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 input 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