Chestnut Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡦⡀⠀⠀⠀⢀⣀⠀⡰
⠀⠀⠀⠀⠀⠊⠀⠂⠀⠀⠀⠐⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⡀⢡⠈⢂⠀⢀⠂⠀⡔⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠆⠀⠀⠐⠀⡜⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⢐⣒⡒⠂⠢⡀⡄⠁⡆⡜⠀⠀⢀⠔⢊⡁⠤⠔⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⢀⡀⡁⠒⠟⣾⣶⣷⣀⣄⡬⠔⢊⡁⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⣤⡀⢂⠶⠾⠾⣿⡿⣷⠆⢖⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⠀⢉⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠐⡷⠈⠦⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠄⠘⠚⠠⣀⡀⣿⣦⡀⠀⠀⠀⢨⣷⡆⡢⣼⢃⢀⡅⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠂⣑⠀⠀⠠⢰⠙⠳⠉⠟⠿⡷⠤⣿⠏⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠐⠀⢰⠃


⠀⠀⠀⠀⢀⣴⠂⠰⣶⡆⠀⠀⠀⠀⡴⠙⢶⡁⠀⠀⠀⠀⠀⠀⣠⠖⠀⠐⣖⠀⠀⠀⠀⠀⢀⠞⠛⠙⠲⡄
⠀⠀⠀⠀⠨⠿⠖⠙⠋⠡⠀⠀⠀⠘⢄⡀⠀⡇⠀⠀⠀⠀⠀⠀⢻⡀⣀⢰⠇⢀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠀⠀⠀⠀⠈⠛⠷⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠰⠅⠀⠠⢁⠌⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⣒⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⡄⢴⢅⠊⠌⣁⢠⢀⡶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠸⣇⠀⢻⣷⠀⠠⠄⠀⠀⠀⠀⢀⠻
⠀⠀⠀⠀⢴⢖⡐⠠⢀⢠⣧⣦⠊⡔⠁⡇⠞⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣤⣿⣄⣠⡏⠀⠀⠀⠡⠁⢄⠀⠀⢰⠢⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠑⠮⠗⣿⣾⣿⣿⣿⣓⠈⠂⠁⢀⠄⠀⠀⠀⣠⣴⡿⠉⠰⠀⠀⠀⠈⠛⠿⠯⠝⠉⠀⠀⠀⠀⠀⠀⠆⠀⠐⢀⠬⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠙⢟⣿⣭⣵⣾⡄⠀⠀⠀⠠⠃⣿⡗⡁⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠘⠶⢄⣂⠄⡀⠀⢟⡆⢸⡂⢀⢀⠎⠐
⠀⠀⠀⡀⠀⠠⠠⢤⣌⠅⠀⠒⣈⣽⣽⡿⠟⢣⡆⠀⠀⠐⣇⢿⣷⠀⣠⣂⡜⠀⠀⣀⣤⢤⣄⠀⠀⠀⠀⠉⠗⡨⣰⣌⢟⡷⠇⡰⠃⠊
⠀⠀⠀⠀⠀⢀⠖⣠⣼⢆⣠⣾⠛⢹⡏⠐⠨⠀⠒⠄⠀⠀⠈⠺⠽⠿⠛⠉⠀⢠⡞⠁⠠⠓⣀⣷⠀⠀⡀⠠⡀⠄⡈⣿⣿⣿⣯⡡⠀⠀⡀
⠀⠀⠀⠀⠀⢃⣾⣧⠃⠈⣾⣷⠀⣼⡷⡈⠁⠀⣲⡁⠀⠀⠀⢀⣠⣤⣤⣀⠀⠸⣿⢳⡆⢹⣿⡟⠀⠀⠉⠂⠠⠀⠀⠁⠀⠀⠀⠉⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠈⢛⣯⣴⣾⢫⠝⣷⣿⢳⡾⡞⠛⠻⠖⠀⠀⠀⣟⠁⣈⢙⣟⣦⠀⠉⠛⠓⠚⠉⠀⣠⣄⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⣺⡯⠊⠀⡀⠅⠌⠪⠑⢦⡜⢆⠀⠀⠀⠀⠈⣿⣦⣀⡰⢿⡟⠀⠀⠀⠀⠀⠀⠰⣝⣛⠉⠛⣋⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣘⠀⠈⠑⠚⠛⠀⠀⠀⠀⠀⠈⠉⠛⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⢾⣏⣯⣴⣾⠿⡿⣿⣿⠟⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠁⠍⠚⠀⢓⣀⣀⣀⣀⣀⣘⡉⡸⣽⣽⣛⣭⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣷⡶⡥⢤⡔⢻⣋⣏⡏⡉⣸⣿⣽⣍⣽⣟⣻⣟⢻⢿⢿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢠⡤⢰⠠⣷⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡞⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠟⠀⠐⠈⡥⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠹⠟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢱⣼⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢼⣾⣯⣾⣧⣾⣿⣿⣿⣿⣿⣿⣿⠳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠿⡿⢿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡁⠀⠀⠀⣴⣶⣾⣿⡿⠉⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣎⠀⠀⠰⢾⣾⣿⣿⣿⠇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣷⣷⢶⣿⣿⣿⣿⣿⣿⣗⢲⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠶⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣯⣿⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠔⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢹⠯⣿⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠐⠳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠈⠳⢮⣝⣋⢻⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣴⢦⢤⣉⣉⣙⢓⣿⡿⣶⣶⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠿⠿⠿⠿⠞⠋⠁





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

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣶⣋⣁⣂⡀⠀⠉⠉⢷⡔
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⠻⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣽⡷⠂⠄⠁⠂⠀⢢⡄⠉⠻⣿⡿⠿⢿⣟⡓⢻⣞⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣾⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⣤⣄⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠺⢿⠋⠀⠀⠀⠀⠀⠀⡆⢀⠠⠈⠀⠀⠠⠉⠿⠿⢿⣿⣿⠆
⠀⠀⠀⠀⠠⠂⠐⠀⠀⠛⠛⠂⢀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣧⡀⠀⠀⠀⠀⠈⠁⣾⣧⣦⣤⣄⡁⢴⣶⣿⣿⣿⡟⠒
⠀⠀⠀⠀⢀⣴⣿⣁⡖⠀⠀⠀⠀⠙⠿⣷⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⣿⣧⠀⢀⣀⡀⢐⣴⡿⠛⢛⡿⣿⣿⣿⣷⣿⡿⠋⡈
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⢀⣄⠀⠀⣾⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡯⢶⣤⣟⣹⣻⣧⣿⣿⡗⠀⢀⣴⣿⣿⣿⣿⠠⠁
⠀⠀⠀⠀⢰⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠛⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢘⣻⣟⠻⠿⠟⠛⠛⢻⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠒⠰⢂⣽⣆⣀⣤⣄⡌⠉⣻⣡⣿⣿⡁⠀⠀⠀⠀⢀⣤⡾⠟⠉⠉⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠜⡃⠸⣿⠴⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⢀⣾⡿⠃⢀⡀⢰⣿⣿⣿⡄⢀⡀⠀⠀⢤⡀⠀⠀⠀⢠⠎⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠄⠀⠁⠀⣠⠄⠀⠀⡀⠾⣿⣿⣏⣉⣿⣿⣿⠿⣿⣿⠋⠀⠀⠀⠀⠙⣷⡀⠀⢻⠀⠀⠀⠀⠀⠈⣹⠟⠀⠀⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠛⠉⢹⣆⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠤⣄⣤⣔⠲⣿⠀⠀⠀⠀⠀⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠈⣀⠄⠀⣿⣿⣿⡷⠁⠀⠀⠀⢼⣿⣿⣍⣠⣤⣤⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⣀⣄⣤⣨⣵⣾⣿⣿⣿⣟⣠⣤⣾⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠘⠁⠈⠉⡑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠐⠀⠀⠀⡁⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠐⢀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣀⣰⣄⣤⣶⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⡤⠤⢤⣀⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⣂⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠋⠉⠉⠁⠐⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⣧⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿
⠀⠀⠀⢸⣇⣠⠀⠀⠀⠀⠀⠐⣀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢻⣷⣚⣄⡁⠀⠀⠀⠀⠀⡀⢠⠇
⠀⠀⠀⠹⡛⠙⡿⢶⣶⣨⣶⣿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣙⠻⣷⢀⠠⡄⠠⣄⣨⡴⠋
⠀⠀⠀⠀⠈⠢⣤⣛⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⢀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠿⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣠⣠⢠⡔⢬⣿⣷⠰⡿⠛⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⡹⠁⢯⣥⢽⠏⠑⢻⣿⣿⣛⣏⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣉⢫⠱⣦⣾⣿⣋⠀⢠⣿⣿⡿⣿⣭⣙⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡚⠋⢟⠻⣳⣬⣸⣟⡃⣴⣿⠗⠙⠉⠀⠈⠉⢳⣦⣙⢦⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣠⣿⣛⡡⣝⠻⣧⠼⠁⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⢷⣿⠛⠛⠻⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⠉⣉⣿⡿⣺⡿⠿⠆⣴⡻⠉⠈⠙⠻⢶⣤⣤⡄⢠⡆⠀⢿⡏⠀⠀⠀⠻⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠦⠉⡽⣲⣿⣟⣲⢁⣿⣃⠆⠀⠀⠀⠀⠀⢿⣧⡈⢇⠠⣾⠃⠀⠀⠀⠀⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢷⢉⣿⣫⣍⡼⢷⣠⣿⠍⡀⠀⠀⠀⠈⠀⠈⠻⣿⣿⣼⠃⠀⠈⠁⠀⢀⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠛⠻⡟⣿⢲⡇⠘⣿⣤⣆⠀⠀⠀⠀⡄⣀⣷⣿⠿⠛⠓⠂⠀⡀⣀⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠛⣤⣿⡼⢿⢿⣇⠀⠙⠻⠿⠿⠛⡛⠋⣉⣁⣤⣤⣖⣿⣿⣷⣾⠻⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣁⣋⣾⢹⣾⣿⣿⡶⣴⣶⣿⣿⣿⠿⣯⠷⣫⣼⡟⢾⣿⣾⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡼⠻⢛⣿⣿⣿⡿⣺⢷⣰⣟⣽⣛⢿⣿⣶⡖⠀⡝⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠍⢚⡡⢿⡵⣦⣻⣿⣿⣿⣿⡻⣶⠛⢍⠀⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣿⠚⠟⠙⣷⡛⠉⣏⠐⢔⠧⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠜⠃⠈⠁⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠃⠀⠐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠢⠄⠔⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠄⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⣀⡄
⠀⠀⠀⢀⠀⡉⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⠄⡀⠀⠐⠀⠐⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠉⠓⠀⠐⠷⢀⡀⠈
⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠁⠰⠄⠀⠀⠀⠀⠀⠀⠈⠀⠠⢀⠀⡠⠀⠀⠠⠂⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⢀⠘⠁
⠀⠀⠀⠀⠚⠀⠀⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠐⠋
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⢀⣤⡀⠀⠀⠀⠂⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑
⠀⠀⠀⠀⠀⠀⢤⡀⠀⡀⢀⡀⠀⠰⠀⠀⠁⠈⠃⠀⠈⠀⠂⢶⡌⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠂⠀⠀⡈⠀⠀⠀⢹⡂⠠⢀⡾⠤⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣬⠓⡁⠂⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠱⣄⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⠤⠄⠀⠀⠀⠀⠓⠒⠈⢀⡰⠅⠀⠀⠀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⣌⡓⢡⡄⠀⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠊⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠄⠐⠀⠀⡀⢸⠍⢋⡄⠀⠀⠀⠀⠀⠙⠒⠂⠀⠒⠚⠁⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡀⠠⠀⠀⠀⠀⠀⠘⠓⠄⢈⠀⢴⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣁⠀⠀⠀⠀⠀⠀⠁⠀⢃⠀⢦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠈⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⡤⠚⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⡄⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣞⢆⠀⠀⢀⣔⠱⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡲⢯⢚⡅⢠⠻⣌⡛⣚⠇
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣛⣈⣤⢮⠱⠬⢭⠏⣀⢠⠀⡖⣶⣶⠂
⠀⠀⠀⠀⣠⣟⣿⣿⢄⠈⠻⠓⠄⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⢯⣺⣒⣺⢦⣟⢞⡿⢺⢹⣸⣴⠻⡬⠁
⠀⠀⠀⢠⣿⢸⣟⡷⠈⢁⡘⢩⢉⣇⠀⠀⠀⠀⠹⣻⢾⢴⣴⣉⡰⣌⣿⣿⣯⡗⣲⡎⣦⡼⢎⡑⠦⠋⠀⠀⠀⠀⡠
⠀⠀⠀⢨⣷⢸⣿⣿⠈⢣⠀⣤⡃⣞⠀⠀⠀⠀⠀⠈⠓⠯⢮⣏⣟⣷⣿⣿⣿⣿⣻⣿⠶⠙⠀⠀⢀⣠⠤⠀⠒⠈
⠀⠀⠀⠀⢿⣎⢿⣿⣇⢴⣺⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠟⢻⣿⣿⣿⡫⣗⣶⣶⡋
⠀⠀⠀⠀⠀⠘⠷⠽⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣞⡁⣀⠀⣈⣷⣳⡿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠢⠤⠀⠙⠲⢶⣗⡖⠀⠉⠉⣠⣶⣾⣿⡿⡟⢋⠛⣾⡀
⠀⠀⠀⠀⠹⣡⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠴⠠⣹⣼⡿⢄⣠⣿⠛⠏⣹⡟⠁⠆⢨⠰⠰⢷⡄
⠀⠀⠀⣠⣖⠻⣯⣭⣵⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⣷⣿⠋⡟⣀⢿⣹⣯⠒⡉⣿⣿⡠⠝⠢⡘⢠⣤⠇
⠀⠀⣼⣿⠋⠁⠸⣿⠁⠙⢛⣿⣧⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⡯⠄⠄⣼⢿⣿⡬⣠⣿⣿⢥⣮⠡⣬⣔⣞⣧
⠀⢸⣿⣿⡀⠀⠀⣿⡆⠀⠨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢉⣷⣴⣾⣿⣿⡼⠾⢯⣭⣿⣋⣿⣽⣏⠙⠛⠓⠛⠁
⠀⠘⣟⣿⣧⣶⣾⣾⣧⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠞⠁⠥⢊⣙⡂⡿⣼⠉⢤⣊⣾⣦
⠀⠀⠈⠿⣿⣿⣿⠟⣻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠸⣎⣷⠬⣧⠀⠐⠧⣙⣳⣾⢇
⠀⠀⠀⠀⠀⠉⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⠷⠇⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣞⣻⣿⣿⡿⢷⣤⡀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠉⠉⠉⠉⠉⠉⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠶⠛⠉⠉⠀⠀⠀⠀⠈⢻⣄⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢻⡆⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣷⢸⣷⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠹⠇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡏⠸⣇⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⢶⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⢀⡾
⠀⠀⠀⠀⣠⡶⠛⢩⣴⠶⠶⠶⠀⠉⠛⢷⣄⠀⢀⣠⡴⠶⠶⠶⢦⣤⣀⣰⠟⠁⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⢻⡄⣠⡾⠁
⣄⣀⣠⡾⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡞⠛⣷⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⣀⡄⠀⠀⠀⠈⠙⠳⠶⣤⣤⣤⣤⡴⠟⠋
⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡏⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠷⠶⢦⣄⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠠⣦⣤⣤⡶⠛⠉⢴⠶⠿⠿⠶⣦⠈⠛⢦⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡟⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠉
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡟⢻⡄⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⣿⣀⣠⡾⠋⠀⠀⠻⣦⡈⠻⣆⡀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠻⢶⣬⣿⣦⣀⣀⣤⡶⠟⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣿⣀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡀⠀⠀⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢿⣿⣿⡀⢀⣤⣶⣶⣶⡆
⠂⠀⠀⠄⠠⠄⠀⠀⠀⠈⣁⠀⠀⠀⡈⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣦⣶⣶⣄⡸⣿⣿⣟⣿⣿⠁⣾⣿⡟⣼⣿⡇
⠀⠄⠀⠐⠠⡀⠈⠀⡀⠀⠲⠀⠀⠐⠀⣀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⡿⣷⣽⣿⣧⢿⡿⣸⡿⣻⣿⣿⠟
⠀⠀⠠⡀⠀⠈⠑⠢⢱⣄⠈⡅⣀⢀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣝⡿⣿⣽⣷⢟⣷⣿⣯⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠄⠀⢀⡉⢓⣽⡧⠥⠾⠭⠤⠤⠠⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣻⣿⣿⣿⢿⣯⣽⣭⣯⣽⣿⣽⣷⠦
⠀⠀⠀⠀⠀⠔⠀⢀⠠⠔⣾⢻⡟⣝⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⢿⣻⣽⣿⣿⣱⣽⢿⡍⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠈⠀⢳⠀⠁⠄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⢣⠙⢿⣽⣆⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠠⠀⣠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⢹⡿⠃⠀⢧⠀⠀⠉⡰⢛⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⠞⠁⠊⠁⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⣾⣷⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠠⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢻⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠟⠛⠉⠀⠀⠈⠙⠻⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣤⡀
⠀⠀⠀⠀⣠⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⡀⠉⠻⢿⣷⣄
⠀⠀⢀⣼⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣶⣄⠀⠙⣿⣧⡀
⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠈⢻⣷⡄
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⢿⣿⡀
⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢹⣿⡀⠀⣠⣴⣾⡿⠟⠋⣩⡁⠀⢠⣄⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣤⡀⠀⠀⢠⣿⡇
⠘⣿⣧⣾⡿⠋⠁⠀⣤⡄⠈⠁⠀⠈⠁⠀⢠⡅⠀⠀⠶⠆⠀⠘⠃⠀⠀⠀⡀⠀⠉⠻⣿⣦⣄⣾⡿
⠀⠘⣿⣿⠀⠀⢰⡆⠀⠀⠀⢴⠆⢀⡀⠀⠈⠁⠀⠀⠀⠀⢰⡆⢀⣀⠀⠘⠛⠀⠰⠷⠀⢹⣿⡿⠁
⠀⠀⠘⢿⣷⣄⡀⠀⠀⣴⡄⠀⠀⠙⠃⠀⠀⠀⠛⠀⠰⡦⠀⠀⠈⢉⠀⠀⠸⠇⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⡀⠸⠗⠀⠀⠛⠁⠀⣤⡄⠀⣴⠄⠀⠙⠃⢀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⡚⠻⠰⢦⠄⠀⠀⠀⠀⠀⠀⠀⠸⣁⣸⣤⡄⣦⣏⡶⣤⣶⣿
⠀⠀⠀⠀⣼⣿⡶⠉⣻⢷⣤⣘⣦
⠀⠀⠀⢀⣿⣿⣿⣟⡛⣷⡟⢩⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣁⣿⣣⣽⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣄⠀⠀⡴⠋⠉⠊⡑⡄
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣯⡙⠉⠀⠀⣧⠀⢷⣦⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣠⣾⠇⠀⠀⠉⠛⠛⠛⠃⠀⢀⣤⡦⣴⠦⣼⣿⣆⠸⣿⣿⣆
⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⡀⠀⣰⣿⠿⣿⢌⡲⡀⠀⠉⠛⠋⠁⣠⠖⠉⠑⢢⡀⠀⠀⢠⣿⡟⢠⡟⣢⣿⣿⢿⣷⣿⣿⠃
⠀⠀⠀⠀⢸⠃⠈⠿⣿⣿⡷⠀⢿⣿⣿⡄⠈⢸⣿⠀⠀⠀⠀⠰⣿⡄⡀⠀⢰⡇⠀⠀⠘⣿⣷⣿⣿⣿⣿⡿⣷⣌⣿⡏
⠀⠀⠀⠀⠘⢤⣰⣿⣿⡿⠃⠀⠈⢻⣿⣿⣷⣿⠟⠀⠀⠀⠀⠀⠙⠿⠿⠿⠞⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣷⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢶⣆⠀⠓⡀⠀⠀⠀⣴⠃⠀⢀⣾⠛⠛⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⣀⡄⠓⡄⠐⡀⠀⠈⠳⣦⠃⠀⠀⠀⠮⠈⠉⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣀⠋⠄⠀⠈⡄⠀⠀⢤⠤⠻⠋⠀⠀⠀⠈⢧⣀⣘⣄⡈⠐⠁⠀⠀⠀⠀⠀⠈⣧⣀⠀⣀⡘
⠀⠀⠀⡀⠻⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠛⠛⠋
⠀⠀⠀⠙⠢⣤⣀⡠⠞⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀⡀⠀⠀⠀⢘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⣰⠋⠉⣿⣷⡄⠀⠀⢀⢨⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⡄⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⢿⠀⠀⣸⣿⡶⠀⠀⠐⠀⠸⣿⣿⣿⡆⠀⢀⣼⣿⣿⢟⣤⣼⣴⣾⣿⡞⠁
⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⡟⠈⠓⠾⠿⠛⠁⠀⠀⠀⠾⣻⣿⣿⣿⣿⡀⢀⣿⡿⣿⣮⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣧⢸⡟⣼⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡎⢀⡀⠀⠀⠀⠀⠈⢹⡿⠿⣿⣿⣿⣿⣿⣾⡾⣛⣋⣉⣠⣤⣀
⠀⠀⠀⠀⠀⠀⢰⠏⠳⡄⠀⢠⡢⣾⡟⠀⠀⣀⣠⠄⠀⠑⠒⠛⠛⠋⠉⡠⡿⣿⣿⣶⣯⣭⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⢆⣐⣻⣄⠊⣿⣋⡶⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡏⠻⢿⡉⠻⢿⡿⠟⠉⠁
⠀⠀⠀⢀⠀⠀⠘⠲⢿⠻⠿⣷⣿⣿⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠁
⠀⠀⠈⢓⠓⠀⠒⣴⣾⣶⣿⣶⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⣀⡀⣀⡀⠰⠀⠀⡠⠀⠀⠠⠀⡄
⠀⠀⠀⠀⠐⠀⠐⠿⠛⠋⣭⡵⡏⠉⠀⠂⠁⠉⠁⠀⢀⣾⡿⢿⣿⣿⣯⣤⡉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⡦⠖⠋⡰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⣼⡟⣿⣿⣿⣿⡎⠉⠁⡀⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠙⣿⣵⣿⣿⣿⡿⠳⠤⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢙⣟⡉⠭⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢘⣿⡄⡀
⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⢀⠀⠀⠀⠀⣀⣤⠀⢠⣀⠀⡄⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢿⣿⠟⠇⠟⣦⣀
⠀⠀⠀⠀⠀⠀⢘⠛⠛⢰⣿⣿⣷⣦⡀⠉⠁⢠⣾⡛⠊⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠀⠟⠃⠀⠀⢀⣸⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠁⣤⢼⣿⠟⠀⠉⠻⢿⣷⡤⠸⣿⣧⣾⠏⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢀⣹⠶⡗⢫⡉⢿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣦⡀⠤⠐⠊⠉⠀⠠⢠⣥⣤⣤⠰⣞⡂⠀⠀⣀⣀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠃⠻⠟⢠⣾⠃⠈⣇⠈⠋⢻⣿⣧
⠀⠀⠀⠀⠀⠀⣭⡻⠟⠋⠸⣷⣌⠳⣄⠀⠀⢀⠎⠀⠈⢛⣶⡘⢿⣟⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠸⡀⠀⠈⠛⢿⣧
⠀⠀⠀⢆⣛⣴⠟⠀⠀⠀⠀⠘⢿⣧⠹⣆⢀⠸⠤⠖⠊⠁⠀⠀⢀⣿⣷⡄⠈⣯⣍⡙⠲⣄⠀⠀⠀⢀⠀⠀⠀⢀⣤⢤⣶⡟⡁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⣤⣶⡇⠀⢀⣾⣀⣀⣀⣀⣘⣩⣭⣤⣶⣿⣿⣿⣷⡈⠃⠀⠀⠂⠀⠀⠔⢋⣤⡾⢋⣮⣤⣤⠶⢁⣼⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣠⡄⠀⠚⠩⢯⡘⢿⠿⠖⠒⣸⣿⣿⡷⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⢛⠁⠀⠛⠢⠰⣇⠀⠀⢀⡼⠹⣿⢟⣾⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠴⣾⠏⠀⠀⠈⠳⣤⠏⠀⠀⢵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠿⠙⠁⣴⣿⣿⢿⠿⠇⠙⠁⢀⣀⣤⡄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣅⣀⣀⠐⠿⠂⠀⠀⣤⣌⠲⠾⠿⠟⠁⣰⢺⡆
⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠠⠤⢠⡶⠊⠉⠉⠁⢀⡠⠀⡠⣶⡌⢣⡀⠸⣿⣷⡿⠛⠻⠦⣀⠠
⢠⣤⣤⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠈⢠⣮⣾⣿⣿⣿⣿⣐⡼⠋⠀⠀⠀⠀⠈⠉⠁
⠈⠿⠛⠛⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣳⠋⣹⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠉⡁⣀⢀⠠⢤⣄
⠀⠀⠀⢀⣦⠀⣠⣤⣤⡶⠛⠉⠙⠓⠶⣶⢦⣷⠀⠰⠞⠳⡄⠙⣻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣀⠀⠠⣤⣤⠆⠀⠤⠼⠟
⢀⣀⣴⠋⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⡌⡏⠐⠀⠀⠀⠀⣰⠌⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠀⠘⣤⣴⣤⣴⡄⣀⠷⠆⢀⡄⠀⠀⠀⠀⡀
⠈⠽⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⢰⡆⠀⢀⣸⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⠿⠯⠁⣴⠿⠛⠇⠀⠘⢡⣾⣌⡙⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠠⠴⠾⠧⠦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣶⠖⠀⠀⠀⠀⠀⠚⠂⠀⠀⣿⡟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠛⠓⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀⣰⣼⣿⡿⠂⢰⡾⠟⣀⣶⡽⠋⠀⠀⠀⠀⠑⣆⠀⠐⠆⠀⢻⣿⣄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⣿⡿⠿⠛⠉⠀⠀⢋⠀⣸⡟⠁⢀⠀⠀⠀⠀⢰⢠⣿⣿⣷⡆⢻⣶⡿⠛⢧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠎⠀⢠⡏⠀⠀⣿⣄⡟⢛⣷⢸⣿⣿⣾⣏⠀⠀⠀⠳⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⣀⣴⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⠚⠇⠀⠀⢠⣾⣿⠿⠛⠉⢠⠷⡄⠴
⠀⠀⠀⠀⠀⠤⢒⣲⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢤⣤⣤⣴⣟⢣⠀⣀⢀⣤⠟⠉⠢⢤⣾⣿⣤⣈⣢⣄⠀⢂
⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡿⢛⡿⠀⠉⠁⠈⠉⡷⠖⠒⡾⣆⣀⠀⣀⣀⣉⠳⠄⠈⠀⠀⠀⢀⣾⣿⠋⠀⠉⠉⠙⢿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣻⣿⣷⠄⠀⠺⠦⠀⠀⠀⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⣴⣤⣶⣶⡲⠄⠀⠾⠿⣥⠀⠀⢀⡀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⣠⠾⠛⠛⠛⠛⠻⢷⣤⣄⣀⠀⠀⠀⢠⣷⡀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣲⣾⣿⠟⠉⢀⣠⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣾⣿⣷⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢉⣦⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡗⠒⠶⣦⣌⠳
⠀⠀⠀⠀⣀⣤⣐⣢⠞⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠉⠉⠁⠀⠀⡰⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡓⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⣄⡀
⠀⠀⠀⠀⣀⣄⡀⠀⡀⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠚⠛⠛⠟⠿⠛⠿⠛⠿⠟⠛⠛⠋⠝⠛⠛⠋⠉⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠠⠤⣶⠄⢠⢄⠽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣟⠟⠉⣳⠀⡄⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠛⠓⢤⡿⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠙⢷⣄⣻⡟⠷⠀⢢⠄⠀⠀⢉⠉⠙⠡⠄⠶⣄⠀⠀⠀⢷⣄⡀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠀⠀⠤⠉⢿⣤⠄⠈⠀⢰⣧⠾⠃⢠⡇⢸⡦⠋⠐⠾⣭⡦⣿⣍⣧⣀⡀
⠀⠀⠀⠀⠀⠀⡷⠶⠾⠧⣤⡀⠀⠠⠈⠁⠀⠤⠀⠄⠒⠀⢸⡟⠀⢀⡾⣩⣿⡽⡦⠾⠿⣷⣶⣚⠣⡀⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠿⡄⡀⠀⢀⣠⡔⠁⠀⠀⠀⢀⡞⠀⠀⣸⣧⣿⢽⡄⡼⣷⢼⣿⣏⠉⠛⣤⣬⣾⣟⢻⡛
⠀⠀⠀⠀⠀⣼⠋⠀⠀⡀⣰⡇⢤⣴⣟⡉⠰⣾⡗⢀⣀⣺⡔⠃⣤⠙⣿⣻⡾⣷⡍⠘⠀⠙⠻⣶⣦⣼⣿⣿⣿⣧⠱⣄⠀⣄
⠀⠀⠀⠀⠀⢁⠂⢠⣶⣹⡏⢷⢠⡉⢻⣿⣿⣿⣿⣶⣯⡙⠓⢊⠁⡀⣿⣿⣧⣿⣷⣶⡦⠀⠀⠈⠻⢤⡈⣿⣿⣿⡟⠻⠂⠻
⠀⠀⠀⠀⢠⡆⡦⢸⠁⣶⣿⡜⣧⢳⣀⡝⠉⢻⣿⢿⣧⣷⠂⠈⢳⡉⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣻⡼⠃⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠓⠀⠀⠀⢹⣷⣿⡈⠂⠻⡇⠀⠘⢻⣷⣙⣯⠅⢠⣤⣿⣿⣿⣯⡘⣿⣿⠀⠀⠀⠀⠀⠠⡆⢻⣃⠀⠀⣰⡷⠂⠀⣰⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠃⠀⢀⠀⠀⠀⠀⠹⣿⣥⣶⢰⢿⣿⣿⣿⢻⡆⢿⡟⠀⠀⠀⠀⠀⠀⠃⡼⠁⠀⠰⣿⣄⡀⠀⠹⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⡖⠁⠀⠀⠀⠀⠀⣿⣿⡟⣼⢿⣿⣿⡟⠻⣿⡈⣿⣄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠇⠀⢰⠋⣧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⡇⢲⣦⣀⠀⠀⠀⢻⣿⠞⠁⠈⡛⠘⣷⣤⣬⣁⡉⣻⣆⠀⠀⠘⣶⠃⠀⠀⠀⠀⠀⣸⠇⠀⠈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣀⢣⡀⠙⣿⣷⠀⠀⠘⠁⢲⣄⣾⣷⠠⢤⣿⢿⠛⠿⢿⠿⣿⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠦⢼⡋⠀⠈⠙⠢⣼⣿⣿⠁⠀⠀⣿⣈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣼⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⣀⡄⠀⠀⢺⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣴⡀⠀⠀⠈⣿⠇⠀⠀⠸⡇⠀⠀⠀⣼⠛⣿⣹⠛⠀⠀⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣿⣷⡀⠀⠀⢸⣷⣇⠀⢸⣿⠀⠀⣤⣿⠷⠛⠋⠀⠀⠀⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠿⡷⠤⢶⣀⠙⢿⣷⠜⣿⣶⣜⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡠⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣶⣶⣾⣥⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣴⣾⣿⡿⡗⠛⢉⠉⠻⢿⣿⣿⣭⣟⣿⣿⣿⣷⣖⢯⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣷⣾⣿⠿⣟⣿⣿⣿⠐⣹⣿⣿⣷⡖⢈⣿⠛⣯⢻⣿⣿⣿⣿⠿⢿⣿⣯⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠙⢟⣏⢻⣾⣿⣿⣿⣿⣷⡃⢚⢛⣢⣵⣾⠁⣰⢿⡏⢿⣿⣿⣿⣷⣾⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠈⢁⣿⣿⣯⣶⣟⠛⠻⠿⣿⠿⢟⣵⣿⣾⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣧⡀
⠀⠀⠀⢀⣤⣤⣶⣾⠀⠀⠀⠀⢠⣿⣛⣽⠟⣿⣩⢰⣶⣞⣩⣴⡿⣹⣿⡿⢫⣾⣿⠿⠋⠉⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⣿⡟⠉⢩⣷⡆⠀⠀⣠⡿⠏⠉⠀⠠⣻⣿⣿⢿⣿⡿⠋⣼⣳⡟⠁⣿⡿⠃⠀⠀⢠⣿⣿⣴⡿⣹⠿⢿⣿⣦⡀
⠀⠀⠀⢿⣿⣧⡿⣿⣷⣦⣾⣿⣶⡁⠀⠀⠀⣹⣿⣿⣾⣿⣿⡲⣾⣿⣆⣤⠠⡆⠀⠀⢀⣾⣿⣿⣿⣷⣿⡄⡜⠛⢻⣿⣦
⠀⠀⠀⠘⢿⣿⣷⣽⡿⣷⣸⠿⣿⣿⣷⣤⣼⣿⣿⣿⢿⣿⠟⠀⠈⡹⢿⣿⣤⣇⠄⢠⣮⣼⣿⣿⠿⠋⠉⡴⠀⠀⣸⣿⣿
⠀⠀⢠⣶⡟⠻⣿⣿⣧⡹⠿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣏⠙⠧⢀⠀⠐⢋⡽⣿⣿⣿⣿⣿⠟⠛⠉⠀⣰⣾⣤⣶⣾⣿⣿⠏
⠀⠀⠀⠹⣷⣄⠈⢿⣿⣿⣆⠀⢻⣿⡻⠿⠿⡿⠇⢻⡿⣿⣶⣦⣤⣤⣤⡴⣿⠋⠉⣁⣠⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠘⢿⣷⡾⠿⣿⣿⣷⡄⠈⠙⠳⠦⣤⣴⣿⠟⠓⢿⣄⣀⣀⣤⣾⣿⣾⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠈⣳⣤⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⣤⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠹⣯⣩⠟⡀⠀⠀⠀⠀⡀⣀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⡀⠀⣅⡰⢀⡠⡷⠐⠚⠛⠋⢉⡀⠙⠟⣦⣄
⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠀⣀⠄⠀⢀⡴⠤⠀⠠⣠⠊⠀⢀⣷⡄⠘⢾⣌⢙⣒⡬⠟⠛⠿⠾⠷⠔⠴⠾⣟
⠀⠀⠀⠀⢿⡉⠻⠏⢛⡻⠟⣵⡿⠟⠁⠀⠀⠀⠀⣸⣦⠀⠈⢳⠛⠁⡤⣽⡯⠁⣄⡀⠀⠀⠀⣴⠀⣠⡄⠈⡧
⠀⠀⠀⠀⠻⣭⡛⠛⢉⣤⠞⡩⡜⠀⠀⠀⠀⠀⠐⠃⠉⢣⡀⠀⠂⠀⠙⠠⠝⠋⠀⠀⠐⠤⠘⣏⢣⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠁⡇⡇⠀⠀⠀⠀⠀⢁⡶⠖⠉⢁⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠢⠰⣶⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠘⠃⠀⠀⠀⠀⢠⣙⣰⠆⠸⡙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⠀⠀⠀⠈⢂⣉⡠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢸⣦⡀⠀⠀⡠⠊⠑⠷⣌⡄⠀⢣⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠡⠼⠃⠉⠂⠈⠀⠀⠀⠀⠀⠁⠐⠒⠒⠷⢄⣀⢢⡀⠀⠀⠀⠲⣯⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⣀⠀⠀⠑⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠐⡧⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠈⠀⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢷⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⢉⣢⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠈


⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣬⣿⣶⣥⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡮⠁⣴⠠⢹⡅⠀⠀⢠⣤⣤⣴⣿⣾⣷⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠒⠨⣛⣇⣀⠀⣿⡿⠿⢛⣥⣾⣿⣿⣿⣗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡗⢿⡿⠿⠛⠛⣷⣴⣵⣾⠿⠿⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣟⠀⠸⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠉⠑⠛
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⢀⣀⠀⢀⠀⢰⠂⠀⠀⠀⠈⠶⣿⠖⢠⡆⠠⣤⣀⣸⡿⠁
⠀⠀⠀⠀⢀⣾⣿⣿⢿⣆⠰⣦⣿⣷⣮⣻⣿⣿⡀⠀⠀⠀⠀⣿⠖⠚⠀⠑⢮⣿⣿⠇
⠀⠀⠀⢀⣿⣿⡿⠛⠚⠉⠀⢸⣽⣜⠯⡁⣿⡟⠿⣷⣦⣤⣤⣽⣇⠰⠇⠀⣠⣿⠿
⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⡓⠀⣿⠇⠀⠀⠈⠉⠉⠉⠛⠛⠛⢼⣷⣟⣶⣤⣀⡀
⢀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠉⠻⣿
⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠐⠂⡀⠀⠀⠴⠶⠾⠟⠁⠀⠀⠀⠀⠘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡀⠀⠀⢀⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠈⠑⠀⠁⠀⠀⠘⠁⠈⠀⠛⢩⠋⠉⠆⠀⠀⡜⡿⠐⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠖⠀⠀⠐⠀⠀⠁⠈⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠰⢦⠍⠀⠀⠰⠶⢶⠆
⠀⠀⠀⢀⠀⠀⠠⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠃⠀⠂⠀⠀⢰⡈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⣾⠆⠀⠀⠄⠀⠀⠈⡀⠛⠀⠀⠄
⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⠄⠘⠃⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠃⠀⠠⢀⠀⠀⠀⠀⠀⠀⠛⠀⡆⠀⠀⠀⠁⠀⠀⣰⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⡀⠀⢰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜⠩⣰⢠⡄⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠃⢀⠈⠀⣶
⠀⠀⣀⠀⠀⠀⠀⠀⡀⣀⢀⣀⠀⢀⡀⢀⣍⠀⠀⠀⠀⠀⠈⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠈⠀⡄
⠀⠀⠈⠙⠒⠀⢰⠀⢹⡇⢸⣇⠀⡾⢷⠀⣶⠁⠀⠀⡀⠀⠀⠰⠈⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠈⠀⠐⠂⠀⠐⠒⠙⢂⠀⠀⠀⢀
⠀⠀⠀⢰⡆⠀⠏⠀⠀⠀⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢂⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠉
⠀⠸⢀⡈⠀⠀⠀⠀⠑⠲⠤⢴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠
⠀⠀⠈⠁⠀⠀⠐⠒⠒⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣄⡀⡠⠀⠉⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡆⠀⠀⡄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⡀⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⢓⠐⢀⡀⡀⠀⠀⠠⡜⠤⠀⢠⠀⠀⡦⠀⠃⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⡀⠘
⠀⠀⡅⢀⠀⢀⣀⣰⢀⣀⡅⠀⢠⠁⠀⠀⠨⠀⠀⡤⠐⠀⠒⠂⠀⠠⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠁⠀⠀⠒⠒⠂⠈⠭⠭⠃⠀⠀⢦⡼⠀⠀⠈⠦⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⢀⠤⢠⣤⣀⡀
⠀⠀⠀⠻⠾⠿⠿⢤⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡑⠤⠀⢀⠀⠀⢀⡎⡖⡆⠀⠀⠀⡤⠒⠊⠉⠉⢀⡘⠫⡝⠢⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠿⡓⢦⣀⠼⣰⠁⠃⢀⠤⡞⠐⠀⠀⠀⠀⠠⠁⠐⢸⡤⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⠦⠬⠥⣕⣷⣲⠨⣤⣒⣒⣷⣦⣶⣶⣒⣪⡭⠳⣌⠠⣃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⣢⢤⠶⢛⡿⢻⣿⡷⣖⡒⠒⠾⠂⠉⠉⠁⠄⠀⠄⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠄⣁⣤⠶⠛⠙⡂⡔⡩⠁⠐⠙⣿⢦⡉⠓⠤⣈⡰⡀⣈⣀⣡⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠛⠻⠡⠄⠤⠰⠒⡹⣹⡤⠓⠋⠐⠻⢌⠻⣶⣖⠀⠈⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⣸⠋⠀⠈⠀⠘⠃⠀⠉⡈⢻⡻⣄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⢸⡇⠀⠀⠄⠀⠀⠀⠘⠀⠑⠈⠙⣮⣕⢤⡀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡾⣧⠂⠀⠀⠀⠀⠄⠰⠀⡰⠀⠀⠁⠘⡗⣿⣤⠀⡀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⠟⠀⢀⠷⢄⡀⠀⣈⣀⣠⠜⠉⠦⢀⠸⠀⠃⠈⠙⠷⣤⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡈⠖⠚⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠑⠒⠄⣄⢀⡀⣌⡑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⡀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢸⣿⠀⠉⢁⠀⠛⡹⢾⠍⠀⠀⠀⢀⣀⣀⡠⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢶⣿⡆⠀⢹⣤⠈⠁⠀⢀⣀⣴⣾⡿⠟⠋⠻⡌⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⠂⢀⣿⠁⠀⣠⣴⣿⡿⠟⠁⠀⠀⠀⠀⠘⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠤⡤⠀⠠⣄⣀⡀⠀⠐⠉⣠⡖⢀⣀⡉⠛⠻⠟⠉⠀⠀⣠⠆⢀⣤⣀⡀⠹⣿⣄⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⠶⠀⠀⠀⡏⠀⠀⠀⠈⣿⡟⣀⣾⣿⠇⣠⣬⣭⣷⡶⠋⠑⣰⠞⠓⢒⣾⠋⠙⠶⠞⣷⡟⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⣶⣿⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢲⠧⠄⠀⠀⠀⢈⠘⠻⣿⠋⢠⠀⠀⠀⠀⠀⠠⡾⠃⠀⢠⣾⠃⠀⠀⠀⠀⠈⠻⣿⠄
⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠠⣿⣃⠀⠀⠀⠀⠀⠀⠀⢮⠳⠒⠲⠤⣄⡀⠉⡖⠼⠂⠀⠀⠀⠀⠀⣤⡀⠁⢀⣴⠟⠁
⠀⢘⣿⣿⣿⣿⣿⣿⣿⡟⣽⠏⠀⠀⠀⠀⢿⣿⣷⣤⣤⣤⣤⠄⠀⢸⢀⡀⠀⠀⠀⠀⠈⢁⠘⠂⣀⣀⠀⠀⠀⠸⣿⣶⣿⡇
⠀⠀⠈⠒⠛⠋⠁⠐⠋⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⠻⠿⠅⡀⠀⢸⠘⢿⣶⣄⡀⠀⠀⣿⠀⠸⡇⠀⠀⠀⣀⠔⢹⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢀⠀⠀⠈⢸⣷⠚⠽⣿⣿⣶⣿⣀⠀⡧⣠⠏⢀⣠⣀⣼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡄⠀⠀⠉⠙⠿⠿⠿⣇⣿⠂⠀⠙⣿⣏⣀⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡀⠈⠋⠉⠉⠉⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢀⣀⣉⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⣸⠆⠀⠈⠻⢿⣤⣤⣤⣤⡘⠷⠀⠀⠀⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⣀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠑⠒⠶⠤⠤⣄⢠⡖⠉⣉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣀⡤⣬⡇⡞⠁⣀⣀⣠⠞⢷⣀⡾⠉⠓⠦⣄⣼⣾⠉⠉⠉⠑⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⢀⡿⠳⠚⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡴⢋⡤⠴⠒⠒⠲⢤⣀⢀⡴⠚⠉⠉⠉⠉⠓⠢⣄⡈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⡾⢥⡏⠀⠀⢠⠖⠒⠲⣄⠀⢠⠟⠫⣷⠀⢀⡤⠖⠲⢤⡀⠀⠈⣇⣠⠽⣖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢩⣟⣹⠾⠯⠷⠶⠶⠶⢶⠖⠚⠲⣼⢦⡤⠿⠤⠬⠤⠤⠤⠤⠧⠤⠶⠿⠴⠶⣾⣷⡒⠲⠆⢀⡠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⡤⠬⢿⠀⠀⠀⡿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡞⡴⠒⠲⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⠋⠀⢀⣀⡤⠤⡖⠒⠒⢛⡗⢒⡞⠉⠉⠙⠓⠒⠒⠒⠤⠤⢤⣀⣀⣀⠀⠀⠀⠉⠙⠒⠲⢧⣇⠳⣀⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡤⣖⠉⠡⡄⠀⠈⠲⣄⡞⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠉⢉⠛⠒⣦⢤⣀⡀⠀⣧⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠋⠀⠈⠳⠤⠞⠀⠀⠀⡾⠀⢀⡷⠤⠤⠤⢤⡤⠤⠴⠖⠚⠉⠀⠀⠀⢰⡃⢀⠜⠁⠀⠀⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠶⠆⠀⠀⠀⠀⠀⠈⠳⣇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠒⠢⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠔⠚⠉⠁⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉





⣿⠿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣛⣿⣿⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠼⠇⠀⠀⠀⠤⣀⠀⠠⠄⠂⠁⠀⣁⣀⣈⠐⠠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠸⢿⣷⣦⡀⠀⠀⠀⠀⠀⣰⡀⠀⢉⠄⠿⠋⡭⢙⣷⠒⠛⣏⢤⣿⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡄⡀⠀⠀⠀⠻⣿⣤⣏⢠⣧⠴⠿⠿⡬⢹⣿⠩⡿⠤⠐⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣾⡏⣹⡷⢦⡜⢿⣮⣷⠀⡙⡿⡟⠛⠛⠛⠙⠛⣯⣵⣫⣾⡯⠭⣐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣿⣿⣿⣿⢷⣦⣿⡟⢿⣿⣿⣶⡇⠀⠀⠂⢰⡀⢀⣿⢯⣿⠏⠉⠀⢸⡀⢤⡈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠛⠲⣿⠏⠛⢷⣙⣷⣹⣿⠋⠀⡆⣠⣼⠞⣿⣷⠿⣅⠔⢌⣠⠏⠀⠀⢉
⠀⠀⠀⠠⣄⡐⠂⢀⠀⠀⠈⠙⠿⣿⣦⣝⡷⣤⣤⣽⣿⢛⣿⡟⠚⢻⣿⣩⣶⡿⢛⡄⠀⡸⠛⡅⠀⣸⢰⠙
⠀⠀⠀⠀⠙⠳⠤⣀⠀⠂⢀⣀⡀⠈⠙⠻⢿⣾⣽⣍⠛⠳⢿⠛⢒⡒⠛⠟⡯⢭⣁⠟⠆⠠⡀⠀⡔⡻⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢧⣮⣁⠀⠀⠀⠀⠈⠛⠿⣷⣦⣙⢦⣼⠇⠀⠂⠙⠶⣿⣉⢦⣤⣾⡿⠋⠀⢔⠍
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣾⣝⡊⠀⠀⠀⠀⠉⠛⠋⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠘⠛⠦⠤⢤⣀⣁⡒⠠⠶⠄⠀⠀⠀⠲⢤⣀⠠⣦⣄⡉⠻⢿⣷⣤⣄⣀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠂⠀⠀⣀⡀⠂⠀⠈⠙⠷⢮⡓⢄⡉⠛⠿⠥⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠦⠀⠙⢦⡙⠂

⣿⣿⢛⠿⣛⠛⣟⢛⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠓⠲⢤⣀⠀⠀⢀⣀⣀⣠⣤⣤⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣠⡇⠀⠀⣠⠬⠛⠋⠉⠁⠀⠀⠀⠀⠈⠉⠓⠒⠮⢭⣓⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⠙⠲⣄
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣙⣦⣀⣀⣀⡀
⣰⠋⠀⠈⠓⣄⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠈⠉⠉⠓⠦⣄
⣇⠀⠀⠀⡴⠋⠙⠲⢤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠈⠙⠢⠤⡇⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢀⡤⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⠴⠚⠉⠀⠀⢸⣄⡠⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢰⠃⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⡄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣤⣀⡀⠀⠀⠀⢸
⠀⠳⢄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⠤⠖⠒⠒⠒⠒⠶⠤⣄⣀⣉⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡰
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠀⠀⠀⠀⢰⣣⠔⠋
⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠖⠛⠺⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠒⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⢯⡛⠉⠻⣤⣴⠞⠉⢀⢀⣀⡁⢔⣺⣿⠿⣯⣄⡀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢄⠘⠛⣿⣤⠞⣽⡿⣇⣠
⠀⠀⠀⠀⠠⢶⣶⡿⠟⠉⠉⠀⠀⠀⠀⣶⣟⣤⣌⠁⠀⠀⢺⡇⣸⣿⣯⠻⠛⠁⠀⠀⠈⠁⠲⠾⠿⠋⣾⠀⠸⣋⣠⣿⠜⣦⣄⠀⠀⣰⠋⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⢿⣪⣿⡿⠀⠀⣴⣿⣿⣿⣝⣏⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣋⡴⠞⠉⠙⠻⠿⢟⣛⡶⢼⠇
⠀⠀⠀⠀⠀⠀⠀⣤⠴⠀⠀⠀⢀⡤⢿⣗⠟⠓⠒⢦⣤⠁⠉⠉⠉⠙⣯⠓⠦⣄⠀⠀⠀⠀⠀⠸⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠐⢄
⠀⠀⠀⠀⠀⣠⢎⠐⠋⠁⠐⠚⡡⠊⠉⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⠂⣜⣆⠀⠀⠈⠃⠀⠻⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠈⠉⢡⠁⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠂⢀⣀⢀⣀⣀⢈⡀
⡀⠀⠀⠤⢤⣤⣤⣤⠤⠬⠭⠭⠭⠯⠽⠽⠿⠿⠿⠿⠧⠛⠓⠉⠉⠁⠀⠁⠁⠀⠈⠀⠉⠉⠀⠈⠙⠋⠍⠸⠿⠭⠿⠉⠉⠉⠙⠁⠉⠉⠁⠉⠁⠈


⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠀⠉⣠⠀⢰⡢⠀⠐⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⡟⠁⢀⠀⠀⠠⣠⠈⠁⠖⢪⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢨⠀⠀⠀⠘⠀⠀⠈⠀⠀⢀⠠⣾⣽⣻⣄⠀⠤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢆⣠⡄⢰⣦⣾⡿⢃⠀⣤⠀⠀⠁⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠤⡐⡀⣼⣏⣤⣴⡧⠛⠀⠀⠀⠾⠀⠲⠄⠃⠀⠀⠉⣻⡷⠀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠀⢨⠀⠐⠹⠝⣻⣤⠇⠀⠨⣄⠀⠀⢀⡈⠠⠴⡖⠃⠀⠋⢉⡝⠂⠐⠦⡊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⣠⡄⣴⡆⠘⠀⣀⡆⠀⠹⡄⣠⠼⠂⢠⡐⠃⠀⠀⠈⠀⣤⣤⡄⢠⠀⠎
⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠈⠋⣤⠴⡁⢀⣘⣶⡤⡜⠁⢻⣤⠀⠄⠈⠀⢄⠙⠰⠄⣶⠘⠀⣀⣈⠀⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠈⡝⢻⣰⠆⠗⢶⢛⠉⠃⠠⠳⣆⣲⠂⠀⣄⠀⡴⠀⢰⠠⠛⠲⠁⠖⠀⣿⠂⢀⠉⠛⢀
⠀⠀⠀⠀⠀⠀⠴⠆⢼⠌⠙⠿⠣⠆⣠⡀⢤⠗⠐⠀⡷⠈⢢⠀⠁⠀⠀⣠⠉⠰⠂⣫⠀⠠⡌⠁⠚⠉⠀⠀⠋
⠀⠀⠀⠀⠀⠈⠷⡤⣴⡁⢠⠄⢠⠄⠛⠁⠀⠀⠠⠬⠁⠐⠛⠀⠘⠁⠸⢿⠁⠖⢂⠁⠠⠙⠃⣠⣴⡚⠃⢰⣄⣠
⠀⠀⠀⠀⠀⠀⠀⣰⢟⣀⠀⠀⠈⠀⠀⣀⡀⢦⡔⢀⡜⢂⠀⠀⢠⣤⡄⢂⣀⣄⠠⠤⠀⠀⠀⠀⠈⢦⡤⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠸⣂⠀⠸⠀⠀⢀⠉⠑⠁⡉⣀⠈⠅⠀⣀⠁⠀⣐⣀⠳⣂⠀⣀⡌⢿⠷⠀⠀⣤⣄⣀⣳⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡈⠀⣀⠄⠀⠈⠄⠀⢹⡿⡈⠉⡁⢀⠐⠛⠣⠙⠄⠀⠐⠖⠀⠘⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡿⣼⣦⢀⣠⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣿⣿⣿⣿⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣿⢹⣿⣿⣿⣿⢻⠻⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡘⠉⠹⢛⡵⣋⠉⠀⠛⡯⠄⠀⠢⣙⣷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠤⠄⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣼⡏
⠀⠀⠂⣤⠤⠴⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⠤⣽⠟⠃⠀⠀⠲⠄⠀⠀⠀⠀⠉⠉⠒⠒⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠶⠚⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠖⠀⠁⠀⠀⠀⠀⢠⡉⠓⠵⣤⡤⠄⠀⢀⠠⠋⠀⠀⠀⠔⠁
⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⣀⡸⠀⠀⠀⠀⡠⣄⡴⠐⠋⠀⢀⣀⡄⠟⠀⠀⠀⠀⠉⠉⢀⡀⠀⠈⠈⠀⠀⠀⠈
⠀⢀⡠⠄⠺⠶⠪⠀⠀⠀⠁⠀⠀⠀⠐⠋⢀⠀⠦⢤⠞⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣛⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠑⠉⡠⠀⡀⠤⢄
⢀⠀⠘⠧⠤⠤⠤⠷⠲⠤⠤⡤⠎⠐⢢⡀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠶⢤⡀⢀⠀⡀⠁⠀⡀⠈⡠⢊⠔⢀⡧
⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣼⠁⠀⠀⠀⣀⠐⡖⠻⠯⢭⣠⡌⠛⡎⠱⢧⣠⣴⣠⣈⠐⡁⢀⣀⠐⠳⣆
⠀⠈⠲⠴⢶⣄⠀⠀⠀⠀⣰⠦⡤⠴⠃⠀⠀⠀⠀⠈⠛⠞⠓⠒⠊⠉⠋⠒⠛⠉⠘⠋⠙⠉⠁⠙⠋⠉⠉⠤⠶⠖
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡤⠖⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⡐⠀⠀⠀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠈⠀⠈⠠
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠂⠀⠔⠁⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠈⢧⣄⡀⠀⠀⣠⢶⠟⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⢀⠀⠀⠐⠀⢀⠄⠀⠀⠄⠀⠀⣱⡇
⠀⠀⠀⠙⠛⠯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⠳⣄⣀⣀⡀⣒⠐⠀⠀⢄⣺⠟⠓⢪⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠉⠠⠘⠘⠒⠛⠓⠛⠁⠈⠈⠈⠀⠁
⠀⠀⠀⠀⣄⠀⠐⠦⢣⡀⠀⠀⠀⠀⠐⠲⣶⡄⢢⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠘⠳⢶⡤⣄⡀⠀⠀⠁⠀⠀⠀⣀⡠⢋⡞⠀⠀⠀⠀⠀⢷⣤⣤⡤⠉⠀⣀⠀⠀⠀⡀⠀⠱⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⢀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⡀⣀⣴⡆⠤⠐⠂⠀⠄⠒⣿⠃

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢀⡠⠴⢂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢆⠀⣴⡀⠁⠀⢠⡄⢀⠀⠉⢩⠀⠈⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⣉⠈⠀⠀⡇⠐⠤⠀⠀⠑⠉⠉⠁⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⣁⣉⠀⠀⠀⡀⣀⡠⠠⠖⠀⠀⠀⢀⠁⢀⠐⠉⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠑⠆⠀⡴⣀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠃⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣆⠀⠀⠛⠨⠁⠀⠀⠀⡘⠂⠄⠀⠀⠙⠶⢞⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⡠⣁⠶⠂⠀⠉⠀⠠⠂⠀⠀⢄⡠⣔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠀⢙⡗⠒⢲⠶⠚⠛⠛⡖⠒⠓⣿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠚⠃⢠⡞⠀⠀⣽⠀⠳⢀⣠⢙⠤⠔⠃⠑⠂⡴⢌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣀⢏⠀⠀⡠⠘⠃⠂⢡⠀⡖⠈⠉⠀⠤⠠⡄⠠⡀⠀⠀⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⠇⡀⠱⠞⠀⣤⢀⡠⠟⠠⠉⡀⠼⠀⡀⢀⢷⠀⢨⠉⠘⠣⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠟⠢⡀⡘⠀⠀⠀⠈⢠⠁⠸⣀⠀⠀⠀⢄⠀⢀⣄⠈⠠⠄⢠⡇⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⡏⠀⠀⠚⠁⠀⢀⠉⠂⢁⠀⠠⠉⠁⡈⠀⢀⠁⠀⢨⠀⢀⠀⠁⠈⡃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡞⠁⠀⠀⡐⠀⠀⠤⣀⢠⠊⠀⡧⠒⠋⠁⠀⠀⠒⠒⢻⠀⠈⠒⠂⢠⡇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⢰⠀⠠⠴⡎⠀⠀⢸⠀⢀⡌⠀⠀⠉⠂⢀⠄⠀⠀⠆⠀⠊⠀⠀⡀⠒⠁⢸⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡼⢆⠀⡰⠁⠀⡀⠀⠈⠉⠀⠀⠀⠀⠂⠉⠀⠀⠸⡀⢀⠾⠀⠀⢑⠦⠀⣼⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡞⠀⠄⠚⠁⠀⠀⠧⠀⠤⠛⠀⠀⠜⠒⠀⡠⠀⠀⢠⠀⠁⢀⠆⠀⢨⠀⠋⠀⡆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⢳⡀⠀⡠⠀⠀⠀⡄⠀⠀⡄⠀⢘⠀⠐⠊⠑⠀⠀⠘⠂⠒⠡⠀⠀⠀⠃⠒⢂⣯⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠉⠉⠛⠲⠦⣤⣄⣄⣀⣀⠀⠀⠀⢸⠢⠄⠀⢀⠂⠀⢀⡀⠀⢀⡀⢀⢀⣃⣠⠮⠜⠂⠀⠡⠀⠡⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⡇⠀⠀⠉⠹⠉⠛⠛⠛⠒⢓⠚⠛⠛⠛⠋⠉⠉⠉⡍⠀⠀⠀⡀⠀⢀⠀⠀⠀⠆⠀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⠀⠀⡇⠀⠀⢘⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢤⠀⣄⢠⣀⣀⣀⣀⣆⣄⠀⠀⠀⠀⣄⢀⣀⠀⠀⠀⠸⠀⠆⠀⠀⠀⢀⣄⣠⠦⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈⠀⠀⠈⠀⠁⠈⠛⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠅⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⣀⡰⢄⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠤⠈
⠀⠀⠠⠴⢒⣒⠀⠈⡀⠀⢀⠀⢀⢠⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠖⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠈⠁⠃⠀⢑⢠⣢⡀⣼⢀⠐⠀⠘⠓⠘⠉⠃⠀⠀⠀⢨⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣠⣒⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢈⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠂⠀⠂⠄⠀⠀⠀⠀⠀⣠⠃⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⡭⠙⠋⠉⣹⠟⠉⠐⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢴⣤⣈⡦⠮⠐⠛⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠁⠀⠀⠀⠂⡙⠲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠢⢪⢟⡏⢲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⠀⠀⠀⠀⠀⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡽⠀⠛⠀⡀⢀⠀⣠⠦
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⢢⠀⠀⡅⠀⠀⠀⢃⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠠⠀⠉⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠄⠀⠆⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠈⠆⠃⠀⠀⠀⠀⠀⠀⢈⠁⢨⡢⡑⠄⠀⣰⣄⠛⠀⣀⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣄⣶⣷⣶⣶⠶⣤⠀⠀⠀⠁⠀⠀⠀⠀⠈⡙⠿⢾⣿⠷⡏⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡀⠠⣀⢠⡀⠀⠙⢫⣯⣼⣥⣦⡴⠿⡇⡄⠀⠀⠀⠂⠈⠁⡀⠐⠊⠸⣸⠂⠐⠠⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠁
⠀⠀⠀⠀⡇⠀⡁⠀⠀⠀⢠⡀⠁⠍⢋⣡⣠⣀⣄⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠄⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠛⠀⠀⠀⠀⠿⠿⠿⠗⠘⢫⣿⣿⣿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠑⡄
⠀⠀⡄⠂⠠⠀⠀⠀⠀⠀⠀⢠⠤⠄⡄⠈⠉⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⣾⡦⡶⠤⣾⣦⠖⠃⠀⢠⠔⠊⠀⠙⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣤⡤⠈⣁⣠⣤⡄⠀⠀⠀⠀⠠⢁⡀⠀⠀⠀⢠⠀⢆⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢎
⠀⠀⠀⠀⠀⠈⠻⠻⢿⣿⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠰⡍⡀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠔⠂⠁⠈⠐⢤⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠈⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⠴⠲⠖⠶⠆⣰⡔⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡰⠞⠋⠀⠀⠈⠙⠋⠐⠂⠐⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠹⣿⡾⠀⢀⣀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣿⣥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣶⣦⡈⠋⠀⣠⣴⣦⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣯⡰⡌⣿⡿⣿⣷⣿⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⠿⠾⠿⠿⠛⠛⠋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣧⡜⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠘⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣏⠄⢴⣠⣴⣿⣿⣿⣿⣴⣶⡒⣤⣾⣿⣎⣷⢪⣆⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡏⠀⢀⣠⣴⣷⣷⣿⡿⠟⠝⠛⠩⡿⠿⣿⠟⠟⠻⠟⠛⢻⣿⠀⠁⣄⠈⢫⣷⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⡉⠁⣠⣴⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠉⠐⠺⠿⣦⣀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⣚⣿⢏⣽⣻⡿⠛⠛⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⢀⡈⣴⡴⢿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⠟⢿⣷⣦
⠀⠀⠀⠀⢸⠏⠻⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⣶⣠⣼⣿⣿⣷⡟⠀⠍⢀⡚⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⠃⢻⣿⠁⠀⠀⢸⣿⣿⢡⣧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠻⠄⠀⢼⡿⠄⢠⠀⢻⡿⡧⡿⠉⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣭⢻⣛⣿⡟⡟⣟⠿⢻⡻⠏⡟⣿⢻⢸⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢩⠇⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠠⠂⠈⢼⠀⠠⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢄⡀⠀⣸⡰⠁⠀⠙⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠈⠑⢿⠣⣠⡹⢑⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡂⠂⠁⡿⢀⠤⣌⡡⢻⢦⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠒⡒⣒⠊⡉⠐⠒⢉⠢⡀⠀⠀⠀⠀⠀⡃⠄⢀⡠⠀⢾⢚⢰⠙⡡⣳⠁⠀⠀⠀⣸⠟⠢⢂⠄⢐⣒⠰⢒⠋⠁
⠀⠀⠀⠀⠀⣌⡷⡦⣄⠀⠈⢆⠈⠉⠧⡐⣌⠠⠇⠄⡎⠀⠀⣯⠚⡡⠆⡴⣩⣀⡔⣃⠂⡃⠘⢀⠜⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⠒⠀⠀⣀⠈⠉⢷⠀⢠⢬⣨⡦⡾⡟⠔⣡⠈⠉⠓⢷⢀⡇⣀⡂⠷⠀⠒⠒⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⣗⠦⠠⠀⠄⠠⠐⠉⠓⢢⣈⣇⠸⠃⡎⢼⠁⣟⠴⠁⡆⠀⠀⣸⠝⠁⣭⡄⠉⠀⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⠀⠐⢤⠀⠀⠔⢀⡀⠀⣻⡬⡽⠳⢄⠱⣘⣆⢳⠂⠀⠀⢠⢚⢧⡂⢀⠐⠂⢀⠖⡾⢢⡤⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣈⠁⡌⠀⠘⢷⢒⠆⠳⢤⣈⠟⠀⣠⡞⠉⠁⠈⢿⡸⠆⠯⠷⠞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣱⣞⡠⣤⠄⡿⠷⡖⠷⡲⢿⡶⠶⡍⠂⡤⠆⢀⣄⠻⢆⣀⣤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡡⠖⢺⡟⢸⠀⠆⠀⠈⢈⢠⢆⣡⠞⠀⠀⠈⠲⣀⣠⠊⣉⣀⢨⡟⢭⣱⡚⠵⠦⠄
⠀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠢⠬⠤⢌⣑⠚⠂⠀⣝⡠⠛⠁⠀⢀⠀⠀⠀⠈⢂⣩⠵⠎⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠻⣷⣆⠀⠀⠀⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⡰⠶⠖⣿⡯⣴⣴⣦⣶⣿⡇⣤⣤⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢻⣷⣷⡾⢿⣿⡿⠁⣬⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢦⣄⣠⢶⡶⣦⣸⡟⠿⣿⣧⣄⣤⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡶⠿⣿⠂⢈⣿⣽⠛⠁⠛⠿⣿⣿⠟⠛⠋⠘⣿⣯⡤⠼⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢶⡏⠡⣤⡴⡀⢼⣿⣿⣿⣿⣤⣤⣾⠛⠇⠙⣿⣶⣤⣷⡿⠿⠷⢶⣿⣿⣿⣯⡀⢠⣴⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣿⣿⣿⡿⣿⠦⢨⣿⣋⢘⣿⠟⠃⠉⢻⣿⣄⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣨⣿⣿⣿⣿⣿⣷⠚⠋⠻⢻⣿⡘⡐⣿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⡶⠞⢻⣷⡌⠈⣁⣴⣿⣿⡿⣧⠼⣁⠀⢶⣤⣿⣿⡟⣀⢀⣹⣿⣾⣿⣯⣿⣿⣿⡙⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⢀⣴⡴⢿⣿⣦⣾⣷⣿⠿⢻⣇⢀⣴⣿⣶⣿⠉⠙⠋⢙⡿⠿⠻⣿⣿⣧⣿⣿⣿⣿⣧⠈⠙⠛⣿⣷⣦⣠⣤⣀
⠀⠀⠀⠀⠀⠲⠿⠀⢾⣿⣿⣿⡿⠁⠀⠀⢘⠿⠁⠈⠻⣿⡶⠤⠶⢾⣆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⢠⣴⢶⣴⣠⣾⣿⠟⣛⠛⣾⣤⣥⣾⣧⣾⠂⢿⣿⣇⡄⣰⣋⡉⠉⣿⡟⢋⢹⣿⣿⡿⣿⣿⣿⣿⣷⣀⡙⠿⣿⣿⣿⡷
⠀⠀⠀⣤⠙⠬⣿⡿⠇⣨⣤⣽⢿⣛⡉⢻⣟⣿⣄⣱⠞⠋⠀⣹⡟⠛⠙⣿⡟⠛⠛⣾⣿⡿⢷⣿⣿⣿⣿⣿⡿⠟⢀⠀⠉⠁
⠀⠀⠀⠰⣿⠴⡿⠿⠈⠉⣿⡿⢰⡝⠉⣤⣿⡿⣧⣈⣦⣥⣴⣾⣧⣌⣸⣿⣿⣶⡶⠾⠿⣥⣼⠛⢻⣿⣿⣿⣦⣿⣿⣿⣄
⠀⠀⣠⣤⣄⢀⣤⣤⣀⡼⢻⣆⣸⣿⣤⣿⡿⣿⠟⠛⠿⠿⢿⣿⣾⣉⣥⣴⣿⣿⣦⠄⢾⡿⠿⣾⠿⣿⣿⣿⣿⣿⣆⣉⣡⣤⣄
⠀⠄⣉⢋⡹⣯⡙⠛⣿⠧⠛⣿⣿⢿⡿⣿⣤⣈⣶⣠⡄⢦⣽⡿⠟⢿⣿⠿⣿⣿⣿⡿⠛⠳⣶⣿⣄⣨⣿⣿⣿⣿⠿⢿⣿⣿⣿
⠀⠘⠛⠉⠙⠻⠿⣾⣻⡞⠿⠛⣡⣾⣷⣿⣯⣭⠙⠛⠛⢿⡯⠀⠀⠈⣿⣶⣿⡿⠻⠷⢶⣀⣼⣿⣿⣉⣿⣿⣿⢿⣦⣶⣌⠀⠈
⠀⠀⡼⣷⢿⣦⣤⢿⣸⣧⣀⣀⣤⣿⡿⢿⣿⠾⠷⣦⣶⣾⣷⣿⠉⢻⣿⣿⣿⠷⣞⣶⣻⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⡉
⠀⠾⢶⠖⣾⣻⣯⠈⡏⢹⣿⣿⣿⣿⣷⠊⠹⠷⣴⣿⣿⣯⣿⣿⣿⠋⠉⢻⣧⣄⣻⣿⣿⣇⣀⣘⣿⣿⣷⣿⣿⣯⣿⣿⣿⣶⣶
⣠⣤⣦⣶⣌⠛⠋⠸⠗⣣⣿⣻⣿⣿⣿⣏⣀⠂⣼⠛⠉⣡⣌⣽⡟⠁⣓⣾⣿⡹⣿⣿⣿⢿⣿⠿⣿⣤⡈⣿⣿⣹⣿⣿⣿⣿⣿
⠈⣻⣙⣃⡙⠁⠀⣶⣼⡾⠋⠁⣭⣼⣿⠿⡟⠛⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠟⠃⠺⣻⡙⢿⡿⢻⣿⣿⣿⣿⣦⣿⣿⠿
⠈⠿⠟⠿⠋⠀⢘⣿⣿⣷⣴⣴⣟⠉⠛⠳⣿⠀⢳⣼⣿⣿⠿⠿⣿⣿⣿⣿⠟⠻⣿⣦⣷⣤⣟⠛⣿⣿⣿⣾⣿⣿⠿⢿⡿⠂
⠀⠀⠀⣤⣦⣤⣾⣿⣿⣯⠉⠈⢡⣴⠾⠚⢻⣾⣟⠛⠋⢠⡶⠄⠸⠿⣿⡇⢀⣤⠸⠿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣍
⠀⠀⣶⣏⣽⠋⡿⠋⢨⣸⣷⣷⣾⣿⣷⣾⡿⠛⠋⠁⢸⣏⠀⠀⢰⣶⡾⠿⣾⣧⣶⡴⠿⠏⢩⣿⡿⣿⣿⣿⣿⣁⣤⣤⡄
⠀⢸⣧⠙⠡⡆⣶⢮⣭⣿⣿⠋⠉⢉⣤⣼⣧⡾⠳⠞⠋⠛⠷⣾⣧⣄⣀⣸⣿⣿⣿⣉⡀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⡄⣉⣷⡿⠃⠁⣤⢴⠛⣯⣿⣋⣶⡁⠂⠠⣄⣰⡟⣹⠿⠿⠙⢻⠀⠉⣿⣅⣀⢹⣟⣻⠿⠛⠃⢰⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠰⣓⡎⠙⠁⠙⣿⣾⣾⣿⠏⠙⢫⣤⣀⡴⠿⠦⢼⣿⣿⣿⣷⣟⣿⣶⣶⣆⣤⣌⣉⠈⠋⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⣹⠿⠿⣿⣷⣏⠀⠘⢻⣿⣿⣟⠁⠸⡛⣏⡉⠀⢷⣄⣸⡿⢋⣽⣿⣿⣿⡻⣿⣿⣿⣿⣿⠄
⠀⢀⣀⣀⡀⠀⠀⠎⠱⢾⣯⣀⢀⣾⢿⣿⣢⡸⣿⣿⣿⣿⣦⣀⣽⢧⠹⡶⠛⠟⢹⣿⣟⣿⠛⣉⣿⣷⡏⠙⠿⠿⠇
⠠⣦⣼⣿⠅⠢⣤⣀⣀⣈⠛⢿⣿⡇⡀⢼⡁⢀⠀⣸⣿⣿⠋⠉⠙⣻⣦⣸⣷⣶⣿⣿⣿⡇⠾⢿⣿⣿⡗
⠀⡿⢛⣿⡶⠾⠿⠷⡉⣿⢠⣾⡟⢉⣏⢸⣿⣿⣿⣿⣿⣿⣧⣶⣶⡿⣯⡟⣶⣿⣿⣿⣿⣧⡐⠛⠟⠋
⠀⠀⠈⠛⠁⠀⠀⠸⢿⡿⠃⠀⢋⣼⣻⠿⣿⣿⣿⣯⡈⢻⣿⣿⣿⣷⣀⡈⣽⡿⠛⠀⠛⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⡿⠧⠿⠿⠟⠀⢿⣷⡼⢿⣿⣿⣿⣿⣿⡹⣻⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠶⢾⠓⠀⠀⠈⠀⠀⠉⠉⠈⣿⡋⣹⡏⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⣷

⠀⠀⠀⠀⠀⠀⣤⡴⠆⢀⠀⠀⠀⢠⣴⡶⢂⡀⠀⠀⣀⣤⠖⣠⣤⡴⢀⡀⠀⠀⠀⠀⠀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤
⠀⠀⣀⣠⣤⣤⣽⣷⣾⡟⣷⣤⣤⣼⣿⣷⣿⣿⣤⣤⣹⣿⣴⣿⣿⣶⡿⢿⣄⣀⣀⣀⣀⣹⣽⣶⣿⢿⡄⠀⠀⣀⣤⣤⣿⣿⣶⣿⣆
⠐⠛⠉⠙⣿⠿⠿⢿⣿⡿⠛⣿⠿⠿⣿⣿⢋⣽⠿⠿⠿⣿⣿⣿⣿⣿⣇⠉⠉⣩⢿⡿⠿⠿⣿⣿⣇⡀⠐⠛⠛⠻⣿⡿⣿⣿⣟
⠀⠀⠀⠀⠙⣆⠀⠀⠃⠁⠀⠈⠦⠤⠼⠬⠞⠁⠀⠀⠠⠇⠘⠧⠄⠈⠳⠤⠊⠁⠏⠀⠀⠀⠀⠘⠄⠑⠀⠀⠀⠀⠹⣦⠀⠘⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⢙⣿⣿⣿⣿⡿⠛⠋⣹⣿⣿⣿⠿⠟⢙⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣿⣿
⣿⣿⣿⡿⠿⠷⠄⠘⠉⠀⠈⠟⠛⠃⠀⠈⠁⠈⠻⠯⠀⠀⠋⠀⠀⠈⠀⠈⠻⣿⣿⠿⡿⠄⠀⠋⠉⠈⢻⣿⣿⡿⠿⠯⠀⠀⠊⠉⢻
⣝⣁⣠⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢰⣷⣎⣉⣁⡀⠀⠀⠀⠀⢀⣶⣤
⣿⣿⣿⣿⣄⠻⣿⢓⣠⢸⣿⣤⠚⠿⠆⠂⠁⣰⣿⡿⠿⢰⣄⠐⢖⠂⠀⠿⣣⣔⢡⣾⣿⣷⣶⣆⢲⡌⢿⣿⣿⣿⡀⠚⢖⠆⡠⣸⣿
⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣦⣼⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣦⣾⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠈⠁⠀⣹⠀⣠⠴⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣄⡀⠀⢀⣠⠔⠛⠳⣍⢀⣠⠴⠒⠚⢁⡼⠁⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠻⣍⡀⠀⠀⠀⢸⣏⡤⠖⠒⢾⡉⠀⢀⣠⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠽⠦⠴⠖⠋⠁⠀⠀⠀⠀⡿⠾⠿⠶⠶⠶⠶⠶⠤⣤⣀
⠀⣠⠴⠖⠒⠚⠛⠛⠋⠉⠉⣩⠟⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⠭⣍⠓⣆
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠥⠤⠶⠶⠖⠒⠒⠲⠦⢤⣀⠀⠀⢀⣿⣀⣈⡇⠈⣧
⠈⡟⠲⣄⡀⣀⣀⣀⣀⣼⠀⠀⣰⡏⠀⠀⢣⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⠞⢹⠉⣁⣠⡴⠟
⠀⢿⠀⠀⠙⠧⣄⠀⠀⠘⣇⠀⠁⣹⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠋⠁⠀⡟⠉⠉
⠀⠈⢧⠀⠀⠀⠈⠑⢦⣀⠈⠳⣄⡱⢄⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣥⠤⠴⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠓⢦⡀⠙⢆⠀⠈⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠶⠖⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠙⡟⠚⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠡⢴⣿⣴⣤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢴⡆⠹⠆⠋⠉⠈⠘⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢀⣤⣾⣤⡂⠉⠀⠀⠀⠀⠰⣾⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡀⣼⡿⠿⠛⠻⢿⠟⠿⠿⣦⡀⠀⢨⡹⣯⠱⣿⡇⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⢀⣤⠿⣇⣸⠂⠀⠀⡠⠃⠀⠀⠀⠀⠉⣳⣮⣠⠚⠋⠉⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠙⠃⢭⣷⠱⣀⣄⡴⡁⠀⠀⠀⠆⠀⠀⠘⣿⣿⣿⣙⡿⢈⠁⠈⠛⢏⠀⠈⠉⠉⠉⠙⠉⠙⠛⠉
⠀⠠⠬⡥⢦⣼⡋⣹⣴⠟⠋⢸⣿⠃⢰⣿⠂⠒⠀⠀⠧⣽⣿⣥⡽⠋⢁⠀⠀⠀⠡
⠀⠀⠐⠀⠀⠈⠉⠁⠀⠀⠀⠀⠹⡤⢈⠛⠢⡀⠀⣀⡴⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣧⣄⠈⠙⣿⣄⣀⣀⣀⡤⠔⠒⢠⡀⠀⠀⠀⡔⠂⠄⠛⢿⠲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠈⠀⠈⠀⠈⠒⠀⠊⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⣇⣬⣷⣦⣤⣄⢂⡰⠀⣤⠰⢆⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠂⡧⣠⣢⣤⢷⣾⣯⣋⣰⣿⣿⣍⢉⣤⣿⣾⣿⣿⡀⢀⣾⣿⣯⣷⡤⢐⣶⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣯⣿⣿⣿⣿⣿⣤⣿⣿⣿⣦⣿⣭⣿⡴⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⢾⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣯⣿⣼⣿⣯⢯⣼⢛⣿⣿⣿⣿⣿⢿⣿⢿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣾⣶⠉⠾⣿⣿⣿⢿⣿⠿⣿⣾⣿⣿⣧⣿⣿⣿⣿⣉⣿⡿⣿⣿⣿⣹⢿⣿⣿⣤⣏⡸⣿⣿⣟⡐
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣠⡽⣿⣿⣿⡿⣿⣿⣮⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡿⣻⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣾⣍⠙⢡⡍⢿⣿⣿⣿⣯⣵⣽⣽⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡿⢫⣿⣧⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣏⢠⣶⣿⣾⣟⣿⣿⣿⣿⢿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣫⣷⡾⠻⠏
⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⢻⣿⣿⣿⠯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⣽⣿⣿⣿⣿⣟⣿⣟⢙⣯⣽⣿⣿⣟⣶⣦
⠀⠀⠀⠀⢀⣉⣭⣿⣿⡿⢿⢾⣿⣿⣾⣷⣿⣟⣿⣿⣿⣿⣿⣟⣏⣿⢿⣿⣿⡟⢿⣻⣿⣿⣿⣾⡁⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⣻⢿⣯⣻⣿⣿⣿⣿⢹⣿⣿⣿⣿⣋⣿⣯⢿⣿⣿⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣿⣿⣷
⠀⠀⠀⣀⡬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⣭⣽⣿⣿⢿⣿⢿⣿⡟⣿⣿⣴⣿⣾⣿⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⠋
⠀⠀⠀⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣼⡿⠿⣿⣷⣿⣿⣿⣷⣿⡷⣾⣿⣿⣿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠛⢿⣿⣿⣿⡿⢿⡿⢉⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⠂
⠀⠀⠀⠹⠿⢛⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣿⣿⡇⣾⣷⣿⣿⡟⢻⣷⢋⣯⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠿⢿⣟⣛⢿⣿⣏⣿⣿⣿⣾⡇⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠁
⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠷⠆⡘⢿⡿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠛⠉⠛⠛⠁⠉⠁⠀⠀⠀⠀⠓⢦⣉⠛⢿⡻⣿⣿⢣⡿⢟⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢿⣿⣿⣿⠃⠀⠀⠀⠉⠉⠈⠹⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠒⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡥⡤⣦⣿⣿⣅⣠⣷⡷⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣷⣭⣶⢿⣭⣿⣾⣿⣿⣿⡻⣷⣽⣦⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠲⡗⠤⢴⣾⠿⠟⠉⢟⣿⣿⣿⣻⣿⣿⠛⣿⠿⣟⣿⣿⣿⣿⣿⠯⡄
⠀⠀⠀⠀⡀⠀⠀⡀⣾⠇⢁⠃⢠⣶⡓⣆⠨⠐⠀⢤⣽⣿⣿⣿⣿⣷⣾⣿⣛⣍⣿⣿⣿⣧⣶⣴
⠀⠀⠀⠡⠀⠀⠀⣴⣿⣴⣦⣄⣘⣿⣗⣂⡗⠀⠀⠀⢀⢀⡋⣿⣿⣿⢟⡟⣯⢯⣿⣏⣻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⡿⢿⣯⠁⠀⠁⠀⡀⠘⠯⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣷⠦
⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠛⠃⠀⠁⠈⠉⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣴⣾⣿⠏
⠀⠀⠀⠀⢀⣀⣐⢿⠟⠓⠀⠀⠟⢂⣤⣄⣠⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢽⡫⡍⣻⣿⣯⠿⣹⣿⣿⣿⣿⠿⠿⠂
⠀⠀⠰⠄⠠⣿⣿⣿⣷⣶⡿⠦⠀⢸⠋⠏⠁⠁⠉⠉⠉⠻⢧⣤⡛⣛⢷⠟⢌⣞⣽⡎⣽⣾⣿⣿⣿⣿⣷⣤⣴⣤⣄⡀
⠀⠀⠀⠀⠴⠌⠝⠻⠛⢿⣵⣿⣄⣼⡁⠀⢠⠁⠵⢶⣶⣿⣿⣿⣿⣟⣉⣂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠂⠀⠀⠀⠀⠀⠰⠟⡿⢻⣿⣿⣤⣤⣴⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣽⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡏⠉⠉⠀⠘⠿⢻⣿⣿⣿⡅
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⣿⠿⡏⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⡿⣿⣿⣿⣿⡏⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠿⢷⣄⣋⣿⣟⣟⣃⠉⢻⡷⡃⠀⠀⢁⠉⢹⠁⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣼⣿⢿⡐⢜⠃⣥⠈⡚⠉⠀⠀⠙⠛⠋⠯⠄⠰⠖⠘⠿⠧⠄⣀⣀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⣷⡘⠟⢋⣉⣉
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠤⡀
⣄⣠⣤⣄⣠⣠⣄⣤⣤⣀⣀⣠⣤⣤⣤⣤⣠⣬⣍⣉⣉⣉⣉⣉⣽⣉⣉⣉⣥⣤⣌⣁⣀⣠⣄⣀⣀⣤⣤⣤⣤⣄⣤⣤⣤
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠋⠙⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣠⣤⣤⣄⡀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣴⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⢠⡄⠀⠀⠀⠀⠀⠀⢠⣾⠏⡜⣦⠛⢽⣉⣷⣤⠀⠄
⠀⠀⣠⣴⡾⠿⣶⣶⣡⠞⢭⡧⠀⠃⠀⠀⠀⠀⠀⣴⢯⣵⡄⣽⠘⢷⣄⣘⡁⠀⢡⣐
⠀⣴⣿⣿⣿⣇⡀⢘⣻⢷⣶⣦⣠⣦⡀⠀⢀⣀⠀⠙⠊⠁⠘⣿⡆⠀⠙⡿⣏⡙⢿⢾⣦⡒⠀⠀⠀⡀
⣰⢿⣿⠯⠟⠻⣿⣶⣬⣛⠿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣆⣤⣄⣹⣿⣄⠀⠁⠙⠿⣼⣾⣿⢃⣷⠀⠀⠘⠿⣷⣦
⠙⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣉⣿⣿⣿⣿⣿⣿⡟⠉⠋⢹⣿⣿⡀⠀⠀⢂⠀⣠⣾⢿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⡟⣷⣿⠿⠛⢿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣷⣤⠀⠛⠻⣏⣉⡲⣿⢀
⠀⠀⠀⠀⠀⢀⠘⣡⠞⠛⠙⠋⠉⠉⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠻⠜⠃
⠀⠀⠀⠀⡀⢈⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣧⠀⠀⠀⠀⢸⡵⠧⡘⠇⠀⠰⡆
⠀⠀⢀⡴⠙⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⢧⣤⡄⠀⠀⠁⠈⠳⡀⠀⠛⠼
⠀⠀⠀⠀⣰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠩⠭⢩⡛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⡟⡳⡄⠀⠀⠀⠁⡍⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠓⠾⣗⢦⠀⠀⠨⠁⢢⡙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠈⢻⡷⣄⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠒⠒⠲⠶⢤⣤⣤⣀⡀⠈⠻⣦⡀⡀⠀⠀⠹⣎⢗⡦⡄⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠔⠒⠈⠀⠂⠀⠀⠀⠀⠀⠠⠙⢦⡀⠈⠻⢦⣤⣀⠀⠈⢳⡳⢷⣀⣼⠇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡆⣿⠀⠀⠀⢈⣹⡿⠗⠒⠿⠟⢻⣇
⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣀⡤⠶⠒⢒⣒⣶⣶⣾⣿⡫⢟⢁⡟⢀⣠⠖⠉⠀⠀⠀⠀⠀⣨⢽⣻⢦⣄
⠀⠀⠀⠀⠀⠀⣿⠤⠶⣛⣥⠴⡾⠾⠟⠛⠋⠉⠀⠀⠀⢁⡾⣴⠋⠀⠀⠀⠀⠀⠀⢠⡞⢡⠟⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢷⡮⠥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠇⠀⠀⠀⠀⠀⢀⣴⢏⣴⠏⠀⡀⡨⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⣀⣠⠶⠋⢸⡟⠂⠀⠀⢠⠶⡛⠋⢡⠋⠁⠀⠀⢈⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠚⠛⠋⠉⠀⠀⠀⢸⣇⠀⣠⡴⠇⢂⡔⠋⠁⠀⢀⠀⠴⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡩⣢⠴⠃⠀⠀⠠⣴⢕⣬⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣴⣔⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⡀⠄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⢛⢉⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠙⢦⡀⠀⣙⠃⠉⠳⠆
⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠢⡀⠀⢙⡂⠉⠻⠦
⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢮⣄⠈⠛⠶⠄⠻⢶⡤⣮⡀
⠀⠀⠀⠘⣿⠟⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠈⠛⠦⠶⢦⡄⢶⣄⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⣤⣀⠴⣤⠰⣇⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡄⠀⠀⠐⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⢳⡄⠀⢹⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣿⢤⣾
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢳⡆⠀⠘⣿⠁
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢸⡇⠀⠀⣿
⠀⠀⠀⣤⣤⣄⣀⡀⠀⢤⣤⣶⣶⣶⣶⣶⣶⣤⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠙⠻⢿⣿⣿⣷⣦⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠂⠀⠰⠀⠀⠈⠃⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠆⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⣆⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⡀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣴⣿⠂⠀⠀⠀⠀⠂⠀⢀⡈⠀⡉⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠚⠉⠁⢀⣀⣠⣷⠾⠃⠀⠀⠀⡠⠖⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢯⡶⣤⣤⣤⣤⣶⣤⣶⣿⣿⣾⣷⣶⣶⣾⣿⣿⠵⠚⠁⠀⠀⠀⠀⢸⣷⠀⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠈⠙⢦⡉⠙⠿⣿⣿⣿⣿⣶⡾⣭⣾⣄⣀⣄⠀⠀⠀⠈⠻⠿⠾⠷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠣⡀⠀⣤⠸⣿⠲⣤⣄⣉⠛⠳⠯⢜⣾⣎⣍⠿⠟⠋⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡵⠳⣌⡲⣿⣿⣿⡟⣿⣿⣿⣿⣷⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠟⠋⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠁⠀⠀⢨⣿⢨⣭⣛⣛⣻⠟⣿⣿⣿⣿⣿⡿⠿⠿⣟⣰⣤⡀⠀⠀⠘⣷⡀⣀⣠⣾⠁
⠀⠀⠀⠀⠀⠠⣼⡯⠁⠀⠀⠈⢳⡀⡀⢸⡿⣼⣿⣿⣿⣿⣿⢿⠛⠙⡙⠿⣿⣷⣄⡀⠩⠛⡩⠄⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠰⣿⣿⠂⠀⠀⣠⣾⡿⠉⠛⠹⠿⣿⣿⣿⣻⣟⠄⠀⢳⣤⡀⢘⣿⣿⣿⡶⣤⣀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠀⡹⣿⣿⣿⣷⣞⣀⠀⣻⣿⣾⣿⣿⡟⢏⣻⠿⠗⠂⠀⠀⠀⣠⣶⠦⣶⠦⣿⣿⣆⠺⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠁⠙⠉⠹⣿⣷⣷⣶⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿⣷⠟⠛⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⡇⣸⡏⣢⣿⣿⢿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⣀⡀⣄⣀⡀⠀⠙⠿⣿⣿⣿⣷⣾⣿⣿⡇⠿⣿⣿⣇⣹⡆⠀⠀⠀⠀⠀⣠⠶⠒⠒⢤⠀⠀⢹⣿⣷⣿⣿⣿⣿⡿⣷⣌⣿⡇
⠀⠀⠀⢠⣮⠱⠛⢟⣻⣿⡀⠀⠀⠈⠀⠉⠀⠙⢿⣿⡃⠀⠀⠉⠛⠓⠃⠀⠀⠀⠀⢰⡇⠀⠀⢼⣿⡇⠀⠀⠙⠻⠿⠿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⢿⣯⣤⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⠿⠿⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠋
⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠄⠀⠀⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢠⣟⠡⣀⠑⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠤⠼⠧⠖⠶⠧⠟⠶⠾⠿⠄⠀⠀⠀⠀⠀⠀⠈⣿⣆⣹⣤⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠋

⠀⢠⣄⢀⡀⣀⠀⣀⣀⢀⡀⣠⡄⢀⣀⢠⢀⡀⡄⣀⢀
⠀⠸⠻⠸⠟⠾⠯⠿⠺⠻⠟⠿⠇⢸⡿⠸⢻⡇⠗⠿⠹
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⣀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠋⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⣶⠀⠀⠀⠀⠀⢼⣧⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⣤⣠⣦⣶⣷⣴⣿⡿⠋⠀⠀⠀⣤⠶⠛⠡⣨⣖⣀
⠀⠀⠀⠀⠀⠀⣿⢁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⢰⣿⡟⡋⠻⣿⡿⢋⠀⣀⣀⣠⠾⠁⡀⢀⣤⣾⢋⡹
⠀⠀⠀⠀⡀⢲⡷⣦⡏⠀⢶⣦⠀⢀⣀⣀⡤⠾⣿⠋⠀⠀⠀⢀⣠⣴⣿⣷⡀⢠⣿⣧⠀⠀⣾⣿⡏⢰⣿⣷⣟⠋⠃⠊
⠀⠀⠀⡁⠀⠀⣶⣿⣷⣤⣚⣡⣶⣿⣿⣿⠄⠀⣸⣧⣤⣤⣼⣿⡿⢿⢿⣦⠉⢩⡋⡙⠒⠚⠙⠷⡑⠚⢉⡣⠜⠅⠂
⠀⠀⢠⢷⡾⠟⠛⠛⠻⢻⠛⢻⣟⡛⡻⠿⡷⠒⠻⣏⢙⢈⡿⣌⠑⢽⣈⠫⠃⢀⣤⣶⠦⠠⣼⡧⠱⠀⢄
⠀⠀⠀⠀⠳⠀⢀⣴⠀⢨⣄⡾⠛⠛⠡⢄⣀⠰⠶⠛⠛⠉⠉⠓⠺⠿⠸⠄⠋⣉⡡⠤⠒⠈⠁
⠀⠀⠀⠀⠈⠓⠚⠉⠒⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠁⠀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⣿⣿⡟⠉⣼⣿⠿⠛⠛⠛⠿⠿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣀⡒⠻⣿⣷⣄⠈⠛⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠶⢂⠞⢻⣀⡤⠀⠙⢯⣽⣶⢤⡟⠀⠀⠀⠀⢒⡫⠽⠟⠂⠀⠀⢠⡄
⠀⠀⠺⣷⣀⡴⣫⠴⢋⠁⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⡆⠀⠀⠀⠀⠀⣀⣠⣤⡾⠁
⣾⠁⠀⢿⡟⠋⣁⣤⠿⣧⠀⠀⠀⠀⠀⠈⠛⠿⠿⠗⠘⣶⣶⣶⡿⠿⠛⠛⠉⠀⠀⠀⠒⠒⠒⠚⠛⠛⠓⠢⣄
⠻⣦⡴⠈⠳⠆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠐⢶⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣷⣄⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠿⠛⢉⣀⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠸⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠿⠛⠻⣿⣿⣿⣿⣿⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣤⠴⠚⠉⠀⣼⡄⠀⠀⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡁⠀⣀⠀⠁⠀⠀⠀⠀⣼⠟⠛⠛⠉⠀⠀⠀⠀⢰⣿⣷⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠛⠋⠉⠉⠀⡴⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢀⣼⡇⠀⠔⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠿⠛⠁⢀⣤⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢀⣀⣸⣿⡿⠃⠀⢀⡴⠂⠀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⢿⠟⠁⠀⠀⢀⡞⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣈⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⣾⣯⢻⡏⣡⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⣶⣤⣀⠀⠀⠀⠀⠀⡡⡞⠓⠻⠻⠉⠻⠆⠓⠀⠀⠀⠀⠀⠄⠁⡀⠶⡒⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠈⡀⠀⠀⠀⢸⣯⣾⠄⠠⢀⡶⠀⣠⣄⡀⠄⠀⠀⠁⠀⠀⢐⣿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠂⣀⠀⠀⠀⣰⣿⣿⠙⣗⢂⣀⣝⠌⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⡮⢹⣣⠼⠉⠹⡆⠉⠁⠤⠰⣄⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠿⠒⠂⠀⣶⠀⠈⠂⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡃⠀⠀⠀⠠⠀⢀⠛⡀⣤⣴⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣾⡃⢠⣿⠀⠀⠒⢼⠋⣽⣿⡿⠃⠺⣷⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⡟⠥⠊⢒⡠⠠⢼⡏⢻⣿⢿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠩⠟⠿⠛⠛⢦⡀⠉⠀⠀⠈⡇⠀⠉⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣷⡶⣥⣄⠀⠀⠀⠃⠀⠀⠀⢀⢔⣤⠤⠤⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣻⣷⡾⠻⢿⣿⣿⣿⡿⠋⠀⣿⠈⢿⣷⣍⢱⣶⣋⡽⡷⠋
⠀⠀⢀⣠⣴⢾⣫⣭⠵⢪⣴⣿⣿⠿⠋⠀⠀⢰⣧⣆⠈⣿⣿⣿⣿⢫⣾⡃
⠀⠀⣌⣸⠞⠋⢁⣤⣴⣿⣿⠟⠁⠀⠀⠀⠀⠐⢹⡏⠀⢹⣿⠀⣱⠃
⠀⠀⠉⠀⢀⣒⡾⠟⢯⠟⠁⠀⠀⠀⠀⠀⠀⣀⣺⣿⠀⡸⣫⣾⠁⠃⠀⠀⢀⣀⣀⣴⡀⢴⣤⡴⣦⡀⠊
⠀⠀⠀⠀⠤⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠄⠉⣼⣿⢟⡼⠻⢻⣧⠉⠀⢠⣾⣟⠟⠉⠉⢣⣿⣷⡄⠹⢷
⠀⠀⠀⠀⢀⣤⣶⠾⠏⢉⣛⡿⠿⣿⣦⣄⠀⠠⣽⢫⡟⠁⠀⠈⠻⡇⣠⣿⡿⠀⠀⠀⠀⠈⣿⣿⣳⡀⠀⠛⡄
⠀⠀⠈⠀⣿⣿⣿⣤⣴⠟⠁⠀⢀⡀⠀⠀⣵⡼⢃⣈⣁⡤⠔⠒⠀⢹⣿⣿⡷⣦⠀⠠⠀⠀⢿⣿⣿⡏⠀⠀⢰
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⣀⣀⣈⣍⣤⣀⡞⣠⠟⠃⠀⠀⠀⠀⠀⢸⣿⣿⡇⣤⡀⠀⠀⠀⣸⣧⣸⡏⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣷⠊⠅⠐⠀⠀⢸⣿⣿⠇⠀⠀⣶
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⠂⣀⢸⣿⡟⢐⣁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠿⣿⣿⣿⡿⢿⠟⠙⠯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠔⠁⡀⠙⢢⠀⠀⠀⠀⠀⢠⠃⣀⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇
⠀⠀⢨⠀⠠⠋⠓⠀⢣⠤⡄⢠⠒⣼⠘⠋⣤⡀⠀⢹⠀⠀⢀⡀⠤⢤⠐⠒⠒⣦⠀⠠⢠⣀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⡠⠀⠀⠀⠈
⠀⠀⢈⠀⢀⡾⠓⠀⢸⠀⣿⢨⠄⡟⠀⠠⣋⡉⠀⣼⠀⠀⡌⠀⡄⠀⠈⣦⠀⠀⠁⢄⠀⠀⡤⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⡀⠀⣰⢦⡀⢸⠀⡇⠀⠇⡇⠀⠴⣫⡓⠀⣿⠀⠀⢰⠀⠈⢢⠂⠀⠑⡄⠁⠀⢣⠊⠈⢴⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⡡⠶⠄⢸⡞⠀⠀⠈⣇⢀⣘⠥⢥⣀⣹⠀⠀⠀⠐⡄⠈⠑⣤⠊⠈⢢⡄⠈⠁⡠⡎⠀⠀⠰⠶⠦⠤⢤⣄⣀⡀⠀⠀⠀⠆
⠀⠀⢰⡗⢚⠃⠉⠉⠙⡇⠀⠀⠀⠸⡅⣠⢠⢠⡆⣸⠀⠀⠀⠃⠈⣦⠂⠀⢡⡀⠀⠈⢂⠈⠑⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠼⠤⡄
⠀⠀⠀⢿⣾⣼⣾⣇⣧⠇⠀⠀⠀⠀⠣⠽⠧⠼⠾⠟⠀⢀⣤⣧⡀⠀⠑⡤⠀⠉⢢⠄⠈⢣⣠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣩⣀⣸⢧⣀⣀⣀⣀⣀⣀⠀⢠⣾⠉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⠀⠀⢀⠀⠀⠀⠀⢽⠒⢻⡵⠊⠁⠀⠀⠉⠉⠉⠉⠛⣌⡿⠽⡇⠀⠀⠀⣴⣂⡤⢄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⣜⣛⣉⣉⣉⣉⣛⣛⣒⣒⣒⡒⠒⠾⠷⠴⡇⠀⠀⣸⠇⣏⠑⡞⠉⣴⡂⢀⡀
⠀⠀⠀⢀⠐⠷⠶⠶⢤⣤⣤⣤⣤⣀⣤⠞⢀⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⡏⠀⠀⣿⢠⢎⣩⠓⢠⠧⣸⠁⠲⢇⡴⢠⡄
⠀⠀⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠈⢆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠟⠲⠤⣍⠸⠁⠶⢥⣝⣉⠖⢀⡟
⠀⠀⢆⡀⠛⠛⠛⠛⠓⠒⠶⠤⠤⠄⠠⣶⣦⡄⠼⡄⠀⢻⢻⡟⠉⠁⠀⠀⠀⠀⠒⠒⠒⠶⢲⠋⠀⢰⡏⠘⠢⣤⣀⠛⢱⠆⣼⠈⡏⢘⡏
⠀⠀⠀⠈⠁⠒⠈⠉⠁⠀⠀⠀⠀⠀⠠⠤⠤⠀⠠⠔⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢀⡴⠋⣤⠋⠰⢠⡍⢉⠓⠲⠤⣤⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣟⡶⠒⠂⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢤⣈⠑⠂⠠⠊⡨⠓⠦⢦⢨⠏
⠀⠀⠀⠀⡠⣶⣶⠯⠷⣻⣿⡿⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⢔⢢⠆⠐⠒⠬⡈⠓⠒⠤⠧⣏⡐⠀⡌
⠀⠀⠠⠊⠙⢯⣿⣾⣻⣯⠟⠁⠀⠤⢀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠌⡀⠴⠋⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠙⠛
⠀⠐⠀⠀⠀⣀⠀⠉⠁⡠⢀⡾⡻⣷⣦⣄⣀⠀⠙⠺⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠠⠀⠀⣶⡟⣽⣷⡀⠈⠀⠈⠳⣕⣦⡟⠁⠈⠁⠉⠉⠁⠊⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠱⡀⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⣀⠀⠀⡰⠃⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢄
⠀⠀⠑⣯⠉⠁⠀⠀⢧⠀⢦⡀⠀⠀⠀⠈⣉⠽⠪⣍⣀⠴⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢌⠀⠀⠈⠻⠀⠀⠀⠈⢂
⠀⠀⠀⠙⠀⠀⠀⠀⠈⢧⠀⣈⠥⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠂⠀⠀⠀⠀⠐⢤⠔⠁⠠⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠄⠀⠀⣀⡀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠈⢆⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠶⠤⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⢤⡖⠰⡤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣨⡧⠀⠀⠠⠔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⢐⠴⢋⡽⢃⡬⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠒⠀⠀⠀⠒⠒⠢⠤⣀⣠⠴⠒⠺⣍⣤⣷⣥⡴⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⣤⣍⠳⡶⠞⠋⠁⠀⠈⠙⠊⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣨⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠀⠚⢸⠁
⠀⠀⠀⠀⢀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⠃
⠀⠀⢠⠾⡧⢈⠓⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠁⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⡾⢋⡴⠃
⠀⠀⢿⣘⣡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣡⠔⠋⠀⠀⢀⣀⣄⡀⠀⠀⠹⡄⠀⠀⠈⠐⠂⠳⠋⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣴⠋⠁⠀⠈⠀⢠⠀⡟⠀⠀⠀⠀⠀⢀⣀⡼⣿⣇⠤⠒⣒⡆
⠀⠀⠀⠀⣠⠐⠒⢴⡋⠿⣦⡃⠁⠠⠀⠀⠀⠀⠀⠀⠻⡘⠆⠀⣤⠤⢃⡴⠃⠀⠀⢀⣀⣤⡾⢞⣿⣿⣤⣦⡼⠗⠠⣄
⠀⠀⠀⠀⣇⠁⠴⢒⡛⡚⠛⠻⠦⣄⡐⠲⢤⡀⣠⠚⠁⠻⡙⠒⠒⠚⠉⢀⠀⢠⢷⡞⠓⣉⣾⣟⠁⠈⠉⠉⠑⣶⣀⣼
⢴⣲⠌⠁⠝⠓⠲⢿⣊⣉⠀⠉⠩⠭⠿⣓⡶⠚⠛⠲⡤⠚⢳⣀⣀⣐⣋⣉⣥⣤⢴⡶⡿⢧⣄⣨⣶⠚⢓⡖⠲⢿⣉⡹⠛⣆
⠀⠈⠑⠒⠤⢀⣀⠀⠀⠈⠉⠉⠙⠭⣉⡉⠢⣥⡤⠜⠧⢤⠴⠿⠭⠭⠽⠭⠥⠶⠚⠙⠒⠋⠀⠉⢉⣉⡉⠀⠀⠀⠉⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠢⠤⠤⠬⠭⠭⣖⣒⣶⣶⣶⣖⣀⣐⣐⣒⣒⣒⣒⣀⣉⣉⣉⡭⠥⠤⠴⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⠕⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢤⣶⢰⣿⠆⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⠋⠁⢤⣾⣿⢼⣿⣧⣤⡖⠀⠀⢤⠀⠀⠀⠀⣠⡆⣀⣧⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⡀⠀⣤⣠⣴⣫⣿⣿⣏⢻⡍⣠⣀⣤⣤⠈⠀⠀⠀⠘⢿⣿⣿⣿⣷⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⢻⣷⡀⣼⣼⣿⣿⣿⣿⣿⣆⠀⠙⣉⣹⠁⠀⠀⣠⣾⣦⡀⠉⠀⠁⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠷⠎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⣿⡆⢀⣠⣿⡿⠛⢡⡎⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠿⠿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣾⣿⡟⠁⣰⣸⣿⣠⡾⠀⠀⠃⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠰⡄⢀⠔⠀⠂⠊⠉⠀⠀⠀⠉⢻⣿⣿⠟⣉⡘⣷⣽⣿⡟⠀⢰⣟⡘⣿⡛⠃⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠂⠄⠀⢀⠀⠀⠸⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣽⣿⠏⠀⠀⡴⠺⣷⡼⣿⡿⡄⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠘⠀⠉⢄⡀⣴⣿⣿⣦⣾⣿⡿⢋⣩⣵⣿⡿⠉⠀⠀⠀⢀⢁⣿⣿⣹⡷⠄⢀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠚⣿⣿⣿⣿⡋⡩⠁⣠⡿⣻⠿⡻⠁⠀⠀⠈⢠⡟⠼⢿⣽⢷⡑⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⡟⢡⠞⠁⠀⠀⡰⠀⠀⠀⠀⠀⣾⠁⣸⣿⣾⣿⣿⣋⡗⢶⣦⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠋⠀⣠⡎⠀⠀⠀⠀⠀⡸⠀⣸⣿⣿⢏⣼⣏⡐⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⢰⡏⠀⣿⣿⣿⣿⡏⠉⠑⠠⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⣿⠇⠀⠀⠀⠀⢠⣧⣴⣿⣯⢱⣿⠋⠁⠙⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⠃⠀⠀⠴⠿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠙⠀⢀⢀⠀⣾⣿⣿⠀⠀⠈⡼⠃⠀⠀⠀⠀⢀⠀⠀⢀⠈⡀⠀⠀⣸⣿⠃⣾⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣄⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣇⠸⢿⣿⣿⣿⢶⣤⡃⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠁⠀⣰⣿⡏⣴⣿⣿⣿⣿⣿⡆
⠀⢀⣠⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡈⣿⣿⣦⣌⢻⣏⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⣦⣤⣈⣉⣉⣩⣩⣿⣿⣿⡇
⠀⢏⣩⣿⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣷⡄⠀⣉⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠈⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⡀⠀⠀⢠⠘⣿⣿⣿⣿⣿⣿⣄⣿⣿⣸⠀⢸⡆⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿
⠀⠀⠀⠴⣿⣿⣿⣿⠿⠿⠿⠿⠛⠁⠀⠀⠘⣧⠀⠀⠘⣷⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣦⣀⣄⠀⠁⠀⢀⣿⣿⣿⠏⢀⣾⠿⢿⣿⣿⡇
⠀⠀⠀⢬⠽⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⠇⠀⠙⢿⣿⣷⣿⣿⠀⠀⠻⠿⢻⡏⢸⡆⣄⣼⣿⣿⣿⠀⠞⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⣿⣿⠀⠀⠀⠀⠉⠛⢿⣿⢠⣶⠀⠀⠋⢠⣿⣿⣿⣿⡿⣀⠀⠀⢀⣴⣿⣿⣿⠿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣔⣾⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⡀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣷⡆⠀⠀⠀⠰⡄⢻⣿⡿⢿⣿⠿⠛⢿⣿⣿⣃⠀⣄⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠹⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣽⣶⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠙⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⢀⠀⠀⠀⠀⠘⢿⣿⡼⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣶⠋⠀⠀⣠⡄⠀⠠⠻⣧⣷⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠀⠐⠾⣿⣿⣠⢀⣄⠉⣉⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⠈⠉⠙⢾⡿⠿⠿⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠠⠂⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠱⣦⣄⡀⠀⢠⣄⣿⣿⣏⣠⠄⠀⢀⣠⣶⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣴⡄⢻⣿⣿⣿⠏⣦⣰⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣽⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠻⠛⠉⠈⠙⠟⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⡤⣞⣡⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠖⠊⠉⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⠙⠲⠤⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⢀⠄⠐⠂⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠐⠀⠀⠂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠐⠂⠉⠀⠀⠀⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠠⣤⠤⣤⣤⣤⣰⣀⣀⣂⣀⣀⣀⣀⡀⢀⠀⠀⡉⠀⠀⠀⣀⡀⠀⣀⡀⣀⣀⣀⣁⣀⣀⣀⣐⣠⣄⣀⣠⣥⣤⠤⣤⣤⠤
⠀⠀⠀⠀⠈⠉⠒⠦⠤⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣭⣭⣯⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣭⣽⣿⣽⣿⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣄⣸⡒⠃⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⣻⡽⣿⠁⠀⠀⣠⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⣿⣄⡻⠦⣀⡴⣻⣿⣿⡿⠿⢿⣿⡄
⠀⠀⠀⣀⣠⣴⣶⣦⣄⠀⠀⠀⠀⡠⠴⢶⣶⣄⣀⣀⣀⣀⣀⣠⢌⠋⢁⣤⣶⣷⣿⣿⣿⠇
⠀⠀⠘⢿⣿⡿⠿⠿⢿⣷⣤⣤⡾⠃⠀⠈⠛⠿⡿⣩⢙⣵⡿⠛⣤⣴⡿⡿⠁⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⣦⣶⣾⣉⡆⠘⠿⠗⢺⣿⣿⣿⣿⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⣿⡿⣿⣿⣿⡗⣦⣤⣼⣿⡿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠃⣿⡿⠋⠃⠽⢿⣿⡿⣽⣦⣨⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⢀⣾⡟⠁⠀⠀⠀⠀⠀⣾⡿⠁⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠉⠙⠲⢤⣀⠀⠀⣸⠏⠀⠀⠀⣈⣿⠇
⠀⠀⠀⠀⠉⠁⠲⠀⠄⠀⠀⠀⠀⠀⠘⣷⠀⢀⣀⣀⣉⣶⠞⠉⠘⠻⠶⠋⠁
⠀⠀⠀⠀⠀⠀⢂⢢⡄⢠⠀⠀⠑⠀⢈⠀⠸⢭⠉⠉⠉⠀⠀⠀⢀⣰⣄⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠙⠻⠿⠛⠛⠻⠿⠟⠛⠒⠛⠛⠘⠒⠂⠋⠑⠛⠻⠉⠋⠛⠙⠃⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⠀⠰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠑⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡉⠀⣸⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠑⠕⠙⣬⣇⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢛⣷⣄⠀⠘⣞⡟⠀⡴⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣇⣄⣑⣒⣒⣒⣒⣒⣶⣥⣬⡵⠢⣾⣯⣽⣆⡇⠀⣅⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠅⠘⠒⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠌⠚⠥⠤⠤⠤⠑⠚⠤⠵⡄
⠀⠀⠀⠀⠀⠀⠀⢧⠀⡠⠠⠤⠠⠄⠀⠠⠤⠄⠤⠤⠤⠀⡀⠠⠠⠤⠤⠤⠤⠤⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⢀⣀⡁⠀⡀⠀⢀⠀⡀⣀⠀⠀⣀⠀⠀⣀⢀⠀⢀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠢⢸⢒⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇⠀⠀⠰⠒⢢⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠉⠀⠀⠀⠀⠀⢣⢱⠀⠀⠀⣧⡀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠀⠀⠀⠀⢀⡴⠃⣜⡔⠲⠀⡗⠷⠂⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⠀⠤⠀⡔⠁⠀⠀⠻⠀⠰⡀⡇⠈⠁⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⢸⠀⠚⠀⢇⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠤⠜⢸⠀⠀⣠⣊⣑⣖⣉⣑⣖⣉⣢⡇⠀⢀⠐⠄⠚⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⠉⠉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⢶⣆⠀⠀⠀⣀⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢘⠁⠀⠈⠏⠀⠀⠀⠉⠁⠉⠁⠀⣸⣷⣤⣷⣾⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠘⡛⣿⣿⠀⠰⣴⣷⣶⣾⡇⣠⠠⣶⣿⣿⡿⠟⠛⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠊⣩⣿⣄⣰⣛⠋⠀⣹⢧⣭⣇⠉⠉⠉⠀⠀⣠⡀⠘⠻⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠁⠋⠈⢉⣿⡿⠿⠃⢸⠃⠈⠃⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⡦⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⠿⠲⠶⣶⣶⣾⡿⠃⣤⣠⡿⠋⠀⠀⣀⠀⠀⡼⠀⠀⠀⢀⠐⢤⣀⠀⣈⣷⣄⡀⠀⣀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠁⢀⠤⢺⡿⢁⣠⣿⠟⣡⣴⣾⣿⣿⣏⣴⠇⠀⠀⠀⣾⣠⣾⡿⠋⠉⠉⠛⢇⠘⠛⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠠⣦⠀⠀⢠⠀⠀⠀⣠⠟⣀⣴⠟⠁⣼⣿⣿⡿⠃⠸⣿⡏⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠰⡿⠀⢰⣧⣖⡀⢀⢡⣴⣟⠁⠀⠸⢻⡇⠈⠁⠀⠀⢿⣧⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⠀⠀⠀⣽⡄⠋⠉⠻⣄⡀⠙⠿⠛⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠙⠷⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢋⡿⢷
⠠⣄⣀⣀⠀⢀⣠⣴⣿⣿⣧⠈⠆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⡿⠚⠁⡿
⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⠀⢸⣿⣷⣄⡀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠸⠿⠟⠛⡿⠟⠁⠀⠀⠀⠀⠹⣦⡄⢸⡏⠻⣿⣿⣦⣄⡈⢿⣿⣧⡔⠀⣀⠀⡀⠀⠀⠐⠢⣿⣾⣁⣠⠆⠀⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠌⡇⠀⠈⠻⣿⣿⣿⣿⡟⢿⣷⠾⡁⠀⠙⢶⡲⠤⠶⢿⣿⣿⠁⠀⠀⠲⣤⣌⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢇⠀⠀⠀⠘⣿⣿⣿⠀⠘⠿⢦⣀⠀⠀⢄⠙⢄⠀⠀⠙⠿⠿⠖⠚⠋⠉⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣠⠘⣦⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠈⠉⠓⠾⣷⣌⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣄⡜⢷⣄⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣍⠙⠮⠻⣿⣿⠀⠀⢠⣤⣴⣦⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡆⠀⠙⢿⣇⠀⠀⠙⠿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣎⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣟⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⡀⣀⣀⡤⠤⠤⠤⠤⠤⠴⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠹⡀⠀⠀⠀⠀⠀⠀⣔⠙⡀⠀⡘⡅⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⢀⡤⠟⠒⠈⠉⠁⠒⠲⡄⠂⠐⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⢍⠑⠂⠤⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠀⠄⡀⢀⠙⢄⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡰⠁⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠈⢣⠀⠀⠀⠠⠈⠳⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⣱⡄⠀⠈⢄⣁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠒⠒⢄⠀⠸⠛⠒⠀⣠⡾⠃⠈⡗⠓⠊⠁⠸⠦⡄⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠣⡀⢀⠜⠀⠀⠀⣠⡾⠋⠀⠀⢰⠀⠀⠀⠀⠀⣀⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠁⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⣠⠗⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠊⠉⠀⠀⠀⠀⣀⡤⠖⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣠⡴⠚⣩⡿⣿⠉⠣⠤⣀⣀⣀⣀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⢸⣇⣤⠞⡿⠁⣿⡇⠀⠦⠄⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⣀⡠⠔⠚⣇
⠀⠀⠀⠀⠀⠀⠉⠀⢸⡇⣰⢿⡇⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠉⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⢸⡷⠀⠉⠁⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠇⢣⡀⠀⠙⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⣄⠠⣠⠀⠈⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠙⠣⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠰⠖⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣖⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⡶⠖⠀⢠⡤⠀⠐⠖⡖⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠱⡄⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡌⠀⠑⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⠀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡈⠧⡏⢇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠿⢷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⣄⠈⠉⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠁⠒⠂⢀⢀⢸⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣰⡄⢠⣼⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣦⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠠⠀⠠⠆⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⢿⣿⣿⣶⣤⣈⢻⣿⣿⣿⣟⡉⠉⠉⠙⢻⣿⣿⣷⣧⠀⠀⠀⢀⡴⠠⠠⠀⠀⠀⠀⠀⢀⠀⣿⠁
⠀⠀⠀⠀⠠⣴⣾⣿⠿⠋⠁⠀⠀⠲⠛⡉⠟⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠹⣿⣿⣿⡂⠀⠀⡋⠂⠀⠀⠀⠀⠀⠠⠀⣁⣿⡶
⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠠⢴⣤⣄⣠⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⠁⣴⣾⡇⢀⣀⣤⡴⠂⠉⣰⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣟⣦⡀⠀⠀⠀⠉⠙⢿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣾⣿⣿⣾⣿⣛⣤⣄⡒⣾⣭⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣤⣀⠀⠀⡀⢈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣠⣾⠿⠟⠛⠃⠁⠚⠛⠛⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠾⠷⠶⠿⠾⠖⠛⠛⠛⠛⠿⠟⢛⣻⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢾⠟⢋⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠄⠁⢠⡏⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⡼⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⢀⡷⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣠⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣶⣶⣶⣶⣶⣖⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣒⣶⣶⣶⣶⣶⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣟⡿⣿⣿⠿⠿⠛⠛⠻⠟⠛⠛⠛⠛⠻⠿⠻⢿⢟⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⡄⠉⢳⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢐⡀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⠀⠀⢀⣠⣀⡈⢷⡄⠀⠐⠀⠀⣰⠃⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡃⢉⣿⠀⠙⠷⠶⠶⠚⣡⣏⡹⠈⠛⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⣙⣓⣿⠀⠀⠀⠀⠀⠐⣯⠢⡅⣢⠜⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢺⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡤⡤⠴⠋⠀⠠⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣇⡀⢸⣒⣔⣶⣘⣆⡠⡤⠀⠀⠀⠀⣰⣶⣶⣼⡆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣒⣻⣿⣿⣻⣶⣒⣦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠉⠉⠉⠹⠿⣛⢛⡛⠛⢛⣛⡛⣛⣛⣛⣛⣛⠛⠛⢻⠋⠋⠋⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⡉⠉⠉⢁⣀⣀⣀⣈⣉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇
⠀⠀⠀⠀⠐⣶⡀⠀⣹⣦⠀⣴⠁⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅
⠀⠀⠀⠀⠀⢻⣿⡷⣾⠗⣿⡿⡄⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣷⢸⢹⣿⠃⣇⣀⣀⣀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣮⣼⣿⠀⠠⠀⠀⡆⢰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣠⣤⣦⣤⣥⡼⠿⠻⠛⠻⢳⣶⣶⣶⣶⣶⣶⠶⠿⠾⠿⠿⢦⣷⣶⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢻⣯⣤⣤⣤⣤⣤⠜⠛⠛⠛⠛⠻⠛⢤⣤⣤⣤⣤⣤⡿⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⣤⣶⣴⣦⣤⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⢄⠀⠀⠀⠁
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠰⡄⠈⠀⠀⢄⠐⠀⠀⠂
⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠀⠄⠓⠀⠐⠀⠀⠀⠀⠁⢀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠙⢿⡿⣿⣻⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠰⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⡐⠂
⠀⠀⠀⠀⢠⣿⣿⣿⠇⢄⡇⠘⡿⡿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⣿⡜⠁⠀⠻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣷⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢈⠉⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠈⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠀⠋⠀⠃⠈⠀⠉⠀⠛⠀⠃⠀⠀⠀⠀⠀⠃⠘⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⢤⣀⣀⣀⠀⠀⠀⣠⠔⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠃⠀⠀⣀⣀⣀⡀⠀⠉⠙⠛⠋⠁⠀⢀⡼⠓⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡥⠴⠒⠛⠉⠉⠉⠉⡭⠉⠉⠉⠓⠒⠦⠤⣤⣾⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⠴⠋⠱⠖⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⡽⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢰⣠⠟⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡾⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠠⢻⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢹⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⡇
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡼⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⠀⠐⠧⠴⠒⠒⠒⠺⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⢸⡀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣷⣤⣀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣈⡳⢤⣄⣀⣀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠐⡆⠀⠀⠀⠀⢀⣰⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⠎⠀⠀⠀⠀⠀⣾⡏⢸⠁⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠗⠁⠀⠀⠀⠀⠀⢸⣿⢀⠇⢠⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠀⣠⣤⡄⠀⠀⠀⣾⣿⡞⠀⣾⢇⠎⠀⠀⢀⣀⠀⡠⠚⠉⢀⡤⠖⠂⣩⠟⡿
⢀⣤⣄⡠⡀⠀⠀⠁⢹⣿⠞⣴⣿⠁⣀⡀⠀⢻⣿⠀⢸⣿⠏⠀⠀⡆⠙⣿⡿⠀⠀⡴⠃⠀⣠⠞⠁⢠⡇
⢠⠿⠣⣅⠓⢰⣀⣀⠈⠉⢰⣿⠇⣼⡏⡼⢀⡞⠻⡤⢾⣿⠀⠀⡼⢧⣠⡿⠃⠀⠀⣳⢶⠊⠀⠀⢀⡜
⠈⢹⠓⠈⠳⢌⡁⢠⡇⠀⢸⣿⠀⣿⣏⣠⠊⠀⠀⠀⢸⣿⣠⠞⠁⠀⠀⠀⠀⠠⠊⠁⠀⠑⠒⠛⣉
⠀⠀⢡⡏⠀⣨⣹⠲⢍⡀⠀⠉⠉⠈⠉⠁⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⡏⠁⠀⠳⣤⡀
⠀⠀⠀⠉⠛⠁⠁⠀⠀⢉⣀⣀⣀⣀⣀⣀⣿⡏⠀⠀⣀⣀⡤⠤⠈⠁⢠⣤⠊⢹⣿⠁⣿⡇⠀⠈⠒⠒⠋⠺⠃
⠀⢠⣶⠛⢢⡀⠀⠀⠐⠉⠀⠀⠈⠉⠉⣻⣿⠛⠋⠉⠉⠁⠀⠀⠀⠀⣾⡏⠀⣼⡇⢰⣿⠃⠀⣀⡀
⢠⣿⢁⣴⣿⠁⠀⣰⣦⠀⠀⣴⡆⠀⠀⣿⡏⠀⢀⣾⠂⠀⣠⡀⠀⠀⡿⠃⠀⠈⠀⢸⣿⠀⠀⣿⡟⠉⢉⣷
⠘⠟⠋⣽⡟⠀⣰⣿⠇⢀⣼⣿⠇⠀⡰⢻⣷⣠⢾⣿⠀⢰⣿⡇⠀⡼⠁⠀⠀⠀⠀⢸⣿⠀⢸⣿⠇⠀⣰⣿
⠀⠀⠀⢿⣇⡼⠉⢿⠴⠋⣼⣿⠀⡼⠁⠀⠉⠀⠘⢿⡴⠚⣿⠀⡼⠃⠀⠀⠀⠀⠀⠐⢿⣀⠼⠟⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢘⣆⣀⣳⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠃⣰⠋⠹⠉⠉⠟⠴⠃⡀⠀⠀⣀⣀⣤⣤⡤⣀⣀⡀
⠀⠀⠀⠀⠀⣤⡄⢀⡀⠀⡤⢼⣄⣿⠀⠀⠀⠀⣀⣤⣴⠿⣿⣿⣭⢽⣶⢛⣿⣉⣿⣉⣿⢲⣄
⠀⠀⠀⠀⡶⣍⠂⢸⡓⡆⠻⠸⠁⠀⠀⣠⡿⠛⠛⠻⡻⠿⠽⣷⣻⣏⣹⣿⡾⣧⣼⣯⣽⠟⠟⠃
⠀⠀⠀⠀⡨⢎⠃⠂⠀⠈⡀⢢⢠⠀⢠⣿⣵⠠⢀⠀⠀⠀⠀⠀⠉⢻⢷⣿⡶⣿⣰⠏⠙⠀⠀⡄
⠀⠀⠀⢀⠭⠒⠿⣲⣾⠿⣿⣾⣿⡿⠟⢛⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⢀⣻⠃⠁⠁⠀⠀⣰⣚⡇
⠀⠀⠀⠐⠋⠠⢺⠋⠉⠀⢸⣿⣏⠀⠀⠀⠀⠂⠀⠀⠙⠻⠿⣶⣼⣦⣬⣾⣀⢀⣤⡶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⢸⣦⡀⢴⣿⣿⣼⣦⣤⣀⡀⠁⠀⠀⠀⠀⠀⢂⡉⢿⣿⣿⢿⣿⡁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⢷⣿⡿⣿⡷⠟⠿⣷⣬⣽⣶⡦⠀⣄⣠⣤⣤⢛⣿⣿⡼⠱⡉⣇⠀⡠⠶⣅⣿⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⠿⢿⣬⣦⣄⠈⠛⠛⠿⢿⣿⣿⡟⢛⣭⣘⡙⢶⠶⠞⠃⣸⠒⠲⣿⣧⡔⠉⠘
⠀⠺⠇⣠⡶⠛⠛⠲⢌⡁⠀⠀⠈⠙⠦⣍⣹⣷⠉⢙⣿⠿⠋⠻⢬⣹⠇⠀⠀⠀⠀⢙⢀⠰⠛⢻⡃⠉⠻
⠀⠀⠰⣟⡉⠉⠁⠒⠤⣵⡀⠛⠓⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢤⣴⠉⠀⠀⠀⠀⠀⠀⢷⣥⣖⣚⣓⣫⡞
⠴⡶⠀⢀⣍⡓⠒⠒⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣁⣀⣀⣀⣀⣾⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠙⠉⠉⠉⠛⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠙⠉⠉⠉⠉⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⣯⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⣧⠀⠀⠀⠀⡇⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⣦⠀⠈⢧⡀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⠚⠁⠀⠀⠈⢳⣄⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣤⣴⠆⠀⠀⠰⣶⣏⢉⣷⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢰⠟⢱⡆⠙⣯⡉⠀⡿⠀⣿⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⢸⠏⣧⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠈⠳⠛⠁⠀⠈⣻⣤⣟⠀⣿⠀⠀⠀⣼⠹⡇
⠀⠀⠀⠀⠀⠀⣿⠀⣻⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡟⢻⣆⣀⣄⠀⠀⠀⠀⢠⣾⠉⣹⣽⠷⣿⠀⠀⠀⣟⠀⣿
⠀⠀⠀⠀⠀⣤⣬⣽⣥⣤⡀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⣩⣟⣥⡀⠀⠀⠀⠈⠻⣏⠉⣿⠀⣿⠀⠀⣤⣬⣯⣥⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⠀⢰⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⢯⣀⣿⠀⠀⠀⢠⡴⢬⡻⣯⡀⣿⠀⠀⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⢸⡇⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢶⣞⣉⣀⣀⣀⣀⣩⣤⠶⠶⣤⣼⣦⣼⣃⣀⣉⣻⡶⠴⡇⠀⠀⠀⣿
⠀⠀⣠⠶⠶⡏⠀⠀⠀⢸⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠶⣇⠀⠀⢸⠷⠾⠿⠿⠿⠿⠿⠶⠶⡇⠀⠀⠀⢹⠶⠶⣄
⣠⡞⣁⡀⣀⣙⠂⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣙⣛⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣛⣓⡋⢀⣀⣈⣳
⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣟
⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹
⠀⠙⡟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠙⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠋⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⠀⠈⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠋
⠀⠀⠀⢻⠀⢀⡴⠛⠛⠻⢦⡀⢠⡿⠒⣶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⢀⡴⠛⠛⠳⣦⠀⠘⡇
⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠘⡇⢸⣇⣀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢰⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢰⡏⠉⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠶⢶⡄⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⡟⠀⢀⣀⣀⡀⠀⠀⣿⡀⢸⡇⠀⣛⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣾⢁⡴⠋⢉⡾⠛⠃⠀⣿⠉⢹⡏⠉⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⢰⡇⣾⠁⠀⠈⣷⠀⠀⠀⣿⠀⠸⣧⣤⣿⠀⣿⠀⠀⠀⠀⢸⡇⢰⡇
⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⣠⣤⣼⡇⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠈⢷⣏⠀⠀⠀⠸⣇⠀⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⠘⡇
⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⡄⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢀⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⢸⡇⠀⠙⠛⢻⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⢺⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⣿⠀⠸⣆⡀⠀⢀⣼⠃⠸⡇⠀⠀⠀⢸⡇⢀⣴⠖⠛⠻⢦⣄⣠⠶⠛⠛⠶⣄⣠⡴⠞⠛⠲⣦⡀⣿⠀⠀⠀⠀⣿⠀⠹⣄⡀⠀⢀⣼⠃⢸⡇
⠀⠀⠀⣿⠀⠀⠈⠙⠛⠋⠁⠀⢐⡇⠀⠀⠀⢸⣇⣼⣁⣀⣀⣀⣀⣹⣇⣀⣀⣀⣀⣸⣏⣀⣀⣀⣀⣈⣧⣿⠀⠀⠀⠀⣿⠀⠀⠈⠙⠛⠋⠁⠀⢘⡇
⠀⠀⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣿⣿⣾⣿⣾⣿⣾⣿⣿⣿⣾⣶⣶⣶⣶⣷⣤
⣿⣿⣿⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣿⡿⠃⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣶⣶⣦⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⡿
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⢀⣚⣿⣿⣿⣿⣿⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠉⠉⠉⠙⠋⠉⠁⠀⠀⠀⠈⠙⠿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠉⠉⠻⣿⡟⠛⠛⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣶⣀⣤⣀⠀⢙⣿⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣈⠙⠉⠉⠉⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠿⡄⠀⢀⢀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢠⣤⣤⡤⣠⡄⠀⠘⠃⠀⠀⡁⠀⢀⠀⠀⠺⠿⠂⠀⢀⣄⣀⣄⡀⠀⠀⠀⠀⡄⠀⠈⠀⢠⡄
⠀⠀⠸⢿⣿⡽⠿⠓⠀⠀⠀⠀⠐⠛⠉⠙⠋⢢⡀⠀⠀⢀⣾⣶⣶⣾⣿⡆⠀⠀⠜⠱⢀⠀⢰⡵⡰
⠀⠀⠀⠀⠁⢻⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⠈⠉⣿⣿⣿⣿⡆⠀⠀⠓⡁⢺⠦⠚⠧⠘
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢠⣤⠤⠀⠀⠁⠀⠀⠀⠀⠙⡿⠀⠘⠇⠀⠀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⢠⣻⣼⣃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⣏⠋⠀⠀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡾⢀⣀⣀⢷⠀⠀⠀⡀⣤⢄⡐⠊⠉⡉⢿⠄⠀⢀⣄⣠⣤⣴⠀⢀
⠀⠀⢰⡧⠛⢡⢤⠘⠿⣧⠀⠘⢻⣯⣿⣯⡼⠃⠀⠰⠡⢷⣓⢀⣀⠀⠓⠋⠀⠀⠉⢻⣿⡿⣯⠔⠉
⠀⠀⠘⡧⣴⠚⢀⣌⣦⣾⠀⠀⢰⠍⠋⢹⠀⠀⠀⠀⠀⠩⠉⠉⠀⠀⠀⠀⡀⠀⠀⠐⠛⢻⠞⠇
⠀⠀⠀⠑⠈⠓⠿⠿⠛⠁⠀⠀⠐⠶⠿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟