{"raw_statement":[{"iden":"problem statement","content":"There are $N$ integers $X_1, X_2, \\cdots, X_N$, and we know that $A_i \\leq X_i \\leq B_i$. Find the number of different values that the median of $X_1, X_2, \\cdots, X_N$ can take."},{"iden":"notes","content":"The median of $X_1, X_2, \\cdots, X_N$ is defined as follows. Let $x_1, x_2, \\cdots, x_N$ be the result of sorting $X_1, X_2, \\cdots, X_N$ in ascending order.\n\n*   If $N$ is odd, the median is $x_{(N+1)/2}$;\n*   if $N$ is even, the median is $(x_{N/2} + x_{N/2+1}) / 2$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A_i \\leq B_i \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $B_1$\n$A_2$ $B_2$\n$:$\n$A_N$ $B_N$"},{"iden":"sample input 1","content":"2\n1 2\n2 3"},{"iden":"sample output 1","content":"3\n\n*   If $X_1 = 1$ and $X_2 = 2$, the median is $\\frac{3}{2}$;\n    \n*   if $X_1 = 1$ and $X_2 = 3$, the median is $2$;\n    \n*   if $X_1 = 2$ and $X_2 = 2$, the median is $2$;\n    \n*   if $X_1 = 2$ and $X_2 = 3$, the median is $\\frac{5}{2}$.\n    \n\nThus, the median can take three values: $\\frac{3}{2}$, $2$, and $\\frac{5}{2}$."},{"iden":"sample input 2","content":"3\n100 100\n10 10000\n1 1000000000"},{"iden":"sample output 2","content":"9991"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}