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 JAVA):

Solution:


import java.util.Arrays;
import java.util.Scanner;

//
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int q = sc.nextInt();

		SqrtDecompositionRSQRUQ sq = new SqrtDecompositionRSQRUQ(n);
		for(int i = 0; i < q; i++){
			int type = sc.nextInt();

			if(type == 0){
				int s = sc.nextInt();
				int t = sc.nextInt();
				int x = sc.nextInt();

				sq.update(s, t + 1, x);
			}
			else {
				int s = sc.nextInt();
				int t = sc.nextInt();

				System.out.println(sq.getSum(s, t + 1));
			}

		}
	}

}

class SqrtDecompositionRSQRUQ {
	int N, K;
	long[] data;
	long[] bucketSum;
	long[] bucketLazyUpdate;
	static final int sqrtN = 512;
	static final int NIL = Integer.MIN_VALUE;

	public SqrtDecompositionRSQRUQ(int n) {
		N = n;
		K = (N + sqrtN - 1) / sqrtN;
		data = new long[K * sqrtN];
		bucketLazyUpdate = new long[K];
		Arrays.fill(bucketLazyUpdate, NIL);
		bucketSum = new long[K];
	}

	// [s, t)
	void update(int s, int t, int x) {
		for (int k = 0; k < K; ++k) {
			int l = k * sqrtN, r = (k + 1) * sqrtN;
			if (r <= s || t <= l)
				continue;
			if (s <= l && r <= t) {
				bucketLazyUpdate[k] = x;
				bucketSum[k] = x*sqrtN;
			} else {
				if(bucketLazyUpdate[k] != NIL){
					for(int i = l; i < r; i++){
						data[i] = bucketLazyUpdate[k];

					}
					bucketLazyUpdate[k] = NIL;
				}
				for (int i = Math.max(s, l); i < Math.min(t, r); ++i) {
					data[i] = x;
				}
				bucketSum[k] = 0;
				for(int i = l; i < r; i++){
					bucketSum[k] += data[i];
				}
			}
//			System.out.println("from "+l+" to "+r+ " bucketSum "+bucketSum[k] );
		}
	}

	//[s,t)
	long getSum(int s, int t) {
		long result = 0;
		for (int k = 0; k < K; ++k) {
			int l = k * sqrtN, r = (k + 1) * sqrtN;
			if (r <= s || t <= l)
				continue;
			if (s <= l && r <= t) {
				result += bucketSum[k];
//				System.out.println("bucket Add " + result);
			}
			else {
				for (int i = Math.max(s, l); i < Math.min(t, r); ++i) {
					if(bucketLazyUpdate[k] != NIL){
						result += bucketLazyUpdate[k];
					}
					else {
						result += data[i];
					}
				}
//				System.out.println("direct Add " + result);
			}
		}

		return result;
	}

	long get(int s) {
		int k = s / sqrtN;
		if(bucketLazyUpdate[k] != NIL){
			return bucketLazyUpdate[k];
		}
		else {
			return data[s];
		}
	}
}