human
What is a the Python program you requested given the following:
Can you solve the below in PYTHON3?
British mathematician John Littlewood once said about Indian mathematician Srinivasa Ramanujan that "every positive integer was one of his personal friends."

It turns out that positive integers can also be friends with each other! You are given an array a of distinct positive integers. 

Define a subarray a_i, a_{i+1}, …, a_j to be a friend group if and only if there exists an integer m ≥ 2 such that a_i mod m = a_{i+1} mod m = … = a_j mod m, where x mod y denotes the remainder when x is divided by y.

Your friend Gregor wants to know the size of the largest friend group in a.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 2⋅ 10^4). 

Each test case begins with a line containing the integer n (1 ≤ n ≤ 2 ⋅ 10^5), the size of the array a.

The next line contains n positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ {10}^{18}), representing the contents of the array a. It is guaranteed that all the numbers in a are distinct.

It is guaranteed that the sum of n over all test cases is less than 2⋅ 10^5.

Output

Your output should consist of t lines. Each line should consist of a single integer, the size of the largest friend group in a.

Example

Input

4
5
1 5 2 4 6
4
8 2 5 10
2
1000 2000
8
465 55 3 54 234 12 45 78

Output

3
3
2
6

Note

In the first test case, the array is [1,5,2,4,6]. The largest friend group is [2,4,6], since all those numbers are congruent to 0 modulo 2, so m=2.

In the second test case, the array is [8,2,5,10]. The largest friend group is [8,2,5], since all those numbers are congruent to 2 modulo 3, so m=3.

In the third case, the largest friend group is [1000,2000]. There are clearly many possible values of m that work.
assistant
#Here is the Python program you requested.

import sys
import math
input = sys.stdin.readline
INF = 10**20
def gcd(a, b):
    if a == INF:
        return b
    if b == INF:
        return a
    return math.gcd(a, b)
class LazySegmentTree:
    def __init__(self, data, default=0, func=min):
        """initialize the lazy segment tree with data"""
        self._default = default
        self._func = func

        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()
        self._lazy = [0] * (2 * _size)

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __len__(self):
        return self._len

    def _push(self, idx):
        """push query on idx to its children"""
        # Let the children know of the queries
        q, self._lazy[idx] = self._lazy[idx], 0

        self._lazy[2 * idx] += q
        self._lazy[2 * idx + 1] += q
        self.data[2 * idx] += q
        self.data[2 * idx + 1] += q

    def _update(self, idx):
        """updates the node idx to know of all queries applied to it via its ancestors"""
        for i in reversed(range(1, idx.bit_length())):
            self._push(idx >> i)

    def _build(self, idx):
        """make the changes to idx be known to its ancestors"""
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) + self._lazy[idx]
            idx >>= 1

    def add(self, start, stop, value):
        """lazily add value to [start, stop)"""
        start = start_copy = start + self._size
        stop = stop_copy = stop + self._size
        while start < stop:
            if start & 1:
                self._lazy[start] += value
                self.data[start] += value
                start += 1
            if stop & 1:
                stop -= 1
                self._lazy[stop] += value
                self.data[stop] += value
            start >>= 1
            stop...