Seep Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠶⠀⠀⠀⠀⠀⠀⢀⣴⣖⣲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⡀⠀⠀⠀⠀⠀⠀⣤⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣟⠀⠀⢒⠲⠒⠠⠴⠶⠦⠁⠉⠑⠶⠀⠩⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⢾⣿⡄⠀⠀⠀⠀⢀⠀⣼⡝⣏⠛⠳⠀⠀⠀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠈⢛⠲⣮⡀⣀⠒⠘⡁⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠒⡿⣿⣷⣄⠀⣲⡖⢘⣾⡉⠓⠂⠉⠉⠙⠀⠄⠠⠀⠤⠀⢠⡀⠀⠀⠀⠠⡈⠲⢘⢣⡌⠙⠣⠉⠘⢠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⣰⣇⣾⣿⣿⣦⣉⣡⣾⣿⠀⠃⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⢐⠂⢀⠃⠀⠀⠈⠻⡆⣨⠓⢄⢠⠀⠚⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢞⣧⢳⢺⠛⣿⣟⢧⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢻⣿⣤⠸⠆⢆⡰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣸⠇⡄⠈⣬⣿⠋⢎⠈⠀⠀⢢⡄⢄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠠⠀⠀⣿⠁⢠⢷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠠⣤⠀⠿⠄⠚⡼⠃⠐⠀⠀⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠈⣀⣀⠁⠀⠀⠄⠁⢸⣖⣻⡟⣩⡷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⢀⠖⠰⠃⠀⠀⠠⡐⡄⠨⠀⢠⣀⡀⠀⠀⠐⠌⡄⠀⠀⠀⠀⠀⠀⠁⢿⢄⣠⡃⠀⢠⠈⠻⣿⣷⠙⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⣦⠁⡢⠀⢈⣦⠈⠀⢧⡅⢠⡀⠸⣧⡀⢀⠰⠇⠲⣿⡄⠀⠀⠙⠀⡈⢀⣀⠂⣼⢉⠀⡈⢁⠀⢸⡿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢠⡟⢡⣤⣯⢁⠒⣤⠈⣷⡈⠹⢇⡿⢦⠀⠆⣀⠀⠸⠳⣶⡀⢷⣀⢷⣼⣫⣄⣴⠿⡞⣠⡤⣎⣿⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣴⠚⠀⢾⣇⣏⠈⠓⣿⢦⡉⢃⠠⣰⣅⠈⣿⣠⣼⣻⣷⣾⢤⡏⣼⢹⣼⣿⣿⡡⣿⡤⢣⢴⣧⢟⠐⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣿⡦⢛⣿⣿⣿⣏⠺⣍⣾⡦⢻⣸⢳⣿⡿⣯⢻⡟⣿⢿⣿⣿⣸⣿⣿⣿⡟⢹⣷⣿⢿⣿⡗⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣯⣿⣾⣿⣿⣿⣿⣿⣯⣿⣷⣾⡇⣧⣽⣿⣛⣿⣿⣿⣶⠻⣾⣷⣿⣟⣿⣿⣿⣿⣷⡾⣿⢷⡆⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣾⡿⣏⡽⣿⣾⠿⠿⠛⢿⣯⣧⠻⠋⠛⢻⣿⡟⣫⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⠟⢻⣿⣿⠟⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⢳⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠀⠀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠼⡄⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠼⠃⠀⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠈⠫⣛⣀⠂⠀⠈⠘⠣⢤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠄⠀⡀⡴⣻⣷⡖⡛⠚⠷⣦⣄⣀⡀⣄⠀⡠⠤⢤⠄⠠⢤⣴⣶⣒⣶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⣘⣸⣿⣿⡆⠈⠀⠀⣮⣕⣁⠒⠐⠀⠀⠀⠀⠀⠀⠁⠁⠾⣫⡥⠀⠀⠉⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⣿⣳⣿⣟⣡⠃⠀⡀⢀⡺⣗⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⢈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡍⠄⠀⠀⠁⣴⣿⣾⣅⢷⡀⠀⠀⠀⠀⠀⠀⠰⠻⡿⠂⠀⠀⠀⢀⢨⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣞⡿⣿⡿⣣⡦⠀⠀⠐⣿⣿⣿⣿⣾⠇⠳⠀⠀⠀⠀⠀⠀⠰⢚⡦⠀⠀⠀⠈⣙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⣿⡿⣴⢿⣇⠀⠀⠀⢸⣿⣿⣿⣷⢴⣦⡄⢀⠀⢀⡄⠀⠖⣽⠇⠄⠀⠈⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⣿⣷⣾⣃⠀⠀⠠⢾⣿⣿⣿⣿⣿⣟⣿⣶⣶⣇⣴⣤⣾⣡⡶⡔⣰⣺⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠄⣿⣯⢀⠀⡠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣹⣭⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣷⣭⣏⡸⠃⠀⠀⠈⠙⠋⠙⠛⠛⠋⠉⠈⠻⣯⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⢿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡟⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⢤⠶⠶⠷⢦⠞⢡⣿⣿⡶⠶⠂⠀⠀⠀⠀⠠⠴⠴⠴⠶⠰⠤⠶⠎⠺⠿⢿⡿⢺⣿⣷⣶⠖⡴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣦⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⠒⠛⠋⠉⠉⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢏⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡤⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠘⢄⣉⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⠶⠆⠀⠀⢰⣶⣄⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⠠⠤⠤⢸⠤⠒⠒⢤⡤⠒⠒⠢⢌⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠲⡀⠀⠀⠀⠀⢀⣧⣀⣀⡀
⠀⠀⠀⡞⠁⠀⠀⣀⣠⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⢣⠀⢀⠞⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⡜⠀⡏⠠⠛⠒⠦⣄
⠀⠀⠀⠉⠓⠚⠉⡡⠚⡅⠀⠘⠻⡀⠀⠀⠶⠀⠀⢸⠉⢳⠤⣀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠈⠒⠤⠤⠓⢄⣀⣀⣀⠴⠃⠀⠈⡇⠀⠙⠦⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢦⠴
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⠂
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢤⠑⡄⠀⠀⠀⠀⠀⠀⠶⡞⠳⠤⠶⠋
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢋⡴⠃⠀⠀⠀⠀⠀⠀⠤⣟
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣿⠀⠀⠀⠀⢢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⣙⣡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⢻⡄⠀⠀⠀⠀⢸⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡤⠞
⠈⠻⣦⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠖⠃
⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠑⠒⠲⠠⣤⡴⢦⢴⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⣆⠀⢀⣠⠞⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢳⣄⣀⡀⠀⠀⣀⣠⣼⠀⠸⠉⠉⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⡏⠉⠉⠁⠀⢸⠀⠀⡇⠀⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⡀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⡇⢸⠦⠤⡇⠀⠀⠀⠀⢸⠉⠉⡇⠀⡗⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⠇⢸⠀⠀⢸⠀⠀⠀⠀⢸⣀⣀⡿⠀⡇⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠛⢲⣤⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠙⢦⣠⠶⠛⠋⣙⣳⡦⢴⣯⣀⡀⠀⠀⠀⠺⠿⠿⠛⢯⡀⠉⠉⠛⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢤⡟⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⠋⠁⠀⠀⠀⠀⠈⠙⢦⡄⠀⠀⢀⣠⠴⠞⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⣠⡤⠤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢹⡇⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣸⣇⠀⢾⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⠏⠘⢦⣈⠙⠋⠁⠀⠀⠀⢀⣠⠞⠁⠙⢷⡀
⠀⠀⣀⣤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⣷⣄⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠈⠛⠒⠶⠶⠖⠚⢻⣧⠀⠀⠀⠀⠙⣦
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡏⡟⠈⠙⠓⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠘⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣇⠀⠀⠀⠀⠀⠘⣧
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⢻
⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠀⣷⡴⢶⠟⠁⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢻⡀⠀⠀⠀⠀⠀⢸
⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣠⡟⠀⠸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⣧⡀⠀⠀⠀⢀⡾
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠚⠋⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⠴⠂⠀⠀⢀⡞⠀⠀⠀⠈⣻⡶⠶⠞⠋
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⠙⠛⣿⠉⠀⠀⠀⢀⣠⠟⠀⠀⠀⠰⡞⠉
⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⢠⡏⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⢻
⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⢀⣠⠞⠁
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠙⠶⢤⣤⠤⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠳⣦⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⣀⠀⠀⢀⣠⡞⠙⣦⡀⠀⠀⠀⠀⢀⡼⠳⣄⠀⠀⠀⠀⢀⣴⢻⡄⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡏⢙⡟⠉⢹⠃⠀⠈⠙⠲⠶⠶⠚⠋⠀⠀⠈⠙⠓⠲⡟⠉⢹⡀⢳⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠁⢸⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣇⠈⢷⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡏⠀⢸⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⠀⠈⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⢆⣉⡀⠀⢉⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⡇⠹⢯⡿⣏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠆⠔⠲⠄⠤⠤⠤⠤⠦⠠⠤⠤⠴⠾⠋⠀⠳⡄⠀⠀⢄⠈⠀⠈⢂
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣐⣴⣴⠧⠀⠨⠍
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇
⠀⠀⠀⠀⠀⣾⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⡇
⠀⠀⠀⠀⠀⣷⠀⠀⢀⡀⠀⠀⢀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠨⣽⠇
⠀⠀⠀⠀⠀⣿⠅⠀⠘⣷⠀⠀⡮⠔⣐⠀⡀⠐⡄⡆⠀⠀⠀⠄⠀⡄⡀⠀⠀⠐⠀⢉⣿
⠀⠀⠀⠀⠀⢻⣿⠄⠀⣿⣷⣿⣺⣤⣽⣷⡿⣿⣿⡧⡀⠀⠀⡰⣞⣷⣿⣱⣕⣆⣤⡼⠃
⠀⠀⠀⠀⠀⢸⡇⠷⢂⣻⡿⣿⣿⣿⣿⣿⣿⠿⠿⠷⣊⠡⠔⣒⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠸⣧⣼⣾⠟⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣷⡟⠀⠀⠻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣿⢹⠁⠀⠀⢸⡷⡇⠀⠀⠀⠀⠀⠀⠀⠧⣾⠃⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⣇⢁⠀⠀⠀⠀⠀⠀⠀⡰⠘⠀⠀⠀⠀⠸⠃⡄
⠀⠀⠀⠀⠀⠀⠸⣦⠓⠀⠀⠀⢾⣌⠀⠀⠀⠀⠀⠀⠀⣅⢠⠀⠀⠀⠀⠰⡆⠡
⠀⠀⠀⠀⣀⣀⣤⣽⣿⣦⣄⢠⣼⣿⣷⢤⡶⠾⠿⢶⣦⣽⣿⣦⣶⢴⣶⣶⣽⣿⣧⠶⡴⢦⣠⡄
⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡤⡂⠁⠀⠀⠈⣱⠊⠉⠀⠀⢹⠏⠆⠁⠀⢈⡀⠠⠄⡀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠹⠖⣦⡀
⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⠋⠃⠀⢀⣽⠊⣐⣦⣀⣾⠈⠃⣀⡀⠀⡈⢡⣈⡷⠖⠈⠑⡆
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠆⠢⠀⠀⠀⠀⠀⠀⠁⣞⠁⠀⠀⣈⠟⠉⠀⠈⠙⢶⠉⠀⠈⠰⠖⠒⠁
⠀⢀⠠⠤⣴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉⢹⠀⠀⠠⠄⠀⢘⠲⠀⠀⠀⠃
⠠⠆⠀⠀⡝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢨⠦⣀⠀⢀⡠⠊⠂⠤⠀⠘⢆
⢣⠀⠀⠀⢣⡤⠀⠀⡐⣡⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣌⡆⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠑⠄⢀⣠⠘⠀⠀⢰⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱
⠀⠀⠀⢻⡤⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⢲⡀⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠁⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠄⠀⠀⠀⠜⠁⣶⠂⠀⠀⠀⠀⠀⠧⠤⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⢳⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠻⠄⠀⠸⡀⠀⠀⠀⠓⠂⠀⠰⡖⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠉⠻⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠘⢠⡶⠀⠙⣦⡀⠀⠀⠀⠀⢠⣁⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⢴⢧⡀⠀⠀⣠⠦⡔⠁⠠⠀⠀⠀⠖⡄⠀⠀⣆⣀⣠⠟⠖⠒⠃⠉⠓⠈⠀⠈⠑⠒⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠈⠏⠋⠀⠀⠈⠐⠛⠣⠤⠤⠜⠳⡶⡎⠁⠹⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢑⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡷⣵⠀⢱⡏⠷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⢼⡀⠘⣜⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡴⠋⠙⠦⡔⠢⠤⣄
⠀⠀⠀⠀⠀⢠⠲⠋⠃⠸⠀⠀⠀⠀⠀⢀⣀⣈⣢⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠚⠒⠊⠑⠖⠒⠦⣀⣀
⢀⣀⠤⠤⠤⣤⡃⠀⣀⣀⠤⠤⠤⠤⠔⢉⠄⠒⠈⠭⣙⣶⣀⠄⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⢤⣀⣀
⢯⣀⠀⠀⠀⠀⠌⠉⠰⠛⠓⢠⣤⣵⡶⠮⠤⠤⠖⠚⠁⠀⠡⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠷⡄
⠀⠈⠙⠒⠶⠴⠞⣻⢐⡒⠄⠀⣎⣅⡞⢆⢀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⢀⡖⠉⠀⢸⠙⠮⠽⠁⠀⠑⠑⠃⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣼⠋⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⡀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⡜⠁⠀⠀⠈⢣⡀⠤⣀⣀⠤⠃⡘⡰⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠗⠀⠀⠀⠀⠀⠱⣄⡈⢀⣠⡔⢡⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢺⠄⠀⠀⠀⠀⠀⠀⢏⠃⠤⠒⣠⠎⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠚
⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠈⡇⠀⠀⠀⠀⠀⢀⣤⣀⠤⠎⠱⠓⢢⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⣠⠎⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠳⡄⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠉⠈⠲⣄⡀⠀⠀⡀⣰⠊
⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⢀⣀⡀⠀⣀⣠⢶⠖⠋⠉⠁⠀⠀⠀⠀⡍⠓⠚⡟⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡸⠲⡀⠀⠀⠀⠀⢀⡄⣠⠖⠋⠉⠉⠙⠉⠉⠉⠉⣹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⢸⠁
⠀⠀⠀⠀⠀⠘⠦⢄⠀⠀⢠⣆⡼⠀⠀⣹⠻⣤⣠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⡏⠀⡏⠀⢰⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠓⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⡇⠀⠈⡧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡄⠀⣸⡇⠀⠀⠀⠀⠀⠀⡼⢉⠉⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣧⠀⠀⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠧⢾⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣤⣤⣼⠂⠀⡗⠶⠶⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠀⠀⢸⡄⠀⣇⣰⠀⢈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠤⣴⣿⣷⡍⠉⠃⠨⠩⣿⣦⡀
⠀⠀⠀⠀⣀⡀⠲⠾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⣷⣤⠄⡀
⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⣿⠉⠀⠀⠀⠀⠀⠰⣿⣷⣶⣶⣦⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⡈⣴⣿⣏⠓⠤⠤⠤⠐⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⢿⣿⣆⠀⢤⣀⠀⣹⡿⣿⣿⣷⣶⢴⡶⠂⠒⠒⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄⣛⢛⣶⣿⣿⢻⣿⠃⠁⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣛⣶⢣⣿⡿⢿⡿⢿⠿⠷⣋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠸⣶⣤⢡
⠀⠀⠀⠀⠀⠀⢸⡿⣽⣥⣤⠦⡑⠿⠴⠂⠒⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡆
⠀⠀⠀⠀⠀⠀⠸⣿⡋⢉⠀⠭⠁⣀⡤⠀⠀⠀⠀⠀⡁⠢⠐⢺⠀⠀⣄⠀⠀⠀⠀⠆⢰⡀⠁⠀⣴⣰⡰⠠⠀⠀⠀⠀⠀⢟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣟⡄⣠⡴⠺⣵⠏⢈⡉⠐⠀⠀⠀⢿⡇⢢⣍⢸⡀⠚⠀⠀⠀⠀⠀⠘⣡⡀⣋⢶⠉⠁⡂⠀⠀⠀⠀⠀⠈⣿⡅
⠀⠀⠀⠀⠀⠀⠀⣿⢶⣩⢀⣼⣿⡴⣭⡤⠄⠀⠀⠀⢸⣧⡄⢻⠈⡑⢂⡈⡇⠀⡴⣄⡀⢜⣿⣿⣇⠀⡀⠁⠀⠀⠀⠀⠈⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣲⣿⣿⣿⡱⢦⠴⠀⠀⠀⣄⣻⣿⣿⣙⣺⡁⡜⣤⠀⠣⣨⣿⣧⣼⣿⣿⣯⣀⠂⢀⠐⠀⠀⠀⢬⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡬⠠⠝⣫⣤⣹⣿⣿⣿⣿⣏⣿⠲⢄⣴⠂⣻⣿⣿⣻⣿⣿⣿⣿⠠⠀⠀⠢⠓⠘⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⠀⠿⠏⣷⣼⣿⣿⣿⣿⣿⣿⣻⣴⣿⣭⣾⣿⡿⠿⠟⢻⣿⣿⣿⣟⡙⢤⣞⠻⢭⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⡇⠘⠒⣻⣿⡿⠀⠈⠁⠈⠉⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠻⣻⣿⣿⣿⣞⣬⣿⣆⠈⠽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡇⠀⠀⢁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠻⠿⣿⣿⣯⠁⠀⠀⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢣⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⢀⣻⠿⣿⣧⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠌⡇⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⢠⠏⠈⢣⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⡟⠀⠀⠀⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡇⠀⠐⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⢀⠃⠀⢀⡿⠁⠀⠀⠀⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣵⣿⢰⣼⡇⠀⣠⣿⣠⢤⣦⡖⣶⡴⣆⢀⠀⢰⠀⠀⢊⢠⡁⣴⣷⣏⣤⣱⣾⠇⠀⣄⢀⡀⣷⣄⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠠⣁⣸⣷⣾⣿⣿⣿⣿⣷⣮⣿⣿⢿⡿⠿⢏⠛⠻⢼⣝⠓⡚⠛⢛⣾⠾⣿⠿⠿⣿⣿⣿⡿⢶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠷⠦⣦
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠒⠓⠊⠛⠈⠃⠘⠈⠙⠋⠉⠋⠀⠈⠀⠀⠀⠀⠀⠐⠒⠂⠘⠀⠒⠀⠢⠀⠁⠀⠐⠀⠈⠘⠋⠙⠉⠋⠉⠹⠙⠛⠑⠐

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠶⠴⠆⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⡆⠀⢸⣷⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢇⡀⠘⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣗⣠⣴⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠄⠀⠀⠀⣸⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣣⡇⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠋⢹⣿⣿⠟⠻⠿⣿⣿⠛⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⢻⠃⠀⠀⠀⢹⡟⠁⠀⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠟⠀⠀⠀⢀⣿⠃⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣴⣿⠀⣾⡆⢀⣀⣄⣼⣿⣀⣤⣄⣀⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠟⠛⠛⠻⠿⠟⠋


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

⠀⠀⠀⠀⠀⣀⡠⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠉⠀⠘⠿⠛⠁⠑
⠀⠀⠀⢀⡄⢠⣀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠄⠀⠀⠂⠀⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠙⢻⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠐⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⣀⠀⠀⠀⠀⣠⣏⣀⢀⣠⢠⡀⣠⣠⢵⣝⠂⠀⠀⠠⢿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⣀⣸⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣿⣿⠁⠈⠉⠉⠉⠋⠛⠛⠋⠀⠈⠹⢿⣦⡀⠙⢖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⠘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⣀⣀⡈⣠⣼⣥⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⢀⣤⣜⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠈⠈
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡺⣿⣦⣤⡠⠤⠀⠁⠀⠀⠀⢀⣴⣿⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣁⠀⠀⠀⠀⠀⡐⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡽⠿⡄⠀⠈⠀⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠼⠁⠀⣾⣿⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠠⢤⡴⠂⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⣴⣮⣿⣇⠤⠶⢢⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠟⠿⠿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢵⠆⠀⠂⡧⢹⡇⡆⠠⡞⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⡀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠰⡄⣿⣿⣿⣧⣘⣱⢢⣤⣄⠀⠀⢰⣠⣿⣯⠀⠀⠀⠀⢀⣖⠀⣈⡛⣃⠸⢛⣪⠛⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣡⣿⣿⣿⣿⣿⣟⡿⣵⣮⣾⡯⣼⣻⣿⣿⣠⠀⠀⠀⠀⢻⣷⣍⣛⣛⣿⠛⢻⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢯⣿⣿⣽⣿⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿⣿⣿⣯⠀⠀⠠⠀⢈⣛⣿⣿⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣾⣿⡟⢹⣿⠿⠻⠋⠀⠀⠀⠀⠀⠈⠉⠉⠋⠹⣿⣾⣄⣄⣴⡾⠿⠛⣿⣿⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠙⡟⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡟⠛⠁⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢻⠀⠀⠀⠀⠻⣄⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⡀⠀⠀⠀⢿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣿⠿⠃⠄⠀⠀⠀⠛⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠓⢦⡀⣠⠴⠶⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠺⢁⡴⠋⠓⣄⠀⠻⠃⢀⡴⠦⣄⠘⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢧⣀⠀⠀⠉⠉⢙⠄⠻⢤⡴⠋⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⡔⠢⠖⢳⡄⢫⣀⡤⣄⣀⡏⠀⠀⣠⠒⢦⣀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⠞⠁⠀⠀⠈⠑⣆⠀⠀⣠⠷⣄⠀⢀⡽⠀⠀⡠⠃⣤⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⠒⠲⡆⠀⣰⠒⠃⠀⣏⠉⠀⢉⡧⠘⠦⠤⣤⠗⠀⢸⡏⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⠴⠋⢹⡀⠈⠛⠁⠀⢀⣤⠘⠦⠞⠉⢀⡼⢦⣀⡀⠀⣀⣼⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣀⡾⠋⠉⠉⢙⡞⠁⠀⠀⢸⡷⢦⣤⣤⣴⣋⠈⠙⠲⠶⠒⠋⠀⣀⣈⡉⠉⠁⣿⠙⠶⢤⣀⣀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡀⠀⠀⠈⠀⠀⠀⢠⡟⠀⠀⠀⣠⢾⡇⢀⡴⠋⢩⣿⣿⣆⠀⠀⠀⣰⠞⢩⣿⣿⣷⡄⡿⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠇⠀⡏⠀⠀⠀⠀⠀⢰⡄⢸⣀⣠⠴⠚⠁⠘⡇⢸⠀⠀⠹⣿⣿⣿⠀⠀⠀⡏⠀⠈⢿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⢀⠑⢤⣤⠴⠓⠶⠚⢀⣀⣀⠀⠀⠀⠀⠀⢷⠘⢧⣀⣀⣈⡽⠋⠀⠀⠀⠹⣦⣀⣀⣨⠟⢹⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣎⠀⡀⣸⠂⢠⠄⠀⠀⠀⠀⣏⠀⠸⠂⠀⠚⠉⢳⠘⣇⠀⠈⠉⠁⠀⠀⣴⠒⠒⢲⠄⠈⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢹⡄⣀⠈⠉⠉⠁⠀⠸⣤⡤⠇⠀⠀⠈⠁⠀⢀⠀⠀⠰⡏⠀⠘⢦⡀⠀⠀⠀⠀⠘⠶⡴⠋⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⡞⢸⠁⠀⠀⠀⢀⡀⠀⢀⡄⠀⠀⠀⠀⠰⡄⠘⢄⣀⡴⠃⠀⠀⠀⠙⢦⣄⣀⠈⠑⠊⠉⢚⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⣇⠘⠦⡄⠀⠀⣸⠃⠀⠸⣄⠀⢀⠀⠀⣠⠇⠀⠀⠀⠀⠈⠳⡄⢀⡤⠤⡀⠉⠉⠛⡟⠋⠉⠁
⠀⠀⠀⠀⢠⠞⠙⢦⣀⠈⠑⠋⣁⠀⠀⠀⢈⣉⡉⠉⠉⠁⠀⠀⢆⠀⠀⣤⠴⠃⢺⡀⠀⠽⠀⠀⢠⡇
⠀⠀⠀⠀⢿⣀⣠⠞⠉⠉⣷⢸⠁⠀⣀⠠⡏⠀⠁⠀⠀⠀⠤⣄⠈⠙⠋⡠⠒⢦⠀⠀⣤⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⣌⠓⠒⢁⡀⠹⣀⣠⠄⠀⡀⠀⣸⠀⠀⠀⠀⢤⠼⠀⣸⠃⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠉⠛⠉⣧⡀⠀⢀⣀⠀⠈⠉⠁⢠⢶⣤⣤⡤⢴⡞⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠙⠛⠋⢹⡗⠦⠤⠖⠋⢸⠀⠀⠀⠀⣷⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣷⠀⠀⠀⢘⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⡄⢀⣀⣠⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⢺⢻⡛⠛⠉⠉⣇⠀⠀⠀⠀⣼⠛⠛⠛⢺⡇⣿⠉⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⢤⡀⣾⠸⡇⣠⠶⣄⣿⠀⠀⠀⠀⣿⣀⡤⣄⢸⠇⢹⣄⡞⠓⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠙⠟⠀⠛⠁⠀⠀⠉⠀⠀⠀⠀⠛⠁⠀⠈⠛⠀⠀⠋

⠀⢸⣷⠀⠀⣿⠉⠀⠀⠀⣿⣧⠄⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⣾⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣷⣄⡆⠀⢸⣿
⠀⢸⡇⠀⠀⣿⣆⠀⠀⠀⣿⣿⡆⡀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⣋⠃⠀⢸⣇
⠀⢸⣿⠀⠀⣿⣍⠀⠀⠀⣿⣿⡟⠁⠀⣼⣿⠀⢠⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠇⠀⢀⣿⢀⣿⠀⠀⠀⠀⢸⣏⢹⠀⠀⢸⣧
⠀⢸⣧⠀⠀⣿⡉⠀⠀⠀⣿⡿⡇⠀⠀⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⣿⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⣹⣿⣻⠀⠀⢼⣿
⠀⢸⡗⠀⠀⢿⣧⠀⠀⠀⣿⡿⡇⠀⠀⣿⣷⠀⢸⠃⠀⠀⠀⠀⠀⢾⡇⠀⠀⡿⣿⠀⠀⢸⣿⠀⠻⠀⠀⠀⠀⣹⣿⣿⠀⠀⢸⣯
⠀⠈⠓⠀⠀⠙⠋⠀⠀⠀⠛⡂⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢼⣿⣽⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡇⠀⠀⣿⣻⠂⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡋⡉
⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⣿⣯⣄⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢺⡏⣿
⣾⣿⣿⣿⣿⣯⣍⣑⣚⣣⣴⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢾⠆
⣠⣤⣶⣶⢉⣉⡉⠩⡉⠍⠉⠙⠛⠀⢶⠀⠀⡶⣖⡒⠂⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢸⡇⠀⠂⠀⠄
⣙⡛⠛⠿⠿⠿⠿⣿⣿⣿⣶⣦⠀⠀⠘⠂⣤⡀⢸⣧⣠⠄⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⡁⠀⠀⠀⠀⢀
⠛⡛⠿⠷⢦⣤⣭⣅⣠⣄⣀⣀⠁⠀⠁⠀⠸⠿⡁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⡄⠀⠀⠈⠘⠋
⠻⢾⠶⢶⣶⣴⣤⣶⡖⠉⢹⣿⡀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠃
⠈⠀⠂⠀⠒⠈⠉⠉⠁⢠⣀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠁
⣄⣀⣤⣄⣤⡄⠀⠀⠀⠸⠿⠄
⠈⠉⠉⠛⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⣿⣿⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠭⣿⣿⢚⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢻⣿⣿⣿⣭⡤⣂
⠀⠀⠀⠀⠀⠀⠀⠀⣓⣾⣿⣿⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠄⠀⠀⠀⠀⠀⠀⠀⡈⠻⢶⣿⣿⣿⣷⣾⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠲⢬⣿⣿⣿⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠀⣀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢀⠓⣶⣿⣿⣷⣶⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢠⠀⠀⢶⣼⣹⣿⣿⣿⣿⣯⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⡿⠿⠋⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠾⣦⣌⣿⣿⣿⣿⣿⣿⣯⣤⣶⠖
⠀⠀⠀⠀⠀⠀⠺⢾⣿⣿⣿⣿⡚⠋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣷⣞⣌⣻⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⠄
⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣛⣡⣤⣠⣄⣀⡀⣀⣀⣀⣠⠰⠂⠀⠀⠀⣉⣻⣿⣋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠧⠶⢯⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⢠⣄⣘⣿⣿⣿⣿⣿⣿⡷⠛⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠘⠚⠛⠛⢿⣿⣿⣿⣿⣿⢿⡾⠈⠁⠀⢸⡆⢰⡆⠀⡄⠀⣧⠘⣧⠠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡛⠶⢢⡂⢀⣀⢸⣇⣼⡇⣀⡏⠀⣷⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣾⣇⣸⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⣠⣄⣤⣀⣠⣀⣄⣀⣠⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣠
⣿⣇⣺⣯⣍⣭⣭⣍⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⢸⡇⢰⢸⠀⠀⣇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⡀⡀⢀⢀⣯⣿⣀⠀⠀⠀⠀⢠⡄⣹⠀⡀⠀⠀⣼⣿⣧⣾⣿⣶⡎⣿⣰⣷⣿⡷⢶⣦
⠀⠀⠀⠀⠀⠀⢀⠀⣼⣷⣾⡇⠣⢺⣿⣿⣿⡇⠀⠀⢨⣶⣾⣷⣿⣿⠃⠀⠑⠛⣿⠃⠈⢻⡿⠥⣏⡷⢻⣾⣡⡎⣻⡆
⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⢷⡞⠐⢿⣿⠏⠃⡀⠀⠈⠋⢻⣿⣿⠛⠂⠤⠦⢴⡇⠀⠀⠀⢿⣩⡿⡗⢺⣋⣾⣷⣨⡇
⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣟⣼⠁⠀⢸⡟⠄⢸⡵⣶⡎⠀⠈⣿⣇⡀⠀⠈⢀⠬⠃⠈⠉⠒⠠⣿⡀⣿⣾⠛⣷⡉⡦⠄
⠀⠀⣼⣿⣿⠿⠿⠛⠛⠉⠉⠃⠀⠀⢸⠃⠤⠈⢷⡿⠁⠤⠐⠙⠛⠛⠛⠿⢾⠀⠀⣤⢴⣤⣤⣏⣿⣷⡟⠀⢿⡙⠫⡀
⠀⠀⠋⠁⠠⡆⠀⠀⠐⢺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠒⠀⠩⡥⠚⣽⡦⢘⣲⣄⣀⣐⣢⡄⠀⠀⠀⠀⠠⣤⣀⣄⠐⢢⡄⠁⠲⡆⠈
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠒⠶⠶⠶⠄⠲⠚⠃⠀⠼⠖⠒⠛
⠀⠁⠀⠀⠒⠿⠿⣥⣶⣤⣿⣆⡀⢰⣦⠀⡀⣰⡄⡄⠀⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣦⣽⣿⣯⣿⣼⣿⣯⣿⣧⣷⡄⠀⠀⡀⠀⠀⣸⣶⡄⠀⣦⠀⠀⠀⢢⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢹⢿⣶⢶⣿⣿⣻⡃⠀⠆⣿⣷⣶⣿⣿⣇⠘⢻⡇⠀⠐⣘⣧⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⢐⡒⠈⠃⠈⠁⣥⠛⢛⡻⣿⣿⣚⣉⣁⠤⠠⣿⣿⠗⠛⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠈⠛⠉⠉⠝⢿⣦⠤⢴⣾⡿⢿⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣲⣱⣦⣄⣀⢀⠀⠀⡀⢀⣀⣴⣦⡀⠀⠀⢠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡉⢛⠙⠉⣴⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠌⠛⣿⣛⠟⠛⢭⡈⠟⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠉⠓⠦⢥⣅⡔⡚⣷⣶⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠋

⠠⠀⢀
⢸⡀⠃⠀⠀⣀⠀⠀⠀⢰⢆⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀⠠⢀⣀⠀⠀⠀⠀⠀⣇⢠⠀⠀⠀⣠⣀⠀⢐⣦⡀⠐⠀⠀⠀⡀⢸⠄
⢠⡅⠀⢀⢟⣞⡼⠀⢀⡋⢎⢫⡽⢀⠀⠀⠀⠀⠠⢀⠆⠀⢨⣿⣶⣻⠏⢀⠀⠀⠀⢀⣼⡲⡇⠀⡄⡟⠿⢧⣸⣽⡄⡄⠀⠀⢸⣷⣟⣖⡆
⠰⣿⡟⠀⡘⢩⠋⢤⣼⡅⠃⢶⣧⠈⠀⠀⠀⠠⢓⣶⡀⣴⣶⣿⠿⣯⣤⣸⠈⠄⠦⡜⢻⡿⣾⡜⠁⣰⣏⣸⣿⣾⣿⠙⠰⢸⡇⣽⣿⣿⣧
⠀⣿⡇⢸⠃⢼⡖⢉⢻⡇⣃⢸⡇⡾⢣⠀⠀⠀⣼⡿⡟⠀⣽⢏⡖⡿⣟⡀⣦⡀⣾⠧⢺⡇⣿⣸⣒⢿⣟⢻⣷⢻⢱⡀⢰⡟⠘⣿⣿⣈⣿
⣴⣿⣈⡟⠀⣸⠘⠈⢸⡄⠙⢾⡇⢸⠏⠐⠀⠀⡼⠀⡇⠀⣿⠻⢀⡇⠛⢇⢸⣇⡇⣀⣸⣻⣿⣋⣣⣼⣦⣹⣣⣿⣟⣆⣸⠀⠀⣿⣿⠼⠾
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣾⣷⣾⣶⣶⣶⣶⣷⣶⣾⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣴⣶⣶⡀⠀⢀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠻⢷⣾⠿⢟⣻⡿⠟⣿⣿⣿⣿⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⠿⢛⡴⠚⠉⠀⠉⠩⣼⣧⠤⠿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣩⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡟⠁⢀⣉⣠⠄⠀⢄⠀⠉⠈⠁⠀⠀⠩⣝⣿⣿⣦⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣶⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣋⡵⢋⣹⣶⡆⠀⢘⡼⠂⠀⠀⠀⠀⣀⣸⠟⣛⠻⣷⣶⣿⣿⣿⣿⣿⣶⣤⡤⠀⢠⣽⣶⠏
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣠⣀⠀⠀⠀⣾⣟⠐⠒⢬⣉⠉⠤⡠⢀⠄⠀⠐⠀⠀⠀⢰⠟⢁⣾⣿⡷⢻⣿⣿⣿⣿⣿⣟⡛⠻⠿⣿⣿⡿⠋
⢀⣴⣿⣿⣿⡿⢻⡿⡛⠿⠿⣷⣄⣸⣿⣏⣰⣷⣮⡉⠳⠀⡊⠀⠀⠀⠀⠀⠘⣦⡆⣠⣾⣿⠿⠆⣿⣿⣿⣿⣧⣄⢾⣿⣶⣶⣿⡿⠁
⢸⣯⣼⣿⣟⣿⣟⣭⣄⠀⢐⣞⣿⣿⣟⣨⣭⣛⠟⠛⠂⣀⠤⠀⠶⠰⠤⠀⠀⠹⡗⠟⠉⠹⡄⠀⣿⣿⣿⡿⣿⣿⠿⠿⠟⠟⠃
⠘⢻⣿⣿⣿⣿⣿⣯⢶⣾⢿⣯⣿⣿⣿⣟⣛⡏⢀⡒⢦⣿⠆⠀⠀⠀⠀⠀⠀⢀⠙⢷⡄⠀⠀⠸⣿⡏⠀⠀⠉
⠀⠀⠀⢹⣿⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⡟⠀⣿⠀⢀⣠⡤⠤⠒⠒⢣⣤⣤⣁⠀⠀⢲⣿⣿⡀
⠀⠀⠀⠀⠀⠙⣹⣿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣷⣄⠀⣴⢣⣶⣿⠅⠀⠀⠒⠋⠉⣠⣿⠻⡆⠀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠈⠁⠀⠀⢀⣿⣿⣿⣿⣸⣿⣿⣧⣤⡀⠀⠀⠀⠀⠸⣿⣷⣄⢹⣦⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡧⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠨⣽⣿⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣧⡿⠁⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣷⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠈⣷⡀⠀⠈⡁⣠⣤⠶⠛⠛⠛⠛⢛⣹⠃⣿⣿⣀⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣷⣦⣙⢿⣿⣟⠉⠁⠀⠀⠀⠀⣀⣀⣾⣏⣼⣿⣿⠿⠛⠉⠛⢷⡀
⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣷⣾⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠚⣿⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠳⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⢸⡏⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⡄⠀⠀⠀⠀⢠⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠃⠀⠀⠀⠀⠘⠁⠘⣿⡉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⢀⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠀⠀⢠⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠈⠛⠀⣼⠀⠚⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠷⢶⡆⠀⠋⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣿⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⠙⡇⠘⣿⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⢸⡟⢀⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠘⣿⠀⠀⣿⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣺⣗⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣳⣶⣿⣶⣚⣁⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⢻⡀⠀⢀⠀⣻⣇⣸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠈⡇⢸⠈⣷⣿⣧⠏⠀⢸⡅
⠀⠀⡀⢨⠉⠒⢦⢰⢿⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢧⠸⠄⠘⣿⡇⠆⠀⣸
⠀⠀⠀⠰⡇⠀⢎⣻⣾⠁⢧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⢘⠀⠀⢸⡐⠀⠆⡻⣿⠀⠀⣿
⠀⠀⠀⣁⡇⠀⠀⣿⡻⠀⢸⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⢨⠄⠀⢸⡇⠀⠀⣿⣿⠀⠀⢹⡀
⠀⠀⠀⠸⡎⠀⣠⣿⡻⠂⣼⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⢰⡇⠀⠀⢹⣿⠀⠀⢸⡇
⠀⠀⠀⡀⣿⠀⢨⣿⠟⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⡇⠀⠀⠀⣿⡆⠀⢸⡇
⠀⠀⠀⠨⣻⠀⣴⠿⣦⠀⢰⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢘⡄⠀⠀⣇⠀⢠⢸⣿⡅⠀⢸⡇
⠀⠀⠀⠂⢹⠀⢹⢢⡄⠀⠈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠁⣿⠀⢸⢸⣿⡇⠀⢸⡇
⠀⠀⠀⡇⢸⡇⢰⣼⡇⠀⠀⣿⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⢸⢀⢹⡀⡌⣸⢸⣷⠀⢸⡇
⠀⠀⠀⡆⢸⡷⢸⡟⡇⠀⠀⣿⠀⢸⡄⠀⠀⠀⢣⠀⡆⠀⠀⠀⢸⠀⠀⢸⡇⢸⢸⢸⣷⢣⣿⢸⣿⡀⢸⡇
⠀⠀⡇⡇⢸⡇⢸⣭⣿⠀⠀⣿⡆⠀⣇⠀⠀⠀⠈⡇⠇⠀⠀⠀⢸⠀⠀⠘⠃⠀⠈⠈⣧⠈⠁⢸⣿⣇⠘⠋
⠀⠀⠀⠇⢸⡇⢼⢻⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣦⡄⠸⠂⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠘⠁⠉⢹⣧⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⣀⣀⣀⣀⣠⣾⡿⣷⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⠁⠈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⢀⣤⣶⣶⣶⣾⣿⠏⠀⠀⣀⣠⣤⣤⣼⡿⠁
⠀⠀⠞⣼⡿⠋⠉⠉⣿⠇⠀⠀⠀⢨⣿⡿⠿⠿⠿⣿⡿⠋⠀⠀⠀⠸⣿⣿⠿⢿⣿⠏⠀⠀⠀⢹⣿⠿⢿⣿⠇
⠀⠀⠀⠇⠇⠀⠀⠀⠹⠄⠀⠀⠀⠸⠍⠇⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⠋⠇⠀⠸⠇⠀⠀⠀⠀⠈⠉⠀⠀⠯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⡀⠀⠀⢠
⠀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣤⠀⠀⠀⠀⣿⣭⣥⣤⣤⣾⡿⠛⠀⠀⢮⠀⠀⠀⠀⣠⣶⡄⠀⠀⣾⣿⣦⣀⣰⡆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣿⣿⠿⠿⣿⡿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⡟⢿⠉⠉⠉⢹⡿⡅⠀⠀⠀⠀⢸⣟⠁⠀⠀⢸⡇⠀⠀⠀⢰⠛⡏⠀⠀⡏⠙⢆⠀⠀⠀⠈⠈⣿⡿⠛⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣠⡄
⠀⠀⣀⣀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠹⣿⣷⣶⣿⣿⡇⠀⠀⠀⢀⣠⣿⡄⠀⠀⢸⣶⣤⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⠀⠰⣦⣀
⠀⠀⠀⠈⠻⣿⣿⠏⠀⠀⠐⢶⣿⣿⡿⠃⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠠⣤⣶⣿⣿⣿⠇⠀⠀⠀⢀⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠉⠿⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⠀⠀⠉⠹⠏⠀⠀⠀⠀⠀⠺⠿⠿⠻⠇

⠓⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⣿⠒⠋⠉⣯⣉⣹⣷⠀⢀⠒⠈⠈⠁⠀⡀⡀⢠⡅⠄⣿⣿⣿⣿⣿
⠉⣉⣓⣟⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠛⠁⠈⣁⡀⠻⠙⠗⣾⡟⠁⠀⠀⣀⡀⠀⢁⠀⠀⠉⠻⠛⠿⠛⠋
⠀⠈⠻⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣅⣾⣟⠀⠀⠀⠁⣰⣾⣿⢤⡀⠀⠀⠉⠱⠴⠈⠓⠦⠀⢀⡀⠋⡋⠴
⠀⠀⠀⣯⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠄⢸⣿⡌⠀⢤⣖⠉⣛⣻⡧⡤⠀⠐⠎⣢⣶⣦⡸⢀⡀⠁⠀⠀⠁
⠀⠀⠀⣿⢤⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢻⣿⣯⡀⢀⣉⣭⠀⠙⢿⡆⠀⠄⢀⠀⠁⠛⠛
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⢸⣿⠋⠹⣮⠽⡇⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢸⡿⠀⠠⢿⣴⣦⠀⠀⠉
⠀⠀⠀⡇⢐⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⡇⠀⠀⠈⢸⠈
⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢸⡇
⠀⠀⢈⣇⡆⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄
⣧⣠⣾⣿⡇⠀⠀⡴⢀⠂⢘⣗⣠⡄⢀⣤⣿⣿⣿⡧⣄⢠⣶⡆⠀⠀⣀⡇
⣋⣤⣹⣿⣧⣀⡂⣾⢾⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⡿⣣⣾⠴⣿⡅⠠⣦⣤⣤⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⡀⠀⣀
⡿⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣯⣹⣃⣿⣷⣾⣿⣿⣿⡆⢴⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣰
⣙⣺⣿⣿⣿⣽⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠸⠿⢿⡿⠟⢹⢿⠁⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣥⣤⣤⣀⡀⣸⣿⢣⣿⣿⣿⣿

⠀⣀⣀⣀⣀⣴⣾⢿⡀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡸⣿⣿⠿⣿⣿⠇⠀⠀⢀⣀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⢰⣿⣿⣿⣿⡿⠙⠂⣀⠀⠀⣠⣤⣤⣾⠋
⠁⢻⠁⠀⠀⣿⠀⠽⠛⡟⠉⠀⠀⡾⡟⠉⠉⢹⡏⠁⠿⢻⠛⠂⠀⢸⠋⠉⠉⡿⠀⠸⢻⠋⠀⠀⠼⠛⠛⡏⢰⡶⡞
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⣤
⣠⣤⣤⣤⣿⠃⠀⠀⠀⢀⣤⣤⣤⣶⠖⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⢠⣆⣀⣠⣶⠄⠀⠀⠀⡄⠀⠀⢀⡀
⣿⡿⠛⣿⡏⣴⣶⠃⠀⢸⡿⠿⢿⠟⣀⣠⠄⠀⣿⡿⣿⣿⣿⠿⢆⣀⠀⠀⣸⠟⠛⣿⠃⣀⣠⠀⠀⣿⠿⢿⣿⠁
⠋⠃⠀⠋⠃⠁⠈⠀⠀⠈⠁⠀⠘⠀⠉⠉⠀⠀⠉⠃⠀⠀⠉⠀⠈⠉⠀⠀⠉⠀⠀⠙⠈⠉⠃⠀⠈⠀⠀⠀⠈⠘⠉

⢀⣤⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⢠⡄
⢸⣿⣿⣷⣶⣿⡀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠐⣶⣄⣤⣾⡇⠀⠀⣀⣀⣀⣾⠂⠀⠀⠀⠀⢠⡶⠀⠀⠀⢀⣀
⠘⠛⢿⣿⣿⠿⢃⡀⠀⠰⣶⣿⡿⣀⡤⠀⠀⠈⠻⣿⠿⢁⠀⠀⠹⣿⣿⠟⠀⠀⢠⣤⣶⣾⠇⡀⠀⠀⣠⣽⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣃⡀⠀⠀⠀⢀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠈⠛⠻⠿⠇⠀⠀⣠⣿⣿⡿⠟⠀⠀⠀⡖⠀⠀⢀⠀⠀⠀⠀⠈⡇⡂
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠁⢠⡀⠀⠀⠀⠂
⠾⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡁⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣄⣀⠀⠀⠀⠀⢠⠆⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣽⣿⣽⣷⣄⠀⣀⣤⣀
⠀⠀⠂⠀⠀⠀⠁⠈⢀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⢠⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠖⠾⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠛⠷⣴⣤⣿⣿⣿⣿⣷⣶⣒⠛⠠⠈⠉⠹⣛⣩⣽⣽⣿⣿⣧⣯⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠠⠀⠙⠚⠀⡠⢸⣿⣿⣿⣟⡶⠾⣿⣟⡁⠈⠰⠀⠀⠈⠁⠈⠛⢷⣿⣿⣕⣄⡀⠀⣀⣿⣿⣷⣤⣶⣦⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡠⠀⠀⡀⠀⠈⠀⠀⠙⠛⣻⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦
⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠿⢿⣿⣿⣿⣿
⠀⠀⠰⠀⠒⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⣿⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠆⠒⠐⣶⣶⣤⣤⣤⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⡤⣰⢆⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⢶⣿⣿⣿⣿⣿⣽⡄⠸⠐⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣴⡏⠀⠀⣻⣭⣦⡝⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠇⠀⠀⣽⣿⠿⣿⣿⣿⠟⠀⠀⠀⠻⠏⠉⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⡀⠀⣿⣿⣿⣿⠎⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⠁⣀⠔⠀⠀⠀⠀⣿⠏⠉⠀⡎⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣦⣴⣻⣿⣿⣿⠉⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⢀⡞⢉⡙⠶⢦⣤⣄⣀⣠⣤⣴⣇⠀⠀⣠⠀⢶⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⢿⠿⣿⡻⣿⡧⢛⣥⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢡⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠛⠳⠶⠨⣅⢈⣿⣩⠡⠀⠀⠀⠀⠀⠀⠲⣀⡇⠉⢀⡘⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⠤⠻⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠠⣤⠀⠀⣿⡀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⢲⡔⣄⢠⣤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠈⢘⢁
⠀⢀⣤⣶⣶⣶⠲⠶⠦⣤⣄⣀⣀⣀⣠⣤⡤⠤⠠⣤⣄⣀⣀⣀⣀⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡜⠛⠶⠞⠋
⠀⢸⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⢰⣾⣿⣿⣿⣿⣿⠿⣟⡧⠀⠀⠀⠀⠀⠀⢦⡠⠠⠢⡔⣀
⠀⢸⣿⠛⣿⢱⡆⠀⠀⣼⣿⣿⣿⣿⣿⠿⠛⠁⠈⠁⢘⣿⣿⣿⣀⣄⡻⢿⣆⡄⠀⠀⠘⠷⢿⡄⠃⢠⣿⣿⣿⣦⠐⠢⣶⣤⣤⣶⣶⣶⣶⣶⣿⢉⡙⢿⣷⣶⡄
⢀⣾⡟⠁⠀⢈⡴⠁⠘⠿⠁⠀⠻⠿⠋⢀⡀⠀⠠⡆⠈⠉⡹⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⣿⣿⣧⣀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣧⡸⠧⠸⢿⣿⣿
⣸⣧⡿⢂⡞⠋⠛⢦⣄⣀⣀⣀⣠⣴⠶⠿⣧⠀⢸⣀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣭⣿⣿⣿⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⢀⠀⠀⢾⣿⣿
⠀⢹⢃⡾⠙⣤⠤⠚⠁⠉⠉⠉⠁⠀⠀⠀⠘⡇⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠆⣴⣶⠐⡌⠉⠉⠁⠉⠁⠀⠀⠘⢣⠀⠀⠘⡇
⠀⢰⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⠀⠉⣻⢇⣷⣄⣀⣀⣠⣤⡶⠺⠏⣈⡱⠀⠀⣧
⠀⠘⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠀⢠⠎⠀⠈⠉⠉⠉⠁⠀⠀⠃⢨⡆⢃⠈⡿
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⢤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡈⠀⠀⡀⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢄⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡐⠀⠀⠀⣇⡇
⠀⠀⠀⠀⢹⣿⣿⣿⡛⢛⡃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠸⣿⣿⣟⠁⠘⠁⠀⣸⣿⣿⣿⣿⡟⠿⣿⠃⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠐⣦⣀
⠀⠀⠀⠀⠀⣿⢻⣯⠀⠀⣼⠀⠈⠛⠉⠙⠿⢰⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠏⢀⠤⣿⣭⣽⣲⡶⠒⢀⣶⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢸⣷⣿⠈⠁⢀⡞⠻⠷⢦⣤⣤⡤⠴⠿⡆⠀⣶⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⢠⣤⣾⠟⣡⣿⣿⡿⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⠛⠀⠿⢲⣤⣀
⠀⠀⠀⠀⠏⡇⢿⠀⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⣼⡿⣏⠰⢈⡟⠛⠋⠁⠀⠀⠀⠈⠓⠀⠈⠹⣿⡟⠷⠀⣶⣿⡿⠿⢿⣿⣿⠍⠀⠀⡄⠀⠻⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠈⢂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢶⡀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣋⡴⠖⠀⠀⠀⢡⣂⡀⠙⠋⠀⠀⠰⡇⢰⡿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠱⠶⠈⢷⡷⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠀⠻⠿⠘⢧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢦⣄⣠⠀⢸⡿⠿⠿⠿⢿⣷⣦⠘⣁⠀⠠⠟⠛⡟⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⣿⡧⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⣶⡄⢠⣿⣿⣤⣿⣿⣶⣶⣿⣿
⠀⣀⡆⢠⣾⣆⠀⠸⣿⣧⣼⣿⣿⣷⢆⣴⣧⡀⠀⣼⠀⠀⢀⣿⡀⠀⣸⣿⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣷⣼⣿⡟⢺⣿⣿⣿⣸⣿⣯⡷⢲⣿⣷⣀⣴⣿⣿⣀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣅⣼⣿⣿⣅⣽⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡎⠀⠀⠀⠀⢀⡀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠚⠋⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠔⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣠⠖⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⢆⠀⠀⡐⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⢿⣿⣤⢠⣁⣷⠀⠀⠀⠀⠆⠀⡞⣄⣠⠀⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠂⢠⠚⠩⠉⠋⠁⠀⠀⠀⠉⠀⠀⠀⠌⠀⣄⠿⣯⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠼⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡄⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠲⣆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠞⢁⣤⠀⠐⣤⣀⡑⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⠉⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐
⠖⠀⠀⠀⠀⣀⠤⡆⢀⡤⠀⠉⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢬
⠀⠀⠀⠀⠁⠀⠀⠘⣿⣁⠀⢀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣖⠁⢀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡽⢾⣻⡏⠀⠀⠀⠰⠀⠀⠈⠀⠀⢠⠀⡄⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢾⣿⣶⣯⣄⠠⠀⠀⠐⡀⠀⠰⠀⢀⣇⣸⢠⢱⠃⠂⠀⠀⠀⠆⣇⠀⢨⣿⠾⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠐⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣹⢻⣿⣷⠀⠂⠸⠆⠈⢀⡷⠀⠙⣿⣿⡀⠁⠃⠀⣀⠀⣁⢻⣽⣀⣿⣿⣿⣿⣄⡀⠰⡄⠀⠀⠀⠀⠘⠀⣄⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣦⣄⠀⠀⠀⠀⠑⠀⢸⣿⣿⣿⣶⣄⡀⢤⠴⣿⣾⣽⣿⣿⣿⣿⡿⠿⠻⣄⣷⡄⠀⠀⠀⠀⢴⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣄⠀⠀⠀⡲⣐⣶⣿⣿⠛⠉⠋⠛⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠉⠳⢄⠀⢀⣰⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣬⣦⣸⠉⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠙⡏⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣤⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡾⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣠⣀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣰⡿⠋⠀⣚⣻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⣉⣼⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢹⣞⣿⠃⠀⣾⠿⠇⠈⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡬⠡⠿⣿⣿⣾⣇⢀⣀⣤⢀⡄⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⠄⠀⠀⠀⠡⣙⣀⠘⠃⢈⠀⠀⠂⠘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠞⢁⣀⣘⣿⣿⣿⣼⣿⢿⡨⠟⠋⠁⠀⠀⠀⠀⠀⢀⣔⣩⠷⡿⠛⠀⠀⠀⣤⢞⡟⠉⠹⣧⠰⢆⠙⠒⠈⠀⠺⠆⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡡⡾⢋⢡⣤⣮⣿⣿⣿⣿⣾⣿⣁⠠⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣎⡀⠀⠀⠀⢈⠇⠀⢠⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣾⢈⣯⠿⣿⣿⣿⢿⣿⡎⠛⠂⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠘⠀⠀⢸⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣷⠟⠁⠈⣿⠃⣽⠀⠰⣻⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠃⢰⠈⠀⠀⢹⡀⠀⠀⠖⢀⠀⠀⣿⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠃⠀⠀⢴⣿⡴⠁⠀⠀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢘⡄⠀⠀⠈⣇⠀⠀⠀⠁⠀⢸⠃⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢹⡄⠀⡁⠀⠁⡞⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠕⠀⢰⠇⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⣾
⠀⠀⠀⠀⢀⠀⠀⣬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⡇
⠀⠀⠀⠀⢸⠆⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣓⣦⣀⢀⣀⣠⣿⡀⢠⡇
⠀⠀⠀⣐⣽⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣴⣇⠨⢠⣋⡼⢛⡉⠭⠜⣼⡇⢸⡇
⠀⠀⠽⣿⢿⣿⢛⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⡥⣪⢤⡄⡤⠉⣡⡴⠋⠄⠶⡶⣿⣟⣸⣷⡆
⠠⢤⣤⣶⢿⣿⣾⣷⣶⠂⢤⡀⣀⣠⣦⣀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢟⡉⠄⣉⡚⡤⠐⢊⣉⣠⣌⢁⣤⢯⣿⣿⣿⣿⣿⠧⠶⠂
⠀⢠⣾⣿⣼⡿⢯⣿⣏⣋⣈⣿⣷⣿⣿⣿⣿⣤⠀⢀⡟⠙⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣿⣿⣥⣤⣶⣶⣬⣭⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠠⣿⣿⣿⠃⠀⠀⠈⠱⣶⣾⣿⣿⡿⢛⡿⠇⠀⢸⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢉⢛⣻⣟⣻⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣈⡛⢻⣷⡀⠻⢦
⠀⣀⣹⠿⢃⣤⠶⣶⣶⣶⣿⢿⡉⠩⠭⡗⠀⠀⠀⠨⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠌⣉⣻⣿⣿⣿⡿⢿⣷⡛⠋⣿⣟⠿⢭⣿⣿⡿⠏⠹⣷⠀⠀⢢
⠀⣩⠖⠁⠀⠀⠀⠡⠶⠏⢁⡴⠄⠀⠀⢀⠤⠀⠀⢰⠀⡆⢸⠄⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣠⠶⠿⠿⣒⠶⣷⢤⣤⢌⡛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠷
⠹⠃⠀⠀⠀⠀⠀⠀⠤⠀⠀⣉⡐⠖⣂⣤⣀⣀⠀⢸⣤⣧⢸⠀⠐⠐⠒⠒⠚⠋⠉⠿⠖⠲⠶⣶⡿⠟⣿⣗⣀⡳⠫⠽⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠣⠳⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠞⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⢀⣄⣄⣴⣤⣶⣦⣄⠀⠈⠀⠀⠀⢀⢀⡔⠀⠀⣼⣷⣲⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣿⠋⠉⣁⠈⢠⣿⣾⣿⣷⣲⣤⣿⣿⡟⠀⢀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠑⢤⣄⢠⣿⣻⣿⣿⣯⣿⣷⣯⡷⠆⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⢿⢿⣿⠿⢿⠿⣿⣿⣿⣤⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⠀⢀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⢻⠁
⠀⠀⠀⠀⠀⠀⡀⠀⡿⠀⠀⠂⠀⠾⣿⠳⡆⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡄⡜
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⠁⠀⠀⠀⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣨⠀⢀⣀⢀⣀⣀⠀⠀⡀⣀⣀⣠⣤⠸⣦⠀⣤⣤⣀⡀⢀⢀⡀
⠀⠀⢤⣤⣤⣤⡄⠲⠶⠆⠸⠷⠶⠶⠿⠘⠟⠂⠘⠛⠛⠉⠉⠁⠈⠙⠛⠙⠛⠉⠀⠉⠀⠉⠙⠛⠛⠉⠛⠋⠀⠁⠁
⠀⠀⠀⠀⠉⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠘⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠑⠠⡀⠀⠀⣠⠔⢪⠃⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⢇⠀⠑⠀⠀⠀⠀⠘⠒⠦⡁⠀⠀⠀⠀⠐⠀⣄⠀⢄⡠⠊⠁⢠⠂⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀
⠀⠀⠀⣀⠄⠊⠀⠀⠀⢨⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⡡⠄⠚⠉⠀⠀⠀⠁⠀⢀⠀⠘⣄⠀⠀⠀⠀⠈⠉⠉
⡠⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠄⠋⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡀⠀⠈⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠉⠂
⠀⠀⠀⠀⠸⡄⢁⠀⢠⢦⠤⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣀⡄⠀⡄⣰⠃⠀⢅⣘⢘⠂⠄⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠛⠡⠎⢥⠀⢨⡤⠔⠀⠰⠤⠀⢀⣌⣀⣘⣃⡐⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠁⢁⢀
⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⠄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡤⠞⠪⢊⠛⠒⣂⠄⡆
⠀⠀⠀⠀⠀⠀⠈⠲⣴⡧⠤⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠙⠌⣀⢸⣷⡬⠼⠃⠀⠀⠀⠂⢾⣙⢠⡏⢸⢸⠇⠘
⠀⠀⠀⠀⠄⠀⢀⡀⢻⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠥⣢⡈⠛⡩⢁⠀⢀⠀⠀⠀⠀⠢⠬⠿⢹⠼⠬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⣀⢠⣤⡀⠉⢱⠛⠋⠅⠭⠅⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣔⡀⡙⠛⢙⠢⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⡙⢷⡀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠺⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠋⠛⠂⠀⠀⠀⠀⠠⠀⠀⠄⠑⠠⢌⡞⢁⡄⠁⠀⡀
⠀⠀⠀⠀⠀⠠⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⡀⢀⡀⠀⠀⠀⠀⠀⠒⢤⣀⢀⢰⠉⡠⢁⣤⠘⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣠⣰⠲⠆⠬⢶⡾⣿⠀⠀⠀⠀⠀⠀⢀⡐⠉⠑⣯⣦⡷⠃⠄⠁⠁
⠀⠀⠀⠨⢄⠶⢐⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⣠⠤⠲⢌⣳⣶⢞⣻⣿⣝⠄⠀⠀⠀⠠⠐⢄⠀⣶⡼⣿⢿⠓
⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣈⡺⢿⠋⠤⡟⡀⠿⠀⠀⠀⠀⠀⠀⠐⠡⠈⡡⠼⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠄⠋⡬⠹⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣴⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠉⠉⠉⢲⡴⠒⠊⠁⠐⣶⠒⡔⠋⠉⠙⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠟⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠈⠙⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠴⠷⠁⠀⢱⡤⠤⢤⡀⠀⡴⠛⠆⠀⠀⠀⠀⠒⠛⢢⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡬⡑⠂⠀⠀⠀⠀⠀⠚⢁⡖⠚⠉⠚⠓⣤⠖⠒⠒⠦⣎⡴⠛⠛⠧⣀⣀⣠⠇
⠀⠀⠀⠀⠀⣠⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡁⣸⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⠤⢾⠁⠀⠀⠀⠀⠘⣀⡀⠀⠀⠈
⠀⡐⠀⠉⢸⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⠁⠀⢠⣅⠁⠀⢀⣄
⡜⠉⠀⠀⢸⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡀⠀⠀⠀⢸⠑⠢⠄⠤⠐⠁⠈⠉⠁⠀⠈⢣⡀
⣱⠂⠀⠀⠈⡖⠂⠀⢠⢃⠶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠼⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠈⠂⠠⣤⠎⠁⠀⠀⢇⣀⡓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹
⠀⠀⠀⠸⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⢺⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣙⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠀⠀⠀⠀⡎⠀⣾⠳⠀⠀⠀⠀⠀⠸⠤⠆⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠸⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠑⠤⠄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢳⡀⠀⠀⠀⠓⠢⠤⠤⢤⠒⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠆⣤⡄⠀⠱⣄⠀⠀⠀⠀⠀⠀⣘⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣰⣅⠀⠀⠀⠀⣄⣠⠔⠁⣀⠀⠀⢀⢤⠀⠀⠀⡄⠀⢀⡼⠦⠤⠴⠃⠓⠧⠚⠉⠙⠢⠤⠄⠠⠜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠈⠑⡖⡖⠋⠀⠘⠢⠴⠶⣁⣀⣀⣢⢇⣠⡴⠛⢚⢏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢠⠃⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡆⠀⣇⣤⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢡⠀⠘⡀⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⢿⠀⠸⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠺⡆⠀⢻⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢿⣿⠟⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⣿⣿⣿⣭⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣗⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢤⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣉⣤⡄
⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣬⡛⢶⣿⣿⣿⣿⣿⡟⢋⣀
⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⡯⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣻⣟⡍⠻⣾⣿⣿⣿⣿⣿⢿⣛⣩⡀
⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣶⡶⢊⣀⢀⡀⠀⠀⠀⠀⣀⡠⠀⠀⠀⡐⢿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠈⠈⠉⠉⠉⠄⠄⠴⠤⢯⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣼⣿⡗
⠀⠀⠀⠀⣤⣈⣿⣿⣿⣿⣿⣿⢚⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡥
⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣛⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀
⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣟⠟⠀⠀⢀⣿⠀⡇⠀⡆⢠⡆⣹⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣹⡆⢰⣤⣿⣞⣧⣴⣧⣸⣷⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⢤⠖⠛⠉⠙⠲⣤⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⣠⡴⠞⠋⢿⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⣻⠙⠳⢦⣄
⠀⢀⡴⠋⠁⠀⠀⠀⢘⣷⠤⠤⠞⠓⠚⠉⠁⠀⠈⠉⠉⠁⠀⠉⠓⠖⠳⣤⣀⣀⣴⡏⠀⠀⠀⠈⠛⢦⡀
⣠⠏⠀⣀⣀⣤⠴⢚⣽⡇⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢸⣯⡓⠦⣤⣀⣀⠀⠹
⢯⡀⠛⢉⣀⣤⠶⠋⢈⡇⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢸⠃⠙⠲⢤⣀⡉⠓⢀
⠀⠉⠉⠉⠁⢀⣠⣤⠞⢷⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⡾⢧⣤⣄⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠞⠉⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⣠⠼⠃⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⢀⢸⡇⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠛⢦⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⣀⠈⠉⠉⠁⢀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⢷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⡼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⠛⠛⡷⠦⠤⠖⠳⠦⠤⣾⠛⠛⡏⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣿⣀⣠⡷⠀⠀⠀⠀⠀⠀⣯⣀⣠⣧⣤⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⢤⣶⡶⠶⠀⠀⣤⣤⠄⠀⠀⠀⠈⠈⠓⠄⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢔⠀⣀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠸⢠⠀⡌⣡⣤⣤⣤⡴⠾⠀⠀⠀⠀⢠⣄⠀⣈⣓⡛⠀⠀⠀⠀⢠⣶⣤⡈⢹⣾⠀⠀⠀⢺⣾⠉⣠⣴⡦⠀⢦⢰⠃⡺⢯⡦⠙⡆
⠀⠀⠙⢧⣀⢁⣈⣉⣹⣿⣿⢶⠁⠀⠀⠀⠿⢿⣿⠿⢿⣷⣴⣶⡀⠀⠀⠙⠿⠿⢾⣿⣆⠀⢀⣾⡿⠾⠿⠞⠁⠀⠀⠀⠈⠷⠉⠀⠈
⠀⠀⠀⠐⢰⡸⣿⣿⣿⣿⣿⠉⠀⠀⠀⣾⣿⣿⣏⠉⠀⠉⣽⣿⣷⣶⡆⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⢤⠀⣠⣾⡆
⠀⠀⢀⡆⢸⡣⣻⣿⣿⣿⣿⣀⡌⠀⠐⠈⠯⠾⢿⣦⣄⣬⣿⣿⡷⠟⠁⠀⠀⠀⠀⠸⠯⡐⡬⡿⠀⢀⣤⡴⠂⣦⣌⠉⠀⠘⠧⠤⠂
⠀⠀⢲⢅⡈⠈⠙⠛⢛⣻⣭⢥⠂⠀⢀⣀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⡶⠃⢀⣫⣾⣿⣿⣭⢿⣧⠀⠀⠀⢀⢀
⠀⠀⠈⠈⠍⢷⣿⣿⣿⣿⠤⠊⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⢄⠀⢀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣽⣿⣼⣟⡄⡿⠀⢨⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣙⣼⠛⢻⣵⣃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⡟⣹⠃⠀⠀⠟⠿⠻⠂
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠇⢞⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢻⣿⣄⣾⣿⡿⠄⠀⠀⠀⠀⠀⠀⣼⣱⡟⠀⣠⠾⠁
⠀⠀⢠⡀⠶⢶⣾⣿⣷⡆⢰⣾⣯⠀⠀⠀⠺⡆⠀⠀⠀⠴⠚⣽⡿⢯⣿⡿⣍⠳⠄⠀⠀⠀⠀⠀⠳⠭⠶⠛⣁⣠⡀⠀⠀⢲⠿⠷⣦
⠀⠀⠈⠿⣶⣄⢙⣿⣿⡿⠿⠿⠟⠁⢀⠈⣗⠨⠄⠀⠀⠀⣰⠃⡷⠴⣿⡇⠹⡆⠀⠀⠀⠀⠀⢠⣤⡦⠀⠀⣿⣿⡷⠀⠀⠀⠀⣠⣬⠄
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⣴⣿⣦⠞⠀⠀⠐⠁⠀⢹⣩⣿⠇⠀⠈⠀⠀⠀⢀⣸⣟⢧⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣷⣌⣳⡿⠛⠀⠀⠀⢀⣠⡄⢦⣽⣿⠆
⠀⠀⠀⠐⠀⠈⠃⠖⠒⠒⠒⠊⠉⠉⠀⠀⣦⣀⠀⠰⢟⢨⣿⡀⢶⣤⣤⣤⡀⢀⣀⣄⠀⠈⣳⣬⣙⣗⣨⡂⠠⣗⡸⢮⣝⢷⣾⡟
⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠀⢠⣿⠉⠀⠀⠈⠘⣿⣿⠀⠻⠿⠿⠋⠘⠏⣠⠀⠀⠈⠓⠿⣽⣿⣷⣭⣽⡷⣭⣛⣷⡾⠁
⠀⠀⠀⠀⠈⠙⢿⣯⠀⣿⣿⣿⣿⣯⡀⢾⠏⠀⠀⠀⠀⠀⢀⡀⢀⣤⣀⣀⠀⠲⡀⠋⡀⠀⠀⣀⣀⠙⢿⣿⣿⣷⣿⣿⡿⠋⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠠⡟⠁⡏⠀⠀⠈⢻⠋⢸⠂⠀⠀⠀⠀⠀⠘⡟⠈⠁⠀⠀⠀⠈⢷⠀⠗⠀⠘⢿⣿⠃⠀⠙⡟⠛⠛⣟⠁⠀⠀⠸⠿⠟
⠀⠀⠀⠀⠀⠀⠁⠁⠸⠀⠀⠀⠀⠊⠀⠎⠀⠀⠀⠀⠀⠀⢀⣀⠔⡄⣤⣦⢴⡤⣁⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠳⠈⠆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠶⠀⠀⠀⠀⠀⠀⢀⣴⣞⣺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⡄⠀⠀⠀⠀⠂⠀⣤⣿⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣿⠀⠀⠒⠶⠒⠠⠴⠶⣦⠁⠉⠓⠶⠀⠭⠄⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣾⣿⡄⠀⠀⠀⠀⢀⠀⣼⡟⣯⠋⠳⠀⠀⠀⡈⠂⠀⠀⢄⠀⠠⠀⠀⠈⠛⠶⣬⡀⣀⠚⠘⡁⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠒⣿⣿⣷⣄⠐⣴⡖⢘⣾⠉⠓⡂⠙⠉⠹⠀⠄⠠⠀⠤⠀⢠⡀⠀⠀⠀⠠⡈⠲⢘⢣⡌⠙⠣⠉⠀⢠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⣰⣇⣼⣿⣿⣦⣉⣡⣾⣿⠀⠓⠀⠂⠀⠀⠀⢀⠄⠀⠀⠀⠀⠘⠀⢐⠢⢀⠃⠀⠀⠈⠻⡆⣨⠓⢄⢠⡀⠚⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠋⢞⣣⢻⢾⠛⣿⣟⢯⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢻⣿⣤⠸⢆⣆⡰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣸⠇⣆⢨⣬⣿⠋⢎⠈⠄⠀⢢⡄⢄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⢠⠀⠀⣿⠡⢠⢷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠠⣤⠀⠿⠄⠚⡽⠃⠲⠀⠀⠀⢈⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠈⣇⣀⠁⠀⠀⠄⠃⢸⣗⣻⡗⣩⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⢀⠜⠰⢋⠀⠠⠠⡐⠄⠨⠀⢠⣀⡀⠄⠀⠐⠌⣄⠀⠀⠀⠀⠀⠀⠀⢿⢤⣠⣁⠀⢠⠈⠻⣿⣧⠙⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⣦⠁⡦⠀⢈⣧⠈⠀⢧⡧⢠⡀⠸⣧⡀⢀⠸⠇⠲⣷⡄⠀⠀⠙⠀⡈⢀⣀⠂⣬⢙⠀⡈⢡⠀⢸⡿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢠⡟⢡⣤⣯⢉⡒⣤⠈⣷⡈⠸⠇⡿⢦⠀⠄⣠⢀⢸⠷⣶⡀⢷⣀⣷⣼⣯⣄⣶⠿⣞⣡⡤⣎⣿⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣴⠚⠀⢾⣇⣏⠘⠳⣿⢦⡉⢃⠠⣰⣇⠈⣿⣠⣼⣻⣷⣾⢤⡏⣼⢻⣼⣿⣿⡡⣿⣴⢣⢴⣧⢟⠐⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣿⡦⢛⣿⣿⣿⣟⢺⣭⣾⡦⢫⣸⢳⣿⡿⣯⢻⡟⣿⢿⣿⣿⣼⣿⣿⣿⡟⢹⣷⣿⢿⣿⡗⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⡇⣯⣽⣿⣿⣿⣿⣿⣶⠻⣾⣷⣿⣟⢿⣿⣿⣿⣿⡿⣿⢷⡆⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣾⡿⣯⡿⣿⣾⠿⠿⠛⢿⣯⣧⠻⠋⠛⢻⣿⡟⣫⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⢿⣿⣿⠟⢻⣿⣿⠟⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⢳⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠀⠀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠼⡀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠃⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠄⠀⢤⠃⠼⠛⣡⠁
⠀⣤⠀⠀⠠⠀⢨⠴⠀⢀⡠⡔⠂
⠀⠀⠐⠇⠀⠀⣞⠀⠀⣄⣁⠀⢤⡀⠀⠀⢤⠄
⠀⠀⠀⠀⠄⠛⠿⡀⠀⠭⠉⠙⠆⠰⣚⠴⠓⣀⠆
⠈⠉⠀⠀⠀⠀⠅⠈⠀⠠⢦⠴⠂⣰⡇⠰⣆⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠋⠰⠀⠘⠁⠁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠄⠀⠀⠀⠀⠀⣤⣴⡂
⠀⠘⠧⠀⠀⠀⠅⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠉⠐⠃⡂⠤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⢂
⠀⠀⠀⡀⠀⠀⡇⠀⠂⠠⢀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠒⠂⠠⠔⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠃⠂⠀⠀⠬⠤⠀⠀⠀⠐⠠⠀⠀⠂
⠀⠀⠀⠉⣤⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠀⠤⠤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⡉⠀⠁⠀⠀⠀⢠⠀⠁⠀⠠⣾⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠉⠁⢀⠀⣄⣄⠀⣀⣈⣧⣀
⠁⠀⠀⡀⠀⢀⣠⣷⣷⣾⠵⠟⠛⠓⠐⠛⠉⠉⠁⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠷⠶⠦⠴⠶⠿⠿⠛⠛⠛⠛⠛
⠛⠻⠻⠿⠋⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣄⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠁⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠙⠻⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⢀⣀⡀⠀⠀⣀⣀⠈⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⠻⣿⣿⣿⣿⣿⡿⣻⠄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣿⣿⣿⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⣿⣿⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠿⠋






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⢂⠀⠀⠀⢄⢀⠠⠄⠄⡀⢀⠄⠐⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠥⢄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠑⠒⠈⠁⠉⠐
⠀⠀⠀⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⡰⢀⠀⢀⡐⠀⠀⠁⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⢈⠇⠐⠄⣀⠠⠒⡈⠀⠈⠠⢄⠀⠀⡠⠤⠐⢃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠁⠀⡐⠁⠀⠀⠀⠀⠀⡀⠀⠈⡉⠀⠀⠁⠀⠛⢄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠄⠊⠀⠀⠐⠀⠠⠀⠀⠇⠀⠀⠄⠀⠠⠀⢠⠀⠀⠢⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⢊⡀⣀⠀⠣⠔⡁⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠆⢀⠄⠈⠐⠄⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⠐⠣⠄⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠄⡀⠀⣀⡠⠊⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠑⠂⠀⠉⡅⠀⠂⠀⠐⠀⠀⠀⢨⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⡀⠈⠋⠀⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠛⠀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠊⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠃⠀⠈⠂

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⡒⢋⠙⠀⠉⠀⢈⠀⠁⠐⠱⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠐⠁⣀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠀⠀⠀⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠉⠀⠀⠉⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡁⠐⣁⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠈⠁⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⣰⣰⣄⣀⣆⣿⣿⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠐⠂⠀⠂⠀⠀⠀⢀⡐⠀⢀⣄⢀⠀⡀⠀⠲⢶⡟⠻⢟⣛⠉⠛⠻⠿⣿⡙⢿⡉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠐⠀⠀⠘⠀⠀⠘⣆⣠⣴⣶⣮⡿⠛⢲⡾⢶⢋⣩⣤⣤⡺⠿⠋⠀⠀⠀⠀⠈⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠉⠔⠠⠃⢠⠄⠘⠄⠀⣰⣶⡋⢡⣴⣿⣿⣧⣶⡏⢠⠈⠈⠻⠿⠿⠛⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⢀⡀⠀⠰⢀⠰⣤⡀⠉⠀⠀⠀⠈⠉⠻⣿⣤⣿⣆⠀⠀⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠁⠀⠀⠀⠀⢀⠈⠀⠀⠀⠰⠦⠶⣦⠀⢶⡾⣿⡙⢠⠈⣸⣆⡙⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡀
⠀⠀⠀⠀⠀⠀⡄⠃⠐⠀⠀⠀⠀⡀⠀⠁⡄⢠⠀⢠⠁⠈⠀⠀⣀⠙⡙⢦⠑⠌⠳⢬⠁⢃⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠈⠀⠀⠀⠈⠀⠄⠨⡂⠉⠀⠐⠆⣨⡘⢦⠈⠁⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⡀
⠀⠀⠀⠀⣠⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠐⠐⢆⠇⠀⡃⢛⠀⣄⣻⠴⠤⠈⠙⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⢤⣄⡀⢀⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠉⠈⠀⢠⠀⡀⠈⠀⡄⢀⠈⠉⢇⣉⠳⣔⡿⡆⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢒⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⠀⠈⠀⠀⠊⠀⠀⠀⠄⠀⠔⠑⠀⣅⢀⢶⣍⠙⢿⣿⡿⣿⣿⠟⠛⠒⠒⠂⠀⠀⣀⣸⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⢠⣈⣛⠀⣠⠟⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠂⢉⣽⡷⠻⢢⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠐⢠⠀⠀⡀⢀⣠⢶⣮⣜⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠤⠀⠎⣤⠘⢫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠠⡀⣉⢳⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡥⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠄
⣆⡅⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣤⣶
⣿⣿⣿⣧⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣻⡄⣿⣿
⣿⣿⣿⣿⣿⣧⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢀⠀⣀⣸⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣧⣾⣇⣠⣸⣀⣆⢀⠀⣴⣆⣠⡄⠀⣄⢀⣴⣤⣶⡆⣀⠀⡧⣾⣦⣤⣿⣇⣼⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣷⣾⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⣤⣶⣾⣿⢿⡟⠧⢃⣖⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⣛⡙⣿⣟⠉⠛⢿⣿⣿⡿⣦⡁⠠⣿⣿⡏⢉⠛⠿⣶⣄⠀⠀⠀⠙⠛⢻⣶⣄⠴⢷⡞⣀
⠀⠀⠀⠀⠀⠀⢀⣴⢛⠃⠸⠛⣻⣿⡄⠒⠂⣺⣿⡿⠖⢌⠳⠄⣿⣿⣷⣼⣧⣶⣄⠉⠀⠀⠀⠀⠀⠀⠙⢻⣧⣾⠇⣴⣦⠄⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⢻⢏⣿⣯⣴⠾⢫⣽⣿⡛⢨⣷⡟⣠⣿⣿⣿⡁⢘⢿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣄⠹⢮⣀⠘⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⡶⣸⣿⡯⠶⣦⣿⣿⡏⢉⣽⡟⣷⣿⣿⣿⣯⡥⢶⡭⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣬⣿⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢡⣿⣿⣡⣴⣽⣿⣿⠑⣻⣿⣴⣿⣿⣿⣿⡿⢛⠨⠭⢷⣤⢁⡀⠀⠀⠀⠀⣀⠀⠀⠈⢿⣿⡜⣿⣧⠰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣿⣿⣯⣾⣿⣿⣏⣼⠿⢁⣿⣿⡿⠿⠛⢀⣠⣤⠶⢦⡀⠈⢳⡀⠀⠀⢰⣿⡆⠀⣀⢸⣿⣧⢸⣿⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⠇⣰⣾⠋⠀⣲⠆⢈⡽⢡⣞⣻⣷⣄⡀⣼⡇⠀⠀⠘⣿⡁⢠⢟⡀⡹⣿⡌⣿⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⠞⣻⣿⣿⣏⣤⣴⣿⣵⣿⠻⢉⡉⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⠿⣧⣸⣿⣇⢈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢃⣴⣿⣿⣿⢿⣿⡿⢿⡏⠻⣷⣾⣾⣿⣿⠏⠀⠀⠀⠀⠙⣿⣧⣭⣵⣿⣿⣿⡜⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⠷⠿⣿⠿⠋⠥⠀⠀⣿⣿⠘⠷⣤⡾⢋⣉⡭⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⣽⢿⡇⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡿⠳⠒⠀⢈⣭⡴⠊⠀⣀⣠⡶⠿⠛⠀⠾⠿⠂⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢌⠻⣼⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡌⠀⠤⠞⢋⣠⣴⣿⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠜⣶⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣭⣠⠄⢀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠀⡀⠘⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣰⠏⢀⡔⣡⣤⠀⠀⠐⠄⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣉⡉⢙⡂⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⣺⡿⠁⢖⣿⣿⢟⣡⠆⠀⠀⠀⠓⢄⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⢿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠀⡼⢻⣿⡿⠓⠉⣉⣉⡉⠓⠊⠓⠀⠀⢻⣿⡾⢻⡐⣤⡀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⡿⠁⠆
⠀⠀⠀⠀⠀⠀⢀⡿⢻⠇⠘⢁⣾⡏⠀⣴⣿⠟⠋⠁⠀⠀⠀⠻⣦⡀⠹⣿⡠⣷⡌⠛⢦⣀⣀⣀⡀⡀⠃⢓⣛⣉⣭⠀⣠
⠀⠀⠀⠀⠀⠐⠋⣀⣠⣆⣤⠞⠛⠀⠜⣿⡱⠀⢀⠠⠐⠂⠀⣈⣉⠭⢤⡈⠻⣿⣿⣷⣬⣉⣥⠹⣿⣿⣿⣿⣿⡏⠉⢰⡏⠃
⠀⠀⠀⠀⠀⠀⠈⣾⡿⣩⣧⠇⠀⠀⠰⠃⠁⠈⠀⠀⣠⠔⠉⠁⠀⠀⠀⣭⣦⣈⠙⢻⣿⣿⣙⠷⣌⠛⠿⠛⠋⠀⠀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠁⢺⣿⣴⣴⣶⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠠⢫⡞⣿⣶⡄⢈⠙⠻⢿⣿⣿⣷⡾⠃⢀⠲⠦⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢸⠉⣿⣧⠀⠀⠶⠲⣶⠦⠀⠀⠀⠀⠀⢑⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⡀⠀⠐⠀⠀⠀⠀⠀⢰⡀⠠⠀⠀⡟⠀⠸⡿⡆⠀⠀⠀⠀⠄⠀⠀⠈⠐⠀⠀⠊⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣰⡆⠀⠀⢰⠀⠀⡇⠀⠀⠈⠃⡀⠈⠙⡀⡀⠀⠐⠤⣄⠀⢀⡀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⣤⢠⠈⠀⠀⠘⠀⠀⢀⠀⠐⠀⠄⢻⡝⠄⢢⠀⡀⠉⠢⡈⡈⠋⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⠇⣄⠀⠀⠀⠀⢸⠀⠑⠀⡘⡆⠁⠀⠀⠄⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡼⢉⡤⢄⠉⢳⡴⠋⢉⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⢰⡉⠀⠈⠓⠒⡄⠼⣁⡽⠂⠙⠛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⡤⠤⠖⡆⠹⣀⡤⣀⣸⠁⠀⡤⠦⣀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡞⠁⠀⠀⠉⢢⠀⣀⡔⢢⡀⢠⠗⠀⢠⠃⣴⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣭⠉⢇⣠⠏⠁⠀⢧⠀⡠⠝⢈⡒⠓⠚⠀⢸⠂⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠶⠒⠦⣤⠚⠁⠈⣧⡀⠀⢀⡠⠓⢬⣉⣀⡴⠋⠑⠲⠤⠖⡿⢤⣀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⠉⠉⠛⠁⠀⠀⡼⠁⠀⠀⣠⡇⢉⡽⠛⣷⣦⡀⠀⠀⢀⠔⢺⣷⣦⡀⡇⠀⠈⠉⠛⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠏⢰⠃⠀⠀⠀⠀⢦⠸⣇⣠⠴⠋⠀⡇⣾⠀⠘⣿⣿⣿⠀⠀⣾⠀⠘⣿⣿⣷⡇
⠀⠀⠀⠀⠀⣠⠋⢀⠀⠀⢄⠓⠤⠔⠓⠒⢁⡤⢄⠀⠀⣀⣀⢻⠘⠦⣄⣬⠽⠁⠀⠀⠘⠦⣤⡤⠞⢹⠃
⠀⠀⠀⠀⠀⣏⠀⠘⠤⠤⠜⠀⡆⠀⡀⠀⠘⠄⠀⠁⠀⠀⣨⠈⢧⠀⠀⠀⠀⠐⢏⠉⡹⠂⠀⠀⢠⠏
⠀⠀⠀⠀⠀⡼⡰⠂⠀⠀⠀⠀⠉⠋⠁⠀⠀⢠⡀⢰⠀⢀⡇⠀⠈⠳⣄⡀⠀⠰⠤⠿⠤⠄⣀⡴⠋
⠀⠀⠀⠀⠀⡇⠣⣄⠀⠀⣸⠀⠰⡇⠀⠀⠀⢀⡇⠀⠉⠉⠐⢢⡀⢀⣀⡉⠓⠒⢶⠖⠒⠋⠁
⠀⠀⠀⢀⡞⠙⣤⣈⠑⠊⣁⠀⠀⢈⣉⠉⠉⠉⠀⠀⣄⠀⣠⠴⠁⢏⠀⠸⠀⠀⣸
⠀⠀⠀⠸⣤⠴⠋⠈⢹⢸⡀⢠⠀⢏⠀⠁⠀⠀⠒⢄⠈⠉⠱⠒⢦⠀⣰⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⣭⡥⣤⠘⠢⠞⠀⠠⠤⠜⢀⡀⠀⠒⢋⡠⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠦⠤⠔⣦⣀⣀⣠⠞⡟⠙⠉⠹⡄⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠒⠒⡿⡗⠚⠉⢹⠀⠀⠀⠀⡟⠒⠒⢺⠹⡏⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠲⣰⡇⣇⡴⠲⢼⡆⠀⠀⢸⣧⠴⢦⣸⠀⢧⠞⠙⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⢀⡤⠂⠊
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⡴⠋⠀⠀⣠⠆
⠀⠀⠻⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠚⠉⠀⠀⠀⠈⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣤⣤⣀⠀⢳⡀⠀⠀⠀⠀⢢⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗
⠀⠀⠈⠳⣬⠙⠄⠀⠀⢠⣮⡿⠙⠢⡄⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠻⣦⠀⢀⣺⣿⡇⠀⠀⡄⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⣸⣿⣄⠀⢀⠀⠀⠀⠘⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⡼⠁⢀⡄⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡗⠀⠀⣴⣾⣄⠀⠀⠉⠻⢆⡀⠳⠆⠀⠀⠀⠠⣾⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⣉⡴⠂⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠁⣠⠖⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢰⠞⠁⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠼⠅⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣟
⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⣼⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡘⠛⠛⠷⠶⠶⣤⣤⣀⡀
⠀⠀⠀⣼⡿⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀⢉⠉⠛⠻⠶⣦⣦⣤⣦⣤⣠⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣼⣿⣿⡿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢀⣼⣿⣿⣿⡿⠤⠸⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⠿⢿⣶⣶⣤⣤⣀⡀
⠛⠛⠛⢿⠿⡁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⣶⣧⣤
⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠻
⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⠉⠊⠀⠀⠀⠀⠀⠀⠈

⠀⢀⣤⣤⣴⣶⣤⣤⣀⣴⣾⣿⣿⣿⣿⣶⣄
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⡀⠀⠈⣉⡀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠀⣀⣈⠀⠈⣆⠒⢿⠦⣀
⣿⡿⠟⠛⠉⣴⣿⡿⠹⡰⠆⢈⠀⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢱⣄⢈⠀⣈⠰⠆⡟⢀⡀⠳⡀⠉⠐⠢⣄
⣟⠀⠀⢀⣾⣿⠿⠁⠀⠑⠚⠿⣵⣾⣿⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠂⢸⠈⠓⠽⠛⠋⠀⠀⠳⣄⠑⢄⠀⠀⢈⠂
⣿⣷⣾⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢻⣿⡿⠋⠀⠀⠀⠀⡘⠀⡸⠀⠀⡱⠀⠀⠀⠀⠀⠀⠳⡀⠉⠉⠁
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠈⢻⠁⠀⠀⠀⠀⡔⠁⢀⠇⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢳
⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠈⠀⠀⠀⠀⢸⠀⢀⠌⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⡘
⣿⣿⣿⣿⣷⣄⠛⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠳⣄⠀⠀⣀⠀⠛⣡⠎
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⡺⠀⠀⠀⢸⠉⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠱⡄⠀⠀⡀
⠛⢻⠉⠁⢸⠛⠛⠛⠿⠿⠿⠟⠛⠛⠉⠁⡇⠀⠀⠙⢆⠀⢀⠞⠀⠀⠘⡍⠒⠂⠠⠄⠀⠀⠀⠤⠤⠔⡖⠉⠐⣶⠆⠐⠹⢄⣀⣀⣀⠞
⢠⠎⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣀⣀⡠⠜⠁⠣⣄⣀⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠙⡄
⣘⣤⣄⣤⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣀⣀⣀⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠻⣿⣧⡀⠀⠀⠀⠀⢀⣾⡿⢱⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⣿⣷⡀⠀⠀⠀⣾⣿⢃⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣌⢿⣇⠀⠀⢰⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠈⠻⣿⣦⢿⡄⠀⢸⣿⠇⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣮⣭⣛⠻⠿⣿⣷⣦⡀⠀⠙⠿⣧⠀⠘⣿⢸⣿⡏⠀⠀⠀⠀⣠⣴⡿⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣦⣍⡛⢿⣦⡀⠀⠘⣷⡀⡿⣾⠟⠀⠀⠀⣠⣾⡿⢋⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣷⣮⣿⣦⡀⠘⣧⣼⠋⠀⠀⠀⣴⣿⠟⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠓⢾⡏⠀⠀⠀⣼⣿⠏⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣝⡻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⣿⢏⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⡻⢿⣿⣦⡀⠀⠀⠀⢸⡇⠀⢸⣏⣾⡿⠋⠀⠀⠀⢀⣀⣤⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⣿⠀⣬⡿⠋⠀⠀⢀⣠⣶⡿⢛⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣙⢿⡄⠀⠀⢻⡾⠋⠀⠀⠀⣴⣿⡿⢋⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠉⠛⠿⣦⣿⡄⠀⢸⡇⠀⠀⢠⣾⣿⢋⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣙⠿⣿⣦⣄⠀⠀⠀⠀⠉⠛⢦⣸⡇⠀⢀⣿⡟⣡⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⡛⢿⣷⣦⠀⠀⠀⠀⠀⢹⡇⠀⣸⢟⣼⣿⠟⠋⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⢸⡇⢠⣿⡾⠟⠁⣀⣴⣾⢟⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡻⣿⡀⠀⠀⢸⣷⠟⠁⠀⣠⣾⡿⢋⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⢦⣄⡀⠀⠈⠛⠿⣷⣜⢷⡀⠀⢸⡇⠀⢀⣾⣿⠟⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡝⢿⣶⣄⠀⠀⠈⠙⠻⢧⡀⢸⡇⢀⣾⡿⣡⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡹⣿⣷⡄⠀⠀⠀⠀⠙⣿⠁⣸⡟⣴⣿⡿⠋⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡌⢿⣿⡄⠀⠀⠀⠀⣿⢀⣿⣾⠟⠋⢀⣤⣶⣾⠿⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣎⢻⣿⡄⠀⠀⢠⣿⠞⠋⠁⣠⣶⣿⠿⣋⣵⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢻⡇⠀⠀⢸⡏⠀⢀⣼⣿⠟⣡⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⠀⠀⣿⠀⢀⣾⢟⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⢠⡏⢀⣾⣣⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣡⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡞⠙⡀⢸⡇⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⣴⡇⠀⠀⠀⠜⠀⠀⢿⡀⢀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⡴⠛⠀⣠⠂⠠⠀⠠⡀⠀⠀⡇⠘⠃⠈⢧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢀⠤⠚⠉⠀⠀⠀⠐⠃⢠⠆⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⡸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⣼⠀⠈⠉⠉⠁⠀⠀⠐⠤⠤⠀⠄⠀⠈⠁⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⣿⣇⢠⣿⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣷⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡀⢀⣿⣿⣿⠼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢼⣿⣿⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠷⠖⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡯⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠙

⡀⠀⠀⡠⠔⠒⠒⠒⠢⢤⡀⠀⠀⠀⢹⠉⢃⠒⠦⣀⠀⠀⠀⠀⢠⡧⣀⡀
⠙⠦⡍⠐⠂⠶⠄⣌⣂⡐⠌⢢⠀⠀⡞⢀⠀⡆⠀⠈⠳⡀⠀⡰⠁⣄⠄⡈⢂
⠀⠀⠈⢦⡀⠀⠀⠄⠐⠙⡛⢮⣇⠀⢣⠀⠀⠹⣆⡠⠀⢧⠀⠃⠐⢧⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠓⠤⠤⠬⠤⠒⠉⠈⠙⠲⢕⣦⣘⠛⢦⡀⠇⠀⠡⣀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⢒⠀⢄⣤⠞⠓⢬⣍⣻⡄⠀⠀⠈⠂⠤⠻⣄⠁
⠀⠀⠀⠀⠀⠀⢀⠜⢀⢀⣈⠖⠒⠋⠉⡸⠀⠀⠀⠀⠈⠉⠓⠒⠦⢄⣀⡀⠈⣧⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠠⢞⠀⠀⠂⢀⡴⠁⠀⠀⡀⠔⠊⠉⠁⣒⢺⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠓⠦⣤
⠀⠀⠀⠀⠀⠀⠈⢄⠐⢀⡠⠤⠔⠉⠀⠀⢀⡎⠀⠀⠀⢒⠴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⡸⠁⠤⠤⠛⠋⢘⡴⠃

⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣣⠊⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡀⠀⠀⠈⢇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡌⠀⠀⢀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢱⡌⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⡴⠃⠀⡜⠀⠀⠀⠈⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠆⠔
⠀⠀⠀⠈⢣⡀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⠀⠀⠀⠀⠰⡆⢠⠏⠀⠀⠀⠀⢄⠀⠀⠀⠀⠸⣸⠂⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠙⢄⣼⠃⠀⢀⠀⠀⠀⢠⠂⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⢹⠏⠀⡄⠀⠂⠀⠘⠇⠀⠀⠃⠀⣷⠀⠀⠀⠀⠀⠆⠀⠙
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⣇⠁⠀⠸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠁
⠸⠇⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣛⣛⢻⡛⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡐⣀⡀⢀
⠀⠀⠀⠀⠀⠈⠟⠁⠉⣦⣾⠿⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠨⠔⠀⠐⢶⣤⡀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠐⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠐⡛⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⡀⠀⠀⠀⠀⠀⣨⡇⣀⠀⢀⡄⣀⠀⣠⣀⣹⣋⠦⠀⠀⠀⢤⣳⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡥⠀⠀⠀⠀⣿⣽⣯⣽⣮⣿⣿⣿⣼⣿⣿⣶⣿⣿⣄⠀⠀⢐⣲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠀⠀⢰⣾⣿⠉⠛⠛⠛⠿⠿⠿⣿⣿⡿⠋⠙⠻⣿⣦⡀⠘⢿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠀⠑⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡠⣀⢄⣤⣠⣀⣄⣀⢠⣶⠧⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠀⢀⣤⣶⣥⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠋⠉⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠁⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡇
⠀⠀⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡋⠀⠀⠀⠀⠀⠀⢠⠆
⣀⠀⠀⢸⣖⠀⠀⠀⠀⣠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠈⠻⠻⣿⣦⣤⠀⠐⢤⡀⠈⠀⡀⢰⡄
⠿⠆⢨⢊⣵⠄⠀⠁⠐⡫⠀⠀⢐⠀⠀⠀⠀⠀⠤⠄⣈⠉⠉⠀⠐⠠⠀⠈⠋⢻⡆⠀⠀⠉⣶⠀⠋⠿⠃⠀⠈⠁
⠰⠀⠠⠋⣙⠧⣀⢰⠊⢠⡀⢀⡎⠱⠲⠦⢀⡄⠲⢤⠍⠀⡒⠄⠄⠀⡀⠀⠀⢈⠙⠆⢀⠆⠽⠂⣰⠄⠤⠀⡀⠰⠆
⠇⡀⢀⣾⢁⠢⡀⣲⣿⣾⠲⣿⣟⣼⣧⣦⣼⣷⣶⡆⣶⣰⡇⣸⣤⣦⣟⣴⣶⣿⣴⣴⣿⣠⣴⣠⣿⣿⣠⣼⣇⡄⣀
⡟⡟⢁⠜⢁⡤⠸⠿⢿⣿⠊⠿⠟⠛⠻⠿⠿⠷⣿⠿⠗⠿⠤⠟⠟⠻⠿⠿⠿⠿⠿⠻⣿⠿⠿⢿⣿⣿⣿⢿⠿⠾⠿
⠀⣴⣋⡼⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠛⠿⠛⠛⠋
⠄⠈⣹⠴⠺⣿⡭⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠉⠉⠁⠀⠀⠀⠉⠉⠉⠙⠋⠙⠛⠛⠿⠿⣷⣶⣦⣄⡀⠀⠀⡄⠒
⠤⠜⠃⣤⢠⣯⣗⢆⠀⠀⠐⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⢀⠀⠐
⠀⠠⠞⠁⣸⣟⢯⠁⠀⠀⠀⠀⠀⠉⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣯⡀⠀⠀⣀
⠁⠀⣼⡟⠹⣿⣧⠧⡄⠀⠀⠀⠀⠀⠀⠘⢠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⠀⠀⠀⠈⠉
⣀⠀⠉⠀⠀⠈⠉⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⠀⠀⣀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⣴⣽⣤⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⢀⢴⣿⣿⣿⣀
⠀⠀⢀⣼⣿⣿⣷⣿⣤⢀⡀⢰⣿⢿⣾⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣭⣿⣫⣍⠛⢿⣶⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢱⣿⣿⣿⢿⠉⠯⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⢀⣠⣶⡄⣘⣿⣿⣿⣟⠻⢿⣿⡿⠟⠿⠆
⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣥⣶⠿⠓⠲⠶
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢬⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣷⣴⣾⡟⣰⣆
⠸⣿⣿⣿⣿⣽⣿⣼⠿⣿⣿⣿⣿⣿⣿⣤⡇⠺⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡛⠓⣿⣾⣿⣿⣿⣿⣿⡏⢹⣏⣿⢋⣹⣿⣿⡇
⣤⣿⣿⣿⣿⣽⣯⣾⣻⡟⢻⣿⣿⢿⢿⠉⡇⠀⣿⠉⢹⡟⣿⢹⣿⣿⣻⣿⣿⣿⠷⡿⢛⡃⣼⣿⣿⡿⠀⢸⡭⢽⣼⣿⣿⣿⣿
⠈⠙⢛⣿⣿⣿⡿⢼⢛⡇⢺⠻⢭⢴⢺⢹⠃⠘⢿⡇⢈⡟⢿⠙⢻⡟⣙⡏⣿⠁⠀⡇⢸⠀⢸⣟⣉⡟⠀⢸⡄⣼⣹⣿⣿⡟⣧
⠀⠀⠠⣿⡏⢙⡇⣻⢀⡇⢸⣾⠀⢸⢸⢸⠁⠀⢸⡇⢐⡇⢹⠀⢸⠀⠉⡇⣸⢰⡂⡇⢸⠀⢸⢨⠀⡇⠀⢸⠀⢸⢸⣿⣿⡗⡃
⠀⠀⠀⡋⣇⠈⡇⢹⠀⡇⢸⣿⣶⢸⢸⢈⠀⡇⢸⣷⣼⣇⢸⢸⣸⠀⠀⡇⣾⣿⣇⡇⢸⠀⢸⣤⠀⡇⠀⢸⠀⢸⠈⠹⠿⡇⠃
⠀⠀⠀⣇⡇⢠⡇⣼⣤⣷⣼⣿⣿⣼⣼⣷⣾⣿⣼⣿⣿⣷⣾⣼⣿⣿⣇⣷⣿⣿⣿⣷⣸⣇⣸⣿⡄⣷⣴⣸⠀⢸⠀⣀⡚⡇⠃
⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠙⠛⠋⢻⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠈⠉⠉⠙⠋⠙⠀⠈⠻⡿⠛⠛⠉⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⡆⠀⠀⣠⠤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⠞⠁⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⣄⠀⠀⠀⠀⠀⠰⣶⠦⡘⢆⣠⠃⣼⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄⢀⡤⠒⠛⡇⠈⠒⠼⠾⣯⠞⣁⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⣠⠃⡟⠀⠀⢀⡇⠀⠀⣠⠞⠳⢏⡁⠀⠀⠀⠀⠈⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⣀⠙⣄⣇⠀⣠⠞⠀⡠⠚⠁⢀⣀⣀⣉⡒⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⣦⠸⡟⠉⠀⣠⣾⣖⠒⠺⣏⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣈⠉⠉⠳⣇⣠⠞⠁⡏⠀⠈⢳⠈⠑⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⢰⠋⢣⠀⢀⡟⠁⠀⠀⢣⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⡄⠀⠀⠀⠘⢆⣸⢠⣯⠖⠋⠉⣹⠂⠈⠑⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣼⠀⣠⠞⡇⠀⢻⡿⢇⣀⠠⠔⢁⡤⠤⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠦⣌⠑⢾⢸⡇⠀⢰⢀⡏⠀⠀⡞⢦⢠⠏⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⠀⢈⡹⠮⣿⣇⠀⡘⢸⠀⢀⣤⠳⣼⡾⠤⠤⣔⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠒⢾⣿⡶⠃⣿⠀⡏⠈⢧⠈⢇⣠⠋⠁⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠻⠾⣿⣧⡀⢿⠀⡇⠀⢸⣸⠏⠙⠢⠤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢨⠏⠉⢻⠀⠸⡄⣼⡟⢀⠔⠊⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠔⢚⣁⣀⡀⠈⣇⠀⠘⣿⡵⠃⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⣳⠼⣦⠞⠉⠓⠢⠤⠄⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠶⠒⠊⣡⣦⠈⢦⡀⠀⠀⣰⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠈⢆⠀⠑⢄⠀⣇⠀⢘⢀⡤⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠲⢤⡳⣀⣸⢀⣖⣚⡷⢮⡲⣼⣏⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢄⣀⣀⣀⡠⠟⠪⣿⠼⠗⠛⠒⠒⠛⠛⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣤⠴⢚⣧⡀⠀⠀⡠⠚⠛⠓⠒⡶⠋⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠃⠀⡞⠀⠙⣆⠀⡇⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠧⡀⠀⡼⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⡇

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⠶⠶⣶⢶⣶⡶⢶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣄⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣀⣀⠀⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠳⣿⠀⠄⢀⠈⣿⣷⣰⠀⠀⠀⡄⡷⠋⠠⠇⠀⠀⠀⠀⠠⣀⠁⢸⡆⠀⡏⡼⠀⡘⠀⡇⢺⡇⣴
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⡀⢠⡸⡇⡘⠁⠀⣿⠊⠁⠀⡴⠒⠃⡧⠀⠀⠀⣠⠆⠀⠀⠀⠸⡄⢸⣧⡮⠁⠖⠀⠘⠀⡇⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠼⠃⣿⠁⠀⠀⣿⣿⠀⠆⠀⠀⢠⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠑⢾⡛⠃⠂⠀⠀⠀⠓⣧⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡀⠸⡆⠀⠀⣿⣿⠀⢀⡀⠀⠘⠒⠛⠉⢅⡀⠀⠀⠀⠀⠀⠀⢸⣏⡘⠀⠈⠀⠀⠀⣿⡁⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣧⡀⠀⣿⣟⠐⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡏⠓⠀⠀⠀⠀⠁⠸⣅⣤⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣇⢸⠀⡀⠄⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣿⣿⡶⣄⡴⠒⠒⠒⠀⠀⠀⠀⠀⠀⣀⣴⣦⣄⠀⡟⢸⣼⣤⣤⡀⠀⢰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢷⡿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⣿⣿⣿⣿⡿⡼⠀⠛⠻⠷⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠃⢀⠀⠀⠀⣠⣴⡾⠋⠉⠛⢿⣿⣿⣿⣿⣷⡅⣷⣤⡀⠀⠀⢾⡄⡤⠞⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⢈⣿⣿⡇⠀⢁⣠⣴⠟⢛⠁⠀⠀⠀⠀⠀⢙⠻⢿⣿⣿⣠⢻⣿⣿⣶⣄⢸⣇⡗⢦⡾⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠀⡙⠛⣿⣿⢣⡶⠛⠉⠰⠊⠐⠀⢀⠄⢀⠀⠠⠜⡆⢄⠙⣿⡉⢸⣿⣿⣿⣿⣿⣷⣇⠈⠿⢿⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠌⠀⣀⡴⣿⡿⠓⡇⠀⠀⣸⠞⠛⠚⠛⠒⠋⠀⠀⠁⡟⢸⠶⣿⣧⡼⢿⣿⣿⣿⣿⡿⣿⠷⢀⣡⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢉⣠⡶⠛⠉⣠⣿⣿⠀⠇⣠⠞⢯⡠⠐⠉⠆⡇⠀⠀⠀⠀⠀⠘⣷⣿⡏⠇⠀⠙⣿⣿⢻⣷⢶⣞⣻⣧⢠⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠋⠁⢀⡀⢠⠀⢹⣶⠦⡾⢻⠀⠀⠉⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⣠⣾⣿⣿⣾⡏⢸⡏⡿⢿⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠡⣾⠀⣀⢀⡷⠾⢄⢸⣿⠀⢉⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⣼⣿⣿⣿⣿⢸⡇⢸⡿⡇⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⡅⠀⠈⢻⣿⡃⢈⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡄⣿⣿⣿⣿⣿⢸⡏⢨⡇⢇⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡃⠀⠃⠀⠀⢸⣿⠃⠬⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⢁⢸⣿⣿⣿⣿⢸⡇⢸⡇⣸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⡀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠁⠇⠀⣠⣾⣿⣿⢼⡸⢿⣽⣿⣿⢸⡇⠈⡇⣿⡅⣇⡄
⠀⠀⢠⣠⡠⠖⣶⣤⣿⣿⣯⠀⠀⠀⠃⢀⠀⢸⢿⣿⢨⠀⠁⠀⠀⠀⠀⠁⠀⠀⠂⢀⣾⣿⣿⣿⣿⢛⠁⣾⣿⣿⡿⣸⡇⣠⠃⣿⡇⣟⡆
⠀⢰⣿⣿⣿⡷⣿⡟⣻⣿⡧⠀⠀⠀⠀⠈⠀⣸⣿⣿⣚⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⡇⣿⠷⣿⡄⣿⠁⣏⡇
⠀⢸⣿⣿⣿⢣⡟⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⠏⠠⣾⣿⣿⣿⣿⣿⣿⣿⣇⡞⣿⣿⣿⡇⢻⡆⣿⣷⣿⣶⣿⠁
⠀⠈⠛⠉⠉⠉⠋⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⢹⡏⢿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣦⠀⠀⡀⣿⣷⠐⠀⠘⠈⠀⣸⡿⠇⠁⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠿⠀⠈⠀⠀⢐⣿
⠀⠠⠀⢠⣄⣤⡤⠄⠀⠤⢤⠤⢤⡤⠶⠴⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⣄⣀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⣀⣠⡾⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢋⣉⣉⡉⠉⣻⠏⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠹⣟⠉⢉⣉⣉⡙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠉⢙⡟⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⡋⠉⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⢼⡇⠀⣠⢤⡀⠀⠘⣿⣿⣿⣿⠁⠀⢀⡠⣄⠀⢸⡧⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⣄⣀⣼⠀⠀⣿⣿⣿⣿⠀⠀⣧⣀⣠⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠛⠛⠋⠀⢠⣿⣿⣿⣿⡀⠀⠙⠛⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⠞⠛⠛⠛⠛⠛⠛⠳⡄⠀⠀⠀⣼⢃⣤⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣦⣄⣸⣦⣀⣛⣀⣀⣛⣀⣴⣇⣤⠴⢾⡁⣞⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⣥⣬⠽⠟⠋⠁⠀⠀⢸⣷⣿⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⣴⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠻⠿⠿⠟⣿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠙⢿⣿⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠋⣉⣉⠉⠳⣤⠖⠋⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⢡⠚⠀⠈⠧⠤⣅⢠⡞⠉⣲⠀⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⡤⡈⢲⠀⢀⠀⠠⡎⠀⠉⣋⡁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡼⠁⠈⠀⠷⢌⠉⠉⢑⣊⠀⠀⢸⠄⠈⢑⠆⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⠤⢤⠀⠀⡤⠜⠀⣖⠋⠀⠳⡄⢧⣠⣀⡇⠀⢻⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡤⠛⢳⠀⠓⠚⠀⠀⣀⠘⠤⠖⠉⢀⠶⣀⠀⠀⣀⡜⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣄⡖⠉⠉⠉⡷⠋⠀⠀⢸⠷⠤⢤⣤⣞⡁⠑⠒⠒⠚⠁⢀⣈⣉⠉⠉⡏⠓⠦⣤⣀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡤⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡠⢾⠀⣰⠊⢡⣿⣿⣦⠀⠀⢀⡞⠁⣾⣿⣷⡄⡇
⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠀⢸⠀⠀⠀⡀⠀⣸⠀⠧⠴⠖⠋⠀⠘⡇⢇⠀⠈⢿⣿⣿⠀⠀⠸⡄⠀⠙⠿⣿⢿⠇
⠀⠀⠀⠀⠀⢠⡎⠀⡠⠀⠀⣄⠙⠒⠊⠉⠉⠁⡤⠢⡄⠀⢀⠤⡀⢷⠈⠳⠤⠤⠚⠁⢀⣀⣀⡙⠦⠤⠖⠋⡼
⠀⠀⠀⠀⠀⢸⡀⠀⠳⠤⠦⠋⠠⡃⠀⡀⠀⠀⠣⠀⠀⠀⠀⢀⡼⠈⢧⠀⠀⠀⠀⠀⢫⡀⣠⠇⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⢠⢣⠖⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡄⠀⡄⠀⢀⠇⠀⠈⠳⣄⡀⠀⠐⠤⠜⠣⠴⢀⣠⠞⠁
⠀⠀⠀⠀⠀⢾⠘⢄⡀⠀⠀⡱⠀⠰⡁⠀⠀⠀⠀⣸⠀⠈⠉⠁⠐⢤⠀⢀⣀⡉⠓⠒⢲⡖⠒⠚⠉
⠀⠀⠀⠀⡰⠛⢦⡀⠑⠒⠚⡁⠀⠀⠉⣒⠋⠒⠚⠁⠀⢠⠀⠀⣀⠼⠀⣏⠀⠸⠀⠀⢰⠇
⠀⠀⠀⠸⣇⣀⠴⠉⠙⡆⡎⠁⢀⠀⡎⠉⠁⠀⠀⠠⢄⠀⠑⠊⡡⠲⡄⠀⢠⢤⣤⠴⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣳⣌⣓⣉⣀⠘⢄⡠⠀⢀⣀⣠⠇⠀⠀⠀⠤⠎⣠⠏⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠉⢹⣄⣀⣠⣤⡀⠀⠀⣠⢷⡶⠶⠖⢺⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⠀⠉⠀⢸⠉⠛⠋⠁⢸⠀⠀⠀⢸⡇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣠⣿⣄⣤⠤⢼⡄⠀⠀⠀⢸⣤⣤⣄⣸⢷⡤⠶⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⢠⡏⡇⢀⣀⠀⡇⠀⠀⠀⢸⠀⣀⠀⢸⠘⡆⢀⢤⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠉⠙⠾⠀⠷⠊⠈⠙⠃⠀⠀⠀⠾⠚⠉⠳⠟⠀⠻⠃⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠶⢶⣶⠾⠛⠻⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇
⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠙⠛⠷⣦⣀
⠀⣠⡾⠛⠁⠀⠀⢀⣀⣀⡾⠛⠷⠶⢦⣄⣀⣀⡀⠀⣀⣀⣀⣀⣤⢾⡅⠀⠀⠀⠀⠈⠙⢷⣄
⣴⠟⠀⣠⠴⠚⠛⠉⢉⡿⢁⣀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠉⠉⠁⠀⠈⣿⠒⠶⠦⣤⣀⠀⠀⠙⢷⣄
⠻⣦⣀⣀⣀⣀⣀⣀⣼⠇⡾⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡆⢹⡆⠀⠀⠀⠉⠛⠦⡄⠀⢻⡆
⠀⠈⠉⠉⠉⢙⣿⣿⣿⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⢸⡷⠶⢦⣤⣤⣤⣄⣤⣤⡾⠃
⠀⠀⠀⠀⢰⡿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣹⣏⠉⠉⠁
⠀⠀⠀⠀⣸⡧⠀⠸⣧⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⣄⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠉⠙⢿⣤⣤⡶⠶⢶⣤⣀⣠⣤⣤⣀
⠀⠀⠀⠰⣿⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠉⢻⡿⠋⠉⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠈⢻⡏⠁⠉⠛⣷⣤⣤⣄
⠀⠀⠀⢠⡿⠃⠀⠀⠈⢷⣄⠀⠀⠀⢤⣄⣼⣇⣤⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠀⠀⠙⣷⣄⡀
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣀⣉⣡⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⣦
⠀⠀⢠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠻⣦⡀
⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⢿
⠀⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿
⠀⠙⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟
⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡏
⠀⠀⠻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠘⢷⣄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣀⣀⣀⣠⣴⢶⡾⠛⠋⠁
⠀⠀⠀⠀⠀⠙⠛⢿⡟⠛⠉⠻⣦⣤⣤⣤⡶⠟⢷⡶⠶⠾⠻⣦⣤⣤⣴⠟⠁⢀⡀⢀⣤⣀⣤⡾⢦⣤⡶⠟⠁⠈⠙⣿⠉⠉⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢸⡏⠀⠙⠛⠛⠛⠛⠛⢹⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣿⠀⠀⠀⠀⢰⡟⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢸⡟⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢰⡟⢠⡄⠀⠀⣿⠀⠀⠀⠀⣼⠃⣠⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢾⣧⣼⣧⣤⣤⡿⠀⠀⠀⠀⢰⣿⣀⣿⣀⣀⣸⡏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋

⠀⣀⠀⠀⠀⠀⠤
⠀⠿⢿⡮⠀⠀⠀⠀⢰⡿⣿⡇⢤⣄⣀⠠⠀⠀⠤⠀⡀⣄⣤⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⠀⡀
⠀⠀⠘⡆⠀⠀⠐⠓⠌⣿⠏⡀⠀⠈⠉⠀⠀⠀⠀⠈⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠙⠋⠁⠈⠙⠛⠿⣦⣄
⠀⠀⡀⠄⠀⠀⠀⣀⣇⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣷
⠀⠀⢿⣿⣥⣤⣶⣿⣿⡽⣿⣿⣿⣷⡟⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⢄⠿⣧⡤⣾⠀⢿
⠀⠀⠀⠀⠀⠀⠙⠛⢿⡄⠙⢿⣿⣿⠅⣤⣾⠀⠙⢷⣿⣦⣀⣶⣆⣧⣄⣾⡆⣴⡀⣠⣾⣿⣿⡑⠀⠉⠋⠉⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠘⠻⢿⣻⣿⣿⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣤⣠⢈⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⢸⣿⣿⣿⣄⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣀⣈⣛⣿⣿⣿⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣢⣤⢿⣷⣽⣿⣿⡤⠮⣿⣿⣿⣿⣿⣿⣿⣟⡀⠠⠍⠉⢹⣿⣧⣿⠻⣿⠙⢻⣶⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣶⣿⣿⣿⡟⠎⠀⠀⠀⠀⠈⠉⠉⢻⠟⠉⠀⠀⠀⠀⠈⣿⣿⣿⠄⠈⢶⣿⡟⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣧⠾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⢻⣷⣄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠇⠀⠀⠀⠀⢿⡇⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠾⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠨⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠃⠀⠀⠀⠀⠀⠠⣖⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣦⣼
⣿⣿⣷⣷⣾⣦⣷⣿⣄⣠⣦⣴⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣤⣰⣴⣠⣷⣷⣾⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣶⣾⣼⣧⣀⣠⣠⡄⠀⢠⣆⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⢤⡚⠳⠾⠖⢂⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⡆⠀⢠⣿⣴⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⠹⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⢰⣶⠂⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣯⣴⣶⣿⡇⣧⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣤⠀⡀⠀⠀⠀⠀⣾⣗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣅⠏⢠⢸⠁⠉⣿⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣓⣬⣉⢀⠉⢹⣿⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣹⣽⣼⢂⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⢹⣿⣿⣿⠿⠿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢸⣿⣿⠏⠀⠀⠀⠘⣿⡿⠂⠀⠀⢹⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢿⣥⡇⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠛⠁⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣆⣠⣿⣿⠀⣾⣧⠀⡀⣠⣄⣴⣿⣟⣄⣤⣆⣀⣸⣿⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⢠⡄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠋⠀⠀⠀⠀⢰⠄⠉⣿⠛⠚⢄⣤⣦⣀⣀⢀⠀⠀⠀⠀⠈⠉⠙⢶⡅
⠀⠀⠀⠀⠀⢀⣤⠦⢀⣤⡄⠀⣠⠿⠃⠀⠀⠀⠀⠀⠛⠀⠀⠽⠠⠀⠈⢿⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⣠⣤⣴⢶
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡏⠀⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⣀⡀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠀⢰⡏⢹⡇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠸⠀⠸⠧⠿⠁⠀⠀⠀⣀⡖⠒⠶⢶⠿⠷
⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣀⣀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠀⠶⢦⠲⠃
⠀⠀⠀⠀⢸⡿⣤⠊⠉⠉⠉⠸⡶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠖
⠀⠀⠀⠀⠸⠧⠹⠦⡠⠄⠀⢸⡧⠛⠀⠀⠀⠀⠀⣰⠶⣶⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⣀⠀⣠⣀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠟⢸⡟⠉⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⠞⠉⢻⠏⠹⡏⠉⠉⠁⣼⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠐⠘⠀⠠⠿⠀⠀⠀⠸⠃

⠀⠀⢀⡀
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⣠⠤
⠀⠀⠀⠀⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡟⠉
⠀⠀⠀⠀⠸⠻⣏⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣿⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠈⢻⣇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣸⠀⠀⢸⠃⠀⢀⡿⠀⣀⣠⡤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣶⡖⠉⣤⢤⡤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠀⠀⢿⠀⠠⠘⠿⢧⣍⣁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣄⡀⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⣿⣷⣴⣷⣬⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⠀⡠⠚⠧⣤⡀⠀⠂⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⠀⠘⠢⠐⠊⠀⠟⠁⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠸⣧⣀⣀⣀⣀⣉⣉⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠉⠳⢤⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣰⢙⡆⠀⡴⠀⡄⠐⡾⠒⢰⠀⣠⠀⡦⡠⡆⡠⣆⠀⡄⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠉⠹⡄⠧⠞⠧⠐⠧⠄⠺⠔⠻⠀⠟⠁⠻⠁⠸⠄⠟⠀⠳⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠀⠀⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠁⠘⣇⠀⠀⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣴⠃⠀⠀⠀⠀⠀⠈⠓⡄⠀⣸⠀⠀⣠⠔⠉⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⡟⠀⠀⠤⠀⠀⠀⠋⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠁⠀⠀⠀⠀⠀⠠⣄⡘⣦⣯⡴⠋⠁⠀⠀⢀⠀⠀⠈⠑⠢⣄⡀⠀⠀⢻⡄⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠛⣿⣏⡉⠉⠉⠉⠉⠁⠀⢀⡐⠀⠀⠙⢷⣄⠘⣿⠀⣠⡟⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢸⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⣿⣦⡟⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⠿⠿⠿⢯⡤⣤⣀⣀⣀⠚
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠒⠤⣀
⠀⠀⠀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⣾⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣏⣿⣻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⡀⣬⣿⣿⡿⣷⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠
⠀⠀⠀⢀⣦⣿⣿⣿⣿⡆⢱⢾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢠⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⢃⣮⢿⣶⡦
⠀⠀⠀⠺⣿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣤⣿⡇⣹⡿⠋⢠⣽⣿⣿⣿⣄
⠀⠀⠀⢶⣿⣿⣯⠌⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠸⣿⣿⣯⣿⡟⠉⠀⠀⡀⣹⣿⣿⣿⣿⠟
⠀⠀⠀⠀⣛⡿⣿⡆⠈⠠⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣇⡐⠀⠸⣿⣿⣿⣿⣿⣷⡶
⠀⠀⠠⣴⣿⡇⢹⡏⠀⣀⣿⠋⠿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⢘⣋⣙⣻⣿⡇⣞⣖⣶⣿⣿⣿⣿⣿⣿⣧⡆
⠀⠀⠀⠈⠛⠳⣸⡇⡴⠏⣿⡶⣶⣿⡗⣑⣗⡀⠀⠀⢀⠀⠸⠟⠛⠋⠁⣿⣧⣿⠟⣿⣿⣿⣿⡿⣿⡿⠋⠁
⠀⠀⠀⠀⢠⣧⣹⡏⠀⡇⣿⡄⡟⣿⡇⣾⣿⣦⢶⠆⣾⠀⠀⣼⡅⠀⠀⣿⡏⣿⠀⣻⢉⣿⢿⡾⣶⣖⣷⠇
⠀⠀⠀⠀⣸⣿⣿⡇⢰⣿⣿⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⡀⣿⣿⣿⣮⣿⣿⣧⢸⣟⠉⠁
⠀⠀⠀⠀⠉⢻⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣇⣤
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠿⠿⠛⠿⠿⠛⠛⠛⠻⠟⠛⠛⠛⠟⠛⠛⠛⠛⠻⢿⣿⣿⠿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠃⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀⠄⠀⠐⠄⢀⠀⢀⠀⡆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⠀⠀⠀⠀⠄⠀⠀⠲⢂⠁⠇⠀⠀⠀⣸⡿⠃⠈⠀⠀⠀⠀⠀⢴⣧⠇⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⢠⠀⠙⢂⡀⠀⠰⠋⢁⡔⠡⠀⠈⠀⠀⠀⠈⡞⣀⠀⠀⠀⡄⠀⠛⢡⣀⣀⣠⣤⠶⠶⠦⠤⠤⠤⠞⠉⠈⢀⣶
⠀⠰⠀⠀⣁⡗⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢶⢀⡀⣬⣯⡄⢀⠀⡀⣠⠀⠠⠀⠀⠀⠀⠀⢰⠌⠀⠀⠀⠀⠀⣴⣾⣭⠿⠚⠛⠚⠛⠓⠂⢄⠴⣤⢠⣍⣉⣉
⠀⠀⠀⠀⢈⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⢿⣿⢶⣤⣴⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢺⣇⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⢀⠀⠈⠿⣭⣟⣻⡾⣷⣦⠘⠤⠶⢖⢀⠛⠁⠂⠀⠀⠀⠀⣇⢸⠀⠀⡃⠰⠀⣀⡀⠀⠀⡀
⠀⠀⡀⠀⢈⣧⠀⠀⢸⢸⡱⠀⠸⢀⣿⣴⠤⣾⠁⠰⠀⠀⠴⠀⠀⢤⠙⡚⠰⠒⠉⠁⡤⠀⡀⠀⠀⠈⠉⠒⠦⢀⡀⠀⠀⠛⢀⡄⠈⠀⢠⡄⢹⢩⢾⢤
⠀⠐⡏⠀⠛⡷⠄⠀⢻⠆⢿⠶⣼⣬⠿⠛⠀⢨⠄⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⡡⠄⠐⠂⠀⠀⠀⠀⠙⠀⣄⠀⠀⠀⠈⠀⠀⠐⡀⣘⠃⢆⠀⢀
⠀⠀⣧⢀⡰⡧⠄⠀⣽⠁⠀⠀⢾⡀⢀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠄
⠀⠈⠉⠀⠰⠀⠀⠁⠀⠐⠆⠀⡸⡀⠀⠀⠐⠚⠄⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠔⣟⣋⣛⣛⣛⣛⣛⣛⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠑⡤⠐⠒⢄⡤⠊⠉⠉⠉⠑⠢⡄⢀⡠⠄⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⢀⢀⠤⠄⣸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⠼⣋⠀⠀⠀⠀⠀⠈⢢⡠⠤⠄⠤⢄⡀
⠀⠀⠀⢀⠔⠀⠃⠀⠀⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠵⠒⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⡖⢒⠲⣄⣀⠀⠀⣀⣀⠀⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠱⠤⡽⠁⣀⠍⠋⠁⢄⡑⠒⢶⠛⣉⡉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢤⡀
⠀⠀⡔⠀⣧⠴⡎⣉⢢⠒⠐⢯⠀⢸⡯⠤⡤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⣳⠞⠁⠀⠑⠟⠛⢿⣇⠜⢸⡼⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢄
⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣒⡒⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡄⠀⠱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⢉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢧⠀⢠⡬⠁⠀⠔⣚⠒⠀⢰⡏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⣀
⠈⠳⢇⣀⠀⠀⠀⢙⣆⠴⠋⢇⠀⠀⠠⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠖⠁⠀⠀⠉
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⡼⢳⡄⣀⣸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠀⠀⠀⢀⠼⠤⢀⣀⡠⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⢤⣟⠀⠀⠀⠀⠀⢹⠒⢲⠒⠉⠓⠤⣀⡀⠀⣀⡠⢴⠋⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⠆⠀⠈⡆⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢀⡏⣀⣸⡀⠀⠀⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠤⠤⠤⠇⠀⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠸⡄⠀⠀⢀⣇⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⡑⠲⢯⠀⠀⠀⠀⠀⠀⠧⠺⠤⠤⠴⠃⠀⠀⢸⠀⠄⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⣺⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠤⠴⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠠⢀⡄⣠⢔⣒⠰⢱⣦⣄⢄⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⣴⣾⣿⣿⣦⣼⣿⣷⣿⣿⣿⣦⡀⠀⠀⠈⡈⠉⠂⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣦⣾⠇⠀⠂⠀⠈⠐⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨
⠀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⢿⣿⣏⡀⡀⠀⠁⠀⠀⣇⠀⠀⠀⡰⠀⠀⣀⠀⣠⢀⢀⡀⠀⠀⠀⠀⢀
⠀⠈⠢⣠⠸⣿⣿⠋⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⠿⣿⠀⠀⢄⠀⠸⡄⡀⢠⠃⠀⣠⡔⢊⣤⠲⣪⣍⢊⣿⣿⣿⣿⡑
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣾⣿⡂⢀⣀⣀⠀⠘⣆⢇⡤⠞⠁⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⡠⢁⠿⠇⠀⣀⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⣄⣧⡼⢸⡤⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠈⠢⢄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠘⠂⢙⠛⢦⣒⣒⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⢹⠇⠀⠂⠀⠠⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠛⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠂⠀⢰⠀⠀⠀⠈⢳⡄⠀⠀⠀⢀⣠⣿⡿⣿⣿⡿⠻⠿⠿⠷
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠊⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢹⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⢯⣿⣷⣶⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣭⢿⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⣝⣸⣿⣾⣿⡾⣯⡙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣼⣟⣾⣿⣿⣏⣿⣿⣿⣿⣧⡿⣗⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣽⣽⣟⣷⣻⣿⣿⣭⣟⣿⣿⣿⡟⣿⣷⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⣼⣫⣼⢏⣿⣿⣼⣿⣹⣯⣷⣿⡟⣻⣏⣼⣿⡛⣿⡽⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢶⣽⣻⣿⣿⣿⣿⣘⣿⣷⣽⣟⣿⣿⣿⣿⣿⣿⣾⣽⣿⠗⣻⣷⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣟⣅⣀⣀⠀⠀⠀⠀⠀⠐⣛⣷⣿⣽⣿⣿⣻⣟⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣽⣿⡾⣫⣿⣿⣖⠀⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠰⣶⣟⣿⣿⣿⣿⣿⣿⣿⣽⡔⣂⠀⠀⢶⣾⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⢓⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣫⣽⣃⡜⣇⣀⠀⢀⠰⣼⣿
⠀⠀⠀⠀⠀⣠⢿⣾⣯⢿⣿⣿⣷⢿⣷⡟⣿⡿⡟⣤⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣫⣭⣟⣿⣷⣮⢟⣻⣿⣿
⠀⠀⠀⠀⠴⢤⣿⢴⣟⣻⣷⣿⣿⣿⣾⣟⣿⡿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣯⣿⢿⣿⢿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣻⣿⡿⣯⣿⣿⣿⣿⣟⣿⠟⢻⣿⣽⣿⣿⣿⣿
⠀⠀⣄⢠⣜⣦⣿⣽⣿⣟⣿⣿⣿⣿⣿⣷⣾⣿⣾⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣏⢋⡽⣯⣿⡟⣋⣽⣿⣟⣷⣿
⠀⣶⢿⣿⣿⣴⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣾⠻⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢠⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣯⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⡿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣏⠞⠻⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⣴⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⡿⠃⠀⠾⠿⣧⠋⢿⣿⣟⣿⣿⡿⡏⠙⢻⣿⣿⣧⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⣿⣿⣿⣿⣿⣿⣿⣀⠀⢙⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⠏⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⢸⣾⣿⣿⣿⣿⣯⡖⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡠⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣞⣿⣿⣿⣿⣿⣿⣆⣦⡄⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠿⢻⣿⣫⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣀⣀⣀⣠⣄⣤⣿⣭⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣯⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣴⣿⣿⡛⠁⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡄⠀⠀⢀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⢸⣧⠴⠚⠉⢿⣿⣦⣍⠉⠛⠿⣿⡿⠿⠛⠉⠀⢀⠀⠀⠀⠀⢀⠀⠠⠍⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣿⡇⠀⢠⠎⠻⣿⣷⣦⠀⠙⠻⠿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠚⢆⠀⠀⠀⠁⢀
⠀⠀⠀⣀⠀⠈⠻⢦⠇⠀⠀⠈⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠹⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠹⣿⣦⠀⢸⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠥
⠀⠀⠀⠀⠙⠛⠷⠾⣾⠉⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢒⡂⠀⠀⠀⠔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⣼⡿⠏⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠠⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⣀⢂⢻⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠖⠉⢈⡇⠀⠀⠀⠀⠀⠐⠀⢍⢻⡋⠕⠩⠀⠀⠀⠀⠀⠘⣷⣄⢸⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⡀⠀⡟⠀⣠⠞⠀⠀⠀⠀⠀⠀⡀⠈⡀⢻⠃⠁⠒⠀⠀⠀⠀⠀⠀⠈⢻⡜⡇⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇⢠⣥⠞⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡈⢺⠓⡢⠑⡆⠀⠀⠀⠀⢠⣄⠀⠙⣷⠎
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢧⢠⣇⠞⣡⠤⠤⠶⣶⠀⠀⠀⠀⠠⠒⠂⠈⢺⠃⢀⠨⠠⠀⠀⠀⠀⠀⠻⣇⠀⢹⠀⢠⣾⠃
⠀⠀⠀⠀⠀⢸⠙⢦⡀⠈⣿⣷⣎⣁⣀⡤⠞⠁⠀⠀⠀⠀⠠⠠⠀⠘⢺⠓⠂⠀⠤⡄⠀⠀⠀⠀⠀⠈⢦⣸⠀⡾⠃
⠀⠀⠀⠀⠀⢸⡀⠀⢳⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠀⠂⢻⠋⠐⠀⠀⡁⠀⠀⠀⠀⣦⡀⠀⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠳⣄⣾⡥⠖⠉⠉⢉⡿⠂⠀⠀⠀⠀⠀⠀⠅⠦⠀⠈⢻⠃⠁⠀⠀⠁⠀⠀⠀⠀⠙⢷⡀⢸⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠁⢾⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢳⣜⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢺⠖⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣼⣿⣿⠏⠀⡀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷
⠀⢠⣯⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠇⠀⣼⣿⡋⠀⠀⢠⡀⠐⠀⠀⢀⠉⠀⠀⠀⠀⣴⣯⠀⠀⠀⠀⣀⠀⠈⠙⠋⠉
⣇⢸⡏⠄⢀⠀⠀⢴⣾⠛⠀⠀⠀⠀⢠⡄⠀⢴⣿⡿⠁⠀⣠⣾⡿⠃⠀⠀⠈⡏⠀⠀⠀⠀⠉⢋⣤⠀⢀⡿⠋⠀⢀⣴⣾⣿⣶⠈⠓
⠷⣿⡧⠀⣾⠃⢠⠆⠿⣷⡀⠈⠁⠀⠈⠀⠀⠺⣿⣣⣴⣿⣿⣿⣦⣄⡀⠀⠀⠛⠀⠀⠀⠀⠀⠼⠿⠀⠈⠁⣠⠖⠋⠈⠈⠁⡄⠀⠀⡉
⢷⣿⡇⠉⣿⡊⣿⠠⣤⠸⣿⣗⠀⠀⠂⢀⠀⠀⠉⠙⠿⠛⠻⠟⠛⠿⣿⠀⢠⠄⠀⢀⣴⡇⠀⠀⠀⢀⡀⠀⠀⢀⡗⢀⡀⣸⡇⣠⢰⡧⣾
⣿⣿⣷⠠⣸⣿⣿⡐⣿⠀⠀⢀⣜⣧⣀⢆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠘⠃⠀⢀⢠⢀⢸⣠⡇⣼⣷⣾⣴⣸⡷⢼⣷⣿⣷⣿⣾⡧⣿
⠙⠛⠛⠛⠻⢿⣿⣦⣿⣴⣾⢾⡷⣮⡷⠞⠀⠀⠿⠇⠀⠘⠟⠿⠿⢶⠾⢾⡶⠀⠀⠺⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⡍⣼⣿⣿⡿⣿⠿⠷⠛
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠉⣀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠘⠛⠟⠉⠀⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⠀⠀⠈⠁⠒⠒⠲⠾⠿⠿⠶⠶⢶⣤⣤⣤⣤⣤⠴⠶⠾⢿⣿⣿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠘⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠛⠂⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢿⣧⣤⣀⣁⣠⣿⣯⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠂
⠀⠀⠀⠁⠀⢠⣦⡌⠙⣿⣷⣴⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡦⠞⠓⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣠⣤⣤
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠉⠛⠿⣿⣗⣂⠉⠉⠀⠈⠙⠿⠿⠿⠷⠚⠃

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠄
⠀⠀⠀⠀⢀⠀⣴⠦⠀⢀⠂⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠳
⠀⠀⠀⠉⠊⠐⢋⠃⠂⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠈⡀⠀⠀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠠⠐⠀⠀⠂⢰⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⣡⠘
⡳⠉⠔⠆⠀⠢⠐⠁⠀⠁⠉⠙⠀⠀⠄⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠁⠀⠊⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠠⠒⠉⠂⠀⠐⢤⠀⠀⠄⠀⠀⠈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠂⠠⠀⢀⣠⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠈⣀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠰
⠄⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⢈⠁
⠐⠀⠀⠈⠁⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⠄⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⢁⠀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢸⠂⠀⠒⠐⠄
⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⣠
⠀⠃⣄⠘⠂⡀⠀⠄⢨⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⠀⣰
⠀⠀⠈⠀⠀⠑⠐⠄⢌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⢠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣆⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠇⠘⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⠁⠀⠀⠀⡀
⠀⠀⢴⣒⢆⢱⢝⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢰⣦⢰⣦⣇⠀⣿⡀⡷⡅⣸⢰⣦⡆⢠⡆⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠙⠈⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠚⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠚⠒⠐⠐⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⡙⠋
⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⢀⣴⣾⣷⣦⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀
⣿⣿⠇⣶⣶⣶⢆⣀⢀⠀⢠⣠⠸⡿⢿⣧⣼⡟⠀⠀⣀⢀⡀⠀⠸⣿⣿⡆⣴⠶⡿⠱⣤⡄⠀⠀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠀⢀⣤⣤⡴⣟
⠷⠶⠴⠷⠴⠷⠾⠷⠬⠿⠶⠶⠴⠾⠿⠿⠿⠿⠷⠾⠧⠿⠶⠶⠦⠶⠶⠤⠾⠤⠶⠴⠦⠶⠶⠴⠿⠶⠿⠷⠮⠶⠿⠿⠿⠿⠷⠶⠷⠿⠽⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⡄
⠀⢀⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⠏⠀⠀⠁⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⠀⠀⠀⠀⠀⠀⢀⣄
⠀⢸⣿⣿⡟⠉⠉⠙⠛⢻⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣴⣶⣷⣶⣶⣾⣿⡿⠃
⠀⠈⡏⢸⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡟⢿⠉⠉⠙⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⣿⡿⠟⠉⠉⠋⠉⣿⡏⠀⠀⠀⠀⢹⣿⠿⠿⢿⣿⠟
⠀⠘⡇⠘⡆⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀⠈⣇⠘⠇⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⢿⠳⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⢸⠣⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⣀⣀⣀⣀⣀⣴⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣴⣾⣿⣿⣿⣷⣶⣤⣄⠀⠀⠐⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢤⣤⣤⣤⣴⣾⡟⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢸⢿⠏⠉⠉⢹⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⡿⠛⠛⢻⡟⠁⠀⠀⠀⠀⠀⣾⣿⠟⠿⢿⡿⠁⠀⠀⢀⢴⣶⣶⣶⡿⠃
⠀⠸⠘⠄⠀⠀⠸⠷⠀⠀⠀⠀⠀⠟⠅⠀⠉⠀⠹⠇⠀⠀⠀⠀⠀⠸⠇⠀⠀⠘⠇⠀⠀⠀⠀⠀⠸⠉⠇⠀⠀⠸⠇⠀⠀⠀⠀⠸⠏⠉⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⢠⣦⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇
⠀⢸⣿⣷⣿⣿⣶⣧⠀⠀⢀⣾⣄⣀⣼⠃⠀⠀⣿⣷⣄⣀⣾⠃⠀⠀⠀⢀⣠⣿⡄⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢦⣀
⠀⠈⠻⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⡿⠁⠀⠀⠈⠻⠿⣿⡿⠁⠀⠐⢶⣿⣿⡿⠁⠀⣠⣤⣶⣿⣿⠆⠀⠀⢀⣀⣴⣿⣿⠇⠀⢀⣴⣶⣾⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠒⠄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣶⠈⠑⣲⠿⠋⠁
⠀⠀⠀⢰⡆⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠧⠀⠰⠂⠀⠐⠀⠀⠀⠀⠘⣀⡰⠓⠀⠀⠀⣸
⠀⠀⠀⠀⠰⠄⠀⠀⠉⠒⡔⠀⠀⢀⠆⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢸⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⣠⠀⠰⠤⠾⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠖⠁⠀⠒⠐⠀⠈⠃⡼⠀⠀⠀⠀⠙⠀⠈⢲⡶⠤⣤⠀⢓⣴⡖⠚⠤⠴⠾⠁⠀⠀⠀⡌⠉⡀⠀⠀⠀⠹⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢡⠀⠀⢀⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠂⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠇⠉⠀⡀⠀⠀⠀⠀⠙⠉⠲⠐⢓⢀⣀⣀⣤⣤⡤⢶⢶⢲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⠳⣤⡀⠀⠀⢸⣦⢈⡁⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⠙⡌⠁⠉⠉⠈⠈⠘⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡖
⠀⠀⠀⠇⠀⠀⠰⡀⠀⠀⠀⠀⠈⢿⣶⣄⣠⠙⠈⠣⠄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠁
⠀⠀⠀⠀⣳⣄⠀⢹⡄⢸⣇⠀⠀⠈⠉⢃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⣀⡤⣤⡄⠀⠰⠁⠀⠀⠀⠀⢠⣀⢀⡀⠸⠇
⠀⠀⠀⠀⠃⡿⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⢘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠈⠙⠄⠸⠀⠀⠀⠀⠀⠀⠹⠰⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠙⠁⠀⠐