Beeswax Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡇⠀⠙⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣬⣦⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣛⣿⣿⢟⣫⣭⣥⣤⢨⣉⡉⠛⠛⠿⠿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⣤⣾⠟⢻⣿⣿⣛⣛⣒⣛⣻⣿⣶⣦⣤⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣸⣿⡷⠒⠒⠒⠒⠒⣿⣌⢹⡿⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⢉⣽⣯⡭⠭⠭⠭⢭⣿⣿⣿⡇⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣭⣿⡿⠛⠿⣿⢃⡾⠉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣫⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⢠⠤⠖⠒⠉⠓⠢⢄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣀⣀⣀⣀⡀⢀⣠⣟⡀
⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⠀⠀⢠⡿⠛⠋⠉⠀⠀⠀⠀⠀⡁⠀⠀⠦⡠⢀⡀⢀⠀⠈⠀⠀⠀⠀⠀⢈⡘⠀⠀⠀⠀⠀⠠⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠈⢸⠆⠀⠉⠁⠨⠛⠢⢠⡶⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⢉⣉⣭⠿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠆⠠⠀⠀⠉⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢐⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⠀⢻⠁⠀⠀⠀⠀⠀⢠⣰⠀⠀⠀⠀⠀⠀⠘⢻⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠂⠒⠂⠶⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣄⡆⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠴⢡⠏
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠛⠋⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠴⠖⠚⠋⢀⡀⠀⠀⠀⠀⠀⠀⢤⣛⡛⠄⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠗⡄⢠⢐⣀⢶⣾⣾⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠤⡴⠒⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⠀⠉⠑⠀⠸⠆⢉⢨⣥⣼⡿⠃
⠀⠀⠀⠀⠀⠐⠢⢤⣶⣤⣀⣀⣠⣄⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠅⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠉⣻⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡁⣾⣧⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣺⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢠⣤⣜⣾⣷⣿⣿⣿⣿⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⣿⣿⣻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣽⣿⣻⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠉⠛⠛⠛⠓⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣃⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠛⠻⠿⠛⡏⠂⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⣀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣿⣉⣗⣻⡷⣯⣷⠕⣧⠼⡘⣳⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⣰⠞⣥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡷⢺⠤⣿⡼⣖⠓⠐⣎⣻⠀⠆⠥⡟⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠆⡁⢼⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣟⣹⡖⢻⠔⣯⢽⣩⣫⢽⣃⣠⠒⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠹⢆⡣⣜⣮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡴⢿⠼⣏⣹⢞⣵⠺⠇⢷⠔⢣⠰⡞⢁⡁⡘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣌⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠞⣻⠶⣧⠼⣏⠹⡫⣟⣩⡏⡨⡘⡇⠉⣰⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣏⣹⡏⣳⠚⣷⠸⡶⢪⡤⣏⠤⣡⢽⢀⠇⢠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⢿⡴⣯⣼⣋⣹⣈⡶⠚⣖⠺⡖⢳⠔⣟⠀⢠⡟⠛⠳⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠈⠀⠀⠈⠀⠹⠛⠻⠙⠓⠛⠐⠉⢳⠏⡐⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⢸⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⠄⠀⡼⠀⠀⠀⠀⡗⡄
⠀⠀⠀⠀⠀⢀⣀⣤⠤⢴⠃⠏⢣⠉⡙⠳⡦⢄⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠯⠵⢛⠒⠒⠒⠚⠒⠶⠶⠦⠤⠤⠴⡃⢰⠀⠀⠰⠄
⠀⠀⠀⠀⢤⡈⠉⢁⡊⢉⢮⣑⡒⢅⡁⠀⡀⠠⠜⠀⣒⡺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣒⣂⣂⣀⣀⡈⠉⠀⠈⠀⠀⣰⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠢⠩⠄⠠⠝⠛⠥⠈⠛⠫⠤⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠐⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠙⢢⡔⠈⠀⠀⠉⢳⠀⠀⠀⠀⠉⠂⡔⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⢁⠀⠀⠀⠀⠘⢈⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠘⠷⡦⠴⡺⠁⠘⢷⣤⢴⡾⠁⠸⢽⡢⠔⡊⠀⠸⢶⠤⢔⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⣀⠴⠣⣄⡀⠀⣀⢜⠃⣀⠀⠀⣠⠄⠰⢄⡀⢀⡠⣞⣧⣀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⢠⠒⠉⠈⠑⢯⢫⠓⠀⠈⠙⠻⠢⠋⠁⠈⠙⠛⠫⠂⠁⠈⠓⠍⡛⠉⠀⠀⠙⠏⠉⠉
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠔⠦⡄⢠⣔⠅⠘⢷⣤⣤⠖⠉⠨⢷⣤⡤⠚⠉⠠⣀⠀⠀⠀⠀⠑⠢⣀⡠⢔⠃⠼⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠈⡈⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠿⣀⠀⠀⢀⡤⠱⡀⠀⠀⢀⠼⢧⡀⠀⠀⢀⡼⠇⡀⠀⠀⢀⠄⠣⣀
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠐⢝⢪⠕⠊⠀⠛⢕⢺⠕⠋⠉⠪⣙⠲⠟⠊⠉⠪⡕⠠⠔⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠈⠲⢄⣠⠴⠊⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢡⡀⢹⡀⣸⣁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢷⣶⣦⣀⣣⣴⢼⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡅⠒⠢⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⣸⠟⠀⠈⠈⠃⠬⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠠⠤⠤⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠺⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣄⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡄⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠸⠂⠰⠚⠃
⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣄⣀⣠⠏⠉⠁⠀⠀⠀⠀⣇⡀⣀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢄⠀⠀⠀⠠⠀⠀⠀⠀⠡⣀⣠⠃⠈⠀⣄⣀⡄⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⡆⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠊⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈
⠀⠀⠀⠀⠀⢀⠀⠒⠀⡀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⣀⠘⠢⢤⡤⠇⠀⢀⠀⠚⠦⣤⠞⠀⠀⠀⢀⢀⣤⣀⠀⣀⣠⠤⡀⠀⠀⠀⣌⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠛⢤⣠⡼⠧⣄⣠⠾⠦⣄⡤⠇⠀⠀⠀⠀⠈⣩⠁⠉⠠⠀⠰⠦⣔⠀⠀⠀⠙⠱⢄⠠⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠈⢱⢀⣀⣨⠧⣀⢀⣼⠇⣀⣀⡴⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣄⠀⠀⠳⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⢀⣿⣀⠀⣠⡏⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠋⠳⢤⡀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⠙⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠁⠠⠤⠚⠃⠀⠀⠀⠀⠀⠆⠈⢻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⢀⢤⡄⢂⠀⠀⠀⠀⠀⠀⡀⢰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠐⠂⠽⢦⡛⠄⠀⠀⠀⠀⠀⠒⣀⠞⠰⣧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠌⣡⠿⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠀⡄⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢾⡟⣅⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡖⢶⡈⠄
⠀⠀⠀⠠⠀⠀⢘⣶⣇⣚⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠺⡀⠈⢄⠀⠁⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢸⠷⣎⠲
⠀⠀⠀⠀⠀⠠⠂⠉⡯⠄⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠑⡄⠈⢂⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢆⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢦⡀⠣⡄⠄⠃⠀⠀⠀⠀⠀⡖⢰⠀⡀⣀⡀⣤⢠⢀⡄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠰⢦⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢾⠘⠋⠓⠃⠈⢸⠁⠀⠀⠀⠀⠀⢀⠣
⠀⠀⠀⠀⠀⠀⠛⠁⠋⠊⠒⠒⠒⠒⠒⠙⠋⡛⠏⢁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢐⠁⡗⠄
⠀⠀⠀⠀⠓⢀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⢨⠈⠈⢯⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠶⢩⠁⠀⠀⠠⣄⠠⠈⠀⠡⠈⢤⠡⠘⡈⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⢤⡄⢃⠀⠀⠀⠸⠵⠖⠇⠀⠀⠀⠀⡟⠳⣀⡀⢠⠱⡈⢂⠁⡀⡀⢊⠐⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢷⣤⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣈⠳⣆⢂⡐⣀⢃⢐⡐⣀⣀⢰⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣳⢿⢶⣴⣴⢶⠒⣟⣋⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣿⢛⡾⠿⠟⠻⠓⠊⠜⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡻⠿⢛⡻⢿⣿⢛⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡠⠐⠒⠠⢄⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢀⠀⠀⠄⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠎⢀⠄⡤⢤⠀⢣⠀⠀⠈⢥⠀⠀⠘⠟⠁⠀⠀⠁⠀⠈⠀⣆⡄⡀⠀⠀⠀⠀⠀⡀⡗⠀⠀⢘⣠⡆⠀⣾⡴⠋
⠀⡄⠘⠤⠢⠕⠁⡘⠀⠀⠀⣉⣤⠄⢠⡄⠀⠀⣠⣌⢻⡆⠀⠋⠃⠰⠄⠈⠀⠀⠀⠔⡂⠀⠀⢉⡠⠁⠀⠈⠀⠈
⠀⠈⠢⠄⠀⠤⠒⠀⠀⠀⢀⣽⣿⠁⠀⠀⣐⣖⡿⣿⣇⠃⠀⢀⣤⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡅
⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⣆⠝⠁⠀⠀⢠⣾⣿⡇⣿⡿⠀⠴⢉⣟⠿⠀⠀⠀⠛⠀⠀⠈⠛⠄⠀⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⢀⡀⠀⠀⠚⠛⠉⠰⡾⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆
⠀⠸⠇⠀⠀⠄⢀⠀⠀⢀⠐⠲⠌⠃⠀⠀⠠⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⢢⢤⠀⠐⠂⠀⣀⠀⠀⠁⠀⢀⢠⠤
⠀⠀⠀⠀⠰⠚⠛⠀⠀⠈⠍⠁⠀⠀⢰⠄⠀⣀⠀⠀⠀⠀⢠⠐⠀⠀⠠⠻⠈⠳⠀⠀⠀⠀⠀⢾⣦⡊⠂⠀⠀⠰⠆
⠀⢐⠂⠀⠀⠲⠁⠀⠀⣐⠄⠀⠀⢠⠀⠀⠀⣯⡅⠀⢠⡦⠈⠀⠀⠀⠈⡁⠀⠐⢠⡆⠀⠀⢸⣿⡍⠀⠀⠀⠠⠄
⠀⠠⠢⠀⠀⠀⢠⡄⠈⢕⠄⠀⠀⠠⡶⠀⠀⢹⣿⣂⡀⠀⠀⣶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢒⡴⠀⠰⠀⡀⠈⣤
⠀⢀⡀⠘⠓⠄⠀⠀⠀⠈⠀⠀⠀⠁⣀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⢠⡀⠆⠀⠀⢰⣆⠀⠀⠀⠀⠀⠁⠓⠞
⠀⠈⠃⢀⠀⠀⠀⠈⣏⠲⠂⢀⠀⠘⢟⠅⠂⠀⢀⣤⡄⠀⠀⢶⠀⠀⠀⢉⠙⠆⠀⠀⠈⠗⠀⠀⠈⠙⢳⢦⡀
⠀⠀⡀⠺⣵⡦⠂⠀⠐⡀⠀⠈⢠⡀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣀⠀⠀⠸⠂⠀⠀⠀⡌⠉⠀⠠⣤⣤⣀⠼⢷⡄
⠀⠀⠀⠁⠙⠣⠀⠀⠀⠁⣀⠀⠀⠨⢦⣀⠀⠀⣴⣆⠂⠀⢀⡐⢉⠀⠀⣤⠀⠀⢀⠑⠐⠂⣀⠀⠻⣿⣻⡿⣿⣶
⠀⠶⠀⠀⢄⢠⡈⠁⠠⣄⡰⠂⠀⠀⢻⣿⠁⠀⠉⠼⠁⠀⠘⢋⡋⠀⠀⠀⠀⠘⠢⠉⠀⠀⠉⠀⠈⠭⢭⣾⣿⠋⡄
⠀⠀⢀⡀⠀⠻⠃⠀⠀⠛⠁⠤⠀⠀⣌⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⡠⠂⠉⠉⠒⢄⠀⠀⠙⣋⣼⠇
⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠉⠀⠀⢤⣦⠀⠀⠀⠄⠀⠀⠀⠘⠀⡔⠠⢒⢀⠀⡆
⠀⢠⣤⡀⠀⠀⠀⣄⠲⠀⠀⠈⠁⠀⠀⠀⠉⠋⣗⣄⠀⠀⠉⠀⠠⠄⠀⠠⠤⠀⠘⡀⠁⠊⠐⠁⢀⠁⠀⠀⠆⣠
⠀⠐⠉⠀⠀⠀⠈⣋⠛⠀⠀⢠⣄⠀⠐⣶⣶⣶⡥⣿⣦⠀⠀⠀⡀⠀⠀⠐⠂⡀⠀⠈⠒⠀⠐⠂⢀⠀⠀⠰⠛⢙
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢴⣶⡀⠀⠈⠩⢿⣋⣿⣿⢠⡀⠀⠉⠀⠴⣰⡘⣇⠀⠀⡀⠀⠀⠀⠸⠇⠀⠀⠐⠇
⠀⠀⢀⡠⠀⠀⠀⣄⠀⠀⠀⠀⢿⠏⡤⡀⠀⠉⠉⠻⢋⣼⠃⠀⢀⡀⠀⠈⠈⠋⠂⠀⠀⣀⠤⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠁⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣀⠤⢄⡀⠀⢀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠈⡆⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣄⡀⣠⢞⣐⣤⣀⣀⠜⠰⣄⠀⢀⡴⣃⢦⡀⢀⠴⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡉⠛⠉⠀⠙⠯⠀⠀⠀⠀⠉⠉⠊⠁⠙⢮⢰⠋⠀⠈⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⣠⠀⣄⠀⠀⢀⡄⢀⠀⠀⢀⡴⠠⡀⠀⠀⡰⠹⣀⠀⢀⡠⠡⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⠓⠁⠐⠙⠚⠉⠀⠘⠛⠂⠁⠈⠙⠪⢒⠉⠀⠉⠛⠏⡽⠂⠐⠊⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠀⠀⢀⡆⠀⠀⠀⢰⠇⠀⠀⠀⢀⡆⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠺⢷⠤⠖⠁⠺⣶⠤⠔⠋⠀⠐⠢⠔⠟⠓⢿⠒⠒⠙⠛⠻⣶⠤⡾⠷⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠔⠥⣢⣄⣠⣀⠤⡲⠤⡀⢀⡨⢝⡢⣄⢔⡯⠼⢗⠦⠴⠃⠑⠦⣀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⢱⠘⠁⠀⠀⠈⡖⠉⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢄⢲⣀⠀⠀⠴⣀⢀⠀⢀⣴⣘⢠⡀⢀⡠⠏⠠⣄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⠁⠈⠋⠉⠐⠉⠉⠁⢉⠋⠉⠈⠙⠂⠉⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⣄⠀⠀⢀⣼⡀⠀⠀⠀⡼⢢⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠔⠋⠀⠀⠑⠒⠁⠀⠓⠦⠴⠊⠀⠀⠉⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣒⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠠⠄⠠⡀⠀⠀⢀⣾⣟⠅⠀⡕⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⢀⣀⣀⡈⠪⡢⡄⠘⠛⠉⠀⠀⠁⠀⠰⠶⠂⠉⠮⠥⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠔⡈⢸⠀⣿⣿⣿⣿⣦⣻⣦⠦⢤⣤⡔⠀⠀⠀⠀⠀⠀⠀⠈⡁⠑⠢⠄⠈
⠀⠀⡠⢖⠚⢃⡈⢁⠘⢄⠙⢿⣿⣿⣿⡷⢻⡖⠿⠿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠐
⠀⢀⡇⡅⢠⣤⣤⣄⠑⢄⠑⢄⠉⠉⠉⠀⡼⠁⠃⣼⣿⣿⣿⣿⡏⣠⣤⣄⣄⣀⣰⣿⠦⡀⠀⠀⠀⠁⠂⠄
⠀⡌⡆⠀⢸⣿⣿⣯⣷⡕⠗⡄⢉⣉⣉⠌⠡⡀⠫⣿⠻⣿⣿⣿⣿⣯⣭⣽⣿⣿⠟⠁⢀⣧
⢠⡐⠢⡑⢌⠻⣿⣿⣿⡇⠀⠁⠈⠀⣤⣤⣤⡈⢢⡏⠢⡈⢉⡹⠋⢀⢟⣻⠟⠁⣀⣴⡿⢻
⢏⠀⠀⠈⠪⡓⣄⣀⣀⣀⠠⠀⡀⠀⣿⣿⣿⣿⣾⠉⢀⠈⢉⠀⠀⣠⢞⠻⡾⠿⠛⠋⣠⡎
⠀⠱⡄⠀⢀⠵⠀⠤⠤⠄⠀⢄⠘⢆⠙⢿⣿⣿⣿⠀⡍⢀⠁⢠⣤⣯⣄⠑⣔⢶⣶⠿⠟⠁
⠀⠀⠈⡎⠀⠀⢰⠀⣤⣤⣴⣄⠑⢄⠑⢄⣀⡀⠀⢀⠇⢘⠀⣿⣿⣿⣿⣷⡼⢳⢰⡎
⠀⠀⢰⠀⠀⢀⢘⠀⣿⣿⣿⣿⣷⠙⢱⠀⡠⠄⠀⠀⠠⡈⠢⡈⠻⣿⣿⣿⠃⢸⢠
⠀⠀⢘⠠⠂⠉⠳⡑⢌⠻⣿⢿⣿⠀⠸⠀⠇⢠⣶⣶⣦⡈⡢⡈⠢⣀⣀⣀⠀⠈
⠀⠀⠈⢢⠀⠀⠀⠈⠢⡑⠤⠀⠤⠤⠆⠠⡀⢸⣿⣿⣿⣿⡎⠟⠆⡆⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠱⡀⠀⠀⠀⡸⠀⠉⠉⠉⡝⠂⠈⠦⡙⢿⡿⠿⠇⠀⠀⠱⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠘⢄⠀⡐⠀⠀⠀⠀⡜⠀⠀⠈⠐⢜⠦⠠⠤⠤⠔⢰⠀⣧⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⠋⠉⠉⠈⠉⠹⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢴⠠⠤⠠⠐⠒⠒⠙⠒⠒⠤⠤⢄⣀⡏
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢫⣯⢾⣿⣍⣼⣿⠛⣳⡤⢤⣠⡄⣤⡄⠒⣶⢐⣾⣀⠈⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢯⣷⣠⣾⣀⣨⣵⡛⢿⡥⢾⡗⠛⢳⡶⠚⠍⣋⣀⢽⡈⢈⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣧⣦⣼⣫⣀⣼⣏⠉⣽⠶⢯⡦⠄⣱⠶⠻⣾⠴⠠⡄⠚⡉⣿⠟⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⣏⣇⣸⣿⠅⢨⣿⠋⢫⡦⢴⣵⣠⣖⣶⠴⣯⣦⠤⠉⠉⠉⡽⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣑⣠⡿⠯⢈⣿⡟⠛⣿⠖⠫⣰⣤⣍⣆⣼⠠⣠⢌⣳⣀⢄⠖⠛⣦⣀⠀⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⠄⣽⣟⠋⣻⡗⠚⣤⣧⢾⣙⣀⣿⣏⢉⣟⢄⣸⣿⡁⢈⣀⡴⠋⠈⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⡋⢙⣿⠛⢻⣾⠴⣞⣃⣀⣿⣅⡨⢫⠉⣻⣫⢁⡜⠯⠈⣫⠃⢀⣠⠞⣠⠃⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢎⡉⣳⡞⠛⣧⣥⠾⣥⣤⣼⣋⢈⢹⠟⣀⡷⢋⢉⡿⡋⠀⢡⠊⠻⡎⠈⠀⣰⡟⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢳⣼⠶⣯⣰⣴⣏⣄⣨⡿⠁⢨⠎⡉⣹⢞⠛⢳⡷⠒⢆⡷⠺⣷⠀⢘⡟⣁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣧⣾⣍⣆⣼⢣⢄⣼⢋⠉⣻⣏⠑⡿⠛⠑⣢⠔⠷⣬⠶⢫⣴⡤⢿⡀⣸⠁⢌⢺⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢮⣖⣠⣟⡄⢨⡿⡉⢹⡟⠛⢻⡶⠚⢷⣼⠴⢧⣵⠴⣏⣆⣰⣷⣆⣠⣿⡟⠀⠀⢃⣻⡿⢛⣳⡶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢻⡟⠁⢻⡖⠻⠾⠴⠾⡵⡤⢾⣄⣆⣸⣓⣆⣸⣣⢀⡘⠃⠀⣽⣧⡀⣱⣼⢋⢊⠵⠢⣌⡃⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠉⢿⠃⠉⠉⠏⢉⡁⠉⠁⢱⢻⣿⠃⢆⠎⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠠⡄⠈⠀⠀⢸⠇⠘⠊⠀⠀⠀⠀⣸⠅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠹⡂⠁⠆⠀⢰⡞⠀⠀⠀⠀⠀⠀⢠⠿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣍⣙⡓⠛⠒⠒⠒⠒⠚⠛⠛⠶⠦⠽⠶⠬⠦⣄⣀⣀⣐⣂⡼⠁⡠⢐⡆⠀⠀⠀⣟⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⢤⣄⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠉⣭⣳⡶⢏⣀⠷⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣭⣀⣀⣈⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠄⣀⣠⡤⠶⠛⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣠⠖⠒⠒⠲⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠞⡱⠁⠀⠀⠀⠀⠙⡆⠃⠀⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⡀⢠⠛⠛⠛⠛⠳⡙⣄⠀⠀⠀⠀⢀⠆⡴⠛⠛⠛⠳⣌⠳
⠀⠀⠀⠀⣼⢡⠇⠀⠀⠀⠀⠀⢻⡘⠦⠴⠶⠄⠋⡞⠁⠀⠀⠀⠀⠈⢳⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠻⣜⣆⠀⠀⠀⠀⢀⣞⡵⠈⠉⠉⠁⢳⣵⡄⠀⠀⠀⠀⢠⢎⡴⠀⠂⠐⣆⢻⣄⣀⣀
⠀⠀⠀⠀⠀⢹⡟⠧⣤⣤⣤⠈⡜⠀⠀⠀⠀⠀⠀⢻⠙⣤⣤⣤⡤⢫⠋⠀⠀⠀⠀⠘⡦⠉⣭⣭⣭⣄
⠀⠀⠀⠀⢠⢏⡼⠛⠛⠛⠀⢦⠳⢄⠀⠀⠀⠀⣠⢏⡴⠘⠛⠛⠐⡜⢦⠀⠀⠀⠀⡠⣡⠞⠁⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⢳⠌⠳⠶⠶⠶⠁⠎⠀⠀⠀⠀⠀⠘⡎⣳⡶⠖⠚⡁⣏⠀⠀⠀⠀⠀⢀⣗
⠀⠀⠀⠀⢰⡸⣆⠀⠀⠀⠀⣠⡟⣠⠟⠉⠉⠉⢣⡱⡄⠀⠀⠀⢀⢜⡽⠁⠀⠀⠀⠘⣜⢧⢀⣀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠷⠙⠁⠛⠛⠛⢋⢰⡁⠀⠀⠀⠀⠀⡳⢙⠤⣿⣿⠋⠨⡄⠀⠀⠀⠀⠀⣸⢀⠴⠒⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠳⣝⢦⣀⣀⣀⣰⣣⠏⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡭⠹⠯⠭⣅⢁⠀⠀⠀⠀⠀⠀⣈⡤⠉⠲⠶⢆⠻⡄⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠞⠀⠀⠀⠀⠘⢦⢳⣀⣀⣀⢠⣾⠟⠁⠀⠀⠀⠀⠳⡜⠦⢀⣀⡰⣫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡞⡰⠾⠾⠗⠒⠘⢦⡀⠀⠀⠀⢀⡼⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣤⣤⠞⣼⠁⠀⠀⠀⠀⠀⡀⠳⠤⠤⠤⠈⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠻⣎⢧⠀⠀⠀⠀⠀⣰⠃⠜⠛⠓⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠇⠤⠤⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⢀⠤⠤⢤⣇⠀⠀⢨⡧⠶⠶⡄⠀⠀⠀⢠⠖⠒⢦
⠀⠀⠀⠑⠀⠂⣼⣴⡦⠀⢮⠀⠀⢀⣯⠿⠿⣿⡅⠀⠀⣸⡤⠤⢤⣯⠀⠀⢀⣷⠶⠶⣄
⠀⠀⠀⠀⠉⠁⣿⠿⣿⡦⠈⡷⠶⣞⣇⠀⠀⢨⣿⠶⠾⣿⠀⠀⠀⣿⡿⠿⢿⣇⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣞⠀⠀⠈⣿⡶⠶⣿⡃⠀⠀⢹⣷⠶⣞⢏⠀⠀⢈⣿⠶⠶⡏⠀⠀⠀⢀⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠾⡏⠀⠀⢘⣷⣶⣶⣿⠁⠀⠈⣻⣷⣶⣾⡏⠀⠀⢘⠆⢠⢶⣬⡄⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣦⡀⠘⣦⣤⢾⡋⠀⠀⢻⣷⣤⣴⣟⠀⠀⠘⣿⣦⣴⡋⢠⣶⣯⣿⡏⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢼⣿⣾⡟⠁⡞⠁⠁⠹⡷⣤⣤⣿⠋⠀⠈⢿⢦⣤⡾⡟⠀⠀⠹⣄⣉⣁⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠁⡀⢀⠆⠉⠀⠀⠱⣄⣀⣼⠏⠀⠈⢻⣦⣤⡴⡿⠁⠀⠙⡵⣤⣤⢾⠏⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⡴⠉⠉⢻⣣⣀⣠⣾⠋⠉⠙⢿⣄⣀⣴⡟⠉⠉⠹⡧⣤⣤⠎⢠⣤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣴⡟⠉⠉⢿⣆⣀⣠⣾⠋⠉⠱⡷⣀⣀⣼⠟⠉⠉⢦⠈⣯⣽⣿⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⡜⠀⠀⠀⠳⣀⣀⣠⡿⠉⠉⢻⣦⣀⣀⡞⠀⠉⠩⡏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠢⢧⣀⣀⡰⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢂⡤⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⡟⣡⣿⣿⡇⣀⡴⠒
⠀⠀⠀⠀⠀⠀⠠⢠⠴⠈⢐⣿⣿⢿⣿⣿⣷⢃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡿⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠘⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄
⠀⠀⠀⠀⠙⠿⣿⣿⠛⠿⣿⠋⢐⠀⠀⠀⢠⣶⣿⣿⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠓⢀⣼⣷⡆⠐⠀⣰⣿⣿⣿⣿⡭⠥⠄⠀⠀⢀⠠⠤⠞⠋
⠀⠀⠀⠀⢀⣀⣠⡄⠀⣀⡌⠛⠁⠂⠤⠛⠋⠉⠉⠉⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡀⢀⣰⣏⣤⡀
⠀⠀⠀⠀⠀⠈⠙⠿⣿⠋⠁⠀⠈⣻⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠈⣷⣄⠀⢀⡴⣄⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣿⠏⠀⠾⢿⣿⣿⣿⣿⣿⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠉⠀⠀⠈⠈⠉⠋⡟⠻⣩⠴⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⡄⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠶⠶⠶⠶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⡼⡉⢉⡤⠈⠉⠹⣌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡔⡛⡛⠛⠛⠛⢦⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⢣⠞⠐⠀⠉⠀⠈⠀⠀⠘⣎⢿⣄⠀⠀⠀⠀⠀⠀⢠⡿⢣⢏⠐⠈⠀⠀⠀⠀⠀⢳⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣛⣛⣛⣛⣛⡛⢧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢂⡿⠛⣛⠛⠛⠛⠛⢿⡅⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡷
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⠎⠂⠀⠀⠀⠀⠙⣎⢧⡱⡄⣁⡀⠀⠀⠀⠀⡼⣡⡟⡴⠫⠀⠀⠀⠀⠉⢦⢻⡜⢆⠠⢀⠀⠀⠀⠀⢀⡼⣡⡿⠁
⠀⠀⠀⠀⠀⠀⣰⡟⣱⠃⠀⠁⠀⠀⠀⠀⠀⠘⢎⢳⡙⠤⠥⠤⠥⠤⠞⣴⢋⡜⡁⠁⠀⠀⠀⠀⠀⠈⢧⠻⣎⢧⣼⣤⣍⣤⣠⠞⣴⠟
⠀⠀⠀⠀⠀⠀⠹⣧⠳⡐⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⠟⣛⣛⣛⣛⣛⡛⢷⡸⡄⢄⠀⠀⠀⠀⠀⠀⠀⢠⢇⡿⠶⠶⠶⠶⠶⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣧⡹⡄⢰⠐⠀⠀⠀⢠⠞⣴⢫⠞⠐⠖⠒⠀⠀⠘⢎⢳⡘⣄⠐⡀⢀⠀⠀⠀⣰⢣⡞⣱⠋⣉⠉⠉⠉⠙⢎⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣘⣒⣒⣒⣒⣒⣋⡾⣡⠋⠀⠀⡀⠀⠀⠀⠀⠈⢧⢻⡜⠢⠤⠤⠤⠤⠞⣡⠟⡼⠁⠢⠀⠀⠀⠀⠀⠈⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣭⡭⣭⡭⢭⡙⢧⡹⡄⠄⠀⠀⠀⠀⠀⠀⠀⡼⢡⠟⣛⣛⣛⣛⣛⡛⢯⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⣽⠇
⠀⠀⠀⠀⠀⠀⠀⣰⡟⡱⠋⠠⠂⠀⠀⠀⠘⣌⢷⡙⡄⠀⠂⠀⠀⠀⢀⡞⣰⢏⡜⠁⡂⠀⠀⠀⠙⣎⢷⡙⡌⢠⠠⣀⠀⢀⠀⣠⢋⣾⡏
⠀⠀⠀⠀⠀⠀⣼⠟⡼⠑⠀⠀⠀⠀⠀⠀⠀⠘⣎⢳⣜⣒⣒⣒⣒⣒⣋⡼⢣⠎⠄⠀⠀⠀⠀⠀⠀⠘⢦⢳⡜⠦⠤⠬⠥⠤⠴⣡⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣦⠳⡘⠀⠈⠀⠀⠀⠀⠀⢠⠞⣼⢋⡭⠭⠭⠭⠭⣍⢷⡹⡄⠀⠀⠂⠀⠀⠀⠀⠀⡸⢣⡟⠛⠛⠛⠛⠛⠛⠋⣀⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠱⡌⢰⠀⠄⠀⠀⣠⢋⡾⣡⢏⠀⠀⠀⠀⠀⠈⢯⢳⡙⡄⢁⣄⣀⠀⠀⢀⡼⣡⠏⠀⠀⠀⠀⠀⠀⣀⣀⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣘⣚⣓⣓⣚⣚⣡⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⣻⣜⠶⠶⠶⠶⠶⢞⡴⣣⣤⡀⣰⣿⡆⠀⢼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⢠⣤⡄⠈⢳⡘⣄⠂⡀⠀⠀⠀⠀⠀⢀⡞⣱⠟⣛⣛⣛⣛⣛⣛⢷⡏⠈⠛⠋⣾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡇⠀⢸⣷⡜⢆⠁⠆⠆⠀⠀⢠⠟⣴⢋⠞⠠⠆⠀⠀⠀⠘⢆⢻⣆⠀⠀⣿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡆⠻⣤⣼⢿⠿⣌⣉⣉⣙⣛⣛⣫⡾⣡⠋⠈⠀⠀⠀⠀⠀⠀⠈⢧⢻⣦⠀⢿⣷⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⡿⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⣼⠆⠀⠀⠸⣯⣠⡀⠀⠀⠀⠀⠀⠀⢳⡘⣄⠆⠒⣤⡔⠄⢀⡞⣱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣀⣴⠟⠀⠀⠀⠀⠈⢹⡇⠀⣀⠀⠀⣠⣄⠀⠻⣜⣒⣒⣒⣒⣒⣋⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠿⣤⣿⠀⠀⢿⠘⣇⠀⠈⠉⠉⠉⠉⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡆⠻⣷⣀⣴⠟⠳⠿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠀⠠⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣿⣯⡅⠛⠀⠸⣻⣿⣷⣄⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⢞⣉⠫⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣇⠁⠀⠀⠀⠀⣿⣿⣿⣿⡋⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⣷⣄⡀⠀⠉⠉⣿⣿⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⢀⣿⠏⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⣿⣿⣿⣿⣷⣾⣷⡄⠀⡀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠟⢻⣿⣿⣿⣿⠀⠙⢷⣤⡴⠟⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢷⡀⠀⠀⠀⠀⢠⣿⡾⠁⠀⢹⣴⡆⠀⠀⠀⠀⢀⡾⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣶⠈⢳⡀⠀⠀⠀⢸⡀⠀⣰⢆⠈⠁⡿⠀⠀⠀⢀⠈⠀⣶⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡀⠀⠀⢻⡄⠀⠀⠈⠳⣤⠏⠈⣧⠶⠁⠀⠀⢠⠟⠀⠀⢀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠤⠤⠤⠤⠤⠤⠤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠤⠤⠤⠤⠤⠤⠤⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡴⣄⣠⣿⣠⡴⠋⠀⢸⡇⠀⠀⢀⡤⢞⡿⢙⡏⠻⡗⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣏⣠⠞⠁⠀⠀⠀⠀⠀⢀⡀⠀⢠⠟⠓⣾⠶⠶⡷⠶⢿⡖⠛⣆⠀⠀⢀⣀⣀⠀⠸⣦⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡀⠀⠀⠀⣠⠀⢈⡇⠀⣏⣀⣀⣇⣀⣀⣇⣀⣸⣇⣀⣸⡀⠀⢸⡇⠉⠙⣄⠀⡇⠀⣠⠴⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠉⠉⢹⡇⠀⢸⡇⠀⣯⠉⠉⡏⠉⠉⡏⠉⢹⡏⠉⣹⠁⠀⠀⠳⢬⡷⣏⠀⡇⢰⣇⡄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣀⣀⣸⡇⠀⢸⡇⠀⠘⢦⡴⢿⡖⠺⡗⠒⣾⠷⣤⠏⠀⠀⠀⠀⠀⠀⠘⢶⡇⢠⡟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠉⠁⠉⠉⠙⠀⢸⡇⠀⠀⠈⠙⠮⣷⣤⣧⣼⠷⠞⠁⠀⠀⠠⣤⣤⣤⠄⠠⣼⣿⣯⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠄⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡼⢷⡀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠀⠀⠀⠀⠀⡼⠁⡀⢳⡄⠀⠀⠀⠘⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡤⠀⠀⠇⠀⠻⡄⠀⠸⡇⠠⡴⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡞⠀⠀⠀⠂⠀⠀⠹⣄⠀⠙⠲⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠁⠈⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⡶⠶⠶⠾⠿⠀⠀⠻⠿⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⠀⠀⠀⣀⣤⣤⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠶⢛⡉⢡⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⣶⡾⠛⣅⣒⣠⣥⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠯⣤⣦⠴⢦⣤⡤⣤⡤⠼⠤⢴⣤⣬⣤⣴⣤⠤⠤⠼⠤⠾⠤⠦⠤⠧⠬⢿⣾⠯⣭⣍⡍⠛⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠈⠙⢦⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⡆⠀⢸⠀⠀⢀⡶⢦⡀⠀⢠⣧⠀⠀⢸⠀⢰⠶⠶⠄⠀⢠⡀⠀⣀⡀⠀⠀⣿⡄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣇⠀⢸⡇⠀⡼⠀⠀⢹⡄⢸⡏⣧⠀⣿⠀⣼⠀⠀⠀⠀⠈⢷⣼⠋⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠤⣿⠶⢾⡷⠀⡇⠀⠀⣼⠁⢸⡇⠘⣧⡿⠀⣿⠛⠛⠂⠀⠀⠘⡇⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⣿⠀⢸⡇⠀⠻⢦⠞⠁⠀⣿⠀⠀⠘⠇⠀⣿⣤⣄⠀⠀⠀⢰⡇⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⠇⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣀⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣝⡲⢄⣠⠴⣚⣓⠦⣄⡠⢖⣫⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢸⡇⣿⣿⣿⣿⢸⡇⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣮⣝⢟⣫⡼⢷⣭⣛⣛⣥⡾⢧⣝⡻⣋⣵⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣵⣿⣶⡍⠛⠻⢶⣷⣮⠙⡿⠥⣺⣦⡍⣿⢫⣶⣿⣾⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢿⣿⡿⢃⠀⠀⠀⠉⠻⣾⣷⣿⣋⢉⣷⣿⡘⢿⣿⡿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⡤⣚⣭⣝⠳⣶⠾⣫⣤⣘⠛⢓⡆⠁⠈⠛⣉⣤⣝⣛⣽⡷⣶⠞⣫⣭⣳⢤
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⡇⣿⢸⣿⣿⠟⢧⠀⢳⡀⠀⠀⢹⣿⣏⣀⣿⡇⣿⢸⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠓⢭⣛⣫⡴⠿⢶⣝⡻⣆⠈⢧⡀⠙⣰⠈⢻⡳⣉⣛⣉⡴⠿⢦⣝⣛⠭⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣾⣿⣷⡌⣿⢻⣶⣾⣯⢰⠏⠀⢸⣿⡎⣿⢡⣾⣿⣷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡻⣿⠿⣣⣿⣘⠿⡿⢟⣀⠀⠀⢸⣿⣃⣿⣜⠿⣿⢟⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⢟⣩⣮⣝⢳⡾⣛⣥⣤⣴⣿⠟⣫⣵⣭⡻⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢸⡇⢿⣿⣿⣿⢸⡇⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣫⠵⠊⠙⠲⢭⡭⠖⠋⠑⠮⣝⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣤⡀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣤⡀⠠⢇⠀⠀⠀⠀⠀⠤⢀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣾⣿⣿⡦⢠⣴⣾⣿⣷⣶⣦⣶⣤⠐⠀⠀⠀⠀⠉⣝⣻⡿⣿⢿⣶⣾⠂⠀⢀⡠⠐⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⣿⣿⣿⣽⡇⢸⡿⣿⣯⣽⣿⣿⣿⣿⠃⠀⣤⣄⣀⣀⠈⣳⠾⠜⣿⠿⣿⣧⡄⠀⢀⡘⠋⠛⠶⠦
⠀⠀⠀⠀⢀⠠⠈⠈⠻⣿⣸⣿⣿⣿⣿⡿⠃⠸⣗⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠤⠿⣄⣐⣿⣿⣿⣿⣧⠤⠤⡃
⠀⡠⠂⠭⣶⣾⣶⣾⣷⣄⡙⠛⠛⠉⣠⣴⣌⣵⣮⣙⠿⣿⡿⠟⣋⣥⡶⠀⠀⠀⠀⠀⠀⡀⢙⠿⣿⡟⠻⠟⢿⣧⣴⡏⠑⢄⢀⡀
⢠⠀⠀⢠⣹⣿⣻⣽⣷⣏⣻⠀⢀⣸⣿⣿⣿⣯⣿⣿⣿⡄⣾⠿⠛⠉⠀⠀⠀⠀⠀⢀⠜⠀⢀⣠⡞⢉⢀⣼⠿⠋⣩⣤⣀⠈⠛⠦⢄⣄⣀
⡄⠀⠀⣿⣿⣽⣿⣿⣿⣿⡏⠀⣿⣿⣾⣿⣿⣿⣿⢶⣽⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⣸⠂⠛⠛⢲⠾⣿⠁⢰⡿⠟⣻⣷⣷
⢇⠀⠠⣿⣟⢿⣿⣿⣿⠿⢃⠐⢿⡯⣿⣿⣿⣿⣿⣿⣿⠀⡀⠘⠀⠀⠀⠀⠤⠀⠀⠊⢻⠀⠀⠀⠘⡄⠹⣶⡏⣠⣾⠿⢻⣶⡆
⠀⠙⠆⠈⠙⠿⢋⣩⣴⣾⠿⠓⠢⣑⠺⣝⣿⠽⠟⣋⣥⣶⣌⡂⢄⡀⠀⠀⢀⠠⠔⠂⠭⡀⠀⠀⠀⠾⡆⠈⠛⢯⣁⣠⣿⣿⡇
⠀⠀⠀⠀⠀⢀⠛⠛⠉⠀⠀⠀⠀⠀⠑⠆⢠⡶⣛⣩⣶⣿⣿⢻⣦⢌⠛⣩⣤⣶⣿⣷⣶⢬⡑⠤⡀⢀⡃⠀⠀⠀⠈⠉⠙⠋
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣇⣿⣟⣿⣿⣿⣿⣾⣶⢸⣿⣷⣾⣟⡿⣇⢀⡀⣠⠁⠀⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⡿⣿⡿⣿⣿⡿⢿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⡿⢸
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⣷⣅⠉⢻⢿⣿⣿⠝⠛⠘⠇⡻⠿⣿⣿⣿⠟⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢌⠙⢿⡧⠿⠿⠋⢀⡠⢾⣷⣦⡙⠺⣿⡿⠟⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⢠⠖⠋⢼⠀⠀⠈⠛⠿⠆⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠉⠻⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠼⠇⠀⠀⠽⢧⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣙⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⠤⣤⠴⠶⠶⠶⠶⠶⠒⠒⠚⠛⠿⠯⠿⠿⠿⠛⠛⠻⠁⠀⠀⠉⣙⣛⣷
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠰⡀⠀⠀⢀⠀⢠⢤⡀⢠⣄⠀⡄⠠⠒⠂⠐⢄⡆⠀⠊⡀⠀⠐⠒⣒⢺⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆⠆⢸⣄⣈⡆⢮⠀⡹⠈⡏⠳⣷⠀⡗⠂⠀⠈⡇⠀⠀⠁⠀⢈⣙⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠐⢠⠈⢯⠀⠃⠈⠛⠁⠀⠛⠀⠉⠀⠙⠉⠀⠀⠃⠀⠀⢶⠀⢀⣀⣒⣺⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⡮⡆⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⠴⢖⣒⣒⣒⣒⣒⡪⠽⠀⠀⢒⣲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠘⠬⠤⠬⠥⠶⠒⠒⠂⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣻⡛⠳⡄⠀⠀⠀⠀⠀⠀⠀⢘⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⢇⠀⠉⠸⠆⡸⠒⠒⠲⡄⠀⠀⠀⠈⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⠃⠀⠀⠀⠈⡦⠤⠤⢴⠁⠀⠀⠀⠘⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⠃⠀⠀⠀⠳⣀⣀⣀⡜⠁⠀⠀⠈⢣⣀⣀⣀⠞⠀⠀⠀⠘⢆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣏⠍⡏⡛⡄⠀⠀⠀⡜⠁⠀⠀⠱⡀⠀⠀⢀⣞⠩⢉⡍⢣⠀⠀⠀⢠⠋⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⠀⠀⠃⡼⠟⠟⠛⣄⠀⠀⠀⢀⠟⠉⣛⡿⡈⠀⠀⠀⢠⣟⢛⡟⢣⡀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠀⠄⢾⢰⠀⠀⠀⢸⠦⠀⠰⣏⠀⠀⠈⠋⣸⡶⠴⢴⡅⠿⠀⠀⠀⣱⡴⣤⡶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢣⠤⠤⢤⠃⠀⠀⠀⠈⣦⣤⡤⣴⠁⣧⠀⠿⠘⡄⠠⠤⡜⠀⠀⢠⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠⠃⠀⠀⠀⢣⡀⢀⢀⡴⠉⢹⠀⠈⢦⡉⠀⢀⡞⠀⠀⠀⠘⣄⠀⠈⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠛⡗⡄⠀⠀⠀⣼⡏⠋⢹⡳⡀⠀⠀⢀⠞⠁⠈⠈⢦⠀⠀⠀⢠⠊⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡜⠒⠒⠚⡄⠘⠃⠈⢀⠟⠒⠒⠻⡀⠀⠀⠀⢠⡗⠖⠒⢣⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠤⠤⢞⠀⠀⠀⠀⢸⠆⠤⠠⡎⠀⠀⠀⠀⣹⠄⠤⠴⡃⠁⠇⠀⠀⣳⣤⣤⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⢣⣀⣀⣠⠋⠀⠀⠀⠈⣆⣀⣀⣰⠁⠀⠀⠀⠙⣄⣀⣀⡜⢱⠌⠐⢸⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠⠏⣉⠩⠄⢣⡀⠀⠀⡰⣿⠀⢨⠈⢆⠀⠀⢀⡜⠀⠀⠀⠘⣄⠀⠀⢈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠱⡀⠉⠀⠀⡴⠉⠉⠉⢣⡀⠀⠘⢀⡜⠉⢛⠛⢦⠀⠀⠀⢠⠎⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠺⡄⠀⠀⠀⢀⠗⠒⠒⠺⡀⠀⠙⠀⢠⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⡎⠀⠀⠀⠀⢱⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⡰⠃

⠀⠀⠀⠀⠀⠠⠏⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣦⣤⣆
⠀⠀⠀⠀⠰⣬⠤⠤⢤⣦⢠⠖⢲⠀⠀⠀⠀⠀⠐⡿⢙⣿⣿⠻⠀⠀⠀⠀⠀⠀⢀⣶⣰⣦⣴⣢⣦⣦⣆⣀
⠀⠀⠀⠀⠀⢄⠀⠀⣴⠟⠃⢄⣘⠀⠀⠀⠀⠀⠀⠀⣿⠧⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢸⡀⢀⡟⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣯⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⡯⣍⢩⣭⡩⡭⢍⡝⠇
⠀⠀⠀⠀⠀⠈⡇⡼⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠶⣽⡆⠀⠀⠀⠀⠀⠀⠀⠿⣏⣙⣽⣋⣪⠟⡏⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⢀⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡶⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠑⠻⣋⣉⣩⣥⢶⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣧⡴⠖⠃⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡿⠁⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣀⠠⠜⠋⠁⠀⠀⠀⠀⠀⠿⠀⠉⠉⠉⠛⠛⣿⠁⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠃⠀⠀⠀⠀⠀⠈⠊⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣘⣛⡀⢀⣤
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠁⠈⠠⠀⢁⠢⠀⠀⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣷⡉
⠀⠀⠀⠀⠀⠀⢉⡉⢉⠉⣉⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⡐⣄⠀⠀⠀⠀⠀⠀⠀⠺⠇⣿⣿⣿⣿⣿⣿⡇⠿⠂
⠀⠀⠀⠀⠀⠀⠈⣡⠈⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢿⣿⣿⡿⢟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⡶⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠁⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢒⡶⠛⢛⠛⠓⠒⠲⠦⣄⣀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⣰⠋⠀⣰⠋⠳⡀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⢀⡜⠁⠀⢰⠃⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠸⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⣀⡴⠒
⠀⠀⠀⢀⡞⠉⠙⠲⠦⢤⣀⣞⡀⠀⣤⣀⠀⠈⢻⠋⠀⢀⣠⡄⠀⣤⣄⣠⠤⠀⠀⠀⠘⣆
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡼⠉⠉⠙⡇⠀⠙⠲⣼⡴⠚⠉⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⡆⠀⢀⣀⣤
⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢻⡀⠀⠀⢹⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉
⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠒⢻⠓⠒⠋⠁⠀⠀⠀⠀⢀⣤⣀⡠⠤⠀⠀⢸⡄
⠀⠀⣿⠒⠒⠒⠒⠒⠒⣿⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠒⠒⠂
⠀⠀⢹⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⢤⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⢸⠁
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠚⠉⠀⠙⠒⠒⠋⠀⠉⠓⠒⠋⠁⠈⠓⡟
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢳⣀⣀⣀⣤⠤⠤⠤⢼⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⡸⠁
⠀⠀⠀⠀⠱⣄⣠⠤⠖⠚⠉⢯⠀⠀⠀⠀⠀⠀⢸⠖⠋⠙⠲⠶⠚⠉⠓⠶⠶⠋⠉⠲⡾⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⣄⠀⠀⠀⢸⣤⠴⠛⠦⣤⣤⠞⠓⢤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠈⠣⡀⠀⢸⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠚⠒⠒⠚⠋⠉

⡆⢢⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⡔
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠂⡆⢸⠀⡜⡄⡮⢅⠀⠀⠨⠀⠀⠪⡀⢹⠀⡅⡄⡎⠈⡂⡧⠁⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡉⠳⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡾⠯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠞⢉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⢸⠀⠀⠐⠊⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠽⠷⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢾⣄⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠂⠀⠀⡇⡿⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⣄⣠⡧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢲⢄⡀⠀⠀⠀⠀⢀⡴⠊⠓⢤⡀⠀⠀⠀⠀⢀⡴⠊⠩⣲⢄⡀
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⠁⠍⠲⢄⣠⠞⠁⠀⠀⠈⠃⢉⠲⣄⣀⠔⠉⠀⠀⠀⠀⠲⠙⢦⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⢧⣀⠀⠀⠀⠀⠀⠀⢀⡠⠧⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢀⡠⠖⠉⠀⠐⠮⢓⢤⡀⢀⡠⠖⠉⠀⠐⠢⢙⡢⣄⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠈⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⣀⠴⠚⠁⠀⠉⠲⢤⣀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⣤⠈⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠑⠉⠗⠘⡏⠀⠀⠀⠀⠀⠀⠀⠈⠋⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣬⠴⡤
⠀⡀⢦⣤⣴⠶⡖⠚⠂⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠐⢳⠃⠀⠀⠀⠀⠀⢠⠀⠞⠛⠛⡉⠉⡄⠁⠀⠀⠀⠀⠀⠀⣀⡠⢶⣩⣾⢛⠞
⢨⡄⠀⣺⡀⢀⣇⣀⡠⠃⠀⠀⠀⠀⠈⠃⢤⡀⡠⣠⡴⠋⠀⠀⠀⠀⠀⠀⡴⠚⠳⡖⠖⠓⢺⠛⢹⠀⠀⠀⠀⠀⢸⣩⣷⠿⣯⡙⠃
⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠿⠤⠤⠼⠖⠚⠁⠀⠀⠀⠀⠞⠋⣹⠗⠉


⢰⠒⠒⠒⠒⠢⠤⠤⠤⡄⠀⠀⠀⠀⠀⢠⣶⣆⡀⢁⣐⣢⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⣖⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⠀⠁⣀⠀⠀⢀⣾⠇⡇⠀⠀⠀⠀⠀⢸⡁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⠀⠉⠙⣎⡇⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢲
⢸⣠⠟⠉⠳⣤⠟⠁⠀⡇⠀⠀⠀⠀⠀⢸⠉⠀⣴⡄⢸⣏⠀⠀⠀⠀⠀⠀⢰⣀⠀⢀⣴⠀⠀⠘⢻⡀⠀⠀⠀⠀⣛⣿⣟⣿⣛⢿⣿⣛⣷
⠸⣤⣦⣤⣄⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠓⣄⣙⣃⣼⣿⠀⠀⠀⠀⠀⠀⠀⠙⢳⣿⡃⠀⠀⠀⡸⠁⠀⠀⠀⠀⣴⣟⢒⣶⣿⣾⣶⣿⡇
⠀⠀⠈⠉⠉⠛⠛⠿⠟⠁⠀⠀⠀⠀⠀⠘⠶⠷⣾⣿⠿⠟⠀⠀⠀⠀⠀⠀⠶⠖⠋⠈⠙⠷⠖⠊⠁⠀⠀⠀⠀⠀⠹⠯⠥⠾⠶⠾⠷⠼⡦
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁

⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⡤⣤⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠒⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⢋⣡⠺⡋⠗⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠻⡉⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠈⠁⠀⣧
⠀⢶⡀⠀⢴⡆⠀⢀⣤⠀⠀⠀⠀⠀⢸⡷⢎⣭⠄⠛⡅⡇⣀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠙⢢⣼⣧⡄⠀⠀⠀⠀⠀⠘⡁⢾⠁⠀⠐⠛⠓⣿
⠀⠀⢱⣤⣿⣴⣤⣾⠁⠀⠀⠀⠀⠀⠈⡛⠣⢅⣢⡀⢿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⠝⠻⣄⠀⠀⠀⢠⡏
⠀⠘⠚⠻⠿⡿⠿⠓⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠿⠛⠿⠿⠿


⢀⠀⠠⡠⠒⢶⠲⡤⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡛⢷⣠⠄
⢸⣿⣶⣬⣽⣿⣾⣶⣾⡇⠀⠀⠀⠀⠈⢻⠯⣙⣛⠛⠟⡿⠃⠀⠀⠀⠀⠀⢀⠀⠀⢠⣘⢀⣼⠄⠀⠀⠀⠀⠀⠀⠀⢠⠼⢷⣿⠤⠶⢤⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⠱⡂⠀⠈⡭⠳⡼⠂⠀⠀⠀⠀⢙⠇⢀⣮⢠⠀⣰⢀⣴⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇
⠈⠻⠿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠈⣀⡤⠡⡍⡐⢘⣣⡀⠀⠀⠀⠀⠀⠈⠚⣏⢻⣼⢸⣿⣋⠝⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠻⠏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠐⢄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣂⣀⠀⠀⠀⠟⠛⠛⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⠤⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣧⣈⡡⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠼⠛⠋⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⠀⠀⠀⠀⠀⢸⡥⠁⠀⠀⠀⠀⡠⠖⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠎⠀⠐⡤⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠓⠀⠀⠛⠛⠶⣤⡀⠀⠘⣇⠀⠀⠀⡌⢀⣵⣤⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠙⣆⠀⠀⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢦⡀⠈⢳⡄⢠⡏⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠿⠀⠀⠀⠀⢀⣀⡤⠖⠋⠛⠋⠓⠦⠒⠒⠒⠚⠻⣶⠟⢀⡼⠀⠀⠈⠻⡌⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠉⠉⠉⢹⠃⠀⠀⠀⠄⠀⠀⠐⠂⠀⠀⠒⠁⣠⡞⣷⠶⣄⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠈⠓⢡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠻⢿⣄⣽
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠻⣧⡀
⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢢⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣷⡀
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠤⠠⠀⠘⣧
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡐⢆⠀⢠⠀⠈⠁⠘⠒⠄⠀⠀⢹⡆
⢸⠇⠀⠀⠀⠀⢀⠃⠃⡜⢱⠀⠜⠁⠐⣰⠚⠢⣐⠀⡶⠖⢠⠓⠒⣦⡆⠔⠀⣀⠴⡆⠀⠀⠀⠈⣧
⣿⠀⠀⠀⠀⠀⢸⠀⠠⠇⠈⢠⢠⠒⡄⣼⠀⣀⠙⠶⣠⠈⠀⠀⠅⠀⠀⠱⡄⢀⠔⠁⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⡠⡄⢀⠘⠐⠄⠃⠄⠀⠁⠑⡄⠈⠀⠘⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢿⠀⠀⠀⠀⠀⠀⢆⣢⢂⠘⠀⢄⡀⣠⠂⣄⡄⠀⠈⠄⣀⠀⣀⠉⢀⠀⠀⡇⠇⠀⠀⠀⠀⠀⢸⠇
⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⢠⡏
⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⣀⣀⣀⣀⣀⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠟⠃⠉⠙⠂⣤⡾⠋⠉⠉⠓⠂⣴⣾⠟⠉⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢀⣠⣿⣀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⠈⠉⢲⣶⠟⠉⠀⠈⠛⢢⡞⠋⠁⠀⠁⣰⣴⣿⣧⣄⡀⣤⣻⢸⣾⠟⠋⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⢿⠿⡟⠉⠁⠉⠈⠺⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⡀⠀⠀⠀⣠⣼⣧⣀⠀⠀⠀⣠⣼⣄⡀⠀⠀⠀⢀⣾⣆⠀⠀⠔⠀⣠⣤⡀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢰⡿⠏⠁⠀⠀⠙⠰⡟⠉⠀⠀⠉⠃⣴⡿⠏⠁⠈⠉⠒⣶⡾⠏⠁⠉⠙⠒⣾⡿⠋⠈⠉⠓⠀⣴⠟⠉⠉⠉⠓⠄
⠀⠀⠀⠀⠀⣸⠃⢴⡆⣸⣠⠀⠀⣀⣤⡂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⡯⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠂⠀⠁⠋⠉⠘⠻⢿⣿⣿⣷⢀⣠⣽⣀⠀⠀⠀⢀⣠⣗⣀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⣀⣼⣇⠀⠀⠀⠀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⠀⠘⠉⢹⣿⡿⠉⠀⠈⠉⠀⣾⠛⠁⠀⠈⠓⢰⣾⠟⠁⠀⠉⠑⣶⡾⠟⠁⠈⠉⠂⣶⡿⠋⠁⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢀⣤⣼⣇⣀⠀⠀⢀⣠⣶⣇⡀⠀⠀⠀⣠⣬⣃⡀⠀⠀⢀⣠⣿⣀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⠁⣶⡿⠋⠀⠀⠉⠁⣶⡿⠋⠁⠈⠙⢁⣾⠟⠁⠀⠈⠙⢲⡶⠿⠋⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⣶⣽⣄⡀⠀⠀⣠⡈⠁⠀⢀⠠⡾⠿⢻⣧⡀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠁⠀⠀⠉⢱⡟⠋⠀⢀⡐⢮⡓⠀⠀⠈⠈⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠛⠂⢣⡀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠤⠄⠤⠠⡤⠀⠄⣤⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢸⣗⣻⡄⣸⠃⢃⠀⣟⠘⣠⣍⠛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠄⢏⣶⠶⣄⠀⠀⢀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠻⠧⠜⣴⡟⢷⡀⠀⠀⣴⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡹
⠀⠈⠿⠶⠏⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⠀⠀⣴⣿⣷⡹⠷⠞⠀⠀⠀⠙⣺⠟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁
⠀⠀⡾⠋⠀⢀⢀⢠⣞⠁⣡⠀⠀⠀⠀⠀⠀⠙⠿⠟⠽⠟⠁⢀⣀⡀⣾⠉⢠⡄⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠠⡟⢛⣧⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠙⣿⠌⠛⠊⢼⡟⠻⡆
⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠛⠈⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡈⢈⢘⢣⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣁⡀
⠀⠀⠀⠰⡀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣠⡀⢺⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠼⠚⠛⢊⠩⠤⠀⠀⠀⠠⠤⢸
⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣞⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⠛⠿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡴⠄⠀⠀⢠⠀⠀⠀⠀⠠⠤⢤⣀⡀⠀⠀⠀⢀⡠⠄⠸⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠶⠶⠶⠒⠒⠒⠶⣿
⠀⠀⠀⠀⠀⢸⡟⢷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣤⣄⡀⠀⠀⠉⡤⠆⠀⠀⠀⡀⢈⣻⡴⠃⠁⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⡐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠑⠿⠀⠀⣀⣂⣀⠀⠐⠁⠁
⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠐
⠀⠀⠀⠀⢥⡀⠀⠀⢿⣗⡀⠀⡀⠀⠀⠀⠐⣶⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣠⠇
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠙⠾⠁⢿⠀⠀⠈⠉⠹⠶⡔⠋⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠂⢤⡼⣴⠀⠀⠀⠈⣉⢿⣿⣛⣟⠛⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢷⠃⠀⠀⠀⠀⠀⣸⠙⢱⡪⡇
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣯⡀⠀⠀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠋⠉⠉⠀⠀⠉⠉⠙⠛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠶⠶⠤⢤⣤⣤⣤⣤⣤⡤⠤⠤⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣷⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⠛⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉⠉⠉⠉⠉⠉⣹⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⠙⠂⣻⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠶⠞⠃⠐⠒⠒⠒⠒⠚⠿⣤⡀
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡀⠀⠀⢰⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡏⢳⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⢀⣀⣸⡟⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⠀⠘⢻⡀
⠀⠀⣀⣸⣯⠉⠉⠳⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁
⣴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠓⣲⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠋⠉
⠙⠶⠦⠴⠶⠶⠶⠶⠦⠤⣤⡄⠀⠀⠀⢀⣼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠀⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡟⣧⣏⣴⢲⡆⣼⢃⡶⣰⢂⡶⠲⣴⢲⡖⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡻⠛⠷⠺⠗⠿⠞⠷⠻⠾⠇⠀⠿⠾⠧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣧⡇⣤⡄⣴⢀⡤⣄⡄⣤⢠⠤⣤⠦⣤⡤⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠸⠸⠛⠧⠘⠾⠛⠖⠙⠗⠷⠟⠀⠻⠔⠿⠐⠾⠃
⠀⠀⠀⠀⠀⣤⣤⡄⠀⣛⣛⣓⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠹⢫⣶⣿⣿⣿⣿⣿⣦⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⡄
⠀⠀⠀⢀⣤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠛⢿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⠋⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⣀⢀⡀⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣤⠻⣿⣿⣿⣿⣿⣿⡿⢃⡀⠀⠀⠀⠀⢄⣿⣱⣿⣿⡷⣯⣽⡿⣾⣽⣷⣼⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠿⠷⠈⠙⣛⣛⡛⠉⠴⠿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠻⡟⢻⠿⠿⠿⠿⡟⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡿⣿⡿⠿⡿⢿⡿⡿⡿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⢻⣥⣳⣾⡿⡿⣷⣞⢫⣭⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⢿⣃⢯⢽⢿⡿⠭⡽⢟⡲⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠚⠑⠛⠛⠓⠛⠛⠒⠚⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣟⣒⠀⠙⢳⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠻⠶⣶⣄⣈⠙⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀⡈⠛⠳⢦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢧⣤⣀⠀⢀⡴⠛⣩⠿⢖⣦⡄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣾⢁⡾⠁⡴⠋⣩⠖⢤⡌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣷⣼⣁⣰⠇⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣿⣶⣿⣿⡟⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣐⡏⢣⣼⠀⣷⠊⣇⣀⠀⠀⣀⣤⠴⠖⠒⣌⠙⢛⣋⡉⢰⠓⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⣦⡈⣿⣶⣿⣴⣧⣴⠋⢉⡵⢛⣡⡴⢶⣛⣫⣥⡽⡦⢤⡤⡟⠀⠐⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠦⠄⣹⣿⣿⣯⣽⣻⣿⢣⠏⣴⣿⡿⣞⣫⣭⠵⠶⠖⣿⢶⢲⡇⠀⠀⠀⠀⢤⡉⠲⡄⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠂⠼⣿⣿⣿⣿⣿⡏⣾⠀⣿⣿⣿⣯⣵⠶⣞⣛⣋⣿⣩⣹⣇⣀⡀⠀⣀⡲⣍⡳⡌⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢬⣉⣟⡽⢦⣼⠉⣏⣱⡿⣽⡜⢮⡻⢿⣿⣿⣿⣯⣭⣥⣿⣬⣼⣿⣽⣛⣿⣶⣿⡿⢛⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⣾⠁⠀⣿⠞⠙⡿⣹⣿⣿⣦⡙⠲⠌⠙⠛⠻⠷⠿⠿⠿⠿⠿⠿⠛⢛⣉⣥⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣏⠉⠓⢾⣄⡀⣸⣄⣤⣟⡄⢀⢱⣿⣿⣙⢿⣝⡳⠶⣤⣀⣀⣀⠐⠒⠒⠒⣚⣛⣻⣿⣿⣿⣿⣿⣿⣿⣫⣿⡄⣀⢠⠶⡄⣠⢤
⠀⠀⢠⠴⠶⠮⢷⣄⣵⣿⣿⣿⣿⣿⣿⣷⡞⣿⣿⣮⡙⠷⢬⣙⠓⠦⠌⠉⠉⠛⠛⢛⣛⣋⣩⣭⣶⠶⢿⣿⣿⣿⣿⣿⣿⣇⡈⠻⣄⣹⣣⣼⠞⢹
⠀⠀⠈⢲⣄⣀⣐⣿⣿⣿⢟⣱⣴⣬⣟⣿⡇⣿⣷⣌⡛⠦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠾⣛⣻⣿⣿⣿⣯⣾⡇⢽⣿⣿⢿⢿⣷⣷⡋⢉⡇
⠀⠀⢞⡉⠀⠀⠉⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢸⣿⣯⣛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠶⠿⣛⣻⣿⣿⣿⣵⣿⠇⠛⣿⣿⣿⣿⣿⣿⡚⠛⢢
⠀⠀⢠⡟⠉⠉⠉⢛⣿⣿⣿⣿⣿⣿⡟⠳⣌⢃⣻⣿⣟⡳⠦⣄⣀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠴⠶⠞⢛⣻⣿⣿⡿⣻⣿⣿⡴⠋⢛⠿⣿⣿⡿⡫⠙⢾⡁
⠀⠀⠀⠙⣻⡛⠋⠉⣉⠿⠋⢀⣿⠀⢱⡀⢨⣿⣿⣿⣿⣿⡷⢦⣬⣉⠀⠀⠀⠀⠀⠤⠴⠶⠶⠾⢟⣿⣿⣿⣿⣟⣿⣿⣿⣶⣾⠃⣠⡏⢹⡁⢹⠓⠚
⠀⠀⠀⠀⠛⠛⠒⣿⣅⣀⣠⣾⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣉⣙⠛⠒⠒⠶⠶⠶⠿⣟⣻⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣾⣿⣧⣬⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣶⣭⣭⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⣛⣛⣓⣒⡒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⣙⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⡉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄
⠀⠀⠀⠀⣠⣤⣬⣧⣄⣖⣄⠀⠀⠀⠀⠀⠲⢉⣃⠀⠀⠀⠀⠀⠀⠀⠙⠇⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠲⡒⠠
⠀⠀⢄⠀⠘⢿⣭⠛⢻⣿⣸⣂⠀⠀⠀⠀⠤⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣿⡿⠛⠈⠀⠀⠀⠂
⠀⠀⠀⠑⠲⢬⣿⡿⠿⣯⡾⢻⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⠚⢿⣏⠻⡆⢀⣀⣀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⢫⡾⣫⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡙⣿⡿⣟⡴⠚⡺⠋⠙⠓⠫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⣤⡘⢡⠈⢱⠏⢢⣼⣧⣤⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⣶⣛⠀⣟⣽⣿⡷⣤⣤⣼⡻⣟⡛⠉⢭⣻⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰⡇⢹⠛⣷⣄⠀⠀⢠⣿⣿⡪⢿⣿⡋⠀⣿⣿⣿⣿⢛⣟⠛⠦⢜⣿⣿⠿⢶⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠏⠩⣿⣷⣧⣼⡿⢿⡟⠠⢶⣿⣏⢄⣡⣿⣿⣿⠆⠛⡛⠛⢫⣾⣿⢻⣷⡞⣿⠖⠚⢏⣿⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣿⣧⠀⠹⣿⢇⠽⣷⣶⣌⣠⢞⣿⣿⡎⢛⣛⡛⢵⣿⣿⣿⣿⣞⢿⣿⡅⣿⢇⣬⣥⣚⠃⡴⡟⢁⣶⡄⡏
⠀⠀⠀⠀⠀⠘⢯⣿⣋⡍⢛⣿⣽⣶⣯⢸⡐⠿⢿⣇⣉⠟⣏⠉⠐⣿⣿⣿⣆⠻⠿⠳⠟⣩⣴⣯⣭⡑⣿⣿⣿⣿⡇⢹⢃⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣌⠙⣿⠇⠁⣒⡊⣃⣤⣴⣿⣷⠘⠿⠭⠽⠋⣶⣾⣷⡌⣿⠿⣿⣿⡧⠻⠭⣿⠟⣋⣀⡉⠛⡥⣒⣰⣦⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢯⣈⣽⣧⣴⣿⣿⣿⡎⢛⣛⡘⢉⠐⣿⣶⣦⡰⣿⣏⣿⢋⣨⣙⡛⢉⢀⣿⣷⣦⢰⣿⣿⣿⡄⠷⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⡿⠃⠣⠄⠛⠇⣧⡿⣿⡆⢴⣻⣿⠿⠃⢤⣤⡐⡤⣿⠿⣿⠈⢬⣌⣝⡿⢈⡛⠿⢛⣴⣤⣭⡉⣴⣾⣶⣄⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣿⣧⢰⢦⠑⣈⠋⣛⠃⡠⢤⣄⠰⣾⣿⣟⠷⠙⡰⡁⢠⢾⣷⣦⡀⢸⣿⣿⣷⢸⢟⣻⣿⡇⢿⣿⣿⡟⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⠻⡿⢀⣭⠘⠬⠗⠐⠃⡀⠨⠽⠀⢈⡉⠁⢘⡆⢀⣥⣜⠀⠌⣿⢃⡀⠈⢘⣡⣬⡉⠙⣭⣤⠈⣭⣿⣶⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⣄⠀⠀⠐⠚⢡⢴⡄⠀⠠⠝⠀⠀⡄⠈⠀⣲⣄⠀⢀⣨⡿⠀⣶⣶⠘⠃⠾⣻⣽⣿⡗⣀⣊⠁⣼⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢶⣦⣞⣼⠆⠈⢛⠃⠀⢀⣄⠀⠘⡃⠀⠀⠻⠿⠀⣠⣥⣄⠀⠠⠰⢶⡆⠀⠤⣭⠉⡄⣸⣿⡇⣨⣷⣞⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⣿⠶⣤⠀⠋⣉⠇⣀⣛⠁⠀⠈⠻⡇⠀⢰⣶⢸⠙⠛⢿⡇⠀⠀⠈⠁⠀⢰⣤⠀⣩⣍⠋⠌⠙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⡿⢿⣷⡤⡀⣿⢃⣀⣀⠛⣃⠀⢨⣅⡀⢉⣠⣏⣁⠂⢟⣿⠆⠂⣠⣟⢰⣈⣻⠯⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣿⣿⣿⣟⣻⣶⡏⢛⣿⣾⡁⠀⢸⣿⡷⣭⠵⠿⠛⠙⠈⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠛⠟⠛⠛⠛⠋⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡷⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠲⢄⡀⠀⠀⣠⠤⠒⠂⠀⠒⠀⠤⣀⠀⠀⡠⠊⠀⠀⠀⠀⠠⠀⠀⠢⡀⢁⠀⡇⠀⠀⠂⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄
⠀⠀⠤⠄⣀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠴⠖⠂⠀⠀⠀⠀⠀⠀⠁⠀⢆⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈
⠀⠀⠉⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⡠⠀⢳⡀⠀⠀⠀⠀⠀⠈⠀⢀⠞⠀⢤⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⢄⣀⣀⣀⡠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠒⠒⠐⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡀⢀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⢀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⢀⠊⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⠀⠀⠀⠄⡀⠀⠤⠔⠂⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠁⠠⣄⡀⠂⠀⢰⠀⢀⡀⠐
⠀⠀⠀⠀⠀⢖⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣠⣷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣾⡛⢦⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣀⣹⠏⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠉⠉⢦⡀⣀⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡰⠞⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣶⡄⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⢯⠶⢛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⣡⣄⣠⡖
⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⠞⠻⣏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⣻⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⡞⡿⠉⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠦⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣠⠴⠖⢛⣛⣛⣍⣉⣍⣉⠭⠭⠭⠭⠽⠿⠯⠤⠭⠭⠭⠭⠭⠭⠭⠵⠶⠶⠶⠶⠶⠶⠶⠞⢾⣿⣗⠶⣤⡀
⣰⠋⣿⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠁⠙⡆
⢱⡄⠈⠛⠲⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠶⠶⠖⠒⠛⠋⠉⠀⠀⠀⠀⠱
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⡇⠀⠀⠀⢀⠴⢦⠀⠀⡇⠀⢍⠀⣠⠎⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⢠⠞⠛⣶
⢸⠃⠀⠀⠀⣼⠆⠘⠦⠞⠀⠀⠈⠛⠁⠀⠀⠀⡇⠀⠀⠀⡴⠚⠛⠲⣄⠀⠀⠀⠀⠀⢠⠁⠀⠘⡇⠀⠀⢀⡄⢀⠜
⡞⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠀⣸⠀⠀⠀⠀⢀⣇⣀⣀⣀⣷⡤⠴⠞⠛⢣
⡇⠀⠀⠀⡸⠛⠓⠲⠖⠒⠒⠒⠒⠒⠒⠒⠂⢸⡇⠀⠀⢸⠓⠒⠒⠛⠉⠛⢳⡀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠂
⠘⣦⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⣿⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠁⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⢸⡄⣠⣤⡤⠤⠖⠚⠉⣧
⢀⡿⠙⠛⠒⠒⠲⠶⠒⠂⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠛⠈⠉⠉⠉⠹⢦⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠘⣗⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡀⢰⠚⢳⡄⠰⠶⣄⣷⠠⡯⠁⠈⢧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠙⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠇⠘⠶⠞⠁⠀⠁⠈⠛⠀⠛⠚⣀⣈⣁⣀⣀⣀⡠⠤⠴⠶⠒⠛⠉⠰⡆
⠀⠸⢇⠀⠈⠉⠉⠉⠉⠉⠓⠒⠒⠃⠘⠀⠋⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠸⣧⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠊
⠀⠀⠀⣹⠓⠦⠤⠤⠤⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠚⠛⠓⠒⠀⠉⠉⠀⢘⡃
⠀⠀⠀⠹⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠙⢧⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠚⡏
⠀⠀⠀⠀⠀⠐⣥⢈⠉⠉⠉⠉⠉⠒⠂⠀⠀⠐⠒⠂⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠹⣷⢋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⠦⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠒⠒⠛⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣂⢔⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⢤⣤⠤⠤⠤⢤⡤⠠⠤⠤⡤⢤⠤⠤⠤⠤⠶⢶⣾⠋⠁⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠈⠐⠄⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢰⠀⢠⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⣘⣦⣠⣿⣿⣿⣦⣾⣥⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠉⠙⠛⣻⣿⣿⣿⣟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠔⣪⠞⠻⠯⠿⠛⠻⠧⢶⡛⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠴⠁⣴⠛⡶⠦⢶⣶⣾⡌⢻⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡿⠿⢾⢿⣿⡟⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢰⡏⠹⢼⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⢿⠶⠾⢿⣿⣿⠀⠸⡷⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀
⠀⠀⠀⠀⠀⠀⠈⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⣿⢿⣿⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣴⠂⡠
⠀⠀⠀⠀⠀⠀⠀⢨⡏⠳⢦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⣿⣿⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⣀⡤⠴⠖⠒⠛⠛⠉⠉⠉⠛⠓⠒⠦⢤⣀⡠⠖⠲⣄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⣢⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣌⣉⣢⠀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠲⠤⠤⠤⠴⠒⠋⠉⠁
⠀⠀⠀⣠⣖⣒⣈⠉⠉⠒⠒⠘⢆⠀⢀⣤⠶⢛⠉⠁⠉⠛⠝⢋⠝⠋⠉⠉⠻⠶⣤⣀⠀⠀⣴⡤
⠀⠀⠀⠀⠀⣀⠤⠙⠃⠀⠀⠀⠀⠳⣭⡤⠞⣫⡇⡀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠘⠋⠉⠓⠁
⠀⠀⠀⠀⠴⠕⠒⠒⠀⠒⠒⠒⠒⠒⠂⠀⠙⢿⡄⣙⠂⠀⠀⠀⠰⡎⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈

⣶⣶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣆⢻⣿⣿⣿⣿⡟⣰⣶⣶⣶⡀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡦⢙⣛⣛⡋⢼⣿⣿⣿⣿⣿⠄⣀⣀⣀⠠⣿⣿⣿⣿⣿⡧⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣡⣿⣿⣿⣿⣌⢿⣿⣿⣿⢏⣼⣿⣿⣿⣧⡹⣿⣿⣿⡿⠡⢿⣿⣿⣟⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⢻⣿⣿⣿⣿⡟⣠⣶⣶⣦⡘⣿⣿⣿⣿⣿⢃⣴⣶⣶⠄⠲⣛⣿⣷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⢛⣛⣛⠛⢴⣿⣿⣿⣿⣷⠜⣛⣛⠛⠃⡞⠛⢟⣷⣾⣄⡟⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣡⣿⣿⣿⣿⡌⢿⣿⣿⣿⠏⣼⣿⣿⣷⣆⠹⣟⣿⣿⣿⣿⣿⠿⢿⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⡿⣻⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⠞⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣫⠔⣋⢉⣤⣶⣷⡌⠓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠁⠀⢧⠻⠿⠛⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠾⠟⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠺⢶⠄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢥⠐⢄⠀⠀⠊⠀⠀⢠⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡄⠀⠀⠀⠀⢀⣀⣼⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡘⠃⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⡴⣫⡄⣠⣥⣤⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠆⠀⡇⠀⣠⣴⠀⠀⠀⢀⣘⠃⠿⠃⠿⡘⣓⡀⠀⠀⠀⣩⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡄⡅⠀⡫⠟⠀⠀⠀⠿⠿⠸⠿⠁⠿⠷⠹⠿⠀⠀⠀⣿⣷⢌⣭⣭⡍⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣘⣧⣊⣀⣀⠀⠀⠀⣿⣷⢸⣿⡆⣿⡗⣸⣿⠀⠀⠀⣿⣿⠸⠿⠿⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠠⠄⠀⠀⠀⠀⠈⠩⣄⢶⡆⣶⢢⡬⠁⠀⠀⠀⣿⣯⣾⣿⣿⣷⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⢁⣛⣓⢘⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⢿⣇⡞⠁⠀⠀⠀⣠⣿⣄⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⠀⠀⠀⠀⣰⣿⣿⣿⢂⣾⣷⡀⠀⠀⢿⣿⠈⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠁




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠿⠆⠀⠸⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠘⠷⣦⠀⠾⠗⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣋⣈⣀⣠⣤⣤⠞⠉⠉⠉⠉⠛⢉⠉⠉⠙⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⢀⡀⠀⠀⠸⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠈⠙⣾⡃
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⢄⠈⢷⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⡀⢀⠀⠀⣀⡀⠀⠀⠀⡄⢀⢤⠀⡔⢆⠀⡄⠀⠁⠐⠒⠀⠀⠘⣇
⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⠃⡇⡇⡇⡌⣀⠈⡸⠉⠢⡅⢸⠻⢹⠁⠬⠞⢰⠐⠤⢊⠆⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠉⠁⠃⡀⡁⠁⡏⠀⠦⡈⠳⠀⢸⢀⣒⠄⠀⠱⠰⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡄⠏⠇⠃⢃⠈⠀⠃⡄⠀⠈⢆⠀⠀⠘⠀⢠⠀⡀⡄⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠃⠀⠂⠀⠁⠈⠀⠉⠀⠀⠈⠉⠀⠉⠐⠁⠀⠙⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⣞⠄⠀⠀⢠⠃⠂⠀⠐
⠀⠀⠀⠄⠠⢄⠀⠄⠀⠀⠀⠀⠀⣠⣤⣄⢾⠀⠀⠀⢈⣎⡭⠭⣅⠁⠀⠀⠀⡐⣠⠤⠤⣄
⠀⠀⠀⠐⢄⠀⠀⢨⢂⣠⠀⢀⡞⠀⠀⠈⢣⢳⣤⣤⢻⠋⠀⠀⠈⣦⣒⣒⣒⢰⠁⠀⠀⠘⣆⣀⣀⣀
⠀⠀⠀⠀⠠⠄⠄⣿⣿⠿⣁⠀⠱⣄⣀⣠⣿⠋⠀⠈⠻⣷⣄⣀⡴⡿⠉⠀⠉⢯⢧⣤⣤⢼⡟⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠛⠎⠻⠿⠃⣠⠚⠛⠳⡽⣄⠀⠀⡴⡷⠛⠛⠳⣳⡀⠀⢀⣾⠟⠉⠉⢻⣧⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⣼⡼⠿⠿⣽⡅⠀⠀⢀⣿⠽⠿⠯⡹⡄⠀⠀⢠⣧⠟⠛⢣⡀⠀⠀⠀⢀⠜⠀⠄⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠚⢿⠀⠀⠀⢈⣟⣶⡶⣞⣏⠀⠀⠀⢹⣽⠶⠶⣿⡇⠀⠀⠀⡱⠀⢰⢶⣤⣥⠐⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣤⡀⠈⠳⠤⠤⢾⠏⠀⠀⠈⣿⢦⣤⡴⢿⠃⠀⠀⠘⡿⣦⣤⡜⠁⢤⣶⣋⣿⣯⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣻⣿⣼⠏⠃⢠⠏⠉⠉⢣⣣⣀⣀⣰⡿⠋⠉⠉⢯⢧⣀⣀⣜⡝⠁⠀⠙⢆⠈⠋⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠹⡙⠿⠁⠀⠹⡄⠀⠀⣰⡷⠛⠛⠳⣷⡀⠀⢀⣼⡗⠒⠚⢮⢧⡀⠀⢠⣾⠞⠛⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠜⠀⠀⠀⠀⠀⡹⠿⠿⡝⡅⠀⠀⢀⣿⡭⠿⠯⣿⡀⠀⠀⢠⣧⠟⠿⢯⣯⡀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣼⠁⠀⠀⢘⣜⣶⣶⣞⣞⠀⠀⠀⢹⣗⣶⣶⡻⡇⠀⠀⠀⣹⣳⣶⣾⡁⠰⢿⣷⣐⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣤⢾⠏⠀⠀⠈⢿⠦⠤⠤⣿⠃⠀⠀⠙⡝⢦⣤⡴⡽⠁⠀⠀⢱⡄⢬⣶⣿⣧⠐⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣠⠃⠂⠀⠀⠘⢆⣀⣀⣴⡟⠉⠉⠙⣿⣆⣀⣀⡞⠀⠈⠉⢰⠠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠐⢊⢧⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⡀⠀⠀⠀⡇⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡛⣙⢟⣉⠛⣻⢛⣹⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣤⡄⢈⡇⠀⣀⠚⠋⠁⢰⣦⡄⢰⡇⠁⠈⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⣶⠶⣿⡟⠁⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⢸⡇⡏⠉⠁⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠀⠀⡋⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃⠘⠃⡇⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣾⣟⣛⣿⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢀⠰⣰⢠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⡿⢯⣌⢿⡇⠀⢀⣠⣴⣿⣿⡷⠂⠀⢈⠄⠰⣣⠀⠀⠀⠐⣿⣿⡗⠀⠀⠬⢵⣿⣿⠯⠄
⠀⠀⠀⠀⠀⠀⢀⣷⣬⣯⣼⡇⠘⠿⠿⠟⠃⠀⠀⠨⡐⠠⠛⠀⠄⢂⠅⠀⠀⣿⣿⡇⠀⠀⠈⠱⢩⠑⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠛⢛⡛⠛⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠶⠟⠠⣟⣿⠀⠀⠀⢨⡅⣶⠠⠆
⠀⠀⠀⠁⣲⣶⢶⣶⣶⣶⣶⣀⠀⠀⠰⣟⡿⠀⠀⠀⡦⠴⣾⣟⣻⣶⠄⠀⠀⠈⣦⠀⠁⠀⢠⣦⣾⣷⣿⣾⣿⣶⣦
⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠛⠉⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡰⠉⢆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡍⣩⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣤⠈⠁⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣒⢂⢀⡀⠀⠈⠿⣿⡿⣿⡿⠟⠀⢸⡗⠀⡀⢺⡇⠀⠀⣶⠘⠏⠸⠂⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⣿⣷⠀⢸⠡⠀⠃⠌⡧⠀⢀⣀⣀⣀⣀⡀⠀⢿⣏⣹⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠙⠛⠁⠝⠛⠋⠀⠊⠛⠀⠀⠙⠁⠀⠸⣿⣿⣿⣿⡏⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⡄⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⣠⣀⠀⠀⢀⣠⡀⠢⣷⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠓⠀⠀⣿⠡⣦⢹⠆⠀⠀⠀⢀⣭⣭⣅⠀⠀⠀⠙⣸⣷⣤⣿⠘⠁⠿⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⡀⠀⠀⠀⢤⠤⣤⣴⠄⠀⠀⠈⠮⠉⠈⠩⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡴⡶⡶⢶⢶⣶⡶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠆⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠒⢸⠁⡄⢻⠈⣶⣂⣀⡤⠴⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⠘⣧⢹⣼⣧⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⢧⣿⢿⡟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡾⠻⠌⠈⠙⣖⣶⡂⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣤⣀⣂⣤⠠⠤⠤⣇⣀⣀⣀⣬⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⣿⣿⣿⣿⣿⣿⡿⠟⠙⠛⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⡸⠉⣹⣿⣿⡿⠀⠀⠀⠀⠀⠘⠳⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⡇⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⣞⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣠⡟⠀⣾⣿⣿⣇⠀⠀⡀⠀⠀⠐⣅⣺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠿⣎⣿⣿⣿⣿⣞⣿⣦⣿⣴⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⣀⣾⣿⢿⣿⣿⣿⡿⣿⣿⣿⣛⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣍⣱⣻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢾⣿⣷⣦⣄⠀⠀⠀⠀⠀⣀⣤⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⣠⡤⠾⠿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⠁⠈⠫⢻⡿⠀⠉⠛⢶⣶⠶⠟⠉⠙⢿⡿⠿⣿⣿⠷⣦⣤⠖⠋⡁⠀⠀⠀⢶⣮⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠷⠀⠀⢀⣨⡅⢤⣀⠀⢸⡟⠀⠀⠀⢀⣠⢄⡀⠀⠈⠁⢸⡇⠼⠋⡉⠐⠤⣌⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠂⠉⠀⠀⠀⠈⠃⣼⡇⢀⡴⠚⠉⠈⠀⠙⠐⢠⠀⢸⡇⣀⣔⡤⠰⠀⠀⢩⡌⠀⠻⣸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⡀⠀⣿⡀⠀⠀⠄⠀⠀⣁⣿⣇⠠⣇⠀⠀⠠⠨⠈⠁⢸⠀⣸⣇⢽⣂⠃⠋⠤⡖⡀⡇⣰⣠⣷⣼⣧
⠀⠀⢀⣠⡤⠶⠛⠿⠿⢿⠻⣶⣥⡘⠤⣀⣤⣶⠿⣿⣿⣭⡓⢦⣝⡤⡘⠰⢈⣠⣴⣾⣿⣿⢷⣯⣟⡿⢶⡧⠓⢃⡻⢿⣿⣿⣿⣤⣀
⠀⣴⣿⣿⣶⡀⠀⠀⠀⠀⠠⣈⠉⢻⣿⣿⣿⠇⠀⠈⠉⣥⣈⠀⠈⠙⢶⣾⢿⣻⠽⠛⠙⠛⠷⠎⠙⠻⣶⣤⣤⡶⠞⠋⠁⠀⠈⢯⣝⣻⣶⣤⡀
⢠⣿⣿⣿⣻⡇⡤⠊⠁⠀⠀⠈⠕⣾⣿⣿⠋⣤⠔⠃⠀⠒⠶⢶⣤⡀⣸⡇⢉⣤⡤⠛⢻⣲⣤⣀⠀⠈⣿⣿⡇⢠⠖⠓⠠⣄⡀⠻⣿⣿⣿⣿⢻
⣸⣿⣿⣯⠉⠠⠇⠀⠀⠀⠀⠠⠀⣿⡟⠈⠀⠇⠀⠀⡀⠐⠐⣤⣘⠃⣿⡇⡇⠀⠀⢀⢀⢈⣙⠙⣷⠀⡟⣿⡇⠠⢀⠂⠀⠀⠉⠓⡊⠙⣫⢻⡸
⣿⣿⣿⡇⠀⣘⡀⠀⠀⠀⠀⠠⣰⣿⡇⠀⠀⠆⠀⠀⡂⡦⠧⠉⢘⠇⣿⡇⠇⡀⠠⠲⠙⠮⡾⢶⣿⢸⠃⢹⣷⢸⠵⠖⠂⡐⡤⡀⡇⢀⣩⣼⣧
⠈⠙⢿⣷⣖⡈⠓⢤⣀⣤⠖⠋⡭⠉⠛⢷⣼⡲⢤⣄⡂⡯⢖⣫⣵⠾⠛⠻⣦⣗⢤⣀⢐⠗⠚⠛⠛⣉⣤⠿⠿⢮⣟⣦⣶⣇⣧⡧⠅⢾⣿⣿⣿
⠀⠀⠘⠾⣿⣿⣶⡟⠉⠠⠞⠊⠀⠀⠀⠀⠈⠛⢶⣬⣵⠾⠿⢋⣤⠤⠐⠀⡀⠙⠿⣾⣥⣤⣤⡶⠟⠉⠀⠀⠀⠀⠈⠙⢷⣧⣅⣀⣠⣷⣿⠟⠉
⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢱⡞⠛⠑⠨⠸⠘⠑⡗⣬⣷⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣟⠋
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⠀⢠⢸⠀⣆⣸⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⣷⡄⠑⠫⠴⢸⡅⡷⣻⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡘⢿⣷⣦⡀⣨⠸⣀⡧⢝⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣄⠈⠃⣿⡍⠓⢁⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣷⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠉⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⣶⣶⡶⠶⠶⠶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣶⡄⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣿⠁⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⣿⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡿⠀⠀⠀⣀⣤⣶⠿⠛⠋⠉⣉⠀⠀⣠⣾⠟⠉⠙
⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣤⣤⣄⡀⠀⠙⣿⣤⡀⠀⣿⡀⠀⣀⣼⡟⠁⢀⣴⡿⠟⠉⠀⢀⣤⣶⠿⠋⢀⣴⡿⠁
⣠⣶⠿⠛⠋⠁⢀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡈⠙⠻⠿⣿⡿⠿⠛⠉⠀⣴⡿⠋⠀⣀⣴⡾⠟⠋⠀⠀⣠⣾⠋
⠙⠿⣶⣤⣀⠀⠛⠻⠿⢶⣶⣦⣄⣀⠀⠙⢿⣦⠀⠀⣿⡇⠀⠀⠀⣸⡟⢀⣴⡾⠟⠉⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠈⠉⠛⠿⢶⣤⣻⣧⠀⣿⠀⠀⠀⢀⣿⣿⠟⠉⢀⣀⣤⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠉⢻⣿⣆⣿⠀⢀⣴⡿⠛⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠛⠛⢿⣿⣴⡿⠋
⠀⠀⣠⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢰⡿⠁⠀⠉⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⢀⣠⣴⡶⠿⠟⠛⠛⠻⠿⠷⢶⣤⣤⣀⣀⣴⣶⣶⣶⣶⣤
⠀⠘⢿⣦⡀⠀⠀⠀⠈⠙⠻⣶⣤⣀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠇⠀⠀⢸⡿
⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠈⠛⣿⣄⣀⣀⣀⣤⣤⣴⣶⡶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣿⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡶⠿⠟⠛⠛⠛⠛⠛⢻⣿⣄⣀⣀⣸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣿⣿⣿⣿⣿⣿⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣛⣛⣃⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠆⠀⢰⠸⡆⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠓⠁⠈⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⣄⣀⣀⣠⣤⣤⣿⣏⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠀⠉⠉⠉⠉⠀⠓⢾⡈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠒⠂⠀⠚⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⢀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⢸⠤⠤⠤⠤⠤⠄⠀⠀⣀⣀⢀⣀⠀⠀⣀⠀⣰⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣰⠶⡶⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠂⢊⢀⡀⠀⠢
⠀⠀⠀⠀⠀⠀⢯⡘⠟⠠⠃⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢣⡽⠳⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠉⠪⡰⠀⢠⢀
⠀⠀⠀⠀⠀⠐⠐⠁⠪⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢀⡀⢀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⡈⠍⠒⢄⠀⠀⣼⠁⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠂⠀⠤⠀⠀⠀⠀⠀⠀⠿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠒⠃⠀⠀⠀⢠⠏⠀⢺⡿⡄
⠀⠀⠀⠐⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠶⠿⡄
⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠒⠂⠂⡀⡀⠀⣰⠆⠀⠀⠀⠀⠀⣄⡀⠀⠈⠀⠀⠈⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⡟⠛⠀⠀⠀⣲⢶⢿⣦
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢾⠀⠀⠀⠀⠀⠀⡟⠛⠛⠀⠀⠀⠂⠘⠻⠛⠀⠀⠀⠀⠀⢀⢋⡴⠀⠀⠀⠀⠘⣶⠦⡿⡆
⠀⠀⠀⠀⠀⠁⠰⠄⠀⠀⠀⠀⣀⠀⡀⠀⢰⠂⠀⠀⠀⠀⠰⣧⠄⢀⡀⠀⠀⣀⣀⣤⡶⠆⠀⠀⠀⠠⠀⠘⠃⠀⠀⠀⠀⠀⢿⠆⣿⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢶⣤⠤⠤⠤⠀⠀⣠⣤⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⣇⣠⠀⠀⠀⢠⠤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣾⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⠀⢀⠀⣴⡿⠀⠀⠀⠀⠀⣘⠿⢫⠡⠴⠶⠆⢠⣠⣽⣿⣷
⠀⠀⠀⠀⠀⢀⠀⠢⠀⢠⢀⣀⠀⠤⠶⠦⠈⠆⠀⠀⠀⠀⠀⠸⣮⡀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⢰⡋⠁⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠙⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡙⣿⣿⣿⡟⣱⣿⣿⣿⣆⠀⠀⠀⠀⢀⣼⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢇⣴⣤⣴⣄⢿⣿⣿⣿⡿⢣⣶⣶⣦⡸⣿⣿⣿⣿⡟⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢙⣛⣛⡃⣾⣿⣿⣿⣿⡎⣛⣛⣛⠱⣿⣿⣿⣿⣷⢘⣛⣛⡋⢠⣽⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡌⠿⠿⠿⠏⣼⣿⣿⣿⣧⡹⠿⠿⠿⢣⣾⣿⢿⣑⡎⡶⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢣⣶⣶⣶⣆⢻⣿⣿⣿⡟⣱⣶⣶⣦⡄⣶⢶⣿⣿⣿⣷⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢿⣿⣿⣿⣿⠇⠉⠉⠉⠰⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⠖⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠻⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⡥⢚⢋⣥⣶⣦⠙⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠈⠀⢸⠘⠟⠋⣁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠋⡡

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⢀⣤⣮⣧⣤⣦⡀⠀⠀⠀⠐⠶⣷⡆⠀⠀⠀⠀⠀⠛⠭⠠⠁⠀⠀⠀⠀⠀⢀⡤⢶⣲
⠀⠀⢄⡀⢻⣷⣋⣹⣧⣷⡌⠈⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣸⡿⠟⠀⠉⢺⠂
⠀⠀⠀⠙⠛⠿⣟⣻⣿⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣮⣻⣏⠳⣠⣤⣤⣺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣯⣾⡏⠢⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⡇⡻⢟⡷⠋⣼⠁⠈⠉⠓⠄
⠀⠀⠀⠀⣠⡀⢀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢀⡴⠉⣹⣿⣦⢀⣁⣸⢠⡾⠿⠿⣧⣾
⠀⠀⠀⠀⢿⡸⠃⠀⠀⢀⠀⠀⢠⠝⢶⣶⣌⠀⠀⣸⣿⠆⣷⣿⠋⠙⣿⣿⣾⠧⠀⣈⣹⣼⣶⣦⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣿⣶⣢⣾⢿⡿⠸⠾⣿⡁⣠⣿⣿⡧⠐⡿⠟⣹⢟⡿⢶⡜⡫⠘⠾⡿⢇⠀⠀⢀
⠀⠀⠀⠀⠀⣾⣿⣾⣷⣶⡄⠙⣿⠃⢻⣶⣼⣴⣿⣿⡿⣉⣉⡉⢾⣿⡿⣿⡿⢾⣅⣽⢣⣭⣄⡊⣕⢉⣷⣷⠿
⠀⠀⠀⠀⠀⠻⣾⡥⣈⣙⠷⣽⣦⠠⠘⠻⡧⡮⠻⣯⢐⣿⡿⢿⡎⣛⣁⢫⣴⣿⣶⡄⡿⢿⣿⣿⠰⣯⣿⠿⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠳⣿⣟⠇⢤⡟⢀⣤⣤⡠⣿⡿⣿⠇⣉⣀⡈⣠⣿⣿⡧⠿⢽⡭⠛⣈⣘⠃⣵⣶⣄⢰⣯⣾⣷⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣳⠻⣿⠋⡙⢻⡗⣶⣶⣄⢊⣿⣿⣿⢙⣛⠛⣔⣿⣷⡄⣓⠛⢿⡇⢿⣿⣿⣈⡻⠿⣋⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣴⣷⣶⡀⣤⠀⠙⠹⡿⠈⢉⡉⢡⣾⣿⣷⠙⢿⠉⣡⣮⣍⠉⣶⣶⣦⢾⣿⣿⡇⣿⣿⣿⡗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⢿⠇⣩⡁⢼⠆⠘⡂⠈⡿⠈⣝⠛⢐⡆⢘⣅⡫⠙⣿⣀⠉⣙⣫⣌⠛⢻⣥⢈⣭⣭⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⡤⠂⢀⡒⢡⢲⡄⠀⠟⠀⢠⡄⠉⢲⣦⡀⢀⣹⠇⣔⡿⠙⠐⠛⢛⣿⠇⣭⡁⣾⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣶⠵⠓⠠⣯⠡⢸⣷⠀⢭⣅⠀⠸⡛⢡⣴⣶⣄⠀⠒⣿⠆⢰⡶⠀⣤⣿⢟⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣻⣇⣴⡞⠁⢺⣧⠀⢘⣿⠇⠠⠿⠘⠌⠙⡿⡀⣤⣄⢠⠊⣿⣦⣶⣦⣇⣨⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣿⣶⣿⡴⣿⣵⢶⣶⣴⠂⢸⣿⣆⣴⣾⣶⠧⠿⠟⠂⠘⠋⠚⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠾⠿⠛⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡴⠟⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠶⢶⡶⠶⣤⡀
⣾⠀⠀⠙⠲⠶⠤⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠼⠃⠀⢸⡇
⣨⡿⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢩⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠈⠹
⣿⠀⠀⠀⠀⠉⠛⠛⠓⠲⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⠾
⠘⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⡇
⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⠀⠀⠘⡏⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢦⣀⣀⡠⠋⠳⠦⠴⠚⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⢸⠉⢳⢰⠛⡆⠀⢀⡴⠒⠶⣄⠀⣤⣤⡀⠀⡴⢦⡄⢀⣤⠤⢤⡀⣀⠀⠀⢀⣤⡄⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⢸⠀⠸⠼⠀⡇⢠⡏⠀⣀⡀⠈⢧⢸⠀⠙⢄⡇⠈⡇⢸⠀⣴⣤⡷⣇⠙⠶⠊⢀⡞⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠈⡆⢠⢦⠀⢱⢸⠀⠀⢯⡽⠀⠈⣿⠀⢀⡈⠁⠀⣇⢸⠀⣉⣹⠀⠈⢳⠀⡞⠉⠀⠀⠀⠀⢸⡇
⠀⠀⢹⠀⠀⠀⠀⡇⢸⢸⠀⢸⠈⢄⠀⠀⠀⠀⣰⢻⠀⢸⠙⢆⠀⢹⢸⠀⠛⠛⠲⡄⢸⠀⢃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡆⠀⠀⠀⠘⠚⠈⠧⠼⠀⠈⠙⠲⠶⠚⠁⠈⠓⠚⠀⠀⠛⠛⠈⠦⠤⠤⠴⠃⠸⠤⠼⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦
⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠷⠀⠀⠐⠻⠿⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣇⣀⠀⠀⠀⣠⡾⠛⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⢙⣧⡀⠸⠛⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠟⠓⠚⠃⣀⣀⣀⣀⣠⠖⠛⠋⠈⠉⠀⠉⠛⠛⠋⠉⠉⠉⠙⢟⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠛⠉⠉⠉⠉⠀⠹⠀⠀⠀⠐⠒⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⢦⣿⡀⢴⡶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠒⠒⠒⠒⠂⠀⠀⠀⠘⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠻⣾⣇⢀⣿
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⠀⠀⠀⡇⠀⠈⠻⣿⣏
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠘⢿⣆
⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⠉⠉⣱⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⡆
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡹⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⡇⢀⡤⠔⢤⠀⠈⣿⡄
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡄⠀⢀⡶⡄⠀⠀⡏⠀⠙⠁⠘⠖⠢⠴⠀⠀⠸⣧
⢰⡟⠀⠀⠀⠀⠀⠀⢰⠋⡆⢰⠒⡆⢀⡔⠚⠑⡆⢠⠒⢄⠸⠀⠀⣧⡼⢄⡼⠤⠽⣄⡴⣠⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⢿
⣼⡇⠀⠀⠀⠀⠀⠀⡎⠀⡇⣘⢰⡇⡘⢀⠤⡀⢸⢸⠀⠀⠹⣆⣨⠇⢸⠀⡇⠰⠒⠛⠁⢳⡀⠉⠚⢁⠞⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁⠈⡇⡇⢸⠀⠳⢸⢸⠀⡖⢄⠈⠹⠶⠸⠄⡇⢘⣒⣦⠀⠀⢹⡆⡴⠃⠀⠀⠀⠀⠀⠀⣸
⣿⡀⠀⠀⠀⠀⠀⠀⢇⠀⡖⠆⠀⡇⢡⠈⠒⠁⢸⠈⠀⢀⠀⠱⣄⠀⠰⠀⠆⠾⠉⠁⠀⠀⠘⠃⡇⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡇⠀⠀⠀⠀⠀⠀⠘⣄⣡⢰⡀⣧⠘⢆⡀⢀⡎⠠⣇⡌⠀⠀⠘⣄⣸⠀⣇⠀⠀⢈⡇⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⢠⡟
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠶⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⢀⣠⣄⡀⠀⠀⣀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠀⢰⠋⠀⠀⠈⢱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣸⠀⠀⠀⢀⣸⡀⠀⠀⢀⠘⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠁⡞⠉⠀⠈⠁⡖⠁⠀⠀⣴⣾⣷⡤⢠⢾⢸⠟⠁⠉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢐⡄⠀⠀⠀⢀⡇⠀⠀⠀⠉⡏⠋
⠀⠀⠀⠀⣴⠞⠉⠉⠐⢤⠞⠉⠉⠒⢠⠶⠋⠉⠒⢠⡴⠞⠙⠒⢠⣴⠟⠉⠒⠀⡤⠞⠉⠒⠄
⠀⠀⠀⠀⡇⠰⡇⣧⣄⣀⣤⣄⡀⠀⢾⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠿⠿⣯⡴⠒⠢⠄⣀⡴⠒⠂⠄⣀⣴⠞⠲⠄⣀⣴⠞⠢⠄⢀⣤⠖⠂⠄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢘⠏⠀⠀⠀⠀⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠼⠧⣀⠀⣠⡴⠧⣄⠀⢀⣤⠥⣀⠀⣀⡤⠧⢄⠀⠀⣠⠼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⢸⠉⠀⠀⠀⢸⠋⠀⠀⣠⣼⡏⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣾⣀⠀⠀⣀⠈⠀⠀⠠⠿⢿⣅⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁⠀⠀⠀⡞⠁⠀⣄⢺⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⢽⡂⡯⠌⢸⠥⠁⠾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠑⠀⠈⠁⠈⠁⠈

⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣤⡀
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⢦⡀
⣿⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣠⡔⣉⠀⠀⢀⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠋⢧⠀⠀⠀⠀⠙⠛⣫⠟⠀⠈⢿⠋⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⣠⡚⡁⠀⢈⡳⣄⠀⣠⢒⣉⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⢠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⠉⣛⠝⠀⠘⢟⠋⠁⠙⢛⡩⠇⠀⠀⠀⠈⠻⡷⡿⠂⠀⣠⠃⠈⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⣴⣯⣅⡀⠀⠀⢀⣙⠺⣍⣥⢦⠆⠀⠀⠐⣟⢧⣌⢦⡀⠸⢷⡆⠠⣶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⡤⠔⠋⠀⠀⠀⣀⠻⣟⠿⠛⠋⠀⠀⠀⠀⠈⢲⣌⠙⠓⡤⠎⠀⠀⠈⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⣷⡮⠏⠀⠀⠈⢯⣷⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⢉⣶⣾⣶⠃⠀⠀⠘⢟⣋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⣥⠀⠀⠀⠀⠀⠀⠙⠫⣄⣠⡔⡷⠀⠀⠀⠀⠀⠈⠣⣴⣷⣿⠃⠀⠘⣷⣦⣿⡀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠁⣀⣴⠄⠀⠀⠀⠀⠻⣝⡻⠞⠁⠀⠀⠀⠀⠀⠀⠈⣩⠿⠁⠀⠀⠀⠀⢉⣢⡀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠛⡩⠋⠀⠀⠀⠀⠀⠀⢀⣙⡆⠀⠀⡀⣀⠀⠘⣦⣞⣻⠇⠀⠀⠀⢠⣄⡈⢻⡓⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⡄⢀⠀⢳⣤⣼⣯⡟⣄⣼⡇⡿⣧⡜⣧⠊⠀⠀⠀⠀⠀⠈⢯⡻⢦⣽⡀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⡷⢾⣴⡾⢇⢾⢷⣼⡀⠉⢹⣾⠉⠀⢱⣧⠀⠿⣿⢾⣡⣶⠃⣀⢠⠀⠀⠑⢄⠈⠃⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⢸⢸⠈⠘⠃⠀⠀⠀⠀⠀⢸⢹⠀⠀⠁⠈⠁⣰⣰⠟⣺⣤⢸⢶⡾⡷⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠻⠃⢰⣧⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⣿⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣧⣼⣤⣤⣤⣤⣤⣤⣤⡼⣥⣼⣤⣤⣤⣤⣤⣤⣤⢧⡼⣤⣤⣤⣤⣤⣤⣤⡤⠴⠞⠁
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⣀⣀⣈⣛⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣛⣉⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠨⠒⠺⡠⠈⠢⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠑⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠜⡠⢀⡠⢉⠄⠀⠀⠀⠀⠀⠠⢆⠰⠄⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠑⠄⠐⢀⠀⠀⠀⠀⠀⠈⡀⠈⠀⠁⢂⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠈⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠠⡺⡩⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⡠⠁⠀⠀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠢⠀⠡
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠰⠀⠀⠐⠄⢀⠀⠀⠀⠀⠂⠀⠀⠁⠡⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠄⡐⠀⠀⡀⠔⠀⠀⠀⠀⠀⠁⢠⡄⢀⡌⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑

⠀⠀⠀⠀⠀⠀⠠⠁⠠⠢⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠑⢄⡀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣄⠀⠀⢠⠒⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⡠⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠌⠀⠈⠆⠀⠀⠖⠁
⠀⠀⠀⠀⠀⡠⢎⢑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⠀⠀⠅⠀⠀⠀⠀⠠⠂⢸⠍⠓⠢
⠀⠀⠀⠀⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⢒⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⢄⠣⢀⠀⠢⢀⠀⢉⠆
⠀⠀⠀⠀⠀⠂⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⠄⠀⡀
⠀⠀⠀⢀⢀⡀⠂⠀⠀⠐⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠔⢂⠕⠀⠀⠀⠀⠐⡈⠂⣀⠀⢀⠄⠒⠠
⠀⠀⠀⣉⡈⡜⡈⠂⠀⠂⠀⠆⢈⣁⠀⠀⢀⠓⠘⢌⠱⢄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠉⣀⣀⡄⠀⠀⠀⠀⠈⠉⠉⢂⡡⢈⡀⠂
⠀⠀⠀⢈⠀⠀⢐⠀⠀⠀⠀⠠⢈⠌⠀⠀⠀⠀⠀⠀⠁⠔⢃⠄⠀⠀⠀⠀⠈⠳⡇⠀⠔⢃⠄
⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠁⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠆⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢘⠤⠤⠤⡎⠀⠀⠀⠀⢱⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⢠⠎⠀⠀⠀⠹⡀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠉⢆⠀⠀⠀⣰⠉⠀⠀⠑⡀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢧⠀⠀⠀⠀⡼⠑⠒⠚⢇⠀⠀⠀⠀⠄⠒⠒⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠐⠀⢾⠁⠀⠀⠀⢈⡶⠆⠄⠎⠀⠀⠀⠀⢈⡶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢓⡄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡜⠁⠀⠀⠀⠣⣀⣀⣀⡎⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⠊⠠⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢀⠏⠀⠀⠀⠳⡀⠀⠀⣠⠃⠀⠀⠀⢂⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⡵⡀⡄⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠱⡀⠀⠀⠀⠠⠋⠉⠉⠣⠀⠀⠀⠀⡰⠀⠋⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡰⡹⠿⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⡱⠤⠴⢔⠁⠀⠀⠀⢀⠆⠐⠲⠀⠀⠀⠀⠀⣼⠇⠼⠄⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⢢⣀⣀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠋⡆⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⠎⠛⠉⠹⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⢯⣂⠀⢀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣳⣾⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣰⡁⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⢆⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠻⡵⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠪⠷⠾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠁⠈⣴⠟⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡉⠠⠀⠀⣸⣧⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠵⠾⣝⢅⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠈⠑⠀⠀⣐⣒⡍⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⢎⣦⣴⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣷⡀⠀⠀⢀⢀⠞⠋⠉⠉⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⠈⠹⢷
⠀⠀⠀⠀⠴⠒⠲⡵⡂⠀⢀⣟⢁⠞⠛⠳⠾⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡅
⠀⠀⠀⠃⠀⠀⠀⠀⠉⠀⠀⠈⠃⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠈⠈
⠀⠀⠀⠀⣐⠂⠂⠃⢀⠀⠀⠂⠀⠀⠒⠂⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⢀⠀⣤⠄⣈⠓⢀
⠀⠀⠀⣾⢁⡾⢃⣼⣿⣇⠀⢀⡀⠤⠀⠀⠀⠀⣠⣴⣾⣿⣶⣄⣀⣠⣶⣿⣷⣦⣄
⠀⠀⢀⡀⠺⢡⣿⣿⣿⣿⣶⣾⣡⠄⠤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠋⠉⠁⠂⠛⠛⠫⣿⣿⣿⣯⣆⠀⠀⠀⢀⢿⣿⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠽⠐⠛⠃⢀⣤⣾⣿⣿⣾⣽⢻⣽⣾⣿⣷⣯⡟⣫⣷⣿⣿⣷⣦⡀⣤⣶⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⢿⣸⢿⣿⣿⣿⡿⢟⡻⣿⣿⣿⣿⡿⣃⠿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⢠⣶⣿⣿⣿⣾⣝⣭⣾⣿⣿⣿⣮⣟⣵⣾⣿⣿⣷⣯⢫⣷⣿⣿⣿⣾⣝⠋⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⣟⣜⡿⣿⣿⣿⡿⣫⣿⢿⣿⣿⣿⢿⣫⡿⠿⣿⢿⣿⣿⣼⣿⣿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣍⣷⣿⣿⣿⣿⣾⢹⣾⣿⣿⣿⣿⣎⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⣟⣭⣛⢿⣿⣿⢿⣻⣼⣻⢿⣿⣿⢟⣯⣝⡿⣿⣿⡿⠟⠃⠛⠿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⡎⣷⣿⣿⣿⣿⣷⣮⣾⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠿⠛⠁⠙⠻⢿⣿⠿⠋⠁⠙⠻⣿⡿⠟⠋

⠀⠀⣠⠴⠒⠛⠛⠛⠛⠛⠛⠛⢛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠦⣄
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠰⠈⠀⠈⢸⠀⠀⠂⠂⡆⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢴⠀⠂⡀⠀⠀⠀⠈⢳
⣾⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⣀⣀⣀⣀⣀⣂⣃⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣭⡭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⡄
⣿⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠀⠀⠀⣰⠊⡱⠋⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⢸⠁⠀⠀⠀⣇⠐⣅⠀⠀⠀⢰⠋⣠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠘⠦⡤⠤⢤⡘⠦⣀⠉⠳⡄⢋⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⣼⢇⠀⠀⠀⠈⠳⠤⠤⢄⠀⠈⢦⢈⡆⠀⢹⠈⡆⠀⢳⢀⡴⠋⣉⣉⣓⣤⡀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⢿⠘⢄⣀⡠⠖⠋⠙⠲⢄⡇⠀⠈⠋⠀⠀⠾⠚⠁⠀⡞⢸⠀⢘⠀⠀⠀⠉⠃⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⣄⣁⡠⠔⠒⢤⠀⠀⢁⡤⠖⠒⠒⠲⢤⡀⠠⠮⠤⠋⠀⠸⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⣄⠀⠀⠀⠀⣠⠖⠒⠀⠘⠃⢠⠏⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡀⠔⢁⠔⠋⣉⠓⢦⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⢫⠳⣄⡀⣠⠃⢀⠴⠦⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠢⠴⠃⢠⠎⠉⠙⢦⣳⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠳⢤⣉⣁⠴⢃⠔⠊⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠇⢠⣄⣀⣠⠤⠋⠀⠀⠀⠀⠙⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⣠⠒⡲⠂⠈⠓⠦⢤⡤⠴⠞⢁⠀⠀⠓⠤⠔⠚⠉⠓⢦⡀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⢀⣀⠀⠀⠀⡇⠀⡇⡰⠁⠀⡤⠶⠀⠀⣠⡀⠀⢸⠓⠦⣄⣀⡤⠚⠉⠱⡄⢧⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠈⠻⢭⣉⣉⣠⠜⠁⢳⡀⠸⡀⢀⠀⠰⡇⠱⡀⠀⠑⠒⠒⢤⡀⠀⠀⠀⢹⡞⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢱⡀⢱⠘⢦⣀⠉⠲⡌⠓⠒⠒⠲⡄⢹⠀⠀⠀⠈⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠊⣠⠏⠀⠀⠈⢙⡆⢸⠀⠀⠀⠀⡇⡼⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⣠⠞⣠⠏⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃
⣿⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠃
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠀⡃⠀⠀⠀⠀⠀⠀⠁⢸⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣀⣀⣙⣳⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣥⣤⣤⣬⣬⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣞⣋⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣉⣉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣠⣴⣶⣄⢀⣦⣌⡀⠀⠀⠠⣴⣦⣄⣤⣀⡄⠀⠀⢂⣥⡾⣿⣿⣿⣿⠗⠂⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣹⣿⣿⣿⢿⣿⠿⠿⠀⣷⣄⢈⡛⠛⠟⢋⢔⣴⡇⠸⠻⢿⣿⣯⣟⣳⣤⣤⣆⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⢻⣿⣿⣿⣿⡜⠷⡀⠻⠋⣤⣚⣿⣿⣶⡈⠿⠃⡰⠋⣸⣿⣿⣿⣯⣿⣿⡟⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠸⠿⠛⠘⠛⠛⠛⠿⠿⠃⠈⠖⠀⣸⣭⠝⣿⣿⣄⠐⠎⠑⠪⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠣⢄⡀
⠀⠀⠀⠀⡀⠄⣂⡥⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢿⡀⠀⣠⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒⡦⠌⠑⠢⡀
⠀⠀⠀⡎⠀⠀⠙⣷⣐⠠⡀⠀⠀⠀⠀⠀⠂⢀⡀⠤⠄⠀⣺⣷⣼⣿⣿⣿⣿⡇⠀⠤⠄⣀⠀⠂⠀⠀⠀⠀⠀⡠⠐⣥⣁⢀⣀⢰⢘
⠀⠀⢀⠂⠀⢰⣷⣿⣾⣿⣮⣀⣀⠂⠈⠁⠀⣠⠦⣀⣄⠀⣀⣿⡿⣿⣿⣿⣟⡀⢀⣀⡠⣦⡀⠀⠉⠀⠂⣀⣨⣼⣿⣿⣻⣿⣿⡞⡄⡄
⠀⠀⠸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⡼⢋⣶⣌⠛⡎⢉⠎⠀⣈⣙⣿⠎⢉⡞⢋⣴⣎⠻⣄⠆⠀⢇⠿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠁
⠀⠀⠘⠤⡀⠛⢿⣧⣽⣿⠿⢛⣩⣶⣶⣌⡘⠯⣿⠃⡜⠉⣿⠿⠛⠛⠻⢿⣷⡏⠹⡄⢻⠿⠓⠨⢴⣶⣶⣌⡘⠲⢿⣿⡿⠟⠂⣠⠐⠁
⠀⠀⠀⠀⠉⠑⠀⠈⠉⣴⣾⡿⠟⠋⠁⠀⠈⠑⠀⣀⡇⢠⣧⣤⠶⠿⣿⣿⣷⣄⠀⣅⡀⠀⠁⠀⠀⠈⠛⠿⣿⣷⡄⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢱⡇⣿⣤⣤⣶⣶⣿⣧⡇⣴⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡁⢸⣇⠸⣅⡉⣉⣽⣯⡝⢸⣿⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⢸⣯⡢⡙⢿⣿⣿⠟⣰⡼⢿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠘⠿⣶⣤⣩⣥⣾⠯⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡈⠙⠉⠁⠀⣠⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣴⠋⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠇⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠱⠦⣀⣯⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠘⠉⠒⠤⣄⣀⠁⠀⠠⠘⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⢀⣻⡌⢯⡑⠂⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣈⢧⠀⠊⠁⠙⢆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⠘⡀⠀⠠⠀⠘⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⢸⡀⠐⠄⢀⣀⠜⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣄⠀⠀⠀⠀⠸⡄⢀⠄⠃⣤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡤⠋⠀⠀⠈⢡
⠀⠀⠀⠈⠒⠴⠤⢄⡀⠟⠀⠀⠀⠉⢀⣀⣤⠤⠲⠄⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠤⣼⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠃⣴⠂⠀⠄⠂⢀⠀⠀⠃⠀⠀⠀⠈⠒⠒⠆⠀⡠⠃⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⢃
⠀⠀⠀⠇⠀⠀⠁⠀⠀⠈⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠙⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣨⠖⠐⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⢀⣀⣀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢻⣤⡀⠤⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠳⣤⣄⣉⡐⠒⠀⠤⠀⢀⣀⠀⠀⠀⢀⡀⠀⣀⣀⢀⣀⠀⠤⢤⣀⣀⡀⠤⠤⠐⠒⠈⠁⢀⣠⠟⡷⠶⠤⣴⣧⠄
⠀⠀⠀⠀⢀⣶⠈⡉⠀⠀⠀⠀⠉⠙⠛⠻⠤⠤⣀⣀⡀⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⠤⠄⠒⠲⠧⡍⠈⠐⠠⢀⣀⠴⠁
⠀⠀⠀⠀⠈⢿⣆⣈⡧⠄⠲⠶⠤⢤⣤⣀⠀⠀⠀⠀⠀⠈⠉⢹⡋⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣒⣶⠾⣇
⠀⠀⠀⠀⠀⠀⢙⠿⣷⣤⣀⣀⣀⠤⠔⠛⠛⠓⠦⣄⣉⠀⠀⢸⠀⣀⠤⠄⠐⢢⠬⣴⣠⡄⢀⠀⣀⡠⠔⠒⠈⠉⠉⠉⠉⠁⠘⡇⠘⢆⣀⠀⠀⠀⠑⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠇⠀⠁⠄⠀⠀⡀⠐⠀⠀⠀⠠⠀⠀⠉⠉⠛⠛⠛⠒⠓⠉⠁⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠠⡀⠂⠀⡀⠀⠀⠰⠠⡀⠀⠱⡆⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⠀⢐⠀⣈⠀⢀⡉⠀⠄⠘⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠤⡈⠀⠂⠀⠰⢤⡀⢲⡾⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠄⠀⠙⠄⠀⠘⠃⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⢿⣿⣧⢠⠀⠀⠀⠀⠘⠀⠀⠀⠠⢺⡏⠉⢹⣯⡋⠁⠀⠘
⠀⠀⠀⠀⠀⠀⢃⠀⢂⠈⠀⠀⠀⠀⠀⠘⡀⠀⢩⢁⢠⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠦⣴⣾⠏⠘⠦⣀⡀⠀⠘⠄⠀⠀⠀⠀⢁⣾⠇⠉⠋⢦
⠀⠀⠀⠀⠀⠀⠈⢆⠈⢂⠀⠀⠀⣀⠓⠀⠠⡄⠀⡄⠨⡧⢾⡦⢀⡖⠳⡄⣧⢶⣤⡉⠗⠙⢾⡇⠀⡇⠀⠀⠁⠀⠄⠐⠀⠀⡄⠀⡀⠀⠀⠊⠈⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠣⡀⠀⠀⠀⠀⠀⢣⠀⣠⣀⠃⠈⠷⠘⠧⠄⠁⠇⠘⠈⠛⠠⣄⠘⠁⢀⡇⠀⠀⡨⠀⠀⠀⢀⠊⠀⠪⡑⢢⡣⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠦⡀⠀⢀⠠⠘⠤⣌⣉⣉⣉⠉⠉⠙⠓⠒⠒⠒⠛⠓⠋⠉⠈⣉⣉⠠⠄⠀⠀⠀⢀⡴⠣⢄⡀⠀⠀⢠⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⡀⠀⢀⠀⠤⠀⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢠⠄⢤⡀⠀⠠⡴⡁⠐⣄⠈⢳⣀⡀⠊⠀⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⠷⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⣸⠀⠀⡴⢇⠀⠈⠑⡎⠉⣇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⣁⠐⠐⠂⠀⠤⠤⠀⠀⠀⠠⠤⠤⠤⠴⠈⠀⠈⠑⢦⠿⢐⠎⠀⢀⣠⣖⣶⢿⣴⣿⣍⠁⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠂⠀⠀⠀⠀⠐⠒⠚⠲⠄⠒⢲⡁⠀⢀⣰⠛⠁⠀⠘⡇⠀⠹⡦⠀⢙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⢀⠀⠀⠉⠛⡆⠉⠙⢲⡶⠘⢷⣀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠀⠀⠀⠛⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⢁⠀⠀⠀⢠⠣⠀⠂⠀⡀
⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢰⠃⠀⠀⠈⢳⢓⣒⣒⡃⡁⠀⠀⠀⢐⢀⣀⣀⣀
⠀⠀⠀⠀⡄⠀⠁⠄⡣⠀⢀⠀⠀⡼⠉⠉⠉⢮⢧⣀⣀⣰⣿⠋⠉⠈⠱⡔⠄⠤⠤⢢⠎⠀⠀⠘⢦
⠀⠀⠀⠀⠈⡁⢈⢰⣷⣾⣿⠄⠘⢧⠀⠀⠀⣼⡷⠛⠛⠳⣷⡀⠀⠀⣠⣿⠒⠒⠒⣞⣆⠀⠀⢀⣾⡞⠛⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠉⢲⣟⠷⣾⣶⠄⢈⣷⣶⣾⣻⡁⠀⠀⠀⡽⣹⠿⠿⣽⣇⠀⠀⠀⢸⣮⠿⠿⢯⣯⠀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡞⠀⠀⠀⢳⡱⣤⣤⡼⡽⠁⠀⠀⠘⣞⢦⣤⣴⢻⠃⠀⠀⠀⢻⢳⣶⣶⡞⠀⠀⠐⠀⠀⢀⠂⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀⣀⣾⠟⠉⠉⠙⣿⣆⣀⣀⣴⡿⠉⠉⠉⢧⢳⣀⣀⣠⣿⠋⠈⠁⠹⡄⠀⢀⣀⡰⡇⢂⠉⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠹⡄⠀⠀⢀⣞⡞⠛⠛⢾⣧⠀⠀⠀⣼⡷⠛⠛⠳⡿⡄⠀⠀⢠⠏⠀⣘⣽⣷⣿⢄⠐⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣦⢤⣶⡆⠀⢈⣟⣟⣏⢾⠀⠀⠀⢈⣿⣿⣿⣾⡻⡁⠀⠀⠀⡹⣹⠿⠿⣇⠀⢾⣿⡷⢿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⠦⣿⣯⣾⣁⠀⣠⠏⠀⠀⠈⢮⢧⣤⣤⢞⡞⠀⠀⠀⠱⡽⠦⠤⠾⣽⠁⠀⠀⠘⣦⢀⣁⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠂⢹⠜⠛⠁⠀⠘⣆⠀⠀⣠⣿⠏⠉⠉⠻⣷⣀⣀⣀⣼⡟⠉⠉⠙⣜⣆⣀⣀⣴⡿⠋⠉⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠃⠀⠀⡀⠀⠀⣨⠿⠿⢯⣻⡀⠀⠀⢠⢿⠞⠛⠻⣼⣄⠀⠀⠀⣼⡖⠛⠛⢮⣧⠀⠀⠀⣰⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⣳⣹⣶⣶⣻⡏⠀⠀⠀⢘⣟⣶⣶⣞⢿⠀⠀⠀⠀⣿⣹⢿⢿⡁⠠⢿⡷⣆⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⡴⡿⠃⠀⠀⠘⣿⢤⣤⡤⢿⠏⠀⠀⠈⢯⠳⣤⣤⢞⡟⠀⠀⠀⠹⡄⢠⣷⣾⣿⡔⢓⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⡀⣰⢣⠂⠀⠀⢈⢦⡀⢀⣠⣿⠏⠉⠉⠹⡷⣀⣀⣀⡼⠁⠀⠉⠁⡆⡀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠇⠀⠀⠀⠀⢨⠭⠭⠥⡻⡀⠀⠀⢀⠏⠈⠉⠉⠀⠀⠀⠀⠀⠁⠀⠑⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢠⠃⠀⠀⠀⢱⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⣠⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣀⣀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠤⠈⠃⠀⠀⠀⣿⣤⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⠇⠀⠀⡴⠉⠀⠀⠀⠀⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡀⠠⣖⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⣷⣄⣀⠜⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠼⠟⠋⠁⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠊⠀⠀⠀⠀⠀⠀⣠⠴⣾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⢻⡇⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⢀⡴⠋⢀⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣏⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠀⡔⠁⠸⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠉⠁⠀⠀⠉⠉⠛⠳⣦⡀⠀⠀⢻⡆⠀⠀⠀⣈⠀⣠⡿⠦⠤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢿⡄⠀⠀⠻⣄⠀⠀⣿⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣄⠀⠙⢷⡄⠉⣼⠇⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡃⣀⡀⠀⠀⠀⠀⠀⣀⣤⠶⢦⠶⠦⣄⣀⣀⣀⣀⣠⡿⣦⣀⣾⠃⢠⡟⠀⠈⠙⢻⡍⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣥⣤⣤⣤⡤⠴⠶⠶⡞⠁⠀⠀⡀⠀⠀⠀⠁⢀⠀⠀⠀⠀⣨⠟⠁⣠⡞⣁⠀⠀⠀⠀⠹⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣁⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠁⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡾⣯⣹⡏⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠻⣿⣤⡿
⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠹⣷
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡤⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡀⠀⠹⣧
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠊⢦⠎⢠⣎⣁⢸⡄⠀⢻⣇
⢀⣿⠀⠀⠀⠀⠀⠀⢀⢄⡀⢀⣀⠀⠀⣀⠤⢀⠀⢀⡀⠀⣷⠀⢀⠈⡀⢀⡄⢹⡄⢠⡟⠀⠀⠀⠀⠁⠙⠋⠀⠀⠘⣿⡀
⢸⡇⠀⠀⠀⠀⠀⠀⡝⠀⠃⠉⢸⠀⠜⠀⠀⠘⡀⡅⠈⠢⣵⠀⣭⢉⡉⣸⢉⣉⣡⡉⣀⡉⠀⣀⠈⣉⠀⠀⠀⠀⠀⢿⡇
⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠶⠆⠈⠀⠂⡎⠹⠀⡇⡇⢀⡀⠘⠲⣭⠀⡇⢨⠈⠄⣀⠀⠈⠳⡀⢀⡔⠃⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⡀⠀⠀⠂⢣⡰⠀⡇⠀⠘⠈⠢⡀⠈⠀⡇⢸⢠⠂⠚⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⣸⠇
⢿⡆⠀⠀⠀⠀⠀⠀⢠⠀⠄⠁⢰⠄⢃⠀⠀⢀⠃⢀⢀⠀⠀⠘⡄⠀⡇⢸⠈⠒⠒⠂⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⢀⡿
⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⠆⠘⠶⠂⠀⠑⠢⠊⠀⠈⠉⠀⠀⠀⠈⠛⠁⠘⠀⠰⠖⠃⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠈⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣯⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣀⣀⣀⡘⠁⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢫⣾⡟⣥⡙⣿⣿⣿⣿⣶⣤⡈⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⣵⣿⡟⣼⣿⣿⡸⣿⣿⣿⣿⣿⣿⣷⣄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡏⣼⣿⣿⣧⡹⢿⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣮⣭⡋⣘⠻⠏⣙⡻⢿⡆⣿⠿⣛⡙⣿⣯⡙⣫⣽⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢰⣿⣿⡇⢿⣿⣶⡁⣴⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣎⡛⠿⡃⡻⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⡃⣿⣿⣿⣿⣿⣿⣿⣷⣦⣵⣾⣿⣿⡇⠀⢤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⢻⣿⣿⣿⠟⣿⣿⣿⡿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⡇⣭⣾⣷⣭⣭⣵⣿⣮⣭⣭⣾⣷⣬
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠜⠿⣛⣛⣛⣫⣭⡁⣿⠟⢿⣿⣿⠟⢿⣿⣿⠟⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣭⣵⣶⣷⡜⣿⣿⣿⣿⣿⡇⣴⣿⣶⣭⣶⣿⣶⣭⣶⣿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣜⢿⣿⣿⣿⡇⣿⡿⠻⣿⣿⡿⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡻⣿⣿⡇⣴⣾⣷⣶⣶⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠈⠛⠃⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠶⠶⠶⠶⠶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣀⣀⣀⣀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣀⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠉⠉⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⠉⠉⠉⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣤⣤⣤⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⠶⠶⠶⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠄⡀⢄⡀⢄⠀⠀⠂⠀⢀⡤⠤⢤⣺⡀⠀⠀⢨⣧⠭⠭⢤⢀⠀⠀⠀⠈⡴⠶⠶⣆
⠀⠀⠀⠈⠢⡀⠌⣰⣃⣤⡀⠠⡏⠀⠀⠀⢳⣳⣶⣶⣻⡃⠀⠀⠈⣷⣁⣀⣈⢼⠁⠀⠀⢈⣇⣤⣤⣄
⠀⠀⠀⠐⠐⠂⢆⣿⣿⣛⣌⡀⠹⣤⣤⡴⣿⠃⠀⠀⠹⡷⣤⣤⠼⡟⠁⠀⠀⢳⣳⣤⣤⣾⡏⠀⠀⠈⢧
⠀⠀⠀⠀⢀⠀⠀⠛⠋⠙⠟⠁⡰⠋⠉⠙⣞⣆⣀⣀⣼⡟⠉⠉⠹⣷⣄⣀⣠⣾⠏⠉⠉⠹⣷⣀⣀⣰⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣼⡞⠛⠛⢾⣆⠀⠀⢠⣿⠞⠛⠳⣝⣄⠀⠀⣰⣷⠛⠛⠳⡄⠀⠀⠀⢠⡊⠔⠊⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢻⡀⠀⠀⢨⢯⠿⠿⢿⣏⠀⠀⠀⣸⡾⠿⠿⣽⣇⠀⠀⠀⡽⠀⢰⣻⣷⣷⣈⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⣄⣴⣶⡄⠀⢳⣲⣒⣻⡋⠀⠀⠈⣿⣳⣶⣶⢿⡁⠀⠀⢘⣿⣶⣶⣞⠐⢶⣿⣧⢿⣷⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⠦⣿⣿⣾⡛⠉⣰⠋⠈⠀⠳⡹⣤⣤⡴⡿⠁⠀⠈⢳⡷⠤⠤⢾⡞⠀⠀⠈⢧⠀⠉⠀⠉⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⢂⢹⠝⠛⠁⠀⠙⣄⢀⣀⣼⡟⠉⠉⠹⣷⣄⣀⣀⣾⠟⠉⠉⢳⣳⣀⣀⣠⣿⠋⠉⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠐⠊⠀⠎⠀⠀⠀⠀⢀⡼⠛⠛⣞⢆⠀⠀⢀⣿⠞⠛⠳⣿⡄⠀⠀⣠⣷⠛⠛⠳⣷⡀⠀⠀⡼⠁⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢾⠀⠀⠀⢈⣮⠿⠿⢯⣏⠀⠀⠀⣸⣯⠿⠿⣝⣇⠀⠀⠀⣽⡽⠿⠿⡅⠐⢿⠿⣾⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠴⢿⡃⠀⠀⠈⣿⠳⠶⠶⢿⠁⠀⠀⠘⣎⣶⣶⣞⣟⠀⠀⠀⢹⠆⢺⣿⠿⠷⠈⢍⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠤⠴⡁⠁⠀⠀⠊⠧⣤⣤⢾⡟⠀⠀⠈⢿⠦⠤⠤⠏⠀⠀⠀⠸⡐⢀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡔⠀⠀⠢⢳⣀⣀⣠⠏⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡄⠀⠀⠘⠓⡶⠀⠀⠀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠙⣶⠳⣄⠀⠀⠘⠁⠀⠀⣠⠁⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠀⠀⠀⠀⠹⣄⣋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⣄⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣆⡽⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⢀⡴⣣⢄⣀⣯⣉⠝⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢦⠈⡏⠀⣠⠴⣆⠀⠀⢀⡴⢺⠟⢻⠙⣗⢦⡀⠀⠈⢾⣡⠞⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⢾⡀⡇⢸⣡⢀⡟⠀⢠⠏⠙⡟⠓⢿⠒⢻⡏⠙⡆⠀⢸⡇⠰⣤⣤⣤⣤⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣇⡼⠋⠉⠀⠀⢸⠶⢶⡇⠀⣼⠀⠾⡷⠶⣿⠀⢸⡇⠀⣯⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠒⢒⣂⣀⣚⠛⢓⡒⠒⠂⠀⠘⣆⣀⣧⣤⣼⣤⣼⣇⣠⠇⠀⢸⡇⠠⠟⠒⠒⠛⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠈⠳⢼⣆⣾⣠⣯⠜⠃⠀⠀⠈⠳⠶⠶⠶⠶⠖⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⠶⢶⡶⢶⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡉⢿⠉⢩⠏⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡜⠀⠹⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣆⣾⡜⠁⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⠀⢸⡈⠀⣦⡀⠃⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⣰⠃⠈⢳⣀⡴⣄⠀⠀⠈⠳⡼⠁⢳⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠏⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠏⠀⠀⣾⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⣼⡿⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⠁⠀⢰⣿⣇⣀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠰⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣀⠀⣿⡏⠀⠀⣾⣟⣻⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠈⢹⣿⡏⠉⠉⠉⠙⠛⠛⢹⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠁⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣷⣦⣼⣿⡇⠀⠀⢀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠉⢹⣿⡇⠀⠀⣿⣷⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⡀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠈⣿⣆⠙⠛⠿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠰⣾⠿⠛⠋⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠓⢦⣄⡀⠀⠀⢀⡤⠞⠉⠀⠈⠙⠷⣄⡀⠀⢀⡴⠚⠁⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠈⠹⡆⡀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⠏⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡳⣤⣀⠀⠀⠀⠀⣀⡴⢋⣠⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⡾⠹⣄⡀⠀⠀⠀⠀⠀⣀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠙⠳⣭⣛⠦⠴⠛⣥⠞⠋⠀⠈⠙⠿⣿⣦⣄⣀⡤⢞⡭⠂⠒⠾⣿⣷⢦⣤⢶⣻⠟⠂⠀⠈⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⣡⡴⠋⠀⠀⠀⠀⠀⠉⢳⢀⡏⠁⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢧⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⠹⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠸⢦⡀⠀⠀⠀⠀⠀⠀⣠⠾⢀⢧⣀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠛⢮⣝⡲⣤⣀⡤⢞⣫⠖⠀⠀⢦⣝⠳⢤⣀⣤⢞⡫⠗⠛⠙⠲⣭⡳⢦⣄⣠⡴⣛⡵⠞⠉⠳⢯⣳⢦⣄⣤⠞⠋⠁
⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠈⠙⡆⢠⠞⠋⠀⠀⠀⠀⠀⠈⠛⢦⣉⡖⠋⠀⠀⠀⠀⠀⠀⠙⠳⣌⢡⠞⠁⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠇⠹⣄⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠸⣦⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⡴⢞⡥⠂⠀⢬⣝⡳⢦⣄⣠⠴⢋⡵⠞⠉⠛⢮⡙⢶⣄⣀⣠⠖⣫⠴⠛⠛⠶⣍⡓⠄⠀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠞⠋⠀⠀⠀⠀⠈⠙⠳⡌⢠⠞⠉⠀⠀⠀⠀⠀⠙⠆⠈⠉⡵⠋⠁⠀⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠘⣦⡀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠳⣤⡀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⢀⣠⠖⠋⠀⠀⠀⠀⠙⠳⢦⣤⠴⠞⠉⠀⠀⠀⠀⠀⠙⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢰⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠐⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⣡⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠲⠶⡴⣅⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣷⠟⠛⢵⣦⡈⢿⣿⡁⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠷⢠⡉⠻⣷⡝⣿⡀⣿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⢀⠙⢻⣦⡿⣿⣾⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠰⡀⠀⡁⠄⢻⣿⡟⢁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠳⠴⠾⢫⡖⠁⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⢉⣉⣁⣀⡉⠀⠘⣁⣀⣉⡉⠉⠉⠉⠀⠐⠒⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⣡⠶⢿⠋⡏⣙⣈⣏⡀⠈⠂⣍⣁⣀⣀⣀⣉⡉⠁⠲⣄⠀⠀⠈⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⢬⡛⠛⠛⣋⠉⠄⠉⡁⠀⠀⠈⠉⠉⠉⠉⠈⠙⠀⠠⡀⠇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠉⠙⠓⠀⠈⠁⠒⠂⠈⠉⠁⠀⠀⠉⠁⠀⠀⡐⠂⠉⡀⠠⢂⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⡷⣾⡇⢠⣶⠀⠀⠀⠀⣤⣄⠠⣴⣤⠀⠄⡀⡇⢐⢀⣣⡔⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡍⠀⠳⠪⣻⠀⠀⠠⠀⡿⠿⢾⠵⠶⠷⠳⠟⠛⠊⠏⠇⠁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠐⠏⠀⠀⠀⠀⡀⠀⠀⠐⠀⡗⢈⠂⠀⡐⠠⢠⠀⠀⠀⠸⢠⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⠀⠀⠀⠀⢀⣤⠀⢀⡅⢠⣿⣦⣶⢄⠀⠀⠂⠄⠀⠀⠃⡈⠀⠁⠘⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢀⣴⠟⠁⠑⠦⠶⢳⣀⡄⡀⠘⣵⠀⠀⠠⠀⡘⠀⠃⠆⠀⠰⢠⠱
⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⡾⠋⣁⠀⠄⠤⠤⣠⣾⣤⣹⢀⡤⠘⡵⡀⠀⠀⠁⠸⢰⠖⠓⢦⡘⠀⢡
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠄⠀⠈⠁⠤⠀⢀⣶⣿⣍⣸⡟⠀⠀⢀⠘⢟⣄⠀⠀⠃⡼⠀⠀⠀⠠⡆⠀⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡐⢀⡠⠤⠤⣀⠾⣷⣬⣿⢻⡇⢀⡴⠀⠀⠜⡄⠀⢀⢀⠹⠀⢦⠀⠀⠀⠠⢰
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠈⡀⠐⠀⡿⢿⣮⡿⡟⡞⡇⠀⢠⠄⡜⠜⠀⠀⠸⡘⢠⠷⣤⡕⠺⠐⠀⢺
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢂⠙⡘⠚⡻⠆⢋⡴⠄⠡⠀⡐⠁⣈⠎⠀⠀⠀⢂⠃⡌⡌⠀⠀⠇⠆⢡⡜
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠁⡰⣑⡔⠄⠈⠀⠀⠀⠘⢀⡼⠂⠀⠰⠀⠀⠈⡐⡰⠀⠀⡌⡐⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠈⠑⠖⠚⠛⢥⣤⢤⢴⠋⠀⠀⢠⠁⠂⠀⠠⢡⢡⠃⡔⠠⠡⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢂⠌⢀⠄⠡⢃⢃⠜⠐⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠨⠀⠩⢶⡬⢀⡁⠒⠠⠂⠈⠈⠀⠀⠠⠠⠂⠂⠊⠀⠁⢃⣀⣄⡾⢋⠔⡡⢊⠐⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⣀⠔⢉⠔⢛⠰⠂⠴⠦⠠⠀⠤⠠⠄⠰⠖⠀⠂⠈⡩⢊⠔⡡⠊⡀⢀⠔⢡⠎⡰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠚⠁⠔⠡⠔⠁⠐⠀⠀⢀⠔⢀⠐⡁⠈⠐⢁⠌⡔⢡⠊⠠⠂⡐⠁⠄⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠙⠿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠉⢿⣿⡿⠛⠻⣿⣿⣿⡿⢿⣿⠏⠉⠙⠻⠿⠛⢿⣿⠋⠀⠹⣿⡿⠛⠻⠿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠉⠉⠀⠀⣿⡆⠀⠀⠀⠀⠀⣾⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠈⠋⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⣀⣤⣀⢀⣠⣄⡀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣄⡀⣠⣤⣀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣭⣷⣷⣮⣹⣾⣷⡍⣵⣿⣦⠀⠀⠀⢿⣿⣿⠿⣿⣿⡿⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢟⣫⡻⡿⣟⣝⠿⢿⣣⣻⠿⠟⠀⠀⠀⠀⠉⣷⣿⣾⢹⣾⣷⣮⠁
⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠿⣟⣼⡻⠿⠋
⠀⠀⠀⣿⡟⠛⢿⡏⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠻⠋⠀⠀⠀⠀⠀⣤⣶⣮⣛⣵⣶⣽⣫⣷⣾⡝⣽⣶⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⢠⣿⡇⠀⣸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣛⡿⣿⢟⣻⢿⡿⣃⡿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠈⠿⠃⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣷⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠈⠙⠛⠁⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⡟⠉⠉⠉⠉⠉⠉⠙⡗⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⣆⡠⣴⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠛⠈⠿⡉⢿⠿⣰⠖⣠⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠀⢱⠁⠴⠟⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⢠⣿⣆⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣷⡀⠀⠀⠀⢾⣿⠿⣿⣾⠀⠀⠀⢀⣾⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⡄⠀⠀⠈⠛⠀⠘⠃⠀⠀⢀⣾⣿⣾⣿⣧

⠀⠀⠀⠀⠀⠀⢀⢄⠀⠘⠉⣡⣶⡆⠀⠀⠀⣠⢠⡄⣄⢤⡀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠑⣫⣾⣿⣿⣿⣿⡇⠀⢀⣶⣧⣭⡅⣭⡄⣶⡄⠀⠀⣀⡀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡏⣻⣿⡋⣿⡇⠀⢨⣭⣨⣭⡅⣭⡅⣭⡅⠀⠀⠹⠟⡂⢸⠀⢠⢾⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠿⠧⣿⡇⠀⠀⠛⣇⢭⡅⣯⢁⡛⠁⠀⠀⠀⠀⠈⢮⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠿⠾⠿⠿⠿⠿⠇⠀⠀⠀⠈⠈⠁⠁⠉⠀⠀⠀⠐⠒⠒⠒⠚⠃⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢀⠀⠀⠀⠀⣰⡟⣧⡀⠀⠀⣴⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⣴⣿⣧⣿⣷⡀⠀⠻⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿