Small Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢸⣏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀
⢀⡴⠖⠛⢉⢉⣀⡀⠀⠀⠀⠀⠉⠙⠻⢶⣄⠀⠀⠀⢻⣼⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁⠀⣀⣄⣠⡤⢤⡽
⠙⠋⢄⡉⠉⠉⠉⠙⠛⠓⠲⠦⣴⣀⠀⠀⡙⢧⡀⠀⠀⢻⣿⡀⠀⠀⠀⢀⣴⠞⠋⠀⣀⣠⣴⣖⠛⠉⠉⢀⡴⠋
⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⣉⣳⣦⣄⠈⢻⡄⠀⠀⣿⡇⠀⠀⣰⠟⠁⠀⣠⡾⠛⠉⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣌⣷⠀⠀⢸⡇⠀⣼⠋⢀⣠⣾⣫⡤⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣀⣀⣀⣈⣿⣆⠀⢸⡇⣸⠇⣠⡾⠋⠉⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠹⣦⢸⡇⢿⣴⢏⣀⣤⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠶⠶⠶⠞⠛⠛⠛⠛⠛⠋⠉⢻⣿⡏⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⠶⢦⣤⣄⣀
⠀⠀⣀⣴⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢶⡄
⠀⠀⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣧
⠀⠀⣿⠈⠉⠛⠳⠷⠶⢶⣤⣶⣶⣿⣭⣭⣉⣉⣉⣉⣉⣉⣹⣽⣏⣉⣉⣉⣩⣭⣭⣽⣷⣶⡶⠶⠶⠞⠛⠉⠀⠀⣿
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠉⠙⠛⡶⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠖⣻⠉
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠖⠛⠉⠁

⡟⠁⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⠀⣎⡑⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠰⢃⣷⣆⣡⣤⡀⠀⠀⠀⠀⠀⢀⣤⢠⣶⡆
⠀⠀⢀⠀⡀⠀⠀⠻⠇⠀⠀⠀⠚⠛⠛⠉⠀⢤⣌⣀⠀⠀⠀⠀⠸⢿⡏⢸⡿⠃⠀⠀⠀⠀⣴⣿⣿⡏⠿⠛⠀⠀⢠⣤⡦⠐⠿⠛⠀⠙⢿⣿⡆
⠀⣠⡺⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⣀⣀⠈⠛⠁⠀⢢⡤⣄⣰⠀⠀⠀⠀⣼⠀⠀⢰⡈⠉⠉⠀⠐⠿⠂⠀⠘⠟⡡⣶⠀⠀⠀⢀⣀⡀
⠀⠙⣿⣿⠀⣤⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠛⠋⠰⠎⠁⠀⠀⠴⣜⣿⠀⡀⢰⡾⠇⠀⠀⠸⣧⡀⠀⢠⣶⠂⠀⠀⠠⣧⡄⠉⠀⠀⠀⠿⡋
⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⣰⣿⡏⣁⡄⠀⣤⣀⠀⠀⡀⠛⠁⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡰⣶⡶⢀⠀⠀⢀⠀⠉⢰⡆⠀⢀⠀⠀⠀⢤⠄
⠀⣿⣿⡁⣿⡄⠅⢉⠉⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⡀⠀⡀⢂⣸⠃⠀⠀⠀⢠⣴⡶⠈⠛⠛⠃⠀⠻⣿⣷⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⢈⣴⢾⡿
⠀⠹⣿⣷⣮⣀⣀⣀⡤⠀⠀⠀⠀⠐⠀⠰⣿⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⢸⠟⢁⣾⠌⠀⠀⠀⣀⡂⠀⠀⠀⠘⠻⠟⠹⠿⣶⠇⠀⠈⠉⠉
⠀⠀⠙⠳⠾⠿⠟⠋⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⠷⠼⠃⠀⠀⠀⠰⣶⡄⠉⠀⠰⠀⠺⠟⠁⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⡠⠶⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⣡⣿⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⡷⠀⠀⢀⣾⡟⢁⣤⠀⣠⣀⠀⠀⢀⠀⣤⣶⡜⢿⣧⣄⠀⠀⠀⠀⢀
⠀⠀⠸⣿⣿⠇⢙⣅⡀⠀⠠⢀⡄⠈⠀⠀⠀⠐⠀⠀⠀⢀⣶⣭⠀⠀⠀⢸⣿⡇⢻⡅⠀⠈⠉⠀⣾⡿⢁⡌⠉⠀⠀⠙⠛⠃⠀⠀⠀⣄⡝⠁
⠀⢸⡆⠀⠀⠀⢀⠉⠀⠀⠄⢘⡗⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠉⠀⠀⠀⠈⢿⣿⢶⣤⣤⣤⡤⠀⢨⡀⠺⠃⠀⠀⣴⡖⠀⠀⠀⠀⢀⡾⣿⡀
⠀⠈⠻⠂⠀⠰⠟⠁⠀⠀⠂⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠀⠀⠀⢀⠀⠉⣰⡄⠀⢀⠀⠀⠀⣄⡀
⠀⣰⣿⡇⣠⡶⠀⣴⣤⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⡄⠀⠀⠃⢀⣀⣄⠰⣾⠿⠆⠛⣷⣶⣄⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⢀⣠⣶⣷
⠀⢿⣿⣇⢷⠆⠂⠀⠀⠀⠀⠉⠀⠀⠀⢰⡷⠀⠀⠀⠐⠀⢹⣶⡀⠀⠀⠀⢸⣿⠇⣤⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⠿⠇⠿⢿⣴⠃⠀⠙⠛⠚
⠀⠘⢿⣿⢳⣤⣤⣤⠖⠀⠀⠀⢂⠀⠀⠐⠁⠀⠀⠀⠀⢠⣟⣻⡇⠀⠀⠀⢰⣄⠈⠿⠀⢠⠀⣴⡶⠂⠀⠀⠀⠀⠀⠀⣰⣟⠋
⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠂⠀⠀⣰⡆⠀⠀⠄⠀⡞⠑⣀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠰⢢⣶⣎⣠⣤⡀⠀⠀⠀⠀⠀⣀⣌⢴⣶⠆
⠀⠀⠀⣀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠺⠛⠛⠋⠀⢤⣘⠆⠀⠀⠀⠀⠸⣿⡇⢹⡿⠃⠀⠀⠀⠀⣴⣿⣿⠏⠿⠋⠀⠀⢠⣴⡆⠘⠟⠛⠀⠙⢿⣿
⠀⠀⣦⣝⢃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣁⡀⠙⠛⠁⠀⢦⡤⣀⠸⠀⠀⠀⢀⣼⠀⠀⣴⠈⠋⠉⠀⠜⠿⠀⠀⠘⠟⢡⡷⠀⠀⠀⠀⣀
⠀⠀⠘⠿⣿⠀⡶⠀⠀⠀⠀⠀⠶⠄⠗⠀⠀⠛⠃⠰⠏⠀⠀⠀⠷⣝⡿⢀⡀⣰⡾⠃⠀⠀⠸⣦⠀⠀⢠⡶⠂⠀⠀⠰⣶⠀⠃⠀⠀⠀⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⡠⠠⢄⡀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠘⣸⣿⣧⣴⣦⠀⠀⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⢠⣾⡏⢁⡀⢀⣀⡀⠀⠀⠀⢀⣤⣦⠺⣿⣀⡀
⠀⠀⣾⣿⣿⠈⢛⣁⠀⠀⠄⢀⡀⠀⠀⢀⠀⠆⠀⠀⠀⢠⣬⣍⠀⠀⠀⣾⣿⡁⣯⡁⠈⠙⠉⠀⣾⡿⣀⠉⠉⠀⠈⠿⠟⠀⠀⠀⠠⣀⡒
⠀⣾⠀⠁⠀⠀⠈⠋⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⠀⠀⠀⢙⠉⠛⠀⠀⠀⠹⣿⣷⣯⣀⣀⣀⡄⠀⣉⠐⢿⠁⠀⢀⣤⠄⠀⠀⠀⠀⢠⣿⣷
⣄⠘⢷⠒⠀⢾⠟⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠓⠿⠿⠛⠉⠀⠀⠙⠃⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢭⠉⠉⠉⠉⠉⠉⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡴⠛⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡡⠋⠀⠀⠀⠱⣌⢣⡤⠤⠤⠤⠤⠤⠤⠤⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠞⠁⠀⠀⠀⠀⠀⠈⠣⡙⢆⣀⣀⣀⣀⣀⣀⣀⣈⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠮⡴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠽⡦⠷⠤⠤⠤⠤⠤⠤⠤⢤⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡤⠤⠤⠤⠤⡄⠀⠀⡇⠀⢀⣤⢤⡤⡤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠐⠀⠀⠀⠂⡇⠀⠀⡇⠀⢸⠀⠀⡀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠁⠈⠁⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠚⠀⡇⠀⠀⡇⠀⠘⠒⠚⠓⠒⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠒⠒⠒⠒⠒⠓⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⣤⣾⣤⣤⣶⣆⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢸⣿
⠀⠀⠛⢿⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣀⣽⣀⣀⣤⡄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⠯⣿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢾⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⣛⣿⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣽⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠶⣾⡶⣶⣶⣦⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿
⠀⠀⠛⢻⠋⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣄⣼⣅⣤⣤⣄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿
⠀⠀⠶⢿⠷⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⣸⡀⢀⣀⡀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢸⣿⡇
⠀⠀⣭⣿⣯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢼⠀⠀⠉⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢸⣿⡇
⠀⠀⣒⣿⣗⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠉⣽⠉⠙⠛⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢸⣿⡇
⠀⠀⣤⣿⣤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠛⢿⠛⠻⠿⠟⠀⠀⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣸⣿
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠀⠀⣿⣿
⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣣⠏
⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠭⠭⠭⠯⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠉⠠⡀⣀⢀⣤⡦⠛⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣦⠀⠸⠟⠀⢀⡀⠒⠙⣛⢻⠟⠁⢀⡀⢻⠾⠛⢱⣤⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⣶⣯⠛⠉⠃⠀⠔⠁⠱⣤⣶⣿⣿⣶⡴⠈⠉⢲⣧⡀⠘⠪⣽⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠓⠒⠒⠚⠛⠓⠒⠒⠛⠛⠛⠛⠛⢥⡀
⠀⠀⠀⠀⠀⠀⡸⠁⣤⣭⣭⣭⡍⢩⣽⣻⢛⠉⠉⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠛⠛⠛⠛⣻⣭⣭⣭⣌⢇
⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡌⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣎⢂
⠀⠀⠀⠀⠀⢠⠄⠤⠭⠭⠭⠭⠥⠬⠍⠓⠒⠒⠐⠂⣿⣿⣿⣿⣿⣿⣿⣾⣿⡗⠒⠒⠒⠂⠋⠟⠛⠛⠛⠋⠀⠡
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣶⣶⣶⣿⠈⠃⠀⠀⠀⣟⠛⠛⠻⠛⠛⠛⠛⢛⡇⠀⠀⠀⠋⢰⣿⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣯⢥⠉⢲⡄⠀⠀⠐⢍⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⡿⡿⠿⠿⣿⣀⠀⠀⠀⠀⣇⠄⠚⠁⠀⠀⠀⠀⣸⡇⠀⠀⠀⣀⣸⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠢⠤⠈⠛⢻⣸⠀⠀⢀⣇⡿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⣏⡍⠀⠀⣸⢸⠇⠠⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣶⣭⠞⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⢮⣵⣮⡵⠋

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⣯⣭⣙⣛⡿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⠿⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⢿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡁⠀⠀⠀⠀⠀⠀⠀⣼⢋⡴⣿⣸⠷⣬⣍⣙⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⢳⡞⠛⠲⠶⣦⣠⡴⠋⣼⠁⠈⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣤⣀⣀⣿⣥⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⣽⠏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠶⢦⣤⣄⣀⠀⠀⠀⠀⢿⣽⣒⡦⠤⢤⣀⣀⣀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡛⣶⠶⢮⣭⣛⡛⠶⢦⣤⣄⣉⣹⠟⣷⠶⢤⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⣾⠈⢷⡈⢷⡀⠀⠉⠉⠛⠳⠶⣬⣽⡏⣰⣏⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⣿⠁⢠⣏⡀⠈⢻⡌⢻⡄⠀⠀⠀⠀⠀⢠⡟⢰⡿⣬⡻⢦⡀⢀⣤⠞⠋⣉⣀⣤⣤⣤⣄⣉⠙⠻⢦⣄
⠀⠀⠀⠀⠀⣠⡴⠟⠉⢀⣀⣤⣴⡏⠀⢸⡏⠙⠶⣤⣻⡄⢻⣄⠀⠀⠀⢀⣾⢁⡿⠀⠈⠻⣦⡙⢿⣥⣴⡟⠋⢻⠀⠀⣸⠀⢉⡿⠶⣤⠙⠳⣄
⠀⠀⠀⢀⡾⠋⢀⣴⠾⡏⠉⢿⣼⠁⠀⣿⢻⣦⡀⠈⢻⣿⣆⠹⣦⠀⠀⣼⢃⣾⠁⠀⠀⣠⡟⢻⣦⣙⠷⣽⡄⠘⡆⠀⡏⠀⡼⠀⠀⢈⣷⡄⠙⣧⡀
⠀⠀⢀⡾⠁⢠⡿⣅⡀⠘⣆⢸⡟⠀⢠⣿⢋⡴⠻⣆⠀⠹⣿⣆⠘⢷⣰⡏⣸⠃⠀⠀⢀⡟⢀⡿⠛⠿⣷⣌⠻⣦⣷⠀⡇⢸⠃⠀⡰⠋⠀⢻⡄⠈⣷
⠀⠀⣼⠃⢀⣿⣄⣀⡙⠲⣌⣾⠇⠀⣸⣷⣫⠴⢚⣙⣧⠀⢻⡽⣦⡾⢛⡛⠻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠺⠿⠾⠷⣧⣤⠞⢀⣠⠴⠚⣷⠀⢸⡇
⠀⠀⣿⠀⢸⡇⣀⣀⣉⣩⡿⣿⡰⢀⣿⣛⣛⣉⣉⣀⣹⡆⢸⡇⣟⢼⢩⣭⢳⡘⣿⠛⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⢦⣤⡀⠙⣿⡉⠀⠀⠀⣹⠀⢸⡇
⠀⠀⣿⠀⠘⣏⠉⠀⣀⠴⢚⡽⢻⢻⠙⢏⠒⠤⣀⠀⢸⡇⢸⡇⢿⣘⡾⠯⠚⣰⠟⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⠶⠶⠶⠛⠁⣠⡿⣉⠉⠙⠒⡿⠀⢸⡇
⠀⠄⠸⣧⠀⢻⣖⠋⠀⢠⠞⠀⡏⠸⡄⠈⠳⣄⠀⢉⡿⠁⣾⠀⢀⡿⠛⠛⠻⠿⠶⠶⠶⢶⡶⢶⣶⢶⡶⠶⢶⡶⠶⡶⠶⣟⠛⣆⠈⠓⢤⣼⠃⢀⡿
⠀⠀⠀⠘⢧⡀⠙⢦⣴⠃⠀⢰⠃⠀⣧⠀⠀⢈⣷⠟⠁⣼⠋⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⢯⣀⣠⠎⠀⢰⠇⠀⢸⠀⠈⣦⣴⠟⠁⣠⡟⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠙⠳⢦⣼⣤⣄⣼⣤⠶⠛⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠉⠛⠶⣤⣼⣤⣤⣼⠷⠞⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣀⣀⣀⣀⣤⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣄⣀⣀⣀⣀⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⢤⡈⠂⠀⠀⠀⠀⠀⣀⢤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠡⠁⡀⠀⠀⠀⠀⠀⠀⠾⠭⠷
⠀⠀⠀⠀⡀⠳⠤⢃⠆⠀⠀⠀⠀⠀⠹⠢⣄⣢⠄⠀⠀⠀⠀⠀⢘⠄⢜⠀⠀⠀⠀⠀⠀⠀⡄⠛⡠
⠀⠀⠀⠀⠈⠀⠈⠁⠚⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠀⠀⠀⠀⠀⠔⠢⠖⠄⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⡡⠓⢀⠀⠀⠀⠀⠀⢀⡐⠀⠄⡁⠀⠀⠀⠀⢠⠖⠉⢙⢢⡀⠀⠀⠀⠀⠀⠀⠀⡁⡢
⠀⠀⠀⠀⠒⡕⠀⠴⢀⠀⠀⠀⠀⠀⠒⠀⢠⠂⠀⠀⠀⠀⠀⠘⣄⡄⢀⡜⠀⠀⠀⠀⠀⢤⠊⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠘⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢈⠑⢤⠀⠀⠀⠀⠀⠀⠀⡔⠤⠈⠑⡄⠀⠀⠀⠀⢰⡇⠀⠀⣼⠀⠀⠀⠀⠰⠣⢂⡀⠌
⠀⠀⠀⠀⢀⣲⡄⠃⠀⠀⠀⠀⠀⠀⠱⢄⡀⠄⡁⠀⠀⠀⠀⢀⠟⠶⠞⢇⠀⠀⠀⠀⠈⢜⠊⠁⡠
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢀⢤⡀⢠⡀⠀⠀⠀⠀⠀⠀⢤⢱⠄⠀⠀⠀⠀⠀⠀⡀⠠⠀⣄⠀⠀⠀⠀⠀⠰⠆⢀
⠀⠀⠀⠀⡥⣔⠀⠌⡉⠄⠀⠀⠀⠀⢠⡌⠡⣆⠀⠀⠀⠀⠀⢠⠀⢐⠐⢂⠀⠀⠀⠀⠀⠓⠠⠎⣁⡦
⠀⠀⠀⠀⠠⢐⣠⢀⠜⠀⠀⠀⠀⠀⢑⢢⠴⠒⠀⠀⠀⠀⠀⢠⢂⠉⣙⢂⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⡖⢲⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣀⣷⠀⠀⢸⣿⣿⠿⠿⢿⣿⠀⠘⢷⣾⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠈⠛⠦⠤⠤⠤⠞⠁⠀⠀⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠉⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡓⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠚⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠶⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠢⠄⣀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⡀⠄⠠⠀⡀⠀⡀⠑⠢⢄⡀⠀⠄⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢇⠀⠀⠀⠈⠀⢈⣀⠁⠀⠀⠀⠈⠑⠢⠄⡀⠀⢀⠀⠀⠀⠒
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰
⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢘⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐
⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠤⠤⠄⠀⠤⠤⠤
⠀⠀⠀⠀⠚⠀⠀⠀⢀⠀⠀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⢸⠂⠃⠀⠅⠀⠅⠀⢩⠀⡅⠀⠨⠰⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠘⠘⠀⠀⢀⠀⠐⠀⠀⠈⠀⠀⠀⡀⠀⢀⠀⢸⠀⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠂⠄⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⢁⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠠⠀⠈⠈⠀⠀⠈⠈⠁⠀⠀⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣲⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠭⠍⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣆⠀⠀⠀⡇⡖⠳⡤⠤⢤⡀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣽⣿⣿⡇⡿⣡⡝⣛⣛⡻⣿⣿⣿⣿
⠀⠀⠠⢶⣚⠞⠓⠀⠀⡇⠙⡞⠉⠉⢳⢳⠀⠀⠀⢸⣿⣿⣟⡉⡭⣥⣽⣿⡇⣿⡎⣵⣶⣶⢹⢸⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠀⠀⠀⣷⣾⠁⠀⠀⢸⢸⠀⠀⠀⢸⣿⣿⣿⣿⣵⣿⣿⣿⣷⠉⠡⣿⣿⣿⢸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣤⣤⢔⡣⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⠛⠛⢛⡯⢞⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠆⢻⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣯⣽⣨⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠤⠤⠤⠴⠷⠤⠤⠼⠦⠤⠄⠀⠀⠀⢸⣿⣿⣿⣿⣟⣛⣛⣛⣋⣘⣛⣛⣃⣛⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠈⠉⠉⠉⠀⠂⢄
⠀⠀⠀⠀⡠⠊⠁⠄⠒⠂⠉⠀⠀⠀⠀⠢⡀⠑⡄
⠀⠀⠀⡐⢁⠎⠀⢀⠔⢀⡀⢁⡁⠐⢄⠀⠈⠄⠘⡄
⠀⠀⢠⠀⠀⠀⢰⠁⠰⠁⠀⠀⠀⢡⠀⠃⠀⠀⡀⠰
⠀⠀⠨⠀⠀⠀⢨⠀⢠⠀⠀⠀⠀⡈⠀⡄⠀⠀⠁⠀⡀
⠀⠀⠀⠣⠀⠂⡀⠣⡀⠱⣄⠤⠊⢀⠔⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠠⠀⣉⢱⡀⠰⠔⠊⠀⠀⠀⠀⠀⢈⠀⢀⠀⠀⠀⣄⣀⣀⡀⠀⠀⠀⠀⣠⣀⣀⣠⠀⠀⠀⠀⢀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠑⠀⠚⠀⠀⠀⠛⠆⠀⠀⠖⡇⠀⠀⠘⠒⠀⠀⠐⠋⠀⠀⠀⠗
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠲⡧⠤⠄⠦⠂⠀⠀⠀⢦⠤⠤⢰⠇⠀⠀⠀⠴⡤⠤⢤⠧
⠀⠀⠀⢰⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠
⠀⠀⠀⠸⠀⠀⠀⠈⢆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸
⢀⠀⠁⠈⠤⠀⠀⢠⠄⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠘⡀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠘
⢠⠄⠀⢀⣦⠀⠈⠐⡒⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠁⠈⠀⠀⠀⣠⠄⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⢀⠀⠀⠀⠤⠀⠂⠀⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠨⠀⠑⢆⡀⠀⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢀⡆⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠂⠒⠐⠐⠂⠒⠒⠒⠒⠐⠂⡖⠐⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠂⠀⠂⠀⠀⠀⠀⠀⡇⠀⢢⠀⠀⠀⠀⠀⢰⠀⠐⠂⠀⠀⠀⠁
⠀⠀⠀⠠⠀⢀⣴⢺⡧⠅⠠⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⣇⣀⡆⠀⠀⠀⠀⠀⢡⣀⣸⠀⠀⠀⠀⠀⠸⣀⣀⠆
⠀⠀⠀⠠⢠⡇⡔⠁⠀⢈⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡄⠀⠀⠐⠘⠛⠧⠀⠔⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢡

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⣀⢀⡀⠀⣀⢀⡀
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠰⠄⠀⠀⠴⠂⠀⠀⢀⠀⢀⠀⠀⠀⠘⠓⠬⣶⠄⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠉⠀⠃⠀⡏⠈⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⡧⠀⢤⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⡄⢉⣀⠉⠀⡉⠀⡉⠀⡁⠀⡁⣰
⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠔⠁⠀⠀⠑⠄⠀⠀⠀⣈⠤⠤⠤⢄⠂⠀⠀⡇⢸⠀⠀⠀⢂⠀⡄⠀⡇⢰⡇⡇
⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇⠀⠰⡔⠒⠒⠒⢒⡄⠀⠀⠀⡏⠀⠀⠀⠘⡇⠀⠀⡇⢸⠀⡄⠀⢀⠀⡇⠀⣇⢸⠇⡇
⠀⠀⣠⠣⠤⠼⢄⠀⠀⠀⠳⠤⠴⠃⠀⠀⠙⠦⠤⠤⠞⠁⠀⠀⠀⠧⠤⠤⠤⠤⠕⠀⠠⡃⠀⠛⠀⠀⠈⠋⠀⠀⠈⠋⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠆⠰⠒⢲⠀⠀⠀⠀⠀⡟⠒⠚⠀⠀⠀⠀⠀⢎⠀⠡⡀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠠⡂⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠨⠀⠀⠀⠀⣞⠀⠡⡀⠈⢄⠀⠀⠀⠀⡀⡔⡀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣀⣂⣀⣂⣐⣀⣘⣀⡄⠀⠀⢰⠋⠀⠉⣇⠀⠀⠀⠀⠀⠀⠈⢫⡈⢣⡀⠀⠀⠠⠐⡃⠀⠀⢸
⠀⠀⠠⠊⠀⠀⠀⠁⢀⠀⢸⠀⡇⢰⠁⢈⡤⣸⠈⠀⠀⢠⠏⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠙⣆⣹⡄⠀⢰⠚⣼⠀⠀⢪
⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⢸⠀⡇⢸⠀⢸⠀⣿⠠⠀⠀⡼⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⠀⠀⠄⠀⢸
⠀⠀⠹⣄⣀⣀⣀⣀⡞⠀⠸⠤⠱⠽⠠⠈⠭⠉⠰⡄⠸⣁⣀⡀⣀⣀⢀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣐⢇⣀⡾

⠀⠀⠐⡭⠉⡕⠀⠀⠀⢸⠉⢹⠀⠀⠀⠀⢫⠉⠹⠀⠀⠀⠀⠀⠯⠉⠝⠀⠀⠸⠍⢩⠇⢺⠍⢩⠂
⠀⠀⠀⡇⠀⡇⠀⠀⠀⢸⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⣇⣸⠀⢰⠈⢿⠀⠀⠀⢠⠿⡄
⠀⠠⠂⠁⠀⠑⠢⠀⠀⢸⢀⣿⠀⠀⠀⢀⠆⠀⠘⡀⠀⠀⢀⠖⣡⡨⠌⠢⡀⠀⣿⣿⠀⢸⠀⣿⠀⠀⠀⡖⠻⢲
⠀⣇⣀⣠⣀⣠⣀⡁⠀⢸⠀⣯⠀⠀⠀⡌⠀⠀⠀⠱⠀⠀⣦⣤⣮⣭⣤⣤⡄⠀⣿⣿⠀⢨⠀⣿⠀⠀⡜⠉⠉⠈⢡
⠀⠹⣿⣿⣿⣿⡿⠁⠀⣸⠐⢿⡀⠀⢸⣿⣿⣿⣿⣷⡇⠀⠘⢿⣼⣿⣿⡿⠃⠀⣿⣿⠀⢸⠐⢻⠀⢸⣶⣶⣿⣶⣶
⠀⠀⢀⠉⠉⠁⠀⠀⠀⠉⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠉
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣖⠒⡲⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⣀⠤⡄⠀⠀⠀⠀⢰⣏⣹⡆
⣀⡀⣸⣇⣀⣀⠀⢀⣀⣇⣀⣇⡀⠀⠀⠀⠀⠀⠀⠈⡄⠈⢣⡜⠁⢠⠃⠀⠀⠀⠀⠈⠛⠛⢧⡀⠀⠀⠀⠀⣠⣀⡄
⠉⠉⢹⡏⠉⠉⠉⠉⡩⢋⡉⠛⢍⠀⠀⠀⠀⣀⠤⠶⠺⣶⢛⡛⣖⠞⠢⠤⣄⠀⠀⠀⠀⠀⠀⣿⡉⣹⡖⠉⠉⠋⠁
⠀⠀⢸⡇⠀⠀⠀⡌⠠⢀⠰⠆⠀⠇⠀⠀⠀⠑⠦⠤⢤⢿⣜⣋⡞⣤⠤⠤⠚⠀⠀⠀⢠⡒⣶⠛⠿⠿⠛⠲⣆⣶
⠀⠀⢸⡇⠀⠀⠀⢸⣿⣻⣷⣿⣿⠇⠀⠀⠀⠀⠀⢀⠆⠀⡸⢇⠀⠸⡆⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⠤⠊⠀⠀⠑⠤⠇⠀⠀⠀⢮⠍⠹⠀⢺⠍⢩⠂⠐⡭⠉⡗
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⣀⠀⠀⠀⠀⢀⣀⣸⣀⡅⣀⢸⣀⣸⢀⡀⣇⣀⣇⣀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⡄⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣤⠔⣧⠀⠀⠀⢸⡏⢸⣿⡇⠈⢸⣿⣿⠈⠁⣿⣿⡇⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠎⠉⠋⠉⢂⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠘⠿⠂⠀⠀⢸⡇⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⡀⣹
⠀⠀⢸⡇⠀⠀⠀⣸⣶⣶⣷⣶⣾⡆⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⡇⣿
⠀⢀⣼⣧⣤⣤⣤⣬⣿⣿⣿⣿⣿⣥⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣼⣧⣬⣭⣥⣤⣤⣭⣥⣤⣤⣭⣭⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⠀⢠⣤⣀⣰⡆⣠⣄⠀⣀⡄⡀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡲⢶⡍⡛⠤⠟⣿⣾⣏⣽⠟⣼⡿⣡⣾⠏⢀⣠⡶⠄
⠀⠀⠈⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠁⠀⠀⢉⣙⣻⣿⣟⣿⢠⣿⠉⣰⣿⠟⠁⢀⣄⣤⢀⡀
⠀⠀⠀⠸⣆⠇⡄⢀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢤⣭⣬⣹⣿⣿⣟⣼⣿⠃⣠⣶⣯⠛⠁⠀⡀
⠀⠀⠀⠄⣿⣆⠃⣰⠀⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠿⣿⣿⣿⣿⣿⣛⣾⣿⠛⣁⣤⣾⡾⠟⠁
⠀⠀⠀⠤⢀⣽⣤⣌⢰⡇⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠿⣿⣽⣿⣿⣿⡟⢢⣾⡿⡟⠋⢀⣠⣦
⠀⠀⠐⠦⢤⣬⣍⣧⡿⠀⢠⡟⠀⠀⢀⡾⠀⠀⠀⢠⠀⠐⠤⣤⢤⢤⣄⢀⡉⢿⣿⣟⣙⣿⣟⣃⣤⣴⡛⠿⠁
⠀⠀⠀⡀⠀⠉⠉⠋⢙⣄⣞⠂⠀⢠⠟⠁⠀⠀⣠⡟⠀⠀⠀⣰⠁⠈⠫⠟⣻⣿⣍⢻⣿⣷⣴⣿⡟⠋⠀⠀⡤
⠀⠀⠀⠙⠶⣤⣴⢴⡶⣼⣧⡀⣰⠟⠁⠀⢀⠚⠉⠀⠀⠀⣰⣿⣄⣄⢀⠀⡀⠖⢛⣻⣯⣤⡟⠃⡀⡴⣸⡙⠓
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣦⣽⣷⡁⠀⣴⡫⠀⠀⠀⣠⠾⠁⠉⠛⠻⠿⣳⢷⣾⣤⡄⣾⣿⣷⡿⢏⠻⣆⣰⡠
⠀⠀⠀⠘⠚⠛⠛⠙⠋⢁⢓⡀⣁⣟⣶⡓⠀⠀⣰⠞⠉⠀⠰⡤⡀⣠⣶⡏⠙⠻⠾⢿⣿⣦⣏⣿⣿⣞⣣⠷⡿
⠀⠀⠀⠀⠀⣀⣀⣴⣦⣾⣿⡿⢹⣿⠿⠉⣦⣰⠍⠀⠀⢀⡠⠖⠫⠽⢷⣿⣸⣤⣴⠉⢩⡿⣿⢿⡟⠛⡉⣁⣠
⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⢀⣠⠴⠶⣓⡟⣛⡿⢄⠀⡴⠋⠂⠁⠀⢀⠉⡨⣕⣤⣿⣴⡄⡀⢿⣤⣿⣾⠟⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣟⣯⣙⣁⣇⣽⣦⡴⣌⣷⡉⠀⠘⢛⣤⢖⣣⣥⢀⡉⠹⢾⣿⣃⠘⣿⡻⠈
⠀⠀⠀⠀⠀⠀⢠⡴⣿⡍⠉⠉⠈⠀⠁⠀⠅⠀⠘⣣⡱⣄⡶⡿⠏⠻⣿⢿⠾⡟⢢⣩⣗⣽⡏⠃⠀⠀⢀⣀⣠
⠀⠀⠀⠀⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣷⢿⡿⣇⠁⠀⣄⡠⡼⢔⡛⣯⣷⣧⣀⣧⣶⣿⣿⣿⠿⠟
⠀⠀⢀⣾⣿⣿⡀⠀⠀⠀⣀⣠⣴⣼⣿⣻⠯⡿⢸⡟⠸⠧⡘⣧⠟⢩⣡⣌⠀⠉⣿⣿⣿⣿⠻⣟⣋⠁⠀⠀⢀
⠀⠀⣸⣿⣿⣿⣷⡐⠛⠛⠛⠛⠛⠉⠉⠀⣠⣠⣤⣝⣷⣤⢷⣿⣆⠙⢿⡿⣗⣦⢴⠸⠞⣟⢛⣩⣤⣤⣶⣶⡿
⠀⠀⣿⣟⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⣀⣲⣬⣿⡏⣿⢻⡿⠸⠟⠹⣆⣦⣷⠙⣬⣷⣿⣶⣿⣿⣿⠿⠛⣙⠈
⠠⠀⢻⣿⣿⡿⣛⡀⠀⠀⣀⡙⠛⠛⠛⠁⠃⠉⠀⣁⣀⣄⣠⣄⣄⣻⡁⠁⠀⠈⠋⠿⣿⠙⢉⠀⣴⣵⠛⣿⡆
⠀⠘⣿⣯⣿⢷⡟⠁⢀⣾⠋⢻⢶⠀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⢀⣤⣯⡤⣿⠉⠻⣭⣭⣿⡟
⠀⠀⠴⠾⠛⠛⠉⠀⠈⢿⣦⡼⠁⠀⠀⠀⠈⠈⠈⠈⠉⠙⠙⠋⠙⠀⢻⣎⡶⡿⠛⢻⡏⠀⣿⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠀⠀⣿⠀⣼⡇⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡆⢠⣾⣿⡄⣿⠇⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣈⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⣠⣤⣼⣇⠸⣷⣾⣿⡿⣰⣿⡟
⠰⠀⡹⢿⣹⣭⠿⡿⠿⡷⣿⣻⣿⣿⣿⡿⢯⠳⠶⢿⢩⣴⡄⠀⣸⣿⡻⣻⣿⣿⣿⣟⣿⣧⣿⣿⠁
⠀⠀⠀⠀⠀⣀⢼⡟⢛⠱⣿⣿⣿⣿⣿⣿⠒⢿⠗⠀⠙⠋⢁⠀⢻⣿⣬⣿⣿⣿⣿⢽⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠑⠛⢶⢗⠾⠿⢹⡿⠳⠎⢲⣿⣼⡦⠀⠀⠈⠀⠀⠈⢛⠿⣷⣿⣟⣙⢓⢻⣿⣿⣧⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠈⠀⠄⠀⠠⠹⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠛⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠚⠀⢲⣿⣿⡧⠀⠁⠉⠛⠀⠀⠒⠀⠀⠀⠚
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠉⣾⣿⠇⠀⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⣀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣠⠋⠀⠀⠀⠀⠄⠀⠀⠀⠐⠻⠍⠀⠀⠀⠀⢀⠠⠤⣀⠀⠀⠁⠢⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣿⡿
⠄⠤⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⠁⠀⠀⠀⠑⡀⠀⠀⠀⠠⣀⣀⡈⠁⠀⠀⠀⠀⠀⠤⠀⣰⣦⣤⣷⣶⣤⣾⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⢳⠎⠈⠀⠁⠀⠀⠄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣿⣿⣿⣶⣶
⠧⠀⠀⠀⠀⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠙⠂⠀⠀⢀⠴⠀⠀⠐⢻⣿⠧⠉⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⣧⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠒⣤⡀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠸⡌⠁⠉⠀⢀⠱⢤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣼⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⡀⠀⠈⠉⠛⣿⣿⣷⢠⣿⣶⣾⣧⠆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⣿⣿⠿⠿⠯⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠐⢃⠀⢀⠆⢀⠠⡤
⠀⠄⠀⡀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣶⠿⣷⡆⠠⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⡀⠀⠀⠀⠠⠀⠉
⠀⠀⠀⠻⣄⠀⠀⡀⠀⠘⠀⠂⠀⠀⠀⠀⣀⡈⠉⡤⠶⢋⠄⡀⠈⠳⡄⠀⠀⠀⠉⠉⠂⠀⠂⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠒⠃
⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠁⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠒⠻⢷⣶⣆⣀⠀⠀⠀⠀⠀⠠
⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠤⠴⣀⡀⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠀⠀⢀⠀⡀⠀⠀⣠
⠀⠀⠀⠰⠠⢄⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣷⡀⣸⣧⣥⣴⡿⠛
⠤⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢳⣿⡀⠀⠀⡰⠃⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⢿⣿⣆⠐⢀⠀⢀⣰⣿⡿⠋⠀⠀⠀⠀⢀⡀⠀⠾⠛⠝⢶⡠⠀⢀⣀
⠤⠀⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠉⠑⠢⡀⠀⠘⠿⣿⣿⠾⠀⣼⣿⣟⡁⠊⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠓⠦⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⢘⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣦⣬⣋⡰⠤⢙⣿⣋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠐⠒⠉⠉⠩⠝⠛⠛⢻⡿⢿⠁⣰⡔⢩⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠲⠀⠱⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⢎⡿⡀⠀⠔⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢂⠀⠀⠀⠀⠀⠈⠐⠼⠓⠒⠂⠉⠈⣀⡀⠀⠀⠈⡆⠉⠿⠟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣭⣽⣆⠀⠀⢀⣴⣞⠳⢶⡇⠀⠀⠀⢰⡿⠿⠿⢿⡶⡀⢱⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠄⠀⠘⠿⢿⣿⣾⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠚⠉⠁⠀⠌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠙⢝⣿⠊⠀⠀⠀⠀⠈⠙⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈
⠀⣀⣀⣀⡀⠀⠀⠿⣿⣿⡿⡆⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠻⢿⣿⣿⠆⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠔⠀⣋⣉⡉⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⡛⠉⠀⢀⣶⠷⠛⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⢰⣿⣿⢶⣯⣭⣭⣖⣛⡒⠦⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢖⣻⠿⠛⠛
⠀⠀⠀⠀⠀⠈⣴⣇⠀⠀⠀⠀⢸⣿⣿⡿⠋⠁⠀⠀⠀⠉⠉⠉⠑⠒⠒⠶⠮⣭⣥⣶⢶⣾⢿⣿⣇⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢳⡄
⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⠞⠁
⠀⠀⠀⠀⢠⣶⣿⣷⣄⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⣼⠋⠹⣷⡄⠀⠀⠀⠀⠀⠀⣾⣇⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⢀⣼⣿⣯⣽⣿⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠹⣿⣄⡀⠀⠀⣀⣼⠿⠋⠀⠀⠀⣠⠴⠶⣄⠀⠀⣠⠎⠉⢻⡅
⠀⣠⣾⠟⡵⠁⢳⡇⠀⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢿⣀⢀⡿⠉⠉⠙⢤⣤⣼⢧⣀⡠⠤⣄
⢸⣿⢳⡾⠦⣤⣤⡧⠠⠤⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣤⣾⠁⠀⠀⢸⣂⠀⣼
⢿⣟⣿⣿⠲⣿⡟⢓⠒⠒⠒⣿⣽⠇⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣿⡆⠀⠀⠀⠙⠛⠋
⠈⠻⠿⣿⣿⣟⣛⣛⣁⣭⡽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣅⡐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⠀⢀⣀⣀⡀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠀⠄⡀⠤⡀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠿⢿⠃
⠀⠀⠀⣿⡿⢿⡿⠀⢻⠭⠽⣿⠀⢻⠿⠿⣽⠃⢻⠯⠭⢿⠃⢸⢼⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣀⣀⡀⠀⠀⢸⠅⠀⠀⢸
⠀⠐⡆⣽⣄⣤⡇⠀⢸⠀⠀⣿⠀⢸⣶⡟⢻⠀⢸⢀⠀⢸⠀⢸⡟⠛⠛⢠⣄⠀⠀⠀⠀⠀⠀⠻⣯⣭⠽⣼⠇⠀⠀⢸⠃⠀⠀⢸
⠰⣺⣧⣼⣿⣿⡷⠀⢾⠀⠀⣿⠀⢾⣿⡇⢰⠀⢸⠛⠑⣻⠀⢸⡇⠀⢀⣖⣿⠛⠀⠀⠀⠀⠀⠀⡇⠁⠀⢸⠀⠀⠀⢸⠃⢀⠀⠘
⠸⢿⡽⠭⡿⢭⠥⡤⠿⡿⠿⢯⣤⠿⠿⠛⡏⢁⠙⠻⡛⢫⡁⠘⢻⡿⣟⣥⣽⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢠⡇⠀⠀⠀⠀⢰
⢰⢾⡏⣻⣿⢿⣿⠉⣿⣟⡿⣿⠉⢹⣿⡟⢹⠉⢹⡿⠛⢻⠉⢹⡟⠛⢻⠉⣿⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡞⠀⠀⠀⠀⠀⠀⢇
⠰⢺⡇⢹⠉⠘⣿⠀⣿⠀⠀⢸⠀⢸⣿⡇⢸⠀⢸⡇⠀⢸⠀⢸⠇⠀⢸⠀⣿⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄⢰⣧⣶⠶⠶⠒⠂⢤⣼⡄
⠀⢸⡇⢸⠀⠀⡿⠀⣿⠀⠀⢸⠀⢸⣿⡇⢸⠀⢸⠀⠀⢸⠀⢸⡀⠀⢸⠀⣿⠀⠀⠀⠀⠀⢀⡴⠇⠀⠀⠘⠧⣿⣯⠉⠉⠉⠋⠉⠉⠁⣷
⠀⢈⡆⢸⠀⠀⡇⠀⣿⠀⠀⢸⠀⢸⣿⠀⢸⠀⢸⡀⠀⢸⠀⢸⠃⠀⢸⠀⣿⠀⠀⠀⢀⡔⠁⢀⣀⠀⠀⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠀⣼
⠸⢠⡇⢸⠀⢀⡏⠀⣿⠀⠀⣼⠀⢸⣿⠀⢸⠀⢸⡇⠀⢸⠀⢸⡄⠀⢸⠀⣿⡃⠀⠀⣿⣯⣭⣍⣈⣁⣀⣀⣀⣨⣽⣿⠀⠀⠀⠀⢀⣾⣿
⠘⢹⡧⣾⣤⣼⡇⡀⢾⣠⣴⡿⡤⢼⣬⣂⡼⠤⢼⣇⢠⣾⠤⢼⣇⣀⣾⢤⣿⠃⠀⠀⣿⣿⣗⠀⡄⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣥⠿⠿
⠰⢺⣁⣙⡛⣻⢷⣤⣤⡍⣉⣙⣉⡀⣙⢿⣥⣄⠀⡙⢛⢋⣍⣉⣹⢿⣿⣧⣽⡧⠀⠀⠘⣿⣿⡀⣤⠀⠀⠀⣼⣵⣿⠃
⢠⣼⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⢻⡟⠀⠀⠀⠈⠛⠿⢿⣿⣶⠾⠿⠛⠁
⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠰⠂⠂⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠂⠣⢠⠀⠀⠀⡂⢈⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣀⣒⠤⠎⠀⠨⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣀⠒⢂
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠱⠀⢆⠀⢧⠠⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢠⠚⠁⠀⠠⠔⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠪⣣⡘⢈⣴⠃⡠⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡉⠁⠈⠆⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⣹⣷⢸⣇⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠁⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣦⣿⡆⠂⣧⣿⢸⣿⡵⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⡇⠠⠈⠙⠘⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣭⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢡⠃⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠂⡀⠀⠀⢈⡙⠒⠢⠄⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⣀⠤⠤⠀⢀⠀⠈⠈⠙⠲⢤⣀⠀⠀⠠⢀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⢰⠊⠉⠀⠀⠀⠸⠁⠘⠏⠀⠋⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠑⢦⡀⠀⠐⠁⠀⠰⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠂⠀⠭⠇
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⣿⠀⡏
⠀⠀⠀⠀⠀⠀⢠⣰⠄⠀⠀⠂⠀⠀⠀⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⢿⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢺⠒⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠆⡀⠄⠀⠀⠀⠀⠀⠀⠖⠐⠐⠁⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠰⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠨⠅⢀⠀⠠⠀⠀⡀⠀⠀⠄⠐⠀⠀⠀⠀⡄⠀⠀⠁⠀⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡐⠀⠀⣀⣀⣀⠀⠀⢀⣁⡂⠂
⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠂
⠀⡀⠀⠀⠀⠉⠀⠀⠀⢈⢀⠶⠀⠀⡖⢢⠀⠨⡁⠀⢈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⡄⠀⠠⡄⠀⢠⠀⠀⣤⠀⢠⡄⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⡇⠀⠈⡅⠀⠭⠀⠀⢡⠀⢸⠅⠀⢠⠀⠿
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠗⠀⠀⢀⠀⠀⠴⠀⠀⠀⢸⠀⡇⠨⠀⠇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠂⠀⠀⠒⠀⢸⠀⡇⢀⠀⡀⠀⢠⠀⠀⢸⠀⠸⠀⠠⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡔⠀⠀⠒⠂⠐⠂⠀⠀⠉⠀⣀⠀⠄⠄⠀⢸⠀⢣⣀⡀⠁⠀⠘⢀⣀⠜⠀⠀⢇⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡀⠀⠀⠀⠀⡠⠀⠀⠉⠀⠀⠀⠀⠼⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢁⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣦⣀⡶
⠀⠀⠀⠀⠀⠀⢥⣭⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠉⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠚⠉⠀⠄
⠀⠀⠀⠀⠀⠀⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠂
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠐⣿⣀⣠⣤⣀⠙⠋⠀⢤⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠆
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠃⠀⠀⠀⠀⠀⠀⢀⡸⠟⠉⠈⠛⢷⣄⠀⠺⡆⢸⠉⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⠗⠃⠀⣠⡤⠈⠻⠀⠀⢱⣾⡀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠛⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠆⠻⡁⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡿⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣿⠖⡟⠛⠿⠟⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣇⣀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠛⠃⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣷⣿⣶⣶⣶⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣠⣄⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠹⣿⣷⡄⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⢀⣈⣽⠿⣟⠛⠃⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠉⠁⠀⠀⠉⠉⠛⢿⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⣀⣴⣶⣿⡿⠋⠁⢠⣿⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣤⣴⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣝⣾⣿⣳⣶⣶⣶⢶⣾⣿⣱⣏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠢⣄⡀⠀⠀⠀⠠⣄⡀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠋⠀⠀⠀⠀⠉⠉⠁⠒⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠶⠦⠤⢿⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛⠛⠛⠿⣿⣷⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠀⠀⣠⣿⣿⡿⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣾⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠞⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢀⣠⡄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠿⠿⠛⠛⠛⠛⠉

⠀⠉⠉⠁
⠀⠘⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡄⠀⠀⣠⠀⠀⠀⡀⠀⠀⣀⠀⢠⠀⠀⠀⡀⠀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠇⢸⠀⣿⠀⡇⠀⡇⢰⠆⣿⠀⡿⢠⡄⢸⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠁

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⣄⣠⣀⣄⡀⠀⠀⠀⠀⠀⠤⠄⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⠶⣤⠀⠤⣴⣤⣠⣀⠀⠀⠀⠀⣰⢺⣿⣿⣷⠹⠆⠀⠀⠀⠘⣾⣿⣿⣷⡄⠀⠈⢀⣤⠖⠒⠂⠀⠀⠀⠀⠀⡈⠉⢉⣤⡦⠀⠀⠀⢾⣂⡀⣀⣤⣤
⠏⢁⠈⣛⢿⣈⠁⠃⠰⠄⠀⠀⠀⠘⠮⡛⠛⠍⠀⠤⠀⠀⠀⠀⠛⠛⠿⠛⠏⠀⠀⠚⢀⠀⠶⣿⡏⠀⠀⠀⠆⠀⠀⣿⢿⠟⣗⠀⠀⠄⣉⣵⢡⣿⣿
⠀⠁⠀⢉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⢠⣀⠂⠀⠀⠀⠁⢨⡈⠁⠀⠀⠀⢼⠋⠰⠟⠁
⢰⣴⣤⡷⠠⠠⠀⠀⣄⣠⢀⡀⡀⡀⠀⠀⠀⡀⣄⣧⣦⡀⠀⠀⠀⠀⠀⡈⠅⣠⠀⠀⠀⠠⠄⡀⣰⣿⣿⣿⡄⠀⣠⡀⠀⠈⠀⢀⡀⠁
⢺⠋⠤⠒⢶⣄⠀⠀⠸⣿⣷⣌⣁⡙⠁⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⢠⣴⣿⣿⡞⠂⠀⠐⣥⠋⠀⠘⠻⣿⣿⣇⠠⢉⠁⢰⣀⡻⡏⠀⠀⠙⡦⠆
⠀⢲⠢⠤⠀⠈⠙⠄⠀⠙⠿⡿⠋⠀⣠⠘⠀⠘⠛⠻⠟⠋⠀⠀⠀⠸⡮⠿⠟⠁⠀⠀⠀⠈⢧⠀⠀⠀⠛⠤⠁⠀⠀⠛⠦⠒⠀⠀⠠⠖⠚⠁⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠉⠉⠉⠁⠒⢄
⠀⠀⠀⠀⡔⠈⡠⠐⠈⠀⠀⠀⠀⠀⠐⢄⠑⠄
⠀⠀⠀⠌⠠⠂⠀⠀⠂⡁⠀⠄⡁⠢⡀⠀⠢⠈⠄
⠀⠀⢸⠀⠃⠀⡌⠀⠊⠀⠀⠀⠘⡄⢱⠀⠀⠀⢰
⠀⠀⠸⠀⢃⠀⢃⠀⢄⠀⠀⠀⡰⠀⡘⠀⠀⠀⠘
⠀⠀⠀⠣⡀⠀⢀⢢⡈⠣⠔⠊⡠⠌⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠈⠒⠠⠤⢡⠀⠓⠁⠀⠀⠀⠀⠀⠘⡀⠡⡀⠀⢠⠤⠤⢴⡄⠀⠀⠀⣠⠤⠤⠤⡀⠀⠀⠀⣰⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠘⠉⠀⠀⠀⡉⠀⠀⠈⢉⠀⠀⠀⡏⠀⠀⠈⢁⠀⠀⠀⠃
⠀⠀⠄⠀⠀⠀⠀⠀⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠘⠋⠀⠀⠈⠙⠛⠓⠸⠋⠀⠀⠈⠙⠛⠒⠘⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠒⣀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠧⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡁⠀⠤⣒⡒⠒⢚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠱⠀⠈⠀⠀⠀⠀⠀⢢⡀
⠈⠁⠐⠒⠃⠀⠀⢀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⣄⠀⡁⠠⠀⢀⠐⠀⠅⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠈⡄⠀⠀⡂⠀⠀⠀⠈⡀⠀⠀⡃
⠀⠀⠀⠀⠀⠈⠑⠠⠠⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⡁⠀⡀⠀⠀⣁⡀⣠⣠⣠⣁⣠⣀⣃⣀⣤⣀⣄⣁⣄⣀⣁⣀⣀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠇⠀⠀⠀⠀⣷⠀⠠⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠂⠀⠀⠀⠀⠛⠀⠀⠃⠀⠘⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠄⡇⠀⠀⠀⠀⠧⠀⠤⡇⠀⠀⠀⠀⢡⠄⠤
⠀⠀⠀⠀⠀⢀⡔⣖⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠇⠀⠀⠀⠀⢰⣀⣰⠇⠀⠀⠀⠀⢸⣀⣠
⠀⠀⠀⠀⢰⢋⠎⠀⠀⣁⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⡤⠠⠄⠤⠼⠿⠄⢠⠂⠀⠠⠈⢢⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡜⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⡜⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣀⢤⡀⠀⠀⠀⠒⠙⠲⢤⣀⠉⠀⠀⠀⠈⠙⠰⢤⣀⠀⠈⠢⠑⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣂⢁
⠀⠀⢠⠔⠚⠉⠉⠀⢨⠆⠀⠖⠀⠘⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢰⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠉⠆
⠀⠀⠈⠳⢄⠀⠀⠀⠎⠀⢀⡄⣴⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢄⣀⠜⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠒⠒⠲⠂⣲⢒
⠀⠀⠀⠀⠀⠑⠄⠈⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⠀⠒⠂⡀⠀⠀⠀⢸⠍⢹
⠀⠀⠀⠀⠀⠀⢐⣐⡄⠀⢀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠄⠀⠐⡀⠀⠀⢠⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠀⢴⠀⡁⠀⠀⠀⠈⠚⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⣀⠀⠐⢤⡀⠀⡀⠀⠀⠸⡀⠀⠀⣭⣀⣀⠇⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠁⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠠⠁⠀⠐⠂⠂⠒⠂⠀⠀⠀⠈⠀⠀⡐⠀⠀⠀⠁⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⡀⠈⠉⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠂⠀⠁⠀⠀⠠⠥⠀⠁⠄⠀⠀⠀⠀⠀⣀⠀⠐⠒⠒⠋⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠴⢃⡀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠐⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠆
⠀⠀⠀⠀⠈⠑⠆⣄⡄⠀⠀⡀⠀⠀⢰⠀⠀⠀⡠⠤⠄⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠠⠀⠤⠤⠠⠀⠄⠠⠤⠀⠀⠀⠀⠤⠤⢠
⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣁⡀⠀⠀⢀⢀⣀⣀⣁⣀⣀⡇⠀⠀⠀⡊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠜⠀⠀⠸⠰⠂⠀⠢⠀⠀⠄⠀⠀⠀⠀⠅⠀⠀⠀⠀⣤⠠⡇⠀⠰⡇⠀⢼⠀⠀⢽⢀⢠⠇⡀⢨⣇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⡏⢹⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⢘⡇⢀⠀⡇⠀⢺⠀⠀⢸⠀⢘⡇⢀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢋⠈⠀⠄⠂⠀⢹⠀⡄⠀⠀⠀⠃⠘⠃⠀⠀⢤⠠⠐⠣⡀⠀⠀⢸⠀⡇⠐⡀⡇⠀⠘⣀⠀⢸⠀⠀⡇⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢀⠀⠌⠀⠃⠀⠀⠀⠈⠉⠀⠀⢀⣀⠈⠁⡠⠈⠁⠀⢸⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠐⡇⠀⠂⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣶⢁⠄⠈⠀⠁⠀⠀⢀⠀⠀⢠⡤⠐⠣⠀⠀⢸⠀⠳⠤⠴⠁⠀⠈⠦⠤⠞⠀⠀⠣⠤⠴⠃⢸
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠐⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠿⢿⣿⣿⣿⡯⡧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠓⠳⠦⢟⡭⡴⠞⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣐⣦⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠲⠲⠶⠦⣨⣗⣶⠾⠞⠟⠛⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⡇
⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⡶⣴⠼⣭⣿⡚⣯⣦⣶⡶⠶⠶⠦⢤⠀⠀⠀⠀⠀⠀⡀⠀⠘⠂⠠⠍
⠀⠚⠿⣺⣮⣇⣸⡇⣰⡿⠁⣠⡴⠗⠀⠁⡀⠀⠴⠔⡄⠀⡘⡷⢌⢁⣄⣆⣤⣀⡀⠢⠁⠀⡀⠀⠂⠀⠀⠀⢀⠉⠐⠄
⠀⠀⠀⢡⢺⣧⠿⢷⣟⣇⣰⣿⡀⢀⣤⡾⠏⢀⢠⣠⣶⠛⠈⢿⣞⠏⠉⣈⡄⠅⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠐⠂
⠀⠀⠀⠰⠋⢠⣼⠿⢸⢛⣏⣽⣤⣺⣿⣿⡀⣼⣿⣛⡀⠃⣿⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡼⠗⠉⣀⣮⡯⣿⢹⡟⢻⡏⢙⢮⣿⣻⣛⡂⢀⠀⡀⣤⣤⣀⠀⠰⠂⠠⠀⠀⠀⠈⠀⠀⠈⠰⣌⠐⣦⠐⣤⣤⣀⡀
⠀⠀⠀⠈⠀⢠⣾⡿⠟⠁⠋⠀⢽⣿⢷⣽⣿⡿⠶⢦⡰⣼⣇⡛⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠿⡐⠻⢾⣿⠟⠉⠉
⠀⠀⠀⠀⢠⠛⠁⠀⠀⠀⠀⢤⣾⢻⡞⢿⠹⣦⠲⢶⣿⣟⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⣀⣤⣤⣀⠈⠓⠦⠈
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣺⣿⠻⡀⠓⢈⣙⣲⣷⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠙⡄⡉⠉⠉⠉⠛⢦
⠀⠀⠀⠀⢀⣀⢀⠀⠀⢠⣿⢈⡀⠀⠀⠀⠶⣞⣻⢿⣿⣏⡛⠀⠀⡄⠀⠀⠀⠀⣶⣇⠀⠀⠹⡐⣇⠁⠀⠠⣄
⠀⢀⡀⠀⠀⠛⣿⣷⣦⣼⠁⡅⣷⣖⡤⡀⠉⣟⣷⠯⡝⠆⠀⢠⠀⠁⠀⠀⠀⠀⡼⠝⣷⣀⣶⣦⣀⣀⢀⣄⣐⣧⣴⣦⣤⡀
⠀⠀⠙⠿⣾⣶⣤⣄⠛⢾⣷⣯⣉⣿⣿⣁⡄⣾⣿⠅⠀⢠⠀⠐⠂⢀⠀⠀⠀⢰⠀⠉⠇⠈⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣟⡛⡀
⠀⠐⠶⡒⠻⣯⣟⠢⢁⡼⢿⡻⠁⢚⣻⠟⣫⢼⡟⠀⠀⠈⡄⠢⠌⠈⠁⠀⠀⡌⠀⡌⠀⠀⣸⣿⣯⣿⠟⡵⠹⠋⣔⡿⣿⣿⠂
⢀⣴⢳⠿⢒⣽⡯⠀⢀⡾⣓⠆⠀⠁⡴⢋⡗⣃⠀⠀⠀⠀⢡⠀⡄⠐⠀⠠⢠⠃⢠⠀⢀⣼⡿⠻⠁⠋⠈⠁⠀⠀⠀⠈⠿⣿⡄
⠐⠝⠸⡆⢉⢼⣽⠀⠀⠼⣩⣧⠀⠀⠀⠊⢿⣿⡇⠀⠂⠀⠸⡄⠇⠀⡆⠀⡼⢠⠃⢠⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⢰⡀⢯⠀⠚⣿⡄⠀⠀⠫⢿⡄⠀⠀⠀⠀⠹⢧⠀⠈⠄⠀⢇⢀⠀⡇⢃⠇⡎⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠠⣶⠃⡀⠃⠀⠙⠷⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠁⠀⠀⡀⢸⡌⡄⡇⣸⣸⡀⠠⠑
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣧⣡⣷⣿⡟⣠⡧
⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣔⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣆⣠⣦⣤⣤⣤⣀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠗⠢⠚⠛⠻⠿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠄⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢠⠀⠄⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⣰⣋⢥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⣀⡀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠫⢄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠓⠎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢀⡔⠓⠚⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠙⠆⠀⡁⣜
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠡⡔⢀⠑⣢⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣄⣀⣁⣁⣀⣤⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅

⠀⠀⠀⠀⠀⢣⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢢
⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⢀⠎⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠜⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠃⠂⠀⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⣠⠒⠶⠶⠶⠶⠶⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠒⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠉⠁⠀⠀⠀⠠⡞⠛⠛⠟⠛⢋⣹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡴⠒⣲⣶⣶⣶⣖⠒⢲⡀⠀⠀⠀⢸⡇⠈⠒⠙⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠤⠤⢤⠞⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⡏⠀⠰⠖⠀⠀⢀⣀⠠⠤⠒⠊⠁⠀⠱⠀⢳⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢸⡇
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡇⢄⠀⣠⢰⡇
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡼⠁⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠙⠦⢬⡤⠞
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣠⠤⠚⠉⠀⠀⡴⠃⠀⢀⡀⠀⠀⠀⣀⣀⢀⣀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠙⠫⢍⣁⣀⣀⡠⠓⢄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⣠⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣖⣀⣺⠩⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣼⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣽⣿⠉⣿
⠀⠀⠀⠀⠘⢦⣦⣄⣸⣷⣿⣿⣿⡟⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⡿⠷⠿⢶⡀⠀⠀⠀⠀⠀⡇⢻⣿⠀⣿⣇
⠀⠀⠀⠀⠠⠶⠿⣿⣻⣿⣿⣿⣿⣮⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⢿⣻⢿⣷⣝⣯⠀⠀⠀⠁⠀⠀⠀⠀⢀⡇⢸⣿⠀⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⡉⠁⠈⠀⠙⢧⠄⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⢀⢠⡄⠈⢰⡖⠋⢀⡜⠉⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⣟⠠⡏⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⣤⣿⡀⠀⣰⠒⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣟⠐⣿⢸⡇⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣳⡀⠉⡙⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⠠⣿⣾⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠦⣈⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢳⣴⠀⠀⠉⣿⡟⣈⠃
⠀⠀⠀⠀⠐⠦⢄⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡰⠁⠀⠀⠀⠀⣠⠶⠟⠋⠉⠀⣤⣿⢿⡇⠀⠀⠀⠀⠸⠋⡀⠀⠀⢺⡇⡟⠁
⠀⠀⠀⠀⡀⠀⠀⠙⢶⢢⠃⢀⡀⢀⡧⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⡔⠀⠀⢀⠠⡞⠍⠀⠀⢀⣰⣾⠿⢉⣼⠃⠀⠀⣰⠟⠀⡐⠀⠀⠀⢹⡗
⠀⠀⠀⠀⠀⠠⣄⣠⣦⣸⣴⣥⢞⣥⡞⠋⠁⠀⠈⠁⠀⠀⠀⠀⣼⠁⢀⣴⠿⠑⠀⢀⣠⣼⡾⠟⠉⣠⡾⠃⠀⠀⠀⣏⠀⣰⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠊⠽⣿⣿⣿⣿⣿⣿⡛⠀⠀⢀⡀⠀⠀⠀⠀⠘⢁⡴⠛⠈⢠⣴⣻⣾⠛⠁⣀⣤⣿⠟⠁⠀⠀⠀⠀⢳⡸⠃⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⡙⠋⠈⣿⠟⠏⠒⠋⠀⠀⠀⠀⠀⡴⠋⢁⣴⣮⠿⠋⠁⠀⢠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠐⠉⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⣶⡿⠟⠃⠀⢀⣴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⣭⣤⡴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⠈⢹⠀⠀⠀⠈⠉⡉⠀⠀⠀⠘⠉⢹⠀⠀⠀⠀⠘⠉⢹⠀⠀⠘⠀⢰⠀⡎⣉⠃
⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⣤⣼⠀⡇⢸⠀⠀⠀⠰⣻
⠀⡔⠁⠀⠀⠁⠄⠀⠀⠀⡇⠀⠀⠀⠌⠀⠈⠆⠀⠀⡔⠡⡦⡂⠈⠄⠀⣿⣿⠀⡇⢸⠀⠀⢀⠇⣍⢡
⠀⢶⣴⣶⣴⣶⡄⠀⠀⠀⡇⠀⠀⣘⣀⣀⣀⣈⡄⠀⣷⡞⣶⣶⣶⡆⠀⣿⡟⠀⡇⢸⠀⢀⣂⣀⣀⣀⣡
⠀⠈⠛⠟⠛⠋⠀⠀⠺⠉⠑⠀⠀⠻⠛⠛⠛⠻⠃⠀⠈⠛⠟⠟⠋⠀⠀⠻⠋⠀⠡⠄⠀⠘⠿⠿⠿⠿⠿
⠀⠀⢰⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠖⣄
⠀⠀⣸⠀⠀⠀⠀⠀⠉⠀⠅⠀⠀⠀⠀⠀⠀⠘⡀⠑⢄⠔⠁⡌⠀⠀⠀⠀⠻⠿⠿⡀⠀⠀⠀⠀⢀⢄
⠛⠛⢻⠛⠛⠛⠛⡛⢛⡛⠛⡃⠀⠀⠀⢀⠠⠤⠳⡰⢛⢢⡴⠥⠤⣀⠀⠀⠀⠀⠀⢸⡎⢹⣶⠊⠙⠛
⠀⠀⢸⠀⠀⠀⢐⠠⢀⠰⢂⠈⠄⠀⠀⠘⠢⠤⣤⢷⣙⡴⢧⠤⠄⠚⠀⠀⠀⣴⣲⡞⠿⠿⠛⠲⣦⡆
⠀⠀⢸⠀⠀⠀⠘⢿⣽⣿⣿⡿⠀⠀⠀⠀⠀⢠⠃⢀⠜⢄⠀⠇⠀⠀⠀⢀⢀⠉⠋⢀⢀
⠀⠀⢸⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠀⡗⠀⠇⠀⡗⠀⠃⠈⡖⠀⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠰⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠐⢠⠀⠀⠀⢠⡦⢁⣤⠁⠄⣧⣤⠠⠆⣧⣴⠰⡆
⠀⠀⢸⠀⠀⠀⠀⠠⠧⡥⠥⡀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣼⡇⠀⠀⢸⡇⢸⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⡇
⠀⠀⢸⠀⠀⠀⢀⣃⣀⣧⣀⣡⠀⠀⠀⠀⠀⣼⣿⠏⠀⠈⠁⠀⠀⢸⡇⢸⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⡇
⠀⢀⣼⣀⣀⣀⣘⣛⣛⣟⣛⣟⡀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⣸⣇⣘⣛⣀⣀⣙⣛⣀⣀⣙⣛⣀⣇
⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢓⠀⠠⣀⠀⠀⠀⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢰⠞⠘⡆⠈⠳⡀⠀⠸⠀⠀⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠂⡠⡀⢀⠈⠘⠀⠀⣧⠠⠀⢹⡀⡆⠀⢸⠃⢀⡰⡇⠀⠀⠀⠀⢀⡠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠈⠪⡻⢄⠀⠀⠀⢸⠀⢣⠜⠃⠙⣶⠁⢠⠃⠀⡄⠀⠀⣀⠔⢉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢮⠳⣅⠀⢀⠀⢸⠀⠀⣇⡇⠀⡞⠀⢠⠃⢠⠞⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀⠀⠀⢠⡣⠙⡈⠃⠀⣜⠀⠀⣿⠇⢠⠁⠀⣎⡔⠁⡠⠋⠀⠀⠀⠀⢀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠀⠈⠀⡁⠀⡀⠀⢰⠀⢀⣸⢇⠈⣷⢚⠏⢀⠜⠁⠀⣀⠤⠂⢉⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠣⡐⠀⢀⢀⢰⠀⠀⠙⠏⣾⠈⢀⡷⠋⣠⠋⢀⠤⠊⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡄⢈⠈⠀⡆⠀⠀⠰⡇⠀⡾⠁⡴⢃⠔⠁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⣻⡀⠀⢱⠀⢀⢀⡇⣸⢃⡞⡡⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⣧⠀⠀⡄⣾⢸⣡⢣⢞⡜⢁⢊⠤⠖⠒⠀⣀⡐⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢹⡄⡀⢁⠉⢸⡇⡟⠞⡰⠋⠁⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⠤⢤⣯⡁⠀⡇⢸⣇⡇⡼⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠘⣇⠈⠷⢸⠘⣰⢡⠎⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠⠐⠀⠀⠀⠀⢻⡄⢣⢸⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⡴⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀




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