Doctors Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠄⠀⠀⠀⠀⠀⢄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡆⠠⡴⠁⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠁⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⠹⣅⠀⠀⠀⠀⠀⢀⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠯⢥⣈⣿⡀⠈⠳⣄⠲⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡰⠯⢄⠀⠀⠀⢰⠋⣷⣀⣀⠬⢣⡶⣯⣦⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⢳⡀⠀⠈⠲⣼⡏⠑⡄⢸⢠⡿⠉⠻⡑⢠
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢣⠀⠀⠀⠈⢻⢄⠘⣼⣸⢻⠀⠀⠹⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡻⡷⣽⣿⠘⣆⣀⠀⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠙⠚⠁⠘⡇⠀⠈⠉⠈⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⢇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢸⠺⡀⠀⠀⠀⠀⣀⠔⠚⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⠀⡇⠀⠀⣀⣀⡼⣅⡑⢦⣤⠴⢊⠁⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢩⣷⠊⠁⠀⠠⢤⣠⠿⠋⡵⡛⠍⣺⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠙⠳⠦⣄⡀⠀⢰⣃⡧⠤⠖⢉⡽⠛⣁⣤⠺⣥⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠃⠀⠚⠑⠒⠉⢹⠉⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣩⣍⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣠⣤⣬⣥⣤⣄⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⣉⣉⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡘⠃⡨⢁⠘⢃⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠋⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⡧⠀⠀⣬⠄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠐⠲⠔⠂⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⠀⠀⠀⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣪⠕⢯⠑⢂⡔⠒⣹⠲⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⣤⣤⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡿⢧⡸⣤⠘⡏⢻⡟⢛⠇⢠⡼⠨⡏⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡦⢄⡡⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⡇⠳⡄⢹⣼⣿⡜⢀⡜⢀⣴⣣⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣀⠀⠀⣨⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⠀⣰⠁⠀⠘⢦⣻⣿⡡⠋⠀⠈⠻⠿⠃⠀⠀⡇⠀⠀⠀⠀⠀⣴⣿⣹⣿⣿⣿⣷⣾⡿⠿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠭⠭⠤⠭⠤⠤⠤⠿⠿⠥⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠶⢂⣩⢇⣄⣀⠈⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣫⠞⢁⣴⣿⢷⣿⣿⣽⣷⣦⣌⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⢏⣴⣀⡾⢋⣾⣿⣿⣿⣿⣿⣯⡆⣈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠄⠀⠀⠛⠿⠿⣿⣿⡿⣿⠞⠋⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⡿⠀⠀⠀⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠃⠈⠁⠀⠀⠀⠰⢶⡶⣍⠛⠀⠀⣴⣶⡶⠶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠿⠟⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠸⣅⠀⢸⣃⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣶⢾⠃⢸⡀⠀⠀⠀⢤⣀⣀⣈⡙⠉⠉⠀⢀⠎
⠀⠠⠴⠖⠒⠛⠋⠉⠉⠁⠀⠀⢠⣞⠗⢹⡇⠈⣇⠀⠳⣄⠀⠀⠀⠈⢉⣉⡙⠛⠀⣠⠂
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣿⡝⠀⠸⣇⠀⠙⣆⠀⠈⠳⣆⡀⠀⠀⠉⠁⢀⣴⣿⡶⢤⣄⡀
⢳⡀⠀⠀⠀⢰⢏⣠⡀⠀⠀⠀⣿⢧⠀⠀⠉⠛⠦⣼⣆⠀⠀⠈⠉⠁⠛⠒⠛⣹⠋⢺⣷⠀⠈⠉⠛⠲⠦⣤⣀⡀
⠈⢧⠀⠀⣰⡿⠋⣽⠁⠀⠀⢀⠿⠸⣆⣀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⢠⡖⣿⠀⠘⣿⡆⠀⠀⠀⣀⡀⠀⠈⠙⡦⢤
⠀⠘⣇⠀⠉⠀⣸⠃⠀⠀⣴⣷⠒⠉⠙⢿⣳⡄⠀⠀⠹⣯⣷⡄⠀⠀⣰⡏⠴⠃⠀⠀⣿⡇⠀⡴⠛⢁⡟⠀⠀⠀⡇⠸⡇
⠀⠀⣿⠀⠀⢰⠏⠀⠀⠀⣿⣇⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠉⢿⣦⡾⢩⡆⠀⠀⠀⠀⣿⣧⠀⠀⠀⣼⠁⠀⠀⠀⡇⠀⢿
⠀⠀⢸⡄⢀⡟⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣽⠃⢸⡇⠀⠀⠀⠀⡿⡇⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠸⣇
⠀⠀⠀⣷⡈⠉⠉⠙⡇⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⢃⡀⢸⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠙⢢⡀⠀⢸⠁⠀⠀⢻⡀
⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⣯⠟⠀⣼⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢳⠀⡟⠀⣠⠞⠈⡇
⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠈⢿⡄⠀⠀⡿⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⣰⢻⡟⢳⡄⠀⠀⠀⠀⠸⣴⢃⡜⠁⡀⠀⢻⡀
⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠀⠀⠈⢻⣄⣸⠃⠀⢠⣤⠀⡟⠹⣄⠀⣿⠀⠀⠀⣷⣾⣆⣠⡇⠀⠀⠀⠀⠀⣽⠏⣠⠞⠁⠀⠀⢷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⣶⣄⣠⠝⠛⠒⠒⠋⠉⢰⠃⠀⢸⡆⣿⠀⠀⢀⣼⣷⣦⢟⣀⣠⠠⠴⠖⢾⣿⢊⣥⠖⠃⠀⠀⠘⢧⡀
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠇⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⠋⠁⠀⠀⣀⠤⠤⣤⠙⢷⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⣷⣤⡀⠀⠀⠀⠀⠀⠀⡟⢠⡔⠋⠀⢸⡆⠀⠀⣧⠈⠉⠉⠉⠉⠉⠁⠸⡟⠁⠀⠀⠀⠈⠁⣠⠞⠁⠀⠀⠻⣄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠢⡙⠦⣀⠀⠀⠀⠀⡇⠠⠬⠝⠃⡘⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⢰⠿⢤⣀⠀⠀⢀⣾⡥⢒⡟⢀⡴⠲⣼⣧⣀
⠠⠤⣄⣀⢸⡇⠀⠀⠀⠀⠀⠀⣀⠤⠛⠓⠚⠷⣄⣀⠀⡇⣠⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠻⣟⠓⠀⠈⠁⣰⠋⢀⡞⠀⢁⣄⠀⠈⠳⠤⣀
⠀⠀⠀⠙⠻⣿⣶⣤⣤⡤⠞⠉⠀⠀⠀⣀⡀⠀⠀⠉⠓⢧⣌⣉⠙⠂⣀⣀⡀⠸⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢹⣦⣄⠀⠰⠟⠀⣼⠁⢠⠞⠙⠛⣀⢀⠀⠘⢧
⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠲⠦⣤⣀⠶⠉⢻⣹⢾⡏⠉⠉⠙⠛⠓⠒⠶⠶⠶⠶⠾⠷⠤⣤⣤⣧⣉⣀⣀⡔⣻⠗⡴⠃⠀⠀⡰⠃⠈⣻⠀⢠
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⣀⠀⢀⡍⠛⢦⣤⠿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠇⡼⠓⣄⢀⡼⠁⢀⡼⢁⡜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠉⣛⠻⢦⡴⢃⣈⣙⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠁⠀⢩⡟⠐⢣⠞⢴⠞⠒⠛
⠀⠀⠀⠀⠶⠦⣤⣀⡀⠀⠀⠀⠈⠙⠛⠛⠛⣉⡿⠛⠛⠉⠉⠉⠉⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⣿⡀⣠⣯⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠓⠛⠛⠛⠋⠉⠙⠳⢦⣄⣀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠿⠛⠙⠳⠦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⣤⣀⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠶⠶⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣤⣤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠚⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛⠛⠁⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣤⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠿⠉⠙⠶⠒⠀⠀⠉⠉⠻⡀⠀⠀⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠐⠂⠀⠀⠲⠀⠀⠀⠀⠛⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣴⡆⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡎⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠃⠀⠀⠈⠁⠀⠀⠀⠀⢠⣶⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡟⠉⠉⠀⠀⠀⣰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⢸⣇⣀⣀⠀⠶⠶⣿⠈⠙⢶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⣹⡇⠘⡏⠈⠁⠀⠀⠀⣿⠀⠀⢸⡇⢹⣿⠗⠂⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣿⡇⠀⠃⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢸⣿⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡇⢸⣿⠀⠀⣠⠛⠀⠱⡆
⠀⠀⠀⠀⢀⡘⢿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠟⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠘⠃⠀⠀⢀⣴⣿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣸⡏⠀⣼⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⢸⠇⠀⠀⠀⣿⣯⣴⣦⢼⣿⣷⠀⠀⠀⠀⣴⠀⠀⠘⠇⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⢀⡇⠀⢰⠀⢰⣿⠁⠀⡏⠀⡿⢿⡇⠀⠀⠀⣿⠀⢀⡾⠿⠿⢿⡄⠀⢿⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠁⠀⢸⠀⣼⡏⠀⠀⡇⠀⡇⢸⣷⠀⠀⠀⣿⠀⣾⠀⠀⠀⠁⢿⠀⠀⣶⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡇⠀⠀⢸⡇⣿⠇⠀⠀⠃⢠⡇⠀⣿⡇⠀⠀⣿⠀⣸⠾⢃⡈⠷⠆⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⢰
⠀⣤⠀⠀⠀⢸⠏⣿⡆⠀⠀⠀⢸⠇⢀⣼⡇⠀⠀⣿⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠘
⠀⠟⠀⠀⠀⢘⠀⠈⠻⣷⣦⠀⣿⣿⡿⠋⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢿
⣦⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⢰⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⡀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠃
⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣴
⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠒⠒⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⢱⡄⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠹⣆⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠾⠋⠳⣄⣀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠻⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⠀⠰⠆⠀⠀⠘⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠓⠛⠛⠛⠒⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠦⠶⠤⠴⠦⢾⠇⠀⠀⠀⣹⡶⠦⠄⢀⣀⣀⠀⣴⠏
⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠶⠋⠀⠀⠀⠈⠉⠁⠀⣿
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠞⠃⠈⢰⠆⠉⠀⠀⠀⠀⠀⠀⣠⠖⠚⠋
⠀⠀⠀⠀⠑⠤⠄⠀⠀⢤⠴⠛⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⡤⠚⠁
⣶⣶⣶⣶⣶⣤⣴⣶⣶⣤⣴⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣤⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⠿⠛⠻⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣻⣝⢶⡀⠀⠀⠙⢶⡄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣎⠀⡽⢠⡗⠲⠦⣄⣀⠁⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⠈⠉⣀⣾⣀⠀⠀⠀⠈⠉⠒⠤⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢌⠙⢋⣩⣀⣯⡙⠓⠶⢤⣄⡀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣏⠁⢾⣷⠋⢰⣿⣽⡷⠀⠀⡾⠉⠙⢲⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠑⠒⠻⣆⣈⣉⠝⠀⠀⢰⠇⢀⣀⣸⡀
⡶⠒⠒⠒⠋⠉⠉⠉⠉⠀⠀⠀⠀⣗⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⠄⠀⠺⣤⠏⠠⢦⠙⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⣠⠏
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢽⠓⠒⠒⠚⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⣿⠉⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⢤⣸⡇⠈⠛⠲⣄⠀⠀⠀⡞
⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⢷⠀⠀⠀⠀⠀⠀⠘⠢⢄⠀⠈⠳⠤⠴⣇
⢀⡰⠤⠖⠒⠒⢦⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⡠⠃⠈⢡⠀⠀⠀⠀⠀⠀⠀⣠⠛⠂⠀⠈⠑⢎⠉⠒⢤⣀
⢫⠀⠠⠶⠖⠚⠛⣦⠀⠀⠀⠀⠀⡇⢣⡀⠀⠀⢰⠃⠀⠀⠈⢶⠖⣿⣥⣀⣀⣀⡵⠂⠀⠀⠀⠀⠘⡄⠀⠀⠘⣆
⠣⣤⠤⠤⠴⠶⠚⣯⠀⠀⠀⠀⠀⡇⠀⣱⠄⣴⠃⠀⠀⠀⠀⢸⠀⡧⠊⠉⣍⣱⡟⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⢻⡀
⠀⣹⠦⣤⣤⠤⠶⠋⠀⠀⠀⠀⠀⡿⠊⠁⡸⡏⠀⠀⠀⠀⠀⢸⠀⡇⢰⡇⢸⡟⡇⢀⠀⠀⠀⠀⢀⣇⡀⢸⡆⠘⡇
⠀⠳⣄⣠⡿⠀⠀⣀⣀⣀⣠⢤⣤⠇⢀⡞⢰⠁⠀⠀⠀⠀⣤⠎⠁⢸⠏⡄⣼⠁⠹⣄⣳⣤⣀⣠⡞⠉⢧⠈⣇⠀⣿
⠀⠀⠈⠷⠚⠛⠻⢬⡉⠉⠙⠲⣄⣠⠞⢀⡏⠀⠀⠀⠀⠀⠈⢆⠀⢸⡀⢷⡟⠀⢀⡜⠁⠀⢨⡟⠀⠀⠘⣆⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠘⠙⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢣⡀⡇⢸⠃⢠⠎⠀⠀⠀⠈⠻⡄⠀⠀⠹⣌⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣸⡇⣰⠏⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠓⠶⠦⢾⣄⣀⣀⣀⡀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣄⠀⠀⠀⠀⠀⠉⠉⢹⠉⠉⣍⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⢧⡀⠀⠀⠀⠀⠀⢹⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠻⡄⠀⠀⠀⠀⠘⡆⠀⠀⠘⢧
⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣧⢤⠤⠤⢿⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢣
⠀⠀⠀⠀⠈⠙⢿⣕⡒⠶⠶⠶⠶⠶⠖⠚⠉⠉⠉⠀⠀⠀⢀⣀⠀⠀⢷⠀⠀⣀⣠⠜⠋⠉⠛⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢦⣤⣤⣀⣀⣀⣤⣤⡤⠶⠚⣉⣏⣠⡤⠾⠓⠛⠉⠀⠀⠀⣰⡆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣛⠛⠛⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⣀⣀⠤⠞⠙⠷⠶⠚⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣶⣶⣶⣶⣶⣶⣶⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠀⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠀⠒⠂⠀⠉⠈⠡⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠶⠀⠀⠰⠦⣄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢉⣵⣄⣠⠒⣉⠐⢄⠀⠀⠀⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢛⠇⢸⠀⠛⠀⡸⠉⠑⠂⠤⣄⡴⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠏⠀⠀⠁⠒⠊⠁⠀⠀⠀⠀⠚⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠄⠀⠀⠀⠄⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡎⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠢⡀
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⣴⠃⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⡘⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠌⢠⠀⠀⠀⠀⡏⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⡀⡆⠀⠐⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠠⠀⠘⠀⠀⡠⠲⠿⠓⢴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠘⣤⠤⠶⠤⢴⣧⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡄⠀⣧⠁⠀⠀⠀⢸⠀⢤⠀⠀⠀⠀⢸⠀⠀⠔⢃⢀⡙⢃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢠⠁⠀⠀⡇⠠⠘⠀⠀⠰⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠈⠀⠁⠀⢘⠀⡁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠆⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠆⣐⠐⡀⠔⠁⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢡
⠀⠐⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⡇⠀⠀⠀⣇⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⡇⠈⠳⣤⣄⠀⠀⢨⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠠⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⢸⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣆⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣨⣇⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣤⡄⠀⠀⢠⣤⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠠⣿⠆⠀⠀⠰⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⢾⣶⣄⣠⣦⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠳⠶⢦⣤⠴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠟⠃⢸⣿⣄⣤⣀⠀⠀⠀⠀⣸⡿⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⠶⠆⣿⣿⠃⠀⠀⢸⣿⠀⠉⠉⠀⠰⠶⠾⠿⠂⠈⢻⣿⡷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢃⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠿⠀⠀⠀⣿⣿⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⣿⣿⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⡆⠀⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠸⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⢸⣿⡇⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⣿⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⣿⣿⣿⣶⣄⠈⠃
⠀⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⣿⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⢹⣿⡀⠙⣿⣷
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⣼⠿⠿⠿⢢⣴⣿⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠟⠿⢿⣿⣼
⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⡀⠙⣷⠆⠰⢎⣹⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠘⢿⣠⣦⠀⠀⠘⢻⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡘⠀⠀⠀⠀⢹⣿
⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠈⠻⣥⣴⣶⣤⢿⣿⠀⠀⠀⠀⢀⣿⡿⠃⠀⢰⣇⠀⠀⠀⢀⣾⣿
⠀⣸⡇⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡇⠀⣿⠀⠀⠀⠀⢸⣿⠇⠀⠀⢸⡿⠀⠀⠀⠈⠻⣿
⠀⠹⠃⠀⠀⠀⠀⠀⢠⣤⠁⠀⠀⣸⡀⠀⠀⠀⠀⠀⠘⠃⢀⣿⠀⠀⠀⠀⢸⣿⣆⠀⠀⣿⡇⠀⠀⢰⠀⢰⣿
⣤⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡇⠀⣠⣾⣿⠿⠟
⣿⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠙⣿⡏
⣿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢿⡇
⠋⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠈⢳⣆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⢱⡄⠀⠀⠀⠀⠀⠈⠛⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⡆
⠀⠀⠘⢃⡀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇
⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⠶⠶⠶⠶⠶⠶⣿⡇⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣀⣤⣤⠚⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠷⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⡰⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⢠⣴⣦⣤⣄⠀⢀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠉⠀⠠⠀⢤⣴⣦⣤⣤⣤⣤⠤⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢰⡇⠈⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⠀⠀⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠙⣦⡄⠀⠀⣿⣶⡄⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠈⠙⢦⣤⣋⣀⣠⠿⠗⢀⣀⣠⣿⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣁⣰⣶⠆⢀⡀⢹⣿⡟⢁⡀⠲⠿⠿⠟⠁⢀⡈⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠴⠿⠿⠟⠁⠀⠙⢣⡀⠀⠀⠀⠀⠙⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣾⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠋⠁⠉⠛⠛⠛⠋⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⣄⠀⠀⠄⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠈⠑⢾⢳⡄⢆⠀⠂⡰⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⢄⠀⢶⠉⠱⡀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢇⠀⡰⠁⠀⠀⠀⠀⠀⠀⢘⢴⠋⠀⠨⢹⠰⡅⠀⠀⠀⠀⢀⠀⠀⡀⠄⠀⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢄⠄⠀⠀⢀⠂⠸⢲⠀⡦⠜⠤⠴⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡎⠀⡶⠚⣥⡃⠀⢀⠀⢡⠀⠀⠙⠒⠁⠀⠦⠀⠀⠀⠐
⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠰⠀⠚⢁⠐⢣⢀⠂⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠱⣄⡀⠀⠀⠀⡅⠀⢸⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠓⠁⠀⠛⠁⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠸⠀⠀⠰⠛⠀⠀⠀⠀⠠⣰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢰⠀⠀⠁⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡘⠀⠀⡀⠈⡀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠀⡀⠀⠀⢰⠀⠀⢠⠀⠀⡀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠐⢁⣀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠸⠀⠀⠀⡠⢀⡞⠁⠀⠀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠉⠣⠀⠠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⠉⢛⣤⣽⠯⢍⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣃⠘⢋⢶⣶⣶⡆⠀⠹⢯⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠛⣻⠀⠘⠘⠛⠋⠀⠀⠀⢣⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⣍⣒⣠⣤⣴⠆⠀⠀⣰⣇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡙⢦⣶⠶⠋⠀⣠⢼⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⢴⡞⠁⢸⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐⠆⠳⠶⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠐⣶⣾⠇⠀⢈⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠘⠯⣁⡀⠊⠀⠀⢀⣀⣀⡿⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠄⣠⠞⣿⡇⠀⣠⡟⢹⡄⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠸⡋⠀⡠⠋⠢⡄⠀⠀⠀⠀⠀⣠⠎⠀⣠⢊⢴⠏⣸⣿⣦⣾⠟⠀⣿⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠈⠑⢄⡀⣠⠞⠁⠀⡜⠁⣈⡿⠀⣿⣿⣿⠏⣤⠾⣟⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠙⢆⠀⠀⠀⡇⠀⣸⡇⢰⣿⣿⠏⡼⠣⠀⢸⡦⠀⠳⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠞⢃⣰⣿⡇⢸⣿⡏⣸⠇⠀⠀⣸⠁⠀⣰⠻⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠒⠉⠀⠀⠘⡛⠾⠃⢸⡟⠠⡿⡄⢀⣰⠏⠀⡴⠃⠀⠘⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡁⠀⠈⠁⠙⠁⢀⡜⠁⠀⠀⢀⡬⠓⠛⠁⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⢀⠀⠀⠀⠀⢠⠎⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠉⠀⠀⠀⡰⡇⢀⡴⠛⡁⠀⠀⠀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢦⠁⠀⠀⠀⠀⡸⠉⠣⣀⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢃⢀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡼⢇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣄⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⠛⠛⠛⠛⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠤⠤⣤⠀⢠⡤⠤⠤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⡄⠀⠹⠿⠆⣀⡀⠾⠿⠁⠀⡼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣽⠖⠒⠋⠉⠀⠈⠉⠓⠒⣾⡍⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⡀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⡴⠚⠛⠁⠀⠀⠀⠀⠀⠀⠹⠶⡖⠤⠤⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⢸⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡸⠀⢹⠀⠀⠀⠀⠉⠑⠒⠦⣀
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢠⡟⠋⢻⡄⠱⡤⠤⠤⠤⠤⡴⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢣⠀⢣⠀⠀⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⡀⠀⢣⠀⢠⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠰⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⡀⠀⡇⠀⠀⢣⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠱
⠀⢠⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠙⣄⡇⠀⢀⣤⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣄⣀⠼⠓⠒⠉⠀⠀⠀⠀⡴⠚⠳⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢆
⠬⣀⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠋⠉⠁⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠁⠀⠰⠶⠀⠀⠀⠀⠰⠖⠀⠀⢸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⠅⠀⠀⠀⣿⡟⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⣄⠀⠀⢀⡄⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠟⠋
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠄⡀⠀⠀⠀⢀⢴⡄
⠀⠘⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠿⠀⠀⠉⠀⠀⠀⠘⡇⠀⠀⡀
⡆⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠥⡀⠀⠀⠀⡠⠌⡁
⢡⣈⡐⠡⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠩⡌⠉⠘⠀⠉
⠀⠓⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇
⠀⠀⠀⠀⠈⠦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠁⠂⠠⠤⠤⡤⠄⠒⠉⠀⡔⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣄⡀⠂⣤⣤⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠨⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢿⣿⡿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣍⣛⣛⣩⣴⡿⠛⠀⣿⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⠋⢈⣿⡿⠿⠛⠉⠀⢀⡼⣁⣀⣐⠟⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⢟⡵⣺⣣⣶⣿⣿⣷⡀⠀⠀⣠⣫⡾⠋⠉⠉⠻⣦⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣴⠏⢺⡄⡿⠁⣿⣿⡟⠁⠳⣄⠞⣡⠋⠀⠀⡔⠀⠀⣿⠀⠀⠀⠀⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠸⠏⢠⡟⠀⡇⣸⣿⣿⣇⠀⣰⠋⡼⠁⠐⣿⠛⠁⢀⣾⠃⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣾⢣⣾⣿⣆⠘⣧⠀⡇⣿⣿⣿⠏⡼⢃⡞⠀⣠⠞⠉⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⡏⠘⢿⡿⠃⠀⢸⣆⣧⣿⣿⡟⣼⢁⡞⢀⡾⠁⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢀⣼⠿⣄⠀⠀⠀⠀⠀⠈⣿⢸⣿⡿⣸⠃⡾⠰⠋⢀⡤⠊⠁⣴⠁⣀⣤⠖⠁⠀⠀⠀⠀⢠⡿
⠀⠀⠀⣰⡟⠁⠀⠈⠀⢰⠀⠀⠀⠀⣿⢸⣿⣷⠟⠦⣧⡤⠖⠉⠀⠀⣼⠋⠉⠉⠀⠀⠀⠀⠀⢀⣠⣾⠃
⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⣿⣿⡟⠀⠀⠈⣙⣣⣶⣾⢯⢭⡅⠀⠀⠀⠀⠠⠴⠚⠋⣹⡏
⠀⣰⡿⠀⠀⡀⠀⠀⣀⣼⣷⣶⣶⣦⣼⣿⣿⣧⣤⣴⣾⣿⣿⣭⠝⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⣼⡟⠀⠀⠀⠈⠙⢾⣿⣿⣿⡿⠋⠀⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⣿⠀⠀⠀⠀⠀⠂⠉⠉⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⢻⡇⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠈⢿⣄⠀⠀⠀⠀⠀⠸⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣿⠁
⠀⠀⠻⢷⣤⣀⠀⠀⠀⠀⠈⠉⢹⣿⣶⣦⣤⣀⣀⠀⠀⠀⠒⠲⠶⠶⢶⣶⠾⣿⠟⠁⠀⣿
⠀⠀⠀⠀⠈⠛⠻⢷⣦⣤⣀⠀⣼⠟⠋⠉⠁⠈⠉⠛⠛⠷⠶⠶⠖⠛⠉⢠⠞⠁⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⠏⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⠿⢿⡿⠋⠁⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠀⠔⣛⢻⣶⡄⢰⣿⣛⣳⠀⢸⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠉⠙⠉⠹⠃⠈⠉⠉⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠰⠋⡈⠙⢊⠁⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠤⠤⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⣠⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣧⡽⠿⠶⠒⠂⠁⡀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⢀⡿⠈⢇⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⢸⠀⠀⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠃⠸⡇⠀⠈⢆⡠⠛⣿⣿⡏⠻⣀⠆⢀⡿⠤⠼⠀⠀⠀⠀⠈⠐⠒⠒⢄
⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢣⡀⣿⣿⣷⠀⡜⢀⣼⢥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠹⣿⣿⣿⡞⢁⡟⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢘⣇⡠⡀⠀⠹⣿⡟⠀⠸⡇⠀⠀⠀⠘⠇⠀⢠⡇
⠀⠀⠀⣼⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢴⠿⠋⠀⠘⠄⠠⡏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢦⣤⣤⠆⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣲
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡀⠀⣠⡦⣼⢧⡇
⠀⠀⠀⢢⠹⡆⠀⠀⠀⠀⠀⠈⣵⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡶⡣⠊⡰⡀⠀⠀⠀⢀
⠀⠀⠀⠈⣇⠘⠀⠀⠀⠀⠀⠀⢹⠛⠒⠦⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢀⠈⡰⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣀⣀⣸⣀⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠁⠀⠒⠒⠶⠏⠀⠀⠈⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣈⣭⣿⡶⢶⣤⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡴⡶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠛⠏⠀⠈⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⣚⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣛⣻⣟⠟⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣻⣶⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣴⣶⣶⣾⣿⣿⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⢿⣿⣿⠋⠉⠉⠘⠻⠇⠀⠛⠛⠋⠿⢹⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡥⠀⠀⠘⢿⢶⠖⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⣷⣆⠀⢲⣖⢲⡶⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣄⣸⣿⣿⣿⣷⣮⡞⠛⠛⠋⠀⢀⣼⣦⣀⠐⠀⠀⢬⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠍⣄⣠⣷⣾⣿⣿⢿⠊⠙⢿⣿⣿⣶⣶⣢⠶⢉⣿⣿⣿⣷⣶⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⢾⣦⠀⠂⢨⣿⡟⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣼⡈⠳⠴⠀⠀⢦⠀⣴⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣽⣿⣷⣦⣤⡀
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠁⡿⣄⠀⢀⢠⣶⠿⣷⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣥⣷⡀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣴⣾⣷⣴⣎⠇⣰⣘⣿⣿⣿⢏⣾⣿⣿⣿⣿⣟⣿⡿⣿⣿⠃⡔⢸⣻⢿⡇
⠀⠀⠀⠙⢿⣯⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣻⡿⣿⣿⠏⠈⠹⠀⣿⣿⣯⠿⢣⣿⡿⢻⣿⣿⣿⣿⣻⡇⣾⢇⡼⠁⡟⢣⢾⠇⡤
⠀⠀⠀⠀⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⡞⡝⣠⣤⠀⢠⣿⡏⠉⣷⣾⣽⢿⣸⡐⠟⣼⣸⢿⡇⡿⣾⢃⠀⣠⢠⡿⣼⡱
⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⠏⠁⠉⠉⣄⢀⡏⠷⠾⠫⠐⡏⡬⢹⡀⣣⡛⡙⣿⡜⣿⡿⠠⢠⠟⢫⣄⣿⠟⠁
⠀⠀⠀⠀⠀⠹⣿⣿⣿⢻⣿⣿⣿⣿⣿⣁⡿⠉⠀⠀⣤⡄⣛⢸⡇⠀⢠⠀⠂⠟⠃⠘⢻⢿⡶⣇⢻⣦⢹⡆⢰⠇⠸⢁⣿⠟
⠀⠀⠀⠀⠀⠀⢻⠟⠋⠯⠉⠞⣿⣿⡿⡏⠁⠀⠀⠈⠉⠁⡧⢸⣿⣀⡈⢤⣓⠀⠟⠈⠀⠈⠁⠁⠈⠈⠀⡇⠊⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠠⡙⠀⠀⠀⠀⠀⣤⠄⡇⠈⣿⢿⣤⡥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡷⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠸⡇⢉⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢾⡄



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⡉⢛⣤⡽⠭⣍⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣳⠘⢋⢶⣶⣶⡆⠀⠹⢯⠁⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⣻⠀⠘⠘⠛⠋⠀⠀⠀⢣⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⣉⣒⣀⣤⣴⡆⠀⠀⣰⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡙⢦⣤⠶⠋⠀⣠⢾⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⢴⡞⠁⢸⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠔⠆⠳⠶⠍⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠐⣶⣾⠇⠀⢈⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠘⠯⣁⡀⠊⠀⠀⠀⣀⣀⡽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠄⣠⠞⣿⠏⠀⣠⡟⢹⡄⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠸⡋⠀⡠⠋⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⣠⢊⢴⠏⣸⣿⣤⣾⠟⠀⡿⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠈⠑⢄⡀⡠⠞⠁⠀⡔⠁⢀⣿⠀⣿⣿⣿⠏⣤⠾⣟⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠙⠆⠀⠀⠀⡆⠀⢸⡇⢰⣿⣿⠏⡼⠡⠀⢸⡦⠀⠳⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠖⢃⢰⣟⡇⢸⣿⠏⣸⠇⠀⠀⣸⠁⠀⣰⠻⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠒⠉⠀⠀⠘⡛⠿⠃⢸⡟⠠⡿⡄⢀⣰⠏⠀⡴⠃⠀⠘⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡁⠀⠈⠁⠙⠋⢀⡜⠁⠀⠀⠀⡨⠒⠛⠁⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⢀⠀⠀⠀⠀⢠⠎⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠉⠀⠀⠀⡰⡇⢀⡴⠛⡁⠀⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠦⠁⠀⠀⠀⠀⡘⠉⠣⣀⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢃⢰⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡼⢇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣄⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢷⡶⢶⣶⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣣⠔⠊⠉⡴⠟⠛⠉⠉⠙⠓⣒⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡞⡽⠛⠛⠳⠶⠶⠶⠤⠤⠤⠤⠤⠤⢤⣤⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠏⠀⠀⣀⣤⡀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠙⢦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣮⣤⠴⠿⠯⣭⣅⡀⠀⠀⢀⣨⣭⠽⠿⠶⣤⣌⣇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠐⠂⠀⠀⣿⠶⠶⣾⠀⠀⠐⠂⠀⠀⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠱⣿⡄⠀⠠⣿⣧⢄⡟⠀⠀⢹⡀⣾⣯⡄⠀⢀⡏⡴⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢏⠙⠶⠶⠿⠷⠟⠀⠀⠀⠀⠙⠾⠿⠶⠶⠛⢀⠇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠼⡄⠀⠀⠁⠈⠀⠠⣀⣀⡠⠀⠀⠀⠀⠀⠀⣸⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡶⠲⢤⡤⠤⢤⠴⠖⢶⢫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡹⢇⡀⣄⢠⠫⠀⡰⢠⢼⢏⠟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠇⠐⠀⠘⡁⠄⡩⠁⣨⠆⠈⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⣤⠎⠀⠀⠀⠁⡀⠡⠊⢀⣁⠀⣄⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣬⠟⠀⠀⠀⠀⠀⡏⠀⠀⡏⠉⢹⠘⢦⡤⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠔⢙⠃⠀⠀⠀⠀⠀⡏⠀⠀⠙⠛⠁⠀⢛⠠⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠸⡀⠈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡌⠀⠀⢠⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠉⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣄⣀⡀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⢀⣀⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⢍⢙⣒⡲⡿⠚⢳⡚⣛⡉⠩⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠀⣀⡧⠀⠸⣀⠀⠀⠀⠀⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠒⠉⠁⠀⠀⠀⠀⠉⠓⠲⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⠛⠛⠛⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠤⠤⠤⠤⠴⠆⠀⠀⠠⠤⠤⠄⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠤⡘⠛⢀⡀⠀⠀⠀⠘⢛⣛⣛⣄⠀⠰⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡀⠀⠀⠠⣶⡆⠀⠴⠒⠆⠀⠈⠿⠇⠀⠀⣀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠿⠁⠀⢀⣀⣉⠀⠀⠀⠀⠈⠀⠄⠤⠠⠄⠀⠉⠓⠭⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠦⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠰⢆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⣀⡀⠤⠤⠀⠀⠀⢦⣤⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⢛⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠉⠁⠀⠂⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⠛⢶⡦⣤⡤⠶⠟⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣫⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡴⠃⠀⡟⢳⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠈⠇⠀⠀⢹⡄⠙⠢⢀⣀⣀⣄⠀⠈⠀⠇⠀⠀⢸⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠰⢄⡀⠀⠷⠀⠀⡄⠀⢀⡼⢇⠀⡞⠀⠀⠀⠀⣴⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠋⠀⠀⠀⢰⠀⠠⠊⠀⠀⠘⣄⡇⠸⣤⡜⠁⢸⡞⠁⠀⠀⠒⠀⣽⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠀⠀⠀⠹⡀⣀⠀⢀⠀⡸⠀⠀⠀⠀⠠⠀⠸⠀⠀⠀⠀⠀⠈⢻⣦⣀
⠀⠀⠀⠊⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⢢⡀⠀⠀⠀⢳⡏⠀⠸⣤⠃⠀⠀⠀⢀⣤⡀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠙⡄⠀⠀⠈⣧⠀⢰⡏⠀⠀⠀⠰⠛⠀⠀⠀⠑⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⢆⠀⠀⢹⡀⡜⠀⢀⠐⠁⢠⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢶⡄⠀⠀⠀⠱⡀⠈⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⢸⠃
⠀⣸⠇⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⣷⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢲
⢰⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠄⠀⠀⠈⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢾
⢸⡇⠀⠀⠀⠀⠀⢿⠆⠶⠦⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡠⢦⣀⣀⠼⣇⠀⢀⣀⠀⠀⠀⠀⣼⡶⠃⠀⠀⠀⠀⠈
⠸⠃⠀⠀⠀⠀⣀⣸⡆⠀⠀⠀⠀⠊⡘⠛⠲⢤⣀⠀⠀⠀⠀⣼⣀⣀⣀⣤⣤⡭⣍⡀⢀⠠⠥⣿⣤⣀⣀⡀⢀⡾⠁
⡄⠀⠀⠀⡴⠋⣩⠟⠛⠛⠛⠛⠛⠒⠓⠒⠒⠚⣛⠻⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⠀⢉⣹⠾⠇⠠
⡧⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⣠⡤⠶⠞⠛⠛⠛⠓⠶⢄
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠙⠦⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠛⠛⢛⠉⠉⠓⠲⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠉⠉⠛⠛⠉⢻⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠷⠶⠶⢶⣦⣤⣤⣤⣤⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶
⣿⣛⣛⣛⣛⣙⣛⣃⣜⣉⣻⣋⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣯⣭⣭⣭⣽⣿⣯⣭⣭⣭⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣷⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠀⣴⣄⡀⠄⠀⠀⠄⣀⣶⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢻⠁⠸⠀⠛⠁⡘⢉⠹⠀⠙⠁⡘⠈⢹⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⡀⠀⠈⠀⠈⢀⡀⢀⠈⠀⠀⠀⠀⣼⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠉⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣭⠁⠀⠀⠀⠀⠀⠀⠉⡽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢈⣀⣿⣀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠇⢻⡇⠐⠠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢰⣾⡿⠛⡛⠻⣿⣧⠀⠀⠀⠀⠀⣠⡿⠀⢸⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣾⡏⠀⠀⠀⠀⢸⣿⣷⣄⣀⣀⣴⣿⠃⠀⣿⠃⠀⠀⡆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⢰⡏⠀⠀⠀⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⡀⠀⠁⠀⡾⡟⠸⣿⣿⣿⡏⠀⢀⣾⠥⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢡⠁⠀⠀⠸⢀⠀⠀⠹⣿⡟⠀⢪⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡄⠀⡈⠈⠀⢀⠀⠈⢀⠀⠣⠂⠨⠂⠀⠀⠹⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠐⠂

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

⠀⠀⠀⠀⠀⠤⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣨⣤⠤⠤⠿⢷⡤⠤⠤⣤⡄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡾⠁⠀⠀⡄⠒⡌⠻⠀⠀⠀⠀⠀⣉⣦⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢶⡶⠛⢰⣶⠷⠀⠀⠀⠀⠀⠀⠙⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠿⠂⠀⢀⡘⠺⠛⠂⠀⠀⠀⢀⡀⠀⣶⣴⠟⠁
⠀⠀⠀⠀⠀⢰⣟⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⣤⣴⠟⠋⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⡄⠀⠠⠄⠒⢊⣁⣀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⣀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⢸⣇⠀⠀⡿⠆⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣄⠁⢠⣍⣀⠴⠷⠄⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠡⠴⠦⠴⠂⠀⠀⣀⣤⣾⣆⡀
⠀⠀⢘⡉⠻⢟⣋⣁⣠⢤⡴⠞⢛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⣀⣀⣀⣠⣤⡶⠾⠛⠉⢠⠇⠈⠙⠳⢦⣄⡀
⠀⣀⣈⠱⣦⡀⠉⣭⡁⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⢯⡉⠛⠋⠉⠉⠁⠀⠀⢀⡴⠋⠀⠀⣀⠀⠀⠉⠛⠳⢦⣄⣀
⢿⣁⠀⠉⠛⠻⢦⠈⡇⣠⢰⡀⠸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⠂⠠⠠⠤⠤⠄⠚⠁⠀⠀⠀⠀⠈⢿⡷⢦⣄⣀⠀⠈⠉⠙⠛⠳⠶⠶
⠀⠉⠙⠛⠛⠲⣆⠀⡇⢻⢸⡁⠀⣦⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⠉⠛⠛⠲⠶⠶⣶⠆⣰
⠀⠀⠀⠀⠀⠀⠘⣇⠃⠀⢸⡁⠀⢸⡶⣦⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢠⡾⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣦⣥⣴⣇⢀⡿⠀⢹⡆⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣰⠋⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣤⠄⠤⣶⡘⢷⡀⠀⠹⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⡾⠃⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢸⡇⠈⢳⡄⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠙⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣄⠀⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢻⠀⢠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⢷⠋⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠙⢙⠟⠛⠛⠛⠿⠿⢿⡾⠗⠾⢿⡶⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡀⠀⣟⠀⠀⠀⠀⠀⠀⡜⠁⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠈⢳⡄⠀⠀⠀⠀⠹⣆⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⡀⠀⠀⠀⠀⠈⢦⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠤⠤⠤⢤⣤⣀⣀⡠⢤⡴⠶⠚⠓⠰⠖⠻⡄⠀⠀⠀⢀⣴⠛⠓⠛⠛⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠁⠀⠀⠀⠀⠖⠘⢁⣠⢶⡄⠀⣿⣀⠴⠞⠋⠱⠀⢀⣶⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠶⠶⣶⡶⠿⠿⠧⠜⠛⠛⠻⠀⠀⠘⠀⢀⣴⠟⠹⠷⠶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⢀⣀⣀⣀⣠⣧⡠⠶⠚⠋
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⢀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⢼⡦⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣀⠲⡗⠂⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠈⢁⣶⣶⠀⠀⣿⣿⣟⡇⠀⠀⠀⢘⣿⣟⠀⠀⠀⠀⠀⠀⠙⠳⡀⠀⢸⠀⠈⠁⠀⡇⠀⠀⢠⣞⠛⡛⡆
⠀⠀⣼⣇⣼⡇⠀⣿⣿⣿⡇⠀⠀⠀⠻⢻⠻⠀⠀⢀⠀⠀⣀⠤⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⠀⠈⠁⠁⠀⠁
⠀⠀⠁⠀⢁⠙⠀⣿⣿⣯⡇⠀⠀⠀⣠⣬⣤⡀⠀⠀⠰⡊⠀⢒⠋⢀⠀⢸⣀⣀⣀⣀⡇⠀⠀⠀⠈⠾
⠀⠀⠀⣠⡄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠈⠀⠐⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢹⡇⠀⠀⣴⠶⢶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠈⠿⠿⠁⠀⣿⢰⢂⠁⡌⠃⣶⣶⢰⠁⡎⡇⢢⣿⡇⣶⡇⣿⢸⠐⣸⠁⢻⠐⢸⡆⢼⣿⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣾⣆⣱⣧⣩⣿⣸⣦⣱⣇⣆⣿⣧⣩⣇⣋⣸⣠⣧⣴⣸⣀⣌⣧⣸⣿⠀⢸⣏⡏
⣀⣦⡀⠠⠄⠀⠀⠈⠉⠉⠉⠉⣉⠉⠉⠉⠉⡉⠉⠉⡉⢉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣸⠗⣇
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠙⠈⠀⠉⠁⠑⠁⠉⠁⠈⠁⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾
⠀⣠⣶⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡤⠀⠀⣀⣠⣀⣠⣄⣀⠈
⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⢻⡻⣿⣿⡇
⠀⠈⠻⣿⣿⠟⠁⢀⣶⣀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠾⠴⠶⠼⠿⠿⠿⣿⠗⠀⠀⢸⣿⣿⣽⣵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠑⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠼⠁⠰⠊⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡝⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⡴⠒⠂⢀⡜⠛⣦⡀⠀⠀⠀⠰⠂⠅⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣆⠇⢴⡧⠎⠰⣿⣿⠉⠀⣀⣤⠶⠖⠺⠟⡛⠛⣦⠀⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣟⣲⡆⠿⠁⠤⠝⠉⠗⠋⠁⠀⠀⠀⠀⠀⠽⢂⡿⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠓⠂⠀⠀⠚⢻⡟⠲⠄⠀⠀⠲⣶⢶⡏⠀⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⡟⠈⡅⡀⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣠⣴⠾⣿⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⡾⠑⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⡀⠀⠛⠚⠻⣤⠴⠊⠀⠀⠀⢠⡞⠋⠛⡖⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢹⢷⡀⠀⠀⡀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣸⠁⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢸⡆⠙⢦⣬⣄⣀⣀⣤⠶⢻⠏⠀⠀⠈⠛⢛⡶⠃⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⡽⢛⠣⡀⡼⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢷⡟⠀⠀⠮⠀⢸⠀⢹⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⢰⠺⠘⠀⠀⢠⣏⡀⠀⠀⠀⡀⠈⠄⡏⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⣨⢸⢀⠀⠀⠀⠈⠙⠶⣄⠀⠡⠀⣼⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠀⠈⠉⠉⠉⠉⠙⡄⠀⠈⠳⣄⢃⡇⣰⠃⠀⠀⠀⠀⢀⣠⠶⠛⠳⣸⡃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠈⠉⠉⠉⠁⢰⡇⠀⠀⠀⠘⣎⣿⣥⡄⠀⢀⣠⠶⠋⠁⠀⠀⢀⠀⠑⠄⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⢷⡤⠴⣄⣀⣤⡤⠾⠶⠒⠚⠛⢹⠋⠀⢰⠋⠉⠁⠀⠀⠀⠀⠀⢠⣄⠉⠲⢄⠐⢆⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠁⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⠳⢤⣀⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣧⣀⣀⣹⠂⠒⠒⢚⣿⠁⢀⡄⠠⡀⠠⡄⠙⡏⠉⡟
⠀⠤⠤⢤⣤⣤⢤⣏⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠶⠾⠛⠋⠩⠠⠤⠤⠬⠤⠤⡄⠈⢀⣼⠀⢘⡇⢰⡇⠀⡇⢀⡷⠚⠲⠒⠶⠐⠶⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠓⠚⠓⠚⠂⠞⠓⠚⠁⠀⠀⠀⢠⡤⡔⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⠒⠒⠒⠒⠒⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢼⣤⣌⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠰⣆⡇⠀⠀⠈⢧⠀⠉⠙⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠡⡄⠤⢀⠀⠀⠀⠀⠀⠀⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠸⡓⠊⠁⠀⠀⢱⡄⠀⠀⠀⠀⠐⡌⢧⠀⠀⠀⠀⠀⢀⡠⠄⠙⢧⡀⠀⠀⠀⢠⡎⠉⠉⠁⠂⢄⡀⠙⢷⣄⠀⠀⠀⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⣀⠀⠥⠐⠁⠀⠀⠀⠀⠀⠘⡌⢧⠀⠀⠀⣊⡥⠶⠛⠁⠀⠙⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠲⣄⡉⠛⠛⠋⠉⠉⠙⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠰⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢣⠀⠈⠁⢀⣀⣠⡤⠶⠶⠟⠃⠀⠀⠻⣤⣬⡴⣈⣑⡄⠀⠈⠻⢶⣄⣀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠲⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠠⡀⣹⢱⡀⠀⠀⠀⠈⠉⠛⠛⠿⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣂⣤⣤⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠿⠟⠻⠿⢿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢌⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠤⣿⡗⣶⡶⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⡿⠋⠉⠙⢛⣿⣿⡿⠁⠛⠶⣤⠔⠀⠀⢠⣟⢦⠠⠤⣶⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣧⣼⣿⡇
⠀⢸⣿⣿⣿⠁⠀⠀⠀⠘⠿⣿⣧⡡⠤⠄⠀⠀⠀⠀⠀⠻⠐⠀⣸⠏⠀⠀⠀⢀⡁⠀⠀⣨⣿⣿⣿⠏⢀⠈⠁
⠀⢸⣿⠟⣇⡄⠄⠀⠀⢠⣀⠈⢛⠛⠀⡀⠀⣀⠄⠀⠠⠆⠻⠋⠙⠂⠀⠀⠀⠨⠇⠀⠄⢀⠈⢥⣿⠚⠿⢻⡄
⠀⢸⠁⠙⠞⠛⠨⣢⠄⢠⠟⠛⠻⠚⠷⠿⠶⠋⠀⠀⣽⠋⠀⢀⡀⠀⣠⠀⠀⠀⣷⡀⠀⠀⣧⢸⡇⠀⠔⢛⡇
⠀⢸⢇⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢩⣆⠻⣾⣏⠁⢴⣿⠀⠈⠀⢼⡇⠘⠀⢹⠀⠛⠀⡀⢸⡇
⠀⢸⠀⠓⠘⠛⠦⠠⣶⣄⡀⠀⠀⢰⣄⠀⡀⠀⠀⠀⢫⡁⡈⠀⡛⠀⠁⣴⢀⡀⠸⠇⠰⠀⣸⠠⠴⡷⣬⣼⡇
⠀⢸⣧⡀⠀⢠⠀⠀⠀⠈⠉⠉⠉⠈⠙⠓⠙⠓⠀⠂⠀⠹⢿⣿⣦⡄⣀⣏⠙⠁⢹⡏⠭⠠⢽⡍⠘⠀⢺⣿⡇
⠀⠸⣿⠷⠼⢿⠿⡶⠷⠷⠄⠶⠶⠄⠀⠦⠰⠄⠠⠠⠄⠶⠦⠈⠙⠿⠏⠻⠄⠀⠸⠤⠟⠡⠤⠿⠃⠀⠉⠹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠛⠋⢻⣿⣷⠀⠀⠀⠀⠁⠀⢤⠄⠀⠉⠀⠀⠀⠀⠀⡿⠛⠉⠙⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⣠⣶⣶⣶⣶⣶⣾⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⣰⣿⡿⠛⠋⠁⠹⣿⣿⡆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣷⡄⢠⡿⠋⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀⠀⠸⣿⡏⠉⠉⣹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡕⠀⠐⡌⣻⣿⡇⢸⣿⣶⡀⠀⠀⠀⠀⢠⣶⣿⠀⠀⠀⠀⢙⡿⠶⠾⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠀⢸⣦⣼⠁⠸⣿⡃⠀⠻⣿⣷⣄⠀⢀⣠⣿⣿⠟⠀⠀⠈⢾⠉⠑⠀⠀⠊⠙⢧⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠃⢀⡠⠈⠛⢹⠄⢰⠏⠻⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⠀⠄⠌⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⡆⠀⠀⣁⡀⢘⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠐⠀⠀⠀⠸⠗⠀⠀⠐⠐⡇⠀⠀⢻⠃⢸⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣶⣶⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠒⠤⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⡦⠤⠤⠤⠤⠤⠤⠼⠀⢘⡰⠂⠀⠀⠀⡀⣀⠀⠀⠀⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠰⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠘⠀⠀⠈⠁⠉⠁⠀⠀⠃⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⢱⠀⠀⠘⠀⠀⠀⠀⠂⠀⡇⠰⠀⠘⠀⠀⠀⠀⠈⠀⠀⠐⠀⠐⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠛⠒⠒⠒⠒⠁⠘⠒⠒⠒⠒⠃⠙⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠃


⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⠈⢧⣀⣴⣊⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠏⠉⠯⣉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⢤⡤⠀⠹⢄⡉⡇
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠶⠌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⣖⠁⠀⢀⣶⢏⠷⡄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠠⡰⠖⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣿⠔⠦⢤⣶⡿⠛⠁⡰⠉⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⢇⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⢶⠋⡇⠀⠸⡇⢀⣾⠛⠒⠒⠉⡠⠀⢀⠤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⡀⠀⡾⣀⣀⣠⠶⠤⠚⠹⡼⢸⠇⠀⠀⣿⣼⠃⠀⠀⠀⡔⠠⣞⣡⡴⡶⡶⣿⡆
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢹⠁⠈⠉⠀⠘⢉⣁⣀⣀⣀⣀⣙⡏⠀⠀⢰⢿⡿⠂⠀⠀⡐⡴⢰⠋⢀⠀⠀⢀⢀⡿
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⠛⠲⢦⣀⣀⣤⠴⠶⠬⣭⣉⢻⡇⢀⣰⢏⡾⠃⠀⠀⠌⡜⢠⡏⠔⢁⡠⠔⠉⣼⡇
⠀⠀⢠⡏⠀⠀⠀⢷⠀⠀⢸⣦⣤⢾⡍⣉⡉⠑⣞⠛⠉⠉⢻⠛⠿⠟⡻⠁⠀⠀⢀⠞⡴⠉⠁⠉⠀⠀⢀⣼⢻⡇
⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⢸⡏⠀⠈⠻⣶⣄⡀⠈⠒⠲⢤⣿⣀⣀⣰⠁⣀⣀⣰⠧⣼⣅⡀⠀⠀⢀⡴⣿⡧⣾⣀⡀
⠀⢠⠇⠀⠀⠀⠀⢸⡄⠀⠈⡇⠀⠀⠀⠀⠀⠙⠦⠤⢼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠀⠰⢋⣾⠃⣠⠇⠈⠉⠛⣦
⠀⠸⡧⠄⠀⠭⣤⠰⢇⠐⠂⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠉⣠⡾⠁⡼⠁⠀⠀⠀⢰⠇
⠀⢸⠃⠀⢒⠒⠛⣏⠈⠳⣄⠀⠈⢦⡀⠀⠀⣀⣀⡤⠾⣁⠀⢀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⡛⠋⢠⣦⣧⣄⣀⠀⢀⡞
⠀⢸⠈⠉⠉⠀⣀⠈⣆⢀⣨⠷⢦⣀⠙⠶⢋⡉⠁⠀⠠⢌⣑⡪⣭⠽⢒⣒⣒⠲⠄⠐⠊⠁⠀⣠⠎⠈⡇⠀⣹⠛⠛⠁
⠀⠀⠀⠀⠀⠉⣉⣀⣉⣐⡁⠀⠀⠈⠑⠲⠤⣼⡷⢤⠀⠀⠀⠀⣀⣀⡀⠀⠠⠤⠤⠄⢀⣀⡘⠁⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢦⣤⣄⣀⣀⢀⠀⠀⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⠀⠀⢀⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡶⠚⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀⠀⢀⣾⡁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠾⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⢀⡠⠊⠀⢀⣴⣿⣿⣿⣿⡿⠟⣋⠡⠤⠒⠈⠁
⠀⠀⢸⡇⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠈⠀⢀⣴⣿⣿⡿⠛⠍⠑⠈⠁
⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠁⡀
⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⣀⣴⡾⢿⣿⠟⠁⠀⠀⠀⡀⠀⠄
⠀⠀⠸⢃⠀⠀⠀⣿⣆⣠⡾⠛⠉
⠀⠀⠀⣿⠀⠀⢀⡟⠉⢹⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⣿⠀⢀⡾⠁⠀⣾⠟⠋⠡⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⢟⣠⡞⢁⣴⠟⠁⣀⠀⠀⠉⠐⠒⠒⠀⠤⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣤⠴⠛⠉⠴⡿⢏⣴⡟⠁⣤⡌⠉⠀⠒⠶⠦⢤⣤⣄⠀⣀⠀⠀⠀⠀⠐⠒⠒⠂⠤⠤⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠹⠈⠃⠀⢀⠀⣾⣿⠅⠺⠋⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢍⠀⢠⠀⠀⠚⠲⠶⠶⠤⣤⣤⣄⣀⣀⣀⠉⣉⣴⡶⣢⣾⡿
⠀⠐⢾⡟⠋⠀⣢⣬⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠃⠸⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣼⣿⣿⡇
⠀⠀⢸⡇⠀⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡧⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⢸⡇⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⢸⠃⠀⠀⣿⣿⡃⠀⠀⠀⠀⠁⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⢱⣬⣿⠄⠀⠀⢀⡀⠀⠠⠀⠀⢠⡀⠀⠀⢸⣿⣿⠁
⠀⢀⡌⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠐⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣸⣿⣷⡦⣀⢧⢀⠈⠁⠀⠈⣿⣿⡟⠀⠁
⠀⠘⠃⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⠚⠉⠟⠋⠃⣏⠀⠈⢰⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⣾⣲⡙⢀⣶⣀⣠⣤⡼⠀⠀⢸⣿⣿⠀⢀⣾
⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢼⠿⢿⠟⣿⠻⠿⣿⡇⠃⠀⠀⣾⣿⠏⢀⣾⣿
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣸⢿⣦⠀⠄⠀⠀⠀⡀⣤⠀⠇⢠⡄⠀⠈⠛⠋⣥⣤⡶⠖⠃⠀⠀⠀⣿⡟⢀⣾⣿⣿
⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⢰⡴⢇⠈⠀⠀⣶⣀⡶⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡸⠟⢃⣼⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠰⣿⢦⣶⠷⡦⢴⣾⣿⢀⣠⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠆⣾⣿⣿⡿⢿
⠀⠀⠀⠀⠀⣿⡗⠀⠀⢀⡞⠉⠘⠛⣀⡀⣼⣾⣇⣀⡉⣸⣿⣿⣿⣶⡖⠂⠠⣤⣤⣀⣀⠀⠀⠀⠀⡸⠁⣼⣿⠟⠉⠀⣛
⠀⠀⠀⠀⠠⠟⠁⠀⠀⣾⠀⣤⠀⠈⠉⠁⢨⣸⠁⠈⠉⠀⠉⠉⠉⠙⠀⠀⠐⠿⠿⠃⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠃⠀⠐⠺⠞⠋⣁⠾⢛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⢠⠾⠉⢫⣄⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⣄⠶⠌⠡⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢻⣆⠀⡤⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⢶⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⠀⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⠿⣿⣿⠿⠋⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣮⠻⣄⡀⠀⠀⢀⣰⠟⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠈⠛⢳⡞⠛⠁⣰⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠻⣿⡆⠀⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠘⢂⣿⣿⡄⢸⡇⢠⣿⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢹⣿⣿⣷⣸⣇⣾⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡛⠿⠟⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⢦⡛⠘⢇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⠀⠈⢢⢹⡄⠈⠁⠸⠒⠒⢒⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⠢⠴⠋⣼⢋⠓⠒⠒⠶⢲⠦⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢛⠟⠷⠶⠚⠙⠛⣷⡤⠤⠤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠉⠙⠳⣄⣰⠟⢩⣵⣤⠊⣩⢵⡼⠂⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⠳⣬⡼⠋⠱⣜⣿⡾⠅⠀⠀⠀⠼⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣤⠀⠀⠀⠀⠀⢀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⣠⠀⠀⠀⠟⠹⣧⠀⠀⠀⠀⠀⠸⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⠾⠛⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠐⢷⣄⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢸⠇
⠀⢀⣀⣀⣤⠤⠴⠖⠒⠛⠛⠋⢉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡇⠀⠀⠀⠈⠉⠉⣡⡴⠟⠀⠀⠀⠀⠀⢀⡿
⢿⠉⠉⠁⠀⢀⠤⠄⠤⢄⡀⠀⢨⢸⡇⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠶⢦⡀
⢸⡀⠀⠀⠀⠁⠀⠀⠀⢀⡈⢆⠀⢸⡇⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢸⠈⠙⡷⣦⣄⣀⣀⣀⣀⣀⣠⣴⠞⠋⠀⠀⠀⢸⠹⣆
⠈⡇⠀⠀⠀⣎⢁⠄⡸⡁⣰⢸⠀⢈⡇⠀⠀⠀⠀⣠⠎⡞⠀⠠⡔⠋⠀⢀⡿⠩⡈⣩⠟⣯⠉⠉⠸⠧⢤⣤⠀⠀⠀⢸⡄⠈⢷⡄
⠀⣧⠀⠀⠀⢄⠀⠀⠑⠀⠠⠃⠀⠀⡇⠀⠀⢀⡜⢁⣼⠁⠀⠀⠘⣆⠀⢸⡇⠀⣿⠁⠀⢸⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⠙⢦⡀⠙⢦⣄
⠀⢻⠀⠀⠀⠀⢧⣤⣤⡤⠆⠀⠀⠀⣿⠀⢀⡞⢀⡞⡌⠀⠀⠀⠀⠘⡄⢸⡇⣸⠘⡇⠀⣾⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⡀⠙⠳⢦⣄
⠀⢸⡆⠀⠀⠀⠀⢀⣤⣖⠂⠀⠀⠀⢹⠖⠋⢁⠞⢠⠀⠀⠀⠀⠀⠀⠰⣼⢡⡏⠀⣿⠀⣿⢠⠟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠴⠚⠛⢀⣀⡬
⠀⠀⠇⠀⠀⠀⡤⡿⠈⡯⠱⡔⢦⠀⢸⡆⠒⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⣸⠁⠀⢹⡀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣏⠁⢀⡴⠛⠁
⠀⠀⢸⣀⣀⣸⡄⢿⠀⡇⠀⡇⣸⠀⠘⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠳⠟
⠀⠀⠀⠈⠣⠐⠈⠈⠛⠉⠚⠉⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⢁⣀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢰⡧⢷⡄⠀⣠⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠞⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠶⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠦⠤⢤⣤⣤⣼⠀⠝⠳⠶⢴⠄⢼⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠀⠀⠀⣼⠀⢨⡏⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⡇⠀⠀⠀⢻⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢏⠀⢧⠀⠀⠀⠘⡆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠓⣦⣄⣀⡀⡀⣸⣀⣸⣆⢀⣀⣀⣿⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠴⣏⠉⠙⠛⠓⠒⠒⠚⠛⠉⠉⠁⠀⣠⡍⠉⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣤⣤⣤⣤⡤⠴⠖⠋⠉⠳⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠞⠛⠛⠛⠛⠛⠛⠷⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣶⣄⡀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣯⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⣶⢦⣤⣨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠘⣦⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡟⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠻⣇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⡿⠀⠀⠘⠋⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠛⠉⠉⠙⠃⠀⠀⠀⠀⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⣿⠀⡷⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⣿⠀⣸⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣸⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠸⣧⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠛⠋⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠶⠾⣋⣼⣿⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣭⣭⣭⣤⣶⣾⣋⣸⡇⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠉⠷⣤⣤⡟⠉⣁⣠⡿⠋⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄⠀⠀⠀⠀⠀⢠⡔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣭⣽⣟⠀⠀⠀⠀⠀⢈⣿⣭⣭⠛⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⣶⣿⡿⠋⢼⣿⡉⠈⠻⣦⡀⠀⠀⣠⡾⠋⠈⣹⣿⠀⠈⠻⣿⣶⣤⣠⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣤⠞⠛⠛⣿⠋⠉⠉⠉⠁⢀⣼⣿⠁⠀⠘⣿⢷⡀⠀⠈⠻⣤⡼⠋⠀⠀⣰⣿⡟⠀⠀⢠⡟⢿⣯⡈⠉⠉⠉⢻⠟⠛⠛⠳⣤⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⢿⡘⢷⡀⣠⡾⠛⠳⣦⡀⣼⠏⣸⠇⠀⠀⣾⠇⢸⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⢸⣧⠀⠀⢸⡇⢨⡿⠋⠀⠀⠀⠈⠻⣏⢰⡏⠀⠀⢰⡏⠀⣸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠇⠈⢿⡀⠀⠀⢻⡏⠻⣤⣀⣀⣀⣠⡾⠋⣿⠁⠀⠀⣸⠇⠀⣿⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣆⠀⢸⡇⠀⠀⠘⣧⠀⣼⠋⠉⠙⢻⡄⢸⠟⠀⠀⢰⡿⠀⢰⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠉⢿⣦⣼⣿⠷⡶⣦⣿⣴⡿⠀⠀⠀⠸⣧⣿⠀⢶⣶⠾⠃⠀⠈⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣶⣿⣛⡿⠷⠶⠶⠛⠛⠛⢿⣛⢯⣿⣿⠁⠀⠀⠀⠀⣿⡇⠀⠀⣿⠇⠀⠀⠀⠙⢿⣷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⢀⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣏⣿⡆⠀⠀⠀⢠⡿⠀⢠⡾⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⣸⠇⣠⡾⠁⢀⣤⡶⠶⠶⣤⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢰⡏⣠⡟⠀⣰⡟⠁⠀⠀⠀⠀⠙⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⣾⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠃⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⠳⣦⣄⣀⣠⣤⠾⠃⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠛⠛⣷⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣤⣴⠟⠉⣳⡄⠀⠀⠀⠀⠀⠸⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠉⠛⠛⠛⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇
⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡆
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡇
⣿⣀⣀⣀⣀⣀⣀⣸⡟⠀⣿⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣸⡇⠀⢸⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠋⠙⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⢋⠀⠀⠀⠀⣀⣤⡶⠿⠿⣿⡷⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣤⠶⠛⠉⣿⢠⣲⡄⠀⣿⠀⠀⠀⠈⠉⠙⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⢻⣄⡉⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠼⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣵⠬⡳⣄⠀⠀⠀⠠⢶⡒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠎⠢⣝⠦⣄⡀⠈⡇⠀⠀⢠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⡀⠀⠈⠑⢬⡙⣶⢿⣄⣀⡀⠀⠉⠉⣹⣟⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢙⣿⠛⠁⠀⠀⠀⠀⠉⢻⡀⠈⠉⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣍⠳⣄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣌⡓⢦⣀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢦⣌⠛⢶⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣤⣄⣀⣈⣙⣿⣿⣤⣤⣤⣤⣤⣤⣴⠾⢿⣦⣀⠀⠀⠀⠀⠀⢀⣤⣾⣇⡜
⠀⠀⠀⠀⠀⢀⣴⠟⣹⡏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⣧⠉⠛⠷⢶⣤⣤⣼⡿⣽⣿⡷
⠀⠀⠀⠀⢠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠉⠻⠿⠟
⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢠⣡⠃
⣠⡤⣾⣿⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢉⡾⢹⠋⣷⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄
⠘⠃⠿⠀⠈⠁⠀⠛⠛⠛⠛⢲⡷⠒⠛⠛⠛⠛⠛⠛⠛⠻⡿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⣶⡞⠙⠓⣦⠀⠀⢀⡼⠿⣶⡞⠛⠓⢲
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣯⣵⣶⣶⣶⣯⣤⣤⣼⣷⣾⣶⣦⣤⣤⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⣠⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠓⠲⠶⠶⠒⠋⠁⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⢉⣀⣼⣇⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣿⠀⠀⠉⠙⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⠟⠉⠉⠉⠻⣦⡀⠈⠳⣄⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⢧⡀⠀⢀⡞⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠹⣤⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠛⠿⠂⠀⠀⠀⠾⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠶⠉⠙⠛⠉⠉⠲⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣀⠀⠀⠀⢁⠀⡐⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠟⠁⠉⠳⣄⡀⠈⠂⠍⠀⣌⣐⣀⡀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⡀⠀⠲⣬⡙⠷⢶⣤⣾⠿⠟⠋⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣉⠀⠀⠀⡈⠻⡀⢀⣀⣤⠤⣤⡞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠴⠀⠟⠀⠀⢾⣿⠀⢰⠘⠏⢀⣀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠚⠅⠀⢠⣀⡀⣬⢥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⢀⣀⣼⠇⠀⠀⡀⠀⠀⠈⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⢀⡼⣦⠀⠀⠀⢻⡀⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⠄⠘⢉⡀⠹⠇⠀⠀⠸⡷⠚⠋
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠙⢀⠈⠳⢦⡀⠀⠀⠀⠀⠀⣠⡶⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠉⠐⢀⣈⠙⠶⢆⣤⡴⠏⣀⣀⡄⢈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣈⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣶⠟⠳⣤⡀
⠠⡞⠋⠉⢉⣄⣨⡟⢁⡴⠎⠉⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⢸⡅⢹⡟⠟⠙⡿⢋⡛⠁⠀⡟⠀⠀⠀⠙⢶⣄
⠀⡈⠙⢓⠀⢠⡏⠀⠸⣦⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠴⠞⠃⠈⠀⠈⣿⠁⣼⠃⠀⣸⠀⠀⠀⢠⠁⠦⣈⠷⣄
⠧⠀⠒⣩⠙⠛⠀⢠⡤⠀⢀⣴⠞⢋⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣾⠃⠈⣦⠏⠀⠀⠉⠁⡰⡦⠈⠈⠁⠀⠀⠈⢡
⠀⢴⠁⠄⠒⠉⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⢀⡜⠁⣼⠃⠀⠀⠀⠀⠀⠈⢆⠀⠀⠸⠀⠀⡟⠀⠀⣠⡴⠊⠁⠀⠸⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢸⡇⠀⠀⠀⢀⠎⠀⣜⠃⠀⠀⠀⠀⠀⡄⠀⠈⠳⡀⠀⡀⣴⢁⡤⠚⠁⠀⠀⠀⠀⠤⠤⢤⣤⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣳⠀⢀⡴⠃⢠⡞⠘⠀⠰⠒⠂⠤⠤⠀⣀⠀⠀⠹⢆⣷⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢹⡴⠛⠁⣠⠋⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠃⣠⠞⠁⠀⠘⠀⠀⠀⠀⠒⠀⠤⠄⣀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡸⠀⠀⢰⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠞⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤⠊⠁⠀⠀⢸⢀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠲⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠉⠉⢛⡿⠛⠿⠶⠶⠾⠿⠶⠾⠿⠿⠟⠛⠛⠛⠻⠋⠉⠻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⠞⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⠶⠿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠁⠀⢀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢰⣆⠀⠉⠛⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠉⠉⠁⠀⠈⠉⠉⠁⠀⢀⣤⡴⠞⣧⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠟⠁⠙⠶⣤⡀⠀⠀⠈⠙⠛⠓⠲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠶⠖⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⣟⢿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⢖⣾⠿⠟⠛⠋⠉⣋⡛⠛⠓⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠋⠉⣐⣤⡴⠋⠀⢈⣦⠖⠛⠛⠛⠺⡗⢶⣶⡦⣄⣀⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣠⠶⡶⣫⠍⡽⣅⡠⣠⡏⢀⡀⠀⠀⠀⠀⠈⣏⠀⣙⠪⡽⣿⢶⠦⣄⢈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣠⠗⠋⠱⠞⠁⠀⠀⠀⠊⠉⣽⠅⠀⠀⠀⠀⠀⠀⡠⢁⠈⠀⠈⠀⠀⠈⢳⡋⠙⠶⣔⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠏⢁⡤⠚⠁⢀⣤⡄⠀⠀⠠⠀⠀⠀⠀⠈⡄⠲⡧⠤⠠⢶⠚⢠⠁⠀⠀⠀⠀⠀⠀⠀⢱⣦⡀⠈⠳⢄⠀⠙⣦
⠀⠀⠀⠀⠀⣠⠾⡑⣤⠋⠑⣦⠖⡋⣸⠶⠀⠀⠀⠀⢀⠀⢀⣦⢁⠶⠃⠀⠀⠂⢰⡈⡰⠂⠀⠀⠀⠀⠀⠈⠶⣃⢙⢦⣴⠋⠱⣆⠌⠳⣄
⠀⠀⠀⠀⡴⠃⢀⡞⠅⢀⡼⠡⠀⢷⡷⢯⠢⣄⠀⢀⢈⢻⡏⠉⡗⠒⠄⢀⠀⠀⠀⠐⡈⢤⡀⠈⠃⢀⡠⠘⡣⣾⡎⠀⠉⢦⡀⠈⢣⡄⠙⣦
⠀⠀⠀⡼⠁⢠⢿⡀⣠⠞⠀⠐⠀⠘⣇⢸⢄⣠⣀⠤⠼⣾⣧⣴⠿⠧⠤⣀⣊⢀⠀⢀⡧⣀⠄⠀⠀⠠⢄⠠⣇⣾⠆⠀⠀⠀⠻⣄⢀⡽⡄⠘⢧
⠀⠀⣼⠅⣰⠏⠀⣼⠛⣇⠀⠀⠀⠀⣿⣽⡞⠉⠁⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⣉⣽⡮⠑⢀⡀⠀⠀⠀⠀⠑⣃⢹⠀⠀⠀⠀⡰⠘⣇⠀⠹⣖⠸⣧
⠀⢰⠃⢀⡏⠀⣰⠇⠒⢊⡲⢄⠄⣞⠢⣍⠻⣶⣄⠀⠀⢸⠀⠀⠀⣀⣤⡶⠟⣋⣡⡴⠞⢋⣹⠀⠀⠀⠀⠀⢩⠟⣆⠀⡰⠚⠑⢒⠸⣆⠀⢹⡀⠘⡆
⢀⣟⡈⣽⢄⣠⡏⠀⠀⢨⠁⠈⣴⠋⠳⣌⠳⢌⡙⢷⣤⣧⣤⠶⠟⣋⣥⠶⠛⢉⣠⠴⠚⠉⢸⡇⠀⠀⠀⢀⡟⠀⠘⣦⠀⠀⠀⡜⠁⢹⣄⠤⣧⠀⢻
⢸⡇⣰⡇⠀⣼⢡⡀⠀⠘⠀⣴⠇⠀⢡⡌⠻⣦⡙⢦⣈⣩⡤⠖⠛⢉⡠⠴⠚⠉⠀⢀⣠⢴⡞⣇⡀⡀⣰⠋⠀⠀⠀⠸⡄⠀⠘⠃⣄⠌⣧⠀⢸⡈⢹
⣾⠀⢸⠁⠀⡟⢠⠉⠒⠒⡋⣼⠀⠀⠀⣾⢣⡌⠙⢦⣹⣁⡠⡴⠚⠉⠈⢀⣠⡶⠎⠥⢼⠸⣇⢸⣪⠞⠁⠀⠀⠀⠀⠀⣇⠑⠚⠚⠁⠄⢻⠀⠘⡗⠐
⣿⠀⢸⣀⣀⡏⠘⡁⡀⠀⠀⡏⠀⠀⠀⠘⡀⣿⣳⣌⡼⣿⡌⣀⡠⠖⠃⢻⢸⠀⣤⠬⠼⠇⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠁⢹⣀⣀⡇
⣿⠀⢼⠀⠈⡧⠈⢰⡁⠐⡀⣧⠀⠀⠀⠀⢳⢈⠓⣿⣿⢹⠉⡇⢣⠤⠚⠹⡄⡇⡀⠀⠀⠂⢻⠀⡆⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⢀⡄⢁⢾⠁⠀⡗
⢹⡂⢸⡆⠀⣗⠉⠚⢓⡚⠠⢹⠀⠀⠀⠀⠈⣇⣄⣏⡙⠏⡇⢰⠀⡠⠔⠋⠁⣼⠠⠤⠤⠔⢸⡀⠇⠀⠀⠀⠀⠀⠀⠀⡏⠌⣓⠚⠻⡋⣾⠀⢰⡇⢐
⢸⡇⠈⣇⠀⣹⡌⠀⠇⠰⠀⢈⣇⠀⠀⠀⠀⢩⡈⠙⣆⢰⢿⠀⠆⠀⠀⠀⢀⢰⠐⠀⠈⠉⠀⡇⢰⠀⠀⠀⠀⠀⠀⣸⠁⠈⠀⣧⠀⣠⣏⠀⣸⢃⣸
⠀⣷⠀⣹⡁⠈⣧⠀⠠⡷⠀⣠⠙⣆⠀⠀⠀⠈⡟⢤⣧⠙⢿⡇⢰⠰⠄⠂⠁⠈⡀⢀⡒⢚⡁⢧⠸⠀⠀⠀⠀⠀⣰⠛⡄⠀⢸⠏⢀⡼⠁⢉⡇⠀⡿
⠀⠘⣧⠘⢧⠀⠘⣇⠒⡠⠚⠁⠁⠘⢆⠀⠀⣀⢼⣢⢩⡦⣸⣷⠈⡄⠇⠀⢀⡇⢳⣆⣀⣀⡡⣼⠀⡆⠀⠀⠀⡴⠃⠈⠈⠓⢜⠒⣹⠃⠀⣞⠀⣸⠃
⠀⠀⠹⡄⠈⢧⢀⡹⣆⠁⠀⡇⠰⠀⠈⠳⣄⠻⣄⠑⢝⢷⠈⡼⡆⢣⠐⡊⠁⠐⠘⠈⠀⠀⣠⠿⢒⣡⠿⣠⠞⠁⢠⠄⢰⠇⠈⣰⣇⠀⡼⠡⣸⠏
⠀⠀⠀⠹⣄⠈⢯⡀⠘⢧⡀⠣⠀⢀⡴⠂⠈⠳⢬⡳⣄⠻⣕⢿⣷⠘⡄⣀⡠⣴⣷⠤⠒⣉⡤⠖⢋⡤⢚⣑⡰⢤⡈⠚⠋⢀⡼⠁⢀⡽⠁⣰⠏
⠀⠀⠀⠀⠙⣦⠀⠳⣄⠀⠻⣭⠉⡏⠀⡂⠄⠀⠀⠍⢛⠷⡌⠳⣿⡆⢳⡿⠟⢋⣡⣴⣚⡭⠴⡚⢹⠈⠁⠠⢐⠀⢱⠉⣥⠏⠀⣠⠏⠀⣵⠋
⠀⠀⠀⠀⠀⠈⢳⣔⠉⢧⡴⠋⠳⢤⡀⢰⢀⠂⣠⠟⢰⡀⠙⢦⡈⠓⣉⣤⠞⠛⢍⠍⠁⠀⢀⡛⠻⡄⠐⡀⡌⢀⡤⠚⠙⣦⣞⠁⣱⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⠘⢳⣄⠀⠙⠳⣏⣊⠑⠀⢸⡧⢼⣵⢹⠟⡫⡤⢤⡅⠘⣄⣦⡧⢼⡆⠀⠎⢑⣻⠞⠋⠀⣠⠞⠁⣀⡿⠋⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣅⠈⠙⠦⣴⠁⠉⠓⠶⢦⣿⣄⠚⠋⠢⡏⠁⠙⢽⠔⠈⠗⣠⣿⡴⠷⠚⠉⢈⣦⠴⡋⠀⣠⠾⠋⠀⠀⠀⠀⠇⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⡙⢳⠦⣄⣀⣸⠉⠉⠙⠓⠛⢻⠛⠛⠛⠋⠉⠉⣆⣀⣤⡴⠚⠋⢀⣤⠼⠛⠁⠀⠀⠀⠀⠀⡠⡿⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣰⡁⠉⠙⢓⠒⠶⠶⠶⠶⠶⡶⠖⠚⠋⠉⣈⣄⣥⠴⠞⠋⠁⠀⠀⠀⠀⡠⠀⡠⠎⠀⠧⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠾⠶⠶⠦⠤⠴⠶⠶⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⠶⢂⣩⢇⣄⣀⠈⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣫⠞⢁⣴⣿⢷⣿⣟⣽⣷⣦⣌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⢏⣴⢀⡾⢫⣾⣿⣿⣿⣿⣿⣯⡆⣈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠄⠀⠀⠻⠿⠿⣿⣿⡿⣿⠞⠋⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⣿⠀⠀⠀⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠃⠈⠁⠀⠀⠀⠰⢶⡶⣍⠛⠀⠀⣴⣶⡶⠶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠿⠟⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠸⣅⠀⢸⣃⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣶⢾⠃⢸⡀⠀⠀⠀⢤⣀⣀⣈⡙⠉⠁⠀⢀⠊
⠀⠤⠴⠖⠒⠛⠋⠉⠉⠁⠀⠀⢠⣾⠟⢹⡇⠈⣇⠀⠳⣄⠀⠀⠀⠈⢉⣉⡙⠛⠀⣠⠃
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣿⡍⠀⠸⣇⠀⠙⣆⠀⠈⠳⣆⡀⠀⠀⠉⠁⢀⣴⢿⡶⢤⣄⡀
⢳⡀⠀⠀⠀⢰⢏⣠⡀⠀⠀⠀⣿⢧⠀⠀⠉⠛⠦⣼⣆⠀⠀⠈⠉⠉⠛⠛⠛⣹⠋⢻⣷⠀⠈⠉⠛⠲⠦⣤⣀⡀
⠈⢷⠀⠀⣰⡿⠋⣽⠁⠀⠀⢀⠿⠸⣆⣀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⢠⡖⣿⠀⠘⣿⡆⠀⠀⠀⣀⡀⠀⠈⠛⡦⢤
⠀⠘⣇⠀⠉⠀⣸⠃⠀⠀⣴⣷⠚⠉⠉⢻⣷⡄⠀⠀⠹⢯⣳⡄⠀⢀⣴⣏⠴⠃⠀⠀⣿⡇⠀⠴⠛⢁⡏⠀⠀⠀⡇⠸⡇
⠀⠀⣿⠀⠀⢰⠏⠀⠀⠀⣿⣇⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠉⢻⣦⡾⢩⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⠁⠀⠀⠀⡇⠀⢿
⠀⠀⢸⡄⢀⡟⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣽⠃⢸⠇⠀⠀⠀⠀⡟⡏⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠸⣇
⠀⠀⠀⣷⡈⠉⠉⠙⡇⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⢃⠀⢸⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠙⢢⡀⠀⢸⠁⠀⠀⢻⡀
⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠞⠀⣼⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢳⠀⡿⠀⣠⠞⠈⡇
⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠈⢿⡄⠀⠀⡿⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⣰⢺⡟⢶⡄⠀⠀⠀⠀⠘⣷⢃⡜⠁⡀⠀⢻⡀
⠀⠀⠀⠀⣧⠀⠀⢸⡇⠀⠀⠀⠀⠈⢻⣄⣸⠃⠀⢠⣤⠀⡟⠱⣄⠀⣿⠀⠀⠀⣷⣾⣇⣠⡇⠀⠀⠀⠀⠀⣿⠏⣠⠞⠁⠀⠈⢷
⠀⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⣴⣶⣄⣠⠜⠛⠒⠚⠛⠉⢰⠇⠀⢸⡆⣿⠀⠀⢀⣼⣷⣦⣟⣀⣠⡤⠴⠶⢾⣿⢊⣥⠞⠃⠀⠀⠘⢧⣀
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠇⢻⠀⠀⠸⡇⠀⠀⠀⢀⡀⠀⠀⠀⣿⡵⠛⠁⠀⠀⣀⠤⠤⣤⠙⢷⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⣷⣤⡀⠀⠀⠀⠀⠀⠀⡟⢠⡴⠋⠀⢸⡇⠀⠀⣧⠈⠉⠉⠉⠉⠉⠁⠸⡟⠁⠀⠀⠀⠈⠁⣠⠞⠁⠀⠀⠻⣄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠢⡙⠦⣀⠀⠀⠀⠀⡇⠠⠬⠝⠂⡘⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢰⠿⢤⣀⠀⠀⢀⣞⡥⢒⡟⢀⡴⠲⣼⣧⣀
⠠⠤⣄⣀⢸⡇⠀⠀⠀⠀⠀⠀⣀⠴⠛⠓⠚⠷⣄⣀⠀⡇⣠⣀⣀⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠻⣟⠓⠀⠈⠁⣰⠋⢀⡾⠀⢁⣄⠀⠙⠳⠤⣀
⠀⠀⠀⠙⠿⣿⣶⣤⣤⡤⠞⠉⠀⠀⠀⣀⠀⠀⠀⠉⠛⢧⣌⣉⠙⠂⣀⣀⡀⠸⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢹⣶⣄⠀⠰⠟⠀⣼⠁⢠⠞⠙⠛⣀⢀⠀⠘⢧
⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠛⠲⠦⣤⣠⠾⠉⢻⣹⢸⡏⠉⠉⠙⠛⠓⠒⠶⠶⠶⠶⠾⠷⠤⣤⣤⣧⣉⣀⣀⡔⣻⠇⡴⠃⠀⠀⡰⠃⠈⣻⠀⢠
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⡀⠀⢀⡍⠛⢦⣤⠿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠇⣼⠓⣄⢀⡼⠁⢀⡼⢁⡜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠉⣛⠻⢶⡴⢃⣀⣙⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠁⠀⢩⡟⠐⢣⠞⢴⠞⠖⠋
⠀⠀⠀⠀⠶⠤⣤⣀⡀⠀⠀⠀⠈⠙⠛⠛⠛⣉⡿⠛⠋⠉⠉⠉⠉⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⣿⡀⣠⣯⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠛⠛⠛⠛⠋⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠙⠳⠦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⣤⣀⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠶⠶⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣤⣤⡤⠤⠤⠤⠴⠶⠒⠒⠒⠚⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣦⣴⡶⠟⠛⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣽⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢿⣿⣿⣧⠀⠀⠀⠀⠀⡎⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⢿⣿⣧⠀⠀⠀⣠⠗⠢⣤⠊⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⢀⡇⠀⠀⣻⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⡐⢿⡗⠛⠉⠙⠤⠴⠋⠙⠛⠡⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢇⢸⡹⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠸⡀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠃⠀⠀⠀⠀⠸⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⡀⠀⠀⠀⠀⢧⠀⠈⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠘⡆⠀⠀⡰⡈⠑⠒⠠⠤⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠤⢼⠙⢦⡀⠀⠀⠸⡀⠀⢐⣥⠀⠀⠀⠀⠀⠀⢠⠒⢲⠉⣄⠔⠁⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠢⢼⡀⠀⠙⠳⣦⣤⣧⠠⠊⡇⠀⠀⠀⠀⠀⠀⡄⢠⣆⠳⢵⡒⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⡀⠉⠐⠒⠀⠤⢬⣏⣷⣥⣀⠀⠀⠀⠀⣠⠇⠈⢸⣦⣤⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠁⠐⠀⠀⠀⣘⠫⡯⣻⣟⢕⢄⠀⡔⠙⣤⣶⠟⢁⠼⠣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢄⠉⠢⣱⠙⢧⠝⠳⠿⠵⠚⠛⢿⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠑⠲⡌⠓⢾⡄⠘⢦⡀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⠑⠤⣀⠀⠀⠀⠀⠀⠛⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⢀⡼⠄⠀⠀⠀⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⠔⠉⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⣲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠓⠒⠒⠒⠒⠒⠀⢐⣿⣉⣀⡠⠊⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⡏⠏⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢹⠉⠈⠒⠂⢱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠭⠭⠶⠶⠤⠤⠀⠀⠀⠀⠀⠬⠤⠤⠤⠴⠶⠭⠭⠭⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢹⣿⣿⣿⣯⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣯⢉⣉⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠾⣟⣡⣔⠻⠟⠀⠀⠀⠀⡀⠋⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡱⡋⠃⠉⠙⠛⠆⠲⠶⠴⠞⠟⢣⣆⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⡟⣛⣳⢶⣄⣈⡰⠞⢿⡭⡉⡂⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡟⠻⠌⠁⡀⢹⠁⠀⢀⣂⣀⡐⠁⠉⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠉⠁⠀⠘⠀⠀⢀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⡀⠀⠹⣾⣦⠖⠀⠳⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡇⡇⠶⠒⠛⠃⠗⠙⠓⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣧⡻⣷⠀⠀⠘⠛⠉⠀⠀⢀⠆⠀⢀⠈⠉⠛⠓⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡶⢬⠳⢄⣀⠀⣀⣀⠔⡁⣸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠉⠙⠋⠉⡹⠿⠿⠿⢿⡇⠨⠙⠆⠀⠉⠉⠁⠈⣀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⣠⠤⢒⡍⠀⠋⠀⢀⢈⡳⠥⡬⡗⠲⠶⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠁⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢳⡀⠀⠀⠀⢀⡤⠋⠀⡰⠋⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢷⠀⠀⠀⢮⡀⠀⠉⠀⡠⠒⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⡇⠀⠀⠸⣇⠒⠒⣀⠀⠠⠊⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠢⠀⠀⠀⠂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠗⠀⠀⠁⠰⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠈⢢⠀⢄⡠⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠘⠉⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢰⠀⡀⠀⠀⠈⠣⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣆⣠⠆⣹⣟⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠑⢉⠒⠤⠀⠐⠦⣤⣀⠀⢄⡀⠘⢿⣶⣿⣿⣀⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣼⣷⣌⠀⠀⠀⠀⢻⠶⣤⣙⠿⢦⣭⣳⢤⣌⠉⠉⠉⠀⠘⠳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⢠⠇⢠⣿⡿⠀⢉⡓⠦⣀⠀⡗⠈⠙⠷⣦⣝⡻⣿⣿⣿⠟⠙⠲⢶⡦⠤⣯⣿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⣾⣿⠡⣴⡟⣿⣦⡌⠹⠷⣦⣀⠀⠀⡽⠻⢇⣸⣿⣖⣛⣛⣛⡛⠾⠿⠿⠞⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⠇⢠⣍⡙⢻⡟⠀⠀⣀⡀⠉⠻⢿⡧⠀⣰⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣉⣙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⠏⠀⢿⣿⢣⡿⠀⠀⠀⣡⣞⣷⣤⣼⠃⣰⣿⣶⣿⣿⣶⣶⣶⣶⣤⣾⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢠⣻⡿⠀⡀⠀⠀⠈⢁⠌⠀⣠⣍⠾⢱⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣽⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⡿⠃⠀⠉⠀⡀⠀⡼⠀⢴⣿⣿⢳⡾⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⣿⠃⠀⠀⠀⣰⡇⣰⠃⠀⠀⠉⠳⠟⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣾⡏⠀⠰⣄⣰⢟⣿⠁⠀⠀⠀⠀⡀⠀⢠⣿⣿⠙⠛⣻⣿⠿⢻⣿⢏⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠁⢠⠁⠀⠀⠀⢀⡴⠀⢠⣿⣿⣿⣿⣧⣿⣿⣿⣿⡏⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⡠⢀⠆⠀⠀⢀⠀⣼⢧⢡⣿⣿⣿⣿⢿⣾⣿⣿⣿⣟⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣿⠏⠀⠀⠀⣰⠃⡘⠀⠀⠀⠀⠘⠛⢪⣿⣿⣿⣿⢿⣾⣿⣿⣽⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣿⡟⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢠⡀⢀⣾⣿⣿⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣾⡿⠁⠀⠀⢣⡄⠰⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠴⠿⣇⡀⠀⠀⣼⡿⠀⠀⠀⠳⣤⣾⠇⣼⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠈⢳⣦⡼⢣⠇⠀⠀⠀⢀⠈⡏⣰⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠙⢦⡌⠀⠀⠀⠀⣿⡾⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠙⢤⡀⡀⢸⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠛⣮⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣿⣼⣿⣿⡿⠿⢟⣛⣭⣭⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣈⣉⣤⣶⣾⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠠⠀⢀⣘⠆⠀⠈⠀⠄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠃⡄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠂⠢⣀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠠⢠
⠀⠀⠀⠀⠀⢠⢀⠀⠐⠂⠀⠄⠀⠀⠀⠀⠀⠋⠉⠑⠛⠂⠄
⠀⠀⠀⠀⠀⠈⠰⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠘⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣄⣠⣆⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠐⠉⡩⠿⢷⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣤⣤⣤⣤⣀⣤⣤⣄⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣨⣂⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣉⡁⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣌⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⡄⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣸⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⠟⠓⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢸⡇⠐⠆⠀⠀⣶⠀⠀⠀⣾⣿⠓⠀⠀⢰⡶⠶⢶⠀⢰⣿⠆⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣷⠀⠀⠀⠀⠸⠇⠀⠀⠈⠁⠀⠀⣀⠾⠁⠀⠘⠇⠀⠀⠀⠀⠀⣰⠿⠃⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡘⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠶⠎⠀⠀⠀⢀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⣼⠏⠀⢀⡀⣴⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠈⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⢂⡰⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠙⢿⡦⠤⠒⣬⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠁⡾⠁⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠳⡀⠀⠙⣝⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⢁⡴⠃⠀⠀⠀⡆⠀⠑⢤⡀⠀⠀⠀⠀⠀⢀⡜⠀⢸⠀⠀⠀⠡⡄⠀⠈⠱⢷⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠁⠀⠀⣸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠀⠀⠀⠀⠰⠀⠀⠀⠎⢱⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡄⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠄⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⠀⠀⠀⡠⠀⠀⠀⠀⠀⣜⠄⠱⣆⡀⠀⠈⢷⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠙⢰⠀⠀⠈⣷
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢈⠀⠀⠀⠸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⢡⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⣄⠀⠀⢸⡄⢀⣀⡠⠊⠁⢀
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⣃⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡿⠀⠀⠰⠋⢁⡼
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢛⣛⡶⡀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢠⠀⠷⠀⠀⠀⠔⠋⠀⠀⠀⠀⡀
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠰⣏⣈⡐⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢰⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣬⣭⡿⠋⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⢰⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢷⠀⠘⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠈⡇⠀⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⡄⡏⠀⠀⠂⠀⠆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡄
⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢳
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏
⣿⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉
⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀
⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣄⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣦⣾⣶⣶⣷⣶⣶⣶⣶⣾⣤⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣛⣉⣉⣙⠛⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣀⠴⠊⡀⠀⠀⠀⢳⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡀⢀⣠⡤⠶⠒⠋⠉⠀⠀⠀⠘⣆⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢔⣡⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢁⠖⡠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⢃⡼⢱⡇⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⣠⣤⠄⠀⣿⡇⠇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠇⡼⠁⢸⠇⠈⠘⠿⠎⠁⠀⡀⠀⠀⠀⠙⠛⠀⠀⡇⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⠃⡆⠘⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⣸⢰⠃⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⡀⠀⢄⡀⠀⠀⡏⣼⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢃⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠄⢠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠈⢆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢠⠇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⢦⠸⡇⠈⠓⠦⠤⠤⠤⠀⠀⢠⡿⢠⣎⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢻⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡎⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡄⠀⡏⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⣆⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠸⡇⠀⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠤⠤⠴⢾⠁⠀⠀⢀⠓⠈⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⢀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢄⠁⠀⠀⠀⠈⡆⠀⠀⠀⠈⠃⢀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠤⠐⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⢧
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣇
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠑⢄⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⠃⠀⠀⢀⡴⠊⢄⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠙⣦⠀⠀⠐⠤⡀⠀⠀⠈⡆⠀⠀⡎⠀⢀⠴⠋⠀⠀⠀⠣⡀⠀⡏⠀⠀⠀⡇⠀⠀⠀⢸⡆
⢀⡇⠀⠀⠀⢰⡄⠀⠀⠀⠈⢧⡀⢀⡿⠀⠀⠀⠀⠈⠀⠀⡀⠘⡄⢰⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⣾⡁⠀⠀⠀⡇⣀⠀⠀⠈⣧
⢸⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢰⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⡬⠁⠈⠀⠠⠆⣷⠃⠀⠀⠀⠻
⡎⠀⠀⠀⠘⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⠏⠄
⣧⣤⣤⣤⣤⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣶⣦⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣧⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣾⣿⣿⣾⣿⣷⣾⣾

⠠⢼⡤⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⠺⡗⠂⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠈⢠⡶⣦⠀⢸⣗⣿⣺⠀⠀⠀⢈⣿⣏⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⡇⠀⠀⠀⡇⠀⠀⢰⣛⠛⢻
⠀⠀⡾⢆⠾⡀⢸⣷⣿⣺⠀⠀⠀⠘⢻⠛⠀⠀⢀⠀⠠⠠⢀⡰⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠤⠁⠸⣷⣿⣺⠀⠀⠀⢰⣾⣶⠀⠀⠀⠱⡁⢈⠌⢀⡄⠀⠧⠤⠤⠤⠇⠀⠀⠀⠀⠇
⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣼⣄⠀⢰⡟⡛⠿⠻⡿⠛⣟⢛⡿⢻⡟⠻⣿⠟⣻⢻⡟⡟⠻⡿⢿⡟⠻⡟⢛⣷
⠀⠀⠈⠉⠉⠀⢸⡇⠃⡆⠷⡀⠺⣿⢸⡀⠇⡀⠸⣿⠀⢿⢸⡇⡇⣰⠃⠘⡇⠸⡇⢸⣿⠀⣴⢰⡄
⠀⡀⠀⠀⠀⠀⠘⢷⣾⣿⣶⣿⣶⣿⣾⣷⣾⣷⣷⣿⣷⣾⣶⣶⣷⣿⣾⣷⣷⣷⣿⣾⠟⠀⢹⢸⠇
⠒⡗⠂⠉⠁⠀⠀⠀⠀⠀⠀⠐⠄⠤⠠⠀⠄⠀⠠⠀⠠⠀⠀⠠⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠚⠘⠒⢀⣤
⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠀⢰⣶⣶⣶⣶⣷⣶
⠀⠹⣿⣿⣿⡿⠁⢀⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣤⢀⡀⣤⣤⣤⣶⣦⠀⠀⢸⣿⣯⡺⣪⣿⣿
⠀⠀⠀⠙⠁⠀⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⣒⣛⣒⠒⠒⠶⠦⢭⣍⣓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢉⣤⣤⣄⡀⠀⢿⣁⣀⣈⡽⠀⢀⣠⣤⣤⡉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠯⣄⣀⣤⠟⠀⣀⡬⠭⠥⣄⠀⠻⣤⣀⣠⠼⢀⡸⠃
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⣀⠻⣤⣤⣤⠞⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⢀⡴⠋⠉⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡭⠟⠛⠉⠙⠓⢦⡀
⠀⠀⣼⣄⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡀⣠⣷
⠀⠀⢸⣠⠏⠉⠛⠿⣍⡽⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣠⡤⢤⡴⠚⠉⠣⣼
⠀⠀⠠⣏⠀⠀⠀⠲⢦⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡷⠋⠀⠀⠀⠀⡼⠂
⠀⠀⣠⠞⠙⠲⣤⣀⢠⠞⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⢳⡀⠀⠀⣠⢞⡓⣄
⠀⢰⠃⡆⠀⡆⢸⠉⠉⠀⣠⢴⡶⠖⠒⠚⠉⠙⢦⠀⠀⠀⢀⣿⡀⠉⠲⣞⢱⡀⠙⣌⣇
⠀⡾⠰⡇⠀⡇⣼⠀⠀⢸⠁⠾⠤⢤⣄⠀⠀⠀⢈⣇⣠⠴⠻⢤⣭⣽⣟⡉⠉⠁⠀⢸⡿⠤⣤⣀
⠀⡇⠀⣇⠀⢹⡇⠀⠀⡿⣆⠀⠀⢀⣈⣷⣤⣠⡼⠋⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠓⢦⠀⠈⠙⢦
⠀⡇⠀⠘⢦⡀⠙⠶⣤⣷⣀⣀⣠⣬⣅⠀⠀⠈⢳⣴⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⡇⠀⠀⠀⢹⡶⢤⣤⣤⣼⠭⠵⠶⠾⠶⠶⠶⠶⠿⠷⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠧⣄
⠀⢻⡛⠛⢛⣛⡇⢿⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣸⠂
⠀⠀⡷⡄⠈⠉⣇⠀⠉⠙⠛⠛⡟⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⢶⡆⠛⠛⠛⠛⡟⠉⠁
⠀⢸⠇⡇⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇
⠀⣼⠀⣿⠀⠀⢸⡀⠀⠀⢀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⣿⠀⠀⢀⣀⣇⣀
⠀⠙⡏⢻⣶⠛⣿⠷⠦⣼⡉⠉⠉⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢿⠛⣷⡟⠙⡏⢀⣾⠉⠉⠉⠉⣹⣄
⠀⢾⣁⣸⣏⣀⣿⣀⣀⣀⣳⠀⠀⠀⣿⣹⡇⠀⠀⠀⠀⠀⠀⣼⣁⣀⣀⣸⣀⣸⣇⣀⣳⣿⣹⡇⠀⠀⠀⣏⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⠙⠦⣀⡐⢡⣤⣤⠄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⠀⠈⠹⠌⢉⣩⣥⡤⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠙⠀⢸⠟⠀⠈⠁⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⣠⠇⠠⡀⠈⠈⢨⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⠀⡠⠿⡄⠀⠸⣈⡹
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠁⠀⠀⠀⢧
⠀⠀⠑⠈⠓⠤⣀⠀⠀⡠⠚⠙⢢⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⢀⣼⡃
⢠⠖⠒⠂⣠⠟⡠⠉⠋⢡⠀⠁⠀⠁⠀⠀⣀⠄⠂⠁⠙⠛⡶⠖⡶⢲⠋⠹⠀⠉⠲⣄
⡀⠀⠈⢰⠃⠘⠆⠀⣠⡇⠀⠀⠀⠀⢠⠎⠀⠀⠀⡖⠈⠀⣀⠻⢀⠇⠠⢇⠀⠀⠠⠈⠳⠄
⠀⣄⠀⠀⠀⠀⢠⡏⠀⡇⠀⠀⠀⠠⢃⡖⠀⠀⠀⠘⠄⠀⠹⠀⡟⠀⣀⠴⠊⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢣⠀⢀⡔⢡⡞⠀⠀⠀⠀⠀⠈⢢⠀⣐⠠⠊⠁⠀⠀⠐⠤⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡤⠊⡠⠃⠀⢘⠀⠈⠉⠀⠂⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣡⠞⠁⠐⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⡶⠦⠤⠤⠧⠤⠤⠴⠶⠶⢶⠒⢲⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⠮⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡤⠀⣰⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣰⢤⡉⠙⠒⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⡠⠴⠊⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠤⠤⠤⠚
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠀⠀⠀⠀⣠⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣶⠀⠀⠘⠛⠒⠒⠋⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⡭⠀⠀⠂⠀⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣶⡄⠀⠺⡝⠁⠀⠀⠠⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⢠⡾⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⠀⠀⠀⠀⣠⠏⢀⡌⠉⠭⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⢀⣠⡾⣵⣾⣟⠀⠀⠀⠘⠂⡙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⡏⠀⢻⣿⣿⡿⢿⡿⢫⣀⠀⢀⡀⠀⠁⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠟⠀⠀⢴⣿⡟⠁⠠⠈⠉⢟⣴⡟⠁⠀⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠀⢀⠒⣛⣿⣆⣤⡀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⣰⠗⠻⠛⠈⢿⣟⣾⣷⡶⢻⣧⠄⠀⠀⢠⣀⠀⠀⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⢀⠉⢰⡆⠀⣀⠀⢹⠛⠙⢦⣘⠻⠀⠀⢀⣀⣉⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⢙⠛⠂⠁⠀⠈⠃⠐⠉⠀⠀⣾⠉⡄⠀⠀⠉⠉⠉⢙⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠘⠀⢀⠟⠀⣶⠀⣿⠀⠀⢠⡄⢀⣵⡄⢠⡈⠂⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠲⠄⢟⣰⣤⡄⢀⡀⣄⠀⠀⢈⡁⢠⣿⡂⠠⣤⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠈⠽⠁⢲⠀⢁⡌⠀⠀⠘⠃⢴⣏⣹⡆⢴⡄⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠐⠉⣡⣄⠀⠀⠠⠀⠀⢤⡗⢀⣈⡁⠁⠀⠘⠃⣾⣍⣽⡆⠐⠦⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣭⢋⣼⠃⠀⠀⠀⣶⣦⣌⣻⠿⠗⠀⠀⠐⠟⠉⠁⢉⣠⠶⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠐⠀⢠⣆⠹⠛⠘⠛⠛⠒⠀⠸⠦⣀⠀⠀⠀⠠⣐⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⡀⠀⠈⢧⣄⠀⠀⠈⠑⠀⠀⠀⠈⠃⠹⡆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠃⣸⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⢸⡟⠈⢶⣢⣡⡏⣀⣈⣄⠀⢠⣤⣤⣄⣠⣀⣤⡄⢴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⠆⣿⠘⠀⠿⠀⣤⠀⢀⡄⣿⠀⠀⣰⣿⡷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣿⠸⠂⣤⠀⠉⠀⠘⠃⢸⡇⠰⠙⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡄⠀⠉⠀⡇⠀⢠⡔⢼⡇⠀⠰⣿⡗⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠛⢧⣴⡃⠀⡀⠀⠙⠁⠈⣧⠞⠁⢻⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠛⠶⣇⣀⣶⠀⢘⣿⡶⠾⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣿⣶⡾⢿⣿⣶⡿⢶⣶⡶⢶⣶⠶⢷⣾⣶⡿⣶⣾⣿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⢸⣇⠘⣿⣿⠃⢸⣿⡇⢸⣿⡄⠸⣿⡿⠀⣿⠁⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⣿⠀⠻⣦⣤⣤⣴⠟⣿⡇⢸⡟⠷⣤⣄⣤⡾⠏⠀⣿⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⠀⠀⠀⠉⠉⠀⠀⢿⣇⣼⡇⠀⠀⠉⠁⠀⠀⠀⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣠⣄⠀⠈⠉⠉⠀⢀⣤⡀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠙⠻⠷⣶⣤⣤⣤⣴⡶⠿⠛⢙⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⢸⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣿⠀⠀⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⣿⡇⠀⠀⠸⣿⣄⠈⠙⢶⣄⠀⣀⣴⠟⠉⠀⣸⣿⠀⠀⠀⢻⣿⢿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣶⠟⢛⣿⡏⢠⣿⡇⠀⠀⠀⢿⣿⣧⡀⠀⢉⣿⣏⠀⠀⣠⣾⣿⡇⠀⠀⠀⢸⣿⠈⣿⣏⠛⢿⣶⣄⡀
⠀⠀⠀⢀⣴⡿⠛⠁⠀⣸⣿⠀⢸⣿⣇⡀⠀⠀⠘⣿⣿⣿⣦⡾⠁⠻⣦⣾⣿⣿⡿⠀⠀⠀⣀⣸⣿⠀⢸⣿⠀⠀⠈⠛⢿⣦⡀
⠀⠀⢠⣾⠟⠀⠀⠀⠀⣿⣿⠀⠈⠛⢛⣿⡿⠀⠀⢻⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⠇⠀⠰⣿⣿⠛⠋⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⡄
⠀⣠⣿⠃⠀⠀⠀⠀⠀⢸⣿⠀⢀⣴⣿⠟⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⢿⣷⣄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣄
⢠⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡀⠸⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⣿⣿⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣸⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠹⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣸⣿⠃⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠹⣿⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣰⣿⠃⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣰⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣀⡀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⣴⡿⠟⠛⠛⠻⢿⣦⡀⠀⠀⠙⣿⡄⠀⠀⠈⣿⡟⠀⠀⠀⣸⡿⠁⠀⠀⢀⣴⡶⠿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠘⣿⣆⠀⠀⠙⠃⠀⠀⣸⡿⠁⠀⠀⣰⡟⣡⠶⠛⠳⣦⡙⣷⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣼⡿⠁⠀⠀⣤⣿⠰⣏⠀⠀⠀⢸⡇⣹⣧⡄⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠘⣿⣆⠀⠀⣼⡿⠁⠀⠀⠀⣿⠻⣧⡙⢦⣤⣤⠞⣡⡿⢹⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣼⡟⠀⠀⠀⠀⠀⣿⠀⠈⠻⠶⢶⠶⠞⠋⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⢠⡄⠀⢀⠚⠁
⠀⠀⠀⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠲⢦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠴⠟⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⡖⠒⠒⠚⠛⠛⣿⡗⠒⠒⠒⠂⠤⣄⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡏⡀⠒⢀⡐⠒⢦⠈⠃⠀⠀⠀⠀⠀⢠⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠙⢻⡟⡏⢹⣶⡾⠂⠀⠀⠀⠀⠀⠀⠉⠠⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡏⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠷⠆⠀⠀⠐⠾⠟⠶⠀⠀⠀⠀⢀⠀⠀⢷⣶⡾⠏
⠀⠀⠀⠀⠀⠀⣶⠾⠻⠟⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⢻⣯⠀⠀⠀⢀⣀⠤⠜⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠠⠤⠶⠃⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡦⠤⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠠⠒⣿⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⠄⢸⣧⠀⠀⣼⠛⠒⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⢀⣀⡁⠀⣸⣦⣤⡴⠿⠦⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠙⠲⠷⡤⠋⠀⠀⣀⣠⣤⣿⣧⣄⡀
⠀⠀⢸⡏⠙⢿⣮⣉⣀⣤⣤⣤⠶⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣀⢀⣀⣀⣤⣴⡶⠾⠛⠁⢠⡟⠀⠉⠻⢶⣤⣀
⠀⠀⠀⠙⢦⡄⠈⠻⣿⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠹⡋⠛⠛⠛⠛⠉⠉⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀
⣾⠛⠙⠛⠸⠿⣦⣀⠹⡄⢠⠀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠁⠄⠀⣀⣀⣀⡀⠠⠖⠉⠀⠀⠀⠀⠈⢿⣶⣤⣄⡀⠀⠀⠉⠛⠛⠶⢶⣤⣤⣤
⠈⠛⠶⠶⠶⢤⣄⠈⠁⡇⢸⠈⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠉⠛⠛⠶⠶⣤⣀⣀⣀⣠⠀⢨
⠀⠀⠀⠀⠀⠀⠈⢷⡀⡷⢸⠀⡇⠀⠈⣷⣠⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠈⢀⡼⠋⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠘⠀⣇⠀⢀⡿⠙⣧⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣠⠟⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠛⠛⠻⣄⣼⠃⠀⠹⣦⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢀⣼⠋⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠒⠿⣾⠟⢦⠀⠀⠹⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡾⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⡀⣀⣿⠀⠈⢷⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠻⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠹⣧⠀⠀⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⡆⠀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢧⣴⠟⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⢁⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠛⠛⢻⡿⠿⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠻⣦⠀⠀⠀⠀⠀⠀⣷⠀⠀⢺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⢳⡄⠀⠀⠀⠀⠈⢳⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢃⠀⠀⠀⠀⠀⠀⢻⣄⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡛⠛⠛⠒⠠⣦⠤⠤⠤⠴⠶⠚⣻⠁⠉⠛⠛⠛⢷⠀⠀⠀⠀⣀⣴⠋⠙⠛⠋⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⡀⡑⠀⠀⠀⠀⠐⠀⠉⢀⣠⡾⣆⠀⣨⣧⣤⠴⠛⢋⡀⠆⢀⣶⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠲⠶⢶⣶⣶⣿⡿⠭⠔⠛⠛⠙⣇⠀⠀⠘⠀⢀⣤⡿⠉⣷⣶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠀⠀⠀⣀⣸⣄⣤⡤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠲⠶⠒⠶⠠⠤⣠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠫⠷⠦⠀⠀⢀⠀⠀⠀⠰⠶⠝⠛⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡜⠁⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⡇⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⠃⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⡿⢁⣀⡤⠴⠖⠒⠒⠒⠚⠛⠛⠛⠛⠁⡐⠢⢄⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⢟⢵⠋⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⢀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠃⠎⣠⣶⣶⣶⣦⣤⡀⠀⠀⠀⠠⣾⣿⡿⠿⠿⢷⡄⢸⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⠖⡿⠋⢀⡀⣉⠉⠉⠁⠀⠀⠀⡤⠀⣰⣾⡷⢦⡀⠁⠀⢻⣿⡿⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢻⣿⣇⠀⠀⠀⠛⠿⠿⠁⠀⣠⣶⣀⣀⡅⢀⣀⣲⣷⣀⣭⣶⠴⢞⣫⡴⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⣏⠛⠛⠛⠛⠶⠷⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠠⠔⡠⠟⡻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⠳⠄⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠛⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠛⣿⡏⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⣠⡞⠁⠀⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠈⠙⠦⣍⠻⢿⣿⣿⡟⢶⠖⢖⢹⡿⠟⣁⠀⠊⠉⢛⡻⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⢦⣄⠻⠀⠀⠉⠘⠻⢿⡷⠾⠶⠿⠿⠋⠃⠀⠀⣠⡴⢁⡴⣼⢟⡿⢿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠛⠉⣰⣿⠀⣸⡏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠄⢀⡼⢋⡴⢋⠾⠃⠘⣷⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⢁⡄⠀⠀⢀⣿⠅⠊⠁⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠠⠒⠁⠀⠀⠀⣿⡆⠀⠀⠀⠀⠈⠙⠻⢿⣿⣀
⠀⠀⠀⢀⣠⣤⡶⠟⠋⠀⢀⣀⣠⣾⣷⠟⠋⠙⡇⠀⠀⠀⠀⠠⠀⠈⠉⠒⠶⠦⠤⢤⣤⡤⠤⠖⢚⣉⣤⠄⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦
⠀⠰⠟⠋⠉⣀⣤⡴⠶⠛⠋⠁⠉⡼⠃⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠉⢉⣤⣶⡿⠋
⠀⠀⠀⢀⡋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠛⠁
⠀⠀⣠⣾⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠉⠁
⠀⠐⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋