Alyona's mother wants to present an array of n non-negative integers to Alyona. The array should be special.

Alyona is a capricious girl so after she gets the array, she inspects m of its subarrays. Subarray is a set of some subsequent elements of the array. The i-th subarray is described with two integers l_i and r_i, and its elements are a[l_i], a[l_i + 1], ..., a[r_i].

Alyona is going to find mex for each of the chosen subarrays. Among these m mexes the girl is going to find the smallest. She wants this minimum mex to be as large as possible.

You are to find an array a of n elements so that the minimum mex among those chosen by Alyona subarrays is as large as possible.

The mex of a set S is a minimum possible non-negative integer that is not in S.

The first line contains two integers n and m (1 ≤ n, m ≤ 10⁵).

The next m lines contain information about the subarrays chosen by Alyona. The i-th of these lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n), that describe the subarray a[l_i], a[l_i + 1], ..., a[r_i].

In the first line print single integer — the maximum possible minimum mex.

In the second line print n integers — the array a. All the elements in a should be between 0 and 10⁹.

It is guaranteed that there is an optimal answer in which all the elements in a are between 0 and 10⁹.

If there are multiple solutions, print any of them.