{"raw_statement":[{"iden":"problem statement","content":"We have an integer sequence $A$ of length $N$, where $A_1 = X, A_{i+1} = A_i + D (1 \\leq i < N )$ holds.\nTakahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others.\nLet $S$ and $T$ be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of $S - T$ are there?"},{"iden":"constraints","content":"*   $-10^8 \\leq X, D \\leq 10^8$\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$ $D$"},{"iden":"sample input 1","content":"3 4 2"},{"iden":"sample output 1","content":"8\n\n$A$ is $(4, 6, 8)$.\nThere are eight ways for (Takahashi, Aoki) to take the elements: $((), (4, 6, 8)), ((4), (6, 8)), ((6), (4, 8)), ((8), (4, 6))), ((4, 6), (8))), ((4, 8), (6))), ((6, 8), (4)))$, and $((4, 6, 8), ())$.\nThe values of $S - T$ in these ways are $-18, -10, -6, -2, 2, 6, 10$, and $18$, respectively, so there are eight possible values of $S - T$."},{"iden":"sample input 2","content":"2 3 -3"},{"iden":"sample output 2","content":"2\n\n$A$ is $(3, 0)$. There are two possible values of $S - T$: $-3$ and $3$."},{"iden":"sample input 3","content":"100 14 20"},{"iden":"sample output 3","content":"49805"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}