Spartan shield Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣐⣒⣶⣬⣽⣿⣿⣯⣥⣶⣒⣂⡤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣺⣭⠷⠛⢻⣏⢩⣤⣴⣶⣶⡦⢸⡟⢠⣭⣍⣙⡛⠾⣭⣗⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣯⠟⣋⣥⣶⠿⣿⡘⣿⣤⣤⡶⠆⢸⡇⠸⢷⣦⣬⣍⢙⣿⠇⣼⡟⣙⠳⣽⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠾⠛⢿⣆⢙⣩⣴⠆⢹⣧⣬⡤⠶⢶⣶⣿⣿⣶⡶⠶⢤⣥⣼⡏⠸⣿⣄⡛⢷⣦⡙⢷⣕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⣡⣾⢿⣦⠹⠟⣩⡴⢞⣯⣽⣶⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣶⣯⣽⡳⢦⣍⠻⠆⣼⡿⢃⣼⡷⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣾⠃⣾⠟⣡⡆⢙⣷⢟⣵⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣮⣻⢾⡋⢴⣿⠉⣴⡘⢷⡳⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣫⠟⠛⢿⣦⡾⢋⡴⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢦⡙⢷⡌⢿⣆⠻⣜⣆
⠀⠀⠀⠀⠀⠀⢰⣳⠏⣼⡿⣶⣌⣡⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣌⣡⣾⠿⢃⣹⣞⡆
⠀⠀⠀⠀⠀⢠⢷⡟⣸⡟⣰⡆⣹⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣏⢰⣾⠟⣋⢻⡾⡄
⠀⠀⠀⠀⠀⡎⣿⣄⣉⢠⡟⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡆⢻⡄⢻⡆⢿⣱
⠀⠀⠀⠀⢰⢹⡏⣉⣉⡛⢁⡾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢷⡈⣃⣸⣧⢸⡇⡆
⠀⠀⠀⠀⡘⣿⢀⣿⠛⡛⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⢛⣋⣉⣠⣿⢃
⠀⠀⠀⠀⣷⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⡏⣉⡉⣿⣾
⠀⠀⠀⠀⡟⣿⣤⣥⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿⡇⣿⢻
⠀⠀⠀⠀⢱⣿⠉⣭⣭⣤⣼⡏⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢹⣧⣤⣤⣿⠁⣿⡎
⠀⠀⠀⠀⠸⣸⡇⢿⡏⢠⡄⣿⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⣿⢠⣤⣭⣉⣸⣇⠇
⠀⠀⠀⠀⠀⢏⢷⠘⣷⠘⣷⠘⣏⢿⣿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⡿⣽⠃⣾⠃⣍⠙⡿⡹
⠀⠀⠀⠀⠀⠘⣞⣧⣤⣴⠿⠃⣹⣞⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣱⣏⡘⠏⣼⡏⣼⢳⠃
⠀⠀⠀⠀⠀⠀⠘⡼⣯⠠⣾⡟⢋⡙⢧⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⡼⢋⣙⠻⣿⠏⣼⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣟⣧⡙⣷⡌⢿⣌⠻⣦⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⣴⠟⣠⡿⠛⢷⣦⣼⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣳⣌⠛⣠⣿⠇⣨⡿⢮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡵⢿⣅⠸⢋⣴⠟⣠⣟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢿⣟⠡⣾⣏⠰⣦⣍⠛⠾⣽⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣯⠷⠛⣩⣴⣦⠹⣷⠟⣩⡾⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢝⡷⣌⡛⢷⣦⠙⣿⡆⣸⡟⣙⡛⠲⠶⠿⢿⡿⠿⠶⠞⢛⣋⢻⣇⠰⠟⣋⣤⠹⣷⣤⢾⡫⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣟⡶⣤⣼⡟⢰⣿⣥⣙⣛⠛⢻⡇⢸⡇⠸⠟⠛⠛⣿⡄⣿⡶⠟⣋⣥⢶⣻⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠭⣟⡶⢦⣭⣉⣙⡃⣼⡇⠘⠛⠛⠛⢛⣃⣹⣷⡴⢶⣛⠭⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠭⠯⠟⢻⣿⣿⡟⠿⠿⠭⠙⠓⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣹⣿⣿⡻⠷⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣿⣫⣿⣿⣿⣏⣿⣶⣤⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠻⡯⣻⣾⣿⣦⡉⠻⣿⣦⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣿⣿⢿⢿⡇⣶⣿⣿⣿⣿⣿⣶⣼⣿⣷⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⣿⢸⡜⣿⡽⣿⣿⣿⡏⠛⠛⠛⠛⣿⣦⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⣿⣸⣧⢸⣷⢻⣿⣿⡗⠀⠀⠀⠀⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⣾⣿⢣⣿⣿⠀⣿⡾⣿⣿⣯⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡏⣾⣿⣿⢀⣿⡇⣿⣿⣿⡀⠀⠀⣼⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢧⣿⣿⡏⣸⣿⢱⣿⣿⣿⣷⢠⣾⡿⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡟⣰⣿⢃⣿⡟⣿⡜⣿⣧⡋⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⡿⣴⡿⣣⡟⣿⣇⣿⣧⣽⣿⡅⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡇⣾⣿⢋⣴⣿⣶⣿⣏⠻⣿⣿⣿⠇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⣾⢃⡿⣡⣾⣯⣭⡍⣱⠇⠀⠈⣿⣣⣾⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣸⡟⣼⢳⣿⣿⡿⣫⣾⠏⠀⠀⠀⣿⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠋⠈⢩⣿⣿⠟⢽⣿⡇⠀⠀⠀⠀⠹⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠙⠃⠀⠀⠀⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠈⠛⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇⠀⠀⠀⣀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⢱⣾⣏⠀⣠⣴⢾⣿⢿⣺⢷⡖⣞⣿⣭⣗⣦⣄⠀⣹⣷⡎⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣉⠈⣻⢿⣿⣻⣺⣼⣷⣿⡟⢿⣿⣾⣧⣟⢞⡽⣿⣟⠁⣉⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⢀⣤⢈⡿⣿⢿⣷⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣿⣾⡮⣞⣿⡁⣤⡀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡸⣄⣾⣛⣯⣿⣿⣿⣿⣿⠏⠀⢀⡀⠀⠹⣿⣿⣿⣿⣿⣩⡿⣷⣠⢇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣋⢹⣿⡯⣽⣿⣿⣿⣿⠏⠀⢀⣾⣷⡀⠀⠹⣿⣿⣿⣿⣯⠿⣽⡏⣙⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⣦⡔⠉⠸⣿⣼⣩⠿⢻⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⡄⠀⠘⣿⣿⣿⡿⣿⣫⣧⣿⠇⠉⢢⡶⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣾⢿⣟⣿⣻⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣄⠀⠘⢿⣿⣟⣻⣾⡷⣷⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠁⣿⣇⠀⠈⢻⣶⣣⢿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⡿⣸⢬⡟⠁⠁⣸⣿⠈⠁⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠶⠛⠋⠀⠀⠀⠘⣿⣧⣄⣘⣷⡟⣿⢗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⡿⣾⣿⣃⣠⣼⣿⠃⠀⠀⠀⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⣮⣻⣗⡯⢻⢿⣿⢿⡿⢿⡿⡟⡽⣮⣗⣿⡿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣯⣿⣽⣾⣻⣟⣗⣯⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠀⢠⢀⡀⠠⠄⣠⠀⠤⠄⡄⣀⢠⡀⠀⠀⠀⠀⠉⠻⠆⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓

⠀⡃⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀⠀⠀⠀⣀⣠⡤⠴⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠛⢻⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⡏
⠀⠀⠀⠠⠶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠻⣍⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣖⣶⣾⣽⡿⠿⠿⣿⣿⣷⣶⣒⣤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⡿⠟⣛⢻⣿⠠⣶⠶⠶⢶⡆⢸⡏⢰⣤⣭⣉⡛⠻⣿⣗⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣿⡟⢋⣥⡶⠟⢿⡆⢿⣶⠶⠶⠆⢸⡇⠸⠷⠶⣦⡬⢹⡿⢡⡿⢋⣙⠳⣿⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⡷⢋⡙⢿⣌⣥⡶⠟⣈⣿⡴⣶⣖⣿⣻⣿⣿⣿⣟⣲⡶⢦⣿⣁⠻⢷⣬⡙⠷⣦⡙⢿⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡾⢫⣶⠟⢿⣌⢛⣡⣶⣻⣽⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣾⣯⣟⡶⣌⡛⣠⡿⢋⣴⡿⢷⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⣏⡰⠟⣡⡾⢀⡿⣻⣵⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣟⢿⡀⢿⣇⠰⣦⡙⣮⣦
⠀⠀⠀⠀⠀⠀⢀⣞⡿⢩⣙⠻⣾⢋⣴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣦⡙⣷⠘⣷⡌⢿⣳⡀
⠀⠀⠀⠀⠀⢀⣞⡾⢡⡿⠛⢷⣦⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢳⣴⠾⢛⣩⣼⣷⣷⡀
⠀⠀⠀⠀⠀⡼⣿⠁⣿⢡⡿⢠⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡄⢿⡏⣥⡈⣿⣧
⠀⠀⠀⠀⢠⢳⡿⢶⣦⣾⢃⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡘⣷⠸⣧⢸⣟⡄
⠀⠀⠀⠀⡸⣿⢠⣶⣦⣤⣼⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣧⣤⣴⣿⠄⣿⢇
⠀⠀⠀⠀⣷⡿⢸⡏⣰⡄⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢠⣴⣶⣶⣿⣿
⠀⠀⠀⠀⣿⡇⠸⠇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢰⡆⢸⣿
⠀⠀⠀⠀⣿⣿⠿⠿⠟⠃⣿⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠘⠋⣸⡇⣾⣿
⠀⠀⠀⠀⢹⣿⠐⣿⠿⠛⢻⡾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡟⠛⠻⠿⢃⣿⡏
⠀⠀⠀⠀⠘⣾⡇⢻⡆⢿⡌⣷⣻⣿⣿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣟⣾⢡⡿⠻⠷⣾⣧⠃
⠀⠀⠀⠀⠀⢳⣿⡘⢛⣸⣷⠘⣯⠿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⢿⣽⠃⣾⢃⣿⢂⣿⡟
⠀⠀⠀⠀⠀⠈⢿⣿⡟⣋⣥⡶⠟⢷⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⡾⠻⢶⣤⣾⢃⡾⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢯⣷⡘⢿⡄⢻⣌⠻⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⠟⣡⡿⣦⣍⣃⣾⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⣌⠻⠆⢹⣷⠈⣷⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⠁⡾⢋⣴⠌⣹⢟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⣾⠟⣡⣾⠋⣬⡙⠾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⠿⢋⣥⡙⣷⣴⠟⣣⡾⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⡷⣌⠻⢶⣬⡛⢷⣦⢩⣿⠳⠾⠯⣽⣿⣿⣿⣿⣯⡽⠷⠞⣿⡍⢴⠾⢛⡙⣷⣌⣡⣾⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣟⣦⣍⣡⣿⢃⣾⣇⡚⠻⠶⢶⡆⢸⡇⠰⠶⠶⠾⣷⠸⣷⣴⠾⢛⣡⣼⣿⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢽⣿⣦⣭⣉⣛⠛⠇⣸⡇⠸⠷⠶⠶⠿⠂⣿⣧⣭⣴⣾⡯⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠭⠿⢟⣿⣿⣷⣶⣾⣿⡿⠿⠭⠛⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣴⣦⣶⣶⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣮⣷⠾⢟⣻⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢛⣩⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠾⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⠿⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⢉⣴⣶⡿⠟⠋⠉⠀⣰⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆⠀⠀⣈⡫⠉⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⡹⠋⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⡋⣻⣿⡇
⠀⠀⠀⢀⣠⣴⠾⢿⣻⣿⠿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠺⠛⠉⠀⠀⠙⢦⡀⠀⠀⠈⠉⠙⠲⣄⡀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣔⠦⣄⣀⡜⣿⣷⣰⣿⣾⣿⡷⢸⡏⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣵⣄⠈⢻⣻⢻⣿⣟⠹⣿⡇⠙⢠⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⢿⣿⣿⣆⢹⡼⣿⣿⣧⡘⠇⠀⡼⠋⣠⣧⣿⢟⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⠏⣾⣿⣿⣿⠀⢻⣿⣿⡿⢟⣲⡿⠭⠭⠭⢿⣟⣻⢿⣟⠋⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⣿⣿⣿⢣⡤⡻⠕⠋⣁⣤⣴⣶⣶⣶⣦⣤⣈⠙⠺⢗⢤⣻⣮⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡄⣿⣿⣿⣿⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠑⠝⣿⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣧⢸⣿⣿⠃⡐⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⣿⠇⣸⣹⣿⣿⣿⣿⣿⣿⣿⡿⡛⡻⣿⣿⣿⣿⣿⣿⣿⣇⠆⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⠀⡇⣿⣿⣿⣿⣿⡿⠿⠝⠈⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡇⣿⣿⡿⠟⠉⠈⠀⣠⣴⣿⣆⠀⠀⠙⢿⣿⣿⣿⣿⢨⠀⣿⡇⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⢱⠛⠉⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⡟⠄⢠⣿⢇⣿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠣⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⠿⠁⢀⣾⡟⢸⣿⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⡿⢡⣿⡿⣷⣕⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⢮⣾⡿⡇⢸⣿⣆⠹⣿⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⣵⣿⡟⢁⣿⣿⣿⡜⢿⣦⣕⢦⣉⠛⠻⠿⢿⣿⡿⠿⠿⠛⣉⡴⣚⣵⣿⠟⣽⣿⡄⢻⣿⣆⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠙⠻⠿⠶⣭⣗⣲⣶⣶⣶⣖⣺⣭⠵⠿⠟⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠶⠶⠶⠶⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠀⡄⠀⠀⠀⣶⠂⢸⠶⡀⠀⠉⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠉⠀⠀⠀⠀⠀⣇⠀⠀⠀⢘⣄⡎⠀⢣⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠠⡇⣿⠄⠀⢀⡔⠛⢿⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⢰⣧⣤⣤⣀⢘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣼⣿⡇⠁⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡷⢶⣮⣿⣿⢁⣠⠟⠀⠀⢠⣾⠛⠙⢢⡀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⠋⣧⣼⡟⠙⠿⣿⠻⢗⣦⢤⣿⠃⣠⠖⠄⢳⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⠟⠀⣿⠟⠣⠤⣄⣈⣳⡋⢀⣾⠟⢠⡏⢀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠷⠄⠠⣿⡆⠀⠀⢈⠀⣸⡍⣿⣿⡆⢸⡇⡼⡆⡆⣇⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣳⣧⣤⣼⣿⣷⠀⠀⠇⠀⢼⢼⣿⣿⡇⢸⣼⠃⢱⡇⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠺⣾⣿⣿⡇⢸⡏⠀⠈⡇⡟⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⢸⣿⡏⠈⣿⣿⣿⣿⣿⣯⠠⠦⣦⡀⣧⣿⣿⢿⣦⠘⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⣰⣿⢿⣿⡟⠀⠀⢀⣿⢿⣇⢰⠏⡿⣿⣿⣟⣉⣲⣤⣭⡟⢻⣿⣿⣿⣿⡄⠹⡄⠀⡸⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠸⣿⡁⣾⣿⣄⢀⣠⣾⢋⣾⠏⠎⡸⢣⣿⢏⣏⢻⠇⣼⠇⠛⠋⣿⢇⠘⢿⣷⣄⣀⡴⠃⠀⠀⠀⠀⢀⣼⣿⡏
⠀⠀⠀⠀⢸⣿⡇⠢⠭⠿⠟⠋⣡⣾⠏⠀⢞⣵⣿⢃⡾⣯⠏⢠⣿⠀⠀⠀⣷⢸⡸⡌⢻⡉⠉⠀⠀⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠸⣿⣷⡆⠀⠀⣠⣴⢟⣡⣴⣾⣿⣿⢁⡞⡰⣿⠀⣸⡇⢰⠀⢀⡇⡄⣇⢻⡄⢻⣄⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⣀⣤⣿⡟⠁⣐⡼⢫⠕⣩⢫⢟⢟⣿⣿⣿⣷⣿⣿⣶⣿⣧⣼⣴⠾⣿⣷⣼⣄⣿⣶⣿⡀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⢨⣿⣧⠶⠊⠁⠀⢁⡼⠁⠁⡠⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠘⣿⣇⣀⣀⣠⢴⣿⠃⢀⣀⣰⣿⠿⢿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠉⢿⣟⠒⠉⣾⡶⠛⠉⠉⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⣏⢸⣉⣭⡍⢹⠠⣏⣛⠛⢿⡟⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠹⡭⠖⣲⠸⣶⣶⣶⡧⢼⣶⣶⣼⠇⣞⠰⢏⡛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⣫⣌⠳⣴⣿⠿⠛⠉⠁⣠⣿⣿⣄⠈⠉⠛⠿⣿⣦⠟⣠⠟⣨⣷⣄
⠀⠀⠀⠀⠀⣴⣯⡙⠶⣡⣾⡾⠋⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⢿⣷⣌⢧⡙⣿⣦
⠀⠀⠀⠀⣼⣿⢃⣌⡛⣿⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⣿⢛⣡⠼⢛⣧
⠀⠀⠀⢸⠿⢧⡎⣼⣿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⣧⢺⡙⣿⡇
⠀⠀⠀⣿⡖⠒⠲⢿⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⡿⠞⠃⣻⣿
⠀⠀⠀⣿⡇⣿⢹⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⡏⣩⣥⣿
⠀⠀⠀⣿⢛⣋⣸⣿⠀⠀⠀⣠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⣿⣇⣿⢸⣿
⠀⠀⠀⣿⣯⢠⡴⣾⡆⠀⣰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣆⠀⢸⣷⠦⠤⠼⣿
⠀⠀⠀⢸⣿⣌⡧⢻⣿⢴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡦⣿⡟⡼⢳⣾⠇
⠀⠀⠀⠀⢻⣥⡔⢋⣥⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣬⡙⢡⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣌⢳⡙⢿⣟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡻⡿⢋⠴⣌⣻⠟
⠀⠀⠀⠀⠀⠀⠙⢿⡋⣴⠋⣴⠻⣿⣶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⣶⣿⠟⢦⡙⣫⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣬⣱⠆⡽⢰⡟⠿⠿⡟⢻⠿⠿⠿⡆⠯⠴⣚⣆⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣼⣷⣤⣭⣹⠂⣇⣘⣛⣩⡇⣹⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠋⢴⣿⣿⣿⣿⣦⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⣷⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣽⣿⣿⣿⣷⣝⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣾⣾⡟⣿⣎⣿⣿⡄⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣧⠻⠳⣾⣿⣿⣿⣿⣶⣄⠀⠀⢻⣿⡄⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⡟⣇⢿⣿⣾⣿⣯⣟⢿⣿⣿⣿⣿⣷⢖⣒⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⢹⡎⣿⣯⣿⠾⣽⣎⣿⣿⠛⠿⠿⢿⠿⢿⣿⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣟⣾⣿⣻⢸⣿⢸⡿⣟⢿⣿⡇⣿⣿⡄⠀⠀⠀⠀⣼⣿⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⡿⢸⣿⡀⣿⣜⢯⡻⣿⣿⣿⣇⠀⠀⠀⣰⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣸⡇⣿⣿⣇⢻⣿⣦⡙⢮⣛⢿⣽⡀⢀⣴⣿⠋⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣇⢹⣿⣿⣆⠻⣿⣿⢷⣭⣳⢮⣟⣻⠟⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⢹⣿⣄⠻⣿⣿⢷⣮⣝⣳⣮⣝⡻⠿⣿⣿⣷⣶⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣌⠻⢷⣯⣟⡛⠿⠿⠿⠗⠒⠈⠉⠙⠛⠛⠛⠛⠻⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⣀⣀⣤⡤⣤⢀⣀⡀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣯⣻⣿⠺⠿⠕⠻⠯⣾⡿⣟⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⢽⢝⣭⣶⣿⣿⣿⣿⣿⣷⣯⣕⢯⣯⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣜⡿⣵⣿⣿⡿⠟⠋⠉⠉⠛⠻⢿⣿⣷⡝⡽⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡾⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⡼⣭⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⢱⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⢿⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡻⣿⣿⣿⣦⣴⣆⠀⠀⠀⢤⣸⣿⣿⣿⣿⡿⣟⡿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣗⢻⣿⣿⣿⣿⣿⣸⡇⠀⠀⣾⣿⣿⣿⣿⢳⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣷⡽⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⡿⣵⣿⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢾⡯⡾⣝⡻⢿⣿⣿⣿⣿⠿⣛⢭⣟⣟⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠑⠻⣟⣫⢿⢟⣲⡬⣻⢿⣻⠯⠓⠁⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⠋⠉⠉⠙⠛⠛⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠘⠋⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⡴⠛⠉⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢦
⠀⠀⡼⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⢧
⠀⣸⠃⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣇
⢠⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸
⣼⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀
⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡞
⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙
⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠞⠁⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⡇
⠘⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢸
⠀⢹⡄⠀⠀⠀⠈⢧⠀⢀⡴⠋⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠙⢦⡀⠀⡼⠁⠀⠀⠀⢀⡏
⠀⠀⠳⣤⣤⣀⠀⠈⢳⡋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢙⡾⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⢤⣤⣄⣀⣀⣠⣤⣤⠤⠟⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⣤⣾⣷⣤⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣤⡚⠋⠉⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠉⠙⢒⣤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠈⠛⢦⡀⠀⠀⠺⣤⣉⣿⡿⣟⣧⠗⠀⠀⢀⡴⠛⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⠢⣄⡤⣀⣽⣿⠛⢾⣀⢤⣠⠔⠋⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢶⡄⠀⠀⣳⡿⢿⣿⣿⠀⠀⠠⣿⣿⡀⠀⢠⡶⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠉⠁⣀⡸⡇⠀⠀⠹⣿⠀⠀⠀⣿⣿⢧⣀⠈⠉⠛⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠸⠋⣴⡿⣶⣦⣶⣿⠀⣶⣿⣿⣿⣦⠙⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣠⣾⠟⡇⣾⣿⣿⣿⠀⣿⠉⢿⣿⠻⣷⣄⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠀⢆⢿⣿⣿⣿⣴⡟⠀⣸⡿⠀⠀⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡟⢧⡀⠀⠈⠊⣿⡟⠋⠙⠃⢠⠛⠁⠀⢀⡼⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⠁⠀⠙⠳⣄⡀⠘⠻⠀⠀⠇⠂⠀⣠⠞⠋⠀⠈⣧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢿⢟⣿⣿⣿⠿⣿⣶⣾⣿⣿⡷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠵⠛⠛⠳⣌⢻⣿⣟⣠⣾⣿⣏⣿⣿⣝⢿⣵⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡾⠁⠀⠀⠀⠀⢈⣷⢿⣿⠟⣵⣿⣭⣿⣿⣟⣽⣻⡿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⠁⠀⣀⣠⠖⣠⣾⣿⣿⣿⣿⠻⠿⣟⣿⣿⣿⢟⣽⣿⣮⡋⣵⡆⡀
⠀⠀⠤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣥⣤⣤⣿⣿⣧⣿⣯⣽⣿⣿⣯⣦⣿⣿⣿⣿⢿⣭⣽⣿⣿⣧⣿⣧⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠹⣎⠛⠚⠁⣻⣿⣿⣿⣿⣃⢩⣿⣿⣿⡞⣿⡿⢏⣾⢟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡯⡀⠀⠀⠀⠀⠀⣰⢃⣿⢿⣏⣿⣿⣿⣿⣛⣿⣛⣬⣶⣟⣭⡾⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⣤⣄⣀⣀⣴⣧⡾⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣩⡾⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣭⣵⣾⣿⠿⠿⠿⠿⢿⣿⣿⠷⠶⢿⣿⣛⡯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣺⣟⠋⡿⠶⠛⠛⢻⠁⡴⠾⢿⣿⣷⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⠗⣋⣅⠸⡆⣛⣋⣩⡇⢸⣀⣙⣓⣲⠄⣽⢁⡾⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢦⡘⢛⣡⣼⣦⣽⠯⠿⢗⢎⣱⡖⠿⠿⣯⣜⣧⣌⡓⢦⡉⢻⡿⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⢿⠟⣡⠶⣄⢛⣿⠿⠋⠁⠀⠀⢀⢮⣾⣷⡵⡀⠀⠀⠈⠙⠿⣿⡋⣠⠋⣠⠾⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣧⣌⡙⢡⣾⣿⠟⠁⠀⠀⠀⠀⢠⣪⣿⣿⣿⣿⣝⡄⠀⠀⠀⠀⠈⠻⣿⣷⡌⢧⡘⢿⣷⡄
⠀⠀⠀⠀⢀⠿⡿⢁⣤⡙⣻⡟⠁⠀⠀⠀⠀⠀⡠⣳⣿⣿⣿⣿⣿⣿⣞⠄⠀⠀⠀⠀⠀⠈⢻⣟⢋⡤⠞⠋⢿⡀
⠀⠀⠀⠀⣞⠾⣅⡞⣰⣿⡏⠀⠀⠀⠀⠀⠀⡰⣽⣿⣿⣿⡟⢻⣿⣿⣿⣮⢆⠀⠀⠀⠀⠀⠀⠹⣟⣆⢺⡉⣿⣷
⠀⠀⠀⢠⢯⡶⠤⢤⣿⡟⠀⠀⠀⠀⠀⠀⣔⣽⣿⣿⣿⣟⠎⠱⣻⣿⣿⣿⣯⣢⠀⠀⠀⠀⠀⠀⢻⣿⡬⠇⢹⡽⡆
⠀⠀⠀⣼⣼⠃⡶⢶⣸⠃⠀⠀⠀⠀⢀⣜⣾⣿⣿⣿⢟⠎⠀⠀⠱⡻⣿⣿⣿⣷⡣⡀⠀⠀⠀⠀⠘⣧⡶⠒⠚⢣⣧
⠀⠀⠀⣿⣿⣤⡇⢸⢸⠀⠀⠀⠀⢀⢮⣾⣿⣿⣿⣯⠃⠀⠀⠀⠀⠘⡽⣿⣿⣿⣷⡵⡀⠀⠀⠀⠀⡧⡇⢸⠉⣿⣿
⠀⠀⠀⢹⣡⡤⠶⠞⢻⡆⠀⠀⢠⣮⣿⣿⣿⣿⡳⠁⠀⠀⠀⠀⠀⠀⠘⢞⣿⣿⣿⣿⣵⡄⠀⠀⢰⡟⠳⠾⢠⡟⡏
⠀⠀⠀⠸⣞⣇⢸⡛⣿⣷⠀⣠⣳⣿⣿⣿⡿⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢿⣿⣿⣿⣞⣄⠀⣜⣿⢛⡓⠚⣿⠃
⠀⠀⠀⠀⢿⣿⣬⠧⠹⣿⡶⣽⣿⣿⣿⡿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣿⣿⣿⣯⢾⣷⠇⡼⢩⡷⡿
⠀⠀⠀⠀⠈⣷⣤⡖⢋⣡⣽⣿⣿⣿⣟⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣯⣌⡙⢁⣾⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣌⠳⡌⢿⣿⣛⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣛⣿⡿⢡⣤⡙⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⢋⡴⢋⡬⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⢧⡙⠶⢋⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⣌⠓⢦⡙⢻⠟⣻⣗⣶⣶⡶⢶⣶⣒⣺⣝⠻⣟⣋⡴⣄⠳⢶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡞⢡⣏⠐⠷⠤⣭⠉⡇⢸⣭⡭⣤⠸⣆⣉⣥⣶⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⢿⣟⣶⣟⣀⣷⣶⣶⢶⣾⣤⡽⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉

⠀⡉⡉

⠀⠀⢀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡀
⠀⠀⣏⡴⠊⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠐⢦⣹
⠀⠀⠙⢷⣞⠁⣨⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣅⠈⣳⡾⠋
⠀⠀⠀⠀⠈⠛⢧⡞⡹⢳⣄⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣠⡞⢏⢳⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣉⡼⢳⣄⡀⠀⠀⢸⡁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⡇⠀⠀⠀⣠⡞⢧⣉⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣉⡤⠛⠲⡎⠉⣠⠖⠉⠀⠀⣀⣤⡤⠶⠶⠚⠛⠛⠲⠶⠦⣤⣀⡀⠀⠀⠉⠳⣄⠉⢱⠖⠛⠦⣉⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢾⣦⠈⣧⡀⣠⡴⠛⠉⠀⠀⣀⠠⠤⠤⠤⢄⡀⠀⠀⠉⠙⠶⣄⡀⢀⣼⠁⣴⡷⢀⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠒⠞⢀⣤⣄⣹⡿⣏⠙⢯⣄⠀⠀⠘⠁⠀⠀⠀⠀⠀⢰⠃⠀⣼⠛⠲⣄⣨⡿⠋⣸⢿⣏⣠⣤⡀⠳⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⡴⠋⠀⠈⢳⣄⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠻⠀⢠⡟⠀⢰⠇⠀⣠⠞⠉⣠⠞⠁⣠⠞⠁⠀⠙⢦⣀⡤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡾⠉⠳⣄⠈⠳⣄⠈⠳⣄⣀⢠⣤⡤⡾⠀⢀⣟⣠⠞⠁⣠⠞⠁⣠⠞⢻⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠁⠈⠳⣄⠈⠳⣄⠈⠛⢦⡖⠒⠲⢦⡬⠛⠁⣠⠞⠁⣠⠞⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠉⠓⠒⠶⠾⢷⣄⠈⠑⢄⠀⠙⢦⡴⠋⠀⡠⠞⠁⣠⡞⠥⠔⠒⢳⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠶⠶⠤⣤⣤⡌⠳⣄⠀⣠⡴⠋⠀⠀⠈⠀⣠⢾⡇⠀⢀⣄⠀⠈⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣇⠀⢀⣀⠀⠈⣷⠀⣻⠟⠁⠀⠀⠀⠀⣠⠾⣅⢸⣇⠀⠈⠉⠀⢰⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⡀⠈⠋⠀⢀⣸⠟⠁⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⣌⠛⠶⣤⣀⡾⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢳⡀⢀⡴⠛⠁⠀⠀⠀⠀⢠⡞⠳⣄⠀⠀⠀⠀⠈⠛⢦⡀⠉⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⡽⠋⠀⠀⠀⠀⠀⢀⡶⢻⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠙⢶⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⠄⠀⠘⡇⠙⢦⡀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⡴⠛⠦⠤⣤⣼⠂⠀⠀⠳⠖⠛⠙⣦⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣀⣤⠴⠚⠉⠛⠲⠦⣤⣤⣀⣀⣀⣠⣤⡴⠶⠛⠉⠉⠓⠦⣤⣀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢔⡖⢿⢩⢿⣹⢯⡿⢲⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢪⣗⡽⣹⠬⢿⣘⣚⣛⣚⡮⠿⣼⢹⣫⢗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣵⠸⣣⢟⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡲⢏⢭⡼⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⢽⢮⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡱⡏⣕⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣽⢳⢣⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡭⠷⡽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣬⣇⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣸⣻⣖⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡽⢦⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⣆⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⣭⣝⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡻⢸⣿⣿⣿⣿⣿⠟⠁⢀⣼⣿⣿⣧⡀⠈⢻⣿⣿⣿⣿⣿⡇⠷⢯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣯⡏⣿⣿⣿⣿⠋⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠙⣿⣿⣿⣿⢩⣻⢮⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣛⠞⡜⣿⡟⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⢣⢿⡺⣳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣫⢽⢮⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⡵⡟⡾⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡳⢞⣵⡪⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⢵⡛⣮⢳⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢔⡾⣱⢯⢲⢖⣉⢭⢭⣍⢷⢲⡯⣻⢽⡬⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠪⠯⣿⣱⣞⣸⣕⣾⠽⠗⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⣶⣶⣶⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣿⣿⣿⣿⣿⣿⣾⣿⠿⠿⠿⠧⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠿⢾⣝⡻⣿⣿⣿⣿⣷⣍⠻⡇⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⣴⣾⣷⣌⠻⣮⡙⣿⣿⣿⣿⢿⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢀⣠⣾⠋
⠀⠀⠀⠀⠠⣌⠻⣿⣦⣄⠀⠀⠀⢠⣞⣵⣿⣿⣟⣥⣍⡻⣷⣌⠻⣏⠻⣿⡿⠀⠀⣰⡟⠁⠀⠀⠀⠀⣠⣴⣿⠟⣡⠄
⠀⠀⠀⠀⠀⠈⠻⣦⣝⡻⢿⣶⣤⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢷⣌⢷⡈⠃⠀⣰⡟⠀⠀⢀⣠⣶⡿⢟⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠨⣝⣻⠿⣾⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣽⡄⣰⠟⣠⣴⣾⣿⣿⣷⠿⣟⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢴⣾⢋⣿⢿⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⡿⣿⡛⣷⡦⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡛⢷⣯⣿⡿⣟⣫⣽⡾⢛⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠷⠛⠛⠿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠟⠋⠻⠏⠀⠀⠀⠀⠀⠀⠹⠟⠙⠻⢿⣶

⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡇⠘⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠰⠄
⠀⠀⠀⠀⡂⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡇⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠
⠀⠀⠀⠀⡇⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡃⠈⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⡷⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡇⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠢⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠄⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⡀⠀⠀⢀⣀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡶⠀⠀⠀⠛⠛⠀⠀⠀⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠒⠀⠤⠂⠚⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⣤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠰⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣁⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠁⠐⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠀⠀⠉⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠂⠀⠀⠉⠉⠁⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢀⠘⢠⡾⠋⠀⠀⠹⠋⠈⣷⣤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠢⡁⠀⠀⠀⠰⡆⠘⢹⠋⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⡌⠀⠀⠀⠀⠀⠐⠀⢀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢰⠛⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠀⢀⣀⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⣆⠀⠀⠈⣀⣾⠏⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠣⠀⠀⡴⠂
⠀⠀⠀⠀⠀⢸⢂⣠⣾⣁⠙⠂⠴⠶⠿⢉⣦⣶⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠀⠀⠈⠋⠉⠛⡻⠟⠓⠶⣶⠛⠛⠁⠙⠃⢢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⡟⠀⠀⠀⡄⠀⢈⡶
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⠉⠀⠀⠄⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⢈⠁⠀⠀⠀⠠⠀⠤⢲⡆⠸⢁⠄⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⢠⠁⠌⠀⠀⣄⡀⢀⢤⡼⢉⡁⠀⠀⠄⠦⠀⠀⡇⠀⠀⠀⠀⠀⢄⡢⠀⢀⣀⡀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀
⠀⠀⠀⠀⠀⠋⠘⠀⠀⢰⢈⣅⣼⡟⠁⠀⠀⠀⠀⠈⢘⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⢀⠈⠀⠁⠀⠀⠀⠉⠀⠀⡌⠙⠛⠻⢛⠏⠁⠉⠋⠁
⠀⠀⠠⠘⠁⠌⢰⠀⠀⠀⢾⠞⠋⠁⢀⠀⠀⠀⠀⠀⠈⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠂⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠦⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠲⡃⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⠎⠐⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣼⡆⠉⠀⢗⡀⠀⠀⢀⠤⠀⠒⠒⠞
⠀⠀⠀⠀⠀⠢⣀⠀⠈⠐⢤⡬⣤⠀⡠⠀⠔⠈⠁⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⢠⣠⣆⠈⣠⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⢄⣀⡀⠀⠀⠀⣰⣧⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠀⠁⠛⠁⠀⠉⠁⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⢻⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠹⣿⣿⣿⣿⠻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠿⢻⣿⡿⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠹⣿⣿⠏⠀⢻⡇⠀⠀⠈⣿⢹⣿⣿⣿⠟⢿⣟⠁⠈⠀⠀⠀⠀⠀⠀⠀⢙⡿⠻⣿⣿⣿⡇⢹⡏⠀⠀⠀⣾⠃⠙⣿⣿⡟⠁
⠀⠀⠀⠀⠘⣧⠎⠀⠈⢧⠀⠀⠀⣿⢸⣿⣿⣷⢀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣀⣸⣿⣿⡇⢸⡇⠀⠀⢰⠇⠀⠀⣩⡟
⠀⠀⠀⠀⠀⠘⢧⠀⠀⠈⣆⠀⠀⣿⢸⣿⣿⡿⠋⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⢿⣿⣿⡇⢸⡇⠀⢠⡏⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⣷⣾⣿⢸⣿⣿⣿⣤⣠⣧⠄⠀⠀⠀⠀⠀⠀⠀⠐⢸⣄⣤⣼⣿⣿⣧⢸⣿⣷⡟⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢿⣿⣸⣿⣿⣿⣿⣿⣷⡀⡀⣠⡀⡄⣀⢠⡀⣀⣸⣿⣿⣿⣿⣿⣿⣸⣿⢏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠻⣉⡄⠀⠀⠀⠀⠀⢰⡾⡄⠀⠀⣀⡤⢶⡾⠂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡿⣧⡀⠂⠀⣾⢹⡏⠀⠀⡌⢀⣴⠟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⢇⣰⣾⣿⣇⣓⢀⣪⣰⡿⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣈⠺⠉⣟⣿⡶⣋⣾⢙⡫⢔⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⡿⣽⡄⡸⣆⣹⣯⣤⢵⣤⣼⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⠶⣲⡟⢛⡛⢛⡅⠘⣋⠉⠛⢉⡋⡉⢀⣀⢀⡀⠐⢶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠛⡆⠙⣷⠲⣡⣳⡎⡀⣿⣀⡀⣏⠀⡉⢼⡿⢾⡇⢰⠞⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⡧⣤⠬⣁⣉⠁⠈⡁⢉⠉⢁⠈⠉⠀⠈⠁⢈⠁⢸⠄⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠐⠖⢄⠀⠀⠀⣀⣠⣤⢤⣄⡤⣤⣤⡀⠀⠀⠀⡴⠲⡆⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⠀⢀⡘⠶⣾⣿⣿⣿⠧⠉⠃⠉⠈⠿⣨⣿⣷⠜⢃⡄⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡜⣿⣷⣤⣉⠛⢤⣀⠀⠀⠀⣀⡤⠟⣉⣤⣾⣿⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣙⣇⠹⣿⣿⣿⣿⣶⣬⣿⠶⠾⣥⣶⣬⣾⣿⣿⡏⣸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⢿⡀⣎⣿⠿⠝⢈⣤⡶⠶⢤⠀⠉⠻⢻⣿⣿⠁⡿⣿⣷⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣭⠎⠀⣧⣸⠃⡀⠀⣾⡃⢀⢺⠂⢹⣦⠐⢀⠉⣿⣠⠀⠙⣏⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡄⠀⣸⡇⠘⠀⢀⣯⣄⢸⡼⢀⠾⣩⣧⠀⢀⢚⣇⠀⢰⣧⡿⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⢻⡥⢞⣿⠄⡇⠀⢰⣿⣯⡥⠀⢰⠃⠀⡧⠀⢸⠘⣿⡳⢬⣿⠇⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢋⣴⣿⣿⡧⠡⢠⣿⣏⡤⠀⠰⠇⣠⠴⠂⠀⠈⣠⣿⣼⣤⣙⢢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⣫⣶⣿⣿⢿⡿⣷⡆⠘⢷⣬⠀⣠⣾⣼⣿⣳⡤⠀⢠⣾⣿⣿⣿⣿⣷⣌⠳⠊⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣀⠭⠭⣭⣭⡤⣤⡭⠽⠮⣀⡹⡛⠿⠻⢛⠛⢩⣐⡼⠟⠫⣭⡭⣭⡭⠉⠨⡄⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢷⡿⣾⣧⡀⠀⠹⠹⣶⣿⣿⣿⢿⠏⡟⠀⢀⣼⣿⣾⣳⠗⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⣿⣯⣽⡒⢷⢹⣿⣿⣿⠉⣼⣷⣊⣼⣿⡍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢾⣭⣻⣇⢻⣿⡟⣸⣿⣿⡹⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠿⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠀⣀⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠛⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠆⠀⢀⣿⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠛⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠛⠁⠀⡀
⠀⠀⠀⠀⠀⢸⣷⡀⠀⠘⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⢀⣾⡇
⠀⠀⠀⠀⡀⠈⠻⠇⠀⣠⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠸⠟⠁
⠀⠀⠀⠀⢳⣤⡀⠀⠘⠛⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠓⠀⢀⣤⡞
⠀⠀⠀⠀⠘⢿⣿⡄⠀⣠⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⠀⣠⣿⡿⠃
⠀⠀⠀⠀⣄⡀⠈⠀⡆⠿⠋⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠙⠟⢠⠀⠁⢀⣠
⠀⠀⠀⠀⠘⣿⣿⣦⡘⡄⢰⣿⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⣿⡆⢠⢃⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠛⠃⠱⡜⠋⢠⣿⣷⢀⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⡀⣾⣿⡄⠙⢣⠎⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠙⢷⣶⣶⣤⣘⢦⡘⣿⠏⢸⣿⣇⢸⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇⣸⣿⡇⠹⣿⢃⡴⣃⣤⣶⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠙⢦⣀⠘⣿⡿⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢿⣿⠃⣀⠴⠋⠀⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣶⣶⣶⣮⠑⠺⢤⣀⣙⠻⠁⠀⠀⠀⠀⠀⠀⠈⠟⣋⣀⡤⠗⠊⣵⣶⣶⣶⣶⣶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⢛⣁⣤⣴⣶⢶⡉⠉⠉⠉⠛⣷⣾⠛⠉⠉⠉⢉⡶⣶⣦⣤⣌⡛⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠿⢿⣿⣿⡿⠟⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠻⢿⣿⣿⡿⠿⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣴⡆⠴⣮⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⣿⡁⠀⠀⠀⠀⢀⣶⣤⣀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⣿⣧⡀⢀⠉⠀⣙⡿⠿⣿⣾⣏⣶⣛⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠻⢶⣟⡛⢳⣴⣿⣦⢈⠈⣀⣿⡤⠀⠉⣉⠟⠛⢛⠿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⠿⠛⠚⠿⠥⠼⠟⠹⠿⠿⠲⠿⠧⠖⠚⠀⠈⠀⠀⠈⠚⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣤⣴⠀⡖⣆⢰⡆⡄⢲⣆⣰⣴⣷⣖⢰⡆⢺⡶⠾⣿⠤⠾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⠿⣿⣼⠇⠇⠘⣤⡾⢸⣿⣿⡉⢡⢸⡚⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠱⣷⣿⣿⣶⣷⣸⣏⣿⢸⣿⣿⠁⡄⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠸⠗⢿⠿⠿⠿⠝⠩⢿⠹⠿⠿⠓⠟⠹⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠚⠀⠀⠀⠀⠀⠄⠀⠸⠇⠀⢰⠀⠀⣙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣬⣴⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣤⠀⠀⠠⠶⠀⠐⠂⠀⠰⠆⠀⣰⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣾⣿⡄⠀⠀⣨⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⣀⣄⠀⠀⢣⣄⣀⣠⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣄⠀⠈⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡀⠛⠿⢿⣿⣿⡿⢷⣦⣄⠙⢿⠟⠋⢁⣀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣷⠦⠄⠀⠉⠃⠀⠉⢉⣤⣈⣿⣶⣿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⡦⠀⠀⢠⣿⣤⣦⣤⣿⣿⣿⣿⣦⢍⣛⠻⣿⡿⣃⠀⠀⢀⣤⠴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡿⣧⣤⠘⠊⠃⠸⠟⢏⣹⡶⣿⣬⡿⢾⣏⠿⠷⠘⠛⠂⠀⠼⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⣿⣿⣷⣤⣶⣠⠀⡀⠐⠛⠄⠙⠋⢀⠠⠀⣶⣦⣤⣶⣾⣋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣿⣿⣮⣹⡿⣿⣿⣦⢶⣤⢦⣤⢯⣥⣴⣾⣿⣟⣿⣿⣿⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⣿⣿⣿⡟⣿⡥⠿⠞⠛⠚⣿⠾⠯⣽⡿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⣿⣯⣙⣋⢀⠀⠀⠀⠀⢀⣉⡄⠀⠈⠙⠿⣹⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠿⡶⢯⣿⡶⢿⣶⣦⠀⠀⠀⠘⣷⠀⠀⠀⠀⠘⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⡿⢁⠘⠋⠙⢻⡏⢸⠛⢣⣴⣦⣼⡆⢀⡄⣠⡄⠈⢷⠿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡰⢃⣾⠛⡇⠈⠳⣾⠀⢦⡙⠘⠀⢸⡟⠡⣿⣿⠈⠁⣹⡁⠀⢸⡿⢿⡄⣄
⠀⠀⠀⠀⠀⠀⣠⠊⣴⣿⣿⢛⡇⠀⠀⠆⠒⣉⡁⢶⠀⠀⠸⣿⠟⠛⣵⡖⢹⠇⠀⢸⡟⢻⣿⣮⡳⣄
⠀⠀⠀⠀⢠⠞⣥⣾⣛⣿⣿⠟⡃⢠⣤⡠⠀⢙⣤⡾⣧⠀⠀⣹⠂⢀⢿⡗⣹⠀⠀⣸⢻⣿⣿⣿⣿⣬⣦⡀
⠀⣰⠶⢶⣯⣿⣿⣿⣿⣿⣿⣿⣛⡌⢻⡁⠀⠛⠛⠳⣌⠷⣤⣸⣇⡈⣿⣷⣤⡶⣀⣛⣿⣿⣿⣿⣿⣿⣿⣏⠦⣀⣀
⢿⣤⣘⡤⢯⣉⣉⡙⠛⠿⠿⢿⣿⣩⣦⠁⠀⢀⡁⠈⠁⠀⠈⣉⣯⣅⣜⣿⢋⣵⣉⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣿⣿
⠀⠀⠉⠀⠀⠀⠈⠉⠉⠓⠒⠖⠀⡝⢷⣿⢳⣯⣉⡋⠉⠉⠋⠉⢉⣉⣽⡟⣿⣼⢿⣯⡿⠿⠿⠟⠛⠋⠉⠁⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⢷⣾⣏⣽⣯⣽⣯⣹⣧⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠻⣿⣿⣿⣿⣯⣿⣿⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣿⣿⣿⣿⣿⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⢿⣿⡟⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡸⠏⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⡱⢤⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣞⢑⠄⣀⠀⡎⢱⠀⣀⠠⡊⣳⠀⠀⠀⠀⣿⣿⣿⣿⣻⡯⣿⣿⣿⢹⡏⣿⣿⣿⢽⣟⣿⣿⣿
⠀⠀⠀⡤⠚⠓⠸⣄⠗⡺⢗⠺⣠⠇⠚⠓⢤⠀⠀⠀⣿⣿⣿⢿⣭⣬⣯⡿⣺⢇⡸⣗⢿⣼⣥⣯⡿⣿⣿
⠀⠀⠀⡇⡇⢰⡉⠉⢁⣳⣞⠈⣉⡉⣂⡸⢸⠀⠀⠀⣿⣿⣿⢿⣿⣯⣷⣷⡾⢜⡫⣷⠶⣾⡽⢿⡇⣿⣿
⠀⠀⠀⠈⡇⡸⡄⠀⢡⠀⢠⠊⢠⠔⢤⠈⢣⠀⠀⠀⣿⣿⣿⣷⣿⣟⢿⣿⣾⣿⡟⣵⡿⣫⡻⣷⣝⣿⣿
⠀⠀⠀⠀⠇⠇⡅⢠⢲⠀⢎⠀⢈⠓⢢⠀⢀⠇⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⣟⣿⣿⣿⣿⣯⣟⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠈⠦⣈⠳⠊⣠⠞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢷⣯⣷⢿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢦⣼⣿⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡗⡂⣸⣧⡴⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⢿⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡶⠿⠶⣭⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⢠⣶⠄⣿⣿⣟⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣽⣿⣿⣿⣿⣿⢻⣿⣿⠠⣶⡄⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⡀⠸⢿⣿⣿⢿⡟⣿⣿⣿⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠟⢾⡿⣿⣿⡿⠇⢀⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣧⡀⠀⠈⠀⠘⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡛⣿⠃⠀⠁⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⠀⢻⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⢰⡟⠀⠀⣀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣼⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⣿⣿⣿⣃⣼⣧⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠟⠹⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡟⣾⠏⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡋⣉⣉⣉⣻⣿⣿⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢶⣾⣿⣿⣿⣭⣍⣽⣿⣿⣿⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⢰⡦⠀⠀⣤⣴⣶⣦⠀⢠⣦⡀⠀⣴⣶⣦⡄⠀⣦⣾⣿⡄⣴⣶⣦⣄⠀⣴⣶⣄⠀⣴⡄⣴⡆⢠⣦⢠⣦⣦⣤
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣯⣭⡅⠀⣾⣿⣇⠀⣿⣿⣿⣿⠀⣿⣭⣭⣿⣿⣏⣹⡿⣿⣿⣬⣉⠀⣿⣿⣿⡇⢸⣿⢸⣿⣉⣿⡇
⠀⠀⠀⠀⠀⢸⣧⣀⡀⣿⣏⣉⣁⢀⣿⣾⣿⠀⣿⣿⣼⡿⠀⣿⣉⣉⣿⣽⡟⢻⣷⣹⣿⣙⣿⠀⣿⣿⣿⡇⢸⣿⢸⣿⠛⠛
⠀⠀⠀⠀⠀⠘⠛⠛⠃⠙⠛⠛⠋⠘⠋⠀⠛⠃⠛⠛⠛⠁⠀⠛⠛⠛⠃⠛⠃⠘⠛⠋⠛⠛⠋⠀⠛⠃⠛⠃⠘⠛⠈⠛







⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⣰⣆⠀⠀⣀⣠⣆⠀⠀⠀⠀⠀⠀⠙⣤⣈⣀⡴⠃⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣧⣤⣠⡴⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠐⡦
⠀⠀⠀⠀⣹⣿⠀⠐⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣾
⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⢹⣧⠺⠛⠒⣾⣿⣿⡷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢼⣿⠀⡟⢸⡇⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠾⠿⠀⠀⠀⠼⠇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠙⠠⠃⠘⠇⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠐⠟
⠀⠀⠀⠀⢼⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟
⠀⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⡿⢿⡿⠃⠀⠀⠀⠀⠀⠈⣿⡏⠀⣿⢻⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠘⢻⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡇⢸⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣿⣧⢸⣿⣹⡇⣸⠻⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⠃⠿⠁⠉⠀⠀⠀⠀⠀⠀⠸⠿⠟⠸⠿⠾⠇⠻⠛⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣬⠀⣀⠉⠀⣘⢁⣤⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡄⠐⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣁⣰⠆
⠀⠀⠀⠞⢹⣿⣶⣿⣧⣸⣿⣯⡄⠀⠀⠀⠀⠀⠈⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢾⣻⣿⡿⡴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣷⡟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣏⢻⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠰⡆⠦⠰⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⢠⡞⠁⣸⠏⣹⡿⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣿
⠀⠀⠀⠋⠀⢾⠻⠟⠉⠧⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⢼⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠄⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⡌⠙⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣶⡀⠀⢰⣶⠶⠖⠂⠀⠀⠀⠀⠈⢳⣶⡞⠁⠀⠀⠀⠀⠀⠠⠄⠠⣿⣿⣿⡇⠀⠀⠙
⠀⠀⠀⠀⠀⢻⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⣶⣄⡀⠹⣿⣿⠓⠀⢀⣾⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠀⠀⠀⢺⣿⡟⠿⠶⡻⠟⠈⠾⢻⣿⣧⠁
⠀⠀⠀⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡗⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀⡿⠺⣇⠀⠀⠀⠀⠀⠘⠛⠛⣿⡿⡇⢹⢀⣿⠛⠛⠛
⠀⠀⠀⠀⠀⣸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣿⡇⠀⠰⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣼⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇⠃⠘⢻⡿⠄
⠀⠀⠀⠀⠀⠁⠀⠈
⣿⢿⠿⠿⡿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣿⣟⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⠀⢀⠀⡀⢀⡀⢀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⣿⠘⡏⢽⣿⢸⣏⢙⡇⢹⠀⣿⢸⡟⣿⡛⣿⢸⡟⡏⢹⣿⢈⡇⢸⢹⡟⣿⢸⣿⣿⢻⡏⢸⡇⣹⡏⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠲⣧⣰⡇⢰⣿⢰⡇⢸⡇⣼⢀⣏⣸⠇⣿⠁⡟⢸⡇⣷⢸⣿⢸⡇⣿⢰⡇⣿⣼⣿⣿⣸⣷⣼⡿⣿⡇⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠀⣿⢸⡏⣿⣿⢸⣧⣸⡇⣿⢸⠋⣿⢀⣿⣷⡇⢿⡀⡟⢸⣿⢠⡇⢿⢸⣷⣿⣿⣟⣿⢹⡗⣹⡇⣿⣇⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣸⡷⣿⣿⣿⣾⡿⡇⣿⢸⠀⣿⠸⡏⢸⡇⣿⣤⡇⣿⣿⢸⡇⢿⣿⣞⠣⣿⣿⣿⢼⢇⣿⣧⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣿⣿⣧⣧⣿⣼⣤⣯⣤⣧⣬⣤⣿⣿⣧⣿⣿⣼⣷⣾⣿⣿⣶⣿⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠉⠉⠁⠹⣧⣤⣽⣾⣏⠉⢹⣿⣥⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣿⣛⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣰⣾⣿⡿⢻⣷⣀⣺⡶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⣷⣿⣽⣿⣿⣽⣿⣴⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⣿⣷⣾⠷⠿⠋⠋⠉⠈⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣇⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⠻⣧⣿⣤⣶⣤⡤⢦⣾⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⡿⠿⡟⢫⡶⢿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠻⠟⠋⢰⠛⠋⠙⢻⡏⠉⠉⠉⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣧⡀⠀⣾⣿⡀⠀⠀⣿⣿⡦⠀⣠⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢳⡈⠻⣦⣿⡿⠛⠛⠛⢛⣿⡿⠛⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⢋⣿⢾⡇⠀⠆⠙⣷⣤⣤⠞⠛⠀⠀⠀⣴⣿⣴⠷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⣆⠀⢠⡟⢳⠟⣇⡾⢁⡾⢿⠀⠀⠀⠉⠁⢠⡬⠀⠀⠀⢠⣿⣆⠉⠀⢸⣿⣿⣤⡀⠀⠀⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡈⠳⣄⣧⠸⠈⡟⣠⣾⠷⢾⡇⠀⣤⡄⠐⠂⣄⠈⠀⠀⣾⡏⢿⣀⠀⠀⠀⠹⠿⣿⣤⠞⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠀⠙⢿⣶⣿⣿⣉⣽⡻⣿⢻⣰⣿⣿⣏⡀⠀⠀⠀⣼⣿⡿⠆⠙⢿⣷⡀⢠⡴⠋⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠳⣮⡽⠟⣫⣥⣾⠟⠓⠛⠟⠛⠛⠿⣶⣿⣝⣻⣿⠀⣀⣹⠟⠁⢀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠀⠄⠴⠤⠈⢳⣾⡿⠏⠁⢀⣠⠤⠀⢤⣤⣄⣀⠉⠛⢿⣿⣿⠛⠁⠀⠀⠬⠁⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡁⠀⠀⠀⠀⣀⣰⣿⠏⢄⡴⠆⣙⡥⠶⢶⡶⠞⣻⡙⢷⣄⠀⢻⣿⣇⡶⢄⡈⠀⠒⢿⣄
⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⣴⣶⣿⡏⠀⠜⢡⡶⠋⠀⠀⢀⣰⠟⢙⣧⠀⠹⣆⢀⢻⣿⡟⠉⠀⣀⢀⣄⡿⢷⣄
⠀⠀⠀⢠⣾⣯⣭⣤⣦⣤⣤⣤⣤⣤⣤⣬⣿⣿⠀⢰⠀⣾⠁⠀⠀⡸⠟⠋⠀⠛⢻⡤⠀⣿⠐⠈⢿⡿⠀⠈⠋⠘⠻⠀⠂⠙⢷⣄⣠⣄
⠀⠀⠀⠀⠙⠉⠉⠉⢩⡏⣿⡍⢉⠉⣽⡍⢿⣿⠀⢸⣧⠙⣦⣄⡀⠁⠀⠀⠀⢀⣾⠁⠄⣿⡇⢀⣾⣿⠶⣶⣶⡶⣾⢶⣶⠶⠶⢿⣭⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣌⢷⣄⠀⡹⣷⠸⣿⡄⠈⢿⣆⠘⡿⠃⠀⢀⣶⣶⣾⣿⠛⢠⡿⢃⠀⣼⡿⢦⠙⣠⠀⢁⣼⡏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣌⠀⣿⠀⡰⣿⣦⣿⣿⣆⠈⠻⢦⣳⡖⢶⡾⠇⠀⠁⣀⣴⠟⠁⢛⣼⡟⢷⣼⢧⣿⠐⢋⡿⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠻⣤⡈⠉⣿⡴⠛⠋⠐⢿⠻⣿⣷⣄⡀⠉⠛⠳⠶⠶⠷⠟⠋⠁⠀⣠⣾⡟⠳⣤⣥⡞⠽⢛⡿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣹⡶⠞⠁⠀⠀⠉⠀⢠⡙⠛⠻⢿⣿⣦⣤⣠⢀⡀⣀⣀⣤⣶⡿⠛⠉⡀⠀⠈⠙⢷⣟⡉
⠀⠈⠀⠀⠀⠀⠀⣴⣟⣁⣤⣤⣄⣀⣀⣀⣀⠀⠂⠀⠀⠀⠙⣿⣿⡿⠿⠿⢻⣿⣿⠆⠀⠀⠆⠀⠀⠂⠀⠀⣹⠟⠳⢦⣤⣄
⠀⢸⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠉⠉⠛⠛⢿⣆⠀⠄⡀⠀⣼⣿⣿⣷⣀⣾⣛⣿⠀⠀⠀⠀⠀⣲⣤⣴⣶⣶⣷⠶⠶⠾⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡤⠄⢰⢼⣿⣉⣿⣿⣿⣿⣟⣹⡇⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣾⡟⣸⣿⣿⣿⠻⣿⢧⣷⠀⠀⣴⡟⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢰⣿⠟⣻⢉⡿⢿⡆⠙⣦⣹⡀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡇⠀⢿⣜⣇⢸⣿⠀⠈⢻⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠿⠛⠻⠇⠀⠀⠈⠉
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠘⠃⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⢀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⠐⣿⣷⡀⠹⣿⣿⠏⠀⠀⠘⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠘⣿⣷⣶⣶⣶⣶⣄⠀⢴⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡟⠃⠀⣿⣿⣿⣿⠛⠁⢰⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠻⣿⠇

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣿⣿⣿⣿⣿⢟⣫⣷⣾⣿⣿⣿⣶⣮⣝⡻⣿⣿⣿⣿⣿⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠈⠉⠑⠢⣄
⠀⠀⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⣿⣿⣿⠃⣿⢙⢩⠋⡍⡏⡙⢹⢩⢹⠉⢹⣿⢸⣿⣿⣿⠀⠀⣿⠐⣧⡖⣖⢶⢰⣶⣶⡞⡆⣾⡆⠈⡇
⠀⠀⣿⣿⣿⣇⢻⣾⣶⣷⣶⣷⣿⣾⣶⣾⣶⣶⠟⣼⣿⣿⣿⠀⠀⢻⡌⠁⠉⠉⠉⠈⠈⠁⠉⠁⠉⠉⣸⠃
⠀⠀⣿⣿⣿⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⠀⠀⠀⠙⠠⣀⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣭⣭⣷⣯⣟⣳⣝⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠛⠓⠦⢝⣦
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⢀⣠⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⢠⠄⣸⣿⢏⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣎⢿⣿⡀⢤
⠀⠀⠀⠀⠀⢰⣿⠀⠿⣃⣼⣶⣿⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣾⣷⣾⣄⠻⠇⢸⣷
⠀⠀⠀⢀⠀⣿⡟⠀⢀⣉⣉⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⣉⣁⠀⠘⣿⡇⢀
⠀⠀⠀⣿⠀⣿⢁⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⢹⡇⢸⡇
⠀⠀⢸⣿⡇⠀⢈⣡⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣉⠀⠀⣿⣿
⠀⢠⠘⣿⡇⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⣿⡟⢠
⠀⢸⣆⠘⠁⠛⣡⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡙⠃⠙⢀⣾
⠀⢸⣿⡆⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⣾⣿
⠀⡄⠻⣷⢸⡿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣿⢰⡿⠃⡄
⠀⢻⣦⡈⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣠⣾⠃
⠀⠈⢿⣷⡄⢸⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣿⠀⣼⣿⠏
⠀⠀⣄⠙⠻⠘⠁⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠙⠸⠛⢁⡄
⠀⠀⠈⢿⣶⣄⠀⢿⣿⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⣿⠇⢀⣴⣾⠏
⠀⠀⠀⠀⠙⠿⣷⡌⠏⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⠏⣴⡿⠟⠁
⠀⠀⠀⠀⠘⢶⣤⣤⣀⠀⢻⣷⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢰⣿⠃⢀⣠⣤⣴⠞
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⠝⠀⠻⣿⣆⠙⣶⣄⡀⠀⠀⠀⠀⣀⣴⡾⢁⣾⡿⠃⠘⠵⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⣶⣦⣤⣬⣛⠆⠙⠻⣿⣦⠀⢠⣾⡿⠛⠁⢚⣫⣤⣤⣶⣦⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣋⣁⣤⣤⣶⣶⠾⠀⠸⣶⣶⣦⣤⣄⣉⡙⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣯⣽⣿⣿⣽⣿

⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠌⠁⠀⠀⠈⠠⡉⠀⠠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠁⠁⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠉⣠⡎⠀⠶⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡔⠁⢀⡀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⢠⠖⠠⠈⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣄
⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠
⠀⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠈⠉⠟⠛⢿⡟⠁⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇
⠀⠅⢲⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣶⣜⢁⣠⡖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣽⣿⢉⣏⣠⠚⠁⠰⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⡄⠀⣀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣍⣠⡤⠒⠀⠀⠀⠀⠈⠳⠠⣆⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡇⢠⣇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠆⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠁⠈⠀⠐⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⣀⠀⠀⠀⢹⡄⠀⣧⣀⣿
⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠀⠀⠀⡆⠈⠀⠀⠀⠁⠀⠀⠠⠧⠀⠀⢀⣴⢶⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⣀⣠⣈⣉⢶⣞⠠⠎⠀⠈⢡⠸⡿⢿⡿
⠀⠁⠀⠀⠀⠁⠈⢰⠆⠀⣾⣷⢀⠀⣁⣀⡇⢸⣆⠀⣴⡆⣠⠄⠀⠀⢠⣉⢞⡇⠙⠷⠀⢳⣆⡀⠀⢢⣄⠀⠀⠈⠀⠀⣀⡈⠉⢉⣻⡟⢿⣧⠶⠺⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣷⣶⣿⣿⣏⣿⣿⡌⢡⣿⣿⠾⢿⣿⣿⣷⠀⠀⣸⣦⡻⠁⠰⣚⠦⠀⡩⠙⣿⢌⣙⣷⣶⣶⢿⣿⣿⡿⠋⡻⠛⠻⣎⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⠛⠛⠩⠿⣾⠻⣿⠻⠃⠀⣼⠁⠀⠉⣿⠉⣿⣿⠛⠉⠠⠈⠀⠀⣿⢠⡅⢸⣿⡿⠅⠻⣷⣴⣿⣄⠊⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠀⡇⠀⠨⠀⠘⣷⣀⣰⡤⢸⣿⣧⣿⠟⠛⢆⢀⣤⣠⡆⢻⡈⠀⠘⢿⡄⠀⠀⢸⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⣧⠀⠀⣴⣦⠀⣾⠛⣽⣷⣿⣿⠂⡁⣰⣦⠘⡿⢻⡝⠂⣾⠁⠉⠀⠀⣧⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠧⠀⠇⠀⣿⠀⠀⡄⢀⠀⣽⠆⢉⠞⣿⠛⠲⠄⠙⠋⠷⠲⣿⡇⠀⣿⠺⠷⠦⣤⡀⣀⡀⠀⣰⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢀⠀⠀⣰⡗⠸⣿⡟⠀⠀⠀⠀⠀⠀⢼⠀⠀⡿⠀⠀⠀⠀⠀⣸⡿⠟⠋⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠉⡀⠀⣧⠸⠁⢸⡿⢷⣤⣿⣇⢧⡸⢀⣦⢰⣦⣾⡄⠐⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡀⢸⡄⡇⠀⣿⣀⠀⢸⠇⢻⡟⣿⢣⣾⣿⡎⣋⣼⣿⣿⡏⠁⠀⠀⠀⢀⣼⣯⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⢸⠃⡧⠀⢹⣇⠀⣸⣇⣼⣧⣧⣼⠟⢿⠿⠠⠿⠿⠿⠇⠀⠀⠀⠠⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠧⠀⠿⠿⠀⠿⠛⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⢦⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠈⠉⢿⣿⣿⣿⣿⠿⠷⢶⡶⠈⠙⠣⣼⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢋⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠷⠊⠀⢀⣠⣿⣿⣿⣧⣀⡀⠀⠀⢀⣀⣀⡀⢀⣰⣶⣤⣤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⠀⠀⠛⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠸⠿⠿⠿⠿⣿⣿⣧⠌⠈⠁⠙⠃⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣏⡁⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠀⢳⡀⠀⠀⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣸⣧⡀⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⣴⣿⠛⢿⣤⠂
⠀⠒⠒⠒⣤⡀⠈⠀⠀⠀⠛⠁⠛⠋
⠀⠈⠛⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠢⠀⠤⣴⠀⠤⠞⠁
⠀⠀⠀⠀⡀

⢠⡄
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠂⢀⡄
⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣀⣨⣤⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠒⠻⣿⠃
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⣤⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡇⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⣰⢄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡶⠂⠀⢸⡇
⠀⠀⣾⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣴⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⠇⠀⠀⠀⠀⠀⢸⣷⣼⣿⠐

⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢗⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⣠
⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣤⣾⣶⡆⠀⠀⠀⠀⠀⠀⣾⣤⣿


⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⡄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⣦⠀⡎⢩⠀⠀⠀⠀⠀⠀⠀⢸⣯⠃
⠀⠀⠀⠺⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠿⠀⠀⠀⠀⠀⠀⠸⠦⠿⠴⠿⠼⠇⠀⠀⠀⠀⠀⠀⠟⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣴⠒⢦⢞⢙⠆⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡀
⠀⠀⠙⢲⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠂⢻⡇⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⣶⣇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⡀
⠀⠈⢿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢠⣞⠉⠙⣷⡌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⠿⡿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⢻⣶⣶⠟⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⡶⠾⢿⡿⠲⣶⡶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣹⡇⣀⣿⡇⡀⣷⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⠁⠨⣭⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣾⡟⠷⣏⢳⣠⣵⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⣂⣴⣿⣿⣿⣿⣿⡄⠈⢹⣿⣿⣿⣿⣿⣿⡆⡰⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⠙⢿⡿⠛⠛⠈⢣⠀⠀⡟⡜⠘⢿⣿⡿⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠈⠑⢤⣤⣿⣶⣶⣾⣄⡤⠞⠉⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣿⣿⣷⣤⣀⣠⣿⡟⢣⡀⢨⣟⣿⣷⣤⣶⣿⣿⣿⣙⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣷⡞⠚⢻⣿⡅⠻⡷⡯⠋⣼⣿⡟⠛⢛⣿⣿⣿⠓⠃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⢀⡼⢿⣿⣦⣤⡜⣊⡿⠋⢑⠢⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⠛⠁⠀⠀⢈⣛⡟⠛⠛⡆⠀⢹⣷⢮⣛⣿⡋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠯⢧⣄⣐⡢⢶⣖⣸⡀⣰⣆⣹⡄⠀⣩⣷⣷⠟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⢿⣿⣯⣷⣿⣿⣿⣷⣤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡏⠾⠙⡟⠻⠁⢨⣽
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⡄
⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡐⢢⢄⢠⡔⠂⣠⣠⣄
⠀⠀⠀⠀⢠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⡀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠆
⠀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠇
⠀⠀⠀⠐⣴⣂⣆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⢀⠤⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣷⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣿⡿⣿⢿⡿⣿⣻⣿⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣛⣧⣿⣤⣟⣿⣾⣧⣿⣽⣭⣿⣧⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⢀⡄⣠⡤⢠⡀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⢧⠤⡄
⠀⠀⠀⠀⠀⠸⡄⠹⠋⢠⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠙⡞⠒⠃
⠀⠀⠀⠀⠀⠦⡤⣤⢴⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⣄⡨⡍⣄⣄⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⣰⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢙⡈⠁⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠠⠞⠸⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛
⠀⠀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀
⠀⠀⢿⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣸
⠀⠀⠘⣧⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢶⡟⠛⠁⠀⠈⠙⢛⣶⠆⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠻⣆⠀⠀⠀⠀⠀⢸⣧⣤⠶⢦⣤⣷⠀⠀⠀⠀⠀⢀⡾⠁⠀⡀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢿⣦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣿⠷⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣠⡴⠟⠉⠛⢦⣄⠀⠀⠀⠀⠀⣀⣴⠞⠉
⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿⠞⠉⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠠⡟⠉⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣾⡁
⠀⠀⠀⠀⠙⣿⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⣶⠞⠁
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠉⠙⠳⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢉⣱⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢀⣀⣠⣶⠿⠋⣉⣿⣿⣿⡆
⠀⠀⠀⠀⠸⢿⠟⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⢀⣤⣶⣦⣷⠿⠿⠟⠋⠁⠀⠀⠈⢿⣿⡉⣿⣧⣀⡀
⠀⠀⠀⣴⣷⣼⣾⣶⠀⠀⢀⣤⣾⣷⣖⣦⡀⠀⠀⠀⣿⠏⢹⣿⣿⣶⣾⡗⠀⠀⠀⠀⠀⠀⣹⠷⣼⡍⢛⡛
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⣼⡏⣼⣿⣿⠛⠿⣶⡦⠀⠛⠀⢸⣿⠟⠉⣿⡇⣀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣧⣤⡄
⠀⠀⢸⡏⣿⣿⣿⠸⡧⠀⠉⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣶⣾⣿⣶⣶⢂⣸⣿⣿⡟⠋⠻⣿⣿⣿⣀
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⡟⣿⣧⠀⠀⠀⠀⠀⣰⡿⠋⢠⣾⣿⡋⠀⢹⣿⣾⣽⣿⣿⣷⣤⣴⣿⣿⣿⠉
⠀⠀⠀⢰⣿⠃⣿⡇⠀⠀⠀⣼⡿⠁⠘⣿⣆⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣿⣶⣿⣿⡀⠛⠙⣿⣿⣿⣿⣿⡟⠙⠁
⣤⣤⣤⣼⣿⣦⣿⣧⣤⣤⣴⣿⣧⣤⣤⣼⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣿⣤⣿⣧⣼⣧⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿