Let’s take a prime P = 200\,003. You are given $N integers A_1, A_2, \ldots, A_N.$ Find the sum of $((A_i \cdot A_j) \bmod P)$ over all $N \cdot (N-1) / 2$ unordered pairs of elements (i < j).

Please note that the sum isn't computed modulo P.

Constraints

• $2 \leq N \leq 200$\,000
• $0 \leq A_i < P = 200$\,003
• All values in input are integers.

Input

Input is given from Standard Input in the following format.

N
$A_1 A_2 \cdots A_N$

Output

Print one integer — the sum over $((A_i \cdot A_j) \bmod P)$.

Examples

Input

4
2019 0 2020 200002

Output

474287

Input

5
1 1 2 2 100000

Output

600013

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