Unfair Nim

There are N piles of stones. The i-th pile has A_i stones.

Aoki and Takahashi are about to use them to play the following game:

• Starting with Aoki, the two players alternately do the following operation:
• Operation: Choose one pile of stones, and remove one or more stones from it.
• When a player is unable to do the operation, he loses, and the other player wins.

When the two players play optimally, there are two possibilities in this game: the player who moves first always wins, or the player who moves second always wins, only depending on the initial number of stones in each pile.

In such a situation, Takahashi, the second player to act, is trying to guarantee his win by moving at least zero and at most (A_1 - 1) stones from the 1-st pile to the 2-nd pile before the game begins.

If this is possible, print the minimum number of stones to move to guarantee his victory; otherwise, print -1 instead.

Constraints

• 2 \leq N \leq 300
• 1 \leq A_i \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

Output

Print the minimum number of stones to move to guarantee Takahashi's win; otherwise, print -1 instead.

Examples

Input

2 5 3

Output

1

Input

2 3 5

Output

-1

Input

3 1 1 2

Output

-1

Input

8 10 9 8 7 6 5 4 3

Output

3

Input

3 4294967297 8589934593 12884901890

Output

1

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

outputFormat

Output

Print the minimum number of stones to move to guarantee Takahashi's win; otherwise, print -1 instead.

Examples

Input

2 5 3

Output

1

Input

2 3 5

Output

-1

Input

3 1 1 2

Output

-1

Input

8 10 9 8 7 6 5 4 3

Output

3

Input

3 4294967297 8589934593 12884901890

Output

1

样例

2
3 5

-1