Technological Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣼⣧⠀⠀⢸⣿⢸⣇⠀⠀⢠⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⣿⣿⢸⡇⠿⢿⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣷⢰⣿⣿⣾⣿⢸⣟⣛⣛⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⣿⣸⣷⣶⣶⠶⠚⠋⠉⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⡶⢲⣴⣿⣿⣿⢱⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣽⣽⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠾⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢐⣒⣲⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠸⠿⠶⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣽⣼⡙⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠲⣾⣧⣿⠸⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣯⣭⡝⡿⠿⠿⠶⢤⣄⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⡽⠇⣿⣿⢿⣿⢸⣯⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢈⣿⣿⣿⢸⡇⣶⣾⢸⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢻⠏⠀⠀⢸⣿⢸⡏⠀⠀⠘⣿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢨⢚⣧⣼⠇⣸⡃⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠛⡿⠆⣼⣷⣿⣏⣣⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢛⡄⠈⠁⣘⣿⣿⣿⠓⣿⣽⣿⣿
⠀⠀⠀⢠⡀⠀⠀⠘⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣘⣴⣾⡿⢿⣿⣿⣜⣿⣟⣿⣿
⠀⠀⠀⠸⡟⠦⣀⣀⡀⠀⠈⢳⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⠀⠠⠁⠈⣁⡤⠁⢙⣿⣿⣾⣿⣼⢿⣿
⠀⠀⠀⠘⣿⠢⣬⣭⣭⣯⣽⣾⣿⠶⣶⣤⡴⢄⣀⣀⣀⣒⠙⠀⢀⣀⡀⢈⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠹⠷⣶⣿⣿⣿⣿⣭⡿⠿⠿⠿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠟⠛⣿⣿⣤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠛⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣏⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⠂⢤⡤⢀⣿⣿⣍⣉⢉⠿⢩⣥⣤⣾⣿⣿⣿⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣀⠰⠲⠠⢆⠀⡈⢿⣿⣿⣷⡨⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠀⠀⠀⠊⠈⠁⠿⠟⠿⢿⡄⢻⡿⣿⡏⣿⣻⣿⣿⢿⡿⣟⢿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣷⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡠⢿⠧⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢹⠑⠲⢅⠀⢸⠀⢠⠵⠂⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⢸⠀⢸⠀⣷⠀⠀⠐⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢸⠀⡧⠀⠀⢀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠢⣀⢸⠀⢸⡀⡿⢀⡠⠿⠧⠈⠙⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⡀⠝⠀⣼⡄⠻⢤⡀⠀⠀⠀⠀⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡄⠀⢀⠠⠐⠁⡀⠐⠊⢉⠉⠓⠦⣈⠑⠦⣄⠀⣠⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠤⠒⠁⡀⠄⠊⢹⠙⠢⢄⡀⠉⠲⢄⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠊⠀⢀⠔⠈⠀⠀⠀⣼⣆⠀⠀⠈⠓⢄⠀⠈⢲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⡀⠔⠀⠉⠉⠑⠢⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⠈





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣦⣀⢀⠀⠀⣸⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡿⣯⡷⠿⢯⡿⡇⢤⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⢿⡷⣏⠰⡷⠀⣿⣿⠆⢻⡃
⠀⠀⠀⠀⠀⠀⠀⣷⣝⡷⣶⣞⣷⡇⣠⣙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠟⠉⢨⣴⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡼⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡘⣃⣦⡀⠀⠀⠱⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟⠀⠀⠀⠀⠙⣄⠀⠀⠀⢸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠇⠀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠑⢆⡠⠅⠐⠊⠁⠠⢠⣤⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠀⠻⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡍⠈⠁⣷⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⢄⡀⠀⠑⠂⠈⠀⣀⠀⣀⣠⣀⣠⡤
⠀⠀⠀⠀⡀⠀⣒⣫⠥⠞⢿⣀⢈⡙⠻⣿⡿⢟⠻⣟⠛⡳⠾⣄⠀⠀⣂⡠⠄⠒⠐⢓⠞⠁⢀⣀⡠⣡⡿⠟⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⣦⠶⠞⠉⠀⠀⠀⠀⠀⠘⢇⠀⠀⣀⣼⠀⢰⣦⣷⠀⠈⠋⠀⠀⠀⠀⠀⡔⡉⣴⠶⢉⡿⠝⠋
⠀⠀⠀⠁⠀⠀⠠⠂⢀⡴⠋⠀⠀⠀⠁⠚⠑⠠⣴⠂⢸⡽⠄⠀⠀⠀⠀⠀⠀⠀⠈⣇⢬⠀⠉⠂
⠀⠀⠀⣄⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠘⠶⠋⠁

⠀⠀⠀⣠⣴⣶⣄⠀⣤⣤⢤⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⢼⣿⣿⣿⡿⠀⠉⠉⠉⠉⠀⠺⣿⠆⠀⠀⢀⢐⡳⠥⣥⡀⢀⣤⡴⠟⠁⠀⠀⠦⠀⠀⠀⠈⣣⣼⡁
⠀⠀⠀⢉⡉⠹⠀⠀⠀⣴⠉⣳⠀⠀⠀⠀⠀⠀⠁⣾⡄⠀⠻⣾⢦⠁⣀⢀⡀⠀⡀⠀⠀⠀⣀⠀⢉⣈⢡⡄⣾⡄
⠀⠀⡰⣿⣿⣿⡶⠖⠋⢹⠟⠋⠄⣨⣦⣼⢤⡆⠀⢿⠇⢀⣀⠛⡸⠸⠡⠚⠉⠼⠙⢀⣀⢸⣭⡧⣿⣙⣯⠻⠟⣷
⠀⢀⡇⠘⢿⣁⣀⠀⣠⣏⠀⣇⠘⢥⣌⣫⡤⠃⠀⠀⠙⠛⠛⠋⣁⢀⡀⣤⢠⡾⢷⡌⣿⣀⣭⡁⠹⣿⡿⠀⢀⠈⣀
⠀⠈⣇⠠⠁⠙⠻⢿⣿⣿⡇⠘⠶⣶⡀⠀⠀⢤⡴⢚⣤⣤⣾⣇⣿⣾⣿⣿⡾⣷⣼⡟⠹⠿⠛⠁⠀⢰⡶⡿⢿⠀⠕
⠀⠀⠙⣶⣄⣀⣀⣀⡼⠛⠁⠀⡀⢁⣠⣴⣶⢄⣠⡼⣯⠙⣉⣿⡙⡷⠻⠙⠋⣨⢁⠀⠀⠈⣇⠀⢀⣸⡷⢦⣼⣤⣤
⢠⣾⣿⣷⣬⣽⣿⣅⠠⠔⠊⠀⠂⠀⠉⢻⣇⢻⣷⣗⠙⠿⠟⠉⠁⢠⠀⠀⢄⠁⠈⣃⠀⠘⠉⠀⠈⠻⣿⣿⣿⣿⠃
⠨⣿⡇⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⢀⠀⠈⠿⠈⠛⠋⠁⢀⣰⢤⣀⠀⠃⠀⠈⠀⠋⢁⣤⣶⣿⣿⣷⠂⠀⠙⠿⠃
⠐⣿⣰⠀⠀⠀⡸⠀⠀⠱⠄⡤⠔⠁⢀⣀⠤⠐⠛⠀⣀⣸⣿⣿⡶⣦⣤⡄⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⡞⠳⣤
⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⡀⠠⠖⠚⣉⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠘⣈⠀⡀⠀⢀⠈⠻⣯⠀⢰⣿⣤⡄⢾⣯
⠀⠀⠀⠀⠀⠀⠐⣠⡂⠀⣧⣴⣶⣿⡿⠿⠿⠟⠛⠛⡉⠉⢹⣿⠏⠀⠀⠀⠈⢀⣀⠠⣾⣷⠀⢿⠀⠸⠟⠋⠀⣻⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣩⡭⢁⡀⠀⠀⠀⣤⣀⣼⠃⠀⣀⠀⠘⢸⡀⠀⡤⢜⠿⠃⣠⠔⢒⡙⠒⢄⠀⠀⡀⠠
⠀⠀⠀⠀⢀⡀⠀⡔⢛⣤⣼⣒⣦⣽⣮⠠⢀⠈⠛⠃⠀⠀⡀⠈⠑⣎⠱⢤⣇⢸⠀⡜⢡⣾⣿⣿⣿⣶⡆⠀⢵⣚⡄
⠀⠀⢠⣶⡈⠃⢸⡿⠟⠛⢿⠉⠀⢀⣈⠳⣇⠁⢰⢀⣴⠿⣿⢿⣿⣜⠳⢦⣿⣯⠀⣇⠸⣿⣿⣿⣿⡿⠃⠀⢸⣿⡇
⠀⠐⢻⡿⠷⠀⣼⣦⡦⢀⣼⣷⣦⣈⢉⡸⠻⣧⠸⠠⣿⠿⣿⢸⢹⣿⠀⠸⣟⠝⢷⣼⣦⣉⣛⣛⣉⠤⠚⣖⣦⡀
⠀⠀⢸⡇⠀⢠⡿⠙⠲⣼⣿⣿⣿⡿⢫⠀⠀⢹⡇⠅⣿⢙⢻⣿⣿⣿⡇⠀⠹⣮⣮⣿⠷⣢⣉⣭⣭⣭⣵⢹⣿⣻⡄
⠀⠀⢸⡇⠀⣸⣇⠀⠀⠳⢭⣝⣋⠤⠎⠀⢀⡜⠗⣆⢹⡟⠟⡿⡟⣿⣇⢸⠀⠈⠛⢻⡜⢕⡂⣙⣏⣈⠜⢀⣿⣿⡇
⠀⠀⣸⣇⢸⠁⡧⣷⡀⠀⢰⠋⠁⢈⠃⠀⢸⣿⡗⣼⢾⣿⡚⣳⣛⣿⣿⣌⠂⠀⠀⠈⣷⣶⣦⣤⣶⣶⣾⣿⣿⡁⡇
⠀⠀⡿⣿⠈⠧⠇⣛⣅⢀⠘⢲⠀⠸⢤⠀⠀⣤⠀⠀⢸⣿⣧⣿⢭⡽⣿⡎⡆⠀⠀⠀⢸⣭⠽⢿⠛⣿⣷⣺⣅⡓⠁
⠀⣸⡟⣿⣆⠀⢘⡛⢩⡆⢀⠼⠴⣠⠃⠈⢻⣿⠟⠀⢸⣿⢿⢸⢠⠃⣿⡇⡣⠀⠀⣴⢿⣿⣿⣿⡆⣿⣿⣿⣿⡿⡆
⠀⠉⠉⠉⠉⠃⠘⠁⠀⠀⠀⠀⠘⠃⠀⠀⠈⠈⠀⠀⠈⠻⠶⠾⠿⠿⠟⠀⠁⠀⠀⠛⠛⠛⠛⠛⠁⠉⠋⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⡦⠸⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠐⠒⠒⠛⠛⠀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡟
⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠐⣦⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠹⢦⣤⣤⣴⣶⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠠⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠠⠄⠀⠬⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠐⠀⠄⠀⠠⠄⠀⠈⠀⠐⠀⠀⢀⠀⠀⢀⠀⠰⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠂⠀⠀⠒⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠄⠀⢀⠀⠀⠀⢠⠐⠀⠄⠂⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠈⠀⠀⠤⠄⠀⡄⠀⠘⠁⠀⠁⠀⠂⠀⠁⠀⠀⠀⠐⠀⠆⠀⠘⠠⠄⠀⢀⠀⠀⠀⠀⡄⢀⠀⠂
⠀⢀⠀⠰⠀⠀⡉⠀⠀⠀⠀⠈⠠⠀⡐⠂⠁⢀⠁⠁⠠⠀⠁⠀⠀⠀⠃⠀⡀⠈⠁⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⣀⡀⡀⢀⠁⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠐⠀⠀⠠⠀⠀⠀⠀⠈⠀⢂⠀⠀⠂
⠀⢐⠀⠈⠀⠈⠀⠀⠐⠂⠀⠀⠀⠆⣀⠀⠄⠀⢀⠀⠁⠀⠀⠀⠐⠀⠠⠀⠀⢐⡂⠐⠀⢀
⠀⠀⠀⠂⠐⠨⠀⠀⠀⠐⠀⠈⠑⠀⠐⠀⠀⠀⠀⠄⠀⢀⠈⢈⠀⠀⡀⠠⠀⠂⠀⠀⠀⠄⠄⠀⠄⡌⠁
⠀⠀⠀⠀⠁⠀⠀⢀⠐⠂⠀⠠⠀⠈⠀⠀⠄⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⠐⢂⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⢀⠀⠠⢄⠠⠀⠀⠀⠀⠀⠀⢐⠂⠴⠀⣀⠀⠃⠰⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠐⠈⠄⠠⠀⠈⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡀⠁⠀⠀⢀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡴⠛⠉⠹⠿⠛⠿⠿⠷⠤⠄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢄⣴⣦⣀⣠⣀⣤⣖⣒⣒⣶⣇⣄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⡏⢉⣉⣉⣉⣉⣉⣉⣉⣉⣓⣒⠔⠴⠢⠶⠶⠒⠄⠠⠂⠀⠂⠉⠩⠭⠍⠭⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⣿⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⣷⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡰⣻⠗
⠀⠀⠀⠀⠀⠀⠀⣉⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣟⣿
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿
⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⡟
⠀⠀⠀⠀⠀⠀⠁⣙⣸⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡏⢠⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⡀⢐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡸⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢱⠈⣦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣺
⠀⠀⠀⠀⠀⠀⢸⠀⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⣆
⠀⠀⠀⠀⠀⠀⢸⠀⠂⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠸⡇⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⠙
⠀⠀⠀⠀⠀⠀⡤⣴⡀⠀⠹⠤⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡇⢸⡂⠀⣀⣀⣈⣱⣌⠑⠦⠠⠄⠶⠷⠄⠤⠤⢠⣴⣀⣂⠥⠶⠶⠶⠶⠶⠤⠶⠶⠶⠶⠶⡄⠤⢀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠡⣈⣉⣋⣋⡿⠊⠁⠉⠳⠤⠤⠤⠤⠤⠤⠔⠋⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠲⣤⣒⣺⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⣀⣀⠀⢸⡟⠟⠝⣅⠀⠴⣶⠰⢌⢠⠀⠀⠐⠖⠀⢀⢠⣤⡄⠀⣀⣀⣀⣂
⠀⠀⠀⡠⠔⠍⡃⢰⣶⣶⣾⣟⣿⣿⡇⠀⢿⣷⣾⣿⣿⠂⠀⠋⠎⠊⢞⠰⠩⢛⣳⡇⡀⠀⠀⠀⢸⣧⠀⠘⣿⡟⠀⠛⠛⠛⠛⠁
⠀⠀⠀⡥⢒⡡⡄⠸⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⠟⠁⠀⣤⣦⣥⣶⣷⡄⠁⠀⢰⡿⢳⡀⢠⠀⠘⣁⠀⡂⢉⣴⣾⠿⠿⣷⣦⡀
⠀⠀⢰⣀⠅⢊⠅⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⣴⡟⠉⠉⠉⠙⢻⣦⡀⠞⢰⠀⠁⠀⠀⢸⣿⠇⠁⣾⡿⣱⣾⣷⣦⡝⣿⡆
⠀⠀⢸⠠⢒⠥⠒⢡⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⣾⣿⠀⠀⠐⠖⠐⠂⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢻⣿⣿⣿⢳⣿⡇
⠀⠀⢸⠒⡡⢊⠸⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣱⠀⠈⢿⣷⣄⣀⡃⣀⣴⠟⠀⠀⠸⠀⠀⢀⠀⠀⠀⠃⠀⠘⠿⣷⣮⣭⣾⡿⠋
⠀⠀⠸⠁⣊⡔⣀⡄⠀⠀⠀⠀⠀⡀⡇⠀⡄⢄⠃⡀⠀⠀⠈⠻⡿⢿⠟⡟⠀⠀⠀⢰⠀⠀⠈⢀⡀⠀⣀⣀⢀⣀⢀⠌⡍⡅⠀⡤⠆
⠀⠀⠀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠂⠐⠁⠀⠈⠢⣿⠔⠂⠀⠀⠈⠓⠀⠒⠇⢠⢦⡄⠘⠀⠠⡶⡦⠙⠛⠓⠛⠒⠒⠂⠒⠂⠊⠊⠁
⠀⠀⠈⠁⠀⠀⣀⠄⣢⣤⣖⡤⡀⠀⠀⠤⡀⠀⣄⠔⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠉⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⡀
⠀⠀⠀⠠⢀⠞⠰⠊⠀⠉⠻⣿⣮⣄⠀⠀⠀⠸⡧⠞⠁⠀⠐⢀⣀⣤⣬⣭⣬⣭⣤⣤⣤⣤⣴⣶⣶⣶⣶⡦⠈⡆⠀⠁⠀⠒⠀⢸⡄⠄
⠀⠀⠀⠀⡅⠲⠁⠀⠀⠀⠀⠹⣿⣿⣀⠀⢰⣶⣧⣴⠀⠀⠀⢸⣿⠉⠉⠁⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⣿⣧⢠⡇⠀⠀⠄⠀⢠⠟
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠸⣿⣿⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣭⣻⣧⠀⢿⣿⢀⡇⠀⠀⠀⣶⡇⢠⣤
⠀⠀⠀⠰⠐⠆⠀⠀⠀⠀⠀⠘⠘⣿⣿⡇⠀⠀⠀⠀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣽⣻⣿⢿⡟⠀⢸⣿⠀⡇⠀⠀⠀⣿⣧⠀⠁
⠀⠀⠀⢐⠈⢓⠒⠤⣄⡀⢀⠤⠐⠛⢿⣿⡀⠀⠸⣿⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⢸⣿⢀⡅⢠⡄⢠⣿⣿
⠀⠀⠀⠠⠐⠈⢿⣦⡈⢿⣆⠀⣰⣿⣆⢿⣧⠀⠀⠉⠁⠀⢀⠸⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⢸⡇⠀⠀⠀⠉⠉
⠀⠀⠀⠀⣴⣾⣦⠻⣿⡌⣿⣰⣿⣿⡿⣸⣿⠀⠃⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣶⣶⢖⣂⣀⣀⣈⣉⣐⣄⠀⠀⠈⠀⠄
⠀⠀⠀⢸⣿⣿⣿⣇⢹⡇⣿⣿⣿⠟⣡⣿⡟⠀⠀⠠⠀⠸⢶⣾⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠄⠀⠁
⠀⠀⠀⠈⢿⣿⣿⡟⢸⣧⠿⣦⣶⣾⠿⡿⠀⠀⠀⠋⠀⠀⠀⠀⠀⣤⡶⠄⣤⠶⠀⣄⠶⠀⣤⣤⡀⢀⠀⠀⠀⣀⣀⣀⣀⣀⠀⡀
⠀⠀⠀⠐⠀⠉⠉⠚⠉⠁⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⢸⣿⣷⠀⠀⠘⢻⣿⠛⣿⡿⠛⣿⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⠀⠀⠐⠁⠁⠀⠚⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠹⣧⠀⣿⡇⠀⣿⠛⣷
⠀⠀⠀⠀⠀⢀⢀⣀⣈⣤⣀⡤⠤⠠⢌⣀⣤⢤⡄⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡄⠀⣿⡆⢸⣿⠀⣿⡾⠏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⢰⣰⣿⣿⣿⣧⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣠⣿⠀⣾⡏⢸⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⠛⣈⠙⠿⣿⡿⠃⢠⠀⠂⠀⠀⢀⣀⣀⠀⡀⡀⡁⠀⠀⠀⠀⢰⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠺⠴⠤⠰⠤⠤⠴⠴⠵⠴⠶⠾⠟⠛⠀⠀⠈⠉⠉⠙⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣶⡆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⠿⢿⠿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⢡⢊⠭⠙⣎⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡘⣌⣀⣢⢎⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣶⣾⣶⣾⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣧⣴⡦⠈⠉⠈⠛⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⡿⠋⠉⠉⠻⣿⣿⠆⠀⢀⣰⣶⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡃⠀⠀⠀⠀⢸⣿⡶⠀⠰⣿⠂⠈⢽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣶⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣄⣀⣀⣠⣿⣿⠄⠀⠈⠹⠷⡶⠿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⠋⠉⠙⢿⡷⠀⠀⠀⠀⣠⣴⣄⠀⣿⣿⡇⠀⣴⣄⡀⠿⠛⣿⡟⠻⠗⠀⠀⠀⠀⠀⡀⣾⣦⣿⣷⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠀⠀⠀⣸⣟⠃⠀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⡀⠀⠀⢀⣴⣴⣶⣆⡀⠚⣿⡿⠋⠁⠈⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠿⣶⠾⡿⠉⠀⠰⣿⣿⣿⣿⠟⢉⣭⣭⣍⡙⢿⣿⣿⣿⡷⠄⠀⢾⡿⡋⣱⣿⡦⠿⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣤⣄⣶⣆⣠⣄⠀⠀⠀⢀⣀⣼⣿⣿⠃⣼⢋⡥⠤⣌⠻⣆⢹⣿⣿⣄⣀⠀⠘⠿⢶⡾⠟⠁⠺⠿⣿⣦⣀⣀⣴⣿⠿
⠀⠀⠀⣿⡀⢈⡷⠀⢰⣶⣿⠟⠛⠛⠿⣷⣶⡄⠀⠸⡿⣿⣿⣿⠸⣇⢸⡀⠀⣸⠀⣿⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠛⢿⡟⠛⠟
⠀⠀⠀⠈⠙⠋⠀⠀⣶⣿⠇⠀⠀⠀⠀⢹⣿⣦⠀⠀⢀⣼⣿⣿⣆⠻⢦⣍⣉⣥⡾⢃⣼⣿⣿⣄⠀⠀⠀⠀⢰⣷⣾⣿⣶⣿⠆
⠀⣀⣀⡀⠀⠀⠀⠀⢨⣿⣧⡀⠀⠀⢀⣼⣿⡅⠀⠀⠈⠿⠿⢿⣿⣷⣦⣭⣭⣥⣴⣿⣿⡿⢿⠟⠀⠀⠐⢿⣿⠟⠉⠀⠉⠻⣿⡟
⢸⡋⠉⣿⠀⠀⠀⠀⠈⠉⣿⡿⣿⡿⢿⡯⠉⢠⡞⠛⢧⠀⠀⢼⣿⡿⠿⣿⣿⡿⠿⣿⣿⠄⠀⠀⠀⠀⠺⢿⣿⠀⠀⠀⠀⠀⣿⡿⠇
⠈⠛⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢧⣤⠞⠀⠀⠀⠈⠁⠀⠛⠛⠃⠀⠈⠀⠀⠀⠀⠀⠂⠐⢿⢿⣦⣄⣀⣠⣾⡿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⣿⠛⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡆⠀⣀⣸⣿⣿⣿⣀⡀⠀⣼⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣿⣿⠿⣛⣫⣭⣥⣶⣶⣮⣭⣭⣛⡻⢿⣿⣿⣷⣾⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡿⣫⣴⣿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣶⣌⡻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣠⣾⣿⡿⢫⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣮⠻⣿⣿⣦⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⣱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡹⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⡇⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣿⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⢿⣿⣷⣜⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠙⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣷⣝⠻⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⣿⣿⣿⣶⣭⣝⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠃⠀⠉⢹⣿⣿⣿⠉⠁⠈⢿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⡧⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣴⢋⣿⠟⠉⠉⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⣠⣾⠿⢿⣶⡀⠀⠀⢰⣤⣼⣧⣴⣎⢀⡀⢹⣏⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣤⣠⡄⠀⢸⠉⠈⣳⠀⠀⠀⠀⣠⣤⣤⡀
⠀⢻⣿⣄⣰⣿⢇⣘⣿⠟⠉⠉⠉⠉⠛⢿⣥⣽⢿⣄⡀⠀⣀⣴⣿⠁⠀⠀⢀⣸⡾⠋⠉⠉⠙⢿⡬⠓⢒⣡⣤⣄⡀⣸⡏⠀⠈⢿⠄
⠀⠀⠙⠛⠛⠉⣈⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣧⡌⠉⠻⠛⠻⣩⣶⣶⣶⣄⠠⣿⠀⠀⠀⠀⠀⠈⣿⢢⣿⠋⠉⠹⣿⡜⢷⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠈⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⠀⠀⠀⢰⣿⡏⠀⢹⣿⠖⢻⣄⠀⠀⠀⢀⣰⣏⠙⣿⣦⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢻⣧⡀⠀⠀⠀⠀⢀⣰⣿⡅⠀⠀⠀⠀⠀⠻⢿⣶⡿⠟⠀⠈⠹⠟⢶⠲⠟⠓⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣶⣶⣶⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⢠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⠰⠤⠄⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢎⣣⡀⠀⠀⠀⠀⠰⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠚⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢪⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠠⡐⠁⠀⠐⠲⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⠉⠀⠀⠀⠀⠀⠀⡰⠢⠤⠁
⠀⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠓⢍⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⢀⠂⠒⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠊⢷⡀⠀⠀⠀⠠⠀⠰⠊⠐⠠⠤⣀⡰⠃⠻⠞⠙⣄⠠⠔⠊⠁
⠀⠉⠚⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐
⠀⢀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠅⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⢃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⢀⢄⡀⢀⠁⠀⠀⠀⠄⠂⠐⢄
⠀⠀⠀⠑⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣈⠅⠀⠀⢀⢀⣀⣄⠀⠀⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠐⠒

⠀⢠⣶⣟⣿⣦⠀⠀⢀⣴⣛⡟⣶⡀⠀⠀⣴⠞⠛⢷⡄⠀⠀⣤⡼⢓⠿⣤⠀⠀⢠⣾⡿⢿⣦⠀⠀⢀⡲⠛⠛⢶⡀
⠀⠸⣟⡧⣟⣾⠀⠀⠘⣧⠚⡟⣼⠇⠀⠀⢿⣀⢀⣸⡇⠀⠀⠼⣍⡆⣳⠷⠀⠀⠸⣟⣤⣼⣽⠃⠀⠀⢧⠀⠀⣸⠃
⠀⠀⠉⠙⠉⠁⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠉⠙
⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⢀⣠⢤⣤⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⣾⠁⠀⠈⣗⠀⠀⣻⠁⠀⠘⣟⠀⠀⣾⢥⠈⡢⢿⠀⠀⢸⣿⡋⣻⣿⠀⠀⢐⡏⠀⠀⢹⡂⠀⠀⡏⠀⠀⢹⡆
⠀⠀⠙⠲⠤⠞⠁⠀⠀⠉⢷⠶⡾⠉⠀⠀⠘⠷⢽⠴⠋⠀⠀⠈⠻⠿⠿⠛⠀⠀⠀⠓⠦⠴⠛⠀⠀⠀⠙⠦⠴⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠠⡄⡤⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢠⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢾⣋⡷⠀⠀⠀⠀⣠⡢⠄⣢⠦⠀⢄⡄⠀⠀⠛⢶⣾⡶⡷⣷⡶⢾⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠘⠋⢀⠆⠀⠀⣠⠖⠶⠦⣄⠀⠀⠉⠀⠀⢀⠔⠛⢇⠀⠀⡷⠀⢀⠞⠛⠷⣄⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡞⢣⢸⣭⠏⡍⢣⠀⠀⢀⢀⡿⢤⡀⠈⢆⠀⣦⢀⠊⠀⣠⠖⠹⣆⠀⠀⣰⠎⠁⡂⠀⢻⣦
⠀⠀⠀⠀⢀⢄⡤⡤⠐⢤⡄⠀⠀⠀⠀⢏⠙⢲⣒⡒⢋⡽⠀⠀⣐⣾⠀⠀⠈⠓⢦⣷⢿⣧⠔⠋⠀⠀⠀⢹⡆⠀⣾⠀⢤⠀⠠⠠⣿⠂
⠀⠀⠀⢠⣳⠋⠁⡔⢠⣜⠀⠑⡄⠀⠀⠈⠛⠥⠼⠬⠛⠁⠀⠀⢐⣾⠉⠉⠉⢉⡹⣿⣤⡿⣉⠉⠉⠉⠉⢸⡂⠀⠘⢦⣀⡁⣀⣤⠋
⠀⠀⠀⣪⣯⠤⢼⠁⠀⢸⡆⢆⡁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⢀⡠⠖⠉⣰⠃⣧⠙⡌⠙⠢⢄⢀⡟⠀⠀⠀⠀⠈⠈⠈
⠀⠀⠀⠀⠹⣄⠀⠃⠂⠚⠀⡠⠃⠆⠀⢀⡄⡶⠻⣭⡬⠚⣶⢄⠀⠐⠸⣀⠀⡰⠁⠀⣿⠀⠘⢆⠀⣠⠾⠀⠀⣠⢔⣚⡾⠞⣒⢤⡀
⠀⠀⠀⠀⠀⠈⠓⠓⠤⠂⠈⠀⠂⠀⢠⣪⣾⣄⠀⣸⡁⢀⡾⠾⢳⡀⠀⠉⠛⢷⢤⣄⣻⣄⡤⡶⠞⠁⠀⠠⡜⠕⠉⡀⠀⣀⠼⠓⣔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⣘⣿⠿⢿⣿⣀⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢼⢈⣄⠀⠤⠐⠀⡤⣄⡈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡰⡛⠉⠛⣶⡀⠈⢅⠟⠉⢉⣿⣷⣾⣏⠀⠀⡋⡗⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠸⡔⠈⠉⠻⡧⠶⠁⠀⠁⣼
⠀⠀⠀⠀⠀⠀⢨⡀⠈⣀⠀⠈⡇⠀⠈⢄⢶⡟⠁⢸⠁⠈⢳⣞⡽⠃⠀⠔⢀⡄⢒⠊⠉⠹⠓⣦⡑⢄⠀⠀⠙⢦⡀⠎⠀⠀⠂⣀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡤⠞⠀⠀⠀⠈⠃⠾⡴⡿⣻⡶⠷⠋⠀⠀⡂⢠⠊⠉⢢⣣⡤⠸⡈⠀⠙⣎⢆⠀⠀⠀⠈⠐⠒⠒⠙
⠀⠀⠀⠀⠀⢀⣠⣆⠀⠀⠀⣠⡖⠶⢶⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠐⣀⣸⠁⠀⠀⣟⡆⡊⢹⢸⠀⠀⠀⣀⣴⣶⣄⣄
⠀⠀⠀⠀⠀⢹⣇⣼⠇⠀⣼⠋⠑⠂⠀⠀⠉⣦⠀⠐⢱⡟⠻⣆⠀⠀⠅⠈⡏⠀⠙⠆⠠⡔⠇⠀⢈⡟⡜⠀⠀⣮⣟⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠊⠙⢤⡾⠒⢛⡟⠀⠀⠼⠳⢞⠃⠁⠀⠈⢀⠙⢆⠀⡃⠀⢀⣀⡼⠋⠔⠀⠀⠀⢿⣿⣧⣄⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣐⠀⠈⣢⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⣀⡴⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠴⠞⠁⠀⠀⠁⠀⠀⠀⠳⠤⠤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢀⣠⡤⠤⢤⣄⡀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠚⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠳⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡞⠻⣄⣀⣠⠞⠓⡆⠀⠀⣏⣀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⣹
⠀⠀⢀⡴⠲⠤⠞⠁⠀⠀⠉⠀⠀⠀⠻⢤⡤⠶⣍⢳⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⠴⠋⠀⠀⢠⠞⠉⠉
⠀⠀⠈⡇⠀⠀⠀⠀⣀⣤⠤⢤⣄⡀⠀⠀⠀⠀⡏⢾⠀⣀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⡄
⣠⠶⠚⠁⠀⠀⡴⠋⠁⠀⠀⠀⠀⠉⠳⡄⠀⠀⠳⢬⣭⠉⠉⢳⠀⠀⣠⣤⣄⠀⢰⠋⣉⡙⠛⠁⠀⣀⡀
⠻⣄⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢠⠞⠁⠀⠈⠒⠞⠁⠀⠈⠳⠛⣸⠋⠑⠦⡤⠞⠉⢹⡀
⠀⣸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣴⠋⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠓⠶⠚⠛⡆
⣾⣁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⣠⠴⠖⠒⠶⢤⣀⠀⠀⠀⢸⠁
⠀⠉⢹⡄⠀⠀⠙⠲⣄⣀⣀⣀⣀⡴⠚⠀⠀⢀⡖⠋⠉⠀⠀⠀⢠⡞⠋⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⠓⠶
⠀⠀⢸⠁⢀⣀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⡖
⠀⠀⠀⠙⠉⠉⢳⡀⠀⣀⣤⣄⠀⢠⠞⠉⠙⠚⠁⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠈⠓⠾⠁⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠈⠳⠤⣤⣤⡤⠴⠋⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣠⠴⠶⣄⠀⡾⠁⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⣸⠗⠛⠛⠺⣧⣀⠀⠀⠀⠀⣀⣸⡷⢿⣿⢾⣇⣀⠀⠀⠀⠀⢀⣴⠋⠉⠉⠙⣦⡀⠀⠀⠀⠀⣀⣸⠷⢺⡗⠾⣇⣀⠀⠀⠀⠀⣀⣼⡻⢿⡽⢟⣧⣀
⠀⢀⣽⠛⣶⠛⠛⣶⠛⣯⡀⠀⠀⢀⣽⠏⣾⡿⢿⣷⠹⣯⡀⠀⠀⠀⣎⠀⢱⡶⢶⡎⠀⢹⠀⠀⠀⢀⣹⢓⠊⠀⠀⠑⠞⣏⡀⠀⠀⢀⣿⣎⣀⡼⢧⣀⣱⢿⡀
⠀⠈⣻⡀⠻⣤⣤⠟⢀⣟⠁⠀⠀⠈⣻⣾⣯⣦⣾⣽⣶⣟⠁⠀⠀⠀⢇⠀⡸⠷⠾⢇⠀⣸⠀⠀⠀⠈⣹⡤⢄⠀⠀⡠⣥⣏⠁⠀⠀⠈⣷⢏⠉⢳⡞⠉⡹⣾⠁
⠀⠀⠉⢹⣦⣼⣧⢴⡏⠉⠀⠀⠀⠀⠉⢹⡷⣦⣴⢾⡏⠉⠀⠀⠀⠀⠈⠻⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠉⢹⡶⢼⡧⢶⡏⠉⠀⠀⠀⠀⠉⢳⣵⣞⣳⣮⡟⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀
⠀⠀⡀⣬⣾⣿⣿⣷⣥⢂⠀⠀⠀⠀⣀⣼⣛⣻⣟⣛⣧⣀⠀⠀⠀⠀⢠⡴⠟⢻⡟⠻⢶⡀⠀⠀⠀⠀⢰⣶⣴⣿⣿⣦⣶⡆⠀⠀⠀⠀⣰⡼⣟⡿⢿⣛⢷⣀
⠀⠐⣾⣿⠑⡤⢤⠊⣿⣷⠀⠀⠀⢀⣿⣸⣿⡿⢿⣿⣏⣿⣀⠀⠀⠐⣿⢷⡶⣻⣟⢶⡶⢿⡀⠀⠀⣀⣴⣿⠋⠀⠀⠙⣿⣦⣀⠀⠀⢐⣿⡼⢿⢗⡸⡿⢯⣿⡂
⠀⠠⢿⣿⡠⠓⠚⢄⣿⡿⠄⠀⠀⠈⣿⢹⣿⣷⣼⣿⡏⣿⠁⠀⠀⠈⣷⠀⣿⣽⣯⣾⢀⣿⠄⠀⠀⠙⠻⣿⣄⠀⠀⣠⣿⠟⠁⠀⠀⠨⣿⣳⣾⡮⠵⣷⣾⣿⠅
⠀⠀⠁⢛⢿⣿⣿⡿⡛⠌⠀⠀⠀⠀⠉⢻⣭⣽⣯⣭⡟⠉⠀⠀⠀⠀⠉⠿⣯⣤⣠⣽⡟⠃⠀⠀⠀⠀⠸⠿⠻⣿⣿⠟⠿⠇⠀⠀⠀⠀⠙⢷⣯⣷⣾⣭⡞⠋
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⣸⣷⠿⠿⣾⣇⣀⠀⠀⠀⠀⣀⡼⠛⢻⡟⠛⢧⣀⠀⠀⠀⠀⣠⡾⠛⢻⡟⠛⢷⣀⠀⠀⠀⠀⣠⡶⢟⣩⣍⡻⢶⣄⠀⠀⠀⠀⣀⡼⣳⣯⣽⣟⢧⣀
⠀⢀⣽⡟⣨⠗⠺⣅⣹⣯⡀⠀⠀⢀⡿⠛⢦⡼⢧⡴⠛⢿⡀⠀⠀⢰⡿⠀⢀⡼⢧⡀⠈⢿⡂⠀⠀⢠⡟⡰⠁⢠⡄⠈⣎⢻⡄⠀⠀⢀⡿⣾⣟⡽⢯⣻⣷⢿⡀
⠀⠈⣻⣏⢙⡦⢴⡋⣸⣟⠁⠀⠀⠈⣷⣤⠞⢳⡞⠳⣤⣾⠁⠀⠀⠨⣷⣤⠞⠳⠞⠳⣤⣾⠅⠀⠀⠘⣧⡱⡔⠉⠉⢢⢎⣽⠃⠀⠀⠈⣳⢿⣯⣳⣞⣽⣟⣾⠁
⠀⠀⠉⢹⡿⣶⣶⢿⡏⠉⠀⠀⠀⠀⠉⢳⣤⣼⣧⣤⡞⠉⠀⠀⠀⠀⠙⢷⣤⣄⣠⣤⡾⠉⠀⠀⠀⠀⠙⠷⣮⣑⣋⣵⠾⠋⠀⠀⠀⠀⠉⢳⣽⣿⣻⢭⡞⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢰⣶⢟⣛⣛⡻⣶⡆⠀⠀⠀⠀⣀⣼⠿⢻⡟⠿⣧⣂⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢰⣶⣿⠛⠛⣿⣶⡆⠀⠀⠀⠀⠰⣦⡶⢿⡿⢶⣴⠆
⠀⢈⣿⢱⢿⡷⢾⡿⡎⣿⡁⠀⠀⢐⣿⠧⢤⡼⢦⡤⠼⣿⡂⠀⠀⠠⣿⣿⣿⢟⡻⣿⣿⣿⡀⠀⠀⢈⣿⠛⠛⣤⣤⠛⠛⣿⡁⠀⠀⢀⣴⣏⡾⢋⡙⢷⣹⣧⡀
⠀⢈⣿⡸⣾⡷⢾⣳⢇⣿⡁⠀⠀⠨⣿⡄⢨⠷⠾⡅⢠⣿⠅⠀⠀⠈⣿⣿⣿⣮⣵⣿⣿⣿⠀⠀⠀⢈⣿⣤⣤⠛⠻⣤⣤⣿⡁⠀⠀⠈⠻⣏⢷⣌⣡⡾⣹⠟⠁
⠀⠀⠸⠿⣮⣭⣭⣵⠿⠇⠀⠀⠀⠀⠉⢻⣷⣤⣤⣾⡟⠍⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠸⠿⣿⣤⣤⣿⠿⠇⠀⠀⠀⠀⠰⠟⠳⣾⣷⠞⠿⠆
⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣼⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢷⣄⠀⠀⠀⠀⢰⡶⠛⠋⠙⠛⣶⡆⠀⠀⠀⠀⣀⣸⡷⢿⡿⢿⣇⣀⠀⠀⠀⠀⣀⣼⢿⣛⣛⡿⣧⣀
⠀⢐⣿⣿⣿⠛⠛⣿⣿⣿⡂⠀⠀⢰⡟⠑⠢⡠⢤⠔⠊⢻⡆⠀⠀⢈⡿⠓⢲⡴⢦⡴⠏⢿⡁⠀⠀⢀⣽⣏⣀⡼⢧⣀⣹⣯⡀⠀⠀⢀⣿⢳⣯⡿⢿⣽⡞⣿⡀
⠀⠨⣿⣿⣿⣤⣤⣿⣿⣿⠅⠀⠀⠸⣧⡠⠔⠑⠊⠢⢄⣼⠇⠀⠀⢈⣷⠀⠈⢳⠞⠁⠀⣾⡁⠀⠀⠈⣻⣏⠉⢳⡞⠉⣹⣟⠁⠀⠀⠈⣿⡼⣟⣷⣾⣻⢧⣿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠙⢷⣄⣀⣀⣤⡾⠋⠀⠀⠀⠀⠸⠷⣤⣜⣧⣤⠾⠇⠀⠀⠀⠀⠉⢹⣷⣾⣷⢾⡏⠉⠀⠀⠀⠀⠉⢻⣾⣭⣭⣷⡟⠉
⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⡴⢦⠀⠀⡼⢳⡀⠀⣠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⣏⠘⢦⣠⡇⠈⢧⣼⠃⠘⣇⡼⠁⢸⠀⣠⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢸⡄⠙⠦⠟⠀⠈⠉⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠛⠃⠀⣟⣀⡴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠓⠾⠃⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⢁⣠⠴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢟⠓⠦⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡼⠃⠀⣀
⠀⠀⠀⠀⠀⢀⣀⣀⡈⣧⠀⠀⣠⠞⠋⠛⢶⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⡴⠛⠙⠳⣄⠀⠛⠚⠋⣹⠃
⠀⠀⠀⠀⠀⠘⢧⡉⠉⠉⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⣀⣤⠴⠖⠒⠚⠓⠒⠲⠦⢤⣀⠀⠀⢸⡀⠀⠀⠀⣹⠀⠀⠀⢾⣁⣠⣤⡀
⠀⠀⠀⢀⣤⣤⣤⡽⠀⠀⠀⠀⠈⠳⠤⠴⠚⢀⡤⠚⣉⡤⠖⠛⠉⠉⠉⠉⠛⠲⢦⣈⠓⢦⡀⠑⠦⠤⠞⠃⠀⠀⠀⠀⠁⣠⠖⠁
⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣠⠞⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠳⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠤⣤
⠀⠀⢀⡤⠴⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⠀⢀⡴⠚⠉⠉⠉⠉⠓⢦⡀⠀⠀⠈⢷⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠈⠓⠦⣄⠀⠀⢀⣠⣤⣀⠀⠀⢰⡇⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣧⠘⡆⠀⠀⣀⣠⣄⡀⠀⠈⠳⠦⠤⣄
⠀⠀⣠⡤⠶⠚⠀⢰⠏⠀⠀⠈⣧⠀⢸⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⣷⠀⣼⠁⠀⠀⠙⡆⠀⣠⠴⠚⠉
⠀⠀⠙⠓⠶⢤⠀⠸⣆⠀⠀⣀⡟⠀⢸⠀⣇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⡿⠀⢻⣄⠀⠀⣰⠇⠀⠙⠲⢤⣀
⠀⠀⢀⡤⠖⠋⠀⠀⠈⠙⠋⠉⠀⠀⠸⡆⢻⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡟⢠⡇⠀⠀⠈⠙⠋⠁⠀⠀⡴⠖⠒⠋
⠀⠀⠈⠓⠲⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢳⡀⠀⠀⠈⠳⢤⣄⣀⣀⣀⡤⠞⠁⠀⠀⢀⡾⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⢦⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡴⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠒⠛
⠀⠀⠀⠈⠓⠛⠛⣳⠀⠀⠀⠀⢀⡴⠒⠲⢤⠈⠓⢦⣉⠓⠦⣤⣀⣀⣀⣀⣤⠴⠞⢋⡤⠞⠁⡤⠖⠒⢦⡄⠀⠀⠀⠀⡀⠙⠢⡀
⠀⠀⠀⠀⠀⢠⡞⣁⣀⣀⠀⠀⣿⠀⠀⠀⠈⡇⠀⠀⠈⠛⠲⠦⠤⣤⡤⠤⠴⠖⠛⠉⠀⠀⢸⠁⠀⠀⠀⣹⠀⠀⠀⢾⡉⠙⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠉⢀⡟⠀⠀⠙⢦⣤⣤⠾⠁⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣠⡴⠋⠀⡴⢤⣄⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡤⠖⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢳⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡤⢶⡄⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⠈⠙⠲⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢸⠃⣠⠖⣦⠀⢀⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣤⡄⠀⣯⠉⠳⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⣏⢠⠞⠙⡇⢀⡞⢻⡄⢠⡏⢳⡀⢸⠀⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠳⠞⠀⠀⢳⡼⠁⠀⠙⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⣀⡈⠙⠛⠛⠛⠋⠉⣁⣀⣀⡴⠶⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠗⠀⢸⠀⠀⠉⠁⠀⠛⠚⠛⠛⠫⣤⣍⢡⡀⠀⠀⢸⡇⠀⡀⢨⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⡀⠶⢾⡀⢶⣿⣟⡄⢱⠄⠀⡎⣿⣶⡞⢀⠙⠀⣰⠚⠓⠐⡇⢸⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⠛⢛⠀⢶⣽⣿⣧⠴⠂⠀⢷⣈⣿⣣⣼⠶⠀⠙⢳⡶⠺⣷⠸⠁⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⢸⠀⠀⠁⢀⡤⠀⠠⣄⠀⠉⠀⠉⠀⡀⠀⠀⢸⡇⠀⠘⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣤⠶⣍⠀⠀⢀⣼⠂⠀⠀⣠⡾⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣄⠀⢀⣷⠴⠛⠁⣀⣠⠾⠋⠀⡃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠉⠛⠿⣥⠤⠚⠟⠋⠉⠀⠀⣿⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠿⢧⡀⠀⠀⠀⠈⠢⣄⠀⡀⠀⢂⣴⠏⠀⠀⣠⡾⠉⠉⠀⠀⠉⣩⡟⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠙⠛⠚⠛⠁⣴⣿⠶⠛⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⡴⠷⢦⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣴⠶⠒⠶⢾⣧
⠀⠀⠀⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠘⠷⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠂⠛⡈⢳⠀⠀⣿⠀⠀⣿⡀⠀⠀⠀⣀⣀⣤⣴⡶⠿
⠀⠀⠀⠀⠀⠀⡏⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠦⣤⠀⣄⠀⣀⠁⢸⠀⠀⣿⠀⠀⠉⠛⠛⣿⡟⠛⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⠛⢿⡷⠶⠶⢦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠉⠀⠀⣿⡀⠀⠀⠀⢀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠳⠶⠶⠶⣶⣤⣤⣤⣀⣀⣽⣇⣠⡶⠞⠋⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠙⠛⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠉⠁⢀⣠⣾⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⣾⣦⣤⣤⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠿⠿⠶⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⣘⣠⣴⠿⠋⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠄⣀⣀⣀⣀⣀⣉⣉⡿⠟⠛⣿⡟⠛⠋⠀⠀⠀⢀⣿⣄⣀⣀⣽⣇
⠀⠀⠀⠘⣧⣀⣀⣀⠀⢀⣾⠀⢀⣀⣠⣤⡤⣾⡇⠀⠀⠀⠤⠀⢉⡉⠉⠉⣉⣉⣤⡴⠛⣿⣇⠀⠀⠀⠀⠀⡏⠁⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠈⣿⠋⠉⣿⠋⠁⠀⣾⢿⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣤⡴⠚⣿⠋⠉⠛⣻⣶⣶⢃⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⡟⠀⠻⣦⠀⠀⠻⢶⣤⣀⣀⠉⠁⠀⠀⠙⠋⣉⣀⣴⠾⢋⣠⡶⠟⠁⠀⡟⠘⣷⠶⠶⠶⣶⠿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⣷⡀⠀⠘⢳⣄⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⣉⣡⡶⠛⠁⠀⠀⠀⣀⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡯⠀⠀⣟⠀⠀⠀⠙⣷⡄⠀⠀⠙⣷⠶⠶⠿⠟⠛⠛⠚⠛⠛⠛⢿⡏⠁⠀⠀⠀⢀⣠⣶⠟⠁⠀⣿⠀⠀⢨⣿
⠀⠀⠀⠀⣰⡷⠶⢶⣏⠀⠀⠀⠀⠈⠻⣦⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⢀⣠⣶⣿⡏⠀⠀⠀⠀⣿⠀⠀⢸⡟
⠀⠀⢀⡾⠁⠀⠀⠀⠙⡿⣆⡀⠀⠀⠀⣿⠻⣾⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣾⠟⠋⠀⣿⡇⠀⠀⠀⠐⣿⣤⣤⡾⢷⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⣰⡟⠀⠀⠀⠀⠀⠀⣇⢸⣧⠀⠀⠀⣿⠀⠈⠉⢹⣟⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⢰⠋⠳⢦⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⣩⡿⣦
⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣻⡀⢀⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⢦⣀⠀⠀⠙⠛⠶⣄⣀⡰⠶⠛⠋⠀⣠⣿⣀⣀
⡿⠒⠦⢤⣤⣤⣀⣸⡀⣿⠿⠾⣿⠇⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡽⠳⣤⣀⠀⠀⣼⠋⣀⣀⣤⠞⠻⣯⣤⣩⡽
⠘⢧⡄⠀⠀⠀⠀⠉⣻⣿⣤⠾⠁⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢰⣯⡀⢠⡞⠛⠳⢾⢿⡖⠉⠉⢳⣤⣤⢾⠇⣏
⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣀⣼⣏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⠙⣶⡶⢾⡏⠀⢸⠄⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠿⢷⣶⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠿⣶⣶⣶⣶⡿⢿⣷⠀⠀⠀⠸⣧⣄⣳⠀⠀⠀⠀⠀⢰⠏⠀⢸⡧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⢷⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠿⠷⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⡁
⠀⠀⠀⠀⠀⣀⣠⠶⠞⠛⠁⠀⠀⠀⠀⢀⣴⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⠉⠉⠉⠛⠶⢦⣀⡀
⠀⢀⣤⣾⣛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⡀⠀⠀⠀⠉⠙⠛⢦⣄⣀
⠀⣼⠋⠉⠉⠙⠛⠶⠶⠶⣤⣤⡶⠋⠁⢀⣴⡟⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠈⠉⣷⣦⡀
⠀⢿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠇⢀⣴⠟⠉⣥⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⡷⣦⡀⠀⠉⢻⡶⠶⠚⠛⠛⠛⠁⢹⡃
⠀⠀⣹⠉⠹⠛⡿⢳⡶⣤⣤⣴⡿⢻⠅⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣶⣾⠃⠈⠻⣦⣄⣸⡇⠀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠹⣄⣼⡄⠁⣼⡀⠠⡄⠀⢀⣼⠷⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠃⣴⠏⠛⠛⠿⠙⡟⢛⠙⡏⢹
⠀⠀⠀⠀⠀⠙⠶⠜⠛⠶⠼⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠹⣆⠀⢀⣸⣠⣷⣀⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⠶⠶⠶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀⣀⣤⣶⠿⠟⠛⠁⠀⠀⠀⠀⠈⠛⠻⠿⣶⣤⣀⢀⣴⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠋⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢾⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠙⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⣠⠞⠁⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠈⠳⣄⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⣰⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⣆⠀⠀⠀⢿⣇
⠀⠀⢠⣤⣤⣤⣿⠃⠀⠀⢰⠇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⡆⠀⠀⠘⣿⣤⣤⣤⡄
⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⣾⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣷⠀⠀⠀⠉⠉⠉⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⣀⣀⡀⠀⠀⠀⢿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡿⠀⠀⠀⢀⣀⣀⣿⡇
⠀⠀⠘⠛⠛⠛⣿⡄⠀⠀⠸⡆⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢰⠇⠀⠀⢠⣿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠹⡄⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⠏⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠙⢦⡀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⢀⡴⠋⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⣀⡴⠋⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣄⣀⣀⣠⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣠⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠟⠁⠉⠛⠿⣶⣦⣤⡀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠛⠉⠈⠻⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⠶⠶⠶⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠉⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠶⠀⢀⠀⠶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠐⠂⠀⠀⠠⠀⠉⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠃⠀⠀⠀⣀⢠⠀⠀⠶⢤⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠁⠀⠂⠀⠀⠒⠐⠈⠀⠀⣠⠔⠀⠀⠀⠀⠱⣀⡧⠴⣁⠴⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⣤⣄⣀⣠⣤⡤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣖⣋⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠒⠈⡋⠈⠉⠁⠈⠓⠈⡶⠠⢄⠀⠀⠀⠀⠀⠀⢀⡕⢤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⢠⠃⠀⠀⠙⠲⠤⠤⠤⠴⠊⠁⠀⠀⢻⠐⢄⣀⡠⡔⢋⡠⠃
⠀⠀⠀⠀⠀⠀⡠⠚⣀⣤⠀⡎⠀⣴⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣇⡀⠴⠊⠁
⠀⠀⠀⠀⠀⣘⢁⠖⠁⠈⢳⠁⠀⠙⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⢀⠴⠣⢿⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡠⠤⡇⠀⠀⢀⡇⠀⠀⡇⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡆
⠫⡤⠊⡽⠲⠶⢮⠙⣆⠀⠈⢑⠒⠤⠤⢀⣀⣀⠂⠀⠀⣀⣀⡀⢬⠴⠚⠁
⠀⠉⠲⠆⢨⠇⠀⠉⠁⠀⠀⢀⢒⡁⠒⢄⠀⠀⠀⢀⠔⠋⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣱⣤⠂⡀⠀⣇⣔⠁⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⢎⠀⠀⠀⠀⠀⢨⠗⠒⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣶⡶⡎⠀⠀⠀⠀⠀⢘⡶⣶⡶⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠰⠴⠣⠄⠤⢱⡀⠀⠀⠀⠀⣸⡡⠤⠤⠣⠤⠤⢄
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠐⠈⠠⠀⠀⠙⢆⠀⢀⠞⠁⠀⠀⠈⠄⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⣏⣩⣉⣹⣉⣹⣉⣩⣉⣹⣹⠀⢸⣸⣁⣋⣈⣛⣀⣙⣈⣋⣘⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⣀⠀⠀⣈⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡟⡄⢎⢸⣉⠆⢸⠰⣉⡇⡜⡕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠵⢧⡬⠭⠭⠤⠤⠭⠭⣤⠵⠵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠋⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡇⠀⡖⢲⠓⡖⢲⠒⡖⢲⡖⢲⠀⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡙⣌⢲⡇⠀⠓⠛⠒⠓⣚⡒⠛⠚⠓⠋⠀⣷⢊⡼⣱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣉⣉⡉⠙⣦⣑⡬⠛⡇⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⡟⠫⣔⣡⡞⠋⣉⣉⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡆⢸⠋⠀⠀⡇⢠⡴⠧⣄⣠⠜⢤⡀⡤⠷⣤⠀⡇⠀⠈⢻⠀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡜⠀⠀⠀⡇⠀⠷⠾⠅⠸⠶⠾⠀⠹⠶⠇⠀⡇⠀⠀⠘⢤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡏⠭⢭⡏⠉⠉⣯⠭⠭⣽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⣒⣒⡇⠀⠀⣗⣒⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠤⠴⡇⠀⠀⡷⠤⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⠭⢭⡇⠀⠀⣯⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣓⣒⣒⣇⡀⣀⣗⣒⣒⣻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠃⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⣴⣿⠿⠛⠻⠿⣿⣤⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣽⠟⠻⣿⣆⠀⠀⣠⣾⡿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⢹⣿⣷⣾⣿⠏⠀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⣸⣿⡄⠀⣴⣶⠀⠀⠀⠀⠀⣀⣿⣧⣤⣴⣾⣿⣿⣿⣿⣦⣄⡀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠇⢹⣿⣿⣿⠋⠉⠉⢹⣿⡟⠋⠛⠻⢿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣦⣴⣿⣦⣿⣷⣄⡀⢸⣿⡇⠀⢀⣴⣿⣏
⠀⠀⠀⠀⠀⢀⡀⢈⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣽⣿⣍⢹⣿⣿⠿⣿⣿⡟⣋⡻⠿⢲⣶⡄⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⠉⠙⢿⣿⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⠿⢿⣿⣿⣿⣿⠋⠘⠿⠃⠀⣸⡿⢋⣿⣿⣶⣿⣿⣷⣾⣿⣿⣄⣠⣶⡄
⠀⠀⠀⢀⣤⣤⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⣷⣤⣤⣼⣿⣿⡿⠋⠀⠀⠹⣿⣿⣿⣶⣶⡄⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡁⣀⣀
⠀⠀⠀⠈⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⠟⣛⡻⢿⣿⡟⠁⠀⠀⠀⠀⢿⣿⣿⣿⠁⢰⣷⣶⣿⣿⣿⠿⣿⣷⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣤⣶⣿⣿⣿⣯⠀⠀⣀⣠⣤⣾⣿⡇⣿⣿⣿⡎⣿⣿⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢹⣿⣿⣿⠃⠀⠘⢿⣿⣦⣤⣴⣿⡿⠃⠈⢿⣿⣿⣦⣤⡄
⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣛⣋⣼⣿⣿⣿⣿⣶⣤⣤⣼⣿⣿⣿⣸⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⠛⠁
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠈⢻⣿⣿⣿⠟⠋⠙⠛⠿⠿⣿⣿⣿⣿⣿⡿⢿⣇⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣸⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣄⠸⠿⢿⣿⣿⣿⡋⠉⠀⠀⢹⣿⣿⠋⠉⠙⠛⢿⣿⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠺⡿⠿⣿⣿⣿⣷⣄⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠛⠛⠀⠀⣴⣿⣿⣿⣿⣦⡀⠀⢸⣿⡿⠀⠀⢀⣠⣾⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⣤⣴⣶⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠛⠛⠙⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⣿⣿⠏⠹⣿⣿⠋⠹⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠁⢸⣿⡏⠀⠙⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠉



⣿⣿⣿⢿⢿⡿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣾⣾⣶⣿⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠇⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢠⣀⢖⡁⠀⠀⠀⠀⠐⠖⡄⠀⣀⠀⠀⠀⡀⠐⠀⢀⠉⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣽⣿⣇⠀⠀⢀⠄⣄⡀⠀⡟⠅⠋⡙⢻⣃⡴⠖⠻⠓⠛⠓⠛⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⠘⡇⠀⢀⡘⢀⣋⢁⠀⡄⣲⣾⣇⣀⣹⡇⢹⠀⠠⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⣰⣤⣶⣛⣡⡶⢰⠇⣰⡇⢈⣽⠊⠙⣿⡇⠘⣧⠀⡆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⡿⠤⣄⠙⢻⣶⣿⡶⠃⠙⠁⠸⣷⣾⣿⠃⠀⠙⢶⣿⣆⢻⣆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⡇⢻⠒⢄⡙⣾⡿⠛⠀⠀⠀⠀⠱⠙⠛⠏⠀⠀⠀⠈⣿⣇⠈⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠁⣇⢸⡐⠲⣬⣿⣷⠀⠀⣠⡄⠀⠀⠀⡎⠀⠀⠀⠀⣰⡟⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣠⣇⠀⠁⢻⡿⣿⣿⣆⠀⣸⣧⣤⣤⣤⣅⣀⡀⠀⣠⣯⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠐⡉⠉⣿⣿⠍⢹⠂⠙⠀⠈⢩⣟⠛⠫⠍⠉⣉⢉⣽⣿⣿⣿⣿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡎⠹⡏⠀⠀⠀⠀⣴⠟⠝⠋⡒⠁⠀⠂⠄⠒⠻⠿⠿⣿⡍⠳⢌⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠀⠑⠈⠀⠀⠀⡏⠙⠓⠶⠀⢠⠀⠀⠀⢰⠀⠸⠗⢺⣟⡠⠀⠙⢺⣤⢶⠄
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⡄⠂⠀⠀⢠⡇⠀⠀⠀⡄⢼⣄⠀⠀⣸⣷⡙⠀⠀⣿⡅⠀⠀⣸⢷⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⣀⣀⡇⠀⠀⠀⢺⣿⣿⠀⣰⣿⣿⠁⠀⠀⢸⣷⣄⣠⣿⢿⡴⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢃⣤⣾⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠹⣿⣿⠉⠀⠀⠀⢻⣷⣿⡟⢈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢺⢀⡾⣡⣿⣿⣿⡟⢻⠄⠈⠃⠀⣻⡇⠀⠀⠀⠘⠿⢷⡀⠄⠀⠀⢻⠛⠙⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠉⣿⠉⠀⢸⣇⡀⠀⠀⣿⣧⠀⠀⠀⣠⣾⣼⣧⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣼⠀⠀⠈⣏⣙⢻⣿⢻⣿⠀⠀⢴⢻⠟⢉⠹⣇⠉⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⣿⢉⣿⣿⢼⡏⠀⣶⣻⣎⣴⠃⢰⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣴⣾⡈⠋⣹⣾⣿⣶⣯⣬⣭⣇⣠⣾⣞⠛⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣶⣿⣿⣿⣿⣇⣰⣯⡽⣿⣿⣿⡇⠀⠈⠉⠘⢿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⢀⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠋⠀⠀⢹⡟⣿⣧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⣄⣀⠀⢸⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣴⣾⣿⣿⣿⣟⠋⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⢃⣤⠀⣀⠀⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠈⠁⠀⠖⠀⠈⠴⣔⢀
⠀⠀⠀⠀⠀⠉⠗⠁⠉⠀⠉⠀⢨⣻⡆⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠋⠀⠀⠀⠀⢀⣄⠀⠲⠘⣎⠤
⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠚⠃⢰⣿⢶⡆⠀⠀⠐⢀⣄⠀⠀⠂⠀⠰⠶⠀⣠⡀⠈⠉⣀⣿⣷⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⣤⣽⣿⠿⠀⠀⠀⠀⠀⠀⢡⣤⣤⣬⡤⢄⡀⢀⡈⣀⣰⣶⡿⢿⣿⢇⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠾⣾⣿⣿⠙⠟⠂⠀⠀⠀⠀⠀⠀⢈⣹⡏⠉⠁⡏⠻⢾⡷⢿⠿⠋⠁⠘⢋⡮
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⢀⣤⣿⣿⠛⠀⢰⠃⢘⣏⠁⠀⠠⠄⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⠡⠼⢿⡼⢿⣟⣹⡷⣠⠋⣀⣻⡄⠀⠀⠀⠀⠄⠀⠀⠰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠈⠀⠀⢈⡩⠞⠁⣶⣼⣿⠖⢀⡀⠀⠀⠀⢠⡌⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⡈⠀⠒⠒⠚⠉⡁⢠⣌⣯⡿⠇⠀⢀⠝⡳⠌⠰⠋⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠳⣤⠀⠊⠀⠁⠈⠉⠈⠙⠒⠊⠁⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠞⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⣄⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣼⣿⣿⣿⣿⡀⠀⠀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣷⣶⣾⣿⣆⠈⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⠛⠛⠛⢉⣉⣠⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣟⠋⣠⣶⣿⣿⣿⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠉⣿⣿⣆⠘⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⣼⣿⣿⣿⠟⠁⠀⠙⢿⣿⡿⠟⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠁⠀⢹⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⡿⠻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⢿⣿⡿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⣿⣿⣿⣷⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣦⣾⣹⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠈⢻⣿⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⣹⣿⣼⡿⣦⣾⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠸⣿⣭⣿⣿⣦⣴⣾⣿⡛⣿⡟
⠀⠀⠀⠀⣠⣤⡶⠶⣦⣤⣹⣿⣿⣾⡁⣹⣿⡿⠁⠀⠀⢀⣴⡿⠛⢻⡏⠙⢻⣷⣿⣿⣿⣉⣿⣿⢛⣿⣿⡟⠁
⠀⠀⢠⡾⢿⣧⠶⠶⠶⣌⠻⣯⡙⠛⠛⠛⠉⠀⠀⠀⠀⣾⠟⠳⣦⣼⣷⣴⠟⠉⣿⡌⠙⠛⠿⠿⠛⠛⠁
⠀⠀⣿⢁⡟⢹⡿⠛⢶⣼⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣿⣧⣠⣿⠷⠶⣾⡇⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⣀⣀
⠀⠀⣿⡈⣧⠘⣷⣤⠾⢡⡟⢸⣇⣴⣿⣟⣿⣦⡀⠀⠀⠹⣯⡀⢠⡿⠙⢿⣄⣠⣿⣷⡿⢿⡅⠀⠈⣹⡿⣷⡀⡞⢷⡬⢷
⠀⠀⠘⢷⣌⣻⡿⠶⠶⢋⣰⡟⢹⣷⣾⠉⢹⣶⣿⠀⠀⠀⠘⠻⢿⣧⣤⣾⠿⠋⢹⡿⠀⠀⣻⠶⢾⡋⠀⢸⣿⠙⠾⠵⠋
⠀⠀⠀⠀⠙⠛⠷⠶⣾⣟⣁⡀⠈⢷⣾⣟⣿⡶⠃⠀⠀⠀⠀⣰⡾⢿⣦⠀⠀⠀⢸⣷⡴⠶⠿⣤⡼⠷⢶⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠹⢷⣾⠟⠀⠀⠀⠀⢻⣦⡀⠀⣾⠆⠀⣠⣿⢏⣤⣤⣦⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣽⣿⣿⠇⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⠻⠿⠿⠿⠟⢫⣽⣿⠋⠁⠀⠀⠀⠉⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⣯⣶⡿⠟⠛⠛⡿⢷⣦⡀⠀⠀⠀⣰⡟⢻⣩⠿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠋⠻⣷⣶⣶⣶⣶⣤⠀⢀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡿⠙⣷⡖⠚⣾⢧⡄⠙⣿⡄⠀⠀⢻⣉⡿⣜⢒⡿⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⣾⣿⡟⠉⢻⣿⣿⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⣃⣿⠟⢻⣦⢿⡶⢿⣷⠀⠀⠀⠛⠶⠾⢿⣷⡶⠿⠿⠶⣶⡄⢹⣧⠀⠀⢻⣿⣷⣤⣾⣿⠏⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠘⣿⡟⠻⣏⢻⡷⠿⣇⡼⠁⣸⡟⠀⠀⠀⠀⠀⣾⡟⠙⣷⣠⣄⣴⠟⠻⣿⣿⣦⡀⠀⠙⣿⠟⠛⠁⠀⢀⣼⠯
⠀⠀⠀⣠⣾⣿⣿⠋⠙⣿⣷⣝⣿⣄⠈⣿⠳⠒⠛⢷⣴⡟⠁⠀⠀⠀⠀⢰⣿⠀⢀⣿⠁⠈⣻⡄⠀⣿⡎⠙⠿⣦⣼⣿⣀⣀⣤⣶⠟⠋
⠀⠀⢰⣿⠁⠉⣿⣶⣶⡿⠛⢿⡎⠙⠻⢿⣶⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠈⣿⡟⠋⠻⢶⡶⠟⠛⢻⣿⠃⠀⠀⠁⠉⠋⠛⠋⠉
⠀⠀⢸⣿⣷⠾⣿⣤⣿⣧⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣷⣷⣦⣼⣿⣦⣄⣸⣇⣀⣴⡟⠃
⠀⠀⠘⢿⣇⠀⣸⣿⠁⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠙⢿⡟⠉⢹⣿⣿⣏⡉⠛⠙⠙⠉⠀⢠⣴⢶⣄
⠀⠀⠀⠈⠙⠿⢿⣿⡷⣾⣋⣁⠀⠀⠀⠀⠀⠀⢐⣿⡿⠿⣷⣶⠿⠿⣶⣾⠟⠛⣿⣗⠀⠀⠀⠀⠀⠸⣷⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣿⣿⣆⠀⠀⠀⠀⣺⣿⣅⣀⣼⡇⠀⠀⠈⣿⣦⣤⣿⣿⡀⣀⣾⣾⡿⠿⠿⣷⣤⠀⢠⠴⣶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣍⣽⡿⣿⠀⠀⠀⠀⢘⣿⣿⠟⠛⢿⣦⣤⣾⡏⠉⢹⣿⣿⣼⡟⣡⡾⣿⠓⢶⣌⢻⣧⢾⡒⣭⠓⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⡷⠋⠀⠀⠀⠀⠀⠻⢿⣧⣤⣾⡏⠀⢹⣿⣶⣿⠟⢫⣿⠀⣏⣰⡟⢻⡶⢿⠋⣿⡍⠙⠛⠋⠉⠻⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⣿⣿⣿⡿⠟⠋⠀⠈⢿⣟⠻⣍⣙⣿⣤⠟⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⣍⣹⣧⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⢸⠃⠀⠀⡇⠀⠀⢸⠃⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⡈⠳⣄⠀⡇⠀⡠⠞⢀⠴⠋⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠁⠀⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠀⠀⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠀⠀⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠶⣄⠙⠋⠛⠛⠛⠛⢻⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡏⠋⠛⠛⠛⠛⠋⢀⡴⠒⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⡈⠲⠶⠶⠶⠶⠶⢾⣿⣿⡇⣿⢸⡇⢿⡇⣿⢸⡇⢿⡇⣿⢸⣿⣿⡷⠶⠶⠶⠶⠶⠖⢉⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣤⣤⣤⣤⣤⣼⣿⣿⡇⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣧⣤⣤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠙⠛⠛⠛⠛⢻⣿⣿⣇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣸⣿⣿⡏⠛⠛⠛⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⣡⠴⠶⠶⠶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠶⠶⠶⠶⢦⡈⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠴⠚⠁⣀⣀⣠⣤⣤⣠⣼⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣇⣀⣤⣤⣤⣤⣄⠙⠦⠤⠶
⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⡇⢸⠀⠀⣇⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⢁⡴⠋⠀⡇⠀⠑⢦⠘⢦⡀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⡄⠀⠀⡇⠀⠀⢸⡅⠀⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠋⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⠄⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⢛⡀⠀⠀⠀⢀⠀⣑⠠⠵⠕⠃⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠁⠀⠀⠀⠀⠘⠘⢀⡀⠈⠁⠀⡄⠀⠈⠈⠀⠀⢸⠀⠀⠀⢠⢫
⠀⠀⠀⠀⠀⠀⠀⣰⣻⠀⡀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠿⠢⠀⠀⡀⠀⠀⠀⣀⢼⣆⠉⠁⢸⡑
⠀⠀⠀⠀⠀⠀⣰⠿⢹⠉⣃⡁⠅⢀⡀⠈⠠⢠⣤⠄⠈⠈⠀⡴⠇⠀⠰⠊⠀⢸⠀⠀⢒⡞
⠀⠀⠀⠀⠀⣰⡝⠃⠀⠀⠀⠁⠀⠀⠉⢣⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡴⠿⣶⣷⣴⣤⣤⡄⡆
⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣖⠀⠐⠞⠁⠆⠀⠀⠀⠰⠀⠈⠃⠣⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠁⠉⠀⠀⠘⠁⠉⠉⠉⢻⠆
⠀⠀⠠⠤⠜⠗⢠⣄⢠⣐⣛⠻⠅⠀⠀⢠⠀⠀⠀⠀⠠⠷⠆
⠀⠀⠀⠀⠈⠉⠛⠙⠻⠉⣹⣿⣯⢭⣿⠩⢥⡦⠄⢦⠽⠿⠶⠶⠮⠷⠖⠒⠺⠥⠟⠿⠷⠮⠥⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⠃⢀⣴⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣦⠀⠙⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠃⢀⣾⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⣸⣿
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⢻⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣦⡀⠙⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠟⠁⢀⣼⣿⠟⠛⠛⠋⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣀⠈⠙⠛⠿⠿⠿⠿⠛⠋⠁⣠⣴⣿⣿⡇⠀⢀⣤⣄⠀⢀⣸⣿⣿⣿⣀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣷⠐⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠉⠈⠉⢻⣿⣿⣿⣿⡟⠉⠁⠙⠻⡿⠟⠁⢠⣿⠟⠉⣠⣴⣾⣿⣿⣷⣶⣤⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⢠⣾⣿⡿⠛⠋⠉⠛⠻⣿⣿⣦⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠘⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣿⠇⢰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣧⡈⠻⣿⣿⣶⣦⣤⣶⣾⣿⡿⠃⣠⣿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣈⠉⠛⠛⠛⠛⠋⢁⣠⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠟⠿⣿⣶⣶⣾⡿⠟⢿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⢀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠁⠀⠁⠀⠀⠁⠀⠁⠈⠀⠀⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⢠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⢰⠀⠀⠐⠂⠀⠀⠀⠀⠀⠦⠀⠀⠰⠄⠀⡀⠀⠀⠠⠀⠀⠀⠀⢀⠀⣌⠀⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠀⠐⡀⠀⠀⠈⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠁⠘⠀⠀⢀⡀⠀⠀⠀⠀⠘⠀⠀⠂⠘⠂⠀⠀⢀⠀⡉⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⢀⠤⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⢄⡀⠀⠀⠈⠀⣁⠘⠀⠀⠠⠄⠀⠀⠀⡀⠶⢈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄
⠀⠀⠀⠈⠁⠀⠀⠴⠤⠀⠀⣄⠀⠀⠈⠁⠀⠈⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠖⠀⠀⠈⠁⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠃
⠀⠀⠀⠀⢠⡀⠀⠀⠐⠂⠀⠐⠀⠀⠀⠐⠂⡀⠀⠀⠆⠈⠃⠀⠙⠀⠆⠀⣀⠐⠂⠀⠀⢀⠀⠰⠀⠀⠀⠈⠓⠀⠀⠐⠂
⠀⠘⠃⠀⠀⠀⠀⠀⠉⠤⠘⠀⠀⠀⠠⠄⠈⠁⠈⠃⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⢠⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⣀⢘⠀⠓⡀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⢠⠀⡤⠀⠰⠆⠀⠀⠓⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⢈⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡁
⠀⠈⠃⠀⠈⠀⠀⠉⠀⠀⠀⠐⠆⠀⠀⠀⠀⠠⠆⢀⠀⠰⠔⠂⠀⢀⠂⠉⠀⠀⠀⠀⠀⠆⠀⠀⣀⠀⠀⠀⢲⠀⠐⠂⠀⢀⡀⠀⠀⠀⠁
⠀⠈⠁⠀⡄⠀⠤⠘⠀⠀⠀⠀⠀⡤⠀⠀⠃⠄⠀⠉⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⡀⠀⠀⠀⢀⠀⠤⠉⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⢤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠘⠀⠀⠆⠁⠀⠰⠀⠈⠀⠀⠀⠀⣠⠀⢈⠁⠉⠘⠘⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠈⣁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡥⠀⠀⠀⠀⠀⠀⠠⡄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠆⠀⠀⠀⠀⠃⠀⠤⠀⠀⠐⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⢀⠀⠜⠇⠀⠀⠀⠀⠀⢠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⠀⣉⠀⠈⠀⠀⠈⠀⣄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣠⠀⠀⠀⠐⠂⢀⡄⠐⢣⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠈⡁⠀⠘⠀⠾⠂⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣦⡠
⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⡀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠷⠾⢓⣆⠀⠂
⠀⠀⠀⢠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣦⠖⣾⣯⡉⠀⠀⡀⠀⣴⣷⣿⣼⣿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠟⣷⢿⡏⠉⠂
⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠐⣴⣷⣏⣩⡅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣄⠀⠀⠀⠀⠀⢤⠿⠙⠍⠋⠈⠀⠀⠀⠀⣠⣤⢰⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⡀⢰⡤⠀⡀⠀⠀⠀⠀⢺⡃⢰⡆⠀⠈⡀⠀⠀⠀⠻⠀⠀⡅⢻⠋
⠀⠀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠁⠰⠆⠀⠀⠈⠁⠀⠙⣦⡀⣿⠀⠀⠀⠘⢶⡰⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢠
⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢶⣴⣇⣀⠀⠀⠀⡀
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⣾⣭⣻⢻⡷⡔⠚⠁
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠈⠀⠀⠐⣟⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⣼⣩⡄⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⣼
⠀⣀⠀⠀⠀⠰⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢀⣠⣞⠁⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠿⠀⠀⠀⠀⠄⠉⠙⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢈⠀⠀⠀⠀⠰⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠈⢘⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡄⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣲⣾⣿⣞⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡚⢲⡄⠀⠀⠘⠟⢻⣿⠛⠃⠀⠀⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠎⣰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠉⠳⡖⠀⠀⢠⠆⠀⠈⠀⠂⠀⠀⠀⡀⠠⢥⣮⣿⣿⣷⡀⠀⠠⠄⠀⣇⠀⠉⢸⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⠻⠟⠑⠦⠀⠀⠀⠉⠀⠀⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣴⠆⠁⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠒⠀⠀⠠⣤⠉⠀⠀⠄⠀⢨⠀⠀⡀⠀⢼⡴⠁⠀⣀⣀
⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⣀⡴⠒⣫⡟⠁⠀⠀⠀⠀⢰⡀⣠⡔⠀⠀⠀⠛⠀⠀⠀⠀⠀⠗⠀⠞⠀⠀⠈⠁⠐⣴⠛⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠐⠘⢿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢄⣸⣿⣯⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣸⣧⠖⠚⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢴⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⢀⣔⣶⣢⡄⠀⠀⣤⣖⣲⣄⠀⠀⣠⢶⣶⢦⠀⠀⢀⠔⣶⠢⡀⠀⠀⡠⡶⣖⣄⠀⠀⣠⠖⡒⢢⡀⠀⢀⠔⣒⡢⡄⠀⠀⡴⡖⡲⢄
⠀⠀⠸⡿⣤⢿⡏⠀⠈⣷⡧⢿⡿⠀⠀⢿⣼⣼⣼⠃⠀⠸⡛⣤⢛⠇⠀⠀⢟⣄⡼⡻⠀⠀⢣⠚⠜⣡⠃⠀⠸⡘⠯⢃⡏⠀⠈⣗⠢⠓⡾
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⢠⣾⠿⣷⡄⠀⢀⣶⣿⣻⣦⠀⠀⣴⢿⣿⢶⡀⠀⢠⡞⣿⢓⣆⠀⢀⣶⣿⢿⣦⠀⠀⣰⢎⣟⢲⡀⠀⢠⣞⣿⡳⣆⠀⢀⡶⣏⡹⢦
⠀⠀⠸⣾⣦⣿⠏⠀⠈⢷⣟⣻⡿⠀⠀⢻⣼⣾⣼⠃⠀⠸⣏⣷⣉⠟⠀⠘⢿⣧⣾⡿⠀⠀⢳⣈⣚⡴⠃⠀⠸⣜⣳⣳⠏⠀⠈⢷⣱⣋⡾
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⢠⣮⠿⣵⡆⠀⠀⣴⣯⣿⣦⠀⠀⣴⢿⢿⢷⡄⠀⢠⣊⠿⣑⡆⠀⠀⣶⠟⢯⣦⠀⠀⡴⢋⢏⡳⡀⠀⢠⢎⣭⡕⡆⠀⠀⠔⠏⡝⢢
⠀⠀⠘⢟⣶⡻⠇⠀⠀⠿⣗⣿⠟⠀⠀⠹⣼⣾⡼⠁⠀⠘⢍⣶⣩⠇⠀⠀⢿⣦⣜⠟⠀⠀⠱⣉⣚⡴⠁⠀⠘⢌⣓⡡⠇⠀⠀⠯⣁⣉⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⣰⣾⢿⣷⡄⠀⠀⠀⣰⣾⣷⣦⠀⠀⠀⢀⡶⠛⠳⣆⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⣤⡿⠺⣧⡄
⠀⠀⢻⣿⣴⣿⠇⠀⠀⠀⢻⣷⣾⡿⠀⠀⠀⠘⣷⣄⣠⡟⠀⠀⠀⠸⣿⣶⣿⠇⠀⠀⠀⠺⣦⣤⡾⠆
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⣰⡾⣛⢶⡀⠀⠀⠀⣴⣾⣻⣦⠀⠀⠀⠀⣴⣾⣷⣄⠀⠀⠀⢠⡖⠛⠲⡄⠀⠀⠀⣰⢾⣻⢶⡀
⠀⠀⢻⣄⣋⣼⠃⠀⠀⠀⢷⣷⣺⡼⠀⠀⠀⠈⢿⣷⣿⠟⠀⠀⠀⠸⣄⣀⣠⠇⠀⠀⠀⢻⣽⣻⣽⠃
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⢠⣶⢳⣴⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⢀⣴⣶⣦⡄⠀⠀⠀⢠⣶⣶⣦
⠀⠀⢹⣴⣛⣼⠃⠀⠀⠀⢿⣇⣢⡿⠀⠀⠀⠸⣿⣧⣽⡿⠀⠀⠀⠺⠿⢠⣿⡿⠀⠀⠀⢿⣧⣤⣿⠇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⣠⣶⠶⣤⠀⠀⠀⠀⣤⣶⣦⡄⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⢀⡤⠦⣄
⠀⠀⢿⣧⣀⣿⡇⠀⠀⠀⢿⣸⣗⣿⠁⠀⠀⠨⣿⣄⣸⡿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢺⡐⠗⣸⠃
⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠉⠋⠋⠁⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠈⠉⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⠿⠯⣏⠀⢈⡯⠿⢷⡀⠀⠀⠀⠀⣴⡿⢿⣏⠁⠀⠀⠈⣹⡿⢿⣦
⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣿⡆⠀⠀⢰⣿⣀⣠⡟⠉⠙⣧⣀⣸⣷⠀⠀⢠⣾⠏⠀⠈⢿⣆⣠⣀⣴⡟⠀⠀⠻⣷
⠀⠀⠀⢺⣿⣿⣿⣇⠀⣬⣿⣿⣿⡇⠀⠀⢸⣷⠉⠙⣧⣀⣠⡟⠉⢳⣿⠀⠀⣼⡏⠀⠀⢀⣾⣿⠿⠿⣻⣧⠀⠀⠀⢻⣇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠹⣦⣴⡏⠀⠉⣗⣤⡾⠁⠀⠀⣿⡿⠿⠿⢿⣿⣇⠀⢀⣽⣿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠋⠀⠀⣄⣰⣄⣠⠈⠙⠻⠲⠚⠛⠉⠀⠀⠀⠀⢹⣧⠀⠀⠀⢻⣷⣿⣿⣿⡋⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⠛⠛⢿⣷⠂⠀⠀⠀⢀⣠⣠⣠⣀⡀⠀⠻⣧⡀⣠⡿⠁⠀⠀⠘⣷⡀⣠⣾⠟
⠀⠀⠀⠀⠀⣠⣴⠶⠶⣦⣄⠀⠙⣿⣇⢀⠀⣸⣿⠃⠀⣀⣾⠿⣿⡋⢹⡿⢿⣶⡀⠈⠻⢿⣧⣤⣠⣠⣤⣼⡿⠛⠁
⠀⠀⠀⠀⣸⡟⢱⠒⠲⡎⢻⡆⠈⠉⡿⢿⡿⢿⠉⠁⢐⣾⡿⣤⣾⠟⠿⣧⡼⢿⣷⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢻⣇⡸⠤⠤⢇⣼⡇⠀⠀⠀⠀⢀⠀⠀⠀⠐⣿⣤⣼⣧⣀⣠⣿⣦⣼⣿⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠙⠷⠶⡶⠿⠋⠀⠀⠀⣤⣷⣾⣾⣧⠆⠀⠻⣿⣄⣼⠛⢻⣧⣸⣿⠃⠀⠀⠀⢐⣾⡿⠋⠋⠉⠙⢽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⣹⣿⠁⠀⠀⢹⣿⡁⠀⠘⠹⠻⢿⠿⠿⠛⠀⠀⠀⠀⠀⣺⣿⡏⠀⠀⠀⠀⠀⣹⣿⡗
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠞⣿⣄⣀⣠⣾⡷⠂⠀⣀⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡢⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣿⣿⣆⠈⠁⠟⠻⠙⠋⠁⠀⢤⣿⣿⣻⡿⣤⠄⠀⠀⣠⣶⣶⣦⡄⠘⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠐⣿⣿⣿⣧⣤⣾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠐⢾⣾⡁⢀⣷⣿⠖⠀⢸⣿⡏⠉⣿⣿⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⢀⣠⣴⡶⣶⢦⣦⣄⠀⠋⣻⢾⡿⢾⠙⠃⠀⠘⢿⣿⣾⣿⠟⠀⠀⣀⣄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢠⣿⠿⡁⠀⡇⠀⣨⠿⣿⡄⠀⠀⠁⣀⣤⣤⣤⣄⡀⠀⠁⠀⢀⣰⡟⢿⣿⣬⣿⡿⢷⣆
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⣃⣀⣈⡶⠛⣾⣁⣀⣸⣷⠀⠀⣴⣿⣿⠿⠿⣿⣿⣦⠀⠀⣲⣿⣿⠫⠊⠉⠑⠽⣿⣿⣆
⠀⠀⠀⠀⣼⡿⡛⢛⢿⣦⠀⣿⡇⠀⣨⠷⡶⠿⡀⠀⣸⣟⠀⢰⣿⣿⢱⡋⢙⢎⣿⣿⡄⠀⢺⣦⣿⣁⠀⠀⠀⢜⡷⣼⡗
⠀⠀⠀⠀⣿⣇⠄⠠⣸⣿⠀⠘⢿⣾⡁⠀⡇⠀⣈⣶⠿⠃⠀⠀⢿⣿⣷⣭⣭⣾⣿⡿⠀⠀⠘⢻⣏⣷⣯⠦⡵⣏⣹⡟
⠀⠀⠀⠀⠘⠻⠿⠿⠟⠁⠀⠀⠈⠘⠛⠻⠿⠟⠏⠋⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠋⠟⠿⠶⠿⠻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠕⠀⠀⡠⠤⠤⠄⠒⠐⠠⢤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢲⣶⣤⠒⣶⣢⡄⡆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⡏⠁⠀⠈⠓⠀⠀⠀⠃⢆⡞⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⡇⢰⠐⠒⠒⠒⠂⢤⢀⢸⡇⠀⠀⣿
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠈⠢⢄⣀⣀⡠⠏⢸⠀⠳⠤⡞⠁
⠀⡴⢢⢫⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠟⠛⠒⠒⠲⠶⣶⠾⠤⢶⠒⠃
⡴⢜⢦⣱⡵⠛⢣⠤⣤⡠⡤⠤⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⢳⣀⣀⡀
⠈⢪⡗⠁⠀⠀⢸⠊⠁⡇⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡇⣏⠀⠀⠀⢸⠛
⠀⠀⠓⢄⡀⠀⣸⠀⠀⠇⡏⠉⢹⠀⠀⠀⠠⠀⠀⠁⢸⢘⠀⠀⢿⠈⠉⢹⠉⢹⢸
⠀⠀⠀⠀⠈⠉⠡⡳⡀⠀⠇⠀⡿⠀⠀⠀⠀⠀⠀⠓⠃⠊⠀⠀⣼⠀⠀⢸⠀⡼⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢾⢳⡀⠀⡇⠀⠀⠀⢀⠀⠤⠀⠨⣈⡄⠀⡇⠀⠀⢸⠀⡇⢸⠀⠀⠀⠀⢩⢱⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡗⣾⠤⠤⠤⡔⠊⠁⠀⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠉⠉⠉⠉⠉⠙⠢⣄⣀⣿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣱⡖⠒⠤⠤⠤⣤⣄⣀⣀⣀⣸⣃⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠏⡝⠉⠓⠚⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠦⣀⠀⠀⠀⠀⠀⡜⠀⢦⡤⠤⠤⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⡆⠀⠀⠀⠈⠉⠒⠒⠒⠛⠂⠉⠁⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⣀⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡏
⠀⠀⠀⠀⠀⠀⢸⠉⠁⠒⠤⡤⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣇⡀
⠀⠀⠀⠀⠀⢴⡋⠑⠠⢄⡀⡇⡠⠔⠊⢉⠦⠀⠀⠀⠀⠀⢰⠚⠭⢄⣀⠲⠃⣈⠥⠶
⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣈⣻⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⢙⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣄⡉⠒⠢⢼⡤⠒⠊⣁⡼⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣤⣧⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠂⠠⢄⣀⣀⠠⠤⠶⢀⠀⠤⡄⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠒⠻⢤⣀⠀⣀⣐⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠰⢠⠏⢿⠁⠀⠉⠙⣶⣦⡀⠀⠀⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠊⢅⠀⢘⢦⣀⣁⡼⠁⢇⣠⠔⣉⢽⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡰⠀⠀⠀⠈⠑⠬⣙⡁⠀⠀⠀⢀⣀⢠⠤⠎⠡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡾⣝⠢⣀⠀⠀⢀⡼⠀⡝⠭⠭⡟⣁⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢈⢀⠃⠈⠐⠁⢰⠀⠃⠀⠰⢀⠇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢱⡀⠀⠀⠀⡘⡠⠀⠀⢠⡆⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡜⠀⠈⠁⢉⠁⠁⠀⠀⠀⠃⡠⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⠄⠀⠀⢀⣠⡊⠀⠀⠀⢀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⢄⡀⡯⠀⠀⠑⣄⠠⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⠈⢳⠤⠖⡊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠣⠄⠀⠀⠀⢠⠄⠒⠁⠤⠀⠤⠀⠀⠀⠳⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠤⢀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⢸⢄⡀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⡀⠀⠀⡈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠠⠀⠀⠉⠒⠒⠠⠐⢦⠀⠈⠉⠒⠒⠂⠤⢤⡄⠐⠁⠀⠀⠀⠈⠀⢀⠄⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠒⠉⠀⠨⡀⠀⠀⠀⢀⠂⠂⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⢠⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣟⣟⣿⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠉⡆⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠵⡒⠁⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⣀⡼⠀⠀⠸⡯⠀⠁⠀⠀⢀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠈⠛⢇⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣼⠁⠀⠁⠀⠀⢸⠀⠀⠘⡏⡇⠀⢀⣤⡈⠀⠑⠀⠀⠀⡀⠀⠀⠀⢱⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠘⠻⢤⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⢀⠊⠈⠁⠀⠀⠃⠀⠀⠙⠿⠿⠿⠋⠀⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡖⠀⠀⡀⠀⠹⡆⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠀⠀⠅⠀⣠⠇⠀⠀⡇⠀⠀⠀⠀⠀⣸⠘⣦⠀⠀⠀⠀⡄⠀⠈⢩⠉⠉⡇⠀⠀⢠⡮⡀⠀⠀⢘
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠈⠟⠛⠟⠛⠏⠀⠀⠀⡇⠀⠀⠀⠀⠉⢻⠀⠉⠻⠉⠉⠋⠁⠀⠀⢸⠀⣗⡇⠀⡖⠉⠀⠀⢀
⠀⠀⣠⣤⣿⣀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣷⣧⣤⣷⣤⣤⣤⣼⣤⣬⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⢻⠉⠉⠹⡆⠀⠀⣴⣖⡒⠒⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠈⣧⣠⣀⣹⣄⣼⠃⠀⠉⠓⠦⣄⣈⣙⣓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃⠀⢠⠏
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠻⣄
⠀⠀⠀⠀⣰⠃⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⣏⣹⠄⠀⠀⠀⠀⡖⢳⡄⠀⠀⠀⠀⠙⣦⢀⣈⣷⡤⠤⠤⠤⡄
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢷⠀⠀⠀⢳
⠀⠀⠐⠧⣄⡀⠀⠀⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⣠⠤⠤⣄⠀⠀⠀⠀⠀⠸⣅⡽⠀⠀⠀⠀⢀⣀⡼⢦⣤⣤⠼⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢰⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⣿⠁
⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠹⣄⠀⠘⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿
⠀⠀⢺⡉⠁⠀⠀⠀⠀⠀⢿⣩⠇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣴⠶⡄⠀⠀⠀⠸⢧⣀⠀⠷⣄⡀
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⢨⡟⠛⠛⢛⡇
⠀⠀⠀⠘⣆⢀⣀⡤⣄⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡞
⠀⠀⠀⠀⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠧⠼⠃⠀⠀⠀⠀⢀⡴⠲⢤⣠⡟⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢀⡤⠞⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⠀⢠⠏⠀⠀⡼⠁⠹⡆⠀⢀⣠⡤⠶⠛⢒⣒⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠚⠁⠀⠀⠻⠿⠭⠤⠴⠖⠛⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢸⣧⢀⣀⣸⣿⣿⣇⣀⡀⢠⣿⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⣿⢸⣿⣿⣟⣟⣻⣿⡭⠿⠿⢸⣿⢸⣇⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣷⣾⣿⣿⣾⣿⣿⣟⣻⣟⣿⣹⣿⣿⢸⣿⣾⣿⣿⢸⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢻⣏⣹⣷⣶⡶⠖⠋⠉⠁⠀⠀⠈⠉⠙⠳⢶⣶⣶⣿⣸⣿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⣐⡓⣶⣾⣿⢸⣿⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣶⢸⣿⢸⣷⣴⣖⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠭⣭⢭⣭⣼⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⣿⣬⣭⣭⡭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⢻⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⢳⡾⡇
⠀⠀⠀⠀⠀⠀⣒⣒⢺⡇⡟⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢻⡇⣿⢒⣒
⠀⠀⠀⠀⠀⠀⠿⠿⢼⡇⣿⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⠼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣚⣃⣋⣛⡸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢸⡟⣘⣙⣃⣓⣂
⠀⠀⠀⠀⠀⠀⠀⠰⡶⠖⢲⣾⣏⣿⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠿⢸⣇⣿⡶⠲⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⣿⣻⡿⠿⠷⠦⣄⣀⡀⠀⠀⢀⣀⣠⡴⠾⠿⠿⡟⣻⣏⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⡿⢿⣿⣿⢿⣿⣿⣯⣽⣯⣿⣹⣿⣿⢸⣿⢿⣿⡇⢿⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢉⣿⢸⣿⣿⣯⣯⣽⣿⣬⡍⣿⢸⣿⢸⡋⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⢸⠏⠈⠉⢹⣿⣿⡏⠁⠁⠸⣿⢸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀
⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡁⢀⠀⣁⣠⢀⡅⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠤⠤⠤⠤⠜⡀⡀
⠀⠌⠀⡄⢠⠆⢀⡀⢠⠀⠀⢹⠁⠀⠉⠈⠀⠀⠀⠀⠈⡇⠀⠆⠰⠀⠠⠤⠄⠂⠁⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠉⠀⠁⠈⡏⢈⠀⠠⡀⠀⣸⠀⣀⠀⠀⡀⠀⠀⠤⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡀⠠⣈⠃⠀⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⠀⠠⠀⠂⣀⠐
⠀⠀⠀⠀⠠⠆⠀⠀⠀⢀⡀⠀⢁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⡑⡄⡅⠀⠀⠀⠐⠠⡤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣁⡒⠀⠠⠀⠒⠈⣀⠀⠐⠀⠀⠀⠀⠈⠀⠐⠄⠀⠀⠠⠄⠀⠆⡄⢀⠀⡆⠀⠑⠁⠀⠀⠀⢎⠀⠀⠀⣀⠘⠀⢀⡂⠶⡅
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠐⡱⠦⠤⠔⠊⠀⠀⠀⣇⢀⠙⣠⠀⢀⠠⠦⠀⢰⠀⠭⠃⢠⠠⡄⠀⠁⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⠁⠀⠀⠐⠀⠀⠀⠀⠘⢦⡀⠈⠁⠉⠁⢂⡠⠬⠀⠀⠉⠀⠋⠀⠠⡀⠀⠀⠐⠈⠐⠉⠐
⠀⠂⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠰⠀⠀⠀⠀⠀⠀⠉⡁⠒⠒⠊⠉⠀⢠⠀⠀⢰⠀⠑⠀⠠⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡊⠐⠀⠄⠀⠘⠀⠑⠁⠦⠀⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⡀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠈⠉⠉⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⡀⢸⣿⠀⠀⢸⠟⠉⢻⡇⣿⡇⢹⡇⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠍⠀⠁
⠀⠀⠀⠀⢨⠈⡅⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠃⢸⣿⠀⠀⢸⣆⣀⣸⡇⢸⣧⣾⠇⠀⠀⢀⣀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠆⠺⠀⠆⡀⠠⡄⠀⠀⠀⠀⠱⡀⢀⠔⠀⢸⣿⠀⠀⢸⡇⠀⢸⡇⢸⡏⣹⡇⠀⠀⢸⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠃⠀⠘⠁⠘⠛⠛⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠂
⢀⠀⠐⠉⠀⠀⠀⡆⠀⠂⠀⠀⠀⢠⢀⠀⠀⣀⠀⠀⢸⡛⡟⣻⠻⢿⠛⢟⣿⢻⡇⠀⠀⠀⡄⠀⠆⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈
⠀⠉⠀⠀⠒⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⣷⢾⡾⣾⡷⣷⡿⡾⡇⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠀⠀⢸⠀⠠⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⢀⠀⠌⠐⢆⡃⠂⠀⠡⠠⢀⡐⠀⠀⠀⠀⠀⠠⡀⠠⠂
⠀⢀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠵⠀⠀⠀⠀⠊⢔⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠁⠀⠂⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠂
⠀⠀⢰⡆⢰⡆⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠐⠁⠊⠁⡐⠀⠀⠀⠉
⠀⠀⢸⣧⣼⡇⡶⣦⠸⣧⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⢸⡇⢀⡿⠀⣿⣸⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠈⠛⠘⠁⠙⠛⠀⠙⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠁⠠⠬⠐⢂⠀⠀⠀⠀⡦⠀⡐⠉⢂⢀⡀⠀⠀⠀⣀⣧⡵⠖
⠀⠀⠀⠀⠀⣥⠜⠁⢢⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠸⡀⠁⠐⠀⠂⢉⡜⠀⠀⠀⠈⢢⡠⣯⡟⣍⣈⠏⠀⠀⢼⠁⢈⡇
⠀⠀⢀⠀⡀⠀⠀⠰⢀⠀⠀⠘⡁⣤⠁⠠⡀⢀⠀⠀⠑⠤⡄⠀⡠⠎⠀⠀⠀⠀⠐⣁⣸⠨⢵⡋⠑⡀⢀⡴⠚⢯⠉
⠀⠀⠈⡉⠅⠀⠠⢂⠌⠀⠀⠀⠐⢄⠀⠀⠐⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠈⠉⠀⠀⠈⠉⠚
⠀⠀⠀⢰⣶⣿⣷⣷⣀⠀⠀⠀⠀⠈⠰⢤⡾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⠑⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⡈⢀⠀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠀⠀⠀⠠⠘⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⡠⢊⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠉⡇⠠⠀⠀⠀⠀⠀⢻⣷⠄⠀⠠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡦⢄⠤⠖⠁⠀⠀⠀⠀⠀⠠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠄⠊
⠀⠀⠀⠀⠀⠠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡡⠀⠀⠀⠀⠈⢤⡐⢀⠆
⠀⠀⠀⠀⢠⠁⠏⠀⠀⠀⠄⢀⠴⠀⠀⠀⢠⠿⢿⠿⣿⣿⡿⠷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠂⠐⠔⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠒⢀⠸⠈⠂⠀⠀⠀⠀⠀⠀⢂⡀⠀⡰⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣈⠁⢈⣤⣤⡗⠀⠀⠀⠀⠀⢠⠊⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡍⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂
⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⡆⠀⠄⣀⠀⠀⠀⠀⠀⠀⡠⢐⣤⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠠⠐⠁⠀⠑⢩⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⣀⣀⠀⡄⠀⠀⠀⢰⡸⠏⠟⢀⢰⠀⠀⠀⠈⡀⣬⢢⠀⠀⡠⡂⠥⠀⠠⠁
⠀⠀⠀⡁⡄⠀⠐⠒⠄⠅⠀⠀⠀⠀⠀⣠⣴⡾⠛⠻⢿⠃⠀⠀⠀⠀⠀⠃⠈⠄⢉⡀⠂⠀⠀⠀⠐⠠⢙⢠⣌⠜⢁⠠
⠀⠀⠀⠑⠈⠀⠒⠨⠈⠀⠀⠀⠀⠀⠠⡈⠛⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⣀⣰⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠓⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠊⠔⢈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡁⠢⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡡⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⢱⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⡀⠀⠀⠀⠀⠀⠀⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⡀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠉⠉⠀⠐⠒⠚⠛⠀⠒⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣄⡄⠀⠠⠐⠒⠒⠤⡀⠀⠀⠀⠄⠀⢉⡐⢄⠀⠁⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠇⠀⢂⠀⠿⠆⠀⡁⠀⠀⢘⠒⢢⣴⡖⠊⠇⠀⠠⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠑⠂⠐⠊⠀⠀⠀⠈⠢⢄⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠒⡄
⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣧⣐⣠⠂
⠀⠀⠀⡄⠨⢊⣦⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣪⠞⠁⣜⡇
⠀⠀⠀⠀⠹⣟⢅⠉⠑⠒⠭⢖⡠⢄⡀⠀⠀⠀⠀⠀⠑⠢⠤⠄⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⢀⠔⣠⠞⠁⠀⡔⡻⠁
⠀⠀⠀⠀⠀⠈⢧⡱⡀⠀⠀⠀⠈⠛⠮⢵⣦⣄⣠⠄⠀⠠⠀⠠⠤⡠⡿⢿⠟⠿⣯⠤⠤⠤⣤⡄⢀⡀⠀⡠⣎⠴⠊⠀⠀⠀⠐⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢌⠢⡀⠀⠀⠀⠀⠀⠈⡿⠁⡖⣤⠀⢰⠒⠒⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠹⢙⡟⠁⠀⠀⠀⢀⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢠⡀⠀⠀⠀⠀⡇⠀⣨⡁⠀⢸⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠲⠞⣛⠚⠃⠀⠙⠀⠀⠀⡠⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢆⠀⠀⠀⡅⠀⠓⠋⠀⢸⠀⠀⠀⠀⣠⠀⠪⡄⠃⠀⣙⠓⠒⢚⡁⠀⢠⣤⡴⢮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⣤⢄⡀⠀⢨⠬⠀⢸⠀⠀⢒⠒⠓⡲⠕⠂⡆⠀⢉⡩⠤⢍⡁⠀⣸⠀⢱⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢎⡗⠀⠴⢢⠀⠀⠉⢉⣉⣉⣉⠀⠀⠈⠁⠀⢨⣑⡚⣉⡀⠀⣿⠀⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢧⠀⠈⠉⠀⠀⠘⠻⠹⣿⠉⡟⠁⠀⠀⠀⢠⡤⠒⢪⡄⠀⠉⠴⣫⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣥⢹⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠛⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢾⣘⡂⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣶⠿⠚⠵⣩⣩⣉⣉⣌⣽⠛⣭⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠉⠀⢀⠉⠳⡀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢀⠀⢤⢠⡎⠀⠀⠤⠱⠸⠀⣃⡗⠀⠐⡀⠀⣰⡀⠲⠢⠠⠀⡀⡀⠉⢶⡠⠀⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉⠐⠈⠐⠂⠙⠒⠺⠓⠷⠛⠍⠃⠅⠂⠥⠂⠅⢂⠍⠋⠖⢲⠤⣥⢤⠴⠪⠐⠍⢂⠔⡩⠢⠓⠡⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⠀⠀⠀⠀⣰⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⡀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⣠⣦⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣦
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣆⣠⣤⣿⣿⣿⣄⣀⣴⣿⣦
⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣾⣿⣆
⠉⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣄
⢀⣤⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠉
⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠻⠿⠋⠀⣿⣿⣿⡄⠀⠀⢠⣶⣶⣤⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣿⣿⠀⣠⣾⣷⣄⣠⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠀⠙⠛⠁⠀⠀⣿⣿⣿⠁⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠹⠿⠿⠛⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣷⣄⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣼⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠰⠁⠀⠀⠀⠀⠀⠀⠀⠉⢟⣿⣿⣿⣿⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠉⠉⠹⣿⣿⣿⠇⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣀⣄⠀⣀⣶⣶⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⣠⠏⠹⣄⣀⠤⣀
⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⢀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀⣀
⠀⠀⠰⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠰⡁⠁⠀⠀⠀⣀⠤⠄⣀⠀⠀⠀⠈⢈⠆
⠀⢀⣀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣧⣀⠀⠀⢀⣠⠇⠀⠀⠀⠎⠀⠀⠀⠀⠱⡀⠀⠀⠸⣄⡀
⠀⠸⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠀⠀⠸⢄⡀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡤⠇
⠀⠀⢀⣿⣿⣿⣿⣷⣄⣀⣀⣤⣾⣿⣿⣿⣇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠑⠤⣀⣀⠤⠊⠀⠀⠀⠸⡀
⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠈⠦⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠴⠁
⠀⠀⠀⠀⠀⠾⡿⠛⠿⣿⣿⠟⠻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⠤⢤⡀⢀⡤⠤⣀⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠶⠛⠤⠐⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⢀⠀⠀⢙⠀⠀⡀⠀⠀⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢂⠀⠀⠛⠁⠀⡬⠀⠙⠁⠀⠀⠆⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠑⠄⠀⠄⠊⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠑⣍⡓⠒⠂⡆⠀⠀⡤⠀⠀⢰⠒⠈⡏⠠⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣇⣀⡀⣇⣀⣀⡸⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠥⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⡋⠘⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⡇⢘⠒⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡤⠄⠳⣀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⡇⡰⠢⢤⡜⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠠⠉⠑⡔⠋⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⡇⠀⠀⠀⠀⣸⠉⠀⠀⠀⠈⠲⡔⠉⠡
⠀⠀⠀⠀⠀⠰⠧⣀⡞⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠐⠐⠂⠐⠂⠐⠀⠐⠒⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⣄⡠⠧
⠀⠀⠀⣀⣠⣅⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣧⣀
⠀⠀⢰⣁⡄⠠⠌⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⡠⠀⣈⣱
⠀⠐⠉⠀⡀⢀⡀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣆⣀⣰⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⣀⠀⡀⠈⠠
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⡇⢀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢹⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⡒⢺⠀⠀⠀⠀⠀⠀⣚⠒⣒⣺⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠀⠀⠀⠉⠑⡄⠀⠀⠀⡔⠉⠁⠀⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣧⡀⠀⠀⠀⣠⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⡿⠟⠛⠹⣿⣷⡀⠀⣴⣿⡿⠛⠻⢿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠉⠀⠀⠀⠀⠀⠙⣿⣷⣾⣿⡟⠁⠀⠀⠀⠈⠉⠛⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣤⣄⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⣀⣀⣤⣤⣶⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠻⠿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠿⠛⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠿⠟⠛⠻⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⣼⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣧
⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡄⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣟⠁
⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠘⠿⣿⣷⣦⣄
⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟
⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣤⣤⣤⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣤⣶⣶⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠛⠛⠉⠁⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠛⠉⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠛⠛⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣤⣀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣶⣤⣄⣼⣿⠟⠀⠘⢿⣿⣆⣠⣤⣶⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⠏⠀⠀⠀⠈⢿⣿⠿⠟⠛⠉


⣶⣿⣿⢿⢿⠷⣿⠷⢶⣿⣷⣿⣷⣾⣿⣶⣿⣷⣾⣿⣷⣿⣿⣾⣿⣷⣿⣷⣾⣿⣷⣿⣿⣾⣿⣶⣿⣿⣾⢿⣷⣿⡷⠿⠿⢷⣿⠷⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣆⠀⢠⣾⣶⣦
⠀⠀⠀⠀⠀⢀⣴⣄⣠⣼⣿⣿⠿⠿⠿⢿⣿⣿⣤⣠⣴⣄
⠀⠀⠀⠀⠐⢿⣿⣿⠟⣋⣥⣶⣾⡀⣺⣶⣦⣍⡻⢿⣿⣿⠇
⠀⠀⠀⣀⣀⣾⡿⢡⣾⡿⢛⡩⠔⠒⠒⠭⣙⠿⣿⣆⠻⣿⣆⣀⡀
⠀⠀⣸⣿⣿⣿⢡⣿⡟⡰⠁⠀⠀⠀⠀⠀⠀⠱⡙⣿⣧⢹⣿⣿⣿
⠀⠀⠈⠙⣿⡇⠘⠻⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃⠹⠻⠀⣿⡟⠉
⠀⠀⣠⣴⣿⣇⢸⣾⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣾⢠⣿⣷⣤⠀⡀⠀⣠⣶⣄⢀⣤⣀
⠀⠀⠸⣿⣿⣿⡌⢿⣷⣜⢦⡀⠀⠀⠀⠀⣠⢞⣴⣿⠇⣼⣿⣿⡟⢾⣿⡾⣟⣛⡛⣛⠿⣿⣄⣤⡀
⠀⠀⠀⠀⠀⣻⣿⣆⠻⢿⣷⣬⣍⡀⣈⣭⣶⣿⠟⣡⣾⣿⠁⣴⣶⡟⣱⡾⡛⠉⠁⠙⠻⣮⡻⣿⠃
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣦⣍⣙⡛⠀⠚⣛⣉⣥⣾⣿⣿⣿⠗⢙⣿⠘⠟⠈⠀⠀⠀⠀⠀⠸⣷⢹⣷⣆
⠀⠀⠀⠀⠀⠀⠉⠁⠀⢹⣿⣿⣿⠿⢿⣿⣿⣿⠁⠀⠉⠁⠸⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⢠⣍⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⣽⣦⠻⣦⣀⠀⠀⣀⣤⡾⣣⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢷⣮⣝⣀⣛⣛⣭⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠙⢿⠿⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣀⣠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⣴⣷⣤⣴⣿⣿⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠈⢻⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄
⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣦⣀⠀⠀⠀⣀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠉⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣷⣾⣿⣦⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⠿⠿⠿⢿⣿⣿⣦⣠⣄⠀⠀⠀⠀⣠⡄⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⠉⠀⣠⣀⣠⣿⣿⣾⣿⣿⣷⣄⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡆⣹⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣿⡿⣵⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⠷⠀⠀⠀⠀⠀⢰⣿⣿⡿
⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢿⣿⣿⣶⣤⣴⣾⣿⣿⠿⢿⠆⢹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⢿⣿⠿⠟⢿⡇⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⠀⠀⠀⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣯⡀⠀⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠙⢻⣿⡿⠿⣿⣿⠋⠉⠛⠁⠀⣠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠋⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢊⡤⣤⡀⠉⡻⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⢀⠔⠉⡔⠀⢿⡀⢀⡇⡰⠁⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐
⠀⠀⠀⠀⠀⠈⠓⣾⡀⠀⠈⠉⢉⢴⠁⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⢪⣿⣿⣷⣤⠔⠁⣜⣀⣀⣸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢠⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠇⣾⡿⢟⣽⠉⡵⠾⠤⠤⠤⢼⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⢰⠤⠤⠤⠤⡄⢸⡇
⠀⠀⠀⠀⢸⣀⠤⠒⠉⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⠀⠐⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⢠⠀⠀⠠⡄⠀⠠⠀⠀⢠⠀⠀⡄⠀⠀⡄⠀⣠⣀⣀⣀⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡃⠀⢀⠀⠀⢸⠀⠀⡇⠀⢀⡗⠋⠀⠀⠀⠀⠀⠑⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠉⠀⠀⠉⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⢙⡤⢄⡒⠭⣒⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣸⣀⣀⣀⡀⠀⠀⠀⠀⢫⢑⣪⣵⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂
⡒⠶⢶⠤⢄⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⠔⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠠
⠠⢀⠀⡇⠀⠀⠀⡠⢤⣶⣆⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢀⠆⠀⠀⠀⠀⠀⠉⢄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠙⠋⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠄⠉⠉⠉⢠⠁⠀⠀⠀⠈⠳⣤⣀⣀⢴⢣⠀⠀⠀⠀⠀⠠⠎⠉⠑⡄⠀⠀⠀⠀⠸
⢀⠇⠀⠀⠐⠄⣀⡀⠀⠀⢀⡀⠈⡀⠤⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡼⠶⣄⠀⠰⠋⠙⠳⡄⠀⠀⠈⠧⣀⡴⠁⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢺⡀⢀⡸⠀⠘⢤⣀⠴⠃⠀⠀⠀⠀⠀⡶⠖⠢⡀
⠀⡠⠶⢤⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡞
⠀⣇⠀⣠⡦⣀⣀⢄⡀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠚⠁
⢀⣈⠉⠁⡸⠋⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠈⢳⠄⣇⠀⠀⠀⢠⠆⠀⠀⠀⢀⠄⢤⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠈⠀⠀⠀⠘⠀⠙⢄⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣀⠠
⢤⠴⠋⠀⠈⠲⠤⠖⠃⠀⠀⠀⠀⠹⢄⣀⠇⠀⠀⠀⠀⢀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⠀⠀⠆⠻⠟⠀⠚⠂⣤⠄⠀⠀⠀⠀⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠁
⢀⣤⠆⢱⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠠⠉⠐
⠉⠀⠀⠀⢢⠀⠀⠘⢅⣀⡼⠓⠢⢼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠾⢁⡤⠦⠠⣄⠀⠀⠀⡠⠄⢄⠀⠀⠀⡠⠲⠶⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⢄⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⡧⠀⠘⢅⣀⡼⠀⠀⠀⠈⡂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠁
⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⠋⠀⠀⠀⠉⢣⠀⠀⠀⠀⢠⠀⠲⡎⠉
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠘⢄⡀⠀⠀⣠⡎⠀⠀⠀⠀⠸⡀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠃⠀⠀⠀⣸⣙⠉⠉⢱⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⢴⠘⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢱⠀⢣⡀⠀⣨⠃
⠀⠀⠀⠀⠀⢠⠒⠒⠄⠀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠡⠀⢀⠌⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⡂⠀⠀⠀⠀⣤
⠀⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡎⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠐⢤⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⣀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠈⠁⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢁⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⡐⣀⡀⠀⠀⠀⠀⠐⠷⠀⢀⠒⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢁⠆⠀⢀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠓⠀⡀
⠚⠀⠠⠀⠀⠀⢀⣄⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠇⡀⠁⡵⠀⠀⠀⠀⠀⠀⠀⠐⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠰⠀⠀⠀⠀⠀⠀⠈⠀⠰⣄⠁⠀⠀⠀⠀⠀⠀⠀⠈⢡⡾⣳⡄⠀⠀⠈⠁⠈⠀⠀⠐⠠⡀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⡀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⣴⠄⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⣀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⢀⡀⣀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠸⠂⢀⠀⠀⡀
⡟⡀⠁⡆⠀⠀⠀⠀⠀⠻⠃⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣴⠀⠀⣔⠲⠀⠀⠀⠎⠀⠀⠤
⣘⣒⣚⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣊⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣾⣀⣀⣊⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡯⠈⠀⣾⣧⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠇⣨⡝⠂⣸⣿⡏⠀⠀⠀⢋⠁⢤⠤⠒⢂⣷
⠀⠀⠀⢀⡀⠀⠀⠐⠀⢠⠥⠄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠒⣞⠀⠈⡀⢠⣿⣿⠁⠤⢤⣄⡐⢠⢯⢐⣦⣍⡿
⠀⠀⠘⡄⠀⠀⠀⢀⣂⣀⣭⣵⣀⣿⡿⠟⠋⠁⣀⣀⣀⣀⠈⠉⠒⠋⠚⠛⠁⠀⠀⠀⠀⠫⠉⠭⠜⠛⠉
⠀⠀⠀⠙⠛⡛⢛⡻⠛⠉⠀⣹⠛⠛⢋⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⢠⠉⣐⢎⠐⠁⠀⠀⠀⠀⡇⢠⣿⣿⣷⣶⣶⣶⣶⣦⣤⣬⣤⣤⡀⠀⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⢰
⠀⡼⠣⢍⡁⢱⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠟⠻⣧⣐⣲⣆⡼⣸
⡘⢠⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠛⣙⣤⣶⣿⣿⣿⢟⡠⠋⠔⠁
⠇⢸⡀⠀⠀⠀⠀⢀⣀⡀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢾⣟⠁⣿⣿⣿⣿⡟⠉
⠈⠀⢱⢤⡒⣈⣭⣤⠄⠀⢀⠗⠘⠛⢛⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿⢤⣤
⠀⡔⠁⠀⠚⠛⠋⣁⡤⠖⠉⠛⢶⣤⣤⣀⣈⣉⠉⠙⢌⠻⣿⣿⣿⣥⠖⣺⣿⣿⣿⢿⣫⣷⣿⣿⠀⣀⡀
⠀⠈⠒⠒⠒⠛⠛⠳⠤⠄⠀⣶⠻⠿⣒⣚⠛⠛⠛⠓⣚⣓⣍⠻⣿⣿⣷⠞⠛⣫⣵⣿⣿⣿⣿⣿⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣐⡒⠫⠉⠩⠉⣙⣓⠒⠓⠾⠛⠿⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠠⠬⠥⢉⣑⣒⠒⠂⠨⠥⠄⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠠⢍⣉⠑⠒⠒⠤⠬⣭⣉⣉⣉⠀⢻⣿⣿⣿⠟⠁⣀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣈⣉⠛⠓⠶⠤⣤⣄⣀⣀⠀⠀⠉⠁⠀⢸⣿⡿⢃⡴⠊⠑⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⡂⠭⢉⡓⠒⠦⠤⢤⣉⣉⡙⠛⠻⠶⠶⠾⠋⠠⡏⠑⢢⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣚⠁⠀⠀⠈⢉⠚⠂⠀⠨⠉⠐⠂⠀⠀⠉⣍⣩⢿⠒⠒⢂⡄⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣀⣀⡉⠒⠒⠀⠀⠀⣠⢮⢟⣰⢃⢞⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣤⣽⣷⣶⡖⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣈⡿⠒⠦⡀⠀⠀⠀⡶⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢦⠀⠀⠙⣶⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣦⣀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢀⠤⠤⢴⣏⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠻⠶⠟⠈⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⡔⠁⠀⠀⠀⠉⠛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣏⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢶⡀⠀⢹⡏⠀⠀⠀⢠⡶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣆⠀⠀⠀⠀⢹⡏⠀⢠⡞⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠟⠀⠀⠘⠷⠶⠶⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠾⠃⠀⠈⠻⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⢾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⡟⠒⠛⠒⠛⠚⠓⠒⢻⠀⠀⠀⠀⠸⣤⣤⣤⣤⣄⠋⠀⠀⠀⠀⣿⠚⠓⠒⠚⠓⠓⠻⣧⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣄⠀⠀⠀⠀⠈⠛⠻⡟⠛⠛⢻⠛⠛⠛⣿⠛⠛⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⣇⠀⢀⡶⠶⣄⠀⠀⠈⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⠜⠁⠀⣠⠾⢦⡀⠀⣿⠀⠀⠀⠉⠉⠙⠷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠟⠒⠚⠁⠀⠀⠀⠹⠦⠾⠁⠀⠹⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠴⣏⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁



⡿⠿⠿⠿⠿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣾⣿⣧⣴⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣶⣾⣿⠿⠿⠿⢿⣿⣿⣧⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡟⠁⠀⠀⠀⠀⠈⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠀⠀⠀⢀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⢙⡛⠛⣿⣿⣶⣤⣴⣶⣿⣿⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⢠⣿⣿⣧⡀⣰⣿⣿⠿⣿⠟⠙⣿⣿⠋⠻⣿⠦⣾⣦⢀⣼⣿⡀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣦⡙⠋⠀⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⣿⣿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⢘⣿⣿⠟⠉⠀⠀⠀⠙⢿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠁⠀⠻⠟⠻⣿⣷⣤⣀⣀⣠⣴⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⡄⠀⠀⢼⣿⠿⢿⣿⣿⢿⣿⣿⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⣤⣀⣀⣠⣤⣾⣿⣿⡟⠛⠛⠛⠃⠀⠀⠀⠁⠀⠘⠿⠇⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠉⠙⣿⣿⡿⠀⠈⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣰⠀⠀⠀⠀⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣢⡞⠀⠀⠀⠀⠀⠘⣦⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣼⣤⣤⣤⣤⣤⣼⠥⠭⠤⠤⠤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⣀⡤⠖⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⡶⠛⠉⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠒⣿⢀⣴⣶⣿⡤⣄⠀⠀⢀⣤⣤⣶⣦⡀⢸⡇⠀⠀⣰⠋⢉⡟⢹⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢪⠀⣿⠀⢸⢿⣿⣷⣏⠀⠀⢸⢸⣿⣧⣼⠛⢸⡇⠀⠀⣿⠀⢸⡁⢇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢤⣿⠀⠀⣉⣉⠁⠁⠀⠀⠘⠈⠉⠉⠛⠀⠘⡇⠀⠀⠘⢦⣬⠷⣼⠒⠁
⠀⣤⠴⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⣄⣀⣀⣀⡀⢈⣙⣟⠁⠀⠀⡇⠀⠀⠀⠀⣠⡴⠛
⢀⡈⠙⢳⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣦⢤⣤⣭⣭⣉⣉⣉⣉⡉⠀⠀⠀⣷⢀⣤⠶⠋⠳⢤⡀
⢾⠙⠲⢛⣷⠓⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠋⢳⡀⠀⠀⠀⠻⣄
⠈⠙⠒⠋⠙⠲⡏⣰⠳⣤⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⣤⣽⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠻⠿⣄⠈⠙⠛⠒⠒⠖⠛⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡏⠀⠀⠀⠀⠈⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⢤⣤⠶⠶⣾⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠷⠾⠿⠿⣶⣶⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠂⠀⢀⡈⡇⠀⠀⠀⠐⠂⠀⠐⢲⠈⡇⠀⠀⠀⣀⡤⣷⠈⣷⡀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⠒⠒⠒⠒⠶⠶⠤⠤⢤⣭⣭⣄⣉⣈⣀⣚⣚⣀⣧⡠⠔⢊⡡⠖⣿⠀⣸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠒⠒⠒⠒⠢⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣈⣉⣉⣯⠤⠚⠉⠀⠀⢸⢻⣉⠉⢉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠀⠀⠀⢸⣰⡋⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣤⢏⡽⠛⢯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠾⠋⢹⠸⡇⠀⣸⠃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⣿⠉⠉⠉⠉⠉⠛⠛⣿⠛⠛⢻⡿⠾⠟⠋⠁⠀⠀⠈⠛⠁⠀⢻⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠐⣿⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠈⠙⢛⡽⢻⡀⠀⠀⠀⠀⣠⠿⣤⣒⣺⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣛⣁⣀⣀⣀⡴⠋⠀⢘⡇⠀⣠⠴⠋⠁⠀⠀⠉⡽⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣬⣭⣭⣽⡤⠖⠛⠉⢰⠻⠷⠦⣤⣤⣀⣀⡾⠁⣠⠟
⡀⠀⢀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡒⠲⠶⣤⣭⣷⢞⡁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿