Problem: There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

* relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$
* diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Constraints

* $2 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq x, y < n$
* $x \ne y$
* $0 \leq z \leq 10000$
* There are no inconsistency in the given information

Input


$n \; q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.


0 $x \; y\; z$


or


1 $x \; y$


where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Example

Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4


Output

2
?
10

Solution (in CPP):

Solution:
#include<vector>
#include<cstdio>
using namespace std;
typedef long long ll;

struct UnionFind {
    vector<int> parent;
    vector< ll > dist;
    UnionFind(int x = 1) {
        parent.resize(x, -1);
        dist.resize(x, 0);
    }
    int find(int x) {
        if (parent[x] < 0) return x;
        int r = find(parent[x]);
        dist[x] += dist[parent[x]];
        return parent[x] = r;
    }
    ll depth(int x) {
        find(x);
        return dist[x];
    }
    bool same(int x, int y) {
        return (find(x) == find(y));
    }
    void unite(int x, int y, ll k = 0) {
        k += depth(y);
        k -= depth(x);
        k *= -1;
        x = find(x);
        y = find(y);
        if (x == y) return;
        parent[y] = x;
        dist[y] = k;
    }
};

int main() {
    int n, q;
    scanf("%d %d", &n, &q);
    UnionFind T(n);
    for (int i = 0; i < q; i++) {
        int type, x, y;
        scanf("%d %d %d", &type, &x, &y);
        if (type == 0) {
            int a;
            scanf("%d", &a);
            T.unite(x, y, a);
        }
        else 
            if (!T.same(x, y)) printf("?\n");
            else printf("%lld\n", T.depth(x) - T.depth(y));
    }
    return 0;
}