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;
typedef long long ll;

struct StarrySkyTree {
    int sz;
    vector<int> sum, mn;
    StarrySkyTree(int n) {
        for(sz = 1; sz < n;)
            sz <<= 1;
        sum.assign(sz << 1, 0);
        mn.assign(sz << 1, 0);
    }

    void add(int a, int b, int x) {
        a += sz;
        b += sz - 1;
        for(int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
            if(l & 1) sum[l++] += x;
            if(r & 1) sum[--r] += x;
        }
        while(a >>= 1)
            mn[a] =
                min(mn[a << 1] + sum[a << 1], mn[a << 1 | 1] + sum[a << 1 | 1]);
        while(b >>= 1)
            mn[b] =
                min(mn[b << 1] + sum[b << 1], mn[b << 1 | 1] + sum[b << 1 | 1]);
    }

    // [a, b) の最大値を取得
    int getmin(int a, int b, int k, int l, int r) {
        if(b <= l || r <= a) return INT_MAX;
        if(a <= l && r <= b) return mn[k] + sum[k];
        int mid = (l + r) >> 1;
        int vl = getmin(a, b, k << 1, l, mid);
        int vr = getmin(a, b, k << 1 | 1, mid, r);
        return min(vl, vr) + sum[k];
    }
    int getmin(int a, int b) { return getmin(a, b, 1, 0, sz); }
};

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int N, Q;
    cin >> N >> Q;

    StarrySkyTree seg(N);

    int a, b, c, d;
    while(Q--) {
        cin >> a;
        if(a) {
            cin >> b >> c;
            cout << seg.getmin(b, c + 1) << "\n";
        } else {
            cin >> b >> c >> d;
            seg.add(b, c + 1, d);
        }
    }
}