Sonya has an array $a_1, a_2, \ldots, a_n$ consisting of $n$ integers and also one non-negative integer $x$. She has to perform $m$ queries of two types:
 -  $1$ $i$ $y$: replace $i$-th element by value $y$, i.e. to perform an operation $a_{i}$ := $y$; -  $2$ $l$ $r$: find the number of pairs ($L$, $R$) that $l\leq L\leq R\leq r$ and bitwise OR of all integers in the range $[L, R]$ is at least $x$ (note that $x$ is a constant for all queries). 
Can you help Sonya perform all her queries?

Bitwise OR is a binary operation on a pair of non-negative integers. To calculate the bitwise OR of two numbers, you need to write both numbers in binary notation. The result is a number, in binary, which contains a one in each digit if there is a one in the binary notation of at least one of the two numbers. For example, $10$ OR $19$ = $1010_2$ OR $10011_2$ = $11011_2$ = $27$.
The first line contains three integers $n$, $m$, and $x$ ($1\leq n, m\leq 10^5$, $0\leq x&lt;2^{20}$) — the number of numbers, the number of queries, and the constant for all queries.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0\leq a_i&lt;2^{20}$) — numbers of the array.

The following $m$ lines each describe an query. A line has one of the following formats:
 -  $1$ $i$ $y$ ($1\leq i\leq n$, $0\leq y&lt;2^{20}$), meaning that you have to replace $a_{i}$ by $y$; -  $2$ $l$ $r$ ($1\leq l\leq r\leq n$), meaning that you have to find the number of subarrays on the segment from $l$ to $r$ that the bitwise OR of all numbers there is at least $x$.
print("_RANDOM_GUESS_1689645210.4479158")# 1689645210.4479356