⠀⠀⠀⠀⠀⠀⠀⡁⡊⠅⡂⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡐⡤⡱⡰⡲⡳⡢⣕⢤⢀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠨⠀⠀Come on balls , don't kill me balls
⠀⠀⠀⠀⡀⡰⡸⡰⡱⡱⡙⡜⡜⢜⢜⢜⢗⢽⡹⡤⣄⢀⠀⠀⠀⠀⠀⠨⠀⠀
⠀⠀⠠⡪⢪⢊⢎⢜⢌⢎⢎⢎⢎⢎⢎⢪⢪⢱⢝⡞⡮⣣⡂⠀⠀⠀⠀⡈⠀⠀
⠀⡐⡕⡕⡕⢵⢱⠱⡱⡑⡕⡜⡔⡕⡕⡕⡕⢕⢕⢽⡹⡪⡮⡀⠀⠀⢠⡲⠀⠀
⠐⡀⢌⠌⢊⠺⠸⠸⠸⡘⡘⢌⠪⡨⡊⣒⡕⢕⢅⢇⢯⡫⡮⣳⠀⠠⡣⡯⣃⠀
⣂⠀⡆⢁⠢⢨⠌⡌⡂⡆⡪⣡⡣⡪⡪⡒⡼⡸⡸⡨⡳⣝⣝⢮⡊⠌⢌⠙⢮⡀
⠕⡕⡕⡕⡕⡅⠘⡜⡜⡜⡜⡔⣊⠪⡪⡪⢪⢱⢱⠱⡑⣧⢳⡳⡣⢑⠠⢑⢎⡇
⠇⡇⡕⡜⡌⡇⣀⠀⠱⣘⠜⡜⠬⡅⣔⠓⠃⠧⡇⡇⡇⣯⡳⡽⡐⠄⢅⢗⣝⡇
⢨⢪⢪⠪⡪⣣⡤⣤⠄⠈⠀⠀⠀⠀⠀⣖⠝⣖⠢⡣⡣⡇⡯⣞⢦⢑⢮⡳⣕⠃
⠀⠪⡆⡇⡇⣃⠣⡁⡃⠀⠀⠀⠀⠀⠀⠐⠄⠂⠨⡪⢌⡗⠃⢯⡳⣝⢵⢝⠾⠀
⠀⠀⠫⠪⢚⣎⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡨⡪⡪⠁⣘⢗⣝⢮⡳⣝⠃⠀
⠀⠀⠀⠀⢀⢮⢦⠀⠀⠀⠈⠊⠃⠀⠀⢀⠀⢱⢱⢑⠅⣔⢗⣝⢮⡳⣝⠂⠀⠀
⠀⠀⠀⠀⡼⡥⡉⠃⡁⠀⡄⣤⡠⠤⢍⠀⠠⡣⡣⠍⣜⢮⡳⣓⣗⢽⠂⠀⠀⠀
⠀⠀⠀⢸⢮⡫⡆⠱⡰⢸⡘⣜⠭⡑⠑⡔⡪⢎⢆⢰⡳⡳⣝⢮⢮⣋⠀⠀⠀⣼
⠀⠀⠀⠀⠙⠙⠑⠀⠈⠢⡱⢨⠪⣸⡀⠈⠪⠊⠀⠜⡮⣫⢮⡳⡳⣕⣖⢤⡺⡚
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣷⣸⡺⣌⡶⡳⡄⠀⠀⠁⠁⠙⢎⡷⢝⣝⢮⢮⠳⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠽⠵⡯⠺⣝⡮⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⡖⣶⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⡅⠈⠙⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⢠⡄⢠⡤⢤⠠⠤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡇⠙⠷⣤⠀⠀⡇⠀ ⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠞⠃ ⠈⠓⠶⠛⠀⠓⠶⠛⠀ ⠃⠀⠀
⢠⣤⠀⠀⣠⣤⠀⣠⡤⢤⣄ ⠀⣤⣄⠀⣤⠀⣤⠀⣤⠀⣠⠄⠀⣠⣄
⢸⡟⣧⢰⠇⣿⠠⣟⠀⠀⣿⠄⣿⠹⣆⣿⠀⣿⠀⣿⢾⡅⠀⢰⣏⣹⡆⠀
⠘⠃⠘⠋⠀⠛⠀⠙⠲⠖⠋⠀⠛⠀⠘⠛⠀ ⠛⠀⠛⠀⠛⠂⠛⠀⠀⠛

⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀
⢸⣀⠜⢄⡀⠀⠰⣶⣤⣀⠀⠀⣠⠔⠚⢛⣛⣦⡀⠀⠀⠀⠀⠀⠀⡐⠉⠉⢶⠄
⠈⢅⠀⡈⠱⣄⠀⠈⠛⠻⢷⡎⡡⣶⣿⣿⣿⢿⣿⡀⠀⠀⠀⠀⣴⣯⣝⣲⠊⠀
⠀⠀⠠⢅⢀⡎⣷⣄⠀⠀⠀⢿⡰⠊⠁⠀⠸⡼⡏⣇⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠈⢻⣾⣿⣿⣷⣤⣀⣼⣧⡀⠀⣠⠴⣗⣳⣼⣄⣴⣿⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⠏⢹⠁⠀⡟⢹⢿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠦⢅⣀⣨⣤⠴⡞⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⠈⠲⢦⡾⣛⣾⣁⣸⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⡿⠟⢻⡔⠚⠚⣷⣼⣾⠉⢹⠃⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⠀⠀⢧⠀⠸⠋⠸⠌⠃⢸⠀⢰⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣸⣤⣤⣶⣶⣶⣶⣾⣤⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⠀⠀⠀⠀⠀⠀⠉⣿⠿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⢸⠀⠀⠀⠂⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣤⣼⣀⣄⣀⡀⡀⢀⣀⡸⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠙⡿⠋⢹⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⣀⣤⡷⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀
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