⠀⠀⠀⠀⠀⠀⠀⠀⡁⡊⠅⡂⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡐⡤⡱⡰⡲⡳⡢⣕⢤⢀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠨⠀⠀
⠀⠀⠀⠀⡀⡰⡸⡰⡱⡱⡙⡜⡜⢜⢜⢜⢗⢽⡹⡤⣄⢀⠀⠀⠀⠀⠀⠨⠀⠀
⠀⠀⠠⡪⢪⢊⢎⢜⢌⢎⢎⢎⢎⢎⢎⢪⢪⢱⢝⡞⡮⣣⡂⠀⠀⠀⠀⡈⠀⠀
⠀⡐⡕⡕⡕⢵⢱⠱⡱⡑⡕⡜⡔⡕⡕⡕⡕⢕⢕⢽⡹⡪⡮⡀⠀⠀⢠⡲⠀⠀
⠐⡀⢌⠌⢊⠺⠸⠸⠸⡘⡘⢌⠪⡨⡊⣒⡕⢕⢅⢇⢯⡫⡮⣳⠀⠠⡣⡯⣃⠀
⣂⠀⡆⢁⠢⢨⠌⡌⡂⡆⡪⣡⡣⡪⡪⡒⡼⡸⡸⡨⡳⣝⣝⢮⡊⠌⢌⠙⢮⡀
⠕⡕⡕⡕⡕⡅⠘⡜⡜⡜⡜⡔⣊⠪⡪⡪⢪⢱⢱⠱⡑⣧⢳⡳⡣⢑⠠⢑⢎⡇
⠇⡇⡕⡜⡌⡇⣀⠀⠱⣘⠜⡜⠬⡅⣔⠓⠃⠧⡇⡇⡇⣯⡳⡽⡐⠄⢅⢗⣝⡇
⢨⢪⢪⠪⡪⣣⡤⣤⠄⠈⠀⠀⠀⠀⠀⣖⠝⣖⠢⡣⡣⡇⡯⣞⢦⢑⢮⡳⣕⠃
⠀⠪⡆⡇⡇⣃⠣⡁⡃⠀⠀⠀⠀⠀⠀⠐⠄⠂⠨⡪⢌⡗⠃⢯⡳⣝⢵⢝⠾⠀
⠀⠀⠫⠪⢚⣎⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡨⡪⡪⠁⣘⢗⣝⢮⡳⣝⠃⠀
⠀⠀⠀⠀⢀⢮⢦⠀⠀⠀⠈⠊⠃⠀⠀⢀⠀⢱⢱⢑⠅⣔⢗⣝⢮⡳⣝⠂⠀⠀
⠀⠀⠀⠀⡼⡥⡉⠃⡁⠀⡄⣤⡠⠤⢍⠀⠠⡣⡣⠍⣜⢮⡳⣓⣗⢽⠂⠀⠀⠀
⠀⠀⠀⢸⢮⡫⡆⠱⡰⢸⡘⣜⠭⡑⠑⡔⡪⢎⢆⢰⡳⡳⣝⢮⢮⣋⠀⠀⠀⣼
⠀⠀⠀⠀⠙⠙⠑⠀⠈⠢⡱⢨⠪⣸⡀⠈⠪⠊⠀⠜⡮⣫⢮⡳⡳⣕⣖⢤⡺⡚
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣷⣸⡺⣌⡶⡳⡄⠀⠀⠁⠁⠙⢎⡷⢝⣝⢮⢮⠳⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠽⠵⡯⠺⣝⡮⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⡖⣶⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⡅⠈⠙⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⢠⡄⢠⡤⢤⠠⠤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡇⠙⠷⣤⠀⠀⡇⠀ ⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠞⠃ ⠈⠓⠶⠛⠀⠓⠶⠛⠀ ⠃⠀⠀
⢠⣤⠀⠀⣠⣤⠀⣠⡤⢤⣄ ⠀⣤⣄⠀⣤⠀⣤⠀⣤⠀⣠⠄⠀⣠⣄
⢸⡟⣧⢰⠇⣿⠠⣟⠀⠀⣿⠄⣿⠹⣆⣿⠀⣿⠀⣿⢾⡅⠀⢰⣏⣹⡆⠀
⠘⠃⠘⠋⠀⠛⠀⠙⠲⠖⠋⠀⠛⠀⠘⠛⠀ ⠛⠀⠛⠀⠛⠂⠛⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀