## SECTORS - Equalize the Sectors

Digo has a cylindrical box which is vertically partitioned into **N** contiguous sectors which are open from the top. Each Sectorial Compartment initially contains a fixed number of coins. Now Digo wants to fill each Sectorial Compartment with equal number of coins. But the problem is that, at a time he is only allowed to increment any two adjacent sectors with one coin each. Given an initial arrangement, you need to tell whether such equalization is possible or not.

Every sector **i** (for all (0 < **i **<** N**)) is adjacent to sector (**i + 1**) and sector **N** is adjacent to sector **1**.

**Input**

In first line, the number of test cases **T.**

Each test case consists of a number **N, **followed by a line containing **N** space seperated integers where **i ^{th}** integer (

**Mi**) denotes the number of coins in

**i**sectorial compartment of the box (initially), in clockwise order.

^{th}**Output**

For every test case output “**YES**” for possible and “**NO**” for which equalization is not possible (Without quotes).

**Constraints**

1 <= **T** <= 1000

3 <= **N **<= 100 (Number of Sectorial Compartments)

1 <= **Mi **<= 10^9 (Number of coins in each Sectorial Compartment)

**Sample Input**

2

3

1 2 3

4

1 2 1 2

**Sample Output**

YES

NO

Added by: | Surya Kiran |

Date: | 2013-09-05 |

Time limit: | 0.130s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | Codeblitz-4 |