Mythical being Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠀⣠⣤⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣤⣀⡨⠁⠀⠀⠈⠀⣀⡠⠆⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠤⠂⣁⡄⠀⠀⠀⠀⠀⠂⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⢩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠙⢢⡙⣆⠀⡄⠆⠀⠀⠀⠀⠈⣽⣿⣷⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢦⡤⠷⣾⠀⠀⡤⠀⠀⢀⣀⣐⣲⣿⣿⡟⢒⣀⠀⠠⠄⠁⣀⣀⣈⣉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠋⠉⠀⢄⣀⢀⣠⠈⢁⡖⠠⣭⣿⣿⣋⣉⠉⢁⣤⣾⣤⡼⠿⠟⠛⠛⠛⠃⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢁⡾⡇⠀⠀⠀⣼⡟⠘⠋⣴⣦⣴⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣾⡄⠀⠀⠀⠀⣻⠃⣾⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡟⠆⠀⠀⠀⢠⡟⠃⠈⠙⣿⣿⣿⣿⡿⠛⢻⣭⣬⣿⡆⠚⢸⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣇⠀⠐⠄⠀⢈⠀⠀⠀⢹⡿⣿⣿⡟⠿⠿⣿⠟⡻⠉⠫⠂⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⣷⣄⡀⠐⢇⠀⠀⠸⢼⣟⠏⠒⠀⠀⠛⠉⣇⠀⠀⠁⠀⠀⢠⣼⢿⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢙⡀⣍⠀⠠⠓⠄⠀⠗⡟⠉⠀⠀⠀⠀⠀⠻⠦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠛⠁⠀⠀⠀⠘⠺⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠆⠀⠀⠀⠀⠀⠀⠈⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣤⣶⣶⣶⣶⢶⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⣠⡎⣰⣅⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢸⡀
⠀⠀⠀⠀⠴⣦⣌⢀⠀⠀⠄⠀⢀⡆⠀⠀⠀⠀⠀⢠⣄⠀⡠⢘⣆⠛⢷⠘⢇⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣾⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠃⠀⠟⠁⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢾⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⠨⠟⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⣿⣿⣶⣤⣤⠤⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠘⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠀⠚⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠈⠀⠧
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⢾⣿⣿⣿⣿⢻⣿⣯⣠⠀⠀⡅
⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠉⣝⡿⠃⠀⠘⠻⢿⠇⠀⠀⢉⢳⡆⢼⡁
⠀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣴⣶⣿⣯⡀⠀⠀⠀⢀⣿⠃⡄⠀⠀⠀⠀⠀⠀⠈⠚⠦⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠀⣇⠀⠀⢀⣾⣿⣌⢷⣴⢠⠀⢰⣠⣎⣀⠙⠒⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⣴⣾⣿⣿⣿⠟⠉⠁⠉⠉⠉⣡⠃⠈⠐⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣟⡿⠋⠀⠀⠀⠀⠀⠀⠗⠀⠀⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠻⡟⡇⠀⠀⠀⠀⠀⠀⠀⢸⠒⢺⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢻⣼⡄⠀⠀⠀⠀⠀⠀⠈⡆⣸⣿⣸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣻⣿⣿⣿⡿⠷⠀⠀⠀⠀⠐⠧⢍⠿⠿⠉⠝⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡮⠡⣴⣦⡈⠭⣥⢡⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠦⠯⣷⣠⣿⣇⠰⣒⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⢁⣀⣈⣋⢉⣿⡇⣻⢾⣶⡍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠛⠋⠉⡻⢿⡿⠛⠛⠛⣿⣿⣷⣶⣿⣿⠂⠄⠀⠤⢦⣀⡀⢀⡴⠛⢱⡏
⠀⠀⠀⠀⠒⡖⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⣿⣼⠿⠿⢷⣶⣶⣿⡿⠋⢿⣿⣿⣿⡾⣷⡄⠀⠀⠀⡛⡟⠏⠁⡸⣿⢷⣶⠂
⠀⠀⠀⠀⢀⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠥⡀⠀⠀⠀⣿⣿⠃⠀⣸⣿⣿⡿⠁⣿⠃⠀⠀⠸⣧⣁⣠⣖⣻⣿⣿⠿⠿⠶
⠀⠀⠠⠾⣥⣙⠆⣄⡀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⣠⠾⠛⠁⣠⣬⠿⢛⣃⣈⣽⡗⠄⠀⠀⠀⣨⠟⠛⠿⠿⠿⠁
⠀⠀⠀⢀⡌⠙⣛⣓⠈⣓⡒⢄⠀⠀⠀⠙⠛⠟⠁⠈⠀⠀⠸⢿⣿⢿⣿⡾⠿⣿⣿⣤⠀⣀⠀⠴⢟⡴⠂⠀⠀⠀⣀
⠀⠀⠀⠈⠉⠉⠁⣌⡟⠁⠹⣾⢧⠀⠀⠀⣠⠀⠀⠀⣠⣖⣓⠲⣻⣿⣵⣿⠶⣷⣿⡡⠺⢁⣀⣤⢅⣤⠤⣤⣁⠯⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢸⣎⣷⣄⡜⠁⠀⠀⠀⠸⠽⢋⣻⠿⣽⠏⣿⣦⣍⣩⣤⣶⣿⠻⢑⠫⠋⠉⠛⠟⣿⣎⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣥⡴⠃⠀⠀⠀⠀⠼⣏⣑⣲⣿⣿⣿⢟⣿⠻⠎⡑⠀⠄⣄⣠⣠⣀⠀⠉⣾⣧⠚⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡘⣿⡄⢀⡄⠀⠀⠀⠈⠿⣽⣿⣿⣻⣍⢫⣕⢢⡒⢦⣷⣾⡿⠟⠻⢿⣿⡄⠈⢿⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣾⡇⠀⠀⠀⢀⣼⣿⣿⣯⣿⢝⢷⣣⣿⣿⣿⡿⠃⠀⠀⠀⠀⢹⡿⡐⣿⡿⠈⠃
⠀⠀⠀⠀⠠⠶⢬⠓⠄⡀⠀⠀⠀⠀⠙⠿⠋⢉⡀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣠⣿⢯⣤⣿⠿⡆
⠀⠀⠀⠀⢀⣔⣉⡛⠳⣴⣤⣤⣴⠴⠶⠚⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⡿⠿⠟⠋⠁⠈⢿⣿⣻⠟⠿⠛⠟⢝⣱⣿⣿
⠀⠀⠀⠀⠉⠈⡹⠿⠟⠾⣊⣼⣳⣐⣭⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠾⠿⠛⠋
⠀⠀⠀⠀⠀⠋⠓⠚⠚⠉⠁⠀⠀⠀⠀⠀⠁

⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⣿⣿⣽⣿⣿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⠟⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣢⣀⢀⣀⣝⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣟⡼⣽⢳⡿⣿⣾⢸⡇⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣷⣷⣿⣺⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣽⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠙⠿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⣤⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⣿⣿⡆⢀⠀⠀⠀⠀⠹⢿⣿⡟⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣼⣷⣶⣤⣤⣤⣤⣤⡀⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⠿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣴⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⠋⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢴⡾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠀⠀⣀⠀⠀⠐⠂⠀⢀⠀⠀⠠⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠐⠄⠅⣀⡀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡋⣸⠄⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡈⠀⣅⠀⠀⠁⢄⠄⡀⠀⠀⠀⢌⡆⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡈⠈⠂⠄⠀⣠⠎⠀⡇⠀⠀⠀⠉⡀⡄⠀⠀⠦⠀⠀⠈⡆⠙⢦⡀⠀⣀⠉⠈⡃⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⡘⠐⠰⠏⠀⣸⣟⠂⠀⡁⠰⠀⠀⠀⢀⠆⠠⠀⣾⠀⠀⠀⠣⠀⢒⣿⡄⠈⠲⠐⡜⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⠀⠰⠇⢠⠀⢲⢰⠇⠨⠀⠀⠑⢦⡄⢀⡐⡏⠃⠀⠀⠍⠀⣠⡤⠃⠀⢘⠁⢷⢠⡄⠀⡀⢸⡄⠈
⠀⠀⠀⠀⠀⠀⢸⠀⢨⡠⠁⠀⠀⢨⠑⠐⠀⠆⠀⠀⣨⣟⢀⡁⠂⠌⣈⣶⠎⠉⠀⠂⠈⠂⠥⠛⠀⢁⠀⠱⡀⡄⠂⡇
⠀⠀⠀⠀⠀⠀⣈⠀⠈⡇⢀⡞⢠⡿⡄⠀⠁⢀⡁⢰⡇⠉⠀⠀⠀⠐⠈⠣⠀⢀⠰⠈⠀⡀⠀⣸⣴⠘⡆⠀⢹⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠙⡐⠀⢠⠆⢠⠸⣇⠻⣄⠀⡀⢤⡄⢷⡀⠄⠀⠀⠀⠀⢠⡌⡀⣀⡉⠀⠀⣱⠏⣸⠃⡐⢁⢀⠀⡄⠛
⠀⠀⠀⠀⠀⠀⢠⡇⠈⠺⡦⠀⠓⢭⠑⠈⠡⠟⠀⠀⠿⠍⠡⠀⠀⠁⠀⠹⠀⡄⠁⠰⣇⠒⡡⠖⣏⡜⠉⣨⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⢰⠧⠸⠡⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⢀⠀⢀⠾⢁⣀⠄⠉⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡄⠀⡖⡄⠀⠙⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣠⠎⠀⠨⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠃⠀⠀⠐⡀⠀⡀⠀⠀⣰⠀⢀⡀⠉⠢⡀⠀⡀⣀⠀⠠⠀⠀⠃⠀⠀⠀⠌⠀⣴⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠆⠈⢠⡟⠀⠐⡡⠶⡎⠟⠀⣀⠓⢊⣰⡌⠀⠔⠂⢲⡆⠠⠂⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠐⠀⠁⠋⠀⢀⠄⠘⢺⣀⠀⠀⠄⠈⡿⠁⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠞⠀⠣⡄⡌⢿⡙⠂⢀⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠁⠀⠀⠀⠀⠀⣀⠀⢱⡇⢰⠇⠂⠐⠐⠈⠜⣆⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠊⠁⠀⠚⠃⠀⠀⢀⠖⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⠀⠀⠀⠐⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠀⠄⣀⣀⡀⠀⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⢸⠂⠄⠀⠙⠃⣾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠤⠐⠁⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠛⠖⠃⠛⠎⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⣤⣤⠤⠤⣤⣀⠀⢀⣤⣿⠑⠢⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣤⡀⠞⡄⡅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣲⡿⠋⠁⠀⠀⠀⡀⠈⣡⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠾⣀⠋⠰⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣳⣟⣴⠶⠑⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠾⠙⡓⠀⠀⠀⢠⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⡨⠗⢠⠿⠁⠀⠀⠀⠀⠀⣈⣿⠟⠁⠀⠀⠀⠀⠀⠀⢐⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⢠⣇⠀⠀⢠⢮⣲⠒⠀⠀⠀⢮⡄⠀⠀⠀⢁⣴⡎⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⢠⣾⠋⠃⠀⡅⠀⡤⣏⠀⠀⠈⠀⠀⠈⠳⢦⣴⣦⠉⣦⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⣀⣼⠏
⠀⠀⠀⠀⣾⠟⠀⠀⠀⠳⣤⢆⠹⢶⡤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠃⠉⠙⠃⠀⠀⠀⠀⠀⢬⣿⢏⣤
⠀⠀⠀⢺⣧⠀⠀⠀⠀⠀⠈⢺⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣂⠐⠀⠀⠀⢀⣀⣼⡿⠗⠛
⠀⠀⠀⠂⠘⢦⡀⠄⡀⠀⠀⠀⠱⢶⡖⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢹⣦⣤⡄⠠⣤⡼⠏
⠀⠀⠂⠀⠀⢿⠍⠲⠤⣀⣀⠀⡀⠈⠛⠶⣤⣀⣀⠀⢀⢄⣤⡆⢐⣠⣿⣿⣿⣿⠿⠿⡟⠲⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⢀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠇⠛⠛⠉⢡⣾⠁⠈⠄⠰⡟⠉⡁⠀⠄

⣶⣶⡶⠶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢂⢈⠀⣧⢩⣶⢸⡏⣙⢸⡇⡏⣷⡏⡇⣿⢸⣿⢱⣿⡇⡏⡟⢱⡟⡀⣿⠀⣿⢸⢹⡏⡉⡟⢱⣏⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣷⣿⣾⣿⣾⣷⣿⣾⣷⣿⣾⣷⣷⣿⣶⣿⣦⣽⣷⣷⣿⣾⣷⣷⣿⣶⣿⣶⣾⣷⣷⣿⣾⣷⣾⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⢠⣷⡈⠁⠀⠀⠀⠀⠀⠘⠦⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠁
⠀⠀⠀⠀⣬⣬⣥⠀⠀⠀⠀⠒⠂⠀⢴⣤⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠓⠀⠀⣀⣀⣤⣤⠤⡄
⠀⠀⠀⠀⠙⠧⣁⣤⠄⠀⠀⢠⡄⠀⠸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠛⢿⡟⠀⠀⠀⠀⠀⠀⣤⣶⣿⠿⣿⣿⡤⠏
⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠙⠿⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠘⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢤⢰⣤⡀
⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠘⠧⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠈⢿⠟⠛⣿⠉⠀⠀⠀⠀⠀⠀⣰⣾⣇⡀
⠀⠀⠀⠀⠀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⠇⠀⠀⠀⠀⠀⣿⡷⢶⣿⠷⠄⠀⠀⠀⠀⠀⠝⠟⢩⣿
⠀⠀⠀⠀⢀⡟⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⢠⡯⠇⠸⢽⡄⠀⠀⠀⠀⠀⠀⠾⠿⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠼⠿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢈⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⠭⠌
⠀⠀⠀⠀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⡶⢶⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠅⢛⠀⠙⠳⠈⠀⠀⠀⠀⠀⠃⠘⡀⠈⠏⠃⠀⠀⠀⠀⠀⣴⣶⣧⡗
⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣾⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣴⣦⣤⣤⣤⣤⣤⣿⣿⣿⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⣶⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⢰⣦⣤⡀⠀⠀⠀⣤⣶⣾⣾⣟⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⠿⠿⠷⢄
⠀⠀⠀⠀⢸⣷⡽⠿⢿⠇⣀⠀⠀⠰⠋⢹⣿⣿⣇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⠁⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠈⠣⡀⢀⠉⠛⠀⠠⣶⢤⣴⣿⠿⠛⢿⣶⣶⣾⣿⣿⣿⣯⣽⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠸⠏⠀⠀⠀⢈⠀⠁⠀⠀⠶⠞⠀⠈⠳⣶⣬⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⢰⣶⢿⣿⣿⣿⣟⠁⠈⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢀⣿⡄⣹⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠘⠁⠀⠈⠉⠿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠹⣿⣿⣷⠂⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠹⣿⣿⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⣠⠿⠛⠛⠟⠛⠿⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣼⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣾⠃⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢀⣿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠙⣦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣤⡾⠿⠛⠻⣷⡀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⠀⠀⠙⠻⣷⣤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠛⠛⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠙⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⠏⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠂⠀⠀⠈⠛⣦⡀⢀⣆⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⢀⡴
⠀⠀⠀⠀⠠⡀⠀⠀⠸⣦⡀⠄⠀⠀⠈⠣⠀⠀⠀⠀⠹⣿⣅⠀⠀⠀⠀⠈⢿⣴⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠙⢦⡰⣄⠀⠂⠀⣤⡀⠀⠀⠈⠙⢧⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠘⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⠀⠛⠾⣟⠷⣤⣌⣙⣦⡀⠀⠀⠀⠻⣦⠀⠀⠀⢸⡀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢠⠈⠳⣄⠉⠛⠛⣷⠶⢶⣤⣤⣿⠃⠀⠀⢨⣇⠀⠀⣠⡟⠁⠀⠀⠀⣠⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠓⢾⣄⠀⠈⢷⡄⠀⣿⡀⠀⠙⠻⣿⣦⡆⠀⠈⢿⣤⣾⠋⠀⠀⠀⢀⣼⣁⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠀⠀⠀⠉⠳⡄⠀⠉⠲⣤⡙⢤⠀⠀⠘⢇⢻⡄⠀⢸⡿⠀⠀⠀⣀⣴⣿⠿⠛⠉⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠹⣆⠀⠐⠛⠛⠻⢷⣦⡀⢸⡀⢿⡄⢸⣷⠀⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⣈⠑⠿⠷⣦⣄⡀⠀⠀⠈⠛⢿⣧⠸⣷⠈⣿⣄⣿⣿⠟⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡻⠛⠶⣄⡉⠻⣍⠳⢶⣤⣀⠀⠹⣆⣻⡇⠈⢻⣿⣇⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣀⠀⠈⠀⠀⡠⠌⡙⣷⣮⡑⠂⢤⣙⠿⣷⣽⣿⣷⡀⢀⠻⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠟⠛⠛⠛⠛⠛⠛⢛⠻⠿⣷⣤⣈⣳⣦⣍⣿⣿⣷⣌⣷⣿⣿⣶⣦⣤⣤⣶⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠖⠊⠉⠉⠉⠙⠛⠛⠶⣶⢶⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠛⠋⠉⠉⢁⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠠⠄⠒⠉⠀⠀⢒⣠⣴⣿⣿⣿⣿⡿⠟⢛⠿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠤⠶⠛⣉⣁⣴⣿⣿⣿⣿⣶⡞⠋⠀⠀⣀⣤⣄⣟⠀⣿⡗⢀⡀⠀⠀⠀⠀⠤⠤⠜⠓⠂
⠀⠀⠀⠀⠀⠀⣠⠶⡞⠛⠙⠛⠁⠀⠀⠀⠀⠛⣉⣽⣿⣿⣿⣿⣿⣿⠁⠀⢆⣴⣿⣶⣿⣧⠀⣿⠀⠈⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢀⣤⡤⠐⣂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣷⡟⠀⠀⠘⠀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠂⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠘⣿⣇⠀⠈⡁⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⣿⣿⣿⣿⣿⣿⠶⠆⠀⣄
⠀⠀⠀⠀⠀⠀⠐⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠿⠛⠃
⠀⠀⠀⠀⠀⡠⠊⢁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣠⠖⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡔⠁⠠⠚⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⡟⠉⠘⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠉⠀⠀⢠⠟⠠⠋⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠟⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣷⠾⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⠁⠀⣱⣷⡴⠂⢀⠀⠀⠀⠀⡐⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢉⠉⢻⣧⣿⡀⢴⠿⢿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡨⠶⣻⡿⣿⣧⠐⡄⢈⣷⣤⣀⣀⣀⣀⣀⣂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⣛⣯⣿⣿⡿⠟⠀⣾⠟⠛⠉⠙⠛⠛⠋⠉⠙⠻⠥⠤⠤⠤⣄⡀
⠀⠀⠀⠀⣠⣴⠛⠿⣂⣴⣾⠟⠛⠋⠑⣀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⡠⠞⠉⠀⢨⣴⣿⡯⡗⠉⠐⣠⣴⡿⠿⢄⣀⣠⣴⣶⣶⣮⣭⣤⣀⣆⣶⡟⠀⠀⠀⠀⠀⠄⡁⢀⡄
⠀⢸⣷⠶⠂⠀⢿⢻⡷⠆⢎⡞⣼⡿⠏⠀⠀⠀⠉⢙⢠⣿⡿⢷⣤⣬⣿⣿⣿⣧⣀⣠⣀⡠⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⠋⣸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⡈⠀⠀⠀⣀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣁⣠⣤⣤⣴⡾⠛⣿⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⡷⠲⠶⣶⣒⣂⣻⣿⣿⣿⣿⣿⡿⠟⢿⡿⠀⠀⢸⡶⢿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⠀⠀⠀⣿⢐⣿⣽⠟⠋⠁⠀⠀⠀⠘⣧⠀⠀⠘⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣽⣻⠛⠋⢹⣷⡀⠀⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣾⣿⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠃⠀⠈⠈⠉⠹⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠈⠻⢿⣿⡿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠀⠀⠀⠈⠙⢿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣉⡅⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠝⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣙⢲⣶⣶⠞⠀⠐⠢⡄⢀⣠⡴⠻⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠚⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡬⠆⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⠀⠀⢠⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢐⡤⠟⠋⠙⠆⠀⠀⠀⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠤⠤⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠠⠃
⠀⠀⠀⠈⠁⠀⠀⢠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠢⠆⢀⠚⠀⢤⠀⡄⠐⡄⠀⠀⠀⠀⠀⠀⡼⠃⠄⠈⠂⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠘⢆⣀⠐⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣈⠀⢀⠀⠀⠀⠀⠡⠰⠀⠠⠀⠐⠂⠤⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠁⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⠄⠀⠮⠀⡔⢀⡂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⠀⠸⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠸⠇⠐⠁⠀⠀⠀⡰⢠⡃⠁⠈⠠⠄⡦⢼⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⢀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⢂⢂⠀⣸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⡪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⣄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠄⠀⠀⠀⠀⢀⡎⢀⣦⠿⠴⠧⠶⠖⠃⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣽⢇⠀⠀⠀⠨⡀⣿⠁⠀⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠁⠉⠁⠀⠀⠀⠳⣌⠀⠀⠠⠎⡀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠲⠧⡀⠀⠀⠀⠉⠙⠛⢻⣭⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠐⠋⠂⠀⣀
⠀⠀⠀⢀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠆⠑⠷⠒
⠀⠀⠀⢿⡟⠘⠛⠓⠀⠀⠀⠀⢠⠀⠀⠀⠘
⠀⠀⠈⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡾⡇⠤⢰⣆
⠀⠀⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⢀⠀⠌⠀⠀⠀⠀⠀⠀⠰⢢⡀⠀⠚⠉⢀⣀⠀⠀⠀⠀⠆⠀⠲⠄⠖⠉⠂⠐⢶⡿⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠐⣂⠀⠀⠀⠀⠀⠠⡸⠀⠢⢥⠄⠀⠐⢂⠀⠀⠀⠀⠀⠀⠤⠴⠀⣰⣷⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⣄⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⡘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠒⠀⠐⠃⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣾⣯⣽⣿⣿⣾⣿⣿⣿⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣬⣹⢿⣿⣿⣷⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢤⡀⢀⣰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⠟⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠂⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⡇
⠀⠀⢶⣶⣿⣿⣧⡄⢀⠀⠀⣀⡀⠀⠠⣼⡿⣿⣿⣟⣿⣿⣿⣿⣿⡏⠑⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁⠈⠿⢿⣷⣾⣶⠘⢿⣷⣦⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⠉⡀⠀⠀⡇⠀⠀⠀⢀⠀⠀⢰⣶⣤⠶⠾⠶⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠇⠀⠀⡇⠀⠀⢀⣆⣠⠾⠛⠋⠛⠀⠀⠀⠀⠻⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡧⢐⠀⠀⡇⢀⣤⣾⡟⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⠹⣷⣤⠐⢢⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢻⠿⣿⡟⠀⠀⠙⢿⡟⢻⠛⠿⣷⣠⣍⣿⣿⣿⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠆⠶⠶⠆⠤⢄⡀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⣀⡀⠀⠀⡀⠈⢣⡀⢀⠴⠊⠁⣀⣀⣀⣀⡀⠈⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠃⣟⠀⢰⡃⡿⠀⣰⣹⠂⠀⡴⠃⣠⢴⡿⠋⠁⠀⠉⠉⢠⡀⠀⠷⢶⣿⡷
⠀⠀⢀⣀⣀⠀⠻⣷⣤⡄⢠⠼⠃⡰⣿⠀⣸⠇⢧⡀⠈⠍⠀⣼⠁⡰⢁⡎⠀⣠⣾⠋⠀⣦⠤⣤⡐⠀⡛⠁
⠀⠘⠻⠿⢦⡉⠄⢻⣿⣕⠒⠒⣉⠴⠃⣠⣏⣀⢀⡟⢁⡤⠀⣀⠘⠃⠉⡁⠀⠉⠁⢀⡼⣡⠖⠋⠡⠀⠾⣄
⠀⠀⠀⠀⢸⠁⢠⠀⠉⠻⠭⢭⡥⠀⠈⠉⣉⡉⠛⢀⡿⢁⠈⣠⡶⡐⠀⢀⣴⠶⠾⠭⣼⡁⢂⣴⡏⠀⡷⣽⡆
⠀⠀⠀⠀⠘⠀⠈⠳⠤⣤⠤⣎⠀⣴⠶⠿⠯⣿⣆⢈⠉⠈⠀⠟⠾⠏⣶⡉⠀⠒⠒⠀⠀⠀⠘⠟⢀⡞⠀⠙⠃
⠀⠀⠀⠀⠀⠈⠢⢄⡀⣀⣀⡀⠀⣀⠶⠛⠛⢶⣿⡙⠀⠀⠀⠀⠀⠀⣩⠿⠥⣤⣀⠀⠐⢒⣨⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣼⠁⠀⠀⠀⢠⢿⠁⠴⠤⠀⠠⠴⠄⠛⠀⠘⠛⠛⢛⡆⠈⣏⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣿⠀⠀⠀⠀⠁⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢰⣿⠁⠀⡇
⠀⠀⣠⡀⠀⠀⠀⠀⠀⠈⢂⡠⠘⣇⠀⠀⠀⠀⠀⠈⠑⣄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⣐⣁⢀⣁⠜
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⣀⣤⠆⠀⣿⡟⠃⠠⣤⣀⡀⡏⠐⠀⠀⣏⠉⠉⠀⠀⣠⣤
⠀⠀⠘⣟⢇⡀⠀⠀⠀⢀⡰⠁⢀⡞⠀⠀⠀⠙⡟⠀⢰⠏⠀⠀⠀⡘⢀⢣⢷⡀⠀⠀⠈⠑⠤⣤⡴⣿⠋
⠀⠀⠀⠘⢦⣉⠓⠲⠚⠉⢀⣠⠞⠀⠀⡄⠀⡜⠀⢀⣿⠀⢀⠀⣰⢣⣷⠋⠀⠉⠢⢤⣅⣠⣀⣀⠄⢣
⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⣇⡾⠀⠀⣼⣿⣧⢣⢠⠃⡟⠁⠀⠀⠀⣴⣤⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢰⣿⠃⣧⣧⡏⡜⡀⠀⢠⠁⠀⠈⠻⣿⡒⣋⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇⣠⠢⣾⣏⢆⠏⡎⣼⡴⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠻⠟⠀⠈⠙⠛⠚⠚⠛⠋⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠉⠉⠙⠛⠻⠷⠶⠾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠛⠛⢛⣿⣷⣶⣶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣿⡏⠀⢀⣴⢀⡹⠛⠉⠙⠃⢈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣤⡘⢿⣿⣿⣷⣄⣠⣿⣿⣷⣦⠄⣠⣄⣀⣀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣀⢀⣀⣀⣀⣴⣤⣾⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣴⣿⣿⠄⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⢣⣿⡿⠀⠉⢩⣿⠋⢹⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣴⠖⣿⡿⣷⣿⣿⠾⣿⣿⣿⡿⣿⣷⣾⣿⣿⣭⠑⣍⣵⣿⣿⣿⣿⣷⣿⣇⠀⢰⣟⣿⡃⣼⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⡆⠘⠯⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣖⣿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡤⠋⢹⣿⣿⣿⣿⣷⣶⣿⣿⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⢧⣼⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⠁⢿⣿⣉⣶⡿⠀⠀⠀⢠⢻⣿⣿⣿⣿⣡⢧⣷⣿⣷⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣯⣜⣯⣽⣾⣌⣭⣭⡿⠟⠁⠀⠈⠻⣿⡿⢠⣆⣄⠀⠀⣽⣿⣿⣿⣿⣿⣧⣉⣰⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣠⠀⢰⡿⠁⠀⠙⠿⠷⢶⣯⣿⣿⣽⣿⣿⠿⡯⣥⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡴⢏⣴⠏⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣾⣍⣱⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⢀⣺⣩⣾⠟⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⠟⠛⠿⣿⡋⠛⠛⠁
⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⣠⣴⣿⡿⠟⠋⠀⡀⠀⠀⠀⢀⣄⣵⣽⠋⠈⠳⠦⣀⣤⣽⠏
⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⢋⣀⣀⢾⣿⣷⣿⣦⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠛⠁
⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⡿⣿⣿⣻⣿⠏
⠀⠀⠘⠿⠿⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣠⣆⡄⢲⣆⣴⣿⣿⣿⣿⣿⡿⢟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⡿⠿⠛⠉⠹⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣙⣿⠀⠀⠀⠀⠀⠙⢿⠿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠈⠙⢿⣧⣿⡀⠀⠀⢀⣠⣴⣶⣤⣤⣙⣿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠄⣐⣿⣷⣤⣶⢾⣿⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣏⣻⣭⣿⣝⣴⡹⣻⣷⣲⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣥⣶⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣶⣻⣟⣿⣯⢥⣈⠉⠉⢾⣽⣿⣷⣽⢻⢿⣿⣳⢾⣽⢳⣄⡀
⠀⢠⣴⣶⣿⣻⣽⣿⣿⣷⣿⣿⡿⠋⠀⠿⠛⢿⣿⣿⣿⣿⢿⣟⡟⡷⣝⣦⠀⠙⠋⢿⣿⣷⣯⣞⣳⢯⡴⠙⡇⠈⠂
⠐⠋⠉⢙⢡⣿⣟⣟⣯⡾⠛⠁⠠⠀⠀⠀⢀⣀⡀⠉⠉⠻⣿⣿⣿⣾⣽⣿⠁⠀⠀⠀⠈⠉⠹⠍⡴⠀⢸⠇
⠀⠀⠛⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠙⠿⡿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣀⠀⠀⡔⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠁
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡡⠀⠠⠀⢄⡀⢤⡂⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡖⠠⠖⠀⠈⠁
⠀⠐⠁⡀⠀⠀⠀⠐⠀⠀⠙⣴⠀⢃⣀⡈⠁⠀⣷⡀⡏⡀⠀⠀⠀⠀⠀⠀⢀⠀⡞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⠿⠿⠇⠿⣻⣷⣤⠀⠉⠁⠛⡁⠀⡀⠀⠀⠀⠈⠀⡉⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠈⡿⠒⠦⠀⠀⡀⠀⠀⠀⠀⠈⠂⠀⠎⠡⠄⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣰⣤⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⠀⠀⠀⠓⠦⢀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⣾⠚⣡⣶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠑⠛⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢨⠇⢰⣿⡉⣿⣋⣿⣿⠶⠀⠂⠀⡀⠉⠀⠀⠀⠀⣠⡶⠀⢄⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢹⢸⣿⣟⣋⣻⣿⣿⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⡴⠋⠛⠾⠲⠀⠳⠤⠂⠠⢄⢀⠎
⠀⠀⠀⠀⠀⠰⣆⣼⣿⣿⣿⣏⣿⠀⠀⠀⢰⡞⠀⠐⠂⢄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠿⡥⣝⢿⢿⢻⠄⠀⡀⠀⠃⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠨⠛⠀⠀⠁⠂⠸⣤⡄⠁⠀⠰⣄⡠
⠀⠀⠀⠀⠀⠱⠄⠶⠂
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣴⠂⠐⢁⠔⡡⢞⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣄⠠⡄⠀⠀⠀⢀⡈⠉⠀⠀⠒⠋⠁⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠀⢸⢸⣷⣞⣀⣷⢬⠧⠤⠤⢶⣶⣶⡒⠀⠉⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⢨⣿⣿⡾⠉⠄⢻⣿⢿⣷⣧⢀⡠⣬⡟⠀⠀⠀⠀⠀⠄⠠⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⢷⣼⣿⣿⣇⠀⠘⠀⢙⠧⢽⡷⢽⣿⣿⡧⣄⠀⣀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣸⣿⣿⣿⣏⠀⡰⠀⢼⡓⢶⡟⠲⢿⡷⣿⣦⣽⣿⡿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡖⣁⣴⠯⢈⣿⠓⢶⣶⣧⣤⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠉⠀⠀⣶⠻⣍⣶⠼⣍⢳⣶⠋⠀⠀⠉⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⠾⠿⠍⣀⠀⠀⠀⠘⠷⣿⢹⣷⡿⠛⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠴⢋⣤⣤⣄⣀⣀⣀⣈⡶⣤⠀⠀⠀⠈⠛⠉⠀⠀⣴⠾⡀⠀⠀⠀⣠⡦⡀
⠀⠀⠀⠀⠸⣷⣠⡾⣿⡟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠈⢷⡀⠀⢾⠁⡀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢸⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢻⣦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠁⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⠀⢠⢿⠆⠀⠀⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⠀⠘⠛⠀⠀⠊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠛⠳⠖⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢝⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⢌⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⠯⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠋⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣾⣅⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠂⠀⠀⠀⠀⢀⣤⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠈⠛⠛⢿⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⣠⣏⡜⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⡼⣛⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡄⢠⣀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠀⢀⣠⡎⠀⠀⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠶⠿⢷⣤⣄⡀⠀⠀⠈⣻⣿⣿⣿⣿⣾⣄⠀⢰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⣟⣟⣟⣻⣿⣿⣿⣿⣿⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣯⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⣿⣿⢻⣿⣿⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢦
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣷⢀
⠀⠀⠀⣀⡠⠀⠀⠀⠀⢀⣿⢾⣿⡿⠇⠀⠈⣿⣿⣿⣿⣿⣳⣾⣿⣿⣿⣦⡀⠀⠀⢀⠤
⠀⠀⠀⠘⢷⣀⠀⡀⠀⠈⣿⣼⣿⣇⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠀⠘⠒⠂
⠀⠀⠀⠀⠀⠻⣦⣙⠦⠀⠉⢿⣿⣿⣇⣹⣿⡿⠿⣿⣿⣿⣹⣿⢿⡿⣧⣤⣄⡀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣄⡠⣿⣿⣿⠏⢁⡶⣾⣞⡛⡛⠿⠀⢀⠀⠀⣌⠙⠀⠀⢠
⠀⠀⠀⠀⣠⣴⣤⣴⣴⠾⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣀⠀⣹⣿⠆⠀⠒⣧⡀
⠀⠀⢀⣾⡟⣡⣶⣿⠶⢛⣥⣶⣶⣌⠻⣿⣿⣿⣿⠹⢷⡏⠈⠀⠺⢻⣧⣿⣿⣿⠐⣰⢌⣓
⠀⠀⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣭⣿⣆⣻⣿⣟⣹⣿⣿⣧⣤⠴⠒⣠⣄⡉⢻⣿⣿⣿⢿⣿⢿⣶⣸⡄⠀⠀⠀⢠⣴
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡿⠿⣿⣿⣷⣶⣶⡿⠂⠀⠈⠉⠉⠙⠙⠻⢿⣿⣿⣷⣀⠉⠫⢧⣀⣤⣀⣼⣿
⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣛⣡⣼⣿⣿⣾⣿⣿⣿⣦⣄⣀⢠⡔⢠⣤⣤⣤⡄⠀⢨⡻⣿⣿⣿⣿⣦⣤⣥⣽⣿⡛⣏
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠛⢛⣛⣿⣿⣷⡿⣶⣦⡰⣶⣤⣄⠀⣣⠙⢿⡟⠉⠛⠿⠿⣿⠟⣛⢿
⢸⣿⣿⣿⣿⣿⣿⠿⠛⢛⣿⣿⣿⣿⣿⣿⣇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣷⠘⢷⠀⠀⠁⠀⡾⠀⢛⣿
⢸⣿⣿⣿⣿⣿⣿⣷⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣷⣌⢧⠀⠀⢀⠃⠀⠈⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⠿⣿⣿⣿⣿⣧⡙⣿⠘⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⡉⠀⠀⢰⣿⣿⣿⣿⣿⣷⣿⣆⢹⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⠀⠀⠠⡜⣿⣿⣿⣿⣿⣿⣿⣾⣷
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⡿⠛⡁⠲⠀⠘⢿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠘
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣀⡀⠀⠿⣿⣿⣿⣿⢛⣿⡿⠋
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⡼⣻⣿⣿⡿⢗⣘⡓⢷⣾⣿⣿⣿⣿⠿⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠁⣀⣩⣾⣿⣿⣿⣿⢿⣿⣷⣤⡹⣿⡛⠋⠁⠀⠀⠀⠆
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣼⠷⠒⠀⠀⠀⣸⣀
⠀⠀⠈⢿⣿⣿⣿⡿⢿⣿⣿⡿⠘⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣯⣉
⠀⠀⠀⢀⣿⣿⠏⣴⣿⣏⣁⣠⣴⣿⣿⣿⡿⣼⣻⣿⣿⣿⣿⣿⣿⠿⠟⠛⠳⠿⣿⡏⣿⣿⣿⣿⣿⣿⠿⠶⡆⠄
⠀⠀⠀⣾⡿⢋⡰⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣶⡶⠄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡷⠶
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣙⣿⣿⣿⣿⡷⠋⠐⠀⠻⠿⣿⣿⣿⣿⠛⠓
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠛⣠⣶⣿⣦⠤⠄⠀⠘⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣄⠀⠀⠀⠀⠺⡟⠷⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⢿⡛⢉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡔⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣘⣋⢀⠀⠀⠀⢳⡔⢀⡀⡦⣈⡇⠀⣤⡀⣰⢚⠎⠀⠀⠀⣻⣷⣶⢞⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣦⡑⢂⣤⣴⣯⠀⠛⠁⠈⠀⠀⠀⠈⠃⠘⢦⣴⣶⣾⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡿⠋⢀⡤⠶⠶⠤⣀⠀⠀⠀⣠⠴⠶⠦⢄⡀⠀⠈⠂⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠒⣴⢯⠆⠀⠀⠀⠈⢣⢠⡞⡵⠀⠀⠀⠀⠱⡀⠀⠀⠹⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠃⣿⡸⡇⠀⣴⣶⡄⣸⢺⡇⢇⠀⢰⣶⡆⢰⠇⠀⠀⠀⢈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢅⡀⠈⢷⣭⣓⣈⣩⡵⠃⠀⠹⢮⣑⣂⣉⡥⠎⠀⠀⠀⠀⠈⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠋⣸⣿⣶⡤⣭⣥⣤⣤⣤⣤⣤⣤⣭⣭⡤⢴⡶⣿⣇⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠄⣿⣿⣿⣷⣴⣿⣦⣼⣿⣤⣾⣷⣴⣿⣶⣾⣿⣿⡟⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠿⢿⣿⣿⣧⠸⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠁⠀⠈⣿⣿⣿⣆⠙⢾⣅⣹⡟⠙⣿⠏⠉⢻⣿⣋⣹⣿⠴⠋⠀⠄⠀⠀⣴⡀⠀⠀⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⢀⣿⣿⣿⡿⠑⠦⢀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠀⡀⠔⠂⠀⠀⠀⣿⡇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠁⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣄⠀⠀⠘⢟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡃⠀⠘⠀⠜⣿⣿⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠀⠀⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⣿⣆⢲⣤⣤⢻⣿⣿⣿⣿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣴⣿⣛⣤⣾⢠⠎⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⣇⠀⠸⠇⢻⣿⣿⣿⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡃⠻⠀⢀⣼⡿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠁⠀⠀⢰⣿⣟⠁⠀⠂⠻⣷⣶⣦⣄⡀⣄⡀⢠⣄⣠⣴⣿⠃⠀⠀⠉⢦⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⢀⡟⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣦⠄⠀⡘⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠘⣿⣷⣤⠄⠠⣇⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣬⣄⣤⣴⣤⣄⣽⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣧⣶⣶⣦⣼⣷⣆⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠻⠛⠋⠙⠛⠛⠟⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋

⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡄⣡⢸⡌⣷⡆⣾⢸⢸⡇⡏⢷⡏⡀⡇⢽⣿⢸⣿⢘⢸⠙⣾⢑⢸⡆⣾⢸⢸⡇⡇⡏⣳⣏⢺⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⢀⡀⠈⠛⠀⣀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡞⠉
⠀⠀⠀⠰⣶⠶⠆⠀⠀⠀⠈⠉⠀⠸⣶⣿⣽⣇⣀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠉⠀⢀⣥⣴⣶⣶⠲⡄
⠀⠀⠀⠀⠈⠃⣶⠟⠀⠀⠐⠖⠀⠈⠻⣿⣿⣿⣿⣧⠀⣀⠀⠀⠀⠀⠉⠿⠀⠀⠀⠀⠀⠀⠲⡿⠟⣻⢿⣿⠚
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠛⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠾⠟

⠀⠀⠀⠀⠰⠶⠲⠆⠀⠀⠀⠀⠘⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣴⡷⠀⠀⠀⠀⠀⠀⢀⣵⡖⠉
⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⢶⡄⠀⠀⠀⠀⢠⣯⣀⣸⣦⡀⠀⠀⠀⠀⠀⣾⡿⢻⡆
⠀⠀⠀⠀⢀⡏⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⢿⠉⡿⡏⠉⠀⠀⠀⠀⠀⣡⣤⡾⠃
⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⠀⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤
⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⡄⠈⠂⠏⠀⠀⠀⠀⠀⠀⠀⠸⣃⠘
⠀⠀⠀⠀⢀⣠⡋⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⡶⣦⠀⠀⠀⠈⠃⣾⣿⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⡄⡠
⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠏⢻⠉⠻⠳⠈⠀⠀⠀⠀⠸⠈⡋⠉⠛⢳⠀⠀⠀⠀⠀⣠⣶⣅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠘⠀⠀⠀⠀⠀⠉⠋⠉

⠀⠀⠠⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠰⠀⠀⠀⠠⠜⢻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⢂⠀⠀⠀⢒⠀⠀⢆⠀⠀⠀⠀⠀⠐⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠒⠀⠀⠁⠀⠀⠁
⠀⠰⠤⣤⡐⠀⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠂⠂⠈⠓⠒⠄⠀⠀⡀⠀⠀⠀⠃⠀⠃⠈⢃⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠠⠀⠒⠋⠀⠀⠖⢀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢁
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⡂⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠅⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⡐⠈⠀⠀⠐⠀⠀⠒
⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠠⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠴⡇⠀⠀⠗⠄⠀⠀⠀⠀⠠⠊⠀⠀⠐⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠚⠃⠀⠈
⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠀⠄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠈⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣤⠄
⠀⠀⠀⢠⠠⡀⠀⠀⠴⠦⠀⠀⠀⠶⠀⠀⠀⠡⠒⠀⠠⡂⠀⠀⠐⠀⠢⠀⠀⠀⠐⠀⠀⠈
⠀⠠⠄⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡈⠀⠁⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠠⠈⢄⠀⢉⠀⠄⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠈⢁⠀⠀⠁⠂⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠠⠉⢀⠀⠀⠐⠒⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⢰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠒⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠰⠔⠊⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⡀⣀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠋⠟⠻⠉⠇⠯⠄⠵⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⣀⠄⠀⠠⣤⠀⠀⢀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⡄⢤⡄⢤⠄⡠⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⡗⢁⠞⣉⣀⣀⣀⣀⣀⠠⠤⠕⠺⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠋⠓⠋⠓⠘⠚⠓⠒⠛⠘⠂⠀⠀⠀⠀⠀⢀⡴⢁⡴⠋⠀⣸⠟⠉⠁⠀⠀⠈⠉⠐⠶⣴⣇⡠⠞⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⢋⡠⠛⢀⣴⣿⣛⣋⣀⠀⠀⠀⠀⠡⠀⢘⣯⣌⣁⠒⠒⠒⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢐⠛⠶⠋⠀⣰⡿⠿⠭⢭⣉⡑⣴⠏⣤⠄⣀⡴⣟⠒⠂⠭⣉⠛⠦⢤⣀⣀⠶⠒
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠋⢸⠶⠁⠀⣀⡤⠾⠥⢤⣐⡶⠞⠁⠲⣥⣴⡒⢛⡉⡑⠢⣌⠤⡀⡀⠉⠑⠒⠬⠵⢶⡶⠶⠚⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⠀⠐⠀⠀⠀⠀⠒⠾⢋⣠⠔⢂⠐⠒⢀⠑⠠⡄⢀⣀⣿⣷⣶⠂⠈⠑⠂⠑⠀⢩⣩⡤⠈⠐⠂⠤⣾⡷⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣷⣾⡀⢰⣾⡷⠒⠊⠀⠀⢀⠙⠓⡀⠈⢠⡴⠓⢄⠂⢀⠀⠀⠀⠀⠈⠑⠢⠤⠤⢤⠐⡞⠩⢉⠉⠙⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠉⠀⠀⠀⠀⠉⠀⡀⠀⠁⠐⠈⠉⣚⠛⠚⠋⠀⠀⠀⢢⠂⢀⠀⠀⠀⠀⠀⢡⠀⠂⢈⠢⡐⠢⣀⠀⠀⡀⢅
⠀⠀⠀⠀⠀⠀⠀⡀⡈⢳⠄⠀⠀⢠⣔⠃⠉⢩⣼⡏⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⢸⠐⢀⡀⠈⠀⣀⠀⠁⡴⣷⠀⠀⠘⠓⠠⠩⣲⡀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠂⠀⠐⠀⠀⡞⠈⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠀⠀⠀⢠⠀⠀⠀⠙⢷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢁⣬⠗⠂⠀⡀⠀⠀⢠⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠉⠀⠀⠀⠂⠀⠸⠀⠀⠳⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⡰⠋⠀⠀⠀⠚⢱⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⡤⠄⢠⠄⠀⠀⣰⠃⠀⠀⠀⠀⠙⠛⠓
⠀⠀⠀⠀⠠⠂⡁⠀⠀⠤⠊⠁⠐⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣰⠋⢀⠀⠀⠀⠀⣸⠋⠀⣦
⠀⠀⠀⠀⠒⠁⠀⠀⠀⣠⠄⡥⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠠⠀⡇⠀⠀⠀⠀⠠⠀⡧⡰⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠔⠀⠀⠀⢷⠀⠀⠀⠀⠀⡂⢰⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠋⠀⠠⠀⠀⠀⠀⠀⠀⣈⡷⣆⡀⠀⠀⠰⢀⠇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⠀⠀⠀⠀⠀⠀⠠⠀⢀⡤⠖⣩⠀⠀⣑⠢⢄⡀⠈⠒⠤⣤
⠀⠀⠀⠠⢠⣈⡒⠀⠀⠀⠒⠀⠠⠀⠀⠀⢀⣀⡴⢋⠀⠀⠀⠀⢂⠀⢂⣠⠴⠊⠉⠀⠐⠃⢠⠐⠁⢠⠀⠉⠓⠦⣄⠄⠂⠀⠀⢤⡀
⠀⠀⠀⠀⢀⣈⣁⠄⠀⣀⡀⠀⠀⠀⠉⠙⢉⡽⠁⠀⠠⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡄⠀⠀⠹⠁⠀⠿⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠙⢢
⠀⠀⠀⠀⠀⠞⢳⡴⠈⠁⠈⠉⣀⡘⠃⠶⣾⠁⠁⠀⠀⠀⡀⢰⡟⠀⠙⠐⠂⠰⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠉⠀⠀⡏⠄⠀⠀⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⡠⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⡀⠀⠀⢿⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠒⠀⡀⠀⣀⠀⠔⠁⠀⠀⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠂⠀⠠⠈⠛⠾⢥⣄⡀⢀⣊⢀⣀⠀⢠⠀⠀⠀⠘⠁⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠂⠐⠀⠂⠀⡀⠀⠈⠉⠓⠾⢤⣦⡤⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⠀⠁⠀⢀⠀⠀⠀⠘⠀⠀⡈⠙⠳⠦⣤⠘⠃⠁⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠶⠶⠶⠚⠶⠒⠶⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠏⠉⡁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠨⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⢀⡀⠀⠀⠀⢠⡀⠀⠈⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠂⠀⠀⢀⡛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠀⠀⢀⣿⠆⠀⠊⢹⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⣼⣇⣴⣄⡀⠸⠀⠀⠀⠀⣠⣤⣿⡎⠁⣿⣷⣦⣤⣴⡇⣧⣸⣶⢷⠾⣿⡂⠛⠀⠈⢹⣷⡀
⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠐⠀⣿⣿⠛⠛⠻⠙⣦⠛⠉⡿⠉⢹⡿⠀⠀⢻⣏⠙⠉⠉⢹⠛⠁⠀⠀⢰⣿⠇⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢀⣿⠏⠁⠀⠂⠀⠀⠀⢸⣿⣆⠀⠀⠀⠇⠀⠀⠀⣠⣾⠀⢰⡄⠀⡿⣆⠀⠀⠘⠀⠀⢀⣠⡟⡅⠀⠀⠀⠀⢀⠐⢻⡄
⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⣶⣤⣶⣤⡶⠾⠏⠁⠀⠀⠁⠀⠀⣿⠛⡷⢶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠁⠀⠂⠼⣷
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⡿⠛⠻⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠛⠛⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⣈⣿⡄
⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣰⣇⢀⣾⣿⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡆⠀⠈⠻⣿
⠀⠀⣼⡏⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣰⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⠂
⠀⢠⣿⠀⠀⠂⠁⠀⠀⠀⠀⠀⢠⣶⣄⡀⢿⣿⡿⢿⣿⣿⣿⣿⣿⣏⣉⡀⢀⣀⣀⣤⣯⡟⢻⡟⣡⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷
⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠷⣾⠉⢡⠀⠸⢷⢬⠛⡛⠿⠿⣿⡟⠛⠉⠃⠸⠃⠘⠃⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡀
⠀⣸⣟⡀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣿⣿⠀⢀⡬⠀⠀⠀⠀⠀⢰⠃⠀⢠⠊⠀⢀⠀⢠⡄⠀⠀⠀⣽⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⣽⡿⠀⠒⠀⠀⠀⠀⢀⠀⠀⢏⣿⡟⢀⠈⠀⠀⠄⢠⠀⠀⡀⠀⢀⠛⢀⠀⠀⠀⠈⠁⠀⠀⠀⣿⡟⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⣿⡇
⠀⣿⠀⣸⡷⠀⠀⠀⠀⠀⠀⢠⢘⣿⣿⡆⠀⠀⡷⠀⠃⠀⠀⠀⣤⣤⣴⡤⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠘⠂⠀⡀⠰⠋⣿⡇
⠠⣿⠦⠛⣄⠀⠀⠀⠀⠀⠆⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣮⣿⣿⣦⡀⠀⠀⠀⠀⢨⣿⣿⡁⠀⠀⠀⠀⢠⠀⡄⠁⠀⠖⣿⡇
⠀⣿⣗⡄⠀⡄⠀⠀⠀⠀⠀⠁⠀⣿⣿⡅⠀⠀⠀⠀⠀⢠⠈⣿⠟⠉⠈⠉⠻⣿⣽⠖⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⣎⢻⡇
⠰⢿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁⢀⠀⠀⠄⣜⣾⡟⠀⠀⠀⠀⠀⠹⣿⡖⡀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠠⠀⠆⣻⣻⡇
⠀⢸⣿⣵⢀⡄⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠈⠀⠀⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣻⣿⡁⠀⠀⠀⢐⣿⡧⠀⠀⠀⠸⠀⠠⠀⠀⣤⠿⣹⡇
⠀⢸⣿⣿⠈⡇⡀⠀⠀⠀⠀⠀⠀⠙⣛⣿⠀⠀⠀⡀⢽⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⢨⣿⠱⠀⠀⠐⠀⠀⠀⠀⢠⣍⡢⣿⡇
⠀⢸⣿⣯⡞⢁⠉⠀⠀⢀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠁⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⢀⠀⢀⣼⠈⡇⢿⡇
⠀⠐⣿⣿⣷⣼⠱⡆⢣⣘⣇⠀⡀⣰⢿⣿⡄⠀⠀⣴⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠈⢰⣿⢺⡛⡄⣤⠀⣀⡔⢫⡟⣷⣮⣿⠃
⠀⠀⢸⣿⣿⣩⣿⣿⣾⣽⣶⣶⣾⡿⠟⠻⣿⠓⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⠀⠀⠀⢸⣿⣾⣟⣇⢋⣠⠇⣴⣻⣵⣟⣷⣿
⠀⠀⠘⠻⣿⣿⡟⠛⢿⠟⠙⠋⠉⠀⠀⠀⠀⠈⠀⡀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⣨⠟⠉⠻⠿⠿⠿⠛⠻⠟⠿⣿⣿⡇
⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢩⡄⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢇⡏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⢀⢀⠀⠀⠇⠀⢀⡀
⠀⠀⠀⠀⠀⠈⡇⠀⢤⠀⠀⠠⠀⠀⢶⠀⠈⣿⣼⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡎⢈⡷⠂⠀⠀⠉⠀⠐⠂⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠀⠀⣀⠀⢀⣇⣠⢟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣼⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⣩⣤⣶⣾⣀⣀⣄⣀⣴⠁
⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⣼⠛⠛⠉⠋⠈⠛⠉⠙⠉⠻⠙⢿⡏⠛⠻⣆
⠀⠀⠀⠔⠋⠁⠠⠊⠀⢠⠆⠀⢀⡀⠀⠀⠀⠀⣀⣤⡶⠦⡀⠀⠀⢦⡀⠀⢰⡏⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠁⠀⠀⣴⠖⠈⠉⠀⠀⠀⠑⠆⠀⠀⠀⠀⢸⣇⠀⢰⡏⠙⠳⣦⣀⣀⠀⠺⢦⡈⠑⢄⠈⠂⠀⠙⢆
⠐⢦⠀⠀⠀⣀⠜⠀⠀⡀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⢻⣆⠀⠹⢦⡀⠀⠉⠛⠷⣤⣀⠉⢢⡀⠱⡀⠙⠀⠘⡄
⠐⢀⡠⠴⠘⠇⠀⢀⡼⠃⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠉⠻⢦⡴⠇⠀⠀⠀⠀⠀⢻⡇⠀⢁⠀⠀⠀⣻⡀⢿⡀
⠀⠀⠀⠀⠰⠤⠒⠉⠱⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⢺⠗⣾⠁⣻⠓⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣠⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿⣶⣶⣾⡷⠶⠤⠤⢖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣛⣯⢿⣿⡥⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠋⠙⠋⠁⠈⠙⡿⠆⠻⠿⢦⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⠀⣄⣼⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⡀⠀⠀⠀⠀⢈⣤
⠀⠀⠀⠀⠀⠀⣤⡂⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣝⡛⠿⣇⠀⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢻⣧⣠⣀⣀⣠⣾⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⡍⠠
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⠟⠛⠋⠁⠈⠀⠑⠀⠘⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢹⣿⣿⣿⣿⣿⣶⡒⠂⠀⠀⡀⣀⠀⢀⡤⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡿⣿⣿⣿⣿⣿⣶⣷⣶⣥⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠦⠀⠀⠈⠀⠹⣿⡿⢿⣿⣿⡿⠿⠻⠶⠶⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⢒⠦⢶⠮⠏⢿⠑⣋⠩⣎⢛⣉⡉⠉⠉⠉⠉⠉⠉⠉⢀⡴⠊
⠀⠀⠀⠀⠀⣀⠀⠤⠒⠢⠄⠐⢒⠟⢠⠃⠀⡰⠀⣚⠑⠤⡤⠳⠔⠤⢀⠏⠉⠣⠙⠂⠀⠀⠀⡤⠤⠋⠁
⠀⠀⠀⠀⠞⠒⣢⣤⠀⠙⠀⠁⡞⠛⢹⠀⡤⡄⠂⠀⠐⠄⡚⠉⠠⣴⡀⠤⢀⣠⣀⣰⠤⠞⠉
⠀⠀⠀⠀⠀⠉⠉⠙⢢⠄⠀⠀⠘⡄⠘⠇⣱⡇⠀⠀⠂⢀⠊⢐⠋⠍⠠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⠀⠀⠘⠺⢼⡜⠖⠁⠀⠐⣁⡟⢑⣄⣢⡷⠥⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣐⡽⢿⣖⠒⡎⠙⢡⡬⠋⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⢔⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠸⣅⣄⣍⣇⣠⠔⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⡗⢍⡂⠞⠵⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠠⠀⠀⡠⠀⠀⠀⠀⠰⣠⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠩⣝⡄⠸⣆⠀⠀⠀⠰⣼⡠⠔⠛⣍⠑⢄⡀⠀⠀⠀⠸⣄⠀⠀⠙⠢⠤⠊
⠀⠀⠀⠀⢀⣀⡀⠀⠀⡜⠀⢀⢌⣂⡷⠿⡀⠀⠐⢂⠇⠀⠀⠀⠀⠙⢢⠙⢦⡤⠄⠄⢈⠉⢭
⠀⠀⠀⠀⠚⡱⣬⡲⠤⣻⠦⠬⠞⠋⠀⠀⠱⣄⣀⠏⠀⠀⠀⢀⠤⠤⠞⢀⡴⠃⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠋⠁⠑⢮⣧⡀⠀⠀⢀⣀⣶⣤⣈⡎⡄⠀⠀⠀⢿⠄⠀⡠⠏⠀⠀⠐⠈⠚⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⢂⢽⣿⠦⠔⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⢀⣀⡀⣠⢂⣴⠛⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠴⣶⡞⢷⣤⣴⣚⣟⡳⣄⣀⣀⣀⡀⣀⡀⠀⠀⠀⢀⠔⣠⡾⠃
⠀⠀⠀⢀⣤⠾⠛⣿⣷⣿⣵⣶⣍⡑⢶⣌⠙⠿⣿⣿⣛⢛⡏⠘⣉⠉⠈⡛⠇⣙⣛⣛⣿⡿⠟⠋⢸⣏⣡⣤⣤⣀⠃⢰⡏⢠⣶⡖⠲⣾
⠀⠀⣠⠞⠁⠀⠀⣠⡟⢫⡄⠀⠈⠙⣦⣽⡄⢀⡀⠙⣿⠞⠁⠤⠀⠄⠈⠡⠀⣿⠛⡟⣿⡃⠀⣰⡾⣿⡴⠒⠂⢽⡄⢸⠀⠟⠉⢻⠀⣿⠇
⠀⠀⡿⠄⠈⣀⣴⣏⡀⢸⡇⠀⣤⠀⣹⢛⡇⢀⣿⠀⣏⡆⠈⠀⠘⠤⠈⠀⠃⢠⡵⣧⠙⠃⣰⣿⣷⣿⣇⣀⣀⠀⣿⠈⢧⡀⢠⠏⣰⠿
⠀⠀⣀⣴⠞⠛⠁⢸⡷⡈⠳⡾⠏⣰⣿⣿⠇⣿⢃⣴⡿⠃⣄⠐⠀⠠⠄⠐⢠⣯⣴⣧⠀⣾⢡⣏⣿⣿⣿⡛⢲⡛⣿⣄⠈⢳⠋⣰⣇⣨⡀
⠀⠀⣏⠀⢰⣾⠃⢸⢄⡇⠀⢀⣼⣿⣿⣼⠃⣸⣿⣿⡿⢷⣮⣿⡂⠲⣿⣤⣤⠟⠿⣿⣷⣿⠸⣿⣿⣿⣿⣷⣼⠇⣹⠙⢦⣜⡀⢻⡾⠋
⠀⠀⣿⠀⠀⠿⣠⠋⣼⠁⣰⣿⣿⣿⣿⡏⠰⠛⡟⣡⡴⣾⣷⣌⣿⣧⢀⣿⣏⣀⣀⣄⡉⢻⣆⢻⡷⣽⢿⣿⣿⣦⠏⠀⠀⠉⣿⣄⠻⣶⠂
⠀⠀⣿⠀⢀⠟⢁⣾⣁⣾⣿⣿⡿⣿⣿⡟⠀⢠⣿⡏⢲⡛⣿⠿⠻⣿⣿⡟⠻⠿⣿⣧⣿⠟⣹⣿⣷⢻⡟⢿⣿⣝⠳⣄⠀⠀⣧⢹⡄⣿
⠀⠀⢁⡴⢉⡴⢛⣼⡟⣿⢿⣿⢡⣟⣿⡅⠀⡾⠀⣷⡘⢷⣟⠀⠀⠹⡿⠀⢠⣞⡼⢣⡿⠞⠻⣿⣿⠈⣿⠘⣿⠿⣧⠈⢷⡀⢈⠿⢠⣿⡄
⠀⠀⠋⣠⠟⢡⣾⠋⣼⠏⢸⡇⣼⡟⣿⣇⠀⢳⡐⢎⢻⣦⡙⠻⡶⢶⡦⣤⡿⠋⣰⡏⠀⠀⠐⡟⣿⠀⣿⠀⠹⣷⠻⣧⠈⣻⠃⣠⣿⠏⠁
⠀⠀⣴⠏⣰⣿⠃⣰⢏⣿⡿⠁⣿⡇⣷⢿⡀⠀⠳⣼⠋⢠⡿⣎⠀⠀⠀⠈⠴⣿⠋⠣⡀⠀⢰⢶⡿⠀⢿⡇⠀⠘⣧⠹⣧⢹⣿⠋⢸
⠀⠀⠿⠋⢀⣯⣸⠋⠈⣿⠃⠀⢿⠇⢹⡎⣷⡀⣼⠃⢀⡾⣿⠂⠰⠶⠦⠀⢾⣿⣧⠀⠹⣦⣼⣼⠇⠀⢸⡇⠀⠀⣿⠀⠹⣧⣿⣤⡎
⠀⠀⣀⡾⠉⣿⣿⠀⠀⢻⡃⠀⢸⡆⠀⢹⡌⢻⣿⠀⣾⢷⣬⣄⠀⠀⠀⢀⡜⠁⢹⡇⢀⡿⢣⡟⠀⠀⣸⠁⠀⢀⣿⠀⠀⣿⣿⡟⠀⢠⡀
⠀⠀⠃⣠⣶⣿⣿⡀⠀⠈⣧⠀⠸⣧⠀⢿⣿⣧⡻⢆⣻⣆⡿⢧⠀⠀⠀⢾⡁⠀⣸⣿⠟⣱⣿⡆⠀⢠⣿⠀⠀⢸⡿⠀⢀⡿⠹⣇⢀⡾⠁
⠀⠀⠀⣷⠋⢸⣟⠷⣄⠀⢹⡆⠀⢿⡀⠈⣻⣿⣿⣾⠿⡏⢠⡿⠀⠀⠀⠈⠙⠛⣿⣧⣼⣿⣿⡟⠀⣿⠃⠀⠀⣾⠃⢠⡞⠀⠀⣿⣼
⠀⠀⠀⡟⣠⠞⠛⡄⠙⠷⣦⣿⠀⢸⣷⠈⣻⣿⡟⠋⠀⢳⠨⣇⠀⠀⠀⠀⠀⠈⠉⠋⡿⣿⣿⡇⢸⡟⠄⠀⢠⣏⣴⠟⠀⠀⠀⣹⡇
⠀⠀⠀⠸⡙⢦⣦⢹⡄⣸⣇⡸⣇⠀⣻⡆⢻⡯⠀⠀⡀⢈⠀⢹⡄⢠⠄⠚⢷⣄⢠⡀⠀⠸⣿⣷⣿⠁⠀⢛⣿⠋⠉⣿⣄⠀⣸⢧⡇⢀
⠀⠀⠀⠀⢹⣌⠻⣆⠻⣿⡀⠙⢿⡟⠛⠻⡞⢁⣀⣴⡷⠊⣀⠜⠁⡋⠀⠁⣼⣿⢻⠻⣴⡆⠈⢿⡍⠛⣦⣾⠷⣤⣰⡏⣽⣠⡟⠈⢧⡀
⠀⠀⠀⠰⣽⠊⢣⠘⣦⠹⠆⠀⠈⠳⠀⡴⣁⣭⣿⣿⢡⡞⠃⠀⠀⠘⢦⡀⠀⣾⣁⢀⣼⣷⡂⠀⠻⣄⣼⣥⣠⠟⡟⣷⢹⠟⢁⡀⠈⢹⠂
⠀⠀⢀⣧⣬⣄⣿⣤⣿⣤⣶⠶⠶⣶⡏⠀⠈⣿⣍⠻⣾⣷⣤⡴⠀⠀⠀⠙⠶⣄⠉⠣⣼⣏⠹⣆⠀⠈⠛⢶⡉⡎⢀⡿⣁⠀⣼⣿⣴⣮⡀
⠀⠀⣿⣸⣆⢹⣿⣼⣧⠀⠌⢉⣧⡈⣖⣠⣾⣧⡘⣷⣨⣍⣉⠀⠀⠀⠀⠀⠀⠙⠷⣄⢀⡿⠓⢉⣷⢾⣦⣬⣷⡉⠙⠃⠉⣍⣿⣽⡟⢙⠁
⠀⠀⠁⡦⠛⢻⣾⣟⡉⢀⣠⠾⠉⠀⡿⣘⠇⡠⠛⠉⠁⣀⣉⠛⡄⠀⠀⠀⠀⣾⠀⢸⠏⣠⠞⢻⡅⢰⣟⡿⠛⢛⡿⠦⣀⠸⣿⣟⠃⠈
⠀⠀⠖⠀⢠⠿⣽⠃⢹⣏⣉⡀⠀⢄⣿⣿⠟⠀⢀⡴⠋⠁⢀⣱⡽⠀⢀⣠⡜⠃⠀⡏⠀⣿⠶⠛⣳⣌⡽⠁⠀⡾⠀⠀⢈⣛⣓⡲⣤⣘
⠀⠀⠀⢠⡿⣦⣹⠀⠀⣿⡛⠻⠴⠛⢡⣿⠀⢠⣿⠃⣰⠿⠟⠋⣠⠔⠋⠁⠀⠀⣠⡇⠀⢻⡎⣸⡏⢿⡷⠞⢸⠇⢠⣿⠋⠉⠉⠙⢦⠹⠇
⠀⠀⠀⢸⡇⠈⢻⡄⠀⠙⣿⣿⣶⣦⣄⡿⠀⡟⢻⡄⠁⠀⣠⠞⠁⠀⠀⢀⣴⠚⡁⣯⠀⠘⣷⢏⣶⣉⡛⢳⣾⠀⢸⡇⠀⠀⠀⠀⣼⡀
⠀⠀⠀⠘⣷⠀⠀⣧⠀⡞⣠⢶⣿⣧⢻⡇⢠⡇⠀⣧⠀⢰⠏⠀⠀⠀⡴⠋⣀⡠⣌⣸⡇⠀⣿⠿⡇⠈⡇⠀⢻⡆⠈⠀⠀⣴⠿⠧⢼⠃
⠀⠀⣦⠀⢹⡆⠀⠈⡿⢰⠃⠈⢿⣿⣼⡇⢸⡇⠀⠘⣧⡟⠀⠀⠀⣸⠁⠀⣀⣤⠄⣸⠃⣠⡿⠂⣩⣭⣿⡓⢿⡙⣄⠀⢸⠃⠀⠀⣸
⠀⠀⠙⣧⠀⢿⡀⢰⠇⢼⣶⠻⣎⠙⣻⡇⠀⣷⡀⠀⢸⡇⠀⠀⠀⢻⡄⠠⠤⢄⣰⠏⣴⠋⢠⣾⡽⠋⠀⣿⣿⠇⠘⣧⡀⠀⠀⢠⠇⢠⡄
⠀⠀⠂⠸⣆⠈⢷⣸⠇⢾⠈⠿⣿⠀⣿⠀⠀⣿⢷⡄⠀⢿⡄⠀⠀⠀⠙⠲⠶⠟⠁⢸⣯⣴⠾⠋⠀⣰⠿⠙⣿⡇⠀⠈⠳⣄⣰⠏⣠⣿⠁
⠀⠀⠀⠀⢻⡀⠈⢻⡇⠘⣷⠀⣿⢠⡏⠀⠀⡿⠀⠹⣦⠀⠙⢦⣀⡀⠀⠀⣀⣠⣤⠞⠋⠀⣀⡴⠺⣧⠀⢰⡟⢧⡀⠀⠀⣼⠋⣰⠟⢠⠄
⠀⠀⣆⠀⢸⡇⠀⢈⣿⣦⡈⢿⣿⣿⠁⠀⢰⣇⠀⠀⠈⣷⡀⠀⠉⠛⠿⠛⣻⠏⠀⢀⣰⠞⠻⡆⠀⢻⣆⠙⠁⣀⠹⣶⠞⠁⣰⠟⣢⣿⠂
⠀⠀⣿⣄⠀⣷⠀⢸⡟⠁⢳⣦⡙⠻⣄⣠⠟⢻⡀⣠⠞⠉⢻⠀⠀⠀⢀⡞⠁⠀⣠⠏⣿⠀⠀⠹⣆⠀⢹⣴⢫⡵⠊⠁⢀⡾⠗⣿⠁
⠀⠀⠈⠻⣦⡽⠀⡼⠀⢀⡏⣠⠿⣦⡈⠛⢧⣸⣷⠋⠀⢀⣾⠀⠀⠀⠞⠀⠀⣸⢇⡼⢿⡇⠀⠀⠹⣦⡜⠋⠁⠀⣠⡖⢻⡀⠀⢿
⠀⠀⠀⠀⢸⡇⢺⠁⠀⠈⣧⠉⠀⢸⣷⣄⠀⠙⣇⢀⡴⠃⣼⠀⠀⡆⠀⠀⠀⣿⡟⠀⠀⣿⠀⠀⠀⠘⣟⠀⢠⡾⠯⣀⣸⠀⠀⣾⠀⠐
⠀⠀⠿⣤⣾⡁⢸⡄⠀⠀⡿⠀⠀⡼⢸⠻⡆⠀⠘⣿⠀⣸⠇⠀⢸⠂⠀⠀⠀⠸⣷⠀⢀⣿⡆⠀⠀⠀⠸⣷⡟⣿⣆⣸⠏⠀⢠⡏⠀⠠
⠀⠀⠂⢈⡿⠀⠈⢣⡀⠀⣇⠀⠀⢳⢸⡀⣷⠀⠀⢙⣦⠋⠀⠀⣏⠀⠀⠀⠀⠀⣻⣇⣸⣧⡇⠀⠀⠀⢛⣿⠀⠘⣸⠏⠀⠀⣸⠇
⠀⠀⠁⠈⠁⠀⠀⠉⠁⠀⠉⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠈⠈
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣁⣀⣀⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⣢⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡾⣿⠿⠉⠉⠉⠙⠺⢝⣛⣦⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⠙⠀⡀⢤⡀⠀⠀⠀⠙⡾⠫⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡀⠀⠀⠀⠐⠙⡦⢒⢲⡄⠀⠠⠖⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠰⢸⣟⣇⠘⠃⠀⢀⢴⠋⠹⠋⠈
⠀⠀⠀⠀⠀⠐⠂⢀⣀⡀⠀⠀⢀⠀⠀⢀⡄⡶⡱⠁⠀⠀⠀⠀⠀⢸⠹⡇⠠⢀⠔⢁⡻⢤⣤⠄⣤⢠
⠀⠀⠀⡂⠀⠼⠖⢒⣿⣿⣤⣄⠀⠀⠀⠀⠐⢰⢇⡠⢀⢀⠀⠐⠃⠘⣿⣦⡴⠋⠀⠀⠀⢸⣇⠀⣁⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢉⠛⣻⣦⣼⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠴⠃⠀⢀⠀⠚⠈⢉⣯⠄⠘
⠀⠀⠀⠀⠀⢁⣈⣤⣀⢀⣠⠟⣉⣤⡌⠋⡃⠂⠀⠀⢀⠀⠀⠀⠀⠉⠈⠢⣄⠀⠐⠉⠀⣀⠀⠚⠈⠙⡶⠤
⠀⠀⡄⠀⣐⢿⡿⢿⣷⠋⠁⣴⢋⡽⠓⡀⠌⠁⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠁⠂⠆⠈⠁⢈⡄⠠⠖⢧⡀
⠀⠀⢀⠘⠁⡉⠀⠹⠋⠀⣀⠈⠛⠿⢈⣱⣄⠀⡠⠄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠝⢲⣄⢀⣤⠀⠈⢢⡀
⠀⠴⠀⠀⠀⣼⡾⢡⢇⠀⣟⣿⢶⣟⣭⣏⣩⣿⢿⣆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⣀⠢⢻⡅⣰⢿⡏⢳
⠀⠀⠀⠐⠈⢱⣧⣥⣽⢆⣸⡿⢛⢳⣺⢿⡟⣿⠟⣿⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⠎⠊⠂⢉⠀⠈⣚⡘⡆⣀⢹⣜⠄
⠀⠀⠀⢁⠈⠹⣿⢻⠃⠈⣯⣢⢶⡀⠁⠀⣀⣠⣤⣄⣈⠙⢿⣗⣦⣤⣀⡁⠤⡙⠊⣀⣀⣠⣀⡠⠒⠗⣿⢫⡉⢹
⠀⠀⠀⠀⠀⠀⠩⣿⠀⠀⢀⢒⠀⠁⣴⣿⡿⠛⠿⣿⣿⣿⣦⣹⣻⡛⡿⣛⣷⡭⠟⠛⠋⠉⢉⠙⣲⢤⡘⠿⠱⠈
⠀⠀⠀⠀⡀⠂⢽⡀⠀⣦⡜⠃⠀⣼⣿⢻⢠⣾⢿⣿⣿⣷⡈⢷⡳⣏⠁⠀⠀⠀⣀⣴⠖⠋⠉⠉⠈⢸⡻⣏⠁
⠀⠀⠀⠂⠒⠀⡾⠓⢄⣦⣟⠁⠀⣿⣯⣀⣈⠛⠻⢿⣿⡯⣵⠋⠙⠻⠦⣄⡀⢠⣿⣿⠂⠀⠀⠐⠀⢰⣷⠇⣿
⠀⠀⠐⠐⡄⠀⠀⢠⡸⢻⣿⡛⠀⠹⣿⣍⣉⠀⠀⣐⡿⣳⠋⠀⠀⠀⣠⣴⣶⣿⣿⡟⠈⠀⠀⠀⠀⢾⣾⣇⡿⠂
⠀⠀⠁⠀⠀⠀⠰⠛⠘⠻⢿⣯⡛⠀⠙⢿⣥⣴⡶⣫⠞⠁⠀⠀⢀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⢻⣸⣿⠇⠿
⠀⠀⠀⠀⠀⡀⠀⢲⣡⠄⢠⠙⣷⣭⢤⠄⣹⣫⠞⠁⠀⠀⢀⣴⣿⣿⡿⠿⠋⠡⠀⠀⠠⠤⣈⢋⣽⡿⠃⠊⠡
⠀⠀⠀⠀⠈⢀⡀⡀⣷⡁⢠⢀⣼⣿⣷⡞⠟⠁⠀⠀⣠⡴⢛⠉⠉⠀⢀⣠⡄⢤⠶⡹⢑⣪⡾⠟⠛⣈⠎⣿
⠀⠀⠀⠀⠀⠈⢑⠓⢝⠶⣴⡿⠿⠟⠋⢀⡀⣠⣤⣿⣅⣓⣉⣑⣜⣛⣐⣋⣑⣮⣴⡾⢛⣯⢠⣬⢶⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠱⠾⡽⠢⠁⠀⠋⠲⠍⠠⠝⠛⠛⠛⠻⠿⠋⠙⠩⠿⠿⠋⠥⠄⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠼⠆⠀⠀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⡀⠀⠀⠀⠈⢣⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠱⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡗⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⢴⣾⣛⠛⣲⠶⢦⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣴⠁⢀⡈⢻⡃⢴⣆⣱⠀⠈⣉⣉⠓⠒⠶⠤⣤⣀⣀⣀⣀⡤⠎⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⡀⠤⢷⠀⠀⠀⠻⣄⡘⣷⡟⠙⠾⠛⢁⡴⠋⠁⠉⠛⢦⠀⠀⠀⠈⠉⠉⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠦⡀⠱⣄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠽⢋⣀⠀⣀⡀⢾⡁⣾⣏⡆⠀⢸⡇⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⢀⡤⠖⢾⠁⠀⠀⠘⢄⠈⠛⠒⠚⠛⠉⢹⡆⠀⠀⠰⡅⠈⢉⣀⣉⡁⠸⢧⡈⠉⠀⢀⡼⡁⠀⢀⣠⡖⠋⠁
⠀⠀⣰⠋⠀⠀⢈⡳⠶⠖⠀⠈⠳⣄⠀⠀⠀⠀⠀⡇⢰⠂⠀⣠⠞⠉⠀⠀⠈⣷⣄⠙⠛⠛⠛⠊⢁⣴⠋⠀⠈⠉⠉⢀⡴⠁⢀⠔⠊⠉⠙⠂
⠀⠀⡏⠀⣀⡀⠀⢻⠀⠀⢀⡀⠀⠈⡆⠀⠀⠀⠀⡇⡼⢠⣾⣥⣤⣤⣴⣤⣴⣿⡈⢦⠀⠀⠀⠀⡼⠉⠛⠲⠶⠶⠒⠉⠀⢰⠃⠀⢀⠀⢁⡞
⠀⠀⠣⡜⠉⣟⣠⢞⣀⡀⢨⡟⢦⠀⢸⠀⠀⠀⠀⣷⣦⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠆⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠈⠙⠉⠙⢦
⠀⠀⠀⠀⢰⠁⠙⠺⡄⠗⠋⠀⢸⠀⢸⠀⠀⠀⢰⣿⡿⠇⠂⠀⠠⠤⢤⣀⣀⣿⠋⠻⣿⣸⠀⣸⠣⡀⠀⠀⠀⠀⢀⡴⠃⠀⣠⠄⣀⡴⠃⠀⠀⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡞⠀⠀⢧⠀⠀⢸⠿⠀⠀⠀⠀⠐⠶⠦⠤⠈⠉⠓⠢⣌⣿⢀⡿⣄⠈⠙⠒⠒⠋⠁⠀⢀⣴⡅⠄⠻⣄⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠙⠒⡿⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣿⠸⡇⠉⠳⠦⣤⣤⣤⠤⠖⠋⠀⠙⠦⣤⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣠⡾⠁⠀⣴⠋⠈⡇⠀⠀⣰⠋⠙⢷⣄⠀⠰⠇⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠉⢀⣠⠞⠁⠀⠀⡇⠀⢀⡏⠀⠀⠀⠙⢦⡀⠀⠐⣄⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⡴⠚⠋⠁⠀⠀⠀⢸⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⡄⠀⠘⣦⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠙⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢹⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢐⡇⠘⡆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢻⡄⠀⢳⡀
⠀⠀⠀⣀⡤⠴⠶⠤⠤⣤⡾⠀⠀⣰⣅⣀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡀⠀⢸⡃⠀⠀⠹⣄⠀⠙⠦⠤⠠⠒⠒⠒⠒⠦⢤⡀
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣠⡤⢄⣀⣼⠄⠀⠀⢸⣀⣀⡀⣀⡤⠼⠧⠀⠘⢧⣄⣀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡗
⠀⠀⠳⣤⣤⡽⢦⣀⣀⠀⣀⣴⣄⣀⣸⣤⠞⠀⣞⠁⠀⢀⡀⠀⠀⠀⠀⠀⢤⡀⠉⠉⣳⠀⢰⡄⠀⠀⠀⠀⢍⣳⡀⢀⣤⡀⠀⣎⣀⡼⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠁⠀⠀⠀⠹⠦⡴⠞⠳⣄⣀⣀⠂⠀⢈⡷⠶⠚⠛⠶⠺⡄⠀⠀⢀⠀⢀⡟⠈⠉⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣣⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣅⣈⡉⠩⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣈⣿⡿⠁⠀⠀⡆⣏⠆⠀⢔⠀⣀⠀⠀⠀⠀⠀⢹⣻⢿⡿⣿⣶⣄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡃⠀⠀⠀⢽⣿⡇⠀⠀⣾⣶⠂⠀⠀⠀⠀⠈⣿⡿⠓⠋⠉⣿⣷⣮⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⣸⣿⣿⣿⠁⠀⠀⠀⠈⠻⣿⠋⢋⣴⠋⠀⠀⠀⠀⠀⠀⢿⣷⣴⣀⡸⢣⣬⣿⣿⣦⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⠟⡞⢿⣿⣷⡀⠀⠀⠀⣰⣿⣷⡿⡙⠀⠀⠀⠀⠀⢠⣾⡿⠋⠛⢻⣆⣿⣿⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡀⠀⠀⣽⣿⣿⣦⢠⣼⣿⣿⣟⣲⢷⠔⠆⡀⣠⣼⡿⠟⠀⠐⠀⢺⣿⣬⡁
⠀⠀⠀⠀⠀⠀⠰⣯⣥⡞⠀⠀⠀⠉⠋⠘⣿⣿⣿⣯⣏⠥⠸⡂⠀⢺⣶⣿⣿⣿⠀⠀⢠⡄⣸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⠂⠈⠱⠀⠀⢀⡈⢿⣿⣿⣥⠖⢊⣷⣾⠗⠉⠻⡿⡿⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠡⠄⠛⣿⣶⣊⡩⠽⣿⣦⣤⣄⣻⠙⠃⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣷⣛⠽⣿⣿⠏⢈⡽⠼⠃⠀⣿
⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢠⣾⡀⣠⣹⣇⣿⡇⠀⠀⡄
⠀⠀⠴⠷⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣽⠇⠙⣿⣿⣿⢳⣿⣿⣿⣿⣿⣟⣻⡃⣠⠄
⣶⡀⠀⠃⠀⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡆⣤⢶⡞⠿⠿⢧⠿⠛⠲⣿⢿⣿⣯⣁⣼⡿⢿⠉⠁⠀⠀⢰⡄⠀⡀
⡿⠃⡀⠀⠀⠒⠃⡔⠲⠀⠠⡖⠀⠀⠀⢈⡻⣷⣀⡷⠲⣤⠾⣴⣤⠄⠥⢛⣃⣶⣿⣿⣿⠀⠀⠀⢀⡀⠘⡃⢀⠀⠀⣤
⡟⠁⠀⠀⠀⡀⠘⡧⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣿⣾⠿⢷⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠉⠁⠀⠁⠘⠉⠈⣤⣴
⣷⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⡿⠅⠻⠿⠿⢗⣋⣛⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⣿⣷⣤⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⣠⣯⠟⠛⠛⢻⡿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣆⢀⣤⣤⣴⣾⣿⣿⣶⣦⣤⣶⣿⣿⣿⣧⣤⣶⣧⣀⣤⣤⣾⣶⣶⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢄⣀⠀⠤⢒⣀⣠⣤⣤⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡢⣄⢤⣀⣤⣤⣴⣮⣵⣶⢾⣷⣽⣾⣽⣿⣬⣮⣽⡿⠿⣿⣿⣟⡲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠮⣛⣩⣔⢟⣯⣫⣝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⠾⢿⣿⣿⣿⣿⣿⣿⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣪⠐⢁⣪⣼⣾⡶⠿⠟⠛⠛⣫⢙⢛⡻⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⢔⣴⣷⣿⣿⡿⡟⢻⠡⡆⢸⢠⠀⣮⡶⣿⣛⢷⣽⡯⣮⣦⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿
⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟⢡⢰⣧⣸⢁⠇⢨⢧⠺⣿⣿⣿⡟⢸⣧⢃⣿⣿⣃⣿⣿⣎⣽⣻⣟⡻⣍⠙⠛⠿⠿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⢰⣿⠟⠋⠋⠁⠀⡌⢷⠙⢦⠺⢠⠈⢸⠀⢹⡿⣥⡴⢏⣠⣾⣿⡿⣻⣿⣿⣿⣿⣟⣁⡈⠀⠀⠦⠬⣶⣾⣍⠾⣹⣿⣿
⠀⠀⠀⠈⠁⠰⣦⣔⢲⣲⠁⣦⠷⢚⣷⢩⣦⣻⡥⣐⣩⣭⡶⢛⣿⡿⢻⣹⡭⢁⣌⣼⣟⣂⣽⣿⣄⡀⠀⠀⢀⢈⠶⠮⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠿⠇⠹⡦⠘⢇⠋⠻⠈⠉⣉⢈⣉⣭⣷⣾⠿⠿⣷⣥⣷⣿⣿⢿⢿⡟⡙⢻⣿⣿⣿⡖⣬⣐⡂⠲⠶⠾⠁
⠀⠀⠀⡶⢀⢄⢦⣬⣆⡸⣡⣀⣠⣶⡁⢖⢓⠻⡟⣟⣿⣽⣧⣾⣿⣿⡯⡼⣏⢎⣏⡖⠐⢥⣄⡿⣿⣿⣷⣄⢔⢄⣀⣀
⠀⠀⠐⢁⣾⢿⣿⣿⣿⣷⣦⣄⣩⠹⡏⠻⣿⠿⢿⣿⡿⣿⡿⢛⠻⠷⠑⡝⡗⡤⠨⠈⡅⠈⠴⢘⠴⣝⣿⣿⣿⣷⡪⠈⠁⠂
⠀⠀⠀⣼⣿⣞⡿⣿⣻⣿⢿⣿⣿⣿⣿⣶⣿⣿⡶⡮⠽⠍⢊⣆⠕⠇⣀⠍⠌⡡⣅⣡⢰⠀⠂⢩⡌⣼⣿⣿⣿⣿⡓⠄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡹⠄⠿⡃⣜⡀⠀⠟⢇⡡⢃⠂⢠⣎⣽⢯⣿⣿⣿⣿⣛⡲⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣭⣐⣮⣾⣴⣼⣴⣷⣦⣿⣿⡿⣾⣿⣿⣿⣿⡟
⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠯⡹⣿⣿⢇⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠔⠖⠠⡶⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⡿⡟⠋⠤⢤⡀⠀⢠⡄⠘⠢
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋⠀⠀⢀⡄⠈⠁⠠⢀⠙⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠈⠉⠙⠛⠛⠛⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠊⠁⢀⡄⠀⠀⠀⡀⠘⠡
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⣿⣿⣿⣿⡿⣿⠆⠀⠀⠀⢰⡦⡤⣾⠟⠁⠀⣤⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢺⠣⠻⣿⠿⠋⣡⢿⡟⠀⠀⡼⢀⠊⠀⢰⠇⠀⠀⠀⠁⠋⠛⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⣴⡿⠃⠀⠀⠀⡀⠀⠀⠠⠾⢃⣀⢀⡀⣠⣴⣶⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠐⠀⠀⠝⠉⢈⣴⣿⣟⣿⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠂⠆⠀⠀⣔⣠⣿⡿⡋⠱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣾⣿⣿⣾⣾⣾⣾⣿⡏⢯⠊⠀⠀⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠅⢡⠀⠀⠀⠁⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣗⣿⡀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠿⠟⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣀⣀⣠⣴⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⣤⣄⠀⢀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣬⠀⠀⠁
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⡴⠿⡿⢟⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣿⣿⣦⡐⠲⠟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⣿⣿⣿⣿⣿⣿⡛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡃⢸⣷⣿⣿⣿⣿⣿⣿⣷⡄⠰⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠻⢿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣷⣠⣤⣄⠀⠀⠀⠀⠀⢠⡇⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠙⣿⡇⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⡇⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠈⢿⣦⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡄⠀⠀⠀⢹⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⡇⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⡿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⡿⡏⠚⠏⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡀⢂⠀⣆⠀⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠻⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣆⡇⢸⠀⣻⠀⣿⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣢⠀⠀⠀⢻⣧⠀⣗⢦⠀⠀⢀⡀⠀⠹⡇⠀⢠⢶⡄⠀⠀⢠⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⡿⠁⡟⠀⡿⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⠀⠈⠂⠘⠮⣷⡀⠸⣿⡀⠀⠀⠀⢼⠀⣧⠀⠀⣾⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⢁⡼⢃⣰⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠣⣧⠀⠠⣶⣄⡀⠀⣀⠈⠓⠀⠀⠀⠀⠀⠹⠶⠶⠟⠀⠿⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡽⠛⠛⠛⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠈⠁⠀⠈⠙⠛⠂⠻⣷⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠶⠀⠀⠀⠉⢛⣳⣦⠀⠀⢠⠏⢠⡏⢠⠏⢀⡎⢀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⣀⣀⠀⠀⠀⠀⠈⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡽⠋⠀⠀⣿⠀⢸⡀⣼⠀⢸⠀⢸⠀⡧
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⣀⠔⠋⠉⠉⢻⡄⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⢰⡞⠒⠶⠶⠶⠚⠋⠀⠀⠀⠀⠘⣆⠘⣇⠹⡄⠸⡄⢸⣴⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⣸⣵⠟⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠛⢦⢿⠶⢿⣏⠁
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⡀⠃⠀⠐⠻⡄⠀⠀⢠⡇⣸⣷⢃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡀⠱⡄⣇⠘⡜⣧
⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡾⠛⣧⣼⡞⠀⠀⠀⢸⠁⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⡇⢠⡇⡟⠀⡇⣼
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⠀⠀⢀⣸⠃⠀⢰⢷⡞⢻⣁⡿⠀⠀⠀⢸⠠⢋⣿⡶⣿⠃⠀⠀⠀⠀⠀⢳⣎⡜⣱⠏⡼⠁⣼⣡⠏
⠀⠀⠀⠀⠀⠀⠹⣄⡀⢀⣠⠞⣽⠓⠲⡚⠁⠀⢀⣟⣠⣿⠞⣿⠀⠀⠀⠀⣾⠀⠈⢉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣾⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⠀⣿⣶⠟⠁⠀⠀⡾⠉⣷⣸⢿⠁⢀⠘⣆⠀⣿⣀⠀⠈⢉⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡇⠀⠀⠀⣸⠳⡟⢹⣥⠾⠀⠘⢦⡈⢷⣯⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣿⡴⢳⣁⣼⣷⠇⠀⠀⠉⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⠀⠀⢀⠀⣀⡀⠀⣀⠀⣠⢶⡦⢶⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⢶⣲⣾⠷⢿⡾⢹⣏⣿⣸⠃⠀⠀⠀⢸⡧⠠⠴⣶⡶⠂⠀⠀⠀⡟⢷⡠⡿⠦⠛⠗⢛⣿⠞⠟⠃⠁⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠛⠿⢭⣍⣹⣿⣹⣷⢻⣏⢿⡼⣧⣶⠛⣯⢹⡇⣹⡇⠀⠀⠀⠸⣷⣶⣿⠵⠶⣶⡶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠷⠿⠷⠿⠶⠦⠤⠴⠶⠶⠶⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣰⣿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⡀⠀⠀⠀⣰⣿⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⣿⣿⡏⢀⠀⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣶⠀⠀⠤⠄⠀⠈⢁⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢟⣿⡿⢠⣿⣰⣿⣿⣿⣧⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠿⠀⡁⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢀⣾⠿⣷⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⢳⠰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣴⠀⠀⠀⠀⠀⠀⣼⡂⠀⠀⠀⠀⢀⣴⣧⣾⠇⢀⣼⣷⣾⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡠⢼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⢠⡟⡄⠀⠀⣠⣴⣿⣿⣿⣷⢀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣫⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠖⠘⠼⠦⣬⠄⣣⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢖⠀⢷⣎⢰⡾⠀⢛⠹⢰⣿⣿⣿⣿⠿⢫⣿⣿⣿⣿⠏⣈⣿⣿⣏⣽⣿⣿⣷⠇
⠀⠀⠀⠃⢠⡄⠀⠀⢀⠇⠀⠡⡔⠀⠀⠀⠀⠀⠀⡤⠀⢠⡀⠱⣧⠀⢈⠉⣾⠒⣩⠎⢀⣿⣿⣿⠋⠀⠐⢁⣿⣿⠋⡤⠚⣿⣿⣿⣿⣿⣿⡟⠁
⢀⠀⠀⢳⠘⠃⠀⠠⣎⠀⠀⠀⢸⣆⡔⠋⢀⡄⡙⠟⠀⠈⠁⠄⠀⠀⠻⠈⢤⣶⠩⠎⣿⣿⣿⠃⠀⠀⠀⠸⢛⠟⠀⢀⣠⣿⡏⠉⣻⠿⠋
⠉⠀⠈⠹⠀⠄⠀⠀⠀⠀⠀⢠⣭⠄⠀⠀⣿⣿⣷⡚⠇⠀⢀⠈⠉⠃⢀⣈⢀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠰⠈⠀⠈⣁⣿⣿⣥⣾⣿⡾⠂
⠀⠀⠀⠀⡀⠺⣀⠀⠀⠀⠀⠀⢠⠇⠰⠀⠈⠀⠀⠀⢀⠀⠈⠀⠀⠀⢈⠀⠀⠀⣠⣾⣿⣿⡿⠃⠀⡀⠀⢀⣈⠉⣙⣿⣃⣠⣴⡟⠋
⠀⠀⠀⠀⢈⠸⠓⠾⣴⣄⣄⣀⠈⠀⠒⠉⠉⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡂⠙⠛⠋⠁⠤⠐⠀⠀⢶⡘⣿⣫⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⢠⣼⠟⡒⣆
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠉⠁⠚⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢠⡀⢰⣶⣿⣿⣉⣘⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠹⠵⠟⠋
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⢿⣾⣾⣤⣾⡷⠿⡿⢾⢾⣿⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠲⠎⢄⠀⠀⠀⠀⠀⠀⠀⡀⢐⡓⢀⡟⠋⢨⡛⠐⣦⣐⣯⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠑⠋⠑⠸⠋⠑⠾⠉⠲⠟⠈⠉⠋⠀⠀⠀⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠰⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⣴⣴⣤⣉⣀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⣦⡀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠲⣶⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢠⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠂⠉⠀⠀⠆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣮

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣀⣤⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡏⣹⠟⢁⣼⣶⠶⢾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠽⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⠿⠷⠒⡿⠋⠙⢳⣎⠉⠛⣯⣀⡀⠀⠀⠁⠈⠀⠄⠀⢆⣀⣀⠤⣄⣒⣤⣷⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⡴⠾⢁⣠⣃⠉⠻⣷⡄⠀⣫⡤⢀⡼⠁⠀⣀⠀⠊⢩⣴⣾⣿⣿⡿⠿⠁⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡿⣿⠟⣿⣿⡀⣸⠀⠀⢸⣷⡁⢂⠔⠁⢀⣶⣿⣿⡿⠛⠋⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢆⣀⡠⢄⣤⠟⠋⠁⣶⡿⠉⢀⠃⠀⠀⣽⠟⡥⠏⣠⣾⣿⣿⣿⣟⣈⣀⣀⣀⣀⣀⠘⠿⢤⡀
⠀⠀⡿⠐⣀⡟⣩⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣹⡭⠿⠋⠀⠀⢈⣿⣿⣦⢸⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠈⠈⠉⡿⠉⠙
⠀⠀⠉⣓⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠊⠉⠈⠁⠀⠀⠀⢾⣾⣿⣟⠙⡟⢻⣿⣿⣿⣿⡤⢀⡀⠀⠀⠀⠀⠀⡌
⠀⣗⣘⠚⠆⠓⠦⣄⠀⠀⠀⠀⠀⣴⠗⠀⠀⠀⠀⠀⢀⣀⡴⠚⠛⠛⠻⠟⣉⣵⣾⣿⣿⡤⢅⡀⠀⠀⠈⠓⠦⣄⣐⣇
⠀⠈⠉⠉⡋⢺⠳⡈⠑⢤⣄⡔⠉⠀⠀⠀⠀⢠⠖⠋⣉⢛⣰⣾⣷⡿⢿⣿⣿⡿⣿⣶⠀⠁⠀⠈⠢⡀⠀⢠⠆⠉⠉⠉⠃
⠀⠀⠀⢀⡷⠜⠀⠈⢶⣴⠋⠀⠀⠀⠀⠀⠔⢣⡾⠟⠉⠀⠁⠀⠘⡁⠈⠀⠀⠁⠀⠈⠂⠠⡀⠀⠀⢁⢐⡏
⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣄⠀⠀⠀⠀⢀⠾⠋⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠹⡆
⠀⠀⠀⠀⠀⠀⢀⣸⣷⡿⠍⠓⠂⠀⠀⠀⠀⠀⢿⡯⢟⣿⢿⣿⣷⣶⣤⣶⡀⣀⣤⣤⣴⣂⡲⢜⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣴⣾⡆⠀⠀⠀⠀⠀⠀⠛⠀⠀⡈⠀⠀⡈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡻⣾⣧⠀⢰⡀⠀⠀⠀⠀⢠⣦⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣵⢿⣇⡧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣾⡉⢻⣟⡿⢿⣣⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡸⠉⠙⠛⠷⣜⡓⣄⣹⠏⠛⠛⠛⠋⠁⠀⠈⠀⠙⣿⡋⢹⡈⢸⡏⡏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠄⠰⠦⢤⣄⣣⠸⢿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣏⢨⡇⠐⣧⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣀⠀⠀⠀⠉⢆⢈⣦⡈⠁⣀⣀⠀⠈⠉⠐⣄⣸⣉⣩⠄⡀⣸⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣞⡽⠛⠚⢲⠦⢀⠀⠈⡄⢿⠟⢀⣭⣟⠉⠛⣷⡀⠀⢿⠄⠁⣠⢣⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡏⠀⠀⠀⠛⠒⣦⡥⠟⠀⣴⣾⠋⠁⠀⠉⠉⠛⠳⡆⠘⣷⣾⢣⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢱⠄⠀⠀⢀⣼⣦⣴⠏⢰⣿⣷⣤⠄⢀⠀⣀⠀⢠⠇⢸⡿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠉⠡⢿⣿⣿⣿⡾⠟⠀⢨⡟⠛⠿⠿⢵⠶⢋⡴⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠒⠚⠋⢁⠤⠀⢄⣚⡷⠶⠶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠴⠷⢶⣾⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⣶⣶⠶⣶⢖⠚⠂
⠀⠀⠀⠀⠀⠀⣈⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⠏⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠁⡠⠲⡇⣀⠦⠄⠀⠀⠀⠀⠀⡤⣶⣒⠤⣄⣀⢀⣀⡤⢒⣿⡷⠿⠲⠦⣀
⠀⠀⠀⠀⠀⢠⣴⠀⠀⢀⢙⠀⠀⠀⠀⠀⠀⡨⠺⠋⠿⠻⠶⣯⣽⠁⣴⣧⠧⠤⣤⣤⡀⠈⢣
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣾⡁⢰⠂⠀⠈⢿⣌⢄⠀⢀⠀⠐⠦⣵⠷⠤⡀
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⠿⠇⠀⠀⠀⠀⠈⠻⢧⡉⢺⣄⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠢⠒⠀⠀⠀⠀⠀⠀⡷⠄⠙⠷⠶⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢇⢦⠀⡇⠀⠀⠀⢀⣠⣴⣶⣶⣤⡀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⢲⠤⠀⠀⠀⡈⢂⠀⠀⠀⠀⢠⣟⠿⡿⡿⢿⡿⣿⣦⠀⠻⣿⢷⣦⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⣆⣦⣤⣾⠇⠀⠀⠀⡄⠀⣾⣿⣿⣿⣿⠿⣿⣾⣿⠄⠀⠸⡆⠹⣧⠀⠀⠀⠟⠻⡧⠀⠀⠀⢀⣤⣤⣤⣤⣄⠒⠁
⠀⠀⢐⣿⡿⠛⠁⠀⢀⠀⠀⠃⠀⠸⣿⣿⣿⣯⣶⣿⣿⡿⠀⠀⠀⢳⡈⣻⡧⡀⢼⠀⢶⠀⠀⠀⣠⣿⣏⣉⣭⠏⠉⠁
⠀⠀⠘⣿⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠙⢥⠔⣼⡿⠀⡴⡴⠖⠾⡏⠀⢈⡵⠋
⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣄⠉⠁⠒⠸⠦⢮⣉⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⢀⢀⣀⡀⠀⠀⠀⢴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⣀⣀⣀⠍⠑⠲⠶⠤⠂
⠀⠀⠀⠀⠠⠶⣿⡷⢰⡿⠻⢫⣞⠁⠀⢹⣿⠁⠢⠀⠈⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋
⠀⠀⠀⠁⢑⡆⣸⠁⣾⠃⠂⣿⣿⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢴⢶⣦⣄⡀⡀
⠀⠀⠀⣰⣾⠒⣥⣾⡿⠟⣸⣿⠏⠀⠀⠘⠂⠈⠂⠀⠀⠀⠀⠀⠀⣟⠛⠻⣟⠛⠛⠫⠰⡄⠀⠀⠀⠀⣄⣀
⠀⠀⠀⡟⠁⠀⢀⣀⣤⣴⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠄⠈⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣥⢄⡀
⠀⠀⠀⡇⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠦⠄⠀⠴⠀⠀⠰⡏⣷⡘⣷⡆
⠀⠀⠀⠱⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡉⠫⠠⠐
⠀⠀⠀⠀⠐⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡏⠀⠐
⠀⠀⠀⠀⢀⡸⣀⠀⣍⡓⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⡀⠀⠀⢰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⠤⢤⣤⣶⣆⠀⠛⢿⣿⣶⣦⣍⣹⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⡀⠀⠀⠤⢤⣤⣤⣄
⠀⠀⠀⡴⠂⠹⠟⣛⢻⣿⡟⣿⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡦⣤⣭⠍⠁
⠀⠀⠀⠁⢀⠤⠿⣾⣿⣿⣾⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣋⠭⠭⢍⣀⠉⠁⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⢠⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⠀⠀⠀⠀⢨⣆⣄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⢀⣾⣿⣦⡀⠀⠀⠀⢻⣿⠛⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⣽⣴⣶⣶⣿⣿⣿⣿⣿⡆⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⣿⣿⠟⠛⠛⠉⠀⢿⣿⣿⡟⠈⠆⡀⠈⢻⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠐⠲⠯⣍⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⣀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⢱⢻⡄
⠀⠀⣀⣠⣶⣶⣴⣾⣿⣶⣶⣤⣶⣦⣴⣿⣤⣤⣤⣴⣶⣾⣿⣿⣿⣥⣤⣤⣤⣶⣶⣶⣿⣟⣻⣧⣤⡄
⠀⠈⠛⠛⠛⠻⠏⠛⠿⠛⠉⠙⠛⠛⠛⠛⠉⠙⠋⠉⠉⠀⠉⠉⠉⠉⠛⠛⠙⠛⠛⠉⠙⠛⠉⠁
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⠲⢶⠧⠖⠀⢀⠀⠀⠀⠀⠁⠀⠐⠶⠿⠇⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠴⠾⠟⣂⠀⠀⠀⠀⠾⠋⠐⢘⠒⠋⠉⠀⠀⠀⠀⠀⠀⣌⠻⣾⡟⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⠏⣴⢠⡀⠀⢀⣴⡶⠈⢷⢦⡄⠀⠀⠀⠀⢠⣶⣜⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠼⡿⢨⣧⡯⠈⣸⠁⠈⠈⠁⠁⠀⠀⠀⢠⡘⣿⠟⠂⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠘⠻⡇⠀⡇⠀⠀⠀⠘⡀⠀⠀⣴⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢯⠀⠈⠠⠄⠀⠀⠐⢿⡏⠃⠀⠀⠀⠀⠈⠁⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⠀⠀⠈⡂⠸⡄⠠⠀⠀⠉⠀⠻⣦⡁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠐⠀⢳⡀⠘⠢⠀⠀⠀⢈⠓⠀⠀⠀⠀⢤⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⢀⠀⠈⣇⠀⢰⡀⠀⠀⠘⠻⠄⠀⠀⠀⠛⢀⣆⠀⠀⢅⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠹⣄⠀⠉⠃⠀⠀⠘⠄⠀⠀⢀⠆⠀⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⡆⠀⢠⠀⠐⣤⢸⠀⠀⠀⡀⠀⠁⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠠⣤⠀⠀⠀⠀⠁⠀⠄⠀⠀⠁⠀⠀⢀⠀⡧⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠄⣸⡧⠀⠀⠘⠁⠐⠀⠀⠀⠂⠈⠀⢀⣰⠁⡄⠀⠌
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠂⠘⠧⠑⠋⠀⠁⠀⡠⠀⡀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠰⡀⢰⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠈⠁⠓⠀⠀⠀⠀⠉⢧⡈⠻⠄⢀⡟⠶⠿⣠⣯⣡⡶⠒⠀⠀⢠⠀⢀⠈⠃⠉
⠀⠀⠀⠊⢠⠊⠑⠦⠄⠀⠀⠀⠄⠀⠈⠋⡀⠀⠖⠈⠀⠀⢅⠀⠀⠀⠀⡀⠐⢫⠴⠠⢈⣤⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠉⠀⠀⠂⠀⠀⠚⠓⠂⠀⠀⠀⠂⠘⠂⠚

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢀⠹⡀⣿⡙⢩⡍⢩⡏⠹⠉⡟⢹⠟⣭⡿⠉⢹⠋⣿⣿⢹⣶⡏⠩⢹⠛⣭⡟⡉⢩⡍⣩⡏⣟⢹⡏⡍⣻⠻⣭⠛⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣴⣧⣽⣧⣿⣧⣼⣧⣼⣤⣯⣼⣦⣻⣥⣦⣼⣥⣿⣿⣘⣻⣧⣴⣽⣤⣿⣥⣦⣽⣧⣽⣧⣭⣼⣧⣦⣽⣬⣿⣽⣾⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⣴⠶⡄
⠀⠀⠀⠀⠀⣰⣗⠀⠁⠀⠀⠀⠀⠀⠀⠘⠳⠄⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠉
⠀⠀⠀⠀⢀⣉⣉⣁⠀⠀⠀⠀⠀⠶⠖⠀⢰⣄⣸⣇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠸⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⢿⣟⠛⢀⣀⠀⠀⠀⠀⢀⠀⢠⣿⣿⣿⣾⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠀⡷
⠀⠀⠀⠀⠀⠀⠈⢹⣿⠋⠀⠀⠀⠙⠁⠀⠀⠙⢻⣿⡿⢿⣿⣿⣆⣀⡤⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⠛⢡⡝⢻⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠃⠀⠀⠐⠾⠟⠁

⠀⠀⠀⠀⠀⢀⣤⣀⣤⠀⠀⠀⠀⠀⠀⢠⠔⣶⣤
⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠐⢷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⣰⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢸⣧⣀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⢿⡆
⠀⠀⠀⠀⠀⠀⡿⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⣿⢿⠉⣹⣿⠉⠉⠀⠀⠀⠀⠀⠀⢁⣤⣤⡿⠇
⠀⠀⠀⠀⠀⠰⠇⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠿⠚⠀⠘⠺⠆⠀⠀⠀⠀⠀⠀⠀⠙⠛⣩⠂

⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⡾⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠂⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠛
⠀⠀⠀⠀⠀⠀⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣤⣄⣤⠀⠀⠀⠀⠀⠻⢀⣤⣶⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⢀
⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⡿⠿⣿⣿⠙⡇⠀⠀⠀⠀⠀⢼⠻⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⡁
⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡇⠀⡈⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⢈⠃⢹⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⠿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠰⠂⠀⠀⠀⠠⣶⡟⠃⠀⠀⠀⠀⠀⢸⡇⢰⣾⣿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠈
⠀⠀⠀⢲⣿⣿⣶⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⢉⣒⣙⡛⢷⣿⣅⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠛⠋⠅
⠀⠀⠀⢾⠻⡟⠛⣿⢿⡟⠻⠷⠀⠀⠀⠀⠰⣿⣏⣉⣛⣛⣻⣿⠆⠀⠀⠀⠀⢼⡦⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠓⠉⠀⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠉⠐⠄⢠⠀⠀⢀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⣼⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡄⠀⡀
⠀⠀⠀⠀⠀⢀⠟⣿⣿⠧⣀⠀⠀⠀⠀⠀⣼⡟⣦⣦⣄⣀⣼⣛⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣏⠀⣿⡿⣄
⠀⠀⠀⠀⢀⣾⣿⡿⢿⡆⠘⠀⠀⠀⠀⠤⠿⠃⣹⣿⠻⠿⢿⡿⠳⡄⠀⠘⠋⣰⣾⠿⣿⣿⣿⣿⣷⣿⣗⡀
⠀⠀⠀⠠⠟⢱⠛⠁⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⢏⠀⠀⢸⠀⠐⠇⠀⠀⠀⢯⡸⢰⣏⡘⢯⠙⣻⡋⠙⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀⠘⠂

⠀⠀⠀⠀⠀⢰⣿⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⢀⣴⣷
⠀⠀⠀⡀⢠⣾⠟⠋⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠐⠹⠆⠀⠀⠀⠀⠘⣿⣇⣰⣏⢠⣿⡿
⠀⠀⠀⠀⣴⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣲⣶⣤⣬⣧⡈⡀⠀⠀⠀⠀⠀⠈⠛⣿⡟⠟⠋⠁
⠀⠀⠀⠀⢿⣿⠁⣀⡀⢠⠀⠀⠀⠀⠀⢠⣾⣿⡞⣿⠉⠛⢿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠚⢳⣦⣤⣄
⠀⠀⠀⠀⠈⠻⣧⣿⡽⠸⠷⠂⠀⠀⠀⠈⠉⠀⡄⠸⠄⠀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠉⠙⢇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢓⠦⠤⢵⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠈⢆⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠈⠢⣛⠛⠛⠿⠿⠟⠋⣠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣤⣤⣶⣶⣾⣿⣭⡉⠓⣰⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⠮⡁⠄⠉⠀⢼⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣫⣬⣝⣚⣷⣆⡲⣈⠻⠽⣿⣷⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣶⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢽⣿⣿⣿⣻⠋⠻⠿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣾⣿⣿⡿⠏⠀⠀⠀⢸⣿⣿⣽⡇⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠁⠀⠈⠻⣿⣿⣇⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢹⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠑⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⣿⣄⢀⣶⣷⣦⡀⠀⢸⡟⠆⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣧⣙⣿⢏⢹⣿⣿⣿⣿⠀⣠⣿⣿⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠻⠉⠙⡩⠾⣿⣿⣿⣷⣮⣭⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⣾⣿⣿⣧⣾⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⣻⠿⠛⣻⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣴⣏⠠⣰⡾⠋⠹⣿⣿⣿⡙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣶⣫⣀⠙⠛⠋⠀⠀⠀⠘⣿⣿⣇⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠿⠛⠛⠛⠻⢿⣿⣶⣤⣀⣀⢀⣾⣿⣏⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣸⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡿⢿⠟⢃⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠈⠛⢸⣿⠰⠶⠦⣆⠠⢠⡄⠀⠀⠀⠀⠠⠴⠶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠈⢿⡀⠀⠀⡨⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠴⠒⠒⠒⠂⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠯⣝⢯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⣶⠖⠛⠉⢹⣷⠛⢛⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠻⠁⠀⠀⠠⠀⠀⠀⠸⠅⠀⢸⠏⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠥⠀⠀⠀⠀⠱⣄⠀⢳⡀⠐⣆⠀⢀⡆⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠓⠒⠂⢀⡀⠹⣾⣷⠼⠛⠛⠋⠭⣭⣽⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠤⠀⢒⣾⣿⣿⡶⠿⠛⠛⠛⠛⠿⢶⣿⣅⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⠤⣒⣿⣿⣿⡿⠋⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠋⠠⢚⣵⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⠿⠛⠋⠙⠛⠛⠉⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⡴⣿⣿⡇⢰⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣉⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠈⣼⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⡼⣟⣿⣿⣷⣴⣿⡟⣹⡏⢻⣿⡇⠈⠁⠀⢀⣀⠀⠀⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠸⠁⣸⡿⣿⣿⣿⠋⢠⣿⡇⠘⢿⣧⣄⠐⠚⠟⠊⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡟⢰⡟⣿⠁⢀⣿⣿⣇⠀⠰⣭⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣾⠁⡿⢀⣨⣿⣿⣿⣿⣶⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣼⠀⡿⠀⠟⣻⣿⣿⣿⣿⠋⠙⠿⣿⠀⠀⠀⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⡀⡇⠀⣰⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⡇⢰⣿⣿⣿⢋⣾⠁⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⣿⣿⡇⢸⡇⠀⢀⣴⣶⡿⠾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣈⠻⢧⡈⢿⠀⣼⣿⠃⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣦⣅⠀⠁⣿⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⡟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠘⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣧⣠⣤⢀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣛⡯⣅⣻⢾⣏⠉⠁⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⣥⣞⣉⠀⣴⡏⠆⣿⡄⡀⠀⠀⡀⠚⠀⠀⢘⠀⠀⠀⢀⡞⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡴⠇⠎⣳⠥⠀⠐⡀⠀⡌⠀⠀⡼⠀⠀⡠⠈⠀⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡈⡠⠣⡨⠃⢀⣴⠏⢰⡼⢀⡀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡠⣀⢠⢏⣠⢦⣿⣿⣶⣿⣷⣿⣤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢇⠘⠫⣟⣿⠽⠷⠿⠾⣿⣿⡁⠀⠀⠀⠀⠊⠀⠀⡐⠁⢀⡀
⠀⠀⠀⠀⠀⠀⣼⠂⠀⠠⢀⣸⣛⣓⢪⣷⣦⠀⣒⠉⠛⡡⠂⠀⠀⠀⡀⠀⠄⣔⣉⢛⢧⣤⡖⠀⡀
⠀⠀⠀⠀⠀⠀⠱⢢⡁⢠⡍⢩⣼⠻⢧⣯⣿⣷⣤⢊⠊⡠⠂⠀⢀⣀⣤⣖⡓⢲⢮⣬⣍⣒⠮⣟⢷⣄⢤⡀
⠀⠀⠀⠀⠀⠀⢨⡏⠃⠸⠛⣍⠑⠠⢠⡄⠉⣽⣑⡵⠊⣀⣴⠚⢡⣾⡿⢻⣿⣈⠈⠀⠀⠈⠙⠛⢝⣷⣑⣯⡁
⠀⠀⠀⠀⠀⠀⢞⠿⣠⠴⠖⠤⠵⢤⣜⣥⣾⠻⣿⣶⡔⢺⣡⡶⣿⠟⢋⣿⣫⠗⠀⠀⠉⠉⠒⠢⠤⣙⢿⣟⣮⣦⡀
⠀⠀⠀⠀⣠⡤⠎⠀⠛⠀⠀⠀⣠⡌⣨⠋⠉⠰⠿⠟⢧⣿⡿⠛⣻⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⡇
⠀⠀⠘⠙⠙⠓⠂⠀⠀⠀⢀⠼⣿⠏⢯⡀⠀⠀⠀⠀⠠⣤⣤⡾⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠩⠁⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣄⡀⣀⢐⣿⠶⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣴⣶⠄⢠⣼⣿⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠥⣬⣀⣲⠾⠛⣻⠍⠐⢹⠇⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠤⠄⠀⠀⠀⠀⠒⠂⠀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣛⠠⠒⠀⣠⠆⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⣾⣯⡀⠀⣠⠞⠁⢀⣴⣶⡏⣿⣧⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⣀⣀⣈⠉⣉⣘⠃⠀⣤⣿⣾⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠛⠉⠉⠙⢻⠇⠀⠐⠋⠉⠁⠈⠛⠛⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢶⣼⡟⠻⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣋⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠁⢠⠀⢿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠈⠀⠸⡇⢸⣿⣿⡏⢿⣟⣷⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⢿⣿⡷⠛⠉⠁⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠛⣧⡼⠁⠁⠀⠀⠀⠀⣸⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢱⡾⠉⠀⠀⠀⠀⠀⠀⠀⠁⠸⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣁⡻⠜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣳⠄⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⠄⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡦⠀⠈⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠃⠀⠀⠚⢸⠁⠀⢠⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠄⢠⡿⠁⠀⠀⠀⠀⠀⠀⡠⠾⠿⣷⣦⣄⣷⡄⠀⠀⣴⠀⠀⢾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣸⡄⢻⠈⠀⠀⠀⢀⢀⡔⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⣦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⡇⢨⠀⠀⢀⡤⠃⣿⡶⠶⣾⠋⢙⠟⡉⠋⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣸⣷⣼⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢡⡎⠀⠀⡟⠁⠀⠸⢣⡶⢁⡼⠋⣴⠿⢸⣧⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠃⠀⠐⢁⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠃⠀⠈⢁⡄⠀⢠⢿⡇⢻⣿⢺⡏⢰⣴⠇⡤⠱⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⠁⠀⠀⢘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠁⠀⠀⠀⢀⠈⡷⣠⡼⢾⣧⠘⣿⣌⠹⠿⠉⠀⢃⢀⣴⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣀⠴⠋⠛⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠸⠟⠃⣿⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢉⠂⠉⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠐⠧⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡞⠃⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠿⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠋⠉⠘⢆⠀⠀⠀⠀⠀⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⢀⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠁⠀⢀⣀⣤⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠇⠈⡁⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠠⠔⠚⠉⠉⢁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡀⠀⠐⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⢾⠁⣾⣶⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡿
⠀⠀⠀⠀⠀⠀⣤⣿⣈⣃⣁⣙⠘⠂⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⣴⡿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠹⢧⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠐⣦⡐⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠂⢀⡘⣾⣿⣿⣿⣿⣷⡄⠀⠀⡀⠀⠀⠀⠀⡄⣄⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣄⢀⣹⣿⣿⣿⣿⣿⣿⣿⣦⣤⣷⣆⢠⣤⠤⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⡁⠀⠀⠀⠀⠰⡼⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡀⠀⠀⢸⣆⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⡿⣶⡯⠿⣿⣿⣿⣿⣿⣷⣌⠀⠀⠘⠻⣦⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠴⠾⠳⣾⣭⠿⣭⣿⣿⣿⣿⣶⣄⣀⣀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠋⠉⠉⡏⣠⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣧⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⠀⠈⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⢈⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣾⣿⣿⣿⣆⠀⠀⠐⠛⢿⡉⠻⠧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢤⠀⠀⣠⣽⣷⣧⣿⣿⣿⣍⣀⠀⠀⠀⠸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣸⣿⣶⣿⡿⠟⢁⡼⠉⢯⠉⠉⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠃⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⠛⢢⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⢤⡀⠇⡈⣦⣊⣰⣀⣹⣜⣁⢸⢀⠴⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⠲⢤⣇⡷⠟⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠓⠶⣨⡃⠤⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢮⣜⡠⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣰⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢄⡀⠀⠀⠀⠀⣇⠀⠈⠻⣬⠀⡟⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡀⠀⠙⡄⠀⠀⢀⡟⠀⠀⠀⡙⢾⡍⡸⢀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠃⠀⣠⠃⠀⢀⡞⢃⠀⠀⠀⢉⣤⡹⣧⠅⣇⣄⠀⠀⢀⢺⣁⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎⢀⡀⠀⠱⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠚⠁⣀⠴⠋⠈⠉⠀⠀⠀⠈⠛⠃⢨⡿⣿⣸⠞⢦⡏⣌⣿⠁⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢇⠘⠋⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠚⠉⠐⠀⠀⠀⠀⠀⠀⠀⠐⢿⡷⢰⡷⢩⣛⠻⢛⣿⠌⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠈⠉⠀⠀⠀⣀⣠⣤⠴⠒⢋⡉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣬⣇⠐⢿⣿⠇⠠⣶⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠠⠤⢤⡤⠶⠲⣛⠉⠡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⣶⣶⠘⠿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⣄⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⢤⠴⢣⡾⠛⠋⠛⠳⢦⡀⢀⣀⣤⡤⠴⠶⠶⣆⠀⢺⠀⠀⢀⡼⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣴⠏⠀⠀⠀⠀⠀⢨⡇⣼⠁⠀⠀⠀⠀⢀⣼⠀⠈⡇⠀⠺⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣉⣉⣠⡿⠀⠀⠀⠀⢸⣭⣤⡤⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢃⡀⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇⠓⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠈⠠⠄⡇⠀⠀⠀⡀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠊⡷⢈⠐⠎⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠐⣲⠀⠀⣠⣤⣿⡐⢶⣿⣷⠏
⠀⠀⠀⠀⠀⠘⠐⢀⠀⠢⡕⠀⠲⢬⣇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠼⢁⢀⠈⠹⣦⣾⡿⠛⢪⣽⡿⠏
⠀⠀⠀⠀⢃⡀⠠⢈⠘⠀⠀⠈⠷⠀⢿⡅⡉⠓⠀⠀⠀⠀⠀⠠⡉⢾⣬⣷⣖⣿⠏⠀⠀⠉⡘⠀⠂⣴⢤⠀⠠
⠀⠀⠀⠙⠀⡁⡄⠘⢄⠐⡆⠘⠦⠦⣨⣰⣆⠄⣀⡀⠀⠀⠀⠰⠀⢙⣻⣟⣿⡟⠀⠀⠀⠘⠀⠀⠀⠀⠄⡀
⠀⠀⡢⢰⠀⠁⠘⠶⢀⢠⣌⢀⢠⣀⠌⠳⣌⢆⠀⠉⠀⠀⠀⢰⠴⠟⢹⣿⢿⠀⠀⠀⠐⣤⠐⢄⠀⣰⠆⠉
⠀⠀⠁⣈⢰⡀⠁⠀⠁⢹⡈⠂⠓⠙⠢⣔⣶⡈⠑⠀⠀⠀⣰⠿⠿⣷⣿⡷⣾⠀⠀⠀⠀⠸⠀⠀⢟⠛⢦⣀⣀⠶
⠀⠀⠁⡅⠈⠀⠀⠃⠐⠆⠦⠰⢎⡘⢣⡠⣿⣷⡄⠳⠦⠀⣾⣧⡄⣠⡿⣷⣧⠀⠀⠀⠀⠀⠱⡀⠀⢳⣄⠈⢽⣦⡄⠂
⠀⠃⠀⠀⠔⠰⡄⠰⠚⠂⡀⢀⠀⠉⡀⡛⠞⠻⣦⣄⠒⠀⠛⢿⠞⡿⢒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠔⠂⠃⠀⡀⢳⠀⢺⡄⠀⠘⠚⢷⠇⡝⡉⢦⣈⠙⠿⢶⣶⣶⣿⣿⣭⣿⣿⠠⣄⡀⢀⣀⡀⠤⣠⡀⠀⠀⠗⠦⢀⡀
⠀⢀⡄⢠⠀⢡⡄⠉⢄⠘⠂⢻⡗⢼⣦⣝⡙⠆⢻⣆⡤⣤⣌⣀⣡⣁⢀⠈⠙⣳⡔⠢⢄⠀⠠⠤⣀⠙⠀⠀⠀⠀⠀⠘⢄
⠀⠈⡈⡀⠆⠁⢰⠈⡀⢦⢀⠈⠙⠆⣻⠭⣽⣶⡀⠈⠻⣦⠆⠉⢉⠟⠙⠋⢛⣝⠃⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⢢⡀⠈⠄⠀⠀⠀⠀⠀⡀⢀
⠀⠈⠁⣀⠸⠀⡀⠠⡍⠈⣼⣼⣿⠃⢀⡁⣤⠉⠻⣢⠄⡀⠙⠦⣀⠀⠃⣈⠈⡙⠁⠀⣄⠀⢤⠀⠀⠀⡀⠀⠀⡤⠀⠃⠀⠴⠃⠉⠀⠀⡄⠁⠨
⠀⠀⠸⢉⡀⡆⠓⠀⠀⢇⢱⠀⠁⢢⣜⡙⢻⣦⡀⠈⠳⣤⠓⠂⠈⠩⣀⢸⣿⠇⢀⠀⠈⠀⠀⡄⠐⢋⡇⠀⠀⠀⠀⠘⢀⡀⠈⠀⠐⠋⢀
⠀⠀⠀⠞⠁⠀⠀⠀⡄⠘⠘⣧⠖⣵⣋⠹⣌⠙⣾⣷⣤⣀⠙⠳⢼⣿⢿⡿⡇⠀⠈⠃⡄⠀⠀⠀⠀⠀⡁⠀⠀⠀⠃⠜⡄⠀⣀⠔⠁⠀⡘
⠀⠀⠀⠀⢰⡄⣶⡀⠇⠀⢦⡄⢲⣜⡙⠠⣦⡀⠈⠻⢾⣏⢺⣶⣤⣉⠺⢇⠁⠀⠀⠀⠰⣄⡀⠄⠄⠉⠙⢦⣴⣧⣶⠖⠓⠒⠃⢀⣀⡼
⠀⠀⠀⢿⠘⠇⠛⣤⢸⠗⢤⠻⣿⢅⣏⠀⠀⠙⢦⣄⠀⠉⠻⢿⣯⠻⣏⢲⡥⣄⠀⠀⠀⠈⢣⣀⢈⠐⠆⠀⠻⣙⡏⠀⠀⠀⡴⠋⠉
⠀⠀⢠⡄⠀⡔⣠⠹⣆⢀⣼⠧⠴⣄⠀⠑⢄⠀⠀⠙⠷⣦⣄⡀⠙⠧⠈⠀⠀⠈⠁⠀⠀⠀⢀⡉⠿⣄⡀⠀⠀⠙⠧⡀⠀⠀⠧⣐⠖
⠀⠀⠀⠱⠈⠈⠁⣷⢘⠾⡟⢇⢤⠈⠑⢄⠀⠀⠠⢀⠀⠙⠿⣿⡁⠒⠄⣀⠀⠀⠀⠀⢀⣴⠋⠔⢀⡼⢩⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⣿⢠⣸⣤⣥⠟⠀⠑⢄⠀⠑⢦⡀⠀⠑⢦⣀⠈⠻⣄⠀⠈⠳⠄⠐⠠⠈⠠⠈⣢⣧⣴⣿⣿⣿⢿⣷⣉⠂
⠀⠀⠀⠀⠀⠀⠈⣌⠉⠡⡈⢄⠘⢆⠀⠡⣄⠀⠙⢷⣄⠀⠻⣷⣦⡈⠳⣤⢦⣤⠠⠴⣴⣦⣿⠛⢿⣿⣿⣿⡻⣧⡉⠳⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠉⢀⠰⡁⠌⠂⠈⠢⡀⠈⠳⣄⠀⠹⣧⡀⠹⡿⣿⣦⡘⣷⠶⠟⠛⠋⠁⢳⡀⠀⠉⠛⡍⢻⣌⠛⢦⡀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠀⠀⠀⠀⠑⡀⠀⠘⣦⡀⠹⣿⡄⢹⣿⡿⣿⣬⣧⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠹⡄⠀⠉⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⡄⠈⢆⠀⠘⣷⡄⠹⡿⣦⣛⠁⠈⠿⣯⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣇⢳⡀⢸⣧⠀⢹⡞⡆⢳⣼⣿⡀⠀⠀⡿⠀⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣸⣧⠈⣿⡆⢸⡗⢱⠸⣿⡟⢧⠀⢀⠛⠀⠀⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣿⣿⣈⡍⢃⣶⣿⣿⣬⡆⠕⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣿⣿⠿⣿⣿⠳⢺⣿⣿⣟⣼⠃⠈⠲⢄⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣁⡼⣻⡏⢈⣿⣿⡇⣾⠛⣿⡎⠏⠀⠀⠀⠀⠑⢄⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢻⡏⣰⢛⣶⣿⣿⠛⠃⠁⠀⠻⠣⠀⠀⠀⠀⠀⠀⠀⠙⢆⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸⡑⣧⠟⠘⠙⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠘⢃⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣀⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⣶
⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠠⣤⡄⠀⢠⡄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⣄⣄⣀⣒⣀⣤⡔⠀⠀⠀⠈⣿⠿⡟⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⣶⣄⠀⠀⠀⠀⠱⠶⠆⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢰⠀⡦⣀⠤⠁⠀⠀⠀⠀⠀⠀⣴⣾⣷⡄⡀⢀⢠⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣽⢰⣟⠟⠠⡒⠄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠉⢀⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢾⡀⢻⣿⣿⣿⠃
⠀⠀⠀⢰⣧⣸⣏⣴⣴⣖⠃⠀⠀⠀⢸⣿⣿⣿⣿⡿⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⣿⠃⠀⠀⠀⠀⣀⡀⠈⡇⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟
⠀⠀⣴⣿⣤⠟⠘⢿⡈⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡴⠿⢴⣦⣻⠀⠀⠀⠀⠈⠉⠉⠀⡇
⠀⠀⢧⣿⠀⠀⣠⣞⡧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⠀⠀⠀⣹⡠⣤⣿⡗⡃⠘⡇⠙⠀⠀⢀⠀⣀⣀⣤⢠⣿⣆⣀⣀⣀
⠀⠀⠈⣿⣤⡾⢿⠉⢡⣇⠀⠀⠀⠀⢠⡇⢸⡇⠀⢀⠀⣿⢸⡇⢸⠇⢹⠿⠈⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤
⠀⠀⠀⣿⡇⠀⣸⠞⠉⠀⠀⠀⠀⠀⢸⣷⢾⡇⣼⣿⡤⣿⣘⠛⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠉⠉⠀⠀⠀⠀⣦
⠀⠀⠀⢹⣧⡼⠃⠀⠀⠀⣀⡀⠀⠀⢸⡇⢸⡇⡟⠙⠁⠛⠉⠀⠀⠀⢀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠈⠿⠃⠀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣦⡄⠠⣴⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣿⡇
⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠆⣁⡆⠀⠀⠀⠀⠛⠀⠀⠻⠀⠀⠘⠀⠀⠀⣿⣿
⠀⠠⠾⠿⠆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠻⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠀⣴⣦⡄⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠂⠀⠀⠀⠀⠈⣿⠇
⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⢶⣆⠀⠀⠀⠉⠁⠿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⡀⢀⣈⡲⢦⣄
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⢉⠉⠉⠙⠶⣿⠳⢦⡄
⠀⠀⠀⠙⣿⡟⣿⠏⣁⡿⠋⠉⠛⣿⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠢⣥⡈⠁⠀⠀⠦⣼⣤⣼⡁
⠀⠀⠀⠀⠸⣿⠏⠀⠉⠀⠀⠀⠀⠚⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠹⣄⠀⠀⣷⡀⠀⠓⣦
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⢿⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣶⣦⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣀⣾⡿⠃
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣿⣿⣿⣿⣿⡙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠃⠸⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣇⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠉⠉⠘⠋⠉⠉⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⣤⣶⣶⣶⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⣷⣷⣤⣄⣀⠀⠀⢠⡀⠠⣜⣶⡀⠀⠞⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣭⣤⣴⣶⣶⣿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢹⣝⠿⣿⣿⣿⣶⣤⣿⣶⣞⣷⣤⡆⠀⠐⠲⠶⣶⢄⠄⠀⠀⠀⢠⣾⣿⣿⣿⠋⡛⣋⡉⠉⣉⣑⣦⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠈⠒⢾⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⢠⣴⠚⠁⠀⠀⠀⠀⣿⣿⡦⠃⣄⣉⣁⠈⠛⠀⣉⠀⠉⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠿⣿⣿⣿⣿⠏⣿⣤⠄⠀⠀⠉⠛⡷⠐⠒⠆⠀⣴⣿⣍⡍⠀⢦⢐⣉⣋⠻⢍⠉⠑⠢⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠛⣿⣯⡜⡟⢉⣿⠂⠂⣠⠞⣷⣀⣠⣴⣾⣟⣿⡏⢠⡷⠒⠤⢁⠉⢁⡠⡀⣠⣄⢉⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⣻⣯⣷⣾⡇⠀⠀⠁⢼⢁⣻⣿⣟⣹⣿⣟⣿⣎⣿⣶⣶⣄⣦⣠⡿⢾⣿⡙⠻⢿⣿⡄⠹⢿⣿⣿⣿⣿⣿⣧⡁⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⣝⠟⢣⣤⣆⢓⠍⣉⣴⡟⣿⣿⣶⣺⠿⣿⣿⣿⣽⡟⣿⠙⢿⠀⠙⠁⠀⠀⠈⠁⠀⠈⠛⢿⣿⣿⣿⣿⣷⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠇⢛⠂⠀⠋⠹⠉⠀⠁⠀⠸⠏⢻⡩⣧⣵⡿⠟⠀⠀⠈⠉⠲⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠟⠻⣿⣿⣿⣿⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠀⢠⡄⠀⢀⡀⣠⠀⠀⠤⣤⣀⣾⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⢙⢷⠠⣄⠀⠉⠠⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠘⢀⠁⢀⡀⠞⠺⠛⣄⢀⣠⠇⡿⣝⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢦⠐⡤⣱⡐⠲⢲⣟⠋⢻⡟⠻⠁⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⢰⣙⣄⡀⣠⠗⠀⣴⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠒⣽⠷⠶⢾⣇⡾⢿⣤⣈⣁⡃⢰⠞⠛⠛⢿⠇⠀⠀⠀⢀⢠⠀⠀⠘⠁⠁⠀⠀⠺⢍⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⣶⠁⠀⠀⠘⠋⠀⢈⡹⣾⠏⠀⠘⡄⣠⣀⠸⠀⠀⠀⠀⠀⠻⡗⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠂⠀⠀⠀⡀⡠⢔⡯⠚⠁⠀⠀⠀⠙⠙⢯⡀⠀⢰⡆⠀⠀⠀⠰⡈⠑⣤⡄⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⡀⢠⣀⣦⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣾⠁⠀⠀⠀⠀⠘⠆⠻⢧⣤⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡏⣜⣠⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⣰⣶⡦⣶⣾⡷⣯⣱⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡶⡯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣿⡄⠀⠀⠀⢠⣤⣤⣄⣄⠸⠁
⠀⠀⠀⠀⠀⠀⠻⡟⠗⠛⠁⠀⣿⣿⡾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⢶⠶⡇⠀⠀⠀⠉⠀⠉⠍⠩
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠸⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⣿⣿⣿⣧⠀⠀⠀⠀⢀⣤⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣧⠀⠀⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣏⣿⡿⣟⣴⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠃⢀⣀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⢉⣹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣒⣃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢙⣿⣿⣿⣿⣿⣯⠙⠿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⢿⣻⣿⣿⣿⣿⣿⣿⡇⠴⠿⣿⣿⣿⣿⣿⣿⣷⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡻⣇⠀⠶⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠂⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠿⢰⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠙⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢀⣸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⢀⣀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⢴⣶⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠁⠈⠉⠁⠈⠙⠛⠿⣿⣿⢛⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠉⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠁⠀⠀⠘⠒⠲⠖⢦⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠆⠀⠀⠀⠀⠀⣠⡲⢆⠀⠁⢢⢴⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣴⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠘⣷⣤⡙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠃⣴⡇⢰⡄⣀⠀⢴⠞⡋⠀⠀⢳⠓⡆⠀⠀⠀⠀⠐⠀⠀⣿⣿⣌⢻⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢻⠇⢸⣧⣹⠀⠂⣸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⣿⠋⠉⠁⢀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⠁⢻⠻⡿⠀⠀⡇⠐⠀⠀⠀⢸⠀⠀⠀⠀⣀⣾⣿⢧⠈⠀⠀⠈
⠀⠀⠀⠀⢀⡠⢀⠀⠀⠄⡀⠀⠀⠀⠈⠀⠀⠀⠰⠀⠠⡧⠀⠀⠀⠀⠀⠐⠀⠀⣀⢸⣿⠻⠆⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⢠
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢓⠀⠀⠀⠀⠀⢀⠄⠀⣈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠇⠀⠀⠀⢈⠀⠘⣆⠀⠂⠀⠀⠀⠀⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⠀⠀⠀⠀⠆⠀⢻⡀⠀⠶⢤⡄⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⢀⡄⠉⠁⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⢵⠂⠀⢀⠀⠀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠀⢸⠇⢀⡑⢀⠀⠙⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠄⠀⢸⡆⠀⠈⢧⣀⠀⠁⠀⠀⣉⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠈⠢⡐⠂⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡈⠁⢀⠀⠀⡆⠀⠀⢀⠀⠀⢦⡀⣸⠀⡀⠀⠀⡀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⡀⠁⠀⠈⠀⠀⠁⠀⠠⠀⠀⠀⠘⠁⠘⠂⠀⠀⠀⡇⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠛⢳⠀⠄⠂⠀⢀⠀⠀⠈⠀⠂⠀⠀⠀⠠⠀⠀⠀⢀⠃⢀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡂⢀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⢠⠇⣰⠞⠗⠀⠀⠀⠀⠀⠀⢈⠀⠀⠄⠈⠀⠀⠀⠢⠤⡜⠀⠄⠀⠐⠃⣀⠂
⠀⠀⠀⠀⠀⠘⠄⢀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠌⢣⠀⠀⠋⠄⠀⠀⡀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⡀⠐⠀⢲⠀⠘⠂⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠒⠲⠦⡀⠀⠀⠀⠀⠙⢯⡀⠒⢶⡀⠀⢰⡇⣤⣾⡞⢀⣇⠉⣠⣦⠰⠀⠀⠀⢀⠀⠀⠀⠘⠄⠘⠁
⠀⠀⠀⠀⡠⠂⢀⠐⠠⡀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠷⠦⠀⠀⢠⡜⠳⠀⠀⢀⠊⠉⠋⠉⠀⠀⠀⠀⣀⠄⢀⡀⠋⡐⠀⠀⢁⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⠁⠀⠂⠀⠀⠈⠐⠀⠀⠀⠀⢄⠀⠘⠂⠀⣀⠀⠀⠧⠄⠀⠀⠀⢀⠤⠀⠀⠘⠉⠁⠁⠐⠷⠀⠨⣤⠐⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠛⠒⠀⠀⠀⠀⠈⠁⠐⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢸⠀⠀⠀⠀⣠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣳⣄⠀⢈⠆⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⡄⣄
⠀⠀⠀⠀⠀⠠⠐⠠⠀⠀⠈⠛⠿⡇⠨⣆⠳⡔⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⠿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠙⢆⠙⠿⣦⣠⣧⣿⠀⢻⡀⢠⣀⢩⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠿⣿⣿⣿⣿⣿⣻⣿⡿⠻⡿⠋⠀⠀⠀⠀⣠⡄⠈⠙
⠀⠀⠀⠀⠀⠀⠀⣸⡷⢄⢨⡟⣡⣿⠀⠈⠲⣷⣛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢉⡤⣌⢻⣿⣿⣿⣿⣿⠛⠚⠀⠀⠀⠀⠀⢰⡝⠋
⠀⢄⠀⠀⠀⠀⣠⡿⢁⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⡘⠃⠀⢃⣼⣿⠋⡙⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠈⠡⠦⠤⣶⠛⠁⢠⠄⠀⣠⣶⠤⠂⠀⢼⡏⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠬⠉⠙⠛⠛⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠛⠉⢢⠀⢠⠻⠧⡄⠀⠀⠈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠓⠀⠀⠑⠤⠤⠤⠀⠑⠆⠀⠊⠐⠒⠒⠁⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊⠻⣿⣶⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠻⢿⠴
⠀⠀⠀⠀⢀⣤⢰⣦⣄⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠰⡇⠀⠀⠀⠈⣇⣠⣞
⠀⠀⠀⠐⠒⠿⣅⣿⣹⣷⠂⠀⠀⠀⠀⢸⣧⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠐⠃⠓⠀⣶⠇⠴⠟⠉⠀⢀⣤⠴⠶⣦⣄⣰⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣻⡾⣆⢾⠙⢖⣀⡈⣧⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠠⠲⡔⢳⠖⠀⡿⢢⡀⢸⣿⣦⣴⣶⣽⢯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡹⢅⠨⣝⡾⣆⠙⢓⡹⡋⠰⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠛⢠⡆⠀⠀⠀⠐⠘⢄⡅⢤⠿⣿⡄⠹⣿⣧⠤
⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢱⡌⠓⠾⣻⡟⢳⣿⢿⣇⡿⠉⠠⠀⠀⠀⠀⠀⠀⣿⡇⠀⢁⠀⠀⠀⠀⠀⠀⠀⠸⠖⠀⣶⡾⡏
⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⢿⣮⡀⠙⠁⡀⠀⠠⠟⠶⢶⣤⠀⠀⠀⠀⠀⠀⠛⠁⠰⠆⠀⠀⠀⢀⣤⣄⡀⠀⠸⠆⠘⢃⡇
⠀⠀⠀⠈⠀⠂⠂⠁⠀⠀⠀⠀⣿⢏⠀⣀⠈⣿⠃⢀⣴⡿⠆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢰⡀⠈⠙⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡳⠀⠘⢇⠀⠈⠹⣧⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠀⠈⠀⠀⠔⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣰⠂⠀⠀⢀⣀⠈⣁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠒⠢⠀⠁⠈⠤⠙⢢⠤⡀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣰⢿⣏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣤⠀⠥⣤⣠⣿⣵⡶⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣧⡖⠰⢿⣿⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣀⣶⣈⣴⢿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⠀⠀⠀⠀⠀⠠⡀⣠⣄⡢⠖⠙⣦⡀⢻⣾⣇
⠀⠀⠀⠀⠀⠀⢠⡗⣿⡏⣼⣿⣿⣶⠀⠀⣠⡴⠀⢈⣡⠔⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠻⢿⣷⠘⡷⣿
⠀⠀⠀⠀⠀⢠⣾⣷⣾⠛⡫⠉⠉⠉⠹⠖⠙⣇⣀⠈⠴⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡍⢶⣾⣿⣾⣿⢠⣷⠏
⠀⠀⠀⠀⠀⣸⣿⢉⡿⢟⣧⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⢠⡉⣿⢷⡿⠾⣿⠁⡼⠃
⠀⠀⠀⠀⠀⠟⠁⠈⠳⡿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⢧
⠀⠀⠀⠀⠀⠂⠀⢀⠀⢣⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢃⡰⣤⢀⣀⠴⢲
⠀⠀⠀⠀⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣤⠜⠁
⠀⠀⠸⠦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈