Jungle cat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠳⢄⠰⢀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⣿⣶⣤⣤⣄⣀⣶⢮⣤⡄⠀⢀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠐⠂⠘⠈⡁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠐⠺⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢋⣿⣿⣿⣷⣄⠂⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣷⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⢿⣿⣿⡟⣿⣧⣽⣿⣿⣿⣿⣿⣟⡿⠁⣭⣥⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢢⣀⣀⣰⣿⣿⠿⣿⣷⣾⣿⣿⡇⣹⡿⣿⣿⢱⣿⣿⣴⣿⠀⠲⢶⣶⣿⣾⡿⢹⣿⣿⠁
⠀⠀⠀⠀⠹⡿⣿⣿⠟⣾⣶⣿⡗⢻⣿⣷⣿⣷⣿⣿⣿⠛⠛⢉⣽⣦⣽⠿⣿⣿⣻⣷⢤⣿⣿⣄⣂⡀
⠀⠀⠀⠀⠀⣿⢿⣿⢷⣽⣾⠻⣷⣿⣦⠀⡼⡛⣶⣾⣵⣶⣿⣿⡿⣿⣿⣷⣿⣿⠏⣈⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⣴⣾⡿⢟⠗⣿⣿⠿⠛⠛⠉⠉⠀⠘⠉⠉⢭⡣⠼⠿⠛⠛⠛⠉
⠀⠀⠀⠒⠂⠀⠉⠛⠙⠛⠋⠉⠁⠀⠀⠂⠉⠁⠀⠀⠀⣀⣤⡬⣦⢠⣤⡦⠤⠄⣀⣀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠤⠤⢠⣤⡤⠐⣶⠷⣯⣴⠿⣯⣥⣅⣤⣤⣞⢙⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠰⠆⠀⢠⣾⣿⡤⣄⡀⠬⠀⠀⣆⠀⠈⠉⠉⠙⠻⣛⠛⢿⣿⣿⣿⡾⣧⣄⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠛⠛⠛⠓⠀⠿⠾⠶⠶⠶⠾⠷⠟⠛⠛⠋⠉⠛⠀⠀⠈⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢸⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠨⡋⡯⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡽⣁⣹⢗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⢁⢠⡼⢀⣠⣤⣴⣤⣀⣀⠀⠀⠀⠀⠀⠀⣰⠻⠀⣋⣴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢬⣑⠂⢠⣈⠀⣈⣽⠿⠋⠀⠓⡉⡇⠀⠉⠉⠹⠿⢿⡛⣿⠃⡤⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣈⠉⣵⣾⣿⡯⢦⣤⣿⣿⣭⣴⣦⣭⢹⣿⢿⣧⣟⣠⣾⣞⣿⡟⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡱⣿⠿⠙⣿⣿⣿⣯⣿⣿⣿⣿⣿⣹⣶⣿⣿⣿⣿⣿⣿⣷⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⣀⣴⡿⠋⠠⡈⣿⣿⣿⣹⣿⣿⡋⣙⠙⣻⠿⠿⢿⣿⣧⠸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⡶⠿⠋⡡⢰⠟⣿⣿⣿⣿⠟⠉⠀⠉⠑⢞⠙⡀⠐⠃⠈⣿⡏⢿⠀⢄⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣧⣾⠅⢡⡘⢛⣷⡂⠀⠀⠀⢿⠋⢠⠄⠷⠺⢷⠤⣺⣇⠄⠀⠀⠃⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⢀⢛⣯⡿⠁⠙⠀⠙⠭⠽⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⡙⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡸⣧⣧⢹⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡘⡇⠿⢹⣈⣉⣱⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢳⣨⡴⠲⢯⣍⡉⢁⠙⢮⡫⢑⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣼⠏⢍⠪⡓⠦⠤⠀⢸⠀⠀⠻⣄⠱⠆⢎⠍⢦⡀⢠⡆⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⣴⡋⡇⠀⠘⡄⠈⠳⠒⠒⠒⠳⢄⣀⡸⣶⠀⢸⡀⠈⣝⢾⣇⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣬⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣈⡘⣧⠋⠀⢀⠿⣿⣷⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠉⠭⣿⣀⠂⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠥⠞⢧⠀⠀⢤⠵⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡉⠛⠛⠒⠿⠀⠀⣀⣀⠀⠀⠀⠀⠀⢁⣀⡀⠀⠈⣦⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠉⠛⠛⢓⣢⠀⠀⠳⠵⢳⠀⠀⠀⡼⠧⢧⠊⠀⠀⠀⠑⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠙⣻⡜⡄⠀⠀⢸⠀⠀⠀⡧⠀⠀⢅⡲⣄⠀⠀⠨⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠒⠯⡓⠲⠤⢥⣤⣉⢁⠈⠺⡄⠀⠸⡀⠀⡐⢀⠀⠀⠀⠙⠀⠀⠐⡀⠄⠠⠛⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣈⡽⠳⠦⢿⡠⠄⠙⢤⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠂⠠⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⢷⣠⠶⡺⣽⢷⠅⠀⠼⠂⠀⠤⠎⠅⠀⢀⠔⠁⢀⠀⠤⡄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠊⡆⠀⣀⠉⡺⠀⠀⠀⠠⠤⢀⠔⢁⠀⠀⠀⢣⠀⠈⠢⡐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠥⣀⣲⡄⠀⠄⢀⠔⠉⠀⠈⠀⢆⠀⠈⢧⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⢡⠀⠘⠀⠀⠀⠀⠄⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠐⡡⠀⠀⠀⣀⡠⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⢛⣿⣿⣿⡝⢿⣿⣿⣿⠯⠿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠙⠀⢻⣿⡿⢿⠉⣿⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠻⣿⣗⠄⠀⢸⣿⣇⠂⠉⣀⡤⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠈⠙⠳⠿⣿⣷⣦⣾⣿⡋⠔⣋⣤⠶⣾⣿⣿⣿⣿⡿⠀⠀⣤⣠⠤
⠀⠀⢀⣀⡀⠀⢸⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠉⠙⣛⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⣿⣿⣶⣌⡇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣿⣦⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⡂
⠀⠀⠀⠻⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⡟
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣋⣁⠀⠘⠛
⠀⠀⠀⠀⠀⠀⡠⠤⠦⠖⠀⠀⠀⠀⠀⠀⣸⣿⡿⣟⠙⣷⣟⣿⣿⣿⣿⡿⠟⠛⠉⢳⣾⣿⡟⠈⠻⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢺⣼⣿⣹⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠁⠀⣠⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣏⣤⡶⠟⠋⠉⠉⠀⠀⠀⠀⢀⣤⠶⠤⣤⣠⣤⣿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣾⣿⣿⠿⣿⣿⣿⣿⡾⢿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣭⣯⠷⠿⠛⠋⠀⠈⢛⣻⠟⣩⣧⢛⠻⠛⡛⠛⠿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣤⣤⣶⣿⠿⠿⢿⠽⢟⠋⠉⠙⠁⠀⠀⠀⠀⠄⠉⠐⠓⣋⠵⠐⠄⠀⠀⠀⠀⡟⠤⢴⡆
⠀⠀⠀⠀⠀⠳⣤⡔⠂⡀⢸⡤⠀⡸⠋⠉⠑⠂⠀⢐⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡁⣞⠤⠀⠀⠀⠀⠀⠀⠈⠼⣶⣯⣴⣦⡄⣤
⠀⠀⠀⠀⠀⠀⠑⠨⡉⠃⠶⠄⢽⡃⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⠅⠈⠈⢀⠀⠀⠀⠀⠀⠀⠄⣀⣻⣿⠛⠻⣿⡏⠐⡀
⠀⠀⠀⠀⡀⠀⣴⡶⠈⠀⠀⠓⡀⠆⠀⠀⠀⠀⠈⠋⠀⠀⠀⠤⠄⠀⢀⠐⣀⢀⢀⣀⠲⠄⢀⣂⣬⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣿⡇⠀⠀⠈⣷⢛⡇
⠀⠀⠀⠀⠁⠀⠉⠀⠉⠀⠠⠔⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠶⠾⠖⠛⠛⠉⠉⠉⠁⠛⠒⢛⠀⠀⠀⠀⣀⢀⣠⠒⠛⢛⣹⣿⡇⠀⠀⠀⣿⣭⣽
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⢀⣀⠀⠀⠀⢐⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠶⠚⢿⣿⣿⣾⣿⣿⣿⣿⣿⣦⡀⠐⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢿⠛⠻⣦⢰⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠾⠿⠁⠀⠈⠙⠻⢿⣟⣻⣿⣿⣿⣯⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠁⠀⢀⠢⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢾⡶⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⢠⡙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⢠⡄⢈⡝
⠀⠀⠀⠀⠀⠀⠀⠀⣂⣈⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢠⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣻⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⡋⢷⡥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣿⣟⡒⠀⢻⣮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⡘⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣱⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⡝⠠⣾⣿⣷⡄⠀⠀⠀⠀⠀⢀⣠⣾⡟⣾⣿⣻⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣖⠈⣿⣿⣿⣜⡟⠓⢶⣶⣾⣿⣿⣿⣳⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣿⣿⣿⠿⣯⡄⠿⣟⣿⠛⠃⠀⠉⠈⠙⢿⣏⡻⢯⡻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⣰⣶⣦⡶⠏⠈⣤⣤⣇⣢⣶⣆⠈⢻⣿⡈⢿⣾⡿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⠃⣀⣶⣿⣿⣿⣿⣝⣿⣿⠀⠀⣿⣿⡈⢿⣿⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢿⢽⡿⢛⣉⠀⢀⣸⡿⢿⣿⣿⣿⣿⡿⢿⣀⡰⢿⣿⣧⢸⣿⣣⣬⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣠⠇⣰⣿⣧⠀⠀⠀⠀⠈⢿⣟⠿⠿⢻⣦⡈⡀⠸⣿⣿⢻⣿⢿⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡸⠓⣴⣿⠿⢛⣧⣀⠈⠠⢼⢷⣝⡳⠶⣿⣿⣧⠀⠐⠻⠟⢻⡶⢋⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡞⢠⣿⡯⠀⠈⠻⢿⣶⡄⢠⣶⣮⣿⠀⠉⣻⣿⣧⠀⠀⡁⠘⣿⣯⣀⡾
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠗⠀⣽⣿⣄⠀⠀⠀⠛⣿⡿⣿⣿⣿⣿⡿⠋⢿⣿⣠⣤⣽⣤⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡀⠀⠻⢿⣷⣄⠀⠀⡮⠀⠈⢿⣿⣷⡦⠤⠄⠙⢿⣶⢨⣧⠟⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠠⢿⣄⠀⠀⠈⣿⣷⣦⣥⠀⠀⠈⢻⣿⣷⣗⠂⣀⣀⢻⡿⣋⣀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠛⠶⢤⣤⣀⣬⢉⣽⣣⣤⣀⠀⠽⣿⣿⣯⣽⣽⣿⣧⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠋⠉⠩⠸⠋⠁⠀⠈⠑⠂⠀⠈⡭⠭⠤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣗⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⣀⣀⣴⢋⣼⣧⣤⣤⡠⢻
⠀⠀⠀⠀⠀⢀⣴⣿⢿⢽⣿⠏⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿
⠀⡄⡀⠀⢠⣿⣿⡛⡀⢙⣟⣾⣿⣟⡏⣈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⣛⣿⣿⡛⣛⠿
⡀⠀⠖⣴⣿⣿⣿⡽⣏⢀⢻⣏⢸⣿⣷⠛⡈⣏⣿⣿⣿⣿⣿⢿⣿⡿⢿⣻⣌⣁⢹⣿⠛⠶⠛⠁
⢡⢂⣼⣿⣿⣿⣿⣳⣿⣦⣏⣹⡄⢻⣭⠁⠈⢹⣟⡛⣉⢉⡇⣿⠝⠢⠩⠛⠟⢻⣾⣭⠿⠒⠁
⠈⣯⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡹⢷⣆⠀⣸⡿⢿⢿⣿⣯⣍⠛⠦⢩⣠⡔
⠄⠣⡝⢷⣺⢿⣿⣿⣷⣾⣿⣿⢟⠛⠿⡭⠿⠿⠾⣧⣤⣀⡉⠻⣇⣀⣀⠈⢻⣗⡅
⠠⠉⠁⠈⠳⣿⡝⣿⣿⣿⡻⡯⠀⠀⠀⠀⠈⠓⠀⠀⠉⢻⣧⠈⢽⣿⣿⣄⠀⠙⣂⡄
⠀⠀⠀⠀⠀⠈⠳⠿⣡⡞⠛⣲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣦⡈⠉⠓⠛⢳⡀⠨⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠤⣼⣇⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠂⠨⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡭⠉⠉⣩⢩⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⣀⣴⡗
⠀⠀⠀⣦⣴⣷⣾⣄⣶⣾⡿⠋⠁
⠀⢠⣿⣿⡿⣿⣿⣿⣿⡟
⡄⣿⡿⢵⣷⣿⣿⣏⡝⣿⡦⠤⠀⡀⣀⣀⣀⣀⡀
⡇⢹⣷⣾⡿⠿⠿⠿⠆⠐⢠⡸⠀⠸⣐⡺⠾⢻⡟⣿⣿⣿⣗⣶⢶⣶⡶⢤⣤⣤⣤⣀
⡇⢹⣿⣟⡃⣄⡛⢷⠀⠀⣹⢧⣒⡔⢹⣤⠥⡄⠑⣻⢓⠽⢾⣿⢛⣍⠓⡻⣿⣟⣿⢿⢻⡶⣤⡀
⡇⠀⠙⣿⣿⣏⡉⠉⠳⣆⣸⠆⡓⠠⣜⣧⡇⠀⠠⠠⠐⠃⠐⠑⢫⢘⢿⢛⠁⣿⡿⠅⣽⣿⠇⢼⣷⡄⢀
⠀⠀⠀⠘⣿⣿⣿⣦⣤⣼⠇⠀⢰⠀⠐⠽⡀⠀⠀⠀⣀⠽⠃⠀⠛⠸⡟⠁⠀⠁⣸⢾⣍⠙⣷⣺⡯⢰⠊⣠
⠀⠀⠀⠀⢻⣻⠿⣿⡿⠃⠀⠀⠰⢂⣦⢽⣷⠀⠀⠠⠠⡆⠆⠐⠀⠀⠦⠀⣠⣶⡿⠄⣿⠨⣾⡿⣽⣻⠏⠀⠣⡀
⠀⠀⠀⠀⠀⢃⣀⣁⠀⠀⠀⠀⠀⠌⠛⠋⠙⠧⠀⡀⠉⠀⠀⠀⠀⠀⠠⡶⠟⠁⠙⢁⣦⣿⣿⣯⠿⠋⠀⠀⠈⣗⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠛⢷⣄⠀⠀⣒⠖⢢⡠⠷⢞⡌⠀⠀⠀⠀⠀⠜⢘⣾⡿⠀⠄⢙⣥⡿⡽⠝⠉⠀⠀⠀⠰⠅⣁
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣙⣿⠗⠤⢰⡾⠚⠂⠾⠛⣄⠀⣀⠀⢐⡇⠈⠀⠈⠀⠀⠝⣊⣧⠖⠀⡆⠀⠀⠀⠀⠀⡤⠦
⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⠉⠀⠀⠀⠀⠐⢄⣰⡦⠴⣉⠀⠀⠀⠉⠐⠢⠀⢀⠀⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⢷⣿⡟⠀⠀⠀⠀⠈⠁⠀⢀⠈⡀⠀⠀⠀⠀⠀⠀⣡⠖⢻⣛⡆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠃⣠⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡅⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣰⠃⠀⠀⠒⠂⠀⡄⠀⠀⠀⠀⠁⠂⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠘⠃⣐⠀⠀⠀⠀⠀⠀⠀⠘⠳⢾⡇⠈⠓⠤⣄⡀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠉⡄⠀⠀⠀⠀⠀⠐⠀⢐⣮⡣⠀⠀⠀⠀⠁⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⢨⠀⠀⠄⠀⠀⠀⠀⠀⡠⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠐⠀⢀⡜⡤⣤⢀⣾⣆⣰⣆⣤⣶⣷⡶⣤⢶⣶⢠⠤⠄⠀⢸⠁⠀⠀⠈⠄
⠀⠀⠠⠀⠀⢀⣄⣠⣀⣤⣪⢤⣶⣶⣴⣴⡄⠆⣄⠻⠷⠯⢶⠶⢾⡷⢧⡴⢷⠾⣷⣦⠎⠀⣷⡄⡄⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠒

⠀⢀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡘⣧⡀⠀⠀⠀⠀⠀⣠⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢽⣷⣀⣀⣀⣠⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡧⢸⡟⠃⠉⠛⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠿⢩⣶⣿⣿⣿⠈⣷⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣿⡀⠈⠙⣿⣿⣯⠈⢻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠉⠹⣦⣨⣽⣏⣻⣧⠈⡘⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⣄⠈⠉⢻⣿⣥⠙⢯⣻⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣉⣟⣦⠀⠹⣿⣶⣾⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣻⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⣤⣄⣀⣠⡄⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⣽⣿⣯⣿⣷⡀⠀⠀⠀⠀⠀⠀⢲⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠧⢼⣿⣿⣿⣦⡀⠀⠀⠀⠶⣄⣹⡶⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠈⣿⣄⣀⣼⣿⣿⣿⣧⠀⠀⠀⡰⢽⣿⣇⡤⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣻⡡⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⡘⠾⣷⠅⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢴⣿⠃⠙⠀⠀⠀⠀⠀⠀⠸⣿⣽⣿⠋⣿⣿⣿⠀⠀⠀⠀⠃⣶⢷⠶⡆⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢘⡿⣴⡀⢀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣿⣿⠆⠀⠒⠶⡌⢹⣎⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣦⣿⠥⠺⠀⠀⠀⠀⢀⠈⠁⠉⠁⠀⠀⠉⠁⠂⠀⠲⡷⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢯⣷⣤⠀⠐⣿⠆⠀⡀⣀⣀⣤⠀⡄⠀⡀⠀⢀⣼⠁⠀⢠⣤⡀⠀⣀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣶⣾⣷⣿⣷⣾⣷⣦⣿⠀⠀⢳⠼⢺⠟⠀⠂⠀⠁⠀⣾⣿⣀⠀⠘⣿⣷⣦⠆⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢿⣿⣧⣦⡖⣏⣡⣽⣂⠸⡇⢰⣾⣶⣿⡿⢿⣷⣿⣻⣿⣧⡄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡿⢹⣿⣿⣧⡟⢸⣿⣿⣟⢿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠷⢼⣿⡷⣿⣿⣿⡗⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠻⣾⣿⣯⣭⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠻⢿⣬⣽⠿⠿⠿⠿⠟⠛⠋⠿⠿⠛⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣻⣿⣶⣤⠁⠀⠀⢳⡀⠀⠀⠀⠀⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⢩⣿⡿⣇⠀⠀⠀⠈⣇⠀⠀⢀⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⣿⠀⠻⠗⠂⣠⡾⠿⠖⠊⣉⣛⣛⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⣿⡀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠈⠉⠛⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣿⣿⣶⣶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣇⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠻⣿⣦⡀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠛⢧⡀⠁⣿⣿⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣴⣶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⢹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣀⣬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠠⢭⣝⣒⡂⠀⠀⢀⡠⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣰⣾⣿⣿⣶⣦⣤⡀⠀⠉⠉⠉⠉⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣽⡿⠋⠉⠉⠛⠳⢶⣶⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⡿⡿⢿⢿⡻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣟⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡄⣰⣶⡀⣶⣶⣦⢰⡆⣴⠆⠀⢰⡆⢰⡆⣶⢰⡆⣶⡄⣶⢴⣶⠆⣶⡶⢰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢹⡇⣿⣆⣿⢸⣿⣿⠀⠀⢸⣧⣼⡇⣿⢸⡇⣿⣿⣿⠀⣿⠀⣿⣄⢸⡇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢾⡗⣿⠉⣿⢸⣟⣿⣀⡀⢸⡏⢹⡇⣿⢸⡇⣿⢿⣿⠀⣿⠀⣿⠁⢸⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠟⠘⣧⡿⢖⣻⠽⡷⠾⠻⠭⠿⢷⡺⠇⠻⠿⠃⠻⠈⠟⠐⠿⠀⠿⠿⠸⠇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠈⠀⠉⣻⣿⠟⢿⣿⣿⡿⠚⠉⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣀⣤⡶⢶⣾⡋⠁⠀⠀⠀⢀⠀⠀⠬⣝⣿⠻⠶⠭⠁⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣶⣿⣿⣤⣼⡟⠀⠀⠀⠀⠀⠀⠁⠀⠱⣮⣻⡂⠀⠀⠀⡠⠚⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣭⣿⣿⣿⣥⣦⡔⠀⠀⠀⠀⠀⡄⠀⠙⣝⣿⣦⠀⣾⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⢠⠀⠀⠀⠃⣠⢻⣎⢻⡎⢅⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣫⣿⣿⣾⡿⣿⣿⢿⢹⠀⠀⠘⠀⠀⣴⢀⣿⣿⣿⣦⣧⠈⣮⠻⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⢏⣼⣿⣿⣾⠈⠎⠀⣰⢃⣼⣿⡎⣿⣿⡿⣿⣿⣦⡉⣦⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⡩⢋⣿⣾⣿⣿⠟⠁⢠⡄⠀⣱⣿⣿⣟⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠤⢂⣨⣿⣿⣿⣿⣼⣰⢟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣙⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢤⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣢⣟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣏⣾⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⢰⣼⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⣼⣦⡀⠀⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⣘⣿⣿⣿⡆⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣦⣀⣄⠿⠛⠉⠀⢀⣤⣶⣤⣤⣤⣀⠘⢷⣄
⠀⠀⠀⣴⠟⠀⠀⠠⣆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠻⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠹⣿⣿⣧⡠⠖⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠛⠉⠁⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣧
⠀⣸⡏⢀⠀⠀⠀⠀⠐⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠛⢉⡏⡰⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣇
⢠⡿⠀⢿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢿
⣸⡇⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀⢸
⣿⠀⢠⡀⣤⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣶⣦⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠈⢻⣿⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡇⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⡿⣿⣿⣷⣀⣀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣷⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣽⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢻⣆⡄⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠻⣧⢸⡄⠀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠙⢿⣇⢰⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣾⣿⡆⡆⡄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣧⣱⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣝⣻⣿⣿⣿⣿⣿⠛⠋⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠾⢿⣿⣤⣴⣴⣦⣶⡶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣠⣶⠃⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢰⣿⡇⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⣿⠀⢠⣿⠀⠀⠈⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣾⡏⠀⠀⢸⣿⣇⢸⣿⡄⠀⠀⠘⣧⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢸⣿⡇⠀⠀⢸⣿⣿⡆⠻⣿⣦⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣤⣾⡿⣿⡇⠀⢹⣿⣧⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠸⣿⣷⡙⠛⠛⣵⡿⠁⠀⠀⣿⣿⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢿⣿⢀⣾⡟⠁⠀⠀⢀⣿⣿⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣾⣿⠀⠀⠀⠀⣼⡿⢹⣿⠏⠀⠀⢰⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣦⣴⣏⠀⠀⢀⣿⣿⣿⣤⣀⣤⠞⡉⢀⣿⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠾⣿⣿⣦⣤⣾⣿⢻⣿⣿⣿⣿⠀⡇⢸⣿⡿⣶⣾⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡛⢿⣿⠀⠻⣿⣿⣿⠀⡷⠄⢀⣴⡿⠉⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣧⣀⠁⠰⣆⠙⠛⠋⢰⠁⣴⣿⣿⡀⢀⣠⡿⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⣠⢀⣿⣿⣷⣦⡈⠻⣶⣶⣿⠀⠻⣿⠟⣿⡿⠋⠀⠀⠀⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⢹⣿⣧⠀⢹⣿⣿⠷⠖⠀⣰⣿⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡙⠛⠋⠁⢸⣿⡏⣴⢿⡟⠁⢀⣴⣾⣿⣿⣀⠀⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣄⠀⠘⠋⢸⣿⠘⠀⠀⣿⣿⣿⠟⠛⠛⠋⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠘⡆⠀⣿⡀⠀⠀⠈⠉⣡⠖⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣰⣿⠇⢀⣵⠀⣽⠹⣦⣤⣤⣾⣿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡟⠀⣾⣿⢾⣿⡀⢻⣿⠏⣿⡿⢸⣿⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠄⠘⠿⠄⢉⣤⠆⠁⣰⠟⠡⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡀⠀⠀⣀⢀⣀⣠⣈⣔⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉⣡⣼⡿⠟⠛⠁⠀⠉⠙⢿⡇⠀⠐⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠒⠒⡭⡵⣫⢂⡤⠂⠉⢉⡴⠛⠷⡄⠀⢀⡆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠁⢲⢏⡼⣱⡷⠋⠀⠁⠐⢠⠖⠛⠻⠇⠀⠀⣧⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢴⣲⣥⣾⡵⠛⠁⢀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⣧⠴⢊⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣂⣿⢋⣁⣉⠀⠀⠀⡀⠀⠀⢀⣾⣶⣄⠀⢠⡆⠀⠀⣿⣦⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⢋⡽⢛⡿⢶⣤⣤⣤⠶⡏⠙⠛⠂⠀⢸⡇⠀⠀⡟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢂⣾⠃⣠⠀⡀⠈⠷⣧⠀⠀⠀⠀⢸⡇⠀⠀⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢈⣗⢼⡇⠁⡟⠀⡆⢘⠀⠘⢧⡀⠠⠂⢸⡇⠀⠀⠞⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠜⢀⡼⡇⠀⢰⡇⠀⠈⣧⠀⠀⣿⠦⣄⣸⠇⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠒⠒⣁⡴⠋⠀⢻⣄⣀⢸⣄⠀⠈⠳⣄⣿⠀⠀⢸⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠔⠛⠉⢉⣹⠷⣄⠀⠈⢻⡄⠀⠸⠀⠀⠀⡟⢻⡆⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡀⠀⠀⠀⢡⣤⣽⠀⡆⣸⡇⠀⠀⠀⠀⠀⡇⢨⣳⣄⠠⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡉⠂⠀⠃⠈⠀⢀⡼⡧⣭⡀⣶⣿⠁⠀⢀⠀⠀⠀⣷⡞⠖⠉⣶⣤⣈⡀⠀⠐⠊⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠉⣿⠡⠒⢨⠉⠉⠈⠳⣄⢸⠀⠀⠀⣽⠀⠀⠀⢹⣧⡀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⡿⠓⣶⡯⢤⠤⣄⡀⠈⢿⠀⠀⠀⣽⠤⠤⣀⠈⣷⣝⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠛⣉⣥⣾⣿⣷⡞⠁⣀⢀⣀⡜⠛⠠⣾⠀⠀⠀⢸⠀⠚⡛⣿⣿⢟⡿⣦⣭⣙⣂⣀⣀⣃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⠶⠿⠟⠋⠁⢨⠿⣿⡀⢸⡁⠈⢹⡸⣦⣾⣿⣠⣤⣄⣼⣘⣤⡞⣸⠁⠀⡑⠀⠉⠙⠛⠛⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢠⠏⠀⢻⣧⠀⠙⠒⠫⠝⣻⢯⣯⣀⠀⣀⣸⣭⠶⢻⣭⡷⠊⠙⢄⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣿⠿⠷⣶⣶⣾⡳⠉⠀⠈⠋⢋⠀⠹⣾⢿⡟⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣤⠖⠛⠒⠉⠉⠉⠁⠉⠉⠉⠉⠹⠋⠀⠀⠀⠀⠀⠠⠀⣘⠀⢸⠃⠀⠀⠀⠀⢀⣠⠼⠛⠙⠛⠛⠶⠦⣄⣀⡇
⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡴⡫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣄⣤⠤⠴⠞⣿⠁⠀⢸⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⡰⠀⠀⢠⡟⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠉⠀⡠⠚⠀⡀⢠⠷⢎⣦⡼⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠱⠀⣠⣾⠓⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⣻⠛⠉⠀⠀⠀⠺⠀⠀⠠⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠒⠊⠉⠉⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣃⠀⠸⡅⠀⠘⡀⢆⣧⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠿⠤⠦⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢋⡏⡄⠀⠔⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡰⠁⠀⠐⠀⢠⠇⠀⡡⢢⡄⢀⡴⢊⠭⢍⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡴⢡⠀⡇⡆⡆⡿⠀⠸⣇⠀⠀⠘⠀⣇⣶⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣇⠰⡀⢧⢸⠸⣿⡀⢆⠉⠳⣄⠐⡄⠻⣝⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠁⠈⠢⣳⡈⢆⢣⠻⣿⣌⢧⢀⠘⣷⠸⡄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⡅⠀⠀⠉⡡⡄⢱⣌⢿⣾⣷⣧⠹⣿⠘⣾⣦⣿⠇⡇⣈⠀⢸⡆⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣺⢩⣛⢦⣿⣿⣿⣶⣿⢀⣿⡿⣫⠞⠁⡡⢀⣼⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠠⡸⠖⠀⢸⠂⠹⣿⣿⣿⣇⣾⣯⡟⢁⣴⣿⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⠀⠀⢤⠀⢿⡄⢆⠹⣯⣿⣿⣿⣿⣷⣿⣴⣆⡀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⠍⢹⠒⡟⣰⠺⢿⣶⣷⣿⣿⠟⠛⠋⠉⠉⠁⠱⠉⠃⠙⠒⣶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠿⠃⣼⠀⠀⠁⠐⣠⠼⠛⠁⠁⠀⠠⠀⠀⠀⠰⢆⠀⡀⠀⣼⢡⢺⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠷⠶⠶⣧⠤⢤⣞⣭⣀⡀⠀⠀⠀⢀⡴⣋⠀⢤⠶⢦⠶⢾⣧⣷⡘⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡗⠀⣤⡤⡀⢀⢸⡀⢀⢮⣹⡆⠀⣨⣾⠛⢿⣃⡏⠠⠄⠀⣼⣿⡍⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡇⢀⡛⡇⠀⣀⣸⣧⣐⣊⣿⢷⣿⡁⠠⠀⠘⣿⡷⢦⠤⠼⠋⢙⡃⢁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠲⠶⢒⣻⠿⢛⠅⠈⢛⢽⠞⠻⢿⣴⣶⠟⠃⠐⠀⠁⠀⠃⠀⠀⠴⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠛⠛⠛⠛⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠂⢉⣀⣀⣄⣀⣤⣄⣠⣄⡀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⠛⢋⣡⣤⡴⠶⠶⠶⢶⣶⠶⢬⣭⣱⠶⣤⡀⠀⠈⢳⡄⢠⡀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⠀⢈⡛⠉⠀⠀⠀⠀⠀⠘⠛⢷⡄⠀⠈⠙⢳⣎⢳⣦⡼⠇⠘⠃⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡇⠀⢀⣴⠖⠀⠀⣠⣤⣄⢻⡆⠀⠀⠀⢿⠋⠀⠀⠀⢸⠇⠾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠛⢉⣩⣶⣟⡁⣠⣄⣙⣿⡀⠀⠀⠈⣧⣠⣄⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠀⢸⠁⢻⣿⣿⡇⠀⢼⣿⣧⣿⠀⠀⠀⠀⠟⠀⣹⠀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⣄⠷⠦⠾⠏⠙⢦⣄⣩⣿⠟⠀⠀⠀⠀⣀⣤⠟⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢶⣄⠀⠀⠀⡋⠀⠀⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣠⣴⠟⠑⢦⡌⠈⠀⠀⢠⡇⠀⠀⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠶⠶⠶⠛⠛⠉⠀⠀⠀⠀⠈⢢⡀⠀⢸⠀⠀⠀⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡤⠶⠚⠁⠈⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠞⣶⡖⢠⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣄⣀⠀⠀⠀⣠⣴⠟⠉⣶⣤⡀⠀⣀⡀⢠⣤⣤⠾⠋⠀⢸⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡙⢋⠁⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⣠⡟⠀⠀⠀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠲⣤⣀⣀⠀⠀⠀⢀⣀⣤⡾⠋⠛⢧⡀⠀⡷⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⡇⠈⠉⠛⠛⠛⣿⠉⠀⠀⠀⢠⡖⢱⣄⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠚⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠁⠃⠸⡁⢸
⠀⠀⣠⡴⠶⠒⠛⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢠⡇⠘⠀⠀⢻⣾
⠀⣾⠁⠀⠀⣠⡀⠀⠀⠀⢀⣀⣤⣴⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠶⠶⠀⠈⢿⡄
⠀⠻⣆⠀⠀⠉⠻⣯⡉⠉⠉⠉⣰⠏⠀⠸⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠸⡇⠀⡆⠀⠀⠘⠹⣦
⠀⠀⠘⢷⣄⠀⠀⠈⠙⣦⢀⡼⠋⠀⠀⠀⢹⡄⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣾⣥⣰⣂⣡⠀⡇⠀⠀⠀⡇⠈⢷⣄
⠀⠀⠀⠀⠙⣧⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠻⣀⣠⠋⠀⠀⠀⠀⠀⠈⢱⣯⠀⠉⠉⠁⠀⠑⢦⣀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⣸⠆⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠠⣎⠁⠀⠀⠀⠀⠀⠀⠈⣿⠉⠻⢦⣤⣀⣀⠉⢷⡄
⠀⠀⠀⠀⢸⡷⠒⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠛⢦⠀⠙⢦
⠀⠀⠀⠀⡞⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⠄⡀⢸⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⣀⣤⡤⠒⠾⣅⡀⢀⡀⠀⠀⢀⣀⣠⣤⡴
⢇⠘⠓⠈⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡇⠀⢩⠀⠀⠀⠀⠀⠉⢹⡏⠉⠁
⠈⠓⠶⠶⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠑⠒⠒⠒⠒⠒⠒⠉⠉⢹⡇⠀⠀⡄⠘⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠓⠶⠤⣤⣤⣤⣤⠶⠖⢺⡇⠀⠀⠐⣄⠡⣄⠀⠀⠘⣷
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢦⡈⠓⢤⣤⠿⣀
⠀⠀⠀⠘⠒⠒⠒⠒⠒⠲⢦⣤⣤⣤⣉⣉⣉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠒⠒⠖⠒⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠉⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⢶⡶⠦⣤⣤⣄⣀⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠙⡞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠓⠒⠒⠒⠒⠀⠤⢶⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣧⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣟⠁⠙⠳⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⡶⠒⠒⠒⠒⠲⢤⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠔⠒⠛⠓⠛⠒⠀⠀⠀⠀⠈⠓⠚⠻⠛⠛⠋⠉⠉⠙⠛⠛⠻⠿⢶⣶⠶⠾⠃
⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠤⠤⢤⣤⡴⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣞⣀⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠚⢉⣸⣿⣿⣿⣿⡾
⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣻⠿⣷⣦⣀
⠀⠀⠀⠀⢠⣾⣿⣿⣷⢻⣿⡻⣶⣿⣿⣿⣿⣿⣖⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄
⠀⠀⠀⢠⣿⣿⣿⢿⣿⢸⣿⢏⣻⣿⣿⠛⠛⠛⢻⣿⠉⠉⠁⠈⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⡏⣿⡿⣟⣿⣿⣿⣿⡿⣿⡏⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⣷⣿⣿⣿⡼⣿⣿⣿⣧⣿⣗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢈⣿⡟⡟⣿⡇⣷⡽⣿⣿⣿⣿⡀⠀⠀⣰⡿
⠀⠀⠀⣼⣿⢹⡇⣿⣧⢹⣿⣮⡻⣟⡿⣥⢀⣴⡿⠁
⠀⠀⠀⠹⣇⢸⣇⢻⣿⣧⣙⢿⣟⠾⣽⣾⣯⣏⣀
⠀⠀⠀⠀⠙⠘⣿⣦⡙⢿⣟⡷⣾⣿⣶⣭⣟⠻⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⠛⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠛⣿⣿⠛⢻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿
⠛⠁⠀⠀⠀⠀⠀⠈⢻⠀⣿⣿⣿⣿⣿⡏⢠⡆⠸⣿⣿⡟⢹⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢻⣿⣿⣡⡟⠃⠀⢹⣿⠇⠀⢸⣹⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠛⣿⠇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣹⠃⠀⠉⡀⠋⠀⠀⠀⠉⠙⠂⣿⣿⣿⣿⣿⣿⣿⣿⣶⠸⠉⠋⢻⣿⣦⣟⠀⣾⣿⠿⠷⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⣧⠀⣿⡇⢠⡄⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢀⣾⡂⠀⠙⠀⠹⡇⠸⣷⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣄⣤⡴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣧⣼⠇⠀⠀⠀⠈⢠⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⠀⠀⠸⣟⣽⣿⣿⣿⣿⣿⢿⠟⠛⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⡏⠀⢀⣠⣿⣿⣿⣿⣿⠿⠃⣸⠀⣴⣈⣿⣿⣿⣟⣿⣿⣿⣿⣷⣤⡅⣿⣿⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡾⢪⣇⣠⣼⣿⣿⣿⣿⣿⡏⠀⠀⢻⠀⠻⣼⣿⡏⣿⣩⠓⢿⣿⣿⣿⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣧⣻⣿⣿⡻⣿⣿⣿⣿⣿⣧⣀⣀⡣⣘⣿⣿⣿⣿⣿⣦⣕⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⢻⣿⣏⣻⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡯⠀⢸⣯⣿⠟⢳⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢱⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣾⡟⠁⠰⠀⢹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡀⠀⠀⠀⢾⣟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠍⣹⣿⣿⡷
⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢇⣿⣿⣿⠇
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢀⣿⢠⠀⠀⣰⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢇⣸⣿⠿⣋⢠⣶
⠀⠘⡟⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡿⢸⠀⣰⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠤⡟⢸⡿
⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣿⡁⢸⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠃⠘⣿⡄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠃
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣼⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⢸
⡧⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⠇⠀⢀⣧⠀⠀⠀⡘
⡗⠀⠀⠀⣿⡌⠀⠀⠀⠀⠀⣾⣿⡇⠀⢈⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⡿⢸⡧⣸⡿⠀⡄⢸⢧⣆⠰
⡇⠄⠀⠀⠿⣿⠀⠀⠀⠀⠀⢻⣿⡇⠀⡎⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⣾⠸⣿⡇⣼⠁⣼⡇⠀⣇⡜⢸⣿⢸
⣧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢨⣿⡇⢸⣷⠀⠀⣿⣿⣿⣽⣿⣿⡟⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠓⢠⣿⠁⠈⠄⢸⡇⣿⡁⠀⣿⡇⠀⣹⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⢸⡟⠀⠀⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⠀⠀⠀⣸⡇⢻⡇⢰⣿⡇⠀⢸⣿
⣿⣆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⣿⠀⣼⡧⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢩⣿⣿⣿⣿⣿⣟⠉⢠⡀⣾⡟⠀⠀⠀⣿⡇⢼⡇⢸⣿⡇⠀⣾⣿
⣿⡟⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⣾⣇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣡⣀⢀⣠⣿⣧⣾⣧⣼⣿⣧⢀⣿⣿
⣿⡇⠸⣿⣴⠆⠀⠀⠀⠀⠀⣧⣿⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣴⠀⢀⣿⢻⣿⣿⣼⣿⠿⣿⣿⣿⣿⣿⣿⣘⣿⣿
⣿⣷⣀⣿⣿⡆⠀⠀⠀⠀⠀⢻⡿⠀⣿⣿⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⠿⠃⠀⠈⠉⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠏⣿⡏⣿
⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠘⡇⠀⢿⣿⠀⠀⠀⢸⣿⡟⠏⠀⠀⠀⠙⢻⣿⣿⠏⠀⠀⠀⠀⠈⠻⣿⠛⠿⠿⠿⠼⠛⠿⠿⠛⠀⠟⠁⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠄⠀⠀⠘⢌⠢⠀⠀⠰⠀⠠⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠊⠀⠘⡠⠀⠀⠀⠠⠑⠀⠀⠀⠐⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⠀⡰⠁⠀⢹⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠁⠄⠘⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠐⢀⠁⠳⠉⢦⣠⠁⠀⠀⢸⠀⠲⢀⡶⢱⠀⢀⠀⠸⠎⠀⠀⡄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⡉⠀⠀⠹⡀⠀⠀⠸⠀⠀⠰⠁⠀⡇⠈⠴⠃⠐⡆⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢾⠣⣄⣠⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠀⡇⠂⠀⠀⢠⠃⠀⠀⣀⢀⡀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⢇⠀⠀⢠⢃⣄⣀⣤⡔⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⢈⠼⠊⢰⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠙⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⢀⠔⢠⠀⠀⠱⠁⠀⠰⠁⡾⠁⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣅⣀⠀⠀⠀⠀⠀⠀⠃⠄⠂⠖⠄⠀⡀⠈⠠⠄⠂⠀⠀⠠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⢐⡖⣻⣉⣉⠉⣩⣽⠶⣀⠀⠀⣀⣠⠤⢤⣀⡄⡦⠀⡠⢦⠐⠠⣤⢄⠂⠠⠾⠿⢷⣿⡂⡀⢰
⠀⠀⠀⠀⠀⠀⠹⠷⠼⠷⠶⠚⢧⡇⢠⣾⣶⣛⡻⣄⣵⢠⣼⠃⣓⢲⠀⢘⣧⡂⠚⢺⣇⣀⡀⡶⡞⣮⣭⠴⣾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠙⠛⠛⠁⠀⠙⠶⠖⠛⠉⠙⠳⠚⠋⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠻⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣾⣷⣶⣊⣽⣷⣄⡀⠀⠀⠀⢀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣖⣛⣏⢻⣷⣿⣿⣷⣀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⠙⡛⣿⣷⣝⠿⣿⣿⣿⣿⣉⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢁⣿⣟⣾⣝⡺⢿⣿⣿⣿⣍⠻⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠁⠟⣛⣿⣷⣬⣓⣬⣿⡆⠘⡄⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡄⠀⢀⡄⠀⣴⣿⠿⣃⠀⠀⢸⡿⢿⣿⣿⣿⣿⡛⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣟⣠⣾⡟⠁⢹⣁⣴⣨⣩⣿⣯⣿⣿⣿⣿⣿⣬⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠋⠁⡴⠞⣿⣿⠋⠛⠿⢻⣿⣿⣿⣿⣯⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⣲⣶⣷⣿⣿⣿⣄⠀⣶⡇⣿⣿⣿⣿⢿⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⠟⡦⠀⢻⣿⣿⣿⣿⢈⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢠⣾⣿⢿⣿⡿⣿⡿⠀⣆⡀⢺⣿⣿⣿⣿⠞⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⢻⠾⠛⠀⠘⠛⠐⢣⠱⣿⠻⢸⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⣮⣭⣽⣭⣭⣵⣖⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣯⠧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⢉⣁⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣽⣾⣿⣿⣿⣿⣿⣿⡿⠃⠙⠿⠟⠳⢯⣷⣿⣿⣿⣿⣿⣿⢟⠞
⠀⠀⠀⠀⠀⠀⠀⣸⣱⣿⣷⣿⣿⠋⠖⠈⠿⠋⢐⣦⣄⡀⠀⠀⠀⠀⠙⠻⢿⣿⣋⣚⣷⣶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢾⣻⣿⣿⢿⡀⠀⠐⠀⠀⠀⠈⠋⠀⠀⠀⠀⠉⠀⠉⠘⠉⠉⠉⠉⠉⢹⣽⠀⠀⣠⣫⢿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣓⣆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠋⢍⣍⡽⠲⣶⣶⣶⣞⡋⣎⣀⣰⣳⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡴⣯⠭⠿⣭⣯⣷⣯⣽⠄⠤⠐⠀⠠⠵⠠⠤⠀⡴⢋⢪⠀⢆⠀⠀⡀⠀⠙⠒⠓⢲⠃⠐⡞⢷⣭⣢
⠀⠀⠀⢀⡤⣤⣴⣹⡇⠀⠀⢀⣀⡀⡠⠀⠀⠀⠀⠀⠐⠒⠀⡤⣴⢣⠈⠀⠀⠈⠂⠤⠄⠃⡴⣲⣒⣚⣦⣴⣷⣾⣟⡽
⠀⠀⡴⡵⠋⠉⠉⠉⠉⠁⠀⠀⠀⠰⠁⠀⠀⠀⠀⠉⠉⠠⢾⣥⣿⣷⣄⠀⠀⠀⠀⠀⣰⣞⣵⠁⠀⠀⠉⠉⠉⠉⠁
⠀⢸⣹⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣄⡀⠀⠀⣈⢀⣀⣾⣿⣿⣿⣿⣷⣤⠤⢤⡔⢿⣿⣮⢦⡀
⠀⠈⢫⡳⣤⣀⣀⣀⡠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠙⢿⣷⡵⣄
⠀⠀⠀⠈⠓⠺⡽⣍⠉⠉⣹⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣞⣆
⠀⠀⠀⠀⠀⠀⠙⢮⣲⣶⣛⡯⠗⠊⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⠠⠄⢀⣴⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡷⢝⡦⠤⣞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠭⠽⢿⣿⣟⣿⣿⣿⠯⠭⠟⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣷⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠻⣿⣧⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣼⠀⠀⠀⠀⢻⣿⡇⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡆⠀⠀⠀⢸⣿⠇⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣄⣀⣠⣿⡿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠈⣿⣿⣿⣿⠃⠀⢀⣾⣿⠏⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣿⣿⣷⣶⣿⣿⡟⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸⣿⣿⡻⣿⣿⣿⣿⡇⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⢀⣼⣿⣿⡇⠸⣿⣿⣿⣿⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠘⠛⠁⢰⣿⣿⣿⣿⣿⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⡄⠀⢰⣿⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⣿⣿⠃⠀⠈⠛⠀⢻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠘⠓⠛⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⢀⠓⠒⠲⢶⣶⣤⣽⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠘⠛⢿⣿⣿⣿⣶⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠠⣾⠟⠹⣍⠙⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⣇⠀⢬⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⡀⠒⠐⠶⣶⢦⣄⡀⠀⢻⣿⣷⣌⢻⣿⡾⠅⠃⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⢙⣿⣦⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠉⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⢠⡶⢶⣶⣶⣦⣦⣤⣍⠉⢈⣉⣻⣽⠟⠉⠙⠋⠋⡻⠀⣀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⣾⠿⣷⡌⠋⠀⠀⠀⢹⣿⠻⠅⠀⠀⠈⠀⠠⠂⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠊⠁⠀⠀⠀⠋⢰⢿⣷⠂⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠃⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣮⣿⣿⣠⣦⠀⡖⢰⠂⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⡟⢻⣿⣿⣤⣇⠸⣦⠀⣇⣀⠄⠀⣇⣾⠉⢿⣿⣧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣿⣿⣿⠁⠈⣿⣻⠉⢿⣇⢻⣿⣾⣿⢀⣼⢹⡿⢃⠘⢿⣿⣁⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣽⣿⡿⠀⠀⣿⣿⣶⣌⣿⣌⢻⣿⣿⣾⣣⣿⡇⢹⡄⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⣄⠙⢻⣿⠛⠿⠿⠛⣛⣛⣿⣻⣿⣷⠀⠰⢆⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡏⠀⠘⠈⣠⡾⢃⣴⡿⠶⣟⣿⣿⣿⣿⣵⣿⡄⠀⠹⡄⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⢠⡉⠼⣋⣴⣿⣿⠿⠚⠛⣱⡿⠋⣹⣿⣿⡀⠀⠀⠱⡆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣝⠀⢈⣵⢾⣿⣿⣿⣷⠀⢠⣾⠟⠀⣼⣿⣿⣿⣁⠀⠀⠀⠛⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠉⢹⣿⠋⣀⣾⠏⡌⢹⣿⣿⠇⢠⡿⠃⠀⣴⣿⣿⣿⢿⡘⠀⠀⠀⠀⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢁⣼⣿⠇⣠⢃⡿⣼⣿⣰⡟⠁⢠⣶⣿⢡⣿⣿⠀⣿⢰⠀⠀⠀⠙⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⠞⢰⡟⡘⣷⡟⣱⠋⢀⣴⣿⣿⡏⣸⣿⡇⢰⡟⠀⠁⠀⠀⠀⠈⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⡟⠀⣰⠏⠐⢁⣴⣿⣿⡿⣿⠃⢿⣿⡇⢸⠀⢰⠀⢀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢡⡟⠀⠀⠁⢀⣴⣿⣿⣿⠟⣰⡟⠀⠀⢿⢡⡇⠀⢸⡄⠸⣆⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢡⡟⢀⣀⣤⣾⣿⣿⣿⡿⠃⣰⣿⡁⢣⠀⠈⠸⡇⠀⠀⢿⡀⢿⡄⠀⠀⠀⠈⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠻⢑⣫⣿⣿⣿⠿⣩⣾⣿⡟⠁⣰⣿⠇⣇⢻⣄⡀⠀⠀⠀⠀⠘⣇⢸⡏⠄⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠁⠀⠚⢹⣿⠿⢿⣶⣿⡟⠀⣇⢸⣿⣇⠀⠀⠘⠂⠀⢸⠀⣄⠂⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣉⣥⣶⣿⣷⣤⣀⣀⣠⣿⠇⢠⠞⢸⣟⠰⠿⣏⠀⠈⠻⣆⠛⠧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢈⣤⡾⢛⣡⣴⣿⣿⣿⠃⣹⡇⠈⠉⠛⠛⣿⠆⣀⣠⣿⣿⠀⠀⠈⠀⠀⠀⠹⣦⣀⣰⣤⣀⣀⠀⡤⠚⢀
⠀⠀⢤⣶⠟⢉⣴⠟⢫⣿⣿⣿⠏⢠⡿⠙⠂⠀⠀⣼⠋⠚⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢥⣿⠁⠀⠀⠘⠃
⠀⠀⡀⢀⣴⡿⠃⢀⣾⣿⣿⡟⢠⣿⠃⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠠⣠⡾⠛⠁⠀⣸⣿⣿⣿⠇⠀⠐⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⢀⡾⠋⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⡜⠁⠀⠀⠀⠀⣺⣿⣿⡿⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣷⣲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠿⠷⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣃⣀⣼⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⢿⠋⠁⢸⠟⠛⠛⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠉⠨⡄⠀⠀⠀⠀⠰⠪⣶⣶⣶⣾⣭⣭⣤⣷⡶⠟⠛⠛⠛⠺⠞⠲⠒⣶⠚⠛⠛⠛⠛⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⠠⠄⠓⠀⠀⢀⠀⠀⠀⠀⠐⣔⡪⠍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣶⠶⠖⠛⡛⠉⠀⠠⣶⣚⣀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⢸⡀⠀⠀⠀⠀⢾⡁⣀⣤⣶⠋⠀⠀⠀⢀⣿⣿⣷⣶⣆⡀⡄⠤⠁⣀⣀⣠⣤⠴⠶
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠙⡯⡟⠁⠀⠀⠀⢀⣿⠏⠙⠛⠻⢻⣿⣿⣶⣼⡿⠋⠉⠈⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠃⠀⠙⢦⣄⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⢿⣦⣤⣴⣿⣿⡿⡇
⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠙⠋⠻⣿⣿⡟⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠄⠀⠀⠉⠁⠀⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢹⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠲⠖⠤⣤⣤⡾⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣿⡟⠛⠻⠷⠶⣶⣤⣄⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠿⣿⣿⣇⠀⠀⠀⠘⡏⣿⡇⠀⠀⠀⠀⠀⢸⡟⣿⠀⠈⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⡘⢷⡀⠀⠀⠈⢿⣿⠀⠀⠀⠀⢳⣸⠇⠀⠀⠀⠀⠀⠘⢰⡇⠀⠀⠀⠀⠀⠈⠛⣶⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠈⣷⠆⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⢸⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠜⠁⣰⠁⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠆⠀⢠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢸⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣼⡄⠀⣿⣾⠀⠀⠀⠀⣸⡇⠀⠀⢀⣼⡇⠀⠀⢀⣴⡟⠁⣀⠄⠀⠀⠀⠀⠤⠤⠴⠶⠾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⠶⠿⠿⠶⠶⠶⠾⠿⣶⣤⣤⣾⣿⡁⠀⣰⣿⠏⣴⣾⠅⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣼⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢠⣶⣶⣿⣿⡿⠿⠛⠃⠀⠀⠀⠀⠉⠙⠛⠿⢿⣧⣾⠟⠁⠀⢀⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡾⠟⠋⠉⣀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⢤⣤⣌⣙⠻⢶⣟⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣠⣤⣶⣿⡿⠟⠛⣉⣉⣤⣤⣴⣶⣶⣶⣶⣦⣤⣄⡀⠉⠛⠶⣿⣿⣍⠉⠉⠉⠛⠛⠒⠲⠤⠄⡀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠛⠋⠁⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣷⣦⡀⠈⠻⣿⣷⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢠⡟⠛⠿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀⠈⢿⣷⣦⣌⡉⠛⠶⣤⣀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⡉⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠈⢿⣯⣉⠛⢶⣄⡀⠉⠻⢶⣄⡀⠀⢿
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣈⡉⠛⠶⣦⣤⣉⡛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠸⣿⡿⣷⣤⡈⠙⢦⡀⠀⠉⠻⢦⣸⡇
⠀⠀⠀⠀⢠⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣛⠶⣤⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣿⣿⡆⠀⣿⣇⠈⠛⢿⣦⡀⠈⠀⠀⠀⠀⣿⡧
⠀⠀⠀⠀⢸⡇⠀⠀⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠃⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⡟⢷⡀⠀⠙⢿⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣼⡇⠀⠀⠛⠛⠛⠛⠛⠛⢛⣋⣉⣉⣉⣭⣭⡥⠴⠿⠧⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢀⣿⣿⡄⠹⡄⠀⠀⠙⢧⡀⠀⠀⣿
⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⠀⣠⠀⣠⠀⣿⢶⡀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣸⣿⣿⣿⡄⠘⠀⠀⠀⢀⠑⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠛⢉⡉⠁⠀⠀⣿⣿⠀⠀⣿⣄⣿⠀⣿⢸⣷⡄⠀⠀⠀⠀⠻⣿⠇⢀⣿⡟⢿⡿⣿⡀⠀⠀⠀⠀⠳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⣋⣴⣾⠟⠁⠀⠀⠀⢻⡇⠀⠀⣿⣿⣿⠀⣿⠘⣿⣿⡄⠀⠀⠀⠀⠈⠀⣾⣿⡃⠈⢿⡘⣷⡀⠀⠀⠀⠀⢹⣾⡏
⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⠛⠛⠋⠁⠀⠀⠀⠀⣰⡿⠃⠀⢰⣿⣿⣿⠀⢿⡇⢿⣿⣿⣆⠠⣄⠀⠀⣼⣿⣿⣇⠀⠈⠇⠘⣷⠀⠀⠀⠀⢸⠟⠃
⠀⠀⠀⠀⠀⠀⣼⠠⠿⠿⣧⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⣾⣿⣿⣿⠀⢸⡇⠈⣿⣿⣿⣦⠙⣷⣼⣿⡟⠀⢿⡀⠀⠀⠀⠸⣇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢰⣏⠀⠀⢠⡝⢧⠀⠀⠀⣰⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⡄⢸⣇⠀⠘⣿⣿⣿⣧⠘⣿⣿⣧⠀⠈⠃⠀⠀⠀⠀⠙⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠉⠛⣿⠉⠀⠈⠃⠀⢸⡇⠀⠀⠀⠛⠉⢉⣴⣿⣿⣿⠆⢸⣿⠀⠀⠸⣿⣿⣿⡇⢹⡇⢿⡆⠀⠀⠀⡀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠒⠒⠀⠀⠸⣧⠀⠀⠀⠀⣠⣾⡿⠟⠋⠀⣠⣼⠟⠀⢀⣀⣹⣿⣿⣇⢸⣇⠘⣿⠀⠀⠀⣇⠀⠀⠀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⣿⡄⠀⠀⠴⠛⠉⢀⣤⣶⣿⡿⢿⣶⣤⡀⠙⠻⣿⣿⣿⠀⣿⠀⢻⣇⠀⠀⢸⡄⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⢀⣸⣧⠀⢀⣠⣴⣾⣿⣿⠟⠁⡀⠀⠉⠛⢿⣷⣤⣀⠉⠻⠆⢹⡆⠈⣿⡀⠀⢸⣧⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⣿⡾⠛⣿⣿⣿⠟⠁⠀⣠⡏⠀⠀⠀⠀⠉⠻⢿⣷⣦⣀⢸⣇⠀⢹⣇⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠿⣿⠀⠈⣿⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣤⣀⠀⠀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣽⣭⣬⣭⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⣶⣦⣶⣿⣿⣿⣯⣽⣼⣽⣷⣯⣽⣿

⣿⡟⡿⢿⠛⢻⠿⠻⡿⠟⢿⠟⠻⡿⠛⢿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣧⣠⣿⣀⣸⣄⣁⣿⣀⣷⣈⣠⣇⣀⣸⣿⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠉⠉⠉⠉⠋⠉⠉⠛⠉⠛⠛⠉⠙⠛⠋⠙⠉⠀⠀⠀⠀⠇⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠋⢂⣀⣠⠖⠖⠲⢢⣄⣀⡔⡙⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣆⠀⣠⠍⠁⠀⠀⠀⠀⠈⠩⣄⠀⣰⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠅⠀⠄⠠⡄⢠⠄⠀⠀⠨⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⡍⠁⠀⡔⡤⠖⠲⠤⢂⠀⠈⢹⠄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣁⣸⡀⠀⠀⠀⢰⠋⠙⢗⠶⢶⡖⢲⡶⠶⡾⠋⠙⡆⠀⠀⠀⢰⣆⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⢣⠀⠀⠀⣎⠈⠸⠈⠑⠚⡇⢘⠓⠊⠀⠂⢀⣵⠈⠀⠀⡞⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⠿⣶⢼⣇⣛⡦⣬⡢⢒⣧⣼⡒⣐⣤⢴⣻⢹⡦⡾⠿⣷⣿⠠⠀⠐⠀⠀⠠⠀⠀⢠⠋⠁⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡠⠒⠛⠛⠍⢿⡇⠢⠱⣯⣶⣶⣽⠎⠔⢸⡿⠩⠛⠓⠒⢄⣽⡇⡠⣤⢤⢤⣀⡤⠦⠀⡀⠄⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠑⠈⠀⠀⠀⠀⠀⢷⠀⠀⠃⠁⠀⠹⠀⢀⡞⠀⠀⠀⠀⢀⠁⠊⠙⠢⣍⡈⠂⠹⡙⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢻⢷⠬⣄⠀⠀⠈⠦⣙⣧⡤⡘⢷⡀⠀⠀⠀⠀⢠⡿⢃⣤⣾⣋⠄⠁⠀⠀⣠⠥⡺⠟⠀⠀⡇⠁⠀⠀⢀⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⠈⠀⠀⠐⠀⠒⠉⠈⠓⠐⣟⠊⠙⠳⣆⣰⠞⠋⠑⣻⠂⠛⠁⠁⠒⠀⠊⠀⠀⠁⡇⠀⠀⡇⠀⢠⣄⣸⣿⣄⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢺⠀⠀⠀⠀⠀⠀⠀⢰⠖⢈⣁⣙⣢⣤⡿⠷⠆⠒⠋⠈⠁⢴⡊⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⡇⢀⣾⣿⣿⡷⠶⠤⣭⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⢀⠀⣺⠛⠁⢡⠉⡈⢰⠁⠀⠀⠀⠀⠀⣀⣾⠧⠀⠀⠀⡠⠀⠀⣸⢰⣷⣰⣧⣾⣿⡿⢿⣷⣿⠛⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⢦⠀⠀⠛⠁⠀⠘⠀⠀⡀⠠⠀⡆⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠈⠛⠀⠀⡾⢹⣺⣿⣿⡿⣛⣿⣶⢿⣿⣿⣿⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡄⠀⠀⠀⡘⠀⠀⡈⠠⣁⡬⣔⣽⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡴⣰⣠⣦⢾⣻⣭⣾⣿⣿⣿⣿⣷⣿⣶⣦⣄⣀⢀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣇⣸⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣯⣩⣶⠤⣝⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠊⣿⠛⠳⢭⡳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⠀⠀⠀⠙⢮⣻⣿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠈⣷⡽⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢤⡙⠶⠦⠦⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣇⣀⣀⣀⣐⣀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢭⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣁⣉⣭⣤⣽⣿⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⠋⠁⣀⡴⢿⣯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠋⠉⢁⣾⣿⣿⣶⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠀⠀⠀⠘⣿⣿⣿⡟⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⡿⠁⢀⢀⡴⣢⣍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣵⣾⣿⣿⣿⣿⠃⣠⣿⣿⠟⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢽⣻⢿⣿⣿⣿⢿⣫⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠵⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⢹⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⡟⡆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣦⢸⢸⠿⡆⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢰⢿⠇⡇⣴⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣿⠀⡼⠹⠘⢸⠀⣷⠀⠀⠀⠀⣶⡰⣭⡆⠀⠀⠸⠈⡇⣇⠏⢣⠀⣿⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣡⣾⢸⣧⣙⣡⣧⠸⣤⣿⠀⠀⠀⣰⣿⣷⣜⠃⠀⠀⣷⡆⡇⣼⣌⣋⣼⠉⣧⣜⣷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣼⡟⣷⢧⡄⡇⢹⣥⣨⢣⣿⣾⠀⢀⢴⣿⡏⣿⢻⡦⡀⠀⣷⣿⡜⣅⣬⠋⢸⢰⡹⡿⢿⣧⢿⡇
⠀⠀⠀⠀⢠⡄⠀⢸⣦⣹⣷⠏⣿⠀⣿⣷⢻⡏⣿⠇⡿⢀⠎⣼⢹⡇⣿⢼⢃⣵⡀⢿⠸⣳⢹⡏⣾⣿⠘⣷⠻⣾⣿⢬⡇⠀⢠⡄
⠀⠀⠀⢠⡿⠀⠀⢸⣟⣹⡏⢆⡏⢸⡏⡏⡌⠑⡎⡀⡇⢸⡟⣿⠘⣇⢹⣧⣸⣿⡇⢸⢀⣿⠸⢡⣿⢻⡆⢣⢁⢹⣏⣾⣇⠀⠀⢿⡄
⠀⠀⢠⠏⣧⠀⣠⠇⡻⣿⣱⡟⣾⢸⡇⢣⢻⣄⠁⡇⢿⡜⣧⡇⣶⢻⡀⣿⣿⣼⣣⡟⣼⠈⣰⡟⡏⢸⡇⣧⢿⡆⣿⣿⠹⣄⠀⡸⢹⡄
⠀⠀⢸⢠⡘⣿⣡⣞⢠⡿⠿⢹⢿⢸⡇⣼⣆⠛⠆⢿⢸⣙⣿⢡⢿⣾⡇⢹⡇⣿⠉⡇⡿⠸⠋⣰⢧⢸⡇⣿⠘⠃⢿⡈⣣⣎⣿⢃⡌⡇
⠀⢠⣼⢼⡇⣹⡶⡽⣾⣷⣇⢸⡿⢸⡇⡟⡿⡜⡟⡌⣼⣿⢃⡿⢸⢸⣇⣼⡇⣏⠿⣏⢃⢿⢱⢿⢸⢸⡆⢿⠀⣼⣾⣇⢯⢶⣏⣼⢱⣧⡄
⢀⡾⢻⡏⣱⠏⣀⡰⣻⢿⡟⣧⢿⣸⠃⠀⠁⡇⡷⣱⢋⣿⣏⣷⡼⢸⡿⣿⢱⢟⣄⠹⣎⢾⢸⠈⢀⠘⡇⠿⣾⢹⡟⣿⣆⣀⠻⣟⢸⡟⣿
⣼⡷⣾⡿⣱⢇⣿⠾⣇⣾⠣⢻⣄⡿⢸⣧⢠⠃⣼⠃⢸⣿⡜⠘⢁⡾⢁⡏⡿⣾⠙⣦⡹⣦⢸⣠⣼⡆⣿⢰⡟⠸⣧⣼⠧⣿⡼⣞⢿⣗⢾
⡏⢻⣿⢣⢻⡘⣯⠘⡿⢣⡶⣸⣿⠇⣦⣿⢸⡾⡏⣶⠸⢀⡖⣸⢹⣧⣾⡗⣧⢣⡆⣼⢣⣿⢿⡇⣿⣰⠸⣿⣇⢶⡘⢯⠃⣽⢣⡟⡜⣿⡞
⢷⡟⢸⡸⠞⠄⣩⢞⣡⡞⣰⠿⡏⢸⣇⢻⠘⠀⡇⠙⠘⠏⡟⢉⠘⠛⡏⢣⠉⠘⠃⠛⠈⣿⠀⠁⡇⢸⡇⢻⠻⣦⠷⣌⠳⡍⢠⠳⢷⡇⣷
⠈⢿⡈⢧⠻⣷⣯⣞⣠⡾⢃⢸⠁⢸⡘⡏⣴⡄⣿⠀⡆⠀⢰⠞⠀⠀⠀⠈⠟⣧⠐⠑⠀⣿⠀⣆⢱⢙⡇⠘⡇⡘⣷⣌⢳⣽⣦⢟⡞⢀⡿
⠀⢬⣳⡌⢳⣿⢋⡞⣿⢣⣿⢸⣸⣇⠻⢠⡏⠀⡿⡄⠀⢸⡄⢶⠀⠀⠀⠳⠀⢹⡄⠎⣸⢿⠀⢹⡌⠟⣼⣇⡇⣿⡘⣟⢿⡙⣷⡞⢠⣞⡤
⠀⢸⣿⠇⢾⡻⣟⠠⣿⢸⣻⠸⣿⠘⡆⢸⢰⢰⡇⢰⣸⡿⡇⣾⢷⡆⢾⡆⢸⠂⣷⢰⡇⠸⠀⣌⡇⢸⠁⣿⢣⣟⡇⣿⢤⣿⢿⡁⣸⣿⡇
⠀⢸⡏⢧⡾⡁⣧⠃⣿⣸⢻⡇⢡⡄⣷⢸⢃⡟⢰⢸⡿⣦⢃⡟⠸⣳⢢⣿⠸⠁⡘⣿⢳⡄⢷⡘⡇⣿⢰⡅⢸⣿⡇⣿⠘⣾⢈⢧⡽⢹⡇
⠀⢸⣷⡜⢱⢃⣿⢷⡟⣿⡟⡴⢛⠃⣿⣴⡟⣠⢿⢸⡇⡿⣸⣇⢠⣏⡎⣿⣴⢸⡇⣿⡞⢳⣌⢻⣦⣿⠸⡛⢆⢻⡇⢿⡾⣿⡸⡎⣡⣾⡇
⠀⢸⡟⣸⠀⣼⣿⢀⡁⣿⢸⢱⡏⢸⢫⢏⣾⡟⡘⣼⠉⣵⡿⡏⣾⢏⡗⢹⡅⣼⠇⡿⢧⠎⣿⣦⡹⡝⡆⢹⡞⡇⣿⢈⡀⡿⣧⠀⣇⢻⡇
⠀⠀⢧⠻⢸⠇⣿⢘⢣⠈⣤⣾⠃⡾⠃⣎⢸⢱⢣⡇⣼⠹⡇⢳⡿⢠⢗⡟⡼⠁⣸⣧⠸⡜⡜⢂⢳⠘⣷⠘⣧⣥⢁⡞⡃⣿⢸⡆⢏⡾
⠀⠀⠈⢷⣼⡆⣿⠸⡾⣇⢿⡘⣸⢃⠸⡹⠘⣿⢸⡿⣏⣆⢳⡀⣷⠺⣬⢡⣽⣼⠋⣿⢿⡇⣿⠸⢾⠀⡘⣇⢇⡟⣸⣣⢇⣿⢸⣧⡾⠁
⠀⠀⠀⠀⠉⠃⠈⢧⡹⣿⣮⢡⡏⣷⡀⣧⡄⢻⠘⠁⣿⢙⣦⠳⣌⠷⠏⢣⡿⣱⡏⣿⠘⢠⡇⢠⡼⡄⣧⢻⡈⡿⣿⢋⡾⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠐⣦⡻⣍⣮⣾⡇⢿⣿⠘⠇⢸⠀⣷⠸⡎⣿⡆⠹⣷⣴⠏⢐⣯⣹⠇⣧⢸⡇⡞⠃⣿⡹⢸⣧⣽⣱⠟
⠀⠀⠀⠀⠀⠀⠀⢫⣳⡹⡏⢿⠀⡟⢸⣠⢰⣾⢰⡏⡄⣿⠘⣷⠀⢻⡏⢺⣘⠃⣿⢰⢹⠸⣇⠇⣄⠃⣷⢸⡇⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣥⢻⣾⡄⡇⣾⡿⡄⢿⡘⣧⡇⣿⠃⡁⣾⢸⣷⠸⡏⢸⣿⢾⣸⢰⡟⢸⣿⢰⣶⢸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣏⣣⢷⠉⡇⢷⢰⣄⠻⠇⣿⢠⣿⡏⣾⠛⣧⢻⢹⣿⠸⠏⣨⡄⣷⢸⢀⡏⣜⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠳⣏⢸⠸⣘⢧⠀⣿⠸⢹⣧⡟⢀⢹⣦⡟⣿⠀⠾⢹⠀⡇⣸⠟⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡻⠄⢿⡀⡆⣿⡼⣼⢹⡇⡿⢸⣿⡕⡿⢸⣠⡟⠰⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣍⣃⠘⣷⡉⢾⡕⣣⡟⣩⣼⢃⣉⣭⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣾⣷⡟⢞⣵⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⢀⠠⢶⠙⢀⠴⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡄⠉⢳⣎⢻⣆⢀⠠⠊⠁⠀⡱⠛⠁
⠀⠀⠀⠀⢶⣂⣀⣲⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⢒⡶⠒⡲⢄⣾⢀⡳⡠⠐⠫⠼⢺⠁⡠⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠆⠀⠀⠀⣠⠔⠂⠉⠀⢀⠘⠀⠀⠈⠀⠐⢠⣿⣏⠟⡐⠓⠱⢛⣿⡎⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡠⠶⠁⠂⠉⠀⠒⢀⠀⠀⢃⠠⠂⠀⠰⡈⣄⢋⠻⠷⣾⡥⢶⣏⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡷⠋⠀⠀⠉⠀⠀⠀⠀⡈⠔⢄⢸⠀⠀⠀⠀⢳⡘⣆⠑⣴⠫⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠠⢎⡀⠀⡠⠒⠛⠉⠁⠢⢈⠑⢄⠀⠙⠀⠀⡿⣀⠀⠙⢌⠳⢥⣾⡽⡼
⠀⠀⠀⠀⠀⡰⠏⠀⠀⠌⠌⠀⠀⠀⠀⠀⠀⢢⠀⢣⠀⢀⡬⠄⠘⢃⡟⠈⢑⠦⣭⡵⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠆⠀⠓⣆⢩⢌⣧⠀⡀⣼⠋⠁
⠀⠀⠀⠀⠸⠀⠀⠀⢠⠄⠀⠀⠸⣃⠄⠀⠀⠀⠀⠀⠏⠀⠂⠹⠂⣀⣤⠗⠉
⠀⠀⠀⠀⠀⢇⠂⠀⠀⢇⠀⠀⠀⠀⢀⠀⡀⢀⠁⠀⣏⣦⡦⠖⢻⠉
⠀⠀⠀⠀⠀⠀⠑⠠⠀⠈⢦⠀⠀⠀⠢⡢⢀⠎⠚⣰⡁⠀⠀⢀⡞⠈⡜
⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠠⢕⠢⣠⠤⣬⢥⡧⡴⡥⢙⠶⢶⠯⡵⢞⠄⠀⠠⠤⠖⠠⠀⠠⠀⠄⠤⠀⠄⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠻⣿⣿⣶⣦⣀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣦⡹⣿⣿⣿⣿⣦⡻⣷⣄⠙⢦⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢿⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣷⡽⣿⣷⣌⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⣬⣻⣿⣿⣿⣿⡏⠙⣿⣿⣿⡻⡼⣿⣿⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠻⣿⣿⡄⠈⢿⣿⠃⠁⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣴⣦⣤⣭⣉⡙⠛⢿⣿⣧⡀⢈⠻⣷⡰⣌⢿⣦⣆⣸⣿⡿⢛⡛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⢿⣿⠿⢿⣿⢿⣷⣤⣨⣽⣿⣎⣿⣾⣿⡿⢿⣛⣿⣿⣿⡼⣫⠽⢦⣻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠁⢀⣹⣿⣿⣭⣍⣀⠈⢭⣭⣿⣿⠿⢛⣩⡶⠟⠛⢉⣩⡍⠉⣶⡇⣾⡆⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢿⣻⣿⣿⣾⠿⣫⡴⢖⡋⠠⠶⣊⣃⡤⠥⢶⣖⣻⣿⣾⣾⣿⣇⠑⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣩⣵⣿⣶⣠⣤⣴⣾⣿⢿⡿⠗⣛⡬⠔⣚⣭⣴⡶⠿⢟⣛⠻⠉⠉⠋⠻⣿⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⣡⣿⣿⣿⣿⣿⢟⣵⡿⢟⣫⣵⠞⢋⣽⣿⠋⣶⣶⡶⣿⣷⣤⣄⣤⣤⡟⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⢡⣿⣿⣿⣿⣿⣯⣾⠟⠿⣥⣾⣿⣿⣿⣆⠈⠻⠉⠘⠉⠋⢹⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢡⣿⡿⢫⣿⣿⣿⣿⣴⣦⠙⡎⡟⠻⣿⡿⡛⢦⡀⠀⠀⠀⠀⠈⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣵⣿⣿⣿⣿⣿⣝⣛⡴⢣⣄⣘⣷⣅⠀⠀⠑⠀⠀⠑⠻⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⣿⣿⣿⣿⣿⡍⠛⠸⣿⣏⣿⣿⣿⣦⡀⠀⠐⠺⣙⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠻⣿⣿⣿⣿⣷⡘⡆⢽⣦⣾⣿⣿⣿⣿⣦⣀⠀⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠳⢬⡻⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡿⣿⡋⠝⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡢⠄⠀⠈⠻⣿⣿⣿⣿⣎⢿⣿⣿⣷⣼⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠱⠙⣿⣿⣿⣿⣧⣻⣿⣿⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⢿⣟⢿⣿⣿⣿⣿⡇⠭⠥⣄⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⠙⠾⡻⢿⣿⣶⣶⡌⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠸⠇⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢻⠀⠀⠀⠀⡇⣸⠃⢀⠀⢠⡈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠁⠀⠀⣰⠃⠀⠀⡞⠀⢈⡇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠸⠁⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠚⢸⡆⠀⢰⡆⠀⠀⣠⠀⢀⡀⠀⠈⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣞⠀⠀⠀⢻⠀⠀⢸⠆⠈⠁⠀⠀⣇⡔⢰⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠋⢠⠀⡄⠀⠀⠀⣀⠀⠀⠀⣼⠀⢉⠀⢸⣧⡇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣼⠃⠀⡠⠀⢀⡀⠆⠀⢀⢉⠀⠀⣧⠁⠀⠈⠀⠏⠏⠀⢰⠀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣇⠐⡇⠀⠀⠁⠀⢸⣷⠀⠃⣾⠀⠀⠂⠈⠀⠀⠁⠆⠀⠀⠀⢸⢃⡁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁⣸⡆⣦⢠⠀⠀⢠⠀⠁⠀⠀⠛⠀⢀⢰⠀⡄⠀⣆⠀⠁⠀⠀⠀⠸⠃⢸⠆⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⡀⣠⠠⠈⡃⠞⠀⠀⠁⡀⠀⠀⢀⠀⢀⠸⠆⣆⠁⡞⠑⠀⡀⣤⠀⠀⣠⠀⠊⠀⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⢳⣉⠀⠁⠑⠰⠓⣠⣷⠇⠀⠰⡌⠂⠰⠀⡄⠉⠀⠇⠐⠾⠁⣸⠀⣶⠀⣶⠄⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠋⡤⠛⠐⣷⡀⠜⠿⣿⡏⣻⣧⡐⠁⢀⠀⢸⡇⠀⠀⠀⠀⢠⣘⡧⣶⠛⣷⣤⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡀⠘⠄⢀⡀⠀⣄⣀⠈⡄⠙⠉⣿⡄⠉⠀⡠⢁⡯⠀⢠⠀⣸⡟⠁⠇⠞⠟⢁⣀⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡄⠙⣻⡆⢨⢉⣠⣿⣾⣏⢀⣔⢃⠈⣁⠀⡀⠇⠋⠛⠀⠀⠀⠋⠅⢡⣴⡀⢸⡇⢦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠓⠉⠙⠛⢾⡌⠙⣿⠇⠁⠈⠛⠙⢷⢈⣤⣅⠀⣄⢂⣼⣷⡀⢰⣾⠆⡿⠃⣾⣿⠆⠘⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⢠⣿⡿⠂⠉⠁⠒⢶⡄⠀⣤⣼⡿⠋⠁⠀⠈⠙⢿⣿⡆⠀⠀⠆⠉⠘⠳⣦⣤⡠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⡒⣶⠞⣻⣟⡀⢀⠀⣀⣼⣮⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⣸⣆⠀⠀⢀⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠯⢉⣛⣛⡽⣿⣦⢠⠞⣿⣿⠦⡀⢀⡀⣰⡿⠿⣿⣿⣯⣾⣽⣷⣀⣫⣾⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠦⠤⠔⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢰⡤⠠⠀⣀⢀⣠⠖⠫⠉⠉⠘⢧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠂⠌⣎⡫⡕⠠⣀⠐⠂⡜⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⡽⠀⠈⣢⣄⣼⡓⢼⠦⡀⠁⠺⢄⠘⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⢲⣴⡋⠁⠀⠀⡽⠀⢀⡤⠓⠀⢀⠉⠪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠧⠤⠴⠻⡙⠁⢀⣠⠞⠁⢀⡽⠀⠀⠀⢀⠰⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠀⠀⠀⠀⢀⠜⠀⠙⠋⠉⠀⠀⠀⢜⣣⣤⡑⣄⠸⠓⠢⢌⠮⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⡀⠀⡠⠔⠉⠢⡀⠀⠀⠀⠀⠀⣠⢈⣀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠑⠤⠤⠴⡒⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⡤⡎⢳⡀⠀⠀⠀⠀⠀⠀⠈⢢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⠲⠦⠒⠉⠀⢻⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠑⠢⣄⡦⣄⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⣠⠜⢉⠇⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⡆⠀⣠⠔⠊⠁⢠⠊⠑⠢⢤⡀
⡴⣦⣶⡄⠤⠄⠀⣀⠀⠀⢀⠤⣤⡀⢶⡒⠈⣠⣤⠹⠞⡀⠒⢄⣰⠃⠀⠀⠀⣸⡁
⠣⠻⣤⣇⣀⣀⣀⣀⢠⠚⡜⠶⣏⠉⠉⠉⠓⠃⠛⠀⠐⠛⠉⢰⡦⢾⣁⡦⠴⣟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⢆⣷⠤⣤⠠⢬⠿⠯⠥⠤⠉⠉⣉⣙⣟⠛⡟⠺⡄⠈⠉⢃⣠⠔⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠁⠐⠀⠠⡤⠤⢼⣏⢢⡈⠙⣟⢯⢮⠣⠄⠁⠈⠽⠵⡧⠛⠉⣶⠁⣔⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣔⡇⣰⢶⡟⡆⢅⠊⣿⡓⠋⠉⠒⠒⠒⠒⠚⢧⠀⠀⠈⠉⠉⠀⠈⠑⠾⠓⠢⢤⣀⡀
⠀⠀⠀⠀⢀⠤⣄⣤⢞⣦⢸⣧⢧⣇⣀⠽⢾⠭⠑⠒⠂⠠⠤⠤⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢠⠧⣠⡞⠪⠚⠉⠉⢈⡅⠁⠀⠀⠯⣄⣀⣀⣀⣠⡤⡾⡏⠙⡑⣄
⠀⠀⠀⠀⠑⠂⠭⠄⠀⢀⢉⣩⠇⠀⠀⠀⠀⠀⠀⠈⡏⠉⣹⣠⠇⣄⢰⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⣆⣊⠟⠀⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣁⢶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠛⠃⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠀⠀⠀⠀⢃⠀⠀⠀⣴⣄⣀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣦⣀⠀⠀⠈⠠⠤⠀⠀⠛⠛⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠣⠀⠀⠀⠀⠀⠀⢀⣶⠟⢛⠛⠃⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠐⠀⠀⠀⠀⠀⣾⣧⡴⠀⠀⠀⣠⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⠙⠃⠀⠘⢢⡼⠟⠙⢣⣀⠀⠀⠀⠀⠄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⢹⠃⠈⠀⠀⠈⠻⣶⡤⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⠄⠘⢇⢃⣤⣿⣧⣄⠀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣎⡷⢶⡀⠰⣿⡿⠉⠻⢿⣿⣿⣿⣯⠀⠸⡏⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⢇⠀⢈⣿⠁⢤⣤⣤⣄⡙⣉⡣⠀⢠⣿⠟⢠⠄⣰⣿⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢦⣼⣿⣏⠋⠉⠙⡁⠀⠀⠃⠀⠀⠀⠘⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠙⣡⡤⠙⢿⡿⣶⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧⠀⠀⢺⡗⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⢀⠀⠈⢩⢻⣶⣤⣀⣩⣄⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⠀⠀⢸⡤⠂⠀⠁⠈⠡⣼⣯⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⡙⠀⠀⠀⠀⠀⢡⣤⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠁⣸⠇⢢⡄⠀⠀⠀⠸⠃⠀⠘⠳⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡾⠁⣾⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠙⠲⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠐⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠲⠀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣀⣴⠀⠀⠀⠀⠀⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠉⠛⢃⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠀⣣⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⣀⣀⣀⣠⠟⠁⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣦⣴⣶⣾⣶⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠁⢀⣠⣿⣿⣿⣿⣟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣤⣾⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⡀⣀⢀⣀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⣉⠽⢿⣭⣭⣯⠉⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀

⠀⣤⡀
⣶⣿⡁⣠⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⢟⣿⣾⣗⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼
⠿⢿⣿⣿⣿⣾⠋⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⢹⣯⠙⠁⠀⠈⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣹⡟⢻
⠀⠀⠈⠻⣄⡀⠀⠀⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⣿⣿⡟
⠀⠀⣀⣴⣿⣅⣠⣾⠿⣿⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢸⣶⣶⣾⡟
⠀⠀⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣾⣼⣿⣿⣿⠃
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⠿⠃
⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠙⠿⠇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠠⢤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡛⠀⠀⠉⢳⠐⠞⢥⡈⠀⠀⣀⠀⡿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠢⢄⠀⠑⢳⣞⠳⡈⠑⠠⡀⣰⠃⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠚⠁⢀⣠⠵⠖⠺⣄⠑⠛⠂⢄⠀⠉⠢⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢈⣶⣿⠀⠀⠀⠀⡜⠀⢀⠄⠂⠁⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡬⠷⠤⠴⠛⢁⠁⠀⢀⡠⠊⠀⠀⡠⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⣃⣀⣀⠀⡀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠈⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠢⣀⣀⣀⡬⠔⠊⠁⠀⠀⠀⠀⠠⣀⠀⠀⠀⡴⠋⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣀⡀⣀⠴⠊⢹⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡆⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⢶⣤⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠤⠃⠨⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠀⠀⣀⡤⠂⠁⠀⡀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⢀⢤⣤⢤⠄⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠠⠀⠀⠀⢠⡈⢷⡞⠁⠢⢄⣀⡔⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢨⠼⣇⢽⠂⠀⠀⠀⠀⠀⡀⢀⣠⣀⡀⠂⠘⠻⠦⠼⠱⠏⠈⣠⢟⣒⣂⣭⣡⡖⢠⣀⣠⡿⢣
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠐⠧⣌⢠⠁⣟⣒⣐⣒⣒⣒⣶⣂⡐⠒⠢⠰⠤⠿⣴⡶⣾⠤⣴⠛⠈⠗⢲⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⣵⠿⡀⠻⡦⣙⣯⢅⢠⠀⠋⠬⠉⠵⢶⣲⡦⣴⢇⣀⠁⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠉⢒⠓⣧⠁⢄⣀⢻⣅⡚⠌⣀⣀⠀⠒⠒⠁⢱⠀⠀⠀⠁⣠⠼⠴⠂⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠀⢿⡿⠉⡆⠰⣅⠀⢎⡀⠀⠀⠀⠀⠈⠉⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠂⠠⢄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢦⠠⡺⣍⡄⣿⢁⢠⣁⠠⠀⠘⠗⠀⠈⠙⠂⠀⠐⠒⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⣠⡎⠓⠒⠃⠈⠁⢀⠀⠀⠀⠀⠸⢤⣀⣀⣀⣀⣠⡴⢾⣭⠉⠫⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠍⢀⡐⣒⡒⠈⣩⠆⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⢹⣀⣜⢠⡀⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠙⣇⠤⣺⠇⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠈⠓⠤⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠪⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡮⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⠿⣝⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠚⠻⢕⣌⡓⢤⡀⠀⠀⠀⢶⠤⣀⠔⠉⠉⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣀⠿⣮⠶⠭⣧⣀⠀⠀⢣⡄⠢⡀⠀⡠⠖⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠀⠀⠹⠀⠀⠀⠈⣄⡄⠻⠀⢷⣄⠀⠉⠢⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⠤⠳⢶⣤⠔⠛⣯⣁⠀⣈⡿⢳⣦⣀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣛⣲⣤⣄⣧⣷⡀⣈⣻⣷⣭⣴⢼⡛⠉⠉⠁⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠠⠽⣿⣿⠿⣛⡻⣄⠐⢄⠀⠉⠳⠘⢮⡉⠀⠀⢇
⠀⠀⠤⠤⢤⣀⣀⣀⣀⣤⠤⠤⠤⠤⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠢⢳⠈⠀⠀⠀⠀⠀⠳⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡒⠒⠚⠓⢤⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠓⠦⣉⠙⠲⠦⣭⣉⣙⠛⠛⠒⠒⠒⠂⠀⠀⣂⣉⣀⣀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠑⠲⢤⣀⠈⠹⣿⣿⣷⣶⣶⡀⠀⠀⠀⠘⡀⠀⠄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⡀⠀⠀⠀⠀⢹⢦⠀⠀⠀⡀⠀⠀⠀⣿⠣⣀⡘⣆⠰⡄⠈⠙⠀⣿⠉⢿⡏⢿⣿⡶⢄⠀⠁⠐⠀⠘⡀⠀⠀⣧
⠰⠀⠂⢄⠀⡿⣀⠀⢹⠱⡙⢂⢠⣠⠀⢹⠀⢣⢠⡀⣿⣆⠈⠂⢸⠀⠙⠹⣿⢆⠃⠀⠀⣠⠟⠀⠀⢿⠈⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠉⠀⠉⠁⠂⠀⠉⠀⠃⠁⢐⡼⠀⠀⠷⠡⡿⠘⠇⠀⢺⠀⠀⠀⠁⠈⠃⠀⠀⣿⡀⠀⠀⠈⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⡾⠁⠀⠀⠀⢀⠀⠀⠐⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠋⠂⡀
⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⠇⠀⠀⢀⡆⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁
⠁⠀⠀⠀⠀⠐⠀⠀⠘⣿⠃⠀⠀⠄⠘⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠆⠀⠀⣿⡇⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⡀
⠀⠀⠀⠉⠉⠰⡀⠀⠠⣿⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠜⠀⢀⡄⠀⡀⠀⠀⠀⠀⣰⣾⠇⢀⣡⠜⢁
⠀⠀⠀⠀⠀⢀⠐⡄⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⡄⢧⠀⠀⡺⣠⣿⠃⡀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠈⣤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⡼⢻⣾
⠀⠐⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢲⡄⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢸⣿
⠀⠀⠀⠀⡀⠀⠀⠀⢸⣏⠃⠀⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⣿⣗⠀⠀⠀⠀⠀⡀
⠀⠲⣠⣾⣇⠀⠀⠀⣻⢇⡀⠀⢸⢻⢀⣠⡄⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⢠⡀⣡⣤⡴
⠐⠄⠀⠉⠛⣃⠀⡀⢻⠏⠿⠀⢸⠿⠿⠿⠈⠉⠀⠩⠄⠀⠛⠁⠀⠀⠐⠐⠛⠖⠧⠀⢿⡆⠀⠀⠀⠀⠀⠀⠤⢼⠿⠿⠷⠦⠜⠓⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠰⠀⠀⠀⠙⠁⠢⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣫⣭⣉⣏⣽⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⣱⣿⢻⣧⠀⠀⠀⠀⠀⠀⢀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿
⠀⠀⠀⠀⢸⣿⠘⣿⡀⠀⠀⠀⠀⠀⠐⢠⠘⣏⢻⢿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢁⣾⡏⠀⠀⠀⠀⠀⠰⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣦
⠀⠀⠀⢰⣼⠀⣤⠛⡇⠀⠀⠀⠀⠀⢰⢿⣿⢃⡀⢸⣶⠂⠀⠀⠀⠀⠀⢸⡇⠋⢀⢸⣯⣔⡇⠀⠀⠀⠀⣾⠉⡀⢸⡇⠀⠀⠀⠠⢠⣠⡾⣿⢠⡌⠹⣷⡀
⠀⠀⠀⢈⣏⠃⡝⣆⣷⠀⠀⠀⠀⠸⣿⠆⢁⡞⣇⠀⢛⡟⠀⠀⠀⠀⠀⠘⢿⣄⢼⣦⣿⡟⠀⠀⠀⠀⠀⣾⠄⣧⣈⡇⠀⠀⢀⣴⠛⢛⣄⣁⣼⣧⡆⡹⠁
⠀⠀⠀⠀⠉⠛⠓⠋⠁⠀⠀⠀⠀⠀⠈⠑⠂⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠚⠃⠀⠀⠀⠀⠀⠈⠑⠛⠉⠀⠀⠀⠘⠛⠀⠛⠈⠉⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⢃⣴⡎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠴⠀⠠⠀⠀⠀⠀⣶⣄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠄⢀
⠀⠀⠀⠀⢾⡟⢿⣷⡈⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠀⣠⣴⣶⡿⠀⠀⠀⠀⠀⠀⢿⣿⠿⣷⣆⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⠁⠀⢀
⠀⠀⠀⠀⣸⡇⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣆⡿⠋⣜⣥⣠⡌⠀⠀⠀⠀⠀⠻⣆⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢃⡴⣿⠠⣶⡿⢻⣿⢀⡴⣯
⠀⠀⠀⠀⠿⣟⢸⡄⡿⠀⠀⠀⠀⢀⣠⣰⣶⠏⣸⠟⢡⠜⠙⠻⢛⡵⠆⠀⠀⠀⠰⡶⣿⢠⡄⢸⣦⠀⠀⠀⣠⣴⣤⡴⠋⣸⡿⢚⡉⣠⢿⡿⠋⣴⠏⡀
⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠠⣿⢋⣛⣡⢦⣠⠶⠻⠴⣦⣤⣀⡶⣧⡀⠀⠀⠀⢹⡦⣾⡁⡸⠃⠀⠀⠞⡋⡉⣩⣞⣀⡀⢴⣋⣈⣥⣠⡄⠚⠟⣻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⣟⣻⣦⢀⠀⠀⠀⠀⠀⣀⠂⢀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠃⠘⣿⡏⢻⣆⠀⠀⠀⢸⣿⣷⣄⡠⢀⣁⣀⣒⣠⣤⣌⡁⠀⠀⠀⠀⠀⠀⣿⡿⣦⣤⣇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣧⠈⡀
⠀⠀⠀⣠⣦⡿⡁⠘⠉⡇⠀⠀⠀⠻⢿⣟⠛⠟⠛⠻⠿⣿⣿⠛⣿⣤⡀⠀⠀⠀⠀⠹⣧⠈⠙⠻⡿⣦⣷⣦⠀⣂⠀⠀⠀⠀⠀⠀⠀⣿⠻⣷⣿⣦⣤
⠀⠀⢼⡏⠋⣼⣧⠄⠸⣿⠀⠀⠀⠀⠐⠉⢻⣷⣶⡄⢲⣤⣈⡆⠙⢿⠇⠀⠀⠀⢀⢳⣾⢷⡄⠰⣤⣤⣍⣉⠻⡟⢷⠀⠀⠀⠀⢀⣗⠾⣆⢉⡛⠈⠻⠿⣆
⠀⠀⠈⠻⠦⠿⠸⠧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠧⠼⠷⠽⠷⠦⠟⠀⠀⠀⠰⠾⠿⠋⠁⠠⠶⠾⠧⠉⠉⠳⠤⠌⠦⠀⠀⠀⠸⠿⠆⠠⠾⠟⠓⠛⠲⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣆⣀⣤⣤⣴⠶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠛⠛⠻⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠋⠀⣿⠋⠛⠀⠀⣰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣶⣴⣿⣦⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠆⠀⠐⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⣿⣿⣿⣿⠟⠙⢤⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣄⠀⠰⠦⠤⠤⠤⡔⠋⠁⠈⠉⠉⠉⢻⡿⠁⠀⠀⠀⠉⠻⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⠬⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠗⠦⣬⣁⠀⢴⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠛⠓⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣞⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣡⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡜⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢋⡿⢻⣿⡿⠀⠀⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠃⠀⢻⣿⢿⠒⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠟⠳⣦⣤⣄⣀⠀⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⣿⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⡛⡆⠀⠀⠀⠀⠉⠀⠀⠴⢢⣄⣆⣸⡇⡀⠀⠀⠀⣀⡀⢦⣴⣾⡇⠀⠀⠘⣿⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣉⠛⠿⣇⣿⣴⣾⣦⣿⠹⠎⣿⣾⠁⠀⠀⠀⢿⣗⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣾⡟⠛⣁⣠⣠⣤⣤⣬⣿⣷⣄⠀⠀⠀⠘⠋⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠁⠉⠁⠀⠛⠛⠛⠛⠛⠁⢿⣿⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣿⠻⠀⠀⠀⠀⢁⣬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⡇⠀⠀⠀⠐⣼⣾⡇⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡷⠀⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠈⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⢸⡏⡗⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣾⠃⠀⡕⠀⡀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⠀⣹⠆⠀⢷⣀⠁⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢴⣶⣾⡇⠀⠀⠘⢧⠖⠀⢀⠀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⠀⠀⠀⠀⠈⢷⣭⡥⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣿⠀⠀⠀⠀⠀⠀⢻⣷⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣇⣿⣿⠀⣠⡀⠀⠀⠀⠈⣿⡈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣾⠿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⢸⣧⢹⣿⣇⢀⣶⣤⡆⠀⣀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⣿⣇⠰⣟⣵⣿⠟⠋⠛⠁⠀⠀⠀⠀⠀⢸⠟⣿⣿⣿⣾⣿⣿⣷⣿⠟⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣴⠈⠀⢺⣾⣿⠿⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣾⣧⣼⢿⣽⣿⣿⠿⠛⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡿⠋⣠⣿⡿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡟⢹⡿⢟⣿⣿⠟⠁



⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⢀⠀⡀⣀⡀⠀⣀⠀⢀
⠀⠀⢀⡗⠀⠀⠀⠀⢀⣴⣿⣾⡆⠀⣼⣿⣷⠀⠀⠀⢀⡀⡀⠀⠀⠐⣾⣿⣷⣿⣿⣿⣾⣿⣿⡿⢀⣉⡇⣨⡽⢃⡀
⠀⢠⣾⣿⣴⡄⠀⠀⣸⣿⣿⣿⣿⡀⠁⠹⠏⠀⡐⡜⣨⡵⣿⣷⣤⡠⠙⠛⠛⡛⠛⣛⣛⣛⣋⠀⡸⣿⣜⡿⢳⡞⣖
⢀⣿⡟⠉⢿⣷⠀⠀⠻⣿⠿⢿⣿⠇⠀⠀⣠⣾⣷⣿⣿⣿⣿⣯⣿⣿⣦⣄⢼⣿⣙⢺⣟⡋⠛⠁⠘⠿⠻⣷⣾⠟⠋
⠀⠛⠄⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣼⣿⣿⠋⠀⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢰⣠⢼⡰⢠⢠⣀⠀⠀⠁⠊⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠀⠢⠀⠀⠰⡄⣠
⠀⠀⠐⡄⠀⢰⣺⣽⣿⣿⣾⣽⣼⣿⣿⠀⠀⠀⠀⠀⣠⣦⣤⣄⠀⠀⠀⠀⠐⠀⠈⠼⠷⠁⣨⢷⣿⢕⠗⠀⢀⣘⡆
⠀⡄⣾⢁⠀⠈⠙⠛⡉⠉⠉⠙⠛⠛⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⠀⣠⢞⢢⡇⠀⠀⢀⣈⣿⣿⣏⣀⠰⣞⣮⣷
⠈⢷⣙⣾⣦⠀⠀⣴⣻⣶⡄⠀⢀⡺⣿⣎⠠⣄⠈⠻⣿⣿⣿⣿⡿⢠⣶⣿⡏⣿⣷⡇⠀⠉⠉⠉⠉⠉⠉⠀⣤⣿⠇
⢀⣾⣼⣿⡏⠀⣼⡏⠹⢿⣿⠀⢢⣹⣯⣟⣵⡝⡄⠠⣿⡿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣗⠀⠀⢀⣠⡄⠀⠀⠈⠻⣧⣄
⠀⠛⠿⠟⠃⠀⠈⠓⠀⠘⠃⠀⠘⠛⠛⠛⠛⠛⠋⠀⠘⠇⠸⠋⠀⠰⠿⠿⠿⠿⠿⠟⠀⠶⠿⠿⠿⠷⠶⠀⠶⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⠿⠝⠛⠛⠛⠛⠛⢝⢦⡀
⠀⠀⠀⠀⠀⠀⣠⢴⢫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⣄
⠀⠀⠀⠀⣠⢞⠕⠁⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⠉⢟⣦⡀
⠀⠀⠀⣴⡳⠁⠀⠀⠄⠀⣀⠤⠒⠊⠉⠁⠀⠀⠹⣯⣿⡦⡩⢷
⠀⠀⢰⡷⠁⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⢰⠟⡙⢿⡁⣷⢹⡇
⠀⠀⣼⠃⠀⠀⣴⣿⡆⠀⠠⠶⠟⢻⡀⠀⠀⠀⠀⠁⠀⠱⣷⠾⢧
⠀⠀⣿⠀⠀⣸⣁⡿⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⢰⠀⠀⠀⢸⡆⢸⡇
⠀⠀⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣢⠞
⠀⠀⣿⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⠃⠀⠀⠀⠀⠀⠀⢀⡤⣤⠞⢋⣷⣤⣄
⠀⠀⣿⠀⢣⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠟⠁⠀⠀⠀⠀⠀⠀⢠⠟⠀⠆⠀⠉⠋⢠⡞⠁
⠀⠀⢿⡀⠀⠉⠉⠉⠉⠑⠒⠄⢀⡠⠔⠒⠒⠒⠒⣮⡇⠀⠀⠀⠀⢀⣀⣤⢶⡟⠀⠀⠀⠀⠀⠂⠻⣧
⠀⠀⠸⣗⡄⢀⠀⠀⠀⠀⢀⢔⣻⡄⠀⠀⠀⠀⠀⣽⠃⣀⡼⣫⡻⠍⠃⠈⠀⠈⠆⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠙⢮⣆⣐⡴⣖⣪⠵⣻⢯⠂⠀⠀⠀⢀⠊⣗⠟⠝⠊⠀⢠⠰⠒⡤⣔⣶⡵⢦⡄⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣰⢯⠃⠀⠀⣁⣠⢼⠉⠃⠄⣀⡠⠔⢦⠀⡜⡾⠁⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡫⠘⡄⠀⠀⠀⠀⠀⢣⡀⣠⠾⠀⠀⢀⢍⡞⠁
⠀⠀⠀⠀⠀⠀⣀⣤⢾⠗⠁⡀⠙⠢⠄⢀⣀⡠⠖⡗⣤⡀⣀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠿⣍⡠⠐⠁⢀⣀⡤⠖⠉⠀⠀⠀⣿⡟⠺⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢮⣟⣉⠀⠀⠀⠀⠀⢠⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶

⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠖⡆⠀⠀⢾⠀⡀⢨⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡀
⢰⠀⠘⡄⠀⠠⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⡀⠂⢸⠀⡖⠀⠀⠀⠉⠁⢰⠄⣠
⡟⠀⠀⢃⠀⠀⠀⠀⡀⠀⠘⢂⣆⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⡃⠀⢸⠀⡇⠀⠀⠀⠀⠆⢸⠂⣈⢀⠀⠀⡠⢨
⠁⠀⠀⠀⠀⠀⠈⠀⠄⣄⢠⠞⡇⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠇⠀⠀⠀⠰⠀⠀⠀⠁⢸⡀⢸⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠋⠀⡆⠀⠀⠀⠸⠀⠸⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁
⢰⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠃⠀⠀⠀⠐⠂⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⠿⠂⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡄⢀⣤⡀
⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠻⠿
⢸⡄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢨⡇⠀⢩⢣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢀⡼⠀⣤⣤
⢨⡏⠀⠘⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⢀⠠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠏⢀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢬⡁⢿⣄⡀⢀⠼⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢞⡟⠶
⠀⠠⡀⣀⣀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠬⠍⠲⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢾⣗⣄⡀⣨⣧

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⠀⠀⠀⠀⣤⠤⠤⠄⣤⣤⢄⣠⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣸⣄⡀⠀⠀⢹⣤⠤⣾⡿⢿⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣶⣿⣧⣿⣿⣻⣶⣶⣶⣶⢾⣿⣛⢿⠋⠉⠁⠘⣳⠞⣡⠴⡗⢶⢾⣿⣿⣿⣿⣿⣿⣿⣿⠞⢋⣿⣿⣿⡿⢁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢽⡿⠿⣿⣟⠲⣄⡜⣠⠞⢁⣠⡤⢴⣤⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⣷⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡶⠷⠦⢤⣙⠳⢌⡰⠁⠒⠉⣚⣲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⣿⣿⡛⣻
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣟⣁⣧⣤⣄⣀⠙⠷⡄⢳⣥⠴⠛⣩⠶⠚⣉⣭⣽⣿⣿⣿⢯⣙⠛⢮⠙⢻⣿⡿⣛⣟
⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣶⠂⠈⠽⠖⠈⠫⠀⠀⠈⢁⣤⢞⡿⣫⡾⣿⡿⢻⣷⡹⣷⣄⠳⣸⠟⠻⣍⠙
⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⠭⣭⣍⣛⠿⢶⣄⣐⠀⠀⢀⡞⢁⡞⢠⡟⢰⠁⡇⠀⠁⠹⣌⢎⠳⡅⢀⣤⣼⣶
⠀⠀⠀⠀⣭⠟⢛⣽⣿⣿⣿⣿⡿⢶⣶⣤⡀⣉⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣄⣇⠀⠀⠀⠘⠎⢣⡸⠋⠉⣠⡶
⠀⠀⠀⠀⠃⡴⡿⣱⣿⠙⣿⣿⠻⣦⡙⣿⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣯⣙⠒⠀⠀⠀⠶⢳⡀⡴⠋
⠀⠀⠀⠀⡞⡸⣱⠋⡏⠀⢸⡌⣇⠙⢷⡌⢷⡄⠙⠆⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⡀⠀⠀⠀⢀⣿⡁
⠀⠀⠀⠀⡼⢡⠏⠘⠀⠀⠘⠀⢿⡀⠀⢉⢠⣷⣶⣶⣶⣤⣤⣄⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⠀⠊⠀⠱⡀⠰
⠀⠀⠀⠀⠃⠎⠀⠀⠀⠀⠀⠀⠈⣧⣶⣿⣧⣿⣿⣿⣿⣿⡟⣙⣮⣙⠂⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢋⣩⠽⠟⠲⢄⠉⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠏⠁⢀⣀⣀⣀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠴⠋⢡⣾⣿⠿⣏⣻⣼⣿⣿⣿⣻⣿⣿⣿⣿⣟⣴⣾⢟⣛⠉⠉⠉⠓⠄⠘⢿⣿⣿⣿⣿⣿⠻⡀⠀⡞
⠀⠀⠀⠀⠀⢀⢠⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⠉⠙⠳⢦⣄⡀⠀⠈⢿⣿⣯⣹⡟⡇⠀⣸⠁
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣉⡑⠆⠀⠀⠀⠉⠑⠀⠈⣿⣿⣿⢹⠀⠀⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡽⢛⣽⣿⣿⣿⡻⣷⠮⣝⠺⢝⡓⠦⡀⠀⠀⠀⠀⠀⣿⣿⣟⢧⠀⢀⡆⣠⣾
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⣼⠟⣴⠋⢠⣿⡏⣼⣿⡿⡇⠈⠑⢌⠙⠦⡙⠲⣄⠀⠀⠀⠀⠀⣿⣿⣿⡌⠳⣾⣶⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⡾⠋⠸⠁⢠⡟⢸⠀⣿⠀⣇⠱⡄⠀⠀⠀⠀⠈⠑⠮⠙⠦⣀⠀⠀⢹⣿⡏⠏⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠛⠚⠓⠁⠈⠚⠛⠓⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠉⠉⠙⠒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠯⢀⡈⠙⠦⣀⡄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⣄⡀⠀⠀⠉⠂⢄⠁⠂⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠉⠀⠁⠢⢄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣦⢂⣀⠀⠀⠀⠉⠒⢄⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠉⠁⠈⠋⠁⠀⠀⠀⠀⠀⠹⣦⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⡀⠀⠀⠀⠠⠀⠀⡀⠀⢈⠉⢣⠼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠉⠛⠻⠿⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠤⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⡠⠀⠀⢇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⣀⡤⠖⡻⠁⠱⠀⢰⢶⠀⠁⠀⠀⡠⠊⠀⠐⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠃
⠀⣀⠤⠒⠉⠁⠀⠈⠑⠀⠀⢀⠋⠈⡇⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠄⠆
⠀⢆⠀⠀⠀⠀⠄⢲⠀⠀⠈⠀⠀⠀⠀⠐⠒⠒⠀⢠⢄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠍⡘⠨
⠀⠀⠣⡀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⠐⠀⢰⠀⠉⠢⢄⡀⠀⠀⠀⠀⠑⣤⡀⠀⠀⡸⢰⢃⠃
⠀⠀⠀⠈⣀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠂⠀⠀⢣⡀⠀⠀⠉⠢⣄⠀⠀⢀⠆⢹⢀⠊⠑⢆⡌
⡦⠓⠲⠞⢹⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠑⢦⡊⢀⡃⠀⠀⢤⡜⠁
⠑⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⠃⡼⠄⢍⠁
⠀⠀⠀⠀⡀⠈⠳⠶⢴⡦⠄⠠⠤⠶⠿⠛⠋⠁⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠰⠸
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠔⠀⠹⠀⢣⠃
⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠄⢰⠃⠀⠦⡀
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⡜⠀⠉
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠂⠄⢀⣀⣀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣀⠀⠀⢀⠊
⠀⠀⢀⣀⠤⠄⠒⠘⠂⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠑⣤⠆
⠀⢮⣥⣤⣤⣤⣤⡤⠤⠴⠶⠂⠴⠤⠤⠤⠤⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⣼⡟⠁⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⢀⣼⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⣼⣿⠁⣸⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⣠⣾⠇⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⢀⠃⢰⣿⣿⢀⡇⢸⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⢀⣼⣿⡏⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⣿⠀⢸⣿⡟⠸⡇⠋
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⣰⣿⣿⡏⠀⣠⣾⣿⣿⣿⣿⠋⢠⠂⠀⢰⡿⠀⢸⡿⢁⡆⠁
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⡇⣸⢿⣿⡟⢀⣾⣿⣿⣿⣿⠟⠁⡰⢃⠆⢠⣿⠇⠀⡞⢁⡾⢱⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⠟⠁⢸⢻⡿⢰⡏⣸⣿⣰⣿⡿⢋⣾⡿⠋⠄⡼⣡⠟⣴⡿⠃⠀⠀⣰⣟⣷⠏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⠏⠀⠀⣼⠈⡇⣿⠀⣿⣿⣿⡟⢀⣾⣿⢃⡏⣼⣷⣯⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⣀
⠀⠀⠀⣶⠀⣼⢿⡀⠀⠀⢸⣿⠀⢠⠀⡟⠀⠃⠟⢸⣿⣿⠛⠀⣾⣿⠇⣾⢡⣿⣿⣿⡟⠀⣰⣿⣿⠟⠁⠀⣠⣴⣿⠇
⠀⠀⠀⣿⠀⠸⣟⣧⠀⠀⢸⡇⠀⣾⣴⡇⠀⠀⠀⢸⣿⠇⠀⢸⣿⡿⢸⣿⢸⣿⣿⣿⡇⣼⣿⣿⠃⢀⣴⣾⣿⡿⠃⢀⠆⢀⠄
⠀⠀⠀⣿⡄⠠⢹⣿⡆⠀⢸⠃⢠⣿⣿⠃⠀⠀⠀⢸⡏⠀⠀⣿⡿⡇⣿⣿⢸⣿⣿⣿⣷⣿⡿⠁⢀⠼⡫⠓⢉⣠⡶⣋⠔⠋
⠀⠀⠀⣿⣧⠀⣧⣻⣷⠀⢸⠀⣼⣿⡿⠀⠀⠀⠀⢸⠃⠀⢠⡿⢰⢱⣿⣿⠸⣿⣿⢹⣿⣿⡇⢀⡾⠋⣠⣶⣿⡿⠛⠁
⠀⠀⠀⢻⣿⣧⢸⣿⣿⠀⡀⢠⣿⣿⠃⠠⠀⠀⠀⣎⠀⠀⢸⢇⡟⣼⣿⣿⢸⣿⣿⠸⣿⣿⡇⢸⠇⣰⣿⣿⡩
⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⢃⣾⣿⠃⠀⢰⠂⠀⠀⠋⠀⢸⣿⡼⢡⣿⣿⢇⣾⣿⡟⣸⣿⣿⡇⠀⢰⣿⣿⠋
⠀⠀⠀⠀⠀⢻⣻⣿⡟⠀⣾⡿⠃⡀⠀⣸⠃⠀⠀⠀⢠⣿⣿⢃⠟⣸⢏⣾⣿⣟⣵⣿⣿⡟⠀⣴⣿⠟⠁⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠈⢿⣿⠃⣼⡿⠁⣼⠃⣰⣿⠀⠀⠀⠀⣾⣿⢃⢂⢠⣫⡾⣻⣿⣿⡿⠟⠋⡠⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡟⣸⡟⠀⣼⠃⣰⣿⡏⠀⠀⢀⣼⡿⠁⢂⣾⣰⣟⣽⣿⠿⠋⠀⢀⣠⠄⠀⢀⣠⣴⠾⠟⢉⣴⠋
⠀⠀⠀⠀⠀⠀⢀⢱⡟⠀⣸⢃⣼⣿⡿⠁⠀⢀⣾⠟⠁⠀⣼⡇⣏⣿⡟⠁⠀⣠⡾⠋⠀⣠⡶⠟⠉⠀⣴⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⣿⣿⣿⡟⠁⠀⢀⣾⠋⠀⠀⣼⣿⣇⢻⡟⠀⢠⣾⡿⠀⢀⠾⠋⠀⢀⣴⣾⢿⣿⡏⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⣿⣿⠋⠀⠀⠀⡾⠁⠀⠀⣼⣿⡟⢻⢸⡇⣰⣿⣿⠃⠀⠁⠀⠀⣰⣿⣿⣳⣿⡟⠀⡜⣯
⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⠃⠀⠀⠀⠀⠁⠀⢀⡾⢋⣿⡧⣀⣼⣠⣿⣿⠏⠀⠀⠀⢀⣼⣿⡿⣷⣿⠟⠀⡰⠁⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣰⠏⣴⣿⣿⡇⣿⣿⣿⣿⠋⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⡰⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡰⢡⣾⣿⣿⣿⣼⣿⠿⠋⠁⠀⠀⠀⣰⣿⣻⣿⡿⠋⠀⢀⡔⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡄⠀⠀⢀⣴⢟⣽⣿⡿⠛⠉⠀⠀⠀⠀⠀⣠⣾⣿⡷⠛⠁⠀⣠⣴⣿⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⣼⠁⠀⢀⠞⣱⡿⠋⠁⠀⠀⣀⣤⣔⣀⡴⠞⠛⠉⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⣳⠏⠀⠀⢊⡞⠁⠀⢀⣤⡾⠿⠋⠁⠉⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⠏⠀⠀⠀⢋⠀⢀⡴⠟⢁⡀⠀⠀⠔⢊⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢀⡴⢃⠤⢊⣠⠞⠁⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⣼⡿⠋⠀⣠⣴⣾⠟⠀⢀⣴⡿⠁⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⣼⠋⢀⣴⣿⡿⠟⠁⣠⡴⠿⠋⠀⠀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠚⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣁
⠀⠀⠀⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠃
⠀⠀⠀⠇⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢀⡀⠒
⠀⠀⠉⠁⠀⠁⠀⠐⠁⠀⠀⢠⣀⠀⠤⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠠
⣀⣀⣀⣄⣘⣁⣀⣀⣀⣐⣒⣀⣀⣄⣀⣐⣛⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣐⣂⣒⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡾⠁⠀⠠⠀⠀⠀⠀⢉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣶⡟⠀⠀⡂⠀⣀⣀⣀⣀⡀⢤⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣿⠆⠛⠀⠀⢁⣴⣭⠀⠖⢨⡝⣟⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⠇⠀⠀⠀⠀⣈⡼⣆⠀⠀⣹⡇⠈⣦⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣿⡅⠀⠀⣠⡞⠁⠀⠸⣦⢀⣿⠿⣿⣿⣿⣿⣿⡏⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣿⡧⣴⣥⡀⠁⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⣧⡶⠖⣀⠒⠒⠂⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡣⢻⣿⠁⠈⢻⣷⣼⣶⡂⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢩⣽⣷⡆⣴⣿⣿⣿⣿⠉⠙⠒⠒⠛⣻⠞⢡⠿⢿⡇⣿⣿⣿⣿⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⣿⡿⡀⠀⠀⠀⡼⠁⣰⡇⢀⣼⣿⣿⠿⡿⠛⣙⡏⢿⣷⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠉⠀⢿⣽⣷⡈⢀⡶⠂⣀⣾⣿⣿⡟⢻⣿⢿⡿⣧⣀⣯⢡⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⣀⣀⠀⠀⠀⠀⠁⡅⢷⣿⣿⣋⡤⠚⡿⣿⣿⣿⡇⢸⣿⣶⣿⣿⣿⣏⣿⣿⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠘⢿⡄⠀⠀⠀⠀⣻⣿⣿⣏⣀⠀⣿⣛⣿⣁⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠂⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣷⡀⠃⠀⠀⡠⢊⣽⣿⠧⠀⠀⠀⠉⡉⣉⣠⣴⠿⣻⣽⣿⣿⣿⣿⣿⠏⡀⢀⠂⢸⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⠇⠀⠀⡠⢡⡞⢻⣿⢶⣶⣤⡀⠀⠀⠀⢀⣀⣙⣻⣿⣿⣍⠻⣿⡏⠀⡀⣡⢀⡼⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠋⠄⠀⠨⠀⠁⠀⢸⠁⠀⢻⣿⢃⠀⠀⠉⠀⠉⠹⣿⣿⣿⡌⠀⢨⠀⢊⣴⢣⣿⡃⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢲⣀⣀⠀⠀⠀⠀⠈⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⢀⣴⠋⠉⠡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⣨⢷⣾⣮⡠⠀⢀⣼⣿⡿⠉⠁⠀⡈⠳⢦⣤⣀⣹⣿⣿⣆⣠⣾⣿⠿⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢃⡀⠀⠀⠛⠻⣿⣦⣾⣿⠏⢀⡀⢀⡠⠈⠀⠐⠀⢭⣭⣿⣿⣯⠿⢿⡯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⣀⣿⣿⡯⠤⣄⠉⠁⠀⠀⠤⣀⣀⣀⣿⣿⠏⠑⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠛⠒⢦⠀⢀⡞⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣼⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⡓⠂⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣭⣴⣶⣾⠿⢿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠨⠙⠀⠀⠙⠁⣀⢄⣀⣀⣀⠤⠤⠦⣤⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠁⠀⠀⠀⠀⠁⠉⢻⠟⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠉⠀⠄⠚
⠀⠀⠀⢀⠀⠀⠀⠱⣄⣀⣀⣀⣠⠤⠴⠖⠀⢀⣤⠄⠘⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠂
⠀⠀⠀⢰⠀⠀⠀⠀⢸⠋⠉⣁⣤⠖⠀⠀⠀⢈⣿⣿⣤⡄⠀⡀⡀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠓⣿⡿⠃⠀⠀⠀⢰⣿⠛⠻⠿⣿⣿⣿⣅⣴⡿⠿⠋⠛⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠸⠀⠈⠲⣄⠀⠀⠀⠀⢀⣴⣿⡏
⠀⠀⠀⠀⡂⠀⠀⠀⠘⢿⣶⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣟⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣛⡽⠿⡛⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢀⡤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣤⠶⠚⠀⠀⠀⠀⠀⠀⠀⢸⣁⣾⣿⡿
⠀⠀⠀⠀⠀⠀⢎⣶⣶⡶⠶⠶⠶⠶⢦⣤⣤⣀⣀⠀⠀⠀⢄⡀⠀⠀⠒⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢻⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⣀⡠⠔⠋⠁⢀⣤⠟⢋⠓⠲⠤⣌⡓⢤⡀⠀⠀⠤⣈⠐⢄⠀⠀⠀⠀⡜⢠⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⠀⡀⠀⠤⠐⣪⠅⠀⠈⠙⠣⠀⡀⠀⠉⠓⢿⣦⡀⠀⠈⢣⠀⠃⠀⠀⡼⢁⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡤⣀⠀⠀⢱⢿⡿⠁⠀⠀⠃⢇⡀⠀⠐⠀⢈⢻⣆⠀⠈⠀⠆⠀⡼⢁⡾⡍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⠿⠿⠀⠀⠁⠀⠀⠀⡴⠃⣌⣷⡆⠀⡀⠁⠘⡿⡘⡔⡀⠀⡼⢁⣾⡝
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣾⣴⡄⠀⡠⠄⠀⠀⠀⠀⠰⠃⣸⠇⠀⢈⠄⠈⣷⣯⣾⣿⣿⣷⣾⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣾⣿⡿⠀⢰⣶⣶⠂⠀⠀⢠⣾⡧⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣭⣂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡷⠐⣠⡯⠀⡀⠤⠞⠛⠟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠈⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠀⠚⣻⣧⠀⠀⠀⠠⠃⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⣠⣴⣿⣿⣶⣦⠖⠃⠀⠀⣰⣾⡿⠛⢹⡿⠿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢤⣾⣿⣿⣿⣿⡟⠀⠀⢀⣼⠛⠋⠀⠀⠄⠠⠄⠈⢻⣿⣿⣿⣷⣤⠀⠀⠀⢠⢤⢶⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⣹⣿⣿⣿⡿⣡⢀⣶⣿⠃⠀⠀⠀⠀⠠⢄⡀⠀⠀⠁⣿⣿⡇⠀⠀⠀⢠⣼⣿⣼⠀⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⠏⠌⣩⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠸⠃⠀⡄⣿⣿⡇⠀⠀⠀⠀⢹⣧⣤⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣋⡔⠀⢸⣿⣿⣿⡉⢸⠀⠛⠤⢀⡀⠀⠘⠄⢰⣸⡿⠙⠃⠀⠀⠀⠐⡘⣿⣿⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠌⠘⢠⣿⣿⣿⣿⣷⡎⠀⣠⠄⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⢸⡇⠛⣹⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⡀⣠⣿⣿⣿⣿⣿⣿⡇⠈⣀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠙⣛⣫⣤⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠁⠒⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⡭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣅⠽⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⡀⠀⠀⣿⠸⡇⠀⠀⢰⡇⠐⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢓⣀⠀⠀⢨⡇⠀⢿⠙⢿⣷
⠀⠀⠀⠀⣤⢀⣄⠀⠀⠘⠇⠀⠎⠆⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣧⢹⣿⠐⠓⣿⡇⠀⢸⣶⣿⡿
⡾⠁⠀⠸⠛⠛⢻⠀⠀⠠⢶⠀⡀⠀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠛⡇⢰⢦⣬⡅⠀⠀⡛⠛⠃
⠗⠀⠀⡄⣰⠻⠸⡄⠀⠐⢨⠀⡇⠀⢁⢻⣿⠀⠀⠀⠀⠀⠀⠀⢀⢡⢹⡃⠘⡁⢨⠜⢻⡇⠀⠠⣦⣤
⠀⠀⠰⠀⠁⠠⠄⡇⠀⠀⠨⠀⡃⠀⢸⣾⣿⡄⠀⠀⠀⠀⠀⢰⠆⡀⣎⠇⢀⣼⠐⣱⠟⡇⠀⢐⡄⠙
⠀⠀⢲⣰⡆⡸⡇⠅⠀⠰⣶⡆⡄⠀⠆⢸⣿⣷⠤⠄⠀⠐⠀⠸⡀⣴⢹⡀⣼⣇⢠⣬⣶⠁⠸⠟⣿⡄
⠀⠂⠈⠁⣧⠇⡜⠇⠀⢰⡟⡇⠁⠀⠀⢸⡿⢛⠂⡉⠄⢇⠀⠷⢷⣗⠻⠘⢂⣺⣉⣹⣋⠄⡀⠀⢯⡀
⠀⠀⠁⠀⠟⣠⣇⡀⠀⢘⡇⣇⢰⠆⠞⣯⣛⡤⡂⠉⡀⠆⠧⡉⠐⠐⠘⠧⢎⡭⡣⠤⠂⠧⠜⣢⢘⡆
⢤⢀⠀⠀⠀⠹⢻⠁⠀⢼⣧⢻⠰⡼⠶⢤⠆⡄⢇⣇⠈⠥⠼⣄⡀⣹⣋⡶⢖⠀⢝⠊⠊⢃⠛⢳⢷⣀⡠
⠸⢮⡧⣠⠀⠀⠺⠄⢀⣤⡅⢸⡇⠱⢤⡬⣴⣶⣽⡺⣆⠀⠘⡦⣥⡺⠧⠏⠎⠠⣌⠒⠴⠠⡀⠀⠉⠁⠁
⣤⣀⠁⢻⣷⣆⠀⠀⠺⡾⢟⡿⠻⠄⣾⠁⣿⣿⣿⠙⠾⢄⡜⠄⠀⠀⠀⠀⠇⠀⢹⡜⣀⡀⠈⠢⡀
⡷⢻⣙⣢⣝⢿⡷⠀⠀⠙⢾⣑⣻⡳⣿⡇⣹⢋⣟⣧⡀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠐⣹⠃⠀⠀⠀⠙⣦⡀
⠐⡶⣚⠿⢟⢹⡇⢠⣧⣄⠈⢽⡿⢿⣾⣿⣭⣊⣫⣿⠇⢀⣰⣶⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠻⠁⠂⣣⡀⣾⠃⠸⠿⢙⠓⠌⠻⠟⠻⣿⣿⣿⠙⣳⣶⣙⣻⣿⠉⠀⢀⣀⣀⡀
⡀⠀⠐⠛⣿⡏⠀⠐⡶⢦⡉⢲⣠⣼⡆⠓⠛⠶⡛⣧⢉⠖⣩⣅⣸⣿⣿⣿⣏⡁⠀⢀⡀⠀⠀⠀⠀⢄⡀
⠀⢀⣄⠀⠉⠋⢐⣧⣱⣿⣿⣿⣟⣿⣟⠛⠉⢹⣭⠉⢣⣾⣿⣿⣿⣿⣫⠉⠙⠓⠒⠂⠀⠀⠀⠀⠀⠀⠙
⣀⣾⣿⢷⠄⠀⠀⠿⣿⣷⣿⣿⣿⡿⠋⠀⠀⠈⠀⠀⠺⣾⣿⣿⠟⢫⡄⠰⣿⠀⠀⠀⠀⠀⠙⠢⡀
⣿⣿⢹⡜⠂⠀⢸⣦⣬⣛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳
⣿⣯⠀⠀⠀⢠⠄⠘⣯⠉⠛⠛⠿⠀⠀⠂⠀⠀⠀⠀⠀⠘⠋⠀⠀⠐⠊⠁
⣿⣿⣧⣤⢤⢤⡄⣽⡛⣷⣄⠀⢰⠀⠀⢠⡄⠠⠀⣠⣤⢤⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⠀⠀⠀⠀⣆⠀⢃⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⡏⠳⢄⠐⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡈⠀⠀⠀⠀⠹⣀⠄⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠌⡇⢀⡄⠀⠀⠀⠐⢤⠀⠀⠙⢆⠀⠀⠀⠀⣠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡏⢸⠱⡀⣀⠀⠀⠀⠑⣄⠀⠈⣇⠀⠀⠌⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠤⠐⡇⠀⠑⠹⡌⣏⢢⡀⠀⢹⢀⠈⢸⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠲⡀⠻⡄⠀⠀⢀⡇⠐⡧⢠⠏⠸⠀⢸⠀⢠⡾⡀
⠀⠀⠀⠀⠸⡗⢄⡀⠀⠀⢳⠀⠡⠈⠢⡈⢢⣀⠞⢠⠀⠿⠁⡐⢀⠀⡜⠀⢸⠁⢇
⠀⠀⠀⠀⠀⠑⢄⠈⢦⠀⠀⠱⣄⠡⠀⠈⢄⠛⡐⠁⠃⡠⠊⠀⠌⡸⠁⣠⠏⠀⢹⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠐⠲⡤⣍⠀⠀⠀⠘⡆⠑⠀⠈⣤⠁⠀⠞⠀⠀⠌⣰⠵⠚⢁⡄⠀⣼⠀⠀⡠⢊⡾
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠉⠢⡀⠀⢸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡁⠔⠂⡑⠀⣰⠃⠀⠨⠐⣉⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⢆⠹⡄⡞⠠⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⡎⢀⡔⠁⣠⢀⡴⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠂⠛⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡞⣰⢾⢃⡎⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠘⡀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⡿⢨⢸⣼⠰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢁⠈⡄⠁⠁⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠀⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠀⠀⠀⣀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠨⠀⠄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠠⠊⠁⠀⠈⠐⠂⠂

⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⢀⣰⣷⡄⠀⠀⢀⢰⣧⠀⠀⠀⠀⣾⣧⠀⠀⠀⢀⣼⣧⡄⠀⠀⠀⣾⣄
⠀⠀⢾⠿⡹⣿⠀⠀⢰⣿⣿⣿⠀⠀⢾⠟⠙⣿⠀⠀⢸⣾⣯⡤⠀⠀⢰⣿⣿⡆⠀⠀⣽⡟⠻⣷⠀⠀⣿⠏⢻⣶
⠀⠀⠈⠘⠃⠉⠀⠀⠈⠛⠛⠁⠀⠀⠈⠃⠐⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠛⠛⠁⠀⠀⠈⠐⠃⠉⠀⠀⠈⠀⠀⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣄
⠀⠀⣰⣾⣿⣧⠀⠀⠀⣼⣿⠀⠀⠀⢀⣿⣷⡀⠀⠀⢀⣿⢷⣄⠀⠀⢠⣾⢿⡆⠀⠀⣠⣿⣿⡀⠀⠀⢠⣶⢿⡄
⠀⠀⠻⢿⡽⠟⠀⠀⠰⣿⣿⠟⠀⠀⠸⡏⠘⠟⠀⠀⠸⣧⣆⠟⠀⠀⢸⡇⠸⡇⠀⠀⢻⣿⣿⡟⠀⠀⢸⣣⡌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣰⣷⡄⠀⠀⠀⢰⣦⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⢰⣶⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⣾⣆
⠀⠀⢴⠟⡈⣷⠀⠀⢨⡟⢹⣶⠀⠀⢰⡿⠹⣧⠀⠀⢀⣿⢿⣀⠀⠀⣰⣿⣿⡇⠀⠀⣤⣿⢿⣧⠀⠀⣤⡟⢹⣧
⠀⠀⠘⠚⠃⠋⠀⠀⠘⠃⠀⠋⠀⠀⠘⠃⠀⠃⠀⠀⠈⠃⠈⠃⠀⠀⠘⠻⠿⠋⠀⠀⠙⠋⠈⠋⠀⠀⠙⠀⠀⠋

⡀⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⢀⣦⠘⣉⣈⣩⠤⢨⣄⠀⠀⣀⣁⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⢸⢿
⡅⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠶⣀⣾⣿⠀⠋⢁⡔⢁⡆⠀⠀⠶⣬⠁⠀⣠⣤⣴⣀⠀⠀⠀⡆⢸⣿⣾
⡇⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠋⠀⢀⣤⣭⣿⣿⣷⣶⠀⣄⡿⢀⠀⠀⢰⣿⠦⠀⠀⠀⠀⠀⢀⡀⠿⡇⢘⣽⣥
⣿⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢀⡞⠁⡞⠀⢠⣾⡿⠋⣾⣿⣿⣿⣧⡈⣵⣿⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠁⠀⠃⠈⠛⠂
⣿⣄⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠘⠁⠀⢸⣿⢻⡟⢿⣿⠉⠨⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠻⣶⣟
⢿⣿⠀⡄⢰⡾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠇⠈⣟⡇⠀⢹⠐⡀⢰⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡿⢘⣷⣮
⡿⢃⣴⡇⣸⣧⢻⣿⣿⡆⠀⠀⠀⢀⡀⠀⢲⡄⠀⠀⠀⠀⠀⠀⡁⠀⣤⣠⠀⠘⠀⠁⠸⠄⠀⠀⠀⠀⠀⣾⣾⡧⠒⡿⠈⣷⣿
⣯⣼⣿⣷⣿⣿⢸⣿⣿⣇⠀⠚⠛⢻⡝⣶⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠩⠜⡀⠈⡀⠀⠠⣶⠀⠀⠀⠀⠐⢻⠋⠆⡻⣿⠀⣌⡁
⣿⣿⢟⣾⣿⣿⣼⣿⣿⣿⣷⡀⠰⠄⠑⠀⡀⠐⠀⠂⠀⠀⠀⠀⠀⡀⡀⣐⠂⢀⡀⠀⠘⣿⡀⠀⠀⠀⠂⢾⢀⡆⢘⡛⣠⣄⠁
⢟⣡⣾⣿⣿⣿⣼⣟⢿⣿⣯⣶⣆⠲⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠸⠀⢸⡇⠀⢀⣿⠃⠀⠠⢰⠾⢛⠨⣉⠹⠃⡀⢫
⣿⣿⠏⣿⣿⣿⡇⣿⡞⣿⣿⠿⠿⠂⠀⠀⠰⠀⢰⡆⢠⡄⠀⡄⢀⠀⠀⢻⠀⢸⣼⢹⢬⣕⠳⡄⠂⢅⠀⡆⢄⠒⠣⢠⠺⣌⣀
⣷⠛⠲⢽⣿⣿⡇⢿⣇⠩⣶⣾⣿⣆⠀⠀⠀⢥⣼⠃⠉⣤⣤⣁⠛⢣⣄⠘⢀⣶⣼⡎⡲⢾⣷⢟⡀⡑⠒⠓⢁⠰⡅⠀⢀
⠒⠀⢠⣿⣿⡏⣿⠘⣿⡀⠘⣿⣿⣿⡄⠠⣽⡾⣿⢻⡇⠀⠉⠹⢿⣦⣽⣷⠀⠑⣿⣶⣿⣾⣿⣆⠈⢀⠀⠀⠀⠀⠻⠁⠀⠑⣄
⠀⠀⣿⣿⣿⣾⣿⡁⢹⣧⡄⠀⠉⠷⠁⠀⠰⢿⣿⢟⣉⡀⠀⠲⠟⢫⣁⡗⠸⢷⠜⠿⢿⣿⡶⣯⣴⣿⠆⠀⣀⠀⠀⠀⠀⠀⠘
⠀⠀⣿⡏⣼⣿⣿⠁⠀⠀⣲⣤⣄⠀⠀⠀⠀⠘⠷⠭⠈⠱⣧⡄⠄⠈⠿⠁⡜⣲⣽⣾⣧⡭⣯⠯⣣⣴⣾⡿⠿⠄⠐⠀⠀⠀⠠
⣆⢠⡿⣧⣿⣯⣿⡳⣄⢰⣿⢿⡿⠦⡀⠀⠀⠀⢸⣿⡛⢢⠙⣧⣼⡷⡄⢀⠿⣿⣿⡿⠃⠀⠉⠀⢿⣿⠛⠅⢰⠀⠀⠀⠀⢄
⣿⡘⣧⡀⠋⢹⡟⣿⣿⣾⣯⠌⠁⠀⠀⠀⠠⣶⠛⠋⢻⣗⣵⣽⣿⠙⠀⠈⢻⡻⠿⠇⠀⠀⠀⠀⠘⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢿⡛⣯⣭⡉⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣿⠹⡟⣶⢶⣿⣿⡟⢡⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢢⠀⠀⠀⠹⣬⡇⣿⠀⠛⣿⣄⡘⠋⠻⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠂⣀⡀⠀⠀⠀⠀⠀⠘⡄⢣⡀⠀⢠⣿⡇⠸⡄⠀⣿⡏⠻⠶⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⢟⣫⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⣧⣠⣾⣿⡇⠀⣿⠛⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⣛⣩⡴⠞⠋⠁⠀⢀⣀⣤⣤⢶⠖⠁⠀⠀⠀⢠⠀⣽⣿⣷⣿⡇⠀⠘⣧⣼⣿⢿⣶⣄
⠀⠠⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⣀⣤⣶⠿⣋⣥⠶⠟⠋⠁⣀⣠⡴⡶⠿⡟⢹⡇⠷⠀⠀⣀⣀⣀⣀⣼⣿⠁⢿⢹⣿⣿⡛⣿⣿⣉⡶⠿⡞⠹⣷⡄
⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣾⡿⠟⠉⠀⢿⣏⣠⣤⣶⢾⡟⣿⢹⡇⢰⠀⡇⣸⣷⣾⡿⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣁⣤⡘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠘⠛⣿⠁⣿⢸⡇⡇⢸⡇⢻⠀⡟⠉⡇⢸⡇⢄⠐⠶⣼⠷⣶⣿⣿⣿⢇⣈⡽⠆⠙⣎⢻⣿⣟⣻⢟⣷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⣿⠘⡇⣿⢸⡇⢸⠀⡇⢸⡇⢸⡇⢸⠀⣴⢻⣄⡻⢿⠿⠋⠜⠭⢙⠇⢠⠁⡎⠹⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⡀⣿⠀⡇⢿⢸⡇⢸⠀⣇⢸⡇⢸⡇⠸⠂⢻⡾⣿⣤⠯⠚⠛⢠⣀⣿⣀⣋⣈⢃⠀⠋⠙⢿⣉⠶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇⢸⢸⡇⠘⠀⡿⢸⡇⢸⡇⣟⠲⠿⣿⡛⠛⢛⣷⣾⣿⣯⣿⠋⠈⢁⣼⣁⢰⡆⠀⠙⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇⢸⢸⡇⡀⠀⣿⢸⡇⢸⡇⢘⡳⠶⠋⠙⡳⣻⠟⠿⣥⣉⣷⣿⣿⣿⠁⠤⣼⣇⠐⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇⠈⢸⡇⡇⠈⣯⢸⡇⣹⠇⢸⡇⠀⠀⢸⠁⣿⠷⠦⠝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇⢠⠘⣷⣿⠂⡻⣌⣷⡈⠀⢸⠁⠀⠀⠹⠶⠛⢦⣴⣿⣿⣿⣿⣿⣿⣿⣟⠿⡙⠿⡿⣿⡛
⠀⠀⠀⠀⠀⢆⣈⡙⢿⠛⣛⣁⡀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇⢸⢀⣿⣿⢶⠛⠪⠹⣷⡄⢾⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣍⠓⢌⡢⡙⢄
⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣻⣿⡇⠀⠀⠀⠀⠀⢸⡇⢻⠀⡇⣸⡿⣏⣄⢈⣛⣾⠂⠈⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠳⢤⡙⢎⣲⣷⠄
⠀⠀⠀⠀⢠⠸⢿⣿⡏⣿⣼⡿⠇⢷⣦⣄⣀⠀⠈⣷⣾⣄⡇⢹⢷⡍⢠⠘⠟⠻⠆⠀⣇⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⢄⡙⠻⣿⣟
⠀⠀⠴⠾⠛⠂⠀⠉⠃⠹⣌⠀⠀⠀⢚⡽⣛⣿⡾⢷⣾⣄⠿⣼⠀⣿⣬⣤⣿⡅⠀⠀⣏⢀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡐⢢⣌⣑⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣿⠰⣯⠞⣣⣶⡿⠿⡿⣿⡶⠿⢤⣘⣿⠛⠀⠀⠘⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣥⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢷⣤⣭⣀⣰⡴⡛⠁⣽⠇⠙⠻⠿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣣⡼⠿⢯⣿⣗⡲⢇⠸⣿⣦⣐⡀⣤⠴⠖⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣴⣻⣷⡴⠶⢧⡄⢀⣿⢠⡟⠀⠈⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⣿⠿⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣟⣅⣾⣿⣿⣿⡗⠠⠼⣦⠉⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⡠⣾⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⡇
⠀⠀⠀⠀⠀⠀⠲⣶⡟⡹⢄⠁⢩⣭⣭⣤⣌⠙⢘⠃⣧⠤⣇⣼⣤⠄⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢆⣡⠟⠀⠀⢀⣹⣆⣠⣴⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣼⡿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢞⣻⣾⣿⣯⣿⣿⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠛⢻⣿⣿⣙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠿⠛⠿⠟⠋⠙⢿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⣀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠦⢌⡀⢼⣿⡄⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢫⣤⡀⠾⠗⢨⣟⣃⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⣴⣶⣾⣿⡿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣷⣿⣿⡟⠀⡽⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣛⣡⢾⣿⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣉⠑⡄
⠀⠀⠀⠀⢴⠖⠂⠀⠀⠀⠀⣆⡂⡀⠆⠐⠛⣿⣿⡿⠁⠻⣿⡄⠈⠋⠀⠀⠀⠀⠀⢀⡜⠁⠀⠙⢄⡀
⠀⠀⠀⠀⠈⢷⣄⣠⣤⣤⣤⣼⠿⠛⠘⡛⠖⠉⢠⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠿⠛⠛⣏⠁⠀⠈⣰⡄⠀⠀⠀⠄⣸⠀⠀⠀⡸⠀⠠⠤⢀⠀⠀⠄⢰⣏⣀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠐⠛⠻⢃⡄⣠⣄⣸⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣴⡄⡀⠀⠀⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⠿⣿⣿⡇⠉⠀⢸⡀⠐⠐⠆⠤⠄⠀⠀⠀⠉⠉⡼⠉⡳⠂⠉⠁⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⢀⣼⠻⣷⠂⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠃⠀⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⣠⠆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠈⠀⠀⠀⢀⠀⠐⠶⠤⠄⠀⠀⢧⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⢻⣛⡭⢅⣠⣤⣶⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣶⣤⣀⠀⠀⠘⠄⠒⠻⢋⢁⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠈⠉⠉⠀⠈⠉⠉⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⡄⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣤⡤⡄⠀⢤⣤⡀⣠⡄⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣦⣤⡴⡄⣤⣾⣿⣿⣿⡮⣸⣿⣧⠀⠀⣘⣻⣿⣿⣿⠁⠀⣴⣶⣼⣿⣿⣿⣿⣿⣻⢖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣘⣷⣦⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⣿⠷⢆⠘⠋⢿⣸⣿⣿⣿⣿⣿⣿⣿⣶⣴⣨⣀
⠀⠀⠀⠀⠛⠌⢅⣹⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠆⢸⣿⣿⡟⠻⠷⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣼⣿⡏⠁⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢗⢢
⠀⠀⠀⠂⡄⣙⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣽⣿⣾⠋⠍⠁⢡⠀⣠⣤⡼⠶⠾⠿⢺⣿⣿⣿⣿⣿⣿⠟⢻⣿⠿⣿⡶⢟
⠀⠀⠀⢇⢩⠄⢀⠀⢤⢄⡸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡯⠠⢤⣄⣠⣥⡉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣮⣿⠿⠁
⠀⠀⠀⡄⣾⠀⠀⠀⠀⠀⠈⠪⢿⡍⣿⣿⣿⣿⣿⣿⣿⡟⣿⠷⢠⣶⣿⣻⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⡃
⠀⠀⠀⡦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠲⠎⢟⡛⣿⣿⣿⣧⣿⣤⠀⠙⠋⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢸⢞⡀
⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠐⠂⠤⢹⣿⣿⢿⣿⣿⣿⣷⡀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⡀
⠀⠀⠀⡰⡘⠀⣤⣲⣮⣤⣼⣷⠀⠀⠀⠀⠀⠀⠙⠓⣬⣾⣿⣿⣿⣿⣿⡁⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠈
⠀⠀⠀⢄⠰⡆⠀⠀⠀⠉⠉⠫⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣛⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠋
⠀⠀⠀⢀⣤⡀⠀⢤⡆⠀⠐⣤⠄⠄⠴⠆⣀⣀⠀⠀⠀⢀⢀⠀⢈⣿⢠⢄⣤⣼⣷⣿⣿⡿⣿⣿⠛⠛⣛⢿⣿⣷⡿⣸⡟⢻⡶⠂
⠀⠀⠀⠰⢿⣆⠀⠈⣓⠠⢸⣿⣿⡷⢒⡶⢙⣿⡠⣠⢈⣻⣆⣓⣄⣿⣿⣿⣿⣿⠿⣿⡿⣿⢿⣿⢿⣿⣿⢿⠿⠿⠷⠿⠓⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠉⠈⠙⢻⠿⠁⠸⠟⠀⠀⠀⠉⠉⠀⠙⠉⠠⠙⠉⠁⠉⠉⠃⠋⠈⠓⠁⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣶⣶⣶⣿⣷⡄⢀⣠⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠠⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣵⣿⣿⣷⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠁⢈⣩⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠈⢀⣀⣀⣻⣿⠏⠉⣧⣀⣀⣀⣀⡠⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⣺⣿⣶⣾⣿⣷⣶⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡋⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡶⣿⣿⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣯⣍
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣦⣆
⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⡰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢄⠀⠀⡆⠀⠀⠀⠀⠀⢀⡄⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⣠⡤⢠⠀⠃⠀⣘⠀⢀⡏⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⠦⠂⢠⠊⡜⠁⠈⠀⢡⡀⠘⠦⠚⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⢧⣀⠄⠀⠀⡇⠀⢀⢻⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸⣆⠀⠀⠇⠀⠀⠀⠀⢰⡥⠔⠁⡸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⡌⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⢃⠀⠈⠓⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⠟⣠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢀⡈⠑⠊⠿⣶⣲⠤⠶⠦⠖⠶⠭⠐⠋⠁⠀⠒⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠂⠀⠀⠩⣒⡦⢤⣀⡈⢉⠥⠔⠒⠈⠁⠀⡀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⣄⣀⠀⢀⠀⠀⠐⠊⠉⠀⠀⠀⠠⠂⢀⡀⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠚⣁⠄⠀⢀⡀⠠⠀⠀⡀⠀⠒⠊⠉⣁⠒⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⡰⢚⡑⢂⠀⠀⠀⠀⣀⡠⠤⠒⠊⠁⠤⢀⣐⡦⠤⢀⠀⠀⠀⢀⠞⠩⣁⢀
⠀⠀⠀⠀⠀⠀⠳⣎⣁⣾⠠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡀⢸⠀⠄⣰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⢀⣴⣶⣶⣶⣄⣤⣶⠾⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠆⢰⣿⣿⣿⣷⣶⣾⣿⣿⣿⠿⣿⣿⣷⣼⣿⣿⣧⣴⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣦⣰⣿⣿⣿⣿⣿⣟⣟⣿⣹⣿⣿⣿⣿⣿⣟⣯⣧⡟⠻⠿⠋⢿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⠟⢻⣿⣿⣿⣿⣦⡙⣫⣿⡟⣻⣿⣿⣿⡿⠛⠷⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⡘⢿⣿⠇⠻⠟⠛⣿⣿⣿⣿⠏⠁⠀⢀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⡴⣀⡘⣧⡀⢈⡿⣭⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠋⢀⠊⣴⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞
⠀⠀⠀⠀⠙⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⢦⠀⡀
⠀⠀⠀⠀⠀⢠⠄⠀⠀⢁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠓⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡦
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠖⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠓⠛⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡄⠀⠸⠿⢟⠁⠀⠀⠀⠀⢠⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⡀⠀⠀⠀⠀⠀⢠⣼⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣴⡴⠛⠁⠀⠀⠀⠀⠴⢻⡏⣿⠿⠃⣿⡆
⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣷⡄⠀⠀⠀⠀⠀⢸⠇⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣠⡀⠈⢿⠃⠀⠀⣿⣶⡄⠀⠀⠀⠻⠀⡄⣀
⠀⠀⠀⠀⠀⣾⣀⡀⡰⠆⠀⠀⣴⠀⠀⠀⠀⠙⠃⠀⠀⣷⣦⣠⣿⣿⡗⠀⠀⠀⠀⠰⣤⠈⠁⠀⠀⠀⠴⠀⢀⠀⠀⠀⠀⠀⠀⠔⣦
⠀⠀⠀⠀⠀⣽⠋⠀⣡⠄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⠟⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⠆⢿⣤⣸⠆⠀⣤⣶⠸⡇⠀⡀⠀⡀
⠀⠀⠀⠀⠀⢿⣇⠀⣏⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢⢤⣹⠆⢲⠇⠉⠟⠀⠀⠙⡅⠀⠀⠌⠛⠼⠰⣄
⠀⠀⠀⠀⠀⠀⣿⠐⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⠀⡀⢀⡤⠐⠋⠀⠀⠐⣄⠀⠀⠀⣿
⠀⠀⠘⠀⠀⠀⢛⠁⠈⢣⠀⢀⣄⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠷⠆⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣍
⠀⠡⣤⠄⠀⠈⠉⠀⠀⣾⣿⣜⡅⠀⠀⠸⠀⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠐⠀⣾⠀⠀⠀⡀⢰⣆⠹⣿⡹⡅⠀⠀⠲⠃⣬⡁⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠐⠀⣒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠐⠀⢿⢠⠀⣀⠁⠀⢻⣦⡛⠻⠅⠀⠀⣠⣆⢸⡇⠀⠀⠀⢿⣴⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢦⣰⣿⠀⠋⠡⢁⠌⠀⠠⡞⠁⠀⠤⠦⠀⠀⢀⡄⣾
⠩⠀⠈⠇⠀⠀⠀⠀⢸⣿⣿⣷⡆⠀⠀⣿⣿⣿⣧⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⡎⠀⢠⣶⡾⣿⣿⣧⠰⢌⣤⠀⠀⠿⠂⠀⠀⠀⠀⠀⠛⡁⢼
⠀⠁⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣿⡀⠀⠀⠀⠰⠟⠀⠃⠀⠟⠋⣼⣿⣿⣿⡷⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⢀⡀⠀⠀⠀⢀⡼⣷⣶⣍⣈⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⣇⠙⣧⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⢹
⡴⠋⠁⠀⠀⠀⠀⠀⠘⠛⠻⠿⠀⠀⠀⢸⣿⣿⣿⠁⣼⣾⣿⢻⣿⣧⠀⢀⣀⣄⡀⠳⠀⠀⠀⠀⠀⠀⢀⣤⡀⠁⠀⠀⠂⠀⠀⠀⢀⣾⣶⢀⡇⠰
⢥⡀⠈⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣾⣿⣿⣿⣸⣿⣯⣄⠈⠁⠚⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⣿⠀⠀⠀⠈⡟⢀⢸⡇
⠂⠀⠀⣈⠡⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢛⣾⣿⣿⣽⣿⣿⣟⣦⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠀⢴⠆⠀⣻⠦⠄⣀⠠⠆⣘⠺⠀⠛
⡦⣿⠀⣏⣠⠟⢿⣦⣤⡀⠀⠀⢄⡈⠀⠀⠀⣠⣾⣿⠏⣿⣿⡏⣷⢻⡿⠿⡟⠀⠀⢠⠀⡄⣠⠀⠀⢀⠀⠱⠄⢸⣄⠾⡏⢀⡂⠁⢀⣀⠁⠀⠀⠬
⠛⠧⣀⣠⢯⣀⡛⢛⣁⡡⢤⠀⣈⡀⠀⠀⠘⣿⡿⠉⢀⣽⣿⢇⣿⡄⢾⣿⣿⡄⠀⡀⣶⣇⡠⠶⢤⣈⠳⣄⠀⢶⡿⢸⣻⣿⠣⡀⠋⠉⠀⢀
⢶⠀⢿⣥⡼⠧⣤⣾⣿⣿⣷⣿⠿⢛⡛⣛⠂⠉⠀⠠⣾⣿⣿⣿⠘⣷⡀⠙⢿⠗⠈⢻⣽⡿⠇⠀⢀⣭⠿⢿⢡⡄⣿⣿⣯⣿⣂⣴⠄
⡾⠃⠈⠉⠐⢂⠀⠀⠀⢩⡌⣥⢻⣿⣿⣯⠁⠠⠀⠀⣿⢩⣿⣿⠀⠈⢡⣤⡀⠀⠀⠀⢻⡄⠙⢶⡄⠀⠹⠏⣰⣦⣤⣮⠿⣛⢿⣭⣴⡷⣆
⠇⠀⣠⣼⣦⣼⣧⠈⠀⠠⠟⠻⣿⣿⣿⣿⣷⣦⣦⢀⡿⢾⣿⣿⣷⣀⣿⢿⠗⠀⠀⠀⢠⣿⡅⠂⢹⣾⡷⠀⣙⣿⣿⠋⠀⠁⠘⡿⠋⠐⠆
⠀⣠⣼⣿⣿⣿⣿⣶⣄⠀⠀⠀⠸⣿⠿⠿⠿⢿⣻⣦⣷⡄⣠⣋⣿⣿⣿⣄⡀⠀⢀⣼⢫⣭⣼⣿⣿⣿⣄⣀⣹⣍⠙⠀⡀⢀⣀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⣽⣯⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢾⣿⣿⣿⣿⣷⣍⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣿⣿⣿⣿⣿⣿⣬⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⣿⣿⣿⣿⣿⣿⣷⡝⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡕⠋⠉⠉⠑⠠⠤⠀⠙⠛⢶⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⢀⣤⡄⠄⠀⢷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢀⠀⠂⠁⠀⠴⠟⣉⠃⠀⠁⠈⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡹⣅⣿⠟⣻⡄⠀⠀⠉⠀⠀⠀⢡⠘⣏⢧⣀⣀⣀⡴⡋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⡿⠀⠩⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⣿⣶⣯⣵⣾⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢳⡀⠀⠈⠀⠀⠀⠀⠁⠄⠀⢠⣤⣿⣿⣿⡿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠁⠢⡄⠀⠀⠀⠀⠀⠀⡠⠀⡟⢛⡛⣥⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣟⣛⢧⣀⠀⠀⠀⠀⠂⠀⠀⣷⣿⣿⣶⣭⣾⣽⣗⣲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣭⣤⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠛⠉⠈⠉⣓⠒⠿⢭⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⣿⣿⣿⣿⠁⠀⠀⢀⠠⢺⣇⣙⣿⡿⠟⠁⠀⠀⠠⣄⠀⠨⠙⡀⢺⡸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⣿⣿⡿⢛⣿⡯⠀⠀⠀⠥⠒⠉⠙⠛⠉⢀⠈⠀⠀⠐⢤⡈⢂⠢⠈⠀⠀⠹⣎⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⡵⠃⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢡⡐⢄⢈⡄⠁⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡯⡞⢁⡴⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠢⢡⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⢷⡱⣄
⠀⠀⠀⠀⠀⠀⢠⢞⡕⠉⠰⢀⠰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⣰⢫⠏⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⣾⡇
⠀⠀⠀⠀⣰⣣⠏⠀⠀⠀⠀⣠⢞⢹⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡾⡾
⠀⠀⣰⣫⠵⠏⠀⠀⠀⢀⡴⡥⣿⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⢻⢡⠀⠀⠀⠀⠀⠀⣋⢧⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣾⡵⡇
⠀⠀⠈⢯⢧⡀⠀⠀⠀⠀⠘⢧⣱⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠀⠀⠀⠀⢀⣼⣿⣿⣧⢣
⠀⠀⠀⠈⢣⡳⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⢄⠀⢀⣴⣿⣿⣿⣿⣿⡎⣇
⠀⠀⠀⠀⠀⠙⢮⡳⢤⣀⠀⠀⠀⢀⡏⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢯⣟⡶⢤⣼⣦⣀⣠⣀⡾⡩⢭⣟⣒⣲⣶⣖⣒⣛⣯⠭⠶⣝⡲⣄⣀⣀⣼⢏⣟⣛⣛⣻⣯⠭⠽⠾⠭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠒⠓⠚⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⠒⠯⠽⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⡇⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠃⠀⢀⣾⠟⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣌⠀⠀⣠⣿⡏⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣠⡾⢻⡿⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⣾⡿⣡⣿⣧⠆⠘⠁⢸⣿⠀⡀⠀⠷⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣟⣵⣿⣿⣇⠀⠀⣠⡾⣿⣿⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣦⡾⣽⣿⣹⣟⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣾⡟⣱⣿⣿⣿⣿⡟⣱⣿⣿⣧⠻⣯⠜⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⢣⣿⡟⣼⢿⣯⣿⣿⣽⢣⠟⣿⣿⠹⣦⠙⢧⣀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡀⡆⢸⣿⠃⣿⡿⢰⡟⣿⡿⣿⣿⣏⠸⡆⢸⣿⣿⣿⡄⡈⢻⣧⡈⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣼⣿⡇⣿⢱⣿⣿⣿⣿⡿⠇⠁⣾⡈⣿⣿⣧⢰⡀⢻⣿⣆⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⠀⢿⣰⡇⡿⠁⣘⡇⢀⣼⣿⠇⢸⢻⣿⢸⡇⠀⣿⣿⠆⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⢻⣿⣿⣀⢸⣿⡇⠀⠀⣧⣷⠘⢿⡏⠀⣿⢹⡏⣸⣇⡀⢸⣿⡇⠀⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⣿⣿⣿⣌⣿⣧⣀⠀⠻⣿⠆⠈⣿⣰⢃⡾⢡⣿⣿⡁⢸⣿⡇⠀⣿⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠻⣿⡿⠿⣧⣼⡻⣷⡄⠉⠀⣰⣯⣿⡾⢡⡞⢹⣿⠁⣸⣿⡇⠀⣿⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣙⠓⠪⡿⠶⣿⣷⣿⣮⡻⣦⣬⣿⡿⠋⠐⠋⠀⣼⠟⣰⣿⡿⠁⢠⡏⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢽⣿⣿⣿⣷⣬⣉⠉⠁⠀⠀⠴⠊⣅⣼⣿⠋⠀⢠⠟⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡏⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⠟⢀⡴⢋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣿⣿⣿⣿⣿⣿⠿⢛⣋⣤⠶⠋⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣷⠶⣿⠶⠶⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡟⠿⡿⠛⡿⠿⣿⠿⢿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣾⣶⣷⣶⣿⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡆⢸⡏⣿⠃⠈⠻⠋⠀⠈⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠉⠁⢈⡟⣯⢠⡞⠂⠢⠸⣶⣾⠏⠘⡳⠀⠴⡴⠄⡀⢢⡀
⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡘⢧⠀⢘⣪⠅⢘⡩⠃⠀⠀⠀⠙⢧⠀⠀⠁⣜⠆⠙⠨⣯⢌⣷⡀⠠
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡀⠀⠁⠀⠈⡀⠀⠀⡀⠦⠮⠊⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠨⠙⠶⡖⢠⡚⠁⠼⠟⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠛⠜⡏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢄⣦⣙⢿
⠀⠀⢠⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠂⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⣿⢻⣿
⠀⠀⢸⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠁⠒⢼⢷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠈⣼⣿
⠀⠀⠀⠀⠀⢸⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢀⣠⠀⠛⠃⣙⣓⠀⢈⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢹⣿
⡃⠀⠀⠀⠀⢸⣧⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢤⣄⠁⣾⣿⡂⠟⠋⠉⡡⢂⡌⠉⠀⢠⣌⡛⠈⠀⠀⣀⣠⡁⠀⠀⠀⠀⡄⣠⣾⢧
⡃⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡴⠀⠀⠀⠘⠲⣾⣿⣆⣀⡄⠈⡀⣾⠁⠀⠀⠀⣹⣧⡀⠐⠉⠉⠉⠉⠂⠀⢠⣾⡇⠸⢿⣛
⣷⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢸⠁⠀⢀⣴⣿⡿⣫⣿⣿⣿⣇⠈⠷⢉⣼⠀⠀⠀⢻⡁⠁⠀⠀⠀⠀⠀⠀⠰⠌⠁⡇⠰⢿⡛
⣿⡇⠀⠀⠀⠀⢾⣿⡆⠀⠀⠀⠀⠀⢀⣼⠃⠀⠏⠀⠀⣿⠟⢋⢠⣿⣿⣿⣿⣿⡷⡼⢾⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣠⠀⣀
⣿⣥⡆⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⠘⣿⠹⣿⣷⠀⢸⢁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡟⠙⡿⢯
⣿⣿⠇⣰⠀⣾⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠛⠀⠨⠿⡄⠀⠚⠈⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⡇⢈⡿⣿
⠿⢃⣤⣿⢀⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⣠⡀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⣄⣅⠀⠘⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⣸⣿⣿⠔⠺⢷⠀⣷⣿
⣯⣨⣾⡿⣾⣿⡇⢸⣿⣿⡇⠀⠐⠚⠛⢻⡹⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⡭⢙⠀⢘⠃⠀⠀⢶⡆⠀⠀⠀⠀⠀⢻⡟⠹⠘⠷⡇⠀⣈⡉
⣿⢿⡿⣱⣿⣿⣿⢸⣿⣿⣿⣶⡄⠀⣤⠈⠃⠉⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠰⢿⣇⠀⠀⠀⢀⠄⢨⡇⢠⠊⡶⠏⢀⣈⠃
⡿⢟⣱⣿⣿⣿⣿⢸⣿⣿⣿⡿⣫⣤⠭⣤⡐⠂⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⡘⢱⠀⣸⡇⠀⠀⢸⣿⠀⠄⠀⢀⣤⡪⠦⠓⠖⠾⠇⠛⢿⠂
⣴⣾⣿⢻⢿⣿⣿⠸⣷⣙⣿⣿⣿⣿⣧⠀⠀⠀⢀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢇⣆⠀⢸⢛⢤⠄⠞⢣⡀⢁⠈⢜⠈⣁⠢⠽⣋⠅⠠⡱⠘
⡟⣿⣁⠸⣿⣿⣿⠀⣿⡅⠻⠏⣛⣉⣅⠀⠀⠀⠀⠃⠀⡿⠀⠾⠆⠀⠇⢰⢄⠀⠀⣏⠀⠸⢻⡜⡛⡺⣐⢸⣅⠀⡃⣂⣭⣜⠂⠀⢈⡁⠉⠚⠶
⠿⠀⠉⢱⣾⣿⣿⡄⢻⣧⠀⢻⣿⣿⣿⣆⠀⠀⢀⠘⣾⣏⣀⠐⠿⣷⣤⣄⡁⢷⣆⠀⠰⡿⣾⠧⢸⡉⣿⣟⠺⢆⠌⠉⠈⠀⠆⢱⣆⠀⠐⡀
⠐⢀⢢⣾⣿⣿⢢⣷⠈⣿⣤⠀⢻⢻⣿⠻⣄⠐⠾⣕⢽⣏⡿⡄⠀⠀⠘⢛⡿⣶⢿⡗⢀⠈⢷⣽⣿⣧⠿⠿⣦⠀⣀⠀⠀⠀⠀⠀⠋⠀⠀⠈⢦
⠀⠈⣾⣿⣿⣳⣿⣿⠀⠹⣷⡤⠀⠈⠈⠗⠀⠀⠘⢿⣷⡟⣋⣉⡀⠀⠓⠾⠁⣎⣸⠃⠾⠳⠌⠿⠻⣿⣿⠛⣧⣜⣿⠆⢀⣀⣀
⠀⠀⣿⡿⢠⣿⣿⣿⠀⠀⠁⢐⣤⣤⡀⠀⠀⠀⠀⠀⢻⠦⡄⠉⢲⣶⡀⠄⠀⠹⣯⢀⢛⣶⣽⣴⣧⣬⠟⡿⠬⣣⣴⣾⣿⠿⣇⠀⠀⠀⠀⠀⠠
⡄⠀⡽⣷⢸⣿⣻⣿⢦⡄⢠⣞⣿⣟⡿⠀⠀⠀⠀⠀⠀⣿⡚⠷⣄⠙⣿⣠⣿⣦⠀⠸⣿⣿⣿⣿⠟⠀⠀⠃⠠⣿⣿⠟⠋⢠⡆⠀⠀⠀⠀⢀
⣿⠀⣷⡈⠹⠟⢿⣿⣿⣿⣼⣟⠃⠙⠁⠀⠃⠀⠀⣀⡼⡿⠻⣱⡎⣦⢻⣿⠿⠎⠀⠹⣶⢿⣿⣏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠁⠀⠀⠀⠀⠀⠁
⣽⣧⣿⡷⣄⢠⣿⣀⣽⣿⣫⣝⣷⣤⣀⠈⠀⢠⡦⡽⢣⣤⣄⡻⣿⢿⣿⣿⣧⣄⣀⠀⡿⣦⡀⢡⠀⢠⠀⠀⣀⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢁⡀⢄⣀⠄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡿⠿⠿⠛⢦⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠻⠟⡂⠛⠋⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣼⣦⣴⣴⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠉⢉⣿⣿⣿⡷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣽⣿⣿⣿⣿⣿⠛⠀⣤⣾⣿⣿⣿⣋⣤⣤⡤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠂⠈⠛⠛⠛⠛⠛⠻⢿⣼⠟⠉⠀⠀⠀⠈⠉⠉⢱⣧⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣿⡿⣾⣤⣤⣠⣀⣤⠀⠀⠀⣤⣻⣶⣶⣶⠶⢾⣶⣠⡧⣼⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⣿⣿⣿⣿⡾⠛⠋⠉⠁⠉⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⠀⣀⣠⣴⣶⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣵⣿⣿⣿⣿⣿⣿⣷⣤⣼⣶⣄⡀⣤⡤⣼⡆⢀⣴⣦⣶⣦⣤⣄⢾⣿⣿⣿⣿⣿⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣬⡍⠛⣿⣿⠟⠋⠀⢹⠟⡉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠟⣉⣸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢿⡏⠀⠀⠀⢻⣆⣡⠆⡄⣄⣤⣤⢀⣀⣤⣴⣖⣿⠟⢛⡫⠈⠙⢍⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⡇⠀⠀⠀⠸⠛⠋⠉⠉⠉⠛⢿⡿⠟⠋⣉⣉⣤⣶⣿⠧⣀⠈⣀⣁⣼⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠾⣇⡀⠀⠀⠀⣶⡏⣤⣶⣯⣶⣞⣷⣾⣿⣿⠟⢛⡏⠀⢀⡀⣹⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⠟⠉⠉⠀⣤⣿⣿⣶⣿⣿⣿⣿⠿⠛⠉⢩⣼⣶⣿⣿⣿⡿⠰⠏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣶⣏⠻⣟⢁⣽⠏⠁⠀⠀⠀⠀⣀⣀⠟⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⣧⣴⢿⡷⢀⠀⢿⣯⡴⣦⣶⡄⣰⣆⣿⣿⠃⣌⣶⣐⣶⣿⡾
⠀⠀⠀⠀⠀⣀⠶⠛⢉⣠⣤⣾⣿⡟⠓⠈⠁⠀⠈⠛⠛⠉⠉⠹⠁⢉⣰⠃⡘⠉⠉⠉⠡⠁⠐
⠀⠀⠀⠀⠀⢣⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⠃⣴⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠿⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⢃⣼⡿⢱⡿⢻⣿⢿⣿⡿⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⣰⡿⠣⠊⠉⠀⠋⠀⠸⠋⠈⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠦⣄⠈⢷⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠻⣎⠻⣦⣀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠸⣆⠀⠀⠀⠀⢹⡆⠈⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⣦⠀⠹⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠁⠀⠘⣇⠀⠘⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡀⢀⡾⠃⠀⠀⠀⠘⢧⣀⣸⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⣇⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡼⠃⣾⡁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢦⡀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⠀⠀⠈⠻⢦⣄⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠹⣦⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠀⠀⠈⠉⢿⠓⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡟⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠃⠀⠀⠀⠀⣠⠞⣿⠇⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⡆⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⠞⠁⠀⢀⣤⠶⠛⠁⣠⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⡇⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠐⣇⠀⣤⠞⠋⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡇⢸⡇⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡀⠀⡼⠃⠀⢀⡼⠁⢸⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⡄⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⡇⠊⠀⠀⠀⣾⠤⠒⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⡄⠀⠰⠾⣡⣶⣟⣯⣤⣦⠀⠀⠈⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣦⡀⠀⠀⠀⠀⢀⡀⠛⢿⣷⣦⣤⣠⣴⣿⣷⣿⣿⠟⠃⠀⠄⠀⠂⠈⢁⣤⣶⡆⠀⠀⠀⠀⠀⣠⡟⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠶⠾⠿⣶⣤⡀⠰⠄⠠⣤⠄⢈⣩⣥⣾⠿⠿⠛⢉⣤⣄⡀⠰⣶⡿⠿⣿⣛⡉⣁⡀⠀⠀⢀⣤⡾⠛⠛⠛⠛⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠛⠛⠋⠉⠉⢛⣿⣶⣦⣤⣤⣿⡿⠛⠿⣶⣶⣦⣬⣽⣿⣿⣿⣶⣄⠈⠙⠛⣛⣩⣷⡶⢾⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⠶⠶⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⣿⡿⠿⢿⣿⣿⣛⣛⣻⣛⡻⠿⢿⣶⡶⠶⠦⠬⣭⡉⠛⠛⠓⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠋⢁⣚⡯⠟⠛⠉⣀⣤⣄⠀⠀⠀⠉⠁⠉⠉⠙⠒⠲⠤⣀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣻⣅⣤⡤⠶⠚⠋⠉⠁⠀⠰⠞⠛⣁⣀⣘⠛⠉⠙⠛⠒⠒⢦⣤⣤⣤⡶⠒⠾⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠋⠉
⣀⡀⣀⣀⡀⣀⣀⣀⢀⣀⢀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⣄⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⠀⠀⠀⠀⠄⠀⠐⡄⠀⠀⠈⠻⣿⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢠⣶⡄⠀⠉⠲⣭⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠃⠀⢀⠠⣄⡀⣤⣴⣮⡆⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⢀⣸⣧⣠⠄⣠⡀⠀⡻⣆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⣿⠿⣭⡀⠀⠐⢾⣿⣧⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢶⡷⠾⠿⢿⣿⣎⢻⣿⡋⠁⠈⠣⡀⠀⠀⠀⢸
⠀⠀⠠⠤⢴⣶⠟⠁⠀⠀⢉⣀⣀⡶⠛⣋⣻⣷⣯⠳⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠄⢀⠐⠛⢻⣷⣴⣼⣿⠿⡟⠋⠀⠀⠀⠀⠉⠀⠀⠀⢸
⠀⠀⠀⠠⣼⣥⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠒⠒⢻⡶⠾⣿⣿⣿⣿⣧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⢻⣿⠟⠋⠀⠀⢉⠉⠉⠉⣟⣿⣿⣿⣿⣉⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣥⣊⡱⠾⣶⡔⠁⠠⠄⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠷⢾⠅⢠⠴⠋⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣙⣿⠉⠻⢿⣿⣤⣴⣾⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠻⠉⠁⠀⠀⠀⠀⠀⠁⠀⣀⣿⢉⣿⣿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⢻⡆⠀⠀⠨⠛⠿⢿⡇⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠰⢶⣦⣤⣿⣥⣼⣿⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠾⠛⠟⠛⡁⢤⣼⡀⠀⠀⣤⣴⣬⣧⣸⡃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠟⠀⠀⠀⠀⠀⠻⠛⠛⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠭⠝⠛⠛⠿⠿⠟⠚⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠐⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠛⠓⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⣶⡀⠀⣠⠚⠋⠀⠰⡇⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⣤⣶⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠉⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣿⣄⡄⠀⠲⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⠄⠀⠀⠙⠲⣤⣿⣯⡁⠀⠀⠀⠀⠈⠉⣽⣿⣄⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣾⣿⣿⣿⣿⣿⣷⢦⣤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣾⣿⣿⣿⡑⠂⠀⠀⢀⠾⠋⠀⠉⠻⠧⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⣟⢁⢹⣿⣿⣿⣿⣶⡿⠛⢦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⢙⣶⣦⣿⣿⣿⣿⣿⣷⣬⣉⣁⡀⠀⠈⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠠⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡿⠋⠁⠉⢉⣿⣿⡿⠟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣍⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠋⠉⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⢿⣿⡿⣿⣿⣧⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡼⣿⡇⢨⣯⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⢀⡿⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠋⠉⣿⠁⠘⠙⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⢾⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠐⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠠⣤⣤⡤⣤⣤⡄⢤⣤⣤⣄⣄⡀⠀⠐⠈⢀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡀⠈⠀⠀⣀⡀⠀⣀⡠
⠀⠀⠰⢦⢲⣦⡹⠿⠇⢉⠈⠡⠘⠉⠚⠋⠙⠋⠓⠝⢺⠛⠾⠾⢮⠒⠺⣻⣇⠽⠏⠿⢿⠟⠻⢿⣷⣂⡦⠆⠉
⠀⠀⠀⠀⠈⠋⠀⠀⠐⢈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠈⠀⢀⡇⠀⠃⠀⠀⠃⠒⡄⠀⠀⠀⠈⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣚⠁⣤⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠄⠀⠀⢴⣦⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠠⣤⠤⣷⢀⣠⣤⣤⣌⡙⠂⣟⢓⢲⡶⠶⢻⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠃⢼⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⡙⠈⠈⠋⠈⠂⠁⠲⠀⠀⠉⠑⠀⢀
⠀⠀⠀⠀⠀⢁⣐⣒⣈⣈⠀⢀⡘⠀⠀⠇⡁⣀⡀⠀⡀⣐⠈⡃⠀⠂⡀⠀⠀⠐⠀⣥⣤⠭⠴⠀⠠
⠀⠀⠀⠀⠈⣉⠋⠁⡈⠠⠀⠀⡄⢰⡄⠃⠀⠉⠛⡓⠉⢀⣀⠄⠠⠶⠴⠒⠀⠁⠰⠈⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠂⠚⠟⢓⣔⡏⢹⢄⠈⠄⣠⠬⢏⡤⠠⠀⠢⠀⠞⠁⢲⡀⡀⠀⠀⠀⡀⡤⡄⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠔⠉⠀⡼⠂⢠⠋⠃⡙⠄⠘⠀⠀⠀⠠⢔⠴⢰⠉⠁⣆⠀⣾⢦⡀⡄⠃⢀⢸⡄⢢⡀⠀⢘⠄
⠀⠀⠀⠁⠈⠐⠀⠟⠁⠀⠈⠀⠠⠋⡒⠀⠑⡉⠘⠘⠀⠀⢮⡆⠀⢃⠀⢨⠀⣁⡀⠀⢃⠀⡈⢢⢇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⡙⢿⣷⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⠀⢹⣿⣿⣷⡌⣿⡆⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⣦⠀⠀⠀⠀⠀⣿⣿⣿⡇⠸⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠙⢶⣦⡀⠀⠀⠀⠀⠸⠀⣾⣿⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠋⢻⡀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀⣤⣴⣿⣿⣿⠁⠀⠘⣷⣦⡀⠀⠀⠹⣿⣷⡄⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣆⠀⠀⢿⡇⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⢠⣿⣿⠃⢀⡀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀⠈⠇⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⡏⠀⠈⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡄⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢒⠢⠄⠀⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢶⣶⣶⡶⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠠⠘⠄⡼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠂⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣄⠀⠀⠀⠳⣧⣄⠀⠀⠀⠀⠀⠀⡦⣄
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠄⡈⡇⠀⠀⠀⠀⠙⡗⠀⠀⠀⠀⠀⡉⠢⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠹⢂⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢘⣀⠀⠠⠌⢀⠁⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢀⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠐⠀⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠐⠁⠀⠘⠀⠀⢀⠀⠀⡄⠠⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⢀⠀⠂⠀⠁⠤⠐⠧⠠⠠⢀⠨⢖⣩⣶⣾⡮⠧⣆⡉⠀⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢊⣍⡙⠚⠉⢀⡀⠈⠈⠐⠁⠻⡂⠀⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠉⢤⠆⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣄⢀⠒⠐⡖⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠷⡿⠀⠀⠧⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⡀⠀⢀⠀⢀⠄⠀⠗⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠁⠀⠈⠀⠘⠐⠀⠀⠉⠘⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠐⠉⠆⡀⠀⠀⠀⠀⠀⢀⠔⠤⠀⠀⠢⡠⢄⠀⠀⠀⠀⠠⠌⡀⢀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠠⣀⠂⠁⠀⠀⡀⡐⠁⠀⠀⠀⠂⢀⡀⠀⠈⠀⠂⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠌⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠄⠠⠃⠁⠈⠁⢠⠄⠁⠀⡁⠀⠀⠠⠶⠢⡀⠀⠀⢤
⠀⠀⠀⠀⠀⡠⠃⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡀⡴⠀⠀⠀⠀⣀⡀⠨⡆⢈⠀⢀⠀⠙⠘⠀⠣⠀⠀⢁
⠀⠀⠀⠀⠉⠀⢀⢐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠨⣶⡄⠀⠢⠸⠃⠀⢨⠀⠐⠁⠀⠆⠀⠀⠐⠂⠂⠄
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⡀⠀⠉⠁⠠⣀⠀⠀⠀⡠⠊⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠎⣂⠤⢀⡀⠀⠀⡀⠠⠞⠁⠀⠠⠂
⠀⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠂⢶⣛⣣⡴⠃⠩⡀⠀⡠⠁
⡠⠊⠀⠀⢀⠀⠀⢀⠀⠀⠁⠂⠀⠤⠄⠀⡢⠋⠀⠀⡠⠀⣠⠔⠤⠄⢠⠄
⢁⠀⢠⠊⠀⠀⣀⣀⣀⡁⠂⠀⠠⠀⠀⠌⠀⠀⣔⠌⡇⠀⠀⠄⠐⠄⠀⡄
⠀⠑⠁⠰⠊⠉⠀⠀⠈⠉⠓⠲⠤⠤⠤⠤⠆⠀⢈⣴⠃⠀⠀⠤⠤⠀⠀⠃
⠀⠀⠀⠀⠠⠐⠊⠉⠉⠛⠒⠦⢤⣄⣀⣀⡤⠟⠀⠈⣄⠀⠀⠉⠉⠀⢀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⠖⠓⠉⠈⠢⡀⡠⠊⠀⠀⡀
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠀⢠⠁⠀⠀⠐⠀⠐⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⠀⠂⠀⠀⠀⠀⠂⠀⢰⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢀⠐⠂⠀⠀⠀⠀⠐⠀⠰⣸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⢁⣀⣀⠀⠀⠀⠀⠀⠀⣄⣅⣀⣉⣉⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⢀⡇⠀⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢠⠂⡄⠀⠀⡇⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠐⠰⠄⠀⠀⠀⠀⠀⣀⣐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢸⣌⠉⢻⣤⣶⡀⢒⢫⡿
⠀⠀⠂⠠⡤⠀⢸⣿⠁⢠⠆⣀⣴⠆⠀⡀⠀⠀⠀⠝⢻⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠐⠐⠉⡆⠀⡐⠈
⠀⠀⠀⠂⠀⠀⡼⣻⡤⠿⠞⠉⠡⠀⠀⠀⠀⡀⠀⢰⠂⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠰⠿⠀⡀⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⣼⣯⠏⠀⠈⠀⠀⠐⠀⢀⠀⠀⡅⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⡐⡀⠀⠀⠋⠃⠚⠚⠀⠂⠀⠀⠈⠉⠉⠀⠁⠈⠠⠄⠀⠀⠸⡄⠀⠀⠀⠀⡳
⠀⠀⠀⢁⣿⠇⠀⠀⠀⠀⠀⠀⠈⢁⣠⣤⣤⡶⠖⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡼⠪⠀⠤
⠀⡀⠀⣸⣿⣷⡀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠒⠠⠤⠤⢤⠠⠄⢠⣄⣀⣀⣤⣀⣀⣈⢀⠀⣩⣴⣂⠀⠠
⠀⢃⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣆⣀⣬⣿⣆⣀⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠿⣿⣏⣹⣿⣿
⣀⣴⣧⡤⢀⠀⠀⢀⣶⣴⣶⣾⣿⣿⠿⠟⠃⠀⠀⠀⠀⣀⣀⣠⣞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠈⠉⠛⢿
⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⢀⣶⣿⣿⠍⠉⠁⠀⢀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠥⠴⣤⣤
⣿⣟⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⡀⠀⠀⠀⠀⠉⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉