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

* $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$.
* $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$.



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 $add(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $find$ query, print the minimum value.

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

-2
0
1
-1

Solution (in CPP):

Solution:
#include"bits/stdc++.h"
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
typedef pair<int, int> P;
const long long mod = 1000000007;
const double eps = 1e-11;
const int inf = 1ll << 61;
int s[100006], t[100006];
struct segtree {
	int n = 1;
	vector<int>node, lazy;
//	vector<bool>lazyF;
	void init(int N) {
		while (n < N)n *= 2;
		node.resize(2 * n - 1);
		lazy.resize(2 * n - 1);
	}

	void eval(int k) {
		if (lazy[k]) {
			node[k] += lazy[k];
			if (k<n-1) {
				lazy[2 * k + 1] += lazy[k];
				lazy[2 * k + 2] += lazy[k];
			}
			lazy[k] = 0;
		}
	}
	void update(int a, int b, int x, int k, int l, int r) {
		eval(k);
		if (r <= a || b <= l)return;
		if (a <= l&&r <= b) {
			lazy[k] += x;
			eval(k);
		}
		else {
			update(a, b, x, k * 2 + 1, l, (l + r) / 2);
			update(a, b, x, k * 2 + 2, (l + r) / 2, r);
			node[k] = min(node[k * 2 + 1], node[k * 2 + 2]);
		}
	}

	int calc(int a, int b, int k, int l, int r) {
		eval(k);
		if (r <= a || b <= l)return inf;
		if (a <= l&&r <= b)return node[k];
		int vl = calc(a, b, k * 2 + 1, l, (l + r) / 2);
		int vr = calc(a, b, k * 2 + 2, (l + r) / 2, r);
		return min(vl, vr);
	}
	void add(int a, int b, int x) {
		update(a, b, x, 0, 0, n);
	}
	int getmin(int a, int b) {
		return calc(a, b, 0, 0, n);
	}
};
segtree seg;
signed main() {
	int n, q; cin >> n >> q;
	seg.init(n);
	rep(x, q) {
		int a; cin >> a;
		if (a) {
			int s, t; cin >> s >> t;
			cout << seg.getmin(s, t + 1)<<endl;
		}
		else {
			int s, t, y; cin >> s >> t >> y;
			seg.add(s, t + 1, y);
		}
	}
}