Table Range Sum with Updates

An $N \times N$ table is filled with natural numbers. The cell in row $i$ and column $j$ is written as $(i, j)$. The sum from $(x_1, y_1)$ to $(x_2, y_2)$ is the sum of the numbers in every cell $(x, y)$ with $x_1 \le x \le x_2$ and $y_1 \le y \le y_2$.

Two kinds of operations arrive mixed together: one replaces the number in a single cell, the other asks for the sum of a rectangle. Consider $N = 4$ with the table below.

The sum from $(2, 2)$ to $(3, 4)$ is $3 + 4 + 5 + 4 + 5 + 6 = 27$. If the number in $(2, 3)$ is then replaced with $7$, the sum over the same rectangle becomes $3 + 7 + 5 + 4 + 5 + 6 = 30$.

Given the initial table and the operations in order, write a program that prints the value for each sum operation.

The first line contains the table size $N$ and the number of operations $M$. ($1 \le N \le 1024$, $1 \le M \le 100\,000$)

Each of the next $N$ lines contains one row of the table, starting from row 1. Each line holds $N$ numbers separated by spaces, and every number in the table is a natural number at most $1000$.

Each of the following $M$ lines contains one operation, given either as four integers $w$, $x$, $y$, $c$ or as five integers $w$, $x_1$, $y_1$, $x_2$, $y_2$. If $w = 0$, replace the number in $(x, y)$ with $c$. If $w = 1$, compute the sum from $(x_1, y_1)$ to $(x_2, y_2)$. ($1 \le x \le N$, $1 \le y \le N$, $1 \le c \le 1000$, $1 \le x_1 \le x_2 \le N$, $1 \le y_1 \le y_2 \le N$)

For each operation with $w = 1$, print the computed sum on its own line, in the order the operations are given.