Postboy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣙⡛⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠘⢧⣤⣇⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣠⠴⣒⣫⣥⡴⡾⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢲⣾⠿⠞⠟⣛⠈⢩⣅⡹⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡃⠀⠀⠒⢙⠀⢡⠴⠁⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⣅⠀⠀⠼⣇⣀⣠⠎⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡖⢚⣭⣥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠛⣷⢦⠉⢹⡆⠀⠀⠈⠉⠘⡆⠀⠀⢘⣇⠀⠀⠀⠀⢀⣀⣼⠀⢻⣒⡇
⠀⠀⠀⠀⠀⢀⣀⣶⠒⠛⣶⡤⠿⠚⢻⠀⣧⠀⠀⠀⢠⠔⣃⣤⡖⣿⡼⣶⠶⠖⠚⠉⢀⡷⠚⠉⠁
⠀⠀⠀⠀⣀⡿⣅⢹⣀⣄⢿⠒⠚⢻⣘⣧⢿⣒⠒⠶⢿⣉⡽⠻⡏⢻⣳⡼⡤⠖⠚⠋⠉⠁
⠀⠀⠀⠀⠹⣄⠘⣾⡄⣹⡼⠶⣺⠟⠉⠀⠀⠈⠉⠛⠻⣏⡳⣄⢻⣄⢻⡇⣇
⠀⠀⠀⠀⠀⠈⡷⠛⠉⢁⡴⠊⣡⣀⣠⠴⢾⡟⠂⠀⠀⠀⠉⠻⡜⣿⡌⣇⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣦⡀⢘⣯⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣹⣿⢼⣾
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣹⠉⠀⡟⢲⠘⡇⠀⠀⠀⠀⠀⠀⢸⡧⠶⢚⡟
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⢹⣲⣣⣳⣼⢘⡇⠀⠤⠶⠚⠃⠀⢸⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠉⠉⣉⣭⡶⢻⡇⠀⠀⠀⠀⠀⢠⡟⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⠶⠛⠉⠀⠀⣼⠁⠀⠀⠀⢀⡴⠿⠶⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣠⣤⡶⠛⣉⣀⣤⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⣉⣠⠟⠛⣻⠏⠁⢠⡟⢀⡾⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⣿⣀⡈⢁⣠⡼⠃⠀⠀⢿⣶⣿⣥⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠘⠛⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠉⠉⠑⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⢐⣇⢀⡀⠐⡶⠒⠻⡇⠤⠤⠤⣀⣀⣰⠁⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠀⠀⠀⠐⠚⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠉⠀⠉⠠⠾⡀
⠀⠀⠀⠴⠀⠠⣠⣌⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠴⠶⠀⠀⢰⣿⠃⠀⠀⠀⢳⠀⠄⠀⠂⡀⣒⡏
⡂⠈⠀⠀⠀⠀⠙⠛⢠⠀⠀⠀⠹⠀⠀⠀⢀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡠⠂⠙⡰⢁⣈
⡇⠀⠀⠀⠀⠀⠀⢠⡏⡰⠠⠀⡀⠀⠀⠀⠻⠤⠤⠤⠤⠤⠐⠒⠒⠚⢣⣀⠀⣀⠄⠀⠀⠀⢹⡩⠴⠚⠁
⡇⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢲⣠⠒⢴⠼⠫⠛⣩⠏⠁⠀⠀⠀⠀⠈⡇
⡇⢰⠀⠀⠀⠀⠀⠀⢸⠉⠢⣴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠒⠶⢿⡿⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀
⠀⣷⠁⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡌⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⣵
⠀⠍⠀⣀⣀⠀⠀⠀⢠⡿⠀⢀⠴⠤⢌⡙⠁⠈⣡⣵⠀⣶⠳⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⣴⢬⡥⠚⠲⠠⠄⣠⠤⢈⡵⢚⠦⣀⢀⡀
⠈⠀⠐⠒⠋⠙⠒⠠⠌⠉⠉⠁⠀⠀⠀⢣⠀⠀⠿⣤⣰⣹⣧⠈⠢⡀⠀⠀⠀⠂⠁⢀⡴⠊⠁⠂⠠⠖⠒⠓⡴⠏⡴⢡⠔⡡⠊⢸⠇⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⡗⢄⢀⡜⠈⣦⠀⣠⠖⠉⠀⠀⠀⠠⢀⣽⡶⠶⠀⠀⡴⠲⢎⣀⠔⠁⠀⢹⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢟⠙⠰⡀⠉⠁⠀⠀⠀⠀⢀⡰⡫⠁⠅⡳⢄⡠⠟⣡⡦⠬⠉⠀⠉⠳⡋⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠙⠀⢳⣄⢐⠀⠀⣀⠞⡁⠈⢀⠀⢀⠔⠁⢠⠞⢹⢀⡀⠀⠀⠀⠈⡇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⣀⠀⠘⡂⠉⠳⣌⡹⣄⠁⢡⣃⣊⡀⣀⠔⠁⠀⡨⠟⠻⢆⠀⢧⢸⠇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂⠙⠄⠀⡳⠀⠐⠢⠉⠻⠶⣤⣧⠟⠋⠀⠀⡠⠪⢀⠄⠀⠈⢧⣸⠎⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⢶⣤⣭⣤⣤⣤⣤⣤⣼⡄⠤⢯⠇⠀⢆⠀⢐⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠛⠛⠛⠛⠛⠻⡀⠀⢣⠀⠀⢆⠈⢞⠄⠂⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠙⠢⢌⠓⢤⡀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠗⢄⡈⢆⢸⢂⢂⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠉⠲⢌⡓⢄⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠐⣺⣾⡇⡆⣢⣱⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⣀⣩⠶⡙⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠭⠊⠉⣩⠞⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣄⠈⠁⣶⠀⠀⠐⠀⠀⠀⠂⠐⠀⠀⠀⠀⡔⠂⠉⠀⠀⠀⠐⢀⡔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⣁⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠶⠶⠾⠶⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠦⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠛⠛⠋⠉⠛⠛⠉⠉⠛⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠄⡀⡀⠀⠀⠀⡀⢀⠀⠀⠀⣀⢀⠀⠀⠠⠀⢠⠀⠀⠀⡀⠄⢀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢎⡉⠱⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣃⣰⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⣼⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣯⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⢭⣽⣦⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⣛⣛⣋⣉⡉⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⢼⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠟⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⡀⠀⢸⢀⣀⣀⣀⣀⣀⡀⠀⣸⡇
⠀⠀⠀⠀⢰⡿⡆⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢠⠿⠀⠀⢀⣴⡿⠋⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⢸⠃⠀⠐⠂⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⡀⢠⡴⠞⠉
⠀⠀⠀⠀⠸⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⣤⣄⣀⣀⣠⣄⣠⣴⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠈⠉⠁⠉⠉⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢱⡆⠀⠀⠀⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⡀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠐⡏⠉⠉⠉⠉⠉⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⡇⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⣤⣤⣄⢀⣤⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢸⣿⣿⣿⣿⣾⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣾⣿⣿⣿⡁⠙⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡶⠆⠀⠀⠀⣼⣿⣧⡀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⡶⠶⣿⠿⠿⢿⣿⣿⣿⣦⡀⠀⠀⠈⠀⠂⠸⠇⣼⣿⡿⣿⣻⠂⢼
⠀⠀⣇⠀⠂⠠⠀⠀⢸⣿⣿⣿⠇⢀⠀⡃⠀⠀⠀⠈⠙⣮⣍⠓⠄⠀⠀⠀⠐⢶⣾⡇⡿⠁⢸⣄⠀⢹
⠀⠀⡇⠀⠆⠀⠀⠀⠸⢿⠿⣿⢀⡟⢀⡇⠀⠀⠀⣠⣼⣿⣿⣽⣦⣴⣆⡀⠀⠘⣿⠞⠃⣀⠀⣉⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⢡⣼⣷⣄⣶⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠀⣻⡀⣼
⠀⠀⡇⠀⠀⠀⠀⢀⠤⠞⠛⠉⣀⣾⣿⣿⣿⣿⣷⡅⣿⣿⣿⡝⠛⠋⠀⠀⠀⠒⣇⠀⠀⡙⠖⠈⠓⢾
⠀⠀⡇⠀⣰⠇⣤⣶⣶⣾⡿⢻⣿⣿⠟⠻⢿⣿⡟⣿⡟⣿⡿⠷⠀⠀⠀⠀⠀⠀⠸⠀⠀⣷⡾⠀⠀⣼
⠀⠀⡏⡸⠗⠘⠻⠉⠉⠀⠀⢸⣿⣿⠀⣶⡵⣾⣭⠃⠐⠻⠃⠀⠀⠀⣀⣽⠀⠀⠀⠀⠀⠜⠁⠀⠀⢻
⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠘⣿⡆⠈⠁⠐⠉⠉⠛⠻⠛⠻⠯⡁⠛⢧⠀⢠⡄⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢸⣿⣿⡆⠀⠀⢸
⠀⠈⣇⠀⠀⠀⠀⠀⢀⣤⣴⣦⣶⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⠛⠋⣹⣷⣭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢸⠙⣿⡇⠀⠀⢸
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢏⣿⠁⠀⠀⢸
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠈⠀⠀⠀⢸
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢸
⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣩⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⡄⠠⢠⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢂⡜⠀⢤⠀⡀⠄⠐⠀⣤⣦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡾⠿⣿⣸⣹⣾⡟⠀⠸⠭⠟⠛⠛⠀⠈⡄⠀⠀⢀⠀⠠⠔⠲
⠀⠀⠀⠀⢀⠄⠀⠸⣿⣿⣿⡇⠈⠁⣀⠉⢸⠃⣀⣤⣴⣶⡄⠀⠀⠠⠒⣂⣉⣠⣶⣼⣷⠀⠄
⠀⠀⠀⠀⡌⠐⠫⠖⠀⠉⠉⠛⡀⠐⠶⠂⣨⣀⠘⠛⠉⠀⠁⠀⠀⠀⠘⠿⠟⠃⠉⠁⠀⠀⠘⡂⢲
⠀⠀⠀⠰⠀⠀⣀⣀⡀⣀⣤⢏⡟⠷⣶⡾⣻⠜⢦⡄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈
⠀⠀⢠⠃⠀⠀⠟⠛⠉⠈⢉⡀⢣⠜⢿⠓⡜⣰⡶⣤⡌⠉⠲⣄⣀⣠⣤⣶⣾⣿⣷⠀⠀⠀⠀⠀⡄⠄
⠀⠀⠀⠉⠐⠂⠀⡄⠐⠛⠋⠙⢮⣂⣿⣷⣰⠏⠐⣿⡷⢂⡆⢸⣿⣿⣿⣿⠿⠟⠋⠀⣀⣠⣤⡔⠀⠰
⠀⠀⠀⠀⠀⡟⠀⢰⠀⠀⠀⠀⠀⢍⠻⠟⠁⠤⠤⣽⣷⣼⣅⡀⠟⠋⣁⣠⠤⠖⠚⠙⠛⠃⠛⠃⠀⠀⡆
⠀⠀⠀⠀⡰⠁⠊⡹⠆⠀⠀⠀⠀⠀⠀⠈⣠⡀⠀⢸⣿⢿⠤⡈⠸⣋⣡⡏⠐⡆⠀⠀⠀⠀⠘⡂⠈⠉
⠀⠀⠀⢀⠁⠖⣄⠀⡇⠀⠀⠘⡄⠀⢐⣪⣤⣤⣶⣶⣿⣧⡓⣀⣤⠹⣿⠃⢠⡤⢴⣀⠀⠀⠀⠃
⠀⠀⢀⣾⢣⠏⠙⠛⢻⣦⣀⣴⣿⣿⣿⡿⠿⠉⠄⠈⣉⣽⠋⠈⠑⠓⣯⠀⣿⡭⠭⠒⠂⠀⣀⡸
⠀⠀⣼⣿⣎⠀⠀⠀⢠⣸⣿⣿⣿⣯⢥⣀⣸⣄⠀⣠⣬⣼⡆⡀⠀⣣⡏⠈⣭⣤⡴⠶⠿⠁
⠀⠀⣿⣿⣷⣶⣶⣤⣬⣻⡟⠁⠀⠐⠿⣿⡿⠛⠿⢿⣿⣿⣶⣶⣿⢇⡇⢠⡭⠤⡀⠀⠀⡆
⠀⠀⠸⣿⣿⠿⣿⣿⣿⡇⢤⣤⣀⣀⣀⡂⢀⣠⡤⠴⠘⣿⡏⠁⡔⠀⢃⠸⠛⠉⣁⡠⠤⠞
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣤⢿⣇⠀⠃⠀⠀⢃⡇
⠀⠀⠀⠀⠀⠐⢻⣿⣿⡟⠉⠉⠛⠉⠉⡏⠉⠉⠉⠀⠈⢻⡿⠤⠀⠂⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣧⣀⠀⣀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠻⡟⡛⢻⡻⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠄⠒⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⠠⠤⠒⠒⣒⣒⣒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⡴⢊⣡⣤⡤⠖⠂⠽⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡰⢋⡇⠀⠚⣵⡉⢢⠤⢾⡭⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣺⣄⠀⠀⠛⠓⢣⣀⡸⠓⠢⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⡉⠛⠁⢀⡄⠀⠰⣀⠁⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠀⠀⠀⠀⠑⢄⡀⠀⠈⢉⡽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠈⠉⠉⠁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⠇⠀⢀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠤⠀⠉⠉⠉⠉⠉⠉⠉⡉⢩⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠤⠁⠙⢄⠓⢄⡈⠑⠒⠖⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠈⠢⣀⠄⠳⣼⢾⠧⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠜⡋⠀⠀⠀⠌⠉⠁
⠀⠀⠀⠀⠀⣴⣉⠐⠀⣀⠜⠀⠀⠀⠀⠀⠁⠀⠀⢩⡌⠀⢰⠀⢀⡠⢆⠀⢀⡠⠄⠂⠁⣀⠀⠀⠒⠓⠀⠀⠀⠄⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢀⠞⠁⠈⠳⡄⢀⣠⡄⠀⠀⣮⢭⣄⣬⡄⡟⠀⢀⡏⠀⠎⠀⠀⠋⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡎⠀⠀⣠⠔⠉⢹⣿⣷⠀⠀⠀⠈⢉⢨⡇⠀⢀⠏⡜⠚⢦⡀⠀⢀⡠⠔⠁
⠀⠀⠀⢁⠀⠀⣧⠀⢠⣿⡟⢸⠁⠀⠈⠉⠊⡍⠀⢀⠎
⠀⠀⠀⢸⠀⠀⡇⢀⣾⡿⠀⢸⠀⠀⠀⠀⢼⡀⣠⠟⠁⠀⠁
⠀⠀⠀⠀⢂⡄⢧⣼⣿⠃⢀⢰⠀⠀⠀⢀⠇⠸⠋⢻⠀⠀⠃
⠀⠀⢀⡋⣙⠃⡖⠒⡤⣍⣉⠚⠳⢆⢠⡎⢠⢁⠀⣸⣀⣀⡔
⠀⡔⢾⣍⠙⠛⠛⠺⢣⡀⠉⢑⠢⡈⡇⢠⣿⠎⠉⠉⠀⠀⢠
⠀⣇⡀⡨⢉⣑⡒⠤⣄⡀⢙⣀⣃⣵⢀⡟⢻⠀⡄⠀⠀⠀⠈
⢈⠙⠁⠘⠳⡆⢉⡃⠀⠀⠉⠉⠀⠉⢈⠀⢸⠀⡆
⢰⢄⠀⠀⠀⠃⢨⢼⠇⠀⠀⠀⠀⡇⠸⠀⢸⠀⢁⠀⠀⠀⢀⡁
⠸⣄⡉⠒⠆⠾⠴⠾⠂⠀⠀⠀⠀⠃⢠⠀⠘⠊⠀⠑⡖⠋⢹⠄
⠀⠂⠈⠑⠠⠤⠤⠦⠄⠀⠀⠀⠀⡄⢠⠀⢨⠀⠀⠀⠇⠀⠀⠇
⠀⠈⢲⣤⣀⣀⣀⣀⡠⠀⠀⠀⠀⡤⣤⣠⠊⠀⠀⢀⡓⠒⠒⠇
⠀⠀⠀⠈⠑⠂⠭⠤⠤⠀⠀⠤⢴⠒⠉⡄⠀⠀⠀⢸⠀⠉⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠁⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⢰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢷⣦⠧⡀⠀⠀⠀⢠⠺⢴⣿⠶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠪⣵⠾⣡⠤⠔⠁⠀⠀⠀⠘⠐⠶⣏⣹⠒⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠰⠅⣀⠠⠽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡝⠢⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡇⠀⠀⠀⠑⠂⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣙⠀⠀⠤⣀⣀⣀⠀⠢
⠀⠀⠀⠀⠀⠀⣀⠴⠊⡇⡀⠀⠀⠀⠀⠈⠉⠛⡻⠷⡛⠀⠀⠀⠈⠒
⠀⠀⠀⣀⠔⠊⠀⠀⠸⠀⠘⢆⠀⠀⠀⠀⢀⣞⠁⠀⠁⠂⢘⣿⣷⣶⡄
⠀⠀⡈⠀⠀⠀⡀⠀⠁⠀⠀⡺⠆⠀⠀⠀⡎⠪⠥⠬⢆⠀⠚⠁⣠⣿⠃⠀⢀⣀⣀⣀
⠀⠀⠘⢄⠀⢰⠀⠀⢀⠐⠎⠀⠀⠀⠀⠀⠑⢈⡰⠻⠃⢀⣀⠴⡺⢫⠉⠁⣰⠀⠀⠀⠀⠀⠸⠕⠀⠀⡡
⠀⠀⠀⠈⠂⣇⠔⠈⠀⢠⣳⢦⠄⣀⣀⣀⠠⠄⢹⣶⣿⢇⠀⢠⡇⠀⠑⠊⠁⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠠⠀⣷⠀⠀⠀⠀⠀⡘⠁⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠂⠀⠀⢫⢧⡀⠀⠀⠀⢀⣴⠟⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⢣⡱⣄⠀⠐⠿⠉⠀⣰⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠋⠀⠀⠀⠀⠀⣀⡠⢵⣌⠑⠦⣄⣠⠞⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣄⠰⠬⠭⠽⠓⠋⠁⠪⢧⣄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠙⠶⣤⣀⡀⠀⠀⢀⡀⠀⠉⠳⣖⢶⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡠⠋⠀⣀⡤⠶⠚⠋⠉⠁⠉⠉⠉⠉⠉⠙⠲⢤⣈⠑⢽⣦⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣳⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣤⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠻⠿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⡿⠋⠁
⠀⠀⠀⠠⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠉⠉⠉⠙⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠈⢀⣠⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⠲⠶⠤⠤⠤⠤⠄⠀⠀⠺⣆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡐⠀⣀⠤⣔⠢⠍⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡴⢋⠑⠈⠁⠀⠀⠀⢀⠀⠀⠀⡀⠬⠉⠀⠈⠉⠉⢨⣥⣻⣤⠞⠁
⠀⠀⠀⠀⣠⠴⠋⠨⠹⡆⠀⠀⠀⠀⠀⠙⢦⡀⢻⠁⡀⠠⣐⠢⠬⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⢀⡤⠾⠀⢸⡇
⠀⢀⡴⠟⠁⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠉⢻⣧⠖⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡡⠀⢣⢸⣧⣀⡀
⣴⠏⣀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⣠⣼⡇⠀⠀⠈⢉⠙⡛⢛⠓⠒⠒⠒⠲⣏⠲⣬⠤⣤⠀⠀⢼⡇⠈⢳⡄
⠘⣧⠀⠈⠁⠐⠄⢴⠀⠀⠀⠙⣦⠀⠀⠀⣾⠁⢀⣧⠀⠀⠀⢨⢰⣿⣆⣴⠀⠀⠀⠀⢧⣼⣿⠧⠀⠀⠀⢸⠇⠀⢸⡇
⠀⠘⢧⣀⡤⢤⣀⢨⠀⠀⠀⠀⠈⢳⡄⠀⣿⠀⠀⢱⠀⠀⠀⠀⠈⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡾
⠀⠀⢈⡟⢀⠊⠉⡷⡄⠀⢀⡀⠀⠀⠙⢦⡘⢷⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣠⣄⠀⠀⠀⠀⠀⢰⡷⠴⠞
⠀⠀⣾⠀⡌⠀⡘⠀⡆⠀⠀⠉⠁⠒⠂⠤⢽⡦⠉⠓⠺⣦⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢀⡞
⠀⠘⣇⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⢀⡴⠋⠀⠀⠀⢀⣼⠷⣄⠛⠻⠿⠿⠿⢟⣉⡛⠛⠛⠛⢉⣠⠛⣷⣄
⠀⠀⢹⡄⠀⠀⠀⠀⠈⢳⣀⠇⣠⠖⠋⠀⠀⢀⣠⠶⢋⠀⠀⢫⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠸⡇⠈⠳⢦⣀
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣻⡿⢷⡄⠀⣠⡴⠛⠁⠀⠈⢧⠀⠀⢳⡀⠉⠳⠦⣀⣀⣀⣤⠶⠋⠀⢠⡟⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⣷⠤⠴⠒⠒⠉⠁⠀⠈⣷⠞⠋⠀⠀⢠⠀⠀⠀⢧⠀⠀⠱⣀⠀⠀⣌⠃⠘⣣⢄⡠⣠⣿⠀⠀⠀⠀⢡⡄⠀⠈⠻⣦
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢀⠴⡄⠀⠀⢰⡇⠀⠀⠀⠈⢣⠀⠀⠙⡶⠶⠉⠀⠀⠈⠃⠙⠛⠃⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢻⣄⠠⠤⠤⠐⠒⠁⠀⢰⠀⠀⢸⠃⠀⠀⠀⠀⠀⢱⡄⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠘⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⢔⡡⢌⠢⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣤⡀⠄⣀⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⡻⣄⢀⠕⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⡀⠀⡀⠀⢈⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⢀⣠⠴⠞⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣡⡎⠀⠉⠢⣀⣀⡀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⠀⡿⠿⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⣹⠷⠒⠒⠉⠉⠉⠑⢤⢨⠤⡴⠆⠔⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⠤⠄⣀⣀⣀⡀⠀⠀⠀⣠⠤⠤⠤⢤⣉⣻⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⡀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣽⣦⡇⠘⡇⠈⢆⠀⠀⠀⢰⣶⣾⣧⡿⠷⠟⠛⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠐⠒⠒⠒⠀⠤⠤⠤⢤⣤⣬⣭⣉⡗⠒⢻⡀⠈⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⠂⠠⡄⠠⠠⡖⠂⠉⠉⢠⣤⠗⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠈⠈⣏⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠉⠛⠉⠒⠒⠒⣒⡚⠛⣉⣛⣋⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠃⢀⣀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⣧⠀⠀⠀⢷⡀⠀⠀⢀⣀⣀⡤⠤⠖⠚⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠉⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⠤⠤⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠤⠄⠀⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠉⠈⠉⠛⠛⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠉⠁⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⣀⣀⣤⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣀⣤⣀⣀⣀⣀⠀⣀⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣻⠋⠉⠉⠉⠙⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢰⠇⠀⠀⠀⠀⠀⠘⣆⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣄⠀⣼⠀⠀⠀⣠⣄⠀⠀⢻⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣧⠬⠿⠤⠿⠶⠶⠶⠾⠷⠶⠶⠾⠶⠽⠽⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣯⣥⡤⠤⢶⡶⠖⠒⠒⠒⠒⠒⠛⠛⠒⠒⠲⣶⠶⠯⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⣿⠀⠀⠸⡇⠀⠖⠀⠀⠀⠀⠀⠀⠛⠂⠀⣿⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣸⠃⠀⠀⣤⠀⠀⠀⠀⠀⣤⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⣿⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣄⣀⡀⠀⠀⣉⠓⠋⠀⣀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠹⣦⠉⠙⣯⡿⠉⡟⢿⣭⡏⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⣠⡟⠳⣤⠟⠀⢰⡇⠀⢨⢇⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠉⢹⠟⠉⠳⡴⠛⠁⣴⠋⠀⢳⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣾⠀⠀⢀⡗⢀⡾⠳⡄⠀⠘⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡤⠾⠋⠛⠛⠉⢙⣛⣧⠀⢹⣆⣠⡟⠛⠋⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⠿⠋⡷⢻⡁⠀⠻⣤⣤⠼⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⠀⠀⠀⢀⣼⣇⣧⠈⣇⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⢉⣷⡈⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⢹⡇⠘⣆⡈⠷⣄⣀⣀⣤⠴⠚⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢠⡏⠀⣇⠀⠈⠙⠲⠦⣭⣀⣀⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠦⢤⣤⣤⣤⡾⠀⠀⢻⣤⣀⣀⣀⣀⣨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣄⣀⣀⣀⣀⣀⡿⠀⠀⠸⣥⣀⣀⣀⣀⣀⣈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⣈⠉⠭⠭⣍⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠈⠁⠀⠀⠀⠀⠀⠙⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠔⠁⠀⠀⠀⠀⠀⣀⡤⠴⠒⠲⢦⡄⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠔⠁⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠊⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠟⢻⡄⠀⠀⠀⡀⢤⣔⣲⣤⣉⠉⠛⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⣶⣺⣷⡖⠀⠀⠀⠰⢋⡽⠾⢿⡧⣤⢤⣤⣾⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠀⠀⠀⠸⣿⡇⢀⣀⢹⣧⣤⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡍⠻⣝⠳⠟⠀⠀⠀⠠⠿⢿⣯⣿⠰⠛⠓⠚⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡀⠀⠀⠀⠀⠀⠐⡇⢠⣀⡿⠃⠀⠀⣠⡄⠀⠀⠀⢁⡝⠁⣀⡀⠀⠀⠀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⢴⢦⠻⣄⠀⠐⢷⡀⠀⠙⠦⠭⣄⠀⠀⠀⠋⠻⣦⡀⠀⠘⠳⠄⠈⠙⠓⠀⠂⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢑⡵⠛⠋⢀⡀⡖⡀⠻⣖⠀⠉⡇⣿⠀⠀⠀⠀⠀⠹⣿⢷⡤⣄⣀⣀⣀⠠⠐⠒⠒⠀⢨⡇⡖⣒⣒⣒⡒⠒⠒⠒⠂⠀⠀⢠
⠀⠀⠀⠀⢀⠔⢀⡠⠀⢈⠠⠐⣂⣀⠺⡵⡜⢜⢄⠙⣦⣀⡻⠿⠒⠀⠉⣿⠀⠀⠘⢦⡙⢦⣄⡼⢻⡀⠀⠀⠀⣠⠊⢸⡗⣁⡀⢴⠃⠀⠀⣴⣷⡖⢀⡎
⠀⠀⠀⣔⠁⠀⠈⢷⡘⢄⢀⣎⠘⠫⡆⠱⡘⣌⢫⢆⠈⢷⡀⠀⠠⡟⣆⢻⠀⠀⠀⠈⠳⣤⠦⠶⠺⣧⠀⢀⠜⠁⠀⣼⠃⠀⠿⠤⠃⠀⠐⢾⣏⠁⣸⢇⣀
⠀⠀⠀⠈⠛⣦⠔⠉⠹⣎⠋⠛⠒⠀⠀⠀⠙⠌⠦⠃⠁⠀⠻⣄⠀⡁⡟⢸⣄⡀⠀⠀⠀⠈⣙⠂⢈⠁⢠⣇⣀⠔⡁⣾⢀⡤⣤⣀⠀⠀⠻⢼⠉⢠⡟⠲⣭⠙⡻
⠀⠀⢀⠠⠊⠴⠋⠒⡒⠘⢧⡀⢀⠀⠐⠒⠒⣦⠤⣄⠀⠀⠀⠙⢶⡴⡇⣀⡆⣏⢷⠒⠲⢤⡈⠉⠁⢠⠧⠈⣁⠀⢻⡏⠘⢧⡒⠉⠙⠳⣄⠀⠀⡾⠢⢞⡁⠊
⣠⣂⣁⣐⣂⣤⡴⠎⠀⢀⠜⠋⠀⠀⠀⠤⠤⣤⣤⠊⠀⠐⡈⢀⡈⠻⣆⡇⣷⠹⣾⡆⢠⣎⣹⣗⣶⡇⡆⠀⣼⡉⡉⠓⠒⠲⢽⣶⣄⠀⠈⢷⣼⠃⡴⠊⢉⠱⠖
⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⢀⠔⠀⠀⠀⠀⠺⠌⢹⠆⠀⠀⠒⠀⠄⠈⢷⣼⡆⢻⡷⠊⣽⢷⡌⠔⢿⡱⠀⣼⡙⠳⠖⠤⣄⠀⠉⠻⣆⠀⠀⢻⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⣤⢤⣭⣁⣈⡀⠀⠀⠀⠀⠁⠀⣤⠞⠉⢳⠈⢷⣤⡋⢠⣦⡄⠈⣧⠰⣮⡛⢧⣄⡀⠈⠳⢦⠀⠀⢀⡖⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡄⠀⠀⠀⠀⠀⠀⠸⢄⠝⠀⠀⣀⡴⠚⠁⠘⢧⡀⠘⣇⠈⠿⢿⣄⠹⣿⣦⠸⡆⢻⣿⣦⣀⠙⢳⣄⠀⠀⢠⠎⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣠⠶⠭⠤⡤⢤⣀⣴⡞⠉⠀⠀⠀⠀⠈⢻⡌⠁⠀⢀⠜⢉⢳⡌⢿⠀⢹⡀⢿⣷⠉⢷⡀⠀⠠⠂⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣈⣁⡰⢫⠏⣿⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⠘⠦⣜⢷⢝⢦⡀⠀⢷⠀⡡⠂⢹⡇⠀⠀⠀⠀⡰⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⣻⠁⠈⣧⠸⠘⠁⠀⠀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠉⠻⣄⠘⠋⠀⠀⣴⡷⣄⣀⠀⣴⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣧⡀⠧⠐⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠈⠳⣄⠘⢧⣀⠜⡴⠈⠛⠦⠀⣉⣄⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⢦⣍⡒⠀⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠃⠀⠀⠈⠳⣌⠋⣸⠁⠀⠀⠀⣼⡻⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣠⡴⡆⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠳⠋⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⡠⠋⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⠀⠀⠀⢰⡶⢤⣄⡀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠊⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠀⠀⠀⠀⠻⣄⠈⠙⢦⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠙⣆⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣻⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⢠⡄⡀⠀⠂⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠖⠚⠛⠛⠛⠛⠛⠛⠓⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡶⠶⠦⠤⠴⠶⠶⠖⠛⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡄⠤⠄⢒⣈⣴⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢶⣶⣾⠶⠚⠛⠋⠉⠀⠀⣨⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠉⢉⠿⠛⠒⠶⠚⠛⣙⣻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠴⠋⠀⢀⣠⣶⣾⠛⣟⣿⡟⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⡋⠀⠈⡷⢌⣉⡀⢀⣀⠏⠉⠛⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢀⣾⢯⣽⠟⠀⣠⠇⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⠛⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠉⠀⠸⠛⣿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⣀⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⣄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⢸⠇⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠳⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⣿⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⠶⠶⠶⡶⠶⠶⣶⠶⣶⣶⣶⠶⢶⠖⠚⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣟⠛⠛⠒⠶⠤⣼⠃⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣇⠀⠀⠀⠀⣿⠀⠀⢹⡾⢣⡜⡿⠀⢸⠀⠀⠀⠀⣸⢟⣧⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣿⣿⠀⠀⠀⢠⡼⠦⠀⠘⣧⡘⢸⡇⠐⠾⣄⠀⠀⣰⠏⣸⠋⠻⣦⡀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⠙⢳⣤⣀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣿⣿⠀⠀⠀⠈⢳⡄⠀⠀⢿⠀⡾⠀⠀⣠⠏⢀⡼⠋⣰⣿⠀⠀⠈⠻⢶⣤⣀⠀⠀⢹⣿⣿⡿⠗⠀⣼⠁⠙⠳⢦⣄⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠙⣦⠀⢸⣿⠃⠀⣰⢋⡴⠏⢀⡼⢻⣿⠀⠀⠀⠀⠀⠉⠛⠻⠷⠾⠟⣿⠀⠀⣰⠇⠀⠀⠀⠀⣉⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠈⢳⡈⣇⠀⣴⡷⠋⢀⡴⠋⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣰⠋⢀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⣠⣶⣿⣿⡀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢤⣽⡿⠞⠉⣠⠶⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠾⠛⠋⠁
⠀⢠⠤⢼⣿⣿⣿⣿⠿⣶⣶⡿⠒⠻⣧⠀⠀⠀⠀⣀⣤⠶⠛⠉⣠⡴⠛⠁⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡟⠀⢸⣿⣿⣿⣿⡄⠈⠉⠀⠀⠀⣿⣍⡶⠶⠛⠉⣀⣤⣶⠛⠛⠀⣶⠒⠒⠒⢂⣈⡩⢼⣿
⢸⡇⠀⠈⠿⠘⢷⡿⢿⡇⠀⠀⠀⢠⡿⣇⣠⡤⠖⠛⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿
⡿⠑⠒⠒⠒⠒⢺⡇⢸⡗⠒⠒⠚⠉⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⡇⠀⠀⠀⠀⠀⠈⠳⠞⠃⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠷⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⢛⣀⣀⣀⣀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠙⠏⠉⠉⠙⠛⣶⡀⠀⠀⢀⡾⠛⠛⠛⠛⢛⠟⠳⠶⣤⡀
⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣾⣶⣶⣾⣷⣾⣇⠀⠀⠘⠷⣷⣶⣶⣤⣶⣤⣤⣶⣾⠿⠀⠀⣀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠺⣉⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣑⠦⣄⣀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠈⠹⣶⠭⣝⣒⣶⠶⠃
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣤⠈⠑⢲⢴⠃
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠀⠀⠀⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣟⢏⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠲
⠀⠀⠀⠀⠀⡠⣾⠦⣄⡀⠘⠶⠄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⢏⡇
⠀⠀⠀⠀⣼⣿⠇⣷⠀⠹⠽⠛⢿⢿⠷⣤⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⢸⣾
⠀⠀⠀⢸⣿⣯⣀⣿⡀⠀⣀⡴⡫⠋⠀⠀⠉⠙⠓⠒⢶⠛⠉⠢⠄⠀⠈⡹⠁⠘⣿⠀⣀⣀⣀⣸⣿
⠀⠀⣴⠏⠀⠀⠀⡈⣿⣎⠵⡻⠃⠫⠁⠀⣀⠰⢢⡀⠀⠈⠉⠉⠉⠐⠊⠀⠀⣰⠋⠉⠛⠓⠒⢺⣿⠒⢻⣿⠛⠛⡟⠛⠛⠛⠛⠛⠛
⠀⢸⢻⡀⠀⠀⢠⡼⠉⣹⠻⡇⣒⡀⠉⠅⠀⠠⢫⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣾⠇⠀⢸⣿⠀⢠⠇
⠀⢸⡀⢿⣷⠒⠋⠀⢀⡏⠀⡵⠐⠀⠉⠁⠀⢲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣟⣀⣤⡶⠟⠁⠀⠀⠀⣿⠀⢸
⠀⠀⠑⠦⣤⣤⣤⠤⣾⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣥⣸⣴⠏
⣀⣀⣠⣾⣉⣉⣹⣆⣰⣟⣉⣉⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣽⣏⣙⣡⣏⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡋⢉⣉⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠳⠀⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠀⡀⠈⠁⡶⠆⠄⡀
⠀⠀⡠⠄⠤⢤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⡦⠂⢠⠀⠀⠀⠹⡆
⠀⠀⠀⠘⠻⡉⠀⡀⠉⡍⠈⠻⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠛⡿⠁⢠⠄⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠓⠀⠀⠒⠒⠒⠒⠇⠀⠀⠀⠀⠀⠀⠠⣄⠀⡦⠀⣠⠀⢠⠀⣶⡖⢀⡀⣷⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠭⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣥⡀⡄⠀⡀⠈⠁⠘⡿⠑⠻⣻⡇
⠀⠀⡆⠀⠀⢠⠀⠒⠒⠒⠂⠀⡄⠀⠀⠀⠀⠀⡰⠶⢾⣇⠑⠤⢲⠀⠉⠙⠊⠒⢤⡿⠛⠒⠘⠶⠄
⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡀⡇⠀⠀⣀⠐⠣⡀⣐⣲⡇⡹⠂⠚⠊⢀⠁⢲⣼⠟⠁⠀⣀⣤⠚⠣⡀
⠀⠀⠑⢲⣶⣾⣶⣶⡖⠐⣎⡀⠠⠝⠀⣄⣆⣠⡾⠋⠁⢈⣿⣦⣀⡀⠀⣠⡟⠙⠲⠒⠚⠉⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠈⠑⠖⠋⠀⠀⠁⠀⢠⠀⢸⡇⠀⠹⣿⣆⠈⢿⣦⣀⠀⠄⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡟⠀⠀⠀⠂⠻⣆⣈⣧⣍⠀⠈⠂⠀⣠⠞⠁
⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⣠⠗⡀⠘⠙⢻⣿⡿⠥⠚⠉
⠀⠀⠀⠸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠁⠀⢂⠈⢿⣇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠚⠀⠀⠀⠂⠘⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⢉⣉⡉⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡃⠴⠈⠂⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢄⡋⠠⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⣀⠔⠁⢀⡄⠗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣡⣍⠉⢁⠲⠢⢉⡅⢐⣠⣄⠀⠀⠀⠀⠁⡀
⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠀⢈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠉⠁⠐⠒⠀⠤⢈⡙⠠⢄⡀⠀⠀⢹⡄
⠀⡠⠊⠀⠀⠀⢠⢤⡠⢦⡄⠠⠤⢨⠆⠀⠀⠀⠀⠀⠀⢀⠔⢉⡌⠑⠲⣾⠵⠤⠤⠤⡄⠀⣤⢠⠥⠒⠬⣑⢰⡄⠂
⠺⠀⠄⠀⠀⣀⡀⠥⠙⠢⡈⠑⠖⠁⠀⠀⠀⠀⠀⠀⠀⢉⠆⠸⠃⡴⣡⣏⡶⠀⠀⢀⠀⠴⢌⠈⠀⠀⢀⠉⢘⠁
⠀⠑⢄⠀⠀⢰⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣆⠀⢦⣙⡡⠃⠀⠀⠈⢸⡟⡎⢠⠀⣤⣀⠙⠈⢧⡀
⠀⠀⠀⠑⢄⠘⢀⡠⠖⣁⠀⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡀⠃⠀⠀⠘⠂⠚⠀⡮⠺⡖⠀⡃⠰⡖⠓
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠑⠤⡀⠀⠀⠀⠉⢠⠆⠱⠒⠂⠠⠄⢳⡀⠈⠻⢍⠑⠠⠟⠀⠀⠀⢀⣀⣁⠔⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠎⢠⠁⠀⠀⠀⢀⠀⡸⠓⠦⡤⢤⣤⡤⠠⢶⠶⠛⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠀⠆⠀⠀⠀⣀⠂⠐⠦⠀⠀⡳⠒⠄⣀⣠⠋⠀⢀⠞⠁⠘⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣜⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⠑⠗⠀⢨⠁⠀⢰⠣⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢠⡝⠉⠉⠙⠂⡆⣤⠀⠀⠇⠀⢤⠃⣣⠀⠀⠀⠀⠀⠀⡤⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢢⠀⢀⡶⠸⠀⠁⠀⢸⠀⣀⡜⠀⠻⢄⠀⠀⠀⣠⠎⣠⠞⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠁⢰⡆⠖⠀⠀⡆⠀⢀⠇⠀⠀⠨⠙⣦⣜⣡⠞⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣀⡠⠄⠒⠂⠛⠐⠷⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⠈⠀⠀⢠⡇⠀⢾⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠈⠠⠄⠀⡇⠑⠂⠚⠑⡄⠀⠀⠀⠀⠀⣤⠀⠀⣘⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡉⠉⠀⠘⠛⠛⠛⠚⡿⠀⠀⠀⠀⢰⡀⠀⠀⢐⡩⠃⠀⠀⡏⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠝⠁⠐⠚⠒⠒⡞⠛⡇⠠⠤⠤⠤⠼⠣⠄⡰⠋⡁⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠤⠷⢀⢳⠀⠠⠤⠤⢼⠀⠘⠒⡙⢡⠀⡀⣤⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣄⠀⠀⠀⢸⠀⠀⣠⠁⠂⣰⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⢱⠀⠉⠉⠉⠉⠉⠁⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠤⢀⣀⣀⣀⠀⣤⠤⠃⠀⠀⠀⣆⠀⠀⠀⢀⣀⠀⣤⠼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠈⠉⠁⠀⢀⣀⡈⠉⠉⠁⢠⠾⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠉⠉⡁⠀⠀⠀⠉⠁⠐⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⣇⠐⢂⡀⠤⠀⠀⠀⠀⠈⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢒⣂⣀⣀⣀⣐⡒⠒⠒⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠋⠄⠐⠒⠒⢒⣒⣒⣒⣀⣀⣀⣀⣀⣒
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⡠⠄⠐⠈⠉⠁⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠆⠀⠀⡐⢂⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡘⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⢄⠐⠒⠒⠠⠤⡄⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠣⡀⠀⠀⢀⠈⠐
⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠬⠵⠶⡶⠾⢷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠀⠁⡀⠂⠀⠀⠠⣄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠰⡀⠁⠀⠀⠀⠀⠀⠂⠀⡀⠃⠀⠐⢁⠄⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠉⠀⠠⣤⠄⣀⠁⡌
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⣠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠐⠀⠑⠂⠐⣀⠀⠈⠑⢄⠈
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠈⢳⠒⠤⠀⠐⡀⠀⠀⠀⠀⡄⠈⠢⣀⠀⠀⢀⠀⠂⠁⠘⢀⡀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠉⠉⠈⠁⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠀⠠⠂⠀⠘⢦⠀⠀⢠⣁⠀⠀⠈⠑⠀⠀⠢⢄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⢤⠄⠐⠀⠁⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠘⡀⠢⢄⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠠⢄⡘⡄⠀⠀⠁⠀⠈⠢⡀⠀⠂⠄⠑⣄⠀⠀⠄⠀⠀⠑⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡆⠀⠈⠉⠙⠒⠒⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠂⡀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠑⠴⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠤⠄⢤⠀⠀⠐⠀⠀⠀⠀⠉⢤⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠨⠁⠒⠤⡀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠒⠂⠤⠄⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠒⡥⠴⢀⣀⣀⡀⠀⣀⡀⠤⢄⡀⢀⣀⣀⣀⠑⢀⠄⠀⡄⠀⠀⠀⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠢⠀⠀⠀⠈⠑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠈⠲⣄⠀⠀⠉⠁⠒⠂
⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠤⠄⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠠⠄⠠⠈⠴
⠀⠀⠀⠀⠀⠀⠙⠠⡀⠀⠀⠀⠆⠁⠀⠂⠀⠤⠜⠀⠁⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢀⢡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡄
⠀⠐⢄⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠀⠰⡀
⠀⠀⠀⠑⠢⢤⣀⠠⠘⠀⠄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀
⣤⣤⣤⣤⣬⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣁⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⢄⣀⣀⣀⣀⣤⠴⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠁⠀⠀⠀⠀⠀⣀⣤⡶⠶⣄⣩⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣧⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢀⣀⣤⠴⡖⣿⣻⡭⠷⣚⣫⡭⠖⠛⠛⠛⠛⠓⢒⣲⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⢥⣤⣴⣶⣿⠯⠿⢺⣏⣿⣭⣔⣚⣉⣉⣀⣀⣠⣤⠤⢶⠻⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯⠤⠶⣶⢻⣿⡇⡇⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⣨⡇⠈⠉⠉⠙⠓⠒⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡼⡟⠺⣝⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠛⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣷⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠁⠹⢄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣰⡛⠋⠉⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣠⣾⣻⢿⡿⢿⣭⣾⠉⠉⡻⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⢴⣶⢶
⠀⣠⠞⣽⡄⠈⡇⠀⢸⡜⠒⢠⣧⣴⣿⣷⡦⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⣀⣧⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣽⣾
⡀⡈⢢⣽⣧⣀⣧⣀⣼⣀⣉⣿⡟⠁⢀⠀⠉⡆⢹⠈⠉⠉⠙⡛⠻⣛⠛⠛⠛⢻⣿⡛⢹⣿⡀⠀⠀⠀⢀⣰⠏⣴⠶⠚⠁⢠⣤⠤⠤⠠⠄⠐⡒⠀⠀⠀⣿
⡇⠁⢹⠒⠒⠲⠿⠶⠬⠭⣽⠋⠀⢰⠏⠀⠀⡌⣸⠀⠀⠀⠀⠘⡄⠈⠑⢦⡔⠁⢸⣎⣻⢸⣿⠓⠦⢶⢯⠹⣄⣷⠀⠀⠀⠀⠚⢲⠩⠭⠭⠬⠥⠀⠀⠀⢹
⠁⠇⢸⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡟⠀⠀⡴⣡⠃⠀⠀⠀⠀⠀⠈⠦⠒⡄⠈⠳⢄⣿⣧⠟⢼⡀⠀⠀⢋⣣⡼⣧⣀⣠⣤⡤⠤⠤⠴⠶⠶⠶⠶⠶⠖⠒⠻
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⣴⣪⠞⢡⣿⠷⡲⠦⣄⣀⠀⠀⠀⠉⠙⠓⠒⠻⡏⠀⠈⡏⠓⠒⠛⠋⠀⠰⣂⣒⠀⠐⠒⠒⠒⠂
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⣇⠀⠀⡸⢯⣀⣠⣞⣈⡙⠁⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⣿
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠹⣄⣔⠔⣱⠏⠩⣭⣤⡟⠁⢀⣾⣯⠏⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣸⠟⠾⠣⣄⡐⠶⣶⠟⢣⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣽⡀⠀⣼⠋⠉⠙⠛⢡⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣧⣀⠀⠀⢀⣾⣿⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⢖⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⠀⠙⢯⣗⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣼⠙⢦⣀⠀⠀⠀⣈⡽⠃⠀⣤⡀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⢀⣠⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠉⠛⠉⠁⠀⢀⡼⠃⢹⣦⡀⠙⠦⣄⠀⠀⠀⢀⡴⠛⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠛⠲⠶⠶⠞⠋⠀⠀⠠⡀⠙⢦⣀⠈⠙⠒⠶⠋⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠍⠻⢦⣄⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠐⠀⡁⠀⢀⠀⠐⠒⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡠⠊⠀⠀⠀⠁⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠉⡠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠀⠒⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂⠀⠀⠀⠰⠥⠤⡀⠀⠀⠀⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⢀⡄⠀⠈⢁⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠄⡠⠂⡡⠀⠐⠐⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⠠⠙⢆⠀⠀⠀⠀⠀⠀⠀⠁⠁⠖⠦⡀⠀⠀⢀⠀⠀⢁⠎⠀⠀⠀⠀⢀⢀⠀⠀⠀⠢⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠼⠀⠀⠐⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⣀⠀⠀⢈⢀⠀⠀⢐⠀⠤⠀⠄⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠄⠠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣀⠠⠄⠚⠁⠀⢻⠘⠀⠀⠀⡈⠂⠄⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⢚⠽⠈⠄⠀⡀⠀⠐⠀⠀⠀⠀⠀⡠⢀⠏
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢌⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⠶⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⠄⢀⢀⣀⣀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢆⠀⠀⠀⠚⠰⠭⣙⣄⠀⠈⠁⠁⠀⠐⠀⣀⠀⠀⠀⠀⠉⠀⠀⡤⢶⣔
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⡓⠀⠀⠂⠒⠂⠨⠥⠴⠤⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠠⣇⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢀⢀⡤⠄⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠄⠐⠂⠀⢀⣉⡤⣤⡈⢆⢀⠔⠁⢸⡉⠀⠆
⠀⠀⠀⠀⠀⢀⠒⠐⠈⡇⠁⠀⠐⠒⠒⠒⠒⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⣵⣀⠇⢸⡇⠀⠀⡆⠈⠑⡆
⠀⠀⠀⠀⠀⠈⠸⠙⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠯⠽⠁⠀⡇⠀⢀⠗⠈⠠
⠀⠀⠀⠀⢀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸
⠀⠀⠀⠀⠀⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠶⠒⠘⠋⠁⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠧⠐⡂⠲⠤⠐⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠠⠨⠅⢀⡀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡠⡄⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣵⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⡛⠻⢿⡿⠂
⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠛⠛⠋⠙⠁⠀⠀⠀⢲⡆⠀⢀⣠⣾⣛⣽⣮⣭⣙⣷⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢱⡀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡞⡟⡏⢻⣴⡶⣶⡛⣁⣀⣸⣩⢿⣿⣿⣿⠛⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠶⠶⠮⠳⣾⣿⡿⠷⠶⠮⢻⣭⣿⣿⢻⣟⣿⣿⣿⡶⣾⣿⣁⢀⠠⠁⡖⠀⠀⠀⠀⠀⠀⠀⡤⣤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⢀⣠⡟⣽⣿⣿⣿⣿⣿⣿⣶⣿⣄⣹⡅⢰⣿⣶⣤⠧⠀⠀⠀⠀⠀⣀⣦⡵⢟⠈⠑⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣹⣿⣿⣿⣿⣿⢰⣿⣤⠃⢠⣬⣥⣈⣛⣛⡿⠀⠷⠶⣤⣶⣞⡉⠻⢤⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣴⣼⠀⠘⣿⡎⢩⣿⢿⠛⠛⠶⣶⣤⣤⢐⠀⠀⠀⠉⠚⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⡇⠀⢿⣷⢸⣿⣟⠀⠀⠂⡾⢦⣿⠀⠂⠀⠀⠀⠀⠀⠻⠓⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣿⡟⣸⢻⣿⣿⣿⣧⣀⢈⣉⢸⣿⣿⣿⣿⣿⣿⣿⡛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠀⠐⣄⣿⣷⡟⣾⣿⣿⣿⣿⡇⠀⣿⡏⣿⣿⣿⣿⣿⣿⣭⣥⣉⣀⢀
⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⠀⠀⣀⣘⣿⢾⣿⣿⣿⣿⣿⣿⣷⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣟⡛⢻⠈⠁
⠀⠀⠀⠀⠀⢾⣿⡿⠁⠀⠀⠀⠈⢻⣷⣾⣿⣿⣿⣯⢾⣿⣿⡀⠀⣾⢿⣿⠿⠿⢿⠉⠉⢛⣧⣼⣄⣠⣄⣀
⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⢸⣿⣿⣾⣿⣿⡇⠀⠘⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⢀⣿⣿⡇⣾⣿⣿⣿⣻⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢸⣼⣿⣷⣿⣿⡿⣟⣿⣿⣿⡇⠀⢸⡿⢟⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⡄⠀⠀⣸⣿⣿⣿⣿⣯⣶⣽⣟⡻⣿⣇⠀⠘⣿⣻⣦⣿⣿⣿⡿⢻⣿⣦⢘⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⢹⣿⣼⣶⡶⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣹⠁⠈⢻⡇⠀⣿⣿⣿⣿⣿⣿⡁⢸⣿⡿⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢀⣸⣿⣿⡿⠛⣁⠔⠊⡉⠉⣻⣿⣿⣿⣿⡟⡏⠈⠙⠺⣇⠀⢻⣿⣿⣿⣷⣶⣝⢿⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⣯⣿⣿⣷⣾⢣⠔⠁⠀⠀⢸⣿⣿⣿⣿⣹⠃⠙⠲⠴⢿⠀⢸⣦⣽⣿⣿⣿⣾⢏⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⡿⣿⣿⠇⣀⣀⣰⣶⣶⡾⢿⣿⣿⡟⠟⠰⢦⣤⣤⣼⡇⠈⡿⢿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣧⢋⣴⡷⣿⣿⣿⣿⢙⡷⣾⣿⣿⢳⡷⣄⡀⢀⣀⣨⣧⠀⢻⠛⠛⠿⣿⣿⡿⣿⠁⣹⣷⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣛⠿⢿⣵⣿⣿⣿⢟⣽⢧⣿⣾⣿⠈⠀⠀⠉⠉⡉⢉⣿⣿⣿⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⠴⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⢷⣶⣯⣿⣿⣿⣿⣿⣿⣿⣦⣤⡤⠤⠤⢭⣍⣉⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠋⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠱⠾⣿⣿⣿⣏⣼⡿⣿⣿⣿⣿⣿⣤⠀⣠⣼⣿⣿⣿⣿⣿⡇⠘⣿⣿⡿⢡⠟⠉⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣄⠈⢁⣰⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉
⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣯⡶⢲⣯⣍⣉⣩⣍⣭⣉⣭⣩⣍⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⡽⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠓⠦⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡿⠛⠒⠒⠒⠚⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣥⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣾⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣾⣤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠋⠉⡇⠈⢛⠒⢒⠢⠄⠤⢀⡄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⣶⡆⠁⠀⠀⠻⠲⠓⠒⠶⠒⠒⠛⠛⠛⠻⣷⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣁⡿⠿⢦⣀⣰⡖⢾⠑⠓⠞⠦⠀⠀⠀⠀⠀⠙⠛⠋⠛⠻⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⣷⣿⣋⡾⠀⢀⠂⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣏⣽⣿⣿⣯⣿⣿⣿⣿⠃⠀⣾⣀⣀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⠯⣤⣶⠇⠀⢸⣿⣿⣿⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠽⠿⣿⣿⣿⣿⣿⠏⠀⢠⣿⣿⣿⣿⡟⠛⠻⠿⢿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⡀⢈⣿⣿⣿⠁⠀⢠⠏⠨⣽⡏⠙⣤⡰⢄⡔⠊⣸⡗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠄⢂⣴⣿⣿⡏⢿⠁⢀⣿⢁⣤⣼⣷⣴⣿⣣⣤⣙⣷⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⡀⠂⡼⣿⣿⣿⣠⠏⢀⣟⣷⠋⣿⣿⣻⣟⣴⢠⣤⠘⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡀⠐⣼⠁⣻⠿⣯⡿⠀⣜⣿⣿⣦⣿⣿⣿⡿⡱⠿⠏⠸⣟⣾
⠀⠀⠀⠀⠀⠀⠀⠐⠤⡼⠀⠀⠀⠠⢰⠿⠶⠏⢰⡟⠀⣸⣿⣿⣿⣿⣿⡟⠈⣿⠆⠦⣵⡿⠻⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠈⢄⣾⣄⠀⣴⣿⠇⢰⣿⣿⣿⡿⠿⣿⣟⣃⣻⣄⣰⣿⣇⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢰⣿⣿⣧⣿⣯⣄⣿⢁⣿⣿⣿⣿⣿⣿⢃⣿⣥⣍⣀⢤⡅
⠀⠀⠀⠀⠀⠀⠀⣀⡌⢀⠀⠄⠀⢼⣿⣿⢀⠙⠱⠿⢿⣾⣿⣧⣿⣿⠿⣿⣽⣼⣯⡽⠏⠘⠃
⠀⣠⣴⣶⣿⣿⣷⣿⡟⠀⠀⡀⢳⣾⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⠿⠿⢿⣿⣀
⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⣀⣀⠀⠙⢷⡄
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣄⣻⡈⠿⠋⠚⠁⠀⠈⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⡿⠷⠞⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢺⡟⢁⣶⣦⣄
⠀⠀⠀⠀⠀⢀⠠⠒⠁⡴⠋⠀⢋⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠒⠂
⠀⠀⣠⡔⠊⠁⠀⢐⢲⡴⠂⢀⡾⠀⠀⠀⠀⠙⢷⣄⠛⠶⠶⠒⠚⠋⢉⣠⠴⠒⠉⠁
⠀⠀⠀⠀⢀⣀⣸⡟⠉⢀⢴⡿⢡⠖⠲⣄⠀⠀⠀⠙⢧⡀⠀⣀⡴⠞⣩⠔⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣴⠞⠉⠉⢿⠉⠙⠲⡌⢠⠃⠀⢀⣈⣵⡦⠄⠀⠀⠉⠉⠁⠀⡠⠁⠀⠀⠠⠚⠉⠉⠉⠉⠓⢦⡀
⠀⡾⠁⢀⡤⠴⡏⠀⠀⠀⢨⡄⠠⠚⠉⠀⠒⠞⠛⠛⠻⠿⠿⠟⠋⣀⡠⠤⠴⠒⠚⠛⠛⠓⣦⠀⠈⢷
⢰⡇⠀⡏⠀⠸⠃⠀⠀⢀⠎⡇⠀⣤⣔⢶⣄⠀⠀⠀⠀⡀⠔⠒⠉⠀⠀⠀⣶⠿⠿⠶⣶⡶⠟⠀⠀⣾
⠀⢷⡀⠁⠀⣀⣀⡠⠖⢁⣼⠃⠀⠈⠻⠄⠙⠦⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⣀⣤⠞⣡⠇
⠀⠈⠻⢦⣄⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣉⣤⣴⠾⠋
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⣰⡆⠀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠠⠔⠚⠐⠒⢂⣉⡭⠖⠛⠉⠁⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠐⠉⠉⢛⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠠⠒⠋
⠈⠀⣠⠖⣀⣤⢶⡿⠦⣜⢦⠀⠀⠒⠈⠉⠉⠒⠦⡀⠀⠻⢦⣤⡤⣤⠖⠂⠀⢀⣤⢖⣩⠭⠭⣗⡦⡀
⢀⡾⢁⣾⠏⠁⡼⣡⣄⠈⢧⠑⡀⠀⠀⠀⢀⡤⠀⠘⡆⠀⠀⣠⠞⠁⠀⠀⢀⡾⠑⢉⡠⠔⠊⠀⢱⡘⣆
⢸⡇⣼⡇⠀⠸⠁⠀⢹⡆⢸⡆⠈⢆⠀⠀⠸⣧⣄⡴⠃⣠⠞⢵⣦⣀⣀⣀⡬⠕⠊⠁⠀⡀⠀⠀⢸⡇⢸
⠸⣇⠸⣧⡀⠀⢀⣠⡟⠁⣸⠁⠀⠀⢳⡄⠀⠈⢁⣠⠞⠁⠀⠀⠈⠉⠁⢀⣀⡠⣤⣒⠉⠀⠀⢀⡾⢃⡾
⠀⠙⢦⣈⠙⠛⠋⠁⢀⡴⠃⠀⠀⠀⣼⣃⣘⡿⠭⠥⠰⠀⠒⠒⠀⠉⠉⠁⠀⠐⣿⡉⠉⠛⠛⢋⣥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡤⣄⡠⢤⣠⠤⣀⡤⢤⣀⡤⣄⣠⠤⣄⣠⠤⣄⣠⠤⣄⡤⢤⣀⡤⣄⡤⢄⣠⢤⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠉⠀⠈⠀⠀⠁⠀⠉⠀⠀⠉⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⠉⠀⠀⠉⠀⠈⠀⠀⠁⠀⠉⠀⣙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠀⢰⠋⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇⠀⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠽⠀⢸⡅⠊⠀⠀⠀⠀⠀⠀⣀⡴⢒⠫⠉⠁⠀⠀⠈⠉⠝⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠀⢸⡄⠀⠂⠀⠀⠀⣠⢞⠅⠺⢄⣀⡤⣧⣴⣤⣤⢴⣀⠈⠑⢭⡳⣄⠀⠀⠀⠀⠀⠀⡇⠀⣖⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡀⢸⡇⠀⠀⠀⢀⡜⡵⠁⠀⠀⣇⣿⡏⣽⣿⣿⠑⣸⣿⣷⣤⠠⠀⢌⢦⠀⠀⠀⠀⠀⡇⠀⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⢸⡇⠀⠀⢀⡞⠜⠀⠀⠀⠀⣧⣤⣄⣈⣉⠉⠐⠿⣿⡿⢐⣴⣀⡀⠀⢳⡀⠀⠀⢀⡇⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⢸⠇⠀⠀⡼⠈⠀⠀⠀⠀⣰⡋⠒⣂⣙⠉⠙⠳⢤⣄⡁⠻⡏⠂⠀⠀⠈⣇⠀⠀⠀⡇⠀⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢸⡅⠀⢰⠃⠀⠀⠀⠀⠀⣿⠴⠶⠼⢿⣿⣷⣶⣬⣙⠻⡶⠁⠀⠀⠀⠀⢸⠀⠀⠨⡇⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⢸⡇⠀⢸⠘⠀⠀⠀⠀⠔⠁⠈⠋⠀⠀⠙⠫⠚⢿⣿⣷⣧⣀⠀⠀⠀⠀⣸⡆⠀⠠⡇⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠂⢸⡇⠀⣺⢀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⢫⡇⠄⢰⡇⠀⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⠀⢸⡇⠀⢹⢸⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⠃⠀⢨⡇⠀⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢸⡇⠀⠸⡌⡀⠀⠀⠀⠐⢄⣀⣀⣠⠀⠀⠈⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣸⠀⠀⠈⡇⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⢸⡇⠀⠀⢧⢀⠀⠀⠀⠀⠀⢀⣠⡴⡶⠀⠟⠛⠉⠉⠙⠳⢦⠀⠀⠀⢤⡇⠀⠀⠀⡇⠀⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠀⢸⡇⠀⠀⠈⢧⢂⠀⠀⠠⣞⡄⠁⠀⠀⠀⠀⠀⠀⠠⠘⡠⠎⠗⢀⣌⡞⠀⠀⠀⠠⡇⠀⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⢸⡇⠀⠀⡴⠬⠶⠷⠒⠂⠒⢌⠙⠓⠄⡀⠀⢀⡠⠚⡡⠒⠐⠒⠾⢾⠴⡆⠀⠀⠀⡇⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⢸⡅⠀⢶⡉⠀⠀⠀⠀⠀⣄⣿⠀⠀⠀⠘⠖⠁⠀⠀⢃⣠⠀⠀⠀⠀⠀⣉⠶⠀⠈⡇⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢸⡅⠀⠀⠉⠙⠒⠛⠉⣻⠀⠉⠉⣴⡒⢒⣲⣒⠒⢋⠉⠘⡏⠉⠙⠓⢋⠁⠀⠀⠐⡇⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣹⠇⣾⠃⠈⣿⡄⠀⠀⢣⠀⠀⠐⠀⠀⠀⠀⢀⡇⠀⢞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣐⠛⠆⠙⠳⠴⠟⣀⣠⡤⠞⠁⠀⠀⠀⠰⠄⠁⠐⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣁⣁⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⡇⠀⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⢀⡀⠈⡈⠁⢀⡁⢀⣁⠀⢁⡁⠀⣀⡀⠀⣀⡀⠁⢀⣀⠀⣀⠀⠁⣈⠀⢉⠈⠈⣙⠁⢀⡀⢑⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠚⠙⠒⠋⠓⠊⠈⠓⠋⠙⠚⠃⠙⠚⠁⠙⠚⠃⠙⠚⠉⠓⠚⠉⠓⠋⠑⠚⠉⠒⠃⠑⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣑⣒⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠟⠛⢦⣀⡀⢀⠄⣰⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⣀⣽⡞⢣⣷⣿⠾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣭⠽⢿⣿⣹⣄⢻⣿⣀⡾⣀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣩⣶⡶⣦⣾⣿⣿⣞⢆⣻⣷⣿⣿⣿⣿⣭⣭⣛⠂
⠀⠀⠀⢀⣶⣧⣶⣶⣤⡀⢀⡞⣛⠛⠻⡏⠱⣬⣉⠛⣿⣿⣿⣎⢻⣭⣶⣤⣬⣿⣿⣿⣷⡌⠳⣄
⠀⠀⢠⡿⣿⣿⢿⡄⢻⣷⣞⣰⣾⣫⣼⣿⣶⣀⡈⢰⣿⣿⡟⡁⣣⡻⠟⠋⠉⠉⢻⣿⣿⣿⡄⢹⣷⡀
⠀⢀⡏⣼⠁⡀⣹⣿⣮⣛⣿⣿⣿⣿⡟⢻⣿⣇⢠⡏⣿⣿⢻⢿⡏⢁⣹⣭⣷⡀⠺⣾⡿⣹⣿⢐⣿⣧
⠀⢸⠧⣯⣾⣦⣼⡏⠩⣿⠛⢻⠿⠿⣿⠿⣻⠇⡞⢡⣿⣿⡀⢸⡇⠈⡿⢿⣫⠃⠦⣿⠇⣿⣿⢸⣿⣿
⠀⠀⣿⣿⡻⣟⢻⣿⣧⣻⣶⣾⡋⢀⣠⣾⡏⣼⣧⣼⡿⣿⣧⡈⣧⠀⢠⣉⣤⣾⡀⢀⣰⣿⣧⣿⣿⡏
⠀⠀⠘⢬⣿⣾⣷⣍⣿⡙⠟⣻⣿⣿⣭⣿⣿⣿⣿⣿⣇⡘⢿⣿⣌⡓⢤⣍⣛⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠛⠿⠿⠿⠟⠓⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠙⠉⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⣠⠤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⡏⠉⠉⠉⠹⣇⠀⢀⡟⠉⠹⣇⡀⢀⣸⠏⠉⠙⢧⣄⣠⡾⠁⠈⢷⣄⣀⡴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢧⣀⠀⠀⣤⣤⡤⣤⠤⠤⠤⠶⠶⠶⠖⣶⣶⣶⣶⣾⣷⣶⡶⠞⠛⠛⠛⢻⡀⠀⢀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⢹⡆⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠉⠁⠀⠀⢀⣠⣴⣾⡇⠀⢺⡀
⠀⠀⠀⠀⠀⡴⠞⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣶⣦⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠛⢾⡆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⢿⡇⠀⠀⣠⣼⡇
⠀⠀⠀⠀⠀⡷⣤⡀⠀⣿⣶⣾⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⢸⡇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⢾⠀⠀⠻⢦⣤
⠀⠀⠀⠀⠘⡟⠋⠀⠀⣿⣿⣿⠿⠋⠀⠀⠀⢀⣠⡴⡶⢶⢶⣤⡤⣤⣴⢾⠏⡇⡇⣿⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⣧⣄⡀⠀⣿⠀⠀⠀⠀⠀⣠⠞⣿⢸⠁⡇⢸⢸⣿⣀⣿⢸⢸⢰⣇⡇⣿⢸⠀⠀⣠⠞⠛
⠀⠀⠀⠀⠀⠁⠈⣷⠀⡧⠀⠀⠀⣠⡞⢻⠀⡇⢸⠀⡇⣸⣸⠋⢉⣳⣾⣸⠾⠛⠳⣿⣸⡀⠀⣯
⠀⠀⠀⠀⠀⣴⠾⠃⠀⡿⢲⠶⡟⢹⣇⣼⠞⠛⠿⣄⣧⣿⣁⢀⣾⣿⣿⣧⣴⣶⣷⣿⣿⠀⠀⠙⠓⢷⠄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣏⢸⠀⣧⡼⠋⢀⣤⣄⢠⣬⣽⣿⣿⣿⣿⣿⣿⣿⠟⣉⣿⣿⣿⠀⠀⠀⣠⣼⠆
⠀⠀⠀⠀⠀⠛⠛⣦⠀⣧⣼⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢿⣿⣿⣿⡀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⣀⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠻⣤⣤
⠀⠀⠀⠀⠀⣿⠉⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠶⢦⡀⠀⠀⣠⠶⠶⣦⡀⠀⣠⡴⠶⣄⠀⠀⢀⡶⠒⢶⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⣄⣀⣠⣼⠃⠀⠀⣿⣤⣴⠏⠀⠀⢸⣧⣴⠏⠀⠀⠿⠶⠖⠾⠁⠀⠀⠿⠶⠖⣲⢿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢒⡲⢶⣆⣾⣶⡀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⡀⢈⡀⠀⢄⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡣⠊⠨⡂⠘⢅⣩⣪⣤⠮⠍⠒⠂⠈⠉⢉⢀⠀⠠⢂⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⣠⡉⠤⠔⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⢂⠀⢀⠆⠌⡀⡠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠐⠘⠁⠉⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⡐⡠⠀⠀⢠⡀
⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣀⠠⠄⠀⠤⢀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠘⣦⠁⡐⠠⢀
⠀⠀⠀⠄⢀⠎⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡀⠈⢀⠀⠄⢀⠄⢂⠊⠢⡀⠙⠄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢳⠀⢀⡰⡠⢳
⠀⠀⠀⠰⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢀⠊⠀⠀⣀⣀⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠸⡆⣪⠎⠀⠀⡄
⠀⠀⠀⠀⠃⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⡆⠀⠀⠀⠀⠀⠡⠀⠀⡄⠀⢠⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠧⠁⠀⠀⠀⠁
⠀⠀⢀⡴⣩⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣰⠀⢃⠀⠁⠆⠀⠀⡠⠀⠀⠰⢀⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⡴⠋⢀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠢⡀⠀⠀⠀⠀⡠⠂⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⡐⡨⠊
⠞⠂⢥⣄⢤⢷⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠂⢄⠈⠀⠒⠀⠁⢀⠠⠊⢀⠀⠀⠀⠀⢀⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠀⠀⠀⠙⠺⢆⣄⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠁⠀⠀⢁⠀⠢⠂⠀⠀⠀⡀⡀⠈⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠈⠉⠒⠠⢠⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠴⢄⡄⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⠋⠐⠀⡠⢀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣀⠀⢀⢀⠀⠁⠀⠰⢀⣸⣊⡠⠀⢀⢌⠔⢁⠄⠐⠠⢀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠰
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠄⣄⠀⠁⢁⠊⠀⠀⠈⠁⠐⠂⠴⠁⠊⠐⠐⠡⢊⠄⠄⠀⠀⠀⠀⠀⢒⠀⠆
⠀⠀⠀⡀⠀⠔⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢠⠀⢊⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀
⠀⠀⠀⠀⡄⠑⡡⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⢀⠕⠐⡡⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠠⢊⠔⡁⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⢀⢌⠄⠔⠐⠀⠁⠁⠀⠀⠀⠀⢀⢀⠀⠀⠖⢀⠖⡠⢋⠔⡡⠊⠀⠁
⠀⠀⠀⠀⠀⢁⠀⡡⢊⠔⠁⢀⠔⠁⡀⠀⠀⠀⠠⠊⢈⠄⠐⡀⠀⠁⠀⠀⠀⠀⠀⢀⡀⢤⠤⢀⠖⡠⢉⠐⢀⠔⡁⠐⠡⠊⠀⠁
⠀⠀⠀⠀⢀⢸⡀⠀⠁⠊⠔⠁⢀⠈⠄⡀⠑⠀⠁⠁⠀⠈⢀⡀⢠⡤⢀⠀⡠⢊⠅⢉⠔⡡⠀⠡⠊⠔⠁
⠀⠀⠀⡀⠐⠈⡁⠐⡡⠂⠀⢁⣀⡀⢤⡄⠠⠆⡐⢂⠝⡩⢊⠔⡡⠔⠡⢊⠔⡡⠂⡠⠊
⠀⠀⠀⠂⢀⠌⡠⢊⠀⡩⢋⠔⠁⠔⡠⢊⠔⢀⠔⡡⢊⠔⡡⠊⠠⠈⠐⠁
⠀⠀⡠⢐⠅⡈⢀⠀⢈⠔⠁⠀⡠⢊⠔⢁⠔⠡⠊⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣿⣿⣿⠿⢶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⣶⣿⣿⣭⣍⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⢛⣉⡉⠙⣿⣷⣯⢿⣿⡷⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠉⠀⠀⢈⣿⣿⣷⠀⠀⠀⠈⠙⠿⠟⠋⠀⠈⠁⠉⠁⠀⠉⠉⠉⠀⢸⡷⠀⠀⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⢿⣿⣿⡛⠿⠿⠛⠁⠀⠀⢤⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠖⠰⣤⣤⣴⣧⡀⠀⣸⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⢻⣷⠄⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⣠⡄⠀⠀⠀⠀⠠⠶⠟⠋⢩⣬⡘⠿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣋⣡⣤⣴⡶⠟⠁⠀⠀⠀⠀⠀⣀⠀⣠⣤⣤⣤⣀⠀⣲⣦⣾⢛⣁⡩⠬⠀⠀⠁⠀⢀⣠⣾⣿⣷⢀⠧⢄⢀⢀
⠀⢦⡀⠠⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠁⠀⣠⣶⡿⠿⠿⢿⣿⣷⣾⣿⢿⣟⣿⠿⢫⡶⠾⣿⢁⡉⡩⠴⠒⠪⠭⢑⡾⢩⢿⣿⣿⣠⠶⠀⣯⣭⣰⢅
⠀⠀⠙⠶⣬⣑⡲⣦⣤⣴⣶⣿⣋⡥⢔⣈⡴⣞⣭⣄⣀⠀⠀⠀⠈⣿⣿⣏⣾⡍⠱⡟⢪⣽⣛⠡⣼⡹⣅⠐⠀⠀⡁⠏⡐⠋⢸⣿⣿⠷⢶⣳⣬⡉⢚⣙⣦
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡷⠾⠛⠁⡞⠉⠉⠙⠻⢿⣶⣶⣾⡿⠿⣿⢻⣿⡿⠫⣛⣯⢻⣿⣅⠀⣹⠏⠀⠀⢰⢉⠋⠉⠛⢻⡏⣅⢿⣿⣽⡿⢂⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣶⣽⣿⣶⢟⡵⠋⠀⠉⠙⠉⠒⠒⠶⠾⠶⠦⠤⠤⠂⢿⡘⢀⡈⢛⠁⣮⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣕⣾⣶⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠒⠛⠛⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⣀⡤⠖⠒⠉⠉⠀⠈⠙⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡬⠟⠲⠦⣤⣠⣎⣥⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣒⡶⢖⡺⠛⢿⣓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠚⡇
⠀⠀⠀⠀⣼⠧⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠔⠋⠀⠀⠀⠈⠙⠀⠉⠒⠤⣀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠀⠀⠀⠀⡿
⠀⠀⠀⢐⡇⣇⠀⠀⠈⠉⠒⠦⢤⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠽⢶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⡇⢸⡄⠀⠀⠀⠀⠀⠀⢸⠉⠑⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⣀⣀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⡇⠀⠀⢹⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⢀⠼⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⡠⠋⠀⠳⣄⠀⠀⢸⡀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢱⠜⠁⠀⠀⠀⠈⠙⠒⢾⣧⣀⣠⠾⠃⠘⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⡀⠀⠀⠀⠈⢦⢸⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣌⣻⣄⠠⠐⠊⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⠒⠒⠒⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢠⣄⡴⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⠒⠒⠒⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣰⠋⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣇⠔⠁⠀⢸⡇
⠀⠀⠀⠀⢠⣾⣯⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠈⠻⢿⣿⣿⣿⠟⠁⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣄⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠈⣩⣿⡿⠛⠙⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣿⡇
⠀⠀⠀⠀⠀⢠⣴⣿⣯⣁⣀⣀⣀⡀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠋⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣴⣿⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⢻⣿⠛⠛⠻⠿⠿⠿⢿⣿⣶⣶⣶⣶⣦⣤⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣴⣿⣷⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⠟⠋⠀⠙⢿⣷⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⣿⣶⣶⣶⣶⣤⣤⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣤⣿⠟⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣦⣤⣤⣤⣤⣀⣼⣿⠀⠀⣿⣿⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠀⠀⣿⣿⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⢿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠉⠉⠙⠛⠓⠶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢛⣉⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⣈⠽⠛⠳⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣉⠥⠖⢊⡩⣴⣆⡀⢀⣨⣙⠶⠀⠀⣀⡠⠖⠋⠁⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣄
⠀⠀⠀⢠⣶⠛⠉⢴⣚⣉⠛⠁⠘⠹⠺⠟⣉⠤⠚⠉⢀⡠⠔⠋⠁⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⣷
⠀⠀⠀⣿⠉⠛⠓⠶⠤⣤⣍⣙⠒⠲⠒⠉⠀⣠⠴⠊⠁⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⢶⠯⣤⣄⣀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢻⠛⠓⠶⠦⣤⣄⣀⣀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠼⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⡇⠀⣼
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣰⡷⢃⣴⠏
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠞⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⢤⣄⣀⡀⢸⣇⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠰⣄⣀⡔⠣⣀⡜⠁⠘⠦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢠⠒⠲⣀⡴⠉⠳⠤⠂⠈⠒⠃⠀⠀⠉⣀⣀⣀⣠⡤⠤⠄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠢⠚⠀⠀⠉⠁⢀⣀⣀⣀⠤⠤⠤⠔⠒⠒⠒⠈⠉⡥⠤⠄⢠⢒⠀⠄⠸⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⡉⠀⠨⠤⠶⠒⠒⠉⣉⣁⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠃⢌⠸⣸⢰⠈⠀⡆⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢃⠀⠀⠁⠰⠋⠀⠀⠉⠂⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⢇⠛⢀⠄⠯⠋⠔⠀⢡⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡢⠸⠀⠀⡀⢣⡈⠖⠛⣧⣤⠚⠁⠀⠋⢂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡁⠀⠆⠀⠀⠆⢐⢂⣄⣀⠄⠤⠥⢀⣐⡊⡀⠀⠀⢀⣠⡤⠤⢤⣀⡀⠀⠀⠀⠀⡆⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢀⠀⠀⠀⠀⠁⣀⣤⣤⣤⣀⡀⠀⠀⠉⢁⠔⣩⠔⢂⡰⠀⠀⠉⠳⡄⠀⠀⢡⠀⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⢨⠀⠀⠀⣠⠊⡠⢂⡤⠀⠀⢉⠒⣄⢀⠎⠐⢡⠊⠁⠀⠀⠀⠀⡀⠐⠀⠀⠸⠈⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡄⠀⠀⡇⠸⢠⠋⠀⠀⠀⠀⠀⠈⠾⠀⠈⠁⠀⠀⠀⡠⢀⠌⡰⠸⠀⠀⠀⡆⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠃⠀⠀⡃⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠎⡠⢂⠌⡀⡐⠀⠀⠀⠃⠈⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡀⢸⠀⠀⢣⠈⠒⠀⠀⠀⠀⠀⠀⠀⡠⢞⡠⢊⠔⡡⢊⡔⠡⠊⠠⠁⠀⠀⠀⠃⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⡄⠀⠀⠱⡀⠘⢔⠨⠔⡡⠔⡩⠔⣡⠔⡡⢊⡔⡡⢖⠕⢡⠃⠀⠀⠀⠀⢰⠀⣈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢢⠀⡅⠀⠀⠀⠈⠢⡀⠒⠡⠔⣉⠔⣊⠔⣊⠔⡡⢊⠔⡁⡠⠁⠀⠀⠀⠀⠀⠸⠀⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⢠⠀⠀⠀⠀⠀⠈⠓⢄⡈⠐⠫⠔⡊⠔⢊⠔⡡⢊⡴⣁⠀⠀⣀⡀⠀⠀⠀⡄⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠘⣀⢀⣀⣠⠋⢑⣀⠀⠈⠒⠤⡉⠐⠪⠕⡪⣲⠟⠘⠉⠁⠘⠉⠛⠀⠀⠀⢃⠘⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠀⠧⠀⠈⠀⠀⢀⠈⠃⠀⠀⠀⠈⠙⠠⢌⠔⠁⢾⣉⣘⣉⠻⠉⠙⠚⠋⠀⢙⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢈⠈⠉⠉⠉⠀⠒⠒⠈⠥⠄⠀⠀⠀⠀⠀⢀⣰⠛⣋⣀⠀⠤⠤⠐⠚⠉⠉⠁⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠈⡀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠀⠒⠂⠈⠉⣀⣀⠀⠀⡠⠤⡀⢡⠂⠒⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠁⠐⠒⠈⠉⠉⢀⣀⡀⢀⡄⢄⠀⡔⠒⢄⡎⠀⠈⠧⠞⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡈⢀⡎⠙⣆⠜⠀⠱⠞⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⡠⠄⡠⢄⡠⢄⡀⠄⣀⠤⣂⡠⢐⡠⢔⡠⠔⣂⠤⣂⠤⣊⠤⢒⠤⢒⡠⠔⡢⠔⠢⠔⠪⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠁⠒⠁⠂⠁⠚⠁⠀⠁⠀⠉⠀⠈⠀⠀⠁⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣴⣦⣦⣄⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣿⢏⡿⣷⠞⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠙⢋⣁⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣠⣿⠇⢱⣮⢷⢾⣿⣿⡷⣀⠄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡜⢿⣻⣷⣾⣿⣿⣿⣿⣶⡀⠀⠈⠉⠛⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣷⣤⣀⠠⢀⡠⠂⠀⠠⢋⣹⣿⠿⠿⢿⣿⠿⠋⢹⣿⣿⣷⣦⣄⠀⢀⠜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡑⢶⠆⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⣿⣶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠉⠛⢿⠟⣠⠞⣿⣿⣷⡲⠷⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠿⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣩⡴⠶⠚⠛⠿⢿⣦⣄⠀⠀⣄⡴⢃⠾⣿⣧⢹⣿⡇⠐⠶⣶⣦⠶⠀⠚⠛⠋⠙⠛⠛⡛⠉⣀⡠
⠀⠀⠀⠀⠀⠀⢀⠏⢠⡞⠡⠀⠈⠉⠉⠙⠲⣌⠙⢿⠆⠁⣼⣿⣷⢹⣿⡼⣏⣷⠄⢄⠈⡃⠀⠀⠀⠀⠡⠀⠑⠄⢈⣀⠈
⠀⠀⠀⠀⠀⠀⡜⠀⡟⠀⠁⠀⡀⠀⣇⣀⣌⠀⠿⠁⢀⣼⣿⣿⣿⡇⣿⣧⡚⣡⠇⣼⣷⣤⣄⠠⡀⠘⡖⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⣧⣼⡇⠆⠀⠀⢸⡏⢀⣴⣴⡋⠀⠰⠋⠹⣿⣿⢿⣿⠛⠹⣧⡹⣲⣿⣿⣇⣽⠃⠐⠂⠘⣶⣆
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠁⠀⠉⢹⣇⠸⣿⣶⡟⡶⠀⠃⠀⢿⡇⠉⣩⢾⣧⢾⡟⢙⣿⣿⠟⢎⢓⠀⠀⠀⠏⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠄⠠⠊⠙⢦⣤⣁⡠⠆⡀⠀⠀⣸⣧⡈⣹⣻⠿⠀⡷⢺⣩⣿⣿⣿⡎⠄⠄⠀⠂⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣌⠠⡀⠘⠀⠀⠡⠀⠀⠀⡅⢀⣿⡇⠥⡷⠟⠛⠚⠓⢫⣌⢋⣿⣿⣿⢐⠈⠁⠀⠀⠀⠀⡀⢴⣶⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣌⡐⠀⠀⠀⠀⠤⠞⣠⣾⠟⠀⠀⡏⣤⣴⡆⢛⣤⣫⡾⣿⣙⣿⠌⠀⠀⠀⢸⣽⣿⣦⠀⠀⠈⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣶⣶⣶⣿⡿⠋⠀⠀⠀⠀⢄⠄⠠⠈⠙⢿⣗⢽⣯⡜⣶⣖⣶⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣀⣹⣳⣿⣿⣻⢿⣩⡛⠏⠉⠅⠉⠙⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣯⣽⠀⠀⢠⣤⢤⡀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⣿⣷⣦⡀⠁⠆⢀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡘⠿⣿⣿⡏⠲⣄⠀⠈⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠜⢻⣷⡁⠠⢐⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠘⠈⢛⠀⠙⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡂⠀⡀⠂⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠉⠉⠛⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠔⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⡴⠚⢹⣅⠒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⣾⣿⣿⠷⢶⣾⣿⡭⠥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣧⠀⠠⠶⠂⢷⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢀⣦⣤⣞⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢈⠿⢿⠀⠀⠀⠈⠋⠉⢹⠃
⠀⢀⠀⠒⠚⠩⣙⣶⡛⠓⢦⣙⣌⠀⠀⠑⢄⠢⢤⣤⡴⢪⣰⠦⣄⡀
⢰⣱⣿⣦⠀⠀⠔⠓⠭⣓⢦⣈⠛⢆⠀⠀⠤⠸⣦⡼⠁⢹⢿⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠘⢻⠟⠻⠀⡘⠀⠀⠀⠈⠣⡈⠳⢌⠒⢿⡄⠀⢸⣿⡆⡄⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⡀⢐⠂⡹⠁⠈
⣤⡸⡀⠀⣷⠁⠀⠀⠀⠀⠀⢱⢦⣠⢵⢤⠙⠂⣻⣿⡷⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⡀⢱⠃
⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⠀⡈⠀⠘⣦⠀⠀⠸⢸⡟⠁⡀⢁⠄⠀⢚⣹⡄⠀⠀⠀⠀⠞⠉⣩⠭⠂
⠀⠀⠈⢻⠁⠀⠀⢐⣂⣤⣤⠧⠤⣤⠇⠀⠀⠀⢱⠇⠌⠀⠉⠁⠉⠀⡯⢳⠤⠤⠤⣤⠄⠀⡜⠑⢄⡀
⠀⠀⠀⢸⠀⠀⠈⠉⡡⠊⠁⠀⢠⡲⣄⣀⡠⣴⠉⣆⢀⠀⢁⠀⢀⡜⣧⠏⠀⠀⠀⢸⣄⠀⣣⣀⡤⠼⠒
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣭⠁⠀⠋⡀⢸⠃⠊⠀⠠⠊⠁⠈⠀⠀⠀⠀⠈⢆⣩⡅
⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⠀⠀⠀⣿⡟⠀⠠⠔⠁⠈⡤⠄⠀⠀⠀⠀⢰⠀⠀⣀⣀⣀⡨⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠛⠻⠭⣄⡀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡈⠏⠉
⠀⠀⠀⠀⠀⠀⠀⡘⠳⢥⣀⡀⠀⠀⢀⠁⠀⠀⠀⠀⢂⠤⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠋⠊⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢣⠀⠀⢀⡠⠖⠁

⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢘⢢⣥⡤⠄⠠⠔⠒⠒⠒⠒⠞⠥⣐⠀⠀⠀⠀⠀⠀⢠⠈⣆⠀⠀⠀⠀⠀⠀⠀⣶⠛⠉⠁⠠⠀⠀⠀⠀⠀⠉⢻⣶
⠀⠀⢸⣿⠀⠀⠠⠶⡀⠘⡄⠀⠀⠀⠒⢾⠀⠀⠀⠀⠀⢠⠾⠛⠿⢆⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠘⣹⠀⣀⣀⣿⡁⠀⢰⣷⣤⣙⣶⣾⠀⠀⠀⠀⠀⣹⣼⣀⣦⣼⠁⠀⠀⠀⠀⠈⣵⣀⡤⢀⢸⡦⠴⣀⠐⢒⡠⣀⣿
⠀⠀⠸⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠩⠀⠀⠀⠤⠋⠙⠛⠉⠁⠫⠜⠣⠀⠀⠀⠀⠛⠻⠿⠷⠩⠤⠤⠍⠸⠾⠿⠿⠟

⠀⠀⠀⠀⠰⠶⢠⣤⣤⣤⣤⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣤⣤⣤⣤⣤⣤⠄⠄
⠀⠀⠀⠀⠀⠒⠊⢉⠉⠉⠉⠉⠘⠂⠀⠀⠀⠀⣾⢒⡀⠤⠄⠀⠀⠀⠰⢲⡆⠀⠀⠀⠀⠒⠈⠉⠉⠈⠉⠉⠉⡙⠒⠆
⠀⠀⠀⠀⠈⠀⠀⠘⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠉⠉⠉⢉⣉⣀⠈⠛⠀⠀⠀⠀⠈⠒⠒⠒⠆⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⢳⡀⠠⠤⠀⠄⠈⠂⠀⠠⡆⠀⠀⠀⠀⢰⠀⠲⣤⣀⡐⠒⠀⠂⢑⡃
⠀⠀⠀⠀⢀⡀⠿⡇⠃⠀⠀⠁⠃⡄⠀⠀⠀⠀⢻⡧⠀⠀⡀⠀⠀⠀⠀⠒⡇⠀⠀⠀⠀⢠⣼⣴⣎⡑⠛⠀⠀⠂⡯⠇
⠀⠀⠀⠀⠘⠒⣗⣛⣋⣛⣛⣛⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠿⠿⣉⣀⣁⣁⡀⠀⠣⡄
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣿⣿
⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣆⠀⠀⠘⣿⣿⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿⣿⡇⠀⠀⣿⣿⡆⠀⠀⣿⣿⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠸⣿⣷⣶⣶⣿⡟⠀⠀⠀⣿⣿⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣿⠿⠋⠉⠻⣿⣧⡀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⠁⠈⠉⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⣿⣿⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⡦⠀⠀⣿⣿⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣶⣿⡟⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⣀⣤⣴⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⣰⠏⢁⣤⠶⢤⣦⠈⢷⡀⠀⠀⠀⠀⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⠻⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢈⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⠿⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡈⠀⠀⠀⠀⠀⠀⠸⣧⣀⠙⠒⠛⠙⣛⡋⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣀⠀⠀⠀⠀⠀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⣠⣾⣿⣿⣿⣶⣤⣶⣾⣿⣿⣷⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠈⠙





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠉⣉⡉⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠃⠆⠈⠆⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠐⢄⢛⡠⠆⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⡠⠖⠁⠘⠠⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢡⣌⣋⣁⠲⠦⠨⡅⢐⡠⣄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⡠⠊⠀⠀⠀⠀⡀⠐⠈⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⠀⠀⠀⠈⠀⠉⠁⠒⠠⠤⢉⠒⠤⣀⠀⠀⠸⡄
⢀⡔⠋⠀⠀⠀⢀⠆⣤⠷⣀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⣀⠔⢣⡜⠙⢢⣴⠶⠆⠠⢤⣤⠤⣤⢤⠜⠒⠠⣁⢪⡤⠂
⠳⡤⠤⠄⠀⢀⠠⠥⠚⢢⠀⠑⠞⠁⠀⠀⠀⠀⠀⠀⠀⢉⠇⢸⠁⡜⣡⣎⡷⠀⠀⢀⡄⡲⢌⠀⠀⠀⢀⣨⠹⠁
⠀⠑⢄⠀⠀⠀⠀⠀⠀⢨⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣌⠀⢣⣙⡡⠃⠀⠀⣾⢸⡟⡎⢠⠀⡴⣀⠉⠀⢣⡀
⠀⠀⠀⠑⢄⠀⡂⡠⢆⡁⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠃⠀⠀⠘⠢⠚⠀⡮⠺⡔⠀⠱⠐⡖⠛
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠦⣀⠀⠀⠀⠉⢲⠎⠐⠂⠠⠄⢀⣳⡄⠀⠙⢅⣘⡃⠞⠀⠀⠀⢀⣀⣡⠴⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⡎⠀⠀⠀⠀⠀⢀⠀⡸⠓⠲⡤⢤⣤⡤⠴⢲⠞⠋⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡌⠀⠀⠀⣄⡎⠘⠒⠂⠀⡻⠚⠢⢄⡰⠃⠀⢠⠞⠁⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⠁⠓⠀⣸⠃⠀⠰⢣⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢴⡹⠀⠈⢩⢀⠇⣤⠀⢠⡟⠂⢠⠃⣧⠁⠀⠀⠀⠀⢀⡴⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠣⡀⢀⠌⡘⠀⠀⠀⣸⠀⢀⡞⠀⠻⢄⡀⠀⠀⣠⠎⣠⠞⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠇⠶⠀⠀⡋⠀⢠⠇⠀⠀⢸⠙⡶⣞⣡⠞⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⢀⠀⠀⠀⡇⠀⢸⣀⡤⠴⠚⠂⠛⠂⢺⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠈⠁⠀⢠⡇⠀⢾⡁⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⢸⢰⡂⠀⡇⠉⠀⠊⠑⡄⠀⠀⠀⠀⢀⡸⠀⠀⣖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠈⠉⢹⠉⠉⠙⡏⡿⠀⠀⠀⠀⢸⡄⠀⠀⢰⡡⠃⠀⢰⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠉⠉⠉⠁⠐⡚⠙⡇⠒⠀⠀⠀⢸⠓⠐⡲⢋⡀⠀⠀⢠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠷⢄⣻⠐⠀⠀⠀⢸⠀⠘⠋⡹⢀⠂⠄⣮⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⢸⡟⢆⣀⠀⠀⢸⣀⢀⣤⢃⢆⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⢸⢰⠀⠉⠉⠉⠉⠉⠁⠈⢻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡆⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠠⡇⠀⠀⢸⡄⠀⠀⠀⠈⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠵⠆⢤⣄⣠⡤⠠⡤⠖⠃⠀⠀⠈⠅⣀⣀⣀⢀⣀⡀⡴⠾⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠋⠉⢀⣀⣀⡀⠀⠀⠤⠀⠀⠰⣾⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⢀⣀⣀⠀⠀⠉⠉⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⣡⠀⠀⠀⠀⠀⠀⠀⣇⠐⠋⠀⠴⠀⠀⠀⠀⠀⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡚⠻⣧⣴⣄
⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡧
⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠆
⠀⠀⠀⠀⠋⠀⣀⣤⣤⣤⣤⡄⠀⢙⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⠻⡆⣀⣀⣀
⠀⠀⠀⠀⢀⣾⡿⠋⠉⠉⠉⠻⣷⡿⢚⣿⣿⣿⣿⣿⣹⣾⣿⣟⣿⡿⠋⣠⣶⣿⣿⣯⠻⢷⣦⡀
⠀⠀⠀⠀⣾⡏⠀⣰⣛⣙⣢⣤⣾⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣾⢫⠇⠰⣿⠃⢹⣿⣿⢤⡀⠹⣷
⠀⠀⠀⠀⢿⣇⠀⠹⣯⣩⠿⠉⢩⣾⢿⣿⣿⣿⣿⣾⣿⣿⣉⡡⠋⠀⠸⣿⠀⠸⣍⠛⣠⠇⢀⣿
⠀⠀⠀⠀⠈⢿⣷⣄⣀⣀⣀⣴⡿⠋⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠹⣷⣄⡈⠉⢁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⠤⠴⠒⠚⠋⠉⠉⢉⠑⠲⠤⣀⡀
⠀⠀⠀⠀⢀⣀⡠⠤⠒⠚⠙⠢⢍⡓⠢⢄⡴⣒⡒⣶⡹⠁⠀⢀⣀⣈⡙⠒⣤⠤⢤⡄
⢀⣴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢆⣿⣺⣿⣴⢤⢞⣽⣶⡷⢚⠿⠓⠈⠉⠙⠲⠤⣀⡀
⡞⢩⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡩⠾⢷⣡⣽⡛⢿⣖⣺⣗⣺⠭⠇⠀⠀⠀⠀⠀⠉⠓⠢⢄
⡇⠈⡆⠀⠀⠀⠉⠓⠦⣄⢀⣀⣤⠖⣊⠭⠕⠒⠉⠀⠀⠈⠀⠙⠢⢍⣓⠦⣄⡀⠀⠀⠀⠀⠀⢀⡠⠔⠒
⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⡏⡴⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣳⠦⡤⠖⠊⠁
⡇⠀⠀⡇⠀⠀⠀⠀⠀⢠⠃⡇⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡆⣧
⣇⠔⠋⠈⠲⣄⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⢀⡠⠔⠊⠉⠀⠀⠀⠀⡗⢻
⠙⠦⣀⠀⠀⠀⠉⠒⢤⣸⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸
⠀⠀⠈⠑⠦⣀⠀⠀⠀⢸⣼⠦⣀⠀⠀⠀⠀⢀⠔⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿
⠀⠀⠀⠀⠀⠈⠓⢤⡀⢸⠈⠀⠀⠑⠢⠤⠴⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠀⠀⠀⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢸⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡗⣇⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠳⢄⡀⠀⠀⠀⠘⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡤⠧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠘⢆⢈⠃⠀⠀⢀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢬⣾⣤⠴⠚⠉

⠐⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣰⠖⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠛⠒⠛⠛⠛⠛⠛⢱⡆
⠀⠀⠛⠀⠂⠒⠀⠂⢐⡀⠘⠀⡂⠀⢂⠀⠂⠛⠀⠃⠐⠀⢻⠁⠀⠐⠂⠃⠐⠃⠀⢂⡀⠃⠀⡀⢀⢀⠈⠀⠐⠂⠐⠃⠚⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡉⠀⠘⠀⠈⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⢀⠀⠈⠀⠓⠀⠃⡀⠈⣁⢒⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣁⣑⣀⣘⣀⣀⣀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠀⢐⣁⣉⣘⣂⣊⣙⣋⣂⣅⣀⣋⣊⣃⣙⣋⣁⠀⠀⡇
⠀⠀⠀⠀⣏⣡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⠀⠀⠀⠀⢸⣿⣵⣧⡆⡨⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇
⠀⠀⡇⠀⣿⢾⠓⠥⠄⠆⠠⠠⠴⠐⠠⠀⢰⠦⠴⠆⠾⠀⢸⠀⠀⠀⠀⢸⡿⡟⠧⠿⠖⢲⠶⠰⡶⠶⡖⠀⡖⠲⡶⠶⠀⠀⡇
⠀⠀⡇⠀⡻⢾⠖⠲⠒⠖⠖⠒⠶⠒⢺⠒⢶⠒⢲⠒⠶⠀⢸⠀⠀⠀⠀⢸⠶⠬⠦⠶⠤⢤⠤⠤⠦⠤⡥⠤⡤⠤⠤⠶⠀⠀⡇
⠀⠀⠁⠀⡇⠺⣿⣾⣷⡆⠁⠀⡽⠀⢸⠀⢸⠀⢸⠀⠸⠀⢸⠀⠀⠀⠀⢸⠀⢼⠀⢵⠀⢸⠀⠀⡃⠨⡇⠀⡇⠀⡇⢰⠀⠀⡇
⠀⠀⠀⠀⣅⣸⣯⣩⣼⡷⣷⠀⣼⣿⢽⢢⢸⠀⢸⠀⢠⠀⢸⠀⠀⠀⠀⢸⠀⠡⠀⠨⢰⢸⠞⢒⡁⠀⡇⠀⡇⠀⡇⠘⠀⠀⡇
⠀⠀⠀⢸⣿⣿⣿⣥⣶⠶⡇⠀⢹⡟⢻⠈⢸⠀⠘⠀⠸⠀⢸⠀⠀⠀⠀⢸⠀⢘⠀⠀⠘⢿⠋⡸⠀⠀⡇⠀⡇⠀⡇⢠⣀⠀⡇
⠀⠀⠀⠀⣀⣽⣟⣟⣁⠀⠇⢞⡋⠰⣹⢠⢰⡮⢠⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⢀⡰⠒⢹⢄⠒⡅⠀⡇⠀⣧⡀⢹⣧⣌⣀⡇
⠀⠀⡤⠈⠁⠀⠀⠀⠁⠱⣕⠀⣓⠀⢹⠠⢸⡗⢱⠀⠸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⠈⢐⠆⠀⠃⠀⡇⠙⣆⢩⠈⠛⠀⡀
⠀⢠⠗⠀⠀⠀⠀⠀⢘⠀⠀⠸⡿⣾⡼⢤⡬⠰⠎⠀⣨⠀⢸⠀⠀⠀⠀⢸⠀⠰⠀⢘⠀⢸⡗⠀⠄⠀⡃⠀⡇⠀⠜⠻⠒⣶⣾⠃⠀⠐
⠀⢸⠰⡀⠀⠀⠀⢘⣿⡗⣮⡀⢹⠖⠛⣉⡈⡟⢛⡛⠻⠀⢸⠀⠀⠀⠀⢸⠛⠛⠚⡛⠛⠺⡗⠚⠓⣒⣓⡲⠟⠀⠀⠀⠘⣿⠂⡌
⠀⠀⢻⠛⠖⠂⠋⣠⣾⡇⠀⢉⣥⣶⣴⡴⠶⠿⠓⠀⠈⠀⢸⠀⠀⣀⠀⠘⠊⠁⠀⠁⠈⠉⠙⠛⠐⠬⢈⡀⣠⡞⠛⠀⠀⢿⡱⣧
⠀⠄⣼⠀⠀⠀⠀⠸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠷⠧⠴⣧⠞⠀⠈⠣⠥⠥⠭⠍⠁⠬⠭⠉⠌⠉⠩⠽⠿⣿⠃⡀⠀⠀⢹⠿⡯
⠀⢰⡇⠀⠀⠀⠀⠀⢿⡧⣤⠤⣬⣤⡤⡤⡤⠤⠤⠤⠤⠤⠏⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠾⠼⢦⡵⠶⠾⣶⣷⠂
⠀⢸⠁⠀⠀⠀⢰⠀⢸⠆⠀⢠⢟⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢸⣻⣧
⠀⡘⢰⠀⠀⡇⠀⠀⢸⡆⠀⡀⣾⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠅⣿⡇
⠀⠇⠈⠀⠀⡇⠀⠀⢸⠃⢰⣧⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⢹⣧
⠀⡴⠀⠀⠅⠇⠀⠀⣰⣀⣭⣿⣿⢟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠃⠘⠸⡆
⠀⡇⠀⢠⡀⠀⠀⢰⣿⣿⢃⣿⢯⣿⣣⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣄⣈⠀⠁
⠀⡷⠶⢰⣤⣴⣶⣿⣿⣿⢸⡷⢱⢻⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⢿⣿⣿⣿⣿⠟⠃⡄
⠠⡇⠀⠀⣻⠘⣿⠹⡟⣿⠃⢿⣷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⠃⣽⣿⣿⠶⡋
⠰⠇⠀⠀⠅⢀⢿⡞⣦⣿⠉⢻⠋⣽⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡿⣿⣏⢠⠖⠁
⠀⠀⢤⣀⣀⣀⣞⣣⣿⣾⣿⣿⠿⠛⠛⣛⣛⣛⡛⠛⠒⣛⣿⡟⢛⣛⣛⠛⣛⣓⣛⣛⣛⡛⠛⠓⠛⠛⠛⠛⠛⢛⢽⣿⣿⣿⢿⣽⡿⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣄⡀⢿⣿⣿⣿⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣉⣋⣉⣉⣉⣿⣿⣿⡿⢀⣠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣦⣍⠻⢿⣿⣿⡿⠟⣩⣴⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣦⣍⣩⣴⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠋⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠋⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠁⠀⠀⠀⣸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⣿
⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢸⣿⣿
⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⢸⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣦⣤⣄⠀⠀⣿⣿⡛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⢸⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠛⠛⠻⣿⣿⠀⠀⣿⣿⡄⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⢸⣿⡏
⠀⠀⠀⣿⣿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣄⠀⠀⣿⣿⣇⣀⣀⣀⣿⣿⠀⠀⣿⣿⠆⠀⠀⠈⠻⣿⣦⣀⠀⠀⢀⣴⣿⣿⠀⠀⠀⢸⣿⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠸⠿⣿⣿⣿⡿⠿⠟⠀⠀⣿⣿⠁⠀⠀⠀⠀⢈⣿⣿⣿⣾⣿⡿⠻⣿⣷⡄⠀⢸⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣿⠏⠉⠉⠀⠀⠀⠈⢿⣿⣦⣸⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠛⠉
⠀⠀⠀⣿⣿⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⡄⣰⣿⡟⠀⠀⢀⣠⣶⣿⡿⠟⠋⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣷⣿⣿⣀⣴⣾⣿⠿⠛⠉
⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣶⡶⠾⠿⠟⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⢶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⠿⠷⠶⣶⠀⣿
⠀⠀⢴⣶⠿⠟⠛⢻⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣫⣽⣿⣛⡋⠀⣿⣄⣿
⠀⠀⢸⣷⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⢾⣿⣭⡥⢀⣿⢹⣿
⠀⠀⠈⣿⡀⠀⠈⢹⣿⠀⠀⠀⣉⣉⣉⣉⣉⣉⡁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⠿⠿⠟⢸⣿
⠀⠀⠀⢿⡇⠀⠀⢹⣿⠀⠀⠀⣄⣀⣀⣈⣉⣉⡀⠀⠀⢸⡇⠀⠀⠀⠚⠒⠒⠲⠀⠠⠤⠤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠈⣿⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⢸⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠛⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⣇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠘⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢻⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⢀⡀⢀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠘⣿⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢀⣀⣠⣤⣤⣶⣶⠾⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠛⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠

⠀⢠⣾⣿⡟⠁⠀⣴⣿⣿⠃⠀⢀⣼⣿⡿⠁⠀⢠⣾⣿⠟⠀⢀⣼⣿⡿⠃⠀⢀⣾⣿⡟⠁⠀⣠⣿⣿⠟⠀⢀⣼⣿⡿⠁⠀⢠⣾⣿
⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⡠⠒⠖⡙⢲
⠀⠀⠀⠀⠀⠀⢀⡴⠤⠞⣒⣋⠬⠥⠐⢒⡉⢭⢱⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢒⣉⣒⣉⣒⣋⣒⣛⣞⣛⢹⠆
⠀⠀⠀⠀⠀⠀⢘⡆⢚⢩⠄⠂⠀⠀⠀⣠⡄⠀⠧⡆⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣮⢸⡧⠆⡴⠒⣦⠴⣲⡢⡸⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠱⡌⣴⠀⠀⣾⣿⣶⣿⡇⠀⠸⣱⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠓⠉⢯⣼⠂⢊⠓⠙⢹⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣄⢧⡇⠀⠈⠻⢿⠟⠀⠀⢀⡃⡇⣞⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡰⢞⣙⡎⡆⢸⠀⡀⢸⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⡘⣀⣀⠠⠄⢐⡒⠬⣉⣂⢰⠈⡵⠀⠀⠀⠀⠀⠀⠐⡧⢸⠣⡢⠭⠤⣣⢾⣶⡸⠸⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢣⢑⠂⠭⣌⠒⠈⣍⡑⠬⠌⡆⢣⡀⠀⠀⠀⠀⠀⠘⡖⠘⠒⠈⠿⠯⠥⠤⠭⠤⠞⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⡀⢌⣓⣂⠬⢅⡒⣂⣍⡥⠦⠎⠁⠀⠀⠀⠀⠀⠀⠉⠚⠙⠙⠚⠉⠚⠓⠚⠚⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢥⣉⠭⡤⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⡠⢆⣀⠴⣀⣠⢦⣀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⣶⠒⠒⠒⠒⠊⠑⠲⣑⡶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢒⣞⣥⠽⠿⣟⣷⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢾⠉⠛⢒⢂⣀⢀⠀⠀⠘⡗⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⣽⢟⡥⣀⣰⣒⣒⠉⠻⣾⡓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⣼⠞⡩⣌⡙⢶⡀⠀⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣼⠃⣩⢪⠛⣉⠉⠙⢕⢎⢪⣷⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⠐⡏⠌⠀⠀⢹⠨⡗⠀⠟⡧⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⡏⡆⡇⡇⠘⣌⢟⡹⠀⣿⠾⢺⣣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⠀⢹⣨⣒⣒⣩⡼⠉⠀⢎⡧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⢠⡱⣱⣀⠘⠁⣀⢜⡜⠀⡾⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽⠀⠰⣒⣋⣙⣒⣒⡂⠀⢧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⢷⣇⡈⠿⣿⡿⠓⠉⣠⣾⣡⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⢄⠀⠉⠋⠋⠙⠉⠁⡠⠱⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠽⢿⣗⣦⡴⠖⣛⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠳⠎⠉⠶⠋⠱⠞⠉⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠋⠁

⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀
⠀⣴⣿⣿⠏⠀⢀⣾⣿⡟⠁⠀⣠⣿⣿⠟⠀⠀⣴⣿⡿⠃⠀⢠⣿⣿⡟⠀⠀⣰⣿⣿⠏⠀⠀⣼⣿⡿⠃⠀⢠⣿⣿⠟⠀⠀⣴⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢀⣀⣀⣀⢀⡀⠀⣀⣀⡀⠀⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠏⠀⠉⠀⠀⠀⠂⠣⣀⢀⡐⠠⠄⠀⠀⢐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⣀⠈⡀⠤⠄⠀⠀⠀⢈⠂⠀⠁⠀⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠃⠀⠀⠀⠀⠁⠀⠈⠐⠒⠀⠀⡀⢀⠀⢁⣂
⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠒⠈⢐⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⢀⠀⠸⠠⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠆⠉⡀⠀⠀⠀⠀⠀⠂⠄⡰⠂⠋⠀⠀⠀⠈⡐⠀⠴⠀⠊⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠊⡇⠰⠁⠀⣠⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠀⠀⠀⠄⢀⠠⠄⠁⠀⢀⢀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⡆⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠁⠁⠂⠀⡐⠁⠀⠁⡁⡀⠀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠠⠀⠀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡀⡀⣀⡠⢀⡈⢢⣁⣂⣴⣀⣠⣂⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⠸⢉⡄⢠⠨⣄⠨⠁⠬⢮⡛⠈⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⢚⢀⠸⡀⢒⠦⠶⠀⠐⠲⡦⠐⠆⣺⠟⠘⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⡀⠀⠑⠀⠈⠠⠤⡀⠁⠈⣁⠀⠀⠀⡔⢁⡤⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠄⠄⣀⣀⠈⠂⠤⠠⠤⢤⡀⡌⠢⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠰⠤⢄⡐⠧⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣄⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠛⡀⢀⠀⠐⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠉⠳⡜⣰⣄⡸⠁
⠀⠀⠀⠀⠠⠢⠄⢀⢼⣁⡀⠀⠀⠊⠈⠉⠙⠛⠋⠁⡐⢀⣀⣠⠄⢀⡀⠀⠀⢀⡹⢈⠀⡀
⠀⠀⠀⠀⢀⣬⠞⠁⣠⡶⠾⠟⠂⠠⠈⠉⠉⠉⠁⣠⡀⠉⠉⡄⠀⠉⠉⠁⠰⠣⠃⡄⠀⠙⠀⠐⠶⠶⠄
⠀⠀⠀⠀⠘⠀⢠⠚⠁⣀⡀⠀⠠⠀⠙⣘⢫⡁⠀⠁⡼⠸⢦⠄⡦⠤⠤⢶⠀⡲⡀⢡⣢⠀⢂⢆⠀⠤⣄⡈⠑⢄
⠀⠀⠀⠈⠀⢠⠁⠠⠬⣍⣀⠸⠁⠱⡀⠟⠃⣉⣉⠫⠼⠦⠂⠀⠙⢢⠀⠀⡄⠁⠃⡈⠁⡔⡪⢻⡆⠙⠷⡝⡆⠈⠆
⠀⠀⠀⠀⠀⠘⠲⠦⠤⢤⣀⣉⠉⠒⠻⠯⠍⣙⢶⣢⠄⠀⢐⠂⠐⠆⣢⡾⣣⠂⠀⡇⠸⡷⡧⠀⠁⠄⠀⡿⢹⠀⢸
⠀⠀⠀⠀⠀⠘⡄⠘⢄⡀⠀⠀⢉⡉⠑⠒⠠⠤⠄⠉⠀⠉⣉⣀⣈⠭⠥⠞⠁⠀⠀⠱⡀⠣⡙⠦⢄⠤⠞⣡⠏⢀⠇
⠀⠀⠀⠀⠀⠀⠈⠦⣀⠉⠉⠉⠉⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠓⠒⠒⠊⢁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣿⠶⢶⡆
⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠚⠋⠉⠀⠀⠀⢸⡇
⠀⠀⢰⣾⠛⠛⠛⠛⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⠋⠉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣿⠐⡏⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠀⠷⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⢦⡀⠀⢀⡴⠛⣆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠀⠀⢀⡾⠀⠈⠳⣴⠋⠀⠀⠘⢧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⣿
⠀⠀⠀⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢚⣉⣡⠤⠄⣿
⠀⠀⠀⢸⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢉⣉⣤⠤⢀⣿
⠀⠀⠀⢸⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣉⣥⠴⠚⠋⠁
⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡇⠀⠀⢀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠿⠷⠖⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠭⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⡳⠀⠀⣠⡀
⠀⠀⠀⠀⣗⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⢀⣰⠼⠁⠂⠁⡼⠁
⠀⠀⠰⡂⢝⣆⠉⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⢀⣤⠴⠒⠋⢁⢀⣀⣀⣤⡎⠤⠔⠊⡽
⡄⡀⣤⡹⣤⡈⠙⠶⢤⣄⣄⡈⢉⠉⠐⠢⡄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢢⠋⢀⡴⠚⢁⣠⠤⠒⠚⠉⠉⠉⠀⠀⠀⢀⣰⠞⡡⡠
⠀⠁⠱⣌⠒⠛⠲⢤⣀⣈⣉⢉⠝⠁⢄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠁⠐⢯⠀⢀⡤⠖⠓⢓⢳⡷⠋⠉⠉⠁⠈⠈
⠀⠀⠀⠈⠳⣶⣀⣀⠀⠈⣉⣉⡀⠸⠿⠤⠀⠀⠠⠤⠀⠠⠤⠠⠤⠄⠠⠤⠤⠄⣀⠀⠉⠢⡀⠀⠃⠈⣠⣶⠺⠭⢓⠂
⠀⠀⠀⠀⠀⢯⣍⠉⠙⠛⠋⠠⠄⠂⠀⠀⠀⠀⠀⡇⠀⠀⡄⢰⣢⣀⠤⢤⣄⣀⠈⡗⢦⡀⠘⡄⠀⢀⣠⣠⡶⡚⠁
⠀⠀⠀⠀⠀⠀⢩⣛⢶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⡇⠘⠉⠙⢀⣈⡉⠸⠀⡯⡲⢝⣲⠇⠀⠈⡉⢁⡥⢃⠄
⠀⠀⠀⠀⠀⠊⠊⠳⢶⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⠇⢆⣀⡀⠬⠕⠂⠃⠀⠑⢬⡲⠋⠈⠻⣿⣚⠉⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠰⣄⣉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡭⢀⠀⠀⠁⠉⠉⠊⠀⠀⠨⡟⢀⠸⣷⢶⠶⠛⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⠀⠀⠀⠀⠀⠀⠀⢸⠍⣷⡈⣿⠞⣻⡒⢈⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠠⡆⠀⠀⠀⠀⠀⡆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⠚⠻⡿⠁⠟⠽⠻⢁⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡄⣆⠀⠀⠀⠀⠀⠃⢸⠄⡀⠀⣀⣀⠀⣄⠀⠦⣀⠤⣼⠦⣴⢀⣤⡇⠈⡎⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣤⢤⡤⡤⣤⢼⠬⣤⢧⡤⠤⣤⢤⡤⣤⣖⠔⢢⠆⢠⠟⣓⡟⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣵⣙⢟⣳⣿⣾⣶⣟⣟⣻⣤⣟⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠉⠉⠙⠛⠛⠓⠛⠓⠛⠚⠛⠛⠛⠛⠛⣃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡀⢀⠀⠀⢀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠂⠅⠠⠀⠨⠀⠀⠀⠀⠈⠠⠔⠠⠀⠄⠨⠀⠄⠀⠄⠬⠊⠔⠠⠂⠅⡨⠀⠅⡢⢀⠅⡠⡴⠤⠤⠤

⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⣿⣿⣿⣿
⣿⣿⡇⠉⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠉⢸⣿
⣿⣿⠇⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⣀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠛⢿⣿⣷⣄⣠⣾⣿⡿⠛⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠉⠻⣿⣿⠟⠉⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⢸⣿
⣿⣿⡇⢀⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⡀⢸⣿
⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠈⠉⠉⠉⠉⠀⣠⣤⣀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⡀⠀⣠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⡏⡿⣿⣿⢿⣿⠛⠛⠛⢿⣿⣿⣿⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⢰⣿⣇⣿⣿⣿⣿⣶⡶⠶⠿⠿⠿⠿⠿⠇
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣨⣯⣧⣿⣿⣿⣿⣿⢀⡐⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢂⡀
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⣾⣿⡇
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣦⣍⠻⣿⣿⣿⣿⣿⠟⣩⣴⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠓⣠⡙⠻⢋⣤⡘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠟⣉⣴⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠻⠇
⠀⠀⠀⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⠋⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣆⠀⠀⠀⠀⠀⠀⠠⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⠟⠛⠉⠀⠀⠀⠀⣰⣾⣿⡿⣷⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢷⣶⠞⢻⡏⢀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣤⣴⣖⠿⢿⠇
⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣴⣦⣾⣿⣶⣤⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢙⣟⣛⠛⣋⣰⡏
⠀⠀⠀⠀⣠⡾⠛⠉⠀⠉⠉⠉⠙⠛⠿⢻⣿⣿⣿⣿⣿⣋⣠⣤⣿⣆⡀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣧⢹⡇⠀⠘⡀⠈
⠀⠀⠀⠀⠹⠃⠀⣤⣶⣶⣶⣤⣀⠀⠀⢠⣝⣿⣿⣿⣿⣿⣿⣿⠟⠉⣈⣿⠉⠁⠀⢸⡏⠉⢻⣿⣿⢿⣧⣥⠀⠀⠂⠂
⠀⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⠀⠄⡑⢶⣴⠉⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⣷⣤⣾⣿⡇⣼⠟⣿⣇⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣾⡟⡀⠀⣤⣤⣐⠉⡂⠁⠀⠱⢶⣶⣶⣶⣦⣿⠟⣛⣿⣿⣟⣿⣟⣿⣿⡿⣩⣿⡟⢿⠃⠀⢹⣿⡄⢌⠸⣿⡆⠑⠢⣄⣀⣀
⠀⠀⠀⠀⠀⣿⡗⢅⢀⣀⠀⠉⠉⠛⠒⠚⠖⠾⠿⠿⠿⠿⢃⣼⣿⣿⣿⣿⡿⣿⣿⣿⣵⣿⣿⣷⠇⠀⡀⠈⢷⢷⣀⡠⠙⢷⡀⠀⠹⣿⣿⡆
⠀⠀⠀⠀⠀⢿⣧⠀⠀⢉⡋⢉⢘⢙⢒⣦⣦⣿⣶⣶⣶⣶⣿⡿⠉⡀⢄⠀⠉⢂⠙⣿⣿⣿⡿⢩⣤⣾⠇⠈⢹⡏⣿⣿⡆⡀⠁⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣷⣌⡉⠂⠠⣀⣀⣈⡉⠉⠛⢻⠻⠿⢿⣿⣧⡀⠃⢈⣀⣬⣤⣤⣼⣿⣿⠃⣾⣿⣿⡇⠀⠀⢿⣿⣿⠇⠄⠐⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⢟⣛⡻⢟⡛⠒⣓⠲⠶⠶⢶⣦⣌⡙⠿⠿⠿⠟⠋⠡⠚⠁⠘⣿⣷⡀⠀⠀⠉⠁⠀⡀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠛⠒⠵⠯⢅⣆⠌⠉⠓⠶⠶⣞⠣⠄⠀⡤⡤⡸⣿⣿⣦⣀⠀⠀⠀⢀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠓⠦⠾⠤⣀⣀⡀⠀⠬⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠱⠮⢭⣙⣛⣫⠭⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠉⠉⠉⠉⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠒⠿⠍⠙⠒⠒⠒⠒⠒⠀⠈⢹⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⣄⡠⢄⠓⠈⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢨⡅⢀⡼⠁
⠀⠀⠀⠀⠀⣠⠴⢶⡀⠀⠀⠀⠀⠀⢧⡀⠀⣯⠐⠈⠀⡀⠠⢀⣐⠠⠬⠑⠒⠒⠀⠀⠀⠀⢀⡶⠒⣿⠞⠁
⠀⠀⢀⡴⠞⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠙⠦⣽⠄⣂⣅⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠏⠡⠀⣿
⣠⡾⠋⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⣸⠏⢁⠋⠿⠷⠶⠦⢤⣄⣀⣀⣠⡴⣛⠁⠀⠁⠀⠃⣼⠓⢶⡀
⠹⡅⠒⠠⠄⣀⠀⡀⠀⠀⠹⣆⠀⠀⠀⣰⠛⢙⣆⠌⠀⠀⠂⣴⣖⢂⡄⠀⠀⠀⣍⢰⣿⠈⠃⠀⠀⣿⠀⠀⡇
⠀⠹⣄⠀⣀⡀⠀⡁⠀⠀⠀⠘⢦⡀⠀⣷⠀⠘⢏⠀⠀⠀⠁⠛⠻⠋⡇⠀⠀⠀⠈⠙⠉⠁⠀⠀⢀⡇⠀⢠⠇
⠀⠀⢹⡟⠀⠟⢳⣅⠂⢀⡀⠀⠀⠹⣄⠸⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣸⣥⡴⠎
⠀⠀⣾⠁⠈⠀⠆⢨⠁⠀⠉⠀⠠⠄⢈⢳⣌⠛⠶⢷⡄⠀⠀⢀⣠⣴⣿⣿⣾⣿⣿⣷⣦⣄⡀⢠⡏
⠀⠐⡇⠀⠀⠈⠀⢸⡀⠀⢀⠀⠀⢀⣠⠞⠁⠀⠀⢀⡽⢦⡘⠻⠿⠿⠿⣟⣛⡻⠿⠛⠛⠋⡱⢻⣦⡀
⠀⠀⢻⡀⠀⠀⠀⠀⠱⣄⠈⣀⡴⠋⠀⠀⢀⣠⠶⢏⠀⠘⡍⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢺⠈⠙⠦⣄⡀
⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸⡿⠿⡄⠀⣠⡴⠋⠁⠀⠈⡆⠀⠐⡄⠈⠓⠶⢤⣤⣤⣤⠖⠃⠀⢨⠃⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠸⡷⠤⠒⠒⠊⠁⠀⠀⢱⠞⠁⠀⠀⠀⠀⠀⠘⡄⠀⠈⢂⡀⠀⣬⠃⠀⢣⢀⡀⣸⡇⠀⠀⠀⠀⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⠔⠆⠀⠀⢰⡇⠀⠀⠀⠘⢄⠀⠀⠳⡒⠊⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢳⡄⠐⠒⠀⠉⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠈⠧⡀⠀⠙⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠘⣦⢎⠕⠢⣔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠴⠆⠐⠰⢄⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣀⡤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡢⠤⢪⠚⢄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠄⠀⠠⠀⠰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠤⠖⠋⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠣⣄⠀⠈⠲⢶⣀⣀⣀⡤⠼⠿⡀⠠⠀⠀⡀⢀⠛⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⠚⠉⠁⠀⠀⠀⠀⠉⠒⠋⠋⠁⠁⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⠉⠐⠒⠒⠂⠀⠀⠀⠸⠏⠩⢩⣙⡖⢻⠈⢢⠀⠀⠀⠀⣠⣠⡄⣴⣦⣾⣾⣦⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠒⠂⠠⠤⠤⠀⢀⣀⣀⣀⣀⠘⠻⠿⡇⠠⡇⠀⢣⠀⠀⠀⠛⠛⠋⠉⠈⠀⠀⠀⠀⢀⣀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠸⡀⠈⢣⠀⠀⠀⠀⣠⠀⠐⠂⠀⡙⡏⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠉⠁⠀⠑⠒⠖⠀⠈⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠉⠉⠐⠒⠒⠒⠂⠤⠀⠒⠒⠒⠒⠒⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠃⠀⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⠛⠛⠋⠙⡆⠀⠀⠹⣄⠀⠀⠀⣀⣀⣠⡤⠴⠶⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠛⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠤⠤⠄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠠⠤⠀⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠦⠤⢀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⠤⠴⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⠤⠖⠒⠚⠉⠉⣑⠒⠤⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠉⠒⠭⣒⠢⡴⣪⣑⡮⡏⠀⣀⡤⠬⣍⣲⡦⣄⣄
⠀⠀⢀⡶⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢽⣿⣿⣷⣎⣾⠿⣛⣽⣋⣍⠀⠈⠙⠒⠤⣀⡀
⠀⠀⢸⠀⡄⠈⠙⠢⢄⡀⠀⠀⠀⠀⣀⠠⢤⣒⠩⠛⠒⠷⠹⡛⠿⣓⠒⠉⠀⠀⠀⠀⠀⠀⠉⣒⢤
⠀⠀⢸⠀⢠⠀⠀⠀⠀⠈⠑⡶⣺⡿⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠺⢭⣒⢤⣄⢀⡠⠔⠂⠉⠀⢸
⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⡗⡇⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠟⡎⣇⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡠⠂⠑⠦⡀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠉⠒⢤⣀⠀⣀⠤⠒⠉⠁⠀⠀⣷⢻⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠢⢄⡀⠀⠈⠑⠢⣤⣹⠁⠀⠀⠀⠀⠀⠀⣀⠔⣛⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⢸⢿⠢⢄⠀⠀⠀⣠⠞⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣸⢸⠀⠀⠉⠒⠊⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠦⣀⠀⠀⠀⠀⢣⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣏⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠈⢧⠀⡇⠀⠀⠀⢀⡠⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣣⣇⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣭⣭⣭⣭⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⢸⡏⠓⡞⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠳⠮⣭⣝⣛⣳⠶⣦⣤⣬⣇⣀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣄⣀⡀⠉⠉⠙⠛⠶⠦⣭⣍⣛⡛⠻⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⣿⠛⣷⣶⠦⣤⣼⣛⡃⠉⠉⠛⠓⠶⢦⣭⣉⣛⠲⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠉⠁⣠⠿⠽⠶⠏⢸⡏⢹⡟⠻⣶⣦⣤⣄⣀⣈⠉⠙⢿⠉⣿⣤⣤⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇⠸⣇⣰⣿⣿⣀⡼⢻⣿⡛⠻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠤⠤⣤⡤⠶⠶⠚⠋⠁⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⢸⣇⣴⡟⠡⣿⠈⠉⢀⡾⠻⠿⠟⠁⠈⠉⠛⠓⠶⠶⠶⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣋⣥⣤⣀⡀⠀⠀⠀⠀⢀⣼⡏⢹⡇⢸⡿⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⣿⠻⠥⣄⣉⠉⠛⢳⣶⣾⣏⣽⡇⢸⡇⢸⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄⣀⣬⠿⠻⠿⣤⣤⣈⡉⠙⢻⡷⢿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⣷⣍⣩⡿⢳⣶⣤⣀⣀⣉⣽⣿⠿⢦⣤⣈⡉⠛⠻⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠉⠉⠀⣸⣿⣦⣬⡿⠻⣷⣬⣄⣀⠀⠉⠙⠛⠳⢶⣤⣌⣉⢛⣿⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠛⠛⠒⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣿⠀⢨⡏⢻⣷⣶⢤⣄⣀⡀⠈⠉⣿⢁⣿⠦⠤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣇⣸⡿⠷⠶⠿⣏⣿⠛⣶⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢶⡏⢸⣏⠀⠀⢀⡿⠛⠛⠁⠀⠉⠛⠲⠶⠶⠶⠶⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣿⠁⢸⡇⢸⡟⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣤⠴⠞⠛⠉⠀⠀⣿⠀⢸⡇⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⢼⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠤⠶⠖⠛⠛⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣸⣇⣼⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⢀

⣾⣿⠷⢴⣿⠿⢶⣾⡿⠶⣾⡿⠷⣶⡿⠷⣴⡿⠿⣦⡾⠿⣷⣾⠿⢷⣶⠿⢿⣦⠾⢿⣶⠾⢿⣷⡶⠿⣿⡶⠿⣿⡶⠾⣿
⢙⡇⠀⠀⠉⠀⠀⠉⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠁⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠈⠀⠀⠉⠀⠀⢸
⣿⡟⠀⢸⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⡿⢿⡉⣻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣼⣧⠀⢸⣿⡿⢻⣿⣿⣿⣾⣿⣿⣿⣿⠛⢥⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠻⡏⠀⢸⣿⣷⣴⣿⣿⣿⣿⢿⣿⣿⣿⡆⠀⠀⠉⣿⠟⢿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣾⡿⠀⢸⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⠏⢹⣿⣿⣦⡟⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢿
⣹⣇⠀⢸⣿⣿⣏⢙⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣸
⢿⡏⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠀⢹
⣼⡷⠀⢸⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡏⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⢾
⢻⣇⠀⠸⢿⣿⣿⣷⣾⣿⣿⣿⡿⠿⣿⣿⣿⡀⠘⣇⠈⠢⣄⣘⣉⡟⢛⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⣸
⣿⡏⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣧⠀⢻⣭⣴⢛⡩⠉⢻⡧⠤⠄⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⢹
⣨⣷⠀⢸⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⢃⠀⠈⣸⣿⡏⠁⢉⣿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⠀⣾
⢿⣇⠀⢸⡏⢙⣿⣿⣿⣿⣿⣿⣿⣟⡀⣿⠁⠘⢁⣴⡿⠿⣿⠐⠾⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠀⣸
⣾⡟⠀⠘⠻⢿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣇⠀⠀⠺⠁⢸⠀⠀⠀⠐⡻⡍⠻⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻
⢙⣧⠀⠀⠀⠀⠈⠉⠛⠿⣾⣿⣿⣿⣿⣿⣿⣶⡄⢠⠇⠀⠀⣠⢊⣜⠀⣆⣽⡿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⣼
⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣧⠉⠀⢀⡜⣡⠎⡛⢘⢿⣿⣷⡀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⠀⢸
⣼⡟⠀⢸⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠇⢀⣮⠞⠁⢀⠁⢸⢀⢻⣿⣿⠀⠀⠠⠏⠀⠈⠙⠻⠿⣿⣿⣿⠀⢻
⠻⣧⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢀⡾⠋⡀⠀⠘⠀⢸⡰⢿⣿⣿⡄⢀⣴⡇⠀⠀⠀⠀⠀⠀⠉⠛⠀⣼
⣾⡇⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⡞⠁⣰⠁⠀⠁⢀⠘⡅⢿⣿⡿⢠⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⢸
⣹⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠆⢠⠃⠀⠀⠀⢸⠀⡇⠸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢿
⢿⣧⠀⢸⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⢠⠎⠀⠀⠀⠀⢈⠀⡇⠀⣿⡟⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠀⣼
⣼⣏⣀⣸⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠘⡇⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠀⢹
⢻⣿⡉⢉⣛⡻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢐⡇⠀⠘⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢾
⣿⣯⡇⢀⡏⠈⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣠⠞⠁⠀⡀⢸⡇⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⣸
⣨⣟⣁⣸⣅⡀⠀⠿⠀⠀⡠⣌⠻⣿⡻⢿⣿⣿⣿⡇⠀⡵⠃⠀⠀⣇⣠⣴⣾⣿⣿⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⠀⢹
⢿⣿⡉⢻⣿⣿⣷⣶⣤⣞⠣⣠⠇⠘⢿⣄⠈⠉⠛⠃⠊⠀⠀⠀⠀⠈⣩⡟⣻⣏⣿⣀⣀⣀⣀⣀⣀⣉⣛⣻⣿⣿⣿⠀⢾
⣾⣟⠋⠹⢿⣿⣿⣿⣿⣿⣿⣷⢶⣶⠾⢿⡶⠒⠞⠛⠛⠛⠛⣛⣿⣿⢛⣋⣻⣏⣿⣿⣿⣭⣉⣉⣉⣉⣉⣉⣉⡉⠉⠀⣸
⢹⣟⠀⠉⠛⠛⠻⠻⠿⣿⣿⡷⣿⣿⠿⣿⣿⣿⣟⡛⠛⢛⠛⣟⢻⣿⣟⣋⣻⣏⣻⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣉⡉⠀⢻
⣿⣿⠗⠀⠉⠛⠛⠛⠿⠞⢿⡿⠺⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⠟⢻⣿⢿⡏⣿⠋⢉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⣾
⣼⣿⣶⡙⣦⠀⠀⠀⢠⡦⢸⣷⢸⣁⡝⢹⠟⣿⠋⢀⡀⣀⣀⣰⣟⣃⣀⣃⡁⠀⠸⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⠀⢸
⠻⡟⢹⣿⣷⣄⡀⠀⠀⠀⢸⣿⠀⠉⠁⢀⡀⣿⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠟⠀⢻
⣾⣷⣾⣿⣿⣿⣿⣷⣶⣀⣾⣇⣈⣷⣶⣾⣷⣿⣀⣴⣄⣀⣴⣦⣀⣠⣦⣀⣠⣦⣀⣠⣦⣀⣠⣶⣄⣠⣶⣄⣀⣴⣄⣀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠾⢭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡤⠴⠖⠛⠛⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠉⠓⣤⣄⣀⠀⠀⣠⠖⢋⣁⣼⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣁⣀⣉⣹⣶⣿⣟⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡄
⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢋⡩⠞⠁⠈⠓⠭⣓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠊⠉⠀⢻
⠀⠀⠀⠀⣼⢏⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣧⠸⡄⠀⠀⠀⠀⠉⠙⠲⢤⣤⣖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⠀⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⠀⠘⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⢀⢷⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⡠⠋⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⢀⡜⠁⠀⠀⠈⠓⠦⢤⣀⡇⠀⠀⣠⡾⠋⢦⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠛⠉⠀⠀⠈⣇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⠀⠀⠀⠀⠳⣄⡇⠀⠀⠀⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠤⠽⠧⠤⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠋⠉⠀⠀⠀⠀⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⣿⣍⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⡴⠾⠛⠋⠉⠀⠀⠀⠀⠙⠻⣦⣄⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡟⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠉⠻⢶⣄⡀⠀⣀⣤⣴⠶⠟⠋⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠉⣿⡟⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣦⣀⠙⠻⣦⣄⠀⢀⣀⣤⣴⠶⠟⠛⠉⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣯⣙⢷⡆⠀⠙⣿⠛⠉⠁⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⣿⠀⠀⣀⣠⣤⡶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠿⠟⠋⠉

⣀⣀⣀⣀⡀
⣿⠿⠟⠿⡇
⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣥⣤⣠⣸⣿⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣙⣛⣛⠛⡛⠛⠻⣿⡆
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣛⣛⠛⢿⣿⠀⣿⠇
⠀⠀⢠⣾⡿⠟⠛⠋⠉⣿⡇⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⣼⣿⣉⣉⠀⢸⢿⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡤⣾⣿⣭⣭⠀⢸⡿⢸⣿
⠀⠀⠀⢻⣧⠀⠀⠘⠉⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠓⠒⠒⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣼⢿⣽⣿⣿⠏⢸⣿
⠀⠀⠀⠸⣿⡀⠀⠀⠄⣿⡇⠀⠀⠀⠚⠛⠛⠒⠒⠒⠒⠂⠀⠀⠀⣿⠀⠀⠀⠀⣠⠤⣤⣤⣀⡀⠀⣀⣀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠉⣿⡇⠀⠀⠀⠛⠛⠒⠲⠶⠖⠒⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠙⠛⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢹⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣄⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠘⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠦⠴⠆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢿⣇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⢤⣄⠀⣀⣀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠉⠈⠀⠘⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣀⣀⣤⣤⣴⣶⣶⠿⠿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠋⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠯⢽⠻⢭⢟⠒⢤⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⠀⠉⣩⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣤⠀⢰⢡⠀⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢉⡠⠔⣊⣥⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠛⡴⣵⠛⢺⢱⠉⠓⢆
⠀⠀⠀⠀⢀⡠⠔⠚⣉⡭⠟⢻⠁⠀⠹⣇⡀⠈⢙⢖⡉⠑⢢⠤⢄⡀⠀⠀⡰⠃⠀⡄⠀⠙⠁⣀⣯⣇⣀⡀⠸
⣀⣤⣖⣋⣁⠤⢒⣩⠴⠀⠀⢸⠀⠀⣀⠭⠛⠷⣮⣅⣨⣧⠎⠀⠀⠉⠑⠶⠁⠀⠀⡇⠀⠀⢰⡟⠀⠀⠀⡏
⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣼⠖⠋⠠⠒⠁⠀⡇⠉⠉⠈⠑⠢⣄⡀⠀⠀⠀⢀⡴⡇⠀⡠⠿⠧⢄⡤⠴⠇
⡇⠀⠀⢸⡇⠀⣀⡤⠖⡋⠁⢸⠀⠀⠀⢀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠁⠀⢳⠀⢧⡀⢀⣀⣇⠀⢀⣀
⡇⠀⠀⢸⠖⠋⠁⠒⠉⠀⠀⢸⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⠛⡯⠤⠬⠏⠉⠈
⡇⠀⠀⢸⡇⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠀⣳
⡇⠀⠀⢸⣃⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠉⠙⢦⡀⠀⠀⣠
⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡆⠀⠉⠉⠉⡇

⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⡆
⠀⠀⠀⡇⠘⠀⠁⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⣀⣠⣿⣿⣿⣷⡄
⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠿⢟⣅⠀⠻⠟⢻⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢇⠈⠉⠀⠄⢠⠜⣤⡀
⠀⠀⠀⡄⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡾⠖⠂⠀⡀⡀⡉⠈⠓⡦⡶⠤⣀
⠀⠀⠀⡇⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡤⣞⠋⢀⠇⠀⢸⠠⠁⠀⠈⠳⢄
⠀⡠⢶⢃⠼⡒⢓⣼⣶⡶⡶⡤⢶⡖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⡗⣿⡓⠹⠀⢴⡎⠀⡄⠀⠀⠀⠼⣇
⢸⠁⠀⠳⢾⡓⠒⠒⠐⠒⠒⡛⡛⠛⠊⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠛⠸⠛⣿⣷⠋⠀⠀⡀⡀⠁⠀⠀⠀⠀⠸⣦⡀
⢸⠀⠀⠀⠀⠹⡄⠀⠘⠲⠀⠑⠟⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⡄⠘⠃⡀⠀⡼⢃⠁⠀⠀⡀⢀⠀⠠⠈⠛⣦
⢸⠀⠀⠀⠀⠀⡟⠒⠐⠒⠒⠛⠛⠛⠛⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣆⠀⠀⣷⠰⠀⠀⡴⠀⠀⣆⠆⢀⣿⣿⡓⠂⣀⠀⣿⣧
⢸⠀⠀⠀⠀⠀⠁⠀⠐⣶⠶⠲⠶⢶⡖⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡸⡄⠉⠀⠀⠌⠁⢀⡄⠿⢬⣈⢹⣿⣖⠊⡭⠶⣾⣿⠁
⢸⡀⠀⠀⠀⠀⠐⠀⠴⡇⠘⠚⠘⠨⢠⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠹⣇⢻⣴⢲⠃⢀⠠⢠⣈⣀⣀⠀⠀⠟⠃⠀⠈⣙⣼⣿⠀⠢
⢸⡃⠀⠀⠀⠀⣼⠀⠀⠮⠖⠘⠶⠞⠞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣾⣿⠈⢸⢠⣀⠸⡇⠀⠉⠉⠙⡳⠋⠓⠢⣄⣹⣿⠿⠷⢾⠄⠓⡦⣤
⢈⡇⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢈⣿⠳⢨⣀⠀⢠⣷⠰⠆⠀⡤⢄⣀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⣠⣯⡀
⢀⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣇⠀⢀⣀⣀⣤⠚⠁⠈⢣⣀⣈⣉⣽⡿⠀⣸⠉⡉⠘⠉⠓⠄⣠⠀⠀⢹⣦⡾⠋⠀⠀⠀⠀⣠⣴⡞⠉⠀⠙⣄
⠀⠧⠤⣤⣄⣀⣼⣀⣠⣤⣤⠤⠤⢴⣚⠁⡠⠀⡉⢻⢤⣀⡈⢗⠀⠀⣠⣯⡿⠛⠋⠁⢃⣷⣾⠀⡀⠑⠀⠤⡀⠒⢀⡿⠲⠶⣦⣤⣤⣴⠞⠋⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠿⠟⠛⡟⠛⠻⣿⣿⠀⠀⠺⠷⠶⢄⡈⠉⠀⢀⡤⠷⠘⠧⡿⠟⠋⠀⢀⠎⠀⢸⣿⠛⠻⢿⣶⣆⡠⣀⠶⣿⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⡆⠀⠀⡇⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠙⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⡇⠀⠀⠈⠿⣿⣿⡆⠀⠹⣿⣷⣄⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⣠⡿⠃⠀⠀⠀⢠⡏⣻⣷⡄⠀⠘⣏⠛⢻⠇⠀⠈⢆⠀⠀⠀⠀⠀⣤⠞
⠀⠀⠀⣧⠀⠀⡇⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡻⠁⠀⠀⠀⠀⠀⡇⠁⠙⢿⣄⣤⣼⣿⣦⣀⣀⡀⠀⠱⢀⣀⡤⠞⠁
⠀⠀⠀⠟⠀⠀⡇⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠃⠀⠀⠀⠀⠀⣰⠛⡄⠀⠘⡋⠛⠿⣿⣿⣿⢿⣁⡤⠞⠉⠁
⠀⠀⠀⢠⠀⠀⠂⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⣠⣶⠟⠀⠸⡄⠀⢱⠀⠀⣿⣿⣿
⠀⠀⠀⢸⠀⠀⠁⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⣰⢿⡏⠀⠀⠀⢱⠀⠀⢧⠀⠀⡿⣿⡆
⠀⠀⠀⠘⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⠁⠀⠀⠘⠃⣾⠁⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠒⠀⠀⠀⣠⠔⠊⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠄⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢋⣀⠤⠤⠐⠚⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠶⠖⠊⠉⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣤⠤⠖⠒⠊⠉⣉⡤⠚⠅⠰⣄⠀⠀⠠⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠈⠙⣆⠀⠀⢈⣀⣀⣤⡤⠶⢒
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡇⠀⠠⠀⠰⠃⠀⠀⢀⣀⣀⡤⠤⠀⠘⡆⠉⠉⠉⠀⣠⣼⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣠⠖⢱⠖⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⡸⠿⣾⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠤⢶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣈⡩⠽⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣬⣄⣠⠤⠤⠐⠂⠀⠀⠀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣭⣿⣿⣿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠛⠋⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢠⣴⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡟⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡅⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⢀⣼⣿⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠻⣿⣦⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⢸⣿⡇⠀⣠⣿⡿⠁⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠘⢿⣷⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠟
⠀⠀⢸⣿⡇⣰⣿⠟⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣤⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⠈⢿⣷⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠋⠁
⠀⠀⢸⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣮⣿⣇⠀⠀⢀⣠⣤⣶⣿⠿⠛⠋⠁
⠀⠀⠘⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣶⣾⣿⠿⠛⠉
⠀⠀⠀⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢰⡟⠹⣿⡛⠛⠛⠛⠛⠛⠛⣛⡛⠛⣃⣽⠏⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢠⡿⢠⣄⡈⠻⣷⣄⠀⠀⠀⣈⣥⠶⠛⠉⢴⢂⡿
⠀⠀⠀⠀⠀⠐⠚⠂⠀⠐⠒⠚⠓⠚⠒⠂⠀⠀⠀⣾⠁⠈⠀⠁⠀⠈⠛⢷⡶⠛⠉⠀⠀⠀⢀⡏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣄⠀⢀⣀⣀⣀⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁




⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢙⣿⣦⣀⣠⣶⣿⡋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⡾⠛⠁⠈⠙⠉⠀⠉⠻⣦⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠷⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣴⡄⠀⣦⠀⢠⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣀⣀⣀⣀⡀⢀⢀⠀⢀⡀⢀⣀⣀⠀⣀⣀⢀⡀⢀⡀⠀⠀⣀⡀⢀⣀⡀⠀⢀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⣿⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢠⣦⣤⣴⣤⣦⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠈⢹⣟⠉⠉⠉⠉⠙⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡧⠘⠿⠟⠟⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣉⣉⣉⣉⣹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠛⠃⠘⠛⠛⢻⣿⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠺⠇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠂⠓⠙⠓⠀⠛⠛⠛⠋⠛⠘⠃⠋⠙⠋⠛⠈⠀⠉⠘⠛⠛⠋⠙⠂⠋⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⢀⣤⣤⣤⡤
⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⠀⡤⡤⣤⢤⡤⠠⡤⢠⣄⡄⢠⣤⠀⠀⠀⠀⠀⠀⣿⣛⣶⣖⣓⣒⣞⣿⡿⠛⠁⠉⠈⠁⠀⠀⢠⣦⠀⡀⠀⠒⠒⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⣬⡁⢭⠌⣭⢤⣤⣤⡌⣭⡍⠈⠀⠀⠀⠀⠀⠀⣿⠿⢛⣛⣛⠛⢫⠍⠘⠂⠀⡀⢀⡀⠀⠀⠘⠿⢁⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢃⣀⣀⠙⠀⢈⣉⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠀⠀⠀⢰⡗⢹⣿⠀⠀⢸⣿⡿⠿⠿⡿⠿⠿⢿⣿⣷⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣶⣦⣶⣾⣻⣿⣿⣷⣦⢸⣯⣭⣽⣭⣭⣭⣽⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠸⠻⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠓⠀⡙⠻⠿⠿⠿⠛⠋⠛⠛⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⡀⣴⣦⠀⣒⡒⠒⠂⠀⠀⠀⠀⢀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢼⣿⠓⣿⡿⠀⠄⠖⠔⠆⠀⠀⠀⠀⠨⠭⠤⠉⠩⠥⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠘⠉⠙⠛⠛⠛⠀⠀⣠⡄
⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣶⣶⣤⣠⣄⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡖⢀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⡀⣀⣀⡀⠀⣀⣠⣤⣤⣄⣀
⣶⣿⣿⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣾⣷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⣀⣤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣬⣝⣤⣁⡜⡆⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢀⠄⠀⠀⠀⣀⣼⣵⣿⣿⣿⣿⡿⡮⠉⠀⠉⠁⠛⠀⠀⠀⣠⠴⠚⠛⠉⠛⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣀⣀⢸⣿⡿⣛⠛⠛⢉⡿⢠⡇⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⡴⢦⣾⠟⠛⠣⠄⠉⣭⢻⣿⣾⠿⣿⠀⠀⠀⠀⠀⠀⣴⢁⠠⢈⠁⡀⠀⠀⢀⣓⡀⠀⠀⣿⣿⣷
⠀⢠⣱⡏⣧⣧⡃⢂⡴⠋⣡⢩⡿⡕⠢⣾⢀⠀⠀⠀⠀⠀⡦⣁⠀⠀⠇⣽⣷⡀⠸⠏⠀⠀⢠⣿⣿⡏
⠀⠈⢌⣻⣉⢛⣃⣴⣀⣦⣆⣾⣷⣁⣾⣿⠟⠀⠀⠀⠀⠀⢿⡈⠢⠘⠁⠉⠛⠙⠀⠀⢀⣴⣿⣿⡟
⠀⠀⠈⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣻⣾⣴⣦⣄⣀⣠⣴⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂

⣾⠟⠒⠿⠓⠻⠛⠺⠟⠲⠿⠓⠾⠛⠲⠟⠳⠟⠛⠾⠛⠶⠛⠳⠞⠛⠶⠛⠷⠛⠳⠞⠻⠖⠛⠷⠚⠿⠒⠻⠗⠛⠟⠚⠿⠒⠻
⣼⡆⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢰
⣽⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣿⣿⣿⣿⠀⢠
⣻⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡋⢕⢤⣯⢰⠟⣿⣿⠀⣠
⢻⡁⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢋⣵⣼⠳⠿⣿⠿⠿⠿⠿⠿⢿⣿⢿⣿⣼⡷⠛⣷⡦⠳⢷⣼⣮⡟⠛⠀⢈
⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣏⠒⢶⣒⠀⢘
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢆⣀⠀⠀⠀⠈⠛⠣⣭⡉⠀⢀⡀⠶⣤⠘⡏⢻⢨⡇⠀⠘
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢻⣧⣀⣀⣶⣤⡀⢹⣿⡍⠹⣿⣧⢨⡛⢧⡰⠦⠀⠀⠸
⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⠀⠀⣀⡤⢼⠀⣀⣈⢿⡆⠆⡼⠛⠓⢾⣧⣷⠰⡈⠉⢹⣧⠈⠈⣧⠁⠀⠰
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠛⠃⠀⣴⠜⠛⣁⣀⡴⠃⠀⢸⡆⠘⠿⢤⣷⠀⣸⠃⠀⠈⡿⣿⢠⡏⠀⠈⢿⣿⡀⢰⠀⠀⢰
⢿⡄⠀⠀⠀⠀⠀⠀⠠⣤⣿⠃⠀⢶⢰⡿⠀⠐⡏⠀⠀⠀⠀⠀⣧⡤⠀⠈⢿⣧⣿⠀⠀⠀⣾⢸⡾⡇⠀⢀⣨⣿⣿⠶⠶⠶⣶
⣾⡅⠀⠀⠖⠃⠀⠀⠒⣾⠏⠀⠀⢸⢿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠉⡇⠀⠀⢨⣜⣿⠀⠀⠀⣿⣼⣷⣷⠞⡫⢡⣿⢸⠬⡁⠈⣿
⣾⡁⠀⠀⠀⠀⣠⠴⠖⢿⠀⠀⠀⠈⢺⡀⠀⠀⣿⣄⠀⠀⠀⠀⠴⣿⠀⠀⠸⣇⣿⢷⣄⠀⢸⣿⡫⢿⣷⣷⠌⣟⣈⣲⣥⣄⣉
⣽⣃⣀⣀⣠⣾⣡⣤⣤⣼⣧⣤⣴⣿⢼⠧⣴⣾⠷⠿⠶⠶⠤⠤⠤⢼⣦⡀⠀⠹⠏⢬⣏⣳⡟⠰⠈⢿⣷⣼⡞⢫⡉⠰⠀⠀⣙
⣹⣯⣭⣭⣥⣤⣤⣤⡤⣴⢶⢿⢿⠶⢶⢶⢷⢾⡷⠒⠒⠒⠲⠶⠶⠶⢾⣯⡱⡄⢠⠾⢫⡿⠷⠘⠋⢩⡟⠉⠏⠈⠁⠀⠀⣠⣿
⢻⡷⠤⠤⠴⠶⠶⠶⠶⠿⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠛⠃⠙⠃⠈⠁⣾⠸⠒⠢⢀⡟⠐⠃⠀⠀⠀⣞⣴⣿⣿
⢿⣦⠤⣶⡤⣶⣤⢴⣦⠴⣦⡤⢶⣤⠴⣦⡴⣦⣤⢶⣤⠶⣤⡴⢦⣤⠶⣤⡶⣤⡴⢦⣿⠶⣶⡶⢼⣷⠿⣴⡦⣾⡷⢿⣷⠤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡖⢄⢀⡠⠖⠋⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠁⠈⢋⠀⠀⠀⠀⠀⣄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠀⠀⠀⠀⢸⡀⠀⠀⠣⡀⢀⠀⠐⠀⠀⠀⢈⡴⠃
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⡀⠀⠠⠆⠀⠀⠀⡘⠁⠰⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⠠⠒⢠⠀⠀⠜⠃⠋⠂⠠⣄⣀⡠⠊
⠀⠀⠀⠀⣀⡠⠞⠂⠀⠀⠀⠠⠉⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠒⠒⣤⡀
⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢃⠀⠀⢀⣠⠀⠀⢀⠠⠂⠁⣸⠁
⠣⡄⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⢒⠈⠀⠀⠑⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⠞⡟⠲⣄
⠀⠐⣄⠉⠀⠠⡄⠀⠔⠀⠀⠀⢀⣠⠤⢏⣀⣀⠀⠀⠀⠀⠀⢡⡼⠀⠀⡠⠊⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠈⢆⠀⠐⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠚⠁⡠⠊⠀⠀⠀⠀⢀⣀⠀⠠⠤⢵
⠀⠀⠀⠀⠳⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡠⠛⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠘⠀⠀⠀⠀⡠⠾⠤⠤⠤⠄⠒⢢⠶⢀⡠⠔⠀⠀⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢱⢄⠀⠀⡀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⡴⠁⠔⠁⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠃⠀⠑⠢⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠌⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠷⠶⠶⠤⠭⠤⠤⠤⠄⣀⣀⣀⣀⣀⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣈⣉⣁⣈⣉⣀⣀⣀⣉⣉⣉⣛⣃⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠶⡞⢀⠀⠖⡀⢾⢉⠆⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠅⢀⡀⠀⠐⠂⠀⠸⠀⠀⠆⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠤⠋⠹⢾⡜⢆⣾⣀⣱⠦⢈⣉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣀⣀⣀⣀⠈⠉⠉⠉⠉⠉⠉⠁⠐⠁⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡅⢻⠉⠉⠉⠉⠙⠛⠛⠒⠒⠲⠶⠶⢦⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣲⣦⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠂⠈⠙⠲⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠶⠿⢆⡀⠀⡐⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⣦⡤⠒⠊⢉⣙⣉⣙⣹⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢼⣿⣿⣿⢿⠿⠿⡿⠿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⡃⠰⢶⡦⠀⢨⣤⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠁⠀⠈⠉⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⡀⠀⢈⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠁⠀⠌⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠃⠀⠀⠠⢐⠂⠀⡴⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠩⠀⠀⠀⠑⠀⠀⠑⣶⡄⠆⠙⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⠀⠀⠀⠱⡀⠀⠀⡈⠀⢀⠙⣿⡓⠀⠲⠃⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠑⢄⠀⠀⠀⠙⠊⢉⡁⠀⠈⠰⣿⣿⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠐⠢⢤⣈⠻⢀⠆⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⣀⣀⣀⣀⣀⣀⣨⡙⡎⠀⠰⠶⠒⣦⡬⢓⣒⡈⣉⣅⣤⠴⠙⡄
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⢀⠇⠈⠉⠉⠉⠀⠀⠀⠀⢀⡀⠇⠀⠘⠄⢼⠁⡈⠉⠀⠀⠀⠀⠀⠂⠀⠘⡄
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⠁⠀⠀⠀⠤⠀⠈⠀⠀⢠⠀⠀⠀⠀⢤⠀⠁⡀⢲⠄⠀⠀⠀⢀⠀⠼
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢲⢏⠀⠈⠀⠠⣀⣀⣀⣧⠊
⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠀⢀⡾⠀⠀⠠⡀⠀⣠⠖⠙⠍⠉⠉⠉⠉⠱⢦⠝⠀⢐⠀⠆⠀⠀⠀⠀⡩
⠀⠀⠀⢠⡿⠛⠉⠉⠛⢻⠶⠶⡷⠊⠀⢤⣈⠘⡅⠀⠂⠂⡀⠐⠀⣠⡄⠁⠀⠀⢿⢆⡠⢤⣤⡖⠊
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠓⣀⠶⠂⠀⠀⠂⠀⠊⠀⡆⠀⠀⠀⠀⣀⠀⠈⢠⠇
⠀⠀⠀⢻⠀⠀⠀⠀⡀⢄⠀⠘⢿⣥⠈⠉⠁⠩⠇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⣦⣤⣭⠴⠋
⠀⠀⠀⠈⠓⠦⣄⣳⣌⣦⣦⣔⣀⠏⠙⠂⠒⠺⠶⠆⠀⠀⠀⠒⠀⢘⠁⠈⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠆⠘⠒⠒⠊⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⣠⢂⣤⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠐⠒⠒⠒⠀⢭⣭⣤⣵⣤⣤⣧⣾⣤⣤⣀⠀⠐⠒⠂⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠒⠂
⠀⢠⠙⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠒⢂⠀⠉⠈⢙⣛⠿⠉⠉⠉⡙⠙⠃⠠⠀⠈⠈⠉⠓⡆
⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢘⠀⠀⠀⠃⡀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠀⠑⡄⠀⠀⠀⡲⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠃⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠠⢿⡄⠀⡷⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⠔⠁⠀⠀⠓⡄⣧⠀⡤⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⡠⠊⠀⠀⠀⠀⠀⠀⠈⡏⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠤⠐⠈⠁
⠀⠀⠉⠐⠂⠄⢀⠀⠀⠀⠐⡧⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠧⠀⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠄⣀⡈⠣⣄⠀⠀⢀⠠⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠿⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣶⡶⢶⣭⣭⣭⣝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⣷⣶⣾⣿⣶⣶⠟⠃⠒⠂⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢳⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣦⣤⣤⣤⣙⣄
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣀⣉⠙⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠳⠄⢠⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⢤⣭⣍⣉⣉⡉⠉⠀⠀⠀⠀⣶⣶⣾⣶⣶⣶⣶⣿⣷⣶⣤⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⠟⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣭⣿⣿⠿⠿⢿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡤⣼⣋⠉⠓⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣸⣿⠟⠁⣠⣤⣤⣤⣤⡉⠻⣧⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠈⠻⢶⣿⡿⠟⠓⣤⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⣴⣿⠃⢀⡾⠉⠀⠀⠈⠛⢿⡆⠈⣿⠁⠀⠀⠀⠀⠀⢀⣠⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢿⣇⠀⣿⣿⣠⢸⣇⠀⢠⣴⠦⠀⢈⣱⠀⢸⡇⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⡀⠀⠀⠀⣸⣾⣿⣿⣁⢾⡹⣷⣼⣧⣾⣿⣿⣏⠄⣼⣇⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⢉⣿⡿⢿⣿⣭⣤⣼⣿⣘⢷⣌⣛⡁⣈⢿⡭⢋⣼⣿⣿⣷⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠇⠈⢿⣤⡽⣿⣿⣿⣿⣿⣷⣯⣭⣭⣭⣥⣦⣽⣿⣿⢿⣅⣾⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣿⣿⣧⣹⣇⣈⣙⣋⣿⣿⣭⣷⣾⣿⣿⣭⣛⣋⣉⣀⢸⡏⠻⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡘⣿⣿⣧⠋⠁⠈⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣯⠉⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⠟⢫⣽⠟⢛⣿⢿⣷⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠶⣟⣛⠛⢛⠛⠛⠿⡆⠀⠀⠈⣿⣿⠀⠀⠹⠋⢉⣉⣀⣠⣌⡙⠙⢳⣤⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⡽⢢⣿⣿⡇⠻⣿⡟⢹⣿⣧⠀⠀⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⣷⡄⢀⣤⡀⠉⢳⣥
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⡽⣰⠇⣽⣿⣅⢺⣿⣿⢺⣿⣿⠀⠀⣿⡟⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢿⣷⣄⣀⣵⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⢿⡃⣾⣿⣿⡇⢼⣿⡏⣸⠿⣿⠀⠀⢿⡅⣹⣶⣶⣶⣶⡾⢿⣿⡿⠛⠛⢿⣿⣿⣿⡇⠀⣿⣿⣿⢿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣷⣾⣿⣿⣷⣾⣿⣶⣿⣾⣟⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣇⠞⠁⠈⢿⢻⣿⣧⠀⠈⠉⠁⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢐⣿⠿⡿⣿⢿⡯⣰⡿⢹⡿⣫⣇⠀⢹⣿⣿⡏⣿⣿⣿⣿⠀⣿⣷⣄⡰⠂⣨⡸⣿⣿⡆⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣷⠐⠛⣹⣿⣿⣻⠗⢋⣼⣷⣨⠀⢘⢹⣿⣿⣿⣿⣿⣿⠈⣿⣿⠛⠀⠰⣿⡇⣿⣿⣿⡄⠀⠀⢀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢣⣶⠀⢀⣴⣿⣿⣿⣟⠀⠀⢸⣿⣿⠟⣿⣿⣿⢰⣿⣿⠀⠰⡄⢸⣇⣿⣿⣿⣇⠀⢀⢼⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠸⢿⣇⢀⠈⣤⠈⣿⡿⣿⣿⣿⡓⠂⢸⡟⣿⠂⣿⣿⣿⢸⣿⣿⣦⡀⠀⣿⣿⠿⢏⣩⠿⣖⠗⠊
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣱⣦⣈⡛⠻⠿⣀⣿⣿⣿⣿⠀⠀⠻⠿⡀⣼⠆⠀⣾⣿⢸⣿⣿⣿⣿⣾⣿⣷⠀⣸⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠍⣽⣿⣿⣿⣿⡏⠉⢷⣦⣤⣐⡉⠿⢙⣿⣷⣶⡖⠋⢻⡖⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⠁⠀⠀⠙⠻⠿⣿⣿⣶⣿⣿⣿⣧⣤⣾⣇⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⡿⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣡⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢷⢻⣿⡇⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⡎⠛⣽⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠰⢠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠿⠿⠿⠿⠿⠟⠋
⣾⣷⡾⠿⢶⣿⣷⣿⣶⣿⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣾⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣿
⣿⣿⡜⢒⣿⣥⣍⣭⣭⣭⣤⣩⣬⣭⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣿⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⣿⠻⢶⣤⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⣤⡶⠟⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠿⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⠿⠋⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⠟⠋⠁⠈⠙⠻⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢿⠛⢳⠶⠦⣄⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡒⢉⠉⠉⣉⣉⣉⣉⣽⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣋⣽⣉⠉⡩⠉⢻⡇⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠈⠀⠁⠀⢘⣥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢻⡦⠔⡆⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠋⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠛⡋⢻⡖⢦⣄⣀
⠀⠀⠀⠀⣀⠤⠤⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⢸⣿⢻⡿⢾⠃⠀⠀⠈⠛⠦⣄
⠀⠀⠀⠀⣳⣞⡆⠀⢸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣸⡆⢿⣼⡇⢸⠀⠀⠀⢠⡄⠀⠈⠙⢦⡀
⠀⠀⠀⠀⢻⠉⠀⠀⡼⢋⣈⠙⢦⣄⣀⠀⠀⠀⣰⠁⢸⠋⣇⠈⢷⣧⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠸⡇⠀⠀⠙⢻⠉⢡⠏⠀⠈⠉⠒⠉⠉⠀⣼⠀⢻⡀⠈⢻⡀⠀⠀⠀⠀⣿⠳⣦⠴⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠛⠂⠉⠛⠯⢤⣟⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⢧⠀⠀⣹⣆⠀⠀⠀⣏⠀⡸⠛⠛⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⠤⣤⣴⡇⠀⠀⠈⢷⡋⠁⣈⣿⠛⠛⠛⣟⠁⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠏⠁⢹⠀⣠⠊⠉⠙⠳⣄⣰⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠈⢹⠂⠀⠀⣸⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠙⠒⢿⣤⠤⠴⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣄⣀⣠⠿⣄⣧⣤⣄⣀⣀⣀⣀⣀⡤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸⠈⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡿⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣸⠁⢷⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⠇⠀⠸⡆⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣞⣡⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡉⠙⠓⠒⠻⣟⠲⢶⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⣄⡈⠉⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠾⠷⠶⠶⠾⠿⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡛⠛⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣽⣿⣿⠿⣻⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⣸⠇⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠮⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣻⣿⣃⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⡻⣿⣿⣿⣿⣿⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠿⠿⠁⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⣴⣾⡟⢿⢿⣽⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡜⠃⠀⠀⠀⠀⠀⠛⠙⠉⠋⠀⠀⠀⢲⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⡀⠀⠀⠀⠨⢧⠤⠒⠊⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⢿⡺⠃⠀⠀⠀⠀⠀⢄⡀⠒⠀⠀⠀⠘⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣸⠆⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠉⠛⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡇⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⣀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⡠⠰⣶⡆⠀⠈⢧⣀⠀⠉⠀⠐⠂⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠿⣽⠹⣷⣀⣠⣤⣄⠀⣤⣤⣄⣀⣤⣿⣿⣅⡤⣾⣒⡀⠀⠘⡆⠀⠀⠀⠂⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣶⣿⣿⣿⡿⡟⡟⢹⣿⣿⣿⣿⡿⠿⣧⠁⠈⠑⢀⠀⠀⠹⠂⠠⠄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⢨⣯⠈⠷⢲⡤⢘⣻⣿⡋⢽⠻⢿⠉⠉⠀⠀⠂⠈⣀⣤⡖⠀⠀⠀⠀⠀⠀⣸⠛⠋⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢺⣿⠿⠛⢙⠛⠳⠀⠚⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠛⠿⠶⠦⠤⠀⠀⠃⠀⠀⠀⢀⣴⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠲⠶⠀⠀⠀⠂⠤⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠛⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠉⠁⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠤⠦⢤⣤⣤⣤⣤⡄⠈⠙⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⣦⠄⠀⠀⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠆⢀⣀⡀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⠀⠋⠓⠀⠈⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⠠⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⢀⣀⣀⣀⣀⠀⢀⣀⡀⢀⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣄⠀⠀⠀⠙⠈⠙⠯⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢻⣿⠟⠁⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠐⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠐

⢾⠟⠺⠛⠺⠛⠺⠛⠺⠛⠺⠛⠲⠛⠲⠛⠳⠛⠳⠛⠳⠛⠳⠛⠳⠛⠳⠚⠳⠚⠻⠚⠻⠚⠻⠚⠻⠚⠻⠚⢿
⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣾⠂⠀⠀⢀⡠⠤⣤⡤⠤⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣾⠂⠀⣾⣻⢷⣄⡛⠁⠼⣿⢠⡿⠁⢸⣿⣶⣤⣄⡀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣾⠂⠀⠙⢷⣯⡿⣿⣷⣄⠁⠈⠁⠂⠞⠻⣿⣿⣿⠟⣰⠏⣄⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣼⠂⠀⠀⠀⠙⢿⣯⠿⣿⣷⣄⠀⠀⠀⠀⠿⠟⣿⠃⠎⣠⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣽⠂⠀⠀⠀⠀⠀⠙⢿⣹⠿⣿⣷⣀⡀⠀⣠⣾⣿⣶⣴⡏⢿⣿⠟⢻⡟⠀⣴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣽⠂⠀⠀⠀⠀⠀⠀⠀⢨⡓⢾⢿⠁⠁⠁⠋⣿⣿⣿⣿⣧⠈⠁⠀⠀⠈⠒⠟⣠⣿⡑⢦⡀⠀⠀⠀⠀⠀⠀⢺
⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⡿⢧⣤⡄⠀⠃⠀⠏⠐⠙⢀⡀⠀⣀⣀⡀⣀⣈⣘⠀⠿⠛⢄⠀⠀⠀⠀⠀⢺
⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣿⡶⠋⠃⠀⣀⣀⣀⠀⢀⣼⣿⢿⣿⣿⣿⡿⣿⢿⢷⣶⣾⡟⢛⠿⠉⠹⣿
⣹⠂⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠙⠦⣧⠀⠀⠀⢀⣯⣼⡛⣿⣿⣛⡶⠿⠼⠶⠷⣿⣾⣿⠿⣿⢟⠀⢭⠇⠠⢿
⣻⠂⠀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⣤⣤⣤⣴⣾⣭⣏⣻⣥⡜⠉⠁⠀⠀⠀⣴⠋⠘⢜⢀⣠⠶⡛⢫⠉⠙⢻
⣻⣏⣉⣭⣭⣭⣭⣭⡭⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠼⡾⠤⠀⠀⠀⠀⠀⣼⠁⠐⠂⢠⠟⠱⠀⠁⠀⠀⣰⣿
⣻⠧⠤⠶⠶⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠗⠒⠂⠀⠀⠀⢀⡇⠓⠒⢠⡏⠘⠀⠀⡀⢜⣶⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠘⠉⠉⠐⡀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢑⣦⣀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣴⣿⣿⣿⣿⣿⣯⣉⣉⡛⢿⣶⣦⣄⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠘⡟⢿⡷⢤⣤⣬⣭⡭⣽⠟⢿⣿⣿⡷⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⡇⣦⡄⣦⠀⠰⢋⡹⡞⠀⠈⢿⣿⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⠁⠧⣴⠇⠀⠘⣬⠑⠁⠀⠀⠈⣿⡋⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣅⠀⠀⣀⠀⠀⠀⠀⠀⠀⡏⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣬⠿⠮⠭⠤⢤⠀⠀⠀⢰⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠢⢄⣀⣀⠤⠊⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡐⠒⠒⠂⠀⢀⡀⢰⡁
⠀⡴⢾⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠋⠀⣸⠙⣿⠳⣄
⠀⠸⡀⢱⡈⢷⠠⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠖⠒⠴⠀⢸⠛⢧⡀⢀⡟⠀⡍⠀⢸⠗⠦⣀⠠⣤⡀
⡇⠐⣄⠀⢱⣤⡷⠙⢄⣀⣴⠋⣩⠇⠀⠀⠀⠀⡎⠀⠀⠀⠀⣠⠃⠀⢸⣠⣴⣿⣿⣄⡾⠀⠀⢸⠀⠠⠁⠀⣰⠋⢙⡦
⠘⢄⠈⠳⢯⠀⠀⠀⠀⠈⠀⡺⠁⠀⠀⠀⠀⣠⡇⠀⠀⠀⢰⡃⠀⠀⢸⠁⡙⢻⠃⢉⠃⠀⠀⡿⠠⠃⠀⡰⠁⠀⠀⢀⡄
⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠉⡇⠀⠀⠀⠈⣿⠁⠀⢸⣄⠃⢸⡅⠎⠀⢠⡶⠃⠁⠀⡰⠁⡐⠀⠀⠈⣇
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣀⠀⠀⠀⢀⡔⠀⠀⢧⠀⠀⠀⠀⠹⣆⠀⠈⡿⠀⠈⡿⠀⠀⡠⠃⠀⠀⡐⠀⡰⠁⢠⡾⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠉⡤⠶⠚⢁⡜⢀⠀⠀⡀⢤⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄⣿⢀⠜⠁⡠⠊⠀⠀⠀⣰⢃⡼⠁⠀⢸⢇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢸⡆⠀⣠⠎⠀⠈⠳⣶⢧⣀⠏⠙⢷⣶⣤⡐⠐⢢⠀⠘⢿⠏⡠⢊⠤⠤⠄⠀⢠⡇⣾⠁⠀⠀⠈⠢⠭⠖⠸⡇
⠀⠀⠀⠀⠀⠀⣾⠿⠛⠁⠀⠀⠀⠀⠈⢳⠏⠀⠀⠈⠳⡈⠙⢶⣤⣀⠀⣮⠈⠀⢸⠀⠀⠀⢀⡟⢠⠹⣆⣀⣀⣀⣀⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠘⢯⡁⠀⣈⠿⠿⠶⠤⣼⣄⣠⠀⣼⣀⣸⣀⡿⢩⣄⡀⠉⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⢀⣠⣤⡄⠀⠀⠈⠙⢛⠙⣏⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠃⠀⠀⠀⠀⢀⣀⣀⣀⣠⠬⠿⠞⠋⠸⣧⠝⠀⡀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠷⣾⣍⡉⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⣿⠀⣀⠜⠀⢠⣾⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢦⣄⠉⠛⠷⣦⣄⡀⠀⠀⠙⣄⠀⠀⠀⢸⣏⣤⢀⣴⡉⠪⣿⣏⣀⣀⣠⣤⠤⠤⠶⠒⠉⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢤⣬⣉⡓⠲⠄⢉⠛⢷⣦⣄⣈⢧⡀⠀⠈⣧⠶⡟⠀⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠉⠙⠛⠻⠿⠷⢦⣄⣻⢻⡇⡇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠁⠺⠇⠇⠸⣿⢧⣀⠀⠀⠀⠀⠀⢠⡎⠱⡆⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⢸⢰⡀⣿⠀⠙⠳⠶⠤⠤⠤⢼⢣⠤⣿⠀⠒⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣠⠄⠘⠧⣄⣸⢸⢸⡇⣹⠀⠀⠀⠀⠀⠀⠀⢸⣾⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠴⠒⠈⠁⠀⠀⠀⠀⠈⡍⢎⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣸⠷⠶⠿⣄⣀⡀⠀⣀⣀⣀⡠⠤⠔⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡤⣤⠤⣤⡤⣤⣤⣤⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣧⣿⣴⣿⣧⣿⣴⡿⡮⢿⢼⠇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡟⣾⠛⣾⡞⣿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠐⣇⣿⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡠⢄⠀⡠⢤⡀⠀⠀⠀⠀⢀⡤⣀⠀⢀⠤⣀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡀⢺⣿⡅⢀⣟⠀⠀⠀⠀⣼⡀⢻⠀⣻⠀⣽⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⠀⠁⠛⠁⠀⠙⠀⠀⠀⠀⠛⠀⠉⠃⠋⠁⠘⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡖⣢⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣎⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⣶⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣾⣿⣿⡜⣿⡞⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣧⣛⣛⣛⣛⣛⣛⣛⣛⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣿⣿⢰⣒⣒⣒⣒⣲⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣿⣿⡸⠿⠿⢿⠿⠿⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣿⣿⠛⢛⣛⣛⣛⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣿⣿⢸⡶⣙⣛⡱⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⡇⣿⡇⣿⣿⣿⣤⣚⣛⣛⣛⣪⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣽⣯⣿⣷⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿




⡟⠉⣿⣻⢻⣛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣿⣿⣟⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠿⠟⢧⡀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⢀⡼⠻⠿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⡻⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⣿⣿⣿⣯⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠛⠉⠙⠋⠉⠀⠀⠀⠙⠷⣤⣀⣰⠀⠈⣿⣶⣆⣀⣤⠾⠋⠀⠀⠀⠈⠙⠋⠉⠛⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣥⡶⠼⠭⣿⣌⢿⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⣷⣯⣶⣾⣷⣶⣳⣾⠂⠎
⠀⠀⠀⠀⠀⠈⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠿⠃⠻⠿⢃⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣸⠀⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⣷⣄⣀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⣤⣄⠀⠀⠈⣿⣏⠀⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣈⣉⣙⣛⣛⣛⣛⣋⣉⣀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠙⢿⣯⣀⣤⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡀⢀⣀⣀⠀⠀⠀⢀⣀⡀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⣿⣿⣿⠀⠀⠀⣿⣿⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠛⠛⠉⢠⣷⣦⣈⣙⣛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡶⠀⠸⠻⣿⣿⠟⢛⠛⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⡤⠀⠀⠘⠟⠰⣿⠁
⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⠁⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠋⣙⣂⠶⠖⡒⣒⣀⡒⠀⣴⣿⣿⣦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣻⣟⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⡿⣿⣤⡌⠁⠀⣿⣿⠀⣿⣿⣿⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⢉⣤⣀⠈⠛⢿⡄⣀⠀⣀⣀
⠀⠀⠣⠁⠀⠻⠿⠗⠲⢲⣟⣉⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢘⣋⣭⡤⠤⣠⣶⣇⠙⢿⣿
⠀⠀⠀⣀⠀⠀⠀⣀⣀⡿⠛⠻⠿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣥⣶⣾⣿⣿⣿⣿⣷⣼⠛⣿⣷⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣠⣶⠴⡾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡼⠟⠛⠻⣦⡀
⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⢸⣿⣿⣿⣿⣿⠿⣿⣻⡿⢒⠉⠀⠀⠘⠉⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⠈⠻⣆⣀⢄⣤⣶⣶⣶⣧⣄⣀⡀
⢠⢴⡴⢞⣿⣿⣿⣿⡿⠿⣿⣿⣷⣝⠿⣛⣽⡾⠛⠉⠈⠁⠽⡷⠄⢘⢷⣤⣄⣀⣴⣶⠂⣠⣿⣧⠀⠀⠀⠀⠀⢨⣧⡀⠙⢿⡛⠋⣩⠛⠻⢿⣶⣄
⡰⢫⣶⣿⣿⠿⢿⠛⠻⠿⣦⣉⠿⢛⣥⡈⠙⣿⣣⣀⣀⣀⣰⠢⠀⠘⣧⠻⢿⣿⠟⣧⡾⠁⣹⠋⡀⠀⠀⠀⢠⣿⣿⠟⠦⡈⠣⣤⣿⣀⠀⠁⢙⢿⣆
⢰⣿⣿⡿⠁⠀⠀⠴⠒⠢⠈⠵⠆⠹⠿⠷⠀⠿⠟⠛⢉⣉⣠⠄⠂⣸⣭⡀⡠⠀⠀⠉⠀⣼⣿⢠⡇⠀⠀⠀⣿⣿⡟⠘⠲⣾⣦⣈⠟⠉⣷⣄⣠⡞⣿
⣿⣿⡏⡇⣀⣀⣀⣀⣀⣄⣤⣤⣤⠀⣤⠀⠀⠀⠐⠛⠋⠀⠀⠀⠐⠈⠉⠀⠘⠒⠂⢀⣾⠟⣡⠌⠀⠀⠀⠀⠋⣿⣇⠀⠀⢿⣈⡿⢶⡉⣹⠇⠀⡀⣿
⢿⣿⣧⢻⣷⡬⠀⠉⠉⢿⣿⣁⠉⣻⣿⢶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣿⣤⠾⠋⠀⠀⠀⠀⠀⠀⠹⣿⡄⢀⡼⠛⠶⠾⢿⡋⠀⡐⣼⡿
⠘⣿⣯⡳⣝⠻⢶⣾⣷⡶⠟⢋⣴⣿⠃⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣄⡀⠀⠀⠈⣁⣤⣾⠟⠁
⠀⠈⠻⣿⣿⣿⣶⣶⣶⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡞⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠎⡽⡜⡸⢰⢩⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡛⡜⡜⢰⢱⢡⢃⠃⡎⠎⡼⣦⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡠⡶⡻⡱⡱⢱⣰⢡⢣⢃⠇⡎⡼⡸⡰⢡⢡⢻⣄
⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠉⠉⠛⠚⠓⠓⠓⠳⠷⠧⠧⠾⣼⣼⣠⣱⢡⢃⢧⢋⢎⡎⡷⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠚⠚⠺⠿⠷⣄⣀⣀⡀
⠀⠀⠀⣀⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⢹⠂
⠀⢠⣎⣽⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⢸⠀⢸
⠀⠸⠈⠳⣼⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡀
⠀⡄⠀⠀⠀⠙⠧⣖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡳⣄
⠀⡇⠀⠀⠀⠀⠀⠈⠳⣮⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣧⣼⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⡔⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣾⠷⠛⠋⡇
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣔⣊⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣺⠝⠚⠉⠀⠀⢘⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠵⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡾⠟⠊⠁⠀⠀⠀⠀⠀⠀⠨⠁⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢥⣒⣪⣄⣠⢄⡠⠀⣔⡮⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠃
⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠉⠁⠀⠈⠉⠲⢯⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸
⣾⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸
⡇⡢⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⡇⠨⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣧⠙⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣖⡠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢻⣴⡊⠁⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣡⠄⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠉⠙⠒⠒⠯⠜⣁⣃⡂⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠬⣐⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣡⠀⠀⠀⡌
⠀⢀⢄⡀⢄⡠⣀⠤⡀⢔⡤⣂⠤⢂⡠⣀⠤⣀⠤⣉⢙⠓⠒⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡄⠀⡇
⠀⠀⠀⠀⠁⠈⠁⠋⠈⠁⠊⠁⠘⠑⠊⠑⠋⠐⠊⠔⠡⠊⠗⠡⠞⡵⢊⢝⡹⢓⡶⣲⠤⣤⢤⣄⣀⣀⡀⠙⣦⣇⡄⣠⢀⣀⢄⡀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⢀⣀⡠⠤⢒⠪⠍⠁⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀
⢀⡤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠞⠛⠋⠳⢄
⢸⡷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠲⠠⠽⣷⣤⣤⡴⠶⠾⢿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⡷⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡶⢶⡾⠟⠛⠛⠿⣶⡒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢼
⠀⡇⢃⠀⠈⠢⣀⣠⣤⠶⠶⠛⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠁
⠀⢏⡉⡄⠀⠀⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⣦⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⠳⣼⠀⠀⣿⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠋⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠈⠳⣄⣿⠀⠀⠀⠘⢦⡀⠀⢀⣠⠤⠒⠊⠁⠀⠀⠀⡀⠠⠀⢾⠃⠀⠀⠀⠀⠀⠀⣀⡠⠞⠊⠁
⠀⠀⠀⠀⠀⠈⢿⡀⠀⢀⣀⠤⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠼⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣎⠀⠀⠀⠀⠀⢀⣀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⠴⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠙⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠋⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠛⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠛⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣦⣀⣀⣀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠛⠉⠀⠀⠈⠉⠉⠁⠀⠀⠈⠛⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣀⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣤⡀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠚⣛⣋⡉⠉⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣆⠀⠀⣏⣀⣧⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⣿⣿⣿⣿⠟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠠⠆⠀⠐⣙⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠀⠀⣀⣈⠥⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠠⣀⣀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣧⡀⠀⣀⠀⡿⢶⡶⢶⡆⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠻⡄⢈⠞⣡⠟⠀⢸⡇⠀⠀⠀⠀⠀⢸⣽⠀⠀⠉⠉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡀⠀⠀⣹⠋⣴⠃⠀⠀⢸⣇⠀⠀⠀⢠⠤⠜⢻⡄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣾⠁⠀⣀⣠⣼⣥⣤⢾⠛⠉⢽⡆⠀⠀⠀⣿⠋⢻⢻⡾⠀⣼⠉⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⢻⠸⡄⠀⣹⡇⠀⠀⠀⣿⠀⢸⢸⣥⣠⡏⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣀⣸⣦⡟⠉⠉⠀⠀⠀⠀⣿⠛⠛⠛⠁⠀⠙⠒⠲⠤⡾
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠚⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⡿⢿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡜⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⠞⠀⠀⠀⠀⠀⢠⣶⠿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣠⠋⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢀⡾⠁⡴⠃⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⢠⡟⢁⡜⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣰⠏⢠⠎⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠸⣿⣴⠋⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢻⣤⣴⠆
⠀⠀⠀⠀⠈⠛⠳⣤⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⣀⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠾⠟⠋⠉⣿⡏⠙⠛⠿⢶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠛⠛⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢿⣆
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣦⣤⣀⠀⠀⣿⡇⠀⢀⣠⣤⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣿⣷⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠸⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠿
⠀⠀⠀⠀⠀⠈⠛⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢀⣿⡇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠰⣿⡷⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢠⣿⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⣸⠏⠀⠀⠀⣿⡇⠀⠀⠈⢿⡀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⣿⡇⠀⢀⣠⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣿⣷⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠄⠀⠈⣙⠦⣄⡀
⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠂⠀⠀⠀⠀⠂⠁⢀⠤⠒⠉⠀⠉⢂⡝⢲⣄
⠀⠀⣾⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠐⠈⠀⠀⠀⠀⠈⠐⠤⡀⠄⣪⠵⠚⠁⣿
⠀⠀⣿⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⣀⡤⠒⠉⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⡇⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⣇⣠⠖⠋