Smallest Missing Coin Sum

You may select any subset of the supplied coins. Each individual coin may be used at most once, even when multiple coins share a value. Find the smallest positive integer amount that no selection can produce.

Implement missing_coin_sum(coins).

Input

coins: The values of the available coins; duplicates represent separate coins.

Output

Return the smallest positive impossible amount.

Constraints

1 ≤ number of coins ≤ 200,000. Each value is between 1 and 1,000,000,000.

Examples

Input:
coins = [1, 1, 4]

Expected output:
expected = 3

Input:
std::vector<long long> coins = {1, 1, 4};

Expected output:
long long expected = 3;

Input:
long[] coins = new long[] {1, 1, 4};

Expected output:
long expected = 3;

Input:
coins = [2, 3]

Expected output:
expected = 1

Input:
std::vector<long long> coins = {2, 3};

Expected output:
long long expected = 1;

Input:
long[] coins = new long[] {2, 3};

Expected output:
long expected = 1;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Missing Coin Sum — 2183