Oceanfront Emojis & Symbols

⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⡀⠀⠀⣄
⠀⠀⠀⢰⠂⠀⠀⠀⠀⠐⣴⠀⠀⠀⠁
⠀⠀⠀⠈⡇⠀⣀⣀⠀⠀⠨⡌⠙⢷⡁⢂⣠⠆
⠀⠀⠀⠀⡅⠀⠁⠈⢁⡀⠀⠀⢀⡈⣻⡗⢧⣄⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠁⡇⠀⡀⠩⡁⢺⠛⣦⣷⢶⣗⢠⣄⣠
⠀⠀⠀⢰⡇⠀⠀⠀⢠⢨⣷⣏⠈⠀⢈⣈⣽⠛⢂⡐⣻⠿⢷⠂
⠀⠀⠀⢸⡇⠀⠀⠀⣴⠛⠈⠁⠀⠀⡜⠛⠇⠈⠀⠀⠁⠆
⠀⠀⠀⣸⠀⠀⠀⠀⡟⠀⠰⠀⠀⢠⠁⠀⠀⠇⠀⠀⡸
⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⡬⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⣀⣀⣀⡀
⠀⠀⢸⡏⠀⠀⠀⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠈⠁
⠀⠀⣾⠃⣀⠀⠀⠀⠃
⠛⢲⡿⠀⠗
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠃
⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀
⠀⣿⣦⣀⣀
⠀⡏⠀⠀⠿⡃⠘⠒⢠
⠀⣏⠉⠀⠀⠀⠲⡄⢹⣷⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢊
⠀⠀⠀⠁⠀⠀⠀⠘⢆⢹⣿⠁⣠⣤⡈⠙⣦⠄⢀⣴⡖⣀⡼⠛⢶⠖⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡻⠧⡴⠯⡤⠀⠘⠢⣆⣄⠀⠈⠃⠀⢤⣀⠀⠀⠀⠈⢋⠀⠀⠄⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠺⡄⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠘⢷⠀⣘
⠀⠀⠀⠀⠀⠀⢰⡤⢶⡄⠈⣉⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⠶⠏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠷⠠⠨⢴⣤⠀⠀⠀⠁⠀⠀⠒⠋⠀⠀⠀⠈⠉⡈⠉⠀⠒⠁
⠀⢀⡀⠀⠀⠀⠀⠳⠴⠓⠀⠉⠻⠛⠃⠀⠀⠀⠀⠞⠀⠀⠀⠒⠂
⠀⠀⠙⢳⢄⠀⠀⠀⠀⠀⠐⠒⠘⠉
⠀⠀⠀⢘⣗⠀⣰⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⡾⢸⡇⣸⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢏⣰⡇⡏⠀⢹⠉⢻⢒
⠀⠀⠀⠀⠀⢰⣒⡲⢖⠖⠂⠐⣨⣭⣤⣦⣤⣤⣀⠀⠐⠻⠞⢩⣆⣿⣀⣚⣲⣖⣆⡀
⠀⠀⠀⠀⠈⢿⣿⠻⠏⡟⠋⠉⠧⠤⠤⢸⡚⡛⢹⣿⣿⣿⢻⣿⣝⣏⠉⢹⣹⢻⣯⢁⡀
⠀⠀⠀⠀⠀⠀⣏⣶⣔⢃⣀⡠⡀⠈⠉⠀⠺⠿⠶⣿⣿⣿⣼⡟⠋⠉⠁⠈⠙⢛⠓⠃
⠀⠀⠀⠀⠀⠀⢻⠉⠉⠋⠉⠁⠓⣶⠆⠀⠐⡂⠀⣿⣸⣇⣿⣄⣸⣸⢠⡆⢸⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠪⠉⠁⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣗⣿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣦⣤⡄
⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣷⣶⣶⣿⣿⣷⡦⠀⠀⠀⠀⠀⠠⢾⣿⣆⠀⣿⠏⠀⣠⡄
⠀⠀⠀⠊⢫⣣⢣⣀⡜⣸⡽⠓⠀⠀⠀⠀⠀⢸⣯⣽⣿⠋⣠⡈⢻⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣈⣛⡷⣯⢴⣿⣿⣧
⠀⠀⠀⠰⠋⠻⣿⣿⣿⠟⠋⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠙⢁⣼⣿⣿⣿⠀⠀⠀⠀⠀⢹⡿⠟⢋⣿⠹⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣄⣤⡶⢄⢀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣤⣤⣶⠏
⠀⠀⠀⠀⡾⢃⣤⠤⣤⡘⢻⡄⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⣥⡖⣺⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⡇
⠀⠀⠀⠐⣽⣿⡀⠀⠀⣽⣿⠂⠀⠀⠀⠀⠀⠀⠀⠟⠸⢷⠀⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣠⡾⠋⢻⣿⣟
⠀⠀⠀⠀⠡⠋⠉⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⡿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⠿⢿⠟⠿⢿
⠀⠀⠀⠀⢀⣰⣶⣿⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣁⠂⠀⠀⠀⢐⠐⠀⣾
⠀⠀⠀⠀⠉⣽⡿⠿⠶⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠺⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⡀⠒⣤⢠⣀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣀⣀⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠈⠙⠛⠻⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠋⠓⠓⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠁⠀⠀⣁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢴⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠐⠀⠦⠀⠀⣼⡄⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣳⡄⠀⠈⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣘⠛⠒⠀⠀⠀⠀⠀⠀⠂⠐⠃⠙⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠈⠻⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣀⣤⣤⣠⣤⣤⣠⣦⣸⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣈⣭⣍⣍⣍⣉⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠒⠶⠠⢄⡀⠀⠀⠀⠀⠆⠆⠀⣀⣤⠶⠚⠛⢉⡉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⠉⠢⣄⠀⠐⠀⠗⠋⣡⢔⣸⠇⢈⡭⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢈⢾⡇⢀⡄⢊⣵⠟⢡⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⢀⣠⠄⠒⣒⣀⣢⣳⣤⣸⣿⣿⡴⠟⣋⣈⣛⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢀⡴⣁⠒⠉⠉⣩⡍⣙⣿⣿⠋⢹⠿⢞⡛⠻⣋⣭⣤⠶⠾⠿⠾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠐⠋⠀⠀⠀⠀⣰⢫⢎⣵⡿⣿⣤⣆⢀⣼⣿⣦⡈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣼⣳⢁⣾⡟⢰⣿⣿⡧⢿⣿⣿⣿⡟⣆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⣸⢳⢋⡾⡛⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⢮⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⢰⠇⣼⠘⣠⠇⢰⠇⣿⣿⣿⡆⢻⡌⢿⡿⠃⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⡾⠀⠁⡀⠁⠃⠈⠸⢿⡿⣿⣿⡈⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢰⡇⡀⠘⠁⠀⢷⢨⣤⠈⡟⢯⣿⣧⠸⣿⣿⣿⣿⣏⠉⠙⠒⠦⣤⣤⠤⠖⢛⣩⣤⣶⣶⣦⣤⣭⡓⠦⢤⣀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⣿⣷⣣⣂⣠⣬⣞⢸⣿⣿⣿⣿⣿⡆⠹⣏⠀⠀⠀⠁⠀⠀⠀⠀⠉⠓⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠾⠛⠉⠀⠀⠈⠙⠲⢤⣀⠀⢸
⠀⠀⢸⣿⣹⠟⣿⣿⣿⣿⣿⣿⠿⠟⠋⢻⣿⡅⠙⣦⠀⢁⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣻⣉⣁⣤⣤⣶⣦⣶⣶⣜⣿⣦⡀⣈⢙⣺
⠀⠀⢸⣧⢿⡾⢛⣵⣿⠋⣉⣀⣤⣼⣿⣟⢿⣿⣥⠘⢷⣾⠁⣀⡖⠉⠉⠀⡀⠀⠒⢤⣀⠀⠠⢄⡉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣻
⠀⠀⠘⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⠛⠻⣿⣦⠄⠻⣄⡟⢰⡤⣲⣶⣼⣶⣄⡀⠈⠙⠲⣤⣉⠓⢦⣤⣤⣬⣝⣛⣿⣿⣿⣽⣻⣎⣾⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣌⠻⢿⣶⡖⢊⡷⣬⣸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣿⠛⣿⠁
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣾⠿⣿⣿⣿⣿⡿⠟⡷⠀⠀⠀⢀⡤⢒⣩⣶⣿⠋⠀⣰⠇
⠀⠀⠀⠀⠀⠹⣄⣤⣀⣄⣀⣀⣀⣉⣲⣦⣤⣉⠛⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣸⣥⣤⣤⣾⣁⣤⣾⣿⣿⣇⣄⣰⠏
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠙⣿⣿⣿⣥⣿⠿⠋⠉⠉⢀⣠⣤⣤⡀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢀⠀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣾⣿⣿⣿⠏⠀⠀⠀⢠⣾⣯⣉⣡⣙⣧⣿⣤⣤⣀⣀⣀⣀⣀⡀⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣉⣉⠉⠉⠉⣹⣿⣋⣿⣿⣿⣿⡿⠁⠀⢀⣀⠀⠈⢿⣿⢿⢿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⡀⢀⣭⣥⣶⣾⣿⣿⣿⣇⣀⣴⣿⣿⣿⣶⣶⣶⣾⣿⣷⣶⣤⣀⣀⣀⣀⣑⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢭⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢭⣭⣍⣉⣉⣉⠓⠲⣶⣶⣶⣶⣶⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⣤⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⡀
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣠⣤⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⡆⣿⣿⣿⡇⢸⣿⣿⣿⢰⠀⢸⣿⣇⠀⠀⠀⢠⣤⡀⢸⣿⣿⣿⡇
⠀⠀⣀⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣷⣶⣶⡆⢸⣿⡇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣼⣿⡇⢸⣿⣿⣿⡇⣿⣿⢀⠀⣠⡄⣠
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠘⠀⠀⠈⠀⠀⠂⢠⣶⣿⣏⠘⣿⣻⡿⣟⡒⠘⠿⣿⣿⣿⣟⣿⠻⣗⣶⣶⣾⣷⣚⡿⠏⣿⡽⢯⣤⣾⡇⢁⠸⡷⠂⠀⣤⡔
⠀⠀⠀⠈⠀⢀⠀⠉⠀⢀⣼⣿⣿⣿⣆⣿⣿⣷⣈⣿⠋⠈⣿⣿⢟⣿⣿⣿⡿⢿⠟⢹⣾⣿⡿⠂⠈⠃⠀⠻⠿⢛⣻⢿⡁⠀⣰⡿⠓
⠀⠀⠀⠀⠀⠉⠀⠀⠀⣛⣻⣿⠃⣛⣿⣿⣿⣿⠏⠇⠀⠀⣽⣿⠋⣿⣿⡟⠁⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣟⠚⢋⣿⠟⣻⢦⠀⢠⣤⢀⡏⢻⠛⠛⠛⠁⠀⠀⠁⠀⠀⠰⢦⣦⠄⠀⠀⠀⠀⢠⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠙⣶⣾⣿⠟⠃⠀⠀⣀⣠⣿⣧⡼⡆⠀⠀⣀⣀⠐⣾⠀⢰⣤⣌⣀⠀⣀⡀⢠⣄⠀⠈⠳⠀⠀⡄⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣵⣶⠾⣶⣋⣩⣿⣿⡁⠀⢳⡀⣤⣷⣿⡟⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠉⢿⣿⠾⠿⣿⣏⣿⣄⢀⠙⠿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠐⠀⠀⠁⠙⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⢡⠀⣿⡿⠀⣹⣤⣴⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⣤⣶⣶⣶⣿⣾
⣿⣿⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢄⡙⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣶⣿⣿⣿⣾⣿⣾⣷⣾⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠿⠁⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢙⣿⣿⣿⠖⠀⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡇⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢉⣫⣅⣼
⣿⣼⣟⣿⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢺⣿⣾⣿
⣿⣿⣿⡿⣿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢿⡿⠿⠿⢿⠿⣿⣿⡿⠿⠿⠿⠋⠘⠹⠿⠻⣿⠟⠛⠛⠻⠿⠿⠿⠛⠛⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⠀⠀⠀⠀⢘⣹⡿⢀⣀⡇⠀⠀⢴⢿⣾⡿⠛⠛⠹⣶⣿⣿⣿⣾⠶⣶⣤⣴⣶⡶⠶⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣴⣿⡏⢠⠴⡆⢢⡀⠹⡷⣾⣯⣯⣭⣥⠤⠀⠀⠀⠀⠊⠁⠉⠉⠙⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠿⢿⠦⣶⠾⣿⠷⠖⠀⠙⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠉
⠀⠲⠀⢠⣀⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆
⠡⢄⡏⠃⢉⠭⠀⠀⢀⡾⠀⠸⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡄
⣤⣾⢓⡈⣀⢶⣷⢾⣭⠶⠿⣦⠔⣧⠾⣄⠀⠀⠐⠒⠂⡔⠂⣀⠂⠠⠀⠀⠀⠀⡀⡀⠀⠀⠀⢷⡟⠄
⣧⣻⣿⣿⣿⡿⣶⠄⢸⣷⢆⣤⣘⣷⣤⣬⠰⣶⡦⢶⡄⣛⠿⢡⠘⡅⢤⠀⠀⠀⢻⠆⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡈⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣆⢰
⠀⠀⠐⠘⠃⠀⠀⠀⠀⠀⠀⢴⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡅⠀⠨⠐⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠃⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠤⠀⠀⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡄⠀⠀⢀⢠⡄⠀⠣⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠆
⠀⠉⠂⠀⠀⠈⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣤⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠒⠄⠠⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠰⠤⠤⠄⠀⠀⠀⠠⠠⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠘⠀⠀⠀⠰⡄⠀⢈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠈⠐⠄⠈⠲⠆⣄⣀⣀
⠀⠡⠀⠀⠀⠑⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠓⠀⠀⢀⣄
⠀⠐⠀⣀⡀⠀⠀⠀⠀⢤⡄⠀⠠⠔⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀⠀⠈⠉⠀⠀⠤
⣀⣀⣀⣀⣢⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣈⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⣧⠀⡠
⠠⠲⠀⣿⠠⠀⠀⠀⢠⠤
⠀⠀⠀⢸⠃⢀
⠀⡀⠀⣸⠀⠈⠊⠀⠋
⠀⠘⡆⣿⠀⠀⢀⡄⠤⣀⠀⠀⠀⠀⠀⠀⡰⠶⠀⠀⠀⠀⠀⠀⣀
⠠⠀⠸⣿⢨⠃⠈⠀⡗⠁⠀⠐⠀⠀⠀⠀⠸⠇⠀⠀⠱⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⣿⠂⣬⢢⠎
⠀⠀⠀⡿⠀⡏⡜
⠀⠀⢰⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀
⠀⠀⢸⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⢀⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡧⠿⠆
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣤⣴⣬⢛⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠯⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠁⣾⠻⠟⡻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠘⠇⠀⠀⠛⢧⠚⠻⠁
⠀⠀⠀⡠⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⡀
⠀⣀⠔⢁⡴⠁⠀⠂⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤
⠀⠉⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⣠⣸⠔⠂⠒⠂⠠⠠⢀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠐⢴⡄⠘⣋⡉⠉⠁
⠀⠀⢸⣾⠂⠀⢀⣼⣳⢶⡴⡗⢐⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣆⣿⣦⣾⣿⣈⡉⠙⠃⠋⠀⠄⠁
⠀⠀⡯⠇⠠⣔⠈⠉⢸⡦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣠⣴⠊⢹⡽⣴⠆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡄⠀⠀⢾⡧⠤⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠃⠀⢸⡯⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⣤⠄⠀⠐⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢀⡀⠀⠀⠀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠐⣆⠀⠀⠀⠐⠐⠀⢒
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠘⠛⠀⠉⠉⠀⠀⠀⠀⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠈⠉⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠈⢉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡽⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡼⠛⠋⠉⠙⠛⠛⢷⡄⢲⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⡦⣻⡀⠀⣤⣿⣶⣋⣼⣼⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⣿⣀⠀⠀⠀⠀⠀⢀⡅⣿⣁⡀⣿⣾⠿⣿⠿⠋⠁⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡍⢡⣄⠈⢹⣿⣿⣿⣇⠀⠀⠀⢠⣿⣠⠿⣿⣡⣦⣄⣀⣁⣀⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣸⢓⣤⣞⣿⣿⣿⣿⣷⣄⠠⢙⡟⢹⠖⢻⠇⢸⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⠏⣿⡿⠏⢠⡭⡿⣿⣿⣿⠖⡋⠇⢸⣼⡤⣆⠺⠛⠉⠀⠀⣠⣞⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣿⠀⣿⣣⡇⢸⣿⣶⣾⡥⠛⢁⣠⣄⠼⢿⣶⣇⠀⣰⣿⣿⠀⠿⣾⣷⡆
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢘⣿⠟⣷⣬⡟⢛⣏⣀⣠⠞⠋⠀⢀⡜⠋⠉⢰⣿⠙⠋⢵⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⣸⣿⡀⣹⣿⣿⡿⠛⠉⠀⢠⠆⢀⣿⣧⣴⣶⣬⣿⠞⠁⠀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣏⣩⣼⡿⠏⢉⠀⣀⢀⢀⣿⣃⣴⣿⣿⣿⡏⢁⣠⣤⡄⠘⡇⣴⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⠟⢠⣤⣴⡏⢰⣿⡄⢹⠿⠟⢿⣿⣻⣿⡧⢸⣿⣿⡇⠀⠈⠁⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⠉⣀⢴⢸⣿⣿⠿⠈⠋⡁⠈⢀⠀⣸⣿⣿⣽⣿⠸⡿⢻⡇⠀⣆⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣄⠀⢳⣈⣇⢈⡏⢼⢸⣿⡅⠀⠀⠁⠀⢸⢥⣿⢻⣿⣿⣿⣿⢀⠁⠀⡄⠀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣶⡖⣶⣶⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢸⠯⡿⢀⠀⣤⣴⣿⣦⣤⠀⠺⠇⠐⣈⣽⣿⣿⣧⣽⣿⢸⣶⠀⡇⠈⠿⠿⠇
⠀⠀⠀⠀⠀⠀⣠⡿⣷⡿⠿⠇⠀⠀⠀⠀⢀⡀⣿⣿⣿⡇⢸⡈⡇⢸⣧⣽⣿⣿⢏⣭⠀⣶⣾⠀⣿⡟⢻⣿⣷⠞⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠾⠋⢀⣤⣤⣶⠄⠰⠛⠻⣾⣿⡇⣿⣿⣿⡇⢸⠃⡇⢙⡏⠀⣻⣿⡏⣻⡄⢿⡙⠆⠹⠃⢸⠿⣿⡿⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠿⠇⣾⡿⢫⡙⠛⠋⢊⡍⠡⢿⣿⣿⡇⢸⢄⡇⢀⡀⢀⠛⣻⣂⠛⠁⠈⠁⠀⠀⠀⠁⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⢀⠀⠶⠆⣿⡀⢊⢻⣈⣥⣼⣷⣦⣾⣿⣏⣁⣻⣛⣧⣨⣧⡈⢸⣿⡏⣿⣷⣠⡀⣶⢺⡗⠀⠀⠀⠹⠿
⠀⠀⠀⠀⠀⠈⠡⡄⢢⣴⣽⣶⣾⠿⠿⠟⠛⢷⠛⣛⣿⣿⣿⣿⣿⠟⢻⡇⠘⠏⣡⣿⣿⠘⢃⡛⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠛⣛⠁⣠⣄⣠⢶⣎⠙⢋⡉⠉⠉⠙⣛⣀⠘⢿⣀⣴⣉⣋⡭⣄⡈⢉⡄⣉⡀⠀⠄⠠⡶⠄
⠀⠀⠀⠀⠀⠀⣤⣰⣆⣿⣆⣘⣀⣘⣉⣋⣛⠹⣥⣟⠁⠽⠷⠟⢋⣥⣀⢈⡙⠉⢉⡛⠿⠿⠷⠾⠶⠾⠿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⣴⠽⠯⢟⠛⠿⢿⣿⣿⣿⣿⣏⠉⠰⢄⠀⠀⣌⣻⣥⣾⡉⠙⠁⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠰⣿⣀⣠⣼⣇⠸⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣷⣮⣛⠈⢻⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠋⠁⣀⣀⣀⣀⠀⣤⠤⡤⠤⠤⢤⠄⠠⠤⠽⠽⠿⠿⠽⠛⠛⠟⠠⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠒⠒⠒⠂⢭⣿⣟⠛⠻⠿⠿⣯⣭⣭⣽⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦
⠀⠀⠀⠠⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⡶⣦⣀⣀⣀⣀⣠⠶⣤⣀⣀⣀⣀⣤⠶⣤⣀⣀⣀⣀⣤⠆⠀⠀⠈⢷⡸⣷⣤⣄⣀⣠⣤⠞⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⢠⡞⢷⡀⠈⢷⡹⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠈⠛⠋⠀⠀⠈⢷⣹⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⡋⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⠇⠀⠀⠀⠀⣠⠟⠉⠀⠀⠉⠻⣦
⠀⠀⠀⢀⣤⡴⠞⠋⣡⡄⢈⣿⠞⢿⡀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣀⣤⣤⣤⣤⡏⠀⠀⢀⣤⣄⠀⢸⡇
⠀⠀⠀⠘⣧⣀⡴⠟⣩⡴⠋⠁⠀⠀⠻⣦⠀⠈⠻⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣤⠶⠛⠋⠉⣠⠶⠂⠀⠉⣀⣴⢿⣄⠙⣷⣼⠇
⠀⠀⠀⠀⠈⠛⠶⠞⠉⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⠓⠒⠒⠒⠚⠋⠁⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢿⡀⠀⢶⡴⢿⣅⢀⣩⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢳⣦⣤⣀⠙⢦⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣃⠀⠉⠛⠻⠿⣭⣹⠟⠋⠉⠻⣦⣤⣄⣀⣀⣤⣤⠴⠶⠛⣿⠛⢻⡟⠛⢷⡄⠘⠷⠶⠶⠶⠶⠶⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢻⡏⠉⠛⠶⣤⣀⡀⠀⠁⠀⠀⣠⠾⠋⠀⠈⠉⠉⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡶⢸⠇⠀⠀⠀⠀⠈⠙⠳⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣸⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⣹⡟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠺⢧⣄⣿⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛⠙⠳⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠲⠶⣄⣠⡴⠶⠛⠛⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⢀⣀⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠋⠀⠀⠀⢰⠆⢀⡶⠈⠻⣦⠀⠀⠀⠀⠀⠀⢸⡇⣹⠟⠉⠀⠀⢨⡝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⣄⠰⠟⠀⠀⠀⠈⠷⢀⣴⠟⠀⠀⠀⠀⠀⠀⣸⣇⣼⢷⣄⣀⣀⣈⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠤⠶⠋⠙⠳⠶⣤⣤⣤⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁
⠿⠿⠿⠿⠿⠿⠛⠛⠀⠛⠁⠘⢥⡴⠛⠂⠠⡤⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠠⣀⣠⣧⣸⣿⣇⣠⣴⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⢿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠘⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣄
⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⡟⠛⠛⠿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡙⠛⠦
⠀⠀⠀⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠒⠀⠄⠀⠀⠀⠀⠀⢀⠀⡄
⣄⣀⠀⠀⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⠻⢿⣦⣄⡀⠀⠀⠀⠂⡀⡠⢋⡕
⣿⣿⣿⣶⣤⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠈⠻⣿⣿⣷⣤⣀⠀⠀⢻⣏⣁⠀⠀⢀⡀
⢿⠛⢿⣿⣿⠿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣙⡿⠿⢿⣿⣿⣦⣤⡿⠉⠓⠠⡀⠈⠀⡀
⠀⠐⠆⠈⠓⠨⠀⠀⠻⢿⣿⣿⠿⢿⡛⠋⢹⢹⣿⣿⣿⣿⣿⣏⡉⠀⠀⠀⠙⢮⠻⠽⣧⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠠
⢰⠀⠀⠀⠀⠀⠀⢾⣶⣷⣶⣤⣠⣀⣙⣤⣾⣿⣿⣿⣿⣤⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣸⠀⠀⣄⣠⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣈⡉⠉⠉⠉⠉⠛⠛⠛⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿
⣿⣀⡈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⣠⣶⣶⣾⣿⡿⣿⣿⡽⢿
⣿⡏⠤⠀⣀⠘⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣷⠶⠆⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⢿⡿⠃⠻⠀⢹⡧⡧⠴
⣿⣷⣾⠀⣿⠀⠀⠀⠀⠀⠉⢤⡽⠷⠨⣍⢉⣿⣸⣟⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⣼⣷⣶⣾
⣿⣿⣿⣦⣿⣆⣆⢰⣶⡀⡀⢀⠀⠀⠀⠈⢻⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣦⣄⣀⡀⡀⠀⢠⠀⠀⣇⢀⣤⣷⣀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⣼⡀⣰⢀⢠⣼⣿⣿⣧⡼⠏⠙⠻⣯⠙⠻⠛⠉⠉⠉⢀⣀⣼⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⡏⢀⠀⠀⡀⣀⣤⣰⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣤⣤⣤⣤⣄⡀⠀⠀⠀⠉⠙⠛⠛⠻⠿⢿⣿⢸⣧⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⡀⠀⣸⣿⣸⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⣩⣭⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⠿⡿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠻⢛⣉⣴⣶⡿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠾⣿⠟⠋⢉⡀⠤⠒⠈⠁⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣀⡀⠀⠐⠂⠠⠶⠖⠉⠀⢀⣀⣀⣼⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⡈⠙⠻⢿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠐⠶⠶⠶⠶⣟⣿⣿⣿⣿⣿
⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⠻⣿⣿⣿⣿⣿⡿⠷⠦⠤⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⢛
⠈⠉⠉⠉⠛⠛⠛⠿⣷⣿⣿⣿⣟⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣭⣿⣿⣿⣤⣴⣶⡿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣾⣥⣤⣈⠙⠻⣟⣉⠛⠿⣿⣶⡤⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠉⠻⠿⠿⣿⣶
⡄⠀⢀⠀⠄⠐⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⡲⣬⣿⣿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣀⡀⠀⠀⠀⠀⠈⠛
⣴⣼⣿⣿⢀⣄⣴⣶⣦⡀⠀⠀⠙⠻⣾⣶⣦⣤⣤⡀⠈⠛⠻⢿⣥⣄⣀⣀⡛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣶⣦⣴
⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣦⣀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣬⣙⢯⣉⠛⠛⠓⠶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠉⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⢺⠅⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣾⣅⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠌⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡃⠀⠙⠷⣤⣄⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⡷⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⢉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠉⠒⠒⠒⠒⠊⠉⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣀⣀⣠⡤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⣀⡠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣂⠉⠉⠑⢆⠀⠀⠙⢧⠈⢻⠑⢤⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠉⠁⠈⠀⠀⠀⠘⠀⢰⠀⠀⠀⠀⠀⠈⠃⠈⡶⡄⠀⠀⠀⠀⠀⢠⡏⠉⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⢄⢸⢀⠤⠀⣀⠤⠀⠀⠀⠆⠘⠞⠆⠀⠀⢀⡟⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⠄⠀⣠⠶⠒⠒⠓⠒⠚⠃⠀⠈⠉⠒⠚⠛⠛⠠⢤⡀⠀⣸⡀⠀⣼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⡜⠁⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⢱⠀⠉⣥⢠⠇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢸⣀⣠⣒⣉⣁⣀⣤⣤⣤⡤⠤⠤⠤⠤⣬⣭⣶⣤⣠⣀⠀⣽⣼⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣋⣭⣭⣭⣦⣤⣤⣤⣤⣤⣀⣀⣤⡴⠶⠶⠶⠶⠶⣦⣤⣭⣍⣛⢧⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣾⠟⠛⠉⣩⡯⠶⠶⠶⠤⣄⠀⢀⣄⠀⠀⣀⣠⡤⠤⣤⣘⡄⠀⠉⢻⠹⣷⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⡏⠀⡐⠀⡧⠒⣲⣶⣶⣤⣾⢷⣻⣉⡓⢯⡤⢒⣊⣉⡒⠺⣿⠀⠀⢸⡇⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣷⠀⡇⠀⡇⠘⠉⣯⣿⡿⡳⢋⡤⠤⡉⢦⣱⡹⣿⣿⠻⣤⠇⢀⡇⠀⡇⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢻⠀⠀⠠⡁⠀⠐⠀⣼⡟⣱⠏⠀⠀⠈⢦⡱⣷⡉⠩⠀⢸⡆⠀⠀⢀⡇⡎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⢌⡓⠦⠤⣵⣄⡤⣾⢏⠞⡉⠀⠂⠀⠀⠀⢿⣜⢿⡢⠤⠼⠷⣒⡿⠽⣊⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣯⡶⣶⣶⡾⠟⠋⠀⠇⠀⡀⠀⢰⠀⢸⠈⠳⠬⠭⣭⠭⢶⡖⠋⣽⠉⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠈⡆⠀⠑⢄⠀⠀⠀⠦⠴⣂⣂⣺⣦⠆⠐⠀⢀⡜⠁⢀⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⡀⠀⠈⠑⠂⠴⠴⢦⣄⡠⠶⡶⠦⠤⠖⣋⣤⠖⠋⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⡒⠒⠚⠛⠛⠛⠛⠚⠛⠉⠉⠁⠀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠐⠓⠶⠶⠶⠶⠶⠶⡶⠶⠒⠒⢚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠓⠒⠒⠛⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣱⢤⣀⣀⣀⣀⣀⣀⡴⠋⠀⠀⣀⡠⠤⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠒⢦⣴⣄⣀⣀⣀⣀⣠⣤⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣠⣴⡏⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢳⣟⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠦⠤⠤⠶⢒⣺⣟⡥⢺⡇⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⢸⠀⢸⡇⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞⠃⡀⠀⠀⠁⠀⠈⢣⠀⣾⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠀⠀⠘⠁⣀⠾⠁⠀⠀⢸⠆⢀⠐⠀⠀⠂⠈⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡆⠀⠀⠐⠀⠀⠀⠠⠤⠀⠠⠄⠀⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣿⣆⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⠀⢰
⠀⠀⠀⠀⠀⠀⢰⡇⢀⣿⣿⣧⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣀⣿⠄
⠀⠀⠀⠀⠀⠀⠚⠻⠚⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣼⣁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⣿⠛⠃⠀⠀⠀⣼⡛⠉⠀⠀⠀⠁⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠉⠙⠂⠀⠑⠂⠀⠀⢀⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠒⠒⠂⠀⠀⠐⠲⠴⠤⠤⠶⠤⡦⠤⠴⠶⠒⠒⠒⠚⠛⠛⠛⠛⠓
⠛⠛⠛⠀⠀⠀⠀⠤⠤⠔⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⢈⠀⡀⡆
⠀⢠⠄⠘⣟⡘⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⡄⡀⢧⡀
⣦⣿⣤⣤⣿⣧⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣧⣿⣶⣧
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠉⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠈⣧⠀⢸⡄
⠀⠀⠀⢠⡶⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠛⠓⠲⣆⠀⢹⡀⠀⣧
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠛⢉⣉⣀⣤⣤⠤⠶⠖⠚⠛⠻⡆⠘⡆⠘⣇⠀⢹
⠀⠀⠸⡇⠀⠀⠀⢀⣴⠟⠋⣉⣤⠤⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢷⠀⢿⠀⠸⡇
⠀⠀⠀⢷⠀⠀⠀⢸⡇⢰⡟⠉⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡄⢸⡆⠀⣧
⠀⠀⠀⠘⢧⡀⠀⠸⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠈⠻⣦⣀⣿⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⠾⠁⣸⠃⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢧⣀⠀⠀⠀⣀⣀⣤⠶⠋⠉⣉⣉⣉⣉⣉⣉⣁⡤⠞⠁⠀⣾⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠉⠛⠛⢋⣉⣁⣤⠴⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡼⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣠⡴⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠉⠉⠀⠈⣿⣁⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⣀⣠⡤⠴⠀⣀⣠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠶⠖⠚⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡓⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠖⠓
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠾⠋
⠀⠀⠀⠀⠀⠀⣀⠒⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠀⠈⣶⣤⣀⢀⡀⡀
⠀⠀⠀⠀⠁⠀⠙⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠻⠙⠠⠀⠈⠐⠂⠁
⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣄⡀⠔⠀⠀⠀⠁⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠠⠀⠀⠀⠀⠀⠠⠂⠀⠀⠐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠒⠀⠀⠄⠘⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⡇⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠈⢳
⠀⠀⠀⠀⠀⠀⠂⠰⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠒⠄⠉⠀⠀⠀⠀⠀⢢⣟⡆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⡁⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠰⢌⣀⡀⠀⢉⡀⠆⠀⠀⠀⠀⣀⣼⠁⣙⢄⡀
⠀⠀⠀⠀⠀⢒⢂⡐⡠⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣸⠆⠀⠃⠀⠠⠄⠤⠤⠀⠚⠀⠀⣍⠀⠀⠀⠈⠀⠀⠀⢉⠄
⠀⠀⠀⠀⠰⠋⠚⠿⢷⠀⠀⠀⠀⠀⠠⠀⠀⠰⠤⠀⠐⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠐⠈⠒⠤⠔⠊
⠀⠀⠀⠀⠠⠠⠲⠰⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⢀⡀⢀⡠⠤⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡴⠐⠐⠤⣬⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠈⠠⠀⠀⠀⠀⠐⠐⠂⠤⠤⠐⠲⠃⠀⠀⠌⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⡆⠦⠆⠤⡄⠀⠀⠀⠀⠀⠀⠈⠀⡜⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⡄⠁
⠀⠀⠀⢠⠧⠠⠠⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⢇⢘⠈⡀⠀⠀⢀⠀⠀⠉⠉
⠀⠀⠀⢰⠤⠰⠰⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠑⡄⠂⠀⠀⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣜⣒⣒⣒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢍⣀⢿⡄⠄⡀⢀
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠛⠑⠞⠖
⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠐⠂⠐⠖⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠂⠀⠒⠒⠐⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡞⠀⠀⠀⢠⡄⠀⠴⠆⠀⠀⠀⡇⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠐⢃⠀⠀⠀⢀⠚⠉⠑⠤⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠠⠤⠤⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠆⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡜⠁⠀⠀⢀⡀⠀⢀⣀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⢇⠀⠀⠀⠈⡡⠐⠬⡉⠀⠀⠀⢰⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢌⠂⠀⠈⠒⠤⠄⠊⠀⠀⠀⠙⠀⠤⠐⠁⠀⠀⡁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⡀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠂⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⡀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⠑⢀⠁⠄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠉⠒⠚⠀⠀⠈⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠈⠣⡤⠤⢤⠜⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠬⠤⠤⠤⠤⠤⠀⣀⡀⠀⠀⠡⠀⠁⠤⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡾⠁⠀⠀⢠⡀⠀⣠⡀⠀⠀⠈⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡄⠻⡀⠀⠀⢈⠔⠒⠪⡀⠀⠀⢀⠟⠠⠘⠀⠐⠀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠈⠁⠀⠀⠀⠁⠐⠒⠉⠀⠀⠀⠄⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠛⠀⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀
⡀⡀⢀⢀⢀⡀⣀⣀⢀⠀⠀⣀⣀⢀⠀⣀⢀⣀⣀⣀⣀⣀⠀⣀⠀⣀⣁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⢀⡀⣀⡀⢀⣀⠀⣀⠀⠀⣀⣀⢀
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣆⠀⣰⡿⠉⢀⣙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡉⣤⣾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣧⣿⠁⢀⡿⡻⠀⠈⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢾⡰⠛⢿⣿⣿⡆⣤⣴⡆⢴⣤⡴⠖⠂⠀⠀⠀⠀⢀⣠⢄⣤⡤⠖⠀⠀⠀⣀⣬⣤⡈⠀⠀⣀⠈⡉⠁⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢋⣤⠶⠾⢿⣿⣿⣿⣟⣥⣊⠁⠀⠀⠀⠀⠀⢀⠴⠫⠞⠫⠋⡅⠀⠀⠲⠋⡏⠀⠘⣷⠘⠃⠈⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠰⡿⣷⣿⣿⣿⣿⡿⣷⡄⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠃⠀⢰⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣟⣴⠟⢹⣿⠛⡟⠙⣻⡄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⡀⠀⠸⠀⠘⡆⠀⠀⢀⠀⠀⠀⢼⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠀⣸⣯⣸⠃⠀⠘⡡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⡀⠀⠀⠸⠄⠀⠈⠀⠂⠀⡾⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠿⠿⠁⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢧⠀⠰⠀⠄⢸⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⠄⠀⡞⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⢣⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣲⣄⠀⠀⢀⣹⣇⠀⣿
⠀⠀⠀⣀⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣎⠠⢡⣏⠜⢛⡉⠭⢣⣿⠀⣿
⠀⠠⢽⡿⣿⡟⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣬⢆⠤⡄⠤⠉⣤⠔⡉⠐⢖⢾⣿⣣⣿⡦
⠠⠤⢼⡿⣿⣿⣿⣶⣃⠢⣄⣂⣤⣦⣄⡀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠸⡉⣀⡬⠽⠤⠐⣈⣈⠤⣌⣱⣾⣽⣿⣿⣿⣿⣓⣚⡂
⠀⢰⣾⣿⣿⠟⠾⠿⣭⠭⢿⣿⣿⣿⣿⣿⠦⠀⢸⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⢿⣿⣿⠿⣟⠋⠁
⠀⠸⣿⣿⠏⠀⠀⠀⠀⣺⣿⣿⣿⣿⡩⠟⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠩⠽⢭⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⢿⣧⣤⣬⣉⣿⣇⠙⠻
⠀⡤⢟⠋⠐⠎⠻⠿⣿⠿⠛⠆⠐⠒⠏⠀⠀⠀⠘⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠋⢠⣴⣿⠿⣿⠿⠛⠿⣭⣡⢿⠿⠛⠚⠛⠛⠛⠈⢻⣆⠀⠙
⣠⡼⠁⠀⠀⠀⠀⠉⠉⠀⠺⠁⢀⠀⠐⠂⠀⠀⢸⢸⡆⡇⠀⠀⠀⢀⣀⡤⠤⣤⣰⣲⡏⣉⣉⣭⣽⡛⣟⡻⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠉⠒⠛⠒⠒⠀⢺⢻⠃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠙⠛⠒⠊⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣍⣬⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢋⣡⣤⣴⣶⣤⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣤⣶⣶⣤⣤⣉⠻⣶⡀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⣧⠘⣷⣠⣿⣀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢀⣾⠋⣠⣶⢶⣦⡉⢻⣆⠀⠀⠀⠀⠀⢀⣿⠀⣿⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⢿⣄⠀⠀⠀⢠⡿⢁⣾⣿⠇⠀⣿⣿⣆⢹⣇⠀⠀⠀⣀⣼⠇⣸⡏⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡙⠻⠷⠶⠟⠁⣼⢃⣿⠀⠀⢸⡇⢿⡄⠛⠷⠶⠿⢛⣡⣾⠟⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡶⠶⠶⠟⠋⢸⡇⠀⠀⠈⣿⠈⠛⠷⠶⠶⣾⡟⠉⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣿⠟⠛⠛⠻⢿⣇⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⢀⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣦⣀⣀⣰⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠛⠋⠀⣼⡇⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠟⠋⠁

⠀⠀⠀⠠⠀⢀⣀⡀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠠⠤⠤⠀⢀⡡⠭⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠒⠒⠚⠁⠀⠴⠦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠆⠀⠀⠀⣈⢉⣁⠄
⠀⠀⠀⠀⢀⣉⠀⠀⢀⠤⠀⠀⠀⠄⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠖⠾⣠⡥⠀⠁⠒⢄⣀⡀⠀⠤⠠⠠⠤⡀
⠀⠀⠀⠀⠦⠤⠀⠈⡵⠒⠀⠒⠚⠂⢢⠀⠀⡂⠀⣰⡀⠀⠀⠀⠀⠀⡀⠝⠓⠚⠚⠓⠓⠠⣶⣴⠴⠔⠃⠐⠂⠒⠒⠐
⠀⠀⠀⠀⠁⠒⠖⠄⠙⠂⠠⠇⠑⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠉⠃⠀⠀⠀⠀⠀⡀⠀⡷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠐⠐⠒⠀⠀⠒⠂⠐⠀⢛⣓⡁⣉⣛⡙⢒⣂⡘⣚⠚⣋⡁⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠁⠀⠀⣀⠈⠉⠈⠉⠁⢉⠉⠉⠈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⡏⠁⠈⠀⠑⠀⠃⠉⠀⢸⠂⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠠⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠌⠀⠀⠀⠀⡠⠀⣀⠀⢰⡛
⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⣰⠿⠟⠁⢠⡾⠂⠀⠀⠀⡀⠀⠀⢀
⠀⠀⢤⠀⠀⠠⠤⠀⠀⠸⠁⢼⣷⡥⢈⣉⠀⠐⣤⣤⠁⠀⠀⠺⢷⡆
⠀⢠⠀⡄⠀⣠⡆⢀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠸⠁⠋⠀⠀⠀⢀⠄⠀⠿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠀⠸⠀⠠
⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠠⠴⠀⠚⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⡶⢾⠿⠿⠿⠗⠶⠶⠶⠶⠶⠶⠛⠛⠉
⠀⠀⠀⠀⠈⠀⠀⣠⣴⣾⣿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠂⠁⠈⠙⠉⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠉⠀⢤⣀
⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠐
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠀⠀⠀⠀⠠⠀⢀⡀
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠑⠾⠡⡆
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠐⠞⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠟⠟⠲⣢⠶⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅
⠀⠀⠀⡀⠀⠀⠲⡁⠀⡀⠰⠂⢀⡘⠂⠀⠀⠀⠀⠀⠀⠐⡚⠗⠷⡄⡔⠀⠀⠀⠀⠀⠠⠀⠰⠀⢀⠔⡀
⠠⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⡇⠀⢐⠂⠈⠉⠉⠉⠐⠒⠛⢢⢀⣈⠱
⠀⠂⠡⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⣀⣔⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠏⣀⢀⡀⠀⡌⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⡏⢌⠘⠛⠃⡯⢐⠂⠄⠀⡀⠀⡃⠀⠀⠀⢀⠂⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠢⠀⠀⠀⢈⣀⡀⡀⠀⠀⠃⡀⠃⠀⠀⠀⢨⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠧⢀⠠⠤⠀⠐⠀⠂⠐⠒⠞
⠀⠀⠀⠀⠀⠀⠄⣈⠀⠀⠀⠀⢀⠀⠁⠀⣀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠙⠉⠉⠀⠀⠀⠀⡉⠐⠐⠀⢀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠁⠙⠁⠀⠑⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠊
⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⢐⠀⢀⠔⠀⠀⠀⢠⡀⠈⣀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠐⠂⠚⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⣾⣴⣦⣀⡀⣄⢀⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⢀⣹⣱⡄⠀⠀⠸⡟⢿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣧⣹⡍⢺⡇⠠⠏⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠛⠉⠡⣿⢟⢹⣧⣦⢿⡏⠘⡏⢳⠙⡏⢹⣯⡽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠚⢡⣽⡉⡆⢰⠙⢸⠀⡀⢸⠏⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⣀⣿⣇⣹⣬⡆⠷⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⢀⣀⡠⣤⣴⣵⡲⣦⠤⡄⠀⠒⠂⠈⠉⠇⢸⡄⠀⢹⠛⡁⠀⢻⡇⡀⠀⣰⣧⣤⣶⣶⣶⣦⣠⣄⡀⠄⠀⠀⡂
⠀⠀⠀⠸⢠⣾⣿⣶⡦⠙⣿⣧⣤⡿⣿⣿⠁⢹⡗⠐⠈⠀⠀⠀⠀⢀⢸⡁⠀⢀⠃⠘⣤⣾⣿⡿⠿⣿⠟⠽⠋⢛⣉⣉⠩⠿⠆⠀⠀⠀⠁
⠀⠀⠀⠀⡿⣿⣿⣿⢷⡦⢻⣿⣿⡏⢘⣿⣀⢿⡟⠀⠀⠀⠠⡿⠛⡏⣽⠗⠃⣾⣠⣴⠥⣿⣿⡇⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⢠⣷⢼⣿⣿⡏⠀⣸⣿⠝⠁⠈⠘⠀⠌⠵⠶⠂⠀⣀⣀⣤⣰⣿⣠⣾⣅⡀⣿⠘⢻⢻⠁⠈⠏⡇⠀⠀⠀⣀⣀⣾⣶⣾⣿⣧⣤⡇
⠀⠀⠀⢈⠁⠚⠛⠋⠠⠘⠋⠛⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠋⠉⣙⡛⢿⡀⡾⠸⠀⠸⠸⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠅
⠀⠀⠀⠀⠄⠀⠄⠀⠤⣒⡀⣲⣶⣶⣴⣿⣿⣿⠿⠻⠝⠲⡦⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣼⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⡃
⠀⠀⠀⢠⡤⢤⣤⣿⢶⢻⣿⣿⣿⣿⡿⠟⢻⠋⠉⠀⠁⠀⣰⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⡇
⠀⠀⠀⢐⠀⠈⣭⣾⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣯⣡⣤⣶⣼⣭⣭⣾⣷⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠗⠀⡆
⠀⠀⠀⠈⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣻⣿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠟⠛⠻⢿⠇⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠻⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⢣⡇
⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢲⣭⣭⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣯⠥⠐⢀⢤⡀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠸⠇⠟⠸⢚⠛⠛⣓⠀⠀⠀⢀⢶⡀⠀⠀⠀⠀⠀⢸⣿⣥⣽⣬⣈⢑⣈⢉⣏⣙⣏⠀⠀⠀⠀⠠⠛⠛
⠀⠀⠀⠀⠀⢰⠄⠈⠉⠁⠀⠉⠉⠉⠉⠁⠉⠉⠀⠠⣀⢸⣶⡇⢀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣶⡆
⠀⠀⠑⠶⢷⢾⠆⠠⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⣿⣿⣿⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⣿⣇⠀⠉⡇
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⢸⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡗⡷⣿⣿⡟⣿⣿⣿⠻⢻⣿⣶⢶⡀⠀⣻⡟⠿⠃⠀⠀⠀⢾⠹⠇⠀⠀⠀⢸⣿⢸⡀⣻⡇
⠀⠀⠀⠀⠀⣗⡇⠀⠀⠀⠀⣽⡄⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⣷⡐⠑⠀⠀⠀⢸⡇⠀⠀⢀⠀⢸⣿⢸⣿⣿⡇
⠀⠀⠀⠀⣴⣷⣷⣶⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣦⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⣏⣉⡘⠃⠀⠀⠀⢘⣧⠀⠀⠀⠀⢸⣿⢸⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⣿⣷⠀⠀⠀⠀⢠⣠⣾⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⣿⠅⠀⡉⠀⠀⠀⠀⢈⣿⣄⢀⠀⠀⢸⣿⢸⢛⣼⣇
⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⢰⣿⡏⠀⠀⠀⣰⣿⣿⣿⢿⣿⣿⣷⠀⢀⡀⠀⠀⠀⣿⣶⣦⣄⡀⠀⠀⠀⢸⣿⢼⡇⠀⠀⠈⠛⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⣇⠳⠀⠘⠛⠛⠿⠿⠎⠿⢿⠏⠳⣿⣿⣤⠀⢸⡿⠃⠠⠬⠃⠀⠀⠀⣮⣥⣬⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣴⣴⣤⡂⠀⠀⠘⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠈⠉⠠⡤⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠻⠟⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡻⠗⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠙⢈⣤⣶⣿⣿⣿⣿⣟⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄⣧⣿⣽⡟⢛⣶⣿⣿⠿⠿⣛⣻⣭⠛⠂⣹⡙⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡿⢛⣛⣻⣧⡘⣯⣽⣿⣿⣶⣿⢿⣶⣾⣯⠴⣛⡀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⢨⠟⠙⠉⣏⣬⣾⣾⣿⣽⣿⢿⣜⣿⣿⣿⣿⣿⣏⣻⣫⣿⣿⣿⣿⣿⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢏⣿⣿⣿⣿⣼⣿⣞⢿⣽⢿⣿⣿⣿⣯⣽⡏⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡝⣾⣿⣿⣿⡛⣿⣿⣷⣫⣿⣸⢉⢿⢻⣿⣿⡇⠇⠛⠛⣿⠿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠍⢏⢹⣿⣿⢿⢿⡳⣿⣿⡿⣟⢹⣇⠀⠁⢸⢿⣿⣿⡳⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠃⠁⠈⠀⠀⣿⣿⣿⣆⠙⠁⢻⣿⡓⠦⠀⣿⠀⠀⠀⠈⠋⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡜⢎⠁⠀⠸⣿⡷⠤⠀⣿⣧⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⣘⣡⢾⣿⢿⡧⠉⠟⢿⡙⢿⣟⠛⠋⠓⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣖⣒⣛⡻⠋⠐⠋⠹⢼⡇⣀⣀⣀⡣⢀⠋⠙⣂⡐⠦⢬⡛⢶⡽⢷⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣀⣤⣀⡀⠀⠉⢉⣉⠉⠉⠉⠿⠿⠿⠯⡽⠷⡶⣸⡯⣁⡈⣍⠁⠨⠽⢿⢋⣙⣷⣽⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣀⣤⠶⠶⠒⠒⠂⠀⠀⠉⠉⣿⡇⢀⡄⣼⣿⢀⡆⣠⠆⠠⠤⢤⣵⣒⣛⣛⣛⢛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠁⣼⢡⢇⣇⣼⢞⡕⣆⡀⠒⠒⠒⣶⣿⣿⣷⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣬⠍⢀⡞⣸⡄⡴⢮⡘⢷⣿⣦⣄⣀⣈⣿⣟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊⠉⠀⣨⠟⠋⠋⠀⠘⠳⠑⠃⠙⠂⠈⠙⠛⠛⠻⠽⠿⠿⠟⠛⠛⠉⠁

⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣄⣤⣤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠉⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠹⠿⠿⠟⠉⠙⠋⠉⢹⣿⣿⣿
⠀⢼⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⣀⡀⠀⢀⣠⣴⣿⣿⣿⣿
⠀⣾⣿⣏⣿⣿⠧⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⠀⢙⣻⣿⣿⣿⣿⣿⣹⣿⣿
⠀⢻⣿⣿⣿⡏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣡⣴⣿⣿⠿⣿⠟⢿⡿⢿⣯
⠀⣸⣿⣿⣿⠀⠒⡒⠂⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣩⣿⣶⣿⣿⣿⣿⣿⡇
⠀⢻⣿⣿⣿⠐⠀⠁⠇⣿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠛⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⠐⠙⠀⠂⣿⣿⣿⣿⣿⣦⣙⣻⣿⣿⣿⣿⣽⣿⢿⣿⡿⠟⠉⠠⠾⢿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠀⠀⣀⢶⣾⣿⣿⣟⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⢸⣿⣿⣿⠇⠀⢀⠐⣿⣿⣆⠀⡉⠻⣿⣿⣿⣿⣿⣿⡿⢀⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏
⠀⢸⣟⣻⣿⡆⠀⠘⢀⣿⣿⣿⣦⡀⠀⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡿⣿⣿⠿⡿⢿⣿⣿⡗⣱⣾⣿⡇
⠀⣸⣿⣿⣿⠄⢰⢰⠀⣿⣿⡿⠉⢃⣀⣠⣾⣿⡿⠿⣟⡿⠿⠿⠇⢸⡿⢿⣿⠿⠿⣟⡇⢿⡿⠿⠛⠻⠮⣿⡀⠿⣿⣚⣿⣾⡿⣻⣛⡿⡇
⠀⣿⢿⣿⣿⡇⢈⢈⠐⣿⣿⣷⣶⢿⣿⣿⣿⣿⡇⠐⠿⠇⠀⠄⠤⠈⡃⠸⠿⠇⠀⠿⠇⢘⡁⠠⠀⠀⠀⠿⠇⢘⠿⣿⡗⣽⣶⣿⣿⣾⡇
⠀⠘⡄⢁⡀⠠⠀⣈⠀⢁⠉⠉⠉⠀⢉⠉⢉⢉⠃⠀⠀⠀⠀⢰⣶⡆⠀⠂⠀⠀⠀⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢀⠈⠈⠉⠉⢉⠃
⠀⠈⠀⠘⠛⠀⠀⠄⠀⠸⡀⠀⠀⠀⠀⢠⠄⠠⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠿⠿⠂⠀⠀⠀⠀⠠⠀⠀⠤⠁⠀⠛⠃⠀⠠⠸⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⠁⠉⠉⠐⠐⠀⠀⠉⠀⠉⣉⣁⠒
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢨⣿⣬⣯⠀⡩⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠈⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁
⠀⡇⣶⡆⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⢠⢤⠀⠀⡀⠀⢠
⠀⡇⠿⠇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⢨⣿⣿⡅⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣾⡇
⠀⡅⠀⠀⠀⠀⢠⠄⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⡇⠀⠇⠀⠀⠀⠀⠘⡷⠾⠃⠀⠉⠉⠁⢸⡇⠘⡇⠀⠀⠀⠀⠀⣤⠛⠃⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⢀⣤⠞⢢⠆⣀⣰⡿⠁⠀⢀⣀⡀⠙⠏⢷⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢻⣧⣄⡀⠀⠀⠈⠹⢁⣴⣶⠟⠛⠑⠦⣤⣤⡽⠋⢙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠋⠲⠲⣤⢴⠋⠁⢀⣀⣤⡀⠙⠃⠱⣄⣰⣦⠀⠈⣰⡆⣸⣇⠀⠀⠛⠁⢀⡄⣾⡇⢠⡏⠢⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠶⠋⢀⠀⢠⡀⢠⡄⠀⡴⠿⠋⠉⠙⠲⢶⣶⠞⠁⠈⠷⢤⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⠄⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣧⣿⣧⣾⣷⠀⠀⠀⠀⣤⡀⠀⠉⠀⠀⠀⠀⠀⢘⣻⣿⣿⣭⣤⣤⣤⣤⣬⣯⣼⣼⣿⣟⣃⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠻⣿⡿⠆⠀⠟⠻⠃⠘⠛⣂⣀⣤⠴⠖⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠒⠂
⠀⠀⠀⠀⠀⢀⣠⠴⠿⣛⡿⠿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠿⠿⢿⣧⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒
⣿⣿⠿⠻⡿⢛⠿⣿⠟⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣤⣤⣤⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⠉⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣿⣿⠀⠀⠀⣼⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠀⠀⠀⢀⣤⣾⣿⣷⣦⡀⠀⢸⠄⣿⣿⡀⠀⠀⣸⣿⡇⠈⠻⣧⣄
⠀⠀⠀⠀⠀⢠⣾⠟⡩⠿⢍⡇⢠⣤⡄⠀⣤⣤⢼⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⢸⠀⣿⣿⡇⠀⢠⣿⣿⡇⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⣰⡿⠋⢸⣿⣶⣿⣿⣿⣿⣿⣿⡟⢿⣷⡇⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⠃⢸⠀⣟⣟⡇⠀⢸⣿⣿⡇⠀⠀⠀⠐⠙⣯⣀
⠀⠀⠀⣼⡿⠁⠀⡎⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⣿⢀⣿⣿⣿⡿⠟⠡⡇⢸⠀⣿⣿⣿⢆⣽⣿⣿⡇⠀⠀⣤⣾⣷⣬⣿⡇
⠀⠀⣼⡿⠁⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠄⣿⣿⣿⡀⣽⣿⣿⡇⠀⠀⠛⣿⣻⠛⠉⢿⡧
⠀⢰⣿⠃⠀⠀⢀⣇⠙⠛⠛⠛⠛⠛⠛⠛⠛⣛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣈⣛⣉⠉⠉⠉⠉⠁⠀⠀⠀⡏⢹⠀⠀⠘⣿⡆
⢀⣿⡏⠀⠀⠀⠸⠿⠀⠀⣀⣀⡀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠶⠶⠶⠶⠶⠶⠶⢤⡇⢸⡇⠀⠀⢹⣿
⢸⡿⠁⠀⠀⠀⣈⣋⠀⠘⣿⠟⠁⡀⣴⣦⠀⣿⢀⡀⣀⡄⠀⢰⣿⣿⣿⣶⣀⢰⠀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠀⣸⡇⢘⣧⠀⠀⠘⣿
⢼⣿⠀⣀⣄⣠⣼⣷⣄⣼⣿⠀⢸⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣼⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿
⢺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠻⢀⣿⡿⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⢸⣿⠀⣟⣽⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⡗⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠈⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⣾⢿⡇⠀⣿⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⠄⠀⠀⠰⢠⣀⣘⣿⣿⣶⣤⣴⡄⠀⠀⠀⠀⠀⣸⣯
⠀⠸⣿⣿⠉⠉⠉⣿⡇⢸⡁⠃⠀⣼⢠⡇⠀⣿⠀⠒⠒⠒⠚⢻⡟⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠁⠀⠀⠀⠀⢠⣿⠇
⠀⠀⢻⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡟
⠀⠀⠀⠹⣿⣄⣠⣴⣶⣶⣦⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⣶⠶⠤⠤⢾⡿⠿⢿⣿⠛⠁⠀⠀⢀⣀⣀⣤⣤⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠤⣧⣀⢀⣀⣤⣤⣤⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⡀
⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄
⠙⢿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⣠⡀⢀
⠀⠀⠈⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢈⡁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣶⣦⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠙⠃

⠀⠀⠀⢠⡖⠋⠓⣺⣷⡄
⠀⠀⠀⢸⠀⠀⠬⠄⣿
⠀⠀⠀⢸⠀⠀⠤⠭⣿
⠀⠀⠀⢸⢀⠀⠶⡫⣿
⠀⠀⠀⠘⠀⠀⢑⠀⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⢸⠀⠀⢝⠄⡇⠀⠀⠀⢀⡴⠅⠒⠛⠉⠙⠛⠛⠷⠶⠶⢤⣤⢤⣤⣤⣤⣤⣴⣒⣂⠩⠄⠐⠒⢚⠛⠿⣦
⠀⠀⠀⢈⡀⣀⣵⣂⡅⢀⣀⣔⡿⣪⣭⣄⣄⣄⣴⣶⣦⣖⣒⣮⣤⣭⣭⡍⣍⣵⣶⢶⠶⠦⠶⠶⢶⣿⣦⡒⢣⣿⣇⡀
⠀⠀⠰⠏⠀⠀⠀⠁⠀⣠⠊⣻⣸⡽⣩⢁⡤⠠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⠙⣌⢢⢿⣻⡃⣰⡀
⠀⠀⢀⠀⡀⠀⠈⠄⠀⣷⣰⠈⢷⠃⡏⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢽⠈⠐⣿⡟⡐
⠀⠀⠀⠒⡏⠉⠉⢉⡞⠛⣧⢸⣻⠀⡇⣀⢸⡆⠀⠀⠀⠀⠀⡀⣿⠃⠀⢹⣟⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡄⠁
⠀⠀⠀⠀⡇⠀⢐⠄⡁⠀⠈⣿⣺⠀⢣⡀⠀⠀⠊⠀⠀⠀⡐⡸⠁⠀⠀⡂⢿⣾⣦⠀⠀⠁⠀⠀⠀⣀⠔⢽⢸⣶⡿⣦
⠀⠀⠀⠀⡁⠀⠘⠀⠀⠀⠀⢸⡿⡄⠀⣈⣙⣛⣛⣛⡡⢋⠔⠀⠀⠀⠀⢆⠘⣿⣎⠩⠉⡥⠀⠩⡡⠐⠐⢗⣿⠈⠳⡽⢡
⠀⠀⠀⠀⠀⠀⢐⠔⠀⠀⠀⠈⠻⠶⠦⢤⣤⣤⣤⣤⣴⠿⠒⠤⡀⡀⡀⢀⠖⢼⣮⣑⣒⡒⣐⣐⣒⣈⣡⣾⠇⠀⠐⣡⣿⠄
⠀⠀⠀⠀⠀⠀⢀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠙⠦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣁⣄⣴⡿⣺⠷⠋
⠀⠀⠀⠀⢐⠀⢐⠁⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣑⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⡯⠗⠊⠉
⠀⠀⠀⠀⢰⢀⣀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣤⣀⣉⠓⠢⠤⣀⣀⢄⡲⡞⣋⠗⠋
⠀⠀⠀⢠⠗⠈⡉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠻⠿⠻⠿⠯⠧⠛⠁
⠀⠀⠀⢸⠀⠀⡀⡀⣠⡀
⠀⠀⠀⢘⠐⣏⣋⣩⣽⠗⡀
⠀⠀⠀⠸⠀⠈⠉⠉⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢰⣤⠀⠀⠀⠀⡤⢤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠋⠛⠿⠶⠖⠶⣶⠚⠋⠂⠁⢹
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠒⠈⠐⠠⣀⠀⠀⠀⠀⠀⠀⠙⣷⠆⠀⠀⠤⠲⢀⡀⠐⠈⡫⠃
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠖⠀⠂⠁⠀⢀⠀⢤⠂⠼⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣈⠊⠀⠀⠌⠀⠄⠄⠀⢀⡠⠔⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠉⠀⡀⠀⠀⢈⠁⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠐⠀⠂⠀⠀⠂⠨⠔⠄⢊⠔⠔⠨⠂⠅⠀⢊⠀⠔⠨⠀⠄⠀⠨⠀⠔⠔⠠⠀⠀⠀⠠⠊⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢿⣿⣶⣦⡀⠀⠀⠀⡀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣾⢿⣯⡉⠑⠀⠀⢠⣬⣿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠂⠙⠂⠀⠀⠀⠙⢻⠻⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⡀⠠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠃⠀⠀⢀⠀⠀⠀⠀⣄⠐⡔⣼⣷⡤⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢀⠀⠀⢀⡘⣁⡀⢀⣄⣱⣶⣿⡿⣿⣿⣫⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣶⡞⣿⣻⢟⣽⣿⠟⣿⣛⣿⡿⣟⡿⣾⣿⡷⠾⡛⢽
⠷⠟⠒⠀⠉⠁⠉⠀⠀⠈⠁⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠋⠙⠉⠋⠉⠉⣉⣉⣉⠍⠩⢉⣩⠥⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣠⡤⠶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠐⠂
⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣔⣾⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⠀⠰
⠀⠀⢢⢸⡆⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡄⡀
⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠙
⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰
⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠠⡀
⠈⠁⠐⠂⢤⡙⠁⠄⠀⠀⠀⠀⠰⠶⠶⠴⠶⢶⡴⠖⠶⣶⣶⣶⣤⠴⠶⠶⠶⠖⠒⠠⠤⢄⠀⠤⠘⠛⠓
⠀⠁⠀⠀⠏⠀⠀⠂⠀⣀⣉⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠙⠀⠠⠤
⠀⡀⠜⠷⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠒⢒⣂⣀⣀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⢀⣀⡀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⢐⡦⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣞⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣁⣀⣀⣀⣀⣈⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠆⠉⠉⠉⠉⠉⠉⠠⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠒⠛⠛⠒⠒⠒⠂⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠻⢶⣶⣤⣤⣤⡒⠒⠊⠉⠉⠙⢋⣉⣉⢹⠋⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠈⢉⣻⣿⣿⣷⣶⣦⠀⢴⠟⠛⠛⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣀⣴⣿⣿⣷⠀⠀⠀⣠⡾⠟⠛⠛⠛⠋⠀⠀⠀⠀⣠⣆⠠⡄⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠈⠀⠀⢀⣤⠤⣄⠀⠀⠀⠀⢿⣿⡆⢸⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣦⠘⠇⠀⠀⠀⢺⣿⣥⠚⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⢶⣶⣍⠻⠃⠀⠀⠀⠀⠀⠈⠻⣯⡼⠃⠀⠀⠀⠀⢙⣿⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠛⠸⠇⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⢛⣤⣤⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⣀⣉⡿⠋⠀⠀⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠤⠴⠰⣿⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠙⠓⠶⠶⢤⡤⠴⠶⣦⠘⠁
⠀⠀⠀⠀⠀⣀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⡈⠳⣄
⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣼⠋⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⣼⣦⣴⣶⣦⡀
⠀⠀⣠⠏⠀⠀⠀⠀⢀⣠⠶⢾⣿⣿⣿⣿⣼⠁⠀⠀⠙⣿⣿⣿⣿⣷⡆⣠⡀⠀⣠⡤⠾⣿⣿⡇⢻⡈⢿⣿⣿⣷⣤⡀
⠀⢰⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠈⠀⠀⠀⠀⢻⣿⡇⠀⢳⡌⣿⣿⣿⣯⠙⢦⡀
⢀⡆⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠹⣸⣿⣿⣿⣇⠈⠳⡄
⠘⠃⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠙⡄
⡇⠀⠀⢠⡍⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⣿⡿⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⢹⡄
⣇⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⣿⡇⠀⢀⡴⠋⠀⣿⣿⣿⡇⠀⠀⠀⢱
⣯⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠙⠛⠛⠓⠂⠤⠤⠤⢀⡀⠀⠹⣿⣧⠀⠀⢻⡇⠰⡏⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣤
⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⣹⣿⣧⠤⣿⣟⢂⣻⣆⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠛
⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠂⢉⣉⡠⠜⠛⠒⠉⠉⠉⠁⠈⠷⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⡇
⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⡃⠀⣴⢿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢇
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⠈⠁⠀⠀⢀⣴⣿⣿⣿⣷⡀⠀⠘⡇⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠸
⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⡀⣱⡀⠀⢀⣤⣽⣿⡿⠋⠉⠉⠻⣷⡀⢠⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⢿⣇⠀⠀⠀⠀⣿⡇⢈⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣴⡾⠋⠀⣿
⠳⢤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⢀⣀⡠
⠀⠀⣿⡏⠀⠒⠒⠂⠉⢹⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠐⠒⠒⠁⢹⠉
⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⢿⡇⠀⠀⠀⠀⠀⢈⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢰
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⠀⢀⡈⠉⢹⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢈⡀⠀⠀⠀⠀⣸
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⠙⠀⠛⠉⠉⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠀⠀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣉⠤⠐⠂⠁⠉⠉⠁⠁⠒⠢⢌⡁⠂⢄⡀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠉⡆⠀⠀⢹⠉⡚
⠀⠀⠀⠀⠀⠀⠘⡀⢨⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⠀⠀⠀⠀⠀⠀⡆⢀⠁⠀⠀⢨⣉⡅
⠀⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⠀⠀⡔⠀⣠⣄⠈⢆⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⣤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠳⣀⣀⠔⠁⡘⢰⠈⡄⠀⠓⠤⡠⠊⣠⠊⠀⠀⠀⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡤⠒⠒⠤⣑⠼⠤⣃⠴⠊⠉⠀⡖⡙⠀⠀⠀⠀⠀⡗⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠑⢄⠀⠀⠀⠈⠀⠀⠀⠀⡠⠎⢠⠃⠀⠀⠀⠀⠀⡏⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⡐⠂⠀⠀⠐⢒⡉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠧⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠍⣉⣉⠉⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠤⠤⠤⢰⠄⠀⢀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⢔⠁⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠑⠒⠒⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡞⢻⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠌⠣⣼⠃⣴
⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀⢠⡴⠶⠶⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⣳⡦⣤⢀⣤⡀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠛
⠀⠀⠀⠀⠀⢀⠀⣰⠀⠈⠀⢀⡄⠀⠀⠦⠌⠀⠀⠀⠀⠀⠀⠀⡤⢤⣤⣅⠉⠠⠄⠀⠀⠀⠀⠀⠂⠀⣁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠣⠀⠀⠤⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⠀⢈⠰⠃⠀⢀⠠⠤⠤⠴⠵⠄⢉⣤⡴⡁⠐⠐⠤
⠊⡂⠅⠀⠀⠀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠖⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠐⠰⠀⠀⠀⠀⡴⠂⠀⡀⡀⠀⢠⠀⠀⠀⠀⡄⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡀⢑⣄⣄⣦⢀⡸⠃⡀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠇⠀⠀⠙⠉⡸⠂⡜⠀⠂⠀⡜⠀⠝⠀⠐⠀⠀⡨⠁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠆⠀⠀⠀⠒⠀⠀⠀⣀⣀⣈⢀⡀⠀⠀⠀⠤⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠤⠄⠀⠒⠐⠃⠒⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠂⠀⠀⠀⠀⡈⠀⢀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⡖⠒⠚⠋⠁⠀⠀⠀⠈⠓⢢⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠢⠤⠤⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠒⡆⠀⠐⠀⠈⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⢸⠒⢐⢒⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣟⢃⡉⠁⠸⠛⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢰⠸⠊⠀⠀⣂⢠⠀⠸⠇
⠀⣸⠿⣶⣻⣋⣹⣿⣻⣯⣿⣌⣩⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠞⢧⠰⠈⠀⠀⠀⡆⢸⠘⠂⢀⠀⢤⣂
⠀⠙⣀⢿⢿⠟⣾⣿⢿⠙⠯⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠸⢰⠘⢀⢀⢰⣼⡄⠃⣠⠔⠛⢭⡄⠀⢿
⠀⠀⢹⣋⣾⢰⡙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡥⡄⠠⢀⢰⠸⠀⣡⣏⡍⢫⢰⡄⠀⡇⠀⢘
⠀⢠⠛⣉⠶⠀⣡⡼⡆⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡰⠏⢙⠀⠀⢘⠀⠀⢠⠘⠈⠠⢚⠫⠐⡖⠠⢸⡇⠀⡳⠒⡎
⠀⠀⢀⣶⠿⢂⠄⡀⣰⠀⠀⠙⠛⢠⢠⠀⠀⠀⠀⣠⠞⢡⠆⡀⠀⠀⣈⣡⠰⢠⠀⢹⠈⠌⡀⡀⣿⠐⢈⠙⠛⠁⡄⢤
⠀⠀⠺⢳⡀⠈⡆⢼⡏⣤⡀⠀⠄⠰⠰⠂⠀⠀⢰⠅⠠⢈⢓⣀⣀⠀⠈⠂⠀⠀⣤⣜⠄⠙⠀⣧⣴⣾⢿⡟⡜⢦⡀⠸⠃
⠀⠀⣴⡄⢠⣄⡭⣟⠇⣿⡀⠀⠀⠜⠀⠀⠀⠀⢠⠇⠠⣬⠧⠧⠀⠀⣸⠂⠴⠐⣉⣤⠑⢿⡇⣿⣍⡇⠏⠁⠀⠘⠁⣠
⠀⠀⡿⠿⠹⢟⢛⡋⠣⣟⣣⢀⣸⡞⣬⠤⢤⡤⣩⡃⢀⢲⣱⣜⣇⡀⡘⢳⣻⠩⣁⡌⣷⠈⡙⠻⠆⠓⠉⠡⠁
⠀⠀⢉⣛⢺⠷⣬⡿⣫⠿⡎⢘⠋⡥⠋⡤⡝⢣⠀⡷⠦⠌⡛⠻⡏⢿⣽⠊⣥⢂⡘⣟⡎⠠⠋⡄⠀⠀⠀⠀⠘⠋⠙⠉
⠀⠘⣤⣯⢈⣵⣙⢳⣟⣿⣙⣻⡇⢿⣧⠟⣵⣤⣅⡆⠀⢀⣧⣖⠀⠀⢀⣈⠟⡍⣽⡛⣿⡦⠟⠃⠀⠠⠤⠀⠀⠉⢉⠉
⠀⠈⢩⣥⣬⣼⡎⢿⠿⢽⡶⠾⠿⠛⠀⠀⠉⠹⠞⠛⠛⠛⠛⠿⠿⠿⠿⠏⠂⠷⠼⠮⠥⠧⣶⠄⣤⣤⣴⣤⣧⣤⣤⣦
⠀⠀⠘⢛⡻⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠹⠿⠥⠾⠿⠆
⠀⠀⠠⠽⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢄⠂⠶⢦⡠⢐⢦⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡭⠭⡅⠓⠂⠀⠙⠂⠑⢮⢪⢣⠀⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠒⠀⢀⣠⢖⡀⢀⡀⢀⡠⠠⠀⣏⡃⠀⠀⠀⠀⠀⠔⠊⠉⠉⠳⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠦⠤⠴⠁⠘⠈⡔⠉⠉⢢⡠⠀⢯⠂⠙⠀⠀⢀⠄⠀⠀⢀⡀⠀⠀⠘⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣄⠀⢄⣲⡆⠀⢀⢸⠀⠀⠀⠰⠑⠀⢀⠃⠰⢰⠊⠉⡶⠊⠉⠉⡃⠀⠀⠀⠈⠅
⠀⢲⠀⠀⠀⠀⠀⣰⣀⠀⣸⠀⠼⡑⡠⠄⠐⢄⡘⠘⢄⣀⣠⢜⠕⢚⠧⠄⡦⡜⠒⠂⠧⠤⢠⠔⠁⠀⠀⠀⠀⠈⠄⠀⢀⠐⢁
⠀⠨⠤⠀⠐⠂⠚⠁⡾⠋⠉⠙⠷⠀⠮⠐⢀⠻⠓⠤⣉⠉⠡⡖⠡⢐⡯⠎⠀⠈⠫⠂⠄⠀⠀⠀⠀⠀⢰⠅⠀⠀⠈⢻⡏⢠⠌
⠀⠀⠀⠀⠀⡀⢀⣀⡄⣆⠀⠈⡄⠀⡠⠖⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⡱⢄⡀⠀⠀⠀⠺⣍⠀⢠⠠⠂⠙⠉⠈⡆
⣀⠄⠂⠁⠀⢀⠼⠏⠿⠮⣂⡀⠌⠚⠀⠑⠕⢢⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠁⠈⠒⠄⠠⠤⠚⠓⢾⠀⠀⠀⠀⠈⠁
⠉⠒⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢠⠀⣤⣴⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡠⢇⢀⣤⣀⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣰⠶⣿⣿⣿⣫⣥⣤⣄⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠈⠉⠀⠀⠀⠉⠀⠋⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⣿⡿⠶⢷⣭⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠘⣡⣾⠸⡈⢳⡄⠉⠛⡌⠺⠀⠀⠀⠀⣠⣾⣶⢒⠶⠄⠀⣐⣆⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣡⣠⢹⣿⡀⠓⢾⡿⣦⠀⠀⠀⠀⠀⠐⣷⣞⣿⣧⡄⠹⢤⣴⢛⣿⣟⢛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⣿⠁⠀⠈⣿⠈⠘⠂⠀⠀⠀⢸⠓⠀⢠⣿⣽⡇⠸⠏⢻⡁⠍⢳⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⡈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠙⠢⣀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⣀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡄⠀⠈⠳⣤⣄⠸⣧
⠀⠀⠀⠀⠀⠐⠒⠛⠛⠓⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠙⣶⣦⠄⠀⠈⢻⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⡤⣤⠤⡤⠤⠤⠖⠛⠉⠄⣀⡀⠐⠙⠁⠀⠀⠈⠁⠠⠈⠻⣯⣦⡀⠀⠻⡄
⠀⠀⠀⠀⠒⠒⠒⠂⠈⠉⠉⠉⠉⠉⠁⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡠⣤⣤⠴⠾⠋⢹⠀⠀⠀⠀⠀⢀⡤⠤⠐⠘⣿⣷⡀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣤⠴⢚⣛⣩⣭⣭⣥⣤⣬⣬⣍⣀⣀⣁⣀⣀⣀⣠⠴⠞⠃⠀⠀⡀⠠⠚⠉⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠠⠄⠤⠤⠤⠔⠒⠂⠐⠋⠉⠉⢁⣀⡠⠌⠀⠠⠤⠚⠉⢉⡉⠉⠊⠀⠁⠀⢀⣔⠚⣏⣴⣠⡤⠖⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠥⠀⠀⢀⣀⠀⠄⠀⠐⠋⠀⠀⠀⠀⣀⢴⣧⡶⢞⣼⣃⣀⡏⠁⠂⠀⠀⠀⡀⣸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠠⠖⠊⠉⠀⠀⠈⠀⠀⠀⠀⠠⠂⠉⠁⠋⠚⠃⠀⠉⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠳⠶⢶⣦⣤⣤⣤⣤⣶⡶⠶⠞⠛⠛⢶⣄⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢠⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠉⠻⣿⣶⣿⠀⠀⣿
⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⣸⠃⠀⢠⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠈⢿⣿⣦⣀⠀⠀⠘⠁⢀⣴⣿⡿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣶⣾⣿⡿⠛⣁⣀⠀⠀⠉⠻⢿⣿⣷⣶⣿⡿⠟⠋⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠙⢷⡄⠀⠀⢠⡾⠋⢉⣿⠀⠀⠀⠀⣿⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⡛⠛⠟⠛⣁⣴⣞⣁⣀⣀⣠⣴⠟⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡛⠛⠉⠉⠉⠙⠉⠉⠁⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣤⣤⣤⡴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛
⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢉⠀⢈⢰
⠀⠀⠀⠀⠨⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣩⡄⠀⠀⡇⠈⢨
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣯⠉⢋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠊
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠿⣴⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣽⠀⠀⠀⠠⠯⠶⢤⠀⠀⠀⠀⠀⠀⣠⡶⢁⠄⠈⠀⠀⠀⠀⢸⠅⠀⠀⡄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⣄⠀⠀⢾⡷⠈⠀⠀⠀⠀⣶⠿⠃⠂⠀⠄⠀⠀⠀⠀⠀⠸⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠛⡛⠀⠁⠀⠈⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⡆⠀⣷⢢⡄⠴⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣇⠀⡏⠀⣁⠄⠀⢀⣀⠐⠀⠀⠀⢀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡇⠀⠀⠀⠀⠈⡌⢳⠀⠀⠀⠉⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡗⠀⡀⠂⠀⠁⠀⠈⠀⠀⠉⠀⣉⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢺⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⣀⣦⣤⣀⡀⢴⣾⣦⡄
⠀⠀⠞⣿⣿⣿⣥⣿⣿⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⢀⣠⣴⣒⣻⣟⣒⣦⣤⣀
⠀⠀⠀⠉⠙⡈⠿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⣿⡟⣻⣛⡉⠁⠀⠀⠀⠀⠀⠈⣿⠉⢹⡏⠉⣿⠉⢹⡇
⠀⠀⠀⠀⠀⠱⡀⢀⣧⣶⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡄⢩⡏⡉⣍⢹⡇⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⢬⣿⣰⣠⣤⣼⠙⠀⠀⠀⠀⠀⠀⠀⣟⢺⣟⡏⣟⢹⡏⡇⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⣇⣸⣿⣀⣼⡇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⣏⢹⡏⣏⣿⢹⡏⣿⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⠿⣿⣿⠿⢿⠿⠆
⠀⠀⠀⠀⠀⠀⠤⠝⠛⠛⠉⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠘⠇⠀⠛⠚⠗⠉⠀⠀⠀⠀⠀⠀⠈⠛⠴⠟⠀⠘⠃⠄⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠂
⠀⠀⠠⠬⠤⠥⣤⣤⣧⣷⢲⠒⡖⠶⠒⠖⠂⠀⠀⠀⠀⠀⢠⣏⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⡏⢹⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⠐⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠰⠿⠇⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⠁⠘⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⡟⣟⣿⣻⣻⣟⣟⣇
⠀⠀⠀⠀⠀⢀⣴⡇⠐⣤⣿⣿⣿⠀⢀⣴⡿⠈⠢⡀⠀⠀⠀⠀⠀⠀⢠⣿⡷⡿⡿⡟⣿⢻⢿⡟⡿⣿⡿⣿⣷
⠀⠀⠀⠀⣠⣾⣿⣣⣾⣿⣿⣿⣇⣴⣿⣿⡇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠸⣿⣿⣟⡿⡿⣿⢿⢿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠉

⢀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣷⡠⣀⠀⠀⠀⠀⣠⣦⣀
⠈⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠛⠳⠶⠶⠞⠛⠉⠙⠳⠶⠶⠞⠛⠉⠙⠻⠶⠶⠶⠛⠉⠀⠀⠀⠀⠘⣷⡉⠛⠛⠛⠛⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣨⣥⣴⣤⣄⡀
⠀⠀⠀⢀⣠⣴⣶⣎⠿⠟⣭⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠠⣶⣿⡿⣛⣵⠿⠋⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⢶⣶⣄⣿⣿⡿⣣⣮⡻⢿⡇
⠀⠙⠵⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡟⣴⣿⡿⣿⠏⢫⣾⣮⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣷⡁⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣶⣤⣀⡀⠈⠛⠛⠛⠛⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠈⠛⠿⣿⣿⣿⣶⣤⣤⣾⣿⣿⡿⠂⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣶⣶⢴⠶
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣿⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⢀⣾⣿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠱⠷⠆
⠀⠀⠀⠀⠀⠉⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢀⣠⣦⣀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠈⠙⠛⠛⠛⠛⠉⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀⣠⣤⣶⣶⣶⣶⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣬⣑⣆
⠀⠀⠀⠀⠀⠀⢹⣿⡟⣼⣿⣿⢿⣿⣧⣿⡟⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣟⢼⣿⣿⣿⣿⢹⣷⠄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠜⢿⣯⣾⣿⣿⣿⣿⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠈⠛⠻⠿⢟⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠛⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⣄⢆⠠⣤⣄
⠀⠀⠀⠀⠀⠉⣈⠖⡎⢿⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣯⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠢⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢐⣧⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢽⡂⠀⠖⣰⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣽⣽⣧⠀⠀⠀⠀⠀⠀⠀⢸⢁⣈⣇⣁⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡌⣧⠀⠀⠀⠀⠀⠀⣼⠀⢁⡈⢉⠉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠛⣭⡿⣆⠀⠀⠀⠀⠀⠉⠀⠈⡃⢻⢸⡇⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣵⢬⣂⣄
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡟⠛⠛⠛⡛⠃⣿⠓⡓⠛⠚⠓⠒⣀⠠⣴⣞⣭⣶⣊⢹⠧⡐⠆⠸⠟⢣⣤⣀⢀
⠐⡿⠛⡋⠙⠋⣸⡴⠀⠀⠀⠀⠈⠙⡟⣿⣤⣤⣤⣷⣀⢄⢸⡇⠀⣼⡅⠒⡸⣿⣯⣦⠐⠉⠉⠐⠶⠒⠲⠆⣾⣖⢛⣛⡿⢋⠀⠀⣀
⠀⠐⠀⠀⠀⢸⡟⠓⠀⠀⢀⠀⠀⠀⠀⡿⠋⠸⠃⠀⠀⢠⢈⣁⡀⠀⠀⠷⢜⡫⢡⡴⠯⣽⡗⢠⡒⠺⢟⣵⣄⠲⢿⡇⠑⠊⠲⠤⡟
⠀⠀⠀⠀⠀⠘⠓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠠⡶⡆⠀⠀⠇⠀⠚⢶⠀⠀⢰⢷⠀⣿⠁⢴⢶⠀⠈⢩⣭⡝⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡇⠀⠂⠃⠀⠸⢿⡀⠐⢸⢸⠆⡽⡀⣸⡻⠀⠀⢰⣾⡄
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡀⠀⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⡋⠁⠀⠀⠀⠙⠀⠉⠁⣿⠨⠉⠈⠁⠈⠈⠉⠉⠃⠈⠀⠀⠀⢠⡄⣠⢀⠀⣴
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠁⠂⣌⣉⠐⠟⢻⣟⣿⣙⢻⣁⢿⣿⠷⢾⠿⠶⣟⠶⣿⣻⣿⢛⣛⠚⠟⠷⠲⠶⢷⡉⢟⣃⠌⣴⠇⣴⠃⡍⢲
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠀⡀⠀⠀⠏⢷⡗⠀⠀⢀⣀⣈⣿⡛⣿⢻⣋⣝⠉⠀⣀⣼⣿⣿⠹⣿⣿⣯⠀⣠⣤⢤⠈⠁⢠⠽⠂⣴⣆⢑⠒⡾⠚
⠀⠀⠚⠆⠀⠀⠀⠀⠀⠀⡄⠀⠠⢥⢠⠀⠀⣁⡄⠀⢲⣏⡇⠀⢰⣯⣭⣹⡞⡻⣿⠈⡏⣯⣅⢸⣯⣻⣿⣿⠀⡆⢱⡏⢰⣿⢿⣿⠀⠀⠘⠗⠠⣿⢿⢿⣿⠇
⠀⠠⡤⢤⠄⢠⣤⣤⣄⠆⠇⠀⠀⣸⠘⠀⣻⣿⣿⠀⡼⡥⠅⠀⢸⣷⣾⣿⡇⡟⣻⠀⡇⣼⡣⣸⣿⣿⣿⣿⠀⠷⢸⡇⢰⣿⣿⣿⠀⣤⢀⠠⣤⣤⣤⢀⣻⡇
⠀⣦⣀⠈⠀⠈⠉⢿⠛⠀⠆⠀⠀⠘⠀⢲⣧⣤⣾⠁⣉⠟⢃⠤⢸⣤⣿⣿⡇⣵⡏⠀⠀⢛⣱⣻⡟⣻⡧⡟⠀⠀⢈⣓⠸⣿⣾⡿⠀⣯⠠⠿⠋⢉⣨⢤⣻⢳⠛
⠀⠈⢭⣿⡆⠀⠀⠀⠀⠀⣀⠀⢀⠘⣀⡻⡛⠛⠛⠓⠋⠐⠾⢀⣸⠿⠿⠻⠃⠛⠓⠀⠰⡜⠹⠋⠉⠉⠉⠁⠐⠐⠈⠉⠁⡄⠀⠄⠈⢓⠐⢂⣀⠘⣿⣻⢿⡟⠇
⠀⠀⠸⣾⠇⠀⠀⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠅⠈⠉⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⣀⣴⡾⠦⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣛⣻⣿⣿⠵⡶⡶⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡿⢛⢿⢿⡛⠻⣶⡄⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⢴⣿⠘⣄⢹⣆⠀⠘⠀⠁⠀⠀⣠⣰⣾⡟⠉⣝⠃⢀⣼⣦⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⢱⠸⣿⡆⠈⢻⣟⠧⢀⠀⠀⠀⠀⣼⠛⠹⣿⢧⡈⢱⡟⣶⠟⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠹⠀⠀⡈⠳⣄⠀⠀⠀⠀⠀⠁⠀⠀⠛⢿⡃⠈⠀⠉⠀⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠙⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠭⠭⠅⠤⠄⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠦⠴⣭⠮⠭⠿⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠈⠙⠦⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠈⠳⣄⡀⠀⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠈⠁⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡉⠳⣴⡄⠀⠈⢛⢠⣉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⢦⠄⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⠶⠤⡵⠦⡙⢿⡦⡴⣎⡄⠛⣲⢬⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠈⠁⠀⠀⠀⣀⡴⠖⠋⠉⠀⣀⡀⠞⠋⢓⢿⣮⣵⢟⠛⠓⢾⣿⣀⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⣭⠀⣠⠆⣀⠞⠋⡄⣔⣠⣾⣦⣽⣿⣾⣾⣄⡆⠪⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣋⣴⣾⣡⣾⡿⣠⣥⢸⣠⣿⠟⠟⠛⠙⠛⠛⡛⠛⢉⠹⠧⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠋⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣀⡀⡴⠀⢀⣀⡄⣀⣖⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠧⠜⠃⠛⡅⠀⠛⠃⠟⠛⠟⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣀⣀⣀⡀⠀⣴⣶⣀⣀⣠⣀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⡿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠜⠁⠙⠋⠛⠂⠀⠏⠈⠁⠛⢻⠋⢟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣟⣟⡧⠙⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣘⣴⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠟⠙⡏⡇⠀⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣐⣛⡗⠚⣦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⣯⣿⡇⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣼⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠛⡗⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⣠⣀⣠⠿⢠⣤⣤⣤⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣓⢠⣉⣻⢫⣿⣿⣿⣿⣞⣛⡒⡛⠛⠛⠛⠛⣿⡿⠻⠿⣿⠃⠀⠸⠿⠟⠃⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⡄⠊⠐⠰⣿⣿⣿⣿⣿⣬⣅⣤⠄⠲⠲⢤⣌⣻⡿⣧⡛⠒⠒⠊⠂⢀⣤⣶⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠀⢸⡇⠀⠈⠹⣿⣿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣾⡁⠀⠀⠀⠀⠿⢧⡏⢀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣨⡇⠀⠀⢐⣿⣯⡠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢖⢷⡀⠀⠀⠀⢀⣀
⠈⠓⠲⠶⠒⠋⠙⠒⠶⠖⠚⠉⠓⠶⠶⠒⠋⠙⠲⠶⠖⠛⠙⠓⠶⠶⠚⢉⡤⣄⠘⣯⢿⠛⠒⠚⠉⠉⠙
⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠓⠋⠀⠘⣎⣧⣀⣀
⠀⠀⢀⣠⡤⠾⣏⣀⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⠇⠀⠀⠀⣰⠋⠁⠀⠈⠻⡄
⢶⠚⢉⣤⢖⣠⠟⠉⢳⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢒⣒⠒⠧⠀⣠⡞⢦⣀⣿
⠈⠷⢯⡴⠋⠀⠀⠀⠀⠙⢦⠀⠙⠦⠤⠤⠴⠖⠛⠛⠲⠴⠖⠛⠉⠁⠀⠀⣿⠁⢠⣠⣿⠉⢙⡶⠛⠃
⠀⠀⠀⠀⠀⠀⡴⠛⣶⢤⣈⡳⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢷⠈⠙⠉
⠀⠀⠀⠀⠀⢰⣇⣠⡯⣄⡈⠉⠛⠻⠿⠋⠉⣙⡷⠦⠤⠤⠶⠒⠛⢹⡏⢹⡏⠉⢧⠈⠓⠒⠒⠒⢲⣖⣶
⠀⠀⠀⠀⢠⡟⣀⢹⠀⠀⠉⠓⠶⢤⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⠳⢤⣈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⢀⡞⢠⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣈⢹⡶⣤
⠀⠀⠀⠺⠦⣼⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣀⣤⡴⠲⢤⣄⣠⡤⠖⠦⡄⣀⡀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣄
⠀⠀⠀⠀⢸⡛⠓⣦⠴⠚⠋⢙⠛⠳⢦⡀⠀⠀⠀⠀⠀⢤⠦⣄⡤⠿⠿⢦⣀
⠀⠀⠀⠀⢸⡇⠰⣇⠀⣤⠀⠋⠀⣏⠀⣹⠆⠀⠀⠀⠀⢸⠀⣯⡀⠀⠀⢇⣹⠇
⠀⠀⠀⠀⢸⣤⡴⠟⠳⢤⣄⣤⣤⡴⠚⠁⠀⠀⠀⠀⠀⠙⠋⠉⠉⠿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠠⠤⠁⠁⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠄⠂⠀⠀⣀⣀⠀⢀⠀⠸⠀⣀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⣀⠘⠇⠀⠇⠀⠀⠀⠀⠀⠠⣄⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠋⠁⠐⠂
⠀⠀⠀⠀⠀⠙⠒⠲⢷⣆⡈⠀⠀⠰⠀⢠⣤⣀⡀⠒⠒⠐⠒⠒⠂⠈⠓⠂⠤⠀⣀⣄⡄⣠⡒⢉⡀⢀⣀⣁⣠⣄⣤⠤⠔⠒⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠄⠈⠁⠀⠀⢈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠁⠼⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢻⡆⠑⠒⠲⠤⢤⣤⡀⠁⣠⣀⡀⠀⠀⠀⠀⢈⣉⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠆⢛⡇⠀⠀⠀⠀⠀⢈⣬⡉⠄⠤⠌⠽⠟⠉⠛⠛⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⢠⡅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⣇
⠀⠀⠀⠲⠀⠤⠤⠶⠶⠖⠚⠀⠀⣀⣿⣾⣷⣶⣦⣤⣶⡆⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠙⠃⠐⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠄⠀⢘⣀⠀⠐⠀⣆⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡇⣩⣤⡆⠀⠀⠀⠙⠄⠄⠀⠩⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠷⠶⠾⠶⠶⠶⠶⠶⠶⠤⠬⣤⣤⣄⣀⣀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡒⠨⠆⡿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⣿⢱⠅⠠⢐⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⡁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⢤⣀⠀⠀⣸⣿⠁⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣿⢠⡞⢁⣭⡀⣭⡭⢠⣌⠉⠨⠀⢶⡆⠀⠠⡄⢈⠉⠒⠦⢄⡀⠀⠀⠀⠈⠙⠦⣿⡏⠿⢆⠀⢀
⠀⠀⠚⢦⠀⠀⠀⠀⣟⣿⠿⠀⢀⣿⣿⠀⠛⠒⠀⠉⠉⠀⠀⠈⠛⢿⡤⠀⠀⠈⠀⠀⠠⣈⠑⠢⢀⠀⠀⠀⠈⠙⢦⡀⠀⢸
⠀⠀⠐⢸⠀⠀⠀⠀⡇⣠⡶⠂⠸⠿⠟⠀⠀⢠⡃⠐⠒⠢⠀⠀⠀⠀⠀⠠⡉⠀⣀⠀⠀⠀⠉⠢⢄⠉⠢⡀⠀⠀⠀⠈⠳⡅⠀⠆⣠
⠀⠀⣰⣿⠀⠀⠀⠀⣷⠟⠁⠈⠉⢀⣠⣴⠶⢃⡀⠘⠛⠛⠲⠆⠀⠀⠀⠀⠈⠛⢿⡆⢀⠀⣀⡠⢀⡨⠢⡀⠑⠀⠀⠀⠀⠈⢾⡂⠙
⠀⠀⠻⣻⠀⠀⠀⠀⣧⣤⡾⠄⠈⠋⣁⣴⠞⠉⣀⣀⣠⣤⣤⣤⢀⠀⠀⠀⠠⣄⠀⠙⢧⣨⣭⣤⡿⣃⢀⢼⣷⡀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⢸⢿⠀⠀⠀⠀⣿⣿⣷⠸⡾⠿⠿⠿⠾⣿⡽⠟⠶⠛⠈⠻⠯⠀⠛⠒⠂⠠⠙⠷⠦⠈⣭⣍⠀⠁⠀⢸⣿⣿⠢⡀⠀⠀⠀⠀⠘⠆
⠀⠀⢰⢸⠀⠀⠀⠀⡏⠋⢂⣈⠀⠒⠓⠒⠀⣀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠉⠡⠀⠀⠀⠀⠀⠈⡖⢸⣆⠐
⠀⠀⠸⣾⠀⠀⠀⠀⡇⠈⠀⠉⠀⠀⠈⠀⠀⠀⠚⠃⠀⠀⠀⠀⢀⠄⠀⢀⠀⠐⠃⡉⠀⠐⠦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢂
⠀⠀⠈⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡴⠖⢤⡤⠶⠶⠢⠀⠞⠁⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢦⠈
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⠷⠀⠀⠐⢛⠟⠉⠂⠀⠀⡀⠀⠀⡇⠀⠀⠀⠄⠁⠲⠀⠈⠀⠀⢀⣀⡠⠠⡀⠀⠀⠘⡄
⠀⠀⠀⠀⡃⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣷⣾⣷⣴⡿⣦⠀⣠⠀⠀⠀⠀⠈⠛⠀⠀⣠⠀⡀⠈⠀⠀⠀⠀⠀⠠⠄⠖⢲⡀⠀⠀⢡
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⡶⠃⠀⠁⡠⠀⠀⢠⡄⠁⠀⠀⠀⠞⠀⠀⢠⡈⠠⢠⡆⣰⠋⠉⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢀⠄⠀⢹⣿⣿⡟⢁⠂⠀⠀⠀⠰⠀⠀⠀⡄⠓⠀⠀⠒⠲⠀⠘⠂⢸⡄⠀⠀⠂⢠⣄⠲⢆⣠⠲⠀⠀⡇
⠀⠀⠀⠖⠁⠀⠀⠀⢻⣄⡇⠀⡤⡟⠉⡉⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⡀⢀⣬⡃⠀⡅⠀⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠁⠂⢄⠐⡀⠸⣆⠐⠒⢲⡶⠶⠶⠶⠶⠶⠶⠶⠶⠾⢯⣿⡙⠉⠈⠩⠟⠀⣠⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⡀⢛⠓⣀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⣿⡾⠧⠴⠒⠐⠦⡀
⠀⠀⠀⠀⠀⠉⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢃⠸⠀⠟⠀⠀⠀⠀⠀⠀⢀⡔⠋⣩⣹⡿⠻⠩⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢱⣆⠀⠀⠠⠂⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠔⠒⠒⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⠊⠋⠀⠀⠶

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⢠⠟⠁⠀⢀⢂⡀⣀⠀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢀⠀⠀⠀⢠⡏⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⢀⡈⠀⠂⣀⡬⠀⡿⠈⠙⠀⠀⠀⢀⠀⠀⢠⣇⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠁⠀⠀⠉⢿⣟⡒⠀⠀⢰⠀⡴⠂⠀⠈⠐⠭⣿⢾⠃⠉⠈⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢯⣹⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠘⠐⠒⠒⠀⠀⠀⠒⠈⠒⢂⣀⢀⣃⡚⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠰⠿⠟⠒⢶⣿⣿⣶⣾⠦⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠅⠀⣸⡀⢈⠆⠀⠀⠘⠈⠙⠀⠗⠲⠀⠖⡆⠐⠾⠶⣦⠀⢀⣿⣿⣹⣿⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠄⣸⣔⠊⠸⠆⠠⠆⠀⠤⠤⡤⣤⣄⡀⠀⠀⠁⠉⠀⠒⠊⠉⠁⠈
⠀⠀⠀⠀⢠⢤⠆⠉⠀⠀⠂⠀⠁⠲⠀⠤⢠⠔⠦⠀⢀⢸⡇⠃⠀⠀⠀⠀⢀⡠⢂⣾⣿⣿⣿⠞⠥⠀⠀⣠⠄⠀⠀⠀⢠⡤
⠈⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡔⠀⠀⠀⠀⠀⠀⠀⡄⠊⠐⠛⣿⣿⣿⣶⡶⠦⡤⣦⣴⣶⣶⣦⣤⣽⣙⣀⡉⣀⡠⠰⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡐⠉⠀⠀⠀⠀⠀⠈⠛⠋⠉⣹⢿⡇⠁⠀⠉⠈⣛⡿⣿⣿⣷⣮⣽⣖⣿⣿⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠅⠀⠀⠀⢄⣙⣻⣿⣦⡍⡭⣽⣿⣿⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠖⠛⠹⠿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡴⠆⠆
⠀⠀⠀⣄⣀⣠⣾⣿⣿⣤⣀⣤⡤⣄⣷⣤⣤⣄⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠶⣶⡶⣽⣆⡘⠂⠀⠐⠄
⠀⠀⠀⠉⠉⠙⠉⠻⠟⠀⠀⠀⠀⠀⠙⠻⠟⠉⠁⠀⠀⠀⣭⢤⣤⢤⠀⠀⠀⠛⠛⠛⠚⠘⠘⠓⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⢤⠤⠄⠤⠄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⣸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡁⢀⡉⢙⠉⠁⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡿⠯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠈⠚⠃⠀⠛⠋⠛⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⢸⣿⢽⡇⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢸⣋⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⡇⠀⢄⣰⠀⡇⢢⢠⡆⡏⢰⠖⠆⡀⣆⣴⠀⡦⢸⢶⠂⢲⡄⠀⠀⠐⣿⠃
⠀⠀⠀⠀⠀⣻⠉⢙⠁⠀⠀⠉⠀⠀⠈⠁⠁⠈⠁⠉⠀⠀⠀⠀⠁⠀⠈⠁⠉⠈⠀⠁⠉⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢈⣿⣇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠎⢄⠠⠐⢶⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠄⠠⠀⠉⡀⠀⠀⠀⠀⠀⢸⣿⡯
⠀⠀⠀⠀⠀⢨⢨⢨⠈⠀⢭⠈⠀⡭⠨⠀⠀⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠾⠧⠿⠷⠿⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⢤⡤⣄⣤⣄⡆⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⣀⣘⣿⣿⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠐⡂⡊⡦⢤⢑⠃⠂⠈⠀⠀⠀⠀⢀⣼⣭⣧⡀⠀⠀⠀⠀⠀⡉⢋⠉⢚⡉⣀⢽⠋⢉⠋⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠄⠄⠄⠄⠄⠀⠆⠀⠀⠀⠀⠀⣼⠟⠛⠻⣇⠀⠀⠀⠀⠀⠠⠁⠀⣷⣁⣭⣸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠉

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿