Insult Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢤⣄
⠀⠀⠀⠀⠀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⣞⠁
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣤⢠⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠙⢦⠀⠀⢷⠀⠀⠀⠀⠈⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⢧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠷⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⢠⡀⠀⠘⣇⠀⠀⣧
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠉⣴⠒⣶⠒⣦⡛⠀⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡇⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⡄⢠⡇⢠⡇⢠⡏⢹⡆⠀⣼⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠐⠗⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠇⣼⠀⣼⠀⣼⠀⣼⠉⣷⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠆⢿⠉⢳⢠⠇⠠⠇⢠⡇⢠⡇⢰⠇⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢸⡆⠘⡿⠀⠀⠀⠀⠀⠘⠀⡾⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠆⣠⠆⠀⠀⠈⣠⣼⣿⣌⣀⠌⠀⢀⣒⢴⣿⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⠃⡄⠠⣠⣴⢀⣸⣟⠀⣻⠟⠫⠖⠈⠁⢙⡿⢲⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⢩⡠⠿⠇⠘⠛⠋⠀⠁⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡴⢀⡁⢸⡗⢥⣮⡀⠀⣤⠤⠒⠈⠁⠐⠄⠀⠀⠰⠃⠀⠀⠀⠒⡀⠀⠀⠀⠀⢴⠄
⠀⠀⠀⠀⠈⠡⣨⣷⣄⢜⢿⣿⣿⡦⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠒⠁⠀⠈
⠀⠀⠀⠀⠀⠀⢨⡛⢿⠎⣾⣿⣟⡧⡀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠶⢺⠗⡦⠀⣟⣿⠟⡇⠉⢀⡀⠀⠐⠉⠀⠀⡇⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠐⠒⠛⣷⠃⠀⣾⠛⠀⡇⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⣸⣿⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⢈⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⣻⡟⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⡆⠀⠈⠛⠁⠀⠉⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⠋⠁⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀



⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡇⠋⠀⠀⠀⠀⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⠀⣿⣿⣷⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡬⠂⠀⢀⣀⣴⣾⣶⣴⣄⣀⣤⣀⣀⢘⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⠵⠒⣲⣛⣿⣿⣿⣿⣿⣿⣿⣋⣿⢿⣿⣿⣿⣿⡆⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⡭⠶⠶⠿⠟⣻⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⡿⢿⡛⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠙⠀⠘⠹⡄⠀⠀⠀⠀⣠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠟⠀⠘⢿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠄⠀⠀⠀⠀⡀⠹⠦⣄⣠⣾⢛⠈⢫⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠈⠀⣿⣿⣿⣿⣿⡿⢢⣄⡀⠁⠀⠀⠀⢀⣘⣻⣿⠑⠛⠛⠛⢶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢠⡀⠀⣿⣿⣿⣿⢿⣵⣂⠀⠙⢦⡀⠀⢾⣀⠉⠛⢿⣦⠀⠂⢠⠺⣿⣿⡋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⣿⠾⢿⣧⡟⠑⠛⠿⠿⣤⡀⢀⣹⡆⠈⠙⣿⣷⣛⠛⠀⠀⣼⢀⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⣾⠃⠀⠈⣿⣿⣿⣷⣤⠤⡿⠋⣠
⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡞⢰⢿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⠇⠀⠀⠀⠀⠀⠸⡾⢤⢄⢀⡀⡇⠚⡿⠀⠀⠀⠀⣿⣿⣿⠿⢻⢿⠹⡟⠑⢿⠙⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⢐⠁⠀⠀⠀⠀⡿⣿⣿⡄⠀⠀⠑⠄⡀⠘⡆
⠀⠀⠀⠀⠀⢠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⠀⠹⣆⣘⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⣼⣁⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢜⣠⣤⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⢃⡘⢋⡉
⠀⠀⠀⢰⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠂⠀⠀⢀⢜⣯⣿⣿⣧⠀⡈⠐⠚⠃⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠋⣼⣿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁

⣾⣷⠿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣴⠋⠀⣾⣙⣧⣴⠟⠀⠀⣤⣾⣤⣿⡤⠀⣿⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⠁⣼⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⣽⠋⠀⢈⣽⢿⡟⢳⠀⠠⣴⣧⣼⣧⠄⠀⠛⠀⠀⢸⠇⠀⠀⠀⠀⠰⠷⡦⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡘⠁⠀⠀⠛⠁⠈⠛⠋⠀⠀⠙⠀⠛⠀⠀⠀⠓⢀⣤⠟⠀⣼⠛⣿⠃⠀⢰⡿⠋⠀⢰⠟⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢦⣀⡟⠛⠛⠉⠁⠀⢰⣇⡘⢻⡶⠀⠀⠁⠀⢀⣟⣀⠛⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢹⣷⠏⠀⠀⠀⠀⠀⠀⠉⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢤⣄⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣠⠞⠛⠉⠛⠳⣄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⢷⡀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣦⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣽⣷⣤⣤⣤⣾⣯⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠙⢿⡉⠁⣠⣤⣤⣤⠤⠶⠶⠖⠐⠂⠘⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣆⠈⣧⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡄⣿⠀⠙⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠈⣇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢷⡀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⢦⣄⠀⠀⠈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⢀⠈⡿⠶⣄⣠⠟⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⠀⢸⣾⠃⠀⠈⠙⠷⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣯⣍⣭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣩⣤⣬⣍⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢁⣾⣿⣿⣿⣿⣧⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣾⣿⠟⣛⠻⣿⣿⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⡀⢲⡄⠀⠀⢸⣿⢰⣿⠇⣾⣿⣿⡿⢃⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⣆⠈⣧⠀⣷⠀⠀⢸⣿⠸⣿⡀⣿⣿⣩⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⡟⠀⡿⠀⣿⠀⠀⠈⣿⡄⣿⣇⢻⣿⣿⡿⢩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠟⠁⠀⠉⢀⡼⠃⠀⠁⠀⠀⠀⢹⣷⠘⣿⣆⠻⣿⣷⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣍⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄⠀⠀⠀⢿⣷⣾⣿⣷⣌⣛⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣴⣌⠻⣿⠟⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣦⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣠⣿⣿⣿⣿⣦⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⠭⢿⡆
⠀⠀⠀⠀⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠸⠶⢾⡇
⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⠋⠙⠿⣿⠟⠙⠿⣿⡿⢻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇
⠀⠀⠈⢻⣿⣿⣿⡇⠘⢿⣄⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇
⠀⠀⢰⣿⣿⣿⣿⣧⠀⠈⢻⣷⣦⡨⡓⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠉⠛⠿⣿⡀⠀⠀⠙⢿⣿⣮⣳⣄⠀⠀⢰⠀⣰⣿⡿⠁⢀⣠⣞⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢻⡓⠲⠽⣿⣿⣿⣗⠀⢸⣾⣿⣟⡠⠖⢩⠏⠸⡆⠀⠀⣰⡶⠚⢛⠉⠀⣦⠀⠀⣸⠀⣸⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠙⢦⡀⠀⠉⣻⠿⣿⢸⡿⠛⡅⠀⢠⠏⢀⠀⢹⡄⢰⣿⠁⠀⠸⠀⠀⠃⠀⠘⠁⠀⣿⠘⢧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣄⠀⠀⠙⠦⣀⣀⡠⡟⠀⢿⡦⠤⠴⠃⢠⡟⡄⣸⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡷
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⢌⡛⠦⣄⡀⠀⠀⣰⠃⠀⠀⠙⠲⠤⠶⠋⢈⡴⠃⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠀⠀⠉⠛⠋⠁⢀⣤⠶⠶⣦⡀⠀⣠⠟⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠈⠻⠀⢹⡀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠲⠶⢶⣦⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇

⠀⠀⢀⣠⣶⣾⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⡀⠀⠀⠀⣿⣿⡟⠉⠀⠀⠙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠚⠂⢸⣿⠃⠀⠀⠀⣿⣿⠀⠓⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣤⣄⣤⣿⡿⠀⠀⠀⠀⠸⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠋⠀⣤⣴⣶⣶⣶⣤⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢛⣟⢿⣿⣿⢛⣙⣿⡟⣿⣿⢻⢿⡿⣻⣻⡿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣪⣕⠿⣸⣿⣌⠻⣿⡇⣿⠆⡖⢰⣷⣽⡽⡵⣛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣛⣛⣥⣛⣿⣛⣩⣾⣟⣿⣷⣧⣿⣿⣟⣾⣯⣛⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠃⢈⡼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⡽⠿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⢈⠉⢠⣤⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠊⣠⣬⠀⠘⠾⣆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠼⠻⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠺⠁⠐⠁⠄⢠⠈⠇⠡⠁⠀⣶⢾⣷⣾⠀⠀⠀⠀⠀⣀⣰⡟⠔⣿⣾⡄⠁⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣟⠀⠠⠀⠀⠀⢠⡎⢠⠅⠁⠀⡟⠃⠀⠀⢀⣴⣾⣿⠥⢰⡦⠀⣿⣷⡐⠷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡽⠈⠦⠄⠀⠀⢀⢼⡇⣼⡆⠀⠀⡀⠀⠈⠛⠋⠈⠁⠬⠀⣾⣿⣶⣿⣿⣧⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠉⠛⠀⢉⠧⣀⠀⠀⢤⢼⡇⢻⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠻⠿⠛⣛⠋⣱⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢁⣴⡄⠀⠰⠇⠀⠀⠀⢂⣨⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠂⠰⣼⣽⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠨⣼⡏⢸⡇⠀⠀⠀⣀⠀⠉⠉⠁⢺⣿⠹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡉⠛⢻⣿⣷
⠀⠀⠀⠀⠀⢀⠀⣾⡀⠀⠀⠀⠀⣹⣿⠇⠀⠀⠀⢸⠉⣦⣽⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠹⠀⠍⠢⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⢰⠄⢁⣸⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⡆⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡸⢀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⣾⠀⠀⠲⣬⣻⣿
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡾⢻⠃⠀⠀⠀⠀⢀⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⡀⠀⠀⢸⡇⣀⢀⣀⣀⢀⣀⠈⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣽⣾⠄⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⡀⠤⠐⡀⢨⠈⠉⠁⠁⠀⠀⠈⠏⠉⠙⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⣿⠀⠀⠀⠀⠐⠀⢸⠃⣤⠀⠀⠀⠀⠀⠀⠁⠁⠠⠀⢩⡭⣁⠀⢻⡄⠘⠿⡿⢿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢢⠺⣿⣯⠀⠁⠀⠀⠀⠀⣿⡰⠦⠈⠀⠀⣀⠀⠀⠀⠀⠀⠆⢸⡇⠀⠱⠘⠀⠀⠸⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⠆⠀⠀⠀⠐⠂⡋⠈⠛⠳⠚⠉⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠀⠙⣕⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣼⠿⣊⠀⠀⠀⠀⠈⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁⠀⠀⠀⠀⢀⣀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠆⠀⠀⠀⠀⢀⣀⣀⣰⣄⣀⣀⡌⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡐⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠐⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⢻⣿⠟⠻⣿⡿⢻⣿⣿⡟⣿⠟⣿⣿⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⡀⢻⣿⣈⠃⠈⠰⢿⣿⣥⢀⡤⢠⣼⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣴⣿⣿⣋⣴⣄⢃⣸⣿⣆⣴⣄⣴⣾⣿⣸⣿⣿⠃⠀⣀⣀⠀⠀⠀⢸⠏⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠟⠟⠻⠛⠛⠟⠻⠛⠿⢿⣿⠟⠟⠛⠋⠁⠀⢰⣿⣏⡀⠀⠀⠀⠀⠀⣸⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠀⠀⠉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣛⣉⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⢀⣀⡀⢠⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡈⣿⠀⠀⠻⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡘⣿⣿⣿⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡙⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⠙⠻⣿⠟⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⡇⠋⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⢹⣿⣿⣿⠀⣿⣿



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⣿⣶⣄⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⣿⣘⣿⣛⣧⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⠂⠀⠀⠉⠙⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠄⠀⠀⠀⠀⠈⠀⠁
⠀⠀⣠⣴⣾⣇⠀⠀⠀⡀⢰⠀⠙⠇⢀⠐⡆⠰⡆⠀⠀⠄⠀⠀⠐
⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡀⣠⣀⣠⡤
⠀⠀⠀⢀⣄⠀⠀⠀⠀⠒⠂⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣟⢙⣿⣧⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠬⠫⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠘⠉⢿⠛⠏⠃⠀⠀⠀⠆⠀⠀⠸⠋⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣽⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠴⠛⠛⠋⠁⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠱⡄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣼⠁⠀⢀⣤⡄⣠⣠⢀⣴⢶⡄⡆⡴⠀⠉⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⡙⠁⠲⡆⣄⣀⣶⣆⠀⠠⣾⡆
⠀⠀⠀⢿⠀⠀⠹⠴⠋⠘⠎⠹⡵⠿⠈⠉⠀⠀⠀⠀⠑⡄⠀⠀⠨⡷⠀⠀⠠⣏⡗⠀⠆⡉⠈⠟⠉⠀⠀⠘⡏
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⢀⣀⣀⣤⠀⠀⠀⡰⠃⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠈⠉⣿⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢉⠇⠀⢀⡰⡫⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠊⠁⠀⠀⠀⠀⠀⠀⠠⠶⠭⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⢀⡄⠀⣠⣄⠀⢀⡄⠀⠀⢠⠀⣠⠀⠀⡌⠉⢳⡄⠀⠀⠀⠀⠀⢠⡶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠴⢿⡤⠀⠷⣼⣷⣏⡀⠀⠚⣿⢛⡟⠃⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⣾⡀⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢰⠋⠀⠀⡴⠋⠿⣼⠇⠀⢻⠟⢻⠛⠁⠀⡄⠀⢠⡟⢀⣤⣤⡄⠀⠉⣿⡞⠁⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⠀⣤⠤⠴⠖⠋⠀⣼⠃⣼⣥⠀⠀⠋⠀⠀⡾⠀⣾⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠛⣷⣴⠋⠀⠀⠀⠀⠘⢻⣇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠁⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢁⣠⠶⠒⠶⢤⡀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⠳⡄⠀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠼⢦⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⠬⠿⠶⠤⠴⠾⠧⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⢿⡉⢀⡤⠶⢶⡶⠶⠖⠒⠀⠃⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣶⠈⣧⢻⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⠀⠀⢸⡄⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣧⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡆⠀⠀⠘⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠻⣤⡀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⢠⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣶⡆⠀⠀⠀⢰⣸⠇⠈⠛⢿⣄⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⢸⠋⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡄⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣠⣶⣄⢀⣴⣾⠟⠋⣁⣠⣴⣶⣶⠿⠿⠿⠿⣶⣶⣦⣄⣈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⣴⣿⠛⠉⠻⣿⣯⣤⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡀⠙⢿⣦⡀
⠀⠀⠀⠀⠘⢿⣦⣀⣤⡈⢉⣍⣙⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡀⠙⣿⣆
⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⣬⣙⣿⡿⠋⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠀⠈⢿⣧
⠀⠀⠀⠀⢰⣿⢹⣿⢴⣦⣹⣿⠏⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⢀⣠⣶⡿⠛⢉⣠⣴⣿⣆⠈⣿⡆
⠀⠀⠀⠀⣿⠇⢸⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣤⣾⠿⣏⢁⣤⣶⠿⠛⠁⠘⣿⡆⠸⣿
⠀⠀⠀⢸⣿⠀⣸⡟⠈⢿⣆⠀⢀⣀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⣀⣤⣾⠟⠋⠁⠀⠀⠀⠀⢻⣇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⣿⡇⠀⠈⢿⣆⠈⢿⣧⣀⣠⣶⡿⠛⠉⣠⣴⡿⠟⠿⣷⣦⣤⣄⣀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢹⣷⠀⠀⠈⢿⣧⣤⣿⠿⠋⢁⣠⣶⠿⠛⠁⠀⠀⠀⠀⠈⠉⠙⠛⢿⣦⣄⣾⡏⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠘⣿⡄⣀⣴⣾⠟⠋⣀⣤⣾⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⢸⣿
⠀⠀⠀⠀⠸⣿⡀⠹⠿⠟⠉⣨⣶⡾⢿⣯⡀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⠇
⠀⠀⠀⠀⠀⠹⣷⡄⠀⣴⣿⠛⠉⠀⠀⠻⣿⣦⡈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣆⠈⠻⣷⣄⡀⠀⠀⠈⠛⢿⣦⡈⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡈⠛⢿⣶⣤⣀⡀⠀⠙⠿⣶⣄⡈⠛⠿⠇⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣈⠉⠛⠻⠿⠿⠿⠿⠿⠿⣶⣦⣤⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣶⣤⣤⣤⣤⣶⣶⡿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢐⢠⣦⢨⡀⠀⠐⠟⢳⣌⢆⡐⠂⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⠀⠀⢉⣥⣬⣦⣤⡀⢠⣄⠀⢀⣷⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢹⣯⣿⡟⣿⡟⢸⣥⣤⣿⣙⢋⣥⡀⠈⢦⡀
⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⠰⠆⠀⠀⣀⠉⢩⠿⢻⢘⣷⣯⠹⠛⠋⣀⠀⣻⡃⠄⠀⠹⣄
⠀⠀⠀⠀⠀⢸⡇⣷⠀⠄⢰⠮⡘⢂⢿⣷⡆⠰⠘⡃⢈⠧⡠⢆⠈⡉⠘⠁⠀⠀⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⡇⢹⣦⣠⡏⠄⠱⢸⡈⠙⢷⣦⣜⠳⠤⢑⣀⡈⠀⠁⠀⠀⠀⠀⠀⠀⣶⢸
⠀⠀⠀⠀⠀⠀⣅⠸⣏⠈⡿⣇⣀⠀⠹⣿⡾⠋⠐⠀⠀⣂⠈⠉⠛⠉⠀⢀⡶⠀⠄⢀⠁⠈⢇
⠀⠀⠀⠀⠀⠀⣿⢀⠉⢠⣀⣈⣿⣦⠖⡋⠗⣂⡞⣜⣿⣿⣿⣿⣿⣾⢤⢸⢻⣾⣿⣿⣿⣇⠞
⠀⠀⠀⠀⠀⠀⢳⡜⣄⣨⠺⠃⣼⣿⠆⠳⢔⡏⠁⣿⣷⣿⣿⣿⣿⣿⠌⠀⣯⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢸⡀⢹⣿⣥⡌⠉⠩⣠⠠⣍⣻⠉⣿⠿⠛⠋⠀⠟⠽⣢⣾⠇⡿⠏⠛⡁⠆
⠀⠀⠀⠀⠀⠀⠈⢧⣰⠛⢸⣇⢻⣆⡿⣶⡌⠉⠰⣌⢶⠷⠰⡾⢠⣾⣿⢻⢰⣧⠟⠛⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣼⠲⢸⢿⡌⣿⢱⣷⠆⣿⠿⣹⠎⢰⡏⠀⠊⠓⠂⡄⠂⢻⣿⣾⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡚⠳⠟⡇⠉⢨⣾⠘⢣⣦⡏⢀⢾⠉⢿⠻⡶⢶⢶⠻⡿⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠂⣇⣁⣄⠈⠟⣸⣶⡜⢃⣾⣷⣿⣿⣿⣷⣾⣶⣟⣋⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⣿⠸⡿⡇⣷⡿⠸⣧⢌⡉⣿⡛⣟⣹⢟⡶⢳⣛⡼⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⡄⡿⣸⡇⠹⣇⣸⡋⢰⠋⣏⠻⠉⡋⠻⠛⠟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣷⣏⢀⠀⠁⢹⢡⠚⠂⣏⡅⣤⣧⣀⣦⡄⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠠⠻⠂⠂⢸⠀⠀⠈⣀⣴⢛⠉⣷⢰⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠄⠀⡄⢸⠰⠂⢰⠿⠩⠀⠀⡉⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠁⠀⢠⠀⢸⠀⠳⠀⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⢸⠀⠸⠀⢰⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠘⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠐⠢⡀⠀⠀⠀⡐⠀⠣⠀⠠⡀⣀⠀⠀⠀⢚⠒⠂⣘⡈⠉⠛⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢀⡠⢂⡊⠦⡼⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⡅⡀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠉⢀⠀⠀⡀⠀⠀⢀⠄⠂⠙⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⣀⠀⣳⠘⠀⠀⠑⠠⢀⣀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡡⣤⠜⢹⠋⢿⠱⣆⣡⡀⠀⠀⢠⣄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠳⠏⠂⠒⠊⠀⠘⣏⡘⠀⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠤⢂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⣆⠈⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡠⠐⠀⠉⠈⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢀⡔⡄⣤⡘⣧⠀⠀⠀⠀⠈⢀⠔⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡇⢰⡐⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠉⠭⠤⠤⠀⠱⠼⠆⠠⠀⠀⡤⠁⠀⠀⠀⠀⢣⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢀⣀⣀⣀⣀⣀⣀⠀⡠⠊⠀⠀⠀⠀⡠⠀⠈⠄⠰⠀⠀⠀⠀⠁⠈⠉⠀⠈⢹⠀⠀⠀⡘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢄⡀⠃⠰⠀⠀⠀⠀⢀⠴⠞⠅⠀⠀⠀⠀⡴⠀⠀⠀⢹⡀⡃⠀⠀⠀⠐⡂⠀⠀⠐⠺⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠁⢀⡠⠀⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⣀⠊⠘⡀⠀⢀⣀⠇⠐⡀⢀⠀⢀⡭⠉⠉⠉⠉⠀⠀⢰⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠥⠼⠤⠬⠆⡀⠀⠐⠀⠀⠒⠂⠀⠤⠎⠀⣄⡊
⠀⠀⡀⠄⢠⠀⠐⠂⠐⠃⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠴⠦⠄⠀⠄⢀⠀⠀⠀⠀⣤⠚⠉⠁⠀⠀⠀⠄⠐
⠀⢮⠀⠠⠁⠀⠀⠄⠂⠀⣼⠂⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠀⠉⠉⠁⠀⠀⠀⠈⠉⠈⠙⠉⠉⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠐⠂
⢀⠁⠀⢀⠀⠀⠀⠀⠀⡴⠹⠖⠒⡖⡶⠒⠀⠰⠶⠀⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠠⠄⠠⠤⠤⠄
⠈⠸⠀⠀⠑⠂⠐⠢⠐⢁⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⢉⠠⠀⡤⢀⡀⠒⠁⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⡇
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠠⠀⡃⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠶⠤⠎⠀⢉⠴⠀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⠤⠤⠤⠆⢧⣄⠤⠄⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⠒⠒⠒⠲⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠒⡄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡤⠊⡴⠁⠀⠈⢳⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡞⢁⣀⣇⠀⠀⠀⠀⢩⠑⢄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣼⠀⢇⠀⠟⢄⠀⠀⠠⣀⠄⠀⠠⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀⠀⠀⠀⠈⠓⢤⡔⣄⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣀⣴⠀⢷⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢼⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⢄⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⣰⣅⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⢀⠉⠗⣄⡠⠁⡵⣀⣉⠒⠢⢤⠀⣀⠀⣀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠢⠜⠀⣀⣈⡋⠁⠚⠀⢩⠉⠘⠂⠄⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠐⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠀⠀⢀⠀⠀⡄⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠺⠒⠛⢻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠁⠀⢸⠀⠀⠩⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠍⠂⠰⠛⠋⠛⠛⠷⠮⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣘⣛⡿⣿⡿⣫⣽⣯⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢶⣾⣾⣛⣛⣻⣿⣷⢿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢣⣿⡿⣭⣟⣿⣿⣿⣮⠻⣿⣿⠿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣭⣛⣻⣏⣾⣿⣿⣾⣿⡿⣻⣽⣵⢞⣲⣖⡣⢾⣭⣟⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⢯⣾⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡀⢈⣯⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏⠁⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠃⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⣀⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠺⠤⠀⠛⠙⠀⠀⣤⣤⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠰⠀⠀⠀⠸⠀⠃⠁⠁⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡇⠀⠃⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠈⠁⠐⡀⠀⠀⠀⠇⢠⣤⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡌⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⠀⠘⠀⠠⠀⢸⠀⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢠⠄⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣦⠞⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠨⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⡀⠀⠀⠀⠀⠀⠈⠠⢰⠺⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠷⡀⡿⠀⠀⠀⠀⣤⣼⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠋⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠙⠓⢦⠀⠀⣦⣀⠀⠀⠀⠀⠀⠄⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣥⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠉⠉⠀⠉⠀⣐⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠋⠁⠐⠖⠒⠂⠀⠀⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣸⡀⠀⢀⡀⠀⠸⠤⢴⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠉⠉⡇⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠄⠀⢨⡄⢠⠧⠠⡧⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⠆⠤⢼⠄⣼⠤⢼⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠀⠀⠷⠀⠞⠂⠶⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣾⣦⣤⡶⠶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⣷⡦⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠛⠉⠁⠀⣠⣾⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠂⠴⠀⠆⠀⠀⠀⠖⠔⠀⠒⠀⠢⠀⠀⠑⠐⠊⠰⠀⠡⠆⠀⡦⠀⠶⢤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣶⣽⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣃⣼⣿⣿⣯⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⢾⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣝⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣽⣯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣠⠶⠶⠶⠄
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠦⣈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢀⣤⣾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡉
⠀⣤⠙⣿⣿⣆⠐⣶⡄⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢀⢴⣓⠀⡀
⠀⣿⣄⠉⢻⣿⣭⣿⣯⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢺⣯⣬⣶⣡⣾⣿⢣⠈⠄
⠀⠻⣬⡆⠀⠙⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⣿⣿⣿⣿⣿⣿⠏⣧⣄⢀⠀⢀⢀⢄
⠀⠀⡝⢿⣦⡀⠈⠻⣿⡟⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⢩⣥⢀⣤⣬⣃⣾⣿⣿⣿⣿⣶⡆
⠀⢠⡧⠈⢻⣷⡄⠀⠘⢧⣿⠻⡇⠀⠀⠀⠠⢀⣀⣀⠀⣠⠏⠀⠀⠀⣀⠴⢷⣿⣼⣿⡯⠀⠀⣀⣬⡟⢉⣿⣿⣿⣿⣿⣿⡡⠂
⠀⢸⣿⣮⠄⠈⢡⣄⠀⠀⢿⡄⢧⣤⣤⣤⣷⣶⣦⣽⣽⣿⣤⣶⣤⣶⣤⣴⣿⣿⣭⣽⣿⣤⣨⣿⣿⣧⣿⣿⣿⣑⣘⣋⠁
⠀⠈⢰⢸⠀⠀⢰⠿⣿⢇⢨⡞⠈⠛⠛⠛⠛⠛⠛⠛⢋⠛⠉⠛⠛⠛⢛⣛⠛⡛⡛⢿⣛⠛⠛⡿⡶⠓⠀⠀⠀⠀⠀⠉⠉⠈⢹⠿⠂
⠀⠐⣠⡀⠀⠀⠀⠀⣟⣀⣩⠁⠀⠀⠀⠀⠈⠉⠉⢉⣉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡏⠉⡉⠉⠈⡹⣽⣟⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⣷⠀⠀⠀⢀⣿⠃⢹⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⣿⠦⠀⠀⢸⢿⣆⣈⣠⣤⣿⣶⣀⣤⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⡇⠆⠀⡟⣸⢯⢉⠁⢩⣿⣏⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⢸⡀⢸⣇⣛⠸⣾⣾⠚⣿⡏⠀⠐⣖⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉
⠀⠀⣸⣿⣷⣾⣿⣿⣶⣧⣄⡈⢹⣿⡇⠉⠉⠏⠉⠉⠉⠙⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⡀⠀⠀⠈⣿⡿⠿⠿⠟⠋⠙⠃
⠀⠐⠿⠿⠿⠟⠉⠉⠫⣿⣭⣽⣼⣙⠃⠁⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠒⠶⣶⣶⡦⠋⠉⠉⠋⠉⠈⠉
⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠈⠁⠀⠃⠀⠈⠁⠈⠀⠀⠀⠀⠁⠁⠑⠈⠁⠁⠃⠉⠁⠘
⠀⠀⡀⠀⢀⠀⠠⠀⡄⡀⢀⠠⠀⡀⢀⠀⢄⢀⠀⠠⠀⢀⠠⠀⠀⢀⠀⠄⠀⠀⢀⠀⣀⠀⠀⡠⠂⡄⡀⠠⢀⠀⡀⠀⠀⠄⠐
⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠤⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⣀⣀⠑⡀⠀⠀⠀⠀⠀⠠⠀⡠⠔⠉
⠀⠀⠀⠀⠁⡀⣀⡴⠉⠘⢶⣤⡀⠈⠀⠀⠀⠀⠘⣛⣛⠃⠠⢄⠛⣉⡽⠁⠐⠀⠁⠀⠠⠄⠀⠌⡡⠈
⠀⠀⠀⢀⠋⠛⣭⡀⠠⣤⠄⢻⠏⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠀⠴⠀⠀⠀⠀⣀⠀⢀⡠⠐⠠⠊⠀⣀
⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠣⠀⠠⣤⠄⣖⠒⣖⠒⣶⠒⡆⠀⠐⠂⠈⠀⠘⡀⠄⠊
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⠀⠹⣷⣿⠛⣜⠽⣫⣿⠃⠀⠀⠒⣀⡀
⠀⠀⠀⠀⡀⢆⡙⠰⠴⣺⣷⣇⠀⠀⠀⠀⠀⠀⠢⡀⠈⠚⠾⠩⠞⠛⠁⢀⠄⠐⠦
⠀⠀⠀⠐⠉⠈⠂⠀⠀⠀⠈⠈⠁⠢⡀⠀⠀⠀⠀⣤⡕⠦⣤⣀⢀⢴⠒⣧⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠊⠀⢸⠀⠁⠒⠠⡄⠀⠈⠁⠁⠌⠉⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠈⡆⠒⠲⣞⣙⡦⠖⠚⠀⠘⣏⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⢃⠀⠀⡟⠉⣇⠀⠀⠐⠠⠁⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⠀⠈⠀⠐⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣦⡀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⣀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠻⠆⠀⠀⡇⣏⠀⠀⢿⣿⡄⢬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢲⡆⠀⠀⠀⢲⣶⠖⠋⠀⠀⡆⡿⠀⠀⠀⠀⠀⢷⣿⠀⠀⠸⣿⣷⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡤⠀⢹⡇⠀⠀⠀⠈⣷⠀⠀⠀⠀⢻⡄⠀⠀⠀⡇⣷⠀⠀⠀⢀⣀⠘⣿⣀⣀⣀⣿⣿⡄⢻⣿⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⣿⡀⠀⠀⠀⣹⡇⠀⠀⠀⡆⣷⣴⠆⠀⢳⡹⣆⠀⠐⠻⢿⣧⢹⣿⠋⠉⠈⢿⣿⠘⣿⣷⣶⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠰⣾⣇⠀⠀⠀⣿⣿⠀⠀⠀⢸⣹⡇⠀⠀⠀⠙⣿⣷⣄⣴⣿⡿⠀⠻⠃⠀⠀⠘⠿⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⣧⠀⢿⣿⡀⠀⠀⠸⣿⣇⠀⠀⠀⢿⣿⣤⣤⠶⠛⠁⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠘⣿⣧⠀⠀⢀⣿⣿⣤⣤⡶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⢹⣿⣶⡶⠏⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠉⠁

⠀⠀⣀⣤⣀⠀⢀⣤⣄
⠀⢸⣿⣹⣿⡆⣿⣿⣿⡧⠀⠀⡴⢾⡤⠦⢤⢤⣤⡄⠘⠏⡥⣤⢶⣤⣤⢤⠀⢠⢤⣤⡴⢸⣏⠤⣄⡠⠤⢤⢤⣤⡄
⠀⠈⠛⠛⠋⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⣄
⠀⠀⠀⢠⣤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠐⠒⠶⣬⣦⢦⣶⣴⣶⡆⠀⠀⠀⠀⠀⣤⡀⠀⠀⣴⣷⣶⣦⠀⠀⠀⣮⣿⣧⢤⢤⣼⣯⡄
⠀⠀⢠⣼⣿⣄⡀⢀⣽⣯⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⢸⣿⠃⠀⠀⠀⠀⣤⡟⢁⣀⠀⣿⣿⣿⣿⠀⠀⠘⠓⣿⣿⡀⢸⣿⣿⡇
⠀⠀⢻⣿⡿⠿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢸⣿⠀⠀⠀⠀⠰⣿⠻⠋⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⢿⡗⠈⣿⣿⠃
⠀⠀⢸⣿⡇⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⢀⣴⣎⢋⡤⢤⣿⡏⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⣧⠀⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢿⡏⠈⠉⠀⣼⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠚⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣧⠞⠛⠁
⠀⠀⡀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⣤⣠⠄
⠀⠀⠷⢻⣿⣲⡄⠀⠀⠀⠀⠀⠀⢀⡻⠟⣠⡶⠛⠓⡄⠀⠀⠀⠀⠀⠀⠠⠀⢸⣷⣀⣀⠴⠀⠀⠀⠘⣿⢿⣇
⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣉⣁⡴⠞⠁⠀⠀⠀⠀⢠⡦⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⢀⣿⡘⡇⣇
⠀⠀⠀⣿⢹⡏⠀⠀⠀⠀⠀⠀⠤⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣧⡞⠉⢸⣿⣿⡆⠀⠀⠀⠀⡼⠏⢥⠅⠸
⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠀⢀⣤⠾⢺⡆⠀⠀⠀⢀⠇⠀⢸⠀⠀⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠘⠀⠀⠈⠘⠛⠛
⠀⠀⠀⠀⣀⡀⢀⡘⠻⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⡤
⠀⠀⠀⣨⣿⣁⢻⣿⣦⣀⡄⠀⠀⠀⠀⣠⣾⡇⢠⣤⡀⠀⠀⠀⠀⠀⠠⣏⡛⠁⣀⢘⡟⡧⠀⠀⠀⢀⣾⣿⣿⡿⢟⡋⠁
⠀⠀⠀⣿⣿⣿⠈⣿⣿⡍⠀⠀⠀⠀⠀⣹⣿⠳⣼⣿⣷⠀⠀⠀⠀⠀⠠⣿⡏⠋⠀⢸⣧⠀⠀⠀⠀⠾⠛⠋⠁⢀⣿⣟⢀⣀
⠀⠀⠀⢻⣿⡟⠀⣾⣿⡇⠀⠀⠀⠀⢸⣿⣿⣤⣿⣿⣿⣤⡄⠀⠀⠀⠸⢿⡷⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣾⣿⡀
⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⠿⠿⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠈⠈⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠟⠛⠛⠛⠛⠛⠻⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⣠⡞⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡄⢀⣠⡄⢀⣠⠄⣠⠄⢀⡤⠀⣠⣄⣠⣶⢠⡿
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠰⣯⡴⢻⣀⣠⠖⣏⣠⠖⢿⡤⠞⠉⠓⠛⠙⠛⠋⠛⠛⠙⠛⠋⠙⠋⠉⠉⠁⣿⣸⠇
⠀⠈⢷⡀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⡀⢹⡏
⠀⠀⠈⢻⡄⢀⡴⠒⠺⠋⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠈⠃⠘⣇⣀⣤⢤⣄
⠀⠀⠀⠀⠙⣿⠀⠀⠷⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡶⠶⠋
⠀⠀⠀⠀⠀⠘⢶⣶⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣀⣀⣀⣤⣶⡃⠀⠀⠀⣶⣋⣱⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠈⠷⠈⢻⡄⠀⠀⠀⠉⠁⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣸⡇⠀⠀⠀⣶⡶⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⢀⣠⡼⠷⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠿⠓⠦⠤⢄⣀⣀⣀⠀⠀⢀⣀⣀⡤⠴⣾⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⣿⣅⠀⠀⠀⣀⣤⡾⠋⠉⠙⢿⣍⡈⠁⠀⣠⠾⠿⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠙⠶⠛⠉⣿⡀⠀⠀⠀⢀⡿⠛⠒⠋⠁⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄⣴⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⣴⠾⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠙⣦⠀⠀⠀⠀⠀⠀⢻⡏⠻⢷⣄⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣠⡿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⢸⣧⠀⠀⠙⣷⡀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣸⡇⠀⢠⣿⠁⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣧⠀⠀⢿
⠀⠀⠀⠀⠀⢀⣿⣇⣀⣸⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡆⠀⠀⠀⣿⠄⠀⢿⡇
⠀⠀⠀⢠⡾⠋⠉⠉⠙⠻⣦⡀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠸⣧⢠⣶⠛⠛⠲⠖⠿⣧
⠀⠀⠀⣿⣴⡟⢠⣶⢠⡶⣾⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⣿⡈⠛⠛⣿⠃⣤⢤⣌
⠀⠀⠀⠀⠘⠿⠛⠻⠿⠁⠀⠀⠀⠀⠻⣶⠶⣤⣤⣄⣀⣀⠀⠀⠙⣧⣀⣼⡁⠀⠀⠀⣀⣀⣤⣤⡾⠁⠀⠸⣷⡾⢿⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣸⡟⠛⠛⠛⠟⠋⠻⠋⠙⠿⠛⢿⡏⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣭⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣽⡇
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⢲⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄⢀⠀⠀⠀⠀⠔⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣮⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠁⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠈⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣷⣦⣄⠀⠈⠛⢛⣋⣠⣤⣴⣶⣾⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⢠⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⣤⣶⣶⣿⡿⠿⠟⠛⠋⢉⣠⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⣰⣿⣿⠋⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⠿⠛⠋⣉⣁⣤⡄⢠⣾⡿⣿⣮⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠘⢋⣉⣡⣤⣶⣶⣿⡿⠿⠟⠛⢉⣉⠀⢤⣴⣶⣶⣄⣿⡟⠋⠁⢸⣿⡀⠈⠁⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣈⣤⣴⣶⣾⣿⠿⠿⠛⠛⠉⢁⣤⣤⣶⡆⣾⡟⠻⠷⠸⣿⣄⣸⣿⢸⣿⡿⠿⠀⣿⣧⢀⣶⣷⠀⢹⣿
⠀⢠⣴⣶⣿⡿⠿⠟⠛⠋⣉⣤⣤⡀⣶⣿⠿⣿⡆⣿⣏⣀⣄⠻⣿⣶⣶⣄⢿⣿⠛⠋⠀⣿⣧⣴⣶⡈⠻⠿⠟⢁⣀⣤⣤⣶⣶⣧
⠀⠀⢉⣩⣤⣤⣄⠸⣿⡰⣿⡋⠙⠛⢸⣿⣤⣾⡟⢸⣿⡛⠋⠀⣤⣄⣸⣿⠸⣿⠄⠀⠀⠘⣉⣉⣤⣴⣶⣾⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠈⣿⡏⠙⣿⡇⢿⣇⠙⠿⠿⢿⣦⣿⣏⠹⣷⣄⣿⣷⡾⠿⠙⠛⢛⣁⣠⣤⣴⣶⣿⡿⠿⠟⠛⠋⢉⣀⣤
⠀⠀⠀⢹⣷⠀⢹⣿⠸⣿⡴⣶⣤⣾⡿⠸⠿⠀⠙⣉⣈⣤⣤⣶⣾⣿⠿⠿⠛⠛⠉⠉⢠⣤⣶⠆⠀⢀⣿⣿⠇
⠀⠀⠀⠈⣿⣷⣾⠟⠀⠛⠃⢈⣉⣡⣤⣴⣶⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⢀⣾⣿⡟
⠀⠀⠀⠀⢉⣁⣤⣤⣶⣶⣿⡿⠿⠛⠛⠉⢉⣤⣴⣦⣄⣀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠟⠁⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠈⠿⠛⠋⠉⠁⠀⠰⣶⣷⣦⡀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠄⡉⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠘⣿
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣰⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⡀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠤⢤⡀⢠⣀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⠤⠴⠒⠛⠛⠛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⣀⠀⠐⠃⠀⠤⢀⣀⠀⠀⠀⣸⡇
⠀⠀⠀⢀⡐⢢⠤⠄⠀⠀⠀⠀⠀⣄⠀⢀⢁⡀⠀⠀⢠⠈⠀⣀⣠⣤⣶⡦⣤⢦⣤⣀⠀⠀⠀⠀⢲⣄⣾⣆⠀⣦⠀⠀⠀⠀⠙⠓⠲⠿⠃
⠀⠀⠀⠀⣉⣹⣶⠆⠀⠀⠀⠀⣀⢻⣷⣬⣷⣽⣀⣀⣡⣞⣉⠁⣀⡈⠁⢀⣤⣶⣾⣿⣶⣄⣰⣧⣿⣿⣿⣿⣾⣿⠆⠀⠀⠀⢰⣷⡼⠂
⠀⠀⠀⠀⢸⣽⣿⠀⠀⢆⣀⠀⣻⣧⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣦⡙⠻⣿⣟⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡄⠀⢸⣿⠀⠨
⠀⠀⠀⠀⠀⠀⢸⣇⠀⣰⣿⣆⠻⢿⣿⣿⣿⣿⣿⡿⠟⣋⣿⣿⣿⣿⣿⣟⠀⠀⠉⠉⠑⠀⢿⣿⣿⣿⣿⣿⣿⡏⣰⣿⡁⠀⣶⠙⠋
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⣌⠻⣿⣿⣿⡟⣠⣾⣿⣿⡿⣿⣿⣿⣿⣷⣄⣠⠀⠀⠀⢰⡟⢻⣿⣿⡿⢋⣼⣿⣿⣿⣿⡇⠀⠠⠸⣧
⠀⠀⠀⠀⠀⢀⢰⠉⢿⣿⣿⣿⣿⣿⡆⠈⠉⢹⡇⢀⣾⣿⠿⠛⡟⠻⢿⣿⣷⣌⠙⠂⠀⠀⣰⡿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠁⠀⠈⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣄⡸⣃⣼⣿⣴⣿⣿⣿⣿⣶⣾⣿⣿⣧⠈⠄⢘⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⢳⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⢿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢰⡟⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣤⣼⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠈⠉⠙⠻⠿⠛⠛⠋⠁⠂⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⣿⡏⠁⢼⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⢿⡿⣿⣿⣿⣿⡿⠶⣶⠿⣿⣿⣿⣿⣿⣿⠳⣀⠙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡋⠁⠀⣀⠀⢀⡾⠛⠲⠌⠄⣿⣧⠜⠁⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠘⡷⠀⠀⢀⣼⠟⠁⠀⠀⠀⢀⣾⡿⣯⠘⠛⠻⠦⠀⠴⠻⠆⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⠀⠋⢽⣿⡃⠀⠀⠀⠀⠀⠉⠲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⣦⣀⠀⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⣿⣷⣶⣶⣶⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢠⡎⣀⣀⣤⣿⠿⠋⠉⠀⠀⠈⠁⠉⠛⢿⣷⡄⠀⣾⣷⡀⠀⠀⠀⠀⠀⣀⣤⣷⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡬⣄⣠⢞⣠⣿⣿⠏⠁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠛⣿⣶⣏⣹⢷⣄⠀⠀⠀⢴⣿⣿⣿⣿⣿⣗⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠻⣟⣾⠁⢾⣿⣿⠃⠀⣄⣤⣴⣷⣿⣶⣶⣶⣾⡟⠀⠀⠈⠙⢿⡧⢠⣿⡀⠀⣐⣿⣿⣿⣿⣿⣯⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣙⣶⣾⣿⣴⣾⣿⣿⡿⠿⠿⠿⠟⠿⠍⠉⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠛⠉⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣴⣄⠀⠠⠶⠿⠛⢁⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⡿⢷⣤⣤⣤⣄⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣤⡀⠉⢀⣤⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠀⡿⠻⣆⠈⠀⣴⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣤⣾⠿⠛⠻⣷⡀
⠀⠀⠀⠀⠀⢠⣿⠀⠙⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⡿⠟⠉⣀⣴⣾⠟⠋⢁⣤⣶⠀⢻⣧
⠀⠀⠀⠀⠀⣼⡟⠀⣶⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⢁⣠⣴⡿⠟⠋⣀⣴⣾⣿⣿⣿⡇⠘⣿⡄
⠀⠀⠀⠀⠀⣿⡇⠀⣿⣷⡀⢻⣿⡉⠹⣿⣿⣿⠿⠋⢁⣤⣶⡿⠛⠁⠀⠰⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣷⡀⠹⣿⡄⠘⠋⣀⣤⣾⠿⠋⢁⣠⣶⣿⣷⣦⣄⣀⣉⠉⠛⢿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⢻⣷⠀⢿⣿⣿⡷⠀⠉⣠⣴⣾⠟⠋⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠘⣿⡆⠘⠛⢁⣠⣶⡿⠟⠉⣠⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣦⣾⠿⠛⢁⣠⣦⡀⠙⢿⣧⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠲⣿⣿⣿⣿⣦⡀⠙⢿⣦⡀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⢿⣿⣿⣿⣦⡀⠙⠿⣷⣄⡈⠙⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡈⠙⠻⠿⠿⣷⣄⠈⠛⠿⣷⣦⣼⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣤⣀⠉⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡄⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⠐⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⠀⠠⢁⣀⣀⠀⠀⠀⢀⣀⣀⠘⡀⠀⡀⠀⠀⠀⠰⢂⣠⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⢀⠜⠁⠹⣦⡂⠀⠁⠀⠀⢀⠀⢚⡛⠛⠃⠠⠀⢛⣋⣉⠁⠀⠀⠁⠀⢠⠔⠡⡤⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⡀⠚⠞⣋⠀⢀⣀⠘⢿⠂⠀⠀⠀⢠⠀⠀⠉⠉⠀⠀⠈⡀⠁⠀⠀⠀⠀⠀⠀⢀⡠⢊⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠐⢤⠈⠉⠀⠈⠉⠀⡈⠀⠀⠀⠀⡆⠀⠀⠀⣀⡨⢬⡥⣤⡄⣀⡀⠀⠩⡀⠐⠁⠀⠄⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠘⣯⣤⣷⡤⠷⢤⠧⣤⡇⠀⠐⣀⡀⠈⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣰⢛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢎⢀⣐⢋⣼⡟⠁⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⡀⣀⠄⠉⠉⠼⣼⣠⠀⠀⠀⠀⠀⠀⠁⢄⠀⠙⠓⠘⠛⠉⠀⡀⠂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠀⠈⠢⠀⠀⠀⠀⠀⣤⡝⠦⣄⣀⣠⠐⠋⣢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠣⠈⠐⠂⢄⡠⠀⠈⠁⠁⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠐⠂⢰⡤⠤⢠⡆⠳⣄⣤⠴⠀⠰⡴⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡗⠶⡏⠀⠀⢀⠀⠊⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠄⢒⠀⠠⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣴⠀⡄⣀⠔⠀⠐⢿⣴⣤⣼⠸⡆⢰⠀⣴⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢽⣶⣳⣾⡀⠄⠀⠀⠉⠻⣧⣶⢿⣾⠠⣏⡜⣤⡦⠐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⡂⠸⣿⣿⣦⣤⢂⠄⠀⠀⠉⠹⣟⠛⣶⣼⣶⠋⣵⠶⠛⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠌⠙⠻⠮⣿⣿⢹⣾⠃⠂⠀⠀⠀⣭⣿⣿⣿⣿⡟⣥⡆⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⡀⡓⠸⣯⡾⠀⠆⠀⠀⠀⠀⠀⠹⣿⢿⣾⣳⠋⣴⡾⠒⠁⣀⡀⠀⠀⡄⠀⠀⠀⡀⣠⣀⣄⣀
⠀⠀⠀⠪⠁⠀⠀⢀⠀⡀⠀⢀⠀⠀⢐⠇⠀⠀⠀⢀⡁⠘⡯⣼⡇⠆⢀⠜⠀⢞⠆⠐⣤⣬⣎⣿⠛⠈⢀⠠⠆⠷⠋⠀⠐⣄⠙⣄⠁⡄⣅⣧⡶⠶⠄
⠀⠀⠀⠀⠈⠀⠠⣀⣆⠐⣂⠰⡔⠸⣿⠴⠄⠀⠀⠀⠀⠀⠷⢮⣿⣡⡌⠀⠀⠖⠀⠀⣸⣷⣿⡍⢟⡿⣶⡄⠁⠀⢷⠈⢆⠘⣶⢸⣄⣿⣪⠥⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣽⣷⣷⣐⣧⠰⠾⠐⡏⠀⠀⠀⠀⠈⠒⢤⣝⢿⠀⠐⠀⢀⢀⢠⣽⠛⠃⠀⣯⣏⣽⢿⣴⣀⠈⣧⠈⣦⣘⣡⠀⢈⣠⣠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢿⠟⡲⢶⣠⣏⠠⢄⡀⠀⠀⠀⠀⠈⠻⣷⡀⣣⣾⡿⠉⢈⡤⣀⢨⣷⣯⡾⡿⣿⡿⠀⣼⣷⣿⣯⠾⠊⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠟⠛⣤⣼⣿⠀⢀⠀⠐⠀⠘⠻⣿⡟⠉⠈⠂⣀⠑⢿⣾⡿⣯⣷⢿⣿⣧⡶⠿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢧⣠⡡⠐⠒⢂⡄⠙⠻⠤⡴⣄⢀⢸⣷⡿⣿⣿⣿⢿⢛⡿⢿⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⡀⠩⡙⢿⠧⠠⣤⡙⢾⣯⣿⣿⣿⢿⣿⢻⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠘⡃⢰⣶⣴⣏⡷⢿⣿⣿⣿⣿⠿⣟⢻⠶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠨⢘⡋⠙⢤⣟⢻⣿⣿⣿⣿⡯⣎⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠐⠷⡌⢳⣈⢻⣿⡛⢿⡟⠯⡱⠈⠌⢿⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⠀⡆⡄⠀⠘⣶⣿⡟⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣸⣀⡇⣧⣀⣇⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⣦⢚⣿⣍⡿⣿⣿⣿⣷⣗⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠈⠙⠾⠿⠿⢷⣷⣮⣿⣋⣛⡛⠛⠛⠉⠊⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣖⣦⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡀⠈⣾⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣿⣿⣿⣿⣿⣿⣿⡶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⣀⣉⣈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣇⣀⡀⢻⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠍⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣄⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⡿⡇⠀⣿⣿⣿⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣿⣧⣶⠏⢸⣿⣿⣿⣕⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣷⣿⡇⠀⣿⣿⣿⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠋⠉⠁⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⣭⣿⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣧⣤⠀⣠⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⣄⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠯⠿⠿⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠀⠽⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⣤⠾⠻⢶⣠⢟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡾⠋⠉⠳⠎⠁⠀⠀⢠⣯⠟⠶⣶⠀⠀⣠⡆
⠀⠀⠀⠀⢀⣤⡶⡖⠷⠚⠛⢀⡤⢾⠁⠀⢴⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⢔⣫⠾⠃
⠀⠀⠀⠀⢼⡏⡌⣶⡒⠚⠋⠉⠀⣸⠀⠀⠀⢨⡟⠋⠀⠀⣷⠿⣄⣀⠀⠀⠀⠰⠏⠲⣏
⠀⠀⠀⠀⠈⠻⠇⢹⠻⡄⠀⠀⢀⡟⠀⠀⠀⠘⢷⠄⡠⠚⠉⠠⡌⠛⠒⣆⣀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣆⠀⣼⢃⠀⠀⠀⠀⢠⡞⠀⠟⠰⠇⠀⠀⠀⠘⠟⡇⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⢧⣿⣸⠀⠀⠀⠀⢸⢠⣄⣑⣠⣄⠀⠀⠠⣄⣰⠃⢀⣹⠆
⠀⠀⠀⠀⠀⡀⢀⡿⠀⠀⠀⢸⣯⡼⢷⡀⠀⠀⠘⢦⡀⠀⠈⠉⠀⠶⣤⡾⠃⣤⠈⢷⡀
⠀⠀⠀⠀⣼⡏⠘⣧⠀⠀⢀⣏⡇⢹⡈⠳⣄⣀⠀⣤⡍⠳⠀⡤⢶⡞⠉⠲⠛⡉⢣⡠⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⢸⣿⢷⡛⡿⣇⠀⣼⠷⠤⣄⠙⠲⠤⣭⣉⡁⢹⡤⠖⠋⠉⠉⠙⠓⠶⡌⢆⡙⢌⢾⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣀⣤⣀⠙⢦⡀
⠀⠀⠀⠘⠟⠛⠛⠓⣿⣰⠓⠲⡄⠙⣦⠀⣀⣠⠞⠁⠀⠀⠀⣰⠏⣉⣉⣹⡆⢹⠈⠣⠈⠛⠋⢥⣄⠀⠀⠀⠀⢰⢋⡤⣠⡌⠋⢛⡛⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣠⠶⠷⢄⡈⠳⣯⠀⠀⠀⠀⠀⣴⣫⠎⠁⢀⢸⠏⣿⠙⢦⡄⠀⣿⣿⣿⠿⣷⣶⡀⢸⣄⣒⣈⣀⠀⠈⣻⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣫⠞⠁⣠⣀⠀⠉⠳⠘⢷⣄⣀⣠⠞⣱⠃⠀⢈⣹⣆⣀⣧⢀⣾⠇⠀⣿⣿⡿⢿⣧⣾⣷⡀⢳⡒⠛⠉⠀⠙⣽⠋
⠀⠀⠀⠀⣿⡀⡶⠋⢀⡴⢚⡁⠉⠛⠶⣤⣄⣀⡭⠟⢁⡼⠁⠀⠀⠈⠁⠋⠃⢁⣾⠟⠀⠸⣿⣻⣤⣿⢿⣎⠈⢿⣆⠉⢓⣦⠴⠦⠼⢦
⠀⠀⠀⠀⣿⣷⣳⠞⣩⡴⠁⣁⣂⣀⣀⣀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠉⠉⣿⠻⣷⣿⣷⠶⠛⣷⠋⠀⣀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠻⠟⠱⠮⢋⡶⠛⠉⠉⠀⠉⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠸⠀⣇⠹⡿⢋⡴⠚⣉⡷⢾⣇⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⡶⢦⣤⣄⡀⣠⣴⣶⠶⠶⢶⣶⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⠙⢁⣠⠞⠁⢀⣤⠟⠒⠀⣤⣤⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠉⠙⢋⣾⠃⠀⠀⠀⢹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣠⠾⠋⣠⠖⠀⠀⠀⣀⡴⣋⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⣀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣇⣠⠞⠁⠀⣴⠚⠋⠉⣻⠳⡌⠧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠘⠀⠅⢠⡿⠡⠌⠡⠄⠀⢤⠄⢻⠆⣿⠀⠠⠦⠀⠃⠠⠤⠀⠀⠘⠃⠰⠆⠑⠎⠠⠙⣧⣠⣤⣤⣤⣤⣀⣀⣿⣤⣝⠒⣲⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠚⠛⠒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢠⡤⡄⠤⡠⠦⠔⠖⠂⠒⠒⠐⠒⠒⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠄⠎⠀⠀⠔⠒⠒⠄⠀⠀⠀⠀⠚⠉⠑⢸⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣅⠀⠀⠀⠀⠀⠀⠀⢄⢠⢴⡀⠠⠴⠄⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠈⠦⣀⠇⠀⢶⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡗⠒⠀⡤⢀⡀⠤⠰⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⠈⠙⠒⠹⢄⢀⠝⠒⠉⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡠⠚⡗⠀⠀⠀⡜⠙⢆⠀⠀⢹⠑⢦⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⢀⡇⠀⠀⡜⠁⠀⠈⡆⠀⠸⡆⠀⣇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣉⣹⡆⢸⠃⠀⠀⠑⣄⠀⢰⠃⠀⠀⣧⠾⣭⣘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠈⡗⠒⡶⠤⠬⠷⠧⠤⡔⠒⡏⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⠃⠀⠀⠀⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⠀⠀⠀⠀⠀⠀⠈⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⠇⠀⠀⠀⠀⠀⠀⠀⠳⡼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⣻⠿⠷⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⣭⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣛⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⣱⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠛⠓⢦⡄⠀⣀⡤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⣀⠀⣠⡶⠛⠛⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⠋⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠙⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⡄⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⠋⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢻⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠘⡆⠀⠀⣀⡤⠤⠶⠦⠬⢥⡀⠀⠈⠃⠀⠀⠀⠀⠀⢸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠞⠁⠀⣞⣉⡙⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⠀⣸⣇⣀⡄⠀⡸⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⢹⠀⢳⡈⢳⡜⠁⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⢇⠀⠁⠀⢹⠀⠀⢀⡀⠀⣰⢋⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣠⠜⠀⠀⢻⣍⡾⠁⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠤⣄⣀⠤⠤⠤⠤⢤⡀⠙⢷⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠻⠴⠚⠁⢀⣠⠴⣖⣛⠉⠉⠁⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠴⠖⠒⠋⠁⠀⠀⠀⠈⠉⠓⢲⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢲⡖⠒⠒⠒⠒⠒⠲⠶⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⣶⣶⣶⣶⣶⣶⣿⣇⣀⡀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⢀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⡀⣀⣸⣿⡇⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⡷⣟⢹⢸⠇⠏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠸⢿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⠁⡎⢼⣿⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠠⠆⠤⠖⠾⠯⠘⠯⠻⠿⠁⠀⠸⠿⠿⠿⠿⠿⠿⠀⠛⠊⠻⠀⠀⠀⠄⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣴⣿⣿⡿⣛⠷⣀⣤⣶⡆
⠀⠀⠀⠀⢠⣿⣿⣿⢟⣴⣾⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⡀
⠀⠀⠀⠀⠈⡏⠉⢀⣿⣿⣿⣿⣿⣿⣿⣷⡄⠋⢸⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣦⣸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⢀⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⣀⣿⣿⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠀⠀⠀⢀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⠙⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠁⣈⣿⢿⣿⣽⢿⣿⣿⣿⣿⡇⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡗⢻⣿⣿⣿⣿⣿⣿⣇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣣⣖⠈⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣵⣿⠋⠁⠲⠄⡀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠆⣿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡦⠀⠀⠀⣀⠀⠐⢴⠶⡶⡶⠶⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⢘⢋⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠀⠀⠀⠀⠀⠸⢨⡅⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡇⠈⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢸⡧⣿⠠⣦⢸⣿⡆⣿⡷⣿⡗⢻⣿⢿⣿⡃⠙⠀⣀⠀⠘⣿⣿⡿⣿⠒⣿⠒⣿⠗⣷⠀⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠘⢻⡟⠞⠛⠚⠛⠓⠛⠀⠛⠛⠛⠛⠛⠺⠻⠇⠀⠉⠃⠠⠻⠛⠙⠿⠛⠛⠻⢿⣿⡿⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢴⠃⠀⠀⠛⠈⠀⢰⣿⠶⡖⣦⣤⣤⠀⢀⡄⣤⢀⣤⣀⣀⣄⣄⣤⣤⣿⢷⣦⣬⣟⠛⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢸⣃⣀⡐⠂⢴⣿⣤⣠⣀⠀⠀⠈⠉⠁⠉⠀⠉⠀⠁⠙⠁⠉⢉⣄⣠⣀⣰⣿⣦⣌⣁⣀⣼⣿⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠃⠀⠀⠈⠛⠉⠋⠛⠛⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡅⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⣄⢀⣄⠀⠀⠀⠀⠀⢀⡾⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠉⠉⠁⠀⠀⠀⠀⣼⣅⣀⣸⠆⢀⣦⣾⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣶⣶⣶⣦⣾⣶⣄⣴⣿⣉⣉⡙⢣⣬⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿
⠀⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⡯⣈⠻⠟⠻⢯⣯⣴⣿⣿⣅⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣿⠇⡀⢺⣿⣶⡾⣿⣿⢟⣁⠸⠿⣯⣽⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⢀⣤⠀⠀⢀⣿⣿⣿⣿⡫⢹⡿⠂⠸⠛⢻⣿⣿⣶⣏⡄⣸⣹⣧⣤⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⣶⣽⣦⢠⣶⣾⡿⠏⣀⣼⣿⣿⣿⣿⣷⣿⣧⣶⣤⡤⣼⣿⣿⡿⢟⣸⣧⠀⠉⣿⣿⣯⢽⣦⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣥⢻⣿⣿⣿⡿⠛⢿⣹⣿⡿⢺⣿⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡹⣿⡟⢿⠁⡀⠸⣽⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠈⠿⣿⡿⢿⡟⢻⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⢿⣿⣿⣿⣇⢀⣠⠀⣿⣿⡷⢾⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢰⣷⣼⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣀⡀⠀⡹⡜⠸⠃⠀⣿⡟⠛⠿⠇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⣾⣍⣿⣿⣿⣿⣿⣝⣿⣿⡏⣿⢿⣿⣿⠿⠿⢗⣨⡥⠽⠟⢿⣿⡟⢰⡶⠁⠀⠀⠟⠷⠛⠂⠀⠀⠀⠀⠀⡀⢀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⢹⣿⣿⣿⣏⣻⣿⣿⣿⣿⡇⣿⣷⣿⠏⣼⣿⢿⣷⠀⠀⠀⠀⠈⠉⠋⠐⠒⠣⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⡇⣸⣿⣷⣾⣿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⣸⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⣿⣿⣿⣌⣿⣷⣾⣿⣿⣿⣿⣿⣏⣴⣿⣿⣯⣽⣿⣷⣼⣄⣻⣿⣿⣻⡦⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠃⠹⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣯⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⣤⢨⣽⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⡀⠀⢀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠉⠛⠻⣟⣛⡁⠛⢷⣿⣿⣿⣿⣷⣾⠿⣿⣿⣧⣄⡉⢻⡷⠶⣶⡋⡀⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡇⠸⡇⠀⢸⣯
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣤⠾⢏⣽⠉⠛⠛⠉⠛⠷⠿⠳⣦⣧⡀⠈⠻⢶⡝⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠓⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⣧⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⣭⠀⢀⡇
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣠⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⡦⠈⠻⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡇⠙⠁⠀⠀⡀⠀⠀⠈⣧⠀⠀⢠⡇⠀⠀⠀⠻⠽⠏⢴⣶⡇⢠⣦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⡀⠀⡼⠀⣀⢀⡠⣄⠀⠀⠀⠀⠀⠘⠷⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠃⠀⠃⠀⣇⠀⠀⢘⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠴⠄⡄⠀⠀⢀⣤⣤⣤⡀⠀⠉⠲⠤⠜⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠁⠀⢠⣿⣿⣿⣿⣿⡆⠀⣀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠀⠀⠘⣿⡉⠙⣿⣿⠃⠀⠉⠁⠛⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣾⣿⣿⣷⣾⣯⣷⣿⣿⣶⣤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠙⠣⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣽⣿⣿⡇⣿⣿⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⣄⢀⣀⢀⣀⡆⢀⢀⣀⢀⣀⠀⣀⡆⣀⢀⣀⠀⣀⠀⣀⡰⢀⡄⢀⠀⡀⢀⠀⢠⡀⠀⡄⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠇⢠⣬⢥⣺⣽⠀⡟⡈⢹⠀⠯⣸⠀⣇⡿⣀⢇⣸⠀⣑⠸⣊⠵⢇⡸⢅⠇⠐⠮⠂⢁⡭⡇⡇⣗⡉⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠤⠤⡄
⠀⠀⢠⣤⡤⢤⣴⠃⠀⢀⣀⣀⢀⣦⡀⠀⠀⣤⠆⠀⠀⠒⠆
⠀⠀⠀⠙⠶⠾⠋⠀⣥⡤⣤⣉⠙⠿⠃⠀⠀⠀⠺⣠⣿⠟⠰⣀
⠀⠀⠀⠀⠀⠈⢢⡀⠈⠠⣴⣮⡿⠁⠤⠂⠀⠲⢦⡄⠄⠀⠀⢧⣵⣦⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠈⢣⠀⠘⢁⣉⣒⠬⠉⠀⠀⢀⡜⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⡐⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⠀⠡⡀⠀⡍⠉⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⠫⣤⣶⠟⠁⠀⠳⣄⢠⣤⣤⡟⠀⠀⡄⢶⡞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢤⠇⠀⠀⠀⠀⠉⢀⣰⠀⠀⡙⢶⡶⠒⣦⣤⠁⠀⠀⠀⠈⡆⢀⢰⡀⠐⣙⣷⠟⠋⠀⠀⠈⣿⣦⣉⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠸⡆⠀⠙⢂⣈⣹⡼⠳⡤⠶⣴⣾⠋⠻⠛⣇⣀⠀⠀⠰⠄⢹⠈⠃⣭⠿⠟⢙⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠀⢧⠀⠀⡸⠁⠹⡄⠀⠙⠛⡟⠁⠀⠀⡇⠈⢁⣁⣨⡿⠋⠀⣧⢠⠏⠀⠀⢸⣃⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠰⠛⢦⠸⡄⣰⠃⠀⠀⠘⢄⠀⠀⢧⠀⠀⠀⢻⠀⠀⣯⠁⠀⠀⠀⢸⣏⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠘⠶⡦⡈⢏⠓⠢⠥⠀⠙⠂⣈⣵⣿⠃⠀⠀⠀⠀⠀⠑⢦⣼⠀⠀⠀⠘⡆⠀⡇⠀⠀⠀⣠⠏⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠐⠒⠛⠛⠉⠉⠈⠉⢷⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠹⣀⡇⠀⠀⡼⠃⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢙⠁⢀⡾⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⣤⠋⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣀⠀⡙⢾⠃⣀⡴⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣀⡀⠪⠅⠀⠀⣽⣧⣭⡤⢒⣿⣅⣉⠟⠣⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣴⣄⢀⠀⡠⠆⣤⣙⣆⣿⡗⠀⢀⣦⡀⠀⡿⠀⠘⢟⠁⢠⡀⠑⠳⢄⣀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⣀⣊⠉⠉⠠⢀⠈⠱⠌⠉⠉⢷⡈⢿⣿⠐⢾⡆⢽⣄⡇⠀⠀⠈⢳⡀⡆⠁⠂⣻⣉⠲⣄⠓⢤
⠀⠀⠀⠀⠀⠀⠀⣀⠌⠅⢤⣬⣾⣿⣿⠢⠄⢀⣤⣵⣄⡘⢇⡀⡘⣇⠘⠙⠀⠘⢿⣶⣿⢁⣀⠀⠀⠀⠱⠀⠀⠀⠙⠉⠦⣈⡑⢾⠃
⠀⠀⠀⠀⠀⣠⣍⢀⡀⣀⣀⣨⠟⣷⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠒⠻⠤⣤⣽⣿⠩⠤⡭⠵⣦⡀⠀⠀⠀⠀⠀⠀⠈⠹⢄⢳
⠀⠀⠀⠀⠀⠀⣠⡶⠗⢋⠁⠐⡀⠈⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⡞⠁⣤⠀⢼⠀⠀⠉⠒⠲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⡈⠀⡴⢘⠀⠖⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢀⣏⠐⠂⠈⢆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠀⠀⣉⠀⡅⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡄
⠀⠀⠀⠀⠙⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡆
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣀⣀⣤⣤⣤⣴⣶⣶⣤⣤⠀⣀⠀⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⢛⠛⣿⣾⣿⣿⣿⣿⣿⣯⣿⣻⠙⠏⣛⣂⡗⢦⣜⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⣭⣿⡟⣼⣿⠹⣿⣿⢍⡀⠀⠁⢀⣤⣷⣿⣿⣿⣿⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡴⢻⣿⠛⣿⢿⢤⣽⣽⡢⢤⣴⣾⣿⣿⠿⢛⣉⡥⠒⠛⢻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⠀⠈⠛⠷⠮⠍⠉⠀⠉⠉⢉⣤⣶⠏⠁⠀⠄⣠⣬⡻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠰⣯⣏⠙⠒⠦⠘⠳⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⡀⠀⠀⠈⣁⣀⠉⠀⠀⠀⠀⠰⣿⣥⣄⣰⣾⣾⣝⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣷⠀⠀⠸⠉⣭⣿⠂⠀⠀⠀⠘⣿⡟⣩⣬⣍⣿⣝⣦⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠟⠀⠀⠀⠌⠉⠥⠄⠀⠀⠀⠀⠈⠁⢿⡢⢰⢿⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⡀⢀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣸⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠈⠀⡙⢁⡦⡀⠀⠀⠀⠀⠀⠀⠐⢫⠚⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⢶⣲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢢⣬⣽⡧⠋⠰⠃⠀⠀⠀⠀⢠⠿⠶⠃⢠⠟
⠀⠀⠀⠀⠀⡠⠒⠛⡁⠀⠀⠀⠀⠙⢿⣀⣍⡺⢖⡊⠵⠀⠢⠄⠀⠀⠀⠀⠹⠀⢭⣥⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⢠⠋
⠀⠀⠀⠀⢸⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠉⠻⣽⡒⣍⡲⢤⣴⠲⢐⡦⢄⠀⠰⣀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⣸⢄
⠀⠀⠀⠀⠈⣇⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣽⡷⣮⣝⣲⢤⣿⣆⡀⡈⠙⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⣠⠔⠁⢸
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⣭⣽⡒⠤⣀⣀⡀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣭⣟⣲⢭⣢⣀⠔⣣⠀⢀⡠⠴⠒⠉⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢘⢻⢦⣀⠓⠥⣾⡳⢌⣲⡌⡙⢦⣄⡒⠤⣄⠀⠀⠀⠀⠀⠉⠉⠛⢿⣟⠳⡼⡜⢅⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡗⢄
⠀⠀⠀⠀⠀⠀⠀⢏⠸⣉⠳⣤⣄⠈⠲⢭⣯⣏⠉⣽⣿⣽⢶⣝⢦⣀⠀⠀⠀⠀⠀⠀⢹⠀⠹⡄⠀⠙⢦⡀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢡⠀⠦⠈⢗⢶⣤⣀⠈⠁⠐⠒⠺⠓⢤⣕⣦⣬⡆⠀⡴⠀⠤⠮⢀⢠⠇⠰⣶⣻⣿⣶⣤⣾⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡆⠸⡀⠘⡗⠈⡏⠙⠳⡶⢦⣤⣀⣉⡀⠀⠀⠉⠉⠉⠒⢠⣄⠀⠉⠲⢄⠀⠙⠿⢿⣷⣿⣿⣿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣧⡀⢠⡀⠉⠒⠄⠘⡌⠻⣯⢝⢍⡉⠙⠛⠛⠋⠉⠉⠙⠓⠀⠀⠀⠑⢄⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠑⢭⣋⠭⢭⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣜⡥⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⢠⠞⢁⣠⠾⠭⢄⣠⠤⠤⢄⣀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⢀⣠⠟⠊⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠀⢀⠇⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⣆⠀⠀⡸⠀⠀⠀⠀⣠⠔⠁
⠀⡼⠁⠈⠑⢦⡀⢠⠞⠁⢀⠀⠀⠀⠀⠀⠈⣶⠰⠧⢤⣀⣠⠞⠁
⢰⠁⠀⠈⣻⡶⠄⠀⠠⠾⣛⠀⠀⠀⠀⠀⠀⢸⣧⡀⡠⠊⠉⠓⢤⡀
⡎⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢫⠀⠀⠀⠀⠀⠉⢢⡀
⢀⠀⠀⠀⠀⢀⡐⠂⠁⠲⣄⠀⠀⠀⠀⠀⠀⢸⡧⣄⣇⠀⠀⠀⠀⠀⠀⠙⢄
⢘⣄⡤⠖⠛⠉⣠⠄⠀⠀⣸⠀⠀⠀⠀⠀⢠⣿⡤⣸⡉⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠁⠹⣄⣠⠔⢋⡴⠂⠒⠊⠁⠀⠀⠀⢀⡴⠋⢸⡃⠘⡳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠐⠋⢓⡴⣏⣀⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⢐⡂⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠸⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣀⠤⠔⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠧⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⠛⠻⠙⡌⠉⠉⠙⡄⠀⣀⡠⣤⠶⡖⠒⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢤⣤⣄⣀⣀⣤⣄⠤⢞⠗⠋⠁⠀⠈⠀⠉⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠤⠤⠤⠔⠶⠖⠒⠛⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⢦⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⣿⠿⠛⠋⠉⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠉⢻⣏⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⣴⠿⠛⠋⠉⠀⠀⠀⠀⠻⡄⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀⠀⠀⠀⣸⣿⡟⠁⠀⢶⡀⠀⠀⠀⠀⠀⠀⣁⣴⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧⣀⢠⡿⠁⢠⡄⠀⠀⠒⠋⠉⠉⠉⠉⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠋⠁⠠⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣠⠟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⣶⣦⣄⣿⣿⣿⣿⣿⣿⣶⣦⣶⠶⠶⠖⢶⠆⠁⠀⠀⠙⠛⠛⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠉⠀⣄⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠀⢀⡿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣤⣤⣭⣤⣤⣄⣤⡄⡀⠀⣀⣠⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠋⢉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠀⠸⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⢀⣀⣀⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠰⠛⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠂⠀⢻⣿⠗⠚⣿⣿⣦⡀⠀⢻⣿⠟⠺⣿⣿⣿⠃⠀⠀⢻⣿⣿⡟⠸⣿⣿⡟⢐⣿⡿⠛⠀⠘⣿⣿⡿⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⠀⠀⣹⣿⣿⣿⣷⣼⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣷⣿⣿⡀⠀⠀⠀⣿⣿⣧⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⣸⣿⠀⠀⣽⣿⠈⠻⣿⣿⣿⠀⠀⣿⣿⣿⠀⢀⣤⢀⣿⣿⡇⠀⣿⣿⡿⢿⣿⣿⣄⠀⠀⣿⣿⡏⠙⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠰⠿⠿⠆⠀⠈⠻⠿⠀⠰⠿⠿⠿⠶⠿⠏⠼⠿⠿⠷⠰⠿⠿⠿⠄⠙⠿⠿⠷⠴⠿⠿⠿⠶⠾⠿⠃





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⠀⣿⣿⣿⣯⣤⢶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢿⢿⣿⠀⣿⣿⣿⡿⢴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⢫⣴⣶⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⣿⣿⣦⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣼⣿⣷⡄⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣁⣄⣀⣀⣤⠄⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⢉⢠⣾⣿⣿⣿⣿⣇⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠁⠉⠁⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡎⠀⢀⠀⠶⠴⠾⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠻⣷⡀⠀⠀⢸⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⠟⢷⣄⠈⠻⣦⡀⠸⠿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⠟⠁⠀⠀⠙⢷⣄⠈⠻⣦⡀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠻⣦⡉⠀⠀⠀⢀⣾⠛⠉⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢿⣦⡀⠀⠸⣿⡀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠉⣠⣶⠆⠈⠛⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡟⠁⣀⠀⠀⠀⣺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣷⡀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣄⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠛⠛⠛⠛⣿⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣧⡈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠀⣀⠀⣿⡇⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⢠⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢿⣦⣾⠋⠀⣿⡇⠀⠀⠀⠀⠀⡀⠻⣷⣄⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠟⢷⣄⠀⣿⡇⠀⠀⠀⠀⠀⣿⡆⠈⠻⣷⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠈⠉⠀⣿⡇⠀⠀⠀⢀⣼⠟⠀⢰⡆⢸⣿⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣀⣀⣀⣀⣠⣿⣄⣀⣀⣀⣀⣀⣄⣿⣇⣠⠀⢠⣾⠋⢀⣴⡟⠁⢸⣿⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣰⡿⠁⣠⡾⠋⠀⠀⢸⣿⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠰⣿⣅⠀⠀⠀⢸⣿⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⡾⠏⠀⠀⠀⠸⠿⠶⠶⠾⠿





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠤⡒⠒⠒⠒⠒⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡡⠖⣩⠴⠞⠛⢻⣧⠀⠀⠀⢀⣶⣶⡄⠉⠓⢦⣀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣣⠖⣭⣦⠀⢹⡀⠀⢀⣾⡏⠀⠀⠐⠋⡿⠀⢀⣴⣦⡀⠙⢷⡀
⠀⠀⠀⠠⡞⢁⠀⢀⡴⠊⠀⢠⡟⣿⡆⠈⣧⣴⣿⡟⠀⠀⠀⠀⠀⠇⠀⠸⣧⡼⠃⠀⢸⣿⡄
⠀⠄⡰⢙⣀⡬⢟⡵⣆⣠⣄⢸⡟⠹⠇⠀⢛⣻⡯⠄⠒⠂⠙⠛⠻⠿⣷⣶⣦⣄⠀⠀⢠⣯⡇⠇
⢠⠠⡇⠀⠀⠀⣮⣼⠟⣡⠏⠘⢃⣤⠶⣿⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⣾⣿⠇⠺⠆
⠀⢻⣧⠀⠀⠀⠈⣿⣶⠋⣠⢾⣟⠁⣸⠁⠀⠀⠠⡞⠙⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⣿⣿⠋⠠
⠀⠀⢻⣷⣄⠀⠀⠈⢛⣾⣿⠏⠈⠤⠇⠠⠀⠀⠰⠉⠀⠐⠒⢦⠀⠀⠃⢠⠀⢣⣿⣿⣃⢀⡤⡀
⠀⠠⠀⠻⣿⣿⣦⣤⣾⠟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⢤⡆⢸⣇⠀⠈⠀⠀⠘⣾⣿⣇⠸⣠⠆⣤
⠠⠀⠀⠀⠈⠙⠻⣿⣯⣷⣶⣶⡀⠀⢀⢞⣿⣿⣿⠿⣿⡀⠃⢸⣿⡀⠰⣤⣏⠀⣿⡿⠎⠛⠛⢿⣷⢸
⢡⠄⢠⠀⡏⠙⡆⠸⢇⣿⣿⡋⣳⠀⢈⠸⣿⣿⣿⣀⣸⡇⠀⢸⣟⣿⢦⡿⠙⣷⠈⠛⠤⢠⣾⣾⡟⣾
⠇⠀⠀⢀⠙⠒⠁⠀⠀⣿⣿⣿⡿⣌⠸⣆⢻⣿⣿⣿⣿⢿⠀⠈⠻⠿⠋⠀⢒⡟⠀⣠⣾⡿⣿⠿⠇
⠀⡄⠀⠀⠀⠀⠀⠀⡸⠾⠿⢛⣽⣿⣆⢺⣷⢿⣿⣿⡿⣫⣴⢶⣏⠀⢀⡆⢎⠀⣾⢯⣫⠔⠂⠀⠀⠀⡆
⠀⠰⣀⠀⢀⣀⠀⢀⡇⠀⠀⣼⡿⠻⠿⣧⠙⠻⠿⠷⠋⣿⡏⠀⠈⢳⠀⠀⢈⠇⠻⣮⢿⠀⠀⠀⠀⠊⠐
⠀⠀⠀⠉⡛⠻⠓⠀⢿⣷⣶⡄⠀⠉⠉⠉⠀⠀⠀⣴⣄⢙⣿⠀⠀⣼⡀⢠⠏⡀⣴⠟⡘⠀⠀⣤⣤⡤⠖
⠀⠀⠀⠀⠈⠓⡀⠀⠀⠙⢻⠃⠀⠀⢀⠀⢰⣶⣤⣼⣿⣿⡿⢀⣼⣟⡤⢘⣄⣿⣧⣤⣿⣦⣴⣧⣀⠈
⠀⠀⠀⡀⠀⠰⢿⡆⠀⠀⣼⣦⣿⣤⣼⣷⣾⣿⠟⠛⡏⢋⣁⣌⣉⣭⣀⣉⣩⣼⣿⠿⠿⠿⠿⣿⣿⣄
⠀⠀⠀⡨⠇⠀⠈⠀⠀⢸⣿⣿⣿⠛⢿⠀⠸⣿⠃⠀⢠⢤⣼⣿⣿⡿⠟⠛⠉⠁⠀⢦⣾⢷⡄⠈⠙⢟⢧
⠀⠀⠊⠀⠠⡀⠀⢀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣯⣿⡿⣻⠛⣷⣤⢤⣰⠛⣶⢸⡟⢸⣇⣴⢶⡌⢾
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢻⣿⣿⣿⣿⣦⣼⣶⣿⡿⠛⠁⠀⠙⣾⠉⣠⡾⠉⠙⠁⠀⠁⠺⢻⡟⠛⠃⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢫⡙⠛⠛⠿⣟⠟⡁⠰⣋⡷⡀⠀⠸⣟⣭⠶⢛⣏⠉⠛⠳⣄⠘⣧⣄⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠱⡄⢠⣤⡌⢿⡍⠳⡍⠛⢁⣴⠞⠉⠀⠆⠀⠁⠀⠀⠀⣽⠇⢀⡴⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢇⠀⢳⠀⠀⠛⣠⣦⡾⡿⠁⠀⢉⠇⠀⠀⢀⣠⣴⣟⡥⠖⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⢰⡘⢶⣬⣴⣶⣾⣟⡿⠏⠀⠀⠀⠋⠐⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣍⡙⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣁⣒⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⠀⠉⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠠⠄⠀⢠⠰⡈⣇⠀⠀⠀⠀⠀⠀⠘⣆⣤⠠⡥⠤⠒⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⣧⢳⠸⡄⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⡌⠇⠁⠀⢺⠉⠂⠀⠀⠀⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠠⠀⠂⠁⠰⢄⠁⠈⠀⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠠⢂⠠⠌⠇⢀⡀⠀⠀⠨⣀⠐⠀⠰⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠣⠌⢤⣢⠇⣸⠙⣄⠀⠀⠈⡄⠀⡀⠂⠀⠀⣠⠀⠀⢀⣀⣀⣤⡤⠴⠒⠉⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⢰⡒⠀⠀⠁⠀⠉⠀⠀⠀⠘⠉⠠⢀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣀⣀⣀⣀⣀⣀⠤⠖⠉⠀⠱⡀
⠀⠀⠀⠀⠸⠵⠁⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠖⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠉⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢸⠀⠱⠃⢸⠀⠀⠀⠀⠀⠀⠀⠲⣄⡴
⠀⠀⠀⠀⠀⠀⢠⠴⡇⠰⠶⠶⠶⠶⠶⠀⡁⠀⠠⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠴⠉⠳
⠀⠀⠀⠀⠀⠀⢸⠀⡇⣟⣉⡇⢘⣛⣛⠀⡄⠀⢀⡤⠴⠤⣄⠀⠀⢄⡀⠀⡟⠲⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⠉⠁⠀⠀⠀⠀⡇⢠⠏⠀⠀⠀⠈⢳⠀⠤⠭⠀⡇⠀⠀⢸⠁⠈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⢠⠇⠸⡄⠀⠀⠀⠀⢸⠀⠖⠋⠀⣇⡤⠤⠾⠛⡟⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠙⣦⣀⣠⣴⠧⣄⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠴⠶⠀⠄⠤⠤⡄⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⠀⠰⣄⣠⠄⠀⣧⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢸⠀⢠⠞⠳⡄⠀⡶⠋⢀⡞⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣤⠇⠀⢸⠀⠀⣼⠉⡇⠀⠀⠀⠀⠀⠀⡗⠦⢤⣀⠀⢩⠗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢳⠤⠤⠴⠖⠒⠒⢻⠀⠀⠈⠙⠛⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣠⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⣸⠁⠀⢸⠀⠀⠀⢠⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡀⠀⠀⢸⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠄⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿
⠀⠀⠀⠀⣿⡷⢀⡀⢶⣩⣾⣦⠀⠀⠀⠀⠀⢠⣤⡄⠀⢠⣿⣿⡞⠁⠀⠀⠀⠀⠀⠍⡅⢨⡁⠺⣿⣿⣿⣆⡀
⠀⠀⠀⢠⣶⠞⠉⠀⠀⢹⣿⣿⡇⠀⠀⠀⢀⣼⣟⣡⣄⣼⣿⣿⣿⠀⠀⠀⢀⣰⣿⣷⣧⣿⣷⣶⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠸⣿⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⣿⡟⠉⠁⠀⠙⣻⣿⡿⠀⠀⣰⢻⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠂⠀⠀⠀⠈⣿⡏⠉⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠁⣿⠀⠀⠀⣻⡿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠛⠋⠁⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣤⡈⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠟⠠⠉⠀⠀⠀⠀⠀⣐⠀⠄
⠀⠀⠀⠀⠀⢙⣏⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢏⣹⠺⡿⠇
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠘⠁⣿⠋⠀⠀⠀⠀⠀⠀⢛⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠙⣿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠾⣿⡟
⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠃⠀⢁⡖⠀⠀⠀⣸⣿⣄
⠀⠀⠀⠀⢸⣿⡟⣳⣀⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷
⠀⠀⠀⠀⢸⣿⡏⠁⠉⢿⢛⡟⢹⡇⠀⠀⠀⠀⢰⢾⣿⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡿⣇⠀⠀⠈⠈⠁⠈⠁⠀⠀⠀⠀⠀⣻⣿⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⣠⣤⣤⣾⡷
⠀⠀⠀⠀⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⡿⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠿⡿⠃
⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠹⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢹⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢻⠉⠛⢻⡿⠁
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣴⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡇
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠙⢿⢿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠻⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣦⡄
⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠛⣿⠉⠉⠁
⠀⠀⠀⠉⠙⣿⠛⠛⠉⠁⠀⠀⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠫⡇⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⣿⣿⡿⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣀⣤⣶⠾⠿⠿⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠉⠉⠛⢿⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⣷⣄⣠⣤⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠉⠁⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡞⢻⣦⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣆
⠀⠀⠀⠀⠀⣰⡟⣰⠟⠀⠀⢿⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡆⠈⣿
⠀⠀⠀⠀⢠⣿⢠⡟⠀⠀⠀⠈⢷⣤⣤⣤⡶⠛⠁⠸⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡅⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣦⣀⣀⣤⠞⠉⢷⡄⠀⠀⠀⠀⢀⡴⠻⣇⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠰⣶⢦⣤⡀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠷⣦⣴⣾⡏⠀⠀⠻⣦⣤⣤⡶⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣀⣠⠟⠋⠀⠀⣤⣄⡀⠀⢶⡄⠀⠀⠙⢦⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⣩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾
⠀⣟⠛⠻⣄⠀⠀⠀⠸⢿⣿⣷⣬⣿⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠞⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠙⣿⠗⠛⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣤⣤⣰⣧
⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠋⠉⠀⠀⠀⣀⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠋⠉⠀⣈⡉⠉
⠀⠐⣿⠀⠀⠀⠀⠀⠙⠓⠛⠃⠀⣠⡶⢛⣛⣿⡿⠿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⡛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⣠
⣴⠾⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣬⣭⡤⠶⠞⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠾⠋
⠙⠿⠿⣏⠁⠀⠀⠀⠀⠀⢀⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣸⡇
⠀⣾⣟⣋⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢸⣧
⠀⠈⢩⣿⣃⣀⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣸⣦⣤⡿⠃
⠀⠀⠀⠉⠉⢿⣧⣶⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⣤⡿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠈⠻⣄⠀⠀⠀⠀⣠⡾⠛⠋⠉⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠘⢷⣄⠀⣴⠏⣀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡀⠀⠙⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⢷⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⡤⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⣀⡀⠀⣼⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠾⣯⢹⡟⠛⠀⠀⢀⣾⠿⠿⢿⡛⠛⠛⢻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⢀⣿⣹⡆⠀⠀⢀⣾⠃⠀⠀⠘⣷⡶⠛⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⢉⣿⠿⠶⠶⠟⠁⠀⠀⠀⠀⠸⣷⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣿⡀
⣄⣠⣀⣠⣤⣄⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣸⣿⣍⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣉⣋⣠⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣀⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢉⡑⠢⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣶⣄⠀⠀⡝⡍⡏⢆⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣤⡖⠺⠧⠑⣄⠹⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠋⠛⢿⠷⣏⠱⢁⠀⠈⠆⠀⠀⠀⠀⠀⢀⣀⠀⠸⡃⢱⢄⡄⠮⠀⠈⠛⡇
⠀⠀⠀⠀⠀⣿⣿⠏⢥⡤⡘⣂⡀⢠⡏⢆⡀⠃⣀⡆⣀⣀⣀⠤⠤⠬⠥⠄⠀⢇⠀⣌⠄⢄⠂⢀⠎⠁
⠀⠀⠀⠀⠀⢍⠁⠿⡴⠒⠚⠁⣸⣸⡿⠆⢉⠁⠀⢃⠀⠀⠀⠀⠒⢒⠉⠀⠀⠈⠢⠜⠶⡮⠔⡏⠉⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠈⣿⣷⣼⣶⠮⠥⢾⡿⠡⠀⡸⠀⠀⠸⡀⠀⠀⠀⡀⠉⠀⡠⢖⢄⣇⠀⠈⡧⠔⠁⠀⠀⠤⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡩⠝⠉⠙⠤⣴⣿⣷⠀⠀⠀⠀⠀⢀⠅⠀⠀⠚⢀⡴⠊⠔⠁⡸⠈⠉⣻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠎⠀⠀⣀⠤⠴⡆⠀⢹⠀⢰⠤⠤⠐⠊⠀⠀⠀⠐⠁⠀⠀⠀⠀⢇⣀⣠⠃⢃⠀⠀⠀⡠⠒⠚⠂⡤⠃
⠀⠀⠀⠀⠸⠀⠀⠉⠀⠀⠀⢡⡠⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠷⠷⠧⠊
⠀⠀⠀⠀⠀⠑⠤⠄⠤⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣼⠃⠀⠀⠤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠳⠐⠀⠈⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠦⢀⣹⣁⡀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠻⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠄⢇⡨⣿⣟⠳⢶⡦⠄⠀⠀⠀⠈⠁⢀⡈⢢⠈⢄
⠀⠀⠀⠀⠀⠀⠀⢴⣷⠂⣤⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠦⠀⠀⠀⠀⢀⢀⡴⠛⢿⣿
⠀⠀⠀⢀⣤⢄⠀⢬⢿⣷⣶⣧⡄⢸⣷⡶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠈⣂⠀⠀⠋⠁⠀⡀⣼⣇⣻⡗⠀⠀⣠⠠⠆
⠀⠀⢠⣿⠿⣦⣡⠏⣿⡛⠛⡿⣷⠐⢪⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣿⡾⢂⡄⣰⣬⠷⠿⣶⠀⠀⢦⣤⣈⢙⠳⣦
⠀⠀⠘⣿⣾⡿⢁⢠⢿⣿⣶⠦⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠻⠿⢷⣏⠁⢀⡀⠈⠻⢎⣋⠿⠿⣆⣠⣀
⢀⡀⠀⣱⡏⠀⣩⠂⡜⢹⣿⡋⢴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢶⣦⣄⡀⠀⠞⠃⠀⠀⢈⠀⡤⠀⣤⣤⣀⠈⢍⠙⠳
⢸⣷⣤⣭⡉⠀⣼⣷⣶⣬⣿⠀⠉⠙⠻⢿⣦⡤⣤⣤⣄⣀⠀⠉⠒⣿⣙⠆⠒⠻⣇⣉⣍⣲⣤⣤⣴⣶⠴⠃⣽⠀⠈⠛⠋⠀⠢⣝⣆
⠈⠉⠉⠛⣿⣦⡿⠟⣃⣿⣻⣤⣠⡀⡀⢀⠈⠣⡈⢻⣿⠿⡧⣀⣀⣿⠿⠇⠀⠀⣏⣉⣿⡿⠟⠛⠋⠁⢀⣾⠿⠶⠒⠂⠀⠀⠀⠀⠙
⣾⣿⣿⣷⣿⣷⣷⣿⠽⠿⠟⠛⠒⠨⠭⠭⠿⡂⠽⠚⠉⠶⠾⢛⠿⠃⠀⢀⣻⡵⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣤⣤⣀⠀⡀
⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠒⠒⠐⠒⠂⠀⠂⠀⠀⠀⠐⠂⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡆⣠⠖⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢦⣬⣷⣼⣿⣷⣾⢯⣩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⡟⢰⡏⢻⣷⡉⢦⡙⢮⡙⢦⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⡾⡿⠁⣾⠀⢸⡇⢸⠈⣧⠀⢻⡄⠙⣦⠻⣤⢿⡿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢿⣿⣤⣩⡏⣼⠃⠘⠏⠀⠀⠓⠸⠇⠘⠃⠀⠻⠀⠘⣧⠘⣾⡇⠀⠹⣿⣷⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⡿⣿⣿⠁⠀⢸⣆⣿⠀⠉⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠙⠀⠀⠀⢹⡜⣮⢳⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⣴⢫⡞⢹⡇⠀⠀⠀⢿⣿⣿⣦⡀⠛⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢠⣤⣄⢀⣌⡙⣦⠀⢻⡈⢷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⠀⣸⠁⠀⠠⣾⢹⣿⣿⡿⠿⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠰⠿⣿⠟⢸⣿⣣⡿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡟⠀⠀⠀⠙⣾⣋⣹⡇⠀⣸⣿⣷⣄⠀⠀⠀⠀⠀⣴⠀⠈⠙⠀⢀⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⢿⡄⢽⣿⠀⠙⢷⣄⠀⣀⣰⠏⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢮⣁⠀⠀⠀⠈⠙⠉⠁⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢚⣿⡗⠛⠛⣿⣏⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⢿⣝⠇⠀⢀⣻⣿⠏⠉⠙⠳⣤⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠴⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠀⠀⠀⠤⠤⣄⠙⠳⣤⡀
⠀⠀⠀⠸⣏⡛⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣇⠀⠀⠠⠤⠤⣤⣤⣤⣴⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣗⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢀⣼⠟⠀⣴⣾⣿⣿⠋⣍⡉⢩⣤⣄⠀⣀⠀⠀⠙⣷⣳⣾⣿⣿⣷⡶⠊⠻⣿⣿⣿⣯⣀⣀⠀⠀⠀⢨⠟⣿⡿⣱⣦⠀⠀⠀⠀⠙⣆
⠀⣠⣶⣯⡷⣶⠄⢾⠟⠁⣴⠿⠶⠿⠶⠾⠶⠿⠞⠛⢿⡛⣿⠙⢿⢻⠟⠉⠁⠀⠀⠠⠀⠸⠿⠿⣿⣿⡗⠀⣈⠈⠙⠑⠟⠁⣦⠀⠀⣠⡾⠁
⠐⠿⠟⢁⣾⣷⢿⣿⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠐⠿⣷⢬⡛⠇⠡⢿⣿⠆⠀⠀⠀⢿⣠⣾⡏
⠀⠀⠀⠸⠿⠃⣾⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⣿⠏⠀⣄⣀⠀⠀⢀⠀⠀⠀⠀⠈⠩⢀⡀⠀⠀⠀⢸⣏⣀⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠄⠀⠠⣽⣛⣿⣿⣷⡆⡀⠀⠈⠀⠴⠄⢃⠀⠀⠀⢿⡞⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡍⠓⠟⠹⠻⠟⠸⠻⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⡄⠀⣶⣦⠄⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣤⣤⣄⣀⣀⣈⣡⣤⡤⠶⠶⠶⠖⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠞⠛⠛⠛⠛⠛⠛⠓⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣆
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡿
⢸⡇
⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠸⣇⢸⠳⠾⠷⢤⡽⢦⣌⡷⣬⡷⢤⣸⠶⣄⣲⢦⡀⢠⣄⡀⠠⣄⡀⠀⢤⣀⠰⡄⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠁⠙⠲⠏⠙⠲⠖⠈⢿⡃⠀⠀⠀⠀⠀⠀⣰⠇
⠀⢀⡏⠀⠀⠀⡾⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⣤⡀⠀⠀⠻⣄⣀⣀⠀⠀⣰⠏
⣞⡛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠙⠆⠀⠀⣨⡄⠉⢧⡼⠃
⣸⠋⠛⠛⠀⢀⣤⣄⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣠⡾
⢻⡄⠀⠀⠀⠛⠶⠞⠃⠀⠀⢠⠟⢻⡷⠒⣶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠉⠉
⠈⢷⣄⠀⠀⣀⣠⡀⠀⠀⠀⡟⠀⠈⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠙⢷⣞⣋⡿⠃⠀⠀⠀⠻⠦⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢉⣛⣛⣛⣛⡛⠛⠉⠉⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⣴⠟⣡⣾⣋⡽⠋⠉⠉⠉⠛⠲⠶⣟⠛⠲⢦⡈⢻⣄
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠉⠙⠳⣦⣄⣀⠀⠀⠀⠀⠙⠶⢄⠷⠀⣿
⠀⠀⠀⠀⠀⠸⣧⣀⣀⣤⣤⠖⠛⠉⠀⠉⠛⠲⢦⣄⣀⡀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠓⠒⠒⠒⠒⠶⠶⠶⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢘⡿⠒⠲⠶⠶⠶⣶⠒⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡾⠁⠀⠀⠀⠀⠀⢸⡇⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠰⣿⣥⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣽⡷
⣿⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣦⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠲⡤⠖⠋⠉⠳⣄⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⣴⠀⠀⠀⡜⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠁⠘⠦⠴⠊⢇⠀⣀⡄⠀⠀⢠⡇⠀⠀⡠⠲⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠊⣀⠀⡀⠰⣢⠀⠉⠀⢈⢶⠾⠁⠑⠒⠋⠀⠀⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⠀⠈⠛⢿⠄⠀⠀⠀⠀⠘⠁⢀⡄⢀⠀⠀⠀⢠⣇⣀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠘⠃⢰⣲⣾⠷⠄⠀⠀⠀⠻⠟⠛⠋⠀⠀⠀⠀⢀⣂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣫⡬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠢⣀⠜⠉⠁⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢆⠀⢸⠀⠀⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣤⠜⠀⣬⣤⠤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠴⡻⠤⠞⠀⠘⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠁⠀⠀⠀⠀⠘⢾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⢰⣿⣿⡆⠸⣿⣿⠃⣰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣿⣿⣿⠅⢸⣿⣿⡇⠨⡿⠃⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⣿⣿⣿⠄⢸⣿⣿⡇⠈⠁⣼⣿⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⡇⠀⣾⣿⣿⡿⢁⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠻⠿⠟⠀⠘⠿⠿⠃⠀⠻⠿⠟⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣶⣶⣶⣿⣷⣶⣶⣾⣿⣶⣴⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢫⠇⢰⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣛⣛⣛⣛⣻⡇⠀⠀⢈⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⡼⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⣩⡍⣿⣏⣉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣬⣥⣿⣶⣶⣾⡇⠀⠀⣠⣾⣿⣿⣶⡀⠀⣈⣙⡂⠀⣿⣿⣿⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡷⠀⢀⡤⠆⠀⣿⡿⠿⠘⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣥⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⣄
⠀⠀⠀⠀⠀⠀⣿⣿⡦⠋⢴⣿⣿⣦⠄⠀⢀⣴⣿⣿⢟⣿⣿⣿⣿⣿⣷⢸⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⣦⣿⣿⠀⠀⠀⣾⣿⡟⠁⢾⣿⣿⣿⣿⣿⣿⡘⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠿⠇⠀⠈⠙⠛⠿⢱⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣭⣭⣴⣶⣶⣶⣧⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⡃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣿⣿⣿⡟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠸⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⠿⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢛⣩⣭⣙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣱⣿⣿⣿⣿⣧⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢡⣿⠟⣋⣛⢿⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⡈⢧⠀⠀⢸⣿⢸⣿⢸⣿⣿⠟⣡⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⣧⠘⡇⢸⡆⠀⠸⣿⢸⣿⢸⣿⣶⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠰⠃⣸⠃⠸⠁⠀⠀⢿⡆⣿⣆⢿⣿⣏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⠻⠟⠛⠉⠀⠀⠀⠘⠃⣤⣦⡄⠀⠀⠘⣿⣌⣿⣦⡙⠿⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⡘⢿⣿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣌⢿⣿⣿⣿⣷⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂⠙⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⡀⢷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢬⡙⠧⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⢈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⡀⠸⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢀⠔⠁⠈⢆⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞⠈⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⢄⠀⠀⣱⡄⠀⠈⣀⠤⣀⠀⠀⠀⢠⠃⠇⠀⢦⠸⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢎⢆⠞⡡⠃⠀⢰⡁⢐⡾⠤⠐⢶⠁⢸⣤⠉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠒⠊⠁⠀⠀⢠⢿⠁⠀⢀⡴⠋⠀⣾⡷⣊⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⠁⠀⠀⣀⡠⠄⢚⡶⠒⠊⠁⠀⠀⠀⠘⠹⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡄⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡴⠋⣀⠤⠒⠋⠉⠀⢀⡴⠃⠠⠀⠀⠀⠀⠀⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⢀⠔⠁⠀⠰⡁⡀⠀⣀⡤⠖⠉⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢣
⢀⣠⡄⣢⠄⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⢀⡞⠀⢀⠔⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢧⢀⡠⣒⡆
⠋⠈⠑⠪⢕⢕⢲⣠⠇⠀⠀⠀⠀⠀⡇⠀⠀⠎⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠳⢯⣏⠒⠀⠈⢇⣠⢿
⠀⠀⠀⠀⠀⠑⢵⣟⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠛⠀⢀⠜⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡀⠀⣠⠔⠁⢠⠂⠣⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠬⢷⡄⠀⠰⠶⠓⠐⠐⠒⠒⠒⠒⠒⠒⠒⢂⠖⠀⠀⠀⢀⠤⡤⠀⢄⠀⠀⠀⠀⢀⡀⠥⡞⣳⠎⠈⠑⠦⠃⠰⡄⠀⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠃⠀⠀⠀⠀⠣⢔⢻⠿⢸⠀⣀⣤⣯⠁⢀⡴⠁⠛⠁⠀⠀⠀⠀⠀⣷⢀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢎⠜⠫⡀⡭⠐⠈⠉⠹⢔⡝⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠟⠋⠙⢧⠀⡠⣫⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢰⡆⠀⠀⣶⠆⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡵⠁⠀⠀⠀⠀⢪⡀⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⡡⠛⢷⡬⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡰⢩⠋⠁⠒⠒⠂⢠⠤⠃⠀⠀⠀⠀⢎⣸⠐⢈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⢻⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠖⠳⠧⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢭⢸⠖⠛⠃⠀⠉⠓⣮⢦⣵⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣱⣄⠸⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠡⠃⠀⠀⠀⠀⠀⠀⠻⠞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⣛⣛⣷⠶⠖⠒⠒⠉

⠀⠀⢠⣤⡤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⣤⡀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⣿⣇⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⡅⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢹⡇
⠀⠀⣿⣿⠀⠀⠉⠀⡌⡀⠁⣈⡀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⣿⠀⠀⠀⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⣸⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢛⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⡇
⠀⠀⠈⠉⠉⠉⠉⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⢰⡿⠛⠛⠻⠛⠛⠛⠛⠛⠒⠻⠿⠟⠛⠷⠶⠶⢶⡄⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠃
⠀⠀⠘⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠾⠷⠶⠶⠶⠶⠖⠾⠂⠀⠀⠹⠶⠺⠿⠿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠿⠃

⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣶⣶⢶⢶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣤⡄
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣴⣿⡟⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⠿⣿⣿⠂
⠀⠀⠀⢿⣿⣻⡿⣿⣽⠏⠀⠀⠀⠀⠀⢸⣿⣿⣛⠛⠻⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠹⡿⠿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣧⡈⠉⠃⠀⠀⠀⠀⠀⠀⠀⣀⣅⣩⣍⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⡶⠖⠀⠀⠀⠀⠀⠀⢩⣤⣥⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣶⣶⣶⡋⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣦⣶⣾⣿⣿⣟⣡⣿⡇⠀⠀⠀⠀⠀⠀⢿⣏⣻⡿⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠋⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠗

⠀⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣿⣿⣷⣥⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⢀⢀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⡟⣻⣿⡿⣿⢹⣏⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⣸⣿⣋⣿⣿⣿⣿⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⢺⣧⣤⣿⣾⣿⣿⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠿⢿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠉⠹⠉⠉⢒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⣠⣤⣴⡟⠀⠀⠀⠀⠀⠀⡄⠀⢻⡇⠀⠀⢤⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂
⠀⠀⢸⣿⣿⣿⣿⠄⠀⠀⠈⠉⠀⠇⠀⠈⠀⠀⠋⠨⠇⠠⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠇⠀⠀⠀⠀⠀⠀⠠⠀⠠⡄
⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣄⣴⣆⣤⣴⡶
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⠀⠒⠊⠀⠁⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⣼⣟⢿⡿⣿⠋⢹⣽⣧⠀⠀⠀⠀⠈⠀⣠⣤⣤⣤⣴⣶⣦⣤
⠀⠀⠀⠀⣙⡏⠄⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣭⣿⣷⣿⣿⣆⠀⠀⠀⡀⠀⠀⣿⣿⣹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠻⣿⡿⣿⠻⠇⠉⠁⠀⢀⡔⠀⠀⠘⣿⠿⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⣶⣶⡶⣶⢶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠒⢮⡈⢙⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡃⠀⠀⠀⠀⠀⠀⠰⢄⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⣀⠠⡤⠀⠀⢠⠃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠁⠄⢀⠀⠀⠈⠣⡮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⢪⡉⣠⠀⠀⠀⠀⠀⢀⡄⠳⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠀⢺⠉⠓⠒⠲⠚⠉⢀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⠤⠤⡤⠤⠤⠤⠤⢠⡄⠇⠀⠀⢣⡀⠀⠀⠀⣠⠎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠈⠉⠐⠒⠞⠀⠘⣄⠀⠀⠈⠑⠒⠉⢁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣀⣀⣀⢀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠈⡷⠂⠤⠤⠐⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠋⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠂⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢨⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⢠⠀⠀⠀⠈⠀⡀⠤⠀⠀⡀⠐⠀⠀⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠈⠁⠀⠀⠀⠀⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠠⠤⢇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠉⠈⠉⠉⠁⠒⠢⢄
⠀⠀⠀⠀⠀⠀⢠⠔⠉⠑⠄⠀⢰⠋⠀⠀⠀⠀⣀⡀⠀⠀⠉⠙⠀⠐⠒⠛⠉⠁⠄⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡔⠀⠀⠀⠀⠀⡇⠀⡠⠊⠒⠐⠒⠷⠤⢀⡀⠀⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⢠⠊⠐⠒⠒⠁⠀⢀⣀⡠⠤⠔⠊⠁
⠈⠁⠂⠒⠄⠀⢹⣀⣀⠴⠂⠐⠒⠁⠀⠀⠀⠉⠉⠐⡲⠖⠀⢀⣀⠼⠋⢈⠇⠀⠀⣠⠖⠋⠁
⠀⠀⠀⠋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠖⠁⠀⠀⢰⠩⠖⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣬⣔⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠇⠀⠀⢳⡀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⢸⠀⠉⠉⠛⠒⢶⡄
⠀⠀⠀⠀⠀⢀⡞⠉⠉⢳⡀⠀⡼⠁⠀⠀⠀⠆⠀⠀⠀⠳⡄⠀⢸⠀⢀⡤⠶⢤⡀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⣰⠇⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⢸⠀⢼⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣨⡭⣭⣥⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣨⠶⢮⠳⠤⠴⠋⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣤⠤⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⡤⠞⠉⡧⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢰⠃⢰⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⡀⠈⣀⡴⠋⠀⠀⢸⢀⣀⠀⠀⠀⢸⡇
⠀⠀⢀⡏⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢓⠚⠁⠀⠀⠀⠀⢸⠈⠉⠀⠀⠀⢸⡇
⠀⠀⠈⠳⠞⣻⠀⢀⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡶⡄⠈⢳⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣸⠃⢹⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢠⡏⠀⢸⡆⠀⣧⠀⠀⠀⢸⠀⠀⠀⣀⣠⡼⠇
⠀⠀⠀⠀⠀⠙⠚⠁⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠙⠚⠁⠀⠀⠀⠸⠖⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠿⠋⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢢⢰⡀⠀⡧⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠉⢉⣠⢴⠖⠂⠒⠁⠀⠀⠀⠀⠀⠀⢸⡁⢀⣼⢠⣠⡏⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢠⠔⡀⠇⡘⡆⠀⠘⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀⡀
⠀⠀⢀⠠⠄⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡉⢈⡲⠀⠀⠀⠀⠀⠀⣡⠇⠸⠀⡏⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠼⠓⠒⠁
⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉
⠀⠀⠀⠀⡴⠊⠁
⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣭⣋⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠉⠉⠁⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠐⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠉⠈⠉⠐⠀⠀⠀⠂⢴⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⡠⠊⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣤⡀⢀⣀⣁⣀⣤⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠆⠀⠀⠈⠛⠛⠀⡀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠙⢿⠿⠿⢿⡿⠃⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠃⠠⠃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡉⠈⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢴⣾⠿⠿⣷⣦⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠈⠑⠁⠐⠋⠈⡀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠉⠈⠑⢄⠀⠀⠀⠀⠀⢉⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠸⠀⠀⠀⢀⠀⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⢤⠄⠒⠄⣀⠠⠖⠃⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠤⠖⠀⠀⠉⠀⢀⡠⣄⡀⠄⠊⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⢠⣤⡇⠀⠉⢁⡀⠀⠄⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠈⠳⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⡀⠳⢤⡀⠀⠀⠀⠀⠀⢠⠄⠤⠠⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⡟⠂⠀⠀⠀⠀⠀⠀⠀⠐⠩
⠀⣉⣉⠀⠉⠀⠁⠀⠸⡀⠀⠀⠀⢠⠃⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⡅
⣠⠤⠶⠂⠀⠀⠀⠀⠀⣠⢤⣔⡒⢼⣦⡶⠉⠢⠀⣀⣀⣀⣀⣀⡀⠄⠮⣥⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠁⠑⠊⠀⠈⠫⡁⣝⠀⠉⠁⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠌⠳⠤⠤⣠⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠢⡀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⢤⠤⡤⠤⠤⠤⠬⠆⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠂⠀⡀⠀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢸⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⢈⠄⠀⠀⢅⠂⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠘⡂⠀⠀⠈⠑⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣆⣦⢲⢲⡆⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⢠⣶⣶⢴⣦⣶⣴⣲⣤⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄⠀⠰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⠛⠿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣷⣶⣶⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠛⠻⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣄⣉⣙⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠟⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣯⣮⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⠿⠋⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣦⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⣿⣴⣿⡿⠃⠀⠀⠀⠀⠀⡘⠘⠃⢻⡇⠉⠃⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⣤⣄⣰⣶⣾⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠏⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠁⠀⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣶⣤⡀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄
⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⣹⣿⣷⡄
⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⣠⣤⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣦⠀⠀⠀⠸⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣤⡀
⠀⠀⠀⠀⣾⡿⠿⠛⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⡿⠀⣠⣶⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣸⣧⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣰⣿⡟⠁⢺⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠿⣿⠿⠿⠿⢟⣻⡋⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣧
⠀⠀⠻⠛⠀⠀⠀⠸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣼⣶⣶⣿⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠉⠛⠛⠋
⣦⣦⣤⣤⣤⣤⣴⣤⣶⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶
⣿⣿⣴⣭⣴⣬⣽⣥⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿