Weighted Union Find Trees

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

inputFormat

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.

outputFormat

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

样例

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

2
?
10

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