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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.StringTokenizer;
class Main{
	public static void main(String[] args) {
		SC sc=new SC(System.in);
		int N=sc.nextInt();
		int Q=sc.nextInt();
		WUnionFindTree uft=new WUnionFindTree(N);
		for(int i=0; i<Q; i++) {
			int com=sc.nextInt();

			if(com==0) {
				int x=sc.nextInt();
				int y=sc.nextInt();
				int z=sc.nextInt();
				uft.union(x,y,z);
			}
			else {
				int x=sc.nextInt();
				int y=sc.nextInt();
				Integer df=(Integer)uft.diff(x,y);
				if(df==null) {
					pl("?");
				}
				else {
					pl(df);
				}
			}
		}
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
	public static class WUnionFindTree{
		int[] par; // 親の番号
		int[] ws;  // 親との重みの差
		public WUnionFindTree(int n){
			par = new int[n+1];
			ws  = new int[n+1];
			for(int i = 0; i <= n; i++){ par[i] = -1; }
		}
		public int find(int x){
			if(par[x] < 0){
				return x;
			}else{
				final int parent = find(par[x]);
				ws[x] += ws[par[x]];
				return par[x] = parent;
			}
		}
		public int weight(int x){
			find(x);
			return ws[x];
		}
		public boolean union(int x, int y, int w){ // x <-(w)- y (x + w = y)
			w += weight(x);
			w -= weight(y);
			x = find(x); y = find(y);
			if(x != y){
				if(par[y] < par[x]) {
					int tmp = x; x = y; y = tmp; w = -w;
				}
				par[x] += par[y]; par[y] = x;
				ws[y] = w;
				return true;
			}else{
				return false;
			}
		}
		public boolean same(int x, int y){
			return find(x) == find(y);
		}
		public Integer diff(int x, int y){ // y - x を求める. 比較不能ならnull.
			if(!same(x, y)){ return null; }
			return this.weight(y) - this.weight(x);
		}
		public int size(int x){
			return -par[find(x)];
		}
	}
}