XOR sum

You have an array of n k-bit numbers a[1], a[2], ..., a[n]. You need to calculate

Operation a + b is bitwise exclusive OR of two numbers a and b. Since the answer can be very large, output it modulo 998 244 353.

Input

The first line of the input contains three integers n, k, x (1 ≤ n, k, n * k ≤ 300 000, 1 ≤ x ≤ 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], ..., s[k-1], consisting of "0" and "1". Then

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 998 244 353.

Examples

Note

In the first test case the array contains the numbers [5, 4, 4], and the resulting sum is (5 xor 4) + (5 xor 4) + (4 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 = 27^3 = 19683.