Socket Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠶⣤⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠟⠛⠛⠛⠿⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠈⠳⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠻⢷⣄⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣸⡿⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⣴⡟⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⢿⣦⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣄⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣈⠛⠷⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⣀⣀⣤⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣷⠼⠗⠛⠋⢉⣡⣤⣤⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⣀⣠⡤⢶⣾⡿⠛⠁⡻⣷⡹⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⠀⠙⣇⢺⣯⣀⣠⣴⡯⠶⣞⣣⣽⠆⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧⠀⠘⣧⣙⣫⡥⠶⠚⠛⠉⠁⠀⢀⣀⡀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡀⠘⣆⠀⠈⠉⠀⠀⣀⣠⡤⠶⠞⠛⠉⠉⢳⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠱⡄⠘⣦⠀⠀⢾⠋⢉⣤⣴⡄⠀⠀⠀⣴⡄⢻⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠙⡄⠘⢧⠀⠈⢷⡀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠹⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⢆⠈⢧⡀⠀⢻⡄⠐⣾⠿⠆⠀⢀⣠⣤⠶⠟⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⢦⠈⢷⡀⠀⠻⣄⣤⠴⠖⠛⣉⣁⣤⡤⠶⠚⣦⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢣⡀⢻⡄⠀⠁⣤⠶⠞⠛⣉⡁⠀⠀⠀⣀⡘⢧⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠱⡄⠹⣄⠀⠹⣦⠀⠻⠛⠃⠀⠀⠀⠻⠗⠈⢷⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⡄⠹⣆⠀⠘⣧⠀⢀⣤⣶⡄⠀⠀⠀⢀⣀⣷⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⢆⠘⣧⠀⠈⢧⡀⢉⣉⣤⠴⠶⠛⠉⠁⠀⢀⣀⣤⣷
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⢦⠈⢷⡀⠈⠛⠋⠁⣀⣠⡤⠶⠶⠛⠋⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢣⠀⢻⡶⠖⠛⠋⠉⠀⠀⠀⠀⣀⣠⠤⠴⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠳⣼⠃⠀⣀⡠⠤⠔⠒⠉⠉⠀⠀⠀⢀⣀⣼
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢹⠋⠉⠀⠀⠀⠀⣀⣠⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣀⣤⡤⠶⠚⠋⠉⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠚⠒⢄⠀⠀⠀⠀⠀⢸⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠩⠑⢸⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠚⠊⢸⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢑⠙⢸⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⠀⠈⡀⡈⢸⠀⠀⠀⠀⠀⣨⣄⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⡀⢸⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠀⢊⠀⢈⢸⠀⠀⠀⠀⠀⠻⠟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠟⢸⡏⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠁⠡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡿⠟
⣶⣶⣶⢶⣶⠶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣼⣾⣶⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢚⡩⠒⠽⡇⠀⠠⡄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⡥⠚⣁⠔⢻⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⠴⠚⣡⠔⠋⢀⣶⢸⠀⣿⠀⢠⣤⣤⣼⡟⣿⢶⠶⠶⢦⣄
⠀⠀⠀⠀⣀⡴⠞⣉⠴⠊⡁⠀⠀⡇⣶⡆⠀⠿⢸⠀⢿⠀⣼⣿⣿⣿⡇⣿⠘⠀⠉⠳⢹⢻⣶⢤⣤⣀⣠⡴⢖⣛⡀
⠀⢀⣤⠞⣋⠔⠋⣀⠴⠊⡇⠀⠀⡇⠿⠃⠀⠀⢸⠀⢸⠀⠉⣉⣉⣹⡇⣿⠠⠀⠤⣊⡾⠛⠉⢹⡷⣾⣿⣿⡉
⠀⢸⡟⡯⢄⠔⠊⠁⢰⣧⢻⠀⠀⡇⠀⢠⣶⠄⢈⣀⣸⠀⠀⠉⠉⠙⠷⠟⠛⠛⠋⠉⠀⠀⣰⢫⡞⠁⠙⣎⢷
⠀⢸⡇⡇⢸⠀⣿⠀⠘⠋⢸⠀⠀⣇⠀⢈⡡⠖⢁⡼⠟⠀⢠⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⡏⡟⠀⠀⠀⢸⣿⡇
⠀⢸⡇⡇⠸⡄⠋⠀⠀⠀⢸⠀⠀⠸⠚⢁⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣧⡀⠀⢀⡼⣻⠃
⠀⢸⡇⡇⠀⡇⠀⣴⡷⢀⡸⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣽⣻⣯⠷⠋
⠀⠈⡇⢇⠀⡇⢀⡠⠖⠉⣀⡴⠟⠁
⠀⠀⣧⢸⠀⠛⠉⣀⡴⠞⠉
⠀⠀⢿⣸⣘⡴⠞⠉
⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⣿⢿⡏⠉⣩⣭⡍⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⢸⡇⠀⣿⢹⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⣸⡇⠀⣿⣼⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⣡⣤⡌⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣷⡿⣷⠆⠀⠀⠀⠿⣿⠟⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⠀⠀⣰⢟⣾⠃⠀⣴⢿⣦⣾⠛⣦⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣍⠻⣾⣫⡾⠙⢷⣾⣣⡿⠷⠿⠿⠿⠶⠶⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠈⠙⠿⣿⣟⠻⣶⡾⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣿⡿⣿⠀⢠⣶⣦⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⠀⢸⣿⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣾⣇⣿⠀⠸⣿⡿⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⣠⡿⠁⠀⠈⠉⢡⣶⣦⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣀⠀⠀⠈⣹⠟⠷⠶⢿⡏⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⣿⣿⢶⡾⠋⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣾⣋⣿⡄⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠿⠿⠿⠷⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢁⣴⠟⠁⠀⠀⠻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⢁⣠⡾⠛⠁
⠀⠀⢀⣀⣠⣤⠶⠛⠋⢁⣠⡶⠟⠉
⠛⠛⠋⠉⢁⣀⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠊⢩⣤⣀⠉⠓⠦⣄⣀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢝⡲⢤⡀⠘⢦⣈⠙⠲⡄⠀⠉⠛⣷⡶⠶⠶⢄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣡⢶⡛⠉⢧⣅⠋⠓⡦⣌⡉⠉⣁⡤⠖⠋⢸⠃⠀⠀⠀⢷⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢋⣡⣀⠘⠣⣝⡢⣽⣆⠀⣙⡟⣲⠌⠐⣩⠏⠁⠀⠀⢀⢼⡄⠀⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣁⡴⠚⠁⢴⡮⠓⠦⣄⠉⠓⠮⣟⠽⠊⣁⡴⠚⠁⠀⣀⠔⠊⠁⢸⡇⠀⠀⣠⣇⣼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣉⣄⡀⠈⠓⢦⣀⣠⣾⠆⠺⠟⢈⣹⠆⠀⣠⠴⠋⠁⢀⡠⠔⠈⠀⢀⣠⠖⢉⣠⢔⣫⢵⣚⡛⢻⣷⣦
⠀⠀⠀⠀⠀⢀⣠⠖⠉⣀⡴⠚⠁⣴⡯⠓⢤⣀⠈⠙⠲⢤⡤⠞⢉⡠⠖⠋⠁⣀⠤⠒⠁⠀⢀⡤⠖⢉⣠⠖⣩⠔⣫⠖⣫⢵⡟⢸⢻⡏
⠀⠀⠀⠀⡶⣏⡀⠀⠈⠳⢤⣀⢴⣾⠆⠺⠗⢈⡹⠆⠀⣀⡴⠚⠉⠀⣀⠤⠊⠀⠀⣀⡤⠚⢉⣠⡶⢋⡴⣋⠴⣋⣴⢟⡵⢋⡴⣣⣾⠇
⠀⠀⠀⠀⡇⠀⠉⠳⢤⣀⠀⠈⠙⠲⢤⡴⠚⢉⣠⠴⠊⠁⠀⡀⠔⠊⠀⠀⣀⡴⠚⢁⣤⣴⠟⣡⠞⡡⢞⡵⣺⣿⠗⣩⣴⡿⣊⠕⠁
⠀⠀⠀⠀⣿⠀⢄⡀⠀⠈⠙⠲⢤⣀⢀⡠⠖⠋⠀⢀⠠⠖⠉⠀⠀⣀⠴⠚⢁⣠⢴⣿⣷⣬⡻⣵⣫⣶⠭⢚⣩⢴⡿⢟⡥⠞⠁
⠀⠀⠀⠀⢿⡀⠀⠈⠑⠤⣀⠀⠀⢸⡇⠀⣀⠄⠊⠁⠀⢀⣠⠴⠋⠁⣠⢖⡿⣺⠽⢋⡥⣾⣷⡮⢿⣴⣺⢽⣺⠵⠚⠁
⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠉⠒⢼⠗⠈⠀⠀⢀⣠⠖⠋⠀⢀⣴⡿⣾⠵⢋⡥⢚⡵⢊⠟⣵⠿⣬⡿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⢸⠇⣀⡤⠚⠉⠀⠀⢀⢔⡽⣫⠞⣡⠞⣩⠶⣫⠞⣡⠞⣡⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⢀⡴⣣⢫⠞⣡⢞⣵⢞⡥⢚⣵⠞⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⢣⠏⣼⣵⡿⠗⣋⣴⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢣⣼⣀⣉⡭⢴⡿⢋⠟⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠤⠴⢚⣩⣴⣯⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣯⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣜⡬⣒⡿⢃⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣈⣽⣻⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⢻⣟⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠀⠀⣿⡏⣻⣷⠀⠀⠀⠀⠀⣰⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣆
⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⣿⡇⣹⣿⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⣿⡇⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⣿⡿⠿⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢀⣠⣤⣿⣧⣿⣯⣤⣤⣤⣿⣧⣽⣿⣤⣀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⡇⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡇⠀⢸⣿⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⣿⡇
⠀⠀⠙⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠟⠁⠀⢸⣿⠀⠀⠀⣿⡏⠀⣤⣶⣦⣄⠀⠀⠀⠀⣠⣴⣶⣄⠀⢹⣿⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⢸⣿⣁⣹⣿⠀⠀⠀⠀⣿⣇⣨⣿⠇⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢿⣇⠀⠙⠛⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⣼⡿⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠹⣿⣄⡀⠀⠀⠀⠀⠀⣀⣴⡿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⣾⡇⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣶⣶⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣶⣿⣿⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣶⣶⣶⣴⣦⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠙⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠻⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣰⠁⠀⢠⢎⠽⢭⡳⡔⠒⠒⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⡱⠁⠀⠀⡿⡎⢰⠛⢷⢱⣀⣀⠤⠒⠋⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⠢⢄⡀⠀⠀⠀⠀⢸⠁⡇⠀⠀⡾⢷⣷⣼⡂⠨⡏⡅⡇⠀⡀⠠⢀⣠⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡙⡄⠀⠀⢀⣠⡀⣧⣤⣞⠀⠸⡀⢷⠪⢗⡇⣏⣏⣠⣴⡾⠛⢹⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⢼⣄⣠⠚⢝⣛⣻⢿⣷⣽⣗⣷⡼⢓⡦⢹⣯⠽⠋⠁⣀⠤⢺⠀⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠓⢾⣻⣾⢉⠒⠒⠊⢁⡧⣌⠛⠿⢊⡥⠖⠻⡼⡀⠔⠊⠀⢀⡼⠀⠀⠹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⣚⡇⠀⠀⢸⡆⣏⡓⠪⠭⣵⡾⢓⣡⠴⠚⠁⠀⡠⠔⠳⡑⣄⡠⠖⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠙⠢⢕⡦⢤⣘⣧⠇⣨⠗⣀⡤⠖⠉⠀⢀⠤⠒⠉⠀⢀⡤⠟⠺⣕⠦
⠀⠀⣠⡔⠊⠉⣤⣖⡋⠙⢓⣲⠖⠉⢂⠀⠉⠚⢒⣩⠔⠋⠁⠀⣀⠔⠊⠁⠀⣀⡤⠚⠁⠀⠀⠀⠀⠁
⠀⠀⡇⠈⠉⠒⠦⠭⣙⡳⠦⣤⡴⠞⠉⣀⡤⠒⠉⠀⠀⡠⠔⠉⠀⠀⣠⠴⠊⠁
⠀⠀⡇⣀⠀⡤⣤⣄⡀⠉⠙⠒⢦⠔⠊⠁⠀⢀⡠⠒⠉⠀⢀⣠⠴⠋
⠀⠀⡇⢀⡭⠟⢛⣻⣿⣀⠀⠀⢸⠀⢀⠤⠒⠁⠀⢀⡠⠖⠉
⠀⣠⠛⢁⣠⣖⠋⠉⠋⠀⠈⠁⢻⠈⠀⠀⢀⡠⠖⠉
⡼⠁⡴⠋⠀⠈⠙⠒⠦⣤⣀⠀⢸⢀⣠⠔⠋
⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋
⠱⣄⠙⢦⡀
⠀⠈⠳⣄⠙⣄
⠀⠀⠀⠸⡆⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⣿⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣸⠏⠀⠀⣰⡿⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⢿⡟⠀⢰⣿⣄⡀⢠⡟⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢠⣿⡀⢀⣿⠉⠙⢻⣿⠁⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⡢⣉⠛⠛⠃⠀⢠⣾⡇⣰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⠻⢾⣷⣦⣄⣀⠀⠙⠻⠟⠁⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣶⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢠⡴⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣤⣄⣀⣀⣹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣩⣿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡿⠿⠿⠿⣟⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⠃⠀⠀⠀⠀⠈⢳⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣼⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡄⠀⠀⠀⠀⢰⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣧⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡆⠀⠀⠀⠸⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣷⠀⠀⠀⠀⠹⣟⢦⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠈⠻⣷⢦⣀⠀⠀⣀⡤⣿⠞
⠀⠀⠀⠀⢻⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠞⠉
⠀⠀⠀⠀⠀⠻⣝⣷⣄⠀⠀⠀⠀⠀⢀⣼⢃⡿
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣶⣶⢶⣛⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⢟⣛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⣛⣫⣵⠶⠞⠛⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⢛⣩⣥⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⣋⣥⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡄⢸⣿
⠀⠀⠀⠀⠀⢀⣤⣾⡿⢛⣩⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⢛⣫⣥⣿⣧⣼⣿⣤⣄
⠀⠀⠀⢀⣶⡿⣫⣵⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⣩⣴⣾⡿⢟⡻⠟⠋⢉⣽⠿⣿⡇
⠀⠀⠀⣿⣿⣽⡏⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡆⢸⣿⠀⣿⣿⣿⣭⣾⣭⣤⣤⡶⢛⣡⣶⣿⣷⣶⣶⣄
⠀⠀⠀⣿⡇⢸⡇⠀⠀⣀⣤⣶⣾⠿⠛⠉⠁⠀⣿⡇⢸⣿⡄⣿⡇⣏⠀⠀⠀⠀⣿⣴⣟⣉⣀⣴⣿⣯⣿⡿
⠀⠀⠀⣿⣷⢸⡇⠀⣾⡿⠋⠉⠀⠀⠀⢀⣄⠀⣿⡇⠀⣿⡇⣿⡇⣿⠀⠀⠀⠀⣿⣿⣭⣹⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢻⣿⢸⡇⠀⣿⣇⠀⣶⡄⠀⠀⠈⠉⠀⢿⣿⠀⣿⡇⣿⣇⣹⣀⣀⣀⢀⣿⣭⣿⣿⠿⠋⠁⠙⣿⣿⣿⡄
⠀⠀⠀⢸⣿⢸⡇⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣷⠘⣻⣿⣿⡿⠿⠿⠿⠟⢹⣿⠀⠀⠀⠀⢹⣿⣿⣧
⠀⠀⠀⢸⣿⡸⣧⠀⢸⣿⠀⠀⠀⠐⠿⠀⠀⠀⢸⣿⠀⢸⣿⠿⠟⠋⠉⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⣿⡇⣿⠀⢸⣿⡄⠀⠀⠀⠀⢀⣤⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⣿⡇⣿⣧
⠀⠀⠀⠀⣿⡇⣿⠀⠀⣿⣇⣀⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡜⣿⣆
⠀⠀⠀⠀⢿⣿⣿⡀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣜⣿⣦
⠀⠀⠀⠀⢸⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠸⣿⣸⣇⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣿⣧⣿⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠛⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⢰⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⢸⣷⡏⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⣍⢳⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡟⡇⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡗⡇⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⣸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⣿⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢸⣿⠀⠀⣠⡾⢋⡥⠶⠒⠒⠦⣍⠻⣦⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⢸⣿⠀⣰⡏⡴⠋⠀⠀⠀⠀⠀⠈⣧⢹⡇⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡏⠀⣿⢸⠁⠀⣰⣿⣿⣿⡆⠀⢸⠈⣿⠀⣿⡇⠀⢸⡇⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣿⠀⠀⣯⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢸⡇⠀⢿⣾⡀⠀⢹⣿⠀⣿⠁⠀⡼⢸⡏⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢸⡇⠀⠘⢷⡻⢤⣸⡏⠀⣿⣤⢞⣵⠟⠁⠀⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠈⠛⠶⣼⣿⠀⣿⡾⠛⠁⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣿⠀⢻⣄⣀⣀⣀⣀⣀⣿⡇⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡀⠀⠉⠉⠉⠉⠉⠉⠉⢻⡆⢸⡟⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠸⣄⣋⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⠈⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣺⣀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢼⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⣽⠶⠶⠛⠛⢉⣉⣁⣠⡀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠉⢁⣀⣤⣤⣶⣶⠟⠛⣿⣏⢷⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠐⣿⠋⣭⠶⠛⠉⢀⣠⣖⣉⣹⣦⢻⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀⣼⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣆⠀⠘⣧⠙⣯⣴⠾⠟⣛⣩⣭⠶⠶⠛⠋⠀⠀⠘⢧⡀⠀⠀⠀⣼⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⢹⡆⠀⠈⢷⣤⠶⠞⠛⠉⠁⠀⠀⢀⣀⣤⡤⣦⠀⠈⢳⡄⢀⡾⣣⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣄⠀⢻⡆⠀⠀⠀⢀⣀⣠⣤⠶⠞⠛⠉⠉⠀⠀⠘⣧⠀⠀⣽⢟⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⢆⠀⠻⣆⠀⠐⣿⠉⠁⣤⣴⣦⠀⠀⠀⠀⣿⣆⠘⣷⡞⣱⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⢧⠀⠹⣆⠀⠘⢷⡀⠉⠉⠀⠀⠀⠀⠀⠈⢁⣴⣟⣼⣧⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢣⡀⠹⣆⠀⠈⢷⡀⠀⢴⣶⣶⠀⠀⠀⣿⠃⠿⠓⣻⣇⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠳⡀⠘⣧⡀⠈⢻⡄⠈⣉⣠⣤⣶⡾⠋⠛⠛⠛⠉⠉⠳⣄⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⡄⠘⢷⡀⠀⠛⠛⠉⠁⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⣆⠈⢷⡄⠀⠀⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣦⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠈⢦⠀⢻⣄⠀⢸⡏⠻⢦⣄⣀⠀⠀⠀⢀⣠⣴⠞⢁⣿⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢳⡀⠹⣆⠀⠙⣶⣄⣈⠉⠙⠛⠛⠋⣁⣠⡴⢟⣉⣷⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠱⡄⠙⣦⠀⠈⢿⡉⠛⢛⣻⣿⡿⠿⠟⠛⠋⠉⠀⣀⣀⣤⣼⡇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⡄⠘⢷⡀⠈⠻⠛⠋⠉⢀⣀⣠⣤⠶⠶⠛⠛⠉⠉⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⣄⠈⢻⣤⣤⠶⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⣀⣀⠤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⢆⢸⡇⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠋⠉⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⢻⣧⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢸⡇⠀⠀⠀⢀⣀⣠⣤⠶⠞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡴⠶⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡴⣾⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠛⢛⡛⠛⢛⡛⠻⣄⠀⠀⠀⢹⠀⠀⠀⣴⡋⠠⣯⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⢸⡇⠀⢸⡇⠀⢸⡆⠀⠀⢸⠀⠀⠀⣸⢟⣠⠞⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣧⠀⠀⠁⣤⠈⠁⠀⣸⠃⠀⠀⢸⠀⠀⠰⠟⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⠶⠶⠶⠶⠶⠶⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⡤⠴⢖⡶⠂
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡖⣢⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡬⠷⠀⠘⣏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠛⣛⠛⠒⣒⠒⢦⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⣿⠀⠀⣿⠀⠈⣧⠀⠀⢸⡇⠀⢀⣀⡀⣰⡶⣤⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡀⠀⠉⢠⡄⠉⠀⢀⡟⠀⠀⢸⡇⠀⠀⠐⠲⠯⣁⣲⠿⠿⠶
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠳⠶⠶⠤⠤⠤⠤⠾⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡴⣻⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠉⢩⡍⠉⢉⣭⠉⠻⣆⠀⠀⠀⢸⡇⠀⠀⠀⢾⣏⡀⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠈⣿⠀⠀⢻⡄⠀⠀⢸⡇⠀⠀⠀⣰⢟⣡⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄⠀⠈⠁⣤⡄⠉⠀⠀⣼⠁⠀⠀⢸⡇⠀⠀⢰⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣦⣤⣤⣬⣥⣤⣤⣴⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢻⣏⡉⣴⡞⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠳⠼⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠶⢿⣯⣭⡤⠬⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠏⢉⣭⠉⠉⣩⡍⠙⢧⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠈⣿⠀⠀⣿⡇⠀⠘⡇⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣿⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⠀⠀⠉⢠⣤⠈⠁⠀⢠⡇⠀⠀⠀⣿⠀⠀⠈⠙⠻⢯⣭⣰⡶⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢧⣤⣤⣬⣭⣤⣤⣤⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢧⡤⢴⢒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣈⣞⠃⠤⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠿⠛⢏⣿⡿⣿⡄⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠒⣿⡽⢿⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢿⡴⠚⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠅⠽⢿⠿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣡⢄⣿⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠿⢿⣻⡟⣿⣶⣿⣅⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠛⡫⢿⣿⡿⣗⣆⣠⣄⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣾⣧⣤⣥⣬⣭⣥⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣍⣩⣬⣩⣏⣽⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⢿⣿⢮⠻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⡑⠌⠳⡀⠙⡄⢻⣿⠸⠟⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠯⣍⡙⠻⢮⡂⠀⠀⠀⠀⠀⢻⠀⠀⢿⡟⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⡛⠛⠒⠢⠄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢻⢫⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⣫⣭⣭⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢣⠞⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⡫⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡄⣤⢄⠀⠀⠀⠀⠁⣠⡾⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⣀⣤⠔⠂⠀⠀⠀⠀⠀⢸⡏⡟⠻⠜⠧⠘⠋⠀⠀⠀⠀⠐⣉⣴⠿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⠟⣉⠀⠀⠀⠀⠀⠀⡄⢠⣶⣶⡇⢸⡇⠀⠀⠀⠀⠀⠠⠔⠋⠉⠚
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡾⠋⢀⠀⠀⠀⠀⠀⠑⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣪⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡴⢣⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣛⣛⣯⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣣⡧⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠐⠢⠤⣤⣤⣬⣽⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣼⣷⠀⠀⣧⠀⠀⠀⠀⠀⠨⡳⣦⣬⣙⣲⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⣿⣴⡄⣿⣧⠘⣄⠈⢦⡐⢌⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣼⣦⡳⣿⣷⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠘⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠖⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠑⠢⠄
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠛⢀⣴⠆⠀⠄⢴⣦⣤⠀⠀⣠⣶⣶⣶⣶⣶⢤⣶⣶⣶⡞⣶⣶⣶⣆⢴⣶⣶⣶⣶⣦⡤⠀⣠⣤⣶⡄⠀⠀⢶⣄⠘⠃
⠀⠀⠀⠀⠰⠀⢸⣇⢠⣤⣄⢸⡘⣻⠟⢛⡛⣿⣿⣿⣿⣿⡸⣿⣿⣿⡇⣿⣿⣿⡟⣸⣿⣿⣿⣿⡟⣛⠟⢿⡛⣸⢀⣤⣤⢀⣿⠀⠘
⠀⠀⠀⠀⢠⠀⠘⠻⠟⠛⠻⠿⠿⠍⠘⠈⠽⠿⠿⠿⠿⠿⠇⠿⠿⠿⢧⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠏⠐⠈⠽⠿⠟⠛⠛⢻⠛⠀⢠
⠀⠀⠀⠀⣇⣀⠀⠀⣀⠠⠠⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⢀⡀⠀⢀⣀⡅
⠀⠀⠀⠀⡄⠉⠀⠀⠛⠛⠛⠛⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⠛⠛⠛⠃⠀⠈⠁⡄
⠀⠀⠀⠀⡇⠀⠈⠉⢻⣿⣾⡏⠀⠀⠁⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠉⠀⠀⡇
⠀⠀⠀⠘⢳⣤⣤⠼⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⡀⣠⣄⣤⣤⣀⣤⣤⣄⣄⣠⣤⣤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠻⢤⣤⣴⠛
⠀⠀⠀⠀⠸⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠿
⠀⠀⠀⢠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦
⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠉





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

⠀⠀⢠⡶⠞⠛⠻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⢸⡇⠀⠀⠀⠀⢿⡟⢧⡀⣀⣀⣀⠀⢀⡼⢿⡟⠉⠀⠈⢻⣆
⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣬⣿⠿⠉⠉⠛⢿⣷⡞⠁⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢻⡄⠀⠀⠀⢰⣿⣿⣿⡶⠄⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡄⠀⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢻⡄⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⣀⣀⣀⣀⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣿⣿⡿⣿
⠀⣿⣿⣧⣸⣿⣾⣿⣿⣿⣿⣟⣛⣛⣛⣛⠛⠛⣻⡿⢿⣿⣿⣿⡇⣿
⠀⣿⣿⣿⡛⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣟⣛⣿⣿⣛⣻⣿⣿⣿⠃⣿
⠀⣿⡇⣿⡇⣿⡏⠙⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⡆⣿⡆
⠀⣿⣇⣿⢧⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⢻⡇
⠀⢻⣿⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⢱⢸⡇
⠀⢸⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣟⣿⣿⣿⢸⡇
⠀⢸⣿⠇⡇⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠻⣿⣿⣿⢸⡇
⠀⢸⣿⡀⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢸⡇
⠀⢸⣿⡇⡏⣿⣷⣶⣶⣶⣶⣶⡶⠶⣶⣶⣿⣿⣿⣷⠶⣶⣿⣧⢻⣸⣇⠀⡀
⠀⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⢸⣿⣿⣷⣿⣿⡟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣸⣿⣿⡟⠿⡟⣿
⢰⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣦⣤⣀
⢸⣿⣿⠛⣴⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⡟⢿⣿⣿⣿⢿⣿⣿⢿⣿⣷⡀
⠘⢿⣄⠻⣿⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠙⡇⠀⠙⢿⣿⣿⣯⣿⡛⠿⣿⢷⡀
⠀⠀⢹⣦⡘⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣷⡝⠳⢿⣧⣇
⠀⠀⢸⣿⣿⣿⣿⣿⡿⡝⢟⣿⣿⡇⠈⢿⣿⣮⡳⣿⡗⠹⣿⣿⡽⣿⣿⣷⣄⠀⠀⠙⢿⣿⣽⣷⣾⡿⠿⠁
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡇⢪⡻⣿⣿⣾⣿⣦⡙⠻⣿⣮⠻⣿⡻⣷⣄⠀⠈⢻⣿⡅⣿⡇
⠀⠀⠀⣿⡿⠙⣿⣿⣿⣿⣿⣿⡿⠼⢿⣆⠑⡌⠈⢿⣿⣯⠿⣆⠈⠻⣷⡌⠙⢿⡿⣧⡀⢸⣿⡇⣿⡇
⠀⠀⠘⣿⢇⢸⣿⡎⢻⣿⣿⡿⣷⣀⣈⣻⣷⣌⣢⣀⣻⣿⣧⣌⣧⣄⡙⣿⣦⣠⡝⣎⣻⣦⣿⣇⣿⡇
⠀⠀⠀⣿⡞⡀⣿⣷⣼⣿⢿⡏⣿⣿⣿⣿⠿⠛⠛⡛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⣿⡇⣽⣿⠀⢻⣿⢺⣇⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡄
⣶⣶⣾⣿⡇⢸⣿⣤⣼⣿⢸⣿⣹⣿⣤⣤⣀⣀⣀⣀⣀⣸⣿⣿⢠⣿⣄⣀⣀⣀⠀⠀⠀⣹⡿⣿⣿⡇
⠸⣿⣿⣿⡇⢸⣿⣿⣿⣿⠈⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣿⣿⠿⡛⠛⢿⣿⣿⡇⢿⣿⣿⡶⣶⣦
⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣦⡀⠀⠀⢸⡇⢸⡿⣿⡇⠉⠹⣧
⠀⠸⣧⠈⠻⣿⣿⣿⣿⣿⣾⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⡇⢸⡟⣿⡇⠀⠀⠹⣇
⠀⠀⣿⡀⠀⠀⠙⢿⣿⣿⠗⣿⣏⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣸⢨⣿⣿⡀⠀⠀⠀⢻⣆
⠀⠀⠸⣧⠀⡀⠀⠀⠙⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠆⠈⠦⠀⠀⠰⢄⠈⠙⠻⢿⢿⢿⡿⠿⣿⠇⠀⠀⡀⠀⢻⡆
⠀⠀⠀⢿⣇⠙⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢈⣿
⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⠿⢿⡿⠛⡿⠿⣿⣿⠿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣶⣼⣷⣴⣧⣤⣿⣴⣼⣿⣴⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣷⣦⣀⠉⠪⡳⣤⡈⠳⣕⢄⠙⢿⣧⡀⠳⡱⡱⠱⢱⡱⢻⡀⠀⠇⡇⠘⡇⠀⢸⠀⠸⠈⢀⡟⢌⣎⠎⢎⢎⠞⢀⣼⡽⡿⡫⣪⠞⢁⣴⢞⠕⠋⣀⣴⣾⡿
⣄⡀⠉⠙⠿⣗⣤⡀⠙⠝⢦⡈⠢⡑⢀⠙⣟⣄⠑⠄⠀⠁⠳⠈⢇⠀⢠⢻⠀⡇⠀⠘⠀⡆⠀⣸⠁⠜⠈⠀⠠⠊⡠⣻⠫⠊⠈⠜⢁⡴⠫⠃⢁⣤⣺⠿⠋⣁⣴
⢈⠙⠳⢤⣀⠈⠙⠪⣖⠀⠀⠙⠲⣄⠀⠀⠈⠻⡢⡈⠀⠀⠀⠁⠘⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠃⠘⠀⠀⠀⢁⢔⠝⠁⠀⠀⣠⠴⠋⠀⠠⣲⠕⠋⠁⣀⣬⣾⡿
⢄⡀⠀⠀⠈⠛⠦⣄⡀⠉⠂⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠐⠈⠀⡠⠔⠪⠛⠋⠁⢀
⣦⣌⣉⠂⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣈⣥
⠀⠀⠉⠙⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⣁⣠
⠷⠶⢶⣤⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⣚⣋⡭⠥
⣉⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⢀⣀
⠓⠶⠶⠭⠥⠄⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠁
⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤
⠶⠶⢶⣒⡒⠬⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀
⠉⠉⠀⠀⠀⢀⡀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⣶⣖⣾⣿⡯⠷⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶
⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢄⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠋⠁⠀⠀⢀⡤⠖⠋⠀⡀⠄⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠢⢄⠀⠀⠂⢄⡀⢀
⢁⣠⣴⡚⠉⢀⣠⢖⠏⠂⠀⣠⠖⠋⠀⠀⢀⣴⠕⠀⠀⠀⠀⡄⢠⠁⠀⢸⠀⠀⠀⠀⡃⠀⠈⡄⢁⠀⠀⠀⠀⠨⣦⡀⠀⠈⠻⣶⣄⠀⠀⠹⡲⣄⡀⠈⢓⠯⣷
⡿⠟⢉⣠⣶⡯⠛⢁⢠⣪⠞⢁⠔⡡⠀⣰⡻⠫⡢⠂⠀⠀⡼⢀⡏⠀⠐⣼⡄⡇⠀⢠⣇⠂⠀⢹⡀⢣⠀⠀⠀⢔⠝⣽⣕⢄⠈⢮⡫⣷⣕⡄⡈⠛⢽⣶⣤⡉⠻
⣤⣾⡿⠟⠉⣠⢔⡵⠛⢁⡴⡻⠊⣠⣾⡟⡕⡵⡱⠀⠀⡼⡱⣼⠁⡀⡆⡇⣿⡇⠀⢸⢸⢰⢀⠈⣧⢎⢧⣆⢆⠈⢮⢪⢻⣷⣷⣄⠙⢮⡻⣟⢮⡢⣄⠉⠻⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠶⣶⣶⣶⣶⣶⡶⠶⠶⡶⢢⣶⠶⠦⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠾⠿⠋⠁⠀⠀⠠⠿⢿⣿⣿⣦⣤⣶⢃⣿⣛⣁⣸⣿⣿⡌⢿⣦⠄⡀
⠀⠀⠀⠀⠀⢀⠠⠄⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠐⠀⠀⢀⠈⠉⠁⠈⠉⠉⠉⠉⠙⠛⠓⠋⠉⠀⠉⠉⠓
⠀⠀⠀⠀⢰⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠲⣶⣺⣷⣄⡀⠀⡐⣡⣶⣦⡀⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠻⣂⡠⡄⠡
⠀⠀⠀⠀⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⣼⣽⣽⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠀⣼⣿⣿⡅
⠀⠀⠀⠐⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠴⠶⡤⠀⠛⠛⢰⣿⣿⡯⣿⣻⡌⠁⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣀⣴⡻⣿⣿⣟⣿⠃⠀⠂⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣷⣶⠟⠁⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣿⣷⣯⣽⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠋⠉⠙⠛⠛⠛⠿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡿⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⢰⡄⠀⠀⠀⠘⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣙⣋⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣻⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡐⠂⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠉⠉⠉⠉⠑⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠉⠉⠉⠉⠙⣄
⣹⣷⣶⣶⣶⣶⣶⣾⡅⠀⠀⠀⠀⠀⠀⠀⠿⢷⣶⢶⣾⣿⡾⠿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣶⣶⣶⣶⣾⡍⠀⠀⠀⠀⠀⠀⠀⠸⠷⣿⣾⣶⣶⣶⠿
⣶⢦⣼⠖⠿⢿⣷⡶⡆⠀⠀⠀⠀⠀⠀⠀⣶⣶⣯⣿⣽⣽⣷⣾⠆⠀⠀⠀⠀⠀⠀⢰⣦⣼⠿⠛⠿⢯⣤⣔⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣟
⠻⠏⠉⠉⠉⠉⠉⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠉⠉⠉⠉⠹⠟⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠿




⢀⡐⠀⠁⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠀⠀⠀⠀⠀⣤
⢨⣷⣶⣶⣶⣶⣶⣯⠁⠀⠀⠀⠀⠀⠀⠈⠟⢻⣿⣷⣶⣿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠸⢧⣤⣤⣤⣤⣤⡼⠗⠀⠀⠀⠀⠀⠀⠀⠞⠛⣿⣿⣿⢿⡟⠛
⣷⣾⣿⣿⣿⣿⣯⢶⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠾⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣶⣞⢛⣛⣛⣛⣶⣶⠀⠀⠀⠀⠀⠀⠀⢛⡻⢿⣿⣿⣿⣷⣿
⠻⠃⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛



⠀⠀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⢠⣌⣀⣀⣀⣀⣘⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠑⣄⡀⠀⠀⠀⠀⠀⠀⠠⣴⣀⣀⣀⣀⣀⣱⡄⠀⠀⠀⠀⠀⠀⠀⣠⡜⠀⠀⠀⠀⠈⣦
⣞⢙⣿⣛⣻⣻⣟⢙⡇⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⠿
⢿⡿⠿⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣯⣿⣛⣛⣛⣻⣿⣽⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⣿
⠘⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠛



⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⢤⣆⢀⣀⣀⣀⣈⣦⠄⠀⠀⠀⠀⠀⠀⠀⢤⣇⣀⣀⣀⣀⣰⡤⠀⠀⠀⠀⠀⠀⠀⠠⣎⣀⣀⣀⣀⣀⣘⡤⠀⠀⠀⠀⠀⠀⠀⢤⣎⣀⣀⣀⣀⡈⣦
⣾⡙⣿⣿⣿⣿⣟⣹⡆⠀⠀⠀⠀⠀⠀⠀⡚⢻⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⢰⡛⣿⣿⣿⣿⣿⡛⣷⠀⠀⠀⠀⠀⠀⠀⣬⣽⣿⣿⣿⣿⣿⣭
⣿⡿⠿⠿⠼⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠭⠭⠭⠽⢿⣿⠀⠀⠀⠀⠀⠀⠀⣷⡾⠯⠭⠭⠽⠿⣷
⣾⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡛⠙⠪⡓⢦⣴⡺⢟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠙⢦⣄⠈⠢⣽⢀⢾⡇⢹⡆
⠀⠀⠀⠀⢀⣠⡀⠀⠐⣏⢿⠪⣗⢦⣴⡫⠋⠓⠛⢉⣮⠟⠀⣸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠑⢝⢦⡀⠀⢠⣾⠋⠀⢰⠇⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠈⣿⣦⡤⠿⢃⣴⡟⠁⠀⣰⠋⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⣴⠿⠋⠀⣠⡾⠁⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⢁⣀⡴⠞⠁⠀⠀⠀⠀⠀⣠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⡀⠀⠀⢀⣠⣞⣡⣞⢝⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠉⠀⠈⠳⣍⡪⡳⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⢿⣜⢌⢷⡥⣤⣴⣚⣋⡭⠟⣒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣾⠟⠋⠙⣏⢎⣧⠀⠀⠀⠈⠉⠙⠒⠯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⣿⠋⠀⠀⠀⢹⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣻⡀⠀⠀⠀⣼⡏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣣⣓⠦⢴⡾⣏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠗⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢰⣮⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢖⡎⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣳⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡮⠭⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠭⠭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠩⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠔⣛⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⠽⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⣎⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠭⣟⡉

⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣭⣿⣷⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠠⠀⠄⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡈⢌⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⢀⣠⣤⡤⠤⠀⠤⠄⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀⢀⣠⣤⣶⣞⣿⣿⠿⠗⠛⠋⠁
⠀⠀⢠⡶⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢾⣟⣿⣿⡿⠟⠛⠉
⠀⢀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣳⡾⠟⠛⠉
⠀⢸⠁⠀⠀⠀⢠⣤⡄⠈⠀⠁⠀⠀⠀⠀⠀⠈⡘⠁
⠀⠈⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠆⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠢

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⢶⣶⢶⣶⠶⠶⣶⣴⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⠀⠀⣴⡞⠛⠛⠉⢉⣩⣿⣿⣿⣿⠿⢿⣋⣁⠀⠀⠀⣀⣤⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣿⣧⣤⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠉⣉⣿⣿⣿⣿⣿⣟⣉⢀⣠⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣤⣶⣿⠿⠛⠋⣁⣠⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢰⠀⠀⢠⠻⠋⠀⠀⠈⠉⣙⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⠿⠿⠋⠉⠁⠈⢉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⢸⠀⠀⣿⠀⠀⣀⣤⣶⣿⡿⢛⣩⣤⣿⣿⣿⣿⠿⣿⣿⣿⣤⣄⣀⣠⣤⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⢸⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠸⠀⠀⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠬⠿⠥⠴⠦⠶⠦⠀⠠⠚⠋⠉⠉⠙⠛⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠷⠀⠀⠀⠀⣀⠰⠶⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⢀⡴⠞⣩⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠹⠀⠀⠀⢀⡴⠋⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢟⣠⣾⣿⣿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣼⣷⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⣾⣿⠟⢻⣯⣍⣩⣭⣉⣩⣭⣭⣭⡉⠉⠉⣩⣭⣉⣹⠍⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠎⠁⣿⠀⠀⠀⠘⠀⣼⣿⡏⢴⣇⣉⣉⣀⣀⠉⠀⠀⠐⠒⠀⠀⠀⢀⣀⣀⣀⣀⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠀⣠⣄⠀⠀⣿⣿⣷⣿⠿⣿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠟⡿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣿⠀⣼⡇⣤⡄⢿⠿⢼⡿⠾⠿⠛⠿⠿⠿⠷⠶⠿⠿⠿⠷⠾⠿⠿⠿⠿⠛⣿⡏⠟⠛⠛⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⠀⠙⠃⣿⡇⠄⠀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠠⠌⠉⠉⠉⠉⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⣿⠀⠀⠀⣿⡇⣶⠀⠻⣷⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣆⠘⣿⡆⠀⠙⠀⠀⠀⠸⣿⣍⠳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⣼⣿⡇⢰⣦⡀⠉⠻⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷
⠀⠀⠀⠀⠀⠀⠛⠀⠈⣷⣿⣿⡇⢸⣿⠛⠿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⣰⠀⡉⠀⣻⣧⣿⣿⡘⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶
⠀⠀⠀⠀⠀⣿⠀⣁⠀⣹⣿⣏⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢠⡿⠁⢿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⣾⠃⠀⢻⣿⠠⠌⣿⣿⣿⣿⣿⣿⣿⡟⣦⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠇⠀⢰⡆⠀⠀⠀⠹⣧⡀⠈⢿⣿⣿⡟⢛⣿⣀⣿⣿⢿⣿⢿⣿⣿⣬⣉⣉⣉⣉⣉⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⣦⣀⣸⣇⠀⣀⠀⣤⠙⣷⡄⠀⢻⡿⢠⣿⣿⠛⠛⣿⣿⣿⣿⡿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⣿⣿⣼⣿⣿⣿⣾⣿⣿⣿⣿⣧⣄⣀⣼⣿⣿⣷⣀⡉⠻⠿⢋⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠳⣆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⠟⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡟⠁⠀⢸⣿⠀⠀⢸⣿⠀⠀⠹⣧⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⢻⣷⠄⠈⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠘⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡿⣁⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣧⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢀⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢶⣞⠛⠉⣉⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠓⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⠋⠀⣤⡄⠀⠀⣠⡄⠀⠙⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⢹⡇⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⠀⠀⣿⡶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⡇⠀⠀⠛⠃⠀⠀⠙⠃⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠉⢭⣭⣛⡛⠁⣬⣝⣻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⣷⡀⠀⠀⠀⠻⠗⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠳⠶⣾⡆⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠻⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠶⢶⣖⠒⣶⡦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣁⠤⠘⠃⠉⠀⠀⢸⣿⠁⠀⠀⠉⠐⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⡀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠋⡾⠥⠽⠶⠶⠶⠶⠶⠶⠶⢾⡟⠷⠶⠶⠶⠾⠷⠶⠶⠀⠙⠷⣤⣀
⠀⠀⠀⢀⣠⡴⠶⠛⠛⠉⠉⠁⠠⠠⠤⠄⠐⠒⠒⠒⠒⠒⠒⠒⢺⡟⠛⠛⠛⠓⠒⠒⠲⠶⠶⠶⠶⡦⠉⠳⣄⡀
⠀⢠⣴⠟⠁⠀⢀⣀⣀⡀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠙⠛⠛⣛⣛⣻⠶⠶⠶⠀⠘⣧
⠀⠀⢿⠀⠀⣪⡽⠶⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣶⣫⡿⠶⠶⣭⡂⠀⠀⠀⢸⡀
⠀⠀⠸⡆⠀⠈⢠⠀⠀⣤⠹⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣾⠀⠁⡄⠀⢠⡌⢳⢀⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠘⢤⡴⠟⢠⠇⠘⠛⠛⠛⠛⠙⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠳⣤⠼⠃⡼⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠐⠠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠠⠤⣀⢀
⠀⠀⠀⠀⣶⣶⣤⠤⢤⣤⣴⣾⣿⣿⢛⡿⣿⣿⣿⡿⠃⢀⣾⣷⢹⣿⣿⣷⣄
⠀⠀⠀⢀⡀⣀⠀⠀⠉⠉⠉⠉⣉⠉⡛⠛⠈⠉⠉⠀⠀⠘⠛⠛⠻⠻⠿⠿⠿⠏⠿⠂
⠀⠀⠀⠾⠿⠿⠀⠀⠀⠀⠀⠸⠿⢿⠿⠆⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠈⠁⢀⣀⣀⠀⣰⣿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⠟⣇
⠀⠀⠠⠆⢠⣶⣌⠉⢙⣛⣀⡀⠀⠀⠀⠀⠀⢀⢠⣿⠰⢩⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠃⡇
⠀⠀⠀⠀⣀⣘⣿⣶⣶⣾⣋⣩⣽⣿⣿⣿⣶⣶⣾⣿⣧⣆⣼⣤⣤⣤⣤⣴⣶⣶⠶⠶⠾⠿⠷⠒⠂
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠖⠒⢲⣶⡖⠒⣒⡒⠒⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠇⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠀⠀⠀⢸⣿⡇⠘⠿⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣤⣤⠀⠀⠀⣾⣿⠄⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⣀⡀⠀⣼⣿⠏⢀⣴⣦⣾⢷⡄⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣿⡋⢳⣾⡿⠷⠿⠿⠷⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣟⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⠿⠿⡀⠛⠛⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠁⠀⠀⢳⡀⠀⠀⠀⣼⣻⡆⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣯⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠁
⠀⣀⣀⣤⣴⣶⣿⣿⣿⠟⠋
⢹⣿⣿⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⠭⠭⠭⢭⣭⣭⣤⣤⠤⢤⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⣇⠀⢀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠉⠙⠳⠮⣕⡢⢄⣀
⠀⠀⠀⢀⢠⣾⣶⣦⣤⣀⡀⠀⠉⡷⢀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠶⢶⣦⣤⣄⡀⠀⠀⠀⣤⣀
⠀⠀⠀⣿⡆⣿⣿⣿⣿⣿⣿⣿⡶⣼⢛⣳⡄⠀⠀⠀⠀⠈⠻⢞⢭⡓⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣀⠀⠨⠓⣦
⠀⠀⠀⣿⣿⢩⣽⠛⠀⠀⠀⠀⢠⣻⣿⣿⣿⡔⣦⡀⢀⠀⠀⠀⠙⠋⣤⣾⣏⡒⢀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠘⠓⠀⡀
⠀⠀⠀⣿⣾⢈⣿⣷⣦⣄⣀⠀⢨⣟⠺⣿⡿⣷⢹⣿⣾⣧⡀⠀⠀⠀⠈⠉⠀⠁⠘⠓⠀⠀⢹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⢹⣿⢼⡿⠿⠿⢿⣿⣿⡞⣿⢹⡚⣸⣿⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣶
⠀⠤⠴⣶⣿⣾⣿⣿⣷⣦⣌⡻⣷⣿⣬⣿⣾⣿⠀⠸⣿⣿⣿⣿⣄⠲⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣦⣵⠿⢿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣷⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠙⣛⣭⣴⣶⣶⣶⣦⣅⠛⣿⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣤⣼⣿⣶⣦⣤⣤⣈⣙⣛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⠟⠛⣛⣛⣋⣉⣩⣭⣤⣼⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⠴⢄⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠒⠒⠁⠀⢀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠔⠀⢁⠤⠒⠉⠉⠁⠀⠈⠉⠉⠒⠦⡀⠀⠀⠈⠓⠢⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡁⠀⢀⠔⡁⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡎⠀⠀⠀⠀⠀⢶⠀⣳⠤⣧⠃⠀⠀⠀⠈⡆⠀⢀⡀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡉⠀⠀⠀⠸⠀⠀⠀⠀⠀⢶⠋⠁⠀⠀⢈⡵⠀⠀⠀⠄⠃⠀⠈⠁⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠐⡄⠀⠀⠀⠀⠈⡆⠀⠀⠀⡞⠀⠀⡀⡄⠂⡇⠀⠤⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠙⣄⠐⣀⠀⠀⢠⠀⠀⢰⠀⠠⠐⠆⢀⡜⠀⠀⠀⡔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠤⣁⠀⠀⠀⠑⠢⢄⠒⠈⢀⡄⡆⠔⠃⣀⠔⠋⠀⣄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠔⠀⠉⠀⢠⣀⣄⣁⣁⣸⠉⠀⠂⠀⡠⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⣄⣠⣄⣀⣸⡀⠁⠉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠊⡵⣻⠟⣚⡿⣆⠑⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣀⢤⡮⣊⠔⠪⠔⡙⢮⡃⠶⣠⡄⢉⡉⡉⠉⠉⠉⠉⠉⢉⡁⠐⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣀⢤⡂⠍⠊⠕⡨⠔⣩⢔⡩⢒⡡⢈⡩⢀⠰⢋⡱⢖⠲⢀⠀⡰⢎⠉⢉⠝⣋⠔⡊⠙⠴⣪⢕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⣺⠟⢁⢠⣀⡀⢀⡡⢒⡿⠡⠋⢉⣙⣮⣕⣈⣥⣊⡕⣪⣕⣞⠐⣳⢞⡝⠋⠙⢺⡔⣨⣖⡩⣒⠴⠉⠻⡝⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣾⠁⠠⣼⠚⠁⡇⢀⡪⡞⢁⠇⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡉⢻⣷⠀⢇⠀⠀⠈⣙⠗⠁⠀⠓⠘
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠹⢷⢄⡀⠉⠐⠗⣄⠡⠁⠀⠀⣜⠀⢥⠶⠶⡄⠀⠀⠀⠀⠀⡤⠌⠥⡀⡇⢸⣹⠀⠈⠲⠤⠎⠀⠀⢀⠔⡴⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠔⡠⡉⢛⠳⡒⣦⣤⣎⠝⡇⣼⡇⡸⠀⠀⠉⠁⠀⠀⢀⠀⠈⠁⣆⡖⠻⠀⠼⣿⠴⠷⢟⠶⣶⣶⣬⣵⡾⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠥⠌⢤⠁⢀⠬⣭⣀⠈⢻⠳⢒⡶⠖⡳⢯⡾⢬⡬⠶⠶⡥⠧⠶⣦⠚⠀⣀⣠⣄⣮⣽⣭⡥⠵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⢊⠤⠊⡉⠿⢊⠡⣐⠟⣂⠅⢂⠡⢐⡡⠄⢡⠀⠸⠅⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣊⠥⢒⠩⢐⡪⠔⢸⠋⢣⠀⢊⠥⢂⠥⢒⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠔⣊⠅⢊⠥⠒⠃⡌⠀⠘⡄⠑⣊⠅⢊⠥⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡩⠔⣊⠡⠔⣊⠁⠇⠀⠀⠇⠨⠔⣊⠥⢐⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠐⡩⠔⣂⠭⡀⢰⢀⠀⢀⢠⠐⡩⠔⣊⠥⢔⠂⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⠄⣴⠁⠀⠀⠀⠀⠀⠀⢀⣠⣬⠕⢊⡡⢞⠀⠀⠉⠒⠩⠥⠀⣸⠥⠂⣠⢔⡠⠂⢀⡤⠀⣀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠤⠛⠱⠖⣒⠶⣚⠝⠋⣉⠤⠊⣡⠔⢊⡱⠦⣄⣀⣀⡠⢖⡡⢒⠽⢊⡡⠔⢊⡡⢒⡩⢖⡩⢒⡡⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠊⠁⠐⠉⠐⠋⠠⠚⠁⠊⠁⠐⠁⠠⠚⠁⠒⠁⠐⠉⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠻⣷⡀
⠀⠀⠀⢠⣾⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠠⠻⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⠈⠀⠰⠄⢀⠀⡀⠀⣄⣀⡀⢠⠚⠆⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠋⠂⠱⠎⢿⡟⠉⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠸⡇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠹⡅⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢀⣼⠃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣼⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣉⣉⣉⣉⣉⣉⣉⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⢿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠉⠉⠛⠓⠦⠀⠀⠀⠀⢀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠑⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠒⠋⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠲⠶⠤⠄⠀⠀⣀⡀⠀⠀⠀⠄⠰⠖⠀⢀⣀⣤⠶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠙⠛⠓⠶⠶⠶⠶⠤⠤⠴⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣙⡓⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣤⡤⠴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠈⣉⡉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠶⢤⣬⣉⣉⣐⡒⠒⠒⠒⠒⠒⠒⢂⣀⣀⣀⣠⣤⡤⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠲⠶⠤⣬⣉⣉⣉⣉⣀⠀⠀⠈⢉⣈⣉⣉⣠⡴⠶⠞⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣤⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠈⠉⠉⠉⠉⠉⠉⠉⢉⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡾⠿⠿⠿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠁⠀⢀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠋⠀⢀⣤⠶⠚⠛⠉⠉⠉⣿⠉⠉⠉⠛⠳⠦⣄⡀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⣿⣆
⠀⠀⠀⠀⠀⣀⣠⣿⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⣿
⠀⠀⠀⣠⣾⠟⠋⠉⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠘⠿⣷⣶⣦⣤⣄⣀
⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣷⣦
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⣠⣿⠟⠉⢀⣀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⣀⡀⠈⠙⢿⣆⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⣀⣀⣠⣿⠇⠀⡼⠋⠉⠙⣆⠀⢹⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟⠀⢰⠟⠉⠉⢳⡀⠈⣿⣆⣀⣀⣀⣿⡇
⠀⠀⠈⠛⠛⠛⠻⣿⡄⠀⢧⡀⠀⣠⡟⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣇⠀⠸⣄⠀⢀⣼⠃⢀⣿⡟⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠉⠉⠉⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠉⠉⠁⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣶⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠠⠄⠀⠀⢸
⠀⠀⠀⠀⢰⠉⠑⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⣶⣶⣄⡞⢁⣤⡀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⡣⠞⡿⠋⢀⣀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡎⠘⡆⠳⣤⠶⣻⠉⠉⡇⣾⣿⠇⠀⠀⠀⠸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢳⣄⣞⡤⠽⠀⠀⣿⣿⣿⠾⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢀⡅⢠⠤⡄⠀⠀⠀⠀⠀⣾⡄⣶⠉⠁⠀⠀⠀⠀⣟⢻⣿⡇⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠨⡀⠷⠀⠀⠀⠀⠀⠀⠿⠄⠩⠤⠞⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠶⠶⠶⠾⠟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠈⠀⠀⠀⠈

⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⡶⠶⠦
⠀⠀⠘⣠⣾⣿⣿⠏⠀⠈⠉⠛⠛⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣼⣿⣿⣿⣿⢶⡆⢐⣒⠀⣲⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣿⣿⣿⣷⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⡜⠁⠈⠉⠤⠉⠉⡽⠛⠋⠛⠛⠙⠙⠉⠋⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⠟⠛⠛⠋⠁
⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣀⣀⣀⡀⠙⢤⣀⡀
⠀⠀⠀⠘⠻⠿⣥⠤⠖⠊⠁⠀⠀⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠴⠦⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣉⣡⡤⠴⠖⢲⠀⣶⠲⠦⢤⣍⣉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡥⠖⠋⠉⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⠀⠉⠙⠓⠦⣌⡙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠐⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠘⠶⠶⠶⠶⠶⠶⠶⠶⠾⠻⠶⠀⠈⠙⠒⠒⠒⠶⠶⠤⢤⣄⣀⡀
⠀⣠⠴⠶⠖⠚⠋⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠉⠓⠦⣄
⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢞⡭⠿⠾⠿⢭⣳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⡭⠿⠿⠿⢿⣦⣄⠀⠀⠀⠈⢧
⢻⠀⠀⠀⠀⠀⠀⠀⣼⣷⢋⡖⠋⠉⠙⠳⡌⢧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⣡⠞⠋⠉⠙⢦⡙⣟⣆⠀⠀⠀⢸
⠈⠳⠤⣤⣀⣀⡀⠀⡟⡇⣿⠀⠀⠀⠀⠀⢹⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡃⡏⠀⠀⠀⠀⠀⣷⢸⢻⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠈⠉⠉⠃⢷⡹⣄⠀⠀⠀⣠⠟⣼⠙⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠾⠈⣇⠳⣄⠀⠀⢀⣰⢇⡞⠘⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢮⣍⣛⣫⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⣛⣩⠵⠋

⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠀⠀⠤⠤⠤⠤⡀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⢄
⠀⠀⠀⠀⠀⠀⡔⠒⠒⠒⠒⠒⠒⠒⠒⠒⢢⠀⢸⠀⠀⠠⠀⢀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄⠀⡇⠀⢸⠀⠠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢈⠀⢸⠀⠀⠀⣠⠀⠀⣤⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⠀⢸⠀⠀⠘⠀⢸⠀⠀⠸⠃⠀⠀⠘⠷⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⣤⡀⠁⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡆⠀⢰⡆⠀⠀⢸⠀⢸⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⡇⠀⢰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠃⣀⠈⠃⠀⠀⢸⠀⢸⠀⠀⠀⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⠈⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢸⠀⢸⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀⠸⠀⢸⠀⠀⠐⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄⠀⡇⠀⢸⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠤⡀⠀⢸
⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠊⠀⠀⢠⠀⢸⠀⢀⠔⠉⠉⠋⠉⠲⠄⠀⡇⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⢀⡏⢀⡀⠀⠀⢀⡀⠸⡆⡇⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆⠙⠃⠀⠁⠘⠋⢠⠇⡇⠀⠁⠀⢸⠀⠀⡇⠀⢀⣀⠀⠀⣀⡀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠙⢄⡀⠀⡀⠀⡠⠊⠀⠃⠀⡄⠀⢸⠀⠀⡇⠀⠈⠁⠀⠀⠈⠁⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⢻⠛⠉⠉⢻⠀⠀⠀⠀⠀⠀⢸⠀⠸⢀⣀⣀⣈⣉⣉⣉⣀⣀⣀⠇⠀⡇⠀⢸⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠒⢲⠛⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠁⠀⠈⠢⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣁⣁⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢰⢱⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⡇⠀⠰⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⡀⠀⢾⠁⠀⠀⠀⠀⢰⠊⠙⢃⢀⢰⢰⢸⢸⠀⠤⠈⣤⠀⠀⠀⠀⠐⠒⡆⠈⠈⠁⡆⢰⠀⡇⠀⢸⠀⠂⢪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡤⢴⠟⠀⠀⠀⠀⠈⠉⠛⠒⠻⣌⣈⣈⣸⢸⠤⠤⠤⠀⠀⠀⠀⠀⠉⠉⠳⠤⠧⡄⠁⠘⠀⡇⠀⠘⠀⠐⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢧⡤⠌⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣦⣽⣶⣦⣭⣮⣶⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣴⠾⠟⠛⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⣠⠖⠋⠉⠉⠉⠻⣿⣷⣦⣭⣙⠻⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣵⢿⣿⠏⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⡁⠀⢀⡀⣀⡀⠠⠽⠛⠉⠉⣁⡤⠂⠀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠆⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⠋⢷⡀⢀⠀⠀⠀⠀⣀⣤⢶⣿⣿⣶⡶⠾⣻⠿⣿⡇
⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠙⠓⠀⠀⠠⠔⠊⠁⠀⢸⣿⣿⡟⠀⢠⡇⣼⣸⠇
⠀⠀⠀⣠⡏⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⣼⡿⢾⡷
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢡⡆⠖⠋⠀⠀⠀⠀⠀⣰⣷⡞⣹⣿⡄⠀⠀⠀⠀⠀⠀⠘⢻⠟⠁⠀⢰⣿⡿⣾⠁
⠀⠀⠘⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠑⠚⠃⣀⡀⠀⠀⠀⠤⢰⡿⠻⣷⡡⣶⣿⡀⠀⠀⣀⣠⠔⠊⣀⣠⣤⣶⣾⣿⣷⠤⠂
⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⡉⠀⠀⠀⠀⠀⠀⣸⣸⣿⣏⡀⣿⣿⣣⣾⣿⣿⣿⡿⠿⠟⠛⠉⠉
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⣄⡀⠙⢿⣿⣿⣷⡄⠀⠀⢀⣀⣼⣿⣿⢓⣼⣿⣿⠿⠟⠛⠉
⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠙⠛⠓⠒⠛⢛⣿⣿⣶⣿⣿⣿⣿⣻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠁
⢀⣀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢀⡀
⠀⠈⠙⠲⢤⣀⠀⠀⠀⠠⣄⡉⠲⢄⠙⠢⣄
⢄⡀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠉⠲⢤⡉⠂⠈⠑⢄
⠤⣄⣁⢦⣤⣀⠀⠀⠈⠙⠳⠦⣄⠀⠈⠓⠄⢀⡀
⠀⠀⠀⠉⠓⠛⠙⠒⠦⢄⡀⢀⣈⠙⠻⠿⣶⣤⣉⠲⢄⡀⢀⡀
⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢄⣀⡈⠉⠒⠢⢄⡉⠛⠷⢦⣈⠐⠉⠢⢄
⠤⠬⢍⣉⡙⠛⠓⠶⠦⠤⣤⣀⡉⠉⠒⠢⠤⠀⠀⠐⢤⣌⡑⠢⠑⠢⢁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀
⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⣒
⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠂⠐⠒⠒⠒⠩⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⠀⠄
⠤⠤⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⢊⣉⡉⠤⠀⠈⠉⠀⢀⠤⠔⠂
⠔⠒⣒⣀⡀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠟⠒⠉
⠉⠉⠁⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠁
⠀⣀⡤⠴⠒⣊⡩⠥⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠔⡀
⠀⣤⡶⠞⠋⠁⠀⠀⠀⠀⠀⣀⡤⠒⠉⢀⡠⠖⣩⠔⠋
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠐⠊⠁
⠀⠀⢀⡠
⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠇⡟⢳⢼⠋⢸⡏⠁⡟⢻⠀⢸⠂⢸⡇⣿⣸⢸⡋⠱⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⡆⡟⠋⢸⡉⢸⡏⠁⣇⣸⠀⢸⡀⢸⡇⡏⣿⢸⡋⢠⣝⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠈⠉⠈⠉⠁⠉⠉⠀⠈⠉⠉⠁⠁⠈⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣤⡀⠀⠀⣿⠉⢳⡀
⠀⠀⠀⠀⢺⡉⢹⡄⠀⢸⡇⠈⣧
⠀⠀⠀⠀⠸⡇⠀⢷⠀⠈⣷⠀⢹⣆⣀⡀
⠀⠀⠀⠀⠀⢿⡀⠸⣧⡤⠞⣧⣀⣿⣽⢷⣄
⠀⠀⠀⠀⠀⣨⢷⣠⣿⠀⠀⢈⣭⠟⠋⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠐⣅⣀⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠈⠫⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡟⠉⠉⠙⣦⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣇⠀⠀⠀⠈⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⣄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⣄⠀⠀⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣞⠃⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣾⠇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⣶⡴⠋⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⢀⣼⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠤⢤⣤⣤⣤⠴⠶⠋⠀⠙⣦⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠲⢽⡶⠶⢤⡤⠴⠞⠋⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣥⣀⣀⣀⣀⣠⡴⠞⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠒⠄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠈⠂⢄⠀⠀⠈⠠⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠈⠂⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠒⠒⠈⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠀⠠⠤⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⡀⠤⠐⠊⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠔⠀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣠⠞⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⡠⠖⠉⠀⡠⠂⠀⠀⢀⠞⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢀⡤⠚⠁⠀⢀⠔⠋⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⣿⣷⣶⣾⣾⡿⣾⣶⣶⣾⣿⣾⣾⣶⣶⣶⣶⣿⣶⣾⣷⣶⣾⣶⣶⣿⣶⣷⣾⣷⣿⣶⣶⣶⣾⣿⣶⣾⣷⣶⣶⣶⣾⣷⡷⣷⡾⢾⣾⢷⣶⣷⠾⠶⡿⠶⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠉⠉⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⠀⠘⣆
⠀⠀⠀⠘⠧⡤⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⣤⠼⠀⠀⠀⠀⠀⠀⣠⠴⠁⠀⢀⣀⣀⣀⣀⣀⣀⡇⢀⣀⣀⣈⣧⠀⠘⢦⡀
⠀⠀⠀⠀⠀⡟⢛⣛⣛⣛⠛⣛⣛⡛⢙⣛⣛⣛⠛⢻⠀⠀⠀⡤⠒⠚⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠉⠓⢦
⠀⠀⠀⠀⠀⡇⠻⠤⠤⠞⠀⠰⠶⠆⠘⠧⠤⠼⠃⢸⠀⠀⢸⠁⠀⠀⢀⡴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠑⡶⠶⢶⡶⠶⠶⠶⠶⠶⢶⠶⠶⢶⠋⠀⠀⠘⠦⠤⠤⣟⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡇⠀⠀⠀⢸⡦⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠳⣤⠼⠁⠀⠀⠀⠀⠀⠘⢦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⡤⠞









⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣧⢸⣿⣿⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠛⣻⣿⢷⡀⠀⠹⣆⠁⢻⡄⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡘⢿⠟⢯⢻⡄⠀⠹⣆⠀⢿⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢷⡹⣆⠀⠹⣆⠈⢿⡀⠀⠈⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⢷⡽⣆⢀⣹⣧⡈⣧⠀⠀⠀⢻⣝⡳⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠻⣽⣿⠟⠋⠉⠙⢷⡀⠀⠈⣿⠉⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠹⣽⣆⠀⠀⠀⠈⠻⠶⠞⠋⢀⣠⣾⡿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢦⣤⣤⣾⠟⠀⠀⠀⡀⣠⣤⣶⣾⡿⠟⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣄⣀⡀⠀⣀⣀⣴⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⣠⣶⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠾⠿⠿⠿⠟⠛⠉⠁⠀⠀⢀⣀⣀⣤⣤⡶⠟⠋⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠶⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢦⣤⣤⣤⣤⣶⠾⠛⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡤⠖⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣸⣇⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⠇⣀⣤⣤⠤⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢛⡟⠀⠀⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢸⡆
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣴⠟⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣴⠏⠀⢿⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠃⠀⠀⠘⣧⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣼⠃⠀⠀⠀⠀⠘⢷⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡏
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠙⠳⣦⣄⣀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⢀⡿
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⣠⡟⠁
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡀⠲⠖⠛⠛⠉⠙⢻⡏⠉⢹⡏⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⠰⢴⣶⣶⣶⣶⣿⣷⣤⣼⣧⣤⣀⣇⠐⣠⡄
⠀⠀⠀⠀⠀⠠⣝⠲⢝⡻⢿⡏⠹⠿⠛⠛⠉⠉⠉⠉⠉⠀⠀⠈
⠀⠀⢢⡀⠀⠀⣼⡟⢦⣌⡑⠒⠭⠙⠒⠦⠤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣦⣾⡟⠃⠀⠈⠿⢶⣤⣤⢀⠀⠀⠐⠀⠩⠉⡛⠛⠛⣻⣿⣿⣶⣔⠆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠘⢿⣷⣼⣄⠀⠀⠀⣨⣝⡻⣾⣷⡦⠀⠀⠀⠀⠀⢠⡹⠿⣿⡿⢛⠯⣤⣰⣤⣷⡿⠂⡄
⠀⠀⠀⠀⠀⠈⢻⣿⣭⡀⠀⠀⣿⣟⣃⠀⠉⠗⡞⢁⡄⣤⠴⠐⠓⠲⠿⣿⣿⣂⣀⣤⣤⣨⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣀⣹⡟⠙⠀⢰⣦⣙⢀⣼⣆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⡇⢀⠀⢼⣿⠧⠀⠉⣇⠛⢻⢛⣛⠛⠍⠉⠁⠒⠐⣤⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⣿⣷⣤⣦⣀⠀⠉⢁⣀⣸⣀⣠⣤⣴⣶⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠻⠿⢝⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠛⠿⠃⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠸⣿⠄⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣄⡀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⣴⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⢀⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣀⣀⠈⠀⢀⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⣄⡀⠀⠀⠠⣾⣍⡙⠿⠃⠈⢽⣻⣯⣤⣉⡙⢒⠦⢄⡀⠀⠀⠀⠀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢈⣙⣿⠿⠶⠒⢒⢹⣿⠛⣿⣿⣽⣟⣶⣹⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠾⠛⠷⣏⣳⣔⡉⠉⠉⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠠⠼⠷⣿⠿⠟⠓⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⠿⣋⠆⠀⠀⣸⢿⣾⣿⣿⣶⡄⠀⠐⠻⠿⢿⠷⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⡡⠀⣈⣭⣴⣶⡶⠿⠿⠛⣛⣙⠛⠻⣿⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⡴⣶⢺⡀⠀⠀⠀⣀⡤⠖⠂⠀⢻⡇⢸⠁⠐⠟⠉⠉⣁⡤⠖⢚⣉⠭⢝⡏⢀⡟⠠⣀⠀⠀⢀⡿⠤⣤⡄
⠀⠀⠀⠀⠀⠘⠆⠈⠀⠁⠀⠀⠋⠁⠀⠀⠀⠀⠀⠙⠚⠓⠒⠒⣚⣭⣤⣶⠾⠿⠿⠿⠛⠒⠉⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢧⡀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢴⠦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⠀⠁⢀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠈⠻⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⡾⡆⢰⠆⠀⣠⠀⠀⠀⢠⡶⠒⠀⠀⠹⣶⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢻⡟⠀⠀⠀⠀⠀⠀⠸⣆⣐⡆⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⡤⠖⣋⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠂⠀⠀⠉⠀⠂⢄
⠀⠀⢀⡠⠴⠚⠋⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⣠⠖⠁⠀⠀⠀⢀⣀⣤⠤⢤⠶⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⡇⠀⠀⢠⣖⠨⠿⠗⠒⠒⠉⠉⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠙⡴⠚⠉⠀⠀⠀⠀⢀⣀⣀⡀⢠⡤⠤⣐⠊⠀⠀⠀⠀⠀⠀⢠⠃
⣾⠀⠀⠀⡤⢶⣾⡯⠭⠥⠲⠆⠒⠂⠀⠀⠙⡆⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⡀⠀⠀⡀⠠⢰⡀
⠹⣦⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⡼⠁⠀⠀⣀⡠⢤⣶⣒⣚⣉⡭⠥⠔⠈⠉⠲⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠒
⢻⡀⠐⢉⡥⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡼⣫⡟⠀⠀⢀⣤⣤⣲⡖⢒⠿⠛⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⠀⢻⠀⠀⢰⠟⠀⠀⠉⠙⡏⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠎
⢸⠀⣀⣐⣚⣉⣤⠤⠤⠤⠤⠧⠤⣤⣀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⡔⠃⠀⠈⢢⠀⠀⠀⠀⠀⠀⠌
⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⡈
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⠂⠀⠀⠀⠱⠀⠀⠀⠀⠀⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠑⢄⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⠀⠀⠀⠀⠼⠤⠤⠤⢶⠃
⠀⠀⠈⡟⠋⠉⠙⠉⠉⠙⠋⠁⠛⠏⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣀⣠⣬⣽⡃⢆
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠐⢂⣐⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠒⠒⠒⠶⠶⠒⣒⡂⢊
⠀⠀⠀⣡⠀⠈⠙⠛⢉⣉⣽⣭⡭⠆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠒⠒⠒⣛⣿⣟⡃⢎
⠀⠀⠀⡳⠈⠉⢉⣉⣉⣉⣶⣲⣷⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠶⠖⠒⢛⣛⣛⠃⢂
⠀⠀⠀⠹⣂⠈⠉⢭⣤⣤⣴⡖⡦⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠛⠛⣻⠟⡴⠁
⠀⠀⠀⠀⠉⠳⡖⠶⠶⠶⣒⢺⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢶⠶⠶⣦⠴
⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣷⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣅⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠒⠢⡀⠀⠀⠀⠔⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠰⠂⠒⠠⠄⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣀⠤⠴⠶⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠒⠀⠀⠀⠈⢢⡀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡴⠋⠁⠀⡀⠀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡇⠀⠀⢸⠀⠀⠄⠀⠀⠀⠊⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⠀⠄⢰⠀⢴⠄⠀⢐⠀⠀⠙⠄⠀⡇⠀⠀⢸⠀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠃⠀⠀⡇⠀⠀⢸⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠠⠀⠀⠀⠄⠈⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠙⠺⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠘⢄⡀⢀⠀⠀⢀⣰⡀⠀⢀⡂⠀⣀⠀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣯⠊⢻⣿⣿⣿⠸⠀⡇⢹⢸⣿⣿⣿⠟⠀⢰⢿⣿⣿⠟⣴⡿⣫⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡙⢿⣷⡀⠹⣟⣿⠀⠁⠁⢸⢸⣿⣿⡏⠀⢠⠏⣾⡿⢣⡾⢋⣾⢟⣫⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣆⠙⢿⣄⠙⡞⣇⠀⠀⠀⢸⣿⣿⠀⠀⠈⢠⠋⡴⢋⣵⢟⣵⢟⢽⡯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣙⢷⣄⠙⢦⡈⠘⠄⠀⠀⠘⢻⠇⠀⠀⠀⠀⠊⡠⢋⠴⠋⠀⠐⠝⣋
⠀⠀⠀⠀⠀⠀⠀⢨⣁⠉⠛⠿⠿⣇⡈⠳⢄⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠠⣬⣍⣒⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⣁⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠨⡥⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⠠⣦⠀⠀⠀⠀⠀⠐⠒⠭⠽⢷⣞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠶⠶⠶⠤⠀⠀⠀⠀⠈⠟⠋⠙⣈⠀⣡⠀⠀⠀⠀⠀⠀⠨⠭⠽⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⠸⠟⠟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠭⣙⡓⠶⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⢦⣈⢷⣦⣄⡀⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠐⣋⢀⣠⡶⣀⠔⡀⢀⡴⠁⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠹⣄⠙⢷⣽⣿⣿⣷⣦⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⢟⣭⢞⣵⣞⣵⠟⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠘⣎⣆⠘⢷⣄⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⡷⣛⣵⣿⣿⡿⠃⣴⠃⡼⠀⠀⡿⠀⣾⢠⠀⡄⠀⢹⣞⣧⠈⢻⣷⣌⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⢁⣼⣟⣼⢁⡾⢸⡇⣿⣿⢸⠀⣷⢀⢸⣿⣿⣷⡀⡹⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠄⠀⠺⣿⣿⣿⠻⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣦⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠁⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠲⠶⠤
⠀⠀⠀⢀⣿⣆⠈⠉⠉⠐⠒⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⡇⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⢠⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⢧⣸⣿⣷⣦⣄⡀⠀⠀⠀⠀⢸⣿⠟⠳⣄⠀⠀⠀⠰⡇⠀⢸⡿⠏⢀⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⣛⣋⣩⣥⣼⡷
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠿⣶⣤⣀⢸⡟⠀⠄⠛⣷⡀⠀⠷⣤⣤⣤⣤⣤⣥⣤⡤⠤⠶⠶⠶⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣧⠀⠄⡐⢿⣿⣷⣄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⣩⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⡀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠘⢿⣿⣷⣄⣀⠀⠀⠀⠀⠀⡄⠀⢹⣿⣷⣤⣀⠀⠀⠈⠛⠛⠀⢀⣠⣶⣿⣿⡿⠃⠀⠀⠀⠁⠀⠰⣾⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣶⡶⠂⠀⠀⠀⠙⠿⣿⣿⣇⣷⣶⠆⠐⢻⣯⣵⡿⠟⠋⠀⠀⠀⠀⢘⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⠁⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⡀⠉⠈⣤⣤⣤⡄⠀⠀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠋⠀⠂⠀⣠⣴⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿⣿⣄⠀⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠈⠈⠀⠀⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⠿⠦⣿⣿⣿⣿⠘⠛⢻⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⢻⣿⣿⣿⠀⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒
⠀⠀⠀⠀⠀⢾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠛⠋⠁⢸⣿⣿⣿⠀⠉⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⣤⣾⣿⣷⣄⠀⠀⠀⠀⠀⢿⣿⣿⡁⠀⠀⠀⠀⠘⡿⠛⠁
⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣦⣤⣄⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠙⠻⠿⠿⣿⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣆⣤⣠⡶⣾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣿⢿⣷⣴⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈






⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⡀⠀⢀⣀⠀⠀⢀⡀⢀⡀⢀⡀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⢠⡄⠙⣶⠀⠀⢸⡷⠀⢠⡤⠈⢳⡄⠀⢀⣀⠘⣷⠀⠀⠀⢹⣷⢤⣴⡏⠀⣿⡇⠘⣷⠤⣤⡿⠀⢠⡴⠀⢙⡶⠀⢠⣤⠈⣷
⠀⠀⠀⠀⠀⢸⠀⠀⣠⣤⣤⡿⠀⠠⣿⡁⠀⢠⣤⣤⣾⠃⠀⠸⠿⢶⡛⠳⠀⢸⣟⠁⠀⢸⡇⠀⠻⠁⢸⡇⠀⢨⡇⠀⢀⠀⢠⣾⡃⠀⢠⣤⣤⣾⠃
⠀⠀⠀⠀⠀⠈⢦⡀⠉⠀⢀⣽⠀⠀⣠⣿⣀⠈⠁⠀⣸⣧⡀⠀⠀⣰⢿⡀⠀⠀⣿⠀⠀⣸⣧⡀⠀⢠⣿⡇⠀⢸⡇⠀⢻⣧⠀⣸⣧⣀⠈⠁⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠛⠛⠋⠀⠉⠛⠛⠛⠁⠀⠙⠛⠛⠉⠈⠛⠛⠛⠋⠛⠛⠋⠈⠛⠛⠋⠀⠙⠛⠋⠙⠛⠛⠁⠛⠋⠀⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡴⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡈⠙⠧⣄⢀⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠉⠲⣄⡈⠙⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠳⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠴⠒⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⡀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⡼⠁⣠⠞⠋⠉⠉⠉⢉⣉⣉⠉⠉⠉⠉⠙⠳⣄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿⣾⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠃⠀⠀⢀⡴⠚⠉⠉⠉⠙⠳⢦⡀⠀⠀⠘⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠀⠀⢠⡏⠀⠀⠠⣏⣹⠄⠀⠀⠹⡄⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⠀⢠⣦⠀⠈⠁⢠⣤⠀⠀⡇⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢸⡀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠞⠁⠀⠀⠀⡇⢸⡇
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⠀⠈⠉⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠈⣇⠈⢧⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀⡾⠁⡼
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠳⢄⣉⣛⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⡤⠞
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇
⠈⢧⡀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣸⠁
⠀⠀⠙⢦⣀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⠤⠶⠖⠒⠛⠉

⣿⣭⣭⣍⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⠿
⣿⣿⣿⣿⣿⣿⠷⠶⠶⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⣶⣶⣶
⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣭⣭⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣽⣯⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿
⣯⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠛⠛⠛⠛⠉⠙⠉⠙⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐
⣟⡛⠛⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⣒⣲⣶⣾
⣿⣿⣿⣛⣛⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣻⣿⣿⣿
⣛⣛⣉⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠿⠿⠿⣿
⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶
⣿⣿⣿⣛⣛⣛⣛⣉⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣚⣛⣿⣿⣿⣿
⣷⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⠛
⣿⣟⣋⣉⣉⣉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣩⣽⣿⣿
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣩
⣿⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶
⣿⣿⣿⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿
⣿⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠻⠿⠿⠿
⣿⣯⣭⣭⣭⣭⣭⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣬⣭
⣓⣒⣒⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠶⠾⠿
⣿⣿⣿⣛⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣼
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣮⣿⣿⣿⣿⣿⣯⣭⣴⢲⣖⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢈⣼⢟⣻⡿⠛⠛⠛⠛⠛⢿⣿⡿⢸⣿⣿⣉⣉⡱⠂⡀⠐⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠈⠤⠾⠿⠵⠿⠭⠤⠤⠤⠤⠤⠤⠾⠿⠧⠴⠶⠟⠛⠛⠀⠀⠀⠀⠠⠤⠤⠌⣀⣠⣀⣤⣦
⠀⠀⠀⠀⣀⡠⠤⠼⢟⡓⠒⢂⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠠⢄⣀⣀⡀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉
⢀⣠⣴⣮⣤⣤⣴⣾⣿⠿⠶⢶⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⡿⠿⠿⢿⣿⣿⣿⣛⣛⣛⣓⠒⠒⣚
⣸⣤⣾⣿⣿⣿⣿⠋⣴⣾⣷⣦⡙⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣰⣿⣿⣿⢋⣶⣿⣿⣶⡙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶
⠁⢢⣤⣶⣾⣿⣿⢸⣽⣷⣷⣿⡇⣽⣿⣿⣟⣿⣿⣿⣟⣻⣿⣛⣛⣻⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⣾⣷⡇⣽⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣼⣿⣿⡿⠟⠻⣿⣝⠿⠽⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣧⣟⣫⣿⡿⠁⠛⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠤⠶⠶⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠖⠒⠒⠒⠒⠒⠒⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⢴⣅⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠹⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠛⠛⠒⠄⡀⠀⠀⠀⠀⠀⠀⠠⡶⠞⢋⡉⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡻⠊⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⡠⢉⠎⠀⠠⣿⣿⠆⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⠃⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢰⠀⣶⢸⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢯⣸⣆⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⡾⠀⢻⡸⣆⠀⠀⠀⢀⣆⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢿⠛⣆⠀⠀⠛⠹⠇⠀⠀⢀⡼⠁⠀⠈⢧⡙⢦⣀⠀⠘⠟⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣙⣲⣤⣤⣤⣤⠖⠋⠀⠀⠀⠀⠀⠑⠦⣍⣛⠒⢒⣶⡶⠟⠁⠀⠀⠀⠀⠀⠀⢸⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠤⠤⠤⠴⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠋






⡿⠿⠿⠿⠿⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠿⢿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⣤⣤⣤⣯⣤⣾⣿⣿⣤⣤⣠⣇⣄⡀⠙⣷⡈⣿⣿⣦⣀
⢠⣠⣂⣀⣀⣰⣶⣀⣒⣒⣒⣖⣲⣄⣉⣭⡄⠀⠈⠉⠀⠀⠀⠀⠀⠉⠃⠀⠀⠉⢩⠈⠀⠀⠉
⢸⡤⣃⢄⣿⣿⣿⣿⣿⣿⣿⣿⡿⢅⠽⣁⣄⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢰
⠐⠐⠁⠀⠁⠀⠀⢲⣄⠀⠉⠉⠉⠹⠶⠌⠉⠁⢀⢸⡿⢻⣿⠇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣫⣿⠃
⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡞⠁⠐⠿⣿⣀⣀⣁⣀⣀⣀⣤⠤⣤⣾⣿⣭⡹⠁
⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠉⠉⠉⠉⠉⠹⣿⣿⣧⣛⣴⠏⠀⠈⠉⠉⠉⠀⠀⠀⠘⠿⠿⠖⠃

⣿⣿⣿⣿⣿⣿⣿⣷⡝⣆⠹⣿⣿⣿⣿⣿⣿⠀⣷⠀⢻⡆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣼⠁⠏⢠⣿⡟⣾⣿⣿⣿⠟⢀⣾⣿⡿⢋⣾⣿
⣿⣿⣿⣿⠋⠻⣿⣿⣿⣌⠣⠘⣿⣿⢿⣿⡿⡆⠘⡆⠘⡇⠀⣿⢸⣿⣿⣿⣿⣿⠇⠇⠈⠀⣾⠏⣼⣿⣿⣿⠋⣰⣿⣿⢟⣵⣿⣿⠿
⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣦⠀⠈⢿⣯⢻⣷⠑⠀⢁⠀⠣⠀⢿⠸⣿⣿⣿⣿⡟⠈⠀⠀⣸⠏⡼⣻⣿⡿⢁⣾⣿⠟⣡⣿⣿⠟⣡⣾
⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣷⡀⠀⠻⣆⢻⣇⠀⠀⠀⠀⠀⢸⠀⣿⢻⣿⣿⠁⠀⠀⢠⠏⠘⣱⡟⠁⣠⣿⠟⣡⣾⡿⠋⣡⣾⠿⣫
⣿⣿⣿⣷⣝⠻⣿⣿⣦⡀⠙⢿⣿⣄⠀⠙⣆⢻⡆⠀⠀⠀⠀⠘⠀⣿⢸⣿⡏⠀⠀⠀⠈⠀⣰⠋⢀⡼⠋⢀⣼⠿⢋⣴⡿⢛⡵⢚⣥
⣿⣿⣿⣿⣿⣷⣮⡙⢿⣿⣦⡀⠙⢿⣦⡀⠘⢆⢻⡀⠀⠀⠀⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠐⠁⡠⠋⢀⣴⠟⢁⣴⠟⠩⢒⡡⢞⣫⠴
⢽⣛⠿⣿⣿⣿⣿⣿⣦⡈⠻⢷⣄⠀⠙⢷⣄⠀⠀⠳⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⡠⠊⢁⠴⠋⠀⠀⠐⠩⠐⠉⣀⡤
⣤⣈⠉⠀⠉⠛⠿⣿⢷⣽⡢⠀⠙⠳⣄⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢒⣩⣵⣾
⣉⠙⠛⠶⢤⣀⡀⠀⠀⠈⠉⠓⠄⠀⠈⠑⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠁
⣻⠿⠷⣶⣤⣄⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣶⡾⣿
⣉⣉⡁⠀⠀⠈⠉⠙⠓⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠄⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⣚⣋⣩⣭⣴⣶⠿⠿
⣿⣭⣭⣭⣍⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡿⢻⡽⣿⢂⢿⣂⢸⡼⠃⠀⠀⠀⠀⠀⠀⠐⣀⣉⣉⣩⣥⣤⣴⣶⣶⣾⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠖⠒⠒⠀⠀⠀⠀⠀⠀⠹⠟⠘⠀⠈⢁⣈⡅⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⠿⠿⣿
⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⣿⣾⢻⣂⢙⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⣓⣶⣶⣿
⡿⠶⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠙⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⣀⡀⠀⠀⢈⣉
⣤⣴⣶⠆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠐⠒⠤⣄⣉⠙⠛⠷⢶⣶
⠛⠉⢀⣀⣤⡴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⢦⡀⠀⠐⢤⣀⠀⠀⠀⠈⠙⠓⠶⣤⣄
⣶⡿⠟⣋⠥⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢷⣌⡓⣮⣛⢶⣦⣤⣀⠀⠀⣀⠉
⡵⠖⠋⣀⠄⢀⡤⣒⠅⢀⠴⠊⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢷⣄⠀⠻⣿⣮⣝⢿⣿⣿⣿⣷⣦⣄⣉
⣠⠴⣊⣵⣞⡽⢊⣡⠞⢁⣴⡄⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠈⢧⠰⡄⠀⠻⣷⣄⠈⠻⣿⣷⣿⡻⣿⣿⣿⣿⣿
⣵⣿⣿⠞⣡⣴⠟⣡⣴⡿⣫⣾⡿⠃⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⢸⠀⡆⠀⡀⠀⠀⠘⣧⠹⣆⠀⠙⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿
⡿⣋⣴⣿⠟⣡⣾⣿⢟⣵⣿⡟⠁⣠⠆⠀⣰⠇⠀⠀⢀⣿⠀⡄⣼⡀⡇⠀⣤⠀⠀⠀⢹⣧⡹⣦⠀⠈⢿⣿⣦⡐⢌⠻⣿⣿⣿⣿⣿
⣾⡿⢋⣵⣾⣿⢟⣵⣿⣿⠏⠀⣰⣯⠎⢰⡏⠀⠀⡆⣸⡟⢠⡀⣿⡇⣧⠀⢹⡆⠀⠀⢀⢿⣷⣹⣷⡀⠀⠻⣿⣿⣦⡳⣝⢿⣿⣿⣿
⣫⣴⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⡟⣰⡿⠀⣸⡿⢀⣿⡇⢸⣿⣿⡇⣿⠀⢸⣷⠀⠄⠘⣾⣿⣷⣿⣿⣄⢢⡙⣿⣿⣿⣮⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣾⣿⡿⣱⣿⠇⣰⣿⠇⣸⣿⠁⣿⣿⣿⡇⣿⠀⠘⣿⣇⢸⡀⣿⣿⣿⣿⣿⣿⣦⠹⣌⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⠤⢤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⢀⣴⡾⠻⠤⣤⡖⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⢀⣼⠎⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀
⠀⠀⠀⡏⡀⠑⢢⣶⣶⣶⡟⡆⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠚⠉⠉⠉⠙⠒⠦⠤⣀⡀
⠀⠀⠀⣧⡀⠑⠌⠛⠛⠛⠷⠼⢶⡒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⡄
⠀⠀⠀⢸⢻⡄⢠⠀⠀⠀⢀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡄
⠀⠀⠀⠀⠘⣻⣿⣄⡀⠀⠈⢀⣤⡀⠀⠀⠀⠈⠑⠢⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⢇⡽⡱⡄
⠀⠀⠀⠀⠀⠉⠉⠉⠻⣦⣄⣿⡿⣿⣦⠀⠀⠀⠀⢸⠁⠀⠀⠉⢲⡒⠒⣶⣿⡿⠿⠛⠋⣉⢔⣫⣤⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣼⣷⣹⣷⠤⢄⣀⡨⠗⠤⣄⡠⠼⠥⠤⠭⠄⢒⣲⠾⠛⠋⣁⡴⣣⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⡇⣿⣧⠀⠀⠀⠀⢀⡤⠖⠒⢦⠀⢰⠊⢁⣀⠤⢒⡫⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣃⣿⣿⡀⠀⠀⠀⣏⠀⠀⢀⡼⠀⠙⣚⡭⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠒⠦⠤⢬⡥⠭⠭⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣴⣿⣶⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢐⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠻⠇⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⣽⠍⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⢸⣿⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣿⠀⠀⠀⢸⣿⢸⣇⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⠁⠈⠁⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠠⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣴⡄⠀⠀⠀⠀⠀⢠⣶⡄⠀⠈⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠛⠁⠀⢘⣿⠀⠀⠀⢸⣿⠀⠀⣤⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠀⢸⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠤⢄⡴⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢆⠀⣰⢤⡶⣤⣤⣖⡠⢤⣤
⠀⠀⠀⠀⠀⠀⣿⢸⡩⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠂⠍⠩⠭⠕⡖⣼⡏
⠀⠀⠀⢀⣠⠞⣡⠚⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠞⢰⣷⢣⠁
⠀⠀⠰⣫⠔⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⣿⠃⠃
⠀⠀⢸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠘⢿⠀⡀
⠀⠀⠸⡄⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⣧⢳
⠀⠀⢠⢣⡆⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠇
⠀⠀⠘⣾⣰⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣸
⠀⠀⠀⡇⡇⠇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿
⠀⠀⠀⡇⡃⢠⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠇
⠀⠀⠀⡇⣇⣸⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡄
⠀⠀⠀⡇⠛⢛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿
⠀⠀⠀⡇⢸⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿
⠀⠀⢸⡇⠘⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡀
⠀⠀⢸⠁⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⡇
⠀⠀⢸⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠃⣧⡇
⠀⠀⢸⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⢸⢨⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⢸
⠀⠀⠸⢸⡌⣇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢰⣱⣧⡏⡿
⠀⠀⢰⠸⣧⠹⣆⠘⢆⡀⠀⠀⠀⠀⠀⡄⠐⠆⠀⢠⠖⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⢴⣵⡟⡾⣱⠃
⠀⠀⢸⡆⠙⢧⡈⠷⣀⠙⢦⡀⠢⡀⠀⢰⡄⠀⠀⣿⣤⣖⣚⣡⡤⠀⠀⠀⠀⣀⣴⠿⣫⠞⣱⡟
⠀⠀⠀⢻⣦⡀⠙⢦⣬⣑⠂⠬⠓⠀⢀⠀⠙⠲⣯⣈⣿⠿⣻⣵⣒⣿⣿⣿⣯⡭⠴⠛⣡⡾⠋
⠀⠀⠀⠀⠙⠿⢶⣦⣤⣭⣭⣷⣒⠲⣕⣿⡀⠀⢸⣏⣴⢿⣿⠿⠶⠶⠶⠶⠶⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣉⣭⣿⡟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡺⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠤⠴⣶⣶⣶⣖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⢿⣿⣍⠁⠀⠀⠀⠀⠀⠐⠒⠲⠶⠿⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣥⣿⠖⠂⠀⠀⠀⠀⠀⠀⠚⣓⣐⣪⣬⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⠆⠀⠀⠀⠀⠀⠠⠤⠶⠶⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣿⣆⠀⠀⠀⠀⠀⠀⢐⣺⣿⣿⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣟⣁⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠴⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣮⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣿⣿⠒⠀⠀⠀⠀⠀⠀⡀⢺⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣿⣿⣿⡽⢂⣀⠀⠀⠀⠀⠘⣫⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠿⠟⠛⠉⠀⠀⠀⠐⡚⢿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣙⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠶⠒⠒⠒⣒⣒⣒⣒⣒⣲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣫⣭⣴⣶⣶⣄⢀⣾⣿⣿⡿⠟⠛⠋⠉⠉⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⠚⢉⡏⠁⠀⢸⠸⡆⢧⢸⣿⣁⣀⣀⠀⠤⠤⠤⣤⣄⣹⣄⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣆⣄⣼⣶⣶⣶⣿⠿⣼⡌⣿⣿⣿⠿⢿⠾⢿⣭⣭⣉⣁⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠿⠿⣶⣶⡶⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⣅⠉⠀⠀⣨⣀⣀⣀⡀⡀⢀⡁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉⠑⣦⣤⡀⣸⡏⠐
⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠒⠲⠤⠄⠤⠤⠤⠀⠀⠀⢩⠶⢄⠀⠀⠀⠰⡷⠿⠛⠁⠁⡻⠶⡊⠻⣧⠖
⠀⠀⠀⠀⠀⠀⣤⢧⣹⣯⡞⠇⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⡑⡀⠀⠀⠀⣰⣿⡒⣨⠙⠂⣀⣒⣲⣦⣤⣤⡀⣴⢿⣻⣀⡄
⠀⠀⠀⢀⣴⣿⣿⣶⣿⣿⣷⣸⣄⣀⣧⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⡜⡄⠀⠐⢿⣻⡿⠏⣠⢽⣿⣿⣿⣿⣿⠻⠀⡷⣿⣅⠻⠀⡀
⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣝⣒⠲⠦⢬⣄⣀⠀⠐⣿⣿⡿⠁⠙⣿⣿⣷⡀⢀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⡿⠃⠀⠀⠉⠠⣟⠁⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣉⡙⣿⣿⣇⠰⠀⣿⣿⣹⣇⠘⠿⠏⠛⠀⠓⠛⠛⠉⠉⢸⡏⠄⠂⢀⣀⣤⣾⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣶⣶⣶⣄⡐⠀⠀⠀⠈⠀⢨⣇⣱⣿⣷⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⠟⠿⠿⠿⠿⣍⠉⠃⠉

⠀⠀⠀⠀⠀⠀⠨⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠐⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠠⠴⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉

⠀⠀⠀⠀⠀⠠⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡷⠀⠀⠀⠀⠀⠈⢹⣿⡟⠉⠀⠀⠀⠀⠀⢀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠒⢲⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠉

⠀⠀⠀⠀⠈⠐⢤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣇⠀⠀⠀⠀⠀⠀⠠⠴⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠁⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠭⠿⠿⠿⠒⠂⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠐⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠴⠂⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⣀⠤⠴⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⠒⠀⠀⠀⠀⠀⢀⣠⣶⡾⠋⠀⠀⠀⠀⢀⣺⠒⠒⠂⣀⣠⡕⠒⠀⠀⠀⠀⠀⢨⡁⠐⢾⠖⠲
⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⢬⣭⠙⡒⠂⠀⠀⠀⠀⠀⠀⡀⣭⣿⣆⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡆
⠀⠀⠀⠀⠀⠒⠚⠨⠭⠥⠀⠀⠀⠀⠀⠀⠀⠬⡝⠓⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣐⣶⡦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡆
⠀⠀⠀⠀⠀⠠⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⢿⣓⣒⣀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡟⠛