Floral leaf Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⠀⠀⠀⠀⠀⠀⠘⢷⡄⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣥⠀⠀⠀⠀⠀⠤⠶⠲⣽⡿⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣷⡀⠀⠀⣀⠀⠀⠀⠀⡀⠭⡫⢐⠀⠀⠀⢀⣀⣠⡴⠦⣜⣉⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⣦⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢢⠀⢠⠀⠀⠀⠀⠀⠠⣄⡀⡈⠀⢠⣮⣃⠀⠀⠀⠀⠨⠷⡖⢍⠔⠀⠀⠀⢉⣡⣤⣄⣀⡉⠳⠄⠁⠀⠀⠀⠀⣀⠸⣆⠘⠟⠳⠖⠒
⠀⠀⠀⠀⠀⢦⢡⡜⡞⠀⠀⠀⠀⠀⠀⠙⠿⣴⡈⠃⠂⠀⣠⠀⠀⠺⠥⣐⡡⠂⠀⠀⠈⠛⣁⣠⣀⣈⠙⢦⡀⠀⠀⠀⠀⢢⡘⣧⠈⠖⠒⣛⠋
⠀⠀⠀⠀⠈⢦⠱⡜⡼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠀⠈⠻⢦⡉⠀⠀⠀⠰⣄⠹⣌⠓⣚⣭⠥
⠀⠀⠀⢈⠑⢦⡑⣤⠃⡞⣰⠃⠀⠀⠘⠳⠢⢦⢦⢠⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⢷⡀⢉⣥⠴⠂
⠀⠀⠀⠀⢍⣲⢍⡪⡜⡱⣡⣲⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠉⣩⣴⠶⠋
⠀⠀⠀⠀⠐⠬⣝⣓⣘⣔⠵⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡀⢹⡄⢻⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⡿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⡛⠀⠀⢤⡀⢻⡌⣿⢸⡆⡿⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⣿⣿⣿⣿⠟⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢻⣆⢿⣸⣿⣧⣇⡿⢀⡴⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣾⢿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣂⣀⠙⣏⣿⣿⣿⡿⣡⢟⣵⠆⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠘⢟⠛⢿⣿⣿⣧⣾⠟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠀⠉⠭⣵⣮⣽⣭⣭⣥⡥⠛⠁⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣦⠀⠀⠈⠛⠛⠟⠋⠉⢁⣀⡀⠀⠀⣠⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⢠⡄⠀⠉⠙⠛⠛⠁⠀⠀⠀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠛⠧⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡛⣡⣤⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⣴⠀⠀⠀⢀⡄⠀⡰⣂⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠆⠀⠋⠀⠀⠀⠀⠥⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠤⠀⠀⣄⠀⠁⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠠⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠀⠀⠟⠀⢀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⡀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠠⠠⠊⠔⠁⠀⢠⠀⣠⠇⠐⢁⡤⠖⠃⠀⠀⠀⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠂
⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠱⠅⠐⠚⠣⠠⠤⣤⣠⡄⠂⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢨⡀
⠀⠈⠂⠀⠀⠀⠀⠀⠀⣘⣻⣿⣋⣙⣻⣧⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠰⠊⠉⠀⠀⠁⠈⢻⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⢄⡀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣸
⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣧⠀⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠄⠁⠈⠀⠀⠀⠀⠀⠴⠀⡄⠀⠀⠀⠀⡇
⠀⠀⠂⠀⠀⠈⠃⢰⠀⢰⠆⠀⠲⢄⠀⠀⠀⠀⡄⠊⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡐⠀⠸⡄⢀⠜
⠀⠀⠆⠀⠀⠀⠀⠀⣰⠃⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⢹
⠀⠀⠀⠈⠶⠒⠖⠊⢁⠂⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡇⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⢀⣴⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠷⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣟⣣⡉⠐⢻⣽⣿⡀⠀⠀⠉⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⡇⠈⢣⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣣⣫⡿⠏⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠟⠻⠛⠋
⠀⠀⠀⠀⠀⡀⠀⢩⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠐⠋⠁


⡿⠿⢿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿

⠃⠈⠳⠌⠉⠁⠀⠀⠠⣦⠀⠈⠛⣫⣥⣄⡀⠀⠀⠀⣤⡿⠿⢞⡿⡵⡺⠇⠀⠀⠀⠛⠿⣿⣷⡄⠋⠀⢠
⠘⢆⡄⠀⠀⡹⠄⣀⠀⣤⡶⣤⡀⢴⣭⡉⠉⠀⠀⠞⠀⠀⢠⣶⣝⠂⠪⠁⠀⠲⣿⣶⡀⠠⣍⠋⠀⣤⠈
⠠⠷⠈⡇⢤⡁⠇⠳⠉⠀⠀⠹⣿⣼⡟⣛⠂⠀⠀⠀⠀⣤⢾⣋⣿⡆⠀⠀⠀⢀⣀⣈⡁⢀⠀⢀⣿⣿⠀⣀⡐
⢖⣈⡔⠒⢂⠐⡃⢆⡆⠤⠀⠀⠈⠙⠁⣿⣷⠀⠀⠀⣶⢗⡟⠨⠓⣕⠀⠀⢠⣿⣿⠟⠁⠘⠀⢸⣿⠃⠀⠖⠹
⡢⠗⡔⡂⣄⡶⠐⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠁⢮⡇⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⣄
⢠⣼⢷⠙⣠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠷
⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣔⠃⢀⣴
⣠⡀⠀⠻⠟⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡉⢀⠞⢸⣿
⠟⠃⠀⠀⣴⡆⠻⣿⠆⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣨⣄⢸⡇⠈⠉
⠀⢰⣶⣤⣌⠀⠀⣶⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠌⠥⠀⠀⠀⠀⠈⣿⠏⠀⠁⣀
⢠⡄⠀⠘⠋⠀⠀⠀⠉⢀⣀⣀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⣄⠀⢘⡂⣫⠄⠀⣠⠄⠀⠉⠀⠀⢀⣸⡆
⠀⠀⠀⠀⣠⡇⠀⠀⠰⠛⠉⠀⠀⠀⠸⣿⣷⡀⠈⠛⠛⠛⠁⠀⠀⠪⢾⢄⡉⠒⠀⡐⠥⠀⠀⠀⠀⠀⠘⣿⡇
⠀⣠⠀⢰⠟⠀⠈⣉⡛⠓⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⠀⢠⠐⡊⣘⠉⠤⠄⢁⡀⠆⠀⠀⠀⣆⠀⣿⠃
⠀⢹⣤⠀⠀⠚⠛⠛⠛⠓⠂⢀⣀⣀⣀⣶⣦⠀⢀⣴⣿⠷⠈⠛⢋⡄⠉⠳⡀⠚⢀⠁⡉⠃⠀⠀⠀⠹⢷⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣿⡀
⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢠⣿⠀⠀⠀⣤⠀⠀⠀⠻⣷⣄
⠀⠀⢠⣾⠁⠀⠀⠀⣾⡐⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆
⠀⠀⣸⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⠀⠀⣠⣶
⠀⢰⣿⠃⠀⠀⠀⠀⢸⣧⠀⣤⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⣠⣾⠋⠀⣿⣠⣾⢫⡏⠀⠀⢀
⠀⢸⣿⠀⠀⠹⣄⠀⠀⢻⣄⠇⠀⠀⠀⠀⢹⣇⠀⠀⠀⣴⡿⠁⠀⠀⣾⡿⠃⣼⠃⣠⡶⣿⡇
⠀⢸⣿⠀⠀⠀⠈⠳⣄⠘⣿⠀⠀⠀⠀⠀⠸⣿⡀⠀⣸⡟⠀⠠⠀⠀⢻⡇⢀⣿⣿⢋⣴⡏
⠀⢸⣿⠁⠀⠀⠀⠀⠈⠳⣽⣆⠀⠀⡀⠀⠀⣿⠇⣰⡟⠀⠀⠃⠀⠀⣼⡇⢸⡿⢻⣿⣿⠁
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⡇⠀⠀⣿⢀⣿⠁⢀⡞⠀⠀⢠⣿⢃⣿⠃⣿⡿⠁
⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⠃⠀⠀⣿⢸⡿⠀⣸⠃⠀⠀⣼⣿⣾⣯⡾⠋
⠀⠀⠀⢻⣄⠀⠀⠀⠐⢠⣄⠀⣿⡇⠀⠀⢰⡿⣸⡇⢠⠟⠀⠀⣸⣿⣿⡿⠛⠁
⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠈⠙⣿⡷⠀⢀⣿⠃⣿⠀⣾⠄⠀⣰⣿⡿⠟
⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⣿⡟⣀⣾⠇⢀⣿⡀⠏⣠⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣶⣴⣿⣿⡿⠋⠀⣸⡟⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⡿⠀⠀⣴⡟⣱⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣼⢏⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡾⣡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣾⠃⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣤⣤⣤⣄⣄⡀⣀⣀⣤⣤⣤⣤⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠃⠀⠀⣀⣤⣶⡿⠛⠛⠉⠉⠁⠀⠀⢀⣿⣭⣿⠟⠻⠛⠛⠉⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⠋⢀⣴⣾⠟⠉⠀⠀⣀⣤⠴⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣿⣿⣥⣄⣠⣔⣋⣁⠀⠀⠀⣤⣿⣻⣿⡟⠀⢀⠠⠊⠀⠀⠀⢠⣼⡿⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⣋⣤⣶⣤⣬⣭⣉⠉⠉⢹⣿⠿⢿⣾⣿⣿⠟⣿⣇⡴⠋⠀⠀⣀⣤⣶⣿⣯⡀⠀⠀⠈⠙⠹⢶⣦⣀
⠀⠀⠀⠀⠀⣴⡟⢁⣶⣿⠿⠛⢹⣇⠀⠈⠻⣷⣼⣾⠻⢷⣾⣿⠛⠉⡀⣿⣿⣶⣶⡾⠿⠛⠛⠛⠛⠛⠛⠻⢶⣶⡆⠀⠀⠉⠛⠻⢶⣤⣄⡀
⠀⠀⠀⢀⣾⠏⣴⣿⠟⠁⠀⠀⠈⣿⡄⠀⠀⠫⠙⠿⢿⣦⣽⣿⣦⣤⣿⣟⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⢤⣄⠀⠀⠀⠈⠙⠛⣿⣷⣶⡤
⠀⠀⠀⣼⠏⣸⣿⡏⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠧⣀⣿⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⣠⣤⡶⠞⠋⠁
⠀⠀⣸⡏⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⣴⡟⠁⠉⣸⣿⣶⡿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢀⣠⣴⡾⠛⠉
⠀⢰⡟⢠⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣸⡟⠀⠀⠜⢁⣿⠋⢿⡌⠛⢿⣷⣤⣀⠀⠀⠀⢀⣴⣿⣿⠾⠿⠋⠁
⠀⣿⠁⣾⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠃⠀⠊⠀⢸⣿⠀⠈⠃⠀⠀⠙⣿⣿⣿⣷⣷⣶⠏⠁
⠀⠋⠀⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠶⠿⢿⣿⡀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⡾⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠐⠀⠀⢀⠀⠀⢠⡆⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠈⢤⡄⠀⠀⠀⠀⢠⡮⠀⠀⠀⠀⢀⠀⢰⡇⣾⠶⠂⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡀⡄⠀⢀⡀⠀⣀⠰⡇⢸⣅⠠⠄⢀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠈⠷⠂⠐⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⢻⡀⠹⣏⢀⣀⠄⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣈⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠙⠂⠉⠉⠀⠀⠀⠈⠀⠀⠀⢠⣶⠀⠀⠀⢀⡀⠀⠀⠀⠀⠹⠛⠟⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠘⠁
⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠈⠉⠑⠠⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢣⠀⡤⠊⠀⠀⠀⠀⠀⠀⠻⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⡀⣀⠔⠀⠀⠀⠀⠀⠀⣾⡏⢀⠀⠀⠀⠀⠘⣌⠂⠗⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢤⣀⡤⠀⠀⢻⢡⠀⣇⡉⠀⠀⠀⠀⢀⣰⣿⣿⡶⠈⠀⠀⠀⠀⡀⠌⣿⣠⠔⡂⠀⠀⠀⠀⠀⢱⡄⠀⠀⣀
⠀⠀⠀⠀⠠⠄⠠⠍⢆⠀⠀⠀⣾⠇⠋⠀⠀⠀⠀⠀⠀⢹⠟⠋⠀⠀⠀⠀⠀⠀⢳⣤⡇⢀⣀⡀⠀⠀⠀⠀⠀⠘⠓⡄⠊
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢁⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠉⠑
⠀⠀⠀⠀⢘⡆⢀⣤⠀⡁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠑⠈⢿⠀⠟⠀⠰⠅⣠⣄⠀⢀⣠⡴⠂⠠⠃⠀⠠⠺⠏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧⠚⠝⠻⠇⠐⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢰⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠤⣄⡄⠠⠂⠐⠀⡤⠊
⠀⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠂⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡀⠀⠉⡓⢄⣧⡊⡀⠐
⠀⠀⠐⠽⠍⢀⠀⠢⣄⠀⠀⠀⠃⢀⣰⠶⣄⠀⠀⠀⠀⠀⠹⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠁⠐⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠓⠬⡳⡀⠰⡄⠀⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢊⠾⠶⡒⠲⠖⠆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠃⢰⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠲⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⢄⣴⣾⡿⠃⠀⠀⠀⠀⡸⠋⠤⠊⣤⣤
⠋⠁⠀⠀⠀⣀⣤⣤⡀⠔⠀⠀⠀⠀⠘⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠈⢲⣶⣦⣄⡀⠈⠙
⠀⠀⠀⢠⣾⣿⠿⠋⠐⡀⠀⠀⠙⢷⣦⣌⢿⡆⠀⣷⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠷⠒
⠀⠀⠀⠟⠉⠀⣀⠰⠐⣿⣦⠀⠠⣤⣬⣿⣍⢫⡀⢹⣿⡆⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢠⡀⢠⡀⢠⡀
⠀⠀⠀⠀⣴⣿⠏⠈⣦⡘⡿⠀⠀⠀⠉⢉⣥⣤⣤⡀⢻⠇⠀⢠⠀⢿⡿⠀⣴⡟⠀⠲⢦⣌⣷⠀⢷⡈⢿⡄⠹
⠇⠀⠀⢸⠛⠁⣠⡆⢻⣷⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠀⠀⠘⣷⣄⣁⢸⡟⠁⠀⠀⢠⠶⠋⣠⣾⠃⣨⡗
⠀⠀⠀⠀⠀⢰⣿⡇⠀⠟⠀⠀⠀⠀⠀⣴⣶⡶⠆⣀⣀⣀⡀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠚⠉⠀⣼⠟⠁⠸
⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⢩⣔⠊⠉⡉⠤⠚⠛⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠈⣷⣦⡀⠙⢿⣿⣶⣤⠀⠀⠀⢴⣾⣶⡦⠤⢨⡀⠀⠀⠀⢻⣦
⢀⣴⡟⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠙⠿⣷⡄⠈⠻⠷⠄⠀⠀⠀⠀⢠⣴⣦⣄⠈⠡⠂⠠⣿⡗⠀⠀⣠⣤⣍⣠
⡾⠟⣠⣾⠀⠀⠀⠀⣿⣧⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠁⢉⣾⡇⠀⠋⠀⠀⠀⢈⣭⣭⣥
⣀⣰⡿⠃⠀⠀⢠⣄⡙⠏⢸⡿⢁⡀⠀⠀⠀⢠⣄⠀⢀⠀⠀⠠⣾⣿⠿⠋⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠉⢉⣉
⠉⠁⠀⠀⠀⠀⠀⢿⣿⡄⡜⢠⣿⡇⠀⠀⢀⣈⣻⡀⢿⣇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⢀⡄⠀⢠⣌⣉⠁⠒⡿⠋⣠⣦⠀⠙⠛⢋⣠⣬⣿⠀⢻⡆⠀⣦⠀⠀⠀⠀⠀⢸⣿⣆⠀⢰⡄
⠀⢀⡀⢿⡇⠀⠀⠻⣿⣿⣄⠁⠠⣿⠏⠀⠀⠀⠈⠛⠋⠀⣠⣬⠗⠀⣘⡧⠀⠀⠀⢀⡀⠙⢿⠀⢸⣿⠀⢀⡀
⠀⠸⣿⣎⣤⡾⠀⠀⠈⠉⠉⠀⠢⡅⠀⠀⠀⠀⢀⣄⠀⠘⠛⠁⠀⣾⡿⠁⠀⠀⠀⠀⠻⢿⣦⡀⡘⠟⠀⢸⣷
⠀⣦⡙⠻⠟⢁⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠟⢀⣤⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢲⣶⣤⡀⠀⢠⣿⣿
⠀⠹⣿⣷⣴⣿⠁⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠙⠛⠛⠉⣁⣀⠀⠀⠀⢀⠀⣿⡟⢀⡤⠀⠀⠈⠉⠉⠐⢸⠿⠃
⠀⠀⠀⠉⠉⠃⠀⢀⠀⣼⣿⠇⠀⣀⠀⠀⠀⠘⠿⠓⠚⠛⠋⠀⠀⠀⣿⣧⠉⣴⡿⠃⠀⠀⠀⠀⠀⠘
⢀⣀⣀⣤⠀⠀⠀⢸⣆⠘⠏⢠⣾⠏⠀⠀⠐⠿⠷⠶⠶⡷⠆⠀⢸⣦⡙⢋⢒⣡⣴⠆⠀⠀⠀⠀⠀⣀⡀⣠⣾
⠿⠿⠟⠁⠀⠀⠀⠈⢿⣷⣤⡾⠁⠀⠀⠐⢶⣦⣀⣀⣤⡀⠀⠀⠘⢿⠇⠰⠛⠛⡁⠀⠀⠀⠀⢠⣾⡟⢠⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡔⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠊⢢⠄⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⢻⡿⠧⠀⠀⠀⠀⠀⠄⠺⢿⠓⣤⡇⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣰⣤⠀⠀⠀⠀⠀⢀⣤⣶⣲⠞⢓⢿⠥⢸⡅⠠⢀⡄⢀⡀⢡⡀⠀⡼⠀⠳⠻⠉⢣⡶⡷⡺⣻⡿⠆⠀⠀⠀⣠⣄⠁
⠀⢀⠀⣤⡈⠁⠀⢀⡠⠄⠀⠈⠙⠛⠿⢀⣀⣾⡤⠊⢢⣳⠯⠄⠀⠠⠀⢘⣿⣆⡑⢴⣣⠠⠴⠯⠞⠋⠁⠀⢀⡄⠀⠀⠘⠉⣀
⠀⠈⠃⠘⠁⠀⠀⠀⠰⠿⠂⣀⣠⣤⣤⠤⠒⢉⣭⠋⠈⠁⠳⠤⠔⠣⠐⠇⠂⠀⠉⣄⣌⠙⠶⣄⠀⠀⠀⠀⣾⠌⠀⠀⠀⠘⠋⠘⠃
⠀⠀⠀⠀⠀⠠⠴⢶⡔⠶⠻⢻⠿⣿⡟⠀⠀⡯⡿⣠⠄⠴⠃⠀⠀⠀⠀⠈⠂⠀⢴⡹⣆⣱⡄⠈⣿⣿⡿⠿⠿⢂⣴⣆
⠀⠀⠀⣀⢤⣤⣦⡈⠀⣠⡞⠁⢸⡿⠁⠀⠀⣿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡜⣆⣣⠀⢿⣿⠈⢶⣄⠈⠁⠐⠂
⠀⣠⣾⣵⣷⡿⢛⣩⡽⢃⣤⣄⠘⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠀⠘⣿⠀⠈⣟⢿⣜⢿⠾⣯⣿⣶⣤
⠀⠀⠀⠀⢀⡴⣻⡟⡤⢺⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡳⣘⣦⢭⡓⠛⠛⠁
⠀⠀⠀⠀⡊⠠⠟⢀⠃⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠏⢊⢇⢱⡄
⠀⠀⠀⠀⣧⣿⠜⠃⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡇⠘⣾⣆⡇
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠻⡇
⢀⣴⡶⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠟⠋⠑⢻⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⢂⣈⡶⠤
⠀⠰⠂⣦⠠⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢣⣾⣧⢀⠂⡀
⠀⠀⣀⠂⢠⠞⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢨⠸⣿
⠀⢸⡻⢇⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⠁
⠀⠀⠉⠉⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣞
⠀⠀⠀⢠⣿⡌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⡇
⠀⠀⠀⢸⡟⠁⣼⢶⣦⡀⠀⠀⠀⢠⡄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢠⣀⠀⠀⠀⡴⢻⣿⡆
⠀⠀⠀⠀⠀⠀⢹⡌⠻⠿⠆⡀⢀⣿⡱⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡙⠷⡸⣏⠁⣠⠎⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠰⣿⢀⡀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⣀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⢸⡘⢶⣄⠠⢀⠀⠀⠀⠀⠀⡘⠓⠴⠺⡇⠀⠀⠀⠀⣠⣤⢀⣠⠞⣡⣄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⡟⣷⣤⢀⣤⣿⣁⠀⣼⣷⣆⠉⣻⣃⠀⢚⣿⡿⡿⠋⠴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠦⣄⠀⠲⠿⣯⣀⡙⠛⢋⠈⣫⠁⠀⠀⡤⠀⠀⠀⠀⠈
⡀⡀⢀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⣞⠁⡈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⠀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢓⣀⡀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⡏⠉⠙⢷⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢘⠷⠖⠀⠀⡧⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠞⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠾⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⣾⠁⠠⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢙⡄⣇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣴⠟⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⢦⠄⣠⢹⡆⠀⠀⣀⣤⠴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⡖⠂⠁⣸⠃⣠⢞⡭⠒⡆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢼⣷⠫⢊⢇⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢆⣀⢀⣴⠁⠀⠀⢡⠀⣤⠾⠛⢤⡀
⠀⠀⠀⠲⣟⠩⣭⢵⣭⣭⣟⡂⠀⠀⢀⣿⣿⣧⣄⡠⠤⠖⢾⡇⠀⠀⠀⢘
⠀⠀⠀⠀⠈⢳⣌⠻⣧⣌⠉⢻⠂⠈⠉⠙⣯⠁⡞⠀⠀⠀⠠⣿⣦⣤⣴⡞⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⠵⢆⠀⠀⠀⢠⡼⠁⠀⠀⠶⠶⣶⣿⣯⣽⣿⠉⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⣤⣶⣿⡅⠀⣀⣀⠀⠀⠀⠒⠛⢻⡛⠳⣄⣀⣴⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⢶⣿⣻⠀⠀⠀⠑⢬⠀⠀⠀⠀⠙⠀⠈⠛⠻⢶⢍⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⢳⡅⠀⠀⠀⠁⢼⣇⢀⣀⣤⠀⠀⠾⡔⠂⢰⣂⡹⠌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⢸⣋⠶⠐⠒⠒⣿⣿⣽⡟⠂⠀⠀⠀⠸⠶⠲⠶⠲⠖⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣱⣿⠖⠆⠆⣭⠁⠀⠀⠀⠀⢹⡟⢹⣷⣄⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢰⠏⡼⢹⣧⢶⡟⠯⢚⡄⢀⠀⠀⢠⠋⠀⠈⠀⠙⣋⢲⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠘⠓⢊⣉⣥⣴⠞⠉⠁⠀⠁⠀⠀⡀⠀⠀⠀⠀⣴⡀⠭⢧⢻⡀
⠀⠀⠀⠀⠀⠀⢸⠷⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠐⢿⣷⣝⡺⢸⡏⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣭⡚⠃⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣄
⠀⠀⠀⣠⠀⠀⠀⣤⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠠⡆⣼⢁⡄⠀⠀⠀⢶⣾⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⢠⣿⠏
⠀⠀⠀⣿⠀⢠⡾⠋⠀⠀⠀⠈⢿⣷⣠⣴⣾⡟⠀⠀⢦⡱⡏⠞⣠⠀⠀⠀⠀⠹⡿⠋⠀⠀⠀⢀⣴⣾⣆⣀⠀⠀⠀⠀⠀⠀⠙⢇⠞⢁⡀
⠀⠀⣦⠘⠆⠃⣰⡆⠀⢰⣶⡄⠈⠉⠛⠋⠁⠀⠀⢰⣌⠹⡥⠚⣁⡖⠀⢠⣾⣷⣠⣄⠀⠀⣀⢺⣿⡿⣟⣻⣗⣀⠀⠀⠀⠀⢠⡼⣰⣿⠇
⠀⠀⠻⣦⡀⠼⠋⢀⡦⠀⠻⣿⡆⠀⣴⣾⡿⠃⠀⣷⡙⢇⡰⠚⢋⣰⠂⠀⠉⠻⠿⠟⠀⢸⣿⣦⣿⣶⣿⣿⣾⣿⡇⠀⠀⢠⣦⣱⡿⠉
⠀⠀⠀⡎⠙⠂⣰⡿⠃⠀⠠⣾⡄⡄⠙⢉⣀⠀⢠⡈⢷⢘⣥⠶⠛⡃⠀⠀⡀⡆⣀⡀⠀⣶⣍⣻⣿⣿⣿⣿⣿⣭⣷⣄⠀⠈⢿⢹⣀
⠀⠀⠀⢿⣄⢠⠋⠀⠀⠀⠀⠹⣿⣧⣾⣿⠟⠀⢈⡻⡄⣏⣴⡶⠛⠁⠀⢾⡿⢿⣿⡧⠀⡻⠿⣿⣽⣿⣿⣿⣿⢿⣿⡿⢀⡀⠈⢿⠉⣠⣶
⠀⠀⠀⠀⠙⠧⢠⡄⠀⠀⠸⣷⣦⡏⣨⣤⡄⠀⠈⢧⠱⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⠟⣿⣟⣹⣷⣮⡁⠹⣿⠀⢸⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠙⠻⣿⡿⠛⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠸⣿⣷⣾⣷⠀⠈⠛⠛⠃⠀⠘⣿⣿⣿⡿⠁⠀⠀⢠⢏⣴⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡼⠛⠛⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠱
⠀⠀⠀⢸⣿⣤⠀⣄⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠘⢿⡇⢠⣶⣿⡆⠀⠀⠀⢀⠀⠀⢹⡇⣰⡆⠀⠀⣿⡇⠀⢠⡄
⠀⠀⠀⠈⣿⣿⠀⠁⣀⣀⡀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡛⠛⠀⠀⠀⠀⠸⣷⡄⠈⢾⡟⠀⠀⠀⠈⠃⠀⣿⠃
⠀⠀⠀⠀⠈⢉⣧⣾⣿⡿⠀⠀⠀⠀⠈⠿⣿⠁⣠⣶⣶⠀⣤⣄⠀⢹⡿⢳⣷⠄⠀⢀⣤⣤⣤⣭⣠⠀⣀⣀⣀⡻⣶⣦⣄⡁⠀⢠⣿⡇
⠀⠀⠀⠀⣀⠀⠹⠟⠉⠀⠀⠀⠀⠀⡀⠀⢉⢸⣿⣿⠏⠀⠙⢛⣁⠀⠁⢠⣤⣤⠀⠘⠿⠋⠀⠀⠘⡎⠉⠙⠛⠁⠀⠉⢀⡑⠀⠹⠛
⠀⠀⢸⣿⣿⣿⣴⡆⣠⣾⣿⣷⠀⢸⣿⣦⡈⣼⠏⠀⢀⣀⠀⢻⣿⣇⠀⠸⠿⠟⠀⠀⢰⣿⣷⠀⢀⢃⣴⣾⡇⠀⠀⠀⠀⠈⢳⠁⠞⠁
⠀⠀⠀⠙⠛⠉⠀⢣⠿⢿⠿⠃⠀⠀⠻⣿⡇⢹⢀⣴⣿⣿⠀⠀⠀⡀⠙⡀⢀⠔⠀⠀⠀⠙⠿⠀⣊⡾⠟⠋⠀⠀⠀⠻⣿⣦⢸
⠀⠀⠀⠀⠀⣠⣤⣼⠀⠀⠀⠀⢀⣀⣀⠀⠙⣼⣿⣿⠿⠋⠀⠀⠀⠈⢦⣠⠏⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣡⠊
⠀⠀⠀⠀⠻⣿⣿⠟⢠⣶⣿⡇⠸⣿⣿⣷⡀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢠⣠⠖⠀⠀⠀⠀⠀⢸⢠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠋⠀⠀⠙⠛⠛⠺⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢃⡞⠀⠀⠀⠀⠀⠀⠀⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡔⠉⠙⡆
⠀⠀⠀⠀⠀⠠⠠⢄⠠⠀⠀⠀⡞⠀⠀⠈⠉⢑⠀⠀⠀⠒⠤⡤⠂⢱⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠢⡀⠀⠁⠀⢄⣼⡠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠁⠀⢰
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢐⣿⡭⠏⠉⠉⠁⡆⢈⠁⠢⡀⠀⠀⢠⠃⠀⠀⠀⠈⠢⢤
⠀⠀⠀⠀⠀⠙⠂⠐⠀⡠⠊⠀⢹⡄⠀⢠⠒⢁⠜⠀⠀⠈⠲⣤⣦⣀⣤⡤⠐⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⡛⣆⢀⡱⠘⠤⣤⢄⣤⠶⠊⢻⡁⠀⠈⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠑⠚⠉⠳⣀⡰⠀⠈⢦⠀⠀⠀⡴⠋⠀⠀⠀⢸⢱⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠑⢄⠀⠑⠒⠢⡀⠀⡼⠀⢇⠀⡯⠑⡄⠈⢦⡀
⠀⠀⠀⠀⠀⡰⠋⠉⠆⠀⡠⠄⠠⡀⠀⠀⠈⢄⠙⢦⡀⠀⠙⠚⠁⠀⠀⡉⠁⠀⠘⢆⠀⢋⠢⡀
⠀⠀⠀⠁⠉⠃⠀⠀⠘⢸⠁⠀⠀⠑⠤⠄⡀⠄⠁⢀⠈⠓⢤⡀⠀⠀⠀⠑⢀⠀⠀⠈⢧⠈⢆⠘⢆
⠀⡀⢀⡱⡀⠀⠀⠀⢰⣼⠀⠀⠀⠀⠀⢀⡔⠀⠀⡀⠀⠂⠄⡉⠳⢤⡀⠀⢀⠀⠢⡀⠈⢧⠘⡀⠀⢣
⠘⡀⠀⠀⠙⠢⡀⠀⠈⡇⠀⢀⡠⠔⠊⠁⠀⠀⠀⠈⠢⡀⠀⠀⠑⠢⢝⠦⣀⢢⠀⠈⢄⠘⡆⢡⠀⠀⠃
⠀⢱⡄⠀⠀⠀⠈⠑⣶⢿⣖⠛⠀⠐⠒⠒⠤⡀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠈⠪⡳⢧⡀⠀⠡⣽⠸⠀⠀⠘
⠀⡎⠀⠀⠀⣀⡤⠖⠉⠉⠧⠀⠀⠀⠀⠀⣠⠞⠐⠢⠤⣀⡀⠀⠑⢄⡀⠀⠀⠈⠢⡑⡄⠀⢹⠀⠀⠀⡆
⠀⠉⠉⠉⡩⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⠀⢄⡀⡀⠀⠀⠉⠉⠒⠲⠬⢦⣄⡀⠀⠘⢌⠂⠀⢆⠀⠰
⠀⠀⠀⠀⠀⠀⡠⠶⡄⠀⠀⠆⠀⠀⠠⠜⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⡀⠑⡅⠸⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠐⠀⠀⠀⠠⠄⠈⣙⣾⣄⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠉⠉⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃
⠀⠀⠀⡀⠀⠀⢄⠈⠃⠀⠀⣾⣶⠄⠀⠀⣾⡁⠂⠀⠀⠐
⠀⠈⠀⠒⠈⠀⠀⢀⠀⠀⠀⠈⠉⠂⠀⢰⠟⠁⣀⣀⡈⠈
⠀⠀⠀⠀⠀⢀⣿⠆⠠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠇⠀⠀⣠⣷⡤⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠁⠀⣀⣤⠀⢠⣆⠀⠀⠀⠀⢐⣾⣷⡆⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠨⠀⠀⠀⠀⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢧⠀⠀⡈⠁⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠁⠀⠚⠁⠀⠀⠀⠀⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠸⠀⢠⠄
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠄⠀⢠⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡀⠀⢠⠁⠀⠀⠀⢉⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠑⠂⠁⠀⣀⠐⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠐⠀⢄⠀⠀⠀⠀⠈⡀⠀⢠⠀⠀⠀⡀⠘⡃⠀⠀⠀⠰⠄⠄⢀⡤⠪⠁
⠀⠀⠀⠀⠀⠈⠀⠀⡈⠁⠉⠀⢠⡀⠈⠁⠀⠀⠀⠀⠁⠀⠈⢷⢄⠀⠈⠀⡀⠀⠀⠀⠀⠅⡠⢊⠂⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠸⠀⠀⠁⠀⠀⠀⠐⡂⢄⠀⠀⠀⠈⠳⢐⠄⠀⠇⠀⠀⠀⠀⢸⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠌⠖⠀⠐⠄⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠄⠓⠢⡖⢄⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠈⠙⠲⠄⡄⠀⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢅⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠂⠂⠀⠈⠈⠀⠀⠀⠀⠈⠀⣀⠤⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠢⠈⠸⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠘⠐⠙⠀⠀⢲⢊⣀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠇⡆⠀⠀⠀⠀⠠⡀⠀⡀⠙⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡌⡌⠀⠀⠉⠙⠁⠈⠀⡀⠀⠀⠠⠂⠒⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠣⠄⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠀⠠⢄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⠀⠰⠀⠠
⠀⠀⠀⠀⠀⢀⠊⠀⢀⠄⠀⠠⡀⠀⠄⠀⠂⠀⠊⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⢀⡀⡠⠢⠈⠢⠀⠀⠀⡁⠀⠀⠄⠠⠀⠂⢁⠀⡀⠀⠉⠀⠀⠀⠀⠠⡀⠀⢃⠀⠀⠀⡄⠂⠀⠀⠀⠁⠐⢀
⠀⠀⠀⠀⢰⠀⠃⠀⠋⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⠀⠰⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⢀⠀⠀⠉⠐⠀⠔
⠀⠀⢀⠀⠀⢧⡀⠀⣠⣂⡀⠃⠀⠀⠖⠈⠀⠀⠀⠀⠁⠀⠀⢀⠤⠂⠠⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠒⠐⠀⢄
⠀⠀⠀⠠⠀⠐⠬⢉⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⡆⠠⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⢂⠀⠈⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢄⠀⠈⠂⠀⠀⡠⠔⠒⠒⠒⢄⠂⠀⠀⠁⠀⠀⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⣀⣈⠀⢀⣀⡀⠀⠀⠁⠀⢡⠔⠒⠀⠤⠤⠤⠄⠀⣑⣌⠂⠠⠀⠀⠀⠊⡀
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠂⠐⡁⢄⠨⠁⠩⠀⠈⢙⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠠⡀⢱⠘⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠡⣀⣆⡂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠤⠔⠀⠀⡠⡀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠤⢀⣒⣀⣀⠖
⠀⠀⠀⠀⡰⠊⠄⡁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠊⠀⠀⢀⠘⠂⠀⠁⠀⠀⠈⠊⢔⡤⠠⡀⠀⠀⠀⠈⠒⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⣀⠀⠄⡀⠀⠀⠑⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⠇⠀⠙⠳⠄⠁⠀⠀⠀⠈⠆⠀⠀⠘⣿⣷⡀⠀⢂⠀⠀⡠⠴⡀⠀⠁
⠀⠀⠀⠀⠀⡀⠑⠄⠑⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠄⠀⠀⠈⣠⡟⠻⡇⢀⡀⠀⠉⠙⠳⠦⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠲⡀⠠⣄⠀⠀⠈⠳⣄⠀⠀⠀⢀⡠⠂⠊⣀⠤⡀
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠖⠀⢸⡿⡃⣶⠊⠉⣠⠔⠉⠀⠀⢧⣄
⠀⠀⠀⠙⠆⠆⠀⠐⡄⠀⠀⣿⣶⢤⣀⣀⠠⠤⢭⣧⠈⢀⡜⠁⠀⢀⠀⠀⠸⣿⡇⠀⠀⠠⠈
⠀⠀⠀⡀⠀⣀⠔⠀⠈⠀⠀⣙⠻⠀⠀⠁⠀⠀⠀⠈⢢⡎⢸⣿⣦⣤⣬⠴⠂⠙⠳⠄⠀⢠⠁⠂
⠀⠀⢦⡀⡎⠀⠀⠀⠀⢀⠂⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⣃⡠⠭⢉⡀
⠀⠀⠀⠉⠉⠁⠀⢀⠤⠒⠉⠉⠀⠣⡀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⢀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣀⣴⣽⣴⡃⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⡴⠃⠤⠿⢿⠿⠀⠀⠀⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠊⡠⠚⠀⠠⢸⠃⠨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⢨⠀⢠⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠒⢀⠀⠀⠒⠂⠀⠠
⠀⠀⠀⠀⠁⠀⠈⠀⢀⡀⠐⠀⡀⠀⣀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠠⠀⠁⡀⠉⡄⠀⠀⠀⢅⠀⠁⠀⠄⠀⠀⠠⠊⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠄⣀⣁⡀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠘⢀⡀⠀⢀⠀⢀⠀⠙⠉⠁⠀⠠⠛⠀⠀⠀⠀⠘⠣⠄⠀⠀⠄⠀⠄⠀⡀
⠀⠀⠈⠀⠁⠀⠀⠁⠁⠤⠤⠐⡀⠡⡔⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠌⠀⠒⠀⠀⡀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠠⢆⠀⡀⠐⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢠⠎⠀⠁⢈⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⠄⢗⡌⠀⠐⠀⠰⠂⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣡⠀⠊⠀⢉⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠘⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠐⡀⠤⢀⠀⠴⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⣀⠔⠓⠀⠐⠁
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⣶⣶⠶⢶⡶⢶

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⢐⣧⡤⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠡⠟⡡⠀⢀⢀⠤⢀⢦⠄⠀⠆
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠒⡀⠀⢀⡀⣾⡦⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠠⠆⠩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠒⠂
⠀⠀⠀⠀⠀⢠⡄⠐⢤⡷⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠀⢀⢠⣾⡃⠀⠐⣷⣠⠀⣠⡶⠀⢐⣤⠀⠀⠀⠺⠆⠆
⠀⠀⠀⠀⠀⠀⠉⠁⠘⢷⡀⠛⠛⠋⠉⠉⠁⡶⠋⢄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠑⠖⠊⠁⠰⠀⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⢀⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠄⠀⠀⠀⣾⠆⠀⠀⠀⠀⠄⠈⡀⠴⠘⡄⠁⠄⠀⠀⠀⠂⣰⠈
⠀⠀⠀⠀⠀⣠⣤⣾⢿⣧⣤⠜⠀⠀⠀⠀⠀⠠⠀⠀⠀⢘⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠀⣴⠁⢌⡱⢐⠀⠀⢀⢈⠇⠈
⠀⠀⠀⠐⠀⢙⣿⣅⣏⣿⡟⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠈⠀⠀⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡉⢀⠒⠢⢀⠀⠀⠀⢀⠚⡆
⠀⠀⠀⠐⠀⠈⠟⠛⠛⠟⠇⠄⠂⠀⠀⢀⡨⠇⠂⢠⡈⢄⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠈⠀⠠⠈⠃⠀⠀⠀⠀⠀⠐⢧⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠐⠀⠀⠀⠀⣤⠼⠀⠀⠀⠈⢁⠀⠀⢰⣿⠛⠁⠀⠁⠀⠀⢄⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢻⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⣾⠁⠀⠀⠀⢀⣰⢠⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠁⠦⠘⠘⠸⠁⠀⠀⡀⠀⠀⠀⠀⢀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢄⠂⠐⣀⢆⠄⠀⠀⠀⣀⣸⣄⠂⠀⠠⠐⣾⡂⠀⠀⠀⠀⠁⠰⡶⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⡀⢀⠀⠀⠀⠀⣰⠇⠂⠀⢌⢄⠂⠤⡩⣚⠌⡄⠀⠈⠔⡷⠾⠉⠂⠀⠀⢸⡇⠁⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⣠⠁⠀⠀⠀⢀⡴⠂
⠀⠀⠄⢢⠼⢦⠂⠀⠀⠅⠀⠀⠠⠂⢌⠦⠐⡖⠀⢂⡱⡁⠀⠀⠀⠀⠀⠀⠀⠐⠸⣇⣀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡏⠀⢀⠀⠁
⠀⠀⠨⠜⠓⠋⠁⠀⠀⠀⠀⠀⠠⠎⠎⡜⠨⡰⢁⠃⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢏⠀⠀⠀⠀⢠⡆⠀⠈⠁⠘⠁⠀⠄⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠈⠚⠱⠱⠑⠂⠉⠀⠀⠀⠀⠀⡐⠈⡄⠀⡀⠀⡀⠈⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠙⠁
⠀⠀⢀⣀⠀⠈⠋⠈⢠⡦⠀⠀⠀⣤⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢥⢀⡖⠀⠀⡀⠁⠀⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠗⣀⠀⢂⠠⠀⢀
⠀⣠⡌⠋⢶⢆⡄⣁⢠⡀⠀⣠⡀⠉⢀⠀⠀⣁⠀⡄⠀⠀⠈⠢⠄⡠⢿⣿⠗⠃⢀⠀⠀⠚⠋⠀⠀⠀⠀⡀⠀⠀⢀⣄⠀⠊⠓⡌⠀⡄⠙
⠀⠀⠁⠨⢄⠈⠁⡄⠈⠳⡶⠙⢁⡀⠀⡔⢆⠉⠀⠁⠜⠠⠀⠀⢠⠀⢀⠋⠠⠀⠀⠄⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣄⠀⠈⡗⠋
⠀⠀⠘⠓⠀⢒⠀⢼⠀⠸⠆⠇⠘⠁⠀⠀⢀⣀⠤⠤⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⠖⠀⠀⠀⠀⠈⢈⠑⡼⠂⣀⢰⠆
⠀⠀⠀⣀⡀⣘⠃⠐⢦⠀⠋⠘⠓⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠴⠏⠀⠀⠄⠀⠟⢠⠀⠀⢹⠄⠒⠉⠀⠀⡀
⠀⠀⢠⡝⠃⡛⠀⠛⢀⢡⠀⠿⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣸⠛⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣇⠄⠀⠀⠀⢀⠇
⠀⠀⠈⠁⠀⣤⠁⠉⠉⠀⢳⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⠀⢸⡀⠀⠀⠄⠀⢀⠋⠉⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠧⠀⠐⠀⠀⡘⠀⠀⠀⠈⠸⡟⠋⠀⠂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢴⡗⠃⠀⠀⠀⠀⠀⢰⣶⡴⣾⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢸⠀⠀⠀⠀⠘⣤⢧⡤⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣾⣯⣝⣿⡷⠤⠂⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠻⢅⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠈⠛⠻⠿⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⠋⠈⠁⠀⠀⠀⠀⠀⠀⣄⣠⣤⣤⠶⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠁⠀⠀⡟⢤⠀⠀⢀⠀⠀⠀⢠⣤⠾⢛⠏⠀⠑⠁⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠹⣿⣿⣿⡿⣯⣶⣶⣿⣇⣀⡤⠊⠀⠀⠀⠀⠀⠈⠁⢀⡞⠁⣴⠁⠓⢄⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠉⠻⣿⠿⠿⢷⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠁⣀⣼⣿⣥⡀⠩⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠓⢄⠀⠬⠷⡆⣅⣹⣵⠤⠤⣶⣶⣤⠤⠤⠖⠛⠻⠉⠿⢝⠋⠢⠅⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠃⣴⠔⠛⠀⠀⠀⠠⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠃⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⡀⣉⠀⠀⣠⠀⠂⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡈⠀⠁⠉⢠⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠠⠄⡄⠀⡩⠄⠁⠐⠂⠀⠀⠀⠀⠠⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠈⠳⣄⠘⠀⣠⠄⢒⠀⠁⠀⠀⠀⠀⢀⠄⠄⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡈⠀⠈⡁⠤
⠀⠀⠀⠀⠀⠻⠂⠀⡀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⢃⠀⠭⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠓⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠠⣀⠰⡌⠁⣀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡅⠊⠤⡶⡱⢄
⠀⠀⠀⠀⠀⠁⠀⢰⠄⠀⠀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠐⡈⠛⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠄⠣⠀⠀⠉⠁
⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠢⠀⢠⡀⠀⣀⡀⠤⡀
⠀⡇⠲⣦⡷⠒⡒⢶⠒⡒⡗⣾⠒⡒⢢⠖⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠆⠘⠂⠁⠀⠀⠒⢀⡇
⠀⡞⢶⠄⣷⠸⠜⢸⢸⠓⡇⣿⢸⢹⢸⡘⠟⢸
⠀⠈⠒⠚⢃⢰⠚⠉⠛⠀⠙⠋⠊⠙⠺⡍⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣾⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡰⠊⢐⢀⠀⠂⡭⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆⠀⠀⢼⠀⠄⠃⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡄⠁⠀⠀⠀⠮⠁⣠⠖
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠁⠀⠠⠀⠘⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢨⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠢⠐⢠⣀⢀⡘⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠂⠀⠀⠀⠂⠀⠀⢠
⠀⠀⠀⠐⠈⠢⢀⠀⠠⠄⠁⠀⠒⠿⣿⣿⣷⡄⠀⣠⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣷⣴⣀⠉⢩⠀⠀⠀⠆⢀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠀⡁⠔⢺⠗⠛⠗⠉⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⡀⠀⢻⠛⠛⢠⠍⠀⡀⠀⠈⠈⢳⣧⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠀⠁⠀⠀⠀⠀⠂⠀⠘⡏⠙⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡈⢄⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠈⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠁⢀⠀⠉⠂⠤⠘⠰⣦⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢠⡴⠂⠘⠃⣐⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⢀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄⠀⢼⣿⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠈⠰⣻⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠂⡖⠀⠈⠑⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠠⠀⠀⠀⠀⠄⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⠐⠡⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⡕⠄⠀⠀⠀⠀⠀⠀⠀⠌⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⡆⡌⡰⠀⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠁⢬⣿⣧⣤⠁⠀⠀⠀⠁⠀⢀⣀⠠⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡔⠂⢈⣷⣯⣴⠂⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠏⠉⢉⠉⠀⠀⠐⠀⠀⠀⠋⢠⣦⣴⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡒⢿⣟⠋⢈⡉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠁⠄⠈⠻⡍⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠔⢫⠄⡀⣸⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⢆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠇⠀⢀⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠴⠁⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡀

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⡤⣡⢅⠀⢀⠀⠀⠀⠀⠀⠀⢠⢁⠀⠀⠀⠀⠀⢰⣦⣀⡰⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠠⠤⠀⠈⠀⠀⠺⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠱⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠙⣯⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠴⠰⠆⠀⠠⠤⠀⠠⠄⠰⠄⠀⠀⡀⠀⠀⠄⠀⠠⠀⠀⢼⡴⣦⡄⢄⡰⠀⠀⠀⠱⠷⠀⠀⡐⠀⠀⠠⡄⣶⣄⠉⠁
⠀⠀⠀⠀⠀⠀⣀⢒⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡄⠒⣠⠐⢦⡤⠀⠀⠀⠉⠁⠀⠀⡄⠀⠀⠀⠀⢠⢞⣁⠑⠄⠀⠠⠖⠈⠀⠲⠶
⠀⠀⠀⠀⠀⢄⡩⡄⡍⢰⣿⠇⠀⢠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⢀⠰⠠⠄
⠀⠀⢠⣶⡄⠈⠙⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠁⠠⠀⢀⠀⡀⢀⠈⠀⠀⣤⠀⠀⡀⢀⠀⢀⡐⣨
⠀⠀⠀⢂⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠆⠀⠀⡤⣶⠆⢃⠀⣀⡀⠀⠀⠀⠀⠘⠿⠀⠸⡿⠁⠀⠈⠀⠀⠙⠎⠀⠀⢱⠇
⠀⠰⠶⣷⠶⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣬⡄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡀⢠⣤⡴⠀⠀⠀⡀⢀⡀⠀⠀⠀⣤
⠀⣄⠀⠀⢀⡀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⡊⠉⢠⣀⡦⣴⡂⡄⠀⢠⠀⢠⠴⣄⠀⢾⢟⠀⠈⠁⠀⠀⠻⠂⠈⠀⠀⠀⠀⠀⠏
⠀⣽⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠈⠀⠃⠙⠁⠙⠉⠉⠋⠉⠉⠁⠀⠀⠀⠂⠀⠀⢤⣆⠒⢸⠴⣪⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠈⠀⠉⠀⠀⠤⠀⠀⠀⡶⠶⠎⠀⠀⠀⠀⠢⠀⠀⢀⣺⣭⢸⠷⢺⢶⣂⡆⡶⢤⡦⣖⣡⠀⠐⠂⠀⠀⠀⠠⡐⢾⠀⠓⠃⠄⠀⠀⠀⠋⠀⠀⠁
⠀⢠⡈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⣹⣉⡱⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⢰⣿⣿⠂⠀⠀⠀⠀⢠⡄⠀⣠⠂⠀⠀⠱⡀⠀⠀⠀⠾⠂
⠀⢀⣟⣛⣧⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠿⢀⣤⣄⠉⠉⠀⠀⠦⠀⠀⡾⠀⠀⠐⠰⣿⣾⢾⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⣄⡄
⠀⠀⠿⠿⠏⠀⢠⣠⠤⣄⠀⢀⣀⡀⠀⢠⣾⣿⣿⣶⡀⠘⣾⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣌⣠⣦⠄⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⠀⡄⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢛⠄⠀⠀⠘⠘⠚⠙⠉⠀⠀⢰⣦⣀
⠀⣰⠀⡠⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⣤⣄⠉⠛⠟⠃⠀⠀⠀⠐⠂⠀⠆⠀⡿⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠸⡟⠀⠃⠚⠒⠂⠀⠙⠑⠂⠈⠛⠉
⠀⣿⢰⠃⠐⢃⠌⠀⠀⠠⣿⣿⡇⠀⠛⠋⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⣤⣤⠄⠀⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⠷⠀⠀⢶⠄⢴⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠀⠦⠶⠢⡀⣰⢰⣠⠖⣣⣴⠐⢀⠀⢀⣦⠛⠀⠀⠀⠀⠐⣄⠀⣀⣀
⠨⠤⢀⡂⠀⣠⡄⣔⠂⡈⠑⡄⠈⠐⠋⠀⠀⢦⠀⠶⢃⢄⡃⣎⡐⣢⣿⡿⠁⠉⠰⠇⡘⢋⠞⣁⣒⠀⠀⠀⠀⠀⠀⣾⣿⠿⢿
⠀⠠⠈⢃⢈⠛⠃⢬⠑⢱⠊⠈⣀⠂⠄⠔⠄⠞⠬⡋⢽⢀⠂⠜⠀⠀⠈⠁⠀⠠⡙⠓⣕⠡⠔⡛⠇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠃⠀⣀⠀⠘⠆⠁⠀⠀⠈⠈⠀⢢⡴⣒⠎⣠⡂⢌⠂⠟⠛⠛⠛⠹⠗⠶⣶⠤⠄⣑⡀⠘⡟⣧⠄⠀⠀⠀⠀⠀⠿⢿⣶⡾
⠶⢂⣠⡄⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠁⡆⠀⠛⠀⠘⠃⠀⠘⠁⠐⠇⠈⣀⣰⣗⠵⣀⠡⠠⠀⠀⠀⠀⠈⠀⠀⠘
⡦⢤⡷⣾⡆⠐⣄⠀⣀⢀⡀⠀⢀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠟⠛⠀⠛⡽⣦⡐⠰⠂
⠃⣸⠍⠈⠅⠀⣼⣿⠿⣿⠳⠆⠀⠸⠆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢀⠀⠀⠙⠉⣸⠠⢲⣀⣀⠀⡀⢀
⠀⠈⠀⠀⠀⢀⣿⣇⢀⣠⣵⠶⠆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠄⠌⠀⣀⡃⢈⣘⣭⢰⠂⠡
⠄⠠⠀⠀⠀⢀⠉⠩⠖⠠⠃⠀⣤⠨⡄⠈⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠃⡀⠉⡃⢉⣂⠘⠤⣀⣀
⠀⠀⠀⠀⠈⠂⡀⠻⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡅⣧⠀⠁⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢤⠎⢯⠛⡟⡄⢚⠏
⠀⢀⠂⠀⢀⠀⠀⢀⡣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣇⢀⡀⣄⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠊⠉⠖⠃⢈⠒
⠀⠀⢐⠐⠂⠀⣶⣾⢦⠙⡡⠀⠀⠀⠀⠀⢠⠂⠀⡀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠀⠀⠘⠇⠲⡉⢀
⠐⢿⢿⠾⠀⠀⠊⠠⢰⣾⣿⡄⠀⠀⠀⠀⠈⢆⠀⠀⡅⢐⡀⠀⠀⠀⠈⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠒⢨⣄⢀⣠⡗⡀⠈⠄
⣴⡡⠀⠀⠀⠁⠀⣄⣶⡊⢢⠠⠀⠀⠀⠀⠀⠈⠀⡏⠀⠈⠀⠀⢀⠀⠀⠘⢀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠠⠆⠩⢀⠜⢛⠁
⠢⢉⡇⠀⠀⢂⠈⠹⠛⢃⡅⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠘⠐⠀⠰⠀⠀⠀⠘⠀⠱⠔⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⡄⠈⠢⡄⠁
⠾⠀⠀⠠⠴⠆⠀⠐⡼⡾⣵⢠⠙⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⢄⠉⡠⠠⠎⠈⡀
⢀⡀⠀⠀⠙⠂⠀⠀⠈⠟⠢⠁⣀⣧⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣗⢾⢲⣿⠓⠀⢺⣶⠄⠁⠈
⠈⠉⠀⠠⡦⠴⠿⠙⢈⠡⠤⢂⡚⠙⠙⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢭⡀⠳⠲⠟⠘⠋⠠⠀⠻⠻⢀⡜⠃
⠀⡀⠀⣤⡄⠠⠄⠶⠀⡔⡰⢓⠂⣠⣦⣯⡶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆⠢⡊⢧⠙⡤⠄⢀⣤⣮⡱⠀⢀⣡⡀⠉
⢀⣄⠀⠈⠀⠀⠘⠦⠠⣾⠕⠉⢳⠪⠊⠉⠀⠥⠈⠍⠙⠛⠶⠷⠶⠾⠚⠗⡛⠉⠁⠐⠂⠁⠀⠀⠀⢊⠊⠟⠙⠌⠀⢸⠿⡇⠤
⠈⢋⠀⢠⢤⠔⣀⢀⣁⠁⢀⠾⠑⣆⠁⠈⠓⠀⠀⠀⠀⠄⠐⡀⠠⠂⠠⢂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠄⠀⠀⠐
⠀⢀⣤⡄⠂⠠⠈⠉⠈⠁⢸⡏⡀⠉⠀⣰⠆⠀⠀⠺⠂⠀⠸⣶⣦⡂⠂⠈⠀⠀⠀⠀⠱⣄⣤⣤⣄⠁⠀⠀⠀⠀⠀⠀⠆⠠⠈
⠀⠀⠁⠀⠀⠂⠐⢀⣬⢀⠉⢠⡟⣿⠁⠈⢀⠀⠄⢜⠀⠈⠀⠀⠀⠑⠀⢀⠀⠀⠂⠀⣼⣿⠛⠛⢿⣿⡀⠀⠀⠀⠀⠠⠀⠀⢄
⠀⠀⠨⣶⠒⠀⠀⠀⠩⠀⠀⢠⠛⠇⠀⠂⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠯⠀⠀⡼⡿⠅⠄⠀⠀⠀⠀⡜⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠀⠀⠀⠈⠁⢀⣆⡀⠀⠀⠀⠈⠀⠀⠀⣁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠑
⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠐⠿⡗⠀⠀⠀⠀⢀⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠚⠖⠀⠀⠀⠒
⠀⠀⠀⠑⢆⠘⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⡀⣠⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡧⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠈⠁⠀⠀⠁⢠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⡀
⠀⠐⣶⡄⠀⠀⠀⠀⣴⣏⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⣘⡒⠓⢲⠔⢢⠆
⠀⢠⣿⡇⠀⠀⠀⡀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢶⣛⡭⠥⠟⠛⠛⣡⡀
⠀⠸⣿⡇⢀⣴⣿⡟⠀⠀⠃⠀⠀⠠⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠐⠠⠁⠰⠒⠃⣀⣊⡠⢔⠂
⠀⠀⠙⠿⠎⠉⠙⠃⠀⠉⠉⠈⠀⠚⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⠀⠈⠆⠠⠄⢠⠞⠁⢀⣹⣿⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⠀⢂⣤⢀⢐⡠⢀⣠⣿⣿⣿⣿⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡤⠜⠁⠀⠀⠙⠛⠋⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢶⡀⠀⠀⠀⢸⠟⠀⠀⢳⣿⣿⣿⣦⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣾⣿⣦⠊⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⡀⠀⢶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠠⣤⣹⣿⣿⡆⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣶⠖⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠁⢀⠀⠠⢈⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣇⠀⠐⣿
⣸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠞⠃⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⠀⠀⠀⢀⣼⣿⣿⣷⣄⡈⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⠄⢻⣿
⣿⡆⠀⢠⣧⠀⠀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢠⣿⠿⠛⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⠛⠉⠙⣿⣿⠉⠉⠉⣽⣿⣿⡤⣾⣿
⣿⡗⠀⣸⣿⡀⢰⡇⠀⠀⢀⣸⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⢾⣿⣿⠶⣿⣿
⣿⣿⡀⣻⣿⡃⣼⣧⠀⠀⠠⣽⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠘⢿⣿⣿⡿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⣿⠄⠀⠴⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣿⣿⡃⢀⣤⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⣀⣄⠀⠲⠐⠂
⠀⠀⠀⠀⠀⢀⡀⣐⡻⠿⡄⣥⠃⠀⠀⠀⠠⠄⠐⠀⠀⣀⣠⠼⠶⠖⠒⠒⠐⣺⢿⠉⠁⠀⠀⢀⣀⡄
⠀⠀⠀⠀⢠⣽⢣⣛⠙⠲⠖⠊⠁⢀⠀⡄⣀⠄⠁⠄⠀⠀⣀⠀⡀⠀⠀⠈⠀⠈⠓⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢠⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣞⠇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠡⠀⠁⠀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠉⠃⠀⠀⠐⠈⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄⢸⣿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠚⢤⠄⠀⢠⠀⡀⡀⠠⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠂⠰⠍
⠀⠀⠀⠐⠀⠀⠄⠀⠀⠆⠀⠠⠀⠠⠀⠈⡐⠉⠉⠑⡃⠀⠁⠀⠀⠠⠤⠀⠀⢰⣶⡄⠀⠀⢰⣖⡆
⠀⠀⠀⠀⠠⠏⠀⢀⠀⠀⡀⠤⠼⠂⠀⠀⢶⣄⠂⠀⠜⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⢪⠐⠀⠀⢀⠀⡄
⠆⠀⠀⠀⠀⠀⢀⡛⠛⠁⠚⠒⠀⣤⣠⡄⠀⠹⣤⡠⢀⠄⠀⠛⠀⠀⠀⠀⠀⠋⠜⡄⠁⠀⢐⢠⠙
⠀⠀⠀⠀⠀⠀⠙⠁⠐⠒⠀⢀⢋⠁⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠲⠗⠐⠀⠈⠀⡛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⢢⡀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠉⠁⠈⠳⡔⠁⠀⠈⢱
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣄⣀⡴⠒⠐⠒⠤⡀⢅⠀⠀⠀⣦⣿⣤⢀⣀⣼
⠀⠘⠛⠒⠒⠺⠿⠷⣶⣵⣤⣤⣤⣾⣷⣿⣿⣉⠀⠁⠀⠀⡴⠊⠉⠙⠻⣿⣧⣿⡿⠋⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⣻⠙⠁⠈⠳⡄⠠⠈⡇⠀⠀⠀⠀⣸⠋⠻⠿⣄⠀⠀⣸⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡟⠀⠀⠀⠀⢡⣀⡀⠑⠒⡤⠴⢻⠁⠀⠀⠀⢘⠗⢒⡗⠀⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠐⠀⠐⠤⠄⣀⡠⠂⠈⠉⢯⣛⣓⣒⠲⠷⢄⠀⡠⠮⠤⣿⡇⠂⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠗⠤⡀⠀⠀⢉⠀⠀⠀⠀⠙⠢⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠹⠀⠀⠀⠈⢢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠄⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠈⠉⠁⠁