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<bits/stdc++.h>
using namespace std;
using Int = long long;

template <typename T,typename E>
struct SegmentTree{
  using F = function<T(T,T)>;
  using G = function<T(T,E)>;
  using H = function<E(E,E)>;
  using P = function<E(E,size_t)>;
  Int n;
  F f;
  G g;
  H h;
  T ti;
  E ei;
  P p;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(Int n_,F f,G g,H h,T ti,E ei,
	      P p=[](E a,size_t b){b++;return a;}):
    f(f),g(g),h(h),ti(ti),ei(ei),p(p){
    init(n_);
  }
  void init(Int n_){
    n=1;
    while(n<n_) n*=2;
    dat.assign(2*n-1,ti);
    laz.assign(2*n-1,ei);
  }
  void build(Int n_, vector<T> v){
    for(Int i=0;i<n_;i++) dat[i+n-1]=v[i];
    for(Int i=n-2;i>=0;i--)
      dat[i]=f(dat[i*2+1],dat[i*2+2]);
  }
  inline void eval(Int len,Int k){
    if(laz[k]==ei) return;
    if(k*2+1<n*2-1){
      laz[k*2+1]=h(laz[k*2+1],laz[k]);
      laz[k*2+2]=h(laz[k*2+2],laz[k]);
    }
    dat[k]=g(dat[k],p(laz[k],len));
    laz[k]=ei;
  }
  T update(Int a,Int b,E x,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return dat[k];
    if(a<=l&&r<=b){
      laz[k]=h(laz[k],x);
      return g(dat[k],p(laz[k],r-l));
    }
    return dat[k]=f(update(a,b,x,k*2+1,l,(l+r)/2),
		    update(a,b,x,k*2+2,(l+r)/2,r));
  }
  T update(Int a,Int b,E x){
    return update(a,b,x,0,0,n);
  }
  T query(Int a,Int b,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return ti;
    if(a<=l&&r<=b) return dat[k];
    T vl=query(a,b,k*2+1,l,(l+r)/2);
    T vr=query(a,b,k*2+2,(l+r)/2,r);
    return f(vl,vr);
  }
  T query(Int a,Int b){
    return query(a,b,0,0,n);
  }
  void update(Int k,T x){
    query(k,k+1);//evaluate
    k+=n-1;
    dat[k]=x;
    while(k){
      k=(k-1)/2;
      dat[k]=f(dat[k*2+1],dat[k*2+2]);
    }
  }
};

//INSERT ABOVE HERE
signed main(){
  Int n,q;
  cin>>n>>q;
  
  Int INF = 1e9;
  SegmentTree<Int, Int>::F f=[&](Int a,Int b){return a+b;};
  SegmentTree<Int, Int>::G g=[&](Int a,Int b){return b==INF?a:b;};
  SegmentTree<Int, Int>::H h=[&](Int a,Int b){return b==INF?a:b;};
  SegmentTree<Int, Int>::P p=[&](Int a,size_t b){return a==INF?a:a*b;};

  SegmentTree<Int, Int> seg(n,f,g,h,0,INF,p);
  seg.build(n,vector<Int>(n,0));

  for(Int i=0;i<q;i++){
    Int c,s,t,x;
    cin>>c>>s>>t;
    t++;
    if(c){
      cout<<seg.query(s,t)<<endl;
    }else{
      cin>>x;
      seg.update(s,t,x);
    }
  }
  
  return 0;
}