# 二次元累積和
class Ruiwa():
    def __init__(self, a):
        self.H = h = len(a)
        self.W = w = len(a[0])
        self.R = r = a
        for i in range(h):
            for j in range(1,w):
                r[i][j] += r[i][j-1]

        for i in range(1,h):
            for j in range(w):
                r[i][j] += r[i-1][j]

    def search(self, x1, y1, x2, y2):
        if x1 > x2 or y1 > y2:
            return 0

        r = self.R
        rr = r[y2][x2]
        if x1 > 0 and y1 > 0:
            return rr - r[y1-1][x2] - r[y2][x1-1] + r[y1-1][x1-1]
        if x1 > 0:
            rr -= r[y2][x1-1]
        if y1 > 0:
            rr -= r[y1-1][x2]

        return rr
