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<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

const int NIL = -1;
const int MAX = 2147483647;
const int N = 100001;
clock_t START, END;
bool debug = false;

ll minv[500000], addv[500000];
ll ql, qr, p, v;
ll _min;

/*void pushdown(int o)
{
	int lc = o * 2, rc = o * 2 + 1;
	if (addv[o] > 0) {
		addv[lc] = addv[rc] = addv[o];
		addv[o] = 0;
	}
}*/

void maintain(ll o, ll L, ll R)
{
	ll lc = o * 2, rc = 2 * o + 1;
	minv[o] = 0;
	if (R > L) {
		minv[o] = min(minv[lc], minv[rc]);
	}
	minv[o] += addv[o];
}

void query(ll o, ll L, ll R, ll add)
{
	ll M = L + (R - L) / 2;
	if (ql <= L && qr >= R) {
		_min = min(_min, minv[o] + add);
	}
	else {
		if (ql <= M)
			query(o * 2, L, M, add + addv[o]);
		if (qr > M)
			query(o * 2 + 1, M + 1, R, add + addv[o]);
	}
}

void update(ll o, ll L, ll R)
{
	ll M = L + (R - L) / 2;
	ll lc = o * 2, rc = o * 2 + 1;
	if (ql <= L && qr >= R) {
		addv[o] += v;
	}
	else {
		if (ql <= M)
			update(lc, L, M);
		if (qr > M)
			update(rc, M + 1, R);
	}
	maintain(o, L, R);
}


int main(void)
{
	if (debug) {
		START = clock();
		freopen("in12.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	}
	int n, q, com;
	scanf("%d%d", &n, &q);
	for (int i = 0; i < q; i++) {
		scanf("%d", &com);
		if (com) {
			scanf("%lld%lld", &ql, &qr);
			ql++;
			qr++;
			_min = MAX;
			query(1, 1, n, 0);
			printf("%lld\n", _min);
		}
		else {
			scanf("%lld%lld%lld", &ql, &qr, &v);
			ql++;
			qr++;
			update(1, 1, n);
		}
	}
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}