Missing Coin Sum

You have n coins with positive integer values. What is the smallest sum you cannot create using a subset of the coins?

Input

The first line has an integer n: the number of coins. The second line has n integers x_1,x_2,\dots,x_n: the value of each coin.

Output

Print one integer: the smallest coin sum.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

5
2 9 1 2 7

Output

6