Description

There is a room with n bulbs labeled from 1 to n. All bulbs are off initially. You turn on exactly one bulb every moment. A bulb changes color to blue only when all bulbs to its left are on. Return the number of moments where all turned-on bulbs are blue.

Examples

Input:light = [2,1,3,5,4]
Output:3
Explanation:

At moments 2, 3, 5 all on bulbs are blue.

Input:light = [1,2,3,4]
Output:4
Explanation:

All bulbs are turned on in order from left to right. At moment 1: bulb 1 is on and blue (no bulbs to its left). At moment 2: bulbs 1,2 are on and both blue. At moment 3: bulbs 1,2,3 are on and all blue. At moment 4: bulbs 1,2,3,4 are on and all blue. Since bulbs are turned on sequentially, all turned-on bulbs are always blue at every moment.

Input:light = [3,1,4,2]
Output:1
Explanation:

At moment 1: bulb 3 is on but not blue (bulbs 1,2 to its left are off). At moment 2: bulbs 3,1 are on, only bulb 1 is blue. At moment 3: bulbs 3,1,4 are on, only bulb 1 is blue (bulb 3 can't be blue because bulb 2 is off). At moment 4: all bulbs 1,2,3,4 are on and all are blue. Only at the final moment are all turned-on bulbs blue.

Constraints

  • n == light.length
  • 1 ≤ n ≤ 5 * 10^4

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