Problem: Mike and some bears are playing a game just for fun. Mike is the judge. All bears except Mike are standing in an n × m grid, there's exactly one bear in each cell. We denote the bear standing in column number j of row number i by (i, j). Mike's hands are on his ears (since he's the judge) and each bear standing in the grid has hands either on his mouth or his eyes.

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They play for q rounds. In each round, Mike chooses a bear (i, j) and tells him to change his state i. e. if his hands are on his mouth, then he'll put his hands on his eyes or he'll put his hands on his mouth otherwise. After that, Mike wants to know the score of the bears.

Score of the bears is the maximum over all rows of number of consecutive bears with hands on their eyes in that row.

Since bears are lazy, Mike asked you for help. For each round, tell him the score of these bears after changing the state of a bear selected in that round. 

Input

The first line of input contains three integers n, m and q (1 ≤ n, m ≤ 500 and 1 ≤ q ≤ 5000).

The next n lines contain the grid description. There are m integers separated by spaces in each line. Each of these numbers is either 0 (for mouth) or 1 (for eyes).

The next q lines contain the information about the rounds. Each of them contains two integers i and j (1 ≤ i ≤ n and 1 ≤ j ≤ m), the row number and the column number of the bear changing his state.

Output

After each round, print the current score of the bears.

Examples

Input

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


Output

3
4
3
3
4

Solution (in PYTHON3):

Solution:
# SOLVED

# solving: 
# from: 


def old():
    invalues = input().strip().split(" ")
    n, m, q = int(invalues[0]), int(invalues[1]), int(invalues[2])
    
    grid = [-1 for _ in range(0, n * m)]

    # Do simulation
    max_val = 0
    for i in range(0, n):
        current_run = 0

        row = input().strip().split(" ")
        for x in range(0, m):
            ch = row[x]
            val = int(ch)

            if val == 1:
                current_run += 1
            elif val == 0:
                if current_run > max_val:
                    max_val = current_run
                
                grid[x + i * m] = current_run
                current_run = 0

    # do rounds
    for round in range(0, q):
        invalues = input().strip().split(" ")
        x, y = int(invalues[0])-1, int(invalues[1])-1

        distance_to_head = 0
        head_value = 0
        
        # NOTE: need to handle cases where two are stiched together
        # TODO: replace a lot of ns with m

        for i in range(y, n):
            if grid[x + y * n + i] != 0:
                distance_to_head = i - y
                head_value = grid[x + y * m + i]
                break
        
        if head_value == 0:
            grid[x + y * n] = 1

        if distance_to_head == 0:
            grid[x + y * n + distance_to_head - 1] = grid[x + y * n + distance_to_head] - 1
            grid[x + y * n + distance_to_head] = 0
            if head_value == max_val:
                max_val -= 1
        elif distance_to_head == head_value - 1:
            grid[x + y * n] -= 1
            if head_value == max_val:
                max_val -= 1
        elif distance_to_head == head_value:
            grid[x + y * n + distance_to_head] += 1
            if head_value == max_val:
                max_val += 1
        elif distance_to_head > head_value:
            grid[x + y * n] = 1
        else:
            # split in half
            grid[x + y * n] = 0
            grid[x + y * n + distance_to_head] = distance_to_head
            grid[x + y * n - 1] = head_value - distance_to_head - 1

            # Recalculate max
            max_val = 0
            for i in range(0, n*m):
                if grid[i] > max_val:
                    max_val = grid[i]

        print("{}".format(max_val))
    

def old1():
    invalues = input().strip().split(" ")
    n, m, q = int(invalues[0]), int(invalues[1]), int(invalues[2])
    
    grid = [0 for _ in range(0, n * m)]
    for i in range(0, n):
        row = input().strip().split(" ")
        for x in range(0, m):
            grid[i * m + x] = int(row[x])

    for round in range(0, q):
        invalues = input().strip().split(" ")
        x, y = int(invalues[1])-1, int(invalues[0])-1

        val = grid[x + y * m]
        if val == 1:
            grid[x + y * m] = 0
        else:
            grid[x + y * m] = 1 

        # Do simulation
        max_val = 0
        current_run = 0
        for i in range(0, n*m):
            if i % m == 0:
                if current_run > max_val:
                    #TODO: break if new max
                    max_val = current_run
                current_run = 0

            if grid[i] == 1:
                current_run += 1
            else:
                if current_run > max_val:
                    #TODO: break if new max
                    max_val = current_run
                current_run = 0
        
        if current_run > max_val:
            #TODO: break if new max
            max_val = current_run

        print("{}".format(max_val))


def get_info_current(grid, x, y, m):
    dist_r = 0
    hit = False
    if x % m != m-1:
        for i in range(x+1, m):
            if grid[i + y * m] != 1:
                dist_r = i - x - 1
                hit = True
                break
        if not hit: dist_r = m - x - 1

    dist_l = 0
    hit = False
    if x % m != 0:
        for i in range(x-1, -1, -1):
            if grid[i + y * m] != 1:
                dist_l = x - i - 1
                hit = True
                break
        if not hit: dist_l = x - (-1) - 1

    return (dist_r, dist_l)

def do_simulation(grid, n, m):
    # Do simulation
    max_val = 0
    current_run = 0
    for i in range(0, n*m):
        if i % m == 0:
            if current_run > max_val:
                max_val = current_run
            current_run = 0

        if grid[i] == 1:
            current_run += 1
        else:
            if current_run > max_val:
                max_val = current_run
            current_run = 0
        
    if current_run > max_val:
        max_val = current_run

    return max_val

def main():
    invalues = input().strip().split(" ")
    n, m, q = int(invalues[0]), int(invalues[1]), int(invalues[2])
    
    # init grid
    grid = [0 for _ in range(0, n * m)]
    for i in range(0, n):
        row = input().strip().split(" ")
        for x in range(0, m):
            grid[i * m + x] = int(row[x])

    max_val = do_simulation(grid, n, m)

    # apply rounds
    for round in range(0, q):
        invalues = input().strip().split(" ")
        x, y = int(invalues[1])-1, int(invalues[0])-1

        dist_r, dist_l = get_info_current(grid, x, y, m)

        #print("{}".format(grid))
        #print("{} {}".format(dist_l, dist_r))

        val = grid[x + y * m]
        if val == 1:
            grid[x + y * m] = 0
            if dist_r + dist_l + 1 == max_val:
                max_val = do_simulation(grid, n, m)
        else:
            grid[x + y * m] = 1 
            if dist_r + dist_l + 1 > max_val:
                max_val = dist_r + dist_l + 1

        print("{}".format(max_val))

main()