Mirko has written the following function:

int fun() {
  int ret = 0;
  for (int a = X1; a <= Y1; ++a)
    for (int b = X2; b <= Y2; ++b)
      ...
        for (int <N-th> = XN; <N-th> <= YN; ++<N-th>)
          ret = (ret + 1) % 1000000007;
  return ret;
}

function fun: longint;
var
  ret: longint;
  a, b, ... , y, z: longint;
begin
  ret := 0;
  for a := X1 to Y1 do
    for b := X2 to Y2 do
      ...
        for <N-th> := XN to YN do
          ret := (ret + 1) mod 1000000007;
  fun := ret;
end;

<N-th> denotes the ~N^{th}~ lowercase letter of the English alphabet. Each ~X_i~ and ~Y_i~ denotes either a positive integer less than or equal to ~100\,000~ or a name of a variable that some outer loop iterates over. For example, X3 can be either ~a~, ~b~, or an integer literal. At least one of ~X_i~ and ~Y_i~ will be an integer literal (i.e. not a variable name) for every ~i~.

Compute the return value of the function.

Input Specification

The first line of input contains the positive integer ~N~ ~(1 \le N \le 26)~.

For the next ~N~ lines, the ~i^{th}~ line contains ~X_i~ and ~Y_i~, separated with a space. If ~X_i~ and ~Y_i~ are both integer literals, then ~X_i \le Y_i~.

Output Specification

The first and only line of output must contain the return value of the function.

Sample Input 1

2
1 2
a 3

Sample Output 1

5

Sample Input 2

3
2 3
1 2
1 a

Sample Output 2

10

Sample Input 3

3
1 2
a 3
1 b

Sample Output 3

11