Happy birthday vasant baby Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣿⣇⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡠⡀⠀⣶⠀⢠⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⣿⡟⠀⢸⡆⠀⢠⣿⠁⣿⠀⠀⣾⡀⠈⣷⠀⣿⠀⠀⣿⢸⣿⢀⣾⡇⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⡇⢠⢿⣧⠞⣿⠀⠐⣿⠀⢸⣿⢠⣿⢀⣺⡟⠈⠿⠋⣸⡧⠐⠉
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⣿⣇⠎⠀⠀⠀⠙⠃⢀⣿⠀⠛⠋⢸⣿⠈⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢳⡀⠀⡤⠆⣰⠄⠀⠘⠃⠀⠙⠋⠀⠀⠀⣀⠀⢀⢸⣿⠀⠀⠀⢸⡟⠀⢀⠄⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡧⡞⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣇⣠⣏⠘⠟⠀⠀⠀⠈⡀⢠⡟⠀⣇⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢹⡏⠉⠉⠉⠉⠉⠁⠀⣾⡇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣌⠀⢀⣀⡀⠀⢰⣿⠀⢸⡇⠰⣆⠀⠀⣰⠟⢳⣿⠁⢠⡖⢠⠀⢠⠀⢰⡄
⠀⠀⠀⠀⠀⠀⢀⡴⣿⣇⠔⠙⡷⢁⣿⢀⠉⣽⡇⠀⣼⣷⢀⣾⣷⢸⣿⠀⢠⣿⠀⣸⣿⠀⣿⢀⢾⣇⢾⡧⢻⡇⢠⡄⠀⡴
⠀⠀⠀⠀⠀⢀⠎⠀⢿⡟⢀⢎⡇⢸⣿⠂⢰⣿⢀⠜⠘⠿⠊⢸⡿⠸⣿⡄⠈⠿⠖⠹⣿⠆⠙⠁⠘⠋⠀⠀⣸⡇⠜⠉⠉
⠀⠀⠀⠀⠀⢸⡄⠀⠸⡇⠘⠛⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣿⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠤⡀⢀⢤⡀⡤⠠⣀⡄⠢⡄⡶⣄⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⢛⠀⣧⠃⠆⣧⠇⡡⠋⡏⡵⠃⠘⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠛⠑⠊⠑⠊⠐⠃⠀⠙⠁⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠍⡇⠘⢣⠨⠠⣱⠾⡍⡽⢂⠳⠏⣆⡏⣍⢆⡸⢀⢳⠸⡱⢎⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡹⢀⡺⢰⡴⢼⠆⢧⠄⠸⡞⢧⠇⢅⡥⠊⣅⠶⣼⠇⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⡤⠤⣤⢤⡀
⠀⠀⠀⠀⠀⠀⣀⠴⣾⠉⢧⣰⠋⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠸⡔⠁⠀⣉⣲⡤⣄⣀
⠀⠀⠀⠐⠫⣉⠏⠑⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠔⢊⣉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣇⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡞⠰⠋⠈⠛⠢⡀⢇⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⡝⠈⠑⡓⠀⠀⣧⡇⢂⠀⠀⡀⢘⣾⠀⢫⠀⡨⠃⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣤⡈⠀⠀⠀⠀⠈⠑⢄⠑⢤⠤⣣⣇⡀⣖⡲⢂⣼⡟⢤⠊⡸⠀⠀⠀⠀⠀⠈⢴⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢓⡎⠀⡞⠀⠈⠫⠝⠁⠈⢣⠀⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⢠⣖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⡠⠖⠉⢉⣆⢤⣤⣏⣱⢦⣄⣸⡯⡉⠓⢤⡀⠀⠉⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠎⠀⢀⡼⠥⢿⠀⠀⠰⠶⠒⢺⡼⠧⢽⡀⠀⢱⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢋⠔⠋⢍⣳⣀⡎⣂⣰⣛⠏⠲⡄⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣉⣁⣀⣀⡤⠔⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠉⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣴⡏⠀⠆⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠐⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡥⠀⠀⠐⠂⠀⢰⡄⠀⣠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠠⡀⠀⠀⠀⠈⣇⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡟⠙⢿⣿⠀⠤⠀⣀⣄⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣏⣈⣽⣿⣆⡈⣛⡇⠀⢸⣿⠟⠛⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡄⢸⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠛⠀⠉⣻⢭⣅⢀⣐⣶⣶⣶⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⠉⠑⠲⢶⣎⡇⠤⠤⢈⣿⣿⢳⡟⢿⣿⣤⠀⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠼⣷⢀⠀⠛⠿⣃⣀⣀⣀⣉⣉⣀⣠⣤⣿⣥⣤⡄⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣰⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⡀
⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠋⠙⢟⣛⣋⣉⣀⣀⣀⣤⣤⣴⣶⣶⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠻⢋⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠛⢦⣀⡉⢿⣿
⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⢷⣦⡈⠻⢿⣷⣯
⠛⠃⠄⢠⣤⣄⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣤⣉⣓⣤⣶⣶⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢃⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣠⠞⠛⠛⠛⣶⡖⠋⢹⡇⣸⡴⠃⠀⠀⠀⢰⢲⢀⡀⢰⣏⠃⠀⣴⣄⣀
⠀⠀⢀⣤⡧⣤⡀⠀⠸⢧⠇⠀⢈⣷⣿⠀⠀⡞⠁⣶⢸⣾⡯⣿⢸⡗⢲⣼⡇⢸⡜⠀⢠⢤
⠀⠀⢾⠀⠑⠾⠃⠀⠀⠀⠀⡰⠋⣿⠸⣇⣰⢧⡴⢧⡴⣯⠛⠃⣞⡇⣹⠋⠛⠋⣧⣠⠾⢏⣀⡤⠴⡶⣤⠠⡀
⠀⠀⠈⠳⣄⠀⡴⠋⣳⣀⠀⠳⠾⢃⢄⣨⣄⡀⢀⡀⠰⣽⠀⢸⢸⡇⠀⣰⠦⡰⢻⡇⠀⠀⠀⠀⠘⢤⠿⠀⢹⡀
⠀⠀⠀⠀⠀⡿⡄⢐⡿⠀⢻⡄⢀⡀⠰⠟⠀⠙⢾⣇⡠⢸⠛⠘⠟⠁⠀⣿⡜⣧⣼⠇⠀⢀⣀⢰⢦⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢰⡇⣿⠈⠁⣀⣼⡇⣴⠀⢺⣇⣀⠀⣿⠀⠀⢸⣇⣀⠀⠀⠀⣿⠁⢠⡖⢀⠀⢸⡙⠘⣏⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠛⠋⠀⢆⣴⠟⢠⡟⢀⡞⣽⠃⡰⣿⠀⣠⣹⡇⣿⢀⡞⢉⣿⠀⣸⣅⣸⣅⠜⠷⢞⢽⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠻⠚⠁⠙⠛⠁⢿⠇⠿⠚⠻⠋⠛⠚⠁⠉⠀⠀⠀⣰⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠁
⠀⠀⠀⠄⠀⠀⢴⠀⠀⠐⠂⠀⢀⡀⠃⣀⠀⠄⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠉⠀⠀⡀
⠀⠄⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠆⢀⠀⠈⡐⠀⠀⠀⠈⢑⡈⠁⠀⠀⠀⠐⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠈
⠀⠈⠀⠀⠈⠁⠀⠀⠀⠠⠀⠈⠁⠸⡀⠂⠀⠁⡀⠀⠀⡀⠓⠩⠚⢄⠄⠀⠀⠀⠀⠲⠀⠀⠀⠀⠠⠀⠁⠁⠀⠀⠀⠀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⡄⡀⠀⠀⠀⠀⠠⠀⠶⠆⠒⠦⠀⢈⡷⠂⠀⠀⠀⠀⠀⠂⠀⠀⣠⠀⢰⠀⠐⠂⠤⠀⡤⠊⠐⠂⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣈⠢⢰⠀⡰⠄⠊⠢⠐⠆⠇⢀⠂⠀⠀⠐⣁⠀⠀⠀⢀⠀⢰⠃⠀⠀⠳⠀⡆⠄⠀⢀⠎⠀⠤⠘⠠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠴⠀⠀⠀⢀⠀⠀⠈⡀⠘⠀⠁⠚⠛⠂⠘⠊⠒⠒⠃⠐⠈⠀⠁⠀⠐⠀⠈⠀⠃⠀⠀⠀⠐⠤⠇⠀⠀⠈⠀⠤⢀⠀⠀⠒⠀⠂⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡤⠤⡄⠀⠀⠀⢀⠀⠴⢐⢐⠰⠀⣀⠀⢠⠀⠀⠀⠂⠀⡄⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣁⣠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⡠⠈⠀⠀⠖⠠⡅⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠀⠀⠈⣐⠦⣅
⠀⠀⡀⠄⠳⠓⠛⠆⡀⡤⠠⠖⡳⠖⠀⠰⢰⠀⠀⠀⠒⠒⠀⠒⡖⠒⡒⠂⠀⠀⠀⠀⠀⠀⣤⠤⡤⠀⢤⣤⣤⣤⠀⠀⠰⠇⢂⠀⠘⠀⠀⠁⠈⡄
⠀⠀⠀⢀⡁⠀⠀⠥⢦⠈⠠⠊⠀⠀⠀⠃⣾⡄⠀⠂⠠⠀⠀⠀⣤⠀⠦⣤⠀⠀⠀⠀⠠⠔⠃⣸⠂⠤⡀⠈⠈⠀⠀⠄⠀⠘⠄⠉⠐⡀⠐⢣⠄⡃
⠀⠈⠉⠀⠁⠀⢠⠒⡂⠈⣇⠀⠀⠠⠈⡀⠖⠁⠐⠀⠀⠀⢠⠚⡛⣆⠀⠘⢤⡤⠦⣀⠼⠁⠠⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠐⠸⠥⠀⠌⠊
⠀⠀⠀⠀⠑⠒⠁⠈⡱⠀⠉⠓⠈⣀⠐⠂⠀⠀⠀⠀⡀⡠⠤⠐⠁⢈⣳⣄⣀⠀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠁⠈⠀⠀⠀⠀⠀⠀⠣⡔⠄⡨⠻⠨⣪⠌⠀⠈⠉⠀⠀⠀⠀⠀⠚⢀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⣀⠀⠛⠿⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⢴⣿⣿⡀⠀⢠⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣴⣤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡈⢿⣿⣧⣀⣼⣿⡿⣠⣤⣄⣄⠀⠀⠀⠀⠀⢸⣿⣯⣀⡾
⠀⠀⣶⣿⣿⣷⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣧⡿⠉⢹⣿⢰⣾⣶⠟⢻⡾⣿⡍⣵⣶⠀⢀⣄⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⠏⠀⣹⣿⣿⠻⣿⣿⠁⣿⣿⡿⣧⣴⢿⣿⢸⣿⣿⣦⠾⠃⠛⠁⠘⣿⣆⣼⡿⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠸⣿⣿⣿⣦⣴⣿⡿⢋⣀⠋⠉⣀⣙⡛⢡⣤⣤⣤⡄⠀⣿⣇⠀⠀⢰⣿⡆⢀⣈⣻⣿⠃⠀⠀⠀⠀⣿⣿⡟
⠀⠀⢀⣿⣿⣿⣿⣿⣭⡀⢿⣿⡰⣿⡟⠛⣷⠛⢻⣿⠛⢣⣦⢌⣥⣤⣀⣼⣿⣁⣬⣛⡛⢵⣶⠀⢀⡀⢰⣿⣿⠃
⠀⠀⣸⣿⣿⣿⠁⢹⣿⣿⢹⣿⠁⣽⣷⣾⠋⠀⢸⣿⣶⣾⡿⣾⡿⠛⢿⣿⣷⡟⠉⣿⡇⠘⣿⣄⣾⠏⣈⠻⠇
⠀⠀⢿⣿⣿⠿⣷⣾⠿⠃⢸⣿⠀⠿⠇⠹⠃⠀⠸⠿⠁⠸⠇⠘⣷⣤⣼⣿⠹⣷⡾⢿⠇⣠⣨⣿⠏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠿⠯⢉⣹⣭⣿⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⢃⠀⠘⢦⠀⠐⣤⢼⡷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢱⢢⡄⡞⠃⠀⠀⠀⠉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡦⠉⠁⠀⠀⠀⠀⠀⠀⣀⡀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⣀⣥⡀⠀⢠⣤⡦⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡀⠀⠀⠉⠉⠀⣀⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣆⠀⠀⠀⠀⢀⣔⣦⠀⠀⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠤⠿⢒⠨⠉⢦⣄⡀⠀⢿⢻⡶⠞⠁⢉⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣠⣄⢀⡥⠚⢂⢀⣠⠖⠁⠐⠹⢀⣀⢡⠚⠉⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠈⣻⣦⠲⡆⠛⠋⠀⢀⡠⠔⠛⠻⣿⣧⠀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠂⠁⠸⣅⠀⠀⣼⠉⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠂⠙⣢⣾⢁⣤⠔⢆⡛⠛⠙⠻⣷⡲⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠒⠤⠀⠤⠔⠦⠭⣿⣦⠀⠠⢾⡿⠒⠀⡰⠃⣡⠽⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠺⣧⠀⠀⠀⠀⠀⠀⠄⢀⡝⡶⣄⣈⢣⣤⣙⣊⢄⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠀⠘⠀⠀⡠⠀⣠⠎⠀⢁⠋⠉⡙⠛⠉⠋⠛⠙⢙⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠀⠀⢤⡀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠎⠀⢰⠇⠀⠀⠀⣠⠟⠈⠀⠀⠀⠘⡗⠒⠶⢤⣀⣀⡀⢀
⠀⠀⠀⠀⢀⣀⢠⠶⢶⠃⠸⡄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠎⠀⠀⠀⡴⠁⠀⠔⢀⠄⠀⠀⢹⡄⠀⠀⠙⣾⣿⣿⣿⡆
⠀⢀⣀⣚⡊⠉⠉⠍⢸⠀⠀⠙⠆⠀⠈⠣⡀⠀⠐⠉⠉⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠁⠀⠐⠦⠌⠙⠟⢿⣿⡀
⡴⠟⠙⣛⣠⡴⡦⠀⠈⢢⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⣠⣤⣀⣤⠤⠴⠶⢤⡀⣹⡇
⡏⠁⠀⠁⠉⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠀⠀⠀⠀⠀⠀⣀⣀⣠⣠⣤⣀⡀⠀⠀⠀⣸⠁⠠⢀⠀⠀⡀⢀⣸⣿⣿⣿
⡗⠖⠀⣀⡠⠀⠐⠋⠑⠚⢹⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠉⠉⠈⠉⢙⣆⠀⣠⣟⣹⣶⡞⠛⠚⠓⠉⠉⠁⠀⠒
⠀⠀⠹⢇⡤⠀⠀⠀⠀⠀⠸⣧⢀⠀⡀⠀⠀⠀⠄⠀⠀⠀⡀⠘⡤⠾⢄⣀⣀⣀⡠⣅⣶⢞⠉⠉⠀⠈⠉⠁⠀⠦⠀⠒⣤⡄⢠⡄
⠀⢀⠀⢀⣒⡉⠀⠀⠀⠀⠀⠀⠀⠱⡄⠴⠛⠓⠦⢌⡀⠀⡸⠒⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠚⢉⠡⢄⡠⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠤⠤⢤⠴⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠠⣆⣐⣂⣠⠶⠿⠿⣿⣄⠀⣀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⡤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠀⠀⠀⣜⢉⠛⠛⠭⠆⠰⠶⠞⠀⠤⠝⠓⠂⠖⠂⠈⠋⠂⠚⠋⠉⠉⠉⠉⠉⠈⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠄⠀⢀⣠
⠀⠀⢠⠀⢈⠄⠀⠀⠂⠐⠂⠉⢑⠒⠀⢤⣄⢀⢀⣀⢁⡀⠀⡁⠀⠀⡀⠀⢠⡤⠀⠲⠋⠉⠃⠀⠂⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠈⠀⠙⠉⠁⠙⠁⠐⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠐⠉⠲⠂⠤⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⡠⠀⠄⠴⠔⠚⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠤⢀⡆⠀⢠⣤⠀⠈⡀⠀⠀⠈⠁⠀⠈⠀⠄⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹
⠀⠀⢀⣀⣀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠈⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠄⠀⠤⡘⠀⠀⡀
⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡄⠀⠀⢄⠚⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠐⠀⣄⠀⡄⢸⠀⡀⠠⡀⠀⠀⠀⢠⠆⠀⠃⠀⠀⠀⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⣻⢂⠻⡺⡆⡟⠶⠛⡂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠉⠀⠆
⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠈⣀⢁⡉⢀⣄⡁⣄⡀⠀⡄⠀⠐⠀⠀⠰⠆⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢸⠰⠃⢰⠀⢽⠂⠍⢈⠟⠀⠄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⢈⠀⠚⠀⡀⠃⠀⠂⠀⠠⠀⠂⠁⠀⠀⠀⠀⣀⠀⢰⡔⠄⣶⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠟⠀⠀⠀⠛⢀⠀⠛⠈⠉⠲⠟
⠀⠀⠀⠀⠀⠀⠂⠀⠾⠃⠀⠀⠀⠘⠀⡓⠬⣀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠁⠐⢀⠀⠀⠀⣀
⠀⠀⢰⡵⠔⣠⡀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠐⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⢸⠀⠀⠰⢿⡀⠀⢀⣀⠀⠀⠀⢹⡍⣶⡖⣞⠇⡀⠀⠀⢈⠀⠀⡇⡇
⠀⠀⠀⠀⠁⡀⠀⠀⠀⢀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠻⣿⡽⢼⡂⠐⠐⢐⠀⠀⠁⠁⠀⢀
⠀⢀⠀⠉⠀⠁⠈⠁⠀⠀⠑⠆⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⡮⢱⡆⠘⠂⠀⠈⠈
⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠀⠀⠀⠀⠶⠀⠠⣄⠀⠀⠀⣀⢴⡀⠀⠁⠀⠁⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢈⠀⢠⣀⠀⠀⠀⠈⠀⠀⡼⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢦⠀⠀⠀⢀⡴⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢳⡤⠞⠁⠀⢳⣀⣠⠞⢻
⠀⠀⠀⠀⠀⢠⡇⢀⡴⠚⠁⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠸⡧⠖
⠀⠀⠀⠀⠀⢸⣥⠋⠀⢀⡴⠚⠁⠀⠉⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠧⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣾⠁⢀⡴⠋⠀⠀⢀⡴⠋⠁⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣀⣀⣀⡀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⢠⠏
⠀⠀⠀⠀⠀⣇⡴⠋⠀⠀⢠⣾⡥⠴⠖⠚⠋⢉⡍⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⠋⠉⠉⠹⠿⠖⠒⠋⠙⣆⢀⣄⠀⠀⠙⢯
⠀⠀⠀⠀⢰⠟⢀⣤⠖⠚⢉⣴⣢⢶⣠⠞⠿⠋⢳⣠⡼⢦⣀⠀⠀⠀⠀⠀⢀⣀⠴⠋⢰⠇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠙⠉⠳⣄⠀⠸⡇
⠀⠀⠀⠀⣸⠟⠉⠀⡴⠶⠋⠙⠁⠀⠁⠀⠀⠀⠀⠉⠀⠀⣹⠀⠀⠀⠀⠀⠈⣻⠖⠀⣸⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠈⡇⠀⡇
⠀⠀⠀⢰⡇⠀⣤⡼⠁⠀⢀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢙⣶⣀⣸⠀⠀⠘⣇⠀⠀⠁⠀⠀⣤⡀⠀⠀⠀⣸⠃⢸⡇
⠀⠀⠀⠠⣧⣤⡏⠀⠀⠀⠈⠀⠀⠐⠖⢃⣀⠀⢲⠂⠀⢸⡇⠀⢀⡴⠶⡄⠀⠀⠉⠉⠙⣆⠀⠀⢻⡷⣤⣤⢴⡞⠁⠀⠀⠀⣰⠃⠀⠈⡇
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡏⠉⢳⠟⠀⠀⣼⠀⠀⢸⡀⣠⠇⠀⠀⠀⠀⣠⠞⢳⠞⢲⡱⢤⠴⠋⠀⠀⠀⣀⠼⠁⠀⠀⣶⠿
⠀⠀⠀⠀⠙⠒⢦⡀⠀⠀⠀⠙⠲⠤⢴⣷⣤⣯⡀⢀⡴⠃⠀⠀⣾⠛⠛⣶⠀⠀⢀⡼⠁⠀⣸⣄⡜⠛⠲⠦⢤⣤⠶⠚⠙⣶⢤⣽⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⢸⡇⠀⠀⡷⠚⢦⡀⠀⠀⣿⠀⠀⣾⠀⢠⠏⠀⠀⢸⠇⠈⢹⡀⢀⡴⠋⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⢿⡉⠉⠉⣇⠀⠀⣇⣀⣀⣽⣦⣤⡟⠀⠀⣯⣤⣏⣀⣀⠀⡼⠀⠀⡏⠳⠋⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⣛⡶⢿⠀⠀⣏⡁⠀⠀⢀⣴⣧⣤⣠⣷⡀⠀⠀⣈⣽⣇⣀⢰⣧⡀⠀⠀⠀⠀⢰⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡤⠚⠁⣴⣛⠒⠒⢫⡝⠃⠀⠀⠿⠶⣄⡴⠶⠟⠂⠀⠉⣷⣀⡉⣉⣳⡍⠲⣄⠀⠀⢸⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⢸⡄⠀⢸⡀⠀⠀⠀⢹
⠀⢀⣀⣀⣨⣇⣀⣀⣀⣀⣹⡖⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣠⣤⣼⣇⣀⣀⣀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠙⠒⠲⠖⠚⠳⠤⠴⠶⢤⣄⣀⣠⠴⠦⣄⣀⣠⡤⠖⠒⠒⠚⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢭⣉⣩⠭⠿⠷⣶⡦⠤⠤⣄⣀⣀⡤⠤⣤⣀⣀⣀⣀⡤⠴⠤⠤⠤⠴⢒⣺⡇
⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡿⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠴⠖⠒⠛⠙⠓⠲⠤⠤⠶⠚⠋⠉⠉⠉⠉⢹⣇⣀
⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠙⠦⣄
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠘⠲⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⠀⠀⠀⠀⠈⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠾⠿⠿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢿⣷⣦⠀⠀⠀⣰⡿⠋⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⢀⣿⡟⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣸⡿⠁⠀⣠⣤⣀⡀⠀⢠⣾⢏⣠⣀⠀⢠⣿⢋⣀⡀⢀⣤⣶⡶⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣾⡿⠿⠛⢻⣿⠗⢀⣾⠟⢉⣿⠃⠀⣾⡿⠋⣸⡿⢀⣿⡷⠋⣼⡟⠈⣽⡟⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣼⡟⠀⣾⡏⣠⢾⡏⢀⣼⣿⣖⣴⡿⠃⣼⣿⣖⣼⡿⠁⢸⡿⢀⢼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⢸⣧⠀⠀⠀⢿⣧⠀⠙⠛⠁⠙⠛⢹⣿⠈⠛⠋⠀⣸⡿⠘⠛⠋⠀⠀⠈⠛⢋⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠃⠀⠀⠀⢠⡶⠖⣻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠙⠿⠾⠛⠁⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⡄⠀⠀⢤⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠉⠼⣿⠷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⠶⠦⣄⠀⠰⠒⠛⠛⠓⠲⠶⠶⣦⣤⣤⣼⣿⣁⣴⡿⠋⠀⠀⠀⣸⣿⠀⢀⣿⠇⠀⠀⠀⠠⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣿⠟⢉⣿⠏⠀⠀⢨⡇⠀⠀⠰⡿⠀⣀⡀⠀⠀⠀⣽⡿⠙⣿⡿⠿⠿⠷⠶⠿⠟⠁⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢢⣾⣿⣶⡶⢾⡋⢀⢴⣶⠆⠀⠸⣧⣿⡀⠀⢰⡿⠁⣸⡟⣠⢶⣿⡟⢀⣴⡶⠿⣿⠏⠀⠀⢠⣾⠟⢻⡷⠀⢠⣿⠋⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣷⠀⣾⠏⠀⣠⡾⣫⡿⠃⣠⣿⠃⢀⣿⡿⠁⣾⠏⢰⡿⠁⠀⣼⡟⠀⢀⣴⣿⠃⣰⣿⠁⢀⣿⠏⢠⣿⡏
⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⣠⣴⠾⠃⠸⣿⡶⠞⠁⠰⣿⣤⠾⣿⡏⠀⢸⡟⠀⠸⣯⠤⠺⢷⡶⠞⠻⢷⣶⠟⠙⢧⠞⠹⠿⠶⠺⣿⠴⣹⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣼⣟⣁⣀⣀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣻⣿⡿⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⠿⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣤⣤⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣤⣶⠶⢶⣶⣶⣤⡀⠀⢀⣤⠾⠛⠛⠻⢿⣿⣦⡀⠀⠀⣠⠶⠛⠛⠛⠿⣿⣶⣄⠀⠀⣠⣴⡶⠶⢶⣶⣶⣤⡀
⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢿⣿⣶⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠞⠁⠀⠀⠀⠀⠀⠈⠻⣿⣧⡞⠉⠀⠀⠀⠀⠀⠙⠻⣿⣦
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⢈⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡄
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠘⠁⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⢻⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢠⡶⠒⠚⠻⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠘⣧⠀⠀⠀⡼⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢀⣀⡤⠴⠶⡄⣴⣾⡁
⠀⠀⠘⢷⣦⠞⠁⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠖⠁⠈⠁⠀⠀⠀⠸⡞⢿⣿⣆
⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠁⠀⠀⠀⠀⠀⢀⢀⠀⠘⡄⢻⣿⡆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣀⡀⠀⠀⠘⠛⠀⠀⠁⠈⣿⣷
⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠛⠃⠀⠀⠀⠀⠀⠘⠆⢀⣿⠇
⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⢀⣀⠀⠁⠄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡤⢾⠘⠇⠒⠲⡀⠂⠀⠀⠀⣀⠀⡄⠀⡈⠀⠀⠀⠀⠀⡀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠸⣤⣤⣤⣤⠤⠦⠀⢤⡍⠤⢤⣤⣤⠌⠂⠀⠀⠀⢠⡿⠻⣄⠀⠀⠀⠀⠀⠀⠤⠀⠉⠒⠂⠀⠀⠀⠈⠉
⠀⠐⠂⠀⠀⣿⣿⠶⠤⠄⢠⠀⡤⢤⡀⢾⣿⠋⠀⠀⢀⣤⠖⠃⠀⠀⠙⠶⢀⣀⡀⢀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣷
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠁⠤⠀⠄⠠⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⠁⠀⠇⠀⠀⠀⠀⠈⠁⣠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠐⠋⠁⠀⠀⠶⠊⠀⠄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⢾⠶⠖⠀⠒⠒⢾⠚⠃⠀⡶⠶⠂⠀⣠⣀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠉⣀⠈⠀⠀⣀⡄⠀⠠⣤⠆⠀⠀⠂⠀⠀⢀⡀⠉⠓⠏⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠠⠳⠂⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠙⠁⢀⡆⠀⠰⣦
⠄⠀⢀⡀⠀⠋⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⣀⣀⢀⡄⣀⡄⡀⠀⠀⠀⠀⠘⠀⢀⡄⠀⠀⠆⠀⠀⠈
⠰⠃⠀⠀⡀⠀⢀⡀⠀⢀⢀⣤⠖⠐⠛⠛⠈⠉⠁⠀⠉⠁⠈⠙⠋⠰⠭⠖⠶⢒⢏⡀⢀⠤
⠀⠀⢀⠀⠁⢠⠎⠴⠚⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⣦⣀⢀⠔⠁
⠀⠀⢀⡶⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣲⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠴⠆⠀⢀⠰⠆⠉⠀⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠠
⠀⡀⠀⠀⠀⠀⠘⣰⠀⠀⠀⠀⢠⡌⠁⠄⠙⠠⠀⠀⠐⠀⠣⠀⠂⠀⠀⠀⠀⠤⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⡀⠒⠁
⠀⠰⠀⠀⠀⠒⠀⠁⠁⠀⡀⠀⠰⠀⠜⠂⠄⠁⠂⠠⠀⠀⠀⠣⡰⣢⣔⠀⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⡀⠒⠐⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠈⠁⠐⠀⠀⠒⠆⠀⢀⠀⠉⠃⠠⠀⡀⠂⠐⣀⣍⠤⣔⠁⠈⠻⣤⡀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠱⡀⢀⢤⠀⠀⡀⢀⠄⢫⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠨⡁⣂⠀⢀⢀⠤⣌⠡⣌⢨⠀⢀⠃⠀⠘⢡⠄⠠⠀⠀⠀⠈⢀⡴⠈⠉⢣⠀⢃⠀⣀⢀⢁⡐⠁⠀⡰⠀⣀⠚
⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠛⠀⠤⠉⣸⠀⠎⣠⣤⡀⠡⡄⣇⣀⣠⠀⡀⢀⠸⠎⠀⣀⠀⠜⠀⣼⠀⠀⠀⠈⡀⢸⠈⠀⠀⠺⠀⠄⠁⠀⠈⣁⠀⡀⠈⢐⠈⠀⠆
⠀⠀⠀⠀⠈⠀⠂⠐⠀⠂⠀⠀⠐⠀⠀⠀⠀⠉⠁⢀⢀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⡀⡀⠀⡀⡉⠉⠁⠀⠀⠀⠀⠁⡂⡀⠔⠀⠀⠀⠀⠀⠀⠪⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠔⢋⡉⢸⠀⠀⠀⠀⠐⠀⣘⠰⠀⠀⡇⠸⠆⠀⡇⠀⠀⠀⠀⠈⡇⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣭⡤⠴⠺⠡⢄⡀
⠀⠀⠀⠀⢀⣸⣰⡀⠀⠀⠈⠁⢈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠈⣀⠀⠤⢭⠲⡄⠐⠘
⠀⠀⠄⠐⠀⢃⠀⢉⠡⠘⡇⠞⡉⠝⠁⠀⡈⢸⠀⠀⠀⠉⠉⠑⠀⠹⠉⠩⠉⠀⠀⠀⠀⠀⠀⠀⡲⠒⡶⡀⠛⢻⡿⡿⠇⠀⢀⠘⢄⠣⣄⠞⠀⠀⣀⠀⢷
⠀⢀⢂⠀⡤⠀⠀⠐⠚⡖⢁⠞⠁⠀⠀⠠⠁⠿⡆⠀⠀⠘⠀⠁⠐⣰⡆⠜⠓⡆⠀⠀⠀⠀⢐⡞⠁⠰⠋⠑⠠⣀⠀⢀⡀⠐⠁⠀⠈⠂⠀⢈⡅⠊⢡⡆⡉
⠀⠀⠀⠀⢀⠀⠀⡎⣹⠀⢸⡄⠀⢀⠰⠁⠌⠊⠁⠈⠀⠀⠀⠠⢞⢩⠹⡄⠀⠙⠦⡖⠓⡤⠞⠀⡰⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⠀⠐⠈
⠀⠀⠀⠀⠈⠛⠉⠀⢀⠦⣀⠉⠉⣁⣤⢘⠂⠀⠀⠀⠀⣃⣀⠗⠒⣙⠄⣨⡶⣤⣄⢀⡀⡄⡀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠙⢤⡢⢤⠟⠇⢝⡥⠂⠀⠀⠀⠀⠈⠀⠀⠀⠘⢀⡀⣀

⠀⡗⣄⡀
⠀⠸⣄⠉⠢⡀
⠀⠀⢹⠀⠰⣾⠓⢄⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢣⠀⠀⠀⠀⠻⣦⠀⢰⠋⠉⡇⠀⠀⠀⢰⡆⠀⠀⣀⣠⡤⠤⠤⣄⢀⡤⠖⠒⠒⠒⠒⢤⣀⡴⢦⡀⠀⠀⡴⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢷⠀⠘⡧⢺⡏⠀⢸⠀⠀⡇⠀⠀⢀⠇⢱⠀⢾⠁⠀⠀⢀⡀⠀⢻⡆⠀⠀⣠⠤⣄⠀⢹⡄⠀⢳⠀⣸⠃⢀⡞⠀⠀⠀⢸⡄⢨⡇⢰⠱⢰⢂
⠀⠀⠀⠀⠘⣤⣾⠀⢸⠃⠀⠀⡆⠀⣇⠀⠀⡞⢀⠀⢧⠘⠒⡆⠘⡏⢉⡇⠈⡏⡇⠀⡇⠀⡼⠀⣸⢧⡀⠈⢷⡏⢀⠞⠀⡀⣀⣸⣼⣀⢨⣡⢠⣠⢴⣸⠤⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⠒⠋⠁⠀⢿⠀⣰⠁⡞⡇⠘⣆⠀⡇⠀⠷⠋⢀⡼⠁⡇⠀⠷⢋⣠⠔⠁⠀⢳⡀⠀⣠⠋⠀⠐⣤⣤⣤⣬⣥⣴⣤⣤⣴⣤⣤⣶⡞
⠀⠀⠀⠀⠀⠀⡖⠃⠀⢀⡀⠤⢤⠀⢸⢠⠃⠸⣥⡵⠀⠹⡀⡇⠀⢠⠖⠋⠀⠀⡇⠀⣾⠉⠀⠀⠀⠀⢰⠃⠀⡇⠀⠀⢀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣇
⠀⠀⠀⠀⠀⠀⠙⢹⠀⢸⠀⠀⢸⠀⢸⠏⠀⢀⣠⣄⠀⠀⢳⡇⠀⠸⡄⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⣸⠀⠀⠇⠀⠀⠀⢷⣿⣿⣾⣿⣿⣿⣿⣶⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⢸⠀⢿⣀⠀⡇⠀⢸⣀⣀⣈⣿⠀⣀⠇⠀⠀⠀⣣⣠⠼⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⢠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠃⠀⢸⠴⠊⠉⠉⠁⠀⠀⠉⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠺⠭⣽⣶⣶⣲⣦⣶⣦⣤⣴⡶⢶⡿⠛⠋
⠀⢀⣠⠴⠒⠋⠉⠙⢳⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡠⠤⠔⠒⠋⠉⢹⡧⢤⡀⢠⠔⢲⣆⡤⠴⠖⠲⠦⣄⠀⠀⢰⢦⠈⢧⡀⠈⢧⠀⢀⡜⠀⣠⠎
⡔⠉⠀⠀⣀⠤⡄⠀⠀⡇⠀⠀⠀⢠⠖⠉⠁⠀⡀⠈⢻⡄⠀⡀⠀⣀⣤⣼⠇⢸⠀⢸⠀⢸⡷⣇⡄⠀⣀⡀⠈⢳⡀⠆⠈⣇⠀⠱⡄⠈⢧⡞⠀⡴⠁
⠹⠔⢦⠀⢳⣠⠇⢀⠜⠁⠀⡏⠉⡆⢳⠀⠰⣏⡼⠂⣸⠋⠉⢡⠀⣿⠀⢸⠀⠘⠶⠚⠀⢸⡇⠀⡇⠀⡇⢸⠆⠀⡟⢀⣆⠘⡆⠀⠘⡆⠀⠀⡞
⠀⠀⠘⡄⠈⠁⠀⠛⠙⠛⢦⡇⠀⡇⠨⡆⠀⠉⢠⡴⠃⠀⠀⣸⠀⢹⠀⢸⠀⠀⣀⣤⠀⢸⡇⠀⡇⠀⣇⡞⠀⣸⠇⢸⣹⡄⢹⡀⠀⡗⠀⠀⡇
⠀⠀⠀⢧⠀⢠⠖⠛⣦⠀⠈⡇⠀⢣⠀⡇⢠⣄⡈⠳⣄⠀⠀⣿⠀⢸⠀⢸⠀⢰⡇⢸⠀⠀⡇⠀⡇⠀⠉⢀⡴⡏⠀⢀⣀⠀⠀⣧⢠⠇⠀⠀⡇
⠀⠀⠀⢸⠀⠈⣧⠔⠁⢀⡼⡇⠀⢘⣼⡇⢨⡇⠳⡄⢈⠗⠀⣿⣀⣘⡆⢸⠀⣸⠅⢸⠀⣠⡇⠀⣧⡤⠖⠋⢰⠃⢀⡏⠉⡇⠀⢸⡾⣤⣀⡀⢁
⠀⠀⠀⠀⠇⠀⣀⡠⠖⠉⠀⠓⠚⠉⠸⠧⠖⠃⠀⠙⠃⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠉⠉⠉⠁⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⣀⣀⡾⠀⠟⣴⣿⣯⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⢻⣄⠀⢉⣡⠀⢀⡶⢸⠏⢀⡶⢀⡟⠻⣦
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣶⣿⠇⣼⠟⠛⠛⡇⠀⠚⠁⡄⠀⢨⣴⠿⢃⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣇⢠⣾⣟⣡⡏⣸⠏⢀⣴⣿⣷⣤⣴⣾⣿⣤⣤⣴⣾⣿⣟⣡⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣻⠟⠋⠉⠉⣀⠉⣀⠛⢁⣴⠀⣸⠃⢈⡤⢀⡉⠀⣡⠄⢈⠁⢀⡟⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠀⣿⠀⡟⠀⠰⠃⢰⡏⢠⡿⠃⢨⠁⣼⠟⠀⡍⠀⠞⠀⠘⣉⠀⠉⣿⡄
⠀⠀⠀⠀⣿⠙⠶⠟⠋⠀⣸⡇⠀⢿⣤⣴⣦⡔⠁⣦⣤⣶⠇⢰⣤⣴⣾⣧⣴⠎⣰⣿⠟⠻⢷⣿⠇
⠀⠀⠀⠀⠹⣷⣄⣀⣠⣾⣿⣧⣀⣀⣿⡍⡿⠀⢸⣿⢉⡏⠀⣿⠃⠘⠷⠟⠃⣰⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠙⠛⠛⠋⠘⣷⣤⣿⠇⣿⣄⣰⣿⣆⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠋⠙⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⠛⠻⠟⠛⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⡥⠄⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠘⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡐⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡤⢴⠆⠀⠀⠠⠂⠀⠀⡠⠀⠁⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢌⣀⣠⡔⢈⡀⠠⣤⠐⠈⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢹⣧⣼⡷⠀⠀⠀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠐⢻⡀⠀⠀⠀⠙⠈⠁⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠁⠀⢀⠠⠀⠐⠛⠊⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠑⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣽⣷⠇⠀⠀⠀⣷⣿⣫⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡻⠃⠀⠀⠀⠀⠘⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠀⠀⠀⢱⣠⠔⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠙⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣄⠐⢀⡜⠁⠄⠀⢀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⣻⠟⡝⡟⢷⣶⣤⣀⣀⠞⠁⠀⢀⠀⠀⠈⠧⠀⠀⢈⣀⡀⠈⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⢀⡬⠐⠋⠘⠁⠁⠀⠐⠦⠙⢷⣦⣀⠀⠈⠙⠂⠀⡠⠚⠉⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣯⡣⡀⠒⠀⡼⠁⣰⠃⠀⠁⠀⠀⠀⢳⠐⠚
⠀⠀⠀⠀⠀⠀⠐⠟⡴⢡⣇⠛⠀⡀⠀⠀⠀⠐⠂⠀⠈⠀⢀⠀⠛⢸⣻⡷⣵⡀⠀⠱⡀⠹⣄⣀⣀⡤⠀⢠⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠏⠀⠇⠻⠁⠀⠀⣹⢶⠤⢍⡭⠤⠖⠁⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠦⢄⣀⣀⡠⠴⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⣀⠀⢰⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠦⠤⠤⠤⠤⠔⠚⢿⢄⡀⠀⠀⣀⢀⡠⠊⠁⠀⠀⠀⡇⠀⠀⢇
⠀⢠⠊⢉⣚⠉⢹⠄⠀⢀⣀⣠⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠑⣾⡷⠏⠀⠀⠀⠀⠀⠀⣃⣀⠀⠈
⠀⢿⢠⠋⢀⢱⠈⠓⡄⠀⠞⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠁⠀⠀⠀⠀⠀⣀⣴⡉⠵⠮⣗⠒⣄
⠀⣰⠛⢻⠾⠊⡤⠞⠁⠀⠀⠀⠀⠘⠓⠋⢹⡏⠉⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣅⢎⣥⡼⢴⠃
⠀⠈⠋⢉⣓⣚⣆⡴⣦⣀⡠⠤⠤⠒⠒⢃⣸⠇⠉⠉⠁⣇⡀⠉⠙⠓⠒⠒⠦⠤⢄⣀⠉⢱⣌⡹⠯⣀⡼
⠀⠀⠀⠈⠓⣮⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⡀
⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⠔⠋⠄⡰⠀⠀⠀⠂⠠⠀⠀⠂⠱⠘⠀⠶⠂⠋⠇⠃⡇⠱⠀⠀⠰⠂⠁⠀⠀⠴⠀⠆⠀⠸⠉⠱⠋⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠰⣆⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠈⢢⠈⠀⡀⠓⢢⡀⠀⣺⠹⣦⠉⠻⢿⠀⠀⡀⠀⠀⠀⠐⢈⠁⠆⣁⠁⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠲⠌⡉⡉⢹⠆⠙⠿⣦⣤⠀⠄⠀⣰⠀⠐⠀⠀⠀⠂⠽⠁⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⣀⠅⠚⠀⢷⠀⠁⠰⠆⠐⠉⠀⠀⠀⠀⠀⠀⠠⠀⠋⡀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢨⡄⠐⠂⠲⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⣀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⢦⡴⠄⠒⠀⠐⠂⠀⠀⠀⢀⡈⣱⢄⠀⠀⠀⠀⠈⡍
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠴⡈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⠉⠈⠁⡀⡄⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢾⠀⠀⠀⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡤⠤⣤⠄⢠⣤⣀⣀⡀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢨⡇⠀⣶⣤⣾⣿⢸⠙⣳⢾⣏⣹⡏⣹⠞⣇⠏
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⣽⡏⠀⠋⠟⠀⠘⠼⠍⠈⢯⠁⠐⠏
⠀⠀⠀⠀⠀⠀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⣼⠟⢳⣖⣴⠦⣶⠶⡔⠿⡿⠺⣿⣂⣀⣻⡿⣿⠿⢷⣤⣴⣦⠄⣠⣀⣠⣄⠁
⠀⠀⠀⠀⠀⠠⢀⣼⡷⢛⣅⣽⣴⣿⡴⠏⠀⡇⠀⢿⡿⠿⢿⣇⣿⣧⣼⢻⡇⢸⡇⢈⣧⣏⢉⡀
⠀⠀⠀⠀⠀⠀⠶⢸⡧⠽⣿⠙⠛⠃⠀⡀⠈⠇⠀⠘⠇⠀⠸⠃⢙⠛⠋⠚⠂⠀⠹⣼⡻⣄⡈⣁
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⠛⢾⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢤⢀⡀⠠⡀⠠⠄⠀⢀⠻⣦⡙⠳⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⣊⡄⠀⠽⢡⣄⣕⠈⠁⠀⠀⣿⡿⠓⠛⠻⠻⢷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⢩⠀⠈⠀⠀⠀⠉⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⢨⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣤⣿⣷⣾⣷⣶⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣼⣿⡏⠀⠀⠀⠉⠉⠈⠙⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⠟⠋⠛⠛⠿⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠏⠋⠉⠈⠁⠀⠈⢻⣿⣿
⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠘⣿⡇
⠀⠀⠀⠈⣜⠀⠀⠀⠁⡀⢀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠗⠎⠀⠄⠀⠁⠄⠠⠀⠀⠀⠀⠐
⠀⠀⠀⢠⣿⣦⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠠⡉⠈⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀
⠀⠀⠀⣸⣿⣿⣿⣿⠗⠐⢿⣿⣷⠀⠀⠀⠂⢀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡛⠃⠓
⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠈⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎
⠀⠀⠀⠈⠉⠉⢱⠀⠀⠀⠀⢈⠁⠀⢠⠀⠀⠀⠀⠀⠈⠩⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠦⠲⠀⠀⠀⠀⠸⠲⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢒⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠥⡄⠈⢴⠀⠀⠉⡙⠀⠀⠀⠀⠈⡤⠏⠘⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠠⢺⠇⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣹⢷⡾⠃⢀⡀⠘⢷⡾⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⢀⣤⣠⠙⠿⣳⡗⢿⡟⢻⡷⢺⣞⠿⠋⣄⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣮⡽⠏⢠⡆⠙⡇⢾⡟⢻⡷⢸⠋⢰⡄⠹⢯⣴⡻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠰⣯⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠢⣽⠆⢹⣦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡌⠀⡗⠊⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠐⢺⠀⢫⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠜⢁⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡈⠳⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡸⣦⣄⠀⠀⠀⠄
⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠸⠃⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠘⠇⡀⠀⠀⠀⠀⠀⣄
⢆⠀⠀⠀⠁⠐⠠⠂⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠉⠐⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⣀⢀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⡴⠃⠀⡏⠼⠁⠼⢡⠏⠼⢡⠏⠰⠡⠟⣴⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠏⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠗⢀⠀⢀⡌⡔⠀⠈⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠶⠁⠏⠞⠼⠱⠱⠡⠃⠎⠎⠜⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⢀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁
⠋⠀⠀⣀⡀⠠⠀⠦⡀⢐⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡂⢀⠴⠀⠄⢀⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣐⡆⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣎⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡎⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠊⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⣡⠀⠗⢀⠸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠇⡀⠺⠀⣜⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡰⣟⠂⠃⢠⠀⠂⢀⡀⢀⠀⠀⡀⢀⠀⠀⢀⡤⠘⠒⡻⢆⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣶⢟⣵⣆⠨⠃⣦⡅⢻⣧⣼⡟⢨⣤⠘⠁⣰⣾⡻⡶⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⠙⣨⣿⠽⠷⢿⣧⣼⡿⠾⠯⣻⣅⠋⠛⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠉⣸⠟⢿⡄⠈⠁⢰⡿⠻⣇⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠣⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠠⠄⣀⣀⡠⠖⠁⢀⣀⠀⠈⢄⠀⠀⠀⠀⠀⠀⡰⠁⠀⠋⢁⣀⣀⠀⠀⠀⠳⡀⣉⣀⠀⠀⠀⢁⡔⠋⠀⠀⠀⠀⠙⢦⠀⣤⠈
⠉⠀⢀⣄⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠈⠩⠇⠀⠀⠈⠁⠀⣠⡄⠂⢄⠀⠀⣠⠞⠁⣀⠀⡞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣈⡀⠈⠁⢀⣀⣀⠉⠁⠀⠀⠀⠀⠐⠀⢀⡤⠒⠛⠛⠒⢤⡉⠀⠀⠀⠈⣙⠅⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉
⠀⠈⠑⠈⠀⠀⠈⢳⡀⠀⠀⠀⣤⠀⢰⠋⠀⠀⠀⠀⠀⠀⠹⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⡀⠀⠀⠈⢧⠀⣠⡀⠐⠄⠀⠀⠀⠀⠀⢀⠜⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⢸⡅⢀⡤⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠑⠤⠐⠉⠯⠄⠑⠢⠤⠋⠀⠉⠁⠒⠀⠑⠢⠤⢤⡖⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠁⠀⠀⠀⠀⠐⠿⠀⠀⠤⠀⠀⠀⠀⠰⠆⠀⢀⠴⠒⠒⠒⢦⡀⠂⠀⠐⠚⠀⠀⣀⠘⡀
⠀⠀⠀⠀⠀⢀⠜⠁⠰⠆⠀⠾⠆⠀⠀⠑⢄⡀⠀⠀⠀⠴⠋⢀⠀⢀⡀⢄⣀⠀⢀⠀⠀⣄⠀⢠⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘
⡙⠢⢤⡤⠔⠁⠀⢠⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠉⢙⣻⠄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⠃⠀⠀⠀⣠⡀
⠁⠀⠀⠘⠀⠀⣀⡄⠀⢀⠔⠉⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠛⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢉⡁⠀⠎⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡄⠀⠛⠀⠃⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠛⠀⠀⠀⠀⠀⠰
⠀⠰⠗⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠜⢀⡀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⠃⡤⠀⠀⣀⣀⠀⠀⠀⢀⣄
⠀⠆⠀⣀⣀⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠀⠀⠀⠰⡖⠀⠀⠑⠶⡆⠀⠀⠈⣁⣀⣀⣀⠀⠀⠠⠀⠀⢠⡤⠄⠈⠠⣶⠀⠰⠋⠀⠀⠙⢦⠀⠘⠁
⡠⠖⠉⠀⠀⠀⠉⠲⡄⢀⠁⠀⠀⢀⣀⠀⠊⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⠀⠀⠉⠁⠀⡰⠋⠁⠀⠀⠀⠙⢦⠀⠀⠘⠶⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁⠂⠀⠉⢀⣀⣠⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢠⣶⠀⠀⠀⠰⠷⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⢀⠔⠉⠀⠀⠀⠈⠙⣄⠀⢠⠄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⠀⠈⡀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣶⠆⠐⢄⠀⠀⠀⠀⡴⠃⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡊⠀⠐⠂⠀⠀⠀⠿⠂⢀⣄⡀⠀⢀⠈⠢⢀⢀⡀⠁⠀⠄
⠑⣄⠀⠀⠀⠀⢠⠊⠀⠀⠈⠁⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⡸⠁⠀⣀⡀⠀⣶⠂⠀⠘⠃⠀⠉⠀⠀⠀⠀⢀⣄⠀⠀⠀⡏⠀⠙⢆⡀⠀⠀⠀⢈⠡⠀⠀⠘
⠀⠈⠓⢤⡤⠐⠁⢀⡈⠁⠀⠈⠀⡀⠀⠀⠀⠈⠑⠄⢀⠀⢀⠔⠁⠀⠀⠈⠁⠀⠀⠰⠆⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠖⠁⠀⠀⠀⠈⠉⢑⡆⠀⠀⠀⠀⠠
⡀⠀⠀⠐⠂⠀⠀⠛⠁⠀⢀⠤⢤⠀⠀⣴⠀⠀⠀⠀⠀⢘⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠈
⠃⠀⠀⠀⠂⡠⠒⠒⠢⠔⠁⠀⠈⡇⠀⠀⠀⠠⡄⠂⠀⠀⣉⢀⣀⠀⠀⣴⡄⠀⡠⠤⠤⢤⡈⢃⡀⢀⡀⠀⠊⠀⠀⠀⠑⡀⠀⠀⢀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⣄⠀⠀⢀⠀⠁⠀⠀⠀⠉⢢⠀⠀⠎⠀⠀⠀⠀⠈⠀⠀⠀⠈⢣⠀⠀⡀⠀⠀⡇⢀⠴⠋⠟⠒⠤⠞⠀⢀⡀⠀⠀⠠
⠄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠛⠀⠀⣉⠁⠀⠂⠀⠀⠄⠀⠀⠛⠀⠀⢀⡀
⠀⡶⠂⠀⠀⢇⠀⢀⣀⣤⡀⠀⠀⠀⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢃⡀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠋⠁
⡀⢠⡄⠀⣀⠀⠀⠀⠀⠂⠈⠢⣄⣠⠇⠀⢠⠷⠀⠐⢄⠀⠀⠀⠀⠠⠊⠀⠀⠀⠙⢄⠀⠀⠀⠀⢀⠔⠁⢀⠀⠁⠀⠀⠀⠈⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀
⠉⠲⡀⠈⠛⠀⠀⠀⠀⣶⡄⠆⢀⣀⡤⠤⣄⣀⠘⠃⠀⠉⠃⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠲⡤⠂⠁⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢠⠞⠉
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠛⠁⠀⠀⠰⠟⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠏
⠀⠀⢨⠀⠀⠻⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⠀⠠⠆⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠘
⠀⠀⡜⠀⡀⠀⢠⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠞⠁⠀⠀⠀⠀⠈⠳⡀⠀⠈⠀⠀⠀⠀⠰⡖⠀⠀⠈⣛⠅⠀⠀⠀⣶⠀⠀⠘⠁⠀⠡⡀
⢀⠜⠀⠘⠛⠀⢀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠊⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢠⡀⠀⠀⢀⠤⢤⡀⠀⣠⠄⠀⠀⢀⡀⠀⠀⣀⡤⣤⣁⠀⠉⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⣶⡏⢠⣿⣿⣀⣤⢤⣤⡤⢤⣄⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢾⠇⠿⠁⠊⡛⣩⠉⡿⠈⣤⢱⠈⡌⠟⣽⢁⡟⣿⣤⠖⠚⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⡆⠀⣶⡀⢿⣇⣩⣀⡅⢠⣀⡆⢠⣠⣷⡤⠈⣁⣾⡏⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢿⣧⣀⣴⣿⣷⣿⣿⣿⣿⣿⣌⡿⣷⣬⠿⣏⢈⣸⣿⣿⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⡶⠶⣦⠀⠙⣿⡟⢛⡿⠛⣟⠉⣉⡉⠀⠻⠇⢰⣿⣿⣿⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢠⡟⠀⢸⣿⡇⠀⣾⠇⢀⣿⡇⢼⣇⢈⠉⣨⣿⠁⣾⣿⠀⡿⠁⢀⣿⢿⡇⠀⢰⣿⡇
⠀⠀⠀⠀⠀⢸⣧⡀⢸⣿⠃⠸⢋⡠⢿⣿⠁⣾⡿⡘⠀⣿⠏⠀⠿⠃⠀⢡⡇⠈⠛⣸⣇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⠾⣿⡀⢰⣿⣿⠀⢹⠀⠉⢡⣧⡀⢀⣼⣤⣤⣾⣦⣾⣿⣦⣶⣿⣿⡀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⠛⠟⠛⠁⢀⣼⡷⠶⠿⣿⣿⣿⡿⠿⣿⢿⣿⠟⣿⡟⢹⠿⣿⡿⠛⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⣠⣤⣴⡟⢁⣴⠀⢰⣦⠙⡿⠁⣴⡄⢸⡟⠀⣿⠀⣾⠆⠈⣷⡀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣿⣆⣸⡟⠀⣿⡿⠀⣇⠀⠉⡀⠈⢁⠀⢁⠄⠋⢀⣴⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢹⣇⠀⡻⠃⢠⣿⣦⣴⣿⣶⡾⢋⡥⠀⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⠋⠁⣠⣿⣿⠛⠛⠋⣿⡀⠈⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣶⣿⣿⠟⠁⠀⠀⠀⢻⣷⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⠀⠤
⠀⠀⢍⠑⠀⠀⠀⠀⠐⠁⠀⠀⢠⠀⠀⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢀⠠⠒⢃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠐⢄⠀⠀⠠⠤⡄⠀⠀⠀⠉⠀⠀⢀⠀⠘⢄⠒⠈⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠐⠂⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⡁
⠀⠀⠀⠀⡇⢀⠀⣤⠀⣇⠨⣀⠀⢰⠀⠀⠀⡆⠠⠀⡏⢠⠂⡄⢰⠂⡀⠀⢰⠀⠀⠀⢠⠀⡀⠀⠁
⠀⢠⠀⠸⠃⠈⣸⠓⠂⢻⠀⣇⡠⠀⡇⠀⠀⡏⠑⠀⠇⢸⠃⠀⠸⠀⡇⠀⢸⡀⢀⣞⠈⢷⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠉⠀⠀⠀⠈⠀⡄⠀⠀⠁⠀⠀⠀⠊⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠠⢀⠀⠀⠔⢀⡀⠀⠀⠀⠀⢖⠆⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠁⠀⠀⢠⠈⢈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠩⢥⠂⢇⠀⠀⠀⠄⠄
⠀⠀⠀⠀⢈⠐⠊⠀⠀⠀⡀⠀⠀⠠⠀⣶⠀⠀⠀⠀⠀⠘⣀⣀⣠⢤⠼⠄⠀⠀⠢⡀⡠⠁⠀⠀⠠⠂
⠁⠀⠁⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⢰⡄⠀⣤⠀⣰⣿⣀⡀
⠀⠀⠀⠀⠈⠳⠤⠝⢲⡿⠉⣀⠿⢂⡀
⠀⠀⠀⠀⠠⣾⡿⢠⣿⠃⠐⠋⢀⢽⡇⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠿⠄⠻⠧⠄⠀⠀⠣⠾⠃⠀⠸⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣾⣿⠧⠀⠒⠒⠒⠋⠉⠓⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣀⣀⠀⠀⣈⣑⡒⠀⠘⠏⡇⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢣⠞⢁⣼⢶⣾⠟⢩⣿⣿⠂⣰⣫⣿⠆⣼⣿⠃⠀⣰⣿⠂⢀⣾⡆⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢋⡞⣽⡟⣿⢏⡴⣿⡿⢃⡴⢳⣿⠃⣸⣿⠃⡠⣾⡿⠁⣠⣾⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠈⠛⠋⠀⠙⠋⠀⠙⠷⠋⠀⠈⠓⠊⠉⠛⠊⠀⠘⠃⢊⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣀⠤⢒⣾⠏⠒⢄⡀⠀⠀⢀⣤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣰⡿⠀⠀⣿⣠⣄⡀⡞⠁⣠⣾⠃⠀⠀⠀⠳⣄⠀⠸⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣀⣠⣿⠓⢀⣿⠆⠀⠘⣃⡙⠛⠋⣵⡞⢓⠀⠀⠀⠘⢦⣀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⡠⢾⣏⣴⣿⢋⣿⠗⣿⠰⣿⠒⡡⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠻⠃⠈⠉⣸⣏⠜⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⣿⣿⣷⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠈⠳⢄⡀
⠀⠀⢰⡶⠒⠶⠦⣤⣴⠆⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠂⢹⠓⢦
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⣦⣶⡖⡶⢰⣰⢴⢶⣰⡆⢦⠆⢀⡖⢰⠀⡦⣶⣦⣦⢰⣶⢲⡆
⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠛⠛⠛⠛⠃⠃⠘⠙⠘⠚⠛⠛⠘⠀⠈⠓⠘⠒⠛⠃⠘⠙⠚⠙⠘⠃
⠀⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⢰⣦⠖⡴⣦⣶⣶⢶⡂
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠉⠓⠙⠋⠋⠋⠚⠁⠀⠀⠀⣰⣿⣿⣦⠀⠀⢀⣶⣿⣷⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣶⣾⣿⡿⠛⠃
⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⢿⣿⣷⡄
⠀⠀⠀⠈⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⠀⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⢠⡄⠀⣠⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠘⡿⠷⠀⠀⠀⠈⠁⠀⠉⠀⣶⠀⡟⠀⠆⡀⠀⠸⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠃⠀⠀⠀⠀⢀⡀⠒⢀⠀⠀⠀⡄⠀⠛⠀⠀⠀⠁⠁⠀⡤⠀⠀⠒⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⠆⠀⠀⠀⠀⠀⠀⢰⡆⠀⠈⢁⡒⠈⠀⠀⠀⠀⠀⠀⠀⣤⣼⣦⡄⠀⠀⡴⣠⠀⠰⠟⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⢴⣶⡶⠶⠂⠀⠀⠁⠀⠀⠈⠁⢰⣷⣰⣦⢠⡞⠀⠀⡼⠻⡏⠀⠀⠘⠱⠃⠀⠀⠀⠀⢀⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠀⠀⣠⠟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠟⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠘⣬⠃⠀⣠⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠘⠃⠀⠾⢧⡤⠀⠀⣸⣿⠟⠳⣆⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠲⠌⠀⠀⡀⠀⠀⣰⠟⠁⠀⢠⣿⡿⠀⣠⡟⠀⣾⠋⢻⠀⠿⠟⠛⢹⣿⠋⣩⡍⠉⠉⠀⣀⡀⠀⠀⠘⠃⠀⠀⢠⣾⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠁⠀⠀⠀⣼⣿⡿⠿⠋⠀⠀⠈⢹⠟⢛⣿⠆⢠⣿⡏⢠⣿⠃⠀⣠⢾⣿⠁⠀⣀⡀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣷⡤⠄⠀⠘⠃⠀⠀⣿⣿⠁⣴⢏⣿⠏⣰⠋⢠⣿⠏⢠⣿⣿⠀⢸⣯⠴⠋⣀⣿⣿⠶⠛⠋⠀⠀⠰⠀⠀⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠟⠹⠏⠀⢀⣀⠀⠀⠀⢸⣿⣿⠀⠿⠋⠻⠞⠁⢠⣿⠏⠀⣾⣿⡇⠀⠀⢀⣴⠟⣻⣿⠃⠀⠀⢠⢀⠀⠀⠀⠀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠰⠆⠀⢶⣿⡛⠉⠀⠀⠀⢸⣿⡏⠀⢚⣛⣛⡀⠀⣸⣿⠀⠀⣿⣿⠁⠀⢰⣟⠁⢠⣿⠏⠀⠀⠐⠂⡌⠀⠀⢹⣾⣷⠶
⠀⠀⠀⠀⠀⠈⡋⠰⠆⠀⣠⡾⠟⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⠁⠀⠀⠘⠿⠶⠿⠋⠀⠀⠀⢀⡀⠀⠀⠀⠘⠙⠇
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⢀⠀⠀⠀⠙⠀⢀⣀⣤⣴⣶⡶⠶⠶⠶⢶⣦⠀⠀⠙⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣾⡤⢶⡇⠀⠀⠀⠐⠖⠒
⠀⠀⠀⠀⠀⠠⠶⠶⠓⠀⠀⠀⠈⡄⠀⠀⠀⡾⠟⠛⢉⣿⠇⢀⡄⠀⠀⢠⣶⠀⠀⣴⢻⣿⠇⢀⣤⣶⠶⡄⠀⠀⠀⠀⣾⣤⠞⠃⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣈⠁⠀⣠⣿⣿⢂⡾⢁⣿⡟⣰⣿⡟⢁⡴⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠿⠀⠀⠀⠀⠒⠀⠂⠀⢠⣿⡇⢠⣿⢀⡞⣿⡿⢻⡿⠁⣸⣿⠃⣿⡿⠛⠋⠀⢀⡤⠀⠀⠀⠀⠂⣈
⠀⠀⠀⠀⠀⠀⠀⢤⠄⠴⠀⠀⣀⣴⠆⠀⠀⠀⠀⢸⣿⠀⠘⣿⠟⢰⣿⡇⠀⠀⢀⣿⣿⠀⣿⣧⡀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠘⠛⠓⣶⠆⠀⠀⠀⠸⠿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⡇⠀⠈⠛⠛⠉⠀⠀⠀⠐⣾⣷⠂⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⠿⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠉⠁⠀⠀⠀⢠⡄⠀⠀⢀⠀⠁⠈⠀⣩⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠆⠀⠀⡀⣀⠀⠀⠀⠖⠀⠀⣠⡄⠀⣀⣀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⣄⢀⡴⠀⠈⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⠞⠁⠷⠚⠁⣿⠀⢀⠀⠰⣶⣿⡤⠀⠸⠃⠹⠞⠀⠀⠰⣌⠳⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠆⠀⠀⠀⡰⠀⠤⠀⠘⠀⠀⠀⠀⠋⠻⠀⠀⡤⡐⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠉⣠⣦⡀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠀⠀⠀⠘⠀⠁⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⠀⡀⡀⡠⢸⠠⡂⢠⠠⡀⡄⡂⠄⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢖⠂⣆⠗⠁⠇⠀⠣⠸⠀⠚⠘⠀⠃⠃⠁⠀⠀⡏⢀⠇⠄⠐⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠤⠄⠤⢄⠈⠁⠀⠈⢁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠎⠉⠀⠁⠈⠀⢀⣀⠀⠈⠑⠒⠖⠢⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⠉⠁⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⡉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠐⠢⠭⢥⡝⠀⠀⠁⠀⣀⠖⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠄
⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠷⣮⡍⠁⠈⢣⠀⢀⣀⠆⠁⠀⠈⠙⠔⠆⠤⠤⠦⠀⠀⢀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⠆⠋⠁⠀⠀⠀⢹⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢇⠀⢁⠏⡼⠀⠀⠀⠀⠀⠠⡘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⠀⠀⠀⠀⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠈⢢⣀⠜⠀⠀⠶⠀⠀⠀⡀⡄⢂⠀⠀⠀⠰⡇⠀⠀⠀⠠⠦⠀⠀⠣⣤⢠⡀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⣦⣀⠀⠀⠀⠀⠀⢀⣠⠞⠓⢤⣀⠀⠐⠐⠀⠀⠀⠀⢀⡠⠔⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠐⠒⢲⣙⠷⡀⠈⠑⠀⠓⠋⠁⠀⠒⠒⠂⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⡿⠃⠀⠸⠄⢠⣆⠀⠀⠀⣀⠀⣀⠐⠤⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⣈⠀⠛⠂⢸⠀⠉⠉⠂⠴⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⢀⠄⠉⠁⠰⠦⢼⡀⢀⢀⠀⡀⡀⢄⡒⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠃⠴⠻⠦⠐⠛⠒⠀⠀⢘⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠐⠀⠀⢀⠀⡀⠐⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡁⠀⢈⢩⡀⠀⠀⡀⣄⡄⠀⢈⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠂⠀⠀⠀⠀⡐⠆⠘⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠉⠀⠈⠠⠈⣅⠀⡀⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠂⠰⠀⠀⣠⡄⠀⠀⠀⠐⢨⠓⠤⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠒⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⠈⠃⠄⠂⠀⠀⠀⠀⠀⠀⢀⠅⠸⠠⠇⠕⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡓⢞⠗⠋⠂⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠈⠁⠀⠀⠀⠀⠀⠀⡅⢸⢸⠂⠁⢀⠈⠁⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠄⠃⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠄⠀⠀⠄⠠⠈⠂⠀⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⣀⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠠⠔⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠈⠁⠰⠀⠀⡀⢀⠀⠰⠄⠀⠀⠀⠀⣀⠄⡁⠀⢀⠰⠂⠀⠀⠀⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠈⠁⠀⠀⠀⢹⣞⣅⡨⠶⠃⠄⠀⠀⠀⠀⠀⡀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠔⠀⠀⡀⠀⠀⠀⠻⢧⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠓⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⣦⡄⠀⠀⠀⢀⣤⣄⠀⣀⣤⣿⣆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣙⠗⠛⣠⣄⣠⣶⡄⠀⢰⡟⠉⠀⢶⣄⣼⠇⣶⡄⠀⣿⡁⣿⠿⢿⡍⠀⠙⠛⣷
⠀⠀⠀⠀⠀⠀⣤⣶⠿⢻⡟⢋⣩⡿⢿⡇⠀⠈⠃⠀⠀⢿⡿⢋⣠⣿⣿⡶⣿⣿⣟⣀⣈⣿⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⢛⣿⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠈⢩⣿⠈⠿⠘⠿⠛⠋⣩⣌⠁⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢿⣻⣹⡿⠀⠀⠀⠀⠀⠀⣀⣉⡀⠈⡋⠀⠀⢠⣄⠀⣾⠏⢁⣀⣤⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡙⣻⡇⠀⠀⣠⣴⡶⢿⣟⠉⣥⡀⢹⣆⣀⣼⣿⠀⣿⡾⠟⠛⢉⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠿⠃⠀⠀⠈⠀⠀⠈⣿⡀⢸⣧⠈⣿⠛⠉⠹⡧⠈⠻⠶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⣶⢶⣄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠓⠀⠻⠋⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣶⡾⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡐⠀⠐⠒⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢟⣛⣩⣭⣭⣛⣓⡀⠀⠀⠀⢮⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⠵⣾⢿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡼⠁⠈⠀⠀⠀⠀⠐⠒⠲⠄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⢀⠤⡀⠀⠔⡡⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⣄⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠃⠀⠈⢀⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⢰⠚⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⣄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢙⠂⠤⠞⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⣠⠔⣻⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢠⢂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢇⡉⣉⡠⣺⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡠⠚⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⣌⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⣀⣠⡴⢾⠁⠒⠒⠉⣁⡠⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢋⡀⢀⡞⢰⠒⠊⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠒⠒⠒⠉⣀⣤⡆⠀⠉⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡴⠂⠤⠤⠤⠤⠖⠚⠦⠔⠒⠋⠁⡼⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⠈⠙⠲⠤⣀⡉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠲⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣄⢀⣀⣠⠋⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡭⢷⡄⠀⢀⣀⣀⣀⣈⠑⠲⠦⢤⣤⣀⣀⡀⠀⣀⡁⠀⠀⠀⠀⠀⢸⠀⡟⠈⠀⠀⠈⠉⠉⠉
⠀⠀⠒⠄⠀⠀⠀⠀⠀⡰⢮⡠⠚⠁⠀⠀⠛⠉⠉⠉⠁⠈⠉⠁⠢⢤⣀⡀⢀⠉⠉⠉⠉⠴⡦⠀⠀⠀⢠⠋⡰⠃
⠘⢌⠢⡀⠈⠑⠢⢄⡘⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⣸⠣⠤⠔⣊⡭⠛⠁
⠀⠈⠱⣈⠢⡀⠀⠀⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠏⠙⠋⠉⠁
⠀⠀⠀⠈⠑⢌⠳⢄⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠾⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣿⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣡⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢼⣿⠿⢛⣹⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢸⣥⣶⣿⣿⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠣⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠱⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣾⣿⣿⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣿⣿⣧⣿⣿⣿⣿⣷⣶⢲⣶⣶⢲⣶⣿⣿⣿⣿⣧⣿⣿⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣹⣿⣿⣸⣿⣿⣸⣿⣿⢸⣿⣿⢸⣿⣿⣼⣿⣿⣹⣿⣿⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣿⣿⡏⣿⣿⣿⣿⣿⣼⣿⣿⣸⣿⣿⣿⣿⡏⣿⣿⣇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣷⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢿⣿⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣾⣿⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡾⣿⣇⣿⣿⢹⣿⡿⣿⣿⣿⣿⢸⣿⣧⣿⡿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⢿⢽⣿⣽⣿⡟⣿⡏⣿⣿⣿⣿⢽⠿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠠⠀⢠⡄⠀⠀⠂⠀⠂⠀⠀⠄⠀⢁⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠃⠀⠱⠀⠀⠛⠀⡢⠀⢀⠐⠛⠀⠐⢆⢨⠃⠀⠀⠒⠀⠀⠈⠁⢄⡄⡐⠀⠠⠾⢦⡃
⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⡀⠀⠀⠐⠂⠀⠱⠀⠢⢃⣀⠀⠀⡀⠀⠀⡄⣨⠀⣀⠰⠀⠀⣀⠀⠀⠀⡀⠀⠀⡀⠔⢀⠀⠄⢀⠎⢀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠀⠀⠑⡀⠰⡏⠠⠀⠰⠊⠃⡈⣤⠀⠉⠀⠄⢠⠉⠀⠋⠀⠠⠁⠀⠗⠰⠉⡀⢴⠈⠃⠨⠦⢔⠁⡀
⠀⠀⠀⠀⠀⠠⠄⠀⠴⠀⠀⠀⠢⠠⠆⠀⢀⠈⢃⠐⠃⠀⡁⠉⠀⠶⠗⠈⡀⠀⠔⠓⠀⠀⢤⡞⠑⠃⠀⢄⡤⠘⠀⠠⢀⡀⠐⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠴⠐⢀⠐⣎⢹⡀⠂⠀⠀⣴⠀⠂⠠⠀⠀⢹⣀⡨⠋⡀⢤⠌⡅⠂⠀⠡⣀⡀⠀⠈⠀⠀⠀⠛⣀⡖⢲⠀⢃
⠀⠀⠀⠀⠀⠀⡀⢄⠃⠘⠷⡆⠀⠀⠁⡁⠀⠀⠀⠐⡊⠀⣀⠀⠀⠀⠀⠄⢀⣄⠁⠂⠁⡀⢰⢈⡆⠈⠆⠎⠀⠞⢀⠠⠉⠈⠉⡉⠉⠀⠄⠁⡀
⠀⠀⠀⠀⠀⠘⢯⠀⠑⠂⠀⠅⠘⠁⢀⡈⠀⢦⡼⠋⠐⣀⣁⣴⠀⠒⠈⠁⢀⢠⡄⠒⠈⠉⢀⠡⠀⠀⠰⢐⠃⠈⡁⠀⠰⠥⠂⡡⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠐⠀⠀⡀⠀⢠⡄⢀⠐⡠⠣⠄⠸⠅⠘⢢⠀⢤⠀⠠⠄⠀⠃⠀⣗⠄⠈⠓⠠⠁⢀⠈⢁⠐⠚⠢⠊⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠣⡀⠀⠀⢀⣦⠘⠈⢁⢁⠀⠆⠠⠇⠀⠀⢢⡄⠀⡀⡈⠀⡤⠀⡰⠀⡀⠈⡀⠀⠄⢠⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⢌⢩⠃⠁⡀⠤⠀⢂⠰⠆⠙⠀⠞⢃⠀⢈⡛⠐⢦⡀⠄⠠⠀⣀⠀⠷⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣁⣈⠤⠤⠤⢶⡖⣢⡺⠄⠂⠖⡒⠶⠲⡗⢳⠠⠄⠤⢏⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠙⠑⠒⠺⡀⠀⠀⠀⣂⣄⣇⣨⣇⣠⠖⠳⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣇⠠⠐⣸⡅⠒⣨⣧⣬⣶⡾⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⠈⠀⠙⢹⠛⣿⡁⣉⡀⣤⡈⣩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⢁⠀⠀⠀⠆⢳⣟⣁⣉⣉⣉⣊⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡊⢀⠵⠀⠀⠀⠀⠨⠋⡏⠉⡏⠈⠝⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠄⡇⠀⠀⠀⠀⡠⣃⠀⢱⠀⠕⢑⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⡀⠀⠀⠀⠀⠐⠄⡪⠀⠐⢽⠀⠀⠘⠀⠰⢺⠀⢻⢂⠢⠔⠊⢔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠉⠉⠉⠚⠚⠑⠛⣘⣀⣀⠧⠬⠚⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠀⣀⠀⠀⠀⠄⡀⢀⠀⠀⢀⠀⠀⢀⠄⡠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠊⠀⠁⠈⠐⠁⠀⠊⠂⠀⠐

⠰⢶⡤⢀⣤⠂⡄⠀⢂⣄⡠⢤⣠⡤⠀⠀⠀⠴⠤⢤⢤⠀⠀⠀⣶⣀⣢⣦⢄⣶⠲⠶⠖⠒⠒⢒⣲⣶⢶⣖⣲⣶⠶
⠈⡌⠅⠀⢀⣑⠢⠀⢛⡴⢚⡥⢄⠈⠐⠯⠌⠱⣎⠴⡐⠀⠀⠈⠋⠀⠐⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠟⠟⢋⣴
⠀⡴⡠⠊⠁⠀⠉⠳⣄⠀⠁⠁⠙⢄⠀⠀⠀⡠⢣⠁⠀⠀⢀⠀⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣈⣨
⠀⢣⠁⠀⠀⠀⠀⠀⢸⢦⠀⠀⠀⡈⠽⠒⠋⠀⠁⠀⠀⠀⢸⢳⡻⠠⡄⠰⣸⢆⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢉⠧⣿
⢀⡿⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡇⣰⣇⡨⢐⠁⠀⡇⠀⠀⠀⠀⡤⠄⡀⣀⣈⠋⢸
⠀⢇⠃⠀⠀⠀⣠⠋⢀⠏⡇⠀⢠⠃⠀⢀⠠⢀⡀⠀⠀⠀⠀⡤⣤⠄⢀⣡⡬⢄⡀⠀⠀⠀⠀⠸⡀⠀⠸⠁⢸⠀⢸
⠀⢫⡓⢤⡔⠊⠁⢠⠎⢠⣁⡔⠁⠀⠀⠀⣗⠄⡸⢶⠀⣌⢿⠀⠸⠤⣄⠀⣗⢣⢱⢄⡀⠠⡆⠐⡟⢦⡀⢀⣏⠤⠚
⠀⠀⠂⢹⠩⠂⠐⠁⢀⢞⠞⠀⠀⠀⠀⠁⣄⠫⠀⡇⠀⡞⠁⢰⢸⡇⣿⠀⢙⡜⡸⣤⡛⡀⡧⡄⡇⢀⡏⠁⠘⠗⡁
⢀⢀⠃⠘⢢⡀⡀⣀⠊⠁⠀⠀⠀⠀⠀⠰⠌⠔⠁⠃⠈⠃⠀⠛⠘⠃⢩⣴⡫⠞⠁⣹⡾⠷⢿⢇⠣⣀⠑⠐⠒⠱⢹
⢸⣦⠄⢨⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣤⣄⡺⠃⠀⠉⠀⠀⠀⠂⢸
⠀⠛⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢠⠀⠀⠀⠀⢸
⢀⡌⡀⣸⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⠈⠀⠌⠀⠀⠀⢸
⢀⢷⢠⠃⠀⠀⠉⠲⣀⣀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠌⠀⡞⠀⠠⠄⠀⠸
⠨⡺⠸⣀⠤⠖⠲⢄⡿⠉⢹⠞⠉⠁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠲⠟⠈⠁⠁⠉⠈⠐⠃⡄⡤
⠀⠰⢀⢸⡏⡿⠯⠽⠧⢤⣼⣓⣦⣄⡂⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠂⠐⣤⠊⠈⣆⡔⠉⡍⠐⡀
⠀⢀⠀⢶⠿⡇⠀⠀⠀⢸⡇⠀⢈⠇⠉⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡍⠄
⠀⢠⠀⠀⠃⡇⠀⠀⡇⢸⠇⠀⢸⠀⣤⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠒⠶⠶⣶⣒⣒⣒⣀⡚⠶⠎⠑
⠀⠀⡄⠀⣠⡇⠀⠀⡇⢸⠀⠀⡆⣀⠈⠉⠉⠙⠒⠶⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢒
⠀⠀⠓⣶⢛⡇⠀⠀⡇⡜⠀⠀⠁⡘⢠⠀⡎⠓⠒⠢⠤⠤⠢⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⡀⠀⢠⠋
⠀⠁⡘⠤⠤⣷⣶⣶⡷⠷⠤⡞⠡⣇⣀⠻⠤⢀⣀⡀⠀⠀⢀⣇⡀⠂⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣
⢀⠄⠶⠯⠤⣤⣤⡬⢥⢤⣬⢽⠇⢒⡒⢶⣖⣲⣶⣤⣤⡼⠟⣲⡯⠙⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠂⠎⠣⠈⠀⠘⠐⠀⠊⠂⠣⠔⠉⠃⠢⠄⠒⠿⠛⠆⠓⠊⠈⠣⠤⠤⠤⠤⠤⠐⠒⠒⠁⠉⠉⠁⠑⠒⠠⠤⠤⠊
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣿⣵⣶⣌⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⣻⣿⣿⣿⣿⣿⣷⡀⢙⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⣿⣽⣿⣿⡗⡸⡿⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡯⠉⠀⠀⠀⠀⠀⠉⠻⣿⣿⠇⢹⢳⣇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⣤⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⣠⣤⣤⡀⠘⣿⣯⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣟⡂⠀⠀⠉⠙⠛⠷⠆⠀⢹⣿⣿⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣣⣄⠠
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣯⠳
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⢤⠀⠀⠀⢰⣴⣿⡿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠠⠹⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⡠⠐⢹⣿⣿⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢫⡑⠒⠒⠈⠁⠀⠀⢸⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢮⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠨⠂⠠⠀⠬⣔⡀⡀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠍⠳⣦⡄
⠀⠀⢔⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠉⠀⠀⠘⡆⠀⠀⠀⢾⣿⠿⣿⡀⠀⠀⠹⣿⡀
⠀⠀⠀⢄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢸⡟⣀⡘⣿⠠⠴⠂⠙⠣
⠀⠀⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠀⠟⠋⠋⠀⠈
⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠘⠀⠀⠀⠰⠶⠄
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠌⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠂⠙⢄
⠀⠰⠀⠀⠀⠀⠉⠐⠒⠀⠒⠂⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠤⢄⡀⠀⠒⠠⠐⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶⠁
⠀⠀⠈⠿⡁⠲⢤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⣀⡤⠶⡎⠁⢰⡄
⠀⠀⠀⢸⠃⠀⢠⠂⠀⠈⠁⠐⠂⠤⠄⣀⠠⠀⠀⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠤⡐⠂⠁⠀⠀⠀⡁
⠀⠀⠀⠸⣣⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠱⠄⠀⠀⢇⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⠀⠀⠀⢹⡟⣼⡂
⠀⠀⠀⠛⠁⠀⠿⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠃⠀⠀⠀⠀⠈⢦⠀⠈⢦⠀⢀⡠⠞⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠉⠑⠠⠀⠀⠃⣀⠄⠲⠒⠲⠀⠷⣀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠡⠠⠏⢁⠔⠚⠂⠀⠒⠠⣍⠃⡀⢀⠄⠄⠀⠦⢄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡇⠰⠁⠀⠀⠀⠀⠠⠀⠀⢠⡗⠁⠀⠀⠀⠀⠀⢣⠀⢀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠄⠀⠀⠀⠀⢠⢁⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠘⠂⠀⢶⡶⠶⠶⠶⠾⠁⣠⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠠⠀⣄⡐⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡑⠤⡀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⣠⣞⠁⠀⠀⠀⠞⢋⡵⡋⠖⣇
⠀⠀⠀⠠⢀⠀⠀⠀⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠣⣀⠀⠋⢘⡣⢑⢦⠀⣀⠽⠢⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠲⠄⠁⠀⠀⠀⠘⢃⠠⡀⠀⠀⠴⠀⠁⠀⡀⠀⠀⢠⠉⠑⢄⢃⠉⠃⠈⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢺⠀⡜⠉⠋⠉⠋⠓⠙⢹⠇⠐⠀⠠⠂⠀⠒⠀⠂⠐⠂⠈⢋⣠⣀⡀⣷⠒⢋⠠⡀⠠⠂⠉⢱⡠⣄
⠀⠀⠠⠀⠀⠀⠀⢸⡐⠅⠠⣂⠀⡠⠀⠀⠨⠜⠃⠀⠀⠑⠀⠀⠐⠃⠀⠰⠀⠀⠀⠉⠛⠁⢽⣉⠋⢝⣺⠛⠛⢦⠂⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡣⠈⠇⠀⡀⠉⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠈⢱⠀⠸⣆⠀⠮⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⡀⠒⢺⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⠆⠊⢩⠺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠤⠀⠉⠂⠤⢀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⢀⠸⡀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠓⠦⣄⡀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠠⢀⡉⠐⠂⠠⠤⠤⠤⠄⠒⠈⢀⣠⠔⠊⠀⠀⠀⠀⠉⠓⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⢸⠉⠙⠓⠒⠒⠒⠒⠂⢩⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠠⠄⠐⠒⠃⠃⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠤⠄⠒⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⢠⠄⠀⠀⠼⠀⠀⠀⠐⢀⠀⠀⠄⠀⠀⠀⠑⠖⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⢧⠀⠀⠀⠈⢂⠀⠀⠀⠀⠄
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠱⠤⠀⠤⠂⠀⠀⠙⠦⣤⡄⠞⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣾⣷⣿⣶⡷⢾⣾⣿⣿⣿⣿⣿⣷⣶⣿⣾⣾⣿⣿⣿⣿⣶⣶⣶⣿⣷⣿⣾⣷⣶⣶⣶⣾⢿⡶⠾⠿⢶⣶⡶⢿⣾⠿⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⠰⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⣀⡀⠀⠐
⠀⠀⠐⠂⠀⠀⡶⠀⠀⠚⠀⠀⠤⠉⢠⠀⠂⠐⠐⢀⡁⢂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⣀
⠀⠂⠀⠀⢀⠀⠔⠀⠀⠀⠀⣘⠀⡌⠀⠄⠀⠀⠀⠀⠠⡌⣀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠦⠀⡀⠀⠄⠠⠀⠄⠉⡐⠙⢦⠂⠀⠀⠀⠀⠃⠀⡀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠠⠀⢀⠀⢀⡐⢂⡙⠇⠉⠓⠀⠠⢋⡁⠀⠀⠀⠀⠈⢀⠀⠰⢆⠀⠆⠀⠁⠐⢀⠂⠁⢨⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢡⣌⠀⡇⠸⢃⣀⡀⢠⠁⡁⠀⠑⠐⠃⠸⡄⠀⠀⠀⡄⠀⠃⠀⠀⠘⠀⣶⠀⠁⢰⠇⢀⠂⠁⠐⢁⠀⠀⠂⠀⠀⡄
⠀⠀⠀⠀⠉⠐⠀⠀⠂⠈⠑⠒⠉⠀⠀⠉⠉⢁⢀⢀⠁⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡉⠉⠀⠀⠈⠀⠉⠢⢀⠄⠁⠈⠁⠀⠁⠰⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡉⢻⠀⠀⠀⠀⠄⢘⠐⠐⠈⠀⠇⠀⢸⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢭⡤⠶⠚⠠⣀
⠀⠀⠀⠀⣀⣇⣇⡀⠀⠈⢀⣹⣀⡀⠀⣀⠀⠀⠀⣀⣀⠀⢁⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠀⢄⠀⠢⡝⢦⠀⠈
⠀⠀⠀⠁⠈⠀⠀⢀⠘⠇⢉⠔⠁⠀⢠⢸⠆⠀⠀⢀⠀⠀⠀⠃⢀⡂⠀⠀⠀⠀⠀⠀⡸⠋⣟⠀⠉⠻⠛⠛⠀⠀⠈⢡⠐⠦⢅⠀⣠⠄⢸⠆
⠀⠀⠤⢘⠂⠀⢨⣉⠇⢰⠁⠀⠀⠠⢀⣌⠇⠀⠀⠈⠀⠀⡠⢿⡀⠉⢧⠀⢀⡀⠀⡽⠀⡐⠁⠈⠐⠆⠀⠄⠀⠀⠀⠀⠁⢄⣰⠃⠀⢻⠔
⠀⠀⠀⠈⢆⡤⠀⠐⡀⠘⠦⠤⠀⠀⡌⠀⠀⠀⠀⠄⢐⣊⡠⠊⠱⣄⠀⠉⠁⠉⠉⢀⠔⠁⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠖⠂⠔⠘⠃⠀⠀⠀⠀⠀⢖⡋⡀⢠⡦⢘⢏⠙⠑⠒⠒⠘⠀⠀⠀⢠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠭⠄⠐⠉⠀⠀⠀⠀⠀⢄⢀⠠⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣄⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⣿⣿⡄⠀⠀⠀⠀⠀⣿⣧⢀⣤⠤⢤⡈⠛⠛⠻⠷⠶⠶⢶⣿⣿⣦⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⣹⣿⠈⠛⠒⠒⢻⡖⠒⢶⣄⠀⠀⢸⣿⡟⠀⠀⠀⠉⠉⠉⠙⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢈⡇⠀⢸⣿⡇⠀⣾⣿⠁⠀⢀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢸⠃⠀⢸⣿⠃⢠⣿⡟⠀⠀⣾⡟⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣠⡿⢃⣴⠗⣶⡿⠀⢸⠀⠀⣿⡿⠀⢸⣿⠇⠀⣸⡿⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢀⡴⠟⢁⣾⠏⢠⣿⠇⠀⠺⠀⢰⣿⠇⠀⣿⣿⠀⠀⣿⠇⠀⢀⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠋⠀⠀⣼⡏⠀⣼⣿⠀⠀⡇⠀⣼⣿⠀⠀⣿⣿⠀⠀⢿⡀⣠⢫⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣿⠀⢰⠻⣿⠀⣸⠁⠀⣿⡇⠀⠀⠹⣿⠀⠀⠈⣉⣡⣿⡿⠤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⢿⣀⠆⠀⠙⠶⠃⠀⠀⠻⡇⠀⠀⢀⡠⠔⠊⠉⣠⣿⠏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⢀⣀⣥⣴⣶⣤⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⡿⠟⠛⠉⠁⠀⠁⢸⣿⠀⠀⡎⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠁⠀⠀⢰⣶⠄⠀⠀⣿⣿⠀⠀⠙⠛⠉⠁⠀⠀⢠⣶⣿⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⣿⣿⣿⡆⠀⢀⣘⠃⠀⠀⢸⣿⡏⠀⣠⡀⢠⢺⣿⠂⣰⣿⠟⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⢹⣿⣿⡇⠀⣾⣿⠇⠀⠀⣼⣿⠇⡞⣼⡵⢁⣿⠃⢰⣿⡯⠔⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⡟⠀⠀⢀⣿⣿⡾⠀⠿⠁⣼⡏⠀⣼⡿⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣿⡇⠀⠀⡜⣿⣿⠃⠀⠀⠀⣿⠁⠀⠸⣷⡀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠸⣇⠀⡰⠀⠙⠿⠀⠀⠀⠀⠙⠁⠀⠀⠈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠉⠛⠁⢀⣀⣠⣤⠴⠶⠒⠒⠛⠋⠋⠉⠉⠉⠉⠛⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⣛⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣍⡙⢿⣿⣿⣯⣍⠛⠿⣿⣿⣿⣍⡉⠉⠙⠻⢿⣿⣿⣿⣷⣄⡉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣍⡉⠉⠉⠉⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛
⠈⠙⠿⣶⣄⡙⠿⣿⣷⣤⡈⠛⠿⣿⣿⣦⣄⠀⠀⠉⠻⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⠿⣦⣄⡉⠻⢿⣷⣄⡀⠙⠻⣿⣿⣦⣄⠀⠀⢉⣻⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⡈⠙⠿⣶⣤⡀⠙⠻⣿⣷⣶⣿⣯⣙⡁⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡈⠙⠻⢷⣄⣠⣿⣿⠏⣷⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⢀⣿⣿⣿⢿⠇⢻⢠⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠈⡃⠸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⡇⢘⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⣿⡆⣇⢨⣀⣿⣀⣀⣀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠃⢘⣉⣩⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣄⣀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠈⣿⣿⣿⣿⢋⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢻⣿⣿⡿⠿⣿⣿⣿⣿⣶
⣤⣤⣄⣤⣤⣤⣴⣶⣶⣶⣤⣤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣦⡘⣿⣿⡴⠒⣿⠟⠉⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣄⣈⣀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠒⠀⣈⠙⠻⠿⢿⣷⡌⠙⠁⠀⠁
⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣦⣶⣶⣦⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣛⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⡷⣿⣿⣿⣿⡷⣬⣍⣉⣳⡞⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁
⢿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⡿⣛⣤⣿⡀
⠀⠻⠟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⡇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠘⣿⡉⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣴⣿⢻⣿⡿⢛⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠃⠈⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⠻⢿⣿⣿⣷⣦⣾⣿⣿⣿⡇⠀⢀⡄
⡀⠀⠀⢀⣿⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⣯⠻⢦⣀⠘⡉⠳⠉⢟⢿⣿⣿⡇⢀⣾⠇⠀⣶⠀⢀
⠃⠀⠀⣿⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⡶⢾⣿⣶⣶⣍⠀⠛⣤⠀⡈⠐⣿⡿⠁⣼⣿⠀⠀⠛
⠀⠀⠀⣸⣿⣿⣿⡶⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣷⣤⡉⢷⣿⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⣶⣦
⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠘⣿⣿⠋⣹⣿⣿⣿⠏⡾⠁⠀⠀⠀⠀⠀⠀⠉⢙⡿
⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⣶⣦⠘⣿⣿⢁⣿⣿⡟⣾⠁⠀⠀⠀⠀⠀⠒⠂⠀⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⡀⠈⢿⡀⠀⠹⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣮⣷⡀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⡙⣿⣿⣿⣷⡀⢸⣿⠃⠀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⣯⣽⣷⣿⡯⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓
⣤⣴⠾⢿⣿⣿⣿⣿⣿⡿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠛⠻⢿⣷⣾⡁⠀⠀⠀⠒
⠒⠈⠑⢪⣿⠟⣿⣿⡿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣄⡀
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣆⣺⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆
⣿⠀⠀⠈⠛⠿⣿⣿⣿⠗⠈⠛⠿⣶⣽⣛⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⣿⣦⡀⠀⠀⠀⠀⣿⠋⠂⠀⠀⠀⠰⢯⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢻⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣧⣀⣀⣀⣰⣿⣿⣿⡿⢿⣶⣮⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣦⠀⣤⣿⡿⣿⣿⣿⣿⣷⣸⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⡏⠈⠋⠛⢹⣿⣿⣿⣿⣿⣯⢿⣿⣿⠙⠻⠆⠻⠿⡧⠸⣿⣿⣿⣿⣿⣻⣷⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡜⣷
⣷⣾⣿⠄⣾⢿⣿⣿⣿⣿⣏⣶⣤⣿⠀⠀⠀⠀⠐⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣆
⣼⣧⣤⠀⠉⣀⣽⣿⣿⣿⣿⣬⡿⠁⠀⠀⢾⣿⣿⡷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣌⠁⠀⢠⣾⣟⢻⣿⣿⣿⣿⣭⣇⠀⠘⢣⡄⢬⣩⡇⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡿⠀⠀⠀⠼⣿⡏⠻⣿⣿⣿⣿⣿⠀⠀⠀⠹⣾⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣷⠀⠀⠀⠀⠸⡇⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠙⢿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⢴⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢯⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⡿⣿⡷⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⠾⣷⣿⣷⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣶⣿⣿⣿⣿⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡏⢸⣿⣿⣿⣿⡧⡯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡼⠿⡟⢻⡿⠉⢿⠉⢉⣻⣟⠛⠿⢧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣭⡀⣰⡆⢸⡇⠀⠃⠀⠸⡆⠸⣿⣿⣷⠀⡆⢀⡍⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⡇⢹⣿⠸⡇⢸⡀⢣⠀⡇⢀⣤⡟⢻⠀⣇⢸⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⢸⡿⠀⢻⡀⣷⣼⡄⢷⠈⠛⠳⣾⡀⣿⣄⠿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢛⡛⠿⣿⠛⠛⢿⡿⠾⠷⠖⣛⣥⣽⢿⣿⣷⠾⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠿⠃⢀⡟⠀⠀⠈⣇⠀⣰⡆⢠⡄⢀⣦⡄⠛⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⢲⡾⢿⡇⠀⠛⠀⢿⠀⠛⢀⣼⡇⢸⣿⣿⡆⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⡋⣰⠿⠧⣜⠅⢤⠸⠀⣄⢺⣿⡇⠈⣿⣿⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠶⠞⠛⠷⠟⠳⠼⠷⢶⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠋⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠀⠀⣼⡟⠀⠀⡀⠀⠀⠀⢠⣾⠂⠀⠀⢀⣶⠆⠀⠁⢀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⠛⣿⠂⢠⣿⡗⢩⣿⠀⣾⡧⠊⣿⠂⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠇⢰⡟⢁⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢤⣼⠟⢀⣿⠃⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠘⠛⣽⡏⠙⠋⠁⢰⡿⠙⠛⠉⠀⠀⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⣴⠞⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⡆⢀⣴⡷⠀⠀⢰⣄⠀⠀⣶⠄⠀⠀⠀⠀⠀⠐⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠉⠉⠉⠛⠛⢻⣾⢿⣶⣿⣯⣤⣀⣠⣼⠟⠀⣼⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣼⠏⢠⡿⢁⣭⣭⡍⢉⣡⣤⣴⡟⠀⠀⢠⣴⠶⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⠀⣴⡿⢁⣼⠇⢀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡃⢀⣀⣤⠟⠁⣿⣧⠶⠋⢰⣿⣥⢾⣿⠀⢸⡟⠁⢼⣇⡤⢿⣤⡶⠻⣧⣴⠞⢿⡥⠊⣿⡤⢺⣿⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠐⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣬⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⡀⢠⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣷⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⢀⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⢸⡀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠉⢩⣭⣿⣿⡏⠉⠉⢩⣯⠉⢹⣿⣿⣿⡿⠋⣩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠘⢿⣿⣿⡏⠀⠸⢿⣿⠀⠀⢛⣛⠉⠀⢸⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⡆⠀⢀⣉⠀⢠⣶⣄⣤⣄⢰⣿⣿⣧⢀⣈⡙⠋⠉⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠀⡀⣿⣿⣷⡸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠆⢼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⠀⣿⣿⣿⣿⣿⣧⣙⣛⣉⣀⣹⣿⣿⣿⣿⣿⠋⢠⣤⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⠀⠹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣿⣿⣿⣿⣀⣀⣀⣀⣀⣼

⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣴⣶⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⣀⣀⣤⣤⣤⣤⣤⡄
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⡩⠝⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠉⠀⠉⠉⠉⠉⠉⠉⠁⠈⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⣿⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣴⣒⠒⠲⠚⠋⣠⣤⣤⣤⣤⣀⣤⣤⣶⣶⡶⠿⠿⠻⠻⠛⠟⠻⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛
⠀⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠉⢙⣿⣿⣿⣿⣾⣽⣿⡋⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠃⠀⣼⣿⣿⣿⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⡏⠀⢠⡿⣿⣿⡟⠀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⠃⠀⣾⣒⣼⡟⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣸⣿⣿⠟⢀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⣿⣿⣯⡾⠟⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣽⣿⠁⠀⠀⠸⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠃⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⣿
⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢰⡿⢾⣶⣶⣤⡀⢀⣴⣶⣿⣿⡿⢷⣄⠀⠀⠀⣼⡿⣿⣦⣄⡀⠀⢈⣿⣿⡀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⡏⢀⣼⠃⠀⠀⠀⠙⠻⣿⠿⠟⠉⢀⣽⣷⣼⡟⠀⢀⣿⡇⠀⠉⠛⠿⢷⢾⣿⠛⠀⠀⠀⢠⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠶⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⢀⣀⡀⠾⡿⠯⣄⡌⣠⠤⣼⠇⣯⣄⢀⡤⡟⢀⣄⣠⡀⣤⠀⠀⠀⠀⠹⡿⢿⡀⢀⡀⠀⠀⣸⠀⣀⠀⠀⢀⡀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⠛⠋⠉⠡⠴⠷⠚⠁⠃⠙⠀⠛⠂⠃⠘⠈⠓⠃⠙⢚⣋⠛⠉⣇⠀⠀⠠⢴⡧⠶⠃⠛⠛⠓⠿⠟⠸⡯⢳⡐⣿⡏⢸⠀⠰⠶⠶⠶⠶⠶⠄⠤⢠⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣃⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣉⣷⠀⣈⠁⢠⣄⣠⡀⣸⡃⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣠⢶⡄⢶⣀⣼⡆⠀⠀⠀⠏⣉⡩⠃⢻⣤⠀⡿⠈⠀⣏⠉⢀⣿⣤⡄⠀⣀⡀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠏⡷⠘⣿⠾⠁⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠋⠘⠇⠾⣍⡉⣿⠁⢀⣀⡀
⠀⠀⢀⠀⢰⣄⢠⡞⢳⡦⠀⢹⡟⠁⠀⢹⡆⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢛⣉⡇⠀⢀
⠀⠀⠘⣷⡞⠻⡆⠙⠋⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⣄⣠
⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠋⠠⡏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠀⠸⢆⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠸⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢄⣀⠀⠀⠀⠉⠀⢀⡀⢐⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⠄⢢⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠃⠀⠀⠀⠀⠰⠆⠀⠀⠐⠢⠺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⠒⠤⠤⠤⠀⠒⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⡀⠠⣤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⣠⢷⢁⡴⠋⡠⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⢀⡴⠋⣡⠾⢅⣠⠞⠁⠀⠘⡇
⠀⠸⠓⠂⢠⠒⡉⠲⡄⠀⢠⠖⡉⠉⣲⠀⢀⣀⠒⠁⢀⡤⠊⠁⢀⠔⠁⣠⠞⠁⢠⠇⠀⠀⢶
⠈⠁⠀⠀⠸⢍⣉⠳⣥⣠⠟⠂⢁⣀⣝⣀⣉⣁⣼⠃⠀⠀⢀⠔⠁⡠⠚⠁⠀⠀⠈⣰⡇⠀⠸
⢀⠀⠀⠈⠙⠋⠙⠛⠛⠛⠚⠛⠉⠉⠉⠉⠉⠀⠀⢢⢀⠴⠋⡠⠊⢠⣎⠀⠀⠀⠀⠹⢠⠀⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠤⠊⠀⠀⢸⣿⠀⠀⠀⠀⠀⡿⠀⠀⢠
⠈⡇⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠲⡶⠒⠀⠀⣴⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢃⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⢖⣄⠀⠀⠅⢸⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠘⢁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠇⣻⢿⡇⢷⠆⠘⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⣀⣀⣀⣠⣄⣀⣥⣀⡀⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠁⠲⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠄⠀⠀⠀⠀⠸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⢠⡔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣩⣤⣤⣤⣤⣄⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣿⣿⠁⢰⣿⡟⠀⠀⣀⣀⡀⠀⠀⢰⣿⡆⡠⢲⣦⠀⡀⠀⠀⢀⣙⠓⠀⣰⣿⡗⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⡉⠑⣾⣿⡏⢀⣿⣿⠃⣰⣾⡟⣹⣿⡇⠀⣾⣿⡏⠁⣾⣿⢠⣿⡆⡰⠋⣿⣧⢠⣿⡿⠁⣴⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠃⢠⣿⡟⠙⣿⣿⠇⢸⣿⣟⡰⣿⣿⢁⣼⣿⡟⣀⣼⣿⠃⣼⣿⡟⣀⣴⣿⠇⢸⣿⣡⢊⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢿⣿⡰⠉⠛⠋⠀⠘⠛⢨⣿⡿⠀⠙⠋⠁⢰⣿⡿⠁⠙⠛⣁⣤⡄⠉⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⢾⡏⠉⣷⡄⠸⣿⠃⠀⣀⠀⠀⣿⣿⠁⢀⡀⠐⣿⡇⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢾⣿⡏⠀⢠⣉⠑⠢⢄⣸⣿⡇⢠⣌⠀⠀⣿⣷⠘⣿⡇⠀⢸⣿⡄⠈⠙⠚⣉⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⡰⠋⣿⡆⠀⣉⡁⢀⣿⡿⠀⠀⢀⣿⣿⠃⣼⣿⣆⡴⠟⠁⠀⠈⠁⢀⣿⣿⠃⠀⠀⢸⣿⠁⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡰⣡⡾⠛⠀⢀⡻⠟⠈⣿⣇⠀⠀⣼⣿⠇⢠⣿⡿⢀⣀⠀⠀⠀⣀⣤⣼⣿⠏⠀⢀⣠⣤⣉⡃⢀⣾⣿⠇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠧⠀⢹⣦⡄⠀⣾⣿⠂⡰⢰⣿⡇⢰⣿⡟⠀⣾⣿⡣⢪⣿⡇⢠⣾⡿⢩⣿⡟⢀⣴⣿⠏⣼⣿⡇⣸⣿⠏⢠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠀⠀⢠⣿⡿⢰⣿⡏⡴⠁⣿⣿⢁⢼⣿⢁⠜⣿⣿⠁⣼⣿⠁⣿⣿⡥⢻⣿⣃⢼⣿⣯⠜⣿⣿⠠⣿⣟⡠⣱⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⢀⣾⡿⠃⠀⠙⠋⠀⠀⠈⠛⠁⠈⠉⠁⠀⠈⠁⠀⢿⣇⠀⠈⣉⡀⠀⠉⠁⠀⠙⢁⣀⡈⠉⠀⠈⠉⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠾⠻⢏⡀⠀⠎⢹⣷⡀⠀⠀⢠⣶⠟⠉⣲⡀⠀⠀⠀⢘⣿⡚⠁⠀⣿⡇⠀⠀⠀⣾⡟⠁⢸⣇⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠾⠟⠀⠀⠀⢸⣿⠀⢶⡿⠁⠀⣠⠔⠋⠈⠛⠒⠚⠛⠁⠀⠀⠀⢿⣇⠘⠿⠃⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉







⣷⣾⣷⣶⣶⡷⢷⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⡶⢷⣶⠶⠶⠿⢶⣾⡶⠶⠶⡷⠶⠷⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⣰⣿⠟⠁⠀⣿⣿⡆⠀⣠⣴⡶⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⡿⠃⠀⠀⢀⣿⣿⠁⢰⣿⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⢀⣼⣿⠇⠀⢺⣿⡇⠀⢰⣿⢀⣤⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢇⣀⠀⣠⣾⡿⠃⠀⠀⠘⣿⣷⡀⣾⠇⠸⢿⣧⣤⣿⣷⠾⠛⠋⠉⠁⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠛⣩⣵⡾⠛⠛⠇⠀⠈⠛⣿⡿⣤⣤⡄⠀⣿⣿⠇⠀⢀⣠⡄⠀⢀⡀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣿⣿⠀⠀⢰⣿⡟⠀⢀⣾⣿⠀⠀⣰⡟⣰⣿⠏⠀⢸⣿⡿⠀⠀⣾⣿⠃⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⢿⣿⠀⣿⣿⠀⠀⢸⣿⣇⣀⡼⣿⣿⣀⣴⠟⢰⣿⡟⠀⠀⣿⣿⡇⠀⢠⣿⡟⠀⢀⣿⣿⠀⠈⣿⣿⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠿⠋⠀⠻⠿⠃⠀⠀⠉⠉⠉⠀⠀⠉⠉⠁⠀⢸⣿⡇⠀⣸⣿⣿⠀⠀⢸⠿⠷⠤⠚⣿⣿⢀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⡀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠶⠶⠶⠶⠶⢶⣦⣄⠘⢿⣷⠾⠛⣿⣿⠀⠀⡾⢀⡴⠖⢺⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⣿⣿⠋⠁⠀⠀⠀⣀⣀⡀⠀⠈⣿⣿⡇⠀⠀⠀⠀⢿⣿⣄⡼⠁⣿⣁⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠸⠿⠿⠃⠀⠘⠛⠋⣠⠞⣿⣷⡄⠈⠙⠋⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⣤⣶⡆⠀⠀⣀⣀⠀⣼⠋⠀⣿⣿⡇⠀⣀⣀⠀⠀⣴⣾⣿⠟⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣼⣿⡿⠀⠀⣰⣿⣿⢸⠇⠀⢸⣿⣿⣠⠟⣽⣿⡇⣼⣿⣿⠃⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⣿⣯⡟⠀⠀⣾⣿⡿⠁⢰⣿⣿⠀⣿⣿⡧⠤⠚⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡄⣀⡴⠛⠿⠟⠀⠀⠀⠻⠟⠃⠀⣾⣿⡇⠀⠹⣿⣿⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⢀⡼⠃⠉⠉⠉⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣧⠤⣤⡀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠤⠴⠋⠀⠀⠀⠀⠀⢸⣿⠃⣼⡿⠀⠀⠀⢀⣠⠴⠻⣿⣷⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣤⣤⡤⠴⠞⠋⠁⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣴⣿⣿⣿⠦⣾⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠘⣿⣿⣿⠀⢸⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⠿⠿⠿⠀⠸⠿⠿⠿⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⡿⠃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢿⣿⣏⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⡏⠁⠐⠒⠂⠀⠀⠀⠒⠂⠉⠒⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠕⠀⠀⢸⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠊⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠟⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⠋⠀⢀⠀⠀⠀⠀⠂⠀⠂⠐⠀⠒⠀⠂⠀⠀⠃⠀⠂⠋⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣝⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣐⠂⠀⠀⢿⣼⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⠇⠙⠋⠟
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡆⠀⠀⠐⠂⠀⠀⣶⡿⠿⠛⠉⠉⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡆⢀⠿⢿⣿⣶⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣏⣿
⣿⣿⠟⠉⠁⠁⠈⡀⠆⠀⠀⢀⠀⠀⠀⡀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠂⠐⠈⠁⠀⠂⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣾⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⣨⣿⣿⣿⣿⣿⣏⣿
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠉⡄⢸⣿⣿⣯⣿⣿⣿⣿
⡋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣷⣤⣀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠅⠐⠀⠨⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠠⠄⠃⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣾⡀⡶⠶⠶⠖⢸⠰⠷⠿⠷⠖⢸⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⢀⡀⠁⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠂⠠⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣈⠀⠘⢿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⣿⣿⠃⡀⠀⠀⡀⠀⠀⠀⠈⠄⢁⠀⠀⠀⠂⠈⠉⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⡟⠋⠑⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⢈⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠈⠀⠀⠀⠑⠀⠹⣿⣿⣿⣦⣬⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠋⠄⠉⠀⠀⠀⠀⠀⠐⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⡀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠛⠇⠈⠉⠀⠀⢀⡤⠁⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⠀⠀⠰⠈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠀⠘⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠃⠀⠄⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣠⠀⣄⣾⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⡀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⢠⣄⣀⣀⣠⠄⡤⢤⣤⣀⣦⣤⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡈⠃⠉⠉⠉⠡⡇⠘⠉⠀⠁⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⠆⠸
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣄⠀⠀⠀⣀⠤⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠘⠉⠁⠒⢄⠀⠀⡀⠀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠳⠶⠚⠁⠀⣡⣀⠔⠁⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠒⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⠟⢉⡍⠀⠀⣇⠀⠉⠉⠓⠛⠒⠒⠒⠒⠒⡟⠀⠀⠰⡟⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢈⡶⢹⠀⠀⠀⡇⠈⠐⠒⠀⠀⠤⠄⠀⠒⡾⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⢻⠀⠀⠀⠸⡆⠀⠀⠤⠄⠀⢀⣠⠞⠀⠀⠀⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⠶⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠃⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠒
⠐⠂⢉⡆⠰⠒⠈⠀⠀⠀⠀⠁⠒⠂⠤⢄⣉⡑⠢⠤⣀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢀⣀⠤⠐⣀⠔⠉⢦⡀⠀⠀⢀⠀⠠⣔
⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣌⡉⠒⠺⠛⣿⠶⠶⠶⣶⠶⠶⠟⠉⠀⢒⣂⣈⣭⠤⠔⠒⠉⠁⠀⠀⠀⠉⠓⠀⢧⠘⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡰⠁⠘⠒⠛⠁⡶⠂⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠉⠑⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⡴⠀⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣠⣤⣴⠞⢉⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠢⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣀⠇
⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⢀⣴⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡦⢙⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡋⣴⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠎⠻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡀
⢠⣿⡟⠁⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠈⢻⣿
⣾⣿⠁⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⡷⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠈⣿
⣿⣿⡄⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢼⡿⠃⠀⠀⠀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⢠⣿
⢹⣿⣷⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⠿⢛⣤⣤⣴⣶⣶⣶⡿⠟⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢠⣾⣿
⠀⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣠⣴⣾⣿⠏⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣄⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⣼⡟⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠘⠛⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⣙⣛⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣛⣋
⠀⢰⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡆
⠀⣿⣿⣿⠏⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠹⣿⣿⣿
⢸⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿
⠸⣿⣿⣇⠀⠀⠀⠀⠈⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠁⠀⠀⠀⠀⣸⣿⣿
⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⢾⣿⡿⠋⠀⠀⠀⠀⠀⠀⢿⣿⡟
⡀⠀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠗⠒⠊⠉⠙⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠇⠀⠀⠀⠀⠀⣀⣀⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠆⠀⠀⠀⡶⠉⠀⠀⢈⠏⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠖⠢⠤⠄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠊⠀⠀⠀⠀⠓⢤⡤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣼⢠⡀⠀⣷⠀⣼⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠆⠐⡞⠁⠀⣿⠀⣀⠀⣰⠁⣤⠀⣸⠀⣰⠇⣼⠀⣠⠃⢰⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⠞⠀⠀⠀⠻⣄⢀⠇⠻⠀⢏⢀⡿⠶⠃⠀⣾⢈⡤⠁⠘⠂⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠲⠦⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡔⢰⡇⠠⠀⠀⢏⡞⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠊⠀⠀⣠⠃⠀⠈⣧⠀⠐⠀⠀⠀⢀⡆⠀⣼⠀⠸⣁⠴⠀⠀⡾⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢠⠏⠀⠀⢀⡟⣰⠂⡄⢀⠀⣸⠁⢨⠏⢉⠁⠀⡠⠀⣸⠃⠀⣀⠄⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠂⠁⠉⠉⠒⢧⣸⠁⣿⠀⡿⠀⣸⠀⢸⠂⣼⠁⡀⣿⠀⣰⠁⣰⠃⢀⠀⢀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠉⠐⢄⠀⠓⢻⣄⡇⠀⠧⠔⠋⠀⢺⡀⠓⠊⠀⣿⠀⢯⠔⢻⠀⢸⣄⢼⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣇⠀⠂⠤⠘⠀⠀⣸⡟⠧⠎⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⡀⠀⠀⠘⠶⠁⠀⢸⠇⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⣀⣀⡴⠋⠐⠀⠒⠒⠀⠂⠀⠈⠀⠀⠀⠠⠀⢀⠀⠒⠀⠀⠀⠀⣸⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⣉⣥⡄⠰⣶⣸⡏⠀⠀⠀⠛⣿⠿⠂⣠⡆⠈⣙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢋⣤⣀⠘⠛⣿⡄⠀⠙⣿⡅⠀⠀⠀⢰⣷⠀⢠⣿⠁⣠⣿⡟⢠⣬⡙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠁⠘⣿⣍⣿⣄⠀⠸⣧⡀⠀⠻⠇⣀⣀⣀⡸⠟⠀⢼⡏⣰⡟⢿⣶⣿⡿⠁⢠⣌⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠠⣶⣦⣄⠈⢿⣏⠹⠷⣀⣭⣶⣾⡿⠿⠿⠟⠿⠿⠿⣿⣷⣶⣭⡐⠗⣡⡟⢁⣴⣿⡛⠷⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢁⣤⣀⠹⣧⣽⠿⡶⣋⣴⣿⠟⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡐⢿⣏⠙⠃⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢠⣿⣉⣿⠇⠘⠿⢠⣾⡿⠋⠀⠀⠀⣀⡀⠀⢴⣿⣿⠂⢰⣾⡦⠀⠀⠀⠀⠀⠙⢿⣷⡍⠀⠀⠀⠀⠀⠀⠈⣻⣷⣄⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠈⠙⠿⣦⠄⣴⣿⠋⠀⠀⠀⠀⠘⠿⠓⠀⠘⠉⠙⠀⠈⠉⠁⢀⣀⣀⣀⣠⣤⣤⣽⣿⣶⣶⣶⣾⣿⠿⠿⠿⠟⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⢉⣁⣀⠀⠀⣤⣤⣄⠀⣶⣶⣿⢿⡇
⠀⠀⠀⠀⢀⣠⣿⢇⣤⣄⣤⣤⣶⣶⣾⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠉⣀⣀⠀⠀⠀⣤⣶⣶⣶⣶⡄⣿⣿⠀⢹⣿⣿⣆⢠⣿⣿⣿⠀⢻⣿⣇⣀⣀
⠀⠀⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠁⣀⣀⣤⣤⣄⠀⢶⣶⣶⣾⣿⡟⣿⣧⢸⣿⡏⠀⠀⠀⠉⠙⣿⣿⠀⠀⢻⣿⡆⢸⣿⣿⣿⣸⣿⢻⣿⡀⢸⣿⡿⠿⠟
⠀⠀⢠⣤⣴⣶⣦⡄⠀⣾⣿⣷⡀⠀⢻⣿⡟⢻⣿⡇⠈⠉⣿⣿⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⣿⣇⢻⣿⣿⢸⣿⡇⠈⣿⣷⣀⣤⡄
⠀⠀⢸⣿⡏⠉⣿⣿⠀⣿⡟⣿⣇⠀⢸⣿⣧⣼⣿⡃⠀⠀⣿⣿⡀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠈⣿⣷⠀⣿⣿⠈⣿⣿⠈⣿⡧⠀⠿⠿⠿⠛⠃
⠀⠀⠀⣿⣿⣶⣿⠟⠀⣿⣇⣸⣿⡆⠈⣿⣿⠉⣻⣿⠀⠀⢸⣿⡇⠀⠀⠀⣿⡿⡀⠀⠀⠀⠀⠀⠸⠷⠇⠀⠀⠛⠛⠀⠉⠉⣀⠈⣀⣀⣤⣤⣤⣴⣶⣶⣶⣷
⠀⠀⠀⣿⣿⡍⠀⠀⢀⣿⡿⠟⢿⣿⡀⣿⣿⠀⢹⣯⡇⠀⠸⠿⠇⠀⠀⠀⠙⠉⠁⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⡿⠿⠟⠛⠛⠛⠋⢹⣿⠉
⠀⠀⠀⢸⣿⡇⠀⠀⠘⠿⠃⠀⠘⠋⠁⢉⣉⣀⣀⣤⣤⣤⣤⣶⣶⣶⣾⣿⡿⠿⠿⠿⠋⠛⠛⠛⠉⠉⠉⠉⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⣤⣤⣤⣤⣶⣶⣶⣶⣿⡿⠿⠿⠿⣿⣟⠛⠛⠉⠉⠉⠉⠀⢀⣀⡀⠀⣄⣠⡄⠀⢴⣶⠄⠀⠀⠀⠀⣴⣿⠏⣰⡗⢠⡀⠀⠀⠀⣾⡿
⠀⠀⠀⠐⠛⠋⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠺⠿⠇⠠⢿⣿⠶⠀⠉⠉⠀⠀⢀⣤⣾⡟⢁⣌⠛⢷⣿⣁⣴⢆⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⢀⣴⡿⣦⡈⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣶⡿⠟⣁⣄⡹⣿⣷⣄⠈⠛⢫⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⣴⡿⠻⣶⠿⢡⣶⣦⠉⠛⠿⠿⣿⣶⣶⣶⣶⣶⣶⣿⠿⠟⢛⣉⢰⣦⠙⢿⣿⢾⣷⡹⢗⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡀⠀⢀⣴⣟⣿⠃⢰⡿⢳⣦⢠⣤⣬⣭⣭⢀⣤⠀⠀⠿⢿⣏⠀⠻⣧⡀⠻⣷⢉⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣝⠉⢽⡏⢀⣿⠿⣿⠋⠀⣾⡏⠀⢻⣿⡏⠀⠀⠀⠈⣿⡆⠀⠹⢗⣠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣶⣤⣜⡛⠰⠿⠀⠀⣿⠇⠀⠀⣿⡇⠀⠀⠀⠀⢘⡋⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣷⣶⣶⣭⣤⣤⣤⣬⣵⣶⣶⣾⡿⠏⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⢷⣦⠀⠀⣰⠟⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣾⠋⠀⣼⠏⠀⠀⠀⠀⠀⣠⡦⠀⠀⢀⣤⠄⠐⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿⠶⢶⡿⢀⣴⠟⣳⠂⢠⣿⠖⣿⠆⣾⡷⢺⡇⢘⣿⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠃⢼⣃⢼⣏⣠⣿⣗⣾⠏⣸⣿⣲⡿⠁⣾⣃⢼⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠧⠀⠀⠻⠦⠈⠁⠀⠉⣼⠇⠈⠀⢠⡟⠈⠁⠀⣀⣈⣡⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠿⠀⠀⠀⠸⠃⠀⠀⠸⠯⠴⠟⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⣠⡄⠀⠠⣄⠀⢀⣄⠀⠀⠀⠀⠀⠸⢿⠆
⠀⠀⠀⠀⢀⣴⠶⣾⠟⠓⢦⠀⠉⣉⡉⠙⠛⠓⠶⢶⣿⣥⣾⣏⣀⣀⣠⡿⠀⣼⠏⠀⠀⠐⠂
⠀⠀⠀⠀⠘⠇⣼⣯⣤⣤⠞⣀⣤⡍⠡⣞⡆⠀⢠⡿⢁⡾⢁⣭⡭⢉⣡⡤⣴⠏⠀⢀⣴⠶⡤⠀⣠⡖⢀⡶
⠀⠀⠀⠀⠀⣸⡏⠈⠀⢈⡇⣸⠏⢀⡴⣫⡟⢀⣾⠁⣸⡷⢫⡿⢡⡟⠁⣰⡏⠀⣠⡿⢁⣾⠃⣰⡟⢠⣿⠃
⠀⠀⠀⠀⠰⢿⣤⣤⠶⠋⠀⠛⠚⠉⠀⠻⠞⣻⡇⠀⠟⠀⠘⠓⠚⠛⢛⡉⠛⠛⠉⠓⠁⠛⠂⠙⠓⣽⠇
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠏⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠲⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣾⣏⣀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢉⣩⣿⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠿⠛⠋⠁⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣯⣽⣿⣭⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠠⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠀⠀⠀⢀⠀⠠⠈⠻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⣀⣄⠀⠀⠀⢀⠂⠀⠐⠀⠀⠀⠀⠀⠀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡁⠀⠈⠋⠀⠀⣆⠉⠀⠀⢰⣦⣤⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠂⠀⠰⠀⠂⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⢰⣦⣰⡆
⠀⠀⠀⠀⢠⣄⠹⠆⠀⠀⠀⠀⠀⠠⠀⠻⡟⠐⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠟⠃
⠀⠀⠀⠂⠄⠈⠇⠀⠀⠠⠀⢸⡄⣤⣼⠦⠙⢠⠍⠀⠘⠆⠀⡀⡀⠀⠄⢀⠀⠀⠂⠂⠰⠀⢀⠀⠀⠀⠐⠄⢀⠃
⠀⠀⢆⡡⠔⢦⡄⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠈⠀⡀⠀⢆⣠⠁⠲⠄⠠⠈⠉⠀⠂⠈⠑⠀⠈⠀⠀⠀⠈
⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢀⢀⠔⡀⠢⡅⠀⠈⠤⠂⠁⠀⠀⠀⢠⠈⠄⠀⠀⠀⠀⡦⠄⠀⠀⠐
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡏⠄⠎⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄⠐⠂
⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⠀⠀⠀⠀⠂⠀⡀⠀⡀⠴
⠀⠀⠠⠄⢀⠀⠒⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠰⠀⠀⡆⠀⠀⠊⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠒⠀⠉⠀⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⢠⣤⡺⡷⠙⠂⠀⠀⠀⠀⠀⠸⠃⠀⠉⠉⠀⠁⠀⠀⠂⠐⠛
⠀⠀⠀⠀⠹⣦⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢳⡀⠀⠀⣻⣶⣷⢶⡄⠀⠠⡀⠀⠀⡀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⣿⣄⠁⣼⡷⠀⠀⠀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡐⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣍⣀⡀⠀⠐⠒⢭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⣫⣭⣭⣭⣭⣇⣀⣀⣀⣐⣾⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⡺⠟⠟⠛⠉⠁⠈⠉⠀⠀⠀⠈⠉⠹⣟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠏⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⢿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠀⠀⠀⢸⢱⠀⠀⠔⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⠙⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⢠⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣠⠔⣣⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⢦⠀⣀⡄⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⠀⠀⠀⠀⠀⢤⠐⠚⠉⠀⡀⣿⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⢂⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠘⢶⠒⠒⣉⢴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⠨⠖⠋⠀⠀⠀⠀⣠⠟⠀⢀⡠⡄⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⣀⠀⠀⠀⠀⣀⣠⠴⡿⠥⠒⠒⢉⣀⠟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢍⠀⣠⠃⡆⠒⠉⠉
⠀⠀⠀⠀⢠⡄⠀⠒⡆⠀⠀⠀⠀⠀⠀⣀⣀⡠⡆⠀⠀⢉⣀⠴⠆⠀⠉⠀⠀⢳
⠀⠀⠀⠀⠀⠤⠀⠁⢁⣀⡠⠜⠒⠒⠒⠒⠒⠚⠳⠒⠊⠉⢀⡞⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡬⢌⣉⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠈⠉⠒⢤⣄⣉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠼⣄⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⣯⠙⡆⠴⠖⠂⠤⠤⠥
⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠊⡠⠚⠉⠹⡦⠴⠖⠒⠒⠒⠤⢀⠉⠉⠛⠒⠲⠶⠶⣂⣀⠀⠀⠀⠀⡏⣸⠁
⠠⡀⡀⠀⠠⢄⡀⢀⠎⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣇⠀⠀⠀⢀⡏⢀⣀⠤⢚⡴⠃
⠀⠑⢌⠲⡀⠀⠈⠙⠦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣼⠢⠤⠒⠊⠁
⠀⠀⠀⠑⢌⡒⢄⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣭⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⢆⠀⢀⠆⠀⠀⠀⣀⠀⠀⠀⠀⢔⠂⠀⡠⡀⠀⢀⡀⢤⡄⠤⠄⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⡄⢀⡀⣀⢀⡀⣀
⠀⡀⠣⠀⡄⠃⢄⠀⡀⠴⢀⠀⡔⡆⠚⠀⠠⢘⣠⡀⠢⠈⠀⡇⠈⣰⠃⢄⠀⣿⢁⣽⢁⠏⠨⣧⢼⣙⢹⡷⠀⡤⠀⠠⣀⡀⠠⣁⡈⠤⠀⣀⠄⠀⢀
⠀⢑⠀⠈⠊⠈⠠⠀⢃⠠⠆⡂⡇⠳⠂⠀⠢⠽⡐⠆⢠⡝⠲⡝⢽⣄⡀⠤⠇⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠘⠀⡦⡄⠎⢀⣴⠈⠆⣀⡀⠃⠠⣤⡄
⠀⠮⠨⠂⠈⠀⢡⠆⡔⠐⢊⠂⠀⠋⠓⠃⠠⠠⠅⠃⠈⢸⡐⠂⢀⠛⠃⠀⡠⣄⠀⠀⠀⠸⠃⠰⢃⠀⠀⣤⠘⠄⠘⢁⡄⠙⠞⢀⠚⠗⠓⣤⠀⠛⡡
⠀⠀⠀⢨⠂⠀⢨⠃⠈⠉⠤⠀⡄⢓⡂⠄⠀⠀⠤⠀⠀⠋⠁⢀⠊⢀⠤⠂⠂⠂⠈⢱⠀⠀⠀⡔⣆⡀⠀⣤⠂⠀⠉⠁⠈⠲⠖⠉⠑⠲⠊⠀⠈⠉
⠀⡠⠪⡔⠀⠋⢠⢀⠃⡠⠛⢀⠆⠑⣉⢰⠀⡠⠛⢄⠀⠀⠑⠊⠀⣧⠐⠀⣀⠐⠀⠈⠧⢄⠀⡇⠀⠂⢸⡁⢽
⠀⡀⠆⠄⡡⠠⢃⠀⢸⠐⠙⠀⠃⠆⠥⠊⠈⠀⠉⠂⠃⠠⠤⠀⢄⠙⠤⠤⠀⠀⢐⡈⠡⠐⠐⠃⢨⡇⠸⠀⢺⠀⡠⣤⠀⠀⢜⠆⠀⠀⢲⢻⡀
⠀⠈⠐⠂⠁⠀⠈⠀⠢⣘⣙⣠⠃⠐⡒⠂⠐⢔⣀⡠⠁⠀⢤⠀⠀⠉⠀⠀⠈⢹⡆⡀⠀⠀⠘⠤⠼⠀⢠⠁⡙⠀⠀⠐⠁⡀⠀⡀⠀⠀⡌⠀⠓⡀
⠀⡀⠀⠀⡈⠈⠔⠂⠁⠢⠀⠼⠦⢤⣬⢤⢤⣤⠤⠤⢤⡄⡤⠠⢤⡄⠐⠂⠙⠘⠓⠀⠀⠀⠠⠒⠀⠐⠨⡀⠁⠀⠀⢀⠀⠀⡀⠀⠀⡜⠐⠃⠁⠑⡀
⠸⠁⢀⡀⠉⠖⠀⣠⣾⣷⡇⠀⠁⠈⢳⣀⠎⠀⢆⠀⡄⠈⢦⢠⠇⠈⠢⣀⠁⠀⠠⠨⠄⢠⠁⠀⠀⠀⠀⠁⠀⠐⢀⠈⠂⡄⠛⡄⢀⢅⠂⠐⠀⠀⢰
⠘⣽⣿⣿⡇⠀⠑⠝⣿⣿⣣⠀⠀⠀⠀⠉⢔⠀⠀⠉⠀⠀⠀⠉⠀⢀⣀⣀⣀⣀⡁⠀⠀⠸⠀⠀⠀⠀⠀⡷⠄⠄⠑⡐⠀⠀⠀⠃⠈⠁⠀⠀⠈⠉
⠀⠹⢟⠻⠂⠀⠀⠀⠀⠀⠘⢦⡄⡄⠀⠀⡏⡆⠀⠀⠈⠀⢀⡆⠉⠉⠈⠀⠀⠉⡉⠨⠁⣆⠑⢄⣀⡤⠊⠁⠀⠀⠀⠱⡀⠐⢨⠀⠀⡀⠀⢤⠖
⠀⠀⢸⡀⠀⠀⠀⡔⠉⠠⠀⠬⠐⠠⠒⠒⠃⠓⠂⠄⠀⠀⡊⠁⣀⠠⢀⢠⢈⡄⡪⠀⡀⠡⠃⠈⠁⠀⠀⠀⠀⠀⡔⠀⠰⡅⡐⠀⠈⠁⢀
⠀⠂⠭⠍⠑⠀⢀⠄⠀⠀⠘⡀⢀⠔⡀⠀⠀⠀⠀⠲⠀⠀⡇⠀⡁⠠⠄⠁⠀⠀⠂⠀⠃⠀⠀⠀⠀⠑⣤⠤⠄⢊⡀⣀⠀⠀⠀⠀⠈⢁⠈⠠⠀⠊
⠀⠀⠀⠀⣤⡀⠸⠂⠀⠀⢐⠃⢸⢨⠔⢑⡀⢀⡊⠡⣚⠀⢋⡀⢀⠀⠐⠴⢢⡄⠀⠤⠀⢀⠇⠀⠀⠀⠀⠀⠀⡦⠀⠠⠇⠀⠀⢀⡀⠈⠃⠀⠓⠄
⠐⠉⠄⣰⠁⢆⠀⢫⠀⠀⢹⢀⢴⠂⠄⠀⡀⠀⠀⠀⢰⡀⠀⠑⠧⢀⣀⣀⣀⣀⣀⡀⠰⠉⠀⢠⡆⢠⣤⣴⡶⠒⠂⠐⠚⢶⣤⣦⠀⠀⠰⠖⢂⠐⠄
⠀⠀⢰⠃⠀⠈⢂⠈⠢⠄⠂⠈⠦⣁⠐⠀⠀⠀⠀⣊⠵⠁⠀⢀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣤⠀⠈⠁⠀⢙⡿⠀⡀⠀⠀⡀⠀⣿⠁⠀⢀⣀⠤⠅⢄⡀
⠀⢀⠇⠀⠀⠀⠘⡄⠀⠀⡄⠰⠶⠀⢜⡭⡀⠉⠁⠀⡴⠠⢱⠃⠐⠀⠀⠴⠡⢀⣁⡠⢊⠴⠀⣖⡄⠀⠀⠰⠀⠀⠀⠀⠀⢀⠇⠃⠐⠡⣀⢀⣀⠆⢸
⠀⠸⠦⠤⠤⠔⠀⠱⠀⢰⠃⠀⠀⠀⠀⠀⡄⠀⢠⠞⠐⠄⠁⢤⢡⡄⠄⠈⠏⠓⠺⡖⠁⠀⡆⠀⠁⢂⠀⠀⠶⠄⡄⢤⠴⢆⠀⠀⠰⡄⠀⠀⠀⢐⠐
⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⠀⡖⠀⠠⠨⠀⡇⢠⠋⠀⠀⣀⡱⠶⠈⠀⠀⠀⠘⡀⠀⢡⠀⡠⠂⣀⠈⠋⠂⠰⣦⣶⣿⣿⣦⣾⠄⠀⠀⠈⠁⠀⠉⣄
⠀⠀⣀⠀⠉⡡⢤⠀⠀⠛⠀⠁⠥⠈⠀⠠⠀⠓⠖⠒⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠐⣻⠂⡦⠤⢤⡤⡤⠬⢥⢤⣤⣤⢤⢤⠀⠀⠆⠐⠻⠁
⠀⠾⡁⢙⣟⡧⡔⠢⡀⠠⠠⠀⠄⠀⠀⠀⡤⡀⠀⠀⢀⡜⠃⠀⠀⠷⡞⠉⠉⠀⠀⠀⢰⠀⡀⠀⠀⣇⣀⢘⠁⠀⠀⢸⢈⠀⡄⠀⢀
⠀⠏⠊⢁⡂⢨⠠⠂⡇⠐⠄⠠⠄⠀⠐⢪⠀⠀⠋⠀⠰⠈⡐⠠⠠⢤⠃⣔⠀⢰⡀⠀⠈⠀⠃⠀⠀⠉⠀⠙⠀⠂⠁⠚⠈⠋⠙⠂⠀⠂⠈⠉
⠀⣔⠈⠀⠃⢠⠠⠀⡇⠠⢤⡀⠀⠠⢄⠈⠻⠏⠁⠀⡇⡠⣀⡉⢐⠊⡄⠁⡎⠀⢰⠀⠀⠠⠀⠠⡄⠰⡄⠠⠂⠀⠀⣤⢄⠀⣄⠄⠄⢠⠄⠀⠤
⠀⠀⠑⠼⠄⠐⠚⠉⠀⠀⢀⠀⠁⠀⠰⠀⠀⢀⠀⢀⠀⢢⠄⠃⠌⠀⠘⡀⠛⠀⣹⠀⠀⠀⠀⠀⡍⠀⡇⠂⠃⡀⢀⡤⠂⢀⡤⠂⢸⠀⠀⠀⠄
⠀⠖⠐⠀⠀⠈⠁⢱⠀⠀⠊⢆⠀⠀⠀⠀⠀⠘⠀⠈⠢⠀⠀⠎⠀⠀⡀⢹⠀⠀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢠⡀⡀⠀⠈⠁⠠⠀⢀⢀⡀
⠀⠀⠀⠸⠍⠇⠀⢸⠀⡀⠀⠈⠀⠀⢰⠀⠀⣀⡆⣀⢤⠤⠤⡤⡄⠥⠼⢆⢢⡰⠁⠀⠨⠅⢠⠀⠀⣉⢼⠀⠀⠉⠀⡓⠀⡇⠀⠉⠂⠀⠰⠀⠀⡆⠁
⠀⠛⠀⠀⠀⠀⠀⠊⠀⠈⠑⠂⠈⠁⠁⠀⠀⠑⠁⠈⠒⠒⠒⠓⠓⠒⠐⠁⠀⠀⠀⠈⠉⠁⠈⠃⠘⠁⠙⠀⠘⠀⠀⠁⠀⠁⠉⠉⠀⠁⠀⠉⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣁⠠⠤⠤⠖⠒⠒⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⡄⠀⠀⣞⢳⡀⠀⠀⠀⠂⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆⠀⣠⡶⢲⡄⠀⢠⣶⣶⣦⣄⣤⡀⠈⢸⠧⣀⡀⠀⣰⣿⣿⠃⠀⢀⣤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡼⠋⣀⣼⡿⣻⣿⠟⢀⣴⣿⣿⠃⢠⡟⣴⣿⠇⢰⣿⡿⠁⠀⣠⣾⡿⠃⠀⣠⣿⡟⠀⠀⠀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣠⠞⣹⣿⢳⣿⠃⡴⢫⣿⡿⠃⣠⠟⣼⣿⠋⢀⣿⣿⠁⢀⢼⣿⡟⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠹⠾⠿⠃⠘⠿⠚⠁⠘⢿⣥⠾⠃⠀⠹⠧⠴⠋⠻⠧⠔⠁⠘⢿⣄⠴⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⢏⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⢀⡴⠚⠉⣴⣿⠃⠀⠈⠳⣄⠀⠀⠀⢠⡾⠛⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢘⣻⡥⠴⢤⣄⠀⠠⡏⠀⢀⣾⡿⠁⠀⠀⠀⠀⠘⢧⡀⠀⠙⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⠀⢀⣿⣿⣡⠤⠒⣿⣥⠀⠀⠀⠠⣿⠇⠀⠙⠛⠛⠉⢀⣴⣶⠖⠲⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠖⣾⣿⠃⠀⠀⣼⣿⡟⠀⣠⣤⣀⡴⣶⣦⢀⣀⡀⢀⣾⣿⠃⢀⠜⠁⠀⠀⠀⠈⠙⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⣠⠞⣿⡟⣀⢼⣿⣿⠋⣸⣿⡿⢫⣿⡟⠸⣿⡿⠊⢁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡤⠞⠁⠀⠈⠉⠁⣾⣿⠃⠀⠻⠟⠁⣼⣿⠁⡰⠻⠧⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢰⣿⣯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⡄⠀⣀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠺⡿⠧⠀⠀⠀⠘⠁⠀⠉⠀⣴⠀⣿⠀⠤⣀⠀⢐⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠛⠀⠀⠀⠀⠁⢀⠀⠦⢀⠀⠀⠀⡄⠀⠿⠀⠁⠀⠃⠉⠀⢀⡈⠀⠐⠂⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡴⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠛⠀⠆⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣆⣀⠀⠀⢠⢄⡄⠀⣴⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠷⢀⣤⣤⡴⡦⠀⠀⠘⠃⠀⠀⠘⠃⢰⡆⢠⣦⢀⣴⠂⠀⣸⠿⣿⠉⠀⠀⠋⠾⠁⠀⠀⠀⠀⢁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠉⣻⠇⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡿⠋⠹⠞⠁⠀⠀⠈⠀⠈⠀⠰⠆⠀⠀⠀⢆⡒⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠶⠀⢠⣾⣁⡀⠀⠀⣶⣶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣍⠃⠀⠀⠀⠀⠀⣴⠟⠁⠀⢰⣿⡟⠀⢸⡗⠀⣴⠶⣦⠀⣾⣿⠿⢿⣿⡟⢛⣛⠛⠻⠃⠀⠀⠀⠀⠀⠴⠀⠀⠀⢠⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠘⠃⠀⠀⠀⣿⣿⣧⣶⠟⠁⠀⠻⢶⡾⠤⣤⡄⢀⣾⡿⠀⣾⡟⠀⠀⣠⣾⡗⠀⠀⠀⠀⠀⠀⠀⠉⣹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣾⣀⣀⠀⠀⡤⠀⠀⢰⣿⣿⠉⣠⢶⣶⠆⢠⠞⢀⣾⡟⠁⣼⣿⠃⢸⣿⣁⡴⠚⢱⣿⣧⣴⠶⠗⠀⠀⣀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⣿⠋⠁⠀⠀⠀⠀⠀⣸⣿⡏⢰⣿⠞⣿⡴⠋⢀⣾⡟⠀⣸⣿⡟⠀⠈⠉⢉⣤⣶⣿⡿⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢉⣤⣴⠶⠆⠀⠀⠀⣿⣿⡇⠀⣤⠤⠬⠀⠀⣸⣿⠁⠀⣿⣿⠇⠀⠀⣴⠟⠁⣸⣿⠃⠀⠀⣈⠁⠖⠀⠠⣦⣴⣆⣀
⠀⠀⠀⠀⠀⠀⠶⢈⣁⠀⠈⢛⣷⣦⠀⠀⠀⠀⠛⠛⠃⠀⠒⠛⠛⠂⠀⢿⡿⠀⠀⠛⠛⠀⠀⠐⣿⣄⣴⣿⠃⠀⠀⠀⠀⠙⠀⠀⠀⡾⣿⠋⠁
⠀⠀⠀⠀⠀⠀⡦⠈⠁⠀⠺⠟⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣀⣄⣠⣄⣀⣀⡀⠀⠀⢴⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢠⡿⢀⣠⠀⠀⠀⠈⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣶⡾⠿⣿⡟⠉⠉⠉⠉⠙⣛⠀⠀⢀⣴⣿⡿⠀⠀⣀⣀⡀⠀⠀⠘⠛⠉⡟⢀⣤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⠀⠀⠘⠀⠀⠀⠘⠋⠁⠀⣼⡿⠀⢶⠆⠀⠀⣼⣿⡀⢠⡞⣹⣿⠃⣰⣾⡟⠉⣿⠀⠀⠀⠀⠘⠟⠋⠁⠀⢨⣽⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢠⣦⠀⣠⣾⣿⣿⣥⡟⢠⣿⡏⣸⣿⣏⣤⠞⠁⠀⠀⠘⠀⠀⢀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⢀⠈⠁⠈⠀⠀⣼⣿⠀⢸⣟⣴⢋⣿⡇⠘⠋⠀⣼⣿⠁⣿⣿⠁⠀⠀⣠⡾⠀⠀⠀⠀⠈⠀⠆⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢃⡘⠃⠀⣠⣾⣋⡁⠀⠀⠀⠀⣿⡟⠀⠈⠛⠁⢸⣿⠃⠀⠀⢀⣿⣿⠀⠻⣿⣤⣤⠾⠋⠀⠀⣀⣤⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⣹⣏⣠⡄⠀⠀⠛⠃⠀⠀⠀⠀⠺⠿⠀⠀⠀⠸⠿⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢹⠿⠏⢠⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠄⠀⠀⠀⢠⣞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢤⣤⣄⠀⠀⠘⠃⠀⣠⠶⡆⣀⡤⣆⠀⠀⠀⠀⠀⣀⠀⠀⢀⡾⢷⢀⡾⠀⠀⠀⣀⠀⠀⢀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⠋⠀⠀⠀⠀⠘⠃⠐⠛⠁⠀⣿⠀⠠⠀⠘⣿⣿⠶⠀⠘⠃⠈⠛⠀⠀⠀⠳⠌⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⠀⢀⡋⠐⠆⠀⠈⠀⠀⠀⠀⠉⠙⠀⠀⠶⣈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣴⣦⠄⠀⠀⠀⢠⠀⡄⠀⢠⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⡄⠀⠀⠀⢀⡞⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣼⣿⣿⠀⠀⠀⢸⣷⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⢸⣷
⠀⠀⣿⡇⠀⠀⢠⣴⣶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠉⠛⠆⠀⠀⣿⡇
⠀⢰⣿⠀⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⣧
⠀⢸⣿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⣿
⠀⢸⡟⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠴⠶⠶⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢶⣶⣶⣦⣤⣤⣤⣤⣶⣶⡶⠾⠿⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣀⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢹⣷⢀⣤⡀⠀⠀⠀⠀⠀⢠⣤⣤⣰⣦⣿⡇⠀⠀⢰⣿⠁⠀⠈⠻⣿⡆⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⢛⡙⣷⣲⣦⣾⡟⣿⣿⣷⣿⠏⠿⢿⣷⢤⣄⠸⣿⡀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣸⣿⢿⣿⣿⠋⢸⣿⠸⣶⠾⢻⣿⢸⡟⠀⠙⠛⠓⠚⠋⢴⡆⣀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠸⠟⣤⡌⠉⢠⣶⠀⠘⠛⠊⠀⠀⠀⠀⢀⡀⣠⡈⠘⣿⣶⣦⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢻⡧⠀⠀⠀⠀⠀⠀⢸⣟⡇⠀⢸⣿⡄⢀⡀⣀⡀⣤⠖⣦⣿⣿⣿⣷⠀⠇⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣸⠃⣶⡄⠀⠀⠾⠗⢸⣿⠃⢀⣼⣿⡇⣿⣿⠿⠿⣿⡔⢃⡼⡿⠹⣿⠌⠈⠚⠉
⠀⠀⠀⠀⣤⣀⣀⠀⢀⣿⣿⣤⡾⠁⠀⣿⣇⣤⡀⣴⡗⢸⣿⠀⣿⣧⣿⣇⣿⡟⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠻⣿⣿⡿⢿⣿⣿⠁⠀⠀⠀⢿⣿⣿⡇⣻⣷⡜⠛⠗⠉⢛⣡⣭⣶⣦⣤⡀⠀⠀⠀⠀⠀⢹⣷⡀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⡼⠟⠈⠛⠁⠀⠀⠀⣠⡞⢋⣶⣶⠆⠘⣿⣿⡆⣴⣫⣿⣷⠀⣿⣧⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣤⠞⠁⠀⣴⠿⣶⡄⠀⢰⣿⡀⠀⣿⣿⡆⠀⢹⣿⣿⢨⣿⣿⣿⣆⣿⣯⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⢸⡟⠀⢸⣿⠀⠸⣿⣿⣿⢹⣿⡇⠀⣸⣿⠇⠘⠛⠃⠉⢉⡤⠖⢿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠈⠙⢿⣾⡇⠀⢸⣿⠀⠀⠀⠉⠀⣸⣿⣇⣴⠟⠋⠀⠀⢀⣤⠞⠋⠀⠀⢸⣿⡆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠙⠃⢀⣿⡟⠀⠀⢀⣶⣏⣽⡿⠁⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣀⠀⣤⣴⣿⠟⠀⠀⠀⠀⠉⠋⠉⢀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠻⣿⣿⣆⠀⠘⣿⣿⡄⠀⢻⣿⡇⠀⢹⣿⡇⠀⣿⣿⠁⠀⣿⣿⠃⠀⣼⣿⡟⠀⢀⣼⣿⡿⠃⠀⢀⣴⣿⣿⡿⠋⠀⠀⢀
⣷⣄⠀⠘⢿⣿⣦⠀⠘⣿⣿⡀⠈⣿⣷⠀⢸⣿⡇⠀⣿⣿⠀⢰⣿⡏⠀⣰⣿⡟⠀⢠⣾⣿⠟⠀⢀⣴⣿⣿⠟⠉⠀⠀⣠⣴⣿
⢿⣿⣧⡀⠀⣹⣿⣷⣦⡈⢿⣷⠀⠸⣿⡄⠀⣿⡇⠀⣿⡏⠀⣾⡿⠀⢰⣿⠏⠀⣰⣿⡿⡁⠀⣠⣿⣿⣿⠇⠀⢀⣴⣾⣿⣿⠿
⠀⠙⢿⣿⣦⣹⣿⣿⣿⣿⡈⢿⣧⠀⢻⣧⠀⢿⡇⠀⣿⡇⢠⣿⠃⢠⣿⣏⣠⣶⣿⣿⣦⣷⣾⣿⡟⣿⣿⣧⣶⣿⣿⣿⣿⣷⣶
⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⠎⢿⣆⠈⣿⡀⢸⡇⠀⣿⠀⣼⡏⢀⣾⠏⢈⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣦⠈⢿⡆⢸⣇⠸⣇⢠⣿⢀⣿⠁⣾⠏⢠⣾⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣤⣿⠀⣿⢸⡇⣸⠇⣼⠏⣰⡟⢁⣴⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢳⠈⡇⠛⢸⠁⡟⣰⢋⡼⢋⣴⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠁⠀⠀⠀⠀⠀⠁⠞⡡⠞⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁
⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣯⣤⣤⣿⣿⣿⡿⢻⣿⣿⣿⡀
⣀⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠩⢯⣩⣉⣉⣽⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣷⡀
⠿⣿⣿⣿⠟⠉⣉⣙⣿⣿⣿⣷⣦⡀⠈⠙⠛⠻⠉⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⣬⣉⣿⣿⣿⠿⠻⠿⠛⠛⠛⠿⢿⡄⠻⣆
⣤⣿⣷⣿⠿⠟⠛⢉⣈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢤⣙⠳⢦⣤⣉⣿⣿⠻⢿⣶⣦⣤⣀⣀⠀⠈⠃⠀⠙⣷⣄
⠛⠉⣽⣁⣤⣶⠿⠛⠉⣸⠿⠛⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢦⣌⠻⢦⣌⠙⠻⢷⣦⣤⣀⠉⠉⠙⠛⠛⠿⢷⣖⣦⣌⣿
⡶⢾⣟⣉⡥⠀⣠⣾⠆⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⢠⠐⣆⠉⠀⠙⠷⣄⠙⠿⢶⣄⠈⠙⠻⢿⣶⣦⣄⣀⡀⡀⠀⠉⠙⠛
⣰⣿⡿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠘⠁⠙⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣄⣰
⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⣤⣤⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢹⣧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣦⣈⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⡀⢀⠀⣹⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿
⣿⣏⣁⡁⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠉⠁⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⡿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⡿⢿⢿⠿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠃⠀⠀⠉⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠋⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿
⢀⣀⠀⠀⠀⠀⣀⠤⠤⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢏⣉⡇⠀⣠⠞⠁⠀⣀⣀⠀⠈⠑⢆
⠈⠉⠀⢠⠃⠀⣴⠛⠉⠉⠙⣦⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⢀⡀⢠⡄
⠀⠀⠀⢸⠀⠀⣯⠀⠀⠀⠀⣸⠇⠀⡇⠀⠀⠀⠀⠈⣅⠗⠀⢦⠰⡂⢻⠀⢢⠆⠀⠸⠀⠇⠉⠠⠣⠘⠆
⠀⠀⠀⠀⠳⡀⠙⠷⣤⣤⡴⠋⢀⡜⠀⠀⠀⠀⠀⠀⠁⠀⠙⠈⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠉⠢⠤⣀⣀⠠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀⡁⢀⠡⠀⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢅⠐⠀⠀⠀⠈⠁⠐⢊⠌⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢀⢀⣀⣀⡁⣀⣀⣀⠠⠠⠛⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⡀⠀⠀⢠⠀⡀⠈⠁⠉⠺⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠁⠀⠀⠐⠉⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠢⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠐⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠠⢀⠀⡀⠊⠀⠀⠀⠀⣀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠂⠀⠊⠀⠇⠀⠂⠀⠄⠀⠀⠀⠀⠒⠁⠀⠀⠀⠐⠠⠀⠀⠀⢈⡂⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⡿⠿⠿⠿⠿⢶⣶⣦⣤⣤⣃⠐⠀⠀⠀⠀⣤⣄⣀⠀⠄⡀⠀⠢⣄⠀⠂⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⠋⠉⠉⠉⠙⠛⠒⠒⠚⠯⠽⣿⡇⠀⠀⠀⣿⣿⣿⣿⣶⣤⣴⡄⡀⠀⠀⠄⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⣚⣛⣉⣉⣉⣉⣙⡒⠒⠤⢤⣀⡃⠀⠀⠀⠋⠉⠻⠿⣿⣿⣿⡷⠀⠀⠀⡀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣭⠅⠤⠠⠰⠶⠆⠄⠍⣭⢙⢓⣲⢬⠁⠠⡀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⢀⠀⠀⠉⠃⠲⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣈⡀⠠⠄⠀⠀⠀⠀⠀⠘⠀⠀⠐⠂⠐⠀⠄⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣻⡄⠭⠭⠭⠭⠭⠭⠭⠭⣽⣿⣛⣛⡷⠶⣤⡔⠀⠀⠀⠀⠀⠄⡀⠀⠀⢀⠀⠀⠀⠀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⢤⣀⣀⡉⠉⠙⡛⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠽⠒⠒⠛⠉⠉⠙⠛⠛⠒⠒⠶⠦⢤⣍⣙⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣐⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠂⠀⠀⠈⠉⠉