⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣬⡺⠟⢛⠛⠋⠙⡈⠙⣱⡂⣆⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠞⠟⡻⠣⠉⠈⠣⠉⠌⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⡘⡿⢛⠩⠰⠛⠃⠉⠀⠀⠀⠀⠀⢀⣠⣄⢀⡴⢶⣶⣷⣖⡲⣆⡠⢮⡀⠤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢧⣔⠤⢤⡴⡶⢟⡛⢷⠄⠋⠁⠀⠀⠀⠀⠀⠀⡠⢶⠻⣏⣽⣷⣿⣿⢿⣿⣿⣿⠶⢇⡨⠉⠺⠿⠢⡀⠀⡑⡉⠂⠙⠙⠒⡢⠄⢀⣀⠀⠀⠀⠀⠀⣱⣆⠠⠁
⠀⠀⠀⠀⠜⠕⣉⠔⠈⠙⠭⣊⣠⠤⡄⠀⠀⢀⡀⢀⠔⠑⢐⣿⢿⣯⠿⢿⣿⣛⢛⣀⣙⠿⠳⢿⡊⠠⡤⡂⠀⢪⡳⢄⠀⠀⠘⠖⠁⠐⠀⠁⡉⠩⠑⠘⠳⠲⡎⡹⠥
⠀⠀⠀⠁⠀⢅⢤⡔⢇⠀⠂⠀⠀⠄⠀⠀⡄⠉⡠⠗⢐⢥⣿⣼⣯⠝⢋⠉⠽⠎⣛⡛⢛⠳⠢⡀⡙⢽⣀⣰⠉⢲⠂⠔⢠⠀⠀⠃⠀⠀⠀⠀⠇⠀⡠⠂⡀⢹⢃⠟⠀⠀
⠀⠀⠀⠉⡀⠂⠀⢆⢣⠀⠀⠀⠀⠀⠐⠀⠀⠘⠟⢀⠶⣿⣛⠯⢗⠐⡊⠀⠸⠿⣷⣶⣷⡾⠿⠂⣨⣸⠄⢩⣷⢟⠌⡔⠃⠐⠀⠁⠀⠀⠀⠀⠀⡜⠁⠀⡴⣗⣝⠄⠀⠀⠀
⠀⠀⠀⠀⠅⠀⠀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⢼⡿⠟⢊⡟⣾⣴⣢⡄⢨⠀⠀⠒⠂⢭⣛⡈⢱⢰⢍⣧⠢⢺⢠⠀⠀⢠⠀⠀⠀⠀⢴⠏⠀⠀⠀⣻⢿⢒⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⣢⠳⣳⠀⠀⠐⠀⠀⢸⢣⣤⣗⠿⣦⣮⣷⣿⣯⣻⣺⢿⢴⢕⢫⠍⣄⣕⢟⣹⣤⣾⡽⣥⡿⣇⢐⣄⣰⠂⠀⢄⠀⢠⠀⠀⡐⠀⠀⠀⣿⡟⠫⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣦⠀⠅⠀⠀⢸⢋⣾⢟⢷⠟⠋⠁⠀⠊⠙⠛⠿⠬⠣⢫⡺⠂⡁⠉⠉⠋⠀⠀⠘⠔⠴⠔⡙⢕⠤⠰⣧⠠⠑⠀⠘⡀⠀⠀⠀⣽⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢟⠅⠀⠀⠀⣺⢸⠃⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠰⢀⠏⡔⠡⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⣜⣿⣠⡆⠠⠀⢈⡁⠀⠀⠀⢻⢐⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⡌⠄⢰⢸⢇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡩⢎⡄⢗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⡘⠁⡆⠀⠀⠁⠀⠀⢐⡣⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⡀⢀⢀⣫⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠰⠀⠁⠀⢻⣠⣣⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⣖⠀⠀⠄⠀⠀⠀⠀⠀⢨⡅⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⡌⡿⢧⣀⣠⢤⡄⠠⣄⣤⣾⠪⡄⡌⠀⠀⠀⠀⠎⢣⠠⡻⣶⣗⠤⡤⢤⢴⠜⡐⠅⣿⠘⢄⠀⠀⠀⠀⠀⠀⡶⢀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣦⠗⠿⡿⡿⠳⢇⣶⠽⡿⢟⢌⡶⠡⠀⠀⠀⠁⡀⠀⠘⢰⢠⢈⡼⠱⠰⣡⠦⡁⢺⡟⡫⢳⣄⠂⠀⠀⠀⠀⣤⣋⡥⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠘⠩⢛⡧⣐⠞⠁⠀⠀⠀⠉⢋⢽⡇⡗⠀⠀⠀⠣⢧⠀⠀⠖⣤⣍⠃⠄⡗⠌⠈⢟⡖⠘⠂⠐⠙⡀⠀⠀⠀⢠⢪⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢷⡀⠀⢨⠠⠉⢌⠂⢀⠀⠀⢂⠀⢀⢇⢙⢚⢖⢖⠀⡉⢰⣑⢞⢀⠆⢎⠫⠈⠈⠀⠀⠀⠀⠀⡀⠀⢈⠋⠀⠀⠀⠎⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣀⠀⠀⠍⠐⣨⠁⠀⠀⠀⠀⡀⡀⢋⢽⢾⢟⡈⢠⠋⡌⡈⣾⣍⢐⠂⠀⡆⠀⠀⢀⠀⠄⠀⠀⢀⠌⡃⠀⢠⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣦⠀⠀⠀⠜⠄⠂⠀⠀⠀⠀⠀⠈⡐⢠⡀⢰⡄⡀⠰⢆⣠⠘⠙⢙⢆⡁⠂⠀⠂⠀⠂⠄⠀⠈⠀⢀⢰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡳⡄⠈⠀⠀⠀⠀⠀⠀⠐⣰⠗⣖⡾⡤⢹⠏⠠⠸⠸⢝⠇⢎⢠⣰⠉⡄⢀⡼⠀⠄⠀⠀⠀⡄⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣛⠀⡄⠀⠀⠀⠀⣀⠉⣄⠊⠇⠃⠁⠈⠁⠂⠀⠀⠸⠀⠈⠐⠈⠂⢈⠬⢀⠄⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢠⠿⣶⣀⠀⠀⠀⠊⠁⠈⠀⠄⢐⡀⠀⠀⠀⠀⠀⠀⠀⢐⠠⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠻⢓⣶⡤⡈⠀⠀⠠⡀⠀⠆⢣⡄⠀⠀⠀⠀⠀⢀⠔⠶⢀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠆⡞⢳⣄⣀⠀⠀⠀⠈⠰⡙⡀⠀⠀⠀⢀⠆⠀⡠⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠭⢢⢓⢼⣳⣦⣀⡀⢘⣽⠀⣤⠖⡁⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠡⠎⢛⠿⣅⠀⢳⣇⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠫⡩⠀⠁⠜⣜⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠊⡊⢒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀