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>

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define FOR(i,n,m) for(int i=(int)(n); i<=(int)(m); i++)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define RITR(x,c) for(__typeof(c.rbegin()) x=c.rbegin();x!=c.rend();x++)
#define setp(n) fixed << setprecision(n)

#define ld long double
#define ll long long
#define vll vector<ll>
#define vi vector<int>
#define pll pair<ll,ll>
#define pi pair<int,int>

#define all(a) (a.begin()),(a.end())
#define rall(a) (a.rbegin()),(a.rend())
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define ins insert

using namespace std;

//-------------------------------------------------
//--Lazy Evaluation Segment tree (Proportional)
//-------------------------------------------------
template<typename T, typename E>
class LazySegmentTree
{
private:
    using F = ::std::function<T(T,T)>;
    using G = ::std::function<T(T,E)>;
    using H = ::std::function<E(E,E)>;
    F f; G g; H h;
    int n, height;
    ::std::vector<T> seg;
    ::std::vector<E> lazy;
    T te; E ee;
public:
    LazySegmentTree(int _n, F f, G g, H h, T te, E ee)
        : f(f),g(g),h(h),te(te),ee(ee)
    {
        init(_n);
    }
    LazySegmentTree(::std::vector<T> &v, F f, G g, H h, T te, E ee)
        : f(f),g(g),h(h),te(te),ee(ee)
    {
        int _n = v.size();
        init(_n);
        for(int i=n; i<n+_n; i++) seg[i] = v[i-n];
        build();
    }
    void init(int _n){
        n = 1; height=0;
        while(n<_n) n<<=1, height++;
        seg.resize(2*n, te);
        lazy.resize(2*n, ee);
    }
    void build(){
        for(int i=n-1; i>0; i--) seg[i] = f(seg[i<<1], seg[i<<1|1]);
    }
    T eval(int k){
        int c = breadth(k);
        return (lazy[k]==ee) ? seg[k] : g(seg[k],quantify(lazy[k], c));
    }
    void waveto(int k){
        for(int i=height; i>0; i--) wave(k>>i);
    }
    void wave(int k){
        seg[k] = eval(k);
        lazy[k<<1] = h(lazy[k<<1],lazy[k]);
        lazy[k<<1|1] = h(lazy[k<<1|1],lazy[k]);
        lazy[k] = ee;
    }
    void recalc(int k){
        for(int i=1; i<=height; i++){
            int m = k>>i;
            seg[m] = f(eval(m<<1), eval(m<<1|1));
        }
    }
    void update(int a, int b, E x){
        if (b<=a) return;
        waveto(a+=n);
        waveto(b+=n-1);
        T L=ee, R=ee;
        int l=a, r=b;
        while(l<=r){
            if (l&1) lazy[l] = h(lazy[l], x), l++;
            if (!(r&1)) lazy[r] = h(lazy[r], x), r--;
            l>>=1; r>>=1;
        }
        recalc(a);
        recalc(b);
    }
    T query(int a, int b){
        waveto(a+=n);
        waveto(b+=n-1);
        T L=te, R=te;
        int l=a, r=b;
        while(l<=r){
            if (l&1) L = f(L, eval(l++));
            if (!(r&1)) R = f(eval(r--), R);
            l>>=1; r>>=1;
        }
        return f(L,R);
    }
    T operator[](int k){return query(k, k+1);};
    inline int breadth(int k){
        int ret = height-31+__builtin_clz(k);
        return 1<<ret;
    }
    //return value proportional to segment's width
    inline E quantify(E laz, int c){
        return laz*c;
    }
};

const ll INF = INT_MAX;

int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n,q; cin>>n>>q;
    vll a(n,0);
    LazySegmentTree<ll,ll> seg(a,
        [](ll x, ll y){return x+y;},
        [](ll x, ll y){return y;},
        [](ll x, ll y){return (y==INF)?x:y;},
        0,INF
    );
    while(q--){
        int c; cin>>c;
        if (c==1){
            int s,t; cin>>s>>t;
            cout<<seg.query(s,t+1)<<endl;
        }else{
            int s,t,x; cin>>s>>t>>x;
            seg.update(s,t+1,x);
        }
    }
    return 0;
}