Symmetry

【题目描述】
The figure shown on the left is left-right symmetric as it is possible to fold the sheet of paper along a vertical line, drawn as a dashed line, and to cut the figure into two identical halves. The figure on the right is not left-right symmetric as it is impossible to find such a vertical line.

Write a program that determines whether a figure, drawn with dots, is left-right symmetric or not. The dots are all distinct.
【输入格式】
The input consists of T test cases. The number of test cases T is given in the first line of the input file. The first line of each test case contains an integer N , where N ( 1≤N≤1, 000) is the number of dots in a figure. Each of the following N lines contains the x-coordinate and y-coordinate of a dot. Both x-coordinates and y-coordinates are integers between -10,000 and 10,000, both inclusive.
【输出格式】
Print exactly one line for each test case. The line should contain ‘YES’ if the figure is left-right symmetric. and `NO’, otherwise.
The following shows sample input and output for three test cases.
【样例输入】
3
5
-2 5
0 0
6 5
4 0
2 3
4
2 3
0 4
4 0
0 0
4
5 14
6 10
5 10
6 14
【样例输出】
YES
NO
YES
【分析】
容易想到，如果存在对称轴，那么对称轴的横坐标一定是最左边的点和最右边的点的中点。为了避免中点是小数 可以将横坐标都乘上2，然后在判断所有点是否有对称点就行了。

var
  x,y:array[0..1001]of longint;
    left,right,i,n,mid,t:longint;
    flag:boolean;
function check(k:longint):boolean;
var
  i:longint;
begin
  for i:=1 to n do
      if (y[i]=y[k])and(x[i]+x[k]=2*mid) then exit(true);
    exit(false);
end;
begin
  readln(t);
    while t>0 do begin
      dec(t);
        left:=1;right:=1;
        readln(n);
        for i:=1 to n do begin
          readln(x[i],y[i]);
            x[i]:=x[i]*2;
            if x[i]<x[left] then left:=i;
            if x[i]>x[right] then right:=i;
        end;
        mid:=(x[left]+x[right]) div 2;
        flag:=true;
        for i:=1 to n do
          if not check(i) then flag:=false;
        if flag then writeln('YES') else writeln('NO');
    end;
end.