You are given matrix *a* of size *n* × *m*, its elements are integers. We will assume that the rows of the matrix are numbered from top to bottom from 1 to *n*, the columns are numbered from left to right from 1 to *m*. We will denote the element on the intersecting of the *i*-th row and the *j*-th column as *a*<sub class="lower-index">*ij*</sub>.

We'll call submatrix *i*<sub class="lower-index">1</sub>, *j*<sub class="lower-index">1</sub>, *i*<sub class="lower-index">2</sub>, *j*<sub class="lower-index">2</sub> (1 ≤ *i*<sub class="lower-index">1</sub> ≤ *i*<sub class="lower-index">2</sub> ≤ *n*; 1 ≤ *j*<sub class="lower-index">1</sub> ≤ *j*<sub class="lower-index">2</sub> ≤ *m*) such elements *a*<sub class="lower-index">*ij*</sub> of the given matrix that *i*<sub class="lower-index">1</sub> ≤ *i* ≤ *i*<sub class="lower-index">2</sub> AND *j*<sub class="lower-index">1</sub> ≤ *j* ≤ *j*<sub class="lower-index">2</sub>. We'll call the area of the submatrix number (*i*<sub class="lower-index">2</sub> - *i*<sub class="lower-index">1</sub> + 1)·(*j*<sub class="lower-index">2</sub> - *j*<sub class="lower-index">1</sub> + 1). We'll call a submatrix inhomogeneous, if all its elements are distinct.

Find the largest (in area) inhomogenous submatrix of the given matrix.
The first line contains two integers *n*, *m* (1 ≤ *n*, *m* ≤ 400) — the number of rows and columns of the matrix, correspondingly.

Each of the next *n* lines contains *m* integers *a*<sub class="lower-index">*ij*</sub> (1 ≤ *a*<sub class="lower-index">*ij*</sub> ≤ 160000) — the elements of the matrix.
print("_RANDOM_GUESS_1689335349.09666")# 1689335349.096705