Problem: Given a permutation p of length n, find its subsequence s_1, s_2, …, s_k of length at least 2 such that:

  * |s_1-s_2|+|s_2-s_3|+…+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2. 
  * Among all such subsequences, choose the one whose length, k, is as small as possible. 



If multiple subsequences satisfy these conditions, you are allowed to find any of them.

A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.

A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.

Input

The first line contains an integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (2 ≤ n ≤ 10^5) — the length of the permutation p.

The second line of each test case contains n integers p_1, p_2, …, p_{n} (1 ≤ p_i ≤ n, p_i are distinct) — the elements of the permutation p.

The sum of n across the test cases doesn't exceed 10^5.

Output

For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, …, s_k — its elements.

If multiple subsequences satisfy these conditions, you are allowed to find any of them.

Example

Input


2
3
3 2 1
4
1 3 4 2


Output


2
3 1 
3
1 4 2 

Note

In the first test case, there are 4 subsequences of length at least 2:

  * [3,2] which gives us |3-2|=1. 
  * [3,1] which gives us |3-1|=2. 
  * [2,1] which gives us |2-1|=1. 
  * [3,2,1] which gives us |3-2|+|2-1|=2. 



So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].

Solution (in JAVA):

Solution:
// var lineIdx = 0;
// var readline = () => {
//   var input = ["2", "3", "3 2 1", "4", "1 3 4 2"]
//   return input[lineIdx++];
// };
// var print = (str) => {
//   console.log(str);
// };

var t = readline().split(" ").map(function (x) { return parseInt(x); })[0];

var step = () => {
  var input = readline().split(" ").map(function (x) { return parseInt(x); });
  var n = input[0];

  var res = new Array()

  var row = readline().split(" ").map(function (x) { return parseInt(x); });
  var dir = 0;
  var cur = row[0];
  res.push(cur)

  for (var j = 1; j < row.length; j++) {
    if (dir == 1) {
      if (cur < row[j]) {
      } else {
        res.push(cur)
        dir = -1
      }
    } else if (dir == -1) {
      if (cur > row[j]) {
      } else {
        res.push(cur)
        dir = 1
      }
    } else if(dir == 0){
      if (cur < row[j]) {
        dir = 1;
      } else {
        dir = -1
      }
    }
    cur = row[j]
  }
  res.push(cur)

  print(res.length)
  print(res.join(' '))
}


for (var i2 = 0; i2 < t; i2++) {
  step();
}