⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢀⢠⢰⡢⢯⡺⡕⡷⡤⡷⣝⢎⢏⠦⣂⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⢐⢐⠅⡂⢀⠆⢮⠪⠣⢏⣗⢵⣫⢯⣫⢞⣗⣽⣲⢽⣲⡺⣔⣅⡂⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢈⢐⢐⢐⠐⢜⢜⢜⢕⢝⢕⡵⡳⣝⢮⡳⡽⣑⢥⡲⣲⡺⣺⡺⡵⣳⠻⣢⢑⢅⢑⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⢂⠂⡂⡐⠄⡣⡱⡱⡱⣕⢗⣝⣝⢮⣳⢭⡺⣪⢳⣝⢞⡮⣳⢽⢝⣞⡵⣪⠗⡔⢅⢕⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢐⠐⡀⠄⡊⡪⡨⠪⡸⣜⢮⢻⢺⡪⢧⣪⡷⣕⡵⣫⢮⢗⡯⣳⠓⣝⣞⢞⣎⢧⡳⡱⢨⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠂⡐⠀⠨⡂⢕⢢⢣⢣⢇⣗⢽⡱⢍⠵⣝⣞⡽⣺⢝⡽⣕⢽⣔⢧⣳⢳⣫⢿⣅⢣⠣⡃⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠅⡂⢐⠀⡑⢌⢢⢣⢱⢕⢧⢳⢕⡝⡢⣟⢞⡮⣞⢷⠝⣜⡼⡯⡾⣽⣺⡳⡕⡯⣞⢌⠕⡑⢕⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠅⡂⠀⠂⠨⢸⠨⡸⡸⡪⣳⡹⣍⢰⢽⢪⡣⢧⢵⡫⣞⣎⡯⡯⣟⣞⡮⣟⡼⡝⡮⣇⢡⢃⢇⢕⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⡢⠐⢈⠠⠈⠄⡃⠇⣳⢹⢜⢞⣆⣩⢮⡺⡮⡭⣽⡙⣗⡯⡯⣯⣗⡷⡯⣷⡹⣢⡉⡆⡇⢕⢌⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠌⡂⡂⠪⢐⢄⠤⢅⢠⡃⢵⡹⣝⢸⠳⠝⠓⠊⠀⠙⠃⢟⡮⡯⡯⣗⣗⡯⣟⢎⣳⢯⢯⡶⡘⢌⢆⢣⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠐⠄⠅⠢⠐⢄⢃⠇⡃⡧⣫⢞⢸⢯⣆⡆⢰⢁⢅⣱⣪⢽⡽⣫⢷⣫⡯⡯⠟⠚⠋⠋⣿⡐⢕⢌⢪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠅⢌⠘⠨⡊⢔⠡⢊⠆⢜⢮⣫⠢⡣⣗⡯⣟⣚⡴⣟⡾⡽⣽⢽⣫⣗⡯⣇⡈⣂⡼⡧⠀⡊⡢⡑⠥⡁⡄⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡂⡂⠅⢕⢀⠂⠌⡘⢜⢔⣰⠡⢳⡣⡇⣪⠵⣻⢽⣺⢽⣳⢯⣟⣗⡯⣗⠷⣻⢽⣺⢴⣻⡝⡡⢐⢅⠪⡊⡬⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡂⡐⠅⠕⢄⠐⢀⠂⡐⠉⠂⠎⠊⢼⢕⢌⢷⢝⡯⡯⣟⡾⣽⣺⣞⣽⢽⣺⢯⣻⣺⣽⣺⠃⢀⠅⡢⠑⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠌⢜⢘⢔⠈⠄⢂⠂⠀⠀⠈⠂⠈⢫⡴⣝⣽⢽⣽⣳⢯⢷⣳⣗⡯⣟⣞⡯⣗⣯⢾⡊⠌⡐⡐⠠⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⢐⠡⡑⢔⠱⢀⢁⠂⠌⠀⠀⠀⠀⠀⠠⡙⢷⡽⣽⣺⢞⣯⢿⢵⣗⢿⢽⣺⡽⣽⣺⠝⡈⡂⢂⠄⡑⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡂⡂⢕⠨⡊⡎⡐⠠⠨⠐⠀⠀⠀⠀⠀⢸⣎⢆⢍⠗⡯⣟⡾⣝⣗⡯⣯⡻⡮⡯⠓⢁⢂⠢⡈⠢⠨⠠⡃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢂⠌⡢⡑⡅⡇⠄⡑⠀⠡⠀⠀⠀⠀⠀⢸⣺⡆⢇⢣⢱⢨⠹⡱⢗⡟⠎⠋⠁⠀⠀⢀⠢⠨⠠⢑⠡⠡⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡐⠠⡑⠔⡌⢆⠇⠅⢂⢁⠁⠀⠀⠀⠀⢀⣾⣺⢽⡜⡌⡆⡣⡑⠔⠄⠀⠀⠀⠀⠀⠀⠀⠠⢑⠨⠐⠌⠌⠄⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠔⠨⠨⡂⢕⠜⡜⠔⡈⠄⡀⠂⠀⠀⢀⡤⣞⣞⢾⢽⢽⡌⡎⡌⢎⠪⡨⡐⡠⠀⡀⠀⢀⠠⡁⡂⡆⠥⡁⡅⡑⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠨⡈⡢⢑⠌⢆⢣⢱⠐⠠⣁⢄⣀⡤⣖⢯⢯⣳⢽⢽⢽⡽⡽⡔⢕⠅⡇⡪⡂⡪⡨⢌⢊⢆⠰⠨⡪⡸⡘⡌⡪⠢⡊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢅⠢⢐⠡⡊⡪⡘⣔⢲⢍⡪⣳⢳⣝⢞⣹⣳⢽⢽⢽⣙⡺⣽⢹⣶⡑⢕⢌⠪⣢⢵⣨⡢⡣⡱⡑⡔⡪⡂⢇⢪⢑⠕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⢐⠈⡢⢑⠌⢆⢇⢇⢗⢵⢝⡴⣓⣗⢯⢞⡮⡯⡯⣳⣳⢽⣺⡳⣳⢽⢬⢮⣺⡳⣫⣞⢽⡺⣕⣗⢼⡠⢊⠪⢢⠡⡱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢅⠢⠡⢂⢕⠸⡘⡜⡜⣜⢕⢗⣝⢵⢪⢯⡳⡽⣝⢞⡵⣳⢝⡮⣞⢗⡽⡵⣫⢞⡮⣳⡳⡽⣝⢞⡮⣳⢽⢔⢑⠡⡑⢌⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠨⢐⠨⢈⠢⡂⢇⢣⢣⢣⢣⡫⡺⡜⡮⣕⢗⣝⢞⢮⡫⣞⢵⡫⡞⡮⡳⡝⢮⡳⣝⢮⡳⡝⡞⡮⡳⣝⢮⡳⡵⡐⡡⠈⡢⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠌⡐⡨⢀⠪⡨⠀⡣⡣⡣⡣⡣⡫⡺⢜⢆⢣⢣⡫⡺⡜⡮⡺⡸⣕⢝⢞⡜⡦⡹⡸⣪⢺⢪⡫⡎⣏⢮⢺⢜⢎⢇⠂⠔⡈⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠐⡐⡐⢄⢑⠌⠄⢣⢪⠪⡪⡪⡺⡨⡣⢓⢕⢕⢕⢝⢜⢜⠎⡇⡇⡫⠪⡪⡬⢌⢤⠡⠅⡇⣇⢋⢪⢪⢲⢰⢪⢃⠅⡀⢊⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠌⡐⡐⢌⢐⢐⠅⠌⡰⡑⡕⢕⢱⢑⢕⢕⠸⡸⡨⠘⡜⢌⠎⡎⢆⠇⡇⡝⢜⢜⢜⠬⡹⡰⡐⡎⢎⠎⡎⢎⢎⢎⠎⡆⠐⢀⠂⢈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢁⠂⠌⢔⠐⡐⡁⡐⠄⢣⠪⡪⡘⢌⠆⡕⡘⢌⢪⠡⡊⢆⢣⢑⠅⡇⢕⠜⢌⠆⡕⢅⠣⡪⡘⡌⡪⠪⡘⡌⢆⢕⠱⡘⡈⠠⠈⠄⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀