Ecological Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠋⠀⠀⢀⣰⣶⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠁⠀⠀⠀⣀⣤⣶⣾⣿⢿⣿⣿⣿⡉⠁⠉⠙⠳⠦⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⡶⣾⠟⢋⣉⣿⣧⡄⠀⠀⠀⠈⢻⣶⣄⠀⡀⠀⠀⠉⠀⠹⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⡡⠿⠛⠛⠿⣙⠻⠁⠠⠾⠛⠿⠿⠟⠁⠠⠄⠀⠀⢹⣿⣿⣷⣷⠂⠀⠀⠒⠀⠉⠉⠉
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡟⡐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠲⠀⠀⠀⣀⣤⡀⠈⣸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣶⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⡆⠀⠒⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⣲⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣦⠀⠗⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠑
⠀⢀⣤⠀⠀⠀⠀⠁⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠈⠁
⠐⠛⠏⠀⠈⠀⠤⠄⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣮⣟⠛⣿⡟⡎⠀⠀⠀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⠟⠉⠀⠸⣿⠀⠀⢀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⠆⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢀⠔⠁⠀⠤⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠰⢄⠀⠂⠀⠀⠘⠿⠦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⠴⡿⠀⠀⠀⣀⠀⠀⣴⣦⠄
⠀⠀⠀⠀⠲⠒⠂⠤⠄⠤⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠉⠁⠈⠁⠄⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⣠⠄⠀⠀⠈⠈⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠖⠀⠀⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣶⣶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢳⠀⠀⠀⠀⠀⡞⠉⠓⣄
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠸⡄⣠⠀⠉⡆⠀⠀⠀⠸⡇⣴⠿⢝⡆
⠀⠀⠀⠀⠀⡏⠀⢏⠣⡀⠀⠀⠀⠀⢻⡟⠆⣀⡼⠀⠀⠀⠀⡇⠁⡰⠿⣷
⠀⠀⠀⠀⠀⠡⡀⠄⠀⡱⡀⠀⠀⠀⠘⡅⠸⠋⠙⢇⠀⠀⠀⣧⡤⠠⣾⣽
⠀⠀⠀⠀⠀⠀⢣⠰⠄⢙⠑⡄⠀⠀⠀⠓⠀⠀⠀⠨⡄⠀⠀⠿⠉⢠⡿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠙⣄⠀⠀⢘⠀⠀⡠⠐⢷⠀⠀⡄⠰⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⢦⠀⠈⣇⠈⠀⠀⠘⡆⠀⡇⠀⠂⠀⠐⠆
⣠⣤⣀⠀⠀⠀⠀⠀⠀⢣⢠⠾⠐⠊⢣⠀⠸⡐⣄⡀⠀⣳⢀⡇⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⠋⠉
⣇⠀⠈⠑⣄⠀⠀⠀⠀⠈⢏⠀⠂⠀⠈⢧⡠⠀⠀⠉⠉⠀⠉⠀⠁⢳⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠁⠎⣰
⠘⢾⡚⠿⠿⠷⢦⣀⠀⠀⠘⢧⠀⠀⣆⠀⠀⠀⢠⣴⠀⠀⠄⠀⠀⢈⠻⢆⣾⡆⠀⠀⠀⠀⠀⠀⡰⢧⣜⣰⡾⣰⠁
⠀⠀⠙⠦⣀⠀⠠⣼⠓⠤⣀⢘⡇⠀⠛⠓⠀⠀⠈⣀⣴⣤⣄⣹⡆⣿⣖⡞⢋⣳⡄⠀⠀⠀⠀⡰⣁⡍⡛⠋⣫⠃
⠀⠀⠀⠀⠈⠫⡼⠛⠒⠄⣀⢁⣀⠐⠂⢀⡄⠀⣴⠿⣛⡋⡉⣁⠀⣝⡭⢡⡄⣿⣝⣦⡀⢀⣴⠃⡁⡄⡸⣠⠏
⠀⠀⠀⠀⠀⠀⠘⢷⡐⠋⠀⠉⠁⡀⠀⡘⠉⠛⠁⠀⠉⣻⡿⣧⣖⣼⠵⠞⡸⢳⣀⠤⠙⠻⠑⠂⢆⡗⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠑⣄⠊⠀⠀⠀⠐⢀⠂⢠⣦⡀⠀⣴⠟⠫⠌⠠⠗⠹⢷⡄⣄⢴⣄⠀⣾⣋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡉⠛⠡⢀⠊⣁⠀⠀⠀⢹⡿⣷⡄⠀⠠⢮⣳⠠⣐⣋⡴⣗⣋⠈⢀⣷⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣿⣿⠃⠀⠀⠈⠃⠼⡟⠀⠀⢀⢈⡀⢂⡤⠀⠼⠿⠃⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⠿⡏⠛⠂⢼⠀⠀⠀⠀⠀⠈⠉⠈⠿⠳⣼⠃⠀⣰⠆⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡄⠤⠀⠈⢅⠀⠀⠐⠶⣦⡔⠀⠀⠈⢺⠀⢿⢿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡁⠀⢀⣠⣀⠀⠤⠶⠶⠂⠒⢒⠀⠀⠚⠳⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣹⣋⡉⠉⠉⣤⣤⣿⠀⠀⠘⠛⠒⠒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⣤⡀⢡⣤⠄⠀⢸⣿⠓⠤⠤⠤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠍⢡⠰⣰⠦⡶⡦⠀⠀⠐⠀⠺⢃⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠗⢦⠟⡤⣰⠆⡀⣇⠸⣐⠀⡼⠁⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⣿⣿⣷⣷⣷⣶⣾⣷⣿⣷⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣅⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣸⠆⣴⣼⣧⣠⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠿⣿⠾⣿⢏⠑⠎⣵⣿⡇⣴⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠎⠛⠿⢃⠲⣶⣶⣭⣾⣧⣆⠻⣫⡄⣠⣿⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣻⡗⣼⡇⢿⣧⣩⡻⠿⡻⡭⠯⢸⣿⠟⠿⠛⢅⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠎⠻⢿⢯⡴⣶⣿⡾⣃⣾⠇⣿⣠⣾⣋⣾⠃⢸⣿⡿⠋⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣃⣛⣦⣄⣿⣄⣚⡷⢿⡇⢦⣿⣋⣤⡼⢿⡷⢏⣿⡃⠸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠹⠿⠟⠰⠟⠀⠈⠙⠿⣿⣿⣿⣿⠛⠁⠀⠈⠉⠈⠻⠿⠄⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⣫⣤⣾⣾⣋⡛⠛⠲⢶⣿⣷⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣦⣿⣿⣿⣿⡿⢎⣡⣄⠀⠀⠀⠙⢿⣿⠋⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣿⣿⣿⣿⣿⣿⠗⠈⠉⠙⠛⠛⠃⠀⠀⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠱⣄⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣀⠀⠀⠀⠀⠈⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⣿⡇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣟⣿⣿⠃⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢺⣿⣿⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠉⠹⢿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠛⠻⢿⣿⡋⠛⠻⠟⠻⢟⣻⡿⠟⡧⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⣿⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠈⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⠑⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⣴⡁⠀⠄⢀⠈⡀⡀⠀⠀⠀⡀⡀⡐⠂⠉⠐⠀⠢⣀⣀⠀⠀⠀⠠
⠀⠀⠀⠸⠀⠀⠠⠀⠀⠒⢠⣶⠁⡀⠐⡿⡇⠨⠼⠲⡉⠀⠀⡷⠖⠀⠂⣵⣦⡀⠀⠀⢰⣶⡄⠀⠐⠲⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⠟⠀⠀⠀⠠⠁⡸⠠⠥⠃⠚⠚⠠⠢⡀⠀⠨⠛⠀⠀⠁⡀⠙⠃⠀⠀⠊
⠀⢀⡖⠐⠧⠄⠠⠤⠖⠀⢀⣀⠀⢤⠂⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠙⠀⣀⡀⠀⠀⢀⣠⠊⠀⠀⡐⠒⢲⡄
⠀⠈⠁⠘⠠⠀⡀⢀⠀⠀⠀⠀⠀⢠⠑⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⣘⢀⣀⠀⠚⠁⠉⠈⠁⠀⠂⠀⠀⣊⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠸⠠⠀⢀⡱⢄⠀⠀⠀⠀⢀⣴⡡⠀⠠⠄⡀⠀⠀⠀⠀⠀⢐⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⡀⠠⠁⠈⠁⠀⠀⠄⠀⠀⠀⠐⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠁⠀⠀⠄⠤⠀⠀⠔⠈⠈⢌⠀⡀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠀⠀⠠⠂⠀⡀⣰⠀⠠⡂⢤⠀⠎⠀⠈⡆⠀⠀⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠆⠀⠂⠂⠀⠉⢤⠀⠀⠔⠂⢈⢭⡒⠀⠊⠀⠁⠀⠀⠂⠈⠄⠀⠈
⠀⠀⠀⠀⢸⡀⠰⠆⡀⠐⠒⠐⠦⡰⢀⠀⠙⣀⡘⠢⠀⡀⠀⠹⢀⠆⢒⢄⣠⠄⠀⡄⠀⠀⠨⠖⢀⡆
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡋⣀⣤⣤⣤⡄⣠⡶⠛⠛⠛⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣸⡿⠃⠘⠳⣼⡿⢹⣯⣀⡀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢠⣾⠟⠉⠁⠀⠀⠀⠀⠀⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠹⠷⠞⠛⢶⣤⣴⠶⣦⡈⢿⣄⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠛⠛⠛⠛⠿⣷⡄⠀⠀⠀⠀⠈⠻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⢹⡇⠀⠀⠀⣀⣴⠟⠀⠀⠀⣀⠀⠀⣀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣇⠀⢀⣾⠋⠁⠀⠀⢠⣿⠟⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⢸⣏⠀⠀⠀⠀⢀⣤⣶⠶⢶⣤⣤⣀⣀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⣿⠛⢷⣦⠀⠀⣿⠋⠀⣀⣀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠈⠙⠛⢷⣯⡛⠛⢿⣆⠀⠀⠀⠀⣠⡴⣦⡄⠀⠀⠀⠀⠘⣿
⠀⢠⣿⠀⠀⣿⡇⠀⣿⠀⠸⢯⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠋⠀⠀⠀⠀⠀⣠⣿⡇⡀⠘⢻⣷⠀⠀⠀⢿⡄⠈⠻⢶⣄⠀⠀⠀⢿⡇
⠀⢸⡟⠀⠀⠹⣷⡼⣿⣤⣤⣤⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢿⣦⣿⢷⣤⣴⠿⠃⠀⠀⢸⣿⠀⠀⣀⣸⡇
⠀⢸⡇⠀⠀⣠⣾⠇⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠾⠿⠿⣷⠀⠀⠘⣿⣠⡾⠋⣿
⠀⢸⣧⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⠉⠀⠀⣿
⠀⠈⣿⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⢻⡆⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠁⠀⠀⢀⣤⡶⠶⠶⣾⡇
⠀⠀⠘⣿⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⣠⣾⠇⠀⠀⢠⣿⠁
⠀⠀⠀⠹⣧⠈⠻⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⣧⣴⣦⠐⣿⡁⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠹⣧⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⣸⡇⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⡇⠰⣿⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⣿⡇⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⢀⣾⠋⠸⡿⠋⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠹⣧⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⢀⣴⡾⠋⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡙⢿⣦⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣌⡻⣮⣙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⣀⣤⣤⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣻⡇⠸⢏⣿⡟⣾⡋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠿⠶⠶⢦⣭⣴⣭⡉⢷⣀⠀⠀⠀⠀⢻⡆⠀⠀⠘⠻⠾⠿⠿⣦⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣹⠃⠀⠀⣠⡼⠃⠀⢀⣀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢻⣄⢀⡾⠁⠀⠀⠀⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣭⣉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢰⡟⠳⣦⠀⢰⡟⠁⣀⣀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠁⠈⠙⠛⢾⣝⠛⣿⣆⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⢹⡆
⠀⢸⡇⠀⢿⡇⢸⡇⠀⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠋⠀⠀⠀⠀⢀⣾⣯⣤⣈⢻⣆⠀⠀⣿⠀⠈⠻⣦⠀⠀⢸⣇
⠀⣸⡇⠀⠈⣿⠚⠷⠚⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⢿⣿⣛⣿⣯⡄⠀⠐⣿⠀⣤⢴⡏
⠀⢻⡇⠀⣾⠏⠀⠀⠀⠀⠈⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠙⠛⠃⢸⡇
⠀⢸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢠⡶⠟⠀⠀⠀⣠⠶⠶⠶⣿
⠀⠀⢹⣏⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣼⠏⠀⠀⣸⡏
⠀⠀⠀⢻⡄⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣷⠀⠀⣰⡟
⠀⠀⠀⠀⢻⡄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢰⣏⣀⣴⡟
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣿⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣾⠉⣿⠞⠁⠈⣩⡿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠹⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⡾⠃⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣙⠷⣄⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⡶⠶⠶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⢶⣶⠶⠶⠶⢶⡶⠶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢐⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢀⣄⠀⠄⠐⢀⣶⣛⡁⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠄⠠⣔⣳⣷⣆⣌⡀⣀⣴⣿⣿⣿⣷⣶⣤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣾⣿⡷⠼⣿⣿⣿⣿⣿⣹⣿⠿⣿⠿⠿⠗⣀⡀⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡤⠀⠈⣀⣤⠟⠀⣿⣅⣠⣏⠁⠐⠚⠛⠛⠉⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⣿⣿⠿⣶⡦⢼⢿⠤⣄⣸⡿⢿⡿⡵⠤⠀⠀⡀⣀⣩⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣸⣧⣼⣿⠛⠛⣵⣶⡿⢃⣿⣿⣿⡀⣠⣷⣞⣡⡀⠀⠎⡶⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⣿⣿⣿⣛⡿⣿⡿⠛⠲⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣮⣴⣯⠉⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⡿⢿⣧⣰⠂⣿⣗⣿⡉⠋⡩⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠷⣠⣡⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⡲⠂⠼⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⠿⣿⣯⡿⠿⢿⡋⠗⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣤⣴⣆⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡀⠇⢌⣿⠒⠉⡅⣺⢇⠻⡏⣴⠿⢥⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⢼⢿⣿⣦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠘⠢⢀⣺⡁⠀⠀⢷⣷⣶⣾⣿⣿⡿⠿⢿⣿⡿⣛⠘⠃⢀⡞⠀⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡼⠏⠁⢠⠿⠚⠀⠘⠉⠉⠑⠋⠃⠒⠛⢻⣶⣖⣠⡶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠃⠀⢶⣶⣤⣅⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠉⢙⡛⡿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢻⣿⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇⠀⠀⠀⠉⠻⠀⠈⠐⠐⠂⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣖⣀⣴⣿⣴⣟⣠⣄⢀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣿⣯⣭⣛⡛⠛⠻⡿⣴⣦⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠁⠀⠀⠀⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠆⠀⣠⠊⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠄⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⢐⡀⠀⠾⢿⡅
⠀⠀⠀⠀⠄⠤⠱⣄⣆⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⢸⣿⠀⠀⠀⠃⠀⠀⠀⠦⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣀⣦⣄⣠⣶⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠀⠀⠀⠈⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠟⠻⠿⠛⠛⠃
⠀⢨⣠⠀⠀⠊⠜⠉⠈⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠦⣄⡀⠀⠀⠀⠐⠀⠁⠐⠠
⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠘⣋⣉⣽⡒⣄⠀⠀⠀⢠⠤⣶⣿⣦⣤⣤⣀⠈⠓
⠀⠀⠀⠔⠒⠳⢆⠀⠀⠀⠈⡠⠒⠒⠠⠀⠀⠀⡄⠀⠀⠀⣰⠂⠴⠶⢾⣿⣿⣿⡎⠁⠀⠀⠉⠀⠀⠀⠈⠋⠉⠉⠃
⠀⠀⡂⠀⣤⠀⠘⠄⠀⢤⣤⠄⣤⡦⠀⢀⠀⠀⠀⠀⠀⠀⣶⣴⣴⣶⡿⠷⠈⠉⠀⢀⠀⠀⠈⡅⠀⢠⠂⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠘⣟⠛⢿⣿⠁⠀⠀⢀⠖⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐
⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⠒⠊⠀⠀⠀⠀⠀⠠⠀⠈⠀⠈⠛⢀⡤⠔⠋⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠭⣭⣽⣿⣿⣿⠿⠶⢦⡀
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠸⠀⠀⠀⠲⠿⠿⠦⣭⠁⠈⠉⢓⠀⠀⠃
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠀⠈⠠⠤⠀⠈⠋⡀⠀⠀⠀⢀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠐⠉⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢀⡇⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠐⡂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⢤⠀⠀⠀⠀⠐⠒⠒⠒⠂⠂⠄⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠠⠅⠅⠄⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠠⢾⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠒⠂⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣿⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣤⣤⣽⣿⣿⣦
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣷⣤⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠉⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⢀⣀⡀⣠⣶⠀⠀⠀⠀⠀⠀⣤⡿⠿⣷⣤⠀⠀⠀⠀⠀⠰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠆⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⣾⣿⠙⠀⠟⡋⠀⠀⠀⠀⠀⠀⢿⣧⣀⣼⡧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣶⣶⠂⠀⠀⠀⠀⣀⣩⣙⠂⣿⣿⣃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄
⠀⠀⠸⡏⣤⣄⠐⢿⡇⠀⠀⠀⠀⠀⠀⢀⡙⣝⣋⠀⠀⠀⠀⠀⠀⠀⠀⢉⣁⣏⣈⡁⠀⠀⠀⠀⠀⠻⠿⣿⣿⠝⠻⠛⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏
⠀⠀⠀⠙⠺⠯⠴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⡄⣴⠟⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠆⣣⣬⣜⡠⠂⠀⠀⠀⠀⢠⣾⣿⣻⣟⣻⣿⡆
⠀⠀⢀⡀⠀⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⢦⢸⣧⢀⡴⠀⠀⠀⠀⡠⠒⠲⠎⡄⠀⠸⠖⠒⣄⠀⠀⠠⠍⣼⠁⠀⠢⣳⠩⠄⠀⠀⠀⢸⢷⣷⢰⣷⢼⣷⣷
⠀⠀⠈⠻⣆⣿⡗⠀⠀⠀⠀⠀⠀⠀⣷⣸⣿⣿⣿⢁⡶⠀⠀⠀⠣⡀⣁⠞⠛⠁⠣⣈⣀⠜⠀⠀⠀⠒⡘⠦⣤⠴⢋⡒⠀⠀⠀⠀⠘⠒⠒⢲⣶⠒⠒⠛
⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠘⠂⠁⠀⠀⠀⠀⠀⠀⠈⠛⠙⠋

⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⣧⣠⣄⡀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⢄⡵⢚⠓⢮⠠⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⡀⢀
⠀⠀⢠⠞⣶⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⠛⠉⠿⠆⠀⠀⠀⠀⠀⠐⠚⣇⢼⡧⣸⠒⠂⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢿⡿⠿⠐⣿⣿⠂
⠀⠀⠀⠀⣟⠛⢋⣣⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⡴⠃⠁⠀⠀⠀⠀⠀⠀⢸⣿⠿⢋⡿⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣸⠃
⠀⠀⠀⠀⠿⠀⠸⠇⠙⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⢠⡤⠤⠤⣤⢤⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄
⠀⠀⢸⡗⠒⠒⣿⡀⢻⡆⠀⠀⠀⠀⠘⢦⡱⠤⢇⡴⠁⠀⠀⠀⠀⠀⣴⠚⡓⢚⡓⡦⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣟⠀⠀⠀⠀⠀⠀⣀⡂⠨⣿⣿⠃
⠀⠀⢸⣿⡿⢾⣿⡇⠀⡇⠀⠀⠀⠀⠀⡇⢙⢶⡃⣶⠀⠀⠀⠀⠀⠀⣴⠀⢀⣤⠀⣟⠀⠀⠀⠀⠀⠀⢸⠋⢶⠘⣿⠀⠀⠀⠀⠀⢰⣿⡿⠄⢀⣄⣀⣀
⠀⠀⣸⣿⣦⣾⣿⡓⠔⠁⠀⠀⠀⠀⢀⡵⠡⠤⠝⢦⡀⠀⠀⠀⠀⠀⣿⠀⠘⠋⠀⡿⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⡟⠀⠀⠀⠀⠀⠈⠿⠀⠄⠺⡿⠿⠃
⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠛⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠓⠀⠀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠴⠇⠀⠀⠀⢀⣴⣄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠀⠠⠀⠠⠀⠀⠀⠀⢠⡟⠀⠙⣆⠀⠛⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦⠀⠀⠀⠀⠆⠀⠆⠀⠰⠀⠰⠀⠀⠀⠀⠀⡟⠀⢀⡤⢸⡟⠉⠛⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⣧⠀⠀⠂⠀⠂⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠹⢦⣉⣠⡾⠁⠀⠀⢸⠇⠲⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠘⣧⣿⣠⠏⠀⠀⠀⠁⠀⠉⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠦⠤⠴⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠉⠳⡄⠀⣿⠀⠀⣀⡤⠶⡆⠀⠀⠀⢀⣠⣤⢶⡶⣤⣄⡀⠀⠀⠚⠁⠀⠀⣦⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡙⣦⡟⠀⣿⠀⣼⠃⡀⠀⡇⠀⢀⣾⣋⣼⡃⢸⡇⣘⣧⣙⣦⡀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣄⣿⠀⢻⣾⣥⠾⠁⢀⡟⠀⢸⡏⠉⢹⡏⠉⢹⡅⠀⢳⡀⢠⡶⢤⣀⠀⠀⠀⠀⠀⢀⣤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣠⠟⠀⠀⠀⠀⢸⡷⠦⢾⡧⠤⢼⡦⠤⢼⡷⠶⢾⡇⠘⡇⠀⢈⡷⠖⠒⠒⠾⣯⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠒⠒⠛⠛⠒⠒⠒⠂⠀⠘⣇⠀⢸⡇⢀⣸⣇⡀⣸⠇⠀⣼⠁⠀⢷⡴⠋⠀⠀⠀⠀⠀⠈⠳⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠘⢿⡛⢿⡉⢹⡏⢉⡟⣙⡿⠃⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠟⠉⣭⡍⠉⡍⠙⡆⠀⠀⠀⠙⠛⠿⠾⠷⠿⠛⠉⠀⠀⠀⢻⡶⠦⣤⣈⠀⣀⡀⢈⣠⡤⠴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣀⣀⣀⣠⠶⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠙⢦⣄⣈⣻⣍⣽⣋⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠲⣴⠋⡉⠉⠻⣆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢿⣁⣸⠉⢻⡆⠀⠀⠀⠛⣏⠀⠀⢠⡴⠟⠛⠛⣻⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋⠉⢿⠋⣹⣤⣀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣏⣀⡽⠀⠀⠈⠁⣀⡀⠀⠀⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⣠⠖⠁⠈⠀⠀⠀⠀⠑⠢⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠋⠁⠠⠖⠀⠀⠀⠀⣈⣵⣦⣀
⠀⡼⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠀⠀⠀⠀⠀⡴⠃⠀⠀⠴⠐⣄⣠⠀⣴⢶⡟⠛⠃⠀⢈⡳⡀
⢐⠃⠀⠀⠰⠥⠀⠐⠉⢀⠈⣡⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⢈⣿⠷⠀⠀⠀⠀⠀⠀⠹⠸⣄
⢈⡀⠀⠀⠀⠈⠠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⡘⠡⠀⠀⠀⠀⠀⢀⡾⣶⠋⠁⠀⠀⠀⠀⠀⠄⠀⠀⢹
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⣀⠐⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⡇⢆⠀⡄⠀⠀⠀⢤⡿⠈⠹⣦⠀⠀⠀⠀⠀⠀⠘⠃⠈
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⢸⠀⠀⡗⠀⢤⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⢠
⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡴⠃⠀⠀⠀⠀⠰⡈⠠⠀⠀⠰⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⡼
⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠫⡐⠀⠁⠀⠀⠈⠁⠀⠀⠀⢀⡈⡰⠁
⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢀⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠎⠀⠀⠀⣪⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡨⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢱
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡏⠙⡉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢙⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢠⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠄⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠘⠃⠈⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠑⠢⢄⡀⣀⠀⠄⠊⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⣹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⢸
⠀⠀⠀⠀⠀⢸⡿⠈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⣧⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⠂⡔⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⣠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉
⠀⠀⠀⠀⢀⢶⡀⠀⡴⣺⣫⣟⣗⢦⠀⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡰⠰⠰⠔⢆⠀⠀⢠⡄
⠀⠀⠀⠀⡜⣸⠀⢸⠥⣯⢬⡧⢼⠤⡇⠀⣇⣳⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣚⡃⣛⢘⣓⢛⡃⠀⠘⣷
⠀⠀⠀⠀⡇⢧⠣⡈⢦⣷⠲⡗⡾⡴⢃⡜⡹⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠘⣃⢩⢨⣏⡛⠃⢀⣾⣿
⠀⠀⠀⠀⠙⣄⠳⠙⢆⠉⠛⠛⠉⣰⠋⠜⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠈⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠈⢧⠀⡜⠀⠀⠀⠀⢣⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠀⠀⠀⠘⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⠀⠀⡠⠄⠀⡄⠄⡄⠀⠀⠀⠀⠄⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠄⡀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⠼⡗
⠀⠀⠀⠁⠈⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠠⠀⠤⡀⠄⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠐⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⠄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠂⠐⠂⠉⠀⠆⠘⠀⠂⠐⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠂⠀⠂⠀⠈⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠐⣀⠀⢇⡂⠘⠉⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠐⠛⣁⠀⠀⠀⠁⠀⢠⣦⡄⠉⠀⢸⢀⠀⠈⢠⣤⡁⠀⠀⠀⠈⡀⠐⠀⠀⠆⡀⠀⠉⠃⢠⡴⠂⢤⡔
⠀⠀⠀⠀⠀⠀⠲⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠆⣀⡃⢰⠈⢈⢀⠀⠀⠀⠘⠃⠀⠼⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠺⠂⠠⣤⢀⡀
⠀⠀⠀⠀⠨⠂⢀⡼⣷⡀⠀⠑⠰⠀⠀⠀⢀⠈⢠⣸⣆⣀⠀⡵⢸⠀⠄⢄⠦⠀⠀⠀⠀⠀⢀⡄⠀⠀⡄⡆⠀⠸⠞⠀⠘⠃⢠⣿⣷⣿⠀⠳
⠀⠀⠀⢀⠀⠀⠈⢏⣀⣠⡀⡂⠀⣀⡆⢠⣾⣌⡄⣘⣿⣹⣶⡇⣬⣰⡤⠘⣫⣅⣄⣴⣠⣦⣤⡷⡖⠀⣽⣷⣗⣴⣴⢶⣔⡄⠀⣩⢸⣿⡇⣡⡦⡄⡀
⠀⠀⠀⠈⠾⠰⠿⠾⠷⠿⠷⠿⠿⠿⠧⠿⠿⠿⠷⠿⠿⠽⠿⠷⠿⠿⠿⠿⠿⠿⠏⠭⠿⠿⠿⠷⠿⠻⠟⠿⠿⠿⠿⠼⠿⠧⠧⠿⠿⠿⠿⠿⠧⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡿⠋⠉⠹⣿⣿⣿⣿⣶⣦⣄⣠⣴⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣿⡄⢀⡴⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣤⣤⣴⣾⣿⣿⣿⣿⣷⣤⠀⠀⢸⡀⠐⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⣴⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣷⡀⢸⡅⠀⢀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢛⡻⠋⠱⠀⠀⠀⠀⢹⣿⣿⡇⠘⣇⠀⢀⠀⢁⡈⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢳⠀⠀⠀⠀⠀⠀⣸⢯⣿⡇⠀⠻⠂⣸⣤⡶⠀⠀⣘⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣶⠋⣿⣿⠉⠇⠀⣶⣾⡋⠀⢠⠚⡿⠧⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠘⠃⠀⠀⠀⣀⠠⠀⠘⠷⠀⠀⣤⡾⢋⣼⣿⠃⠘⠆⠐⣻⠿⠃⠀⣸⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⣤⣀⢻⠃⣠⣾⣿⣿⡆⣦⢀⡄⢻⡗⠀⠀⢉⣩⢠⡾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠉⢹⡀⠉⢹⣷⡾⠟⠉⠻⢿⣿⡀⢹⣤⠴⡃⣰⣇⣈⣧⣿⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠀⠀⠀⠂⠀⣾⠇⠀⠋⠁⠀⠀⠀⠀⠀⠈⠀⠈⢧⡴⠇⢿⣀⣩⡶⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢾⣆⠀⠀⠀⠀⠀⣀⣄⡀⢀⣿⣇⣀⣀⣹⣍⣀⣩⡿⠋
⠀⠀⠀⠀⠀⠀⢠⣼⣧⠀⢄⠀⠀⠘⠀⠀⠀⢀⣀⣴⣿⡄⠀⠀⢀⣾⣿⣿⢷⡟⠋⠙⠋⠹⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢾⡇⠀⠀⠀⢂⠀⠂⣙⣿⣿⡇⠀⠀⣼⣿⣿⡉⠀⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣷⡀⠱⢣⣏⣤⣾⡿⣿⣿⠁⠀⠀⣿⣿⣏⠁⠈⠀⢤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣛⣿⡗⣿⣫⣽⣿⣿⡿⠃⠀⠀⠀⣿⣿⡿⠇⠀⢸⠘⢖⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣵⠀⣾⣇⣸⣗⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡐⠞⠷⢶⣤⣀⣠⣤⣤⣴⣿⣿⡿⠿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠋⠀⡀⢻⠠⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣆⣀⠐⢡⣀⣤⣼⠏⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⢿⣧⠀⠀⠠⠄⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠤⣄⠀⠀⠀⠀⠀⡠⠔⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠔⠒⢒⡬⠖⠒⠒⠒⠾⣵⠒⠒⢄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄⢨⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⢠⣤⡀⠀⣀⠀⢠⣤⡀⢹⠋⠀⢸⣳⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠚⠁⡜⠈⡇⠈⠛⠁⢸⠀⠀⣠⡏⢞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠹⣤⠃⣠⠖⢳⠊⠀⠀⡇⠙⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡑⠒⠒⣾⠁⣀⠏⠀⠀⠀⠳⢤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⢺⣀⡵⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢸⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠋⠉⢢⡀⢸⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢦⡀⠀⠀⠀⠈⠉⠒⠒⠲⡄⠀⠉⠒⠲⠤⠒⠊⣡⠜⢢⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⣄⠈⠓⢤⡀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠀⢀⡴⠊⠁⢀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠢⡄⠀⠉⢦⠀⠀⠀⠀⠀⠈⠛⠀⡴⠋⠀⠀⡴⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠇⠠⡡⠰⡹⠀⠠⠀⡎⠐⠁⢺⠰⠈⠉⢢⠂⠀⠰⡱⢘⠅⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠆⢰⠶⠔⠂⠢⠖⠶⠀⠆⠐⠢⠰⠰⠴⠄⠶⠆⠆⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠔⠁⠈⠈⠓⡄⠀⢸⠀⠀⠀⠰⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢀⡤⠖⠊⢉⠉⠉⠉⠑⠲⢄⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠐⠈⠁⠉⢲⠀⢸⠀⢰⠀⠀⠀⠀⠀⡇⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⡀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠈⠉⠛⠒⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢡⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⢀⠈⠀⠀⠀⠓⠀⠒⠊⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠐⠂⣀⢀⠀⠁⠐⠀⠈⠀⠀⠊
⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡎⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠀⠘⠃⡈⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠈⠉⠉⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡈⡸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠸⠁⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣄⣀⣀⣀⣀⣠⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠞⠛⠋⠉⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢉⠉⠉⠉⢉⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠄⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠌⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠐⠆⡠⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠄⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠋⡀⠀⠁⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠁⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠠⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠠⠀⠀⢠⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠰⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⠳⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠐⠁⠀⡐⠂⠐⠂⠀⠑⠒⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠀⠀⠀⠼⢤⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠂⢤⣀⣀⡁⠀⠀⢧⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠂⠠⡂⠀⠀⠀⣠⠄⠀⠀⠠⠀⠀⠀⠀⠐⢄⠀⠀⠀⠁⡦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⡎⠀⢀⡀⠀⠀⠐⠀⠀⢀⡀⠀⢐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⡈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠓⠤⠀⠀⠠⠔⠊⠉⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣔⣉⠀⣀⣀⠈⡅⠀⠀⢰⠁⠀⣀⣈⡑⢄⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⣈⠑⢦⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⢄⠀⠉⠁⠀⠀⠀⠁⠀⠀⠘⡠⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠈⡗⠉⢧⠀⠀⠀⠀⠀⢀⣄⠀⢠⠁⠘⡄⠀⣀⡀⠀⠀⠀⠀⠀⡜⠓⢾⠛⠆⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡼⠷⠀⠛⠀⠀⠀⠀⠀⠘⠟⢀⠃⠀⠀⠡⠀⠻⠟⠀⠀⠀⠀⠀⡇⠀⣼⡄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢱⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠺⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⡖⠚⠒⠊⠑⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠺⠅⠽⠊⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠛⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⣀⣀⣤⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⠀⢀⡜⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠢⠤⠜⠑⠂⠒⠁⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗
⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⠀⢙⡷
⣖⣀⣠⣦⠄⠀⠀⠀⠂⢠⠄⠀⠀⡀⠀⣸⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠛⠟⢟
⠻⠿⣿⣿⣿⣴⠀⠀⠀⣠⠄⠀⠀⠀⠰⠅⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠀⠀⢡⡀⠀⢂⠀⣤⣤
⣤⠀⠀⠀⠸⣿⠀⠀⠰⠿⠋⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⣿⠀⠄⠀⠀⠀⠰⠂⠀⠀⠱⣿⣸⡇⢹⣿
⠛⠀⠀⠀⠀⢹⠃⠀⠐⣮⠀⢀⠰⠀⠉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠚⠛⠀⠫⡀⠀⠀⠁⠀⠀⠈⣿⠷⠼⣿
⠀⠀⠀⠀⢠⣿⣆⡄⠀⢻⣂⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣀⠀⠊⠀⠀⢠⣿⣀⠀⠹
⠀⠀⠀⢠⡿⠟⠛⠁⠄⠐⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣶⣿⠀⠀⢯⠀⠀⠀⣠⣿⣿⠿⠆
⠀⠀⡠⠈⠀⡀⠀⠀⠈⠾⣿⡆⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠿⠀⢠⡎⠀⠀⢶⣿⠏
⢀⡼⠃⠀⠀⠂⠀⠀⠀⠀⠘⠃⡀⢠⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠠⠟⠁⠀⣰⣾⠃
⠈⡀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⡇⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⢲⣴⡟⠀⠀⠀⠀⠰⠀⠄
⠾⣷⢂⣤⠆⠙⠮⠁⠈⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠀⠀⠉⠀⠀⢄⡄⠀⠀⠀⠠
⣾⣿⠟⠋⠉⠺⠠⠄⠀⠀⠁⠀⣀⠀⠀⠀⢀⣀⣀⡀⠀⣀⢀⠀⠀⠀⢀⣀⣠⣄⣀⣀⣀⣄⣤⣴⡄⠘⠒⠀⢀⠀⢀⠀⠠⢂⡀⢀
⠛⢁⠀⠀⠀⡀⢲⣿⣧⣼⣾⣿⣿⣿⡿⠛⠛⠙⠉⠙⠛⠛⠛⠓⠒⠻⠟⠻⠿⠿⠋⢙⡛⠛⠻⠿⣿⣦⣼⣽⡟⣋⠀⠀⠀⢩⣦⣼⢷
⣄⣠⡀⠨⣤⣴⡾⠋⠙⠛⠿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⣿⣾⣿⣶⣶⣤⣾⣿⣿⠿
⠛⠿⣷⣶⢿⣿⣿⣶⣦⣄⣀⣤⡾⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠷⠶⠾⠿⠿⠿⠟⠛⠋⠁⠀⠤⠖
⠀⠀⢿⢿⣶⣤⡭⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠥⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢄⣀⠀⠀⡤⠒⠀⠀⠀⠈⠀⠀⠈⠁⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠑⠈⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠃⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⢀⠀⠀⠀⠀⢠⠃⠀⠔⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠂⠁⣠⠀⢢⢬⠰⠂⢀⢁⠀⠀⠐⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠔⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⣉⢀⠀⠋⠉⠀⠀⢈⢀⠈⠅⠰⠒⠋⠐⠠⣄
⢀⡠⠴⠮⠹⡇⠃⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣢⢼⠁⠀⣀⠀⠀⡦⠄⠀⠧⡒⠠⠤⠚
⡎⠀⠀⠀⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣠⠔⠀⡇⠀⠢⡀⠀⢀⠴⠥⠄⠊⠀⠈⠲⡄
⠈⢲⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠘⢦⣀⠵⣤⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⠈⠢⠁⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠄⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠂⠀⠀⢀
⠀⠀⠀⠀⠈⢦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠺⡀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢀⠀⠀⠀⠀⣠⡹⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢲⠤⠤⠓⡆⠀⠀⠀⠀⣀⡸⠂⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠶⠶⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⡏⠉⠒⠒⣻⠁⡇⢸⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣇⣀⡇⠀⠀⠀⣾⠀⡇⢸⡤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠚⠀⡏⠀⠁⠀⠀⠀⠘⠉⢃⢸⣀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⢀⠼⣿⣄⡠⣾⡷⢄⣰⣿⡗⢄⣀⣀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⠻⣧⡀⠁⠀⡟⢧⡴⠛⠛⢆⠀⣿⠉⠀⢀⣼⣿⢷⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣄⠀⠀⠙⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢱⠇⠈⣼⡟⠇
⠀⠀⠀⠀⠀⣴⣤⡤⠚⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠈⠢⣤⣤⡄
⠀⠀⠀⡀⠀⢀⡟⠻⢦⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⣠⣾⠟⢻⠁
⠀⠀⠘⢿⣿⣷⣤⣄⠀⣱⣶⣴⡾⢿⡥⠉⣿⡿⠟⠋⠀⠀⣠⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣷⡌⠀⠀⢈⣢⣴⣦
⠀⠀⠀⢈⠂⠉⠳⠄⣾⣿⣿⣅⣰⣷⣆⠀⠉⠀⠀⠀⠠⣦⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠴⠿⠋⠹
⠀⢠⣴⣧⣤⣀⠀⣼⣿⣿⣿⣿⠿⠃⠉⠀⠀⠀⠀⠀⢰⣾⣛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀⣉⣤⣠⡀
⠀⠈⠙⠻⠋⢉⢁⣿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⢉⡽⢿⠟⠉⠁
⠀⢠⣴⣮⣾⠁⠈⠿⣧⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⠀⠀⢹⡏⠀⠙⠛⠈⢹⣦⣷⣄⡀
⠀⠀⠈⢣⡙⣦⡀⠀⠀⠉⠒⣾⣶⣦⣄⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠳⢠⠴⢋⠛⠉
⠀⢠⣴⡿⠿⠥⠄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⣷⣤⡄
⠀⠀⠀⠑⡄⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠉
⠀⠀⢀⣠⣧⣾⠟⠁⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣤⣰
⠀⠀⠈⠛⠉⢰⠀⢀⣠⡀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⣩⠿⠿⠿
⠀⠀⠀⠀⠀⣼⣶⡿⠋⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡄
⠀⠀⠀⠀⠀⠈⠁⠉⠑⡀⣠⡾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⡄⢰⠊⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠥⡄⣼⣠⠆⠀⠀⣄⠀⡀⠀⠀⣠⡀⣠⠀⠀⢿⣦⠀⣀⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣇⢠⡀⣼⣿⣀⡱⣶⡶⣃⣳⣿⠀⡤⠌⣿⣟⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⣿⡟⠁⠈⢻⡟⠁⠘⣿⡋⠀⠀⠀⠋
⠀⡀⡀
⠀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⣋⣉⡁⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢰⠏⠁⠀⠉⢳⡀⠀⠀⠀⠰⠶⠶⠶⠶⠿⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⠶⠶⠆⢻⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠙⠁⠘⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣥⠉⠉⠀⠀⠀⠙⠶⠤⠖⠋⠀⠀⠀⠀⠀⠀⣠⣾⠷⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣤⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡏⠀⠈⠣⣄⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣀⡤⠏⣼⠁⠘⢦⡀⠀⠀⠀⠀⠀⣠⢶⠏⠀⠈⣧⠀⠀⠀⠀⠙⢲⡄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⡞⠁⣠⣾⠁⠀⠀⠀⠙⠦⣄⠀⣠⠞⢱⠏⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠙⠦⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡴⠋⠀⠈⣡⠇⢀⡀⠀⠀⠀⠀⠈⣻⠧⡜⠉⠀⠀⣀⠀⢀⠀⠀⠀⠀⣾⡇⢴⡦⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠁⣠⣄⠀⠁⢘⣿⣟⠀⠀⠀⠀⣚⣿⣓⠙⣆⠀⢰⣿⠆⣿⡇⠀⣀⡤⠼⠧⠽⠯⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⢈⣽⣯⡡⣤⣐⣻⠓⠀⢀⣄⠀⠚⣿⠓⢀⡬⠷⠒⠛⠒⠛⠙⣛⣷⠄⠀⠀⣠⣧⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⢾⡷⠄⠀⣀⣩⠷⠆⣫⣯⡓⠉⠙⠛⠛⠓⠂⢀⡤⣶⣿⡿⠿⠋⣰⡀⢈⣩⣯⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⣓⠛⠉⠁⠀⠀⠀⠵⡿⠭⠀⠀⠀⠀⠀⢀⣸⠆⢳⢉⡳⡄⢉⣽⣍⠁⡴⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣿⡓⢀⣠⢤⣴⣞⠓⢷⡀⣠⠶⠒⣿⠉⠩⠴⠚⠿⢞⣳⠇⣩⣼⣭⡡⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⠈⠁⠀⠈⠉⣁⣈⣤⠟⢸⠣⣞⠉⣴⢢⠖⠋⠉⠀⠀⠤⢾⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠖⣻⠭⢗⣛⠀⣚⠉⢀⡨⢇⡼⠊⢳⡄⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⠃⡾⢉⡴⢋⡵⢚⣩⢖⡃⣠⠴⠋⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡇⢸⠇⡜⢠⠏⢠⠏⣸⠛⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠇⢰⢀⡇⡟⢰⢸⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠆⢸⠘⠃⡇⢾⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠘⣠⣧⣼⣸⡆⡇⣴⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⢷⣄⣠⠸⢃⣠⣬⡼⢷⡇⡾⠞⢳⡆⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢈⡅⠟⡋⠛⠳⠀⠠⠷⠞⠃⡀⣲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠹⠴⠦⠟⠲⠚⠓⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠚⠉⠉⠛⢦⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⠃⠀⠀⠀⠀⣠⠞⠉⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢠⡴⠚⠛⠃⠀⠀⠀⠀⠀⠀⠸⣦⣍⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⢀⡴⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣴⠃⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠉⠙⠳⡴⠖⠒⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠋⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⣦⠀⢸⡇⠀⠀⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠶⣠⠞⠉⠽⢤⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢘⣧⢸⠃⠠⣄⣿⠀⠀⢸⡇
⠀⠀⠀⠀⡴⠚⠋⠁⢠⡤⠶⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⠘⢧⡟⠀⠀⠈⣿⠀⠀⠀⢳⡀
⠀⠀⠀⡼⠁⠀⠃⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⣯⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷
⠀⠀⠀⠳⢤⢤⡄⠀⠀⠀⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⠐⡇⠀⠀⠀⠀⣿⠀⣠⠆⠀⣸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠶⠆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣿⠀⢻⡀⠀⠀⠀⣿⠞⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠂⣿⠰⠶⠻⢦⣀⠀⣿⢀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⡿⠀⡖⠘⢦⣄⣀⠀⣠⠶⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀⣀⣀⣀⣈⡁⣿⠈⠁
⠀⠀⠀⠀⠰⠯⠥⠞⠁⠰⠯⠭⠥⠤⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠉⠉⠁⠀⠀⠉⠁⠟⠘⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠠⣤⠀⣤⡄⠠⡤⠘⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢢⡖⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡒⢤⡀⠀⠀⠀⠀⠀⠄⠁⠐⠂⠙⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⡠⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡈⠁⠠⢀⡜⠤⠃⠀⠀⠀⠀⣠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢀⢠⡤⠛⢢⠤⠠⡄⠔⠀⡷⠀⠀⠀⠢⢀⣀⠠⢤⠀⠲⡓⠠⠀⠂⠅
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢄⠤⢀⠀⠀⠀⠁⠀⠰⠆⢀⣠⠂⠀⠀⠀⠠⡄⠀⠌⡆⠀⠀⠀⠀⡀⠋⠑⠤⠀⠀⠀⠀⠀⢀⣠⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣤⠀⠀⠀⢡⡔⠛⢄⡤⠀⠀⣛⣁⠀⠀⠀⠀⡬⣅⠲⠀⠀⣄⠀⠀⠀⠴⡋⠉⠈⢃⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⣠⠄⡹⠈⠀⠀⠀⠀⠀⡴⡢⠈⠋⠈⠀⠁⠈⠀⠀⢪⢟⣤⡈⠀⠀⠀⠉⠁⠂⠲⣤⢧⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⡘⠁⣨⠖⡀⣀⢠⠆⠀⠈⠠⠀⠀⠀⡀⠐⠁⠈⠀⠀⠙⠢⡀⠀⠀⣶⠐⣆⡀⠹⣃⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠹⢟⡀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⡐⠠⠀⠠⠄⠑⣄⣤⠻⢷⡌⠁⠀⡏⠁
⠀⠀⠀⠀⠀⠤⠄⠐⠂⠠⣄⠀⠚⠀⠀⠀⠀⡘⠀⠁⠀⠅⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠈⠆⠀⠀⠀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠤⢁⠐⢤⠠⠐⠀⠀⠠⣴⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⡀⠀⡠⠖⠠⠀⠀⠀⢀⠀⠘⡄⠀⠠⢀⣀
⠀⠀⠀⢀⢀⡆⠀⠠⠃⠩⡉⠈⠐⠠⠀⠈⠱⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⣦⣀⡌⠠⠓⠄⠼⠠⡔⠀⠐⣸⠛⢂
⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠁⡆⠀⠀⠀⠀⢸⠀⠀⠀⠐⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠴⠊⠉⠱⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡴⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⢀⠜⠁⠀⠚⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠠⠀⠄⠠⠞⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⢠⡂⡀⠀⠠⡂⢘⠇⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⠂⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠅⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠒⣦⡤⡐⠐⠀⠀⠀⠀⠀⠀⠒⠙⠎⢡⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠈⢙⣙⠉⠀⠀⠀⠀⠀⠀⠄⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠰⠉⠈⢐⠁⠀⠀⡀⡀⠀⢠⠂⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠐⠂⠄⠀⠀⠱⣔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣎⡀⣀⠀⡐⠣⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠾⡄⣁⣠⡈⠛⢁⡀⠀⢀⣀⣀⢹⣿⡬⠁⠀⠄⠶⡇⠀⠰⠐⠛⣰⢦⠀⣶⣿⠂
⠀⠀⠀⠀⠀⣀⣀⡘⢋⣼⣿⣀⣾⣿⡷⠛⠉⠉⢉⠇⠀⠀⢿⡄⢠⡷⠀⠧⠀⢀⠈⠈⠀⠙⠹⠀⡀
⠀⠀⠀⠀⠙⠛⠋⠐⠛⢿⣿⡿⣿⣿⠃⠀⠀⠀⣶⣿⠀⢠⡘⣠⡿⠁⠀⣴⣠⢱⡧⠀⠀⢨⠀⣦⠃
⠀⠀⠀⠀⠀⢶⣦⣾⣷⣶⡏⠀⣹⡟⠄⠀⢀⣠⠛⠻⠵⠿⠟⠋⠀⠀⠀⠈⢿⣮⠀⠀⠀⠘⡇⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣦⣼⠷⢛⡿⣯⣤⠾⠿⠿⠟⠱⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡧⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠈⢹⠏⠰⠀⠛⠛⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣊⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤
⠀⠀⠀⠀⠀⠀⢀⡈⠈⠛⣡⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠸⠿⠷⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠉⠾⠟⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠆⠀⠀⠀⠀⠀⢸⣷⣶⣿⠿⣾⠄⠀⠀⠀⠈⢛⣿⣨⣷⣦⠀⠀⠀⠀⣺⠇⣶⡀
⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⡿⠀⠀⠀⣀⠀⠀⠻⠿⠋⠻⠋⠀⠀⠀⠈⠛⠲⠗⠀⠀⠀⢠⣶⣦⡀
⠉⠿⠃⠀⠀⠀⠀⢾⡷⠸⡷⠄⠀⠀⠀⠀⣀⣠⡀⠈⠉⠁⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢾⡧⢰⡷⠀⠀⠀⠀⢘⣿⣹⣯⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀⠀⢀⠀⠀⣤⣶⡄⣠⣀⠀⠀⠀⠀⢀⣀
⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⣠⣄⡀⣠⡀⠀⠈⠛⠛⠛⠀⠀⠀⠀⢈⣻⡇⠁⢿⠿⠆⠀⠀⠀⣿⣾
⠿⠏⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢿⣽⣻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣤⣿⣷⠀⠀⠀⢴⣾⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⢈⣟⡿⣯⣾⠟⠁⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠈⠛⠋
⠀⢀⣀⣤⡀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠘⢮⣻⠟⠈⠃⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⢻⣯⣿⡆⠀⠀⠀⠸⣿⣿⣧⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣶⢤⠀⠘⣿⣿⠃
⠀⠈⠉⠈⠀⠀⠀⠠⣶⣾⣇⣼⣟⡛⠁⠀⠀⠀⠀⠀⠀⢺⣿⣟⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠢⣼⣿⣟⣕⣄⠀⠀⠉
⣦⡀⠀⠀⠀⠀⠀⠀⠛⠟⠹⣿⠿⠇⠀⠂⠀⠀⠀⠀⣿⣿⣧⣼⡿⠷⠀⠀⠀⠀⣾⠗⠛⢟⡀⠀⠀⠀⠀⣾⣿⣺⣿⣿⢻⠇⠀⠀⠀⠀⢀
⣿⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠿⠿⠇⠀⠀⠀⠀⠀⠰⣶⡖⠿⠃⠀⠀⠀⠀⠙⠾⠯⠈⠛⠋⠀⠀⠀⠀⠀⣾
⠛⠋⠀⠀⣄⡙⠻⣴⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠙⢳⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⣻⡁⣯⡄⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⠀⠀⠀⠀⣴⠤⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⢿⣿⠿⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡅⠀⠀⠀⢾⡶⠶⠆⠀⡀
⢠⣄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⢀⣤⣤⡄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢶⡦⠀⠀⠉⠉⠺⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣤
⠿⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣻⡿⣧⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠿⠆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣌⡿
⡠⣾⣿⡏⠀⠀⣴⣶⣦⠀⠀⠀⠀⢹⣿⣿⣤⣽⡻⠟⠀⠀⠀⣀⠀⣤⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠰⣿⡿⠁
⣿⡆⠉⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⡿⠿⠇⠀⠀⠀⢾⣿⣳⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⢰⣷
⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠠⠟⣿⣿⠟⠀⠀⠀⠰⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢺⣿⣇⣤⡀⠀⠀⠀⠈
⠀⢠⣶⢾⡶⠀⠀⠀⠀⠀⣤⣤⣶⡆⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣧⣽⡻⠃
⠀⠀⠾⠞⠟⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠀⠀⠈⠁⢀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣏⣩⣿⣿⡇⠀⠀⠀⠀⠀⠻⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣗⠈⢻⣏⣄⠀⠒⠀⠀⠀⠀⠈⢰⣿⣿⡌⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣷⣦⡀
⠀⠀⠀⣀⣀⠀⠀⠀⢠⡴⣲⣦⣰⣶⣄⠀⠀⠀⠈⢙⣽⣤⡴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⣡⣿⣿⣳⣯
⠀⠀⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⢿⣿⡟⠀⠀⠀⠀⠈⠙⠟⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠸⢟⢿⡿⣻⡾
⠀⠀⠀⠈⠉⠀⠀⠀⠀⣾⢾⣽⡟⢯⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⢀⣴⣆⣾⣷⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠙
⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣭⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⡻⣿⣿⣿⣿⣿⣶⣬⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡙⢿⣷⢹⣿⣿⣿⡿⠟⣛⣋⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⠉⣡⣶⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣟⣃⣼⣧⣝⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣯⣽⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣡⣦⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢟⣿⣿⣿⣿⣿⣯⣍⢻⣿⣿⣿⢫⣙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⣻⣯⣙⣛⣛⣟⣩⣽⣿⢿⠿⣿⣦⠹⣶⣶⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠳⣮⣩⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⡿⢿⣟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⣿⣦⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣬⠻⣿⣿⣿⣿⣿⣿⣷⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⡿⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢃⣿⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡜⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡹⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⢱⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣮⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠸⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⡆⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢼⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠻⡎⢃⠀⡇⠀⣰⢿⡇⠀⠀⠠⠖⢴⡇⣷⠔⠦⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡃⢀⡅⠛⠁⠀⢰⣿⢳⡿⡇⣾⡧⢻⣷⠀⠀⣤⣄⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠀⠀⠀⠀⢰⣶⢰⣶⡆⣶⡦⣰⣶⠀⠀⢹⢏⣴⣾⣿⣷⣮⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣅⢭⡅⣭⢅⡭⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣛⣿⣿⡆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢭⣟⣛⠿⠿⠿⣛⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣄⡀⠀⠀⠀⠉⠛⠃⠉⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⢰⣄⠀⠀⠀⠂⢸⣿⡿⣃⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢶⢂⡀⠀⠀⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣾⣿⡆
⢰⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟
⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⢴⢤⣶⣶⣁⡅⡠⠤⠀⠉⠛⠙⢿⠋
⣿⣿⣿⣿⣏⣀⣀⣰⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⢿⠇⠛⠛⠉⠁⠀⠉⠀⣀⣉⣁⣀⣀⠀⠀⠀⠀⠀⢸⡆
⠿⣿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣆⣠⣠⣄⣀⡀⠀⠀⠀⠤⠤⠄⠀⠀⠉⠉⠀⣀⣀⣀⣀⡀⠀⣠⣤⣤⣿⣷⣶
⠀⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠛⠛
⢸⡟⡴⢁⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⣰⣖⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣾⣟⡔⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠿⠿⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠋⠉⠀⡁
⣿⣿⠟⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡶⠖⢒⡠⡖⠁⠀⠀⠀⠀⠀⠀⠄⠦⠤⠴⠄
⣿⣿⠃⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠛⠋⠀⠀⠿⠿⢿⣿⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠖⣚⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿
⠶⠒⠒⠒⠶⠶⠶⠿⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣃⣶⣤⣤⣤⣾⣦⣤⣶⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠦⣤⠴⠒⠀⢲⡶⢄⠀⠯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢀⣤⡀⠀⠀⢸⡇⣸⠃⠀⠀⣠⡔⢲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠉⠙⠛⠛⠉⠀⠀⠀⠘⠧⠞⠉⣖⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠰⠆⠠⣀⠀⠀⠀⠀⠀⠈⠓⠶⠃
⠀⠀⠀⠀⠀⠀⢠⡏⠀⡀⠀⢠⡇⠀⣀⣴⠄⠀⣀⣤⣤⣤⣀⠈⠙⢦⡀⠠⣀⠴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠈⣧⣎⢀⣠⠞⠀⠈⡽⠹⢠⠾⣵⣧⣼⣬⣯⠷⣄⠀⢳⠐⣿⠀⠀⠴⠓⢒⡶⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⢠⡇⠀⣯⣤⣯⣤⣼⣤⣼⣤⣼⠀⠘⡇⠸⠄⠀⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣣⣀⣜⠀⡀⣇⠀⢳⣀⣿⣀⣼⣀⣼⣀⡼⣀⢸⠃⠀⠈⢓⣶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡾⠭⣤⠭⣶⠃⠘⣆⠀⠙⢬⣧⣽⣰⡧⠟⠁⣿⡯⠆⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⡖⣇⠁⣿⠈⣸⢲⠀⠈⠓⢤⡀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⣦⢤⡖
⠀⠀⠀⠀⠀⠀⠀⠁⣼⠓⠿⠚⣧⠈⠀⢀⠤⢄⡀⢈⣁⣀⠀⣠⠤⣄⢀⡜⠉⣽⣹⣏⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠞⠉⣉⣩⣉⠉⠓⣄⡿⠀⠐⠛⢳⣰⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡞⣵⠒⣺⢳⡀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢧⣈⣻⣁⣸⠃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣉⣉⣉⡉⠛⢯⡷⠚⢉⣉⣉⡉⠛⢯⡛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡴⠛⠉⠀⠈⠙⠳⡄⣠⠞⠉⠉⠉⠉⠳⣄⠙⣆⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠁⠀⢀⣠⠤⢤⣀⢹⡏⣀⣤⣤⣄⠀⠀⢸⡆⢸⡄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡀⢰⠋⠀⠀⠀⠈⢿⡟⠁⠀⠀⠈⠻⡄⢰⡇⢸⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢧⣿⠀⠀⣀⣤⣄⡘⢁⣠⣄⡀⠀⠀⣇⡞⢀⡞⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠦⠼⢧⠈⠻⣇⢰⠃⠀⠀⢹⠏⠀⠀⢹⡄⣼⠟⢀⡾⠥⠾⠧⠴⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣁⡤⠶⠶⠶⣦⣤⣄⣀⠙⢿⣆⠀⠀⠀⠀⠀⢀⣼⠟⢁⣀⣤⣤⣶⠶⠶⠦⣤⡈⠳⣌⠙⢦
⠀⠀⠀⠀⠀⠀⡾⠁⡼⠉⠀⢀⡖⠋⠉⠉⣩⠽⠿⠷⢿⣧⣀⠀⠀⣠⣾⠷⠾⠿⠯⣍⠉⠉⠙⢦⡀⠀⠙⣦⠈⣧⠈⢳
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⢳⡞⠉⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⡇⠀⠀⢸⡆⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠈⣇⠘⢧⠀⠀⠘⢦⡀⠀⠀⠙⢶⡶⠀⠀⠀⢠⡏⢳⡀⠀⠀⠀⢦⡶⢋⠀⠀⣀⡼⠁⠀⢀⡼⠀⡾⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠘⢦⡈⠛⠶⠤⣤⠽⡽⠋⠁⢿⠀⠀⠀⣠⡿⠀⠈⣷⡀⠀⠀⢀⡇⠈⠻⣿⢯⣤⠤⠶⠋⣠⠞⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⡾⠁⢸⡇⠀⠀⠈⠓⠶⢚⡿⠁⡼⣆⠘⣿⡲⠖⠛⠁⠀⠀⢸⠀⠘⣦⠀⣾⠁⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠳⣄⡀⠀⣀⣴⡿⠁⡼⠁⣸⣆⠘⢷⣤⣀⠀⢀⣠⠞⠀⠀⢸⠀⣹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢳⡀⠀⠀⠈⠉⢉⣡⠟⢀⡞⢁⣼⠃⣼⢧⡈⠳⣍⠉⠉⠀⠀⠀⣠⠟⢀⡟⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡉⠓⠶⠶⠒⠋⣁⡴⣋⡴⡿⠃⢠⡏⠀⠙⢦⣈⠙⠲⠶⠖⠚⢁⡤⢏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠚⠛⠛⠛⢉⡼⠁⠀⡼⠀⠀⠀⠀⠉⠛⠒⠒⠒⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⣅⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣽⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣠⡴⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠟⠻⣿⣿⣿⣿⣤⣤⣀⣀⣨⣿⣿⣿⣿⡿⠛⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣴⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣄⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠋⠤⠀⠤⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠁⢀⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠃⠀⢄⠙⢿⣿⣿⡉⠉⠉⠉⢻⣿
⣿⣿⣿⣧⣠⣴⣿⠟⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠙⣿⣧⠀⢀⣶⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠄⠤⡘⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠂⠁⢸⣿⡿⢿⣿⣿
⡏⠉⠁⠀⣿⡇⠀⠀⠀⠈⢂⠀⠀⠀⠂⠀⠀⠈⠬⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠙
⣿⣦⣄⣰⣿⡇⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢠⣿⣆⣠⣿⣾
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠖⣜⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⢠⠀⢠⣿⣿⠿⣿⣿⣿
⣿⣿⠟⠿⠁⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄⣠⣿⠟⠁⠀⠸⣿⣿
⣿⣿⣤⣀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣀⣾⣿⣷⣤⣴⣄⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⣤⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢻⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⡟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⡯⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢋⡴⠞⠀⠀⠀⠀⠀⠀⡵⢼⠀⠤⢤⡀⠀⠀⠀⢀⡾⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣠⠃⢀⠤⠢⡀⠀⠀⡷⢼⠀⠀⠀⠈⢢⢀⠴⡃
⠀⠀⠀⠉⠀⢸⠬⠐⠲⣀⡀⠀⠀⠀⠀⡅⠀⠀⢙⢶⡢⣉⠉⠁⢲⠀⠀⠼⠋⣄⠁
⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠉⢢⣀⠀⢀⡇⠀⣀⣠⣰⣵⠶⠤⠶⣮⣿⠤⢶⡈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⣿⡀⢲⣴⣾⣻⣿⣿⠗⠀⠀⠀⠀⠈⠑⢾⣹⡆⠐⠂⡀⣈⡅⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⢁⡆⣰⣿⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠡⠿⠦⣄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣴⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡐⠂⠤⣶⣓⠄
⠀⠀⠀⠀⠀⠄⣀⡀⢳⠶⣶⣶⣿⣿⠠⠶⣆⣄⣈⡉⠀⠈⠂⠀⠀⠀⠀⠀⣠⡀⢹⣇⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣭⣻⣿⠃⠀⠀⠉⠉⠙⠁⠀⠀⠒⠀⢲⣦⣄⠀⣿⣿⢸⣿⣀⢂⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣧⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⣠⣾⣿⣿⣷⣶⣿⣿⡇⡀⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠁⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡿⢁⠃⠙⡇
⠀⠀⠀⠀⠀⠘⡂⠀⢠⠤⠂⡀⣠⣾⢿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠲⢤⣢⢀
⠀⠀⠀⠀⠐⠃⠠⡆⠀⠀⢀⡽⠋⢀⢦⡽⢻⣧⣀⡀⠀⠀⣼⣁⣾⣿⡿⣿⡷⡠⠦⠀⠉⠑⠤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠳⢋⠎⠠⠋⡻⠟⡹⣻⠛⠯⣟⢀⠙⡶⡋⠒⠤⡞⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠘⠳⠚⠁⠈⠀⠡⠀⠀⠀⠘⢳⠗⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⣾⣿⣿⡆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⡄⢹⣿⠋⢾⣿⣿⣦
⠀⠀⠀⠀⢀⣴⣿⣷⣦⠀⣰⣾⣿⣶⡄⠘⠻⠿⣷⣿⢸⡿⠶⠿⠿⠟⠋⠀⣴⣾⣿⣶⠀⣰⣾⣿⣷⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢿⣿⣿⢋⣤⣶⣿⣦⠀⢹⣿⠃⠀⢶⣦⣾⣿⣷⣌⢻⣿⣿⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢈⣛⡛⠃⠹⣆⠈⣿⣿⣾⣿⣾⣿⠷⣶⡿⣿⢸⣿⣦⡙⠻⣿⣾⣿⣾⣿⠃⢰⡏⠘⢛⣛⣉
⠀⠀⠀⣰⣿⣿⡿⠿⢶⣿⡄⠹⣿⠟⠉⢠⣄⣰⣏⡄⣿⡆⣍⠛⣡⣦⡄⠀⠙⣿⠏⢠⣿⠶⠟⢿⣿⣿⣷
⠀⠀⠀⠹⣿⣿⣿⣃⣀⣈⣿⣦⡹⣧⠀⢿⣿⣿⣿⡇⢸⡇⣿⣾⣿⣿⡿⢀⣼⢏⣴⣿⣡⣀⣘⡿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣻⣿⡿⢿⣷⣌⢿⣿⣞⠃⢸⡇⠛⣱⣿⡟⢡⣾⡿⢟⣿⣟⣻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠻⠿⠛⠹⣿⡇⠙⠦⠉⢿⣦⡙⠛⠁⢸⡇⠘⠋⠁⣴⡿⠋⠰⠛⠱⣿⠏⠙⠿⠟⠁
⠀⠀⣴⣿⣿⣷⡄⠀⣴⣶⣶⡄⠀⣀⣀⠀⠙⣿⣄⠀⢸⡇⠀⣠⣾⠟⠀⢀⣀⡀⢠⣶⣶⣦⡀⢠⣾⣿⣿⣦
⣰⣶⣿⡿⣿⣿⠇⠸⣿⣿⡿⢣⣾⣿⣫⣴⣦⠈⢿⣧⣸⣿⣴⡿⠃⣤⣦⣜⣻⣿⣌⠻⣿⣿⡇⠘⣿⣿⢿⣿⣶
⢻⣿⣯⣥⡌⢻⣆⣴⠟⠋⠐⢙⣛⣛⣛⡛⠓⠆⠀⢻⣿⣿⡿⠁⠠⠚⢛⣛⣛⣛⣛⠓⠈⠻⣧⣰⡿⠁⣬⣿⣿
⠀⠈⠉⠷⠶⠿⠻⢷⣴⣾⠿⠛⣛⣛⡛⠛⠻⢷⣄⠀⣿⣿⠁⣠⡶⠟⠛⢛⣛⣛⠛⠻⣷⣦⡾⠟⠿⠶⠾⠋⠁
⣼⣿⣿⣿⣷⠶⣶⡿⠛⢻⣷⣿⣿⣿⠋⠵⠶⠾⢿⡇⣿⣿⢰⡿⠷⠶⠊⠙⣿⣿⣿⣾⡟⠙⢿⣶⡶⠶⣿⣿⣿
⠹⣿⣿⣷⣀⢠⡟⠀⣴⣿⣿⣿⣝⣻⣷⣆⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣴⣿⣟⣽⣿⣿⣿⣆⠀⢻⡄⣀⠺⣿⣿
⠀⠀⣾⣿⣿⣿⡇⣸⣿⣿⣧⠸⣿⡟⠛⠋⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠛⠛⣿⡿⠃⣿⣿⣿⡇⢸⣿⣿⣿⣷
⠀⠀⠻⣿⣿⡿⠃⠻⢿⣿⠿⠃⠈⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠷⣦⡘⠿⣿⣿⠿⠀⣀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠿⠶⢟⣋⠳⣌⠻⢶⣶⣶⠾⠿⢛⣋⣭⣭⣭⣙⡛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠘⠻⣶⣶⣶⡶⠿⠛⠋⠉⠉⠉⠉⠻⢷⡈⠳⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣋⣯⣩⣟⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠒⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣻⣾⡷⠐⠀⠀⡶⠀⠀⠀⡴⠀⠀⠀⠀⠈⠀⣸⡩⢟⣖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠩⣽⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⡄⠀⠀⠀⠀⠿⠶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢫⡥⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠿⠃⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⡇⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠄⠀⠀⠀⣿⣤⢀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠃⢸⠀⠀⠀⢸⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⣿⣊⡥⠐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠲⣽⡆⣼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⣿⢃⡒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠛⣷⡾⠇⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡬⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣡⠀⠀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⢠⠴⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣦⠀⣾⡛⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⡹⠗
⠀⠀⠀⠀⠐⠀⠐⠊⠐⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣁
⠀⠀⠀⢲⣶⠎⠉⠉⠀⠀⠀⠀⣠⣤⡤⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣩⣤⣦⣴⢤⣄
⠀⠀⠲⢾⠃⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠋⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣿⣫⣴⣚⠁
⠀⠀⠘⢩⡏⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠃⠀⠀⠀⠸⣟⣋⠁
⠀⠀⠶⣶⡆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠂
⠀⠀⣚⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⢀⡀⠀⠀⠀⠠⠀⠀⠐⠶⡦⣀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠦⠀⠀⠀⠁⠀⠈⢉⠀⠀⠐⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡄⣻⣶⣤⣀⣀⡀⠀⠀⠀⣀⣤⠞⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣤⡎⢀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠇
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣻⣿⣿⣟⣻⣯⣿⣿⣟⣾⣻⡿⣻⡟⣻⡿⣻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠏
⢀⣠⡴⠾⠟⠛⣿⣶⡛⠀⠙⠻⣮⣉⣠⣤⣤⣥⣿⡬⢥⣬⣧⣭⣠⣟⣘⠛⠁⠋⠘⠋⠾⠇⠸⠟⠹⡿⢻⣿⣿⣿⡿⣶⣦⣤⣤⣾⣷⣶⡟
⠀⠙⢣⡀⣀⠻⠿⠟⠀⠀⢀⠀⣻⡟⡟⠓⠉⠉⠈⠉⠉⣁⣀⣨⠭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠾⠿⢿⣿⣿⣻⡅
⠙⠻⢦⣥⣞⡃⠀⠀⠀⠀⣴⡀⣿⣓⣳⣤⣤⠖⠈⠉⠉⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠉⠁⠉⠀⠀⠀⠀⠻⣝⠛⢻⡀
⠀⠀⠀⠀⠉⠛⠻⠶⣶⣮⣿⣿⡟⣛⣛⣿⣿⣿⣭⣭⣭⣵⣶⣶⠶⠶⢷⣴⣤⣶⣴⣶⣶⣾⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣯⣭⣭⣭⡭⠽⠿⠿⠿⠟⠛⠛⠛⠻⣿⡻⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣷⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣮⣄⣤⡤⠤⠶⠄⠀⠀⠈⠀⠀⢁⡉⡉⠀⢠⡄⠀⡄
⠀⠀⠧⠂⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠠⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠂⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢘⠀⠛⠛⠛⠁⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⣤⣤⠄⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠉⠁
⠀⠀⠀⠀⠀⢠⣴⠶⠀⣀⣀⡀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⡄⠻⠿⣾⣤⣤⣀
⠀⠀⡔⠂⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠀⡀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⢹⣾⡿⢻⣄⡀
⠀⠠⣇⠀⠀⠀⢸⡿⢻⡿⠟⢸⣿⣿⣸⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⣾⣿⣇⣿⣿⡇
⠀⠀⣶⣾⣴⣿⣹⡿⣿⣿⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠟⢹⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⠿⠿⠉⠁
⠀⠀⣛⡻⣿⣡⢨⡿⢫⣼⣿⣿⣿⡋⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢰
⠀⠀⣿⣿⣿⣿⡄⢰⣦⠁⣾⢿⣿⣏⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⠗⠀⠀⠀⠐⠤
⠀⠰⣿⣾⣿⡿⢁⡸⡟⢀⢻⣼⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⡄⢀⡒⠀⠄
⠀⢰⣿⡟⣽⣷⡞⢳⠛⡟⡏⣽⣛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡚⠋⠉⠁
⠀⢸⣿⣿⣍⣉⣈⣑⠚⢚⣛⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⠒⠒⠒⣷⣶
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣴⣦⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠛⠛⠋
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠶⠶⠶⠶⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⡀⠀⠀⠀⠀⠐⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⡄⠐⠂⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⣰⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⢸⣿⣿⠿⣛⠁⠴⠀⠙⠀⢀⣤⣶⣶⣶⠦⢘⣭⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣘⠋⠷⠀⠉⠀⠀⠀⡄⠀⠿⣿⠏⣿⣿⡿⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠠⣾⣏⣁⣠⠀⠉⠀⠀⠀⠀⠀⠀⠘⢻⣤⣶⣶⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣼⣧⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⣤⣬⡿⠋⠻⣿⣿⣿⣍⣍⣻⣯⠸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣽⣿⣿⣿⣙⠋⠀⠀⠀⠀⠀⠀⢙⣯⣶⣶⣄⠀⢙⠛⠛⢛⣿⣿⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢰⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣛⡿⠿⠿⣿⣿⣆
⠀⠀⠀⢀⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣎⢿⣿⣿⡿⠃⠀⠘⣿⣿⡄
⠀⠀⠀⣸⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠐⢶⠧⡄⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⣉⣭⠄⠀⠀⠀⠘⢿⣷
⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⣿⣿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠋⠉⠹⣿⣿⣟⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⢻⠿⣷⣿⣿⡿⠛⠛⠛⠁⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⡇⠀⠀⠐⠦⣶⣼⣇⠈⠻⣿⣿⣧⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⣿⣿⣿⠋⢰⣿⠃⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣇⠀⠀⠀⠀⣸⠏⠻⢦⠀⠀⠉⠉⠙⠿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠛⠿⠟⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢻⡀⠀⠀⣈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠀⡀⢀⣶⣿⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠁⠳⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠈⣇⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠸⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡃⢀⡀⢠⠀⣠⠀⣄⠀⡀⢠⠏
⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣟⣿⣭⡿⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠈⠿⣋⣿⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣯⣴⣆⡸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡀⢀⠀⣀⠀⣤⠀⠄⠐⠂⠘⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉

⠀⢠⣴⠶⢶⣶⡿⠿⣶⣤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⠁⣼⡤⣏⠰⠶⣿⠰⠶⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⢔⢐⣴⡆⡄⣀⠴⢄⢤⠢⣖⠂⠀⢈⠄⠀⠀⠀⠀⠀⡄⠃⢀
⠀⠙⠷⠤⠴⠻⢷⣾⡿⠿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⣀⣀⣀⡀⢀⡀⢀⣠⠜⠀⠀⡠⠊⡀⢸⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠗⠁⠀⠀⠀⠐⠁⠀⠡⠞⢩⠙⠂⠤⣈⠂
⠀⠀⢀⡶⠀⠀⠀⠀⠀⠲⡔⢒⡊⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠛⠖⠚⠀⠀⠀⠥
⠀⡰⠁⡇⠑⡀⠀⠀⠎⡔⠉⠀⠀⠀⢢⡀⠄⠀⠀⠀⠀⠳⣴⣫⠗⣠⠞⠆⢠⠎⠙⣧⢀⣡⢀⡞⠀⠀⠀⢘⡿⡅⠈⠀⠀⠐⢄⠀⢰⠀⠀⠀⡠⠂
⠀⣇⠀⡇⠀⡱⠈⢰⠰⡀⠁⠀⠀⠈⠀⠇⡀⠒⠀⠀⠀⠀⠻⠤⠴⠻⣤⡤⠛⣦⡤⠎⠀⠈⠉⠀⠐⠀⢀
⠀⠈⠒⡇⠀⠀⠀⠄⢀⠱⣀⠠⠤⠊⠠⠁⢋⡀⠀⠀⡀⠀⠠⢄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠘⢘⠀⢢⢤⣀⠖⠃⠀⠀⠀⢸⠀⠒⠒⠃⢠⠁⣠⣈⡧⢀⠄⢀⡉⢢⡀⠀⢠⠁⠀⠒⠤⢠⡤⠴⠊⠁⠀⠀⠇⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⣀⣠⡀⢸⡀⠔⠂⠀⠀⠘⠀⠀⠀⢸⠀⠁⢹⠀⣇⠀⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠁
⡰⠨⢤⠉⠄⠀⢀⢰⠂⠐⠊⠐⢀⠀⠀⠰⠁⠀⠉⠿⢤⣀⣀⠀⠸⣄⣀⣀⡀⠸⣀⡀⠈⣠⠇⠀⠀⠀⣀⠤⠒⠁⠀⠈⠱⠄⠀⠀⡀⠀⠀⠐⠄
⠑⠊⠩⠔⠂⠀⠀⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠀⠀⠙⠛⠛⠁⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⣾⡆⠀⠈
⠀⠀⢀⣤⡖⠒⠂⠒⠒⣲⣤⡀⠀⠀⠀⠀⠀⠀⣰⣊⡉⠉⠉⢱⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠄⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⣠⡙⢻⡷⠀⠄⠐⣋⣭⣿⣿⣦⠀⠀⠀⠀⢠⠀⠇⢮⡁⢠⣷⠣⢹⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠱⣀⠀⠀⠂⠁⢈⠕⠀⠀⡐⠀⠀⠀⠀⠂
⢰⠹⠟⣃⡀⠀⠀⠼⠛⠟⠿⢿⣿⡇⠀⠀⠀⠎⠀⠈⠉⠑⠆⠘⡇⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⡇⢸⠒⠊
⢸⣷⣿⣿⠁⠀⠀⢠⣾⣿⣧⣙⠿⡇⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀
⠀⣿⠉⢁⡀⠀⠀⠙⠿⠿⣿⡿⢡⠇⠀⠀⠀⢸⠈⢀⡀⠀⠀⡰⠁⠀⠀⡎⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠰⠿⠿⠿⠇
⠀⠘⢿⣿⣿⣶⠀⠀⠀⠀⢿⡧⠊⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠇⠀⠀⠀⠣⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⣀⠀⠀⠀⠀⢀⣀⣀⣈⣥⣤⣄⠀⠀⠀⠀⢰⣁⠯⠆⡈
⠀⢠⠊⠁⢀⠀⠀⢀⠀⠀⠀⠄⠸⠀⠘⠇⠒⠒⠒⠀⠀⠀⠀⠏⠀⠀⢀⡤⠚⠙⠀⠀⠀⠘⡇⠀⠀⢠⣿⢩⡍⢹⠁⠌⣿⡇⠀⠀⠀⠀⠀⠐⠁
⠀⠸⣀⡡⠃⠉⠡⠏⠌⢹⠐⠂⠂⠀⠀⠀⠀⢠⠀⠀⠠⡄⠀⠀⠀⢰⠏⠠⠀⠀⠀⡀⢀⣀⠇⠀⠀⠈⠻⢶⣶⡿⢗⣶⡿⢶⣦⡀⠀⠂⠀⢶⡄
⠀⠀⠀⠐⠒⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⡀⠠⠀⠀⠀⠀⣄⠀⠀⢀⠴⠭⠤⢤⡟⠐⠀⠀⠀⠀⢀⣿⣇⡛⣉⣇⣄⣻⡷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⠈⠀⣀⣠⠭⠶⠆⠀⠀⠀⠀⠠⠀⣀⣀⣀⠠⠆⠀⠀⠉⠀⠠⠋⠀⣀⡴⠋⠀⡘⠀⠀⠀⣼⡏⠛⢹⡏⣿⢩⣹⣿⠁⠀⠀⠀⢀
⠀⢀⡀⠀⠞⠋⠋⠁⣀⠔⠁⠀⠀⠀⠀⠖⠰⢠⠂⠖⡔⠂⠀⡇⠀⠀⠀⣜⣴⣞⡉⠤⠀⠀⠀⠀⠀⠀⠻⣧⣷⣾⡷⢿⣮⣿⡿⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠛⠛⠛⠛⠛⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⣶⠶⠛⢛⢛⡛⠛⠛⢻⡇⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⣿⠀⢰⣼⣿⣷⣶⠀⢸⡇⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢀⣿⠀⠘⠛⠽⠈⠙⠀⢸⡇⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⣤⣼⣿⠶⠶⠾⠿⠿⠿⠿⠿⠿⠷⠶⠶⣶⣤⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⡶⠶⠿⠛⠛⠛⠛⠛⠶⠶⢶⣦⣄⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⢀⣴⡿⠛⠛⢻⡄⠈⠳⣤⣀⠀⠀⢀⣴⣤⣀⠀⣠⠀⠹⣆⠀⢀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢠⡿⢿⠃⠀⢳⡄⣿⠀⠀⢈⣿⠁⠀⠀⠴⢞⣿⡛⠋⠀⠸⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⣸⡇⢸⡆⠀⣾⠁⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠚⠁⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⠀⢿⡀⠈⠀⢸⡇⠀⠘⣧⠀⠀⢀⣠⣤⣤⣾⣅⣀⣀⡀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣿⣶⠂⢸⡇⠀⠀⠙⢷⣄⣀⣠⡾⠛⠉⠉⠉⠉⠛⢿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠙⠷⣾⡇⠀⠀⢴⣶⡛⠛⠉⣀⣤⠞⢉⡉⠛⠳⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢶⣶⣤⣀⠘⣿⡀⠀⠀⠈⠙⠛⠛⠉⠻⣦⣀⣉⣻⣦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⢦⣤⣀⣀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡟⠙⠛⠻⠿⠷⠶⣶⣾⠿⠆



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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣠⣤⣤⠤⠤⠤⣤⠤⣤⣀⡀⣀⣤⣰⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣍⠻⣗⡒⠰⣟⡳⢉⣽⣟⢿⣿⡿⣶⣭⣟⠯⣫⡿⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢸⠐⣽⡧⠹⡿⠑⠺⡻⡿⠻⠍⡣⢛⢿⣿⡿⣿⣿⣮⣔⢩⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣏⣶⣘⣿⡀⠇⢠⢀⡇⠀⠀⠐⠀⢸⣆⡠⢃⣿⣿⣿⣿⣷⣻⣽⣿⡀
⠀⠀⠀⠀⠀⠀⣴⢛⣭⣍⣉⡉⠘⠒⠋⢙⣷⠦⠤⠤⢔⣘⣠⠔⣨⠀⢛⣹⣿⣿⣿⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣦⡐⠀⠀⠉⠉⣛⣯⣤⣤⣄⣤⣾⣉⣁⠚⣠⣿⣿⣾⣽⣿⡿⣿⡾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣴⡖⠮⢿⣿⡿⢿⡛⠷⠊⠁⠀⠙⢿⣿⣿⡿⢛⣭⣬⣿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣴⣤⣄⣀⡀⠀⠈⠁⠀⠙⢛⣫⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠙⣿⣯⡹⣿⠀⠀⠀⠀⠐⣿⢿⢿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠓⠦⢼⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⡄⣤⣄⡀⢰⣾⢷⡏⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣀⣀⣀⣀⣀⡼⠃⣽⡿⣷⣝⣯⣿⡾⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⣿⣿⠀⠀⢹⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡯⢿⣿⣤⡐⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣽⢿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣡⢿⡿⠁⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣯⣉⣙⣛⡻⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣷⣿⣿⠉⠉⣉⣼⣿⠘⢿⣽⣷⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣽⣾⣿⣿⣿⣿⣼⣿⣷⣦⡀⠀⠉⠁⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⣿⣿⣿⡿⠿⠿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣿⣟⢁⣀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠀⠀⠀⠈⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣤⣄⣄⣶⣂⣀⣤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠀⣠⡴⢤⡀⣠⡴⣤⡀⢠⡤⠦⡄⢤⡀⣠⡄⣠⡤⢤⡄⠤⣤⡤⠄⣤⠤⠄⢠⣤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠀⣿⠀⠀⠸⣿⠀⢸⡇⠘⠳⢶⡄⠈⢿⡟⠀⠙⠷⢶⡄⠀⣿⠀⠀⣿⠒⠂⢸⡟⣷⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠉⠛⠛⠁⠙⠛⠋⠁⠘⠛⠛⠁⠀⠘⠃⠀⠙⠛⠋⠁⠀⠛⠀⠀⠛⠛⠃⠘⠃⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠫⠝⡇⠀⠸⣋⡣⠀⠀⠀⠠⠂⡰⠁⣤⠀⢀⠀⠀⠀⠀⠐⠑⢨⢂⣀⣀⠀⠀⠀⠀⣠⠈⠫⡭⢙⠀⡄⠀⠀⠀⠀⠀⢻⣀⣞
⠀⠀⠀⠀⠀⠘⠁⠊⡡⡒⡄⠁⠘⠀⠀⠀⢀⠀⠠⠆⠀⠄⢁⠀⠀⠀⢠⡜⡃⠰⡀⠓⢐⣤⠀⠀⢐⢠⠜⡒⠒⠨⢥⣀⠀⠀⠀⡆⡛⡿⠵⢹⠟⠈
⠀⠀⠀⠀⠀⢰⠠⠀⡈⠒⠡⠀⠠⠀⠀⠀⠀⠂⢀⠀⢀⠈⠀⠂⠀⠀⡅⠀⢈⠢⠀⢀⡋⠀⠀⠀⠘⡀⠖⣱⢔⡃⡖⡀⠀⠀⠀⠃⡁⠷⠭⠾⢆⡰⠂
⠀⠀⠀⠀⠀⠘⠳⠤⠇⠀⠸⠎⠈⠀⠀⠀⠈⠂⠈⠓⠋⠄⠂⠀⠀⠀⠈⠃⠀⠀⠀⠯⠏⠀⠀⠀⠀⠉⠠⢄⣀⠤⠐⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠄

⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠤⠠⠀⠀⠀⡠⠀⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠓⠈⢠
⠀⠀⠀⠀⠀⠀⡌⠉⠤⠀⠁⠊⢀⠀⠀⠀⡂⡉⢰⠒⠑⠊⠛⡄⠀⠀⠐⠀⠒⠂⠂⠀⠂⠂⠀⠀⠐⡀⠘⠛⡤⠀⡐⠀⠀⠀⠀⡐⠗⠀⠘⠤⠄⠰⡆
⠀⠀⠀⠀⠀⠈⢓⠲⠀⡌⡔⡀⠘⠀⠀⠀⠀⢀⢦⢛⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣸⠀⣿⡞⠀⠀⠀⢇⠠⠆⠀⢀⢴⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠰⡬⠏⠉⠀⠀⠀⠀⠀⠈⢧⣣⡜⠆⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠔⠘⠉⠉⠄⠐⠀⠀⠀⠈⠠⠤⣀⡈⠳⠂

⠀⠀⠀⠀⠀⠐⢀⠤⠀⠀⡀⠂⠠⠀⠀⠀⡔⠀⢀⠀⠢⢀⢀⠀⠀⠀⢀⢀⠢⠄⠄⠄⠀⢠⠀⠀⠀⠄⢄⠐⠀⠄⠐⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠡⠀⠔⠒⠬⠁⠁⠀⠀⠀⠀⠈⠠⠐⠠⠁⠀⡁⠀⠀⠁⠀⠁⠒⠒⠉⠍⠁⠀⠀⠀⠼⠤⠒⠒⢌⠸⠅⠀⠀⠀⠀⠀⠈⣀⡃⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠒⡤⠊⠀⠀⠀⠀⠀⠠⠆⠐⢴⠔⡘⢠⠄⠀⠀⢆⡆⠀⢠⡔⣠⢶⣆⠀⠀⠀⠁⠈⠣⡬⠊⠀⠈⠀⠀⠀⡀⠀⡘⢿⠗⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⠈⠉⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠐⠈⠃⠐⠀⠀⠀⠀⠀⠀⠅⡀⠀⢐⣰⣆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢤⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠄⣈⢣⡟⠾⡁⢄⠀⠀⠀⠠⠀⢤⢬⣤⠄⠠⠀⠀⠀⢠⡴⢉⣀⡁⠈⢢⡄⠀⠀⠀⠀⡄⡤⠥⡄⡄⡀⠀⠀⠀⠀⠀⣖⣹⣸⡃
⠀⠀⠀⠀⠀⠠⡤⣭⢃⠜⣑⢷⢤⠀⠀⠀⠀⠶⠚⡧⠈⠰⠇⠀⠀⠀⢰⡀⠀⠋⠨⠀⢀⡅⠀⠀⠈⠀⣸⡀⣗⣸⡀⠠⠀⠀⠀⠀⢀⣈⢹⡭⣀
⠀⠀⠀⠀⠀⠀⡄⠹⠮⠵⠄⡇⠰⠀⠀⠀⠀⢀⠀⢀⠠⢁⠀⠀⠀⠀⠀⠘⠔⡤⢤⠂⠃⠀⠀⠀⠀⠀⡁⠈⠎⠁⠀⠀⠀⠀⠀⠀⠇⡸⢫⡁⠈⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠃
⠀⠀⠠⡄⠐⠀⠀⢠⣴⡴⠛⣡⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡇
⠀⠀⠀⠀⠐⠀⡋⠅⠨⠀⣙⣷⢿⡿⠛⢖⡤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠠⢈⣿⣿⠑⣒⠛⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠰⠆⢹⣍⢞⣓⡢⣆⣍⡍⣰⣰⣦⣤⡄⠀⠀⠀⠠⡤⠀⠀⢀⣀⣀⡀⢀⠀⣀⠀⣼⡾⣧⠮⢴⣨⣅⣰⣮⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣤⡈⢶⢘⣷⣿⡴⢋⠛⣮⣵⣷⡛⠀⠉⠉⠁⠀⠀⠀⣰⠌⠁⣉⣹⣶⠟⠀⠀⠀⢀⣠⣿⡟⣻⣿⣻⣭⡷⠿⢭⣭⣴⡻⣶⢭⡅
⠀⠀⠀⠀⠀⢀⣀⠈⠫⣤⣀⣼⣿⣯⣶⢛⠟⡻⢿⠛⣭⡐⠺⠀⠀⠁⠛⠀⡟⢿⣟⣟⣥⡞⠉⠀⠀⣳⣿⡯⠛⣡⣷⣿⠿⠀⣨⡀⡌⣷⡾⠿⠿⠋
⠀⠀⠀⠘⠛⠉⣉⣙⡓⠲⢿⣶⣤⣶⣷⣿⠈⣠⡟⢷⠘⠋⠀⠀⠀⠀⠀⠀⠠⡚⢛⣻⡟⠀⠀⠀⠀⠉⠉⠀⠀⠿⢟⣿⣤⣠⣿⣷⣿⣿⠷⠚⣓⠉⠉
⠀⠀⠀⠘⢲⣤⡌⣥⡄⣤⢠⣾⣷⣚⣙⣯⣛⣙⡏⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⣿⣟⣿⣏⣩⣿⠿⠿⠟⠓⠒⣀⡄
⠀⠀⠀⠀⡈⣀⠀⠀⠀⢉⣛⣋⣩⣿⣏⣉⣉⣭⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣴⣾⣿⡇⡀⢀⠀⣐⣩⣅⣽⡿⠃⠈⣻⠯⡍⢀⠀⢀⣰⣤⣾⠷⠚⠉
⠀⠀⠀⠀⠁⠛⢛⡁⠀⠀⣀⣀⣀⠉⣩⣛⣿⣿⣿⣴⠂⠀⢀⠀⠀⣀⠀⣼⣾⣽⣿⡏⠀⠀⠀⠀⠘⣿⣿⠟⠁⠃⣿⣶⣶⠶⠟⣋⣉⠩⢍⣁⣀⣠⠄
⠀⠀⠶⣤⠶⣤⣼⠧⢤⣄⠁⠀⢉⣝⣯⣿⠏⠉⠈⠀⠀⠀⠈⠘⠐⠀⠀⠀⠛⣿⣿⠧⠤⢄⡀⠠⠤⡿⣿⠖⠘⠣⣼⣌⠤⠀⠀⠀⠀⢀⡳⢌⡟⠉
⠀⠀⠀⠀⢨⡇⠹⠈⠳⠦⣤⡤⠀⠉⢻⡷⠀⠀⠀⠋⠀⠀⠀⠀⠒⠂⠦⠄⣄⣤⡠⠄⠀⠀⠤⣀⡀⠀⠈⠀⢀⣠⣈⣥⡤⠾⠧⡎⠛⠀⠸⣿⡉⠋⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠿⠁⠀⠀⠀⠒⠂⠀⠀⠁⠀⠁⠀⢀⢀⡄⠀⢀⠀⠀⠉⠁⠀⠀⠶⠐⠋⠛⠋⠀⠴⠶⠂⠙⠰⠆


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠛⠋⠉⠑⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠍⠁⢈⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢴⣶⣿⣿⣠⣶⣦⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⠈⠛⣿⣿⣿⡿⣿⠆⠀⠀⣘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣉⡩⣤⠀⠀⠈⠉⢿⣿⡿⢤⣒⣬⣶⣶⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣀⠀⠀⠀⠛⣿⠀⠀⠀⢸⠀⣀⣤⢶⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⡄⢤⣴⣾⣛⡻⣿⡆⠙⣿⣿⡿⢫⡶⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢉⡿⠁⠀⠹⣏⠙⠻⠟⠁⠀⠈⠟⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⠶⢤⣤⠶⠾⠀⢄⠀⠀⠀⠀⢻⣿⣦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣤⣄⡠⠤⠤⢄⣴⠀⠀⠀⠀⢸⡇⠘⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠫⣭⡀⠀⠤⠤⠄⠀⢢⠀⠀⠀⢈⠃⢀⠲⠶⠶⠚⠋⠁⠀⠀⠀⠀⣡⠁⣾⡏
⠀⠀⠀⠀⠀⠀⢰⠗⣶⠛⠈⠂⠀⠀⠀⢸⠀⠀⠀⠘⣇⡈⠳⠶⠖⠉⠀⠀⠀⠀⣸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠿⢁⣤⠀⢀⣤⡀⠾⣴⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣶⣶⡶⢀⡿⢸⠀⠀⡀⠀⡸⠏⠀⢈⣀⣵⣾⣿⣿⡿⣿⣿⣿⡿⣿⣯⡑⠒⠠⠤⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠳⣆⡉⢻⣿⣿⣷⣿⢺⡇⠘⠀⠀⢛⢸⣇⡶⣦⣾⣿⡿⢿⣿⣫⡾⢫⣿⡛⢁⣿⣿⣷⣦⡠⠀⢠⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠛⢻⣿⣿⡇⣾⠀⡸⠀⣠⣾⣿⣿⣧⣾⣿⣿⣿⢿⣽⣿⣿⣤⠞⠀⣸⠛⣿⣟⡟⠀⡰⡌⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢨⡉⠒⠒⣿⣿⢅⡏⣰⠃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣼⢻⠃⡼⠉⠛⠙⠷⢇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠠⢅⣈⣙⣿⣿⢾⡇⡁⢠⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣧⡘⢣⡜⠀⠀⠀⠀⢀⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⠃⡼⣿⣿⣿⡿⠁⠀⢠⣿⣿⣿⡿⢿⢉⣵⠚⠁⠀⠀⠀⢀⡆⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⣻⢫⡟⠐⢹⢏⠙⢻⠀⠀⠀⣼⠏⣿⣿⣿⣀⣸⣞⣴⣦⣤⡤⡡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠰⠁⠂⠀⠀⠸⠀⠀⠏⠀⠀⠀⢁⠂⠿⠟⠛⠙⡥⠟⠀⠁⠫⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠛⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣤⣶⠒⢲⣶⣶⠆⠀⠀⢒⣀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠐⠛⢻⣿⣿⣿⣿⣉⣵⣯⠀⠙⠁⠀⠁⣀⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠠⣼⠛⠿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⠃⡀
⠀⠀⠀⠀⠀⠹⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠈⠛⠧⣀⣄⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠻⠃⠈⠻⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⡀⠀⠀⠈⠁⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⠔⠗⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⢃⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⢀⡠⠄⠶⠒⠶⠦⠤⣤⣠⡤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢤⡤⣀⣀
⠀⡔⢡⡄⠀⢀⡀⠤⠦⢶⣭⣀⠀⠀⣤⠈⠉⠳⣶⠤⣠⡔⣥⠐⡄⠀⠀⠀⢀⣀⠤⠤⠒⠒⠉⠉⠀⠀⠀⢀⡔⠙⡄⠀⠈⠉⠒⠦⣄⡀
⢠⡇⢨⠳⣀⣎⣀⣀⡠⣄⣀⠈⠻⣀⡟⡄⠀⣤⠹⣷⠎⠠⠄⠰⢟⣔⠛⠛⢺⡧⢤⡴⠊⠉⠻⡉⠉⢲⠊⠉⠙⠲⢇⠀⠀⠀⠀⢀⡀⠹⣦⡀
⢸⣿⡘⢄⡞⠁⠀⠀⠀⠀⠈⡷⠤⠋⣰⠁⠀⣿⠀⡝⠀⢄⠀⢀⡈⢿⡴⣷⣿⣇⠜⣰⡟⢀⠀⢱⣄⣼⠄⠀⠀⠀⢌⠳⣤⣄⠀⢸⠙⡄⢹⣷
⠀⣿⣇⠈⡇⠀⠀⠀⡠⠤⠤⠳⣶⠞⠉⡻⣤⣿⣳⠧⠤⠴⠴⠮⠴⣞⣿⣿⣿⠀⡼⢻⣵⡏⠀⠈⡆⠁⠈⠄⠀⠈⠀⠀⡸⠀⢳⣼⠀⠹⡀⣿⣧
⢸⣿⡜⣆⠹⠀⠀⢰⠀⠚⠃⠀⠉⠉⠛⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣻⣎⠻⣧⣸⣿⡇⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠑⠒⢻⠃⠀⠀⢣⢹⢸
⢸⡏⢿⣿⡇⠀⠀⡜⠀⠀⠀⠀⢰⠆⠀⠇⣿⣿⣿⢆⠀⢀⠔⠀⠀⡿⠁⡀⠈⠙⢦⡙⠻⣝⢦⣀⠀⠻⡆⠀⠀⠀⠿⠂⡀⠀⠈⠦⣀⣀⡼⢾⣘
⠀⣿⣮⣿⡏⢄⣠⠀⡄⠀⠀⣠⡞⠀⣰⣧⠟⣉⣀⣮⡀⠬⠤⠔⠚⠉⠉⠁⠉⠉⠉⠛⠚⠛⠲⠬⠯⣶⣌⢦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⡄⢹
⠀⢸⡏⠛⢷⣬⠯⢚⣥⣀⣰⣃⡠⠴⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⠷⠦⠤⠤⣤⣧⠺⣹⠀⣩⣴⣿
⠀⠈⣿⠀⠀⠸⣭⣁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠋⣰⢫⡏
⠀⠀⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⣀⡀⢀⠀⠀⢀⡄⠀⠀⢀⠀⡀⠀⢀⠠⡀⠀⣀⠀⠀⠀⢠⡄⠀⢀⡀⠀⡄⠀⣄⠤⡀⢀⡠⠡⢸
⠀⠀⢻⢻⡄⠀⠀⢰⠀⠀⠀⠀⣊⠒⠾⠀⣂⠐⠢⠃⠀⡈⡀⠀⠠⡱⠒⠅⠀⡮⠒⠴⠀⣱⠀⠀⠀⡀⠃⠀⢸⢠⠀⡇⢸⡴⠒⡀⣸⣿⡀⢸
⠀⠀⣾⢸⡇⣀⡀⣸⡇⢀⢤⡜⡇⡀⠤⡀⡙⢒⠕⠀⠀⡸⢣⠀⠐⠧⠐⠢⠸⠣⠔⠒⡀⣺⠀⠀⢀⡿⢻⠀⢸⣾⢠⡇⢸⡇⠀⣯⢸⡟⣷⠸
⠀⢠⣿⢸⣿⣇⢹⣿⣿⡝⣰⠇⠇⠁⣳⠀⢴⡜⠄⠀⢰⡉⠅⡇⠈⠉⠀⡧⠀⠉⠁⢁⡇⢿⠀⠀⢘⡈⢥⠃⢸⡍⠼⠇⠸⡇⢀⢃⠈⣏⠘⢳⡆
⠀⣾⣯⡿⣹⣼⡿⣤⠀⣸⡇⢠⠣⠐⡇⠀⠸⠈⢎⢄⡜⠀⠀⢰⠘⠇⠔⡕⠰⠣⠄⡰⠀⠹⠤⢤⢸⠀⠈⡀⢸⠇⠐⠀⠨⠧⢊⠂⠀⢻⠀⠀⣇
⠀⣿⣟⣽⣿⣛⣧⠀⢾⣿⠇⠀⠑⠈⠀⠀⠉⠀⠀⠉⠉⠀⠀⠉⠈⠐⠈⠀⠀⠑⠊⠀⠀⠑⠈⠁⠉⠀⠀⠁⠈⠁⠀⠁⠈⢢⣥⣄⣤⣼⢾⣄⣿
⠀⣿⣿⣿⣿⣻⣿⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⣑⡤⠤⠤⠤⣔⢩⠛⢿⣿⣿⣿
⠀⣿⣾⣿⣟⣼⠃⠀⠀⠠⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⠏⠀⠀⠀⠀⠀⠙⡆⢸⢿⣿⣿
⢰⢣⣿⣿⣽⠇⠀⠀⠀⠆⠀⡸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⠻⠀⠀⠚⠃⠀⡸⡳⣾⣿⡿
⢸⣼⣿⢿⡿⡀⠳⡀⠀⢇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣧⠀⠰⡀⠈⢶⡴⠃⡆⡠⢁⢿⣿⣿⡇
⢸⡟⣿⣿⣴⣧⠀⠉⠢⣌⢣⣸⡇⠀⠀⠀⠀⢀⡀⠀⢀⡄⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣸⣇⡰⢙⢷⡚⠓⣲⠛⣡⣏⣀⣿⣏⢻
⠘⣧⣿⣿⡇⣿⠴⠦⣧⠈⡆⢹⣸⣤⠆⠀⠀⣼⢁⡶⠁⢀⣠⢠⣄⣾⡟⣦⢳⣀⠀⠀⣠⠏⢰⡄⣸⣾⣿⣿⡆⠘⡄⠉⠉⣠⠜⠀⡇⣿⣿⣿⡹
⠀⣿⣸⢻⣿⢡⡄⠀⣿⣷⣦⣾⢿⣏⣴⣣⣾⣷⣿⣥⢾⡟⠁⣾⣿⡝⣷⣿⡿⣟⣧⡾⣿⢀⣾⣧⣿⣿⡿⢿⣷⢀⡾⠠⠊⠀⠀⠀⢿⣿⣿⣿⡇
⠀⣿⣿⣸⣧⡀⣿⣼⣿⣿⣰⣏⣾⣿⣿⣱⡿⢻⣿⣷⣿⣠⡞⣽⡟⢳⣿⣿⣷⣿⣿⣿⢿⢿⡿⣿⢿⣿⢳⣿⣿⢻⡃⠀⠀⠁⢀⢀⣸⡏⣿⢿⡇
⠀⠹⣏⠿⣮⣻⣿⣸⣿⣿⣡⣟⡟⣼⣿⠛⣠⡼⡃⠸⣻⣯⡾⢯⣤⣿⠿⠬⠿⣿⣿⡻⢯⣼⣓⡇⢸⡿⣾⣿⣯⠞⠛⠒⠈⠁⣹⢟⣡⡿⢫⡞
⠀⠀⠈⠻⢌⣙⢾⣿⣿⡿⢫⣞⡼⠿⠷⠾⣭⣤⣬⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡽⠿⠟⠛⠛⢻⣿⣏⠥⠀⠀⢀⣾⠗⣛⣡⠖⠋
⣀⣀⣀⣀⣀⣉⣙⣛⣿⣟⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣻⣿⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⡀⠀⢀⢀⣀⢀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠘⠐⠂⡤⠀⡸⠀⢸⠀⡠⠠⠄⠀⡇⠐⠀⠒⢄⠑⡆⠀⠈⢠⠤⡄⠱
⠀⠀⠀⠀⠀⠀⡜⠁⡔⠁⠀⢸⠀⣀⣀⡀⠀⡇⠠⡠⠠⠊⢀⠂⠀⠀⠆⠀⢠⠀⡀
⠀⠀⠀⠀⢀⠎⢀⠌⠀⠀⠀⢸⠀⡤⠤⠃⠀⠇⠀⢄⠀⠂⠁⠀⢰⠀⠀⠀⠘⠀⡃
⠀⠀⠀⢀⠎⠠⠏⠀⠠⡀⠀⠸⠀⠇⢀⡀⠀⠀⢦⠈⢢⠀⠀⠀⠀⡀⠣⠠⠂
⠀⠀⠀⠘⠤⠤⠤⠤⠤⠂⠀⠰⠤⠤⠤⠃⠀⠦⠂⠁⠤⠃⠀⠀⠀⠐⠠⠠⠐⠁

⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠒⢲⠀⠀⠔⠐⠄⠀⠀⢀⠖⠉⠉⠲⡀⢰⠀⠀⠀⠀⠈⠀⠀⡀⠀⠖⠂⠀⠐
⠀⠀⠀⠈⡄⢰⠀⠀⡠⠤⡀⠀⠀⠃⡀⠀⠐⠀⠀⠘⠀⠀⡂⢰⠁⠀⠉⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⡇⠈⠉⠉
⠀⠀⠀⠀⢡⠀⡆⠰⢡⡄⢱⠀⠰⢀⠁⠀⡀⢈⠁⠀⠀⠀⠑⠄⢉⣁⠐⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠰⠤⠤
⠀⠀⠀⠀⠘⡄⠰⠇⠎⢸⠘⡀⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⡖⠀⠈
⠀⠀⠀⠀⠀⢃⠀⡜⠀⠈⡄⠓⠁⠇⠀⢈⠀⠔⡄⠀⠀⢐⠁⣀⣀⠠⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠣⠤⢤
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠒⠊⠀⠀⠐⠐⠀⠑⠒⠀⠀⠑⠂⠀⠒⠁⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠘⠂⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠁⠀⢻⣏⠀⢀⣿⠀⠀⠀⢉⣿⣶⡖⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⠋⠹⠀⠀⠀⠀⢿⣿⡀⠀⢻⡀⠀⠀⢀⣀⣈⠙⠇⢼⣷⠄⠀⠃⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣓⡀⠀⢀⣠⠸⣶⣦⡜⣩⣷⣸⣏⠃⢀⡔⡏⠉⢋⠆⠀⠘⣁⣄⠀⢀⣷⡜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠿⠿⠂⠚⠑⢻⡀⣄⡠⠿⢿⣿⡿⣦⣩⡀⠀⣠⣿⣧⣤⣼⣿⣿⣷⣟⠁⠀⠀⠁⣀⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠿⣦⣀⣻⣃⡠⠞⠉⠁⠀⠀⠀⠀⠀⠉⠀⠘⠛⠳⣽⠆⢈⢿⡍⠻⣿⣿⠧⢤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠁⠀⠀⠀⢠⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣯⣇⠼⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠸⠷⠚⠉⠀⢀⣠⣴⣇⣤⣀⠀⠀⠀⠀⠘⣭⣙⢦⣾⠿⠛⢇
⠀⠀⠀⠀⠀⠰⢛⣻⣷⣶⡶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠏⢀⡀⠀⠈⠀⠀⠀⢁⡴⢌⣀⣀⠐⠆⠱⠄
⠀⠀⠀⣤⡀⠀⢘⣿⣿⣭⡤⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠐⠀⢀⠤⠓⠒⠛⠋⠉⠓⠀⡀⠰⠆
⠀⠀⠀⠈⠃⠀⣄⣙⣫⠽⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⣤⠦⣄⠈⠁⠀⠀⠀⠀⠀⢰⠀⢠⡴
⠀⠀⠀⠀⣀⡀⠁⢰⣶⢆⣸⠿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⡯⠐⠙⠓⠈
⠀⠀⠀⠀⠈⠁⠀⡈⢻⣿⣿⣄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣞⠀⠀⠀⠀⠀⢀⡼⠄⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣇⡀⠸⠿⢿⠷⡷⡄⠀⠀⠀⠻⠀⠀⠘⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⣼⣷⠚⢻⣟⣡⡶⠉
⠀⠀⠀⠀⠀⠀⠋⢯⡀⠀⠺⢺⣧⣨⠟⣦⣤⡤⠽⢾⣿⣶⣇⡀⠀⡀⠀⠀⠀⣆⠳⠚⢿⠹⣷⠿⠛⢉⡀⣴
⠀⠀⠀⠀⠀⠀⢷⣄⠀⠐⠢⡶⢿⢿⣿⣧⣈⣷⢲⣬⠡⠤⣀⣋⢀⣀⣗⡴⠊⠀⠀⠠⠆⠀⠸⡄⠀⠡⠙⠛
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣤⡼⡺⢼⠛⢿⣿⣇⠀⠀⠀⠀⠡⠟⢐⣾⣿⠈⡠⣶⣿⠀⠀⠀⢠⠛⠉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣤⣠⡓⠚⠋⠁⢻⣆⠂⠀⠀⠆⠋⠀⠰⠚⠛⠋⢙⠀⠀⠠⠀⠂⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣟⣿⣿⣷⣄⣀⠀⢹⠠⢤⡄⢠⣴⡶⠀⠀⠐⠒⠁⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠈⠇⠘⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠛⠻⣭⠁⠀⠀⠉⠈⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⣠⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠄⠀⠄⠀⠀⡰⠃⠱⡀⢠⠇⢩⠀⠀⠈⢣⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠄⢠⠄⠘⠄⠀⠀⠱⡴⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠙⠻⠧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠶⡒⠒⠂⠀⠉⠹⡀⠂⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢀⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡦⠀⠀⡀⠀⠱⡀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⡔⡥⠦⠤⠠⠤⠄⡄⠁⠀⠀⠀⡠⠃⠪⠤⠤⠤⠤⠤⠬⠴⠖⠗⢠⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⡄⢸⡎⠀⠀⠀⠀⠀⠀⡏⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠑⢦⡀⠀⠠⠀⠀⠃⢀⠀⠀⠘⢦⠀⢰⡂⠀⠀⣀⣀⡤⢞⡙⢫⣄⠀⠀⢀⠀⠴⡉⢋⠒⢄
⠐⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠈⠠⡀⠀⠀⠑⢾⠉⠉⠁⢍⠀⢴⣿⣦⣥⡍⠀⠄⠠⠾⠾⣿⣿⣣⢨
⠛⠄⠀⠛⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠈⠢⢅⣇⠠⠉⠁⠈⠄⠀⠘⠦⣉⣋⣡⠎
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⡀⠸⠄⢲⠾⠑⠀⠀⢤⡄⣠⡾⠳⠄⢀⡀⠊⠀⠠⠤⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣉⠡⣤⣰⢶⠠⢶⣤⣤⠶⠲⡿⠟⣻⣿⣿⣭⣴⣈⣴⣠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠺⣶⣤⣌⣿⠟⣤⢠⠀⣄⠰⣶⣯⣿⠟⣿⠁⡸⢿⠿⣿⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⣱⣿⣰⡞⢺⠃⢾⠀⠈⢀⣿⡿⡵⣇⠛⠀⠐⠚⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡐⠛⠛⣶⠘⢡⡼⠀⡌⠈⠀⠀⠀⢸⣿⡇⠂⠁⠀⠀⠀⠀⢻⡐⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⡤⢦⣄⠉⣦⣰⠅⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣵⣎⡭⠀⠀⢀⡠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⡄⠀⠐⢲⣦⣾⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⡀⠀⠀⢱⣾⡧⠀⠠⣁⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣬⠿⠃⣄⣴⣿⣿⢁⠔⢀⣶⣄⠀⠆⠀⢸⣿⡂⠋⠙⠆⠀⠀⠴⣷⣤⡸⠶⠚⣃⣨⡿⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡤⣴⡉⢀⣀⡙⢦⣄⣨⣿⠃⠀⢲⡾⢩⣿⣿⣄⠀⠀⠀⠙⠄⠀⠀⠀⠴⣶⣚⣻⣽⣿⣟⡛⠫⠁⠲⡿⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡝⠲⠋⢳⣦⡀⢿⣿⡿⣋⠁⡄⢠⣿⡾⠛⣿⣿⠡⡄⡀⢀⡀⡄⠀⠀⢰⣾⠿⢭⣴⣿⣗⠻⣷⠀⢀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⣿⡿⣿⡿⡼⠁⠐⠀⢸⣋⣴⣶⣾⡿⠀⠁⠁⠈⠁⠀⠀⠈⠀⡟⠀⠈⣿⣩⣿⣆⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣥⣾⠋⣩⣥⡾⠁⠀⠀⠀⠀⡯⡥⠀⢚⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠐⠋⠉⢚⣿⡇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⣷⣯⡿⠁⠀⠀⠀⠀⠀⠶⠿⠶⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⠀⠤⠐⣡⢌⣵⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠺⣿⣀⣎⣿⠇⢀⠀⠀⠀⠀⣶⣶⠾⢛⣭⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠁⠀⠀⢈⣭⣼⣷⣶⡆⢁⣄⡏
⠀⠀⠀⠀⢴⡀⠀⠚⡛⠿⣆⣡⣴⠟⠿⠀⠚⠴⠀⠀⠀⣿⠇⣤⣾⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠂⣠⠶⣟⢛⡛⣹⡟⠃⠀⠿⠁
⠀⠀⠀⠀⠀⠁⣀⣀⣰⣿⣻⣿⣡⣠⣆⡠⣤⢀⠠⣦⣤⣶⣞⣿⡿⠿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣠⡄⠸⢉⣿⣷⣤⡀⠀⣲⡀
⠀⠀⠀⢀⣀⣆⣽⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣋⡿⠿⠧⠙⢿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⡴⢞⣡⣼⣿⠉⠃⢘⠛⢃
⠀⠀⠀⠀⣠⣼⢿⣿⣶⣿⡟⣸⠟⢶⣿⣿⣿⢡⡿⢿⣶⣿⣶⣾⡎⡗⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⠑⠯⠙⠻⢿⡀⢤⣀⢬⡻⡄
⠀⠠⣶⣾⡯⠻⠆⢻⣿⣿⡄⣃⢰⡟⡻⠿⡏⣼⠁⠘⢸⣿⢿⣿⡇⠅⠀⠘⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣀⣀⣀⣰⣾⡇⠀⠛⠈⢷⠱⡄
⠀⠀⠹⡇⠀⠀⠤⣸⡟⣸⠷⣼⣿⠁⠝⣿⠁⠏⠀⠀⣸⡿⣾⢿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢻⡿⠟⢋⣹⣄⠀⠀⠀⠈⠇⠸⠃
⠀⠀⠀⣧⠂⢰⣿⡿⣱⢆⡾⢏⠋⠀⠐⣡⢸⠀⢀⡄⣿⠢⠔⣶⣿⠂⠘⠂⠀⠹⠀⠀⠀⠀⠀⠀⢀⣠⡾⢿⣿⣏⣤⣾⣿⣿⣿⣷⠀⠀⠀⠘
⠀⠀⣰⣿⣄⣤⢿⠃⠁⣺⡇⠸⠁⠀⣰⡇⠀⠀⠙⠂⣿⣄⣄⡀⣿⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢰⣿⣤⣶⣾⠿⡿⠋⠀⠹⡏⠈⣷⣄
⠀⠹⠟⠋⠘⠿⠀⠀⡀⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣛⣿⣿⣿⠇⡶⠀⠀⠀⠀⢻⡇⠀⠀⣸⣿⡿⠉⠗⠈⡿⠁⠀⠀⠐⠏⠉⢨⣷
⠀⠀⠀⣤⣤⣘⠀⢀⢩⡇⠀⠀⠆⠀⣿⠅⠀⠀⣀⢸⡟⠋⠉⠰⣾⡀⠀⠀⠀⢀⣀⠘⡇⡀⢠⡟⣁⣠⣶⣀⣦⣀⣀⣀⠐⠀⣦⣲⣿⣿
⠀⠀⠀⠘⠲⡟⠀⠈⠈⠀⠀⠀⠀⢠⣿⠀⠀⣄⠁⠀⣿⡿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠁⠸⣿⣿⣿⣿⣯⢿⣿⣛⣿⡿⢺⣿⠾⠛⠟⣦⡀
⠀⠀⢰⡿⠿⠃⠀⠀⠀⠀⠀⢸⣇⢼⠟⢰⡔⠛⠀⠰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠇⠉⠘⠛⣁⣈⣿⡁⣀⣷⣿⣥⡀⠳⡄⣹⠊⢶⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠿⠻⠻⣿⠋⠉⠀⢬⣌⠛⣿⣿⣶⣿⠛⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣉⣁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠛⠶⠶⠞⠉⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡶⠶⢶⣿⣿⣿⣿⣿⣗⣦⣀⣐⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠺⠽⠚⠒⠣⠾⡆⢀⣀⣠⣯⣳⢿⣿⠋⠉⠛⢿⠟⡳⡤⡈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⡀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠁⠀⠘⢟⣩⡖⢆⠀⢙⡿⣋⣿⠀⠀⢙⣕⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⢂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣶⠽⠷⣶⣍⠀⢠⣽⣫⢘⡃⠈⠐⠀⠁⠘⣦⡀
⠀⠀⠀⠀⠀⡠⡺⢡⡔⢯⣦⠀⠀⢐⡈⠥⠀⠀⠀⠀⠀⠀⠀⢮⠰⢈⢔⢅⡿⠀⠙⣟⣿⣻⣪⡴⣻⠀⠀⣔⡲⡁⣉⡳⢄
⠀⠀⠀⠀⢨⡌⣔⠪⡂⢕⢸⠀⠀⠀⠒⠈⠈⠀⠀⠀⠀⠀⠀⠈⠘⠪⣴⡵⠇⠀⠀⠉⠀⣿⣯⠿⣒⡭⠶⠋⢛⠡⠘⠬⠋⠣⡀
⠀⠀⢀⠎⡈⢔⠲⣪⡐⠩⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠧⠃⠀⠀⠀⠀⠀⠈⠳⡞⢍⡢⠑⣀⠤⢒⠠⠔⠂⠀⡑⡄
⠀⢀⠆⠐⠌⡐⠍⡢⢙⠳⣢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢲⠒⠞⠐⡄⠡⢐⠨⠐⢊⡠⠔⠊⠀⠰⢳⠘⡀
⠀⡌⠀⢌⡁⠊⠕⣊⢔⡣⠞⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⣀⢤⡨⢙⠢⣉⠉⢈⡠⠔⢊⠡⠐⢀⡀⠀⠈⠙⡷⠡
⠰⠀⠀⠀⢀⠁⠒⠂⠬⠍⡇⠀⠀⠀⠈⠀⢊⠡⠒⠁⠀⠀⠀⠄⢀⠀⠀⣠⢒⠃⣂⠤⢒⡨⠔⣊⠡⠐⢈⡠⠔⡪⠕⠀⠀⠄⠤⠧⢀
⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢑⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠂⠉⠐⢈⠠⠒⢈⠠⠐⡪⠄⠊⢁⠠⠐⠈⠐⠄⢢⢀⡏
⡇⠀⠀⢒⣂⠀⠨⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡔⠊⠐⡂⠡⢒⡈⠤⢒⠨⠔⢂⡁⠤⢒⡈⠔⣂⠁⢐⡂⠬⢲⠉⠉
⡇⠀⠈⡁⠤⠒⣊⠥⠀⡀⠀⠈⢿⠦⡀⠀⠀⠀⡌⢝⠡⢐⠄⢄⣈⢀⠡⠐⠊⠅⠂⣈⠠⠐⢊⡡⠔⣊⠥⠒⢈⠠⠀⠐⢂⢁⠊⠀⠂
⠃⠀⠀⠐⡈⠥⢐⠢⢑⡠⢐⡀⠈⠃⠑⠀⠀⠐⡋⠕⡪⢴⢡⠂⣂⠤⡒⠡⠀⠂⠁⠄⢒⡉⠄⢒⡩⠄⠒⣉⠠⠐⠀⠊⠀⡆
⢀⠀⠀⠀⠐⡈⠄⢂⠡⢒⠡⢊⠅⠀⠈⠒⠄⣀⠐⠊⠀⣜⣵⢒⠔⡉⢷⠩⣸⠄⢀⠔⡪⢄⠀⠡⠔⣂⠩⠐⡈⠁⠀⡂⢠⠃⢀⡭⠔
⠈⡄⠀⠀⡡⠔⣈⠄⠊⡡⠒⡡⠒⡡⠀⡀⠀⡀⠈⠁⠒⢆⠀⠁⡊⠂⣁⢎⣀⠊⢑⡩⠲⢑⠠⡀⠉⠔⣂⠡⠄⠀⠀⡂⠀⢢⠀⢀⢀
⠀⢰⠀⠀⠐⠉⡠⠐⢉⠔⢊⠔⢊⠔⢋⡠⠊⡀⠀⠀⠀⠀⠑⠛⢪⠊⠀⠀⠀⣀⠀⠈⠢⠠⡈⠐⠄⠀⠐⠂⠀⠀⢀⡂⠅⡀⠁⠁⠊
⠀⠀⢣⠀⠀⢉⠤⠊⡡⠂⢁⠔⢁⠔⢁⠤⠊⡀⠔⠁⠀⢂⠄⠀⡰⠀⡠⢔⠩⠒⠀⠀⠀⠀⠈⢤⣀⠀⠀⠀⠀⠨⠐⡀⠅⡪⠀⠌
⠀⠀⠀⢢⠀⠀⠐⢊⠤⠊⡠⠐⡁⠔⢁⠠⠊⡠⠀⠀⠨⢔⠁⠸⠀⠀⠀⢑⠨⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⢢⢀⡨⠕⡢⡑⢈⠌
⠀⠀⠀⠀⠱⡀⠀⠁⠤⢊⠠⠊⡠⠔⣁⠔⡩⠂⡀⠄⠀⠡⢂⠌⢢⠀⠀⠀⡊⠄⠀⠀⠀⠠⡂⠀⠀⠀⠔⠡⠄⡂⢅⡨⡠⠂
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⣉⠔⢊⠤⢊⠔⢊⠔⡀⠀⠈⠠⢂⠅⠑⠤⡀⠀⠄⠀⠠⡐⠌⠀⠀⠀⡠⠀⢀⠥⠂⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠂⠁⢊⠤⢊⠥⢊⠠⢂⢄⠀⠐⠨⢢⠀⠘⠀⠁⠀⠀⠈⠀⢀⠒⠁⣀⠠⠔⡢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠁⠒⠁⠪⠔⠅⡪⢀⠀⠀⠀⠆⠀⠀⠀⠀⣀⠔⠂⠀⠄⣂⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠄⠀⢀⠤⠊⢁⣀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⡠⠤⠒⠒⠒⢤⠀⠀⠀⠀⡤⠒⠒⠒⠠⢄⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡤⠼⢤⣄⣰⡇⠴⠶⠶⢤⣤⣸⠀⠀⠀⠀⣇⣤⡤⠶⠶⠦⣸⣆⣀⡤⠧⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⣀⠙⠆⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⠑⠶⠖⠊⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⡆⠰⢃⣀⡈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠉⢙⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠔⠠⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⠉⠙⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣾⣿⠛⡌⢿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃⠀⠀⠘⣜⢿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠙⣿⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢻⠏⠀⡜⠒⠬⣝⣛⣛⣛⣛⡭⡺⠃⠀⠀⠀⠀⠘⣗⢭⣛⣛⣛⣛⣫⠥⠚⢳⠀⠹⠇⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⣃⠀⠀⠀⠀⠀⠀⣀⠤⠚⠓⠢⣄⣤⠔⠚⠓⠤⣀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⡋⠑⠒⠂⠄⠒⠊⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠑⠒⠠⠐⠒⠊⢹⠃⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⢗⡒⠠⠤⠤⠤⠔⠒⠉⠀⠀⠉⠒⠠⠤⠤⠤⠄⠒⡺⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⡤⣿⣀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠛⠋⠀⠈⣯⣠⡿⠶⡄⠀⠰⢦⣴⢛⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠙⠓⣶⠀⠀⠀⠀⠀⠈⠻⠶⠶⠃⠀⠐⢻⡇⠀⠁⣠⡼⠷⠒⠒⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣀⣤⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⡛⠉⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠠⠤⠄⢀⣀⠀⠀⠀⠉⢀⡀⠀⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠒⠒⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠉⢻⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⡀⠀⠀⠀⠀⣤⢶⣿⡇⠀⢀⡤⢶⡿⢻⠛⢷⠶⣄⠀⠀⠙⣦⠀⠙⠟⠃⠀⠀⢀⡞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡀⢻⡄⠀⠀⠀⢀⡟⠸⠇⣴⠿⢦⣿⣤⣼⣤⣬⣷⠼⠷⡄⠀⠈⣧⠀⠀⠀⠀⠠⠟⢀⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠘⠃⠀⠹⣄⠀⠀⢸⠁⠀⢰⡇⠀⢸⠃⠀⢸⡀⠀⢸⡄⠀⢻⠀⠀⢸⡆⠀⠀⣠⠆⠀⠘⠃⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠐⠂⠀⠀⠙⣆⠀⢸⠀⠀⢸⡟⠛⢻⠛⠛⢻⠛⠛⢻⡟⠛⢻⠀⠀⢸⡇⠀⣰⠋⠀⠀⠐⠂⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠸⣇⠀⠈⢧⣀⣼⣧⡤⣼⡦⢤⣾⣄⣠⡟⢠⠀⣼⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠻⢦⣹⣄⢸⣃⣴⣣⡼⠋⠀⣾⣼⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣳⣤⣴⡃⢀⡀⠘⢷⣄⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠛⠋⠁⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣭⣥⣭⣿⡾⠂⠀⠀⠈⠛⠶⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡗⠲⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠂⢸⠐⠂⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⢉⡟⢙⡏⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣳⣄⣼⣠⣼⡃⠘⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠘⢦⡤⢾⡉⠉⣹⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠉⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠸⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠠⠄⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣠⣄⠠⣤⣤⠄⣀⣠⠄⣄⣤⣤⣤⠀⠀⢤⡄⠀⣠⡄⠀⠀⣀⡄⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠁⡎⣿⡁⢳⣿⠛⠀⣿⡿⢿⢻⠀⢰⡿⠛⠀⣼⡿⢂⢸⣿⢖⡟⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⠏⠸⡟⠰⠆⠘⣤⣠⠋⠀⢼⠿⠀⢳⠈⡇⠘⠈⣩⠾⠃⢀
⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⣀⠀⠁⡶⢵⠙⠉⠣⢄⡃⠀⠀⠈⣦⡃⠀⠠⠃⣠⣤⠊
⠀⠀⣰⣶⡀⠀⠘⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡆⠐⢷⠀⠀⠀⠑⠄⠀⠀⡟⠀⡠⠃⠸⡹⠋
⠀⠀⢹⣿⣿⣆⣀⡆⠹⣿⣿⣿⣿⣿⣓⠦⣀⠀⣀⢠⣐⡒⠢⠀⠀⠹⡀⠘⡄⠀⠀⠀⢇⠀⡴⠛⠉⠀⣠⠏⠀⠀⠀⢀⡀
⠀⠀⠘⠻⢿⣿⣿⣧⡀⣿⣿⣿⣿⣷⣌⡛⠆⢝⢷⣿⣿⠿⠷⣬⣦⠀⠈⠒⠷⠤⢤⣄⡈⣾⠁⠀⣠⣥⣏⣠⠄⣀⠁⣤⣢⡵
⠀⠀⠀⣶⣄⠉⠻⣿⣷⣿⣿⢿⣿⣿⣿⢟⢦⡑⠁⠘⢿⣷⣔⣽⠟⢳⠂⠤⢀⣀⠀⣀⠹⣧⠀⠸⣿⡟⢩⡑⣌⡀⣤⣾⡟⢲
⠀⠀⣠⣿⡓⠀⠀⠈⠛⢿⣿⣷⣍⢻⡿⣵⣷⡙⢦⡀⠀⢝⢿⣿⣿⣄⡀⠀⠀⠀⠹⡇⣰⣷⣤⣶⣿⣿⣾⢿⣿⣿⣿⣿⠟⠛
⠀⠀⣿⣿⣃⠀⠀⠀⡀⠀⣿⣿⣿⣅⠑⡈⠻⣿⣆⠳⣌⢈⢻⣿⣿⣾⠟⠿⠶⣤⣶⣿⣟⠉⠉⠉⠛⠛⢷⡀⠀⠀⠈⣿
⠀⠀⣿⣿⣻⣴⣀⣀⣷⡆⡿⠻⢿⣿⣻⣿⣦⡙⢞⢷⡙⣧⡰⡻⣿⣿⣿⣿⣵⣾⣿⣿⣯⣴⡢⠀⢀⣤⣸⣧⠀⣠⠂⣸⣄⠀⡀
⠀⠀⠻⠿⣿⣿⣿⣿⣿⣵⣆⡀⡀⢹⣿⣿⣿⣿⣌⣿⣷⣜⣷⣱⣻⣿⣿⣿⣿⣁⣽⣿⣿⣿⣧⠿⢿⣿⡿⠿⠚⠷⢏⠀⠀⠉⡁
⠀⢸⣀⠀⠀⠉⠉⠀⠈⠙⡿⠛⠓⠛⠛⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⡋⣧⣄⣀⠀⠀⠀⠀⠀⠈⣦⣤⣴⠇
⠀⢸⣿⣾⣆⠀⡀⠀⢨⣄⣿⡖⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⣿⣿⣿⣿⢿⠿⠃⠀⠀⠀⠀⠀⢿⣿⠇
⠀⢸⣿⣿⣿⣿⣿⡧⢘⣼⣿⣿⠀⠀⠀⠀⣀⡀⠀⢈⣿⣷⡮⣙⠛⢟⡻⢬⣭⡙⠻⠿⠿⣿⣿⡇⣳⣤⣀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⣿⠿⠿⠛⠛⠛⠻⣿⣿⣯⣀⠀⣶⣿⡿⣴⣶⣭⡻⢿⣿⣿⢧⣠⣌⠲⢌⡙⣷⡦⣀⡁⠛⢿⣾⣧⣿⣗⣄⡀⠀⠀⠈⡷
⠀⠀⠁⠟⢛⡀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣛⣜⢧⡉⠻⣿⠷⣽⡻⣓⠈⠋⠛⢦⡙⠷⣍⠀⢭⠢⣄⠈⠻⡿⣧⣴⣉⣿⡷⠞⠃
⠀⢸⢸⢿⡟⡒⠀⠀⠐⣿⣿⣿⣭⡇⠀⠈⢹⣷⣝⢧⡈⠳⠄⠙⢮⠳⣿⣦⡀⠙⠷⣌⠻⣦⡉⠀⠱⣄⠈⠪⣙⢿⡉
⠀⢸⣸⣴⣯⣅⠀⢀⡞⣿⣿⡛⢯⡓⠀⠀⠸⣿⣿⣅⡱⣄⢠⡀⠢⡑⢌⠻⣿⣦⠀⠘⢷⣌⠻⣦⡀⠪⡻⣄⠈⠳⣿⢦
⠀⢸⣺⣿⣿⣷⣯⡾⣣⣿⡏⢈⣧⡑⡄⠀⠀⢻⡿⠛⠳⠿⣿⣿⣄⠙⣦⠣⡈⢻⣷⠀⠰⣿⣷⡜⢿⣄⠙⣞⢷⡕⣌⢳⣷⣄
⠀⢸⣙⣻⣿⡿⠿⠋⠁⠙⢷⡀⠺⢳⣗⣦⠄⣸⣿⡤⠀⠀⠈⠙⠛⠂⠸⣷⡙⣆⠻⣦⠀⠘⣿⣿⣆⠙⢷⡈⢳⡻⣟⢦⠙⣧
⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠋⠉⠓⠒⠚⠛⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠛⠓⠘⠂⠙⠃⠀⠘⠛⠙⠃⠀⠑⠀⠛⠛⠋⠓⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁