⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⠢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠠⢀⠐⠀⡀⡠⡠⡲⠸⠐⠀⠂⠅⢀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⡀⠄⠐⢀⠐⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⡢⡑⠅⢁⢂⢌⠜⡜⡸⠈⠠⠐⠀⠅⢈⠠⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠐⡀⠂⠁⠀⠀⠄⠀⠀⠀⢀⠠⠀⠂⠁⠀⡀⠀⠠⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⡢⣕⠼⠰⡑⡥⡱⡰⢑⠁⠠⠀⠂⠀⠁⠀⠀⠀⠀⠀⠁⢀⠀⡀⢀⠀⢀⠠⠠⠁⠀⠀⠐⠈⠀⠐⠀⠀⢈⠠⠐⠀⢀⠐⠀⠠⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡢⣪⢣⢣⢢⢣⡫⠎⠊⢈⢀⠠⠀⡂⠄⠁⠌⠠⠑⡈⡢⣑⢌⠢⣂⡐⠄⠆⠒⠀⠁⠀⠀⠀⠁⢀⠠⠀⠄⡠⡨⠂⠁⠀⡀⠂⠁⠀⠁⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢪⢢⡣⣇⢇⢇⠣⠁⡀⠄⠌⠀⠀⠀⠀⢀⢠⢰⢰⢸⡸⡪⡮⠺⠊⢉⠀⠄⠂⠐⠈⠀⠄⠁⡈⡄⣅⢤⢢⢪⠪⠂⠁⠠⢈⠔⡀⡐⡌⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠀⠀⠀⠀⢀⠰⣑⢕⣕⢧⢳⠹⠈⢀⠀⢂⠠⠀⠀⠀⢄⠢⢸⢸⣸⡱⡽⡵⡙⠉⡀⠂⢁⠠⠐⠀⡂⢄⢂⡅⠆⡓⣉⢮⢎⡧⠳⠉⢀⠠⠈⠔⢐⢨⢰⡱⠁⠀⠀⠄⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡪⣪⡳⡕⡕⠕⢁⢐⢠⠢⠂⠀⠀⡠⡣⠀⢔⡇⣳⣳⢙⠁⢂⠀⢂⠐⢈⢠⡰⣔⠵⠕⡉⣄⡴⡴⡺⠊⡉⢁⠠⠐⡀⡄⡔⡌⣎⢎⣎⢾⢨⠂⠀⠀⡀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠠⡢⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢁⠀⠀⢪⢪⣞⢮⠣⢁⢐⠐⢰⡕⡕⠀⠐⢀⡷⡅⣢⣟⡝⢎⠂⠠⡀⠢⢈⣠⢼⡺⣓⣋⣤⠵⡚⠍⢁⠂⡀⠄⠐⡀⣄⢆⡧⢧⢳⡹⣪⡺⡺⡪⠓⠁⢀⠀⠀⠀⡀⠄⠠⠠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡙⡌⠎⢆⡂⡢⡀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠂⠁⢐⠠⠀⠀⢣⢣⢫⣏⠊⠄⡂⠨⡪⡞⡬⡤⣜⣾⣻⣪⢗⠇⢊⢀⠢⢑⠈⡂⡧⣗⣿⡞⢏⠋⠄⠡⠐⠐⡀⣠⡠⣦⢷⣟⣞⢽⢼⣵⢳⠝⠎⠊⠈⠀⠀⠂⠀⡀⡠⡁⡂⢅⠪⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠂⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠄⠀⠐⠀⠀⠁⠀⠀⠀⠀⠣⡅⠄⠑⠪⠪⡪⡪⡢⡄⡄⠀⡀⠁⠀⠠⠀⠢⡡⡀⠐⠀⡈⡇⡯⠀⠅⣢⢣⣩⣪⡾⡽⣞⢧⡳⠩⠡⠈⠄⡐⠈⣄⣦⢾⡻⢋⠣⠨⢐⣈⣌⡴⣜⢞⣞⣮⣾⣽⣿⣾⣾⣟⡟⠊⠁⠀⠀⡀⠄⠀⡀⠢⠑⠈⠀⡀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⢂⠐⠀⠐⠀⡀⠀⠁⠀⠄⠠⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠆⡄⠀⠈⠈⢇⠣⡳⡕⡎⡆⡄⡀⠀⠠⠘⡜⣆⡂⠌⠨⢈⠠⣱⠫⠫⣺⡪⣯⠫⠪⠊⠄⡁⡂⢣⢱⢔⠯⢓⠉⢅⣂⣥⣮⡾⣷⣳⢷⠻⣪⣯⡾⣿⣽⣾⣿⡿⠊⠁⠀⠀⠀⡔⡕⡌⡄⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠈⠀⠄⠀⠄⠀⠀⠀⠀⠀⠁⢀⠠⠀⠀⠀⠁⠠⠈⠀⢁⠀⠠⠀⠀⠀⠀⠈⠐⠀⠁⠨⠱⡱⡱⡹⣜⢎⢎⡆⡂⢅⢘⣼⡂⠡⠐⡀⠬⠂⢄⢕⣕⢟⠜⠈⡀⠂⢡⡰⠜⡑⠡⣡⣬⣦⣷⢿⢷⢻⣺⣹⢵⣵⣺⣯⣷⡿⣻⢫⡳⠟⠉⠀⠀⠀⠄⠀⠈⡮⡪⡎⡎⡂⡣⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠈⢀⠀⠂⠈⠀⠀⢀⠠⠀⠁⠀⠀⡀⠁⠐⠐⡄⢄⠀⠐⠀⠀⢀⠠⠀⠀⢀⠀⠁⠣⢑⠹⢆⢯⢎⢆⢮⡗⡑⡀⠅⡸⡈⢌⡦⡻⠜⠈⠄⣡⡰⡝⠅⣐⣔⣼⢿⣫⣳⣵⣷⣿⣿⣿⣿⣿⡿⣿⣻⡽⠾⠛⠩⠉⠀⠀⠀⠀⠐⠆⡠⢁⢜⢎⠎⢎⠰⡨⡐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⠠⠁⠀⠀⠀⡀⠁⠄⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠐⠀⠀⠀⠈⠠⠨⠐⢡⢱⢀⠂⠠⠀⠂⠡⠠⡐⠨⠐⠤⠱⣕⢽⣝⢮⣗⠇⢅⢐⠨⣪⢮⡳⡝⠨⠈⣌⣼⣾⣹⣼⣞⢿⣹⣵⣿⣿⡿⣿⣻⣞⠿⠞⠗⠋⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⡀⢂⡠⠂⠠⢪⢊⢊⠢⡑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⢀⠁⢀⠀⠐⠈⠄⠀⠀⠀⠂⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡀⠁⠂⠅⠕⢄⠠⠀⠐⠀⠐⠀⠅⠡⠨⡊⡜⣵⢕⢯⡗⠅⡂⡢⡽⣵⠟⢈⢐⢨⣜⣾⣿⢿⣹⣼⢞⣟⢽⠽⠾⠓⠛⠉⠁⠀⠀⢀⢀⢀⢄⢄⣄⠔⠀⠀⠀⠀⠀⡔⢈⠀⠀⠰⠁⢜⠜⠈⠀⠠⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠀⡂⡐⠀⠈⠠⢁⢀⠀⠐⠀⠀⠀⠂⠈⠀⢀⠠⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠁⠁⠂⠅⠃⡃⠊⠎⠮⣎⣆⡕⡨⡊⠝⡹⣯⡯⡂⢢⣞⡿⢃⢐⢰⣼⢷⣿⢿⣹⡵⠫⠊⠃⠁⠀⠀⠀⢀⢀⢄⡢⡼⡼⣞⡾⣻⢻⢝⠎⠊⠀⠀⠀⡀⠎⠀⠀⠀⠀⠅⢰⠣⡃⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡑⡐⡀⡀⠀⠑⠐⠐⠄⢅⢐⢀⠀⠀⠀⠀⠄⠁⢀⠀⠠⠀⠀⠐⠀⠀⠈⠀⡀⠁⠠⠈⡀⠐⠸⡌⡍⠋⠌⣔⢯⣿⣣⡃⣺⡿⢑⣰⣴⡿⡗⣛⡼⡕⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠉⠈⠁⠁⠈⠀⠁⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⣔⢇⠃⠄⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠨⠈⠊⠂⢆⢂⠀⠈⠑⠪⣰⡀⡂⡀⠀⢀⠀⠐⠀⠐⠀⠐⠀⠀⠄⠀⠐⠀⢀⠠⠀⢄⠠⠈⢈⢚⢮⣯⣿⣯⣎⣿⣿⣼⣾⠟⠨⡪⠓⠁⠀⢀⠠⠠⠂⠂⠊⠈⠀⠂⠐⠀⠂⠐⠐⠠⠄⢄⠠⡀⡐⠀⠁⢀⢀⠀⠀⠀⣀⢤⡲⡜⠜⠀⠀⠀⠀⠄⠌⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡈⡂⠀⠀⠠⠑⢕⠦⣢⡀⡀⠉⠳⠮⡮⣦⣤⣅⣄⣂⡠⠠⠀⠠⠀⠀⠠⠀⠀⡀⠎⠂⠀⠀⠂⠠⠑⣜⢿⣾⢯⡫⣫⡿⣏⠪⡐⡁⠀⠠⠈⡀⠄⣐⠴⣴⣤⣥⣑⢤⣔⣄⣄⣀⡀⢄⠀⢄⣀⣀⣀⣈⣀⣀⡠⡤⠶⠻⠋⠋⠁⠀⠀⡀⠄⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⢌⢂⠀⠀⠄⠀⠑⠱⡙⡮⣲⡲⡤⣠⠀⠈⠉⠓⠻⠋⠉⠉⠁⠀⡀⠄⡀⡆⠎⠂⠀⠁⠄⠐⠀⡀⠪⣏⢯⢷⡝⡔⣽⠣⡑⠁⠀⡀⠵⢈⣀⣬⣴⠾⡞⡟⠞⣟⢟⠝⢍⢋⠋⡋⢉⠋⢉⠉⠉⠉⠈⠂⠂⠀⡀⣀⠠⠠⠠⠐⠠⡁⢄⠐⡈⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠑⢄⠀⠀⠂⠄⡑⠹⡸⣪⡫⡮⣯⣣⡄⡀⠀⠀⠂⠐⠈⠀⠀⡀⠎⢜⢔⢔⢴⡰⣔⣤⡁⡀⢀⠐⢕⡯⡻⣜⡾⠨⢀⢼⢕⣠⣿⡿⡟⡯⣲⠭⠎⠒⠉⠂⠂⠈⠀⡀⡀⡠⣀⢄⠢⡌⡎⡕⡕⡵⠬⢆⠦⡢⠢⢃⠪⠈⠂⠂⠀⠀⢀⠠⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠑⡐⠄⢌⠢⡑⡆⡗⡽⣜⢾⣽⡺⣦⡀⠂⠑⢄⠐⠀⢀⠈⠀⠀⢀⠀⠨⡦⣁⡋⠲⡐⠔⠇⠑⣜⣞⠇⢁⢪⣵⢿⢻⣹⡼⢚⠉⣀⣤⡴⡴⣞⢾⢝⣽⢽⠽⠽⠺⠱⠋⠋⠊⠃⠃⠁⠁⠉⠈⠈⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠨⠨⢘⠨⡙⡚⢷⢭⡳⡳⣯⢂⠀⠀⠑⢥⢠⠀⠐⠀⡀⠀⡀⠀⡀⠀⠁⠉⠉⢚⠄⣵⡇⢀⣮⣫⣮⢷⢫⣰⣒⣥⣾⢾⡾⠾⠟⣛⣩⡩⡤⡰⡨⢄⢢⡐⡔⡌⢆⠆⠆⠢⠑⡐⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⢉⠪⡘⠒⢆⢄⠀⠈⡱⡹⣄⠀⡀⠄⠀⠠⠀⠀⠁⠀⠂⢐⠳⡱⣯⡸⡷⢁⡵⣵⣿⢷⢻⣹⡸⣕⢮⢞⢯⢯⢮⢛⢮⢳⠹⠊⢅⠕⠕⠨⠐⢀⠅⢅⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠌⢆⢢⢀⠈⠀⠸⠸⡪⠷⣄⠀⠀⠀⠈⠀⠂⠀⡀⡃⠁⠈⡫⠫⡊⣳⣽⡵⡷⡻⣝⡮⡺⡸⣜⡮⡯⡃⡧⡻⡪⠪⡈⢨⠨⠨⠈⠄⠨⠈⢈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠂⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠂⢎⠄⠀⠀⠁⡊⡢⡑⠳⢔⠀⠀⠀⡀⠀⢀⠀⠁⠠⠀⢈⢎⢺⣸⢺⣪⡽⡞⡵⡹⠩⠑⠌⢢⠪⢊⠂⠇⡑⠀⠂⠁⠅⠁⠀⡀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢐⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠪⡣⡊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠪⡊⠢⡂⡆⠃⡪⠡⠀⠡⠠⡂⡄⠄⠁⠀⠄⡂⠅⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠂⠠⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠘⢜⢄⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠑⢀⠡⡑⡌⠎⠊⠠⠀⡨⡊⢂⠐⠀⠀⠅⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡅⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠨⠨⠈⠄⠁⠀⡂⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⠀⠄⠀⠂⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⢁⠀⠂⡀⠈⠐⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⡀⠂⠀⠀⠀⠀⠀⠑⠄⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠄⠁⠡⠂⠄⠈⠢⢢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠈⠐⡈⠄⢀⠈⠐⠠⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⢈⠈⡂⠅⠌⡈⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠠⠀⠀⠄⠠⠀⠀⡀⠠⠀⠀⡀⠠⠀⠀⠠⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀