XOR sum — Eolymp

Input

The first line of the input contains three integers $n$ , $k$ , $x$ ( $1 \leq n, k, n \times k \leq 300000$ 1 \le n, k, n \times k \le 300\ 000, $1 \leq x \leq 3$ 1 \le x \le 3) - length of an array, number of bits in each number and the power of exclusive OR operations results in the sum.

Next $n$ lines contain array elements. The $i$ -th of them contains string $s_{0}, s_{1}, \dots, s_{k - 1}$ s_0, s_1, \ldots, s_{k-1}, consisting of " $0$ " and " $1$ ". Then

![prb8647_1.gif](https://static.e-olymp.com/content/c3/c3107b00316da88a8810798e492cddd92a4e7166.gif)

Output

Print one number - the remainder of division of the sum of $x$ -th powers of exclusive OR results of all pairs of numbers in the array by $998244353$ .

Examples

Example 1

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Example 2

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Note

In the first test case the array contains the numbers $[5, 4, 4]$ [5, 4, 4], and the resulting sum is $(5 xor 4) + (5 xor 4) + (4 xor 4) = 1 + 1 + 0 = 2$ (5 \mathrm{\ xor}\ 4) + (5 \mathrm{\ xor}\ 4) + (4 \mathrm{\ xor}\ 4) = 1 + 1 + 0 = 2.

In the second test case the array contains the numbers $[61, 38]$ , and the resulting sum is $(61 xor 38)^{3} = 2 7^{3} = 19683$ (61 \mathrm{\ xor}\ 38)^3 = 27^3 = 19683.