Description

Farmer John's N (1 <= N <= 100,000) cows, conveniently numbered 1..N, are once again standing in a row. Cow i has height $H_i$ (1 <= $H_i$ <= 1,000,000).

Each cow is looking to her left toward those with higher index numbers. We say that cow i 'looks up' to cow j if i < j and $H_i$ < $H_j$. For each cow i, FJ would like to know the index of the first cow in line looked up to by cow i.

Format

Input

• Line 1: A single integer: N
• Lines 2..N+1: Line i+1 contains the single integer: $H_i$

Output

• Lines 1..N: Line i contains a single integer representing the smallest index of a cow up to which cow i looks. If no such cow exists, print 0.

Samples

123 500

623

Details

INPUT DETAILS:

FJ has six cows of heights 3, 2, 6, 1, 1, and 2.

OUTPUT DETAILS:

Cows 1 and 2 both look up to cow 3; cows 4 and 5 both look up to cow 6; and cows 3 and 6 do not look up to any cow.

Limitation

about 50% of the test data will have N <= 1,000.