New Year and Ascent Sequence

A sequence a = [a_1, a_2, …, a_l] of length l has an ascent if there exists a pair of indices (i, j) such that 1 ≤ i < j ≤ l and a_i < a_j. For example, the sequence [0, 2, 0, 2, 0] has an ascent because of the pair (1, 4), but the sequence [4, 3, 3, 3, 1] doesn't have an ascent.

Let's call a concatenation of sequences p and q the sequence that is obtained by writing down sequences p and q one right after another without changing the order. For example, the concatenation of the [0, 2, 0, 2, 0] and [4, 3, 3, 3, 1] is the sequence [0, 2, 0, 2, 0, 4, 3, 3, 3, 1]. The concatenation of sequences p and q is denoted as p+q.

Gyeonggeun thinks that sequences with ascents bring luck. Therefore, he wants to make many such sequences for the new year. Gyeonggeun has n sequences s_1, s_2, …, s_n which may have different lengths.

Gyeonggeun will consider all n^2 pairs of sequences s_x and s_y (1 ≤ x, y ≤ n), and will check if its concatenation s_x + s_y has an ascent. Note that he may select the same sequence twice, and the order of selection matters.

Please count the number of pairs (x, y) of sequences s_1, s_2, …, s_n whose concatenation s_x + s_y contains an ascent.

Input

The first line contains the number n (1 ≤ n ≤ 100 000) denoting the number of sequences.

The next n lines contain the number l_i (1 ≤ l_i) denoting the length of s_i, followed by l_i integers s_{i, 1}, s_{i, 2}, …, s_{i, l_i} (0 ≤ s_{i, j} ≤ 10^6) denoting the sequence s_i.

It is guaranteed that the sum of all l_i does not exceed 100 000.

Output

Print a single integer, the number of pairs of sequences whose concatenation has an ascent.

Examples

Input

5 1 1 1 1 1 2 1 4 1 3

Output

9

Input

3 4 2 0 2 0 6 9 9 8 8 7 7 1 6

Output

7

Input

10 3 62 24 39 1 17 1 99 1 60 1 64 1 30 2 79 29 2 20 73 2 85 37 1 100

Output

72

Note

For the first example, the following 9 arrays have an ascent: [1, 2], [1, 2], [1, 3], [1, 3], [1, 4], [1, 4], [2, 3], [2, 4], [3, 4]. Arrays with the same contents are counted as their occurences.

inputFormat

Input

The first line contains the number n (1 ≤ n ≤ 100 000) denoting the number of sequences.

The next n lines contain the number l_i (1 ≤ l_i) denoting the length of s_i, followed by l_i integers s_{i, 1}, s_{i, 2}, …, s_{i, l_i} (0 ≤ s_{i, j} ≤ 10^6) denoting the sequence s_i.

It is guaranteed that the sum of all l_i does not exceed 100 000.

outputFormat

Output

Print a single integer, the number of pairs of sequences whose concatenation has an ascent.

Examples

Input

5 1 1 1 1 1 2 1 4 1 3

Output

9

Input

3 4 2 0 2 0 6 9 9 8 8 7 7 1 6

Output

7

Input

10 3 62 24 39 1 17 1 99 1 60 1 64 1 30 2 79 29 2 20 73 2 85 37 1 100

Output

72

Note

For the first example, the following 9 arrays have an ascent: [1, 2], [1, 2], [1, 3], [1, 3], [1, 4], [1, 4], [2, 3], [2, 4], [3, 4]. Arrays with the same contents are counted as their occurences.

样例

5
1 1
1 1
1 2
1 4
1 3

9

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