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 <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef vector<ll> vl;
typedef pair<ll, ll> PP;
#define rep(i, n) for (ll i = 0; i < ll(n); i++)
#define all(v) v.begin(), v.end()
bool chmin(ll& a, ll b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
bool chmax(ll& a, ll b) {
    if (b > a) {
        a = b;
        return 1;
    }
    return 0;
}
const ll INF = 999999999999999;
const ll MOD = 1000000007;
const ll MAX_N = 500010;
ll a, b, c, d, e, f, p, t, x, y, z, q, m, n, r, h, k, w, l, ans;
template <class Abel>
struct UnionFind {
    vector<ll> par;
    vector<ll> rank;
    vector<Abel> diff_weight;

    UnionFind(ll n = 1, Abel SUM_UNITY = 0) { init(n, SUM_UNITY); }

    void init(ll n = 1, Abel SUM_UNITY = 0) {
        par.resize(n);
        rank.resize(n);
        diff_weight.resize(n);
        for (ll i = 0; i < n; ++i)
            par[i] = i, rank[i] = 0, diff_weight[i] = SUM_UNITY;
    }

    ll root(ll x) {
        if (par[x] == x) {
            return x;
        } else {
            ll r = root(par[x]);
            diff_weight[x] += diff_weight[par[x]];
            return par[x] = r;
        }
    }

    Abel weight(ll x) {
        root(x);
        return diff_weight[x];
    }

    bool same(ll x, ll y) { return root(x) == root(y); }

    bool merge(ll x, ll y, Abel w) {
        w += weight(x);
        w -= weight(y);
        x = root(x);
        y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y), w = -w;
        if (rank[x] == rank[y]) ++rank[x];
        par[y] = x;
        diff_weight[y] = w;
        return true;
    }

    Abel diff(ll x, ll y) { return weight(y) - weight(x); }
};
int main() {
    cin >> n;
    cin >> q;
    UnionFind<ll> U(n,0);

    while (q--) {
        cin >> x;
        if (x == 0) {
            cin >> a >> b >> c;
            U.merge(a, b, c);
        }
        else{
          cin>>a>>b;
          if(!U.same(a,b))cout<<"?"<<endl;
          else cout << U.diff(a, b) << endl;
        }
    }
}