{"raw_statement":[{"iden":"problem statement","content":"There are $N$ piles of stones. The $i$\\-th pile has $A_i$ stones.\nAoki and Takahashi are about to use them to play the following game:\n\n*   Starting with Aoki, the two players alternately do the following operation:\n    *   Operation: Choose one pile of stones, and remove one or more stones from it.\n*   When a player is unable to do the operation, he loses, and the other player wins.\n\nWhen 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.\nIn 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.\nIf this is possible, print the minimum number of stones to move to guarantee his victory; otherwise, print `-1` instead."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 300$\n*   $1 \\leq A_i \\leq 10^{12}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"2\n5 3"},{"iden":"sample output 1","content":"1\n\nWithout moving stones, if Aoki first removes $2$ stones from the $1$\\-st pile, Takahashi cannot win in any way.\nIf Takahashi moves $1$ stone from the $1$\\-st pile to the $2$\\-nd before the game begins so that both piles have $4$ stones, Takahashi can always win by properly choosing his actions."},{"iden":"sample input 2","content":"2\n3 5"},{"iden":"sample output 2","content":"\\-1\n\nIt is not allowed to move stones from the $2$\\-nd pile to the $1$\\-st."},{"iden":"sample input 3","content":"3\n1 1 2"},{"iden":"sample output 3","content":"\\-1\n\nIt is not allowed to move all stones from the $1$\\-st pile."},{"iden":"sample input 4","content":"8\n10 9 8 7 6 5 4 3"},{"iden":"sample output 4","content":"3"},{"iden":"sample input 5","content":"3\n4294967297 8589934593 12884901890"},{"iden":"sample output 5","content":"1\n\nWatch out for overflows."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}