠀⠘⡧⣀⠀⠀⠀⡀⢂⣬⠷⣿⠋⣻⣷⠶⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠑⠀⠀⡂⠀⢤⡀⠀⣢⠈⠉⠸⣿⠀⠁⠀⠰⢀⣿⠃⠀⠄⠀⣼⡏⠀⠛⠘⠛⢁⠠⡄⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣆⠈⠛⢷⠀⡄⠉⣠⣿⡞⣯⠉⣤⡙⡄⠉⡀⠀⠀⠃⠉⠙⠁⠀⠀⠀⠙⠅⢀⡤⠀⠀⣿⠀⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣦⠟⠒⠚⠛⠷⣧⡙⠛⢿⠇⠉⠀⠙⠗⢻⣦⠉⣤⣁⠀⣀⠐⢠⣿⣆⠀⢴⣶⠄⢻⠇⢰⣿⣦⡄⠾⠽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢰⣿⡷⠆⠉⠀⠠⢤⣄⠀⠀⣀⣼⣿⠟⠋⠉⠈⠛⢿⣿⣷⡌⠉⠀⠄⠐⠀⠷⣤⣀⡀⢠⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⡤⢤⣤⣶⣿⡟⠁⠀⠀⠀⡀⢢⠋⠀⠀⠉⣻⠃⠀⠀⠀⠀⠀⠀⠙⣯⠀⠀⠀⠀⡆⠀⠀⠀⠹⡿⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠓⠒⠛⢾⡆⠲⠦⠶⢖⣿⣄⠀⢀⡾⣿⣦⡀⠀⠀⠀⠀⣠⣶⣿⣷⢤⡴⣢⡿⣶⠠⠠⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠛⠛⠙⠿⠷⠦⠴⠿⢯⣄⣒⠂⠒⠚⢋⣋⡸⠛⠛⠛⠻⠟⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣀⣼⠿⠛⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠈⠻⣿⠁⠈⢿⣿⡆⠀⠀⠀⠈⢿⣿⢻⣿⣿⣿⣿⣿⡟⠁⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣿⣷⣦⣀⡀⢀⣽⣆⠀⠀⠈⠃⠀⠀⠀⠀⠸⠏⠀⢿⣿⣿⡿⠋⣠⢾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⡆⢻⣿⣿⣿⣿⡿⢿⣿⣆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣼⡿⢋⡴⠛⠁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣧⠀⠙⠛⢀⡄⢸⣿⣧⠀⠀⠀⣠⣾⣁⣀⣤⣶⡏⢰⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⡄⠀⠀⠈⢿⣶⣿⣿⣧⣷⠘⠛⠉⢡⣿⣿⡟⢀⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣌⠛⢿⣷⡄⠀⣷⣾⣿⣿⣿⣟⣁⠀⣀⣴⣿⠿⢋⣴⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣦⣉⠛⢦⣜⣿⣿⣿⣿⣿⣧⠾⠟⣋⣥⣶⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⣤⣭⣭⣭⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢛⣥⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣭⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣹⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠻⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⢸⣇⠀⠀⢠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⠟⠁⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡾⡄⠀⢰⠏⢧⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⡞⠀⠹⣤⠏⠀⠘⣇⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣼⠀⠀⠀⠈⠀⠀⠀⢹⡀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢦⡀⠀⠀⠀⠀⣠⢟⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣛⠻⠶⣦⣤⣀⣀⠀⠉⠛⠻⠿⣷⣶⣶⠿⠿⠛⠉⠀⢀⣀⣤⣴⠶⠟⢛⣛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠦⣭⣉⡀⠀⠈⠉⠛⠻⠶⣶⣤⣄⣀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠁⠀⠀⣈⣩⡤⠶⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠰⠦⣬⣉⡛⠲⠦⣬⣙⣓⣶⣤⣽⠿⠟⣛⣩⡥⠶⢚⣋⣡⠤⠶⢚⣋⣩⠤⠖⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣬⣭⣿⡶⠶⠟⠛⠉⠀⠐⠚⣋⠉⠀⠀⢈⣉⡅⠀⠀⣛⣩⣥⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣿⣋⣩⠤⠖⢚⣋⣥⠴⠖⠛⠉⠁⠀⢐⣛⣩⣥⣶⡾⠻⠿⣭⣙⣿⡷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢡⠖⠲⣌⢻⡆⠀⣈⣩⡥⠴⢒⣋⣤⣴⠶⣾⣿⣙⡛⠶⢤⣍⣉⠀⢠⣿⢡⠶⠲⣎⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠹⣤⣠⠟⣸⣇⣈⣭⣴⠶⠟⠛⠉⠁⠀⠀⠀⠈⠉⠛⠻⠶⣶⣭⣁⣘⣷⡸⢦⣠⠞⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⣶⠾⠛

⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣼⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠵
⠀⠀⠀⣼⠱⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠸⣿⠂⠁⠀⠀⠀⡌⣄⠀⠀⠀⠀⠀⠀⣐⠀⢠
⠀⠀⢸⡍⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢂⣰⠂⡗⢰⡀⠀⠀⠀⢡⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠃⢰⠀⡀
⠀⠀⢸⡄⡇⡄⠄⠀⠀⠀⢸⠘⡇⠀⢠⠀⠀⢈⢋⣤⢀⡧⢄⠀⠀⠀⠀⣸⢠⠀⠀⠀⢠⠃⣸⡆⠀⠀⠀⠀⡘⠀⣾⢀⠁
⠀⠀⠈⠇⠀⠱⢸⠀⠀⠀⢦⠀⢱⠀⡆⠀⠀⣏⠈⠹⣏⠃⢛⠀⠀⠀⠈⡭⠔⠁⠀⠀⡎⠀⣿⠀⠀⠀⠀⠀⣇⡈⢸⡚⡰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢺⠄⠾⢠⡝⠀⠀⠘⠀⡷⠀⠰⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⡆⢣⠀⠀⠀⠀⠀⡿⣱⢨⡧⢠
⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⢸⡆⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⡇⣷⠸⣇⠀⠀⠀⠀⠁⠃⠘⡇⣶
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠛⢧⡉⠀⠀⠀⠀⢸⢀⡆⢳⠇
⠀⠀⠀⢿⡇⠀⠀⠀⢀⡀⠀⡀⣸⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠘⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠈⠀⣦⠠⡌
⠀⠀⡇⣼⠓⠀⠀⠀⣾⠀⣐⢡⡟⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⠄⡁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⢻⠃
⢦⠀⢰⣯⠁⠀⠀⠰⣿⠀⢧⡟⠀⠠⢐⣀⡇⠀⠀⠀⢀⠀⠀⠈⠀⡁⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠁
⢸⡄⢄⠟⠀⠀⠀⠀⢃⠀⢻⡇⠀⠀⡜⣸⡧⠀⠀⠀⣼⡀⣸⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢀⢀⡆⡀
⠀⣇⠾⣇⠀⠀⠀⠀⠀⠃⢦⠁⡇⡔⠀⣣⡇⠀⠀⠀⣿⠩⠏⡀⠈⣟⡟⢀⠃⠀⠀⠀⠀⢆⢀⢢⠃⡆⠘⢁⠇
⢀⣿⠀⢹⠸⠀⠀⠀⠀⢀⢸⡴⢱⡇⣼⠟⠀⠀⠀⠀⠈⣗⣺⡇⠘⡝⡼⠆⠀⠀⠀⠀⠀⠀⢸⣬⠐⡔⠀⢸⠀⠘
⢠⠇⠇⣼⠀⠀⠀⠀⠀⢾⡸⡇⠀⢦⡏⠀⠀⠀⠀⠀⠀⢲⢺⡇⢠⢱⡇⡾⠀⠀⠀⢠⠀⠀⢼⡇⠀⠀⡆⢸⡆⢀
⣤⢰⠀⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠨⡆⠁⠀⠀⠀⠀⠀⡄⠀⠠⢹⡴⠀⢣⠈⢧⠘⡆
⠸⠸⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠃⢱⠹⡌⠃⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠀⢀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢺⡇⡷⠆⢄⢀⠀⡆⢀⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⡄⡆⠀⠆⢰⡄⠀⢆⠀⡰⠁⢰⠁⡄⢀⠀⠀⠀⠀⢇⠀⢇⠀⠘⠀⡄⢹⠸⠏⢠⠀⠞⢀⡄⡎
⠀⢰⡀⢠⠀⠾⡀⡄⠀⠀⡏⠁⠀⠸⠀⢸⠃⠹⠐⠁⡆⠘⢁⢇⢾⡀⠀⠀⠀⡘⠐⠸⠇⢇⠀⡇⠘⠀⣤⡾⢀⠧⠫⢾⠆
⠀⠈⢁⡄⢣⣾⢹⡿⠀⣇⠀⠇⢠⠀⢰⠀⠀⡀⢀⠰⡇⡄⣼⠸⠀⡿⢰⠀⠀⠀⢀⡀⢀⡈⠳⠐⠀⠀⠉⣠⠏⠀⡠⠂
⠀⠀⠉⠳⠀⠃⠀⠑⠀⠈⠀⠇⠈⠂⠘⠀⠞⠀⠘⠃⠁⠁⠈⠀⠀⠟⠘⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠾⠚⠁⠒⠛⠂
⣿⣶⠿⠷⠾⢿⣿⣾⣶⣷⣶⣾⣷⣾⣷⣿⣾⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣾⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡄⠀⠀⠄⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠐⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠀⣀⣤⡴⣾⣿⠀⡄⠀⠀⢸⣷⠶⢦⣤⣀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⡾⠛⣏⠀⠁⢸⣿⡄⠀⠐⢠⣿⡟⠀⠄⠀⡹⢛⠶⣄⠐⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡟⠁⠀⠀⠈⣦⣴⠶⢟⣻⣿⣿⣿⣿⣶⣦⣄⡼⠁⠀⠀⠙⢷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣰⡟⠉⠳⣀⣴⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣦⣂⡤⠞⢳⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡟⠀⠀⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡽⣧⠀⣀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠢⡞⣹⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠹⣿⣿⣿⣿⣿⣷⠹⣄⡤⠤⢺⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⠀⣨⢤⡇⣿⣿⣿⣿⡿⢿⣿⠁⠈⠋⠀⠐⣿⡿⢿⣿⣿⣿⡆⣿⠀⠂⠰⣷⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠦⢼⣃⣿⣿⣿⡿⠀⢸⡇⠀⢰⣆⡀⣰⠏⠀⠘⣿⣿⣿⡇⢿⣀⣤⣤⡟⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡇⠐⣒⢘⣿⣿⣿⣿⡇⣄⠸⣿⣠⣸⣿⣇⣿⢀⡄⠀⠸⢿⣿⣧⣿⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣶⣶⣼⣿⣿⣿⡈⣳⠸⣦⣹⣿⣿⣿⣿⣿⣼⣿⡇⠀⣼⣿⣿⣿⣀⣂⡀⡿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠉⠉⠙⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣧⣿⠛⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣏⣠⣄⣹⣿⣿⣿⣿⣗⠶⣤⣀⡿⣿⣾⣿⣷⣤⡴⢾⣿⣿⣿⣷⣿⠀⠀⠀⡏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠶⢼⡿⠿⠷⢶⣿⣿⡿⢿⢿⣿⣾⣿⣿⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡟⠋⠐⢒⣒⣒⣒⣒⣒⣶⣖⣒⣠⣤⣴⣖⣒⣒⣀⣀⣀⣀⣐⣀⣈⣛⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠭⠽⠿⠿⠯⠉⠩⠀⠈⠀⠨⠤⠤⠀⠴⠶⠦⠂⠀⠀⣀⡀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠖⠀⠀⠀⠈⠉⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⡏⠀⠀⠀⠀⠀⠓⢻⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⡜⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢹⡀⡇⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⢇⣠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠀⠀⢸⠁⢱⠀⡀⠀⠀⠀⠘⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⣀⣊⠀⠀⠀⠀⠀⡜⠑⠃⠀⠈⠚⠹⡀⠀⠀⠀⠀⢱⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠖⠇⠀⠀⠀⠀⠀⠀⠀⠸⠊⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠈⠒⠤⣀⣀⡠⠴⠊⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣟⠒⠤⢄⣀⣀⠤⠤⢄⣀⣀⡠⠤⠒⣾⡵⢮⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠏⡿⡀⠀⠀⣰⠁⡆⡞⢝⡟⣄⣀⡀⠀⡿⣝⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠯⠼⠒⠊⠉⠘⢄⠣⣉⡭⢃⠇⠀⠈⠉⠉⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉