⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠴⠇⢀⠟⡃⠈⡀⡆⡤⡐⡀⠀⠀⢠⡶⠶⠶⠶⠐⠲⠦⡀⠀⠀⠀
⠀⠀⠀⠀⢀⡾⡗⢸⡞⢀⡞⡄⡠⢣⢡⡲⡕⡮⢡⡂⢀⡇⣤⣀⡀⡀⡀⡀⢈⣳⡄⠀⠀
⠀⠀⠀⠀⣴⡣⣜⠜⢇⡠⡜⠆⡄⣍⣸⢽⣜⠛⡜⡐⣬⣍⣙⡍⡌⢢⠉⡪⡪⢫⢵⡆⠀
⠀⠀⠀⠈⣵⣛⡡⢃⠑⡄⠢⣆⡡⢊⣬⣺⣧⣸⢃⢝⣝⡪⡺⡨⣰⡂⡌⡜⡫⠟⡉⡄⠀
⠀⠀⠀⠈⠑⡍⣇⠧⠦⣃⣡⡳⣴⡞⢙⡹⣣⢤⠫⡊⡆⡪⡽⣧⢧⢲⠂⠰⡩⣵⠂⠄⠀
⠀⠀⠀⠀⠀⢸⡈⡧⢽⣦⢘⡎⣻⢧⡽⡛⠫⡆⡸⣁⢸⡽⡝⠜⡇⢅⡀⡒⠄⡹⠂⠆⠀
⠀⠀⠀⠀⠀⠈⠋⢙⣣⡮⡓⣸⣞⢫⡞⡮⡨⡤⢡⡪⢹⢙⡳⡂⠑⢣⢜⠦⢀⡢⡐⡄⠀
⠀⠀⠀⠀⠀⠀⢰⡩⡮⡽⡿⢹⡸⢞⠕⡘⡖⡆⢠⢵⡢⢅⡑⡬⢠⡜⡪⡬⣔⢬⠈⠇⠀
⠀⠀⠀⠀⠀⠀⠈⡇⢜⠪⢫⡼⣇⠰⢙⢙⡞⢌⡣⣓⢒⡚⢓⡼⡌⣊⡤⡢⠢⠢⡁⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠆⠗⡾⣄⡸⡱⡄⡳⡐⡃⣷⠣⣡⣂⡸⢌⡢⠚⢊⡜⡦⢐⢄⡄⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡏⠧⢡⡘⢢⢍⠍⣌⡞⡼⡺⢲⢽⠅⢰⢣⡑⣇⡒⡅⠅⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡲⢦⣧⡕⠢⠪⡳⡘⡪⡢⣎⡲⡜⢧⡆⠇⢸⡐⡀⡁⠨⡑⠂⠀
⠀⠀⠀⠀⠀⠀⠀⡐⡝⢢⣹⢧⡎⡮⡶⡵⣈⡸⣕⢳⠞⢊⡝⡔⢡⠄⡣⡐⡬⡵⢍⡇⠀
⠀⠀⠀⠀⠀⠀⢘⢒⢝⣆⢸⢱⠢⢥⢤⡂⢧⢄⡸⡑⢙⡵⡂⢜⡆⢢⢨⠬⡍⣋⠅⢂⠀
⠀⠀⠀⠀⠀⠀⢸⡇⢸⠽⠜⣍⡕⢺⡜⡘⡆⡯⣄⢦⠱⠳⢆⡄⢀⠈⡗⡀⠒⢌⢤⡃⠀
⠀⠀⠀⠀⠀⠀⠈⠣⡐⡜⢪⢩⠎⢮⢝⢞⡵⢮⡡⡪⡜⡵⡆⠒⡕⡀⡬⠰⡆⢣⢆⡃⠀
⠀⠀⠀⠀⠀⠀⢢⠊⡬⢸⢼⢌⢌⢡⡝⡌⡅⡚⡞⡣⡤⢫⡦⢪⡐⢡⣇⡩⡆⢆⢬⢠⠀
⠀⠀⠀⠀⠀⠀⠈⠑⡂⢢⡱⢪⡌⣷⢹⢡⡪⡂⣎⡆⠮⡧⠬⡬⢒⡼⠸⣔⡵⡂⡐⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠣⢁⠊⡣⢪⡼⢱⡇⣣⢡⠍⡕⠝⢅⢔⠒⢊⡪⠡⡪⢳⢣⠨⢀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡣⡝⢪⡢⡑⡬⡸⠪⢉⣈⣊⢊⡢⢸⡇⢹⢱⢹⢩⢈⢎⢃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⡨⢡⡺⡣⡬⢜⡜⡕⢈⡱⢂⡉⠦⢠⠍⡑⡔⢐⠑⢑⢅⡸⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢐⠬⢑⡃⢣⠨⠌⢤⡪⣢⢐⢞⠑⡢⡤⡐⡊⢪⠡⡐⡌⡃⢡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⢌⡑⡨⢃⢍⡃⠐⢢⡏⡎⣤⡣⡄⠬⢨⢀⡘⠢⢡⡠⡠⡅⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡪⠂⡜⠜⠢⢔⠨⠦⢐⠙⢞⠠⡅⡆⠨⡄⠂⡁⡘⡑⡄⡂⢄⡃⠀