Baby bear Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣀⣀⡀⠀⠈⢻⣤⣤⡶⠶⠶⠶⠶⠶⠶⠦⣤⣀⡀⣰⠛⠉⢀⣀⣀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣺⣯⣿⢟⡴⠚⠉⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠉⠓⢦⣾⣿⣧⣈⠁⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠁⣹⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡴⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣆⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠸⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣇⢀⣠⣶⣶⣦⡄⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣾⡿⠈⠉⠉⠁⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣠⡖⠓⠒⠲⢤⣀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣀⣀⣀⣤⣀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⠛⠳⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣠⣇⣀⣀⡤⠗⠀⠀⠀⠀⣠⣞⣥⠶⠚⠉⠉⠀⠀⠀⠘⣆
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠠⢍⠀⠀⠉⠻⣷⣦⣤⣀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠞⠁⠈⠙⠿⢭⣛⣲⠦⣤⣤⣤⣤⢤⣶⣶⣾⡯⠟⠁⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⢉⣿⠟⡟⢸⣷⡾⣷⠈⣯⢳⡀⠀⠀⠈⢷⡀⠀⣠⠄⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⠜⣡⣿⢹⡇⣟⠦⠞⢸⠇⠀⠀⠀⠘⣧⠀⠘⠭⠖⢀⣀⣴⠾⠃
⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢱⠃⣸⡇⣸⡗⠒⠋⠀⠀⠀⠀⠀⢻⣦⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡿⡇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢀⣠⢤⣶⡤⢤⣷⡴⠶⠗⠲⠶⣄⡀⠀⠀⠀⠀⠯⠤⠼⠁⠛⠛⠃⠀⠀⠀⠀⠀⢀⣤⠴⣿⣤⣀
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠙⢦⡈⠳⣦⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⣴⠏⢠⠞⠁⠀⠙⢷⡄
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠙⣆⠘⣷⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣰⠏⣠⠋⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢠⡏⢠⠏⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣾⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣿⣠⣰⢠⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢀⡾⠷⢤⣄⣀⠀⠀⠀⣈⣿⡀⠀⢰⡏⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⣿⣿⢸⠀⠠⡆⡄⠀⠀⡟⣰⡟⣀⡴⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢷⡀⢸⡇⠀⡇⢀⡇⡇⡇⣼⠇⠀⢰⡏
⠀⠀⠀⠀⠈⠻⣿⣼⣆⣇⣇⣃⣀⣼⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⡀⡇⠘⠓⠂⠃⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⣄⣀⣀⣤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣤⠤⠀⠶⠀⠁⠀⠀⠂⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡀⠉⠉⠐⢷⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠊⠙⢷⡦⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠟⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠛⠈⠉⠀⠈⠙⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⢴⣶⣶⡄⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⢩⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⡧
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣖⠀⠾⢈⠹⣇⠀⠀⢰⣶⣿⣷⣶⡄⠀⡀⢀⣿⡄⠀⠀⠀⠠⢉⡗
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⠺⠇⢹⡄⠀⠈⢿⢿⣿⠟⠁⠀⣠⣾⠗⢬⢂⡀⠓⠂⠀⠓
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣽⢿⣷⣬⠛⠷⠶⠞⠛⠛⠶⡶⣴⡟⣋⣤⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⣤⢳⣦⣤⣦⣦⣶⢷⡾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠉⠻⠿⠟⠁
⠀⠀⠀⠀⠄⠀⠀⠀⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠘⠹⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣐⣷⡀⠀⢀⠀⠀⠀⢀⣤⠀⠂⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢉⢱⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢇⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠗⣿⢾⣤⡀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡟⢳⣷⣎⣀⠀⠀⠀⠀⠌⣹⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣯⣿⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣟⢻⣿⣧⣴⣂⣀⣀⣶⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠘⡙⠈⠐⠄⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⢺⡿⠋⠈⠉⠉⠓⠛⠻⡇⠀⠀⠀⠀⠀⠀⠐⣄⠀⡄⠀⠀⠀⠸⣿⣿⣰⡟⠁⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠈⠸⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠰⠀⣰⣾⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⣰⣇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠋⠶⠿⢾⡿⠯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⣄⠀⠀⣄⠀⢤⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠐⠻⠦⠄⢼⡤⠾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡤⢀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⢸⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡘⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢣⡄⠀⢦⠀⢻⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠦⠀⠻⠶⠾⠷⠜⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⢤
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠤⠀⠀⠀⠈⠉⠉⠓⢤⣠⡤⠤⠤⠤⢤⣄⡀⠀⠀⠀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣀⣀⣀⣉⠙⠛⠉⠁⠀⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠠⣿⣧⡀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠛⣋⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠻⢭⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠛⢲⡤⠤⡴⠒⠚⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠰⠋⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠛⠀⠀⠀⠀⠑⣤⣀⠀⠀⠀⠀⠀⠀⣧⠤⢦⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡀⠀⠀⠀⠀⠀⢀⡸⢃⡟⠀⠀⠀⠀⠀⢰⣇⣀⣨⠽⠆⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⡟⠋⠉⠀⠀⠀⠀⠀⣠⠎⠀⣏⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠖⠋⠁⠀⠀⠈⠉⠉⠛⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⡌⢻⣟⣶⣿⣿⣿⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠁⠀⠀⠀⠘⠙⠿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄⣠⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣠⢀⣿⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⣠⣦⣀⡀⠀⠀⠀⠀⣠⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⣰⣿⣿⣿⡷⠀⠀⠰⢾⣿⣿⣿⣷⡀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⣤⣤⠀⠀⠈⢻⣿⣿⠟⠁⠀⠀⠀⠀⠙⣿⣿⣿⠃⠀⠀⠀⢰⡆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠠⡀⠀⣶⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠹⣧⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣤⣿⡿⠆⠀⠀⠠⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣦⠈⠛⣶⣿⣿⠀⢀⣤⣤⣤⡄⠀⠀⠀⣀⢹⣿⣿⣿⡿⠁⠀⢀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⢸⣇⣬⣽⣿⡅⢾⣿⣿⣿⣇⡀⠀⣀⠀⣸⣿⣿⣿⣥⣴⣾⣿⣛⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠰⡆⠻⣿⣿⣿⣦⣿⣿⣿⠿⣳⣾⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠋⢠⣄⠀⠻⣶⣾⣿⣿⣿⣇⡈⠉⠒⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⠀⢘⡏⣸⡇⠴⢤⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⢻⣿⢿⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣉⡻⠟⠈⠃⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡟⠁⠀⠀⠀⠀⠘⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⡅⠋⣶⠀⠀⣾⠟⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⠳⢤⣤⣶⣶⣤⣶⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢠⣄⣠⣿⣿⣿⣿⣿⣦⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣴⣶⣌⠙⠛⠛⠛⣿⡿⠓⠛⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣀⣼⣿⣇⠀⠀⠀⢻⣅⠚⢀⣶⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠙⣿⣿⣿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣛⣿⣿⣿⣿⡋⠛⠉⠁⠀⠐⣿⡿⣿⣿⠛⠿⣷⣄⣴⢂⠘⢿⠃⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⣨⣿⣿⣷⡟⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⢠⠔⠀⠘⠃



⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠈⠈⠐⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠤⠄⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⢁⠀⢈⠖⠈⠀⠒⣄
⠀⠀⠀⠀⠀⢰⠡⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⣆⠀⠺⢳⢸⠁
⠀⠀⠀⠀⠀⠀⠑⠢⡄⠀⠀⡠⢤⣄⠀⠀⠀⣀⠈⣡⢅⣘⢟⣶⡄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠻⢿⡏⠠⠤⠄⠤⠤⢿⣿⠿⡞⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡐⠁⠀⣴⣒⣶⣦⡀⢀⣈⣧⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠃⠀⠀⠛⠿⡿⠟⠁⡸⡯⢟⠯⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣇⡀⠀⡀⠀⡇⢀⣝⣔⣴⣏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠙⠻⠛⢫⣵⣞⣟⣟⢗⣾⡿⢫⡻⣄
⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠴⡶⠁⠂⢊⢊⡉⡋⡢⠹⣮⠠⠈⠑⠤⡄
⠀⠀⠀⠀⠀⡐⠁⠀⡀⢢⡟⠁⠀⠀⠀⠁⠁⡪⠂⢐⢽⣆⠀⠀⠘⠜⣆
⠀⠀⠀⢀⠂⠁⠀⡰⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠔⢹⣇⠀⠀⠐⡸⣄
⠀⠀⣀⡾⠶⠤⣐⣄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢑⢁⢷⢄⢀⡠⠠⠌⠣⣀
⠠⠉⠀⣀⡀⠀⠈⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⢄⢝⢷⠃⠀⠀⠀⠀⠈⠳⣄
⠆⡰⠉⠀⠀⠉⠒⢌⠪⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⢕⢕⢕⢕⡏⠀⠀⡠⠒⠉⠒⢄⢙⠆
⡆⡇⠀⠀⠀⠠⠀⠈⢢⣺⡤⠂⠀⠀⠀⠀⠀⠀⠀⠕⢑⢔⠿⠀⢀⠊⠀⠀⠀⠠⠀⠇⣽
⠃⢁⠀⠀⠀⠨⠀⡈⠈⡞⣷⠀⠅⠀⠀⠀⠀⠀⢀⢕⢕⢕⠇⠀⡎⠀⠀⠀⠐⠂⠀⣖⡞
⠐⣌⣆⠀⠀⠀⠭⠀⢀⡏⣗⡀⠀⠀⢀⡀⣕⢖⢕⠴⡫⡻⡇⢠⠀⠀⠀⠄⠠⡁⣰⡷⠛⢓⠦⣤⣀
⠀⠈⠻⣦⣀⠀⠳⠄⡼⣽⣏⣛⣟⢻⠿⣿⠟⠛⠟⠛⢾⣾⣇⡆⠀⠀⠄⠤⢁⣴⡽⠯⠀⠩⠐⠒⠲⠶
⠀⠀⠀⠈⠻⠛⠿⠿⠾⢉⣄⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠽⣾⣄⣈⣭⣶⡭⠟⢆⣐⢚⡏⠓⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣧⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣟⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⣾⡟⠛⠂⠀⠀⠀⠀⢀⡴⢶⣶⣆⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠀⠘⠁⣾⣷⠐⠀⠀⠀⢿⣿⡆⢻⠧⠄⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠘⠋⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣀⣠⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢦⡙⣦⡀⣾⣿⣿⣷⣾⣠⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣬⣷⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣷⣼⣼⣶⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠴⣸⡿⠉⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣯⣄⣋⠙⡋⠳⠂⠉⠛⢌⠛⠹⣿⣿⣿⣿⠇⠚⠉⠁⠀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠉⠉⠍⢹⣿⣿⡆⠀⠀⠀⠈⠆⠈⠳⣼⣿⠿⠁⣀⣤⡄⠀⠀⡀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢀⠼⠉⠀⠀⢰⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣟⣹⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣦⣰⣾⣿⣽⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣯⣽⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢠⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣿⣻⣿⢉⣿⣋⣹⣿⣷⡄⠀⠀⠁⠀⠀⠀⠈⢿⣿⣿⡟⠋⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣯⣿⡿⢿⣿⣮⡿⠛⠛⠿⢿⣿⣿⣤⡀⣀⣠⣠⢤⠀⠘⢿⣿⠿⠂⠀⠀⠀⣄⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠁⠁⠼⣿⣿⣿⣤⠀⠀⠀⠙⠿⠿⣿⣿⣏⣰⣶⣆⣁⢼⣡⠄⠀⠀⠰⣾⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⠷⠞⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣟⡥⠂⠀⡀⠀⢴⡖⢛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⠙⣿⡿⢥⡿⠿⠀⠀⠁⢀⠀⠈⠿⡤⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣦⣈⢀⣀⣀⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠉



⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠠⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⢀⡶⠀⢠⣄⣀⠀⠀⢀⠻⠃⣰⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⡄⠀⢸⠀⠀⠈⢡⣶⣀⣿⠛⠀⠀⠸⣿⠛⠁⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠘⡇⠀⢹⣧⣠⣦⡸⣿⣿⣧⣄⡴⠋⠀⠙⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢃⠒⠚⣿⣿⣿⣿⣿⣷⣽⣿⠇⠀⠀⠀⠘⢷⡄⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠘⣄⣽⣿⠣⣷⣿⣏⡏⠉⠘⣄⠀⣀⣰⢃⣼⡇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣀⣀⠙⢻⡏⠁⠉⠈⠈⠁⠀⠀⠙⢷⣾⣷⡾⣟⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢠⣿⣿⣧⠀⣿⡀⠀⠀⠀⠀⠀⣰⣺⠟⣡⣌⠹⣿⣧⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⡋⢰⣿⡆⣿⣿⣄⠀⠀⠀⠀⣸⠃⡼⠘⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⡿⣡⣿⢷⣿⣷⣦⣤⣼⡧⢸⣷⣾⣿⡧⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠶⢤⡴⠿⠿⠟⠋⠀⠀⠀⠀⠀⠹⢿⣿⠿⢣⡿⠃⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠀⠀⣀⡠⠀⠀⣤⣀⣀⣂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡁⠀⠀⠀⣀⣀⠙⠀⣤⣤⣙⡻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠐⢿⣿⠃⠀⠀⠘⣿⣿⡿⠉⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠘⠇⠀⠀⠀⠀⠈⢿⣷⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣆⠀⠀⢰⣾⣿⣷⡀⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣼⣛⣿⣿⣧⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢀⡔⠛⠓⢦⡀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⢸⢰⡏⠙⢦⣳⣮⡤⠤⠶⠒⢒⠒⠲⠦⢤⣄⡀⢀⡞⣡⠤⢄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠈⣏⣧⠴⠚⠉⠀⠙⡌⠃⣤⠈⠁⠖⣠⠋⠀⠉⠛⠾⣅⠀⡼⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠹⡤⠀⡄⠘⣰⠃⠀⠀⠀⠀⠀⠈⠻⣵⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡀⠀⠈⢧
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢰⡆⢳⣀⠀⢳⠃⢰⡄⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣠⠞⠉⠀⠀⢠⡀⠀⠈⠁⢀⡀⢸⡄
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠓⠦⠴⢋⣠⠼⠧⠼⢯⡀⠈⠧⣄⣠⠔⠀⠀⠀⠀⠈⡇⢠⡇⠀⠀⠀⠀⠈⠀⠐⠃⠀⠈⠁⢘⣧⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡤⠚⠉⢧⡀⠀⠀⢀⡽⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠚⠀⠀⠀⠠⠀⠀⣸⠁⢹⡀
⠀⠀⠀⠀⣇⠀⠀⠀⣰⠋⠀⠀⠀⠀⡉⢹⠋⠉⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⡏⠀⢳⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⠧⣄⣸⠃
⠀⠀⠀⠀⠘⢦⠀⢠⣇⣠⠤⠤⣄⡀⠙⠾⠞⠁⢀⣀⣀⣀⣳⠀⠀⠀⠀⢀⡼⢡⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠑⡞⠁⠀⠀⠀⠀⠙⢦⠀⠀⡴⠉⠀⠀⠀⠈⠑⣄⣀⣴⣫⠤⢿⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠦⢤⣀⣀⣀⣀⡼⠤⠼⢇⣀⣀⣀⣀⣠⣠⠞⠉⠀⠀⠀⠀⠑⠦⠤⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⢤⣤⣴⣦⣤⣤⣤⣤⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⣛⠻⣿⣿⡿⠿⣿⣿⣁⠙⠿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⢉⡁⠶⠏⠁⠀⡀⣿⣿⠂⣀⣠⣌⡻⣷⣄⡹⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣴⣿⢤⣴⣤⣝⠺⢿⣿⣫⣿⣿⣿⣭⡻⢿⣿⡏⢉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠙⠟⢿⣿⣿⣿⣿⣆⢹⣿⠿⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⣿⣯⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠙⠫⣽⣫⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⣿⣿⢿⠿⠃⠤⠨⣽⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⠇⢔⣼⣶⣿⣿⡿⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣷⣻⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠃
⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠈⠀⠙⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠛⠋⠉⠉⠉⠻⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠋⠉⠘⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠀⠀⠀⢰⣿⣵⠀⠀⠀⠀⠘⢿⠾⠁⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⡴⢒⣛⣓⣦⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⢁⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⠔⢊⠤⢄⠀⠠⠄
⠀⠀⠀⠀⠀⠒⠀⠀⠂⠤⢀⣀⣀⣀⣀⡀⠠⠘⠐⠠⣀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠂⠀⠀⠈⠉⠀⠀⡇⠀⠀⠑⠀⠠⠄
⠀⠀⠀⠀⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠡⢀⣶⠀⠀⡰⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠲⠀⢐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠀⠀⠀⠐⠄⠑⠒⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⡀⠢⠠⠞⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⢀⠆⠀⠀⠀⠀⠀⠉⠒⠘⡃⠠⠀⠀⠀⠀⢀⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⢀⡀⠄⠐⠃⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠒⠂⠤⡀⠀⡀⠠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠔⠂⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⣈⡀⠑⠂
⠀⠀⠀⠀⠀⣀⡖⠒⠉⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠜⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠁⢠⠊⠈⠑⢄⠀⠀⠡⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢁⢸⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠄⠒⠒⠒⠒⠒⠛⠓⠒⠒⠒⠛⠓⠂⠀⠒⠒⠒⠂⠀⠠⠄⠀⠈⠀⣈⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡐⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣼⣤⡀⠰⡄⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⣿⣽⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⢋⢹⣿⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⠀⠀⣾⣿⣿⣿⣷⠀⠠⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⣀⣠⠴⠖⠛⠛⠉⠉⠙⠛⠒⠲⠤⣀⢀⡤⠖⠛⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣀⣀⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⠖⠒⠒⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠁⠀⠈⢹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⡀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣠⡟⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⢡⣬⣧⠀⠀⠀⠀⠀⣴⢫⣍⢳⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⢀⣾⣀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠹⣦⡀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠋⠉⠛⠲⢤⣄⡀⠀⠀⠀⢀⡾⠁⠈⠙⠲⣤⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠻⢦⣀⠀⠀⣧⠀⠀⠀⢰⣾⣿⣶⡆⠀⢈⡿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⠳⢾⣄⠀⠀⠀⠙⡿⠛⠀⢀⡾⠤⠶⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠙⠓⠶⠤⠴⠷⠤⠖⠋⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣏⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣧⡤⣤⣀⣀⣀⣀⣀⣴
⢻⣦⡀⠀⢀⣀⣤⠶⣿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠀⠀⠀⠈⠙⠻⣦⠀⠀⠉⠉⠉⠁
⠀⠈⠙⠛⠋⠉⠀⢰⠇⠀⠀⠀⠀⡴⠢⡄⢠⠶⢦⡀⠹⣄⠀⠀⣼⠁⢀⡤⢦⠀⣠⠖⢲⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡾⠛⠢⡄⢧⠀⢹⠘⣆⠀⣷⠀⢹⣤⣼⡇⠀⣾⠀⢸⠀⣏⠀⡼⣠⠔⠛⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⣄⣀⡿⠈⢓⣛⣀⣈⠛⠁⠀⠀⣇⢸⡇⠀⠙⠒⠋⠀⠈⠉⠁⢿⣀⣠⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⡴⠚⠉⠀⠀⠈⠙⠲⢤⡀⢹⠸⡇⠀⢠⠖⠚⠉⠉⠉⠲⢄⠉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⢻⡄⠸⣆⠀⠀⠀⠀⠀⢀⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠙⠓⠲⠶⠶⠚⠁⢀⡞⠀⠀⢻⣄⠈⠙⠒⠒⠒⠒⠋⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⡤⠴⠚⠉⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠒⠀⠀⠀⠐⠪⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣤⣶⣶⣶⣦⣜⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠰⣀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢂⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠾⢂⢀⣀⠰⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⡿⣿⣿⣏⣹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠁⢶⠆⠑⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣾⡉⣻⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠘⢄⠚⢒⠔⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡿⣭⡿⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠜⠑⠀⠀⠀⠐⠘⢤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣧⡀⣀⡀
⠀⠀⠀⡠⠒⠈⠁⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠀⠢⡄⠀⠀⣠⣴⣶⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢈⠀⠀⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠑⠀⠀⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠐⠀⠐⠁⠀⠀⠈⠛⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠛⠉
⠀⠀⠀⠀⠀⢀⠂⠁⠀⠁⠢⡀⠀⠀⠀⠀⡠⠂⠁⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣟⣿⣿⣿⣿⣿⢿⣽⣿⣿⣶⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢠⡃⠀⠀⣡⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠿⣿⡿⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠁⠀⠀⠀⠀⠁⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⢶⣶⣤⣄⡀⠀⣀⣤⣶⣶⣶⣶⣦⣄
⠀⣰⡿⠋⠁⠀⠀⠀⠈⣻⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⡉⠀⠀⠀⠀⠉⠻⣷⡄
⢰⣿⠁⠀⠀⠀⠀⣰⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⢹⣿
⢸⣿⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢸⣿
⠈⢿⣧⡀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⣿⠏
⠀⠀⠙⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠁
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⢀⣤⣴⣦⣤⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⣿⡿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣿⣇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⡟⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠘⣿⡻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠻⣷⣄
⠀⠀⠀⢀⣴⡿⠋⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⠙⢷⣄
⠀⢀⣴⡿⠋⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠈⠹⣷⣄
⢠⡿⠋⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⢻⣷
⣿⡇⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣀⠀⠀⠀⠀⣿
⠙⠿⠶⠶⠿⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠿⠿⠶⠾⠟
⠀⠀⠀⠀⣀⡴⠾⠛⠛⠓⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠛⠛⠻⠶⣄⡀
⠀⠀⠀⣼⢋⡴⠛⠉⢉⡓⢦⡈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⠞⢋⠉⣙⠳⣌⢻⡄
⠀⠀⢸⣧⡏⡔⠀⠀⠀⠀⢆⢻⡀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⢡⠎⠀⠀⠀⠁⡌⣧⣿
⠀⠀⢸⣿⢰⠀⠀⠀⠀⠀⢸⢸⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢨⠀⠀⠀⠀⠀⣸⢸⣿
⠀⠀⠈⢻⣎⡳⣄⣀⣀⡤⢋⣾⡾⠿⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠿⢷⣿⣜⢦⣀⣀⣀⡴⣣⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠋⠉⠀⠀⠈⠉⠻⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⠟⠋⠉⠉⠉⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠛⠛⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠈⠙⠋⣡⣴⡶⠶⠶⠶⣶⣤⡈⠛⠛⠁⠀⠀⠀⠀⢸⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⢠⣶⣶⣦⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠹⣷⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⢿⡇⠀⢶⣄⣀⣴⢿⣄⣀⣠⡦⢀⣿⠃⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠈⢿⣄⠀⠉⠉⠁⠀⠉⠉⠉⢀⣾⠏⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄⣀⣹⣿⣷⣦⡀⠀⠙⢷⣦⣄⣀⣀⣠⣤⣶⠟⠁⠀⣠⣶⣿⣿⣃⢀⣤⣶⣶⣿⣿⣿⣶⣦⣄⡀
⠀⢀⣴⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⡿⠛⠁⠉⠻⢷⣦⣤⣀⣉⣉⣉⣉⣁⣠⣤⣶⠿⠋⠁⠙⠻⣿⣿⡿⠛⠉⠉⠁⠉⠉⠛⢿⣿⣦
⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠈⠻⣿⣿⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠉⢹⣿⣇⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠁⠀⠀⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠁⠈⠉⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠛⠛⠛⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢉⣁⡤⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠐⠁⠀⡄⠈⠓⠤⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣣⠜⠊⠁⠁⠁⢴⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠂⠀⢋⠀⢠⡄⠁⠀⠀⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠜⠁⠚⠁⠀⠀⠙⠀⠙⢄⠗
⠀⢀⡠⠤⣀⠀⢀⣸⢀⣀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢒⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠸⠀⠀⠀⠓⠀⠀⠀⢄
⡔⠁⠀⠀⠀⠛⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠔⠑⠖⠈⠂⠀⠀⠀⢈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠀⠤⠀⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⠤⡞⠋⠁⠒⢄⠀⠁⡠⠤⠤⠤⣴⠋
⠘⢄⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠲⡉⠀⠀⠀⠀⠀⠀⠀⡴⠁⠘⢄⠀⠀⠀⠀⠑⠋⠀⠀⠀⢀⡸⠑⢄
⠀⠀⠑⢄⡀⠀⢀⡠⢖⠟⠉⠁⠒⠀⠤⠤⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣸
⠀⠀⠀⢠⠟⠞⢡⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡀⠀⠀⠀⠀⠀⠀⠑⠖⡾⡀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⠖⠁
⠀⠀⠀⡇⠀⠀⠈⠀⡇⠀⠀⢀⠒⠩⠓⠖⠁⠉⠂⢹⢹⠂⠀⠠⠊⠉⠉⠘⠘⠀⠈⠒⢄⠀⠀⢀⡠⠒⠉⠄⠐⠓⠒⠒⢦
⠀⠀⠀⢣⠀⠀⠀⠀⢱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠣⢄⡠⠤⠒⠳⢄⡈⣆⠀⠀⠀⠀⢀⣀⠜⠀⠀⠀⠰⡀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⢀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣴⣶⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣀⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣹⡇
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣦⡿
⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣤⣀⠀⠀⣀⣤⡤⠴⠶⠶⠦⢤⣄⣀⠀⠀⢀⣠⠴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠐⠂⠒⠂⣹⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣟⣁⠰⠂⠲⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡌⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⡥⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⠄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠴⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡟⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣷⣥⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢛⡵⠚⠉⢉⠉⠉⠓⢾⡛⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⣿⠆⠀⠀⢷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠓⠶⠶⠶⠶⠚⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡷⣤⡤⢤⣄⣀⣀⣀⢀⣠⡤⢤⡴⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣻⠏⢀⡏⠀⠀⠈⡟⠀⠈⣿⠁⠀⠀⢹⠈⠻⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣼⠃⠀⠈⣧⡀⠀⣀⡿⠤⠴⢿⣀⠀⢀⡼⠀⠀⠹⣆⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠈⠉⠉⠁⠀⡤⠀⠀⠈⠉⠉⠀⠀⠀⠀⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻
⠀⠀⠀⠀⣠⡴⠶⠶⢤⡀⢠⡾⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⡄⢀⡴⠒⠒⠶⣄
⠀⠀⠀⣼⠷⠀⣤⠀⠀⠻⡏⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⠏⠀⠀⠴⠐⠞⣧
⠀⠀⢰⡇⠀⠀⠀⠳⠀⠀⢹⣤⠶⠖⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠓⠶⢴⠏⠀⢀⡛⠀⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠈⣃⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢸⠃
⠀⠀⠀⣷⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠶⢤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠖⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡿
⠀⠀⠀⠸⣆⠀⠀⠀⠰⠆⠀⠀⢀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⡀⠀⠰⠆⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠙⠒⠶⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠿⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠾⠿⠷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣧⣀⣀⣤⣤⣤⣶⣶⣶⣤⣤⣤⣀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠈⠉⠙⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⠶⠶⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⣀⣀⡀⠀⠈⠛⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠸⣿⣿⣿⣿⡿⠂⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⢹⣿⠋⠀⠀⠀⣀⠀⢸⡇⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⢿⡄⠀⠻⣆⡀⠀⢸⣿⠀⠀⢀⡼⠃⠀⣼⠇⠀⠀⣠⣾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⢿⣷⣤⡈⠻⣄⠀⠈⠛⠶⠾⠿⠶⠞⠋⠀⢀⣼⠏⣀⣴⣾⣟⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⢀⣾⡿⠙⠿⣷⣿⣿⣦⣤⣀⣀⣀⣀⣀⣤⣶⣿⣷⣾⠿⠋⠉⢿⣷⡀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣤⣶⡿⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣶⣤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⢉⣡⣤⣴⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣤⣀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠉⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠛⠉⠉⠉⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣷⣶⣤⣤⣤⣤⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠉⠉⠉⠁⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⢀⣀⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⠀⢀⣀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠋⠁


⣿⣿⣿⣿⠿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠉⠒⢄⣀⠤⠔⠒⠒⠒⠒⠒⠒⠤⠄⣀⠤⠒⠉⠉⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠒⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠃⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠤⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠡⠴⠒⠐⠐⠲⠤⢅⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠊⠁⠀⠀⡊⠉⠉⠂⠀⠀⠉⢢⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⠀⠀⠈⢹⠋⠀⠀⡀⠀⠀⡂⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠢⢄⠣⡀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠀⢠⣁⠔⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠛⠦⠄⣀⣁⣀⣀⣀⡠⠤⠞⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡸⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢇⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠰⢧⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡷⠔⠒⠒⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠤⠠⠄⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠄⠂⠒⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⠈⢂⠀⡗⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢺⠀⡔⠀⠀⠀⠀⠀⢁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢠⠀⠀⠀⠀⠀⠈⢠⠓⠤⢀⣈⠀⠒⠒⠒⠂⢉⡀⠴⠚⡄⠀⠀⠀⠀⠀⠀⡄⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢥⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⡬⠔⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⢀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣄⡀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠶⢤⣄⡀⠀⣀⡴⠖⠚⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⣠⣄⣀⡀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⡴⠖⠛⠛⠓⢦⡀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠉⠀⠀⠉⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⡗⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡄⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⡟⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣷⡿⠀⠀⠀⠀⠀⠀⢸⣇⣶⣦⣿⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠛⠛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣾⠃⠈⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢸⡉⠀⠀⠀⠀⣤⣶⣶⣤⣤⠀⠈⠙⣷⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⣦⣤⣈⣇⠀⠀⠀⠀⠙⢿⣿⣿⠏⠀⠀⣼⠁⢀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⠉⠉⠛⠻⢦⣀⠀⠀⠀⠈⡏⠀⠀⣠⡾⠋⠉⠉⠙⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡄⠀⠀⠀⠀⠈⠉⠓⢲⠚⠛⢲⠚⠉⠀⠀⠀⠀⢸⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⣀⠼⣄⣀⣸⣀⣀⣀⡀⠀⠀⣘⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉⠙⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣠⡤⠴⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢶⣿⣿⡓⠶⠶⠤⣤⣤⣤⣤⣾⠟
⠹⣷⣄⣀⣀⣀⣠⣴⡾⠟⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠈⠉⠛⠛⠛⠉⠁⠀⣼⠃⠀⠀⠀⠀⢠⡤⠤⣄⠀⣴⢶⣤⡀⠙⣷⡀⠀⠀⣰⡏⠀⢀⣤⣦⡀⠀⣴⠒⢳⡆⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⠶⢦⣀⠈⣇⠀⠸⡆⢻⠀⠈⢷⠀⠘⣧⣀⣠⣿⠀⠀⡞⠁⢸⡇⢸⠃⠀⣼⠂⣠⠴⠶⣦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣏⠀⠀⠘⡇⠹⣄⣤⠇⠈⠳⣤⡾⠀⠀⢸⡏⢹⡟⠀⠈⣧⣀⡼⠁⠘⠷⠶⠋⢼⠁⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠶⠾⠃⣀⡤⠴⠖⠲⠦⣄⡀⠀⠀⠀⣧⢸⡇⠀⠀⠈⠁⣀⣀⣀⣄⣀⡀⠘⠷⠶⠞⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⣿⠘⣿⠀⠀⣼⠋⠉⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣾⠀⢹⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠉⠛⠲⠶⢤⣤⠴⠾⠋⠀⢀⡟⠀⠀⠹⣧⡀⠈⠛⠲⠶⠶⠶⠶⠛⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⣀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⠀⢀⣀⣠⣴⡿⠋

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⡈⠤⠴⠒⠒⠒⠒⠂⠂⠤⢅⣀⣤⣶⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣈⣉⣉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⡀⠀⠀⢀⠙⠦⣀⠀⡀⠀⣀⠴⠊⠀⠀⠀⢀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠻⣷⣤⣀⡑⣤⡤⠉⠉⡉⢄⣤⣊⣤⣴⣾⠟⠀⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣾⣿⡟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠦⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣬⣉⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣁⣤⣤⣤⣌⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣌⠢⠀⠀⠀⠀⠀⠊⣠⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠤⠤⠤⠀⢿⣿⣿⣿⣿⣿⠟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣈⡙⠛⠛⣉⠠⠀⠀⠀⠀⠀⠀⣉⠛⢛⣉⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⠉⠁⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⢍⠶⠂⠀⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠊⣴⣶⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠘⣆⠀⠾⢓⡤⡇
⠀⠀⠀⠀⠀⠀⠑⠬⣡⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠐⢊⣂⠸⡿⣣⡤⠨⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠸⣶⣿⠇⣀⣀⣀⣕⣄⣿⣾⣿⡴⢡⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⡔⠋⠁⡠⢤⣤⣄⠀⠈⠙⣦⢱⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢸⠀⠀⠘⢷⣿⣿⣿⠃⢸⣿⣿⡺⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣾⠀⠀⠀⠀⢸⠉⠀⡲⣁⢧⡞⢨⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣿⣷⣆⠬⡶⣜⡶⣖⡽⣾⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⣱⡠⢋⠟⡟⠳⡶⡴⠛⢷⡌⡪⡙⢦⡀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⣀⢪⡽⠁⠀⠈⠊⠮⠢⡢⡪⢊⢽⡈⠈⠀⠪⡻⡄
⠀⠀⠀⠀⢀⠜⠀⠀⡰⢠⡟⠁⠀⠀⠀⠀⠀⠈⠪⢔⢕⢙⢷⡄⠀⠀⠪⡸⡄
⠀⠀⠀⢠⡁⠀⠀⠐⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠕⡡⡺⣷⠀⠀⠈⠢⢝⢦
⠀⡠⠤⠛⠉⠙⠲⢦⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠨⠠⡻⣦⣠⠖⠈⠊⠉⡱⣄⡀
⠜⠀⡠⠤⠤⢄⡀⠀⠹⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡠⡢⡪⣿⠀⠀⠀⠀⠀⠈⠿⠿⠆
⠃⡜⠀⠀⠀⠀⠈⠳⡍⡺⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⠪⡊⡟⠀⢀⠔⠉⠀⠀⠙⢦⠝⡆
⡇⡇⠀⠀⠀⢐⠀⠂⡘⡮⣿⠊⢁⠀⠀⠀⠀⠀⠀⠀⡪⡪⡪⣺⠀⢀⠎⠀⠀⠀⡀⠆⠘⡆⣯
⠁⢰⠀⠀⠀⠀⢎⡨⢀⢺⣹⡇⠠⠀⠀⠀⠀⠀⠀⡠⠪⣪⣢⡇⠀⡌⠀⠀⠀⠀⠁⠐⢰⢭⣃
⠈⢦⣧⠀⠀⠀⢕⠢⠀⡾⣺⣣⡀⡀⡀⣴⢨⣮⣫⣨⣞⠉⡩⣧⠠⠀⠀⠀⣨⣁⠂⢠⣿⠿⢉⣑⠢⠤
⠀⠀⠙⣷⣄⣀⠐⠅⡲⢏⣿⢈⡭⠉⠽⠻⡿⠟⠛⠛⠛⣛⣛⣯⣸⠀⠀⠰⠠⠄⣠⣯⠿⠆⠀⠐⠒⢙⡛⠛⠂
⠀⠀⠀⠀⠹⠛⠻⠿⡷⠋⣐⡀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠭⣮⣦⣠⣭⣱⡮⠜⠣⣖⡚⠛⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠓⢦⣀⡤⠖⠒⠒⠒⠶⢴⣃⠀⠀⠄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢁⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⢀⠀⢀⠔⠂⠀⠄⣴⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⣆⠀⠀⠀⠛⠠⠀⠄⠀⠑⡀⠡⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠳⣄⠀⠀⠁⢀⣄⡀⠄⣸⡄⢡⡴⠋⢳⠀⠀⠀⡠⠶⠲⢄⣀⣀⣀⣀⣀⢀⡠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠙⠲⢆⠈⠿⣿⣿⠿⢃⡞⠀⠀⢸⡄⠀⢸⠁⢀⡠⠊⠉⠀⠀⠀⠉⠛⢆⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠙⠲⠶⠿⠖⠋⠀⠀⠀⣸⠙⢦⠈⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡤⠏
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⢄⣀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⢧⣸⠀⠀⣤⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠁⠀⡐⠀⠀⢻⡀⠀⠀⡅⠀⠂⠀⠉⠀⠀⣸⠃
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠈⠀⢀⣤⢚⠉⠺⣄⢻⡿⠃⣠⠤⠴⠺⠁
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡞⠉⠀⠀⡄⠀⠈⠛⠛⠋⠀⠔⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠐⠊⠉⠓⠲⢤⣐⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣆⡠⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡙⠲⢤⣄⣀⡀⠀⠀⢀⣀⣠⢴⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡀
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠈⠉⠉⠉⠉⠑⢯⣄⣠⣄⠀⠀⠀⠀⠀⠀⣠⣤⠔⠉⠀⠈⣧
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠶⢲⢦⡀⠀⠀⠀⢸⠋⠀⠯⠳⣤⠄⠐⠶⠛⠙⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⡉⠄⡁⣷⠀⢀⠂⢠⠉⡄⠀⠀⢿⠘⠀⠀⠀⡇⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡀⡿⠀⠀⠀⢈⣳⡐⠄⠀⣼⡇⠀⡡⢠⠇⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠤⢤⣤⣤⣤⣤⠬⠦⠤⠴⠛⠙⠉⠉⠉⠁⠈⠛⠋⠉⠳⠤⠖⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⢁⣀⡈⠑⢆⠀⠀⡀⠀⠀⠀⠀⣀⠀⢀⠔⠉⣀⢀⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠁⠀⠈⢢⠄⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⢤⠊⠀⠀⠑⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠰⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡰⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢈⠇⠀⠀⠀⢾⠗⢀⠠⠤⠤⠄⠀⢿⠆⠀⠀⠀⢋⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠊⠀⠀⠄⠤⠀⠈⠢⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⡶⡆⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠰⡀⠀⠈⠉⠀⠈⠁⠀⠀⠠⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠑⠢⢀⣀⣀⣀⡀⠤⠐⠁⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⠀⣑⠢⠄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠴⣎⠈⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠐⣎⠁⠀⠀⢀⡀⠟⠉⡏⠉⡇⢄⠀⠀⠀⠈⠖⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠⠉⠢⣀⠔⠉⣀⠃⠀⣧⠀⢐⠀⠑⢄⣠⠊⢆⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⠔⠁⣍⡀⠀⠇⠀⠀⡉⠢⡀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠠⠂⠙⠀⠀⡰⠁⠀⠀⠀⠀⠈⠁⠁⠁⠀⠀⠘⠄⠀⠀⠓⠢⢀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠊⠁⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⢄⡀⠙⠂⠤⠀⣀⣀⠀⠤⠒⠉⢀⠠⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⠰⠂⠀⠀⠀⠀⠖⠒⠈⠀⠀⠀⠁
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠁⠢⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡠⠊
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠄⠐⠊

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⡀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡄
⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢠⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⢠⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣼⣿⣄⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠈⠉⠉⠛⠲⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠤⣀⡉⠉⠓⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠲⣤⠤⠤⣌⡑⠢⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⣼
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣤⣤⠀⠀⠀⠛⠄⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⢠⡟
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⠁
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⡟⠰⣀⠔⢋⣤⣶⣿⣷⣶⣶⣶⣶⣦⣤⡄⢸⡄⠀⠀⠀⠀⢘⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡈⢳⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣉⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⢿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣿⣿⣷⣶⣿⡿⠋⠁⠀⠀⠀⠀⠙⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠈⠉⣩⣴⠶⠾⠿⠷⢶⣤⡉⠋⠁⠀⠀⠀⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⠏⠁⢠⣾⣿⣶⠀⠈⠻⣦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⣾⠇⠀⠀⠘⠿⠿⠟⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣿⠀⢀⡀⠀⢀⣤⠀⠀⢀⡀⢸⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠹⣧⠈⠛⠶⠛⠉⠳⠶⠋⢁⡿⠁⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⢹⣿⣷⣄⠀⠙⠷⣦⣀⣀⣀⣀⣠⣴⠟⠁⢀⣤⣾⣿⡃⢀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣿⣿⠟⠋⠙⠻⢶⣤⣌⣉⣙⣛⣋⣉⣠⣴⠾⠛⠉⠙⠿⣿⣿⠟⠋⠉⠉⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣏⣁⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣼⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠉⠉⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠘⢿⣿⣶⣶⣴⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁

⣿⣿⡿⠿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠙⠋⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠁⠀⠀⣤⣦⠰⣦⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢺⣷⡿⠛⠛⢦⣌⣛⣾⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠉⠁⠀⠀⠀⠀⣛⣛⠛⠛⠒⢺⡷⠶⠶⠦⠤⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠉⠉⠉⠉⠛⢻⡟⠓⠒⠲⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⠟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣾⣿⣿⣷⣶⣦⣾⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠆
⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠉⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣶⣦⡀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢑⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡠⠐⠂⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠔⠁⢠⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠌⠀⡠⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⡠⠈⠁⠀⢀⡀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠠⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡔⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠈⠂⠀⢀⣴⠓⡁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠈⠛⠻⡟⠁⠀⠀⠀⠀⠀⢀⣀⡴⢋⣀⡠⠐⢀⡿⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠁⠀⢀⠠⠂⣀⢴⠿⣭⠐⠩⠅⠀⠐⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠐⠒⠚⠃⠀⠁⠀⠸⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠈⠀⠀⢱⡄⠀⠀⣀⣀⣀⣀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠢⠀⠀⢤⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠠⠐⠈⢀⠔⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠐⠉⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⡠⠤⡀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠁⠢⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢰⠀⠀⠀⡎⠀⠀⠐⠆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡀⠀⠀⠀⡦⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠲⠂⠀⢀⡀⠀⠈⢆⠀⠍⠐⠠⠀⢀⣀⡀⠠⠄⠐⠊⠀⠐⢄⠀⠀⠀⠈⡀⠀⠈⢄⠀⢀⡔⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⠑⠀⠀⠸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠱⡀⠀⠀⠈⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢄⡀⠀⠀⠀⢠⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡈⠑⠠⠴⠀⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠉⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠻⡇⠙⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠠⠒⠈⠀⠀⠀⣿⣏⠀⠔⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢁⠀⣀⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠂⠀⠀⠀⡐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢄⢈⢀⡁⠀⠨⣒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣉⣁⣧⡀⠀⠈⠘⠢⠄⡀⠀⠀⠀⠀⠐⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡗⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠉⠀⠀⠀⠃⠀⠀⠀⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠄⠀⠐⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⡄⠀⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠁⠠⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠉⠉⠉⠉⠒⠲⣄⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄
⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⠞⠉⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡖⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠸⡀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⣄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⡻⠥⠤⠤⠄⣀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣰⠋⠀⠀⢠⠤⠤⢤⡈⠑⠦⡘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢧⠀⠀⠀⠘⢄⣀⣀⡨⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠵⢤⡘⣆⠀⢢⣀⣠⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠛⠳⢄⡀⠀⠙⠚⠁⣀⡤⠞⠀⠀⣀⣠⢴⡊
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢠⠀⠀⠀⠀⠉⠉⠉⠋⠉⠙⠓⠛⡉⠉⠉⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡠⠖⠒⠢⣷⠤⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣀⣀⡼⠷⠲⠤⣄
⠀⣼⠁⠀⠀⠀⠈⠣⠈⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠞⡱⠋⠀⠀⠀⠀⠈⣇
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠐⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇
⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠤⣀⣀⣀⣀⣀⣀⣠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠉⠓⠲⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣀⢀⡀⠑⢄⠀⡀⠠⠤⠤⠄⢀⠀⡠⠊⠁⡀⣀⡀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⢈⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣁⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠡⢀⠔⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠢⡀⠜⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡌⠀⠀⠀⠘⠛⡠⠀⠒⠒⠂⠄⡛⠃⠀⠀⠀⢡⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠊⠀⢠⠂⠐⡆⠀⠈⠄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⣀⠜⠣⣀⠀⠀⢰⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠢⡀⠀⠈⠁⠐⠒⠒⠒⠈⠁⠀⢀⡀⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⣀⠔⠊⠉⠐⠂⣠⠤⣤⠤⣄⠒⠈⠉⠑⠠⣀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡘⢂⠀⠀⡠⠊⡐⠀⢸⠀⠀⠑⠤⡀⠀⡰⡀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠤⠲⠁⠀⠸⠀⠈⠦⢀⠈⠊⠀⠠⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡀⠔⡇⠀⠀⠔⠁⠀⠈⠀⠂⠂⠂⠀⠘⠀⠑⡀⠀⠀⠦⢀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠘⢄⣀⣀⠠⠐⠈⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⠀⠁⠢⠄⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠤⡀⠈⠢⠄⠀⠀⡀⠀⠀⠤⠊⢀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠂⡄⠄⠀⠀⠄⠤⠐⠈⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠉⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠣⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⣰⡎⠀⠀⠀⠀⠀⠘⠃⠀⠀⠛⠀⠀⠀⠀⠄⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢠⣶⣆⣤⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⠀⠠⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢈⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠐⢾⣟⡛⠻⠷⠂⠀⠠⠄⠀⢀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢶⣌⣿⢿⠐⠶⠤⣍⣑⣲⠟⢹⠋⢻⠇⢿⠉⡿⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⠜⠓⠉⢀⣼⣿⣦⣸⠃⣼⠛⣷⣾⣦⣾⣶⠾⠛⠉⣻⣤⠀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠀⠀⠀⠠⠖⣿⠛⣯⡯⣀⡯⢈⡇⢸⢉⡛⡻⠀⠀⠀⢘⣿⣶⣦⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣬⣶⣿⠟⠁⣤⡼⠃⣼⢅⡸⢬⣿⣏⠀⠀⠀⠈⢘⣿⣿⣷⡂⢀⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢉⣿⣦⠛⠁⡀⠤⠂⣼⠱⣾⠉⠉⠀⠀⠀⠀⠈⢽⡏⣉⠛⣺⣧⡬⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠿⣿⣿⡟⢁⡠⠞⢁⣰⢿⡀⠀⠀⠀⠀⠀⣾⣤⠇⠈⠩⠿⣅⠀⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡀⢠⡤⠉⢄⣁⣿⣿⣿⠩⠔⢻⣯⣸⡺⠷⠀⠀⠀⠀⢠⣿⢼⠇⠀⠀⠀⠈⠓⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠻⣿⣤⠴⠛⠛⠿⡉⠀⠀⠀⠀⠀⠈⢻⣾⡇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⠀⠈⢃⠀⠀⠀⠀⣸⣿⣿⠅⠀⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠂⠀⠀⠂⠀⠀⠀⠘⠀⠀⠒⢐⣿⡧⠁⠀⠀⠀⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠒⠛⠉⠹⣿⠦⣄⡀⠀⠀⢀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣿⠀⠀⠂⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠟⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠷⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⠤⢤⣤⣀⡀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠉⠻⢶⣴⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡴⠛⠁⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠉⠀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⡶⠛⠛⠓⠶⣤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡋⠀⠀⠀⠀⠙⣷⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⣼⡏⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠘⣷⣤⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢛⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⣦⡗⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⢀⣾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠛⠉⠛⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⣾⠉⠀⠀⠀⠀⣠⣤⣦⣤⣤⡀⠈⠉⢻⡦⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣶⣤⣀⣸⡆⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁⠀⢀⡞⠁⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡾⠉⠛⠻⠷⣄⠀⠀⠀⠀⠈⣿⠋⠀⠀⣠⡿⠋⠉⠉⢻⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⠀⠀⠀⠀⠈⠙⠒⠶⢤⡴⠿⠦⡴⠚⠉⠀⠀⠀⠀⣸⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⡁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠙⠶⠦⠤⠤⠤⠴⠖⠚⠉⠙⠛⠛⠉⠙⠛⠛⠒⠒⠚⠛⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣠⣿
⠸⣧⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡶⠛⠛⠉⠉⠉⠉⠉⠙⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠉⠙⠛⠛⠻⢿⣮⣍⠉⠙⠛⠛⠛⠿⠿⠛⠁
⠀⠙⢿⣦⣤⣤⣴⣶⠿⠟⢉⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢼⠛⠳⣆⠀⡿⠛⢷⡄⠀⢻⣆⠀⠀⢰⡟⠀⠀⣴⠞⢷⡀⢀⡞⠉⢙⡇⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⠟⠛⠦⣄⢸⡄⠀⢸⡆⢻⡀⠀⢹⡀⠀⢻⣤⣤⣿⡇⠀⢸⠃⠀⢸⠇⢼⠀⠀⣼⢁⡠⠞⠛⢳⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡀⠀⠀⢹⠄⠻⣤⠾⠃⠈⠓⠶⠞⠀⠀⠘⣯⠉⣿⠀⠀⠸⣦⡤⠟⠀⠘⠛⠚⠃⢸⡃⠀⠀⣨⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠛⠳⠶⠟⢀⣤⠶⠖⠛⠒⠶⢤⣀⠀⠀⠀⢿⡀⣿⠀⠀⠀⠀⣀⣠⣤⡤⢤⣤⡀⠈⠳⠶⠛⠋⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⢸⡇⢻⡇⠀⢠⡟⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡇⠘⣷⡀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠈⠙⠳⠶⢦⣤⣤⣤⠶⠟⠁⠀⣾⠀⠀⠘⢿⣄⠀⠙⠳⠶⠶⠤⠴⠶⠾⠋⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⡀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⡀⣠⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⡶⠿⠿⠿⢿⣿⣯⣽⣶⣿⣭⠔⠻⡟⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠻⠯⣼⣗⣦⣶⢆⣠⡼⠓
⠀⢀⡤⠶⠚⠓⠒⢒⣾⣾⡿⢟⣍⣻⢯⡞⠁⠀⡘⢀⡠⠔⠒⠈⠛⠁⠒⠢⢤⡀⠀⠀⠀⢰⣆⠀⠀⠈⡻⠉⣧⠙⣒⡦⠄
⠰⠋⠀⠀⠀⣠⡾⠛⠋⠁⢠⣬⣳⠁⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠎⣿⢗⠄⠚⠒⠉⠈⠉⠁⠀⠘⠛⠃
⠀⠀⠈⠀⠈⠁⠀⠀⣠⠀⠛⠃⠁⠀⠀⠀⣰⠃⠀⠀⠰⠆⢀⠁⡄⠈⡄⠐⠂⠀⠀⠘⢆⠀⠀⠘⣷⣄
⠀⠀⠀⠀⢰⣷⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢩⡄⠡⣀⣣⣧⣼⣀⠌⣤⠋⠀⠀⠘⡄⠐⠰⢻⡙⠃
⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⢠⣤⠀⢸⠀⠀⣈⠀⠈⣐⣾⡷⣾⢎⣷⡊⡠⠄⡉⠀⠀⡇⢀⠆⠀⣿⣄⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠈⡄⠀⠀⢀⠛⡐⠛⡿⢲⢫⠉⢂⠘⣃⠀⠀⢠⠃⢎⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⠄⠀⠱⡀⠀⠀⠀⠄⠐⡁⠐⢀⠁⠠⠄⠀⠀⠀⠌⠀⠈⠀⢠⢿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣌⠓⠀⠀⠘⠄⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠿⡠⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠸⣿⡟⠷⢦⣄⡀⠀⠀⡶⠀⠀⢀⣀⠀⠠⡤⠐⠀⠀⠀⠀⢀⡀⡀⠃⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠀⢻⠀⢨⡦⡈⠙⢆⠀⠃⠀⠀⠀⡋⠀⠀⡅⠀⠀⠀⠀⠰⡸⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣆⠈⠁⣨⡅⠘⠀⢰⠄⢲⡀⠀⢨⡇⠀⠀⠀⠃⠀⠀⠀⠀⡘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠓⢀⠀⣰⠀⠈⠁⠀⠸⡻⣦⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡃⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠸⠀⠁⡑⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢃⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⠿⠿⣷⣶⣤⣄
⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠻⣷⣆
⠀⣼⡿⠋⠀⠀⣀⣤⣶⣶⣤⣅⢠⠀⢸⣿⣤⣤⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣀⣿⡏⢀⣤⣨⣤⣶⣶⣤⣄⠀⠀⠈⢿⣷
⣸⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣷⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⢿
⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸
⢿⣷⠀⠀⢿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡿⠀⠀⣼
⠈⢿⣧⡀⠘⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠃⣀⣼⡿
⠀⠀⠙⠿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⠿⠋
⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⣁⡠⠤⠒⠒⠒⠲⠤⣄⡘⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⣠⣶⣶⣤⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢠⡀⣰⣿⣿⣀⢀⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠈⠛⠛⠁⠈⠛⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⣠⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣶⣾⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣷⣶⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣾⠟
⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣤⣴⣶⡿⠛⠻⢿⣶⣤⣤⣤⣤⣤⣶⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣠⠖⠛⠛⠛⠓⢦⡀
⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⠀⠀⣴⡛⠓⠈⠳⢦⣀⣰⠃⠀⣠⠔⠒⢤⠀⠙⡆
⢠⡞⠉⠀⣀⣀⠀⠀⠈⢧⣠⠶⠋⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⢧⣀⣠⠆⠀⠀⡿
⣿⠀⢰⠋⠀⠈⢱⡀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠲⢿⣿⣶⡄⠀⠀⠀⣀⠼⠁
⢻⡀⠀⠳⠤⠤⠞⠁⠀⠀⣴⣿⠿⠋⠀⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀⠀⠈⠛⠶⣤
⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢦⣄⠀⠀⠀⠀⢸⣋⣦⠈⢧⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⡏⠀⣤⣿⣧⠀⠀⠀⠸⣿⣿⠃⣸⠀⠀⠀⠀⠀⠐⢿
⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⢧⠀⠻⣿⣿⠀⡠⠤⠀⠘⠳⠖⠛⠋⠀⠀⠀⠀⠀⣈⡷⠶⠶⠚⠓⢦⣀⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠴⠞⠓⠤⠞⢁⣤⠒⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠠⣼⠀⠀⢀⡤⢄⠀⠀⢹
⠀⠀⠀⠈⢧⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⡶⠋⡧⠀⢫⣀⡸⠀⢀⡼
⠀⠀⠀⠀⠀⠳⠶⢦⡀⠀⣀⠤⠄⠠⢀⠀⠀⠀⠉⢻⠀⣄⠀⠀⠀⠠⣀⣼⢋⣠⠞⠁⠀⠀⠀⠀⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠁⠀⠀⠀⠀⠱⣄⡀⠐⠾⠟⢀⡀⠄⠀⠀⠈⢻⠉⠁⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠄⠀⢀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠎⠀⢀⠔⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⡆⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢰⠇⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⢽⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣮⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢀⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠂⢸⡿⠛⢳⡖⠂⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠠⠄⠘⠷⢤⡀⢀⡼⠇⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡀⢀⣽⣏⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⢴⠧⠞⠁⠈⠳⠤⠴⣤⣠⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠉⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡔⠋⠉⠓⣄⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⣀⣀⡤⠴⠚⠚⠒⠦⠤⣄⡀⡴⣉⣤⣄⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡅⠀⠀⠙⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⡟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠭⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡤⠬⣿⣀⣀⡀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠁⠀⠸⣿⣿⣿⣿⡝⠫⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡞⠙⠢⣝⠲⠤⢤⣀⣀⣀⠤⠚⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡞⢀⣀⣀⣀⣉⡓⠲⠤⠤⠤⠤⠤⢤⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢀⡎⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡴⠒⢶⡲⠤⣼⣦⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⣸⠟⢠⣦⣇⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣷⣿⣷⠀⡏⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢹⡿⠋⡼⠁⠀⠀⠀⠀⠘⢷⠦⣀⠀⠀⢀⠔⠊⢉⠉⠛⢶⡦⡀⠀⢸⢻⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠛⠋⠉⠙⠮⣝⢲⢿⣶⠄⠻⠟⣠⣄⢱⠹⣄⡟⠀⠉⠙⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣴⣾⣷⣶⣌⠋⣸⠀⡏⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⠷⠃⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠭⠤⠴⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⠟⠋
⣟⣀
⣿⣿⡷
⣿⣁⡀
⣿⣿⡿⠄
⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣤⡀
⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣼⣿⣄⣀⣀⣤⣾⣿⣿⣁⣠⣤⣠⣤⣤⣤⣄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣴⣤⣄⠀⠀⠀⠀⠀⠀⠼⡿⠋⠻⠿⣿⣿⣧⠀⠀⠀⣀⠀⢀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⣿⣿⠀⠀⠀⣱⣘⣙⣋⣜⠛⣟⣋⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠁⠉⠁⠉⠉⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣁⡐⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠋⠛⣭⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⡀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢀⣴⣀⣀⡄⠀⠀⠻⢿⠁⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⡀⠛⠀⠀⠀⢶⣾⣿⡶⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣄⠈⠀⠀⠓
⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣄⡀⠀⠉⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀
⠀⠀⠀⢸⣿⣟⣿⠹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡇⡁⢁⠄
⠀⠀⠀⠀⢻⣿⣴⣦⣿⣿⣿⣿⣿⣿⡟⢩⣿⢿⢿⡿⢱⣻⣹⣷⡧⣤⡈⠻⣿⣿⡿⢿⣿⠿⠿⢿⣷⡇
⠀⠀⠀⠀⠸⣯⣭⣤⣤⣬⣿⣿⣿⣻⠖⢬⠛⠛⠷⠉⠀⠻⠏⠫⡱⢏⣴⣤⣬⣥⣤⣿⣷⣶⣦⣤⣴⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣤⠀⠀⠈⠀⠈⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠀⠴⠄⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠋⠀⠀⠁⣶⠂
⠿⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⢠⠔⠁
⣾⣶⣖⢸⡟⣳⣶⣤⣄⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠌⠀⢀⠉
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢰⡴⠁⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣶⣿⢯⣭⣤⡤⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣾⣁⣈⠀⢀⣤⣤⠀⢘⡿⣷⢽⣻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣤⣤⣤⣤⣤⣤⣄⣀⣀⣰⣿⣉⣀⣀⣀⣀⡙⢒⣾⣒⣺⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⣉⡁⠈⠉⠈⣿⣿⡉⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⡈⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⠤⠶⠤⣄⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣠⠶⠖⠲⢤⣀
⠀⠀⠀⢀⣾⡟⠋⠀⠀⠀⠀⢙⣦⢶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠻⡶⣮⡀⠀⣀⡀⠀⠋⡷⣄
⠀⠀⠀⢸⠁⠀⢠⠞⠉⢹⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⢻⡉⠉⢳⡀⠀⢹
⠀⠀⠀⢸⡄⠀⠘⢆⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⠜⠁⠀⣼
⠀⠀⠀⠀⠻⣄⣀⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠞⣧⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣹⠛⡎⠁⠀⠀⢠⣤⡄⢀⡤⠶⣲⣶⡖⠤⢄⣠⣶⣦⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣶⡆⠀⠀⠀⠈⢛⡟⠁⠀⠐⣿⣿⡿⠀⠀⠉⢫⠁⠀⠀⠀⠀⠃⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡄⡄⠀⠀⠀⠀⢸⠀⢤⡤⠀⠀⡯⠀⠀⣦⠤⠀⡇⠀⠀⠀⠀⠚⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢄⢰⣀⣀⠀⠸⡄⠀⠙⠦⠤⠧⠤⠞⠁⠀⢀⠃⠀⡤⣀⣞⠀⠁
⠀⠀⠀⠀⣀⠤⠶⠴⠶⠿⡿⠿⠭⣷⣝⣤⡀⠀⠀⠀⠀⠀⣀⣴⣠⡯⠾⣿⠿⡥⢀⡀⠀⠀⣀
⠀⠀⢠⡞⣁⠀⠀⠀⢡⢄⡐⡡⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡪⣁⢔⠂⠁⠀⠀⠀⠙⢦
⠀⠀⢸⠏⠁⠀⠀⠀⠀⢠⠞⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣷⡀⠀⠀⠀⠀⠚⠚⣇
⠀⠀⢿⣄⡀⠀⠀⠀⣠⠏⠃⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⢙⣆⠀⠀⢀⣀⣠⡏
⠀⠀⠘⢷⣀⠀⠀⣰⢣⡿⣿⡶⠲⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠲⢴⣎⣿⣦⢤⡤⠼⠋
⠀⠀⠀⠀⠉⠙⢻⡿⠋⠐⠃⢀⣀⡀⠓⠉⠳⡀⠀⠀⠀⠀⣠⠞⣁⠋⠀⡠⢤⡀⠉⠉⠻⡆
⠀⠀⠀⠀⠀⢠⡟⢀⡞⢳⡀⣏⢀⡇⢰⠋⣷⠹⡄⠀⠀⣸⠃⢸⡉⣳⠀⢧⡰⠃⡴⠒⡆⢹⡄
⠀⠀⠀⠀⠀⣿⠀⠈⠷⢞⣁⣬⣭⣤⣌⠛⠁⠀⢹⡀⠀⡏⠀⠀⠉⣡⠤⠤⠤⠤⣝⠋⠁⠀⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⣟⠀⠀⠀⠀⠈⣷⠀⠀⣸⡘⠻⢳⠀⠀⢸⣀⡀⠀⠀⠀⣸⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠘⢷⠄⠀⠉⠛⠛⠓⠒⠛⠁⢀⡴⢿⣿⣸⣧⠷⣄⣀⠈⠉⠉⠉⠉⢁⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠒⠒⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⣠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠴⠒⠦⡈⣳⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣞⣡⠖⠒⢦⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡇⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡖⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⢀⣀⣀⣀⠀⠀⠀⢴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⠴⠚⢯⡁⠀⣩⠟⠲⢤⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣇⡀⠀⠀⠀⠲⠤⠾⠳⠤⠖⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣠⠏⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠈⢳⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢹⠀⠀⠀⠀⠀⠀⠙⣶⠒⠒⢲⠞⠁⠀⠀⠀⠀⠀⢸⠁⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢠⠞⣇⠀⠀⣀⣠⠤⠖⠋⢳⣞⠋⠙⠲⢤⣀⡀⠀⠀⡾⠙⣆⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⡏⠀⠈⠉⠙⢯⠀⠀⠀⠀⡼⢹⡄⠀⠀⠀⢨⠟⠉⠉⠀⠀⠘⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣠⠾⠀⠀⠀⠀⠀⠈⠳⣄⠀⢰⠇⠀⣧⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠹⢤⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡾⠀⠀⢸⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡴⠲⣄⣠⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⢤⣤⢖⡲⣄⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡵⣌⢸⢙⠬⣷⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣟⡇⣏⡽⣰⢲⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠳⢞⡴⠛⠛⠛⢦⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡴⠋⠉⠙⠳⣝⠚⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡅⠀⠀⠀⠀⡿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⡳⠤⠤⠴⣋⡴⠓⠲⠦⠤⠤⠤⠤⠤⠤⠤⠶⠒⠚⠳⣍⣓⣦⠴⣚⡡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄⣀⣠⠤⠤⡤⠦⠤⢤⣠⠒⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠞⠁⠀⢀⠎⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢠⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡏⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣘⢿⠶⠶⢶⠼⢿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡜⠁⠘⠦⠤⠚⠀⠀⠱⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢇⢀⠀⢠⡀⠀⡠⠀⢠⠇⠀⠀⣠⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠙⠪⢷⣿⣥⣤⣒⣒⣒⣡⠤⠖⠋⠀⠀⠈⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠑⣄⠀⠀⠀⢸⠁⠀⠀⠹⣄⣉⠔⠁⢠⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⡼⠶⠶⢤⣄⡀⠀⣸⠀⠀⠀⣾⠀⠀⠀⠀⠉⠁⠀⠀⢸⡀⠀⠀⣀⣀⣀⡼⠁
⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠈⠙⠿⣏⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠚⠉⠁⠉⠉⠛⢦⡀
⠀⠀⠀⢸⠃⢠⠞⠛⠓⢦⡀⠀⠀⠈⢷⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡴⠋⢀⡤⠖⠚⠶⣦⡄⠀⢳⡀
⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠙⢦⠀⠀⠈⣇⠀⠀⢳⠀⠀⠀⠀⠀⢸⠃⣰⠋⠀⠀⠀⠀⠈⢻⡀⢸⡇
⠀⠀⠀⠈⣇⣧⠀⠀⠀⠀⠀⢸⡇⠀⢀⡏⠀⠀⠀⢣⡀⠀⠀⠀⢻⡀⡇⠀⠀⠀⠀⠀⠀⣸⠃⣸⠃
⠀⠀⠀⠀⠘⢾⣦⡀⠀⠀⢀⡼⠁⢀⡼⣁⠤⠤⢄⣀⣱⣄⣠⣤⡼⢷⣧⣀⠀⠀⠀⣀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣞⣫⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⡭⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠐⠂⠐⠂⢄⠈⠢⠄⠂⠀⠈⠉⠉⠁⠀⠐⠠⠆⣀⡠⠐⠂⠐⠂⠄⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠁⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡜⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠆⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⢰⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠠⠆⠉⠁⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⢠⠄⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⡔⠀⢡⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠡⡀⠈⠢⢀⠀⠀⠀⢀⠠⠐⠀⢀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠑⢄⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⢀⠠⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠈⠀⡄⢀⠀⠀⠉⠀⠈⠉⠀⠀⡀⠤⠂⠁⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠃⠀⠘⢦⠀⠡⡀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠉⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠀⣀⠠⠐⠃⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠂⢄⡀⠀⠀⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢀⡤⠒⠋⠓⠒⢤⡀⠑⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠒⠊⠑⠲⢤⠀⠑⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢀⡜⠁⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢂⠀⠀⡌⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠀⢰⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠁⠹⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠌⠀⠀⢢⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠉⠒⠤⠤⠴⠒⠋⡠⠔⠁⠀⠀⠀⠀⠈⠢⢈⠙⠒⠤⠤⠴⠚⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠐⠈

⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⠖⠒⠒⢤⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠁⠀⠀⣀⣀⣧⣼⣀⣀⣀⠀⠀⠀⢠⠖⠋⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡷⠖⠋⠉⠀⠀⠀⠀⠀⠉⠙⠲⢤⣯⠖⠋⠙⠲⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢀⣰⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡭⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣀⣈⣛⣁⣀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠞⠁⠀⢰⣿⣿⣿⣿⣿⠺⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⠀⠀⠀⠙⠿⠿⠿⠛⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣣⡈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡽⠁⠈⠳⢬⣙⠓⠶⠤⠤⠤⠤⠖⠋⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡾⠀⣀⣠⣤⣤⣈⣙⠒⠶⠤⠤⠤⠤⠤⠴⣶⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢀⣴⠿⠛⠉⠁⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⡼⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⡇⠀⠀⠀⠈⢧
⠀⢀⣤⣤⣄⣀⡀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⡇⠀⠀⠀⠀⠈⢧
⢠⣯⠀⠈⢳⡈⠉⠛⠻⠦⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⠀⠀⠀⠀⠀⠀⠘⡆
⡾⣉⡐⠿⠟⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⡆⢸⠃⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇
⢻⡻⠟⣠⠏⠀⠀⠀⠀⠀⠀⠻⣗⢤⣀⠀⠀⠀⡠⠞⠉⢉⠉⠙⠻⣶⢄⡀⠀⢸⠸⣄⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠙⠚⠓⠶⠶⠶⠒⠒⠒⠚⠛⠉⠳⢬⡓⠦⣼⣷⣦⠐⠿⠿⢀⣀⡈⣆⢳⠀⡞⠀⠈⠙⢒⡖⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⢉⣥⣶⣶⣤⣘⠻⠃⣼⠈⡟⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⣿⣿⣿⣿⣿⣇⡰⠃⢰⠧⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠿⠿⠟⠋⢀⡴⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣶⣶⣶⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⡠⠐⠒⠀⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⣄⡘⠃⣨⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠳⢴⣾⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠄⠁⠈⠉⠁⠀⠉⠀⠄
⠀⠀⠀⠀⠀⣀⠤⠐⠁⠀⠀⣠⣀⡀⣮⡷⠀⠀⢧⣐⡠⡁⢠⣠⣤⡀⢀⣤⣔⡜⡁⠀⢈⠀⠀⠀⠀⠀⠀⢀⡘⠋⠑⠠
⠀⠀⠀⠀⠀⡇⠚⣷⣆⢠⢤⡌⣋⣵⣨⡻⡞⢠⣿⣅⡁⢳⡄⠉⠱⣤⣤⡍⠹⢼⡾⠀⣼⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣀⣨⣟⡎⢛⣵⠳⢶⣿⣀⣢⠎⠈⠏⠀⠀⣹⠓⣶⣔⣛⣲⡶⠞⠛⠲⠏⠐⠀⢀⡀⠀⠀⡜⠃⡁⠐⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣬⣭⣤⣠⣡⠞⠉⠀⢀⡏⠠⠀⡏⠀⢌⢠⠉⣡⣈⠠⢀⠁⡸⣦⢴⡆⢣⣾⣥⣤⡶⠁⠀⡄⠄⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠶⠤⢒⣘⠾⢈⠀⢀⠔⠀⠠⠋⡨⠢⢼⡀⠀⠾⡐⠀⠈⡓⣶⣦⣶⠖⠋⡂⠀⠠⠀⠲⠀⠄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠒⠈⠉⠉⠉⠉⠉⠉⠃⡠⢀⡄⠀⠠⠔⢤⡒⢠⡔⠀⠀⡠⠼⢋⣀⣀⣒⣐⣿⠀⠀⠀⠀⣇⠢⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢼⠀⠀⠀⠀⠀⢁⠴⠀⢀⠔⠁⢀⠀⠀⠀⠈⠉⡻⠀⠀⢀⢎⠀⢠⠄⡏
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠠⠆⢈⡁⠀⡠⠆⠀⠀⣤⢀⢜⠠⠄⠀⠂⠀⠀⢀⡜⠀⠀⢠⠀⠀⠁⡈⠔⢃
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠀⡀⢀⡇⠀⢀⠔⡡⢘⣹
⠀⢀⣀⣀⡀⠀⣀⠀⢤⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⣠⢚⠝⡩⠞⢡⠟
⠀⣀⠄⠀⣀⣀⠀⠀⣤⣤⡤⠠⠌⢀⣈⣛⣿⠦⣤⡀⠌⠀⢀⡴⡄⠲⠤⣤⣤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⢤⣡⣪⠤⠊
⢰⠕⠊⠉⠁⠀⠀⠀⠀⠀⠁⠉⠃⠈⠀⠒⠛⠶⢢⣥⣦⡙⠖⠇⠤⠑⠂⠀⠈⠀⠉⠉⠉⠁⣀⠀⠀⠠⠔⢁⠀⠈⠾⠈⠁
⢨⣮⣐⣒⣂⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀⡀⠀⠀⢫⣀⠤⡔⠁
⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣙⣛⣒⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⢉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠖⠀⠤⢄⣀⣠⣤⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⡀⠒⠀⠀⠀⠀⠀⠀⠬⠽⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁⠀⠐⠁⢀⠀⡀⣄⠀⠀⠀⠀⣀⣀⣀⡈⢻⠇⢀
⠀⠀⠀⠀⠀⠀⣸⣷⡀⡀⢀⣼⠿⢋⣡⡴⢚⣀⣠⡴⠞⠛⠋⢀⣠⣴⣾⠿⠋⠉⠉⠻⢿⣶⡾
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣿⡴⢛⣭⠶⠛⠉⠀⣀⣤⣶⣿⠿⠿⠓⠒⠲⠶⢦⣤⣀⣀⠙⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣾⠟⠀⢠⣴⣿⣿⡿⠟⢉⣁⣠⣴⠞⠛⠒⠒⠲⠶⢶⣽⣦
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠋⣄⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡃⠀⠀⢀⢠⣤⡤⢾⣿⣦
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣍⠛⠋⢉⣻⣿⣿⣿⣿⣿⣵⣶⣤⣶⣿⢿⣾⣯⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⠟⡋⠁⠀⣴⣿⣿⣿⣿⣿⣁⣘⣤⢾⣿⣿⣷⣴⣦⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⡿⠿⡿⡿⠟⠋⢻⠿⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠁⣝⣛⣽⠏⠀⠀⠀⠘⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡮⠉⠀⣴⣀⣀⣠⣤⣬⡻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡻⢟⣿⣿⣿⣿⡿⠿⡃⣀⣠⣾⠙⠿⡿⢿⣿⣿⣷⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣦⣀⣠⣤⣭⡟⠁⢀⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠻⣿⣿⣯⣽⠏⢀⣴⠏⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢾⣧⡄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣿⣿⠋⠀⣸⠏⢠⡾⠋⣸⠟⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣁⣀⠀⠀⠀⠀⠀⢸⡟⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⡈⠁⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠻⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⠀⢄⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⣀⠠⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠰⠁⠀⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⣧⠀⠀⠀⠀⠀⢀⠖⠐⠢⠀⠁⠢⡀⠀⠀⠀⠀⢻⡀⠂⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠙⠒⠢⢄⣹⡀⠀⠀⠀⠀⠈⠳⠦⠖⠁⠀⠀⠐⠀⠀⠀⠀⣼⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡈⠳⢤⣀⣀⣀⣀⣀⠠⠊⠀⠀⢠⡟⣀⣀⡤⠤⠖⠒⠉⠉⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⡤⠤⠄⠀⠀⠈⠛⠶⣤⣀⡀⠁⠀⠀⠀⣀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⠒⠶⠶⠶⠒⠛⠉
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡏⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⡴⣋⡀⠀⠀⠉⠙⠒⠒⠖⠚⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⣸⡎⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⢹⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁
⠀⠀⠻⣦⡀⢀⠇⠀⠀⠀⠀⢀⣀⣴⠟⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠻⣄⡀
⠀⠀⠀⠈⠙⠛⠷⠶⠶⠖⠛⠛⠉⠀⠀⠀⠈⠙⠻⢶⣤⣤⣀⣀⣀⣀⣀⣤⡤⠶⣾⠛⠉⠀⠀⠀⠀⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡠⠊⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢸⠁⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠷⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀⠀⠤⡔⢷⣦⣠⣀⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢠⡍⠉⣁⣬⣆⣻⣿⣿⣷⣯⣏⡛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣠⣶⡿⣿⡏⢉⣉⣁⡸⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡖⢠⣾⠟⠁⠈⠋⣠⣿⠋⠁⠀⠙⠻⠮⣝⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⡞⢠⡿⢁⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⠳⠙⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣾⢡⡟⢀⠀⠀⢀⣼⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⡟⠀⠄⢀⠀⣾⠃⠈⠀⠀⢀⣤⣤⣤⣄⠀⠀⢰⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡿⢰⣾⢡⠇⣸⣿⡇⠀⠀⠰⢃⡀⢈⣿⡞⢿⡀⠸⣯⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠗⠊⣿⠏⣰⣿⣿⠇⠀⠀⠐⠿⠏⠛⠐⠁⠈⢷⡄⠱⣦⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⢸⣦⣿⣟⠗⢶⡄⠿⢿⠿⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢧⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣠⠿⢿⣿⣯⣽⣿⣿⣆⠸⣷⡀⠀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⢄⣠⣾⣷⣦⠴⢶⣆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣴⣟⣭⣅⣠⣤⣿⣿⣄⡈⠑⣶⡀⠀⠀⠈⢤⠘⢷⡄⠀⠀⠀⠀⠀⢀⣼⡇⣠⣶⡆⢻⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⢀⢺⣿⣋⣩⣽⣿⣿⣷⣿⢻⣿⣶⡟⠳⣄⠀⠀⠀⠀⢿⠁⠀⠀⠀⢴⣶⣋⣙⣧⣼⡏⢧⠸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⠿⠖⣉⣛⠉⠹⠏⢻⡛⠛⠛⠋⣿⠃⠀⠉⢓⠤⣀⠀⠘⠀⠀⠀⠀⠀⠀⢛⣡⠟⠋⠀⠀⣠⡿⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣴⣿⡂⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⢄⣤⣤⣴⡶⠛⠁⠀⠀⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⢾⡭⠉⢉⣛⠿⡦⠀⠀⠀⠈⢦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣛⣾⠇⣤⣄⣴⡀⠀⡀
⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢄⠀⠈⠳⣤⣀⠂⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣸⠿⣿⡇⠘⣿⣿⡇⢻⠇
⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣀⠂⠀⢹⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⡿⠀⣿⡇⠀⠘⣿⣧⠀⠆
⠀⠀⠀⠀⣸⣿⠀⠀⢰⡁⠀⠀⠀⠂⠀⠀⡀⠀⠘⣿⣷⡀⠉⢻⣷⣄⠀⠀⠀⢰⠋⢸⡿⠀⡇⢺⣿⡇⠀⠀⢹⣧⠀⢠
⠀⠀⠀⢠⡏⣿⡀⠀⠈⠀⠀⠀⠀⠀⣀⣢⠈⠀⠀⠸⣿⣧⠀⡌⣆⠉⠀⢤⡄⠀⠀⢸⡇⢰⠇⠀⣿⡇⠀⠀⢰⣿⡄⢸
⠀⠀⠀⣾⠀⠻⠇⠀⠀⠤⠤⠀⠀⠂⠉⠻⢿⡳⠆⠀⣿⣿⡄⢁⢹⡄⠀⠀⡤⠀⠀⣿⠀⣾⠀⠀⣿⡇⠀⠀⠈⣿⡇⠀⡆
⠀⠀⢰⡏⠀⣠⣴⣶⣶⡶⠶⠶⠶⠦⢤⣤⣀⣁⠀⡀⢹⣿⡇⢸⠈⣷⠀⢸⡇⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣷
⠀⠀⢸⠁⠀⠈⠓⠾⢿⡇⠉⠁⠀⠀⠀⠀⠈⠉⠝⠛⢼⣿⡇⢸⡆⢻⡄⡺⠁⠀⠀⠀⠀⠀⠀⣼⠏⠃⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿