public int maxEnvelopes(int[][] envelopes) {

Arrays.sort(envelopes, (a, b) -> a[0] == b[0] ? Integer.compare(b[1], a[1])

: Integer.compare(a[0], b[0]));

final int[] lis = new int[envelopes.length];

int len = 0;

for (int[] envelope : envelopes) {

final int idx = lowerBound(lis, len, envelope[1]);

lis[idx] = envelope[1];

if (len == idx) {

len++;

}

}

return len;

}

private static int lowerBound(int[] arr, int to, int target) {

int lo = 0;

int hi = to;

while (lo < hi) {

final int mid = lo + hi >>> 1;

if (arr[mid] < target) {

lo = mid + 1;

} else {

hi = mid;

}

}

return lo;

}