Planetary Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠓⢲⣄⣠⠖⢛⣹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⡿⣿⠿⠿⢿⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠉⢀⣠⡾⠛⠁⣱⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⣀⠈⠭⠤⠐⠀⠈⠁⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⣀⣠⣴⡞⠛⠉⣀⡴⢞⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠋⠉⠀⣠⠴⢚⣥⠖⢋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⢰⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣵⣶⣯⠵⠞⢉⣠⣾⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠘⢦⡍⣄⢠⠤⠤⠤⠄⢒⣲⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠑⠒⠺⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣖⡲⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⡀⢀⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⣸⣫⡿⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⠐⠃⠈⠀⠉⠁⢅⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣇⣤⠀⢀⣴⣟⢕⣷⡆⠈⣆⠀⡀⠀⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠐⠀⡀⢀⠀⣈⠠⠀⢔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣣⠈⠚⢱⣿⣿⣿⠀⢸⠁⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠀⠀⠌⠠⠀⡱⠈⠆⠀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠙⠤⡄⠀⠈⢹⢛⠿⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⡀⠘⠤⣉⡀⠜⠀⠀⢈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⡁⢠⣿⣦⣰⢋⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⠌⠂⠄⠀⠠⠄⢂⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠘⠛⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢱⢠⠢⠔⠖⠢⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠔⠂⢉⠟⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣤⠖⠀⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠠⠀⢂⠀⢬⣿⡄⠀⣠⠊⢀⢀⣀⠅⠀⠀⠤⢈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⢃⠀⡟⢦
⠀⠀⠀⠀⠠⠒⢉⠄⠀⠀⠀⠀⠀⠏⣀⠁⠀⠀⢀⡠⠀⠀⢎⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡏⠀⢠⠀⠸⣀⠤⡠⠀⠎⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠅⢪⠀⠀⠀⠀⠀⣀⢤⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠁⠀⣀⢄⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠬⠇⠀⠀⠀⢀⠑⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣉⠀⠀⠁⢲⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⣠⠀⠀⠾⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣖⣯⣼⣟⢲⣦⣽⣤⡀⢠⠀⠀⠈⠀⣠⣦⡙⣅⠀⠙⠷⣦⡀⠀⠀⠀⠀⣠⡴⠖⣲⢤⡀
⠀⠀⠀⠀⣰⣶⣯⡿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡌⠄⣄⠀⠐⢅⠀⠑⢤⡐⢄⡀⠈⢑⡀⠀⠀⠐⠋⡀⠈⢁⣼⣿⡀
⠀⠀⠀⠀⣿⢄⣽⣷⡌⠻⠿⢿⣿⠭⣭⣁⣿⣷⡠⠏⠀⠀⠀⠑⢄⠀⠉⠲⢌⡑⠺⡇⠀⠀⠘⣁⠀⣠⠔⡻⣿⠁
⠀⠀⢀⣈⡟⢻⡿⣛⣿⣿⣷⣾⣧⡴⣿⣿⡟⡿⠃⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⣨⡿⠀⠀⠀⠀⠈⠛⠿⠷⠚⠁
⠀⢠⡼⢃⣀⣘⣿⡏⠙⣋⠈⠛⢋⡄⠈⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠵⠈
⠀⠀⠈⠑⠻⢏⠙⣻⣿⣧⣦⣿⣼⡳⢾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠿⣿⠟⠋⠑⠁⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠂⣐⣦⣤⡀⠀⠀⣤⣄⡰⣧⢠⡇
⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣚⣃⣀⡀⠐⣒⣀⡀⣘⣻⣦⠀⠀⠲⠥⠤⠚⠁
⠀⠸⣏⣉⠉⢉⠀⠀⠀⢀⣴⣯⣤⠀⡟⣳⣦⡀⠀⠀⠉⠉⠙⠇⠈⠈⠉⠉⠛⢨⠙⠩⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠛⠛⠋⠀⠀⠀⢶⣶⠿⣏⠛⣉⡿⢿⣷⠀⢰⣶⣦⣤⡤⣤⣶⣄⠠⢤⣤⣤⣼⡧⠀⠀⣤⡾⠿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣷⣾⣿⡀⣠⡟⠀⠈⠋⠛⡛⠿⠿⠓⠛⠛⠙⠉⠉⢿⠇⠀⢸⣏⠤⠴⠛⠿⠶⣿⡆
⠀⠀⠀⠀⣴⣞⢦⠀⠀⠀⠉⠉⣉⣿⣿⣿⠟⠀⠀⠀⠈⠺⣉⣛⡛⡛⢛⣛⣛⣿⡿⠋⠀⠀⠘⣷⣶⣶⣶⣖⣲⡾⠁
⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠈⠓⠂⠀⠀⠛⡯⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢠⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⣀⣀⡀⢠⡤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢢⠀⠀⠐⠂⠄
⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀
⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠂⠀⠒⠀⠀⡀
⠀⡀⠀⣀⡀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⡡⣤⡀⠈⠉⠉⢠⠉⠳⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⢟
⣥⣰⣀⣉⣁⣀⣞⣋⣲⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣿⣲⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠐⠚⢻⣯⠀⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⣤⣄⣹⡾⠛⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⣀⠀⠀⢼⣿⠖⠀⠀⣐⠻⣮⣿⢹⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣿⠴⠁⠰⣿⣶⠀⠿⠗⠉⠀⠻⠁⠛⠯⠹⢿⣿⡿⣷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣝⣯⣟⣏⣔⣠⢦⣼⡿⡄⠀⠀⠀⠀⠀⠆⠀⢀⠀⠉⣉⠂⣽⣷⣤⣤⣆
⠀⠀⠀⠀⠀⠀⢰⡿⣼⡿⢾⣿⣿⣿⣿⣿⣿⡯⠎⠈⢠⣶⢊⠜⠀⠀⠀⢈⠅⠀⢸⣧⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠒⠁⡯⣀⣼⣿⣿⣹⣿⣿⡿⠀⡀⠀⠈⠁⠈⠀⠀⠠⠈⠁⠀⠀⣴⠎⠙⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⢢⡈⣹⣿⣿⣿⣿⣧⡀⠀⠀⢀⣶⣄⣠⡴⡆⠀⣤⠒⠂⠀⠘⠀⠁⣤⣿⠁
⠀⠀⠀⠀⠀⠀⢷⡞⠻⣿⢟⡺⣿⠿⣿⣷⣧⣴⢲⣬⣽⣿⣿⠁⢁⡚⠀⠀⠀⠀⠁⠀⢀⣽⡏
⠀⠀⠀⠀⠀⠀⠸⣟⠆⠺⣮⢱⣊⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⢂⣶⣿⣆⡀⠀⢐⣧⣄⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠁⠛⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⡿⣭⠟⠉⠀⠀⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⠀⠀⠁⣜⡛⢿⡿⠐⠀⠀⠀⠘⣿⡷⠁⠆⠰⠀⠤⠀⣀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡃⠈⠙⠑⠻⠿⣄⡀⠀⢐⣶⣿⣤⣐⣤⢀⣂⣤⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣒⣦⠠⣰⣦⣥⢉⣼⣿⣟⢻⣿⣿⣯⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠺⠯⠍⢟⣶⣿⡫⠴⠿⠟⠋⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣤⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠿⠛⣛⠫⠭⠉⡀⢶⠀⠀⠀⠀⣼⣏⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⠶⡿⢀
⠀⠀⠀⠀⢠⡖⣶⣿⣿⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⢿⣟⢻⠀⡀⠀⠆⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡞⠄⠀⠀⠀⠀⠀⠀⠹⢞⡖⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠉⠐⠠
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸⣿⣭⡴⠶⠒⠛⢻⡆⠀⠀⠀⠀⢸⣿⣿⠀⣀⡤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⣠⡾⠀⠀⠀⠀⠀⠸⣿⡛⢉⡀⠀⠀⠈⡇⠀⠀⠀⠀⣴⢿⣿⣟⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠘⢿⣿⣦⡀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠷⣿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡤⠀⠀⠀⠀⠀⠀⢀⣄⣠⠄⢠⣤⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⣻⢿⣿⠀⠀⠀⠀⢀⣤⣶⣖⡒⠄
⠀⠀⠀⠀⠀⠀⠸⠿⢾⣶⣋⠐⠚⠀⠀⠀⠀⠀⠂⣠⡝⠀⠘⠛⣃⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⣴⠎⢻⡶⠃⠀⠀⠀⠀⣾⣿⡿⠖⠈⠂⢠
⠀⠀⠀⠀⠀⠀⠻⣿⣟⣳⣦⠶⠒⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠀⠛⢿⣦⠀⠀⠀⠀⠀⠀⠁⢠⢻⣧⠶⢛⡕⠀⠀⠀⠀⠀⢻⣿⣷⣬⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠶⠖⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠁⠰⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⢎⠓⡚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⡄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠂⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⠐⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⠀⢀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡇⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢴⡀⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢨⠀⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠚⠀⢰⠶⠂⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⡠⢔⢢⠉⢤⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠠⣀
⠀⠀⠀⠀⠀⡣⠗⠁⠀⠀⠀⠀⠱⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣇⠀⠀⠀⠠⠀⠀⣍⠹
⠀⠀⠀⠀⠀⠰⡙⢄⠠⠀⠀⣰⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠰⠎⠒⠥⠤⠍⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠞⠁⠀⠀⠈⢱⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠃⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠁⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣀⠼⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣄⠤⠛⠛⠄⣀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠒⠒⠂⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢞⠅

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠃⠀⠀⠀⠈⠑⡴⠂
⠀⠀⠀⠀⠀⠞⣿⣤⡄⢀⡠⠀⣤⣼⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢽⢄⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠓⢢⡴⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡂
⠀⠀⠀⠀⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠈
⠀⠀⠈⠀⠀⢠⡀⣠⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⠠⠖⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⠐⠐⢲⢤⡀⠀⠀⠀⠀⠀⠔⠀⠀⠤⠒⠖⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠚⠶⠆⠚⠛⠷⠛⡀⠀⠀⠀⢁⠄⠈⠀⠀⣠⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣶⣾⠷⠹⠞⢻⠁⠀⠀⡠⠁⣀⡤⡲⠋⠁⡘
⠀⠈⠀⠈⢀⠄⠁⠈⠀⠀⠈⠫⠭⠭⠭⠟⠃⠀⠠⠊⠀⡢⠕⠂⠒⠐⠈⠀⠀⠀⠈⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡀⢴⣒⣶⣤⣄⠀⠀⣀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡤⠖⠒⠂⢄
⠀⠀⠀⠀⢀⠉⠉⠉⢐⣓⣏⣉⡤⠂⠄⠀⠀⠀⠀⠀⠀⡀⠰⠓⠰⠂⠀⠀⠀⢀
⠀⣀⠤⢦⢂⣴⣾⣾⠭⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⡞⠉⠈⠈⠂⡀⠂
⠨⠗⠒⠛⠻⡏⠁⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠲⠀⢀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢋⣉⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡛⣹⠛⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⢛⠟⢛⠖⢦⣄
⠀⠀⠀⠀⠀⠀⢠⠞⡁⠶⠀⠸⠜⠃⠀⣴⠈⢷⡀⠀⠀⠀⠀⠀⣴⠋⢀⡘⠁⠙⠤⠤⠤⠤⠽⣆⠀⠀⠀⠀⠀⢀⡾⠉⢀⠠⠁⠒⠁⡰⠁⡨⢷⡀
⠀⠀⠀⠀⠀⠀⡟⢀⠔⠢⠀⠘⠃⠤⢠⢤⠐⠀⣷⠀⠀⠀⠀⢰⠋⠀⠀⠀⢉⡷⢠⣤⢠⡖⠒⣸⡆⠀⠀⠀⠀⣾⡤⠊⢀⠔⠂⠉⢉⠠⠊⣁⠔⣷
⠀⠀⠀⠀⠀⠀⣇⠈⠲⠞⠀⢠⠒⢲⡈⠉⠀⠀⣿⠀⠀⠀⠀⢸⣏⣉⡁⠉⣉⠀⣀⣤⠤⠀⠀⢠⡇⠀⠀⠀⠀⣿⠰⠒⣁⠤⢐⣈⠠⠐⢊⡡⣖⣿
⠀⠀⠀⠀⠀⠀⠹⡄⣌⡆⠀⡈⠙⠋⠀⠐⠇⣰⠏⠀⠀⠀⠀⠈⢷⡒⠋⣈⠉⠀⠑⠒⠒⠒⢂⡾⠁⠀⠀⠀⠀⠸⣿⣊⠔⡈⠠⠐⣈⣉⠠⠈⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠤⠤⠥⠝⢀⡯⠟⠁⠀⠀⠀⠀⠀⠀⠘⠷⣍⡔⣊⠁⠠⠄⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⠭⠀⣀⣈⣉⡳⣦⡀⠀⢠⠂⡀⢂⠖⠶⣶⠾⠛⠋⠉⠭⠉⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⡉⠉⡀⠤⢉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠉⠢⢄⠀⠀⠀⠀⠔⠂⠹⡄⠰⡀⢆⠸⡀⠻⣋⠒⠒⠶⠤⠤⠤⠤⠒⠚⣷⡀⠀⠀⠀⠀⢠⢏⣠⠈⠁⠀⡐⠯⢪⠂⣶⠹⡄
⠀⠀⠀⠀⠀⠀⡿⠦⣄⣀⠀⠈⠁⠒⠒⠂⠒⠒⣿⠀⠑⢄⠑⢨⣦⣌⠙⠓⢒⣒⠒⠒⠚⠉⣩⣽⣧⡀⠀⠀⠀⣿⠐⠉⠂⠀⠲⠀⠁⡀⢠⣤⠀⢻
⠀⠀⠀⠀⠀⠀⣇⢠⣶⡄⠀⠈⠉⠀⣉⣉⡁⠁⡿⠀⠀⠀⠑⢦⡈⠁⠽⡖⢤⣈⠁⠒⠬⢥⣀⢐⣿⢻⣷⡄⠀⢿⠀⢠⡣⠜⡄⠀⠀⣁⠀⠠⠄⣼
⠀⠀⠀⠀⠀⠀⠘⣆⡠⠄⠂⠈⠁⠀⠀⢴⢀⡽⠃⠀⠀⠀⠀⠀⠻⣕⠢⢄⡉⠂⠬⢐⠂⠤⢀⣀⠀⠴⢀⠈⠆⠘⢧⠰⠉⠈⠀⠀⡏⠤⢙⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣈⣁⠂⣀⣉⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⣛⠶⣦⣤⣀⣈⡁⠀⢀⣀⡠⠂⠀⠈⠛⢦⣄⣉⣀⣈⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠈⢹⠆⠀⢹⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠟⢑⢃⠒⠘⢄⢨⠟⣦⡀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣀⣒⣂⣁⡠⠟⣳⣄
⠀⠀⠀⠀⠀⠀⣸⠇⠀⣀⠠⠖⠊⠀⢀⣻⣆⣻⣆⠀⠀⠀⠀⢀⡾⡀⠀⢠⢂⣠⠈⠉⢼⡸⣁⢻⡀⠀⠀⠀⠀⣼⣓⠒⠰⢤⣄⣀⡤⠴⠊⠁⣸⣆
⠀⠀⠀⠀⠀⠀⡇⠘⠦⢉⠆⠢⣄⡀⢯⣀⠀⠀⣿⠀⠀⠀⠀⢸⢇⡘⠤⠬⡓⠒⠊⡹⠀⣇⣈⢹⡇⠀⠀⠀⠀⡿⠬⢍⣉⡐⠒⠒⣒⣒⣍⣛⠒⣿
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠄⠀⠀⡙⠀⠀⡇⠀⡟⠀⠀⠀⠀⠸⣆⢹⡀⠴⠣⡀⠀⠈⠠⠤⠄⣺⠃⠀⠀⠀⠀⢿⡁⠒⠒⠀⠶⢚⣈⣉⠴⠚⢉⡿
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢸⠀⡜⠀⠀⠀⣸⡞⠁⠀⠀⠀⠀⠀⠹⣮⠀⠀⠐⠁⠰⣆⢠⠀⡼⠋⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠐⠂⠠⣉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣭⣤⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⢤⣍⣦⠼⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣈⣉⣩⠴⠞⠋



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠈⠁⠀⠻⢿⣆⠀⠀⠀⠀⠀⠀⢻⠽⣷⡄⠀⠀⠀⡴⠿⠮⡈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠿⣿⣦
⠀⠰⠅⢀⡀⢀⡈⢸⣿⡆⠀⠀⠀⠀⢠⢸⢀⣽⣿⠀⠀⢸⣄⡀⠀⢈⣿⣿⣷⠀⠀⠀⠠⣄⣤⣤⣼⣿⡇
⠀⠀⠀⡀⠀⠀⢘⣾⡿⠀⠀⠀⠀⠀⠀⢴⣿⣿⡟⠀⠀⠀⠹⣿⠀⣾⣿⣿⠇⠀⠀⠀⠀⡒⠦⡿⣺⡿⠃
⠀⠀⠀⠐⠐⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠙⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠶⠦⣄⠀⠀⠀⠀⠀⡴⠖⡶⣦⣤⠴⣶⠀⠀⠀⠀⠂⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠒⣤⡀
⠀⠀⠀⢀⣤⣤⣬⣭⣷⡀⠀⠀⠀⠀⠀⢈⣴⣿⡷⠋⠀⠀⠀⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⢀⣨⣿⡄
⠀⠀⠀⠴⢶⣦⢶⣶⣾⠃⠀⡀⠀⠀⠀⠩⠞⣡⡾⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇
⠀⠀⠀⠀⢀⣠⣤⡼⠋⠀⠀⠀⠀⢀⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣿⠟⠁⠀⠀⠀⠀⠀⢉⣽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠲⠄
⠀⠀⠀⠀⡃⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⡂⠀⠀⠀⠀⠀⠄⠀⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠠⠄⠀⠀⠠⠀⠄⠠⠉⠁⠀⠀⠀⠀⠀⠀⠒⣭⡤⡷⠁⠀⠀⠀⢈⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⢐⠐⠀⠈⡐⣀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣈⠁⠛⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗
⠀⠀⡀⠐⠨⠃⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠘⢭⠇⣤⣄⣤⢄⢠⣤⣁⣝⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⠠⠠⠄⠀⠈⣠⠀⡢
⢸⠐⠆⡄⣀⠀⠀⠈⣀⡈⠁⡈⡭⠀⠀⠀⠀⡈⠠⢌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⠢⢄⣀⢀⡀⠷⠠⠉
⢸⢀⡀⠑⠁⠘⠐⢊⡉⠋⠁⠁⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⣤⠁⠀⢀⡠⡐⠐⡺
⠈⢟⠓⠊⠀⠀⠂⠨⠯⠷⠄⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⠀⠀⠖⠂
⠀⠀⠑⢆⡰⠍⠁⠀⡐⣒⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⡠⠀⠃⣀⠂⡀⠀⠈⠀⠢⢅⠄
⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⡡⠂⠀⠀⠀⡐⠀⠀⢀⠱⢆⠒⠦⠀⣤⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠆⠈⠃⠀⣠⡝⠢⠰⠄⠀⠐⠀⣌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⣀⡠⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣀⡀⠀⠂⢡⠀⠀⠀⢠⠀⠦⢎⠙⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠂⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⡶⡤⠀⣤⠀⠀⠀⠀⠀⠱⠀⣀⠀⠲⠸⡆⠐⠚⢿⠗⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠰
⠠⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠁⡌⠥⡀⠶⠁⠀⠀⠀⠀⡀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣄⠀⠀⠀⠀⡠⠒⠂⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠆⠀⠀⠀⢀⣄⠀⠀⠀⡎⠀⠀⠀⠀⠈⢳⠀⠀⠀⣀⢀⢀⠐⣰
⠀⠀⠀⢀⠀⠀⡀⠀⠁⠀⠀⠀⠈⢁⠉⠀⠀⠀⠀⠙⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠁⠎⠬⠵⠋
⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠢⢤⣤⠤⠞⠁
⠀⠀⢘⣶⣯⡀⠀⠀⠀⠀⠀⡖⠁⢈⢣⠀⠀⡀⠈⠆⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠉⠹⠁⠀⠀⠀⠀⠀⠀⠙⠒⠾⣬⢧⣤⢤⣤⠦⠴⠃⠀⠀⠈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡌⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡂
⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⢠⣶⠄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠀⣀⠀⠀⠀⠉⠏⠁
⠀⠀⢃⠀⠀⠀⢀⠌⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣶⡆⠀⠀⡌⠀⠀⠀⠈⠣⠀⠀⠀⠀⠈⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠠⠤⣄⠀⠃⠀⠀⠐⡄⠀⠀⠀⢀⠀⠅⠀⠀⠀⠀⣴⣧⡤⢈⣩⣦
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠑⢌⡀⣀⠤⠊⠀⢰⣧⠄⠀⢿⡏⠀⠛⢿⣿
⠀⠀⠀⠚⡿⠳⠄⢠⠒⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠳⠶⠄⠄
⠀⠀⠈⠀⠁⠀⠀⣇⠀⠑⣤⣴⢚⠡⠔⠀⠀⢶⡖⠀⠀⠀⠀⠀⠰⠀⠀⡇⠀⢉⣱⠶⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠁⠀⢁⠀⠀⠈⠉⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣧⡴⠋⠄⢄⠈⢦⠀⠀⠀⠛⠋
⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⢠⠎⠡⠨⡀⢕⡄⠀⠀⠀⠀⠀⠀⠀⣀⣦⡤⠈⢢⡀⠀⢁⠤⡀⠳⣄⣄⡐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⢁⢀⠀⡐⠀⠀⠀⠐⠃⠀⠀⠘⠛⠀⠀⠀⠙⢄⠈⠒⣃⣔⡁⠀⠱⣄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣂⡸⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠊⠹⡀⠘⢆⡠⠞⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⣴⣧⡀⠀⠀⢞⠙⢦⡀⢈⠦⠌⡇
⠀⠀⠀⠈⠦⣀⣀⡠⠞⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⠓⠤⣝⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡟⠁⠘⠗⠐⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠙⠉⠀⠀⠀⠀⣴⠿⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢴⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⢏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠐⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠔⠀⢀⣴⣶⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢞⡼⠻⠋⣰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣴⡷⠟⠀⢀⣹⡿⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⡴⣭⠟⠀⠀⢀⡜⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠹⣿⢄⡀⠀⠀⢀⣤⣶⡟⢁⣀⡴⣫⡾⠁⠀⢀⡴⠏⠁⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⣿⣿⣶⣿⣿⣿⣃⣼⡿⣫⣾⠟⠀⢀⣤⠞⠁⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⠟⣫⣾⣿⣡⣴⣶⡟⠁⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠂⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠒⠤⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢘⠀⢠⠄⠂⠀⢀⣾⢱⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠞⠁⠀⠀⠀⢈⣧⣄⣀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⡗⠐⠀⠀⢀⢑⣡⢂⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠀⢀⡀⠀⠠⠈⢹⠄
⠀⠀⠀⠀⠀⠀⡅⠠⣀⠀⣀⣀⣤⠶⢟⡞⠁⣼⠏⠀⠀⠀⠀⠀⠁⠀⢻⡍⠀⠒⠋⠀⠀⢀⢈⡤⠀⠐⠂
⠀⠀⠀⠀⠀⢄⠷⣄⢉⣉⡥⣜⣶⡾⠋⢀⠾⣉⡰⠂⠀⠀⠀⠀⠉⠀⠀⠘⠶⢭⣈⣬⣥⠴⡋
⠀⠀⠀⠀⠀⡇⢀⠈⠉⠓⠺⠟⠉⠀⢠⠋⠌⠹⣿⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠣⠈⠃⠀⠈⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠁⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠤⠦⡀⠀⢀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠰⠂⠀⠀⠀⠂⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠠⣿⡼⡧⠀⠀⠠⠛⠓⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠕⣄⡠⠖⠰⠀⠀⣀⢤⠃
⠀⠀⠀⠀⠀⠉⠀⠯⠵⣅⣤⠴⠀⠐⠒⠠⠡⠄⠀⠀⠀⠀⠀⠀⠀⠘⠎⠠⠄⠀⡇⢀⠒⠫⣺⠏
⠀⠀⠀⠀⠀⠃⠀⠠⠒⠀⠀⠲⠀⠒⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠠⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠱⢤⡀⣀⠀⢈⠁⣁⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⡀⢘⡃⠠⠀⠐⠄⣠⠐⠇⠀⠀⠀⠀⠀⠫⢤⢧⣠⣤⣽⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢤⠁⠈⢰⠀⠀⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠥⣀⣀⠹⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⡿⠿⢿⠛⠿⣿⣿⣷⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢿⣃⡾⠀⡐⠌⠐⠋⠈⠀⠙⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢛⡛⣉⣉⣁⣄⣀⣤⣀⣀⣀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣬⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⠛⠃⠒⠟⠛⠹⠟⠟⠻⠿⠟⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠹⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⣤⣤⣤⣄⠀⠀⠀⠀⢀⢛⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠝⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣿⣿⣿⣿⣷⣾⣿⣿⣧⡄⠀⠀⡤⢈⢩⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣉⠛⠂⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⢎⣉⣉⡿⠿⠷⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣘⣛⣿⣷⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⡀⣀⢀⣤⢀⣄⡄⣠⠾⠆⠤⠐⠐⠒⠊⠁⠆⠀⠀⠀⠉⠛⡿⠉⠋⢭⣿⣿⣧⣍⢋⡉⠹⣿⣿⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠟⠙⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠈⠙⠧⡄⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣤⣴⣤⣶⣶⣶⣶⣶⣾⣷⣶⣪⣴⣶⣶⣆⠴⣦⡶⣦⣤⣄⣀⣐⣠⣤⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⣨⣴⣿⣿⣿⣿⣿⣿⠿⡛⠛⠙⠉⠋⠉⠉⠉⠉⠛⠉⠀⠁⠀⠘⠻⠻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣡⢀⣂⣤⣠⣤⣴⣶⣶⣶⣤⣤⣴⣤⣀⣀⠀⠀⠀⠀⣹⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⢻⣿⣿⣷⣾⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠏⢛⣿⣛⡛⠻⠙⢟⢿⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣽⣀⡆⠠⠦⡌⠠⡝⢛⡚⢢⣮⣾⣿⣿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣥⣶⣷⣿⣿⣷⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⡴⠶⣚⣛⠋⣁⠐⢢⢱⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠿⠿⠛⠋⠁⢠⠈⣆⠀⣬⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⢜⡜⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⢿⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⡅
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠐
⠀⠀⠀⠀⢀⡴⣫⣾⠟⠁⠀⠀⠈⢀⠀⠀⣀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠐⠁
⠀⠀⢀⡴⡁⠀⡍⠸⣀⣀⠀⣀⣤⣴⣷⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⠄⠊
⠀⠠⢱⠰⡀⠐⠀⠒⣒⣒⣭⠿⠟⠛⠉⠀⠀⠁⠀⠐⠒⠂⠀⠈
⠀⠐⠠⠅⠤⠉⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⠸⢿⣷⣶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⠋⠀⠀⠀⣺⠟⣩⣿⣿⣿⣿⣟⠛⠛⠻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⣾⠋⠁⢘⣿⣿⣿⣧⡀⣰⢇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⠐⠉⠁⠀⣰⣿⣿⣿⣿⣿⡷⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣾⠿⣋⣿⣿⡿⢋⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⢁⣴⣿⡿⣋⠔⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⣾⡿⠟⡡⢊⣥⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⣡⠔⣉⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣖⣤⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⢤⣀⣀⣠⡬⠥⠖⣚⣩⣴⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠃⠈⠃⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠖⠛⢋⣉⠙⠓⠦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⡤⠶⡟⢹⠋⠛⠲⢤⡀⠀⠀⢤⡞⣦⠤⠀⠀⣠⡴⡺⢛⠟⢉⠗⢶⣄
⠀⠀⢠⠞⡁⠶⠀⠻⠞⠀⠀⣶⠈⢷⡀⠙⣯⣨⡟⠁⣰⢛⢒⢒⠁⠘⠤⠤⠤⠤⠽⢆⠀⣼⠛⠻⠀⢀⡾⠉⢁⠀⠄⠒⠁⡰⠁⣨⠷⡀
⠀⠀⡟⢠⠔⠦⠀⠘⠂⠆⢠⢤⠐⠀⣧⠘⠋⠈⠓⢰⠏⠉⠈⠀⢉⡇⢠⣦⠠⣖⣒⣛⡆⠀⠀⠀⠀⣾⡤⠊⢁⠔⠂⠈⢉⠤⠊⣀⠴⢻
⠀⠀⡇⠘⠲⠚⠀⢠⠚⢲⠈⠉⠀⠀⣿⠀⣀⣀⡀⢸⣋⣉⡉⠉⣉⠀⣀⠤⠤⠤⠤⢤⡇⢀⠤⢄⠀⣿⠔⣒⠥⠐⠒⠬⠅⢒⣊⢅⡮⣿
⠀⠀⢻⡄⣞⡆⠀⡈⠛⠋⠀⠰⠆⣰⠇⢰⠋⠬⢳⠀⢷⡐⠋⡈⠋⠀⠑⠒⠒⠒⢒⡾⠁⠺⣘⡺⠀⠘⣯⣊⠕⡀⠬⠄⠉⣀⠠⡀⢭⡟
⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠠⡈⠓⠒⠋⠀⠀⠻⢭⣭⠭⠭⠭⠝⢀⣯⠟⠁⠀⠀⠀⠀⢄⠀⠈⠳⣏⡴⢊⠩⠤⠀⣂⡴⠋
⠀⠀⠀⡰⠀⠈⠙⠛⠚⠛⠋⠁⠐⠄⠀⠀⠄⢀⣤⢠⣄⠀⠀⢉⠙⠛⠛⠛⠉⠀⠜⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⢋⡁
⠀⠉⢊⠁⣉⠈⠀⠀⠀⠀⣴⢶⡄⠐⠉⠐⠀⣾⢤⣻⢾⠀⠢⠀⠀⠀⠀⠀⠳⡈⠀⠈⡀⠒⠂⠠⠀⡒⢀⠀⠠⢿⡿⠆⠀⠻⠟⠠⠶
⠀⠀⠄⠉⠑⠄⣀⣀⣀⣀⡈⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠐⠀⣀⣀⣀⡀⠀⠤⠒⠄⡇⠀⠐⠂⢿⡽⢀⠀⠀⢉⣋⣀⣀⡀
⠀⠀⠀⢀⡴⠾⢉⡐⠀⠈⠉⣳⣤⡀⠀⢠⠂⡡⠐⠶⢶⣶⡶⠛⠩⠭⠭⠟⠻⢶⣄⠀⠈⠀⠀⠘⠀⠂⢀⡴⠞⠉⠉⣉⠉⣉⠓⢦⡀
⠀⠀⣰⠋⠙⠢⢀⡀⠀⠀⠀⡔⡤⠳⡄⠸⡀⢆⠡⡀⠻⡛⠒⠒⠦⠤⠤⠤⠤⠖⠚⢧⠀⠀⠺⠒⠀⢠⣞⡀⡈⠁⠈⡐⠯⣊⠂⣶⠹⣆
⠀⠀⡿⠤⣀⡀⠀⠈⠉⠒⠒⠒⠒⠒⣷⠀⠑⢄⠑⢬⣦⣈⠙⠶⣒⣒⣒⣒⣒⣉⣉⣹⣧⡀⠀⠀⠀⣾⠘⠭⠀⠀⠶⠀⠀⡀⢀⣤⠀⢹
⠀⠀⣇⢠⣶⡄⠉⠉⠀⠒⢂⣀⡉⠉⡿⠀⠀⠀⠑⢤⡉⠋⠭⡦⢄⣉⠙⠲⢄⣈⡀⢠⣿⢿⣷⡄⠀⢿⠀⢠⠫⠕⡄⠀⠀⣁⠀⠠⠄⣸
⠀⠀⠹⣄⠉⠄⠒⠈⣀⠀⠀⣤⠄⣼⠃⠀⠀⠀⡀⠀⠻⡑⠦⣌⡙⠂⠌⠐⡢⠤⢀⣈⢁⡴⢈⠜⡆⠘⣧⠰⠉⠊⠁⠀⡎⠡⢱⠄⣰⠏
⠀⠀⠀⠈⠳⣆⣉⡀⠆⢀⣉⡶⠞⠁⠀⢋⠐⢨⠁⢠⠀⠙⠷⣤⣛⡓⠦⣤⣄⣈⡉⠁⠀⠀⢁⡠⠃⠀⠈⠳⢤⣀⣛⠀⢈⣁⣥⠞⠁
⠀⠘⠃⠠⠆⠀⠉⠉⠉⠉⣁⠔⢀⠀⠠⠆⠒⠲⠆⠀⠀⠄⠀⠀⢈⡉⠉⠉⠡⠄⠀⠈⠉⠉⢠⣲⡀⠺⡗⠀⠀⠈⠉⠉⠉⠁⠀⠀⣴⡄
⠀⠀⠀⡁⠈⠐⠀⠀⠀⠈⠂⢀⠠⠁⠀⠀⡜⢢⠀⠈⡀⠀⠀⠐⠄⡐⠀⠘⢄⡀⠓⠠⠄⡤⠒⠁⠓⠠⠠⠄⠐⣶⠆⠀⠀⠀⢠⠀⠉⠁
⠀⠀⠀⠘⠀⢀⣠⣤⣤⣤⣈⡀⠈⠠⡔⠊⠀⠀⠑⣠⠀⠀⠀⣀⣨⣤⣤⣄⣀⠠⢶⠀⠀⢀⠀⡀⠀⠐⠁⠀⢀⣠⣤⣤⣤⣀⡀⠀⠺⠂
⠀⠀⠀⣠⠞⠉⠓⠒⢱⠄⠀⢹⢦⡀⠀⠑⠄⠠⠋⠀⠀⣠⠞⡉⢃⠵⠸⣄⢉⠿⣦⡀⠀⠆⠁⠐⠢⠠⣠⣞⣛⣀⣀⣒⣊⣠⠝⢳⣄
⠀⠀⣰⡇⠀⣀⣠⠔⠚⠀⢀⣻⣂⣿⡄⠀⠘⠁⠀⢀⣾⡁⠀⢠⢖⢠⡐⠋⢼⢰⡉⢳⡀⠀⠀⠀⠀⣰⡇⠒⠤⣄⣀⣀⣀⠤⠒⠁⢘⣆
⠀⠀⡇⠑⠌⣓⠤⠤⣀⠀⣏⣀⠀⠈⣿⢀⡖⢦⠀⢸⣅⠸⠤⢌⡢⠥⠖⢲⠀⣇⢉⣹⡇⠀⠈⠀⠀⡿⢭⣙⡒⠒⠰⠶⠶⣒⣒⣿⣗⣻
⠀⠀⣧⠀⠀⠘⡄⠀⠀⡑⠀⠈⡇⠀⡟⠀⠙⡋⠀⢸⡄⢹⡆⢤⠃⡀⠀⠘⠤⠬⠅⢾⠇⠀⠀⠀⠀⢿⡒⠲⠮⢭⡽⢿⣛⣉⡭⠖⢋⣿
⠀⠀⠘⢦⡀⠀⢸⢀⡔⠁⠀⠀⢹⡜⠁⣴⢋⡍⣷⠀⠻⣬⠥⠤⠤⠃⠠⡄⢒⠴⣴⠏⠀⢠⣼⣧⡄⠈⢷⡩⠍⣂⠒⠤⠤⠤⢆⣈⡽⠃
⠀⠀⠀⠈⠙⠦⣬⣚⣀⣀⡤⠖⠋⠀⠀⠙⢶⡴⠟⠀⠀⠈⠲⢶⣄⣐⣤⣹⠾⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠙⠷⢦⣐⣒⣂⣴⠶⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠛⢲⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣠⡞⠁⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⠃⢀⣼⠏⠀⠀⢀⣠⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣜⣦⡔⡵⠃⠀⣠⡾⠋⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠈⠁⠀⠙⢷⣤⣾⠋⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⡀⠀⡤⠤⢄⣄⣈⢑⠆⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⠤⠀⢠⠄⠈⠀⢘⡃⡼⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⢶⡇⠀⠀⠪⠄⠪⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣪⡤⠾⠉⣄⠀⢀⠀⠀⢈⣩⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠋⠌⠀⠀⠂⠰⠎⠙⠢⠿⢚⡿⠋⢙⡴⠛⠳⡄⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠖⠁⡐⢄⡙⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠋⠀⠀⠀⢳⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠇⣀⠀⢈⢶⡓⠀⠀⠀⠀⡄⠀⣰⠏⠀⠀⢀⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⡰⢋⡾⡷⠊⢘⣷⣄⣀⠀⠀⢻⡾⠃⠀⠀⠀⡂⣠⣄⠀⠀⠀⠀⢳⡀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢞⡵⠋⠀⣧⠀⢀⡿⣍⠉⠁⢀⡞⠁⡐⠀⠀⢰⠋⢸⡆⠁⠀⠀⠀⠀⢳⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⡟⠀⠀⠀⢸⣀⡼⠃⢹⣄⣠⠟⢀⡞⢠⠀⠀⣸⠠⠿⣿⣄⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⡇⡀⠀⠀⣸⠏⠁⢀⠆⠛⢁⣴⠏⣰⠃⢠⠀⡏⠀⣰⣿⠙⣦⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⠴⠛⠲⢤⣼⣀⠒⠛⢁⡴⠃⢀⡏⠀⣷⣾⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠒⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠙⠂⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠘⠳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⣠⠀⠈⠏⠀⠀⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠄⠀⠄⠒⢁⠀⠀⠀⠐⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠐⠔⠀⠤⠋⠀⠀⠊⠙⡇⠀⠐⠰⣦⠸⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠠⡄⣀⠀⠈⠃⠀⠜⠒⠃⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠱⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⣁⠙⠃⠀⠀⠀⡠⠀⠀⠀⢤⡆⠀⠀⠀⡀⠒⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘
⠀⠀⠀⠀⠀⠘⣦⠀⠐⠁⠈⢧⠀⠀⠀⢰⠇⠀⠀⠈⠁⢿⡄⠀⠀⠀⣀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⢻⣀⡀⠀⠀⢀⡴⢚⠁⠀⠔⠋⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡑⠂⡊⠀⠢⠟⠫⠉⠁⠊⠐⠻⠁⠀⠀⠀⠀⠀⠁⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⢀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀⠆⠀⠀⠉⠛⠃⠠⣤⡐⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⣁⠀⠈⣀⠀⠠⣀⠈⠂⠀⠀⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢸⡉⠙⢿⢥⡀⠀⢀⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠀⠀⢙⠟⠀⠐⠠⠉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣒⣲⠦⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⡴⠁⠀⠀⠀⠀⠉⠀⠱⣤⣴⣶⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣦⠀⠀⠤⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣼⠁⠀⠀⠀⠀⠀⠂⣀⣠⡽⣿⡯⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣽⡿⠿⣃⡤⠔⠋
⠀⠀⠀⡴⢺⣽⣛⣹⣤⣤⣤⣶⣶⠿⠿⠛⠛⡹⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠀⣛⣛⡛⠫⢭⣑⣒⣬⣵⠆⠀⡀
⠀⠀⠀⠉⠛⠛⠛⢋⠻⣍⠁⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⠀⠲⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⢫⣾⣿⣷⣶⣵⣿⠛⠛⢛⢿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠀⠈⠉⠃⠙⣿⣿⣿⢿⣧
⠀⠀⠀⢰⣿⣿⡿⠟⠃⣿⣿⣿⣿⡿⠿⠟⠃⣓⣬⣾⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⣐⣀⣤⣼⣿⣽⣾⣿
⠀⠀⠀⠈⣿⣕⣦⣘⣧⡉⣋⣤⣤⣶⣶⡿⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣶⠾⠿⠛⠛⠋⠉⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣭⣛⣻⣛⣯⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣤⣀⣠⣴⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠩⠁⠀⠀⠉⠉⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⠠⠣
⠀⠔⠂⢈⠭⠍⠩⠥⠴⠆⢐⡖⠀⡀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢣
⠀⠑⢄⠈⠢⢄⠀⠀⠀⠀⢀⠅⠈⢀⠁⠀⠀⠈⠪⠿⠁⠈⠉⠁⠻⠧⠃⠀⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠁⠢⢄⡉⠒⠤⣀⢸⠂⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠂⠀⠖⠀⠠⠁⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠑⠂⠤⣄⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠠⢄⣈⠁⠒⠢⠄⣀⡀⠀⠀⠊⠀⠈⢀⠀⠀⠀⠀⠰⠁⠒⠭⣒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠂⠀⠉⠒⠂⠤⣄⣈⠉⠙⠛⠠⠄⣀⡀⠀⠁⡰⠃⠀⠀⠀⠀⠉⠒⢅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠠⠄⠀⠤⢀⠀⠈⠛⠒⠒⠠⢤⣀⣉⠉⠑⠒⠂⠠⠤⠤⠀⠀⠀⠕⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠤⠄⠀⣀⠤⠊⠁⠀⠉⠁⠀⠐⠒⠒⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣴⣿⣿⣿⣿⣷⣄
⠀⠀⠐⠇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣾⣿⣿⠟⠘⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣼⣿⣿⣿⡏⠀⠀⠈⣉⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⠻⠛⠛⠙⠿⡿⠿⠟⣻⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣰⣿⢿⠿⣛⣛⡻⠟⠋⠉⠉⠉⠙⠻⢿⡟⣷⣶⣤⣀⠀⠙⠆⢀⣬⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢿⣿⣦⣴⣾⣿⣷⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⡿⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⡆⣈⠈⣏⣛⢄⠀⢄
⠀⠀⠀⠀⠀⠀⣠⠎⣰⠟⣵⣾⣷⣬⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡙⡦⢹⣿⣿⠱⣄⠠⡀
⠀⠀⠀⠀⢀⠞⣡⣾⣯⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢹⣿⣧⠷⠠⣿⣿⡇⣿⣦⡈⢢
⠀⠀⢀⡴⢋⣼⣟⠻⢿⣌⠛⢿⣿⣿⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⣿⣿⠃⣾⣿⣿⣆⠑⢄
⠀⠀⠘⣄⠻⣿⣿⣳⣌⠛⠿⣶⣾⣿⠀⠀⠈⠃⢰⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣾⣿⡟⢠⣿⣿⣿⡿⠃⡴⠃
⠀⠀⠀⠈⠳⡈⢻⣷⣬⣿⣶⣤⣽⣿⠀⠀⠀⠀⠀⢰⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣸⣿⡟⡿⠟⢋⣴⣿⣿⣿⠟⡠⠊
⠀⠀⠀⠀⠀⠘⢦⡙⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣶⣿⣿⣴⣶⣾⣿⣿⣿⡿⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣌⠻⣿⣿⣿⣿⣯⡻⣅⢀⡀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⡀⢀⣽⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⡿⠋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢿⣿⣿⣿⡆⠘⢷⣶⣷⣴⣀⣀⠀⡈⠻⣍⣿⣽⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⢿⣿⣿⣷⣷⣌⡻⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⢟⣩⣾⡿⠏⠿⣿⡟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠻⣿⣿⣿⣿⣿⣶⣶⣬⣭⣙⣋⣛⣻⣭⣿⣿⢺⣿⣿⣿⣶⣄⡿⢋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡩⠀⠛⠿⢿⣿⠟⡠⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⣠⣶⠟⠁⠞⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠴⠄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⣿⣿⣿⣿⠟⣫⣭⢀⣭⣝⣿⣦⡿⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢿⣿⠃⣼⣿⡇⢾⣿⣿⣼⠏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣿⣿⣿⣶⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣭⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡄⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠑⠛⠃⠀⠀⠀⣀⠄⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⡠⠔⠚⠭⢭⡉⠓⠦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠁⠀⠀⠀⢀⠾⢷⣴⡤⣀⠐⠈⢑⠢⣌⢢⠀⠀⢳⡤⠚⢲⡀⠒⢄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡀⠰⠁⠀⠁⠄⠀⣶⣦⣼⣿⣿⠂⢀⡵⠬⠍⠱⡀⢨⣀⠀⠀⠉⠓⠿⠷⣄⡁⠢⠙⡇⠀⠌⠀⠀⠀⠙⢦⢀⡣⠀⠰⠁⠀⢠⣭⣳⡀⢠⣏⣀⣋⣽⡄
⠀⠀⠤⠾⠁⡇⠴⢄⠀⡘⠀⣿⣿⣏⣽⣿⠇⠸⣄⠀⠀⡀⠀⢸⠿⣿⢿⣷⣶⣤⣀⠈⠙⠦⣌⡇⠀⢃⠀⠀⠀⠀⠈⡟⡞⠀⠸⣀⠀⣿⣿⣿⠃⠐⠈⠓⠊⣉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠙⠛⠛⠉⠀⠀⠈⢡⡌⠀⠀⠈⢆⠀⠀⠛⠻⢿⣿⣷⣦⣀⡜⠀⠀⠀⠳⠄⣢⣀⣾⡛⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣦⣀⣀⣈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠯
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⢟⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣻⣛⣿⣟⣛⣿⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡣⣽⠆⣏⠊⠀⠀⠀⠀⠀⢀⡄⠒⠐⢲⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠥⠤⠇⠙⠀⠋⡈⠀⠀⠀⠀⠀⠘⣿⣶⣾⣩⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⢀⣀⣤⠤⢤⣤⡴⢋⠉⢉⠟⢢⡒⢲⠸⡇⠀⠀⠀⠀⠀⠀⠠⠉⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠰⣧⣇⠀⠻⡄⡠⠤⠰⡄⡎⠀⠀⠀⠀⠀⡰⠡⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠉⢿⣰⣶⠊⠤⡬⠡⢤⡏⠓⢤⡀⢀⡼⡱⡟⡜⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⢷⡀⠀⠀⣰⠁⠀⠀⠀⠀⠙⢻⠃⠀⠀⠀⠀⠃⠀⠀⠹⠛⠶⣕⡱⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠙⠦⣴⣳⠤⢄⣀⣀⠀⠀⠀⢀⠄⠀⠀⡴⢣⠀⠀⠀⠀⣀⣈⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢉⣙⡲⠦⣤⣄⣹⠆⠸⠀⠉⠛⣦⡞⠀⠙⠗⠉⣠⣿⣤⢾⣇⣰⠋⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡜⠉⠋⣿⠀⠉⠀⠀⠀⠀⢀⣯⣉⣛⠲⠦⣾⣭⡀⠀⠀⢙⣧⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠸⣄⠀⢀⣀⡤⠶⠛⠛⢛⡉⠙⠓⠲⠦⣭⣙⡚⠷⢯⠁⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⣀⠀⠀⣠⣴⣛⣙⣒⣒⣌⠭⠭⠒⢂⣈⡤⠖⠊⠁⠀⠉⢹⣛⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣨⣽⣟⣉⣉⣁⡀⠤⠤⠴⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠶⠦⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠷⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠉⠙⠻⢿⣿⡿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣄⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⣀⣀⣤⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⠛⠛⠛⠛⠻⣷⣶⠚⠉⢉⣠⡶⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣨⣿⣶⣿⣿⠗⢁⣨⣽⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠺⠿⠟⢉⣁⣤⣴⣾⣿⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⣤⡶⠾⢛⠿⠟⣻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⠹⣅⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣷⡶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⡉⠙⠛⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠙⠁⠀⠀⠀⠈⠉⠙⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣴⣶⣶⡦⣤⣴⣄⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠷⠄⠈⠈⠀⠉⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐⠀⠀⠀⠂⠂⠂⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣁⡀⣀⠹⢤⣅⣿⣦⣴⣴⢶⣤⣶⣅⣥⠸⢁⡀⣄⡠⠀⢀
⠀⠀⠀⠀⠀⠑⠀⠑⣆⣀⠀⠩⠻⠐⢢⡟⠙⢦⠀⡿⠗⢴⠖⢻⣧⡐⠼⠩⠁⢀⣄⡶⠁⠐⠃
⠀⠀⠀⠀⠀⠀⣆⣀⠬⡻⠃⣀⢀⣽⢟⣁⠀⠀⠀⠀⠀⠀⠀⠀⣙⢿⣅⢀⡀⠛⡨⢄⣀⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⣿⠹⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣤⡀
⠀⠀⠀⠀⠀⠛⠓⣖⡀⠌⣿⣷⠀⠀⠀⠀⠒⣶⣤⠊⢠⣴⡶⠂⠀⠀⠐⢷⣽⣏⠄⣑⡖⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⡿⢤⠆⠀⠀⠀⠉⠀⠀⠂⠈⠁⠀⠀⠐⣤⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠹⡿⠛⠉⠀⠀⢠⡀⠀⠂⢀⠒⠀⠀⡀⠀⠀⠈⠱⣮⣿⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢽⣧⡀⠃⣠⢀⢊⠁⢠⠮⠉⠵⠄⠺⡇⡄⢠⢀⣴⣿⣿⠗⠈
⠀⠀⠀⠀⠀⠀⠰⠲⢶⣿⣿⣿⡟⡃⠀⠀⢢⣧⡀⠀⠀⠘⣀⠈⠀⠀⠚⢿⣿⣿⣷⡶⠲⠂
⠀⠀⠀⠀⠀⠈⣋⣠⠞⠋⠋⢩⣿⢿⡄⠉⠘⠈⠶⡂⡸⡈⠁⠀⣠⡶⢠⣾⡿⡯⠛⢦⣈⣋⢀
⠀⠀⠀⠀⠀⣉⢉⠁⠀⠀⠴⣿⠷⠚⠁⢀⣀⣲⣶⡿⢰⢁⢰⣞⡉⠻⠎⢻⡷⠄⠀⠀⢉⣉⡡
⠀⠀⠀⠙⢦⣈⣿⠉⡑⢰⣾⣿⠷⣄⣸⣿⣿⠋⣿⠤⠈⠓⢹⣿⡏⢁⣴⢾⣿⣶⠀⡉⢹⣏⣤⠞⠁
⠀⠀⠀⠀⠀⠘⢛⡼⡛⠉⣸⢡⣴⣌⠛⠙⠁⠉⢸⡆⢚⡌⣿⣿⠓⡫⣽⣦⢻⠻⠻⡻⣜⠛
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣸⣏⡙⣇⡀⣀⣤⣭⡁⢀⡇⡿⠋⠀⠊⣉⣿⣸⡇⠀⠀⠈⠁
⠀⠀⠀⠀⣀⡀⠀⠀⣀⣠⢠⡁⣄⢢⠘⠃⣸⣟⠛⠚⠿⠋⣡⡄⠛⣠⢂⣄⣩⢠⣀⣀⠀⠀⣀⡄
⠀⠀⠀⠤⠬⠟⢁⡉⠀⣀⣼⠟⠘⠁⠁⠈⠁⠈⠀⠀⠀⠀⠈⠋⠀⢁⡟⠩⢿⣄⡀⠈⣁⢙⠯⠤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠚⠛⠛⠛⠛⠓⠒⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣭⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠈⠉⠙⠛⠿⣝⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠻⣍⣉⣭⠤⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⢙⣛⣛⣛⣛⣛⣋⣉⣭⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢣⡈⠉⠙⠓⠲⠤⢤⣤⡤⠴⠚⠁⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⠀⠀⠀⣴⠶⠶⠶⠶⠚⢳⡀
⠀⠀⠀⠀⠀⣠⣏⣀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⣠⣤⠤⠤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠷⠦⣬⣉⣉⣀⣀⣀⣠⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠦⠤⠤⣄⡀⠀⠀⠀⠀⢀⣠⠤⠼⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠛⠛⠉⠉⠉⠉⠉⠛⠛⠒⠦⢤⣀⡀⠀⠳⢤⣀⣀⡴⠋⠀⠀⠀⠸⡆
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠓⠶⠤⣤⣤⣀⣀⣀⣠⣤⠴⢿
⠀⠀⢸⠧⠤⠤⣤⡤⠤⠴⠖⠚⠉⠀⣠⠞⠉⣷⠀⠀⠀⢀⣠⡤⠖⠚⠋⠉⠉⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇
⠀⠀⣾⠀⠀⠀⢀⡤⠴⠶⠶⠶⠖⠋⠁⠀⣰⠃⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠓⠶⠤⠤⠤⠶⠒⠒⠛⠉⠉⣠⣷
⠀⠀⣿⣀⠀⠀⠈⢧⣄⣀⠀⠀⠀⠀⣀⡴⠃⣠⠜⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠀⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⣿
⠀⠀⢿⠈⠉⠓⠦⢤⣄⣉⣉⣉⣉⣭⠥⠖⠋⠁⠀⠀⢀⡤⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠀⠀⠀⢀⡿
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣀⡀⢀⣀⣠⠴⠚⢩⡇
⠀⠀⠀⣧⠀⣀⣠⠤⠖⣒⣛⣛⣉⣙⣛⡓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⣼⠁
⠀⠀⠀⠸⡏⠁⣠⠖⠋⠉⠁⠀⠀⠀⠉⠉⠙⠲⠦⣍⡓⠦⣄⡀⠀⠀⠘⠶⠤⣤⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⢩⠇
⠀⠀⠀⠀⠹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠛⠲⠦⠤⣤⣤⣄⣀⣠⣄⣤⣤⠤⠶⠖⠛⠉⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠹⣤⠶⠚⠋⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣖⠛⠉⠉⣩⠏
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠈⠳⢤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠉⠛⠒⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠉⠙⢲⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣠⠞⠋⠛⠲⣄⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⡤⠟⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣄⣀⠀⠀⠈⠙⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⣄⣠⣤⣤⡤⠤⠶⠚⠋⠉

⡶⣶⢶⢶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⢶⣶⡶⠶⢶⡶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣵⣵⣵⢕⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⠝⢿⣟⠗⡡⡪⠊⡠⠂⠠⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢁⠔⠑⠡⡪⡪⡺⠪⢂⠶⢀⢔⠕⡵⡀⡀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⢀⠞⢕⠕⡡⡫⡪⣪⢎⢊⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠪⠚⢠⢞⢕⡵⡑⠕⡠
⠀⠀⠀⠀⠀⠀⣴⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠠⠊⢀⢔⠕⡫⡪⡪⡪⢊⢄⢀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠔⠕⠁⠈⡨⠊⢁⢔⢑⠔⡡⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠀⡨⡈⢐⠕⠁⡡⠪⡪⢊⠄⠀⠀⢊⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠕⡵⡪⡪⢊⢔⠕⢐⠀⠴⢟⠔⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠈⠐⠕⢀⡠⣪⢔⢕⢕⣔⣕⢄⠔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⢄⡀⠄⠀⠀⠀⡠⣀⠄⡪⠒⠁⠀⠀⠀⠀⢀⢕⡩⣪⣷⣝⢕⣵⢟⡵⡫⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣥⣶⣿⣿⣿⣿⣾⣕⡦⣒⣝⡪⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⡪⣺⣿⣵⣿⣿⣯⡮⡠⠊⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣭⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢵⣫⣿⣿⣟⣿⣿⣫⣮⢔⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⣵⣼⣿⣿⣿⣿⣿⣯⣿⣕⢄⡠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡢⣠⣍⣭⣤⣿⣿⣿⣿⣿⣿⣵⠿⡪⡎⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⡷⣶⣶⣶⣷⣶⣶⣶⡴⣶⢄⠄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⠤⣖⠯⡂⢕⣾⣿⣿⣿⣿⣿⣿⡿⡚⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡒⠯⢐⠫⣔⠮⣂⢵⣾⣿⣿⣿⣿⣿⡿⣟⠟⡢⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣀⡢⠤⠴⡆⠒⠉⣙⠢⠵⣚⠭⣔⠯⢗⣯⡾⣿⢿⣻⣿⡿⣟⠿⡚⠑⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡆⣻⠃⠒⠈⠁⠐⠊⠁⠊⢉⠐⢉⡠⠔⠯⣟⠿⣻⢽⠋⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⡿⠒⠓⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠑⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣋⣩⣟⣿⠟⠿⣶⣆⠀⠀⠀⠈⠙⢲⣄⡀⠀⠀⠀⠀⠀⠄⠀⢼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢤⣶⠞⣿⣿⣿⣿⡿⣿⡿⠙⢋⣤⣶⣾⣿⣿⠗⠀⠀⠀⠀⠠⣿⣿⣦⣰⣄⡀⠀⠀⣀⠈⡿⠿⠷
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠚⠉⠁⠀⠈⠱⠎⠁⠀⠈⠉⠈⡙⠋⠁⠀⠀⠁⠀⠠⡄⣿⣿⣿⣿⣏
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⡾⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⣴⣶⣦⣄⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⢀⡿⠿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⡼⠀⠈⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠋⠻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠤⠀⠀⢐⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣶⣦⠀⠋⠾⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠐⠈⠃
⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠉
⠐⠾⠿⠀⠈⠁⠠⣄⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⣽⡛⢻⣿⡏⡇⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⠟⠁⠀⢻⡼⠀⠀⢀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣩⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠐⠁⢀⣀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣠⣎⠀⠀⠈⠁⠀⠀⢀⣄⡀
⠀⠀⠀⠀⢀⣀⣈⠁⠀⠀⢀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⢡⠄⠀⠀⠴⠋⠙⠁⠀⠀⠀⠒⠀⠀⠿⠋⠁
⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠁⠀⠰⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠿⠿⠛⠻⠿⠿⠷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠋⠁⠈⠙⠛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⢀⣤⣶⠶⠿⠛⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣠⡾⠟⠉⢀⣠⣤⡶⠾⠟⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣠⡾⠋⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⣴⡿⠃⣼⡇⠸⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣠⡾⠋⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄
⠀⠀⠀⢀⣼⠟⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡾⠟⠁⠀⣠⣾⠏⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠈⢿⣆
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣴⠟⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⢻⣆
⠀⠀⣾⠃⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡏⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⢀⣀⣤⡾⠋⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⢀⡿⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢉⣩⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⣦⠀⠀⠀⠀⢠⣾⠏⠘⣧
⢸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⢠⣿⠁⠀⠀⢠⡿⠃⠀⠀⢿
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⡿⠁⠀⠀⣰⡿⠁⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⡿⠋⠀⠀⢀⣼⠟⠀⠀⠀⣠⡿⢻
⣿⠀⠀⣀⣤⣶⠶⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⣀⣀⣤⣶⠟⠋⠀⠀⠀⣠⣾⠋⠀⠀⠀⣴⡟⠁⢸
⣿⣠⣾⠟⠁⠀⣠⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣠⣾⠋⠀⢠⣿
⢹⡟⠁⠀⣠⡾⠋⠁⠀⠀⠀⠈⠉⠛⠿⢶⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⣠⡿⣿
⠘⣧⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⣴⡟⢁⡿
⠀⢻⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣠⣶⠟⠁⠀⠀⣠⣾⠋⠀⣼⠃
⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁⠀⢀⣤⡾⠛⠁⠀⠀⣠⡾⠟⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠁⠀⣀⣤⡾⠟⠉⠀⠀⣠⣴⠿⠋⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠀⣀⣤⣶⠿⠛⠉⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⣀⣴⡶⠟⠋⠁⠀⣀⣤⣶⠾⠛⠉⠀⢠⡀⣠⡄⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢀⣿⠃⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣠⣶⠿⠛⠉⠀⠀⢠⣦⢠⣿⠱⠿⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⡇⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⣿⠃⠈⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⠀⠀⠀⣰⡿⠃⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢾⣿⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠈⠑⢦⡄⠂⠀⠀⠀⠀⠀⠀⣴⠊⢉⡠⠊⠉⠳⣄
⠀⠀⠀⠀⠀⢀⠔⡁⠀⡴⣀⠾⠉⠠⣀⠾⢹⠂⠀⠀⠀⠀⠀⢸⠃⠂⠁⠐⠀⠠⠠⢼⡖⠦⠄
⠀⠀⠀⠀⠀⡌⠀⠐⠃⠋⠁⢀⣨⣖⡵⢁⣿⠀⠀⠀⠀⠠⠔⢻⡤⠖⣀⡔⠀⠀⠑⠄⠓⢀⡀
⠀⠀⠀⠠⠄⢲⠀⠑⠴⠒⣺⣉⡴⠊⢀⡿⢁⡀⠀⠀⠀⠠⠤⠘⠣⣤⡤⠄⠰⢀⣠⠏
⠀⠀⠀⠀⢨⠁⠙⠺⠮⣵⡿⠋⠀⡠⢋⠺⣶⠀⠀⠀⠀⠀⠐⠈⠀⠨⢉⠛⠋⠍
⠀⠀⠀⠀⠸⠀⠳⠀⠐⠀⠀⢀⠔⠀⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠃⠲⠷⡔⠀⠄⠹⡄
⠀⠀⠀⠀⠀⢀⢠⢠⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⡀⠁⢀⠈⠀⣁
⠀⠀⠀⠀⠠⠠⢿⢿⠏⠀⠀⢊⣉⡀⢗⠃⠀⠀⠀⠀⠀⠀⠸⡄⠏⠵⢾⡏⠙⣀⣴⣾⠇
⠀⠀⠀⠀⢠⠄⠛⢉⠑⠛⡍⠀⢉⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡃⠘⠃⠂⢀⡼⠋
⠀⠀⠀⠀⠀⠲⣀⠀⠀⠐⠡⠄⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠇⠦⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣀
⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⡀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠓⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠐⠊
⠀⠀⠀⠀⢰⠀⠄⠌⢤⡁⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⢠⡄⠇⠀⠀⣀⢴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠜⠀⢸⠃⠳⠀⠐⠠⠆⠃⠀⠀⠀⠀⠈⠳⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠐⢄⣀⡸⠀⠀⠆⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⠀⠀⠀⠈⢉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⡀⠀⠈⠛⠂⢱⣤⠔⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢀⠀⠒⠀⠈⠀⠀⠀⡔⣰⠄⠀⢱⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡠⢾⣿⡄⠉⠀⢰⠉⠙⣷⠀⠀⠀⠀⣆⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁
⠀⠀⣴⠟⠁⠸⣿⣿⣂⣀⡈⠃⡚⢃⣤⣶⣤⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢘⠉⢄⠀⠀⠛⢛⣛⣩⣭⡲⠖⠛⠋⠉⢱⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⣠⣤⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣀⣴⣿⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⠓⡀⠉
⠀⠀⠀⠀⢃⡐⠙⠀⢿⣶⣿⣷⣿⣿⣿⣿⡉⠀⢉⣄⡀⠁⠀⠀⢠
⠀⠀⠀⢀⡄⠀⠀⠐⢿⣿⣿⣿⠹⢿⣿⠟⠛⠂⠈⠛⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣾⢠⣶⡀⠀⠈⠙⢻⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣾⣿⣿⣷⣠⣤⢈⣿⠉⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⢿⣿⣿⣿⣿⠙⠟⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠐⢀⡻⣿⡏⠀⠀⠀⠈⠀⠀⠒⠒⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⣾⣅⠀⢳⠤⠀⠀⠀⠀⠳⣾⠣⠟⣹⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣾⣶⡤⠖⢃⣄⠉⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠟⠓⠄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠾⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⡤⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠴⠾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠀⠴⠀⣀⣢⣄⣄⡀⠀⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⢀⣽⡏⠉⡀⠀⢀⣨⢿⣶⣄⣤⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠖⠒⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢈⡟⠙⢦⣤⡄⢻⠇⠡⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⠀⠀⠂⠀⠀⠀⠀⠘⢦⠀⡀
⠀⠀⠀⠀⠀⢠⣼⡃⠀⣿⠉⠀⠀⣷⣄⡀⠀⣨⣿⣷⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⡆⢉⠠⠤⣈⡳⠾⢧⡀⡀⠀⠘⢂⠀⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⡶⡄⣤⣼⠁⠉⠻⣯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠳⣤⡀⠻⢄⣀⣀⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠉⣷⠀⠀⠘⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠠⡀⠉⠿⣀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢏⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠆⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠛⠻⠿⢶⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣔⣋⡀⠀⠀⠐⢾⣓⣫⢤⡀⠉⠉⠉⠓⠒⠒⠒⣒⣒⣒⣒⣒⣒⣻⠦⡀
⠀⠀⠀⠀⠀⡴⠋⠹⡄⠉⠉⠓⠲⠦⠴⠒⠋⠀⢀⣠⠤⠖⠚⠉⠉⠁⠀⠀⠀⡖⠒⠒⠒⠛⢦
⠀⠀⠀⢀⣞⠓⠤⠤⠋⠀⠀⠀⢀⣀⣠⠤⠒⠋⠉⠀⠀⠀⠀⢴⣒⣒⡒⠒⠊⠁⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⡞⠀⠉⠙⠒⠒⠚⠋⠉⠉⢀⣀⡤⠤⠤⠖⠒⠒⠒⠶⠤⠤⣈⡉⠉⠙⢆⣀⣀⡠⠚⠉⠉⢳
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⠴⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠙⠒⠦⢭⣍⣀⣀⣀⡤⠴⣇
⠀⠀⡟⠒⠶⠶⠖⠒⠚⠉⢀⡴⠋⢹⠆⠀⢀⡠⠴⠒⠉⠉⠉⠈⠉⠙⠢⢄⡀⠀⠀⠀⠀⢀⣀⣀⡤⢼
⠀⢰⡇⠀⠀⢰⠋⠉⠉⠉⠁⠀⢠⠎⢀⡴⠉⠀⠀⠀⠀⢀⡤⠤⠶⠲⠤⣀⠉⠉⠛⠉⠉⠉⠁⢀⡤⢺⡄
⠀⠸⡟⠒⠤⣄⣉⡓⠒⢒⣒⣚⡥⠖⠁⠀⢀⣠⠤⠤⠖⠃⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠖⠚⠁⠀⢸⠇
⠀⠀⣇⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⣀⣀⣠⠤⠚⣹
⠀⠀⢸⣄⠤⠖⣒⡭⠭⠭⠭⠭⣍⣓⠲⢤⣀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⡏
⠀⠀⠀⢣⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢮⡙⠲⢤⣀⣈⠉⠛⠋⠉⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁⡜
⠀⠀⠀⠈⢣⣠⠤⠖⠒⠒⠲⠤⡀⠀⠀⠀⠀⠈⠲⢤⣀⣈⣩⣭⣭⣉⡉⠉⠉⠁⠀⣤⠖⠒⢒⡟⠁
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠈⠲⣤⠎
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⣀⣀⠉⠉⠉⠉⠉⠉⠉⠓⠒⠦⡄⠀⠀⠀⠀⠈⣹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣞⡁⠀⠈⠓⠤⣀⡞⠉⠉⠛⠒⠒⠋⠁⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠷⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠤⣄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⢣⢀⠔⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⢀⡀⠀⡏⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⢇⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⢸⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠓⠒⠒⠚⠦⣄⣀⣠⡴⠧⠼⢦⣀⣀⡴⠏⠤⠤⠤⠽⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠘⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠇⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢀⣠⠴⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⢤⣀
⠀⠀⠀⢠⠖⠉⢀⡤⠖⢿⡖⠢⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠔⠒⠒⣺⠗⠦⣄⠈⠓⢦
⠀⠀⢰⠋⠀⡰⠋⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⢳⡀⠈⢳
⠀⢀⡏⠀⢸⡇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣷⠀⠈⣇
⠀⢈⡁⠀⠸⣇⡀⠀⠀⠀⠀⠀⠻⣯⡐⠒⠒⠒⠢⠤⠤⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⣀⡿⠀⠀⣻
⠀⡴⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠳⡄
⣸⠁⠀⣠⣤⡀⠈⠉⡧⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠙⠛⠛⣚⣳⡾⠛⠁⠀⠀⠀⠀⠀⠀⠰⡏⠉⠀⣀⣤⡀⠀⢹
⡏⠀⢰⡏⢧⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣦⣤⣤⣤⣤⣶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⠏⣷⠀⠈
⠳⣤⡼⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠛⠛⠓⠲⠦⣼⡇⢸⡇⣿⠀⣿⡤⠶⠒⠛⠛⠛⠛⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⠀⣀⡀⢀⠀⠀⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⢖⠀⠀⠑⢡⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⠂⠄⠀⡈⠀⡀⠀⠀⢀⠈⠶⠅⠄⠈⠂⠑⠈⠀⠀⡀⠈⡁⠠⠆
⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⠈⠀⠅⢈⠂⠀⠁⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠐⢀⢈⠂⠂⠀⣟⠂⠐⣀⠆
⠀⠀⠈⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠔⠠⠀⠀⠄⠀⠆⠀⢲⠀⣀⠀⠀⠀⠐⠀⠢⠄⢎⠀⡐⠐⢄⠀⠈⠉
⠀⠈⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠠⠄⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⡀⣀⠀⠄⢎⠀⡑⠰⡀⠒⣦⣀⠀⢆⢄⡀
⠀⠐⠀⡀⠀⠀⡀⢀⠀⠐⠾⠠⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠈⠉⠀⠀⠀⠀⠀⠁⢀⣀⣀⣃⣀⡀⠀⢀⣀⠀⠂⠈⠻⠆⠐⠤⠃
⠀⠀⠀⠧⡈⢀⢁⢸⠀⠀⠈⠋⠁⠀⠐⠉⠑⠀⡛⢣⠼⠆⠀⠓⠃⡀⠀⣀⠀⠀⠀⠀⠄⠀⠒⡒⡒⣒⡒⠓⠀⠐⠀⠀⠡⠂⠀⠀⣀
⠀⠀⠁⢀⡤⠀⣬⡀⠀⠀⠀⠀⠀⠨⢅⠆⠀⡀⠙⠮⠞⢁⡀⠆⠆⠈⠀⡉⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀
⠀⡰⠒⢂⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⢣⡄⠠⡃⡂⠠⢂⡀⠰⠠⠌⠁⠐⠁⠀⠀⠀⠂⠐⠀⠀⣰⣆⡰⠿⠚⠇⠀⠀⠦⢂⣤⠀⡀⠨⢀
⠀⡁⠤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢠⠀⠈⠀⠀⠀⡁⠀⠀⠀⢈⡃⠀⢢⠀⢀⣀⠐⠀⣀⠈⢉⣩⠔⢉⡀⠀⠠⢐⠂⠩⣆⠀⠂
⠀⠈⠒⠁⠀⠀⠐⡄⠁⠀⠀⠒⠒⠒⠂⠈⢀⡀⠀⡀⠀⡡⠀⠠⠀⠀⠁⠀⠀⠄⠈⠋⠀⠀⠍⠁⠉⠀⠠⠀⠀⠀⢴⡆⠀⠀⠀⠐⠸⠆⠁
⠀⠀⡟⠄⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⠛⠀⠀⠀⡀⠀⡐⠀⠀⡎⠀⠑⠀⠄⠡⡡⢀⠀⠄⠈⠁⢸⠂⠉⠀⠀⠀⠐⡁
⠀⠀⠋⠁⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠀⠁⠀⠀⢀⠠⣠⣄⢈⠄⠀⠐⠀⠀⠈⠒⠪⠀⠀⡐⠐⡐⠀⢀⠄⠀⠐⠀⠀⠀⡐
⢀⣐⢢⠢⢠⠀⠀⠀⠀⠀⠙⢹⠀⠁⠆⣠⠂⠈⠀⠐⠈⠨⠚⠋⠉⠆⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⡠⡀⠁⠀⠀⠀⠁⠀⠘⠠⢠⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠱⠊⠀⠠⠆⠈⠒⠇⠘⠄⠀⠁⠔⢀⠀⠀⡄⠢⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠈⠀⠀⠋⠃⠀⠀⠀⠄⠀⠀⠬⠄⠀⠀⠀⠀⠀⢂⠂⡀⠒⢐⠀⠀⠁⢀⠀⠅⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠉⠙⡧⠀⠈⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⠀⡞⠹⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠶⣦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⣐⠰⣟⠀⠀⠀⢰⠉⢻⠇⢠⠀⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣰⠋⠙⣿⠀⠀⠀⠀⠐⠪⠃⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠠⡀⠳⡴⠛⠀⢀⡈⢁⣀⡪⢊⣠⠾⠛⠟⣻⣿⡷⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣖⣫⣿⣶⣮⣝⢿⢜⣋⣠⢦⣿⠁⠀⠀⠀⢱⣿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡆⢿⡘⣿⣧⠻⢆⡀⣀⣠⣬⠁⠃⠂⠀⠀⠀⢀⣴⢿⣿⣦⠀⠀⠀⠀⣀⠁⠈⡇
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣇⣛⣽⣿⣿⣿⣿⣿⣿⣏⡚⠋⡁⡘⠉⠁⠁⢀⡀⠀⠀⣼⠀⠀⠘⡿⢃⠀⡄⠀⠘⢆⠀⡄⠰⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣷⡔⠜⠆⣤⠝⠳⠟⠀⠀⠈⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣀⢄⣀⣠⣤⣴⣄⣤⡤⡄⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠙⢿⣿⣿⣿⣿⣿⣿⣅⠹⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠰⠆⠀⢠⠉⢸⠟⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡄⠀⠛⠁⠀⣀⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣒⡔⣄⣶⣶⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣆⠹⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣛⣉⣩⣭⣽⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠉⣲⣤⡀⠀⠀⠀⠀⢠⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⢀⣠⠴⠾⢦⣤⣄⣰⠟⣥⣾⣿⡳⣄⠀⠀⢸⡆⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⢤⣄⣀⡀⠄⠴⢿⣖⢲⣀⣀⣄⣴⣿⣾⣯⠄⠀⠀⠀⠈⠙⢏⠈⣇⠁⣯⡾⢍⡑⢄⣸⣧⠏⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣛⠒⠀⠀⠄⢀⡈⣙⣿⣷⣄⠀⠀⠈⠉⠀⠀⢹⣿⡃⠟⠿⠆⠀⠀⠀⠀⠈⣆⣿⠀⣌⣿⣤⠉⢾⠉⠀⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠲⠄⠀⠀⠀⠀⠊⠉⠉⣿⣿⣿⣂⡰⠞⠚⠛⠓⢺⡏⠑⣀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠃⣹⣿⠟⠀⢸⡗⣺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⢀⣼⠃⠀⠈⣻⣶⣦⣤⣀⡀⠀⠉⠿⠾⠟⠋⠀⣀⣼⠂⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠛⠲⠿⣷⣮⡀⠀⠀⢸⣿⠃⠀⠀⠀⣴⠞⠻⣧⡴⠚⠛⠉⠉⣿⢻⡿⠿⢿⣿⣿⡶⠿⠿⢿⡛⠛⠋⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⣷⣄⣼⠃⠀⠀⢀⣾⠁⠀⠀⠈⢻⡷⠄⠀⣰⠁⢸⡇⠀⠀⠙⣿⣝⠢⠀⠀⠈⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣦⡀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⢀⣾⡏⠀⠀⠀⠀⡼⠻⠶⣾⡧⠀⣼⠃⠀⠀⠀⠸⡌⠀⠀⠀⠀⣤⣤⡾⠁
⠀⠀⠀⠀⡀⠀⢀⡾⠀⠀⠀⠈⢻⣄⠀⢀⡠⠛⡽⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠃⠀⢀⣿⣧⢠⡏⠀⠀⠀⠀⠀⣇⣀⣤⣴⠾⠟⠉
⠀⠀⠀⢰⣧⣄⣸⠣⠀⠀⠀⠀⠀⠹⠁⠁⠀⠀⣧⣀⢠⠀⠀⣾⡇⠀⠀⠀⠀⠰⠀⠀⣼⣿⡏⡾⠀⠀⠀⠀⠀⣼⠛⠉⠉
⠀⠀⢀⣼⡿⠛⠻⣄⢐⣶⣦⣴⣄⡀⣧⠀⠀⠰⢻⣿⣿⣿⣿⠟⠀⠀⡀⢀⠀⢸⡀⢰⡿⠹⡿⠁⠀⠀⠀⢀⡼⠃
⠀⢠⠊⢸⠀⠀⠀⠀⠙⠉⠁⠈⠉⠻⢿⣷⢶⣶⣧⣼⠩⢻⠏⠀⢰⣼⣴⣿⣦⣦⣳⣜⡇⠀⠁⠤⣤⣤⡶⠋
⠀⡜⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠈⢻⣷⠈⠑⢿⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠛⠛⠻⠶⠶⠶⠾⠋
⠀⡇⠀⢸⡆⢠⠀⠀⢳⣤⠀⠀⣸⠁⠀⠀⠿⠀⠀⠈⣦⠀⢤⣶⠟⠁⠀⠈⠙⠛⠶⢦⣤⣤⡤⠤⠂
⠀⢷⡀⢸⣇⠘⣷⣄⣀⠙⣷⣤⣟⠀⠀⠀⠀⠀⠀⣠⠟⣠⠼⠋
⠀⠘⠙⣺⣷⠀⣼⠋⠉⠋⠙⠿⠟⠢⠤⠤⠤⠐⠚⠋⠉
⠀⢴⣼⣿⣿⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⣹⠟⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠷⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⡤⠴⠞⠋⠁⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣄
⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠛⠉⠁⠘⣧
⠀⠀⠀⠀⠀⣰⣏⣀⣠⣤⡤⠶⠚⠋⠉⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆
⠀⠀⠀⠀⣾⣀⣀⣀⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠒⠛⠛⠋⠉⠁⣷
⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠛⠉⠉⠉⠉⠛⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⠤⡿
⠀⠀⠀⠀⣯⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠖⠛⠋⠉⠉⠙⠛⠓⠶⠦⢤⣤⣀⣀⣀⣀⣀⣠⣤⢴⡞
⠀⠀⠀⠀⠀⠀⠻⣟⠓⠒⠶⠶⠶⠖⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣉⣿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠯⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡸⠀⠘⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⢀⠄⠑⡶⠏⡁⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠸⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠩⠠⠄⠷⠀⡰⣘⠗⠃⠙⡀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠍⠑⠀⠔⠂⠀⠀⠀⠐⡀
⠀⠀⠀⠀⡀⠃⠀⠀⠀⢀⠎⠀⠋⠀⠁⠀⠡⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠄⠈⠀⠀⠀⠀⠀⠄⢠⠳
⠀⠀⠀⠂⠃⢢⡀⢸⠀⡞⠂⠁⠈⠀⡀⠀⠆⢠⠄⢀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⡀⠀⠐⡂⣤⣠⠀⠀⢀⡃
⠀⠀⠀⠀⠘⠀⠑⠈⢆⢿⠀⠄⠀⠀⠀⣤⠏⠄⣌⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢾⠃⢘⠁⡼⣵⡿⠘⡱⢿⠡⡟⢹⢘⡃
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠚⢄⢰⠜⢠⠾⠃⡈⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠥⠀⠀⢀⡪⠍⠀⠀⠠⠈⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠐⣐⡝⠤⠠⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠫⠀⠀⠐⠍⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⡄⠀⠀⠀⠢⠐⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣤⣄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⡏⠐⠤⡀⢀⠄⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠡⢭⠯⢽⡐⢤⡀
⠀⠀⠀⠀⢀⣼⢁⠄⠴⠢⠃⠋⠘⡾⢣⠚⠓⡻⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⢰⢋⡠⠉⠂⠤⢄⡒⠼⠄⢳
⠀⠀⠀⠀⠚⠈⠀⣀⠈⠠⠈⣀⠐⡀⠄⠡⠊⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⢹⠂⢠⣀⠀⢸⡀⠂⠖⣑⣦⣴⣥⣖⠄⡸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠐⠉⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⢃⡰⣚⢉⠩⡅⠻⢴⡋⢩⡈⡙⠉⢺⠞⠁⢰⢐⠀⠉⠉⢀
⠀⠀⡴⣻⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⢠⠅⠀⠀⠀⠸⡭⣄⣅⣂⣓⡒⠠⣐⢈⠒⡄⡀⠀⢣⣀⠐⠀⡀⠈⠀⠄⠘⡆
⠀⡸⢠⠛⡝⠀⠦⠢⢤⡀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠁⠀⢰⡜⢀⢾⠀⠀⠀⣽⣼⠟⠛⠿⣽⣷⣬⠳⡍⠄⠁⠈⠩⠫⠖⠑⠒⠮⣅⡊⠰⠃
⠀⡄⢨⡆⠐⣤⣀⡔⠀⠱⠀⠀⠀⠀⢀⠘⠁⠠⠠⠐⢠⠿⠱⠀⡸⠀⠀⠀⠉⠿⠂⠀⠀⠈⠻⣟⢷⣎⡲⢄⣀⣰⠇⠀⡀⠀⠀⠈⠻
⠀⠱⠰⡙⣀⠘⢎⡉⠃⠹⠆⠀⠀⠀⢨⠈⠀⠀⢀⣴⡃⠀⣠⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢣⡂⢅⡀⣆⡈⠀⢠⡀⠀⡀
⠀⠀⠀⠊⠸⢄⠙⡵⠇⡀⢐⠀⠀⠀⠸⣄⣰⠟⢉⣐⣈⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣈⠀⠀⠀⢏⡀⢋⡁⢠⡿
⠀⠀⠀⠀⠀⠈⠈⠳⠂⠙⠚⠃⠀⠶⠒⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣐⡹⠴⠊
⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⡀⡸⡟⡃⠀⠀⠀⠀⡺⣿⡇⠀⣀⣀

⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⡀⡀⢀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⣿⣿⡿⠟⠛⠻⢿⣿⣿⡿⠛⠉⠉⠉⠙⢿⣿⣿⣿⠿⠛⠻⠯⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⣿⠁⠠⠄⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⣶⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠦⡀⠀⣏⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠔⠄⣬⣄⠀⠀⠀⠀⠀⠻⡆⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⢀⠀⣤⣴⢆⣤⡀⣠⣤⡄
⠀⡠⣤⣠⣾⣿⣿⣿⣦⣤⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠆⠰⣿⡿⣡⣌⣻⣿⣿⡇
⠀⠷⠹⢿⠿⣿⣿⠿⠇⠘⣿⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⢃⣻⣅⣟⣥⠎⠛⠙⡇
⠀⠛⠛⠛⠋⠙⠿⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⢲⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣍⠟⣷⣷⠄⠀⣿⡀
⠀⠄⢀⣦⢴⣶⣶⣶⣶⣴⣦⣟⢰⣾⣯⣿⡥⢦⡀⣿⣷⠞⣷⢦⣄⣰⣾⣤⢀⠂⠀⣃⣶⠧⣿⣮⣿⣯⣏⣾⣿⣅⣴⣯⡇
⠀⠄⣰⣥⣰⣿⣿⣧⣻⢏⣿⣿⠿⢻⣿⣽⣿⣦⣥⣟⣿⢷⠙⡳⣿⣿⣿⣿⣏⡯⢬⣷⣿⠗⠘⠋⢻⣵⣽⣿⣿⣼⣥⣿⡇
⠀⣷⣿⣿⣿⣯⣿⣿⣭⣡⣤⣘⠿⢿⣿⣿⣿⠿⣈⣙⡋⠙⠙⠻⣿⠛⣹⣿⣿⠀⢀⠿⢿⣆⡀⠐⡉⢸⣯⣽⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣼⣿⡟⡛⣩⣿⣛⣿⣻⣉⣾⣿⣏⣿⡻⠴⢬⣿⣿⣾⣿⣿⢿⣿⣿⣷⣴⣾⣿⣗⢺⢿⣿⣏⣭⣵⣾⡇
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣾⣷⣿⣿⣿⡿⣜⣫⣽⣵⣿⣿⣿⣿⣿⣻⣧⣾⠟⢁⣾⣿⣿⣿⢿⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⠿⠿⣿⡿⠿⠿⣿⠿⢽⣿⢿⣿⠿⣿⢿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠯⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢣⡀⠀⡎⠀⣹⠟⢧⣌⣧⣠⠏⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡂
⠀⠀⠀⠀⠀⣾⢙⣯⣸⡆⠀⠀⠁⠀⠀⠁⠀⠁⠃⠀⠁⠀⠀⠁⠀⠀⠑⢼⣷⠋⠀⠀⢀⣨⠟⠁
⠀⠀⠀⠀⠀⠹⢿⣤⡿⠃⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡄⣦⡔⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢠⣴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠄⠀⠀⡀⢧⣙⠂⠁⠠⣄⠀⠀⠀⠀⠨⠃⠀⠀⠀⠙⠀⠉⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠻⠁
⠀⠄⠀⠀⠀⠀⠀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠂⠀⠀⠐⠲⠢⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠂⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄⠐⠀⠀⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⣀⠐⠿⠇⠀⠀⠀⠀⠀⠀⠀⠎⠀⠄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀
⠀⠀⠴⠀⠀⠀⠀⠀⠀⠺⠿⠈⣿⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡀⠀⠀⢀⠄⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠄⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⠈⠀⠀⡄⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠁⠀⠀⠀⠀⢠⣿⣿⣿⠁
⠀⠐⠠⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠀⢸⣿⣿⣿
⠠⠀⠀⠀⠶⢠⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⢀⣨⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⠟⠀⠀⠀⣀⠌⢿⣿⣿⣆
⠀⠄⠀⠙⠀⡐⠀⡉⠀⠀⠾⠃⠀⠀⠀⠀⠁⠄⠁⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡾⢦⡀⠀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⢤⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⢠⠀⡀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠗⠀⠀⠀⠀⠙⠁⠀⠀⠀⢸⡟⣯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠈⠐⠀⠵⠀⠄⠁⠈⠀⠀⠀⠠⠀⠀⠀⢁⣠⡄⠀⠀⠀⠀⠀⠀⢤⣤⡄⠈⠻⣷⡿⠀⠀⠉⠃⠂⠀⠀⠀⠁
⠈⠀⠀⠀⠀⠀⢠⣶⡄⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠔⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⣤⡶⠀⠀⠻⠿⠃⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⡴⢿⠗⣦⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠸⣿⡗
⠀⠀⠲⣀⠀⢀⣾⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⡀⠀⠀⠀⢠⣤⣤⡄⠀⠰⣾⣿⠆⠀⠘⣧⡞⢹⣿⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠲⢁⠀⢸⣯⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠃⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠦⢁⠀⠀⠹⠿⠋⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢃
⠀⠀⠀⠁⠀⢀⡀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⢀⠀⠀⠀⠀⠸⠷⠅⠀⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠚⠛⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠈⠀⢠⡄⠀⠀⡴⠀⠀⣤⠀⠈⠀⠀⠃⠀⠀⢀⡤⠔⣶⡖⠒⠦⣄⠀⠀⠀⠀⠀⠀⣴⠀⢰⡦⠀⠀⠀⠀⠀⠠
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⢀⡔⠁⠀⢰⠃⢳⡀⠀⠈⠳⡄⠀⠀⠀⠀⠐⠃⠀⠀⠁⠜⣃⠀⠌
⠴⢁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣖⠒⠒⡿⠒⠚⢿⡒⢛⡻⢿⠀⠀⠀⣘⠂⠀⠘⠀⡐⠀⠁⠀⠀⢡⡉⠡
⡂⠲⡒⠘⠀⠀⠘⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⢶⣧⡀⠀⢈⣷⡋⠀⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣂⣜⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⢿⣯⠉⠉⠉⠹⣿⣟⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠠⣾⣿⣍⠀⠀⠀⠀⠈⢹⣿⣠⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠈⣻⡇⠀⠀⠀⠀⢸⣿⠟⠃⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣀⣀⠀⣠⣤⣾⠟⠁⠀⠀⠀⠀⠀⠉⢀⣀⣀⣀⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠹⣷⣼⡟⢻⣷⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠛⠛⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣿⣷⣄⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠙⠛⢀⣴⡶⠿⢶⣤⣤⡀⠀⠀⠀⠙⠿⠾⠟⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⠁⠀⠀⠀⠉⠹⠷⢶⣦⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⢾⣏⠀⣠⡾⠟⠛⠋⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⣿⣛⣋⣁⣀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⢻⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⣀⡀⣠⡤⠤⠀⢸⣧⣤⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⠿⠀⠘⠋⠀⢀⡀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⢀⣀⠀⣶⣶⣾⣿⣧⣀⣰⣬⠻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⢀⣴⣿⡟⢀⠈⢿⢿⠏⢽⣿⣿⡗⠆⢻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣾⣿⣿⣷⡆⠀⠰⠖⠀⠀⠙⠋⠁⣀⣀⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠘⣿⣾⠟⠯⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣿⣯⠂⠀⡀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⠙⣷⣳⣢⠀⠀⠀⠀⠀⠀⠙⢀⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠋⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⣿⣿⣿⣿⣿⣏⢹⣦⡔⡂⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⡈⠁⢀⠈⢀⡀⠀⠀⠀⣾⢿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣽⣶⡟⠀⠀⠈⠁⠈⠁⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣿⢋⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠂⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠕⠈⠀⠈⠁⠂⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⠥
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⠀⠡⠀⠀⠀⠀⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡦⠀⢀⡉⠉⠐⠠⠄⢀⠀⠀⠀⠀⢳⠀⠀⠑⠄⠠⠀⠀⠀⠀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠂⠀⠁
⠀⠀⠀⠉⠢⡀⠀⠉⠀⠐⠂⠄⢈⡁⠒⠠⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠐⠂⠀⠀⡁⠠⠀⠤⠤⠤⠀⡄
⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⢀⡠⠔⡠⢁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠁⠀⠀⠀⠀⢀⡀⠄⠐⠂⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡠⠐⠂⠉⠀⢈⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠒⠒⠊⠉⠀⡠⠔⠁⢀⠔⠁⠀⠀⢀⠠⠐⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠂⠐⠒⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢔⠒⠠⠄⢀⣀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠛⠛⠛⠛⠒⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢭⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠈⠉⠙⠓⠻⣽⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠻⣍⣉⣭⠤⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣭⣭⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢳⡈⠉⠉⠓⠲⠦⠤⠤⠤⠴⠚⠁⠀⠀⢀⣠⡤⠶⠒⠛⠉⠉⠁⠀⠀⠀⣴⠖⠲⠶⠖⠚⢳⡀
⠀⠀⠀⠀⠀⣠⢯⣀⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠓⠦⣬⣉⣉⣀⣀⣀⣤⡤⠤⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠶⠦⠤⣤⡀⠀⠀⠀⠀⢀⣠⠤⠼⣆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠛⠒⠶⢤⣀⡀⠀⠱⢤⣀⣀⡴⠉⠀⠀⠀⠸⡆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠉⠛⠲⠤⢤⣤⣄⣀⣀⣤⡤⠴⢿
⠀⠀⢸⠧⠤⠤⠤⠤⠤⠴⠒⠛⠉⢀⡠⠞⠉⣷⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⣼⠀⠀⠀⢀⡤⠶⠶⠶⠶⠖⠋⠀⠀⣰⠃⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠓⠶⠤⠤⠶⠶⠒⠚⠋⠉⠁⣠⣧
⠀⠀⣿⣀⡀⠀⠈⠧⣄⣀⡀⠀⠀⣀⣀⡴⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠁⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⣿
⠀⠀⢻⠀⠉⠓⠲⠤⣄⣈⣉⣉⣉⡭⠵⠖⠋⠁⠀⠀⢠⠤⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠋⠉⠀⠀⠀⣀⡟
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣀⣀⣀⣀⣠⠴⠚⢩⡇
⠀⠀⠀⣧⢀⣀⣤⠴⢖⣚⣋⣉⣉⣉⣙⣛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⣼
⠀⠀⠀⠘⡏⠁⡤⠞⠉⠁⠀⠀⠀⠀⠈⠉⠙⠓⠦⣌⡙⠲⢤⣀⠀⠀⠘⠲⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⢱⠇
⠀⠀⠀⠀⠹⡞⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⠙⠒⠶⠤⠤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠚⠋⠉⢀⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠙⣦⠖⠛⠉⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⠶⠶⠶⠦⢤⡀⠀⠀⠀⠀⠀⣞⠉⠉⠉⣡⠏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠈⠓⢦⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠙⠛⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠈⠙⢓⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⡴⠚⠉⠙⠲⢤⡀⠀⢀⡤⠤⠤⠤⢤⣤⣤⠴⠚⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⣤⣤⣤⣤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣤⡀
⠀⠀⢹⣿⣿⣿⣿⣿⣼⣷⣦⣤⣀⣀⡀⠀⠀⠉⠛⠷⣶⣦⡀
⠀⠀⠀⢻⣿⣿⣿⣿⡟⠻⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⡏⠙⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⢠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⠀⠀⠀⣿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠻⡭⢿⡒⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⣿⣶⣿⣜⠇⣠⢿⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢀⣷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣿⣏⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⣟⢿⡃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠷⠾⠀⣤⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⡿⠽⣷⣄⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠈⠀⠀⠀⠀⠙⢿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠉⠉⠙⠻⢿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣻⣾⣝⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⢿⣿⣦⣀⣀⣈⣉⣛⡻⠿⠋⠀⠀⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⣿⣷⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣴⣿⡿⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦
⠀⠀⠀⢀⣾⣿⡟⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡙⣷⡀
⠀⠀⢀⣾⣿⠏⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢹⣷⡀
⠀⠀⣾⣿⡟⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣷
⠀⣸⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠛⠛⢿⣇
⢀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣿
⢸⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⣿⣦⣄⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣾⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⢫⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠈⠻⠿⣷⣄⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣀⣀⣀⣠⣴⣶⣿⣿⡇⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⢿⣿⣿⡄⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⢈⣿⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠁⠀⠀⠘⡇⠀⢻
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠺⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⢀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠻⣿⠇⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣦⣀⠀⠀⢀⣿⣠⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁
⣶⣶⣶⣶⣶⡷⣿⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣷⣶⣿⣿⣶⣶⣶⣿⣶⢿⡿⠷⠿⢷⣶⠿⠿⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⡀⠀⠰
⠀⠀⠀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠄⠀⠤⠀⡰⡳⠀⠀⠀⠀⠀⢘⠂⠆⠁⠄⢰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠲⠄⠀⠀⠂⠈⠀⠒⠀⠚⠁
⠀⠀⠂⠀⠀⠀⠓⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡐⣂⠂⠀⠀⠀⠀⠀⠈⠢⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠀⠀⠀⠒⠈⠀⠀⠀⠀⠂⠀⠀⠨⠈⡡⠀⠀⠁⠀⠀⠐⠊⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠄⠈⡐⠀⠀⢁
⠀⠀⠀⠄⠀⠀⠀⠀⢀⡄⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠠⡀⢠⠀⠁⠉⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠘⠁⠀⠀⢀⢀⠠⠀⠀⠀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⢡⠸⠄⠀⠊⡄⠂⠀⢄
⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠈⠁⠊⠀⠀⣀⣀⣀⣃⣀⣀⡀⠀⠀⠁⠀⣠⡀⢠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠁⠈⠂
⠀⠀⠃⠁⠀⠑⠿⡀⠾⠦⠀⠀⠄⣀⡀⠀⠄⠐⠀⡀⠀⠰⢓⠒⠶⠒⠒⠒⠣⠀⠀⠂⠀⠁⠀⠀⠉⠁⡀⠀⠈⡀⡂⢐⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⢄⣁⠴⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠐⠀⠉⠠
⠀⡰⠀⠑⡄⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⢶⠆⠀⡴⠲⣦⠀⣴⠀⠀⢀⡴⠲⣦⠀⣠⠖⠶⠄⠐⣆⠀⣴⠀⠀⠀⠀⠁⠊⠀⠀⢠⠂⢰
⠀⠇⢀⠀⠰⠰⠀⠿⠈⠂⠀⢸⡷⣏⠀⢸⠀⢸⡇⠀⢸⠄⣿⠀⠀⢸⡇⠀⣹⠀⡿⠀⠰⡤⠀⠘⣾⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠉
⠀⠀⠤⠄⠁⠀⠀⡀⠀⠀⠀⠸⠧⠞⠀⠾⠆⠈⠷⠶⠛⠀⠻⠶⠶⠈⠷⠶⠛⠀⠻⠶⠾⠃⠀⠰⠏⠀⠀⠠⠀⠀⠀⠀⠂⠂⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠰⡆⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⡁⠀⠀⠁⠀⠀⠀⣴⠀⠰⣿⡇⠹⠃⠀⠀⠀⢀⠃⠠
⠀⡠⡆⠀⠐⠀⠀⣤⡀⠀⠁⠀⠨⣗⠀⠀⠀⡀⠐⠀⠀⠀⠘⠒⠀⠀⠀⠉⡁⠀⠀⠀⢀⠁⠈⠋⠉⢉⣀⠄⠉⠀⠀⠀⠐⠁⠀⠐⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠀⠐⠸⠀⠀⠀⠖⠉⠀⠀⠊⠁⠀⠠⡀
⠀⡤⡙⡀⠠⠠⡄⠀⠀⣀⠑⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠠⠠⠀⠀⠀⠈⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⡉⠉⢀⢀⡠⡀
⠀⠀⠀⠁⡀⡀⠁⠀⠀⢀⠆⢠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠂⠈⠀⠀⠀⠀⠀⠒⠒⢀⢀⡘⠀⠂
⠀⠀⠈⠆⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠐⡊⠠⠀⠠⠰⡤⠀⠀⠀⠀⠀⠂⠀⠠⢀⠠⠌⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⡄⠐⠀⠀⠀⠀⢄⡁⠀⠀⠣⠤⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠄⡀⠈⠀⠐⠀⣅⠀⠀⠈
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠲⠀⠀⠀⡀⠀⠘⠃⠀⠠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠀⠀⠀⢀⠄⠀⠁
⠀⠀⠰⢀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠘⠃⠀⣀⠣⠀⠁⠀⠀⠂⠂⠀⠀⠀⠅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢀
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⢻⣿⣿⣿⣧⡀⠘⠷⣭⡙⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⢈⡉⠉⠻⠃⠀⢸⣿⣷⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣠⣶⣶⣤⡀⠀⡀⠀⠀⠀⠀⠀⠘⠁⠟⠻⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣯⣙⣫⣀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣥⣽⠋⢁⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⢸⡆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⣼⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠛⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠈⠹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠳⠌⠙⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣻⡟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠛⠿⠿⠋⠀⠀⠀⠀⣼⣏⡿⠿⠛⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠀⡀⣀⡀

⠀⠀⠀⢠⣴⣾⣿⣷⣦⡄⠀⠀⠀⣠⣤⡀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⠠
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡏⠐⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠓⡔⠁
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣧⡀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢣⣠⠾⠃
⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠙⠻⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⡿⣻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣽⣭⣯⣯⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉