## PERMPATT - Check 1324

Given a permutation P[1...n] of {1,2,...n}, you should output if the permutation contains a pattern of the form 1324. That is, do there exist indices 1 <= i1 < i2 < i3 < i4 <= n such that P[i1] < P[i3] < P[i2] < P[i4]. For example, P = 6 8 5 4 9 3 7 2 1 10 contains one: the indices 1, 2, 7, 10 correspond to the sequence 6 8 7 10 which is a 1324 pattern.

### Input

First line contains T, the number of test cases

Each of the next T lines contains **n **(1 <= n <= 100000), followed by **n** integers, representing a permutation of [1,2,..,n].

SUM( n * log_{2}(n)) over all test cases <= 10^{8}. Do not assume anything else about the number of test cases or their distribution.

### Output

Output T lines, one per test case: "yes"(without quotes) if the permutation contains a 1324 pattern or "no" (without quotes) otherwise.

**Warning: **Huge I/O

### Example

Input:2 10 6 8 5 4 9 3 7 2 1 10 10 5 3 4 7 9 10 8 6 2 1Output:yes no

Added by: | konqueror |

Date: | 2010-07-23 |

Time limit: | 0.564s-6.325s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: NODEJS OBJC PERL6 SQLITE VB.NET |