Alice has recently received an array a_1, a_2, ..., a_n for her birthday! She is very proud of her array, and when she showed her friend Bob the array, he was very happy with her present too!

However, soon Bob became curious, and as any sane friend would do, asked Alice to perform q operations of two types on her array:

  * 1 x y: update the element a_x to y (set a_x = y). 
  * 2 l r: calculate how many non-decreasing subarrays exist within the subarray [a_l, a_{l+1}, ..., a_r]. More formally, count the number of pairs of integers (p,q) such that l ≤ p ≤ q ≤ r and a_p ≤ a_{p+1} ≤ ... ≤ a_{q-1} ≤ a_q. 



Help Alice answer Bob's queries!

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^5) — the size of the array, and the number of queries, respectively.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the elements of Alice's array.

The next q lines consist of three integers each. The first integer of the i-th line is t_i, the operation being performed on the i-th step (t_i = 1 or t_i = 2).

If t_i = 1, the next two integers are x_i and y_i (1 ≤ x_i ≤ n; 1 ≤ y_i ≤ 10^9), updating the element at position x_i to y_i (setting a_{x_i} = y_i).

If t_i = 2, the next two integers are l_i and r_i (1 ≤ l_i ≤ r_i ≤ n), the two indices Bob asks Alice about for the i-th query.

It's guaranteed that there is at least one operation of the second type.

Output

For each query of type 2, print a single integer, the answer to the query.

Example

Input


5 6
3 1 4 1 5
2 2 5
2 1 3
1 4 4
2 2 5
1 2 6
2 2 5


Output


6
4
10
7

Note

For the first query, l = 2 and r = 5, and the non-decreasing subarrays [p,q] are [2,2], [3,3], [4,4], [5,5], [2,3] and [4,5].
 
import java.io.*;
import java.util.StringTokenizer;

public class Main {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] intArr(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] longArr(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

    static FastReader in = new FastReader();

    public static void main(String args[]) {
        resolve();
    }


    private static class SegmentTree {
        private int[] originalArray;
        private Segment[] segmentTreeStore;

        private static class Segment {
            int prefix;
            int prefixElementQuantity;
            int suffix;
            int suffixElementQuantity;
            boolean isNonDecInTotalSegment;
            long nonDecSeqInMiddleSegment;

            @Override
            public String toString() {
                return "Segment{" +
                        "prefix=" + prefix +
                        ", prefixElementQuantity=" + prefixElementQuantity +
                        ", suffix=" + suffix +
                        ", suffixElementQuantity=" + suffixElementQuantity +
                        ", isNonDecInTotalSegment=" + isNonDecInTotalSegment +
                        ", nonDecSeqInMiddleSegment=" + nonDecSeqInMiddleSegment +
                        '}';
            }
        }

        public SegmentTree(int[] originalArray) {
            this.originalArray = originalArray;
            this.segmentTreeStore = new Segment[4 * originalArray.length];
            build(1, 0, originalArray.length - 1);
        }

        private void build(int index, int left, int right) {
            // System.out.println(left + " " + right);
            if (left == right) {
                segmentTreeStore[index] = createSegment(left, right);
                //System.out.println(segmentTreeStore[index].toString());
            } else {
                int leftChildIndex = index * 2;
                int rightChildIndex = index * 2 + 1;
                int seg = right - left;
                build(leftChildIndex, left, left + seg / 2);
                build(rightChildIndex, left + seg / 2 + 1, right);
                segmentTreeStore[index] = merge(leftChildIndex, rightChildIndex);
            }
        }

        private Segment createSegment(int left, int right) {
            Segment result = new Segment();
            result.prefix = originalArray[left];
            result.prefixElementQuantity = 1;
            result.suffix = originalArray[right];
            result.suffixElementQuantity = 1;
            result.isNonDecInTotalSegment = true;
            result.nonDecSeqInMiddleSegment = 0;
            return result;
        }

        public void update(int index, int value) {
            update(1, 0, originalArray.length - 1, index, value);
        }

        private void update(int currentIndex, int left, int right, int index, int value) {
            //System.out.println(currentIndex + " " + left + " " + right + " " + index + " " + value);
            if (left == right) {
                segmentTreeStore[currentIndex].prefix = value;
                segmentTreeStore[currentIndex].suffix = value;
                return;
            } else if (left <= index && index <= left + (right - left) / 2) {
                update(currentIndex * 2, left, getMiddleElementIndexOnSegment(left, right), index, value);
            } else {
                update(currentIndex * 2 + 1, getMiddleElementIndexOnSegment(left, right) + 1, right, index, value);
            }
            segmentTreeStore[currentIndex] = merge(currentIndex * 2, currentIndex * 2 + 1);
            //System.out.println(segmentTreeStore[currentIndex]);
        }

        private Segment merge(int leftChildIndex, int rightChildIndex) {
            return merge(segmentTreeStore[leftChildIndex], segmentTreeStore[rightChildIndex]);
        }

        public long get(int left, int right) {
            //System.out.println(left + " " + right);
            Segment result = findSegment(
                    1,
                    0,
                    originalArray.length - 1,
                    left,
                    right);
            return result.isNonDecInTotalSegment ?
                    calculateNonDecreasingSequencesQuantity(result.prefixElementQuantity) :
                    calculateNonDecreasingSequencesQuantity(result.prefixElementQuantity) +
                            result.nonDecSeqInMiddleSegment +
                            calculateNonDecreasingSequencesQuantity(result.suffixElementQuantity);
        }

        private Segment findSegment(int currentSegmentIndex, int leftSegment, int rightSegment, int findLeft, int findRight) {
//            System.out.println(currentSegmentIndex + " " + leftSegment + " " + rightSegment + " "
//            + findLeft + " " +findRight);

            Segment segment = segmentTreeStore[currentSegmentIndex];
//            System.out.println(segment.toString());

            if (leftSegment == findLeft && rightSegment == findRight) {
                return segment;
            } else if (leftSegment <= findLeft &&
                    findRight <= leftSegment + (rightSegment - leftSegment) / 2) {
                return findSegment(currentSegmentIndex * 2,
                        leftSegment,
                        leftSegment + (rightSegment - leftSegment) / 2,
                        findLeft,
                        findRight);
            } else if (leftSegment + (rightSegment - leftSegment) / 2 + 1 <= findLeft &&
                    findRight <= rightSegment) {
                return findSegment(currentSegmentIndex * 2 + 1,
                        leftSegment + (rightSegment - leftSegment) / 2 + 1,
                        rightSegment,
                        findLeft, findRight);
            } else {
                Segment lSegment = findSegment(
                        currentSegmentIndex * 2,
                        leftSegment,
                        leftSegment + (rightSegment - leftSegment) / 2,
                        findLeft,
                        leftSegment + (rightSegment - leftSegment) / 2);
                Segment rSegment = findSegment(
                        currentSegmentIndex * 2 + 1,
                        leftSegment + (rightSegment - leftSegment) / 2 + 1,
                        rightSegment,
                        leftSegment + (rightSegment - leftSegment) / 2 + 1,
                        findRight);

                return merge(lSegment, rSegment);
            }
        }

        private Segment merge(Segment leftChildSegment, Segment rightChildSegment) {
            Segment segment = new Segment();

            if (!leftChildSegment.isNonDecInTotalSegment && !rightChildSegment.isNonDecInTotalSegment) {
                segment.prefix = leftChildSegment.prefix;
                segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity;

                segment.nonDecSeqInMiddleSegment = leftChildSegment.nonDecSeqInMiddleSegment + rightChildSegment.nonDecSeqInMiddleSegment;
                segment.nonDecSeqInMiddleSegment += leftChildSegment.suffix <= rightChildSegment.prefix ?
                        calculateNonDecreasingSequencesQuantity(
                                leftChildSegment.suffixElementQuantity + rightChildSegment.prefixElementQuantity
                        ) :
                        calculateNonDecreasingSequencesQuantity(leftChildSegment.suffixElementQuantity) +
                                calculateNonDecreasingSequencesQuantity(rightChildSegment.prefixElementQuantity);


                segment.suffix = rightChildSegment.suffix;
                segment.suffixElementQuantity = rightChildSegment.suffixElementQuantity;

                segment.isNonDecInTotalSegment = false;
            } else if (!leftChildSegment.isNonDecInTotalSegment && rightChildSegment.isNonDecInTotalSegment) {
                segment.prefix = leftChildSegment.prefix;
                segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity;

                if (leftChildSegment.suffix <= rightChildSegment.prefix) {
                    segment.nonDecSeqInMiddleSegment = leftChildSegment.nonDecSeqInMiddleSegment;
                    segment.suffixElementQuantity = leftChildSegment.suffixElementQuantity + rightChildSegment.prefixElementQuantity;
                } else {
                    segment.nonDecSeqInMiddleSegment = leftChildSegment.nonDecSeqInMiddleSegment
                            + calculateNonDecreasingSequencesQuantity(leftChildSegment.suffixElementQuantity);

                    segment.suffixElementQuantity = rightChildSegment.prefixElementQuantity;
                }
                segment.suffix = rightChildSegment.suffix;

                segment.isNonDecInTotalSegment = false;
            } else if (leftChildSegment.isNonDecInTotalSegment && !rightChildSegment.isNonDecInTotalSegment) {
                segment.prefix = leftChildSegment.prefix;

                if (leftChildSegment.suffix <= rightChildSegment.prefix) {
                    segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity + rightChildSegment.prefixElementQuantity;
                    segment.nonDecSeqInMiddleSegment = rightChildSegment.nonDecSeqInMiddleSegment;
                } else {
                    segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity;
                    segment.nonDecSeqInMiddleSegment = calculateNonDecreasingSequencesQuantity(rightChildSegment.prefixElementQuantity)
                            + rightChildSegment.nonDecSeqInMiddleSegment;
                }

                segment.suffix = rightChildSegment.suffix;
                segment.suffixElementQuantity = rightChildSegment.suffixElementQuantity;

                segment.isNonDecInTotalSegment = false;
            } else {
                segment.prefix = leftChildSegment.prefix;

                if (leftChildSegment.suffix <= rightChildSegment.prefix) {
                    segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity + rightChildSegment.prefixElementQuantity;
                    segment.suffixElementQuantity = segment.prefixElementQuantity;
                    segment.nonDecSeqInMiddleSegment = 0;
                    segment.isNonDecInTotalSegment = true;
                } else {
                    segment.prefixElementQuantity = leftChildSegment.prefixElementQuantity;
                    segment.suffixElementQuantity = rightChildSegment.prefixElementQuantity;
                    segment.nonDecSeqInMiddleSegment = 0;
                    segment.isNonDecInTotalSegment = false;
                }

                segment.suffix = rightChildSegment.suffix;
            }

//            System.out.println(segment.toString());
            return segment;
        }

        private int getMiddleElementIndexOnSegment(int left, int right) {
            return left + (right - left) / 2;
        }

        private long calculateNonDecreasingSequencesQuantity(int elementQuantity) {
            return (long) elementQuantity * (elementQuantity + 1) / 2;
        }
    }

    private static SegmentTree segmentTree;
    private static int quotationQuantity;

    public static void resolve() {
        input();

        for (int i = 0; i < quotationQuantity; i++) {
            int c = in.nextInt();
            int l = in.nextInt();
            int r = in.nextInt();
//            System.out.println(c + " " + l + " " + r);
            if (c == 1) {
                segmentTree.update(l - 1, r);
            } else {
                output(segmentTree.get(l - 1, r - 1));
            }
        }

    }

    private static void input() {
        int n = in.nextInt();
        int[] arr = new int[n];
        quotationQuantity = in.nextInt();

        for (int i = 0; i < arr.length; i++) {
            arr[i] = in.nextInt();
        }

        segmentTree = new SegmentTree(arr);
    }

    private static void output(long value) {
        System.out.println(value);
    }

}

