Scuba Emojis & Symbols

⠈⠛⠷⢦⣤⡀
⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⢿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣇⣀⣀
⠀⠀⠀⢀⣠⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠰⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⡿⠿⣿⣷⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠚⠛⠛⠓⠲⠶⣤⡀⢰⠋⢑⡄⠀⠀⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⢠⠞⠉⠉⠳⡄⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⡓⠋⠀⣰⠋⠉⠙⡆⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢸⣄⠀⠀⣠⠇⠀⠀⠀⢰⡿⢃⣠⠆⠀⠀⢀⡠⠊⠉⠢⡄⠀⠀⠈⣷⣠⢤⡹⣤⣀⡴⠃
⠀⠀⠀⠀⠀⣀⣉⠓⠛⠁⠀⠀⠀⠀⢸⣏⣉⣁⣒⣂⣩⣥⣶⣲⣦⣄⢈⣄⠤⠖⢻⡷⠶⠃⠀⠀⠀⠀⠀⠀⠀⡴⠒⢢⡀
⠀⠀⠀⠀⣞⠁⠀⢳⠀⠀⠀⠀⠀⢰⣟⣿⡽⠿⠯⠍⠉⠒⢒⡒⢮⢿⣿⠀⠀⢀⣸⣧⣤⣤⣄⠀⠀⠀⠀⠀⠈⢧⣀⡴⠃
⠀⠀⠀⠀⠘⠲⠖⠃⠀⠀⠀⠀⠀⢸⣿⣿⡁⢰⢉⣀⣀⣀⠸⢬⠆⣏⣿⠴⠚⠉⣼⠟⠉⠉⢿⣷⠀⠀⠀⠀⠀⢀⡤⣄⠀⢰⣚⡆
⠀⠀⡴⠋⢳⡀⢀⣀⡀⠀⠀⠀⠀⠀⢿⣯⣷⣈⣂⣽⠿⢿⣷⣤⣾⡿⠋⠀⠀⣰⣟⣓⣒⣒⣛⣿⠷⠦⣄⡀⠀⠘⠶⠊⠀⣀⡀
⠀⠀⠙⠦⠞⠀⣏⣀⡽⠀⠀⠀⠀⠀⠀⠙⠻⣟⠛⢉⣤⣤⣍⠉⠉⠀⢀⣤⠾⠷⠾⢶⠶⢦⣄⠀⠀⠀⠈⢳⡄⠀⠀⢰⠏⠉⠙⣦
⠀⠀⠀⠀⣠⣄⠀⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣧⡴⠞⠉⠀⠀⠀⠀⡎⠀⠀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⢦⣄⡤⠏
⠀⠀⠀⠈⠧⠞⠀⠘⠚⠀⠀⠀⣀⠀⠀⣠⣞⣿⣿⣿⣧⣦⣖⣂⣺⣤⣤⣄⠀⠀⢠⠁⠀⠀⠀⠈⣇⢀⣀⣀⣿⠀⠀⠀⠀⠀⣀⡤⣀
⠀⠀⠀⢀⣴⣶⣿⣻⣿⣻⣶⢮⣍⡙⠶⣿⣸⣷⣿⢹⠉⠉⠉⠉⠉⠉⠉⠉⣇⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠄⣿⠀⠀⠀⠀⢰⡃⠀⠈⡇
⠀⢀⡴⣿⡿⣛⠉⠉⠉⣿⡳⠶⢬⣙⠳⠈⠙⢿⡇⠘⢤⣤⣤⣤⣤⣤⣤⡤⠇⠀⢸⠀⠀⠀⠀⠀⣿⢘⣿⣯⣿⠀⠀⠀⠀⠀⠙⠒⠚⠁
⣤⣌⣿⣿⠏⢻⠀⠀⠀⢿⣍⡳⠶⠬⠅⠀⠀⠀⠙⡆⠰⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣨⣬⣯⣿⠀⠀⢰⢲⡄
⠁⠟⠌⣵⡂⢸⡀⠀⠀⠀⣈⡿⠉⠑⠂⠤⣄⣀⢀⡇⠀⠀⡇⠈⠉⠒⠂⠤⠄⣀⣈⡀⠀⠀⠀⠀⣯⠤⣄⠀⢸⠀⠀⠀⠉
⡚⠉⠉⣑⡦⠀⠙⢛⣛⠿⣍⠁⠀⠀⠀⢀⣾⢿⣷⠼⢁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠆⢸⡇⠀⢠⠤⡄
⠀⠹⣿⣿⣦⣀⠀⣰⠆⠀⢹⠂⠀⠀⣠⠟⣿⣿⡿⡄⠀⠀⠉⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⡥⠊⠀⢸⡇⠀⠘⠒⠃
⠀⠀⠈⠻⠿⣿⣿⣤⣠⣴⣿⣤⠴⠞⠃⠀⢹⣿⣿⣷⢀⠀⠀⠀⠀⠀⢀⣈⣉⣱⡶⣶⣤⡤⣶⣿⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣿⣶⣤⣬⣬⣭⡽⠟⠛⣾⠁⠀⠂⢹⣿⣛⠟⣿⠦⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⣴⣖⡒⠲⣄
⠀⠀⠀⠀⠀⠰⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠿⠿⣯⣭⣟⠛⠛⣹⣄⡀⢀⣸⢟⡥⠊⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⣠⠴⠾⣁⠀⠈⢢⢸⡆
⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠦⣄⡀⠉⠉⠀⠉⠉⠋⡡⠋⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⣠⠞⠙⠦⣀⣈⠆⠀⢈⣼⢿⡀
⠀⠀⠀⠀⠀⠀⠰⠷⣠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠀⠀⠈⠑⠢⢄⡀⠀⡜⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⣠⠞⠁⠀⠀⢀⣴⣿⣦⣴⣾⢿⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⣧⠀⠀⠀⠀⠀⠈⠙⡅⠀⠀⠀⠀⠀⠈⣧⢤⣤⠟⠁⠀⠀⢀⣴⠋⢸⡇⢸⢉⣼⠀⡆⠘⣇
⠀⠀⠀⠀⢰⡞⢳⠀⠉⠛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠀⣠⠟⠁⠀⢸⡇⢸⠀⣇⡄⢳⠀⢻
⠀⠀⠀⠀⠈⠑⠋⠀⠐⢺⡷⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠃⠀⠀⢠⡾⠁⠀⠀⠀⢸⠁⠸⠀⢇⡇⢸⠀⠘
⠀⠀⠀⠀⠀⢀⣀⠀⠸⣿⣯⣯⠁⠀⠀⠀⠀⠀⢺⡴⢃⡀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣾⠀⡇⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠈⠛⣀⡤⠹⡯⢒⡲⠀⠀⣠⡶⡊⢹⣟⣿⠅⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠘⠷⣀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⠇⠀⠈⣷⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢉⣾⡟⢿⣿⡗⠀⣀⣨⣿⡟⠋⠀⣠⢀⣠⡀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⣹⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡄⠀⠀⣿⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⣿⡇⠀⣸⣿⣿⢁⠀⣀⣿⣿⣗⡏⠀⠀⠀⠀⠀⠀⠙⢦⣄⣠⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⣄⣀⠀⡯⢀⣀⣃
⠀⠀⠀⠀⠀⠀⡤⢶⡄⠀⠸⢿⣶⣀⣟⢳⣾⣇⡲⢟⠵⣎⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠘⢷⡿⠋⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠸⠂⠦⡤⠀⢉⠀⠡⠄
⠁⠀⠀⠀⠀⠘⠠⠀⣀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠃⠀⠑⠀⠐⣂⡍⠀⣠⣔⣿⣀⢀⡀⠀⠴⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⡀⠄⣀⠁⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⠀⠀⠀⠀⠀⠈⠀⡠⠠⠞⠻⡤⠀⢣⠀⡏⠀⠉⠳⡺⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠄⠀⠀⠀⠰⢆⠁⠀⠀⠀⠀⠀⠀⢀⢀⠠⠐⠁⠐⠀⠈⠄⠈⠲⣼⣄⣌⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢄⠀⠀⠈⡀⠀⠀⠀⣀⠤⠒⠚⠺⠅⠀⠀⠀⡇⢀⡆⠀⠀⣈⠌⠈⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⢀⠚⠀⠈⠕⠀⠀⠀⠐⢤⠂⠀⠀⠀⠠⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢀⠌⠀⠀⠀⠀⠀⡊⢁⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠐⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠉
⠀⠀⣀⠠⠀⢂⡡⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐

⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⢀⣤⠠
⠀⠀⠀⠉⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣾⣦⡀⠀⣀⣀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢈⣽⣛⠻⢿⣧⣀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢀⣀⠴⠞⠛⠛⠻⢿⣶⣮⣿⣿⣦⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣦⡀
⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠽⠟⠀⠀⠀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣰⣿⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠛⠿⠿⣿⡿⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣹⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡏⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠁⠈⠻⢿⣿⣟⠛⠛⠿⠟⠀⠀⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⣀⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⠿⠟⠋⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⢀⣾⣿⠟⠉⠁⠀⠀⠀⢀⣄⣀⣠⣼⣿⣿⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣻⣿⣿⠋⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⢀⣾⣿⠃⠀⠀⠀⠀⣀⣴⡿⠿⠟⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠁⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣤⡀
⢀⣿⣿⠃⠀⠀⠀⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆
⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢻⣿⣿⡇
⠀⣀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠘⣿⣿⠇
⠳⢾⣷⣄⣸⣿⠿⣿⣿⣿⣿⣿⣿⣷⣤⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⣿⣿
⠀⠀⠀⠙⠿⠟⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠛⠛⠛⠻⢿⣿⣷⣤⣀⣀⣤⣾⠟⠉⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡏⠀⠀⠀⠀⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⣴⣶⣶⣶⣶⣶⣬⣤⣶⣶⣶⣦⣄⡀
⠠⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣏⣹⠧⣈⠻⣿⣿⣿⣿⣿⣿⠯⠝⠉⠉⠓
⠀⠉⠙⠛⠳⣦⣤⣀⠀⠀⠀⠀⢿⢾⣿⣿⣿⣿⣿⣿⣏⠁⠋⠉⣙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⡿⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⡀⠀⠀⣸⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠈⠻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡶⠶⠾⠿⠿⠿⠿⠟⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣀⣀⣤⣤⣤⣤⣴⡶⠾⠿⠿⢿⣿⣿⣿⣿⡶⠶⠦⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠛⠿⠿⠿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢷⣄⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣙⣷⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣾⣤⡝⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣏⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠙⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢨⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⢁⣀⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⢀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣤⠁⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢰⣦⠀⠑⠛⠁⠀⠀⠐⡪⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠧⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣦⣤⣶⣿⣶⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣃⡈⠁⠛⠿⣿⡀⣥⠀⠠⡀⠀⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣠⣴⣼⠾⠁⠈⢿⣿⠗⣲⠲⢾⡇⢩⠂⠐⡃⠀⠀⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⣠⣤⣬⡾⠿⠏⡀⢀⢄⠀⣣⣼⡿⠓⠃⠈⢂⡀⢀⣽⠊⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠛⠉⠉⠠⢁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⡌⠳⢫⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠀⠀⣠⣿⣻⣿⣶⣤⡤⢀⣀⣤⣤⣶⢍⣐⣠⣿⡏⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢸⣠⣾⣿⣿⣿⡿⠟⠋⠀⠀⢉⡁⠀⠁⠛⠛⠛⠋⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠁⠀⠀⡴⢾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⣀⣀⣀⣠⡤⡤⠤⠊⠀⠀⢙⡿⠟⠁⠀⠀⠀⣀⣀⣤⡄⠀⠀⠘
⠀⠀⠲⠀⠀⠀⠀⠉⠀⠀⣤⣤⡖⠊⠀⠈⠉⠉⠁⠉⠀⠀⢀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠘⠂
⠀⠀⠀⠈⢆⢹⣦⣄⣀⣴⢿⣥⠖⠃⠙⠒⠒⠒⠒⠂⠐⠈
⠀⠀⠀⠀⢠⡯⣿⣿⢋⣴⠟⠁
⠀⠀⠀⢀⣎⣀⡿⠟⠋⠁

⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣧⣤
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡋⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣿⣟⠿⠇
⠀⠀⠀⠀⢰⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣿⣿⣧
⠀⠀⠀⠀⢸⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠿⣯⡉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠻⣷⡶⠖⠚⠛⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠸⣧⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⣄⣾⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⠉⠉⠻⠿⠟⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣤
⠀⠀⢀⡿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⣾⣿⣿⣿⣿⣿⡻⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣏⠹⡀
⠀⠉⠛⠛⠀⠹⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⣿⠻⣿⠈⠃
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⣿⡿⠿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⣣⠀⠀⠀⠀⠀⠀⣀⡴⠇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⢴⡿⠋⠀⠀⠀⠀⢻⣷

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢀⣠⣶⣶⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀
⠀⠀⣀⣤⣤⣄⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⢀⣾⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣴⣾⣿⡿⠋⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⣶⣶⣄
⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠠⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⠿⠋⠁⠀⠀⠙⠛⠛⠿⢿⡿⠿⠿⠟
⠀⠀⠈⠛⠛⠁⠉⢪⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠋⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡤⠶⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠁⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡈⢣⡀⠀⠀⢌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠶⣭⣓⠦⣄⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⡶⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡆⣆⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣋⣠⠃⠀⠀⠀⠠⡂⠀⠀⠀⣠⠾⣩⡽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢈⡇⢠⢞⠭⢵⣦⡀⢀⣸⡟⠟⢳⢦⠠⠤⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⢾⡎⢀⣠⣹⡙⣝⣦⠀⣶⠄⠠⢻⡃⠀⡎⢳
⠀⠀⡤⠄⣀⣀⣀⣀⠤⠒⣒⣤⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠓⠛⣛⡳⣄⣹⡙⠍⠈⢳⡄⢀⡀⢱⠃⠈⠇⢸
⠀⠀⡇⠀⠄⠀⡤⠒⠂⡽⠋⠙⢆⠀⠀⠀⠀⠀⢀⣎⣉⠶⠖⠒⠉⠀⢤⣸⠙⣜⠷⣐⡠⡗⠙⠋⢀⣸⠀⣰⠏
⠀⢰⠁⠸⠀⡀⢇⣀⠔⠛⣄⠀⠀⠳⣄⣀⠤⠒⢻⡀⢇⠀⢀⠠⠄⠂⠁⡈⠑⢞⢳⣄⣐⣙⡶⠶⡾⠷⠊⠁
⠀⠀⠉⠑⢢⣠⡾⠁⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢣⠈⢁⠀⠀⠀⠀⠃⢘⡴⠋⠻⣄⠀⠀⠀⣀⢤⣀⡀
⠀⠀⠀⠀⢮⠜⠁⠀⠀⠀⠀⠈⠢⢄⣀⣀⡠⢤⡀⠀⠳⡈⠢⣀⡠⢴⡾⠛⠉⢢⡀⠀⠉⠉⠉⢹⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⢻⠛⠓⠒⠒⠒⠒⠉⠀⠀⢀⠝⠛⠓⠊⠁⠀⠀⠀⠀⠉⠒⠒⠒⠚⠋⠙⠚⠃
⠀⠀⠀⠀⠀⠀⣠⢞⢴⠏⢸⣀⣀⡀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⢀⠔⢊⠔⠁⡎⠀⡼⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠈⠱⡈⢀⠅⠣⣴⠁
⠀⠀⠀⠀⠀⢇⣲⣈⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠁⢢
⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⠄⡐⠂⢨⡥⠀⠚⠠
⠀⠀⠠⠁⠀⠀⠀⠉⠒⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⣁⣀⢠⠀⠀⠀⠤⠀⢰⠔⠦⡀
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠉⠐⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠁⠀⢄⢄⠀⠒⣠⠏⠀⠀⡨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡁⢀⠔⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠁⠑⢉⣡⢖⠀⠉
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠗⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢤⠀⢄⢘⠩⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⠢⢠⠞⠳⠂⠐⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢆⠀⠑⣄⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠊⡂⢠⠀⠀⠈⡄⠀⠀⠀⠀⠠⠡⠊⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠄⣀⠬⠃⡀⠀⠀⠀⠃⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠦⠀⠨⠐⠀⢣⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠑⠦⣀⠀⠀⠀⠀⠠⠃⠀⠣⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠀⡁⠀⠀⠀⢈⠵⠶⢤⣄⣈⣹⡈⠙⢄⠀⠀⠀⠀⠀⠀⠉⢓⡶⠶⠶⠒⠂⠁⠀⠠⠠⠂⠈⡂
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⠁⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⢉⠟⠉⠀⠀⠁⠐⠀⠀⠀⠲⢾⠉⠀⠀⠀⠀⠁⠀⢒⠁⠀⠚⠭⠁
⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠔⠛⡀⠈⠀⠄
⡠⠐⠉⠀⢀⠔⠀⠀⡠⠊⠀⠀⠀⠈⠉⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢁⠀⠀⠊⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠢⡀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⣴⡾⠿⣶⣀⣀⣤⡾⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠞⠉⠀⠀⠀⠀⡍⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⣠⡾⠁⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⠶⠀⣠⠶⠆⣸⠟⠁⠀⣰⠟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠞⢁⣠⠞⠁⠀⠀⡴⠃⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡜⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠋⢠⣴⣞⡉⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢠⡴⢿⣥⣀⠀⠈⠉⠙⠳⠶⣤⣾⣿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠰⣮⣥⣤⡀⠈⠙⢷⣶⣶⡶⠶⠾⢿⡋⠀⠀⣠⣼⠷⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠉⠙⠛⣶⣿⣿⠋⠀⠀⢀⣾⣿⠟⠛⢉⣤⣶⣿⠿⠿⠛⠻⣷⡄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⢰⣿⣿⠁⠀⠀⣠⣿⣿⠋⢀⣾⠿⠟⠋⠁⠀⠀⢀⣠⣼⣿⡄⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⡏⠀⠀⢠⣿⣿⣧⠞⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⠟⢻⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⣤⣤⣾⡿⠉⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋⠁⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣾⣿⣿⠿⠿⠛⠉⠁⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣦⣤⣤⣤⣶⣶⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⠛⠿⠛⠉⠁⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣶⣤⣤⢀⣠⡤⠀⠀⠀⠀⢀⣴⠟⠋⣉⣤⣀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠛⠛⠋⠑⠋⠁⠀⠀⠀⠀⣴⠟⠁⣠⠞⢛⡝⠋⠀⣈⣤⣄
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣤⣀⣀⣀⣤⣤⣤⣶⡇⠀⠀⠀⣼⠇⠀⠘⠁⠐⠊⠀⣰⣾⠋⠉⠹⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠰⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣶⣠⡟⠁⠀⠀⠀⢀⣀⣀⠀⢀⡀⣸⣇
⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣀⣀⣀⡠⠤⠠⢶⣾⣿⣿⣿⡟⠀⠁⠔⠀⠰⠏⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⢻⠋⡩⠽⣇⠀⠀⠀⠀⠀⠀⢤⣤⠂⠀⠐⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⠉⠉⠙⣄⡀⠀⠀⠱⣾⢀⡐⠀⡌⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⢙⣦
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣴⣿⡇⠀⠀⠀⢹⣿⣷⣄⠁⠀⠀⠀⣰⠿⠋⠉⠀⠀⠰⠟⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠿⢿⡇⠀⠀⠀⠀⠛⠀⣿⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡜⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣾⣇⠀⠀⠀⠀⣷⣶⣿⣇⠀⠀⠀⠀⠈⠳⢄⣀⣀⠴⠛⣠⡟
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⠀⠙⢷⣄⡀⠀⠀⠀⠛⠉⠉⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣅⠀⠀⠀⠀⠙⣿⠛⢷⡖⠒⠒⠉
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣆⠀⠀⠀⢸⣿⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣧⠀⠀⢰⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⡀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⡤⠤⠒⠛⢋⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⡇⠀⠀⢻⣇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠌⠀⠒⢛⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢠⠀⠀⠈⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣈⣁⣤⡤⠒⠒⠉⠉⠀⡉⠈⠉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⢙⡇⠀⣇⣰⠶⡆
⠀⣤⡤⠶⠖⠋⠉⠁⠀⢀⣀⣤⣴⣶⣾⣿⣶⣦⣄⣀⠀⠉⠻⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣤⡴⠲⠻⢧⣤⠿⠋⢸⣧⡴⠛⣿
⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⠀⠀⣀⣠⣤⠶⢋⣁⠴⠞⠁
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⢇⠀⠀⢰⠋
⠈⠛⠛⠋⠈⠛⠿⣿⣿⠿⠟⠛⠛⠉⠁⠀⣀⡀⠀⠤⠤⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⠘⣇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠖⠛⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⡀⢰⠉⡄⢻⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⢸⠀⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢾⣀⣧⣤⣽⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⣦⣴⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣠⣤⡴⢦⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡤⠤⣀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣤⣴
⠀⠀⠭⠥⠶⠦⣌⣿⣿⣿⣿⣿⡇⠀⠀⠐⠋⠹⠶⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣋⣭⣭⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⣤⠤⠤⣤⠀⠀⠀⠀⠉⠋⠀⢰⣶⣿⣿⣿⣷⣓⣰⠛⠒⠀⠈⠉⠈⠛⠉⠀⠀⠙⠛
⠀⠰⢶⣶⠶⢦⡀⠀⢠⣤⣄⡀⠀⠀⠤⠦⣬⣷⣤⣿⣿⣿⣶⡄⠈⠙⣿⣿⡿⠋⠉⠁⠀⢾⣿⣿⣿⣷⠆⣀⡴⣶⡒⠲⠆
⠀⠀⢀⣠⠶⣌⣷⣴⣶⣿⣿⣿⣦⠀⠀⠀⠀⠈⠉⢉⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠻⠿⠋⠉⠉⠁⠉
⠀⠈⠉⠀⠀⠈⠛⠋⠁⠹⢟⡉⠿⠀⠀⠀⠀⠀⢀⣠⣴⣾⣧⡄⢀⣀⣀⣀⣠⣼⣧⣠⡴⠚⠉⠀⣶⣿⣷⣦⣤⠶⢆⡀
⠀⠀⠀⣀⣠⠶⣄⠀⢠⣤⣤⣧⣤⣀⠀⠀⢠⣤⡴⣾⣿⣿⣿⡀⠀⠁⠈⠉⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⢷⣤⡟⠙⠒
⠀⠀⣘⡿⠷⠶⠿⠶⠿⠿⣿⣿⡿⡟⠀⠰⠶⠛⠗⣻⡋⠁⠈⢧⡀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⣀
⠐⠋⠉⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⡄⠙⣷⣄⠀⣀⠀⠀⣀⣷⠎⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⣀⡾⣹⠟⠛⠂
⠀⢰⡒⠊⠉⠙⢦⡀⢠⣶⣶⣿⣶⣦⠀⠀⠀⠈⠹⣿⣿⣷⣿⡾⠇⠀⠉⠟⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋⠀⣀
⠀⠀⠙⠚⠛⠶⢬⣽⠿⠻⡿⣿⠻⠉⠛⠉⠁⠀⠀⠻⡿⡿⠟⠁⠀⠠⣤⣄⣀⣀⡀⠀⠰⠚⠁⠋⠉⠀⠀⠀⠀⢾⣽⣧⣐
⠀⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⡠⠖⠚⣿⣿⡇⠈⢀⣠⣶⣶⣶⡂⠀⣠⢦⡤⠄⢼⣿⣿⡏
⠀⢹⣿⣿⣿⠿⣾⣿⣿⣟⠁⠰⣿⣿⣿⣿⣿⣤⣞⣩⢭⣀⠈⠀⠀⠀⣿⡿⠁⠀⠈⡿⠿⢿⠿⠿⢾⠿⠉⠑⠀⣸⠿⣿
⠀⠀⣉⣚⠟⠳⠟⠉⠛⠋⠁⠀⠀⠉⠋⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⣰⠁⠀⠈⣀⣀⠀⠀⠀⠀⡾⠁⠀⡿
⠸⢿⣿⣿⣿⣿⣆⣀⣤⡴⡶⠄⠀⠀⢀⣶⣶⡄⠀⣀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠀⠀⢰⣆⣤⣭⣿⡇⠀⠀⢸⡇⠀⢰⡇
⠀⣤⠙⠛⠏⠛⠻⠿⠋⠀⠈⠑⠀⣠⣼⣿⣿⢿⣄⡏⠙⠛⠛⠃⠀⣲⣄⣀⣠⠤⠒⠂⠉⢿⣿⣿⣿⡴⣷⡀⠀⠀⠘⠓
⢀⣈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⠻⠃⠈⠉⠁⠀⠀⠒⠒⠛⢿⣿⣿⡀⠀⠀⠀⡀⢰⡟⢉⡏⠀⠀⠀⠀⢀⣆
⠀⠉⠉⠹⣷⣄⣰⣶⣾⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠀⠀⠀⠀⠓⢬⡁⠀⣀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠙⠛⠛⠻⡿⠿⢿⣷⠤⠀⠀⢠⣤⠀⠀⠀⠀⠀⣀⣘⣷⠋⠀⠀⣀⣀⣀⣀⣀⠀⢙⣷⣿⣧⡀⠴⠹⣿⣿⡿⣇
⠀⠀⠀⢀⡀⠀⠀⣠⢁⣀⣀⠀⢠⡄⠀⠘⣿⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠘⠻⠷⠦⠭⣽⣿⣿⡿⠛⠱⣄⠀⣿⢿⡇⠈
⠀⠀⢘⣻⣿⣷⣶⣋⡾⠀⠀⣀⣀⣻⣀⣼⣿⣯⣄⣤⠤⠒⠃⠀⠀⢀⣀⣀⣀⣀⠀⢀⡴⠛⠚⠒⢦⠀⠀⠀⠀⠹⡌⣧
⢀⡴⠟⣿⣿⣿⣿⡟⠁⠀⠀⠈⠀⠹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⠞⣁⣤⠶⠒⠋⠀⠀⠀⠀⣰⡇⣿
⠈⠁⠀⠉⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⠟⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠿

⠠⣴⣶⣶⣶⣶⣶⣶⣶⡆⠄⣤⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣹⣿⣧⡀
⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⢹⣿⣿⣿⣥⣄
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠻⠿⣷⣿⣷
⢀⣶⣤⡻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣿⣼⣿⣿⣶⠄
⠀⠀⢹⣧⡛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢿⣿⣿⠇
⠘⢷⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠠⣴⢮⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣷⣬⣠⣤⢀⣀⣻⣿⣿⣷⡄⠀⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⡇
⠀⠁⠉⠀⢈⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣤⣸⡿⢿⢿⣽⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣵⠾⣼⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠖⠒⠲⢜⡆
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⣤⣄⡀⠀⠹⡄
⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⢠⠊⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣶⣶⣾⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠈⠉⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣶⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣤⣆⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣖⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⢉⡙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡹⣦⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢹⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⣠⠔⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⡇⠀⠀⠀⠀⢰⣦⠀⣹⠀⠀⠀⠻⠷⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⠀⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠼⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣠⠔⠀⠋⠀⠈⠱⣶⠊⢀⡀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠛⠓⠒⠊⠉⢈⠇⠀⠀⠀⠐⣦⡀⠈⠒⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⣀⣄⣀⣀⣀⠀⠀⣀⡼⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⡤⡄⠀⣾⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⠉⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⢺
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡔⠁⠀⠀⣠⠶⠒⠲⣶⠒⠴⠶⠚⠉⠢⡤⣤⡄⡤⠔⠻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⡰⠊⠉⠈⠳⡄⠈⠙⠓⠶⠶⣄⠀⠀⠀⠀⣠⡄⠀⠘⢆⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠱⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠙⣆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⢠⠶⡄⠀⠐⢀⡴⠋⠀⠀⠀⠙⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣡⣤⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⢀⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⢀⣴⡿⠡⠆⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⡄⠀⠀⣸⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⢠⣾⡟⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⠏⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⣼⠻⡴⢋⣰⣿⠟⠀⠀⠙⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡼⠃⠀⠀⠀⠀⠛⠀⠈⠻⢦⣀⠀⣸⡿⠀⠙⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⡏⠀⠀⠀⡰⠚⠛⢦⠀⠀⠀⠀⠙⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣦⡀⠀⠀⠀⣰⢶⣶⣶⡄⠀⠀⣾⣷⣿⣿⣿⣿⡿⠇⠀⢀⣀⣀⣠⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣈⣻⣶⣾⣿⣿⠿⠿⣏⠀⠀⠀⠉⠙⢿⣿⣿⡿⡿⢿⠿⠿⠟⠛⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠤⠶⠛⠛⠃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⣿⣷⡄⠀⢀⣿⣿⣿⠁⠀⠀⢀⣠⡤⡖⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⢧⠀⠠⢾⣿⣿⢻⣿⡀⠸⣿⣿⡿⠀⠀⠈⠉⠉⠀⠀⣀⡀⠀⠀⢰⣧⡴⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠀⠈⢀⣠⣾⣿⠿⠋⠿⠃⠀⢻⣿⣇⠀⠀⠀⠀⠰⠾⠿⠋⢀⣠⣴⡾⠃⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣷⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⢠⣀⠀⢀⣠⣿⡟⠋⠀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣦⠀⠀⠀⢀⡞⠀⠀⣿⡀⠀⣸⢿⣿⣿⠿⢻⡀⠀⠚⠉⠩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⢀⣿⡄⠀⠀⠸⡇⠀⠀⣿⠃⠀⠘⢾⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠳⣄⡈⢷⡀⠀⠙⠛⠛⠁⠀⣢⠆⠀⠀⢸⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣷⣽⣤⠀⠀⠀⠀⠀⠀⠈⢧⡀⣷⣄⠀⠀⠀⠤⠴⣿⣶⡶⠆⠘⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⡌⠙⠳⠶⠦⣤⣤⣀⠀⠀⠈⠛⢻⣿⣿⣷⣦⡀⠀⠈⠉⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⣦⣄⡀⠈⠛⠿⡿⠀⠀⠀⠉⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣩⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢡⡾⠉⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⡟⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠁⢠⡅⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⢠⡜⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠃⠀⠀⣠⡾⠁⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣴⠟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡾⠋⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⢠⡄⠀⣠⠋⠀⢀⡀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠘⠁⣴⠟⠀⢠⡟⠃⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣀⣀⣀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣾⣿⣿⣿⣿⣷⣦⣉⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⠿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠁⠀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⠟⠁⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⠿⠿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢤⣶⣤⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⣿⠇⠀⢻⣿⣿⠿⠋
⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣀⣤⣤⠴⠒⠒⠒⠲⣦⣄⠀⠀⠀⠀⠀⠸⣿⠀⢴⣯⣀⠀⢸⣏⠁
⠀⠀⠀⠂⠀⠀⠀⣠⡾⠛⢻⣀⠀⠀⠀⣠⣶⠶⠟⠙⠛⣶⣄⠀⠀⠀⢹⡇⠈⠀⢹⣷⠀⣿⡆
⠀⠀⠀⣦⠀⣀⠾⠉⠀⠀⠀⠙⠷⠶⠾⠟⠁⠀⠀⠀⠀⠀⠙⣷⠀⠀⢸⡇⠀⣠⡿⠃⠀⣿⡇
⠀⠀⠀⢸⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡦⠀⠀⠀⠈⠿⡀⢸⣧⡴⠟⠁⠀⠀⣿⡇
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⠻⣷⣄⠀⠶⠶⠶⢦⣀⠀⠀⠀⠀⠀⣿⡶⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⣄⡀⠈⠻⢷⡀⢀⣤⡀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠘⠛⠿⣆⠈⡇⠀⠙⠛⠀⠉⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠋⢱⡆⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⡟⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠒⠂⣤⣤⣈⡉⠙⠻⠿⠟⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣽⡏⠈⠛⠃⢤⡤⠤⡤⠛⠁⠅⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣀⡾⠁⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⣀⡴⠋⠀⠀⢀⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣿⣤⡾⠋⠁⠀⠀⣤⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⣄⣉⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣿⠛⢀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡛⣽⢳⣴⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣗⡹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡿⠟⢯⣿⣿⣿⣿⣿⣿⣿⣧⠇⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣤⡴⣚⢻⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⢍⣜⢿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠇⣵⠀⢀⣿⠃⠈⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⠋⢀⣼⣿⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⡀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⢀⣴⡿⠋⠀⣰⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣴⠿⠋⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠈⠁⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣎⣀⣀⡸⡄
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠹⣆⠀⠿⠯⡉⠉⢣⣧
⠀⠀⠀⠀⠀⢠⠊⠀⠉⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢠⠊⢻⣄⠀⠤⠛⠀⠀⢀⠛⡍⠉⠉⡆
⠀⠀⠀⠀⠀⠮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⣀⣀⣀⣀⡀⠀⠐⢊⣥⣔⣃⠞⠒⠂⠉⠄⠀⠠⠐⢀⠜⠀⠈⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠐⠂⠒⠠⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⣄⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠖⠀⠀⠂⡠⢎⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⠠⠤⠤⠒⠀⠉⠁⢀⡠⠒⣆⢠⡘
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠒⠁⠀⣀⠠⠖⠂⠒⠂⠉⠉⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡠⠄⠊




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢄⠀⠈⠓⢿⡦⢔⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠠⠤⠤⠀⠐⠒⠐⠒⠒⠒⠒⠛⠚⠢⢄⡀⣂⠌⠀⠀⠘⢣⢋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢗⡀⡠⠀⠀⠀⠀⠀⠀⠀⠐⡤⠄⣀⠀⠀⠀⠀⠀⡰⠙⡁⠀⠀⠀⠰⡀⢉⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⡔⠉⠀⠀⡠⠊⠉⠒⠒⠉⠀⠀⠰⣠⠐⠉⠒⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⣄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⡩⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁
⠀⢀⣀⠠⠤⠤⠤⠤⠤⠀⠀⠠⠤⠀⠀⠠⡄⠠⠤⠀⠒⠂⠀⠉⠐⠒⠂⠩⠁⠀⠀⠀⡰⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠂
⡎⠁⡠⠤⠄⠐⠒⠒⠒⠂⠀⠐⠄⠀⠀⣈⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢠⠀⠀⡠⠊⠀⠀⠀⠀⠀⣱⠄⠒⠈⢁⠔⢁⡠⠊
⠱⡀⠢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⡠⠚⢡⡄⠀⠐⡁⠔⠁
⠀⠸⠀⠇⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⣀⠔⠉⠀⠀⣞⣷⡠⠜
⠀⠘⣀⣑⡠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⡁⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠔⠉⠉⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⡠⠊⠀⠀⠀⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠔⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠤⢀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⠡⣀⢌⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀
⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠟⡟⠻⢿⣿⣿⣿⣿⣿⣿⠿⠶⠄
⠀⠀⠀⠚⠓⢦⣄⣀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣷⣟⠘⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣄⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣳⢤⣀⣠⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠶⢾⣿⠿⠇⠉⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣭⣤⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣶⣿⣿⣿⣛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠑⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠳⣌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡝⣷⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢤⠀⠓⠲⠤⠀⢈⡀⠠⠄
⠁⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠐⠀⠙⣴⡀⠀⢶⠼⣇⣀⣀⡀⠰⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⡀⠄⠞⡩⢷⡂⠘⡆⢨⣀⡀⠙⠟⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⠂⠠⠐⠀⠈⡲⡷⣴⠼⡉⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢂⢀⠀⢀⡤⠒⠉⠉⠝⠢⠀⠀⠀⠀⠸⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠉⠂⠀⠊⠀⠀⠀⠀⡶⡀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠆⠴⠀⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠠⠊⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠋
⠀⠀⠀⢀⠀⠄⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠂⢄⠀⢀⣶⠋⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣬⣦⣄⣙⣿⣿⣿⣇⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⣠⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⢀⣀⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⢰⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⠟⠀⠐⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠟⠛⢦⣀⡤⠾⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠶⠶⠤⠶⠈⠀⠀⠀⠀⡠⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠙⠂⠉⠀⠀⠀⠀⠀⢀⠄⠀⣴⠞⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠥⠀⠀⢀⣀⢀⣠⡖⠁⢀⡾⠃⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢁⡠⠞⣩⡼⠋⠀⣠⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣡⠞⠁⠀⠀⣰⠏⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡾⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣏⠀⠈⠙⠓⠲⢤⣄⣤⣶⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢤⣆⣈⡀⠉⠛⢷⣶⣶⣶⠤⣾⡟⠉⠀⢀⣨⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⡀⠀⠀⠈⠉⠙⠓⢶⣾⣿⠋⠀⠀⣼⣿⡷⠞⢋⣡⣴⣿⣿⡿⠿⢶⣄⠀⠀⠀⢸⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⢠⣿⣿⠃⠀⢀⣾⣿⠏⢀⣴⡿⠟⠉⠁⠀⠀⢀⣼⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡏⠀⠀⣼⣿⡧⠒⠋⠁⠀⠀⣀⣠⣴⣾⣿⠟⢻⡿⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠧⠤⢴⡿⠋⠀⣀⣠⣤⣶⣿⣿⣿⠿⠛⠁⠀⣸⠇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣿⠿⠿⠟⠋⠉⠁⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠈⠉⠉⠀⠀⠉⠁⠀⠀⢀⣠⡴⠤⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⠿⣧⠶⠛⠀⠀⠀⢀⣾⠟⢁⣤⣶⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡿⠁⠰⠋⢠⠊⠀⣠⡴⠶⠦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣧⣀⡼⠋⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⠀⢤⣶⣾⣿⣿⡿⠁⢋⡄⠀⡴⠋⠈⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠛⠉⠿⢇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠈⠹⢀⡀⠀⠀⢢⢀⡀⠐⡬⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠘⢻⡄
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣤⣴⣿⡆⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠜⠏⠀⠀⠀⠀⠟⠛⠘⡏
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⢻⡇⠀⠀⠀⡇⠀⣯⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⠄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡇⠀⠀⠀⣿⠿⠿⣆⠀⠀⠀⠀⠈⣓⠀⠀⠐⠉⣠⠏
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⡁⠀⠀⠈⠳⣤⣄⣀⣀⣉⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢧⡀⠀⠀⠀⢸⣏⠉⢻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢳⡄⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⣀⣤⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢸⡇⠀⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⢀⣀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠒⠉⠉⡏⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿⠀⠀⠘⣿⠀⣿⢠⣤⡄
⠀⠠⠤⠔⠒⠋⠉⠁⢀⣀⣠⣤⣴⣶⣿⣶⣤⣀⡀⠉⠛⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣤⡤⠶⢿⣤⣿⠞⢺⣃⣠⠖⣶
⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠉⠀⠀⢀⠀⡀⠴⢛⣩⡤⠞⠋
⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡀⠀⢰⠋
⠀⠈⠉⠀⠀⠉⠻⠿⠟⠛⠉⠁⠀⢀⣀⣠⠄⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⡄⡦⢰⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡇⢸⢀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢷⡾⠾⠿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣤⣤⣄⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⣤⣭⣭⣿⣿⣧⣶⠾⠶⢷⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣾⡟⠁⠀⢀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⢻⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣾⠋⢀⣾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣏⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣹⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠟⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⠋
⠀⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣀⡈⠙⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⡆⣠⣤⣀
⠈⠻⢦⣄⣀⣀⣀⠹⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠋⠀⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢀⡠⠤⣄⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⢠⠴⠒⠒⠂⠀⠀⢀⠌⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⣶⡈⠀⠀⠀⢀⡤⠀⡴⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⢚⡽⠋⢀⡞⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠋⠀⣠⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣴⡁⠘⠓⠤⢄⣠⣶⠶⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠲⠤⢄⢉⣿⡷⠒⢺⣯⣀⠤⠾⣦⣤⣤⡀⠀⠀⠀⡇⠀⠈
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⢀⣾⡿⠀⢠⣾⠟⣡⡶⠟⠋⠉⢉⣽⣆⠀⢸⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⢀⣿⠟⠈⠁⢀⣠⣴⣾⡿⠋⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣹⣧⣤⣶⠿⠿⠛⠋⠁⢀⣴⠃⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣉⣀⣀⣀⣀⣀⣤⣴⠶⠋⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠛⠛⠛⠛⠛⠉⢀⣀⡀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⡿⠶⠶⠒⠀⠀⣠⠞⢋⡴⡦
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣤⣤⣤⣤⣴⡇⠀⢠⠏⠀⠁⠀⠀⠔⠋⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠉⠙⠙⠋⠉⠀⣠⣀⠞⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣤⣤⠖⠐⢺⣿⢿⡏⠈⠆⠐⠁⠀⠀⠀⠘⡀⠀⠀⠀⢨
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠙⠇⡀⠀⢀⢀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⢧
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣾⡇⠀⠈⠟⢦⠀⠀⠀⠘⠀⠀⠀⠋⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⡇⠀⠀⣦⢾⡄⠀⠀⠀⠂⠀⠠⠂⡸
⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡁⠀⠈⢲⣤⣤⣨⣤⠴⠊
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠱⡀⠀⢸⣷⠀⡆
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⠀⠘⡇⠀⢻
⠀⠀⠀⠀⠃⠀⠀⡒⠚⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡇⠀⢷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣈⠥⠤⠐⢚⡛⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡇⠀⠸⡇⣸⢠⡄
⠀⠐⠊⢉⣁⣤⣤⣶⣶⣿⣿⣶⣤⣄⡉⠳⠆⠀⠀⠀⠀⠀⠀⠈⢷⠐⠖⠛⠳⠞⣉⠦⢒⡿
⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢆⠈⡵⠋⠉
⠀⠉⠀⠈⠙⠛⠉⠉⠀⠤⠀⠀⣒⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⠀⡇⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⢤⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠐⠁⠀⠀⢀⠄⣨⠁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡧⢁⠁⠀⠀⠀⠀⣈⠴⣶⠎⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠠⠁⠀⣠⣤⡾⠿⠕⠊⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⡤⠴⡂⠈⠀⠀⠀⠠⠐⠈⠄⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⢀⣤⡶⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⢭⡃⠀⠀⠉⠙⠒⠂⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠠⣸⢉⠋⠓⢂⢀⡀⠀⠀⠀⠀⠘⠛⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⢠⠁⠀⠐⣀⣠⣤⣀⠀⠀⢹⠉⢉⣩⢌⡤⠀⠀⠀⠀⠀⠀⠀⠈⡥⠱⡄⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠉⠥⠠⠀⠀⡀⢲⣶⠡⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠇⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠄⠀⢄⣲⣤⣄⡼⠗⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠛
⠀⠀⠔⠉⠀⡏⠀⠀⠀⠁⢶⣹⠆⠘⠁⠀⠀⠀⠀⠀⡁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⡄⠀⠄
⠀⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠋
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠁⠴⠀⠁
⠀⠀⠀⡤⣀
⠀⢀⣜⣿⡟⠁
⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢀⢠⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⣀
⠀⠀⠀⠀⣀⡀⠰⠖⠈⠘⠁⠀⠀⠀⠀⠀⠓⣰⡦⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⣀
⠀⢠⢖⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠊⠁⠀⠀⠀⠉⠢⠤⣤⡀⡎⠑⢄⠀⠀⠀⠀⠀⠀⠉⠐
⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡀⠈⠒⡄
⣎⡀⠀⢀⣀⣀⢀⣠⠔⠚⠈⠀⠈⠧⡄⠀⣠⠤⢤⡀⠸⡓⠒⠤⣀⠀⠀⠀⠀⢀⠧⠇⠰⡀⠘⠤⡀
⠀⠀⠀⠀⠈⢩⡀⢈⣆⡎⠉⠑⣄⠀⠣⡼⠱⠛⢀⠇⢰⠀⠀⠀⠀⠑⣄⢰⢀⢼⡒⠒⡴⢣⢠⡹⠁
⠀⠀⠀⠀⠀⠀⢹⠁⠀⢣⡀⠀⡸⠀⠠⡄⠀⢴⠭⡖⠁⠀⠀⠀⢀⡴⠛⣯⠁⠀⠱⡀⠑⠉⠉
⠀⠀⠀⠀⢀⠔⠚⠓⠒⠉⠈⠩⠁⠀⢀⡿⡀⠀⠉⢁⠔⠲⡈⢲⠉⠑⠊⠀⠑⠄⠀⠑⢦
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣀⠄⠀⠀⢀⡼⢾⣧⠀⠰⠁⠀⠀⠈⢦⠱⡀⠀⠀⠘⠷⠧⠗⠚
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠏⠠⠤⠒⠉⠀⢀⡟⢠⠃⠀⠀⠀⠀⠀⠱⡘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⡷⣲⠁⠀⠀⠀⠀⠐⢏⣋⣁⠀⠉⢊⣉⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡍⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢦⢤⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⡱⢂⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠏⠴⠇⠜⠠⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠄⢀⡠⠒⠠⠤⠠⠔⠒⠤⣀⣀⡶⠢⠤⣀⣀⠀⠀⣀⡖⠢⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⢀⡀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⡀⠀⠀⠘⣧⢤⣀⣀⣀⣀⣴⣦⣀
⠀⠉⠛⠛⠋⠉⠀⠉⠛⠛⠋⠉⠀⠉⠛⠛⠋⠉⠀⠉⠛⠛⠋⠉⠀⠉⠛⠛⠋⠉⠀⣀⠀⠀⠘⣧⠉⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠘⠇⢀⡀
⠀⠀⠀⠀⣀⣤⡰⣿⢿⣫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆
⢠⣴⣶⠿⣫⡿⠋⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣸⣿⣿⢟⣝⡿⣿
⠀⠋⠵⠟⠋⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⣀⣤⣤⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⢱⣾⡿⡿⠛⣵⣮⣟⠛⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣷⡀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡏⣾⣷⣦⣤⣀⡉⠉⣩⣽⣭⣛⠿⢿⣿⣿⠿⠿⠛⠛⢛⣿⡟⠋⠈⢿⣷⣀⣀⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⣼⣭⠁⠀⠉⠛⠿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⠻⠿⠿⠿⠿⠿⠇⠋⠁
⠀⠀⠀⠀⠀⣼⣏⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⣼⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠶⠦
⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⣤⣤⠶⠳⢦⣤⣤⣤⠶⠳⢦⣤⣤⡤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⣤⣤⣀⢀⣠⣤⣶⣶⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣈⣑⣢
⠀⠀⠀⠀⠀⢹⣿⣫⣿⣿⢿⣿⣵⣿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣳⣿⣿⣿⣟⣿⡆
⠀⠀⠀⠀⠀⣾⣿⠗⠙⢿⣾⣿⣿⣿⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠛⢛⡻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿