Inna loves sweets very much. That's why she wants to play the "Sweet Matrix" game with Dima and Sereja. But Sereja is a large person, so the game proved small for him. Sereja suggested playing the "Large Sweet Matrix" game.

The "Large Sweet Matrix" playing field is an n × m matrix. Let's number the rows of the matrix from 1 to n, and the columns — from 1 to m. Let's denote the cell in the i-th row and j-th column as (i, j). Each cell of the matrix can contain multiple candies, initially all cells are empty. The game goes in w moves, during each move one of the two following events occurs:

  1. Sereja chooses five integers x1, y1, x2, y2, v (x1 ≤ x2, y1 ≤ y2) and adds v candies to each matrix cell (i, j) (x1 ≤ i ≤ x2; y1 ≤ j ≤ y2). 
  2. Sereja chooses four integers x1, y1, x2, y2 (x1 ≤ x2, y1 ≤ y2). Then he asks Dima to calculate the total number of candies in cells (i, j) (x1 ≤ i ≤ x2; y1 ≤ j ≤ y2) and he asks Inna to calculate the total number of candies in the cells of matrix (p, q), which meet the following logical criteria: (p < x1 OR p > x2) AND (q < y1 OR q > y2). Finally, Sereja asks to write down the difference between the number Dima has calculated and the number Inna has calculated (D - I). 



Unfortunately, Sereja's matrix is really huge. That's why Inna and Dima aren't coping with the calculating. Help them!

Input

The first line of the input contains three integers n, m and w (3 ≤ n, m ≤ 4·106; 1 ≤ w ≤ 105).

The next w lines describe the moves that were made in the game. 

  * A line that describes an event of the first type contains 6 integers: 0, x1, y1, x2, y2 and v (1 ≤ x1 ≤ x2 ≤ n; 1 ≤ y1 ≤ y2 ≤ m; 1 ≤ v ≤ 109). 
  * A line that describes an event of the second type contains 5 integers: 1, x1, y1, x2, y2 (2 ≤ x1 ≤ x2 ≤ n - 1; 2 ≤ y1 ≤ y2 ≤ m - 1). 



It is guaranteed that the second type move occurs at least once. It is guaranteed that a single operation will not add more than 109 candies.

Be careful, the constraints are very large, so please use optimal data structures. Max-tests will be in pretests.

Output

For each second type move print a single integer on a single line — the difference between Dima and Inna's numbers.

Examples

Input

4 5 5
0 1 1 2 3 2
0 2 2 3 3 3
0 1 5 4 5 1
1 2 3 3 4
1 3 4 3 4


Output

2
-21

Note

Note to the sample. After the first query the matrix looks as: 
    
    
      
    22200  
    22200   
    00000  
    00000  
    

After the second one it is: 
    
    
      
    22200  
    25500  
    03300   
    00000  
    

After the third one it is: 
    
    
      
    22201  
    25501  
    03301  
    00001  
    

For the fourth query, Dima's sum equals 5 + 0 + 3 + 0 = 8 and Inna's sum equals 4 + 1 + 0 + 1 = 6. The answer to the query equals 8 - 6 = 2. For the fifth query, Dima's sum equals 0 and Inna's sum equals 18 + 2 + 0 + 1 = 21. The answer to the query is 0 - 21 = -21.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt(), q = in.nextInt();
        /*for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                int x = in.nextInt();
                A[i] += x;
                B[j] += x;
            }
        }*/

            FenwickTree S1 = new FenwickTree(n);
            FenwickTree S2 = new FenwickTree(m);

            while (q-- > 0) {
                int type = in.nextInt();
                int x1 = in.nextInt() - 1, y1 = in.nextInt() - 1;
                int x2 = in.nextInt() - 1, y2 = in.nextInt() - 1;
                if (type == 1) {
                    long s1 = S1.query(0, x1 - 1) + S1.query(x2 + 1, n - 1) +
                            S2.query(0, y1 - 1) + S2.query(y2 + 1, m - 1);
                    long s2 = S1.query(x1, x2) + S2.query(y1, y2);
                    out.println((s2 - s1) / 2);
                } else {
                    int v = in.nextInt();
                    S1.update(x1, x2, (y2 - y1 + 1) * v);
                    S2.update(y1, y2, (x2 - x1 + 1) * v);
                }
            }
        }

        private class FenwickTree {
            private long[] sum;
            private long[] coef;
            private int size;

            FenwickTree(int n) {
                sum = new long[n + 1];
                coef = new long[n + 1];
                size = n;
            }

            public void update(int left, int right, int value) {
                ++left;
                ++right;
                for (int i = left; i <= size; i += i & -i) {
                    coef[i] += value;
                }
                for (int i = right + 1; i <= size; i += i & -i) {
                    coef[i] -= value;
                }
                long add = (long) (left - 1) * value;
                for (int i = left; i <= size; i += i & -i) {
                    sum[i] -= add;
                }
                for (int i = right + 1; i <= size; i += i & -i) {
                    sum[i] += add;
                    sum[i] += (long) (right - left + 1) * value;
                }
            }

            private long getSum(int pos) {
                long c = 0, s = 0;
                for (int i = ++pos; i > 0; i -= i & -i) {
                    c += coef[i];
                    s += sum[i];
                }
                return pos * c + s;
            }

            public long query(int left, int right) {
                return getSum(right) - getSum(left - 1);
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

