Problem: Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations:

* $update(s, t, x)$: change $a_s, a_{s+1}, ..., a_t$ to $x$.
* $getSum(s, t)$: print the sum of $a_s, a_{s+1}, ..., a_t$.



Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0.

Constraints

* $1 ≤ n ≤ 100000$
* $1 ≤ q ≤ 100000$
* $0 ≤ s ≤ t < n$
* $-1000 ≤ x ≤ 1000$

Input


$n$ $q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$-th query $query_i$ is given in the following format:


0 $s$ $t$ $x$


or


1 $s$ $t$


The first digit represents the type of the query. '0' denotes $update(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $getSum$ query, print the sum in a line.

Example

Input

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5


Output

-5
1
6
8

Solution (in CPP):

Solution:
#include <iostream>
#define int long long
using namespace std;

const int DEPTH = 17;

struct SegTree {
	int lazyT[1 << DEPTH + 1];
	int lazyV[1 << DEPTH + 1];
	int segSum[1 << DEPTH + 1];
	
	SegTree() {
		for (int i = 0; i < (1 << DEPTH + 1); i++) {
			lazyT[i] = -1;
			lazyV[i] = 0;
			segSum[i] = 0;
		}
	}
	
	void lazy_evaluate(int id, int len) {
		if (lazyT[id] == -1) return;
		
		segSum[id] = lazyV[id] * len;
		if (id < (1 << DEPTH) - 1) {
			if (lazyT[id * 2 + 1] < lazyT[id]) {
				lazyT[id * 2 + 1] = lazyT[id];
				lazyV[id * 2 + 1] = lazyV[id];
			}
			if (lazyT[id * 2 + 2] < lazyT[id]) {
				lazyT[id * 2 + 2] = lazyT[id];
				lazyV[id * 2 + 2] = lazyV[id];
			}
		}
		lazyT[id] = -1;
	}
	
	void update(int l, int r, int x, int Time, int a = 0, int b = 1 << DEPTH, int id = 0) {
		lazy_evaluate(id, b - a);
		
		if (a >= r || b <= l) return;
		if (l <= a && b <= r) {
			lazyT[id] = Time;
			lazyV[id] = x;
			lazy_evaluate(id, b - a);
			return;
		}
		
		update(l, r, x, Time, a, (a + b) / 2, id * 2 + 1);
		update(l, r, x, Time, (a + b) / 2, b, id * 2 + 2);
		segSum[id] = segSum[id * 2 + 1] + segSum[id * 2 + 2];
	}
	
	int getSum(int l, int r, int a = 0, int b = 1 << DEPTH, int id = 0) {
		if (a >= r || b <= l) return 0;
		
		lazy_evaluate(id, b - a);
		if (l <= a && b <= r) {
			return segSum[id];
		}
		
		int res1 = getSum(l, r, a, (a + b) / 2, id * 2 + 1);
		int res2 = getSum(l, r, (a + b) / 2, b, id * 2 + 2);
		return res1 + res2;
	}
};

SegTree seg;

signed main() {
	int n, q;
	cin >> n >> q;
	
	for (int i = 0; i < q; i++) {
		int type;
		cin >> type;
		if (type == 0) {
			int s, t, x;
			cin >> s >> t >> x;
			seg.update(s, t + 1, x, i);
		}
		else {
			int s, t;
			cin >> s >> t;
			cout << seg.getSum(s, t + 1) << endl;
		}
	}
	return 0;
}