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 vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using ll = long long int;
using vll = vector<ll>; using vvll = vector<vll>; using vvvll = vector<vvll>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using cdouble = complex<double>;

const double eps = 1e-7;
#define Loop(i, n) for(int i = 0; i < int(n); i++)
#define Loopll(i, n) for(ll i = 0; i < ll(n); i++)
#define Loop1(i, n) for(int i = 1; i <= int(n); i++)
#define Loopll1(i, n) for(ll i = 1; i <= ll(n); i++)
#define Loopr(i, n) for(int i = int(n) - 1; i >= 0; i--)
#define Looprll(i, n) for(ll i = ll(n) - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = int(n); i >= 1; i--)
#define Looprll1(i, n) for(ll i = ll(n); i >= 1; i--)
#define Foreach(buf, container) for(const auto &buf : container)
#define Loopdiag(i, j, h, w, sum) for(int i = ((sum) >= (h) ? (h) - 1 : (sum)), j = (sum) - i; i >= 0 && j < (w); i--, j++)
#define Loopdiagr(i, j, h, w, sum) for(int j = ((sum) >= (w) ? (w) - 1 : (sum)), i = (sum) - j; j >= 0 && i < (h); j--, i++)
#define Loopdiagsym(i, j, h, w, gap) for (int i = ((gap) >= 0 ? (gap) : 0), j = i - (gap); i < (h) && j < (w); i++, j++)
#define Loopdiagsymr(i, j, h, w, gap) for (int i = ((gap) > (h) - (w) - 1 ? (h) - 1 : (w) - 1 + (gap)), j = i - (gap); i >= 0 && j >= 0; i--, j--)
#define Loopitr(itr, container) for(auto itr = container.begin(); itr != container.end(); itr++)
#define printv(vector) Loop(ex_i, vector.size()) { cout << vector[ex_i] << " "; } cout << endl;
#define printmx(matrix) Loop(ex_i, matrix.size()) { Loop(ex_j, matrix[ex_i].size()) { cout << matrix[ex_i][ex_j] << " "; } cout << endl; }
#define quickio() ios::sync_with_stdio(false); cin.tie(0);
#define bitmanip(m,val) static_cast<bitset<(int)m>>(val)
#define Comp(type_t) bool operator<(const type_t &another) const
#define fst first
#define snd second
#define INF INFINITY
bool feq(double x, double y) { return abs(x - y) <= eps; }
bool inrange(ll x, ll t) { return x >= 0 && x < t; }
bool inrange(vll xs, ll t) { Foreach(x, xs) if (!(x >= 0 && x < t)) return false; return true; }
int ceillog2(ll x) { return int(ceil(log2(x))); }
int floorlog2(ll x) { return int(floor(log2(x))); }
ll rndf(double x) { return (ll)(x + (x >= 0 ? 0.5 : -0.5)); }
ll floorsqrt(ll x) { ll m = (ll)sqrt((double)x); return m + (m * m <= x ? 0 : -1); }
ll ceilsqrt(ll x) { ll m = (ll)sqrt((double)x); return m + (x <= m * m ? 0 : 1); }
ll rnddiv(ll a, ll b) { return (a / b + (a % b * 2 >= b ? 1 : 0)); }
ll ceildiv(ll a, ll b) { return (a / b + (a % b == 0 ? 0 : 1)); }
ll gcd(ll m, ll n) { if (n == 0) return m; else return gcd(n, m % n); }
ll lcm(ll m, ll n) { return m * n / gcd(m, n); }

//========================================================================//

class SegTreeSum {
	using val_t = ll;
private:
	struct segval_t {
		bool enable;
		val_t upd, add, sum;
	};
	int n, N; // n is the original size, while N is the extended size
	int base;
	vector<segval_t> nodes;
	vi idl, idr, cover_size;
	void merge(int id) {
		nodes[id].sum = nodes[idl[id]].sum + nodes[idl[id]].add * cover_size[idl[id]]
			+ nodes[idr[id]].sum + nodes[idr[id]].add * cover_size[idr[id]];
	}
	void lazy(int id) {
		if (id >= base) return;
		if (nodes[id].enable) {
			val_t upd = nodes[id].upd + nodes[id].add;
			nodes[idl[id]] = { true, upd, 0, upd * cover_size[idl[id]] };
			nodes[idr[id]] = { true, upd, 0, upd * cover_size[idr[id]] };
			nodes[id] = { false, 0, 0, upd * cover_size[id] };
		}
		else {
			nodes[idl[id]].add += nodes[id].add;
			nodes[idr[id]].add += nodes[id].add;
			nodes[id].add = 0;
			merge(id);
		}
	}
	enum change_t {
		UPD, ADD
	};
	void change_rec(int s, int t, int l, int r, int id, val_t x, change_t op) {
		if (s == l && t == r) {
			if (op == UPD) nodes[id] = { true, x, 0, x * cover_size[id] };
			else if (op == ADD) nodes[id].add += x;
		}
		else {
			lazy(id);
			int m = (l + r) >> 1;
			if (s < m && m < t) {
				change_rec(s, m, l, m, idl[id], x, op);
				change_rec(m, t, m, r, idr[id], x, op);
			}
			else if (s < m) {
				change_rec(s, t, l, m, idl[id], x, op);
			}
			else if (m < t) {
				change_rec(s, t, m, r, idr[id], x, op);
			}
			merge(id);
		}
	}
	val_t solve_rec(int s, int t, int l, int r, int id) {
		val_t v = 0;
		if (s == l && t == r) {
			v = nodes[id].sum;
		}
		else {
			lazy(id);
			int m = (l + r) >> 1;
			if (s < m && m < t) {
				val_t v0 = solve_rec(s, m, l, m, idl[id]);
				val_t v1 = solve_rec(m, t, m, r, idr[id]);
				v = v0 + v1;
			}
			else if (s < m) {
				v = solve_rec(s, t, l, m, idl[id]);
			}
			else if (m < t) {
				v = solve_rec(s, t, m, r, idr[id]);
			}
		}
		v += nodes[id].add * (t - s);
		return v;
	}
	void common_init() {
		idl.resize(base + N, -1);
		idr.resize(base + N, -1);
		Loop(i, base) {
			idl[i] = (i << 1) + 1;
			idr[i] = (i << 1) + 2;
		}
		cover_size.resize(base + N);
		Loop(i, n) {
			cover_size[base + i] = 1;
		}
		Loopr(i, base) {
			cover_size[i] = cover_size[idl[i]] + cover_size[idr[i]];
		}
	}
public:
	SegTreeSum(int n, val_t init = 0) {
		this->n = n;
		N = 1 << ceillog2(n);
		base = N - 1;
		nodes = vector<segval_t>(base + N, { false, 0, 0, 0 });
		common_init();
		upd(0, n, init);
	}
	SegTreeSum(const vector<val_t> &a) {
		this->n = a.size();
		N = 1 << ceillog2(n);
		base = N - 1;
		nodes = vector<segval_t>(base + N, { false, 0, 0, 0 });
		common_init();
		Loop(i, n) {
			nodes[base + i] = { true, a[i], 0, a[i] };
		}
		Loopr(i, base) {
			merge(i);
		}
	}
	void upd(int s, int t, val_t x) {
		change_rec(s, t, 0, N, 0, x, UPD);
	}
	void add(int s, int t, val_t x) {
		change_rec(s, t, 0, N, 0, x, ADD);
	}
	val_t sumof(int s, int t) {
		return solve_rec(s, t, 0, N, 0);
	}
};

int main() {
	quickio();
	int n, q; cin >> n >> q;
	SegTreeSum st(n);
	Loop(_, q) {
		int op; cin >> op;
		int s, t; cin >> s >> t; t++;
		if (op == 0) {
			ll x; cin >> x;
			st.upd(s, t, x);
		}
		else {
			cout << st.sumof(s, t) << endl;
		}
	}
}