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문제

Pasha is playing the video game "DiaBro III". He is fighting against $n \cdot m$ monsters in this game. The monsters are arranged into $n$ rows of $m$ columns each. Rows are numbered with sequential integers from $1$ to $n$ and columns --- with sequential integers from $1$ to $m$.

Each monster has one of $k$ types. The $i$-th monster type is described by two integers $q_{i}$ and $g_{i}$: Pasha can kill a monster of $i$-th type only if amount of his experience is at least $q_{i}$, and after killing each monster of this type --- Pasha will gain $g_{i}$ units of experience.

Pasha wants to choose a rectangle by fixing four integers $r_{1}$, $r_{2}$, $c_{1}$ and $c_{2}$ such that $1 \leq r_{1} \leq r_{2} \leq n$ and $1 \leq c_{1} \leq c_{2} \leq m$. Then Pasha starts to kill monsters in the chosen rectangle --- at cells $(r, c)$ such that $r_{1} \leq r \leq r_{2}$ and $c_{1} \leq c \leq c_{2}$. Initially, he has no experience at all. The rectangle is good if it is possible to kill all monsters inside the rectangle in some order without killing any monster which is not in the rectangle.

You are to write a program that will find the number of different good rectangles.

입력

The first line of input contains two integers $n$ and $m$ ($1 \leq n, m \leq 200$) --- the number of rows and columns of monsters respectively.

Each of the following $n$ lines contains exactly $m$ lowercase Latin letters. The $j$-th character of $i$-th line denotes the type of monster with row number $i$ and column number $j$. Monsters of the same type are denoted with the same lowercase Latin letter. 

The next line contain the only integer $k$ ($1 \leq k \leq 26$) --- the number of monster types.

Each of the following $k$ lines contains the description of some monster type. The description of $i$-th monster type consists of character $l_{i}$ --- the lowercase Latin letter corresponding to this monster type --- and two integers $q_{i}$ and $g_{i}$ ($0 \leq q_{i} \leq 10^{9}, 1 \leq g_{i} \leq 10^{9}$) --- the amount of experience required to kill a monster of this type and the amount of experience obtained after killing each monster of this type respectively. The values of $l_{i}$, $q_{i}$ and $g_{i}$ are separated by single spaces.

It is guaranteed that there is no monster of type that is not described in the input.

출력

The only line of output should contain one integer --- the number of ways to choose values $r_{1}$, $r_{2}$, $c_{1}$ and $c_{2}$ to satisfy all the conditions given above.

예제 입력 1

2 3
aba
baa
2
a 0 2
b 4 100

예제 출력 1

11

예제 입력 2

4 6
aaaaaa
abbaaa
aaacba
aaabba
3
a 0 1
b 3 2
c 12 5

예제 출력 2

128

힌트

There are $11$ possible values of $r_{1}$, $r_{2}$, $c_{1}$ and $c_{2}$ in the first sample:

  1. $r_{1} = 1,~~~r_{2} = 1,~~~c_{1} = 1,~~~c_{2} = 1$;
  2. $r_{1} = 1,~~~r_{2} = 1,~~~c_{1} = 1,~~~c_{2} = 3$;
  3. $r_{1} = 1,~~~r_{2} = 1,~~~c_{1} = 3,~~~c_{2} = 3$;
  4. $r_{1} = 1,~~~r_{2} = 2,~~~c_{1} = 1,~~~c_{2} = 2$;
  5. $r_{1} = 1,~~~r_{2} = 2,~~~c_{1} = 1,~~~c_{2} = 3$;
  6. $r_{1} = 1,~~~r_{2} = 2,~~~c_{1} = 2,~~~c_{2} = 3$;
  7. $r_{1} = 1,~~~r_{2} = 2,~~~c_{1} = 3,~~~c_{2} = 3$;
  8. $r_{1} = 2,~~~r_{2} = 2,~~~c_{1} = 1,~~~c_{2} = 3$;
  9. $r_{1} = 2,~~~r_{2} = 2,~~~c_{1} = 2,~~~c_{2} = 2$;
  10. $r_{1} = 2,~~~r_{2} = 2,~~~c_{1} = 2,~~~c_{2} = 3$;
  11. $r_{1} = 2,~~~r_{2} = 2,~~~c_{1} = 3,~~~c_{2} = 3$.