Dough Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠉⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠹⠻⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣷⣕⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⢀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠻⢿⣿⡛⠳⠆⠀⠂⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣠⠄⠀⠀⠀⢠⠊⠉⠁⠀⠚⠓⠒⠂⠤⠤⠤⠄⣄⣀⣂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⠣⠤⣤⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡝⠉⣆⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⢀⣀⣀⣀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⡇⢎⡉⠀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐⠂⠒⠒⠂⠀⠷⠊⠈⠙⠒⠒⠒⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠃⠀⠀⠀⠀⢤⣴⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠄⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⢀
⠀⢐⢀⠀⠀⠤⡤⠀⠀⠀⣀⠀⠐⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⢨⡑⠳⠶⠄⠠⠤⠤⠤⠤⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠁⠀⠀⠭
⠀⠀⠙⢗⠤⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠔⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠠⣄⣀⠈⠙⠂
⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⡀⡀⠀⣠⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠛⠋⠉⢉⡅⠻⠉⠉⢐⢊⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠄⣀⠀⡄⠀⢀⣉⠠⢄⣀⠀⠀⠀⠀⠘⠻⠄⠁⠤⠤⣤⣤⠬⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⢸⢯⡉⢦⣀⠛⠦⠰⠀⠡⡀⢰⠀⠀⠀⠀⠀⢂⠒⢀⠀⠀⠈⠐⠀⠀⠐⡠⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠘⢾⣴⢲⡾⠳⣜⣃⠉⡗⠘⠓⠟⠧⢁⡀⠀⠀⠑⠅⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠈⢿⣉⣙⡊⢶⠉⠈⠙⠑⠒⠒⠠
⠀⠀⠀⠀⠀⠙⠿⡝⠈⠦⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠛⠢⠵⢠⣄⠄⢀⡀⠂⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠦⠈⠂⠈⠁⠈⠁⠀⠀⠀⠀⠙⠤⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣈⣀⠀⠒⠒⠲⢶⡶⡶⡄⠐⡄⠀⠐⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⣓⠬⠤⠔⠁⠉⠛⠁⠸⠴⠤⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠶⡶⠿⡴⢄⣀⣀⠀⡀
⠀⠀⠀⠀⠠⠉⠒⠂⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢮⠙⡈⢏⣰⣄⣠⢐⣄⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢐⠢⠤⠤⠈⡧⠬⠤⠀⠫⠄
⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡤⠀⠀⠀⠈⠁⠀⠀⢀
⡄⠈⠈⡍⣉⣙⣛⡓⠒⢓⠒⠶⠶⠂⠴⠾⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⡶⠶⠓⠓⠷⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⣤⣴⣶⣶⣿⢿⠾⢶⣶⣦⣬⣋⠛⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⣾⠟⠋⠁⢉⡞⠁⠀⢀⡼⠟⠉⢻⡿⢿⣦⡐⠻⣷⣄
⠀⠀⠀⠀⠀⢠⡾⢋⣴⣿⠟⠉⠀⣀⡔⠻⠀⠀⠔⠙⠦⣀⠔⠀⠀⠠⡏⠘⢦⡘⢝⢦⡀
⠀⠀⠀⠀⢰⡟⢀⣾⠛⠻⣀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠉⠂⣀⠀⠀⠀⠂⡀⠑⡌⢻⣿⡆
⠀⠀⠀⢠⡟⠀⣾⢿⣆⡀⠉⠒⢄⠀⠈⠐⢦⡠⠊⠑⠤⣠⠆⠀⠑⠤⠀⠀⢀⠎⠠⠈⢿⣧
⠀⠀⠀⣼⠃⢸⣏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠠⠖⠀⠀⡠⠛⠄⠀⡆⠈⢿
⠀⠀⠀⣿⠄⢸⡟⠀⠀⢀⠔⠣⡀⢀⡴⣣⣄⠠⣴⣛⣷⣿⣄⠁⠠⡀⠾⡁⠀⠀⠘⣿⠀⣿
⠀⠀⠀⣿⡄⢸⡇⠀⠰⢇⠀⠀⢀⣿⡀⠈⠛⠛⠻⣿⣉⢉⡻⣦⣄⠈⠀⢌⡢⣄⠀⣼⠀⣿
⠀⠀⠀⢸⡇⠘⣿⡀⠀⠀⠰⢄⡀⠉⠹⠓⢦⡀⠀⠈⠙⢿⣷⠟⠉⠓⢦⡄⠠⡨⠿⣿⢢⡿
⠀⠀⠀⠈⣿⡄⠹⣯⢢⠄⠀⠀⢹⠖⠀⠀⠀⠙⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡁⣰⢃⣾⠃
⠀⠀⠀⠀⠈⢿⣄⠙⠇⠀⣠⠞⠁⠂⠀⣠⠎⠀⢀⡴⠛⠀⠀⢀⠴⠂⠀⢀⢘⡿⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠧⠀⠀⠠⣄⠀⠀⠘⠛⡀⠀⠀⠐⠷⣄⠀⢢⡽⠋⢀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠄⠈⢳⣤⠀⠀⠙⣦⡄⡀⠀⠠⠟⢋⣤⡼⠛⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡈⠈⠙⠛⠋⠋⣀⣁⣤⠴⠞⢋⣥⣤⣴⣶⣶⣶⢤⣄⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠛⠛⣿⠟⠛⠛⣩⡴⢞⣽⠛⠁⠀⠀⢠⠀⠙⠳⣬⣜⡳⢦⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⣹⠂⠀⢠⡞⠁⣤⢴⣾⣩⣷⣿⠃⠀⢀⠀⠀⠀⠀⠐⠀⢻⡟⠏⠶⣿⣷⡀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⡟⠀⢠⡟⠁⠀⣾⣷⣿⡋⡇⣿⠀⠀⠀⠀⢀⢁⣄⠀⠀⢸⣿⡆⠀⠈⡟⢻⣆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣾⠃⠀⣾⠁⠀⣼⣿⡿⣻⠧⣅⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠙⢣⠀⢀⠇⠸⢿⡆⠀⠘⣧
⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⢠⣿⣿⢹⡿⡴⢛⣣⣉⠟⠶⣤⣄⣠⣤⣾⠇⣀⣦⣰⣴⣤⠆⣳⠀⢿⠀⠀⣿⡀
⠀⠀⣴⠋⠀⣠⡤⠶⠤⣄⠀⠀⣿⠀⢸⡇⠀⠸⣿⠃⢀⡾⠛⠉⠉⠉⠛⠲⢾⡉⠀⢹⣷⠟⠉⠁⠉⠉⠙⠳⣟⠃⢸⠀⠀⢸⡇
⠀⣸⠃⢠⡞⠁⠀⠀⠀⠀⠳⠀⢸⡇⠘⣇⠀⠀⣿⢠⡟⠀⠀⣀⠀⠀⠀⠁⠀⢳⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⠀⠀⣸⡇
⠀⣏⠀⢾⠀⠀⠀⠀⠀⠀⠈⠆⢸⡇⠀⢻⡄⠀⠹⣿⠀⠀⠀⠀⣉⠀⠈⠀⠀⢸⣾⡇⠀⠀⠀⠤⢤⠬⠣⡀⢀⣿⠀⠀⢠⣿⠃
⠀⢻⡀⠘⢇⠀⠀⠀⠀⢀⠐⠀⣼⠃⠀⠘⣷⡀⠀⢻⠀⠈⠀⠉⠀⠀⠀⠀⠀⢸⡏⣷⡀⠀⠐⠀⠀⢀⠀⠁⣼⠇⠀⢠⣿⡟
⠀⠈⠻⣆⡀⠈⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠘⣷⡀⠀⠑⣤⣀⠀⠀⠀⠀⢀⣴⠃⠀⡏⠷⣤⣀⡀⠀⣀⣠⡾⠋⠀⣰⢿⡟
⠀⠀⠀⠈⠙⠻⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠈⠻⢿⡶⠖⠚⣿⠁⠀⠀⡇⠀⠈⣝⢙⡉⠉⠁⠀⣠⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠉⠁⠀⠛⠤⠀⠠⠴⠄⠀⠉⠀⠀⢀⣠⢾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⣤⣄⣀⣀⣀⠀⢀⣀⣀⢠⡴⣾⣻⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀
⠀⠀⢰⡚⠛⠉⠁⡀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⡦
⠀⠀⠀⠉⠣⣄⠀⠀⠀⠁⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠖⠋⠉
⠀⠀⠀⠀⠀⣈⣙⣓⣚⡋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣺⠿⠗⠋⠉
⠀⠀⢰⡞⠛⠉⠀⠀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⣀⡠⢴⣲⡯⠗⠛⠉
⠀⠀⠀⠉⢧⠀⠁⠀⠀⢀⣠⡤⠏⢀⡠⢤⣒⡭⠗⠚⠉
⠀⠀⠀⠀⠈⠓⠒⠒⢚⣉⣤⣶⠿⠗⠋⠉
⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠻⠶⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠒⣒⣋⣽
⠀⠀⢀⣼⡿⠋⠀⠀⠄⠀⠊⣰⠋⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣯⠭⠿⠶⠒⠛⠛⠉⠉⠁
⠀⠀⠸⢤⡀⠀⠀⠀⣀⣠⣶⣥⣤⣶⣶⠶⠿⠭⠽⠒⠚⠋⠉⠉⠉
⠀⠀⠀⠀⠾⠿⠿⠛⠛⠛⠉⠉⠁

⠶⢤⠴⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠤⠀⣀⡀
⠄⡘⢀⡇⠼⠒⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⣤⣤⣤⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣈⠉⠙⠎⠙⡓⠲
⣒⣛⣚⣓⣗⣓⣚⡳⢤⡀⠀⠀⠀⠀⠀⣠⣾⢿⣲⡶⠤⠾⠥⢤⣄⣸⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠢⢐⣤⠴⢯
⢀⠴⠒⠞⠛⠳⣦⠉⠓⣽⡄⠀⠀⠀⠀⢿⡞⣩⢂⡰⠶⢠⡢⢦⡰⠈⢗⣼⠇⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣴⠊⠀⠀⣈⡆
⣇⢀⡁⠊⠀⢔⣽⡧⠔⡿⠀⠀⠀⠀⠀⠘⢿⣾⣧⣼⣿⣷⣶⣷⣿⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡙⠻⠶⠶⠶⠿⠷
⡈⠉⠉⠉⠉⠉⢁⡤⠊⠀⠀⠀⡄⠀⠀⠀⠀⠙⣶⠬⠭⣭⡭⠯⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠦⠤⠤⠴
⠛⠷⣶⣶⣶⡾⠟⠀⣀⠀⡴⠒⠋⠀⠀⠀⠀⠈⢻⣦⣀⣀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⡎⢙⡏⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣞⠛⠛⢶
⣠⠶⠦⣄⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣥⠞⣫⣾⠋⣿⡁
⠃⢄⠀⠸⡆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡄⠐⠁⣪⢿⠾⠦⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣋⣡⠉⡀⠜⢙⠉⠃
⠀⠀⣱⢞⣁⣀⠀⠀⠀⠘⡄⠈⠁⠀⠀⠀⢀⠀⢠⠖⠛⠙⣤⣀⣽⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠞⠁⢏⠩⢚⠰
⠛⠚⡱⠋⠀⠈⠙⢦⠉⠉⠁⠀⠀⠀⠀⠠⢂⠀⢾⠐⠀⠀⡼⡇⠀⠹⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣤⣦⣤⣤⡴⠾
⠀⢸⠃⠈⢲⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⢠⡤⠊⠁⠛⡂⢰⡑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⣒⣂⣰⣤
⠀⠘⢆⡀⣸⣂⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟⢺⢂⠘⠀⠀⠀⠀⠹⠇⠷⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢈⠝⠂⠀⠀⠀⢚⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣀⣀⡀
⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣱⢳⢳⢃⡟⣹⢋⠟⡿
⠉⠁⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⠟⠀⠀⠀⠀⠀⠀⢰⣧⢏⢯⠇⡞⣴⢣⢏⠞⣰
⠖⣱⢶⡶⣤⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⣴⣟⡤⠤⢶⡷⠦⠀⠀⣿⡟⡘⡜⡘⣼⢡⢣⠊⣼⡿
⣾⠿⢷⣸⡉⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡤⠚⠉⠹⣿⣶⣾⠟⠁⠀⢠⡞⠀⠀⠀⢰⡏⠁⠙⠁⢰⢣⠣⠃⣼⡿⣱
⣌⣱⡴⣷⣦⣙⣧⠏⠀⠀⠀⣠⣿⠃⠀⠀⣠⠋⠀⠀⣠⣾⠿⠙⢿⣦⣀⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠌⠀⣼⠟⣱⠏
⠈⢹⣷⠥⢿⡶⠀⠀⣀⣤⣾⠟⠁⠀⠠⡾⠿⠤⠶⠞⡿⠃⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⢸⡏⣰⠏
⣶⣶⣶⣶⣶⣶⡾⠿⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣁⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣶⣶⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⢛⠛⣛⡿⠖⠛⢋⣉⡤⠄⢖⣊⣳⡂⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠘⠷⠶⠖⠛⠉⠁⠀⣀⣀⣤⣬⣽⣦⠘⣄⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠛⠛⠻⠷⢖⡤⡒⠋⠉⢉⣒⣂⣠⣬⣧⠘⣦⣤⣄⣬⡍⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣈⣛⣛⣛⠻⠿⠿⠿⠿⣛⣛⣛⣫⣭⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠘⠲⠤⣤⣤⣀⣤⡔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⣧⠈⣉⡉⢁⠀⢀⡀⣀⣀⣀⣀⠤⠴⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⢿⡀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣤⣄⣀⠀⢀⣠⣤⠤⠀⠀⠤⠤⠤⣤⣤⣤⣤⣴⣾⣍⣀⣀⣻⡀⠉⠉⠉⠉⠉⡼⠋⠉⠈⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡿⠛⠁⠀⢠⡰⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⡍⠉⠛⠛⠛⠲⡾⠷⠶⢤⣤⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠋⠁⠀⠀⠀⠀⠀⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣇⣤⡶⠶⠟⣾⠓⠚⠓⠲⢦⡀⠀⠈⠉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⣄⠀⠀⢀⣤⠶⠚⣩⣶⡾⠛⠁⠀⠀⠁⠶⠞⠃⠀⠀⠀⢹⣦⣤⠞⠁⢸
⠀⠀⠀⠀⠀⢠⣶⡛⠋⠙⣇⠀⠉⠉⠛⠛⠛⠷⠶⢶⣤⣤⣤⣤⠼⡧⡙⡂⠜⣋⡤⠖⢿⣿⡟⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠾⠿⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⣷⣽⣿⠞⢉⣤⣴⠋⣹⡇⠼⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠾⣷⣶⣾⣍⣷⡀⣀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠂⣰⢂⡿⠂⠀⠀⠀⠀⠀⡔⠒⠲⠦⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡷⠟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⡜⢀⠀⠈⠣⣄⣀⣀⣀⣀⡀⢀⣀⣴⠏⠀⣴⠃⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣒⣒⣂⠀⠀⠀⠀⠈⠉⠉⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠶⠶⠞⠛⠉⠀⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⢀⡤⢖⡚⠩⠭⠭⣍⡛⣒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡀⢀
⠀⠀⠀⠀⣠⢞⢩⢾⡃⠠⠔⠥⠀⠀⠀⠉⠁⠨⡑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣙⠢⣑⢄⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⡀
⠀⠀⠀⣰⢣⡏⠀⠦⠾⠚⣆⢣⡀⠀⠀⠠⠀⠀⣸⣮⢳⡀⠀⠀⠀⠀⠀⠉⠑⠒⠚⢛⣾⣿⡿⠁⠀⠀⠀⠈⢿⠻⠣⠎⠈⠁⠈
⠀⠀⢠⠇⣿⠁⠀⠀⠀⣠⣿⡘⣿⠶⣤⣤⡤⠚⠿⠙⣇⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⡁⣀⠀⣀⡄⢀⡸⠟⠒⢄⠀⠀⡠⢰⢦
⠀⠀⢸⢰⡇⣀⠀⢰⣯⣨⡼⡈⣷⠠⣿⣿⠀⠀⠀⠀⠨⣹⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⠿⢿⣿⣿⣾⣿⣿⣟⠁⠀⠀⢸⣷⡾⢷⣫⡞
⠀⠀⠸⡄⣿⣿⣤⣾⣻⣟⠒⠽⣯⣼⣿⠇⠀⠀⠀⠀⡖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣭⣭⣭⣭⣤⣤⣶⣶⣾⣿⡿⠁
⠀⠀⠀⢳⡸⣿⣿⣿⢷⣽⣻⣟⣿⣿⣿⡤⡄⠀⢠⡔⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠙⢌⡻⣯⡺⣿⣿⣿⣿⣿⣿⣿⣧⠴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠢⢭⣛⣛⠛⠛⣛⣛⣫⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡀⡀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣷⣿⣯⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣠⡾⠏⠣⢄⣀⣀⡔⠁⠀⠈⢙
⠀⠀⠀⢀⣴⣶⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠞⠻⣶⣧⣄⠀⠀⠀⢠⡑⠒⠂⠈⣀⠀⠀⣀⡜⠏⠋⠀⠀⠀⢀⣾⡳⡄
⠀⠀⠐⢜⡿⣾⡏⠈⢽⣷⣿⣿⠉⠉⠋⠙⠉⠉⠆⠀⠀⠀⣼⡿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣋⡁⠀⢀⡠⠦⠴⡿⠟⣋⠴⠁
⠀⠀⠀⠀⠉⠒⠯⠤⣜⣛⣿⡿⠤⠤⠤⠤⠤⣄⣘⣢⡤⠭⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⠀⠉⠉⠀⠈⠛⠛⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠤⠀⣀⠀⣰⡧⠴⡗⠚⣻⣁⣸⣦⡤⠖
⠀⠀⠀⠀⠀⠀⠤⠴⣿⣚⡽⠛⠁⢸⠀⢠⡿⡆⢸⠀⢰⡇⢰⡇⢈⡽⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣟⣁⡤⢤⡤⢼⠁⢸⠃⢻⣼⠀⢸⡇⠀⠛⠋⢠⠀⠀⢀⠀⠀⢀⡼⣣⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠉⣇⡤⠖⠋⠀⠻⠴⠺⠀⠀⠛⣤⠀⢠⡄⣷⠖⣾⡴⣦⠞⠀⢀⣞⢞⡵⠊
⠀⠀⠀⠀⠀⢀⡤⠾⡏⠀⠀⠀⠀⠀⢠⣀⣿⣠⠄⡟⠿⠿⢹⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣦⢶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢀⣀⣤⣾⡜⠳⣻⠿⠂⠧⠖⠂⢀⣀⢀⣀⣤⣴⠶⣖⣉⣉⣉⠉⠒⢬⡁⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣲⣾⡧⠛⠉⡏⠟⠈⠋⠀⠀⣀⡠⠊⠁⠀⠫⣴⢣⣀⠷⠈⡧⢄⠈⢳⠀⠀⠈⠳⢄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⡰⠂⡏⠀⠸⠀⠀⠀⠁⢀⣠⣴⡖⠉⡱⠁⠀⠀⠀⠁⠙⢗⣭⠷⣴⡳⠌⡇⢸⠯⡉⢳⡀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠑⠞⠁⠀⠀⣀⡤⠖⠋⠁⡟⠋⡻⢤⡃⠀⡔⠒⠂⠉⢂⡜⠁⠂⠀⠙⣞⣠⠷⣄⡹⢸⡣⢚⣶⠤⡈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⡀⢀⡀⠄⠠⡈⠒⠌⠒⢦⣶⣆⡀⡌⠀⠀⠀⣀⣀⠈⢏⡲⠗⠧⣞⠔⣱⠋⡰⣁⠠⢠⠈⠲⡀
⠀⠀⠀⠀⠀⠀⣼⠡⣴⢤⠐⠢⣀⠢⡕⠂⢁⠠⠐⡧⠠⠠⡈⠛⢶⡃⠀⡎⠀⠀⠈⣤⠋⠀⠀⠀⠈⢾⠃⢜⠔⢁⠔⡦⢀⡦⢿
⠀⠀⠀⠀⠀⠀⡟⣆⠀⠸⡇⠦⠀⠂⠒⣈⠠⡄⠰⣄⠢⠀⣴⣦⣶⡌⠑⠧⣶⡄⢐⠁⢠⠄⠐⠒⢢⠈⢟⠳⣪⡭⠞⠋⠁⠀⡼
⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡃⠘⠙⠣⠉⢮⢹⣈⠃⢈⣀⠴⢯⡁⡠⠛⠉⠙⢪⡑⠧⡀⢢⢠⢰⣄⣤⠤⠚⠋⡁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠳⣍⡀⡳⡜⠛⠛⡿⠉⠀⠀⠀⡸⢁⡴⠒⢢⠀⣇⣀⣨⠽⠚⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠉⠳⢤⣀⢸⠁⢠⠊⠑⡄⣇⣸⣠⡤⠜⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⣚⠋⠉⠁⠀⠀⠒⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠁⠁⢀⣀⡤⠴⠒⠋⠁⠀⢀⠀⣠⡀⣴⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠙⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⢠⠟⣷⠁⠿⠘⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⡀
⣿⣯⢭⣟⡛⣛⣛⠛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠋⢉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣎⠻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣟⠋⢍⢢⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⢶⣾⣿⣿⣿⣿⡿⠟⠣⡺⣝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠈⣇⢀⣉⣁⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⣿⣿⡿⣿⣿⣿⢟⣩⣀⠀⠀⣽⣝⢷⣝⠻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢳⣀⣀⣤⣶⣶⢳⣟⣿⣿⣿⠙⠿⠋⣿⣿⣯⣿⣿⣠⣾⣿⣿⣦⠻⣷⣮⡻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠈⠋⢻⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣻⣭⣽⣿⣿⣟⢿⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣜⢿⣿⣿⣿⣿⠿⣻⣿⠿⣛⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣶⣶⣶⣿⣿⡇⣾⣿⣿⣿⣿⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣶⣭⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠴⣾⠋⣽⣹⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠖⢋⣩⠖⠁⠀⠀⣀⠀⣾⣰⡇⡜⣿⢸⣇⠞⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣠⠖⡋⠁⣧⠴⠟⠒⠛⣻⠆⢰⡷⡟⡿⠑⠟⠀⠏⠀⡁⠀⢰⠇⣰⠇⠀⢀⣠
⠀⠀⠀⠀⣴⡯⠖⠋⠀⠀⣧⠀⠀⣠⠞⠁⠈⠙⠚⢠⠀⢀⢠⠀⣤⢸⣷⢛⣾⠞⢹⠀⠀⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠀⣸⠀⠿⠻⠞⣿⣼⠙⠋⣿⠀⠘⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠀⠀⠀⣠⢤⡖⠀⠀⣿⣠⡴⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠋⠁⠀⠀⠀⢀⣀⡠⢤⠔⠶⣒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠛⠉⠁⢢⡗⠀⠒⢠⠙⢆⠈⢲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠊⠁⠀⠀⣠⡄⡰⠒⠾⢭⡢⢤⡊⢀⣠⠤⠃⡠⠗⠒⠐⢸⠀⡰⢀⡬⠔⢊⣉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣄⠎⠲⠃⠈⠁⠀⠀⣀⠓⠂⠉⠒⢤⣠⠊⢀⡀⠴⣒⠡⠶⠵⢍⠀⢎⢹⣂⠇⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠃⡄⠀⠀⠀⠀⠀⠀⠤⠏⠁⣨⡤⠒⠂⣏⢙⠤⣠⠊⢠⠂⡏⠌⡲⠑⣤⣈⡤⠖⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠐⠀⢀⣀⣶⣲⠃⠀⠀⡇⢀⣀⣰⣾⠄⠑⢩⠛⠲⣝⣓⣨⠴⠚⠉⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠳⢤⣀⡔⡉⠀⠀⠀⣱⠼⠾⣔⠋⠀⠀⠈⢣⣀⣠⠷⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠙⠧⣄⣀⡞⠠⠀⠀⠈⣧⣠⠴⠒⠉⠁⠀⠀⠀⠈⠁⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠈⠉⢛⣒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣈⣁⣀⡤⠴⠚⠉⠁⠀⠀⠀⣀⡴⡴⠖⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⢀⠤⠔⠒⠒⠢⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⡀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠒⠢⠤⠋⠙⣦⣀
⠀⡠⠔⠋⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠁⠑⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠜⡠⠔⠒⠒⠠⠄⣶⠤⣑⠂⣄
⠸⣀⠀⠀⢠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠃⠀⠨⠀⠀⠀⡠⡔⠋⠀⠀⠂⠈⡹⠯⠶⡄⡀
⠀⠈⠑⢢⢄⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠂⢡⠁⠀⡄⠀⠂⢇⡔⠉⠀⠀⠀⢋⠤⠒⠉⠠⠄⠀⢹⣌⡑⠢⣄
⠀⠀⠀⢸⠀⠉⠒⠤⡈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⠤⠀⠀⠘⠢⡀⠀⠄⢀⣠⣦⡲⠀⡀⠂⠁⠀⠈⢀⡀⠄⠊⠁⣠⢹⠀⠀⠉⠂⢄
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠑⠢⢌⠑⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⡋⠀⣰⠥⠴⢦⣤⣌⡂⢁⠈⠢⢄⢩⣴⡶⢶⠵⣄⠑⢀⣞⡉⠀⠂⠀⠀⠁⠀⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠉⠒⠄⡉⠒⠀⠒⠊⠀⡰⠧⢭⣚⡥⢤⣥⣇⣀⣼⠚⠉⠉⠂⠆⠀⠀⢰⠁⠀⠀⠙⠉⠁⠙⢢⣀⣀⠀⠀⣀⢇⡠⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠈⠑⠠⢀⠀⠀⠑⢤⢾⡁⠀⠀⠀⠀⠉⠛⢦⠀⢀⠀⢠⣄⠠⡀⢀⠠⠴⡁⠀⠀⠀⠈⠂⠈⡉⠄⠊⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠉⠒⢄⡀⠉⠃⠀⠀⠀⠀⢀⡀⠜⣀⣀⢠⣌⡨⠏⣘⠁⡀⢠⠈⠁⠀⢀⡠⠒⠉⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠁⠀⡎⠀⢀⠀⠀⢙⡄⠃⠀⠓⠁⣀⠤⠊⠁⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠁⠢⢄⡀⠀⠃⠐⠀⠀⠀⠈⠃⢀⡠⠔⠈⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠈⠐⠤⣀⠀⠀⣀⠤⠂⠁⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⣀⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⡀⠀⣐⣲⣶⡒⠠⢀⠀⠀⠀⢤⠤⠦⠴⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢄
⠀⠀⠀⠀⠀⠀⠈⠴⠀⠂⠈⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠡⠆⠐⠈⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣶⣍⣩⣥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖
⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠰⠂⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⣴⠋
⠀⠀⡴⠟⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣷⣶⡋⠀⠀⢠⡏⠀⠀⠀⠀⣠⠾⠁⠀⢀⣀⢀⠄
⢀⡾⠃⠀⢀⣔⡑⢂⣠⣴⠀⠀⠀⠀⠐⢤⣤⣤⣾⣧⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣀⡌⠐⣀⣴⡆⠀⠀⠀⠀⠦⣤
⠀⠁⠀⠀⠀⣿⣿⡏⢩⣿⠀⣀⠀⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠉⣽⠇⢀⡀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠈⣷
⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠶⢬⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠸⢦⣿⠀⠀⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠈⢷
⠀⢤⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⣠⠀⠀⢸⡗⢦⣬⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠘⠃
⢠⣶⡶⣃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠠⠀⠘⢧⣸⣿⣋⡔⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣞⡀⠀⠀⠀⠘⠃
⠸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠉⣷⢤⣇⣴⣴⠀⠀⠀⠀⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣻⣿⣿
⠀⠀⡀⠀⠠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢄⡃⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴
⠀⠒⢠⠶⠦⠶⡎⠀⠴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⠂⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠂⠴⠦⠰⢶⠁⠠⠄⢠
⠐⠻⠇⢀⣛⣁⣼⣞⣲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠌⠖⠀⠀⠀⠀⢰⣄⡈⣋⡀⠿⠚⠿⠀⣈⣁⣤⣷⣓⣾⡿
⢀⣉⣤⢾⣿⣷⡟⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣨⣿⢦⣀⣈⣡⡴⣿⣿⣾⠛⠛⠋⠁⠀⠀⠀⠀⠀⡀
⢸⣿⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢼⣿⣿⣿⡷⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⠉⠀⠀⠀⠀⠀⢰⣤⠄⡀⠀⠀⠀⡀⠈⠻⢿⠿⠟⠥⣀⠀⠀⠀⢤⠤⠤⠴⠠⣤⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠰⠁⠂⠈⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠆⠰⠈⠀⠀⠀⢾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣭⣉⣩⣭⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡧
⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡄⠰⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣤⠏
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣴⣶⣴⣶⣴⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢨⡿⠀⣰⡿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠃⢠⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣼⠇⢠⡿⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⢠⡿⠃⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡟⠀⣾⠗⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀⠠⠄⠒⠂⣈⣉⠉⠥⠀⢀⡿⢠⡿⠀⣼⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠰⠁⠀⠀⠞⠁⠀⠀⠀⠀⠀⣾⠃⣾⠁⣰⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢢⡀⠀⠀⠀⠈⠲⠄⣀⠙⠲⢄⠀⠀⠀⣸⠏⣼⠇⢠⡟⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⡙⠫⣝⢷⣦⣀⣀⣩⣭⣭⣴⣦⣤⣤⣦⣤⣶⣤⣤⣰⡟⣰⡏⢀⡿⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⢡⣤⡙⢿⣍⣉⣳⣈⠻⠿⣍⡠⠤⣄⠠⡤⣘⠀⠡⣄⠀⢈⣿⢡⡿⠻⣿⢁⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⡘⠓⢽⡿⢧⣌⠁⢞⠈⢷⠀⠈⠀⠀⠈⢄⡀⠀⠀⣸⠃⡼⠁⡼⢁⣾⠋⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⣹⡿⠿⠷⣶⣯⣉⡑⣭⡀⢸⡶⢄⠀⠨⠀⢀⠁⢰⣶⣧⣼⡧⣾⠷⢾⣷⣶⣤⣄⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣠⣾⠋⠁⠀⢒⡂⠀⠍⠉⠻⠿⠛⣷⣶⡏⡐⠀⠈⣀⠜⡋⠀⠌⠀⡤⠀⣤⣞⣉⣍⢙⠻⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣾⡯⠄⠀⢾⡶⣤⣥⣤⣤⣄⣘⠆⠈⠠⣼⣦⣑⣤⠞⡡⠀⡠⢀⠔⡠⠄⠀⢿⣻⡿⢻⣿⡷⠾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⡟⢻⠿⣯⣽⡇⢀⠀⠈⠉⠙⣯⡀⢢⡒⢡⣾⡿⡡⢊⡤⢊⣤⡪⢶⣤⣠⣴⣼⣿⠟⠻⣿⠀⣄⣞⡷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⢧⣎⢘⣷⠐⠚⢇⡀⠀⠈⢻⡅⣰⡿⢋⠜⡰⣡⢜⡠⢋⠔⢉⡿⡁⠠⠁⣬⠆⢘⣿⣷⣎⣁⣠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠷⢶⣾⣦⣿⣄⣐⣂⢻⣀⡐⣾⡷⣛⢖⡡⣚⢚⡵⣿⣷⣥⣶⣽⣇⣵⣾⣯⣷⣶⠿⠿⠟⠛⠋⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠳⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⠶⠶⠿⠛⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣮⣦⣤⣀⣀⣀⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣯⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣿⣿⣿⣿⠟⢉⣉⣈⣹⡿⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⣿⣿⣿⣤⣿⡇⢺⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠘⣿⣿⠁⢠⣾⣿⠿⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⣿⣿⣿⠀⣿⡇⢻⡇⢸⡇⢸⢿⡧⢾⡏⠴⣦⣽⣧⠈⣶⣾⣿⡿⠁⢰⣿⣿⡄⠘⣿⠀⠸⣟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣿⠇⣿⡃⢸⡇⠘⡇⠀⠊⠁⢸⡟⠳⠖⢸⣷⠀⠿⢿⡿⢧⣰⠿⠟⠛⠻⠀⠘⡧⣀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢿⣿⠿⠋⠁⠂⠀⠐⠒⠁⠈⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠶⠋⣠⢞⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⣋⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠋⣠⡶⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠉⣤⢞⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠷⣄⡀⡀⠀⠀⠀⣀⡴⠞⢁⡴⢚⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣀⣉⣛⣛⣛⣋⣉⡤⠶⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⠉⠉⠉⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⢉⣉⣉⣉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣒⣚⣓⡒⠦⣤⡀
⠀⠀⠀⠀⣠⠞⢁⣤⣪⡬⠶⣶⠶⡦⢯⣷⣤⠈⠳⡀⠀⠀⠀⢀⡔⣩⡴⠿⠛⢣⠹⠇⠛⠛⠲⣍⠳⣄
⠀⠀⠀⣰⠃⣽⣿⡿⠹⡇⠀⡇⠀⠇⠀⡄⠙⢷⡄⠙⡄⠀⢠⢏⣾⠧⠤⠐⢀⠀⠀⠀⠂⠘⠀⠨⠷⠙⣆
⠀⠀⠀⡇⢰⣿⢿⡵⢜⡷⠔⣤⣴⡅⣠⢡⣠⢼⢻⠀⢹⢀⡏⣾⣁⣤⠀⢂⡠⠀⠠⣄⢲⡄⢠⡠⠔⠢⢸⡀
⠀⠀⠰⡇⢸⡇⢨⠀⠸⠀⠈⠁⢸⠋⠈⠋⢹⠈⠁⠀⢸⢸⡷⣿⡄⠘⠀⢸⠀⢠⣴⡟⠈⡅⠀⡀⠠⠀⠘⡇
⠀⠀⠀⢧⠈⢧⡲⢀⣶⢀⣾⣀⡼⣀⣼⣤⣜⢰⡘⠀⣾⠸⣇⠟⠂⠀⠁⠀⠀⠻⣏⣿⠀⢀⡠⠤⠀⢷⢰⠇
⠀⠀⠀⠘⢧⠈⠿⠑⡟⠑⡗⠉⡖⠋⡙⠋⣙⠝⢁⣼⠃⠀⠹⡌⢀⠀⢀⠠⠆⠀⢟⠉⠁⡀⡀⠀⡦⢃⡞
⠀⠀⠀⠀⠈⠳⣄⡉⠓⠀⠧⠀⠧⠀⠗⠂⢀⣴⡿⠃⠀⠀⠀⠻⢦⡄⢤⣄⠀⡃⠈⠀⢈⣅⣡⢀⡵⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣿⣓⣐⣛⣨⠭⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠠⠀⠂⢄⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⠠⠂⠁⠀⢀⡠⠖⠃⠂⢄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⡀⡀⣤⣦⣀⠀⡤⠒⠁⠀⠀⢀⠠⠚⠁⠂⠄⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⡄⣤⣤⢤⣀⠈⢁⡬⡝⣦⣤⣤⡀⠂⠁⠀⠀⢀⠠⠊⠉⠑⠀⡀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⢠⠔⠋⠁⠀⠀⢀⣤⣤⣤⣀⠈⠁⡬⡜⢶⣶⢧⣅⠈⠁⡀⡥⡤⢄⡀⠊⠀⠀⠀⢀⣠⡞⠉⣹⡤⠠⡀⠀⠀⠉⠓⢤
⠀⠀⠀⢸⠀⠀⠀⠀⠰⠋⠉⠛⢉⣽⣧⣄⣡⡄⠀⠁⠀⢈⢀⣺⠉⠀⠀⠀⠈⡆⠀⣠⡞⠅⣹⠭⢾⠿⢀⣴⠷⠉⠁⠀⠀⠸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠋⠁⡌⠗⠚⠲⢤⠋⠀⠈⢱⠒⠀⠨⠤⣕⢤⣌⣩⣞⣧⢀⣼⠗⠋⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠂⠀⠀⢀⡀⠇⣀⡄⠘⠠⢀⠀⠀⢢⠤⠙⢩⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠈⠉⠁⡠⢒⣂⠳⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠟⠀⠀⢀⠁⠀⠀⠀⠙⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡖⠀⠀⠀⠀⠁⠀⠈⠃⠐⡏⠀⢘⠆⠀⠁⢲⠀⠀⣀⠇⠀⢠⠞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠃⠀⡆⠰⢀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠘⢧⡀
⠀⣀⠀⠀⠠⠯⢸⠢⢠⢠⡈⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠐⠓⡀⠀⠈⠁
⠀⡁⣀⡀⠀⠀⠙⠱⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⢀
⠐⢻⠵⠂⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠄⠁⠀⠐⠀⠁⠀⠀⠀⠰⣁⠈⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⣀⣀
⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠦⣵⢿⡷⣯⣤
⠀⣏⠀⢳⣔⡀⠀⠀⠀⡀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⣂⡿⢿⣟⡶⡿⣗⠈
⠀⡏⠻⠾⠏⡦⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡽⠷⣴⠷⡍⡛⠒⠀⠆
⠀⡇⡂⠘⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣄⢠⣾⠧⢓⡀⠀⠀⡤
⠀⠁⠑⢀⠉⢀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣜⠹⣀
⠠⡆⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠔⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠁

⠀⠀⠀⠀⠤⡤⢀⡀⠀⠀⠴⠶⢤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠰⢤⡤⣀⣀⢀⠃⠒⠒⢦⢈⠗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠘⢩⠏⡧⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠠⣵⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠃⠀⠀⣠⠞⠀⠑⢬⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠆⠀⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀⠉⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⢀⣿⠗⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⣀⠀⠀⣠⠴⢥⣌⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣆⣀⡀⣸⠵⠓⠲⣄⣹⢾⠈⠉⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⠃⠀⠀⠀⡽⣽⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠨⢤⡍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠠⠀⠂⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣷⣿⣧⠀⣀⠀⢷⠃⠀⠀⠀⠀⡀⠄⠀⠉⡁⠀⢃⣬⡁⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠁⠀⠉⠀⠁⠀⠀⠀⢀⠈⠀⡄⠀⠀⢰⣦⡼⡿⠛⠉⠀⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢰⣶⣴⠿⠛⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠒⠠⠃⠒⠦⠿⠿⠿⠿⠛⢷⣝⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠲⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣠⣶⡶⣿⣿⠿⠿⠛⣿⣶⣶⣯⣉⠻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⣿⠋⠁⢈⡴⠃⠀⣀⡜⠛⠁⠸⢟⠿⡷⢌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢠⡾⢁⣾⣿⠋⠀⠐⡴⠊⠑⢤⠐⠁⠉⠲⡎⠀⠀⠘⠃⠈⠳⡌⢮⢧⣄
⠀⠀⠀⠀⠀⢠⡟⢠⣿⡇⠈⠳⣄⠀⠠⡠⢀⠀⢁⢤⡀⠀⢈⠶⢄⠀⠀⠉⠦⡨⠆⢻⣿
⠀⠀⠀⠀⠀⣿⠀⣾⠋⢿⠂⠀⠈⠑⠀⠀⠀⠙⠁⠀⢈⠟⠁⠀⣀⠉⠀⢀⣔⠀⢈⠈⢿⡆
⠀⠀⠀⠀⢠⣯⢀⣿⠟⠁⠀⢠⡔⠀⠀⣠⢀⠀⢀⡴⢦⣤⣀⠜⠁⠀⣴⠃⠈⠁⢾⡆⢰⡇
⠀⠀⠀⠀⠸⣏⠈⡷⠀⢠⡜⠁⠈⡠⣾⠀⠻⠷⠿⣶⠾⠛⢿⣄⡀⠑⠈⡣⣀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣿⡄⠀⠈⢢⡀⠈⠻⣷⠦⣀⠀⠈⠻⢿⣷⡾⠋⠢⣄⡜⠉⢻⢶⡯⣸⠇
⠀⠀⠀⠀⠀⢹⣇⠘⣟⢤⡄⠁⠈⢳⠖⠁⠀⠈⠛⠀⠀⣠⠋⠀⠀⠀⠈⠀⠀⠃⡼⠡⡿
⠀⠀⠀⠀⠀⠀⠻⣧⠘⢏⡀⣠⠞⠁⠀⠀⣠⠃⠀⣠⠔⠁⠀⢀⣴⡂⠀⣀⢸⡟⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⠧⠀⠀⠠⡄⠀⠀⠛⢃⠀⠀⠈⠻⢄⡀⣺⡿⢋⣴⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠤⠈⣳⣄⠀⠈⢳⡤⣀⠀⠠⠟⣉⣤⠟⠋⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⣤⣀⣈⣉⣉⣉⣠⣤⡶⢞⡛⣭⣴⠶⠶⠶⣶⣖⠤⣄⡀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠉⠉⣹⠟⠋⠉⣥⣶⣋⡼⠋⠀⠀⠀⠢⠀⡉⢳⣶⣿⢷⣦⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣿⠀⢀⡾⠁⠘⣶⣿⡷⡿⢿⠁⠀⠀⠀⠀⡀⠀⠁⠈⣷⡝⠘⠻⣿⣆⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣸⠇⠀⣼⠁⠀⣼⣿⣿⣇⠇⣸⠀⠀⠀⠀⠀⠘⠢⠀⢀⡟⡇⠀⠀⡇⢸⣧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⣿⠀⢰⡇⠀⢸⣿⡿⣼⣏⡷⣌⠷⣤⡀⠀⠀⠀⢀⣴⠊⢁⢉⡃⡐⡃⢾⠹⣇⠀⠘⡇
⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⠀⠀⠀⣿⠀⢸⠁⠀⣾⣿⠃⢃⣮⠶⠾⠾⢥⣍⡿⠟⠛⣿⣩⠶⠟⠛⠳⠾⣥⡶⡄⢻⠀⠀⣿
⠀⠀⠀⣼⠃⣠⠞⠉⠁⠈⠉⢆⠀⢻⡀⢸⡅⠀⢸⡇⣰⠏⠀⡀⠀⠀⠀⠀⠙⣆⢠⡟⠁⠀⠀⠀⠁⠀⠀⠹⡄⠘⠀⠀⣿
⠀⠀⢰⡗⠀⡏⠀⠀⠀⠀⠀⠈⡄⢸⡇⠈⣇⠀⠘⣷⡏⠀⠀⠈⠐⡀⠀⠀⠀⣽⣾⠀⠀⠀⠀⠀⣀⠤⠀⠀⣿⠃⠀⢸⣿
⠀⠀⠈⣇⠀⠳⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⢹⣆⠀⠸⡇⠀⠈⠁⠉⠀⠀⠀⠀⣸⢻⣆⠀⠤⠤⠚⠁⠀⠁⣼⡏⠀⢠⣿⠇
⠀⠀⠀⠙⢦⡀⠈⠒⠀⠀⠈⣠⡾⠃⠀⠀⠀⢻⣆⠀⠙⢤⡀⠀⠀⠀⠀⢀⡴⠃⢸⡟⢦⣀⠀⠀⠀⣀⣼⠋⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⢿⣶⡖⠒⡟⠁⠀⢸⠅⠀⢉⡛⣏⠝⠉⠀⣀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠈⠁⠀⠓⠂⠀⠜⠒⠂⠈⠁⠀⢀⣠⢾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠞⠛⠙⠉⠉⠉⠉⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡠⣤⡴⠶⠒⠒⠶⠶⢤⣀⡀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⢀⣴⡾⣋⡠⣶⡶⣾⢸⠿⢷⡖⣶⣦⣝⣳⢤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠰⣿⣶⣯⢼⡿⢿⣷⠀⠀⢸⢸⠀⢈⠃⠀⠋⣽⢸⠿⣿⣦⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠀⢠⣿⣷⣿⢸⠀⢸⡟⠀⠁⡾⠀⠀⢸⠀⠀⠀⡟⠀⠀⢹⢹⣷⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢹⡆
⠀⠀⠀⠀⢠⡏⠀⢀⣿⣿⣋⡿⡲⣄⢶⢳⠄⢠⡟⣀⣠⣬⠖⠀⠀⢧⠆⠀⡞⣸⠹⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⢸⣿⡏⠿⣻⠋⠉⣦⡵⠋⠃⣈⡵⢍⣿⠟⣢⡺⡴⣗⡲⡞⢨⡂⢹⡆⠀⢸⡇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⢠⡇⠀⠀⣿⠀⠀⢸⠁⠀⠀⡟⠏⠀⢸⠹⠁⢻⡇⠊⠉⠀⡇⠀⢸⡇⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⡇⠀⠘⣯⠀⢸⡀⠀⢠⡏⠀⠀⣾⠀⠀⠀⣧⠀⠀⣸⠀⠀⢀⡇⠄⠀⡰⠀⠀⢸⡇⢠⡾⠁⢀⡤⠤⠤⢤⡀⠠⢸⡇
⠀⠀⠀⠀⠀⢻⡄⠀⠹⣤⡘⡃⢄⣸⣅⢄⣨⣽⡅⢀⣤⢱⣀⣐⡟⢧⡤⣨⡁⢞⠃⠇⠀⢠⣿⢣⡏⠀⡴⠋⠀⠀⠀⠀⢙⠄⠸⡇
⠀⠀⠀⠀⠀⠘⣷⡀⠀⢻⣧⡝⢪⡽⡽⠦⣰⣿⡷⠟⠛⠛⠛⠛⠿⠿⠿⢿⢶⣯⡞⠀⢠⣿⡟⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠙⣇⠀⣼⠾⠛⢋⣡⣴⣶⡾⢻⣿⡿⢿⣿⣶⣤⣉⡛⠿⡷⣿⡟⠀⠘⣇⠀⠳⡀⠀⠀⠀⠀⡠⠁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣨⠟⠁⣴⣾⢿⢟⡟⠀⠀⡼⠛⠀⡀⠛⠂⡾⠀⠙⠶⢌⠲⣿⣷⡀⠙⢷⣀⠈⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⣠⣾⠏⠀⠀⣾⠁⠀⡼⠉⠒⠴⢀⠀⠀⠀⠀⠓⠠⢌⠃⡌⢻⣷⡀⠀⠉⠛⠲⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣰⣿⠟⠂⢤⡞⠀⠉⠒⠄⢀⡀⠀⠀⠌⠑⠢⡄⠀⠀⣌⠀⠀⣄⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣸⡿⠿⣀⠀⠀⠈⠰⠠⢤⣀⠋⠉⠓⡞⠀⠀⣴⠀⠀⡼⠁⠉⠐⢿⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⣧⡀⠈⠁⠒⠴⠀⠀⠀⠁⠀⠀⣌⣠⣤⣠⠂⠠⣘⠓⠤⣀⡀⠀⢿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⣿⠉⠟⠀⠀⠀⠀⠀⢀⡆⣄⡠⣾⣭⣾⠟⠻⢦⣤⣀⠀⠈⠊⠉⣻⢿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⡞⠁⠀⠠⠋⠂⢀⣜⠈⠛⠛⠛⠛⢶⣶⣾⣷⡏⠈⠙⠻⠁⠀⠁⢰⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⡧⠀⠰⢧⡀⠀⠐⠻⠿⡶⠢⣤⣠⠀⠀⢈⡟⠀⠀⢀⠀⠀⠀⠾⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢻⣦⠀⠀⠈⠗⠠⢤⡤⠁⠀⠀⠉⠀⢀⣼⠀⠀⢀⠾⠁⢂⣾⡞⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠻⣗⡰⡖⠀⢀⡼⠁⠀⠀⡼⠀⢀⡾⠁⠀⠁⠛⠒⠤⣤⡟⣁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⢆⣀⡼⠁⠀⠀⣌⠀⠀⠈⠁⠲⢤⣀⢀⡀⠔⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣈⠙⠂⠀⠀⡀⠉⣲⣦⣀⣤⠾⠃⣉⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⡒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣷⣴⡁⠔⠐⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⢀⣼⢳⣒⡭⢛⡷⢺⣿⡟⢸⢿⠃⠀⠀⠀⠠⠐⠁⠀⠂⢀⡠⠄⠤⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⡴⣽⣺⣎⢻⣭⠏⠑⠤⣠⣇⠿⠿⠶⠤⠤⣀⠁⠀⡀⣄⡤⠊⠀⠀⠀⠐⡀⢠⠀⠈⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠐⠐⠉⠁⠀⠈⠓⠳⣽⡗⠣⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⣈⣧⡖⠉⠠⠁⠀⠀⡀⠐⠂⣁⡀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⡠⠒⠁⡀⠐⠀⠂⠀⢀⣄⢠⠬⡁⠂⢇⣀⠀⠀⠀⠀⠀⠠⣠⠊⣠⣤⣤⣈⠃⠤⡆⠁⠀⠀⠀⠀⠙⠀⠀⠇
⠀⠀⠀⠁⠀⠀⡄⠁⠀⠀⠈⠁⣾⠆⠀⢧⠘⠚⣀⠇⠀⢀⣀⠉⠂⢀⡀⠀⠀⠃⠀⠈⠀⠀⠉⠀⠀⠈⡄
⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠓⠊⠀⠀⠀⠈⠂⠰⣆⠀⠀⠀⠀⠀⠶⣛⠀⢠
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⡀⠀⠸⡱⠀⠀⠀⢀⠀⠀⠀⡤⠒⠒⠦⡀⠔⢢⠀⠀⠈⠢⣐⠲⠶⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠣⠞⡵⠀⡸⠈⠁⠀⠀⠀⠀⠀⠙⠈⣁⠄⠂⠁⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⠠⠴⠀⢉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡤⠖⣚⣋⣉⣉⣉⣁⣀⣀⣤⣤⣬⣭⠭⠭⠭⠭⠥⠤⠤⠤⠭⠭⠭⠭⠭⠽⣷⣶⣤⣀⡀
⠀⠐⣏⠙⢛⣻⣿⣿⡿⠿⠿⠿⠿⠿⠭⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⠥⠤⠤⠤⠤⣤⣬⡉⢧
⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠟
⠀⠀⠀⠈⠲⠿⠶⠒⠒⠒⠶⠚⣶⣄⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⡶⢄⡤⠶⢶⠻⠋
⠀⠀⠀⠀⢀⠀⣨⠿⢟⣿⠿⠷⢿⡿⠯⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⠝⠋⠀⠂⢸
⠀⠀⠀⠀⡾⡜⢡⠖⠉⠀⠀⠀⢸⣷⠃⣀⡬⠓⢦⠀⠀⠀⠀⠀⣠⠔⢋⣩⠽⠋⠁⢠⣤⢀⠀⢸⡷⣄
⠀⠀⠀⢰⢇⣷⠃⠀⠠⠴⠶⣦⢼⠿⠋⠀⠀⠀⠈⢳⡀⠀⠀⣴⣧⠴⠋⠁⠀⠀⠀⠈⠁⠘⠃⠘⡇⠀⠙⢆
⠀⠀⠀⣸⢸⡇⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠚⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠃
⠀⠀⠀⡏⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⢸⣠⠾⠃
⠀⠀⠀⡇⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡤⣴⡄⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⠦⢼⣿⡆
⠀⠀⢸⡇⡏⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣹⣍⡉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣠⣿⣤⣼⢸⠁
⠀⠀⠀⢧⢧⡀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⣿⠯⣙⠓⠒⠚⠛⠛⣉⣭⣿⣟⣛⠻⢧⣤⣄⣸⣿
⠀⠀⠀⠈⢷⠬⣝⣛⣛⣓⣒⣒⣒⣒⡿⣺⣥⣄⡏⠈⠳⠈⠉⠓⣖⣚⠉⢁⡼⣍⣛⣿⢻⡽⢯⣉⡏⡧
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠉⠉⠉⢸⣿⠁⠘⢿⣲⣠⣶⣤⣴⣚⣁⣘⣞⣉⣀⣉⣩⣯⠬⠤⠚⡹
⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣀⣀⣀⣘⣋⣀⣀⣀⣀⣉⣀⣀⡀⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⢒⣛⣛⣶⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⣋⣉⣭⣤⡶⠾⠟⠛⠋⢉⣙⣯⡳⣝⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢲⠞⢁⣴⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠼⠳⠽⠟⠛⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⢉⣀⣀⡴⠃⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⡪⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠿⣄⠀⠀⣠⣖⠋⠀⠉⢑⣲⣾⣆⠀⢀⡀⠤⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠊⠉⠀⢀⡠⠝⢳
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠛⢲⡏⠉⠛⠳⣾⡿⠟⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠉⠁⢀⣀⡤⠴⠒⠊⠉⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢸⠃⠀⠀⠀⣿⠤⣄⣀⣀⠀⠉⠁⠒⠀⠠⠤⠐⠒⠉⠁⢀⣀⣤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣝⣲⢶⡾⣶⣦⣄⠀⣿⠀⠀⠈⠉⠛⠛⠶⠶⠦⠤⠤⠴⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⢒⣋⣭⢴⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠻⣇⣤⢄⢹⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠖⢚⣋⣭⢴⠶⠟⠛⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡄⠀⡏⠰⠜⢸⣿⡯⢭⣙⡓⠲⠤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡶⠶⠞⢛⣋⣥⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡿⡇⡇⠉⠙⠛⠶⢶⣤⣭⣉⣉⣉⣩⣭⣤⡶⠾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠠⢄⢸⡿⡇⡇⠁⠒⠠⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⠀⠘⢮⣊⣼⠟⠃⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡉⠒⠠⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣈⡉⠒⠠⢄⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⣟⠟⠀⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠐⠀⠀⠈⠁⠀⠀⣄⣀⠀⠂⠈⠉⠀⠈⠁⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢰⣆⣠⣀⢈⣉⣁⣤⣄⣈⢀⣺⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣛⣽⣿⡄⠀⠀⠀⠀⠘⠛⠻⢃⣬⠉⢙⡛⠛⠉⠜⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠋⠉⠛⠁⠀⠀⠀⠀⡆⠀⠀⣤⡾⠛⡾⣿⢿⣿⠿⣷⠀⠀⠈
⠀⠀⠀⠀⣄⣰⠐⡠⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⢦⣆⣾⣶⣾⣴⣦⣴⡄⠀⠠
⠀⠀⠀⠀⠈⠉⠉⠳⠮⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⡉⠉⠉⠛⠭⠯⣉⡙⠁⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣿⣷⡼⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠠⠀⠮⠽⠿⠄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠱⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠲⣦⣖⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢉⡞⣳⣛⣻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠫⢠⣥⣼⣷⢚⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⡁⠀⠀⠀⠀⠀⣰⣾⡯⣽⣿⣧⣴⡀
⠀⠀⠀⢀⣴⡀⠂⢀⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⣤⢀⣄⡀
⠀⠀⠀⠀⠙⠛⠃⠭⠀⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠩⠿⠿⠏⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠠⠀⠀⢀⣀⣠⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⢿⣿⢵⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠷⠶⠒⠛⠁⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦
⠀⢀⠀⠀⠠⣰⡏⠡⢄⡅⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡶⠶⠶⠆
⠀⠀⠁⠀⠀⠀⠁⠙⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣄⠤⣄⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⡦⠛⢉⣠⡴⠋⣀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠱⠟⠐⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⣹⠀⠴⠻⠯⠃⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⠂⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣄⠀⠀⢀⡀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠁⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⡈⠀⠀⢸⢷⣔⣂⣐⢶⣉⡫⣥⣾
⠀⠀⠀⠄⠀⣀⣤⣨⣧⡤⠀⠀⠀⠀⠀⢀⠆⠐⢦⠀⠀⢀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠉⠒⠉⠉⠛⢋⡁⠁
⠀⠀⠀⠀⠒⠈⡞⠯⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠛⠡⠀⠀⡹⠖⠲⠾⢾⣧⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⣂⠀⣀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢀⢀⠀⠀⠀⠀⠀⠀⡐⢈⠁⠶⠡⠠⡄⠂⠀⠀⠀⠀⠀⠀⠐⠓⠐⠀⠒⣲⠂
⠀⠀⠀⠀⢐⡄⠀⠂⠀⠈⢂⠀⠀⠀⣉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⡄⣀⣀⠉⠀⠀⠆⠉
⠀⠀⠀⠀⠀⡙⣄⣠⣰⣤⡤⠷⠒⠚⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠞⣈⣭⣷⠇⠁⡂⠀⠀⠀⢀⠄
⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢴⡀⠀⠀⠀⠀⠒⠾⠀⣠⣾⣯⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠐⠢⢄⡀⠀⠈⠉⠀⠠⠀⠀⠈
⠀⠀⠐⠲⠊⠀⠀⠀⠀⠀⠀⠠⠀⠘⣢⠤⠠⠀⠐⠀⠀⡀⡀⢠⣆⠀⠀⠀⠀⠈⠑⠪⢄⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠒⠀⠒⠉⠀⠐⠀⠀⠉⠃⠀⠀⠀⠀⠘⠤⡀⠂⢀⣶⠈⠀⠀⠈⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⢀⣠⠤⠀⠒⠒⠒⠒⠂⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠃⠀⢨⡄
⠀⠀⡀⠋⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⡀⢳⡄⢀⠀⠨⠤⠴⠂⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠤⢸⠦⠄⠀⠀⠀⠀⡟
⠀⠀⡕⠀⣤⡶⣞⠿⢭⢵⣿⡆⠤⠤⢴⡚⡏⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠙⠲⢵⣛⢩⡙⢶⠾⠵⠞⣚⣤⠟⠉⠁⠀⠀⠀⠀⢀⠈⠀⠐⠘⡇⠐⠈⢉⠀⠠⠀⠀⠀⠀⠀⠀⠑⢄⣀
⠀⠀⠀⠀⠠⡀⠀⠉⠙⠋⠉⠉⣁⡄⠈⠀⠀⠀⠑⠀⠀⠉⠂⠀⡤⠚⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⢄⣀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⠶⣏⠈⢻⣖⣚⣛⣛⣛⢩⣉⣭⣭⣿⣷⠶⠖⠛⠛⣷⣎⢧⡀
⠀⠀⠀⠀⠀⣿⢡⣶⣶⣾⡉⠷⣔⠊⢍⡚⠻⣿⣿⣿⣿⡎⢿⣿⠟⢁⣠⣴⠶⠚⠉⠛⢻⣧⣳⡀
⠀⠀⠀⠀⠀⢻⣆⢿⡗⠀⠙⢦⡀⠙⣄⠙⣄⠹⣽⣽⣶⣷⡞⢿⣷⠏⠀⣀⣀⠤⠀⠂⣺⣿⡷⠻⣄
⠀⠀⠀⠀⠀⢸⣿⡌⣧⠀⠀⠀⠻⣄⠘⡆⠸⣦⠿⠿⠿⠿⢟⣘⣛⣃⠈⣭⣤⡴⢲⡶⠶⢾⣿⣶⡙⣦
⠀⠀⠀⠀⠀⢸⣿⣷⡘⢒⣂⣠⣤⡭⢤⣶⣶⠶⠖⡻⠟⠛⣩⣌⡙⢿⣷⡹⠁⣇⠀⢿⡟⠛⠛⣻⣿⣜⢧⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣧⢹⣿⡉⠐⣝⡦⠈⠀⠐⠮⠁⠀⣀⠠⡅⠀⣠⣌⠛⢄⠸⢦⡈⠻⣿⣛⣉⣉⣽⡮⠿⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⢻⣿⣦⡀⠀⣼⠃⠄⢂⣀⠘⠽⢲⣴⠦⠀⢁⣶⣛⣒⣦⣭⣭⣿⣿⣷⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣼⣿⣿⣿⣦⣬⣥⣤⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁