Background

No, Commander-in-Chief.

Problem Description

There are $n$ outposts on the battlefield, numbered from $1$ to $n$. There is a bidirectional road between every pair of outposts.

One day, the Commander-in-Chief came to inspect the war zone. After walking for a while, he got lost, so he angrily gave an order: you must change every bidirectional road into a one-way road, such that these roads contain no cycles (otherwise the Commander-in-Chief will get lost). However, since the outposts have different sizes, for outpost $i$, the number of outposts that the Commander-in-Chief can directly reach by following one-way roads must be within $[l_i, r_i]$. In other words, the outdegree of node $i$ must be within $[l_i, r_i]$. You need to tell the Commander-in-Chief whether it is possible to satisfy his requirements.

Input Format

This problem has multiple test cases.

The first line contains an integer $T$, representing the number of test cases.

For each test case:

The first line contains an integer $n$, representing the number of outposts.

The second line contains $n$ integers $l_1, l_2, \dots, l_n$.

The third line contains $n$ integers $r_1, r_2, \dots, r_n$.

Output Format

For each test case:

Output one line with a string. If the Commander-in-Chief's requirements can be satisfied, output YES; otherwise, output NO.

2
5
0 1 4 0 0
3 4 4 1 3
3
1 2 2
2 2 2

YES
NO

见下发文件 road2.in

见下发文件 road2.out

Hint

Explanation for Sample #1

Below is one feasible solution for the first test case:

Explanation for Sample #2

This sample satisfies the constraints of test points $3 \sim 6$.

Constraints

The scores of the test points are not equally distributed.

For $100\%$ of the testdata, $1 \leq n \leq 10^5$, $0 \leq l_i \leq r_i < n$, and $1 \leq T \leq 10$.

Translated by ChatGPT 5