Lu

LU decomposition

Syntax

lu(A)

A is a square matrix

Returns an upper triangular matrix in U, a lower triangular matrix L with a unit diagonal, and a permutation matrix P, such that L*U = P*A.

Examples

Input

Output

lu([2+i, -3i, -4; 1+i, -1+i, 4+2i; 3+2i, -2+2i, 3-i])

<L,U,P> =

lu([2+i, -3i, -4; 1+i, -1+i, 4+2i; 3+2i, -2+2i, 3-i])