Problem: Nuske has a grid with N rows and M columns of squares. The rows are numbered 1 through N from top to bottom, and the columns are numbered 1 through M from left to right. Each square in the grid is painted in either blue or white. If S_{i,j} is 1, the square at the i-th row and j-th column is blue; if S_{i,j} is 0, the square is white. For every pair of two blue square a and b, there is at most one path that starts from a, repeatedly proceeds to an adjacent (side by side) blue square and finally reaches b, without traversing the same square more than once.

Phantom Thnook, Nuske's eternal rival, gives Q queries to Nuske. The i-th query consists of four integers x_{i,1}, y_{i,1}, x_{i,2} and y_{i,2} and asks him the following: when the rectangular region of the grid bounded by (and including) the x_{i,1}-th row, x_{i,2}-th row, y_{i,1}-th column and y_{i,2}-th column is cut out, how many connected components consisting of blue squares there are in the region?

Process all the queries.

Constraints

* 1 ≤ N,M ≤ 2000
* 1 ≤ Q ≤ 200000
* S_{i,j} is either 0 or 1.
* S_{i,j} satisfies the condition explained in the statement.
* 1 ≤ x_{i,1} ≤ x_{i,2} ≤ N(1 ≤ i ≤ Q)
* 1 ≤ y_{i,1} ≤ y_{i,2} ≤ M(1 ≤ i ≤ Q)

Input

The input is given from Standard Input in the following format:


N M Q
S_{1,1}..S_{1,M}
:
S_{N,1}..S_{N,M}
x_{1,1} y_{i,1} x_{i,2} y_{i,2}
:
x_{Q,1} y_{Q,1} x_{Q,2} y_{Q,2}


Output

For each query, print the number of the connected components consisting of blue squares in the region.

Examples

Input

3 4 4
1101
0110
1101
1 1 3 4
1 1 3 1
2 2 3 4
1 2 2 4


Output

3
2
2
2


Input

5 5 6
11010
01110
10101
11101
01010
1 1 5 5
1 2 4 5
2 3 3 4
3 3 3 3
3 1 3 5
1 1 3 4


Output

3
2
1
1
3
2

Solution (in PYTHON3):

Solution:
def examA():
    N, A, B = LI()
    if N==1:
        if A==B:
            print(1)
        else:
            print(0)
        return
    ans = (N-2)*max(B-A,0) + 1
    if B<A:
        ans = 0
    print(ans)
    return

def examB():
    S = SI()
    N = len(S)
    cnt = 0
    for i,s in enumerate(S):
        cnt += N-1
        if s=="U":
            cnt += i
        else:
            cnt += (N-i-1)
    ans = cnt
    print(ans)
    return

def examC():
    N, M, q = LI()
    S = [SI()for _ in range(N)]
    Q = [LI()for _ in range(q)]
    S1 = [[0]*(M+1) for _ in range(N+1)]
    S2 = [[0]*(M+1) for _ in range(N+1)]
    S3 = [[0]*(M+1) for _ in range(N+1)]
    for i in range(N):
        now = 0
        for j in range(M):
            now += int(S[i][j])
            S1[i+1][j+1] = S1[i][j+1]+now
    for i in range(N):
        now = 0
        for j in range(M-1):
            if S[i][j]=="1" and S[i][j+1]=="1":
                now += 1
            S2[i+1][j+1] += S2[i][j+1]+now
    for i in range(M):
        now = 0
        for j in range(N-1):
            if S[j][i]=="1" and S[j+1][i]=="1":
                now += 1
            S3[j+1][i+1] += S3[j+1][i]+now
    ans = [0]*q
    #print(S2)
    #print(S3)
    for i in range(q):
        x1, y1, x2, y2 = Q[i]
        #print(x1,y1,x2,y2)
        x1 -= 1; y1 -= 1
        cur = S1[x2][y2] - S1[x1][y2] - S1[x2][y1] + S1[x1][y1]
        cur -= S2[x2][y2-1] - S2[x1][y2-1] - S2[x2][y1] + S2[x1][y1]
        cur -= S3[x2-1][y2] - S3[x1][y2] - S3[x2-1][y1] + S3[x1][y1]
        ans[i] = cur
    for v in ans:
        print(v)
    return

def examD():
    A = I()
    B = I()

    ans = 0
    print(ans)
    return

def examE():
    ans = 0
    print(ans)
    return

def examF():
    ans = 0
    print(ans)
    return

def test():

    return

import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-12)
alphabet = [chr(ord('a') + i) for i in range(26)]

sys.setrecursionlimit(10**7)

if __name__ == '__main__':
    examC()

"""
3 4 4 
1101 
0110 
1101 
1 1 3 4 
1 1 3 1 
2 2 3 4 
1 2 2 4 
"""